pax_global_header00006660000000000000000000000064140061266750014521gustar00rootroot0000000000000052 comment=cce93db5277ce2618dafdc84c42186bbafe2a6b6 statsmodels-0.12.2/000077500000000000000000000000001400612667500141455ustar00rootroot00000000000000statsmodels-0.12.2/.codacy.yml000066400000000000000000000001641400612667500162110ustar00rootroot00000000000000--- engines: pylint: enabled: true python_version: 3 exclude_paths: - '**/_version.py' - 'versioneer.py' statsmodels-0.12.2/.gitattributes000066400000000000000000000000621400612667500170360ustar00rootroot00000000000000* text=auto statsmodels/_version.py export-subst statsmodels-0.12.2/.github/000077500000000000000000000000001400612667500155055ustar00rootroot00000000000000statsmodels-0.12.2/.github/ISSUE_TEMPLATE/000077500000000000000000000000001400612667500176705ustar00rootroot00000000000000statsmodels-0.12.2/.github/ISSUE_TEMPLATE/bug_report.md000066400000000000000000000032411400612667500223620ustar00rootroot00000000000000--- name: Bug report about: Create a report to help us improve title: '' labels: '' assignees: '' --- #### Describe the bug [A clear and concise description of what the bug is. This should explain **why** the current behaviour is a problem and why the expected output is a better solution.] #### Code Sample, a copy-pastable example if possible ```python # Your code here that produces the bug # This example should be self-contained, and so not rely on external data. # It should run in a fresh ipython session, and so include all relevant imports. ```
**Note**: As you can see, there are many issues on our GitHub tracker, so it is very possible that your issue has been posted before. Please check first before submitting so that we do not have to handle and close duplicates. **Note**: Please be sure you are using the latest released version of `statsmodels`, or a recent build of `master`. If your problem has been fixed in an unreleased version, you might be able to use `master` until a new release occurs. **Note**: If you are using a released version, have you verified that the bug exists in the master branch of this repository? It helps the limited resources if we know problems exist in the current master so that they do not need to check whether the code sample produces a bug in the next release.
If the issue has not been resolved, please file it in the issue tracker. #### Expected Output A clear and concise description of what you expected to happen. #### Output of ``import statsmodels.api as sm; sm.show_versions()``
[paste the output of ``import statsmodels.api as sm; sm.show_versions()`` here below this line]
statsmodels-0.12.2/.github/ISSUE_TEMPLATE/feature_request.md000066400000000000000000000011121400612667500234100ustar00rootroot00000000000000--- name: Feature request about: Suggest an idea for this project title: '' labels: '' assignees: '' --- #### Is your feature request related to a problem? Please describe A clear and concise description of what the problem is. Ex. I'm always frustrated when [...] #### Describe the solution you'd like A clear and concise description of what you want to happen. #### Describe alternatives you have considered A clear and concise description of any alternative solutions or features you have considered. #### Additional context Add any other context about the feature request here.statsmodels-0.12.2/.github/PULL_REQUEST_TEMPLATE.md000066400000000000000000000023401400612667500213050ustar00rootroot00000000000000- [ ] closes #xxxx - [ ] tests added / passed. - [ ] code/documentation is well formatted. - [ ] properly formatted commit message. See [NumPy's guide](https://docs.scipy.org/doc/numpy-1.15.1/dev/gitwash/development_workflow.html#writing-the-commit-message).
**Notes**: * It is essential that you add a test when making code changes. Tests are not needed for doc changes. * When adding a new function, test values should usually be verified in another package (e.g., R/SAS/Stata). * When fixing a bug, you must add a test that would produce the bug in master and then show that it is fixed with the new code. * New code additions must be well formatted. Changes should pass flake8. If on Linux or OSX, you can verify you changes are well formatted by running ``` git diff upstream/master -u -- "*.py" | flake8 --diff --isolated ``` assuming `flake8` is installed. This command is also available on Windows using the Windows System for Linux once `flake8` is installed in the local Linux environment. While passing this test is not required, it is good practice and it help improve code quality in `statsmodels`. * Docstring additions must render correctly, including escapes and LaTeX.
statsmodels-0.12.2/.gitignore000066400000000000000000000042221400612667500161350ustar00rootroot00000000000000*.py[oc] # setup.py working directory build # setup.py dist directory dist #docs build and others #generated #not yet? generated for dataset not rebuild docs/source/generated docs/source/dev/generated docs/source/examples/generated docs/source/datasets/generated docs/source/examples/notebooks/generated docs/source/datasets/statsmodels.datasets.* docs/source/savefig docs/gettingstarted_0.png examples/executed # generated c source and built extensions *.c *.so *.pyd # repository directories for bzr-git .bzr .git marks.git marks.bzr # virtualenv stuff .venv # Editor temporary/working/backup files *$ .*.sw[nop] .sw[nop] *~ [#]*# .#* *.bak *.tmp /.idea *.tgz *.rej *.org .project *.diff .settings/ *.svn/ *.log.py # Egg metadata *.egg-info # The shelf plugin uses this dir .shelf # Mac droppings .DS_Store help # Coverage report output .coverage coverage_html_report/ # Idea IDE .idea/ # VS Code .vscode/ # Project specific statsmodels/version.py statsmodels.egg-info/ iterate.dat hash_dict.pickle rehab.table salary.table .ipynb_checkpoints statsmodels/tsa/statespace/_statespace.pyx statsmodels/tsa/innovations/_arma_innovations.pyx statsmodels/tsa/regime_switching/_hamilton_filter.pyx statsmodels/tsa/regime_switching/_kim_smoother.pyx statsmodels/tsa/statespace/_initialization.pyx statsmodels/tsa/statespace/_representation.pyx statsmodels/tsa/statespace/_kalman_filter.pyx statsmodels/tsa/statespace/_kalman_smoother.pyx statsmodels/tsa/statespace/_simulation_smoother.pyx statsmodels/tsa/statespace/_cfa_simulation_smoother.pyx statsmodels/tsa/statespace/_tools.pyx statsmodels/tsa/statespace/_filters/_conventional.pyx statsmodels/tsa/statespace/_filters/_inversions.pyx statsmodels/tsa/statespace/_filters/_univariate.pyx statsmodels/tsa/statespace/_filters/_univariate_diffuse.pyx statsmodels/tsa/statespace/_smoothers/_conventional.pyx statsmodels/tsa/statespace/_smoothers/_univariate.pyx statsmodels/tsa/statespace/_smoothers/_univariate_diffuse.pyx statsmodels/tsa/statespace/_smoothers/_alternative.pyx statsmodels/tsa/statespace/_smoothers/_classical.pyx #pytest .cache .pytest_cache # Temporary copies for packaging statsmodels/setup.cfg statsmodels/LICENSE.txt statsmodels-0.12.2/.mailmap000066400000000000000000000160001400612667500155630ustar00rootroot00000000000000Alexander W Blocker Alexander W Blocker Alex Griffing alex Alexis Roche Alexis Roche Ana Martinez Pardo Ana Martinez Pardo Ana Martinez Pardo Ana Martinez Pardo anov anov avishaylivne avishaylivne Bart Baker Bart Baker Bart Baker bartbkr Bart Baker bartbkr@gmail.com Ben Duffield benduffield Benjamin Thyreau benjamin.thyreau <> brian.hawthorne <> brian.hawthorne <> Bruno Rodrigues Bruno Rodrigues Carl Vogel Carl Vogel Chad Fulton Chad Fulton Chris Jordan-Squire Chris Jordan-Squire Christian Prinoth Christian Prinoth Christopher Burns cburns <> Christopher Burns Chris Christopher Burns Christopher Burns Cindee Madison Cindee Madison Daniel B. Smith Daniel B. Smith davclark <> davclark <> dengemann dengemann Dieter Vandenbussche Dieter Vandenbussche Dougal Sutherland Dougal Sutherland Enrico Giampieri Enrico Giampieri Eric Chiang ericchiang evelynmitchell evelynmitchell Evgeni Burovski Zhenya Fernando Perez fdo.perez <> Fernando Perez Fernando Perez Gael Varoquaux Gael Varoquaux George Panterov George Panterov Grayson Grayson Jan Schulz Jan Schulz Jarrod Millman jarrod.millman <> Jarrod Millman Jarrod Millman Jeff Reback jreback Jonathan Taylor jonathan.taylor <> Jonathan Taylor Jonathan Taylor Jonathan Taylor Jonathan Taylor Jonathan Taylor Jonathan Taylor Jonathan Taylor Jonathan Taylor Jonathan Taylor jtaylo Josef Perktold Josef Perktold Justin Grana Justin Grana langmore langmore Matthew Brett matthew.brett <> Matthew Brett Matthew Brett <> Matthew Brett Matthew Brett Matthew Brett Matthew Brett Matthieu Brucher Matthieu Brucher michael.castelle <> michael.castelle <> Mike Crowe Mike Crowe Mike Crowe Mike Crowe Mike Crowe Mike Nathaniel J. Smith Nathaniel J. Smith otterb otterb Padarn Wilson padarn Padarn Wilson Padarn Paris Sprint Account Paris Sprint Account Paul Hobson Paul Hobson Peter Prettenhofer Peter Prettenhofer Pietro Battiston Pietro Battiston Ralf Gommers Ralf Gommers Richard T. Guy Richard T. Guy Robert Cimrman Robert Cimrman Roger Lew Roger Lew scottpiraino scottpiraino sebastien.meriaux <> sebastien.meriaux <> Skipper Seabold jsseabold <> Skipper Seabold jsseabold Skipper Seabold Skipper Seabold skipper seabold skipper seabold Skipper Seabold skipper Skipper Seabold skipper Steve Genoud Steve Genoud Thomas Haslwanter Thomas Haslwanter Thomas Kluyver Thomas Kluyver tim.leslie <> tim.leslie <> timmie timmie Tom Augspurger TomAugspurger Tom Augspurger Tom Augspurger Tom Waite Tom Waite Tom Waite twaite Trent Hauck Trent Hauck Trent Hauck tshauck tylerhartley tylerhartley Vincent Arel-Bundock Vincent Arel-Bundock Vincent Davis Vincent Davis VirgileFritsch VirgileFritsch Wes McKinney Wes McKinney Wes McKinney Wes McKinney Yaroslav Halchenko Yaroslav Halchenko zed zed statsmodels-0.12.2/.pep8speaks.yml000066400000000000000000000002341400612667500170300ustar00rootroot00000000000000scanner: diff_only: True linter: flake8 flake8: max-line-length: 79 ignore: # Errors and warnings to ignore - W503 - W504 statsmodels-0.12.2/.travis.yml000066400000000000000000000123731400612667500162640ustar00rootroot00000000000000# Travis script that uses miniconda in place of the system installed python # versions. Allows substantial flexibility for choosing versions of # required packages and is simpler to use to test up-to-date scientific Python # stack dist: bionic language: python cache: - directories: - $HOME/.cache/pip - $TRAVIS_BUILD_DIR/docs/source/examples/notebooks git: depth: 10000 env: # Default values for common packages, override as needed global: - OPTIONAL= - COVERAGE=false - USE_MATPLOTLIB=true - USE_CVXOPT=true - MATPLOTLIB= - DOCBUILD=false - LINT=false - MKL_NUM_THREADS=1 # Enforce single thread - NUMEXPR_NUM_THREADS=1 - OMP_NUM_THREADS=1 - OPENBLAS_NUM_THREADS=1 - PYTHONHASHSEED=0 # Ensure tests are correctly gathered by xdist - BLAS="mkl blas=*=mkl" # Use Intel MKL by default - BUILD_INIT=tools/ci/travis_conda.sh - DEPEND_ALWAYS="pyyaml joblib pip colorama" - # Doctr deploy key for statsmodels/statsmodels.github.io - secure: "AzwB23FWdilHKVcEJnj57AsoY5yKTWT8cQKzsH2ih9i08wIXvZXP/Ui8XRDygV9tDKfqGVltC7HpBBDE3C4ngeMlis4uuKWlkp0O1757YQe+OdDnimuDZhrh3ILEk7xW3ab5YizjLeyv3iiBW7cNS5z8W3Yu8HeJPkr6Ck30gAA=" - SM_CYTHON_COVERAGE=false # Run takes > 1 hour and so not feasible - PYTEST_OPTIONS=--skip-slow # skip slow on travis since tested on azure - XDIST_OPTS="" matrix: fast_finish: true include: # Documentation build (on Python 3.7 + cutting edge packages). Slowest build - python: 3.8 env: - BUILD_INIT=tools/ci/travis_pip.sh - USE_MATPLOTLIB=false - USE_CVXOPT=false - LINT=true - python: 3.7 env: - PYTHON=3.7 - DOCBUILD=true # Python 3.7 + fixed pandas - python: 3.7 env: - PYTHON=3.7 - PANDAS=0.25 - NUMPY=1.17 - SCIPY=1.4 - COVERAGE=true - PYTEST_OPTIONS= # Python 3.6 + legacy blas + older pandas - python: 3.6 env: - PYTHON=3.6 - NUMPY=1.16 - PANDAS=0.24 - SCIPY=1.3 - BLAS="nomkl blas=*=openblas" - COVERAGE=true - PYTEST_OPTIONS= # Python 3.6 + oldest packages - python: 3.6 env: - PYTHON=3.6 - NUMPY=1.15 - SCIPY=1.2 - PANDAS=0.23 - MATPLOTLIB=2 - LINT=true # Latest pre-release packages - python: 3.8 env: - PIP_PRE=true - BUILD_INIT=tools/ci/travis_pip.sh - os: osx language: generic env: - PYTHON=3.7 allow_failures: # pre-testing is a little fragile. Make it an FYI. - python: 3.8 env: - PIP_PRE=true - BUILD_INIT=tools/ci/travis_pip.sh notifications: email: on_success: always before_install: # Skip if commit message contains [skip travis] or [travis skip] - COMMIT_MESSAGE=$(git show -s $TRAVIS_COMMIT_RANGE | awk 'BEGIN{count=0}{if ($1=="Author:") count++; if (count==1) print $0}') - if [[ $TRAVIS_PULL_REQUEST == false ]]; then COMMIT_MESSAGE=${TRAVIS_COMMIT_MESSAGE}; fi - if echo "$COMMIT_MESSAGE" | grep -E '\[(skip travis|travis skip)\]'; then exit 0 ; fi # Show information about CPU running job to understand BLAS issues - if [ "$TRAVIS_OS_NAME" = "linux" ]; then sudo lshw -class processor; fi - if [ "$TRAVIS_OS_NAME" = "osx" ]; then sysctl -a | grep machdep.cpu; fi # Fix for headless TravisCI - "export DISPLAY=:99.0" - if [ "$TRAVIS_OS_NAME" = "linux" ]; then ( sh -e /etc/init.d/xvfb start )& fi - if [ "$TRAVIS_OS_NAME" = "osx" ]; then ( sudo Xvfb :99 -ac -screen 0 1024x768x8; echo ok )& fi # Avoid noise from matplotlib - mkdir -p $HOME/.config/matplotlib - SRCDIR=$PWD # Source recipe to install packages - source $BUILD_INIT - pip install pytest pip pytest-randomly nose jupyter_client nbformat # Moved to enable Python 3.8 since cvxopt wheel is not available - if [ ${USE_CVXOPT} = true ]; then pip install cvxopt; fi # Pin to 1.29 for now due to test discovery issues - if [ "$TRAVIS_OS_NAME" = "osx" ]; then pip install "pytest-xdist==1.29"; fi; - | if [ ${COVERAGE} = true ]; then pip install codecov coverage coveralls pytest-cov export COVERAGE_OPTS="--cov=statsmodels --cov-report=" echo "Cython coverage:" ${SM_CYTHON_COVERAGE} else export COVERAGE_OPTS="" fi - pip install flake8 - pip list - export SRCDIR=$PWD # Install packages install: # Bug in NumPy < 1.16.1 that raises ValueError on size mismatch - if [[ ${NUMPY} != "1.15" ]]; then pip install -e .; else python setup.py develop; fi before_script: - if [[ ${DOCBUILD} = true ]]; then source tools/ci/docbuild_install.sh; fi; - if [[ ${TRAVIS_OS_NAME} = "osx" ]]; then export XDIST_OPTS="-n 2"; fi script: # Show versions - python -c 'import statsmodels.api as sm; sm.show_versions();' # docbuild or run tests - | if [[ ${DOCBUILD} = true ]]; then cd ${SRCDIR}/docs source ${SRCDIR}/tools/ci/docbuild.sh; else echo pytest -r a ${COVERAGE_OPTS} statsmodels --skip-examples ${XDIST_OPTS} ${PYTEST_OPTIONS} pytest -r a ${COVERAGE_OPTS} statsmodels --skip-examples ${XDIST_OPTS} ${PYTEST_OPTIONS} fi - cd $SRCDIR - ./lint.sh after_success: - if [[ ${COVERAGE} = true ]]; then coveralls; fi - if [[ ${COVERAGE} = true ]]; then codecov; fi statsmodels-0.12.2/CHANGES.md000066400000000000000000000003661400612667500155440ustar00rootroot00000000000000Release Notes ============= The list of changes for each statsmodels release can be found [here](https://www.statsmodels.org/devel/release/index.html). Full details are available in the [commit logs](https://github.com/statsmodels/statsmodels). statsmodels-0.12.2/CONTRIBUTING.rst000066400000000000000000000112761400612667500166150ustar00rootroot00000000000000Contributing guidelines ======================= This page explains how you can contribute to the development of `statsmodels` by submitting patches, statistical tests, new models, or examples. `statsmodels` is developed on `Github `_ using the `Git `_ version control system. Submitting a Bug Report ~~~~~~~~~~~~~~~~~~~~~~~ - Include a short, self-contained code snippet that reproduces the problem - Specify the statsmodels version used. You can do this with ``sm.version.full_version`` - If the issue looks to involve other dependencies, also include the output of ``sm.show_versions()`` Making Changes to the Code ~~~~~~~~~~~~~~~~~~~~~~~~~~ For a pull request to be accepted, you must meet the below requirements. This greatly helps in keeping the job of maintaining and releasing the software a shared effort. - **One branch. One feature.** Branches are cheap and github makes it easy to merge and delete branches with a few clicks. Avoid the temptation to lump in a bunch of unrelated changes when working on a feature, if possible. This helps us keep track of what has changed when preparing a release. - Commit messages should be clear and concise. This means a subject line of less than 80 characters, and, if necessary, a blank line followed by a commit message body. We have an `informal commit format standard `_ that we try to adhere to. You can see what this looks like in practice by ``git log --oneline -n 10``. If your commit references or closes a specific issue, you can close it by mentioning it in the `commit message `_. (*For maintainers*: These suggestions go for Merge commit comments too. These are partially the record for release notes.) - Code submissions must always include tests. See our `notes on testing `_. - Each function, class, method, and attribute needs to be documented using docstrings. We conform to the `numpy docstring standard `_. - If you are adding new functionality, you need to add it to the documentation by editing (or creating) the appropriate file in ``docs/source``. - Make sure your documentation changes parse correctly. Change into the top-level ``docs/`` directory and type:: make clean make html Check that the build output does not have *any* warnings due to your changes. - Finally, please add your changes to the release notes. Open the ``docs/source/release/versionX.X.rst`` file that has the version number of the next release and add your changes to the appropriate section. Linting ~~~~~~~ Due to the way we have the CI builds set up, the linter will not do anything unless the environmental variable $LINT is set to a truthy value. - On MacOS/Linux LINT=true ./lint.sh - Dependencies: flake8, git How to Submit a Pull Request ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ So you want to submit a patch to `statsmodels` but are not too familiar with github? Here are the steps you need to take. 1. `Fork `_ the `statsmodels repository `_ on Github. 2. `Create a new feature branch `_. Each branch must be self-contained, with a single new feature or bugfix. 3. Make sure the test suite passes. This includes testing on Python 3. The easiest way to do this is to either enable `Travis-CI `_ on your fork, or to make a pull request and check there. 4. Document your changes by editing the appropriate file in ``docs/source/``. If it is a big, new feature add a note and an example to the latest ``docs/source/release/versionX.X.rst`` file. See older versions for examples. If it's a minor change, it will be included automatically in our release notes. 5. Add an example. If it is a big, new feature please submit an example notebook by following `these instructions `_. 6. `Submit a pull request `_ Mailing List ~~~~~~~~~~~~ Conversations about development take place on the `statsmodels mailing list `__. Learn More ~~~~~~~~~~ The ``statsmodels`` documentation's `developer page `_ offers much more detailed information about the process. License ~~~~~~~ statsmodels is released under the `Modified (3-clause) BSD license `_. statsmodels-0.12.2/COPYRIGHTS.txt000066400000000000000000000267241400612667500164140ustar00rootroot00000000000000 The license of statsmodels can be found in LICENSE.txt statsmodels contains code or derivative code from several other packages. Some modules also note the author of individual contributions, or author of code that formed the basis for the derived or translated code. The copyright statements for the datasets are attached to the individual datasets, most datasets are in public domain, and we do not claim any copyright on any of them. In the following, we collect copyright statements of code from other packages, all of which are either a version of BSD or MIT licensed: numpy scipy pandas matplotlib scikit-learn qsturng-py http://code.google.com/p/qsturng-py/ numpy (statsmodels.compatnp contains copy of entire model) ---------------------------------------------------------- Copyright (c) 2005-2009, NumPy Developers. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the NumPy Developers nor the names of any contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. --------------------------------------------------------------------- scipy ----- Copyright (c) 2001, 2002 Enthought, Inc. All rights reserved. Copyright (c) 2003-2009 SciPy Developers. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: a. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. b. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. c. Neither the name of the Enthought nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. --------------------------------------------------------------------------- pandas ------ Copyright (c) 2008-2009 AQR Capital Management, LLC All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the copyright holder nor the names of any contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDER AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ---------------------------------------------------------------------- matplotlib (copied from license.py) ----------------------------------- LICENSE AGREEMENT FOR MATPLOTLIB %(version)s -------------------------------------- 1. This LICENSE AGREEMENT is between John D. Hunter ("JDH"), and the Individual or Organization ("Licensee") accessing and otherwise using matplotlib software in source or binary form and its associated documentation. 2. Subject to the terms and conditions of this License Agreement, JDH hereby grants Licensee a nonexclusive, royalty-free, world-wide license to reproduce, analyze, test, perform and/or display publicly, prepare derivative works, distribute, and otherwise use matplotlib %(version)s alone or in any derivative version, provided, however, that JDH's License Agreement and JDH's notice of copyright, i.e., "Copyright (c) 2002-%(year)d John D. Hunter; All Rights Reserved" are retained in matplotlib %(version)s alone or in any derivative version prepared by Licensee. 3. In the event Licensee prepares a derivative work that is based on or incorporates matplotlib %(version)s or any part thereof, and wants to make the derivative work available to others as provided herein, then Licensee hereby agrees to include in any such work a brief summary of the changes made to matplotlib %(version)s. 4. JDH is making matplotlib %(version)s available to Licensee on an "AS IS" basis. JDH MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR IMPLIED. BY WAY OF EXAMPLE, BUT NOT LIMITATION, JDH MAKES NO AND DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF MATPLOTLIB %(version)s WILL NOT INFRINGE ANY THIRD PARTY RIGHTS. 5. JDH SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF MATPLOTLIB %(version)s FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS AS A RESULT OF MODIFYING, DISTRIBUTING, OR OTHERWISE USING MATPLOTLIB %(version)s, OR ANY DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF. 6. This License Agreement will automatically terminate upon a material breach of its terms and conditions. 7. Nothing in this License Agreement shall be deemed to create any relationship of agency, partnership, or joint venture between JDH and Licensee. This License Agreement does not grant permission to use JDH trademarks or trade name in a trademark sense to endorse or promote products or services of Licensee, or any third party. 8. By copying, installing or otherwise using matplotlib %(version)s, Licensee agrees to be bound by the terms and conditions of this License Agreement. -------------------------------------------------------------------------- scikits-learn ------------- New BSD License Copyright (c) 2007 - 2010 Scikit-Learn Developers. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: a. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. b. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. c. Neither the name of the Scikit-learn Developers nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. --------------------------------------------------------------------------- qsturng-py (code included in statsmodels.stats.libqsturng) -------------------------------------------------------------- Copyright (c) 2011, Roger Lew [see LICENSE.txt] All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the organizations affiliated with the contributors or the names of its contributors themselves may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ---------------------------------------------------------- statsmodels-0.12.2/INSTALL.txt000066400000000000000000000050711400612667500160170ustar00rootroot00000000000000Dependencies ------------ python >= 3.6 www.python.org numpy >= 1.15 www.numpy.org scipy >= 1.1 www.scipy.org pandas >= 0.23 pandas.pydata.org patsy >= 0.5.1 patsy.readthedocs.org cython >= 0.29 https://cython.org/ Cython is required if you are building the source from github. However, if you have are building from source distribution archive then the generated C files are included and Cython is not necessary. Earlier versions may be ok for earlier versions of Python. Optional Dependencies --------------------- X-12-ARIMA or X-13ARIMA-SEATS https://www.census.gov/srd/www/x13as/ If available, time-series analysis can be conducted using either X-12-ARIMA or the newer X-13ARIMA-SEATS. You should place the appropriate executable on your PATH or set the X12PATH or X13PATH environmental variable to take advantage. matplotlib >= 2.2 https://matplotlib.org/ Matplotlib is needed for plotting functionality and running many of the examples. sphinx >= 1.3 http://sphinx.pocoo.org/ Sphinx is used to build the documentation. pytest >= 3.0 http://readthedocs.org/docs/pytest/en/latest/ Pytest is needed to run the tests. IPython >= 5.0 Needed to build the docs. Installing ---------- To get the latest release using pip pip install statsmodels --upgrade-strategy only-if-needed The additional parameter pip --upgrade-strategy only-if-needed will ensure that dependencies, e.g. NumPy or pandas, are not upgraded unless required. Ubuntu/Debian ------------- On Ubuntu you can get dependencies through: sudo apt-get install python python-dev python-setuptools python-numpy python-scipy pip install cython pandas Alternatively, you can install from the NeuroDebian repository: http://neuro.debian.net Installing from Source ---------------------- Download and extract the source distribution from PyPI or github https://pypi.python.org/pypi/statsmodels https://github.com/statsmodels/statsmodels/tags Or clone the bleeding edge code from our repository on github at git clone git://github.com/statsmodels/statsmodels.git In the statsmodels directory do (with proper permissions) python setup.py install You will need a C compiler installed. Installing from Source on Windows --------------------------------- See https://www.statsmodels.org/devel/install.html#windows. Documentation ------------- You may find more information about the project and installation in our documentation https://www.statsmodels.org/devel/install.html statsmodels-0.12.2/LICENSE.txt000066400000000000000000000031441400612667500157720ustar00rootroot00000000000000Copyright (C) 2006, Jonathan E. Taylor All rights reserved. Copyright (c) 2006-2008 Scipy Developers. All rights reserved. Copyright (c) 2009-2018 statsmodels Developers. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: a. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. b. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. c. Neither the name of statsmodels nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL STATSMODELS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. statsmodels-0.12.2/MANIFEST.in000066400000000000000000000013751400612667500157110ustar00rootroot00000000000000global-include *.csv *.py *.txt *.pyx *.pyx.in *.pxd *.pxi *.c *.h *.pkl include MANIFEST.in include README.rst recursive-exclude build * recursive-exclude dist * recursive-exclude tools * graft statsmodels/datasets graft statsmodels/sandbox/regression/data graft statsmodels/sandbox/tests graft statsmodels/sandbox/tsa/examples recursive-include docs/source * exclude docs/source/generated/* recursive-include docs/sphinxext * recursive-include docs/themes * recursive-exclude docs/build * recursive-exclude docs/build/htmlhelp * include statsmodels/statsmodelsdoc.chm include docs/make.bat include docs/Makefile recursive-include examples * prune */__pycache__ global-exclude *~ *.swp *.pyc *.pyo *.bak include versioneer.py include statsmodels/_version.py statsmodels-0.12.2/README.rst000066400000000000000000000144261400612667500156430ustar00rootroot00000000000000|PyPI Version| |Conda Version| |License| |Travis Build Status| |Azure CI Build Status| |Appveyor Build Status| |Coveralls Coverage| |PyPI downloads| |Conda downloads| About statsmodels ================= statsmodels is a Python package that provides a complement to scipy for statistical computations including descriptive statistics and estimation and inference for statistical models. Documentation ============= The documentation for the latest release is at https://www.statsmodels.org/stable/ The documentation for the development version is at https://www.statsmodels.org/dev/ Recent improvements are highlighted in the release notes https://www.statsmodels.org/stable/release/version0.9.html Backups of documentation are available at https://statsmodels.github.io/stable/ and https://statsmodels.github.io/dev/. Main Features ============= * Linear regression models: - Ordinary least squares - Generalized least squares - Weighted least squares - Least squares with autoregressive errors - Quantile regression - Recursive least squares * Mixed Linear Model with mixed effects and variance components * GLM: Generalized linear models with support for all of the one-parameter exponential family distributions * Bayesian Mixed GLM for Binomial and Poisson * GEE: Generalized Estimating Equations for one-way clustered or longitudinal data * Discrete models: - Logit and Probit - Multinomial logit (MNLogit) - Poisson and Generalized Poisson regression - Negative Binomial regression - Zero-Inflated Count models * RLM: Robust linear models with support for several M-estimators. * Time Series Analysis: models for time series analysis - Complete StateSpace modeling framework - Seasonal ARIMA and ARIMAX models - VARMA and VARMAX models - Dynamic Factor models - Unobserved Component models - Markov switching models (MSAR), also known as Hidden Markov Models (HMM) - Univariate time series analysis: AR, ARIMA - Vector autoregressive models, VAR and structural VAR - Vector error correction modle, VECM - exponential smoothing, Holt-Winters - Hypothesis tests for time series: unit root, cointegration and others - Descriptive statistics and process models for time series analysis * Survival analysis: - Proportional hazards regression (Cox models) - Survivor function estimation (Kaplan-Meier) - Cumulative incidence function estimation * Multivariate: - Principal Component Analysis with missing data - Factor Analysis with rotation - MANOVA - Canonical Correlation * Nonparametric statistics: Univariate and multivariate kernel density estimators * Datasets: Datasets used for examples and in testing * Statistics: a wide range of statistical tests - diagnostics and specification tests - goodness-of-fit and normality tests - functions for multiple testing - various additional statistical tests * Imputation with MICE, regression on order statistic and Gaussian imputation * Mediation analysis * Graphics includes plot functions for visual analysis of data and model results * I/O - Tools for reading Stata .dta files, but pandas has a more recent version - Table output to ascii, latex, and html * Miscellaneous models * Sandbox: statsmodels contains a sandbox folder with code in various stages of development and testing which is not considered "production ready". This covers among others - Generalized method of moments (GMM) estimators - Kernel regression - Various extensions to scipy.stats.distributions - Panel data models - Information theoretic measures How to get it ============= The master branch on GitHub is the most up to date code https://www.github.com/statsmodels/statsmodels Source download of release tags are available on GitHub https://github.com/statsmodels/statsmodels/tags Binaries and source distributions are available from PyPi https://pypi.org/project/statsmodels/ Binaries can be installed in Anaconda conda install statsmodels Installing from sources ======================= See INSTALL.txt for requirements or see the documentation https://statsmodels.github.io/dev/install.html Contributing ============ Contributions in any form are welcome, including: * Documentation improvements * Additional tests * New features to existing models * New models https://www.statsmodels.org/stable/dev/test_notes for instructions on installing statsmodels in *editable* mode. License ======= Modified BSD (3-clause) Discussion and Development ========================== Discussions take place on the mailing list https://groups.google.com/group/pystatsmodels and in the issue tracker. We are very interested in feedback about usability and suggestions for improvements. Bug Reports =========== Bug reports can be submitted to the issue tracker at https://github.com/statsmodels/statsmodels/issues .. |Travis Build Status| image:: https://travis-ci.org/statsmodels/statsmodels.svg?branch=master :target: https://travis-ci.org/statsmodels/statsmodels .. |Azure CI Build Status| image:: https://dev.azure.com/statsmodels/statsmodels-testing/_apis/build/status/statsmodels.statsmodels?branch=master :target: https://dev.azure.com/statsmodels/statsmodels-testing/_build/latest?definitionId=1&branch=master .. |Appveyor Build Status| image:: https://ci.appveyor.com/api/projects/status/gx18sd2wc63mfcuc/branch/master?svg=true :target: https://ci.appveyor.com/project/josef-pkt/statsmodels/branch/master .. |Coveralls Coverage| image:: https://coveralls.io/repos/github/statsmodels/statsmodels/badge.svg?branch=master :target: https://coveralls.io/github/statsmodels/statsmodels?branch=master .. |PyPI downloads| image:: https://img.shields.io/pypi/dm/statsmodels.svg?label=Pypi%20downloads :target: https://pypi.org/project/statsmodels/ .. |Conda downloads| image:: https://img.shields.io/conda/dn/conda-forge/statsmodels.svg?label=Conda%20downloads :target: https://anaconda.org/conda-forge/statsmodels/ .. |PyPI Version| image:: https://img.shields.io/pypi/v/statsmodels.svg :target: https://pypi.org/project/statsmodels/ .. |Conda Version| image:: https://anaconda.org/conda-forge/statsmodels/badges/version.svg :target: https://anaconda.org/conda-forge/statsmodels/ .. |License| image:: https://img.shields.io/pypi/l/statsmodels.svg :target: https://github.com/statsmodels/statsmodels/blob/master/LICENSE.txt statsmodels-0.12.2/README_l1.txt000066400000000000000000000023771400612667500162500ustar00rootroot00000000000000What the l1 addition is ======================= A slight modification that allows l1 regularized LikelihoodModel. Regularization is handled by a fit_regularized method. Main Files ========== l1_demo/demo.py $ python demo.py --get_l1_slsqp_results logit does a quick demo of the regularization using logistic regression. l1_demo/sklearn_compare.py $ python sklearn_compare.py Plots a comparison of regularization paths. Modify the source to use different datasets. statsmodels/base/l1_cvxopt.py fit_l1_cvxopt_cp() Fit likelihood model using l1 regularization. Use the CVXOPT package. Lots of small functions supporting fit_l1_cvxopt_cp statsmodels/base/l1_slsqp.py fit_l1_slsqp() Fit likelihood model using l1 regularization. Use scipy.optimize Lots of small functions supporting fit_l1_slsqp statsmodels/base/l1_solvers_common.py Common methods used by l1 solvers statsmodels/base/model.py Likelihoodmodel.fit() 3 lines modified to allow for importing and calling of l1 fitting functions statsmodels/discrete/discrete_model.py L1MultinomialResults class Child of MultinomialResults MultinomialModel.fit() 3 lines re-directing l1 fit results to the L1MultinomialResults class statsmodels-0.12.2/appveyor.yml000066400000000000000000000026431400612667500165420ustar00rootroot00000000000000skip_tags: true clone_depth: 50 os: Visual Studio 2015 environment: # Undefining will run test from installation PYTEST_DIRECTIVES: --skip-slow PYTHONHASHSEED: 0 # Ensure tests are correctly gathered by xdist MKL_NUM_THREADS: 1 NUMEXPR_NUM_THREADS: 1 OMP_NUM_THREADS: 1 OPENBLAS_NUM_THREADS: 1 matrix: # Pip builds - PYTHON: C:\Python38 PYTEST_DIRECTIVES: - PY_MAJOR_VER: 3 PYTHON_ARCH: "x86" - PY_MAJOR_VER: 3 PYTHON_ARCH: "x86_64" TEST_INSTALL: "true" platform: - x64 build_script: # Search for [appveyor skip] or [skip appveyor] and exit if found in full commit message - ps: $commit=$env:APPVEYOR_REPO_COMMIT_MESSAGE + $env:APPVEYOR_REPO_COMMIT_MESSAGE_EXTENDED - ps: $skip_appveyor=$commit.Contains("[skip appveyor]") -Or $commit.Contains("[appveyor skip]") - ps: If ($skip_appveyor) { echo "[skip appveyor]"; Exit-AppVeyorBuild } # Show information about CPU running job to understand BLAS issues - wmic cpu get caption, name, numberofcores - If Defined PY_MAJOR_VER ( call tools\ci\appveyor_conda.bat ) else ( call tools\ci\appveyor_pip.bat ) # Pin to 1.29 for now due to test discovery issues - python -m pip install --upgrade pip "setuptools<50.0" - pip install pytest "pytest-xdist==1.29" pytest-randomly - if Defined PYTEST_DIRECTIVES ( pip install -e . --no-build-isolation ) else ( pip install . ) test_script: - call tools\ci\run_test.bat statsmodels-0.12.2/archive/000077500000000000000000000000001400612667500155665ustar00rootroot00000000000000statsmodels-0.12.2/archive/README.md000066400000000000000000000003231400612667500170430ustar00rootroot00000000000000This directory holds files that were once part of statsmodels but are no longer maintained. 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write_file.close() os.remove(read_file_path) os.rename(write_file_path, read_file_path) statsmodels-0.12.2/archive/docs/source/000077500000000000000000000000001400612667500200165ustar00rootroot00000000000000statsmodels-0.12.2/archive/docs/source/genericmle.rst.TXT000066400000000000000000000000001400612667500233260ustar00rootroot00000000000000statsmodels-0.12.2/archive/tsa/000077500000000000000000000000001400612667500163555ustar00rootroot00000000000000statsmodels-0.12.2/archive/tsa/ex_arma.py000066400000000000000000000056671400612667500203610ustar00rootroot00000000000000''' does not seem to work so well anymore even with nobs=1000 ??? works ok if noise variance is large ''' import numpy as np import statsmodels.api as sm from statsmodels.tsa.arima_process import arma_generate_sample from statsmodels.tsa.arma_mle import Arma as Arma from statsmodels.tsa.arima_process import ARIMA as ARIMA_old from statsmodels.sandbox.tsa.garch import Arma as Armamle_old print("\nExample 1") ar = [1.0, -0.6, 0.1] ma = [1.0, 0.5, 0.3] nobs = 1000 y22 = arma_generate_sample(ar, ma, nobs+1000, 0.5)[-nobs:] y22 -= y22.mean() start_params = [0.1, 0.1, 0.1, 0.1] start_params_lhs = [-0.1, -0.1, 0.1, 0.1] print('truelhs', np.r_[ar[1:], ma[1:]]) ###bug in current version, fixed in Skipper and 1 more ###arr[1:q,:] = params[p+k:p+k+q] # p to p+q short params are MA coeffs ###ValueError: array dimensions are not compatible for copy ##from statsmodels.tsa.arima import ARMA as ARMA_kf ##arma22 = ARMA_kf(y22, constant=False, order=(2,2)) ##res = arma22.fit(start_params=start_params) ##print res.params print('\nARIMA new') arest2 = Arma(y22) naryw = 4 #= 30 resyw = sm.regression.yule_walker(y22, order=naryw, inv=True) arest2.nar = naryw arest2.nma = 0 e = arest2.geterrors(np.r_[1, -resyw[0]]) x=sm.tsa.tsatools.lagmat2ds(np.column_stack((y22,e)),3,dropex=1, trim='both') yt = x[:,0] xt = x[:,1:] res_ols = sm.OLS(yt, xt).fit() print('hannan_rissannen') print(res_ols.params) start_params = res_ols.params start_params_mle = np.r_[-res_ols.params[:2], res_ols.params[2:], #res_ols.scale] #areste.var()] np.sqrt(res_ols.scale)] #need to iterate, ar1 too large ma terms too small #fix large parameters, if hannan_rissannen are too large start_params_mle[:-1] = (np.sign(start_params_mle[:-1]) * np.minimum(np.abs(start_params_mle[:-1]),0.75)) print('conditional least-squares') #print rhohat2 print('with mle') arest2.nar = 2 arest2.nma = 2 # res = arest2.fit_mle(start_params=start_params_mle, method='nm') #no order in fit print(res.params) rhohat2, cov_x2a, infodict, mesg, ier = arest2.fit((2,2)) print('\nARIMA_old') arest = ARIMA_old(y22) rhohat1, cov_x1, infodict, mesg, ier = arest.fit((2,0,2)) print(rhohat1) print(np.sqrt(np.diag(cov_x1))) err1 = arest.errfn(x=y22) print(np.var(err1)) print('bse ls, formula not checked') print(np.sqrt(np.diag(cov_x1))*err1.std()) print('bsejac for mle') #print arest2.bsejac #TODO:check bsejac raises singular matrix linalg error #in model.py line620: return np.linalg.inv(np.dot(jacv.T, jacv)) print('\nyule-walker') print(sm.regression.yule_walker(y22, order=2, inv=True)) print('\nArmamle_old') arma1 = Armamle_old(y22) arma1.nar = 2 arma1.nma = 2 #arma1res = arma1.fit(start_params=np.r_[-0.5, -0.1, 0.1, 0.1, 0.5], method='fmin') # maxfun=1000) arma1res = arma1.fit(start_params=res.params*0.7, method='fmin') print(arma1res.params) statsmodels-0.12.2/archive/tsa/notes_organize.txt000066400000000000000000000152621400612667500221520ustar00rootroot00000000000000 scikits.statsmodels.sandbox.tsa.kalmanf --------------------------------------- ARMA : ARMA model using the exact Kalman Filter StateSpaceModel : kalmanfilter : Returns the negative log-likelihood of y conditional on the information set kalmansmooth : updatematrices : TODO: change API, update names scikits.statsmodels.sandbox.tsa.arima ------------------------------------- runs ok, no refactoring bugs has examples and monte carlo that can be split up into example files ARIMA : currently ARMA only, no differencing used - no I arma2ar : get the AR representation of an ARMA process arma2ma : get the impulse response function (MA representation) for ARMA process arma_acf : theoretical autocovariance function of ARMA process arma_acovf : theoretical autocovariance function of ARMA process arma_generate_sample : generate an random sample of an ARMA process arma_impulse_response : get the impulse response function (MA representation) for ARMA process arma_pacf : partial autocorrelation function of an ARMA process deconvolve : Deconvolves divisor out of signal, division of polynomials for n terms index2lpol : expand coefficients to lag poly lpol2index : remove zeros from lagpolynomial, squeezed representation with index mcarma22 : run Monte Carlo for ARMA(2,2) scikits.statsmodels.sandbox.tsa.varma ------------------------------------- just filter experiments needed to fix import for acf example VAR : multivariate linear filter VARMA : multivariate linear filter scikits.statsmodels.sandbox.tsa.varma_tools ------------------------------------------- Helper and filter functions for VAR and VARMA, and basic VAR class needed import fix in top of module maybe rename to varma_process in "main" example for VarmaPoly, and some Var fit Var could be used for Granger Causality tests, otherwise it's pretty limited Var : simultaneous OLS estimation VarmaPoly : class to keep track of Varma polynomial format working with and transforming VARMA Lag-Polynomials (3d) ar2full : make reduced lagpolynomial into a right side lagpoly array ar2lhs : convert full (rhs) lagpolynomial into a reduced, left side lagpoly array padone : pad with zeros along one axis, currently only axis=0 trimone : trim number of array elements along one axis varfilter : apply an autoregressive filter to a series x vargenerate : generate an VAR process with errors u varinversefilter : creates inverse ar filter (MA representation) recursively scikits.statsmodels.sandbox.tsa.try_fi -------------------------------------- (not included by script that generates this list) various functions to build lag-polynomials for fractional and seasonal integration and function ar2arma minimizes distance in terms of impulse response function move these to a module or rename scikits.statsmodels.sandbox.tsa.try_var_convolve.py --------------------------------------------------- (not included by script that generates this list) two functions: arfilter : autoregressive filter for 1d, 2d and 3d fftconvolve : multidimensional filtering using fft many examples, but I'm not sure this (fft) is correct incompletely copied for interpreter session currently raises exception because a variable (imp) is not defined scikits.statsmodels.sandbox.tsa.try_var_convolve.py --------------------------------------------------- (not included by script that generates this list) includes functions for detrending, (theoretical) acovf and similar for special cases acf plot functions (partially copied from matplotlib.mlab) currently exception: FIXED uses arima.ARIMA class without data in constructor, and order now has 3 values and is keyword with tuple as value move plot function to new graphics directory ? scikits.statsmodels.sandbox.regression.mle ------------------------------------------ one refactoring bug fixed, because arima.ARIMA needs data, use class method instead runs without exception, but I did not look at any results "main" has quite a lot AR : Notes Arma : univariate Autoregressive Moving Average model Garch : Garch model gjrgarch (t-garch) Garch0 : Garch model, GarchX : Garch model, LikelihoodModel : Likelihood model is a subclass of Model. TSMLEModel : univariate time series model for estimation with maximum likelihood garchplot : generate_garch : simulate standard garch generate_gjrgarch : simulate gjr garch process generate_kindofgarch : simulate garch like process but not squared errors in arma gjrconvertparams : flat to matrix loglike_GARCH11 : miso_lfilter : use nd convolution to merge inputs, normloglike : test_gjrgarch : test_misofilter : Other ----- diffusion: continuous time processes, produce nice graphs but parameterization is a bit inconsistent. script files ============ sandbox/tsa/try_arma_more.py ---------------------------- imports scikits.talkbox which is not compiled against my current numpy and does not run contains arma_periodogram : theoretical periodogram Proposed Structure (preliminary) ================================ arima_estimation ---------------- ARIMA class for estimation, wrapper or containing different estimators other wrappers: here or in separate ??? - support for choosing lag-length arma_process ------------ all theoretical properties for given parameters simulation method with options: initial conditions, errors, (?) not sure what else varma_process ------------- including VarmaPoly and impulse response functions filters ------- miso_filter (should be in cython eventually) ar_filter : fast VAR filter with convolution or fft convolution (not sure what's the relationship between the two) others ??? stattools --------- empirical properties acf, ... tsatools -------- helper functions lagmat detrend ??? others, unclear --------------- ??? open questions ============== support for exog ---------------- is incomplete or missing from some implementations not clear parameterization - ARMAX A(L)y_t = C(L)x_t + B(L)e_t - ARMAX-simple A(L)y_t = beta x_t + B(L)e_t Note: covers previous version by extending x_t - ARMA residuals y_t = beta x_t + u_t, and A(L)u_t = B(L)e_t - ARMAX 2-step A(L)(y_t - beta x_t) = B(L)e_t Note: looks the same as ARMA residuals, implies A(L)y_t = A(L)x_t + B(L)e_t - ARMAX A(L)(y_t - A^{-1}(L) C(L) x_t) = B(L)e_t this does not look useful, unless we cutoff A^{-1}(L) problem: signal.lfilter can only handle ARMAX residuals model (I think) deterministic trend have ARMAX-simple model, e.g. in unit root tests support for seasonal and "sparse" lag-polynomials ------------------------------------------------- - fit functions need support for different lag structures, e.g. zeros, multiplicative - support for pre-filters, e.g. (seasonal) differencing statsmodels-0.12.2/azure-pipelines.yml000066400000000000000000000011571400612667500200100ustar00rootroot00000000000000# https://docs.microsoft.com/en-us/azure/devops/pipelines/process/templates?view=azure-devops#passing-parameters trigger: - master variables: MKL_NUM_THREADS: 1 NUMEXPR_NUM_THREADS: 1 OMP_NUM_THREADS: 1 VML_NUM_THREADS: 1 OPENBLAS_NUM_THREADS: 1 PYTHONHASHSEED: 0 # Ensure tests are correctly gathered by xdist jobs: - template: tools/ci/azure_template.yml parameters: name: Linux vmImage: ubuntu-20.04 - template: tools/ci/azure_template.yml parameters: name: macOS vmImage: macOS-10.15 - template: tools/ci/azure_template.yml parameters: name: Windows vmImage: windows-2019 statsmodels-0.12.2/codecov.yml000066400000000000000000000003301400612667500163060ustar00rootroot00000000000000codecov: branch: master notify: require_ci_to_pass: no after_n_builds: 1 comment: off coverage: status: project: default: target: '82' patch: default: target: '50' statsmodels-0.12.2/docs/000077500000000000000000000000001400612667500150755ustar00rootroot00000000000000statsmodels-0.12.2/docs/Makefile000066400000000000000000000037071400612667500165440ustar00rootroot00000000000000# Minimal makefile for Sphinx documentation # # You can set these variables from the command line. SPHINXOPTS = SPHINXBUILD = sphinx-build SPHINXPROJ = statsmodels SOURCEDIR = source BUILDDIR = build PAPER = TOOLSPATH = ../tools/ DATASETBUILD = dataset_rst.py NOTEBOOKBUILD = nbgenerate.py # Internal variables. PAPEROPT_a4 = -D latex_paper_size=a4 PAPEROPT_letter = -D latex_paper_size=letter ALLSPHINXOPTS = $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) # Put it first so that "make" without argument is like "make help". help: @$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(ALLSPHINXOPTS) $(O) .PHONY: help Makefile cleanall: @$(SPHINXBUILD) -M clean "$(SOURCEDIR)" "$(BUILDDIR)" $(ALLSPHINXOPTS) $(O) -rm source/examples/generated/* -rm -rf source/examples/notebooks/generated/* -rm -rf ../tools/hash_dict.pickle -rm -rf source/datasets/generated/* notebooks: @echo "Generating notebooks from examples/notebooks folder" $(TOOLSPATH)$(NOTEBOOKBUILD) --execute=True --allow_errors=True html: # make directories for images @echo "Make static directory for images" mkdir -p $(BUILDDIR)/html/_static # generate the examples rst files @echo "Generating datasets from installed statsmodels.datasets" $(TOOLSPATH)$(DATASETBUILD) @echo "Executing notebooks from examples/notebooks folder" mkdir -p $(BUILDDIR)/source/examples/notebooks/generated # Black list notebooks from doc build here $(TOOLSPATH)$(NOTEBOOKBUILD) --parallel --report-errors --skip-existing --execute-only --execution-blacklist statespace_custom_models @echo "Running sphinx-build" @echo @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(ALLSPHINXOPTS) $(O) @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(ALLSPHINXOPTS) $(O) # Catch-all target: route all unknown targets to Sphinx using the new # "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS). %: Makefile @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(ALLSPHINXOPTS) $(O) statsmodels-0.12.2/docs/README.md000066400000000000000000000021141400612667500163520ustar00rootroot00000000000000# Documentation Documentation We use a combination of sphinx and Jupyter notebooks for the documentation. Jupyter notebooks should be used for longer, self-contained examples demonstrating a topic. Sphinx is nice because we get the tables of contents and API documentation. ## Build Process Building the docs requires a few additional dependencies. You can get most of these with ```bash pip install -e .[docs] ``` From the root of the project. Some of the examples rely on `rpy2` to execute R code from the notebooks. It's not included in the setup requires since it's known to be difficult to install. To generate the HTML docs, run ``make html`` from the ``docs`` directory. This executes a few distinct builds 1. datasets 2. notebooks 3. sphinx # Notebook Builds We're using `nbconvert` to execute the notebooks, and then convert them to HTML. The conversion is handled by `statsmodels/tools/nbgenerate.py`. The default python kernel (embedded in the notebook) is `python3`. You need at least `nbconvert==4.2.0` to specify a non-default kernel, which can be passed in the Makefile. statsmodels-0.12.2/docs/make.bat000066400000000000000000000033601400612667500165040ustar00rootroot00000000000000@ECHO OFF pushd %~dp0 REM Command file for Sphinx documentation if "%SPHINXBUILD%" == "" ( set SPHINXBUILD=sphinx-build ) set SOURCEDIR=source set BUILDDIR=build set SPHINXPROJ=statsmodels set SPHINXOPTS= set TOOLSPATH=../tools set DATASETBUILD=dataset_rst.py set NOTEBOOKBUILD=nbgenerate.py if "%1" == "" goto help %SPHINXBUILD% >NUL 2>NUL if errorlevel 9009 ( echo. echo.The 'sphinx-build' command was not found. Make sure you have Sphinx echo.installed, then set the SPHINXBUILD environment variable to point echo.to the full path of the 'sphinx-build' executable. Alternatively you echo.may add the Sphinx directory to PATH. echo. echo.If you do not have Sphinx installed, grab it from echo.http://sphinx-doc.org/ exit /b 1 ) if "%1" == "html" ( echo mkdir %BUILDDIR%\html\_static mkdir %BUILDDIR%\html\_static echo python %TOOLSPATH%/%NOTEBOOKBUILD% --parallel --report-errors --skip-existing rem Black list notebooks from doc build here python %TOOLSPATH%/%NOTEBOOKBUILD% --parallel --report-errors --skip-existing --execution-blacklist statespace_custom_models echo python %TOOLSPATH%/%DATASETBUILD% python %TOOLSPATH%/%DATASETBUILD% ) echo %SPHINXBUILD% -b %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %SPHINXBUILD% -b %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% if errorlevel 1 exit /b 1 if "%1" == "html" ( echo xcopy /s /y source\examples\notebooks\generated\*.html %BUILDDIR%\html\examples\notebooks\generated\*.html xcopy /s /y source\examples\notebooks\generated\*.html %BUILDDIR%\html\examples\notebooks\generated\*.html if NOT EXIST %BUILDDIR%/html/examples/notebooks/generated mkdir %BUILDDIR%\html\examples\notebooks\generated ) goto end :help %SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% :end popd statsmodels-0.12.2/docs/source/000077500000000000000000000000001400612667500163755ustar00rootroot00000000000000statsmodels-0.12.2/docs/source/_static/000077500000000000000000000000001400612667500200235ustar00rootroot00000000000000statsmodels-0.12.2/docs/source/_static/blogger.png000066400000000000000000000126531400612667500221610ustar00rootroot00000000000000‰PNG  IHDRrp*ŽgUrIDATxœíÝAH\Y¢‡ñÿ<šç(…%ØÖŒð ž ¹“¬!|‹Z¤'>dÕz‹Y¼G z#MCÛL½ cCÓ³ Lõn&daH/|‹06ˆ®:”Ðy0Ræ• 1h«žE™´1jÝ[uî=÷Ôù~‹¡›ÖòŒ–Ÿçž{ø駟æü‹íè4d€ad€ad€ad€ad€aïØ@Ûv·ôbËö £òúeÆö ZçBV^îéyUÛU½ØÒvU’6+¶Ç$¥+£¼$åõ*;¨\`{LMü"¥Ûáv·T«h³¢Z…ÉpÒ@^¹@¹@CA ç5)ËÊvUOU«èyÕöPG ÊO(?¡ì í¡IGV^îé颞.R uÿ6¡ü„Þ/Ú‡õ¬lWõäž.ÚÐIº2º4­Ñ¢ÅÉ‹½¬Ô*Z)³ø Äe´¨±’•¸ØÈÊî–¿$(@.Mk¬”ð²n²Yy¹§Õ²žà‘ƣУˆ˜•—{¬ÔÞY)GúðˆYaªx(â„%JV˜ªÞŠ2a‰’•ê2SÀS›í†Ýþ%+œ|º¡³²]e«>àµÐ{ùCg…UÀs‡{!oÅ:+­^t s„ë@¸¬Ô*,ÖùœÒpYaª !D BÏV@¡j"+»[\¯ 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position: absolute; top: 0; left: 0; z-index: 100; text-align: left; } #facebox .popup{ position:relative; border:3px solid rgba(0,0,0,0); -webkit-border-radius:5px; -moz-border-radius:5px; border-radius:5px; -webkit-box-shadow:0 0 18px rgba(0,0,0,0.4); -moz-box-shadow:0 0 18px rgba(0,0,0,0.4); box-shadow:0 0 18px rgba(0,0,0,0.4); } #facebox .content { display:table; width: 370px; padding: 10px; background: #fff; -webkit-border-radius:4px; -moz-border-radius:4px; border-radius:4px; } #facebox .content > p:first-child{ margin-top:0; } #facebox .content > p:last-child{ margin-bottom:0; } #facebox .close{ position:absolute; top:5px; right:5px; padding:2px; background:#fff; } #facebox .close img{ opacity:0.3; } #facebox .close:hover img{ opacity:1.0; } #facebox .loading { text-align: center; } #facebox .image { text-align: center; } #facebox img { border: 0; margin: 0; } #facebox_overlay { position: fixed; top: 0px; left: 0px; height:100%; width:100%; } .facebox_hide { z-index:-100; } .facebox_overlayBG { background-color: #000; z-index: 99; }statsmodels-0.12.2/docs/source/_static/facebox.js000066400000000000000000000220431400612667500217710ustar00rootroot00000000000000/* * Facebox (for jQuery) * version: 1.3 * @requires jQuery v1.2 or later * @homepage https://github.com/defunkt/facebox * * Licensed under the MIT: * http://www.opensource.org/licenses/mit-license.php * * Copyright Forever Chris Wanstrath, Kyle Neath * * Usage: * * jQuery(document).ready(function() { * jQuery('a[rel*=facebox]').facebox() * }) * * Terms * Loads the #terms div in the box * * Terms * Loads the terms.html page in the box * * Terms * Loads the terms.png image in the box * * * You can also use it programmatically: * * jQuery.facebox('some html') * jQuery.facebox('some html', 'my-groovy-style') * * The above will open a facebox with "some html" as the content. * * jQuery.facebox(function($) { * $.get('blah.html', function(data) { $.facebox(data) }) * }) * * The above will show a loading screen before the passed function is called, * allowing for a better ajaxy experience. * * The facebox function can also display an ajax page, an image, or the contents of a div: * * jQuery.facebox({ ajax: 'remote.html' }) * jQuery.facebox({ ajax: 'remote.html' }, 'my-groovy-style') * jQuery.facebox({ image: 'stairs.jpg' }) * jQuery.facebox({ image: 'stairs.jpg' }, 'my-groovy-style') * jQuery.facebox({ div: '#box' }) * jQuery.facebox({ div: '#box' }, 'my-groovy-style') * * Want to close the facebox? Trigger the 'close.facebox' document event: * * jQuery(document).trigger('close.facebox') * * Facebox also has a bunch of other hooks: * * loading.facebox * beforeReveal.facebox * reveal.facebox (aliased as 'afterReveal.facebox') * init.facebox * afterClose.facebox * * Simply bind a function to any of these hooks: * * $(document).bind('reveal.facebox', function() { ...stuff to do after the facebox and contents are revealed... }) * */ (function($) { $.facebox = function(data, klass) { $.facebox.loading(data.settings || []) if (data.ajax) fillFaceboxFromAjax(data.ajax, klass) else if (data.image) fillFaceboxFromImage(data.image, klass) else if (data.div) fillFaceboxFromHref(data.div, klass) else if ($.isFunction(data)) data.call($) else $.facebox.reveal(data, klass) } /* * Public, $.facebox methods */ $.extend($.facebox, { settings: { opacity : 0.2, overlay : true, loadingImage : '/facebox/loading.gif', closeImage : '/facebox/closelabel.png', imageTypes : [ 'png', 'jpg', 'jpeg', 'gif' ], faceboxHtml : '\ ' }, loading: function() { init() if ($('#facebox .loading').length == 1) return true showOverlay() $('#facebox .content').empty(). append('
') $('#facebox').show().css({ top: getPageScroll()[1] + (getPageHeight() / 10), left: $(window).width() / 2 - ($('#facebox .popup').outerWidth() / 2) }) $(document).bind('keydown.facebox', function(e) { if (e.keyCode == 27) $.facebox.close() return true }) $(document).trigger('loading.facebox') }, reveal: function(data, klass) { $(document).trigger('beforeReveal.facebox') if (klass) $('#facebox .content').addClass(klass) $('#facebox .content').empty().append(data) $('#facebox .popup').children().fadeIn('normal') $('#facebox').css('left', $(window).width() / 2 - ($('#facebox .popup').outerWidth() / 2)) $(document).trigger('reveal.facebox').trigger('afterReveal.facebox') }, close: function() { $(document).trigger('close.facebox') return false } }) /* * Public, $.fn methods */ $.fn.facebox = function(settings) { if ($(this).length == 0) return init(settings) function clickHandler() { $.facebox.loading(true) // support for rel="facebox.inline_popup" syntax, to add a class // also supports deprecated "facebox[.inline_popup]" syntax var klass = this.rel.match(/facebox\[?\.(\w+)\]?/) if (klass) klass = klass[1] fillFaceboxFromHref(this.href, klass) return false } return this.bind('click.facebox', clickHandler) } /* * Private methods */ // called one time to setup facebox on this page function init(settings) { if ($.facebox.settings.inited) return true else $.facebox.settings.inited = true $(document).trigger('init.facebox') makeCompatible() var imageTypes = $.facebox.settings.imageTypes.join('|') $.facebox.settings.imageTypesRegexp = new RegExp('\\.(' + imageTypes + ')(\\?.*)?$', 'i') if (settings) $.extend($.facebox.settings, settings) $('body').append($.facebox.settings.faceboxHtml) var preload = [ new Image(), new Image() ] preload[0].src = $.facebox.settings.closeImage preload[1].src = $.facebox.settings.loadingImage $('#facebox').find('.b:first, .bl').each(function() { preload.push(new Image()) preload.slice(-1).src = $(this).css('background-image').replace(/url\((.+)\)/, '$1') }) $('#facebox .close') .click($.facebox.close) .append('') } // getPageScroll() by quirksmode.com function getPageScroll() { var xScroll, yScroll; if (self.pageYOffset) { yScroll = self.pageYOffset; xScroll = self.pageXOffset; } else if (document.documentElement && document.documentElement.scrollTop) { // Explorer 6 Strict yScroll = document.documentElement.scrollTop; xScroll = document.documentElement.scrollLeft; } else if (document.body) {// all other Explorers yScroll = document.body.scrollTop; xScroll = document.body.scrollLeft; } return new Array(xScroll,yScroll) } // Adapted from getPageSize() by quirksmode.com function getPageHeight() { var windowHeight if (self.innerHeight) { // all except Explorer windowHeight = self.innerHeight; } else if (document.documentElement && document.documentElement.clientHeight) { // Explorer 6 Strict Mode windowHeight = document.documentElement.clientHeight; } else if (document.body) { // other Explorers windowHeight = document.body.clientHeight; } return windowHeight } // Backwards compatibility function makeCompatible() { var $s = $.facebox.settings $s.loadingImage = $s.loading_image || $s.loadingImage $s.closeImage = $s.close_image || $s.closeImage $s.imageTypes = $s.image_types || $s.imageTypes $s.faceboxHtml = $s.facebox_html || $s.faceboxHtml } // Figures out what you want to display and displays it // formats are: // div: #id // image: blah.extension // ajax: anything else function fillFaceboxFromHref(href, klass) { // div if (href.match(/#/)) { var url = window.location.href.split('#')[0] var target = href.replace(url,'') if (target == '#') return $.facebox.reveal($(target).html(), klass) // image } else if (href.match($.facebox.settings.imageTypesRegexp)) { fillFaceboxFromImage(href, klass) // ajax } else { fillFaceboxFromAjax(href, klass) } } function fillFaceboxFromImage(href, klass) { var image = new Image() image.onload = function() { $.facebox.reveal('
', klass) } image.src = href } function fillFaceboxFromAjax(href, klass) { $.facebox.jqxhr = $.get(href, function(data) { $.facebox.reveal(data, klass) }) } function skipOverlay() { return $.facebox.settings.overlay == false || $.facebox.settings.opacity === null } function showOverlay() { if (skipOverlay()) return if ($('#facebox_overlay').length == 0) $("body").append('
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statsmodels-0.12.2/docs/source/_templates/000077500000000000000000000000001400612667500205325ustar00rootroot00000000000000statsmodels-0.12.2/docs/source/_templates/autosummary/000077500000000000000000000000001400612667500231205ustar00rootroot00000000000000statsmodels-0.12.2/docs/source/_templates/autosummary/attribute.rst000066400000000000000000000001651400612667500256570ustar00rootroot00000000000000:orphan: {{ fullname | escape | underline}} .. currentmodule:: {{ module }} .. auto{{ objtype }}:: {{ objname }} statsmodels-0.12.2/docs/source/_templates/autosummary/class.rst000066400000000000000000000012761400612667500247650ustar00rootroot00000000000000{{ fullname | escape | underline}} .. currentmodule:: {{ module }} .. autoclass:: {{ objname }} :exclude-members: {% block methods %} {% if methods %} .. rubric:: Methods .. autosummary:: :toctree: {% for item in methods %} {%- if not item.startswith('_') or item in ['__call__'] %} ~{{ name }}.{{ item }} {% endif %} {%- endfor %} {% endif %} {% endblock %} {% block attributes %} {% if attributes %} .. rubric:: Properties .. autosummary:: :toctree: {% for item in attributes %} {%- if not item.startswith('_') or item in ['__call__'] %} ~{{ name }}.{{ item }} {% endif %} {%- endfor %} {% endif %} {% endblock %} statsmodels-0.12.2/docs/source/_templates/autosummary/member.rst000066400000000000000000000001661400612667500251240ustar00rootroot00000000000000:orphan: {{ fullname | escape | underline}} .. currentmodule:: {{ module }} .. auto{{ objtype }}:: {{ objname }} statsmodels-0.12.2/docs/source/_templates/autosummary/method.rst000066400000000000000000000001651400612667500251340ustar00rootroot00000000000000:orphan: {{ fullname | escape | underline}} .. currentmodule:: {{ module }} .. auto{{ objtype }}:: {{ objname }} statsmodels-0.12.2/docs/source/_templates/autosummary/minimal_module.rst000066400000000000000000000001611400612667500266430ustar00rootroot00000000000000{{ fullname | escape | underline}} .. automodule:: {{ fullname }} {% block docstring %} {% endblock %} statsmodels-0.12.2/docs/source/_templates/layout.html000066400000000000000000000015211400612667500227340ustar00rootroot00000000000000{# Import the theme's layout. #} {% extends "!layout.html" %} {%- block htmltitle %} {{ super() }} {%- endblock %} statsmodels-0.12.2/docs/source/about.rst000066400000000000000000000120201400612667500202340ustar00rootroot00000000000000.. module:: statsmodels :synopsis: Statistical analysis in Python .. currentmodule:: statsmodels ***************** About statsmodels ***************** Background ---------- The ``models`` module of ``scipy.stats`` was originally written by Jonathan Taylor. For some time it was part of scipy but was later removed. During the Google Summer of Code 2009, ``statsmodels`` was corrected, tested, improved and released as a new package. Since then, the statsmodels development team has continued to add new models, plotting tools, and statistical methods. Testing ------- Most results have been verified with at least one other statistical package: R, Stata or SAS. The guiding principle for the initial rewrite and for continued development is that all numbers have to be verified. Some statistical methods are tested with Monte Carlo studies. While we strive to follow this test-driven approach, there is no guarantee that the code is bug-free and always works. Some auxiliary function are still insufficiently tested, some edge cases might not be correctly taken into account, and the possibility of numerical problems is inherent to many of the statistical models. We especially appreciate any help and reports for these kind of problems so we can keep improving the existing models. Code Stability ^^^^^^^^^^^^^^ The existing models are mostly settled in their user interface and we do not expect many large changes going forward. For the existing code, although there is no guarantee yet on API stability, we have long deprecation periods in all but very special cases, and we try to keep changes that require adjustments by existing users to a minimal level. For newer models we might adjust the user interface as we gain more experience and obtain feedback. These changes will always be noted in our release notes available in the documentation. Reporting Bugs ^^^^^^^^^^^^^^ If you encounter a bug or an unexpected behavior, please report it on `the issue tracker `_. Use the ``show_versions`` command to list the installed versions of statsmodels and its dependencies. .. autosummary:: :toctree: generated/ ~statsmodels.tools.print_version.show_versions Financial Support ----------------- We are grateful for the financial support that we obtained for the development of statsmodels: * Google `www.google.com `_ : Google Summer of Code (GSOC) 2009-2017. * AQR `www.aqr.com `_ : financial sponsor for the work on Vector Autoregressive Models (VAR) by Wes McKinney We would also like to thank our hosting providers, `github `_ for the public code repository, `github.io `_ for hosting our documentation and `python.org `_ for making our downloads available on PyPi. We also thank our continuous integration providers, `Travis CI `_ and `AppVeyor `_ for unit testing, and `Codecov `_ and `Coveralls `_ for code coverage. Brand Marks ----------- Please make use of the statsmodels logos when preparing demonstrations involving statsmodels code. Color ^^^^^ +----------------+---------------------+ | Horizontal | |color-horizontal| | +----------------+---------------------+ | Vertical | |color-vertical| | +----------------+---------------------+ | Logo Only | |color-notext| | +----------------+---------------------+ Monochrome (Dark) ^^^^^^^^^^^^^^^^^ +----------------+---------------------+ | Horizontal | |dark-horizontal| | +----------------+---------------------+ | Vertical | |dark-vertical| | +----------------+---------------------+ | Logo Only | |dark-notext| | +----------------+---------------------+ Monochrome (Light) ^^^^^^^^^^^^^^^^^^ .. note:: The light brand marks are light grey on transparent, and so are difficult to see on this page. They are intended for use on a dark background. +----------------+---------------------+ | Horizontal | |light-horizontal| | +----------------+---------------------+ | Vertical | |light-vertical| | +----------------+---------------------+ | Logo Only | |light-notext| | +----------------+---------------------+ .. |color-horizontal| image:: images/statsmodels-logo-v2-horizontal.svg :width: 50% .. |color-vertical| image:: images/statsmodels-logo-v2.svg :width: 14% .. |color-notext| image:: images/statsmodels-logo-v2-no-text.svg :width: 9% .. |dark-horizontal| image:: images/statsmodels-logo-v2-horizontal-dark.svg :width: 50% .. |dark-vertical| image:: images/statsmodels-logo-v2-dark.svg :width: 14% .. |dark-notext| image:: images/statsmodels-logo-v2-no-text-dark.svg :width: 9% .. |light-horizontal| image:: images/statsmodels-logo-v2-horizontal-light.svg :width: 50% .. |light-vertical| image:: images/statsmodels-logo-v2-light.svg :width: 14% .. |light-notext| image:: images/statsmodels-logo-v2-no-text-light.svg :width: 9% statsmodels-0.12.2/docs/source/anova.rst000066400000000000000000000021361400612667500202350ustar00rootroot00000000000000.. currentmodule:: statsmodels.stats.anova .. _anova: ANOVA ===== Analysis of Variance models containing anova_lm for ANOVA analysis with a linear OLSModel, and AnovaRM for repeated measures ANOVA, within ANOVA for balanced data. Examples -------- .. ipython:: python import statsmodels.api as sm from statsmodels.formula.api import ols moore = sm.datasets.get_rdataset("Moore", "carData", cache=True) # load data data = moore.data data = data.rename(columns={"partner.status": "partner_status"}) # make name pythonic moore_lm = ols('conformity ~ C(fcategory, Sum)*C(partner_status, Sum)', data=data).fit() table = sm.stats.anova_lm(moore_lm, typ=2) # Type 2 ANOVA DataFrame print(table) A more detailed example for `anova_lm` can be found here: * `ANOVA `__ Module Reference ---------------- .. module:: statsmodels.stats.anova :synopsis: Analysis of Variance .. autosummary:: :toctree: generated/ anova_lm AnovaRM statsmodels-0.12.2/docs/source/api-structure.rst000066400000000000000000000100451400612667500217360ustar00rootroot00000000000000.. _importpaths: Import Paths and Structure -------------------------- We offer two ways of importing functions and classes from statsmodels: 1. `API import for interactive use`_ + Allows tab completion 2. `Direct import for programs`_ + Avoids importing unnecessary modules and commands API Import for interactive use ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ For interactive use the recommended import is: .. code-block:: python import statsmodels.api as sm Importing `statsmodels.api` will load most of the public parts of statsmodels. This makes most functions and classes conveniently available within one or two levels, without making the "sm" namespace too crowded. To see what functions and classes available, you can type the following (or use the namespace exploration features of IPython, Spyder, IDLE, etc.): .. code-block:: python >>> dir(sm) ['GLM', 'GLS', 'GLSAR', 'Logit', 'MNLogit', 'OLS', 'Poisson', 'Probit', 'RLM', 'WLS', '__builtins__', '__doc__', '__file__', '__name__', '__package__', 'add_constant', 'categorical', 'datasets', 'distributions', 'families', 'graphics', 'iolib', 'nonparametric', 'qqplot', 'regression', 'robust', 'stats', 'test', 'tools', 'tsa', 'version'] >>> dir(sm.graphics) ['__builtins__', '__doc__', '__file__', '__name__', '__package__', 'abline_plot', 'beanplot', 'fboxplot', 'interaction_plot', 'qqplot', 'rainbow', 'rainbowplot', 'violinplot'] >>> dir(sm.tsa) ['AR', 'ARMA', 'SVAR', 'VAR', '__builtins__', '__doc__', '__file__', '__name__', '__package__', 'acf', 'acovf', 'add_lag', 'add_trend', 'adfuller', 'ccf', 'ccovf', 'datetools', 'detrend', 'filters', 'grangercausalitytests', 'interp', 'lagmat', 'lagmat2ds', 'pacf', 'pacf_ols', 'pacf_yw', 'periodogram', 'q_stat', 'stattools', 'tsatools', 'var'] Notes ^^^^^ The `api` modules may not include all the public functionality of statsmodels. If you find something that should be added to the api, please file an issue on github or report it to the mailing list. The subpackages of statsmodels include `api.py` modules that are mainly intended to collect the imports needed for those subpackages. The `subpackage/api.py` files are imported into statsmodels api, for example :: from .nonparametric import api as nonparametric Users do not need to load the `subpackage/api.py` modules directly. Direct import for programs ~~~~~~~~~~~~~~~~~~~~~~~~~~ ``statsmodels`` submodules are arranged by topic (e.g. `discrete` for discrete choice models, or `tsa` for time series analysis). Our directory tree (stripped down) looks something like this:: statsmodels/ __init__.py api.py discrete/ __init__.py discrete_model.py tests/ results/ tsa/ __init__.py api.py tsatools.py stattools.py arima_model.py arima_process.py vector_ar/ __init__.py var_model.py tests/ results/ tests/ results/ stats/ __init__.py api.py stattools.py tests/ tools/ __init__.py tools.py decorators.py tests/ The submodules that can be import heavy contain an empty `__init__.py`, except for some testing code for running tests for the submodules. The intention is to change all directories to have an `api.py` and empty `__init__.py` in the next release. Import examples ^^^^^^^^^^^^^^^ Functions and classes:: from statsmodels.regression.linear_model import OLS, WLS from statsmodels.tools.tools import rank, add_constant Modules :: from statsmodels.datasets import macrodata import statsmodels.stats import diagnostic Modules with aliases :: import statsmodels.regression.linear_model as lm import statsmodels.stats.diagnostic as smsdia import statsmodels.stats.outliers_influence as oi We do not have currently a convention for aliases of submodules. statsmodels-0.12.2/docs/source/api.rst000066400000000000000000000166451400612667500177140ustar00rootroot00000000000000API Reference ============= The main statsmodels API is split into models: * ``statsmodels.api``: Cross-sectional models and methods. Canonically imported using ``import statsmodels.api as sm``. * ``statsmodels.tsa.api``: Time-series models and methods. Canonically imported using ``import statsmodels.tsa.api as tsa``. * ``statsmodels.formula.api``: A convenience interface for specifying models using formula strings and DataFrames. This API directly exposes the ``from_formula`` class method of models that support the formula API. Canonically imported using ``import statsmodels.formula.api as smf`` The API focuses on models and the most frequently used statistical test, and tools. :ref:`api-structure:Import Paths and Structure` explains the design of the two API modules and how importing from the API differs from directly importing from the module where the model is defined. See the detailed topic pages in the :ref:`user-guide:User Guide` for a complete list of available models, statistics, and tools. ``statsmodels.api`` ------------------- Regression ~~~~~~~~~~ .. autosummary:: ~statsmodels.regression.linear_model.OLS ~statsmodels.regression.linear_model.GLS ~statsmodels.regression.linear_model.GLSAR ~statsmodels.regression.linear_model.WLS ~statsmodels.regression.recursive_ls.RecursiveLS ~statsmodels.regression.rolling.RollingOLS ~statsmodels.regression.rolling.RollingWLS Imputation ~~~~~~~~~~ .. autosummary:: ~statsmodels.imputation.bayes_mi.BayesGaussMI ~statsmodels.genmod.bayes_mixed_glm.BinomialBayesMixedGLM ~statsmodels.multivariate.factor.Factor ~statsmodels.imputation.bayes_mi.MI ~statsmodels.imputation.mice.MICE ~statsmodels.imputation.mice.MICEData Generalized Estimating Equations ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. autosummary:: ~statsmodels.genmod.generalized_estimating_equations.GEE ~statsmodels.genmod.generalized_estimating_equations.NominalGEE ~statsmodels.genmod.generalized_estimating_equations.OrdinalGEE Generalized Linear Models ~~~~~~~~~~~~~~~~~~~~~~~~~ .. autosummary:: ~statsmodels.genmod.generalized_linear_model.GLM ~statsmodels.gam.generalized_additive_model.GLMGam ~statsmodels.genmod.bayes_mixed_glm.PoissonBayesMixedGLM Discrete and Count Models ~~~~~~~~~~~~~~~~~~~~~~~~~ .. autosummary:: ~statsmodels.discrete.discrete_model.GeneralizedPoisson ~statsmodels.discrete.discrete_model.Logit ~statsmodels.discrete.discrete_model.MNLogit ~statsmodels.discrete.discrete_model.Poisson ~statsmodels.discrete.discrete_model.Probit ~statsmodels.discrete.discrete_model.NegativeBinomial ~statsmodels.discrete.discrete_model.NegativeBinomialP ~statsmodels.discrete.count_model.ZeroInflatedGeneralizedPoisson ~statsmodels.discrete.count_model.ZeroInflatedNegativeBinomialP ~statsmodels.discrete.count_model.ZeroInflatedPoisson Multivariate Models ~~~~~~~~~~~~~~~~~~~ .. autosummary:: ~statsmodels.multivariate.manova.MANOVA ~statsmodels.multivariate.pca.PCA Misc Models ~~~~~~~~~~~ .. autosummary:: ~statsmodels.regression.mixed_linear_model.MixedLM ~statsmodels.duration.hazard_regression.PHReg ~statsmodels.regression.quantile_regression.QuantReg ~statsmodels.robust.robust_linear_model.RLM ~statsmodels.duration.survfunc.SurvfuncRight Graphics ~~~~~~~~ .. autosummary:: ~statsmodels.graphics.gofplots.ProbPlot ~statsmodels.graphics.gofplots.qqline ~statsmodels.graphics.gofplots.qqplot ~statsmodels.graphics.gofplots.qqplot_2samples Statistics ~~~~~~~~~~ .. autosummary:: ~statsmodels.stats.descriptivestats.Description ~statsmodels.stats.descriptivestats.describe Tools ~~~~~ .. autosummary:: ~statsmodels.__init__.test ~statsmodels.tools.tools.add_constant ~statsmodels.iolib.smpickle.load_pickle ~statsmodels.tools.print_version.show_versions ~statsmodels.tools.web.webdoc ``statsmodels.tsa.api`` ----------------------- Statistics and Tests ~~~~~~~~~~~~~~~~~~~~ .. autosummary:: ~statsmodels.tsa.stattools.acf ~statsmodels.tsa.stattools.acovf ~statsmodels.tsa.stattools.adfuller ~statsmodels.tsa.stattools.bds ~statsmodels.tsa.stattools.ccf ~statsmodels.tsa.stattools.ccovf ~statsmodels.tsa.stattools.coint ~statsmodels.tsa.stattools.kpss ~statsmodels.tsa.stattools.pacf ~statsmodels.tsa.stattools.pacf_ols ~statsmodels.tsa.stattools.pacf_yw ~statsmodels.tsa.stattools.q_stat Univariate Time-Series Analysis ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. autosummary:: ~statsmodels.tsa.ar_model.AutoReg ~statsmodels.tsa.arima.model.ARIMA ~statsmodels.tsa.statespace.sarimax.SARIMAX ~statsmodels.tsa.stattools.arma_order_select_ic ~statsmodels.tsa.arima_process.arma_generate_sample ~statsmodels.tsa.arima_process.ArmaProcess Exponential Smoothing ~~~~~~~~~~~~~~~~~~~~~ .. autosummary:: ~statsmodels.tsa.holtwinters.ExponentialSmoothing ~statsmodels.tsa.holtwinters.Holt ~statsmodels.tsa.holtwinters.SimpleExpSmoothing ~statsmodels.tsa.statespace.exponential_smoothing.ExponentialSmoothing ~statsmodels.tsa.exponential_smoothing.ets.ETSModel Multivariate Time Series Models ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. autosummary:: ~statsmodels.tsa.statespace.dynamic_factor.DynamicFactor ~statsmodels.tsa.statespace.dynamic_factor_mq.DynamicFactorMQ ~statsmodels.tsa.vector_ar.var_model.VAR ~statsmodels.tsa.statespace.varmax.VARMAX ~statsmodels.tsa.vector_ar.svar_model.SVAR ~statsmodels.tsa.vector_ar.vecm.VECM ~statsmodels.tsa.statespace.structural.UnobservedComponents Filters and Decompositions ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. autosummary:: ~statsmodels.tsa.seasonal.seasonal_decompose ~statsmodels.tsa.seasonal.STL ~statsmodels.tsa.filters.bk_filter.bkfilter ~statsmodels.tsa.filters.cf_filter.cffilter ~statsmodels.tsa.filters.hp_filter.hpfilter Markov Regime Switching Models ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. autosummary:: ~statsmodels.tsa.regime_switching.markov_autoregression.MarkovAutoregression ~statsmodels.tsa.regime_switching.markov_regression.MarkovRegression Forecasting ~~~~~~~~~~~ .. autosummary:: ~statsmodels.tsa.forecasting.stl.STLForecast ~statsmodels.tsa.forecasting.theta.ThetaModel Time-Series Tools ~~~~~~~~~~~~~~~~~ .. autosummary:: ~statsmodels.tsa.tsatools.add_lag ~statsmodels.tsa.tsatools.add_trend ~statsmodels.tsa.tsatools.detrend ~statsmodels.tsa.tsatools.lagmat ~statsmodels.tsa.tsatools.lagmat2ds ~statsmodels.tsa.deterministic.DeterministicProcess X12/X13 Interface ~~~~~~~~~~~~~~~~~ .. autosummary:: ~statsmodels.tsa.x13.x13_arima_analysis ~statsmodels.tsa.x13.x13_arima_select_order ``statsmodels.formula.api`` --------------------------- Models ~~~~~~ The function descriptions of the methods exposed in the formula API are generic. See the documentation for the parent model for details. .. autosummary:: :toctree: generated/ ~statsmodels.formula.api.gls ~statsmodels.formula.api.wls ~statsmodels.formula.api.ols ~statsmodels.formula.api.glsar ~statsmodels.formula.api.mixedlm ~statsmodels.formula.api.glm ~statsmodels.formula.api.rlm ~statsmodels.formula.api.mnlogit ~statsmodels.formula.api.logit ~statsmodels.formula.api.probit ~statsmodels.formula.api.poisson ~statsmodels.formula.api.negativebinomial ~statsmodels.formula.api.quantreg ~statsmodels.formula.api.phreg ~statsmodels.formula.api.ordinal_gee ~statsmodels.formula.api.nominal_gee ~statsmodels.formula.api.gee ~statsmodels.formula.api.glmgam statsmodels-0.12.2/docs/source/conf.py000066400000000000000000000351101400612667500176740ustar00rootroot00000000000000# -*- coding: utf-8 -*- # # statsmodels documentation build configuration file, created by # sphinx-quickstart on Sat Jan 22 11:17:58 2011. # # This file is execfile()d with the current directory set to its # containing dir. # # Note that not all possible configuration values are present in this # autogenerated file. # # All configuration values have a default; values that are commented out # serve to show the default. import contextlib from distutils.version import LooseVersion import os from os.path import dirname, join import sys import yaml from numpydoc.xref import DEFAULT_LINKS import sphinx_material from statsmodels import __version__ # -- Monkey Patch ---------------------------------------------------------- # Monkey patch contextlib.contextmanager.__doc__ to avoid noise contextlib.contextmanager.__doc__ = '' # If extensions (or modules to document with autodoc) are in another directory, # add these directories to sys.path here. 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Default is True. # html_show_sphinx = True # If true, '(C) Copyright ...' is shown in the HTML footer. Default is True. # html_show_copyright = True # If true, an OpenSearch description file will be output, and all pages will # contain a tag referring to it. The value of this option must be the # base URL from which the finished HTML is served. # html_use_opensearch = '' # This is the file name suffix for HTML files (e.g. '.xhtml'). # html_file_suffix = None # Output file base name for HTML help builder. htmlhelp_basename = 'statsmodelsdoc' # Options for LaTeX output # The paper size ('letter' or 'a4'). # latex_paper_size = 'letter' # The font size ('10pt', '11pt' or '12pt'). # latex_font_size = '10pt' # Grouping the document tree into LaTeX files. List of tuples # (source start file, target name, title, author, # documentclass [howto/manual]). latex_documents = [ ('index', 'statsmodels.tex', u'statsmodels Documentation', u'Josef Perktold, Skipper Seabold', 'manual'), ] # The name of an image file (relative to this directory) to place at the top of # the title page. # latex_logo = None # For 'manual' documents, if this is true, then toplevel headings are parts, # not chapters. # latex_use_parts = False # If true, show page references after internal links. # latex_show_pagerefs = False # If true, show URL addresses after external links. # latex_show_urls = False # Additional stuff for the LaTeX preamble. # latex_preamble = '' # Documents to append as an appendix to all manuals. # latex_appendices = [] # If false, no module index is generated. # latex_domain_indices = True # imgmath options imgmath_image_format = 'png' imgmath_latex_preamble = r'\usepackage[active]{preview}' imgmath_use_preview = True # Options for manual page output # One entry per manual page. List of tuples # (source start file, name, description, authors, manual section). man_pages = [ ('index', 'statsmodels', u'statsmodels Documentation', [u'Josef Perktold, Skipper Seabold, Jonathan Taylor'], 1) ] # Options for Epub output # Bibliographic Dublin Core info. epub_title = u'statsmodels' epub_author = u'Josef Perktold, Skipper Seabold' epub_publisher = u'Josef Perktold, Skipper Seabold' epub_copyright = u'2009-2019, Josef Perktold, Skipper Seabold, ' \ u'Jonathan Taylor, statsmodels-developers' # The language of the text. It defaults to the language option # or en if the language is not set. # epub_language = '' # The scheme of the identifier. Typical schemes are ISBN or URL. # epub_scheme = '' # The unique identifier of the text. This can be a ISBN number # or the project homepage. # epub_identifier = '' # A unique identification for the text. # epub_uid = '' # HTML files that should be inserted before the pages created by sphinx. # The format is a list of tuples containing the path and title. # epub_pre_files = [] # HTML files shat should be inserted after the pages created by sphinx. # The format is a list of tuples containing the path and title. # epub_post_files = [] # A list of files that should not be packed into the epub file. # epub_exclude_files = [] # The depth of the table of contents in toc.ncx. # epub_tocdepth = 3 # Allow duplicate toc entries. # epub_tocdup = True # Numpydoc options # numpydoc_attributes_as_param_list = True # numpydoc_show_class_members = False # numpydoc_show_inherited_class_members = True # Create xrefs numpydoc_xref_param_type = True numpydoc_class_members_toctree = False numpydoc_xref_aliases = DEFAULT_LINKS.copy() numpydoc_xref_aliases.update({ 'Figure': 'matplotlib.figure.Figure', 'Axes': 'matplotlib.axes.Axes', 'AxesSubplot': 'matplotlib.axes.Axes', 'DataFrame': 'pandas.DataFrame', 'Series': 'pandas.Series', 'MLEResults': 'statsmodels.tsa.statespace.mlemodel.MLEResults' }) # NBSphinx options nbsphinx_execute = "never" # Example configuration for intersphinx: refer to the Python standard library. # Example configuration for intersphinx: refer to the Python standard library. intersphinx_mapping = { 'numpy': ('https://docs.scipy.org/doc/numpy/', None), 'python': ('https://docs.python.org/3/', None), 'pydagogue': ('https://matthew-brett.github.io/pydagogue/', None), 'matplotlib': ('https://matplotlib.org/', None), 'scipy': ('https://docs.scipy.org/doc/scipy/reference/', None), 'pandas': ('https://pandas.pydata.org/pandas-docs/stable/', None), } plot_basedir = join(dirname(dirname(os.path.abspath(__file__))), 'source') # ghissue config github_project_url = 'https://github.com/statsmodels/statsmodels' example_context = yaml.safe_load(open('examples/landing.yml')) html_context.update({'examples': example_context}) # --------------- DOCTEST ------------------- doctest_global_setup = """ import statsmodels.api as sm import statsmodels.tsa.api as tsa import statsmodels.formula.api as smf import numpy as np import scipy.stats as stats import matplotlib.pyplot as plt import pandas as pd """ extlinks = {'pr': ('https://github.com/statsmodels/statsmodels/pull/%s', 'PR #'), 'issue': ('https://github.com/statsmodels/statsmodels/issues/%s', 'Issue #') } autosectionlabel_prefix_document = True def rstjinja(app, docname, source): """ Render our pages as a jinja template for fancy templating goodness. """ # http://ericholscher.com/blog/2016/jul/25/integrating-jinja-rst-sphinx/ # Make sure we're outputting HTML if app.builder.format != "html": return src = source[0] # Skip converted notebooks if 'nbconvert_exporter' in src: return try: rendered = app.builder.templates.render_string(src, app.config.html_context) source[0] = rendered except Exception as exc: from sphinx.util import logging logger = logging.getLogger(__name__) logger.warning(exc) logger.warning(source[0]) def setup(app): app.connect("source-read", rstjinja) return {'parallel_read_safe': True, 'parallel_write_safe': True} statsmodels-0.12.2/docs/source/contingency_tables.rst000066400000000000000000000233451400612667500230100ustar00rootroot00000000000000.. currentmodule:: statsmodels.stats.contingency_tables .. _contingency_tables: Contingency tables ================== statsmodels supports a variety of approaches for analyzing contingency tables, including methods for assessing independence, symmetry, homogeneity, and methods for working with collections of tables from a stratified population. The methods described here are mainly for two-way tables. Multi-way tables can be analyzed using log-linear models. statsmodels does not currently have a dedicated API for loglinear modeling, but Poisson regression in :class:`statsmodels.genmod.GLM` can be used for this purpose. A contingency table is a multi-way table that describes a data set in which each observation belongs to one category for each of several variables. For example, if there are two variables, one with :math:`r` levels and one with :math:`c` levels, then we have a :math:`r \times c` contingency table. The table can be described in terms of the number of observations that fall into a given cell of the table, e.g. :math:`T_{ij}` is the number of observations that have level :math:`i` for the first variable and level :math:`j` for the second variable. Note that each variable must have a finite number of levels (or categories), which can be either ordered or unordered. In different contexts, the variables defining the axes of a contingency table may be called **categorical variables** or **factor variables**. They may be either **nominal** (if their levels are unordered) or **ordinal** (if their levels are ordered). The underlying population for a contingency table is described by a **distribution table** :math:`P_{i, j}`. The elements of :math:`P` are probabilities, and the sum of all elements in :math:`P` is 1. Methods for analyzing contingency tables use the data in :math:`T` to learn about properties of :math:`P`. The :class:`statsmodels.stats.Table` is the most basic class for working with contingency tables. We can create a ``Table`` object directly from any rectangular array-like object containing the contingency table cell counts: .. ipython:: python import numpy as np import pandas as pd import statsmodels.api as sm df = sm.datasets.get_rdataset("Arthritis", "vcd").data tab = pd.crosstab(df['Treatment'], df['Improved']) tab = tab.loc[:, ["None", "Some", "Marked"]] table = sm.stats.Table(tab) Alternatively, we can pass the raw data and let the Table class construct the array of cell counts for us: .. ipython:: python data = df[["Treatment", "Improved"]] table = sm.stats.Table.from_data(data) Independence ------------ **Independence** is the property that the row and column factors occur independently. **Association** is the lack of independence. If the joint distribution is independent, it can be written as the outer product of the row and column marginal distributions: .. math:: P_{ij} = \sum_k P_{ij} \cdot \sum_k P_{kj} \quad \text{for all} \quad i, j We can obtain the best-fitting independent distribution for our observed data, and then view residuals which identify particular cells that most strongly violate independence: .. ipython:: python print(table.table_orig) print(table.fittedvalues) print(table.resid_pearson) In this example, compared to a sample from a population in which the rows and columns are independent, we have too many observations in the placebo/no improvement and treatment/marked improvement cells, and too few observations in the placebo/marked improvement and treated/no improvement cells. This reflects the apparent benefits of the treatment. If the rows and columns of a table are unordered (i.e. are nominal factors), then the most common approach for formally assessing independence is using Pearson's :math:`\chi^2` statistic. It's often useful to look at the cell-wise contributions to the :math:`\chi^2` statistic to see where the evidence for dependence is coming from. .. ipython:: python rslt = table.test_nominal_association() print(rslt.pvalue) print(table.chi2_contribs) For tables with ordered row and column factors, we can us the **linear by linear** association test to obtain more power against alternative hypotheses that respect the ordering. The test statistic for the linear by linear association test is .. math:: \sum_k r_i c_j T_{ij} where :math:`r_i` and :math:`c_j` are row and column scores. Often these scores are set to the sequences 0, 1, .... This gives the 'Cochran-Armitage trend test'. .. ipython:: python rslt = table.test_ordinal_association() print(rslt.pvalue) We can assess the association in a :math:`r\times x` table by constructing a series of :math:`2\times 2` tables and calculating their odds ratios. There are two ways to do this. The **local odds ratios** construct :math:`2\times 2` tables from adjacent row and column categories. .. ipython:: python print(table.local_oddsratios) taloc = sm.stats.Table2x2(np.asarray([[7, 29], [21, 13]])) print(taloc.oddsratio) taloc = sm.stats.Table2x2(np.asarray([[29, 7], [13, 7]])) print(taloc.oddsratio) The **cumulative odds ratios** construct :math:`2\times 2` tables by dichotomizing the row and column factors at each possible point. .. ipython:: python print(table.cumulative_oddsratios) tab1 = np.asarray([[7, 29 + 7], [21, 13 + 7]]) tacum = sm.stats.Table2x2(tab1) print(tacum.oddsratio) tab1 = np.asarray([[7 + 29, 7], [21 + 13, 7]]) tacum = sm.stats.Table2x2(tab1) print(tacum.oddsratio) A mosaic plot is a graphical approach to informally assessing dependence in two-way tables. .. ipython:: python from statsmodels.graphics.mosaicplot import mosaic fig, _ = mosaic(data, index=["Treatment", "Improved"]) Symmetry and homogeneity ------------------------ **Symmetry** is the property that :math:`P_{i, j} = P_{j, i}` for every :math:`i` and :math:`j`. **Homogeneity** is the property that the marginal distribution of the row factor and the column factor are identical, meaning that .. math:: \sum_j P_{ij} = \sum_j P_{ji} \forall i Note that for these properties to be applicable the table :math:`P` (and :math:`T`) must be square, and the row and column categories must be identical and must occur in the same order. To illustrate, we load a data set, create a contingency table, and calculate the row and column margins. The :class:`Table` class contains methods for analyzing :math:`r \times c` contingency tables. The data set loaded below contains assessments of visual acuity in people's left and right eyes. We first load the data and create a contingency table. .. ipython:: python df = sm.datasets.get_rdataset("VisualAcuity", "vcd").data df = df.loc[df.gender == "female", :] tab = df.set_index(['left', 'right']) del tab["gender"] tab = tab.unstack() tab.columns = tab.columns.get_level_values(1) print(tab) Next we create a :class:`SquareTable` object from the contingency table. .. ipython:: python sqtab = sm.stats.SquareTable(tab) row, col = sqtab.marginal_probabilities print(row) print(col) The ``summary`` method prints results for the symmetry and homogeneity testing procedures. .. ipython:: python print(sqtab.summary()) If we had the individual case records in a dataframe called ``data``, we could also perform the same analysis by passing the raw data using the ``SquareTable.from_data`` class method. :: sqtab = sm.stats.SquareTable.from_data(data[['left', 'right']]) print(sqtab.summary()) A single 2x2 table ------------------ Several methods for working with individual 2x2 tables are provided in the :class:`sm.stats.Table2x2` class. The ``summary`` method displays several measures of association between the rows and columns of the table. .. ipython:: python table = np.asarray([[35, 21], [25, 58]]) t22 = sm.stats.Table2x2(table) print(t22.summary()) Note that the risk ratio is not symmetric so different results will be obtained if the transposed table is analyzed. .. ipython:: python table = np.asarray([[35, 21], [25, 58]]) t22 = sm.stats.Table2x2(table.T) print(t22.summary()) Stratified 2x2 tables --------------------- Stratification occurs when we have a collection of contingency tables defined by the same row and column factors. In the example below, we have a collection of 2x2 tables reflecting the joint distribution of smoking and lung cancer in each of several regions of China. It is possible that the tables all have a common odds ratio, even while the marginal probabilities vary among the strata. The 'Breslow-Day' procedure tests whether the data are consistent with a common odds ratio. It appears below as the `Test of constant OR`. The Mantel-Haenszel procedure tests whether this common odds ratio is equal to one. It appears below as the `Test of OR=1`. It is also possible to estimate the common odds and risk ratios and obtain confidence intervals for them. The ``summary`` method displays all of these results. Individual results can be obtained from the class methods and attributes. .. ipython:: python data = sm.datasets.china_smoking.load_pandas() mat = np.asarray(data.data) tables = [np.reshape(x.tolist(), (2, 2)) for x in mat] st = sm.stats.StratifiedTable(tables) print(st.summary()) Module Reference ---------------- .. module:: statsmodels.stats.contingency_tables :synopsis: Contingency table analysis .. currentmodule:: statsmodels.stats.contingency_tables .. autosummary:: :toctree: generated/ Table Table2x2 SquareTable StratifiedTable mcnemar cochrans_q See also -------- Scipy_ has several functions for analyzing contingency tables, including Fisher's exact test which is not currently in statsmodels. .. _Scipy: https://docs.scipy.org/doc/scipy-0.18.0/reference/stats.html#contingency-table-functions statsmodels-0.12.2/docs/source/contrasts.rst000066400000000000000000000252331400612667500211540ustar00rootroot00000000000000:orphan: Patsy: Contrast Coding Systems for categorical variables =========================================================== .. note:: This document is based on `this excellent resource from UCLA `__. A categorical variable of K categories, or levels, usually enters a regression as a sequence of K-1 dummy variables. This amounts to a linear hypothesis on the level means. That is, each test statistic for these variables amounts to testing whether the mean for that level is statistically significantly different from the mean of the base category. This dummy coding is called Treatment coding in R parlance, and we will follow this convention. There are, however, different coding methods that amount to different sets of linear hypotheses. In fact, the dummy coding is not technically a contrast coding. This is because the dummy variables add to one and are not functionally independent of the model's intercept. On the other hand, a set of *contrasts* for a categorical variable with `k` levels is a set of `k-1` functionally independent linear combinations of the factor level means that are also independent of the sum of the dummy variables. The dummy coding is not wrong *per se*. It captures all of the coefficients, but it complicates matters when the model assumes independence of the coefficients such as in ANOVA. Linear regression models do not assume independence of the coefficients and thus dummy coding is often the only coding that is taught in this context. To have a look at the contrast matrices in Patsy, we will use data from UCLA ATS. First let's load the data. .. ipython:: :suppress: In [1]: import numpy as np ...: np.set_printoptions(precision=4, suppress=True) ...: ...: from patsy.contrasts import ContrastMatrix ...: ...: def _name_levels(prefix, levels): ...: return ["[%s%s]" % (prefix, level) for level in levels] In [2]: class Simple(object): ...: def _simple_contrast(self, levels): ...: nlevels = len(levels) ...: contr = -1./nlevels * np.ones((nlevels, nlevels-1)) ...: contr[1:][np.diag_indices(nlevels-1)] = (nlevels-1.)/nlevels ...: return contr ...: ...: def code_with_intercept(self, levels): ...: contrast = np.column_stack((np.ones(len(levels)), ...: self._simple_contrast(levels))) ...: return ContrastMatrix(contrast, _name_levels("Simp.", levels)) ...: ...: def code_without_intercept(self, levels): ...: contrast = self._simple_contrast(levels) ...: return ContrastMatrix(contrast, _name_levels("Simp.", levels[:-1])) ...: Example Data ------------ .. ipython:: python import pandas url = 'https://stats.idre.ucla.edu/stat/data/hsb2.csv' hsb2 = pandas.read_csv(url) It will be instructive to look at the mean of the dependent variable, write, for each level of race ((1 = Hispanic, 2 = Asian, 3 = African American and 4 = Caucasian)). .. ipython:: python hsb2.groupby('race')['write'].mean() Treatment (Dummy) Coding ------------------------ Dummy coding is likely the most well known coding scheme. It compares each level of the categorical variable to a base reference level. The base reference level is the value of the intercept. It is the default contrast in Patsy for unordered categorical factors. The Treatment contrast matrix for race would be .. ipython:: python from patsy.contrasts import Treatment levels = [1,2,3,4] contrast = Treatment(reference=0).code_without_intercept(levels) print(contrast.matrix) Here we used `reference=0`, which implies that the first level, Hispanic, is the reference category against which the other level effects are measured. As mentioned above, the columns do not sum to zero and are thus not independent of the intercept. To be explicit, let's look at how this would encode the `race` variable. .. ipython:: python contrast.matrix[hsb2.race-1, :][:20] This is a bit of a trick, as the `race` category conveniently maps to zero-based indices. If it does not, this conversion happens under the hood, so this will not work in general but nonetheless is a useful exercise to fix ideas. The below illustrates the output using the three contrasts above .. ipython:: python from statsmodels.formula.api import ols mod = ols("write ~ C(race, Treatment)", data=hsb2) res = mod.fit() print(res.summary()) We explicitly gave the contrast for race; however, since Treatment is the default, we could have omitted this. Simple Coding ------------- Like Treatment Coding, Simple Coding compares each level to a fixed reference level. However, with simple coding, the intercept is the grand mean of all the levels of the factors. See :ref:`user-defined` for how to implement the Simple contrast. .. ipython:: python contrast = Simple().code_without_intercept(levels) print(contrast.matrix) mod = ols("write ~ C(race, Simple)", data=hsb2) res = mod.fit() print(res.summary()) Sum (Deviation) Coding ---------------------- Sum coding compares the mean of the dependent variable for a given level to the overall mean of the dependent variable over all the levels. That is, it uses contrasts between each of the first k-1 levels and level k In this example, level 1 is compared to all the others, level 2 to all the others, and level 3 to all the others. .. ipython:: python from patsy.contrasts import Sum contrast = Sum().code_without_intercept(levels) print(contrast.matrix) mod = ols("write ~ C(race, Sum)", data=hsb2) res = mod.fit() print(res.summary()) This corresponds to a parameterization that forces all the coefficients to sum to zero. Notice that the intercept here is the grand mean where the grand mean is the mean of means of the dependent variable by each level. .. ipython:: python hsb2.groupby('race')['write'].mean().mean() Backward Difference Coding -------------------------- In backward difference coding, the mean of the dependent variable for a level is compared with the mean of the dependent variable for the prior level. This type of coding may be useful for a nominal or an ordinal variable. .. ipython:: python from patsy.contrasts import Diff contrast = Diff().code_without_intercept(levels) print(contrast.matrix) mod = ols("write ~ C(race, Diff)", data=hsb2) res = mod.fit() print(res.summary()) For example, here the coefficient on level 1 is the mean of `write` at level 2 compared with the mean at level 1. Ie., .. ipython:: python res.params["C(race, Diff)[D.1]"] hsb2.groupby('race').mean()["write"][2] - \ hsb2.groupby('race').mean()["write"][1] Helmert Coding -------------- Our version of Helmert coding is sometimes referred to as Reverse Helmert Coding. The mean of the dependent variable for a level is compared to the mean of the dependent variable over all previous levels. Hence, the name 'reverse' being sometimes applied to differentiate from forward Helmert coding. This comparison does not make much sense for a nominal variable such as race, but we would use the Helmert contrast like so: .. ipython:: python from patsy.contrasts import Helmert contrast = Helmert().code_without_intercept(levels) print(contrast.matrix) mod = ols("write ~ C(race, Helmert)", data=hsb2) res = mod.fit() print(res.summary()) To illustrate, the comparison on level 4 is the mean of the dependent variable at the previous three levels taken from the mean at level 4 .. ipython:: python grouped = hsb2.groupby('race') grouped.mean()["write"][4] - grouped.mean()["write"][:3].mean() As you can see, these are only equal up to a constant. Other versions of the Helmert contrast give the actual difference in means. Regardless, the hypothesis tests are the same. .. ipython:: python k = 4 1./k * (grouped.mean()["write"][k] - grouped.mean()["write"][:k-1].mean()) k = 3 1./k * (grouped.mean()["write"][k] - grouped.mean()["write"][:k-1].mean()) Orthogonal Polynomial Coding ---------------------------- The coefficients taken on by polynomial coding for `k=4` levels are the linear, quadratic, and cubic trends in the categorical variable. The categorical variable here is assumed to be represented by an underlying, equally spaced numeric variable. Therefore, this type of encoding is used only for ordered categorical variables with equal spacing. In general, the polynomial contrast produces polynomials of order `k-1`. Since `race` is not an ordered factor variable let's use `read` as an example. First we need to create an ordered categorical from `read`. .. ipython:: python _, bins = np.histogram(hsb2.read, 3) try: # requires numpy master readcat = np.digitize(hsb2.read, bins, True) except: readcat = np.digitize(hsb2.read, bins) hsb2['readcat'] = readcat hsb2.groupby('readcat').mean()['write'] .. ipython:: python from patsy.contrasts import Poly levels = hsb2.readcat.unique().tolist() contrast = Poly().code_without_intercept(levels) print(contrast.matrix) mod = ols("write ~ C(readcat, Poly)", data=hsb2) res = mod.fit() print(res.summary()) As you can see, readcat has a significant linear effect on the dependent variable `write` but not a significant quadratic or cubic effect. .. _user-defined: User-Defined Coding ------------------- If you want to use your own coding, you must do so by writing a coding class that contains a code_with_intercept and a code_without_intercept method that return a `patsy.contrast.ContrastMatrix` instance. .. ipython:: In [1]: from patsy.contrasts import ContrastMatrix ...: ...: def _name_levels(prefix, levels): ...: return ["[%s%s]" % (prefix, level) for level in levels] In [2]: class Simple(object): ...: def _simple_contrast(self, levels): ...: nlevels = len(levels) ...: contr = -1./nlevels * np.ones((nlevels, nlevels-1)) ...: contr[1:][np.diag_indices(nlevels-1)] = (nlevels-1.)/nlevels ...: return contr ...: ...: def code_with_intercept(self, levels): ...: contrast = np.column_stack((np.ones(len(levels)), ...: self._simple_contrast(levels))) ...: return ContrastMatrix(contrast, _name_levels("Simp.", levels)) ...: ...: def code_without_intercept(self, levels): ...: contrast = self._simple_contrast(levels) ...: return ContrastMatrix(contrast, _name_levels("Simp.", levels[:-1])) In [3]: mod = ols("write ~ C(race, Simple)", data=hsb2) ...: res = mod.fit() ...: print(res.summary()) statsmodels-0.12.2/docs/source/datasets/000077500000000000000000000000001400612667500202055ustar00rootroot00000000000000statsmodels-0.12.2/docs/source/datasets/index.rst000066400000000000000000000070501400612667500220500ustar00rootroot00000000000000.. _datasets: .. currentmodule:: statsmodels.datasets .. ipython:: python :suppress: import numpy as np np.set_printoptions(suppress=True) The Datasets Package ==================== ``statsmodels`` provides data sets (i.e. data *and* meta-data) for use in examples, tutorials, model testing, etc. Using Datasets from Stata ------------------------- .. autosummary:: :toctree: ./ webuse Using Datasets from R --------------------- The `Rdatasets project `__ gives access to the datasets available in R's core datasets package and many other common R packages. All of these datasets are available to statsmodels by using the :func:`get_rdataset` function. The actual data is accessible by the ``data`` attribute. For example: .. ipython:: python import statsmodels.api as sm duncan_prestige = sm.datasets.get_rdataset("Duncan", "carData") print(duncan_prestige.__doc__) duncan_prestige.data.head(5) R Datasets Function Reference ----------------------------- .. autosummary:: :toctree: ./ get_rdataset get_data_home clear_data_home Available Datasets ------------------ .. toctree:: :maxdepth: 1 :glob: generated/* Usage ----- Load a dataset: .. ipython:: python import statsmodels.api as sm data = sm.datasets.longley.load_pandas() The `Dataset` object follows the bunch pattern. The full dataset is available in the ``data`` attribute. .. ipython:: python data.data Most datasets hold convenient representations of the data in the attributes `endog` and `exog`: .. ipython:: python data.endog.iloc[:5] data.exog.iloc[:5,:] Univariate datasets, however, do not have an `exog` attribute. Variable names can be obtained by typing: .. ipython:: python data.endog_name data.exog_name If the dataset does not have a clear interpretation of what should be an `endog` and `exog`, then you can always access the `data` or `raw_data` attributes. This is the case for the `macrodata` dataset, which is a collection of US macroeconomic data rather than a dataset with a specific example in mind. The `data` attribute contains a record array of the full dataset and the `raw_data` attribute contains an ndarray with the names of the columns given by the `names` attribute. .. ipython:: python type(data.data) type(data.raw_data) data.names Loading data as pandas objects ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ For many users it may be preferable to get the datasets as a pandas DataFrame or Series object. Each of the dataset modules is equipped with a ``load_pandas`` method which returns a ``Dataset`` instance with the data readily available as pandas objects: .. ipython:: python data = sm.datasets.longley.load_pandas() data.exog data.endog The full DataFrame is available in the ``data`` attribute of the Dataset object .. ipython:: python data.data With pandas integration in the estimation classes, the metadata will be attached to model results: .. ipython:: python :okwarning: y, x = data.endog, data.exog res = sm.OLS(y, x).fit() res.params res.summary() Extra Information ^^^^^^^^^^^^^^^^^ If you want to know more about the dataset itself, you can access the following, again using the Longley dataset as an example :: >>> dir(sm.datasets.longley)[:6] ['COPYRIGHT', 'DESCRLONG', 'DESCRSHORT', 'NOTE', 'SOURCE', 'TITLE'] Additional information ---------------------- * The idea for a datasets package was originally proposed by David Cournapeau. * To add datasets, see the :ref:`notes on adding a dataset `. statsmodels-0.12.2/docs/source/dev/000077500000000000000000000000001400612667500171535ustar00rootroot00000000000000statsmodels-0.12.2/docs/source/dev/dataset_notes.rst000066400000000000000000000051011400612667500225370ustar00rootroot00000000000000.. _add_data: Datasets ======== For a list of currently available datasets and usage instructions, see the :ref:`datasets page `. License ------- To be considered for inclusion in `statsmodels`, a dataset must be in the public domain, distributed under a BSD-compatible license, or we must obtain permission from the original author. Adding a dataset: An example ---------------------------- The Nile River data measures the volume of the discharge of the Nile River at Aswan for the years 1871 to 1970. The data are copied from the paper of Cobb (1978). **Step 1**: Create a directory `datasets/nile/` **Step 2**: Add `datasets/nile/nile.csv` and a new file `datasets/__init__.py` which contains :: from data import * **Step 3**: If `nile.csv` is a transformed/cleaned version of the original data, create a `nile/src` directory and include the original raw data there. In the `nile` case, this step is not necessary. **Step 4**: Copy `datasets/template_data.py` to `nile/data.py`. Edit `nile/data.py` by filling-in strings for COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCLONG, and NOTE. :: COPYRIGHT = """This is public domain.""" TITLE = """Nile River Data""" SOURCE = """ Cobb, G.W. 1978. The Problem of the Nile: Conditional Solution to a Changepoint Problem. Biometrika. 65.2, 243-251, """ DESCRSHORT = """Annual Nile River Volume at Aswan, 1871-1970"" DESCRLONG = """Annual Nile River Volume at Aswan, 1871-1970. The units of measurement are 1e9 m^{3}, and there is an apparent changepoint near 1898.""" NOTE = """ Number of observations: 100 Number of variables: 2 Variable name definitions: year - Year of observation volume - Nile River volume at Aswan The data were originally used in Cobb (1987, See SOURCE). The author acknowledges that the data were originally compiled from various sources by Dr. Barbara Bell, Center for Astrophysics, Cambridge, Massachusetts. The data set is also used as an example in many textbooks and software packages. """ **Step 5:** Edit the docstring of the `load` function in `data.py` to specify which dataset will be loaded. Also edit the path and the indices for the `endog` and `exog` attributes. In the `nile` case, there is no `exog`, so everything referencing `exog` is not used. The `year` variable is also not used. **Step 6:** Edit the `datasets/__init__.py` to import the directory. That's it! The result can be found `here `_ for reference. statsmodels-0.12.2/docs/source/dev/examples.rst000066400000000000000000000044531400612667500215310ustar00rootroot00000000000000.. _examples: Examples ======== Examples are invaluable for new users who hope to get up and running quickly with `statsmodels`, and they are extremely useful to those who wish to explore new features of `statsmodels`. We hope to provide documentation and tutorials for as many models and use-cases as possible! Please consider submitting an example with any PR that introduces new functionality. User-contributed examples/tutorials/recipes can be placed on the `statsmodels examples wiki page `_ That wiki page is freely editable. Please post your cool tricks, examples, and recipes on there! If you would rather have your example file officially accepted to the `statsmodels` distribution and posted on this website, you will need to go through the normal `patch submission process `_ and follow the instructions that follow. File Format ----------- Examples are best contributed as IPython notebooks. Save your notebook with all output cells cleared in ``examples/notebooks``. From the notebook save the pure Python output to ``examples/python``. The first line of the Notebook *must* be a header cell that contains a title for the notebook, if you want the notebook to be included in the documentation. The Example Gallery ------------------- We have a gallery of example notebooks available `here `_. If you would like your example to show up in this gallery, add a link to the notebook in ``docs/source/examples/landing.json``. For the thumbnail, take a screenshot of what you think is the best "hook" for the notebook. The image will be displayed at 360 x 225 (W x H). It's best to save the image as a PNG with a resolution that is some multiple of 360 x 225 (720 x 450 is preferred). Please remember to shrink the PNG file, if you can. `This website `_ can help with that. Before submitting a PR ---------------------- To save you some time and to make the new examples nicely fit into the existing ones consider the following points. **Look at examples source code** to get a feel for how statsmodels examples should look like. **Build the docs** by running `make html` from the docs directory to see how your example looks in the fully rendered html pages. statsmodels-0.12.2/docs/source/dev/get_involved.rst000066400000000000000000000022571400612667500224000ustar00rootroot00000000000000Get Involved ============ Where to Start? --------------- Use grep or download a tool like `grin `__ to search the code for TODO notes:: grin -i -I "*.py*" todo This shows almost 700 TODOs in the code base right now. Feel free to inquire on the `mailing list `_ about any of these. Sandbox ------- We currently have a large amount code in the :ref:`sandbox`. The medium term goal is to move much of this to feature branches as it gets worked on and remove the sandbox folder. Many of these models and functions are close to done, however, and we welcome any and all contributions to complete them, including refactoring, documentation, and tests. These models include generalized additive models (GAM), information theoretic models such as maximum entropy, survival models, systems of equation models, restricted least squares, panel data models, and time series models such as (G)ARCH. .. .. toctree:: .. :maxdepth: 4 .. .. ../sandbox Contribute an Example --------------------- Contribute an :ref:`example `, add some technical documentation, or contribute a statistics tutorial. statsmodels-0.12.2/docs/source/dev/git_notes.rst000066400000000000000000000225701400612667500217060ustar00rootroot00000000000000.. _git_notes: Working with the statsmodels Code ================================= Github ------ The `statsmodels` code base is hosted on `Github `_. To contribute you will need to `sign up for a free Github account `_. Version Control and Git ----------------------- We use the `Git `_ version control system for development. Git allows many people to work together on the same project. In a nutshell, it allows you to make changes to the code independent of others who may also be working on the code and allows you to easily contribute your changes to the codebase. It also keeps a complete history of all changes to the code, so you can easily undo changes or see when a change was made, by whom, and why. To install and configure Git, and to setup SSH keys, see `setting up git `_. To learn more about Git, you may want to visit: + `Git documentation (book and videos) `_ + `Github help pages `_ + `NumPy documentation `_ + `Matthew Brett's Pydagogue `_ Below, we describe the bare minimum git commands you need to contribute to `statsmodels`. statsmodels Git/Github Workflow ------------------------------- Forking and cloning ~~~~~~~~~~~~~~~~~~~ After setting up git, you need to fork the main `statsmodels` repository. To do this, visit the `statsmodels project page `_ and hit the fork button (see instructions for `forking a repo `_ for details). This should take you to your fork's page. Then, you want to clone the fork to your machine:: git clone https://github.com/your-user-name/statsmodels cd statsmodels git remote add upstream https://github.com/statsmodels/statsmodels git fetch --all The third line sets-up a read-only connection to the upstream statsmodels repository. This will allow you to periodically update your local code with changes in the upstream. The final command fetches both your repository and the upstream statsmodels repository. Create a Branch ~~~~~~~~~~~~~~~ All changes to the code should be made in a feature branch. To create a branch, type:: git checkout master git rebase upstream/master git checkout -b shiny-new-feature The first two lines ensure you are starting from an up-to-date version of the upstream statsmodels repository. The third creates and checkout a new branch. Doing:: git branch will give something like:: * shiny-new-feature master to indicate that you are now on the `shiny-new-feature` branch. Making changes ~~~~~~~~~~~~~~ Hack away! Make any changes that you want, but please keep the work in your branch completely confined to one specific topic, bugfix, or feature implementation. You can work across multiple files and have many commits, but the changes should all be related to the feature of the feature branch, whatever that may be. Now imagine that you changed the file `foo.py`. You can see your changes by typing:: git status This will print something like:: # On branch shiny-new-feature # Changes not staged for commit: # (use "git add ..." to update what will be committed) # (use "git checkout -- ..." to discard changes in working directory) # # modified: relative/path/to/foo.py # no changes added to commit (use "git add" and/or "git commit -a") Before you can commit these changes, you have to `add`, or `stage`, the changes. You can do this by typing:: git add path/to/foo.py Then check the status to make sure your commit looks okay:: git status should give something like:: # On branch shiny-new-feature # Changes to be committed: # (use "git reset HEAD ..." to unstage) # # modified: /relative/path/to/foo.py # Pushing your changes ~~~~~~~~~~~~~~~~~~~~ At any time you can push your feature branch (and any changes) to your github (fork) repository by:: git push although the first time you will need to run git push --set-upstream origin shiny-new-feature to instruct git to set the current branch to track its corresponding branch in your github repository. You can see the remote repositories by:: git remote -v If you added the upstream repository as described above you will see something like:: origin https://github.com/yourname/statsmodels.git (fetch) origin https://github.com/yourname/statsmodels.git (push) upstream https://github.com/statsmodels/statsmodels.git (fetch) upstream https://github.com/statsmodels/statsmodels.git (push) Before you push any commits, however, it is *highly* recommended that you make sure what you are pushing makes sense and looks clean. You can review your change history by:: git log --oneline --graph It pays to take care of things locally before you push them to github. So when in doubt, do not push. Also see the advice on keeping your history clean in :ref:`merge-vs-rebase`. .. _pull-requests: Pull Requests ~~~~~~~~~~~~~ When you are ready to ask for a code review, we recommend that you file a pull request. Before you do so you should check your changeset yourself. You can do this by using `compare view `__ on github. #. Navigate to your repository on github. #. Click on `Branch List` #. Click on the `Compare` button for your feature branch, `shiny-new-feature`. #. Select the `base` and `compare` branches, if necessary. This will be `master` and `shiny-new-feature`, respectively. #. From here you will see a nice overview of your changes. If anything is amiss, you can fix it. If everything looks good you are read to make a `pull request `__. #. Navigate to your repository on github. #. Click on the `Pull Request` button. #. You can then click on `Commits` and `Files Changed` to make sure everything looks okay one last time. #. Write a description of your changes in the `Preview Discussion` tab. #. Click `Send Pull Request`. Your request will then be reviewed. If you need to go back and make more changes, you can make them in your branch and push them to github and the pull request will be automatically updated. One last thing to note. If there has been a lot of work in upstream/master since you started your patch, you might want to rebase. However, you can probably get away with not rebasing if these changes are unrelated to the work you have done in the `shiny-new-feature` branch. If you can avoid it, then do not rebase. If you have to, try to do it once and when you are at the end of your changes. Read on for some notes on :ref:`merge-vs-rebase`. Advanced Topics --------------- .. _merge-vs-rebase: Merging vs. Rebasing ~~~~~~~~~~~~~~~~~~~~ This is a topic that has been discussed at great length and with considerable more expertise than we can offer here. This section will provide some resources for further reading and some advice. The focus, though, will be for those who wish to submit pull requests for a feature branch. For these cases rebase should be preferred. A rebase replays commits from one branch on top of another branch to preserve a linear history. Recall that your commits were tested against a (possibly) older version of master from which you started your branch, so if you rebase, you could introduce bugs. However, if you have only a few commits, this might not be such a concern. One great place to start learning about rebase is :ref:`rebasing without tears `. In particular, `heed the warnings `__. Namely, **always make a new branch before doing a rebase**. This is good general advice for working with git. I would also add **never use rebase on work that has already been published**. If another developer is using your work, do not rebase!! As for merging, **never merge from trunk into your feature branch**. You will, however, want to check that your work will merge cleanly into trunk. This will help out the reviewers. You can do this in your local repository by merging your work into your master (or any branch that tracks remote master) and :ref:`run-tests`. Deleting Branches ~~~~~~~~~~~~~~~~~ Once your feature branch is accepted into upstream, you might want to get rid of it. First you'll want to merge upstream master into your branch. That way git will know that it can safely delete your branch:: git fetch upstream git checkout master git merge upstream/master Then you can just do:: git branch -d shiny-new-feature Make sure you use a lower-case -d. That way, git will complain if your feature branch has not actually been merged. The branch will still exist on github however. To delete the branch on github, do:: git push origin :shiny-new-feature branch .. Squashing with Rebase .. ^^^^^^^^^^^^^^^^^^^^^ .. You have made a bunch of incremental commits, but you think they might be better off together as one .. commit. You can do this with an interactive rebase. As usual, **only do this when you have local .. commits. Do not edit the history of changes that have been pushed.** .. see this reference http://gitready.com/advanced/2009/02/10/squashing-commits-with-rebase.html statsmodels-0.12.2/docs/source/dev/images/000077500000000000000000000000001400612667500204205ustar00rootroot00000000000000statsmodels-0.12.2/docs/source/dev/images/git_merge.png000066400000000000000000001055401400612667500230750ustar00rootroot00000000000000‰PNG  IHDRÏž}È.tiCCPicmxÚíÚUP–Ñ×(ðõ~1Q†¶¶VðŸ˜Pð‰Š [Ðøp?5¹übɽó¶÷[¨Ùð_{´‹«b Œ ¿¹?0|ÿæ ÀØ €äÃ/ØÇ©ùh;cä‘ä`g @š R}ìŒØ_©>>ÑA¼_€éãÀÇö7÷ àSf¼_P,Ÿ-žáÀôÀëûÄøHžÿ¿p)"؆‡GúH¹€´_Tt,€Ô!wqucþ}–O€æ‚õj᧚×xŽý§&U À{ Ýî?µe;@áz¨¦ Õ÷rssY€P°^°¹¹znss½ó 7Ì/.:þï},ÈÀ à!iPUÐ]0S°pWð?†pˆ†}©¹'¡ÎÂy¸MÐ× ú`F` Á4ÌÂø_á¬"B@¨áA„ DQA¶ úˆ)b‰Ø!®ˆ7ˆ„#qH’†ä …Ȥ ¹€´ H/2„Œ!SÈ,²€,!+(ŠRP*€J Š¨j€Z ö¨ˆF¡ûÑ4ô(z­BÐ+h:ŒN¢3èô;º‰!c81LŒF c„±Æ¸b0Q˜$Læ¦Óˆ¹Ž¹ǼÄ|ÄüÆb±ìX!¬œ4N g†sÂàbqGpE¸j\;n7›Ç-ã1x^¯7Å;áƒð øl| ¾?ŠŸÅ#`œ)‚6ÁŠàIˆ"¤N.º£„9Âw"‘ÈOT"ˆ¡Ädb!±–ØI%Α¨$’&É’äMŠ#å*IWH#¤YÒO2•,JÖ&ÛÈIäBòEr/ù y‘‚£RÔ)–?J"¥ˆÒ@ <£,S©TqªÕ‰AͤVQ;©ÔÏ4É ËÚɦËvÈ~”’³“Ëë”[”•w’Ï‘ï‘ÿ® £à©P¤0¤°®¨¦¢X¡8©DQ2TÚ§Ô¤ôZ™_ÙN9[¹Où·Š²JÊY•'ª¬ªæª‡T;T—ÔdÕüÔÊÔ©³ª›«VïVÿ©¡¬ªQ£1£É§é¨™¯9¢…×2ÒJÖº®õc‹Ê–ð-õ[Þj‹i{k—kOëpë8èê<Ð¥éZêfëÞÙŠßj²5mk¿¢g —¢×£·¡¯¯Ÿ¬ScÛ¶m)Ûz ÀÀÐà°Á-Cœ¡™a–á°Õh§QÑ„1—±‹q©ñK““ &ŸL•McM;L׶lOß>lÆbfovÆ쥹˜yˆy³ùº;Rwܱ`±p´(µxe)k¹×²Ã ¬Ì­ò­¦¬™ÖÁÖ­Ö+;væí|d#ddÓj³jkj{Üöé.ñ]»®ÛaílìJìÞØ«Ø'Ù90¼.9üqÜîXè8ã$ïtÀéŽ3ÃÙ×¹ÅyÃÅÊ¥ÄeÁu‹k†ë#7q·X·ww?÷6Œ‡½GµÇ÷Ý&»Oî~ë©å™í9í%ï•ì5æ-êë}LJ×'̧Ǘîà{ÝêçíwÙŸèïá߀ p hĺ6aƒÜ‚Z‚ñÁÁm!¤¯«¡´PÿÐî={öìã‹   O ¡‘1©Yù9Ê,ª*ju¯ÓÞ–hJt`t_Œ@LBÌD¬Rlnì»8ã¸Ê¸µx×ø«û8öEíMKÈNx·ßtõô€÷žD¡Äƒ‰Ï“¶&•&­t?Ø•ÌŸœ”üÆ}Üü”ó™ësÕ¢übÇ“/c_=¾.,Å}C¿_X®ÿ®õýöûs?#nüÊûÍÿ»þöŸ»+®+ïWÖˆkgÖeÖ;7,7žoFü³À? ü³À? ü³À? ü³À? ü³À? ü³À? ü³À? ü³Àÿ¿ˆò‰ö  ßêh®cÌ÷üïå@œ  ^P ï $ù„z Ó?Ììyœ'^ ÿ›0E" ‘Ç(Ï©?Yh¬Zl»ÙÓéãŒ\tn m^>S~#eAn!Tèƒð$ó†H½h±XŽx²D´dˆ”—´³Œ³¬³œ³¼»B€b¸Ò~ål•ÕFµõU-î-[µÝu’tó·–ë5èwlë7x`8c´h¼fJÛ.d¦bn¸c—Ee¢Õqëš6#¶ó»VìÙ¤·9¹8ǹ»öº}ñÜmáïUí=æ ~ªþ¾ÅÁ”¡y{&Ãù"B"»öÒ£Ãc†ãdãí›HX<‰lIâÕ“MSly¦M‹>•šéše‘­‘#œ‹Í}—w÷hͱCÇwçÈÒ WŠæOŒœ¼|ªôtZqøçãR¥2þrRùŸŠgg*'«î»]}ã|gMMmF]Øû‹[ê™ Ä†/S—šššK[2Z£Û¼Ú­/ë^‘½Ê{ wí[ÇÌõ‘κ®”n§J7É7ßôô÷Vô%÷{Ü’¸M»ýcpî΃¡›w[†kFÊîÝÏÝ÷ `l×C½qÙ ¾IÂäGo?~rwªûiëtݳ³ÏO¿(zyt&w6k.ãUÞ|Áëü7Ùo¾‹y²àóÁçcЧ„Ïe‹ã_E—N-Ë~ýóñïÕÕÈ ÉÍM €ØÂ)ø‰è YÈkÔíÀhcîaqÜm|6Á¨Mb’¹(üTš‹«'Û~öbúUŽIÆ.àfááåáâç@Þ >º.\Å̉õ³7•P“”–”f•¡ÉåyD§HR¢)sªð«Jªiªo×pÓ Õ:¼å´v½N›nËÖ&½Kú·Õ\4¬7ª7n4i2mÝÞnvÕ¼sG¯ÅmË»V£ÖwNÙÌؾÞõÁnÉþ#ΉËYÑÅÒ5Øíˆ{¥ÇÝÏ|Ü>_¿@¶»[ôíÄ›“S§îŸ(î:Ó^ÒRÚTÖTÞZqålwe_Õй®êòó™51µ^uÖ¶^”¯j 77.-7-4϶LµÞk»ÝÞu¹ñJÅÕüki ×÷tîî²í6¾¡yS¦G —­Ó÷³ÿãÀÜ­ÉÛ÷îtµß½4\?R{ïâýžÑéßÆ&T&Ù?x?•õ´tºåÙàó¹+3|³ºsÞ¯2ç›_?}K~§ó>l¡öÃëObŸƒÛ¾¢KNßê¿cøÿ¼ý[êϱ•kîë77¹77, úÅðáFœrdµD[1"˜b,¶§‹{†O!Èž HÖdVò0%—º“ÆF»Ïr„U‡õ [9»9ûgz‡8Ç †3c‰3—KŠë·–§š×”wï¿ÿ AUÁy¡"aá?ÌF?QaÑgb§Å$x$¦$OJYJ}—®”±’ù%{^Î^#E!HQ@ñ¡R¦ò6å•+ª{Õ”Õ>©×k„hÊk~ÔjØ¡­¢ýCçšnâVc=²Þ¸~É6_9ƒŸ†}FG=LMÖMl?o–hn³CÆc1cÙmUb°ÓÕFÉfÃöÞ®2»{C^‡¯Ž#Nœ3\B]­Ý4Ü™4µÝŸ<_zMxùôú^ókò?Px8(2Ø;Ä>tûÝ0¥pÉf$_÷^ÎhŽz,GW<ß>¡‰ýòTÕ’x“–%ŸM‰>d–Ê›ºp¸+íØŸtõ BƳ̶¬Ülßœm¹¹+yOv+;¾7ߤ€»`±ðnQ݉¬“{N96)Ö8£T"_ªP¦V®_auÖ³2¶êø¹†êçjnÕÖ ]½ø¤~¶áSãZ¥Y¨E­Õ¼Í«=þòÑ+uWo^›êøÒIì2쮾±ÒcÑ{¶oc øÖì`øýžûãcÒãý.>eyÁòJô}ï²Àæ&Àßy:^à à4àˆ(hŠà&ØÒ´%ë²2ˆdàÿþ?8@LÁ  à6ÌÀ„(#VH(’‰Ô"ƒÈ;”Œ*¢hZ‡N`0 L(¦ó+Ž Â6b—qº¸tܼ>ßI vZˆ8¢;±…D$ù:É ò^ò}Š,%“ò–jF­¥‘ha´G,&,WX%YËØl¹ìXööuúú G"Ç&#“ÌYÀÅÏUíÊÝÏcÏóŠ7žÂwŽ_‡B L+X&¤"tGØ[x…yZD]dR4VŒ!vUÜM|]¢\ÒHòT®´¢ô™8Y^Ù.9Oy?§`¢ðV1WI^iTù€Š‰ª êµ'êíÅš‰ZA[viëèéªmÕÔÛ¦o±ÍÛ ÑðœÑ=ÔT{{²ÙкÅ.Ë|«É¼6¾¶—vmØÛ8T9þr¶p©v]wwô¸ä‰÷òò¾æËêæ?¨Ôb:f>õ;:=–3®fßÖ„‡B“0+StÍÎ>¢š>›Ùš}<7æ¨ÝqµFáê‰éS7Š+JÊœ+”+‰U3Õ—k2êœ.Ê4¿5Í·Lµ_¾uµ¿£§ózwÇÍ+½mýÍ·. 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«íÖ­[E¿.]ºô+µ–––¼q㆟ŸŸh3±¯ÔVä{zzjkk³ãOŸ>©¨¨0u&µ%B¾€ö)((ˆvZ„ÚŠºYAóæÍ7n\XCÿúë/¶X\\Ü¿ù¶ßUÛÈÈHü‰æ8Ú„<’““£¥¥/U¤¶B¡Š‰cx¯jjj‡*¬¡ð…•””bcc?|ø0räHœôòò*¦Ú^ºtIò[\“ÚQVèÝ»÷Š+Dj;vìX[[[H¤ªªêüùóÙy‘†Â«íÑ£þjjjº`Á\¾|¹˜j;±ÊpR[‚SÂÃÃÍÌÌXg‚¨ß6>>Þë¿ýË«W¯>~üX¢oINN611ùÉù¤¶Að›™3g9räó7oÉJ‘-[¶¬Y³†²šÔ– ˆ|,--EóÇR[‚ R[‚ ‚Ô– ‚Ô– ‚Ô– ‚ µ%‚àÿnSÀí&ŸIEND®B`‚statsmodels-0.12.2/docs/source/dev/index.rst000066400000000000000000000110031400612667500210070ustar00rootroot00000000000000Developer Page ============== This page explains how you can contribute to the development of `statsmodels` by submitting patches, statistical tests, new models, or examples. `statsmodels` is developed on `Github `_ using the `Git `_ version control system. Submitting a Bug Report ----------------------- - Include a short, self-contained code snippet that reproduces the problem - Specify the statsmodels version used. You can do this with ``sm.version.full_version`` - If the issue looks to involve other dependencies, also include the output of ``sm.show_versions()`` Making Changes to the Code -------------------------- First, review the :ref:`git_notes` section for an intro to the git version control system. For a pull request to be accepted, you must meet the below requirements. This greatly helps the job of maintaining and releasing the software a shared effort. - **One branch. One feature.** Branches are cheap and github makes it easy to merge and delete branches with a few clicks. Avoid the temptation to lump in a bunch of unrelated changes when working on a feature, if possible. This helps us keep track of what has changed when preparing a release. - Commit messages should be clear and concise. This means a subject line of less than 80 characters, and, if necessary, a blank line followed by a commit message body. We have an `informal commit format standard `_ that we try to adhere to. You can see what this looks like in practice by ``git log --oneline -n 10``. If your commit references or closes a specific issue, you can close it by mentioning it in the `commit message `_. (*For maintainers*: These suggestions go for Merge commit comments too. These are partially the record for release notes.) - Code submissions must always include tests. See our notes on :ref:`testing`. - Each function, class, method, and attribute needs to be documented using docstrings. We conform to the `numpy docstring standard `_. - If you are adding new functionality, you need to add it to the documentation by editing (or creating) the appropriate file in ``docs/source``. - Make sure your documentation changes parse correctly. Change into the top-level ``docs/`` directory and type:: make clean make html Check that the build output does not have *any* warnings due to your changes. - Follow `PEP8 `_ style guidelines wherever possible. Compare your code to what's in master by running ``git diff upstream/master -u -- "*.py" | flake8 --diff`` prior to submitting. - Finally, please add your changes to the release notes. Open the ``docs/source/release/versionX.X.rst`` file that has the version number of the next release and add your changes to the appropriate section. How to Submit a Pull Request ---------------------------- So you want to submit a patch to `statsmodels` but are not too familiar with github? Here are the steps you need to take. 1. `Fork `_ the `statsmodels repository `_ on Github. 2. `Create a new feature branch `_. Each branch must be self-contained, with a single new feature or bugfix. 3. Make sure the test suite passes. This includes testing on Python 3. The easiest way to do this is to either enable `Travis-CI `_ on your fork, or to make a pull request and check there. 4. `Submit a pull request `_ Pull requests are thoroughly reviewed before being accepted into the codebase. If your pull request becomes out of date, rebase your pull request on the latest version in the central repository. Mailing List ------------ Conversations about development take place on the `statsmodels mailing list `__. License ------- statsmodels is released under the `Modified (3-clause) BSD license `_. Contents -------- .. toctree:: :maxdepth: 1 git_notes maintainer_notes test_notes naming_conventions warnings-and-exceptions dataset_notes examples get_involved internal testing statsmodels-0.12.2/docs/source/dev/internal.rst000066400000000000000000000037651400612667500215340ustar00rootroot00000000000000.. _model: Internal Classes ================ The following summarizes classes and functions that are not intended to be directly used, but of interest only for internal use or for a developer who wants to extend on existing model classes. Module Reference ---------------- Model and Results Classes ^^^^^^^^^^^^^^^^^^^^^^^^^ These are the base classes for both the estimation models and the results. They are not directly useful, but layout the structure of the subclasses and define some common methods. .. module:: statsmodels.base.model :synopsis: Base classes that are inherited by models .. currentmodule:: statsmodels.base.model .. autosummary:: :toctree: generated/ Model LikelihoodModel GenericLikelihoodModel Results LikelihoodModelResults ResultMixin GenericLikelihoodModelResults .. module:: statsmodels.stats.contrast :synopsis: Classes for statistical test .. currentmodule:: statsmodels.stats.contrast .. autosummary:: :toctree: generated/ ContrastResults .. inheritance-diagram:: statsmodels.base.model statsmodels.discrete.discrete_model statsmodels.regression.linear_model statsmodels.miscmodels.count :parts: 3 .. inheritance-diagram:: statsmodels.regression.linear_model.GLS statsmodels.regression.linear_model.WLS statsmodels.regression.linear_model.OLS statsmodels.regression.linear_model.GLSAR :parts: 1 Linear Model ^^^^^^^^^^^^ .. inheritance-diagram:: statsmodels.regression.linear_model :parts: 1 Generalized Linear Model ^^^^^^^^^^^^^^^^^^^^^^^^ .. inheritance-diagram:: statsmodels.genmod.generalized_linear_model statsmodels.genmod.families.family statsmodels.genmod.families.links :parts: 1 Discrete Model ^^^^^^^^^^^^^^ .. inheritance-diagram:: statsmodels.discrete.discrete_model :parts: 1 Robust Model ^^^^^^^^^^^^ .. inheritance-diagram:: statsmodels.robust.robust_linear_model :parts: 1 Vector Autoregressive Model ^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. inheritance-diagram:: statsmodels.tsa.vector_ar.var_model :parts: 3 statsmodels-0.12.2/docs/source/dev/maintainer_notes.rst000066400000000000000000000176741400612667500232630ustar00rootroot00000000000000Maintainer Notes ================ This is for those with read-write access to upstream. It is recommended to name the upstream remote something to remind you that it is read-write:: git remote add upstream-rw git@github.com:statsmodels/statsmodels.git git fetch upstream-rw Git Workflow ------------ Grabbing Changes from Others ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ If you need to push changes from others, you can link to their repository by doing:: git remote add contrib-name git://github.com/contrib-name/statsmodels.git get fetch contrib-name git branch shiny-new-feature --track contrib-name/shiny-new-feature git checkout shiny-new-feature The rest of the below assumes you are on your or someone else's branch with the changes you want to push upstream. .. _rebasing: Rebasing ^^^^^^^^ If there are only a few commits, you can rebase to keep a linear history:: git fetch upstream-rw git rebase upstream-rw/master Rebasing will not automatically close the pull request however, if there is one, so do not forget to do this. .. _merging: Merging ^^^^^^^ If there is a long series of related commits, then you'll want to merge. You may ask yourself, :ref:`ff-no-ff`? See below for more on this choice. Once decided you can do:: git fetch upstream-rw git merge --no-ff upstream-rw/master Merging will automatically close the pull request on github. Check the History ^^^^^^^^^^^^^^^^^ This is very important. Again, any and all fixes should be made locally before pushing to the repository:: git log --oneline --graph This shows the history in a compact way of the current branch. This:: git log -p upstream-rw/master.. shows the log of commits excluding those that can be reached from upstream-rw/master, and including those that can be reached from current HEAD. That is, those changes unique to this branch versus upstream-rw/master. See :ref:`Pydagogue ` for more on using dots with log and also for using :ref:`dots with diff `. Push Your Feature Branch ^^^^^^^^^^^^^^^^^^^^^^^^ All the changes look good? You can push your feature branch after :ref:`merging` or :ref:`rebasing` by:: git push upstream-rw shiny-new-feature:master Cherry-Picking ^^^^^^^^^^^^^^ Say you are interested in some commit in another branch, but want to leave the other ones for now. You can do this with a cherry-pick. Use `git log --oneline` to find the commit that you want to cherry-pick. Say you want commit `dd9ff35` from the `shiny-new-feature` branch. You want to apply this commit to master. You simply do:: git checkout master git cherry-pick dd9ff35 And that's all. This commit is now applied as a new commit in master. .. _ff-no-ff: Merging: To Fast-Forward or Not To Fast-Forward ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ By default, `git merge` is a fast-forward merge. What does this mean, and when do you want to avoid this? .. figure:: images/git_merge.png :alt: git merge diagram :scale: 100% :align: center (source `nvie.com `__, post `"A successful Git branching model" `__) The fast-forward merge does not create a merge commit. This means that the existence of the feature branch is lost in the history. The fast-forward is the default for Git basically because branches are cheap and, therefore, *usually* short-lived. If on the other hand, you have a long-lived feature branch or are following an iterative workflow on the feature branch (i.e. merge into master, then go back to feature branch and add more commits), then it makes sense to include only the merge in the main branch, rather than all the intermediate commits of the feature branch, so you should use:: git merge --no-ff Handling Pull Requests ^^^^^^^^^^^^^^^^^^^^^^ You can apply a pull request through `fetch `__ and `merge `__. In your local copy of the main repo:: git checkout master git remote add contrib-name git://github.com/contrib-name/statsmodels.git git fetch contrib-name git merge contrib-name/shiny-new-feature Check that the merge applies cleanly and the history looks good. Edit the merge message. Add a short explanation of what the branch did along with a 'Closes gh-XXX.' string. This will auto-close the pull request and link the ticket and closing commit. To automatically close the issue, you can use any of:: gh-XXX GH-XXX #XXX in the commit message. Any and all problems need to be taken care of locally before doing:: git push origin master Releasing --------- 1. Checkout master:: git checkout statsmodels/master 2. Clean the working tree with:: git clean -xdf But you might want to do a dry-run first:: git clean -xdfn 3. **Locally** tag the release. For a release candidate, for example:: git tag -a v0.10.0rc1 -m "Version 0.10.0 Release Candidate 1" 7b2fb29 or just:: git tag -a v0.10.0rc1 -m "Version 0.10.0 Release Candidate 1" to use the last commit in master. 4. Checkout the tag:: git checkout tags/v0.10.0rc1 5. Build a sdist to ensure that that the build is clean:: python setup.py sdist --formats=gztar It is important that the build on the tar.gz file is the same as the tag. It must not be **dirty** 6. If on a new minor release (major.minor.micro format) start a new maintenance branch, for example:: git checkout -b maintenance/0.10.x Any bug fixes and maintenance commits intended for the next micro release should be made against master as usual, but tagged with the milestone for the micro release it is intended for. Then merge into master as usual. When ready to do the backports, use the file ``tools/backport_pr.py`` to identify which PRs need to be backported and to apply them to the maintenance branch. The tag for the release should be made in the maintenance branch. 7. Upload the source distribution to PyPI:: twine upload dist/* You might want to upload to test first:: twine upload --repository-url https://test.pypi.org/legacy/ dist/* 8. Go back to the master branch, and add an empty commit:: git checkout statsmodels/master git commit --allow-empty -m "Start of 0.11.0 development" git tag -a v0.11.0.dev0 -m "Start of 0.11.0 development" 9. Push everything to statsmodels:: git push --tags If a new branch was created:: git push --set-upstream origin maintenance/0.10.x 10. Make an announcement, and inform maintainers of wheel builders. 11. Profit? Releasing from Maintenance Branch --------------------------------- Once any patches have been backported to a maintenance branch, the release steps are 1. Checkout the branch:: git checkout maintenance/0.10.x 2. Clean up thoroughly:: git clean -xdf 3. **Locally** tag the release:: git tag -a v0.10.0 -m "Version 0.10.0" 4. Checkout the tag:: git checkout tags/v0.10.0 5. Build a sdist to ensure that that the build is clean:: python setup.py sdist --formats=gztar It is important that the build on the tar.gz file is the same as the tag. It must not be **dirty**. 6. Upload the source distribution to PyPI ot PyPI test:: twine upload dist/* or:: twine upload --repository-url https://test.pypi.org/legacy/ dist/* 7. Push the tag to statsmodels:: git push --tags 8. Make an announcement, and inform maintainers of wheel builders. Commit Comments --------------- Prefix commit messages in the master branch of the main shared repository with the following:: ENH: Feature implementation BUG: Bug fix STY: Coding style changes (indenting, braces, code cleanup) DOC: Sphinx documentation, docstring, or comment changes CMP: Compiled code issues, regenerating C code with Cython, etc. REL: Release related commit TST: Change to a test, adding a test. Only used if not directly related to a bug. REF: Refactoring changes statsmodels-0.12.2/docs/source/dev/naming_conventions.rst000066400000000000000000000075301400612667500236100ustar00rootroot00000000000000Naming Conventions ------------------ File and Directory Names ~~~~~~~~~~~~~~~~~~~~~~~~ Our directory tree stripped down looks something like:: statsmodels/ __init__.py api.py discrete/ __init__.py discrete_model.py tests/ results/ tsa/ __init__.py api.py tsatools.py stattools.py arima_model.py arima_process.py vector_ar/ __init__.py var_model.py tests/ results/ tests/ results/ stats/ __init__.py api.py stattools.py tests/ tools/ __init__.py tools.py decorators.py tests/ The submodules are arranged by topic, `discrete` for discrete choice models, or `tsa` for time series analysis. The submodules that can be import heavy contain an empty __init__.py, except for some testing code for running tests for the submodules. The namespace to be imported is in `api.py`. That way, we can import selectively and do not have to import a lot of code that we do not need. Helper functions are usually put in files named `tools.py` and statistical functions, such as statistical tests are placed in `stattools.py`. Everything has directories for :ref:`tests `. `endog` & `exog` ~~~~~~~~~~~~~~~~ Our working definition of a statistical model is an object that has both endogenous and exogenous data defined as well as a statistical relationship. In place of endogenous and exogenous one can often substitute the terms left hand side (LHS) and right hand side (RHS), dependent and independent variables, regressand and regressors, outcome and design, response variable and explanatory variable, respectively. The usage is quite often domain specific; however, we have chosen to use `endog` and `exog` almost exclusively, since the principal developers of statsmodels have a background in econometrics, and this feels most natural. This means that all of the models are objects with `endog` and `exog` defined, though in some cases `exog` is None for convenience (for instance, with an autoregressive process). Each object also defines a `fit` (or similar) method that returns a model-specific results object. In addition there are some functions, e.g. for statistical tests or convenience functions. See also the related explanation in :ref:`endog_exog`. Variable Names ~~~~~~~~~~~~~~ All of our models assume that data is arranged with variables in columns. Thus, internally the data is all 2d arrays. By convention, we will prepend a `k_` to variable names that indicate moving over axis 1 (columns), and `n_` to variables that indicate moving over axis 0 (rows). The main exception to the underscore is that `nobs` should indicate the number of observations. For example, in the time-series ARMA model we have:: `k_ar` - The number of AR lags included in the RHS variables `k_ma` - The number of MA lags included in the RHS variables `k_trend` - The number of trend variables included in the RHS variables `k_exog` - The number of exogenous variables included in the RHS variables excluding the trend terms `n_totobs` - The total number of observations for the LHS variables including the pre-sample values Options ~~~~~~~ We are using similar options in many classes, methods and functions. They should follow a standardized pattern if they recur frequently. :: `missing` ['none', 'drop', 'raise'] define whether inputs are checked for nans, and how they are treated `alpha` (float in (0, 1)) significance level for hypothesis tests and confidence intervals, e.g. `alpha=0.05` patterns :: `return_xxx` : boolean to indicate optional or different returns (not `ret_xxx`) statsmodels-0.12.2/docs/source/dev/test_notes.rst000066400000000000000000000174511400612667500221040ustar00rootroot00000000000000.. _testing: Testing ======= Setting up development environment locally ------------------------------------------ Follow our :ref:`installation instructions ` and set up a suitable environment to build statsmodels from source. We recommend that you develop using a development install of statsmodels by running: .. code-block:: bash pip install -e . from the root directory of the git repository. The flag ``-e`` is for editable. This command compiles the C code and add statsmodels to your activate python environment by creating links from your python environment's libraries to the statsmodels source code. Therefore, changes to pure python code will be immediately available to the user without a re-install. Changes to C code or Cython code require rerunning ``pip install -e .`` before these changes are available. Test Driven Development ----------------------- We strive to follow a `Test Driven Development (TDD) `_ pattern. All models or statistical functions that are added to the main code base are to have tests versus an existing statistical package, if possible. Introduction to pytest ---------------------- Like many packages, statsmodels uses the `pytest testing system `__ and the convenient extensions in `numpy.testing `__. Pytest will find any file, directory, function, or class name that starts with ``test`` or ``Test`` (classes only). Test function should start with ``test``, test classes should start with ``Test``. These functions and classes should be placed in files with names beginning with ``test`` in a directory called ``tests``. .. _run-tests: Running Tests ------------- Test are run from the command line by calling ``pytest``. Directly running tests using pytest requires that statsmodels is installed using ``pip install -e .`` as described above. Tests can be run at different levels of granularity: * Project level, which runs all tests. Running the entire test suite is slow and normally this would only be needed if making deep changes to statsmodels. .. code-block:: bash pytest statsmodels * Folder level, which runs all tests below a folder .. code-block:: bash pytest statsmodels/regression/tests * File level, which runs all tests in a file .. code-block:: bash pytest statsmodels/regression/tests/test_regression.py * Class level, which runs all tests in a class .. code-block:: bash pytest statsmodels/regression/tests/test_regression.py::TestOLS * Test level, which runs a single test. The first example runs a test in a class. The second runs a stand alone test. .. code-block:: bash pytest statsmodels/regression/tests/test_regression.py::TestOLS::test_missing pytest statsmodels/regression/tests/test_regression.py::test_ridge How To Write A Test ------------------- NumPy provides a good introduction to unit testing with pytest and NumPy extensions `here `__. It is worth a read for some more details. Here, we will document a few conventions we follow that are worth mentioning. Often we want to test a whole model at once rather than just one function, for example. The following is a pared down version test_discrete.py. In this case, several different models with different options need to be tested. The tests look something like .. code-block:: python from numpy.testing import assert_almost_equal import statsmodels.api as sm from results.results_discrete import Spector class CheckDiscreteResults(object): """ res2 are the results. res1 are the values from statsmodels """ def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, 4) decimal_tvalues = 4 def test_tvalues(self): assert_almost_equal(self.res1.params, self.res2.params, self.decimal_tvalues) # ... as many more tests as there are common results class TestProbitNewton(CheckDiscreteResults): """ Tests the Probit model using Newton's method for fitting. """ @classmethod def setup_class(cls): # set up model data = sm.datasets.spector.load() data.exog = sm.add_constant(data.exog) cls.res1 = sm.Probit(data.endog, data.exog).fit(method='newton', disp=0) # set up results res2 = Spector.probit cls.res2 = res2 # set up precision cls.decimal_tvalues = 3 def test_model_specifc(self): assert_almost_equal(self.res1.foo, self.res2.foo, 4) The main workhorse is the `CheckDiscreteResults` class. Notice that we can set the level of precision for `tvalues` to be different than the default in the subclass `TestProbitNewton`. All of the test classes have a ``@classmethod`` called ``setup_class``. Otherwise, pytest would reinstantiate the class before every single test method. If the fitting of the model is time consuming, then this is clearly undesirable. Finally, we have a script at the bottom so that we can run the tests should be running the Python file. Test Results ------------ The test results are the final piece of the above example. For many tests, especially those for the models, there are many results against which you would like to test. It makes sense then to separate the hard-coded results from the actual tests to make the tests more readable. If there are only a few results it's not necessary to separate the results. We often take results from some other statistical package. It is important to document where you got the results from and why they might differ from the results that we get. Each tests folder has a results subdirectory. Consider the folder structure for the discrete models:: tests/ __init__.py test_discrete.py results/ __init__.py results_discrete.py nbinom_resids.csv It is up to you how best to structure the results. In the discrete model example, you will notice that there are result classes based around particular datasets with a method for loading different model results for that dataset. You can also include text files that hold results to be loaded by results classes if it is easier than putting them in the class itself. Speeding up full runs --------------------- Running the full test suite is slow. Fortunately it is only necessary to run the full suite when making low-level changes (e.g., to ``statsmodels.base``) There are two methods available to speed up runs of the full test suite when needed. * Use the pytest-xdist package .. code-block:: bash pip install pytest-xdist export MKL_NUM_THREADS=1 export OMP_NUM_THREADS=1 pytest -n auto statsmodels * Skip slow tests using ``--skip-slow`` .. code-block:: bash pytest --skip-slow statsmodels You can combine these two approaches for faster runs. .. code-block:: bash export MKL_NUM_THREADS=1 && export OMP_NUM_THREADS=1 pytest -n auto --skip-slow statsmodels The ``test()`` method --------------------- The root of statsmodels and all submodules expose a ``test()`` method which can be used to run all tests either in the package (``statsmodels.test()``) or in a module (``statsmodels.regression.test()``). This method allows tests to be run from an install copy of statsmodels even it is was not installed using the *editable* flag as described above. This method is required for testing wheels in release builds and is **not** recommended for development. Using this method, all tests are run using: .. code-block:: python import statsmodels.api as sm sm.test() Submodules tests are run using: .. code-block:: python sm.discrete.test() .. autosummary:: :toctree: generated/ ~statsmodels.__init__.test statsmodels-0.12.2/docs/source/dev/testing.rst000066400000000000000000000013221400612667500213600ustar00rootroot00000000000000Testing on Build Machines ------------------------- There are currently several places that statsmodels is automatically built and tested against different dependency and Python versions and architectures. Check these logs periodically, make sure everything looks okay, and fix any failures: * `Travis CI `_ * `Appveyor `_ The test coverage pages are here: * `Coveralls `_ * `codecov `_ We use `Codacy `_ to monitor code quality. statsmodels-0.12.2/docs/source/dev/warnings-and-exceptions.rst000066400000000000000000000024331400612667500244560ustar00rootroot00000000000000======================= Exceptions and Warnings ======================= Exceptions ---------- Errors derive from Exception or another custom error. Custom errors are only needed if standard errors, for example ValueError or TypeError, are not accurate descriptions of the cause for the error. .. module:: statsmodels.tools.sm_exceptions :synopsis: Exceptions and Warnings .. currentmodule:: statsmodels.tools.sm_exceptions .. autosummary:: :toctree: generated/ ParseError PerfectSeparationError X13NotFoundError X13Error Warnings -------- Warnings derive from either an existing warning or another custom warning, and are often accompanied by a string using the format ``warning_name_doc`` that services as a generic message to use when the warning is raised. .. currentmodule:: statsmodels.tools.sm_exceptions .. autosummary:: :toctree: generated/ X13Warning IOWarning ModuleUnavailableWarning ModelWarning ConvergenceWarning CacheWriteWarning IterationLimitWarning InvalidTestWarning NotImplementedWarning OutputWarning DomainWarning ValueWarning EstimationWarning SingularMatrixWarning HypothesisTestWarning InterpolationWarning PrecisionWarning SpecificationWarning HessianInversionWarning CollinearityWarning statsmodels-0.12.2/docs/source/diagnostic.rst000066400000000000000000000176331400612667500212650ustar00rootroot00000000000000:orphan: .. _diagnostics: Regression Diagnostics and Specification Tests ============================================== Introduction ------------ In many cases of statistical analysis, we are not sure whether our statistical model is correctly specified. For example when using ols, then linearity and homoscedasticity are assumed, some test statistics additionally assume that the errors are normally distributed or that we have a large sample. Since our results depend on these statistical assumptions, the results are only correct of our assumptions hold (at least approximately). One solution to the problem of uncertainty about the correct specification is to use robust methods, for example robust regression or robust covariance (sandwich) estimators. The second approach is to test whether our sample is consistent with these assumptions. The following briefly summarizes specification and diagnostics tests for linear regression. Heteroscedasticity Tests ------------------------ For these test the null hypothesis is that all observations have the same error variance, i.e. errors are homoscedastic. The tests differ in which kind of heteroscedasticity is considered as alternative hypothesis. They also vary in the power of the test for different types of heteroscedasticity. :py:func:`het_breuschpagan ` Lagrange Multiplier Heteroscedasticity Test by Breusch-Pagan :py:func:`het_white ` Lagrange Multiplier Heteroscedasticity Test by White :py:func:`het_goldfeldquandt ` test whether variance is the same in 2 subsamples Autocorrelation Tests --------------------- This group of test whether the regression residuals are not autocorrelated. They assume that observations are ordered by time. :py:func:`durbin_watson ` - Durbin-Watson test for no autocorrelation of residuals - printed with summary() :py:func:`acorr_ljungbox ` - Ljung-Box test for no autocorrelation of residuals - also returns Box-Pierce statistic :py:func:`acorr_breusch_godfrey ` - Breusch-Pagan test for no autocorrelation of residuals missing - ? Non-Linearity Tests ------------------- :py:func:`linear_harvey_collier ` - Multiplier test for Null hypothesis that linear specification is correct :py:func:`acorr_linear_rainbow ` - Multiplier test for Null hypothesis that linear specification is correct. :py:func:`acorr_linear_lm ` - Lagrange Multiplier test for Null hypothesis that linear specification is correct. This tests against specific functional alternatives. :py:func:`spec_white ` - White's two-moment specification test with null hypothesis of homoscedastic and correctly specified. Tests for Structural Change, Parameter Stability ------------------------------------------------ Test whether all or some regression coefficient are constant over the entire data sample. Known Change Point ^^^^^^^^^^^^^^^^^^ OneWayLS : - flexible ols wrapper for testing identical regression coefficients across predefined subsamples (eg. groups) missing - predictive test: Greene, number of observations in subsample is smaller than number of regressors Unknown Change Point ^^^^^^^^^^^^^^^^^^^^ :py:func:`breaks_cusumolsresid ` - cusum test for parameter stability based on ols residuals :py:func:`breaks_hansen ` - test for model stability, breaks in parameters for ols, Hansen 1992 :py:func:`recursive_olsresiduals ` Calculate recursive ols with residuals and cusum test statistic. This is currently mainly helper function for recursive residual based tests. However, since it uses recursive updating and does not estimate separate problems it should be also quite efficient as expanding OLS function. missing - supLM, expLM, aveLM (Andrews, Andrews/Ploberger) - R-structchange also has musum (moving cumulative sum tests) - test on recursive parameter estimates, which are there? Multicollinearity Tests -------------------------------- conditionnum (statsmodels.stattools) - -- needs test vs Stata -- - cf Grene (3rd ed.) pp 57-8 numpy.linalg.cond - (for more general condition numbers, but no behind the scenes help for design preparation) Variance Inflation Factors This is currently together with influence and outlier measures (with some links to other tests here: http://www.stata.com/help.cgi?vif) Normality and Distribution Tests -------------------------------- :py:func:`jarque_bera ` - printed with summary() - test for normal distribution of residuals Normality tests in scipy stats need to find list again :py:func:`omni_normtest ` - test for normal distribution of residuals - printed with summary() :py:func:`normal_ad ` - Anderson Darling test for normality with estimated mean and variance :py:func:`kstest_normal ` :py:func:`lilliefors ` Lilliefors test for normality, this is a Kolmogorov-Smirnov tes with for normality with estimated mean and variance. lilliefors is an alias for kstest_normal qqplot, scipy.stats.probplot other goodness-of-fit tests for distributions in scipy.stats and enhancements - kolmogorov-smirnov - anderson : Anderson-Darling - likelihood-ratio, ... - chisquare tests, powerdiscrepancy : needs wrapping (for binning) Outlier and Influence Diagnostic Measures ----------------------------------------- These measures try to identify observations that are outliers, with large residual, or observations that have a large influence on the regression estimates. Robust Regression, RLM, can be used to both estimate in an outlier robust way as well as identify outlier. The advantage of RLM that the estimation results are not strongly influenced even if there are many outliers, while most of the other measures are better in identifying individual outliers and might not be able to identify groups of outliers. :py:class:`RLM ` example from example_rlm.py :: import statsmodels.api as sm ### Example for using Huber's T norm with the default ### median absolute deviation scaling data = sm.datasets.stackloss.load() data.exog = sm.add_constant(data.exog) huber_t = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT()) hub_results = huber_t.fit() print(hub_results.weights) And the weights give an idea of how much a particular observation is down-weighted according to the scaling asked for. :py:class:`Influence ` Class in stats.outliers_influence, most standard measures for outliers and influence are available as methods or attributes given a fitted OLS model. This is mainly written for OLS, some but not all measures are also valid for other models. Some of these statistics can be calculated from an OLS results instance, others require that an OLS is estimated for each left out variable. - resid_press - resid_studentized_external - resid_studentized_internal - ess_press - hat_matrix_diag - cooks_distance - Cook's Distance `Wikipedia `_ (with some other links) - cov_ratio - dfbetas - dffits - dffits_internal - det_cov_params_not_obsi - params_not_obsi - sigma2_not_obsi statsmodels-0.12.2/docs/source/discretemod.rst000066400000000000000000000077141400612667500214420ustar00rootroot00000000000000.. currentmodule:: statsmodels.discrete.discrete_model .. _discretemod: Regression with Discrete Dependent Variable =========================================== Regression models for limited and qualitative dependent variables. The module currently allows the estimation of models with binary (Logit, Probit), nominal (MNLogit), or count (Poisson, NegativeBinomial) data. Starting with version 0.9, this also includes new count models, that are still experimental in 0.9, NegativeBinomialP, GeneralizedPoisson and zero-inflated models, ZeroInflatedPoisson, ZeroInflatedNegativeBinomialP and ZeroInflatedGeneralizedPoisson. See `Module Reference`_ for commands and arguments. Examples -------- .. ipython:: python :okwarning: # Load the data from Spector and Mazzeo (1980) import statsmodels.api as sm spector_data = sm.datasets.spector.load_pandas() spector_data.exog = sm.add_constant(spector_data.exog) # Logit Model logit_mod = sm.Logit(spector_data.endog, spector_data.exog) logit_res = logit_mod.fit() print(logit_res.summary()) Detailed examples can be found here: * `Overview `__ * `Examples `__ Technical Documentation ----------------------- Currently all models are estimated by Maximum Likelihood and assume independently and identically distributed errors. All discrete regression models define the same methods and follow the same structure, which is similar to the regression results but with some methods specific to discrete models. Additionally some of them contain additional model specific methods and attributes. References ^^^^^^^^^^ General references for this class of models are:: A.C. Cameron and P.K. Trivedi. `Regression Analysis of Count Data`. Cambridge, 1998 G.S. Madalla. `Limited-Dependent and Qualitative Variables in Econometrics`. Cambridge, 1983. W. Greene. `Econometric Analysis`. Prentice Hall, 5th. edition. 2003. Module Reference ---------------- .. module:: statsmodels.discrete.discrete_model :synopsis: Models for discrete data The specific model classes are: .. autosummary:: :toctree: generated/ Logit Probit MNLogit Poisson NegativeBinomial NegativeBinomialP GeneralizedPoisson .. currentmodule:: statsmodels.discrete.count_model .. module:: statsmodels.discrete.count_model .. autosummary:: :toctree: generated/ ZeroInflatedPoisson ZeroInflatedNegativeBinomialP ZeroInflatedGeneralizedPoisson .. currentmodule:: statsmodels.discrete.conditional_models .. module:: statsmodels.discrete.conditional_models .. autosummary:: :toctree: generated/ ConditionalLogit ConditionalMNLogit ConditionalPoisson The specific result classes are: .. currentmodule:: statsmodels.discrete.discrete_model .. autosummary:: :toctree: generated/ LogitResults ProbitResults CountResults MultinomialResults NegativeBinomialResults GeneralizedPoissonResults .. currentmodule:: statsmodels.discrete.count_model .. autosummary:: :toctree: generated/ ZeroInflatedPoissonResults ZeroInflatedNegativeBinomialResults ZeroInflatedGeneralizedPoissonResults :class:`DiscreteModel` is a superclass of all discrete regression models. The estimation results are returned as an instance of one of the subclasses of :class:`DiscreteResults`. Each category of models, binary, count and multinomial, have their own intermediate level of model and results classes. This intermediate classes are mostly to facilitate the implementation of the methods and attributes defined by :class:`DiscreteModel` and :class:`DiscreteResults`. .. currentmodule:: statsmodels.discrete.discrete_model .. autosummary:: :toctree: generated/ DiscreteModel DiscreteResults BinaryModel BinaryResults CountModel MultinomialModel .. currentmodule:: statsmodels.discrete.count_model .. autosummary:: :toctree: generated/ GenericZeroInflated statsmodels-0.12.2/docs/source/distributions.rst000066400000000000000000000041351400612667500220340ustar00rootroot00000000000000.. module:: statsmodels.sandbox.distributions :synopsis: Probability distributions .. currentmodule:: statsmodels.sandbox.distributions .. _distributions: Distributions ============= This section collects various additional functions and methods for statistical distributions. Empirical Distributions ----------------------- .. module:: statsmodels.distributions.empirical_distribution :synopsis: Tools for working with empirical distributions .. currentmodule:: statsmodels.distributions.empirical_distribution .. autosummary:: :toctree: generated/ ECDF StepFunction monotone_fn_inverter Distribution Extras ------------------- .. module:: statsmodels.sandbox.distributions.extras :synopsis: Probability distributions and random number generators .. currentmodule:: statsmodels.sandbox.distributions.extras *Skew Distributions* .. autosummary:: :toctree: generated/ SkewNorm_gen SkewNorm2_gen ACSkewT_gen skewnorm2 *Distributions based on Gram-Charlier expansion* .. autosummary:: :toctree: generated/ pdf_moments_st pdf_mvsk pdf_moments NormExpan_gen *cdf of multivariate normal* wrapper for scipy.stats .. autosummary:: :toctree: generated/ mvstdnormcdf mvnormcdf Univariate Distributions by non-linear Transformations ------------------------------------------------------ Univariate distributions can be generated from a non-linear transformation of an existing univariate distribution. `Transf_gen` is a class that can generate a new distribution from a monotonic transformation, `TransfTwo_gen` can use hump-shaped or u-shaped transformation, such as abs or square. The remaining objects are special cases. .. module:: statsmodels.sandbox.distributions.transformed :synopsis: Experimental probability distributions and random number generators .. currentmodule:: statsmodels.sandbox.distributions.transformed .. autosummary:: :toctree: generated/ TransfTwo_gen Transf_gen ExpTransf_gen LogTransf_gen SquareFunc absnormalg invdnormalg loggammaexpg lognormalg negsquarenormalg squarenormalg squaretg statsmodels-0.12.2/docs/source/duration.rst000066400000000000000000000156261400612667500207660ustar00rootroot00000000000000.. module:: statsmodels.duration :synopsis: Models for durations .. currentmodule:: statsmodels.duration .. _duration: Methods for Survival and Duration Analysis ========================================== :mod:`statsmodels.duration` implements several standard methods for working with censored data. These methods are most commonly used when the data consist of durations between an origin time point and the time at which some event of interest occurred. A typical example is a medical study in which the origin is the time at which a subject is diagnosed with some condition, and the event of interest is death (or disease progression, recovery, etc.). Currently only right-censoring is handled. Right censoring occurs when we know that an event occurred after a given time `t`, but we do not know the exact event time. Survival function estimation and inference ------------------------------------------ The :class:`statsmodels.api.SurvfuncRight` class can be used to estimate a survival function using data that may be right censored. ``SurvfuncRight`` implements several inference procedures including confidence intervals for survival distribution quantiles, pointwise and simultaneous confidence bands for the survival function, and plotting procedures. The ``duration.survdiff`` function provides testing procedures for comparing survival distributions. Here we create a ``SurvfuncRight`` object using data from the `flchain` study, which is available through the R datasets repository. We fit the survival distribution only for the female subjects. .. code-block:: python import statsmodels.api as sm data = sm.datasets.get_rdataset("flchain", "survival").data df = data.loc[data.sex == "F", :] sf = sm.SurvfuncRight(df["futime"], df["death"]) The main features of the fitted survival distribution can be seen by calling the ``summary`` method: .. code-block:: python sf.summary().head() We can obtain point estimates and confidence intervals for quantiles of the survival distribution. Since only around 30% of the subjects died during this study, we can only estimate quantiles below the 0.3 probability point: .. code-block:: python sf.quantile(0.25) sf.quantile_ci(0.25) To plot a single survival function, call the ``plot`` method: .. code-block:: python sf.plot() Since this is a large dataset with a lot of censoring, we may wish to not plot the censoring symbols: .. code-block:: python fig = sf.plot() ax = fig.get_axes()[0] pt = ax.get_lines()[1] pt.set_visible(False) We can also add a 95% simultaneous confidence band to the plot. Typically these bands only plotted for central part of the distribution. .. code-block:: python fig = sf.plot() lcb, ucb = sf.simultaneous_cb() ax = fig.get_axes()[0] ax.fill_between(sf.surv_times, lcb, ucb, color='lightgrey') ax.set_xlim(365, 365*10) ax.set_ylim(0.7, 1) ax.set_ylabel("Proportion alive") ax.set_xlabel("Days since enrollment") Here we plot survival functions for two groups (females and males) on the same axes: .. code-block:: python gb = data.groupby("sex") ax = plt.axes() sexes = [] for g in gb: sexes.append(g[0]) sf = sm.SurvfuncRight(g[1]["futime"], g[1]["death"]) sf.plot(ax) li = ax.get_lines() li[1].set_visible(False) li[3].set_visible(False) plt.figlegend((li[0], li[2]), sexes, "center right") plt.ylim(0.6, 1) ax.set_ylabel("Proportion alive") ax.set_xlabel("Days since enrollment") We can formally compare two survival distributions with ``survdiff``, which implements several standard nonparametric procedures. The default procedure is the logrank test: .. code-block:: python stat, pv = sm.duration.survdiff(data.futime, data.death, data.sex) Here are some of the other testing procedures implemented by survdiff: .. code-block:: python # Fleming-Harrington with p=1, i.e. weight by pooled survival time stat, pv = sm.duration.survdiff(data.futime, data.death, data.sex, weight_type='fh', fh_p=1) # Gehan-Breslow, weight by number at risk stat, pv = sm.duration.survdiff(data.futime, data.death, data.sex, weight_type='gb') # Tarone-Ware, weight by the square root of the number at risk stat, pv = sm.duration.survdiff(data.futime, data.death, data.sex, weight_type='tw') Regression methods ------------------ Proportional hazard regression models ("Cox models") are a regression technique for censored data. They allow variation in the time to an event to be explained in terms of covariates, similar to what is done in a linear or generalized linear regression model. These models express the covariate effects in terms of "hazard ratios", meaning the the hazard (instantaneous event rate) is multiplied by a given factor depending on the value of the covariates. .. code-block:: python import statsmodels.api as sm import statsmodels.formula.api as smf data = sm.datasets.get_rdataset("flchain", "survival").data del data["chapter"] data = data.dropna() data["lam"] = data["lambda"] data["female"] = (data["sex"] == "F").astype(int) data["year"] = data["sample.yr"] - min(data["sample.yr"]) status = data["death"].values mod = smf.phreg("futime ~ 0 + age + female + creatinine + " "np.sqrt(kappa) + np.sqrt(lam) + year + mgus", data, status=status, ties="efron") rslt = mod.fit() print(rslt.summary()) See :ref:`statsmodels-examples` for more detailed examples. There are some notebook examples on the Wiki: `Wiki notebooks for PHReg and Survival Analysis `_ .. todo:: Technical Documentation References ^^^^^^^^^^ References for Cox proportional hazards regression model:: T Therneau (1996). Extending the Cox model. Technical report. http://www.mayo.edu/research/documents/biostat-58pdf/DOC-10027288 G Rodriguez (2005). Non-parametric estimation in survival models. http://data.princeton.edu/pop509/NonParametricSurvival.pdf B Gillespie (2006). Checking the assumptions in the Cox proportional hazards model. http://www.mwsug.org/proceedings/2006/stats/MWSUG-2006-SD08.pdf Module Reference ---------------- .. module:: statsmodels.duration.survfunc :synopsis: Models for Survival Analysis .. currentmodule:: statsmodels.duration.survfunc The class for working with survival distributions is: .. autosummary:: :toctree: generated/ SurvfuncRight .. module:: statsmodels.duration.hazard_regression :synopsis: Proportional hazards model for Survival Analysis .. currentmodule:: statsmodels.duration.hazard_regression The proportional hazards regression model class is: .. autosummary:: :toctree: generated/ PHReg The proportional hazards regression result class is: .. autosummary:: :toctree: generated/ PHRegResults The primary helper class is: .. autosummary:: :toctree: generated/ rv_discrete_floatstatsmodels-0.12.2/docs/source/emplike.rst000066400000000000000000000035521400612667500205620ustar00rootroot00000000000000.. currentmodule:: statsmodels.emplike .. _emplike: Empirical Likelihood :mod:`emplike` ==================================== Introduction ------------ Empirical likelihood is a method of nonparametric inference and estimation that lifts the obligation of having to specify a family of underlying distributions. Moreover, empirical likelihood methods do not require re-sampling but still uniquely determine confidence regions whose shape mirrors the shape of the data. In essence, empirical likelihood attempts to combine the benefits of parametric and nonparametric methods while limiting their shortcomings. The main difficulties of empirical likelihood is the computationally intensive methods required to conduct inference. :mod:`statsmodels.emplike` attempts to provide a user-friendly interface that allows the end user to effectively conduct empirical likelihood analysis without having to concern themselves with the computational burdens. Currently, :mod:`emplike` provides methods to conduct hypothesis tests and form confidence intervals for descriptive statistics. Empirical likelihood estimation and inference in a regression, accelerated failure time and instrumental variable model are currently under development. References ^^^^^^^^^^ The main reference for empirical likelihood is:: Owen, A.B. "Empirical Likelihood." Chapman and Hall, 2001. Examples -------- .. ipython:: python import numpy as np import statsmodels.api as sm # Generate Data x = np.random.standard_normal(50) # initiate EL el = sm.emplike.DescStat(x) # confidence interval for the mean el.ci_mean() # test variance is 1 el.test_var(1) Module Reference ---------------- .. module:: statsmodels.emplike :synopsis: Empirical likelihood tools .. autosummary:: :toctree: generated/ descriptive.DescStat descriptive.DescStatUV descriptive.DescStatMV statsmodels-0.12.2/docs/source/endog_exog.rst000066400000000000000000000072561400612667500212570ustar00rootroot00000000000000.. _endog_exog: ``endog``, ``exog``, what's that? ================================= statsmodels is using ``endog`` and ``exog`` as names for the data, the observed variables that are used in an estimation problem. Other names that are often used in different statistical packages or text books are, for example, ===================== ====================== endog exog ===================== ====================== y x y variable x variable left hand side (LHS) right hand side (RHS) dependent variable independent variable regressand regressors outcome design response variable explanatory variable ===================== ====================== The usage is quite often domain and model specific; however, we have chosen to use `endog` and `exog` almost exclusively. A mnemonic hint to keep the two terms apart is that exogenous has an "x", as in x-variable, in its name. `x` and `y` are one letter names that are sometimes used for temporary variables and are not informative in itself. To avoid one letter names we decided to use descriptive names and settled on ``endog`` and ``exog``. Since this has been criticized, this might change in future. Background ---------- Some informal definitions of the terms are `endogenous`: caused by factors within the system `exogenous`: caused by factors outside the system *Endogenous variables designates variables in an economic/econometric model that are explained, or predicted, by that model.* http://stats.oecd.org/glossary/detail.asp?ID=794 *Exogenous variables designates variables that appear in an economic/econometric model, but are not explained by that model (i.e. they are taken as given by the model).* http://stats.oecd.org/glossary/detail.asp?ID=890 In econometrics and statistics the terms are defined more formally, and different definitions of exogeneity (weak, strong, strict) are used depending on the model. The usage in statsmodels as variable names cannot always be interpreted in a formal sense, but tries to follow the same principle. In the simplest form, a model relates an observed variable, y, to another set of variables, x, in some linear or nonlinear form :: y = f(x, beta) + noise y = x * beta + noise However, to have a statistical model we need additional assumptions on the properties of the explanatory variables, x, and the noise. One standard assumption for many basic models is that x is not correlated with the noise. In a more general definition, x being exogenous means that we do not have to consider how the explanatory variables in x were generated, whether by design or by random draws from some underlying distribution, when we want to estimate the effect or impact that x has on y, or test a hypothesis about this effect. In other words, y is *endogenous* to our model, x is *exogenous* to our model for the estimation. As an example, suppose you run an experiment and for the second session some subjects are not available anymore. Is the drop-out relevant for the conclusions you draw for the experiment? In other words, can we treat the drop-out decision as exogenous for our problem. It is up to the user to know (or to consult a text book to find out) what the underlying statistical assumptions for the models are. As an example, ``exog`` in ``OLS`` can have lagged dependent variables if the error or noise term is independently distributed over time (or uncorrelated over time). However, if the error terms are autocorrelated, then OLS does not have good statistical properties (is inconsistent) and the correct model will be ARMAX. ``statsmodels`` has functions for regression diagnostics to test whether some of the assumptions are justified or not. statsmodels-0.12.2/docs/source/example_formulas.rst000066400000000000000000000137251400612667500225020ustar00rootroot00000000000000.. _formula_examples: Fitting models using R-style formulas ===================================== Since version 0.5.0, ``statsmodels`` allows users to fit statistical models using R-style formulas. Internally, ``statsmodels`` uses the `patsy `_ package to convert formulas and data to the matrices that are used in model fitting. The formula framework is quite powerful; this tutorial only scratches the surface. A full description of the formula language can be found in the ``patsy`` docs: - `Patsy formula language description `_ Loading modules and functions ----------------------------- .. ipython:: python import statsmodels.api as sm import statsmodels.formula.api as smf import numpy as np import pandas Notice that we called ``statsmodels.formula.api`` in addition to the usual ``statsmodels.api``. In fact, ``statsmodels.api`` is used here only to load the dataset. The ``formula.api`` hosts many of the same functions found in ``api`` (e.g. OLS, GLM), but it also holds lower case counterparts for most of these models. In general, lower case models accept ``formula`` and ``df`` arguments, whereas upper case ones take ``endog`` and ``exog`` design matrices. ``formula`` accepts a string which describes the model in terms of a ``patsy`` formula. ``df`` takes a `pandas `_ data frame. ``dir(smf)`` will print a list of available models. Formula-compatible models have the following generic call signature: ``(formula, data, subset=None, *args, **kwargs)`` OLS regression using formulas ----------------------------- To begin, we fit the linear model described on the `Getting Started `_ page. Download the data, subset columns, and list-wise delete to remove missing observations: .. ipython:: python df = sm.datasets.get_rdataset("Guerry", "HistData").data df = df[['Lottery', 'Literacy', 'Wealth', 'Region']].dropna() df.head() Fit the model: .. ipython:: python mod = smf.ols(formula='Lottery ~ Literacy + Wealth + Region', data=df) res = mod.fit() print(res.summary()) Categorical variables --------------------- Looking at the summary printed above, notice that ``patsy`` determined that elements of *Region* were text strings, so it treated *Region* as a categorical variable. ``patsy``'s default is also to include an intercept, so we automatically dropped one of the *Region* categories. If *Region* had been an integer variable that we wanted to treat explicitly as categorical, we could have done so by using the ``C()`` operator: .. ipython:: python res = smf.ols(formula='Lottery ~ Literacy + Wealth + C(Region)', data=df).fit() print(res.params) Examples more advanced features ``patsy``'s categorical variables function can be found here: `Patsy: Contrast Coding Systems for categorical variables `_ Operators --------- We have already seen that "~" separates the left-hand side of the model from the right-hand side, and that "+" adds new columns to the design matrix. Removing variables ~~~~~~~~~~~~~~~~~~ The "-" sign can be used to remove columns/variables. For instance, we can remove the intercept from a model by: .. ipython:: python res = smf.ols(formula='Lottery ~ Literacy + Wealth + C(Region) -1 ', data=df).fit() print(res.params) Multiplicative interactions ~~~~~~~~~~~~~~~~~~~~~~~~~~~ ":" adds a new column to the design matrix with the product of the other two columns. "\*" will also include the individual columns that were multiplied together: .. ipython:: python res1 = smf.ols(formula='Lottery ~ Literacy : Wealth - 1', data=df).fit() res2 = smf.ols(formula='Lottery ~ Literacy * Wealth - 1', data=df).fit() print(res1.params) print(res2.params) Many other things are possible with operators. Please consult the `patsy docs `_ to learn more. Functions --------- You can apply vectorized functions to the variables in your model: .. ipython:: python res = smf.ols(formula='Lottery ~ np.log(Literacy)', data=df).fit() print(res.params) Define a custom function: .. ipython:: python def log_plus_1(x): return np.log(x) + 1.0 res = smf.ols(formula='Lottery ~ log_plus_1(Literacy)', data=df).fit() print(res.params) .. _patsy-namespaces: Namespaces ---------- Notice that all of the above examples use the calling namespace to look for the functions to apply. The namespace used can be controlled via the ``eval_env`` keyword. For example, you may want to give a custom namespace using the :class:`patsy:patsy.EvalEnvironment` or you may want to use a "clean" namespace, which we provide by passing ``eval_func=-1``. The default is to use the caller's namespace. This can have (un)expected consequences, if, for example, someone has a variable names ``C`` in the user namespace or in their data structure passed to ``patsy``, and ``C`` is used in the formula to handle a categorical variable. See the `Patsy API Reference `_ for more information. Using formulas with models that do not (yet) support them --------------------------------------------------------- Even if a given ``statsmodels`` function does not support formulas, you can still use ``patsy``'s formula language to produce design matrices. Those matrices can then be fed to the fitting function as ``endog`` and ``exog`` arguments. To generate ``numpy`` arrays: .. ipython:: python import patsy f = 'Lottery ~ Literacy * Wealth' y, X = patsy.dmatrices(f, df, return_type='matrix') print(y[:5]) print(X[:5]) ``y`` and ``X`` would be instances of ``patsy.DesignMatrix`` which is a subclass of ``numpy.ndarray``. To generate pandas data frames: .. ipython:: python f = 'Lottery ~ Literacy * Wealth' y, X = patsy.dmatrices(f, df, return_type='dataframe') print(y[:5]) print(X[:5]) .. ipython:: python print(sm.OLS(y, X).fit().summary()) statsmodels-0.12.2/docs/source/examples/000077500000000000000000000000001400612667500202135ustar00rootroot00000000000000statsmodels-0.12.2/docs/source/examples/README000066400000000000000000000004671400612667500211020ustar00rootroot00000000000000The format for landing.json should be self-explanatory. The images should be placed in docs/source/_static/images/. They will be displayed at 360 x 225 (W x H). It's best to save them as a png with a resolution of a multiple of at least 720 x 450. If you want, you can use png crush to make the images smaller. statsmodels-0.12.2/docs/source/examples/index.rst000066400000000000000000000023321400612667500220540ustar00rootroot00000000000000:orphan: .. _statsmodels-examples: Examples ======== This page provides a series of examples, tutorials and recipes to help you get started with ``statsmodels``. Each of the examples shown here is made available as an IPython Notebook and as a plain python script on the `statsmodels github repository `_. We also encourage users to submit their own examples, tutorials or cool `statsmodels` trick to the `Examples wiki page `_ .. toctree:: {# This content is white space sensitive. Do not reformat #} {% for category in examples%} {% set underscore = "-" * (category.header | length) %} .. raw:: html

 
{{ category.header }} {{ underscore }} .. toctree:: :maxdepth: 1 :hidden: {% for notebook in category.links %} {{ notebook.target | replace('.html','') }} {% endfor %} {%- for notebook in category.links %} {% set heading = "`" ~ notebook.text ~ " <" ~ notebook.target|e ~ ">`_" %} .. container:: example {{ heading }} .. image:: {{ notebook.img }} :target: {{ notebook.target }} :width: 240px {%- endfor %} {% endfor %} statsmodels-0.12.2/docs/source/examples/landing.yml000066400000000000000000000235761400612667500223670ustar00rootroot00000000000000# Add new notebook here # To add a new notebook, create an image in _static/images/.png, # set the target to .html, and add the text name of the notebook # Care is needed with special characters, especially : (use single quotes) # # New sections are added by adding header and id to the top level - header: Linear Regression Models id: regression links: - img: ../_static/images/ols.png target: notebooks/generated/ols.html text: Ordinary Least Squares - img: ../_static/images/gls.png target: notebooks/generated/gls.html text: Generalized Least Squares - img: ../_static/images/quantile_regression.png target: notebooks/generated/quantile_regression.html text: Quantile Regression - img: ../_static/images/recursive_ls.png target: notebooks/generated/recursive_ls.html text: Recursive Least Squares - img: ../_static/images/rolling_ls.png target: notebooks/generated/rolling_ls.html text: Rolling Least Squares - img: ../_static/images/regression_diagnostics.png target: notebooks/generated/regression_diagnostics.html text: Regression Diagnostics - img: ../_static/images/wls.png target: notebooks/generated/wls.html text: Weighted Least Squares - img: ../_static/images/mixed_lm.png target: notebooks/generated/mixed_lm_example.html text: Linear Mixed-Effects - img: ../_static/images/variance_components.png target: notebooks/generated/variance_components.html text: Variance Component Analysis - header: Plotting id: plotting links: - img: ../_static/images/regression_plots.png target: notebooks/generated/regression_plots.html text: Regression Plots - img: ../_static/images/categorical_interaction_plot.png target: notebooks/generated/categorical_interaction_plot.html text: Categorical Interactions - img: ../_static/images/plots_boxplots.png target: notebooks/generated/plots_boxplots.html text: Box Plots - header: Discrete Choice Models id: discrete links: - img: ../_static/images/discrete_overview.png target: notebooks/generated/discrete_choice_overview.html text: Getting Started - img: ../_static/images/fairs_data.png target: notebooks/generated/discrete_choice_example.html text: Fair's Affairs Data - header: Nonparametric Statistics id: nonparametric links: - img: ../_static/images/kde_overview.png target: notebooks/generated/kernel_density.html text: Univariate Kernel Density Estimator - header: Generalized Linear Models id: glm links: - img: ../_static/images/glm_overview.png target: notebooks/generated/glm.html text: Generalized Linear Models Overview - img: ../_static/images/glm_formulas.png target: notebooks/generated/glm_formula.html text: Using Formulas with GLMs - img: ../_static/images/glm_weights.png target: notebooks/generated/glm_weights.html text: Weighting Observations with GLMs - img: ../_static/images/influence_glm_logit.png target: notebooks/generated/influence_glm_logit.html text: Influence Measures for GLMs - img: ../_static/images/quasibinomial.png target: notebooks/generated/quasibinomial.html text: Quasi-binomial regression - header: Robust Regression id: robust links: - img: ../_static/images/rlm_overview.png target: notebooks/generated/robust_models_1.html text: M-estimators for Robust Regression - img: ../_static/images/rlm.png target: notebooks/generated/robust_models_0.html text: Comparing OLS and RLM - header: Generalized Estimating Equations id: robust links: - img: ../_static/images/gee-cov-struct.png target: notebooks/generated/gee_nested_simulation.html text: GEE Nested Covariance Structure - img: ../_static/images/gee-score-tests.png target: notebooks/generated/gee_score_test_simulation.html text: GEE Score Tests - header: Statistics id: stats links: - img: ../_static/images/anova.png target: notebooks/generated/interactions_anova.html text: ANOVA - img: ../_static/images/metaanalysis1.png target: notebooks/generated/metaanalysis1.html text: Meta-Analysis in statsmodels - img: ../_static/images/mediation_survival.png target: notebooks/generated/mediation_survival.html text: Mediation analysis with duration data - header: Time Series Analysis id: stats links: - img: ../_static/images/autoregressions.png target: notebooks/generated/autoregressions.html text: Autoregressions - img: ../_static/images/deterministics.png target: notebooks/generated/deterministics.html text: Deterministic Terms - img: ../_static/images/tsa_arma0.png target: notebooks/generated/tsa_arma_0.html text: 'ARMA: Sunspots Data' - img: ../_static/images/tsa_arma1.png target: notebooks/generated/tsa_arma_1.html text: 'ARMA: Artificial Data' - img: ../_static/images/tsa_filters.png target: notebooks/generated/tsa_filters.html text: Time Series Filters - img: ../_static/images/markov_regression.png target: notebooks/generated/markov_regression.html text: Markov switching dynamic regression - img: ../_static/images/markov_autoregression.png target: notebooks/generated/markov_autoregression.html text: Markov switching autoregression - img: ../_static/images/exponential_smoothing.png target: notebooks/generated/exponential_smoothing.html text: Exponential Smoothing - img: ../_static/images/stl_decomposition.png target: notebooks/generated/stl_decomposition.html text: Seasonal Decomposition - img: ../_static/images/stationarity_detrending_adf_kpss.png target: notebooks/generated/stationarity_detrending_adf_kpss.html text: Stationarity and detrending (ADF/KPSS) - header: State space models id: statespace links: - img: ../_static/images/statespace_sarimax_stata.png target: notebooks/generated/statespace_sarimax_stata.html text: 'SARIMAX: Introduction' - img: ../_static/images/statespace_sarimax_internet.png target: notebooks/generated/statespace_sarimax_internet.html text: 'SARIMAX: Model selection, missing data' - img: ../_static/images/statespace_varmax.png target: notebooks/generated/statespace_varmax.html text: 'VARMAX: introduction' - img: ../_static/images/statespace_dfm_coincident.png target: notebooks/generated/statespace_dfm_coincident.html text: 'Dynamic Factor Models: Application' - img: ../_static/images/statespace_structural_harvey_jaeger.png target: notebooks/generated/statespace_structural_harvey_jaeger.html text: 'Unobserved Components: Application' - img: ../_static/images/statespace_cycles.png target: notebooks/generated/statespace_cycles.html text: Trends and cycles in unemployment - img: ../_static/images/statespace_local_linear_trend.png target: notebooks/generated/statespace_local_linear_trend.html text: 'State space modeling: Local Linear Trends' - img: ../_static/images/statespace_arma0.png target: notebooks/generated/statespace_arma_0.html text: 'Statespace ARMA: Sunspots Data' - img: ../_static/images/statespace_seasonal.png target: notebooks/generated/statespace_seasonal.html text: Seasonality in Time Series Data - img: ../_static/images/statespace_fixed_params.png target: notebooks/generated/statespace_fixed_params.html text: Fixed / constrained parameters in state space models - img: ../_static/images/statespace_tvpvar_mcmc_cfa.png target: notebooks/generated/statespace_tvpvar_mcmc_cfa.html text: TVP-VAR, MCMC, and sparse simulation smoothing - img: ../_static/images/statespace_sarimax_pymc3.png target: notebooks/generated/statespace_sarimax_pymc3.html text: SARIMAX estimation with Bayesian methods - img: ../_static/images/statespace_news.png target: notebooks/generated/statespace_news.html text: 'Forecasting, updating datasets, and the "news"' - img: ../_static/images/statespace_custom_models.png target: notebooks/generated/statespace_custom_models.html text: 'Statespace: Custom Models' - img: ../_static/images/ets.png target: notebooks/generated/ets.html text: 'ETS models' - header: State space models - Technical notes id: statespace_notes links: - img: ../_static/images/statespace_concentrated_scale.png target: notebooks/generated/statespace_concentrated_scale.html text: 'State space models: concentrating out the scale' - img: ../_static/images/statespace_chandrasekhar.png target: notebooks/generated/statespace_chandrasekhar.html text: 'State space models: Chandrasekhar recursions' - header: Forecasting id: forecasting links: - img: ../_static/images/theta-model.png target: notebooks/generated/theta-model.html text: 'Forecasting using the Theta Model' - header: Multivariate Methods id: multivariate links: - img: ../_static/images/pca_fertility_factors.png target: notebooks/generated/pca_fertility_factors.html text: Principal Component Analysis - header: User Notes id: user links: - img: ../_static/images/contrasts.png target: notebooks/generated/contrasts.html text: Contrasts - img: ../_static/images/formulas_intro.png target: notebooks/generated/formulas.html text: Formulas - img: ../_static/images/prediction.png target: notebooks/generated/predict.html text: Prediction - img: ../_static/images/statespace_forecasting.png target: notebooks/generated/statespace_forecasting.html text: Forecasting in statsmodels - img: ../_static/images/generic_mle.png target: notebooks/generated/generic_mle.html text: Generic Maximum Likelihood - img: ../_static/images/tsa_dates.png target: notebooks/generated/tsa_dates.html text: Dates in Time-Series Models - img: ../_static/images/chi2_fitting.png target: notebooks/generated/chi2_fitting.html text: Least squares fitting of models to data - img: ../_static/images/distributed_estimation.png target: notebooks/generated/distributed_estimation.html text: Distributed Estimations statsmodels-0.12.2/docs/source/extending.rst.TXT000066400000000000000000000000001400612667500215600ustar00rootroot00000000000000statsmodels-0.12.2/docs/source/faq.rst000066400000000000000000000055351400612667500177060ustar00rootroot00000000000000:orphan: .. currentmodule:: statsmodels .. _faq: Frequently Asked Question ========================= What is statsmodels? -------------------- statsmodels is a Python package that provides a collection of widely-used statistical models. While statsmodels historically has an econometrics-heavy user base, the package is designed to be useful to a large variety of statistical use cases. In comparison with other Python-based modelling tools, statsmodels focuses more heavily on the statistics and diagnostics underlying the models than having the most cutting-edge or predictive models. .. _endog-exog-faq: What do endog and exog mean? ---------------------------- These are shorthand for endogenous and exogenous variables. You might be more comfortable with the common ``y`` and ``X`` notation in linear models. Sometimes the endogenous variable ``y`` is called a dependent variable. Likewise, sometimes the exogenous variables ``X`` are called the independent variables. You can read about this in greater detail at :ref:`endog_exog` .. _missing-faq: How does statsmodels handle missing data? ----------------------------------------- Missing data can be handled via the ``missing`` keyword argument. Every model takes this keyword. You can find more information in the docstring of :class:`statsmodels.base.Model `. .. _build-faq: Why will not statsmodels build? ------------------------------- Remember that to build, you must have: - The appropriate dependencies (numpy, pandas, scipy, Cython) installed - A suitable C compiler - A working python installation Please review our :ref:`installation instructions ` for details. You might also try cleaning up your source directory by running: .. code-block:: bash pip uninstall statsmodels python setup.py clean And then attempting to re-compile. If you want to be more aggressive, you could also reset git to a prior version by: .. code-block:: bash git reset --hard git clean -xdf git checkout master python setup.py clean I'd like to contribute. Where do I start? ----------------------------------------- Check out our :doc:`development pages ` for a guide on how to get involved. We accept Pull Requests on our GitHub page for bugfixes and topics germane to statistics and statistical modeling. In addition, usability and quality of life enhancements are greatly appreciated as well. What if my question is not answered here? ----------------------------------------- You may find answers for questions that have not yet been added here on GitHub under the `FAQ issues tag `_. If not, please ask your question on stackoverflow using the `statsmodels tag `_ or on the `mailing list `_. statsmodels-0.12.2/docs/source/gam.rst000066400000000000000000000067451400612667500177070ustar00rootroot00000000000000.. currentmodule:: statsmodels.gam.api .. _gam: Generalized Additive Models (GAM) ================================= Generalized Additive Models allow for penalized estimation of smooth terms in generalized linear models. See `Module Reference`_ for commands and arguments. Examples -------- The following illustrates a Gaussian and a Poisson regression where categorical variables are treated as linear terms and the effect of two explanatory variables is captured by penalized B-splines. The data is from the automobile dataset https://archive.ics.uci.edu/ml/datasets/automobile We can load a dataframe with selected columns from the unit test module. .. ipython:: python import statsmodels.api as sm from statsmodels.gam.api import GLMGam, BSplines # import data from statsmodels.gam.tests.test_penalized import df_autos # create spline basis for weight and hp x_spline = df_autos[['weight', 'hp']] bs = BSplines(x_spline, df=[12, 10], degree=[3, 3]) # penalization weight alpha = np.array([21833888.8, 6460.38479]) gam_bs = GLMGam.from_formula('city_mpg ~ fuel + drive', data=df_autos, smoother=bs, alpha=alpha) res_bs = gam_bs.fit() print(res_bs.summary()) # plot smooth components res_bs.plot_partial(0, cpr=True) res_bs.plot_partial(1, cpr=True) alpha = np.array([8283989284.5829611, 14628207.58927821]) gam_bs = GLMGam.from_formula('city_mpg ~ fuel + drive', data=df_autos, smoother=bs, alpha=alpha, family=sm.families.Poisson()) res_bs = gam_bs.fit() print(res_bs.summary()) # Optimal penalization weights alpha can be obtaine through generalized # cross-validation or k-fold cross-validation. # The alpha above are from the unit tests against the R mgcv package. gam_bs.select_penweight()[0] gam_bs.select_penweight_kfold()[0] References ^^^^^^^^^^ * Hastie, Trevor, and Robert Tibshirani. 1986. Generalized Additive Models. Statistical Science 1 (3): 297-310. * Wood, Simon N. 2006. Generalized Additive Models: An Introduction with R. Texts in Statistical Science. Boca Raton, FL: Chapman & Hall/CRC. * Wood, Simon N. 2017. Generalized Additive Models: An Introduction with R. Second edition. Chapman & Hall/CRC Texts in Statistical Science. Boca Raton: CRC Press/Taylor & Francis Group. Module Reference ---------------- .. module:: statsmodels.gam.generalized_additive_model :synopsis: Generalized Additive Models .. currentmodule:: statsmodels.gam.generalized_additive_model Model Class ^^^^^^^^^^^ .. autosummary:: :toctree: generated/ GLMGam LogitGam Results Classes ^^^^^^^^^^^^^^^ .. autosummary:: :toctree: generated/ GLMGamResults Smooth Basis Functions ^^^^^^^^^^^^^^^^^^^^^^ .. module:: statsmodels.gam.smooth_basis :synopsis: Classes for Spline and other Smooth Basis Function .. currentmodule:: statsmodels.gam.smooth_basis Currently there is verified support for two spline bases .. autosummary:: :toctree: generated/ BSplines CyclicCubicSplines `statsmodels.gam.smooth_basis` includes additional splines and a (global) polynomial smoother basis but those have not been verified yet. Families and Link Functions ^^^^^^^^^^^^^^^^^^^^^^^^^^^ The distribution families in `GLMGam` are the same as for GLM and so are the corresponding link functions. Current unit tests only cover Gaussian and Poisson, and GLMGam might not work for all options that are available in GLM. statsmodels-0.12.2/docs/source/gee.rst000066400000000000000000000100061400612667500176640ustar00rootroot00000000000000.. currentmodule:: statsmodels.genmod.generalized_estimating_equations .. _gee: Generalized Estimating Equations ================================ Generalized Estimating Equations estimate generalized linear models for panel, cluster or repeated measures data when the observations are possibly correlated withing a cluster but uncorrelated across clusters. It supports estimation of the same one-parameter exponential families as Generalized Linear models (`GLM`). See `Module Reference`_ for commands and arguments. Examples -------- The following illustrates a Poisson regression with exchangeable correlation within clusters using data on epilepsy seizures. .. ipython:: python import statsmodels.api as sm import statsmodels.formula.api as smf data = sm.datasets.get_rdataset('epil', package='MASS').data fam = sm.families.Poisson() ind = sm.cov_struct.Exchangeable() mod = smf.gee("y ~ age + trt + base", "subject", data, cov_struct=ind, family=fam) res = mod.fit() print(res.summary()) Several notebook examples of the use of GEE can be found on the Wiki: `Wiki notebooks for GEE `_ References ^^^^^^^^^^ * KY Liang and S Zeger. "Longitudinal data analysis using generalized linear models". Biometrika (1986) 73 (1): 13-22. * S Zeger and KY Liang. "Longitudinal Data Analysis for Discrete and Continuous Outcomes". Biometrics Vol. 42, No. 1 (Mar., 1986), pp. 121-130 * A Rotnitzky and NP Jewell (1990). "Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster correlated data", Biometrika, 77, 485-497. * Xu Guo and Wei Pan (2002). "Small sample performance of the score test in GEE". http://www.sph.umn.edu/faculty1/wp-content/uploads/2012/11/rr2002-013.pdf * LA Mancl LA, TA DeRouen (2001). A covariance estimator for GEE with improved small-sample properties. Biometrics. 2001 Mar;57(1):126-34. Module Reference ---------------- .. module:: statsmodels.genmod.generalized_estimating_equations :synopsis: Generalized estimating equations Model Class ^^^^^^^^^^^ .. autosummary:: :toctree: generated/ GEE NominalGEE OrdinalGEE .. module:: statsmodels.genmod.qif :synopsis: Quadratic inference functions .. currentmodule:: statsmodels.genmod.qif .. autosummary:: :toctree: generated/ QIF Results Classes ^^^^^^^^^^^^^^^ .. currentmodule:: statsmodels.genmod.generalized_estimating_equations .. autosummary:: :toctree: generated/ GEEResults GEEMargins .. currentmodule:: statsmodels.genmod.qif .. autosummary:: :toctree: generated/ QIFResults Dependence Structures ^^^^^^^^^^^^^^^^^^^^^ The dependence structures currently implemented are .. module:: statsmodels.genmod.cov_struct :synopsis: Covariance structures for Generalized Estimating Equations (GEE) .. currentmodule:: statsmodels.genmod.cov_struct .. autosummary:: :toctree: generated/ CovStruct Autoregressive Exchangeable GlobalOddsRatio Independence Nested Families ^^^^^^^^ The distribution families are the same as for GLM, currently implemented are .. module:: statsmodels.genmod.families.family :synopsis: Generalized Linear Model (GLM) families .. currentmodule:: statsmodels.genmod.families.family .. autosummary:: :toctree: generated/ Family Binomial Gamma Gaussian InverseGaussian NegativeBinomial Poisson Tweedie Link Functions ^^^^^^^^^^^^^^ The link functions are the same as for GLM, currently implemented are the following. Not all link functions are available for each distribution family. The list of available link functions can be obtained by :: >>> sm.families.family..links .. currentmodule:: statsmodels.genmod.families.links .. autosummary:: :toctree: generated/ Link CDFLink CLogLog Log Logit NegativeBinomial Power cauchy cloglog identity inverse_power inverse_squared log logit nbinom probit statsmodels-0.12.2/docs/source/gettingstarted.rst000066400000000000000000000152271400612667500221660ustar00rootroot00000000000000Getting started =============== This very simple case-study is designed to get you up-and-running quickly with ``statsmodels``. Starting from raw data, we will show the steps needed to estimate a statistical model and to draw a diagnostic plot. We will only use functions provided by ``statsmodels`` or its ``pandas`` and ``patsy`` dependencies. Loading modules and functions ----------------------------- After `installing statsmodels and its dependencies `_, we load a few modules and functions: .. ipython:: python import statsmodels.api as sm import pandas from patsy import dmatrices `pandas `_ builds on ``numpy`` arrays to provide rich data structures and data analysis tools. The ``pandas.DataFrame`` function provides labelled arrays of (potentially heterogenous) data, similar to the ``R`` "data.frame". The ``pandas.read_csv`` function can be used to convert a comma-separated values file to a ``DataFrame`` object. `patsy `_ is a Python library for describing statistical models and building `Design Matrices `_ using ``R``-like formulas. .. note:: This example uses the API interface. See :ref:`importpaths` for information on the difference between importing the API interfaces (``statsmodels.api`` and ``statsmodels.tsa.api``) and directly importing from the module that defines the model. Data ---- We download the `Guerry dataset `_, a collection of historical data used in support of Andre-Michel Guerry's 1833 *Essay on the Moral Statistics of France*. The data set is hosted online in comma-separated values format (CSV) by the `Rdatasets `_ repository. We could download the file locally and then load it using ``read_csv``, but ``pandas`` takes care of all of this automatically for us: .. ipython:: python df = sm.datasets.get_rdataset("Guerry", "HistData").data The `Input/Output doc page `_ shows how to import from various other formats. We select the variables of interest and look at the bottom 5 rows: .. ipython:: python vars = ['Department', 'Lottery', 'Literacy', 'Wealth', 'Region'] df = df[vars] df[-5:] Notice that there is one missing observation in the *Region* column. We eliminate it using a ``DataFrame`` method provided by ``pandas``: .. ipython:: python df = df.dropna() df[-5:] Substantive motivation and model -------------------------------- We want to know whether literacy rates in the 86 French departments are associated with per capita wagers on the Royal Lottery in the 1820s. We need to control for the level of wealth in each department, and we also want to include a series of dummy variables on the right-hand side of our regression equation to control for unobserved heterogeneity due to regional effects. The model is estimated using ordinary least squares regression (OLS). Design matrices (*endog* & *exog*) ---------------------------------- To fit most of the models covered by ``statsmodels``, you will need to create two design matrices. The first is a matrix of endogenous variable(s) (i.e. dependent, response, regressand, etc.). The second is a matrix of exogenous variable(s) (i.e. independent, predictor, regressor, etc.). The OLS coefficient estimates are calculated as usual: .. math:: \hat{\beta} = (X'X)^{-1} X'y where :math:`y` is an :math:`N \times 1` column of data on lottery wagers per capita (*Lottery*). :math:`X` is :math:`N \times 7` with an intercept, the *Literacy* and *Wealth* variables, and 4 region binary variables. The ``patsy`` module provides a convenient function to prepare design matrices using ``R``-like formulas. You can find more information `here `_. We use ``patsy``'s ``dmatrices`` function to create design matrices: .. ipython:: python y, X = dmatrices('Lottery ~ Literacy + Wealth + Region', data=df, return_type='dataframe') The resulting matrices/data frames look like this: .. ipython:: python y[:3] X[:3] Notice that ``dmatrices`` has * split the categorical *Region* variable into a set of indicator variables. * added a constant to the exogenous regressors matrix. * returned ``pandas`` DataFrames instead of simple numpy arrays. This is useful because DataFrames allow ``statsmodels`` to carry-over meta-data (e.g. variable names) when reporting results. The above behavior can of course be altered. See the `patsy doc pages `_. Model fit and summary --------------------- Fitting a model in ``statsmodels`` typically involves 3 easy steps: 1. Use the model class to describe the model 2. Fit the model using a class method 3. Inspect the results using a summary method For OLS, this is achieved by: .. ipython:: python mod = sm.OLS(y, X) # Describe model res = mod.fit() # Fit model print(res.summary()) # Summarize model The ``res`` object has many useful attributes. For example, we can extract parameter estimates and r-squared by typing: .. ipython:: python res.params res.rsquared Type ``dir(res)`` for a full list of attributes. For more information and examples, see the `Regression doc page `_ Diagnostics and specification tests ----------------------------------- ``statsmodels`` allows you to conduct a range of useful `regression diagnostics and specification tests `_. For instance, apply the Rainbow test for linearity (the null hypothesis is that the relationship is properly modelled as linear): .. ipython:: python sm.stats.linear_rainbow(res) Admittedly, the output produced above is not very verbose, but we know from reading the `docstring `_ (also, ``print(sm.stats.linear_rainbow.__doc__)``) that the first number is an F-statistic and that the second is the p-value. ``statsmodels`` also provides graphics functions. For example, we can draw a plot of partial regression for a set of regressors by: .. ipython:: python @savefig gettingstarted_0.png sm.graphics.plot_partregress('Lottery', 'Wealth', ['Region', 'Literacy'], data=df, obs_labels=False) Documentation ------------- Documentation can be accessed from an IPython session using :func:`~statsmodels.tools.web.webdoc`. .. autosummary:: :nosignatures: :toctree: generated/ ~statsmodels.tools.web.webdoc More ---- Congratulations! You're ready to move on to other topics in the `Table of Contents `_ statsmodels-0.12.2/docs/source/glm.rst000066400000000000000000000210741400612667500177120ustar00rootroot00000000000000.. currentmodule:: statsmodels.genmod.generalized_linear_model .. _glm: Generalized Linear Models ========================= Generalized linear models currently supports estimation using the one-parameter exponential families. See `Module Reference`_ for commands and arguments. Examples -------- .. ipython:: python :okwarning: # Load modules and data import statsmodels.api as sm data = sm.datasets.scotland.load(as_pandas=False) data.exog = sm.add_constant(data.exog) # Instantiate a gamma family model with the default link function. gamma_model = sm.GLM(data.endog, data.exog, family=sm.families.Gamma()) gamma_results = gamma_model.fit() print(gamma_results.summary()) Detailed examples can be found here: * `GLM `__ * `Formula `__ Technical Documentation ----------------------- .. ..glm_techn1 .. ..glm_techn2 The statistical model for each observation :math:`i` is assumed to be :math:`Y_i \sim F_{EDM}(\cdot|\theta,\phi,w_i)` and :math:`\mu_i = E[Y_i|x_i] = g^{-1}(x_i^\prime\beta)`. where :math:`g` is the link function and :math:`F_{EDM}(\cdot|\theta,\phi,w)` is a distribution of the family of exponential dispersion models (EDM) with natural parameter :math:`\theta`, scale parameter :math:`\phi` and weight :math:`w`. Its density is given by :math:`f_{EDM}(y|\theta,\phi,w) = c(y,\phi,w) \exp\left(\frac{y\theta-b(\theta)}{\phi}w\right)\,.` It follows that :math:`\mu = b'(\theta)` and :math:`Var[Y|x]=\frac{\phi}{w}b''(\theta)`. The inverse of the first equation gives the natural parameter as a function of the expected value :math:`\theta(\mu)` such that :math:`Var[Y_i|x_i] = \frac{\phi}{w_i} v(\mu_i)` with :math:`v(\mu) = b''(\theta(\mu))`. Therefore it is said that a GLM is determined by link function :math:`g` and variance function :math:`v(\mu)` alone (and :math:`x` of course). Note that while :math:`\phi` is the same for every observation :math:`y_i` and therefore does not influence the estimation of :math:`\beta`, the weights :math:`w_i` might be different for every :math:`y_i` such that the estimation of :math:`\beta` depends on them. ================================================= ============================== ============================== ======================================== =========================================== ============================================================================ ===================== Distribution Domain :math:`\mu=E[Y|x]` :math:`v(\mu)` :math:`\theta(\mu)` :math:`b(\theta)` :math:`\phi` ================================================= ============================== ============================== ======================================== =========================================== ============================================================================ ===================== Binomial :math:`B(n,p)` :math:`0,1,\ldots,n` :math:`np` :math:`\mu-\frac{\mu^2}{n}` :math:`\log\frac{p}{1-p}` :math:`n\log(1+e^\theta)` 1 Poisson :math:`P(\mu)` :math:`0,1,\ldots,\infty` :math:`\mu` :math:`\mu` :math:`\log(\mu)` :math:`e^\theta` 1 Neg. Binom. :math:`NB(\mu,\alpha)` :math:`0,1,\ldots,\infty` :math:`\mu` :math:`\mu+\alpha\mu^2` :math:`\log(\frac{\alpha\mu}{1+\alpha\mu})` :math:`-\frac{1}{\alpha}\log(1-\alpha e^\theta)` 1 Gaussian/Normal :math:`N(\mu,\sigma^2)` :math:`(-\infty,\infty)` :math:`\mu` :math:`1` :math:`\mu` :math:`\frac{1}{2}\theta^2` :math:`\sigma^2` Gamma :math:`N(\mu,\nu)` :math:`(0,\infty)` :math:`\mu` :math:`\mu^2` :math:`-\frac{1}{\mu}` :math:`-\log(-\theta)` :math:`\frac{1}{\nu}` Inv. Gauss. :math:`IG(\mu,\sigma^2)` :math:`(0,\infty)` :math:`\mu` :math:`\mu^3` :math:`-\frac{1}{2\mu^2}` :math:`-\sqrt{-2\theta}` :math:`\sigma^2` Tweedie :math:`p\geq 1` depends on :math:`p` :math:`\mu` :math:`\mu^p` :math:`\frac{\mu^{1-p}}{1-p}` :math:`\frac{\alpha-1}{\alpha}\left(\frac{\theta}{\alpha-1}\right)^{\alpha}` :math:`\phi` ================================================= ============================== ============================== ======================================== =========================================== ============================================================================ ===================== The Tweedie distribution has special cases for :math:`p=0,1,2` not listed in the table and uses :math:`\alpha=\frac{p-2}{p-1}`. Correspondence of mathematical variables to code: * :math:`Y` and :math:`y` are coded as ``endog``, the variable one wants to model * :math:`x` is coded as ``exog``, the covariates alias explanatory variables * :math:`\beta` is coded as ``params``, the parameters one wants to estimate * :math:`\mu` is coded as ``mu``, the expectation (conditional on :math:`x`) of :math:`Y` * :math:`g` is coded as ``link`` argument to the ``class Family`` * :math:`\phi` is coded as ``scale``, the dispersion parameter of the EDM * :math:`w` is not yet supported (i.e. :math:`w=1`), in the future it might be ``var_weights`` * :math:`p` is coded as ``var_power`` for the power of the variance function :math:`v(\mu)` of the Tweedie distribution, see table * :math:`\alpha` is either * Negative Binomial: the ancillary parameter ``alpha``, see table * Tweedie: an abbreviation for :math:`\frac{p-2}{p-1}` of the power :math:`p` of the variance function, see table References ^^^^^^^^^^ * Gill, Jeff. 2000. Generalized Linear Models: A Unified Approach. SAGE QASS Series. * Green, PJ. 1984. “Iteratively reweighted least squares for maximum likelihood estimation, and some robust and resistant alternatives.†Journal of the Royal Statistical Society, Series B, 46, 149-192. * Hardin, J.W. and Hilbe, J.M. 2007. “Generalized Linear Models and Extensions.†2nd ed. Stata Press, College Station, TX. * McCullagh, P. and Nelder, J.A. 1989. “Generalized Linear Models.†2nd ed. Chapman & Hall, Boca Rotan. Module Reference ---------------- .. module:: statsmodels.genmod.generalized_linear_model :synopsis: Generalized Linear Models (GLM) Model Class ^^^^^^^^^^^ .. autosummary:: :toctree: generated/ GLM Results Class ^^^^^^^^^^^^^ .. autosummary:: :toctree: generated/ GLMResults PredictionResults .. _families: Families ^^^^^^^^ The distribution families currently implemented are .. module:: statsmodels.genmod.families.family .. currentmodule:: statsmodels.genmod.families.family .. autosummary:: :toctree: generated/ Family Binomial Gamma Gaussian InverseGaussian NegativeBinomial Poisson Tweedie .. _links: Link Functions ^^^^^^^^^^^^^^ The link functions currently implemented are the following. Not all link functions are available for each distribution family. The list of available link functions can be obtained by :: >>> sm.families.family..links .. module:: statsmodels.genmod.families.links .. currentmodule:: statsmodels.genmod.families.links .. autosummary:: :toctree: generated/ Link CDFLink CLogLog Log Logit NegativeBinomial Power cauchy cloglog identity inverse_power inverse_squared log logit nbinom probit .. _varfuncs: Variance Functions ^^^^^^^^^^^^^^^^^^ Each of the families has an associated variance function. You can access the variance functions here: :: >>> sm.families..variance .. module:: statsmodels.genmod.families.varfuncs .. currentmodule:: statsmodels.genmod.families.varfuncs .. autosummary:: :toctree: generated/ VarianceFunction constant Power mu mu_squared mu_cubed Binomial binary NegativeBinomial nbinom statsmodels-0.12.2/docs/source/glm_techn1.rst.TXT000066400000000000000000000002251400612667500216250ustar00rootroot00000000000000.. currentmodule:: statsmodels.glm .. _glm_techn1: Technical Documentation ======================= Introduction ------------ Just a placeholder statsmodels-0.12.2/docs/source/glm_techn2.rst.TXT000066400000000000000000000002671400612667500216340ustar00rootroot00000000000000.. currentmodule:: statsmodels.glm .. _glm_techn2: Technical Documentation - part 2 ================================ Implementation Notes -------------------- Just a placeholder statsmodels-0.12.2/docs/source/gmm.rst000066400000000000000000000026211400612667500177100ustar00rootroot00000000000000.. currentmodule:: statsmodels.sandbox.regression.gmm .. _gmm: Generalized Method of Moments :mod:`gmm` ======================================== :mod:`statsmodels.gmm` contains model classes and functions that are based on estimation with Generalized Method of Moments. Currently the general non-linear case is implemented. An example class for the standard linear instrumental variable model is included. This has been introduced as a test case, it works correctly but it does not take the linear structure into account. For the linear case we intend to introduce a specific implementation which will be faster and numerically more accurate. Currently, GMM takes arbitrary non-linear moment conditions and calculates the estimates either for a given weighting matrix or iteratively by alternating between estimating the optimal weighting matrix and estimating the parameters. Implementing models with different moment conditions is done by subclassing GMM. In the minimal implementation only the moment conditions, `momcond` have to be defined. .. currentmodule:: statsmodels.sandbox.regression.gmm Module Reference """""""""""""""" .. module:: statsmodels.sandbox.regression.gmm :synopsis: A framework for implementing Generalized Method of Moments (GMM) .. autosummary:: :toctree: generated/ GMM GMMResults IV2SLS IVGMM IVGMMResults IVRegressionResults LinearIVGMM NonlinearIVGMM statsmodels-0.12.2/docs/source/gmm_techn1.rst.TXT000066400000000000000000000035321400612667500216320ustar00rootroot00000000000000.. currentmodule:: statsmodels.sandbox.regression.gmm .. _gmm_techn1: Technical Documentation ======================= Introduction ------------ Generalized Method of Moments is an extension of the Method of Moments if there are more moment conditions than parameters that are estimated. simple example General Structure and Implementation ------------------------------------ The main class for GMM estimation, makes little assumptions about the moment conditions. It is designed for the general case when moment conditions are given as function by the user. :: def momcond(params) which should return a two dimensional array with observation in rows and moment conditions in columns. Denote this function by `$g(\theta)$`. Then the GMM estimator is given as the solution to the maximization problem: ..math: max_{\theta) g(theta)' W g(theta) (1) The weighting matrix can be estimated in several different ways. The basic method `fitgmm` takes the weighting matrix as argument or if it is not given takes the identity matrix and maximizes (1) taking W as given. Since the optimizing functions solve minimization problems, we usually minimizes the negative of the objective function. `fit_iterative` calculates the optimal weighting matrix and maximizes the criterion function in alternating steps. The number of iterations can be given as an argument to this fit method. The optimal weighting matrix, which is the covariance matrix of the moment conditions, can be estimated in different ways. Kernel and shrinkage estimators are planned but not yet implemented. TODO The GMM class itself does not define any moment conditions. To get an estimator for given moment conditions, GMM needs to be subclassed. The basic structure of writing new models based on the generic MLE or GMM framework and subclassing is described in `extending.rst` (TODO: link) As an example statsmodels-0.12.2/docs/source/graphics.rst000066400000000000000000000035601400612667500207330ustar00rootroot00000000000000.. currentmodule:: statsmodels.graphics.gofplots .. _graphics: Graphics ======== .. automodule:: statsmodels.graphics Goodness of Fit Plots --------------------- .. currentmodule:: statsmodels.graphics.gofplots .. autosummary:: :toctree: generated/ qqplot qqline qqplot_2samples ProbPlot Boxplots -------- .. currentmodule:: statsmodels.graphics.boxplots .. autosummary:: :toctree: generated/ violinplot beanplot Correlation Plots ------------------ .. currentmodule:: statsmodels.graphics.correlation .. autosummary:: :toctree: generated/ plot_corr plot_corr_grid .. currentmodule:: statsmodels.graphics.plot_grids .. autosummary:: :toctree: generated/ scatter_ellipse Dot Plots --------- .. currentmodule:: statsmodels.graphics.dotplots .. autosummary:: :toctree: generated/ dot_plot Functional Plots ---------------- .. currentmodule:: statsmodels.graphics.functional .. autosummary:: :toctree: generated/ hdrboxplot fboxplot rainbowplot banddepth Regression Plots ---------------- .. currentmodule:: statsmodels.graphics.regressionplots .. autosummary:: :toctree: generated/ plot_fit plot_regress_exog plot_partregress plot_partregress_grid plot_ccpr plot_ccpr_grid plot_ceres_residuals abline_plot influence_plot plot_leverage_resid2 Time Series Plots ----------------- .. currentmodule:: statsmodels.graphics.tsaplots .. autosummary:: :toctree: generated/ plot_acf plot_pacf month_plot quarter_plot Other Plots ----------- .. currentmodule:: statsmodels.graphics.factorplots .. autosummary:: :toctree: generated/ interaction_plot .. currentmodule:: statsmodels.graphics.mosaicplot .. autosummary:: :toctree: generated/ mosaic .. currentmodule:: statsmodels.graphics.agreement .. autosummary:: :toctree: 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The basic idea is to treat each variable with missing values as the dependent variable in a regression, with some or all of the remaining variables as its predictors. The MICE procedure cycles through these models, fitting each in turn, then uses a procedure called "predictive mean matching" (PMM) to generate random draws from the predictive distributions determined by the fitted models. These random draws become the imputed values for one imputed data set. By default, each variable with missing variables is modeled using a linear regression with main effects for all other variables in the data set. Note that even when the imputation model is linear, the PMM procedure preserves the domain of each variable. Thus, for example, if all observed values for a given variable are positive, all imputed values for the variable will always be positive. The user also has the option to specify which model is used to produce imputed values for each variable. .. code Classes ------- .. currentmodule:: statsmodels.imputation.mice .. autosummary:: :toctree: generated/ MICE MICEData .. currentmodule:: statsmodels.imputation.bayes_mi .. autosummary:: :toctree: generated/ MI BayesGaussMI Implementation Details ---------------------- Internally, this function uses `pandas.isnull `_. Anything that returns True from this function will be treated as missing data. statsmodels-0.12.2/docs/source/index.rst000066400000000000000000000051441400612667500202420ustar00rootroot00000000000000.. image:: images/statsmodels-logo-v2-horizontal.svg :width: 50% :alt: statsmodels :align: left :ref:`statsmodels ` is a Python module that provides classes and functions for the estimation of many different statistical models, as well as for conducting statistical tests, and statistical data exploration. An extensive list of result statistics are available for each estimator. The results are tested against existing statistical packages to ensure that they are correct. The package is released under the open source Modified BSD (3-clause) license. The online documentation is hosted at `statsmodels.org `__. Introduction ============ ``statsmodels`` supports specifying models using R-style formulas and ``pandas`` DataFrames. Here is a simple example using ordinary least squares: .. ipython:: python import numpy as np import statsmodels.api as sm import statsmodels.formula.api as smf # Load data dat = sm.datasets.get_rdataset("Guerry", "HistData").data # Fit regression model (using the natural log of one of the regressors) results = smf.ols('Lottery ~ Literacy + np.log(Pop1831)', data=dat).fit() # Inspect the results print(results.summary()) You can also use ``numpy`` arrays instead of formulas: .. ipython:: python import numpy as np import statsmodels.api as sm # Generate artificial data (2 regressors + constant) nobs = 100 X = np.random.random((nobs, 2)) X = sm.add_constant(X) beta = [1, .1, .5] e = np.random.random(nobs) y = np.dot(X, beta) + e # Fit regression model results = sm.OLS(y, X).fit() # Inspect the results print(results.summary()) Have a look at `dir(results)` to see available results. Attributes are described in `results.__doc__` and results methods have their own docstrings. Citation ======== Please use following citation to cite statsmodels in scientific publications: Seabold, Skipper, and Josef Perktold. "`statsmodels: Econometric and statistical modeling with python. `_" *Proceedings of the 9th Python in Science Conference.* 2010. Bibtex entry:: @inproceedings{seabold2010statsmodels, title={statsmodels: Econometric and statistical modeling with python}, author={Seabold, Skipper and Perktold, Josef}, booktitle={9th Python in Science Conference}, year={2010}, } .. toctree:: :maxdepth: 1 install gettingstarted user-guide examples/index api about dev/index release/index Index ===== :ref:`genindex` :ref:`modindex` statsmodels-0.12.2/docs/source/install.rst000066400000000000000000000116241400612667500206010ustar00rootroot00000000000000:orphan: .. _install: Installing statsmodels ====================== The easiest way to install statsmodels is to install it as part of the `Anaconda `_ distribution, a cross-platform distribution for data analysis and scientific computing. This is the recommended installation method for most users. Instructions for installing from PyPI, source or a development version are also provided. Python Support -------------- statsmodels supports Python 3.6, 3.7 and 3.8. Anaconda -------- statsmodels is available through conda provided by `Anaconda `__. The latest release can be installed using: .. code-block:: bash conda install -c conda-forge statsmodels PyPI (pip) ---------- To obtain the latest released version of statsmodels using pip: .. code-block:: bash pip install statsmodels Follow `this link to our PyPI page `__ to directly download wheels or source. For Windows users, unofficial recent binaries (wheels) are occasionally available `here `__. Obtaining the Source -------------------- We do not release very often but the master branch of our source code is usually fine for everyday use. You can get the latest source from our `github repository `__. Or if you have git installed: .. code-block:: bash git clone git://github.com/statsmodels/statsmodels.git If you want to keep up to date with the source on github just periodically do: .. code-block:: bash git pull in the statsmodels directory. Installation from Source ------------------------ You will need a C compiler installed to build statsmodels. If you are building from the github source and not a source release, then you will also need Cython. You can follow the instructions below to get a C compiler setup for Windows. If your system is already set up with pip, a compiler, and git, you can try: .. code-block:: bash pip install git+https://github.com/statsmodels/statsmodels If you do not have pip installed or want to do the installation more manually, you can also type: .. code-block:: bash python setup.py install Or even more manually .. code-block:: bash python setup.py build python setup.py install statsmodels can also be installed in `develop` mode which installs statsmodels into the current python environment in-place. The advantage of this is that edited modules will immediately be re-interpreted when the python interpreter restarts without having to re-install statsmodels. .. code-block:: bash python setup.py develop Compilers ~~~~~~~~~ Linux ^^^^^ If you are using Linux, we assume that you are savvy enough to install `gcc` on your own. More than likely, it is already installed. Windows ^^^^^^^ It is strongly recommended to use 64-bit Python if possible. Getting the right compiler is especially confusing for Windows users. Over time, Python has been built using a variety of different Windows C compilers. `This guide `_ should help clarify which version of Python uses which compiler by default. Mac ^^^ Installing statsmodels on MacOS requires installing `gcc` which provides a suitable C compiler. We recommend installing Xcode and the Command Line Tools. Dependencies ------------ The current minimum dependencies are: * `Python `__ >= 3.6 * `NumPy `__ >= 1.15 * `SciPy `__ >= 1.2 * `Pandas `__ >= 0.23 * `Patsy `__ >= 0.5.1 Cython is required to build from a git checkout but not to run or install from PyPI: * `Cython `__ >= 0.29 is required to build the code from github but not from a source distribution. Given the long release cycle, statsmodels follows a loose time-based policy for dependencies: minimal dependencies are lagged about one and a half to two years. Our next planned update of minimum versions is expected in the first half of 2020. Optional Dependencies --------------------- * `cvxopt `__ is required for regularized fitting of some models. * `Matplotlib `__ >= 2.2 is needed for plotting functions and running many of the examples. * If installed, `X-12-ARIMA `__ or `X-13ARIMA-SEATS `__ can be used for time-series analysis. * `pytest `__ is required to run the test suite. * `IPython `__ >= 5.0 is required to build the docs locally or to use the notebooks. * `joblib `__ >= 0.9 can be used to accelerate distributed estimation for certain models. * `jupyter `__ is needed to run the notebooks. statsmodels-0.12.2/docs/source/iolib.rst000066400000000000000000000023521400612667500202270ustar00rootroot00000000000000.. currentmodule:: statsmodels.iolib .. _iolib: Input-Output :mod:`iolib` ========================= ``statsmodels`` offers some functions for input and output. These include a reader for STATA files, a class for generating tables for printing in several formats and two helper functions for pickling. Users can also leverage the powerful input/output functions provided by :ref:`pandas.io `. Among other things, ``pandas`` (a ``statsmodels`` dependency) allows reading and writing to Excel, CSV, and HDF5 (PyTables). Examples -------- `SimpleTable: Basic example `__ Module Reference ---------------- .. module:: statsmodels.iolib :synopsis: Tools for reading datasets and producing summary output .. autosummary:: :toctree: generated/ foreign.StataReader foreign.StataWriter foreign.genfromdta foreign.savetxt table.SimpleTable table.csv2st smpickle.save_pickle smpickle.load_pickle The following are classes and functions used to return the summary of estimation results, and mostly intended for internal use. There are currently two versions for creating summaries. .. autosummary:: :toctree: generated/ summary.Summary summary2.Summary statsmodels-0.12.2/docs/source/large_data.rst000066400000000000000000000050371400612667500212170ustar00rootroot00000000000000.. module:: statsmodels.base.distributed_estimation .. currentmodule:: statsmodels.base.distributed_estimation Working with Large Data Sets ============================ Big data is something of a buzzword in the modern world. While statsmodels works well with small and moderately-sized data sets that can be loaded in memory--perhaps tens of thousands of observations--use cases exist with millions of observations or more. Depending your use case, statsmodels may or may not be a sufficient tool. statsmodels and most of the software stack it is written on operates in memory. Resultantly, building models on larger data sets can be challenging or even impractical. With that said, there are 2 general strategies for building models on larger data sets with statsmodels. Divide and Conquer - Distributing Jobs -------------------------------------- If your system is capable of loading all the data, but the analysis you are attempting to perform is slow, you might be able to build models on horizontal slices of the data and then aggregate the individual models once fit. A current limitation of this approach is that it generally does not support `patsy `_ so constructing your design matrix (known as `exog`) in statsmodels, is a little challenging. A detailed example is available `here `_. .. autosummary:: :toctree: generated/ DistributedModel DistributedResults Subsetting your data -------------------- If your entire data set is too large to store in memory, you might try storing it in a columnar container like `Apache Parquet `_ or `bcolz `_. Using the patsy formula interface, statsmodels will use the `__getitem__` function (i.e. data['Item']) to pull only the specified columns. .. code-block:: python import pyarrow as pa import pyarrow.parquet as pq import statsmodels.formula.api as smf class DataSet(dict): def __init__(self, path): self.parquet = pq.ParquetFile(path) def __getitem__(self, key): try: return self.parquet.read([key]).to_pandas()[key] except: raise KeyError LargeData = DataSet('LargeData.parquet') res = smf.ols('Profit ~ Sugar + Power + Women', data=LargeData).fit() Additionally, you can add code to this example `DataSet` object to return only a subset of the rows until you have built a good model. Then, you can refit your final model on more data. statsmodels-0.12.2/docs/source/miscmodels.rst000066400000000000000000000035461400612667500212760ustar00rootroot00000000000000 .. module:: statsmodels.miscmodels .. currentmodule:: statsmodels.miscmodels .. _miscmodels: Other Models :mod:`miscmodels` ============================== :mod:`statsmodels.miscmodels` contains model classes and that do not yet fit into any other category, or are basic implementations that are not yet polished and will most likely still change. Some of these models were written as examples for the generic maximum likelihood framework, and there will be others that might be based on general method of moments. The models in this category have been checked for basic cases, but might be more exposed to numerical problems than the complete implementation. For example, count.Poisson has been added using only the generic maximum likelihood framework, the standard errors are based on the numerical evaluation of the Hessian, while discretemod.Poisson uses analytical Gradients and Hessian and will be more precise, especially in cases when there is strong multicollinearity. On the other hand, by subclassing GenericLikelihoodModel, it is easy to add new models, another example can be seen in the zero inflated Poisson model, miscmodels.count. Count Models :mod:`count` -------------------------- .. module:: statsmodels.miscmodels.count .. currentmodule:: statsmodels.miscmodels.count .. autosummary:: :toctree: generated/ PoissonGMLE PoissonOffsetGMLE PoissonZiGMLE Linear Model with t-distributed errors -------------------------------------- This is a class that shows that a new model can be defined by only specifying the method for the loglikelihood. All result statistics are inherited from the generic likelihood model and result classes. The results have been checked against R for a simple case. .. module:: statsmodels.miscmodels.tmodel .. currentmodule:: statsmodels.miscmodels.tmodel .. autosummary:: :toctree: generated/ TLinearModel statsmodels-0.12.2/docs/source/missing.rst000066400000000000000000000026741400612667500206110ustar00rootroot00000000000000:orphan: .. _missing_data: Missing Data ------------ All of the models can handle missing data. For performance reasons, the default is not to do any checking for missing data. If, however, you would like for missing data to be handled internally, you can do so by using the missing keyword argument. The default is to do nothing .. ipython:: python import statsmodels.api as sm data = sm.datasets.longley.load(as_pandas=False) data.exog = sm.add_constant(data.exog) # add in some missing data missing_idx = np.array([False] * len(data.endog)) missing_idx[[4, 10, 15]] = True data.endog[missing_idx] = np.nan ols_model = sm.OLS(data.endog, data.exog) ols_fit = ols_model.fit() print(ols_fit.params) This silently fails and all of the model parameters are NaN, which is probably not what you expected. If you are not sure whether or not you have missing data you can use `missing = 'raise'`. This will raise a `MissingDataError` during model instantiation if missing data is present so that you know something was wrong in your input data. .. ipython:: python :okexcept: ols_model = sm.OLS(data.endog, data.exog, missing='raise') If you want statsmodels to handle the missing data by dropping the observations, use `missing = 'drop'`. .. ipython:: python ols_model = sm.OLS(data.endog, data.exog, missing='drop') We are considering adding a configuration framework so that you can set the option with a global setting. statsmodels-0.12.2/docs/source/mixed_glm.rst000066400000000000000000000034021400612667500210730ustar00rootroot00000000000000.. currentmodule:: statsmodels.genmod.bayes_mixed_glm Generalized Linear Mixed Effects Models ======================================= Generalized Linear Mixed Effects (GLIMMIX) models are generalized linear models with random effects in the linear predictors. statsmodels currently supports estimation of binomial and Poisson GLIMMIX models using two Bayesian methods: the Laplace approximation to the posterior, and a variational Bayes approximation to the posterior. Both methods provide point estimates (posterior means) and assessments of uncertainty (posterior standard deviation). The current implementation only supports independent random effects. Technical Documentation ----------------------- Unlike statsmodels mixed linear models, the GLIMMIX implementation is not group-based. Groups are created by interacting all random effects with a categorical variable. Note that this creates large, sparse random effects design matrices `exog_vc`. Internally, `exog_vc` is converted to a scipy sparse matrix. When passing the arguments directly to the class initializer, a sparse matrix may be passed. When using formulas, a dense matrix is created then converted to sparse. For very large problems, it may not be feasible to use formulas due to the size of this dense intermediate matrix. References ^^^^^^^^^^ Blei, Kucukelbir, McAuliffe (2017). Variational Inference: A review for Statisticians https://arxiv.org/pdf/1601.00670.pdf Module Reference ---------------- .. module:: statsmodels.genmod.bayes_mixed_glm :synopsis: Bayes Mixed Generalized Linear Models The model classes are: .. autosummary:: :toctree: generated/ BinomialBayesMixedGLM PoissonBayesMixedGLM The result class is: .. autosummary:: :toctree: generated/ BayesMixedGLMResults statsmodels-0.12.2/docs/source/mixed_linear.rst000066400000000000000000000162151400612667500215740ustar00rootroot00000000000000.. currentmodule:: statsmodels.regression.mixed_linear_model .. _mixedlmmod: Linear Mixed Effects Models =========================== Linear Mixed Effects models are used for regression analyses involving dependent data. Such data arise when working with longitudinal and other study designs in which multiple observations are made on each subject. Some specific linear mixed effects models are * *Random intercepts models*, where all responses in a group are additively shifted by a value that is specific to the group. * *Random slopes models*, where the responses in a group follow a (conditional) mean trajectory that is linear in the observed covariates, with the slopes (and possibly intercepts) varying by group. * *Variance components models*, where the levels of one or more categorical covariates are associated with draws from distributions. These random terms additively determine the conditional mean of each observation based on its covariate values. The statsmodels implementation of LME is primarily group-based, meaning that random effects must be independently-realized for responses in different groups. There are two types of random effects in our implementation of mixed models: (i) random coefficients (possibly vectors) that have an unknown covariance matrix, and (ii) random coefficients that are independent draws from a common univariate distribution. For both (i) and (ii), the random effects influence the conditional mean of a group through their matrix/vector product with a group-specific design matrix. A simple example of random coefficients, as in (i) above, is: .. math:: Y_{ij} = \beta_0 + \beta_1X_{ij} + \gamma_{0i} + \gamma_{1i}X_{ij} + \epsilon_{ij} Here, :math:`Y_{ij}` is the :math:`j^\rm{th}` measured response for subject :math:`i`, and :math:`X_{ij}` is a covariate for this response. The "fixed effects parameters" :math:`\beta_0` and :math:`\beta_1` are shared by all subjects, and the errors :math:`\epsilon_{ij}` are independent of everything else, and identically distributed (with mean zero). The "random effects parameters" :math:`\gamma_{0i}` and :math:`\gamma_{1i}` follow a bivariate distribution with mean zero, described by three parameters: :math:`{\rm var}(\gamma_{0i})`, :math:`{\rm var}(\gamma_{1i})`, and :math:`{\rm cov}(\gamma_{0i}, \gamma_{1i})`. There is also a parameter for :math:`{\rm var}(\epsilon_{ij})`. A simple example of variance components, as in (ii) above, is: .. math:: Y_{ijk} = \beta_0 + \eta_{1i} + \eta_{2j} + \epsilon_{ijk} Here, :math:`Y_{ijk}` is the :math:`k^\rm{th}` measured response under conditions :math:`i, j`. The only "mean structure parameter" is :math:`\beta_0`. The :math:`\eta_{1i}` are independent and identically distributed with zero mean, and variance :math:`\tau_1^2`, and the :math:`\eta_{2j}` are independent and identically distributed with zero mean, and variance :math:`\tau_2^2`. statsmodels MixedLM handles most non-crossed random effects models, and some crossed models. To include crossed random effects in a model, it is necessary to treat the entire dataset as a single group. The variance components arguments to the model can then be used to define models with various combinations of crossed and non-crossed random effects. The statsmodels LME framework currently supports post-estimation inference via Wald tests and confidence intervals on the coefficients, profile likelihood analysis, likelihood ratio testing, and AIC. Examples -------- .. ipython:: python import statsmodels.api as sm import statsmodels.formula.api as smf data = sm.datasets.get_rdataset("dietox", "geepack").data md = smf.mixedlm("Weight ~ Time", data, groups=data["Pig"]) mdf = md.fit() print(mdf.summary()) Detailed examples can be found here * `Mixed LM `__ There are some notebook examples on the Wiki: `Wiki notebooks for MixedLM `_ Technical Documentation ----------------------- The data are partitioned into disjoint groups. The probability model for group :math:`i` is: .. math:: Y = X\beta + Z\gamma + Q_1\eta_1 + \cdots + Q_k\eta_k + \epsilon where * :math:`n_i` is the number of observations in group :math:`i` * :math:`Y` is a :math:`n_i` dimensional response vector * :math:`X` is a :math:`n_i * k_{fe}` dimensional matrix of fixed effects coefficients * :math:`\beta` is a :math:`k_{fe}`-dimensional vector of fixed effects slopes * :math:`Z` is a :math:`n_i * k_{re}` dimensional matrix of random effects coefficients * :math:`\gamma` is a :math:`k_{re}`-dimensional random vector with mean 0 and covariance matrix :math:`\Psi`; note that each group gets its own independent realization of gamma. * :math:`Q_j` is a :math:`n_i \times q_j` dimensional design matrix for the :math:`j^\rm{th}` variance component. * :math:`\eta_j` is a :math:`q_j`-dimensional random vector containing independent and identically distributed values with variance :math:`\tau_j^2`. * :math:`\epsilon` is a :math:`n_i` dimensional vector of i.i.d normal errors with mean 0 and variance :math:`\sigma^2`; the :math:`\epsilon` values are independent both within and between groups :math:`Y, X, \{Q_j\}` and :math:`Z` must be entirely observed. :math:`\beta`, :math:`\Psi`, and :math:`\sigma^2` are estimated using ML or REML estimation, and :math:`\gamma`, :math:`\{\eta_j\}` and :math:`\epsilon` are random so define the probability model. The marginal mean structure is :math:`E[Y|X,Z] = X*\beta`. If only the marginal mean structure is of interest, GEE is a good alternative to mixed models. Notation: * :math:`cov_{re}` is the random effects covariance matrix (referred to above as :math:`\Psi`) and :math:`scale` is the (scalar) error variance. There is also a single estimated variance parameter :math:`\tau_j^2` for each variance component. For a single group, the marginal covariance matrix of endog given exog is :math:`scale*I + Z * cov_{re} * Z`, where :math:`Z` is the design matrix for the random effects in one group. References ^^^^^^^^^^ The primary reference for the implementation details is: * MJ Lindstrom, DM Bates (1988). *Newton Raphson and EM algorithms for linear mixed effects models for repeated measures data*. Journal of the American Statistical Association. Volume 83, Issue 404, pages 1014-1022. See also this more recent document: * http://econ.ucsb.edu/~doug/245a/Papers/Mixed%20Effects%20Implement.pdf All the likelihood, gradient, and Hessian calculations closely follow Lindstrom and Bates. The following two documents are written more from the perspective of users: * https://r-forge.r-project.org/scm/viewvc.php/*checkout*/www/lMMwR/lrgprt.pdf?revision=949&root=lme4&pathrev=1781 * http://lme4.r-forge.r-project.org/slides/2009-07-07-Rennes/3Longitudinal-4.pdf .. Class hierarchy: TODO General references for this class of models are Module Reference ---------------- .. module:: statsmodels.regression.mixed_linear_model :synopsis: Mixed Linear Models The model class is: .. autosummary:: :toctree: generated/ MixedLM The result class is: .. autosummary:: :toctree: generated/ MixedLMResults statsmodels-0.12.2/docs/source/multivariate.rst000066400000000000000000000030171400612667500216360ustar00rootroot00000000000000.. module:: statsmodels.multivariate :synopsis: Models for multivariate data .. currentmodule:: statsmodels.multivariate .. _multivariate: Multivariate Statistics :mod:`multivariate` =========================================== This section includes methods and algorithms from multivariate statistics. Principal Component Analysis ---------------------------- .. module:: statsmodels.multivariate.pca :synopsis: Principal Component Analaysis .. currentmodule:: statsmodels.multivariate.pca .. autosummary:: :toctree: generated/ PCA pca Factor Analysis --------------- .. currentmodule:: statsmodels.multivariate.factor .. autosummary:: :toctree: generated/ Factor FactorResults Factor Rotation --------------- .. currentmodule:: statsmodels.multivariate.factor_rotation .. autosummary:: :toctree: generated/ rotate_factors target_rotation procrustes promax Canonical Correlation --------------------- .. currentmodule:: statsmodels.multivariate.cancorr .. autosummary:: :toctree: generated/ CanCorr MANOVA ------ .. currentmodule:: statsmodels.multivariate.manova .. autosummary:: :toctree: generated/ MANOVA MultivariateOLS --------------- `_MultivariateOLS` is a model class with limited features. Currently it supports multivariate hypothesis tests and is used as backend for MANOVA. .. currentmodule:: statsmodels.multivariate.multivariate_ols .. autosummary:: :toctree: generated/ _MultivariateOLS _MultivariateOLSResults MultivariateTestResults statsmodels-0.12.2/docs/source/names_wordlist.txt000066400000000000000000000043421400612667500221730ustar00rootroot00000000000000Abdelhakim Akaike Aknouche Amund Ananyev Anders Andrews Anscombe Argia Armitage Arpin Assimakopoulos Athanasopoulos Atticus Augspurger Azzalini Bai Bakirov Balazs Banbura Baran Batakrishna BaÅ„bura Behrens Benjamini Bera Berndt Billah Biometrical Biopharmaceutical Biostatistics Blunck Bok Borenstein Brandyn Breslow Breusch Brockwell Bronwyn Broyden Caratelli Chadrasekhar Chantal Charlier Chaudhuri Chichester Cinthia Clauss Commandeur Conaway Coster Cribbie Daniele Degreeds Denton Devan Domenico Doornik Driscoll Durbin ETSModel Econometrica Efron Eiker El Elsevier Engle Escanciano Fama Fayçal Ferre Filardo Finney Fioruci Fleiss Forsythe Galuzio Gangat Gelman Geng Gentonb Giannone Gibb Goldfarb Goldfeld Gommers Granger Gruman Grunfeld Gu Guglielmo Gwowen Hallock Hamdi Hampel Hannan Hanszel Haoyu Hartung Hassan Hastie Hauck Hausman Helmert Helmut Henning Herbst Hertzprung Hobson Hochberg Hodrick Hoffmann Hotellings Hurvich Hyndman Inggs Itzikovitch Jacoby Jaeger Jarque Jeliazkov Johansen Jong Jonkman Joonsuk Josef Jurgen Kacker Kaplan Karakus Kerby Kibirige Knotek Koehler Koenker Kolmogorov Koopman Kotz Kraay Kumar Kwiatkowski Lakhotia Larralde Levene Levinson Liang Lickert Liu Ljung Lobato Longley Louzada Lucrezia Lyttle Löning Lütkepohl MacKinnon Mahalanobis Mandel Manmeet Markus Mazon Mehrotra Merothra Methodologist Miettinen Mirzayev Modugno Murasawa Nelder Newey Nikolopoulos Nino Nurminen Nychkac OaxacaBlinder Omer Oneway Ord Ozen Paule Paulo Pellegrini Pelletier Penrose Perktold Petropoulos Piet Ploberger Pölsterl Pratyush Qi Qingqing Quackenbush Raphson Reichlin Rencher Reuille Ridout Rizzo Ruecker Saeed Saggiorato Sahu Samesh Sandu Satterthwait Sbordone Scherrer Scholl Schucany Schwarz Schwert Seabold Shanno Sharan Shedden Shephard Shieh Sidak Sidik Siem Silverman Sitka Smirnov Spector Springer Sriram Staley Startz Stata Steiger Surico Szekely Tambalotti Tanaka Theano Tibshirani Tukey Ursu Varga Varun Vedal Warne Welch Wellek Wes Wichern Wishart Wouter Yao Yasine Yasutomo Yichuan Yuen Zaman Zeger Zha Zhiqing Zivot adrienpacifico aeturrell bashtage comatrion eirki gliptak hannan luxiform oaxaca partev seabold zveryansky Řehůřek 郭飞 Physica Rousseeuw Croux Bivolaru Ezequiel Smucler Giulio Beseghi Marchand das soham tagomastatsmodels-0.12.2/docs/source/nonparametric.rst000066400000000000000000000113521400612667500217730ustar00rootroot00000000000000.. currentmodule:: statsmodels.nonparametric .. _nonparametric: Nonparametric Methods :mod:`nonparametric` ========================================== This section collects various methods in nonparametric statistics. This includes kernel density estimation for univariate and multivariate data, kernel regression and locally weighted scatterplot smoothing (lowess). sandbox.nonparametric contains additional functions that are work in progress or do not have unit tests yet. We are planning to include here nonparametric density estimators, especially based on kernel or orthogonal polynomials, smoothers, and tools for nonparametric models and methods in other parts of statsmodels. Kernel density estimation ------------------------- The kernel density estimation (KDE) functionality is split between univariate and multivariate estimation, which are implemented in quite different ways. Univariate estimation (as provided by `KDEUnivariate`) uses FFT transforms, which makes it quite fast. Therefore it should be preferred for *continuous, univariate* data if speed is important. It supports using different kernels; bandwidth estimation is done only by a rule of thumb (Scott or Silverman). Multivariate estimation (as provided by `KDEMultivariate`) uses product kernels. It supports least squares and maximum likelihood cross-validation for bandwidth estimation, as well as estimating mixed continuous, ordered and unordered data. The default kernels (Gaussian, Wang-Ryzin and Aitchison-Aitken) cannot be altered at the moment however. Direct estimation of the conditional density (:math:`P(X | Y) = P(X, Y) / P(Y)`) is supported by `KDEMultivariateConditional`. `KDEMultivariate` can do univariate estimation as well, but is up to two orders of magnitude slower than `KDEUnivariate`. Kernel regression ----------------- Kernel regression (as provided by `KernelReg`) is based on the same product kernel approach as `KDEMultivariate`, and therefore has the same set of features (mixed data, cross-validated bandwidth estimation, kernels) as described above for `KDEMultivariate`. Censored regression is provided by `KernelCensoredReg`. Note that code for semi-parametric partial linear models and single index models, based on `KernelReg`, can be found in the sandbox. References ---------- * B.W. Silverman, "Density Estimation for Statistics and Data Analysis" * J.S. Racine, "Nonparametric Econometrics: A Primer," Foundation and Trends in Econometrics, Vol. 3, No. 1, pp. 1-88, 2008. * Q. Li and J.S. Racine, "Nonparametric econometrics: theory and practice", Princeton University Press, 2006. * Hastie, Tibshirani and Friedman, "The Elements of Statistical Learning: Data Mining, Inference, and Prediction", Springer, 2009. * Racine, J., Li, Q. "Nonparametric Estimation of Distributions with Categorical and Continuous Data." Working Paper. (2000) * Racine, J. Li, Q. "Kernel Estimation of Multivariate Conditional Distributions Annals of Economics and Finance 5, 211-235 (2004) * Liu, R., Yang, L. "Kernel estimation of multivariate cumulative distribution function." Journal of Nonparametric Statistics (2008) * Li, R., Ju, G. "Nonparametric Estimation of Multivariate CDF with Categorical and Continuous Data." Working Paper * Li, Q., Racine, J. "Cross-validated local linear nonparametric regression" Statistica Sinica 14(2004), pp. 485-512 * Racine, J.: "Consistent Significance Testing for Nonparametric Regression" Journal of Business & Economics Statistics * Racine, J., Hart, J., Li, Q., "Testing the Significance of Categorical Predictor Variables in Nonparametric Regression Models", 2006, Econometric Reviews 25, 523-544 Module Reference ---------------- .. module:: statsmodels.nonparametric :synopsis: Nonparametric estimation of densities and curves The public functions and classes are .. currentmodule:: statsmodels.nonparametric.smoothers_lowess .. autosummary:: :toctree: generated/ lowess .. currentmodule:: statsmodels.nonparametric.kde .. autosummary:: :toctree: generated/ KDEUnivariate .. currentmodule:: statsmodels.nonparametric.kernel_density .. autosummary:: :toctree: generated/ KDEMultivariate KDEMultivariateConditional EstimatorSettings .. currentmodule:: statsmodels.nonparametric.kernel_regression .. autosummary:: :toctree: generated/ KernelReg KernelCensoredReg helper functions for kernel bandwidths .. currentmodule:: statsmodels.nonparametric.bandwidths .. autosummary:: :toctree: generated/ bw_scott bw_silverman select_bandwidth There are some examples for nonlinear functions in :mod:`statsmodels.nonparametric.dgp_examples` The sandbox.nonparametric contains additional insufficiently tested classes for testing functional form and for semi-linear and single index models. statsmodels-0.12.2/docs/source/optimization.rst000066400000000000000000000150701400612667500216600ustar00rootroot00000000000000.. module:: statsmodels.base.optimizer .. currentmodule:: statsmodels.base.optimizer Optimization ============ statsmodels uses three types of algorithms for the estimation of the parameters of a model. 1. Basic linear models such as :ref:`WLS and OLS ` are directly estimated using appropriate linear algebra. 2. :ref:`RLM ` and :ref:`GLM `, use iteratively re-weighted least squares. However, you can optionally select one of the scipy optimizers discussed below. 3. For all other models, we use `optimizers `_ from `scipy `_. Where practical, certain models allow for the optional selection of a scipy optimizer. A particular scipy optimizer might be default or an option. Depending on the model and the data, choosing an appropriate scipy optimizer enables avoidance of a local minima, fitting models in less time, or fitting a model with less memory. statsmodels supports the following optimizers along with keyword arguments associated with that specific optimizer: - ``newton`` - Newton-Raphson iteration. While not directly from scipy, we consider it an optimizer because only the score and hessian are required. tol : float Relative error in params acceptable for convergence. - ``nm`` - scipy's ``fmin_nm`` xtol : float Relative error in params acceptable for convergence ftol : float Relative error in loglike(params) acceptable for convergence maxfun : int Maximum number of function evaluations to make. - ``bfgs`` - Broyden–Fletcher–Goldfarb–Shanno optimization, scipy's ``fmin_bfgs``. gtol : float Stop when norm of gradient is less than gtol. norm : float Order of norm (np.Inf is max, -np.Inf is min) epsilon If fprime is approximated, use this value for the step size. Only relevant if LikelihoodModel.score is None. - ``lbfgs`` - A more memory-efficient (limited memory) implementation of ``bfgs``. Scipy's ``fmin_l_bfgs_b``. m : int The maximum number of variable metric corrections used to define the limited memory matrix. (The limited memory BFGS method does not store the full hessian but uses this many terms in an approximation to it.) pgtol : float The iteration will stop when ``max{|proj g_i | i = 1, ..., n} <= pgtol`` where pg_i is the i-th component of the projected gradient. factr : float The iteration stops when ``(f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr * eps``, where eps is the machine precision, which is automatically generated by the code. Typical values for factr are: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy. See Notes for relationship to ftol, which is exposed (instead of factr) by the scipy.optimize.minimize interface to L-BFGS-B. maxfun : int Maximum number of iterations. epsilon : float Step size used when approx_grad is True, for numerically calculating the gradient approx_grad : bool Whether to approximate the gradient numerically (in which case func returns only the function value). - ``cg`` - Conjugate gradient optimization. Scipy's ``fmin_cg``. gtol : float Stop when norm of gradient is less than gtol. norm : float Order of norm (np.Inf is max, -np.Inf is min) epsilon : float If fprime is approximated, use this value for the step size. Can be scalar or vector. Only relevant if Likelihoodmodel.score is None. - ``ncg`` - Newton conjugate gradient. Scipy's ``fmin_ncg``. fhess_p : callable f'(x, \*args) Function which computes the Hessian of f times an arbitrary vector, p. Should only be supplied if LikelihoodModel.hessian is None. avextol : float Stop when the average relative error in the minimizer falls below this amount. epsilon : float or ndarray If fhess is approximated, use this value for the step size. Only relevant if Likelihoodmodel.hessian is None. - ``powell`` - Powell's method. Scipy's ``fmin_powell``. xtol : float Line-search error tolerance ftol : float Relative error in loglike(params) for acceptable for convergence. maxfun : int Maximum number of function evaluations to make. start_direc : ndarray Initial direction set. - ``basinhopping`` - Basin hopping. This is part of scipy's ``basinhopping`` tools. niter : integer The number of basin hopping iterations. niter_success : integer Stop the run if the global minimum candidate remains the same for this number of iterations. T : float The "temperature" parameter for the accept or reject criterion. Higher "temperatures" mean that larger jumps in function value will be accepted. For best results `T` should be comparable to the separation (in function value) between local minima. stepsize : float Initial step size for use in the random displacement. interval : integer The interval for how often to update the `stepsize`. minimizer : dict Extra keyword arguments to be passed to the minimizer `scipy.optimize.minimize()`, for example 'method' - the minimization method (e.g. 'L-BFGS-B'), or 'tol' - the tolerance for termination. Other arguments are mapped from explicit argument of `fit`: - `args` <- `fargs` - `jac` <- `score` - `hess` <- `hess` - ``minimize`` - Allows the use of any scipy optimizer. min_method : str, optional Name of minimization method to use. Any method specific arguments can be passed directly. For a list of methods and their arguments, see documentation of `scipy.optimize.minimize`. If no method is specified, then BFGS is used. Model Class ----------- Generally, there is no need for an end-user to directly call these functions and classes. However, we provide the class because the different optimization techniques have unique keyword arguments that may be useful to the user. .. autosummary:: :toctree: generated/ Optimizer _fit_newton _fit_bfgs _fit_lbfgs _fit_nm _fit_cg _fit_ncg _fit_powell _fit_basinhopping statsmodels-0.12.2/docs/source/pitfalls.rst000066400000000000000000000076501400612667500207550ustar00rootroot00000000000000Pitfalls ======== This page lists issues which may arise while using statsmodels. These can be the result of data-related or statistical problems, software design, "non-standard" use of models, or edge cases. statsmodels provides several warnings and helper functions for diagnostic checking (see this `blog article `_ for an example of misspecification checks in linear regression). The coverage is of course not comprehensive, but more warnings and diagnostic functions will be added over time. While the underlying statistical problems are the same for all statistical packages, software implementations differ in the way extreme or corner cases are handled. Please report corner cases for which the models might not work, so we can treat them appropriately. Repeated calls to fit with different parameters ----------------------------------------------- Result instances often need to access attributes from the corresponding model instance. Fitting a model multiple times with different arguments can change model attributes. This means that the result instance may no longer point to the correct model attributes after the model has been re-fit. It is therefore best practice to create separate model instances when we want to fit a model using different fit function arguments. For example, this works without problem because we are not keeping the results instance for further use :: mod = AR(endog) aic = [] for lag in range(1,11): res = mod.fit(maxlag=lag) aic.append(res.aic) However, when we want to hold on to two different estimation results, then it is recommended to create two separate model instances. :: mod1 = RLM(endog, exog) res1 = mod1.fit(scale_est='mad') mod2 = RLM(endog, exog) res2 = mod2.fit(scale_est=sm.robust.scale.HuberScale()) Unidentified Parameters ----------------------- Rank deficient exog, perfect multicollinearity ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Models based on linear models, GLS, RLM, GLM and similar, use a generalized inverse. This means that: + Rank deficient matrices will not raise an error + Cases of almost perfect multicollinearity or ill-conditioned design matrices might produce numerically unstable results. Users need to manually check the rank or condition number of the matrix if this is not the desired behavior Note: statsmodels currently fails on the NIST benchmark case for Filip if the data is not rescaled, see `this blog `_ Incomplete convergence in maximum likelihood estimation ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In some cases, the maximum likelihood estimator might not exist, parameters might be infinite or not unique (e.g. (quasi-)separation in models with binary endogenous variable). Under the default settings, statsmodels will print a warning if the optimization algorithm stops without reaching convergence. However, it is important to know that the convergence criteria may sometimes falsely indicate convergence (e.g. if the value of the objective function converged but not the parameters). In general, a user needs to verify convergence. For binary Logit and Probit models, statsmodels raises an exception if perfect prediction is detected. There is, however, no check for quasi-perfect prediction. Other Problems -------------- Insufficient variation in the data ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It is possible that there is insufficient variation in the data for small datasets or for data with small groups in categorical variables. In these cases, the results might not be identified or some hidden problems might occur. The only currently known case is a perfect fit in robust linear model estimation. For RLM, if residuals are equal to zero, then it does not cause an exception, but having this perfect fit can produce NaNs in some results (scale=0 and 0/0 division) (issue #55). statsmodels-0.12.2/docs/source/plots/000077500000000000000000000000001400612667500175365ustar00rootroot00000000000000statsmodels-0.12.2/docs/source/plots/arma_predict_plot.py000066400000000000000000000007521400612667500236040ustar00rootroot00000000000000import matplotlib.pyplot as plt import pandas as pd import warnings import statsmodels.api as sm dta = sm.datasets.sunspots.load_pandas().data[['SUNACTIVITY']] dta.index = pd.date_range(start='1700', end='2009', freq='A') with warnings.catch_warnings(): warnings.simplefilter("ignore") res = sm.tsa.ARMA(dta, (3, 0)).fit(disp=0) fig, ax = plt.subplots() ax = dta.loc['1950':].plot(ax=ax) res.plot_predict('1990', '2012', dynamic=True, ax=ax, plot_insample=False) statsmodels-0.12.2/docs/source/plots/bkf_plot.py000066400000000000000000000003361400612667500217120ustar00rootroot00000000000000import matplotlib.pyplot as plt from load_macrodata import dta import statsmodels.api as sm cycles = sm.tsa.filters.bkfilter(dta[['realinv']], 6, 24, 12) fig, ax = plt.subplots() cycles.plot(ax=ax, style=['r--', 'b-']) statsmodels-0.12.2/docs/source/plots/cff_plot.py000066400000000000000000000003511400612667500217030ustar00rootroot00000000000000import matplotlib.pyplot as plt from load_macrodata import dta import statsmodels.api as sm cf_cycles, cf_trend = sm.tsa.filters.cffilter(dta[["infl", "unemp"]]) fig, ax = plt.subplots() cf_cycles.plot(ax=ax, style=['r--', 'b-']) statsmodels-0.12.2/docs/source/plots/graphics-mean_diff_plot.py000066400000000000000000000006411400612667500246550ustar00rootroot00000000000000# -*- coding: utf-8 -*- # Test Bland-Altman """ Author: Joses Ho """ import matplotlib.pyplot as plt import numpy as np import statsmodels.api as sm # Seed the random number generator. # This ensures that the results below are reproducible. np.random.seed(9999) m1 = np.random.random(20) m2 = np.random.random(20) f, ax = plt.subplots(1, figsize = (8,5)) sm.graphics.mean_diff_plot(m1, m2, ax = ax) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_boxplot_beanplot.py000066400000000000000000000016211400612667500253430ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri May 04 00:22:40 2012 Author: Ralf Gommers """ import matplotlib.pyplot as plt import numpy as np import statsmodels.api as sm data = sm.datasets.anes96.load_pandas() party_ID = np.arange(7) labels = ["Strong Democrat", "Weak Democrat", "Independent-Democrat", "Independent-Indpendent", "Independent-Republican", "Weak Republican", "Strong Republican"] plt.rcParams['figure.subplot.bottom'] = 0.23 # keep labels visible age = [data.exog['age'][data.endog == id] for id in party_ID] fig = plt.figure() ax = fig.add_subplot(111) sm.graphics.beanplot(age, ax=ax, labels=labels, plot_opts={'cutoff_val':5, 'cutoff_type':'abs', 'label_fontsize':'small', 'label_rotation':30}) ax.set_xlabel("Party identification of respondent.") ax.set_ylabel("Age") #plt.show() statsmodels-0.12.2/docs/source/plots/graphics_boxplot_violinplot.py000066400000000000000000000016271400612667500257440ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri May 04 00:11:32 2012 Author: Ralf Gommers """ import matplotlib.pyplot as plt import numpy as np import statsmodels.api as sm data = sm.datasets.anes96.load_pandas() party_ID = np.arange(7) labels = ["Strong Democrat", "Weak Democrat", "Independent-Democrat", "Independent-Indpendent", "Independent-Republican", "Weak Republican", "Strong Republican"] plt.rcParams['figure.subplot.bottom'] = 0.23 # keep labels visible age = [data.exog['age'][data.endog == id] for id in party_ID] fig = plt.figure() ax = fig.add_subplot(111) sm.graphics.violinplot(age, ax=ax, labels=labels, plot_opts={'cutoff_val':5, 'cutoff_type':'abs', 'label_fontsize':'small', 'label_rotation':30}) ax.set_xlabel("Party identification of respondent.") ax.set_ylabel("Age") #plt.show() statsmodels-0.12.2/docs/source/plots/graphics_correlation_plot_corr.py000066400000000000000000000005541400612667500264000ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Create a plot of correlation among many variables in a grid """ import matplotlib.pyplot as plt import numpy as np import statsmodels.api as sm import statsmodels.graphics.api as smg hie_data = sm.datasets.randhie.load_pandas() corr_matrix = np.corrcoef(hie_data.data.T) smg.plot_corr(corr_matrix, xnames=hie_data.names) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_correlation_plot_corr_grid.py000066400000000000000000000010761400612667500274050ustar00rootroot00000000000000# -*- coding: utf-8 -*- ''' In this example we just reuse the same correlation matrix several times. Of course in reality one would show a different correlation (measuring a another type of correlation, for example Pearson (linear) and Spearman, Kendall (nonlinear) correlations) for the same variables. ''' import matplotlib.pyplot as plt import numpy as np import statsmodels.api as sm hie_data = sm.datasets.randhie.load_pandas() corr_matrix = np.corrcoef(hie_data.data.T) sm.graphics.plot_corr_grid([corr_matrix] * 8, xnames=hie_data.names) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_functional_fboxplot.py000066400000000000000000000017511400612667500260530ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri May 04 11:10:51 2012 Author: Ralf Gommers """ #Load the El Nino dataset. Consists of 60 years worth of Pacific Ocean sea #surface temperature data. import matplotlib.pyplot as plt import numpy as np import statsmodels.api as sm data = sm.datasets.elnino.load(as_pandas=False) #Create a functional boxplot. We see that the years 1982-83 and 1997-98 are #outliers; these are the years where El Nino (a climate pattern #characterized by warming up of the sea surface and higher air pressures) #occurred with unusual intensity. fig = plt.figure() ax = fig.add_subplot(111) res = sm.graphics.fboxplot(data.raw_data[:, 1:], wfactor=2.58, labels=data.raw_data[:, 0].astype(int), ax=ax) ax.set_xlabel("Month of the year") ax.set_ylabel("Sea surface temperature (C)") ax.set_xticks(np.arange(13, step=3) - 1) ax.set_xticklabels(["", "Mar", "Jun", "Sep", "Dec"]) ax.set_xlim([-0.2, 11.2]) #plt.show() statsmodels-0.12.2/docs/source/plots/graphics_functional_hdrboxplot.py000066400000000000000000000017151400612667500264030ustar00rootroot00000000000000# coding: utf-8 #Load the El Nino dataset. Consists of 60 years worth of Pacific Ocean sea #surface temperature data. import matplotlib.pyplot as plt import numpy as np import statsmodels.api as sm data = sm.datasets.elnino.load(as_pandas=False) #Create a HDR functional boxplot. We see that the years 1982-83 and 1997-98 are #outliers; these are the years where El Nino (a climate pattern #characterized by warming up of the sea surface and higher air pressures) #occurred with unusual intensity. fig = plt.figure() ax = fig.add_subplot(111) fig, res = sm.graphics.hdrboxplot(data.raw_data[:, 1:], labels=data.raw_data[:, 0].astype(int), ax=ax) ax.plot([0, 10], [25, 25]) ax.set_xlabel("Month of the year") ax.set_ylabel("Sea surface temperature (C)") ax.set_xticks(np.arange(13, step=3) - 1) ax.set_xticklabels(["", "Mar", "Jun", "Sep", "Dec"]) ax.set_xlim([-0.2, 11.2]) plt.show() print(res) statsmodels-0.12.2/docs/source/plots/graphics_functional_rainbowplot.py000066400000000000000000000012371400612667500265550ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri May 04 11:08:56 2012 Author: Ralf Gommers """ #Load the El Nino dataset. Consists of 60 years worth of Pacific Ocean sea #surface temperature data. import matplotlib.pyplot as plt import numpy as np import statsmodels.api as sm data = sm.datasets.elnino.load(as_pandas=False) #Create a rainbow plot: fig = plt.figure() ax = fig.add_subplot(111) res = sm.graphics.rainbowplot(data.raw_data[:, 1:], ax=ax) ax.set_xlabel("Month of the year") ax.set_ylabel("Sea surface temperature (C)") ax.set_xticks(np.arange(13, step=3) - 1) ax.set_xticklabels(["", "Mar", "Jun", "Sep", "Dec"]) ax.set_xlim([-0.2, 11.2]) #plt.show() statsmodels-0.12.2/docs/source/plots/graphics_gofplots_qqplot.py000066400000000000000000000036071400612667500252330ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun May 06 05:32:15 2012 Author: Josef Perktold editted by: Paul Hobson (2012-08-19) """ # example with the new ProbPlot class from matplotlib import pyplot as plt import numpy as np from scipy import stats import statsmodels.api as sm #example from docstring data = sm.datasets.longley.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=True) mod_fit = sm.OLS(data.endog, data.exog).fit() res = mod_fit.resid left = -1.8 #x coordinate for text insert fig = plt.figure() ax = fig.add_subplot(2, 2, 1) sm.graphics.qqplot(res, ax=ax) top = ax.get_ylim()[1] * 0.75 txt = ax.text(left, top, 'no keywords', verticalalignment='top') txt.set_bbox(dict(facecolor='k', alpha=0.1)) ax = fig.add_subplot(2, 2, 2) sm.graphics.qqplot(res, line='s', ax=ax) top = ax.get_ylim()[1] * 0.75 txt = ax.text(left, top, "line='s'", verticalalignment='top') txt.set_bbox(dict(facecolor='k', alpha=0.1)) ax = fig.add_subplot(2, 2, 3) sm.graphics.qqplot(res, line='45', fit=True, ax=ax) ax.set_xlim(-2, 2) top = ax.get_ylim()[1] * 0.75 txt = ax.text(left, top, "line='45', \nfit=True", verticalalignment='top') txt.set_bbox(dict(facecolor='k', alpha=0.1)) ax = fig.add_subplot(2, 2, 4) sm.graphics.qqplot(res, dist=stats.t, line='45', fit=True, ax=ax) ax.set_xlim(-2, 2) top = ax.get_ylim()[1] * 0.75 txt = ax.text(left, top, "dist=stats.t, \nline='45', \nfit=True", verticalalignment='top') txt.set_bbox(dict(facecolor='k', alpha=0.1)) fig.tight_layout() plt.gcf() x = np.random.normal(loc=8.25, scale=3.5, size=37) y = np.random.normal(loc=8.00, scale=3.25, size=37) pp_x = sm.ProbPlot(x, fit=True) pp_y = sm.ProbPlot(y, fit=True) # probability of exceedance fig2 = pp_x.probplot(exceed=True) # compare x quantiles to y quantiles fig3 = pp_x.qqplot(other=pp_y, line='45') # same as above with probabilities/percentiles fig4 = pp_x.ppplot(other=pp_y, line='45') statsmodels-0.12.2/docs/source/plots/graphics_gofplots_qqplot_2samples.py000066400000000000000000000006241400612667500270350ustar00rootroot00000000000000''' Create Q-Q Plot of two samples quanitiles of randomnly generated data. ''' import matplotlib.pyplot as plt import numpy as np import statsmodels.api as sm from statsmodels.graphics.gofplots import qqplot_2samples x = np.random.normal(loc=8.5, scale=2.5, size=37) y = np.random.normal(loc=8.0, scale=3.0, size=37) pp_x = sm.ProbPlot(x) pp_y = sm.ProbPlot(y) qqplot_2samples(pp_x, pp_y) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_gofplots_qqplot_qqline.py000066400000000000000000000010071400612667500265740ustar00rootroot00000000000000''' Import the food expenditure dataset. Plot annual food expenditure on x-axis and household income on y-axis. Use qqline to add regression line into the plot. ''' import matplotlib.pyplot as plt import statsmodels.api as sm from statsmodels.graphics.gofplots import qqline foodexp = sm.datasets.engel.load(as_pandas=False) x = foodexp.exog y = foodexp.endog ax = plt.subplot(111) plt.scatter(x, y) ax.set_xlabel(foodexp.exog_name[0]) ax.set_ylabel(foodexp.endog_name) qqline(ax, 'r', x, y) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_mosaicplot_mosaic.py000066400000000000000000000036271400612667500255050ustar00rootroot00000000000000# -*- coding: utf-8 -*- from itertools import product import matplotlib.pyplot as plt import numpy as np import pandas as pd from statsmodels.graphics.mosaicplot import mosaic # The most simple use case is to take a dictionary and plot the result data = {'a': 10, 'b': 15, 'c': 16} mosaic(data, title='basic dictionary') plt.show() # A more useful example is given by a dictionary with multiple indices. In # this case we use a wider gap to a better visual separation of the resulting # plot data = {('a', 'b'): 1, ('a', 'c'): 2, ('d', 'b'): 3, ('d', 'c'): 4} mosaic(data, gap=0.05, title='complete dictionary') plt.show() # The same data can be given as a simple or hierarchical indexed Series rand = np.random.random tuples = list(product(['bar', 'baz', 'foo', 'qux'], ['one', 'two'])) index = pd.MultiIndex.from_tuples(tuples, names=['first', 'second']) data = pd.Series(rand(8), index=index) mosaic(data, title='hierarchical index series') plt.show() # The third accepted data structure is the np array, for which a very simple # index will be created. rand = np.random.random data = 1+rand((2, 2)) mosaic(data, title='random non-labeled array') plt.show() # If you need to modify the labeling and the coloring you can give a function # to create the labels and one with the graphical properties starting from the # key tuple def props(key): return {'color': 'r' if 'a' in key else 'gray'} def labelizer(key): return {('a',): 'first', ('b',): 'second', ('c',): 'third'}[key] data = {'a': 10, 'b': 15, 'c': 16} mosaic(data, title='colored dictionary', properties=props, labelizer=labelizer) plt.show() # Using a DataFrame as source, specifying the name of the columns of interest gender = ['male', 'male', 'male', 'female', 'female', 'female'] pet = ['cat', 'dog', 'dog', 'cat', 'dog', 'cat'] data = pd.DataFrame({'gender': gender, 'pet': pet}) mosaic(data, ['pet', 'gender'], title='DataFrame as Source') plt.show() statsmodels-0.12.2/docs/source/plots/graphics_plot_fit_ex.py000066400000000000000000000013331400612667500243040ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Monday April 1st 2013 Author: Padarn Wilson """ # Load the Statewide Crime data set and perform linear regression with # 'poverty' and 'hs_grad' as variables and 'murder' as the response import matplotlib.pyplot as plt import numpy as np import statsmodels.api as sm data = sm.datasets.statecrime.load_pandas().data murder = data['murder'] X = data[['poverty', 'hs_grad']].copy() X['constant'] = 1 y = murder model = sm.OLS(y, X) results = model.fit() # Create a plot just for the variable 'Poverty': fig, ax = plt.subplots() fig = sm.graphics.plot_fit(results, 0, ax=ax) ax.set_ylabel("Murder Rate") ax.set_xlabel("Poverty Level") ax.set_title("Linear Regression") plt.show() statsmodels-0.12.2/docs/source/plots/graphics_plot_grids_scatter_ellipse.py000066400000000000000000000006041400612667500274000ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Create of grid of scatter plots with confidence ellipses from the statecrime dataset """ import matplotlib.pyplot as plt import statsmodels.api as sm from statsmodels.graphics.plot_grids import scatter_ellipse data = sm.datasets.statecrime.load_pandas().data fig = plt.figure(figsize=(8, 8)) scatter_ellipse(data, varnames=data.columns, fig=fig) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_regression_abline.py000066400000000000000000000010761400612667500254660ustar00rootroot00000000000000# -*- coding: utf-8 -*- ''' Using the state crime dataset separately plot the effect of the each variable on the on the outcome, murder rate while accounting for the effect of all other variables in the model. ''' import matplotlib.pyplot as plt import numpy as np import statsmodels.api as sm np.random.seed(12345) X = sm.add_constant(np.random.normal(0, 20, size=30)) y = np.dot(X, [25, 3.5]) + np.random.normal(0, 30, size=30) mod = sm.OLS(y, X).fit() fig = sm.graphics.abline_plot(model_results=mod) ax = fig.axes[0] ax.scatter(X[:, 1], y) ax.margins(.1) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_regression_ccpr.py000066400000000000000000000011171400612667500251570ustar00rootroot00000000000000# -*- coding: utf-8 -*- ''' Using the state crime dataset plot the effect of the rate of single households ('single') on the murder rate while accounting for high school graduation rate ('hs_grad'), percentage of people in an urban area, and rate of poverty ('poverty'). ''' import matplotlib.pyplot as plt import statsmodels.api as sm import statsmodels.formula.api as smf crime_data = sm.datasets.statecrime.load_pandas() results = smf.ols('murder ~ hs_grad + urban + poverty + single', data=crime_data.data).fit() sm.graphics.plot_ccpr(results, 'single') plt.show() statsmodels-0.12.2/docs/source/plots/graphics_regression_ccpr_grid.py000066400000000000000000000010671400612667500261700ustar00rootroot00000000000000# -*- coding: utf-8 -*- ''' Using the state crime dataset separately plot the effect of the each variable on the on the outcome, murder rate while accounting for the effect of all other variables in the model. ''' import matplotlib.pyplot as plt import statsmodels.api as sm import statsmodels.formula.api as smf fig = plt.figure(figsize=(8, 8)) crime_data = sm.datasets.statecrime.load_pandas() results = smf.ols('murder ~ hs_grad + urban + poverty + single', data=crime_data.data).fit() sm.graphics.plot_ccpr_grid(results, fig=fig) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_regression_ceres_residuals.py000066400000000000000000000010401400612667500273770ustar00rootroot00000000000000# -*- coding: utf-8 -*- ''' Using a model built from the the state crime dataset, make a CERES plot with the rate of Poverty as the focus variable. ''' import matplotlib.pyplot as plt import statsmodels.api as sm import statsmodels.formula.api as smf from statsmodels.graphics.regressionplots import plot_ceres_residuals crime_data = sm.datasets.statecrime.load_pandas() results = smf.ols('murder ~ hs_grad + urban + poverty + single', data=crime_data.data).fit() plot_ceres_residuals(results, 'poverty') plt.show() statsmodels-0.12.2/docs/source/plots/graphics_regression_influence.py000066400000000000000000000010561400612667500262020ustar00rootroot00000000000000# -*- coding: utf-8 -*- ''' Using a model built from the the state crime dataset, plot the influence in regression. Observations with high leverage, or large residuals will be labeled in the plot to show potential influence points. ''' import matplotlib.pyplot as plt import statsmodels.api as sm import statsmodels.formula.api as smf crime_data = sm.datasets.statecrime.load_pandas() results = smf.ols('murder ~ hs_grad + urban + poverty + single', data=crime_data.data).fit() sm.graphics.influence_plot(results) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_regression_leverage_resid2.py000066400000000000000000000010521400612667500272700ustar00rootroot00000000000000# -*- coding: utf-8 -*- ''' Using a model built from the the state crime dataset, plot the leverage statistics vs. normalized residuals squared. Observations with Large-standardized Residuals will be labeled in the plot. ''' import matplotlib.pyplot as plt import statsmodels.api as sm import statsmodels.formula.api as smf crime_data = sm.datasets.statecrime.load_pandas() results = smf.ols('murder ~ hs_grad + urban + poverty + single', data=crime_data.data).fit() sm.graphics.plot_leverage_resid2(results) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_regression_partregress.py000066400000000000000000000010461400612667500265720ustar00rootroot00000000000000# -*- coding: utf-8 -*- ''' Load the statewide dataset and plot partial regression of high school graduation on murder rate after removing the effects of rate of urbanization, poverty, and rate of single household. ''' import matplotlib.pyplot as plt import statsmodels.api as sm crime_data = sm.datasets.statecrime.load_pandas() sm.graphics.plot_partregress(endog='murder', exog_i='hs_grad', exog_others=['urban', 'poverty', 'single'], data=crime_data.data, obs_labels=False) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_regression_partregress_grid.py000066400000000000000000000012541400612667500276000ustar00rootroot00000000000000# -*- coding: utf-8 -*- ''' Using the state crime dataset separately plot the effect of the each variable on the on the outcome, murder rate while accounting for the effect of all other variables in the model visualized with a grid of partial regression plots. ''' import matplotlib.pyplot as plt import statsmodels.api as sm import statsmodels.formula.api as smf from statsmodels.graphics.regressionplots import plot_partregress_grid fig = plt.figure(figsize=(8, 6)) crime_data = sm.datasets.statecrime.load_pandas() results = smf.ols('murder ~ hs_grad + urban + poverty + single', data=crime_data.data).fit() plot_partregress_grid(results, fig=fig) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_regression_regress_exog.py000066400000000000000000000015461400612667500267320ustar00rootroot00000000000000# -*- coding: utf-8 -*- ''' Load the Statewide Crime data set and build a model with regressors including the rate of high school graduation (hs_grad), population in urban areas (urban), households below poverty line (poverty), and single person households (single). Outcome variable is the murder rate (murder). Build a 2 by 2 figure based on poverty showing fitted versus actual murder rate, residuals versus the poverty rate, partial regression plot of poverty, and CCPR plot for poverty rate. ''' import matplotlib.pyplot as plt import statsmodels.api as sm import statsmodels.formula.api as smf fig = plt.figure(figsize=(8, 6)) crime_data = sm.datasets.statecrime.load_pandas() results = smf.ols('murder ~ hs_grad + urban + poverty + single', data=crime_data.data).fit() sm.graphics.plot_regress_exog(results, 'poverty', fig=fig) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_tsa_month_plot.py000066400000000000000000000006261400612667500250260ustar00rootroot00000000000000import pandas as pd import statsmodels.api as sm dta = sm.datasets.elnino.load_pandas().data dta['YEAR'] = dta.YEAR.astype(int).astype(str) dta = dta.set_index('YEAR').T.unstack() dates = pd.to_datetime(list(map(lambda x: '-'.join(x) + '-1', dta.index.values))) dta.index = pd.DatetimeIndex(list(dates), freq='MS') dta.name = 'temp' fig = sm.graphics.tsa.month_plot(dta) statsmodels-0.12.2/docs/source/plots/graphics_tsa_plot_acf.py000066400000000000000000000006311400612667500244260ustar00rootroot00000000000000# -*- coding: utf-8 -*- ''' Load Sunspots Data and plot the autocorrelation of the number of sunspots per year. ''' import matplotlib.pyplot as plt import pandas as pd import statsmodels.api as sm dta = sm.datasets.sunspots.load_pandas().data dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008')) del dta["YEAR"] sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_tsa_plot_pacf.py000066400000000000000000000006421400612667500246100ustar00rootroot00000000000000# -*- coding: utf-8 -*- ''' Load Sunspots Data and plot the partial autocorrelation of the number of sunspots per year. ''' import matplotlib.pyplot as plt import pandas as pd import statsmodels.api as sm dta = sm.datasets.sunspots.load_pandas().data dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008')) del dta["YEAR"] sm.graphics.tsa.plot_pacf(dta.values.squeeze(), lags=40) plt.show() statsmodels-0.12.2/docs/source/plots/graphics_tsa_quarter_plot.py000066400000000000000000000006041400612667500253600ustar00rootroot00000000000000import pandas as pd import statsmodels.api as sm dta = sm.datasets.elnino.load_pandas().data dta['YEAR'] = dta.YEAR.astype(int).astype(str) dta = dta.set_index('YEAR').T.unstack() dates = pd.to_datetime(list(map(lambda x: '-'.join(x) + '-1', dta.index.values))) dta.index = dates.to_period('Q') dta.name = 'temp' fig = sm.graphics.tsa.quarter_plot(dta) statsmodels-0.12.2/docs/source/plots/hpf_plot.py000066400000000000000000000006411400612667500217240ustar00rootroot00000000000000import matplotlib.pyplot as plt import pandas as pd from load_macrodata import dta import statsmodels.api as sm cycle, trend = sm.tsa.filters.hpfilter(dta.realgdp, 1600) gdp_decomp = dta[['realgdp']].copy() gdp_decomp["cycle"] = cycle gdp_decomp["trend"] = trend fig, ax = plt.subplots() gdp_decomp[["realgdp", "trend"]]["2000-03-31":].plot(ax=ax, fontsize=16) statsmodels-0.12.2/docs/source/plots/load_macrodata.py000066400000000000000000000003431400612667500230420ustar00rootroot00000000000000import pandas as pd import statsmodels.api as sm dta = sm.datasets.macrodata.load_pandas().data dates = sm.tsa.datetools.dates_from_range('1959Q1', '2009Q3') index = pd.DatetimeIndex(dates) dta.set_index(index, inplace=True) statsmodels-0.12.2/docs/source/plots/mice_example_1.txt000066400000000000000000000015751400612667500231570ustar00rootroot00000000000000 Results: MICE ================================================================= Method: MICE Sample size: 1000 Model: OLS Scale 1.00 Dependent variable: y Num. imputations 10 ----------------------------------------------------------------- Coef. Std.Err. t P>|t| [0.025 0.975] FMI ----------------------------------------------------------------- Intercept -0.0234 0.0318 -0.7345 0.4626 -0.0858 0.0390 0.0128 x1 1.0305 0.0578 17.8342 0.0000 0.9172 1.1437 0.0309 x2 -0.0134 0.0162 -0.8282 0.4076 -0.0451 0.0183 0.0236 x3 -1.0260 0.0328 -31.2706 0.0000 -1.0903 -0.9617 0.0169 x4 -0.0253 0.0336 -0.7520 0.4521 -0.0911 0.0406 0.0269 ================================================================= statsmodels-0.12.2/docs/source/plots/stl_plot.py000066400000000000000000000004751400612667500217560ustar00rootroot00000000000000import matplotlib.pyplot as plt from pandas.plotting import register_matplotlib_converters from statsmodels.datasets import co2 from statsmodels.tsa.seasonal import STL register_matplotlib_converters() data = co2.load(True).data data = data.resample('M').mean().ffill() res = STL(data).fit() res.plot() plt.show() statsmodels-0.12.2/docs/source/plots/var_plot_acorr.py000066400000000000000000000000571400612667500231260ustar00rootroot00000000000000from var_plots import plot_acorr plot_acorr() statsmodels-0.12.2/docs/source/plots/var_plot_fevd.py000066400000000000000000000000551400612667500227420ustar00rootroot00000000000000from var_plots import plot_fevd plot_fevd() statsmodels-0.12.2/docs/source/plots/var_plot_forecast.py000066400000000000000000000000651400612667500236250ustar00rootroot00000000000000from var_plots import plot_forecast plot_forecast() statsmodels-0.12.2/docs/source/plots/var_plot_input.py000066400000000000000000000000571400612667500231570ustar00rootroot00000000000000from var_plots import plot_input plot_input() statsmodels-0.12.2/docs/source/plots/var_plot_irf.py000066400000000000000000000000531400612667500225740ustar00rootroot00000000000000from var_plots import plot_irf plot_irf() statsmodels-0.12.2/docs/source/plots/var_plot_irf_cum.py000066400000000000000000000000631400612667500234410ustar00rootroot00000000000000from var_plots import plot_irf_cum plot_irf_cum() statsmodels-0.12.2/docs/source/plots/var_plots.py000066400000000000000000000015521400612667500221240ustar00rootroot00000000000000import numpy as np import pandas from statsmodels.api import datasets as ds from statsmodels.tsa.api import VAR from statsmodels.tsa.base.datetools import dates_from_str mdata = ds.macrodata.load_pandas().data # prepare the dates index dates = mdata[['year', 'quarter']].astype(int) quarterly = [str(yr) + 'Q' + str(mo) for yr, mo in zip(dates["year"], dates["quarter"])] quarterly = dates_from_str(quarterly) mdata = mdata[['realgdp','realcons','realinv']] mdata.index = pandas.DatetimeIndex(quarterly) data = np.log(mdata).diff().dropna() model = VAR(data) est = model.fit(maxlags=2) def plot_input(): est.plot() def plot_acorr(): est.plot_acorr() def plot_irf(): est.irf().plot() def plot_irf_cum(): irf = est.irf() irf.plot_cum_effects() def plot_forecast(): est.plot_forecast(10) def plot_fevd(): est.fevd(20).plot() statsmodels-0.12.2/docs/source/regression.rst000066400000000000000000000157711400612667500213220ustar00rootroot00000000000000.. currentmodule:: statsmodels.regression.linear_model .. _regression: Linear Regression ================= Linear models with independently and identically distributed errors, and for errors with heteroscedasticity or autocorrelation. This module allows estimation by ordinary least squares (OLS), weighted least squares (WLS), generalized least squares (GLS), and feasible generalized least squares with autocorrelated AR(p) errors. See `Module Reference`_ for commands and arguments. Examples -------- .. ipython:: python # Load modules and data import numpy as np import statsmodels.api as sm spector_data = sm.datasets.spector.load(as_pandas=False) spector_data.exog = sm.add_constant(spector_data.exog, prepend=False) # Fit and summarize OLS model mod = sm.OLS(spector_data.endog, spector_data.exog) res = mod.fit() print(res.summary()) Detailed examples can be found here: * `OLS `__ * `WLS `__ * `GLS `__ * `Recursive LS `__ * `Rolling LS `__ Technical Documentation ----------------------- The statistical model is assumed to be :math:`Y = X\beta + \mu`, where :math:`\mu\sim N\left(0,\Sigma\right).` Depending on the properties of :math:`\Sigma`, we have currently four classes available: * GLS : generalized least squares for arbitrary covariance :math:`\Sigma` * OLS : ordinary least squares for i.i.d. errors :math:`\Sigma=\textbf{I}` * WLS : weighted least squares for heteroskedastic errors :math:`\text{diag}\left (\Sigma\right)` * GLSAR : feasible generalized least squares with autocorrelated AR(p) errors :math:`\Sigma=\Sigma\left(\rho\right)` All regression models define the same methods and follow the same structure, and can be used in a similar fashion. Some of them contain additional model specific methods and attributes. GLS is the superclass of the other regression classes except for RecursiveLS, RollingWLS and RollingOLS. .. Class hierachy: TODO .. yule_walker is not a full model class, but a function that estimate the .. parameters of a univariate autoregressive process, AR(p). It is used in GLSAR, .. but it can also be used independently of any models. yule_walker only .. calculates the estimates and the standard deviation of the lag parameters but .. not the additional regression statistics. We hope to include yule-walker in .. future in a separate univariate time series class. A similar result can be .. obtained with GLSAR if only the constant is included as regressors. In this .. case the parameter estimates of the lag estimates are not reported, however .. additional statistics, for example aic, become available. References ^^^^^^^^^^ General reference for regression models: * D.C. Montgomery and E.A. Peck. "Introduction to Linear Regression Analysis." 2nd. Ed., Wiley, 1992. Econometrics references for regression models: * R.Davidson and J.G. MacKinnon. "Econometric Theory and Methods," Oxford, 2004. * W.Green. "Econometric Analysis," 5th ed., Pearson, 2003. .. toctree:: .. :maxdepth: 1 .. .. regression_techn1 Attributes ^^^^^^^^^^ The following is more verbose description of the attributes which is mostly common to all regression classes pinv_wexog : array The `p` x `n` Moore-Penrose pseudoinverse of the whitened design matrix. It is approximately equal to :math:`\left(X^{T}\Sigma^{-1}X\right)^{-1}X^{T}\Psi`, where :math:`\Psi` is defined such that :math:`\Psi\Psi^{T}=\Sigma^{-1}`. cholsimgainv : array The `n` x `n` upper triangular matrix :math:`\Psi^{T}` that satisfies :math:`\Psi\Psi^{T}=\Sigma^{-1}`. df_model : float The model degrees of freedom. This is equal to `p` - 1, where `p` is the number of regressors. Note that the intercept is not counted as using a degree of freedom here. df_resid : float The residual degrees of freedom. This is equal `n - p` where `n` is the number of observations and `p` is the number of parameters. Note that the intercept is counted as using a degree of freedom here. llf : float The value of the likelihood function of the fitted model. nobs : float The number of observations `n` normalized_cov_params : array A `p` x `p` array equal to :math:`(X^{T}\Sigma^{-1}X)^{-1}`. sigma : array The `n` x `n` covariance matrix of the error terms: :math:`\mu\sim N\left(0,\Sigma\right)`. wexog : array The whitened design matrix :math:`\Psi^{T}X`. wendog : array The whitened response variable :math:`\Psi^{T}Y`. Module Reference ---------------- .. module:: statsmodels.regression.linear_model :synopsis: Least squares linear models Model Classes ^^^^^^^^^^^^^ .. autosummary:: :toctree: generated/ OLS GLS WLS GLSAR yule_walker burg .. module:: statsmodels.regression.quantile_regression :synopsis: Quantile regression .. currentmodule:: statsmodels.regression.quantile_regression .. autosummary:: :toctree: generated/ QuantReg .. module:: statsmodels.regression.recursive_ls :synopsis: Recursive least squares using the Kalman Filter .. currentmodule:: statsmodels.regression.recursive_ls .. autosummary:: :toctree: generated/ RecursiveLS .. module:: statsmodels.regression.rolling :synopsis: Rolling (moving) least squares .. currentmodule:: statsmodels.regression.rolling .. autosummary:: :toctree: generated/ RollingWLS RollingOLS .. module:: statsmodels.regression.process_regression :synopsis: Process regression .. currentmodule:: statsmodels.regression.process_regression .. autosummary:: :toctree: generated/ GaussianCovariance ProcessMLE .. module:: statsmodels.regression.dimred :synopsis: Dimension reduction methods .. currentmodule:: statsmodels.regression.dimred .. autosummary:: :toctree: generated/ SlicedInverseReg PrincipalHessianDirections SlicedAverageVarianceEstimation Results Classes ^^^^^^^^^^^^^^^ Fitting a linear regression model returns a results class. OLS has a specific results class with some additional methods compared to the results class of the other linear models. .. currentmodule:: statsmodels.regression.linear_model .. autosummary:: :toctree: generated/ RegressionResults OLSResults PredictionResults .. currentmodule:: statsmodels.base.elastic_net .. autosummary:: :toctree: generated/ RegularizedResults .. currentmodule:: statsmodels.regression.quantile_regression .. autosummary:: :toctree: generated/ QuantRegResults .. currentmodule:: statsmodels.regression.recursive_ls .. autosummary:: :toctree: generated/ RecursiveLSResults .. currentmodule:: statsmodels.regression.rolling .. autosummary:: :toctree: generated/ RollingRegressionResults .. currentmodule:: statsmodels.regression.process_regression .. autosummary:: :toctree: generated/ ProcessMLEResults .. currentmodule:: statsmodels.regression.dimred .. autosummary:: :toctree: generated/ DimReductionResults statsmodels-0.12.2/docs/source/regression_techn1.rst.TXT000066400000000000000000000002431400612667500232260ustar00rootroot00000000000000.. currentmodule:: statsmodels.regression .. _regression-techn1: Technical Documentation ======================= Introduction ------------ Just a placeholder statsmodels-0.12.2/docs/source/release/000077500000000000000000000000001400612667500200155ustar00rootroot00000000000000statsmodels-0.12.2/docs/source/release/index.rst000066400000000000000000000006071400612667500216610ustar00rootroot00000000000000.. _whatsnew_index: ============= Release Notes ============= .. toctree:: :maxdepth: 1 version0.12.2 version0.12.1 version0.12 version0.11.1 version0.11 version0.10.2 version0.10.1 version0.10 version0.9 version0.8 version0.7 version0.6 version0.5 For an overview of changes that occurred previous to the 0.5.0 release see :ref:`old_changes`. statsmodels-0.12.2/docs/source/release/old_changes.rst000066400000000000000000000153771400612667500230320ustar00rootroot00000000000000:orphan: .. _old_changes: Pre 0.5.0 Release History ========================= 0.5.0 ----- *Main Changes and Additions* * Add patsy dependency *Compatibility and Deprecation* * cleanup of import paths (lowess) * *Bug Fixes* * input shapes of tools.isestimable * *Enhancements and Additions* * formula integration based on patsy (new dependency) * Time series analysis - ARIMA modeling - enhanced forecasting based on pandas datetime handling * expanded margins for discrete models * OLS outlier test * empirical likelihood - Google Summer of Code 2012 project - inference for descriptive statistics - inference for regression models - accelerated failure time models * expanded probability plots * improved graphics - plotcorr - acf and pacf * new datasets * new and improved tools - numdiff numerical differentiation 0.4.3 ----- The only change compared to 0.4.2 is for compatibility with python 3.2.3 (changed behavior of 2to3) 0.4.2 ----- This is a bug-fix release, that affects mainly Big-Endian machines. *Bug Fixes* * discrete_model.MNLogit fix summary method * tsa.filters.hp_filter do not use umfpack on Big-Endian machine (scipy bug) * the remaining fixes are in the test suite, either precision problems on some machines or incorrect testing on Big-Endian machines. 0.4.1 ----- This is a backwards compatible (according to our test suite) release with bug fixes and code cleanup. *Bug Fixes* * build and distribution fixes * lowess correct distance calculation * genmod correction CDFlink derivative * adfuller _autolag correct calculation of optimal lag * het_arch, het_lm : fix autolag and store options * GLSAR: incorrect whitening for lag>1 *Other Changes* * add lowess and other functions to api and documentation * rename lowess module (old import path will be removed at next release) * new robust sandwich covariance estimators, moved out of sandbox * compatibility with pandas 0.8 * new plots in statsmodels.graphics - ABLine plot - interaction plot 0.4.0 ----- *Main Changes and Additions* * Added pandas dependency. * Cython source is built automatically if cython and compiler are present * Support use of dates in timeseries models * Improved plots - Violin plots - Bean Plots - QQ Plots * Added lowess function * Support for pandas Series and DataFrame objects. Results instances return pandas objects if the models are fit using pandas objects. * Full Python 3 compatibility * Fix bugs in genfromdta. Convert Stata .dta format to structured array preserving all types. Conversion is much faster now. * Improved documentation * Models and results are pickleable via save/load, optionally saving the model data. * Kernel Density Estimation now uses Cython and is considerably faster. * Diagnostics for outlier and influence statistics in OLS * Added El Nino Sea Surface Temperatures dataset * Numerous bug fixes * Internal code refactoring * Improved documentation including examples as part of HTML *Changes that break backwards compatibility* * Deprecated scikits namespace. The recommended import is now:: import statsmodels.api as sm * model.predict methods signature is now (params, exog, ...) where before it assumed that the model had been fit and omitted the params argument. * For consistency with other multi-equation models, the parameters of MNLogit are now transposed. * tools.tools.ECDF -> distributions.ECDF * tools.tools.monotone_fn_inverter -> distributions.monotone_fn_inverter * tools.tools.StepFunction -> distributions.StepFunction 0.3.1 ----- * Removed academic-only WFS dataset. * Fix easy_install issue on Windows. 0.3.0 ----- *Changes that break backwards compatibility* Added api.py for importing. So the new convention for importing is:: import statsmodels.api as sm Importing from modules directly now avoids unnecessary imports and increases the import speed if a library or user only needs specific functions. * sandbox/output.py -> iolib/table.py * lib/io.py -> iolib/foreign.py (Now contains Stata .dta format reader) * family -> families * families.links.inverse -> families.links.inverse_power * Datasets' Load class is now load function. * regression.py -> regression/linear_model.py * discretemod.py -> discrete/discrete_model.py * rlm.py -> robust/robust_linear_model.py * glm.py -> genmod/generalized_linear_model.py * model.py -> base/model.py * t() method -> tvalues attribute (t() still exists but raises a warning) *Main changes and additions* * Numerous bugfixes. * Time Series Analysis model (tsa) - Vector Autoregression Models VAR (tsa.VAR) - Autoregressive Models AR (tsa.AR) - Autoregressive Moving Average Models ARMA (tsa.ARMA) optionally uses Cython for Kalman Filtering use setup.py install with option --with-cython - Baxter-King band-pass filter (tsa.filters.bkfilter) - Hodrick-Prescott filter (tsa.filters.hpfilter) - Christiano-Fitzgerald filter (tsa.filters.cffilter) * Improved maximum likelihood framework uses all available scipy.optimize solvers * Refactor of the datasets sub-package. * Added more datasets for examples. * Removed RPy dependency for running the test suite. * Refactored the test suite. * Refactored codebase/directory structure. * Support for offset and exposure in GLM. * Removed data_weights argument to GLM.fit for Binomial models. * New statistical tests, especially diagnostic and specification tests * Multiple test correction * General Method of Moment framework in sandbox * Improved documentation * and other additions 0.2.0 ----- *Main changes* * renames for more consistency RLM.fitted_values -> RLM.fittedvalues GLMResults.resid_dev -> GLMResults.resid_deviance * GLMResults, RegressionResults: lazy calculations, convert attributes to properties with _cache * fix tests to run without rpy * expanded examples in examples directory * add PyDTA to lib.io -- functions for reading Stata .dta binary files and converting them to numpy arrays * made tools.categorical much more robust * add_constant now takes a prepend argument * fix GLS to work with only a one column design *New* * add four new datasets - A dataset from the American National Election Studies (1996) - Grunfeld (1950) investment data - Spector and Mazzeo (1980) program effectiveness data - A US macroeconomic dataset * add four new Maximum Likelihood Estimators for models with a discrete dependent variables with examples - Logit - Probit - MNLogit (multinomial logit) - Poisson *Sandbox* * add qqplot in sandbox.graphics * add sandbox.tsa (time series analysis) and sandbox.regression (anova) * add principal component analysis in sandbox.tools * add Seemingly Unrelated Regression (SUR) and Two-Stage Least Squares for systems of equations in sandbox.sysreg.Sem2SLS * add restricted least squares (RLS) 0.1.0b1 ------- * initial release statsmodels-0.12.2/docs/source/release/version0.10.1.rst000066400000000000000000000030231400612667500226700ustar00rootroot00000000000000:orphan: ============== Release 0.10.1 ============== Release summary =============== This is a bug fix-only release Development summary and credits =============================== Besides receiving contributions for new and improved features and for bugfixes, important contributions to general maintenance for this release came from * Chad Fulton * Brock Mendel * Peter Quackenbush * Kerby Shedden * Kevin Sheppard and the general maintainer and code reviewer * Josef Perktold These lists of names are automatically generated based on git log, and may not be complete. Merged Pull Requests -------------------- The following Pull Requests were merged since the last release: * :pr:`5784`: MAINT: implement parts of #5220, deprecate ancient aliases * :pr:`5892`: BUG: fix pandas compat * :pr:`5893`: BUG: exponential smoothing - damped trend gives incorrect param, predictions * :pr:`5895`: DOC: improvements to BayesMixedGLM docs, argument checking * :pr:`5897`: MAINT: Use pytest.raises to check error message * :pr:`5903`: BUG: Fix kwargs update bug in linear model fit_regularized * :pr:`5917`: BUG: TVTP for Markov regression * :pr:`5921`: BUG: Ensure exponential smoothers has continuous double data * :pr:`5930`: BUG: Limit lags in KPSS * :pr:`5933`: MAINT: Fix test that fails with positive probability * :pr:`5935`: CLN: port parts of #5220 * :pr:`5940`: MAINT: Fix linting failures * :pr:`5944`: BUG: Restore ResettableCache * :pr:`5951`: BUG: Fix mosaic plot with missing category * :pr:`5971`: BUG: Fix a future issue in ExpSmooth statsmodels-0.12.2/docs/source/release/version0.10.2.rst000066400000000000000000000024631400612667500227000ustar00rootroot00000000000000:orphan: ============== Release 0.10.2 ============== Release summary =============== This is a bug release and adds compatibility with Python 3.8. Development summary and credits =============================== Besides receiving contributions for new and improved features and for bugfixes, important contributions to general maintenance for this release came from * Chad Fulton * Qingqing Mao * Diego Mazon * Brock Mendel * Guglielmo Saggiorato * Kevin Sheppard * Tim Staley Merged Pull Requests -------------------- The following Pull Requests were merged since the last release: * :pr:`5935`: CLN: port parts of #5220 * :pr:`5951`: BUG: Fix mosaic plot with missing category * :pr:`5996`: BUG: Limit lags in KPSS * :pr:`5998`: Replace alpha=0.05 with alpha=alpha * :pr:`6030`: Turn relative import into an absolute import * :pr:`6044`: DOC: Fix notebook due to pandas index change * :pr:`6046`: DOC: Remove DynamicVAR * :pr:`6091`: MAINT/SEC: Remove unnecessary pickle use * :pr:`6092`: MAINT: Ensure r download cache works * :pr:`6093`: MAINT: Fix new cache name * :pr:`6117`: BUG: Remove extra LICENSE.txt and setup.cfg * :pr:`6105`: Update correlation_tools.py * :pr:`6050`: BUG: MLEModel now passes nobs to Representation * :pr:`6205`: MAINT: Exclude pytest-xdist 1.30 * :pr:`6246`: TST: Add Python 3.8 environment statsmodels-0.12.2/docs/source/release/version0.10.rst000066400000000000000000001317631400612667500225460ustar00rootroot00000000000000:orphan: ============== Release 0.10.0 ============== Release summary =============== statsmodels is using github to store the updated documentation. Two version are available: * `Stable `_, the latest release * `Development `_, the latest build of the master branch **Warning** API stability is not guaranteed for new features, although even in this case changes will be made in a backwards compatible way if possible. The stability of a new feature depends on how much time it was already in statsmodels master and how much usage it has already seen. If there are specific known problems or limitations, then they are mentioned in the docstrings. Stats ----- **Issues Closed**: 1052 **Pull Requests Merged**: 469 The list of pull requests for this release can be found on `github `_ (The list does not include some pull request that were merged before the 0.9 release but not included in 0.9.) The Highlights ============== Generalized Additive Models --------------------------- :class:`~statsmodels.gam.generalized_additive_model.GLMGam` adds support for Generalized additive models. .. note:: **Status: experimental**. This class has full unit test coverage for the core results with Gaussian and Poisson (without offset and exposure). Other options and additional results might not be correctly supported yet. (Binomial with counts, i.e. with n_trials, is most likely wrong in parts. User specified var or freq weights are most likely also not correct for all results.) :class:`~statsmodels.gam.generalized_additive_model.LogitGam` adds a Logit version, although this is unfinished. Conditional Models ------------------ Three conditional limited dependent variables models have been added: :class:`~statsmodels.discrete.conditional_models.ConditionalLogit`, :class:`~statsmodels.discrete.conditional_models.ConditionalMNLogit` and :class:`~statsmodels.discrete.conditional_models.ConditionalPoisson`. These are known as fixed effect models in Econometrics. Dimension Reduction Methods --------------------------- Three standard methods to perform dimension reduction when modeling data have been added: :class:`~statsmodels.regression.dimred.SlicedInverseReg`, :class:`~statsmodels.regression.dimred.PrincipalHessianDirections`, and :class:`~statsmodels.regression.dimred.SlicedAverageVarianceEstimation`. Regression using Quadratic Inference Functions (QIF) ---------------------------------------------------- Quadratic Inference Function, :class:`~statsmodels.genmod.qif.QIF`, improve the estimation of GEE models. Gaussian Process Regression --------------------------- :class:`~statsmodels.regression.process_regression.GaussianCovariance` implements Gaussian process regression which is a nonparametric kernel-based method to model data. :class:`~statsmodels.regression.process_regression.ProcessMLE` is a generic class that can be used for other types of process regression. The results are returned in a :class:`~statsmodels.regression.process_regression.ProcessMLEResults`. :func:`~statsmodels.stats.correlation_tools.kernel_covariance` provides a method that uses kernel averaging to estimate a multivariate covariance function. Burg's Method ------------- Burg's method, :func:`~statsmodels.regression.linear_model.burg`, provides an alternative estimator for the parameters of AR models that is known to work well in small samples. It minimizes the forward and backward errors. Time series Tools ----------------- A number of common helper function for decomposing a time series have been added: :func:`~statsmodels.tsa.innovations.arma_innovations.arma_innovations`, :func:`~statsmodels.tsa.stattools.innovations_algo`, and :func:`~statsmodels.tsa.stattools.innovations_filter`. Two new PACF estimators have been added: :func:`~statsmodels.tsa.stattools.levinson_durbin_pacf` and :func:`~statsmodels.tsa.stattools.pacf_burg`. Other ----- Knockoff effect estimation has been added for a many models: :class:`~statsmodels.stats.knockoff_regeffects.RegModelEffects`, :class:`~statsmodels.stats.knockoff_regeffects.CorrelationEffects`, :class:`~statsmodels.stats.knockoff_regeffects.OLSEffects`, :class:`~statsmodels.stats.knockoff_regeffects.ForwardEffects`, and :class:`~statsmodels.stats.knockoff_regeffects.OLSEffects`. Influence functions are available for GLM and generic MLE models: :class:`~statsmodels.stats.outliers_influence.GLMInfluence` and :class:`~statsmodels.stats.outliers_influence.MLEInfluence`. What's new - an overview ======================== The following lists the main new features of statsmodels 0.10. In addition, release 0.10 includes bug fixes, refactorings and improvements in many areas. Submodules ---------- ``base`` ~~~~~~~~ - Add ``ModelWarning`` base class to avoid warning filter on standard UserWarning (:pr:`4712`) - Add ultra-high screening with SCAD (:pr:`4683`) - Add penalized mle scad (:pr:`4576`, :issue:`3677`, :issue:`2374`) - Add score/LM conditional moment tests (:pr:`2096`) - Fixed a bug which resulted in weights not being used in penalized models (:pr:`5762`, :issue:`4725`) - Allow the constant index to be located even when ``hasconst=False`` (:pr:`5680`) - Ensure ``mle_retvals`` is always set even when ``full_output=False`` (:pr:`5681`, :issue:`2752`) - Fix a bug in Wald tests when testing a single constraint (:pr:`5684`, :issue:`5475`) - Improve performance by skipping constant check when ``hasconst=True`` (:pr:`5698`) - Deprecated ``scale`` parameter in the base model class (:pr:`5614`, :issue:`4598`) - Fixed a bug that raised an error when a multi-index DataFrame was input into a model (:pr:`5634`, :issue:`5415`, :issue:`5414`) - Fix bug in use of ``self.score`` in GenericLikelihoodModel (:pr:`5130`, :issue:`4453`) ``discrete`` ~~~~~~~~~~~~ - Improve performance by only computing matrix_rank(exog) once in DiscreteModel.initialize (:pr:`4805`) - Improve performance in discrete models by avoiding repeated calculations (:pr:`4515`) - Add ``cov_type`` to summary of discrete models (:pr:`5672`, :issue:`4581`) - Add conditional multinomial logit (:pr:`5510`) - Add conditional logistic and Poisson regression (:pr:`5304`) ``genmod`` ~~~~~~~~~~ - Fix arguments in poisson version of ``BayesMixedLM`` (:pr:`4809`) - Ensure that column names are properly attached to the model (:pr:`4788`) - Change ``cov_params`` in ``BayesMixedLM`` to act more like it does in other models (:pr:`4788`) - Add missing predict and fit methods to ``BayesMixedGLM`` (:pr:`4702`) - Add influence function support for GLM (:pr:`4732`, :issue:`4268`, :issue:`4257`) - Fixed a bug in GEE where history was not saved (:pr:`5789`) - Enable ``missing='drop'`` in GEE (:pr:`5771`) - Improve score test to allow the submodel to be provided as a GEEResults object instead of as linear constraints (:pr:`5435`) - Use GLM to get starting values for GEE (:pr:`5440`) - Added regularized GEE (:pr:`5450`) - Added Generalized Additive Models (GAM) (:pr:`5481`, :issue:`5370`, :issue:`5296`, :issue:`4575`, :issue:`2744`, :issue:`2435`) - Added tweedie log-likelihood (:pr:`5521`) - Added ridge regression by gradient for all GLM (:pr:`5521`) - Added Tweedie EQL quasi-likelihood (:pr:`5543`) - Allow ``dep_data`` to be specified using formula or names (:pr:`5345`) - Fix a bug in stationary cov_struct for GEE (:pr:`5390`) - Add QIC for GEE (:pr:`4909`) ``graphics`` ~~~~~~~~~~~~ - Allow QQ plots using samples with different sizes (:pr:`5673`, :issue:`2896`, :issue:`3169`) - Added examples of many graphics functions to the documentation (:pr:`5607`, :issue:`5309`) - Fixed a bug in ``interaction_plot`` which lost information in a ``pd.Series`` index (:pr:`5548`) - Remove change of global pickle method in functional plots (:pr:`4963`) ``imputation`` ~~~~~~~~~~~~~~ - Add formula support to MI multiple imputation (:pr:`4722`) - Saves the column names from ``pd.DataFrames`` and returns the imputed results as a DataFrame in ``BayesMI`` (:pr:`4722`) - Fixed warnings in ``MICEData`` related to setting on copy (:pr:`5606`, :issue:`5431`) - Allow results to be stored for multiple imputation (:pr:`5093`) - Fixed a bug where MICEData sets initial imputation incorrectly (:pr:`5301`, :issue:`5254`) ``iolib`` ~~~~~~~~~ - Deprecate ``StataReader``, ``StataWriter``, and ``genfromdta`` in favor of pandas equivalents (:pr:`5770`) - Improve string escaping when exporting to LaTeX (:pr:`5683`, :issue:`5297`) - Fixed a bug in ``summary2`` that ignored user float formatting (:pr:`5655`, :issue:`1964`, :issue:`1965`) - Remove ``$$`` from LaTeX output (:pr:`5588`,:issue:`5444`) ``multivariate`` ~~~~~~~~~~~~~~~~ - Fixed a bug that only allowed ``MANOVA`` to work correctly when called using the formula interface (:pr:`5646`, :issue:`4903`, :issue:`5578`) - Fix pickling bug in ``PCA`` (:pr:`4963`) ``nonparametric`` ~~~~~~~~~~~~~~~~~ - Added input protection ``lowess` to ensure ``frac`` is always in bounds. (:pr:`5556`) - Add check of inputs in ``KernelReg`` (:pr:`4968`, :issue:`4873`) ``regression`` ~~~~~~~~~~~~~~ - Fix bug in random effects covariance getter for ``MixedLM`` (:pr:`4704`) - Add exact diffuse filtering for ``RecursiveLS`` (:pr:`4699`) - Add Gaussian process regression (:pr:`4691`) - Add linear restrictions to ``RecursiveLS`` (:pr:`4133`) - Added regression with quadratic inference functions :class:`~statsmodels.genmod.qif.QIF` (:pr:`5803`) - Allow mediation to be used with MixedLM as a mediator and/or outcome model (:pr:`5489`) - Add square root LASSO (:pr:`5516`) - Add dimension reduction regression methods: ``SlicedInverseReg``, ``PHD`` and ``SAVE`` (:pr:`5518`) - Increased the number of methods available to optimize ``MixedLM`` models (:pr:`5551`) - Added label to R2 when model is uncentered (:pr:`5083`, :issue:`5078`) - Allow several optimizers to be tried in sequence for MixedLM (:pr:`4819`) - Fix bug in Recursive LS with multiple constraints (:pr:`4826`) - Fix a typo in ``ColinearityWarning`` (:pr:`4889`, :issue:`4671`) - Add a finite check for ``_MinimalWLS`` (:pr:`4960`) - Fix definition of R2 in ``GLS`` (:pr:`4967`, :issue:`1252`, :issue:`1171`) - Add Burgs algorithm for estimating parameters of AR models (:pr:`5016`) ``sandbox`` ~~~~~~~~~~~ - Add copulas (:pr:`5076`) ``stats`` ~~~~~~~~~ - Implements a simple method of moments estimator of a spatial covariance in ``kernel_covariance`` (:pr:`4726`) - Fixed a bug in multiple function in ``~statsmodels.stats.moment_helpers`` which prevents in-place modification of inputs (:pr:`5671`, :issue:`3362`, :issue:`2928`) - Fixed a bug in contingency tables where shift was not correctly applied (:pr:`5654`, :issue:`3603`, :issue:`3579`) - Added White's two-moment specification test with null hypothesis of homoskedastic and correctly specified(:pr:`5602`, :issue:`4721`) - Added adjusted p-values for Tukey's HSD (:issue:`5418`, :pr:`5625`) - Fixed a bug in ``medcouple`` that produced the incorrect estimate when there are ties in the data (:pr:`5397`, :issue:`5395`) - Combine the real and knockoff features in init (:pr:`4920`) - Modifying exog in-place leads to incorrect scaling (:pr:`4920`) - Add Provide Knockoff+ (guaranteed to control FDR but slightly conservative) as well as Knockoff FDR (:pr:`4920`) - Add RegModelEffects allows the user to specify which model is used for parameter estimation (:pr:`4920`) ``tools`` ~~~~~~~~~ - Fixed a bug in ``group_sums`` that raised ``NameError`` (:pr:`5127`) ``tsa`` ~~~~~~~ - Fix k_params in seasonal MAs (:pr:`4790`, :issue:`4789`) - Fix prediction index in VAR predict (:pr:`4785`, :issue:`4784`) - Standardized forecast error in state space when using Cholesky methods with partial missing data (:pr:`4770`) - Add and fix VARMAX trend, exog. timing and polynomial trends (:pr:`4766`) - Fix bug in exact diffuse filtering in complex data type case (:pr:`4743`) - SARIMAX warns for non-stationary starting params (:pr:`4739`) - Make arroots and maroots have consistent return type (:pr:`4559`) - Add exact diffuse initialization to state space models (:pr:`4418`, :issue:`4042`) - Allow concentrating scale out of log-likelihood in state space models (:pr:`3480`) - Fixed a bug in ``coint_johansen`` that prevented it from running with 0 lags (:pr:`5783`) - Improved performance in ``kpss`` using ``np.sum`` (:pr:`5774`) - Enforce maximum number of lags in ``kpss`` (:pr:`5707`) - Add ``arma_innovations`` to compute the innovations from an ARMA process (:pr:`5704`) - Limit maximum lag length in ``adfuller`` so that model can always be estimated (:pr:`5699`, :issue:`5432`, :issue:`3330`) - Added automatic data-dependent lag length selection in ``kpss`` (:pr:`5670`, :issue:`2781`, :issue:`5522`) - Fixed a bug in ``VARMAX`` where the wrong form of the intercept was used when creating starting values (:pr:`5652`, :issue:`5651`) - Fixed a bug ``sirf_errband_mc`` (:pr:`5641`, :issue:`5280`) - Clarified error when input to ARMA is not a 1-d array (:pr:`5640`, :issue:`2575`) - Improved the numerical stability of parameter transformation in ARIMA estimation (:pr:`5569`) - Fixed a bug in the acf of a ``VAR`` which produced incorrect values (:pr:`5501`) - Expose additional alternative estimation methods in ``pacf`` (:pr:`5153`, :issue:`3862`) - Removed original implementation of Kalman Filter in favor of Cythonized version in ``statsmodels.tsa.statespace`` (:pr:`5171`) - Issue warning when using ``VARResults.cov_params`` that it will become a method in the future (:pr:`5244`) - Fix a bug in statespace models' ``predict`` that would fail when using row labels (:pr:`5250`) - Allow ``summary`` even if filter_results=None, which happens after ``save`` and ``load`` (:pr:`5252`) - Fixed a bug in sequential simulation in models with state_intercept (:pr:`5257`) - Add an analytic version of ``arma_acovf`` (:pr:`5324`) - Add a fast ARMA innovation algorithm and loglike computation (:pr:`5360`) - Fix a bug in the Initialization of simulation smoother with exact diffuse initialization (:pr:`5383`) - Fix bug in simulation smoothed measurement disturbance with FILTER_COLLAPSED (:pr:`4810`, :issue:`4800`) - Improve SARIMAX for time series close to non-stationary (:pr:`4815`) - Use Cython to improve speed of Exponential Smoothing models (:pr:`4845`) - Fix a bug in ``arma_order_selection`` when data is passed in as a list (:pr:`4890`, :issue:`4727`) - Add explicit exceptions in ARMA/ARIMA forecast with missing or wrong exog (:pr:`4915`, :issue:`3737`) - Remove incorrect endog from results if constraints (:pr:`4921`) - Add ``nlag`` argument to ``acovf`` (:pr:`4937`) - Set reasonable default lags for acf/pacf plots (:pr:`4949`) - Add innovations algorithm to convert acov to MA (:pr:`5042`) - Add and innovations filter to filter for observations in a MA (:pr:`5042`) - Fix a bug in initialization when simulating in state space models (:pr:`5043`) ``maintenance`` ~~~~~~~~~~~~~~~ - Switch to standard setup.py so that ``pip install statsmodels`` can succeed in an empty virtual environment - General compatibility fixes for recent versions of numpy, scipy and pandas - Added new CI using Azure Pipelines (:pr:`5617`) - Enable linting on travis to ensure code is up to standards (:pr:`4820`) - Add coverage for Cython code (:pr:`4871`) - Improve import speed (:pr:`5831`) - Make all version of docs available (:pr:`5879`) bug-wrong --------- A new issue label `type-bug-wrong` indicates bugs that cause that incorrect numbers are returned without warnings. (Regular bugs are mostly usability bugs or bugs that raise an exception for unsupported use cases.) `see tagged issues `_ - :issue:`5475` - :issue:`5316` Major Bugs Fixed ================ See github issues for a list of bug fixes included in this release - `Closed bugs `_ - `Closed bugs (wrong result) `_ Development summary and credits =============================== Besides receiving contributions for new and improved features and for bugfixes, important contributions to general maintenance for this release came from * Chad Fulton * Brock Mendel * Peter Quackenbush * Kerby Shedden * Kevin Sheppard and the general maintainer and code reviewer * Josef Perktold Additionally, many users contributed by participation in github issues and providing feedback. Thanks to all of the contributors for the 0.10 release (based on git log): * Amir Masoud Abdol * Andrew Davis * Andrew Kittredge * Andrew Theis * bertrandhaut * bksahu * Brock Mendel * Chad Fulton * Chris Snow * Chris Down * Daniel Saxton * donbeo * Emlyn Price * equinaut * Eric Larson * Evgeny Zhurko * fourpoints * Gabriel Reid * Harry Moreno * Hauke Jürgen Mönck * Hugo * hugovk * Huize Wang * JarnoRFB * Jarrod Millman * jcdang * Jefferson Tweed * Josef Perktold * jtweeder * Julian Taylor * Kerby Shedden * Kevin Sheppard * Loknar * Matthew Brett * Max Ghenis * Ming Li * Mitch Negus * Michael Handley * Moritz Lotze * Nathan Perkins * Nathaniel J. Smith * Niklas H * Peter Quackenbush * QuentinAndre * Ralf Gommers * Rebecca N. Palmer * Rhys Ulerich * Richard Barnes * RonLek * Stefaan Lippens * Tad seldovia * thequackdaddy * Tom Augspurger * Torsten Wörtwein * Varanelli * xrr * Yichuan Liu * zveryansky * 郭飞 These lists of names are automatically generated based on git log, and may not be complete. Merged Pull Requests -------------------- Thie following Pull Requests were merged since the last release: * :pr:`2096`: Score/LM conditional moment tests * :pr:`3480`: ENH: State space: allow concentrating scale out of log-likelihood * :pr:`4048`: Remove redundant code for dropped Python 2.6 * :pr:`4133`: ENH: Add linear restrictions to RecursiveLS * :pr:`4316`: ensure MultinomialResults has J, K. Get rid of unnecessary lmap usage * :pr:`4322`: Make DiscreteResults Unchanging * :pr:`4371`: catch the correct exception, make assertions not-pointless * :pr:`4418`: ENH: State space: Exact diffuse initialization * :pr:`4458`: De-duplicate a bunch of identical code * :pr:`4468`: remove unused resetlist * :pr:`4487`: Get rid of non-standard imports and one-line functions * :pr:`4494`: Fix imports math.foo -->np.foo in vecm * :pr:`4501`: xfail test instead of commenting it out * :pr:`4515`: PERF: Simplify algebra in discrete_model * :pr:`4559`: REF: make arroots and maroots have consistent return type * :pr:`4560`: Document and cleanup bits of cython code * :pr:`4576`: Penalized mle scad rebased2 * :pr:`4593`: DOC:ArmaProcess class documentation typo fix * :pr:`4594`: TEST/DOC: SMW linalg routines documentation and test * :pr:`4640`: BF: DataTimeIndex.to_datetime removed in pandas * :pr:`4648`: BUG/TEST: Make pattern order for multiple imputation deterministic * :pr:`4650`: DISCUSS/BLD: Update minimum versions. * :pr:`4653`: REF/MAINT: avoid dict with pandas * :pr:`4658`: BLD: Use older version of Pandas for docbuild * :pr:`4683`: ENH: add ultra-high screening with SCAD * :pr:`4686`: TEST: Docstring edits and variable name changes for clarity * :pr:`4689`: PERF: Declare temporary output for hessian * :pr:`4691`: ENH: Gaussian process regression * :pr:`4692`: DOC: Add GLM varfuncs and weights notebook to documentation * :pr:`4696`: Configure doctr * :pr:`4698`: REF: Remove compatibility mode for state space * :pr:`4699`: ENH: Exact diffuse filtering for RecursiveLS * :pr:`4702`: BUG: Add missing predict and fit methods to BayesMixedGLM * :pr:`4704`: BUG Fix random effects covariance getter for MixedLM * :pr:`4712`: BUG: add ModelWarning base class to avoid warning filter on standard UserWarning. * :pr:`4717`: TST: allclose instead of exact match for floats and use machine precision * :pr:`4720`: fix syntax-like error * :pr:`4722`: ENH: Add formula support to MI multiple imputation * :pr:`4726`: ENH Kernel covariance * :pr:`4728`: TST: Openblas appveyor fixes * :pr:`4732`: ENH: add GLMInfluence * :pr:`4736`: DOC: Make custom function take effect * :pr:`4739`: REF: SARIMAX: only warn for non stationary starting params * :pr:`4743`: BUG: state space: exact diffuse filtering in complex data type case * :pr:`4750`: DOC: Fix indentation of math formulas * :pr:`4753`: DOC: Add notebook on concentrated scale in ssm * :pr:`4758`: DOC: Added missing notebooks to examples * :pr:`4760`: CLN: Provide better name for pooled risk ratio * :pr:`4763`: replace copy/pasted code with import * :pr:`4766`: BUG/ENH: VARMAX Fix trend / exog. timing. Add polynomial trends. * :pr:`4767`: MAINT: gitignore univariate_diffuse pyx files. * :pr:`4770`: BUG: State space: standardized forecast error when using Cholesky methods with partial missing data * :pr:`4777`: MAINT: conda specify numpy-base * :pr:`4785`: BUG: Get prediction index in VAR predict. * :pr:`4786`: CLEAN: fix indentation by four typos * :pr:`4788`: BUG: bayes mixed GLM maintenance * :pr:`4790`: BUG: k_params if seasonal MA * :pr:`4805`: Only compute matrix_rank(exog) once in DiscreteModel.initialize * :pr:`4809`: BUG: fix arguments in poisson mixed model * :pr:`4810`: BUG: simulation smoothed measurement disturbance with FILTER_COLLAPSED * :pr:`4814`: CLEAN: Removed unnecessary and non-informative print * :pr:`4815`: ENH/BUG: Improve SARIMAX for time series close to non-stationary * :pr:`4819`: ENH: Allow several optimizers to be tried in sequence for MixedLM * :pr:`4820`: Implement basic linting for Travis * :pr:`4823`: Fix deprecation warnings * :pr:`4826`: BUG/ENH: Recursive LS: fix bug w/ multiple constraints * :pr:`4834`: Implement full flake8 checking for a subset of files in good condition * :pr:`4835`: CLEAN: Fix tab indentation, lint for it * :pr:`4842`: CLN: Flake8 fixups and linting for statespace files (but not tests) * :pr:`4844`: CLN: Fully lint regime_switching * :pr:`4845`: ENH: Improve speed in Exponential Smoothing * :pr:`4853`: CLN/REF: Remove recarrays from datasets * :pr:`4855`: BUG: Attach vc_names for mixed Poisson models * :pr:`4858`: MAINT: Delete migrate_issues_gh * :pr:`4859`: Fix some NameErrors, do not delete unused [...] * :pr:`4861`: DOC: Fix small doc errors * :pr:`4864`: CLN: fix and lint for W391 blank line at end of file * :pr:`4869`: Update setup.cfg * :pr:`4871`: BLD: Refactor Setup * :pr:`4872`: MAINT: Remove nose and related references * :pr:`4879`: CLN: Fix documentation for Levinson-Durbin * :pr:`4883`: CLN: remove empty __main__ sections * :pr:`4886`: CLN: Fully lint recursive_ls.py * :pr:`4889`: REF: Rename ColinearityWarning * :pr:`4890`: BUG: Add check to ensure array in arma order selection * :pr:`4891`: BLD: Fix linting and move coverage * :pr:`4893`: TST: Restore incorrectly disabled test * :pr:`4895`: CLN: Fix and lint for misleading indentation E125,E129 * :pr:`4896`: CLN: Fix and lint for potential double-negatives E713,E714 * :pr:`4897`: CLN: Fix and lint for multiple spaces after keyword E271 * :pr:`4900`: CLN: Lint for missing whitespace around modulo operator E228,E401 * :pr:`4901`: CLN: Fix and lint for E124 closing bracket does not match visual indentation * :pr:`4909`: ENH: QIC for GEE * :pr:`4910`: CLN: Blank Lines E301,E302,E303,E305,E306 in examples, tools, sm.base * :pr:`4911`: MAINT: Remove future errors and warnings * :pr:`4912`: BLD: Rebased ci improvements * :pr:`4913`: TST: Add a fixture to close all plots * :pr:`4914`: CLN: Blanks E301,E302,E303,E305,E306 in tsa * :pr:`4915`: ENH: explicit exceptions in ARMA/ARIMA forecast with missing or wrong exog * :pr:`4920`: BUG/ENH: Two bug fixes and several enhancements to knockoff filter (regression fdr) * :pr:`4921`: BUG: remove faux endog from results if constraints * :pr:`4924`: CLN: E242 space after tab, enforce all passing rules * :pr:`4925`: CLN: Enforce E721, use isinstance * :pr:`4926`: CLN: Enforce E306, blank lines in nested funcs * :pr:`4927`: CLN: Enforce E272, multiple spaces * :pr:`4929`: BLD: Add linting for any new files * :pr:`4933`: Remove unused patsy import in quantile_regression.ipynb * :pr:`4937`: ENH: Add nlag argument to acovf * :pr:`4941`: MAINT: remove exact duplicate file datamlw.py * :pr:`4943`: TST: Relax tolerance on failing test * :pr:`4944`: BLD: Add pinned numpy on appveyor * :pr:`4949`: BUG: Set default lags for acf/pacf plots * :pr:`4950`: DOC: Fix small typo in unit root testing example * :pr:`4953`: DOC: Fix nagging issues in docs * :pr:`4954`: BUG: disallow use_self=False * :pr:`4959`: DOC: Clean up tsa docs * :pr:`4960`: BUG: Add finite check for _MinimalWLS * :pr:`4963`: BUG: Remove change of global pickle method * :pr:`4967`: BUG: Fix definition of GLS r2 * :pr:`4968`: BUG: Check inputs in KernelReg * :pr:`4971`: DOC: Switch to https where used * :pr:`4972`: MAINT/CLN Remove .bzrignore * :pr:`4977`: [BUG/MAINT] Fix NameErrors caused by missing kwargs * :pr:`4978`: [MAINT/Test] skip test instead of mangling name in test_generic_methods * :pr:`4979`: [MAINT/TST] remove np.testing.dec unused imports (nose dependency) * :pr:`4980`: [MAINT/TST] skip/xfail tests instead of mangling/commenting-out in genmod, regression * :pr:`4981`: [MAINT] Remove info.py * :pr:`4982`: DOC Fix typo Parameters-->Parameters * :pr:`4983`: [TST] xfail/skip instead of commenting-out/mangling discrete tests * :pr:`4984`: [TST/DOC] make commented-out code in tests/results into readable docs * :pr:`4985`: [TST/DOC] Make test comments more readable * :pr:`4986`: [MAINT/TST] turn commented-out code into readable docs in results_arma * :pr:`4987`: [TST/MAINT] turn commented-out code into readable docs in results_ar,… * :pr:`4988`: [TST/MAINT] de-duplicate get_correction_factor code * :pr:`4989`: [MAINT/CLN] Remove code made unusable due to license issue * :pr:`4990`: [MAINT/CLN] remove numdiff __main__ section explicitly marked as scratch work * :pr:`4993`: [TST/CLN] Turn decorators __main__ section into tests * :pr:`4995`: [TST] make tools.linalg __main__ section into tests * :pr:`4998`: [CLN/TST] Follow instructions to remove function * :pr:`4999`: [MAINT] remove wrappers.py * :pr:`5000`: [MAINT] update compat to remove unusable shims e.g. py26 * :pr:`5002`: [MAINT] add missing import * :pr:`5003`: MAINT: fix invalid exception messages * :pr:`5005`: [MAINT] remove unused imports in examples+tools * :pr:`5007`: MAINT: unused imports in robust * :pr:`5011`: [MAINT] remove text file relics from scikits/statsmodels * :pr:`5012`: [MAINT/TST] move misplaced results files in regressions/tests * :pr:`5013`: [MAINT] fix typo deprecated-->deprecated * :pr:`5014`: [MAINT] typo in __init__ signature * :pr:`5015`: [MAINT] move misplaced test_tsa_indexes * :pr:`5016`: ENH: Burgs algorithm * :pr:`5020`: MAINT: fix incorrect docstring summary-->summary2 * :pr:`5021`: MAINT: fix typo duplicated References in docstring * :pr:`5024`: MAINT: silenced as_pandas warnings in documentation * :pr:`5027`: MAINT: remove functions duplicated from scipy * :pr:`5029`: MAINT: strict linting for sm.stats files _close_ to already passing * :pr:`5040`: MAINT: clean up x13.py, delete main * :pr:`5042`: ENH: Add innovations algorithm * :pr:`5043`: BUG: Initialization when simulating * :pr:`5045`: MAINT: strict linting for tsa.statespace.tests.results * :pr:`5057`: BUG: Correct check for callable * :pr:`5058`: BUG: Do not use mutable default values * :pr:`5059`: BLD: Add line displaying CPU info to CI * :pr:`5065`: TST: Fix incorrect assertion * :pr:`5070`: MAINT: remove file that just says to remove it * :pr:`5071`: MAINT: remove example file corresponding to removed module * :pr:`5074`: MAINT: strict lint test_var.py * :pr:`5075`: MAINT: strict linting test_univariate.py * :pr:`5076`: ENH: more work on copula (deriv, classes) * :pr:`5079`: MAINT: linting statespace tests * :pr:`5080`: FIX failure caused by #5076 * :pr:`5083`: ENH: Add "(uncentered)" after rsquared label in .summary, .summary2 when appropriate * :pr:`5086`: TST: parametrize tests instead of using for loops * :pr:`5088`: DOC: Add javascript to link to other doc versions * :pr:`5090`: MAINT: Chrome does not like having a secure link with an unsecure image * :pr:`5093`: Allow results to be stored for multiple imputation * :pr:`5096`: ENH remove unneeded restriction on QIC (GEE) * :pr:`5099`: MAINT: fix and lint for W292 newline at end of file * :pr:`5103`: BUG: fix missing new_branch_dir arg in upload_pdf * :pr:`5105`: BUG/DOC: Description of k_posdef * :pr:`5114`: MAINT: many but not all trailing whitespace * :pr:`5119`: CLN: remove unused imports in tools, sm.tsa * :pr:`5120`: BUG: Ensure internal tester exits with error if needed * :pr:`5121`: MAINT: Avoid star imports * :pr:`5122`: MAINT: Modernize R-->py script, lint output * :pr:`5123`: CLN: Move results files to a location that is copied to install * :pr:`5124`: MAINT: fix generated double whitespace * :pr:`5127`: BUG: Fix NameError in grouputils, make __main__ into tests * :pr:`5130`: BUG: incorrect self.score in GenericLikelihoodModel; closes #4453 * :pr:`5133`: TST: apply stacklevel to warning in Family.__init__ * :pr:`5135`: MAINT: Fix warnings * :pr:`5136`: TST: improve testing util functions; de-duplicate * :pr:`5138`: CLN: Use cache_readonly instead of OneTimeProperty * :pr:`5141`: MAINT: Delete bspline source files * :pr:`5143`: ENH/BUG Bootstrap clone rebased * :pr:`5146`: Clean up the smf namespace * :pr:`5148`: REF/TST: add seed to hdrboxplot, Use random order in pytest * :pr:`5149`: TST: Theil test randomseed * :pr:`5152`: REF: Use iterative cumsum_n * :pr:`5153`: ENH: Add additional options for pacf ols * :pr:`5156`: TST: Remove __main__ sections in tests * :pr:`5162`: TST: Fix incorrect test closes #4325 * :pr:`5164`: BF: drop tolerance of a zero_constrained test * :pr:`5165`: MAINT: Add decorator for tests that use matplotlib * :pr:`5166`: DOC: Fix section title in QIC * :pr:`5167`: TST/BUG: Fix missing SkipTest * :pr:`5170`: DEPR: Remove items deprecated in previous versions * :pr:`5171`: MAINT: Remove kalmanf StateSpace code supplanted by tsa.statespace * :pr:`5176`: TST: Fix random generation issue * :pr:`5177`: DOC: Improve Holt Winters documentation * :pr:`5178`: TST: Fix scale in test * :pr:`5180`: TST: Change assert_approx_equal to assert_allclose * :pr:`5184`: TST: parametrize tests in test_lme * :pr:`5188`: BLD/TST: Add coverage for Cython files * :pr:`5191`: MAINT: Remove selected __main__ sections * :pr:`5192`: MAINT: Fix incorrect pass statements * :pr:`5193`: MAINT: raise specific exceptions instead of just Exception * :pr:`5194`: MAINT: fix incorrect TypeError --> ValueError * :pr:`5195`: BLD: Include License in Wheel * :pr:`5196`: TST: Set seed when using basin hopping * :pr:`5198`: TST/CLN/BUG: Fix corr nearest factor * :pr:`5200`: TST: Alter test condition due to parameter scale * :pr:`5201`: TST/CLN: test_arima_exog_predict, Rescale data to avoid convergence issues * :pr:`5203`: BUG: raise instead of return ValueError * :pr:`5204`: MAINT: Avoid/Fix FutureWarnings * :pr:`5207`: TST: Ensure random numbers are reproducible * :pr:`5208`: TST/CLN: Tighten tol to reduce spurious test failure * :pr:`5210`: BLD: Ensure master is available when linting * :pr:`5211`: MAINT: Import instead of copy/pasting utils * :pr:`5213`: MAINT: Move misplaced duration results files * :pr:`5214`: MAINT: remove example-like file that could never run * :pr:`5217`: MAINT: Remove outdated pandas compat shims * :pr:`5218`: MAINT: Move misplaced genmod results files * :pr:`5219`: fixed typo * :pr:`5222`: MAINT: fully lint formula * :pr:`5223`: MAINT: fully lint compat * :pr:`5224`: REF: raise early on invalid method * :pr:`5227`: MAINT: docstring and whitespace fixups * :pr:`5228`: DOC: Fix many small errors in examples * :pr:`5230`: DOC: Fix small doc build errors * :pr:`5232`: TST: mark smoketests * :pr:`5237`: TST: Add mac testing * :pr:`5239`: BLD/TST: Add platform-specific skips to CI testing * :pr:`5240`: MAINT: remove cythonize.py made unnecessary by #4871 * :pr:`5242`: DOC: Update release instructions [skip ci] * :pr:`5244`: DEPR: warn that VARResults.cov_params will become method * :pr:`5246`: DOC: Added documentation of elements in anova_lm * :pr:`5248`: DOC: Revert incorrect docstring change [skip ci] * :pr:`5249`: MAINT: Add Script to convert notebooks * :pr:`5250`: BUG/TST: TSA models: _get_index_label_loc failed when using row labels. * :pr:`5251`: DOC: Use correct “autoregressive†in docstring * :pr:`5252`: BUG: Allow `summary` even if filter_results=None (e.g. after `save`, `load` * :pr:`5257`: BUG: Sequential simulation in models with state_intercept * :pr:`5260`: MAINT: avoid pandas FutureWarning by checking specific condition * :pr:`5262`: MAINT: fix typos in pca, wrap long lines * :pr:`5263`: BLD: Only unshallow when required * :pr:`5265`: MAINT: Prefer signature over formatargspec * :pr:`5267`: MAINT: implement _wrap_derivative_exog for de-duplication * :pr:`5269`: MAINT: De-duplicate code in iolib.summary * :pr:`5272`: WIP/MAINT: Identify defunct code in summary methods * :pr:`5273`: Fix incorrect parameter name in docstring * :pr:`5274`: MAINT: remove self.table pinning * :pr:`5275`: ENH/BUG Modify GEE indexing to remove numpy warnings * :pr:`5277`: DOC: Clarify/fix docs on GLM scale estimation for negative binomial * :pr:`5292`: DOC: Remove only_directive * :pr:`5295`: TST: Added random seed to test_gee and verified working * :pr:`5300`: DOC fix docstring in stattools.py * :pr:`5301`: BUG: MICEData sets initial imputation incorrectly * :pr:`5304`: ENH: conditional logistic and Poisson regression * :pr:`5306`: DOC: Workarounds to fix docbuild * :pr:`5308`: REF: Collect covtype descriptions, de-duplicate normalization func * :pr:`5314`: DOC: minor fix on documentation on Durbin Watson test * :pr:`5322`: DOC: Move magic * :pr:`5324`: ENH: analytic version of arma_acovf * :pr:`5325`: BUG/TST: Fix innovations_filter, add test vs Kalman filter * :pr:`5335`: MAINT: eliminate some pytest warnings * :pr:`5345`: ENH: Allow dep_data to be specified using formula or names * :pr:`5348`: Set python3 as interpreter for doc tools * :pr:`5352`: CLN: Fix F901 and E306 mixups * :pr:`5353`: CLN: W605 fixups in vector_ar * :pr:`5359`: BUG: raise correct error * :pr:`5360`: ENH: Fast ARMA innovation algorithm and loglike computation * :pr:`5369`: MAINT: disable pytest minversion check (broken in pytest 3.10.0) * :pr:`5383`: BUG: Initialization of simulation smoother with exact diffuse initialization * :pr:`5390`: BUG/ENH: modify stationary cov_struct for GEE * :pr:`5397`: BUG: Fix medcouple with ties * :pr:`5399`: CLN: Fix some invalid escapes * :pr:`5421`: CLN: informative names for test functions * :pr:`5424`: MAINT: conda-forge use gcc7 * :pr:`5426`: Misspelling in the documentation proportions_ztest * :pr:`5435`: ENH Score test enhancements for GEE * :pr:`5440`: ENH: Use GLM to get starting values for GEE * :pr:`5449`: ENH/DOC: Added linting instruction in CONTRIBUTING.rst * :pr:`5450`: ENH: regularized GEE * :pr:`5462`: Fixed broken link for Guerry Dataset * :pr:`5471`: Fix broken link * :pr:`5481`: ENH: Generalized Additive Models and splines (Gam 2744 rebased4) * :pr:`5484`: DOC: fix gam.rst * :pr:`5485`: MAINT: Travis fixes * :pr:`5489`: ENH: Mediation for Mixedlm * :pr:`5494`: BUG: Bad escapes * :pr:`5497`: Fix typo in docstring * :pr:`5501`: BUG: Correct error in VAR ACF * :pr:`5510`: ENH Conditional multinomial logit * :pr:`5513`: DOC: Fix spelling * :pr:`5516`: ENH square root lasso * :pr:`5518`: ENH dimension reduction regression * :pr:`5521`: ENH: Tweedie log-likelihood (+ridge regression by gradient for all GLM) * :pr:`5532`: DOC/ENH Docstring updates for clogit * :pr:`5541`: DOC: Describe binomial endog formats * :pr:`5542`: BUG/TEST: py27 needs slacker tolerances * :pr:`5543`: BUG: Tweedie EQL quasi-likelihood * :pr:`5548`: keep index of series when recoding a series * :pr:`5551`: ENH: extend mixedlm optimizer attempts * :pr:`5556`: Update _smoothers_lowess.pyx * :pr:`5566`: Add project_urls to setup * :pr:`5567`: Correct a spell mistake * :pr:`5569`: ENH: Improve numerical stability of _ar_transparams, _ar_invtransparams * :pr:`5582`: Jbrockmendel w605b * :pr:`5583`: MAINT: Set language level for Cython * :pr:`5584`: MAINT: Remov deprecation issues * :pr:`5586`: DOC: Add issue and pr templates * :pr:`5587`: MAINT: Resolve additional deprecations * :pr:`5588`: BUG: Replace $$ in generated LaTeX * :pr:`5589`: DOC: Updated the `for all i, j` * :pr:`5590`: MAINT: Reorder travis so that legacy fails early * :pr:`5591`: Jbrockmendel manywarns3 * :pr:`5592`: Jbrockmendel pversion * :pr:`5593`: MAINT: remove never-needed callable and never-used compat functions * :pr:`5594`: TST: Ensure test is identical in all runs * :pr:`5595`: MAINT: Remove warnings from tests * :pr:`5596`: TST: Explicitly set seed in basinhopping * :pr:`5597`: MAINT: Remove unavailable imports * :pr:`5599`: DOC: More emphasis and fix reference * :pr:`5600`: TST: Relax tolerance for OpenBlas issue * :pr:`5601`: Update mixed_linear.rst * :pr:`5602`: ENH: White spec test (clean commit for PR 4721) * :pr:`5604`: MAINT: Update template to encourage master check * :pr:`5605`: Guofei9987 modify comments proportion confint * :pr:`5606`: Mattwigway mice setting with copy warning * :pr:`5607`: Jtweeder graphics addgraphics * :pr:`5611`: BUG: Stop hardcoding parameters in results * :pr:`5612`: MAINT: Ensure no warnings are produced by foreign * :pr:`5613`: DOC: Improve PR template [skip ci] * :pr:`5614`: MAINT: Deprecate scale in test function * :pr:`5615`: Thequackdaddy docs * :pr:`5616`: Bulleted list and minor typos in ttest_ind * :pr:`5617`: CI: Implement azure-pipelines with multi-platform support * :pr:`5621`: CLN: simplify lint configuration, fix some invalid escapes * :pr:`5622`: DOC: Restore import * :pr:`5625`: Andrew d davis tukey pvals * :pr:`5626`: MAINT: Improve user-facing error message * :pr:`5627`: BLD: Remove redundant travis config * :pr:`5628`: MAINT: Relax tolerance on OSX only * :pr:`5630`: MAINT: Enable xdist on azure * :pr:`5631`: MAINT: Allow webuse fail * :pr:`5633`: TST: change skip to xfail for test_compare_numdiff on OSX * :pr:`5634`: Gabrielreid pandas multiindex handling bug * :pr:`5635`: MAINT: Add a codecov config file * :pr:`5636`: DOC: Update badges [skip ci] * :pr:`5637`: CLN: strict linting for tools directory * :pr:`5638`: MAINT: remove file with note to remove in 0.5.0 * :pr:`5640`: ENH: Improve error when ARMA endog is not 1d * :pr:`5641`: Josef pkt svar irf errband 5280 * :pr:`5642`: TST: Relax tolerance on OSX for OpenBlas issues * :pr:`5643`: MAINT: Consolidate platform checks * :pr:`5644`: CLN/DOC: Remove unused module, vbench references * :pr:`5645`: TST: Allow network failure in web tests * :pr:`5646`: BUG: Fix MANOVA when not using formulas * :pr:`5647`: TST: Adjust test_irf atol * :pr:`5648`: BUG: Replace midrule with hline * :pr:`5649`: CLN: strict linting for robust/tests directory * :pr:`5650`: MAINT: Fix error in lint script * :pr:`5652`: ENH/BUG: Use intercept form of trend / exog in VARMAX start params (not mean form) * :pr:`5653`: MAINT: Reformat exceptions * :pr:`5654`: Evgenyzhurko fix contingency table * :pr:`5655`: BUG: summary2 use float_format when creating `_simple_tables` see #1964 * :pr:`5656`: BLD: Add linting to azure * :pr:`5657`: TST: Protect multiprocess using test * :pr:`5658`: BLD: Match requirements in setup and requirements * :pr:`5659`: TST: Allow corr test to fail on Win32 * :pr:`5660`: MAINT: Fix make.bat [skip ci] * :pr:`5661`: TST: Relax test tolerance on OSX * :pr:`5662`: TST: Protect multiprocess on windows * :pr:`5663`: MAINT: Add test runners * :pr:`5664`: CLN: Fix and lint for E703 statements ending in semicolon * :pr:`5666`: TST: Relax tolerance for irf test on windows * :pr:`5667`: TST: Adjust tol and reset random state * :pr:`5668`: TST: Adjust tolerance for test on windows * :pr:`5669`: MAINT: Remove unused code * :pr:`5670`: Jim varanelli issue2781 * :pr:`5671`: BUG: fix stats.moment_helpers inplace modification * :pr:`5672`: ENH: Add cov type to summary for discrete models * :pr:`5673`: ENH: Allow comparing two samples with different sizes * :pr:`5675`: CLN: strict linting for emplike/tests * :pr:`5679`: DOC: Clarify that predict expects arrays in dicts [skip ci] * :pr:`5680`: ENH: Allow const idx to be found * :pr:`5681`: BUG: Always set mle_retvals * :pr:`5683`: BUG: Escape strings for latex output * :pr:`5684`: BUG: fix df in summary for single constraint in wald_test_terms * :pr:`5685`: Spelling * :pr:`5686`: DOC: Fix parameter description in weightstats * :pr:`5691`: MAINT: Near-duplicate example file, remove dominated version * :pr:`5693`: CLN: Fix invalid escapes where possible * :pr:`5694`: MAINT: Fix NameErrors in correlation_structures * :pr:`5695`: MAINT: remove NameError-having version of levinson_durbin, just keep … * :pr:`5696`: CLN: remove identical functions from garch * :pr:`5697`: CLN: strict linting for examples/ * :pr:`5698`: PERF: Avoid implicit check when hasconst * :pr:`5699`: BUG: Limit lag length in adf * :pr:`5700`: MAINT: Update import of URLError * :pr:`5701`: MAINT: missing imports, typos, fixes several NameErrors * :pr:`5702`: MAINT: clean up docstring'd-out failure in __main__ block * :pr:`5703`: MAINT: confirm that docstring'd-out traceback no longer raises; remove * :pr:`5704`: ENH: expose innovations computation method to API. * :pr:`5705`: WIP: TST: Sort dicts in test_multi * :pr:`5707`: ENH: KPSS - detailed error message when lags > nobs * :pr:`5709`: TST: Fix bad bash * :pr:`5710`: CLN: clean up over/under indentation in tsa.tests.results, E12 codes * :pr:`5712`: CLN: fix invalid escapes in test_stattools introduced in #5707 * :pr:`5713`: CLN/EX: Troubleshoot broken example, clean up now-working scratch paper * :pr:`5715`: CLN: ellipses-out invalid escapes traceback * :pr:`5716`: MAINT: Fix incorrect specification of loglike arg * :pr:`5717`: MAINT: fix non-working example ex_pandas * :pr:`5720`: CLN: remove impossible commented-out imports, close several * :pr:`5721`: CLN: strict linting for dimred, processreg, and their tests. * :pr:`5723`: Spelling fix in ValueError message * :pr:`5724`: MAINT: close assorted small issues * :pr:`5726`: DOC: Remove redundant attributes in GLM * :pr:`5728`: CLN: remove and lint for unused imports * :pr:`5729`: MAINT: use dummy_sparse func within method, see GH#5687 * :pr:`5730`: CLN: strict linting for discrete.tests.results * :pr:`5732`: CLN: strict linting for genmod/tests/results * :pr:`5734`: CLN: codes with only a few violations apiece * :pr:`5736`: CLN: strict linting for regression/tests/results * :pr:`5737`: CLN: strict linting for tsa.filters * :pr:`5738`: CLN: strict linting for stats/tests/results/ * :pr:`5740`: CLN: strict linting for tsa.tests.results * :pr:`5742`: CLN: strict linting for remaining results directories * :pr:`5743`: CLN: strict linting for results files in sandbox/regression/tests/ * :pr:`5744`: CLN: Fix/lint for dangerous redefinitions and comparisons * :pr:`5746`: MAINT: fix missing or redundant imports * :pr:`5748`: CLN: clean up adfvalues, avoid using `eval` * :pr:`5750`: CLN: E131 hanging indentation alignment * :pr:`5758`: CLN: lint for ambiguous variable names * :pr:`5760`: TST: test for intentionally emitted warnings, avoid some unintentional ones * :pr:`5762`: BUG: rename wts to weights issue #4725 * :pr:`5765`: BUG/TST: Fix+test pieces of code that would raise NameError * :pr:`5770`: DEPR: deprecate StataReader, StataWriter, genfromdta * :pr:`5771`: ENH: improve missing data handling for GEE * :pr:`5774`: PERF: use np.sum(...) instead of sum(...) * :pr:`5778`: CLN: strict linting for test_varmax * :pr:`5780`: TST: Protext against SSLError * :pr:`5781`: CLN: Replace #5779 * :pr:`5783`: BUG: Ensure coint_johansen runs with 0 lags * :pr:`5789`: BUG: GEE fit_history * :pr:`5791`: Holder bunch * :pr:`5792`: MAINT: matplotlib normed -> density * :pr:`5793`: MAINT: Adjust tolerance for random fail on OSX * :pr:`5796`: CLN: test_data.py * :pr:`5798`: BUG: ignore bugs instead of fixing them * :pr:`5801`: CI: Consolidate coveragerc spec * :pr:`5803`: ENH: QIF regression * :pr:`5805`: REF/CLN: collect imports at top of file, de-duplicate imports * :pr:`5815`: CLN: test_gee.py * :pr:`5816`: CLN: genmod/families/ * :pr:`5818`: CLN: qif * :pr:`5825`: MAINT: use correct key name to check cov params presence * :pr:`5830`: DOC: Add docstring for base class * :pr:`5831`: PERF: Import speed * :pr:`5833`: BUG: ARIMA fit with trend and constant exog * :pr:`5834`: DOC: Fix small errors in release notes * :pr:`5839`: MAINT: RangeIndex._start deprecated in pandas 0.25 * :pr:`5836`: CLN: over-indentation E117 * :pr:`5837`: CLN: invalid escapes in linear_model * :pr:`5843`: MAINT: Catch intentional warnings * :pr:`5846`: DOC: Update maintainer * :pr:`5847`: BUG: Allow NumPy ints # * :pr:`5848`: BUG: Warn rather than print * :pr:`5850`: MAINT: Improve error message * :pr:`5851`: BUG: Refactor method used to name variables * :pr:`5853`: BUG: Add check for xnames length * :pr:`5854`: BUG: Fix MNLogit summary with float values * :pr:`5857`: BUG: Allow categorical to accept pandas dtype * :pr:`5858`: BUG: Fix default alignment for SimpleTable * :pr:`5859`: DOC: fix incorrect ARResults.predict docstring, closes #4498 * :pr:`5860`: Cdown gofplot typerror * :pr:`5863`: MAINT: Use pd.Categorical() instead of .astype('categorical') * :pr:`5868`: BUG: State space univariate smoothing w/ time-varying transition matrix: wrong transition matrix used * :pr:`5869`: DOC: Improve ExponentialSmoothing docstring * :pr:`5875`: DOC: Improve bug report template * :pr:`5876`: BUG: Ensure keywords exist in partial reg plot * :pr:`5879`: DOC: Update version dropdown javascript statsmodels-0.12.2/docs/source/release/version0.11.1.rst000066400000000000000000000023071400612667500226750ustar00rootroot00000000000000:orphan: ============== Release 0.11.1 ============== Release summary =============== This is a bug release. Development summary and credits =============================== Besides receiving contributions for new and improved features and for bugfixes, important contributions to general maintenance for this release came from * Kerby Shedden * Josef Perktold * Alex Lyttle * Chad Fulton * Kevin Sheppard * Wouter De Coster Merged Pull Requests -------------------- The following Pull Requests were merged since the last release: * :pr:`6433`: TST/BUG: use reset_randomstate * :pr:`6438`: BUG: Change default optimizer for glm/ridge and make it user-settable * :pr:`6453`: DOC: Fix the version that appears in the documentation * :pr:`6456`: DOC: Send log to dev/null/ * :pr:`6461`: MAINT: correcting typo * :pr:`6465`: MAINT: Avoid noise in f-pvalue * :pr:`6469`: MAINT: Fix future warnings * :pr:`6470`: BUG: fix tukey-hsd for 1 pvalue * :pr:`6471`: MAINT: Fix issue with ragged array * :pr:`6474`: BLD: Use pip on Azure * :pr:`6515`: BUG: fix #6511 * :pr:`6520`: BUG: fix GAM for 1-dim exog_linear * :pr:`6534`: MAINT: Relax tolerance on test that occasionally fails * :pr:`6535`: MAINT: Restrict to Python 3.5+ statsmodels-0.12.2/docs/source/release/version0.11.rst000066400000000000000000001135241400612667500225420ustar00rootroot00000000000000:orphan: ============== Release 0.11.0 ============== Release summary =============== statsmodels is using github to store the updated documentation. Two version are available: - `Stable `_, the latest release - `Development `_, the latest build of the master branch **Warning** API stability is not guaranteed for new features, although even in this case changes will be made in a backwards compatible way if possible. The stability of a new feature depends on how much time it was already in statsmodels master and how much usage it has already seen. If there are specific known problems or limitations, then they are mentioned in the docstrings. Stats ----- **Issues Closed**: 335 **Pull Requests Merged**: 301 The Highlights ============== Regression ---------- Rolling OLS and WLS are implemented in :class:`~statsmodels.regression.rolling.RollingOLS` and :class:`~statsmodels.regression.rolling.RollingWLS`. These function similarly to the estimators recently removed from pandas. Statistics ---------- Add the Oaxaca-Blinder decomposition (:class:`~statsmodels.stats.oaxaca.OaxacaBlinder`) that decomposes the difference in group means into with and between components. Add the Distance dependence measures statistics (:func:`~statsmodels.stats.dist_dependence_measures.distance_statistics`) and the Distance Covariance test (:func:`~statsmodels.stats.dist_dependence_measures.distance_covariance_test`). Statespace Models ----------------- Linear exponential smoothing models ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - Model class: :class:`~statsmodels.tsa.statespace.ExponentialSmoothing` - Alternative to :class:`~statsmodels.tsa.statespace.exponential_smoothing.ExponentialSmoothing` - Only supports linear models - Is part of the class of state space models and so inherits some additional functionality. Methods to apply parameters fitted on one dataset to another dataset ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - Methods: ``extend``, ``append``, and ``apply``, for state space results classes - These methods allow applying fitted parameters from a training dataset to a test dataset in various ways - Useful for conveniently performing cross-validation exercises Method to hold some parameters fixed at known values ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - Methods: :func:`statsmodels.tsa.statespace.mlemodel.MLEModel.fix_params` and :func:`statsmodels.tsa.statespace.mlemodel.MLEModel.fit_constrained` for state space model classes. - These methods allow setting some parameters to known values and then estimating the remaining parameters Option for low memory operations ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - Argument: ``low_memory=True``, for ``fit``, ``filter``, and ``smooth`` - Only a subset of results are available when using this option, but it does allow for prediction, diagnostics, and forecasting - Useful to speed up cross-validation exercises Improved access to state estimates ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - Attribute: ``states``, for state space results classes - Wraps estimated states (predicted, filtered, smoothed) as Pandas objects with the appropriate index. - Adds human-readable names for states, where possible. Improved simulation and impulse responses for time-varying models ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - Argument: ``anchor`` allows specifying the period after which to begin the simulation. - Example: to simulate data following the sample period, use ``anchor='end'`` Time-Series Analysis -------------------- STL Decomposition ~~~~~~~~~~~~~~~~~ - Class implementing the STL decomposition :class:`~statsmodels.tsa.seasonal.STL`. New AR model ~~~~~~~~~~~~ - Model class: :class:`~statsmodels.tsa.ar_model.AutoReg` - Estimates parameters using conditional MLE (OLS) - Adds the ability to specify exogenous variables, include time trends, and add seasonal dummies. - The function :class:`~statsmodels.tsa.ar_model.ar_select_order` performs lag length selection for AutoReg models. New ARIMA model ~~~~~~~~~~~~~~~ - Model class: :class:`~statsmodels.tsa.arima.model.ARIMA` - Incorporates a variety of SARIMA estimators - MLE via state space methods (SARIMA models) - MLE via innovations algorithm (SARIMA models) - Hannan-Rissanen (ARIMA models) - Burg's method (AR models) - Innovations algorithm (MA models) - Yule-Walker (AR models) - Handles exogenous regressors via GLS or by MLE with state space methods. - Is part of the class of state space models and so inherits some additional functionality. Zivot-Andrews Test ~~~~~~~~~~~~~~~~~~ The Zivot-Andrews test for unit roots in the presence of structural breaks has been added in :func:`~statsmodels.tsa.stattools.zivot_andrews`. More robust regime switching models ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - Implementation of the Hamilton filter and Kim smoother in log space avoids underflow errors. What's new - an overview ======================== The following lists the main new features of statsmodels 0.11. In addition, release 0.11 includes bug fixes, refactorings and improvements in many areas. Major Feature ------------- - Allow fixing parameters in state space models (:pr:`5735`) - Add new version of ARIMA-type estimators (AR, ARIMA, SARIMAX) (:pr:`5827`) - Add STL decomposition for time series (:pr:`5926`) - Functional SIR (:pr:`5963`) - Zivot Andrews test (:pr:`6014`) - Added Oaxaca-Blinder Decomposition (:pr:`6026`) - Add rolling WLS and OLS (:pr:`6028`) - Replacement for AR (:pr:`6087`) Performance Improvements ------------------------ - Cythonize innovations algo and filter (:pr:`5947`) - Only perform required predict iterations in state space models (:pr:`6064`) - State space: Improve low memory usability; allow in fit, loglike (:pr:`6071`) Submodules ---------- ``base`` ~~~~~~~~ - Clarify xname length and purpose (:pr:`5957`) - Remove unnecessary pickle use (:pr:`6091`) - Fix accepting of eval environment for formula (:pr:`6152`) - Workaround NumPy ptp issue (:pr:`6316`) ``discrete`` ~~~~~~~~~~~~ - Test_constrained (:pr:`5821`) - Improve the cvxopt not found error (:pr:`6163`) ``genmod`` ~~~~~~~~~~ - Improvements to BayesMixedGLM docs, argument checking (:pr:`5895`) - Scale parameter handling in GEE (:pr:`6208`) - Add example notebook for GEE score tests (:pr:`6299`) - Fix bug in ridge for vector alpha (:pr:`6442`) ``graphics`` ~~~~~~~~~~~~ - Plot only unique censored points (:pr:`6124`) - Add missing keyword argument to plot_acf (:pr:`6227`) - And vlines option to plot_fit (:pr:`6266`) - Pass arguments through in plot_leverage_resid2 (:pr:`6281`) ``io`` ~~~~~~ - Clarify summary2 documentation (:pr:`6118`) ``nonparametric`` ~~~~~~~~~~~~~~~~~ - Ensure BW is not 0 (:pr:`6292`) - Check dtype in KDEUnivariate (:pr:`6314`) - Supporting custom kernel in local linear kernel regression (:pr:`6375`) ``regression`` ~~~~~~~~~~~~~~ - Test for anova_nistcertified (:pr:`5797`) - Remove no-longer-needed HC_se lookups (:pr:`5841`) - Dimension reduction for covariance matrices (:pr:`5852`) - Use class to define MixedLM variance components structure (:pr:`5898`) - Add rolling WLS and OLS (:pr:`6028`) - Prepare for Rolling Least Squares (:pr:`6056`) - Improve regression doc strings (:pr:`6077`) - Fix summary table header for mixedlm (:pr:`6217`) ``robust`` ~~~~~~~~~~ - Robust (:pr:`5819`) - Make mad function behave correctly when used on empty inputs (:pr:`5968`) ``stats`` ~~~~~~~~~ - Lilliefors min nobs not set (:pr:`5610`) - Replace alpha=0.05 with alpha=alpha (:pr:`5998`) - Added Oaxaca-Blinder Decomposition (:pr:`6026`) - Improve Ljung-Box (:pr:`6079`) - Correct thresholding in correlation tools (:pr:`6105`) - Use self.data consistently (:pr:`6144`) - Better argument checking for StratifiedTable (:pr:`6294`) - Restore multicomp (:pr:`6320`) - Improve Ljung Box diagnostics (:pr:`6324`) - Correct standardization in robust skewness (:pr:`6374`) - Distance dependence measures (:pr:`6401`) - Improve diagnostics (:pr:`6410`) ``tools`` ~~~~~~~~~ - Fix error introduced in isestimable (:pr:`6081`) - Fix axis in irq (:pr:`6391`) ``tsa`` ~~~~~~~ - Use cython fused types to simplify statespace code (:pr:`5283`) - Allow fixing parameters in state space models (:pr:`5735`) - Markov switching in log space: Hamilton filter / Kim smoother (:pr:`5826`) - Add new version of ARIMA-type estimators (AR, ARIMA, SARIMAX) (:pr:`5827`) - Exponential smoothing - damped trend gives incorrect param, predictions (:pr:`5893`) - State space: add methods to apply fitted parameters to new observations or new dataset (:pr:`5915`) - TVTP for Markov regression (:pr:`5917`) - Add STL decomposition for time series (:pr:`5926`) - Cythonize innovations algo and filter (:pr:`5947`) - Zivot Andrews test (:pr:`6014`) - Improve ARMA startparams (:pr:`6018`) - Fix ARMA so that it works with exog when trend=nc (:pr:`6070`) - Clean tsatools docs (:pr:`6075`) - Improve Ljung-Box (:pr:`6079`) - Replacement for AR (:pr:`6087`) - Incorrect TSA index if loc resolves to slice (:pr:`6130`) - Division by zero in exponential smoothing if damping_slope=0 (:pr:`6232`) - Forecasts now ignore non-monotonic period index (:pr:`6242`) - Hannan-Rissanen third stage is invalid if non-stationary/invertible (:pr:`6258`) - Fix notebook (:pr:`6279`) - Correct VAR summary when model contains exog variables (:pr:`6286`) - Fix conf interval with MI (:pr:`6297`) - Ensure inputs are finite in granger causality test (:pr:`6318`) - Fix trend due to recent changes (:pr:`6321`) - Improve Ljung Box diagnostics (:pr:`6324`) - Documentation for release v0.11 (:pr:`6338`) - Fix _get_index_loc with date strings (:pr:`6340`) - Use correct exog names (:pr:`6389`) ``tsa.statespace`` ~~~~~~~~~~~~~~~~~~ - Use cython fused types to simplify statespace code (:pr:`5283`) - Allow fixing parameters in state space models (:pr:`5735`) - Add new version of ARIMA-type estimators (AR, ARIMA, SARIMAX) (:pr:`5827`) - MLEModel now passes nobs to Representation (:pr:`6050`) - Only perform required predict iterations in state space models (:pr:`6064`) - State space: Improve low memory usability; allow in fit, loglike (:pr:`6071`) - State space: cov_params computation in fix_params context (:pr:`6072`) - Add conserve memory tests. (:pr:`6073`) - Improve cov_params in append, extend, apply (:pr:`6074`) - Seasonality in SARIMAX Notebook (:pr:`6096`) - Improve SARIMAX start_params if too few nobs (:pr:`6102`) - Fix score computation with fixed params (:pr:`6104`) - Add exact diffuse initialization as an option for SARIMAX, UnobservedComponents (:pr:`6111`) - Compute standardized forecast error in diffuse period if possible (:pr:`6131`) - Start_params for VMA model with exog. (:pr:`6133`) - Adds state space version of linear exponential smoothing models (:pr:`6179`) - State space: add wrapped states and, where possible, named states (:pr:`6181`) - Allow dynamic factor starting parameters computation with NaNs values (:pr:`6231`) - Dynamic factor model use AR model for error start params if error_var=False (:pr:`6233`) - SARIMAX index behavior with simple_differencing=True (:pr:`6239`) - Parameter names in DynamicFactor for unstructured error covariance matrix (:pr:`6240`) - SARIMAX: basic validation for order, seasonal_order (:pr:`6241`) - Update SARIMAX to use SARIMAXSpecification for more consistent input handling (:pr:`6250`) - State space: Add finer-grained memory conserve settings (:pr:`6254`) - Cloning of arima.ARIMA models. (:pr:`6260`) - State space: saving fixed params w/ extend, apply, append (:pr:`6261`) - State space: Improve simulate, IRF, prediction (:pr:`6280`) - State space: deprecate out-of-sample w/ unsupported index (:pr:`6332`) - State space: integer params can cause imaginary output (:pr:`6333`) - Append, extend check that index matches model (:pr:`6334`) - Fix k_exog, k_trend in arima.ARIMA; raise error when cloning a model with exog if no new exog given (:pr:`6337`) - Documentation for release v0.11 (:pr:`6338`) - RecursiveLS should not allow `fix_params` method. (:pr:`6415`) - More descriptive error message for recursive least squares parameter constraints. (:pr:`6424`) - Diffuse multivariate case w/ non-diagonal observation innovation covariance matrix (:pr:`6425`) ``tsa.vector.ar`` ~~~~~~~~~~~~~~~~~ - Raise in GC test for VAR(0) (:pr:`6285`) - Correct VAR summary when model contains exog variables (:pr:`6286`) - Use correct exog names (:pr:`6389`) Build ----- - Ignore warns on 32 bit linux (:pr:`6005`) - Travis CI: The sudo: tag is deprecated in Travis (:pr:`6161`) - Relax precision for ppc64el (:pr:`6222`) Documentation ------------- - Remove orphaned docs files (:pr:`5832`) - Array-like -> array_like (:pr:`5929`) - Change some more links to https (:pr:`5937`) - Fix self-contradictory minimum dependency versions (:pr:`5939`) - Fix formula for log-like in WLS (:pr:`5946`) - Fix typo (:pr:`5949`) - Add parameters for CountModel predict (:pr:`5986`) - Fix many spelling errors (:pr:`5992`) - Small fixups after the spell check (:pr:`5994`) - Clarify that GARCH models are deprecated (:pr:`6000`) - Added content for two headings in VAR docs (:pr:`6022`) - Fix regression doc strings (:pr:`6031`) - Add doc string check to doc build (:pr:`6036`) - Apply documentation standardizations (:pr:`6038`) - Fix spelling (:pr:`6041`) - Merge pull request #6041 from bashtage/doc-fixes (:pr:`6042`) - Fix notebook due to pandas index change (:pr:`6044`) - Remove warning due to deprecated features (:pr:`6045`) - Remove DynamicVAR (:pr:`6046`) - Small doc site improvements (:pr:`6048`) - Small fix ups for modernized size (:pr:`6052`) - More small doc fixes (:pr:`6053`) - Small changes to doc building (:pr:`6054`) - Use the working branch of numpy doc (:pr:`6055`) - Fix spelling in notebooks (:pr:`6057`) - Fix missing spaces around colon (:pr:`6058`) - Continue fixing docstring formatting (:pr:`6060`) - Fix web font size (:pr:`6062`) - Fix web font size (:pr:`6063`) - Fix doc errors affecting build (:pr:`6067`) - Improve docs in tools and ar_model (:pr:`6080`) - Improve filter docstrings (:pr:`6082`) - Spelling and notebook link (:pr:`6085`) - Website fix (:pr:`6089`) - Changes summary_col's docstring to match variables (:pr:`6106`) - Update spelling in CONTRIBUTING.rst (:pr:`6107`) - Update link in CONTRIBUTING.rst (:pr:`6108`) - Update PR template Numpy guide link (:pr:`6110`) - Added interpretations to LogitResults.get_margeff (:pr:`6113`) - Improve docstrings (:pr:`6116`) - Switch doc theme (:pr:`6119`) - Add initial API doc (:pr:`6120`) - Small improvements to docs (:pr:`6122`) - Switch doc icon (:pr:`6123`) - Fix doc build failure (:pr:`6125`) - Update templates and add missing API functions (:pr:`6126`) - Add missing functions from the API (:pr:`6134`) - Restructure the documentation (:pr:`6136`) - Add a new logo (:pr:`6142`) - Fix validator so that it works (:pr:`6143`) - Add formula API (:pr:`6145`) - Fix sidebar TOC (:pr:`6160`) - Warn that only trusted files should be unpickled (:pr:`6162`) - Update pickle warning (:pr:`6166`) - Fix warning format (:pr:`6167`) - Clarify req for cvxopt (:pr:`6198`) - Spelling and Doc String Fixes (:pr:`6204`) - Fix a typo (:pr:`6214`) - Fix typos in install.rst (:pr:`6215`) - Fix a typo (:pr:`6216`) - Docstring fixes (:pr:`6235`) - Fix spelling in notebooks (:pr:`6257`) - Clarify patsy 0.5.1 is required (:pr:`6275`) - Fix notebook (:pr:`6279`) - Close issues (:pr:`6283`) - Doc string changes (:pr:`6289`) - Correct spells (:pr:`6298`) - Add simple, documented script to get github info (:pr:`6303`) - Update test running instructions (:pr:`6317`) - Restore test() autosummary (:pr:`6319`) - Fix alpha description for GLMGam (:pr:`6322`) - Move api docs (:pr:`6327`) - Update Release Note (:pr:`6342`) - Fix documentation errors (:pr:`6343`) - Fixes in preparation for release (:pr:`6344`) - Further doc fixes (:pr:`6345`) - Fix minor doc errors (:pr:`6347`) - Git notes (:pr:`6348`) - Finalize release notes for 0.11 (:pr:`6349`) - Add version dropdown (:pr:`6350`) - Finalize release note (:pr:`6353`) - Change generated path (:pr:`6363`) - Doc updates (:pr:`6368`) - Improve doc strings (:pr:`6369`) - Clarify demeaning in ljungbox (:pr:`6390`) - Fix ridge regression formula in hpfilter (:pr:`6398`) - Fix link (:pr:`6407`) - Update release note for v0.11.0rc2 (:pr:`6416`) - Replace array with ndarray (:pr:`6447`) - Final release note change for 0.11 (:pr:`6450`) Maintenance ----------- - Implement cached_value, cached_data proof of concept (:pr:`4421`) - Use Appender pattern for docstrings (:pr:`5235`) - Remove sandbox.formula, supplanted by patsy (:pr:`5692`) - Remove docstring'd-out traceback for code that no longer raises (:pr:`5757`) - Enable/mark mangled/commented-out tests (:pr:`5768`) - Implement parts of #5220, deprecate ancient aliases (:pr:`5784`) - Catch warnings produced during tests (:pr:`5799`) - Parts of iolib (:pr:`5814`) - E701 multiple statements on one line (colon) (:pr:`5842`) - Remove ex_pairwise file dominated by try_tukey_hsd (:pr:`5856`) - Fix pandas compat (:pr:`5892`) - Use pytest.raises to check error message (:pr:`5897`) - Bump dependencies (:pr:`5910`) - Fix pandas imports (:pr:`5922`) - Remove Python 2.7 from Appveyor (:pr:`5927`) - Relax tol on test that randomly fails (:pr:`5931`) - Fix test that fails with positive probability (:pr:`5933`) - Port parts of #5220 (:pr:`5935`) - Remove Python 2.7 from travis (:pr:`5938`) - Fix linting failures (:pr:`5940`) - Drop redundant travis configs (:pr:`5950`) - Mark MPL test as MPL (:pr:`5954`) - Deprecate periodogram (:pr:`5958`) - Ensure seaborn is available for docbuild (:pr:`5960`) - Cython cleanups (:pr:`5962`) - Remove PY3 (:pr:`5965`) - Remove future and Python 2.7 (:pr:`5969`) - Remove string_types in favor of str (:pr:`5972`) - Restore ResettableCache (:pr:`5976`) - Cleanup legacy imports (:pr:`5977`) - Follow-up to #5956 (:pr:`5982`) - Clarify breusch_pagan is for scalars (:pr:`5984`) - Add W605 to lint codes (:pr:`5987`) - Follow-up to #5928 (:pr:`5988`) - Add spell checking (:pr:`5990`) - Remove comment no longer relevant (:pr:`5991`) - Refactor X13 testing (:pr:`6001`) - Standardized on nlags for acf/pacf (:pr:`6002`) - Rename forecast years to forecast periods (:pr:`6007`) - Improve testing of seasonal decompose (:pr:`6011`) - Remove notes about incorrect test (:pr:`6015`) - Turn relative import into an absolute import (:pr:`6030`) - Change types for future changes in NumPy (:pr:`6039`) - Move garch to archive/ (:pr:`6059`) - Fix small lint issue (:pr:`6066`) - Stop testing on old, buggy SciPy (:pr:`6069`) - Small fixes in preparation for larger changes (:pr:`6088`) - Add tools for programatically manipulating docstrings (:pr:`6090`) - Ensure r download cache works (:pr:`6092`) - Fix new cache name (:pr:`6093`) - Fix wrong test (:pr:`6094`) - Remove extra LICENSE.txt and setup.cfg (:pr:`6117`) - Be compatible with scipy 1.3 (:pr:`6164`) - Don't assume that 'python' is Python 3 (:pr:`6165`) - Exclude pytest-xdist 1.30 (:pr:`6205`) - Add Python 3.8 environment (:pr:`6246`) - Ignore vscode (:pr:`6255`) - Update test tolerance (:pr:`6288`) - Remove open_help method (:pr:`6290`) - Remove deprecated code in preparation for release (:pr:`6291`) - Deprecate recarray support (:pr:`6310`) - Reduce test size to prevent 32-bit crash (:pr:`6311`) - Remove chain dot (:pr:`6312`) - Catch and fix warnings (:pr:`6313`) - Use NumPy's linalg when available (:pr:`6315`) - Pin xdist (:pr:`6392`) - Unify pandas testing import (:pr:`6394`) - Clarify codecov (:pr:`6406`) - Port non-diagnostic changes (:pr:`6412`) - Fixes for future SciPY and pandas (:pr:`6414`) - Fixes for rc2 (:pr:`6419`) - Switch to bionic (:pr:`6423`) - Improve test that randomly fails (:pr:`6426`) - Fix future issues (:pr:`6440`) - Disable cvxopt for windows (:pr:`6445`) - Reduce tolerance on basin hopping test (:pr:`6448`) - Remove unused import (:pr:`6449`) bug-wrong --------- A new issue label `type-bug-wrong` indicates bugs that cause that incorrect numbers are returned without warnings. (Regular bugs are mostly usability bugs or bugs that raise an exception for unsupported use cases.) `see tagged issues `_ Major Bugs Fixed ================ See github issues for a list of bug fixes included in this release - `Closed bugs `_ - `Closed bugs (wrong result) `_ Development summary and credits =============================== Besides receiving contributions for new and improved features and for bugfixes, important contributions to general maintenance for this release came from - Chad Fulton - Brock Mendel - Peter Quackenbush - Kerby Shedden - Kevin Sheppard and the general maintainer and code reviewer - Josef Perktold Additionally, many users contributed by participation in github issues and providing feedback. Thanks to all of the contributors for the 0.10 release (based on git log): - Atticus Yang - Austin Adams - Balazs Varga - Brock Mendel - Chad Fulton - Christian Clauss - Emil Mirzayev - Graham Inggs - Guglielmo Saggiorato - Hassan Kibirige - Ian Preston - Jefferson Tweed - Josef Perktold - Keller Scholl - Kerby Shedden - Kevin Sheppard - Lucas Roberts - Mandy Gu - Omer Ozen - Padarn Wilson - Peter Quackenbush - Qingqing Mao - Rebecca N. Palmer - Ron Itzikovitch - Samesh Lakhotia - Sandu Ursu - Tim Staley - Varun Sriram - Yasine Gangat - comatrion - luxiform - partev - vegcev - 郭飞 These lists of names are automatically generated based on git log, and may not be complete. Merged Pull Requests -------------------- The following Pull Requests were merged since the last release: - :pr:`4421`: ENH: Implement cached_value, cached_data proof of concept - :pr:`5235`: STY: use Appender pattern for docstrings - :pr:`5283`: ENH: Use cython fused types to simplify statespace code - :pr:`5610`: BUG: Lilliefors min nobs not set - :pr:`5692`: MAINT: remove sandbox.formula, supplanted by patsy - :pr:`5735`: ENH: Allow fixing parameters in state space models - :pr:`5757`: MAINT: Remove docstring'd-out traceback for code that no longer raises - :pr:`5768`: WIP/TST: enable/mark mangled/commented-out tests - :pr:`5784`: MAINT: implement parts of #5220, deprecate ancient aliases - :pr:`5797`: TST: test for anova_nistcertified - :pr:`5799`: TST: Catch warnings produced during tests - :pr:`5814`: CLN: parts of iolib - :pr:`5819`: CLN: robust - :pr:`5821`: CLN: test_constrained - :pr:`5826`: ENH/REF: Markov switching in log space: Hamilton filter / Kim smoother - :pr:`5827`: ENH: Add new version of ARIMA-type estimators (AR, ARIMA, SARIMAX) - :pr:`5832`: DOC: remove orphaned docs files - :pr:`5841`: MAINT: remove no-longer-needed HC_se lookups - :pr:`5842`: CLN: E701 multiple statements on one line (colon) - :pr:`5852`: ENH: Dimension reduction for covariance matrices - :pr:`5856`: MAINT: remove ex_pairwise file dominated by try_tukey_hsd - :pr:`5892`: BUG: fix pandas compat - :pr:`5893`: BUG: exponential smoothing - damped trend gives incorrect param, predictions - :pr:`5895`: DOC: improvements to BayesMixedGLM docs, argument checking - :pr:`5897`: MAINT: Use pytest.raises to check error message - :pr:`5898`: ENH: use class to define MixedLM variance components structure - :pr:`5903`: BUG: Fix kwargs update bug in linear model fit_regularized - :pr:`5910`: MAINT: Bump dependencies - :pr:`5915`: ENH: state space: add methods to apply fitted parameters to new observations or new dataset - :pr:`5917`: BUG: TVTP for Markov regression - :pr:`5921`: BUG: Ensure exponential smoothers has continuous double data - :pr:`5922`: MAINT: Fix pandas imports - :pr:`5926`: ENH: Add STL decomposition for time series - :pr:`5927`: MAINT: Remove Python 2.7 from Appveyor - :pr:`5928`: ENH: Add array_like function to simplify input checking - :pr:`5929`: DOC: array-like -> array_like - :pr:`5930`: BUG: Limit lags in KPSS - :pr:`5931`: MAINT: Relax tol on test that randomly fails - :pr:`5933`: MAINT: Fix test that fails with positive probability - :pr:`5935`: CLN: port parts of #5220 - :pr:`5937`: DOC: Change some more links to https - :pr:`5938`: MAINT: Remove Python 2.7 from travis - :pr:`5939`: DOC: Fix self-contradictory minimum dependency versions - :pr:`5940`: MAINT: Fix linting failures - :pr:`5946`: DOC: Fix formula for log-like in WLS - :pr:`5947`: PERF: Cythonize innovations algo and filter - :pr:`5948`: ENH: Normalize eigenvectors from coint_johansen - :pr:`5949`: DOC: Fix typo - :pr:`5950`: MAINT: Drop redundant travis configs - :pr:`5951`: BUG: Fix mosaic plot with missing category - :pr:`5952`: ENH: Improve RESET test stability - :pr:`5953`: ENH: Add type checkers/converts for int, float and bool - :pr:`5954`: MAINT: Mark MPL test as MPL - :pr:`5956`: BUG: Fix multidimensional model cov_params when using pandas - :pr:`5957`: DOC: Clarify xname length and purpose - :pr:`5958`: MAINT: Deprecate periodogram - :pr:`5960`: MAINT: Ensure seaborn is available for docbuild - :pr:`5962`: CLN: cython cleanups - :pr:`5963`: ENH: Functional SIR - :pr:`5964`: ENH: Add start_params to RLM - :pr:`5965`: MAINT: Remove PY3 - :pr:`5966`: ENH: Add JohansenResults class - :pr:`5967`: BUG/ENH: Improve RLM in the case of perfect fit - :pr:`5968`: BUG: Make mad function behave correctly when used on empty inputs - :pr:`5969`: MAINT: Remove future and Python 2.7 - :pr:`5971`: BUG: Fix a future issue in ExpSmooth - :pr:`5972`: MAINT: Remove string_types in favor of str - :pr:`5976`: MAINT: Restore ResettableCache - :pr:`5977`: MAINT: Cleanup legacy imports - :pr:`5982`: CLN: follow-up to #5956 - :pr:`5983`: BUG: Fix return for RegressionResults - :pr:`5984`: MAINT: Clarify breusch_pagan is for scalars - :pr:`5986`: DOC: Add parameters for CountModel predict - :pr:`5987`: MAINT: add W605 to lint codes - :pr:`5988`: CLN: follow-up to #5928 - :pr:`5990`: MAINT/DOC: Add spell checking - :pr:`5991`: MAINT: Remove comment no longer relevant - :pr:`5992`: DOC: Fix many spelling errors - :pr:`5994`: DOC: Small fixups after the spell check - :pr:`5995`: ENH: Add R-squared and Adj. R_squared to summary_col - :pr:`5996`: BUG: Limit lags in KPSS - :pr:`5997`: ENH/BUG: Add check to AR instance to prevent bugs - :pr:`5998`: BUG: Replace alpha=0.05 with alpha=alpha - :pr:`5999`: ENH: Add summary to AR - :pr:`6000`: DOC: Clarify that GARCH models are deprecated - :pr:`6001`: MAINT: Refactor X13 testing - :pr:`6002`: MAINT: Standardized on nlags for acf/pacf - :pr:`6003`: BUG: Do not fit when fit=False - :pr:`6004`: ENH/BUG: Allow ARMA predict to swallow typ - :pr:`6005`: MAINT: Ignore warns on 32 bit linux - :pr:`6006`: BUG/ENH: Check exog in ARMA and ARIMA predict - :pr:`6007`: MAINT: Rename forecast years to forecast periods - :pr:`6008`: ENH: Allow GC testing for specific lags - :pr:`6009`: TST: Verify categorical is supported for MNLogit - :pr:`6010`: TST: Improve test that is failing due to precision issues - :pr:`6011`: MAINT/BUG/TST: Improve testing of seasonal decompose - :pr:`6012`: BUG: Fix t-test and f-test for multidimensional params - :pr:`6014`: ENH: Zivot Andrews test - :pr:`6015`: CLN: Remove notes about incorrect test - :pr:`6016`: TST: Add check for dtypes in Binomial - :pr:`6017`: ENH: Set limit for number of endog variables when using formulas - :pr:`6018`: ENH: Improve ARMA startparams - :pr:`6019`: BUG: Fix ARMA cov_params - :pr:`6020`: TST: Correct test to use trend not level - :pr:`6022`: DOC: added content for two headings in VAR docs - :pr:`6023`: TST: Verify missing exog raises in ARIMA - :pr:`6026`: WIP: Added Oaxaca-Blinder Decomposition - :pr:`6028`: ENH: Add rolling WLS and OLS - :pr:`6030`: MAINT: Turn relative import into an absolute import - :pr:`6031`: DOC: Fix regression doc strings - :pr:`6036`: BLD/DOC: Add doc string check to doc build - :pr:`6038`: DOC: Apply documentation standardizations - :pr:`6039`: MAINT: Change types for future changes in NumPy - :pr:`6041`: DOC: Fix spelling - :pr:`6042`: DOC: Merge pull request #6041 from bashtage/doc-fixes - :pr:`6044`: DOC: Fix notebook due to pandas index change - :pr:`6045`: DOC/MAINT: Remove warning due to deprecated features - :pr:`6046`: DOC: Remove DynamicVAR - :pr:`6048`: DOC: Small doc site improvements - :pr:`6050`: BUG: MLEModel now passes nobs to Representation - :pr:`6052`: DOC: Small fix ups for modernized size - :pr:`6053`: DOC: More small doc fixes - :pr:`6054`: DOC: Small changes to doc building - :pr:`6055`: DOC: Use the working branch of numpy doc - :pr:`6056`: MAINT: Prepare for Rolling Least Squares - :pr:`6057`: DOC: Fix spelling in notebooks - :pr:`6058`: DOC: Fix missing spaces around colon - :pr:`6059`: REF: move garch to archive/ - :pr:`6060`: DOC: Continue fixing docstring formatting - :pr:`6062`: DOC: Fix web font size - :pr:`6063`: DOC: Fix web font size - :pr:`6064`: ENH/PERF: Only perform required predict iterations in state space models - :pr:`6066`: MAINT: Fix small lint issue - :pr:`6067`: DOC: Fix doc errors affecting build - :pr:`6069`: MAINT: Stop testing on old, buggy SciPy - :pr:`6070`: BUG: Fix ARMA so that it works with exog when trend=nc - :pr:`6071`: ENH: state space: Improve low memory usability; allow in fit, loglike - :pr:`6072`: BUG: state space: cov_params computation in fix_params context - :pr:`6073`: TST: Add conserve memory tests. - :pr:`6074`: ENH: Improve cov_params in append, extend, apply - :pr:`6075`: DOC: Clean tsatools docs - :pr:`6077`: DOC: Improve regression doc strings - :pr:`6079`: ENH/DOC: Improve Ljung-Box - :pr:`6080`: DOC: Improve docs in tools and ar_model - :pr:`6081`: BUG: Fix error introduced in isestimable - :pr:`6082`: DOC: Improve filter docstrings - :pr:`6085`: DOC: Spelling and notebook link - :pr:`6087`: ENH: Replacement for AR - :pr:`6088`: MAINT: Small fixes in preparation for larger changes - :pr:`6089`: DOC: Website fix - :pr:`6090`: ENH/DOC: Add tools for programatically manipulating docstrings - :pr:`6091`: MAINT/SEC: Remove unnecessary pickle use - :pr:`6092`: MAINT: Ensure r download cache works - :pr:`6093`: MAINT: Fix new cache name - :pr:`6094`: TST: Fix wrong test - :pr:`6096`: DOC: Seasonality in SARIMAX Notebook - :pr:`6102`: ENH: Improve SARIMAX start_params if too few nobs - :pr:`6104`: BUG: Fix score computation with fixed params - :pr:`6105`: BUG: Correct thresholding in correlation tools - :pr:`6106`: DOC: Changes summary_col's docstring to match variables - :pr:`6107`: DOC: Update spelling in CONTRIBUTING.rst - :pr:`6108`: DOC: Update link in CONTRIBUTING.rst - :pr:`6110`: DOC: Update PR template Numpy guide link - :pr:`6111`: ENH: Add exact diffuse initialization as an option for SARIMAX, UnobservedComponents - :pr:`6113`: DOC: added interpretations to LogitResults.get_margeff - :pr:`6116`: DOC: Improve docstrings - :pr:`6117`: MAINT: Remove extra LICENSE.txt and setup.cfg - :pr:`6118`: DOC: Clarify summary2 documentation - :pr:`6119`: DOC: Switch doc theme - :pr:`6120`: DOC: Add initial API doc - :pr:`6122`: DOC: Small improvements to docs - :pr:`6123`: DOC: Switch doc icon - :pr:`6124`: ENH: Plot only unique censored points - :pr:`6125`: DOC: Fix doc build failure - :pr:`6126`: DOC: Update templates and add missing API functions - :pr:`6130`: BUG: Incorrect TSA index if loc resolves to slice - :pr:`6131`: ENH: Compute standardized forecast error in diffuse period if possible - :pr:`6133`: BUG: start_params for VMA model with exog. - :pr:`6134`: DOC: Add missing functions from the API - :pr:`6136`: DOC: Restructure the documentation - :pr:`6142`: DOC: Add a new logo - :pr:`6143`: DOC: Fix validator so that it works - :pr:`6144`: BUG: use self.data consistently - :pr:`6145`: DOC: Add formula API - :pr:`6152`: BUG: Fix accepting of eval environment for formula - :pr:`6160`: DOC: fix sidebar TOC - :pr:`6161`: BLD: Travis CI: The sudo: tag is deprecated in Travis - :pr:`6162`: DOC/SEC: Warn that only trusted files should be unpickled - :pr:`6163`: ENH: Improve the cvxopt not found error - :pr:`6164`: MAINT: Be compatible with scipy 1.3 - :pr:`6165`: MAINT: Don't assume that 'python' is Python 3 - :pr:`6166`: DOC: Update pickle warning - :pr:`6167`: DOC: Fix warning format - :pr:`6179`: ENH: Adds state space version of linear exponential smoothing models - :pr:`6181`: ENH: state space: add wrapped states and, where possible, named states - :pr:`6198`: DOC: Clarify req for cvxopt - :pr:`6204`: DOC: Spelling and Doc String Fixes - :pr:`6205`: MAINT: Exclude pytest-xdist 1.30 - :pr:`6208`: ENH: Scale parameter handling in GEE - :pr:`6214`: DOC: fix a typo - :pr:`6215`: DOC: fix typos in install.rst - :pr:`6216`: DOC: fix a typo - :pr:`6217`: BUG: Fix summary table header for mixedlm - :pr:`6222`: MAINT: Relax precision for ppc64el - :pr:`6227`: ENH: Add missing keyword argument to plot_acf - :pr:`6231`: BUG: allow dynamic factor starting parameters computation with NaNs values - :pr:`6232`: BUG: division by zero in exponential smoothing if damping_slope=0 - :pr:`6233`: BUG: dynamic factor model use AR model for error start params if error_var=False - :pr:`6235`: DOC: docstring fixes - :pr:`6239`: BUG: SARIMAX index behavior with simple_differencing=True - :pr:`6240`: BUG: parameter names in DynamicFactor for unstructured error covariance matrix - :pr:`6241`: BUG: SARIMAX: basic validation for order, seasonal_order - :pr:`6242`: BUG: Forecasts now ignore non-monotonic period index - :pr:`6246`: TST: Add Python 3.8 environment - :pr:`6250`: ENH: Update SARIMAX to use SARIMAXSpecification for more consistent input handling - :pr:`6254`: ENH: State space: Add finer-grained memory conserve settings - :pr:`6255`: MAINT: Ignore vscode - :pr:`6257`: DOC: Fix spelling in notebooks - :pr:`6258`: BUG: Hannan-Rissanen third stage is invalid if non-stationary/invertible - :pr:`6260`: BUG: cloning of arima.ARIMA models. - :pr:`6261`: BUG: state space: saving fixed params w/ extend, apply, append - :pr:`6266`: ENH: and vlines option to plot_fit - :pr:`6275`: MAINT/DOC: Clarify patsy 0.5.1 is required - :pr:`6279`: DOC: Fix notebook - :pr:`6280`: ENH: State space: Improve simulate, IRF, prediction - :pr:`6281`: BUG: Pass arguments through in plot_leverage_resid2 - :pr:`6283`: MAINT/DOC: Close issues - :pr:`6285`: BUG: Raise in GC test for VAR(0) - :pr:`6286`: BUG: Correct VAR summary when model contains exog variables - :pr:`6288`: MAINT: Update test tolerance - :pr:`6289`: DOC: doc string changes - :pr:`6290`: MAINT: Remove open_help method - :pr:`6291`: MAINT: Remove deprecated code in preparation for release - :pr:`6292`: BUG: Ensure BW is not 0 - :pr:`6294`: ENH: better argument checking for StratifiedTable - :pr:`6297`: BUG: Fix conf interval with MI - :pr:`6298`: DOC: Correct spells - :pr:`6299`: DOC: Add example notebook for GEE score tests - :pr:`6303`: DOC/MAINT: Add simple, documented script to get github info - :pr:`6310`: MAINT: Deprecate recarray support - :pr:`6311`: TST: Reduce test size to prevent 32-bit crash - :pr:`6312`: MAINT: Remove chain dot - :pr:`6313`: MAINT: Catch and fix warnings - :pr:`6314`: BUG: Check dtype in KDEUnivariate - :pr:`6315`: MAINT: Use NumPy's linalg when available - :pr:`6316`: MAINT: Workaround NumPy ptp issue - :pr:`6317`: DOC: Update test running instructions - :pr:`6318`: BUG: Ensure inputs are finite in granger causality test - :pr:`6319`: DOC: Restore test() autosummary - :pr:`6320`: BUG: Restore multicomp - :pr:`6321`: BUG: Fix trend due to recent changes - :pr:`6322`: DOC: fix alpha description for GLMGam - :pr:`6324`: ENH: Improve Ljung Box diagnostics - :pr:`6327`: DOC: Move api docs - :pr:`6332`: DEPR: state space: deprecate out-of-sample w/ unsupported index - :pr:`6333`: BUG: state space: integer params can cause imaginary output - :pr:`6334`: ENH: append, extend check that index matches model - :pr:`6337`: BUG: fix k_exog, k_trend in arima.ARIMA; raise error when cloning a model with exog if no new exog given - :pr:`6338`: DOC: Documentation for release v0.11 - :pr:`6340`: BUG: fix _get_index_loc with date strings - :pr:`6342`: DOC: Update Release Note - :pr:`6343`: DOC: Fix documentation errors - :pr:`6344`: DOC: Fixes in preparation for release - :pr:`6345`: DOC: Further doc fixes - :pr:`6347`: DOC: Fix minor doc errors - :pr:`6348`: DOC: git notes - :pr:`6349`: DOC: Finalize release notes for 0.11 - :pr:`6350`: DOC: Add version dropdown - :pr:`6353`: DOC: Finalize release note - :pr:`6363`: DOC: Change generated path - :pr:`6368`: Doc updates - :pr:`6369`: DOC: Improve doc strings - :pr:`6374`: BUG: Correct standardization in robust skewness - :pr:`6375`: ENH: Supporting custom kernel in local linear kernel regression - :pr:`6389`: BUG: Use correct exog names - :pr:`6390`: DOC: Clarify demeaning in ljungbox - :pr:`6391`: BUG: Fix axis in irq - :pr:`6392`: MAINT: Pin xdist - :pr:`6394`: MAINT: Unify pandas testing import - :pr:`6398`: DOC: fix ridge regression formula in hpfilter - :pr:`6401`: ENH: Distance dependence measures - :pr:`6406`: MAINT: Clarify codecov - :pr:`6407`: DOC: Fix link - :pr:`6410`: ENH/CLN: Improve diagnostics - :pr:`6412`: CLN/MAINT: Port non-diagnostic changes - :pr:`6414`: CLN: Fixes for future SciPY and pandas - :pr:`6415`: BUG: RecursiveLS should not allow `fix_params` method. - :pr:`6416`: DOC: Update release note for v0.11.0rc2 - :pr:`6419`: MAINT: Fixes for rc2 - :pr:`6422`: BUG: Improve executable detection - :pr:`6423`: MAINT: Switch to bionic - :pr:`6424`: REF: More descriptive error message for recursive least squares parameter constraints. - :pr:`6425`: BUG/ENH: Diffuse multivariate case w/ non-diagonal observation innovation covariance matrix - :pr:`6426`: TST: Improve test that randomly fails - :pr:`6440`: MAINT: Fix future issues - :pr:`6442`: BUG: Fix bug in ridge for vector alpha - :pr:`6445`: MAINT: Disable cvxopt for windows - :pr:`6447`: DOC: Replace array with ndarray - :pr:`6448`: MAINT: Reduce tolerance on basin hopping test - :pr:`6449`: MAINT: Remove unused import - :pr:`6450`: DOC: Final release note change for 0.11 statsmodels-0.12.2/docs/source/release/version0.12.1.rst000066400000000000000000000027651400612667500227060ustar00rootroot00000000000000:orphan: ============== Release 0.12.1 ============== Release summary =============== This is a bug fix release. Development summary and credits =============================== Besides receiving contributions for new and improved features and for bugfixes, important contributions to general maintenance for this release came from * Kevin Sheppard * Chad Fulton * Josef Perktold * Kerby Shedden * Pratyush Sharan Merged Pull Requests -------------------- The following Pull Requests were merged since the last release: * :pr:`7016`: BLD: avoid setuptools version 50, windows build problem * :pr:`7017`: BUG: param names with higher order trend in VARMAX * :pr:`7020`: REF: Don't validate specification in SARIMAX when cloning to get extended time varying matrices * :pr:`7025`: BUG: Ensure bestlag is defined in autolag * :pr:`7028`: BUG: Correct axis None case * :pr:`7040`: Bug fix ets get prediction * :pr:`7052`: ENH: handle/warn for singularities in MixedLM * :pr:`7055`: BUG: Fix squeeze when nsimulation is 1 * :pr:`7073`: DOC: fix several doc issues in stats functions * :pr:`7088`: DOC: augmented docstrings from statsmodels.base.optimizer * :pr:`7090`: DOC: Fix contradicting KPSS-statistics interpretations in stationarity_detrending_adf_kpss.ipynb * :pr:`7093`: BUG: Correct prediction intervals for ThetaModel * :pr:`7109`: some fixes in the doc of grangercausalitytests * :pr:`7116`: BUG: don't raise error in impacts table if no news. * :pr:`7118`: MAINT: Fix issues in master branches of dependencies statsmodels-0.12.2/docs/source/release/version0.12.2.rst000066400000000000000000000043401400612667500226760ustar00rootroot00000000000000:orphan: ============== Release 0.12.2 ============== Release summary =============== Statsmodels 0.12.2 is a bug-fix release with no new features compared to 0.12.1. Notable changes include fixes for a bug that could lead to incorrect results in forecasts with the new ARIMA model (when `d > 0` and `trend='t'`) and a bug in the LM test for autocorrelation. Documentation ------------- Documentation for the current release and for ongoing development are available at: - `Stable `_, the latest release - `Development `_, the latest build of the master branch Stats ----- **Issues Closed**: 42 **Pull Requests Merged**: 4 Major Bugs Fixed ================ The primary bugs fixed include: - :pr:`7250`: Bug in forecasting with new ARIMA model when `d > 0` and `trend='t'`. - :pr:`7259`: Bug in LM test for autocorrelation See github issues for a list of all bug fixes included in this release - `Closed bugs `_ - `Closed bugs (wrong result) `_ Development summary and credits =============================== Besides receiving contributions for new and improved features and for bugfixes, important contributions to general maintenance for this release came from - Chad Fulton - Brock Mendel - Peter Quackenbush - Kerby Shedden - Kevin Sheppard and the general maintainer and code reviewer - Josef Perktold Additionally, many users contributed by participation in github issues and providing feedback. Thanks to all of the contributors for the 0.12.2 release (based on git log): - Chad Fulton - Graham Inggs - Joris Van Den Bossche - Josef Perktold - Kevin Sheppard - Mike Ovyan - Natalie Heer These lists of names are automatically generated based on git log, and may not be complete. Merged Pull Requests -------------------- The following Pull Requests were merged since the last release: - :pr:`7123`: DOC: Port missed doc fix - :pr:`7221`: MAINT: Backport fixes for 0.12.2 compat release - :pr:`7222`: Backports - :pr:`7291`: Backports statsmodels-0.12.2/docs/source/release/version0.12.rst000066400000000000000000001325601400612667500225440ustar00rootroot00000000000000:orphan: ============== Release 0.12.0 ============== Release summary =============== statsmodels is using github to store the updated documentation. Two version are available: - `Stable `_, the latest release - `Development `_, the latest build of the master branch **Warning** API stability is not guaranteed for new features, although even in this case changes will be made in a backwards compatible way if possible. The stability of a new feature depends on how much time it was already in statsmodels master and how much usage it has already seen. If there are specific known problems or limitations, then they are mentioned in the docstrings. Stats ----- **Issues Closed**: 239 **Pull Requests Merged**: 221 The Highlights ============== Statistics ---------- New functions for hypothesis tests return a `HolderTuple` instance which allows tuple indexing and unpacking for ``(statistic, pvalue)``, but also has attribute access for those and for additional results statistics. Meta-Analysis ~~~~~~~~~~~~~ Functions for Meta-Analysis have been added in :mod:`~statsmodels.stats.meta_analysis`. The function :func:`~statsmodels.stats.meta_analysis.combine_effects` performs fixed effects and random effects analysis. Several methods such as Paule-Mandel and DerSimonian-Laird are available to estimate the random effects variance. The module also includes effect size functions for standardized mean difference and for proportions that can be used with :func:`~statsmodels.stats.meta_analysis.combine_effects`. A notebook illustrates the usage of the new features for meta-analysis. New hypothesis test for 2 samples ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Hypothesis tests, confidence intervals and power functions have been added for proportions from two independent samples. Inferential statistics are available for difference, ratio and odds-ratio of the two proportions. Equivalence testing for two independent proportions is available based on two one-sided tests TOST. Hypothesis tests including equivalence test, for the ratio of two independent Poisson rates are now available in :func:`~statsmodels.stats.rates.test_poisson_2indep` and :func:`~statsmodels.stats.rates.tost_poisson_2indep` Oneway ANOVA-type analysis ~~~~~~~~~~~~~~~~~~~~~~~~~~ Several statistical methods for ANOVA-type analysis of k independent samples have been added in module :mod:`~statsmodels.stats.oneway`. This includes standard Anova, Anova for unequal variances (Welch, Brown-Forsythe for mean), Anova based on trimmed samples (Yuen anova) and equivalence testing using the method of Wellek. Anova for equality of variances or dispersion are available for several transformations. This includes Levene test and Browne-Forsythe test for equal variances as special cases. It uses the `anova_oneway` function, so unequal variance and trimming options are also available for tests on variances. Several functions for effect size measures have been added, that can be used for reporting or for power and sample size computation. Multivariate statistics ~~~~~~~~~~~~~~~~~~~~~~~ The new module :mod:`~statsmodels.stats.multivariate` includes one and two sample tests for multivariate means, Hotelling's t-tests', :func:`~statsmodels.stats.multivariate.test_mvmean`, :func:`~statsmodels.stats.multivariate.test_mvmean_2indep` and confidence intervals for one-sample multivariate mean :func:`~statsmodels.stats.multivariate.confint_mvmean` Additionally, hypothesis tests for covariance patterns, and for oneway equality of covariances are now available in several ``test_cov`` functions. Time-Series Analysis -------------------- New exponential smoothing model: ETS (Error, Trend, Seasonal) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - Class implementing ETS models :class:`~statsmodels.tsa.exponential_smoothing.ets.ETSModel`. - Includes linear and non-linear exponential smoothing models - Supports parameter fitting, in-sample prediction and out-of-sample forecasting, prediction intervals, simulation, and more. - Based on the innovations state space approach. Statespace Models ----------------- New dynamic factor model for large datasets and monthly / quarterly mixed frequency models ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - New dynamic factor model :class:`~statsmodels.tsa.statespace.dynamic_factor_mq.DynamicFactorMQ`. - Allows for hundreds of observed variables, by fitting with the EM algorithm - Allows specifying factors that load only on a specific group of variables - Allows for monthly / quarterly mixed frequency models. For example, this supports one popular approach to "Nowcasting" GDP Decomposition of forecast updates based on the "news" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - New :meth:`~statsmodels.tsa.statespace.mlemodel.MLEResults.news` method for state space model results objects - Links updated data to changes in forecasts - Supports "nowcasting" exercises that progressively incorporate more and more information as time goes on Sparse Cholesky Simulation Smoother ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - New option for simulation smoothing in state space models via the "Cholesky factor algorithm" (CFA) approach in :class:`~statsmodels.tsa.statespace.cfa_simulation_smoother.CFASimulationSmoother` - Takes advantage of algorithms for sparse Cholesky factorization, rather than using the typical simulation smoother based on Kalman filtering and smoothing Option to use Chadrasekhar recursions ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - New option for state space models to use Chandrasekhar recursions rather than than the typical Kalman filtering recursions by setting ``filter_chandrasekhar=True``. - Improved performance for some models with large state vectors Forecasting Methods ~~~~~~~~~~~~~~~~~~~ Two popular method for forecasting time series, forecasting after STL decomposition (:class:`~statsmodels.tsa.forecasting.stl.STLForecast`) and the Theta model (:class:`~statsmodels.tsa.forecasting.theta.ThetaModel`) have been added. Complex Deterministic Terms ~~~~~~~~~~~~~~~~~~~~~~~~~~~ :class:`~statsmodels.tsa.deterministic.DeterministicProcess` can be used to generate deterministic processes containing time trends, seasonal dummies and Fourier components. A :class:`~statsmodels.tsa.deterministic.DeterministicProcess` can be used to produce in-sample regressors or out-of-sample values suitable for forecasting. What's new - an overview ======================== The following lists the main new features of statsmodels 0.12.0. In addition, release 0.12.0 includes bug fixes, refactorings and improvements in many areas. Submodules ---------- ``Documentation`` ~~~~~~~~~~~~~~~~~ - Fix the version that appears in the documentation (:pr:`6452`) - Send log to dev/null/ (:pr:`6456`) - Correct spelling of various (:pr:`6518`) - Fix typos (:pr:`6531`) - Update interactions_anova.ipynb (:pr:`6601`) - Fix `true` type on statespace docs page (:pr:`6616`) - Minor fixes for holtwinters simulate (:pr:`6631`) - Change OLS example to use datasets (:pr:`6656`) - Fix AutoReg docstring (:pr:`6662`) - Fix `fdrcorrection` docstring missing `is_sorted` parameter (:pr:`6680`) - Add new badges (:pr:`6704`) - Fix number if notebook text (:pr:`6709`) - Improve Factor and related docstrings (:pr:`6719`) - Improve explantion of missing values in ACF and related (:pr:`6726`) - Notebook for quasibinomial regression (:pr:`6732`) - Improve "conservative" doc (:pr:`6738`) - Update broken link (:pr:`6742`) - Fix broken links with 404 error (:pr:`6746`) - Demonstrate variance components analysis (:pr:`6758`) - Make deprecations more visible (:pr:`6775`) - Numpydoc signatures (:pr:`6825`) - Correct reference in docs (:pr:`6837`) - Include dot_plot (:pr:`6841`) - Updated durbin_watson Docstring and Tests (:pr:`6848`) - Explain low df in cluster (:pr:`6853`) - Fix common doc errors (:pr:`6862`) - Small doc fixes (:pr:`6874`) - Fix issues in docs related to exponential smoothing (:pr:`6879`) - Spelling and other doc fixes (:pr:`6902`) - Correct spacing around colon in docstrings (:pr:`6903`) - Initial 0.12 Release Note (:pr:`6923`) - Fix doc errors and silence warning (:pr:`6931`) - Clarify deprecations (:pr:`6932`) - Document exceptions and warnings (:pr:`6943`) - Update pandas function in hp_filter example (:pr:`6946`) - Prepare docs (:pr:`6948`) - Fix final issues in release note (:pr:`6951`) - Final doc fixed for 0.12.0rc0 (:pr:`6965`) - Update DeterministicProcess docs (:pr:`6968`) - Add docstring to string_like method (:pr:`6972`) - Fix LaTeX in seasonal notebook (:pr:`6976`) - Add new stats to release notes for 0.12 (:pr:`7001`) ``Performance`` ~~~~~~~~~~~~~~~ - State space: add Chandrasekhar recursions (:pr:`6411`) - Speed up HC2/HC3 standard error calculation, using less memory (:pr:`6664`) - Sparse matrices in MixedLM (:pr:`6766`) ``backport`` ~~~~~~~~~~~~ - `MLEResults.states.predicted` has wrong index (:pr:`6580`) - State space: simulate with time-varying covariance matrices. (:pr:`6607`) - State space: error with collapsed observations when missing (:pr:`6613`) - Dataframe/series concatenation in statespace results append (:pr:`6768`) - Pass cov_type, cov_kwargs through ARIMA.fit (:pr:`6770`) ``base`` ~~~~~~~~ - Don't attach patsy constraint instance (:pr:`6521`) - Fix constraints and bunds when use scipy.optimize.minimize (:pr:`6657`) - Correct shape of fvalue and f_pvalue (:pr:`6831`) - Correct dimension when data removed (:pr:`6888`) ``build`` ~~~~~~~~~ - Use pip on Azure (:pr:`6474`) - Attempt to cache key docbuild files (:pr:`6490`) - Improve doc caching (:pr:`6491`) - Azure: Mac OSX 10.13 -> 10.14 (:pr:`6587`) ``discrete`` ~~~~~~~~~~~~ - Don't attach patsy constraint instance (:pr:`6521`) - Sparse matrices in MixedLM (:pr:`6766`) - Catch warnings in discrete (:pr:`6836`) - Add improved .cdf() and .ppf() to discrete distributions (:pr:`6938`) - Remove k_extra from effects_idx (:pr:`6939`) - Improve count model tests (:pr:`6940`) ``docs`` ~~~~~~~~ - Fix doc errors and silence warning (:pr:`6931`) - Prepare docs (:pr:`6948`) ``duration`` ~~~~~~~~~~~~ - Allow more than 2 groups for survdiff in statsmodels.duration (:pr:`6626`) ``gam`` ~~~~~~~ - Fix GAM for 1-dim exog_linear (:pr:`6520`) - Fixed BSplines to match existing docs (:pr:`6915`) ``genmod`` ~~~~~~~~~~ - Change default optimizer for glm/ridge and make it user-settable (:pr:`6438`) - Fix exposure/offset handling in GEEResults (:pr:`6475`) - Use GLM starting values for QIF (:pr:`6514`) - Don't attach patsy constraint instance (:pr:`6521`) - Allow GEE weights to vary within clusters (:pr:`6582`) - Calculate AR covariance parameters for gridded data (:pr:`6621`) - Warn for non-convergence in elastic net (:pr:`6697`) - Gh 6627 (:pr:`6852`) - Change of BIC formula in GLM (:pr:`6941`) - Make glm's predict function return numpy array even if exposure is a pandas series (:pr:`6942`) - Fix check for offset_exposure in null (:pr:`6957`) - Add test for offset exposure null (:pr:`6959`) ``graphics`` ~~~~~~~~~~~~ - Include figsize as parameter for IRF plot (:pr:`6590`) - Speed up banddepth calculations (:pr:`6744`) - Fix logic in labeling corr plot (:pr:`6818`) - Enable qqplot_2sample to handle uneven samples (:pr:`6906`) - Support frozen dist in ProbPlots (:pr:`6910`) ``io`` ~~~~~~ - Handle pathlib.Path objects (:pr:`6654`) - Added label option to summary.to_latex() (:pr:`6895`) - Fixed the shifted column names in summary.to_latex() (:pr:`6900`) - Removed additional hline between tabulars (:pr:`6905`) ``maintenance`` ~~~~~~~~~~~~~~~ - Special docbuild (:pr:`6457`) - Special docbuild" (:pr:`6460`) - Correcting typo (:pr:`6461`) - Avoid noise in f-pvalue (:pr:`6465`) - Replace Python 3.5 with 3.8 on Azure (:pr:`6466`) - Update supported versions (:pr:`6467`) - Fix future warnings (:pr:`6469`) - Fix issue with ragged array (:pr:`6471`) - Avoid future error (:pr:`6473`) - Silence expected visible deprecation warning (:pr:`6477`) - Remove Python 3.5 references (:pr:`6492`) - Avoid calling depr code (:pr:`6493`) - Use travis cache and optimize build times (:pr:`6495`) - Relax tolerance on test that occasionally fails (:pr:`6534`) - Relax tolerance on test that randomly fails (:pr:`6588`) - Fix appveyor/conda (:pr:`6653`) - Delete empty directory (:pr:`6671`) - Flake8 fixes (:pr:`6710`) - Remove deprecated keyword (:pr:`6712`) - Remove OrderedDict (:pr:`6715`) - Remove dtype np.integer for avoid Dep Warning (:pr:`6728`) - Update pip-pre links (:pr:`6733`) - Spelling and small fixes (:pr:`6752`) - Remove error on FutureWarning (:pr:`6811`) - Fix failing tests (:pr:`6817`) - Replace Warnings with Notes in regression summary (:pr:`6828`) - Numpydoc should work now (:pr:`6842`) - Deprecate categorical (:pr:`6843`) - Remove redundant definition (:pr:`6845`) - Relax tolerance on test that fails Win32 (:pr:`6849`) - Fix error on nightly build (:pr:`6850`) - Correct debugging info (:pr:`6855`) - Mark VAR from_formula as NotImplemented (:pr:`6865`) - Allow skip if rdataset fails (:pr:`6871`) - Improve lint (:pr:`6885`) - Change default lag in serial correlation tests (:pr:`6893`) - Ensure setuptools is imported first (:pr:`6894`) - Remove FutureWarnings (:pr:`6920`) - Add tool to simplify documenting API in release notes (:pr:`6922`) - Relax test tolerance for future compat (:pr:`6945`) - Fixes for failures in wheel building (:pr:`6952`) - Fixes for wheel building (:pr:`6954`) - Remove print statements (:pr:`6985`) - Update Azure images (:pr:`6992`) ``multivariate`` ~~~~~~~~~~~~~~~~ - Multivariate mean tests and confint (:pr:`4107`) - Improve missing value handling in PCA (:pr:`6705`) ``nonparametric`` ~~~~~~~~~~~~~~~~~ - Fix #6511 (:pr:`6515`) - Fix domain check (:pr:`6547`) - Ensure sigma estimate is positive in KDE (:pr:`6713`) - Fix access to normal_reference_constant (:pr:`6806`) - Add xvals param to lowess smoother (:pr:`6908`) - Return self from KDEUnivariate fit (:pr:`6991`) - Allow custom bandwidth functions in KDEUnivariate fit (:pr:`7002`) ``regression`` ~~~~~~~~~~~~~~ - Statsmodels.regression.linear_model.OLS.fit_regularized fails to generate correct answer (#6604) (:pr:`6608`) - Change OLS example to use datasets (:pr:`6656`) - Speed up HC2/HC3 standard error calculation, using less memory (:pr:`6664`) - Fix summary col R2 ordering (:pr:`6714`) - Insufficient input checks in QuantReg (:pr:`6747`) - Add expanding initialization to RollingOLS/WLS (:pr:`6838`) - Add a note when R2 is uncentered (:pr:`6844`) ``robust`` ~~~~~~~~~~ - Add normalized iqr to robust.scales (:pr:`6969`) - Robust.scale.iqr does need centering, since quantiles are translation equivariant (:pr:`6973`) - Add robust qn scale (:pr:`6990`) - Fix bug where mad ignores center if center is not callable (:pr:`7000`) ``stats`` ~~~~~~~~~ - Multivariate mean tests and confint (:pr:`4107`) - Fix tukey-hsd for 1 pvalue (:pr:`6470`) - Add option for original Breusch-Pagan heteroscedasticity test (:pr:`6508`) - ENH Allow optional regularization in local fdr (:pr:`6622`) - Add meta-analysis (basic methods) (:pr:`6632`) - Add two independent proportion inference rebased (:pr:`6675`) - Rates, poisson means two-sample comparison rebased (:pr:`6677`) - Stats.base, add HolderTuple, Holder class with indexing (:pr:`6678`) - Add covariance structure hypothesis tests (:pr:`6693`) - Raise exception when recursive residual is not well defined (:pr:`6727`) - Mediation support for PH regression (:pr:`6782`) - Stats robust rebased2 (:pr:`6789`) - Hotelling's Two Sample Mean Test (:pr:`6810`) - Stats moment_helpers use random state in unit test (:pr:`6835`) - Updated durbin_watson Docstring and Tests (:pr:`6848`) - Add recent stats addition to docs (:pr:`6859`) - REF/DOC docs and refactor of recent stats (:pr:`6872`) - Api cleanup and improve docstrings in stats, round 3 (:pr:`6897`) - Improve descriptivestats (:pr:`6944`) - Catch warning (:pr:`6964`) ``tools`` ~~~~~~~~~ - Return column information in add_constant (:pr:`6830`) - Add QR-based matrix rank (:pr:`6834`) - Add Root Mean Square Percentage Error (:pr:`6926`) ``tsa`` ~~~~~~~ - Fixes #6553, sliced predicted values according to predicted index (:pr:`6556`) - Holt-Winters simulations (:pr:`6560`) - Example notebook (r): stationarity and detrending (ADF/KPSS) (:pr:`6614`) - Ensure text comparison is lower (:pr:`6628`) - Minor fixes for holtwinters simulate (:pr:`6631`) - New exponential smoothing implementation (:pr:`6699`) - Improve warning message in KPSS (:pr:`6711`) - Change trend initialization in STL (:pr:`6722`) - Add check in test_whiteness (:pr:`6723`) - Raise on incorrectly sized exog (:pr:`6730`) - Add deterministic processes (:pr:`6751`) - Add Theta forecasting method (:pr:`6767`) - Automatic lag selection for Box-Pierce, Ljung-Box #6645 (:pr:`6785`) - Fix missing str (:pr:`6827`) - Add support for PeriodIndex to AutoReg (:pr:`6829`) - Error in append for ARIMA model with trend (:pr:`6832`) - Add QR-based matrix rank (:pr:`6834`) - Rename unbiased to adjusted (:pr:`6839`) - Ensure PACF lag length is sensible (:pr:`6846`) - Allow Series as exog in predict (:pr:`6847`) - Raise on nonstationary parameters when attempting to use GLS (:pr:`6854`) - Relax test tolerance (:pr:`6856`) - Limit maxlags in VAR (:pr:`6867`) - Fix indexing with HoltWinters's forecast (:pr:`6869`) - Refactor Holt-Winters (:pr:`6870`) - Fix raise exception on granger causality test (:pr:`6877`) - Get_prediction method for ETS (:pr:`6882`) - Ets: test for simple exponential smoothing convergence (:pr:`6884`) - Added diagnostics test to ETS model (:pr:`6892`) - Stop transforming ES components (:pr:`6904`) - Fix extend in VARMAX with trend (:pr:`6909`) - Add STL Forecasting method (:pr:`6911`) - Dynamic is incorrect when not an int in statespace get_prediction (:pr:`6917`) - Correct IRF nobs with exog (:pr:`6925`) - Add get_prediction to AutoReg (:pr:`6927`) - Standardize forecast API (:pr:`6933`) - Fix small issues post ETS get_prediction merge (:pr:`6934`) - Modify failing test on Windows (:pr:`6949`) - Improve ETS / statespace documentation and highlights for v0.12 (:pr:`6950`) - Remove FutureWarnings (:pr:`6958`) ``tsa.statespace`` ~~~~~~~~~~~~~~~~~~ - State space: add Chandrasekhar recursions (:pr:`6411`) - Use reset_randomstate (:pr:`6433`) - State space: add "Cholesky factor algorithm" simulation smoothing (:pr:`6501`) - Bayesian estimation of SARIMAX using PyMC3 NUTS (:pr:`6528`) - State space: compute smoothed state autocovariance matrices for arbitrary lags (:pr:`6579`) - `MLEResults.states.predicted` has wrong index (:pr:`6580`) - State space: simulate with time-varying covariance matrices. (:pr:`6607`) - State space: error with collapsed observations when missing (:pr:`6613`) - Notebook describing how to create state space custom models (:pr:`6682`) - Fix covariance estimation in parameterless models (:pr:`6688`) - Fix state space linting errors. (:pr:`6698`) - Decomposition of forecast updates in state space models due to the "news" (:pr:`6765`) - Dataframe/series concatenation in statespace results append (:pr:`6768`) - Pass cov_type, cov_kwargs through ARIMA.fit (:pr:`6770`) - Improve univariate smoother performance (:pr:`6797`) - Add `news` example notebook image. (:pr:`6800`) - Fix extend in VARMAX with trend (:pr:`6909`) - Dynamic is incorrect when not an int in statespace get_prediction (:pr:`6917`) - Add dynamic factor model with EM algorithm, option for monthly/quarterly mixed frequency model (:pr:`6937`) - Improve ETS / statespace documentation and highlights for v0.12 (:pr:`6950`) - SARIMAX throwing different errors when length of endogenous var is too low (:pr:`6961`) - Fix start params computation with few nobs (:pr:`6962`) - Relax tolerance on random failure (:pr:`6963`) ``tsa.vector.ar`` ~~~~~~~~~~~~~~~~~ - Include figsize as parameter for IRF plot (:pr:`6590`) - Raise on incorrectly sized exog (:pr:`6730`) - Correct IRF nobs with exog (:pr:`6925`) bug-wrong --------- A new issue label `type-bug-wrong` indicates bugs that cause that incorrect numbers are returned without warnings. (Regular bugs are mostly usability bugs or bugs that raise an exception for unsupported use cases.) `see tagged issues `_ Major Bugs Fixed ================ See github issues for a list of bug fixes included in this release - `Closed bugs `_ - `Closed bugs (wrong result) `_ Development summary and credits =============================== Besides receiving contributions for new and improved features and for bugfixes, important contributions to general maintenance for this release came from - Chad Fulton - Brock Mendel - Peter Quackenbush - Kerby Shedden - Kevin Sheppard and the general maintainer and code reviewer - Josef Perktold Additionally, many users contributed by participation in github issues and providing feedback. Thanks to all of the contributors for the 0.12.0 release (based on git log): - Alex Lyttle - Amund Vedal - Baran Karakus - Batakrishna Sahu - Chad Fulton - Cinthia M. Tanaka - Dorian Bivolaru - Ezequiel Smucler - Giulio Beseghi - Haoyu Qi - Hassan Kibirige - He Yang - Henning Blunck - Jimmy2027 - Joon Ro - Joonsuk Park - Josef Perktold - Kerby Shedden - Kevin Rose - Kevin Sheppard - Manmeet Kumar Chaudhuri - Markus Löning - Martin Larralde - Nolan Conaway - Paulo Galuzio - Peter Prescott - Peter Quackenbush - Samuel Scherrer - Sean Lane - Sebastian Pölsterl - Skipper Seabold - Thomas Brooks - Thomas Marchand - Tim Gates - Victor Ananyev - Wouter De Coster - Zhiqing Xiao - adrienpacifico - aeturrell - cd - das-soham - eirki - pag - partev - tagoma - w31ha0 These lists of names are automatically generated based on git log, and may not be complete. Merged Pull Requests -------------------- The following Pull Requests were merged since the last release: - :pr:`4107`: ENH: multivariate mean tests and confint - :pr:`6411`: ENH: state space: add Chandrasekhar recursions - :pr:`6433`: TST/BUG: use reset_randomstate - :pr:`6438`: BUG: Change default optimizer for glm/ridge and make it user-settable - :pr:`6452`: DOC: Fix the version that appears in the documentation - :pr:`6456`: DOC: Send log to dev/null/ - :pr:`6457`: DOC: Special docbuild - :pr:`6460`: Revert "DOC: Special docbuild" - :pr:`6461`: MAINT: correcting typo - :pr:`6465`: MAINT: Avoid noise in f-pvalue - :pr:`6466`: MAINT: Replace Python 3.5 with 3.8 on Azure - :pr:`6467`: MAINT: Update supported versions - :pr:`6469`: MAINT: Fix future warnings - :pr:`6470`: BUG: fix tukey-hsd for 1 pvalue - :pr:`6471`: MAINT: Fix issue with ragged array - :pr:`6473`: MAINT: Avoid future error - :pr:`6474`: BLD: Use pip on Azure - :pr:`6475`: BUG: Fix exposure/offset handling in GEEResults - :pr:`6477`: BUG: Silence expected visible deprecation warning - :pr:`6490`: BLD: Attempt to cache key docbuild files - :pr:`6491`: BLD: Improve doc caching - :pr:`6492`: MAINT: Remove Python 3.5 references - :pr:`6493`: MAINT: Avoid calling depr code - :pr:`6495`: MAINT: Use travis cache and optimize build times - :pr:`6501`: ENH: state space: add "Cholesky factor algorithm" simulation smoothing - :pr:`6508`: ENH: Add option for original Breusch-Pagan heteroscedasticity test - :pr:`6514`: ENH: use GLM starting values for QIF - :pr:`6515`: BUG: fix #6511 - :pr:`6518`: DOC: Fix simple typo: various - :pr:`6520`: BUG: fix GAM for 1-dim exog_linear - :pr:`6521`: REF/BUG: don't attach patsy constraint instance - :pr:`6528`: DOC: Bayesian estimation of SARIMAX using PyMC3 NUTS - :pr:`6531`: DOC: fix typos - :pr:`6534`: MAINT: Relax tolerance on test that occasionally fails - :pr:`6547`: BUG: Fix domain check - :pr:`6556`: BUG: fixes #6553, sliced predicted values according to predicted index - :pr:`6560`: ENH: Holt-Winters simulations - :pr:`6579`: ENH: state space: compute smoothed state autocovariance matrices for arbitrary lags - :pr:`6580`: BUG: `MLEResults.states.predicted` has wrong index - :pr:`6582`: ENH: Allow GEE weights to vary within clusters - :pr:`6587`: BLD: Azure: Mac OSX 10.13 -> 10.14 - :pr:`6588`: MAINT: Relax tolerance on test that randomly fails - :pr:`6590`: ENH: Include figsize as parameter for IRF plot - :pr:`6601`: DOC: Update interactions_anova.ipynb - :pr:`6607`: BUG: state space: simulate with time-varying covariance matrices. - :pr:`6608`: BUG: statsmodels.regression.linear_model.OLS.fit_regularized fails to generate correct answer (#6604) - :pr:`6613`: BUG: state space: error with collapsed observations when missing - :pr:`6614`: DOC/ENH: example notebook (r): stationarity and detrending (ADF/KPSS) - :pr:`6616`: DOC: Fix `true` type on statespace docs page - :pr:`6621`: ENH: Calculate AR covariance parameters for gridded data - :pr:`6622`: ENH Allow optional regularization in local fdr - :pr:`6626`: ENH: allow more than 2 groups for survdiff in statsmodels.duration - :pr:`6628`: BUG: Ensure text comparison is lower - :pr:`6631`: DOC/TST: minor fixes for holtwinters simulate - :pr:`6632`: ENH: add meta-analysis (basic methods) - :pr:`6653`: MAINT: Fix appveyor/conda - :pr:`6654`: ENH: Handle pathlib.Path objects - :pr:`6656`: DOC: change OLS example to use datasets - :pr:`6657`: BUG: fix constraints and bunds when use scipy.optimize.minimize - :pr:`6662`: DOC: Fix AutoReg docstring - :pr:`6664`: PERF: Speed up HC2/HC3 standard error calculation, using less memory - :pr:`6671`: MAINT: Delete empty directory - :pr:`6675`: ENH: add two independent proportion inference rebased - :pr:`6677`: ENH: rates, poisson means two-sample comparison rebased - :pr:`6678`: ENH: stats.base, add HolderTuple, Holder class with indexing - :pr:`6680`: DOC: Fix `fdrcorrection` docstring missing `is_sorted` parameter - :pr:`6682`: ENH/DOC: Notebook describing how to create state space custom models - :pr:`6688`: BUG: Fix covariance estimation in parameterless models - :pr:`6693`: ENH: add covariance structure hypothesis tests - :pr:`6697`: ENH: Warn for non-convergence in elastic net - :pr:`6698`: CLN: Fix state space linting errors. - :pr:`6699`: ENH: New exponential smoothing implementation - :pr:`6704`: DOC: Add new badges - :pr:`6705`: BUG\ENH: Improve missing value handling in PCA - :pr:`6709`: DOC: Fix number if notebook text - :pr:`6710`: MAINT: Flake8 fixes - :pr:`6711`: ENH: Improve warning message in KPSS - :pr:`6712`: MAINT: Remove deprecated keyword - :pr:`6713`: BUG: Ensure sigma estimate is positive in KDE - :pr:`6714`: BUG: Fix summary col R2 ordering - :pr:`6715`: MAINT: Remove OrderedDict - :pr:`6719`: DOC: Improve Factor and related docstrings - :pr:`6722`: BUG: Change trend initialization in STL - :pr:`6723`: ENH: Add check in test_whiteness - :pr:`6726`: DOC: Improve explantion of missing values in ACF and related - :pr:`6727`: ENH: Raise exception when recursive residual is not well defined - :pr:`6728`: MAINT: Remove dtype np.integer for avoid Dep Warning - :pr:`6730`: BUG: Raise on incorrectly sized exog - :pr:`6732`: DOC: Notebook for quasibinomial regression - :pr:`6733`: MAINT: Update pip-pre links - :pr:`6738`: DOC: Improve "conservative" doc - :pr:`6742`: Update broken link - :pr:`6744`: ENH: Speed up banddepth calculations - :pr:`6746`: DOC: Fix broken links with 404 error - :pr:`6747`: BUG: Insufficient input checks in QuantReg - :pr:`6751`: ENH: Add deterministic processes - :pr:`6752`: MAINT: Spelling and small fixes - :pr:`6758`: DOC: Demonstrate variance components analysis - :pr:`6765`: ENH: Decomposition of forecast updates in state space models due to the "news" - :pr:`6766`: PERF: Sparse matrices in MixedLM - :pr:`6767`: ENH: Add Theta forecasting method - :pr:`6768`: BUG: dataframe/series concatenation in statespace results append - :pr:`6770`: BUG: pass cov_type, cov_kwargs through ARIMA.fit - :pr:`6775`: DOC: Make deprecations more visible - :pr:`6782`: ENH: Mediation support for PH regression - :pr:`6785`: ENH: automatic lag selection for Box-Pierce, Ljung-Box #6645 - :pr:`6789`: ENH: Stats robust rebased2 - :pr:`6797`: ENH: improve univariate smoother performance - :pr:`6800`: DOC: Add `news` example notebook image. - :pr:`6806`: BUG: Fix access to normal_reference_constant - :pr:`6810`: ENH: Hotelling's Two Sample Mean Test - :pr:`6811`: MAINT: Remove error on FutureWarning - :pr:`6817`: MAINT: Fix failing tests - :pr:`6818`: BUG: Fix logic in labeling corr plot - :pr:`6825`: DOC: Numpydoc signatures - :pr:`6827`: BUG: Fix missing str - :pr:`6828`: MAINT: Replace Warnings with Notes in regression summary - :pr:`6829`: ENH: Add support for PeriodIndex to AutoReg - :pr:`6830`: ENH: Return column information in add_constant - :pr:`6831`: BUG: Correct shape of fvalue and f_pvalue - :pr:`6832`: BUG: error in append for ARIMA model with trend - :pr:`6834`: ENH: Add QR-based matrix rank - :pr:`6835`: TST: stats moment_helpers use random state in unit test - :pr:`6836`: MAINT: Catch warnings in discrete - :pr:`6837`: DOC: Correct reference in docs - :pr:`6838`: ENH: Add expanding initialization to RollingOLS/WLS - :pr:`6839`: REF: Rename unbiased to adjusted - :pr:`6841`: DOC: Include dot_plot - :pr:`6842`: MAINT: numpydoc should work now - :pr:`6843`: MAINT: Deprecate categorical - :pr:`6844`: ENH: Add a note when R2 is uncentered - :pr:`6845`: MAINT: Remove redundant definition - :pr:`6846`: BUG: Ensure PACF lag length is sensible - :pr:`6847`: BUG: Allow Series as exog in predict - :pr:`6848`: Updated durbin_watson Docstring and Tests - :pr:`6849`: TST: Relax tolerance on test that fails Win32 - :pr:`6850`: MAINT: Fix error on nightly build - :pr:`6852`: Gh 6627 - :pr:`6853`: DOC: Explain low df in cluster - :pr:`6854`: BUG: Raise on nonstationary parameters when attempting to use GLS - :pr:`6855`: MAINT: Correct debugging info - :pr:`6856`: MAINT: Relax test tolerance - :pr:`6859`: DOC: add recent stats addition to docs - :pr:`6862`: DOC: Fix common doc errors - :pr:`6865`: MAINT: Mark VAR from_formula as NotImplemented - :pr:`6867`: BUG: Limit maxlags in VAR - :pr:`6868`: TST: Refactor factor tests again - :pr:`6869`: BUG: Fix indexing with HoltWinters's forecast - :pr:`6870`: REF: Refactor Holt-Winters - :pr:`6871`: MAINT: Allow skip if rdataset fails - :pr:`6872`: REF/DOC docs and refactor of recent stats - :pr:`6874`: DOC: Small doc fixes - :pr:`6877`: BUG: fix raise exception on granger causality test - :pr:`6879`: DOC: Fix issues in docs related to exponential smoothing - :pr:`6882`: ENH: get_prediction method for ETS - :pr:`6884`: TST: ets: test for simple exponential smoothing convergence - :pr:`6885`: MAINT: Improve lint - :pr:`6888`: BUG: Correct dimension when data removed - :pr:`6892`: ENH: added diagnostics test to ETS model - :pr:`6893`: MAINT: Change default lag in serial correlation tests - :pr:`6894`: MAINT: Ensure setuptools is imported first - :pr:`6895`: ENH: Added label option to summary.to_latex() - :pr:`6897`: REF/DOC: api cleanup and improve docstrings in stats, round 3 - :pr:`6900`: ENH: Fixed the shifted column names in summary.to_latex() - :pr:`6902`: DOC: Spelling and other doc fixes - :pr:`6903`: DOC: Correct spacing around colon in docstrings - :pr:`6904`: BUG: Stop transforming ES components - :pr:`6905`: ENH: removed additional hline between tabulars - :pr:`6906`: ENH: Enable qqplot_2sample to handle uneven samples - :pr:`6908`: ENH: Add xvals param to lowess smoother - :pr:`6909`: BUG: fix extend in VARMAX with trend - :pr:`6910`: ENH: Support frozen dist in ProbPlots - :pr:`6911`: ENH: Add STL Forecasting method - :pr:`6915`: BUG: Fixed BSplines to match existing docs - :pr:`6917`: BUG: dynamic is incorrect when not an int in statespace get_prediction - :pr:`6920`: MAINT: Remove FutureWarnings - :pr:`6922`: ENH: Add tool to simplify documenting API in release notes - :pr:`6923`: DOC: Initial 0.12 Release Note - :pr:`6925`: BUG: Correct IRF nobs with exog - :pr:`6926`: ENH: Add Root Mean Square Percentage Error - :pr:`6927`: ENH: Add get_prediction to AutoReg - :pr:`6931`: DOC/MAINT: Fix doc errors and silence warning - :pr:`6932`: DOC: Clarify deprecations - :pr:`6933`: MAINT: Standardize forecast API - :pr:`6934`: MAINT: Fix small issues post ETS get_prediction merge - :pr:`6937`: ENH: Add dynamic factor model with EM algorithm, option for monthly/quarterly mixed frequency model - :pr:`6938`: ENH: Add improved .cdf() and .ppf() to discrete distributions - :pr:`6939`: BUG: remove k_extra from effects_idx - :pr:`6940`: TST: Improve count model tests - :pr:`6941`: REF: Change of BIC formula in GLM - :pr:`6942`: BUG: Make glm's predict function return numpy array even if exposure is a pandas series - :pr:`6943`: DOC: Document exceptions and warnings - :pr:`6944`: ENH: improve descriptivestats - :pr:`6945`: MAINT: Relax test tolerance for future compat - :pr:`6946`: DOC: update pandas function in hp_filter example - :pr:`6948`: Prepare docs - :pr:`6949`: TST: Modify failing test on Windows - :pr:`6950`: DOC: improve ETS / statespace documentation and highlights for v0.12 - :pr:`6951`: DOC: Fix final issues in release note - :pr:`6952`: MAINT: Fixes for failures in wheel building - :pr:`6954`: MAINT: Fixes for wheel building - :pr:`6957`: BUG: Fix check for offset_exposure in null - :pr:`6958`: MAINT: Remove FutureWarnings - :pr:`6959`: TST: Add test for offset exposure null - :pr:`6961`: BUG: SARIMAX throwing different errors when length of endogenous var is too low - :pr:`6962`: BUG: Fix start params computation with few nobs - :pr:`6963`: TST: Relax tolerance on random failure - :pr:`6964`: MAINT: Catch warning - :pr:`6965`: DOC: Final doc fixed for 0.12.0rc0 - :pr:`6968`: DOC: Update DeterministicProcess docs - :pr:`6969`: ENH add normalized iqr to robust.scales - :pr:`6972`: DOC: Add docstring to string_like method - :pr:`6973`: ENH/BUG: robust.scale.iqr does need centering, since quantiles are translation equivariant - :pr:`6976`: DOC: Fix LaTeX in seasonal notebook - :pr:`6985`: MAINT: Remove print statements - :pr:`6990`: ENH: Add robust qn scale - :pr:`6991`: ENH: Return self from KDEUnivariate fit - :pr:`6992`: MAINT: Update Azure images - :pr:`7000`: BUG: fix bug where mad ignores center if center is not callable - :pr:`7001`: DOC: add new stats to release notes for 0.12 - :pr:`7002`: ENH: Allow custom bandwidth functions in KDEUnivariate fit API Changes =========== Notable New Classes ------------------- * :class:`statsmodels.stats.descriptivestats.Description` * :class:`statsmodels.stats.meta_analysis.CombineResults` * :class:`statsmodels.stats.robust_compare.TrimmedMean` * :class:`statsmodels.tools.sm_exceptions.ParseError` * :class:`statsmodels.tsa.base.prediction.PredictionResults` * :class:`statsmodels.tsa.deterministic.CalendarDeterministicTerm` * :class:`statsmodels.tsa.deterministic.CalendarFourier` * :class:`statsmodels.tsa.deterministic.CalendarSeasonality` * :class:`statsmodels.tsa.deterministic.CalendarTimeTrend` * :class:`statsmodels.tsa.deterministic.DeterministicProcess` * :class:`statsmodels.tsa.deterministic.DeterministicTerm` * :class:`statsmodels.tsa.deterministic.Fourier` * :class:`statsmodels.tsa.deterministic.FourierDeterministicTerm` * :class:`statsmodels.tsa.deterministic.Seasonality` * :class:`statsmodels.tsa.deterministic.TimeTrend` * :class:`statsmodels.tsa.deterministic.TimeTrendDeterministicTerm` * :class:`statsmodels.tsa.exponential_smoothing.ets.ETSModel` * :class:`statsmodels.tsa.exponential_smoothing.ets.ETSResults` * :class:`statsmodels.tsa.forecasting.stl.STLForecast` * :class:`statsmodels.tsa.forecasting.stl.STLForecastResults` * :class:`statsmodels.tsa.forecasting.theta.ThetaModel` * :class:`statsmodels.tsa.forecasting.theta.ThetaModelResults` * :class:`statsmodels.tsa.statespace.cfa_simulation_smoother.CFASimulationSmoother` * :class:`statsmodels.tsa.statespace.dynamic_factor_mq.DynamicFactorMQ` * :class:`statsmodels.tsa.statespace.dynamic_factor_mq.DynamicFactorMQResults` * :class:`statsmodels.tsa.statespace.news.NewsResults` Moved or Removed Classes ------------------------ * ``statsmodels.base._penalties.L2ContraintsPenalty`` * ``statsmodels.tools.docstring.ParseError`` * ``statsmodels.tsa.holtwinters.ExponentialSmoothing`` * ``statsmodels.tsa.holtwinters.Holt`` * ``statsmodels.tsa.holtwinters.HoltWintersResults`` * ``statsmodels.tsa.holtwinters.HoltWintersResultsWrapper`` * ``statsmodels.tsa.holtwinters.SimpleExpSmoothing`` * ``statsmodels.tsa.stattools.ResultsStore`` New Methods ----------- * :meth:`statsmodels.genmod.generalized_linear_model.GLMResults.bic` * :meth:`statsmodels.tsa.ar_model.AutoRegResults.forecast` * :meth:`statsmodels.tsa.ar_model.AutoRegResults.get_prediction` * :meth:`statsmodels.tsa.arima.model.ARIMAResults.append` * :meth:`statsmodels.tsa.base.prediction.PredictionResults.predicted_mean` * :meth:`statsmodels.tsa.base.prediction.PredictionResults.row_labels` * :meth:`statsmodels.tsa.base.prediction.PredictionResults.t_test` * :meth:`statsmodels.tsa.base.prediction.PredictionResults.tvalues` * :meth:`statsmodels.tsa.base.prediction.PredictionResults.var_pred_mean` * :meth:`statsmodels.tsa.statespace.kalman_smoother.SmootherResults.news` * :meth:`statsmodels.tsa.statespace.kalman_smoother.SmootherResults.smoothed_state_autocovariance` * :meth:`statsmodels.tsa.statespace.kalman_smoother.SmootherResults.smoothed_state_gain` * :meth:`statsmodels.tsa.statespace.mlemodel.MLEResults.news` * :meth:`statsmodels.tsa.statespace.representation.Representation.diff_endog` * :meth:`statsmodels.tsa.vector_ar.var_model.VAR.from_formula` Removed Methods --------------- * ``statsmodels.base.model.GEEResults.remove_data`` * ``statsmodels.base.model.NominalGEEResults.remove_data`` * ``statsmodels.base.model.OrdinalGEEResults.remove_data`` * ``statsmodels.base.model.VAR.from_formula`` * ``statsmodels.genmod._prediction.PredictionResults.se_obs`` * ``statsmodels.genmod._prediction.PredictionResults.t_test`` * ``statsmodels.genmod._prediction.PredictionResults.tvalues`` * ``statsmodels.genmod.generalized_estimating_equations.GEE.predict`` * ``statsmodels.genmod.generalized_estimating_equations.NominalGEE.predict`` * ``statsmodels.genmod.generalized_estimating_equations.OrdinalGEE.predict`` * ``statsmodels.tsa.statespace.mlemodel.ARIMAResults.append`` Methods with New Arguments -------------------------- * :meth:`statsmodels.discrete.discrete_model.BinaryModel`: ``check_rank`` * :meth:`statsmodels.discrete.discrete_model.CountModel`: ``check_rank`` * :meth:`statsmodels.discrete.discrete_model.DiscreteModel`: ``check_rank`` * :meth:`statsmodels.discrete.discrete_model.GeneralizedPoisson`: ``check_rank`` * :meth:`statsmodels.discrete.discrete_model.Logit`: ``check_rank`` * :meth:`statsmodels.discrete.discrete_model.MNLogit`: ``check_rank`` * :meth:`statsmodels.discrete.discrete_model.MultinomialModel`: ``check_rank`` * :meth:`statsmodels.discrete.discrete_model.NegativeBinomial`: ``check_rank`` * :meth:`statsmodels.discrete.discrete_model.NegativeBinomialP`: ``check_rank`` * :meth:`statsmodels.discrete.discrete_model.Poisson`: ``check_rank`` * :meth:`statsmodels.discrete.discrete_model.Probit`: ``check_rank`` * :meth:`statsmodels.duration.hazard_regression.PHReg`: ``pred_only`` * :meth:`statsmodels.duration.hazard_regression.rv_discrete_float`: ``n`` * :meth:`statsmodels.genmod.cov_struct.Autoregressive`: ``grid`` * :meth:`statsmodels.iolib.summary2.Summary`: ``label`` * :meth:`statsmodels.regression.mixed_linear_model.MixedLMResults`: ``fit_kwargs`` * :meth:`statsmodels.regression.recursive_ls.RecursiveLSResults`: ``copy_initialization`` * :meth:`statsmodels.regression.rolling.RollingOLS`: ``expanding`` * :meth:`statsmodels.regression.rolling.RollingWLS`: ``expanding`` * :meth:`statsmodels.stats.mediation.Mediation`: ``outcome_predict_kwargs`` * :meth:`statsmodels.tsa.ar_model.AutoReg`: ``deterministic``, ``old_names`` * :meth:`statsmodels.tsa.arima.model.ARIMAResults`: ``copy_initialization`` * :meth:`statsmodels.tsa.statespace.dynamic_factor.DynamicFactorResults`: ``copy_initialization`` * :meth:`statsmodels.tsa.statespace.exponential_smoothing.ExponentialSmoothingResults`: ``copy_initialization`` * :meth:`statsmodels.tsa.statespace.kalman_smoother.KalmanSmoother`: ``update_smoother``, ``update_filter``, ``update_representation`` * :meth:`statsmodels.tsa.statespace.mlemodel.MLEResults`: ``copy_initialization`` * :meth:`statsmodels.tsa.statespace.sarimax.SARIMAXResults`: ``copy_initialization`` * :meth:`statsmodels.tsa.statespace.simulation_smoother.SimulationSmoother`: ``update_smoother``, ``update_filter``, ``update_representation`` * :meth:`statsmodels.tsa.statespace.structural.UnobservedComponentsResults`: ``copy_initialization`` * :meth:`statsmodels.tsa.statespace.varmax.VARMAXResults`: ``truncate_endog_names`` * :meth:`statsmodels.tsa.vector_ar.irf.IRAnalysis`: ``figsize`` Methods with Changed Arguments ------------------------------ * :meth:`statsmodels.regression.mixed_linear_model.MixedLM` * New: ``MixedLM(start_params, reml, niter_sa, do_cg, fe_pen, cov_pen, free, full_output, method, fit_kwargs)`` * Old: ``MixedLM(start_params, reml, niter_sa, do_cg, fe_pen, cov_pen, free, full_output, method, kwargs)`` New Functions ------------- * :func:`statsmodels.robust.scale.iqr` * :func:`statsmodels.robust.scale.qn_scale` * :func:`statsmodels.stats.contrast.wald_test_noncent` * :func:`statsmodels.stats.contrast.wald_test_noncent_generic` * :func:`statsmodels.stats.descriptivestats.describe` * :func:`statsmodels.stats.meta_analysis.combine_effects` * :func:`statsmodels.stats.meta_analysis.effectsize_2proportions` * :func:`statsmodels.stats.meta_analysis.effectsize_smd` * :func:`statsmodels.stats.multivariate.confint_mvmean` * :func:`statsmodels.stats.multivariate.confint_mvmean_fromstats` * :func:`statsmodels.stats.multivariate.test_cov` * :func:`statsmodels.stats.multivariate.test_cov_blockdiagonal` * :func:`statsmodels.stats.multivariate.test_cov_diagonal` * :func:`statsmodels.stats.multivariate.test_cov_oneway` * :func:`statsmodels.stats.multivariate.test_cov_spherical` * :func:`statsmodels.stats.multivariate.test_mvmean` * :func:`statsmodels.stats.multivariate.test_mvmean_2indep` * :func:`statsmodels.stats.oneway.anova_generic` * :func:`statsmodels.stats.oneway.anova_oneway` * :func:`statsmodels.stats.oneway.confint_effectsize_oneway` * :func:`statsmodels.stats.oneway.confint_noncentrality` * :func:`statsmodels.stats.oneway.convert_effectsize_fsqu` * :func:`statsmodels.stats.oneway.effectsize_oneway` * :func:`statsmodels.stats.oneway.equivalence_oneway` * :func:`statsmodels.stats.oneway.equivalence_oneway_generic` * :func:`statsmodels.stats.oneway.equivalence_scale_oneway` * :func:`statsmodels.stats.oneway.f2_to_wellek` * :func:`statsmodels.stats.oneway.fstat_to_wellek` * :func:`statsmodels.stats.oneway.power_equivalence_oneway` * :func:`statsmodels.stats.oneway.simulate_power_equivalence_oneway` * :func:`statsmodels.stats.oneway.test_scale_oneway` * :func:`statsmodels.stats.oneway.wellek_to_f2` * :func:`statsmodels.stats.power.normal_power_het` * :func:`statsmodels.stats.power.normal_sample_size_one_tail` * :func:`statsmodels.stats.proportion.confint_proportions_2indep` * :func:`statsmodels.stats.proportion.power_proportions_2indep` * :func:`statsmodels.stats.proportion.samplesize_proportions_2indep_onetail` * :func:`statsmodels.stats.proportion.score_test_proportions_2indep` * :func:`statsmodels.stats.proportion.test_proportions_2indep` * :func:`statsmodels.stats.proportion.tost_proportions_2indep` * :func:`statsmodels.stats.rates.etest_poisson_2indep` * :func:`statsmodels.stats.rates.test_poisson_2indep` * :func:`statsmodels.stats.rates.tost_poisson_2indep` * :func:`statsmodels.stats.robust_compare.scale_transform` * :func:`statsmodels.stats.robust_compare.trim_mean` * :func:`statsmodels.stats.robust_compare.trimboth` * :func:`statsmodels.tools.eval_measures.rmspe` Removed Functions ----------------- * ``statsmodels.compat.python.iteritems`` * ``statsmodels.compat.python.iterkeys`` * ``statsmodels.compat.python.itervalues`` * ``statsmodels.stats.diagnostic.unitroot_adf`` * ``statsmodels.tools.decorators.nottest`` * ``statsmodels.tsa.stattools.periodogram`` Functions with New Arguments ---------------------------- * :func:`statsmodels.graphics.gofplots.qqline`: ``lineoptions`` * :func:`statsmodels.nonparametric.smoothers_lowess.lowess`: ``xvals`` * :func:`statsmodels.stats.diagnostic.acorr_ljungbox`: ``auto_lag`` * :func:`statsmodels.stats.diagnostic.het_breuschpagan`: ``robust`` * :func:`statsmodels.stats.diagnostic.linear_harvey_collier`: ``skip`` * :func:`statsmodels.stats.multitest.local_fdr`: ``alpha`` * :func:`statsmodels.tsa.ar_model.ar_select_order`: ``old_names`` Functions with Changed Arguments -------------------------------- * :func:`statsmodels.graphics.tsaplots.plot_acf` * New: ``plot_acf(x, ax, lags, alpha, use_vlines, adjusted, fft, missing, title, zero, vlines_kwargs, kwargs)`` * Old: ``plot_acf(x, ax, lags, alpha, use_vlines, unbiased, fft, missing, title, zero, vlines_kwargs, kwargs)`` * :func:`statsmodels.tsa.stattools.acf` * New: ``acf(x, adjusted, nlags, qstat, fft, alpha, missing)`` * Old: ``acf(x, unbiased, nlags, qstat, fft, alpha, missing)`` * :func:`statsmodels.tsa.stattools.acovf` * New: ``acovf(x, adjusted, demean, fft, missing, nlag)`` * Old: ``acovf(x, unbiased, demean, fft, missing, nlag)`` * :func:`statsmodels.tsa.stattools.ccf` * New: ``ccf(x, y, adjusted)`` * Old: ``ccf(x, y, unbiased)`` * :func:`statsmodels.tsa.stattools.ccovf` * New: ``ccovf(x, y, adjusted, demean)`` * Old: ``ccovf(x, y, unbiased, demean)`` * :func:`statsmodels.tsa.stattools.pacf_ols` * New: ``pacf_ols(x, nlags, efficient, adjusted)`` * Old: ``pacf_ols(x, nlags, efficient, unbiased)`` statsmodels-0.12.2/docs/source/release/version0.5.rst000066400000000000000000001067711400612667500224730ustar00rootroot00000000000000============= Release 0.5.0 ============= statsmodels 0.5 is a large and very exciting release that brings together a year of work done by 38 authors, including over 2000 commits. It contains many new features and a large amount of bug fixes detailed below. See the :ref:`list of fixed issues ` for specific closed issues. The following major new features appear in this version. Support for Model Formulas via Patsy ==================================== statsmodels now supports fitting models with a formula. This functionality is provided by `patsy `_. Patsy is now a dependency for statsmodels. Models can be individually imported from the ``statsmodels.formula.api`` namespace or you can import them all as:: import statsmodels.formula.api as smf Alternatively, each model in the usual ``statsmodels.api`` namespace has a ``from_formula`` classmethod that will create a model using a formula. Formulas are also available for specifying linear hypothesis tests using the ``t_test`` and ``f_test`` methods after model fitting. A typical workflow can now look something like this. .. code-block:: python import numpy as np import pandas as pd import statsmodels.formula.api as smf url = 'https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/csv/HistData/Guerry.csv' data = pd.read_csv(url) # Fit regression model (using the natural log of one of the regressors) results = smf.ols('Lottery ~ Literacy + np.log(Pop1831)', data=data).fit() See :ref:`here for some more documentation of using formulas in statsmodels ` Empirical Likelihood (Google Summer of Code 2012 project) --------------------------------------------------------- Empirical Likelihood-Based Inference for moments of univariate and multivariate variables is available as well as EL-based ANOVA tests. EL-based linear regression, including the regression through the origin model. In addition, the accelerated failure time model for inference on a linear regression model with a randomly right censored endogenous variable is available. Analysis of Variance (ANOVA) Modeling ------------------------------------- Support for ANOVA is now available including type I, II, and III sums of squares. See :ref:`anova`. .. currentmodule:: statsmodels.nonparametric Multivariate Kernel Density Estimators (GSoC 2012 project) ---------------------------------------------------------- Kernel density estimation has been extended to handle multivariate estimation as well via product kernels. It is available as :class:`sm.nonparametric.KDEMultivariate `. It supports least squares and maximum likelihood cross-validation for bandwidth estimation, as well as mixed continuous, ordered, and unordered categorical data. Conditional density estimation is also available via :class:`sm.nonparametric.KDEMUltivariateConditional `. Nonparameteric Regression (GSoC 2012 project) --------------------------------------------- Kernel regression models are now available via :class:`sm.nonparametric.KernelReg `. It is based on the product kernel mentioned above, so it also has the same set of features including support for cross-validation as well as support for estimation mixed continuous and categorical variables. Censored kernel regression is also provided by `kernel_regression.KernelCensoredReg`. Quantile Regression Model ------------------------- .. currentmodule:: statsmodels.regression.quantile_regression Quantile regression is supported via the :class:`sm.QuantReg ` class. Kernel and bandwidth selection options are available for estimating the asymptotic covariance matrix using a kernel density estimator. Negative Binomial Regression Model ---------------------------------- .. currentmodule:: statsmodels.discrete.discrete_model It is now possible to fit negative binomial models for count data via maximum-likelihood using the :class:`sm.NegativeBinomial ` class. ``NB1``, ``NB2``, and ``geometric`` variance specifications are available. l1-penalized Discrete Choice Models ----------------------------------- A new optimization method has been added to the discrete models, which includes Logit, Probit, MNLogit and Poisson, that makes it possible to estimate the models with an l1, linear, penalization. This shrinks parameters towards zero and can set parameters that are not very different from zero to zero. This is especially useful if there are a large number of explanatory variables and a large associated number of parameters. `CVXOPT `_ is now an optional dependency that can be used for fitting these models. New and Improved Graphics ------------------------- .. currentmodule:: statsmodels.graphics * **ProbPlot**: A new `ProbPlot` object has been added to provide a simple interface to create P-P, Q-Q, and probability plots with options to fit a distribution and show various reference lines. In the case of Q-Q and P-P plots, two different samples can be compared with the `other` keyword argument. :func:`sm.graphics.ProbPlot ` .. code-block:: python import numpy as np import statsmodels.api as sm x = np.random.normal(loc=1.12, scale=0.25, size=37) y = np.random.normal(loc=0.75, scale=0.45, size=37) ppx = sm.ProbPlot(x) ppy = sm.ProbPlot(y) fig1 = ppx.qqplot() fig2 = ppx.qqplot(other=ppy) * **Mosaic Plot**: Create a mosaic plot from a contingency table. This allows you to visualize multivariate categorical data in a rigorous and informative way. Available with :func:`sm.graphics.mosaic `. * **Interaction Plot**: Interaction plots now handle categorical factors as well as other improvements. :func:`sm.graphics.interaction_plot `. * **Regression Plots**: The regression plots have been refactored and improved. They can now handle pandas objects and regression results instances appropriately. See :func:`sm.graphics.plot_fit `, :func:`sm.graphics.plot_regress_exog `, :func:`sm.graphics.plot_partregress `, :func:`sm.graphics.plot_ccpr `, :func:`sm.graphics.abline_plot `, :func:`sm.graphics.influence_plot `, and :func:`sm.graphics.plot_leverage_resid2 `. .. currentmodule:: statsmodels.stats.power Power and Sample Size Calculations ---------------------------------- The power module (``statsmodels.stats.power``) currently implements power and sample size calculations for the t-tests (:class:`sm.stats.TTestPower `, :class:`sm.stats.TTestIndPower `), normal based test (:class:`sm.stats.NormIndPower `), F-tests (:class:`sm.stats.FTestPower `, `:class:sm.stats.FTestAnovaPower `) and Chisquare goodness of fit (:class:`sm.stats.GofChisquarePower `) test. The implementation is class based, but the module also provides three shortcut functions, :func:`sm.stats.tt_solve_power `, :func:`sm.stats.tt_ind_solve_power ` and :func:`sm.stats.zt_ind_solve_power ` to solve for any one of the parameters of the power equations. See this `blog post `_ for a more in-depth description of the additions. Other important new features ---------------------------- * **IPython notebook examples**: Many of our examples have been converted or added as IPython notebooks now. They are available `here `_. * **Improved marginal effects for discrete choice models**: Expanded options for obtaining marginal effects after the estimation of nonlinear discrete choice models are available. See :py:meth:`get_margeff `. * **OLS influence outlier measures**: After the estimation of a model with OLS, the common set of influence and outlier measures and a outlier test are now available attached as methods ``get_influnce`` and ``outlier_test`` to the Results instance. See :py:class:`OLSInfluence ` and :func:`outlier_test `. * **New datasets**: New :ref:`datasets ` are available for examples. * **Access to R datasets**: We now have access to many of the same datasets available to R users through the `Rdatasets project `_. You can access these using the :func:`sm.datasets.get_rdataset ` function. This function also includes caching of these datasets. * **Improved numerical differentiation tools**: Numerical differentiation routines have been greatly improved and expanded to cover all the routines discussed in:: Ridout, M.S. (2009) Statistical applications of the complex-step method of numerical differentiation. The American Statistician, 63, 66-74 See the :ref:`sm.tools.numdiff ` module. * **Consistent constant handling across models**: Result statistics no longer rely on the assumption that a constant is present in the model. * **Missing value handling across models**: Users can now control what models do in the presence of missing values via the ``missing`` keyword available in the instantiation of every model. The options are ``'none'``, ``'drop'``, and ``'raise'``. The default is ``'none'``, which does no missing value checks. To drop missing values use ``'drop'``. And ``'raise'`` will raise an error in the presence of any missing data. .. currentmodule:: statsmodels.iolib * **Ability to write Stata datasets**: Added the ability to write Stata ``.dta`` files. See :class:`sm.iolib.StataWriter `. .. currentmodule:: statsmodels.tsa.arima_model * **ARIMA modeling**: statsmodels now has support for fitting Autoregressive Integrated Moving Average (ARIMA) models. See :class:`ARIMA` and :class:`ARIMAResults` for more information. * **Support for dynamic prediction in AR(I)MA models**: It is now possible to obtain dynamic in-sample forecast values in :class:`ARMA` and :class:`ARIMA` models. * **Improved Pandas integration**: statsmodels now supports all frequencies available in pandas for time-series modeling. These are used for intelligent dates handling for prediction. These features are available, if you pass a pandas Series or DataFrame with a DatetimeIndex to a time-series model. .. currentmodule:: statsmodels * **New statistical hypothesis tests**: Added statistics for calculating interrater agreement including Cohen's kappa and Fleiss' kappa (See :ref:`interrater`), statistics and hypothesis tests for proportions (See :ref:`proportion stats `), Tukey HSD (with plot) was added as an enhancement to the multiple comparison tests (:class:`sm.stats.multicomp.MultiComparison `, :func:`sm.stats.multicomp.pairwise_tukeyhsd `). Weighted statistics and t tests were enhanced with new options. Tests of equivalence for one sample and two independent or paired samples were added based on t tests and z tests (See :ref:`tost`). Major Bugs fixed ---------------- * Post-estimation statistics for weighted least squares that depended on the centered total sum of squares were not correct. These are now correct and tested. See :issue:`501`. * Regression through the origin models now correctly use uncentered total sum of squares in post-estimation statistics. This affected the :math:`R^2` value in linear models without a constant. See :issue:`27`. Backwards incompatible changes and deprecations ----------------------------------------------- * Cython code is now non-optional. You will need a C compiler to build from source. If building from github and not a source release, you will also need Cython installed. See the :ref:`installation documentation `. * The ``q_matrix`` keyword to `t_test` and `f_test` for linear models is deprecated. You can now specify linear hypotheses using formulas. .. currentmodule:: statsmodels.tsa * The ``conf_int`` keyword to :func:`sm.tsa.acf ` is deprecated. * The ``names`` argument is deprecated in :class:`sm.tsa.VAR ` and `sm.tsa.SVAR `. This is now automatically detected and handled. .. currentmodule:: statsmodels.tsa * The ``order`` keyword to :py:meth:`sm.tsa.ARMA.fit ` is deprecated. It is now passed in during model instantiation. .. currentmodule:: statsmodels.distributions * The empirical distribution function (:class:`sm.distributions.ECDF `) and supporting functions have been moved to ``statsmodels.distributions``. Their old paths have been deprecated. * The ``margeff`` method of the discrete choice models has been deprecated. Use ``get_margeff`` instead. See above. Also, the vague ``resid`` attribute of the discrete choice models has been deprecated in favor of the more descriptive ``resid_dev`` to indicate that they are deviance residuals. .. currentmodule:: statsmodels.nonparametric.kde * The class ``KDE`` has been deprecated and renamed to :class:`KDEUnivariate` to distinguish it from the new ``KDEMultivariate``. See above. Development summary and credits ------------------------------- The previous version (statsmodels 0.4.3) was released on July 2, 2012. Since then we have closed a total of 380 issues, 172 pull requests and 208 regular issues. The :ref:`detailed list` can be viewed. This release is a result of the work of the following 38 authors who contributed total of 2032 commits. If for any reason, we have failed to list your name in the below, please contact us: * Ana Martinez Pardo * anov * avishaylivne * Bruno Rodrigues * Carl Vogel * Chad Fulton * Christian Prinoth * Daniel B. Smith * dengemann * Dieter Vandenbussche * Dougal Sutherland * Enrico Giampieri * evelynmitchell * George Panterov * Grayson * Jan Schulz * Josef Perktold * Jeff Reback * Justin Grana * langmore * Matthew Brett * Nathaniel J. Smith * otterb * padarn * Paul Hobson * Pietro Battiston * Ralf Gommers * Richard T. Guy * Robert Cimrman * Skipper Seabold * Thomas Haslwanter * timmie * Tom Augspurger * Trent Hauck * tylerhartley * Vincent Arel-Bundock * VirgileFritsch * Zhenya .. note:: Obtained by running ``git log v0.4.3..HEAD --format='* %aN <%aE>' | sed 's/@/\-at\-/' | sed 's/<>//' | sort -u``. .. _issues_list_05: Issues closed in the 0.5.0 development cycle ============================================ Issued closed in 0.5.0 ----------------------- GitHub stats for release 0.5.0 (07/02/2012/ - 08/14/2013/). We closed a total of 380 issues, 172 pull requests and 208 regular issues. This is the full list (generated with the script :file:`tools/github_stats.py`): This list is automatically generated, and may be incomplete: Pull Requests (172): * :pr:`1015`: DOC: Bump version. Remove done tasks. * :pr:`1010`: DOC/RLS: Update release notes workflow. Help Needed! * :pr:`1014`: DOC: nbgenerate does not like the comment at end of line. * :pr:`1012`: DOC: Add link to notebook and crosslink ref. Closes #924. * :pr:`997`: misc, tests, diagnostic * :pr:`1009`: MAINT: Add .mailmap file. * :pr:`817`: Add 3 new unit tests for arima_process * :pr:`1001`: BUG include_package_data for install closes #907 * :pr:`1005`: GITHUB: Contributing guidelines * :pr:`1007`: Cleanup docs for release * :pr:`1003`: BUG: Workaround for bug in sphinx 1.1.3. See #1002. * :pr:`1004`: DOC: Update maintainer notes with branching instructions. * :pr:`1000`: BUG: Support pandas 0.8.0. * :pr:`996`: BUG: Handle combo of pandas 0.8.0 and dateutils 1.5.0 * :pr:`995`: ENH: Print dateutil version. * :pr:`994`: ENH: Fail gracefully for version not found. * :pr:`993`: More conservative error catching in TimeSeriesModel * :pr:`992`: Misc fixes 12: adjustments to unit test * :pr:`985`: MAINT: Print versions script. * :pr:`986`: ENH: Prefer to_offset to get_offset. Closes #964. * :pr:`984`: COMPAT: Pandas 0.8.1 compatibility. Closes #983. * :pr:`982`: Misc fixes 11 * :pr:`978`: TST: generic mle pareto disable bsejac tests with estimated loc * :pr:`977`: BUG python 3.3 fix for numpy str TypeError, see #633 * :pr:`975`: Misc fixes 10 numdiff * :pr:`970`: BUG: array too long, raises exception with newer numpy closes #967 * :pr:`965`: Vincent summary2 rebased * :pr:`933`: Update and improve GenericlikelihoodModel and miscmodels * :pr:`950`: BUG/REF mcnemar fix exact pvalue, allow table as input * :pr:`951`: Pylint emplike formula genmod * :pr:`956`: Fix a docstring in KDEMultivariateConditional. * :pr:`949`: BUG fix lowess sort when nans closes #946 * :pr:`932`: ENH: support basinhopping solver in LikelihoodModel.fit() * :pr:`927`: DOC: clearer minimal example * :pr:`919`: OLS summary crash * :pr:`918`: Fixes10 emplike lowess * :pr:`909`: Bugs in GLM pvalues, more tests, pylint * :pr:`906`: ENH: No fmax with Windows SDK so define inline. * :pr:`905`: MAINT more fixes * :pr:`898`: Misc fixes 7 * :pr:`896`: Quantreg rebase2 * :pr:`895`: Fixes issue #832 * :pr:`893`: ENH: Remove unneeded restriction on low. Closes #867. * :pr:`894`: MAINT: Remove broken function. Keep deprecation. Closes #781. * :pr:`856`: Carljv improved lowess rebased2 * :pr:`884`: Pyflakes cleanup * :pr:`887`: BUG: Fix kde caching * :pr:`883`: Fixed pyflakes issue in discrete module * :pr:`882`: Update predstd.py * :pr:`871`: Update of sandbox doc * :pr:`631`: WIP: Correlation positive semi definite * :pr:`857`: BLD: apt get dependencies from Neurodebian, whitespace cleanup * :pr:`855`: AnaMP issue 783 mixture rvs tests rebased * :pr:`854`: Enrico multinear rebased * :pr:`849`: Tyler tukeyhsd rebased * :pr:`848`: BLD TravisCI use python-dateutil package * :pr:`784`: Misc07 cleanup multipletesting and proportions * :pr:`841`: ENH: Add load function to main API. Closes #840. * :pr:`820`: Ensure that tuples are not considered as data, not as data containers * :pr:`822`: DOC: Update for Cython changes. * :pr:`765`: Fix build issues * :pr:`800`: Automatically generate output from notebooks * :pr:`802`: BUG: Use two- not one-sided t-test in t_test. Closes #740. * :pr:`806`: ENH: Import formula.api in statsmodels.api namespace. * :pr:`803`: ENH: Fix arima error message for bad start_params * :pr:`801`: DOC: Fix ANOVA section titles * :pr:`795`: Negative Binomial Rebased * :pr:`787`: Origintests * :pr:`794`: ENH: Allow pandas-in/pandas-out in tsa.filters * :pr:`791`: Github stats for release notes * :pr:`779`: added np.asarray call to durbin_watson in stattools * :pr:`772`: Anova docs * :pr:`776`: BUG: Fix dates_from_range with length. Closes #775. * :pr:`774`: BUG: Attach prediction start date in AR. Closes #773. * :pr:`767`: MAINT: Remove use of deprecated from examples and docs. * :pr:`762`: ENH: Add new residuals to wrapper * :pr:`754`: Fix arima predict * :pr:`760`: ENH: Adjust for k_trend in information criteria. Closes #324. * :pr:`761`: ENH: Fixes and tests sign_test. Closes #642. * :pr:`759`: Fix 236 * :pr:`758`: DOC: Update VAR docs. Closes #537. * :pr:`752`: Discrete cleanup * :pr:`750`: VAR with 1d array * :pr:`748`: Remove reference to new_t_test and new_f_test. * :pr:`739`: DOC: Remove outdated note in docstring * :pr:`732`: BLD: Check for patsy dependency at build time + docs * :pr:`731`: Handle wrapped * :pr:`730`: Fix opt fulloutput * :pr:`729`: Get rid of warnings in docs build * :pr:`698`: update url for hsb2 dataset * :pr:`727`: DOC: Fix indent and add missing params to linear models. Closes #709. * :pr:`726`: CLN: Remove unused method. Closes #694 * :pr:`725`: BUG: Should call anova_single. Closes #702. * :pr:`723`: Rootfinding for Power * :pr:`722`: Handle pandas.Series with names in make_lags * :pr:`714`: Fix 712 * :pr:`668`: Allow for any pandas frequency to be used in TimeSeriesModel. * :pr:`711`: Misc06 - bug fixes * :pr:`708`: BUG: Fix one regressor case for conf_int. Closes #706. * :pr:`700`: Bugs rebased * :pr:`680`: BUG: Swap arguments in fftconvolve for scipy >= 0.12.0 * :pr:`640`: Misc fixes 05 * :pr:`663`: a typo in runs.py doc string for mcnemar test * :pr:`652`: WIP: fixing pyflakes / pep8, trying to improve readability * :pr:`619`: DOC: intro to formulas * :pr:`648`: BF: Make RLM stick to Huber's description * :pr:`649`: Bug Fix * :pr:`637`: Pyflakes cleanup * :pr:`634`: VAR DOC typo * :pr:`623`: Slowtests * :pr:`621`: MAINT: in setup.py, only catch ImportError for pandas. * :pr:`590`: Cleanup test output * :pr:`591`: Interrater agreement and reliability measures * :pr:`618`: Docs fix the main warnings and errors during sphinx build * :pr:`610`: nonparametric examples and some fixes * :pr:`578`: Fix 577 * :pr:`575`: MNT: Remove deprecated scikits namespace * :pr:`499`: WIP: Handle constant * :pr:`567`: Remove deprecated * :pr:`571`: Dataset docs * :pr:`561`: Grab rdatasets * :pr:`570`: DOC: Fixed links to Rdatasets * :pr:`524`: DOC: Clean up discrete model documentation. * :pr:`506`: ENH: Re-use effects if model fit with QR * :pr:`556`: WIP: L1 doc fix * :pr:`564`: TST: Use native integer to avoid issues in dtype asserts * :pr:`543`: Travis CI using M.Brett nipy hack * :pr:`558`: Plot cleanup * :pr:`541`: Replace pandas DataMatrix with DataFrame * :pr:`534`: Stata test fixes * :pr:`532`: Compat 323 * :pr:`531`: DOC: Add ECDF to distributions docs * :pr:`526`: ENH: Add class to write Stata binary dta files * :pr:`521`: DOC: Add abline plot to docs * :pr:`518`: Small fixes: interaction_plot * :pr:`508`: ENH: Avoid taking cholesky decomposition of diagonal matrix * :pr:`509`: DOC: Add ARIMA to docs * :pr:`510`: DOC: realdpi is disposable personal income. Closes #394. * :pr:`507`: ENH: Protect numdifftools import. Closes #45 * :pr:`504`: Fix weights * :pr:`498`: DOC: Add patys requirement to install docs * :pr:`491`: Make _data a public attribute. * :pr:`494`: DOC: Fix pandas links * :pr:`492`: added intersphinx for pandas * :pr:`422`: Handle missing data * :pr:`485`: ENH: Improve error message for pandas objects without dates in index * :pr:`428`: Remove other data * :pr:`483`: Arima predict bug * :pr:`482`: TST: Do array-array comparison when using numpy.testing * :pr:`471`: Formula rename df -> data * :pr:`473`: Vincent docs tweak rebased * :pr:`468`: Docs 050 * :pr:`462`: El aft rebased * :pr:`461`: TST: numpy 1.5.1 compatibility * :pr:`460`: Emplike desc reg rebase * :pr:`410`: Discrete model marginal effects * :pr:`417`: Numdiff cleanup * :pr:`398`: Improved plot_corr and plot_corr_grid functions. * :pr:`401`: BUG: Finish refactoring margeff for dummy. Closes #399. * :pr:`400`: MAINT: remove lowess.py, which was kept in 0.4.x for backwards compatibi... * :pr:`371`: BF+TEST: fixes, checks and tests for isestimable * :pr:`351`: ENH: Copy diagonal before write for upcoming numpy changes * :pr:`384`: REF: Move mixture_rvs out of sandbox. * :pr:`368`: ENH: Add polished version of acf/pacf plots with confidence intervals * :pr:`378`: Infer freq * :pr:`374`: ENH: Add Fair's extramarital affair dataset. From tobit-model branch. * :pr:`358`: ENH: Add method to OLSResults for outlier detection * :pr:`369`: ENH: allow predict to pass through patsy for transforms * :pr:`352`: Formula integration rebased * :pr:`360`: REF: Deprecate order in fit and move to ARMA init * :pr:`366`: Version fixes * :pr:`359`: DOC: Fix sphinx warnings Issues (208): * :issue:`1036`: Series no longer inherits from ndarray * :issue:`1038`: DataFrame with integer names not handled in ARIMA * :issue:`1028`: Test fail with windows and Anaconda - Low priority * :issue:`676`: acorr_breush_godfrey undefined nlags * :issue:`922`: lowess returns inconsistent with option * :issue:`425`: no bse in robust with norm=TrimmedMean * :issue:`1025`: add_constant incorrectly detects constant column * :issue:`533`: py3 compatibility ``pandas.read_csv(urlopen(...))`` * :issue:`662`: doc: install instruction: explicit about removing scikits.statsmodels * :issue:`910`: test failure Ubuntu TestARMLEConstant.test_dynamic_predict * :issue:`80`: t_model: f_test, t_test do not work * :issue:`432`: GenericLikelihoodModel change default for score and hessian * :issue:`454`: BUG/ENH: HuberScale instance is not used, allow user defined scale estimator * :issue:`98`: check connection or connect summary to variable names in wrappers * :issue:`418`: BUG: MNLogit loglikeobs, jac * :issue:`1017`: nosetests warnings * :issue:`924`: DOCS link in notebooks to notebook for download * :issue:`1011`: power ttest endless loop possible * :issue:`907`: BLD data_files for stats.libqsturng * :issue:`328`: consider moving example scripts into IPython notebooks * :issue:`1002`: Docs will not build with Sphinx 1.1.3 * :issue:`69`: Make methods like compare_ftest work with wrappers * :issue:`503`: summary_old in RegressionResults * :issue:`991`: TST precision of normal_power * :issue:`945`: Installing statsmodels from github? * :issue:`964`: Prefer to_offset not get_offset in tsa stuff * :issue:`983`: bug: pandas 0.8.1 incompatibility * :issue:`899`: build_ext inplace does not cythonize * :issue:`923`: location of initialization code * :issue:`980`: auto lag selection in S_hac_simple * :issue:`968`: genericMLE Ubuntu test failure * :issue:`633`: python 3.3 compatibility * :issue:`728`: test failure for solve_power with fsolve * :issue:`971`: numdiff test cases * :issue:`976`: VAR Model does not work in 1D * :issue:`972`: numdiff: epsilon has no minimum value * :issue:`967`: lowes test failure Ubuntu * :issue:`948`: nonparametric tests: mcnemar, cochranq unit test * :issue:`963`: BUG in runstest_2sample * :issue:`946`: Issue with lowess() smoother in statsmodels * :issue:`868`: k_vars > nobs * :issue:`917`: emplike emplikeAFT stray dimensions * :issue:`264`: version comparisons need to be made more robust (may be just use LooseVersion) * :issue:`674`: failure in test_foreign, pandas testing * :issue:`828`: GLMResults inconsistent distribution in pvalues * :issue:`908`: RLM missing test for tvalues, pvalues * :issue:`463`: formulas missing in docs * :issue:`256`: discrete Nbin has zero test coverage * :issue:`831`: test errors running bdist * :issue:`733`: Docs: interrater cohens_kappa is missing * :issue:`897`: lowess failure - sometimes * :issue:`902`: test failure tsa.filters precision too high * :issue:`901`: test failure stata_writer_pandas, newer versions of pandas * :issue:`900`: ARIMA.__new__ errors on python 3.3 * :issue:`832`: notebook errors * :issue:`867`: Baxter King has unneeded limit on value for low? * :issue:`781`: discreteResults margeff method not tests, obsolete * :issue:`870`: discrete unit tests duplicates * :issue:`630`: problems in regression plots * :issue:`885`: Caching behavior for KDEUnivariate icdf * :issue:`869`: sm.tsa.ARMA(..., order=(p,q)) gives "__init__() got an unexpected keyword argument 'order'" error * :issue:`783`: statsmodels.distributions.mixture_rvs.py no unit tests * :issue:`824`: Multicomparison w/Pandas Series * :issue:`789`: presentation of multiple comparison results * :issue:`764`: BUG: multipletests incorrect reject for Holm-Sidak * :issue:`766`: multipletests - status and tests of 2step FDR procedures * :issue:`763`: Bug: multipletests raises exception with empty array * :issue:`840`: sm.load should be in the main API namespace * :issue:`830`: invalid version number * :issue:`821`: Fail gracefully when extensions are not built * :issue:`204`: Cython extensions built twice? * :issue:`689`: tutorial notebooks * :issue:`740`: why does t_test return one-sided p-value * :issue:`804`: What goes in statsmodels.formula.api? * :issue:`675`: Improve error message for ARMA SVD convergence failure. * :issue:`15`: arma singular matrix * :issue:`559`: Add Rdatasets to optional dependencies list * :issue:`796`: Prediction Standard Errors * :issue:`793`: filters are not pandas aware * :issue:`785`: Negative R-squared * :issue:`777`: OLS residuals returned as Pandas series when endog and exog are Pandas series * :issue:`770`: Add ANOVA to docs * :issue:`775`: Bug in dates_from_range * :issue:`773`: AR model pvalues error with Pandas * :issue:`768`: multipletests: numerical problems at threshold * :issue:`355`: add draw if interactive to plotting functions * :issue:`625`: Exog is not correctly handled in ARIMA predict * :issue:`626`: ARIMA summary does not print exogenous variable coefficients * :issue:`657`: order (0,1) breaks ARMA forecast * :issue:`736`: ARIMA predict problem for ARMA model * :issue:`324`: ic in ARResults, aic, bic, hqic, fpe inconsistent definition? * :issue:`642`: sign_test check * :issue:`236`: AR start_params broken * :issue:`235`: tests hang on Windows * :issue:`156`: matplotlib deprecated legend ? var plots * :issue:`331`: Remove stale tests * :issue:`592`: test failures in datetools * :issue:`537`: Var Models * :issue:`755`: Unable to access AR fit parameters when model is estimated with pandas.DataFrame * :issue:`670`: discrete: numerically useless clipping * :issue:`515`: MNLogit residuals raise a TypeError * :issue:`225`: discrete models only define deviance residuals * :issue:`594`: remove skiptest in TestProbitCG * :issue:`681`: Dimension Error in discrete_model.py When Running test_dummy_* * :issue:`744`: DOC: new_f_test * :issue:`549`: Ship released patsy source in statsmodels * :issue:`588`: patsy is a hard dependency? * :issue:`716`: Tests missing for functions if pandas is used * :issue:`715`: statsmodels regression plots not working with pandas datatypes * :issue:`450`: BUG: full_output in optimizers Likelihood model * :issue:`709`: DOCstrings linear models do not have missing params * :issue:`370`: BUG weightstats has wrong cov * :issue:`694`: DiscreteMargins duplicate method * :issue:`702`: bug, pylint stats.anova * :issue:`423`: Handling of constant across models * :issue:`456`: BUG: ARMA date handling incompatibility with recent pandas * :issue:`514`: NaNs in Multinomial * :issue:`405`: Check for existing old version of scikits.statsmodels? * :issue:`586`: Segmentation fault with OLS * :issue:`721`: Unable to run AR on named time series objects * :issue:`125`: caching pinv_wexog broke iterative fit - GLSAR * :issue:`712`: TSA bug with frequency inference * :issue:`319`: Timeseries Frequencies * :issue:`707`: .summary with alpha ignores parsed value * :issue:`673`: nonparametric: bug in _kernel_base * :issue:`710`: test_power failures * :issue:`706`: .conf_int() fails on linear regression without intercept * :issue:`679`: Test Baxter King band-pass filter fails with scipy 0.12 beta1 * :issue:`552`: influence outliers breaks when regressing on constant * :issue:`639`: test folders not on python path * :issue:`565`: omni_normtest does not propagate the axis argument * :issue:`563`: error in doc generation for AR.fit * :issue:`109`: TestProbitCG failure on Ubuntu * :issue:`661`: from scipy import comb fails on the latest scipy 0.11.0 * :issue:`413`: DOC: example_discrete.py missing from 0.5 documentation * :issue:`644`: FIX: factor plot + examples broken * :issue:`645`: STY: pep8 violations in many examples * :issue:`173`: doc sphinx warnings * :issue:`601`: bspline.py dependency on old scipy.stats.models * :issue:`103`: ecdf and step function conventions * :issue:`18`: Newey-West sandwich covariance is missing * :issue:`279`: cov_nw_panel not tests, example broken * :issue:`150`: precision in test_discrete.TestPoissonNewton.test_jac ? * :issue:`480`: rescale loglike for optimization * :issue:`627`: Travis-CI support for scipy * :issue:`622`: mark tests as slow in emplike * :issue:`589`: OLS F-statistic error * :issue:`572`: statsmodels/tools/data.py Stuck looking for la.py * :issue:`580`: test errors in graphics * :issue:`577`: PatsyData detection buglet * :issue:`470`: remove deprecated features * :issue:`573`: lazy imports are (possibly) very slow * :issue:`438`: New results instances are not in online documentation * :issue:`542`: Regression plots fail when Series objects passed to sm.OLS * :issue:`239`: release 0.4.x * :issue:`530`: l1 docs issues * :issue:`539`: test for statawriter (failure) * :issue:`490`: Travis CI on PRs * :issue:`252`: doc: distributions.rst refers to sandbox only * :issue:`85`: release 0.4 * :issue:`65`: MLE fit of AR model has no tests * :issue:`522`: ``test`` does not propagate arguments to nose * :issue:`517`: missing array conversion or shape in linear model * :issue:`523`: test failure with ubuntu decimals too large * :issue:`520`: web site documentation, source not updated * :issue:`488`: Avoid cholesky decomposition of diagonal matrices in linear regression models * :issue:`394`: Definition in macrodata NOTE * :issue:`45`: numdifftools dependency * :issue:`501`: WLS/GLS post estimation results * :issue:`500`: WLS fails if weights is a pandas.Series * :issue:`27`: add hasconstant indicator for R-squared and df calculations * :issue:`497`: DOC: add patsy? * :issue:`495`: ENH: add footer SimpleTable * :issue:`402`: model._data -> model.data? * :issue:`477`: VAR NaN Bug * :issue:`421`: Enhancement: Handle Missing Data * :issue:`489`: Expose model._data as model.data * :issue:`315`: tsa models assume pandas object indices are dates * :issue:`440`: arima predict is broken for steps > q and q != 1 * :issue:`458`: TST BUG? comparing pandas and array in tests, formula * :issue:`464`: from_formula signature * :issue:`245`: examples in docs: make nicer * :issue:`466`: broken example, pandas * :issue:`57`: Unhelpful error from bad exog matrix in model.py * :issue:`271`: ARMA.geterrors requires model to be fit * :issue:`350`: Writing to array returned np.diag * :issue:`354`: example_rst does not copy unchanged files over * :issue:`467`: Install issues with Pandas * :issue:`444`: ARMA example on stable release website not working * :issue:`377`: marginal effects count and discrete adjustments * :issue:`426`: "svd" method not supported for OLS.fit() * :issue:`409`: Move numdiff out of the sandbox * :issue:`416`: Switch to complex-step Hessian for AR(I)MA * :issue:`415`: bug in kalman_loglike_complex * :issue:`397`: plot_corr axis text labeling not working (with fix) * :issue:`399`: discrete errors due to incorrect in-place operation * :issue:`389`: VAR test_normality is broken with KeyError * :issue:`388`: Add tsaplots to graphics.api as graphics.tsa * :issue:`387`: predict date was not getting set with start = None * :issue:`386`: p-values not returned from acf * :issue:`385`: Allow AR.select_order to work without model being fit * :issue:`383`: Move mixture_rvs out of sandbox. * :issue:`248`: ARMA breaks with a 1d exog * :issue:`273`: When to give order for AR/AR(I)MA * :issue:`363`: examples folder -> tutorials folder * :issue:`346`: docs in sitepackages * :issue:`353`: PACF docs raise a sphinx warning * :issue:`348`: python 3.2.3 test failure zip_longest statsmodels-0.12.2/docs/source/release/version0.6.rst000066400000000000000000001215711400612667500224670ustar00rootroot00000000000000:orphan: ============= Release 0.6.1 ============= statsmodels 0.6.1 is a bugfix release. All users are encouraged to upgrade to 0.6.1. See the :ref:`list of fixed issues ` for specific backported fixes. ============= Release 0.6.0 ============= statsmodels 0.6.0 is another large release. It is the result of the work of 37 authors over the last year and includes over 1500 commits. It contains many new features, improvements, and bug fixes detailed below. See the :ref:`list of fixed issues ` for specific closed issues. The following major new features appear in this version. Generalized Estimating Equations -------------------------------- Generalized Estimating Equations (GEE) provide an approach to handling dependent data in a regression analysis. Dependent data arise commonly in practice, such as in a longitudinal study where repeated observations are collected on subjects. GEE can be viewed as an extension of the generalized linear modeling (GLM) framework to the dependent data setting. The familiar GLM families such as the Gaussian, Poisson, and logistic families can be used to accommodate dependent variables with various distributions. Here is an example of GEE Poisson regression in a data set with four count-type repeated measures per subject, and three explanatory covariates. .. code-block:: python import numpy as np import statsmodels.api as sm import statsmodels.formula.api as smf data = sm.datasets.get_rdataset("epil", "MASS").data md = smf.gee("y ~ age + trt + base", "subject", data, cov_struct=sm.cov_struct.Independence(), family=sm.families.Poisson()) mdf = md.fit() print mdf.summary() The dependence structure in a GEE is treated as a nuisance parameter and is modeled in terms of a "working dependence structure". The statsmodels GEE implementation currently includes five working dependence structures (independent, exchangeable, autoregressive, nested, and a global odds ratio for working with categorical data). Since the GEE estimates are not maximum likelihood estimates, alternative approaches to some common inference procedures have been developed. The statsmodels GEE implementation currently provides standard errors, Wald tests, score tests for arbitrary parameter contrasts, and estimates and tests for marginal effects. Several forms of standard errors are provided, including robust standard errors that are approximately correct even if the working dependence structure is misspecified. Seasonality Plots ----------------- Adding functionality to look at seasonality in plots. Two new functions are :func:`sm.graphics.tsa.month_plot` and :func:`sm.graphics.tsa.quarter_plot`. Another function :func:`sm.graphics.tsa.seasonal_plot` is available for power users. .. code-block:: python import statsmodels.api as sm import pandas as pd dta = sm.datasets.elnino.load_pandas().data dta['YEAR'] = dta.YEAR.astype(int).astype(str) dta = dta.set_index('YEAR').T.unstack() dates = map(lambda x : pd.datetools.parse('1 '+' '.join(x)), dta.index.values) dta.index = pd.DatetimeIndex(dates, freq='M') fig = sm.tsa.graphics.month_plot(dta) .. currentmodule:: statsmodels.tsa Seasonal Decomposition ---------------------- We added a naive seasonal decomposition tool in the same vein as R's ``decompose``. This function can be found as :func:`sm.tsa.seasonal_decompose `. .. plot:: :include-source: import statsmodels.api as sm dta = sm.datasets.co2.load_pandas().data # deal with missing values. see issue dta.co2.interpolate(inplace=True) res = sm.tsa.seasonal_decompose(dta.co2) res.plot() Addition of Linear Mixed Effects Models (MixedLM) Linear Mixed Effects Models --------------------------- Linear Mixed Effects models are used for regression analyses involving dependent data. Such data arise when working with longitudinal and other study designs in which multiple observations are made on each subject. Two specific mixed effects models are "random intercepts models", where all responses in a single group are additively shifted by a value that is specific to the group, and "random slopes models", where the values follow a mean trajectory that is linear in observed covariates, with both the slopes and intercept being specific to the group. The statsmodels MixedLM implementation allows arbitrary random effects design matrices to be specified for the groups, so these and other types of random effects models can all be fit. Here is an example of fitting a random intercepts model to data from a longitudinal study: .. code-block:: python import statsmodels.api as sm import statsmodels.formula.api as smf data = sm.datasets.get_rdataset('dietox', 'geepack', cache=True).data md = smf.mixedlm("Weight ~ Time", data, groups=data["Pig"]) mdf = md.fit() print mdf.summary() The statsmodels LME framework currently supports post-estimation inference via Wald tests and confidence intervals on the coefficients, profile likelihood analysis, likelihood ratio testing, and AIC. Some limitations of the current implementation are that it does not support structure more complex on the residual errors (they are always homoscedastic), and it does not support crossed random effects. We hope to implement these features for the next release. Wrapping X-12-ARIMA/X-13-ARIMA ------------------------------ It is now possible to call out to X-12-ARIMA or X-13ARIMA-SEATS from statsmodels. These libraries must be installed separately. .. code-block:: python import statsmodels.api as sm dta = sm.datasets.co2.load_pandas().data dta.co2.interpolate(inplace=True) dta = dta.resample('M').last() res = sm.tsa.x13_arima_select_order(dta.co2) print(res.order, res.sorder) results = sm.tsa.x13_arima_analysis(dta.co2) fig = results.plot() fig.set_size_inches(12, 5) fig.tight_layout() Other important new features ---------------------------- * The AR(I)MA models now have a :func:`plot_predict ` method to plot forecasts and confidence intervals. * The Kalman filter Cython code underlying AR(I)MA estimation has been substantially optimized. You can expect speed-ups of one to two orders of magnitude. * Added :func:`sm.tsa.arma_order_select_ic`. A convenience function to quickly get the information criteria for use in tentative order selection of ARMA processes. * Plotting functions for timeseries is now imported under the ``sm.tsa.graphics`` namespace in addition to ``sm.graphics.tsa``. * New `distributions.ExpandedNormal` class implements the Edgeworth expansion for weakly non-normal distributions. * **New datasets**: Added new :ref:`datasets ` for examples. ``sm.datasets.co2`` is a univariate time-series dataset of weekly co2 readings. It exhibits a trend and seasonality and has missing values. * Added robust skewness and kurtosis estimators in :func:`sm.stats.stattools.robust_skewness` and :func:`sm.stats.stattools.robust_kurtosis`, respectively. An alternative robust measure of skewness has been added in :func:`sm.stats.stattools.medcouple`. * New functions added to correlation tools: `corr_nearest_factor` finds the closest factor-structured correlation matrix to a given square matrix in the Frobenius norm; `corr_thresholded` efficiently constructs a hard-thresholded correlation matrix using sparse matrix operations. * New `dot_plot` in graphics: A dotplot is a way to visualize a small dataset in a way that immediately conveys the identity of every point in the plot. Dotplots are commonly seen in meta-analyses, where they are known as "forest plots", but can be used in many other settings as well. Most tables that appear in research papers can be represented graphically as a dotplot. * statsmodels has added custom warnings to ``statsmodels.tools.sm_exceptions``. By default all of these warnings will be raised whenever appropriate. Use ``warnings.simplefilter`` to turn them off, if desired. * Allow control over the namespace used to evaluate formulas with patsy via the ``eval_env`` keyword argument. See the :ref:`patsy-namespaces` documentation for more information. Major Bugs fixed ---------------- * NA-handling with formulas is now correctly handled. :issue:`805`, :issue:`1877`. * Better error messages when an array with an object dtype is used. :issue:`2013`. * ARIMA forecasts were hard-coded for order of integration with ``d = 1``. :issue:`1562`. .. currentmodule:: statsmodels.tsa Backwards incompatible changes and deprecations ----------------------------------------------- * RegressionResults.norm_resid is now a readonly property, rather than a function. * The function ``statsmodels.tsa.filters.arfilter`` has been removed. This did not compute a recursive AR filter but was instead a convolution filter. Two new functions have been added with clearer names :func:`sm.tsa.filters.recursive_filter ` and :func:`sm.tsa.filters.convolution_filter `. Development summary and credits ------------------------------- The previous version (0.5.0) was released August 14, 2014. Since then we have closed a total of 528 issues, 276 pull requests, and 252 regular issues. Refer to the :ref:`detailed list` for more information. This release is a result of the work of the following 37 authors who contributed a total of 1531 commits. If for any reason we have failed to list your name in the below, please contact us: A blurb about the number of changes and the contributors list. * Alex Griffing * Alex Parij * Ana Martinez Pardo * Andrew Clegg * Ben Duffield * Chad Fulton * Chris Kerr * Eric Chiang * Evgeni Burovski * gliptak * Hans-Martin von Gaudecker * Jan Schulz * jfoo * Joe Hand * Josef Perktold * jsphon * Justin Grana * Kerby Shedden * Kevin Sheppard * Kyle Beauchamp * Lars Buitinck * Max Linke * Miroslav Batchkarov * m * Padarn Wilson * Paul Hobson * Pietro Battiston * Radim Řehůřek * Ralf Gommers * Richard T. Guy * Roy Hyunjin Han * Skipper Seabold * Tom Augspurger * Trent Hauck * Valentin Haenel * Vincent Arel-Bundock * Yaroslav Halchenko .. note:: Obtained by running ``git log v0.5.0..HEAD --format='* %aN <%aE>' | sed 's/@/\-at\-/' | sed 's/<>//' | sort -u``. .. _issues_list_06: Issues closed in the 0.6.0 development cycle ============================================ Issues closed in 0.6.0 ---------------------- GitHub stats for 2013/08/14 - 2014/10/15 (tag: v0.5.0) We closed a total of 528 issues, 276 pull requests and 252 regular issues; this is the full list (generated with the script :file:`tools/github_stats.py`): This list is automatically generated and may be incomplete. Pull Requests (276): * :pr:`2044`: ENH: Allow unit interval for binary models. Closes #2040. * :pr:`1426`: ENH: Import arima_process stuff into tsa.api * :pr:`2042`: Fix two minor typos in contrast.py * :pr:`2034`: ENH: Handle missing for extra data with formulas * :pr:`2035`: MAINT: Remove deprecated code for 0.6 * :pr:`1325`: ENH: add the Edgeworth expansion based on the normal distribution * :pr:`2032`: DOC: What it is what it is. * :pr:`2031`: ENH: Expose patsy eval_env to users. * :pr:`2028`: ENH: Fix numerical issues in links and families. * :pr:`2029`: DOC: Fix versions to match other docs. * :pr:`1647`: ENH: Warn on non-convergence. * :pr:`2014`: BUG: Fix forecasting for ARIMA with d == 2 * :pr:`2013`: ENH: Better error message on object dtype * :pr:`2012`: BUG: 2d 1 columns -> 1d. Closes #322. * :pr:`2009`: DOC: Update after refactor. Use code block. * :pr:`2008`: ENH: Add wrapper for MixedLM * :pr:`1954`: ENH: PHReg formula improvements * :pr:`2007`: BLD: Fix build issues * :pr:`2006`: BLD: Do not generate cython on clean. Closes #1852. * :pr:`2000`: BLD: Let pip/setuptools handle dependencies that are not installed at all. * :pr:`1999`: Gee offset exposure 1994 rebased * :pr:`1998`: BUG/ENH Lasso emptymodel rebased * :pr:`1989`: BUG/ENH: WLS generic robust cov_type did not use whitened, * :pr:`1587`: ENH: Wrap X12/X13-ARIMA AUTOMDL. Closes #442. * :pr:`1563`: ENH: Add plot_predict method to ARIMA models. * :pr:`1995`: BUG: Fix issue #1993 * :pr:`1981`: ENH: Add api for covstruct. Clear __init__. Closes #1917. * :pr:`1996`: DEV: Ignore .venv file. * :pr:`1982`: REF: Rename jac -> score_obs. Closes #1785. * :pr:`1987`: BUG tsa pacf, base bootstrap * :pr:`1986`: Bug multicomp 1927 rebased * :pr:`1984`: Docs add gee.rst * :pr:`1985`: Bug uncentered latex table 1929 rebased * :pr:`1983`: BUG: Fix compat asunicode * :pr:`1574`: DOC: Fix math. * :pr:`1980`: DOC: Documentation fixes * :pr:`1974`: REF/Doc beanplot change default color, add notebook * :pr:`1978`: ENH: Check input to binary models * :pr:`1979`: BUG: Typo * :pr:`1976`: ENH: Add _repr_html_ to SimpleTable * :pr:`1977`: BUG: Fix import refactor victim. * :pr:`1975`: BUG: Yule walker cast to float * :pr:`1973`: REF: Move and expose webuse * :pr:`1972`: TST: Add testing against NumPy 1.9 and matplotlib 1.4 * :pr:`1939`: ENH: Binstar build files * :pr:`1952`: REF/DOC: Misc * :pr:`1940`: REF: refactor and speedup of mixed LME * :pr:`1937`: ENH: Quick access to online documentation * :pr:`1942`: DOC: Rename Change README type to rst * :pr:`1938`: ENH: Enable Python 3.4 testing * :pr:`1924`: Bug gee cov type 1906 rebased * :pr:`1870`: robust covariance, cov_type in fit * :pr:`1859`: BUG: Do not use negative indexing with k_ar == 0. Closes #1858. * :pr:`1914`: BUG: LikelihoodModelResults.pvalues use df_resid_inference * :pr:`1899`: TST: fix assert_equal for pandas index * :pr:`1895`: Bug multicomp pandas * :pr:`1894`: BUG fix more ix indexing cases for pandas compat * :pr:`1889`: BUG: fix ytick positions closes #1561 * :pr:`1887`: Bug pandas compat asserts * :pr:`1888`: TST test_corrpsd Test_Factor: add noise to data * :pr:`1886`: BUG pandas 0.15 compatibility in grouputils labels * :pr:`1885`: TST: corr_nearest_factor, more informative tests * :pr:`1884`: Fix: Add compat code for pd.Categorical in pandas>=0.15 * :pr:`1883`: BUG: add _ctor_param to TransfGen distributions * :pr:`1872`: TST: fix _infer_freq for pandas .14+ compat * :pr:`1867`: Ref covtype fit * :pr:`1865`: Disable tst distribution 1864 * :pr:`1856`: _spg_optim returns history of objective function values * :pr:`1854`: BLD: Do not hard-code path for building notebooks. Closes #1249 * :pr:`1851`: MAINT: Cor nearest factor tests * :pr:`1847`: Newton regularize * :pr:`1623`: BUG Negbin fit regularized * :pr:`1797`: BUG/ENH: fix and improve constant detection * :pr:`1770`: TST: anova with `-1` noconstant, add tests * :pr:`1837`: Allow group variable to be passed as variable name when using formula * :pr:`1839`: BUG: GEE score * :pr:`1830`: BUG/ENH Use t * :pr:`1832`: TST error with scipy 0.14 location distribution class * :pr:`1827`: fit_regularized for linear models rebase 1674 * :pr:`1825`: Phreg 1312 rebased * :pr:`1826`: Lme api docs * :pr:`1824`: Lme profile 1695 rebased * :pr:`1823`: Gee cat subclass 1694 rebase * :pr:`1781`: ENH: Glm add score_obs * :pr:`1821`: Glm maint #1734 rebased * :pr:`1820`: BUG: revert change to conf_int in PR #1819 * :pr:`1819`: Docwork * :pr:`1772`: REF: cov_params allow case of only cov_params_default is defined * :pr:`1771`: REF numpy >1.9 compatibility, indexing into empty slice closes #1754 * :pr:`1769`: Fix ttest 1d * :pr:`1766`: TST: TestProbitCG increase bound for fcalls closes #1690 * :pr:`1709`: BLD: Made build extensions more flexible * :pr:`1714`: WIP: fit_constrained * :pr:`1706`: REF: Use fixed params in test. Closes #910. * :pr:`1701`: BUG: Fix faulty logic. Do not raise when missing='raise' and no missing data. * :pr:`1699`: TST/ENH StandardizeTransform, reparameterize TestProbitCG * :pr:`1697`: Fix for statsmodels/statsmodels#1689 * :pr:`1692`: OSL Example: redundant cell in example removed * :pr:`1688`: Kshedden mixed rebased of #1398 * :pr:`1629`: Pull request to fix bandwidth bug in issue 597 * :pr:`1666`: Include pyx in sdist but do not install * :pr:`1683`: TST: GLM shorten random seed closes #1682 * :pr:`1681`: Dotplot kshedden rebased of 1294 * :pr:`1679`: BUG: Fix problems with predict handling offset and exposure * :pr:`1677`: Update docstring of RegressionModel.predict() * :pr:`1635`: Allow offset and exposure to be used together with log link; raise except... * :pr:`1676`: Tests for SVAR * :pr:`1671`: ENH: avoid hard-listed bandwidths -- use present dictionary (+typos fixed) * :pr:`1643`: Allow matrix structure in covariance matrices to be exploited * :pr:`1657`: BUG: Fix refactor victim. * :pr:`1630`: DOC: typo, "intercept" * :pr:`1619`: MAINT: Dataset docs cleanup and automatic build of docs * :pr:`1612`: BUG/ENH Fix negbin exposure #1611 * :pr:`1610`: BUG/ENH fix llnull, extra kwds to recreate model * :pr:`1582`: BUG: wls_prediction_std fix weight handling, see 987 * :pr:`1613`: BUG: Fix proportions allpairs #1493 * :pr:`1607`: TST: adjust precision, CI Debian, Ubuntu testing * :pr:`1603`: ENH: Allow start_params in GLM * :pr:`1600`: CLN: Regression plots fixes * :pr:`1592`: DOC: Additions and fixes * :pr:`1520`: CLN: Refactored so that there is no longer a need for 2to3 * :pr:`1585`: Cor nearest 1384 rebased * :pr:`1553`: Gee maint 1528 rebased * :pr:`1583`: BUG: For ARMA(0,0) ensure 1d bse and fix summary. * :pr:`1580`: DOC: Fix links. [skip ci] * :pr:`1572`: DOC: Fix link title [skip ci] * :pr:`1566`: BLD: Fix copy paste path error for >= 3.3 Windows builds * :pr:`1524`: ENH: Optimize Cython code. Use scipy blas function pointers. * :pr:`1560`: ENH: Allow ARMA(0,0) in order selection * :pr:`1559`: MAINT: Recover lost commits from vbench PR * :pr:`1554`: Silenced test output introduced in medcouple * :pr:`1234`: ENH: Robust skewness, kurtosis and medcouple measures * :pr:`1484`: ENH: Add naive seasonal decomposition function * :pr:`1551`: COMPAT: Fix failing test on Python 2.6 * :pr:`1472`: ENH: using human-readable group names instead of integer ids in MultiComparison * :pr:`1437`: ENH: accept non-int definitions of cluster groups * :pr:`1550`: Fix test gmm poisson * :pr:`1549`: TST: Fix locally failing tests. * :pr:`1121`: WIP: Refactor optimization code. * :pr:`1547`: COMPAT: Correct bit_length for 2.6 * :pr:`1545`: MAINT: Fix missed usage of deprecated tools.rank * :pr:`1196`: REF: ensure O(N log N) when using fft for acf * :pr:`1154`: DOC: Add links for build machines. * :pr:`1546`: DOC: Fix link to wrong notebook * :pr:`1383`: MAINT: Deprecate rank in favor of np.linalg.matrix_rank * :pr:`1432`: COMPAT: Add NumpyVersion from scipy * :pr:`1438`: ENH: Option to avoid "center" environment. * :pr:`1544`: BUG: Travis miniconda * :pr:`1510`: CLN: Improve warnings to avoid generic warnings messages * :pr:`1543`: TST: Suppress RuntimeWarning for L-BFGS-B * :pr:`1507`: CLN: Silence test output * :pr:`1540`: BUG: Correct derivative for exponential transform. * :pr:`1536`: BUG: Restores coveralls for a single build * :pr:`1535`: BUG: Fixes for 2.6 test failures, replacing astype(str) with apply(str) * :pr:`1523`: Travis miniconda * :pr:`1533`: DOC: Fix link to code on github * :pr:`1531`: DOC: Fix stale links with linkcheck * :pr:`1530`: DOC: Fix link * :pr:`1527`: DOCS: Update docs add FAQ page * :pr:`1525`: DOC: Update with Python 3.4 build notes * :pr:`1518`: DOC: Ask for release notes and example. * :pr:`1516`: DOC: Update examples contributing docs for current practice. * :pr:`1517`: DOC: Be clear about data attribute of Datasets * :pr:`1515`: DOC: Fix broken link * :pr:`1514`: DOC: Fix formula import convention. * :pr:`1506`: BUG: Format and decode errors in Python 2.6 * :pr:`1505`: TST: Test co2 load_data for Python 3. * :pr:`1504`: BLD: New R versions require NAMESPACE file. Closes #1497. * :pr:`1483`: ENH: Some utility functions for working with dates * :pr:`1482`: REF: Prefer filters.api to __init__ * :pr:`1481`: ENH: Add weekly co2 dataset * :pr:`1474`: DOC: Add plots for standard filter methods. * :pr:`1471`: DOC: Fix import * :pr:`1470`: DOC/BLD: Log code exceptions from nbgenerate * :pr:`1469`: DOC: Fix bad links * :pr:`1468`: MAINT: CSS fixes * :pr:`1463`: DOC: Remove defunct argument. Change default kw. Closes #1462. * :pr:`1452`: STY: import pandas as pd * :pr:`1458`: BUG/BLD: exclude sandbox in relative path, not absolute * :pr:`1447`: DOC: Only build and upload docs if we need to. * :pr:`1445`: DOCS: Example landing page * :pr:`1436`: DOC: Fix auto doc builds. * :pr:`1431`: DOC: Add default for getenv. Fix paths. Add print_info * :pr:`1429`: MAINT: Use ip_directive shipped with IPython * :pr:`1427`: TST: Make tests fit quietly * :pr:`1424`: ENH: Consistent results for transform_slices * :pr:`1421`: ENH: Add grouping utilities code * :pr:`1419`: Gee 1314 rebased * :pr:`1414`: TST temporarily rename tests probplot other to skip them * :pr:`1403`: Bug norm expan shapes * :pr:`1417`: REF: Let subclasses keep kwds attached to data. * :pr:`1416`: ENH: Make handle_data overwritable by subclasses. * :pr:`1410`: ENH: Handle missing is none * :pr:`1402`: REF: Expose missing data handling as classmethod * :pr:`1387`: MAINT: Fix failing tests * :pr:`1406`: MAINT: Tools improvements * :pr:`1404`: Tst fix genmod link tests * :pr:`1396`: REF: Multipletests reduce memory usage * :pr:`1380`: DOC :Update vector_ar.rst * :pr:`1381`: BLD: Do not check dependencies on egg_info for pip. Closes #1267. * :pr:`1302`: BUG: Fix typo. * :pr:`1375`: STY: Remove unused imports and comment out unused libraries in setup.py * :pr:`1143`: DOC: Update backport notes for new workflow. * :pr:`1374`: ENH: Import tsaplots into tsa namespace. Closes #1359. * :pr:`1369`: STY: Pep-8 cleanup * :pr:`1370`: ENH: Support ARMA(0,0) models. * :pr:`1368`: STY: Pep 8 cleanup * :pr:`1367`: ENH: Make sure mle returns attach to results. * :pr:`1365`: STY: Import and pep 8 cleanup * :pr:`1364`: ENH: Get rid of hard-coded lbfgs. Closes #988. * :pr:`1363`: BUG: Fix typo. * :pr:`1361`: ENH: Attach mlefit to results not model. * :pr:`1360`: ENH: Import adfuller into tsa namespace * :pr:`1346`: STY: PEP-8 Cleanup * :pr:`1344`: BUG: Use missing keyword given to ARMA. * :pr:`1340`: ENH: Protect against ARMA convergence failures. * :pr:`1334`: ENH: ARMA order select convenience function * :pr:`1339`: Fix typos * :pr:`1336`: REF: Get rid of plain assert. * :pr:`1333`: STY: __all__ should be after imports. * :pr:`1332`: ENH: Add Bunch object to tools. * :pr:`1331`: ENH: Always use unicode. * :pr:`1329`: BUG: Decode metadata to utf-8. Closes #1326. * :pr:`1330`: DOC: Fix typo. Closes #1327. * :pr:`1185`: Added support for pandas when pandas was installed directly from git trunk * :pr:`1315`: MAINT: Change back to path for build box * :pr:`1305`: TST: Update hard-coded path. * :pr:`1290`: ENH: Add seasonal plotting. * :pr:`1296`: BUG/TST: Fix ARMA forecast when start == len(endog). Closes #1295 * :pr:`1292`: DOC: cleanup examples folder and webpage * :pr:`1286`: Make sure PeriodIndex passes through tsa. Closes #1285. * :pr:`1271`: Silverman enhancement - Issue #1243 * :pr:`1264`: Doc work GEE, GMM, sphinx warnings * :pr:`1179`: REF/TST: `ProbPlot` now uses `resettable_cache` and added some kwargs to plotting fxns * :pr:`1225`: Sandwich mle * :pr:`1258`: Gmm new rebased * :pr:`1255`: ENH add GEE to genmod * :pr:`1254`: REF: Results.predict convert to array and adjust shape * :pr:`1192`: TST: enable tests for llf after change to WLS.loglike see #1170 * :pr:`1253`: Wls llf fix * :pr:`1233`: sandbox kernels bugs uniform kernel and confint * :pr:`1240`: Kde weights 1103 823 * :pr:`1228`: Add default value tags to adfuller() docs * :pr:`1198`: fix typo * :pr:`1230`: BUG: numerical precision in resid_pearson with perfect fit #1229 * :pr:`1214`: Compare lr test rebased * :pr:`1200`: BLD: do not install \*.pyx \*.c MANIFEST.in * :pr:`1202`: MAINT: Sort backports to make applying easier. * :pr:`1157`: Tst precision master * :pr:`1161`: add a fitting interface for simultaneous log likelihood and score, for lbfgs, tested with MNLogit * :pr:`1160`: DOC: update scipy version from 0.7 to 0.9.0 * :pr:`1147`: ENH: add lbfgs for fitting * :pr:`1156`: ENH: Raise on 0,0 order models in AR(I)MA. Closes #1123 * :pr:`1149`: BUG: Fix small data issues for ARIMA. * :pr:`1092`: Fixed duplicate svd in RegressionModel * :pr:`1139`: TST: Silence tests * :pr:`1135`: Misc style * :pr:`1088`: ENH: add predict_prob to poisson * :pr:`1125`: REF/BUG: Some GLM cleanup. Used trimmed results in NegativeBinomial variance. * :pr:`1124`: BUG: Fix ARIMA prediction when fit without a trend. * :pr:`1118`: DOC: Update gettingstarted.rst * :pr:`1117`: Update ex_arma2.py * :pr:`1107`: REF: Deprecate stand_mad. Add center keyword to mad. Closes #658. * :pr:`1089`: ENH: exp(poisson.logpmf()) for poisson better behaved. * :pr:`1077`: BUG: Allow 1d exog in ARMAX forecasting. * :pr:`1075`: BLD: Fix build issue on some versions of easy_install. * :pr:`1071`: Update setup.py to fix broken install on OSX * :pr:`1052`: DOC: Updating contributing docs * :pr:`1136`: RLS: Add IPython tools for easier backporting of issues. * :pr:`1091`: DOC: minor git typo * :pr:`1082`: coveralls support * :pr:`1072`: notebook examples title cell * :pr:`1056`: Example: reg diagnostics * :pr:`1057`: COMPAT: Fix py3 caching for get_rdatasets. * :pr:`1045`: DOC/BLD: Update from nbconvert to IPython 1.0. * :pr:`1026`: DOC/BLD: Add LD_LIBRARY_PATH to env for docs build. Issues (252): * :issue:`2040`: enh: fractional Logit, Probit * :issue:`1220`: missing in extra data (example sandwiches, robust covariances) * :issue:`1877`: error with GEE on missing data. * :issue:`805`: nan with categorical in formula * :issue:`2036`: test in links require exact class so Logit cannot work in place of logit * :issue:`2010`: Go over deprecations again for 0.6. * :issue:`1303`: patsy library not automatically installed * :issue:`2024`: genmod Links numerical improvements * :issue:`2025`: GEE requires exact import for cov_struct * :issue:`2017`: Matplotlib warning about too many figures * :issue:`724`: check warnings * :issue:`1562`: ARIMA forecasts are hard-coded for d=1 * :issue:`880`: DataFrame with bool type not cast correctly. * :issue:`1992`: MixedLM style * :issue:`322`: acf / pacf do not work on pandas objects * :issue:`1317`: AssertionError: attr is not equal [dtype]: dtype('object') != dtype('datetime64[ns]') * :issue:`1875`: dtype bug object arrays (raises in clustered standard errors code) * :issue:`1842`: dtype object, glm.fit() gives AttributeError: sqrt * :issue:`1300`: Doc errors, missing * :issue:`1164`: RLM cov_params, t_test, f_test do not use bcov_scaled * :issue:`1019`: 0.6.0 Roadmap * :issue:`554`: Prediction Standard Errors * :issue:`333`: ENH tools: squeeze in R export file * :issue:`1990`: MixedLM does not have a wrapper * :issue:`1897`: Consider depending on setuptools in setup.py * :issue:`2003`: pip install now fails silently * :issue:`1852`: do not cythonize when cleaning up * :issue:`1991`: GEE formula interface does not take offset/exposure * :issue:`442`: Wrap x-12 arima * :issue:`1993`: MixedLM bug * :issue:`1917`: API: GEE access to genmod.covariance_structure through api * :issue:`1785`: REF: rename jac -> score_obs * :issue:`1969`: pacf has incorrect standard errors for lag 0 * :issue:`1434`: A small bug in GenericLikelihoodModelResults.bootstrap() * :issue:`1408`: BUG test failure with tsa_plots * :issue:`1337`: DOC: HCCM are now available for WLS * :issue:`546`: influence and outlier documentation * :issue:`1532`: DOC: Related page is out of date * :issue:`1386`: Add minimum matplotlib to docs * :issue:`1068`: DOC: keeping documentation of old versions on sourceforge * :issue:`329`: link to examples and datasets from module pages * :issue:`1804`: PDF documentation for statsmodels * :issue:`202`: Extend robust standard errors for WLS/GLS * :issue:`1519`: Link to user-contributed examples in docs * :issue:`1053`: inconvenient: logit when endog is (1,2) instead of (0,1) * :issue:`1555`: SimpleTable: add repr html for ipython notebook * :issue:`1366`: Change default start_params to .1 in ARMA * :issue:`1869`: yule_walker (from `statsmodels.regression`) raises exception when given an integer array * :issue:`1651`: statsmodels.tsa.ar_model.ARResults.predict * :issue:`1738`: GLM robust sandwich covariance matrices * :issue:`1779`: Some directories under statsmodels dont have __init_.py * :issue:`1242`: No support for (0, 1, 0) ARIMA Models * :issue:`1571`: expose webuse, use cache * :issue:`1860`: ENH/BUG/DOC: Bean plot should allow for separate widths of bean and violins. * :issue:`1831`: TestRegressionNM.test_ci_beta2 i386 AssertionError * :issue:`1079`: bugfix release 0.5.1 * :issue:`1338`: Raise Warning for HCCM use in WLS/GLS * :issue:`1430`: scipy min version / issue * :issue:`276`: memoize, last argument wins, how to attach sandwich to Results? * :issue:`1943`: REF/ENH: LikelihoodModel.fit optimization, make hessian optional * :issue:`1957`: BUG: Re-create OLS model using _init_keys * :issue:`1905`: Docs: online docs are missing GEE * :issue:`1898`: add python 3.4 to continuous integration testing * :issue:`1684`: BUG: GLM NegativeBinomial: llf ignores offset and exposure * :issue:`1256`: REF: GEE handling of default covariance matrices * :issue:`1760`: Changing covariance_type on results * :issue:`1906`: BUG: GEE default covariance is not used * :issue:`1931`: BUG: GEE subclasses NominalGEE do not work with pandas exog * :issue:`1904`: GEE Results does not have a Wrapper * :issue:`1918`: GEE: required attributes missing, df_resid * :issue:`1919`: BUG GEE.predict uses link instead of link.inverse * :issue:`1858`: BUG: arimax forecast should special case k_ar == 0 * :issue:`1903`: BUG: pvalues for cluster robust, with use_t do not use df_resid_inference * :issue:`1243`: kde silverman bandwidth for non-gaussian kernels * :issue:`1866`: Pip dependencies * :issue:`1850`: TST test_corr_nearest_factor fails on Ubuntu * :issue:`292`: python 3 examples * :issue:`1868`: ImportError: No module named compat [ from statsmodels.compat import lmap ] * :issue:`1890`: BUG tukeyhsd nan in group labels * :issue:`1891`: TST test_gmm outdated pandas, compat * :issue:`1561`: BUG plot for tukeyhsd, MultipleComparison * :issue:`1864`: test failure sandbox distribution transformation with scipy 0.14.0 * :issue:`576`: Add contributing guidelines * :issue:`1873`: GenericLikelihoodModel is not picklable * :issue:`1822`: TST failure on Ubuntu pandas 0.14.0 , problems with frequency * :issue:`1249`: Source directory problem for notebook examples * :issue:`1855`: anova_lm throws error on models created from api.ols but not formula.api.ols * :issue:`1853`: a large number of hardcoded paths * :issue:`1792`: R² adjusted strange after including interaction term * :issue:`1794`: REF: has_constant, k_constant, include implicit constant detection in base * :issue:`1454`: NegativeBinomial missing fit_regularized method * :issue:`1615`: REF DRYing fit methods * :issue:`1453`: Discrete NegativeBinomialModel regularized_fit ValueError: matrices are not aligned * :issue:`1836`: BUG Got an TypeError trying to import statsmodels.api * :issue:`1829`: BUG: GLM summary show "t" use_t=True for summary * :issue:`1828`: BUG summary2 does not propagate/use use_t * :issue:`1812`: BUG/ REF conf_int and use_t * :issue:`1835`: Problems with installation using easy_install * :issue:`1801`: BUG 'f_gen' missing in scipy 0.14.0 * :issue:`1803`: Error revealed by numpy 1.9.0r1 * :issue:`1834`: stackloss * :issue:`1728`: GLM.fit maxiter=0 incorrect * :issue:`1795`: singular design with offset ? * :issue:`1730`: ENH/Bug cov_params, generalize, avoid ValueError * :issue:`1754`: BUG/REF: assignment to slices in numpy >= 1.9 (emplike) * :issue:`1409`: GEE test errors on Debian Wheezy * :issue:`1521`: ubuntu failures: tsa_plot and grouputils * :issue:`1415`: test failure test_arima.test_small_data * :issue:`1213`: df_diff in anova_lm * :issue:`1323`: Contrast Results after t_test summary broken for 1 parameter * :issue:`109`: TestProbitCG failure on Ubuntu * :issue:`1690`: TestProbitCG: 8 failing tests (Python 3.4 / Ubuntu 12.04) * :issue:`1763`: Johansen method does not give correct index values * :issue:`1761`: doc build failures: ipython version ? ipython directive * :issue:`1762`: Unable to build * :issue:`1745`: UnicodeDecodeError raised by get_rdataset("Guerry", "HistData") * :issue:`611`: test failure foreign with pandas 0.7.3 * :issue:`1700`: faulty logic in missing handling * :issue:`1648`: ProbitCG failures * :issue:`1689`: test_arima.test_small_data: SVD fails to converge (Python 3.4 / Ubuntu 12.04) * :issue:`597`: BUG: nonparametric: kernel, efficient=True changes bw even if given * :issue:`1606`: BUILD from sdist broken if cython available * :issue:`1246`: test failure test_anova.TestAnova2.test_results * :issue:`50`: t_test, f_test, model.py for normal instead of t-distribution * :issue:`1655`: newey-west different than R? * :issue:`1682`: TST test failure on Ubuntu, random.seed * :issue:`1614`: docstring for regression.linear_model.RegressionModel.predict() does not match implementation * :issue:`1318`: GEE and GLM scale parameter * :issue:`519`: L1 fit_regularized cleanup, comments * :issue:`651`: add structure to example page * :issue:`1067`: Kalman Filter convergence. How close is close enough? * :issue:`1281`: Newton convergence failure prints warnings instead of warning * :issue:`1628`: Unable to install statsmodels in the same requirements file as numpy, pandas, etc. * :issue:`617`: Problem in installing statsmodels in Fedora 17 64-bit * :issue:`935`: ll_null in likelihoodmodels discrete * :issue:`704`: datasets.sunspot: wrong link in description * :issue:`1222`: NegativeBinomial ignores exposure * :issue:`1611`: BUG NegativeBinomial ignores exposure and offset * :issue:`1608`: BUG: NegativeBinomial, llnul is always default 'nb2' * :issue:`1221`: llnull with exposure ? * :issue:`1493`: statsmodels.stats.proportion.proportions_chisquare_allpairs has hardcoded value * :issue:`1260`: GEE test failure on Debian * :issue:`1261`: test failure on Debian * :issue:`443`: GLM.fit does not allow start_params * :issue:`1602`: Fitting GLM with a pre-assigned starting parameter * :issue:`1601`: Fitting GLM with a pre-assigned starting parameter * :issue:`890`: regression_plots problems (pylint) and missing test coverage * :issue:`1598`: Is "old" string formatting Python 3 compatible? * :issue:`1589`: AR vs ARMA order specification * :issue:`1134`: Mark knownfails * :issue:`1259`: Parameterless models * :issue:`616`: python 2.6, python 3 in single codebase * :issue:`1586`: Kalman Filter errors with new pyx * :issue:`1565`: build_win_bdist*_py3*.bat are using the wrong compiler * :issue:`843`: UnboundLocalError When trying to install OS X * :issue:`713`: arima.fit performance * :issue:`367`: unable to install on RHEL 5.6 * :issue:`1548`: testtransf error * :issue:`1478`: is sm.tsa.filters.arfilter an AR filter? * :issue:`1420`: GMM poisson test failures * :issue:`1145`: test_multi noise * :issue:`1539`: NegativeBinomial strange results with bfgs * :issue:`936`: vbench for statsmodels * :issue:`1153`: Where are all our testing machines? * :issue:`1500`: Use Miniconda for test builds * :issue:`1526`: Out of date docs * :issue:`1311`: BUG/BLD 3.4 compatibility of cython c files * :issue:`1513`: build on osx -python-3.4 * :issue:`1497`: r2nparray needs NAMESPACE file * :issue:`1502`: coveralls coverage report for files is broken * :issue:`1501`: pandas in/out in predict * :issue:`1494`: truncated violin plots * :issue:`1443`: Crash from python.exe using linear regression of statsmodels * :issue:`1462`: qqplot line kwarg is broken/docstring is wrong * :issue:`1457`: BUG/BLD: Failed build if "sandbox" anywhere in statsmodels path * :issue:`1441`: wls function: syntax error "unexpected EOF while parsing" occurs when name of dependent variable starts with digits * :issue:`1428`: ipython_directive does not work with ipython master * :issue:`1385`: SimpleTable in Summary (e.g. OLS) is slow for large models * :issue:`1399`: UnboundLocalError: local variable 'fittedvalues' referenced before assignment * :issue:`1377`: TestAnova2.test_results fails with pandas 0.13.1 * :issue:`1394`: multipletests: reducing memory consumption * :issue:`1267`: Packages cannot have both pandas and statsmodels in install_requires * :issue:`1359`: move graphics.tsa to tsa.graphics * :issue:`356`: docs take up a lot of space * :issue:`988`: AR.fit no precision options for fmin_l_bfgs_b * :issue:`990`: AR fit with bfgs: large score * :issue:`14`: arma with exog * :issue:`1348`: reset_index + set_index with drop=False * :issue:`1343`: ARMA does not pass missing keyword up to TimeSeriesModel * :issue:`1326`: formula example notebook broken * :issue:`1327`: typo in docu-code for "Outlier and Influence Diagnostic Measures" * :issue:`1309`: Box-Cox transform (some code needed: lambda estimator) * :issue:`1059`: sm.tsa.ARMA making ma invertibility * :issue:`1295`: Bug in ARIMA forecasting when start is int len(endog) and dates are given * :issue:`1285`: tsa models fail on PeriodIndex with pandas * :issue:`1269`: KPSS test for stationary processes * :issue:`1268`: Feature request: Exponential smoothing * :issue:`1250`: DOCs error in var_plots * :issue:`1032`: Poisson predict breaks on list * :issue:`347`: minimum number of observations - document or check ? * :issue:`1170`: WLS log likelihood, aic and bic * :issue:`1187`: sm.tsa.acovf fails when both unbiased and fft are True * :issue:`1239`: sandbox kernels, problems with inDomain * :issue:`1231`: sandbox kernels confint missing alpha * :issue:`1245`: kernels cosine differs from Stata * :issue:`823`: KDEUnivariate with weights * :issue:`1229`: precision problems in degenerate case * :issue:`1219`: select_order * :issue:`1206`: REF: RegressionResults cov-HCx into cached attributes * :issue:`1152`: statsmodels failing tests with pandas master * :issue:`1195`: pyximport.install() before import api crash * :issue:`1066`: gmm.IV2SLS has wrong predict signature * :issue:`1186`: OLS when exog is 1d * :issue:`1113`: TST: precision too high in test_normality * :issue:`1159`: scipy version is still >= 0.7? * :issue:`1108`: SyntaxError: unqualified exec is not allowed in function 'test_EvalEnvironment_capture_flag * :issue:`1116`: Typo in Example Doc? * :issue:`1123`: BUG : arima_model._get_predict_out_of_sample, ignores exogenous of there is no trend ? * :issue:`1155`: ARIMA - The computed initial AR coefficients are not stationary * :issue:`979`: Win64 binary cannot find Python installation * :issue:`1046`: TST: test_arima_small_data_bug on current master * :issue:`1146`: ARIMA fit failing for small set of data due to invalid maxlag * :issue:`1081`: streamline linear algebra for linear model * :issue:`1138`: BUG: pacf_yw does not demean * :issue:`1127`: Allow linear link model with Binomial families * :issue:`1122`: no data cleaning for statsmodels.genmod.families.varfuncs.NegativeBinomial() * :issue:`658`: robust.mad is not being computed correctly or is non-standard definition; it returns the median * :issue:`1076`: Some issues with ARMAX forecasting * :issue:`1073`: easy_install sandbox violation * :issue:`1115`: EasyInstall Problem * :issue:`1106`: bug in robust.scale.mad? * :issue:`1102`: Installation Problem * :issue:`1084`: DataFrame.sort_index does not use ascending when then value is a list with a single element * :issue:`393`: marginal effects in discrete choice do not have standard errors defined * :issue:`1078`: Use pandas.version.short_version * :issue:`96`: deepcopy breaks on ResettableCache * :issue:`1055`: datasets.get_rdataset string decode error on python 3 * :issue:`46`: tsa.stattools.acf confint needs checking and tests * :issue:`957`: ARMA start estimate with numpy master * :issue:`62`: GLSAR incorrect initial condition in whiten * :issue:`1021`: from_formula() throws error - problem installing * :issue:`911`: noise in stats.power tests * :issue:`472`: Update roadmap for 0.5 * :issue:`238`: release 0.5 * :issue:`1006`: update nbconvert to IPython 1.0 * :issue:`1038`: DataFrame with integer names not handled in ARIMA * :issue:`1036`: Series no longer inherits from ndarray * :issue:`1028`: Test fail with windows and Anaconda - Low priority * :issue:`676`: acorr_breush_godfrey undefined nlags * :issue:`922`: lowess returns inconsistent with option * :issue:`425`: no bse in robust with norm=TrimmedMean * :issue:`1025`: add_constant incorrectly detects constant column statsmodels-0.12.2/docs/source/release/version0.7.rst000066400000000000000000000167341400612667500224740ustar00rootroot00000000000000:orphan: ============= Release 0.7.0 ============= Release summary --------------- **Note:** This version has never been officially released. Several models have been refactored, improved or bugfixed in 0.8. The following major new features appear in this version. Principal Component Analysis ---------------------------- Author: Kevin Sheppard A new class-based Principal Component Analysis has been added. This class replaces the function-based PCA that previously existed in the sandbox. This change bring a number of new features, including: * Options to control the standardization (demeaning/studentizing) * Scree plotting * Information criteria for selecting the number of factors * R-squared plots to assess component fit * NIPALS implementation when only a small number of components are required and the dataset is large * Missing-value filling using the EM algorithm .. code-block:: python import statsmodels.api as sm from statsmodels.multivariate.pca import PCA data = sm.datasets.fertility.load_pandas().data columns = map(str, range(1960, 2012)) data.set_index('Country Name', inplace=True) dta = data[columns] dta = dta.dropna() pca_model = PCA(dta.T, standardize=False, demean=True) pca_model.plot_scree() *Note* : A function version is also available which is compatible with the call in the sandbox. The function version is just a thin wrapper around the class-based PCA implementation. Regression graphics for GLM/GEE ------------------------------- Author: Kerby Shedden Added variable plots, partial residual plots, and CERES residual plots are available for GLM and GEE models by calling the methods `plot_added_variable`, `plot_partial_residuals`, and `plot_ceres_residuals` that are attached to the results classes. State Space Models ------------------ Author: Chad Fulton State space methods provide a flexible structure for the estimation and analysis of a wide class of time series models. The statsmodels implementation allows specification of state models, fast Kalman filtering, and built-in methods to facilitate maximum likelihood estimation of arbitrary models. One of the primary goals of this module is to allow end users to create and estimate their own models. Below is a short example demonstrating the ease with which a local level model can be specified and estimated: .. code-block:: python import numpy as np import statsmodels.api as sm import pandas as pd data = sm.datasets.nile.load_pandas().data data.index = pd.DatetimeIndex(data.year.astype(int).astype(str), freq='AS') # Setup the state space representation class LocalLevel(sm.tsa.statespace.MLEModel): def __init__(self, endog): # Initialize the state space model super(LocalLevel, self).__init__( endog, k_states=1, initialization='approximate_diffuse') # Setup known components of state space representation matrices self.ssm['design', :] = 1. self.ssm['transition', :] = 1. self.ssm['selection', :] = 1. # Describe how parameters enter the model def update(self, params, transformed=True): params = super(LocalLevel, self).update(params, transformed) self.ssm['obs_cov', 0, 0] = params[0] self.ssm['state_cov', 0, 0] = params[1] def transform_params(self, params): return params**2 # force variance parameters to be positive # Specify start parameters and parameter names @property def start_params(self): return [np.std(self.endog)]*2 @property def param_names(self): return ['sigma2.measurement', 'sigma2.level'] # Fit the model with maximum likelihood estimation mod = LocalLevel(data['volume']) res = mod.fit() print res.summary() The documentation and example notebooks provide further examples of how to form state space models. Included in this release is a full-fledged model making use of the state space infrastructure to estimate SARIMAX models. See below for more details. Time Series Models (ARIMA) with Seasonal Effects ------------------------------------------------ Author: Chad Fulton A model for estimating seasonal autoregressive integrated moving average models with exogenous regressors (SARIMAX) has been added by taking advantage of the new state space functionality. It can be used very similarly to the existing `ARIMA` model, but works on a wider range of specifications, including: * Additive and multiplicative seasonal effects * Flexible trend specification * Regression with SARIMA errors * Regression with time-varying coefficients * Measurement error in the endogenous variables Below is a short example fitting a model with a number of these components, including exogenous data, a linear trend, and annual multiplicative seasonal effects. .. code-block:: python import statsmodels.api as sm import pandas as pd data = sm.datasets.macrodata.load_pandas().data data.index = pd.DatetimeIndex(start='1959-01-01', end='2009-09-01', freq='QS') endog = data['realcons'] exog = data['m1'] mod = sm.tsa.SARIMAX(endog, exog=exog, order=(1,1,1), trend='t', seasonal_order=(0,0,1,4)) res = mod.fit() print res.summary() Generalized Estimating Equations GEE ------------------------------------ Author: Kerby Shedden Enhancements and performance improvements for GEE: * EquivalenceClass covariance structure allows covariances to be specified by arbitrary collections of equality constraints #2188 * add weights #2090 * refactored margins #2158 MixedLM ------- Author: Kerby Shedden with Saket Choudhary Enhancements to MixedLM (#2363): added variance components support for MixedLM allowing a wider range of random effects structures to be specified; also performance improvements from use of sparse matrices internally for random effects design matrices. Other important new features ---------------------------- * GLM: add scipy-based gradient optimization to fit #1961 (Kerby Shedden) * wald_test_terms: new method of LikelihoodModels to compute wald tests (F or chi-square) for terms or sets of coefficients #2132 (Josef Perktold) * add cov_type with fixed scale in WLS to allow chi2-fitting #2137 #2143 (Josef Perktold, Christoph Deil) * VAR: allow generalized IRF and FEVD computation #2067 (Josef Perktold) * get_prediction new method for full prediction results (new API convention) Major Bugs fixed ---------------- * see github issues for a full list * bug in ARMA/ARIMA predict with `exog` #2470 * bugs in VAR * x13: python 3 compatibility Backwards incompatible changes and deprecations ----------------------------------------------- * List backwards incompatible changes Development summary and credits ------------------------------- .. note:: Thanks to all of the contributors for the 0.7 release: .. note:: * Alex Griffing * Antony Lee * Chad Fulton * Christoph Deil * Daniel Sullivan * Hans-Martin von Gaudecker * Jan Schulz * Joey Stockermans * Josef Perktold * Kerby Shedden * Kevin Sheppard * Kiyoto Tamura * Louis-Philippe Lemieux Perreault * Padarn Wilson * Ralf Gommers * Saket Choudhary * Skipper Seabold * Tom Augspurger * Trent Hauck * Vincent Arel-Bundock * chebee7i * donbeo * gliptak * hlin117 * jerry dumblauskas * jonahwilliams * kiyoto * neilsummers * waynenilsen These lists of names are automatically generated based on git log, and may not be complete. statsmodels-0.12.2/docs/source/release/version0.8.rst000066400000000000000000000231271400612667500224670ustar00rootroot00000000000000:orphan: ============= Release 0.8.0 ============= See also changes in the unreleased 0.7 Release summary --------------- The main features of this release are several new time series models based on the statespace framework, multiple imputation using MICE as well as many other enhancements. The codebase also has been updated to be compatible with recent numpy and pandas releases. statsmodels is using now github to store the updated documentation which is available under https://www.statsmodels.org/stable for the last release, and https://www.statsmodels.org/devel/ for the development version. This is the last release that supports Python 2.6. **Warning** API stability is not guaranteed for new features, although even in this case changes will be made in a backwards compatible way if possible. The stability of a new feature depends on how much time it was already in statsmodels master and how much usage it has already seen. If there are specific known problems or limitations, then they are mentioned in the docstrings. The following major new features appear in this version. Statespace Models ----------------- Building on the statespace framework and models added in 0.7, this release includes additional models that build on it. Authored by Chad Fulton largely during GSOC 2015 Kalman Smoother ^^^^^^^^^^^^^^^ The Kalman smoother (introduced in #2434) allows making inference on the unobserved state vector at each point in time using data from the entire sample. In addition to this improved inference, the Kalman smoother is required for future improvements such as simulation smoothing and the expectation maximization (EM) algorithm. As a result of this improvement, all state space models now inherit a `smooth` method for producing results with smoothed state estimates. In addition, the `fit` method will return results with smoothed estimates at the maximum likelihood estimates. Postestimation ^^^^^^^^^^^^^^ Improved post-estimation output is now available to all state space models (introduced in #2566). This includes the new methods `get_prediction` and `get_forecast`, providing standard errors and confidence intervals as well as point estimates, `simulate`, providing simulation of time series following the given state space process, and `impulse_responses`, allowing computation of impulse responses due to innovations to the state vector. Diagnostics ^^^^^^^^^^^ A number of general diagnostic tests on the residuals from state space estimation are now available to all state space models (introduced in #2431). These include: * `test_normality` implements the Jarque-Bera test for normality of residuals * `test_heteroskedasticity` implements a test for homoskedasticity of residuals similar to the Goldfeld-Quandt test * `test_serial_correlation` implements the Ljung-Box (or Box-Pierce) test for serial correlation of residuals These test statistics are also now included in the `summary` method output. In addition, a `plot_diagnostics` method is available which provides four plots to visually assess model fit. Unobserved Components ^^^^^^^^^^^^^^^^^^^^^ The class of univariate Unobserved Components models (also known as structural time series models) are now available (introduced in #2432). This includes as special cases the local level model and local linear trend model. Generically it allows decomposing a time series into trend, cycle, seasonal, and irregular components, optionally with exogenous regressors and / or autoregressive errors. Multivariate Models ^^^^^^^^^^^^^^^^^^^ Two standard multivariate econometric models - vector autoregressive moving-average model with exogenous regressors (VARMAX) and Dynamic Factors models - are now available (introduced in #2563). The first is a popular reduced form method of exploring the covariance in several time series, and the second is a popular reduced form method of extracting a small number of common factors from a large dataset of observed series. Recursive least squares ^^^^^^^^^^^^^^^^^^^^^^^ A model for recursive least squares, also known as expanding-window OLS, is now available in `statsmodels.regression` (introduced in #2830). Miscellaneous ^^^^^^^^^^^^^ Other improvements to the state space framework include: * Improved missing data handling #2770, #2809 * Ongoing refactoring and bug fixes in fringes and corner cases Time Series Analysis -------------------- Markov Switching Models ^^^^^^^^^^^^^^^^^^^^^^^ Markov switching dynamic regression and autoregression models are now available (introduced in #2980 by Chad Fulton). These models allow regression effects and / or autoregressive dynamics to differ depending on an unobserved "regime"; in Markov switching models, the regimes are assumed to transition according to a Markov process. Statistics ^^^^^^^^^^ * KPSS stationarity, unit root test #2775 (N-Wouda) * The Brock Dechert Scheinkman (BDS) test for nonlinear dependence is now available (introduced in #934 by Chad Fulton) * Augmented Engle/Granger cointegration test (refactor hidden function) #3146 (Josef Perktold) New functionality in statistics ------------------------------- Contingency Tables #2418 (Kerby Shedden) Local FDR, multiple testing #2297 (Kerby Shedden) Mediation Analysis #2352 (Kerby Shedden) Confidence intervals for multinomial proportions #3162 (Sebastien Lerique, Josef Perktold) other: * weighted quantiles in DescrStatsW #2707 (Kerby Shedden) Duration -------- Kaplan Meier Survival Function #2614 (Kerby Shedden) Cumulative incidence rate function #3016 (Kerby Shedden) other: * frequency weights in Kaplan-Meier #2992 (Kerby Shedden) * entry times for Kaplan-Meier #3126 (Kerby Shedden) * intercept handling for PHReg #3095 (Kerby Shedden) Imputation ---------- new subpackage in `statsmodels.imputation` MICE #2076 (Frank Cheng GSOC 2014 and Kerby Shedden) Imputation by regression on Order Statistic #3019 (Paul Hobson) Penalized Estimation -------------------- Elastic net: fit_regularized with L1/L2 penalization has been added to OLS, GLM and PHReg (Kerby Shedden) GLM --- Tweedie is now available as new family #2872 (Peter Quackenbush, Josef Perktold) other: * frequency weights for GLM (currently without full support) # * more flexible convergence options #2803 (Peter Quackenbush) Multivariate ------------ new subpackage that currently contains PCA PCA was added in 0.7 to statsmodels.tools and is now in statsmodels.multivariate Documentation ------------- New doc build with latest jupyter and Python 3 compatibility (Tom Augspurger) Other important improvements ---------------------------- several existing functions have received improvements * seasonal_decompose: improved periodicity handling #2987 (ssktotoro ?) * tools add_constant, add_trend: refactoring and pandas compatibility #2240 (Kevin Sheppard) * acf, pacf, acovf: option for missing handling #3020 (joesnacks ?) * acf, pacf plots: allow array of lags #2989 (Kevin Sheppard) * pickling support for ARIMA #3412 (zaemyung) * io SimpleTable (summary): allow names with special characters #3015 (tvanessa ?) * tsa tools lagmat, lagmat2ds: pandas support #2310 #3042 (Kevin Sheppard) * CompareMeans: from_data, summary methods #2754 (Valery Tyumen) * API cleanup for robust, sandwich covariances #3162 (Josef Perktold) * influence plot used swapped arguments (bug) #3158 Major Bugs fixed ---------------- * see github issues While most bugs are usability problems, there is now a new label `type-bug-wrong` for bugs that cause that silently incorrect numbers are returned. https://github.com/statsmodels/statsmodels/issues?q=label%3Atype-bug-wrong+is%3Aclosed Backwards incompatible changes and deprecations ----------------------------------------------- * predict now returns a pandas Series if the exog argument is a DataFrame, including missing/NaN values * PCA moved to multivariate compared to 0.7 Development summary and credits ------------------------------- Besides receiving contributions for new and improved features and for bugfixes, important contributions to general maintenance came from * Kevin Sheppard * Pierre Barbier de Reuille * Tom Augsburger and the general maintainer and code reviewer * Josef Perktold Additionally, many users contributed by participation in github issues and providing feedback. Thanks to all of the contributors for the 0.8 release (based on git log): .. note:: * Ashish * Brendan * Brendan Condon * BrianLondon * Chad Fulton * Chris Fonnesbeck * Christian Lorentzen * Christoph T. Weidemann * James Kerns * Josef Perktold * Kerby Shedden * Kevin Sheppard * Leoyzen * Matthew Brett * Niels Wouda * Paul Hobson * Pierre Barbier de Reuille * Pietro Battiston * Ralf Gommers * Roman Ring * Skipper Seabold * Soren Fuglede Jorgensen * Thomas Cokelaer * Tom Augspurger * ValeryTyumen * Vanessa * Yaroslav Halchenko * dhpiyush * joesnacks * kokes * matiumerca * rlan * ssktotoro * thequackdaddy * vegcev Thanks to all of the contributors for the 0.7 release: .. note:: * Alex Griffing * Antony Lee * Chad Fulton * Christoph Deil * Daniel Sullivan * Hans-Martin von Gaudecker * Jan Schulz * Joey Stockermans * Josef Perktold * Kerby Shedden * Kevin Sheppard * Kiyoto Tamura * Louis-Philippe Lemieux Perreault * Padarn Wilson * Ralf Gommers * Saket Choudhary * Skipper Seabold * Tom Augspurger * Trent Hauck * Vincent Arel-Bundock * chebee7i * donbeo * gliptak * hlin117 * jerry dumblauskas * jonahwilliams * kiyoto * neilsummers * waynenilsen These lists of names are automatically generated based on git log, and may not be complete. statsmodels-0.12.2/docs/source/release/version0.9.rst000066400000000000000000000345371400612667500224770ustar00rootroot00000000000000:orphan: ============= Release 0.9.0 ============= Release summary --------------- statsmodels is using github to store the updated documentation which is available under https://www.statsmodels.org/stable for the last release, and https://www.statsmodels.org/devel/ for the development version. **Warning** API stability is not guaranteed for new features, although even in this case changes will be made in a backwards compatible way if possible. The stability of a new feature depends on how much time it was already in statsmodels master and how much usage it has already seen. If there are specific known problems or limitations, then they are mentioned in the docstrings. The list of pull requests for this release can be found on github https://github.com/statsmodels/statsmodels/pulls?utf8=%E2%9C%93&q=is%3Apr+is%3Amerged+milestone%3A0.9 (The list does not include some pull request that were merged before the 0.8 release but not included in 0.8.) The Highlights -------------- - statespace refactoring, Markov Switching Kim smoother - 3 Google summer of code (GSOC) projects merged - distributed estimation - VECM and enhancements to VAR (including cointegration test) - new count models: GeneralizedPoisson, zero inflated models - Bayesian mixed GLM - Gaussian Imputation - new multivariate methods: factor analysis, MANOVA, repeated measures within ANOVA - GLM var_weights in addition to freq_weights - Holt-Winters and Exponential Smoothing What's new - an overview ------------------------ The following lists the main new features of statsmodels 0.9. In addition, release 0.9 includes bug fixes, refactorings and improvements in many areas. **base** - distributed estimation #3396 (Leland Bybee GSOC, Kerby Shedden) - optimization option scipy minimize #3193 (Roman Ring) - Box-Cox #3477 (Niels Wouda) - t_test_pairwise #4365 (Josef Perktold) **discrete** - new count models (Evgeny Zhurko GSOC, Josef Perktold) - NegativeBinomialP #3832 merged in #3874 - GeneralizedPoisson #3727 merged in #3795 - zero-inflated count models #3755 merged in #3908 - discrete optimization improvements #3921, #3928 (Josef Perktold) - extend discrete margin when extra params, NegativeBinomial #3811 (Josef Perktold) **duration** - dependent censoring in survival/duration #3090 (Kerby Shedden) - entry times for Kaplan-Meier #3126 (Kerby Shedden) **genmod** - Bayesian GLMM #4189, #4540 (Kerby Shedden) - GLM add var_weights #3692 (Peter Quackenbush) - GLM: EIM in optimization #3646 (Peter Quackenbush) - GLM correction to scale handling, loglike #3856 (Peter Quackenbush) **graphics** - graphics HDR functional boxplot #3876 merged in #4049 (Pamphile ROY) - graphics Bland-Altman or Tukey mean difference plot #4112 merged in #4200 (Joses W. Ho) - bandwidth options in violinplots #4510 (Jim Correia) **imputation** - multiple imputation via Gaussian model #4394, #4520 (Kerby Shedden) - regularized fitting in MICE #4319 (Kerby Shedden) **iolib** - improvements of summary_coll #3702 merged #4064 (Natasha Watkins, Kevin Sheppard) **multivariate** - multivariate: MANOVA, CanCorr #3327 (Yichuan Liu) - Factor Analysis #4161, #4156, #4167, #4214 (Yichuan Liu, Kerby Shedden, Josef Perktold) - statsmodels now includes the rotation code by .... **regression** - fit_regularized for WLS #3581 (Kerby Shedden) **stats** - Knockoff FDR # 3204 (Kerby Shedden) - Repeated measures ANOVA #3303 merged in #3663, #3838 (Yichuan Liu, Richard Höchenberger) - lilliefors test for exponential distribution #3837 merged in #3936 (Jacob Kimmel, Josef Perktold) **tools** - quasi-random, Halton sequences #4104 (Pamphile ROY) **tsa** - VECM #3246 (Aleksandar Karakas GSOC, Josef Perktold) - exog support in VAR, incomplete for extra results, part of VECM #3246, #4538 (Aleksandar Karakas GSOC, Josef Perktold) - Markov switching, Kim smoother #3141 (Chad Fulton) - Holt-Winters #3817 merged in #4176 (tvanzyl) - seasonal_decompose: trend extrapolation and vectorized 2-D #3031 (kernc, Josef Perktold) - add frequency domain seasonal components to UnobservedComponents #4250 (Jordan Yoder) - refactoring of date handling in tsa #3276, #4457 (Chad Fulton) - SARIMAX without AR, MA #3383 (Chad Fulton) **maintenance** - switch to pytest #3804 plus several other PRs (Kevin Sheppard) - general compatibility fixes for recent versions of numpy, scipy and pandas `bug-wrong` ~~~~~~~~~~~ A new issue label `type-bug-wrong` indicates bugs that cause that incorrect numbers are returned without warnings. (Regular bugs are mostly usability bugs or bugs that raise an exception for unsupported use cases.) see https://github.com/statsmodels/statsmodels/issues?q=is%3Aissue+label%3Atype-bug-wrong+is%3Aclosed+milestone%3A0.9 - scale in GLM fit_constrained, #4193 fixed in #4195 cov_params and bse were incorrect if scale is estimated as in Gaussian. (This did not affect families with scale=1 such as Poisson) - incorrect `pearson_chi2` with binomial counts, #3612 fixed as part of #3692 - null_deviance and llnull in GLMResults were wrong if exposure was used and when offset was used with Binomial counts. - GLM Binomial in the non-binary count case used incorrect endog in recreating models which is used by fit_regularized and fit_constrained #4599. - GLM observed hessian was incorrectly computed if non-canonical link is used, fixed in #4620 This fix improves convergence with gradient optimization and removes a usually numerically small error in cov_params. - discrete predict with offset or exposure, #3569 fixed in #3696 If either offset or exposure are not None but exog is None, then offset and exposure arguments in predict were ignored. - discrete margins had wrong dummy and count effect if constant is prepended, #3695 fixed in #3696 - OLS outlier test, wrong index if order is True, #3971 fixed in #4385 - tsa coint ignored the autolag keyword, #3966 fixed in #4492 This is a backwards incompatible change in default, instead of fixed maxlag it defaults now to 'aic' lag selection. The default autolag is now the same as the adfuller default. - wrong confidence interval in contingency table summary, #3822 fixed in #3830 This only affected the summary and not the corresponding attribute. - incorrect results in summary_col if regressor_order is used, #3767 fixed in #4271 Description of selected new feature ----------------------------------- The following provides more information about a selected set of new features. Vector Error Correction Model (VECM) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The VECM framework developed during GSOC 2016 by Aleksandar Karakas adds support for non-stationary cointegrated VAR processes to statsmodels. Currently, the following topics are implemented * Parameter estimation for cointegrated VAR * forecasting * testing for Granger-causality and instantaneous causality * testing for cointegrating rank * lag order selection. New methods have been added also to the existing VAR model, and VAR has now limited support for user provided explanatory variables. New Count Models ---------------- New count models have been added as part of GSOC 2017 by Evgeny Zhurko. Additional models that are not yet finished will be added for the next release. The new models are: * NegativeBinomialP (NBP): This is a generalization of NegativeBinomial that allows the variance power parameter to be specified in the range between 1 and 2. The current NegativeBinomial support NB1 and NB2 which are two special cases of NBP. * GeneralizedPoisson (GPP): Similar to NBP this allows a large range of dispersion specification. GPP also allow some amount of under dispersion * ZeroInflated Models: Based on a generic base class, zeroinflated models are now available for Poisson, GeneralizedPoisson and NegativeBinomialP. Generalized linear mixed models ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Limited support for GLIMMIX models is now included in the genmod module. Binomial and Poisson models with independent random effects can be fit using Bayesian methods (Laplace and mean field approximations to the posterior). Multiple imputation ~~~~~~~~~~~~~~~~~~~ Multiple imputation using a multivariate Gaussian model is now included in the imputation module. The model is fit via Gibbs sampling from the joint posterior of the mean vector, covariance matrix, and missing data values. A convenience function for fitting a model to the multiply imputed data sets and combining the results is provided. This is an alternative to the existing MICE (Multiple Imputation via Chained Equations) procedures. Exponential smoothing models ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Exponential smoothing models are now available (introduced in #4176 by Terence L van Zyl). These models are conceptually simple, decomposing a time series into level, trend, and seasonal components that are constructed from weighted averages of past observations. Nonetheless, they produce forecasts that are competitive with more advanced models and which may be easier to interpret. Available models include: - Simple exponential smoothing - Holt's method - Holt-Winters exponential smoothing Improved time series index support ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Handling of indexes for time series models has been overhauled (#3272) to take advantage of recent improvements in Pandas and to shift to Pandas much of the special case handling (especially for date indexes) that had previously been done in statsmodels. Benefits include more consistent behavior, a reduced number of bugs from corner cases, and a reduction in the maintenance burden. Although an effort was made to maintain backwards compatibility with this change, it is possible that some undocumented corner cases that previously worked will now raise warnings or exceptions. State space models ~~~~~~~~~~~~~~~~~~ The state space model infrastructure has been rewritten and improved (#2845). New features include: - Kalman smoother rewritten in Cython for substantial performance improvements - Simulation smoother (Durbin and Koopman, 2002) - Fast simulation of time series for any state space model - Univariate Kalman filtering and smoothing (Koopman and Durbin, 2000) - Collapsed Kalman filtering and smoothing (Jungbacker and Koopman, 2014) - Optional computation of the lag-one state autocovariance - Use of the Scipy BLAS functions for Cython interface if available (`scipy.linalg.cython_blas` for Scipy >= 0.16) These features yield new features and improve performance for the existing state space models (`SARIMAX`, `UnobservedComopnents`, `DynamicFactor`, and `VARMAX`), and they also make Bayesian estimation by Gibbs-sampling possible. **Warning**: this will be the last version that includes the original state space code and supports Scipy < 0.16. The next release will only include the new state space code. Unobserved components models: frequency-domain seasonals ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Unobserved components models now support modeling seasonal factors from a frequency-domain perspective with user-specified period and harmonics (introduced in #4250 by Jordan Yoder). This not only allows for multiple seasonal effects, but also allows the representation of seasonal components with fewer unobserved states. This can improve computational performance and, since it allows for a more parsimonious model, may also improve the out-of-sample performance of the model. Major Bugs fixed ---------------- * see github issues for a list of bug fixes included in this release https://github.com/statsmodels/statsmodels/pulls?utf8=%E2%9C%93&q=is%3Apr+is%3Amerged+milestone%3A0.9+label%3Atype-bug https://github.com/statsmodels/statsmodels/pulls?q=is%3Apr+is%3Amerged+milestone%3A0.9+label%3Atype-bug-wrong * Refitting elastic net regularized models using the `refit=True` option now returns the unregularized parameters for the coefficients selected by the regularized fitter, as documented. #4213 * In MixedLM, a bug that produced exceptions when calling `random_effects_cov` on models with variance components has been fixed. Backwards incompatible changes and deprecations ----------------------------------------------- * DynamicVAR and DynamicPanelVAR is deprecated and will be removed in a future version. It used rolling OLS from pandas which has been removed in pandas. * In MixedLM, names for the random effects variance and covariance parameters have changed from, e.g. G RE to G Var or G x F Cov. This impacts summary output, and also may require modifications to user code that extracted these parameters from the fitted results object by name. * In MixedLM, the names for the random effects realizations for variance components have been changed. When using formulas, the random effect realizations are named using the column names produced by Patsy when parsing the formula. Development summary and credits ------------------------------- Besides receiving contributions for new and improved features and for bugfixes, important contributions to general maintenance for this release came from * Kevin Sheppard * Peter Quackenbush * Brock Mendel and the general maintainer and code reviewer * Josef Perktold Additionally, many users contributed by participation in github issues and providing feedback. Thanks to all of the contributors for the 0.9 release (based on git log): .. note:: * Aleksandar Karakas * Alex Fortin * Alexander Belopolsky * Brock Mendel * Chad Fulton * ChadFulton * Christian Lorentzen * Dave Willmer * Dror Atariah * Evgeny Zhurko * Gerard Brunick * Greg Mosby * Jacob Kimmel * Jamie Morton * Jarvis Miller * Jasmine Mou * Jeroen Van Goey * Jim Correia * Joon Ro * Jordan Yoder * Jorge C. Leitao * Josef Perktold * Joses W. Ho * José Lopez * Joshua Engelman * Juan Escamilla * Justin Bois * Kerby Shedden * Kernc * Kevin Sheppard * Leland Bybee * Maxim Uvarov * Michael Kaminsky * Mosky Liu * Natasha Watkins * Nick DeRobertis * Niels Wouda * Pamphile ROY * Peter Quackenbush * Quentin Andre * Richard Höchenberger * Rob Klooster * Roman Ring * Scott Tsai * Soren Fuglede Jorgensen * Tom Augspurger * Tommy Odland * Tony Jiang * Yichuan Liu * ftemme * hugovk * kiwirob * malickf * tvanzyl * weizhongg * zveryansky These lists of names are automatically generated based on git log, and may not be complete. statsmodels-0.12.2/docs/source/rlm.rst000066400000000000000000000042271400612667500177260ustar00rootroot00000000000000.. currentmodule:: statsmodels.robust .. _rlm: Robust Linear Models ==================== Robust linear models with support for the M-estimators listed under `Norms`_. See `Module Reference`_ for commands and arguments. Examples -------- .. ipython:: python # Load modules and data import statsmodels.api as sm data = sm.datasets.stackloss.load(as_pandas=False) data.exog = sm.add_constant(data.exog) # Fit model and print summary rlm_model = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT()) rlm_results = rlm_model.fit() print(rlm_results.params) Detailed examples can be found here: * `Robust Models 1 `__ * `Robust Models 2 `__ Technical Documentation ----------------------- .. toctree:: :maxdepth: 1 rlm_techn1 References ^^^^^^^^^^ * PJ Huber. ‘Robust Statistics’ John Wiley and Sons, Inc., New York. 1981. * PJ Huber. 1973, ‘The 1972 Wald Memorial Lectures: Robust Regression: Asymptotics, Conjectures, and Monte Carlo.’ The Annals of Statistics, 1.5, 799-821. * R Venables, B Ripley. ‘Modern Applied Statistics in S’ Springer, New York, * C Croux, PJ Rousseeuw, 'Time-efficient algorithms for two highly robust estimators of scale' Computational statistics. Physica, Heidelberg, 1992. Module Reference ---------------- .. module:: statsmodels.robust Model Classes ^^^^^^^^^^^^^ .. module:: statsmodels.robust.robust_linear_model .. currentmodule:: statsmodels.robust.robust_linear_model .. autosummary:: :toctree: generated/ RLM Model Results ^^^^^^^^^^^^^ .. autosummary:: :toctree: generated/ RLMResults .. _norms: Norms ^^^^^ .. module:: statsmodels.robust.norms .. currentmodule:: statsmodels.robust.norms .. autosummary:: :toctree: generated/ AndrewWave Hampel HuberT LeastSquares RamsayE RobustNorm TrimmedMean TukeyBiweight estimate_location Scale ^^^^^ .. module:: statsmodels.robust.scale .. currentmodule:: statsmodels.robust.scale .. autosummary:: :toctree: generated/ Huber HuberScale mad hubers_scale iqr qn_scale statsmodels-0.12.2/docs/source/rlm_techn1.rst000066400000000000000000000006721400612667500211700ustar00rootroot00000000000000.. module:: statsmodels.rlm :synopsis: Outlier robust linear models .. currentmodule:: statsmodels.rlm .. _rlm_techn1: Weight Functions ---------------- Andrew's Wave .. image:: images/aw.png Hampel 17A .. image:: images/hl.png Huber's t .. image:: images/ht.png Least Squares .. image:: images/ls.png Ramsay's Ea .. image:: images/re.png Trimmed Mean .. image:: images/tm.png Tukey's Biweight .. image:: images/tk.png statsmodels-0.12.2/docs/source/sandbox.rst000066400000000000000000000122311400612667500205640ustar00rootroot00000000000000.. _sandbox: Sandbox ======= This sandbox contains code that is for various reasons not ready to be included in statsmodels proper. It contains modules from the old stats.models code that have not been tested, verified and updated to the new statsmodels structure: cox survival model, mixed effects model with repeated measures, generalized additive model and the formula framework. The sandbox also contains code that is currently being worked on until it fits the pattern of statsmodels or is sufficiently tested. All sandbox modules have to be explicitly imported to indicate that they are not yet part of the core of statsmodels. The quality and testing of the sandbox code varies widely. Examples -------- There are some examples in the `sandbox.examples` folder. Additional examples are directly included in the modules and in subfolders of the sandbox. Module Reference ---------------- Time Series analysis :mod:`tsa` ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In this part we develop models and functions that will be useful for time series analysis. Most of the models and function have been moved to :mod:`statsmodels.tsa`. Moving Window Statistics """""""""""""""""""""""" Most moving window statistics, like rolling mean, moments (up to 4th order), min, max, mean, and variance, are covered by the functions for `Moving (rolling) statistics/moments `_ in Pandas. .. module:: statsmodels.sandbox.tsa :synopsis: Experimental time-series analysis models .. currentmodule:: statsmodels.sandbox.tsa .. autosummary:: :toctree: generated/ movstat.movorder movstat.movmean movstat.movvar movstat.movmoment Regression and ANOVA ^^^^^^^^^^^^^^^^^^^^ .. module:: statsmodels.sandbox.regression.anova_nistcertified :synopsis: Experimental ANOVA estimator .. currentmodule:: statsmodels.sandbox.regression.anova_nistcertified The following two ANOVA functions are fully tested against the NIST test data for balanced one-way ANOVA. ``anova_oneway`` follows the same pattern as the oneway anova function in scipy.stats but with higher precision for badly scaled problems. ``anova_ols`` produces the same results as the one way anova however using the OLS model class. It also verifies against the NIST tests, with some problems in the worst scaled cases. It shows how to do simple ANOVA using statsmodels in three lines and is also best taken as a recipe. .. autosummary:: :toctree: generated/ anova_oneway anova_ols The following are helper functions for working with dummy variables and generating ANOVA results with OLS. They are best considered as recipes since they were written with a specific use in mind. These function will eventually be rewritten or reorganized. .. module:: statsmodels.sandbox.regression :synopsis: Experimental regression tools .. currentmodule:: statsmodels.sandbox.regression .. autosummary:: :toctree: generated/ try_ols_anova.data2dummy try_ols_anova.data2groupcont try_ols_anova.data2proddummy try_ols_anova.dropname try_ols_anova.form2design The following are helper functions for group statistics where groups are defined by a label array. The qualifying comments for the previous group apply also to this group of functions. .. autosummary:: :toctree: generated/ try_catdata.cat2dummy try_catdata.convertlabels try_catdata.groupsstats_1d try_catdata.groupsstats_dummy try_catdata.groupstatsbin try_catdata.labelmeanfilter try_catdata.labelmeanfilter_nd try_catdata.labelmeanfilter_str Additional to these functions, sandbox regression still contains several examples, that are illustrative of the use of the regression models of statsmodels. Systems of Regression Equations and Simultaneous Equations ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The following are for fitting systems of equations models. Though the returned parameters have been verified as accurate, this code is still very experimental, and the usage of the models will very likely change significantly before they are added to the main codebase. .. module:: statsmodels.sandbox.sysreg :synopsis: Experimental system regression models .. currentmodule:: statsmodels.sandbox.sysreg .. autosummary:: :toctree: generated/ SUR Sem2SLS Miscellaneous ^^^^^^^^^^^^^ .. module:: statsmodels.sandbox.tools.tools_tsa :synopsis: Experimental tools for working with time-series .. currentmodule:: statsmodels.sandbox.tools.tools_tsa Descriptive Statistics Printing """"""""""""""""""""""""""""""" .. module:: statsmodels.sandbox :synopsis: Experimental tools that have not been fully vetted .. currentmodule:: statsmodels.sandbox .. autosummary:: :toctree: generated/ descstats.sign_test descstats.descstats Original stats.models ^^^^^^^^^^^^^^^^^^^^^ None of these are fully working. 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trent tri tricube trimboth triw triweight tsa tsaplots tsatools tss tstat tt ttest ttost tukey tukeyQcrit tukeyhsd tuple tuples tvalues tvanessa tvanzyl tvtp tw tweedie twosided twostage txt ty tyleha tylerhartley typerror typlist ub uiowa uk umfpack umich un unadjusted uncentered uncommenting unconstrain undamped underdispersion undifferenced unibo uniq uniquenesses unitroot univariate unmodeled unnormalized unordered unpenalized unpickle unpickled unregularized unreplicated unrotated unscaled unsecure unshallow unsqueeze unsqueezed untransform untransformed unweight unweighted unwhitened upp urls usecase useic useranks usevar utf valentin vals varanelli varcorrection vare varel varfuncs variates variational varimax varlist varma varmax varname varnames vbench vc vcov vcp vec vecm vectorized vegcev venv versa verterical violinplot violinplots virgile vlblist vlines vname von vscode vstack vstackarma vtype wald wallis wargs warnflag watson waynenilsen webdoc webuse weightmatrix weightstats weigths weizhongg wellek wendog wexog wilsonp windowsize windsize winsorized wls wmean wo worN wresid wts wusing www xdist xfail xfunc xk xlabel xname xnames xopt xpoints xranks xrr xtol xtscc xvals ybar ylabel ylimit yname ynames ys ytick yw ywadjusted ywm ywmle ywunbiased zaemyung zconfint zcu zero'd zeroinflated zivot zscores zstat zt ztest ztost zvalues qn Qn statsmodels-0.12.2/docs/source/statespace.rst000066400000000000000000001037301400612667500212670ustar00rootroot00000000000000.. module:: statsmodels.tsa.statespace :synopsis: Statespace models for time-series analysis .. currentmodule:: statsmodels.tsa.statespace .. _statespace: Time Series Analysis by State Space Methods :mod:`statespace` ============================================================= :mod:`statsmodels.tsa.statespace` contains classes and functions that are useful for time series analysis using state space methods. A general state space model is of the form .. math:: y_t & = Z_t \alpha_t + d_t + \varepsilon_t \\ \alpha_{t+1} & = T_t \alpha_t + c_t + R_t \eta_t \\ where :math:`y_t` refers to the observation vector at time :math:`t`, :math:`\alpha_t` refers to the (unobserved) state vector at time :math:`t`, and where the irregular components are defined as .. math:: \varepsilon_t \sim N(0, H_t) \\ \eta_t \sim N(0, Q_t) \\ The remaining variables (:math:`Z_t, d_t, H_t, T_t, c_t, R_t, Q_t`) in the equations are matrices describing the process. Their variable names and dimensions are as follows Z : `design` :math:`(k\_endog \times k\_states \times nobs)` d : `obs_intercept` :math:`(k\_endog \times nobs)` H : `obs_cov` :math:`(k\_endog \times k\_endog \times nobs)` T : `transition` :math:`(k\_states \times k\_states \times nobs)` c : `state_intercept` :math:`(k\_states \times nobs)` R : `selection` :math:`(k\_states \times k\_posdef \times nobs)` Q : `state_cov` :math:`(k\_posdef \times k\_posdef \times nobs)` In the case that one of the matrices is time-invariant (so that, for example, :math:`Z_t = Z_{t+1} ~ \forall ~ t`), its last dimension may be of size :math:`1` rather than size `nobs`. This generic form encapsulates many of the most popular linear time series models (see below) and is very flexible, allowing estimation with missing observations, forecasting, impulse response functions, and much more. **Example: AR(2) model** An autoregressive model is a good introductory example to putting models in state space form. Recall that an AR(2) model is often written as: .. math:: y_t = \phi_1 y_{t-1} + \phi_2 y_{t-2} + \epsilon_t, \quad \epsilon_t \sim N(0, \sigma^2) This can be put into state space form in the following way: .. math:: y_t & = \begin{bmatrix} 1 & 0 \end{bmatrix} \alpha_t \\ \alpha_{t+1} & = \begin{bmatrix} \phi_1 & \phi_2 \\ 1 & 0 \end{bmatrix} \alpha_t + \begin{bmatrix} 1 \\ 0 \end{bmatrix} \eta_t Where .. math:: Z_t \equiv Z = \begin{bmatrix} 1 & 0 \end{bmatrix} and .. math:: T_t \equiv T & = \begin{bmatrix} \phi_1 & \phi_2 \\ 1 & 0 \end{bmatrix} \\ R_t \equiv R & = \begin{bmatrix} 1 \\ 0 \end{bmatrix} \\ \eta_t \equiv \epsilon_{t+1} & \sim N(0, \sigma^2) There are three unknown parameters in this model: :math:`\phi_1, \phi_2, \sigma^2`. Models and Estimation --------------------- The following are the main estimation classes, which can be accessed through `statsmodels.tsa.statespace.api` and their result classes. Seasonal Autoregressive Integrated Moving-Average with eXogenous regressors (SARIMAX) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The `SARIMAX` class is an example of a fully fledged model created using the statespace backend for estimation. `SARIMAX` can be used very similarly to :ref:`tsa ` models, but works on a wider range of models by adding the estimation of additive and multiplicative seasonal effects, as well as arbitrary trend polynomials. .. autosummary:: :toctree: generated/ sarimax.SARIMAX sarimax.SARIMAXResults For an example of the use of this model, see the `SARIMAX example notebook `__ or the very brief code snippet below: .. code-block:: python # Load the statsmodels api import statsmodels.api as sm # Load your dataset endog = pd.read_csv('your/dataset/here.csv') # We could fit an AR(2) model, described above mod_ar2 = sm.tsa.SARIMAX(endog, order=(2,0,0)) # Note that mod_ar2 is an instance of the SARIMAX class # Fit the model via maximum likelihood res_ar2 = mod_ar2.fit() # Note that res_ar2 is an instance of the SARIMAXResults class # Show the summary of results print(res_ar2.summary()) # We could also fit a more complicated model with seasonal components. # As an example, here is an SARIMA(1,1,1) x (0,1,1,4): mod_sarimax = sm.tsa.SARIMAX(endog, order=(1,1,1), seasonal_order=(0,1,1,4)) res_sarimax = mod_sarimax.fit() # Show the summary of results print(res_sarimax.summary()) The results object has many of the attributes and methods you would expect from other statsmodels results objects, including standard errors, z-statistics, and prediction / forecasting. Behind the scenes, the `SARIMAX` model creates the design and transition matrices (and sometimes some of the other matrices) based on the model specification. Unobserved Components ^^^^^^^^^^^^^^^^^^^^^ The `UnobservedComponents` class is another example of a statespace model. .. autosummary:: :toctree: generated/ structural.UnobservedComponents structural.UnobservedComponentsResults For examples of the use of this model, see the `example notebook `__ or a notebook on using the unobserved components model to `decompose a time series into a trend and cycle `__ or the very brief code snippet below: .. code-block:: python # Load the statsmodels api import statsmodels.api as sm # Load your dataset endog = pd.read_csv('your/dataset/here.csv') # Fit a local level model mod_ll = sm.tsa.UnobservedComponents(endog, 'local level') # Note that mod_ll is an instance of the UnobservedComponents class # Fit the model via maximum likelihood res_ll = mod_ll.fit() # Note that res_ll is an instance of the UnobservedComponentsResults class # Show the summary of results print(res_ll.summary()) # Show a plot of the estimated level and trend component series fig_ll = res_ll.plot_components() # We could further add a damped stochastic cycle as follows mod_cycle = sm.tsa.UnobservedComponents(endog, 'local level', cycle=True, damped_cycle=True, stochastic_cycle=True) res_cycle = mod_cycle.fit() # Show the summary of results print(res_cycle.summary()) # Show a plot of the estimated level, trend, and cycle component series fig_cycle = res_cycle.plot_components() Vector Autoregressive Moving-Average with eXogenous regressors (VARMAX) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The `VARMAX` class is an example of a multivariate statespace model. .. autosummary:: :toctree: generated/ varmax.VARMAX varmax.VARMAXResults For an example of the use of this model, see the `VARMAX example notebook `__ or the very brief code snippet below: .. code-block:: python # Load the statsmodels api import statsmodels.api as sm # Load your (multivariate) dataset endog = pd.read_csv('your/dataset/here.csv') # Fit a local level model mod_var1 = sm.tsa.VARMAX(endog, order=(1,0)) # Note that mod_var1 is an instance of the VARMAX class # Fit the model via maximum likelihood res_var1 = mod_var1.fit() # Note that res_var1 is an instance of the VARMAXResults class # Show the summary of results print(res_var1.summary()) # Construct impulse responses irfs = res_ll.impulse_responses(steps=10) Dynamic Factor Models ^^^^^^^^^^^^^^^^^^^^^ Statsmodels has two classes that support dynamic factor models: `DynamicFactorMQ` and `DynamicFactor`. Each of these models has strengths, but in general the `DynamicFactorMQ` class is recommended. This is because it fits parameters using the Expectation-Maximization (EM) algorithm, which is more robust and can handle including hundreds of observed series. In addition, it allows customization of which variables load on which factors. However, it does not yet support including exogenous variables, while `DynamicFactor` does support that feature. .. autosummary:: :toctree: generated/ dynamic_factor_mq.DynamicFactorMQ dynamic_factor_mq.DynamicFactorMQResults For an example of the `DynamicFactorMQ` class, see the very brief code snippet below: .. code-block:: python # Load the statsmodels api import statsmodels.api as sm # Load your dataset endog = pd.read_csv('your/dataset/here.csv') # Create a dynamic factor model mod_dfm = sm.tsa.DynamicFactorMQ(endog, k_factors=1, factor_order=2) # Note that mod_dfm is an instance of the DynamicFactorMQ class # Fit the model via maximum likelihood, using the EM algorithm res_dfm = mod_dfm.fit() # Note that res_dfm is an instance of the DynamicFactorMQResults class # Show the summary of results print(res_ll.summary()) # Show a plot of the r^2 values from regressions of # individual estimated factors on endogenous variables. fig_dfm = res_ll.plot_coefficients_of_determination() The `DynamicFactor` class is suitable for models with a smaller number of observed variables .. autosummary:: :toctree: generated/ dynamic_factor.DynamicFactor dynamic_factor.DynamicFactorResults For an example of the use of the `DynamicFactor` model, see the `Dynamic Factor example notebook `__ Linear Exponential Smoothing Models ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The `ExponentialSmoothing` class is an implementation of linear exponential smoothing models using a state space approach. **Note**: this model is available at `sm.tsa.statespace.ExponentialSmoothing`; it is not the same as the model available at `sm.tsa.ExponentialSmoothing`. See below for details of the differences between these classes. .. autosummary:: :toctree: generated/ exponential_smoothing.ExponentialSmoothing exponential_smoothing.ExponentialSmoothingResults A very brief code snippet follows: .. code-block:: python # Load the statsmodels api import statsmodels.api as sm # Load your dataset endog = pd.read_csv('your/dataset/here.csv') # Simple exponential smoothing, denoted (A,N,N) mod_ses = sm.tsa.statespace.ExponentialSmoothing(endog) res_ses = mod_ses.fit() # Holt's linear method, denoted (A,A,N) mod_h = sm.tsa.statespace.ExponentialSmoothing(endog, trend=True) res_h = mod_h.fit() # Damped trend model, denoted (A,Ad,N) mod_dt = sm.tsa.statespace.ExponentialSmoothing(endog, trend=True, damped_trend=True) res_dt = mod_dt.fit() # Holt-Winters' trend and seasonality method, denoted (A,A,A) # (assuming that `endog` has a seasonal periodicity of 4, for example if it # is quarterly data). mod_hw = sm.tsa.statespace.ExponentialSmoothing(endog, trend=True, seasonal=4) res_hw = mod_hw.fit() **Differences between Statsmodels' exponential smoothing model classes** There are several differences between this model class, available at `sm.tsa.statespace.ExponentialSmoothing`, and the model class available at `sm.tsa.ExponentialSmoothing`. - This model class only supports *linear* exponential smoothing models, while `sm.tsa.ExponentialSmoothing` also supports multiplicative models. - This model class puts the exponential smoothing models into state space form and then applies the Kalman filter to estimate the states, while `sm.tsa.ExponentialSmoothing` is based on exponential smoothing recursions. In some cases, this can mean that estimating parameters with this model class will be somewhat slower than with `sm.tsa.ExponentialSmoothing`. - This model class can produce confidence intervals for forecasts, based on an assumption of Gaussian errors, while `sm.tsa.ExponentialSmoothing` does not support confidence intervals. - This model class supports concentrating initial values out of the objective function, which can improve performance when there are many initial states to estimate (for example when the seasonal periodicity is large). - This model class supports many advanced features available to state space models, such as diagnostics and fixed parameters. **Note**: this class is based on a "multiple sources of error" (MSOE) state space formulation and not a "single source of error" (SSOE) formulation. Custom state space models ^^^^^^^^^^^^^^^^^^^^^^^^^ The true power of the state space model is to allow the creation and estimation of custom models. Usually that is done by extending the following two classes, which bundle all of state space representation, Kalman filtering, and maximum likelihood fitting functionality for estimation and results output. .. autosummary:: :toctree: generated/ mlemodel.MLEModel mlemodel.MLEResults For a basic example demonstrating creating and estimating a custom state space model, see the `Local Linear Trend example notebook `__. For a more sophisticated example, see the source code for the `SARIMAX` and `SARIMAXResults` classes, which are built by extending `MLEModel` and `MLEResults`. In simple cases, the model can be constructed entirely using the MLEModel class. For example, the AR(2) model from above could be constructed and estimated using only the following code: .. code-block:: python import numpy as np from scipy.signal import lfilter import statsmodels.api as sm # True model parameters nobs = int(1e3) true_phi = np.r_[0.5, -0.2] true_sigma = 1**0.5 # Simulate a time series np.random.seed(1234) disturbances = np.random.normal(0, true_sigma, size=(nobs,)) endog = lfilter([1], np.r_[1, -true_phi], disturbances) # Construct the model class AR2(sm.tsa.statespace.MLEModel): def __init__(self, endog): # Initialize the state space model super(AR2, self).__init__(endog, k_states=2, k_posdef=1, initialization='stationary') # Setup the fixed components of the state space representation self['design'] = [1, 0] self['transition'] = [[0, 0], [1, 0]] self['selection', 0, 0] = 1 # Describe how parameters enter the model def update(self, params, transformed=True, **kwargs): params = super(AR2, self).update(params, transformed, **kwargs) self['transition', 0, :] = params[:2] self['state_cov', 0, 0] = params[2] # Specify start parameters and parameter names @property def start_params(self): return [0,0,1] # these are very simple # Create and fit the model mod = AR2(endog) res = mod.fit() print(res.summary()) This results in the following summary table:: Statespace Model Results ============================================================================== Dep. Variable: y No. Observations: 1000 Model: AR2 Log Likelihood -1389.437 Date: Wed, 26 Oct 2016 AIC 2784.874 Time: 00:42:03 BIC 2799.598 Sample: 0 HQIC 2790.470 - 1000 Covariance Type: opg ============================================================================== coef std err z P>|z| [0.025 0.975] ------------------------------------------------------------------------------ param.0 0.4395 0.030 14.730 0.000 0.381 0.498 param.1 -0.2055 0.032 -6.523 0.000 -0.267 -0.144 param.2 0.9425 0.042 22.413 0.000 0.860 1.025 =================================================================================== Ljung-Box (Q): 24.25 Jarque-Bera (JB): 0.22 Prob(Q): 0.98 Prob(JB): 0.90 Heteroskedasticity (H): 1.05 Skew: -0.04 Prob(H) (two-sided): 0.66 Kurtosis: 3.02 =================================================================================== Warnings: [1] Covariance matrix calculated using the outer product of gradients (complex-step). The results object has many of the attributes and methods you would expect from other statsmodels results objects, including standard errors, z-statistics, and prediction / forecasting. More advanced usage is possible, including specifying parameter transformations, and specifying names for parameters for a more informative output summary. Overview of usage ----------------- All state space models follow the typical Statsmodels pattern: 1. Construct a **model instance** with an input dataset 2. Apply parameters to the model (for example, using `fit`) to construct a **results instance** 3. Interact with the results instance to examine the estimated parameters, explore residual diagnostics, and produce forecasts, simulations, or impulse responses. An example of this pattern is as follows: .. code-block:: python # Load in the example macroeconomic dataset dta = sm.datasets.macrodata.load_pandas().data # Make sure we have an index with an associated frequency, so that # we can refer to time periods with date strings or timestamps dta.index = pd.date_range('1959Q1', '2009Q3', freq='QS') # Step 1: construct an SARIMAX model for US inflation data model = sm.tsa.SARIMAX(dta.infl, order=(4, 0, 0), trend='c') # Step 2: fit the model's parameters by maximum likelihood results = model.fit() # Step 3: explore / use results # - Print a table summarizing estimation results print(results.summary()) # - Print only the estimated parameters print(results.params) # - Create diagnostic figures based on standardized residuals: # (1) time series graph # (2) histogram # (3) Q-Q plot # (4) correlogram results.plot_diagnostics() # - Examine diagnostic hypothesis tests # Jarque-Bera: [test_statistic, pvalue, skewness, kurtosis] print(results.test_normality(method='jarquebera')) # Goldfeld-Quandt type test: [test_statistic, pvalue] print(results.test_heteroskedasticity(method='breakvar')) # Ljung-Box test: [test_statistic, pvalue] for each lag print(results.test_serial_correlation(method='ljungbox')) # - Forecast the next 4 values print(results.forecast(4)) # - Forecast until 2020Q4 print(results.forecast('2020Q4')) # - Plot in-sample dynamic prediction starting in 2005Q1 # and out-of-sample forecasts until 2010Q4 along with # 90% confidence intervals predict_results = results.get_prediction(start='2005Q1', end='2010Q4', dynamic=True) predict_df = predict_results.summary_frame(alpha=0.10) fig, ax = plt.subplots() predict_df['mean'].plot(ax=ax) ax.fill_between(predict_df.index, predict_df['mean_ci_lower'], predict_df['mean_ci_upper'], alpha=0.2) # - Simulate two years of new data after the end of the sample print(results.simulate(8, anchor='end')) # - Impulse responses for two years print(results.impulse_responses(8)) Basic methods and attributes for estimation / filtering / smoothing ------------------------------------------------------------------- The most-used methods for a state space model are: - :py:meth:`fit ` - estimate parameters via maximum likelihood and return a results object (this object will have also performed Kalman filtering and smoothing at the estimated parameters). This is the most commonly used method. - :py:meth:`smooth ` - return a results object associated with a given vector of parameters after performing Kalman filtering and smoothing - :py:meth:`loglike ` - compute the log-likelihood of the data using a given vector of parameters Some useful attributes of a state space model are: - :py:meth:`param_names ` - names of the parameters used by the model - :py:meth:`state_names ` - names of the elements of the (unobserved) state vector - :py:meth:`start_params ` - initial parameter estimates used a starting values for numerical maximum likelihood optimization Other methods that are used less often are: - :py:meth:`filter ` - return a results object associated with a given vector of parameters after only performing Kalman filtering (but not smoothing) - :py:meth:`simulation_smoother ` - return an object that can perform simulation smoothing Output and postestimation methods and attributes ------------------------------------------------ Commonly used methods include: - :py:meth:`summary ` - construct a table that presents model fit statistics, estimated parameters, and other summary output - :py:meth:`predict ` - compute in-sample predictions and out-of-sample forecasts (point estimates only) - :py:meth:`get_prediction ` - compute in-sample predictions and out-of-sample forecasts, including confidence intervals - :py:meth:`forecast ` - compute out-of-sample forecasts (point estimates only) (this is a convenience wrapper around `predict`) - :py:meth:`get_forecast ` - compute out-of-sample forecasts, including confidence intervals (this is a convenience wrapper around `get_prediction`) - :py:meth:`simulate ` - simulate new data according to the state space model - :py:meth:`impulse_responses ` - compute impulse responses from the state space model Commonly used attributes include: - :py:meth:`params ` - estimated parameters - :py:meth:`bse ` - standard errors of estimated parameters - :py:meth:`pvalues ` - p-values associated with estimated parameters - :py:meth:`llf ` - log-likelihood of the data at the estimated parameters - :py:meth:`sse `, :py:meth:`mse `, and :py:meth:`mae ` - sum of squared errors, mean square error, and mean absolute error - Information criteria, including: :py:meth:`aic `, :py:meth:`aicc `, :py:meth:`bic `, and :py:meth:`hquc ` - :py:meth:`fittedvalues ` - fitted values from the model (note that these are one-step-ahead predictions) - :py:meth:`resid ` - residuals from the model (note that these are one-step-ahead prediction errors) Estimates and covariances of the unobserved state ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ It can be useful to compute estimates of the unobserved state vector conditional on the observed data. These are available in the results object :py:meth:`states `, which contains the following elements: - `states.filtered` - filtered (one-sided) estimates of the state vector. The estimate of the state vector at time `t` is based on the observed data up to and including time `t`. - `states.smoothed` - smoothed (two-sided) estimates of the state vector. The estimate of the state vector at time `t` is based on all observed data in the sample. - `states.filtered_cov` - filtered (one-sided) covariance of the state vector - `states.smoothed_cov` - smoothed (two-sided) covariance of the state vector Each of these elements are Pandas `DataFrame` objects. As an example, in a "local level + seasonal" model estimated via the `UnobservedComponents` components class we can get an estimates of the underlying level and seasonal movements of a series over time. .. code-block:: python fig, axes = plt.subplots(3, 1, figsize=(8, 8)) # Retrieve monthly retail sales for clothing from pandas_datareader.data import DataReader clothing = DataReader('MRTSSM4481USN', 'fred', start='1992').asfreq('MS')['MRTSSM4481USN'] # Construct a local level + seasonal model model = sm.tsa.UnobservedComponents(clothing, 'llevel', seasonal=12) results = model.fit() # Plot the data, the level, and seasonal clothing.plot(ax=axes[0]) results.states.smoothed['level'].plot(ax=axes[1]) results.states.smoothed['seasonal'].plot(ax=axes[2]) Residual diagnostics ^^^^^^^^^^^^^^^^^^^^ Three diagnostic tests are available after estimation of any statespace model, whether built in or custom, to help assess whether the model conforms to the underlying statistical assumptions. These tests are: - :py:meth:`test_normality ` - :py:meth:`test_heteroskedasticity ` - :py:meth:`test_serial_correlation ` A number of standard plots of regression residuals are available for the same purpose. These can be produced using the command :py:meth:`plot_diagnostics `. Applying estimated parameters to an updated or different dataset ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ There are three methods that can be used to apply estimated parameters from a results object to an updated or different dataset: - :py:meth:`append ` - retrieve a new results object with additional observations that follow after the end of the current sample appended to it (so the new results object contains both the current sample and the additional observations) - :py:meth:`extend ` - retrieve a new results object for additional observations that follow after end of the current sample (so the new results object contains only the new observations but NOT the current sample) - :py:meth:`apply ` - retrieve a new results object for a completely different dataset One cross-validation exercise on time-series data involves fitting a model's parameters based on a training sample (observations through time `t`) and then evaluating the fit of the model using a test sample (observations `t+1`, `t+2`, ...). This can be conveniently done using either `apply` or `extend`. In the example below, we use the `extend` method. .. code-block:: python # Load in the example macroeconomic dataset dta = sm.datasets.macrodata.load_pandas().data # Make sure we have an index with an associated frequency, so that # we can refer to time periods with date strings or timestamps dta.index = pd.date_range('1959Q1', '2009Q3', freq='QS') # Separate inflation data into a training and test dataset training_endog = dta['infl'].iloc[:-1] test_endog = dta['infl'].iloc[-1:] # Fit an SARIMAX model for inflation training_model = sm.tsa.SARIMAX(training_endog, order=(4, 0, 0)) training_results = training_model.fit() # Extend the results to the test observations test_results = training_results.extend(test_endog) # Print the sum of squared errors in the test sample, # based on parameters computed using only the training sample print(test_results.sse) Understanding the Impact of Data Revisions ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Statespace model results expose a :meth:`~mlemodel.MLEModel.news` method that can be used to understand the impact of data revisions -- news -- on model parameters. .. autosummary:: :toctree: generated/ news.NewsResults Additional options and tools ---------------------------- All state space models have the following options and tools: Holding some parameters fixed and estimating the rest ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The :py:meth:`fit_constrained ` method allows fixing some parameters to known values and then estimating the rest via maximum likelihood. An example of this is: .. code-block:: python # Construct a model model = sm.tsa.SARIMAX(endog, order=(1, 0, 0)) # To find out the parameter names, use: print(model.param_names) # Fit the model with a fixed value for the AR(1) coefficient: results = model.fit_constrained({'ar.L1': 0.5}) Alternatively, you can use the :py:meth:`fix_params ` context manager: .. code-block:: python # Construct a model model = sm.tsa.SARIMAX(endog, order=(1, 0, 0)) # Fit the model with a fixed value for the AR(1) coefficient using the # context manager with model.fix_params({'ar.L1': 0.5}): results = model.fit() Low memory options ^^^^^^^^^^^^^^^^^^ When the observed dataset is very large and / or the state vector of the model is high-dimensional (for example when considering long seasonal effects), the default memory requirements can be too large. For this reason, the `fit`, `filter`, and `smooth` methods accept an optional `low_memory=True` argument, which can considerably reduce memory requirements and speed up model fitting. Note that when using `low_memory=True`, not all results objects will be available. However, residual diagnostics, in-sample (non-dynamic) prediction, and out-of-sample forecasting are all still available. Low-level state space representation and Kalman filtering --------------------------------------------------------- While creation of custom models will almost always be done by extending `MLEModel` and `MLEResults`, it can be useful to understand the superstructure behind those classes. Maximum likelihood estimation requires evaluating the likelihood function of the model, and for models in state space form the likelihood function is evaluated as a byproduct of running the Kalman filter. There are two classes used by `MLEModel` that facilitate specification of the state space model and Kalman filtering: `Representation` and `KalmanFilter`. The `Representation` class is the piece where the state space model representation is defined. In simple terms, it holds the state space matrices (`design`, `obs_intercept`, etc.; see the introduction to state space models, above) and allows their manipulation. `FrozenRepresentation` is the most basic results-type class, in that it takes a "snapshot" of the state space representation at any given time. See the class documentation for the full list of available attributes. .. autosummary:: :toctree: generated/ representation.Representation representation.FrozenRepresentation The `KalmanFilter` class is a subclass of Representation that provides filtering capabilities. Once the state space representation matrices have been constructed, the :py:meth:`filter ` method can be called, producing a `FilterResults` instance; `FilterResults` is a subclass of `FrozenRepresentation`. The `FilterResults` class not only holds a frozen representation of the state space model (the design, transition, etc. matrices, as well as model dimensions, etc.) but it also holds the filtering output, including the :py:attr:`filtered state ` and loglikelihood (see the class documentation for the full list of available results). It also provides a :py:meth:`predict ` method, which allows in-sample prediction or out-of-sample forecasting. A similar method, :py:meth:`predict `, provides additional prediction or forecasting results, including confidence intervals. .. autosummary:: :toctree: generated/ kalman_filter.KalmanFilter kalman_filter.FilterResults kalman_filter.PredictionResults The `KalmanSmoother` class is a subclass of `KalmanFilter` that provides smoothing capabilities. Once the state space representation matrices have been constructed, the :py:meth:`filter ` method can be called, producing a `SmootherResults` instance; `SmootherResults` is a subclass of `FilterResults`. The `SmootherResults` class holds all the output from `FilterResults`, but also includes smoothing output, including the :py:attr:`smoothed state ` and loglikelihood (see the class documentation for the full list of available results). Whereas "filtered" output at time `t` refers to estimates conditional on observations up through time `t`, "smoothed" output refers to estimates conditional on the entire set of observations in the dataset. .. autosummary:: :toctree: generated/ kalman_smoother.KalmanSmoother kalman_smoother.SmootherResults The `SimulationSmoother` class is a subclass of `KalmanSmoother` that further provides simulation and simulation smoothing capabilities. The :py:meth:`simulation_smoother ` method can be called, producing a `SimulationSmoothResults` instance. The `SimulationSmoothResults` class has a `simulate` method, that allows performing simulation smoothing to draw from the joint posterior of the state vector. This is useful for Bayesian estimation of state space models via Gibbs sampling. .. autosummary:: :toctree: generated/ simulation_smoother.SimulationSmoother simulation_smoother.SimulationSmoothResults cfa_simulation_smoother.CFASimulationSmoother Statespace Tools ---------------- There are a variety of tools used for state space modeling or by the SARIMAX class: .. autosummary:: :toctree: generated/ tools.companion_matrix tools.diff tools.is_invertible tools.constrain_stationary_univariate tools.unconstrain_stationary_univariate tools.constrain_stationary_multivariate tools.unconstrain_stationary_multivariate tools.validate_matrix_shape tools.validate_vector_shape statsmodels-0.12.2/docs/source/stats.rst000066400000000000000000000405701400612667500202730ustar00rootroot00000000000000.. module:: statsmodels.stats :synopsis: Statistical methods and tests .. currentmodule:: statsmodels.stats .. _stats: Statistics :mod:`stats` ======================= This section collects various statistical tests and tools. Some can be used independently of any models, some are intended as extension to the models and model results. API Warning: The functions and objects in this category are spread out in various modules and might still be moved around. We expect that in future the statistical tests will return class instances with more informative reporting instead of only the raw numbers. .. _stattools: Residual Diagnostics and Specification Tests -------------------------------------------- .. module:: statsmodels.stats.stattools :synopsis: Statistical methods and tests that do not fit into other categories .. currentmodule:: statsmodels.stats.stattools .. autosummary:: :toctree: generated/ durbin_watson jarque_bera omni_normtest medcouple robust_skewness robust_kurtosis expected_robust_kurtosis .. module:: statsmodels.stats.diagnostic :synopsis: Statistical methods and tests to diagnose model fit problems .. currentmodule:: statsmodels.stats.diagnostic .. autosummary:: :toctree: generated/ acorr_breusch_godfrey acorr_ljungbox acorr_lm breaks_cusumolsresid breaks_hansen recursive_olsresiduals compare_cox compare_encompassing compare_j het_arch het_breuschpagan het_goldfeldquandt het_white spec_white linear_harvey_collier linear_lm linear_rainbow linear_reset Outliers and influence measures ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. module:: statsmodels.stats.outliers_influence :synopsis: Statistical methods and measures for outliers and influence .. currentmodule:: statsmodels.stats.outliers_influence .. autosummary:: :toctree: generated/ OLSInfluence GLMInfluence MLEInfluence variance_inflation_factor See also the notes on :ref:`notes on regression diagnostics ` Sandwich Robust Covariances --------------------------- The following functions calculate covariance matrices and standard errors for the parameter estimates that are robust to heteroscedasticity and autocorrelation in the errors. Similar to the methods that are available for the LinearModelResults, these methods are designed for use with OLS. .. currentmodule:: statsmodels.stats .. autosummary:: :toctree: generated/ sandwich_covariance.cov_hac sandwich_covariance.cov_nw_panel sandwich_covariance.cov_nw_groupsum sandwich_covariance.cov_cluster sandwich_covariance.cov_cluster_2groups sandwich_covariance.cov_white_simple The following are standalone versions of the heteroscedasticity robust standard errors attached to LinearModelResults .. autosummary:: :toctree: generated/ sandwich_covariance.cov_hc0 sandwich_covariance.cov_hc1 sandwich_covariance.cov_hc2 sandwich_covariance.cov_hc3 sandwich_covariance.se_cov Goodness of Fit Tests and Measures ---------------------------------- some tests for goodness of fit for univariate distributions .. module:: statsmodels.stats.gof :synopsis: Goodness of fit measures and tests .. currentmodule:: statsmodels.stats.gof .. autosummary:: :toctree: generated/ powerdiscrepancy gof_chisquare_discrete gof_binning_discrete chisquare_effectsize .. currentmodule:: statsmodels.stats.diagnostic .. autosummary:: :toctree: generated/ anderson_statistic normal_ad kstest_exponential kstest_fit kstest_normal lilliefors Non-Parametric Tests -------------------- .. module:: statsmodels.sandbox.stats.runs :synopsis: Experimental statistical methods and tests to analyze runs .. currentmodule:: statsmodels.sandbox.stats.runs .. autosummary:: :toctree: generated/ mcnemar symmetry_bowker median_test_ksample runstest_1samp runstest_2samp cochrans_q Runs .. currentmodule:: statsmodels.stats.descriptivestats .. autosummary:: :toctree: generated/ sign_test Descriptive Statistics ---------------------- .. module:: statsmodels.stats.descriptivestats :synopsis: Descriptive statistics .. currentmodule:: statsmodels.stats.descriptivestats .. autosummary:: :toctree: generated/ describe Description .. _interrater: Interrater Reliability and Agreement ------------------------------------ The main function that statsmodels has currently available for interrater agreement measures and tests is Cohen's Kappa. Fleiss' Kappa is currently only implemented as a measures but without associated results statistics. .. module:: statsmodels.stats.inter_rater .. currentmodule:: statsmodels.stats.inter_rater .. autosummary:: :toctree: generated/ cohens_kappa fleiss_kappa to_table aggregate_raters Multiple Tests and Multiple Comparison Procedures ------------------------------------------------- `multipletests` is a function for p-value correction, which also includes p-value correction based on fdr in `fdrcorrection`. `tukeyhsd` performs simultaneous testing for the comparison of (independent) means. These three functions are verified. GroupsStats and MultiComparison are convenience classes to multiple comparisons similar to one way ANOVA, but still in development .. module:: statsmodels.sandbox.stats.multicomp :synopsis: Experimental methods for controlling size while performing multiple comparisons .. currentmodule:: statsmodels.stats.multitest .. autosummary:: :toctree: generated/ multipletests fdrcorrection .. currentmodule:: statsmodels.sandbox.stats.multicomp .. autosummary:: :toctree: generated/ GroupsStats MultiComparison TukeyHSDResults .. module:: statsmodels.stats.multicomp :synopsis: Methods for controlling size while performing multiple comparisons .. currentmodule:: statsmodels.stats.multicomp .. autosummary:: :toctree: generated/ pairwise_tukeyhsd .. module:: statsmodels.stats.multitest :synopsis: Multiple testing p-value and FDR adjustments .. currentmodule:: statsmodels.stats.multitest .. autosummary:: :toctree: generated/ local_fdr fdrcorrection_twostage NullDistribution RegressionFDR .. module:: statsmodels.stats.knockoff_regeffects :synopsis: Regression Knock-Off Effects .. currentmodule:: statsmodels.stats.knockoff_regeffects .. autosummary:: :toctree: generated/ CorrelationEffects OLSEffects ForwardEffects OLSEffects RegModelEffects The following functions are not (yet) public .. currentmodule:: statsmodels.sandbox.stats.multicomp .. autosummary:: :toctree: generated/ varcorrection_pairs_unbalanced varcorrection_pairs_unequal varcorrection_unbalanced varcorrection_unequal StepDown catstack ccols compare_ordered distance_st_range ecdf get_tukeyQcrit homogeneous_subsets maxzero maxzerodown mcfdr qcrit randmvn rankdata rejectionline set_partition set_remove_subs tiecorrect .. _tost: Basic Statistics and t-Tests with frequency weights --------------------------------------------------- Besides basic statistics, like mean, variance, covariance and correlation for data with case weights, the classes here provide one and two sample tests for means. The t-tests have more options than those in scipy.stats, but are more restrictive in the shape of the arrays. Confidence intervals for means are provided based on the same assumptions as the t-tests. Additionally, tests for equivalence of means are available for one sample and for two, either paired or independent, samples. These tests are based on TOST, two one-sided tests, which have as null hypothesis that the means are not "close" to each other. .. module:: statsmodels.stats.weightstats :synopsis: Weighted statistics .. currentmodule:: statsmodels.stats.weightstats .. autosummary:: :toctree: generated/ DescrStatsW CompareMeans ttest_ind ttost_ind ttost_paired ztest ztost zconfint weightstats also contains tests and confidence intervals based on summary data .. currentmodule:: statsmodels.stats.weightstats .. autosummary:: :toctree: generated/ _tconfint_generic _tstat_generic _zconfint_generic _zstat_generic _zstat_generic2 Power and Sample Size Calculations ---------------------------------- The :mod:`power` module currently implements power and sample size calculations for the t-tests, normal based test, F-tests and Chisquare goodness of fit test. The implementation is class based, but the module also provides three shortcut functions, ``tt_solve_power``, ``tt_ind_solve_power`` and ``zt_ind_solve_power`` to solve for any one of the parameters of the power equations. .. module:: statsmodels.stats.power :synopsis: Power and size calculations for common tests .. currentmodule:: statsmodels.stats.power .. autosummary:: :toctree: generated/ TTestIndPower TTestPower GofChisquarePower NormalIndPower FTestAnovaPower FTestPower normal_power_het normal_sample_size_one_tail tt_solve_power tt_ind_solve_power zt_ind_solve_power .. _proportion_stats: Proportion ---------- Also available are hypothesis test, confidence intervals and effect size for proportions that can be used with NormalIndPower. .. module:: statsmodels.stats.proportion :synopsis: Tests for proportions .. currentmodule:: statsmodels.stats.proportion .. autosummary:: :toctree: generated proportion_confint proportion_effectsize binom_test binom_test_reject_interval binom_tost binom_tost_reject_interval multinomial_proportions_confint proportions_ztest proportions_ztost proportions_chisquare proportions_chisquare_allpairs proportions_chisquare_pairscontrol proportion_effectsize power_binom_tost power_ztost_prop samplesize_confint_proportion Statistics for two independent samples Status: experimental, API might change, added in 0.12 .. autosummary:: :toctree: generated test_proportions_2indep confint_proportions_2indep power_proportions_2indep tost_proportions_2indep samplesize_proportions_2indep_onetail score_test_proportions_2indep _score_confint_inversion Rates ----- Statistical functions for rates. This currently includes hypothesis tests for two independent samples. Status: experimental, API might change, added in 0.12 .. module:: statsmodels.stats.rates :synopsis: Tests for Poisson rates .. currentmodule:: statsmodels.stats.rates .. autosummary:: :toctree: generated test_poisson_2indep etest_poisson_2indep tost_poisson_2indep Multivariate ------------ Statistical functions for multivariate samples. This includes hypothesis test and confidence intervals for mean of sample of multivariate observations and hypothesis tests for the structure of a covariance matrix. Status: experimental, API might change, added in 0.12 .. module:: statsmodels.stats.multivariate :synopsis: Statistical functions for multivariate samples. .. currentmodule:: statsmodels.stats.multivariate .. autosummary:: :toctree: generated test_mvmean confint_mvmean confint_mvmean_fromstats test_mvmean_2indep test_cov test_cov_blockdiagonal test_cov_diagonal test_cov_oneway test_cov_spherical .. _oneway_stats: Oneway Anova ------------ Hypothesis test, confidence intervals and effect size for oneway analysis of k samples. Status: experimental, API might change, added in 0.12 .. module:: statsmodels.stats.oneway :synopsis: Statistical functions for oneway analysis, Anova. .. currentmodule:: statsmodels.stats.oneway .. autosummary:: :toctree: generated anova_oneway anova_generic equivalence_oneway equivalence_oneway_generic power_equivalence_oneway _power_equivalence_oneway_emp test_scale_oneway equivalence_scale_oneway confint_effectsize_oneway confint_noncentrality convert_effectsize_fsqu effectsize_oneway f2_to_wellek fstat_to_wellek wellek_to_f2 _fstat2effectsize scale_transform simulate_power_equivalence_oneway .. _robust_stats: Robust, Trimmed Statistics -------------------------- Statistics for samples that are trimmed at a fixed fraction. This includes class TrimmedMean for one sample statistics. It is used in `stats.oneway` for trimmed "Yuen" Anova. Status: experimental, API might change, added in 0.12 .. module:: statsmodels.stats.robust_compare :synopsis: Trimmed sample statistics. .. currentmodule:: statsmodels.stats.robust_compare .. autosummary:: :toctree: generated TrimmedMean scale_transform trim_mean trimboth Moment Helpers -------------- When there are missing values, then it is possible that a correlation or covariance matrix is not positive semi-definite. The following three functions can be used to find a correlation or covariance matrix that is positive definite and close to the original matrix. .. module:: statsmodels.stats.correlation_tools :synopsis: Procedures for ensuring correlations are positive semi-definite .. currentmodule:: statsmodels.stats.correlation_tools .. autosummary:: :toctree: generated/ corr_clipped corr_nearest corr_nearest_factor corr_thresholded cov_nearest cov_nearest_factor_homog FactoredPSDMatrix kernel_covariance These are utility functions to convert between central and non-central moments, skew, kurtosis and cummulants. .. module:: statsmodels.stats.moment_helpers :synopsis: Tools for converting moments .. currentmodule:: statsmodels.stats.moment_helpers .. autosummary:: :toctree: generated/ cum2mc mc2mnc mc2mvsk mnc2cum mnc2mc mnc2mvsk mvsk2mc mvsk2mnc cov2corr corr2cov se_cov Mediation Analysis ------------------ Mediation analysis focuses on the relationships among three key variables: an 'outcome', a 'treatment', and a 'mediator'. Since mediation analysis is a form of causal inference, there are several assumptions involved that are difficult or impossible to verify. Ideally, mediation analysis is conducted in the context of an experiment such as this one in which the treatment is randomly assigned. It is also common for people to conduct mediation analyses using observational data in which the treatment may be thought of as an 'exposure'. The assumptions behind mediation analysis are even more difficult to verify in an observational setting. .. module:: statsmodels.stats.mediation :synopsis: Mediation analysis .. currentmodule:: statsmodels.stats.mediation .. autosummary:: :toctree: generated/ Mediation MediationResults Oaxaca-Blinder Decomposition ---------------------------- The Oaxaca-Blinder, or Blinder-Oaxaca as some call it, decomposition attempts to explain gaps in means of groups. It uses the linear models of two given regression equations to show what is explained by regression coefficients and known data and what is unexplained using the same data. There are two types of Oaxaca-Blinder decompositions, the two-fold and the three-fold, both of which can and are used in Economics Literature to discuss differences in groups. This method helps classify discrimination or unobserved effects. This function attempts to port the functionality of the oaxaca command in STATA to Python. .. module:: statsmodels.stats.oaxaca :synopsis: Oaxaca-Blinder Decomposition .. currentmodule:: statsmodels.stats.oaxaca .. autosummary:: :toctree: generated/ OaxacaBlinder OaxacaResults Distance Dependence Measures ---------------------------- Distance dependence measures and the Distance Covariance (dCov) test. .. module:: statsmodels.stats.dist_dependence_measures :synopsis: Distance Dependence Measures .. currentmodule:: statsmodels.stats.dist_dependence_measures .. autosummary:: :toctree: generated/ distance_covariance_test distance_statistics distance_correlation distance_covariance distance_variance Meta-Analysis ------------- Functions for basic meta-analysis of a collection of sample statistics. Examples can be found in the notebook * `Meta-Analysis `__ Status: experimental, API might change, added in 0.12 .. module:: statsmodels.stats.meta_analysis :synopsis: Meta-Analysis .. currentmodule:: statsmodels.stats.meta_analysis .. autosummary:: :toctree: generated/ combine_effects effectsize_2proportions effectsize_smd CombineResults The module also includes internal functions to compute random effects variance. .. autosummary:: :toctree: generated/ _fit_tau_iter_mm _fit_tau_iterative _fit_tau_mm statsmodels-0.12.2/docs/source/tools.rst000066400000000000000000000050121400612667500202650ustar00rootroot00000000000000.. currentmodule:: statsmodels.tools .. _tools: Tools ===== Our tool collection contains some convenience functions for users and functions that were written mainly for internal use. Additional to this tools directory, several other subpackages have their own tools modules, for example :mod:`statsmodels.tsa.tsatools` Module Reference ---------------- .. module:: statsmodels.tools :synopsis: Tools for variable transformation and common numerical operations Basic tools :mod:`tools` ^^^^^^^^^^^^^^^^^^^^^^^^ These are basic and miscellaneous tools. The full import path is `statsmodels.tools.tools`. .. autosummary:: :toctree: generated/ tools.add_constant The next group are mostly helper functions that are not separately tested or insufficiently tested. .. autosummary:: :toctree: generated/ tools.clean0 tools.fullrank tools.isestimable tools.recipr tools.recipr0 tools.unsqueeze .. currentmodule:: statsmodels.tools .. _numdiff: Numerical Differentiation ^^^^^^^^^^^^^^^^^^^^^^^^^ .. autosummary:: :toctree: generated/ numdiff.approx_fprime numdiff.approx_fprime_cs numdiff.approx_hess1 numdiff.approx_hess2 numdiff.approx_hess3 numdiff.approx_hess_cs Measure for fit performance :mod:`eval_measures` ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The first group of function in this module are standalone versions of information criteria, aic bic and hqic. The function with `_sigma` suffix take the error sum of squares as argument, those without, take the value of the log-likelihood, `llf`, as argument. The second group of function are measures of fit or prediction performance, which are mostly one liners to be used as helper functions. All of those calculate a performance or distance statistic for the difference between two arrays. For example in the case of Monte Carlo or cross-validation, the first array would be the estimation results for the different replications or draws, while the second array would be the true or observed values. .. currentmodule:: statsmodels.tools .. autosummary:: :toctree: generated/ eval_measures.aic eval_measures.aic_sigma eval_measures.aicc eval_measures.aicc_sigma eval_measures.bic eval_measures.bic_sigma eval_measures.hqic eval_measures.hqic_sigma eval_measures.bias eval_measures.iqr eval_measures.maxabs eval_measures.meanabs eval_measures.medianabs eval_measures.medianbias eval_measures.mse eval_measures.rmse eval_measures.rmspe eval_measures.stde eval_measures.vare statsmodels-0.12.2/docs/source/tsa.rst000066400000000000000000000303071400612667500177210ustar00rootroot00000000000000.. module:: statsmodels.tsa :synopsis: Time-series analysis .. currentmodule:: statsmodels.tsa .. _tsa: Time Series analysis :mod:`tsa` =============================== :mod:`statsmodels.tsa` contains model classes and functions that are useful for time series analysis. Basic models include univariate autoregressive models (AR), vector autoregressive models (VAR) and univariate autoregressive moving average models (ARMA). Non-linear models include Markov switching dynamic regression and autoregression. It also includes descriptive statistics for time series, for example autocorrelation, partial autocorrelation function and periodogram, as well as the corresponding theoretical properties of ARMA or related processes. It also includes methods to work with autoregressive and moving average lag-polynomials. Additionally, related statistical tests and some useful helper functions are available. Estimation is either done by exact or conditional Maximum Likelihood or conditional least-squares, either using Kalman Filter or direct filters. Currently, functions and classes have to be imported from the corresponding module, but the main classes will be made available in the statsmodels.tsa namespace. The module structure is within statsmodels.tsa is - stattools : empirical properties and tests, acf, pacf, granger-causality, adf unit root test, kpss test, bds test, ljung-box test and others. - ar_model : univariate autoregressive process, estimation with conditional and exact maximum likelihood and conditional least-squares - arima_model : univariate ARMA process, estimation with conditional and exact maximum likelihood and conditional least-squares - statespace : Comprehensive statespace model specification and estimation. See the :ref:`statespace documentation `. - vector_ar, var : vector autoregressive process (VAR) and vector error correction models, estimation, impulse response analysis, forecast error variance decompositions, and data visualization tools. See the :ref:`vector_ar documentation `. - kalmanf : estimation classes for ARMA and other models with exact MLE using Kalman Filter - arma_process : properties of arma processes with given parameters, this includes tools to convert between ARMA, MA and AR representation as well as acf, pacf, spectral density, impulse response function and similar - sandbox.tsa.fftarma : similar to arma_process but working in frequency domain - tsatools : additional helper functions, to create arrays of lagged variables, construct regressors for trend, detrend and similar. - filters : helper function for filtering time series - regime_switching : Markov switching dynamic regression and autoregression models Some additional functions that are also useful for time series analysis are in other parts of statsmodels, for example additional statistical tests. Some related functions are also available in matplotlib, nitime, and scikits.talkbox. Those functions are designed more for the use in signal processing where longer time series are available and work more often in the frequency domain. .. currentmodule:: statsmodels.tsa Descriptive Statistics and Tests """""""""""""""""""""""""""""""" .. autosummary:: :toctree: generated/ stattools.acovf stattools.acf stattools.pacf stattools.pacf_yw stattools.pacf_ols stattools.pacf_burg stattools.ccovf stattools.ccf stattools.adfuller stattools.kpss stattools.zivot_andrews stattools.coint stattools.bds stattools.q_stat stattools.grangercausalitytests stattools.levinson_durbin stattools.innovations_algo stattools.innovations_filter stattools.levinson_durbin_pacf stattools.arma_order_select_ic x13.x13_arima_select_order x13.x13_arima_analysis Estimation """""""""" The following are the main estimation classes, which can be accessed through statsmodels.tsa.api and their result classes Univariate Autoregressive Processes (AR) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The basic autoregressive model in Statsmodels is: .. currentmodule:: statsmodels.tsa .. autosummary:: :toctree: generated/ ar_model.AutoReg ar_model.AutoRegResults ar_model.ar_select_order The `ar_model.AutoReg` model estimates parameters using conditional MLE (OLS), and supports exogenous regressors (an AR-X model) and seasonal effects. AR-X and related models can also be fitted with the `arima.ARIMA` class and the `SARIMAX` class (using full MLE via the Kalman Filter). Finally, the old class, `ar_model.AR`, is still available but it has been deprecated. .. autosummary:: :toctree: generated/ ar_model.AR ar_model.ARResults Autoregressive Moving-Average Processes (ARMA) and Kalman Filter ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Basic ARIMA model and results classes are as follows: .. currentmodule:: statsmodels.tsa .. autosummary:: :toctree: generated/ arima.model.ARIMA arima.model.ARIMAResults This model allows estimating parameters by various methods (including conditional MLE via the Hannan-Rissanen method and full MLE via the Kalman filter). It is a special case of the `SARIMAX` model, and it includes a large number of inherited features from the :ref:`state space ` models (including prediction / forecasting, residual diagnostics, simulation and impulse responses, etc.). Prior to version 0.11, the basic ARIMA model and results classes were the following: .. autosummary:: :toctree: generated/ arima_model.ARMA arima_model.ARMAResults arima_model.ARIMA arima_model.ARIMAResults These classes are still available, but they are no longer recommended. Exponential Smoothing ~~~~~~~~~~~~~~~~~~~~~ Linear and non-linear exponential smoothing models are available: .. currentmodule:: statsmodels.tsa.holtwinters .. autosummary:: :toctree: generated/ ExponentialSmoothing SimpleExpSmoothing Holt HoltWintersResults Separately, linear and non-linear exponential smoothing models have also been implemented based on the "innovations" state space approach. In addition to the usual support for parameter fitting, in-sample prediction, and out-of-sample forecasting, these models also support prediction intervals, simulation, and more. .. currentmodule:: statsmodels.tsa .. autosummary:: :toctree: generated/ exponential_smoothing.ets.ETSModel exponential_smoothing.ets.ETSResults Finally, linear exponential smoothing models have also been separately implemented as a special case of the general state space framework (this is separate from the "innovations" state space approach described above). Although this approach does not allow for the non-linear (multiplicative) exponential smoothing models, it includes all features of :ref:`state space ` models (including prediction / forecasting, residual diagnostics, simulation and impulse responses, etc.). .. currentmodule:: statsmodels.tsa .. autosummary:: :toctree: generated/ statespace.exponential_smoothing.ExponentialSmoothing statespace.exponential_smoothing.ExponentialSmoothingResults ARMA Process """""""""""" The following are tools to work with the theoretical properties of an ARMA process for given lag-polynomials. .. autosummary:: :toctree: generated/ arima_process.ArmaProcess arima_process.ar2arma arima_process.arma2ar arima_process.arma2ma arima_process.arma_acf arima_process.arma_acovf arima_process.arma_generate_sample arima_process.arma_impulse_response arima_process.arma_pacf arima_process.arma_periodogram arima_process.deconvolve arima_process.index2lpol arima_process.lpol2index arima_process.lpol_fiar arima_process.lpol_fima arima_process.lpol_sdiff .. currentmodule:: statsmodels.sandbox.tsa.fftarma .. autosummary:: :toctree: generated/ ArmaFft .. currentmodule:: statsmodels.tsa Statespace Models """"""""""""""""" See the :ref:`statespace documentation `. Vector ARs and Vector Error Correction Models """"""""""""""""""""""""""""""""""""""""""""" See the :ref:`vector_ar documentation. ` Regime switching models """"""""""""""""""""""" .. currentmodule:: statsmodels.tsa.regime_switching.markov_regression .. autosummary:: :toctree: generated/ MarkovRegression .. currentmodule:: statsmodels.tsa.regime_switching.markov_autoregression .. autosummary:: :toctree: generated/ MarkovAutoregression Time Series Filters """"""""""""""""""" .. currentmodule:: statsmodels.tsa.filters.bk_filter .. autosummary:: :toctree: generated/ bkfilter .. currentmodule:: statsmodels.tsa.filters.hp_filter .. autosummary:: :toctree: generated/ hpfilter .. currentmodule:: statsmodels.tsa.filters.cf_filter .. autosummary:: :toctree: generated/ cffilter .. currentmodule:: statsmodels.tsa.filters.filtertools .. autosummary:: :toctree: generated/ convolution_filter recursive_filter miso_lfilter fftconvolve3 fftconvolveinv .. currentmodule:: statsmodels.tsa.seasonal .. autosummary:: :toctree: generated/ seasonal_decompose STL DecomposeResult TSA Tools """"""""" .. currentmodule:: statsmodels.tsa.tsatools .. autosummary:: :toctree: generated/ add_lag add_trend detrend lagmat lagmat2ds VARMA Process """"""""""""" .. currentmodule:: statsmodels.tsa.varma_process .. autosummary:: :toctree: generated/ VarmaPoly Interpolation """"""""""""" .. currentmodule:: statsmodels.tsa.interp.denton .. autosummary:: :toctree: generated/ dentonm Deterministic Processes """"""""""""""""""""""" Deterministic processes simplify creating deterministic sequences with time trend or seasonal patterns. They also provide methods to simplify generating deterministic terms for out-of-sample forecasting. A :class:`~statsmodels.tsa.deterministic.DeterministicProcess` can be directly used with :class:`~statsmodels.tsa.ar_model.AutoReg` to construct complex deterministic dynamics and to forecast without constructing exogenous trends. .. currentmodule:: statsmodels.tsa.deterministic .. autosummary:: :toctree: generated/ DeterministicProcess TimeTrend Seasonality Fourier CalendarTimeTrend CalendarSeasonality CalendarFourier DeterministicTerm CalendarDeterministicTerm FourierDeterministicTerm TimeTrendDeterministicTerm Users who wish to write custom deterministic terms must subclass :class:`~statsmodels.tsa.deterministic.DeterministicTerm`. .. currentmodule:: statsmodels.tsa.deterministic .. autosummary:: :toctree: generated/ DeterministicTerm Forecasting Models """""""""""""""""" .. module:: statsmodels.tsa.forecasting :synopsis: Models designed for forecasting .. currentmodule:: statsmodels.tsa.forecasting The Theta Model ~~~~~~~~~~~~~~~ The Theta model is a simple forecasting method that combines a linear time trend with a Simple Exponential Smoother (Assimakopoulos & Nikolopoulos). An estimator for the parameters of the Theta model and methods to forecast are available in: .. module:: statsmodels.tsa.forecasting.theta :synopsis: Models designed for forecasting .. currentmodule:: statsmodels.tsa.forecasting.theta .. autosummary:: :toctree: generated/ ThetaModel ThetaModelResults Forecasting after STL Decomposition ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ :class:`statsmodels.tsa.seasonal.STL` is commonly used to remove seasonal components from a time series. The deseasonalized time series can then be modeled using a any non-seasonal model, and forecasts are constructed by adding the forecast from the non-seasonal model to the estimates of the seasonal component from the final full-cycle which are forecast using a random-walk model. .. module:: statsmodels.tsa.forecasting.stl :synopsis: Models designed for forecasting .. currentmodule:: statsmodels.tsa.forecasting.stl .. autosummary:: :toctree: generated/ STLForecast STLForecastResults Prediction Results """""""""""""""""" Most forecasting methods support a ``get_prediction`` method that return a ``PredictionResults`` object that contains both the prediction, its variance and can construct a prediction interval. Results Class ~~~~~~~~~~~~~ .. module:: statsmodels.tsa.base.prediction :synopsis: Shared objects for predictive methods .. currentmodule:: statsmodels.tsa.base.prediction .. autosummary:: :toctree: generated/ PredictionResults statsmodels-0.12.2/docs/source/tsastats.rst.TXT000066400000000000000000000010511400612667500214500ustar00rootroot00000000000000.. currentmodule:: statsmodels.tsa.tsatools Time Series Analysis ==================== These are some of the helper functions for doing time series analysis. First we can load some a some data from the US Macro Economy 1959:Q1 - 2009:Q3. :: >>> data = sm.datasets.macrodata.load(as_pandas=False) The macro dataset is a structured array. :: >>> data = data.data[['year','quarter','realgdp','tbilrate','cpi','unemp']] We can add a lag like so :: >>> data = sm.tsa.add_lag(data, 'realgdp', lags=2) TODO: -scikits.timeseries -link in to var docs statsmodels-0.12.2/docs/source/user-guide.rst000066400000000000000000000015731400612667500212060ustar00rootroot00000000000000User Guide ========== Background ---------- .. toctree:: :maxdepth: 1 endog_exog api-structure example_formulas pitfalls Regression and Linear Models ---------------------------- .. toctree:: :maxdepth: 1 regression glm gee gam rlm mixed_linear discretemod mixed_glm anova Time Series Analysis -------------------- .. toctree:: :maxdepth: 1 tsa statespace vector_ar Other Models ------------ .. toctree:: :maxdepth: 1 duration nonparametric gmm miscmodels multivariate Statistics and Tools -------------------- .. toctree:: :maxdepth: 1 stats contingency_tables imputation emplike distributions graphics iolib tools large_data optimization Data Sets --------- .. toctree:: :maxdepth: 1 datasets/index Sandbox ------- .. toctree:: :maxdepth: 1 sandbox statsmodels-0.12.2/docs/source/vector_ar.rst000066400000000000000000000320361400612667500211170ustar00rootroot00000000000000:orphan: .. module:: statsmodels.tsa.vector_ar.var_model :synopsis: Vector autoregressions .. currentmodule:: statsmodels.tsa.vector_ar.var_model .. _var: Vector Autoregressions :mod:`tsa.vector_ar` =========================================== :mod:`statsmodels.tsa.vector_ar` contains methods that are useful for simultaneously modeling and analyzing multiple time series using :ref:`Vector Autoregressions (VAR) ` and :ref:`Vector Error Correction Models (VECM) `. .. _var_process: VAR(p) processes ---------------- We are interested in modeling a :math:`T \times K` multivariate time series :math:`Y`, where :math:`T` denotes the number of observations and :math:`K` the number of variables. One way of estimating relationships between the time series and their lagged values is the *vector autoregression process*: .. math:: Y_t = \nu + A_1 Y_{t-1} + \ldots + A_p Y_{t-p} + u_t u_t \sim {\sf Normal}(0, \Sigma_u) where :math:`A_i` is a :math:`K \times K` coefficient matrix. We follow in large part the methods and notation of `Lutkepohl (2005) `__, which we will not develop here. Model fitting ~~~~~~~~~~~~~ .. note:: The classes referenced below are accessible via the :mod:`statsmodels.tsa.api` module. To estimate a VAR model, one must first create the model using an `ndarray` of homogeneous or structured dtype. When using a structured or record array, the class will use the passed variable names. Otherwise they can be passed explicitly: .. ipython:: python :suppress: import pandas as pd pd.options.display.max_rows = 10 import matplotlib import matplotlib.pyplot as plt matplotlib.style.use('ggplot') .. ipython:: python :okwarning: # some example data import numpy as np import pandas import statsmodels.api as sm from statsmodels.tsa.api import VAR mdata = sm.datasets.macrodata.load_pandas().data # prepare the dates index dates = mdata[['year', 'quarter']].astype(int).astype(str) quarterly = dates["year"] + "Q" + dates["quarter"] from statsmodels.tsa.base.datetools import dates_from_str quarterly = dates_from_str(quarterly) mdata = mdata[['realgdp','realcons','realinv']] mdata.index = pandas.DatetimeIndex(quarterly) data = np.log(mdata).diff().dropna() # make a VAR model model = VAR(data) .. note:: The :class:`VAR` class assumes that the passed time series are stationary. Non-stationary or trending data can often be transformed to be stationary by first-differencing or some other method. For direct analysis of non-stationary time series, a standard stable VAR(p) model is not appropriate. To actually do the estimation, call the `fit` method with the desired lag order. Or you can have the model select a lag order based on a standard information criterion (see below): .. ipython:: python :okwarning: results = model.fit(2) results.summary() Several ways to visualize the data using `matplotlib` are available. Plotting input time series: .. ipython:: python :okwarning: @savefig var_plot_input.png results.plot() Plotting time series autocorrelation function: .. ipython:: python @savefig var_plot_acorr.png results.plot_acorr() Lag order selection ~~~~~~~~~~~~~~~~~~~ Choice of lag order can be a difficult problem. Standard analysis employs likelihood test or information criteria-based order selection. We have implemented the latter, accessible through the :class:`VAR` class: .. ipython:: python model.select_order(15) When calling the `fit` function, one can pass a maximum number of lags and the order criterion to use for order selection: .. ipython:: python results = model.fit(maxlags=15, ic='aic') Forecasting ~~~~~~~~~~~ The linear predictor is the optimal h-step ahead forecast in terms of mean-squared error: .. math:: y_t(h) = \nu + A_1 y_t(h − 1) + \cdots + A_p y_t(h − p) We can use the `forecast` function to produce this forecast. Note that we have to specify the "initial value" for the forecast: .. ipython:: python lag_order = results.k_ar results.forecast(data.values[-lag_order:], 5) The `forecast_interval` function will produce the above forecast along with asymptotic standard errors. These can be visualized using the `plot_forecast` function: .. ipython:: python @savefig var_forecast.png results.plot_forecast(10) Class Reference ~~~~~~~~~~~~~~~ .. module:: statsmodels.tsa.vector_ar :synopsis: Vector autoregressions and related tools .. currentmodule:: statsmodels.tsa.vector_ar.var_model .. autosummary:: :toctree: generated/ VAR VARProcess VARResults Post-estimation Analysis ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Several process properties and additional results after estimation are available for vector autoregressive processes. .. currentmodule:: statsmodels.tsa.vector_ar.var_model .. autosummary:: :toctree: generated/ LagOrderResults .. currentmodule:: statsmodels.tsa.vector_ar.hypothesis_test_results .. autosummary:: :toctree: generated/ HypothesisTestResults NormalityTestResults WhitenessTestResults Impulse Response Analysis ------------------------- *Impulse responses* are of interest in econometric studies: they are the estimated responses to a unit impulse in one of the variables. They are computed in practice using the MA(:math:`\infty`) representation of the VAR(p) process: .. math:: Y_t = \mu + \sum_{i=0}^\infty \Phi_i u_{t-i} We can perform an impulse response analysis by calling the `irf` function on a `VARResults` object: .. ipython:: python :okwarning: irf = results.irf(10) These can be visualized using the `plot` function, in either orthogonalized or non-orthogonalized form. Asymptotic standard errors are plotted by default at the 95% significance level, which can be modified by the user. .. note:: Orthogonalization is done using the Cholesky decomposition of the estimated error covariance matrix :math:`\hat \Sigma_u` and hence interpretations may change depending on variable ordering. .. ipython:: python @savefig var_irf.png irf.plot(orth=False) Note the `plot` function is flexible and can plot only variables of interest if so desired: .. ipython:: python @savefig var_realgdp.png irf.plot(impulse='realgdp') The cumulative effects :math:`\Psi_n = \sum_{i=0}^n \Phi_i` can be plotted with the long run effects as follows: .. ipython:: python @savefig var_irf_cum.png irf.plot_cum_effects(orth=False) .. currentmodule:: statsmodels.tsa.vector_ar.irf .. autosummary:: :toctree: generated/ IRAnalysis Forecast Error Variance Decomposition (FEVD) -------------------------------------------- Forecast errors of component j on k in an i-step ahead forecast can be decomposed using the orthogonalized impulse responses :math:`\Theta_i`: .. math:: \omega_{jk, i} = \sum_{i=0}^{h-1} (e_j^\prime \Theta_i e_k)^2 / \mathrm{MSE}_j(h) \mathrm{MSE}_j(h) = \sum_{i=0}^{h-1} e_j^\prime \Phi_i \Sigma_u \Phi_i^\prime e_j These are computed via the `fevd` function up through a total number of steps ahead: .. ipython:: python fevd = results.fevd(5) fevd.summary() They can also be visualized through the returned :class:`FEVD` object: .. ipython:: python @savefig var_fevd.png results.fevd(20).plot() .. currentmodule:: statsmodels.tsa.vector_ar.var_model .. autosummary:: :toctree: generated/ FEVD Statistical tests ----------------- A number of different methods are provided to carry out hypothesis tests about the model results and also the validity of the model assumptions (normality, whiteness / "iid-ness" of errors, etc.). Granger causality ~~~~~~~~~~~~~~~~~ One is often interested in whether a variable or group of variables is "causal" for another variable, for some definition of "causal". In the context of VAR models, one can say that a set of variables are Granger-causal within one of the VAR equations. We will not detail the mathematics or definition of Granger causality, but leave it to the reader. The :class:`VARResults` object has the `test_causality` method for performing either a Wald (:math:`\chi^2`) test or an F-test. .. ipython:: python results.test_causality('realgdp', ['realinv', 'realcons'], kind='f') Normality ~~~~~~~~~ As pointed out in the beginning of this document, the white noise component :math:`u_t` is assumed to be normally distributed. While this assumption is not required for parameter estimates to be consistent or asymptotically normal, results are generally more reliable in finite samples when residuals are Gaussian white noise. To test whether this assumption is consistent with a data set, :class:`VARResults` offers the `test_normality` method. .. ipython:: python results.test_normality() Whiteness of residuals ~~~~~~~~~~~~~~~~~~~~~~ To test the whiteness of the estimation residuals (this means absence of significant residual autocorrelations) one can use the `test_whiteness` method of :class:`VARResults`. .. currentmodule:: statsmodels.tsa.vector_ar.hypothesis_test_results .. autosummary:: :toctree: generated/ HypothesisTestResults CausalityTestResults NormalityTestResults WhitenessTestResults .. _svar: Structural Vector Autoregressions --------------------------------- There are a matching set of classes that handle some types of Structural VAR models. .. module:: statsmodels.tsa.vector_ar.svar_model :synopsis: Structural vector autoregressions and related tools .. currentmodule:: statsmodels.tsa.vector_ar.svar_model .. autosummary:: :toctree: generated/ SVAR SVARProcess SVARResults .. _vecm: Vector Error Correction Models (VECM) ------------------------------------- Vector Error Correction Models are used to study short-run deviations from one or more permanent stochastic trends (unit roots). A VECM models the difference of a vector of time series by imposing structure that is implied by the assumed number of stochastic trends. :class:`VECM` is used to specify and estimate these models. A VECM(:math:`k_{ar}-1`) has the following form .. math:: \Delta y_t = \Pi y_{t-1} + \Gamma_1 \Delta y_{t-1} + \ldots + \Gamma_{k_{ar}-1} \Delta y_{t-k_{ar}+1} + u_t where .. math:: \Pi = \alpha \beta' as described in chapter 7 of [1]_. A VECM(:math:`k_{ar} - 1`) with deterministic terms has the form .. math:: \Delta y_t = \alpha \begin{pmatrix}\beta' & \eta'\end{pmatrix} \begin{pmatrix}y_{t-1} \\ D^{co}_{t-1}\end{pmatrix} + \Gamma_1 \Delta y_{t-1} + \dots + \Gamma_{k_{ar}-1} \Delta y_{t-k_{ar}+1} + C D_t + u_t. In :math:`D^{co}_{t-1}` we have the deterministic terms which are inside the cointegration relation (or restricted to the cointegration relation). :math:`\eta` is the corresponding estimator. To pass a deterministic term inside the cointegration relation, we can use the `exog_coint` argument. For the two special cases of an intercept and a linear trend there exists a simpler way to declare these terms: we can pass ``"ci"`` and ``"li"`` respectively to the `deterministic` argument. So for an intercept inside the cointegration relation we can either pass ``"ci"`` as `deterministic` or `np.ones(len(data))` as `exog_coint` if `data` is passed as the `endog` argument. This ensures that :math:`D_{t-1}^{co} = 1` for all :math:`t`. We can also use deterministic terms outside the cointegration relation. These are defined in :math:`D_t` in the formula above with the corresponding estimators in the matrix :math:`C`. We specify such terms by passing them to the `exog` argument. For an intercept and/or linear trend we again have the possibility to use `deterministic` alternatively. For an intercept we pass ``"co"`` and for a linear trend we pass ``"lo"`` where the `o` stands for `outside`. The following table shows the five cases considered in [2]_. The last column indicates which string to pass to the `deterministic` argument for each of these cases. ==== =============================== =================================== ============= Case Intercept Slope of the linear trend `deterministic` ==== =============================== =================================== ============= I 0 0 ``"nc"`` II :math:`- \alpha \beta^T \mu` 0 ``"ci"`` III :math:`\neq 0` 0 ``"co"`` IV :math:`\neq 0` :math:`- \alpha \beta^T \gamma` ``"coli"`` V :math:`\neq 0` :math:`\neq 0` ``"colo"`` ==== =============================== =================================== ============= .. currentmodule:: statsmodels.tsa.vector_ar.vecm .. autosummary:: :toctree: generated/ VECM coint_johansen JohansenTestResult select_order select_coint_rank VECMResults CointRankResults References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. .. [2] Johansen, S. 1995. *Likelihood-Based Inference in Cointegrated * *Vector Autoregressive Models*. Oxford University Press. statsmodels-0.12.2/examples/000077500000000000000000000000001400612667500157635ustar00rootroot00000000000000statsmodels-0.12.2/examples/incomplete/000077500000000000000000000000001400612667500201225ustar00rootroot00000000000000statsmodels-0.12.2/examples/incomplete/arima.py000066400000000000000000000030651400612667500215710ustar00rootroot00000000000000from statsmodels.datasets.macrodata import load_pandas from statsmodels.tsa.base.datetools import dates_from_range from statsmodels.tsa.arima_model import ARIMA import matplotlib.pyplot as plt import numpy as np from scipy import stats import statsmodels.api as sm plt.interactive(False) # let's examine an ARIMA model of CPI cpi = load_pandas().data['cpi'] dates = dates_from_range('1959q1', '2009q3') cpi.index = dates res = ARIMA(cpi, (1, 1, 1), freq='Q').fit() print(res.summary()) # we can look at the series cpi.diff().plot() # maybe logs are better log_cpi = np.log(cpi) # check the ACF and PCF plots acf, confint_acf = sm.tsa.acf(log_cpi.diff().values[1:], confint=95) # center the confidence intervals about zero # TODO: demean? --> confint_acf -= confint_acf.mean(1)[:, None] pacf = sm.tsa.pacf(log_cpi.diff().values[1:], method='ols') # confidence interval is now an option to pacf confint_pacf = stats.norm.ppf(1 - .025) * np.sqrt(1 / 202.) fig = plt.figure() ax = fig.add_subplot(121) ax.set_title('Autocorrelation') ax.plot(range(41), acf, 'bo', markersize=5) ax.vlines(range(41), 0, acf) ax.fill_between(range(41), confint_acf[:, 0], confint_acf[:, 1], alpha=.25) fig.tight_layout() ax = fig.add_subplot(122, sharey=ax) ax.vlines(range(41), 0, pacf) ax.plot(range(41), pacf, 'bo', markersize=5) ax.fill_between(range(41), -confint_pacf, confint_pacf, alpha=.25) # TODO: you'll be able to just to this when tsa-plots is in master # sm.graphics.acf_plot(x, nlags=40) # sm.graphics.pacf_plot(x, nlags=40) # still some seasonality # try an arma(1, 1) with ma(4) term statsmodels-0.12.2/examples/incomplete/arma2.py000066400000000000000000000015401400612667500214760ustar00rootroot00000000000000""" Autoregressive Moving Average (ARMA) Model """ import numpy as np import pandas as pd import statsmodels.api as sm # Generate some data from an ARMA process from statsmodels.tsa.arima_process import arma_generate_sample np.random.seed(12345) arparams = np.array([.75, -.25]) maparams = np.array([.65, .35]) # The conventions of the arma_generate function require that we specify a # 1 for the zero-lag of the AR and MA parameters and that the AR parameters # be negated. ar = np.r_[1, -arparams] ma = np.r_[1, maparams] nobs = 250 y = arma_generate_sample(ar, ma, nobs) # Now, optionally, we can add some dates information. For this example, # we'll use a pandas time series. dates = sm.tsa.datetools.dates_from_range('1980m1', length=nobs) y = pd.Series(y, index=dates) arma_mod = sm.tsa.ARMA(y, order=(2, 2)) arma_res = arma_mod.fit(trend='nc', disp=-1) statsmodels-0.12.2/examples/incomplete/dates.py000066400000000000000000000023551400612667500216010ustar00rootroot00000000000000""" Using dates with timeseries models """ import statsmodels.api as sm import pandas as pd # Getting started # --------------- data = sm.datasets.sunspots.load() # Right now an annual date series must be datetimes at the end of the year. dates = sm.tsa.datetools.dates_from_range('1700', length=len(data.endog)) # Using Pandas # ------------ # Make a pandas Series or DataFrame with DatetimeIndex endog = pd.Series(data.endog, index=dates) # and instantiate the model ar_model = sm.tsa.AR(endog, freq='A') pandas_ar_res = ar_model.fit(maxlag=9, method='mle', disp=-1) # Let's do some out-of-sample prediction pred = pandas_ar_res.predict(start='2005', end='2015') print(pred) # Using explicit dates # -------------------- ar_model = sm.tsa.AR(data.endog, dates=dates, freq='A') ar_res = ar_model.fit(maxlag=9, method='mle', disp=-1) pred = ar_res.predict(start='2005', end='2015') print(pred) # This just returns a regular array, but since the model has date information # attached, you can get the prediction dates in a roundabout way. print(ar_res.data.predict_dates) # This attribute only exists if predict has been called. It holds the dates # associated with the last call to predict. # TODO: should this be attached to the results instance? statsmodels-0.12.2/examples/incomplete/glsar.py000066400000000000000000000111421400612667500216030ustar00rootroot00000000000000""" Generalized Least Squares with AR Errors 6 examples for GLSAR with artificial data """ # .. note: These examples were written mostly to cross-check results. It is # still being written, and GLSAR is still being worked on. import numpy as np import numpy.testing as npt from scipy import signal import statsmodels.api as sm from statsmodels.regression.linear_model import GLSAR, yule_walker examples_all = range(10) + ['test_copy'] examples = examples_all # [5] if 0 in examples: print('\n Example 0') X = np.arange(1, 8) X = sm.add_constant(X, prepend=False) Y = np.array((1, 3, 4, 5, 8, 10, 9)) rho = 2 model = GLSAR(Y, X, 2) for i in range(6): results = model.fit() print('AR coefficients:', model.rho) rho, sigma = yule_walker(results.resid, order=model.order) model = GLSAR(Y, X, rho) par0 = results.params print('params fit', par0) model0if = GLSAR(Y, X, 2) res = model0if.iterative_fit(6) print('iterativefit beta', res.params) results.tvalues # TODO: is this correct? it does equal params/bse # but is not the same as the AR example (which was wrong) print(results.t_test([0, 1])) # are sd and t correct? vs print(results.f_test(np.eye(2))) rhotrue = np.array([0.5, 0.2]) nlags = np.size(rhotrue) beta = np.array([0.1, 2]) noiseratio = 0.5 nsample = 2000 x = np.arange(nsample) X1 = sm.add_constant(x, prepend=False) wnoise = noiseratio * np.random.randn(nsample + nlags) # .. noise = noise[1:] + rhotrue*noise[:-1] # wrong this is not AR # .. find my drafts for univariate ARMA functions # generate AR(p) if np.size(rhotrue) == 1: # replace with scipy.signal.lfilter, keep for testing arnoise = np.zeros(nsample + 1) for i in range(1, nsample + 1): arnoise[i] = rhotrue * arnoise[i - 1] + wnoise[i] noise = arnoise[1:] an = signal.lfilter([1], np.hstack((1, -rhotrue)), wnoise[1:]) print('simulate AR(1) difference', np.max(np.abs(noise - an))) else: noise = signal.lfilter([1], np.hstack((1, -rhotrue)), wnoise)[nlags:] # generate GLS model with AR noise y1 = np.dot(X1, beta) + noise if 1 in examples: print('\nExample 1: iterative_fit and repeated calls') mod1 = GLSAR(y1, X1, 1) res = mod1.iterative_fit() print(res.params) print(mod1.rho) mod1 = GLSAR(y1, X1, 2) for i in range(5): res1 = mod1.iterative_fit(2) print(mod1.rho) print(res1.params) if 2 in examples: print('\nExample 2: iterative fitting of first model') print('with AR(0)', par0) parold = par0 mod0 = GLSAR(Y, X, 1) for i in range(5): res0 = mod0.iterative_fit(1) print('rho', mod0.rho) parnew = res0.params print('params', parnew,) print('params change in iteration', parnew - parold) parold = parnew # generate pure AR(p) process Y = noise # example with no regressor, # results now have same estimated rho as yule-walker directly if 3 in examples: print('\nExample 3: pure AR(2), GLSAR versus Yule_Walker') model3 = GLSAR(Y, rho=2) for i in range(5): results = model3.fit() print("AR coefficients:", model3.rho, results.params) rho, sigma = yule_walker(results.resid, order=model3.order) model3 = GLSAR(Y, rho=rho) if 'test_copy' in examples: xx = X.copy() rhoyw, sigmayw = yule_walker(xx[:, 0], order=2) print(rhoyw, sigmayw) print((xx == X).all()) # test for unchanged array (fixed) yy = Y.copy() rhoyw, sigmayw = yule_walker(yy, order=2) print(rhoyw, sigmayw) print((yy == Y).all()) # test for unchanged array (fixed) if 4 in examples: print('\nExample 4: demeaned pure AR(2), GLSAR versus Yule_Walker') Ydemeaned = Y - Y.mean() model4 = GLSAR(Ydemeaned, rho=2) for i in range(5): results = model4.fit() print("AR coefficients:", model3.rho, results.params) rho, sigma = yule_walker(results.resid, order=model4.order) model4 = GLSAR(Ydemeaned, rho=rho) if 5 in examples: print('\nExample 5: pure AR(2), GLSAR iterative_fit versus Yule_Walker') model3a = GLSAR(Y, rho=1) res3a = model3a.iterative_fit(5) print(res3a.params) print(model3a.rho) rhoyw, sigmayw = yule_walker(Y, order=1) print(rhoyw, sigmayw) npt.assert_array_almost_equal(model3a.rho, rhoyw, 15) for i in range(6): model3b = GLSAR(Y, rho=0.1) print(i, model3b.iterative_fit(i).params, model3b.rho) model3b = GLSAR(Y, rho=0.1) for i in range(6): print(i, model3b.iterative_fit(2).params, model3b.rho) print(np.array(res.history['params'])) print(np.array(res.history['rho'])) statsmodels-0.12.2/examples/incomplete/ols_table.py000066400000000000000000000037161400612667500224470ustar00rootroot00000000000000"""Example: statsmodels.OLS """ from statsmodels.datasets.longley import load import statsmodels.api as sm from statsmodels.iolib.table import SimpleTable, default_txt_fmt import numpy as np data = load() data_orig = (data.endog.copy(), data.exog.copy()) # Note: In this example using zscored/standardized variables has no effect on # regression estimates. Are there no numerical problems? rescale = 0 # 0: no rescaling, 1:demean, 2:standardize, 3:standardize and transform back rescale_ratio = data.endog.std() / data.exog.std(0) if rescale > 0: # rescaling data.endog -= data.endog.mean() data.exog -= data.exog.mean(0) if rescale > 1: data.endog /= data.endog.std() data.exog /= data.exog.std(0) # skip because mean has been removed, but dimension is hardcoded in table data.exog = sm.tools.add_constant(data.exog, prepend=False) ols_model = sm.OLS(data.endog, data.exog) ols_results = ols_model.fit() # the Longley dataset is well known to have high multicollinearity # one way to find the condition number is as follows # Find OLS parameters for model with one explanatory variable dropped resparams = np.nan * np.ones((7, 7)) res = sm.OLS(data.endog, data.exog).fit() resparams[:, 0] = res.params indall = range(7) for i in range(6): ind = indall[:] del ind[i] res = sm.OLS(data.endog, data.exog[:, ind]).fit() resparams[ind, i + 1] = res.params if rescale == 1: pass if rescale == 3: resparams[:-1, :] *= rescale_ratio[:, None] txt_fmt1 = default_txt_fmt numformat = '%10.4f' txt_fmt1 = dict(data_fmts=[numformat]) rowstubs = data.names[1:] + ['const'] headers = ['all'] + ['drop %s' % name for name in data.names[1:]] tabl = SimpleTable(resparams, headers, rowstubs, txt_fmt=txt_fmt1) nanstring = numformat % np.nan nn = len(nanstring) nanrep = ' ' * (nn - 1) nanrep = nanrep[:nn // 2] + '-' + nanrep[nn // 2:] print('Longley data - sensitivity to dropping an explanatory variable') print(str(tabl).replace(nanstring, nanrep)) statsmodels-0.12.2/examples/incomplete/ols_tftest.py000066400000000000000000000132651400612667500226710ustar00rootroot00000000000000"""examples for usage of F-test on linear restrictions in OLS linear restriction is R \beta = 0 R is (nr,nk), beta is (nk,1) (in matrix notation) TODO: clean this up for readability and explain Notes ----- This example was written mostly for cross-checks and refactoring. """ import numpy as np import numpy.testing as npt from scipy import stats import statsmodels.api as sm print('\n\n Example 1: Longley Data, high multicollinearity') data = sm.datasets.longley.load() data.exog = sm.add_constant(data.exog, prepend=False) res = sm.OLS(data.endog, data.exog).fit() # test pairwise equality of some coefficients R2 = [[0, 1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 1, -1, 0]] Ftest = res.f_test(R2) print(repr((Ftest.fvalue, Ftest.pvalue))) # use repr to get more digits # 9.740461873303655 0.0056052885317360301 # Compare to R (after running R_lm.s in the longley folder) # # > library(car) # > linear.hypothesis(m1, c("GNP = UNEMP","POP = YEAR")) # Linear hypothesis test # # Hypothesis: # GNP - UNEMP = 0 # POP - YEAR = 0 # # Model 1: TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR # Model 2: restricted model # # Res.Df RSS Df Sum of Sq F Pr(>F) # 1 9 836424 # 2 11 2646903 -2 -1810479 9.7405 0.005605 ** print('Regression Results Summary') print(res.summary()) print('\n F-test whether all variables have zero effect') R = np.eye(7)[:-1, :] Ftest0 = res.f_test(R) print(repr((Ftest0.fvalue, Ftest0.pvalue))) print('%r' % res.fvalue) npt.assert_almost_equal(res.fvalue, Ftest0.fvalue, decimal=9) ttest0 = res.t_test(R[0, :]) print(repr((ttest0.tvalue, ttest0.pvalue))) betatval = res.tvalues betatval[0] npt.assert_almost_equal(betatval[0], ttest0.tvalue, decimal=15) """ # several ttests at the same time # currently not checked for this, but it (kind of) works >>> ttest0 = res.t_test(R[:2,:]) >>> print(repr((ttest0.t, ttest0.pvalue)) (array([[ 0.17737603, NaN], [ NaN, -1.06951632]]), array([[ 0.43157042, 1. ], [ 1. , 0.84365947]])) >>> ttest0 = res.t_test(R) >>> ttest0.t array([[ 1.77376028e-01, NaN, NaN, NaN, -1.43660623e-02, 2.15494063e+01], [ NaN, -1.06951632e+00, -1.62440215e+01, -1.78173553e+01, NaN, NaN], [ NaN, -2.88010561e-01, -4.13642736e+00, -4.06097408e+00, NaN, NaN], [ NaN, -6.17679489e-01, -7.94027056e+00, -4.82198531e+00, NaN, NaN], [ 4.23409809e+00, NaN, NaN, NaN, -2.26051145e-01, 2.89324928e+02], [ 1.77445341e-01, NaN, NaN, NaN, -8.08336103e-03, 4.01588981e+00]]) >>> betatval array([ 0.17737603, -1.06951632, -4.13642736, -4.82198531, -0.22605114, 4.01588981, -3.91080292]) >>> ttest0.t array([ 0.17737603, -1.06951632, -4.13642736, -4.82198531, -0.22605114, 4.01588981]) """ print('\nsimultaneous t-tests') ttest0 = res.t_test(R2) t2 = ttest0.tvalue print(ttest0.tvalue) print(t2) t2a = np.r_[res.t_test(np.array(R2)[0, :]).tvalue, res.t_test(np.array(R2)[1, :]).tvalue] print(t2 - t2a) t2pval = ttest0.pvalue print('%r' % t2pval) # reject # array([ 9.33832896e-04, 9.98483623e-01]) print('reject') print('%r' % (t2pval < 0.05)) # f_test needs 2-d currently Ftest2a = res.f_test(np.asarray(R2)[:1, :]) print(repr((Ftest2a.fvalue, Ftest2a.pvalue))) Ftest2b = res.f_test(np.asarray(R2)[1:2, :]) print(repr((Ftest2b.fvalue, Ftest2b.pvalue))) print('\nequality of t-test and F-test') print(t2a**2 - np.array((Ftest2a.fvalue, Ftest2b.fvalue))) npt.assert_almost_equal(t2a**2, np.vstack((Ftest2a.fvalue, Ftest2b.fvalue))) npt.assert_almost_equal(t2pval * 2, np.c_[Ftest2a.pvalue, Ftest2b.pvalue].squeeze()) print('\n\n Example 2: Artificial Data') nsample = 100 ncat = 4 sigma = 2 xcat = np.linspace(0, ncat - 1, nsample).round()[:, np.newaxis] dummyvar = (xcat == np.arange(ncat)).astype(float) beta = np.array([0., 2, -2, 1])[:, np.newaxis] ytrue = np.dot(dummyvar, beta) X = sm.tools.add_constant(dummyvar[:, :-1], prepend=False) y = ytrue + sigma * np.random.randn(nsample, 1) mod2 = sm.OLS(y[:, 0], X) res2 = mod2.fit() print(res2.summary()) R3 = np.eye(ncat)[:-1, :] Ftest = res2.f_test(R3) print(repr((Ftest.fvalue, Ftest.pvalue))) R3 = np.atleast_2d([0, 1, -1, 2]) Ftest = res2.f_test(R3) print(repr((Ftest.fvalue, Ftest.pvalue))) print('simultaneous t-test for zero effects') R4 = np.eye(ncat)[:-1, :] ttest = res2.t_test(R4) print(repr((ttest.tvalue, ttest.pvalue))) R5 = np.atleast_2d([0, 1, 1, 2]) np.dot(R5, res2.params) Ftest = res2.f_test(R5) print(repr((Ftest.fvalue, Ftest.pvalue))) ttest = res2.t_test(R5) print(repr((ttest.tvalue, ttest.pvalue))) R6 = np.atleast_2d([1, -1, 0, 0]) np.dot(R6, res2.params) Ftest = res2.f_test(R6) print(repr((Ftest.fvalue, Ftest.pvalue))) ttest = res2.t_test(R6) print(repr((ttest.tvalue, ttest.pvalue))) R7 = np.atleast_2d([1, 0, 0, 0]) np.dot(R7, res2.params) Ftest = res2.f_test(R7) print(repr((Ftest.fvalue, Ftest.pvalue))) ttest = res2.t_test(R7) print(repr((ttest.tvalue, ttest.pvalue))) print('\nExample: 2 categories: replicate stats.glm and stats.ttest_ind') mod2 = sm.OLS(y[xcat.flat < 2][:, 0], X[xcat.flat < 2, :][:, (0, -1)]) res2 = mod2.fit() R8 = np.atleast_2d([1, 0]) np.dot(R8, res2.params) Ftest = res2.f_test(R8) print(repr((Ftest.fvalue, Ftest.pvalue))) print(repr((np.sqrt(Ftest.fvalue), Ftest.pvalue))) ttest = res2.t_test(R8) print(repr((ttest.tvalue, ttest.pvalue))) print(stats.glm(y[xcat < 2].ravel(), xcat[xcat < 2].ravel())) print(stats.ttest_ind(y[xcat == 0], y[xcat == 1])) # TODO: compare with f_oneway statsmodels-0.12.2/examples/incomplete/wls_extended.py000066400000000000000000000373121400612667500231670ustar00rootroot00000000000000""" Weighted Least Squares example is extended to look at the meaning of rsquared in WLS, at outliers, compares with RLM and a short bootstrap """ import numpy as np import statsmodels.api as sm import matplotlib.pyplot as plt data = sm.datasets.ccard.load() data.exog = sm.add_constant(data.exog, prepend=False) ols_fit = sm.OLS(data.endog, data.exog).fit() # perhaps the residuals from this fit depend on the square of income incomesq = data.exog[:, 2] plt.scatter(incomesq, ols_fit.resid) # @savefig wls_resid_check.png plt.grid() # If we think that the variance is proportional to income**2 # we would want to weight the regression by income # the weights argument in WLS weights the regression by its square root # and since income enters the equation, if we have income/income # it becomes the constant, so we would want to perform # this type of regression without an explicit constant in the design wls_fit = sm.WLS(data.endog, data.exog[:, :-1], weights=1/incomesq).fit() # This however, leads to difficulties in interpreting the post-estimation # statistics. statsmodels does not yet handle this elegantly, but # the following may be more appropriate # explained sum of squares ess = wls_fit.uncentered_tss - wls_fit.ssr # rsquared rsquared = ess/wls_fit.uncentered_tss # mean squared error of the model mse_model = ess/(wls_fit.df_model + 1) # add back the dof of the constant # f statistic fvalue = mse_model/wls_fit.mse_resid # adjusted r-squared rsquared_adj = 1 - (wls_fit.nobs)/(wls_fit.df_resid)*(1-rsquared) # Trying to figure out what's going on in this example # ---------------------------------------------------- # JP: I need to look at this again. Even if I exclude the weight variable # from the regressors and keep the constant in then the reported rsquared # stays small. Below also compared using squared or sqrt of weight variable. # TODO: need to add 45 degree line to graphs wls_fit3 = sm.WLS(data.endog, data.exog[:, (0, 1, 3, 4)], weights=1/incomesq).fit() print(wls_fit3.summary()) print('corrected rsquared') print((wls_fit3.uncentered_tss - wls_fit3.ssr)/wls_fit3.uncentered_tss) plt.figure() plt.title('WLS dropping heteroscedasticity variable from regressors') plt.plot(data.endog, wls_fit3.fittedvalues, 'o') plt.xlim([0, 2000]) # @savefig wls_drop_het.png plt.ylim([0, 2000]) print('raw correlation of endog and fittedvalues') print(np.corrcoef(data.endog, wls_fit.fittedvalues)) print('raw correlation coefficient of endog and fittedvalues squared') print(np.corrcoef(data.endog, wls_fit.fittedvalues)[0, 1]**2) # compare with robust regression, # heteroscedasticity correction downweights the outliers rlm_fit = sm.RLM(data.endog, data.exog).fit() plt.figure() plt.title('using robust for comparison') plt.plot(data.endog, rlm_fit.fittedvalues, 'o') plt.xlim([0, 2000]) # @savefig wls_robust_compare.png plt.ylim([0, 2000]) # What is going on? A more systematic look at the data # ---------------------------------------------------- # two helper functions def getrsq(fitresult): '''calculates rsquared residual, total and explained sums of squares Parameters ---------- fitresult : instance of Regression Result class, or tuple of (resid, endog) arrays regression residuals and endogenous variable Returns ------- rsquared residual sum of squares (centered) total sum of squares explained sum of squares (for centered) ''' if hasattr(fitresult, 'resid') and hasattr(fitresult, 'model'): resid = fitresult.resid endog = fitresult.model.endog nobs = fitresult.nobs else: resid = fitresult[0] endog = fitresult[1] nobs = resid.shape[0] rss = np.dot(resid, resid) tss = np.var(endog)*nobs return 1-rss/tss, rss, tss, tss-rss def index_trim_outlier(resid, k): '''returns indices to residual array with k outliers removed Parameters ---------- resid : array_like, 1d data vector, usually residuals of a regression k : int number of outliers to remove Returns ------- trimmed_index : ndarray, 1d index array with k outliers removed outlier_index : ndarray, 1d index array of k outliers Notes ----- Outliers are defined as the k observations with the largest absolute values. ''' sort_index = np.argsort(np.abs(resid)) # index of non-outlier trimmed_index = np.sort(sort_index[:-k]) outlier_index = np.sort(sort_index[-k:]) return trimmed_index, outlier_index # Comparing estimation results for ols, rlm and wls with and without outliers # --------------------------------------------------------------------------- olskeep, olsoutl = index_trim_outlier(ols_fit.resid, 2) print('ols outliers', olsoutl, ols_fit.resid[olsoutl]) ols_fit_rm2 = sm.OLS(data.endog[olskeep], data.exog[olskeep, :]).fit() rlm_fit_rm2 = sm.RLM(data.endog[olskeep], data.exog[olskeep, :]).fit() results = [ols_fit, ols_fit_rm2, rlm_fit, rlm_fit_rm2] # Note: I think incomesq is already square for weights in [1/incomesq, 1/incomesq**2, np.sqrt(incomesq)]: print('\nComparison OLS and WLS with and without outliers') wls_fit0 = sm.WLS(data.endog, data.exog, weights=weights).fit() wls_fit_rm2 = sm.WLS(data.endog[olskeep], data.exog[olskeep, :], weights=weights[olskeep]).fit() wlskeep, wlsoutl = index_trim_outlier(ols_fit.resid, 2) print('2 outliers candidates and residuals') print(wlsoutl, wls_fit.resid[olsoutl]) # redundant because ols and wls outliers are the same: # wls_fit_rm2_ = sm.WLS(data.endog[wlskeep], data.exog[wlskeep, :], # weights=1/incomesq[wlskeep]).fit() print('outliers ols, wls:', olsoutl, wlsoutl) print('rsquared') print('ols vs ols rm2', ols_fit.rsquared, ols_fit_rm2.rsquared) print('wls vs wls rm2', wls_fit0.rsquared, wls_fit_rm2.rsquared) print('compare R2_resid versus R2_wresid') print('ols minus 2', getrsq(ols_fit_rm2)[0],) print(getrsq((ols_fit_rm2.wresid, ols_fit_rm2.model.wendog))[0]) print('wls ', getrsq(wls_fit)[0],) print(getrsq((wls_fit.wresid, wls_fit.model.wendog))[0]) print('wls minus 2', getrsq(wls_fit_rm2)[0]) # next is same as wls_fit_rm2.rsquared for cross checking print(getrsq((wls_fit_rm2.wresid, wls_fit_rm2.model.wendog))[0]) results.extend([wls_fit0, wls_fit_rm2]) print(' ols ols_rm2 rlm rlm_rm2 ' 'wls (lin) wls_rm2 (lin) ' 'wls (squ) wls_rm2 (squ) ' 'wls (sqrt) wls_rm2 (sqrt)') print('Parameter estimates') print(np.column_stack([r.params for r in results])) print('R2 original data, next line R2 weighted data') print(np.column_stack([getattr(r, 'rsquared', None) for r in results])) print('Standard errors') print(np.column_stack([getattr(r, 'bse', None) for r in results])) print('Heteroscedasticity robust standard errors (with ols)') print('with outliers') print(np.column_stack([getattr(ols_fit, se, None) for se in ['HC0_se', 'HC1_se', 'HC2_se', 'HC3_se']])) ''' # .. # .. # .. ols ols_rm2 rlm rlm_rm2 wls (lin) wls_rm2 (lin) wls (squ) wls_rm2 (squ) wls (sqrt) wls_rm2 (sqrt) # ..Parameter estimates # ..[[ -3.08181404 -5.06103843 -4.98510966 -5.34410309 -2.69418516 -3.1305703 -1.43815462 -1.58893054 -3.57074829 -6.80053364] # .. [ 234.34702702 115.08753715 129.85391456 109.01433492 158.42697752 128.38182357 60.95113284 100.25000841 254.82166855 103.75834726] # .. [ -14.99684418 -5.77558429 -6.46204829 -4.77409191 -7.24928987 -7.41228893 6.84943071 -3.34972494 -16.40524256 -4.5924465 ] # .. [ 27.94090839 85.46566835 89.91389709 95.85086459 60.44877369 79.7759146 55.9884469 60.97199734 -3.8085159 84.69170048] # .. [-237.1465136 39.51639838 -15.50014814 31.39771833 -114.10886935 -40.04207242 -6.41976501 -38.83583228 -260.72084271 117.20540179]] # .. # ..R2 original data, next line R2 weighted data # ..[[ 0.24357792 0.31745994 0.19220308 0.30527648 0.22861236 0.3112333 0.06573949 0.29366904 0.24114325 0.31218669]] # ..[[ 0.24357791 0.31745994 None None 0.05936888 0.0679071 0.06661848 0.12769654 0.35326686 0.54681225]] # .. # ..-> R2 with weighted data is jumping all over # .. # ..standard errors # ..[[ 5.51471653 3.31028758 2.61580069 2.39537089 3.80730631 2.90027255 2.71141739 2.46959477 6.37593755 3.39477842] # .. [ 80.36595035 49.35949263 38.12005692 35.71722666 76.39115431 58.35231328 87.18452039 80.30086861 86.99568216 47.58202096] # .. [ 7.46933695 4.55366113 3.54293763 3.29509357 9.72433732 7.41259156 15.15205888 14.10674821 7.18302629 3.91640711] # .. [ 82.92232357 50.54681754 39.33262384 36.57639175 58.55088753 44.82218676 43.11017757 39.31097542 96.4077482 52.57314209] # .. [ 199.35166485 122.1287718 94.55866295 88.3741058 139.68749646 106.89445525 115.79258539 105.99258363 239.38105863 130.32619908]] # .. # ..robust standard errors (with ols) # ..with outliers # .. HC0_se HC1_se HC2_se HC3_se' # ..[[ 3.30166123 3.42264107 3.4477148 3.60462409] # .. [ 88.86635165 92.12260235 92.08368378 95.48159869] # .. [ 6.94456348 7.19902694 7.19953754 7.47634779] # .. [ 92.18777672 95.56573144 95.67211143 99.31427277] # .. [ 212.9905298 220.79495237 221.08892661 229.57434782]] # .. # ..removing 2 outliers # ..[[ 2.57840843 2.67574088 2.68958007 2.80968452] # .. [ 36.21720995 37.58437497 37.69555106 39.51362437] # .. [ 3.1156149 3.23322638 3.27353882 3.49104794] # .. [ 50.09789409 51.98904166 51.89530067 53.79478834] # .. [ 94.27094886 97.82958699 98.25588281 102.60375381]] # .. # .. # .. ''' # noqa:E501 # a quick bootstrap analysis # -------------------------- # # (I did not check whether this is fully correct statistically) # **With OLS on full sample** nobs, nvar = data.exog.shape niter = 2000 bootres = np.zeros((niter, nvar*2)) for it in range(niter): rind = np.random.randint(nobs, size=nobs) endog = data.endog[rind] exog = data.exog[rind, :] res = sm.OLS(endog, exog).fit() bootres[it, :nvar] = res.params bootres[it, nvar:] = res.bse np.set_printoptions(linewidth=200) print('Bootstrap Results of parameters and parameter standard deviation OLS') print('Parameter estimates') print('median', np.median(bootres[:, :5], 0)) print('mean ', np.mean(bootres[:, :5], 0)) print('std ', np.std(bootres[:, :5], 0)) print('Standard deviation of parameter estimates') print('median', np.median(bootres[:, 5:], 0)) print('mean ', np.mean(bootres[:, 5:], 0)) print('std ', np.std(bootres[:, 5:], 0)) plt.figure() for i in range(4): plt.subplot(2, 2, i+1) plt.hist(bootres[:, i], 50) plt.title('var%d' % i) # @savefig wls_bootstrap.png plt.figtext(0.5, 0.935, 'OLS Bootstrap', ha='center', color='black', weight='bold', size='large') # **With WLS on sample with outliers removed** data_endog = data.endog[olskeep] data_exog = data.exog[olskeep, :] incomesq_rm2 = incomesq[olskeep] nobs, nvar = data_exog.shape niter = 500 # a bit slow bootreswls = np.zeros((niter, nvar*2)) for it in range(niter): rind = np.random.randint(nobs, size=nobs) endog = data_endog[rind] exog = data_exog[rind, :] res = sm.WLS(endog, exog, weights=1/incomesq[rind, :]).fit() bootreswls[it, :nvar] = res.params bootreswls[it, nvar:] = res.bse print('Bootstrap Results of parameters and parameter standard deviation',) print('WLS removed 2 outliers from sample') print('Parameter estimates') print('median', np.median(bootreswls[:, :5], 0)) print('mean ', np.mean(bootreswls[:, :5], 0)) print('std ', np.std(bootreswls[:, :5], 0)) print('Standard deviation of parameter estimates') print('median', np.median(bootreswls[:, 5:], 0)) print('mean ', np.mean(bootreswls[:, 5:], 0)) print('std ', np.std(bootreswls[:, 5:], 0)) plt.figure() for i in range(4): plt.subplot(2, 2, i+1) plt.hist(bootreswls[:, i], 50) plt.title('var%d' % i) # @savefig wls_bootstrap_rm2.png plt.figtext(0.5, 0.935, 'WLS rm2 Bootstrap', ha='center', color='black', weight='bold', size='large') # ..plt.show() # ..plt.close('all') ''' # :: # # The following a random variables not fixed by a seed # # Bootstrap Results of parameters and parameter standard deviation # OLS # # Parameter estimates # median [ -3.26216383 228.52546429 -14.57239967 34.27155426 -227.02816597] # mean [ -2.89855173 234.37139359 -14.98726881 27.96375666 -243.18361746] # std [ 3.78704907 97.35797802 9.16316538 94.65031973 221.79444244] # # Standard deviation of parameter estimates # median [ 5.44701033 81.96921398 7.58642431 80.64906783 200.19167735] # mean [ 5.44840542 86.02554883 8.56750041 80.41864084 201.81196849] # std [ 1.43425083 29.74806562 4.22063268 19.14973277 55.34848348] # # Bootstrap Results of parameters and parameter standard deviation # WLS removed 2 outliers from sample # # Parameter estimates # median [ -3.95876112 137.10419042 -9.29131131 88.40265447 -44.21091869] # mean [ -3.67485724 135.42681207 -8.7499235 89.74703443 -46.38622848] # std [ 2.96908679 56.36648967 7.03870751 48.51201918 106.92466097] # # Standard deviation of parameter estimates # median [ 2.89349748 59.19454402 6.70583332 45.40987953 119.05241283] # mean [ 2.97600894 60.14540249 6.92102065 45.66077486 121.35519673] # std [ 0.55378808 11.77831934 1.69289179 7.4911526 23.72821085] # # # # Conclusion: problem with outliers and possibly heteroscedasticity # ----------------------------------------------------------------- # # in bootstrap results # # * bse in OLS underestimates the standard deviation of the parameters # compared to standard deviation in bootstrap # * OLS heteroscedasticity corrected standard errors for the original # data (above) are close to bootstrap std # * using WLS with 2 outliers removed has a relatively good match between # the mean or median bse and the std of the parameter estimates in the # bootstrap # # We could also include rsquared in bootstrap, and do it also for RLM. # The problems could also mean that the linearity assumption is violated, # e.g. try non-linear transformation of exog variables, but linear # in parameters. # # # for statsmodels # # * In this case rsquared for original data looks less random/arbitrary. # * Do not change definition of rsquared from centered tss to uncentered # tss when calculating rsquared in WLS if the original exog contains # a constant. The increase in rsquared because of a change in definition # will be very misleading. # * Whether there is a constant in the transformed exog, wexog, or not, # might affect also the degrees of freedom calculation, but I have not # checked this. I would guess that the df_model should stay the same, # but needs to be verified with a textbook. # * df_model has to be adjusted if the original data does not have a # constant, e.g. when regressing an endog on a single exog variable # without constant. This case might require also a redefinition of # the rsquare and f statistic for the regression anova to use the # uncentered tss. # This can be done through keyword parameter to model.__init__ or # through autodedection with hasconst = (exog.var(0)<1e-10).any() # I'm not sure about fixed effects with a full dummy set but # without a constant. In this case autodedection would not work this # way. Also, I'm not sure whether a ddof keyword parameter can also # handle the hasconst case. ''' # noqa:E501 statsmodels-0.12.2/examples/notebooks/000077500000000000000000000000001400612667500177665ustar00rootroot00000000000000statsmodels-0.12.2/examples/notebooks/autoregressions.ipynb000066400000000000000000000461011400612667500242670ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": true, "pycharm": { "name": "#%% md\n" } }, "source": [ "# Autoregressions\n", "\n", "This notebook introduces autoregression modeling using the `AutoReg` model. It also covers aspects of `ar_select_order` assists in selecting models that minimize an information criteria such as the AIC. \n", "An autoregressive model has dynamics given by \n", "\n", "$$ y_t = \\delta + \\phi_1 y_{t-1} + \\ldots + \\phi_p y_{t-p} + \\epsilon_t. $$\n", "\n", "`AutoReg` also permits models with:\n", "\n", "* Deterministic terms (`trend`)\n", " * `n`: No deterministic term \n", " * `c`: Constant (default)\n", " * `ct`: Constant and time trend\n", " * `t`: Time trend only\n", "* Seasonal dummies (`seasonal`)\n", " * `True` includes $s-1$ dummies where $s$ is the period of the time series (e.g., 12 for monthly)\n", "* Custom deterministic terms (`deterministic`)\n", " * Accepts a `DeterministicProcess`\n", "* Exogenous variables (`exog`)\n", " * A `DataFrame` or `array` of exogenous variables to include in the model\n", "* Omission of selected lags (`lags`)\n", " * If `lags` is an iterable of integers, then only these are included in the model.\n", "\n", "The complete specification is\n", "\n", "$$ y_t = \\delta_0 + \\delta_1 t + \\phi_1 y_{t-1} + \\ldots + \\phi_p y_{t-p} + \\sum_{i=1}^{s-1} \\gamma_i d_i + \\sum_{j=1}^{m} \\kappa_j x_{t,j} + \\epsilon_t. $$\n", "\n", "where:\n", "\n", "* $d_i$ is a seasonal dummy that is 1 if $mod(t, period) = i$. Period 0 is excluded if the model contains a constant (`c` is in `trend`).\n", "* $t$ is a time trend ($1,2,\\ldots$) that starts with 1 in the first observation.\n", "* $x_{t,j}$ are exogenous regressors. **Note** these are time-aligned to the left-hand-side variable when defining a model.\n", "* $\\epsilon_t$ is assumed to be a white noise process." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This first cell imports standard packages and sets plats to appear inline." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import pandas_datareader as pdr\n", "import seaborn as sns\n", "from statsmodels.tsa.ar_model import AutoReg, ar_select_order\n", "from statsmodels.tsa.api import acf, pacf, graphics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This cell sets the plotting style, registers pandas date converters for matplotlib, and sets the default figure size." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sns.set_style('darkgrid')\n", "pd.plotting.register_matplotlib_converters()\n", "# Default figure size\n", "sns.mpl.rc('figure',figsize=(16, 6))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first set of examples uses the month-over-month growth rate in U.S. Housing starts that has not been seasonally adjusted. The seasonality is evident by the regular pattern of peaks and troughs. We set the frequency for the time series to \"MS\" (month-start) to avoid warnings when using `AutoReg`." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "data = pdr.get_data_fred('HOUSTNSA', '1959-01-01', '2019-06-01')\n", "housing = data.HOUSTNSA.pct_change().dropna()\n", "# Scale by 100 to get percentages\n", "housing = 100 * housing.asfreq('MS')\n", "fig, ax = plt.subplots()\n", "ax = housing.plot(ax=ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can start with an AR(3). While this is not a good model for this data, it demonstrates the basic use of the API." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = AutoReg(housing, 3, old_names=False)\n", "res = mod.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`AutoReg` supports the same covariance estimators as `OLS`. Below, we use `cov_type=\"HC0\"`, which is White's covariance estimator. While the parameter estimates are the same, all of the quantities that depend on the standard error change." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res = mod.fit(cov_type=\"HC0\")\n", "print(res.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "sel = ar_select_order(housing, 13, old_names=False)\n", "sel.ar_lags\n", "res = sel.model.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`plot_predict` visualizes forecasts. Here we produce a large number of forecasts which show the string seasonality captured by the model." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = res.plot_predict(720, 840)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`plot_diagnositcs` indicates that the model captures the key features in the data." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(16,9))\n", "fig = res.plot_diagnostics(fig=fig, lags=30)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Seasonal Dummies" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`AutoReg` supports seasonal dummies which are an alternative way to model seasonality. Including the dummies shortens the dynamics to only an AR(2)." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "sel = ar_select_order(housing, 13, seasonal=True, old_names=False)\n", "sel.ar_lags\n", "res = sel.model.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The seasonal dummies are obvious in the forecasts which has a non-trivial seasonal component in all periods 10 years in to the future." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = res.plot_predict(720, 840)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "fig = plt.figure(figsize=(16,9))\n", "fig = res.plot_diagnostics(lags=30, fig=fig)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Seasonal Dynamics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While `AutoReg` does not directly support Seasonal components since it uses OLS to estimate parameters, it is possible to capture seasonal dynamics using an over-parametrized Seasonal AR that does not impose the restrictions in the Seasonal AR. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "yoy_housing = data.HOUSTNSA.pct_change(12).resample(\"MS\").last().dropna()\n", "_, ax = plt.subplots()\n", "ax = yoy_housing.plot(ax=ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We start by selecting a model using the simple method that only chooses the maximum lag. All lower lags are automatically included. The maximum lag to check is set to 13 since this allows the model to next a Seasonal AR that has both a short-run AR(1) component and a Seasonal AR(1) component, so that\n", "\n", "$$ (1-\\phi_s L^{12})(1-\\phi_1 L)y_t = \\epsilon_t $$\n", "which becomes\n", "$$ y_t = \\phi_1 y_{t-1} +\\phi_s Y_{t-12} - \\phi_1\\phi_s Y_{t-13} + \\epsilon_t $$\n", "\n", "when expanded. `AutoReg` does not enforce the structure, but can estimate the nesting model \n", "\n", "$$ y_t = \\phi_1 y_{t-1} +\\phi_{12} Y_{t-12} - \\phi_{13} Y_{t-13} + \\epsilon_t. $$\n", "\n", "We see that all 13 lags are selected." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sel = ar_select_order(yoy_housing, 13, old_names=False)\n", "sel.ar_lags" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It seems unlikely that all 13 lags are required. We can set `glob=True` to search all $2^{13}$ models that include up to 13 lags.\n", "\n", "Here we see that the first three are selected, as is the 7th, and finally the 12th and 13th are selected. This is superficially similar to the structure described above.\n", "\n", "After fitting the model, we take a look at the diagnostic plots that indicate that this specification appears to be adequate to capture the dynamics in the data." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "sel = ar_select_order(yoy_housing, 13, glob=True, old_names=False)\n", "sel.ar_lags\n", "res = sel.model.fit()\n", "print(res.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(16,9))\n", "fig = res.plot_diagnostics(fig=fig, lags=30)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also include seasonal dummies. These are all insignificant since the model is using year-over-year changes." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "sel = ar_select_order(yoy_housing, 13, glob=True, seasonal=True, old_names=False)\n", "sel.ar_lags\n", "res = sel.model.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "source": [ "## Industrial Production\n", "\n", "We will use the industrial production index data to examine forecasting." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "data = pdr.get_data_fred('INDPRO', '1959-01-01', '2019-06-01')\n", "ind_prod = data.INDPRO.pct_change(12).dropna().asfreq('MS')\n", "_, ax = plt.subplots(figsize=(16,9))\n", "ind_prod.plot(ax=ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will start by selecting a model using up to 12 lags. An AR(13) minimizes the BIC criteria even though many coefficients are insignificant." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "sel = ar_select_order(ind_prod, 13, 'bic', old_names=False)\n", "res = sel.model.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also use a global search which allows longer lags to enter if needed without requiring the shorter lags. Here we see many lags dropped. The model indicates there may be some seasonality in the data. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "sel = ar_select_order(ind_prod, 13, 'bic', glob=True, old_names=False)\n", "sel.ar_lags\n", "res_glob = sel.model.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`plot_predict` can be used to produce forecast plots along with confidence intervals. Here we produce forecasts starting at the last observation and continuing for 18 months." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "ind_prod.shape" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "fig = res_glob.plot_predict(start=714, end=732)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The forecasts from the full model and the restricted model are very similar. I also include an AR(5) which has very different dynamics" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_ar5 = AutoReg(ind_prod, 5, old_names=False).fit()\n", "predictions = pd.DataFrame({\"AR(5)\": res_ar5.predict(start=714, end=726),\n", " \"AR(13)\": res.predict(start=714, end=726),\n", " \"Restr. AR(13)\": res_glob.predict(start=714, end=726)})\n", "_, ax = plt.subplots()\n", "ax = predictions.plot(ax=ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The diagnostics indicate the model captures most of the the dynamics in the data. The ACF shows a patters at the seasonal frequency and so a more complete seasonal model (`SARIMAX`) may be needed." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "fig = plt.figure(figsize=(16,9))\n", "fig = res_glob.plot_diagnostics(fig=fig, lags=30)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Forecasting\n", "\n", "Forecasts are produced using the `predict` method from a results instance. The default produces static forecasts which are one-step forecasts. Producing multi-step forecasts requires using `dynamic=True`. \n", "\n", "In this next cell, we produce 12-step-heard forecasts for the final 24 periods in the sample. This requires a loop.\n", "\n", "**Note**: These are technically in-sample since the data we are forecasting was used to estimate parameters. Producing OOS forecasts requires two models. The first must exclude the OOS period. The second uses the `predict` method from the full-sample model with the parameters from the shorter sample model that excluded the OOS period." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "start = ind_prod.index[-24]\n", "forecast_index = pd.date_range(start, freq=ind_prod.index.freq, periods=36)\n", "cols = ['-'.join(str(val) for val in (idx.year, idx.month)) for idx in forecast_index]\n", "forecasts = pd.DataFrame(index=forecast_index,columns=cols)\n", "for i in range(1, 24):\n", " fcast = res_glob.predict(start=forecast_index[i], end=forecast_index[i+12], dynamic=True)\n", " forecasts.loc[fcast.index, cols[i]] = fcast\n", "_, ax = plt.subplots(figsize=(16, 10))\n", "ind_prod.iloc[-24:].plot(ax=ax, color=\"black\", linestyle=\"--\")\n", "ax = forecasts.plot(ax=ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparing to SARIMAX\n", "\n", "`SARIMAX` is an implementation of a Seasonal Autoregressive Integrated Moving Average with eXogenous regressors model. It supports:\n", "\n", "* Specification of seasonal and nonseasonal AR and MA components\n", "* Inclusion of Exogenous variables\n", "* Full maximum-likelihood estimation using the Kalman Filter\n", "\n", "This model is more feature rich than `AutoReg`. Unlike `SARIMAX`, `AutoReg` estimates parameters using OLS. This is faster and the problem is globally convex, and so there are no issues with local minima. The closed-form estimator and its performance are the key advantages of `AutoReg` over `SARIMAX` when comparing AR(P) models. `AutoReg` also support seasonal dummies, which can be used with `SARIMAX` if the user includes them as exogenous regressors. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.api import SARIMAX\n", "\n", "sarimax_mod = SARIMAX(ind_prod, order=((1,5,12,13),0, 0), trend='c')\n", "sarimax_res = sarimax_mod.fit()\n", "print(sarimax_res.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sarimax_params = sarimax_res.params.iloc[:-1].copy()\n", "sarimax_params.index = res_glob.params.index\n", "params = pd.concat([res_glob.params, sarimax_params], axis=1, sort=False)\n", "params.columns = [\"AutoReg\", \"SARIMAX\"]\n", "params" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Custom Deterministic Processes\n", "\n", "The `deterministic` parameter allows a custom `DeterministicProcess` to be used. This allows for more complex deterministic terms to be constructed, for example one that includes seasonal components with two periods, or, as the next example shows, one that uses a Fourier series rather than seasonal dummies." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.deterministic import DeterministicProcess\n", "dp = DeterministicProcess(housing.index, constant=True, period=12, fourier=2)\n", "mod = AutoReg(housing,2, trend=\"n\",seasonal=False, deterministic=dp)\n", "res = mod.fit()\n", "print(res.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = res.plot_predict(720, 840)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 1 }statsmodels-0.12.2/examples/notebooks/categorical_interaction_plot.ipynb000066400000000000000000000037231400612667500267500ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Plot Interaction of Categorical Factors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example, we will visualize the interaction between categorical factors. First, we will create some categorical data. Then, we will plot it using the interaction_plot function, which internally re-codes the x-factor categories to integers." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "from statsmodels.graphics.factorplots import interaction_plot" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "np.random.seed(12345)\n", "weight = pd.Series(np.repeat(['low', 'hi', 'low', 'hi'], 15), name='weight')\n", "nutrition = pd.Series(np.repeat(['lo_carb', 'hi_carb'], 30), name='nutrition')\n", "days = np.log(np.random.randint(1, 30, size=60))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(6, 6))\n", "fig = interaction_plot(x=weight, trace=nutrition, response=days, \n", " colors=['red', 'blue'], markers=['D', '^'], ms=10, ax=ax)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 } statsmodels-0.12.2/examples/notebooks/chi2_fitting.ipynb000066400000000000000000000151241400612667500234050ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Least squares fitting of models to data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a quick introduction to `statsmodels` for physical scientists (e.g. physicists, astronomers) or engineers.\n", "\n", "Why is this needed?\n", "\n", "Because most of `statsmodels` was written by statisticians and they use a different terminology and sometimes methods, making it hard to know which classes and functions are relevant and what their inputs and outputs mean." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assume you have data points with measurements `y` at positions `x` as well as measurement errors `y_err`.\n", "\n", "How can you use `statsmodels` to fit a straight line model to this data?\n", "\n", "For an extensive discussion see [Hogg et al. (2010), \"Data analysis recipes: Fitting a model to data\"](https://arxiv.org/abs/1008.4686) ... we'll use the example data given by them in Table 1.\n", "\n", "So the model is `f(x) = a * x + b` and on Figure 1 they print the result we want to reproduce ... the best-fit parameter and the parameter errors for a \"standard weighted least-squares fit\" for this data are:\n", "* `a = 2.24 +- 0.11`\n", "* `b = 34 +- 18`" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "data = \"\"\"\n", " x y y_err\n", "201 592 61\n", "244 401 25\n", " 47 583 38\n", "287 402 15\n", "203 495 21\n", " 58 173 15\n", "210 479 27\n", "202 504 14\n", "198 510 30\n", "158 416 16\n", "165 393 14\n", "201 442 25\n", "157 317 52\n", "131 311 16\n", "166 400 34\n", "160 337 31\n", "186 423 42\n", "125 334 26\n", "218 533 16\n", "146 344 22\n", "\"\"\"\n", "try:\n", " from StringIO import StringIO\n", "except ImportError:\n", " from io import StringIO\n", "data = pd.read_csv(StringIO(data), delim_whitespace=True).astype(float)\n", "\n", "# Note: for the results we compare with the paper here, they drop the first four points\n", "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To fit a straight line use the weighted least squares class [WLS](https://www.statsmodels.org/devel/generated/statsmodels.regression.linear_model.WLS.html) ... the parameters are called:\n", "* `exog` = `sm.add_constant(x)`\n", "* `endog` = `y`\n", "* `weights` = `1 / sqrt(y_err)`\n", "\n", "Note that `exog` must be a 2-dimensional array with `x` as a column and an extra column of ones. Adding this column of ones means you want to fit the model `y = a * x + b`, leaving it off means you want to fit the model `y = a * x`.\n", "\n", "And you have to use the option `cov_type='fixed scale'` to tell `statsmodels` that you really have measurement errors with an absolute scale. If you do not, `statsmodels` will treat the weights as relative weights between the data points and internally re-scale them so that the best-fit model will have `chi**2 / ndf = 1`." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "exog = sm.add_constant(data['x'])\n", "endog = data['y']\n", "weights = 1. / (data['y_err'] ** 2)\n", "wls = sm.WLS(endog, exog, weights)\n", "results = wls.fit(cov_type='fixed scale')\n", "print(results.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Check against scipy.optimize.curve_fit" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# You can use `scipy.optimize.curve_fit` to get the best-fit parameters and parameter errors.\n", "from scipy.optimize import curve_fit\n", "\n", "def f(x, a, b):\n", " return a * x + b\n", "\n", "xdata = data['x']\n", "ydata = data['y']\n", "p0 = [0, 0] # initial parameter estimate\n", "sigma = data['y_err']\n", "popt, pcov = curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma=True)\n", "perr = np.sqrt(np.diag(pcov))\n", "print('a = {0:10.3f} +- {1:10.3f}'.format(popt[0], perr[0]))\n", "print('b = {0:10.3f} +- {1:10.3f}'.format(popt[1], perr[1]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Check against self-written cost function" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# You can also use `scipy.optimize.minimize` and write your own cost function.\n", "# This does not give you the parameter errors though ... you'd have\n", "# to estimate the HESSE matrix separately ...\n", "from scipy.optimize import minimize\n", "\n", "def chi2(pars):\n", " \"\"\"Cost function.\n", " \"\"\"\n", " y_model = pars[0] * data['x'] + pars[1]\n", " chi = (data['y'] - y_model) / data['y_err']\n", " return np.sum(chi ** 2)\n", "\n", "result = minimize(fun=chi2, x0=[0, 0])\n", "popt = result.x\n", "print('a = {0:10.3f}'.format(popt[0]))\n", "print('b = {0:10.3f}'.format(popt[1]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Non-linear models" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# TODO: we could use the examples from here:\n", "# http://probfit.readthedocs.org/en/latest/api.html#probfit.costfunc.Chi2Regression" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3.0 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }statsmodels-0.12.2/examples/notebooks/contrasts.ipynb000066400000000000000000000350461400612667500230610ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Contrasts Overview" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import statsmodels.api as sm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This document is based heavily on this excellent resource from UCLA http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A categorical variable of K categories, or levels, usually enters a regression as a sequence of K-1 dummy variables. This amounts to a linear hypothesis on the level means. That is, each test statistic for these variables amounts to testing whether the mean for that level is statistically significantly different from the mean of the base category. This dummy coding is called Treatment coding in R parlance, and we will follow this convention. There are, however, different coding methods that amount to different sets of linear hypotheses.\n", "\n", "In fact, the dummy coding is not technically a contrast coding. This is because the dummy variables add to one and are not functionally independent of the model's intercept. On the other hand, a set of *contrasts* for a categorical variable with `k` levels is a set of `k-1` functionally independent linear combinations of the factor level means that are also independent of the sum of the dummy variables. The dummy coding is not wrong *per se*. It captures all of the coefficients, but it complicates matters when the model assumes independence of the coefficients such as in ANOVA. Linear regression models do not assume independence of the coefficients and thus dummy coding is often the only coding that is taught in this context.\n", "\n", "To have a look at the contrast matrices in Patsy, we will use data from UCLA ATS. First let's load the data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example Data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "url = 'https://stats.idre.ucla.edu/stat/data/hsb2.csv'\n", "hsb2 = pd.read_table(url, delimiter=\",\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "hsb2.head(10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It will be instructive to look at the mean of the dependent variable, write, for each level of race ((1 = Hispanic, 2 = Asian, 3 = African American and 4 = Caucasian))." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "hsb2.groupby('race')['write'].mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Treatment (Dummy) Coding" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dummy coding is likely the most well known coding scheme. It compares each level of the categorical variable to a base reference level. The base reference level is the value of the intercept. It is the default contrast in Patsy for unordered categorical factors. The Treatment contrast matrix for race would be" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from patsy.contrasts import Treatment\n", "levels = [1,2,3,4]\n", "contrast = Treatment(reference=0).code_without_intercept(levels)\n", "print(contrast.matrix)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we used `reference=0`, which implies that the first level, Hispanic, is the reference category against which the other level effects are measured. As mentioned above, the columns do not sum to zero and are thus not independent of the intercept. To be explicit, let's look at how this would encode the `race` variable." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "hsb2.race.head(10)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(contrast.matrix[hsb2.race-1, :][:20])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "pd.get_dummies(hsb2.race.values, drop_first=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a bit of a trick, as the `race` category conveniently maps to zero-based indices. If it does not, this conversion happens under the hood, so this will not work in general but nonetheless is a useful exercise to fix ideas. The below illustrates the output using the three contrasts above" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.formula.api import ols\n", "mod = ols(\"write ~ C(race, Treatment)\", data=hsb2)\n", "res = mod.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We explicitly gave the contrast for race; however, since Treatment is the default, we could have omitted this." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simple Coding" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Like Treatment Coding, Simple Coding compares each level to a fixed reference level. However, with simple coding, the intercept is the grand mean of all the levels of the factors. Patsy does not have the Simple contrast included, but you can easily define your own contrasts. To do so, write a class that contains a code_with_intercept and a code_without_intercept method that returns a patsy.contrast.ContrastMatrix instance" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from patsy.contrasts import ContrastMatrix\n", "\n", "def _name_levels(prefix, levels):\n", " return [\"[%s%s]\" % (prefix, level) for level in levels]\n", "\n", "class Simple(object):\n", " def _simple_contrast(self, levels):\n", " nlevels = len(levels)\n", " contr = -1./nlevels * np.ones((nlevels, nlevels-1))\n", " contr[1:][np.diag_indices(nlevels-1)] = (nlevels-1.)/nlevels\n", " return contr\n", "\n", " def code_with_intercept(self, levels):\n", " contrast = np.column_stack((np.ones(len(levels)),\n", " self._simple_contrast(levels)))\n", " return ContrastMatrix(contrast, _name_levels(\"Simp.\", levels))\n", "\n", " def code_without_intercept(self, levels):\n", " contrast = self._simple_contrast(levels)\n", " return ContrastMatrix(contrast, _name_levels(\"Simp.\", levels[:-1]))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "hsb2.groupby('race')['write'].mean().mean()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "contrast = Simple().code_without_intercept(levels)\n", "print(contrast.matrix)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = ols(\"write ~ C(race, Simple)\", data=hsb2)\n", "res = mod.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sum (Deviation) Coding" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sum coding compares the mean of the dependent variable for a given level to the overall mean of the dependent variable over all the levels. That is, it uses contrasts between each of the first k-1 levels and level k In this example, level 1 is compared to all the others, level 2 to all the others, and level 3 to all the others." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from patsy.contrasts import Sum\n", "contrast = Sum().code_without_intercept(levels)\n", "print(contrast.matrix)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = ols(\"write ~ C(race, Sum)\", data=hsb2)\n", "res = mod.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This corresponds to a parameterization that forces all the coefficients to sum to zero. Notice that the intercept here is the grand mean where the grand mean is the mean of means of the dependent variable by each level." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "hsb2.groupby('race')['write'].mean().mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Backward Difference Coding" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In backward difference coding, the mean of the dependent variable for a level is compared with the mean of the dependent variable for the prior level. This type of coding may be useful for a nominal or an ordinal variable." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from patsy.contrasts import Diff\n", "contrast = Diff().code_without_intercept(levels)\n", "print(contrast.matrix)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = ols(\"write ~ C(race, Diff)\", data=hsb2)\n", "res = mod.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For example, here the coefficient on level 1 is the mean of `write` at level 2 compared with the mean at level 1. Ie.," ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res.params[\"C(race, Diff)[D.1]\"]\n", "hsb2.groupby('race').mean()[\"write\"][2] - \\\n", " hsb2.groupby('race').mean()[\"write\"][1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Helmert Coding" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our version of Helmert coding is sometimes referred to as Reverse Helmert Coding. The mean of the dependent variable for a level is compared to the mean of the dependent variable over all previous levels. Hence, the name 'reverse' being sometimes applied to differentiate from forward Helmert coding. This comparison does not make much sense for a nominal variable such as race, but we would use the Helmert contrast like so:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from patsy.contrasts import Helmert\n", "contrast = Helmert().code_without_intercept(levels)\n", "print(contrast.matrix)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = ols(\"write ~ C(race, Helmert)\", data=hsb2)\n", "res = mod.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To illustrate, the comparison on level 4 is the mean of the dependent variable at the previous three levels taken from the mean at level 4" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "grouped = hsb2.groupby('race')\n", "grouped.mean()[\"write\"][4] - grouped.mean()[\"write\"][:3].mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, these are only equal up to a constant. Other versions of the Helmert contrast give the actual difference in means. Regardless, the hypothesis tests are the same." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "k = 4\n", "1./k * (grouped.mean()[\"write\"][k] - grouped.mean()[\"write\"][:k-1].mean())\n", "k = 3\n", "1./k * (grouped.mean()[\"write\"][k] - grouped.mean()[\"write\"][:k-1].mean())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Orthogonal Polynomial Coding" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coefficients taken on by polynomial coding for `k=4` levels are the linear, quadratic, and cubic trends in the categorical variable. The categorical variable here is assumed to be represented by an underlying, equally spaced numeric variable. Therefore, this type of encoding is used only for ordered categorical variables with equal spacing. In general, the polynomial contrast produces polynomials of order `k-1`. Since `race` is not an ordered factor variable let's use `read` as an example. First we need to create an ordered categorical from `read`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "hsb2['readcat'] = np.asarray(pd.cut(hsb2.read, bins=3))\n", "hsb2.groupby('readcat').mean()['write']" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from patsy.contrasts import Poly\n", "levels = hsb2.readcat.unique().tolist()\n", "contrast = Poly().code_without_intercept(levels)\n", "print(contrast.matrix)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = ols(\"write ~ C(readcat, Poly)\", data=hsb2)\n", "res = mod.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, readcat has a significant linear effect on the dependent variable `write` but not a significant quadratic or cubic effect." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/deterministics.ipynb000066400000000000000000000341261400612667500240650ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Deterministic Terms in Time Series Models" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "\n", "plt.rc(\"figure\", figsize=(16, 9))\n", "plt.rc(\"font\", size=16)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basic Use\n", "\n", "Basic configurations can be directly constructed through `DeterministicProcess`. These can include a constant, a time trend of any order, and either a seasonal or a Fourier component.\n", "\n", "The process requires an index, which is the index of the full-sample (or in-sample).\n", "\n", "First, we initialize a deterministic process with a constant, a linear time trend, and a 5-period seasonal term. The `in_sample` method returns the full set of values that match the index." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.deterministic import DeterministicProcess\n", "\n", "index = pd.RangeIndex(0, 100)\n", "det_proc = DeterministicProcess(\n", " index, constant=True, order=1, seasonal=True, period=5\n", ")\n", "det_proc.in_sample()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `out_of_sample` returns the next `steps` values after the end of the in-sample." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "det_proc.out_of_sample(15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`range(start, stop)` can also be used to produce the deterministic terms over any range including in- and out-of-sample.\n", "\n", "### Notes\n", "\n", "* When the index is a pandas `DatetimeIndex` or a `PeriodIndex`, then `start` and `stop` can be date-like (strings, e.g., \"2020-06-01\", or Timestamp) or integers.\n", "* `stop` is always included in the range. While this is not very Pythonic, it is needed since both statsmodels and Pandas include `stop` when working with date-like slices." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "det_proc.range(190, 210)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using a Date-like Index\n", "\n", "Next, we show the same steps using a `PeriodIndex`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "index = pd.period_range(\"2020-03-01\", freq=\"M\", periods=60)\n", "det_proc = DeterministicProcess(index, constant=True, fourier=2)\n", "det_proc.in_sample().head(12)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "det_proc.out_of_sample(12)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`range` accepts date-like arguments, which are usually given as strings." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "det_proc.range(\"2025-01\", \"2026-01\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is equivalent to using the integer values 58 and 70." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "det_proc.range(58, 70)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Advanced Construction\n", "\n", "Deterministic processes with features not supported directly through the constructor can be created using `additional_terms` which accepts a list of `DetermisticTerm`. Here we create a deterministic process with two seasonal components: day-of-week with a 5 day period and an annual captured through a Fourier component with a period of 365.25 days." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.deterministic import Fourier, Seasonality, TimeTrend\n", "\n", "index = pd.period_range(\"2020-03-01\", freq=\"D\", periods=2 * 365)\n", "tt = TimeTrend(constant=True)\n", "four = Fourier(period=365.25, order=2)\n", "seas = Seasonality(period=7)\n", "det_proc = DeterministicProcess(index, additional_terms=[tt, seas, four])\n", "det_proc.in_sample().head(28)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Custom Deterministic Terms\n", "\n", "The `DetermisticTerm` Abstract Base Class is designed to be subclassed to help users write custom deterministic terms. We next show two examples. The first is a broken time trend that allows a break after a fixed number of periods. The second is a \"trick\" deterministic term that allows exogenous data, which is not really a deterministic process, to be treated as if was deterministic. This lets use simplify gathering the terms needed for forecasting.\n", "\n", "These are intended to demonstrate the construction of custom terms. They can definitely be improved in terms of input validation." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.deterministic import DeterministicTerm\n", "\n", "\n", "class BrokenTimeTrend(DeterministicTerm):\n", " def __init__(self, break_period: int):\n", " self._break_period = break_period\n", "\n", " def __str__(self):\n", " return \"Broken Time Trend\"\n", "\n", " def _eq_attr(self):\n", " return (self._break_period,)\n", "\n", " def in_sample(self, index: pd.Index):\n", " nobs = index.shape[0]\n", " terms = np.zeros((nobs, 2))\n", " terms[self._break_period :, 0] = 1\n", " terms[self._break_period :, 1] = np.arange(\n", " self._break_period + 1, nobs + 1\n", " )\n", " return pd.DataFrame(\n", " terms, columns=[\"const_break\", \"trend_break\"], index=index\n", " )\n", "\n", " def out_of_sample(\n", " self, steps: int, index: pd.Index, forecast_index: pd.Index = None\n", " ):\n", " # Always call extend index first\n", " fcast_index = self._extend_index(index, steps, forecast_index)\n", " nobs = index.shape[0]\n", " terms = np.zeros((steps, 2))\n", " # Assume break period is in-sample\n", " terms[:, 0] = 1\n", " terms[:, 1] = np.arange(nobs + 1, nobs + steps + 1)\n", " return pd.DataFrame(\n", " terms, columns=[\"const_break\", \"trend_break\"], index=fcast_index\n", " )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "btt = BrokenTimeTrend(60)\n", "tt = TimeTrend(constant=True, order=1)\n", "index = pd.RangeIndex(100)\n", "det_proc = DeterministicProcess(index, additional_terms=[tt, btt])\n", "det_proc.range(55, 65)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we write a simple \"wrapper\" for some actual exogenous data that simplifies constructing out-of-sample exogenous arrays for forecasting." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "class ExogenousProcess(DeterministicTerm):\n", " def __init__(self, data):\n", " self._data = data\n", "\n", " def __str__(self):\n", " return \"Custom Exog Process\"\n", "\n", " def _eq_attr(self):\n", " return (id(self._data),)\n", "\n", " def in_sample(self, index: pd.Index):\n", " return self._data.loc[index]\n", "\n", " def out_of_sample(\n", " self, steps: int, index: pd.Index, forecast_index: pd.Index = None\n", " ):\n", " forecast_index = self._extend_index(index, steps, forecast_index)\n", " return self._data.loc[forecast_index]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "gen = np.random.default_rng(98765432101234567890)\n", "exog = pd.DataFrame(\n", " gen.integers(100, size=(300, 2)), columns=[\"exog1\", \"exog2\"]\n", ")\n", "exog.head()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ep = ExogenousProcess(exog)\n", "tt = TimeTrend(constant=True, order=1)\n", "# The in-sample index\n", "idx = exog.index[:200]\n", "det_proc = DeterministicProcess(idx, additional_terms=[tt, ep])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "det_proc.in_sample().head()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "det_proc.out_of_sample(10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model Support\n", "\n", "The only model that directly supports `DeterministicProcess` is `AutoReg`. A custom term can be set using the `deterministic` keyword argument. \n", "\n", "**Note**: Using a custom term requires that `trend=\"n\"` and `seasonal=False` so that all deterministic components must come from the custom deterministic term." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulate Some Data\n", "\n", "Here we simulate some data that has an weekly seasonality captured by a Fourier series." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "gen = np.random.default_rng(98765432101234567890)\n", "idx = pd.RangeIndex(200)\n", "det_proc = DeterministicProcess(idx, constant=True, period=52, fourier=2)\n", "det_terms = det_proc.in_sample().to_numpy()\n", "params = np.array([1.0, 3, -1, 4, -2])\n", "exog = det_terms @ params\n", "y = np.empty(200)\n", "y[0] = det_terms[0] @ params + gen.standard_normal()\n", "for i in range(1, 200):\n", " y[i] = 0.9 * y[i - 1] + det_terms[i] @ params + gen.standard_normal()\n", "y = pd.Series(y, index=idx)\n", "ax = y.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model is then fit using the `deterministic` keyword argument. `seasonal` defaults to False but `trend` defaults to `\"c\"` so this needs to be changed." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.api import AutoReg\n", "\n", "mod = AutoReg(y, 1, trend=\"n\", deterministic=det_proc)\n", "res = mod.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the `plot_predict` to show the predicted values and their prediction interval. The out-of-sample deterministic values are automatically produced by the deterministic process passed to `AutoReg`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = res.plot_predict(200, 200 + 2 * 52, True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "auto_reg_forecast = res.predict(200, 211)\n", "auto_reg_forecast" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using with other models\n", "\n", "Other models do not support `DeterministicProcess` directly. We can instead manually pass any deterministic terms as `exog` to model that support exogenous values.\n", "\n", "Note that `SARIMAX` with exogenous variables is OLS with SARIMA errors so that the model is \n", "\n", "$$\n", "\\begin{align*}\n", "\\nu_t & = y_t - x_t \\beta \\\\\n", "(1-\\phi(L))\\nu_t & = (1+\\theta(L))\\epsilon_t.\n", "\\end{align*}\n", "$$\n", "\n", "The parameters on deterministic terms are not directly comparable to `AutoReg` which evolves according to the equation\n", "\n", "$$\n", "(1-\\phi(L)) y_t = x_t \\beta + \\epsilon_t.\n", "$$\n", "\n", "When $x_t$ contains only deterministic terms, these two representation are equivalent (assuming $\\theta(L)=0$ so that there is no MA).\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.api import SARIMAX\n", "\n", "det_proc = DeterministicProcess(idx, period=52, fourier=2)\n", "det_terms = det_proc.in_sample()\n", "\n", "mod = SARIMAX(y, order=(1, 0, 0), trend=\"c\", exog=det_terms)\n", "res = mod.fit(disp=False)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The forecasts are similar but differ since the parameters of the `SARIMAX` are estimated using MLE while `AutoReg` uses OLS." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sarimax_forecast = res.forecast(12, exog=det_proc.out_of_sample(12))\n", "df = pd.concat([auto_reg_forecast, sarimax_forecast], axis=1)\n", "df.columns = columns = [\"AutoReg\", \"SARIMAX\"]\n", "df" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 4 }statsmodels-0.12.2/examples/notebooks/discrete_choice_example.ipynb000066400000000000000000000334541400612667500256710ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Discrete Choice Models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fair's Affair data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A survey of women only was conducted in 1974 by *Redbook* asking about extramarital affairs." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from scipy import stats\n", "import matplotlib.pyplot as plt\n", "import statsmodels.api as sm\n", "from statsmodels.formula.api import logit" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(sm.datasets.fair.SOURCE)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print( sm.datasets.fair.NOTE)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dta = sm.datasets.fair.load_pandas().data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dta['affair'] = (dta['affairs'] > 0).astype(float)\n", "print(dta.head(10))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(dta.describe())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "affair_mod = logit(\"affair ~ occupation + educ + occupation_husb\"\n", " \"+ rate_marriage + age + yrs_married + children\"\n", " \" + religious\", dta).fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(affair_mod.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How well are we predicting?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "affair_mod.pred_table()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coefficients of the discrete choice model do not tell us much. What we're after is marginal effects." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mfx = affair_mod.get_margeff()\n", "print(mfx.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "respondent1000 = dta.iloc[1000]\n", "print(respondent1000)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "resp = dict(zip(range(1,9), respondent1000[[\"occupation\", \"educ\",\n", " \"occupation_husb\", \"rate_marriage\",\n", " \"age\", \"yrs_married\", \"children\",\n", " \"religious\"]].tolist()))\n", "resp.update({0 : 1})\n", "print(resp)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mfx = affair_mod.get_margeff(atexog=resp)\n", "print(mfx.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`predict` expects a `DataFrame` since `patsy` is used to select columns." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "respondent1000 = dta.iloc[[1000]]\n", "affair_mod.predict(respondent1000)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "affair_mod.fittedvalues[1000]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "affair_mod.model.cdf(affair_mod.fittedvalues[1000])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The \"correct\" model here is likely the Tobit model. We have an work in progress branch \"tobit-model\" on github, if anyone is interested in censored regression models." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise: Logit vs Probit" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "support = np.linspace(-6, 6, 1000)\n", "ax.plot(support, stats.logistic.cdf(support), 'r-', label='Logistic')\n", "ax.plot(support, stats.norm.cdf(support), label='Probit')\n", "ax.legend();" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "support = np.linspace(-6, 6, 1000)\n", "ax.plot(support, stats.logistic.pdf(support), 'r-', label='Logistic')\n", "ax.plot(support, stats.norm.pdf(support), label='Probit')\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare the estimates of the Logit Fair model above to a Probit model. Does the prediction table look better? Much difference in marginal effects?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generalized Linear Model Example" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(sm.datasets.star98.SOURCE)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(sm.datasets.star98.DESCRLONG)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(sm.datasets.star98.NOTE)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dta = sm.datasets.star98.load_pandas().data\n", "print(dta.columns)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(dta[['NABOVE', 'NBELOW', 'LOWINC', 'PERASIAN', 'PERBLACK', 'PERHISP', 'PERMINTE']].head(10))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(dta[['AVYRSEXP', 'AVSALK', 'PERSPENK', 'PTRATIO', 'PCTAF', 'PCTCHRT', 'PCTYRRND']].head(10))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "formula = 'NABOVE + NBELOW ~ LOWINC + PERASIAN + PERBLACK + PERHISP + PCTCHRT '\n", "formula += '+ PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Aside: Binomial distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Toss a six-sided die 5 times, what's the probability of exactly 2 fours?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "stats.binom(5, 1./6).pmf(2)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from scipy.special import comb\n", "comb(5,2) * (1/6.)**2 * (5/6.)**3" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.formula.api import glm\n", "glm_mod = glm(formula, dta, family=sm.families.Binomial()).fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(glm_mod.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The number of trials " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "glm_mod.model.data.orig_endog.sum(1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "glm_mod.fittedvalues * glm_mod.model.data.orig_endog.sum(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First differences: We hold all explanatory variables constant at their means and manipulate the percentage of low income households to assess its impact\n", "on the response variables:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "exog = glm_mod.model.data.orig_exog # get the dataframe" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "means25 = exog.mean()\n", "print(means25)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "means25['LOWINC'] = exog['LOWINC'].quantile(.25)\n", "print(means25)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "means75 = exog.mean()\n", "means75['LOWINC'] = exog['LOWINC'].quantile(.75)\n", "print(means75)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, `predict` expects a `DataFrame` since `patsy` is used to select columns." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "resp25 = glm_mod.predict(pd.DataFrame(means25).T)\n", "resp75 = glm_mod.predict(pd.DataFrame(means75).T)\n", "diff = resp75 - resp25" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The interquartile first difference for the percentage of low income households in a school district is:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(\"%2.4f%%\" % (diff[0]*100))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "nobs = glm_mod.nobs\n", "y = glm_mod.model.endog\n", "yhat = glm_mod.mu" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.graphics.api import abline_plot\n", "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111, ylabel='Observed Values', xlabel='Fitted Values')\n", "ax.scatter(yhat, y)\n", "y_vs_yhat = sm.OLS(y, sm.add_constant(yhat, prepend=True)).fit()\n", "fig = abline_plot(model_results=y_vs_yhat, ax=ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Plot fitted values vs Pearson residuals" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pearson residuals are defined to be\n", "\n", "$$\\frac{(y - \\mu)}{\\sqrt{(var(\\mu))}}$$\n", "\n", "where var is typically determined by the family. E.g., binomial variance is $np(1 - p)$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111, title='Residual Dependence Plot', xlabel='Fitted Values',\n", " ylabel='Pearson Residuals')\n", "ax.scatter(yhat, stats.zscore(glm_mod.resid_pearson))\n", "ax.axis('tight')\n", "ax.plot([0.0, 1.0],[0.0, 0.0], 'k-');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Histogram of standardized deviance residuals with Kernel Density Estimate overlaid" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The definition of the deviance residuals depends on the family. For the Binomial distribution this is\n", "\n", "$$r_{dev} = sign\\left(Y-\\mu\\right)*\\sqrt{2n(Y\\log\\frac{Y}{\\mu}+(1-Y)\\log\\frac{(1-Y)}{(1-\\mu)}}$$\n", "\n", "They can be used to detect ill-fitting covariates" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "resid = glm_mod.resid_deviance\n", "resid_std = stats.zscore(resid)\n", "kde_resid = sm.nonparametric.KDEUnivariate(resid_std)\n", "kde_resid.fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111, title=\"Standardized Deviance Residuals\")\n", "ax.hist(resid_std, bins=25, density=True);\n", "ax.plot(kde_resid.support, kde_resid.density, 'r');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### QQ-plot of deviance residuals" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "fig = sm.graphics.qqplot(resid, line='r', ax=ax)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/discrete_choice_overview.ipynb000066400000000000000000000152501400612667500260760ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Discrete Choice Models Overview" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import statsmodels.api as sm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data\n", "\n", "Load data from Spector and Mazzeo (1980). Examples follow Greene's Econometric Analysis Ch. 21 (5th Edition)." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "spector_data = sm.datasets.spector.load(as_pandas=False)\n", "spector_data.exog = sm.add_constant(spector_data.exog, prepend=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inspect the data:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(spector_data.exog[:5,:])\n", "print(spector_data.endog[:5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Probability Model (OLS)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "lpm_mod = sm.OLS(spector_data.endog, spector_data.exog)\n", "lpm_res = lpm_mod.fit()\n", "print('Parameters: ', lpm_res.params[:-1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Logit Model" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "logit_mod = sm.Logit(spector_data.endog, spector_data.exog)\n", "logit_res = logit_mod.fit(disp=0)\n", "print('Parameters: ', logit_res.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Marginal Effects" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "margeff = logit_res.get_margeff()\n", "print(margeff.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As in all the discrete data models presented below, we can print a nice summary of results:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(logit_res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Probit Model " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "probit_mod = sm.Probit(spector_data.endog, spector_data.exog)\n", "probit_res = probit_mod.fit()\n", "probit_margeff = probit_res.get_margeff()\n", "print('Parameters: ', probit_res.params)\n", "print('Marginal effects: ')\n", "print(probit_margeff.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multinomial Logit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Load data from the American National Election Studies:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "anes_data = sm.datasets.anes96.load(as_pandas=False)\n", "anes_exog = anes_data.exog\n", "anes_exog = sm.add_constant(anes_exog, prepend=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inspect the data:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(anes_data.exog[:5,:])\n", "print(anes_data.endog[:5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit MNL model:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mlogit_mod = sm.MNLogit(anes_data.endog, anes_exog)\n", "mlogit_res = mlogit_mod.fit()\n", "print(mlogit_res.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Poisson\n", "\n", "Load the Rand data. Note that this example is similar to Cameron and Trivedi's `Microeconometrics` Table 20.5, but it is slightly different because of minor changes in the data. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "rand_data = sm.datasets.randhie.load(as_pandas=False)\n", "rand_exog = rand_data.exog.view(float).reshape(len(rand_data.exog), -1)\n", "rand_exog = sm.add_constant(rand_exog, prepend=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit Poisson model: " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "poisson_mod = sm.Poisson(rand_data.endog, rand_exog)\n", "poisson_res = poisson_mod.fit(method=\"newton\")\n", "print(poisson_res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Negative Binomial\n", "\n", "The negative binomial model gives slightly different results. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mod_nbin = sm.NegativeBinomial(rand_data.endog, rand_exog)\n", "res_nbin = mod_nbin.fit(disp=False)\n", "print(res_nbin.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Alternative solvers\n", "\n", "The default method for fitting discrete data MLE models is Newton-Raphson. You can use other solvers by using the ``method`` argument: " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mlogit_res = mlogit_mod.fit(method='bfgs', maxiter=250)\n", "print(mlogit_res.summary())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }statsmodels-0.12.2/examples/notebooks/distributed_estimation.ipynb000066400000000000000000000122751400612667500256160ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Distributed Estimation \n", "\n", "This notebook goes through a couple of examples to show how to use `distributed_estimation`. We import the `DistributedModel` class and make the exog and endog generators." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.stats.distributions import norm\n", "from statsmodels.base.distributed_estimation import DistributedModel\n", "\n", "def _exog_gen(exog, partitions):\n", " \"\"\"partitions exog data\"\"\"\n", "\n", " n_exog = exog.shape[0]\n", " n_part = np.ceil(n_exog / partitions)\n", "\n", " ii = 0\n", " while ii < n_exog:\n", " jj = int(min(ii + n_part, n_exog))\n", " yield exog[ii:jj, :]\n", " ii += int(n_part)\n", "\n", "def _endog_gen(endog, partitions):\n", " \"\"\"partitions endog data\"\"\"\n", "\n", " n_endog = endog.shape[0]\n", " n_part = np.ceil(n_endog / partitions)\n", "\n", " ii = 0\n", " while ii < n_endog:\n", " jj = int(min(ii + n_part, n_endog))\n", " yield endog[ii:jj]\n", " ii += int(n_part)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we generate some random data to serve as an example." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "X = np.random.normal(size=(1000, 25))\n", "beta = np.random.normal(size=25)\n", "beta *= np.random.randint(0, 2, size=25)\n", "y = norm.rvs(loc=X.dot(beta))\n", "m = 5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the most basic fit, showing all of the defaults, which are to use OLS as the model class, and the debiasing procedure." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "debiased_OLS_mod = DistributedModel(m)\n", "debiased_OLS_fit = debiased_OLS_mod.fit(zip(_endog_gen(y, m), _exog_gen(X, m)),\n", " fit_kwds={\"alpha\": 0.2})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we run through a slightly more complicated example which uses the GLM model class." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [], "source": [ "from statsmodels.genmod.generalized_linear_model import GLM\n", "from statsmodels.genmod.families import Gaussian\n", "\n", "debiased_GLM_mod = DistributedModel(m, model_class=GLM,\n", " init_kwds={\"family\": Gaussian()})\n", "debiased_GLM_fit = debiased_GLM_mod.fit(zip(_endog_gen(y, m), _exog_gen(X, m)),\n", " fit_kwds={\"alpha\": 0.2})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also change the `estimation_method` and the `join_method`. The below example show how this works for the standard OLS case. Here we using a naive averaging approach instead of the debiasing procedure." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.base.distributed_estimation import _est_regularized_naive, _join_naive\n", "\n", "\n", "naive_OLS_reg_mod = DistributedModel(m, estimation_method=_est_regularized_naive,\n", " join_method=_join_naive)\n", "naive_OLS_reg_params = naive_OLS_reg_mod.fit(zip(_endog_gen(y, m), _exog_gen(X, m)),\n", " fit_kwds={\"alpha\": 0.2})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can also change the `results_class` used. The following example shows how this work for a simple case with an unregularized model and naive averaging." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.base.distributed_estimation import _est_unregularized_naive, DistributedResults\n", "\n", "\n", "naive_OLS_unreg_mod = DistributedModel(m, estimation_method=_est_unregularized_naive,\n", " join_method=_join_naive,\n", " results_class=DistributedResults)\n", "naive_OLS_unreg_params = naive_OLS_unreg_mod.fit(zip(_endog_gen(y, m), _exog_gen(X, m)),\n", " fit_kwds={\"alpha\": 0.2})" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.14" } }, "nbformat": 4, "nbformat_minor": 1 }statsmodels-0.12.2/examples/notebooks/ets.ipynb000066400000000000000000000313721400612667500216320ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# ETS models\n", "\n", "The ETS models are a family of time series models with an underlying state space model consisting of a level component, a trend component (T), a seasonal component (S), and an error term (E).\n", "\n", "This notebook shows how they can be used with `statsmodels`. For a more thorough treatment we refer to [1], chapter 8 (free online resource), on which the implementation in statsmodels and the examples used in this notebook are based.\n", "\n", "`statsmodels` implements all combinations of:\n", "- additive and multiplicative error model\n", "- additive and multiplicative trend, possibly dampened\n", "- additive and multiplicative seasonality\n", "\n", "However, not all of these methods are stable. Refer to [1] and references therein for more info about model stability.\n", "\n", "[1] Hyndman, Rob J., and George Athanasopoulos. *Forecasting: principles and practice*, 3rd edition, OTexts, 2019. https://www.otexts.org/fpp3/7" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "%matplotlib inline\n", "from statsmodels.tsa.exponential_smoothing.ets import ETSModel" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plt.rcParams['figure.figsize'] = (12, 8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simple exponential smoothing\n", "\n", "The simplest of the ETS models is also known as *simple exponential smoothing*. In ETS terms, it corresponds to the (A, N, N) model, that is, a model with additive errors, no trend, and no seasonality. The state space formulation of Holt's method is:\n", "\n", "\\begin{align}\n", "y_{t} &= y_{t-1} + e_t\\\\\n", "l_{t} &= l_{t-1} + \\alpha e_t\\\\\n", "\\end{align}\n", "\n", "This state space formulation can be turned into a different formulation, a forecast and a smoothing equation (as can be done with all ETS models):\n", "\n", "\\begin{align}\n", "\\hat{y}_{t|t-1} &= l_{t-1}\\\\\n", "l_{t} &= \\alpha y_{t-1} + (1 - \\alpha) l_{t-1}\n", "\\end{align}\n", "\n", "Here, $\\hat{y}_{t|t-1}$ is the forecast/expectation of $y_t$ given the information of the previous step. In the simple exponential smoothing model, the forecast corresponds to the previous level. The second equation (smoothing equation) calculates the next level as weighted average of the previous level and the previous observation." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "oildata = [\n", " 111.0091, 130.8284, 141.2871, 154.2278,\n", " 162.7409, 192.1665, 240.7997, 304.2174,\n", " 384.0046, 429.6622, 359.3169, 437.2519,\n", " 468.4008, 424.4353, 487.9794, 509.8284,\n", " 506.3473, 340.1842, 240.2589, 219.0328,\n", " 172.0747, 252.5901, 221.0711, 276.5188,\n", " 271.1480, 342.6186, 428.3558, 442.3946,\n", " 432.7851, 437.2497, 437.2092, 445.3641,\n", " 453.1950, 454.4096, 422.3789, 456.0371,\n", " 440.3866, 425.1944, 486.2052, 500.4291,\n", " 521.2759, 508.9476, 488.8889, 509.8706,\n", " 456.7229, 473.8166, 525.9509, 549.8338,\n", " 542.3405\n", "]\n", "oil = pd.Series(oildata, index=pd.date_range('1965', '2013', freq='AS'))\n", "oil.plot()\n", "plt.ylabel(\"Annual oil production in Saudi Arabia (Mt)\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot above shows annual oil production in Saudi Arabia in million tonnes. The data are taken from the R package `fpp2` (companion package to prior version [1]).\n", "Below you can see how to fit a simple exponential smoothing model using statsmodels's ETS implementation to this data. Additionally, the fit using `forecast` in R is shown as comparison." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model = ETSModel(oil, error='add', trend='add', damped_trend=True)\n", "fit = model.fit(maxiter=10000)\n", "oil.plot(label='data')\n", "fit.fittedvalues.plot(label='statsmodels fit')\n", "plt.ylabel(\"Annual oil production in Saudi Arabia (Mt)\");\n", "\n", "# obtained from R\n", "params_R = [0.99989969, 0.11888177503085334, 0.80000197, 36.46466837, 34.72584983]\n", "yhat = model.smooth(params_R).fittedvalues\n", "yhat.plot(label='R fit', linestyle='--')\n", "\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By default the initial states are considered to be fitting parameters and are estimated by maximizing log-likelihood. Additionally it is possible to only use a heuristic for the initial values. In this case this leads to better agreement with the R implementation." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model_heuristic = ETSModel(oil, error='add', trend='add', damped_trend=True,\n", " initialization_method='heuristic')\n", "fit_heuristic = model_heuristic.fit()\n", "oil.plot(label='data')\n", "fit.fittedvalues.plot(label='estimated')\n", "fit_heuristic.fittedvalues.plot(label='heuristic', linestyle='--')\n", "plt.ylabel(\"Annual oil production in Saudi Arabia (Mt)\");\n", "\n", "# obtained from R\n", "params = [0.99989969, 0.11888177503085334, 0.80000197, 36.46466837, 34.72584983]\n", "yhat = model.smooth(params).fittedvalues\n", "yhat.plot(label='with R params', linestyle=':')\n", "\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fitted parameters and some other measures are shown using `fit.summary()`. Here we can see that the log-likelihood of the model using fitted initial states is a bit lower than the one using a heuristic for the initial states.\n", "Additionally, we see that $\\beta$ (`smoothing_trend`) is at the boundary of the default parameter bounds, and therefore it's not possible to estimate confidence intervals for $\\beta$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(fit.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(fit_heuristic.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Holt-Winters' seasonal method\n", "\n", "The exponential smoothing method can be modified to incorporate a trend and a seasonal component. In the additive Holt-Winters' method, the seasonal component is added to the rest. This model corresponds to the ETS(A, A, A) model, and has the following state space formulation:\n", "\n", "\\begin{align}\n", "y_t &= l_{t-1} + b_{t-1} + s_{t-m} + e_t\\\\\n", "l_{t} &= l_{t-1} + b_{t-1} + \\alpha e_t\\\\\n", "b_{t} &= b_{t-1} + \\beta e_t\\\\\n", "s_{t} &= s_{t-m} + \\gamma e_t\n", "\\end{align}\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "austourists_data = [\n", " 30.05251300, 19.14849600, 25.31769200, 27.59143700,\n", " 32.07645600, 23.48796100, 28.47594000, 35.12375300, \n", " 36.83848500, 25.00701700, 30.72223000, 28.69375900, \n", " 36.64098600, 23.82460900, 29.31168300, 31.77030900,\n", " 35.17787700, 19.77524400, 29.60175000, 34.53884200,\n", " 41.27359900, 26.65586200, 28.27985900, 35.19115300,\n", " 42.20566386, 24.64917133, 32.66733514, 37.25735401,\n", " 45.24246027, 29.35048127, 36.34420728, 41.78208136,\n", " 49.27659843, 31.27540139, 37.85062549, 38.83704413,\n", " 51.23690034, 31.83855162, 41.32342126, 42.79900337,\n", " 55.70835836, 33.40714492, 42.31663797, 45.15712257,\n", " 59.57607996, 34.83733016, 44.84168072, 46.97124960,\n", " 60.01903094, 38.37117851, 46.97586413, 50.73379646,\n", " 61.64687319, 39.29956937, 52.67120908, 54.33231689,\n", " 66.83435838, 40.87118847, 51.82853579, 57.49190993,\n", " 65.25146985, 43.06120822, 54.76075713, 59.83447494,\n", " 73.25702747, 47.69662373, 61.09776802, 66.05576122,\n", "]\n", "index = pd.date_range(\"1999-03-01\", \"2015-12-01\", freq=\"3MS\")\n", "austourists = pd.Series(austourists_data, index=index)\n", "austourists.plot()\n", "plt.ylabel('Australian Tourists');" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# fit in statsmodels\n", "model = ETSModel(austourists, error=\"add\", trend=\"add\", seasonal=\"add\",\n", " damped_trend=True, seasonal_periods=4)\n", "fit = model.fit()\n", "\n", "# fit with R params\n", "params_R = [\n", " 0.35445427, 0.03200749, 0.39993387, 0.97999997, 24.01278357, \n", " 0.97770147, 1.76951063, -0.50735902, -6.61171798, 5.34956637\n", "]\n", "fit_R = model.smooth(params_R)\n", "\n", "austourists.plot(label='data')\n", "plt.ylabel('Australian Tourists')\n", "\n", "fit.fittedvalues.plot(label='statsmodels fit')\n", "fit_R.fittedvalues.plot(label='R fit', linestyle='--')\n", "plt.legend();" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(fit.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Predictions\n", "\n", "The ETS model can also be used for predicting. There are several different methods available:\n", "- `forecast`: makes out of sample predictions\n", "- `predict`: in sample and out of sample predictions\n", "- `simulate`: runs simulations of the statespace model\n", "- `get_prediction`: in sample and out of sample predictions, as well as prediction intervals\n", "\n", "We can use them on our previously fitted model to predict from 2014 to 2020." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "pred = fit.get_prediction(start='2014', end='2020')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "df = pred.summary_frame(alpha=0.05)\n", "df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case the prediction intervals were calculated using an analytical formula. This is not available for all models. For these other models, prediction intervals are calculated by performing multiple simulations (1000 by default) and using the percentiles of the simulation results. This is done internally by the `get_prediction` method.\n", "\n", "We can also manually run simulations, e.g. to plot them. Since the data ranges until end of 2015, we have to simulate from the first quarter of 2016 to the first quarter of 2020, which means 17 steps." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "simulated = fit.simulate(anchor=\"end\", nsimulations=17, repetitions=100)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "for i in range(simulated.shape[1]):\n", " simulated.iloc[:,i].plot(label='_', color='gray', alpha=0.1)\n", "df[\"mean\"].plot(label='mean prediction')\n", "df[\"pi_lower\"].plot(linestyle='--', color='tab:blue', label='95% interval')\n", "df[\"pi_upper\"].plot(linestyle='--', color='tab:blue', label='_')\n", "pred.endog.plot(label='data')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, we chose \"end\" as simulation anchor, which means that the first simulated value will be the first out of sample value. It is also possible to choose other anchor inside the sample." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.4" } }, "nbformat": 4, "nbformat_minor": 2 }statsmodels-0.12.2/examples/notebooks/exponential_smoothing.ipynb000066400000000000000000000546231400612667500254600ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exponential smoothing\n", "\n", "Let us consider chapter 7 of the excellent treatise on the subject of Exponential Smoothing By Hyndman and Athanasopoulos [1].\n", "We will work through all the examples in the chapter as they unfold.\n", "\n", "[1] [Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014.](https://www.otexts.org/fpp/7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Loading data\n", "\n", "First we load some data. We have included the R data in the notebook for expedience." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:15.020317Z", "start_time": "2017-12-07T12:39:14.263100Z" } }, "outputs": [], "source": [ "import os\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from statsmodels.tsa.api import ExponentialSmoothing, SimpleExpSmoothing, Holt\n", "%matplotlib inline\n", "\n", "data = [446.6565, 454.4733, 455.663 , 423.6322, 456.2713, 440.5881, 425.3325, 485.1494, 506.0482, 526.792 , 514.2689, 494.211 ]\n", "index= pd.date_range(start='1996', end='2008', freq='A')\n", "oildata = pd.Series(data, index)\n", "\n", "data = [17.5534, 21.86 , 23.8866, 26.9293, 26.8885, 28.8314, 30.0751, 30.9535, 30.1857, 31.5797, 32.5776, 33.4774, 39.0216, 41.3864, 41.5966]\n", "index= pd.date_range(start='1990', end='2005', freq='A')\n", "air = pd.Series(data, index)\n", "\n", "data = [263.9177, 268.3072, 260.6626, 266.6394, 277.5158, 283.834 , 290.309 , 292.4742, 300.8307, 309.2867, 318.3311, 329.3724, 338.884 , 339.2441, 328.6006, 314.2554, 314.4597, 321.4138, 329.7893, 346.3852, 352.2979, 348.3705, 417.5629, 417.1236, 417.7495, 412.2339, 411.9468, 394.6971, 401.4993, 408.2705, 414.2428]\n", "index= pd.date_range(start='1970', end='2001', freq='A')\n", "livestock2 = pd.Series(data, index)\n", "\n", "data = [407.9979 , 403.4608, 413.8249, 428.105 , 445.3387, 452.9942, 455.7402]\n", "index= pd.date_range(start='2001', end='2008', freq='A')\n", "livestock3 = pd.Series(data, index)\n", "\n", "data = [41.7275, 24.0418, 32.3281, 37.3287, 46.2132, 29.3463, 36.4829, 42.9777, 48.9015, 31.1802, 37.7179, 40.4202, 51.2069, 31.8872, 40.9783, 43.7725, 55.5586, 33.8509, 42.0764, 45.6423, 59.7668, 35.1919, 44.3197, 47.9137]\n", "index= pd.date_range(start='2005', end='2010-Q4', freq='QS-OCT')\n", "aust = pd.Series(data, index)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simple Exponential Smoothing\n", "Lets use Simple Exponential Smoothing to forecast the below oil data." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:15.189907Z", "start_time": "2017-12-07T12:39:15.022229Z" } }, "outputs": [], "source": [ "ax=oildata.plot()\n", "ax.set_xlabel(\"Year\")\n", "ax.set_ylabel(\"Oil (millions of tonnes)\")\n", "print(\"Figure 7.1: Oil production in Saudi Arabia from 1996 to 2007.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we run three variants of simple exponential smoothing:\n", "1. In ```fit1``` we do not use the auto optimization but instead choose to explicitly provide the model with the $\\alpha=0.2$ parameter\n", "2. In ```fit2``` as above we choose an $\\alpha=0.6$\n", "3. In ```fit3``` we allow statsmodels to automatically find an optimized $\\alpha$ value for us. This is the recommended approach." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:15.785068Z", "start_time": "2017-12-07T12:39:15.191930Z" } }, "outputs": [], "source": [ "fit1 = SimpleExpSmoothing(oildata, initialization_method=\"heuristic\").fit(smoothing_level=0.2,optimized=False)\n", "fcast1 = fit1.forecast(3).rename(r'$\\alpha=0.2$')\n", "fit2 = SimpleExpSmoothing(oildata, initialization_method=\"heuristic\").fit(smoothing_level=0.6,optimized=False)\n", "fcast2 = fit2.forecast(3).rename(r'$\\alpha=0.6$')\n", "fit3 = SimpleExpSmoothing(oildata, initialization_method=\"estimated\").fit()\n", "fcast3 = fit3.forecast(3).rename(r'$\\alpha=%s$'%fit3.model.params['smoothing_level'])\n", "\n", "plt.figure(figsize=(12, 8))\n", "plt.plot(oildata, marker='o', color='black')\n", "plt.plot(fit1.fittedvalues, marker='o', color='blue')\n", "line1, = plt.plot(fcast1, marker='o', color='blue')\n", "plt.plot(fit2.fittedvalues, marker='o', color='red')\n", "line2, = plt.plot(fcast2, marker='o', color='red')\n", "plt.plot(fit3.fittedvalues, marker='o', color='green')\n", "line3, = plt.plot(fcast3, marker='o', color='green')\n", "plt.legend([line1, line2, line3], [fcast1.name, fcast2.name, fcast3.name])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Holt's Method\n", "\n", "Lets take a look at another example.\n", "This time we use air pollution data and the Holt's Method.\n", "We will fit three examples again.\n", "1. In ```fit1``` we again choose not to use the optimizer and provide explicit values for $\\alpha=0.8$ and $\\beta=0.2$\n", "2. In ```fit2``` we do the same as in ```fit1``` but choose to use an exponential model rather than a Holt's additive model.\n", "3. In ```fit3``` we used a damped versions of the Holt's additive model but allow the dampening parameter $\\phi$ to be optimized while fixing the values for $\\alpha=0.8$ and $\\beta=0.2$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:16.114361Z", "start_time": "2017-12-07T12:39:15.786542Z" } }, "outputs": [], "source": [ "fit1 = Holt(air, initialization_method=\"estimated\").fit(smoothing_level=0.8, smoothing_trend=0.2, optimized=False)\n", "fcast1 = fit1.forecast(5).rename(\"Holt's linear trend\")\n", "fit2 = Holt(air, exponential=True, initialization_method=\"estimated\").fit(smoothing_level=0.8, smoothing_trend=0.2, optimized=False)\n", "fcast2 = fit2.forecast(5).rename(\"Exponential trend\")\n", "fit3 = Holt(air, damped_trend=True, initialization_method=\"estimated\").fit(smoothing_level=0.8, smoothing_trend=0.2)\n", "fcast3 = fit3.forecast(5).rename(\"Additive damped trend\")\n", "\n", "plt.figure(figsize=(12, 8))\n", "plt.plot(air, marker='o', color='black')\n", "plt.plot(fit1.fittedvalues, color='blue')\n", "line1, = plt.plot(fcast1, marker='o', color='blue')\n", "plt.plot(fit2.fittedvalues, color='red')\n", "line2, = plt.plot(fcast2, marker='o', color='red')\n", "plt.plot(fit3.fittedvalues, color='green')\n", "line3, = plt.plot(fcast3, marker='o', color='green')\n", "plt.legend([line1, line2, line3], [fcast1.name, fcast2.name, fcast3.name])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Seasonally adjusted data\n", "Lets look at some seasonally adjusted livestock data. We fit five Holt's models.\n", "The below table allows us to compare results when we use exponential versus additive and damped versus non-damped.\n", " \n", "Note: ```fit4``` does not allow the parameter $\\phi$ to be optimized by providing a fixed value of $\\phi=0.98$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:16.605618Z", "start_time": "2017-12-07T12:39:16.116424Z" } }, "outputs": [], "source": [ "fit1 = SimpleExpSmoothing(livestock2, initialization_method=\"estimated\").fit()\n", "fit2 = Holt(livestock2, initialization_method=\"estimated\").fit()\n", "fit3 = Holt(livestock2,exponential=True, initialization_method=\"estimated\").fit()\n", "fit4 = Holt(livestock2,damped_trend=True, initialization_method=\"estimated\").fit(damping_trend=0.98)\n", "fit5 = Holt(livestock2,exponential=True, damped_trend=True, initialization_method=\"estimated\").fit()\n", "params = ['smoothing_level', 'smoothing_trend', 'damping_trend', 'initial_level', 'initial_trend']\n", "results=pd.DataFrame(index=[r\"$\\alpha$\",r\"$\\beta$\",r\"$\\phi$\",r\"$l_0$\",\"$b_0$\",\"SSE\"] ,columns=['SES', \"Holt's\",\"Exponential\", \"Additive\", \"Multiplicative\"])\n", "results[\"SES\"] = [fit1.params[p] for p in params] + [fit1.sse]\n", "results[\"Holt's\"] = [fit2.params[p] for p in params] + [fit2.sse]\n", "results[\"Exponential\"] = [fit3.params[p] for p in params] + [fit3.sse]\n", "results[\"Additive\"] = [fit4.params[p] for p in params] + [fit4.sse]\n", "results[\"Multiplicative\"] = [fit5.params[p] for p in params] + [fit5.sse]\n", "results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plots of Seasonally Adjusted Data\n", "The following plots allow us to evaluate the level and slope/trend components of the above table's fits." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:17.105928Z", "start_time": "2017-12-07T12:39:16.607306Z" } }, "outputs": [], "source": [ "for fit in [fit2,fit4]:\n", " pd.DataFrame(np.c_[fit.level,fit.trend]).rename(\n", " columns={0:'level',1:'slope'}).plot(subplots=True)\n", "plt.show()\n", "print('Figure 7.4: Level and slope components for Holt’s linear trend method and the additive damped trend method.')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparison\n", "Here we plot a comparison Simple Exponential Smoothing and Holt's Methods for various additive, exponential and damped combinations. All of the models parameters will be optimized by statsmodels." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:18.038995Z", "start_time": "2017-12-07T12:39:17.108323Z" } }, "outputs": [], "source": [ "fit1 = SimpleExpSmoothing(livestock2, initialization_method=\"estimated\").fit()\n", "fcast1 = fit1.forecast(9).rename(\"SES\")\n", "fit2 = Holt(livestock2, initialization_method=\"estimated\").fit()\n", "fcast2 = fit2.forecast(9).rename(\"Holt's\")\n", "fit3 = Holt(livestock2, exponential=True, initialization_method=\"estimated\").fit()\n", "fcast3 = fit3.forecast(9).rename(\"Exponential\")\n", "fit4 = Holt(livestock2, damped_trend=True, initialization_method=\"estimated\").fit(damping_trend=0.98)\n", "fcast4 = fit4.forecast(9).rename(\"Additive Damped\")\n", "fit5 = Holt(livestock2, exponential=True, damped_trend=True, initialization_method=\"estimated\").fit()\n", "fcast5 = fit5.forecast(9).rename(\"Multiplicative Damped\")\n", "\n", "ax = livestock2.plot(color=\"black\", marker=\"o\", figsize=(12,8))\n", "livestock3.plot(ax=ax, color=\"black\", marker=\"o\", legend=False)\n", "fcast1.plot(ax=ax, color='red', legend=True)\n", "fcast2.plot(ax=ax, color='green', legend=True)\n", "fcast3.plot(ax=ax, color='blue', legend=True)\n", "fcast4.plot(ax=ax, color='cyan', legend=True)\n", "fcast5.plot(ax=ax, color='magenta', legend=True)\n", "ax.set_ylabel('Livestock, sheep in Asia (millions)')\n", "plt.show()\n", "print('Figure 7.5: Forecasting livestock, sheep in Asia: comparing forecasting performance of non-seasonal methods.')" ] }, { "cell_type": "markdown", "metadata": { "ExecuteTime": { "end_time": "2017-10-05T09:40:15.958575Z", "start_time": "2017-10-05T09:40:15.615Z" } }, "source": [ "## Holt's Winters Seasonal\n", "Finally we are able to run full Holt's Winters Seasonal Exponential Smoothing including a trend component and a seasonal component.\n", "statsmodels allows for all the combinations including as shown in the examples below:\n", "1. ```fit1``` additive trend, additive seasonal of period ```season_length=4``` and the use of a Box-Cox transformation.\n", "1. ```fit2``` additive trend, multiplicative seasonal of period ```season_length=4``` and the use of a Box-Cox transformation..\n", "1. ```fit3``` additive damped trend, additive seasonal of period ```season_length=4``` and the use of a Box-Cox transformation.\n", "1. ```fit4``` additive damped trend, multiplicative seasonal of period ```season_length=4``` and the use of a Box-Cox transformation.\n", "\n", "The plot shows the results and forecast for ```fit1``` and ```fit2```.\n", "The table allows us to compare the results and parameterizations." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:28.375871Z", "start_time": "2017-12-07T12:39:18.040674Z" } }, "outputs": [], "source": [ "fit1 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='add', use_boxcox=True, initialization_method=\"estimated\").fit()\n", "fit2 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='mul', use_boxcox=True, initialization_method=\"estimated\").fit()\n", "fit3 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='add', damped_trend=True, use_boxcox=True, initialization_method=\"estimated\").fit()\n", "fit4 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='mul', damped_trend=True, use_boxcox=True, initialization_method=\"estimated\").fit()\n", "results=pd.DataFrame(index=[r\"$\\alpha$\",r\"$\\beta$\",r\"$\\phi$\",r\"$\\gamma$\",r\"$l_0$\",\"$b_0$\",\"SSE\"])\n", "params = ['smoothing_level', 'smoothing_trend', 'damping_trend', 'smoothing_seasonal', 'initial_level', 'initial_trend']\n", "results[\"Additive\"] = [fit1.params[p] for p in params] + [fit1.sse]\n", "results[\"Multiplicative\"] = [fit2.params[p] for p in params] + [fit2.sse]\n", "results[\"Additive Dam\"] = [fit3.params[p] for p in params] + [fit3.sse]\n", "results[\"Multiplica Dam\"] = [fit4.params[p] for p in params] + [fit4.sse]\n", "\n", "ax = aust.plot(figsize=(10,6), marker='o', color='black', title=\"Forecasts from Holt-Winters' multiplicative method\" )\n", "ax.set_ylabel(\"International visitor night in Australia (millions)\")\n", "ax.set_xlabel(\"Year\")\n", "fit1.fittedvalues.plot(ax=ax, style='--', color='red')\n", "fit2.fittedvalues.plot(ax=ax, style='--', color='green')\n", "\n", "fit1.forecast(8).rename('Holt-Winters (add-add-seasonal)').plot(ax=ax, style='--', marker='o', color='red', legend=True)\n", "fit2.forecast(8).rename('Holt-Winters (add-mul-seasonal)').plot(ax=ax, style='--', marker='o', color='green', legend=True)\n", "\n", "plt.show()\n", "print(\"Figure 7.6: Forecasting international visitor nights in Australia using Holt-Winters method with both additive and multiplicative seasonality.\")\n", "\n", "results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Internals\n", "It is possible to get at the internals of the Exponential Smoothing models. \n", "\n", "Here we show some tables that allow you to view side by side the original values $y_t$, the level $l_t$, the trend $b_t$, the season $s_t$ and the fitted values $\\hat{y}_t$. Note that these values only have meaningful values in the space of your original data if the fit is performed without a Box-Cox transformation." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fit1 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='add', initialization_method=\"estimated\").fit()\n", "fit2 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='mul', initialization_method=\"estimated\").fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:28.399765Z", "start_time": "2017-12-07T12:39:28.377215Z" } }, "outputs": [], "source": [ "df = pd.DataFrame(np.c_[aust, fit1.level, fit1.trend, fit1.season, fit1.fittedvalues],\n", " columns=[r'$y_t$',r'$l_t$',r'$b_t$',r'$s_t$',r'$\\hat{y}_t$'],index=aust.index)\n", "df.append(fit1.forecast(8).rename(r'$\\hat{y}_t$').to_frame(), sort=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:28.574783Z", "start_time": "2017-12-07T12:39:28.401234Z" } }, "outputs": [], "source": [ "df = pd.DataFrame(np.c_[aust, fit2.level, fit2.trend, fit2.season, fit2.fittedvalues], \n", " columns=[r'$y_t$',r'$l_t$',r'$b_t$',r'$s_t$',r'$\\hat{y}_t$'],index=aust.index)\n", "df.append(fit2.forecast(8).rename(r'$\\hat{y}_t$').to_frame(), sort=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally lets look at the levels, slopes/trends and seasonal components of the models." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:29.636548Z", "start_time": "2017-12-07T12:39:28.576279Z" } }, "outputs": [], "source": [ "states1 = pd.DataFrame(np.c_[fit1.level, fit1.trend, fit1.season], columns=['level','slope','seasonal'], index=aust.index)\n", "states2 = pd.DataFrame(np.c_[fit2.level, fit2.trend, fit2.season], columns=['level','slope','seasonal'], index=aust.index)\n", "fig, [[ax1, ax4],[ax2, ax5], [ax3, ax6]] = plt.subplots(3, 2, figsize=(12,8))\n", "states1[['level']].plot(ax=ax1)\n", "states1[['slope']].plot(ax=ax2)\n", "states1[['seasonal']].plot(ax=ax3)\n", "states2[['level']].plot(ax=ax4)\n", "states2[['slope']].plot(ax=ax5)\n", "states2[['seasonal']].plot(ax=ax6)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulations and Confidence Intervals\n", "\n", "By using a state space formulation, we can perform simulations of future values. The mathematical details are described in Hyndman and Athanasopoulos [2] and in the documentation of `HoltWintersResults.simulate`.\n", "\n", "Similar to the example in [2], we use the model with additive trend, multiplicative seasonality, and multiplicative error. We simulate up to 8 steps into the future, and perform 1000 simulations. As can be seen in the below figure, the simulations match the forecast values quite well.\n", "\n", "[2] [Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice, 2nd edition. OTexts, 2018.](https://otexts.com/fpp2/ets.html)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fit = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='mul', initialization_method=\"estimated\").fit()\n", "simulations = fit.simulate(8, repetitions=100, error='mul')\n", "\n", "ax = aust.plot(figsize=(10,6), marker='o', color='black', \n", " title=\"Forecasts and simulations from Holt-Winters' multiplicative method\" )\n", "ax.set_ylabel(\"International visitor night in Australia (millions)\")\n", "ax.set_xlabel(\"Year\")\n", "fit.fittedvalues.plot(ax=ax, style='--', color='green')\n", "simulations.plot(ax=ax, style='-', alpha=0.05, color='grey', legend=False)\n", "fit.forecast(8).rename('Holt-Winters (add-mul-seasonal)').plot(ax=ax, style='--', marker='o', color='green', legend=True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulations can also be started at different points in time, and there are multiple options for choosing the random noise." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fit = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='mul', initialization_method=\"estimated\").fit()\n", "simulations = fit.simulate(16, anchor='2009-01-01', repetitions=100, error='mul', random_errors='bootstrap')\n", "\n", "ax = aust.plot(figsize=(10,6), marker='o', color='black', \n", " title=\"Forecasts and simulations from Holt-Winters' multiplicative method\" )\n", "ax.set_ylabel(\"International visitor night in Australia (millions)\")\n", "ax.set_xlabel(\"Year\")\n", "fit.fittedvalues.plot(ax=ax, style='--', color='green')\n", "simulations.plot(ax=ax, style='-', alpha=0.05, color='grey', legend=False)\n", "fit.forecast(8).rename('Holt-Winters (add-mul-seasonal)').plot(ax=ax, style='--', marker='o', color='green', legend=True)\n", "plt.show()" ] } ], "metadata": { "anaconda-cloud": {}, "hide_input": false, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "colors": { "hover_highlight": "#DAA520", "navigate_num": "#000000", "navigate_text": "#333333", "running_highlight": "#FF0000", "selected_highlight": "#FFD700", "sidebar_border": "#EEEEEE", "wrapper_background": "#FFFFFF" }, "moveMenuLeft": true, "nav_menu": { "height": "98px", "width": "252px" }, "navigate_menu": true, "number_sections": false, "sideBar": true, "threshold": 4, "toc_cell": false, "toc_section_display": "block", "toc_window_display": true, "widenNotebook": false } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/formulas.ipynb000066400000000000000000000231351400612667500226650ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Formulas: Fitting models using R-style formulas" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since version 0.5.0, ``statsmodels`` allows users to fit statistical models using R-style formulas. Internally, ``statsmodels`` uses the [patsy](http://patsy.readthedocs.org/) package to convert formulas and data to the matrices that are used in model fitting. The formula framework is quite powerful; this tutorial only scratches the surface. A full description of the formula language can be found in the ``patsy`` docs: \n", "\n", "* [Patsy formula language description](http://patsy.readthedocs.org/)\n", "\n", "## Loading modules and functions" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np # noqa:F401 needed in namespace for patsy\n", "import statsmodels.api as sm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Import convention" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can import explicitly from statsmodels.formula.api" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from statsmodels.formula.api import ols" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternatively, you can just use the `formula` namespace of the main `statsmodels.api`." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sm.formula.ols" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or you can use the following convention" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import statsmodels.formula.api as smf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These names are just a convenient way to get access to each model's `from_formula` classmethod. See, for instance" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sm.OLS.from_formula" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All of the lower case models accept ``formula`` and ``data`` arguments, whereas upper case ones take ``endog`` and ``exog`` design matrices. ``formula`` accepts a string which describes the model in terms of a ``patsy`` formula. ``data`` takes a [pandas](https://pandas.pydata.org/) data frame or any other data structure that defines a ``__getitem__`` for variable names like a structured array or a dictionary of variables. \n", "\n", "``dir(sm.formula)`` will print a list of available models. \n", "\n", "Formula-compatible models have the following generic call signature: ``(formula, data, subset=None, *args, **kwargs)``" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## OLS regression using formulas\n", "\n", "To begin, we fit the linear model described on the [Getting Started](./regression_diagnostics.html) page. Download the data, subset columns, and list-wise delete to remove missing observations:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "dta = sm.datasets.get_rdataset(\"Guerry\", \"HistData\", cache=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "df = dta.data[['Lottery', 'Literacy', 'Wealth', 'Region']].dropna()\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit the model:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mod = ols(formula='Lottery ~ Literacy + Wealth + Region', data=df)\n", "res = mod.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Categorical variables\n", "\n", "Looking at the summary printed above, notice that ``patsy`` determined that elements of *Region* were text strings, so it treated *Region* as a categorical variable. `patsy`'s default is also to include an intercept, so we automatically dropped one of the *Region* categories.\n", "\n", "If *Region* had been an integer variable that we wanted to treat explicitly as categorical, we could have done so by using the ``C()`` operator: " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res = ols(formula='Lottery ~ Literacy + Wealth + C(Region)', data=df).fit()\n", "print(res.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Patsy's mode advanced features for categorical variables are discussed in: [Patsy: Contrast Coding Systems for categorical variables](./contrasts.html)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Operators\n", "\n", "We have already seen that \"~\" separates the left-hand side of the model from the right-hand side, and that \"+\" adds new columns to the design matrix. \n", "\n", "## Removing variables\n", "\n", "The \"-\" sign can be used to remove columns/variables. For instance, we can remove the intercept from a model by: " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res = ols(formula='Lottery ~ Literacy + Wealth + C(Region) -1 ', data=df).fit()\n", "print(res.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multiplicative interactions\n", "\n", "\":\" adds a new column to the design matrix with the interaction of the other two columns. \"*\" will also include the individual columns that were multiplied together:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res1 = ols(formula='Lottery ~ Literacy : Wealth - 1', data=df).fit()\n", "res2 = ols(formula='Lottery ~ Literacy * Wealth - 1', data=df).fit()\n", "print(res1.params, '\\n')\n", "print(res2.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Many other things are possible with operators. Please consult the [patsy docs](https://patsy.readthedocs.org/en/latest/formulas.html) to learn more." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Functions\n", "\n", "You can apply vectorized functions to the variables in your model: " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res = smf.ols(formula='Lottery ~ np.log(Literacy)', data=df).fit()\n", "print(res.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define a custom function:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def log_plus_1(x):\n", " return np.log(x) + 1.\n", "res = smf.ols(formula='Lottery ~ log_plus_1(Literacy)', data=df).fit()\n", "print(res.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Any function that is in the calling namespace is available to the formula." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using formulas with models that do not (yet) support them\n", "\n", "Even if a given `statsmodels` function does not support formulas, you can still use `patsy`'s formula language to produce design matrices. Those matrices \n", "can then be fed to the fitting function as `endog` and `exog` arguments. \n", "\n", "To generate ``numpy`` arrays: " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import patsy\n", "f = 'Lottery ~ Literacy * Wealth'\n", "y,X = patsy.dmatrices(f, df, return_type='matrix')\n", "print(y[:5])\n", "print(X[:5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To generate pandas data frames: " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "f = 'Lottery ~ Literacy * Wealth'\n", "y,X = patsy.dmatrices(f, df, return_type='dataframe')\n", "print(y[:5])\n", "print(X[:5])" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(sm.OLS(y, X).fit().summary())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }statsmodels-0.12.2/examples/notebooks/gee_nested_simulation.ipynb000066400000000000000000000131031400612667500253750ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## GEE nested covariance structure simulation study\n", "\n", "This notebook is a simulation study that illustrates and evaluates the performance of the GEE nested covariance structure.\n", "\n", "A nested covariance structure is based on a nested sequence of groups, or \"levels\". The top level in the hierarchy is defined by the `groups` argument to GEE. Subsequent levels are defined by the `dep_data` argument to GEE." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set the number of covariates." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "p = 5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These parameters define the population variance for each level of grouping." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "groups_var = 1\n", "level1_var = 2\n", "level2_var = 3\n", "resid_var = 4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set the number of groups" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "n_groups = 100" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set the number of observations at each level of grouping. Here, everything is balanced, i.e. within a level every group has the same size." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "group_size = 20\n", "level1_size = 10\n", "level2_size = 5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculate the total sample size." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "n = n_groups * group_size * level1_size * level2_size" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Construct the design matrix." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "xmat = np.random.normal(size=(n, p))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Construct labels showing which group each observation belongs to at each level." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "groups_ix = np.kron(np.arange(n // group_size), np.ones(group_size)).astype(np.int)\n", "level1_ix = np.kron(np.arange(n // level1_size), np.ones(level1_size)).astype(np.int)\n", "level2_ix = np.kron(np.arange(n // level2_size), np.ones(level2_size)).astype(np.int)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulate the random effects." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "groups_re = np.sqrt(groups_var) * np.random.normal(size=n // group_size)\n", "level1_re = np.sqrt(level1_var) * np.random.normal(size=n // level1_size)\n", "level2_re = np.sqrt(level2_var) * np.random.normal(size=n // level2_size)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulate the response variable." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "y = groups_re[groups_ix] + level1_re[level1_ix] + level2_re[level2_ix]\n", "y += np.sqrt(resid_var) * np.random.normal(size=n)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Put everything into a dataframe." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "df = pd.DataFrame(xmat, columns=[\"x%d\" % j for j in range(p)])\n", "df[\"y\"] = y + xmat[:, 0] - xmat[:, 3]\n", "df[\"groups_ix\"] = groups_ix\n", "df[\"level1_ix\"] = level1_ix\n", "df[\"level2_ix\"] = level2_ix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit the model." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "cs = sm.cov_struct.Nested()\n", "dep_fml = \"0 + level1_ix + level2_ix\"\n", "m = sm.GEE.from_formula(\"y ~ x0 + x1 + x2 + x3 + x4\", cov_struct=cs,\n", " dep_data=dep_fml, groups=\"groups_ix\", data=df)\n", "r = m.fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The estimated covariance parameters should be similar to `groups_var`, `level1_var`, etc. as defined above." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "r.cov_struct.summary()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 2 } statsmodels-0.12.2/examples/notebooks/gee_score_test_simulation.ipynb000066400000000000000000000223221400612667500262700ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# GEE score tests\n", "\n", "This notebook uses simulation to demonstrate robust GEE score tests. These tests can be used in a GEE analysis to compare nested hypotheses about the mean structure. The tests are robust to miss-specification of the working correlation model, and to certain forms of misspecification of the variance structure (e.g. as captured by the scale parameter in a quasi-Poisson analysis).\n", "\n", "The data are simulated as clusters, where there is dependence within but not between clusters. The cluster-wise dependence is induced using a copula approach. The data marginally follow a negative binomial (gamma/Poisson) mixture.\n", "\n", "The level and power of the tests are considered below to assess the performance of the tests." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "from scipy.stats.distributions import norm, poisson\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function defined in the following cell uses a copula approach to simulate correlated random values that marginally follow a negative binomial distribution. The input parameter `u` is an array of values in (0, 1). The elements of `u` must be marginally uniformly distributed on (0, 1). Correlation in `u` will induce correlations in the returned negative binomial values. The array parameter `mu` gives the marginal means, and the scalar parameter `scale` defines the mean/variance relationship (the variance is `scale` times the mean). The lengths of `u` and `mu` must be the same." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 1 }, "outputs": [], "source": [ "def negbinom(u, mu, scale):\n", " p = (scale - 1) / scale\n", " r = mu * (1 - p) / p\n", " x = np.random.gamma(r, p / (1 - p), len(u))\n", " return poisson.ppf(u, mu=x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below are some parameters that govern the data used in the simulation." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Sample size\n", "n = 1000\n", "\n", "# Number of covariates (including intercept) in the alternative hypothesis model\n", "p = 5\n", "\n", "# Cluster size\n", "m = 10\n", "\n", "# Intraclass correlation (controls strength of clustering)\n", "r = 0.5\n", "\n", "# Group indicators\n", "grp = np.kron(np.arange(n/m), np.ones(m))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The simulation uses a fixed design matrix." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Build a design matrix for the alternative (more complex) model\n", "x = np.random.normal(size=(n, p))\n", "x[:, 0] = 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The null design matrix is nested in the alternative design matrix. It has rank two less than the alternative design matrix." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "x0 = x[:, 0:3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The GEE score test is robust to dependence and overdispersion. Here we set the overdispersion parameter. The variance of the negative binomial distribution for each observation is equal to `scale` times its mean value." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Scale parameter for negative binomial distribution\n", "scale = 10" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the next cell, we set up the mean structures for the null and alternative models" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# The coefficients used to define the linear predictors\n", "coeff = [[4, 0.4, -0.2], [4, 0.4, -0.2, 0, -0.04]]\n", "\n", "# The linear predictors\n", "lp = [np.dot(x0, coeff[0]), np.dot(x, coeff[1])]\n", "\n", "# The mean values\n", "mu = [np.exp(lp[0]), np.exp(lp[1])]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below is a function that carries out the simulation." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# hyp = 0 is the null hypothesis, hyp = 1 is the alternative hypothesis.\n", "# cov_struct is a statsmodels covariance structure\n", "def dosim(hyp, cov_struct=None, mcrep=500):\n", " \n", " # Storage for the simulation results\n", " scales = [[], []]\n", " \n", " # P-values from the score test\n", " pv = []\n", " \n", " # Monte Carlo loop\n", " for k in range(mcrep):\n", "\n", " # Generate random \"probability points\" u that are uniformly \n", " # distributed, and correlated within clusters\n", " z = np.random.normal(size=n)\n", " u = np.random.normal(size=n//m)\n", " u = np.kron(u, np.ones(m))\n", " z = r*z +np.sqrt(1-r**2)*u\n", " u = norm.cdf(z)\n", "\n", " # Generate the observed responses\n", " y = negbinom(u, mu=mu[hyp], scale=scale)\n", "\n", " # Fit the null model\n", " m0 = sm.GEE(y, x0, groups=grp, cov_struct=cov_struct, family=sm.families.Poisson())\n", " r0 = m0.fit(scale='X2')\n", " scales[0].append(r0.scale)\n", " \n", " # Fit the alternative model\n", " m1 = sm.GEE(y, x, groups=grp, cov_struct=cov_struct, family=sm.families.Poisson())\n", " r1 = m1.fit(scale='X2')\n", " scales[1].append(r1.scale)\n", " \n", " # Carry out the score test\n", " st = m1.compare_score_test(r0)\n", " pv.append(st[\"p-value\"])\n", "\n", " pv = np.asarray(pv)\n", " rslt = [np.mean(pv), np.mean(pv < 0.1)]\n", " \n", " return rslt, scales" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run the simulation using the independence working covariance structure. We expect the mean to be around 0 under the null hypothesis, and much lower under the alternative hypothesis. Similarly, we expect that under the null hypothesis, around 10% of the p-values are less than 0.1, and a much greater fraction of the p-values are less than 0.1 under the alternative hypothesis." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "rslt, scales = [], []\n", "\n", "for hyp in 0, 1:\n", " s, t = dosim(hyp, sm.cov_struct.Independence())\n", " rslt.append(s)\n", " scales.append(t)\n", " \n", "rslt = pd.DataFrame(rslt, index=[\"H0\", \"H1\"], columns=[\"Mean\", \"Prop(p<0.1)\"])\n", "\n", "print(rslt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we check to make sure that the scale parameter estimates are reasonable. We are assessing the robustness of the GEE score test to dependence and overdispersion, so here we are confirming that the overdispersion is present as expected." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "_ = plt.boxplot([scales[0][0], scales[0][1], scales[1][0], scales[1][1]])\n", "plt.ylabel(\"Estimated scale\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we conduct the same analysis using an exchangeable working correlation model. Note that this will be slower than the example above using independent working correlation, so we use fewer Monte Carlo repetitions." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "rslt, scales = [], []\n", "\n", "for hyp in 0, 1:\n", " s, t = dosim(hyp, sm.cov_struct.Exchangeable(), mcrep=100)\n", " rslt.append(s)\n", " scales.append(t)\n", " \n", "rslt = pd.DataFrame(rslt, index=[\"H0\", \"H1\"], columns=[\"Mean\", \"Prop(p<0.1)\"])\n", "\n", "print(rslt)" ] } ], "metadata": { "jupytext": { "cell_metadata_filter": "-all", "main_language": "python", "notebook_metadata_filter": "-all" }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 2 } statsmodels-0.12.2/examples/notebooks/generic_mle.ipynb000066400000000000000000000323311400612667500233040ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Maximum Likelihood Estimation (Generic models)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This tutorial explains how to quickly implement new maximum likelihood models in `statsmodels`. We give two examples: \n", "\n", "1. Probit model for binary dependent variables\n", "2. Negative binomial model for count data\n", "\n", "The `GenericLikelihoodModel` class eases the process by providing tools such as automatic numeric differentiation and a unified interface to ``scipy`` optimization functions. Using ``statsmodels``, users can fit new MLE models simply by \"plugging-in\" a log-likelihood function. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1: Probit model" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "from scipy import stats\n", "import statsmodels.api as sm\n", "from statsmodels.base.model import GenericLikelihoodModel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ``Spector`` dataset is distributed with ``statsmodels``. You can access a vector of values for the dependent variable (``endog``) and a matrix of regressors (``exog``) like this:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "data = sm.datasets.spector.load_pandas()\n", "exog = data.exog\n", "endog = data.endog\n", "print(sm.datasets.spector.NOTE)\n", "print(data.exog.head())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Them, we add a constant to the matrix of regressors:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "exog = sm.add_constant(exog, prepend=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To create your own Likelihood Model, you simply need to overwrite the loglike method." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "class MyProbit(GenericLikelihoodModel):\n", " def loglike(self, params):\n", " exog = self.exog\n", " endog = self.endog\n", " q = 2 * endog - 1\n", " return stats.norm.logcdf(q*np.dot(exog, params)).sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Estimate the model and print a summary:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sm_probit_manual = MyProbit(endog, exog).fit()\n", "print(sm_probit_manual.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare your Probit implementation to ``statsmodels``' \"canned\" implementation:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sm_probit_canned = sm.Probit(endog, exog).fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(sm_probit_canned.params)\n", "print(sm_probit_manual.params)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(sm_probit_canned.cov_params())\n", "print(sm_probit_manual.cov_params())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the ``GenericMaximumLikelihood`` class provides automatic differentiation, so we did not have to provide Hessian or Score functions in order to calculate the covariance estimates." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "## Example 2: Negative Binomial Regression for Count Data\n", "\n", "Consider a negative binomial regression model for count data with\n", "log-likelihood (type NB-2) function expressed as:\n", "\n", "$$\n", " \\mathcal{L}(\\beta_j; y, \\alpha) = \\sum_{i=1}^n y_i ln \n", " \\left ( \\frac{\\alpha exp(X_i'\\beta)}{1+\\alpha exp(X_i'\\beta)} \\right ) -\n", " \\frac{1}{\\alpha} ln(1+\\alpha exp(X_i'\\beta)) + ln \\Gamma (y_i + 1/\\alpha) - ln \\Gamma (y_i+1) - ln \\Gamma (1/\\alpha)\n", "$$\n", "\n", "with a matrix of regressors $X$, a vector of coefficients $\\beta$,\n", "and the negative binomial heterogeneity parameter $\\alpha$. \n", "\n", "Using the ``nbinom`` distribution from ``scipy``, we can write this likelihood\n", "simply as:\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "from scipy.stats import nbinom" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def _ll_nb2(y, X, beta, alph):\n", " mu = np.exp(np.dot(X, beta))\n", " size = 1/alph\n", " prob = size/(size+mu)\n", " ll = nbinom.logpmf(y, size, prob)\n", " return ll" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### New Model Class\n", "\n", "We create a new model class which inherits from ``GenericLikelihoodModel``:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from statsmodels.base.model import GenericLikelihoodModel" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "class NBin(GenericLikelihoodModel):\n", " def __init__(self, endog, exog, **kwds):\n", " super(NBin, self).__init__(endog, exog, **kwds)\n", " \n", " def nloglikeobs(self, params):\n", " alph = params[-1]\n", " beta = params[:-1]\n", " ll = _ll_nb2(self.endog, self.exog, beta, alph)\n", " return -ll \n", " \n", " def fit(self, start_params=None, maxiter=10000, maxfun=5000, **kwds):\n", " # we have one additional parameter and we need to add it for summary\n", " self.exog_names.append('alpha')\n", " if start_params == None:\n", " # Reasonable starting values\n", " start_params = np.append(np.zeros(self.exog.shape[1]), .5)\n", " # intercept\n", " start_params[-2] = np.log(self.endog.mean())\n", " return super(NBin, self).fit(start_params=start_params, \n", " maxiter=maxiter, maxfun=maxfun, \n", " **kwds) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two important things to notice: \n", "\n", "+ ``nloglikeobs``: This function should return one evaluation of the negative log-likelihood function per observation in your dataset (i.e. rows of the endog/X matrix). \n", "+ ``start_params``: A one-dimensional array of starting values needs to be provided. The size of this array determines the number of parameters that will be used in optimization.\n", " \n", "That's it! You're done!\n", "\n", "### Usage Example\n", "\n", "The [Medpar](https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/doc/COUNT/medpar.html)\n", "dataset is hosted in CSV format at the [Rdatasets repository](https://raw.githubusercontent.com/vincentarelbundock/Rdatasets). We use the ``read_csv``\n", "function from the [Pandas library](https://pandas.pydata.org) to load the data\n", "in memory. We then print the first few columns: \n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import statsmodels.api as sm" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "medpar = sm.datasets.get_rdataset(\"medpar\", \"COUNT\", cache=True).data\n", "\n", "medpar.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model we are interested in has a vector of non-negative integers as\n", "dependent variable (``los``), and 5 regressors: ``Intercept``, ``type2``,\n", "``type3``, ``hmo``, ``white``.\n", "\n", "For estimation, we need to create two variables to hold our regressors and the outcome variable. These can be ndarrays or pandas objects." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "y = medpar.los\n", "X = medpar[[\"type2\", \"type3\", \"hmo\", \"white\"]].copy()\n", "X[\"constant\"] = 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then, we fit the model and extract some information: " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mod = NBin(y, X)\n", "res = mod.fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Extract parameter estimates, standard errors, p-values, AIC, etc.:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print('Parameters: ', res.params)\n", "print('Standard errors: ', res.bse)\n", "print('P-values: ', res.pvalues)\n", "print('AIC: ', res.aic)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As usual, you can obtain a full list of available information by typing\n", "``dir(res)``.\n", "We can also look at the summary of the estimation results." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Testing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check the results by using the statsmodels implementation of the Negative Binomial model, which uses the analytic score function and Hessian." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_nbin = sm.NegativeBinomial(y, X).fit(disp=0)\n", "print(res_nbin.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(res_nbin.params)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(res_nbin.bse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or we could compare them to results obtained using the MASS implementation for R:\n", "\n", " url = 'https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/csv/COUNT/medpar.csv'\n", " medpar = read.csv(url)\n", " f = los~factor(type)+hmo+white\n", " \n", " library(MASS)\n", " mod = glm.nb(f, medpar)\n", " coef(summary(mod))\n", " Estimate Std. Error z value Pr(>|z|)\n", " (Intercept) 2.31027893 0.06744676 34.253370 3.885556e-257\n", " factor(type)2 0.22124898 0.05045746 4.384861 1.160597e-05\n", " factor(type)3 0.70615882 0.07599849 9.291748 1.517751e-20\n", " hmo -0.06795522 0.05321375 -1.277024 2.015939e-01\n", " white -0.12906544 0.06836272 -1.887951 5.903257e-02\n", "\n", "### Numerical precision \n", "\n", "The ``statsmodels`` generic MLE and ``R`` parameter estimates agree up to the fourth decimal. The standard errors, however, agree only up to the second decimal. This discrepancy is the result of imprecision in our Hessian numerical estimates. In the current context, the difference between ``MASS`` and ``statsmodels`` standard error estimates is substantively irrelevant, but it highlights the fact that users who need very precise estimates may not always want to rely on default settings when using numerical derivatives. In such cases, it is better to use analytical derivatives with the ``LikelihoodModel`` class." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 } statsmodels-0.12.2/examples/notebooks/glm.ipynb000066400000000000000000000220771400612667500216200ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Generalized Linear Models" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import statsmodels.api as sm\n", "from scipy import stats\n", "from matplotlib import pyplot as plt\n", "\n", "plt.rc(\"figure\", figsize=(16,8))\n", "plt.rc(\"font\", size=14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## GLM: Binomial response data\n", "\n", "### Load Star98 data\n", "\n", " In this example, we use the Star98 dataset which was taken with permission\n", " from Jeff Gill (2000) Generalized linear models: A unified approach. Codebook\n", " information can be obtained by typing: " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(sm.datasets.star98.NOTE)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Load the data and add a constant to the exogenous (independent) variables:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = sm.datasets.star98.load(as_pandas=False)\n", "data.exog = sm.add_constant(data.exog, prepend=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " The dependent variable is N by 2 (Success: NABOVE, Failure: NBELOW): " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(data.endog[:5,:])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " The independent variables include all the other variables described above, as\n", " well as the interaction terms:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(data.exog[:2,:])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fit and summary" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "glm_binom = sm.GLM(data.endog, data.exog, family=sm.families.Binomial())\n", "res = glm_binom.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Quantities of interest" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print('Total number of trials:', data.endog[0].sum())\n", "print('Parameters: ', res.params)\n", "print('T-values: ', res.tvalues)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First differences: We hold all explanatory variables constant at their means and manipulate the percentage of low income households to assess its impact on the response variables: " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "means = data.exog.mean(axis=0)\n", "means25 = means.copy()\n", "means25[0] = stats.scoreatpercentile(data.exog[:,0], 25)\n", "means75 = means.copy()\n", "means75[0] = lowinc_75per = stats.scoreatpercentile(data.exog[:,0], 75)\n", "resp_25 = res.predict(means25)\n", "resp_75 = res.predict(means75)\n", "diff = resp_75 - resp_25" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The interquartile first difference for the percentage of low income households in a school district is:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(\"%2.4f%%\" % (diff*100))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plots\n", "\n", " We extract information that will be used to draw some interesting plots: " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "nobs = res.nobs\n", "y = data.endog[:,0]/data.endog.sum(1)\n", "yhat = res.mu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot yhat vs y:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.graphics.api import abline_plot" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots()\n", "ax.scatter(yhat, y)\n", "line_fit = sm.OLS(y, sm.add_constant(yhat, prepend=True)).fit()\n", "abline_plot(model_results=line_fit, ax=ax)\n", "\n", "\n", "ax.set_title('Model Fit Plot')\n", "ax.set_ylabel('Observed values')\n", "ax.set_xlabel('Fitted values');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot yhat vs. Pearson residuals:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots()\n", "\n", "ax.scatter(yhat, res.resid_pearson)\n", "ax.hlines(0, 0, 1)\n", "ax.set_xlim(0, 1)\n", "ax.set_title('Residual Dependence Plot')\n", "ax.set_ylabel('Pearson Residuals')\n", "ax.set_xlabel('Fitted values')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Histogram of standardized deviance residuals:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from scipy import stats\n", "\n", "fig, ax = plt.subplots()\n", "\n", "resid = res.resid_deviance.copy()\n", "resid_std = stats.zscore(resid)\n", "ax.hist(resid_std, bins=25)\n", "ax.set_title('Histogram of standardized deviance residuals');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "QQ Plot of Deviance Residuals:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels import graphics\n", "graphics.gofplots.qqplot(resid, line='r')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## GLM: Gamma for proportional count response\n", "\n", "### Load Scottish Parliament Voting data\n", "\n", " In the example above, we printed the ``NOTE`` attribute to learn about the\n", " Star98 dataset. statsmodels datasets ships with other useful information. For\n", " example: " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(sm.datasets.scotland.DESCRLONG)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Load the data and add a constant to the exogenous variables:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data2 = sm.datasets.scotland.load()\n", "data2.exog = sm.add_constant(data2.exog, prepend=False)\n", "print(data2.exog[:5,:])\n", "print(data2.endog[:5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model Fit and summary" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "glm_gamma = sm.GLM(data2.endog, data2.exog, family=sm.families.Gamma(sm.families.links.log()))\n", "glm_results = glm_gamma.fit()\n", "print(glm_results.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## GLM: Gaussian distribution with a noncanonical link\n", "\n", "### Artificial data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "nobs2 = 100\n", "x = np.arange(nobs2)\n", "np.random.seed(54321)\n", "X = np.column_stack((x,x**2))\n", "X = sm.add_constant(X, prepend=False)\n", "lny = np.exp(-(.03*x + .0001*x**2 - 1.0)) + .001 * np.random.rand(nobs2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fit and summary (artificial data)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "gauss_log = sm.GLM(lny, X, family=sm.families.Gaussian(sm.families.links.log()))\n", "gauss_log_results = gauss_log.fit()\n", "print(gauss_log_results.summary())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 1 }statsmodels-0.12.2/examples/notebooks/glm_formula.ipynb000066400000000000000000000060771400612667500233470ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Generalized Linear Models (Formula)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook illustrates how you can use R-style formulas to fit Generalized Linear Models.\n", "\n", "To begin, we load the ``Star98`` dataset and we construct a formula and pre-process the data:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import statsmodels.api as sm\n", "import statsmodels.formula.api as smf\n", "star98 = sm.datasets.star98.load_pandas().data\n", "formula = 'SUCCESS ~ LOWINC + PERASIAN + PERBLACK + PERHISP + PCTCHRT + \\\n", " PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF'\n", "dta = star98[['NABOVE', 'NBELOW', 'LOWINC', 'PERASIAN', 'PERBLACK', 'PERHISP',\n", " 'PCTCHRT', 'PCTYRRND', 'PERMINTE', 'AVYRSEXP', 'AVSALK',\n", " 'PERSPENK', 'PTRATIO', 'PCTAF']].copy()\n", "endog = dta['NABOVE'] / (dta['NABOVE'] + dta.pop('NBELOW'))\n", "del dta['NABOVE']\n", "dta['SUCCESS'] = endog" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then, we fit the GLM model:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mod1 = smf.glm(formula=formula, data=dta, family=sm.families.Binomial()).fit()\n", "print(mod1.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we define a function to operate customized data transformation using the formula framework:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def double_it(x):\n", " return 2 * x\n", "formula = 'SUCCESS ~ double_it(LOWINC) + PERASIAN + PERBLACK + PERHISP + PCTCHRT + \\\n", " PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF'\n", "mod2 = smf.glm(formula=formula, data=dta, family=sm.families.Binomial()).fit()\n", "print(mod2.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, the coefficient for ``double_it(LOWINC)`` in the second model is half the size of the ``LOWINC`` coefficient from the first model:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(mod1.params[1])\n", "print(mod2.params[1] * 2)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }statsmodels-0.12.2/examples/notebooks/glm_weights.ipynb000066400000000000000000000600341400612667500233450ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Weighted Generalized Linear Models" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import statsmodels.formula.api as smf\n", "import statsmodels.api as sm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Weighted GLM: Poisson response data\n", "\n", "### Load data\n", "\n", "In this example, we'll use the affair dataset using a handful of exogenous variables to predict the extra-marital affair rate. \n", "\n", "Weights will be generated to show that `freq_weights` are equivalent to repeating records of data. On the other hand, `var_weights` is equivalent to aggregating data. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(sm.datasets.fair.NOTE)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Load the data into a pandas dataframe." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "data = sm.datasets.fair.load_pandas().data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " The dependent (endogenous) variable is ``affairs``" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "data.describe()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "data[:3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the following we will work mostly with Poisson. While using decimal affairs works, we convert them to integers to have a count distribution." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "data[\"affairs\"] = np.ceil(data[\"affairs\"])\n", "data[:3]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "(data[\"affairs\"] == 0).mean()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "np.bincount(data[\"affairs\"].astype(int))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Condensing and Aggregating observations\n", "\n", "We have 6366 observations in our original dataset. When we consider only some selected variables, then we have fewer unique observations. In the following we combine observations in two ways, first we combine observations that have values for all variables identical, and secondly we combine observations that have the same explanatory variables." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dataset with unique observations\n", "\n", "We use pandas's groupby to combine identical observations and create a new variable `freq` that count how many observation have the values in the corresponding row." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "data2 = data.copy()\n", "data2['const'] = 1\n", "dc = data2['affairs rate_marriage age yrs_married const'.split()].groupby('affairs rate_marriage age yrs_married'.split()).count()\n", "dc.reset_index(inplace=True)\n", "dc.rename(columns={'const': 'freq'}, inplace=True)\n", "print(dc.shape)\n", "dc.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dataset with unique explanatory variables (exog)\n", "\n", "For the next dataset we combine observations that have the same values of the explanatory variables. However, because the response variable can differ among combined observations, we compute the mean and the sum of the response variable for all combined observations.\n", "\n", "We use again pandas ``groupby`` to combine observations and to create the new variables. We also flatten the ``MultiIndex`` into a simple index." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "gr = data['affairs rate_marriage age yrs_married'.split()].groupby('rate_marriage age yrs_married'.split())\n", "df_a = gr.agg(['mean', 'sum','count'])\n", "def merge_tuple(tpl):\n", " if isinstance(tpl, tuple) and len(tpl) > 1:\n", " return \"_\".join(map(str, tpl))\n", " else:\n", " return tpl\n", " \n", "df_a.columns = df_a.columns.map(merge_tuple)\n", "df_a.reset_index(inplace=True)\n", "print(df_a.shape)\n", "df_a.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After combining observations with have a dataframe `dc` with 467 unique observations, and a dataframe `df_a` with 130 observations with unique values of the explanatory variables." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print('number of rows: \\noriginal, with unique observations, with unique exog')\n", "data.shape[0], dc.shape[0], df_a.shape[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analysis\n", "\n", "In the following, we compare the GLM-Poisson results of the original data with models of the combined observations where the multiplicity or aggregation is given by weights or exposure.\n", "\n", "\n", "### original data" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "glm = smf.glm('affairs ~ rate_marriage + age + yrs_married',\n", " data=data, family=sm.families.Poisson())\n", "res_o = glm.fit()\n", "print(res_o.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_o.pearson_chi2 / res_o.df_resid" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### condensed data (unique observations with frequencies)\n", "\n", "Combining identical observations and using frequency weights to take into account the multiplicity of observations produces exactly the same results. Some results attribute will differ when we want to have information about the observation and not about the aggregate of all identical observations. For example, residuals do not take ``freq_weights`` into account." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "glm = smf.glm('affairs ~ rate_marriage + age + yrs_married',\n", " data=dc, family=sm.families.Poisson(), freq_weights=np.asarray(dc['freq']))\n", "res_f = glm.fit()\n", "print(res_f.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_f.pearson_chi2 / res_f.df_resid" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### condensed using ``var_weights`` instead of ``freq_weights``\n", "\n", "Next, we compare ``var_weights`` to ``freq_weights``. It is a common practice to incorporate ``var_weights`` when the endogenous variable reflects averages and not identical observations.\n", "I do not see a theoretical reason why it produces the same results (in general).\n", "\n", "This produces the same results but ``df_resid`` differs the ``freq_weights`` example because ``var_weights`` do not change the number of effective observations. \n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "glm = smf.glm('affairs ~ rate_marriage + age + yrs_married',\n", " data=dc, family=sm.families.Poisson(), var_weights=np.asarray(dc['freq']))\n", "res_fv = glm.fit()\n", "print(res_fv.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dispersion computed from the results is incorrect because of wrong ``df_resid``. \n", "It is correct if we use the original ``df_resid``." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_fv.pearson_chi2 / res_fv.df_resid, res_f.pearson_chi2 / res_f.df_resid" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### aggregated or averaged data (unique values of explanatory variables)\n", "\n", "For these cases we combine observations that have the same values of the explanatory variables. The corresponding response variable is either a sum or an average.\n", "\n", "#### using ``exposure``\n", "\n", "If our dependent variable is the sum of the responses of all combined observations, then under the Poisson assumption the distribution remains the same but we have varying `exposure` given by the number of individuals that are represented by one aggregated observation.\n", "\n", "The parameter estimates and covariance of parameters are the same with the original data, but log-likelihood, deviance and Pearson chi-squared differ" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "glm = smf.glm('affairs_sum ~ rate_marriage + age + yrs_married',\n", " data=df_a, family=sm.families.Poisson(), exposure=np.asarray(df_a['affairs_count']))\n", "res_e = glm.fit()\n", "print(res_e.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_e.pearson_chi2 / res_e.df_resid" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### using var_weights\n", "\n", "We can also use the mean of all combined values of the dependent variable. In this case the variance will be related to the inverse of the total exposure reflected by one combined observation." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "glm = smf.glm('affairs_mean ~ rate_marriage + age + yrs_married',\n", " data=df_a, family=sm.families.Poisson(), var_weights=np.asarray(df_a['affairs_count']))\n", "res_a = glm.fit()\n", "print(res_a.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparison\n", "\n", "We saw in the summary prints above that ``params`` and ``cov_params`` with associated Wald inference agree across versions. We summarize this in the following comparing individual results attributes across versions.\n", "\n", "Parameter estimates `params`, standard errors of the parameters `bse` and `pvalues` of the parameters for the tests that the parameters are zeros all agree. However, the likelihood and goodness-of-fit statistics, `llf`, `deviance` and `pearson_chi2` only partially agree. Specifically, the aggregated version do not agree with the results using the original data.\n", "\n", "**Warning**: The behavior of `llf`, `deviance` and `pearson_chi2` might still change in future versions.\n", "\n", "Both the sum and average of the response variable for unique values of the explanatory variables have a proper likelihood interpretation. However, this interpretation is not reflected in these three statistics. Computationally this might be due to missing adjustments when aggregated data is used. However, theoretically we can think in these cases, especially for `var_weights` of the misspecified case when likelihood analysis is inappropriate and the results should be interpreted as quasi-likelihood estimates. There is an ambiguity in the definition of ``var_weights`` because they can be used for averages with correctly specified likelihood as well as for variance adjustments in the quasi-likelihood case. We are currently not trying to match the likelihood specification. However, in the next section we show that likelihood ratio type tests still produce the same result for all aggregation versions when we assume that the underlying model is correctly specified." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "results_all = [res_o, res_f, res_e, res_a]\n", "names = 'res_o res_f res_e res_a'.split()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pd.concat([r.params for r in results_all], axis=1, keys=names)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pd.concat([r.bse for r in results_all], axis=1, keys=names)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pd.concat([r.pvalues for r in results_all], axis=1, keys=names)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pd.DataFrame(np.column_stack([[r.llf, r.deviance, r.pearson_chi2] for r in results_all]), \n", " columns=names, index=['llf', 'deviance', 'pearson chi2'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Likelihood Ratio type tests\n", "\n", "We saw above that likelihood and related statistics do not agree between the aggregated and original, individual data. We illustrate in the following that likelihood ratio test and difference in deviance agree across versions, however Pearson chi-squared does not.\n", "\n", "As before: This is not sufficiently clear yet and could change.\n", "\n", "As a test case we drop the `age` variable and compute the likelihood ratio type statistics as difference between reduced or constrained and full or unconstrained model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### original observations and frequency weights" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "glm = smf.glm('affairs ~ rate_marriage + yrs_married',\n", " data=data, family=sm.families.Poisson())\n", "res_o2 = glm.fit()\n", "#print(res_f2.summary())\n", "res_o2.pearson_chi2 - res_o.pearson_chi2, res_o2.deviance - res_o.deviance, res_o2.llf - res_o.llf" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "glm = smf.glm('affairs ~ rate_marriage + yrs_married',\n", " data=dc, family=sm.families.Poisson(), freq_weights=np.asarray(dc['freq']))\n", "res_f2 = glm.fit()\n", "#print(res_f2.summary())\n", "res_f2.pearson_chi2 - res_f.pearson_chi2, res_f2.deviance - res_f.deviance, res_f2.llf - res_f.llf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### aggregated data: ``exposure`` and ``var_weights``\n", "\n", "Note: LR test agrees with original observations, ``pearson_chi2`` differs and has the wrong sign." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "glm = smf.glm('affairs_sum ~ rate_marriage + yrs_married',\n", " data=df_a, family=sm.families.Poisson(), exposure=np.asarray(df_a['affairs_count']))\n", "res_e2 = glm.fit()\n", "res_e2.pearson_chi2 - res_e.pearson_chi2, res_e2.deviance - res_e.deviance, res_e2.llf - res_e.llf" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "glm = smf.glm('affairs_mean ~ rate_marriage + yrs_married',\n", " data=df_a, family=sm.families.Poisson(), var_weights=np.asarray(df_a['affairs_count']))\n", "res_a2 = glm.fit()\n", "res_a2.pearson_chi2 - res_a.pearson_chi2, res_a2.deviance - res_a.deviance, res_a2.llf - res_a.llf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Investigating Pearson chi-square statistic\n", "\n", "First, we do some sanity checks that there are no basic bugs in the computation of `pearson_chi2` and `resid_pearson`. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_e2.pearson_chi2, res_e.pearson_chi2, (res_e2.resid_pearson**2).sum(), (res_e.resid_pearson**2).sum()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_e._results.resid_response.mean(), res_e.model.family.variance(res_e.mu)[:5], res_e.mu[:5]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "(res_e._results.resid_response**2 / res_e.model.family.variance(res_e.mu)).sum()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_e2._results.resid_response.mean(), res_e2.model.family.variance(res_e2.mu)[:5], res_e2.mu[:5]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "(res_e2._results.resid_response**2 / res_e2.model.family.variance(res_e2.mu)).sum()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "(res_e2._results.resid_response**2).sum(), (res_e._results.resid_response**2).sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One possible reason for the incorrect sign is that we are subtracting quadratic terms that are divided by different denominators. In some related cases, the recommendation in the literature is to use a common denominator. We can compare pearson chi-squared statistic using the same variance assumption in the full and reduced model. \n", "\n", "In this case we obtain the same pearson chi2 scaled difference between reduced and full model across all versions. (Issue [#3616](https://github.com/statsmodels/statsmodels/issues/3616) is intended to track this further.)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "((res_e2._results.resid_response**2 - res_e._results.resid_response**2) / res_e2.model.family.variance(res_e2.mu)).sum()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "((res_a2._results.resid_response**2 - res_a._results.resid_response**2) / res_a2.model.family.variance(res_a2.mu)\n", "* res_a2.model.var_weights).sum()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "((res_f2._results.resid_response**2 - res_f._results.resid_response**2) / res_f2.model.family.variance(res_f2.mu) \n", " * res_f2.model.freq_weights).sum()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "((res_o2._results.resid_response**2 - res_o._results.resid_response**2) / res_o2.model.family.variance(res_o2.mu)).sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Remainder\n", "\n", "The remainder of the notebook just contains some additional checks and can be ignored." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "np.exp(res_e2.model.exposure)[:5], np.asarray(df_a['affairs_count'])[:5]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_e2.resid_pearson.sum() - res_e.resid_pearson.sum()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_e2.mu[:5]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_a2.pearson_chi2, res_a.pearson_chi2, res_a2.resid_pearson.sum(), res_a.resid_pearson.sum()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "((res_a2._results.resid_response**2) / res_a2.model.family.variance(res_a2.mu) * res_a2.model.var_weights).sum()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "((res_a._results.resid_response**2) / res_a.model.family.variance(res_a.mu) * res_a.model.var_weights).sum()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "((res_a._results.resid_response**2) / res_a.model.family.variance(res_a2.mu) * res_a.model.var_weights).sum()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_e.model.endog[:5], res_e2.model.endog[:5]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_a.model.endog[:5], res_a2.model.endog[:5]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_a2.model.endog[:5] * np.exp(res_e2.model.exposure)[:5]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_a2.model.endog[:5] * res_a2.model.var_weights[:5]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy import stats\n", "stats.chi2.sf(27.19530754604785, 1), stats.chi2.sf(29.083798806764687, 1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_o.pvalues" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(res_e2.summary())\n", "print(res_e.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(res_f2.summary())\n", "print(res_f.summary())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.0" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/gls.ipynb000066400000000000000000000120751400612667500216230ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Generalized Least Squares" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import statsmodels.api as sm\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Longley dataset is a time series dataset: " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "data = sm.datasets.longley.load(as_pandas=False)\n", "data.exog = sm.add_constant(data.exog)\n", "print(data.exog[:5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", " Let's assume that the data is heteroskedastic and that we know\n", " the nature of the heteroskedasticity. We can then define\n", " `sigma` and use it to give us a GLS model\n", "\n", " First we will obtain the residuals from an OLS fit" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ols_resid = sm.OLS(data.endog, data.exog).fit().resid" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assume that the error terms follow an AR(1) process with a trend:\n", "\n", "$\\epsilon_i = \\beta_0 + \\rho\\epsilon_{i-1} + \\eta_i$\n", "\n", "where $\\eta \\sim N(0,\\Sigma^2)$\n", "\n", "and that $\\rho$ is simply the correlation of the residual a consistent estimator for rho is to regress the residuals on the lagged residuals" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "resid_fit = sm.OLS(ols_resid[1:], sm.add_constant(ols_resid[:-1])).fit()\n", "print(resid_fit.tvalues[1])\n", "print(resid_fit.pvalues[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " While we do not have strong evidence that the errors follow an AR(1)\n", " process we continue" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "rho = resid_fit.params[1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we know, an AR(1) process means that near-neighbors have a stronger\n", " relation so we can give this structure by using a toeplitz matrix" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy.linalg import toeplitz\n", "\n", "toeplitz(range(5))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "order = toeplitz(range(len(ols_resid)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "so that our error covariance structure is actually rho**order\n", " which defines an autocorrelation structure" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sigma = rho**order\n", "gls_model = sm.GLS(data.endog, data.exog, sigma=sigma)\n", "gls_results = gls_model.fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course, the exact rho in this instance is not known so it it might make more sense to use feasible gls, which currently only has experimental support.\n", "\n", "We can use the GLSAR model with one lag, to get to a similar result:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "glsar_model = sm.GLSAR(data.endog, data.exog, 1)\n", "glsar_results = glsar_model.iterative_fit(1)\n", "print(glsar_results.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comparing gls and glsar results, we see that there are some small\n", " differences in the parameter estimates and the resulting standard\n", " errors of the parameter estimate. This might be do to the numerical\n", " differences in the algorithm, e.g. the treatment of initial conditions,\n", " because of the small number of observations in the longley dataset." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(gls_results.params)\n", "print(glsar_results.params)\n", "print(gls_results.bse)\n", "print(glsar_results.bse)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/influence_glm_logit.ipynb000066400000000000000000000125541400612667500250450ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Influence Measures for GLM Logit\n", "\n", "\n", "Based on draft version for GLMInfluence, which will also apply to discrete Logit, Probit and Poisson, and eventually be extended to cover most models outside of time series analysis.\n", "\n", "The example for logistic regression was used by Pregibon (1981) \"Logistic Regression diagnostics\" and is based on data by Finney (1947).\n", "\n", "GLMInfluence includes the basic influence measures but still misses some measures described in Pregibon (1981), for example those related to deviance and effects on confidence intervals." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import os.path\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "\n", "from statsmodels.genmod.generalized_linear_model import GLM\n", "from statsmodels.genmod import families\n", "plt.rc(\"figure\", figsize=(16,8))\n", "plt.rc(\"font\", size=14)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import statsmodels.stats.tests.test_influence\n", "test_module = statsmodels.stats.tests.test_influence.__file__\n", "cur_dir = cur_dir = os.path.abspath(os.path.dirname(test_module))\n", "\n", "file_name = 'binary_constrict.csv'\n", "file_path = os.path.join(cur_dir, 'results', file_name)\n", "df = pd.read_csv(file_path, index_col=0)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res = GLM(df['constrict'], df[['const', 'log_rate', 'log_volumne']],\n", " family=families.Binomial()).fit(attach_wls=True, atol=1e-10)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## get the influence measures\n", "\n", "GLMResults has a `get_influence` method similar to OLSResults, that returns and instance of the GLMInfluence class. This class has methods and (cached) attributes to inspect influence and outlier measures.\n", "\n", "This measures are based on a one-step approximation to the the results for deleting one observation. One-step approximations are usually accurate for small changes but underestimate the magnitude of large changes. Event though large changes are underestimated, they still show clearly the effect of influential observations\n", "\n", "In this example observation 4 and 18 have a large standardized residual and large Cook's distance, but not a large leverage. Observation 13 has the largest leverage but only small Cook's distance and not a large studentized residual.\n", "\n", "Only the two observations 4 and 18 have a large impact on the parameter estimates." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "infl = res.get_influence(observed=False)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "summ_df = infl.summary_frame()\n", "summ_df.sort_values('cooks_d', ascending=False)[:10]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig = infl.plot_influence()\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig = infl.plot_index(y_var='cooks', threshold=2 * infl.cooks_distance[0].mean())\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig = infl.plot_index(y_var='resid', threshold=1)\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig = infl.plot_index(y_var='dfbeta', idx=1, threshold=0.5)\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig = infl.plot_index(y_var='dfbeta', idx=2, threshold=0.5)\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig = infl.plot_index(y_var='dfbeta', idx=0, threshold=0.5)\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.4" } }, "nbformat": 4, "nbformat_minor": 1 }statsmodels-0.12.2/examples/notebooks/interactions_anova.ipynb000066400000000000000000000474741400612667500247370ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Interactions and ANOVA" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note: This script is based heavily on Jonathan Taylor's class notes https://web.stanford.edu/class/stats191/notebooks/Interactions.html\n", "\n", "Download and format data:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from urllib.request import urlopen\n", "import numpy as np\n", "np.set_printoptions(precision=4, suppress=True)\n", "\n", "import pandas as pd\n", "pd.set_option(\"display.width\", 100)\n", "import matplotlib.pyplot as plt\n", "from statsmodels.formula.api import ols\n", "from statsmodels.graphics.api import interaction_plot, abline_plot\n", "from statsmodels.stats.anova import anova_lm\n", "\n", "try:\n", " salary_table = pd.read_csv('salary.table')\n", "except: # recent pandas can read URL without urlopen\n", " url = 'http://stats191.stanford.edu/data/salary.table'\n", " fh = urlopen(url)\n", " salary_table = pd.read_table(fh)\n", " salary_table.to_csv('salary.table')\n", "\n", "E = salary_table.E\n", "M = salary_table.M\n", "X = salary_table.X\n", "S = salary_table.S" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Take a look at the data:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plt.figure(figsize=(6,6))\n", "symbols = ['D', '^']\n", "colors = ['r', 'g', 'blue']\n", "factor_groups = salary_table.groupby(['E','M'])\n", "for values, group in factor_groups:\n", " i,j = values\n", " plt.scatter(group['X'], group['S'], marker=symbols[j], color=colors[i-1],\n", " s=144)\n", "plt.xlabel('Experience');\n", "plt.ylabel('Salary');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit a linear model:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "formula = 'S ~ C(E) + C(M) + X'\n", "lm = ols(formula, salary_table).fit()\n", "print(lm.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Have a look at the created design matrix: " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "lm.model.exog[:5]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or since we initially passed in a DataFrame, we have a DataFrame available in" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "lm.model.data.orig_exog[:5]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We keep a reference to the original untouched data in" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "lm.model.data.frame[:5]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Influence statistics" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "infl = lm.get_influence()\n", "print(infl.summary_table())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or get a dataframe" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "df_infl = infl.summary_frame()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "df_infl[:5]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now plot the residuals within the groups separately:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "resid = lm.resid\n", "plt.figure(figsize=(6,6));\n", "for values, group in factor_groups:\n", " i,j = values\n", " group_num = i*2 + j - 1 # for plotting purposes\n", " x = [group_num] * len(group)\n", " plt.scatter(x, resid[group.index], marker=symbols[j], color=colors[i-1],\n", " s=144, edgecolors='black')\n", "plt.xlabel('Group');\n", "plt.ylabel('Residuals');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will test some interactions using anova or f_test" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "interX_lm = ols(\"S ~ C(E) * X + C(M)\", salary_table).fit()\n", "print(interX_lm.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Do an ANOVA check" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.stats.api import anova_lm\n", "\n", "table1 = anova_lm(lm, interX_lm)\n", "print(table1)\n", "\n", "interM_lm = ols(\"S ~ X + C(E)*C(M)\", data=salary_table).fit()\n", "print(interM_lm.summary())\n", "\n", "table2 = anova_lm(lm, interM_lm)\n", "print(table2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The design matrix as a DataFrame" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "interM_lm.model.data.orig_exog[:5]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The design matrix as an ndarray" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "interM_lm.model.exog\n", "interM_lm.model.exog_names" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "infl = interM_lm.get_influence()\n", "resid = infl.resid_studentized_internal\n", "plt.figure(figsize=(6,6))\n", "for values, group in factor_groups:\n", " i,j = values\n", " idx = group.index\n", " plt.scatter(X[idx], resid[idx], marker=symbols[j], color=colors[i-1],\n", " s=144, edgecolors='black')\n", "plt.xlabel('X');\n", "plt.ylabel('standardized resids');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks like one observation is an outlier." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "drop_idx = abs(resid).argmax()\n", "print(drop_idx) # zero-based index\n", "idx = salary_table.index.drop(drop_idx)\n", "\n", "lm32 = ols('S ~ C(E) + X + C(M)', data=salary_table, subset=idx).fit()\n", "\n", "print(lm32.summary())\n", "print('\\n')\n", "\n", "interX_lm32 = ols('S ~ C(E) * X + C(M)', data=salary_table, subset=idx).fit()\n", "\n", "print(interX_lm32.summary())\n", "print('\\n')\n", "\n", "\n", "table3 = anova_lm(lm32, interX_lm32)\n", "print(table3)\n", "print('\\n')\n", "\n", "\n", "interM_lm32 = ols('S ~ X + C(E) * C(M)', data=salary_table, subset=idx).fit()\n", "\n", "table4 = anova_lm(lm32, interM_lm32)\n", "print(table4)\n", "print('\\n')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Replot the residuals" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "resid = interM_lm32.get_influence().summary_frame()['standard_resid']\n", "\n", "plt.figure(figsize=(6,6))\n", "resid = resid.reindex(X.index)\n", "for values, group in factor_groups:\n", " i,j = values\n", " idx = group.index\n", " plt.scatter(X.loc[idx], resid.loc[idx], marker=symbols[j], color=colors[i-1],\n", " s=144, edgecolors='black')\n", "plt.xlabel('X[~[32]]');\n", "plt.ylabel('standardized resids');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Plot the fitted values" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "lm_final = ols('S ~ X + C(E)*C(M)', data = salary_table.drop([drop_idx])).fit()\n", "mf = lm_final.model.data.orig_exog\n", "lstyle = ['-','--']\n", "\n", "plt.figure(figsize=(6,6))\n", "for values, group in factor_groups:\n", " i,j = values\n", " idx = group.index\n", " plt.scatter(X[idx], S[idx], marker=symbols[j], color=colors[i-1],\n", " s=144, edgecolors='black')\n", " # drop NA because there is no idx 32 in the final model\n", " fv = lm_final.fittedvalues.reindex(idx).dropna()\n", " x = mf.X.reindex(idx).dropna()\n", " plt.plot(x, fv, ls=lstyle[j], color=colors[i-1])\n", "plt.xlabel('Experience');\n", "plt.ylabel('Salary');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From our first look at the data, the difference between Master's and PhD in the management group is different than in the non-management group. This is an interaction between the two qualitative variables management,M and education,E. We can visualize this by first removing the effect of experience, then plotting the means within each of the 6 groups using interaction.plot." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "U = S - X * interX_lm32.params['X']\n", "\n", "plt.figure(figsize=(6,6))\n", "interaction_plot(E, M, U, colors=['red','blue'], markers=['^','D'],\n", " markersize=10, ax=plt.gca())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Minority Employment Data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "try:\n", " jobtest_table = pd.read_table('jobtest.table')\n", "except: # do not have data already\n", " url = 'http://stats191.stanford.edu/data/jobtest.table'\n", " jobtest_table = pd.read_table(url)\n", "\n", "factor_group = jobtest_table.groupby(['MINORITY'])\n", "\n", "fig, ax = plt.subplots(figsize=(6,6))\n", "colors = ['purple', 'green']\n", "markers = ['o', 'v']\n", "for factor, group in factor_group:\n", " ax.scatter(group['TEST'], group['JPERF'], color=colors[factor],\n", " marker=markers[factor], s=12**2)\n", "ax.set_xlabel('TEST');\n", "ax.set_ylabel('JPERF');" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "min_lm = ols('JPERF ~ TEST', data=jobtest_table).fit()\n", "print(min_lm.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(6,6));\n", "for factor, group in factor_group:\n", " ax.scatter(group['TEST'], group['JPERF'], color=colors[factor],\n", " marker=markers[factor], s=12**2)\n", "\n", "ax.set_xlabel('TEST')\n", "ax.set_ylabel('JPERF')\n", "fig = abline_plot(model_results = min_lm, ax=ax)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "min_lm2 = ols('JPERF ~ TEST + TEST:MINORITY',\n", " data=jobtest_table).fit()\n", "\n", "print(min_lm2.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(6,6));\n", "for factor, group in factor_group:\n", " ax.scatter(group['TEST'], group['JPERF'], color=colors[factor],\n", " marker=markers[factor], s=12**2)\n", "\n", "fig = abline_plot(intercept = min_lm2.params['Intercept'],\n", " slope = min_lm2.params['TEST'], ax=ax, color='purple');\n", "fig = abline_plot(intercept = min_lm2.params['Intercept'],\n", " slope = min_lm2.params['TEST'] + min_lm2.params['TEST:MINORITY'],\n", " ax=ax, color='green');" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "min_lm3 = ols('JPERF ~ TEST + MINORITY', data = jobtest_table).fit()\n", "print(min_lm3.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(6,6));\n", "for factor, group in factor_group:\n", " ax.scatter(group['TEST'], group['JPERF'], color=colors[factor],\n", " marker=markers[factor], s=12**2)\n", "\n", "fig = abline_plot(intercept = min_lm3.params['Intercept'],\n", " slope = min_lm3.params['TEST'], ax=ax, color='purple');\n", "fig = abline_plot(intercept = min_lm3.params['Intercept'] + min_lm3.params['MINORITY'],\n", " slope = min_lm3.params['TEST'], ax=ax, color='green');" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "min_lm4 = ols('JPERF ~ TEST * MINORITY', data = jobtest_table).fit()\n", "print(min_lm4.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(8,6));\n", "for factor, group in factor_group:\n", " ax.scatter(group['TEST'], group['JPERF'], color=colors[factor],\n", " marker=markers[factor], s=12**2)\n", "\n", "fig = abline_plot(intercept = min_lm4.params['Intercept'],\n", " slope = min_lm4.params['TEST'], ax=ax, color='purple');\n", "fig = abline_plot(intercept = min_lm4.params['Intercept'] + min_lm4.params['MINORITY'],\n", " slope = min_lm4.params['TEST'] + min_lm4.params['TEST:MINORITY'],\n", " ax=ax, color='green');" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# is there any effect of MINORITY on slope or intercept?\n", "table5 = anova_lm(min_lm, min_lm4)\n", "print(table5)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# is there any effect of MINORITY on intercept\n", "table6 = anova_lm(min_lm, min_lm3)\n", "print(table6)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# is there any effect of MINORITY on slope\n", "table7 = anova_lm(min_lm, min_lm2)\n", "print(table7)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# is it just the slope or both?\n", "table8 = anova_lm(min_lm2, min_lm4)\n", "print(table8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## One-way ANOVA" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "try:\n", " rehab_table = pd.read_csv('rehab.table')\n", "except:\n", " url = 'http://stats191.stanford.edu/data/rehab.csv'\n", " rehab_table = pd.read_table(url, delimiter=\",\")\n", " rehab_table.to_csv('rehab.table')\n", "\n", "fig, ax = plt.subplots(figsize=(8,6))\n", "fig = rehab_table.boxplot('Time', 'Fitness', ax=ax, grid=False)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "rehab_lm = ols('Time ~ C(Fitness)', data=rehab_table).fit()\n", "table9 = anova_lm(rehab_lm)\n", "print(table9)\n", "\n", "print(rehab_lm.model.data.orig_exog)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(rehab_lm.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two-way ANOVA" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "try:\n", " kidney_table = pd.read_table('./kidney.table')\n", "except:\n", " url = 'http://stats191.stanford.edu/data/kidney.table'\n", " kidney_table = pd.read_csv(url, delim_whitespace=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Explore the dataset" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "kidney_table.head(10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Balanced panel" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "kt = kidney_table\n", "plt.figure(figsize=(8,6))\n", "fig = interaction_plot(kt['Weight'], kt['Duration'], np.log(kt['Days']+1),\n", " colors=['red', 'blue'], markers=['D','^'], ms=10, ax=plt.gca())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You have things available in the calling namespace available in the formula evaluation namespace" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "kidney_lm = ols('np.log(Days+1) ~ C(Duration) * C(Weight)', data=kt).fit()\n", "\n", "table10 = anova_lm(kidney_lm)\n", "\n", "print(anova_lm(ols('np.log(Days+1) ~ C(Duration) + C(Weight)',\n", " data=kt).fit(), kidney_lm))\n", "print(anova_lm(ols('np.log(Days+1) ~ C(Duration)', data=kt).fit(),\n", " ols('np.log(Days+1) ~ C(Duration) + C(Weight, Sum)',\n", " data=kt).fit()))\n", "print(anova_lm(ols('np.log(Days+1) ~ C(Weight)', data=kt).fit(),\n", " ols('np.log(Days+1) ~ C(Duration) + C(Weight, Sum)',\n", " data=kt).fit()))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sum of squares\n", "\n", " Illustrates the use of different types of sums of squares (I,II,II)\n", " and how the Sum contrast can be used to produce the same output between\n", " the 3.\n", "\n", " Types I and II are equivalent under a balanced design.\n", "\n", " Do not use Type III with non-orthogonal contrast - ie., Treatment" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sum_lm = ols('np.log(Days+1) ~ C(Duration, Sum) * C(Weight, Sum)',\n", " data=kt).fit()\n", "\n", "print(anova_lm(sum_lm))\n", "print(anova_lm(sum_lm, typ=2))\n", "print(anova_lm(sum_lm, typ=3))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "nosum_lm = ols('np.log(Days+1) ~ C(Duration, Treatment) * C(Weight, Treatment)',\n", " data=kt).fit()\n", "print(anova_lm(nosum_lm))\n", "print(anova_lm(nosum_lm, typ=2))\n", "print(anova_lm(nosum_lm, typ=3))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/kernel_density.ipynb000066400000000000000000000332451400612667500240570ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Kernel Density Estimation\n", "\n", "Kernel density estimation is the process of estimating an unknown probability density function using a *kernel function* $K(u)$. While a histogram counts the number of data points in somewhat arbitrary regions, a kernel density estimate is a function defined as the sum of a kernel function on every data point. The kernel function typically exhibits the following properties:\n", "\n", "1. Symmetry such that $K(u) = K(-u)$.\n", "2. Normalization such that $\\int_{-\\infty}^{\\infty} K(u) \\ du = 1$ .\n", "3. Monotonically decreasing such that $K'(u) < 0$ when $u > 0$.\n", "4. Expected value equal to zero such that $\\mathrm{E}[K] = 0$.\n", "\n", "For more information about kernel density estimation, see for instance [Wikipedia - Kernel density estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation).\n", "\n", "A univariate kernel density estimator is implemented in `sm.nonparametric.KDEUnivariate`.\n", "In this example we will show the following:\n", "\n", "* Basic usage, how to fit the estimator.\n", "* The effect of varying the bandwidth of the kernel using the `bw` argument.\n", "* The various kernel functions available using the `kernel` argument." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "from scipy import stats\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "from statsmodels.distributions.mixture_rvs import mixture_rvs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A univariate example" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.random.seed(12345) # Seed the random number generator for reproducible results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We create a bimodal distribution: a mixture of two normal distributions with locations at `-1` and `1`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Location, scale and weight for the two distributions\n", "dist1_loc, dist1_scale, weight1 = -1 , .5, .25\n", "dist2_loc, dist2_scale, weight2 = 1 , .5, .75\n", "\n", "# Sample from a mixture of distributions\n", "obs_dist = mixture_rvs(prob=[weight1, weight2], size=250,\n", " dist=[stats.norm, stats.norm],\n", " kwargs = (dict(loc=dist1_loc, scale=dist1_scale),\n", " dict(loc=dist2_loc, scale=dist2_scale)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The simplest non-parametric technique for density estimation is the histogram." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "\n", "# Scatter plot of data samples and histogram\n", "ax.scatter(obs_dist, np.abs(np.random.randn(obs_dist.size)),\n", " zorder=15, color='red', marker='x', alpha=0.5, label='Samples')\n", "lines = ax.hist(obs_dist, bins=20, edgecolor='k', label='Histogram')\n", "\n", "ax.legend(loc='best')\n", "ax.grid(True, zorder=-5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitting with the default arguments" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The histogram above is discontinuous. To compute a continuous probability density function,\n", "we can use kernel density estimation.\n", "\n", "We initialize a univariate kernel density estimator using `KDEUnivariate`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "kde = sm.nonparametric.KDEUnivariate(obs_dist)\n", "kde.fit() # Estimate the densities" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We present a figure of the fit, as well as the true distribution." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "\n", "# Plot the histrogram\n", "ax.hist(obs_dist, bins=20, density=True, label='Histogram from samples',\n", " zorder=5, edgecolor='k', alpha=0.5)\n", "\n", "# Plot the KDE as fitted using the default arguments\n", "ax.plot(kde.support, kde.density, lw=3, label='KDE from samples', zorder=10)\n", "\n", "# Plot the true distribution\n", "true_values = (stats.norm.pdf(loc=dist1_loc, scale=dist1_scale, x=kde.support)*weight1\n", " + stats.norm.pdf(loc=dist2_loc, scale=dist2_scale, x=kde.support)*weight2)\n", "ax.plot(kde.support, true_values, lw=3, label='True distribution', zorder=15)\n", "\n", "# Plot the samples\n", "ax.scatter(obs_dist, np.abs(np.random.randn(obs_dist.size))/40,\n", " marker='x', color='red', zorder=20, label='Samples', alpha=0.5)\n", "\n", "ax.legend(loc='best')\n", "ax.grid(True, zorder=-5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the code above, default arguments were used. We can also vary the bandwidth of the kernel, as we will now see." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Varying the bandwidth using the `bw` argument" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The bandwidth of the kernel can be adjusted using the `bw` argument.\n", "In the following example, a bandwidth of `bw=0.2` seems to fit the data well." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "\n", "# Plot the histrogram\n", "ax.hist(obs_dist, bins=25, label='Histogram from samples',\n", " zorder=5, edgecolor='k', density=True, alpha=0.5)\n", "\n", "# Plot the KDE for various bandwidths\n", "for bandwidth in [0.1, 0.2, 0.4]:\n", " kde.fit(bw=bandwidth) # Estimate the densities\n", " ax.plot(kde.support, kde.density, '--', lw=2, color='k', zorder=10,\n", " label='KDE from samples, bw = {}'.format(round(bandwidth, 2)))\n", "\n", "# Plot the true distribution\n", "ax.plot(kde.support, true_values, lw=3, label='True distribution', zorder=15)\n", "\n", "# Plot the samples\n", "ax.scatter(obs_dist, np.abs(np.random.randn(obs_dist.size))/50,\n", " marker='x', color='red', zorder=20, label='Data samples', alpha=0.5)\n", "\n", "ax.legend(loc='best')\n", "ax.set_xlim([-3, 3])\n", "ax.grid(True, zorder=-5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparing kernel functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the example above, a Gaussian kernel was used. Several other kernels are also available." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.nonparametric.kde import kernel_switch\n", "list(kernel_switch.keys())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The available kernel functions" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create a figure\n", "fig = plt.figure(figsize=(12, 5))\n", "\n", "# Enumerate every option for the kernel\n", "for i, (ker_name, ker_class) in enumerate(kernel_switch.items()):\n", "\n", " # Initialize the kernel object\n", " kernel = ker_class()\n", "\n", " # Sample from the domain\n", " domain = kernel.domain or [-3, 3]\n", " x_vals = np.linspace(*domain, num=2**10)\n", " y_vals = kernel(x_vals)\n", "\n", " # Create a subplot, set the title\n", " ax = fig.add_subplot(2, 4, i + 1)\n", " ax.set_title('Kernel function \"{}\"'.format(ker_name))\n", " ax.plot(x_vals, y_vals, lw=3, label='{}'.format(ker_name))\n", " ax.scatter([0], [0], marker='x', color='red')\n", " plt.grid(True, zorder=-5)\n", " ax.set_xlim(domain)\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The available kernel functions on three data points" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now examine how the kernel density estimate will fit to three equally spaced data points." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create three equidistant points\n", "data = np.linspace(-1, 1, 3)\n", "kde = sm.nonparametric.KDEUnivariate(data)\n", "\n", "# Create a figure\n", "fig = plt.figure(figsize=(12, 5))\n", "\n", "# Enumerate every option for the kernel\n", "for i, kernel in enumerate(kernel_switch.keys()):\n", "\n", " # Create a subplot, set the title\n", " ax = fig.add_subplot(2, 4, i + 1)\n", " ax.set_title('Kernel function \"{}\"'.format(kernel))\n", "\n", " # Fit the model (estimate densities)\n", " kde.fit(kernel=kernel, fft=False, gridsize=2**10)\n", "\n", " # Create the plot\n", " ax.plot(kde.support, kde.density, lw=3, label='KDE from samples', zorder=10)\n", " ax.scatter(data, np.zeros_like(data), marker='x', color='red')\n", " plt.grid(True, zorder=-5)\n", " ax.set_xlim([-3, 3])\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A more difficult case\n", "\n", "The fit is not always perfect. See the example below for a harder case." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "obs_dist = mixture_rvs([.25, .75], size=250, dist=[stats.norm, stats.beta],\n", " kwargs = (dict(loc=-1, scale=.5), dict(loc=1, scale=1, args=(1, .5))))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "kde = sm.nonparametric.KDEUnivariate(obs_dist)\n", "kde.fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "ax.hist(obs_dist, bins=20, density=True, edgecolor='k', zorder=4, alpha=0.5)\n", "ax.plot(kde.support, kde.density, lw=3, zorder=7)\n", "# Plot the samples\n", "ax.scatter(obs_dist, np.abs(np.random.randn(obs_dist.size))/50,\n", " marker='x', color='red', zorder=20, label='Data samples', alpha=0.5)\n", "ax.grid(True, zorder=-5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The KDE is a distribution\n", "\n", "Since the KDE is a distribution, we can access attributes and methods such as:\n", "\n", "- `entropy`\n", "- `evaluate`\n", "- `cdf`\n", "- `icdf`\n", "- `sf`\n", "- `cumhazard`" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "obs_dist = mixture_rvs([.25, .75], size=1000, dist=[stats.norm, stats.norm],\n", " kwargs = (dict(loc=-1, scale=.5), dict(loc=1, scale=.5)))\n", "kde = sm.nonparametric.KDEUnivariate(obs_dist)\n", "kde.fit(gridsize=2**10)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "kde.entropy" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "kde.evaluate(-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cumulative distribution, it's inverse, and the survival function" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "\n", "ax.plot(kde.support, kde.cdf, lw=3, label='CDF')\n", "ax.plot(np.linspace(0, 1, num = kde.icdf.size), kde.icdf, lw=3, label='Inverse CDF')\n", "ax.plot(kde.support, kde.sf, lw=3, label='Survival function')\n", "ax.legend(loc = 'best')\n", "ax.grid(True, zorder=-5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Cumulative Hazard Function" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "ax.plot(kde.support, kde.cumhazard, lw=3, label='Cumulative Hazard Function')\n", "ax.legend(loc = 'best')\n", "ax.grid(True, zorder=-5)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/markov_autoregression.ipynb000066400000000000000000000337661400612667500255000ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Markov switching autoregression models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook provides an example of the use of Markov switching models in statsmodels to replicate a number of results presented in Kim and Nelson (1999). It applies the Hamilton (1989) filter the Kim (1994) smoother.\n", "\n", "This is tested against the Markov-switching models from E-views 8, which can be found at http://www.eviews.com/EViews8/ev8ecswitch_n.html#MarkovAR or the Markov-switching models of Stata 14 which can be found at http://www.stata.com/manuals14/tsmswitch.pdf." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "import requests\n", "from io import BytesIO\n", "\n", "# NBER recessions\n", "from pandas_datareader.data import DataReader\n", "from datetime import datetime\n", "usrec = DataReader('USREC', 'fred', start=datetime(1947, 1, 1), end=datetime(2013, 4, 1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hamilton (1989) switching model of GNP\n", "\n", "This replicates Hamilton's (1989) seminal paper introducing Markov-switching models. The model is an autoregressive model of order 4 in which the mean of the process switches between two regimes. It can be written:\n", "\n", "$$\n", "y_t = \\mu_{S_t} + \\phi_1 (y_{t-1} - \\mu_{S_{t-1}}) + \\phi_2 (y_{t-2} - \\mu_{S_{t-2}}) + \\phi_3 (y_{t-3} - \\mu_{S_{t-3}}) + \\phi_4 (y_{t-4} - \\mu_{S_{t-4}}) + \\varepsilon_t\n", "$$\n", "\n", "Each period, the regime transitions according to the following matrix of transition probabilities:\n", "\n", "$$ P(S_t = s_t | S_{t-1} = s_{t-1}) =\n", "\\begin{bmatrix}\n", "p_{00} & p_{10} \\\\\n", "p_{01} & p_{11}\n", "\\end{bmatrix}\n", "$$\n", "\n", "where $p_{ij}$ is the probability of transitioning *from* regime $i$, *to* regime $j$.\n", "\n", "The model class is `MarkovAutoregression` in the time-series part of `statsmodels`. In order to create the model, we must specify the number of regimes with `k_regimes=2`, and the order of the autoregression with `order=4`. The default model also includes switching autoregressive coefficients, so here we also need to specify `switching_ar=False` to avoid that.\n", "\n", "After creation, the model is `fit` via maximum likelihood estimation. Under the hood, good starting parameters are found using a number of steps of the expectation maximization (EM) algorithm, and a quasi-Newton (BFGS) algorithm is applied to quickly find the maximum." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Get the RGNP data to replicate Hamilton\n", "dta = pd.read_stata('https://www.stata-press.com/data/r14/rgnp.dta').iloc[1:]\n", "dta.index = pd.DatetimeIndex(dta.date, freq='QS')\n", "dta_hamilton = dta.rgnp\n", "\n", "# Plot the data\n", "dta_hamilton.plot(title='Growth rate of Real GNP', figsize=(12,3))\n", "\n", "# Fit the model\n", "mod_hamilton = sm.tsa.MarkovAutoregression(dta_hamilton, k_regimes=2, order=4, switching_ar=False)\n", "res_hamilton = mod_hamilton.fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_hamilton.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We plot the filtered and smoothed probabilities of a recession. Filtered refers to an estimate of the probability at time $t$ based on data up to and including time $t$ (but excluding time $t+1, ..., T$). Smoothed refers to an estimate of the probability at time $t$ using all the data in the sample.\n", "\n", "For reference, the shaded periods represent the NBER recessions." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, axes = plt.subplots(2, figsize=(7,7))\n", "ax = axes[0]\n", "ax.plot(res_hamilton.filtered_marginal_probabilities[0])\n", "ax.fill_between(usrec.index, 0, 1, where=usrec['USREC'].values, color='k', alpha=0.1)\n", "ax.set_xlim(dta_hamilton.index[4], dta_hamilton.index[-1])\n", "ax.set(title='Filtered probability of recession')\n", "\n", "ax = axes[1]\n", "ax.plot(res_hamilton.smoothed_marginal_probabilities[0])\n", "ax.fill_between(usrec.index, 0, 1, where=usrec['USREC'].values, color='k', alpha=0.1)\n", "ax.set_xlim(dta_hamilton.index[4], dta_hamilton.index[-1])\n", "ax.set(title='Smoothed probability of recession')\n", "\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the estimated transition matrix we can calculate the expected duration of a recession versus an expansion." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(res_hamilton.expected_durations)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, it is expected that a recession will last about one year (4 quarters) and an expansion about two and a half years." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Kim, Nelson, and Startz (1998) Three-state Variance Switching\n", "\n", "This model demonstrates estimation with regime heteroskedasticity (switching of variances) and no mean effect. The dataset can be reached at http://econ.korea.ac.kr/~cjkim/MARKOV/data/ew_excs.prn.\n", "\n", "The model in question is:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\varepsilon_t \\\\\n", "\\varepsilon_t & \\sim N(0, \\sigma_{S_t}^2)\n", "\\end{align}\n", "$$\n", "\n", "Since there is no autoregressive component, this model can be fit using the `MarkovRegression` class. Since there is no mean effect, we specify `trend='nc'`. There are hypothesized to be three regimes for the switching variances, so we specify `k_regimes=3` and `switching_variance=True` (by default, the variance is assumed to be the same across regimes)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Get the dataset\n", "ew_excs = requests.get('http://econ.korea.ac.kr/~cjkim/MARKOV/data/ew_excs.prn').content\n", "raw = pd.read_table(BytesIO(ew_excs), header=None, skipfooter=1, engine='python')\n", "raw.index = pd.date_range('1926-01-01', '1995-12-01', freq='MS')\n", "\n", "dta_kns = raw.loc[:'1986'] - raw.loc[:'1986'].mean()\n", "\n", "# Plot the dataset\n", "dta_kns[0].plot(title='Excess returns', figsize=(12, 3))\n", "\n", "# Fit the model\n", "mod_kns = sm.tsa.MarkovRegression(dta_kns, k_regimes=3, trend='nc', switching_variance=True)\n", "res_kns = mod_kns.fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_kns.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we plot the probabilities of being in each of the regimes; only in a few periods is a high-variance regime probable." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, axes = plt.subplots(3, figsize=(10,7))\n", "\n", "ax = axes[0]\n", "ax.plot(res_kns.smoothed_marginal_probabilities[0])\n", "ax.set(title='Smoothed probability of a low-variance regime for stock returns')\n", "\n", "ax = axes[1]\n", "ax.plot(res_kns.smoothed_marginal_probabilities[1])\n", "ax.set(title='Smoothed probability of a medium-variance regime for stock returns')\n", "\n", "ax = axes[2]\n", "ax.plot(res_kns.smoothed_marginal_probabilities[2])\n", "ax.set(title='Smoothed probability of a high-variance regime for stock returns')\n", "\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Filardo (1994) Time-Varying Transition Probabilities\n", "\n", "This model demonstrates estimation with time-varying transition probabilities. The dataset can be reached at http://econ.korea.ac.kr/~cjkim/MARKOV/data/filardo.prn.\n", "\n", "In the above models we have assumed that the transition probabilities are constant across time. Here we allow the probabilities to change with the state of the economy. Otherwise, the model is the same Markov autoregression of Hamilton (1989).\n", "\n", "Each period, the regime now transitions according to the following matrix of time-varying transition probabilities:\n", "\n", "$$ P(S_t = s_t | S_{t-1} = s_{t-1}) =\n", "\\begin{bmatrix}\n", "p_{00,t} & p_{10,t} \\\\\n", "p_{01,t} & p_{11,t}\n", "\\end{bmatrix}\n", "$$\n", "\n", "where $p_{ij,t}$ is the probability of transitioning *from* regime $i$, *to* regime $j$ in period $t$, and is defined to be:\n", "\n", "$$\n", "p_{ij,t} = \\frac{\\exp\\{ x_{t-1}' \\beta_{ij} \\}}{1 + \\exp\\{ x_{t-1}' \\beta_{ij} \\}}\n", "$$\n", "\n", "Instead of estimating the transition probabilities as part of maximum likelihood, the regression coefficients $\\beta_{ij}$ are estimated. These coefficients relate the transition probabilities to a vector of pre-determined or exogenous regressors $x_{t-1}$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Get the dataset\n", "filardo = requests.get('http://econ.korea.ac.kr/~cjkim/MARKOV/data/filardo.prn').content\n", "dta_filardo = pd.read_table(BytesIO(filardo), sep=' +', header=None, skipfooter=1, engine='python')\n", "dta_filardo.columns = ['month', 'ip', 'leading']\n", "dta_filardo.index = pd.date_range('1948-01-01', '1991-04-01', freq='MS')\n", "\n", "dta_filardo['dlip'] = np.log(dta_filardo['ip']).diff()*100\n", "# Deflated pre-1960 observations by ratio of std. devs.\n", "# See hmt_tvp.opt or Filardo (1994) p. 302\n", "std_ratio = dta_filardo['dlip']['1960-01-01':].std() / dta_filardo['dlip'][:'1959-12-01'].std()\n", "dta_filardo['dlip'][:'1959-12-01'] = dta_filardo['dlip'][:'1959-12-01'] * std_ratio\n", "\n", "dta_filardo['dlleading'] = np.log(dta_filardo['leading']).diff()*100\n", "dta_filardo['dmdlleading'] = dta_filardo['dlleading'] - dta_filardo['dlleading'].mean()\n", "\n", "# Plot the data\n", "dta_filardo['dlip'].plot(title='Standardized growth rate of industrial production', figsize=(13,3))\n", "plt.figure()\n", "dta_filardo['dmdlleading'].plot(title='Leading indicator', figsize=(13,3));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The time-varying transition probabilities are specified by the `exog_tvtp` parameter.\n", "\n", "Here we demonstrate another feature of model fitting - the use of a random search for MLE starting parameters. Because Markov switching models are often characterized by many local maxima of the likelihood function, performing an initial optimization step can be helpful to find the best parameters.\n", "\n", "Below, we specify that 20 random perturbations from the starting parameter vector are examined and the best one used as the actual starting parameters. Because of the random nature of the search, we seed the random number generator beforehand to allow replication of the result." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod_filardo = sm.tsa.MarkovAutoregression(\n", " dta_filardo.iloc[2:]['dlip'], k_regimes=2, order=4, switching_ar=False,\n", " exog_tvtp=sm.add_constant(dta_filardo.iloc[1:-1]['dmdlleading']))\n", "\n", "np.random.seed(12345)\n", "res_filardo = mod_filardo.fit(search_reps=20)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_filardo.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we plot the smoothed probability of the economy operating in a low-production state, and again include the NBER recessions for comparison." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(12,3))\n", "\n", "ax.plot(res_filardo.smoothed_marginal_probabilities[0])\n", "ax.fill_between(usrec.index, 0, 1, where=usrec['USREC'].values, color='gray', alpha=0.2)\n", "ax.set_xlim(dta_filardo.index[6], dta_filardo.index[-1])\n", "ax.set(title='Smoothed probability of a low-production state');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the time-varying transition probabilities, we can see how the expected duration of a low-production state changes over time:\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_filardo.expected_durations[0].plot(\n", " title='Expected duration of a low-production state', figsize=(12,3));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "During recessions, the expected duration of a low-production state is much higher than in an expansion." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/markov_regression.ipynb000066400000000000000000000300331400612667500245670ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Markov switching dynamic regression models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook provides an example of the use of Markov switching models in statsmodels to estimate dynamic regression models with changes in regime. It follows the examples in the Stata Markov switching documentation, which can be found at http://www.stata.com/manuals14/tsmswitch.pdf." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "\n", "# NBER recessions\n", "from pandas_datareader.data import DataReader\n", "from datetime import datetime\n", "usrec = DataReader('USREC', 'fred', start=datetime(1947, 1, 1), end=datetime(2013, 4, 1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Federal funds rate with switching intercept\n", "\n", "The first example models the federal funds rate as noise around a constant intercept, but where the intercept changes during different regimes. The model is simply:\n", "\n", "$$r_t = \\mu_{S_t} + \\varepsilon_t \\qquad \\varepsilon_t \\sim N(0, \\sigma^2)$$\n", "\n", "where $S_t \\in \\{0, 1\\}$, and the regime transitions according to\n", "\n", "$$ P(S_t = s_t | S_{t-1} = s_{t-1}) =\n", "\\begin{bmatrix}\n", "p_{00} & p_{10} \\\\\n", "1 - p_{00} & 1 - p_{10}\n", "\\end{bmatrix}\n", "$$\n", "\n", "We will estimate the parameters of this model by maximum likelihood: $p_{00}, p_{10}, \\mu_0, \\mu_1, \\sigma^2$.\n", "\n", "The data used in this example can be found at https://www.stata-press.com/data/r14/usmacro." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Get the federal funds rate data\n", "from statsmodels.tsa.regime_switching.tests.test_markov_regression import fedfunds\n", "dta_fedfunds = pd.Series(fedfunds, index=pd.date_range('1954-07-01', '2010-10-01', freq='QS'))\n", "\n", "# Plot the data\n", "dta_fedfunds.plot(title='Federal funds rate', figsize=(12,3))\n", "\n", "# Fit the model\n", "# (a switching mean is the default of the MarkovRegession model)\n", "mod_fedfunds = sm.tsa.MarkovRegression(dta_fedfunds, k_regimes=2)\n", "res_fedfunds = mod_fedfunds.fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_fedfunds.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the summary output, the mean federal funds rate in the first regime (the \"low regime\") is estimated to be $3.7$ whereas in the \"high regime\" it is $9.6$. Below we plot the smoothed probabilities of being in the high regime. The model suggests that the 1980's was a time-period in which a high federal funds rate existed." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_fedfunds.smoothed_marginal_probabilities[1].plot(\n", " title='Probability of being in the high regime', figsize=(12,3));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the estimated transition matrix we can calculate the expected duration of a low regime versus a high regime." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(res_fedfunds.expected_durations)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A low regime is expected to persist for about fourteen years, whereas the high regime is expected to persist for only about five years." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Federal funds rate with switching intercept and lagged dependent variable\n", "\n", "The second example augments the previous model to include the lagged value of the federal funds rate.\n", "\n", "$$r_t = \\mu_{S_t} + r_{t-1} \\beta_{S_t} + \\varepsilon_t \\qquad \\varepsilon_t \\sim N(0, \\sigma^2)$$\n", "\n", "where $S_t \\in \\{0, 1\\}$, and the regime transitions according to\n", "\n", "$$ P(S_t = s_t | S_{t-1} = s_{t-1}) =\n", "\\begin{bmatrix}\n", "p_{00} & p_{10} \\\\\n", "1 - p_{00} & 1 - p_{10}\n", "\\end{bmatrix}\n", "$$\n", "\n", "We will estimate the parameters of this model by maximum likelihood: $p_{00}, p_{10}, \\mu_0, \\mu_1, \\beta_0, \\beta_1, \\sigma^2$." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Fit the model\n", "mod_fedfunds2 = sm.tsa.MarkovRegression(\n", " dta_fedfunds.iloc[1:], k_regimes=2, exog=dta_fedfunds.iloc[:-1])\n", "res_fedfunds2 = mod_fedfunds2.fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_fedfunds2.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are several things to notice from the summary output:\n", "\n", "1. The information criteria have decreased substantially, indicating that this model has a better fit than the previous model.\n", "2. The interpretation of the regimes, in terms of the intercept, have switched. Now the first regime has the higher intercept and the second regime has a lower intercept.\n", "\n", "Examining the smoothed probabilities of the high regime state, we now see quite a bit more variability." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_fedfunds2.smoothed_marginal_probabilities[0].plot(\n", " title='Probability of being in the high regime', figsize=(12,3));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, the expected durations of each regime have decreased quite a bit." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(res_fedfunds2.expected_durations)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Taylor rule with 2 or 3 regimes\n", "\n", "We now include two additional exogenous variables - a measure of the output gap and a measure of inflation - to estimate a switching Taylor-type rule with both 2 and 3 regimes to see which fits the data better.\n", "\n", "Because the models can be often difficult to estimate, for the 3-regime model we employ a search over starting parameters to improve results, specifying 20 random search repetitions." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Get the additional data\n", "from statsmodels.tsa.regime_switching.tests.test_markov_regression import ogap, inf\n", "dta_ogap = pd.Series(ogap, index=pd.date_range('1954-07-01', '2010-10-01', freq='QS'))\n", "dta_inf = pd.Series(inf, index=pd.date_range('1954-07-01', '2010-10-01', freq='QS'))\n", "\n", "exog = pd.concat((dta_fedfunds.shift(), dta_ogap, dta_inf), axis=1).iloc[4:]\n", "\n", "# Fit the 2-regime model\n", "mod_fedfunds3 = sm.tsa.MarkovRegression(\n", " dta_fedfunds.iloc[4:], k_regimes=2, exog=exog)\n", "res_fedfunds3 = mod_fedfunds3.fit()\n", "\n", "# Fit the 3-regime model\n", "np.random.seed(12345)\n", "mod_fedfunds4 = sm.tsa.MarkovRegression(\n", " dta_fedfunds.iloc[4:], k_regimes=3, exog=exog)\n", "res_fedfunds4 = mod_fedfunds4.fit(search_reps=20)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_fedfunds3.summary()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_fedfunds4.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Due to lower information criteria, we might prefer the 3-state model, with an interpretation of low-, medium-, and high-interest rate regimes. The smoothed probabilities of each regime are plotted below." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig, axes = plt.subplots(3, figsize=(10,7))\n", "\n", "ax = axes[0]\n", "ax.plot(res_fedfunds4.smoothed_marginal_probabilities[0])\n", "ax.set(title='Smoothed probability of a low-interest rate regime')\n", "\n", "ax = axes[1]\n", "ax.plot(res_fedfunds4.smoothed_marginal_probabilities[1])\n", "ax.set(title='Smoothed probability of a medium-interest rate regime')\n", "\n", "ax = axes[2]\n", "ax.plot(res_fedfunds4.smoothed_marginal_probabilities[2])\n", "ax.set(title='Smoothed probability of a high-interest rate regime')\n", "\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Switching variances\n", "\n", "We can also accommodate switching variances. In particular, we consider the model\n", "\n", "$$\n", "y_t = \\mu_{S_t} + y_{t-1} \\beta_{S_t} + \\varepsilon_t \\quad \\varepsilon_t \\sim N(0, \\sigma_{S_t}^2)\n", "$$\n", "\n", "We use maximum likelihood to estimate the parameters of this model: $p_{00}, p_{10}, \\mu_0, \\mu_1, \\beta_0, \\beta_1, \\sigma_0^2, \\sigma_1^2$.\n", "\n", "The application is to absolute returns on stocks, where the data can be found at https://www.stata-press.com/data/r14/snp500." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Get the federal funds rate data\n", "from statsmodels.tsa.regime_switching.tests.test_markov_regression import areturns\n", "dta_areturns = pd.Series(areturns, index=pd.date_range('2004-05-04', '2014-5-03', freq='W'))\n", "\n", "# Plot the data\n", "dta_areturns.plot(title='Absolute returns, S&P500', figsize=(12,3))\n", "\n", "# Fit the model\n", "mod_areturns = sm.tsa.MarkovRegression(\n", " dta_areturns.iloc[1:], k_regimes=2, exog=dta_areturns.iloc[:-1], switching_variance=True)\n", "res_areturns = mod_areturns.fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_areturns.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first regime is a low-variance regime and the second regime is a high-variance regime. Below we plot the probabilities of being in the low-variance regime. Between 2008 and 2012 there does not appear to be a clear indication of one regime guiding the economy." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "res_areturns.smoothed_marginal_probabilities[0].plot(\n", " title='Probability of being in a low-variance regime', figsize=(12,3));" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.3" } }, "nbformat": 4, "nbformat_minor": 0 } statsmodels-0.12.2/examples/notebooks/mediation_survival.ipynb000066400000000000000000000132401400612667500247350ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Mediation analysis with duration data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook demonstrates mediation analysis when the\n", "mediator and outcome are duration variables, modeled\n", "using proportional hazards regression. These examples\n", "are based on simulated data." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import statsmodels.api as sm\n", "from statsmodels.stats.mediation import Mediation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make the notebook reproducible." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.random.seed(3424)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Specify a sample size." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "n = 1000" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate an exposure variable." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 1 }, "outputs": [], "source": [ "exp = np.random.normal(size=n)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate a mediator variable." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 1 }, "outputs": [], "source": [ "def gen_mediator():\n", " mn = np.exp(exp)\n", " mtime0 = -mn * np.log(np.random.uniform(size=n))\n", " ctime = -2 * mn * np.log(np.random.uniform(size=n))\n", " mstatus = (ctime >= mtime0).astype(np.int)\n", " mtime = np.where(mtime0 <= ctime, mtime0, ctime)\n", " return mtime0, mtime, mstatus" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate an outcome variable." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 1 }, "outputs": [], "source": [ "def gen_outcome(otype, mtime0):\n", " if otype == \"full\":\n", " lp = 0.5*mtime0\n", " elif otype == \"no\":\n", " lp = exp\n", " else:\n", " lp = exp + mtime0\n", " mn = np.exp(-lp)\n", " ytime0 = -mn * np.log(np.random.uniform(size=n))\n", " ctime = -2 * mn * np.log(np.random.uniform(size=n))\n", " ystatus = (ctime >= ytime0).astype(np.int)\n", " ytime = np.where(ytime0 <= ctime, ytime0, ctime)\n", " return ytime, ystatus" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Build a dataframe containing all the relevant variables." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 1 }, "outputs": [], "source": [ "def build_df(ytime, ystatus, mtime0, mtime, mstatus):\n", " df = pd.DataFrame({\"ytime\": ytime, \"ystatus\": ystatus,\n", " \"mtime\": mtime, \"mstatus\": mstatus,\n", " \"exp\": exp})\n", " return df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run the full simulation and analysis, under a particular\n", "population structure of mediation." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 1 }, "outputs": [], "source": [ "def run(otype):\n", "\n", " mtime0, mtime, mstatus = gen_mediator()\n", " ytime, ystatus = gen_outcome(otype, mtime0)\n", " df = build_df(ytime, ystatus, mtime0, mtime, mstatus)\n", "\n", " outcome_model = sm.PHReg.from_formula(\"ytime ~ exp + mtime\", status=\"ystatus\", data=df)\n", " mediator_model = sm.PHReg.from_formula(\"mtime ~ exp\", status=\"mstatus\", data=df)\n", "\n", " med = Mediation(outcome_model, mediator_model, \"exp\", \"mtime\",\n", " outcome_predict_kwargs={\"pred_only\": True})\n", " med_result = med.fit(n_rep=20)\n", " print(med_result.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run the example with full mediation" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "run(\"full\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run the example with partial mediation" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "run(\"partial\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run the example with no mediation" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "run(\"no\")" ] } ], "metadata": { "jupytext": { "cell_metadata_filter": "-all", "main_language": "python", "notebook_metadata_filter": "-all" }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 2 } statsmodels-0.12.2/examples/notebooks/metaanalysis1.ipynb000066400000000000000000000475461400612667500236240ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Meta-Analysis in statsmodels\n", "\n", "Statsmodels include basic methods for meta-analysis. This notebook illustrates the current usage.\n", "\n", "Status: The results have been verified against R meta and metafor packages. However, the API is still experimental and will still change. Some options for additional methods that are available in R meta and metafor are missing.\n", "\n", "The support for meta-analysis has 3 parts:\n", "\n", "- effect size functions: this currently includes\n", " ``effectsize_smd`` computes effect size and their standard errors for standardized mean difference, \n", " ``effectsize_2proportions`` computes effect sizes for comparing two independent proportions using risk difference, (log) risk ratio, (log) odds-ratio or arcsine square root transformation\n", "- The `combine_effects` computes fixed and random effects estimate for the overall mean or effect. The returned results instance includes a forest plot function.\n", "- helper functions to estimate the random effect variance, tau-squared\n", "\n", "The estimate of the overall effect size in `combine_effects` can also be performed using WLS or GLM with var_weights.\n", "\n", "Finally, the meta-analysis functions currently do not include the Mantel-Hanszel method. However, the fixed effects results can be computed directly using `StratifiedTable` as illustrated below." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from scipy import stats, optimize\n", "\n", "from statsmodels.regression.linear_model import WLS\n", "from statsmodels.genmod.generalized_linear_model import GLM\n", "\n", "from statsmodels.stats.meta_analysis import (\n", " effectsize_smd, effectsize_2proportions, combine_effects,\n", " _fit_tau_iterative, _fit_tau_mm, _fit_tau_iter_mm)\n", "\n", "# increase line length for pandas\n", "pd.set_option('display.width', 100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = [\n", "[\"Carroll\", 94, 22,60,92, 20,60],\n", "[\"Grant\", 98, 21,65, 92,22, 65],\n", "[\"Peck\", 98, 28, 40,88 ,26, 40],\n", "[\"Donat\", 94,19, 200, 82,17, 200],\n", "[\"Stewart\", 98, 21,50, 88,22 , 45],\n", "[\"Young\", 96,21,85, 92 ,22, 85]]\n", "colnames = [\"study\",\"mean_t\",\"sd_t\",\"n_t\",\"mean_c\",\"sd_c\",\"n_c\"]\n", "rownames = [i[0] for i in data]\n", "dframe1 = pd.DataFrame(data, columns=colnames)\n", "rownames" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mean2, sd2, nobs2, mean1, sd1, nobs1 = np.asarray(dframe1[[\"mean_t\",\"sd_t\",\"n_t\",\"mean_c\",\"sd_c\",\"n_c\"]]).T\n", "rownames = dframe1[\"study\"]\n", "rownames.tolist()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.array(nobs1 + nobs2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### estimate effect size standardized mean difference" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "eff, var_eff = effectsize_smd(mean2, sd2, nobs2, mean1, sd1, nobs1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using one-step chi2, DerSimonian-Laird estimate for random effects variance tau\n", "\n", "Method option for random effect `method_re=\"chi2\"` or `method_re=\"dl\"`, both names are accepted.\n", "This is commonly referred to as the DerSimonian-Laird method, it is based on a moment estimator based on pearson chi2 from the fixed effects estimate." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res3 = combine_effects(eff, var_eff, method_re=\"chi2\", use_t=True, row_names=rownames)\n", "# TODO: we still need better information about conf_int of individual samples\n", "# We don't have enough information in the model for individual confidence intervals\n", "# if those are not based on normal distribution.\n", "res3.conf_int_samples(nobs=np.array(nobs1 + nobs2))\n", "print(res3.summary_frame())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res3.cache_ci" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res3.method_re" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = res3.plot_forest()\n", "fig.set_figheight(6)\n", "fig.set_figwidth(6)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res3 = combine_effects(eff, var_eff, method_re=\"chi2\", use_t=False, row_names=rownames)\n", "# TODO: we still need better information about conf_int of individual samples\n", "# We don't have enough information in the model for individual confidence intervals\n", "# if those are not based on normal distribution.\n", "res3.conf_int_samples(nobs=np.array(nobs1 + nobs2))\n", "print(res3.summary_frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using iterated, Paule-Mandel estimate for random effects variance tau\n", "\n", "The method commonly referred to as Paule-Mandel estimate is a method of moment estimate for the random effects variance that iterates between mean and variance estimate until convergence.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res4 = combine_effects(eff, var_eff, method_re=\"iterated\", use_t=False, row_names=rownames)\n", "res4_df = res4.summary_frame()\n", "print(\"method RE:\", res4.method_re)\n", "print(res4.summary_frame())\n", "fig = res4.plot_forest()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example Kacker interlaboratory mean\n", "\n", "In this example the effect size is the mean of measurements in a lab. We combine the estimates from several labs to estimate and overall average." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "eff = np.array([61.00, 61.40, 62.21, 62.30, 62.34, 62.60, 62.70,\n", " 62.84, 65.90])\n", "var_eff = np.array([0.2025, 1.2100, 0.0900, 0.2025, 0.3844, 0.5625,\n", " 0.0676, 0.0225, 1.8225])\n", "rownames = ['PTB', 'NMi', 'NIMC', 'KRISS', 'LGC', 'NRC', 'IRMM', 'NIST', 'LNE']" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res2_DL = combine_effects(eff, var_eff, method_re=\"dl\", use_t=True, row_names=rownames)\n", "print(\"method RE:\", res2_DL.method_re)\n", "print(res2_DL.summary_frame())\n", "fig = res2_DL.plot_forest()\n", "fig.set_figheight(6)\n", "fig.set_figwidth(6)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res2_PM = combine_effects(eff, var_eff, method_re=\"pm\", use_t=True, row_names=rownames)\n", "print(\"method RE:\", res2_PM.method_re)\n", "print(res2_PM.summary_frame())\n", "fig = res2_PM.plot_forest()\n", "fig.set_figheight(6)\n", "fig.set_figwidth(6)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Meta-analysis of proportions\n", "\n", "In the following example the random effect variance tau is estimated to be zero. \n", "I then change two counts in the data, so the second example has random effects variance greater than zero." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import io" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "\n", "ss = \"\"\"\\\n", " study,nei,nci,e1i,c1i,e2i,c2i,e3i,c3i,e4i,c4i\n", " 1,19,22,16.0,20.0,11,12,4.0,8.0,4,3\n", " 2,34,35,22.0,22.0,18,12,15.0,8.0,15,6\n", " 3,72,68,44.0,40.0,21,15,10.0,3.0,3,0\n", " 4,22,20,19.0,12.0,14,5,5.0,4.0,2,3\n", " 5,70,32,62.0,27.0,42,13,26.0,6.0,15,5\n", " 6,183,94,130.0,65.0,80,33,47.0,14.0,30,11\n", " 7,26,50,24.0,30.0,13,18,5.0,10.0,3,9\n", " 8,61,55,51.0,44.0,37,30,19.0,19.0,11,15\n", " 9,36,25,30.0,17.0,23,12,13.0,4.0,10,4\n", " 10,45,35,43.0,35.0,19,14,8.0,4.0,6,0\n", " 11,246,208,169.0,139.0,106,76,67.0,42.0,51,35\n", " 12,386,141,279.0,97.0,170,46,97.0,21.0,73,8\n", " 13,59,32,56.0,30.0,34,17,21.0,9.0,20,7\n", " 14,45,15,42.0,10.0,18,3,9.0,1.0,9,1\n", " 15,14,18,14.0,18.0,13,14,12.0,13.0,9,12\n", " 16,26,19,21.0,15.0,12,10,6.0,4.0,5,1\n", " 17,74,75,,,42,40,,,23,30\"\"\"\n", "df3 = pd.read_csv(io.StringIO(ss))\n", "df_12y = df3[[\"e2i\", \"nei\", \"c2i\", \"nci\"]]\n", "# TODO: currently 1 is reference, switch labels\n", "count1, nobs1, count2, nobs2 = df_12y.values.T\n", "dta = df_12y.values.T" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "eff, var_eff = effectsize_2proportions(*dta, statistic=\"rd\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "eff, var_eff" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res5 = combine_effects(eff, var_eff, method_re=\"iterated\", use_t=False)#, row_names=rownames)\n", "res5_df = res5.summary_frame()\n", "print(\"method RE:\", res5.method_re)\n", "print(\"RE variance tau2:\", res5.tau2)\n", "print(res5.summary_frame())\n", "fig = res5.plot_forest()\n", "fig.set_figheight(8)\n", "fig.set_figwidth(6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### changing data to have positive random effects variance" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dta_c = dta.copy()\n", "dta_c.T[0, 0] = 18\n", "dta_c.T[1, 0] = 22\n", "dta_c.T" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "eff, var_eff = effectsize_2proportions(*dta_c, statistic=\"rd\")\n", "res5 = combine_effects(eff, var_eff, method_re=\"iterated\", use_t=False)#, row_names=rownames)\n", "res5_df = res5.summary_frame()\n", "print(\"method RE:\", res5.method_re)\n", "print(res5.summary_frame())\n", "fig = res5.plot_forest()\n", "fig.set_figheight(8)\n", "fig.set_figwidth(6)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res5 = combine_effects(eff, var_eff, method_re=\"chi2\", use_t=False)\n", "res5_df = res5.summary_frame()\n", "print(\"method RE:\", res5.method_re)\n", "print(res5.summary_frame())\n", "fig = res5.plot_forest()\n", "fig.set_figheight(8)\n", "fig.set_figwidth(6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replicate fixed effect analysis using GLM with var_weights\n", "\n", "`combine_effects` computes weighted average estimates which can be replicated using GLM with var_weights or with WLS.\n", "The `scale` option in `GLM.fit` can be used to replicate fixed meta-analysis with fixed and with HKSJ/WLS scale" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.genmod.generalized_linear_model import GLM" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "eff, var_eff = effectsize_2proportions(*dta_c, statistic=\"or\")\n", "res = combine_effects(eff, var_eff, method_re=\"chi2\", use_t=False)\n", "res_frame = res.summary_frame()\n", "print(res_frame.iloc[-4:])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We need to fix scale=1 in order to replicate standard errors for the usual meta-analysis." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "weights = 1 / var_eff\n", "mod_glm = GLM(eff, np.ones(len(eff)),\n", " var_weights=weights)\n", "res_glm = mod_glm.fit(scale=1.)\n", "print(res_glm.summary().tables[1])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# check results\n", "res_glm.scale, res_glm.conf_int() - res_frame.loc[\"fixed effect\", [\"ci_low\", \"ci_upp\"]].values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using HKSJ variance adjustment in meta-analysis is equivalent to estimating the scale using pearson chi2, which is also the default for the gaussian family." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_glm = mod_glm.fit(scale=\"x2\")\n", "print(res_glm.summary().tables[1])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# check results\n", "res_glm.scale, res_glm.conf_int() - res_frame.loc[\"fixed effect\", [\"ci_low\", \"ci_upp\"]].values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mantel-Hanszel odds-ratio using contingency tables\n", "\n", "The fixed effect for the log-odds-ratio using the Mantel-Hanszel can be directly computed using StratifiedTable.\n", "\n", "We need to create a 2 x 2 x k contingency table to be used with `StratifiedTable`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "t, nt, c, nc = dta_c\n", "counts = np.column_stack([t, nt - t, c, nc - c])\n", "ctables = counts.T.reshape(2, 2, -1)\n", "ctables[:, :, 0]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "counts[0]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dta_c.T[0]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import statsmodels.stats.api as smstats" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "st = smstats.StratifiedTable(ctables.astype(np.float64))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "compare pooled log-odds-ratio and standard error to R meta package" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "st.logodds_pooled, st.logodds_pooled - 0.4428186730553189 # R meta" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "st.logodds_pooled_se, st.logodds_pooled_se - 0.08928560091027186 # R meta" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "st.logodds_pooled_confint()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(st.test_equal_odds())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(st.test_null_odds())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "check conversion to stratified contingency table\n", "\n", "Row sums of each table are the sample sizes for treatment and control experiments" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ctables.sum(1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "nt, nc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Results from R meta package**\n", "\n", "```\n", "> res_mb_hk = metabin(e2i, nei, c2i, nci, data=dat2, sm=\"OR\", Q.Cochrane=FALSE, method=\"MH\", method.tau=\"DL\", hakn=FALSE, backtransf=FALSE)\n", "> res_mb_hk\n", " logOR 95%-CI %W(fixed) %W(random)\n", "1 2.7081 [ 0.5265; 4.8896] 0.3 0.7\n", "2 1.2567 [ 0.2658; 2.2476] 2.1 3.2\n", "3 0.3749 [-0.3911; 1.1410] 5.4 5.4\n", "4 1.6582 [ 0.3245; 2.9920] 0.9 1.8\n", "5 0.7850 [-0.0673; 1.6372] 3.5 4.4\n", "6 0.3617 [-0.1528; 0.8762] 12.1 11.8\n", "7 0.5754 [-0.3861; 1.5368] 3.0 3.4\n", "8 0.2505 [-0.4881; 0.9892] 6.1 5.8\n", "9 0.6506 [-0.3877; 1.6889] 2.5 3.0\n", "10 0.0918 [-0.8067; 0.9903] 4.5 3.9\n", "11 0.2739 [-0.1047; 0.6525] 23.1 21.4\n", "12 0.4858 [ 0.0804; 0.8911] 18.6 18.8\n", "13 0.1823 [-0.6830; 1.0476] 4.6 4.2\n", "14 0.9808 [-0.4178; 2.3795] 1.3 1.6\n", "15 1.3122 [-1.0055; 3.6299] 0.4 0.6\n", "16 -0.2595 [-1.4450; 0.9260] 3.1 2.3\n", "17 0.1384 [-0.5076; 0.7844] 8.5 7.6\n", "\n", "Number of studies combined: k = 17\n", "\n", " logOR 95%-CI z p-value\n", "Fixed effect model 0.4428 [0.2678; 0.6178] 4.96 < 0.0001\n", "Random effects model 0.4295 [0.2504; 0.6086] 4.70 < 0.0001\n", "\n", "Quantifying heterogeneity:\n", " tau^2 = 0.0017 [0.0000; 0.4589]; tau = 0.0410 [0.0000; 0.6774];\n", " I^2 = 1.1% [0.0%; 51.6%]; H = 1.01 [1.00; 1.44]\n", "\n", "Test of heterogeneity:\n", " Q d.f. p-value\n", " 16.18 16 0.4404\n", "\n", "Details on meta-analytical method:\n", "- Mantel-Haenszel method\n", "- DerSimonian-Laird estimator for tau^2\n", "- Jackson method for confidence interval of tau^2 and tau\n", "\n", "> res_mb_hk$TE.fixed\n", "[1] 0.4428186730553189\n", "> res_mb_hk$seTE.fixed\n", "[1] 0.08928560091027186\n", "> c(res_mb_hk$lower.fixed, res_mb_hk$upper.fixed)\n", "[1] 0.2678221109331694 0.6178152351774684\n", " \n", "```\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(st.summary())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 2 }statsmodels-0.12.2/examples/notebooks/mixed_lm_example.ipynb000066400000000000000000000422731400612667500243520ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Linear Mixed Effects Models" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import statsmodels.formula.api as smf\n", "from statsmodels.tools.sm_exceptions import ConvergenceWarning" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note**: The R code and the results in this notebook has been converted to markdown so that R is not required to build the documents. The R results in the notebook were computed using R 3.5.1 and lme4 1.1." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```ipython\n", "%load_ext rpy2.ipython\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```ipython\n", "%R library(lme4)\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```\n", "array(['lme4', 'Matrix', 'tools', 'stats', 'graphics', 'grDevices',\n", " 'utils', 'datasets', 'methods', 'base'], dtype=' .2].values" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.3" } }, "nbformat": 4, "nbformat_minor": 0 }statsmodels-0.12.2/examples/notebooks/plots_boxplots.ipynb000066400000000000000000000227661400612667500241410ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Box Plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following illustrates some options for the boxplot in statsmodels. These include `violin_plot` and `bean_plot`." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import statsmodels.api as sm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bean Plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following example is taken from the docstring of `beanplot`.\n", "\n", "We use the American National Election Survey 1996 dataset, which has Party\n", "Identification of respondents as independent variable and (among other\n", "data) age as dependent variable." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = sm.datasets.anes96.load_pandas()\n", "party_ID = np.arange(7)\n", "labels = [\"Strong Democrat\", \"Weak Democrat\", \"Independent-Democrat\",\n", " \"Independent-Independent\", \"Independent-Republican\",\n", " \"Weak Republican\", \"Strong Republican\"]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Group age by party ID, and create a violin plot with it:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plt.rcParams['figure.subplot.bottom'] = 0.23 # keep labels visible\n", "plt.rcParams['figure.figsize'] = (10.0, 8.0) # make plot larger in notebook\n", "age = [data.exog['age'][data.endog == id] for id in party_ID]\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "plot_opts={'cutoff_val':5, 'cutoff_type':'abs',\n", " 'label_fontsize':'small',\n", " 'label_rotation':30}\n", "sm.graphics.beanplot(age, ax=ax, labels=labels,\n", " plot_opts=plot_opts)\n", "ax.set_xlabel(\"Party identification of respondent.\")\n", "ax.set_ylabel(\"Age\")\n", "#plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def beanplot(data, plot_opts={}, jitter=False):\n", " \"\"\"helper function to try out different plot options\n", " \"\"\"\n", " fig = plt.figure()\n", " ax = fig.add_subplot(111)\n", " plot_opts_ = {'cutoff_val':5, 'cutoff_type':'abs',\n", " 'label_fontsize':'small',\n", " 'label_rotation':30}\n", " plot_opts_.update(plot_opts)\n", " sm.graphics.beanplot(data, ax=ax, labels=labels,\n", " jitter=jitter, plot_opts=plot_opts_)\n", " ax.set_xlabel(\"Party identification of respondent.\")\n", " ax.set_ylabel(\"Age\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = beanplot(age, jitter=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = beanplot(age, plot_opts={'violin_width': 0.5, 'violin_fc':'#66c2a5'})" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = beanplot(age, plot_opts={'violin_fc':'#66c2a5'})" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = beanplot(age, plot_opts={'bean_size': 0.2, 'violin_width': 0.75, 'violin_fc':'#66c2a5'})" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = beanplot(age, jitter=True, plot_opts={'violin_fc':'#66c2a5'})" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = beanplot(age, jitter=True, plot_opts={'violin_width': 0.5, 'violin_fc':'#66c2a5'})" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Advanced Box Plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Based of example script `example_enhanced_boxplots.py` (by Ralf Gommers)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import statsmodels.api as sm\n", "\n", "\n", "# Necessary to make horizontal axis labels fit\n", "plt.rcParams['figure.subplot.bottom'] = 0.23\n", "\n", "data = sm.datasets.anes96.load_pandas()\n", "party_ID = np.arange(7)\n", "labels = [\"Strong Democrat\", \"Weak Democrat\", \"Independent-Democrat\",\n", " \"Independent-Independent\", \"Independent-Republican\",\n", " \"Weak Republican\", \"Strong Republican\"]\n", "\n", "# Group age by party ID.\n", "age = [data.exog['age'][data.endog == id] for id in party_ID]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create a violin plot.\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "\n", "sm.graphics.violinplot(age, ax=ax, labels=labels,\n", " plot_opts={'cutoff_val':5, 'cutoff_type':'abs',\n", " 'label_fontsize':'small',\n", " 'label_rotation':30})\n", "\n", "ax.set_xlabel(\"Party identification of respondent.\")\n", "ax.set_ylabel(\"Age\")\n", "ax.set_title(\"US national election '96 - Age & Party Identification\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create a bean plot.\n", "fig2 = plt.figure()\n", "ax = fig2.add_subplot(111)\n", "\n", "sm.graphics.beanplot(age, ax=ax, labels=labels,\n", " plot_opts={'cutoff_val':5, 'cutoff_type':'abs',\n", " 'label_fontsize':'small',\n", " 'label_rotation':30})\n", "\n", "ax.set_xlabel(\"Party identification of respondent.\")\n", "ax.set_ylabel(\"Age\")\n", "ax.set_title(\"US national election '96 - Age & Party Identification\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create a jitter plot.\n", "fig3 = plt.figure()\n", "ax = fig3.add_subplot(111)\n", "\n", "plot_opts={'cutoff_val':5, 'cutoff_type':'abs', 'label_fontsize':'small',\n", " 'label_rotation':30, 'violin_fc':(0.8, 0.8, 0.8),\n", " 'jitter_marker':'.', 'jitter_marker_size':3, 'bean_color':'#FF6F00',\n", " 'bean_mean_color':'#009D91'}\n", "sm.graphics.beanplot(age, ax=ax, labels=labels, jitter=True,\n", " plot_opts=plot_opts)\n", "\n", "ax.set_xlabel(\"Party identification of respondent.\")\n", "ax.set_ylabel(\"Age\")\n", "ax.set_title(\"US national election '96 - Age & Party Identification\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create an asymmetrical jitter plot.\n", "ix = data.exog['income'] < 16 # incomes < $30k\n", "age = data.exog['age'][ix]\n", "endog = data.endog[ix]\n", "age_lower_income = [age[endog == id] for id in party_ID]\n", "\n", "ix = data.exog['income'] >= 20 # incomes > $50k\n", "age = data.exog['age'][ix]\n", "endog = data.endog[ix]\n", "age_higher_income = [age[endog == id] for id in party_ID]\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "\n", "plot_opts['violin_fc'] = (0.5, 0.5, 0.5)\n", "plot_opts['bean_show_mean'] = False\n", "plot_opts['bean_show_median'] = False\n", "plot_opts['bean_legend_text'] = 'Income < \\$30k'\n", "plot_opts['cutoff_val'] = 10\n", "sm.graphics.beanplot(age_lower_income, ax=ax, labels=labels, side='left',\n", " jitter=True, plot_opts=plot_opts)\n", "plot_opts['violin_fc'] = (0.7, 0.7, 0.7)\n", "plot_opts['bean_color'] = '#009D91'\n", "plot_opts['bean_legend_text'] = 'Income > \\$50k'\n", "sm.graphics.beanplot(age_higher_income, ax=ax, labels=labels, side='right',\n", " jitter=True, plot_opts=plot_opts)\n", "\n", "ax.set_xlabel(\"Party identification of respondent.\")\n", "ax.set_ylabel(\"Age\")\n", "ax.set_title(\"US national election '96 - Age & Party Identification\")\n", "\n", "\n", "# Show all plots.\n", "#plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/predict.ipynb000066400000000000000000000105051400612667500224640ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Prediction (out of sample)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import statsmodels.api as sm\n", "\n", "plt.rc(\"figure\", figsize=(16,8))\n", "plt.rc(\"font\", size=14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Artificial data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "nsample = 50\n", "sig = 0.25\n", "x1 = np.linspace(0, 20, nsample)\n", "X = np.column_stack((x1, np.sin(x1), (x1-5)**2))\n", "X = sm.add_constant(X)\n", "beta = [5., 0.5, 0.5, -0.02]\n", "y_true = np.dot(X, beta)\n", "y = y_true + sig * np.random.normal(size=nsample)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimation " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "olsmod = sm.OLS(y, X)\n", "olsres = olsmod.fit()\n", "print(olsres.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## In-sample prediction" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ypred = olsres.predict(X)\n", "print(ypred)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create a new sample of explanatory variables Xnew, predict and plot" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "x1n = np.linspace(20.5,25, 10)\n", "Xnew = np.column_stack((x1n, np.sin(x1n), (x1n-5)**2))\n", "Xnew = sm.add_constant(Xnew)\n", "ynewpred = olsres.predict(Xnew) # predict out of sample\n", "print(ynewpred)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot comparison" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(x1, y, 'o', label=\"Data\")\n", "ax.plot(x1, y_true, 'b-', label=\"True\")\n", "ax.plot(np.hstack((x1, x1n)), np.hstack((ypred, ynewpred)), 'r', label=\"OLS prediction\")\n", "ax.legend(loc=\"best\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Predicting with Formulas" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using formulas can make both estimation and prediction a lot easier" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.formula.api import ols\n", "\n", "data = {\"x1\" : x1, \"y\" : y}\n", "\n", "res = ols(\"y ~ x1 + np.sin(x1) + I((x1-5)**2)\", data=data).fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the `I` to indicate use of the Identity transform. Ie., we do not want any expansion magic from using `**2`" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res.params" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we only have to pass the single variable and we get the transformed right-hand side variables automatically" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res.predict(exog=dict(x1=x1n))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 }statsmodels-0.12.2/examples/notebooks/quantile_regression.ipynb000066400000000000000000000142451400612667500251210ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Quantile regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "This example page shows how to use ``statsmodels``' ``QuantReg`` class to replicate parts of the analysis published in \n", "\n", "* Koenker, Roger and Kevin F. Hallock. \"Quantile Regression\". Journal of Economic Perspectives, Volume 15, Number 4, Fall 2001, Pages 143–156\n", "\n", "We are interested in the relationship between income and expenditures on food for a sample of working class Belgian households in 1857 (the Engel data). \n", "\n", "## Setup\n", "\n", "We first need to load some modules and to retrieve the data. Conveniently, the Engel dataset is shipped with ``statsmodels``." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import statsmodels.formula.api as smf\n", "import matplotlib.pyplot as plt\n", "\n", "data = sm.datasets.engel.load_pandas().data\n", "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Least Absolute Deviation\n", "\n", "The LAD model is a special case of quantile regression where q=0.5" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = smf.quantreg('foodexp ~ income', data)\n", "res = mod.fit(q=.5)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualizing the results\n", "\n", "We estimate the quantile regression model for many quantiles between .05 and .95, and compare best fit line from each of these models to Ordinary Least Squares results. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Prepare data for plotting\n", "\n", "For convenience, we place the quantile regression results in a Pandas DataFrame, and the OLS results in a dictionary." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "quantiles = np.arange(.05, .96, .1)\n", "def fit_model(q):\n", " res = mod.fit(q=q)\n", " return [q, res.params['Intercept'], res.params['income']] + \\\n", " res.conf_int().loc['income'].tolist()\n", " \n", "models = [fit_model(x) for x in quantiles]\n", "models = pd.DataFrame(models, columns=['q', 'a', 'b', 'lb', 'ub'])\n", "\n", "ols = smf.ols('foodexp ~ income', data).fit()\n", "ols_ci = ols.conf_int().loc['income'].tolist()\n", "ols = dict(a = ols.params['Intercept'],\n", " b = ols.params['income'],\n", " lb = ols_ci[0],\n", " ub = ols_ci[1])\n", "\n", "print(models)\n", "print(ols)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### First plot\n", "\n", "This plot compares best fit lines for 10 quantile regression models to the least squares fit. As Koenker and Hallock (2001) point out, we see that:\n", "\n", "1. Food expenditure increases with income\n", "2. The *dispersion* of food expenditure increases with income\n", "3. The least squares estimates fit low income observations quite poorly (i.e. the OLS line passes over most low income households)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "x = np.arange(data.income.min(), data.income.max(), 50)\n", "get_y = lambda a, b: a + b * x\n", "\n", "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "for i in range(models.shape[0]):\n", " y = get_y(models.a[i], models.b[i])\n", " ax.plot(x, y, linestyle='dotted', color='grey')\n", " \n", "y = get_y(ols['a'], ols['b'])\n", "\n", "ax.plot(x, y, color='red', label='OLS')\n", "ax.scatter(data.income, data.foodexp, alpha=.2)\n", "ax.set_xlim((240, 3000))\n", "ax.set_ylim((240, 2000))\n", "legend = ax.legend()\n", "ax.set_xlabel('Income', fontsize=16)\n", "ax.set_ylabel('Food expenditure', fontsize=16);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Second plot\n", "\n", "The dotted black lines form 95% point-wise confidence band around 10 quantile regression estimates (solid black line). The red lines represent OLS regression results along with their 95% confidence interval.\n", "\n", "In most cases, the quantile regression point estimates lie outside the OLS confidence interval, which suggests that the effect of income on food expenditure may not be constant across the distribution." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "n = models.shape[0]\n", "p1 = plt.plot(models.q, models.b, color='black', label='Quantile Reg.')\n", "p2 = plt.plot(models.q, models.ub, linestyle='dotted', color='black')\n", "p3 = plt.plot(models.q, models.lb, linestyle='dotted', color='black')\n", "p4 = plt.plot(models.q, [ols['b']] * n, color='red', label='OLS')\n", "p5 = plt.plot(models.q, [ols['lb']] * n, linestyle='dotted', color='red')\n", "p6 = plt.plot(models.q, [ols['ub']] * n, linestyle='dotted', color='red')\n", "plt.ylabel(r'$\\beta_{income}$')\n", "plt.xlabel('Quantiles of the conditional food expenditure distribution')\n", "plt.legend()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/quasibinomial.ipynb000066400000000000000000000132061400612667500236700ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Quasi-binomial regression\n", "\n", "This notebook demonstrates using custom variance functions and non-binary data\n", "with the quasi-binomial GLM family to perform a regression analysis using\n", "a dependent variable that is a proportion.\n", "\n", "The notebook uses the barley leaf blotch data that has been discussed in\n", "several textbooks. See below for one reference:\n", "\n", "https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_glimmix_sect016.htm" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import statsmodels.api as sm\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from io import StringIO" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The raw data, expressed as percentages. We will divide by 100\n", "to obtain proportions." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "raw = StringIO(\"\"\"0.05,0.00,1.25,2.50,5.50,1.00,5.00,5.00,17.50\n", "0.00,0.05,1.25,0.50,1.00,5.00,0.10,10.00,25.00\n", "0.00,0.05,2.50,0.01,6.00,5.00,5.00,5.00,42.50\n", "0.10,0.30,16.60,3.00,1.10,5.00,5.00,5.00,50.00\n", "0.25,0.75,2.50,2.50,2.50,5.00,50.00,25.00,37.50\n", "0.05,0.30,2.50,0.01,8.00,5.00,10.00,75.00,95.00\n", "0.50,3.00,0.00,25.00,16.50,10.00,50.00,50.00,62.50\n", "1.30,7.50,20.00,55.00,29.50,5.00,25.00,75.00,95.00\n", "1.50,1.00,37.50,5.00,20.00,50.00,50.00,75.00,95.00\n", "1.50,12.70,26.25,40.00,43.50,75.00,75.00,75.00,95.00\"\"\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The regression model is a two-way additive model with\n", "site and variety effects. The data are a full unreplicated\n", "design with 10 rows (sites) and 9 columns (varieties)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "df = pd.read_csv(raw, header=None)\n", "df = df.melt()\n", "df[\"site\"] = 1 + np.floor(df.index / 10).astype(np.int)\n", "df[\"variety\"] = 1 + (df.index % 10)\n", "df = df.rename(columns={\"value\": \"blotch\"})\n", "df = df.drop(\"variable\", axis=1)\n", "df[\"blotch\"] /= 100" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit the quasi-binomial regression with the standard variance\n", "function." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model1 = sm.GLM.from_formula(\"blotch ~ 0 + C(variety) + C(site)\",\n", " family=sm.families.Binomial(), data=df)\n", "result1 = model1.fit(scale=\"X2\")\n", "print(result1.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot below shows that the default variance function is\n", "not capturing the variance structure very well. Also note\n", "that the scale parameter estimate is quite small." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 1 }, "outputs": [], "source": [ "plt.clf()\n", "plt.grid(True)\n", "plt.plot(result1.predict(linear=True), result1.resid_pearson, 'o')\n", "plt.xlabel(\"Linear predictor\")\n", "plt.ylabel(\"Residual\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An alternative variance function is mu^2 * (1 - mu)^2." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 1 }, "outputs": [], "source": [ "class vf(sm.families.varfuncs.VarianceFunction):\n", " def __call__(self, mu):\n", " return mu**2 * (1 - mu)**2\n", "\n", " def deriv(self, mu):\n", " return 2*mu - 6*mu**2 + 4*mu**3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit the quasi-binomial regression with the alternative variance\n", "function." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "bin = sm.families.Binomial()\n", "bin.variance = vf()\n", "model2 = sm.GLM.from_formula(\"blotch ~ 0 + C(variety) + C(site)\", family=bin, data=df)\n", "result2 = model2.fit(scale=\"X2\")\n", "print(result2.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the alternative variance function, the mean/variance relationship\n", "seems to capture the data well, and the estimated scale parameter is\n", "close to 1." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plt.clf()\n", "plt.grid(True)\n", "plt.plot(result2.predict(linear=True), result2.resid_pearson, 'o')\n", "plt.xlabel(\"Linear predictor\")\n", "plt.ylabel(\"Residual\")" ] } ], "metadata": { "jupytext": { "cell_metadata_filter": "-all", "main_language": "python", "notebook_metadata_filter": "-all" }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 2 } statsmodels-0.12.2/examples/notebooks/recursive_ls.ipynb000066400000000000000000000232021400612667500235350ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Recursive least squares\n", "\n", "Recursive least squares is an expanding window version of ordinary least squares. In addition to availability of regression coefficients computed recursively, the recursively computed residuals the construction of statistics to investigate parameter instability.\n", "\n", "The `RecursiveLS` class allows computation of recursive residuals and computes CUSUM and CUSUM of squares statistics. Plotting these statistics along with reference lines denoting statistically significant deviations from the null hypothesis of stable parameters allows an easy visual indication of parameter stability.\n", "\n", "Finally, the `RecursiveLS` model allows imposing linear restrictions on the parameter vectors, and can be constructed using the formula interface." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "from pandas_datareader.data import DataReader\n", "\n", "np.set_printoptions(suppress=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1: Copper\n", "\n", "We first consider parameter stability in the copper dataset (description below)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(sm.datasets.copper.DESCRLONG)\n", "\n", "dta = sm.datasets.copper.load_pandas().data\n", "dta.index = pd.date_range('1951-01-01', '1975-01-01', freq='AS')\n", "endog = dta['WORLDCONSUMPTION']\n", "\n", "# To the regressors in the dataset, we add a column of ones for an intercept\n", "exog = sm.add_constant(dta[['COPPERPRICE', 'INCOMEINDEX', 'ALUMPRICE', 'INVENTORYINDEX']])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, construct and fit the model, and print a summary. Although the `RLS` model computes the regression parameters recursively, so there are as many estimates as there are datapoints, the summary table only presents the regression parameters estimated on the entire sample; except for small effects from initialization of the recursions, these estimates are equivalent to OLS estimates." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = sm.RecursiveLS(endog, exog)\n", "res = mod.fit()\n", "\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The recursive coefficients are available in the `recursive_coefficients` attribute. Alternatively, plots can generated using the `plot_recursive_coefficient` method." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(res.recursive_coefficients.filtered[0])\n", "res.plot_recursive_coefficient(range(mod.k_exog), alpha=None, figsize=(10,6));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The CUSUM statistic is available in the `cusum` attribute, but usually it is more convenient to visually check for parameter stability using the `plot_cusum` method. In the plot below, the CUSUM statistic does not move outside of the 5% significance bands, so we fail to reject the null hypothesis of stable parameters at the 5% level." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(res.cusum)\n", "fig = res.plot_cusum();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another related statistic is the CUSUM of squares. It is available in the `cusum_squares` attribute, but it is similarly more convenient to check it visually, using the `plot_cusum_squares` method. In the plot below, the CUSUM of squares statistic does not move outside of the 5% significance bands, so we fail to reject the null hypothesis of stable parameters at the 5% level." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res.plot_cusum_squares();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Example 2: Quantity theory of money\n", "\n", "The quantity theory of money suggests that \"a given change in the rate of change in the quantity of money induces ... an equal change in the rate of price inflation\" (Lucas, 1980). Following Lucas, we examine the relationship between double-sided exponentially weighted moving averages of money growth and CPI inflation. Although Lucas found the relationship between these variables to be stable, more recently it appears that the relationship is unstable; see e.g. Sargent and Surico (2010)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "start = '1959-12-01'\n", "end = '2015-01-01'\n", "m2 = DataReader('M2SL', 'fred', start=start, end=end)\n", "cpi = DataReader('CPIAUCSL', 'fred', start=start, end=end)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def ewma(series, beta, n_window):\n", " nobs = len(series)\n", " scalar = (1 - beta) / (1 + beta)\n", " ma = []\n", " k = np.arange(n_window, 0, -1)\n", " weights = np.r_[beta**k, 1, beta**k[::-1]]\n", " for t in range(n_window, nobs - n_window):\n", " window = series.iloc[t - n_window:t + n_window+1].values\n", " ma.append(scalar * np.sum(weights * window))\n", " return pd.Series(ma, name=series.name, index=series.iloc[n_window:-n_window].index)\n", "\n", "m2_ewma = ewma(np.log(m2['M2SL'].resample('QS').mean()).diff().iloc[1:], 0.95, 10*4)\n", "cpi_ewma = ewma(np.log(cpi['CPIAUCSL'].resample('QS').mean()).diff().iloc[1:], 0.95, 10*4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After constructing the moving averages using the $\\beta = 0.95$ filter of Lucas (with a window of 10 years on either side), we plot each of the series below. Although they appear to move together prior for part of the sample, after 1990 they appear to diverge." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(13,3))\n", "\n", "ax.plot(m2_ewma, label='M2 Growth (EWMA)')\n", "ax.plot(cpi_ewma, label='CPI Inflation (EWMA)')\n", "ax.legend();" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "endog = cpi_ewma\n", "exog = sm.add_constant(m2_ewma)\n", "exog.columns = ['const', 'M2']\n", "\n", "mod = sm.RecursiveLS(endog, exog)\n", "res = mod.fit()\n", "\n", "print(res.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res.plot_recursive_coefficient(1, alpha=None);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The CUSUM plot now shows substantial deviation at the 5% level, suggesting a rejection of the null hypothesis of parameter stability." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res.plot_cusum();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, the CUSUM of squares shows substantial deviation at the 5% level, also suggesting a rejection of the null hypothesis of parameter stability." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res.plot_cusum_squares();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Example 3: Linear restrictions and formulas" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear restrictions\n", "\n", "It is not hard to implement linear restrictions, using the `constraints` parameter in constructing the model." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "endog = dta['WORLDCONSUMPTION']\n", "exog = sm.add_constant(dta[['COPPERPRICE', 'INCOMEINDEX', 'ALUMPRICE', 'INVENTORYINDEX']])\n", "\n", "mod = sm.RecursiveLS(endog, exog, constraints='COPPERPRICE = ALUMPRICE')\n", "res = mod.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Formula\n", "\n", "One could fit the same model using the class method `from_formula`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = sm.RecursiveLS.from_formula(\n", " 'WORLDCONSUMPTION ~ COPPERPRICE + INCOMEINDEX + ALUMPRICE + INVENTORYINDEX', dta,\n", " constraints='COPPERPRICE = ALUMPRICE')\n", "res = mod.fit()\n", "print(res.summary())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 1 }statsmodels-0.12.2/examples/notebooks/regression_diagnostics.ipynb000066400000000000000000000135341400612667500256060ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Regression diagnostics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This example file shows how to use a few of the ``statsmodels`` regression diagnostic tests in a real-life context. You can learn about more tests and find out more information about the tests here on the [Regression Diagnostics page.](https://www.statsmodels.org/stable/diagnostic.html)\n", "\n", "Note that most of the tests described here only return a tuple of numbers, without any annotation. A full description of outputs is always included in the docstring and in the online ``statsmodels`` documentation. For presentation purposes, we use the ``zip(name,test)`` construct to pretty-print short descriptions in the examples below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate a regression model" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.compat import lzip\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.formula.api as smf\n", "import statsmodels.stats.api as sms\n", "import matplotlib.pyplot as plt\n", "\n", "# Load data\n", "url = 'https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/master/csv/HistData/Guerry.csv'\n", "dat = pd.read_csv(url)\n", "\n", "# Fit regression model (using the natural log of one of the regressors)\n", "results = smf.ols('Lottery ~ Literacy + np.log(Pop1831)', data=dat).fit()\n", "\n", "# Inspect the results\n", "print(results.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Normality of the residuals" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Jarque-Bera test:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "name = ['Jarque-Bera', 'Chi^2 two-tail prob.', 'Skew', 'Kurtosis']\n", "test = sms.jarque_bera(results.resid)\n", "lzip(name, test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Omni test:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "name = ['Chi^2', 'Two-tail probability']\n", "test = sms.omni_normtest(results.resid)\n", "lzip(name, test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Influence tests\n", "\n", "Once created, an object of class ``OLSInfluence`` holds attributes and methods that allow users to assess the influence of each observation. For example, we can compute and extract the first few rows of DFbetas by:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.stats.outliers_influence import OLSInfluence\n", "test_class = OLSInfluence(results)\n", "test_class.dfbetas[:5,:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Explore other options by typing ``dir(influence_test)``\n", "\n", "Useful information on leverage can also be plotted:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.graphics.regressionplots import plot_leverage_resid2\n", "fig, ax = plt.subplots(figsize=(8,6))\n", "fig = plot_leverage_resid2(results, ax = ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Other plotting options can be found on the [Graphics page.](https://www.statsmodels.org/stable/graphics.html)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multicollinearity\n", "\n", "Condition number:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.linalg.cond(results.model.exog)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Heteroskedasticity tests\n", "\n", "Breush-Pagan test:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "name = ['Lagrange multiplier statistic', 'p-value',\n", " 'f-value', 'f p-value']\n", "test = sms.het_breuschpagan(results.resid, results.model.exog)\n", "lzip(name, test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Goldfeld-Quandt test" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "name = ['F statistic', 'p-value']\n", "test = sms.het_goldfeldquandt(results.resid, results.model.exog)\n", "lzip(name, test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linearity\n", "\n", "Harvey-Collier multiplier test for Null hypothesis that the linear specification is correct:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "name = ['t value', 'p value']\n", "test = sms.linear_harvey_collier(results)\n", "lzip(name, test)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/regression_plots.ipynb000066400000000000000000000407751400612667500244470ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Regression Plots" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from statsmodels.compat import lzip\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import statsmodels.api as sm\n", "from statsmodels.formula.api import ols\n", "\n", "plt.rc(\"figure\", figsize=(16,8))\n", "plt.rc(\"font\", size=14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Duncan's Prestige Dataset" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Load the Data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use a utility function to load any R dataset available from the great Rdatasets package." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "prestige = sm.datasets.get_rdataset(\"Duncan\", \"carData\", cache=True).data" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "prestige.head()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "prestige_model = ols(\"prestige ~ income + education\", data=prestige).fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "print(prestige_model.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Influence plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Influence plots show the (externally) studentized residuals vs. the leverage of each observation as measured by the hat matrix.\n", "\n", "Externally studentized residuals are residuals that are scaled by their standard deviation where \n", "\n", "$$var(\\hat{\\epsilon}_i)=\\hat{\\sigma}^2_i(1-h_{ii})$$\n", "\n", "with\n", "\n", "$$\\hat{\\sigma}^2_i=\\frac{1}{n - p - 1 \\;\\;}\\sum_{j}^{n}\\;\\;\\;\\forall \\;\\;\\; j \\neq i$$\n", "\n", "$n$ is the number of observations and $p$ is the number of regressors. $h_{ii}$ is the $i$-th diagonal element of the hat matrix\n", "\n", "$$H=X(X^{\\;\\prime}X)^{-1}X^{\\;\\prime}$$\n", "\n", "The influence of each point can be visualized by the criterion keyword argument. Options are Cook's distance and DFFITS, two measures of influence." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fig = sm.graphics.influence_plot(prestige_model, criterion=\"cooks\")\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see there are a few worrisome observations. Both contractor and reporter have low leverage but a large residual.
\n", "RR.engineer has small residual and large leverage. Conductor and minister have both high leverage and large residuals, and,
\n", "therefore, large influence." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Partial Regression Plots (Duncan)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since we are doing multivariate regressions, we cannot just look at individual bivariate plots to discern relationships.
\n", "Instead, we want to look at the relationship of the dependent variable and independent variables conditional on the other
\n", "independent variables. We can do this through using partial regression plots, otherwise known as added variable plots.
\n", "\n", "In a partial regression plot, to discern the relationship between the response variable and the $k$-th variable, we compute
\n", "the residuals by regressing the response variable versus the independent variables excluding $X_k$. We can denote this by
\n", "$X_{\\sim k}$. We then compute the residuals by regressing $X_k$ on $X_{\\sim k}$. The partial regression plot is the plot
\n", "of the former versus the latter residuals.
\n", "\n", "The notable points of this plot are that the fitted line has slope $\\beta_k$ and intercept zero. The residuals of this plot
\n", "are the same as those of the least squares fit of the original model with full $X$. You can discern the effects of the
\n", "individual data values on the estimation of a coefficient easily. If obs_labels is True, then these points are annotated
\n", "with their observation label. You can also see the violation of underlying assumptions such as homoskedasticity and
\n", "linearity." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fig = sm.graphics.plot_partregress(\"prestige\", \"income\", [\"income\", \"education\"], data=prestige)\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fig = sm.graphics.plot_partregress(\"prestige\", \"income\", [\"education\"], data=prestige)\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see the partial regression plot confirms the influence of conductor, minister, and RR.engineer on the partial relationship between income and prestige. The cases greatly decrease the effect of income on prestige. Dropping these cases confirms this." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "subset = ~prestige.index.isin([\"conductor\", \"RR.engineer\", \"minister\"])\n", "prestige_model2 = ols(\"prestige ~ income + education\", data=prestige, subset=subset).fit()\n", "print(prestige_model2.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a quick check of all the regressors, you can use plot_partregress_grid. These plots will not label the
\n", "points, but you can use them to identify problems and then use plot_partregress to get more information." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fig = sm.graphics.plot_partregress_grid(prestige_model)\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Component-Component plus Residual (CCPR) Plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The CCPR plot provides a way to judge the effect of one regressor on the
\n", "response variable by taking into account the effects of the other
\n", "independent variables. The partial residuals plot is defined as
\n", "$\\text{Residuals} + B_iX_i \\text{ }\\text{ }$ versus $X_i$. The component adds $B_iX_i$ versus
\n", "$X_i$ to show where the fitted line would lie. Care should be taken if $X_i$
\n", "is highly correlated with any of the other independent variables. If this
\n", "is the case, the variance evident in the plot will be an underestimate of
\n", "the true variance." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fig = sm.graphics.plot_ccpr(prestige_model, \"education\")\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see the relationship between the variation in prestige explained by education conditional on income seems to be linear, though you can see there are some observations that are exerting considerable influence on the relationship. We can quickly look at more than one variable by using plot_ccpr_grid." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fig = sm.graphics.plot_ccpr_grid(prestige_model)\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Single Variable Regression Diagnostics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot_regress_exog function is a convenience function that gives a 2x2 plot containing the dependent variable and fitted values with confidence intervals vs. the independent variable chosen, the residuals of the model vs. the chosen independent variable, a partial regression plot, and a CCPR plot. This function can be used for quickly checking modeling assumptions with respect to a single regressor." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fig = sm.graphics.plot_regress_exog(prestige_model, \"education\")\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fit Plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot_fit function plots the fitted values versus a chosen independent variable. It includes prediction confidence intervals and optionally plots the true dependent variable." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fig = sm.graphics.plot_fit(prestige_model, \"education\")\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Statewide Crime 2009 Dataset" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare the following to http://www.ats.ucla.edu/stat/stata/webbooks/reg/chapter4/statareg_self_assessment_answers4.htm\n", "\n", "Though the data here is not the same as in that example. You could run that example by uncommenting the necessary cells below." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#dta = pd.read_csv(\"http://www.stat.ufl.edu/~aa/social/csv_files/statewide-crime-2.csv\")\n", "#dta = dta.set_index(\"State\", inplace=True).dropna()\n", "#dta.rename(columns={\"VR\" : \"crime\",\n", "# \"MR\" : \"murder\",\n", "# \"M\" : \"pctmetro\",\n", "# \"W\" : \"pctwhite\",\n", "# \"H\" : \"pcths\",\n", "# \"P\" : \"poverty\",\n", "# \"S\" : \"single\"\n", "# }, inplace=True)\n", "#\n", "#crime_model = ols(\"murder ~ pctmetro + poverty + pcths + single\", data=dta).fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "dta = sm.datasets.statecrime.load_pandas().data" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "crime_model = ols(\"murder ~ urban + poverty + hs_grad + single\", data=dta).fit()\n", "print(crime_model.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Partial Regression Plots (Crime Data)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fig = sm.graphics.plot_partregress_grid(crime_model)\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fig = sm.graphics.plot_partregress(\"murder\", \"hs_grad\", [\"urban\", \"poverty\", \"single\"], data=dta)\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Leverage-Resid2 Plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Closely related to the influence_plot is the leverage-resid2 plot." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fig = sm.graphics.plot_leverage_resid2(crime_model)\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Influence Plot" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fig = sm.graphics.influence_plot(crime_model)\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using robust regression to correct for outliers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Part of the problem here in recreating the Stata results is that M-estimators are not robust to leverage points. MM-estimators should do better with this examples." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from statsmodels.formula.api import rlm" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rob_crime_model = rlm(\"murder ~ urban + poverty + hs_grad + single\", data=dta, \n", " M=sm.robust.norms.TukeyBiweight(3)).fit(conv=\"weights\")\n", "print(rob_crime_model.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#rob_crime_model = rlm(\"murder ~ pctmetro + poverty + pcths + single\", data=dta, M=sm.robust.norms.TukeyBiweight()).fit(conv=\"weights\")\n", "#print(rob_crime_model.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is not yet an influence diagnostics method as part of RLM, but we can recreate them. (This depends on the status of [issue #888](https://github.com/statsmodels/statsmodels/issues/808))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "weights = rob_crime_model.weights\n", "idx = weights > 0\n", "X = rob_crime_model.model.exog[idx.values]\n", "ww = weights[idx] / weights[idx].mean()\n", "hat_matrix_diag = ww*(X*np.linalg.pinv(X).T).sum(1)\n", "resid = rob_crime_model.resid\n", "resid2 = resid**2\n", "resid2 /= resid2.sum()\n", "nobs = int(idx.sum())\n", "hm = hat_matrix_diag.mean()\n", "rm = resid2.mean()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from statsmodels.graphics import utils\n", "fig, ax = plt.subplots(figsize=(16,8))\n", "ax.plot(resid2[idx], hat_matrix_diag, 'o')\n", "ax = utils.annotate_axes(range(nobs), labels=rob_crime_model.model.data.row_labels[idx], \n", " points=lzip(resid2[idx], hat_matrix_diag), offset_points=[(-5,5)]*nobs,\n", " size=\"large\", ax=ax)\n", "ax.set_xlabel(\"resid2\")\n", "ax.set_ylabel(\"leverage\")\n", "ylim = ax.get_ylim()\n", "ax.vlines(rm, *ylim)\n", "xlim = ax.get_xlim()\n", "ax.hlines(hm, *xlim)\n", "ax.margins(0,0)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 1 }statsmodels-0.12.2/examples/notebooks/robust_models_0.ipynb000066400000000000000000000146241400612667500241400ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Robust Linear Models" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "from statsmodels.sandbox.regression.predstd import wls_prediction_std" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimation\n", "\n", "Load data:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = sm.datasets.stackloss.load(as_pandas=False)\n", "data.exog = sm.add_constant(data.exog)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Huber's T norm with the (default) median absolute deviation scaling" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "huber_t = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT())\n", "hub_results = huber_t.fit()\n", "print(hub_results.params)\n", "print(hub_results.bse)\n", "print(hub_results.summary(yname='y',\n", " xname=['var_%d' % i for i in range(len(hub_results.params))]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Huber's T norm with 'H2' covariance matrix" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "hub_results2 = huber_t.fit(cov=\"H2\")\n", "print(hub_results2.params)\n", "print(hub_results2.bse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Andrew's Wave norm with Huber's Proposal 2 scaling and 'H3' covariance matrix" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "andrew_mod = sm.RLM(data.endog, data.exog, M=sm.robust.norms.AndrewWave())\n", "andrew_results = andrew_mod.fit(scale_est=sm.robust.scale.HuberScale(), cov=\"H3\")\n", "print('Parameters: ', andrew_results.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "See ``help(sm.RLM.fit)`` for more options and ``module sm.robust.scale`` for scale options\n", "\n", "## Comparing OLS and RLM\n", "\n", "Artificial data with outliers:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "nsample = 50\n", "x1 = np.linspace(0, 20, nsample)\n", "X = np.column_stack((x1, (x1-5)**2))\n", "X = sm.add_constant(X)\n", "sig = 0.3 # smaller error variance makes OLS<->RLM contrast bigger\n", "beta = [5, 0.5, -0.0]\n", "y_true2 = np.dot(X, beta)\n", "y2 = y_true2 + sig*1. * np.random.normal(size=nsample)\n", "y2[[39,41,43,45,48]] -= 5 # add some outliers (10% of nsample)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 1: quadratic function with linear truth\n", "\n", "Note that the quadratic term in OLS regression will capture outlier effects. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res = sm.OLS(y2, X).fit()\n", "print(res.params)\n", "print(res.bse)\n", "print(res.predict())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Estimate RLM:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "resrlm = sm.RLM(y2, X).fit()\n", "print(resrlm.params)\n", "print(resrlm.bse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Draw a plot to compare OLS estimates to the robust estimates:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "ax.plot(x1, y2, 'o',label=\"data\")\n", "ax.plot(x1, y_true2, 'b-', label=\"True\")\n", "prstd, iv_l, iv_u = wls_prediction_std(res)\n", "ax.plot(x1, res.fittedvalues, 'r-', label=\"OLS\")\n", "ax.plot(x1, iv_u, 'r--')\n", "ax.plot(x1, iv_l, 'r--')\n", "ax.plot(x1, resrlm.fittedvalues, 'g.-', label=\"RLM\")\n", "ax.legend(loc=\"best\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 2: linear function with linear truth\n", "\n", "Fit a new OLS model using only the linear term and the constant:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "X2 = X[:,[0,1]]\n", "res2 = sm.OLS(y2, X2).fit()\n", "print(res2.params)\n", "print(res2.bse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Estimate RLM:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "resrlm2 = sm.RLM(y2, X2).fit()\n", "print(resrlm2.params)\n", "print(resrlm2.bse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Draw a plot to compare OLS estimates to the robust estimates:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "prstd, iv_l, iv_u = wls_prediction_std(res2)\n", "\n", "fig, ax = plt.subplots(figsize=(8,6))\n", "ax.plot(x1, y2, 'o', label=\"data\")\n", "ax.plot(x1, y_true2, 'b-', label=\"True\")\n", "ax.plot(x1, res2.fittedvalues, 'r-', label=\"OLS\")\n", "ax.plot(x1, iv_u, 'r--')\n", "ax.plot(x1, iv_l, 'r--')\n", "ax.plot(x1, resrlm2.fittedvalues, 'g.-', label=\"RLM\")\n", "legend = ax.legend(loc=\"best\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/robust_models_1.ipynb000066400000000000000000000557751400612667500241550ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# M-Estimators for Robust Linear Modeling" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.compat import lmap\n", "import numpy as np\n", "from scipy import stats\n", "import matplotlib.pyplot as plt\n", "\n", "import statsmodels.api as sm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* An M-estimator minimizes the function \n", "\n", "$$Q(e_i, \\rho) = \\sum_i~\\rho \\left (\\frac{e_i}{s}\\right )$$\n", "\n", "where $\\rho$ is a symmetric function of the residuals \n", "\n", "* The effect of $\\rho$ is to reduce the influence of outliers\n", "* $s$ is an estimate of scale. \n", "* The robust estimates $\\hat{\\beta}$ are computed by the iteratively re-weighted least squares algorithm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* We have several choices available for the weighting functions to be used" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "norms = sm.robust.norms" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def plot_weights(support, weights_func, xlabels, xticks):\n", " fig = plt.figure(figsize=(12,8))\n", " ax = fig.add_subplot(111)\n", " ax.plot(support, weights_func(support))\n", " ax.set_xticks(xticks)\n", " ax.set_xticklabels(xlabels, fontsize=16)\n", " ax.set_ylim(-.1, 1.1)\n", " return ax" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Andrew's Wave" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "help(norms.AndrewWave.weights)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "a = 1.339\n", "support = np.linspace(-np.pi*a, np.pi*a, 100)\n", "andrew = norms.AndrewWave(a=a)\n", "plot_weights(support, andrew.weights, ['$-\\pi*a$', '0', '$\\pi*a$'], [-np.pi*a, 0, np.pi*a]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hampel's 17A" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "help(norms.Hampel.weights)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "c = 8\n", "support = np.linspace(-3*c, 3*c, 1000)\n", "hampel = norms.Hampel(a=2., b=4., c=c)\n", "plot_weights(support, hampel.weights, ['3*c', '0', '3*c'], [-3*c, 0, 3*c]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Huber's t" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "help(norms.HuberT.weights)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "t = 1.345\n", "support = np.linspace(-3*t, 3*t, 1000)\n", "huber = norms.HuberT(t=t)\n", "plot_weights(support, huber.weights, ['-3*t', '0', '3*t'], [-3*t, 0, 3*t]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Least Squares" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "help(norms.LeastSquares.weights)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "support = np.linspace(-3, 3, 1000)\n", "lst_sq = norms.LeastSquares()\n", "plot_weights(support, lst_sq.weights, ['-3', '0', '3'], [-3, 0, 3]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Ramsay's Ea" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "help(norms.RamsayE.weights)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "a = .3\n", "support = np.linspace(-3*a, 3*a, 1000)\n", "ramsay = norms.RamsayE(a=a)\n", "plot_weights(support, ramsay.weights, ['-3*a', '0', '3*a'], [-3*a, 0, 3*a]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Trimmed Mean" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "help(norms.TrimmedMean.weights)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "c = 2\n", "support = np.linspace(-3*c, 3*c, 1000)\n", "trimmed = norms.TrimmedMean(c=c)\n", "plot_weights(support, trimmed.weights, ['-3*c', '0', '3*c'], [-3*c, 0, 3*c]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Tukey's Biweight" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "help(norms.TukeyBiweight.weights)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "c = 4.685\n", "support = np.linspace(-3*c, 3*c, 1000)\n", "tukey = norms.TukeyBiweight(c=c)\n", "plot_weights(support, tukey.weights, ['-3*c', '0', '3*c'], [-3*c, 0, 3*c]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Scale Estimators" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Robust estimates of the location" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "x = np.array([1, 2, 3, 4, 500])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* The mean is not a robust estimator of location" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "x.mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* The median, on the other hand, is a robust estimator with a breakdown point of 50%" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.median(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Analogously for the scale\n", "* The standard deviation is not robust" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "x.std()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Median Absolute Deviation\n", "\n", "$$ median_i |X_i - median_j(X_j)|) $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Standardized Median Absolute Deviation is a consistent estimator for $\\hat{\\sigma}$\n", "\n", "$$\\hat{\\sigma}=K \\cdot MAD$$\n", "\n", "where $K$ depends on the distribution. For the normal distribution for example,\n", "\n", "$$K = \\Phi^{-1}(.75)$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "stats.norm.ppf(.75)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(x)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sm.robust.scale.mad(x)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.array([1,2,3,4,5.]).std()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another robust estimator of scale is the Interquartile Range (IQR)\n", "\n", "$$\\left(\\hat{X}_{0.75} - \\hat{X}_{0.25}\\right),$$\n", "\n", "where $\\hat{X}_{p}$ is the sample p-th quantile and $K$ depends on the distribution. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The standardized IQR, given by $K \\cdot \\text{IQR}$ for\n", "$$K = \\frac{1}{\\Phi^{-1}(.75) - \\Phi^{-1}(.25)} \\approx 0.74,$$\n", "is a consistent estimator of the standard deviation for normal data." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sm.robust.scale.iqr(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The IQR is less robust than the MAD in the sense that it has a lower breakdown point: it can withstand 25\\% outlying observations before being completely ruined, whereas the MAD can withstand 50\\% outlying observations. However, the IQR is better suited for asymmetric distributions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yet another robust estimator of scale is the $Q_n$ estimator, introduced in Rousseeuw & Croux (1993), 'Alternatives to the Median Absolute Deviation'. Then $Q_n$ estimator is given by\n", "$$\n", "Q_n = K \\left\\lbrace \\vert X_{i} - X_{j}\\vert : i 2])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(infl.summary_frame().loc['minister'])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sidak = ols_model.outlier_test('sidak')\n", "sidak.sort_values('unadj_p', inplace=True)\n", "print(sidak)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fdr = ols_model.outlier_test('fdr_bh')\n", "fdr.sort_values('unadj_p', inplace=True)\n", "print(fdr)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "rlm_model = rlm('prestige ~ income + education', prestige).fit()\n", "print(rlm_model.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(rlm_model.weights)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hertzprung Russell data for Star Cluster CYG 0B1 - Leverage Points" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Data is on the luminosity and temperature of 47 stars in the direction of Cygnus." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dta = sm.datasets.get_rdataset(\"starsCYG\", \"robustbase\", cache=True).data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from matplotlib.patches import Ellipse\n", "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111, xlabel='log(Temp)', ylabel='log(Light)', title='Hertzsprung-Russell Diagram of Star Cluster CYG OB1')\n", "ax.scatter(*dta.values.T)\n", "# highlight outliers\n", "e = Ellipse((3.5, 6), .2, 1, alpha=.25, color='r')\n", "ax.add_patch(e);\n", "ax.annotate('Red giants', xy=(3.6, 6), xytext=(3.8, 6),\n", " arrowprops=dict(facecolor='black', shrink=0.05, width=2),\n", " horizontalalignment='left', verticalalignment='bottom',\n", " clip_on=True, # clip to the axes bounding box\n", " fontsize=16,\n", " )\n", "# annotate these with their index\n", "for i,row in dta.loc[dta['log.Te'] < 3.8].iterrows():\n", " ax.annotate(i, row, row + .01, fontsize=14)\n", "xlim, ylim = ax.get_xlim(), ax.get_ylim()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from IPython.display import Image\n", "Image(filename='star_diagram.png')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "y = dta['log.light']\n", "X = sm.add_constant(dta['log.Te'], prepend=True)\n", "ols_model = sm.OLS(y, X).fit()\n", "abline_plot(model_results=ols_model, ax=ax)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "rlm_mod = sm.RLM(y, X, sm.robust.norms.TrimmedMean(.5)).fit()\n", "abline_plot(model_results=rlm_mod, ax=ax, color='red')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Why? Because M-estimators are not robust to leverage points." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "infl = ols_model.get_influence()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "h_bar = 2*(ols_model.df_model + 1 )/ols_model.nobs\n", "hat_diag = infl.summary_frame()['hat_diag']\n", "hat_diag.loc[hat_diag > h_bar]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sidak2 = ols_model.outlier_test('sidak')\n", "sidak2.sort_values('unadj_p', inplace=True)\n", "print(sidak2)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fdr2 = ols_model.outlier_test('fdr_bh')\n", "fdr2.sort_values('unadj_p', inplace=True)\n", "print(fdr2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Let's delete that line" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "l = ax.lines[-1]\n", "l.remove()\n", "del l" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "weights = np.ones(len(X))\n", "weights[X[X['log.Te'] < 3.8].index.values - 1] = 0\n", "wls_model = sm.WLS(y, X, weights=weights).fit()\n", "abline_plot(model_results=wls_model, ax=ax, color='green')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* MM estimators are good for this type of problem, unfortunately, we do not yet have these yet. \n", "* It's being worked on, but it gives a good excuse to look at the R cell magics in the notebook." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "yy = y.values[:,None]\n", "xx = X['log.Te'].values[:,None]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note**: The R code and the results in this notebook has been converted to markdown so that R is not required to build the documents. The R results in the notebook were computed using R 3.5.1 and robustbase 0.93." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "```ipython\n", "%load_ext rpy2.ipython\n", "\n", "%R library(robustbase)\n", "%Rpush yy xx\n", "%R mod <- lmrob(yy ~ xx);\n", "%R params <- mod$coefficients;\n", "%Rpull params\n", "```" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "```ipython\n", "%R print(mod)\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```\n", "Call:\n", "lmrob(formula = yy ~ xx)\n", " \\--> method = \"MM\"\n", "Coefficients:\n", "(Intercept) xx \n", " -4.969 2.253 \n", "```" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "params = [-4.969387980288108, 2.2531613477892365] # Computed using R\n", "print(params[0], params[1])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "abline_plot(intercept=params[0], slope=params[1], ax=ax, color='red')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise: Breakdown points of M-estimator" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.random.seed(12345)\n", "nobs = 200\n", "beta_true = np.array([3, 1, 2.5, 3, -4])\n", "X = np.random.uniform(-20,20, size=(nobs, len(beta_true)-1))\n", "# stack a constant in front\n", "X = sm.add_constant(X, prepend=True) # np.c_[np.ones(nobs), X]\n", "mc_iter = 500\n", "contaminate = .25 # percentage of response variables to contaminate" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "all_betas = []\n", "for i in range(mc_iter):\n", " y = np.dot(X, beta_true) + np.random.normal(size=200)\n", " random_idx = np.random.randint(0, nobs, size=int(contaminate * nobs))\n", " y[random_idx] = np.random.uniform(-750, 750)\n", " beta_hat = sm.RLM(y, X).fit().params\n", " all_betas.append(beta_hat)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "all_betas = np.asarray(all_betas)\n", "se_loss = lambda x : np.linalg.norm(x, ord=2)**2\n", "se_beta = lmap(se_loss, all_betas - beta_true)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Squared error loss" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.array(se_beta).mean()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "all_betas.mean(0)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "beta_true" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "se_loss(all_betas.mean(0) - beta_true)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/rolling_ls.ipynb000066400000000000000000000161521400612667500232020ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Rolling Regression\n", "\n", "Rolling OLS applies OLS across a fixed windows of observations and then rolls \n", "(moves or slides) the window across the data set. They key parameter is `window` \n", "which determines the number of observations used in each OLS regression. By \n", "default, `RollingOLS` drops missing values in the window and so will estimate \n", "the model using the available data points.\n", "\n", "Estimated values are aligned so that models estimated using data points \n", "$i, i+1, ... i+window$ are stored in location $i+window$. \n", "\n", "Start by importing the modules that are used in this notebook." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false } }, "outputs": [], "source": [ "import pandas_datareader as pdr\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "from statsmodels.regression.rolling import RollingOLS\n", "import matplotlib.pyplot as plt\n", "import seaborn\n", "seaborn.set_style('darkgrid')\n", "pd.plotting.register_matplotlib_converters()\n", "%matplotlib inline\n" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "`pandas-datareader` is used to download data from\n", "[Ken French's website](https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html). \n", "The two data sets downloaded are the 3 Fama-French factors and the 10 industry portfolios. \n", "Data is available from 1926. \n", "\n", "The data are monthly returns for the factors or industry portfolios." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "factors = pdr.get_data_famafrench('F-F_Research_Data_Factors', start='1-1-1926')[0]\n", "print(factors.head())\n", "industries = pdr.get_data_famafrench('10_Industry_Portfolios', start='1-1-1926')[0]\n", "print(industries.head())" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "The first model estimated is a rolling version of the CAPM that regresses\n", "the excess return of Technology sector firms on the excess return of the market.\n", "\n", "The window is 60 months, and so results are available after the first 60 (`window`) \n", "months. The first 59 (`window - 1`) estimates are all `nan` filled." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "endog = industries.HiTec - factors.RF.values\n", "exog = sm.add_constant(factors['Mkt-RF'])\n", "rols = RollingOLS(endog, exog, window=60)\n", "rres = rols.fit()\n", "params = rres.params\n", "print(params.head())\n", "print(params.tail())" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "We next plot the market loading along with a 95% point-wise confidence interval.\n", "The `alpha=False` omits the constant column, if present. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "fig = rres.plot_recursive_coefficient(variables=['Mkt-RF'], figsize=(14,6))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, the model is expanded to include all three factors, the excess market, the size factor\n", "and the value factor. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "exog_vars = ['Mkt-RF', 'SMB', 'HML']\n", "exog = sm.add_constant(factors[exog_vars])\n", "rols = RollingOLS(endog, exog, window=60)\n", "rres = rols.fit()\n", "fig = rres.plot_recursive_coefficient(variables=exog_vars, figsize=(14,18))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Formulas\n", "\n", "`RollingOLS` and `RollingWLS` both support model specification using the formula interface. The example below is equivalent to the 3-factor model estimated previously. Note that one variable is renamed to have a valid Python variable name." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "joined = pd.concat([factors, industries], axis=1)\n", "joined['Mkt_RF'] = joined['Mkt-RF']\n", "mod = RollingOLS.from_formula('HiTec ~ Mkt_RF + SMB + HML', data=joined, window=60)\n", "rres = mod.fit()\n", "print(rres.params.tail())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## `RollingWLS`: Rolling Weighted Least Squares \n", "\n", "The `rolling` module also provides `RollingWLS` which takes an optional `weights` input to perform rolling weighted least squares. It produces results that match `WLS` when applied to rolling windows of data. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fit Options\n", "\n", "Fit accepts other optional keywords to set the covariance estimator. Only two estimators are supported, `'nonrobust'` (the classic OLS estimator) and `'HC0'` which is White's heteroskedasticity robust estimator.\n", "\n", "You can set `params_only=True` to only estimate the model parameters. This is substantially faster than computing the full set of values required to perform inference. \n", "\n", "Finally, the parameter `reset` can be set to a positive integer to control estimation error in very long samples. `RollingOLS` avoids the full matrix product when rolling by only adding the most recent observation and removing the dropped observation as it rolls through the sample. Setting `reset` uses the full inner product every `reset` periods. In most applications this parameter can be omitted. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "%timeit rols.fit()\n", "%timeit rols.fit(params_only=True)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.8" }, "pycharm": { "stem_cell": { "cell_type": "raw", "metadata": { "collapsed": false }, "source": [] } } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/star_diagram.png000066400000000000000000005267061400612667500231510ustar00rootroot00000000000000‰PNG  IHDRHE©âŸ&sRGB®ÎébKGDÿÿÿ ½§“ pHYs a Äî–@µtIMEÜ6xá IDATxÚì½]¬¬ÛU%6Æ\_Õ9þiÿ`·Œ!ü…tÓ`Àjµ€ü!"H“ˆ— ¡ÄHoH<€DìÒÀ‹_HH-E$J@<@D;Q'nºóg‡Vè@‹"è¸}}N}kΑ‡9×úVí½Ïõ½— 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Xÿ8'OžüàƒþŸ.þÞ{ïݸqC,ß»wïâÅ‹t×ÐÇdøðá§OŸÆC kl 󰶶~êØÄ<'kDÜ f(w1˜Ç¯0 ƒƒÁ`0X°a0 óø@%OʵÉò¹IEND®B`‚statsmodels-0.12.2/examples/notebooks/statespace_arma_0.ipynb000066400000000000000000000155751400612667500244210ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Autoregressive Moving Average (ARMA): Sunspots data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook replicates the existing ARMA notebook using the `statsmodels.tsa.statespace.SARIMAX` class rather than the `statsmodels.tsa.ARMA` class." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "from scipy import stats\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "\n", "import statsmodels.api as sm" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from statsmodels.graphics.api import qqplot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sunspots Data" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(sm.datasets.sunspots.NOTE)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "dta = sm.datasets.sunspots.load_pandas().data" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "dta.index = pd.Index(pd.date_range(\"1700\", end=\"2009\", freq=\"A-DEC\"))\n", "del dta[\"YEAR\"]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "dta.plot(figsize=(12,4));" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax1 = fig.add_subplot(211)\n", "fig = sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40, ax=ax1)\n", "ax2 = fig.add_subplot(212)\n", "fig = sm.graphics.tsa.plot_pacf(dta, lags=40, ax=ax2)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "arma_mod20 = sm.tsa.statespace.SARIMAX(dta, order=(2,0,0), trend='c').fit(disp=False)\n", "print(arma_mod20.params)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "arma_mod30 = sm.tsa.statespace.SARIMAX(dta, order=(3,0,0), trend='c').fit(disp=False)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(arma_mod20.aic, arma_mod20.bic, arma_mod20.hqic)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(arma_mod30.params)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(arma_mod30.aic, arma_mod30.bic, arma_mod30.hqic)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Does our model obey the theory?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sm.stats.durbin_watson(arma_mod30.resid)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,4))\n", "ax = fig.add_subplot(111)\n", "ax = plt.plot(arma_mod30.resid)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "resid = arma_mod30.resid" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "stats.normaltest(resid)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,4))\n", "ax = fig.add_subplot(111)\n", "fig = qqplot(resid, line='q', ax=ax, fit=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax1 = fig.add_subplot(211)\n", "fig = sm.graphics.tsa.plot_acf(resid, lags=40, ax=ax1)\n", "ax2 = fig.add_subplot(212)\n", "fig = sm.graphics.tsa.plot_pacf(resid, lags=40, ax=ax2)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "r,q,p = sm.tsa.acf(resid, fft=True, qstat=True)\n", "data = np.c_[range(1,41), r[1:], q, p]\n", "table = pd.DataFrame(data, columns=['lag', \"AC\", \"Q\", \"Prob(>Q)\"])\n", "print(table.set_index('lag'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* This indicates a lack of fit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* In-sample dynamic prediction. How good does our model do?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "predict_sunspots = arma_mod30.predict(start='1990', end='2012', dynamic=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(12, 8))\n", "dta.loc['1950':].plot(ax=ax)\n", "predict_sunspots.plot(ax=ax, style='r');" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def mean_forecast_err(y, yhat):\n", " return y.sub(yhat).mean()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mean_forecast_err(dta.SUNACTIVITY, predict_sunspots)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.3" } }, "nbformat": 4, "nbformat_minor": 0 }statsmodels-0.12.2/examples/notebooks/statespace_chandrasekhar.ipynb000066400000000000000000000415641400612667500260550ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## State space models - Chandrasekhar recursions" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "\n", "from pandas_datareader.data import DataReader" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although most operations related to state space models rely on the Kalman filtering recursions, in some special cases one can use a separate method often called \"Chandrasekhar recursions\". These provide an alternative way to iteratively compute the conditional moments of the state vector, and in some cases they can be substantially less computationally intensive than the Kalman filter recursions. For complete details, see the paper \"Using the 'Chandrasekhar Recursions' for Likelihood Evaluation of DSGE Models\" (Herbst, 2015). Here we just sketch the basic idea." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### State space models and the Kalman filter\n", "\n", "Recall that a time-invariant state space model can be written:\n", "\n", "$$\n", "\\begin{aligned}\n", "y_t &= Z \\alpha_t + \\varepsilon_t, \\qquad \\varepsilon_t \\sim N(0, H) \\\\\n", "\\alpha_{t+1} & = T \\alpha_t + R \\eta_t, \\qquad \\eta_t \\sim N(0, Q) \\\\\n", "\\alpha_1 & \\sim N(a_1, P_1)\n", "\\end{aligned}\n", "$$\n", "\n", "where $y_t$ is a $p \\times 1$ vector and $\\alpha_t$ is an $m \\times 1$ vector.\n", "\n", "Each iteration of the Kalman filter, say at time $t$, can be split into three parts:\n", "\n", "1. **Initialization**: specification of $a_t$ and $P_t$ that define the conditional state distribution, $\\alpha_t \\mid y^{t-1} \\sim N(a_t, P_t)$.\n", "2. **Updating**: computation of $a_{t|t}$ and $P_{t|t}$ that define the conditional state distribution, $\\alpha_t \\mid y^{t} \\sim N(a_{t|t}, P_{t|t})$.\n", "3. **Prediction**: computation of $a_{t+1}$ and $P_{t+1}$ that define the conditional state distribution, $\\alpha_{t+1} \\mid y^{t} \\sim N(a_{t+1}, P_{t+1})$.\n", "\n", "Of course after the first iteration, the prediction part supplies the values required for initialization of the next step." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Focusing on the prediction step, the Kalman filter recursions yield:\n", "\n", "$$\n", "\\begin{aligned}\n", "a_{t+1} & = T a_{t|t} \\\\\n", "P_{t+1} & = T P_{t|t} T' + R Q R' \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "where the matrices $T$ and $P_{t|t}$ are each $m \\times m$, where $m$ is the size of the state vector $\\alpha$. In some cases, the state vector can become extremely large, which can imply that the matrix multiplications required to produce $P_{t+1}$ can be become computationally intensive." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example: seasonal autoregression\n", "\n", "As an example, notice that an AR(r) model (we use $r$ here since we already used $p$ as the dimension of the observation vector) can be put into state space form as:\n", "\n", "$$\n", "\\begin{aligned}\n", "y_t &= \\alpha_t \\\\\n", "\\alpha_{t+1} & = T \\alpha_t + R \\eta_t, \\qquad \\eta_t \\sim N(0, Q)\n", "\\end{aligned}\n", "$$\n", "\n", "where:\n", "\n", "\n", "$$\n", "\\begin{aligned}\n", "T = \\begin{bmatrix}\n", "\\phi_1 & \\phi_2 & \\dots & \\phi_r \\\\\n", "1 & 0 & & 0 \\\\\n", "\\vdots & \\ddots & & \\vdots \\\\\n", "0 & & 1 & 0 \\\\\n", "\\end{bmatrix} \\qquad\n", "R = \\begin{bmatrix}\n", "1 \\\\\n", "0 \\\\\n", "\\vdots \\\\\n", "0\n", "\\end{bmatrix} \\qquad\n", "Q = \\begin{bmatrix}\n", "\\sigma^2\n", "\\end{bmatrix}\n", "\\end{aligned}\n", "$$\n", "\n", "In an AR model with daily data that exhibits annual seasonality, we might want to fit a model that incorporates lags up to $r=365$, in which case the state vector would be at least $m = 365$. The matrices $T$ and $P_{t|t}$ then each have $365^2 = 133225$ elements, and so most of the time spent computing the likelihood function (via the Kalman filter) can become dominated by the matrix multiplications in the prediction step." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### State space models and the Chandrasekhar recursions\n", "\n", "The Chandrasekhar recursions replace equation $P_{t+1} = T P_{t|t} T' + R Q R'$ with a different recursion:\n", "\n", "$$\n", "P_{t+1} = P_t + W_t M_t W_t'\n", "$$\n", "\n", "but where $W_t$ is a matrix with dimension $m \\times p$ and $M_t$ is a matrix with dimension $p \\times p$, where $p$ is the dimension of the observed vector $y_t$. These matrices themselves have recursive formulations. For more general details and for the formulas for computing $W_t$ and $M_t$, see Herbst (2015).\n", "\n", "**Important note**: unlike the Kalman filter, the Chandrasekhar recursions can not be used for every state space model. In particular, the latter has the following restrictions (that are not required for the use of the former):\n", "\n", "- The model must be time-invariant, except that time-varying intercepts are permitted.\n", "- Stationary initialization of the state vector must be used (this rules out all models in non-stationary components)\n", "- Missing data is not permitted" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To understand why this formula can imply more efficient computations, consider again the SARIMAX case, above. In this case, $p = 1$, so that $M_t$ is a scalar and we can rewrite the Chandrasekhar recursion as:\n", "\n", "$$\n", "P_{t+1} = P_t + M_t \\times W_t W_t'\n", "$$\n", "\n", "The matrices being multiplied, $W_t$, are then of dimension $m \\times 1$, and in the case $r=365$, they each only have $365$ elements, rather than $365^2$ elements. This implies substantially fewer computations are required to complete the prediction step." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Convergence\n", "\n", "A factor that complicates a straightforward discussion of performance implications is the well-known fact that in time-invariant models, the predicted state covariance matrix will converge to a constant matrix. This implies that there exists an $S$ such that, for every $t > S$, $P_t = P_{t+1}$. Once convergence has been achieved, we can eliminate the equation for $P_{t+1}$ from the prediction step altogether.\n", "\n", "In simple time series models, like AR(r) models, convergence is achieved fairly quickly, and this can limit the performance benefit to using the Chandrasekhar recursions. Herbst (2015) focuses instead on DSGE (Dynamic Stochastic General Equilibrium) models instead, which often have a large state vector and often a large number of periods to achieve convergence. In these cases, the performance gains can be quite substantial." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Practical example\n", "\n", "As a practical example, we will consider monthly data that has a clear seasonal component. In this case, we look at the inflation rate of apparel, as measured by the consumer price index. A graph of the data indicates strong seasonality." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "cpi_apparel = DataReader('CPIAPPNS', 'fred', start='1986')\n", "cpi_apparel.index = pd.DatetimeIndex(cpi_apparel.index, freq='MS')\n", "inf_apparel = np.log(cpi_apparel).diff().iloc[1:] * 1200\n", "inf_apparel.plot(figsize=(15, 5));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will construct two model instances. The first will be set to use the Kalman filter recursions, while the second will be set to use the Chandrasekhar recursions. This setting is controlled by the `ssm.filter_chandrasekhar` property, as shown below.\n", "\n", "The model we have in mind is a seasonal autoregression, where we include the first 6 months as lags as well as the given month in each of the previous 15 years as lags. This implies that the state vector has dimension $m = 186$, which is large enough that we might expect to see some substantial performance gains by using the Chandrasekhar recursions.\n", "\n", "**Remark**: We set `tolerance=0` in each model - this has the effect of preventing the filter from ever recognizing that the prediction covariance matrix has converged. *This is not recommended in practice*. We do this here to highlight the superior performance of the Chandrasekhar recursions when they are used in every period instead of the typical Kalman filter recursions. Later, we will show the performance in a more realistic setting that we do allow for convergence." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Model that will apply Kalman filter recursions\n", "mod_kf = sm.tsa.SARIMAX(inf_apparel, order=(6, 0, 0), seasonal_order=(15, 0, 0, 12), tolerance=0)\n", "print(mod_kf.k_states)\n", "\n", "# Model that will apply Chandrasekhar recursions\n", "mod_ch = sm.tsa.SARIMAX(inf_apparel, order=(6, 0, 0), seasonal_order=(15, 0, 0, 12), tolerance=0)\n", "mod_ch.ssm.filter_chandrasekhar = True" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We time computation of the log-likelihood function, using the following code:\n", "\n", "```python\n", "%timeit mod_kf.loglike(mod_kf.start_params)\n", "%timeit mod_ch.loglike(mod_ch.start_params)\n", "```\n", "\n", "This results in:\n", "\n", "```\n", "171 ms ± 19.7 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", "85 ms ± 4.97 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", "```\n", "\n", "The implication is that in this experiment, the Chandrasekhar recursions improved performance by about a factor of 2." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we mentioned above, in the previous experiment we disabled convergence of the predicted covariance matrices, so the results there are an upper bound. Now we allow for convergence, as usual, by removing the `tolerance=0` argument:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Model that will apply Kalman filter recursions\n", "mod_kf = sm.tsa.SARIMAX(inf_apparel, order=(6, 0, 0), seasonal_order=(15, 0, 0, 12))\n", "print(mod_kf.k_states)\n", "\n", "# Model that will apply Chandrasekhar recursions\n", "mod_ch = sm.tsa.SARIMAX(inf_apparel, order=(6, 0, 0), seasonal_order=(15, 0, 0, 12))\n", "mod_ch.ssm.filter_chandrasekhar = True" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we time computation of the log-likelihood function, using the following code:\n", "\n", "```python\n", "%timeit mod_kf.loglike(mod_kf.start_params)\n", "%timeit mod_ch.loglike(mod_ch.start_params)\n", "```\n", "\n", "This results in:\n", "\n", "```\n", "114 ms ± 7.64 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", "70.5 ms ± 2.43 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", "```\n", "\n", "The Chandrasekhar recursions still improve performance, but now only by about 33%. The reason for this is that after convergence, we no longer need to compute the predicted covariance matrices, so that for those post-convergence periods, there will be no difference in computation time between the two approaches. Below we check the period in which convergence was achieved:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_kf = mod_kf.filter(mod_kf.start_params)\n", "print('Convergence at t=%d, of T=%d total observations' %\n", " (res_kf.filter_results.period_converged, res_kf.nobs))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since convergence happened relatively early, we are already avoiding the expensive matrix multiplications in more than half of the periods.\n", "\n", "However, as mentioned above, larger DSGE models may not achieve convergence for most or all of the periods in the sample, and so we could perhaps expect to achieve performance gains more similar to the first example. In their 2019 paper \"Euro area real-time density forecasting with financial or labor market frictions\", McAdam and Warne note that in their applications, \"Compared with the standard Kalman filter, it is our experience that these recursions speed up\n", "the calculation of the log-likelihood for the three models by roughly 50 percent\". This is about the same result as we found in our first example." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Aside on multithreaded matrix algebra routines\n", "\n", "The timings above are based on the Numpy installation installed via Anaconda, which uses Intel's MKL BLAS and LAPACK libraries. These implement multithreaded processing to speed up matrix algebra, which can be particularly helpful for operations on the larger matrices we're working with here. To get a sense of how this affects results, we could turn off multithreading by putting the following in the first cell of this notebook.\n", "\n", "```python\n", "import os\n", "os.environ[\"MKL_NUM_THREADS\"] = \"1\"\n", "```\n", "\n", "When we do this, the timings of the first example change to:\n", "\n", "```\n", "307 ms ± 3.08 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n", "97.5 ms ± 1.64 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", "```\n", "\n", "and the timings of the second example change to:\n", "\n", "```\n", "178 ms ± 2.78 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n", "78.9 ms ± 950 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n", "```\n", "\n", "Both are slower, but the typical Kalman filter is affected much more.\n", "\n", "This is not unexpected; the performance differential between single and multithreaded linear algebra is much greater in the typical Kalman filter case, because the whole point of the Chandrasekhar recursions is to reduce the size of the matrix operations. It means that if multithreaded linear algebra is unavailable, the Chandrasekhar recursions offer even greater performance gains." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Chandrasekhar recursions and the univariate filtering approach\n", "\n", "It is also possible to combine the Chandrasekhar recursions with the univariate filtering approach of Koopman and Durbin (2000), by making use of the results of Aknouche and Hamdi in their 2007 paper \"Periodic Chandrasekhar recursions\". An initial implementation of this combination is included in Statsmodels. However, experiments suggest that this tends to degrade performance compared to even the usual Kalman filter. This accords with the computational savings reported for the univariate filtering method, which suggest that savings are highest when the state vector is small relative to the observation vector." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Bibliography\n", "\n", "Aknouche, Abdelhakim, and Fayçal Hamdi. \"Periodic Chandrasekhar recursions.\" arXiv preprint arXiv:0711.3857 (2007).\n", "\n", "Herbst, Edward. \"Using the “Chandrasekhar Recursions†for likelihood evaluation of DSGE models.\" Computational Economics 45, no. 4 (2015): 693-705.\n", "\n", "Koopman, Siem J., and James Durbin. \"Fast filtering and smoothing for multivariate state space models.\" Journal of Time Series Analysis 21, no. 3 (2000): 281-296.\n", "\n", "McAdam, Peter, and Anders Warne. \"Euro area real-time density forecasting with financial or labor market frictions.\" International Journal of Forecasting 35, no. 2 (2019): 580-600." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 } statsmodels-0.12.2/examples/notebooks/statespace_concentrated_scale.ipynb000066400000000000000000000305721400612667500270740ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## State space models - concentrating the scale out of the likelihood function" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "\n", "dta = sm.datasets.macrodata.load_pandas().data\n", "dta.index = pd.date_range(start='1959Q1', end='2009Q4', freq='Q')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Introduction\n", "\n", "(much of this is based on Harvey (1989); see especially section 3.4)\n", "\n", "State space models can generically be written as follows (here we focus on time-invariant state space models, but similar results apply also to time-varying models):\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = Z \\alpha_t + \\varepsilon_t, \\quad \\varepsilon_t \\sim N(0, H) \\\\\n", "\\alpha_{t+1} & = T \\alpha_t + R \\eta_t \\quad \\eta_t \\sim N(0, Q)\n", "\\end{align}\n", "$$\n", "\n", "Often, some or all of the values in the matrices $Z, H, T, R, Q$ are unknown and must be estimated; in statsmodels, estimation is often done by finding the parameters that maximize the likelihood function. In particular, if we collect the parameters in a vector $\\psi$, then each of these matrices can be thought of as functions of those parameters, for example $Z = Z(\\psi)$, etc.\n", "\n", "Usually, the likelihood function is maximized numerically, for example by applying quasi-Newton \"hill-climbing\" algorithms, and this becomes more and more difficult the more parameters there are. It turns out that in many cases we can reparameterize the model as $[\\psi_*', \\sigma_*^2]'$, where $\\sigma_*^2$ is the \"scale\" of the model (usually, it replaces one of the error variance terms) and it is possible to find the maximum likelihood estimate of $\\sigma_*^2$ analytically, by differentiating the likelihood function. This implies that numerical methods are only required to estimate the parameters $\\psi_*$, which has dimension one less than that of $\\psi$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: local level model\n", "\n", "(see, for example, section 4.2 of Harvey (1989))\n", "\n", "As a specific example, consider the local level model, which can be written as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\alpha_t + \\varepsilon_t, \\quad \\varepsilon_t \\sim N(0, \\sigma_\\varepsilon^2) \\\\\n", "\\alpha_{t+1} & = \\alpha_t + \\eta_t \\quad \\eta_t \\sim N(0, \\sigma_\\eta^2)\n", "\\end{align}\n", "$$\n", "\n", "In this model, $Z, T,$ and $R$ are all fixed to be equal to $1$, and there are two unknown parameters, so that $\\psi = [\\sigma_\\varepsilon^2, \\sigma_\\eta^2]$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Typical approach\n", "\n", "First, we show how to define this model without concentrating out the scale, using statsmodels' state space library:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "class LocalLevel(sm.tsa.statespace.MLEModel):\n", " _start_params = [1., 1.]\n", " _param_names = ['var.level', 'var.irregular']\n", "\n", " def __init__(self, endog):\n", " super(LocalLevel, self).__init__(endog, k_states=1, initialization='diffuse')\n", "\n", " self['design', 0, 0] = 1\n", " self['transition', 0, 0] = 1\n", " self['selection', 0, 0] = 1\n", "\n", " def transform_params(self, unconstrained):\n", " return unconstrained**2\n", "\n", " def untransform_params(self, unconstrained):\n", " return unconstrained**0.5\n", "\n", " def update(self, params, **kwargs):\n", " params = super(LocalLevel, self).update(params, **kwargs)\n", "\n", " self['state_cov', 0, 0] = params[0]\n", " self['obs_cov', 0, 0] = params[1]\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are two parameters in this model that must be chosen: `var.level` $(\\sigma_\\eta^2)$ and `var.irregular` $(\\sigma_\\varepsilon^2)$. We can use the built-in `fit` method to choose them by numerically maximizing the likelihood function.\n", "\n", "In our example, we are applying the local level model to consumer price index inflation." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = LocalLevel(dta.infl)\n", "res = mod.fit(disp=False)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can look at the results from the numerical optimizer in the results attribute `mle_retvals`:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(res.mle_retvals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Concentrating out the scale" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, there are two ways to reparameterize this model as above:\n", "\n", "1. The first way is to set $\\sigma_*^2 \\equiv \\sigma_\\varepsilon^2$ so that $\\psi_* = \\psi / \\sigma_\\varepsilon^2 = [1, q_\\eta]$ where $q_\\eta = \\sigma_\\eta^2 / \\sigma_\\varepsilon^2$.\n", "2. The second way is to set $\\sigma_*^2 \\equiv \\sigma_\\eta^2$ so that $\\psi_* = \\psi / \\sigma_\\eta^2 = [h, 1]$ where $h = \\sigma_\\varepsilon^2 / \\sigma_\\eta^2$.\n", "\n", "In the first case, we only need to numerically maximize the likelihood with respect to $q_\\eta$, and in the second case we only need to numerically maximize the likelihood with respect to $h$.\n", "\n", "Either approach would work well in most cases, and in the example below we will use the second method." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To reformulate the model to take advantage of the concentrated likelihood function, we need to write the model in terms of the parameter vector $\\psi_* = [g, 1]$. Because this parameter vector defines $\\sigma_\\eta^2 \\equiv 1$, we now include a new line `self['state_cov', 0, 0] = 1` and the only unknown parameter is $h$. Because our parameter $h$ is no longer a variance, we renamed it here to be `ratio.irregular`.\n", "\n", "The key piece that is required to formulate the model so that the scale can be computed from the Kalman filter recursions (rather than selected numerically) is setting the flag `self.ssm.filter_concentrated = True`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "class LocalLevelConcentrated(sm.tsa.statespace.MLEModel):\n", " _start_params = [1.]\n", " _param_names = ['ratio.irregular']\n", "\n", " def __init__(self, endog):\n", " super(LocalLevelConcentrated, self).__init__(endog, k_states=1, initialization='diffuse')\n", "\n", " self['design', 0, 0] = 1\n", " self['transition', 0, 0] = 1\n", " self['selection', 0, 0] = 1\n", " self['state_cov', 0, 0] = 1\n", " \n", " self.ssm.filter_concentrated = True\n", "\n", " def transform_params(self, unconstrained):\n", " return unconstrained**2\n", "\n", " def untransform_params(self, unconstrained):\n", " return unconstrained**0.5\n", "\n", " def update(self, params, **kwargs):\n", " params = super(LocalLevelConcentrated, self).update(params, **kwargs)\n", " self['obs_cov', 0, 0] = params[0]\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we can use the built-in `fit` method to find the maximum likelihood estimate of $h$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod_conc = LocalLevelConcentrated(dta.infl)\n", "res_conc = mod_conc.fit(disp=False)\n", "print(res_conc.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The estimate of $h$ is provided in the middle table of parameters (`ratio.irregular`), while the estimate of the scale is provided in the upper table. Below, we will show that these estimates are consistent with those from the previous approach." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we can again look at the results from the numerical optimizer in the results attribute `mle_retvals`. It turns out that two fewer iterations were required in this case, since there was one fewer parameter to select. Moreover, since the numerical maximization problem was easier, the optimizer was able to find a value that made the gradient for this parameter slightly closer to zero than it was above." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(res_conc.mle_retvals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Comparing estimates\n", "\n", "Recall that $h = \\sigma_\\varepsilon^2 / \\sigma_\\eta^2$ and the scale is $\\sigma_*^2 = \\sigma_\\eta^2$. Using these definitions, we can see that both models produce nearly identical results:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print('Original model')\n", "print('var.level = %.5f' % res.params[0])\n", "print('var.irregular = %.5f' % res.params[1])\n", "\n", "print('\\nConcentrated model')\n", "print('scale = %.5f' % res_conc.scale)\n", "print('h * scale = %.5f' % (res_conc.params[0] * res_conc.scale))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: SARIMAX\n", "\n", "By default in SARIMAX models, the variance term is chosen by numerically maximizing the likelihood function, but an option has been added to allow concentrating the scale out." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Typical approach\n", "mod_ar = sm.tsa.SARIMAX(dta.cpi, order=(1, 0, 0), trend='ct')\n", "res_ar = mod_ar.fit(disp=False)\n", "\n", "# Estimating the model with the scale concentrated out\n", "mod_ar_conc = sm.tsa.SARIMAX(dta.cpi, order=(1, 0, 0), trend='ct', concentrate_scale=True)\n", "res_ar_conc = mod_ar_conc.fit(disp=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These two approaches produce about the same loglikelihood and parameters, although the model with the concentrated scale was able to improve the fit very slightly:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print('Loglikelihood')\n", "print('- Original model: %.4f' % res_ar.llf)\n", "print('- Concentrated model: %.4f' % res_ar_conc.llf)\n", "\n", "print('\\nParameters')\n", "print('- Original model: %.4f, %.4f, %.4f, %.4f' % tuple(res_ar.params))\n", "print('- Concentrated model: %.4f, %.4f, %.4f, %.4f' % (tuple(res_ar_conc.params) + (res_ar_conc.scale,)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This time, about 1/3 fewer iterations of the optimizer are required under the concentrated approach:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print('Optimizer iterations')\n", "print('- Original model: %d' % res_ar.mle_retvals['iterations'])\n", "print('- Concentrated model: %d' % res_ar_conc.mle_retvals['iterations'])" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 } statsmodels-0.12.2/examples/notebooks/statespace_custom_models.ipynb000066400000000000000000001053451400612667500261320ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Custom statespace models\n", "\n", "The true power of the state space model is to allow the creation and estimation of custom models. This notebook shows various statespace models that subclass `sm.tsa.statespace.MLEModel`.\n", "\n", "Remember the general state space model can be written in the following general way:\n", "\n", "$$\n", "\\begin{aligned}\n", "y_t & = Z_t \\alpha_{t} + d_t + \\varepsilon_t \\\\\n", "\\alpha_{t+1} & = T_t \\alpha_{t} + c_t + R_t \\eta_{t}\n", "\\end{aligned}\n", "$$\n", "\n", "You can check the details and the dimensions of the objects [in this link](https://www.statsmodels.org/stable/statespace.html#custom-state-space-models)\n", "\n", "Most models won't include all of these elements. For example, the design matrix $Z_t$ might not depend on time ($\\forall t \\;Z_t = Z$), or the model won't have an observation intercept $d_t$.\n", "\n", "We'll start with something relatively simple and then show how to extend it bit by bit to include more elements.\n", "\n", "+ Model 1: time-varying coefficients. One observation equation with two state equations\n", "+ Model 2: time-varying parameters with non identity transition matrix\n", "+ Model 3: multiple observation and multiple state equations\n", "+ Bonus: pymc3 for Bayesian estimation" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "from collections import OrderedDict\n", "plt.rc(\"figure\", figsize=(16,8))\n", "plt.rc(\"font\", size=15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model 1: time-varying coefficients\n", "\n", "$$\n", "\\begin{aligned}\n", "y_t & = d + x_t \\beta_{x,t} + w_t \\beta_{w,t} + \\varepsilon_t \\hspace{4em} \\varepsilon_t \\sim N(0, \\sigma_\\varepsilon^2)\\\\\n", "\\begin{bmatrix} \\beta_{x,t} \\\\ \\beta_{w,t} \\end{bmatrix} & = \\begin{bmatrix} \\beta_{x,t-1} \\\\ \\beta_{w,t-1} \\end{bmatrix} + \\begin{bmatrix} \\zeta_{x,t} \\\\ \\zeta_{w,t} \\end{bmatrix} \\hspace{3.7em} \\begin{bmatrix} \\zeta_{x,t} \\\\ \\zeta_{w,t} \\end{bmatrix} \\sim N \\left ( \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}, \\begin{bmatrix} \\sigma_{\\beta, x}^2 & 0 \\\\ 0 & \\sigma_{\\beta, w}^2 \\end{bmatrix} \\right )\n", "\\end{aligned}\n", "$$\n", "\n", "The observed data is $y_t, x_t, w_t$. With $x_t, w_t$ being the exogenous variables. Notice that the design matrix is time-varying, so it will have three dimensions (`k_endog x k_states x nobs`)\n", "\n", "The states are $\\beta_{x,t}$ and $\\beta_{w,t}$. The state equation tells us these states evolve with a random walk. Thus, in this case the transition matrix is a 2 by 2 identity matrix.\n", "\n", "We'll first simulate the data, the construct a model and finally estimate it." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def gen_data_for_model1():\n", " nobs = 1000\n", "\n", " rs = np.random.RandomState(seed=93572)\n", "\n", " d = 5\n", " var_y = 5\n", " var_coeff_x = 0.01\n", " var_coeff_w = 0.5\n", "\n", " x_t = rs.uniform(size=nobs)\n", " w_t = rs.uniform(size=nobs)\n", " eps = rs.normal(scale=var_y**0.5, size=nobs)\n", "\n", " beta_x = np.cumsum(rs.normal(size=nobs, scale=var_coeff_x**0.5))\n", " beta_w = np.cumsum(rs.normal(size=nobs, scale=var_coeff_w**0.5))\n", "\n", " y_t = d + beta_x * x_t + beta_w * w_t + eps\n", " return y_t, x_t, w_t, beta_x, beta_w \n", "\n", "y_t, x_t, w_t, beta_x, beta_w = gen_data_for_model1()\n", "_ = plt.plot(y_t)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "class TVRegression(sm.tsa.statespace.MLEModel):\n", " def __init__(self, y_t, x_t, w_t):\n", " exog = np.c_[x_t, w_t] # shaped nobs x 2\n", "\n", " super(TVRegression, self).__init__(\n", " endog=y_t, exog=exog, k_states=2,\n", " initialization='diffuse')\n", "\n", " # Since the design matrix is time-varying, it must be\n", " # shaped k_endog x k_states x nobs\n", " # Notice that exog.T is shaped k_states x nobs, so we\n", " # just need to add a new first axis with shape 1\n", " self.ssm['design'] = exog.T[np.newaxis, :, :] # shaped 1 x 2 x nobs\n", " self.ssm['selection'] = np.eye(self.k_states)\n", " self.ssm['transition'] = np.eye(self.k_states)\n", " \n", " #Which parameters need to be positive?\n", " self.positive_parameters = slice(1, 4)\n", "\n", " @property\n", " def param_names(self):\n", " return ['intercept', 'var.e', 'var.x.coeff', 'var.w.coeff']\n", "\n", " @property\n", " def start_params(self):\n", " \"\"\"\n", " Defines the starting values for the parameters\n", " The linear regression gives us reasonable starting values for the constant\n", " d and the variance of the epsilon error\n", " \"\"\"\n", " exog = sm.add_constant(self.exog)\n", " res = sm.OLS(self.endog, exog).fit()\n", " params = np.r_[res.params[0], res.scale, 0.001, 0.001]\n", " return params\n", "\n", " def transform_params(self, unconstrained):\n", " \"\"\"\n", " We constraint the last three parameters\n", " ('var.e', 'var.x.coeff', 'var.w.coeff') to be positive, \n", " because they are variances\n", " \"\"\"\n", " constrained = unconstrained.copy()\n", " constrained[self.positive_parameters] = constrained[self.positive_parameters]**2\n", " return constrained\n", "\n", " def untransform_params(self, constrained):\n", " \"\"\"\n", " Need to unstransform all the parameters you transformed\n", " in the `transform_params` function\n", " \"\"\"\n", " unconstrained = constrained.copy()\n", " unconstrained[self.positive_parameters] = unconstrained[self.positive_parameters]**0.5\n", " return unconstrained\n", "\n", " def update(self, params, **kwargs):\n", " params = super(TVRegression, self).update(params, **kwargs)\n", "\n", " self['obs_intercept', 0, 0] = params[0]\n", " self['obs_cov', 0, 0] = params[1]\n", " self['state_cov'] = np.diag(params[2:4])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### And then estimate it with our custom model class" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = TVRegression(y_t, x_t, w_t)\n", "res = mod.fit()\n", "\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The values that generated the data were:\n", "\n", "+ intercept = 5\n", "+ var.e = 5\n", "+ var.x.coeff = 0.01\n", "+ var.w.coeff = 0.5\n", "\n", "\n", "As you can see, the estimation recovered the real parameters pretty well.\n", "\n", "We can also recover the estimated evolution of the underlying coefficients (or states in Kalman filter talk)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, axes = plt.subplots(2, figsize=(16, 8))\n", "\n", "ss = pd.DataFrame(res.smoothed_state.T, columns=['x', 'w'])\n", "\n", "axes[0].plot(beta_x, label='True')\n", "axes[0].plot(ss['x'], label='Smoothed estimate')\n", "axes[0].set(title='Time-varying coefficient on x_t')\n", "axes[0].legend()\n", "\n", "axes[1].plot(beta_w, label='True')\n", "axes[1].plot(ss['w'], label='Smoothed estimate')\n", "axes[1].set(title='Time-varying coefficient on w_t')\n", "axes[1].legend()\n", "\n", "fig.tight_layout();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model 2: time-varying parameters with non identity transition matrix\n", "\n", "This is a small extension from Model 1. Instead of having an identity transition matrix, we'll have one with two parameters ($\\rho_1, \\rho_2$) that we need to estimate. \n", "\n", "\n", "$$\n", "\\begin{aligned}\n", "y_t & = d + x_t \\beta_{x,t} + w_t \\beta_{w,t} + \\varepsilon_t \\hspace{4em} \\varepsilon_t \\sim N(0, \\sigma_\\varepsilon^2)\\\\\n", "\\begin{bmatrix} \\beta_{x,t} \\\\ \\beta_{w,t} \\end{bmatrix} & = \\begin{bmatrix} \\rho_1 & 0 \\\\ 0 & \\rho_2 \\end{bmatrix} \\begin{bmatrix} \\beta_{x,t-1} \\\\ \\beta_{w,t-1} \\end{bmatrix} + \\begin{bmatrix} \\zeta_{x,t} \\\\ \\zeta_{w,t} \\end{bmatrix} \\hspace{3.7em} \\begin{bmatrix} \\zeta_{x,t} \\\\ \\zeta_{w,t} \\end{bmatrix} \\sim N \\left ( \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}, \\begin{bmatrix} \\sigma_{\\beta, x}^2 & 0 \\\\ 0 & \\sigma_{\\beta, w}^2 \\end{bmatrix} \\right )\n", "\\end{aligned}\n", "$$\n", "\n", "\n", "What should we modify in our previous class to make things work?\n", "+ Good news: not a lot!\n", "+ Bad news: we need to be careful about a few things" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1) Change the starting parameters function\n", "\n", "We need to add names for the new parameters $\\rho_1, \\rho_2$ and we need to start corresponding starting values.\n", "\n", "The `param_names` function goes from:\n", "\n", "```python\n", "def param_names(self):\n", " return ['intercept', 'var.e', 'var.x.coeff', 'var.w.coeff']\n", "```\n", "\n", "\n", "to \n", "\n", "```python\n", "def param_names(self):\n", " return ['intercept', 'var.e', 'var.x.coeff', 'var.w.coeff',\n", " 'rho1', 'rho2']\n", "```\n", "\n", "and we change the `start_params` function from \n", "\n", "```python\n", "def start_params(self):\n", " exog = sm.add_constant(self.exog)\n", " res = sm.OLS(self.endog, exog).fit()\n", " params = np.r_[res.params[0], res.scale, 0.001, 0.001]\n", " return params\n", "```\n", "\n", "to\n", "\n", "```python\n", "def start_params(self):\n", " exog = sm.add_constant(self.exog)\n", " res = sm.OLS(self.endog, exog).fit()\n", " params = np.r_[res.params[0], res.scale, 0.001, 0.001, 0.8, 0.8]\n", " return params\n", "```\n", "\n", "2) Change the `update` function\n", "\n", "It goes from\n", "\n", "```python\n", "def update(self, params, **kwargs):\n", " params = super(TVRegression, self).update(params, **kwargs)\n", "\n", " self['obs_intercept', 0, 0] = params[0]\n", " self['obs_cov', 0, 0] = params[1]\n", " self['state_cov'] = np.diag(params[2:4])\n", "```\n", "\n", "\n", "to \n", "\n", "```python\n", "def update(self, params, **kwargs):\n", " params = super(TVRegression, self).update(params, **kwargs)\n", "\n", " self['obs_intercept', 0, 0] = params[0]\n", " self['obs_cov', 0, 0] = params[1]\n", " self['state_cov'] = np.diag(params[2:4])\n", " self['transition', 0, 0] = params[4]\n", " self['transition', 1, 1] = params[5]\n", "```\n", "\n", "\n", "3) (optional) change `transform_params` and `untransform_params`\n", "\n", "This is not required, but you might wanna restrict $\\rho_1, \\rho_2$ to lie between -1 and 1.\n", "In that case, we first import two utility functions from `statsmodels`.\n", "\n", "\n", "```python\n", "from statsmodels.tsa.statespace.tools import (\n", " constrain_stationary_univariate, unconstrain_stationary_univariate)\n", "```\n", "\n", "`constrain_stationary_univariate` constraint the value to be within -1 and 1. \n", "`unconstrain_stationary_univariate` provides the inverse function.\n", "The transform and untransform parameters function would look like this\n", "(remember that $\\rho_1, \\rho_2$ are in the 4 and 5th index):\n", "\n", "```python\n", "def transform_params(self, unconstrained):\n", " constrained = unconstrained.copy()\n", " constrained[self.positive_parameters] = constrained[self.positive_parameters]**2\n", " constrained[4] = constrain_stationary_univariate(constrained[4:5])\n", " constrained[5] = constrain_stationary_univariate(constrained[5:6])\n", " return constrained\n", "\n", "def untransform_params(self, constrained):\n", " unconstrained = constrained.copy()\n", " unconstrained[self.positive_parameters] = unconstrained[self.positive_parameters]**0.5\n", " unconstrained[4] = unconstrain_stationary_univariate(constrained[4:5])\n", " unconstrained[5] = unconstrain_stationary_univariate(constrained[5:6])\n", " return unconstrained\n", "```\n", "\n", "I'll write the full class below (without the optional changes I have just discussed)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "class TVRegressionExtended(sm.tsa.statespace.MLEModel):\n", " def __init__(self, y_t, x_t, w_t):\n", " exog = np.c_[x_t, w_t] # shaped nobs x 2\n", "\n", " super(TVRegressionExtended, self).__init__(\n", " endog=y_t, exog=exog, k_states=2,\n", " initialization='diffuse')\n", "\n", " # Since the design matrix is time-varying, it must be\n", " # shaped k_endog x k_states x nobs\n", " # Notice that exog.T is shaped k_states x nobs, so we\n", " # just need to add a new first axis with shape 1\n", " self.ssm['design'] = exog.T[np.newaxis, :, :] # shaped 1 x 2 x nobs\n", " self.ssm['selection'] = np.eye(self.k_states)\n", " self.ssm['transition'] = np.eye(self.k_states)\n", " \n", " #Which parameters need to be positive?\n", " self.positive_parameters = slice(1, 4)\n", "\n", " @property\n", " def param_names(self):\n", " return ['intercept', 'var.e', 'var.x.coeff', 'var.w.coeff',\n", " 'rho1', 'rho2']\n", "\n", " @property\n", " def start_params(self):\n", " \"\"\"\n", " Defines the starting values for the parameters\n", " The linear regression gives us reasonable starting values for the constant\n", " d and the variance of the epsilon error\n", " \"\"\"\n", "\n", " exog = sm.add_constant(self.exog)\n", " res = sm.OLS(self.endog, exog).fit()\n", " params = np.r_[res.params[0], res.scale, 0.001, 0.001, 0.7, 0.8]\n", " return params\n", "\n", " def transform_params(self, unconstrained):\n", " \"\"\"\n", " We constraint the last three parameters\n", " ('var.e', 'var.x.coeff', 'var.w.coeff') to be positive, \n", " because they are variances\n", " \"\"\"\n", " constrained = unconstrained.copy()\n", " constrained[self.positive_parameters] = constrained[self.positive_parameters]**2\n", " return constrained\n", "\n", " def untransform_params(self, constrained):\n", " \"\"\"\n", " Need to unstransform all the parameters you transformed\n", " in the `transform_params` function\n", " \"\"\"\n", " unconstrained = constrained.copy()\n", " unconstrained[self.positive_parameters] = unconstrained[self.positive_parameters]**0.5\n", " return unconstrained\n", "\n", " def update(self, params, **kwargs):\n", " params = super(TVRegressionExtended, self).update(params, **kwargs)\n", "\n", " self['obs_intercept', 0, 0] = params[0]\n", " self['obs_cov', 0, 0] = params[1]\n", " self['state_cov'] = np.diag(params[2:4])\n", " self['transition', 0, 0] = params[4]\n", " self['transition', 1, 1] = params[5]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To estimate, we'll use the same data as in model 1 and expect the $\\rho_1, \\rho_2$ to be near 1.\n", "\n", "The results look pretty good!\n", "Note that this estimation can be quite sensitive to the starting value of $\\rho_1, \\rho_2$. If you try lower values, you'll see it fails to converge." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = TVRegressionExtended(y_t, x_t, w_t)\n", "res = mod.fit(maxiter=2000) #it doesn't converge with 50 iters\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model 3: multiple observation and state equations\n", "\n", "We'll keep the time-varying parameters, but this time we'll also have two observation equations.\n", "\n", "### Observation equations\n", "\n", "$\\hat{i_t}, \\hat{M_t}, \\hat{s_t}$ are observed each period.\n", "\n", "The model for the observation equation has two equations:\n", "\n", "$$ \\hat{i_t} = \\alpha_1 * \\hat{s_t} + \\varepsilon_1 $$\n", "\n", "$$ \\hat{M_t} = \\alpha_2 + \\varepsilon_2 $$\n", "\n", "Following the [general notation from state space models](https://www.statsmodels.org/stable/statespace.html), the endogenous part of the observation equation is $y_t = (\\hat{i_t}, \\hat{M_t})$ and we only have one exogenous variable $\\hat{s_t}$\n", "\n", "\n", "### State equations\n", "\n", "\n", "$$ \\alpha_{1, t+1} = \\delta_1 \\alpha_{1, t} + \\delta_2 \\alpha_{2, t} + W_1 $$\n", "\n", "$$ \\alpha_{2, t+1} = \\delta_3 \\alpha_{2, t} + W_2 $$\n", "\n", "\n", "### Matrix notation for the state space model\n", "\n", "$$\n", "\\begin{aligned}\n", "\\begin{bmatrix} \\hat{i_t} \\\\ \\hat{M_t} \\end{bmatrix} &= \n", "\\begin{bmatrix} \\hat{s_t} & 0 \\\\ 0 & 1 \\end{bmatrix} \\begin{bmatrix} \\alpha_{1, t} \\\\ \\alpha_{2, t} \\end{bmatrix} + \\begin{bmatrix} \\varepsilon_{1, t} \\\\ \\varepsilon_{1, t} \\end{bmatrix} \\hspace{6.5em} \\varepsilon_t \\sim N \\left ( \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}, \\begin{bmatrix} \\sigma_{\\varepsilon_1}^2 & 0 \\\\ 0 & \\sigma_{\\varepsilon_2}^2 \\end{bmatrix} \\right )\n", "\\\\\n", "\\begin{bmatrix} \\alpha_{1, t+1} \\\\ \\alpha_{2, t+1} \\end{bmatrix} & = \\begin{bmatrix} \\delta_1 & \\delta_1 \\\\ 0 & \\delta_3 \\end{bmatrix} \\begin{bmatrix} \\alpha_{1, t} \\\\ \\alpha_{2, t} \\end{bmatrix} + \\begin{bmatrix} W_1 \\\\ W_2 \\end{bmatrix} \\hspace{3.em} \\begin{bmatrix} W_1 \\\\ W_2 \\end{bmatrix} \\sim N \\left ( \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}, \\begin{bmatrix} \\sigma_{W_1}^2 & 0 \\\\ 0 & \\sigma_{W_2}^2 \\end{bmatrix} \\right )\n", "\\end{aligned}\n", "$$\n", "\n", "I'll simulate some data, talk about what we need to modify and finally estimate the model to see if we're recovering something reasonable.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "true_values = {'var_e1': 0.01, 'var_e2': 0.01,\n", " 'var_w1': 0.01, 'var_w2': 0.01,\n", " 'delta1': 0.8, 'delta2': 0.5, 'delta3': 0.7}\n", "\n", "def gen_data_for_model3():\n", " #Starting values\n", " alpha1_0 = 2.1\n", " alpha2_0 = 1.1\n", "\n", " t_max = 500\n", "\n", " def gen_i(alpha1, s):\n", " return alpha1*s + np.sqrt(true_values['var_e1'])*np.random.randn()\n", "\n", " def gen_m_hat(alpha2):\n", " return 1*alpha2 + np.sqrt(true_values['var_e2'])*np.random.randn()\n", "\n", " def gen_alpha1(alpha1, alpha2):\n", " w1 = np.sqrt(true_values['var_w1'])*np.random.randn()\n", " return true_values['delta1'] * alpha1 + true_values['delta2'] * alpha2 + w1\n", "\n", " def gen_alpha2(alpha2):\n", " w2 = np.sqrt(true_values['var_w2'])*np.random.randn()\n", " return true_values['delta3'] * alpha2 + w2\n", "\n", " s_t = 0.3 + np.sqrt(1.4)*np.random.randn(t_max)\n", " i_hat = np.empty(t_max)\n", " m_hat = np.empty(t_max)\n", "\n", " current_alpha1 = alpha1_0\n", " current_alpha2 = alpha2_0\n", " for t in range(t_max):\n", " #Obs eqns\n", " i_hat[t] = gen_i(current_alpha1, s_t[t])\n", " m_hat[t] = gen_m_hat(current_alpha2)\n", "\n", " #state eqns\n", " new_alpha1 = gen_alpha1(current_alpha1, current_alpha2)\n", " new_alpha2 = gen_alpha2(current_alpha2)\n", "\n", " #Update states for next period\n", " current_alpha1 = new_alpha1\n", " current_alpha2 = new_alpha2\n", " \n", " return i_hat, m_hat, s_t\n", "\n", "i_hat, m_hat, s_t = gen_data_for_model3()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### What do we need to modify?\n", "\n", "Once again, we don't need to change much, but we need to be careful about the dimensions.\n", "\n", "#### 1) The `__init__` function changes from\n", "\n", "\n", "```python\n", "def __init__(self, y_t, x_t, w_t):\n", " exog = np.c_[x_t, w_t]\n", "\n", " super(TVRegressionExtended, self).__init__(\n", " endog=y_t, exog=exog, k_states=2,\n", " initialization='diffuse')\n", "\n", " self.ssm['design'] = exog.T[np.newaxis, :, :] # shaped 1 x 2 x nobs\n", " self.ssm['selection'] = np.eye(self.k_states)\n", " self.ssm['transition'] = np.eye(self.k_states)\n", "```\n", "\n", "to\n", "\n", "\n", "```python\n", "def __init__(self, i_t: np.array, s_t: np.array, m_t: np.array):\n", "\n", " exog = np.c_[s_t, np.repeat(1, len(s_t))] # exog.shape => (nobs, 2)\n", " \n", " super(MultipleYsModel, self).__init__(\n", " endog=np.c_[i_t, m_t], exog=exog, k_states=2,\n", " initialization='diffuse')\n", " \n", " self.ssm['design'] = np.zeros((self.k_endog, self.k_states, self.nobs))\n", " self.ssm['design', 0, 0, :] = s_t\n", " self.ssm['design', 1, 1, :] = 1\n", "```\n", "\n", "Note that we did not have to specify `k_endog` anywhere. The initialization does this for us after checking the dimensions of the `endog` matrix.\n", "\n", "\n", "#### 2) The `update()` function \n", "\n", "changes from \n", "\n", "```python\n", "def update(self, params, **kwargs):\n", " params = super(TVRegressionExtended, self).update(params, **kwargs)\n", "\n", " self['obs_intercept', 0, 0] = params[0]\n", " self['obs_cov', 0, 0] = params[1]\n", " \n", " self['state_cov'] = np.diag(params[2:4])\n", " self['transition', 0, 0] = params[4]\n", " self['transition', 1, 1] = params[5]\n", "```\n", "\n", "\n", "to\n", "\n", "\n", "```python\n", "def update(self, params, **kwargs):\n", " params = super(MultipleYsModel, self).update(params, **kwargs)\n", " \n", " \n", " #The following line is not needed (by default, this matrix is initialized by zeroes),\n", " #But I leave it here so the dimensions are clearer\n", " self['obs_intercept'] = np.repeat([np.array([0, 0])], self.nobs, axis=0).T\n", " self['obs_cov', 0, 0] = params[0]\n", " self['obs_cov', 1, 1] = params[1]\n", "\n", " self['state_cov'] = np.diag(params[2:4])\n", " #delta1, delta2, delta3\n", " self['transition', 0, 0] = params[4]\n", " self['transition', 0, 1] = params[5]\n", " self['transition', 1, 1] = params[6]\n", "```\n", "\n", "The rest of the methods change in pretty obvious ways (need to add parameter names, make sure the indexes work, etc). The full code for the function is right below" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "starting_values = {'var_e1': 0.2, 'var_e2': 0.1,\n", " 'var_w1': 0.15, 'var_w2': 0.18,\n", " 'delta1': 0.7, 'delta2': 0.1, 'delta3': 0.85}\n", "\n", "\n", "class MultipleYsModel(sm.tsa.statespace.MLEModel):\n", " def __init__(self, i_t: np.array, s_t: np.array, m_t: np.array):\n", "\n", " exog = np.c_[s_t, np.repeat(1, len(s_t))] # exog.shape => (nobs, 2)\n", " \n", " super(MultipleYsModel, self).__init__(\n", " endog=np.c_[i_t, m_t], exog=exog, k_states=2,\n", " initialization='diffuse')\n", " \n", " self.ssm['design'] = np.zeros((self.k_endog, self.k_states, self.nobs))\n", " self.ssm['design', 0, 0, :] = s_t\n", " self.ssm['design', 1, 1, :] = 1\n", " \n", " #These have ok shape. Placeholders since I'm changing them\n", " #in the update() function\n", " self.ssm['selection'] = np.eye(self.k_states)\n", " self.ssm['transition'] = np.eye(self.k_states)\n", " \n", " #Dictionary of positions to names\n", " self.position_dict = OrderedDict(var_e1=1, var_e2=2, \n", " var_w1=3, var_w2=4,\n", " delta1=5, delta2=6, delta3=7)\n", " self.initial_values = starting_values\n", " self.positive_parameters = slice(0, 4)\n", " \n", "\n", " @property\n", " def param_names(self):\n", " return list(self.position_dict.keys())\n", "\n", " @property\n", " def start_params(self):\n", " \"\"\"\n", " Initial values\n", " \"\"\"\n", " #(optional) Use scale for var_e1 and var_e2 starting values\n", " params = np.r_[self.initial_values['var_e1'],\n", " self.initial_values['var_e2'],\n", " self.initial_values['var_w1'],\n", " self.initial_values['var_w2'],\n", " self.initial_values['delta1'],\n", " self.initial_values['delta2'],\n", " self.initial_values['delta3']]\n", " return params\n", "\n", " def transform_params(self, unconstrained):\n", " \"\"\"\n", " If you need to restrict parameters\n", " For example, variances should be > 0\n", " Parameters maybe have to be within -1 and 1\n", " \"\"\"\n", " constrained = unconstrained.copy()\n", " constrained[self.positive_parameters] = constrained[self.positive_parameters]**2\n", " return constrained\n", "\n", " def untransform_params(self, constrained):\n", " \"\"\"\n", " Need to reverse what you did in transform_params()\n", " \"\"\"\n", " unconstrained = constrained.copy()\n", " unconstrained[self.positive_parameters] = unconstrained[self.positive_parameters]**0.5\n", " return unconstrained\n", "\n", " def update(self, params, **kwargs):\n", " params = super(MultipleYsModel, self).update(params, **kwargs)\n", " \n", " #The following line is not needed (by default, this matrix is initialized by zeroes),\n", " #But I leave it here so the dimensions are clearer\n", " self['obs_intercept'] = np.repeat([np.array([0, 0])], self.nobs, axis=0).T\n", " \n", " self['obs_cov', 0, 0] = params[0]\n", " self['obs_cov', 1, 1] = params[1]\n", " \n", " self['state_cov'] = np.diag(params[2:4])\n", " \n", " #delta1, delta2, delta3\n", " self['transition', 0, 0] = params[4]\n", " self['transition', 0, 1] = params[5]\n", " self['transition', 1, 1] = params[6]\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = MultipleYsModel(i_hat, s_t, m_hat)\n", "res = mod.fit()\n", "\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bonus: pymc3 for fast Bayesian estimation\n", "\n", "In this section I'll show how you can take your custom state space model and easily plug it to `pymc3` and estimate it with Bayesian methods. In particular, this example will show you an estimation with a version of Hamiltonian Monte Carlo called the No-U-Turn Sampler (NUTS).\n", "\n", "I'm basically copying the ideas contained [in this notebook](https://www.statsmodels.org/dev/examples/notebooks/generated/statespace_sarimax_pymc3.html), so make sure to check that for more details." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#Extra requirements\n", "import theano\n", "import theano.tensor as tt\n", "import pymc3 as pm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We need to define some helper functions to connect theano to the likelihood function that is implied in our model" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "class Loglike(tt.Op):\n", "\n", " itypes = [tt.dvector] # expects a vector of parameter values when called\n", " otypes = [tt.dscalar] # outputs a single scalar value (the log likelihood)\n", "\n", " def __init__(self, model):\n", " self.model = model\n", " self.score = Score(self.model)\n", "\n", " def perform(self, node, inputs, outputs):\n", " theta, = inputs # contains the vector of parameters\n", " llf = self.model.loglike(theta)\n", " outputs[0][0] = np.array(llf) # output the log-likelihood\n", "\n", " def grad(self, inputs, g):\n", " # the method that calculates the gradients - it actually returns the\n", " # vector-Jacobian product - g[0] is a vector of parameter values\n", " theta, = inputs # our parameters\n", " out = [g[0] * self.score(theta)]\n", " return out\n", "\n", "\n", "class Score(tt.Op):\n", " itypes = [tt.dvector]\n", " otypes = [tt.dvector]\n", "\n", " def __init__(self, model):\n", " self.model = model\n", "\n", " def perform(self, node, inputs, outputs):\n", " theta, = inputs\n", " outputs[0][0] = self.model.score(theta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll simulate again the data we used for model 1.\n", "We'll also `fit` it again and save the results to compare them to the Bayesian posterior we get." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "y_t, x_t, w_t, beta_x, beta_w = gen_data_for_model1()\n", "plt.plot(y_t)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = TVRegression(y_t, x_t, w_t)\n", "res_mle = mod.fit(disp=False)\n", "print(res_mle.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayesian estimation\n", "\n", "We need to define a prior for each parameter and the number of draws and burn-in points" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Set sampling params\n", "ndraws = 3000 # 3000 number of draws from the distribution\n", "nburn = 600 # 600 number of \"burn-in points\" (which will be discarded)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Construct an instance of the Theano wrapper defined above, which\n", "# will allow PyMC3 to compute the likelihood and Jacobian in a way\n", "# that it can make use of. Here we are using the same model instance\n", "# created earlier for MLE analysis (we could also create a new model\n", "# instance if we preferred)\n", "loglike = Loglike(mod)\n", "\n", "with pm.Model():\n", " # Priors\n", " intercept = pm.Uniform('intercept', 1, 10)\n", " var_e = pm.InverseGamma('var.e', 2.3, 0.5)\n", " var_x_coeff = pm.InverseGamma('var.x.coeff', 2.3, 0.1)\n", " var_w_coeff = pm.InverseGamma('var.w.coeff', 2.3, 0.1)\n", "\n", " # convert variables to tensor vectors\n", " theta = tt.as_tensor_variable([intercept, var_e, var_x_coeff, var_w_coeff])\n", "\n", " # use a DensityDist (use a lamdba function to \"call\" the Op)\n", " pm.DensityDist('likelihood', lambda v: loglike(v), observed={'v': theta})\n", "\n", " # Draw samples\n", " trace = pm.sample(ndraws, tune=nburn, discard_tuned_samples=True, cores=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### How does the posterior distribution compare with the MLE estimation?\n", "\n", "The clearly peak around the MLE estimate." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "results_dict = {'intercept': res_mle.params[0], 'var.e': res_mle.params[1],\n", " 'var.x.coeff': res_mle.params[2], 'var.w.coeff': res_mle.params[3]}\n", "plt.tight_layout()\n", "_ = pm.traceplot(trace,\n", " lines=[(k, {}, [v]) for k, v in dict(results_dict).items()],\n", " combined=True,\n", " figsize=(12, 12))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 4 } statsmodels-0.12.2/examples/notebooks/statespace_cycles.ipynb000066400000000000000000000150051400612667500245300ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Trends and cycles in unemployment\n", "\n", "Here we consider three methods for separating a trend and cycle in economic data. Supposing we have a time series $y_t$, the basic idea is to decompose it into these two components:\n", "\n", "$$\n", "y_t = \\mu_t + \\eta_t\n", "$$\n", "\n", "where $\\mu_t$ represents the trend or level and $\\eta_t$ represents the cyclical component. In this case, we consider a *stochastic* trend, so that $\\mu_t$ is a random variable and not a deterministic function of time. Two of methods fall under the heading of \"unobserved components\" models, and the third is the popular Hodrick-Prescott (HP) filter. Consistent with e.g. Harvey and Jaeger (1993), we find that these models all produce similar decompositions.\n", "\n", "This notebook demonstrates applying these models to separate trend from cycle in the U.S. unemployment rate." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from pandas_datareader.data import DataReader\n", "endog = DataReader('UNRATE', 'fred', start='1954-01-01')\n", "endog.index.freq = endog.index.inferred_freq" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hodrick-Prescott (HP) filter\n", "\n", "The first method is the Hodrick-Prescott filter, which can be applied to a data series in a very straightforward method. Here we specify the parameter $\\lambda=129600$ because the unemployment rate is observed monthly." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "hp_cycle, hp_trend = sm.tsa.filters.hpfilter(endog, lamb=129600)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Unobserved components and ARIMA model (UC-ARIMA)\n", "\n", "The next method is an unobserved components model, where the trend is modeled as a random walk and the cycle is modeled with an ARIMA model - in particular, here we use an AR(4) model. The process for the time series can be written as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\mu_t + \\eta_t \\\\\n", "\\mu_{t+1} & = \\mu_t + \\epsilon_{t+1} \\\\\n", "\\phi(L) \\eta_t & = \\nu_t\n", "\\end{align}\n", "$$\n", "\n", "where $\\phi(L)$ is the AR(4) lag polynomial and $\\epsilon_t$ and $\\nu_t$ are white noise." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod_ucarima = sm.tsa.UnobservedComponents(endog, 'rwalk', autoregressive=4)\n", "# Here the powell method is used, since it achieves a\n", "# higher loglikelihood than the default L-BFGS method\n", "res_ucarima = mod_ucarima.fit(method='powell', disp=False)\n", "print(res_ucarima.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Unobserved components with stochastic cycle (UC)\n", "\n", "The final method is also an unobserved components model, but where the cycle is modeled explicitly.\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\mu_t + \\eta_t \\\\\n", "\\mu_{t+1} & = \\mu_t + \\epsilon_{t+1} \\\\\n", "\\eta_{t+1} & = \\eta_t \\cos \\lambda_\\eta + \\eta_t^* \\sin \\lambda_\\eta + \\tilde \\omega_t \\qquad & \\tilde \\omega_t \\sim N(0, \\sigma_{\\tilde \\omega}^2) \\\\\n", "\\eta_{t+1}^* & = -\\eta_t \\sin \\lambda_\\eta + \\eta_t^* \\cos \\lambda_\\eta + \\tilde \\omega_t^* & \\tilde \\omega_t^* \\sim N(0, \\sigma_{\\tilde \\omega}^2)\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod_uc = sm.tsa.UnobservedComponents(\n", " endog, 'rwalk',\n", " cycle=True, stochastic_cycle=True, damped_cycle=True,\n", ")\n", "# Here the powell method gets close to the optimum\n", "res_uc = mod_uc.fit(method='powell', disp=False)\n", "# but to get to the highest loglikelihood we do a\n", "# second round using the L-BFGS method.\n", "res_uc = mod_uc.fit(res_uc.params, disp=False)\n", "print(res_uc.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Graphical comparison\n", "\n", "The output of each of these models is an estimate of the trend component $\\mu_t$ and an estimate of the cyclical component $\\eta_t$. Qualitatively the estimates of trend and cycle are very similar, although the trend component from the HP filter is somewhat more variable than those from the unobserved components models. This means that relatively mode of the movement in the unemployment rate is attributed to changes in the underlying trend rather than to temporary cyclical movements." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, axes = plt.subplots(2, figsize=(13,5));\n", "axes[0].set(title='Level/trend component')\n", "axes[0].plot(endog.index, res_uc.level.smoothed, label='UC')\n", "axes[0].plot(endog.index, res_ucarima.level.smoothed, label='UC-ARIMA(2,0)')\n", "axes[0].plot(hp_trend, label='HP Filter')\n", "axes[0].legend(loc='upper left')\n", "axes[0].grid()\n", "\n", "axes[1].set(title='Cycle component')\n", "axes[1].plot(endog.index, res_uc.cycle.smoothed, label='UC')\n", "axes[1].plot(endog.index, res_ucarima.autoregressive.smoothed, label='UC-ARIMA(2,0)')\n", "axes[1].plot(hp_cycle, label='HP Filter')\n", "axes[1].legend(loc='upper left')\n", "axes[1].grid()\n", "\n", "fig.tight_layout();" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 1 }statsmodels-0.12.2/examples/notebooks/statespace_dfm_coincident.ipynb000066400000000000000000001136041400612667500262170ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Dynamic factors and coincident indices\n", "\n", "Factor models generally try to find a small number of unobserved \"factors\" that influence a substantial portion of the variation in a larger number of observed variables, and they are related to dimension-reduction techniques such as principal components analysis. Dynamic factor models explicitly model the transition dynamics of the unobserved factors, and so are often applied to time-series data.\n", "\n", "Macroeconomic coincident indices are designed to capture the common component of the \"business cycle\"; such a component is assumed to simultaneously affect many macroeconomic variables. Although the estimation and use of coincident indices (for example the [Index of Coincident Economic Indicators](http://www.newyorkfed.org/research/regional_economy/coincident_summary.html)) pre-dates dynamic factor models, in several influential papers Stock and Watson (1989, 1991) used a dynamic factor model to provide a theoretical foundation for them.\n", "\n", "Below, we follow the treatment found in Kim and Nelson (1999), of the Stock and Watson (1991) model, to formulate a dynamic factor model, estimate its parameters via maximum likelihood, and create a coincident index." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Macroeconomic data\n", "\n", "The coincident index is created by considering the comovements in four macroeconomic variables (versions of these variables are available on [FRED](https://research.stlouisfed.org/fred2/); the ID of the series used below is given in parentheses):\n", "\n", "- Industrial production (IPMAN)\n", "- Real aggregate income (excluding transfer payments) (W875RX1)\n", "- Manufacturing and trade sales (CMRMTSPL)\n", "- Employees on non-farm payrolls (PAYEMS)\n", "\n", "In all cases, the data is at the monthly frequency and has been seasonally adjusted; the time-frame considered is 1972 - 2005." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "\n", "np.set_printoptions(precision=4, suppress=True, linewidth=120)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from pandas_datareader.data import DataReader\n", "\n", "# Get the datasets from FRED\n", "start = '1979-01-01'\n", "end = '2014-12-01'\n", "indprod = DataReader('IPMAN', 'fred', start=start, end=end)\n", "income = DataReader('W875RX1', 'fred', start=start, end=end)\n", "sales = DataReader('CMRMTSPL', 'fred', start=start, end=end)\n", "emp = DataReader('PAYEMS', 'fred', start=start, end=end)\n", "# dta = pd.concat((indprod, income, sales, emp), axis=1)\n", "# dta.columns = ['indprod', 'income', 'sales', 'emp']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note**: in a recent update on FRED (8/12/15) the time series CMRMTSPL was truncated to begin in 1997; this is probably a mistake due to the fact that CMRMTSPL is a spliced series, so the earlier period is from the series HMRMT and the latter period is defined by CMRMT.\n", "\n", "This has since (02/11/16) been corrected, however the series could also be constructed by hand from HMRMT and CMRMT, as shown below (process taken from the notes in the Alfred xls file)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# HMRMT = DataReader('HMRMT', 'fred', start='1967-01-01', end=end)\n", "# CMRMT = DataReader('CMRMT', 'fred', start='1997-01-01', end=end)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# HMRMT_growth = HMRMT.diff() / HMRMT.shift()\n", "# sales = pd.Series(np.zeros(emp.shape[0]), index=emp.index)\n", "\n", "# # Fill in the recent entries (1997 onwards)\n", "# sales[CMRMT.index] = CMRMT\n", "\n", "# # Backfill the previous entries (pre 1997)\n", "# idx = sales.loc[:'1997-01-01'].index\n", "# for t in range(len(idx)-1, 0, -1):\n", "# month = idx[t]\n", "# prev_month = idx[t-1]\n", "# sales.loc[prev_month] = sales.loc[month] / (1 + HMRMT_growth.loc[prev_month].values)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dta = pd.concat((indprod, income, sales, emp), axis=1)\n", "dta.columns = ['indprod', 'income', 'sales', 'emp']\n", "dta.index.freq = dta.index.inferred_freq" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dta.loc[:, 'indprod':'emp'].plot(subplots=True, layout=(2, 2), figsize=(15, 6));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Stock and Watson (1991) report that for their datasets, they could not reject the null hypothesis of a unit root in each series (so the series are integrated), but they did not find strong evidence that the series were co-integrated.\n", "\n", "As a result, they suggest estimating the model using the first differences (of the logs) of the variables, demeaned and standardized." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create log-differenced series\n", "dta['dln_indprod'] = (np.log(dta.indprod)).diff() * 100\n", "dta['dln_income'] = (np.log(dta.income)).diff() * 100\n", "dta['dln_sales'] = (np.log(dta.sales)).diff() * 100\n", "dta['dln_emp'] = (np.log(dta.emp)).diff() * 100\n", "\n", "# De-mean and standardize\n", "dta['std_indprod'] = (dta['dln_indprod'] - dta['dln_indprod'].mean()) / dta['dln_indprod'].std()\n", "dta['std_income'] = (dta['dln_income'] - dta['dln_income'].mean()) / dta['dln_income'].std()\n", "dta['std_sales'] = (dta['dln_sales'] - dta['dln_sales'].mean()) / dta['dln_sales'].std()\n", "dta['std_emp'] = (dta['dln_emp'] - dta['dln_emp'].mean()) / dta['dln_emp'].std()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dynamic factors\n", "\n", "A general dynamic factor model is written as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\Lambda f_t + B x_t + u_t \\\\\n", "f_t & = A_1 f_{t-1} + \\dots + A_p f_{t-p} + \\eta_t \\qquad \\eta_t \\sim N(0, I)\\\\\n", "u_t & = C_1 u_{t-1} + \\dots + C_q u_{t-q} + \\varepsilon_t \\qquad \\varepsilon_t \\sim N(0, \\Sigma)\n", "\\end{align}\n", "$$\n", "\n", "where $y_t$ are observed data, $f_t$ are the unobserved factors (evolving as a vector autoregression), $x_t$ are (optional) exogenous variables, and $u_t$ is the error, or \"idiosyncratic\", process ($u_t$ is also optionally allowed to be autocorrelated). The $\\Lambda$ matrix is often referred to as the matrix of \"factor loadings\". The variance of the factor error term is set to the identity matrix to ensure identification of the unobserved factors.\n", "\n", "This model can be cast into state space form, and the unobserved factor estimated via the Kalman filter. The likelihood can be evaluated as a byproduct of the filtering recursions, and maximum likelihood estimation used to estimate the parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model specification\n", "\n", "The specific dynamic factor model in this application has 1 unobserved factor which is assumed to follow an AR(2) process. The innovations $\\varepsilon_t$ are assumed to be independent (so that $\\Sigma$ is a diagonal matrix) and the error term associated with each equation, $u_{i,t}$ is assumed to follow an independent AR(2) process.\n", "\n", "Thus the specification considered here is:\n", "\n", "$$\n", "\\begin{align}\n", "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\\\\n", "u_{i,t} & = c_{i,1} u_{1,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n", "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n", "\\end{align}\n", "$$\n", "\n", "where $i$ is one of: `[indprod, income, sales, emp ]`.\n", "\n", "This model can be formulated using the `DynamicFactor` model built-in to statsmodels. In particular, we have the following specification:\n", "\n", "- `k_factors = 1` - (there is 1 unobserved factor)\n", "- `factor_order = 2` - (it follows an AR(2) process)\n", "- `error_var = False` - (the errors evolve as independent AR processes rather than jointly as a VAR - note that this is the default option, so it is not specified below)\n", "- `error_order = 2` - (the errors are autocorrelated of order 2: i.e. AR(2) processes)\n", "- `error_cov_type = 'diagonal'` - (the innovations are uncorrelated; this is again the default)\n", "\n", "Once the model is created, the parameters can be estimated via maximum likelihood; this is done using the `fit()` method.\n", "\n", "**Note**: recall that we have demeaned and standardized the data; this will be important in interpreting the results that follow.\n", "\n", "**Aside**: in their empirical example, Kim and Nelson (1999) actually consider a slightly different model in which the employment variable is allowed to also depend on lagged values of the factor - this model does not fit into the built-in `DynamicFactor` class, but can be accommodated by using a subclass to implement the required new parameters and restrictions - see Appendix A, below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Parameter estimation\n", "\n", "Multivariate models can have a relatively large number of parameters, and it may be difficult to escape from local minima to find the maximized likelihood. In an attempt to mitigate this problem, I perform an initial maximization step (from the model-defined starting parameters) using the modified Powell method available in Scipy (see the minimize documentation for more information). The resulting parameters are then used as starting parameters in the standard LBFGS optimization method." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Get the endogenous data\n", "endog = dta.loc['1979-02-01':, 'std_indprod':'std_emp']\n", "\n", "# Create the model\n", "mod = sm.tsa.DynamicFactor(endog, k_factors=1, factor_order=2, error_order=2)\n", "initial_res = mod.fit(method='powell', disp=False)\n", "res = mod.fit(initial_res.params, disp=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimates\n", "\n", "Once the model has been estimated, there are two components that we can use for analysis or inference:\n", "\n", "- The estimated parameters\n", "- The estimated factor" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Parameters\n", "\n", "The estimated parameters can be helpful in understanding the implications of the model, although in models with a larger number of observed variables and / or unobserved factors they can be difficult to interpret.\n", "\n", "One reason for this difficulty is due to identification issues between the factor loadings and the unobserved factors. One easy-to-see identification issue is the sign of the loadings and the factors: an equivalent model to the one displayed below would result from reversing the signs of all factor loadings and the unobserved factor.\n", "\n", "Here, one of the easy-to-interpret implications in this model is the persistence of the unobserved factor: we find that exhibits substantial persistence." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(res.summary(separate_params=False))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Estimated factors\n", "\n", "While it can be useful to plot the unobserved factors, it is less useful here than one might think for two reasons:\n", "\n", "1. The sign-related identification issue described above.\n", "2. Since the data was differenced, the estimated factor explains the variation in the differenced data, not the original data.\n", "\n", "It is for these reasons that the coincident index is created (see below).\n", "\n", "With these reservations, the unobserved factor is plotted below, along with the NBER indicators for US recessions. It appears that the factor is successful at picking up some degree of business cycle activity." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(13,3))\n", "\n", "# Plot the factor\n", "dates = endog.index._mpl_repr()\n", "ax.plot(dates, res.factors.filtered[0], label='Factor')\n", "ax.legend()\n", "\n", "# Retrieve and also plot the NBER recession indicators\n", "rec = DataReader('USREC', 'fred', start=start, end=end)\n", "ylim = ax.get_ylim()\n", "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Post-estimation\n", "\n", "Although here we will be able to interpret the results of the model by constructing the coincident index, there is a useful and generic approach for getting a sense for what is being captured by the estimated factor. By taking the estimated factors as given, regressing them (and a constant) each (one at a time) on each of the observed variables, and recording the coefficients of determination ($R^2$ values), we can get a sense of the variables for which each factor explains a substantial portion of the variance and the variables for which it does not.\n", "\n", "In models with more variables and more factors, this can sometimes lend interpretation to the factors (for example sometimes one factor will load primarily on real variables and another on nominal variables).\n", "\n", "In this model, with only four endogenous variables and one factor, it is easy to digest a simple table of the $R^2$ values, but in larger models it is not. For this reason, a bar plot is often employed; from the plot we can easily see that the factor explains most of the variation in industrial production index and a large portion of the variation in sales and employment, it is less helpful in explaining income." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res.plot_coefficients_of_determination(figsize=(8,2));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Coincident Index\n", "\n", "As described above, the goal of this model was to create an interpretable series which could be used to understand the current status of the macroeconomy. This is what the coincident index is designed to do. It is constructed below. For readers interested in an explanation of the construction, see Kim and Nelson (1999) or Stock and Watson (1991).\n", "\n", "In essence, what is done is to reconstruct the mean of the (differenced) factor. We will compare it to the coincident index on published by the Federal Reserve Bank of Philadelphia (USPHCI on FRED)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "usphci = DataReader('USPHCI', 'fred', start='1979-01-01', end='2014-12-01')['USPHCI']\n", "usphci.plot(figsize=(13,3));" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dusphci = usphci.diff()[1:].values\n", "def compute_coincident_index(mod, res):\n", " # Estimate W(1)\n", " spec = res.specification\n", " design = mod.ssm['design']\n", " transition = mod.ssm['transition']\n", " ss_kalman_gain = res.filter_results.kalman_gain[:,:,-1]\n", " k_states = ss_kalman_gain.shape[0]\n", "\n", " W1 = np.linalg.inv(np.eye(k_states) - np.dot(\n", " np.eye(k_states) - np.dot(ss_kalman_gain, design),\n", " transition\n", " )).dot(ss_kalman_gain)[0]\n", "\n", " # Compute the factor mean vector\n", " factor_mean = np.dot(W1, dta.loc['1972-02-01':, 'dln_indprod':'dln_emp'].mean())\n", " \n", " # Normalize the factors\n", " factor = res.factors.filtered[0]\n", " factor *= np.std(usphci.diff()[1:]) / np.std(factor)\n", "\n", " # Compute the coincident index\n", " coincident_index = np.zeros(mod.nobs+1)\n", " # The initial value is arbitrary; here it is set to\n", " # facilitate comparison\n", " coincident_index[0] = usphci.iloc[0] * factor_mean / dusphci.mean()\n", " for t in range(0, mod.nobs):\n", " coincident_index[t+1] = coincident_index[t] + factor[t] + factor_mean\n", " \n", " # Attach dates\n", " coincident_index = pd.Series(coincident_index, index=dta.index).iloc[1:]\n", " \n", " # Normalize to use the same base year as USPHCI\n", " coincident_index *= (usphci.loc['1992-07-01'] / coincident_index.loc['1992-07-01'])\n", " \n", " return coincident_index" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we plot the calculated coincident index along with the US recessions and the comparison coincident index USPHCI." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(13,3))\n", "\n", "# Compute the index\n", "coincident_index = compute_coincident_index(mod, res)\n", "\n", "# Plot the factor\n", "dates = endog.index._mpl_repr()\n", "ax.plot(dates, coincident_index, label='Coincident index')\n", "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n", "ax.legend(loc='lower right')\n", "\n", "# Retrieve and also plot the NBER recession indicators\n", "ylim = ax.get_ylim()\n", "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Appendix 1: Extending the dynamic factor model\n", "\n", "Recall that the previous specification was described by:\n", "\n", "$$\n", "\\begin{align}\n", "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\\\\n", "u_{i,t} & = c_{i,1} u_{1,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n", "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n", "\\end{align}\n", "$$\n", "\n", "Written in state space form, the previous specification of the model had the following observation equation:\n", "\n", "$$\n", "\\begin{bmatrix}\n", "y_{\\text{indprod}, t} \\\\\n", "y_{\\text{income}, t} \\\\\n", "y_{\\text{sales}, t} \\\\\n", "y_{\\text{emp}, t} \\\\\n", "\\end{bmatrix} = \\begin{bmatrix}\n", "\\lambda_\\text{indprod} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\lambda_\\text{income} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\lambda_\\text{sales} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\lambda_\\text{emp} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", "\\end{bmatrix}\n", "\\begin{bmatrix}\n", "f_t \\\\\n", "f_{t-1} \\\\\n", "u_{\\text{indprod}, t} \\\\\n", "u_{\\text{income}, t} \\\\\n", "u_{\\text{sales}, t} \\\\\n", "u_{\\text{emp}, t} \\\\\n", "u_{\\text{indprod}, t-1} \\\\\n", "u_{\\text{income}, t-1} \\\\\n", "u_{\\text{sales}, t-1} \\\\\n", "u_{\\text{emp}, t-1} \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "and transition equation:\n", "\n", "$$\n", "\\begin{bmatrix}\n", "f_t \\\\\n", "f_{t-1} \\\\\n", "u_{\\text{indprod}, t} \\\\\n", "u_{\\text{income}, t} \\\\\n", "u_{\\text{sales}, t} \\\\\n", "u_{\\text{emp}, t} \\\\\n", "u_{\\text{indprod}, t-1} \\\\\n", "u_{\\text{income}, t-1} \\\\\n", "u_{\\text{sales}, t-1} \\\\\n", "u_{\\text{emp}, t-1} \\\\\n", "\\end{bmatrix} = \\begin{bmatrix}\n", "a_1 & a_2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & c_{\\text{indprod}, 1} & 0 & 0 & 0 & c_{\\text{indprod}, 2} & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & c_{\\text{income}, 1} & 0 & 0 & 0 & c_{\\text{income}, 2} & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & c_{\\text{sales}, 1} & 0 & 0 & 0 & c_{\\text{sales}, 2} & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & c_{\\text{emp}, 1} & 0 & 0 & 0 & c_{\\text{emp}, 2} \\\\\n", "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", "\\end{bmatrix} \n", "\\begin{bmatrix}\n", "f_{t-1} \\\\\n", "f_{t-2} \\\\\n", "u_{\\text{indprod}, t-1} \\\\\n", "u_{\\text{income}, t-1} \\\\\n", "u_{\\text{sales}, t-1} \\\\\n", "u_{\\text{emp}, t-1} \\\\\n", "u_{\\text{indprod}, t-2} \\\\\n", "u_{\\text{income}, t-2} \\\\\n", "u_{\\text{sales}, t-2} \\\\\n", "u_{\\text{emp}, t-2} \\\\\n", "\\end{bmatrix}\n", "+ R \\begin{bmatrix}\n", "\\eta_t \\\\\n", "\\varepsilon_{t}\n", "\\end{bmatrix}\n", "$$\n", "\n", "the `DynamicFactor` model handles setting up the state space representation and, in the `DynamicFactor.update` method, it fills in the fitted parameter values into the appropriate locations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The extended specification is the same as in the previous example, except that we also want to allow employment to depend on lagged values of the factor. This creates a change to the $y_{\\text{emp},t}$ equation. Now we have:\n", "\n", "$$\n", "\\begin{align}\n", "y_{i,t} & = \\lambda_i f_t + u_{i,t} \\qquad & i \\in \\{\\text{indprod}, \\text{income}, \\text{sales} \\}\\\\\n", "y_{i,t} & = \\lambda_{i,0} f_t + \\lambda_{i,1} f_{t-1} + \\lambda_{i,2} f_{t-2} + \\lambda_{i,2} f_{t-3} + u_{i,t} \\qquad & i = \\text{emp} \\\\\n", "u_{i,t} & = c_{i,1} u_{i,t-1} + c_{i,2} u_{i,t-2} + \\varepsilon_{i,t} \\qquad & \\varepsilon_{i,t} \\sim N(0, \\sigma_i^2) \\\\\n", "f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \\eta_t \\qquad & \\eta_t \\sim N(0, I)\\\\\n", "\\end{align}\n", "$$\n", "\n", "Now, the corresponding observation equation should look like the following:\n", "\n", "$$\n", "\\begin{bmatrix}\n", "y_{\\text{indprod}, t} \\\\\n", "y_{\\text{income}, t} \\\\\n", "y_{\\text{sales}, t} \\\\\n", "y_{\\text{emp}, t} \\\\\n", "\\end{bmatrix} = \\begin{bmatrix}\n", "\\lambda_\\text{indprod} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\lambda_\\text{income} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\lambda_\\text{sales} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\lambda_\\text{emp,1} & \\lambda_\\text{emp,2} & \\lambda_\\text{emp,3} & \\lambda_\\text{emp,4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", "\\end{bmatrix}\n", "\\begin{bmatrix}\n", "f_t \\\\\n", "f_{t-1} \\\\\n", "f_{t-2} \\\\\n", "f_{t-3} \\\\\n", "u_{\\text{indprod}, t} \\\\\n", "u_{\\text{income}, t} \\\\\n", "u_{\\text{sales}, t} \\\\\n", "u_{\\text{emp}, t} \\\\\n", "u_{\\text{indprod}, t-1} \\\\\n", "u_{\\text{income}, t-1} \\\\\n", "u_{\\text{sales}, t-1} \\\\\n", "u_{\\text{emp}, t-1} \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "Notice that we have introduced two new state variables, $f_{t-2}$ and $f_{t-3}$, which means we need to update the transition equation:\n", "\n", "$$\n", "\\begin{bmatrix}\n", "f_t \\\\\n", "f_{t-1} \\\\\n", "f_{t-2} \\\\\n", "f_{t-3} \\\\\n", "u_{\\text{indprod}, t} \\\\\n", "u_{\\text{income}, t} \\\\\n", "u_{\\text{sales}, t} \\\\\n", "u_{\\text{emp}, t} \\\\\n", "u_{\\text{indprod}, t-1} \\\\\n", "u_{\\text{income}, t-1} \\\\\n", "u_{\\text{sales}, t-1} \\\\\n", "u_{\\text{emp}, t-1} \\\\\n", "\\end{bmatrix} = \\begin{bmatrix}\n", "a_1 & a_2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & c_{\\text{indprod}, 1} & 0 & 0 & 0 & c_{\\text{indprod}, 2} & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & c_{\\text{income}, 1} & 0 & 0 & 0 & c_{\\text{income}, 2} & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & c_{\\text{sales}, 1} & 0 & 0 & 0 & c_{\\text{sales}, 2} & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 0 & c_{\\text{emp}, 1} & 0 & 0 & 0 & c_{\\text{emp}, 2} \\\\\n", "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", "\\end{bmatrix} \n", "\\begin{bmatrix}\n", "f_{t-1} \\\\\n", "f_{t-2} \\\\\n", "f_{t-3} \\\\\n", "f_{t-4} \\\\\n", "u_{\\text{indprod}, t-1} \\\\\n", "u_{\\text{income}, t-1} \\\\\n", "u_{\\text{sales}, t-1} \\\\\n", "u_{\\text{emp}, t-1} \\\\\n", "u_{\\text{indprod}, t-2} \\\\\n", "u_{\\text{income}, t-2} \\\\\n", "u_{\\text{sales}, t-2} \\\\\n", "u_{\\text{emp}, t-2} \\\\\n", "\\end{bmatrix}\n", "+ R \\begin{bmatrix}\n", "\\eta_t \\\\\n", "\\varepsilon_{t}\n", "\\end{bmatrix}\n", "$$\n", "\n", "This model cannot be handled out-of-the-box by the `DynamicFactor` class, but it can be handled by creating a subclass when alters the state space representation in the appropriate way." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, notice that if we had set `factor_order = 4`, we would almost have what we wanted. In that case, the last line of the observation equation would be:\n", "\n", "$$\n", "\\begin{bmatrix}\n", "\\vdots \\\\\n", "y_{\\text{emp}, t} \\\\\n", "\\end{bmatrix} = \\begin{bmatrix}\n", "\\vdots & & & & & & & & & & & \\vdots \\\\\n", "\\lambda_\\text{emp,1} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", "\\end{bmatrix}\n", "\\begin{bmatrix}\n", "f_t \\\\\n", "f_{t-1} \\\\\n", "f_{t-2} \\\\\n", "f_{t-3} \\\\\n", "\\vdots\n", "\\end{bmatrix}\n", "$$\n", "\n", "\n", "and the first line of the transition equation would be:\n", "\n", "$$\n", "\\begin{bmatrix}\n", "f_t \\\\\n", "\\vdots\n", "\\end{bmatrix} = \\begin{bmatrix}\n", "a_1 & a_2 & a_3 & a_4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "\\vdots & & & & & & & & & & & \\vdots \\\\\n", "\\end{bmatrix} \n", "\\begin{bmatrix}\n", "f_{t-1} \\\\\n", "f_{t-2} \\\\\n", "f_{t-3} \\\\\n", "f_{t-4} \\\\\n", "\\vdots\n", "\\end{bmatrix}\n", "+ R \\begin{bmatrix}\n", "\\eta_t \\\\\n", "\\varepsilon_{t}\n", "\\end{bmatrix}\n", "$$\n", "\n", "Relative to what we want, we have the following differences:\n", "\n", "1. In the above situation, the $\\lambda_{\\text{emp}, j}$ are forced to be zero for $j > 0$, and we want them to be estimated as parameters.\n", "2. We only want the factor to transition according to an AR(2), but under the above situation it is an AR(4).\n", "\n", "Our strategy will be to subclass `DynamicFactor`, and let it do most of the work (setting up the state space representation, etc.) where it assumes that `factor_order = 4`. The only things we will actually do in the subclass will be to fix those two issues.\n", "\n", "First, here is the full code of the subclass; it is discussed below. It is important to note at the outset that none of the methods defined below could have been omitted. In fact, the methods `__init__`, `start_params`, `param_names`, `transform_params`, `untransform_params`, and `update` form the core of all state space models in statsmodels, not just the `DynamicFactor` class." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.statespace import tools\n", "class ExtendedDFM(sm.tsa.DynamicFactor):\n", " def __init__(self, endog, **kwargs):\n", " # Setup the model as if we had a factor order of 4\n", " super(ExtendedDFM, self).__init__(\n", " endog, k_factors=1, factor_order=4, error_order=2,\n", " **kwargs)\n", "\n", " # Note: `self.parameters` is an ordered dict with the\n", " # keys corresponding to parameter types, and the values\n", " # the number of parameters of that type.\n", " # Add the new parameters\n", " self.parameters['new_loadings'] = 3\n", "\n", " # Cache a slice for the location of the 4 factor AR\n", " # parameters (a_1, ..., a_4) in the full parameter vector\n", " offset = (self.parameters['factor_loadings'] +\n", " self.parameters['exog'] +\n", " self.parameters['error_cov'])\n", " self._params_factor_ar = np.s_[offset:offset+2]\n", " self._params_factor_zero = np.s_[offset+2:offset+4]\n", "\n", " @property\n", " def start_params(self):\n", " # Add three new loading parameters to the end of the parameter\n", " # vector, initialized to zeros (for simplicity; they could\n", " # be initialized any way you like)\n", " return np.r_[super(ExtendedDFM, self).start_params, 0, 0, 0]\n", " \n", " @property\n", " def param_names(self):\n", " # Add the corresponding names for the new loading parameters\n", " # (the name can be anything you like)\n", " return super(ExtendedDFM, self).param_names + [\n", " 'loading.L%d.f1.%s' % (i, self.endog_names[3]) for i in range(1,4)]\n", "\n", " def transform_params(self, unconstrained):\n", " # Perform the typical DFM transformation (w/o the new parameters)\n", " constrained = super(ExtendedDFM, self).transform_params(\n", " unconstrained[:-3])\n", "\n", " # Redo the factor AR constraint, since we only want an AR(2),\n", " # and the previous constraint was for an AR(4)\n", " ar_params = unconstrained[self._params_factor_ar]\n", " constrained[self._params_factor_ar] = (\n", " tools.constrain_stationary_univariate(ar_params))\n", "\n", " # Return all the parameters\n", " return np.r_[constrained, unconstrained[-3:]]\n", "\n", " def untransform_params(self, constrained):\n", " # Perform the typical DFM untransformation (w/o the new parameters)\n", " unconstrained = super(ExtendedDFM, self).untransform_params(\n", " constrained[:-3])\n", "\n", " # Redo the factor AR unconstrained, since we only want an AR(2),\n", " # and the previous unconstrained was for an AR(4)\n", " ar_params = constrained[self._params_factor_ar]\n", " unconstrained[self._params_factor_ar] = (\n", " tools.unconstrain_stationary_univariate(ar_params))\n", "\n", " # Return all the parameters\n", " return np.r_[unconstrained, constrained[-3:]]\n", "\n", " def update(self, params, transformed=True, **kwargs):\n", " # Peform the transformation, if required\n", " if not transformed:\n", " params = self.transform_params(params)\n", " params[self._params_factor_zero] = 0\n", " \n", " # Now perform the usual DFM update, but exclude our new parameters\n", " super(ExtendedDFM, self).update(params[:-3], transformed=True, **kwargs)\n", "\n", " # Finally, set our new parameters in the design matrix\n", " self.ssm['design', 3, 1:4] = params[-3:]\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So what did we just do?\n", "\n", "**`__init__`**\n", "\n", "The important step here was specifying the base dynamic factor model which we were operating with. In particular, as described above, we initialize with `factor_order=4`, even though we will only end up with an AR(2) model for the factor. We also performed some general setup-related tasks.\n", "\n", "**`start_params`**\n", "\n", "`start_params` are used as initial values in the optimizer. Since we are adding three new parameters, we need to pass those in. If we had not done this, the optimizer would use the default starting values, which would be three elements short.\n", "\n", "**`param_names`**\n", "\n", "`param_names` are used in a variety of places, but especially in the results class. Below we get a full result summary, which is only possible when all the parameters have associated names.\n", "\n", "**`transform_params`** and **`untransform_params`**\n", "\n", "The optimizer selects possibly parameter values in an unconstrained way. That's not usually desired (since variances cannot be negative, for example), and `transform_params` is used to transform the unconstrained values used by the optimizer to constrained values appropriate to the model. Variances terms are typically squared (to force them to be positive), and AR lag coefficients are often constrained to lead to a stationary model. `untransform_params` is used for the reverse operation (and is important because starting parameters are usually specified in terms of values appropriate to the model, and we need to convert them to parameters appropriate to the optimizer before we can begin the optimization routine).\n", "\n", "Even though we do not need to transform or untransform our new parameters (the loadings can in theory take on any values), we still need to modify this function for two reasons:\n", "\n", "1. The version in the `DynamicFactor` class is expecting 3 fewer parameters than we have now. At a minimum, we need to handle the three new parameters.\n", "2. The version in the `DynamicFactor` class constrains the factor lag coefficients to be stationary as though it was an AR(4) model. Since we actually have an AR(2) model, we need to re-do the constraint. We also set the last two autoregressive coefficients to be zero here.\n", "\n", "**`update`**\n", "\n", "The most important reason we need to specify a new `update` method is because we have three new parameters that we need to place into the state space formulation. In particular we let the parent `DynamicFactor.update` class handle placing all the parameters except the three new ones in to the state space representation, and then we put the last three in manually." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create the model\n", "extended_mod = ExtendedDFM(endog)\n", "initial_extended_res = extended_mod.fit(maxiter=1000, disp=False)\n", "extended_res = extended_mod.fit(initial_extended_res.params, method='nm', maxiter=1000)\n", "print(extended_res.summary(separate_params=False))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although this model increases the likelihood, it is not preferred by the AIC and BIC measures which penalize the additional three parameters.\n", "\n", "Furthermore, the qualitative results are unchanged, as we can see from the updated $R^2$ chart and the new coincident index, both of which are practically identical to the previous results." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "extended_res.plot_coefficients_of_determination(figsize=(8,2));" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(13,3))\n", "\n", "# Compute the index\n", "extended_coincident_index = compute_coincident_index(extended_mod, extended_res)\n", "\n", "# Plot the factor\n", "dates = endog.index._mpl_repr()\n", "ax.plot(dates, coincident_index, '-', linewidth=1, label='Basic model')\n", "ax.plot(dates, extended_coincident_index, '--', linewidth=3, label='Extended model')\n", "ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI')\n", "ax.legend(loc='lower right')\n", "ax.set(title='Coincident indices, comparison')\n", "\n", "# Retrieve and also plot the NBER recession indicators\n", "ylim = ax.get_ylim()\n", "ax.fill_between(dates[:-3], ylim[0], ylim[1], rec.values[:-4,0], facecolor='k', alpha=0.1);" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/statespace_fixed_params.ipynb000066400000000000000000000252021400612667500257100ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimating or specifying parameters in state space models\n", "\n", "In this notebook we show how to fix specific values of certain parameters in statsmodels' state space models while estimating others.\n", "\n", "In general, state space models allow users to:\n", "\n", "1. Estimate all parameters by maximum likelihood\n", "2. Fix some parameters and estimate the rest\n", "3. Fix all parameters (so that no parameters are estimated)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "from importlib import reload\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "\n", "from pandas_datareader.data import DataReader" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To illustrate, we will use the Consumer Price Index for Apparel, which has a time-varying level and a strong seasonal component." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "endog = DataReader('CPIAPPNS', 'fred', start='1980').asfreq('MS')\n", "endog.plot(figsize=(15, 3));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is well known (e.g. Harvey and Jaeger [1993]) that the HP filter output can be generated by an unobserved components model given certain restrictions on the parameters.\n", "\n", "The unobserved components model is:\n", "\n", "$$\n", "\\begin{aligned}\n", "y_t & = \\mu_t + \\varepsilon_t & \\varepsilon_t \\sim N(0, \\sigma_\\varepsilon^2) \\\\\n", "\\mu_t &= \\mu_{t-1} + \\beta_{t-1} + \\eta_t & \\eta_t \\sim N(0, \\sigma_\\eta^2) \\\\\n", "\\beta_t &= \\beta_{t-1} + \\zeta_t & \\zeta_t \\sim N(0, \\sigma_\\zeta^2) \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "For the trend to match the output of the HP filter, the parameters must be set as follows:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\frac{\\sigma_\\varepsilon^2}{\\sigma_\\zeta^2} & = \\lambda \\\\\n", "\\sigma_\\eta^2 & = 0\n", "\\end{aligned}\n", "$$\n", "\n", "where $\\lambda$ is the parameter of the associated HP filter. For the monthly data that we use here, it is usually recommended that $\\lambda = 129600$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Run the HP filter with lambda = 129600\n", "hp_cycle, hp_trend = sm.tsa.filters.hpfilter(endog, lamb=129600)\n", "\n", "# The unobserved components model above is the local linear trend, or \"lltrend\", specification\n", "mod = sm.tsa.UnobservedComponents(endog, 'lltrend')\n", "print(mod.param_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The parameters of the unobserved components model (UCM) are written as:\n", "\n", "- $\\sigma_\\varepsilon^2 = \\text{sigma2.irregular}$\n", "- $\\sigma_\\eta^2 = \\text{sigma2.level}$\n", "- $\\sigma_\\zeta^2 = \\text{sigma2.trend}$\n", "\n", "To satisfy the above restrictions, we will set $(\\sigma_\\varepsilon^2, \\sigma_\\eta^2, \\sigma_\\zeta^2) = (1, 0, 1 / 129600)$.\n", "\n", "Since we are fixing all parameters here, we do not need to use the `fit` method at all, since that method is used to perform maximum likelihood estimation. Instead, we can directly run the Kalman filter and smoother at our chosen parameters using the `smooth` method." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res = mod.smooth([1., 0, 1. / 129600])\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The estimate that corresponds to the HP filter's trend estimate is given by the smoothed estimate of the `level` (which is $\\mu_t$ in the notation above):" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ucm_trend = pd.Series(res.level.smoothed, index=endog.index)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is easy to see that the estimate of the smoothed level from the UCM is equal to the output of the HP filter:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(15, 3))\n", "\n", "ax.plot(hp_trend, label='HP estimate')\n", "ax.plot(ucm_trend, label='UCM estimate')\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding a seasonal component" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, unobserved components models are more flexible than the HP filter. For example, the data shown above is clearly seasonal, but with time-varying seasonal effects (the seasonality is much weaker at the beginning than at the end). One of the benefits of the unobserved components framework is that we can add a stochastic seasonal component. In this case, we will estimate the variance of the seasonal component by maximum likelihood while still including the restriction on the parameters implied above so that the trend corresponds to the HP filter concept.\n", "\n", "Adding the stochastic seasonal component adds one new parameter, `sigma2.seasonal`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Construct a local linear trend model with a stochastic seasonal component of period 1 year\n", "mod = sm.tsa.UnobservedComponents(endog, 'lltrend', seasonal=12, stochastic_seasonal=True)\n", "print(mod.param_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, we will continue to restrict the first three parameters as described above, but we want to estimate the value of `sigma2.seasonal` by maximum likelihood. Therefore, we will use the `fit` method along with the `fix_params` context manager.\n", "\n", "The `fix_params` method takes a dictionary of parameters names and associated values. Within the generated context, those parameters will be used in all cases. In the case of the `fit` method, only the parameters that were not fixed will be estimated." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Here we restrict the first three parameters to specific values\n", "with mod.fix_params({'sigma2.irregular': 1, 'sigma2.level': 0, 'sigma2.trend': 1. / 129600}):\n", " # Now we fit any remaining parameters, which in this case\n", " # is just `sigma2.seasonal`\n", " res_restricted = mod.fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternatively, we could have simply used the `fit_constrained` method, which also accepts a dictionary of constraints:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_restricted = mod.fit_constrained({'sigma2.irregular': 1, 'sigma2.level': 0, 'sigma2.trend': 1. / 129600})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The summary output includes all parameters, but indicates that the first three were fixed (and so were not estimated)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(res_restricted.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For comparison, we construct the unrestricted maximum likelihood estimates (MLE). In this case, the estimate of the level will no longer correspond to the HP filter concept." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_unrestricted = mod.fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can retrieve the smoothed estimates of the trend and seasonal components." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Construct the smoothed level estimates\n", "unrestricted_trend = pd.Series(res_unrestricted.level.smoothed, index=endog.index)\n", "restricted_trend = pd.Series(res_restricted.level.smoothed, index=endog.index)\n", "\n", "# Construct the smoothed estimates of the seasonal pattern\n", "unrestricted_seasonal = pd.Series(res_unrestricted.seasonal.smoothed, index=endog.index)\n", "restricted_seasonal = pd.Series(res_restricted.seasonal.smoothed, index=endog.index)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comparing the estimated level, it is clear that the seasonal UCM with fixed parameters still produces a trend that corresponds very closely (although no longer exactly) to the HP filter output.\n", "\n", "Meanwhile, the estimated level from the model with no parameter restrictions (the MLE model) is much less smooth than these." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(15, 3))\n", "\n", "ax.plot(unrestricted_trend, label='MLE, with seasonal')\n", "ax.plot(restricted_trend, label='Fixed parameters, with seasonal')\n", "ax.plot(hp_trend, label='HP filter, no seasonal')\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, the UCM with the parameter restrictions is still able to pick up the time-varying seasonal component quite well." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(15, 3))\n", "\n", "ax.plot(unrestricted_seasonal, label='MLE')\n", "ax.plot(restricted_seasonal, label='Fixed parameters')\n", "ax.legend();" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.2" } }, "nbformat": 4, "nbformat_minor": 2 } statsmodels-0.12.2/examples/notebooks/statespace_forecasting.ipynb000066400000000000000000000565111400612667500255610ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Forecasting in statsmodels\n", "\n", "This notebook describes forecasting using time series models in statsmodels.\n", "\n", "**Note**: this notebook applies only to the state space model classes, which are:\n", "\n", "- `sm.tsa.SARIMAX`\n", "- `sm.tsa.UnobservedComponents`\n", "- `sm.tsa.VARMAX`\n", "- `sm.tsa.DynamicFactor`" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "\n", "macrodata = sm.datasets.macrodata.load_pandas().data\n", "macrodata.index = pd.period_range('1959Q1', '2009Q3', freq='Q')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basic example\n", "\n", "A simple example is to use an AR(1) model to forecast inflation. Before forecasting, let's take a look at the series:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "endog = macrodata['infl']\n", "endog.plot(figsize=(15, 5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Constructing and estimating the model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next step is to formulate the econometric model that we want to use for forecasting. In this case, we will use an AR(1) model via the `SARIMAX` class in statsmodels.\n", "\n", "After constructing the model, we need to estimate its parameters. This is done using the `fit` method. The `summary` method produces several convenient tables showing the results." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Construct the model\n", "mod = sm.tsa.SARIMAX(endog, order=(1, 0, 0), trend='c')\n", "# Estimate the parameters\n", "res = mod.fit()\n", "\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Forecasting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Out-of-sample forecasts are produced using the `forecast` or `get_forecast` methods from the results object.\n", "\n", "The `forecast` method gives only point forecasts." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# The default is to get a one-step-ahead forecast:\n", "print(res.forecast())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `get_forecast` method is more general, and also allows constructing confidence intervals." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Here we construct a more complete results object.\n", "fcast_res1 = res.get_forecast()\n", "\n", "# Most results are collected in the `summary_frame` attribute.\n", "# Here we specify that we want a confidence level of 90%\n", "print(fcast_res1.summary_frame(alpha=0.10))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The default confidence level is 95%, but this can be controlled by setting the `alpha` parameter, where the confidence level is defined as $(1 - \\alpha) \\times 100\\%$. In the example above, we specified a confidence level of 90%, using `alpha=0.10`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Specifying the number of forecasts\n", "\n", "Both of the functions `forecast` and `get_forecast` accept a single argument indicating how many forecasting steps are desired. One option for this argument is always to provide an integer describing the number of steps ahead you want." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(res.forecast(steps=2))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fcast_res2 = res.get_forecast(steps=2)\n", "# Note: since we did not specify the alpha parameter, the\n", "# confidence level is at the default, 95%\n", "print(fcast_res2.summary_frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, **if your data included a Pandas index with a defined frequency** (see the section at the end on Indexes for more information), then you can alternatively specify the date through which you want forecasts to be produced:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(res.forecast('2010Q2'))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fcast_res3 = res.get_forecast('2010Q2')\n", "print(fcast_res3.summary_frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the data, forecasts, and confidence intervals\n", "\n", "Often it is useful to plot the data, the forecasts, and the confidence intervals. There are many ways to do this, but here's one example" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(15, 5))\n", "\n", "# Plot the data (here we are subsetting it to get a better look at the forecasts)\n", "endog.loc['1999':].plot(ax=ax)\n", "\n", "# Construct the forecasts\n", "fcast = res.get_forecast('2011Q4').summary_frame()\n", "fcast['mean'].plot(ax=ax, style='k--')\n", "ax.fill_between(fcast.index, fcast['mean_ci_lower'], fcast['mean_ci_upper'], color='k', alpha=0.1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Note on what to expect from forecasts\n", "\n", "The forecast above may not look very impressive, as it is almost a straight line. This is because this is a very simple, univariate forecasting model. Nonetheless, keep in mind that these simple forecasting models can be extremely competitive." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prediction vs Forecasting\n", "\n", "The results objects also contain two methods that all for both in-sample fitted values and out-of-sample forecasting. They are `predict` and `get_prediction`. The `predict` method only returns point predictions (similar to `forecast`), while the `get_prediction` method also returns additional results (similar to `get_forecast`).\n", "\n", "In general, if your interest is out-of-sample forecasting, it is easier to stick to the `forecast` and `get_forecast` methods." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cross validation\n", "\n", "**Note**: some of the functions used in this section were first introduced in statsmodels v0.11.0.\n", "\n", "A common use case is to cross-validate forecasting methods by performing h-step-ahead forecasts recursively using the following process:\n", "\n", "1. Fit model parameters on a training sample\n", "2. Produce h-step-ahead forecasts from the end of that sample\n", "3. Compare forecasts against test dataset to compute error rate\n", "4. Expand the sample to include the next observation, and repeat\n", "\n", "Economists sometimes call this a pseudo-out-of-sample forecast evaluation exercise, or time-series cross-validation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will conduct a very simple exercise of this sort using the inflation dataset above. The full dataset contains 203 observations, and for expositional purposes we'll use the first 80% as our training sample and only consider one-step-ahead forecasts." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A single iteration of the above procedure looks like the following:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Step 1: fit model parameters w/ training sample\n", "training_obs = int(len(endog) * 0.8)\n", "\n", "training_endog = endog[:training_obs]\n", "training_mod = sm.tsa.SARIMAX(\n", " training_endog, order=(1, 0, 0), trend='c')\n", "training_res = training_mod.fit()\n", "\n", "# Print the estimated parameters\n", "print(training_res.params)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Step 2: produce one-step-ahead forecasts\n", "fcast = training_res.forecast()\n", "\n", "# Step 3: compute root mean square forecasting error\n", "true = endog.reindex(fcast.index)\n", "error = true - fcast\n", "\n", "# Print out the results\n", "print(pd.concat([true.rename('true'),\n", " fcast.rename('forecast'),\n", " error.rename('error')], axis=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To add on another observation, we can use the `append` or `extend` results methods. Either method can produce the same forecasts, but they differ in the other results that are available:\n", "\n", "- `append` is the more complete method. It always stores results for all training observations, and it optionally allows refitting the model parameters given the new observations (note that the default is *not* to refit the parameters).\n", "- `extend` is a faster method that may be useful if the training sample is very large. It *only* stores results for the new observations, and it does not allow refitting the model parameters (i.e. you have to use the parameters estimated on the previous sample).\n", "\n", "If your training sample is relatively small (less than a few thousand observations, for example) or if you want to compute the best possible forecasts, then you should use the `append` method. However, if that method is infeasible (for example, because you have a very large training sample) or if you are okay with slightly suboptimal forecasts (because the parameter estimates will be slightly stale), then you can consider the `extend` method." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A second iteration, using the `append` method and refitting the parameters, would go as follows (note again that the default for `append` does not refit the parameters, but we have overridden that with the `refit=True` argument):" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Step 1: append a new observation to the sample and refit the parameters\n", "append_res = training_res.append(endog[training_obs:training_obs + 1], refit=True)\n", "\n", "# Print the re-estimated parameters\n", "print(append_res.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that these estimated parameters are slightly different than those we originally estimated. With the new results object, `append_res`, we can compute forecasts starting from one observation further than the previous call:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Step 2: produce one-step-ahead forecasts\n", "fcast = append_res.forecast()\n", "\n", "# Step 3: compute root mean square forecasting error\n", "true = endog.reindex(fcast.index)\n", "error = true - fcast\n", "\n", "# Print out the results\n", "print(pd.concat([true.rename('true'),\n", " fcast.rename('forecast'),\n", " error.rename('error')], axis=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Putting it altogether, we can perform the recursive forecast evaluation exercise as follows:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Setup forecasts\n", "nforecasts = 3\n", "forecasts = {}\n", "\n", "# Get the number of initial training observations\n", "nobs = len(endog)\n", "n_init_training = int(nobs * 0.8)\n", "\n", "# Create model for initial training sample, fit parameters\n", "init_training_endog = endog.iloc[:n_init_training]\n", "mod = sm.tsa.SARIMAX(training_endog, order=(1, 0, 0), trend='c')\n", "res = mod.fit()\n", "\n", "# Save initial forecast\n", "forecasts[training_endog.index[-1]] = res.forecast(steps=nforecasts)\n", "\n", "# Step through the rest of the sample\n", "for t in range(n_init_training, nobs):\n", " # Update the results by appending the next observation\n", " updated_endog = endog.iloc[t:t+1]\n", " res = res.append(updated_endog, refit=False)\n", " \n", " # Save the new set of forecasts\n", " forecasts[updated_endog.index[0]] = res.forecast(steps=nforecasts)\n", "\n", "# Combine all forecasts into a dataframe\n", "forecasts = pd.concat(forecasts, axis=1)\n", "\n", "print(forecasts.iloc[:5, :5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now have a set of three forecasts made at each point in time from 1999Q2 through 2009Q3. We can construct the forecast errors by subtracting each forecast from the actual value of `endog` at that point." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Construct the forecast errors\n", "forecast_errors = forecasts.apply(lambda column: endog - column).reindex(forecasts.index)\n", "\n", "print(forecast_errors.iloc[:5, :5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To evaluate our forecasts, we often want to look at a summary value like the root mean square error. Here we can compute that for each horizon by first flattening the forecast errors so that they are indexed by horizon and then computing the root mean square error fore each horizon." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Reindex the forecasts by horizon rather than by date\n", "def flatten(column):\n", " return column.dropna().reset_index(drop=True)\n", "\n", "flattened = forecast_errors.apply(flatten)\n", "flattened.index = (flattened.index + 1).rename('horizon')\n", "\n", "print(flattened.iloc[:3, :5])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Compute the root mean square error\n", "rmse = (flattened**2).mean(axis=1)**0.5\n", "\n", "print(rmse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Using `extend`\n", "\n", "We can check that we get similar forecasts if we instead use the `extend` method, but that they are not exactly the same as when we use `append` with the `refit=True` argument. This is because `extend` does not re-estimate the parameters given the new observation." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Setup forecasts\n", "nforecasts = 3\n", "forecasts = {}\n", "\n", "# Get the number of initial training observations\n", "nobs = len(endog)\n", "n_init_training = int(nobs * 0.8)\n", "\n", "# Create model for initial training sample, fit parameters\n", "init_training_endog = endog.iloc[:n_init_training]\n", "mod = sm.tsa.SARIMAX(training_endog, order=(1, 0, 0), trend='c')\n", "res = mod.fit()\n", "\n", "# Save initial forecast\n", "forecasts[training_endog.index[-1]] = res.forecast(steps=nforecasts)\n", "\n", "# Step through the rest of the sample\n", "for t in range(n_init_training, nobs):\n", " # Update the results by appending the next observation\n", " updated_endog = endog.iloc[t:t+1]\n", " res = res.extend(updated_endog)\n", " \n", " # Save the new set of forecasts\n", " forecasts[updated_endog.index[0]] = res.forecast(steps=nforecasts)\n", "\n", "# Combine all forecasts into a dataframe\n", "forecasts = pd.concat(forecasts, axis=1)\n", "\n", "print(forecasts.iloc[:5, :5])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Construct the forecast errors\n", "forecast_errors = forecasts.apply(lambda column: endog - column).reindex(forecasts.index)\n", "\n", "print(forecast_errors.iloc[:5, :5])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Reindex the forecasts by horizon rather than by date\n", "def flatten(column):\n", " return column.dropna().reset_index(drop=True)\n", "\n", "flattened = forecast_errors.apply(flatten)\n", "flattened.index = (flattened.index + 1).rename('horizon')\n", "\n", "print(flattened.iloc[:3, :5])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Compute the root mean square error\n", "rmse = (flattened**2).mean(axis=1)**0.5\n", "\n", "print(rmse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By not re-estimating the parameters, our forecasts are slightly worse (the root mean square error is higher at each horizon). However, the process is faster, even with only 200 datapoints. Using the `%%timeit` cell magic on the cells above, we found a runtime of 570ms using `extend` versus 1.7s using `append` with `refit=True`. (Note that using `extend` is also faster than using `append` with `refit=False`)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Indexes\n", "\n", "Throughout this notebook, we have been making use of Pandas date indexes with an associated frequency. As you can see, this index marks our data as at a quarterly frequency, between 1959Q1 and 2009Q3." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(endog.index)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In most cases, if your data has an associated data/time index with a defined frequency (like quarterly, monthly, etc.), then it is best to make sure your data is a Pandas series with the appropriate index. Here are three examples of this:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Annual frequency, using a PeriodIndex\n", "index = pd.period_range(start='2000', periods=4, freq='A')\n", "endog1 = pd.Series([1, 2, 3, 4], index=index)\n", "print(endog1.index)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Quarterly frequency, using a DatetimeIndex\n", "index = pd.date_range(start='2000', periods=4, freq='QS')\n", "endog2 = pd.Series([1, 2, 3, 4], index=index)\n", "print(endog2.index)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Monthly frequency, using a DatetimeIndex\n", "index = pd.date_range(start='2000', periods=4, freq='M')\n", "endog3 = pd.Series([1, 2, 3, 4], index=index)\n", "print(endog3.index)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In fact, if your data has an associated date/time index, it is best to use that even if does not have a defined frequency. An example of that kind of index is as follows - notice that it has `freq=None`:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "index = pd.DatetimeIndex([\n", " '2000-01-01 10:08am', '2000-01-01 11:32am',\n", " '2000-01-01 5:32pm', '2000-01-02 6:15am'])\n", "endog4 = pd.Series([0.2, 0.5, -0.1, 0.1], index=index)\n", "print(endog4.index)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can still pass this data to statsmodels' model classes, but you will get the following warning, that no frequency data was found:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = sm.tsa.SARIMAX(endog4)\n", "res = mod.fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What this means is that you cannot specify forecasting steps by dates, and the output of the `forecast` and `get_forecast` methods will not have associated dates. The reason is that without a given frequency, there is no way to determine what date each forecast should be assigned to. In the example above, there is no pattern to the date/time stamps of the index, so there is no way to determine what the next date/time should be (should it be in the morning of 2000-01-02? the afternoon? or maybe not until 2000-01-03?).\n", "\n", "For example, if we forecast one-step-ahead:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res.forecast(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The index associated with the new forecast is `4`, because if the given data had an integer index, that would be the next value. A warning is given letting the user know that the index is not a date/time index.\n", "\n", "If we try to specify the steps of the forecast using a date, we will get the following exception:\n", "\n", " KeyError: 'The `end` argument could not be matched to a location related to the index of the data.'\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Here we'll catch the exception to prevent printing too much of\n", "# the exception trace output in this notebook\n", "try:\n", " res.forecast('2000-01-03')\n", "except KeyError as e:\n", " print(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ultimately there is nothing wrong with using data that does not have an associated date/time frequency, or even using data that has no index at all, like a Numpy array. However, if you can use a Pandas series with an associated frequency, you'll have more options for specifying your forecasts and get back results with a more useful index." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 2 } statsmodels-0.12.2/examples/notebooks/statespace_local_linear_trend.ipynb000066400000000000000000000306011400612667500270650ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# State space modeling: Local Linear Trends" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook describes how to extend the statsmodels statespace classes to create and estimate a custom model. Here we develop a local linear trend model.\n", "\n", "The Local Linear Trend model has the form (see Durbin and Koopman 2012, Chapter 3.2 for all notation and details):\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\mu_t + \\varepsilon_t \\qquad & \\varepsilon_t \\sim\n", " N(0, \\sigma_\\varepsilon^2) \\\\\n", "\\mu_{t+1} & = \\mu_t + \\nu_t + \\xi_t & \\xi_t \\sim N(0, \\sigma_\\xi^2) \\\\\n", "\\nu_{t+1} & = \\nu_t + \\zeta_t & \\zeta_t \\sim N(0, \\sigma_\\zeta^2)\n", "\\end{align}\n", "$$\n", "\n", "It is easy to see that this can be cast into state space form as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\begin{pmatrix} 1 & 0 \\end{pmatrix} \\begin{pmatrix} \\mu_t \\\\ \\nu_t \\end{pmatrix} + \\varepsilon_t \\\\\n", "\\begin{pmatrix} \\mu_{t+1} \\\\ \\nu_{t+1} \\end{pmatrix} & = \\begin{bmatrix} 1 & 1 \\\\ 0 & 1 \\end{bmatrix} \\begin{pmatrix} \\mu_t \\\\ \\nu_t \\end{pmatrix} + \\begin{pmatrix} \\xi_t \\\\ \\zeta_t \\end{pmatrix}\n", "\\end{align}\n", "$$\n", "\n", "Notice that much of the state space representation is composed of known values; in fact the only parts in which parameters to be estimated appear are in the variance / covariance matrices:\n", "\n", "$$\n", "\\begin{align}\n", "H_t & = \\begin{bmatrix} \\sigma_\\varepsilon^2 \\end{bmatrix} \\\\\n", "Q_t & = \\begin{bmatrix} \\sigma_\\xi^2 & 0 \\\\ 0 & \\sigma_\\zeta^2 \\end{bmatrix}\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "from scipy.stats import norm\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To take advantage of the existing infrastructure, including Kalman filtering and maximum likelihood estimation, we create a new class which extends from `statsmodels.tsa.statespace.MLEModel`. There are a number of things that must be specified:\n", "\n", "1. **k_states**, **k_posdef**: These two parameters must be provided to the base classes in initialization. The inform the statespace model about the size of, respectively, the state vector, above $\\begin{pmatrix} \\mu_t & \\nu_t \\end{pmatrix}'$, and the state error vector, above $\\begin{pmatrix} \\xi_t & \\zeta_t \\end{pmatrix}'$. Note that the dimension of the endogenous vector does not have to be specified, since it can be inferred from the `endog` array.\n", "2. **update**: The method `update`, with argument `params`, must be specified (it is used when `fit()` is called to calculate the MLE). It takes the parameters and fills them into the appropriate state space matrices. For example, below, the `params` vector contains variance parameters $\\begin{pmatrix} \\sigma_\\varepsilon^2 & \\sigma_\\xi^2 & \\sigma_\\zeta^2\\end{pmatrix}$, and the `update` method must place them in the observation and state covariance matrices. More generally, the parameter vector might be mapped into many different places in all of the statespace matrices.\n", "3. **statespace matrices**: by default, all state space matrices (`obs_intercept, design, obs_cov, state_intercept, transition, selection, state_cov`) are set to zeros. Values that are fixed (like the ones in the design and transition matrices here) can be set in initialization, whereas values that vary with the parameters should be set in the `update` method. Note that it is easy to forget to set the selection matrix, which is often just the identity matrix (as it is here), but not setting it will lead to a very different model (one where there is not a stochastic component to the transition equation).\n", "4. **start params**: start parameters must be set, even if it is just a vector of zeros, although often good start parameters can be found from the data. Maximum likelihood estimation by gradient methods (as employed here) can be sensitive to the starting parameters, so it is important to select good ones if possible. Here it does not matter too much (although as variances, they should't be set zero).\n", "5. **initialization**: in addition to defined state space matrices, all state space models must be initialized with the mean and variance for the initial distribution of the state vector. If the distribution is known, `initialize_known(initial_state, initial_state_cov)` can be called, or if the model is stationary (e.g. an ARMA model), `initialize_stationary` can be used. Otherwise, `initialize_approximate_diffuse` is a reasonable generic initialization (exact diffuse initialization is not yet available). Since the local linear trend model is not stationary (it is composed of random walks) and since the distribution is not generally known, we use `initialize_approximate_diffuse` below.\n", "\n", "The above are the minimum necessary for a successful model. There are also a number of things that do not have to be set, but which may be helpful or important for some applications:\n", "\n", "1. **transform / untransform**: when `fit` is called, the optimizer in the background will use gradient methods to select the parameters that maximize the likelihood function. By default it uses unbounded optimization, which means that it may select any parameter value. In many cases, that is not the desired behavior; variances, for example, cannot be negative. To get around this, the `transform` method takes the unconstrained vector of parameters provided by the optimizer and returns a constrained vector of parameters used in likelihood evaluation. `untransform` provides the reverse operation.\n", "2. **param_names**: this internal method can be used to set names for the estimated parameters so that e.g. the summary provides meaningful names. If not present, parameters are named `param0`, `param1`, etc." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "\"\"\"\n", "Univariate Local Linear Trend Model\n", "\"\"\"\n", "class LocalLinearTrend(sm.tsa.statespace.MLEModel):\n", " def __init__(self, endog):\n", " # Model order\n", " k_states = k_posdef = 2\n", "\n", " # Initialize the statespace\n", " super(LocalLinearTrend, self).__init__(\n", " endog, k_states=k_states, k_posdef=k_posdef,\n", " initialization='approximate_diffuse',\n", " loglikelihood_burn=k_states\n", " )\n", "\n", " # Initialize the matrices\n", " self.ssm['design'] = np.array([1, 0])\n", " self.ssm['transition'] = np.array([[1, 1],\n", " [0, 1]])\n", " self.ssm['selection'] = np.eye(k_states)\n", "\n", " # Cache some indices\n", " self._state_cov_idx = ('state_cov',) + np.diag_indices(k_posdef)\n", "\n", " @property\n", " def param_names(self):\n", " return ['sigma2.measurement', 'sigma2.level', 'sigma2.trend']\n", "\n", " @property\n", " def start_params(self):\n", " return [np.std(self.endog)]*3\n", "\n", " def transform_params(self, unconstrained):\n", " return unconstrained**2\n", "\n", " def untransform_params(self, constrained):\n", " return constrained**0.5\n", "\n", " def update(self, params, *args, **kwargs):\n", " params = super(LocalLinearTrend, self).update(params, *args, **kwargs)\n", " \n", " # Observation covariance\n", " self.ssm['obs_cov',0,0] = params[0]\n", "\n", " # State covariance\n", " self.ssm[self._state_cov_idx] = params[1:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using this simple model, we can estimate the parameters from a local linear trend model. The following example is from Commandeur and Koopman (2007), section 3.4., modeling motor vehicle fatalities in Finland." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import requests\n", "from io import BytesIO\n", "from zipfile import ZipFile\n", " \n", "# Download the dataset\n", "ck = requests.get('http://staff.feweb.vu.nl/koopman/projects/ckbook/OxCodeAll.zip').content\n", "zipped = ZipFile(BytesIO(ck))\n", "df = pd.read_table(\n", " BytesIO(zipped.read('OxCodeIntroStateSpaceBook/Chapter_2/NorwayFinland.txt')),\n", " skiprows=1, header=None, sep='\\s+', engine='python',\n", " names=['date','nf', 'ff']\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since we defined the local linear trend model as extending from `MLEModel`, the `fit()` method is immediately available, just as in other statsmodels maximum likelihood classes. Similarly, the returned results class supports many of the same post-estimation results, like the `summary` method.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Load Dataset\n", "df.index = pd.date_range(start='%d-01-01' % df.date[0], end='%d-01-01' % df.iloc[-1, 0], freq='AS')\n", "\n", "# Log transform\n", "df['lff'] = np.log(df['ff'])\n", "\n", "# Setup the model\n", "mod = LocalLinearTrend(df['lff'])\n", "\n", "# Fit it using MLE (recall that we are fitting the three variance parameters)\n", "res = mod.fit(disp=False)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can do post-estimation prediction and forecasting. Notice that the end period can be specified as a date." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Perform prediction and forecasting\n", "predict = res.get_prediction()\n", "forecast = res.get_forecast('2014')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(10,4))\n", "\n", "# Plot the results\n", "df['lff'].plot(ax=ax, style='k.', label='Observations')\n", "predict.predicted_mean.plot(ax=ax, label='One-step-ahead Prediction')\n", "predict_ci = predict.conf_int(alpha=0.05)\n", "predict_index = np.arange(len(predict_ci))\n", "ax.fill_between(predict_index[2:], predict_ci.iloc[2:, 0], predict_ci.iloc[2:, 1], alpha=0.1)\n", "\n", "forecast.predicted_mean.plot(ax=ax, style='r', label='Forecast')\n", "forecast_ci = forecast.conf_int()\n", "forecast_index = np.arange(len(predict_ci), len(predict_ci) + len(forecast_ci))\n", "ax.fill_between(forecast_index, forecast_ci.iloc[:, 0], forecast_ci.iloc[:, 1], alpha=0.1)\n", "\n", "# Cleanup the image\n", "ax.set_ylim((4, 8));\n", "legend = ax.legend(loc='lower left');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### References\n", "\n", " Commandeur, Jacques J. F., and Siem Jan Koopman. 2007.\n", " An Introduction to State Space Time Series Analysis.\n", " Oxford ; New York: Oxford University Press.\n", "\n", " Durbin, James, and Siem Jan Koopman. 2012.\n", " Time Series Analysis by State Space Methods: Second Edition.\n", " Oxford University Press." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 } statsmodels-0.12.2/examples/notebooks/statespace_news.ipynb000066400000000000000000001016151400612667500242250ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Forecasting, updating datasets, and the \"news\"\n", "\n", "In this notebook, we describe how to use Statsmodels to compute the impacts of updated or revised datasets on out-of-sample forecasts or in-sample estimates of missing data. We follow the approach of the \"Nowcasting\" literature (see references at the end), by using a state space model to compute the \"news\" and impacts of incoming data.\n", "\n", "**Note**: this notebook applies to Statsmodels v0.12+. In addition, it only applies to the state space models or related classes, which are: `sm.tsa.statespace.ExponentialSmoothing`, `sm.tsa.arima.ARIMA`, `sm.tsa.SARIMAX`, `sm.tsa.UnobservedComponents`, `sm.tsa.VARMAX`, and `sm.tsa.DynamicFactor`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "\n", "macrodata = sm.datasets.macrodata.load_pandas().data\n", "macrodata.index = pd.period_range('1959Q1', '2009Q3', freq='Q')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Forecasting exercises often start with a fixed set of historical data that is used for model selection and parameter estimation. Then, the fitted selected model (or models) can be used to create out-of-sample forecasts. Most of the time, this is not the end of the story. As new data comes in, you may need to evaluate your forecast errors, possibly update your models, and create updated out-of-sample forecasts. This is sometimes called a \"real-time\" forecasting exercise (by contrast, a pseudo real-time exercise is one in which you simulate this procedure).\n", "\n", "If all that matters is minimizing some loss function based on forecast errors (like MSE), then when new data comes in you may just want to completely redo model selection, parameter estimation and out-of-sample forecasting, using the updated datapoints. If you do this, your new forecasts will have changed for two reasons:\n", "\n", "1. You have received new data that gives you new information\n", "2. Your forecasting model or the estimated parameters are different\n", "\n", "In this notebook, we focus on methods for isolating the first effect. The way we do this comes from the so-called \"nowcasting\" literature, and in particular BaÅ„bura, Giannone, and Reichlin (2011), BaÅ„bura and Modugno (2014), and BaÅ„bura et al. (2014). They describe this exercise as computing the \"**news**\", and we follow them in using this language in Statsmodels.\n", "\n", "These methods are perhaps most useful with multivariate models, since there multiple variables may update at the same time, and it is not immediately obvious what forecast change was created by what updated variable. However, they can still be useful for thinking about forecast revisions in univariate models. We will therefore start with the simpler univariate case to explain how things work, and then move to the multivariate case afterwards." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note on revisions**: the framework that we are using is designed to decompose changes to forecasts from newly observed datapoints. It can also take into account *revisions* to previously published datapoints, but it does not decompose them separately. Instead, it only shows the aggregate effect of \"revisions\"." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note on `exog` data**: the framework that we are using only decomposes changes to forecasts from newly observed datapoints for *modeled* variables. These are the \"left-hand-side\" variables that in Statsmodels are given in the `endog` arguments. This framework does not decompose or account for changes to unmodeled \"right-hand-side\" variables, like those included in the `exog` argument." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simple univariate example: AR(1)\n", "\n", "We will begin with a simple autoregressive model, an AR(1):\n", "\n", "$$y_t = \\phi y_{t-1} + \\varepsilon_t$$\n", "\n", "- The parameter $\\phi$ captures the persistence of the series\n", "\n", "We will use this model to forecast inflation.\n", "\n", "To make it simpler to describe the forecast updates in this notebook, we will work with inflation data that has been de-meaned, but it is straightforward in practice to augment the model with a mean term.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# De-mean the inflation series\n", "y = macrodata['infl'] - macrodata['infl'].mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Step 1: fitting the model on the available dataset" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, we'll simulate an out-of-sample exercise, by constructing and fitting our model using all of the data except the last five observations. We'll assume that we haven't observed these values yet, and then in subsequent steps we'll add them back into the analysis." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "y_pre = y.iloc[:-5]\n", "y_pre.plot(figsize=(15, 3), title='Inflation');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To construct forecasts, we first estimate the parameters of the model. This returns a results object that we will be able to use produce forecasts." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod_pre = sm.tsa.arima.ARIMA(y_pre, order=(1, 0, 0), trend='n')\n", "res_pre = mod_pre.fit()\n", "print(res_pre.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Creating the forecasts from the results object `res` is easy - you can just call the `forecast` method with the number of forecasts you want to construct. In this case, we'll construct four out-of-sample forecasts." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Compute the forecasts\n", "forecasts_pre = res_pre.forecast(4)\n", "\n", "# Plot the last 3 years of data and the four out-of-sample forecasts\n", "y_pre.iloc[-12:].plot(figsize=(15, 3), label='Data', legend=True)\n", "forecasts_pre.plot(label='Forecast', legend=True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the AR(1) model, it is also easy to manually construct the forecasts. Denoting the last observed variable as $y_T$ and the $h$-step-ahead forecast as $y_{T+h|T}$, we have:\n", "\n", "$$y_{T+h|T} = \\hat \\phi^h y_T$$\n", "\n", "Where $\\hat \\phi$ is our estimated value for the AR(1) coefficient. From the summary output above, we can see that this is the first parameter of the model, which we can access from the `params` attribute of the results object." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Get the estimated AR(1) coefficient\n", "phi_hat = res_pre.params[0]\n", "\n", "# Get the last observed value of the variable\n", "y_T = y_pre.iloc[-1]\n", "\n", "# Directly compute the forecasts at the horizons h=1,2,3,4\n", "manual_forecasts = pd.Series([phi_hat * y_T, phi_hat**2 * y_T,\n", " phi_hat**3 * y_T, phi_hat**4 * y_T],\n", " index=forecasts_pre.index)\n", "\n", "# We'll print the two to double-check that they're the same\n", "print(pd.concat([forecasts_pre, manual_forecasts], axis=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Step 2: computing the \"news\" from a new observation\n", "\n", "Suppose that time has passed, and we have now received another observation. Our dataset is now larger, and we can evaluate our forecast error and produce updated forecasts for the subsequent quarters." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Get the next observation after the \"pre\" dataset\n", "y_update = y.iloc[-5:-4]\n", "\n", "# Print the forecast error\n", "print('Forecast error: %.2f' % (y_update.iloc[0] - forecasts_pre.iloc[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To compute forecasts based on our updated dataset, we will create an updated results object `res_post` using the `append` method, to append on our new observation to the previous dataset.\n", "\n", "Note that by default, the `append` method does not re-estimate the parameters of the model. This is exactly what we want here, since we want to isolate the effect on the forecasts of the new information only." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create a new results object by passing the new observations to the `append` method\n", "res_post = res_pre.append(y_update)\n", "\n", "# Since we now know the value for 2008Q3, we will only use `res_post` to\n", "# produce forecasts for 2008Q4 through 2009Q2\n", "forecasts_post = pd.concat([y_update, res_post.forecast('2009Q2')])\n", "print(forecasts_post)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, the forecast error is quite large - inflation was more than 10 percentage points below the AR(1) models' forecast. (This was largely because of large swings in oil prices around the global financial crisis)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To analyse this in more depth, we can use Statsmodels to isolate the effect of the new information - or the \"**news**\" - on our forecasts. This means that we do not yet want to change our model or re-estimate the parameters. Instead, we will use the `news` method that is available in the results objects of state space models.\n", "\n", "Computing the news in Statsmodels always requires a *previous* results object or dataset, and an *updated* results object or dataset. Here we will use the original results object `res_pre` as the previous results and the `res_post` results object that we just created as the updated results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once we have previous and updated results objects or datasets, we can compute the news by calling the `news` method. Here, we will call `res_pre.news`, and the first argument will be the updated results, `res_post` (however, if you have two results objects, the `news` method could can be called on either one).\n", "\n", "In addition to specifying the comparison object or dataset as the first argument, there are a variety of other arguments that are accepted. The most important specify the \"impact periods\" that you want to consider. These \"impact periods\" correspond to the forecasted periods of interest; i.e. these dates specify with periods will have forecast revisions decomposed.\n", "\n", "To specify the impact periods, you must pass two of `start`, `end`, and `periods` (similar to the Pandas `date_range` method). If your time series was a Pandas object with an associated date or period index, then you can pass dates as values for `start` and `end`, as we do below." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Compute the impact of the news on the four periods that we previously\n", "# forecasted: 2008Q3 through 2009Q2\n", "news = res_pre.news(res_post, start='2008Q3', end='2009Q2')\n", "# Note: one alternative way to specify these impact dates is\n", "# `start='2008Q3', periods=4`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The variable `news` is an object of the class `NewsResults`, and it contains details about the updates to the data in `res_post` compared to `res_pre`, the new information in the updated dataset, and the impact that the new information had on the forecasts in the period between `start` and `end`.\n", "\n", "One easy way to summarize the results are with the `summary` method." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(news.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Summary output**: the default summary for this news results object printed four tables:\n", "\n", "1. Summary of the model and datasets\n", "2. Details of the news from updated data\n", "3. Summary of the impacts of the new information on the forecasts between `start='2008Q3'` and `end='2009Q2'`\n", "4. Details of how the updated data led to the impacts on the forecasts between `start='2008Q3'` and `end='2009Q2'`\n", "\n", "These are described in more detail below.\n", "\n", "*Notes*:\n", "\n", "- There are a number of arguments that can be passed to the `summary` method to control this output. Check the documentation / docstring for details.\n", "- Table (4), showing details of the updates and impacts, can become quite large if the model is multivariate, there are multiple updates, or a large number of impact dates are selected. It is only shown by default for univariate models." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**First table: summary of the model and datasets**\n", "\n", "The first table, above, shows:\n", "\n", "- The type of model from which the forecasts were made. Here this is an ARIMA model, since an AR(1) is a special case of an ARIMA(p,d,q) model.\n", "- The date and time at which the analysis was computed.\n", "- The original sample period, which here corresponds to `y_pre`\n", "- The endpoint of the updated sample period, which here is the last date in `y_post`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Second table: the news from updated data**\n", "\n", "This table simply shows the forecasts from the previous results for observations that were updated in the updated sample.\n", "\n", "*Notes*:\n", "\n", "- Our updated dataset `y_post` did not contain any *revisions* to previously observed datapoints. If it had, there would be an additional table showing the previous and updated values of each such revision." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Third table: summary of the impacts of the new information**\n", "\n", "*Columns*:\n", "\n", "The third table, above, shows:\n", "\n", "- The previous forecast for each of the impact dates, in the \"estimate (prev)\" column\n", "- The impact that the new information (the \"news\") had on the forecasts for each of the impact dates, in the \"impact of news\" column\n", "- The updated forecast for each of the impact dates, in the \"estimate (new)\" column\n", "\n", "*Notes*:\n", "\n", "- In multivariate models, this table contains additional columns describing the relevant impacted variable for each row.\n", "- Our updated dataset `y_post` did not contain any *revisions* to previously observed datapoints. If it had, there would be additional columns in this table showing the impact of those revisions on the forecasts for the impact dates.\n", "- Note that `estimate (new) = estimate (prev) + impact of news`\n", "- This table can be accessed independently using the `summary_impacts` method.\n", "\n", "*In our example*:\n", "\n", "Notice that in our example, the table shows the values that we computed earlier:\n", "\n", "- The \"estimate (prev)\" column is identical to the forecasts from our previous model, contained in the `forecasts_pre` variable.\n", "- The \"estimate (new)\" column is identical to our `forecasts_post` variable, which contains the observed value for 2008Q3 and the forecasts from the updated model for 2008Q4 - 2009Q2." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Fourth table: details of updates and their impacts**\n", "\n", "The fourth table, above, shows how each new observation translated into specific impacts at each impact date.\n", "\n", "*Columns*:\n", "\n", "The first three columns table described the relevant **update** (an \"updated\" is a new observation):\n", "\n", "- The first column (\"update date\") shows the date of the variable that was updated.\n", "- The second column (\"forecast (prev)\") shows the value that would have been forecasted for the update variable at the update date based on the previous results / dataset.\n", "- The third column (\"observed\") shows the actual observed value of that updated variable / update date in the updated results / dataset.\n", "\n", "The last four columns described the **impact** of a given update (an impact is a changed forecast within the \"impact periods\").\n", "\n", "- The fourth column (\"impact date\") gives the date at which the given update made an impact.\n", "- The fifth column (\"news\") shows the \"news\" associated with the given update (this is the same for each impact of a given update, but is just not sparsified by default)\n", "- The sixth column (\"weight\") describes the weight that the \"news\" from the given update has on the impacted variable at the impact date. In general, weights will be different between each \"updated variable\" / \"update date\" / \"impacted variable\" / \"impact date\" combination.\n", "- The seventh column (\"impact\") shows the impact that the given update had on the given \"impacted variable\" / \"impact date\".\n", "\n", "*Notes*:\n", "\n", "- In multivariate models, this table contains additional columns to show the relevant variable that was updated and variable that was impacted for each row. Here, there is only one variable (\"infl\"), so those columns are suppressed to save space.\n", "- By default, the updates in this table are \"sparsified\" with blanks, to avoid repeating the same values for \"update date\", \"forecast (prev)\", and \"observed\" for each row of the table. This behavior can be overridden using the `sparsify` argument.\n", "- Note that `impact = news * weight`.\n", "- This table can be accessed independently using the `summary_details` method.\n", "\n", "*In our example*:\n", "\n", "- For the update to 2008Q3 and impact date 2008Q3, the weight is equal to 1. This is because we only have one variable, and once we have incorporated the data for 2008Q3, there is no no remaining ambiguity about the \"forecast\" for this date. Thus all of the \"news\" about this variable at 2008Q3 passes through to the \"forecast\" directly." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Addendum: manually computing the news, weights, and impacts\n", "\n", "For this simple example with a univariate model, it is straightforward to compute all of the values shown above by hand. First, recall the formula for forecasting $y_{T+h|T} = \\phi^h y_T$, and note that it follows that we also have $y_{T+h|T+1} = \\phi^h y_{T+1}$. Finally, note that $y_{T|T+1} = y_T$, because if we know the value of the observations through $T+1$, we know the value of $y_T$.\n", "\n", "**News**: The \"news\" is nothing more than the forecast error associated with one of the new observations. So the news associated with observation $T+1$ is:\n", "\n", "$$n_{T+1} = y_{T+1} - y_{T+1|T} = Y_{T+1} - \\phi Y_T$$\n", "\n", "**Impacts**: The impact of the news is the difference between the updated and previous forecasts, $i_h \\equiv y_{T+h|T+1} - y_{T+h|T}$.\n", "\n", "- The previous forecasts for $h=1, \\dots, 4$ are: $\\begin{pmatrix} \\phi y_T & \\phi^2 y_T & \\phi^3 y_T & \\phi^4 y_T \\end{pmatrix}'$. \n", "- The updated forecasts for $h=1, \\dots, 4$ are: $\\begin{pmatrix} y_{T+1} & \\phi y_{T+1} & \\phi^2 y_{T+1} & \\phi^3 y_{T+1} \\end{pmatrix}'$.\n", "\n", "The impacts are therefore:\n", "\n", "$$\\{ i_h \\}_{h=1}^4 = \\begin{pmatrix} y_{T+1} - \\phi y_T \\\\ \\phi (Y_{T+1} - \\phi y_T) \\\\ \\phi^2 (Y_{T+1} - \\phi y_T) \\\\ \\phi^3 (Y_{T+1} - \\phi y_T) \\end{pmatrix}$$\n", "\n", "**Weights**: To compute the weights, we just need to note that it is immediate that we can rewrite the impacts in terms of the forecast errors, $n_{T+1}$.\n", "\n", "$$\\{ i_h \\}_{h=1}^4 = \\begin{pmatrix} 1 \\\\ \\phi \\\\ \\phi^2 \\\\ \\phi^3 \\end{pmatrix} n_{T+1}$$\n", "\n", "The weights are then simply $w = \\begin{pmatrix} 1 \\\\ \\phi \\\\ \\phi^2 \\\\ \\phi^3 \\end{pmatrix}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check that this is what the `news` method has computed." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Print the news, computed by the `news` method\n", "print(news.news)\n", "\n", "# Manually compute the news\n", "print()\n", "print((y_update.iloc[0] - phi_hat * y_pre.iloc[-1]).round(6))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Print the total impacts, computed by the `news` method\n", "# (Note: news.total_impacts = news.revision_impacts + news.update_impacts, but\n", "# here there are no data revisions, so total and update impacts are the same)\n", "print(news.total_impacts)\n", "\n", "# Manually compute the impacts\n", "print()\n", "print(forecasts_post - forecasts_pre)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Print the weights, computed by the `news` method\n", "print(news.weights)\n", "\n", "# Manually compute the weights\n", "print()\n", "print(np.array([1, phi_hat, phi_hat**2, phi_hat**3]).round(6))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Multivariate example: dynamic factor\n", "\n", "In this example, we'll consider forecasting monthly core price inflation based on the Personal Consumption Expenditures (PCE) price index and the Consumer Price Index (CPI), using a Dynamic Factor model. Both of these measures track prices in the US economy and are based on similar source data, but they have a number of definitional differences. Nonetheless, they track each other relatively well, so modeling them jointly using a single dynamic factor seems reasonable.\n", "\n", "One reason that this kind of approach can be useful is that the CPI is released earlier in the month than the PCE. One the CPI is released, therefore, we can update our dynamic factor model with that additional datapoint, and obtain an improved forecast for that month's PCE release. A more involved version of this kind of analysis is available in Knotek and Zaman (2017)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We start by downloading the core CPI and PCE price index data from [FRED](https://fred.stlouisfed.org/), converting them to annualized monthly inflation rates, removing two outliers, and de-meaning each series (the dynamic factor model does not " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import pandas_datareader as pdr\n", "levels = pdr.get_data_fred(['PCEPILFE', 'CPILFESL'], start='1999', end='2019').to_period('M')\n", "infl = np.log(levels).diff().iloc[1:] * 1200\n", "infl.columns = ['PCE', 'CPI']\n", "\n", "# Remove two outliers and de-mean the series\n", "infl['PCE'].loc['2001-09':'2001-10'] = np.nan" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To show how this works, we'll imagine that it is April 14, 2017, which is the data of the March 2017 CPI release. So that we can show the effect of multiple updates at once, we'll assume that we haven't updated our data since the end of January, so that:\n", "\n", "- Our **previous dataset** will consist of all values for the PCE and CPI through January 2017\n", "- Our **updated dataset** will additionally incorporate the CPI for February and March 2017 and the PCE data for February 2017. But it will not yet the PCE (the March 2017 PCE price index was not released until May 1, 2017)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Previous dataset runs through 2017-02\n", "y_pre = infl.loc[:'2017-01'].copy()\n", "const_pre = np.ones(len(y_pre))\n", "print(y_pre.tail())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# For the updated dataset, we'll just add in the\n", "# CPI value for 2017-03\n", "y_post = infl.loc[:'2017-03'].copy()\n", "y_post.loc['2017-03', 'PCE'] = np.nan\n", "const_post = np.ones(len(y_post))\n", "\n", "# Notice the missing value for PCE in 2017-03\n", "print(y_post.tail())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We chose this particular example because in March 2017, core CPI prices fell for the first time since 2010, and this information may be useful in forecast core PCE prices for that month. The graph below shows the CPI and PCE price data as it would have been observed on April 14th$^\\dagger$.\n", "\n", "-----\n", "\n", "$\\dagger$ This statement is not entirely true, because both the CPI and PCE price indexes can be revised to a certain extent after the fact. As a result, the series that we're pulling are not exactly like those observed on April 14, 2017. This could be fixed by pulling the archived data from [ALFRED](https://alfred.stlouisfed.org/) instead of [FRED](https://fred.stlouisfed.org/), but the data we have is good enough for this tutorial." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Plot the updated dataset\n", "fig, ax = plt.subplots(figsize=(15, 3))\n", "y_post.plot(ax=ax)\n", "ax.hlines(0, '2009', '2017-06', linewidth=1.0)\n", "ax.set_xlim('2009', '2017-06');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To perform the exercise, we first construct and fit a `DynamicFactor` model. Specifically:\n", "\n", "- We are using a single dynamic factor (`k_factors=1`)\n", "- We are modeling the factor's dynamics with an AR(6) model (`factor_order=6`)\n", "- We have included a vector of ones as an exogenous variable (`exog=const_pre`), because the inflation series we are working with are not mean-zero." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod_pre = sm.tsa.DynamicFactor(y_pre, exog=const_pre, k_factors=1, factor_order=6)\n", "res_pre = mod_pre.fit()\n", "print(res_pre.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the fitted model in hand, we now construct the news and impacts associated with observing the CPI for March 2017. The updated data is for February 2017 and part of March 2017, and we'll examining the impacts on both March and April.\n", "\n", "In the univariate example, we first created an updated results object, and then passed that to the `news` method. Here, we're creating the news by directly passing the updated dataset.\n", "\n", "Notice that:\n", "\n", "1. `y_post` contains the entire updated dataset (not just the new datapoints)\n", "2. We also had to pass an updated `exog` array. This array must cover **both**:\n", " - The entire period associated with `y_post`\n", " - Any additional datapoints after the end of `y_post` through the last impact date, specified by `end`\n", "\n", " Here, `y_post` ends in March 2017, so we needed our `exog` to extend one more period, to April 2017." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [], "source": [ "# Create the news results\n", "# Note\n", "const_post_plus1 = np.ones(len(y_post) + 1)\n", "news = res_pre.news(y_post, exog=const_post_plus1, start='2017-03', end='2017-04')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Note**:\n", ">\n", "> In the univariate example, above, we first constructed a new results object, and then passed that to the `news` method. We could have done that here too, although there is an extra step required. Since we are requesting an impact for a period beyond the end of `y_post`, we would still need to pass the additional value for the `exog` variable during that period to `news`:\n", "> \n", "> ```python\n", "res_post = res_pre.apply(y_post, exog=const_post)\n", "news = res_pre.news(res_post, exog=[1.], start='2017-03', end='2017-04')\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have computed the `news`, printing `summary` is a convenient way to see the results." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Show the summary of the news results\n", "print(news.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because we have multiple variables, by default the summary only shows the news from updated data along and the total impacts.\n", "\n", "From the first table, we can see that our updated dataset contains three new data points, with most of the \"news\" from these data coming from the very low reading in March 2017.\n", "\n", "The second table shows that these three datapoints substantially impacted the estimate for PCE in March 2017 (which was not yet observed). This estimate revised down by nearly 1.5 percentage points.\n", "\n", "The updated data also impacted the forecasts in the first out-of-sample month, April 2017. After incorporating the new data, the model's forecasts for CPI and PCE inflation in that month revised down 0.29 and 0.17 percentage point, respectively." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While these tables show the \"news\" and the total impacts, they do not show how much of each impact was caused by each updated datapoint. To see that information, we need to look at the details tables.\n", "\n", "One way to see the details tables is to pass `include_details=True` to the `summary` method. To avoid repeating the tables above, however, we'll just call the `summary_details` method directly." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(news.summary_details())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This table shows that most of the revisions to the estimate of PCE in April 2017, described above, came from the news associated with the CPI release in March 2017. By contrast, the CPI release in February had only a little effect on the April forecast, and the PCE release in February had essentially no effect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bibliography\n", "\n", "BaÅ„bura, Marta, Domenico Giannone, and Lucrezia Reichlin. \"Nowcasting.\" The Oxford Handbook of Economic Forecasting. July 8, 2011.\n", "\n", "BaÅ„bura, Marta, Domenico Giannone, Michele Modugno, and Lucrezia Reichlin. \"Now-casting and the real-time data flow.\" In Handbook of economic forecasting, vol. 2, pp. 195-237. Elsevier, 2013.\n", "\n", "BaÅ„bura, Marta, and Michele Modugno. \"Maximum likelihood estimation of factor models on datasets with arbitrary pattern of missing data.\" Journal of Applied Econometrics 29, no. 1 (2014): 133-160.\n", "\n", "Knotek, Edward S., and Saeed Zaman. \"Nowcasting US headline and core inflation.\" Journal of Money, Credit and Banking 49, no. 5 (2017): 931-968." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 2 } statsmodels-0.12.2/examples/notebooks/statespace_sarimax_internet.ipynb000066400000000000000000000203741400612667500266270ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# SARIMAX: Model selection, missing data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The example mirrors Durbin and Koopman (2012), Chapter 8.4 in application of Box-Jenkins methodology to fit ARMA models. The novel feature is the ability of the model to work on datasets with missing values." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from scipy.stats import norm\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import requests\n", "from io import BytesIO\n", "from zipfile import ZipFile\n", "\n", "# Download the dataset\n", "dk = requests.get('http://www.ssfpack.com/files/DK-data.zip').content\n", "f = BytesIO(dk)\n", "zipped = ZipFile(f)\n", "df = pd.read_table(\n", " BytesIO(zipped.read('internet.dat')),\n", " skiprows=1, header=None, sep='\\s+', engine='python',\n", " names=['internet','dinternet']\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model Selection\n", "\n", "As in Durbin and Koopman, we force a number of the values to be missing." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Get the basic series\n", "dta_full = df.dinternet[1:].values\n", "dta_miss = dta_full.copy()\n", "\n", "# Remove datapoints\n", "missing = np.r_[6,16,26,36,46,56,66,72,73,74,75,76,86,96]-1\n", "dta_miss[missing] = np.nan" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we can consider model selection using the Akaike information criteria (AIC), but running the model for each variant and selecting the model with the lowest AIC value.\n", "\n", "There are a couple of things to note here:\n", "\n", "- When running such a large batch of models, particularly when the autoregressive and moving average orders become large, there is the possibility of poor maximum likelihood convergence. Below we ignore the warnings since this example is illustrative.\n", "- We use the option `enforce_invertibility=False`, which allows the moving average polynomial to be non-invertible, so that more of the models are estimable.\n", "- Several of the models do not produce good results, and their AIC value is set to NaN. This is not surprising, as Durbin and Koopman note numerical problems with the high order models." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import warnings\n", "\n", "aic_full = pd.DataFrame(np.zeros((6,6), dtype=float))\n", "aic_miss = pd.DataFrame(np.zeros((6,6), dtype=float))\n", "\n", "warnings.simplefilter('ignore')\n", "\n", "# Iterate over all ARMA(p,q) models with p,q in [0,6]\n", "for p in range(6):\n", " for q in range(6):\n", " if p == 0 and q == 0:\n", " continue\n", " \n", " # Estimate the model with no missing datapoints\n", " mod = sm.tsa.statespace.SARIMAX(dta_full, order=(p,0,q), enforce_invertibility=False)\n", " try:\n", " res = mod.fit(disp=False)\n", " aic_full.iloc[p,q] = res.aic\n", " except:\n", " aic_full.iloc[p,q] = np.nan\n", " \n", " # Estimate the model with missing datapoints\n", " mod = sm.tsa.statespace.SARIMAX(dta_miss, order=(p,0,q), enforce_invertibility=False)\n", " try:\n", " res = mod.fit(disp=False)\n", " aic_miss.iloc[p,q] = res.aic\n", " except:\n", " aic_miss.iloc[p,q] = np.nan" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the models estimated over the full (non-missing) dataset, the AIC chooses ARMA(1,1) or ARMA(3,0). Durbin and Koopman suggest the ARMA(1,1) specification is better due to parsimony.\n", "\n", "$$\n", "\\text{Replication of:}\\\\\n", "\\textbf{Table 8.1} ~~ \\text{AIC for different ARMA models.}\\\\\n", "\\newcommand{\\r}[1]{{\\color{red}{#1}}}\n", "\\begin{array}{lrrrrrr}\n", "\\hline\n", "q & 0 & 1 & 2 & 3 & 4 & 5 \\\\\n", "\\hline\n", "p & {} & {} & {} & {} & {} & {} \\\\\n", "0 & 0.00 & 549.81 & 519.87 & 520.27 & 519.38 & 518.86 \\\\\n", "1 & 529.24 & \\r{514.30} & 516.25 & 514.58 & 515.10 & 516.28 \\\\\n", "2 & 522.18 & 516.29 & 517.16 & 515.77 & 513.24 & 514.73 \\\\\n", "3 & \\r{511.99} & 513.94 & 515.92 & 512.06 & 513.72 & 514.50 \\\\\n", "4 & 513.93 & 512.89 & nan & nan & 514.81 & 516.08 \\\\\n", "5 & 515.86 & 517.64 & nan & nan & nan & nan \\\\\n", "\\hline\n", "\\end{array}\n", "$$\n", "\n", "For the models estimated over missing dataset, the AIC chooses ARMA(1,1)\n", "\n", "$$\n", "\\text{Replication of:}\\\\\n", "\\textbf{Table 8.2} ~~ \\text{AIC for different ARMA models with missing observations.}\\\\\n", "\\begin{array}{lrrrrrr}\n", "\\hline\n", "q & 0 & 1 & 2 & 3 & 4 & 5 \\\\\n", "\\hline\n", "p & {} & {} & {} & {} & {} & {} \\\\\n", "0 & 0.00 & 488.93 & 464.01 & 463.86 & 462.63 & 463.62 \\\\\n", "1 & 468.01 & \\r{457.54} & 459.35 & 458.66 & 459.15 & 461.01 \\\\\n", "2 & 469.68 & nan & 460.48 & 459.43 & 459.23 & 460.47 \\\\\n", "3 & 467.10 & 458.44 & 459.64 & 456.66 & 459.54 & 460.05 \\\\\n", "4 & 469.00 & 459.52 & nan & 463.04 & 459.35 & 460.96 \\\\\n", "5 & 471.32 & 461.26 & nan & nan & 461.00 & 462.97 \\\\\n", "\\hline\n", "\\end{array}\n", "$$\n", "\n", "**Note**: the AIC values are calculated differently than in Durbin and Koopman, but show overall similar trends." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Postestimation\n", "\n", "Using the ARMA(1,1) specification selected above, we perform in-sample prediction and out-of-sample forecasting." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Statespace\n", "mod = sm.tsa.statespace.SARIMAX(dta_miss, order=(1,0,1))\n", "res = mod.fit(disp=False)\n", "print(res.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# In-sample one-step-ahead predictions, and out-of-sample forecasts\n", "nforecast = 20\n", "predict = res.get_prediction(end=mod.nobs + nforecast)\n", "idx = np.arange(len(predict.predicted_mean))\n", "predict_ci = predict.conf_int(alpha=0.5)\n", "\n", "# Graph\n", "fig, ax = plt.subplots(figsize=(12,6))\n", "ax.xaxis.grid()\n", "ax.plot(dta_miss, 'k.')\n", "\n", "# Plot\n", "ax.plot(idx[:-nforecast], predict.predicted_mean[:-nforecast], 'gray')\n", "ax.plot(idx[-nforecast:], predict.predicted_mean[-nforecast:], 'k--', linestyle='--', linewidth=2)\n", "ax.fill_between(idx, predict_ci[:, 0], predict_ci[:, 1], alpha=0.15)\n", "\n", "ax.set(title='Figure 8.9 - Internet series');" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 } statsmodels-0.12.2/examples/notebooks/statespace_sarimax_pymc3.ipynb000066400000000000000000000520721400612667500260320ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Fast Bayesian estimation of SARIMAX models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "This notebook will show how to use fast Bayesian methods to estimate SARIMAX (Seasonal AutoRegressive Integrated Moving Average with eXogenous regressors) models. These methods can also be parallelized across multiple cores.\n", "\n", "Here, fast methods means a version of Hamiltonian Monte Carlo called the No-U-Turn Sampler (NUTS) developed by Hoffmann and Gelman: see [Hoffman, M. D., & Gelman, A. (2014). The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15(1), 1593-1623.](https://arxiv.org/abs/1111.4246). As they say, \"the cost of HMC per independent sample from a target distribution of dimension $D$ is roughly $\\mathcal{O}(D^{5/4})$, which stands in sharp contrast with the $\\mathcal{O}(D^{2})$ cost of random-walk Metropolis\". So for problems of larger dimension, the time-saving with HMC is significant. However it does require the gradient, or Jacobian, of the model to be provided.\n", "\n", "This notebook will combine the Python libraries [statsmodels](https://www.statsmodels.org/stable/index.html), which does econometrics, and [PyMC3](https://docs.pymc.io/), which is for Bayesian estimation, to perform fast Bayesian estimation of a simple SARIMAX model, in this case an ARMA(1, 1) model for US CPI.\n", "\n", "Note that, for simple models like AR(p), base PyMC3 is a quicker way to fit a model; there's an [example here](https://docs.pymc.io/notebooks/AR.html). The advantage of using statsmodels is that it gives access to methods that can solve a vast range of statespace models.\n", "\n", "The model we'll solve is given by\n", "\n", "$$\n", "y_t = \\phi y_{t-1} + \\varepsilon_t + \\theta_1 \\varepsilon_{t-1}, \\qquad \\varepsilon_t \\sim N(0, \\sigma^2)\n", "$$\n", "\n", "with 1 auto-regressive term and 1 moving average term. In statespace form it is written as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\underbrace{\\begin{bmatrix} 1 & \\theta_1 \\end{bmatrix}}_{Z} \\underbrace{\\begin{bmatrix} \\alpha_{1,t} \\\\ \\alpha_{2,t} \\end{bmatrix}}_{\\alpha_t} \\\\\n", " \\begin{bmatrix} \\alpha_{1,t+1} \\\\ \\alpha_{2,t+1} \\end{bmatrix} & = \\underbrace{\\begin{bmatrix}\n", " \\phi & 0 \\\\\n", " 1 & 0 \\\\\n", " \\end{bmatrix}}_{T} \\begin{bmatrix} \\alpha_{1,t} \\\\ \\alpha_{2,t} \\end{bmatrix} +\n", " \\underbrace{\\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}}_{R} \\underbrace{\\varepsilon_{t+1}}_{\\eta_t} \\\\\n", "\\end{align}\n", "$$\n", "\n", "The code will follow these steps:\n", "1. Import external dependencies\n", "2. Download and plot the data on US CPI\n", "3. Simple maximum likelihood estimation (MLE) as an example\n", "4. Definitions of helper functions to provide tensors to the library doing Bayesian estimation\n", "5. Bayesian estimation via NUTS\n", "6. Application to US CPI series\n", "\n", "Finally, Appendix A shows how to re-use the helper functions from step (4) to estimate a different state space model, `UnobservedComponents`, using the same Bayesian methods." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1. Import external dependencies" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import theano\n", "import theano.tensor as tt\n", "import pymc3 as pm\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import statsmodels.api as sm\n", "import pandas as pd\n", "from pandas_datareader.data import DataReader\n", "from pandas.plotting import register_matplotlib_converters\n", "plt.style.use('seaborn')\n", "register_matplotlib_converters()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2. Download and plot the data on US CPI\n", "\n", "We'll get the data from FRED:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "cpi = DataReader('CPIAUCNS', 'fred', start='1971-01', end='2018-12')\n", "cpi.index = pd.DatetimeIndex(cpi.index, freq='MS')\n", "\n", "# Define the inflation series that we'll use in analysis\n", "inf = np.log(cpi).resample('QS').mean().diff()[1:] * 400\n", "print(inf.head())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Plot the series \n", "fig, ax = plt.subplots(figsize=(9, 4), dpi=300)\n", "ax.plot(inf.index, inf, label=r'$\\Delta \\log CPI$', lw=2)\n", "ax.legend(loc='lower left')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3. Fit the model with maximum likelihood\n", "\n", "Statsmodels does all of the hard work of this for us - creating and fitting the model takes just two lines of code. The model order parameters correspond to auto-regressive, difference, and moving average orders respectively." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create an SARIMAX model instance - here we use it to estimate\n", "# the parameters via MLE using the `fit` method, but we can\n", "# also re-use it below for the Bayesian estimation\n", "mod = sm.tsa.statespace.SARIMAX(inf, order=(1, 0, 1))\n", "\n", "res_mle = mod.fit(disp=False)\n", "print(res_mle.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's a good fit. We can also get the series of one-step ahead predictions and plot it next to the actual data, along with a confidence band.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "predict_mle = res_mle.get_prediction()\n", "predict_mle_ci = predict_mle.conf_int()\n", "lower = predict_mle_ci['lower CPIAUCNS']\n", "upper = predict_mle_ci['upper CPIAUCNS']\n", "\n", "# Graph\n", "fig, ax = plt.subplots(figsize=(9,4), dpi=300)\n", "\n", "# Plot data points\n", "inf.plot(ax=ax, style='-', label='Observed')\n", "\n", "# Plot predictions\n", "predict_mle.predicted_mean.plot(ax=ax, style='r.', label='One-step-ahead forecast')\n", "ax.fill_between(predict_mle_ci.index, lower, upper, color='r', alpha=0.1)\n", "ax.legend(loc='lower left')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4. Helper functions to provide tensors to the library doing Bayesian estimation\n", "\n", "We're almost on to the magic but there are a few preliminaries. Feel free to skip this section if you're not interested in the technical details." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Technical Details\n", "\n", "PyMC3 is a Bayesian estimation library (\"Probabilistic Programming in Python: Bayesian Modeling and Probabilistic Machine Learning with Theano\") that is a) fast and b) optimized for Bayesian machine learning, for instance [Bayesian neural networks](https://docs.pymc.io/notebooks/bayesian_neural_network_advi.html). To do all of this, it is built on top of a Theano, a library that aims to evaluate tensors very efficiently and provide symbolic differentiation (necessary for any kind of deep learning). It is the symbolic differentiation that means PyMC3 can use NUTS on any problem formulated within PyMC3.\n", "\n", "We are not formulating a problem directly in PyMC3; we're using statsmodels to specify the statespace model and solve it with the Kalman filter. So we need to put the plumbing of statsmodels and PyMC3 together, which means wrapping the statsmodels SARIMAX model object in a Theano-flavored wrapper before passing information to PyMC3 for estimation.\n", "\n", "Because of this, we can't use the Theano auto-differentiation directly. Happily, statsmodels SARIMAX objects have a method to return the Jacobian evaluated at the parameter values. We'll be making use of this to provide gradients so that we can use NUTS." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Defining helper functions to translate models into a PyMC3 friendly form\n", "\n", "First, we'll create the Theano wrappers. They will be in the form of 'Ops', operation objects, that 'perform' particular tasks. They are initialized with a statsmodels `model` instance.\n", "\n", "Although this code may look somewhat opaque, it is generic for any state space model in statsmodels." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "class Loglike(tt.Op):\n", "\n", " itypes = [tt.dvector] # expects a vector of parameter values when called\n", " otypes = [tt.dscalar] # outputs a single scalar value (the log likelihood)\n", "\n", " def __init__(self, model):\n", " self.model = model\n", " self.score = Score(self.model)\n", "\n", " def perform(self, node, inputs, outputs):\n", " theta, = inputs # contains the vector of parameters\n", " llf = self.model.loglike(theta)\n", " outputs[0][0] = np.array(llf) # output the log-likelihood\n", "\n", " def grad(self, inputs, g):\n", " # the method that calculates the gradients - it actually returns the\n", " # vector-Jacobian product - g[0] is a vector of parameter values\n", " theta, = inputs # our parameters\n", " out = [g[0] * self.score(theta)]\n", " return out\n", "\n", " \n", "class Score(tt.Op):\n", " itypes = [tt.dvector]\n", " otypes = [tt.dvector]\n", "\n", " def __init__(self, model):\n", " self.model = model\n", "\n", " def perform(self, node, inputs, outputs):\n", " theta, = inputs\n", " outputs[0][0] = self.model.score(theta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5. Bayesian estimation with NUTS\n", "\n", "The next step is to set the parameters for the Bayesian estimation, specify our priors, and run it." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Set sampling params\n", "ndraws = 3000 # number of draws from the distribution\n", "nburn = 600 # number of \"burn-in points\" (which will be discarded)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now for the fun part! There are three parameters to estimate: $\\phi$, $\\theta_1$, and $\\sigma$. We'll use uninformative uniform priors for the first two, and an inverse gamma for the last one. Then we'll run the inference optionally using as many computer cores as I have." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Construct an instance of the Theano wrapper defined above, which\n", "# will allow PyMC3 to compute the likelihood and Jacobian in a way\n", "# that it can make use of. Here we are using the same model instance\n", "# created earlier for MLE analysis (we could also create a new model\n", "# instance if we preferred)\n", "loglike = Loglike(mod)\n", "\n", "with pm.Model():\n", " # Priors\n", " arL1 = pm.Uniform('ar.L1', -0.99, 0.99)\n", " maL1 = pm.Uniform('ma.L1', -0.99, 0.99)\n", " sigma2 = pm.InverseGamma('sigma2', 2, 4)\n", "\n", " # convert variables to tensor vectors\n", " theta = tt.as_tensor_variable([arL1, maL1, sigma2])\n", "\n", " # use a DensityDist (use a lamdba function to \"call\" the Op)\n", " pm.DensityDist('likelihood', lambda v: loglike(v), observed={'v': theta})\n", " \n", " # Draw samples\n", " trace = pm.sample(ndraws, tune=nburn, discard_tuned_samples=True, cores=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the NUTS sampler is auto-assigned because we provided gradients. PyMC3 will use Metropolis or Slicing samplers if it does not find that gradients are available. There are an impressive number of draws per second for a \"block box\" style computation! However, note that if the model can be represented directly by PyMC3 (like the AR(p) models mentioned above), then computation can be substantially faster.\n", "\n", "Inference is complete, but are the results any good? There are a number of ways to check. The first is to look at the posterior distributions (with lines showing the MLE values):" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plt.tight_layout()\n", "# Note: the syntax here for the lines argument is required for\n", "# PyMC3 versions >= 3.7\n", "# For version <= 3.6 you can use lines=dict(res_mle.params) instead\n", "_ = pm.traceplot(trace,\n", " lines=[(k, {}, [v]) for k, v in dict(res_mle.params).items()],\n", " combined=True,\n", " figsize=(12, 12))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The estimated posteriors clearly peak close to the parameters found by MLE. We can also see a summary of the estimated values:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "pm.summary(trace)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here $\\hat{R}$ is the Gelman-Rubin statistic. It tests for lack of convergence by comparing the variance between multiple chains to the variance within each chain. If convergence has been achieved, the between-chain and within-chain variances should be identical. If $\\hat{R}<1.2$ for all model parameters, we can have some confidence that convergence has been reached.\n", "\n", "Additionally, the highest posterior density interval (the gap between the two values of HPD in the table) is small for each of the variables.\n", "\n", "### 6. Application of Bayesian estimates of parameters\n", "\n", "We'll now re-instigate a version of the model but using the parameters from the Bayesian estimation, and again plot the one-step-ahead forecasts." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Retrieve the posterior means\n", "params = pm.summary(trace)['mean'].values\n", "\n", "# Construct results using these posterior means as parameter values\n", "res_bayes = mod.smooth(params)\n", "\n", "predict_bayes = res_bayes.get_prediction()\n", "predict_bayes_ci = predict_bayes.conf_int()\n", "lower = predict_bayes_ci['lower CPIAUCNS']\n", "upper = predict_bayes_ci['upper CPIAUCNS']\n", "\n", "# Graph\n", "fig, ax = plt.subplots(figsize=(9,4), dpi=300)\n", "\n", "# Plot data points\n", "inf.plot(ax=ax, style='-', label='Observed')\n", "\n", "# Plot predictions\n", "predict_bayes.predicted_mean.plot(ax=ax, style='r.', label='One-step-ahead forecast')\n", "ax.fill_between(predict_bayes_ci.index, lower, upper, color='r', alpha=0.1)\n", "ax.legend(loc='lower left')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Appendix A. Application to `UnobservedComponents` models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can reuse the `Loglike` and `Score` wrappers defined above to consider a different state space model. For example, we might want to model inflation as the combination of a random walk trend and autoregressive error term:\n", "\n", "$$\n", "\\begin{aligned}\n", "y_t & = \\mu_t + \\varepsilon_t \\\\\n", "\\mu_t & = \\mu_{t-1} + \\eta_t \\\\\n", "\\varepsilon_t &= \\phi \\varepsilon_t + \\zeta_t\n", "\\end{aligned}\n", "$$\n", "\n", "This model can be constructed in Statsmodels with the `UnobservedComponents` class using the `rwalk` and `autoregressive` specifications. As before, we can fit the model using maximum likelihood via the `fit` method." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Construct the model instance\n", "mod_uc = sm.tsa.UnobservedComponents(inf, 'rwalk', autoregressive=1)\n", "\n", "# Fit the model via maximum likelihood\n", "res_uc_mle = mod_uc.fit()\n", "print(res_uc_mle.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As noted earlier, the Theano wrappers (`Loglike` and `Score`) that we created above are generic, so we can re-use essentially the same code to explore the model with Bayesian methods." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Set sampling params\n", "ndraws = 3000 # number of draws from the distribution\n", "nburn = 600 # number of \"burn-in points\" (which will be discarded)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Here we follow the same procedure as above, but now we instantiate the\n", "# Theano wrapper `Loglike` with the UC model instance instead of the\n", "# SARIMAX model instance\n", "loglike_uc = Loglike(mod_uc)\n", "\n", "with pm.Model():\n", " # Priors\n", " sigma2level = pm.InverseGamma('sigma2.level', 1, 1)\n", " sigma2ar = pm.InverseGamma('sigma2.ar', 1, 1)\n", " arL1 = pm.Uniform('ar.L1', -0.99, 0.99)\n", "\n", " # convert variables to tensor vectors\n", " theta_uc = tt.as_tensor_variable([sigma2level, sigma2ar, arL1])\n", "\n", " # use a DensityDist (use a lamdba function to \"call\" the Op)\n", " pm.DensityDist('likelihood', lambda v: loglike_uc(v), observed={'v': theta_uc})\n", " \n", " # Draw samples\n", " trace_uc = pm.sample(ndraws, tune=nburn, discard_tuned_samples=True, cores=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And as before we can plot the marginal posteriors. In contrast to the SARIMAX example, here the posterior modes are somewhat different from the MLE estimates." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plt.tight_layout()\n", "# Note: the syntax here for the lines argument is required for\n", "# PyMC3 versions >= 3.7\n", "# For version <= 3.6 you can use lines=dict(res_mle.params) instead\n", "_ = pm.traceplot(trace_uc,\n", " lines=[(k, {}, [v]) for k, v in dict(res_uc_mle.params).items()],\n", " combined=True,\n", " figsize=(12, 12))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "pm.summary(trace_uc)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Retrieve the posterior means\n", "params = pm.summary(trace_uc)['mean'].values\n", "\n", "# Construct results using these posterior means as parameter values\n", "res_uc_bayes = mod_uc.smooth(params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One benefit of this model is that it gives us an estimate of the underling \"level\" of inflation, using the smoothed estimate of $\\mu_t$, which we can access as the \"level\" column in the results objects' `states.smoothed` attribute. In this case, because the Bayesian posterior mean of the level's variance is larger than the MLE estimate, its estimated level is a little more volatile." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Graph\n", "fig, ax = plt.subplots(figsize=(9,4), dpi=300)\n", "\n", "# Plot data points\n", "inf['CPIAUCNS'].plot(ax=ax, style='-', label='Observed data')\n", "\n", "# Plot estimate of the level term\n", "res_uc_mle.states.smoothed['level'].plot(ax=ax, label='Smoothed level (MLE)')\n", "res_uc_bayes.states.smoothed['level'].plot(ax=ax, label='Smoothed level (Bayesian)')\n", "\n", "ax.legend(loc='lower left');" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 2 }statsmodels-0.12.2/examples/notebooks/statespace_sarimax_stata.ipynb000066400000000000000000000632301400612667500261110ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# SARIMAX: Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook replicates examples from the Stata ARIMA time series estimation and postestimation documentation.\n", "\n", "First, we replicate the four estimation examples http://www.stata.com/manuals13/tsarima.pdf:\n", "\n", "1. ARIMA(1,1,1) model on the U.S. Wholesale Price Index (WPI) dataset.\n", "2. Variation of example 1 which adds an MA(4) term to the ARIMA(1,1,1) specification to allow for an additive seasonal effect.\n", "3. ARIMA(2,1,0) x (1,1,0,12) model of monthly airline data. This example allows a multiplicative seasonal effect.\n", "4. ARMA(1,1) model with exogenous regressors; describes consumption as an autoregressive process on which also the money supply is assumed to be an explanatory variable.\n", "\n", "Second, we demonstrate postestimation capabilities to replicate http://www.stata.com/manuals13/tsarimapostestimation.pdf. The model from example 4 is used to demonstrate:\n", "\n", "1. One-step-ahead in-sample prediction\n", "2. n-step-ahead out-of-sample forecasting\n", "3. n-step-ahead in-sample dynamic prediction" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from scipy.stats import norm\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "from datetime import datetime\n", "import requests\n", "from io import BytesIO\n", "# Register converters to avoid warnings\n", "pd.plotting.register_matplotlib_converters()\n", "plt.rc(\"figure\", figsize=(16,8))\n", "plt.rc(\"font\", size=14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ARIMA Example 1: Arima\n", "\n", "As can be seen in the graphs from Example 2, the Wholesale price index (WPI) is growing over time (i.e. is not stationary). Therefore an ARMA model is not a good specification. In this first example, we consider a model where the original time series is assumed to be integrated of order 1, so that the difference is assumed to be stationary, and fit a model with one autoregressive lag and one moving average lag, as well as an intercept term.\n", "\n", "The postulated data process is then:\n", "\n", "$$\n", "\\Delta y_t = c + \\phi_1 \\Delta y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\epsilon_{t}\n", "$$\n", "\n", "where $c$ is the intercept of the ARMA model, $\\Delta$ is the first-difference operator, and we assume $\\epsilon_{t} \\sim N(0, \\sigma^2)$. This can be rewritten to emphasize lag polynomials as (this will be useful in example 2, below):\n", "\n", "$$\n", "(1 - \\phi_1 L ) \\Delta y_t = c + (1 + \\theta_1 L) \\epsilon_{t}\n", "$$\n", "\n", "where $L$ is the lag operator.\n", "\n", "Notice that one difference between the Stata output and the output below is that Stata estimates the following model:\n", "\n", "$$\n", "(\\Delta y_t - \\beta_0) = \\phi_1 ( \\Delta y_{t-1} - \\beta_0) + \\theta_1 \\epsilon_{t-1} + \\epsilon_{t}\n", "$$\n", "\n", "where $\\beta_0$ is the mean of the process $y_t$. This model is equivalent to the one estimated in the statsmodels SARIMAX class, but the interpretation is different. To see the equivalence, note that:\n", "\n", "$$\n", "(\\Delta y_t - \\beta_0) = \\phi_1 ( \\Delta y_{t-1} - \\beta_0) + \\theta_1 \\epsilon_{t-1} + \\epsilon_{t} \\\\\n", "\\Delta y_t = (1 - \\phi_1) \\beta_0 + \\phi_1 \\Delta y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\epsilon_{t}\n", "$$\n", "\n", "so that $c = (1 - \\phi_1) \\beta_0$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Dataset\n", "wpi1 = requests.get('https://www.stata-press.com/data/r12/wpi1.dta').content\n", "data = pd.read_stata(BytesIO(wpi1))\n", "data.index = data.t\n", "# Set the frequency\n", "data.index.freq=\"QS-OCT\"\n", "\n", "# Fit the model\n", "mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(1,1,1))\n", "res = mod.fit(disp=False)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thus the maximum likelihood estimates imply that for the process above, we have:\n", "\n", "$$\n", "\\Delta y_t = 0.0943 + 0.8742 \\Delta y_{t-1} - 0.4120 \\epsilon_{t-1} + \\epsilon_{t}\n", "$$\n", "\n", "where $\\epsilon_{t} \\sim N(0, 0.5257)$. Finally, recall that $c = (1 - \\phi_1) \\beta_0$, and here $c = 0.0943$ and $\\phi_1 = 0.8742$. To compare with the output from Stata, we could calculate the mean:\n", "\n", "$$\\beta_0 = \\frac{c}{1 - \\phi_1} = \\frac{0.0943}{1 - 0.8742} = 0.7496$$\n", "\n", "**Note**: This value is virtually identical to the value in the Stata documentation, $\\beta_0 = 0.7498$. The slight difference is likely down to rounding and subtle differences in stopping criterion of the numerical optimizers used." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ARIMA Example 2: Arima with additive seasonal effects\n", "\n", "This model is an extension of that from example 1. Here the data is assumed to follow the process:\n", "\n", "$$\n", "\\Delta y_t = c + \\phi_1 \\Delta y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\theta_4 \\epsilon_{t-4} + \\epsilon_{t}\n", "$$\n", "\n", "The new part of this model is that there is allowed to be a annual seasonal effect (it is annual even though the periodicity is 4 because the dataset is quarterly). The second difference is that this model uses the log of the data rather than the level.\n", "\n", "Before estimating the dataset, graphs showing:\n", "\n", "1. The time series (in logs)\n", "2. The first difference of the time series (in logs)\n", "3. The autocorrelation function\n", "4. The partial autocorrelation function.\n", "\n", "From the first two graphs, we note that the original time series does not appear to be stationary, whereas the first-difference does. This supports either estimating an ARMA model on the first-difference of the data, or estimating an ARIMA model with 1 order of integration (recall that we are taking the latter approach). The last two graphs support the use of an ARMA(1,1,1) model." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Dataset\n", "data = pd.read_stata(BytesIO(wpi1))\n", "data.index = data.t\n", "data.index.freq=\"QS-OCT\"\n", "\n", "data['ln_wpi'] = np.log(data['wpi'])\n", "data['D.ln_wpi'] = data['ln_wpi'].diff()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Graph data\n", "fig, axes = plt.subplots(1, 2, figsize=(15,4))\n", "\n", "# Levels\n", "axes[0].plot(data.index._mpl_repr(), data['wpi'], '-')\n", "axes[0].set(title='US Wholesale Price Index')\n", "\n", "# Log difference\n", "axes[1].plot(data.index._mpl_repr(), data['D.ln_wpi'], '-')\n", "axes[1].hlines(0, data.index[0], data.index[-1], 'r')\n", "axes[1].set(title='US Wholesale Price Index - difference of logs');" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Graph data\n", "fig, axes = plt.subplots(1, 2, figsize=(15,4))\n", "\n", "fig = sm.graphics.tsa.plot_acf(data.iloc[1:]['D.ln_wpi'], lags=40, ax=axes[0])\n", "fig = sm.graphics.tsa.plot_pacf(data.iloc[1:]['D.ln_wpi'], lags=40, ax=axes[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To understand how to specify this model in statsmodels, first recall that from example 1 we used the following code to specify the ARIMA(1,1,1) model:\n", "\n", "```python\n", "mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(1,1,1))\n", "```\n", "\n", "The `order` argument is a tuple of the form `(AR specification, Integration order, MA specification)`. The integration order must be an integer (for example, here we assumed one order of integration, so it was specified as 1. In a pure ARMA model where the underlying data is already stationary, it would be 0).\n", "\n", "For the AR specification and MA specification components, there are two possibilities. The first is to specify the **maximum degree** of the corresponding lag polynomial, in which case the component is an integer. For example, if we wanted to specify an ARIMA(1,1,4) process, we would use:\n", "\n", "```python\n", "mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(1,1,4))\n", "```\n", "\n", "and the corresponding data process would be:\n", "\n", "$$\n", "y_t = c + \\phi_1 y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\theta_2 \\epsilon_{t-2} + \\theta_3 \\epsilon_{t-3} + \\theta_4 \\epsilon_{t-4} + \\epsilon_{t}\n", "$$\n", "\n", "or\n", "\n", "$$\n", "(1 - \\phi_1 L)\\Delta y_t = c + (1 + \\theta_1 L + \\theta_2 L^2 + \\theta_3 L^3 + \\theta_4 L^4) \\epsilon_{t}\n", "$$\n", "\n", "When the specification parameter is given as a maximum degree of the lag polynomial, it implies that all polynomial terms up to that degree are included. Notice that this is *not* the model we want to use, because it would include terms for $\\epsilon_{t-2}$ and $\\epsilon_{t-3}$, which we do not want here.\n", "\n", "What we want is a polynomial that has terms for the 1st and 4th degrees, but leaves out the 2nd and 3rd terms. To do that, we need to provide a tuple for the specification parameter, where the tuple describes **the lag polynomial itself**. In particular, here we would want to use:\n", "\n", "```python\n", "ar = 1 # this is the maximum degree specification\n", "ma = (1,0,0,1) # this is the lag polynomial specification\n", "mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(ar,1,ma)))\n", "```\n", "\n", "This gives the following form for the process of the data:\n", "\n", "$$\n", "\\Delta y_t = c + \\phi_1 \\Delta y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\theta_4 \\epsilon_{t-4} + \\epsilon_{t} \\\\\n", "(1 - \\phi_1 L)\\Delta y_t = c + (1 + \\theta_1 L + \\theta_4 L^4) \\epsilon_{t}\n", "$$\n", "\n", "which is what we want." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Fit the model\n", "mod = sm.tsa.statespace.SARIMAX(data['ln_wpi'], trend='c', order=(1,1,(1,0,0,1)))\n", "res = mod.fit(disp=False)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ARIMA Example 3: Airline Model\n", "\n", "In the previous example, we included a seasonal effect in an *additive* way, meaning that we added a term allowing the process to depend on the 4th MA lag. It may be instead that we want to model a seasonal effect in a multiplicative way. We often write the model then as an ARIMA $(p,d,q) \\times (P,D,Q)_s$, where the lowercase letters indicate the specification for the non-seasonal component, and the uppercase letters indicate the specification for the seasonal component; $s$ is the periodicity of the seasons (e.g. it is often 4 for quarterly data or 12 for monthly data). The data process can be written generically as:\n", "\n", "$$\n", "\\phi_p (L) \\tilde \\phi_P (L^s) \\Delta^d \\Delta_s^D y_t = A(t) + \\theta_q (L) \\tilde \\theta_Q (L^s) \\epsilon_t\n", "$$\n", "\n", "where:\n", "\n", "- $\\phi_p (L)$ is the non-seasonal autoregressive lag polynomial\n", "- $\\tilde \\phi_P (L^s)$ is the seasonal autoregressive lag polynomial\n", "- $\\Delta^d \\Delta_s^D y_t$ is the time series, differenced $d$ times, and seasonally differenced $D$ times.\n", "- $A(t)$ is the trend polynomial (including the intercept)\n", "- $\\theta_q (L)$ is the non-seasonal moving average lag polynomial\n", "- $\\tilde \\theta_Q (L^s)$ is the seasonal moving average lag polynomial\n", "\n", "sometimes we rewrite this as:\n", "\n", "$$\n", "\\phi_p (L) \\tilde \\phi_P (L^s) y_t^* = A(t) + \\theta_q (L) \\tilde \\theta_Q (L^s) \\epsilon_t\n", "$$\n", "\n", "where $y_t^* = \\Delta^d \\Delta_s^D y_t$. This emphasizes that just as in the simple case, after we take differences (here both non-seasonal and seasonal) to make the data stationary, the resulting model is just an ARMA model.\n", "\n", "As an example, consider the airline model ARIMA $(2,1,0) \\times (1,1,0)_{12}$, with an intercept. The data process can be written in the form above as:\n", "\n", "$$\n", "(1 - \\phi_1 L - \\phi_2 L^2) (1 - \\tilde \\phi_1 L^{12}) \\Delta \\Delta_{12} y_t = c + \\epsilon_t\n", "$$\n", "\n", "Here, we have:\n", "\n", "- $\\phi_p (L) = (1 - \\phi_1 L - \\phi_2 L^2)$\n", "- $\\tilde \\phi_P (L^s) = (1 - \\phi_1 L^12)$\n", "- $d = 1, D = 1, s=12$ indicating that $y_t^*$ is derived from $y_t$ by taking first-differences and then taking 12-th differences.\n", "- $A(t) = c$ is the *constant* trend polynomial (i.e. just an intercept)\n", "- $\\theta_q (L) = \\tilde \\theta_Q (L^s) = 1$ (i.e. there is no moving average effect)\n", "\n", "It may still be confusing to see the two lag polynomials in front of the time-series variable, but notice that we can multiply the lag polynomials together to get the following model:\n", "\n", "$$\n", "(1 - \\phi_1 L - \\phi_2 L^2 - \\tilde \\phi_1 L^{12} + \\phi_1 \\tilde \\phi_1 L^{13} + \\phi_2 \\tilde \\phi_1 L^{14} ) y_t^* = c + \\epsilon_t\n", "$$\n", "\n", "which can be rewritten as:\n", "\n", "$$\n", "y_t^* = c + \\phi_1 y_{t-1}^* + \\phi_2 y_{t-2}^* + \\tilde \\phi_1 y_{t-12}^* - \\phi_1 \\tilde \\phi_1 y_{t-13}^* - \\phi_2 \\tilde \\phi_1 y_{t-14}^* + \\epsilon_t\n", "$$\n", "\n", "This is similar to the additively seasonal model from example 2, but the coefficients in front of the autoregressive lags are actually combinations of the underlying seasonal and non-seasonal parameters.\n", "\n", "Specifying the model in statsmodels is done simply by adding the `seasonal_order` argument, which accepts a tuple of the form `(Seasonal AR specification, Seasonal Integration order, Seasonal MA, Seasonal periodicity)`. The seasonal AR and MA specifications, as before, can be expressed as a maximum polynomial degree or as the lag polynomial itself. Seasonal periodicity is an integer.\n", "\n", "For the airline model ARIMA $(2,1,0) \\times (1,1,0)_{12}$ with an intercept, the command is:\n", "\n", "```python\n", "mod = sm.tsa.statespace.SARIMAX(data['lnair'], order=(2,1,0), seasonal_order=(1,1,0,12))\n", "```" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Dataset\n", "air2 = requests.get('https://www.stata-press.com/data/r12/air2.dta').content\n", "data = pd.read_stata(BytesIO(air2))\n", "data.index = pd.date_range(start=datetime(data.time[0], 1, 1), periods=len(data), freq='MS')\n", "data['lnair'] = np.log(data['air'])\n", "\n", "# Fit the model\n", "mod = sm.tsa.statespace.SARIMAX(data['lnair'], order=(2,1,0), seasonal_order=(1,1,0,12), simple_differencing=True)\n", "res = mod.fit(disp=False)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that here we used an additional argument `simple_differencing=True`. This controls how the order of integration is handled in ARIMA models. If `simple_differencing=True`, then the time series provided as `endog` is literally differenced and an ARMA model is fit to the resulting new time series. This implies that a number of initial periods are lost to the differencing process, however it may be necessary either to compare results to other packages (e.g. Stata's `arima` always uses simple differencing) or if the seasonal periodicity is large.\n", "\n", "The default is `simple_differencing=False`, in which case the integration component is implemented as part of the state space formulation, and all of the original data can be used in estimation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ARIMA Example 4: ARMAX (Friedman)\n", "\n", "This model demonstrates the use of explanatory variables (the X part of ARMAX). When exogenous regressors are included, the SARIMAX module uses the concept of \"regression with SARIMA errors\" (see http://robjhyndman.com/hyndsight/arimax/ for details of regression with ARIMA errors versus alternative specifications), so that the model is specified as:\n", "\n", "$$\n", "y_t = \\beta_t x_t + u_t \\\\\n", " \\phi_p (L) \\tilde \\phi_P (L^s) \\Delta^d \\Delta_s^D u_t = A(t) +\n", " \\theta_q (L) \\tilde \\theta_Q (L^s) \\epsilon_t\n", "$$\n", "\n", "Notice that the first equation is just a linear regression, and the second equation just describes the process followed by the error component as SARIMA (as was described in example 3). One reason for this specification is that the estimated parameters have their natural interpretations.\n", "\n", "This specification nests many simpler specifications. For example, regression with AR(2) errors is:\n", "\n", "$$\n", "y_t = \\beta_t x_t + u_t \\\\\n", "(1 - \\phi_1 L - \\phi_2 L^2) u_t = A(t) + \\epsilon_t\n", "$$\n", "\n", "The model considered in this example is regression with ARMA(1,1) errors. The process is then written:\n", "\n", "$$\n", "\\text{consump}_t = \\beta_0 + \\beta_1 \\text{m2}_t + u_t \\\\\n", "(1 - \\phi_1 L) u_t = (1 - \\theta_1 L) \\epsilon_t\n", "$$\n", "\n", "Notice that $\\beta_0$ is, as described in example 1 above, *not* the same thing as an intercept specified by `trend='c'`. Whereas in the examples above we estimated the intercept of the model via the trend polynomial, here, we demonstrate how to estimate $\\beta_0$ itself by adding a constant to the exogenous dataset. In the output, the $beta_0$ is called `const`, whereas above the intercept $c$ was called `intercept` in the output." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Dataset\n", "friedman2 = requests.get('https://www.stata-press.com/data/r12/friedman2.dta').content\n", "data = pd.read_stata(BytesIO(friedman2))\n", "data.index = data.time\n", "data.index.freq = \"QS-OCT\"\n", "\n", "# Variables\n", "endog = data.loc['1959':'1981', 'consump']\n", "exog = sm.add_constant(data.loc['1959':'1981', 'm2'])\n", "\n", "# Fit the model\n", "mod = sm.tsa.statespace.SARIMAX(endog, exog, order=(1,0,1))\n", "res = mod.fit(disp=False)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ARIMA Postestimation: Example 1 - Dynamic Forecasting\n", "\n", "Here we describe some of the post-estimation capabilities of statsmodels' SARIMAX.\n", "\n", "First, using the model from example, we estimate the parameters using data that *excludes the last few observations* (this is a little artificial as an example, but it allows considering performance of out-of-sample forecasting and facilitates comparison to Stata's documentation)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Dataset\n", "raw = pd.read_stata(BytesIO(friedman2))\n", "raw.index = raw.time\n", "raw.index.freq = \"QS-OCT\"\n", "data = raw.loc[:'1981']\n", "\n", "# Variables\n", "endog = data.loc['1959':, 'consump']\n", "exog = sm.add_constant(data.loc['1959':, 'm2'])\n", "nobs = endog.shape[0]\n", "\n", "# Fit the model\n", "mod = sm.tsa.statespace.SARIMAX(endog.loc[:'1978-01-01'], exog=exog.loc[:'1978-01-01'], order=(1,0,1))\n", "fit_res = mod.fit(disp=False, maxiter=250)\n", "print(fit_res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we want to get results for the full dataset but using the estimated parameters (on a subset of the data)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = sm.tsa.statespace.SARIMAX(endog, exog=exog, order=(1,0,1))\n", "res = mod.filter(fit_res.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `predict` command is first applied here to get in-sample predictions. We use the `full_results=True` argument to allow us to calculate confidence intervals (the default output of `predict` is just the predicted values).\n", "\n", "With no other arguments, `predict` returns the one-step-ahead in-sample predictions for the entire sample." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# In-sample one-step-ahead predictions\n", "predict = res.get_prediction()\n", "predict_ci = predict.conf_int()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also get *dynamic predictions*. One-step-ahead prediction uses the true values of the endogenous values at each step to predict the next in-sample value. Dynamic predictions use one-step-ahead prediction up to some point in the dataset (specified by the `dynamic` argument); after that, the previous *predicted* endogenous values are used in place of the true endogenous values for each new predicted element.\n", "\n", "The `dynamic` argument is specified to be an *offset* relative to the `start` argument. If `start` is not specified, it is assumed to be `0`.\n", "\n", "Here we perform dynamic prediction starting in the first quarter of 1978." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Dynamic predictions\n", "predict_dy = res.get_prediction(dynamic='1978-01-01')\n", "predict_dy_ci = predict_dy.conf_int()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can graph the one-step-ahead and dynamic predictions (and the corresponding confidence intervals) to see their relative performance. Notice that up to the point where dynamic prediction begins (1978:Q1), the two are the same." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Graph\n", "fig, ax = plt.subplots(figsize=(9,4))\n", "npre = 4\n", "ax.set(title='Personal consumption', xlabel='Date', ylabel='Billions of dollars')\n", "\n", "# Plot data points\n", "data.loc['1977-07-01':, 'consump'].plot(ax=ax, style='o', label='Observed')\n", "\n", "# Plot predictions\n", "predict.predicted_mean.loc['1977-07-01':].plot(ax=ax, style='r--', label='One-step-ahead forecast')\n", "ci = predict_ci.loc['1977-07-01':]\n", "ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], color='r', alpha=0.1)\n", "predict_dy.predicted_mean.loc['1977-07-01':].plot(ax=ax, style='g', label='Dynamic forecast (1978)')\n", "ci = predict_dy_ci.loc['1977-07-01':]\n", "ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], color='g', alpha=0.1)\n", "\n", "legend = ax.legend(loc='lower right')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, graph the prediction *error*. It is obvious that, as one would suspect, one-step-ahead prediction is considerably better." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Prediction error\n", "\n", "# Graph\n", "fig, ax = plt.subplots(figsize=(9,4))\n", "npre = 4\n", "ax.set(title='Forecast error', xlabel='Date', ylabel='Forecast - Actual')\n", "\n", "# In-sample one-step-ahead predictions and 95% confidence intervals\n", "predict_error = predict.predicted_mean - endog\n", "predict_error.loc['1977-10-01':].plot(ax=ax, label='One-step-ahead forecast')\n", "ci = predict_ci.loc['1977-10-01':].copy()\n", "ci.iloc[:,0] -= endog.loc['1977-10-01':]\n", "ci.iloc[:,1] -= endog.loc['1977-10-01':]\n", "ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], alpha=0.1)\n", "\n", "# Dynamic predictions and 95% confidence intervals\n", "predict_dy_error = predict_dy.predicted_mean - endog\n", "predict_dy_error.loc['1977-10-01':].plot(ax=ax, style='r', label='Dynamic forecast (1978)')\n", "ci = predict_dy_ci.loc['1977-10-01':].copy()\n", "ci.iloc[:,0] -= endog.loc['1977-10-01':]\n", "ci.iloc[:,1] -= endog.loc['1977-10-01':]\n", "ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], color='r', alpha=0.1)\n", "\n", "legend = ax.legend(loc='lower left');\n", "legend.get_frame().set_facecolor('w')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/statespace_seasonal.ipynb000066400000000000000000000470461400612667500250650ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Seasonality in time series data\n", "\n", "Consider the problem of modeling time series data with multiple seasonal components with different periodicities. Let us take the time series $y_t$ and decompose it explicitly to have a level component and two seasonal components.\n", "\n", "$$\n", "y_t = \\mu_t + \\gamma^{(1)}_t + \\gamma^{(2)}_t\n", "$$\n", "\n", "where $\\mu_t$ represents the trend or level, $\\gamma^{(1)}_t$ represents a seasonal component with a relatively short period, and $\\gamma^{(2)}_t$ represents another seasonal component of longer period. We will have a fixed intercept term for our level and consider both $\\gamma^{(2)}_t$ and $\\gamma^{(2)}_t$ to be stochastic so that the seasonal patterns can vary over time.\n", "\n", "In this notebook, we will generate synthetic data conforming to this model and showcase modeling of the seasonal terms in a few different ways under the unobserved components modeling framework." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "\n", "plt.rc(\"figure\", figsize=(16,8))\n", "plt.rc(\"font\", size=14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Synthetic data creation\n", "\n", "We will create data with multiple seasonal patterns by following equations (3.7) and (3.8) in Durbin and Koopman (2012). We will simulate 300 periods and two seasonal terms parametrized in the frequency domain having periods 10 and 100, respectively, and 3 and 2 number of harmonics, respectively. Further, the variances of their stochastic parts are 4 and 9, respectively." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# First we'll simulate the synthetic data\n", "def simulate_seasonal_term(periodicity, total_cycles, noise_std=1.,\n", " harmonics=None):\n", " duration = periodicity * total_cycles\n", " assert duration == int(duration)\n", " duration = int(duration)\n", " harmonics = harmonics if harmonics else int(np.floor(periodicity / 2))\n", "\n", " lambda_p = 2 * np.pi / float(periodicity)\n", "\n", " gamma_jt = noise_std * np.random.randn((harmonics))\n", " gamma_star_jt = noise_std * np.random.randn((harmonics))\n", "\n", " total_timesteps = 100 * duration # Pad for burn in\n", " series = np.zeros(total_timesteps) \n", " for t in range(total_timesteps):\n", " gamma_jtp1 = np.zeros_like(gamma_jt)\n", " gamma_star_jtp1 = np.zeros_like(gamma_star_jt)\n", " for j in range(1, harmonics + 1):\n", " cos_j = np.cos(lambda_p * j)\n", " sin_j = np.sin(lambda_p * j)\n", " gamma_jtp1[j - 1] = (gamma_jt[j - 1] * cos_j\n", " + gamma_star_jt[j - 1] * sin_j\n", " + noise_std * np.random.randn())\n", " gamma_star_jtp1[j - 1] = (- gamma_jt[j - 1] * sin_j\n", " + gamma_star_jt[j - 1] * cos_j\n", " + noise_std * np.random.randn())\n", " series[t] = np.sum(gamma_jtp1)\n", " gamma_jt = gamma_jtp1\n", " gamma_star_jt = gamma_star_jtp1\n", " wanted_series = series[-duration:] # Discard burn in\n", "\n", " return wanted_series" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "duration = 100 * 3\n", "periodicities = [10, 100]\n", "num_harmonics = [3, 2]\n", "std = np.array([2, 3])\n", "np.random.seed(8678309)\n", "\n", "terms = []\n", "for ix, _ in enumerate(periodicities):\n", " s = simulate_seasonal_term(\n", " periodicities[ix],\n", " duration / periodicities[ix],\n", " harmonics=num_harmonics[ix],\n", " noise_std=std[ix])\n", " terms.append(s)\n", "terms.append(np.ones_like(terms[0]) * 10.)\n", "series = pd.Series(np.sum(terms, axis=0))\n", "df = pd.DataFrame(data={'total': series,\n", " '10(3)': terms[0],\n", " '100(2)': terms[1],\n", " 'level':terms[2]})\n", "h1, = plt.plot(df['total'])\n", "h2, = plt.plot(df['10(3)'])\n", "h3, = plt.plot(df['100(2)'])\n", "h4, = plt.plot(df['level'])\n", "plt.legend(['total','10(3)','100(2)', 'level'])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Unobserved components (frequency domain modeling)\n", "\n", "The next method is an unobserved components model, where the trend is modeled as a fixed intercept and the seasonal components are modeled using trigonometric functions with primary periodicities of 10 and 100, respectively, and number of harmonics 3 and 2, respectively. Note that this is the correct, generating model. The process for the time series can be written as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\mu_t + \\gamma^{(1)}_t + \\gamma^{(2)}_t + \\epsilon_t\\\\\n", "\\mu_{t+1} & = \\mu_t \\\\\n", "\\gamma^{(1)}_{t} &= \\sum_{j=1}^2 \\gamma^{(1)}_{j, t} \\\\\n", "\\gamma^{(2)}_{t} &= \\sum_{j=1}^3 \\gamma^{(2)}_{j, t}\\\\\n", "\\gamma^{(1)}_{j, t+1} &= \\gamma^{(1)}_{j, t}\\cos(\\lambda_j) + \\gamma^{*, (1)}_{j, t}\\sin(\\lambda_j) + \\omega^{(1)}_{j,t}, ~j = 1, 2, 3\\\\\n", "\\gamma^{*, (1)}_{j, t+1} &= -\\gamma^{(1)}_{j, t}\\sin(\\lambda_j) + \\gamma^{*, (1)}_{j, t}\\cos(\\lambda_j) + \\omega^{*, (1)}_{j, t}, ~j = 1, 2, 3\\\\\n", "\\gamma^{(2)}_{j, t+1} &= \\gamma^{(2)}_{j, t}\\cos(\\lambda_j) + \\gamma^{*, (2)}_{j, t}\\sin(\\lambda_j) + \\omega^{(2)}_{j,t}, ~j = 1, 2\\\\\n", "\\gamma^{*, (2)}_{j, t+1} &= -\\gamma^{(2)}_{j, t}\\sin(\\lambda_j) + \\gamma^{*, (2)}_{j, t}\\cos(\\lambda_j) + \\omega^{*, (2)}_{j, t}, ~j = 1, 2\\\\\n", "\\end{align}\n", "$$\n", "\n", "\n", "where $\\epsilon_t$ is white noise, $\\omega^{(1)}_{j,t}$ are i.i.d. $N(0, \\sigma^2_1)$, and $\\omega^{(2)}_{j,t}$ are i.i.d. $N(0, \\sigma^2_2)$, where $\\sigma_1 = 2.$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [], "source": [ "model = sm.tsa.UnobservedComponents(series.values, \n", " level='fixed intercept', \n", " freq_seasonal=[{'period': 10,\n", " 'harmonics': 3},\n", " {'period': 100,\n", " 'harmonics': 2}])\n", "res_f = model.fit(disp=False)\n", "print(res_f.summary())\n", "# The first state variable holds our estimate of the intercept\n", "print(\"fixed intercept estimated as {0:.3f}\".format(res_f.smoother_results.smoothed_state[0,-1:][0]))\n", "\n", "res_f.plot_components()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.ssm.transition[:, :, 0]" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Observe that the fitted variances are pretty close to the true variances of 4 and 9. Further, the individual seasonal components look pretty close to the true seasonal components. The smoothed level term is kind of close to the true level of 10. Finally, our diagnostics look solid; the test statistics are small enough to fail to reject our three tests." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Unobserved components (mixed time and frequency domain modeling)\n", "\n", "The second method is an unobserved components model, where the trend is modeled as a fixed intercept and the seasonal components are modeled using 10 constants summing to 0 and trigonometric functions with a primary periodicities of 100 with 2 harmonics total. Note that this is not the generating model, as it presupposes that there are more state errors for the shorter seasonal component than in reality. The process for the time series can be written as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\mu_t + \\gamma^{(1)}_t + \\gamma^{(2)}_t + \\epsilon_t\\\\\n", "\\mu_{t+1} & = \\mu_t \\\\\n", "\\gamma^{(1)}_{t + 1} &= - \\sum_{j=1}^9 \\gamma^{(1)}_{t + 1 - j} + \\omega^{(1)}_t\\\\\n", "\\gamma^{(2)}_{j, t+1} &= \\gamma^{(2)}_{j, t}\\cos(\\lambda_j) + \\gamma^{*, (2)}_{j, t}\\sin(\\lambda_j) + \\omega^{(2)}_{j,t}, ~j = 1, 2\\\\\n", "\\gamma^{*, (2)}_{j, t+1} &= -\\gamma^{(2)}_{j, t}\\sin(\\lambda_j) + \\gamma^{*, (2)}_{j, t}\\cos(\\lambda_j) + \\omega^{*, (2)}_{j, t}, ~j = 1, 2\\\\\n", "\\end{align}\n", "$$\n", "\n", "where $\\epsilon_t$ is white noise, $\\omega^{(1)}_{t}$ are i.i.d. $N(0, \\sigma^2_1)$, and $\\omega^{(2)}_{j,t}$ are i.i.d. $N(0, \\sigma^2_2)$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model = sm.tsa.UnobservedComponents(series, \n", " level='fixed intercept', \n", " seasonal=10,\n", " freq_seasonal=[{'period': 100,\n", " 'harmonics': 2}])\n", "res_tf = model.fit(disp=False)\n", "print(res_tf.summary())\n", "# The first state variable holds our estimate of the intercept\n", "print(\"fixed intercept estimated as {0:.3f}\".format(res_tf.smoother_results.smoothed_state[0,-1:][0]))\n", "\n", "fig = res_tf.plot_components()\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plotted components look good. However, the estimated variance of the second seasonal term is inflated from reality. Additionally, we reject the Ljung-Box statistic, indicating we may have remaining autocorrelation after accounting for our components." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Unobserved components (lazy frequency domain modeling)\n", "\n", "The third method is an unobserved components model with a fixed intercept and one seasonal component, which is modeled using trigonometric functions with primary periodicity 100 and 50 harmonics. Note that this is not the generating model, as it presupposes that there are more harmonics then in reality. Because the variances are tied together, we are not able to drive the estimated covariance of the non-existent harmonics to 0. What is lazy about this model specification is that we have not bothered to specify the two different seasonal components and instead chosen to model them using a single component with enough harmonics to cover both. We will not be able to capture any differences in variances between the two true components. The process for the time series can be written as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & = \\mu_t + \\gamma^{(1)}_t + \\epsilon_t\\\\\n", "\\mu_{t+1} &= \\mu_t\\\\\n", "\\gamma^{(1)}_{t} &= \\sum_{j=1}^{50}\\gamma^{(1)}_{j, t}\\\\\n", "\\gamma^{(1)}_{j, t+1} &= \\gamma^{(1)}_{j, t}\\cos(\\lambda_j) + \\gamma^{*, (1)}_{j, t}\\sin(\\lambda_j) + \\omega^{(1}_{j,t}, ~j = 1, 2, \\dots, 50\\\\\n", "\\gamma^{*, (1)}_{j, t+1} &= -\\gamma^{(1)}_{j, t}\\sin(\\lambda_j) + \\gamma^{*, (1)}_{j, t}\\cos(\\lambda_j) + \\omega^{*, (1)}_{j, t}, ~j = 1, 2, \\dots, 50\\\\\n", "\\end{align}\n", "$$\n", "\n", "where $\\epsilon_t$ is white noise, $\\omega^{(1)}_{t}$ are i.i.d. $N(0, \\sigma^2_1)$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model = sm.tsa.UnobservedComponents(series, \n", " level='fixed intercept', \n", " freq_seasonal=[{'period': 100}])\n", "res_lf = model.fit(disp=False)\n", "print(res_lf.summary())\n", "# The first state variable holds our estimate of the intercept\n", "print(\"fixed intercept estimated as {0:.3f}\".format(res_lf.smoother_results.smoothed_state[0,-1:][0]))\n", "\n", "fig = res_lf.plot_components()\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that one of our diagnostic tests would be rejected at the .05 level." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Unobserved components (lazy time domain seasonal modeling)\n", "\n", "The fourth method is an unobserved components model with a fixed intercept and a single seasonal component modeled using a time-domain seasonal model of 100 constants. The process for the time series can be written as:\n", "\n", "$$\n", "\\begin{align}\n", "y_t & =\\mu_t + \\gamma^{(1)}_t + \\epsilon_t\\\\\n", "\\mu_{t+1} &= \\mu_{t} \\\\\n", "\\gamma^{(1)}_{t + 1} &= - \\sum_{j=1}^{99} \\gamma^{(1)}_{t + 1 - j} + \\omega^{(1)}_t\\\\\n", "\\end{align}\n", "$$\n", "\n", "where $\\epsilon_t$ is white noise, $\\omega^{(1)}_{t}$ are i.i.d. $N(0, \\sigma^2_1)$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model = sm.tsa.UnobservedComponents(series,\n", " level='fixed intercept',\n", " seasonal=100)\n", "res_lt = model.fit(disp=False)\n", "print(res_lt.summary())\n", "# The first state variable holds our estimate of the intercept\n", "print(\"fixed intercept estimated as {0:.3f}\".format(res_lt.smoother_results.smoothed_state[0,-1:][0]))\n", "\n", "fig = res_lt.plot_components()\n", "fig.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The seasonal component itself looks good--it is the primary signal. The estimated variance of the seasonal term is very high ($>10^5$), leading to a lot of uncertainty in our one-step-ahead predictions and slow responsiveness to new data, as evidenced by large errors in one-step ahead predictions and observations. Finally, all three of our diagnostic tests were rejected. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparison of filtered estimates\n", "\n", "The plots below show that explicitly modeling the individual components results in the filtered state being close to the true state within roughly half a period. The lazy models took longer (almost a full period) to do the same on the combined true state." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Assign better names for our seasonal terms\n", "true_seasonal_10_3 = terms[0]\n", "true_seasonal_100_2 = terms[1]\n", "true_sum = true_seasonal_10_3 + true_seasonal_100_2\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "time_s = np.s_[:50] # After this they basically agree\n", "fig1 = plt.figure()\n", "ax1 = fig1.add_subplot(111)\n", "idx = np.asarray(series.index)\n", "h1, = ax1.plot(idx[time_s], res_f.freq_seasonal[0].filtered[time_s], label='Double Freq. Seas')\n", "h2, = ax1.plot(idx[time_s], res_tf.seasonal.filtered[time_s], label='Mixed Domain Seas')\n", "h3, = ax1.plot(idx[time_s], true_seasonal_10_3[time_s], label='True Seasonal 10(3)')\n", "plt.legend([h1, h2, h3], ['Double Freq. Seasonal','Mixed Domain Seasonal','Truth'], loc=2)\n", "plt.title('Seasonal 10(3) component')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "time_s = np.s_[:50] # After this they basically agree\n", "fig2 = plt.figure()\n", "ax2 = fig2.add_subplot(111)\n", "h21, = ax2.plot(idx[time_s], res_f.freq_seasonal[1].filtered[time_s], label='Double Freq. Seas')\n", "h22, = ax2.plot(idx[time_s], res_tf.freq_seasonal[0].filtered[time_s], label='Mixed Domain Seas')\n", "h23, = ax2.plot(idx[time_s], true_seasonal_100_2[time_s], label='True Seasonal 100(2)')\n", "plt.legend([h21, h22, h23], ['Double Freq. Seasonal','Mixed Domain Seasonal','Truth'], loc=2)\n", "plt.title('Seasonal 100(2) component')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [ "time_s = np.s_[:100]\n", "\n", "fig3 = plt.figure()\n", "ax3 = fig3.add_subplot(111)\n", "h31, = ax3.plot(idx[time_s], res_f.freq_seasonal[1].filtered[time_s] + res_f.freq_seasonal[0].filtered[time_s], label='Double Freq. Seas')\n", "h32, = ax3.plot(idx[time_s], res_tf.freq_seasonal[0].filtered[time_s] + res_tf.seasonal.filtered[time_s], label='Mixed Domain Seas')\n", "h33, = ax3.plot(idx[time_s], true_sum[time_s], label='True Seasonal 100(2)')\n", "h34, = ax3.plot(idx[time_s], res_lf.freq_seasonal[0].filtered[time_s], label='Lazy Freq. Seas')\n", "h35, = ax3.plot(idx[time_s], res_lt.seasonal.filtered[time_s], label='Lazy Time Seas')\n", "\n", "plt.legend([h31, h32, h33, h34, h35], ['Double Freq. Seasonal','Mixed Domain Seasonal','Truth', 'Lazy Freq. Seas', 'Lazy Time Seas'], loc=1)\n", "plt.title('Seasonal components combined')\n", "plt.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Conclusions\n", "\n", "In this notebook, we simulated a time series with two seasonal components of different periods. We modeled them using structural time series models with (a) two frequency domain components of correct periods and numbers of harmonics, (b) time domain seasonal component for the shorter term and a frequency domain term with correct period and number of harmonics, (c) a single frequency domain term with the longer period and full number of harmonics, and (d) a single time domain term with the longer period. We saw a variety of diagnostic results, with only the correct generating model, (a), failing to reject any of the tests. Thus, more flexible seasonal modeling allowing for multiple components with specifiable harmonics can be a useful tool for time series modeling. Finally, we can represent seasonal components with fewer total states in this way, allowing for the user to attempt to make the bias-variance trade-off themselves instead of being forced to choose \"lazy\" models, which use a large number of states and incur additional variance as a result." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/statespace_structural_harvey_jaeger.ipynb000066400000000000000000000446051400612667500303610ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Detrending, Stylized Facts and the Business Cycle\n", "\n", "In an influential article, Harvey and Jaeger (1993) described the use of unobserved components models (also known as \"structural time series models\") to derive stylized facts of the business cycle.\n", "\n", "Their paper begins:\n", "\n", " \"Establishing the 'stylized facts' associated with a set of time series is widely considered a crucial step\n", " in macroeconomic research ... For such facts to be useful they should (1) be consistent with the stochastic\n", " properties of the data and (2) present meaningful information.\"\n", " \n", "In particular, they make the argument that these goals are often better met using the unobserved components approach rather than the popular Hodrick-Prescott filter or Box-Jenkins ARIMA modeling techniques.\n", "\n", "statsmodels has the ability to perform all three types of analysis, and below we follow the steps of their paper, using a slightly updated dataset." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "\n", "from IPython.display import display, Latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Unobserved Components\n", "\n", "The unobserved components model available in statsmodels can be written as:\n", "\n", "$$\n", "y_t = \\underbrace{\\mu_{t}}_{\\text{trend}} + \\underbrace{\\gamma_{t}}_{\\text{seasonal}} + \\underbrace{c_{t}}_{\\text{cycle}} + \\sum_{j=1}^k \\underbrace{\\beta_j x_{jt}}_{\\text{explanatory}} + \\underbrace{\\varepsilon_t}_{\\text{irregular}}\n", "$$\n", "\n", "see Durbin and Koopman 2012, Chapter 3 for notation and additional details. Notice that different specifications for the different individual components can support a wide range of models. The specific models considered in the paper and below are specializations of this general equation.\n", "\n", "### Trend\n", "\n", "The trend component is a dynamic extension of a regression model that includes an intercept and linear time-trend.\n", "\n", "$$\n", "\\begin{align}\n", "\\underbrace{\\mu_{t+1}}_{\\text{level}} & = \\mu_t + \\nu_t + \\eta_{t+1} \\qquad & \\eta_{t+1} \\sim N(0, \\sigma_\\eta^2) \\\\\\\\\n", "\\underbrace{\\nu_{t+1}}_{\\text{trend}} & = \\nu_t + \\zeta_{t+1} & \\zeta_{t+1} \\sim N(0, \\sigma_\\zeta^2) \\\\\n", "\\end{align}\n", "$$\n", "\n", "where the level is a generalization of the intercept term that can dynamically vary across time, and the trend is a generalization of the time-trend such that the slope can dynamically vary across time.\n", "\n", "For both elements (level and trend), we can consider models in which:\n", "\n", "- The element is included vs excluded (if the trend is included, there must also be a level included).\n", "- The element is deterministic vs stochastic (i.e. whether or not the variance on the error term is confined to be zero or not)\n", "\n", "The only additional parameters to be estimated via MLE are the variances of any included stochastic components.\n", "\n", "This leads to the following specifications:\n", "\n", "| | Level | Trend | Stochastic Level | Stochastic Trend |\n", "|----------------------------------------------------------------------|-------|-------|------------------|------------------|\n", "| Constant | ✓ | | | |\n", "| Local Level
(random walk) | ✓ | | ✓ | |\n", "| Deterministic trend | ✓ | ✓ | | |\n", "| Local level with deterministic trend
(random walk with drift) | ✓ | ✓ | ✓ | |\n", "| Local linear trend | ✓ | ✓ | ✓ | ✓ |\n", "| Smooth trend
(integrated random walk) | ✓ | ✓ | | ✓ |\n", "\n", "### Seasonal\n", "\n", "The seasonal component is written as:\n", "\n", "$$\n", "\\gamma_t = - \\sum_{j=1}^{s-1} \\gamma_{t+1-j} + \\omega_t \\qquad \\omega_t \\sim N(0, \\sigma_\\omega^2)\n", "$$\n", "\n", "The periodicity (number of seasons) is `s`, and the defining character is that (without the error term), the seasonal components sum to zero across one complete cycle. The inclusion of an error term allows the seasonal effects to vary over time.\n", "\n", "The variants of this model are:\n", "\n", "- The periodicity `s`\n", "- Whether or not to make the seasonal effects stochastic.\n", "\n", "If the seasonal effect is stochastic, then there is one additional parameter to estimate via MLE (the variance of the error term).\n", "\n", "### Cycle\n", "\n", "The cyclical component is intended to capture cyclical effects at time frames much longer than captured by the seasonal component. For example, in economics the cyclical term is often intended to capture the business cycle, and is then expected to have a period between \"1.5 and 12 years\" (see Durbin and Koopman).\n", "\n", "The cycle is written as:\n", "\n", "$$\n", "\\begin{align}\n", "c_{t+1} & = c_t \\cos \\lambda_c + c_t^* \\sin \\lambda_c + \\tilde \\omega_t \\qquad & \\tilde \\omega_t \\sim N(0, \\sigma_{\\tilde \\omega}^2) \\\\\\\\\n", "c_{t+1}^* & = -c_t \\sin \\lambda_c + c_t^* \\cos \\lambda_c + \\tilde \\omega_t^* & \\tilde \\omega_t^* \\sim N(0, \\sigma_{\\tilde \\omega}^2)\n", "\\end{align}\n", "$$\n", "\n", "The parameter $\\lambda_c$ (the frequency of the cycle) is an additional parameter to be estimated by MLE. If the seasonal effect is stochastic, then there is one another parameter to estimate (the variance of the error term - note that both of the error terms here share the same variance, but are assumed to have independent draws).\n", "\n", "### Irregular\n", "\n", "The irregular component is assumed to be a white noise error term. Its variance is a parameter to be estimated by MLE; i.e.\n", "\n", "$$\n", "\\varepsilon_t \\sim N(0, \\sigma_\\varepsilon^2)\n", "$$\n", "\n", "In some cases, we may want to generalize the irregular component to allow for autoregressive effects:\n", "\n", "$$\n", "\\varepsilon_t = \\rho(L) \\varepsilon_{t-1} + \\epsilon_t, \\qquad \\epsilon_t \\sim N(0, \\sigma_\\epsilon^2)\n", "$$\n", "\n", "In this case, the autoregressive parameters would also be estimated via MLE.\n", "\n", "### Regression effects\n", "\n", "We may want to allow for explanatory variables by including additional terms\n", "\n", "$$\n", "\\sum_{j=1}^k \\beta_j x_{jt}\n", "$$\n", "\n", "or for intervention effects by including\n", "\n", "$$\n", "\\begin{align}\n", "\\delta w_t \\qquad \\text{where} \\qquad w_t & = 0, \\qquad t < \\tau, \\\\\\\\\n", "& = 1, \\qquad t \\ge \\tau\n", "\\end{align}\n", "$$\n", "\n", "These additional parameters could be estimated via MLE or by including them as components of the state space formulation.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data\n", "\n", "Following Harvey and Jaeger, we will consider the following time series:\n", "\n", "- US real GNP, \"output\", ([GNPC96](https://research.stlouisfed.org/fred2/series/GNPC96))\n", "- US GNP implicit price deflator, \"prices\", ([GNPDEF](https://research.stlouisfed.org/fred2/series/GNPDEF))\n", "- US monetary base, \"money\", ([AMBSL](https://research.stlouisfed.org/fred2/series/AMBSL))\n", "\n", "The time frame in the original paper varied across series, but was broadly 1954-1989. Below we use data from the period 1948-2008 for all series. Although the unobserved components approach allows isolating a seasonal component within the model, the series considered in the paper, and here, are already seasonally adjusted.\n", "\n", "All data series considered here are taken from [Federal Reserve Economic Data (FRED)](https://research.stlouisfed.org/fred2/). Conveniently, the Python library [Pandas](https://pandas.pydata.org/) has the ability to download data from FRED directly." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Datasets\n", "from pandas_datareader.data import DataReader\n", "\n", "# Get the raw data\n", "start = '1948-01'\n", "end = '2008-01'\n", "us_gnp = DataReader('GNPC96', 'fred', start=start, end=end)\n", "us_gnp_deflator = DataReader('GNPDEF', 'fred', start=start, end=end)\n", "us_monetary_base = DataReader('AMBSL', 'fred', start=start, end=end).resample('QS').mean()\n", "recessions = DataReader('USRECQ', 'fred', start=start, end=end).resample('QS').last().values[:,0]\n", "\n", "# Construct the dataframe\n", "dta = pd.concat(map(np.log, (us_gnp, us_gnp_deflator, us_monetary_base)), axis=1)\n", "dta.columns = ['US GNP','US Prices','US monetary base']\n", "dta.index.freq = dta.index.inferred_freq\n", "dates = dta.index._mpl_repr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get a sense of these three variables over the timeframe, we can plot them:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Plot the data\n", "ax = dta.plot(figsize=(13,3))\n", "ylim = ax.get_ylim()\n", "ax.xaxis.grid()\n", "ax.fill_between(dates, ylim[0]+1e-5, ylim[1]-1e-5, recessions, facecolor='k', alpha=0.1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model\n", "\n", "Since the data is already seasonally adjusted and there are no obvious explanatory variables, the generic model considered is:\n", "\n", "$$\n", "y_t = \\underbrace{\\mu_{t}}_{\\text{trend}} + \\underbrace{c_{t}}_{\\text{cycle}} + \\underbrace{\\varepsilon_t}_{\\text{irregular}}\n", "$$\n", "\n", "The irregular will be assumed to be white noise, and the cycle will be stochastic and damped. The final modeling choice is the specification to use for the trend component. Harvey and Jaeger consider two models:\n", "\n", "1. Local linear trend (the \"unrestricted\" model)\n", "2. Smooth trend (the \"restricted\" model, since we are forcing $\\sigma_\\eta = 0$)\n", "\n", "Below, we construct `kwargs` dictionaries for each of these model types. Notice that rather that there are two ways to specify the models. One way is to specify components directly, as in the table above. The other way is to use string names which map to various specifications." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Model specifications\n", "\n", "# Unrestricted model, using string specification\n", "unrestricted_model = {\n", " 'level': 'local linear trend', 'cycle': True, 'damped_cycle': True, 'stochastic_cycle': True\n", "}\n", "\n", "# Unrestricted model, setting components directly\n", "# This is an equivalent, but less convenient, way to specify a\n", "# local linear trend model with a stochastic damped cycle:\n", "# unrestricted_model = {\n", "# 'irregular': True, 'level': True, 'stochastic_level': True, 'trend': True, 'stochastic_trend': True,\n", "# 'cycle': True, 'damped_cycle': True, 'stochastic_cycle': True\n", "# }\n", "\n", "# The restricted model forces a smooth trend\n", "restricted_model = {\n", " 'level': 'smooth trend', 'cycle': True, 'damped_cycle': True, 'stochastic_cycle': True\n", "}\n", "\n", "# Restricted model, setting components directly\n", "# This is an equivalent, but less convenient, way to specify a\n", "# smooth trend model with a stochastic damped cycle. Notice\n", "# that the difference from the local linear trend model is that\n", "# `stochastic_level=False` here.\n", "# unrestricted_model = {\n", "# 'irregular': True, 'level': True, 'stochastic_level': False, 'trend': True, 'stochastic_trend': True,\n", "# 'cycle': True, 'damped_cycle': True, 'stochastic_cycle': True\n", "# }" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now fit the following models:\n", "\n", "1. Output, unrestricted model\n", "2. Prices, unrestricted model\n", "3. Prices, restricted model\n", "4. Money, unrestricted model\n", "5. Money, restricted model" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Output\n", "output_mod = sm.tsa.UnobservedComponents(dta['US GNP'], **unrestricted_model)\n", "output_res = output_mod.fit(method='powell', disp=False)\n", "\n", "# Prices\n", "prices_mod = sm.tsa.UnobservedComponents(dta['US Prices'], **unrestricted_model)\n", "prices_res = prices_mod.fit(method='powell', disp=False)\n", "\n", "prices_restricted_mod = sm.tsa.UnobservedComponents(dta['US Prices'], **restricted_model)\n", "prices_restricted_res = prices_restricted_mod.fit(method='powell', disp=False)\n", "\n", "# Money\n", "money_mod = sm.tsa.UnobservedComponents(dta['US monetary base'], **unrestricted_model)\n", "money_res = money_mod.fit(method='powell', disp=False)\n", "\n", "money_restricted_mod = sm.tsa.UnobservedComponents(dta['US monetary base'], **restricted_model)\n", "money_restricted_res = money_restricted_mod.fit(method='powell', disp=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once we have fit these models, there are a variety of ways to display the information. Looking at the model of US GNP, we can summarize the fit of the model using the `summary` method on the fit object." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "print(output_res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For unobserved components models, and in particular when exploring stylized facts in line with point (2) from the introduction, it is often more instructive to plot the estimated unobserved components (e.g. the level, trend, and cycle) themselves to see if they provide a meaningful description of the data.\n", "\n", "The `plot_components` method of the fit object can be used to show plots and confidence intervals of each of the estimated states, as well as a plot of the observed data versus the one-step-ahead predictions of the model to assess fit." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fig = output_res.plot_components(legend_loc='lower right', figsize=(15, 9));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, Harvey and Jaeger summarize the models in another way to highlight the relative importances of the trend and cyclical components; below we replicate their Table I. The values we find are broadly consistent with, but different in the particulars from, the values from their table." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Create Table I\n", "table_i = np.zeros((5,6))\n", "\n", "start = dta.index[0]\n", "end = dta.index[-1]\n", "time_range = '%d:%d-%d:%d' % (start.year, start.quarter, end.year, end.quarter)\n", "models = [\n", " ('US GNP', time_range, 'None'),\n", " ('US Prices', time_range, 'None'),\n", " ('US Prices', time_range, r'$\\sigma_\\eta^2 = 0$'),\n", " ('US monetary base', time_range, 'None'),\n", " ('US monetary base', time_range, r'$\\sigma_\\eta^2 = 0$'),\n", "]\n", "index = pd.MultiIndex.from_tuples(models, names=['Series', 'Time range', 'Restrictions'])\n", "parameter_symbols = [\n", " r'$\\sigma_\\zeta^2$', r'$\\sigma_\\eta^2$', r'$\\sigma_\\kappa^2$', r'$\\rho$',\n", " r'$2 \\pi / \\lambda_c$', r'$\\sigma_\\varepsilon^2$',\n", "]\n", "\n", "i = 0\n", "for res in (output_res, prices_res, prices_restricted_res, money_res, money_restricted_res):\n", " if res.model.stochastic_level:\n", " (sigma_irregular, sigma_level, sigma_trend,\n", " sigma_cycle, frequency_cycle, damping_cycle) = res.params\n", " else:\n", " (sigma_irregular, sigma_level,\n", " sigma_cycle, frequency_cycle, damping_cycle) = res.params\n", " sigma_trend = np.nan\n", " period_cycle = 2 * np.pi / frequency_cycle\n", " \n", " table_i[i, :] = [\n", " sigma_level*1e7, sigma_trend*1e7,\n", " sigma_cycle*1e7, damping_cycle, period_cycle,\n", " sigma_irregular*1e7\n", " ]\n", " i += 1\n", " \n", "pd.set_option('float_format', lambda x: '%.4g' % np.round(x, 2) if not np.isnan(x) else '-')\n", "table_i = pd.DataFrame(table_i, index=index, columns=parameter_symbols)\n", "table_i" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }statsmodels-0.12.2/examples/notebooks/statespace_tvpvar_mcmc_cfa.ipynb000066400000000000000000001067751400612667500264170ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## TVP-VAR, MCMC, and sparse simulation smoothing" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "from importlib import reload\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "\n", "from scipy.stats import invwishart, invgamma\n", "\n", "# Get the macro dataset\n", "dta = sm.datasets.macrodata.load_pandas().data\n", "dta.index = pd.date_range('1959Q1', '2009Q3', freq='QS')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Background\n", "\n", "Bayesian analysis of linear Gaussian state space models via Markov chain Monte Carlo (MCMC) methods has become both commonplace and relatively straightforward in recent years, due especially to advances in sampling from the joint posterior of the unobserved state vector conditional on the data and model parameters (see especially Carter and Kohn (1994), de Jong and Shephard (1995), and Durbin and Koopman (2002)). This is particularly useful for Gibbs sampling MCMC approaches.\n", "\n", "While these procedures make use of the forward/backward application of the recursive Kalman filter and smoother, another recent line of research takes a different approach and constructs the posterior joint distribution of the entire vector of states at once - see in particular Chan and Jeliazkov (2009) for an econometric time series treatment and McCausland et al. (2011) for a more general survey. In particular, the posterior mean and precision matrix are constructed explicitly, with the latter a sparse band matrix. Advantage is then taken of efficient algorithms for Cholesky factorization of sparse band matrices; this reduces memory costs and can improve performance. Following McCausland et al. (2011), we refer to this method as the \"Cholesky Factor Algorithm\" (CFA) approach.\n", "\n", "The CFA-based simulation smoother has some advantages and some drawbacks compared to that based on the more typical Kalman filter and smoother (KFS).\n", "\n", "**Advantages of CFA**:\n", "\n", "- Derivation of the joint posterior distribution is relatively straightforward and easy to understand.\n", "- In some cases can be both faster and less memory-intensive than the KFS approach\n", " - In the Appendix at the end of this notebook, we briefly discuss the performance of the two simulation smoothers for the TVP-VAR model. In summary: simple tests on a single machine suggest that for the TVP-VAR model, the CFA and KFS implementations in Statsmodels have about the same runtimes, while both implementations are about twice as fast as the replication code, written in Matlab, provided by Chan and Jeliazkov (2009).\n", "\n", "**Drawbacks of CFA**:\n", "\n", "The main drawback is that this method has not (at least so far) reached the generality of the KFS approach. For example:\n", "\n", "- It can not be used with models that have reduced-rank error terms in the observation or state equations.\n", " - One implication of this is that the typical state space model trick of including identities in the state equation to accommodate, for example, higher-order lags in autoregressive models is not applicable. These models can still be handled by the CFA approach, but at the cost of requiring a slightly different implementation for each lag that is included.\n", " - As an example, standard ways of representing ARMA and VARMA processes in state space form do include identities in the observation and/or state equations, and so the basic formulas presented in Chan and Jeliazkov (2009) do not apply immediately to these models.\n", "- Less flexibility is available in the state initialization / prior." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementation in Statsmodels\n", "\n", "A CFA simulation smoother along the lines of the basic formulas presented in Chan and Jeliazkov (2009) has been implemented in Statsmodels.\n", "\n", "**Notes**:\n", "\n", "- Therefore, the CFA simulation smoother in Statsmodels so-far only supports the case that the state transition is truly a first-order Markov process (i.e. it does not support a p-th order Markov process that has been stacked using identities into a first-order process).\n", "- By contrast, the KFS smoother in Statsmodels is fully general any can be used for any state space model, including those with stacked p-th order Markov processes or other identities in the observation and state equations.\n", "\n", "Either a KFS or the CFA simulation smoothers can be constructed from a state space model using the `simulation_smoother` method. To show the basic idea, we first consider a simple example." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Local level model\n", "\n", "A local level model decomposes an observed series $y_t$ into a persistent trend $\\mu_t$ and a transitory error component\n", "\n", "$$\n", "\\begin{aligned}\n", "y_t & = \\mu_t + \\varepsilon_t, \\qquad \\varepsilon_t \\sim N(0, \\sigma_\\text{irregular}^2) \\\\\n", "\\mu_t & = \\mu_{t-1} + \\eta_t, \\quad ~ \\eta_t \\sim N(0, \\sigma_\\text{level}^2)\n", "\\end{aligned}\n", "$$\n", "\n", "This model satisfies the requirements of the CFA simulation smoother because both the observation error term $\\varepsilon_t$ and the state innovation term $\\eta_t$ are non-degenerate - that is, their covariance matrices are full rank.\n", "\n", "We apply this model to inflation, and consider simulating draws from the posterior of the joint state vector. That is, we are interested in sampling from\n", "\n", "$$p(\\mu^t \\mid y^t, \\sigma_\\text{irregular}^2, \\sigma_\\text{level}^2)$$\n", "\n", "where we define $\\mu^t \\equiv (\\mu_1, \\dots, \\mu_T)'$ and $y^t \\equiv (y_1, \\dots, y_T)'$.\n", "\n", "In Statsmodels, the local level model falls into the more general class of \"unobserved components\" models, and can be constructed as follows:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Construct a local level model for inflation\n", "mod = sm.tsa.UnobservedComponents(dta.infl, 'llevel')\n", "\n", "# Fit the model's parameters (sigma2_varepsilon and sigma2_eta)\n", "# via maximum likelihood\n", "res = mod.fit()\n", "print(res.params)\n", "\n", "# Create simulation smoother objects\n", "sim_kfs = mod.simulation_smoother() # default method is KFS\n", "sim_cfa = mod.simulation_smoother(method='cfa') # can specify CFA method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The simulation smoother objects `sim_kfs` and `sim_cfa` have `simulate` methods that perform simulation smoothing. Each time that `simulate` is called, the `simulated_state` attribute will be re-populated with a new simulated draw from the posterior.\n", "\n", "Below, we construct 20 simulated paths for the trend, using the KFS and CFA approaches, where the simulation is at the maximum likelihood parameter estimates." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "nsimulations = 20\n", "simulated_state_kfs = pd.DataFrame(\n", " np.zeros((mod.nobs, nsimulations)), index=dta.index)\n", "simulated_state_cfa = pd.DataFrame(\n", " np.zeros((mod.nobs, nsimulations)), index=dta.index)\n", "\n", "for i in range(nsimulations):\n", " # Apply KFS simulation smoothing\n", " sim_kfs.simulate()\n", " # Save the KFS simulated state\n", " simulated_state_kfs.iloc[:, i] = sim_kfs.simulated_state[0]\n", "\n", " # Apply CFA simulation smoothing\n", " sim_cfa.simulate()\n", " # Save the CFA simulated state\n", " simulated_state_cfa.iloc[:, i] = sim_cfa.simulated_state[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the observed data and the simulations created using each method below, it is not too hard to see that these two methods are doing the same thing." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Plot the inflation data along with simulated trends\n", "fig, axes = plt.subplots(2, figsize=(15, 6))\n", "\n", "# Plot data and KFS simulations\n", "dta.infl.plot(ax=axes[0], color='k')\n", "axes[0].set_title('Simulations based on KFS approach, MLE parameters')\n", "simulated_state_kfs.plot(ax=axes[0], color='C0', alpha=0.25, legend=False)\n", "\n", "# Plot data and CFA simulations\n", "dta.infl.plot(ax=axes[1], color='k')\n", "axes[1].set_title('Simulations based on CFA approach, MLE parameters')\n", "simulated_state_cfa.plot(ax=axes[1], color='C0', alpha=0.25, legend=False)\n", "\n", "# Add a legend, clean up layout\n", "handles, labels = axes[0].get_legend_handles_labels()\n", "axes[0].legend(handles[:2], ['Data', 'Simulated state'])\n", "fig.tight_layout();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Updating the model's parameters\n", "\n", "The simulation smoothers are tied to the model instance, here the variable `mod`. Whenever the model instance is updated with new parameters, the simulation smoothers will take those new parameters into account in future calls to the `simulate` method.\n", "\n", "This is convenient for MCMC algorithms, which repeatedly (a) update the model's parameters, (b) draw a sample of the state vector, and then (c) draw new values for the model's parameters.\n", "\n", "Here we will change the model to a different parameterization that yields a smoother trend, and show how the simulated values change (for brevity we only show the simulations from the KFS approach, but simulations from the CFA approach would be the same)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(15, 3))\n", "\n", "# Update the model's parameterization to one that attributes more\n", "# variation in inflation to the observation error and so has less\n", "# variation in the trend component\n", "mod.update([4, 0.05])\n", "\n", "# Plot simulations\n", "for i in range(nsimulations):\n", " sim_kfs.simulate()\n", " ax.plot(dta.index, sim_kfs.simulated_state[0],\n", " color='C0', alpha=0.25, label='Simulated state')\n", "\n", "# Plot data\n", "dta.infl.plot(ax=ax, color='k', label='Data', zorder=-1)\n", " \n", "# Add title, legend, clean up layout\n", "ax.set_title('Simulations with alternative parameterization yielding a smoother trend')\n", "handles, labels = ax.get_legend_handles_labels()\n", "ax.legend(handles[-2:], labels[-2:])\n", "fig.tight_layout();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Application: Bayesian analysis of a TVP-VAR model by MCMC\n", "\n", "One of the applications that Chan and Jeliazkov (2009) consider is the time-varying parameters vector autoregression (TVP-VAR) model, estimated with Bayesian Gibb sampling (MCMC) methods. They apply this to model the co-movements in four macroeconomic time series:\n", "\n", "- Real GDP growth\n", "- Inflation\n", "- Unemployment rate\n", "- Short-term interest rates\n", "\n", "We will replicate their example, using a very similar dataset that is included in Statsmodels." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Subset to the four variables of interest\n", "y = dta[['realgdp', 'cpi', 'unemp', 'tbilrate']].copy()\n", "y.columns = ['gdp', 'inf', 'unemp', 'int']\n", "\n", "# Convert to real GDP growth and CPI inflation rates\n", "y[['gdp', 'inf']] = np.log(y[['gdp', 'inf']]).diff() * 100\n", "y = y.iloc[1:]\n", "\n", "fig, ax = plt.subplots(figsize=(15, 5))\n", "y.plot(ax=ax)\n", "ax.set_title('Evolution of macroeconomic variables included in TVP-VAR exercise');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### TVP-VAR model\n", "\n", "**Note**: this section is based on Chan and Jeliazkov (2009) section 3.1, which can be consulted for additional details.\n", "\n", "The usual (time-invariant) VAR(1) model is typically written:\n", "\n", "$$\n", "\\begin{aligned}\n", "y_t & = \\mu + \\Phi y_{t-1} + \\varepsilon_t, \\qquad \\varepsilon_t \\sim N(0, H)\n", "\\end{aligned}\n", "$$\n", "\n", "where $y_t$ is a $p \\times 1$ vector of variables observed at time $t$ and $H$ is a covariance matrix.\n", "\n", "The TVP-VAR(1) model generalizes this to allow the coefficients to vary over time according. Stacking all the parameters into a vector according to $\\alpha_t = \\text{vec}([\\mu_t : \\Phi_t])$, where $\\text{vec}$ denotes the operation that stacks columns of a matrix into a vector, we model their evolution over time according to:\n", "\n", "$$\\alpha_{i,t+1} = \\alpha_{i, t} + \\eta_{i,t}, \\qquad \\eta_{i, t} \\sim N(0, \\sigma_i^2)$$\n", "\n", "In other words, each parameter evolves independently according to a random walk.\n", "\n", "Note that there are $p$ coefficients in $\\mu_t$ and $p^2$ coefficients in $\\Phi_t$, so the full state vector $\\alpha$ is shaped $p * (p + 1) \\times 1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Putting the TVP-VAR(1) model into state-space form is relatively straightforward, and in fact we just have to re-write the observation equation into SUR form:\n", "\n", "$$\n", "\\begin{aligned}\n", "y_t & = Z_t \\alpha_t + \\varepsilon_t, \\qquad \\varepsilon_t \\sim N(0, H) \\\\\n", "\\alpha_{t+1} & = \\alpha_t + \\eta_t, \\qquad \\eta_t \\sim N(0, \\text{diag}(\\{\\sigma_i^2\\}))\n", "\\end{aligned}\n", "$$\n", "\n", "where\n", "\n", "$$\n", "Z_t = \\begin{bmatrix}\n", "1 & y_{t-1}' & 0 & \\dots & & 0 \\\\\n", "0 & 0 & 1 & y_{t-1}' & & 0 \\\\\n", "\\vdots & & & \\ddots & \\ddots & \\vdots \\\\\n", "0 & 0 & 0 & 0 & 1 & y_{t-1}' \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "As long as $H$ is full rank and each of the variances $\\sigma_i^2$ is non-zero, the model satisfies the requirements of the CFA simulation smoother.\n", "\n", "We also need to specify the initialization / prior for the initial state, $\\alpha_1$. Here we will follow Chan and Jeliazkov (2009) in using $\\alpha_1 \\sim N(0, 5 I)$, although we could also model it as diffuse." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Aside from the time-varying coefficients $\\alpha_t$, the other parameters that we will need to estimate are terms in the covariance matrix $H$ and the random walk variances $\\sigma_i^2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### TVP-VAR model in Statsmodels\n", "\n", "Constructing this model programatically in Statsmodels is also relatively straightforward, since there are basically four steps:\n", "\n", "1. Create a new `TVPVAR` class as a subclass of `sm.tsa.statespace.MLEModel`\n", "2. Fill in the fixed values of the state space system matrices\n", "3. Specify the initialization of $\\alpha_1$\n", "4. Create a method for updating the state space system matrices with new values of the covariance matrix $H$ and the random walk variances $\\sigma_i^2$.\n", "\n", "To do this, first note that the general state space representation used by Statsmodels is:\n", "\n", "$$\n", "\\begin{aligned}\n", "y_t & = d_t + Z_t \\alpha_t + \\varepsilon_t, \\qquad \\varepsilon_t \\sim N(0, H_t) \\\\\n", "\\alpha_{t+1} & = c_t + T_t \\alpha_t + R_t \\eta_t, \\qquad \\eta_t \\sim N(0, Q_t) \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "Then the TVP-VAR(1) model implies the following specializations:\n", "\n", "- The intercept terms are zero, i.e. $c_t = d_t = 0$\n", "- The design matrix $Z_t$ is time-varying but its values are fixed as described above (i.e. its values contain ones and lags of $y_t$)\n", "- The observation covariance matrix is not time-varying, i.e. $H_t = H_{t+1} = H$\n", "- The transition matrix is not time-varying and is equal to the identity matrix, i.e. $T_t = T_{t+1} = I$\n", "- The selection matrix $R_t$ is not time-varying and is also equal to the identity matrix, i.e. $R_t = R_{t+1} = I$\n", "- The state covariance matrix $Q_t$ is not time-varying and is diagonal, i.e. $Q_t = Q_{t+1} = \\text{diag}(\\{\\sigma_i^2\\})$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# 1. Create a new TVPVAR class as a subclass of sm.tsa.statespace.MLEModel\n", "class TVPVAR(sm.tsa.statespace.MLEModel):\n", " # Steps 2-3 are best done in the class \"constructor\", i.e. the __init__ method\n", " def __init__(self, y):\n", " # Create a matrix with [y_t' : y_{t-1}'] for t = 2, ..., T\n", " augmented = sm.tsa.lagmat(y, 1, trim='both', original='in', use_pandas=True)\n", " # Separate into y_t and z_t = [1 : y_{t-1}']\n", " p = y.shape[1]\n", " y_t = augmented.iloc[:, :p]\n", " z_t = sm.add_constant(augmented.iloc[:, p:])\n", "\n", " # Recall that the length of the state vector is p * (p + 1)\n", " k_states = p * (p + 1)\n", " super().__init__(y_t, exog=z_t, k_states=k_states)\n", "\n", " # Note that the state space system matrices default to contain zeros,\n", " # so we don't need to explicitly set c_t = d_t = 0.\n", "\n", " # Construct the design matrix Z_t\n", " # Notes:\n", " # -> self.k_endog = p is the dimension of the observed vector\n", " # -> self.k_states = p * (p + 1) is the dimension of the observed vector\n", " # -> self.nobs = T is the number of observations in y_t\n", " self['design'] = np.zeros((self.k_endog, self.k_states, self.nobs))\n", " for i in range(self.k_endog):\n", " start = i * (self.k_endog + 1)\n", " end = start + self.k_endog + 1\n", " self['design', i, start:end, :] = z_t.T\n", "\n", " # Construct the transition matrix T = I\n", " self['transition'] = np.eye(k_states)\n", "\n", " # Construct the selection matrix R = I\n", " self['selection'] = np.eye(k_states)\n", "\n", " # Step 3: Initialize the state vector as alpha_1 ~ N(0, 5I)\n", " self.ssm.initialize('known', stationary_cov=5 * np.eye(self.k_states))\n", "\n", " # Step 4. Create a method that we can call to update H and Q\n", " def update_variances(self, obs_cov, state_cov_diag):\n", " self['obs_cov'] = obs_cov\n", " self['state_cov'] = np.diag(state_cov_diag)\n", "\n", " # Finally, it can be convenient to define human-readable names for\n", " # each element of the state vector. These will be available in output\n", " @property\n", " def state_names(self):\n", " state_names = np.empty((self.k_endog, self.k_endog + 1), dtype=object)\n", " for i in range(self.k_endog):\n", " endog_name = self.endog_names[i]\n", " state_names[i] = (\n", " ['intercept.%s' % endog_name] +\n", " ['L1.%s->%s' % (other_name, endog_name) for other_name in self.endog_names])\n", " return state_names.ravel().tolist()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above class defined the state space model for any given dataset. Now we need to create a specific instance of it with the dataset that we created earlier containing real GDP growth, inflation, unemployment, and interest rates." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create an instance of our TVPVAR class with our observed dataset y\n", "mod = TVPVAR(y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Preliminary investigation with ad-hoc parameters in H, Q" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In our analysis below, we will need to begin our MCMC iterations with some initial parameterization. Following Chan and Jeliazkov (2009) we will set $H$ to be the sample covariance matrix of our dataset, and we will set $\\sigma_i^2 = 0.01$ for each $i$.\n", "\n", "Before discussing the MCMC scheme that will allow us to make inferences about the model, first we can consider the output of the model when simply plugging in these initial parameters. To fill in these parameters, we use the `update_variances` method that we defined earlier and then perform Kalman filtering and smoothing conditional on those parameters.\n", "\n", "**Warning: This exercise is just by way of explanation - we must wait for the output of the MCMC exercise to study the actual implications of the model in a meaningful way**. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "initial_obs_cov = np.cov(y.T)\n", "initial_state_cov_diag = [0.01] * mod.k_states\n", "\n", "# Update H and Q\n", "mod.update_variances(initial_obs_cov, initial_state_cov_diag)\n", "\n", "# Perform Kalman filtering and smoothing\n", "# (the [] is just an empty list that in some models might contain\n", "# additional parameters. Here, we don't have any additional parameters\n", "# so we just pass an empty list)\n", "initial_res = mod.smooth([])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `initial_res` variable contains the output of Kalman filtering and smoothing, conditional on those initial parameters. In particular, we may be interested in the \"smoothed states\", which are $E[\\alpha_t \\mid y^t, H, \\{\\sigma_i^2\\}]$.\n", "\n", "First, lets create a function that graphs the coefficients over time, separated into the equations for equation of the observed variables." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def plot_coefficients_by_equation(states):\n", " fig, axes = plt.subplots(2, 2, figsize=(15, 8))\n", "\n", " # The way we defined Z_t implies that the first 5 elements of the\n", " # state vector correspond to the first variable in y_t, which is GDP growth\n", " ax = axes[0, 0]\n", " states.iloc[:, :5].plot(ax=ax)\n", " ax.set_title('GDP growth')\n", " ax.legend()\n", "\n", " # The next 5 elements correspond to inflation\n", " ax = axes[0, 1]\n", " states.iloc[:, 5:10].plot(ax=ax)\n", " ax.set_title('Inflation rate')\n", " ax.legend();\n", "\n", " # The next 5 elements correspond to unemployment\n", " ax = axes[1, 0]\n", " states.iloc[:, 10:15].plot(ax=ax)\n", " ax.set_title('Unemployment equation')\n", " ax.legend()\n", "\n", " # The last 5 elements correspond to the interest rate\n", " ax = axes[1, 1]\n", " states.iloc[:, 15:20].plot(ax=ax)\n", " ax.set_title('Interest rate equation')\n", " ax.legend();\n", " \n", " return ax\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we are interested in the smoothed states, which are available in the `states.smoothed` attribute out our results object `initial_res`.\n", "\n", "As the graph below shows, the initial parameterization implies substantial time-variation in some of the coefficients." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Here, for illustration purposes only, we plot the time-varying\n", "# coefficients conditional on an ad-hoc parameterization\n", "\n", "# Recall that `initial_res` contains the Kalman filtering and smoothing,\n", "# and the `states.smoothed` attribute contains the smoothed states\n", "plot_coefficients_by_equation(initial_res.states.smoothed);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Bayesian estimation via MCMC\n", "\n", "We will now implement the Gibbs sampler scheme described in Chan and Jeliazkov (2009), Algorithm 2.\n", "\n", "\n", "We use the following (conditionally conjugate) priors:\n", "\n", "$$\n", "\\begin{aligned}\n", "H & \\sim \\mathcal{IW}(\\nu_1^0, S_1^0) \\\\\n", "\\sigma_i^2 & \\sim \\mathcal{IG} \\left ( \\frac{\\nu_{i2}^0}{2}, \\frac{S_{i2}^0}{2} \\right )\n", "\\end{aligned}\n", "$$\n", "\n", "where $\\mathcal{IW}$ denotes the inverse-Wishart distribution and $\\mathcal{IG}$ denotes the inverse-Gamma distribution. We set the prior hyperparameters as:\n", "\n", "$$\n", "\\begin{aligned}\n", "v_1^0 = T + 3, & \\quad S_1^0 = I \\\\\n", "v_{i2}^0 = 6, & \\quad S_{i2}^0 = 0.01 \\qquad \\text{for each} ~ i\\\\\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Prior hyperparameters\n", "\n", "# Prior for obs. cov. is inverse-Wishart(v_1^0=k + 3, S10=I)\n", "v10 = mod.k_endog + 3\n", "S10 = np.eye(mod.k_endog)\n", "\n", "# Prior for state cov. variances is inverse-Gamma(v_{i2}^0 / 2 = 3, S+{i2}^0 / 2 = 0.005)\n", "vi20 = 6\n", "Si20 = 0.01" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before running the MCMC iterations, there are a couple of practical steps:\n", "\n", "1. Create arrays to store the draws of our state vector, observation covariance matrix, and state error variances.\n", "2. Put the initial values for H and Q (described above) into the storage vectors\n", "3. Construct the simulation smoother object associated with our `TVPVAR` instance to make draws of the state vector" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Gibbs sampler setup\n", "niter = 11000\n", "nburn = 1000\n", "\n", "# 1. Create storage arrays\n", "store_states = np.zeros((niter + 1, mod.nobs, mod.k_states))\n", "store_obs_cov = np.zeros((niter + 1, mod.k_endog, mod.k_endog))\n", "store_state_cov = np.zeros((niter + 1, mod.k_states))\n", "\n", "# 2. Put in the initial values\n", "store_obs_cov[0] = initial_obs_cov\n", "store_state_cov[0] = initial_state_cov_diag\n", "mod.update_variances(store_obs_cov[0], store_state_cov[0])\n", "\n", "# 3. Construct posterior samplers\n", "sim = mod.simulation_smoother(method='cfa')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As before, we could have used either the simulation smoother based on the Kalman filter and smoother or that based on the Cholesky Factor Algorithm." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "for i in range(niter):\n", " mod.update_variances(store_obs_cov[i], store_state_cov[i])\n", " sim.simulate()\n", "\n", " # 1. Sample states\n", " store_states[i + 1] = sim.simulated_state.T\n", "\n", " # 2. Simulate obs cov\n", " fitted = np.matmul(mod['design'].transpose(2, 0, 1), store_states[i + 1][..., None])[..., 0]\n", " resid = mod.endog - fitted\n", " store_obs_cov[i + 1] = invwishart.rvs(v10 + mod.nobs, S10 + resid.T @ resid)\n", "\n", " # 3. Simulate state cov variances\n", " resid = store_states[i + 1, 1:] - store_states[i + 1, :-1]\n", " sse = np.sum(resid**2, axis=0)\n", " \n", " for j in range(mod.k_states):\n", " rv = invgamma.rvs((vi20 + mod.nobs - 1) / 2, scale=(Si20 + sse[j]) / 2)\n", " store_state_cov[i + 1, j] = rv" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After removing a number of initial draws, the remaining draws from the posterior allow us to conduct inference. Below, we plot the posterior mean of the time-varying regression coefficients.\n", "\n", "(**Note**: these plots are different from those in Figure 1 of the published version of Chan and Jeliazkov (2009), but they are very similar to those produced by the Matlab replication code available at http://joshuachan.org/code/code_TVPVAR.html)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Collect the posterior means of each time-varying coefficient\n", "states_posterior_mean = pd.DataFrame(\n", " np.mean(store_states[nburn + 1:], axis=0),\n", " index=mod._index, columns=mod.state_names)\n", "\n", "# Plot these means over time\n", "plot_coefficients_by_equation(states_posterior_mean);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Python also has a number of libraries to assist with exploring Bayesian models. Here we'll just use the [arviz](https://arviz-devs.github.io/arviz/index.html) package to explore the credible intervals of each of the covariance and variance parameters, although it makes available a much wider set of tools for analysis." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": false }, "outputs": [], "source": [ "import arviz as az\n", "\n", "# Collect the observation error covariance parameters\n", "az_obs_cov = az.convert_to_inference_data({\n", " ('Var[%s]' % mod.endog_names[i] if i == j else\n", " 'Cov[%s, %s]' % (mod.endog_names[i], mod.endog_names[j])):\n", " store_obs_cov[nburn + 1:, i, j]\n", " for i in range(mod.k_endog) for j in range(i, mod.k_endog)})\n", "\n", "# Plot the credible intervals\n", "az.plot_forest(az_obs_cov, figsize=(8, 7));" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Collect the state innovation variance parameters\n", "az_state_cov = az.convert_to_inference_data({\n", " r'$\\sigma^2$[%s]' % mod.state_names[i]: store_state_cov[nburn + 1:, i]\n", " for i in range(mod.k_states)})\n", "\n", "# Plot the credible intervals\n", "az.plot_forest(az_state_cov, figsize=(8, 7));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Appendix: performance\n", "\n", "Finally, we run a few simple tests to compare the performance of the KFS and CFA simulation smoothers by using the `%timeit` Jupyter notebook magic.\n", "\n", "One caveat is that the KFS simulation smoother can produce a variety of output beyond just simulations of the posterior state vector, and these additional computations could bias the results. To make the results comparable, we will tell the KFS simulation smoother to only compute simulations of the state by using the `simulation_output` argument." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.statespace.simulation_smoother import SIMULATION_STATE\n", "\n", "sim_cfa = mod.simulation_smoother(method='cfa')\n", "sim_kfs = mod.simulation_smoother(simulation_output=SIMULATION_STATE)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we can use the following code to perform a basic timing exercise:\n", "\n", "```python\n", "%timeit -n 10000 -r 3 sim_cfa.simulate()\n", "%timeit -n 10000 -r 3 sim_kfs.simulate()\n", "```\n", "\n", "On the machine this was tested on, this resulted in the following:\n", "\n", "```\n", "2.06 ms ± 26.5 µs per loop (mean ± std. dev. of 3 runs, 10000 loops each)\n", "2.02 ms ± 68.4 µs per loop (mean ± std. dev. of 3 runs, 10000 loops each)\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These results suggest that - at least for this model - there are not noticeable computational gains from the CFA approach relative to the KFS approach. However, this does not rule out the following:\n", "\n", "1. The Statsmodels implementation of the CFA simulation smoother could possibly be further optimized\n", "2. The CFA approach may only show improvement for certain models (for example with a large number of `endog` variables)\n", "\n", "One simple way to take a first pass at assessing the first possibility is to compare the runtime of the Statsmodels implementation of the CFA simulation smoother to the Matlab implementation in the replication codes of Chan and Jeliazkov (2009), available at http://joshuachan.org/code/code_TVPVAR.html.\n", "\n", "While the Statsmodels version of the CFA simulation smoother is written in Cython and compiled to C code, the Matlab version takes advantage of the Matlab's sparse matrix capabilities. As a result, even though it is not compiled code, we might expect it to have relatively good performance.\n", "\n", "On the machine this was tested on, the Matlab version typically ran the MCMC loop with 11,000 iterations in 70-75 seconds, while the MCMC loop in this notebook using the Statsmodels CFA simulation smoother (see above), also with 11,0000 iterations, ran in 40-45 seconds. This is some evidence that the Statsmodels implementation of the CFA smoother already performs relatively well (although it does not rule out that there are additional gains possible)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bibliography\n", "\n", "Carter, Chris K., and Robert Kohn. \"On Gibbs sampling for state space models.\" Biometrika 81, no. 3 (1994): 541-553.\n", "\n", "Chan, Joshua CC, and Ivan Jeliazkov. \"Efficient simulation and integrated likelihood estimation in state space models.\" International Journal of Mathematical Modelling and Numerical Optimisation 1, no. 1-2 (2009): 101-120.\n", "\n", "De Jong, Piet, and Neil Shephard. \"The simulation smoother for time series models.\" Biometrika 82, no. 2 (1995): 339-350.\n", "\n", "Durbin, James, and Siem Jan Koopman. \"A simple and efficient simulation smoother for state space time series analysis.\" Biometrika 89, no. 3 (2002): 603-616.\n", "\n", "McCausland, William J., Shirley Miller, and Denis Pelletier. \"Simulation smoothing for state–space models: A computational efficiency analysis.\" Computational Statistics & Data Analysis 55, no. 1 (2011): 199-212." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 2 } statsmodels-0.12.2/examples/notebooks/statespace_varmax.ipynb000066400000000000000000000123221400612667500245430ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# VARMAX models\n", "\n", "This is a brief introduction notebook to VARMAX models in statsmodels. The VARMAX model is generically specified as:\n", "$$\n", "y_t = \\nu + A_1 y_{t-1} + \\dots + A_p y_{t-p} + B x_t + \\epsilon_t +\n", "M_1 \\epsilon_{t-1} + \\dots M_q \\epsilon_{t-q}\n", "$$\n", "\n", "where $y_t$ is a $\\text{k_endog} \\times 1$ vector." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "dta = sm.datasets.webuse('lutkepohl2', 'https://www.stata-press.com/data/r12/')\n", "dta.index = dta.qtr\n", "dta.index.freq = dta.index.inferred_freq\n", "endog = dta.loc['1960-04-01':'1978-10-01', ['dln_inv', 'dln_inc', 'dln_consump']]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model specification\n", "\n", "The `VARMAX` class in statsmodels allows estimation of VAR, VMA, and VARMA models (through the `order` argument), optionally with a constant term (via the `trend` argument). Exogenous regressors may also be included (as usual in statsmodels, by the `exog` argument), and in this way a time trend may be added. Finally, the class allows measurement error (via the `measurement_error` argument) and allows specifying either a diagonal or unstructured innovation covariance matrix (via the `error_cov_type` argument)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1: VAR\n", "\n", "Below is a simple VARX(2) model in two endogenous variables and an exogenous series, but no constant term. Notice that we needed to allow for more iterations than the default (which is `maxiter=50`) in order for the likelihood estimation to converge. This is not unusual in VAR models which have to estimate a large number of parameters, often on a relatively small number of time series: this model, for example, estimates 27 parameters off of 75 observations of 3 variables." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "exog = endog['dln_consump']\n", "mod = sm.tsa.VARMAX(endog[['dln_inv', 'dln_inc']], order=(2,0), trend='n', exog=exog)\n", "res = mod.fit(maxiter=1000, disp=False)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the estimated VAR model, we can plot the impulse response functions of the endogenous variables." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ax = res.impulse_responses(10, orthogonalized=True).plot(figsize=(13,3))\n", "ax.set(xlabel='t', title='Responses to a shock to `dln_inv`');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2: VMA\n", "\n", "A vector moving average model can also be formulated. Below we show a VMA(2) on the same data, but where the innovations to the process are uncorrelated. In this example we leave out the exogenous regressor but now include the constant term." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mod = sm.tsa.VARMAX(endog[['dln_inv', 'dln_inc']], order=(0,2), error_cov_type='diagonal')\n", "res = mod.fit(maxiter=1000, disp=False)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Caution: VARMA(p,q) specifications\n", "\n", "Although the model allows estimating VARMA(p,q) specifications, these models are not identified without additional restrictions on the representation matrices, which are not built-in. For this reason, it is recommended that the user proceed with error (and indeed a warning is issued when these models are specified). Nonetheless, they may in some circumstances provide useful information." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mod = sm.tsa.VARMAX(endog[['dln_inv', 'dln_inc']], order=(1,1))\n", "res = mod.fit(maxiter=1000, disp=False)\n", "print(res.summary())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.3" } }, "nbformat": 4, "nbformat_minor": 0 }statsmodels-0.12.2/examples/notebooks/stationarity_detrending_adf_kpss.ipynb000066400000000000000000000227001400612667500276410ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Stationarity and detrending (ADF/KPSS)\n", "\n", "Stationarity means that the statistical properties of a time series i.e. mean, variance and covariance do not change over time. Many statistical models require the series to be stationary to make effective and precise predictions.\n", "\n", "Two statistical tests would be used to check the stationarity of a time series – Augmented Dickey Fuller (“ADFâ€) test and Kwiatkowski-Phillips-Schmidt-Shin (“KPSSâ€) test. A method to convert a non-stationary time series into stationary series shall also be used." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This first cell imports standard packages and sets plots to appear inline." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import statsmodels.api as sm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sunspots dataset is used. It contains yearly (1700-2008) data on sunspots from the National Geophysical Data Center." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sunspots = sm.datasets.sunspots.load_pandas().data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some preprocessing is carried out on the data. The \"YEAR\" column is used in creating index." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sunspots.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008'))\n", "del sunspots[\"YEAR\"]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data is plotted now." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sunspots.plot(figsize=(12,8))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ADF test\n", "\n", "ADF test is used to determine the presence of unit root in the series, and hence helps in understand if the series is stationary or not. The null and alternate hypothesis of this test are:\n", "\n", "Null Hypothesis: The series has a unit root.\n", "\n", "Alternate Hypothesis: The series has no unit root.\n", "\n", "If the null hypothesis in failed to be rejected, this test may provide evidence that the series is non-stationary.\n", "\n", "A function is created to carry out the ADF test on a time series." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.stattools import adfuller\n", "def adf_test(timeseries):\n", " print ('Results of Dickey-Fuller Test:')\n", " dftest = adfuller(timeseries, autolag='AIC')\n", " dfoutput = pd.Series(dftest[0:4], index=['Test Statistic','p-value','#Lags Used','Number of Observations Used'])\n", " for key,value in dftest[4].items():\n", " dfoutput['Critical Value (%s)'%key] = value\n", " print (dfoutput)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## KPSS test\n", "\n", "KPSS is another test for checking the stationarity of a time series. The null and alternate hypothesis for the KPSS test are opposite that of the ADF test.\n", "\n", "Null Hypothesis: The process is trend stationary.\n", "\n", "Alternate Hypothesis: The series has a unit root (series is not stationary).\n", "\n", "A function is created to carry out the KPSS test on a time series." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.stattools import kpss\n", "def kpss_test(timeseries):\n", " print ('Results of KPSS Test:')\n", " kpsstest = kpss(timeseries, regression='c', nlags=\"auto\")\n", " kpss_output = pd.Series(kpsstest[0:3], index=['Test Statistic','p-value','Lags Used'])\n", " for key,value in kpsstest[3].items():\n", " kpss_output['Critical Value (%s)'%key] = value\n", " print (kpss_output)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ADF tests gives the following results – test statistic, p value and the critical value at 1%, 5% , and 10% confidence intervals.\n", "\n", "ADF test is now applied on the data." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "adf_test(sunspots['SUNACTIVITY'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Based upon the significance level of 0.05 and the p-value of ADF test, the null hypothesis can not be rejected. Hence, the series is non-stationary." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The KPSS tests gives the following results – test statistic, p value and the critical value at 1%, 5% , and 10% confidence intervals.\n", "\n", "KPSS test is now applied on the data." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "kpss_test(sunspots['SUNACTIVITY'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Based upon the significance level of 0.05 and the p-value of KPSS test, there is evidence for rejecting the null hypothesis in favor of the alternative. Hence, the series is non-stationary as per the KPSS test.\n", "\n", "It is always better to apply both the tests, so that it can be ensured that the series is truly stationary. Possible outcomes of applying these stationary tests are as follows:\n", "\n", "Case 1: Both tests conclude that the series is not stationary - The series is not stationary \n", "Case 2: Both tests conclude that the series is stationary - The series is stationary \n", "Case 3: KPSS indicates stationarity and ADF indicates non-stationarity - The series is trend stationary. Trend needs to be removed to make series strict stationary. The detrended series is checked for stationarity. \n", "Case 4: KPSS indicates non-stationarity and ADF indicates stationarity - The series is difference stationary. Differencing is to be used to make series stationary. The differenced series is checked for stationarity. \n", "\n", "Here, due to the difference in the results from ADF test and KPSS test, it can be inferred that the series is trend stationary and not strict stationary. The series can be detrended by differencing or by model fitting." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Detrending by Differencing\n", "\n", "It is one of the simplest methods for detrending a time series. A new series is constructed where the value at the current time step is calculated as the difference between the original observation and the observation at the previous time step.\n", "\n", "Differencing is applied on the data and the result is plotted." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sunspots['SUNACTIVITY_diff'] = sunspots['SUNACTIVITY'] - sunspots['SUNACTIVITY'].shift(1)\n", "sunspots['SUNACTIVITY_diff'].dropna().plot(figsize=(12,8))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ADF test is now applied on these detrended values and stationarity is checked." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "adf_test(sunspots['SUNACTIVITY_diff'].dropna())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Based upon the p-value of ADF test, there is evidence for rejecting the null hypothesis in favor of the alternative. Hence, the series is strict stationary now." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "KPSS test is now applied on these detrended values and stationarity is checked." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "kpss_test(sunspots['SUNACTIVITY_diff'].dropna())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Based upon the p-value of KPSS test, the null hypothesis can not be rejected. Hence, the series is stationary." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "\n", "Two tests for checking the stationarity of a time series are used, namely ADF test and KPSS test. Detrending is carried out by using differencing. Trend stationary time series is converted into strict stationary time series. Requisite forecasting model can now be applied on a stationary time series data." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.9" } }, "nbformat": 4, "nbformat_minor": 2 }statsmodels-0.12.2/examples/notebooks/stl_decomposition.ipynb000066400000000000000000000323241400612667500245730ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Seasonal-Trend decomposition using LOESS (STL)\n", "\n", "This note book illustrates the use of `STL` to decompose a time series into three components: trend, season(al) and residual. STL uses LOESS (locally estimated scatterplot smoothing) to extract smooths estimates of the three components. The key inputs into `STL` are:\n", "\n", "* `season` - The length of the seasonal smoother. Must be odd.\n", "* `trend` - The length of the trend smoother, usually around 150% of `season`. Must be odd and larger than `season`.\n", "* `low_pass` - The length of the low-pass estimation window, usually the smallest odd number larger than the periodicity of the data.\n", "\n", "First we import the required packages, prepare the graphics environment, and prepare the data. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "from pandas.plotting import register_matplotlib_converters\n", "register_matplotlib_converters()\n", "sns.set_style('darkgrid')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plt.rc('figure',figsize=(16,12))\n", "plt.rc('font',size=13)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Atmospheric CO2\n", "\n", "The example in Cleveland, Cleveland, McRae, and Terpenning (1990) uses CO2 data, which is in the list below. This monthly data (January 1959 to December 1987) has a clear trend and seasonality across the sample. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "co2 = [315.58, 316.39, 316.79, 317.82, 318.39, 318.22, 316.68, 315.01, 314.02, 313.55, \n", " 315.02, 315.75, 316.52, 317.10, 317.79, 319.22, 320.08, 319.70, 318.27, 315.99, \n", " 314.24, 314.05, 315.05, 316.23, 316.92, 317.76, 318.54, 319.49, 320.64, 319.85, \n", " 318.70, 316.96, 315.17, 315.47, 316.19, 317.17, 318.12, 318.72, 319.79, 320.68, \n", " 321.28, 320.89, 319.79, 317.56, 316.46, 315.59, 316.85, 317.87, 318.87, 319.25, \n", " 320.13, 321.49, 322.34, 321.62, 319.85, 317.87, 316.36, 316.24, 317.13, 318.46, \n", " 319.57, 320.23, 320.89, 321.54, 322.20, 321.90, 320.42, 318.60, 316.73, 317.15, \n", " 317.94, 318.91, 319.73, 320.78, 321.23, 322.49, 322.59, 322.35, 321.61, 319.24, \n", " 318.23, 317.76, 319.36, 319.50, 320.35, 321.40, 322.22, 323.45, 323.80, 323.50, \n", " 322.16, 320.09, 318.26, 317.66, 319.47, 320.70, 322.06, 322.23, 322.78, 324.10, \n", " 324.63, 323.79, 322.34, 320.73, 319.00, 318.99, 320.41, 321.68, 322.30, 322.89, \n", " 323.59, 324.65, 325.30, 325.15, 323.88, 321.80, 319.99, 319.86, 320.88, 322.36, \n", " 323.59, 324.23, 325.34, 326.33, 327.03, 326.24, 325.39, 323.16, 321.87, 321.31, \n", " 322.34, 323.74, 324.61, 325.58, 326.55, 327.81, 327.82, 327.53, 326.29, 324.66, \n", " 323.12, 323.09, 324.01, 325.10, 326.12, 326.62, 327.16, 327.94, 329.15, 328.79, \n", " 327.53, 325.65, 323.60, 323.78, 325.13, 326.26, 326.93, 327.84, 327.96, 329.93, \n", " 330.25, 329.24, 328.13, 326.42, 324.97, 325.29, 326.56, 327.73, 328.73, 329.70, \n", " 330.46, 331.70, 332.66, 332.22, 331.02, 329.39, 327.58, 327.27, 328.30, 328.81, \n", " 329.44, 330.89, 331.62, 332.85, 333.29, 332.44, 331.35, 329.58, 327.58, 327.55, \n", " 328.56, 329.73, 330.45, 330.98, 331.63, 332.88, 333.63, 333.53, 331.90, 330.08, \n", " 328.59, 328.31, 329.44, 330.64, 331.62, 332.45, 333.36, 334.46, 334.84, 334.29, \n", " 333.04, 330.88, 329.23, 328.83, 330.18, 331.50, 332.80, 333.22, 334.54, 335.82, \n", " 336.45, 335.97, 334.65, 332.40, 331.28, 330.73, 332.05, 333.54, 334.65, 335.06, \n", " 336.32, 337.39, 337.66, 337.56, 336.24, 334.39, 332.43, 332.22, 333.61, 334.78, \n", " 335.88, 336.43, 337.61, 338.53, 339.06, 338.92, 337.39, 335.72, 333.64, 333.65, \n", " 335.07, 336.53, 337.82, 338.19, 339.89, 340.56, 341.22, 340.92, 339.26, 337.27, \n", " 335.66, 335.54, 336.71, 337.79, 338.79, 340.06, 340.93, 342.02, 342.65, 341.80, \n", " 340.01, 337.94, 336.17, 336.28, 337.76, 339.05, 340.18, 341.04, 342.16, 343.01, \n", " 343.64, 342.91, 341.72, 339.52, 337.75, 337.68, 339.14, 340.37, 341.32, 342.45, \n", " 343.05, 344.91, 345.77, 345.30, 343.98, 342.41, 339.89, 340.03, 341.19, 342.87, \n", " 343.74, 344.55, 345.28, 347.00, 347.37, 346.74, 345.36, 343.19, 340.97, 341.20, \n", " 342.76, 343.96, 344.82, 345.82, 347.24, 348.09, 348.66, 347.90, 346.27, 344.21, \n", " 342.88, 342.58, 343.99, 345.31, 345.98, 346.72, 347.63, 349.24, 349.83, 349.10, \n", " 347.52, 345.43, 344.48, 343.89, 345.29, 346.54, 347.66, 348.07, 349.12, 350.55, \n", " 351.34, 350.80, 349.10, 347.54, 346.20, 346.20, 347.44, 348.67]\n", "co2 = pd.Series(co2, index=pd.date_range('1-1-1959', periods=len(co2), freq='M'), name = 'CO2')\n", "co2.describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The decomposition requires 1 input, the data series. If the data series does not have a frequency, then you must also specify `period`. The default value for `seasonal` is 7, and so should also be changed in most applications." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.seasonal import STL\n", "stl = STL(co2, seasonal=13)\n", "res = stl.fit()\n", "fig = res.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Robust Fitting\n", "Setting `robust` uses a data-dependent weighting function that re-weights data when estimating the LOESS (and so is using LOWESS). Using robust estimation allows the model to tolerate larger errors that are visible on the bottom plot.\n", "\n", "Here we use a series the measures the production of electrical equipment in the EU." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.datasets import elec_equip as ds\n", "elec_equip = ds.load(as_pandas=True).data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we estimate the model with and without robust weighting. The difference is minor and is most pronounced during the financial crisis of 2008. The non-robust estimate places equal weights on all observations and so produces smaller errors, on average. The weights vary between 0 and 1." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def add_stl_plot(fig, res, legend):\n", " \"\"\"Add 3 plots from a second STL fit\"\"\"\n", " axs = fig.get_axes()\n", " comps = ['trend', 'seasonal', 'resid']\n", " for ax, comp in zip(axs[1:], comps):\n", " series = getattr(res, comp)\n", " if comp == 'resid':\n", " ax.plot(series, marker='o', linestyle='none')\n", " else:\n", " ax.plot(series)\n", " if comp == 'trend':\n", " ax.legend(legend, frameon=False) \n", " \n", "\n", "stl = STL(elec_equip, period=12, robust=True)\n", "res_robust = stl.fit()\n", "fig = res_robust.plot()\n", "res_non_robust = STL(elec_equip, period=12, robust=False).fit()\n", "add_stl_plot(fig, res_non_robust, ['Robust','Non-robust'])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(16,5))\n", "lines = plt.plot(res_robust.weights, marker='o', linestyle='none')\n", "ax = plt.gca()\n", "xlim = ax.set_xlim(elec_equip.index[0], elec_equip.index[-1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## LOESS degree\n", "The default configuration estimates the LOESS model with both a constant and a trend. This can be changed to only include a constant by setting `COMPONENT_deg` to 0. Here the degree makes little difference except in the trend around the financial crisis of 2008." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "stl = STL(elec_equip, period=12, seasonal_deg=0, trend_deg=0, low_pass_deg=0, robust=True)\n", "res_deg_0 = stl.fit()\n", "fig = res_robust.plot()\n", "add_stl_plot(fig, res_deg_0, ['Degree 1','Degree 0'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Performance\n", "Three options can be used to reduce the computational cost of the STL decomposition:\n", "\n", "* `seasonal_jump`\n", "* `trend_jump`\n", "* `low_pass_jump`\n", "\n", "When these are non-zero, the LOESS for component `COMPONENT` is only estimated ever `COMPONENT_jump` observations, and linear interpolation is used between points. These values should not normally be more than 10-20% of the size of `seasonal`, `trend` or `low_pass`, respectively. \n", "\n", "The example below shows how these can reduce the computational cost by a factor of 15 using simulated data with both a low-frequency cosinusoidal trend and a sinusoidal seasonal pattern." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "rs = np.random.RandomState(0xA4FD94BC)\n", "tau = 2000\n", "t = np.arange(tau)\n", "period = int(0.05 * tau)\n", "seasonal = period + ((period % 2) == 0) # Ensure odd\n", "e = .25*rs.standard_normal(tau)\n", "y = np.cos(t / tau * 2 * np.pi) + 0.25 * np.sin(t / period * 2 * np.pi) + e\n", "plt.plot(y)\n", "plt.title('Simulated Data')\n", "xlim = plt.gca().set_xlim(0, tau)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, the base line model is estimated with all jumps equal to 1. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = STL(y, period=period, seasonal=seasonal)\n", "%timeit mod.fit()\n", "res = mod.fit()\n", "fig = res.plot(observed=False, resid=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The jumps are all set to 15% of their window length. Limited linear interpolation makes little difference to the fit of the model." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "low_pass_jump = seasonal_jump = int(0.15 * (period + 1))\n", "trend_jump = int(0.15 * 1.5 * (period + 1))\n", "mod = STL(y, period=period, seasonal=seasonal, seasonal_jump=seasonal_jump, \n", " trend_jump=trend_jump, low_pass_jump=low_pass_jump)\n", "%timeit mod.fit()\n", "res = mod.fit()\n", "fig = res.plot(observed=False, resid=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Forecasting with STL\n", "\n", "``STLForecast`` simplifies the process of using STL to remove seasonalities and then using a standard time-series model to forecast the trend and cyclical components. \n", "\n", "Here we use STL to handle the seasonality and then an ARIMA(1,1,0) to model the deseasonalized data. The seasonal component is forecast from the find full cycle where \n", "\n", "$$E[S_{T+h}|\\mathcal{F}_T]=\\hat{S}_{T-k}$$\n", "\n", "where $k= m - h + m \\lfloor \\frac{h-1}{m} \\rfloor$. The forecast automatically adds the seasonal component forecast to the ARIMA forecast." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.forecasting.stl import STLForecast\n", "from statsmodels.tsa.arima.model import ARIMA\n", "\n", "elec_equip.index.freq = elec_equip.index.inferred_freq\n", "stlf = STLForecast(elec_equip, ARIMA, model_kwargs=dict(order=(1,1,0), trend=\"t\"))\n", "stlf_res = stlf.fit()\n", "\n", "forecast = stlf_res.forecast(24)\n", "plt.plot(elec_equip)\n", "plt.plot(forecast)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "``summary`` contains information about both the time-series model and the STL decomposition." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(stlf_res.summary())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 2 } statsmodels-0.12.2/examples/notebooks/theta-model.ipynb000066400000000000000000000244671400612667500232510ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The Theta Model\n", "\n", "The Theta model of Assimakopoulos & Nikolopoulos (2000) is a simple method for forecasting the involves fitting two $\\theta$-lines, forecasting the lines using a Simple Exponential Smoother, and then combining the forecasts from the two lines to produce the final forecast. The model is implemented in steps:\n", "\n", "\n", "1. Test for seasonality\n", "2. Deseasonalize if seasonality detected\n", "3. Estimate $\\alpha$ by fitting a SES model to the data and $b_0$ by OLS.\n", "4. Forecast the series\n", "5. Reseasonalize if the data was deseasonalized.\n", "\n", "The seasonality test examines the ACF at the seasonal lag $m$. If this lag is significantly different from zero then the data is deseasonalize using `statsmodels.tsa.seasonal_decompose` use either a multiplicative method (default) or additive. \n", "\n", "The parameters of the model are $b_0$ and $\\alpha$ where $b_0$ is estimated from the OLS regression\n", "\n", "$$\n", "X_t = a_0 + b_0 (t-1) + \\epsilon_t\n", "$$\n", "\n", "and $\\alpha$ is the SES smoothing parameter in\n", "\n", "$$\n", "\\tilde{X}_t = (1-\\alpha) X_t + \\alpha \\tilde{X}_{t-1}\n", "$$\n", "\n", "The forecasts are then \n", "\n", "$$\n", " \\hat{X}_{T+h|T} = \\frac{\\theta-1}{\\theta} \\hat{b}_0\n", " \\left[h - 1 + \\frac{1}{\\hat{\\alpha}}\n", " - \\frac{(1-\\hat{\\alpha})^T}{\\hat{\\alpha}} \\right]\n", " + \\tilde{X}_{T+h|T}\n", "$$\n", "\n", "Ultimately $\\theta$ only plays a role in determining how much the trend is damped. If $\\theta$ is very large, then the forecast of the model is identical to that from an Integrated Moving Average with a drift,\n", "\n", "$$\n", "X_t = X_{t-1} + b_0 + (\\alpha-1)\\epsilon_{t-1} + \\epsilon_t.\n", "$$\n", "\n", "Finally, the forecasts are reseasonalized if needed.\n", "\n", "This module is based on:\n", "\n", "* Assimakopoulos, V., & Nikolopoulos, K. (2000). The theta model: a decomposition\n", " approach to forecasting. International journal of forecasting, 16(4), 521-530.\n", "* Hyndman, R. J., & Billah, B. (2003). Unmasking the Theta method.\n", " International Journal of Forecasting, 19(2), 287-290.\n", "* Fioruci, J. A., Pellegrini, T. R., Louzada, F., & Petropoulos, F.\n", " (2015). The optimized theta method. arXiv preprint arXiv:1503.03529." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Imports\n", "\n", "We start with the standard set of imports and some tweaks to the default matplotlib style." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import pandas_datareader as pdr\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "plt.rc(\"figure\",figsize=(16,8))\n", "plt.rc(\"font\",size=15)\n", "plt.rc(\"lines\",linewidth=3)\n", "sns.set_style(\"darkgrid\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Load some Data\n", "\n", "We will first look at housing starts using US data. This series is clearly seasonal but does not have a clear trend during the same. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "reader = pdr.fred.FredReader([\"HOUST\"], start=\"1980-01-01\", end=\"2020-04-01\")\n", "data = reader.read()\n", "housing = data.HOUST\n", "housing.index.freq = housing.index.inferred_freq\n", "ax = housing.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We fit specify the model without any options and fit it. The summary shows that the data was deseasonalized using the multiplicative method. The drift is modest and negative, and the smoothing parameter is fairly low. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.forecasting.theta import ThetaModel\n", "tm = ThetaModel(housing)\n", "res = tm.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model is first and foremost a forecasting method. Forecasts are produced using the `forecast` method from fitted model. Below we produce a hedgehog plot by forecasting 2-years ahead every 2 years. \n", "\n", "**Note**: the default $\\theta$ is 2." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "forecasts = {\"housing\": housing}\n", "for year in range(1995, 2020, 2):\n", " sub = housing[:str(year)]\n", " res = ThetaModel(sub).fit()\n", " fcast = res.forecast(24)\n", " forecasts[str(year)] = fcast\n", "forecasts = pd.DataFrame(forecasts)\n", "ax = forecasts[\"1995\":].plot(legend=False)\n", "children = ax.get_children()\n", "children[0].set_linewidth(4)\n", "children[0].set_alpha(0.3)\n", "children[0].set_color(\"#000000\")\n", "ax.set_title(\"Housing Starts\")\n", "plt.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We could alternatively fir the log of the data. Here it makes more sense to force the deseasonalizing to use the additive method, if needed. We also fit the model parameters using MLE. This method fits the IMA\n", "\n", "$$ X_t = X_{t-1} + \\gamma\\epsilon_{t-1} + \\epsilon_t $$\n", "\n", "where $\\hat{\\alpha}$ = $\\min(\\hat{\\gamma}+1, 0.9998)$ using `statsmodels.tsa.SARIMAX`. The parameters are similar although the drift is closer to zero." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "tm = ThetaModel(np.log(housing), method=\"additive\")\n", "res = tm.fit(use_mle=True)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The forecast only depends on the forecast trend component,\n", "$$\n", "\\hat{b}_0\n", " \\left[h - 1 + \\frac{1}{\\hat{\\alpha}}\n", " - \\frac{(1-\\hat{\\alpha})^T}{\\hat{\\alpha}} \\right],\n", "$$\n", "\n", "the forecast from the SES (which does not change with the horizon), and the seasonal. These three components are available using the `forecast_components`. This allows forecasts to be constructed using multiple choices of $\\theta$ using the weight expression above. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res.forecast_components(12)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Personal Consumption Expenditure\n", "\n", "We next look at personal consumption expenditure. This series has a clear seasonal component and a drift. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "reader = pdr.fred.FredReader([\"NA000349Q\"], start=\"1980-01-01\", end=\"2020-04-01\")\n", "pce = reader.read()\n", "pce.columns = [\"PCE\"]\n", "_ = pce.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since this series is always positive, we model the $\\ln$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod = ThetaModel(np.log(pce))\n", "res = mod.fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we explore differenced in the forecast as $\\theta$ changes. When $\\theta$ is close to 1, the drift is nearly absent. As $\\theta$ increases, the drift becomes more obvious." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "forecasts = pd.DataFrame({\"ln PCE\":np.log(pce.PCE),\n", " \"theta=1.2\": res.forecast(12, theta=1.2),\n", " \"theta=2\": res.forecast(12),\n", " \"theta=3\": res.forecast(12, theta=3),\n", " \"No damping\": res.forecast(12, theta=np.inf)\n", " })\n", "_ = forecasts.tail(36).plot()\n", "plt.title(\"Forecasts of ln PCE\")\n", "plt.tight_layout(pad=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, `plot_predict` can be used to visualize the predictions and prediction intervals which are constructed assuming the IMA is true." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ax = res.plot_predict(24, theta=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We conclude be producing a hedgehog plot using 2-year non-overlapping samples." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "ln_pce = np.log(pce.PCE)\n", "forecasts = {\"ln PCE\": ln_pce}\n", "for year in range(1995,2020,3):\n", " sub = ln_pce[:str(year)]\n", " res = ThetaModel(sub).fit()\n", " fcast = res.forecast(12)\n", " forecasts[str(year)] = fcast\n", "forecasts = pd.DataFrame(forecasts)\n", "ax = forecasts[\"1995\":].plot(legend=False)\n", "children = ax.get_children()\n", "children[0].set_linewidth(4)\n", "children[0].set_alpha(0.3)\n", "children[0].set_color(\"#000000\")\n", "ax.set_title(\"ln PCE\")\n", "plt.tight_layout(pad=1.0)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 4 }statsmodels-0.12.2/examples/notebooks/tsa_arma_0.ipynb000066400000000000000000000250601400612667500230420ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Autoregressive Moving Average (ARMA): Sunspots data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy import stats\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "\n", "import statsmodels.api as sm\n", "from statsmodels.tsa.arima.model import ARIMA" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.graphics.api import qqplot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sunspots Data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(sm.datasets.sunspots.NOTE)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dta = sm.datasets.sunspots.load_pandas().data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008'))\n", "del dta[\"YEAR\"]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dta.plot(figsize=(12,8));" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax1 = fig.add_subplot(211)\n", "fig = sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40, ax=ax1)\n", "ax2 = fig.add_subplot(212)\n", "fig = sm.graphics.tsa.plot_pacf(dta, lags=40, ax=ax2)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arma_mod20 = ARIMA(dta, order=(2, 0, 0)).fit()\n", "print(arma_mod20.params)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arma_mod30 = ARIMA(dta, order=(3, 0, 0)).fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(arma_mod20.aic, arma_mod20.bic, arma_mod20.hqic)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(arma_mod30.params)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(arma_mod30.aic, arma_mod30.bic, arma_mod30.hqic)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Does our model obey the theory?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sm.stats.durbin_watson(arma_mod30.resid.values)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "ax = arma_mod30.resid.plot(ax=ax);" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "resid = arma_mod30.resid" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "stats.normaltest(resid)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "fig = qqplot(resid, line='q', ax=ax, fit=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax1 = fig.add_subplot(211)\n", "fig = sm.graphics.tsa.plot_acf(resid.values.squeeze(), lags=40, ax=ax1)\n", "ax2 = fig.add_subplot(212)\n", "fig = sm.graphics.tsa.plot_pacf(resid, lags=40, ax=ax2)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "r,q,p = sm.tsa.acf(resid.values.squeeze(), fft=True, qstat=True)\n", "data = np.c_[range(1,41), r[1:], q, p]\n", "table = pd.DataFrame(data, columns=['lag', \"AC\", \"Q\", \"Prob(>Q)\"])\n", "print(table.set_index('lag'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* This indicates a lack of fit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* In-sample dynamic prediction. How good does our model do?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "predict_sunspots = arma_mod30.predict('1990', '2012', dynamic=True)\n", "print(predict_sunspots)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def mean_forecast_err(y, yhat):\n", " return y.sub(yhat).mean()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mean_forecast_err(dta.SUNACTIVITY, predict_sunspots)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise: Can you obtain a better fit for the Sunspots model? (Hint: sm.tsa.AR has a method select_order)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulated ARMA(4,1): Model Identification is Difficult" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from statsmodels.tsa.arima_process import ArmaProcess" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.random.seed(1234)\n", "# include zero-th lag\n", "arparams = np.array([1, .75, -.65, -.55, .9])\n", "maparams = np.array([1, .65])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's make sure this model is estimable." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arma_t = ArmaProcess(arparams, maparams)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arma_t.isinvertible" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arma_t.isstationary" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* What does this mean?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "ax.plot(arma_t.generate_sample(nsample=50));" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arparams = np.array([1, .35, -.15, .55, .1])\n", "maparams = np.array([1, .65])\n", "arma_t = ArmaProcess(arparams, maparams)\n", "arma_t.isstationary" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arma_rvs = arma_t.generate_sample(nsample=500, burnin=250, scale=2.5)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax1 = fig.add_subplot(211)\n", "fig = sm.graphics.tsa.plot_acf(arma_rvs, lags=40, ax=ax1)\n", "ax2 = fig.add_subplot(212)\n", "fig = sm.graphics.tsa.plot_pacf(arma_rvs, lags=40, ax=ax2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* For mixed ARMA processes the Autocorrelation function is a mixture of exponentials and damped sine waves after (q-p) lags.\n", "* The partial autocorrelation function is a mixture of exponentials and dampened sine waves after (p-q) lags." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arma11 = ARIMA(arma_rvs, order=(1, 0, 1)).fit()\n", "resid = arma11.resid\n", "r,q,p = sm.tsa.acf(resid, fft=True, qstat=True)\n", "data = np.c_[range(1,41), r[1:], q, p]\n", "table = pd.DataFrame(data, columns=['lag', \"AC\", \"Q\", \"Prob(>Q)\"])\n", "print(table.set_index('lag'))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arma41 = ARIMA(arma_rvs, order=(4, 0, 1)).fit()\n", "resid = arma41.resid\n", "r,q,p = sm.tsa.acf(resid, fft=True, qstat=True)\n", "data = np.c_[range(1,41), r[1:], q, p]\n", "table = pd.DataFrame(data, columns=['lag', \"AC\", \"Q\", \"Prob(>Q)\"])\n", "print(table.set_index('lag'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise: How good of in-sample prediction can you do for another series, say, CPI" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "macrodta = sm.datasets.macrodata.load_pandas().data\n", "macrodta.index = pd.Index(sm.tsa.datetools.dates_from_range('1959Q1', '2009Q3'))\n", "cpi = macrodta[\"cpi\"]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Hint: " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "ax = cpi.plot(ax=ax);\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "P-value of the unit-root test, resoundingly rejects the null of a unit-root." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(sm.tsa.adfuller(cpi)[1])" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 1 }statsmodels-0.12.2/examples/notebooks/tsa_arma_1.ipynb000066400000000000000000000060171400612667500230440ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Autoregressive Moving Average (ARMA): Artificial data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "\n", "from statsmodels.graphics.tsaplots import plot_predict\n", "from statsmodels.tsa.arima_process import arma_generate_sample\n", "from statsmodels.tsa.arima.model import ARIMA\n", "\n", "np.random.seed(12345)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate some data from an ARMA process:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arparams = np.array([.75, -.25])\n", "maparams = np.array([.65, .35])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The conventions of the arma_generate function require that we specify a 1 for the zero-lag of the AR and MA parameters and that the AR parameters be negated." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "arparams = np.r_[1, -arparams]\n", "maparams = np.r_[1, maparams]\n", "nobs = 250\n", "y = arma_generate_sample(arparams, maparams, nobs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Now, optionally, we can add some dates information. For this example, we'll use a pandas time series." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dates = pd.date_range('1980-1-1', freq=\"M\", periods=nobs)\n", "y = pd.Series(y, index=dates)\n", "arma_mod = ARIMA(y, order=(2, 0, 2), trend='n')\n", "arma_res = arma_mod.fit()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(arma_res.summary())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "y.tail()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "fig, ax = plt.subplots(figsize=(10,8))\n", "fig = plot_predict(arma_res, start='1999-06-30', end='2001-05-31', ax=ax)\n", "legend = ax.legend(loc='upper left')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/tsa_dates.ipynb000066400000000000000000000057561400612667500230150ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Dates in timeseries models" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "\n", "import statsmodels.api as sm\n", "from statsmodels.tsa.ar_model import AutoReg, ar_select_order\n", "\n", "plt.rc(\"figure\", figsize=(16,8))\n", "plt.rc(\"font\", size=14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Getting started" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "data = sm.datasets.sunspots.load()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Right now an annual date series must be datetimes at the end of the year." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from datetime import datetime\n", "dates = pd.date_range('1700-1-1', periods=len(data.endog), freq=\"A-DEC\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using Pandas\n", "\n", "Make a pandas TimeSeries or DataFrame" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "endog = pd.Series(data.endog, index=dates)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Instantiate the model" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "selection_res = ar_select_order(endog, 9, old_names=True, seasonal=True, period=11)\n", "pandas_ar_res = selection_res.model.fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Out-of-sample prediction" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "pred = pandas_ar_res.predict(start='2005', end='2027')\n", "print(pred)\n" ] }, { "cell_type": "code", "execution_count": null, "outputs": [], "source": [ "fig = pandas_ar_res.plot_predict(start='2005', end='2027')" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }statsmodels-0.12.2/examples/notebooks/tsa_filters.ipynb000066400000000000000000000205351400612667500233550ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Time Series Filters" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "\n", "import statsmodels.api as sm" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dta = sm.datasets.macrodata.load_pandas().data" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "index = pd.Index(sm.tsa.datetools.dates_from_range('1959Q1', '2009Q3'))\n", "print(index)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "dta.index = index\n", "del dta['year']\n", "del dta['quarter']" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(sm.datasets.macrodata.NOTE)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(dta.head(10))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "dta.realgdp.plot(ax=ax);\n", "legend = ax.legend(loc = 'upper left');\n", "legend.prop.set_size(20);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hodrick-Prescott Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Hodrick-Prescott filter separates a time-series $y_t$ into a trend $\\tau_t$ and a cyclical component $\\zeta_t$ \n", "\n", "$$y_t = \\tau_t + \\zeta_t$$\n", "\n", "The components are determined by minimizing the following quadratic loss function\n", "\n", "$$\\min_{\\\\{ \\tau_{t}\\\\} }\\sum_{t}^{T}\\zeta_{t}^{2}+\\lambda\\sum_{t=1}^{T}\\left[\\left(\\tau_{t}-\\tau_{t-1}\\right)-\\left(\\tau_{t-1}-\\tau_{t-2}\\right)\\right]^{2}$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "gdp_cycle, gdp_trend = sm.tsa.filters.hpfilter(dta.realgdp)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "gdp_decomp = dta[['realgdp']].copy()\n", "gdp_decomp[\"cycle\"] = gdp_cycle\n", "gdp_decomp[\"trend\"] = gdp_trend" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "gdp_decomp[[\"realgdp\", \"trend\"]][\"2000-03-31\":].plot(ax=ax, fontsize=16);\n", "legend = ax.get_legend()\n", "legend.prop.set_size(20);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Baxter-King approximate band-pass filter: Inflation and Unemployment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Explore the hypothesis that inflation and unemployment are counter-cyclical." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Baxter-King filter is intended to explicitly deal with the periodicity of the business cycle. By applying their band-pass filter to a series, they produce a new series that does not contain fluctuations at higher or lower than those of the business cycle. Specifically, the BK filter takes the form of a symmetric moving average \n", "\n", "$$y_{t}^{*}=\\sum_{k=-K}^{k=K}a_ky_{t-k}$$\n", "\n", "where $a_{-k}=a_k$ and $\\sum_{k=-k}^{K}a_k=0$ to eliminate any trend in the series and render it stationary if the series is I(1) or I(2).\n", "\n", "For completeness, the filter weights are determined as follows\n", "\n", "$$a_{j} = B_{j}+\\theta\\text{ for }j=0,\\pm1,\\pm2,\\dots,\\pm K$$\n", "\n", "$$B_{0} = \\frac{\\left(\\omega_{2}-\\omega_{1}\\right)}{\\pi}$$\n", "$$B_{j} = \\frac{1}{\\pi j}\\left(\\sin\\left(\\omega_{2}j\\right)-\\sin\\left(\\omega_{1}j\\right)\\right)\\text{ for }j=0,\\pm1,\\pm2,\\dots,\\pm K$$\n", "\n", "where $\\theta$ is a normalizing constant such that the weights sum to zero.\n", "\n", "$$\\theta=\\frac{-\\sum_{j=-K^{K}b_{j}}}{2K+1}$$\n", "\n", "$$\\omega_{1}=\\frac{2\\pi}{P_{H}}$$\n", "\n", "$$\\omega_{2}=\\frac{2\\pi}{P_{L}}$$\n", "\n", "$P_L$ and $P_H$ are the periodicity of the low and high cut-off frequencies. Following Burns and Mitchell's work on US business cycles which suggests cycles last from 1.5 to 8 years, we use $P_L=6$ and $P_H=32$ by default." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "bk_cycles = sm.tsa.filters.bkfilter(dta[[\"infl\",\"unemp\"]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* We lose K observations on both ends. It is suggested to use K=12 for quarterly data." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(12,10))\n", "ax = fig.add_subplot(111)\n", "bk_cycles.plot(ax=ax, style=['r--', 'b-']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Christiano-Fitzgerald approximate band-pass filter: Inflation and Unemployment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Christiano-Fitzgerald filter is a generalization of BK and can thus also be seen as weighted moving average. However, the CF filter is asymmetric about $t$ as well as using the entire series. The implementation of their filter involves the\n", "calculations of the weights in\n", "\n", "$$y_{t}^{*}=B_{0}y_{t}+B_{1}y_{t+1}+\\dots+B_{T-1-t}y_{T-1}+\\tilde B_{T-t}y_{T}+B_{1}y_{t-1}+\\dots+B_{t-2}y_{2}+\\tilde B_{t-1}y_{1}$$\n", "\n", "for $t=3,4,...,T-2$, where\n", "\n", "$$B_{j} = \\frac{\\sin(jb)-\\sin(ja)}{\\pi j},j\\geq1$$\n", "\n", "$$B_{0} = \\frac{b-a}{\\pi},a=\\frac{2\\pi}{P_{u}},b=\\frac{2\\pi}{P_{L}}$$\n", "\n", "$\\tilde B_{T-t}$ and $\\tilde B_{t-1}$ are linear functions of the $B_{j}$'s, and the values for $t=1,2,T-1,$ and $T$ are also calculated in much the same way. $P_{U}$ and $P_{L}$ are as described above with the same interpretation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The CF filter is appropriate for series that may follow a random walk." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(sm.tsa.stattools.adfuller(dta['unemp'])[:3])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(sm.tsa.stattools.adfuller(dta['infl'])[:3])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "cf_cycles, cf_trend = sm.tsa.filters.cffilter(dta[[\"infl\",\"unemp\"]])\n", "print(cf_cycles.head(10))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(14,10))\n", "ax = fig.add_subplot(111)\n", "cf_cycles.plot(ax=ax, style=['r--','b-']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Filtering assumes *a priori* that business cycles exist. Due to this assumption, many macroeconomic models seek to create models that match the shape of impulse response functions rather than replicating properties of filtered series. See VAR notebook." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 } statsmodels-0.12.2/examples/notebooks/variance_components.ipynb000066400000000000000000000246671400612667500251050ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Variance Component Analysis\n", "\n", "This notebook illustrates variance components analysis for two-level\n", "nested and crossed designs." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import statsmodels.api as sm\n", "from statsmodels.regression.mixed_linear_model import VCSpec\n", "import pandas as pd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make the notebook reproducible" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_next_cell": 1 }, "outputs": [], "source": [ "np.random.seed(3123)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Nested analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In our discussion below, \"Group 2\" is nested within \"Group 1\". As a\n", "concrete example, \"Group 1\" might be school districts, with \"Group\n", "2\" being individual schools. The function below generates data from\n", "such a population. In a nested analysis, the group 2 labels that\n", "are nested within different group 1 labels are treated as\n", "independent groups, even if they have the same label. For example,\n", "two schools labeled \"school 1\" that are in two different school\n", "districts are treated as independent schools, even though they have\n", "the same label." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_end_of_cell_marker": 0, "lines_to_next_cell": 1 }, "outputs": [], "source": [ "def generate_nested(n_group1=200, n_group2=20, n_rep=10, group1_sd=2,\n", " group2_sd=3, unexplained_sd=4):\n", "\n", " # Group 1 indicators\n", " group1 = np.kron(np.arange(n_group1), np.ones(n_group2 * n_rep))\n", "\n", " # Group 1 effects\n", " u = group1_sd * np.random.normal(size=n_group1)\n", " effects1 = np.kron(u, np.ones(n_group2 * n_rep))\n", "\n", " # Group 2 indicators\n", " group2 = np.kron(np.ones(n_group1), np.kron(np.arange(n_group2), np.ones(n_rep)))\n", "\n", " # Group 2 effects\n", " u = group2_sd * np.random.normal(size=n_group1*n_group2)\n", " effects2 = np.kron(u, np.ones(n_rep))\n", "\n", " e = unexplained_sd * np.random.normal(size=n_group1 * n_group2 * n_rep)\n", " y = effects1 + effects2 + e\n", "\n", " df = pd.DataFrame({\"y\":y, \"group1\": group1, \"group2\": group2})\n", "\n", " return df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate a data set to analyze." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "df = generate_nested()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using all the default arguments for `generate_nested`, the population\n", "values of \"group 1 Var\" and \"group 2 Var\" are 2^2=4 and 3^2=9,\n", "respectively. The unexplained variance, listed as \"scale\" at the\n", "top of the summary table, has population value 4^2=16." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_end_of_cell_marker": 0, "lines_to_next_cell": 1 }, "outputs": [], "source": [ "model1 = sm.MixedLM.from_formula(\"y ~ 1\", re_formula=\"1\", vc_formula={\"group2\": \"0 + C(group2)\"},\n", " groups=\"group1\", data=df)\n", "result1 = model1.fit()\n", "print(result1.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we wish to avoid the formula interface, we can fit the same model\n", "by building the design matrices manually." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_end_of_cell_marker": 0, "lines_to_next_cell": 1 }, "outputs": [], "source": [ "def f(x):\n", " n = x.shape[0]\n", " g2 = x.group2\n", " u = g2.unique()\n", " u.sort()\n", " uv = {v: k for k, v in enumerate(u)}\n", " mat = np.zeros((n, len(u)))\n", " for i in range(n):\n", " mat[i, uv[g2.iloc[i]]] = 1\n", " colnames = [\"%d\" % z for z in u]\n", " return mat, colnames" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we set up the variance components using the VCSpec class." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "vcm = df.groupby(\"group1\").apply(f).to_list()\n", "mats = [x[0] for x in vcm]\n", "colnames = [x[1] for x in vcm]\n", "names = [\"group2\"]\n", "vcs = VCSpec(names, [colnames], [mats])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we fit the model. It can be seen that the results of the\n", "two fits are identical." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_end_of_cell_marker": 0, "lines_to_next_cell": 1 }, "outputs": [], "source": [ "oo = np.ones(df.shape[0])\n", "model2 = sm.MixedLM(df.y, oo, exog_re=oo, groups=df.group1, exog_vc=vcs)\n", "result2 = model2.fit()\n", "print(result2.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Crossed analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In a crossed analysis, the levels of one group can occur in any\n", "combination with the levels of the another group. The groups in\n", "Statsmodels MixedLM are always nested, but it is possible to fit a\n", "crossed model by having only one group, and specifying all random\n", "effects as variance components. Many, but not all crossed models\n", "can be fit in this way. The function below generates a crossed data\n", "set with two levels of random structure." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_end_of_cell_marker": 0, "lines_to_next_cell": 1 }, "outputs": [], "source": [ "def generate_crossed(n_group1=100, n_group2=100, n_rep=4, group1_sd=2,\n", " group2_sd=3, unexplained_sd=4):\n", "\n", " # Group 1 indicators\n", " group1 = np.kron(np.arange(n_group1, dtype=np.int),\n", " np.ones(n_group2 * n_rep, dtype=np.int))\n", " group1 = group1[np.random.permutation(len(group1))]\n", "\n", " # Group 1 effects\n", " u = group1_sd * np.random.normal(size=n_group1)\n", " effects1 = u[group1]\n", "\n", " # Group 2 indicators\n", " group2 = np.kron(np.arange(n_group2, dtype=np.int),\n", " np.ones(n_group2 * n_rep, dtype=np.int))\n", " group2 = group2[np.random.permutation(len(group2))]\n", "\n", " # Group 2 effects\n", " u = group2_sd * np.random.normal(size=n_group2)\n", " effects2 = u[group2]\n", "\n", " e = unexplained_sd * np.random.normal(size=n_group1 * n_group2 * n_rep)\n", " y = effects1 + effects2 + e\n", "\n", " df = pd.DataFrame({\"y\":y, \"group1\": group1, \"group2\": group2})\n", "\n", " return df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate a data set to analyze." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "df = generate_crossed()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we fit the model, note that the `groups` vector is constant.\n", "Using the default parameters for `generate_crossed`, the level 1\n", "variance should be 2^2=4, the level 2 variance should be 3^2=9, and\n", "the unexplained variance should be 4^2=16." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "lines_to_end_of_cell_marker": 0, "lines_to_next_cell": 1 }, "outputs": [], "source": [ "vc = {\"g1\": \"0 + C(group1)\", \"g2\": \"0 + C(group2)\"}\n", "oo = np.ones(df.shape[0])\n", "model3 = sm.MixedLM.from_formula(\"y ~ 1\", groups=oo, vc_formula=vc, data=df)\n", "result3 = model3.fit()\n", "print(result3.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we wish to avoid the formula interface, we can fit the same model\n", "by building the design matrices manually." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def f(g):\n", " n = len(g)\n", " u = g.unique()\n", " u.sort()\n", " uv = {v: k for k, v in enumerate(u)}\n", " mat = np.zeros((n, len(u)))\n", " for i in range(n):\n", " mat[i, uv[g.iloc[i]]] = 1\n", " colnames = [\"%d\" % z for z in u]\n", " return [mat], [colnames]\n", "\n", "vcm = [f(df.group1), f(df.group2)]\n", "print(vcm)\n", "mats = [x[0] for x in vcm]\n", "colnames = [x[1] for x in vcm]\n", "names = [\"group1\", \"group2\"]\n", "vcs = VCSpec(names, colnames, mats)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we fit the model without using formulas, it is simple to check\n", "that the results for models 3 and 4 are identical." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "oo = np.ones(df.shape[0])\n", "model4 = sm.MixedLM(df.y, oo[:, None], exog_re=None, groups=oo, exog_vc=vcs)\n", "result4 = model4.fit()\n", "print(result4.summary())" ] } ], "metadata": { "jupytext": { "cell_metadata_filter": "-all", "main_language": "python", "notebook_metadata_filter": "-all" }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 2 } statsmodels-0.12.2/examples/notebooks/wls.ipynb000066400000000000000000000132621400612667500216420ustar00rootroot00000000000000{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Weighted Least Squares" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy import stats\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "from statsmodels.sandbox.regression.predstd import wls_prediction_std\n", "from statsmodels.iolib.table import (SimpleTable, default_txt_fmt)\n", "np.random.seed(1024)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## WLS Estimation\n", "\n", "### Artificial data: Heteroscedasticity 2 groups \n", "\n", "Model assumptions:\n", "\n", " * Misspecification: true model is quadratic, estimate only linear\n", " * Independent noise/error term\n", " * Two groups for error variance, low and high variance groups" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "nsample = 50\n", "x = np.linspace(0, 20, nsample)\n", "X = np.column_stack((x, (x - 5)**2))\n", "X = sm.add_constant(X)\n", "beta = [5., 0.5, -0.01]\n", "sig = 0.5\n", "w = np.ones(nsample)\n", "w[nsample * 6//10:] = 3\n", "y_true = np.dot(X, beta)\n", "e = np.random.normal(size=nsample)\n", "y = y_true + sig * w * e \n", "X = X[:,[0,1]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### WLS knowing the true variance ratio of heteroscedasticity\n", "\n", "In this example, `w` is the standard deviation of the error. `WLS` requires that the weights are proportional to the inverse of the error variance." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "mod_wls = sm.WLS(y, X, weights=1./(w ** 2))\n", "res_wls = mod_wls.fit()\n", "print(res_wls.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## OLS vs. WLS\n", "\n", "Estimate an OLS model for comparison: " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "res_ols = sm.OLS(y, X).fit()\n", "print(res_ols.params)\n", "print(res_wls.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare the WLS standard errors to heteroscedasticity corrected OLS standard errors:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "se = np.vstack([[res_wls.bse], [res_ols.bse], [res_ols.HC0_se], \n", " [res_ols.HC1_se], [res_ols.HC2_se], [res_ols.HC3_se]])\n", "se = np.round(se,4)\n", "colnames = ['x1', 'const']\n", "rownames = ['WLS', 'OLS', 'OLS_HC0', 'OLS_HC1', 'OLS_HC3', 'OLS_HC3']\n", "tabl = SimpleTable(se, colnames, rownames, txt_fmt=default_txt_fmt)\n", "print(tabl)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculate OLS prediction interval:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "covb = res_ols.cov_params()\n", "prediction_var = res_ols.mse_resid + (X * np.dot(covb,X.T).T).sum(1)\n", "prediction_std = np.sqrt(prediction_var)\n", "tppf = stats.t.ppf(0.975, res_ols.df_resid)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "prstd_ols, iv_l_ols, iv_u_ols = wls_prediction_std(res_ols)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Draw a plot to compare predicted values in WLS and OLS:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "prstd, iv_l, iv_u = wls_prediction_std(res_wls)\n", "\n", "fig, ax = plt.subplots(figsize=(8,6))\n", "ax.plot(x, y, 'o', label=\"Data\")\n", "ax.plot(x, y_true, 'b-', label=\"True\")\n", "# OLS\n", "ax.plot(x, res_ols.fittedvalues, 'r--')\n", "ax.plot(x, iv_u_ols, 'r--', label=\"OLS\")\n", "ax.plot(x, iv_l_ols, 'r--')\n", "# WLS\n", "ax.plot(x, res_wls.fittedvalues, 'g--.')\n", "ax.plot(x, iv_u, 'g--', label=\"WLS\")\n", "ax.plot(x, iv_l, 'g--')\n", "ax.legend(loc=\"best\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Feasible Weighted Least Squares (2-stage FWLS)\n", "\n", "Like `w`, `w_est` is proportional to the standard deviation, and so must be squared." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "resid1 = res_ols.resid[w==1.]\n", "var1 = resid1.var(ddof=int(res_ols.df_model)+1)\n", "resid2 = res_ols.resid[w!=1.]\n", "var2 = resid2.var(ddof=int(res_ols.df_model)+1)\n", "w_est = w.copy()\n", "w_est[w!=1.] = np.sqrt(var2) / np.sqrt(var1)\n", "res_fwls = sm.WLS(y, X, 1./((w_est ** 2))).fit()\n", "print(res_fwls.summary())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 }statsmodels-0.12.2/examples/python/000077500000000000000000000000001400612667500173045ustar00rootroot00000000000000statsmodels-0.12.2/examples/python/categorical_interaction_plot.py000066400000000000000000000020361400612667500255710ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook categorical_interaction_plot.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Plot Interaction of Categorical Factors # In this example, we will visualize the interaction between categorical # factors. First, we will create some categorical data are initialized. Then # plotted using the interaction_plot function which internally re-codes the # x-factor categories to integers. import numpy as np import matplotlib.pyplot as plt import pandas as pd from statsmodels.graphics.factorplots import interaction_plot np.random.seed(12345) weight = pd.Series(np.repeat(['low', 'hi', 'low', 'hi'], 15), name='weight') nutrition = pd.Series(np.repeat(['lo_carb', 'hi_carb'], 30), name='nutrition') days = np.log(np.random.randint(1, 30, size=60)) fig, ax = plt.subplots(figsize=(6, 6)) fig = interaction_plot( x=weight, trace=nutrition, response=days, colors=['red', 'blue'], markers=['D', '^'], ms=10, ax=ax) statsmodels-0.12.2/examples/python/chi2_fitting.py000066400000000000000000000102211400612667500222230ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook chi2_fitting.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Least squares fitting of models to data # This is a quick introduction to `statsmodels` for physical scientists # (e.g. physicists, astronomers) or engineers. # # Why is this needed? # # Because most of `statsmodels` was written by statisticians and they use # a different terminology and sometimes methods, making it hard to know # which classes and functions are relevant and what their inputs and outputs # mean. import numpy as np import pandas as pd import statsmodels.api as sm # ## Linear models # Assume you have data points with measurements `y` at positions `x` as # well as measurement errors `y_err`. # # How can you use `statsmodels` to fit a straight line model to this data? # # For an extensive discussion see [Hogg et al. (2010), "Data analysis # recipes: Fitting a model to data"](https://arxiv.org/abs/1008.4686) ... # we'll use the example data given by them in Table 1. # # So the model is `f(x) = a * x + b` and on Figure 1 they print the result # we want to reproduce ... the best-fit parameter and the parameter errors # for a "standard weighted least-squares fit" for this data are: # * `a = 2.24 +- 0.11` # * `b = 34 +- 18` data = """ x y y_err 201 592 61 244 401 25 47 583 38 287 402 15 203 495 21 58 173 15 210 479 27 202 504 14 198 510 30 158 416 16 165 393 14 201 442 25 157 317 52 131 311 16 166 400 34 160 337 31 186 423 42 125 334 26 218 533 16 146 344 22 """ try: from StringIO import StringIO except ImportError: from io import StringIO data = pd.read_csv(StringIO(data), delim_whitespace=True).astype(float) # Note: for the results we compare with the paper here, they drop the # first four points data.head() # To fit a straight line use the weighted least squares class [WLS](https: # //www.statsmodels.org/devel/generated/statsmodels.regression.linear_model. # WLS.html) ... the parameters are called: # * `exog` = `sm.add_constant(x)` # * `endog` = `y` # * `weights` = `1 / sqrt(y_err)` # # Note that `exog` must be a 2-dimensional array with `x` as a column and # an extra column of ones. Adding this column of ones means you want to fit # the model `y = a * x + b`, leaving it off means you want to fit the model # `y = a * x`. # # And you have to use the option `cov_type='fixed scale'` to tell # `statsmodels` that you really have measurement errors with an absolute # scale. If you do not, `statsmodels` will treat the weights as relative # weights between the data points and internally re-scale them so that the # best-fit model will have `chi**2 / ndf = 1`. exog = sm.add_constant(data['x']) endog = data['y'] weights = 1. / (data['y_err']**2) wls = sm.WLS(endog, exog, weights) results = wls.fit(cov_type='fixed scale') print(results.summary()) # ### Check against scipy.optimize.curve_fit # You can use `scipy.optimize.curve_fit` to get the best-fit parameters # and parameter errors. from scipy.optimize import curve_fit def f(x, a, b): return a * x + b xdata = data['x'] ydata = data['y'] p0 = [0, 0] # initial parameter estimate sigma = data['y_err'] popt, pcov = curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma=True) perr = np.sqrt(np.diag(pcov)) print('a = {0:10.3f} +- {1:10.3f}'.format(popt[0], perr[0])) print('b = {0:10.3f} +- {1:10.3f}'.format(popt[1], perr[1])) # ### Check against self-written cost function # You can also use `scipy.optimize.minimize` and write your own cost # function. # This does not give you the parameter errors though ... you'd have # to estimate the HESSE matrix separately ... from scipy.optimize import minimize def chi2(pars): """Cost function. """ y_model = pars[0] * data['x'] + pars[1] chi = (data['y'] - y_model) / data['y_err'] return np.sum(chi**2) result = minimize(fun=chi2, x0=[0, 0]) popt = result.x print('a = {0:10.3f}'.format(popt[0])) print('b = {0:10.3f}'.format(popt[1])) # ## Non-linear models # TODO: we could use the examples from here: # http://probfit.readthedocs.org/en/latest/api.html#probfit.costfunc.Chi2R # egression statsmodels-0.12.2/examples/python/contrasts.py000066400000000000000000000214741400612667500217060ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook contrasts.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Contrasts Overview import numpy as np import statsmodels.api as sm # This document is based heavily on this excellent resource from UCLA # http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm # A categorical variable of K categories, or levels, usually enters a # regression as a sequence of K-1 dummy variables. This amounts to a linear # hypothesis on the level means. That is, each test statistic for these # variables amounts to testing whether the mean for that level is # statistically significantly different from the mean of the base category. # This dummy coding is called Treatment coding in R parlance, and we will # follow this convention. There are, however, different coding methods that # amount to different sets of linear hypotheses. # # In fact, the dummy coding is not technically a contrast coding. This is # because the dummy variables add to one and are not functionally # independent of the model's intercept. On the other hand, a set of # *contrasts* for a categorical variable with `k` levels is a set of `k-1` # functionally independent linear combinations of the factor level means # that are also independent of the sum of the dummy variables. The dummy # coding is not wrong *per se*. It captures all of the coefficients, but it # complicates matters when the model assumes independence of the # coefficients such as in ANOVA. Linear regression models do not assume # independence of the coefficients and thus dummy coding is often the only # coding that is taught in this context. # # To have a look at the contrast matrices in Patsy, we will use data from # UCLA ATS. First let's load the data. # #### Example Data import pandas as pd url = 'https://stats.idre.ucla.edu/stat/data/hsb2.csv' hsb2 = pd.read_table(url, delimiter=",") hsb2.head(10) # It will be instructive to look at the mean of the dependent variable, # write, for each level of race ((1 = Hispanic, 2 = Asian, 3 = African # American and 4 = Caucasian)). hsb2.groupby('race')['write'].mean() # #### Treatment (Dummy) Coding # Dummy coding is likely the most well known coding scheme. It compares # each level of the categorical variable to a base reference level. The base # reference level is the value of the intercept. It is the default contrast # in Patsy for unordered categorical factors. The Treatment contrast matrix # for race would be from patsy.contrasts import Treatment levels = [1, 2, 3, 4] contrast = Treatment(reference=0).code_without_intercept(levels) print(contrast.matrix) # Here we used `reference=0`, which implies that the first level, # Hispanic, is the reference category against which the other level effects # are measured. As mentioned above, the columns do not sum to zero and are # thus not independent of the intercept. To be explicit, let's look at how # this would encode the `race` variable. hsb2.race.head(10) print(contrast.matrix[hsb2.race - 1, :][:20]) sm.categorical(hsb2.race.values) # This is a bit of a trick, as the `race` category conveniently maps to # zero-based indices. If it does not, this conversion happens under the # hood, so this will not work in general but nonetheless is a useful exercise # to fix ideas. The below illustrates the output using the three contrasts # above from statsmodels.formula.api import ols mod = ols("write ~ C(race, Treatment)", data=hsb2) res = mod.fit() print(res.summary()) # We explicitly gave the contrast for race; however, since Treatment is # the default, we could have omitted this. # ### Simple Coding # Like Treatment Coding, Simple Coding compares each level to a fixed # reference level. However, with simple coding, the intercept is the grand # mean of all the levels of the factors. Patsy does not have the Simple # contrast included, but you can easily define your own contrasts. To do so, # write a class that contains a code_with_intercept and a # code_without_intercept method that returns a patsy.contrast.ContrastMatrix # instance from patsy.contrasts import ContrastMatrix def _name_levels(prefix, levels): return ["[%s%s]" % (prefix, level) for level in levels] class Simple(object): def _simple_contrast(self, levels): nlevels = len(levels) contr = -1. / nlevels * np.ones((nlevels, nlevels - 1)) contr[1:][np.diag_indices(nlevels - 1)] = (nlevels - 1.) / nlevels return contr def code_with_intercept(self, levels): contrast = np.column_stack((np.ones(len(levels)), self._simple_contrast(levels))) return ContrastMatrix(contrast, _name_levels("Simp.", levels)) def code_without_intercept(self, levels): contrast = self._simple_contrast(levels) return ContrastMatrix(contrast, _name_levels("Simp.", levels[:-1])) hsb2.groupby('race')['write'].mean().mean() contrast = Simple().code_without_intercept(levels) print(contrast.matrix) mod = ols("write ~ C(race, Simple)", data=hsb2) res = mod.fit() print(res.summary()) # ### Sum (Deviation) Coding # Sum coding compares the mean of the dependent variable for a given level # to the overall mean of the dependent variable over all the levels. That # is, it uses contrasts between each of the first k-1 levels and level k In # this example, level 1 is compared to all the others, level 2 to all the # others, and level 3 to all the others. from patsy.contrasts import Sum contrast = Sum().code_without_intercept(levels) print(contrast.matrix) mod = ols("write ~ C(race, Sum)", data=hsb2) res = mod.fit() print(res.summary()) # This corresponds to a parameterization that forces all the coefficients # to sum to zero. Notice that the intercept here is the grand mean where the # grand mean is the mean of means of the dependent variable by each level. hsb2.groupby('race')['write'].mean().mean() # ### Backward Difference Coding # In backward difference coding, the mean of the dependent variable for a # level is compared with the mean of the dependent variable for the prior # level. This type of coding may be useful for a nominal or an ordinal # variable. from patsy.contrasts import Diff contrast = Diff().code_without_intercept(levels) print(contrast.matrix) mod = ols("write ~ C(race, Diff)", data=hsb2) res = mod.fit() print(res.summary()) # For example, here the coefficient on level 1 is the mean of `write` at # level 2 compared with the mean at level 1. Ie., res.params["C(race, Diff)[D.1]"] hsb2.groupby('race').mean()["write"][2] - hsb2.groupby( 'race').mean()["write"][1] # ### Helmert Coding # Our version of Helmert coding is sometimes referred to as Reverse # Helmert Coding. The mean of the dependent variable for a level is compared # to the mean of the dependent variable over all previous levels. Hence, the # name 'reverse' being sometimes applied to differentiate from forward # Helmert coding. This comparison does not make much sense for a nominal # variable such as race, but we would use the Helmert contrast like so: from patsy.contrasts import Helmert contrast = Helmert().code_without_intercept(levels) print(contrast.matrix) mod = ols("write ~ C(race, Helmert)", data=hsb2) res = mod.fit() print(res.summary()) # To illustrate, the comparison on level 4 is the mean of the dependent # variable at the previous three levels taken from the mean at level 4 grouped = hsb2.groupby('race') grouped.mean()["write"][4] - grouped.mean()["write"][:3].mean() # As you can see, these are only equal up to a constant. Other versions of # the Helmert contrast give the actual difference in means. Regardless, the # hypothesis tests are the same. k = 4 1. / k * (grouped.mean()["write"][k] - grouped.mean()["write"][:k - 1].mean()) k = 3 1. / k * (grouped.mean()["write"][k] - grouped.mean()["write"][:k - 1].mean()) # ### Orthogonal Polynomial Coding # The coefficients taken on by polynomial coding for `k=4` levels are the # linear, quadratic, and cubic trends in the categorical variable. The # categorical variable here is assumed to be represented by an underlying, # equally spaced numeric variable. Therefore, this type of encoding is used # only for ordered categorical variables with equal spacing. In general, the # polynomial contrast produces polynomials of order `k-1`. Since `race` is # not an ordered factor variable let's use `read` as an example. First we # need to create an ordered categorical from `read`. hsb2['readcat'] = np.asarray(pd.cut(hsb2.read, bins=3)) hsb2.groupby('readcat').mean()['write'] from patsy.contrasts import Poly levels = hsb2.readcat.unique().tolist() contrast = Poly().code_without_intercept(levels) print(contrast.matrix) mod = ols("write ~ C(readcat, Poly)", data=hsb2) res = mod.fit() print(res.summary()) # As you can see, readcat has a significant linear effect on the dependent # variable `write` but not a significant quadratic or cubic effect. statsmodels-0.12.2/examples/python/discrete_choice_example.py000066400000000000000000000137631400612667500245170ustar00rootroot00000000000000# DO NOT EDIT # Autogenerated from the notebook discrete_choice_example.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT #!/usr/bin/env python # coding: utf-8 # # Discrete Choice Models # ## Fair's Affair data # A survey of women only was conducted in 1974 by *Redbook* asking about # extramarital affairs. import numpy as np import pandas as pd from scipy import stats import matplotlib.pyplot as plt import statsmodels.api as sm from statsmodels.formula.api import logit print(sm.datasets.fair.SOURCE) print(sm.datasets.fair.NOTE) dta = sm.datasets.fair.load_pandas().data dta['affair'] = (dta['affairs'] > 0).astype(float) print(dta.head(10)) print(dta.describe()) affair_mod = logit( "affair ~ occupation + educ + occupation_husb" "+ rate_marriage + age + yrs_married + children" " + religious", dta).fit() print(affair_mod.summary()) # How well are we predicting? affair_mod.pred_table() # The coefficients of the discrete choice model do not tell us much. What # we're after is marginal effects. mfx = affair_mod.get_margeff() print(mfx.summary()) respondent1000 = dta.iloc[1000] print(respondent1000) resp = dict( zip( range(1, 9), respondent1000[[ "occupation", "educ", "occupation_husb", "rate_marriage", "age", "yrs_married", "children", "religious" ]].tolist())) resp.update({0: 1}) print(resp) mfx = affair_mod.get_margeff(atexog=resp) print(mfx.summary()) # `predict` expects a `DataFrame` since `patsy` is used to select columns. respondent1000 = dta.iloc[[1000]] affair_mod.predict(respondent1000) affair_mod.fittedvalues[1000] affair_mod.model.cdf(affair_mod.fittedvalues[1000]) # The "correct" model here is likely the Tobit model. We have an work in # progress branch "tobit-model" on github, if anyone is interested in # censored regression models. # ### Exercise: Logit vs Probit fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111) support = np.linspace(-6, 6, 1000) ax.plot(support, stats.logistic.cdf(support), 'r-', label='Logistic') ax.plot(support, stats.norm.cdf(support), label='Probit') ax.legend() fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111) support = np.linspace(-6, 6, 1000) ax.plot(support, stats.logistic.pdf(support), 'r-', label='Logistic') ax.plot(support, stats.norm.pdf(support), label='Probit') ax.legend() # Compare the estimates of the Logit Fair model above to a Probit model. # Does the prediction table look better? Much difference in marginal # effects? # ### Generalized Linear Model Example print(sm.datasets.star98.SOURCE) print(sm.datasets.star98.DESCRLONG) print(sm.datasets.star98.NOTE) dta = sm.datasets.star98.load_pandas().data print(dta.columns) print(dta[[ 'NABOVE', 'NBELOW', 'LOWINC', 'PERASIAN', 'PERBLACK', 'PERHISP', 'PERMINTE' ]].head(10)) print(dta[[ 'AVYRSEXP', 'AVSALK', 'PERSPENK', 'PTRATIO', 'PCTAF', 'PCTCHRT', 'PCTYRRND' ]].head(10)) formula = 'NABOVE + NBELOW ~ LOWINC + PERASIAN + PERBLACK + PERHISP + PCTCHRT ' formula += '+ PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF' # #### Aside: Binomial distribution # Toss a six-sided die 5 times, what's the probability of exactly 2 fours? stats.binom(5, 1. / 6).pmf(2) from scipy.special import comb comb(5, 2) * (1 / 6.)**2 * (5 / 6.)**3 from statsmodels.formula.api import glm glm_mod = glm(formula, dta, family=sm.families.Binomial()).fit() print(glm_mod.summary()) # The number of trials glm_mod.model.data.orig_endog.sum(1) glm_mod.fittedvalues * glm_mod.model.data.orig_endog.sum(1) # First differences: We hold all explanatory variables constant at their # means and manipulate the percentage of low income households to assess its # impact # on the response variables: exog = glm_mod.model.data.orig_exog # get the dataframe means25 = exog.mean() print(means25) means25['LOWINC'] = exog['LOWINC'].quantile(.25) print(means25) means75 = exog.mean() means75['LOWINC'] = exog['LOWINC'].quantile(.75) print(means75) # Again, `predict` expects a `DataFrame` since `patsy` is used to select # columns. resp25 = glm_mod.predict(pd.DataFrame(means25).T) resp75 = glm_mod.predict(pd.DataFrame(means75).T) diff = resp75 - resp25 # The interquartile first difference for the percentage of low income # households in a school district is: print("%2.4f%%" % (diff[0] * 100)) nobs = glm_mod.nobs y = glm_mod.model.endog yhat = glm_mod.mu from statsmodels.graphics.api import abline_plot fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111, ylabel='Observed Values', xlabel='Fitted Values') ax.scatter(yhat, y) y_vs_yhat = sm.OLS(y, sm.add_constant(yhat, prepend=True)).fit() fig = abline_plot(model_results=y_vs_yhat, ax=ax) # #### Plot fitted values vs Pearson residuals # Pearson residuals are defined to be # # $$\frac{(y - \mu)}{\sqrt{(var(\mu))}}$$ # # where var is typically determined by the family. E.g., binomial variance # is $np(1 - p)$ fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111, title='Residual Dependence Plot', xlabel='Fitted Values', ylabel='Pearson Residuals') ax.scatter(yhat, stats.zscore(glm_mod.resid_pearson)) ax.axis('tight') ax.plot([0.0, 1.0], [0.0, 0.0], 'k-') # #### Histogram of standardized deviance residuals with Kernel Density # Estimate overlaid # The definition of the deviance residuals depends on the family. For the # Binomial distribution this is # # $$r_{dev} = sign\left(Y-\mu\right)*\sqrt{2n(Y\log\frac{Y}{\mu}+(1-Y)\log # \frac{(1-Y)}{(1-\mu)}}$$ # # They can be used to detect ill-fitting covariates resid = glm_mod.resid_deviance resid_std = stats.zscore(resid) kde_resid = sm.nonparametric.KDEUnivariate(resid_std) kde_resid.fit() fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111, title="Standardized Deviance Residuals") ax.hist(resid_std, bins=25, density=True) ax.plot(kde_resid.support, kde_resid.density, 'r') # #### QQ-plot of deviance residuals fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111) fig = sm.graphics.qqplot(resid, line='r', ax=ax) statsmodels-0.12.2/examples/python/discrete_choice_overview.py000066400000000000000000000053121400612667500247210ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook discrete_choice_overview.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Discrete Choice Models Overview import numpy as np import statsmodels.api as sm # ## Data # # Load data from Spector and Mazzeo (1980). Examples follow Greene's # Econometric Analysis Ch. 21 (5th Edition). spector_data = sm.datasets.spector.load() spector_data.exog = sm.add_constant(spector_data.exog, prepend=False) # Inspect the data: print(spector_data.exog[:5, :]) print(spector_data.endog[:5]) # ## Linear Probability Model (OLS) lpm_mod = sm.OLS(spector_data.endog, spector_data.exog) lpm_res = lpm_mod.fit() print('Parameters: ', lpm_res.params[:-1]) # ## Logit Model logit_mod = sm.Logit(spector_data.endog, spector_data.exog) logit_res = logit_mod.fit(disp=0) print('Parameters: ', logit_res.params) # Marginal Effects margeff = logit_res.get_margeff() print(margeff.summary()) # As in all the discrete data models presented below, we can print a nice # summary of results: print(logit_res.summary()) # ## Probit Model probit_mod = sm.Probit(spector_data.endog, spector_data.exog) probit_res = probit_mod.fit() probit_margeff = probit_res.get_margeff() print('Parameters: ', probit_res.params) print('Marginal effects: ') print(probit_margeff.summary()) # ## Multinomial Logit # Load data from the American National Election Studies: anes_data = sm.datasets.anes96.load() anes_exog = anes_data.exog anes_exog = sm.add_constant(anes_exog, prepend=False) # Inspect the data: print(anes_data.exog[:5, :]) print(anes_data.endog[:5]) # Fit MNL model: mlogit_mod = sm.MNLogit(anes_data.endog, anes_exog) mlogit_res = mlogit_mod.fit() print(mlogit_res.params) # ## Poisson # # Load the Rand data. Note that this example is similar to Cameron and # Trivedi's `Microeconometrics` Table 20.5, but it is slightly different # because of minor changes in the data. rand_data = sm.datasets.randhie.load() rand_exog = rand_data.exog.view(float).reshape(len(rand_data.exog), -1) rand_exog = sm.add_constant(rand_exog, prepend=False) # Fit Poisson model: poisson_mod = sm.Poisson(rand_data.endog, rand_exog) poisson_res = poisson_mod.fit(method="newton") print(poisson_res.summary()) # ## Negative Binomial # # The negative binomial model gives slightly different results. mod_nbin = sm.NegativeBinomial(rand_data.endog, rand_exog) res_nbin = mod_nbin.fit(disp=False) print(res_nbin.summary()) # ## Alternative solvers # # The default method for fitting discrete data MLE models is Newton- # Raphson. You can use other solvers by using the ``method`` argument: mlogit_res = mlogit_mod.fit(method='bfgs', maxiter=100) print(mlogit_res.summary()) statsmodels-0.12.2/examples/python/distributed_estimation.py000066400000000000000000000057261400612667500244460ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook distributed_estimation.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # This notebook goes through a couple of examples to show how to use # `distributed_estimation`. We import the `DistributedModel` class and make # the exog and endog generators. import numpy as np from scipy.stats.distributions import norm from statsmodels.base.distributed_estimation import DistributedModel def _exog_gen(exog, partitions): """partitions exog data""" n_exog = exog.shape[0] n_part = np.ceil(n_exog / partitions) ii = 0 while ii < n_exog: jj = int(min(ii + n_part, n_exog)) yield exog[ii:jj, :] ii += int(n_part) def _endog_gen(endog, partitions): """partitions endog data""" n_endog = endog.shape[0] n_part = np.ceil(n_endog / partitions) ii = 0 while ii < n_endog: jj = int(min(ii + n_part, n_endog)) yield endog[ii:jj] ii += int(n_part) # Next we generate some random data to serve as an example. X = np.random.normal(size=(1000, 25)) beta = np.random.normal(size=25) beta *= np.random.randint(0, 2, size=25) y = norm.rvs(loc=X.dot(beta)) m = 5 # This is the most basic fit, showing all of the defaults, which are to # use OLS as the model class, and the debiasing procedure. debiased_OLS_mod = DistributedModel(m) debiased_OLS_fit = debiased_OLS_mod.fit( zip(_endog_gen(y, m), _exog_gen(X, m)), fit_kwds={"alpha": 0.2}) # Then we run through a slightly more complicated example which uses the # GLM model class. from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod.families import Gaussian debiased_GLM_mod = DistributedModel( m, model_class=GLM, init_kwds={"family": Gaussian()}) debiased_GLM_fit = debiased_GLM_mod.fit( zip(_endog_gen(y, m), _exog_gen(X, m)), fit_kwds={"alpha": 0.2}) # We can also change the `estimation_method` and the `join_method`. The # below example show how this works for the standard OLS case. Here we # using a naive averaging approach instead of the debiasing procedure. from statsmodels.base.distributed_estimation import _est_regularized_naive, _join_naive naive_OLS_reg_mod = DistributedModel( m, estimation_method=_est_regularized_naive, join_method=_join_naive) naive_OLS_reg_params = naive_OLS_reg_mod.fit( zip(_endog_gen(y, m), _exog_gen(X, m)), fit_kwds={"alpha": 0.2}) # Finally, we can also change the `results_class` used. The following # example shows how this work for a simple case with an unregularized model # and naive averaging. from statsmodels.base.distributed_estimation import _est_unregularized_naive, DistributedResults naive_OLS_unreg_mod = DistributedModel( m, estimation_method=_est_unregularized_naive, join_method=_join_naive, results_class=DistributedResults) naive_OLS_unreg_params = naive_OLS_unreg_mod.fit( zip(_endog_gen(y, m), _exog_gen(X, m)), fit_kwds={"alpha": 0.2}) statsmodels-0.12.2/examples/python/exponential_smoothing.py000066400000000000000000000305361400612667500243020ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook exponential_smoothing.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Tutorial # # Let us consider chapter 7 of the excellent treatise on the subject of # Exponential Smoothing By Hyndman and Athanasopoulos [1]. # We will work through all the examples in the chapter as they unfold. # # [1] [Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles # and practice. OTexts, 2014.](https://www.otexts.org/fpp/7) # # Exponential smoothing # # First we load some data. We have included the R data in the notebook for # expedience. import os import numpy as np import pandas as pd import matplotlib.pyplot as plt from statsmodels.tsa.api import ExponentialSmoothing, SimpleExpSmoothing, Holt data = [ 446.6565, 454.4733, 455.663, 423.6322, 456.2713, 440.5881, 425.3325, 485.1494, 506.0482, 526.792, 514.2689, 494.211 ] index = pd.DatetimeIndex(start='1996', end='2008', freq='A') oildata = pd.Series(data, index) oildata.index = pd.DatetimeIndex( oildata.index, freq=pd.infer_freq(oildata.index)) data = [ 17.5534, 21.86, 23.8866, 26.9293, 26.8885, 28.8314, 30.0751, 30.9535, 30.1857, 31.5797, 32.5776, 33.4774, 39.0216, 41.3864, 41.5966 ] index = pd.DatetimeIndex(start='1990', end='2005', freq='A') air = pd.Series(data, index) air.index = pd.DatetimeIndex(air.index, freq=pd.infer_freq(air.index)) data = [ 263.9177, 268.3072, 260.6626, 266.6394, 277.5158, 283.834, 290.309, 292.4742, 300.8307, 309.2867, 318.3311, 329.3724, 338.884, 339.2441, 328.6006, 314.2554, 314.4597, 321.4138, 329.7893, 346.3852, 352.2979, 348.3705, 417.5629, 417.1236, 417.7495, 412.2339, 411.9468, 394.6971, 401.4993, 408.2705, 414.2428 ] index = pd.DatetimeIndex(start='1970', end='2001', freq='A') livestock2 = pd.Series(data, index) livestock2.index = pd.DatetimeIndex( livestock2.index, freq=pd.infer_freq(livestock2.index)) data = [407.9979, 403.4608, 413.8249, 428.105, 445.3387, 452.9942, 455.7402] index = pd.DatetimeIndex(start='2001', end='2008', freq='A') livestock3 = pd.Series(data, index) livestock3.index = pd.DatetimeIndex( livestock3.index, freq=pd.infer_freq(livestock3.index)) data = [ 41.7275, 24.0418, 32.3281, 37.3287, 46.2132, 29.3463, 36.4829, 42.9777, 48.9015, 31.1802, 37.7179, 40.4202, 51.2069, 31.8872, 40.9783, 43.7725, 55.5586, 33.8509, 42.0764, 45.6423, 59.7668, 35.1919, 44.3197, 47.9137 ] index = pd.DatetimeIndex(start='2005', end='2010-Q4', freq='QS') aust = pd.Series(data, index) aust.index = pd.DatetimeIndex(aust.index, freq=pd.infer_freq(aust.index)) # ## Simple Exponential Smoothing # Lets use Simple Exponential Smoothing to forecast the below oil data. ax = oildata.plot() ax.set_xlabel("Year") ax.set_ylabel("Oil (millions of tonnes)") plt.show() print("Figure 7.1: Oil production in Saudi Arabia from 1996 to 2007.") # Here we run three variants of simple exponential smoothing: # 1. In ```fit1``` we do not use the auto optimization but instead choose # to explicitly provide the model with the $\alpha=0.2$ parameter # 2. In ```fit2``` as above we choose an $\alpha=0.6$ # 3. In ```fit3``` we allow statsmodels to automatically find an optimized # $\alpha$ value for us. This is the recommended approach. fit1 = SimpleExpSmoothing(oildata).fit(smoothing_level=0.2, optimized=False) fcast1 = fit1.forecast(3).rename(r'$\alpha=0.2$') fit2 = SimpleExpSmoothing(oildata).fit(smoothing_level=0.6, optimized=False) fcast2 = fit2.forecast(3).rename(r'$\alpha=0.6$') fit3 = SimpleExpSmoothing(oildata).fit() fcast3 = fit3.forecast(3).rename( r'$\alpha=%s$' % fit3.model.params['smoothing_level']) ax = oildata.plot(marker='o', color='black', figsize=(12, 8)) fcast1.plot(marker='o', ax=ax, color='blue', legend=True) fit1.fittedvalues.plot(marker='o', ax=ax, color='blue') fcast2.plot(marker='o', ax=ax, color='red', legend=True) fit2.fittedvalues.plot(marker='o', ax=ax, color='red') fcast3.plot(marker='o', ax=ax, color='green', legend=True) fit3.fittedvalues.plot(marker='o', ax=ax, color='green') plt.show() # ## Holt's Method # # Lets take a look at another example. # This time we use air pollution data and the Holt's Method. # We will fit three examples again. # 1. In ```fit1``` we again choose not to use the optimizer and provide # explicit values for $\alpha=0.8$ and $\beta=0.2$ # 2. In ```fit2``` we do the same as in ```fit1``` but choose to use an # exponential model rather than a Holt's additive model. # 3. In ```fit3``` we used a damped versions of the Holt's additive model # but allow the dampening parameter $\phi$ to be optimized while fixing the # values for $\alpha=0.8$ and $\beta=0.2$ fit1 = Holt(air).fit(smoothing_level=0.8, smoothing_slope=0.2, optimized=False) fcast1 = fit1.forecast(5).rename("Holt's linear trend") fit2 = Holt( air, exponential=True).fit( smoothing_level=0.8, smoothing_slope=0.2, optimized=False) fcast2 = fit2.forecast(5).rename("Exponential trend") fit3 = Holt(air, damped=True).fit(smoothing_level=0.8, smoothing_slope=0.2) fcast3 = fit3.forecast(5).rename("Additive damped trend") ax = air.plot(color="black", marker="o", figsize=(12, 8)) fit1.fittedvalues.plot(ax=ax, color='blue') fcast1.plot(ax=ax, color='blue', marker="o", legend=True) fit2.fittedvalues.plot(ax=ax, color='red') fcast2.plot(ax=ax, color='red', marker="o", legend=True) fit3.fittedvalues.plot(ax=ax, color='green') fcast3.plot(ax=ax, color='green', marker="o", legend=True) plt.show() # ### Seasonally adjusted data # Lets look at some seasonally adjusted livestock data. We fit five Holt's # models. # The below table allows us to compare results when we use exponential # versus additive and damped versus non-damped. # # Note: ```fit4``` does not allow the parameter $\phi$ to be optimized by # providing a fixed value of $\phi=0.98$ fit1 = SimpleExpSmoothing(livestock2).fit() fit2 = Holt(livestock2).fit() fit3 = Holt(livestock2, exponential=True).fit() fit4 = Holt(livestock2, damped=True).fit(damping_slope=0.98) fit5 = Holt(livestock2, exponential=True, damped=True).fit() params = [ 'smoothing_level', 'smoothing_slope', 'damping_slope', 'initial_level', 'initial_slope' ] results = pd.DataFrame( index=[r"$\alpha$", r"$\beta$", r"$\phi$", r"$l_0$", "$b_0$", "SSE"], columns=['SES', "Holt's", "Exponential", "Additive", "Multiplicative"]) results["SES"] = [fit1.params[p] for p in params] + [fit1.sse] results["Holt's"] = [fit2.params[p] for p in params] + [fit2.sse] results["Exponential"] = [fit3.params[p] for p in params] + [fit3.sse] results["Additive"] = [fit4.params[p] for p in params] + [fit4.sse] results["Multiplicative"] = [fit5.params[p] for p in params] + [fit5.sse] results # ### Plots of Seasonally Adjusted Data # The following plots allow us to evaluate the level and slope/trend # components of the above table's fits. for fit in [fit2, fit4]: pd.DataFrame(np.c_[fit.level, fit.slope]).rename(columns={ 0: 'level', 1: 'slope' }).plot(subplots=True) plt.show() print( 'Figure 7.4: Level and slope components for Holt’s linear trend method and the additive damped trend method.' ) # ## Comparison # Here we plot a comparison Simple Exponential Smoothing and Holt's # Methods for various additive, exponential and damped combinations. All of # the models parameters will be optimized by statsmodels. fit1 = SimpleExpSmoothing(livestock2).fit() fcast1 = fit1.forecast(9).rename("SES") fit2 = Holt(livestock2).fit() fcast2 = fit2.forecast(9).rename("Holt's") fit3 = Holt(livestock2, exponential=True).fit() fcast3 = fit3.forecast(9).rename("Exponential") fit4 = Holt(livestock2, damped=True).fit(damping_slope=0.98) fcast4 = fit4.forecast(9).rename("Additive Damped") fit5 = Holt(livestock2, exponential=True, damped=True).fit() fcast5 = fit5.forecast(9).rename("Multiplicative Damped") ax = livestock2.plot(color="black", marker="o", figsize=(12, 8)) livestock3.plot(ax=ax, color="black", marker="o", legend=False) fcast1.plot(ax=ax, color='red', legend=True) fcast2.plot(ax=ax, color='green', legend=True) fcast3.plot(ax=ax, color='blue', legend=True) fcast4.plot(ax=ax, color='cyan', legend=True) fcast5.plot(ax=ax, color='magenta', legend=True) ax.set_ylabel('Livestock, sheep in Asia (millions)') plt.show() print( 'Figure 7.5: Forecasting livestock, sheep in Asia: comparing forecasting performance of non-seasonal methods.' ) # ## Holt's Winters Seasonal # Finally we are able to run full Holt's Winters Seasonal Exponential # Smoothing including a trend component and a seasonal component. # statsmodels allows for all the combinations including as shown in the # examples below: # 1. ```fit1``` additive trend, additive seasonal of period # ```season_length=4``` and the use of a Box-Cox transformation. # 1. ```fit2``` additive trend, multiplicative seasonal of period # ```season_length=4``` and the use of a Box-Cox transformation.. # 1. ```fit3``` additive damped trend, additive seasonal of period # ```season_length=4``` and the use of a Box-Cox transformation. # 1. ```fit4``` additive damped trend, multiplicative seasonal of period # ```season_length=4``` and the use of a Box-Cox transformation. # # The plot shows the results and forecast for ```fit1``` and ```fit2```. # The table allows us to compare the results and parameterizations. fit1 = ExponentialSmoothing( aust, seasonal_periods=4, trend='add', seasonal='add').fit(use_boxcox=True) fit2 = ExponentialSmoothing( aust, seasonal_periods=4, trend='add', seasonal='mul').fit(use_boxcox=True) fit3 = ExponentialSmoothing( aust, seasonal_periods=4, trend='add', seasonal='add', damped=True).fit(use_boxcox=True) fit4 = ExponentialSmoothing( aust, seasonal_periods=4, trend='add', seasonal='mul', damped=True).fit(use_boxcox=True) results = pd.DataFrame(index=[ r"$\alpha$", r"$\beta$", r"$\phi$", r"$\gamma$", r"$l_0$", "$b_0$", "SSE" ]) params = [ 'smoothing_level', 'smoothing_slope', 'damping_slope', 'smoothing_seasonal', 'initial_level', 'initial_slope' ] results["Additive"] = [fit1.params[p] for p in params] + [fit1.sse] results["Multiplicative"] = [fit2.params[p] for p in params] + [fit2.sse] results["Additive Dam"] = [fit3.params[p] for p in params] + [fit3.sse] results["Multiplica Dam"] = [fit4.params[p] for p in params] + [fit4.sse] ax = aust.plot( figsize=(10, 6), marker='o', color='black', title="Forecasts from Holt-Winters' multiplicative method") ax.set_ylabel("International visitor night in Australia (millions)") ax.set_xlabel("Year") fit1.fittedvalues.plot(ax=ax, style='--', color='red') fit2.fittedvalues.plot(ax=ax, style='--', color='green') fit1.forecast(8).rename('Holt-Winters (add-add-seasonal)').plot( ax=ax, style='--', marker='o', color='red', legend=True) fit2.forecast(8).rename('Holt-Winters (add-mul-seasonal)').plot( ax=ax, style='--', marker='o', color='green', legend=True) plt.show() print( "Figure 7.6: Forecasting international visitor nights in Australia using Holt-Winters method with both additive and multiplicative seasonality." ) results # ### The Internals # It is possible to get at the internals of the Exponential Smoothing # models. # # Here we show some tables that allow you to view side by side the # original values $y_t$, the level $l_t$, the trend $b_t$, the season $s_t$ # and the fitted values $\hat{y}_t$. df = pd.DataFrame( np.c_[aust, fit1.level, fit1.slope, fit1.season, fit1.fittedvalues], columns=[r'$y_t$', r'$l_t$', r'$b_t$', r'$s_t$', r'$\hat{y}_t$'], index=aust.index) df.append(fit1.forecast(8).rename(r'$\hat{y}_t$').to_frame(), sort=True) df = pd.DataFrame( np.c_[aust, fit2.level, fit2.slope, fit2.season, fit2.fittedvalues], columns=[r'$y_t$', r'$l_t$', r'$b_t$', r'$s_t$', r'$\hat{y}_t$'], index=aust.index) df.append(fit2.forecast(8).rename(r'$\hat{y}_t$').to_frame(), sort=True) # Finally lets look at the levels, slopes/trends and seasonal components # of the models. states1 = pd.DataFrame( np.c_[fit1.level, fit1.slope, fit1.season], columns=['level', 'slope', 'seasonal'], index=aust.index) states2 = pd.DataFrame( np.c_[fit2.level, fit2.slope, fit2.season], columns=['level', 'slope', 'seasonal'], index=aust.index) fig, [[ax1, ax4], [ax2, ax5], [ax3, ax6]] = plt.subplots(3, 2, figsize=(12, 8)) states1[['level']].plot(ax=ax1) states1[['slope']].plot(ax=ax2) states1[['seasonal']].plot(ax=ax3) states2[['level']].plot(ax=ax4) states2[['slope']].plot(ax=ax5) states2[['seasonal']].plot(ax=ax6) plt.show() statsmodels-0.12.2/examples/python/formulas.py000066400000000000000000000121221400612667500215040ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook formulas.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Formulas: Fitting models using R-style formulas # Since version 0.5.0, ``statsmodels`` allows users to fit statistical # models using R-style formulas. Internally, ``statsmodels`` uses the # [patsy](http://patsy.readthedocs.org/) package to convert formulas and # data to the matrices that are used in model fitting. The formula framework # is quite powerful; this tutorial only scratches the surface. A full # description of the formula language can be found in the ``patsy`` docs: # # * [Patsy formula language description](http://patsy.readthedocs.org/) # # ## Loading modules and functions import numpy as np # noqa:F401 needed in namespace for patsy import statsmodels.api as sm # #### Import convention # You can import explicitly from statsmodels.formula.api from statsmodels.formula.api import ols # Alternatively, you can just use the `formula` namespace of the main # `statsmodels.api`. sm.formula.ols # Or you can use the following convention import statsmodels.formula.api as smf # These names are just a convenient way to get access to each model's # `from_formula` classmethod. See, for instance sm.OLS.from_formula # All of the lower case models accept ``formula`` and ``data`` arguments, # whereas upper case ones take ``endog`` and ``exog`` design matrices. # ``formula`` accepts a string which describes the model in terms of a # ``patsy`` formula. ``data`` takes a [pandas](https://pandas.pydata.org/) # data frame or any other data structure that defines a ``__getitem__`` for # variable names like a structured array or a dictionary of variables. # # ``dir(sm.formula)`` will print a list of available models. # # Formula-compatible models have the following generic call signature: # ``(formula, data, subset=None, *args, **kwargs)`` # # ## OLS regression using formulas # # To begin, we fit the linear model described on the [Getting # Started](gettingstarted.html) page. Download the data, subset columns, and # list-wise delete to remove missing observations: dta = sm.datasets.get_rdataset("Guerry", "HistData", cache=True) df = dta.data[['Lottery', 'Literacy', 'Wealth', 'Region']].dropna() df.head() # Fit the model: mod = ols(formula='Lottery ~ Literacy + Wealth + Region', data=df) res = mod.fit() print(res.summary()) # ## Categorical variables # # Looking at the summary printed above, notice that ``patsy`` determined # that elements of *Region* were text strings, so it treated *Region* as a # categorical variable. `patsy`'s default is also to include an intercept, # so we automatically dropped one of the *Region* categories. # # If *Region* had been an integer variable that we wanted to treat # explicitly as categorical, we could have done so by using the ``C()`` # operator: res = ols(formula='Lottery ~ Literacy + Wealth + C(Region)', data=df).fit() print(res.params) # Patsy's mode advanced features for categorical variables are discussed # in: [Patsy: Contrast Coding Systems for categorical # variables](contrasts.html) # ## Operators # # We have already seen that "~" separates the left-hand side of the model # from the right-hand side, and that "+" adds new columns to the design # matrix. # # ### Removing variables # # The "-" sign can be used to remove columns/variables. For instance, we # can remove the intercept from a model by: res = ols(formula='Lottery ~ Literacy + Wealth + C(Region) -1 ', data=df).fit() print(res.params) # ### Multiplicative interactions # # ":" adds a new column to the design matrix with the interaction of the # other two columns. "*" will also include the individual columns that were # multiplied together: res1 = ols(formula='Lottery ~ Literacy : Wealth - 1', data=df).fit() res2 = ols(formula='Lottery ~ Literacy * Wealth - 1', data=df).fit() print(res1.params, '\n') print(res2.params) # Many other things are possible with operators. Please consult the [patsy # docs](https://patsy.readthedocs.org/en/latest/formulas.html) to learn # more. # ## Functions # # You can apply vectorized functions to the variables in your model: res = smf.ols(formula='Lottery ~ np.log(Literacy)', data=df).fit() print(res.params) # Define a custom function: def log_plus_1(x): return np.log(x) + 1. res = smf.ols(formula='Lottery ~ log_plus_1(Literacy)', data=df).fit() print(res.params) # Any function that is in the calling namespace is available to the # formula. # ## Using formulas with models that do not (yet) support them # # Even if a given `statsmodels` function does not support formulas, you # can still use `patsy`'s formula language to produce design matrices. Those # matrices # can then be fed to the fitting function as `endog` and `exog` arguments. # # To generate ``numpy`` arrays: import patsy f = 'Lottery ~ Literacy * Wealth' y, X = patsy.dmatrices(f, df, return_type='matrix') print(y[:5]) print(X[:5]) # To generate pandas data frames: f = 'Lottery ~ Literacy * Wealth' y, X = patsy.dmatrices(f, df, return_type='dataframe') print(y[:5]) print(X[:5]) print(sm.OLS(y, X).fit().summary()) statsmodels-0.12.2/examples/python/generic_mle.py000066400000000000000000000170011400612667500221260ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook generic_mle.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Maximum Likelihood Estimation (Generic models) # This tutorial explains how to quickly implement new maximum likelihood # models in `statsmodels`. We give two examples: # # 1. Probit model for binary dependent variables # 2. Negative binomial model for count data # # The `GenericLikelihoodModel` class eases the process by providing tools # such as automatic numeric differentiation and a unified interface to # ``scipy`` optimization functions. Using ``statsmodels``, users can fit new # MLE models simply by "plugging-in" a log-likelihood function. # ## Example 1: Probit model import numpy as np from scipy import stats import statsmodels.api as sm from statsmodels.base.model import GenericLikelihoodModel # The ``Spector`` dataset is distributed with ``statsmodels``. You can # access a vector of values for the dependent variable (``endog``) and a # matrix of regressors (``exog``) like this: data = sm.datasets.spector.load_pandas() exog = data.exog endog = data.endog print(sm.datasets.spector.NOTE) print(data.exog.head()) # Them, we add a constant to the matrix of regressors: exog = sm.add_constant(exog, prepend=True) # To create your own Likelihood Model, you simply need to overwrite the # loglike method. class MyProbit(GenericLikelihoodModel): def loglike(self, params): exog = self.exog endog = self.endog q = 2 * endog - 1 return stats.norm.logcdf(q * np.dot(exog, params)).sum() # Estimate the model and print a summary: sm_probit_manual = MyProbit(endog, exog).fit() print(sm_probit_manual.summary()) # Compare your Probit implementation to ``statsmodels``' "canned" # implementation: sm_probit_canned = sm.Probit(endog, exog).fit() print(sm_probit_canned.params) print(sm_probit_manual.params) print(sm_probit_canned.cov_params()) print(sm_probit_manual.cov_params()) # Notice that the ``GenericMaximumLikelihood`` class provides automatic # differentiation, so we did not have to provide Hessian or Score functions # in order to calculate the covariance estimates. # # # ## Example 2: Negative Binomial Regression for Count Data # # Consider a negative binomial regression model for count data with # log-likelihood (type NB-2) function expressed as: # # $$ # \mathcal{L}(\beta_j; y, \alpha) = \sum_{i=1}^n y_i ln # \left ( \frac{\alpha exp(X_i'\beta)}{1+\alpha exp(X_i'\beta)} \right # ) - # \frac{1}{\alpha} ln(1+\alpha exp(X_i'\beta)) + ln \Gamma (y_i + # 1/\alpha) - ln \Gamma (y_i+1) - ln \Gamma (1/\alpha) # $$ # # with a matrix of regressors $X$, a vector of coefficients $\beta$, # and the negative binomial heterogeneity parameter $\alpha$. # # Using the ``nbinom`` distribution from ``scipy``, we can write this # likelihood # simply as: # import numpy as np from scipy.stats import nbinom def _ll_nb2(y, X, beta, alph): mu = np.exp(np.dot(X, beta)) size = 1 / alph prob = size / (size + mu) ll = nbinom.logpmf(y, size, prob) return ll # ### New Model Class # # We create a new model class which inherits from # ``GenericLikelihoodModel``: from statsmodels.base.model import GenericLikelihoodModel class NBin(GenericLikelihoodModel): def __init__(self, endog, exog, **kwds): super(NBin, self).__init__(endog, exog, **kwds) def nloglikeobs(self, params): alph = params[-1] beta = params[:-1] ll = _ll_nb2(self.endog, self.exog, beta, alph) return -ll def fit(self, start_params=None, maxiter=10000, maxfun=5000, **kwds): # we have one additional parameter and we need to add it for summary self.exog_names.append('alpha') if start_params == None: # Reasonable starting values start_params = np.append(np.zeros(self.exog.shape[1]), .5) # intercept start_params[-2] = np.log(self.endog.mean()) return super(NBin, self).fit( start_params=start_params, maxiter=maxiter, maxfun=maxfun, **kwds) # Two important things to notice: # # + ``nloglikeobs``: This function should return one evaluation of the # negative log-likelihood function per observation in your dataset (i.e. # rows of the endog/X matrix). # + ``start_params``: A one-dimensional array of starting values needs to # be provided. The size of this array determines the number of parameters # that will be used in optimization. # # That's it! You're done! # # ### Usage Example # # The [Medpar](https://raw.githubusercontent.com/vincentarelbundock/Rdatas # ets/doc/COUNT/medpar.html) # dataset is hosted in CSV format at the [Rdatasets repository](https://ra # w.githubusercontent.com/vincentarelbundock/Rdatasets). We use the # ``read_csv`` # function from the [Pandas library](https://pandas.pydata.org) to load the # data # in memory. We then print the first few columns: # import statsmodels.api as sm medpar = sm.datasets.get_rdataset("medpar", "COUNT", cache=True).data medpar.head() # The model we are interested in has a vector of non-negative integers as # dependent variable (``los``), and 5 regressors: ``Intercept``, # ``type2``, # ``type3``, ``hmo``, ``white``. # # For estimation, we need to create two variables to hold our regressors # and the outcome variable. These can be ndarrays or pandas objects. y = medpar.los X = medpar[["type2", "type3", "hmo", "white"]].copy() X["constant"] = 1 # Then, we fit the model and extract some information: mod = NBin(y, X) res = mod.fit() # Extract parameter estimates, standard errors, p-values, AIC, etc.: print('Parameters: ', res.params) print('Standard errors: ', res.bse) print('P-values: ', res.pvalues) print('AIC: ', res.aic) # As usual, you can obtain a full list of available information by typing # ``dir(res)``. # We can also look at the summary of the estimation results. print(res.summary()) # ### Testing # We can check the results by using the statsmodels implementation of the # Negative Binomial model, which uses the analytic score function and # Hessian. res_nbin = sm.NegativeBinomial(y, X).fit(disp=0) print(res_nbin.summary()) print(res_nbin.params) print(res_nbin.bse) # Or we could compare them to results obtained using the MASS # implementation for R: # # url = 'https://raw.githubusercontent.com/vincentarelbundock/Rdataset # s/csv/COUNT/medpar.csv' # medpar = read.csv(url) # f = los~factor(type)+hmo+white # # library(MASS) # mod = glm.nb(f, medpar) # coef(summary(mod)) # Estimate Std. Error z value Pr(>|z|) # (Intercept) 2.31027893 0.06744676 34.253370 3.885556e-257 # factor(type)2 0.22124898 0.05045746 4.384861 1.160597e-05 # factor(type)3 0.70615882 0.07599849 9.291748 1.517751e-20 # hmo -0.06795522 0.05321375 -1.277024 2.015939e-01 # white -0.12906544 0.06836272 -1.887951 5.903257e-02 # # ### Numerical precision # # The ``statsmodels`` generic MLE and ``R`` parameter estimates agree up # to the fourth decimal. The standard errors, however, agree only up to the # second decimal. This discrepancy is the result of imprecision in our # Hessian numerical estimates. In the current context, the difference # between ``MASS`` and ``statsmodels`` standard error estimates is # substantively irrelevant, but it highlights the fact that users who need # very precise estimates may not always want to rely on default settings # when using numerical derivatives. In such cases, it is better to use # analytical derivatives with the ``LikelihoodModel`` class. statsmodels-0.12.2/examples/python/glm.py000066400000000000000000000100311400612667500204300ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook glm.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Generalized Linear Models import numpy as np import statsmodels.api as sm from scipy import stats from matplotlib import pyplot as plt # ## GLM: Binomial response data # # ### Load data # # In this example, we use the Star98 dataset which was taken with # permission # from Jeff Gill (2000) Generalized linear models: A unified approach. # Codebook # information can be obtained by typing: print(sm.datasets.star98.NOTE) # Load the data and add a constant to the exogenous (independent) # variables: data = sm.datasets.star98.load() data.exog = sm.add_constant(data.exog, prepend=False) # The dependent variable is N by 2 (Success: NABOVE, Failure: NBELOW): print(data.endog[:5, :]) # The independent variables include all the other variables described # above, as # well as the interaction terms: print(data.exog[:2, :]) # ### Fit and summary glm_binom = sm.GLM(data.endog, data.exog, family=sm.families.Binomial()) res = glm_binom.fit() print(res.summary()) # ### Quantities of interest print('Total number of trials:', data.endog[0].sum()) print('Parameters: ', res.params) print('T-values: ', res.tvalues) # First differences: We hold all explanatory variables constant at their # means and manipulate the percentage of low income households to assess its # impact on the response variables: means = data.exog.mean(axis=0) means25 = means.copy() means25[0] = stats.scoreatpercentile(data.exog[:, 0], 25) means75 = means.copy() means75[0] = lowinc_75per = stats.scoreatpercentile(data.exog[:, 0], 75) resp_25 = res.predict(means25) resp_75 = res.predict(means75) diff = resp_75 - resp_25 # The interquartile first difference for the percentage of low income # households in a school district is: print("%2.4f%%" % (diff * 100)) # ### Plots # # We extract information that will be used to draw some interesting # plots: nobs = res.nobs y = data.endog[:, 0] / data.endog.sum(1) yhat = res.mu # Plot yhat vs y: from statsmodels.graphics.api import abline_plot fig, ax = plt.subplots() ax.scatter(yhat, y) line_fit = sm.OLS(y, sm.add_constant(yhat, prepend=True)).fit() abline_plot(model_results=line_fit, ax=ax) ax.set_title('Model Fit Plot') ax.set_ylabel('Observed values') ax.set_xlabel('Fitted values') # Plot yhat vs. Pearson residuals: fig, ax = plt.subplots() ax.scatter(yhat, res.resid_pearson) ax.hlines(0, 0, 1) ax.set_xlim(0, 1) ax.set_title('Residual Dependence Plot') ax.set_ylabel('Pearson Residuals') ax.set_xlabel('Fitted values') # Histogram of standardized deviance residuals: from scipy import stats fig, ax = plt.subplots() resid = res.resid_deviance.copy() resid_std = stats.zscore(resid) ax.hist(resid_std, bins=25) ax.set_title('Histogram of standardized deviance residuals') # QQ Plot of Deviance Residuals: from statsmodels import graphics graphics.gofplots.qqplot(resid, line='r') # ## GLM: Gamma for proportional count response # # ### Load data # # In the example above, we printed the ``NOTE`` attribute to learn about # the # Star98 dataset. statsmodels datasets ships with other useful # information. For # example: print(sm.datasets.scotland.DESCRLONG) # Load the data and add a constant to the exogenous variables: data2 = sm.datasets.scotland.load() data2.exog = sm.add_constant(data2.exog, prepend=False) print(data2.exog[:5, :]) print(data2.endog[:5]) # ### Fit and summary glm_gamma = sm.GLM(data2.endog, data2.exog, family=sm.families.Gamma()) glm_results = glm_gamma.fit() print(glm_results.summary()) # ## GLM: Gaussian distribution with a noncanonical link # # ### Artificial data nobs2 = 100 x = np.arange(nobs2) np.random.seed(54321) X = np.column_stack((x, x**2)) X = sm.add_constant(X, prepend=False) lny = np.exp(-(.03 * x + .0001 * x**2 - 1.0)) + .001 * np.random.rand(nobs2) # ### Fit and summary gauss_log = sm.GLM(lny, X, family=sm.families.Gaussian(sm.families.links.log)) gauss_log_results = gauss_log.fit() print(gauss_log_results.summary()) statsmodels-0.12.2/examples/python/glm_formula.py000066400000000000000000000032251400612667500221640ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook glm_formula.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Generalized Linear Models (Formula) # This notebook illustrates how you can use R-style formulas to fit # Generalized Linear Models. # # To begin, we load the ``Star98`` dataset and we construct a formula and # pre-process the data: import statsmodels.api as sm import statsmodels.formula.api as smf star98 = sm.datasets.star98.load_pandas().data formula = 'SUCCESS ~ LOWINC + PERASIAN + PERBLACK + PERHISP + PCTCHRT + PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF' dta = star98[[ 'NABOVE', 'NBELOW', 'LOWINC', 'PERASIAN', 'PERBLACK', 'PERHISP', 'PCTCHRT', 'PCTYRRND', 'PERMINTE', 'AVYRSEXP', 'AVSALK', 'PERSPENK', 'PTRATIO', 'PCTAF' ]].copy() endog = dta['NABOVE'] / (dta['NABOVE'] + dta.pop('NBELOW')) del dta['NABOVE'] dta['SUCCESS'] = endog # Then, we fit the GLM model: mod1 = smf.glm(formula=formula, data=dta, family=sm.families.Binomial()).fit() mod1.summary() # Finally, we define a function to operate customized data transformation # using the formula framework: def double_it(x): return 2 * x formula = 'SUCCESS ~ double_it(LOWINC) + PERASIAN + PERBLACK + PERHISP + PCTCHRT + PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF' mod2 = smf.glm(formula=formula, data=dta, family=sm.families.Binomial()).fit() mod2.summary() # As expected, the coefficient for ``double_it(LOWINC)`` in the second # model is half the size of the ``LOWINC`` coefficient from the first model: print(mod1.params[1]) print(mod2.params[1] * 2) statsmodels-0.12.2/examples/python/glm_weights.py000066400000000000000000000330651400612667500221760ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook glm_weights.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Weighted Generalized Linear Models import numpy as np import pandas as pd import statsmodels.formula.api as smf import statsmodels.api as sm # ## Weighted GLM: Poisson response data # # ### Load data # # In this example, we'll use the affair dataset using a handful of # exogenous variables to predict the extra-marital affair rate. # # Weights will be generated to show that `freq_weights` are equivalent to # repeating records of data. On the other hand, `var_weights` is equivalent # to aggregating data. print(sm.datasets.fair.NOTE) # Load the data into a pandas dataframe. data = sm.datasets.fair.load_pandas().data # The dependent (endogenous) variable is ``affairs`` data.describe() data[:3] # In the following we will work mostly with Poisson. While using decimal # affairs works, we convert them to integers to have a count distribution. data["affairs"] = np.ceil(data["affairs"]) data[:3] (data["affairs"] == 0).mean() np.bincount(data["affairs"].astype(int)) # ## Condensing and Aggregating observations # # We have 6366 observations in our original dataset. When we consider only # some selected variables, then we have fewer unique observations. In the # following we combine observations in two ways, first we combine # observations that have values for all variables identical, and secondly we # combine observations that have the same explanatory variables. # ### Dataset with unique observations # # We use pandas's groupby to combine identical observations and create a # new variable `freq` that count how many observation have the values in the # corresponding row. data2 = data.copy() data2['const'] = 1 dc = data2['affairs rate_marriage age yrs_married const'.split()].groupby( 'affairs rate_marriage age yrs_married'.split()).count() dc.reset_index(inplace=True) dc.rename(columns={'const': 'freq'}, inplace=True) print(dc.shape) dc.head() # ### Dataset with unique explanatory variables (exog) # # For the next dataset we combine observations that have the same values # of the explanatory variables. However, because the response variable can # differ among combined observations, we compute the mean and the sum of the # response variable for all combined observations. # # We use again pandas ``groupby`` to combine observations and to create # the new variables. We also flatten the ``MultiIndex`` into a simple index. gr = data['affairs rate_marriage age yrs_married'.split()].groupby( 'rate_marriage age yrs_married'.split()) df_a = gr.agg(['mean', 'sum', 'count']) def merge_tuple(tpl): if isinstance(tpl, tuple) and len(tpl) > 1: return "_".join(map(str, tpl)) else: return tpl df_a.columns = df_a.columns.map(merge_tuple) df_a.reset_index(inplace=True) print(df_a.shape) df_a.head() # After combining observations with have a dataframe `dc` with 467 unique # observations, and a dataframe `df_a` with 130 observations with unique # values of the explanatory variables. print('number of rows: \noriginal, with unique observations, with unique exog') data.shape[0], dc.shape[0], df_a.shape[0] # ## Analysis # # In the following, we compare the GLM-Poisson results of the original # data with models of the combined observations where the multiplicity or # aggregation is given by weights or exposure. # # # ### original data glm = smf.glm( 'affairs ~ rate_marriage + age + yrs_married', data=data, family=sm.families.Poisson()) res_o = glm.fit() print(res_o.summary()) res_o.pearson_chi2 / res_o.df_resid # ### condensed data (unique observations with frequencies) # # Combining identical observations and using frequency weights to take # into account the multiplicity of observations produces exactly the same # results. Some results attribute will differ when we want to have # information about the observation and not about the aggregate of all # identical observations. For example, residuals do not take # ``freq_weights`` into account. glm = smf.glm( 'affairs ~ rate_marriage + age + yrs_married', data=dc, family=sm.families.Poisson(), freq_weights=np.asarray(dc['freq'])) res_f = glm.fit() print(res_f.summary()) res_f.pearson_chi2 / res_f.df_resid # ### condensed using ``var_weights`` instead of ``freq_weights`` # # Next, we compare ``var_weights`` to ``freq_weights``. It is a common # practice to incorporate ``var_weights`` when the endogenous variable # reflects averages and not identical observations. # I do not see a theoretical reason why it produces the same results (in # general). # # This produces the same results but ``df_resid`` differs the # ``freq_weights`` example because ``var_weights`` do not change the number # of effective observations. # glm = smf.glm( 'affairs ~ rate_marriage + age + yrs_married', data=dc, family=sm.families.Poisson(), var_weights=np.asarray(dc['freq'])) res_fv = glm.fit() print(res_fv.summary()) # Dispersion computed from the results is incorrect because of wrong # ``df_resid``. # It is correct if we use the original ``df_resid``. res_fv.pearson_chi2 / res_fv.df_resid, res_f.pearson_chi2 / res_f.df_resid # ### aggregated or averaged data (unique values of explanatory variables) # # For these cases we combine observations that have the same values of the # explanatory variables. The corresponding response variable is either a sum # or an average. # # #### using ``exposure`` # # If our dependent variable is the sum of the responses of all combined # observations, then under the Poisson assumption the distribution remains # the same but we have varying `exposure` given by the number of individuals # that are represented by one aggregated observation. # # The parameter estimates and covariance of parameters are the same with # the original data, but log-likelihood, deviance and Pearson chi-squared # differ glm = smf.glm( 'affairs_sum ~ rate_marriage + age + yrs_married', data=df_a, family=sm.families.Poisson(), exposure=np.asarray(df_a['affairs_count'])) res_e = glm.fit() print(res_e.summary()) res_e.pearson_chi2 / res_e.df_resid # #### using var_weights # # We can also use the mean of all combined values of the dependent # variable. In this case the variance will be related to the inverse of the # total exposure reflected by one combined observation. glm = smf.glm( 'affairs_mean ~ rate_marriage + age + yrs_married', data=df_a, family=sm.families.Poisson(), var_weights=np.asarray(df_a['affairs_count'])) res_a = glm.fit() print(res_a.summary()) # ### Comparison # # We saw in the summary prints above that ``params`` and ``cov_params`` # with associated Wald inference agree across versions. We summarize this in # the following comparing individual results attributes across versions. # # Parameter estimates `params`, standard errors of the parameters `bse` # and `pvalues` of the parameters for the tests that the parameters are # zeros all agree. However, the likelihood and goodness-of-fit statistics, # `llf`, `deviance` and `pearson_chi2` only partially agree. Specifically, # the aggregated version do not agree with the results using the original # data. # # **Warning**: The behavior of `llf`, `deviance` and `pearson_chi2` might # still change in future versions. # # Both the sum and average of the response variable for unique values of # the explanatory variables have a proper likelihood interpretation. # However, this interpretation is not reflected in these three statistics. # Computationally this might be due to missing adjustments when aggregated # data is used. However, theoretically we can think in these cases, # especially for `var_weights` of the misspecified case when likelihood # analysis is inappropriate and the results should be interpreted as quasi- # likelihood estimates. There is an ambiguity in the definition of # ``var_weights`` because they can be used for averages with correctly # specified likelihood as well as for variance adjustments in the quasi- # likelihood case. We are currently not trying to match the likelihood # specification. However, in the next section we show that likelihood ratio # type tests still produce the same result for all aggregation versions when # we assume that the underlying model is correctly specified. results_all = [res_o, res_f, res_e, res_a] names = 'res_o res_f res_e res_a'.split() pd.concat([r.params for r in results_all], axis=1, keys=names) pd.concat([r.bse for r in results_all], axis=1, keys=names) pd.concat([r.pvalues for r in results_all], axis=1, keys=names) pd.DataFrame( np.column_stack( [[r.llf, r.deviance, r.pearson_chi2] for r in results_all]), columns=names, index=['llf', 'deviance', 'pearson chi2']) # ### Likelihood Ratio type tests # # We saw above that likelihood and related statistics do not agree between # the aggregated and original, individual data. We illustrate in the # following that likelihood ratio test and difference in deviance agree # across versions, however Pearson chi-squared does not. # # As before: This is not sufficiently clear yet and could change. # # As a test case we drop the `age` variable and compute the likelihood # ratio type statistics as difference between reduced or constrained and # full or unconstrained model. # #### original observations and frequency weights glm = smf.glm( 'affairs ~ rate_marriage + yrs_married', data=data, family=sm.families.Poisson()) res_o2 = glm.fit() #print(res_f2.summary()) res_o2.pearson_chi2 - res_o.pearson_chi2, res_o2.deviance - res_o.deviance, res_o2.llf - res_o.llf glm = smf.glm( 'affairs ~ rate_marriage + yrs_married', data=dc, family=sm.families.Poisson(), freq_weights=np.asarray(dc['freq'])) res_f2 = glm.fit() #print(res_f2.summary()) res_f2.pearson_chi2 - res_f.pearson_chi2, res_f2.deviance - res_f.deviance, res_f2.llf - res_f.llf # #### aggregated data: ``exposure`` and ``var_weights`` # # Note: LR test agrees with original observations, ``pearson_chi2`` # differs and has the wrong sign. glm = smf.glm( 'affairs_sum ~ rate_marriage + yrs_married', data=df_a, family=sm.families.Poisson(), exposure=np.asarray(df_a['affairs_count'])) res_e2 = glm.fit() res_e2.pearson_chi2 - res_e.pearson_chi2, res_e2.deviance - res_e.deviance, res_e2.llf - res_e.llf glm = smf.glm( 'affairs_mean ~ rate_marriage + yrs_married', data=df_a, family=sm.families.Poisson(), var_weights=np.asarray(df_a['affairs_count'])) res_a2 = glm.fit() res_a2.pearson_chi2 - res_a.pearson_chi2, res_a2.deviance - res_a.deviance, res_a2.llf - res_a.llf # ### Investigating Pearson chi-square statistic # # First, we do some sanity checks that there are no basic bugs in the # computation of `pearson_chi2` and `resid_pearson`. res_e2.pearson_chi2, res_e.pearson_chi2, (res_e2.resid_pearson **2).sum(), (res_e.resid_pearson **2).sum() res_e._results.resid_response.mean(), res_e.model.family.variance( res_e.mu)[:5], res_e.mu[:5] (res_e._results.resid_response**2 / res_e.model.family.variance( res_e.mu)).sum() res_e2._results.resid_response.mean(), res_e2.model.family.variance( res_e2.mu)[:5], res_e2.mu[:5] (res_e2._results.resid_response**2 / res_e2.model.family.variance( res_e2.mu)).sum() (res_e2._results.resid_response**2).sum(), (res_e._results.resid_response **2).sum() # One possible reason for the incorrect sign is that we are subtracting # quadratic terms that are divided by different denominators. In some # related cases, the recommendation in the literature is to use a common # denominator. We can compare pearson chi-squared statistic using the same # variance assumption in the full and reduced model. # # In this case we obtain the same pearson chi2 scaled difference between # reduced and full model across all versions. (Issue # [#3616](https://github.com/statsmodels/statsmodels/issues/3616) is # intended to track this further.) ((res_e2._results.resid_response**2 - res_e._results.resid_response**2) / res_e2.model.family.variance(res_e2.mu)).sum() ((res_a2._results.resid_response**2 - res_a._results.resid_response**2) / res_a2.model.family.variance(res_a2.mu) * res_a2.model.var_weights).sum() ((res_f2._results.resid_response**2 - res_f._results.resid_response**2) / res_f2.model.family.variance(res_f2.mu) * res_f2.model.freq_weights).sum() ((res_o2._results.resid_response**2 - res_o._results.resid_response**2) / res_o2.model.family.variance(res_o2.mu)).sum() # ## Remainder # # The remainder of the notebook just contains some additional checks and # can be ignored. np.exp(res_e2.model.exposure)[:5], np.asarray(df_a['affairs_count'])[:5] res_e2.resid_pearson.sum() - res_e.resid_pearson.sum() res_e2.mu[:5] res_a2.pearson_chi2, res_a.pearson_chi2, res_a2.resid_pearson.sum( ), res_a.resid_pearson.sum() ((res_a2._results.resid_response**2) / res_a2.model.family.variance(res_a2.mu) * res_a2.model.var_weights).sum() ((res_a._results.resid_response**2) / res_a.model.family.variance(res_a.mu) * res_a.model.var_weights).sum() ((res_a._results.resid_response**2) / res_a.model.family.variance(res_a2.mu) * res_a.model.var_weights).sum() res_e.model.endog[:5], res_e2.model.endog[:5] res_a.model.endog[:5], res_a2.model.endog[:5] res_a2.model.endog[:5] * np.exp(res_e2.model.exposure)[:5] res_a2.model.endog[:5] * res_a2.model.var_weights[:5] from scipy import stats stats.chi2.sf(27.19530754604785, 1), stats.chi2.sf(29.083798806764687, 1) res_o.pvalues print(res_e2.summary()) print(res_e.summary()) print(res_f2.summary()) print(res_f.summary()) statsmodels-0.12.2/examples/python/gls.py000066400000000000000000000046761400612667500204600ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook gls.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Generalized Least Squares import statsmodels.api as sm # The Longley dataset is a time series dataset: data = sm.datasets.longley.load() data.exog = sm.add_constant(data.exog) print(data.exog[:5]) # # Let's assume that the data is heteroskedastic and that we know # the nature of the heteroskedasticity. We can then define # `sigma` and use it to give us a GLS model # # First we will obtain the residuals from an OLS fit ols_resid = sm.OLS(data.endog, data.exog).fit().resid # Assume that the error terms follow an AR(1) process with a trend: # # $\epsilon_i = \beta_0 + \rho\epsilon_{i-1} + \eta_i$ # # where $\eta \sim N(0,\Sigma^2)$ # # and that $\rho$ is simply the correlation of the residual a consistent # estimator for rho is to regress the residuals on the lagged residuals resid_fit = sm.OLS(ols_resid[1:], sm.add_constant(ols_resid[:-1])).fit() print(resid_fit.tvalues[1]) print(resid_fit.pvalues[1]) # While we do not have strong evidence that the errors follow an AR(1) # process we continue rho = resid_fit.params[1] # As we know, an AR(1) process means that near-neighbors have a stronger # relation so we can give this structure by using a toeplitz matrix from scipy.linalg import toeplitz toeplitz(range(5)) order = toeplitz(range(len(ols_resid))) # so that our error covariance structure is actually rho**order # which defines an autocorrelation structure sigma = rho**order gls_model = sm.GLS(data.endog, data.exog, sigma=sigma) gls_results = gls_model.fit() # Of course, the exact rho in this instance is not known so it it might # make more sense to use feasible gls, which currently only has experimental # support. # # We can use the GLSAR model with one lag, to get to a similar result: glsar_model = sm.GLSAR(data.endog, data.exog, 1) glsar_results = glsar_model.iterative_fit(1) print(glsar_results.summary()) # Comparing gls and glsar results, we see that there are some small # differences in the parameter estimates and the resulting standard # errors of the parameter estimate. This might be do to the numerical # differences in the algorithm, e.g. the treatment of initial conditions, # because of the small number of observations in the longley dataset. print(gls_results.params) print(glsar_results.params) print(gls_results.bse) print(glsar_results.bse) statsmodels-0.12.2/examples/python/influence_glm_logit.py000066400000000000000000000052701400612667500236670ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook influence_glm_logit.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Influence Measures for GLM Logit # # # Based on draft version for GLMInfluence, which will also apply to # discrete Logit, Probit and Poisson, and eventually be extended to cover # most models outside of time series analysis. # # The example for logistic regression was used by Pregibon (1981) # "Logistic Regression diagnostics" and is based on data by Finney (1947). # # GLMInfluence includes the basic influence measures but still misses some # measures described in Pregibon (1981), for example those related to # deviance and effects on confidence intervals. import os.path import numpy as np import pandas as pd from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod import families import statsmodels.stats.tests.test_influence test_module = statsmodels.stats.tests.test_influence.__file__ cur_dir = cur_dir = os.path.abspath(os.path.dirname(test_module)) file_name = 'binary_constrict.csv' file_path = os.path.join(cur_dir, 'results', file_name) df = pd.read_csv(file_path, index_col=0) res = GLM( df['constrict'], df[['const', 'log_rate', 'log_volumne']], family=families.Binomial()).fit( attach_wls=True, atol=1e-10) print(res.summary()) # ## get the influence measures # # GLMResults has a `get_influence` method similar to OLSResults, that # returns and instance of the GLMInfluence class. This class has methods and # (cached) attributes to inspect influence and outlier measures. # # This measures are based on a one-step approximation to the the results # for deleting one observation. One-step approximations are usually accurate # for small changes but underestimate the magnitude of large changes. Event # though large changes are underestimated, they still show clearly the # effect of influential observations # # In this example observation 4 and 18 have a large standardized residual # and large Cook's distance, but not a large leverage. Observation 13 has # the largest leverage but only small Cook's distance and not a large # studentized residual. # # Only the two observations 4 and 18 have a large impact on the parameter # estimates. infl = res.get_influence(observed=False) summ_df = infl.summary_frame() summ_df.sort_values('cooks_d', ascending=False)[:10] infl.plot_influence() infl.plot_index(y_var='cooks', threshold=2 * infl.cooks_distance[0].mean()) infl.plot_index(y_var='resid', threshold=1) infl.plot_index(y_var='dfbeta', idx=1, threshold=0.5) infl.plot_index(y_var='dfbeta', idx=2, threshold=0.5) infl.plot_index(y_var='dfbeta', idx=0, threshold=0.5) statsmodels-0.12.2/examples/python/interactions_anova.py000066400000000000000000000255551400612667500235600ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook interactions_anova.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Interactions and ANOVA # Note: This script is based heavily on Jonathan Taylor's class notes # http://www.stanford.edu/class/stats191/interactions.html # # Download and format data: from statsmodels.compat import urlopen import numpy as np np.set_printoptions(precision=4, suppress=True) import pandas as pd pd.set_option("display.width", 100) import matplotlib.pyplot as plt from statsmodels.formula.api import ols from statsmodels.graphics.api import interaction_plot, abline_plot from statsmodels.stats.anova import anova_lm try: salary_table = pd.read_csv('salary.table') except: # recent pandas can read URL without urlopen url = 'http://stats191.stanford.edu/data/salary.table' fh = urlopen(url) salary_table = pd.read_table(fh) salary_table.to_csv('salary.table') E = salary_table.E M = salary_table.M X = salary_table.X S = salary_table.S # Take a look at the data: plt.figure(figsize=(6, 6)) symbols = ['D', '^'] colors = ['r', 'g', 'blue'] factor_groups = salary_table.groupby(['E', 'M']) for values, group in factor_groups: i, j = values plt.scatter( group['X'], group['S'], marker=symbols[j], color=colors[i - 1], s=144) plt.xlabel('Experience') plt.ylabel('Salary') # Fit a linear model: formula = 'S ~ C(E) + C(M) + X' lm = ols(formula, salary_table).fit() print(lm.summary()) # Have a look at the created design matrix: lm.model.exog[:5] # Or since we initially passed in a DataFrame, we have a DataFrame # available in lm.model.data.orig_exog[:5] # We keep a reference to the original untouched data in lm.model.data.frame[:5] # Influence statistics infl = lm.get_influence() print(infl.summary_table()) # or get a dataframe df_infl = infl.summary_frame() df_infl[:5] # Now plot the residuals within the groups separately: resid = lm.resid plt.figure(figsize=(6, 6)) for values, group in factor_groups: i, j = values group_num = i * 2 + j - 1 # for plotting purposes x = [group_num] * len(group) plt.scatter( x, resid[group.index], marker=symbols[j], color=colors[i - 1], s=144, edgecolors='black') plt.xlabel('Group') plt.ylabel('Residuals') # Now we will test some interactions using anova or f_test interX_lm = ols("S ~ C(E) * X + C(M)", salary_table).fit() print(interX_lm.summary()) # Do an ANOVA check from statsmodels.stats.api import anova_lm table1 = anova_lm(lm, interX_lm) print(table1) interM_lm = ols("S ~ X + C(E)*C(M)", data=salary_table).fit() print(interM_lm.summary()) table2 = anova_lm(lm, interM_lm) print(table2) # The design matrix as a DataFrame interM_lm.model.data.orig_exog[:5] # The design matrix as an ndarray interM_lm.model.exog interM_lm.model.exog_names infl = interM_lm.get_influence() resid = infl.resid_studentized_internal plt.figure(figsize=(6, 6)) for values, group in factor_groups: i, j = values idx = group.index plt.scatter( X[idx], resid[idx], marker=symbols[j], color=colors[i - 1], s=144, edgecolors='black') plt.xlabel('X') plt.ylabel('standardized resids') # Looks like one observation is an outlier. drop_idx = abs(resid).argmax() print(drop_idx) # zero-based index idx = salary_table.index.drop(drop_idx) lm32 = ols('S ~ C(E) + X + C(M)', data=salary_table, subset=idx).fit() print(lm32.summary()) print('\n') interX_lm32 = ols('S ~ C(E) * X + C(M)', data=salary_table, subset=idx).fit() print(interX_lm32.summary()) print('\n') table3 = anova_lm(lm32, interX_lm32) print(table3) print('\n') interM_lm32 = ols('S ~ X + C(E) * C(M)', data=salary_table, subset=idx).fit() table4 = anova_lm(lm32, interM_lm32) print(table4) print('\n') # Replot the residuals try: resid = interM_lm32.get_influence().summary_frame()['standard_resid'] except: resid = interM_lm32.get_influence().summary_frame()['standard_resid'] plt.figure(figsize=(6, 6)) for values, group in factor_groups: i, j = values idx = group.index plt.scatter( X[idx], resid[idx], marker=symbols[j], color=colors[i - 1], s=144, edgecolors='black') plt.xlabel('X[~[32]]') plt.ylabel('standardized resids') # Plot the fitted values lm_final = ols('S ~ X + C(E)*C(M)', data=salary_table.drop([drop_idx])).fit() mf = lm_final.model.data.orig_exog lstyle = ['-', '--'] plt.figure(figsize=(6, 6)) for values, group in factor_groups: i, j = values idx = group.index plt.scatter( X[idx], S[idx], marker=symbols[j], color=colors[i - 1], s=144, edgecolors='black') # drop NA because there is no idx 32 in the final model plt.plot( mf.X[idx].dropna(), lm_final.fittedvalues[idx].dropna(), ls=lstyle[j], color=colors[i - 1]) plt.xlabel('Experience') plt.ylabel('Salary') # From our first look at the data, the difference between Master's and PhD # in the management group is different than in the non-management group. # This is an interaction between the two qualitative variables management,M # and education,E. We can visualize this by first removing the effect of # experience, then plotting the means within each of the 6 groups using # interaction.plot. U = S - X * interX_lm32.params['X'] plt.figure(figsize=(6, 6)) interaction_plot( E, M, U, colors=['red', 'blue'], markers=['^', 'D'], markersize=10, ax=plt.gca()) # ## Minority Employment Data try: jobtest_table = pd.read_table('jobtest.table') except: # do not have data already url = 'http://stats191.stanford.edu/data/jobtest.table' jobtest_table = pd.read_table(url) factor_group = jobtest_table.groupby(['MINORITY']) fig, ax = plt.subplots(figsize=(6, 6)) colors = ['purple', 'green'] markers = ['o', 'v'] for factor, group in factor_group: ax.scatter( group['TEST'], group['JPERF'], color=colors[factor], marker=markers[factor], s=12**2) ax.set_xlabel('TEST') ax.set_ylabel('JPERF') min_lm = ols('JPERF ~ TEST', data=jobtest_table).fit() print(min_lm.summary()) fig, ax = plt.subplots(figsize=(6, 6)) for factor, group in factor_group: ax.scatter( group['TEST'], group['JPERF'], color=colors[factor], marker=markers[factor], s=12**2) ax.set_xlabel('TEST') ax.set_ylabel('JPERF') fig = abline_plot(model_results=min_lm, ax=ax) min_lm2 = ols('JPERF ~ TEST + TEST:MINORITY', data=jobtest_table).fit() print(min_lm2.summary()) fig, ax = plt.subplots(figsize=(6, 6)) for factor, group in factor_group: ax.scatter( group['TEST'], group['JPERF'], color=colors[factor], marker=markers[factor], s=12**2) fig = abline_plot( intercept=min_lm2.params['Intercept'], slope=min_lm2.params['TEST'], ax=ax, color='purple') fig = abline_plot( intercept=min_lm2.params['Intercept'], slope=min_lm2.params['TEST'] + min_lm2.params['TEST:MINORITY'], ax=ax, color='green') min_lm3 = ols('JPERF ~ TEST + MINORITY', data=jobtest_table).fit() print(min_lm3.summary()) fig, ax = plt.subplots(figsize=(6, 6)) for factor, group in factor_group: ax.scatter( group['TEST'], group['JPERF'], color=colors[factor], marker=markers[factor], s=12**2) fig = abline_plot( intercept=min_lm3.params['Intercept'], slope=min_lm3.params['TEST'], ax=ax, color='purple') fig = abline_plot( intercept=min_lm3.params['Intercept'] + min_lm3.params['MINORITY'], slope=min_lm3.params['TEST'], ax=ax, color='green') min_lm4 = ols('JPERF ~ TEST * MINORITY', data=jobtest_table).fit() print(min_lm4.summary()) fig, ax = plt.subplots(figsize=(8, 6)) for factor, group in factor_group: ax.scatter( group['TEST'], group['JPERF'], color=colors[factor], marker=markers[factor], s=12**2) fig = abline_plot( intercept=min_lm4.params['Intercept'], slope=min_lm4.params['TEST'], ax=ax, color='purple') fig = abline_plot( intercept=min_lm4.params['Intercept'] + min_lm4.params['MINORITY'], slope=min_lm4.params['TEST'] + min_lm4.params['TEST:MINORITY'], ax=ax, color='green') # is there any effect of MINORITY on slope or intercept? table5 = anova_lm(min_lm, min_lm4) print(table5) # is there any effect of MINORITY on intercept table6 = anova_lm(min_lm, min_lm3) print(table6) # is there any effect of MINORITY on slope table7 = anova_lm(min_lm, min_lm2) print(table7) # is it just the slope or both? table8 = anova_lm(min_lm2, min_lm4) print(table8) # ## One-way ANOVA try: rehab_table = pd.read_csv('rehab.table') except: url = 'http://stats191.stanford.edu/data/rehab.csv' rehab_table = pd.read_table(url, delimiter=",") rehab_table.to_csv('rehab.table') fig, ax = plt.subplots(figsize=(8, 6)) fig = rehab_table.boxplot('Time', 'Fitness', ax=ax, grid=False) rehab_lm = ols('Time ~ C(Fitness)', data=rehab_table).fit() table9 = anova_lm(rehab_lm) print(table9) print(rehab_lm.model.data.orig_exog) print(rehab_lm.summary()) # ## Two-way ANOVA try: kidney_table = pd.read_table('./kidney.table') except: url = 'http://stats191.stanford.edu/data/kidney.table' kidney_table = pd.read_csv(url, delim_whitespace=True) # Explore the dataset kidney_table.head(10) # Balanced panel kt = kidney_table plt.figure(figsize=(8, 6)) fig = interaction_plot( kt['Weight'], kt['Duration'], np.log(kt['Days'] + 1), colors=['red', 'blue'], markers=['D', '^'], ms=10, ax=plt.gca()) # You have things available in the calling namespace available in the # formula evaluation namespace kidney_lm = ols('np.log(Days+1) ~ C(Duration) * C(Weight)', data=kt).fit() table10 = anova_lm(kidney_lm) print( anova_lm( ols('np.log(Days+1) ~ C(Duration) + C(Weight)', data=kt).fit(), kidney_lm)) print( anova_lm( ols('np.log(Days+1) ~ C(Duration)', data=kt).fit(), ols('np.log(Days+1) ~ C(Duration) + C(Weight, Sum)', data=kt).fit())) print( anova_lm( ols('np.log(Days+1) ~ C(Weight)', data=kt).fit(), ols('np.log(Days+1) ~ C(Duration) + C(Weight, Sum)', data=kt).fit())) # ## Sum of squares # # Illustrates the use of different types of sums of squares (I,II,II) # and how the Sum contrast can be used to produce the same output between # the 3. # # Types I and II are equivalent under a balanced design. # # Do not use Type III with non-orthogonal contrast - ie., Treatment sum_lm = ols( 'np.log(Days+1) ~ C(Duration, Sum) * C(Weight, Sum)', data=kt).fit() print(anova_lm(sum_lm)) print(anova_lm(sum_lm, typ=2)) print(anova_lm(sum_lm, typ=3)) nosum_lm = ols( 'np.log(Days+1) ~ C(Duration, Treatment) * C(Weight, Treatment)', data=kt).fit() print(anova_lm(nosum_lm)) print(anova_lm(nosum_lm, typ=2)) print(anova_lm(nosum_lm, typ=3)) statsmodels-0.12.2/examples/python/kernel_density.py000066400000000000000000000212141400612667500226750ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook kernel_density.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Kernel Density Estimation # # Kernel density estimation is the process of estimating an unknown # probability density function using a *kernel function* $K(u)$. While a # histogram counts the number of data points in somewhat arbitrary regions, # a kernel density estimate is a function defined as the sum of a kernel # function on every data point. The kernel function typically exhibits the # following properties: # # 1. Symmetry such that $K(u) = K(-u)$. # 2. Normalization such that $\int_{-\infty}^{\infty} K(u) \ du = 1$ . # 3. Monotonically decreasing such that $K'(u) < 0$ when $u > 0$. # 4. Expected value equal to zero such that $\mathrm{E}[K] = 0$. # # For more information about kernel density estimation, see for instance # [Wikipedia - Kernel density # estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation). # # A univariate kernel density estimator is implemented in # `sm.nonparametric.KDEUnivariate`. # In this example we will show the following: # # * Basic usage, how to fit the estimator. # * The effect of varying the bandwidth of the kernel using the `bw` # argument. # * The various kernel functions available using the `kernel` argument. import numpy as np from scipy import stats import statsmodels.api as sm import matplotlib.pyplot as plt from statsmodels.distributions.mixture_rvs import mixture_rvs # ## A univariate example np.random.seed( 12345) # Seed the random number generator for reproducible results # We create a bimodal distribution: a mixture of two normal distributions # with locations at `-1` and `1`. # Location, scale and weight for the two distributions dist1_loc, dist1_scale, weight1 = -1, .5, .25 dist2_loc, dist2_scale, weight2 = 1, .5, .75 # Sample from a mixture of distributions obs_dist = mixture_rvs( prob=[weight1, weight2], size=250, dist=[stats.norm, stats.norm], kwargs=(dict(loc=dist1_loc, scale=dist1_scale), dict(loc=dist2_loc, scale=dist2_scale))) # The simplest non-parametric technique for density estimation is the # histogram. fig = plt.figure(figsize=(12, 5)) ax = fig.add_subplot(111) # Scatter plot of data samples and histogram ax.scatter( obs_dist, np.abs(np.random.randn(obs_dist.size)), zorder=15, color='red', marker='x', alpha=0.5, label='Samples') lines = ax.hist(obs_dist, bins=20, edgecolor='k', label='Histogram') ax.legend(loc='best') ax.grid(True, zorder=-5) # ## Fitting with the default arguments # The histogram above is discontinuous. To compute a continuous # probability density function, # we can use kernel density estimation. # # We initialize a univariate kernel density estimator using # `KDEUnivariate`. kde = sm.nonparametric.KDEUnivariate(obs_dist) kde.fit() # Estimate the densities # We present a figure of the fit, as well as the true distribution. fig = plt.figure(figsize=(12, 5)) ax = fig.add_subplot(111) # Plot the histrogram ax.hist( obs_dist, bins=20, normed=True, label='Histogram from samples', zorder=5, edgecolor='k', alpha=0.5) # Plot the KDE as fitted using the default arguments ax.plot(kde.support, kde.density, lw=3, label='KDE from samples', zorder=10) # Plot the true distribution true_values = ( stats.norm.pdf(loc=dist1_loc, scale=dist1_scale, x=kde.support) * weight1 + stats.norm.pdf(loc=dist2_loc, scale=dist2_scale, x=kde.support) * weight2) ax.plot(kde.support, true_values, lw=3, label='True distribution', zorder=15) # Plot the samples ax.scatter( obs_dist, np.abs(np.random.randn(obs_dist.size)) / 40, marker='x', color='red', zorder=20, label='Samples', alpha=0.5) ax.legend(loc='best') ax.grid(True, zorder=-5) # In the code above, default arguments were used. We can also vary the # bandwidth of the kernel, as we will now see. # ## Varying the bandwidth using the `bw` argument # The bandwidth of the kernel can be adjusted using the `bw` argument. # In the following example, a bandwidth of `bw=0.2` seems to fit the data # well. fig = plt.figure(figsize=(12, 5)) ax = fig.add_subplot(111) # Plot the histrogram ax.hist( obs_dist, bins=25, label='Histogram from samples', zorder=5, edgecolor='k', normed=True, alpha=0.5) # Plot the KDE for various bandwidths for bandwidth in [0.1, 0.2, 0.4]: kde.fit(bw=bandwidth) # Estimate the densities ax.plot( kde.support, kde.density, '--', lw=2, color='k', zorder=10, label='KDE from samples, bw = {}'.format(round(bandwidth, 2))) # Plot the true distribution ax.plot(kde.support, true_values, lw=3, label='True distribution', zorder=15) # Plot the samples ax.scatter( obs_dist, np.abs(np.random.randn(obs_dist.size)) / 50, marker='x', color='red', zorder=20, label='Data samples', alpha=0.5) ax.legend(loc='best') ax.set_xlim([-3, 3]) ax.grid(True, zorder=-5) # ## Comparing kernel functions # In the example above, a Gaussian kernel was used. Several other kernels # are also available. from statsmodels.nonparametric.kde import kernel_switch list(kernel_switch.keys()) # ### The available kernel functions # Create a figure fig = plt.figure(figsize=(12, 5)) # Enumerate every option for the kernel for i, (ker_name, ker_class) in enumerate(kernel_switch.items()): # Initialize the kernel object kernel = ker_class() # Sample from the domain domain = kernel.domain or [-3, 3] x_vals = np.linspace(*domain, num=2**10) y_vals = kernel(x_vals) # Create a subplot, set the title ax = fig.add_subplot(2, 4, i + 1) ax.set_title('Kernel function "{}"'.format(ker_name)) ax.plot(x_vals, y_vals, lw=3, label='{}'.format(ker_name)) ax.scatter([0], [0], marker='x', color='red') plt.grid(True, zorder=-5) ax.set_xlim(domain) plt.tight_layout() # ### The available kernel functions on three data points # We now examine how the kernel density estimate will fit to three equally # spaced data points. # Create three equidistant points data = np.linspace(-1, 1, 3) kde = sm.nonparametric.KDEUnivariate(data) # Create a figure fig = plt.figure(figsize=(12, 5)) # Enumerate every option for the kernel for i, kernel in enumerate(kernel_switch.keys()): # Create a subplot, set the title ax = fig.add_subplot(2, 4, i + 1) ax.set_title('Kernel function "{}"'.format(kernel)) # Fit the model (estimate densities) kde.fit(kernel=kernel, fft=False, gridsize=2**10) # Create the plot ax.plot( kde.support, kde.density, lw=3, label='KDE from samples', zorder=10) ax.scatter(data, np.zeros_like(data), marker='x', color='red') plt.grid(True, zorder=-5) ax.set_xlim([-3, 3]) plt.tight_layout() # ## A more difficult case # # The fit is not always perfect. See the example below for a harder case. obs_dist = mixture_rvs([.25, .75], size=250, dist=[stats.norm, stats.beta], kwargs=(dict(loc=-1, scale=.5), dict(loc=1, scale=1, args=(1, .5)))) kde = sm.nonparametric.KDEUnivariate(obs_dist) kde.fit() fig = plt.figure(figsize=(12, 5)) ax = fig.add_subplot(111) ax.hist(obs_dist, bins=20, normed=True, edgecolor='k', zorder=4, alpha=0.5) ax.plot(kde.support, kde.density, lw=3, zorder=7) # Plot the samples ax.scatter( obs_dist, np.abs(np.random.randn(obs_dist.size)) / 50, marker='x', color='red', zorder=20, label='Data samples', alpha=0.5) ax.grid(True, zorder=-5) # ## The KDE is a distribution # # Since the KDE is a distribution, we can access attributes and methods # such as: # # - `entropy` # - `evaluate` # - `cdf` # - `icdf` # - `sf` # - `cumhazard` obs_dist = mixture_rvs([.25, .75], size=1000, dist=[stats.norm, stats.norm], kwargs=(dict(loc=-1, scale=.5), dict(loc=1, scale=.5))) kde = sm.nonparametric.KDEUnivariate(obs_dist) kde.fit(gridsize=2**10) kde.entropy kde.evaluate(-1) # ### Cumulative distribution, it's inverse, and the survival function fig = plt.figure(figsize=(12, 5)) ax = fig.add_subplot(111) ax.plot(kde.support, kde.cdf, lw=3, label='CDF') ax.plot( np.linspace(0, 1, num=kde.icdf.size), kde.icdf, lw=3, label='Inverse CDF') ax.plot(kde.support, kde.sf, lw=3, label='Survival function') ax.legend(loc='best') ax.grid(True, zorder=-5) # ### The Cumulative Hazard Function fig = plt.figure(figsize=(12, 5)) ax = fig.add_subplot(111) ax.plot(kde.support, kde.cumhazard, lw=3, label='Cumulative Hazard Function') ax.legend(loc='best') ax.grid(True, zorder=-5) statsmodels-0.12.2/examples/python/markov_autoregression.py000066400000000000000000000241331400612667500243110ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook markov_autoregression.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # ## Markov switching autoregression models # This notebook provides an example of the use of Markov switching models # in statsmodels to replicate a number of results presented in Kim and # Nelson (1999). It applies the Hamilton (1989) filter the Kim (1994) # smoother. # # This is tested against the Markov-switching models from E-views 8, which # can be found at http://www.eviews.com/EViews8/ev8ecswitch_n.html#MarkovAR # or the Markov-switching models of Stata 14 which can be found at # http://www.stata.com/manuals14/tsmswitch.pdf. import numpy as np import pandas as pd import statsmodels.api as sm import matplotlib.pyplot as plt import requests from io import BytesIO # NBER recessions from pandas_datareader.data import DataReader from datetime import datetime usrec = DataReader( 'USREC', 'fred', start=datetime(1947, 1, 1), end=datetime(2013, 4, 1)) # ### Hamilton (1989) switching model of GNP # # This replicates Hamilton's (1989) seminal paper introducing Markov- # switching models. The model is an autoregressive model of order 4 in which # the mean of the process switches between two regimes. It can be written: # # $$ # y_t = \mu_{S_t} + \phi_1 (y_{t-1} - \mu_{S_{t-1}}) + \phi_2 (y_{t-2} - # \mu_{S_{t-2}}) + \phi_3 (y_{t-3} - \mu_{S_{t-3}}) + \phi_4 (y_{t-4} - # \mu_{S_{t-4}}) + \varepsilon_t # $$ # # Each period, the regime transitions according to the following matrix of # transition probabilities: # # $$ P(S_t = s_t | S_{t-1} = s_{t-1}) = # \begin{bmatrix} # p_{00} & p_{10} \\ # p_{01} & p_{11} # \end{bmatrix} # $$ # # where $p_{ij}$ is the probability of transitioning *from* regime $i$, # *to* regime $j$. # # The model class is `MarkovAutoregression` in the time-series part of # `statsmodels`. In order to create the model, we must specify the number of # regimes with `k_regimes=2`, and the order of the autoregression with # `order=4`. The default model also includes switching autoregressive # coefficients, so here we also need to specify `switching_ar=False` to # avoid that. # # After creation, the model is `fit` via maximum likelihood estimation. # Under the hood, good starting parameters are found using a number of steps # of the expectation maximization (EM) algorithm, and a quasi-Newton (BFGS) # algorithm is applied to quickly find the maximum. # Get the RGNP data to replicate Hamilton dta = pd.read_stata('https://www.stata-press.com/data/r14/rgnp.dta').iloc[1:] dta.index = pd.DatetimeIndex(dta.date, freq='QS') dta_hamilton = dta.rgnp # Plot the data dta_hamilton.plot(title='Growth rate of Real GNP', figsize=(12, 3)) # Fit the model mod_hamilton = sm.tsa.MarkovAutoregression( dta_hamilton, k_regimes=2, order=4, switching_ar=False) res_hamilton = mod_hamilton.fit() res_hamilton.summary() # We plot the filtered and smoothed probabilities of a recession. Filtered # refers to an estimate of the probability at time $t$ based on data up to # and including time $t$ (but excluding time $t+1, ..., T$). Smoothed refers # to an estimate of the probability at time $t$ using all the data in the # sample. # # For reference, the shaded periods represent the NBER recessions. fig, axes = plt.subplots(2, figsize=(7, 7)) ax = axes[0] ax.plot(res_hamilton.filtered_marginal_probabilities[0]) ax.fill_between( usrec.index, 0, 1, where=usrec['USREC'].values, color='k', alpha=0.1) ax.set_xlim(dta_hamilton.index[4], dta_hamilton.index[-1]) ax.set(title='Filtered probability of recession') ax = axes[1] ax.plot(res_hamilton.smoothed_marginal_probabilities[0]) ax.fill_between( usrec.index, 0, 1, where=usrec['USREC'].values, color='k', alpha=0.1) ax.set_xlim(dta_hamilton.index[4], dta_hamilton.index[-1]) ax.set(title='Smoothed probability of recession') fig.tight_layout() # From the estimated transition matrix we can calculate the expected # duration of a recession versus an expansion. print(res_hamilton.expected_durations) # In this case, it is expected that a recession will last about one year # (4 quarters) and an expansion about two and a half years. # ### Kim, Nelson, and Startz (1998) Three-state Variance Switching # # This model demonstrates estimation with regime heteroskedasticity # (switching of variances) and no mean effect. The dataset can be reached at # http://econ.korea.ac.kr/~cjkim/MARKOV/data/ew_excs.prn. # # The model in question is: # # $$ # \begin{align} # y_t & = \varepsilon_t \\ # \varepsilon_t & \sim N(0, \sigma_{S_t}^2) # \end{align} # $$ # # Since there is no autoregressive component, this model can be fit using # the `MarkovRegression` class. Since there is no mean effect, we specify # `trend='nc'`. There are hypothesized to be three regimes for the switching # variances, so we specify `k_regimes=3` and `switching_variance=True` (by # default, the variance is assumed to be the same across regimes). # Get the dataset ew_excs = requests.get( 'http://econ.korea.ac.kr/~cjkim/MARKOV/data/ew_excs.prn').content raw = pd.read_table( BytesIO(ew_excs), header=None, skipfooter=1, engine='python') raw.index = pd.date_range('1926-01-01', '1995-12-01', freq='MS') dta_kns = raw.loc[:'1986'] - raw.loc[:'1986'].mean() # Plot the dataset dta_kns[0].plot(title='Excess returns', figsize=(12, 3)) # Fit the model mod_kns = sm.tsa.MarkovRegression( dta_kns, k_regimes=3, trend='nc', switching_variance=True) res_kns = mod_kns.fit() res_kns.summary() # Below we plot the probabilities of being in each of the regimes; only in # a few periods is a high-variance regime probable. fig, axes = plt.subplots(3, figsize=(10, 7)) ax = axes[0] ax.plot(res_kns.smoothed_marginal_probabilities[0]) ax.set(title='Smoothed probability of a low-variance regime for stock returns') ax = axes[1] ax.plot(res_kns.smoothed_marginal_probabilities[1]) ax.set( title='Smoothed probability of a medium-variance regime for stock returns') ax = axes[2] ax.plot(res_kns.smoothed_marginal_probabilities[2]) ax.set( title='Smoothed probability of a high-variance regime for stock returns') fig.tight_layout() # ### Filardo (1994) Time-Varying Transition Probabilities # # This model demonstrates estimation with time-varying transition # probabilities. The dataset can be reached at # http://econ.korea.ac.kr/~cjkim/MARKOV/data/filardo.prn. # # In the above models we have assumed that the transition probabilities # are constant across time. Here we allow the probabilities to change with # the state of the economy. Otherwise, the model is the same Markov # autoregression of Hamilton (1989). # # Each period, the regime now transitions according to the following # matrix of time-varying transition probabilities: # # $$ P(S_t = s_t | S_{t-1} = s_{t-1}) = # \begin{bmatrix} # p_{00,t} & p_{10,t} \\ # p_{01,t} & p_{11,t} # \end{bmatrix} # $$ # # where $p_{ij,t}$ is the probability of transitioning *from* regime $i$, # *to* regime $j$ in period $t$, and is defined to be: # # $$ # p_{ij,t} = \frac{\exp\{ x_{t-1}' \beta_{ij} \}}{1 + \exp\{ x_{t-1}' # \beta_{ij} \}} # $$ # # Instead of estimating the transition probabilities as part of maximum # likelihood, the regression coefficients $\beta_{ij}$ are estimated. These # coefficients relate the transition probabilities to a vector of pre- # determined or exogenous regressors $x_{t-1}$. # Get the dataset filardo = requests.get( 'http://econ.korea.ac.kr/~cjkim/MARKOV/data/filardo.prn').content dta_filardo = pd.read_table( BytesIO(filardo), sep=' +', header=None, skipfooter=1, engine='python') dta_filardo.columns = ['month', 'ip', 'leading'] dta_filardo.index = pd.date_range('1948-01-01', '1991-04-01', freq='MS') dta_filardo['dlip'] = np.log(dta_filardo['ip']).diff() * 100 # Deflated pre-1960 observations by ratio of std. devs. # See hmt_tvp.opt or Filardo (1994) p. 302 std_ratio = dta_filardo['dlip']['1960-01-01':].std( ) / dta_filardo['dlip'][:'1959-12-01'].std() dta_filardo[ 'dlip'][:'1959-12-01'] = dta_filardo['dlip'][:'1959-12-01'] * std_ratio dta_filardo['dlleading'] = np.log(dta_filardo['leading']).diff() * 100 dta_filardo['dmdlleading'] = dta_filardo['dlleading'] - dta_filardo[ 'dlleading'].mean() # Plot the data dta_filardo['dlip'].plot( title='Standardized growth rate of industrial production', figsize=(13, 3)) plt.figure() dta_filardo['dmdlleading'].plot( title='Leading indicator', figsize=(13, 3)) # The time-varying transition probabilities are specified by the # `exog_tvtp` parameter. # # Here we demonstrate another feature of model fitting - the use of a # random search for MLE starting parameters. Because Markov switching models # are often characterized by many local maxima of the likelihood function, # performing an initial optimization step can be helpful to find the best # parameters. # # Below, we specify that 20 random perturbations from the starting # parameter vector are examined and the best one used as the actual starting # parameters. Because of the random nature of the search, we seed the random # number generator beforehand to allow replication of the result. mod_filardo = sm.tsa.MarkovAutoregression( dta_filardo.iloc[2:]['dlip'], k_regimes=2, order=4, switching_ar=False, exog_tvtp=sm.add_constant(dta_filardo.iloc[1:-1]['dmdlleading'])) np.random.seed(12345) res_filardo = mod_filardo.fit(search_reps=20) res_filardo.summary() # Below we plot the smoothed probability of the economy operating in a # low-production state, and again include the NBER recessions for # comparison. fig, ax = plt.subplots(figsize=(12, 3)) ax.plot(res_filardo.smoothed_marginal_probabilities[0]) ax.fill_between( usrec.index, 0, 1, where=usrec['USREC'].values, color='gray', alpha=0.2) ax.set_xlim(dta_filardo.index[6], dta_filardo.index[-1]) ax.set(title='Smoothed probability of a low-production state') # Using the time-varying transition probabilities, we can see how the # expected duration of a low-production state changes over time: # res_filardo.expected_durations[0].plot( title='Expected duration of a low-production state', figsize=(12, 3)) # During recessions, the expected duration of a low-production state is # much higher than in an expansion. statsmodels-0.12.2/examples/python/markov_regression.py000066400000000000000000000170311400612667500234170ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook markov_regression.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # ## Markov switching dynamic regression models # This notebook provides an example of the use of Markov switching models # in statsmodels to estimate dynamic regression models with changes in # regime. It follows the examples in the Stata Markov switching # documentation, which can be found at # http://www.stata.com/manuals14/tsmswitch.pdf. import numpy as np import pandas as pd import statsmodels.api as sm import matplotlib.pyplot as plt # NBER recessions from pandas_datareader.data import DataReader from datetime import datetime usrec = DataReader( 'USREC', 'fred', start=datetime(1947, 1, 1), end=datetime(2013, 4, 1)) # ### Federal funds rate with switching intercept # # The first example models the federal funds rate as noise around a # constant intercept, but where the intercept changes during different # regimes. The model is simply: # # $$r_t = \mu_{S_t} + \varepsilon_t \qquad \varepsilon_t \sim N(0, # \sigma^2)$$ # # where $S_t \in \{0, 1\}$, and the regime transitions according to # # $$ P(S_t = s_t | S_{t-1} = s_{t-1}) = # \begin{bmatrix} # p_{00} & p_{10} \\ # 1 - p_{00} & 1 - p_{10} # \end{bmatrix} # $$ # # We will estimate the parameters of this model by maximum likelihood: # $p_{00}, p_{10}, \mu_0, \mu_1, \sigma^2$. # # The data used in this example can be found at https://www.stata- # press.com/data/r14/usmacro. # Get the federal funds rate data from statsmodels.tsa.regime_switching.tests.test_markov_regression import fedfunds dta_fedfunds = pd.Series( fedfunds, index=pd.date_range('1954-07-01', '2010-10-01', freq='QS')) # Plot the data dta_fedfunds.plot(title='Federal funds rate', figsize=(12, 3)) # Fit the model # (a switching mean is the default of the MarkovRegession model) mod_fedfunds = sm.tsa.MarkovRegression(dta_fedfunds, k_regimes=2) res_fedfunds = mod_fedfunds.fit() res_fedfunds.summary() # From the summary output, the mean federal funds rate in the first regime # (the "low regime") is estimated to be $3.7$ whereas in the "high regime" # it is $9.6$. Below we plot the smoothed probabilities of being in the high # regime. The model suggests that the 1980's was a time-period in which a # high federal funds rate existed. res_fedfunds.smoothed_marginal_probabilities[1].plot( title='Probability of being in the high regime', figsize=(12, 3)) # From the estimated transition matrix we can calculate the expected # duration of a low regime versus a high regime. print(res_fedfunds.expected_durations) # A low regime is expected to persist for about fourteen years, whereas # the high regime is expected to persist for only about five years. # ### Federal funds rate with switching intercept and lagged dependent # variable # # The second example augments the previous model to include the lagged # value of the federal funds rate. # # $$r_t = \mu_{S_t} + r_{t-1} \beta_{S_t} + \varepsilon_t \qquad # \varepsilon_t \sim N(0, \sigma^2)$$ # # where $S_t \in \{0, 1\}$, and the regime transitions according to # # $$ P(S_t = s_t | S_{t-1} = s_{t-1}) = # \begin{bmatrix} # p_{00} & p_{10} \\ # 1 - p_{00} & 1 - p_{10} # \end{bmatrix} # $$ # # We will estimate the parameters of this model by maximum likelihood: # $p_{00}, p_{10}, \mu_0, \mu_1, \beta_0, \beta_1, \sigma^2$. # Fit the model mod_fedfunds2 = sm.tsa.MarkovRegression( dta_fedfunds.iloc[1:], k_regimes=2, exog=dta_fedfunds.iloc[:-1]) res_fedfunds2 = mod_fedfunds2.fit() res_fedfunds2.summary() # There are several things to notice from the summary output: # # 1. The information criteria have decreased substantially, indicating # that this model has a better fit than the previous model. # 2. The interpretation of the regimes, in terms of the intercept, have # switched. Now the first regime has the higher intercept and the second # regime has a lower intercept. # # Examining the smoothed probabilities of the high regime state, we now # see quite a bit more variability. res_fedfunds2.smoothed_marginal_probabilities[0].plot( title='Probability of being in the high regime', figsize=(12, 3)) # Finally, the expected durations of each regime have decreased quite a # bit. print(res_fedfunds2.expected_durations) # ### Taylor rule with 2 or 3 regimes # # We now include two additional exogenous variables - a measure of the # output gap and a measure of inflation - to estimate a switching Taylor- # type rule with both 2 and 3 regimes to see which fits the data better. # # Because the models can be often difficult to estimate, for the 3-regime # model we employ a search over starting parameters to improve results, # specifying 20 random search repetitions. # Get the additional data from statsmodels.tsa.regime_switching.tests.test_markov_regression import ogap, inf dta_ogap = pd.Series( ogap, index=pd.date_range('1954-07-01', '2010-10-01', freq='QS')) dta_inf = pd.Series( inf, index=pd.date_range('1954-07-01', '2010-10-01', freq='QS')) exog = pd.concat((dta_fedfunds.shift(), dta_ogap, dta_inf), axis=1).iloc[4:] # Fit the 2-regime model mod_fedfunds3 = sm.tsa.MarkovRegression( dta_fedfunds.iloc[4:], k_regimes=2, exog=exog) res_fedfunds3 = mod_fedfunds3.fit() # Fit the 3-regime model np.random.seed(12345) mod_fedfunds4 = sm.tsa.MarkovRegression( dta_fedfunds.iloc[4:], k_regimes=3, exog=exog) res_fedfunds4 = mod_fedfunds4.fit(search_reps=20) res_fedfunds3.summary() res_fedfunds4.summary() # Due to lower information criteria, we might prefer the 3-state model, # with an interpretation of low-, medium-, and high-interest rate regimes. # The smoothed probabilities of each regime are plotted below. fig, axes = plt.subplots(3, figsize=(10, 7)) ax = axes[0] ax.plot(res_fedfunds4.smoothed_marginal_probabilities[0]) ax.set(title='Smoothed probability of a low-interest rate regime') ax = axes[1] ax.plot(res_fedfunds4.smoothed_marginal_probabilities[1]) ax.set(title='Smoothed probability of a medium-interest rate regime') ax = axes[2] ax.plot(res_fedfunds4.smoothed_marginal_probabilities[2]) ax.set(title='Smoothed probability of a high-interest rate regime') fig.tight_layout() # ### Switching variances # # We can also accommodate switching variances. In particular, we consider # the model # # $$ # y_t = \mu_{S_t} + y_{t-1} \beta_{S_t} + \varepsilon_t \quad # \varepsilon_t \sim N(0, \sigma_{S_t}^2) # $$ # # We use maximum likelihood to estimate the parameters of this model: # $p_{00}, p_{10}, \mu_0, \mu_1, \beta_0, \beta_1, \sigma_0^2, \sigma_1^2$. # # The application is to absolute returns on stocks, where the data can be # found at https://www.stata-press.com/data/r14/snp500. # Get the federal funds rate data from statsmodels.tsa.regime_switching.tests.test_markov_regression import areturns dta_areturns = pd.Series( areturns, index=pd.date_range('2004-05-04', '2014-5-03', freq='W')) # Plot the data dta_areturns.plot(title='Absolute returns, S&P500', figsize=(12, 3)) # Fit the model mod_areturns = sm.tsa.MarkovRegression( dta_areturns.iloc[1:], k_regimes=2, exog=dta_areturns.iloc[:-1], switching_variance=True) res_areturns = mod_areturns.fit() res_areturns.summary() # The first regime is a low-variance regime and the second regime is a # high-variance regime. Below we plot the probabilities of being in the low- # variance regime. Between 2008 and 2012 there does not appear to be a clear # indication of one regime guiding the economy. res_areturns.smoothed_marginal_probabilities[0].plot( title='Probability of being in a low-variance regime', figsize=(12, 3)) statsmodels-0.12.2/examples/python/mixed_lm_example.py000066400000000000000000000263121400612667500231730ustar00rootroot00000000000000# DO NOT EDIT # Autogenerated from the notebook mixed_lm_example.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT #!/usr/bin/env python # coding: utf-8 # # Linear Mixed Effects Models import numpy as np import pandas as pd import statsmodels.api as sm import statsmodels.formula.api as smf # **Note**: The R code and the results in this notebook has been converted # to markdown so that R is not required to build the documents. The R # results in the notebook were computed using R 3.5.1 and lme4 1.1. # ```ipython # %load_ext rpy2.ipython # ``` # ```ipython # %R library(lme4) # ``` # ``` # array(['lme4', 'Matrix', 'tools', 'stats', 'graphics', 'grDevices', # 'utils', 'datasets', 'methods', 'base'], dtype=' .2].values statsmodels-0.12.2/examples/python/plots_boxplots.py000066400000000000000000000144511400612667500227560ustar00rootroot00000000000000# DO NOT EDIT # Autogenerated from the notebook plots_boxplots.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT #!/usr/bin/env python # coding: utf-8 # # Box Plots # The following illustrates some options for the boxplot in statsmodels. # These include `violin_plot` and `bean_plot`. import numpy as np import matplotlib.pyplot as plt import statsmodels.api as sm # ## Bean Plots # The following example is taken from the docstring of `beanplot`. # # We use the American National Election Survey 1996 dataset, which has # Party # Identification of respondents as independent variable and (among other # data) age as dependent variable. data = sm.datasets.anes96.load_pandas() party_ID = np.arange(7) labels = [ "Strong Democrat", "Weak Democrat", "Independent-Democrat", "Independent-Independent", "Independent-Republican", "Weak Republican", "Strong Republican" ] # Group age by party ID, and create a violin plot with it: plt.rcParams['figure.subplot.bottom'] = 0.23 # keep labels visible plt.rcParams['figure.figsize'] = (10.0, 8.0) # make plot larger in notebook age = [data.exog['age'][data.endog == id] for id in party_ID] fig = plt.figure() ax = fig.add_subplot(111) plot_opts = { 'cutoff_val': 5, 'cutoff_type': 'abs', 'label_fontsize': 'small', 'label_rotation': 30 } sm.graphics.beanplot(age, ax=ax, labels=labels, plot_opts=plot_opts) ax.set_xlabel("Party identification of respondent.") ax.set_ylabel("Age") #plt.show() def beanplot(data, plot_opts={}, jitter=False): """helper function to try out different plot options """ fig = plt.figure() ax = fig.add_subplot(111) plot_opts_ = { 'cutoff_val': 5, 'cutoff_type': 'abs', 'label_fontsize': 'small', 'label_rotation': 30 } plot_opts_.update(plot_opts) sm.graphics.beanplot(data, ax=ax, labels=labels, jitter=jitter, plot_opts=plot_opts_) ax.set_xlabel("Party identification of respondent.") ax.set_ylabel("Age") fig = beanplot(age, jitter=True) fig = beanplot(age, plot_opts={'violin_width': 0.5, 'violin_fc': '#66c2a5'}) fig = beanplot(age, plot_opts={'violin_fc': '#66c2a5'}) fig = beanplot(age, plot_opts={ 'bean_size': 0.2, 'violin_width': 0.75, 'violin_fc': '#66c2a5' }) fig = beanplot(age, jitter=True, plot_opts={'violin_fc': '#66c2a5'}) fig = beanplot(age, jitter=True, plot_opts={ 'violin_width': 0.5, 'violin_fc': '#66c2a5' }) # ## Advanced Box Plots # Based of example script `example_enhanced_boxplots.py` (by Ralf Gommers) import numpy as np import matplotlib.pyplot as plt import statsmodels.api as sm # Necessary to make horizontal axis labels fit plt.rcParams['figure.subplot.bottom'] = 0.23 data = sm.datasets.anes96.load_pandas() party_ID = np.arange(7) labels = [ "Strong Democrat", "Weak Democrat", "Independent-Democrat", "Independent-Independent", "Independent-Republican", "Weak Republican", "Strong Republican" ] # Group age by party ID. age = [data.exog['age'][data.endog == id] for id in party_ID] # Create a violin plot. fig = plt.figure() ax = fig.add_subplot(111) sm.graphics.violinplot(age, ax=ax, labels=labels, plot_opts={ 'cutoff_val': 5, 'cutoff_type': 'abs', 'label_fontsize': 'small', 'label_rotation': 30 }) ax.set_xlabel("Party identification of respondent.") ax.set_ylabel("Age") ax.set_title("US national election '96 - Age & Party Identification") # Create a bean plot. fig2 = plt.figure() ax = fig2.add_subplot(111) sm.graphics.beanplot(age, ax=ax, labels=labels, plot_opts={ 'cutoff_val': 5, 'cutoff_type': 'abs', 'label_fontsize': 'small', 'label_rotation': 30 }) ax.set_xlabel("Party identification of respondent.") ax.set_ylabel("Age") ax.set_title("US national election '96 - Age & Party Identification") # Create a jitter plot. fig3 = plt.figure() ax = fig3.add_subplot(111) plot_opts = { 'cutoff_val': 5, 'cutoff_type': 'abs', 'label_fontsize': 'small', 'label_rotation': 30, 'violin_fc': (0.8, 0.8, 0.8), 'jitter_marker': '.', 'jitter_marker_size': 3, 'bean_color': '#FF6F00', 'bean_mean_color': '#009D91' } sm.graphics.beanplot(age, ax=ax, labels=labels, jitter=True, plot_opts=plot_opts) ax.set_xlabel("Party identification of respondent.") ax.set_ylabel("Age") ax.set_title("US national election '96 - Age & Party Identification") # Create an asymmetrical jitter plot. ix = data.exog['income'] < 16 # incomes < $30k age = data.exog['age'][ix] endog = data.endog[ix] age_lower_income = [age[endog == id] for id in party_ID] ix = data.exog['income'] >= 20 # incomes > $50k age = data.exog['age'][ix] endog = data.endog[ix] age_higher_income = [age[endog == id] for id in party_ID] fig = plt.figure() ax = fig.add_subplot(111) plot_opts['violin_fc'] = (0.5, 0.5, 0.5) plot_opts['bean_show_mean'] = False plot_opts['bean_show_median'] = False plot_opts['bean_legend_text'] = 'Income < \$30k' plot_opts['cutoff_val'] = 10 sm.graphics.beanplot(age_lower_income, ax=ax, labels=labels, side='left', jitter=True, plot_opts=plot_opts) plot_opts['violin_fc'] = (0.7, 0.7, 0.7) plot_opts['bean_color'] = '#009D91' plot_opts['bean_legend_text'] = 'Income > \$50k' sm.graphics.beanplot(age_higher_income, ax=ax, labels=labels, side='right', jitter=True, plot_opts=plot_opts) ax.set_xlabel("Party identification of respondent.") ax.set_ylabel("Age") ax.set_title("US national election '96 - Age & Party Identification") # Show all plots. #plt.show() statsmodels-0.12.2/examples/python/predict.py000066400000000000000000000033021400612667500213060ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook predict.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Prediction (out of sample) import numpy as np import statsmodels.api as sm # ## Artificial data nsample = 50 sig = 0.25 x1 = np.linspace(0, 20, nsample) X = np.column_stack((x1, np.sin(x1), (x1 - 5)**2)) X = sm.add_constant(X) beta = [5., 0.5, 0.5, -0.02] y_true = np.dot(X, beta) y = y_true + sig * np.random.normal(size=nsample) # ## Estimation olsmod = sm.OLS(y, X) olsres = olsmod.fit() print(olsres.summary()) # ## In-sample prediction ypred = olsres.predict(X) print(ypred) # ## Create a new sample of explanatory variables Xnew, predict and plot x1n = np.linspace(20.5, 25, 10) Xnew = np.column_stack((x1n, np.sin(x1n), (x1n - 5)**2)) Xnew = sm.add_constant(Xnew) ynewpred = olsres.predict(Xnew) # predict out of sample print(ynewpred) # ## Plot comparison import matplotlib.pyplot as plt fig, ax = plt.subplots() ax.plot(x1, y, 'o', label="Data") ax.plot(x1, y_true, 'b-', label="True") ax.plot( np.hstack((x1, x1n)), np.hstack((ypred, ynewpred)), 'r', label="OLS prediction") ax.legend(loc="best") # ## Predicting with Formulas # Using formulas can make both estimation and prediction a lot easier from statsmodels.formula.api import ols data = {"x1": x1, "y": y} res = ols("y ~ x1 + np.sin(x1) + I((x1-5)**2)", data=data).fit() # We use the `I` to indicate use of the Identity transform. Ie., we do not # want any expansion magic from using `**2` res.params # Now we only have to pass the single variable and we get the transformed # right-hand side variables automatically res.predict(exog=dict(x1=x1n)) statsmodels-0.12.2/examples/python/quantile_regression.py000066400000000000000000000077211400612667500237470ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook quantile_regression.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Quantile regression # # This example page shows how to use ``statsmodels``' ``QuantReg`` class # to replicate parts of the analysis published in # # * Koenker, Roger and Kevin F. Hallock. "Quantile Regressioin". Journal # of Economic Perspectives, Volume 15, Number 4, Fall 2001, Pages 143–156 # # We are interested in the relationship between income and expenditures on # food for a sample of working class Belgian households in 1857 (the Engel # data). # # ## Setup # # We first need to load some modules and to retrieve the data. # Conveniently, the Engel dataset is shipped with ``statsmodels``. import numpy as np import pandas as pd import statsmodels.api as sm import statsmodels.formula.api as smf import matplotlib.pyplot as plt data = sm.datasets.engel.load_pandas().data data.head() # ## Least Absolute Deviation # # The LAD model is a special case of quantile regression where q=0.5 mod = smf.quantreg('foodexp ~ income', data) res = mod.fit(q=.5) print(res.summary()) # ## Visualizing the results # # We estimate the quantile regression model for many quantiles between .05 # and .95, and compare best fit line from each of these models to Ordinary # Least Squares results. # ### Prepare data for plotting # # For convenience, we place the quantile regression results in a Pandas # DataFrame, and the OLS results in a dictionary. quantiles = np.arange(.05, .96, .1) def fit_model(q): res = mod.fit(q=q) return [q, res.params['Intercept'], res.params['income'] ] + res.conf_int().loc['income'].tolist() models = [fit_model(x) for x in quantiles] models = pd.DataFrame(models, columns=['q', 'a', 'b', 'lb', 'ub']) ols = smf.ols('foodexp ~ income', data).fit() ols_ci = ols.conf_int().loc['income'].tolist() ols = dict( a=ols.params['Intercept'], b=ols.params['income'], lb=ols_ci[0], ub=ols_ci[1]) print(models) print(ols) # ### First plot # # This plot compares best fit lines for 10 quantile regression models to # the least squares fit. As Koenker and Hallock (2001) point out, we see # that: # # 1. Food expenditure increases with income # 2. The *dispersion* of food expenditure increases with income # 3. The least squares estimates fit low income observations quite poorly # (i.e. the OLS line passes over most low income households) x = np.arange(data.income.min(), data.income.max(), 50) get_y = lambda a, b: a + b * x fig, ax = plt.subplots(figsize=(8, 6)) for i in range(models.shape[0]): y = get_y(models.a[i], models.b[i]) ax.plot(x, y, linestyle='dotted', color='grey') y = get_y(ols['a'], ols['b']) ax.plot(x, y, color='red', label='OLS') ax.scatter(data.income, data.foodexp, alpha=.2) ax.set_xlim((240, 3000)) ax.set_ylim((240, 2000)) legend = ax.legend() ax.set_xlabel('Income', fontsize=16) ax.set_ylabel( 'Food expenditure', fontsize=16) # ### Second plot # # The dotted black lines form 95% point-wise confidence band around 10 # quantile regression estimates (solid black line). The red lines represent # OLS regression results along with their 95% confidence interval. # # In most cases, the quantile regression point estimates lie outside the # OLS confidence interval, which suggests that the effect of income on food # expenditure may not be constant across the distribution. n = models.shape[0] p1 = plt.plot(models.q, models.b, color='black', label='Quantile Reg.') p2 = plt.plot(models.q, models.ub, linestyle='dotted', color='black') p3 = plt.plot(models.q, models.lb, linestyle='dotted', color='black') p4 = plt.plot(models.q, [ols['b']] * n, color='red', label='OLS') p5 = plt.plot(models.q, [ols['lb']] * n, linestyle='dotted', color='red') p6 = plt.plot(models.q, [ols['ub']] * n, linestyle='dotted', color='red') plt.ylabel(r'$\beta_{income}$') plt.xlabel('Quantiles of the conditional food expenditure distribution') plt.legend() plt.show() statsmodels-0.12.2/examples/python/recursive_ls.py000066400000000000000000000141401400612667500223630ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook recursive_ls.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Recursive least squares # # Recursive least squares is an expanding window version of ordinary least # squares. In addition to availability of regression coefficients computed # recursively, the recursively computed residuals the construction of # statistics to investigate parameter instability. # # The `RecursiveLS` class allows computation of recursive residuals and # computes CUSUM and CUSUM of squares statistics. Plotting these statistics # along with reference lines denoting statistically significant deviations # from the null hypothesis of stable parameters allows an easy visual # indication of parameter stability. # # Finally, the `RecursiveLS` model allows imposing linear restrictions on # the parameter vectors, and can be constructed using the formula interface. import numpy as np import pandas as pd import statsmodels.api as sm import matplotlib.pyplot as plt from pandas_datareader.data import DataReader np.set_printoptions(suppress=True) # ## Example 1: Copper # # We first consider parameter stability in the copper dataset (description # below). print(sm.datasets.copper.DESCRLONG) dta = sm.datasets.copper.load_pandas().data dta.index = pd.date_range('1951-01-01', '1975-01-01', freq='AS') endog = dta['WORLDCONSUMPTION'] # To the regressors in the dataset, we add a column of ones for an # intercept exog = sm.add_constant( dta[['COPPERPRICE', 'INCOMEINDEX', 'ALUMPRICE', 'INVENTORYINDEX']]) # First, construct and fit the model, and print a summary. Although the # `RLS` model computes the regression parameters recursively, so there are # as many estimates as there are datapoints, the summary table only presents # the regression parameters estimated on the entire sample; except for small # effects from initialization of the recursions, these estimates are # equivalent to OLS estimates. mod = sm.RecursiveLS(endog, exog) res = mod.fit() print(res.summary()) # The recursive coefficients are available in the `recursive_coefficients` # attribute. Alternatively, plots can generated using the # `plot_recursive_coefficient` method. print(res.recursive_coefficients.filtered[0]) res.plot_recursive_coefficient( range(mod.k_exog), alpha=None, figsize=(10, 6)) # The CUSUM statistic is available in the `cusum` attribute, but usually # it is more convenient to visually check for parameter stability using the # `plot_cusum` method. In the plot below, the CUSUM statistic does not move # outside of the 5% significance bands, so we fail to reject the null # hypothesis of stable parameters at the 5% level. print(res.cusum) fig = res.plot_cusum() # Another related statistic is the CUSUM of squares. It is available in # the `cusum_squares` attribute, but it is similarly more convenient to # check it visually, using the `plot_cusum_squares` method. In the plot # below, the CUSUM of squares statistic does not move outside of the 5% # significance bands, so we fail to reject the null hypothesis of stable # parameters at the 5% level. res.plot_cusum_squares() # # Example 2: Quantity theory of money # # The quantity theory of money suggests that "a given change in the rate # of change in the quantity of money induces ... an equal change in the rate # of price inflation" (Lucas, 1980). Following Lucas, we examine the # relationship between double-sided exponentially weighted moving averages # of money growth and CPI inflation. Although Lucas found the relationship # between these variables to be stable, more recently it appears that the # relationship is unstable; see e.g. Sargent and Surico (2010). start = '1959-12-01' end = '2015-01-01' m2 = DataReader('M2SL', 'fred', start=start, end=end) cpi = DataReader('CPIAUCSL', 'fred', start=start, end=end) def ewma(series, beta, n_window): nobs = len(series) scalar = (1 - beta) / (1 + beta) ma = [] k = np.arange(n_window, 0, -1) weights = np.r_[beta**k, 1, beta**k[::-1]] for t in range(n_window, nobs - n_window): window = series.iloc[t - n_window:t + n_window + 1].values ma.append(scalar * np.sum(weights * window)) return pd.Series( ma, name=series.name, index=series.iloc[n_window:-n_window].index) m2_ewma = ewma( np.log(m2['M2SL'].resample('QS').mean()).diff().iloc[1:], 0.95, 10 * 4) cpi_ewma = ewma( np.log(cpi['CPIAUCSL'].resample('QS').mean()).diff().iloc[1:], 0.95, 10 * 4) # After constructing the moving averages using the $\beta = 0.95$ filter # of Lucas (with a window of 10 years on either side), we plot each of the # series below. Although they appear to move together prior for part of the # sample, after 1990 they appear to diverge. fig, ax = plt.subplots(figsize=(13, 3)) ax.plot(m2_ewma, label='M2 Growth (EWMA)') ax.plot(cpi_ewma, label='CPI Inflation (EWMA)') ax.legend() endog = cpi_ewma exog = sm.add_constant(m2_ewma) exog.columns = ['const', 'M2'] mod = sm.RecursiveLS(endog, exog) res = mod.fit() print(res.summary()) res.plot_recursive_coefficient( 1, alpha=None) # The CUSUM plot now shows substantial deviation at the 5% level, # suggesting a rejection of the null hypothesis of parameter stability. res.plot_cusum() # Similarly, the CUSUM of squares shows substantial deviation at the 5% # level, also suggesting a rejection of the null hypothesis of parameter # stability. res.plot_cusum_squares() # # Example 3: Linear restrictions and formulas # ### Linear restrictions # # It is not hard to implement linear restrictions, using the `constraints` # parameter in constructing the model. endog = dta['WORLDCONSUMPTION'] exog = sm.add_constant( dta[['COPPERPRICE', 'INCOMEINDEX', 'ALUMPRICE', 'INVENTORYINDEX']]) mod = sm.RecursiveLS(endog, exog, constraints='COPPERPRICE = ALUMPRICE') res = mod.fit() print(res.summary()) # ### Formula # # One could fit the same model using the class method `from_formula`. mod = sm.RecursiveLS.from_formula( 'WORLDCONSUMPTION ~ COPPERPRICE + INCOMEINDEX + ALUMPRICE + INVENTORYINDEX', dta, constraints='COPPERPRICE = ALUMPRICE') res = mod.fit() print(res.summary()) statsmodels-0.12.2/examples/python/regression_diagnostics.py000066400000000000000000000060371400612667500244330ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook regression_diagnostics.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Regression diagnostics # This example file shows how to use a few of the ``statsmodels`` # regression diagnostic tests in a real-life context. You can learn about # more tests and find out more information abou the tests here on the # [Regression Diagnostics # page.](https://www.statsmodels.org/stable/diagnostic.html) # # Note that most of the tests described here only return a tuple of # numbers, without any annotation. A full description of outputs is always # included in the docstring and in the online ``statsmodels`` documentation. # For presentation purposes, we use the ``zip(name,test)`` construct to # pretty-print short descriptions in the examples below. # ## Estimate a regression model from statsmodels.compat import lzip import numpy as np import pandas as pd import statsmodels.formula.api as smf import statsmodels.stats.api as sms import matplotlib.pyplot as plt # Load data url = 'https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/master/csv/HistData/Guerry.csv' dat = pd.read_csv(url) # Fit regression model (using the natural log of one of the regressors) results = smf.ols('Lottery ~ Literacy + np.log(Pop1831)', data=dat).fit() # Inspect the results print(results.summary()) # ## Normality of the residuals # Jarque-Bera test: name = ['Jarque-Bera', 'Chi^2 two-tail prob.', 'Skew', 'Kurtosis'] test = sms.jarque_bera(results.resid) lzip(name, test) # Omni test: name = ['Chi^2', 'Two-tail probability'] test = sms.omni_normtest(results.resid) lzip(name, test) # ## Influence tests # # Once created, an object of class ``OLSInfluence`` holds attributes and # methods that allow users to assess the influence of each observation. For # example, we can compute and extract the first few rows of DFbetas by: from statsmodels.stats.outliers_influence import OLSInfluence test_class = OLSInfluence(results) test_class.dfbetas[:5, :] # Explore other options by typing ``dir(influence_test)`` # # Useful information on leverage can also be plotted: from statsmodels.graphics.regressionplots import plot_leverage_resid2 fig, ax = plt.subplots(figsize=(8, 6)) fig = plot_leverage_resid2(results, ax=ax) # Other plotting options can be found on the [Graphics # page.](https://www.statsmodels.org/stable/graphics.html) # ## Multicollinearity # # Condition number: np.linalg.cond(results.model.exog) # ## Heteroskedasticity tests # # Breush-Pagan test: name = ['Lagrange multiplier statistic', 'p-value', 'f-value', 'f p-value'] test = sms.het_breuschpagan(results.resid, results.model.exog) lzip(name, test) # Goldfeld-Quandt test name = ['F statistic', 'p-value'] test = sms.het_goldfeldquandt(results.resid, results.model.exog) lzip(name, test) # ## Linearity # # Harvey-Collier multiplier test for Null hypothesis that the linear # specification is correct: name = ['t value', 'p value'] test = sms.linear_harvey_collier(results) lzip(name, test) statsmodels-0.12.2/examples/python/regression_plots.py000066400000000000000000000230531400612667500232620ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook regression_plots.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Regression Plots from statsmodels.compat import lzip import numpy as np import matplotlib.pyplot as plt import statsmodels.api as sm from statsmodels.formula.api import ols # ## Duncan's Prestige Dataset # ### Load the Data # We can use a utility function to load any R dataset available from the # great Rdatasets # package. prestige = sm.datasets.get_rdataset("Duncan", "carData", cache=True).data prestige.head() prestige_model = ols("prestige ~ income + education", data=prestige).fit() print(prestige_model.summary()) # ### Influence plots # Influence plots show the (externally) studentized residuals vs. the # leverage of each observation as measured by the hat matrix. # # Externally studentized residuals are residuals that are scaled by their # standard deviation where # # $$var(\hat{\epsilon}_i)=\hat{\sigma}^2_i(1-h_{ii})$$ # # with # # $$\hat{\sigma}^2_i=\frac{1}{n - p - 1 \;\;}\sum_{j}^{n}\;\;\;\forall # \;\;\; j \neq i$$ # # $n$ is the number of observations and $p$ is the number of regressors. # $h_{ii}$ is the $i$-th diagonal element of the hat matrix # # $$H=X(X^{\;\prime}X)^{-1}X^{\;\prime}$$ # # The influence of each point can be visualized by the criterion keyword # argument. Options are Cook's distance and DFFITS, two measures of # influence. fig, ax = plt.subplots(figsize=(12, 8)) fig = sm.graphics.influence_plot(prestige_model, ax=ax, criterion="cooks") # As you can see there are a few worrisome observations. Both contractor # and reporter have low leverage but a large residual.
# RR.engineer has small residual and large leverage. Conductor and # minister have both high leverage and large residuals, and,
# therefore, large influence. # ### Partial Regression Plots # Since we are doing multivariate regressions, we cannot just look at # individual bivariate plots to discern relationships.
# Instead, we want to look at the relationship of the dependent variable # and independent variables conditional on the other
# independent variables. We can do this through using partial regression # plots, otherwise known as added variable plots.
# # In a partial regression plot, to discern the relationship between the # response variable and the $k$-th variable, we compute
# the residuals by regressing the response variable versus the independent # variables excluding $X_k$. We can denote this by
# $X_{\sim k}$. We then compute the residuals by regressing $X_k$ on # $X_{\sim k}$. The partial regression plot is the plot
# of the former versus the latter residuals.
# # The notable points of this plot are that the fitted line has slope # $\beta_k$ and intercept zero. The residuals of this plot
# are the same as those of the least squares fit of the original model # with full $X$. You can discern the effects of the
# individual data values on the estimation of a coefficient easily. If # obs_labels is True, then these points are annotated
# with their observation label. You can also see the violation of # underlying assumptions such as homoskedasticity and
# linearity. fig, ax = plt.subplots(figsize=(12, 8)) fig = sm.graphics.plot_partregress( "prestige", "income", ["income", "education"], data=prestige, ax=ax) fix, ax = plt.subplots(figsize=(12, 14)) fig = sm.graphics.plot_partregress( "prestige", "income", ["education"], data=prestige, ax=ax) # As you can see the partial regression plot confirms the influence of # conductor, minister, and RR.engineer on the partial relationship between # income and prestige. The cases greatly decrease the effect of income on # prestige. Dropping these cases confirms this. subset = ~prestige.index.isin(["conductor", "RR.engineer", "minister"]) prestige_model2 = ols( "prestige ~ income + education", data=prestige, subset=subset).fit() print(prestige_model2.summary()) # For a quick check of all the regressors, you can use # plot_partregress_grid. These plots will not label the
# points, but you can use them to identify problems and then use # plot_partregress to get more information. fig = plt.figure(figsize=(12, 8)) fig = sm.graphics.plot_partregress_grid(prestige_model, fig=fig) # ### Component-Component plus Residual (CCPR) Plots # The CCPR plot provides a way to judge the effect of one regressor on the #
# response variable by taking into account the effects of the other
# independent variables. The partial residuals plot is defined as
# $\text{Residuals} + B_iX_i \text{ }\text{ }$ versus $X_i$. The # component adds $B_iX_i$ versus
# $X_i$ to show where the fitted line would lie. Care should be taken if # $X_i$
# is highly correlated with any of the other independent variables. If # this
# is the case, the variance evident in the plot will be an underestimate # of
# the true variance. fig, ax = plt.subplots(figsize=(12, 8)) fig = sm.graphics.plot_ccpr(prestige_model, "education", ax=ax) # As you can see the relationship between the variation in prestige # explained by education conditional on income seems to be linear, though # you can see there are some observations that are exerting considerable # influence on the relationship. We can quickly look at more than one # variable by using plot_ccpr_grid. fig = plt.figure(figsize=(12, 8)) fig = sm.graphics.plot_ccpr_grid(prestige_model, fig=fig) # ### Regression Plots # The plot_regress_exog function is a convenience function that gives a # 2x2 plot containing the dependent variable and fitted values with # confidence intervals vs. the independent variable chosen, the residuals of # the model vs. the chosen independent variable, a partial regression plot, # and a CCPR plot. This function can be used for quickly checking modeling # assumptions with respect to a single regressor. fig = plt.figure(figsize=(12, 8)) fig = sm.graphics.plot_regress_exog(prestige_model, "education", fig=fig) # ### Fit Plot # The plot_fit function plots the fitted values versus a chosen # independent variable. It includes prediction confidence intervals and # optionally plots the true dependent variable. fig, ax = plt.subplots(figsize=(12, 8)) fig = sm.graphics.plot_fit(prestige_model, "education", ax=ax) # ## Statewide Crime 2009 Dataset # Compare the following to http://www.ats.ucla.edu/stat/stata/webbooks/reg # /chapter4/statareg_self_assessment_answers4.htm # # Though the data here is not the same as in that example. You could run # that example by uncommenting the necessary cells below. #dta = # pd.read_csv("http://www.stat.ufl.edu/~aa/social/csv_files/statewide- # crime-2.csv") #dta = dta.set_index("State", inplace=True).dropna() #dta.rename(columns={"VR" : "crime", # "MR" : "murder", # "M" : "pctmetro", # "W" : "pctwhite", # "H" : "pcths", # "P" : "poverty", # "S" : "single" # }, inplace=True) # #crime_model = ols("murder ~ pctmetro + poverty + pcths + single", # data=dta).fit() dta = sm.datasets.statecrime.load_pandas().data crime_model = ols( "murder ~ urban + poverty + hs_grad + single", data=dta).fit() print(crime_model.summary()) # ### Partial Regression Plots fig = plt.figure(figsize=(12, 8)) fig = sm.graphics.plot_partregress_grid(crime_model, fig=fig) fig, ax = plt.subplots(figsize=(12, 8)) fig = sm.graphics.plot_partregress( "murder", "hs_grad", ["urban", "poverty", "single"], ax=ax, data=dta) # ### Leverage-Resid2 Plot # Closely related to the influence_plot is the leverage-resid2 # plot. fig, ax = plt.subplots(figsize=(8, 6)) fig = sm.graphics.plot_leverage_resid2(crime_model, ax=ax) # ### Influence Plot fig, ax = plt.subplots(figsize=(8, 6)) fig = sm.graphics.influence_plot(crime_model, ax=ax) # ### Using robust regression to correct for outliers. # Part of the problem here in recreating the Stata results is that # M-estimators are not robust to leverage points. MM-estimators should do # better with this examples. from statsmodels.formula.api import rlm rob_crime_model = rlm( "murder ~ urban + poverty + hs_grad + single", data=dta, M=sm.robust.norms.TukeyBiweight(3)).fit(conv="weights") print(rob_crime_model.summary()) #rob_crime_model = rlm("murder ~ pctmetro + poverty + pcths + single", # data=dta, M=sm.robust.norms.TukeyBiweight()).fit(conv="weights") #print(rob_crime_model.summary()) # There is not yet an influence diagnostics method as part of RLM, but we # can recreate them. (This depends on the status of [issue # #888](https://github.com/statsmodels/statsmodels/issues/808)) weights = rob_crime_model.weights idx = weights > 0 X = rob_crime_model.model.exog[idx.values] ww = weights[idx] / weights[idx].mean() hat_matrix_diag = ww * (X * np.linalg.pinv(X).T).sum(1) resid = rob_crime_model.resid resid2 = resid**2 resid2 /= resid2.sum() nobs = int(idx.sum()) hm = hat_matrix_diag.mean() rm = resid2.mean() from statsmodels.graphics import utils fig, ax = plt.subplots(figsize=(12, 8)) ax.plot(resid2[idx], hat_matrix_diag, 'o') ax = utils.annotate_axes( range(nobs), labels=rob_crime_model.model.data.row_labels[idx], points=lzip(resid2[idx], hat_matrix_diag), offset_points=[(-5, 5)] * nobs, size="large", ax=ax) ax.set_xlabel("resid2") ax.set_ylabel("leverage") ylim = ax.get_ylim() ax.vlines(rm, *ylim) xlim = ax.get_xlim() ax.hlines(hm, *xlim) ax.margins(0, 0) statsmodels-0.12.2/examples/python/robust_models_0.py000066400000000000000000000061421400612667500227610ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook robust_models_0.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Robust Linear Models import numpy as np import statsmodels.api as sm import matplotlib.pyplot as plt from statsmodels.sandbox.regression.predstd import wls_prediction_std # ## Estimation # # Load data: data = sm.datasets.stackloss.load() data.exog = sm.add_constant(data.exog) # Huber's T norm with the (default) median absolute deviation scaling huber_t = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT()) hub_results = huber_t.fit() print(hub_results.params) print(hub_results.bse) print( hub_results.summary( yname='y', xname=['var_%d' % i for i in range(len(hub_results.params))])) # Huber's T norm with 'H2' covariance matrix hub_results2 = huber_t.fit(cov="H2") print(hub_results2.params) print(hub_results2.bse) # Andrew's Wave norm with Huber's Proposal 2 scaling and 'H3' covariance # matrix andrew_mod = sm.RLM(data.endog, data.exog, M=sm.robust.norms.AndrewWave()) andrew_results = andrew_mod.fit( scale_est=sm.robust.scale.HuberScale(), cov="H3") print('Parameters: ', andrew_results.params) # See ``help(sm.RLM.fit)`` for more options and ``module sm.robust.scale`` # for scale options # # ## Comparing OLS and RLM # # Artificial data with outliers: nsample = 50 x1 = np.linspace(0, 20, nsample) X = np.column_stack((x1, (x1 - 5)**2)) X = sm.add_constant(X) sig = 0.3 # smaller error variance makes OLS<->RLM contrast bigger beta = [5, 0.5, -0.0] y_true2 = np.dot(X, beta) y2 = y_true2 + sig * 1. * np.random.normal(size=nsample) y2[[39, 41, 43, 45, 48]] -= 5 # add some outliers (10% of nsample) # ### Example 1: quadratic function with linear truth # # Note that the quadratic term in OLS regression will capture outlier # effects. res = sm.OLS(y2, X).fit() print(res.params) print(res.bse) print(res.predict()) # Estimate RLM: resrlm = sm.RLM(y2, X).fit() print(resrlm.params) print(resrlm.bse) # Draw a plot to compare OLS estimates to the robust estimates: fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111) ax.plot(x1, y2, 'o', label="data") ax.plot(x1, y_true2, 'b-', label="True") prstd, iv_l, iv_u = wls_prediction_std(res) ax.plot(x1, res.fittedvalues, 'r-', label="OLS") ax.plot(x1, iv_u, 'r--') ax.plot(x1, iv_l, 'r--') ax.plot(x1, resrlm.fittedvalues, 'g.-', label="RLM") ax.legend(loc="best") # ### Example 2: linear function with linear truth # # Fit a new OLS model using only the linear term and the constant: X2 = X[:, [0, 1]] res2 = sm.OLS(y2, X2).fit() print(res2.params) print(res2.bse) # Estimate RLM: resrlm2 = sm.RLM(y2, X2).fit() print(resrlm2.params) print(resrlm2.bse) # Draw a plot to compare OLS estimates to the robust estimates: prstd, iv_l, iv_u = wls_prediction_std(res2) fig, ax = plt.subplots(figsize=(8, 6)) ax.plot(x1, y2, 'o', label="data") ax.plot(x1, y_true2, 'b-', label="True") ax.plot(x1, res2.fittedvalues, 'r-', label="OLS") ax.plot(x1, iv_u, 'r--') ax.plot(x1, iv_l, 'r--') ax.plot(x1, resrlm2.fittedvalues, 'g.-', label="RLM") legend = ax.legend(loc="best") statsmodels-0.12.2/examples/python/robust_models_1.py000066400000000000000000000217411400612667500227640ustar00rootroot00000000000000# DO NOT EDIT # Autogenerated from the notebook robust_models_1.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT #!/usr/bin/env python # coding: utf-8 # # M-Estimators for Robust Linear Modeling from statsmodels.compat import lmap import numpy as np from scipy import stats import matplotlib.pyplot as plt import statsmodels.api as sm # * An M-estimator minimizes the function # # $$Q(e_i, \rho) = \sum_i~\rho \left (\frac{e_i}{s}\right )$$ # # where $\rho$ is a symmetric function of the residuals # # * The effect of $\rho$ is to reduce the influence of outliers # * $s$ is an estimate of scale. # * The robust estimates $\hat{\beta}$ are computed by the iteratively re- # weighted least squares algorithm # * We have several choices available for the weighting functions to be # used norms = sm.robust.norms def plot_weights(support, weights_func, xlabels, xticks): fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111) ax.plot(support, weights_func(support)) ax.set_xticks(xticks) ax.set_xticklabels(xlabels, fontsize=16) ax.set_ylim(-.1, 1.1) return ax # ### Andrew's Wave help(norms.AndrewWave.weights) a = 1.339 support = np.linspace(-np.pi * a, np.pi * a, 100) andrew = norms.AndrewWave(a=a) plot_weights(support, andrew.weights, ['$-\pi*a$', '0', '$\pi*a$'], [-np.pi * a, 0, np.pi * a]) # ### Hampel's 17A help(norms.Hampel.weights) c = 8 support = np.linspace(-3 * c, 3 * c, 1000) hampel = norms.Hampel(a=2., b=4., c=c) plot_weights(support, hampel.weights, ['3*c', '0', '3*c'], [-3 * c, 0, 3 * c]) # ### Huber's t help(norms.HuberT.weights) t = 1.345 support = np.linspace(-3 * t, 3 * t, 1000) huber = norms.HuberT(t=t) plot_weights(support, huber.weights, ['-3*t', '0', '3*t'], [-3 * t, 0, 3 * t]) # ### Least Squares help(norms.LeastSquares.weights) support = np.linspace(-3, 3, 1000) lst_sq = norms.LeastSquares() plot_weights(support, lst_sq.weights, ['-3', '0', '3'], [-3, 0, 3]) # ### Ramsay's Ea help(norms.RamsayE.weights) a = .3 support = np.linspace(-3 * a, 3 * a, 1000) ramsay = norms.RamsayE(a=a) plot_weights(support, ramsay.weights, ['-3*a', '0', '3*a'], [-3 * a, 0, 3 * a]) # ### Trimmed Mean help(norms.TrimmedMean.weights) c = 2 support = np.linspace(-3 * c, 3 * c, 1000) trimmed = norms.TrimmedMean(c=c) plot_weights(support, trimmed.weights, ['-3*c', '0', '3*c'], [-3 * c, 0, 3 * c]) # ### Tukey's Biweight help(norms.TukeyBiweight.weights) c = 4.685 support = np.linspace(-3 * c, 3 * c, 1000) tukey = norms.TukeyBiweight(c=c) plot_weights(support, tukey.weights, ['-3*c', '0', '3*c'], [-3 * c, 0, 3 * c]) # ### Scale Estimators # * Robust estimates of the location x = np.array([1, 2, 3, 4, 500]) # * The mean is not a robust estimator of location x.mean() # * The median, on the other hand, is a robust estimator with a breakdown # point of 50% np.median(x) # * Analogously for the scale # * The standard deviation is not robust x.std() # Median Absolute Deviation # # $$ median_i |X_i - median_j(X_j)|) $$ # Standardized Median Absolute Deviation is a consistent estimator for # $\hat{\sigma}$ # # $$\hat{\sigma}=K \cdot MAD$$ # # where $K$ depends on the distribution. For the normal distribution for # example, # # $$K = \Phi^{-1}(.75)$$ stats.norm.ppf(.75) print(x) sm.robust.scale.mad(x) np.array([1, 2, 3, 4, 5.]).std() # * The default for Robust Linear Models is MAD # * another popular choice is Huber's proposal 2 np.random.seed(12345) fat_tails = stats.t(6).rvs(40) kde = sm.nonparametric.KDEUnivariate(fat_tails) kde.fit() fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111) ax.plot(kde.support, kde.density) print(fat_tails.mean(), fat_tails.std()) print(stats.norm.fit(fat_tails)) print(stats.t.fit(fat_tails, f0=6)) huber = sm.robust.scale.Huber() loc, scale = huber(fat_tails) print(loc, scale) sm.robust.mad(fat_tails) sm.robust.mad(fat_tails, c=stats.t(6).ppf(.75)) sm.robust.scale.mad(fat_tails) # ### Duncan's Occupational Prestige data - M-estimation for outliers from statsmodels.graphics.api import abline_plot from statsmodels.formula.api import ols, rlm prestige = sm.datasets.get_rdataset("Duncan", "carData", cache=True).data print(prestige.head(10)) fig = plt.figure(figsize=(12, 12)) ax1 = fig.add_subplot(211, xlabel='Income', ylabel='Prestige') ax1.scatter(prestige.income, prestige.prestige) xy_outlier = prestige.loc['minister', ['income', 'prestige']] ax1.annotate('Minister', xy_outlier, xy_outlier + 1, fontsize=16) ax2 = fig.add_subplot(212, xlabel='Education', ylabel='Prestige') ax2.scatter(prestige.education, prestige.prestige) ols_model = ols('prestige ~ income + education', prestige).fit() print(ols_model.summary()) infl = ols_model.get_influence() student = infl.summary_frame()['student_resid'] print(student) print(student.loc[np.abs(student) > 2]) print(infl.summary_frame().loc['minister']) sidak = ols_model.outlier_test('sidak') sidak.sort_values('unadj_p', inplace=True) print(sidak) fdr = ols_model.outlier_test('fdr_bh') fdr.sort_values('unadj_p', inplace=True) print(fdr) rlm_model = rlm('prestige ~ income + education', prestige).fit() print(rlm_model.summary()) print(rlm_model.weights) # ### Hertzprung Russell data for Star Cluster CYG 0B1 - Leverage Points # * Data is on the luminosity and temperature of 47 stars in the direction # of Cygnus. dta = sm.datasets.get_rdataset("starsCYG", "robustbase", cache=True).data from matplotlib.patches import Ellipse fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot( 111, xlabel='log(Temp)', ylabel='log(Light)', title='Hertzsprung-Russell Diagram of Star Cluster CYG OB1') ax.scatter(*dta.values.T) # highlight outliers e = Ellipse((3.5, 6), .2, 1, alpha=.25, color='r') ax.add_patch(e) ax.annotate( 'Red giants', xy=(3.6, 6), xytext=(3.8, 6), arrowprops=dict(facecolor='black', shrink=0.05, width=2), horizontalalignment='left', verticalalignment='bottom', clip_on=True, # clip to the axes bounding box fontsize=16, ) # annotate these with their index for i, row in dta.loc[dta['log.Te'] < 3.8].iterrows(): ax.annotate(i, row, row + .01, fontsize=14) xlim, ylim = ax.get_xlim(), ax.get_ylim() from IPython.display import Image Image(filename='star_diagram.png') y = dta['log.light'] X = sm.add_constant(dta['log.Te'], prepend=True) ols_model = sm.OLS(y, X).fit() abline_plot(model_results=ols_model, ax=ax) rlm_mod = sm.RLM(y, X, sm.robust.norms.TrimmedMean(.5)).fit() abline_plot(model_results=rlm_mod, ax=ax, color='red') # * Why? Because M-estimators are not robust to leverage points. infl = ols_model.get_influence() h_bar = 2 * (ols_model.df_model + 1) / ols_model.nobs hat_diag = infl.summary_frame()['hat_diag'] hat_diag.loc[hat_diag > h_bar] sidak2 = ols_model.outlier_test('sidak') sidak2.sort_values('unadj_p', inplace=True) print(sidak2) fdr2 = ols_model.outlier_test('fdr_bh') fdr2.sort_values('unadj_p', inplace=True) print(fdr2) # * Let's delete that line l = ax.lines[-1] l.remove() del l weights = np.ones(len(X)) weights[X[X['log.Te'] < 3.8].index.values - 1] = 0 wls_model = sm.WLS(y, X, weights=weights).fit() abline_plot(model_results=wls_model, ax=ax, color='green') # * MM estimators are good for this type of problem, unfortunately, we do # not yet have these yet. # * It's being worked on, but it gives a good excuse to look at the R cell # magics in the notebook. yy = y.values[:, None] xx = X['log.Te'].values[:, None] # **Note**: The R code and the results in this notebook has been converted # to markdown so that R is not required to build the documents. The R # results in the notebook were computed using R 3.5.1 and robustbase 0.93. # ```ipython # %load_ext rpy2.ipython # # %R library(robustbase) # %Rpush yy xx # %R mod <- lmrob(yy ~ xx); # %R params <- mod$coefficients; # %Rpull params # ``` # ```ipython # %R print(mod) # ``` # ``` # Call: # lmrob(formula = yy ~ xx) # \--> method = "MM" # Coefficients: # (Intercept) xx # -4.969 2.253 # ``` params = [-4.969387980288108, 2.2531613477892365] # Computed using R print(params[0], params[1]) abline_plot(intercept=params[0], slope=params[1], ax=ax, color='red') # ### Exercise: Breakdown points of M-estimator np.random.seed(12345) nobs = 200 beta_true = np.array([3, 1, 2.5, 3, -4]) X = np.random.uniform(-20, 20, size=(nobs, len(beta_true) - 1)) # stack a constant in front X = sm.add_constant(X, prepend=True) # np.c_[np.ones(nobs), X] mc_iter = 500 contaminate = .25 # percentage of response variables to contaminate all_betas = [] for i in range(mc_iter): y = np.dot(X, beta_true) + np.random.normal(size=200) random_idx = np.random.randint(0, nobs, size=int(contaminate * nobs)) y[random_idx] = np.random.uniform(-750, 750) beta_hat = sm.RLM(y, X).fit().params all_betas.append(beta_hat) all_betas = np.asarray(all_betas) se_loss = lambda x: np.linalg.norm(x, ord=2)**2 se_beta = lmap(se_loss, all_betas - beta_true) # #### Squared error loss np.array(se_beta).mean() all_betas.mean(0) beta_true se_loss(all_betas.mean(0) - beta_true) statsmodels-0.12.2/examples/python/statespace_arma_0.py000066400000000000000000000046451400612667500232420ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook statespace_arma_0.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Autoregressive Moving Average (ARMA): Sunspots data # This notebook replicates the existing ARMA notebook using the # `statsmodels.tsa.statespace.SARIMAX` class rather than the # `statsmodels.tsa.ARMA` class. import numpy as np from scipy import stats import pandas as pd import matplotlib.pyplot as plt import statsmodels.api as sm from statsmodels.graphics.api import qqplot # ## Sunspots Data print(sm.datasets.sunspots.NOTE) dta = sm.datasets.sunspots.load_pandas().data dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008')) del dta["YEAR"] dta.plot(figsize=(12, 4)) fig = plt.figure(figsize=(12, 8)) ax1 = fig.add_subplot(211) fig = sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40, ax=ax1) ax2 = fig.add_subplot(212) fig = sm.graphics.tsa.plot_pacf(dta, lags=40, ax=ax2) arma_mod20 = sm.tsa.statespace.SARIMAX( dta, order=(2, 0, 0), trend='c').fit(disp=False) print(arma_mod20.params) arma_mod30 = sm.tsa.statespace.SARIMAX( dta, order=(3, 0, 0), trend='c').fit(disp=False) print(arma_mod20.aic, arma_mod20.bic, arma_mod20.hqic) print(arma_mod30.params) print(arma_mod30.aic, arma_mod30.bic, arma_mod30.hqic) # * Does our model obey the theory? sm.stats.durbin_watson(arma_mod30.resid) fig = plt.figure(figsize=(12, 4)) ax = fig.add_subplot(111) ax = plt.plot(arma_mod30.resid) resid = arma_mod30.resid stats.normaltest(resid) fig = plt.figure(figsize=(12, 4)) ax = fig.add_subplot(111) fig = qqplot(resid, line='q', ax=ax, fit=True) fig = plt.figure(figsize=(12, 8)) ax1 = fig.add_subplot(211) fig = sm.graphics.tsa.plot_acf(resid, lags=40, ax=ax1) ax2 = fig.add_subplot(212) fig = sm.graphics.tsa.plot_pacf(resid, lags=40, ax=ax2) r, q, p = sm.tsa.acf(resid, qstat=True) data = np.c_[range(1, 41), r[1:], q, p] table = pd.DataFrame(data, columns=['lag', "AC", "Q", "Prob(>Q)"]) print(table.set_index('lag')) # * This indicates a lack of fit. # * In-sample dynamic prediction. How good does our model do? predict_sunspots = arma_mod30.predict(start='1990', end='2012', dynamic=True) fig, ax = plt.subplots(figsize=(12, 8)) dta.loc['1950':].plot(ax=ax) predict_sunspots.plot( ax=ax, style='r') def mean_forecast_err(y, yhat): return y.sub(yhat).mean() mean_forecast_err(dta.SUNACTIVITY, predict_sunspots) statsmodels-0.12.2/examples/python/statespace_concentrated_scale.py000066400000000000000000000216611400612667500257200ustar00rootroot00000000000000# DO NOT EDIT # Autogenerated from the notebook statespace_concentrated_scale.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT #!/usr/bin/env python # coding: utf-8 # ## State space models - concentrating the scale out of the likelihood # function import numpy as np import pandas as pd import statsmodels.api as sm dta = sm.datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959Q1', end='2009Q4', freq='Q') # ### Introduction # # (much of this is based on Harvey (1989); see especially section 3.4) # # State space models can generically be written as follows (here we focus # on time-invariant state space models, but similar results apply also to # time-varying models): # # $$ # \begin{align} # y_t & = Z \alpha_t + \varepsilon_t, \quad \varepsilon_t \sim N(0, H) \\ # \alpha_{t+1} & = T \alpha_t + R \eta_t \quad \eta_t \sim N(0, Q) # \end{align} # $$ # # Often, some or all of the values in the matrices $Z, H, T, R, Q$ are # unknown and must be estimated; in statsmodels, estimation is often done by # finding the parameters that maximize the likelihood function. In # particular, if we collect the parameters in a vector $\psi$, then each of # these matrices can be thought of as functions of those parameters, for # example $Z = Z(\psi)$, etc. # # Usually, the likelihood function is maximized numerically, for example # by applying quasi-Newton "hill-climbing" algorithms, and this becomes more # and more difficult the more parameters there are. It turns out that in # many cases we can reparameterize the model as $[\psi_*', \sigma_*^2]'$, # where $\sigma_*^2$ is the "scale" of the model (usually, it replaces one # of the error variance terms) and it is possible to find the maximum # likelihood estimate of $\sigma_*^2$ analytically, by differentiating the # likelihood function. This implies that numerical methods are only required # to estimate the parameters $\psi_*$, which has dimension one less than # that of $\psi$. # ### Example: local level model # # (see, for example, section 4.2 of Harvey (1989)) # # As a specific example, consider the local level model, which can be # written as: # # $$ # \begin{align} # y_t & = \alpha_t + \varepsilon_t, \quad \varepsilon_t \sim N(0, # \sigma_\varepsilon^2) \\ # \alpha_{t+1} & = \alpha_t + \eta_t \quad \eta_t \sim N(0, \sigma_\eta^2) # \end{align} # $$ # # In this model, $Z, T,$ and $R$ are all fixed to be equal to $1$, and # there are two unknown parameters, so that $\psi = [\sigma_\varepsilon^2, # \sigma_\eta^2]$. # #### Typical approach # # First, we show how to define this model without concentrating out the # scale, using statsmodels' state space library: class LocalLevel(sm.tsa.statespace.MLEModel): _start_params = [1., 1.] _param_names = ['var.level', 'var.irregular'] def __init__(self, endog): super(LocalLevel, self).__init__(endog, k_states=1, initialization='diffuse') self['design', 0, 0] = 1 self['transition', 0, 0] = 1 self['selection', 0, 0] = 1 def transform_params(self, unconstrained): return unconstrained**2 def untransform_params(self, unconstrained): return unconstrained**0.5 def update(self, params, **kwargs): params = super(LocalLevel, self).update(params, **kwargs) self['state_cov', 0, 0] = params[0] self['obs_cov', 0, 0] = params[1] # There are two parameters in this model that must be chosen: `var.level` # $(\sigma_\eta^2)$ and `var.irregular` $(\sigma_\varepsilon^2)$. We can use # the built-in `fit` method to choose them by numerically maximizing the # likelihood function. # # In our example, we are applying the local level model to consumer price # index inflation. mod = LocalLevel(dta.infl) res = mod.fit(disp=False) print(res.summary()) # We can look at the results from the numerical optimizer in the results # attribute `mle_retvals`: print(res.mle_retvals) # #### Concentrating out the scale # Now, there are two ways to reparameterize this model as above: # # 1. The first way is to set $\sigma_*^2 \equiv \sigma_\varepsilon^2$ so # that $\psi_* = \psi / \sigma_\varepsilon^2 = [1, q_\eta]$ where $q_\eta = # \sigma_\eta^2 / \sigma_\varepsilon^2$. # 2. The second way is to set $\sigma_*^2 \equiv \sigma_\eta^2$ so that # $\psi_* = \psi / \sigma_\eta^2 = [h, 1]$ where $h = \sigma_\varepsilon^2 / # \sigma_\eta^2$. # # In the first case, we only need to numerically maximize the likelihood # with respect to $q_\eta$, and in the second case we only need to # numerically maximize the likelihood with respect to $h$. # # Either approach would work well in most cases, and in the example below # we will use the second method. # To reformulate the model to take advantage of the concentrated # likelihood function, we need to write the model in terms of the parameter # vector $\psi_* = [g, 1]$. Because this parameter vector defines # $\sigma_\eta^2 \equiv 1$, we now include a new line `self['state_cov', 0, # 0] = 1` and the only unknown parameter is $h$. Because our parameter $h$ # is no longer a variance, we renamed it here to be `ratio.irregular`. # # The key piece that is required to formulate the model so that the scale # can be computed from the Kalman filter recursions (rather than selected # numerically) is setting the flag `self.ssm.filter_concentrated = True`. class LocalLevelConcentrated(sm.tsa.statespace.MLEModel): _start_params = [1.] _param_names = ['ratio.irregular'] def __init__(self, endog): super(LocalLevelConcentrated, self).__init__(endog, k_states=1, initialization='diffuse') self['design', 0, 0] = 1 self['transition', 0, 0] = 1 self['selection', 0, 0] = 1 self['state_cov', 0, 0] = 1 self.ssm.filter_concentrated = True def transform_params(self, unconstrained): return unconstrained**2 def untransform_params(self, unconstrained): return unconstrained**0.5 def update(self, params, **kwargs): params = super(LocalLevelConcentrated, self).update(params, **kwargs) self['obs_cov', 0, 0] = params[0] # Again, we can use the built-in `fit` method to find the maximum # likelihood estimate of $h$. mod_conc = LocalLevelConcentrated(dta.infl) res_conc = mod_conc.fit(disp=False) print(res_conc.summary()) # The estimate of $h$ is provided in the middle table of parameters # (`ratio.irregular`), while the estimate of the scale is provided in the # upper table. Below, we will show that these estimates are consistent with # those from the previous approach. # And we can again look at the results from the numerical optimizer in the # results attribute `mle_retvals`. It turns out that two fewer iterations # were required in this case, since there was one fewer parameter to select. # Moreover, since the numerical maximization problem was easier, the # optimizer was able to find a value that made the gradient for this # parameter slightly closer to zero than it was above. print(res_conc.mle_retvals) # #### Comparing estimates # # Recall that $h = \sigma_\varepsilon^2 / \sigma_\eta^2$ and the scale is # $\sigma_*^2 = \sigma_\eta^2$. Using these definitions, we can see that # both models produce nearly identical results: print('Original model') print('var.level = %.5f' % res.params[0]) print('var.irregular = %.5f' % res.params[1]) print('\nConcentrated model') print('scale = %.5f' % res_conc.scale) print('h * scale = %.5f' % (res_conc.params[0] * res_conc.scale)) # ### Example: SARIMAX # # By default in SARIMAX models, the variance term is chosen by numerically # maximizing the likelihood function, but an option has been added to allow # concentrating the scale out. # Typical approach mod_ar = sm.tsa.SARIMAX(dta.cpi, order=(1, 0, 0), trend='ct') res_ar = mod_ar.fit(disp=False) # Estimating the model with the scale concentrated out mod_ar_conc = sm.tsa.SARIMAX(dta.cpi, order=(1, 0, 0), trend='ct', concentrate_scale=True) res_ar_conc = mod_ar_conc.fit(disp=False) # These two approaches produce about the same loglikelihood and # parameters, although the model with the concentrated scale was able to # improve the fit very slightly: print('Loglikelihood') print('- Original model: %.4f' % res_ar.llf) print('- Concentrated model: %.4f' % res_ar_conc.llf) print('\nParameters') print('- Original model: %.4f, %.4f, %.4f, %.4f' % tuple(res_ar.params)) print('- Concentrated model: %.4f, %.4f, %.4f, %.4f' % (tuple(res_ar_conc.params) + (res_ar_conc.scale, ))) # This time, about 1/3 fewer iterations of the optimizer are required # under the concentrated approach: print('Optimizer iterations') print('- Original model: %d' % res_ar.mle_retvals['iterations']) print('- Concentrated model: %d' % res_ar_conc.mle_retvals['iterations']) statsmodels-0.12.2/examples/python/statespace_cycles.py000066400000000000000000000106431400612667500233600ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook statespace_cycles.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Trends and cycles in unemployment # # Here we consider three methods for separating a trend and cycle in # economic data. Supposing we have a time series $y_t$, the basic idea is to # decompose it into these two components: # # $$ # y_t = \mu_t + \eta_t # $$ # # where $\mu_t$ represents the trend or level and $\eta_t$ represents the # cyclical component. In this case, we consider a *stochastic* trend, so # that $\mu_t$ is a random variable and not a deterministic function of # time. Two of methods fall under the heading of "unobserved components" # models, and the third is the popular Hodrick-Prescott (HP) filter. # Consistent with e.g. Harvey and Jaeger (1993), we find that these models # all produce similar decompositions. # # This notebook demonstrates applying these models to separate trend from # cycle in the U.S. unemployment rate. import numpy as np import pandas as pd import statsmodels.api as sm import matplotlib.pyplot as plt from pandas_datareader.data import DataReader endog = DataReader('UNRATE', 'fred', start='1954-01-01') # ### Hodrick-Prescott (HP) filter # # The first method is the Hodrick-Prescott filter, which can be applied to # a data series in a very straightforward method. Here we specify the # parameter $\lambda=129600$ because the unemployment rate is observed # monthly. hp_cycle, hp_trend = sm.tsa.filters.hpfilter(endog, lamb=129600) # ### Unobserved components and ARIMA model (UC-ARIMA) # # The next method is an unobserved components model, where the trend is # modeled as a random walk and the cycle is modeled with an ARIMA model - in # particular, here we use an AR(4) model. The process for the time series # can be written as: # # $$ # \begin{align} # y_t & = \mu_t + \eta_t \\ # \mu_{t+1} & = \mu_t + \epsilon_{t+1} \\ # \phi(L) \eta_t & = \nu_t # \end{align} # $$ # # where $\phi(L)$ is the AR(4) lag polynomial and $\epsilon_t$ and $\nu_t$ # are white noise. mod_ucarima = sm.tsa.UnobservedComponents(endog, 'rwalk', autoregressive=4) # Here the powell method is used, since it achieves a # higher loglikelihood than the default L-BFGS method res_ucarima = mod_ucarima.fit(method='powell', disp=False) print(res_ucarima.summary()) # ### Unobserved components with stochastic cycle (UC) # # The final method is also an unobserved components model, but where the # cycle is modeled explicitly. # # $$ # \begin{align} # y_t & = \mu_t + \eta_t \\ # \mu_{t+1} & = \mu_t + \epsilon_{t+1} \\ # \eta_{t+1} & = \eta_t \cos \lambda_\eta + \eta_t^* \sin \lambda_\eta + # \tilde \omega_t \qquad & \tilde \omega_t \sim N(0, \sigma_{\tilde # \omega}^2) \\ # \eta_{t+1}^* & = -\eta_t \sin \lambda_\eta + \eta_t^* \cos \lambda_\eta # + \tilde \omega_t^* & \tilde \omega_t^* \sim N(0, \sigma_{\tilde # \omega}^2) # \end{align} # $$ mod_uc = sm.tsa.UnobservedComponents( endog, 'rwalk', cycle=True, stochastic_cycle=True, damped_cycle=True, ) # Here the powell method gets close to the optimum res_uc = mod_uc.fit(method='powell', disp=False) # but to get to the highest loglikelihood we do a # second round using the L-BFGS method. res_uc = mod_uc.fit(res_uc.params, disp=False) print(res_uc.summary()) # ### Graphical comparison # # The output of each of these models is an estimate of the trend component # $\mu_t$ and an estimate of the cyclical component $\eta_t$. Qualitatively # the estimates of trend and cycle are very similar, although the trend # component from the HP filter is somewhat more variable than those from the # unobserved components models. This means that relatively mode of the # movement in the unemployment rate is attributed to changes in the # underlying trend rather than to temporary cyclical movements. fig, axes = plt.subplots( 2, figsize=(13, 5)) axes[0].set(title='Level/trend component') axes[0].plot(endog.index, res_uc.level.smoothed, label='UC') axes[0].plot(endog.index, res_ucarima.level.smoothed, label='UC-ARIMA(2,0)') axes[0].plot(hp_trend, label='HP Filter') axes[0].legend(loc='upper left') axes[0].grid() axes[1].set(title='Cycle component') axes[1].plot(endog.index, res_uc.cycle.smoothed, label='UC') axes[1].plot( endog.index, res_ucarima.autoregressive.smoothed, label='UC-ARIMA(2,0)') axes[1].plot(hp_cycle, label='HP Filter') axes[1].legend(loc='upper left') axes[1].grid() fig.tight_layout() statsmodels-0.12.2/examples/python/statespace_dfm_coincident.py000066400000000000000000000733241400612667500250500ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook statespace_dfm_coincident.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Dynamic factors and coincident indices # # Factor models generally try to find a small number of unobserved # "factors" that influence a substantial portion of the variation in a larger # number of observed variables, and they are related to dimension-reduction # techniques such as principal components analysis. Dynamic factor models # explicitly model the transition dynamics of the unobserved factors, and so # are often applied to time-series data. # # Macroeconomic coincident indices are designed to capture the common # component of the "business cycle"; such a component is assumed to # simultaneously affect many macroeconomic variables. Although the # estimation and use of coincident indices (for example the [Index of # Coincident Economic Indicators](http://www.newyorkfed.org/research/regiona # l_economy/coincident_summary.html)) pre-dates dynamic factor models, in # several influential papers Stock and Watson (1989, 1991) used a dynamic # factor model to provide a theoretical foundation for them. # # Below, we follow the treatment found in Kim and Nelson (1999), of the # Stock and Watson (1991) model, to formulate a dynamic factor model, # estimate its parameters via maximum likelihood, and create a coincident # index. # ## Macroeconomic data # # The coincident index is created by considering the comovements in four # macroeconomic variables (versions of thse variables are available on # [FRED](https://research.stlouisfed.org/fred2/); the ID of the series used # below is given in parentheses): # # - Industrial production (IPMAN) # - Real aggregate income (excluding transfer payments) (W875RX1) # - Manufacturing and trade sales (CMRMTSPL) # - Employees on non-farm payrolls (PAYEMS) # # In all cases, the data is at the monthly frequency and has been # seasonally adjusted; the time-frame considered is 1972 - 2005. import numpy as np import pandas as pd import statsmodels.api as sm import matplotlib.pyplot as plt np.set_printoptions(precision=4, suppress=True, linewidth=120) from pandas_datareader.data import DataReader # Get the datasets from FRED start = '1979-01-01' end = '2014-12-01' indprod = DataReader('IPMAN', 'fred', start=start, end=end) income = DataReader('W875RX1', 'fred', start=start, end=end) sales = DataReader('CMRMTSPL', 'fred', start=start, end=end) emp = DataReader('PAYEMS', 'fred', start=start, end=end) # dta = pd.concat((indprod, income, sales, emp), axis=1) # dta.columns = ['indprod', 'income', 'sales', 'emp'] # **Note**: in a recent update on FRED (8/12/15) the time series CMRMTSPL # was truncated to begin in 1997; this is probably a mistake due to the fact # that CMRMTSPL is a spliced series, so the earlier period is from the # series HMRMT and the latter period is defined by CMRMT. # # This has since (02/11/16) been corrected, however the series could also # be constructed by hand from HMRMT and CMRMT, as shown below (process taken # from the notes in the Alfred xls file). # HMRMT = DataReader('HMRMT', 'fred', start='1967-01-01', end=end) # CMRMT = DataReader('CMRMT', 'fred', start='1997-01-01', end=end) # HMRMT_growth = HMRMT.diff() / HMRMT.shift() # sales = pd.Series(np.zeros(emp.shape[0]), index=emp.index) # # Fill in the recent entries (1997 onwards) # sales[CMRMT.index] = CMRMT # # Backfill the previous entries (pre 1997) # idx = sales.loc[:'1997-01-01'].index # for t in range(len(idx)-1, 0, -1): # month = idx[t] # prev_month = idx[t-1] # sales.loc[prev_month] = sales.loc[month] / (1 + # HMRMT_growth.loc[prev_month].values) dta = pd.concat((indprod, income, sales, emp), axis=1) dta.columns = ['indprod', 'income', 'sales', 'emp'] dta.loc[:, 'indprod':'emp'].plot( subplots=True, layout=(2, 2), figsize=(15, 6)) # Stock and Watson (1991) report that for their datasets, they could not # reject the null hypothesis of a unit root in each series (so the series # are integrated), but they did not find strong evidence that the series # were co-integrated. # # As a result, they suggest estimating the model using the first # differences (of the logs) of the variables, demeaned and standardized. # Create log-differenced series dta['dln_indprod'] = (np.log(dta.indprod)).diff() * 100 dta['dln_income'] = (np.log(dta.income)).diff() * 100 dta['dln_sales'] = (np.log(dta.sales)).diff() * 100 dta['dln_emp'] = (np.log(dta.emp)).diff() * 100 # De-mean and standardize dta['std_indprod'] = ( dta['dln_indprod'] - dta['dln_indprod'].mean()) / dta['dln_indprod'].std() dta['std_income'] = ( dta['dln_income'] - dta['dln_income'].mean()) / dta['dln_income'].std() dta['std_sales'] = ( dta['dln_sales'] - dta['dln_sales'].mean()) / dta['dln_sales'].std() dta['std_emp'] = ( dta['dln_emp'] - dta['dln_emp'].mean()) / dta['dln_emp'].std() # ## Dynamic factors # # A general dynamic factor model is written as: # # $$ # \begin{align} # y_t & = \Lambda f_t + B x_t + u_t \\ # f_t & = A_1 f_{t-1} + \dots + A_p f_{t-p} + \eta_t \qquad \eta_t \sim # N(0, I)\\ # u_t & = C_1 u_{t-1} + \dots + C_q u_{t-q} + \varepsilon_t \qquad # \varepsilon_t \sim N(0, \Sigma) # \end{align} # $$ # # where $y_t$ are observed data, $f_t$ are the unobserved factors # (evolving as a vector autoregression), $x_t$ are (optional) exogenous # variables, and $u_t$ is the error, or "idiosyncratic", process ($u_t$ is # also optionally allowed to be autocorrelated). The $\Lambda$ matrix is # often referred to as the matrix of "factor loadings". The variance of the # factor error term is set to the identity matrix to ensure identification # of the unobserved factors. # # This model can be cast into state space form, and the unobserved factor # estimated via the Kalman filter. The likelihood can be evaluated as a # byproduct of the filtering recursions, and maximum likelihood estimation # used to estimate the parameters. # ## Model specification # # The specific dynamic factor model in this application has 1 unobserved # factor which is assumed to follow an AR(2) process. The innovations # $\varepsilon_t$ are assumed to be independent (so that $\Sigma$ is a # diagonal matrix) and the error term associated with each equation, # $u_{i,t}$ is assumed to follow an independent AR(2) process. # # Thus the specification considered here is: # # $$ # \begin{align} # y_{i,t} & = \lambda_i f_t + u_{i,t} \\ # u_{i,t} & = c_{i,1} u_{1,t-1} + c_{i,2} u_{i,t-2} + \varepsilon_{i,t} # \qquad & \varepsilon_{i,t} \sim N(0, \sigma_i^2) \\ # f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \eta_t \qquad & \eta_t \sim N(0, # I)\\ # \end{align} # $$ # # where $i$ is one of: `[indprod, income, sales, emp ]`. # # This model can be formulated using the `DynamicFactor` model built-in to # statsmodels. In particular, we have the following specification: # # - `k_factors = 1` - (there is 1 unobserved factor) # - `factor_order = 2` - (it follows an AR(2) process) # - `error_var = False` - (the errors evolve as independent AR processes # rather than jointly as a VAR - note that this is the default option, so it # is not specified below) # - `error_order = 2` - (the errors are autocorrelated of order 2: i.e. # AR(2) processes) # - `error_cov_type = 'diagonal'` - (the innovations are uncorrelated; # this is again the default) # # Once the model is created, the parameters can be estimated via maximum # likelihood; this is done using the `fit()` method. # # **Note**: recall that we have demeaned and standardized the data; this # will be important in interpreting the results that follow. # # **Aside**: in their empirical example, Kim and Nelson (1999) actually # consider a slightly different model in which the employment variable is # allowed to also depend on lagged values of the factor - this model does # not fit into the built-in `DynamicFactor` class, but can be accommodated by # using a subclass to implement the required new parameters and restrictions # - see Appendix A, below. # ## Parameter estimation # # Multivariate models can have a relatively large number of parameters, # and it may be difficult to escape from local minima to find the maximized # likelihood. In an attempt to mitigate this problem, I perform an initial # maximization step (from the model-defined starting parameters) using the # modified Powell method available in Scipy (see the minimize documentation # for more information). The resulting parameters are then used as starting # parameters in the standard LBFGS optimization method. # Get the endogenous data endog = dta.loc['1979-02-01':, 'std_indprod':'std_emp'] # Create the model mod = sm.tsa.DynamicFactor(endog, k_factors=1, factor_order=2, error_order=2) initial_res = mod.fit(method='powell', disp=False) res = mod.fit(initial_res.params, disp=False) # ## Estimates # # Once the model has been estimated, there are two components that we can # use for analysis or inference: # # - The estimated parameters # - The estimated factor # ### Parameters # # The estimated parameters can be helpful in understanding the # implications of the model, although in models with a larger number of # observed variables and / or unobserved factors they can be difficult to # interpret. # # One reason for this difficulty is due to identification issues between # the factor loadings and the unobserved factors. One easy-to-see # identification issue is the sign of the loadings and the factors: an # equivalent model to the one displayed below would result from reversing # the signs of all factor loadings and the unobserved factor. # # Here, one of the easy-to-interpret implications in this model is the # persistence of the unobserved factor: we find that exhibits substantial # persistence. print(res.summary(separate_params=False)) # ### Estimated factors # # While it can be useful to plot the unobserved factors, it is less useful # here than one might think for two reasons: # # 1. The sign-related identification issue described above. # 2. Since the data was differenced, the estimated factor explains the # variation in the differenced data, not the original data. # # It is for these reasons that the coincident index is created (see # below). # # With these reservations, the unobserved factor is plotted below, along # with the NBER indicators for US recessions. It appears that the factor is # successful at picking up some degree of business cycle activity. fig, ax = plt.subplots(figsize=(13, 3)) # Plot the factor dates = endog.index._mpl_repr() ax.plot(dates, res.factors.filtered[0], label='Factor') ax.legend() # Retrieve and also plot the NBER recession indicators rec = DataReader('USREC', 'fred', start=start, end=end) ylim = ax.get_ylim() ax.fill_between( dates[:-3], ylim[0], ylim[1], rec.values[:-4, 0], facecolor='k', alpha=0.1) # ## Post-estimation # # Although here we will be able to interpret the results of the model by # constructing the coincident index, there is a useful and generic approach # for getting a sense for what is being captured by the estimated factor. By # taking the estimated factors as given, regressing them (and a constant) # each (one at a time) on each of the observed variables, and recording the # coefficients of determination ($R^2$ values), we can get a sense of the # variables for which each factor explains a substantial portion of the # variance and the variables for which it does not. # # In models with more variables and more factors, this can sometimes lend # interpretation to the factors (for example sometimes one factor will load # primarily on real variables and another on nominal variables). # # In this model, with only four endogenous variables and one factor, it is # easy to digest a simple table of the $R^2$ values, but in larger models it # is not. For this reason, a bar plot is often employed; from the plot we # can easily see that the factor explains most of the variation in # industrial production index and a large portion of the variation in sales # and employment, it is less helpful in explaining income. res.plot_coefficients_of_determination(figsize=(8, 2)) # ## Coincident Index # # As described above, the goal of this model was to create an # interpretable series which could be used to understand the current status # of the macroeconomy. This is what the coincident index is designed to do. # It is constructed below. For readers interested in an explanation of the # construction, see Kim and Nelson (1999) or Stock and Watson (1991). # # In essence, what is done is to reconstruct the mean of the (differenced) # factor. We will compare it to the coincident index on published by the # Federal Reserve Bank of Philadelphia (USPHCI on FRED). usphci = DataReader( 'USPHCI', 'fred', start='1979-01-01', end='2014-12-01')['USPHCI'] usphci.plot(figsize=(13, 3)) dusphci = usphci.diff()[1:].values def compute_coincident_index(mod, res): # Estimate W(1) spec = res.specification design = mod.ssm['design'] transition = mod.ssm['transition'] ss_kalman_gain = res.filter_results.kalman_gain[:, :, -1] k_states = ss_kalman_gain.shape[0] W1 = np.linalg.inv( np.eye(k_states) - np.dot(np.eye(k_states) - np.dot(ss_kalman_gain, design), transition) ).dot(ss_kalman_gain)[0] # Compute the factor mean vector factor_mean = np.dot( W1, dta.loc['1972-02-01':, 'dln_indprod':'dln_emp'].mean()) # Normalize the factors factor = res.factors.filtered[0] factor *= np.std(usphci.diff()[1:]) / np.std(factor) # Compute the coincident index coincident_index = np.zeros(mod.nobs + 1) # The initial value is arbitrary; here it is set to # facilitate comparison coincident_index[0] = usphci.iloc[0] * factor_mean / dusphci.mean() for t in range(0, mod.nobs): coincident_index[t + 1] = coincident_index[t] + factor[t] + factor_mean # Attach dates coincident_index = pd.Series(coincident_index, index=dta.index).iloc[1:] # Normalize to use the same base year as USPHCI coincident_index *= ( usphci.loc['1992-07-01'] / coincident_index.loc['1992-07-01']) return coincident_index # Below we plot the calculated coincident index along with the US # recessions and the comparison coincident index USPHCI. fig, ax = plt.subplots(figsize=(13, 3)) # Compute the index coincident_index = compute_coincident_index(mod, res) # Plot the factor dates = endog.index._mpl_repr() ax.plot(dates, coincident_index, label='Coincident index') ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI') ax.legend(loc='lower right') # Retrieve and also plot the NBER recession indicators ylim = ax.get_ylim() ax.fill_between( dates[:-3], ylim[0], ylim[1], rec.values[:-4, 0], facecolor='k', alpha=0.1) # ## Appendix 1: Extending the dynamic factor model # # Recall that the previous specification was described by: # # $$ # \begin{align} # y_{i,t} & = \lambda_i f_t + u_{i,t} \\ # u_{i,t} & = c_{i,1} u_{1,t-1} + c_{i,2} u_{i,t-2} + \varepsilon_{i,t} # \qquad & \varepsilon_{i,t} \sim N(0, \sigma_i^2) \\ # f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \eta_t \qquad & \eta_t \sim N(0, # I)\\ # \end{align} # $$ # # Written in state space form, the previous specification of the model had # the following observation equation: # # $$ # \begin{bmatrix} # y_{\text{indprod}, t} \\ # y_{\text{income}, t} \\ # y_{\text{sales}, t} \\ # y_{\text{emp}, t} \\ # \end{bmatrix} = \begin{bmatrix} # \lambda_\text{indprod} & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ # \lambda_\text{income} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ # \lambda_\text{sales} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ # \lambda_\text{emp} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ # \end{bmatrix} # \begin{bmatrix} # f_t \\ # f_{t-1} \\ # u_{\text{indprod}, t} \\ # u_{\text{income}, t} \\ # u_{\text{sales}, t} \\ # u_{\text{emp}, t} \\ # u_{\text{indprod}, t-1} \\ # u_{\text{income}, t-1} \\ # u_{\text{sales}, t-1} \\ # u_{\text{emp}, t-1} \\ # \end{bmatrix} # $$ # # and transition equation: # # $$ # \begin{bmatrix} # f_t \\ # f_{t-1} \\ # u_{\text{indprod}, t} \\ # u_{\text{income}, t} \\ # u_{\text{sales}, t} \\ # u_{\text{emp}, t} \\ # u_{\text{indprod}, t-1} \\ # u_{\text{income}, t-1} \\ # u_{\text{sales}, t-1} \\ # u_{\text{emp}, t-1} \\ # \end{bmatrix} = \begin{bmatrix} # a_1 & a_2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ # 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ # 0 & 0 & c_{\text{indprod}, 1} & 0 & 0 & 0 & c_{\text{indprod}, 2} & # 0 & 0 & 0 \\ # 0 & 0 & 0 & c_{\text{income}, 1} & 0 & 0 & 0 & c_{\text{income}, 2} # & 0 & 0 \\ # 0 & 0 & 0 & 0 & c_{\text{sales}, 1} & 0 & 0 & 0 & c_{\text{sales}, # 2} & 0 \\ # 0 & 0 & 0 & 0 & 0 & c_{\text{emp}, 1} & 0 & 0 & 0 & c_{\text{emp}, # 2} \\ # 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ # 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ # 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ # 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ # \end{bmatrix} # \begin{bmatrix} # f_{t-1} \\ # f_{t-2} \\ # u_{\text{indprod}, t-1} \\ # u_{\text{income}, t-1} \\ # u_{\text{sales}, t-1} \\ # u_{\text{emp}, t-1} \\ # u_{\text{indprod}, t-2} \\ # u_{\text{income}, t-2} \\ # u_{\text{sales}, t-2} \\ # u_{\text{emp}, t-2} \\ # \end{bmatrix} # + R \begin{bmatrix} # \eta_t \\ # \varepsilon_{t} # \end{bmatrix} # $$ # # the `DynamicFactor` model handles setting up the state space # representation and, in the `DynamicFactor.update` method, it fills in the # fitted parameter values into the appropriate locations. # The extended specification is the same as in the previous example, # except that we also want to allow employment to depend on lagged values of # the factor. This creates a change to the $y_{\text{emp},t}$ equation. Now # we have: # # $$ # \begin{align} # y_{i,t} & = \lambda_i f_t + u_{i,t} \qquad & i \in \{\text{indprod}, # \text{income}, \text{sales} \}\\ # y_{i,t} & = \lambda_{i,0} f_t + \lambda_{i,1} f_{t-1} + \lambda_{i,2} # f_{t-2} + \lambda_{i,2} f_{t-3} + u_{i,t} \qquad & i = \text{emp} \\ # u_{i,t} & = c_{i,1} u_{i,t-1} + c_{i,2} u_{i,t-2} + \varepsilon_{i,t} # \qquad & \varepsilon_{i,t} \sim N(0, \sigma_i^2) \\ # f_t & = a_1 f_{t-1} + a_2 f_{t-2} + \eta_t \qquad & \eta_t \sim N(0, # I)\\ # \end{align} # $$ # # Now, the corresponding observation equation should look like the # following: # # $$ # \begin{bmatrix} # y_{\text{indprod}, t} \\ # y_{\text{income}, t} \\ # y_{\text{sales}, t} \\ # y_{\text{emp}, t} \\ # \end{bmatrix} = \begin{bmatrix} # \lambda_\text{indprod} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ # \lambda_\text{income} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ # \lambda_\text{sales} & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ # \lambda_\text{emp,1} & \lambda_\text{emp,2} & \lambda_\text{emp,3} & # \lambda_\text{emp,4} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ # \end{bmatrix} # \begin{bmatrix} # f_t \\ # f_{t-1} \\ # f_{t-2} \\ # f_{t-3} \\ # u_{\text{indprod}, t} \\ # u_{\text{income}, t} \\ # u_{\text{sales}, t} \\ # u_{\text{emp}, t} \\ # u_{\text{indprod}, t-1} \\ # u_{\text{income}, t-1} \\ # u_{\text{sales}, t-1} \\ # u_{\text{emp}, t-1} \\ # \end{bmatrix} # $$ # # Notice that we have introduced two new state variables, $f_{t-2}$ and # $f_{t-3}$, which means we need to update the transition equation: # # $$ # \begin{bmatrix} # f_t \\ # f_{t-1} \\ # f_{t-2} \\ # f_{t-3} \\ # u_{\text{indprod}, t} \\ # u_{\text{income}, t} \\ # u_{\text{sales}, t} \\ # u_{\text{emp}, t} \\ # u_{\text{indprod}, t-1} \\ # u_{\text{income}, t-1} \\ # u_{\text{sales}, t-1} \\ # u_{\text{emp}, t-1} \\ # \end{bmatrix} = \begin{bmatrix} # a_1 & a_2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ # 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ # 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ # 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ # 0 & 0 & 0 & 0 & c_{\text{indprod}, 1} & 0 & 0 & 0 & # c_{\text{indprod}, 2} & 0 & 0 & 0 \\ # 0 & 0 & 0 & 0 & 0 & c_{\text{income}, 1} & 0 & 0 & 0 & # c_{\text{income}, 2} & 0 & 0 \\ # 0 & 0 & 0 & 0 & 0 & 0 & c_{\text{sales}, 1} & 0 & 0 & 0 & # c_{\text{sales}, 2} & 0 \\ # 0 & 0 & 0 & 0 & 0 & 0 & 0 & c_{\text{emp}, 1} & 0 & 0 & 0 & # c_{\text{emp}, 2} \\ # 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ # 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ # 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ # 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ # \end{bmatrix} # \begin{bmatrix} # f_{t-1} \\ # f_{t-2} \\ # f_{t-3} \\ # f_{t-4} \\ # u_{\text{indprod}, t-1} \\ # u_{\text{income}, t-1} \\ # u_{\text{sales}, t-1} \\ # u_{\text{emp}, t-1} \\ # u_{\text{indprod}, t-2} \\ # u_{\text{income}, t-2} \\ # u_{\text{sales}, t-2} \\ # u_{\text{emp}, t-2} \\ # \end{bmatrix} # + R \begin{bmatrix} # \eta_t \\ # \varepsilon_{t} # \end{bmatrix} # $$ # # This model cannot be handled out-of-the-box by the `DynamicFactor` # class, but it can be handled by creating a subclass when alters the state # space representation in the appropriate way. # First, notice that if we had set `factor_order = 4`, we would almost # have what we wanted. In that case, the last line of the observation # equation would be: # # $$ # \begin{bmatrix} # \vdots \\ # y_{\text{emp}, t} \\ # \end{bmatrix} = \begin{bmatrix} # \vdots & & & & & & & & & & & \vdots \\ # \lambda_\text{emp,1} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ # \end{bmatrix} # \begin{bmatrix} # f_t \\ # f_{t-1} \\ # f_{t-2} \\ # f_{t-3} \\ # \vdots # \end{bmatrix} # $$ # # # and the first line of the transition equation would be: # # $$ # \begin{bmatrix} # f_t \\ # \vdots # \end{bmatrix} = \begin{bmatrix} # a_1 & a_2 & a_3 & a_4 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ # \vdots & & & & & & & & & & & \vdots \\ # \end{bmatrix} # \begin{bmatrix} # f_{t-1} \\ # f_{t-2} \\ # f_{t-3} \\ # f_{t-4} \\ # \vdots # \end{bmatrix} # + R \begin{bmatrix} # \eta_t \\ # \varepsilon_{t} # \end{bmatrix} # $$ # # Relative to what we want, we have the following differences: # # 1. In the above situation, the $\lambda_{\text{emp}, j}$ are forced to # be zero for $j > 0$, and we want them to be estimated as parameters. # 2. We only want the factor to transition according to an AR(2), but # under the above situation it is an AR(4). # # Our strategy will be to subclass `DynamicFactor`, and let it do most of # the work (setting up the state space representation, etc.) where it # assumes that `factor_order = 4`. The only things we will actually do in # the subclass will be to fix those two issues. # # First, here is the full code of the subclass; it is discussed below. It # is important to note at the outset that none of the methods defined below # could have been omitted. In fact, the methods `__init__`, `start_params`, # `param_names`, `transform_params`, `untransform_params`, and `update` form # the core of all state space models in statsmodels, not just the # `DynamicFactor` class. from statsmodels.tsa.statespace import tools class ExtendedDFM(sm.tsa.DynamicFactor): def __init__(self, endog, **kwargs): # Setup the model as if we had a factor order of 4 super(ExtendedDFM, self).__init__( endog, k_factors=1, factor_order=4, error_order=2, **kwargs) # Note: `self.parameters` is an ordered dict with the # keys corresponding to parameter types, and the values # the number of parameters of that type. # Add the new parameters self.parameters['new_loadings'] = 3 # Cache a slice for the location of the 4 factor AR # parameters (a_1, ..., a_4) in the full parameter vector offset = (self.parameters['factor_loadings'] + self.parameters['exog'] + self.parameters['error_cov']) self._params_factor_ar = np.s_[offset:offset + 2] self._params_factor_zero = np.s_[offset + 2:offset + 4] @property def start_params(self): # Add three new loading parameters to the end of the parameter # vector, initialized to zeros (for simplicity; they could # be initialized any way you like) return np.r_[super(ExtendedDFM, self).start_params, 0, 0, 0] @property def param_names(self): # Add the corresponding names for the new loading parameters # (the name can be anything you like) return super(ExtendedDFM, self).param_names + [ 'loading.L%d.f1.%s' % (i, self.endog_names[3]) for i in range(1, 4) ] def transform_params(self, unconstrained): # Perform the typical DFM transformation (w/o the new parameters) constrained = super(ExtendedDFM, self).transform_params(unconstrained[:-3]) # Redo the factor AR constraint, since we only want an AR(2), # and the previous constraint was for an AR(4) ar_params = unconstrained[self._params_factor_ar] constrained[self._params_factor_ar] = ( tools.constrain_stationary_univariate(ar_params)) # Return all the parameters return np.r_[constrained, unconstrained[-3:]] def untransform_params(self, constrained): # Perform the typical DFM untransformation (w/o the new parameters) unconstrained = super(ExtendedDFM, self).untransform_params(constrained[:-3]) # Redo the factor AR unconstrained, since we only want an AR(2), # and the previous unconstrained was for an AR(4) ar_params = constrained[self._params_factor_ar] unconstrained[self._params_factor_ar] = ( tools.unconstrain_stationary_univariate(ar_params)) # Return all the parameters return np.r_[unconstrained, constrained[-3:]] def update(self, params, transformed=True, complex_step=False): # Peform the transformation, if required if not transformed: params = self.transform_params(params) params[self._params_factor_zero] = 0 # Now perform the usual DFM update, but exclude our new parameters super(ExtendedDFM, self).update( params[:-3], transformed=True, complex_step=complex_step) # Finally, set our new parameters in the design matrix self.ssm['design', 3, 1:4] = params[-3:] # So what did we just do? # # #### `__init__` # # The important step here was specifying the base dynamic factor model # which we were operating with. In particular, as described above, we # initialize with `factor_order=4`, even though we will only end up with an # AR(2) model for the factor. We also performed some general setup-related # tasks. # # #### `start_params` # # `start_params` are used as initial values in the optimizer. Since we are # adding three new parameters, we need to pass those in. If we had not done # this, the optimizer would use the default starting values, which would be # three elements short. # # #### `param_names` # # `param_names` are used in a variety of places, but especially in the # results class. Below we get a full result summary, which is only possible # when all the parameters have associated names. # # #### `transform_params` and `untransform_params` # # The optimizer selects possibly parameter values in an unconstrained way. # That's not usually desired (since variances cannot be negative, for # example), and `transform_params` is used to transform the unconstrained # values used by the optimizer to constrained values appropriate to the # model. Variances terms are typically squared (to force them to be # positive), and AR lag coefficients are often constrained to lead to a # stationary model. `untransform_params` is used for the reverse operation # (and is important because starting parameters are usually specified in # terms of values appropriate to the model, and we need to convert them to # parameters appropriate to the optimizer before we can begin the # optimization routine). # # Even though we do not need to transform or untransform our new parameters # (the loadings can in theory take on any values), we still need to modify # this function for two reasons: # # 1. The version in the `DynamicFactor` class is expecting 3 fewer # parameters than we have now. At a minimum, we need to handle the three new # parameters. # 2. The version in the `DynamicFactor` class constrains the factor lag # coefficients to be stationary as though it was an AR(4) model. Since we # actually have an AR(2) model, we need to re-do the constraint. We also set # the last two autoregressive coefficients to be zero here. # # #### `update` # # The most important reason we need to specify a new `update` method is # because we have three new parameters that we need to place into the state # space formulation. In particular we let the parent `DynamicFactor.update` # class handle placing all the parameters except the three new ones in to # the state space representation, and then we put the last three in # manually. # Create the model extended_mod = ExtendedDFM(endog) initial_extended_res = extended_mod.fit(maxiter=1000, disp=False) extended_res = extended_mod.fit( initial_extended_res.params, method='nm', maxiter=1000) print(extended_res.summary(separate_params=False)) # Although this model increases the likelihood, it is not preferred by the # AIC and BIC measures which penalize the additional three parameters. # # Furthermore, the qualitative results are unchanged, as we can see from # the updated $R^2$ chart and the new coincident index, both of which are # practically identical to the previous results. extended_res.plot_coefficients_of_determination(figsize=(8, 2)) fig, ax = plt.subplots(figsize=(13, 3)) # Compute the index extended_coincident_index = compute_coincident_index(extended_mod, extended_res) # Plot the factor dates = endog.index._mpl_repr() ax.plot(dates, coincident_index, '-', linewidth=1, label='Basic model') ax.plot( dates, extended_coincident_index, '--', linewidth=3, label='Extended model') ax.plot(usphci.index._mpl_repr(), usphci, label='USPHCI') ax.legend(loc='lower right') ax.set(title='Coincident indices, comparison') # Retrieve and also plot the NBER recession indicators ylim = ax.get_ylim() ax.fill_between( dates[:-3], ylim[0], ylim[1], rec.values[:-4, 0], facecolor='k', alpha=0.1) statsmodels-0.12.2/examples/python/statespace_local_linear_trend.py000066400000000000000000000231641400612667500257200ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook statespace_local_linear_trend.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # State space modeling: Local Linear Trends # This notebook describes how to extend the statsmodels statespace classes # to create and estimate a custom model. Here we develop a local linear # trend model. # # The Local Linear Trend model has the form (see Durbin and Koopman 2012, # Chapter 3.2 for all notation and details): # # $$ # \begin{align} # y_t & = \mu_t + \varepsilon_t \qquad & \varepsilon_t \sim # N(0, \sigma_\varepsilon^2) \\ # \mu_{t+1} & = \mu_t + \nu_t + \xi_t & \xi_t \sim N(0, \sigma_\xi^2) \\ # \nu_{t+1} & = \nu_t + \zeta_t & \zeta_t \sim N(0, \sigma_\zeta^2) # \end{align} # $$ # # It is easy to see that this can be cast into state space form as: # # $$ # \begin{align} # y_t & = \begin{pmatrix} 1 & 0 \end{pmatrix} \begin{pmatrix} \mu_t \\ # \nu_t \end{pmatrix} + \varepsilon_t \\ # \begin{pmatrix} \mu_{t+1} \\ \nu_{t+1} \end{pmatrix} & = \begin{bmatrix} # 1 & 1 \\ 0 & 1 \end{bmatrix} \begin{pmatrix} \mu_t \\ \nu_t \end{pmatrix} # + \begin{pmatrix} \xi_t \\ \zeta_t \end{pmatrix} # \end{align} # $$ # # Notice that much of the state space representation is composed of known # values; in fact the only parts in which parameters to be estimated appear # are in the variance / covariance matrices: # # $$ # \begin{align} # H_t & = \begin{bmatrix} \sigma_\varepsilon^2 \end{bmatrix} \\ # Q_t & = \begin{bmatrix} \sigma_\xi^2 & 0 \\ 0 & \sigma_\zeta^2 # \end{bmatrix} # \end{align} # $$ import numpy as np import pandas as pd from scipy.stats import norm import statsmodels.api as sm import matplotlib.pyplot as plt # To take advantage of the existing infrastructure, including Kalman # filtering and maximum likelihood estimation, we create a new class which # extends from `statsmodels.tsa.statespace.MLEModel`. There are a number of # things that must be specified: # # 1. **k_states**, **k_posdef**: These two parameters must be provided to # the base classes in initialization. The inform the statespace model about # the size of, respectively, the state vector, above $\begin{pmatrix} \mu_t # & \nu_t \end{pmatrix}'$, and the state error vector, above # $\begin{pmatrix} \xi_t & \zeta_t \end{pmatrix}'$. Note that the dimension # of the endogenous vector does not have to be specified, since it can be # inferred from the `endog` array. # 2. **update**: The method `update`, with argument `params`, must be # specified (it is used when `fit()` is called to calculate the MLE). It # takes the parameters and fills them into the appropriate state space # matrices. For example, below, the `params` vector contains variance # parameters $\begin{pmatrix} \sigma_\varepsilon^2 & \sigma_\xi^2 & # \sigma_\zeta^2\end{pmatrix}$, and the `update` method must place them in # the observation and state covariance matrices. More generally, the # parameter vector might be mapped into many different places in all of the # statespace matrices. # 3. **statespace matrices**: by default, all state space matrices # (`obs_intercept, design, obs_cov, state_intercept, transition, selection, # state_cov`) are set to zeros. Values that are fixed (like the ones in the # design and transition matrices here) can be set in initialization, whereas # values that vary with the parameters should be set in the `update` method. # Note that it is easy to forget to set the selection matrix, which is often # just the identity matrix (as it is here), but not setting it will lead to # a very different model (one where there is not a stochastic component to # the transition equation). # 4. **start params**: start parameters must be set, even if it is just a # vector of zeros, although often good start parameters can be found from # the data. Maximum likelihood estimation by gradient methods (as employed # here) can be sensitive to the starting parameters, so it is important to # select good ones if possible. Here it does not matter too much (although # as variances, they should't be set zero). # 5. **initialization**: in addition to defined state space matrices, all # state space models must be initialized with the mean and variance for the # initial distribution of the state vector. If the distribution is known, # `initialize_known(initial_state, initial_state_cov)` can be called, or if # the model is stationary (e.g. an ARMA model), `initialize_stationary` can # be used. Otherwise, `initialize_approximate_diffuse` is a reasonable # generic initialization (exact diffuse initialization is not yet # available). Since the local linear trend model is not stationary (it is # composed of random walks) and since the distribution is not generally # known, we use `initialize_approximate_diffuse` below. # # The above are the minimum necessary for a successful model. There are # also a number of things that do not have to be set, but which may be # helpful or important for some applications: # # 1. **transform / untransform**: when `fit` is called, the optimizer in # the background will use gradient methods to select the parameters that # maximize the likelihood function. By default it uses unbounded # optimization, which means that it may select any parameter value. In many # cases, that is not the desired behavior; variances, for example, cannot be # negative. To get around this, the `transform` method takes the # unconstrained vector of parameters provided by the optimizer and returns a # constrained vector of parameters used in likelihood evaluation. # `untransform` provides the reverse operation. # 2. **param_names**: this internal method can be used to set names for # the estimated parameters so that e.g. the summary provides meaningful # names. If not present, parameters are named `param0`, `param1`, etc. """ Univariate Local Linear Trend Model """ class LocalLinearTrend(sm.tsa.statespace.MLEModel): def __init__(self, endog): # Model order k_states = k_posdef = 2 # Initialize the statespace super(LocalLinearTrend, self).__init__( endog, k_states=k_states, k_posdef=k_posdef, initialization='approximate_diffuse', loglikelihood_burn=k_states) # Initialize the matrices self.ssm['design'] = np.array([1, 0]) self.ssm['transition'] = np.array([[1, 1], [0, 1]]) self.ssm['selection'] = np.eye(k_states) # Cache some indices self._state_cov_idx = ('state_cov', ) + np.diag_indices(k_posdef) @property def param_names(self): return ['sigma2.measurement', 'sigma2.level', 'sigma2.trend'] @property def start_params(self): return [np.std(self.endog)] * 3 def transform_params(self, unconstrained): return unconstrained**2 def untransform_params(self, constrained): return constrained**0.5 def update(self, params, *args, **kwargs): params = super(LocalLinearTrend, self).update(params, *args, **kwargs) # Observation covariance self.ssm['obs_cov', 0, 0] = params[0] # State covariance self.ssm[self._state_cov_idx] = params[1:] # Using this simple model, we can estimate the parameters from a local # linear trend model. The following example is from Commandeur and Koopman # (2007), section 3.4., modeling motor vehicle fatalities in Finland. import requests from io import BytesIO from zipfile import ZipFile # Download the dataset ck = requests.get( 'http://staff.feweb.vu.nl/koopman/projects/ckbook/OxCodeAll.zip').content zipped = ZipFile(BytesIO(ck)) df = pd.read_table( BytesIO( zipped.read('OxCodeIntroStateSpaceBook/Chapter_2/NorwayFinland.txt')), skiprows=1, header=None, sep='\s+', engine='python', names=['date', 'nf', 'ff']) # Since we defined the local linear trend model as extending from # `MLEModel`, the `fit()` method is immediately available, just as in other # statsmodels maximum likelihood classes. Similarly, the returned results # class supports many of the same post-estimation results, like the # `summary` method. # # Load Dataset df.index = pd.date_range( start='%d-01-01' % df.date[0], end='%d-01-01' % df.iloc[-1, 0], freq='AS') # Log transform df['lff'] = np.log(df['ff']) # Setup the model mod = LocalLinearTrend(df['lff']) # Fit it using MLE (recall that we are fitting the three variance # parameters) res = mod.fit(disp=False) print(res.summary()) # Finally, we can do post-estimation prediction and forecasting. Notice # that the end period can be specified as a date. # Perform prediction and forecasting predict = res.get_prediction() forecast = res.get_forecast('2014') fig, ax = plt.subplots(figsize=(10, 4)) # Plot the results df['lff'].plot(ax=ax, style='k.', label='Observations') predict.predicted_mean.plot(ax=ax, label='One-step-ahead Prediction') predict_ci = predict.conf_int(alpha=0.05) predict_index = np.arange(len(predict_ci)) ax.fill_between( predict_index[2:], predict_ci.iloc[2:, 0], predict_ci.iloc[2:, 1], alpha=0.1) forecast.predicted_mean.plot(ax=ax, style='r', label='Forecast') forecast_ci = forecast.conf_int() forecast_index = np.arange(len(predict_ci), len(predict_ci) + len(forecast_ci)) ax.fill_between( forecast_index, forecast_ci.iloc[:, 0], forecast_ci.iloc[:, 1], alpha=0.1) # Cleanup the image ax.set_ylim((4, 8)) legend = ax.legend(loc='lower left') # ### References # # Commandeur, Jacques J. F., and Siem Jan Koopman. 2007. # An Introduction to State Space Time Series Analysis. # Oxford ; New York: Oxford University Press. # # Durbin, James, and Siem Jan Koopman. 2012. # Time Series Analysis by State Space Methods: Second Edition. # Oxford University Press. statsmodels-0.12.2/examples/python/statespace_sarimax_internet.py000066400000000000000000000131171400612667500254510ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook statespace_sarimax_internet.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # SARIMAX: Model selection, missing data # The example mirrors Durbin and Koopman (2012), Chapter 8.4 in # application of Box-Jenkins methodology to fit ARMA models. The novel # feature is the ability of the model to work on datasets with missing # values. import numpy as np import pandas as pd from scipy.stats import norm import statsmodels.api as sm import matplotlib.pyplot as plt import requests from io import BytesIO from zipfile import ZipFile # Download the dataset dk = requests.get('http://www.ssfpack.com/files/DK-data.zip').content f = BytesIO(dk) zipped = ZipFile(f) df = pd.read_table( BytesIO(zipped.read('internet.dat')), skiprows=1, header=None, sep='\s+', engine='python', names=['internet', 'dinternet']) # ### Model Selection # # As in Durbin and Koopman, we force a number of the values to be missing. # Get the basic series dta_full = df.dinternet[1:].values dta_miss = dta_full.copy() # Remove datapoints missing = np.r_[6, 16, 26, 36, 46, 56, 66, 72, 73, 74, 75, 76, 86, 96] - 1 dta_miss[missing] = np.nan # Then we can consider model selection using the Akaike information # criteria (AIC), but running the model for each variant and selecting the # model with the lowest AIC value. # # There are a couple of things to note here: # # - When running such a large batch of models, particularly when the # autoregressive and moving average orders become large, there is the # possibility of poor maximum likelihood convergence. Below we ignore the # warnings since this example is illustrative. # - We use the option `enforce_invertibility=False`, which allows the # moving average polynomial to be non-invertible, so that more of the models # are estimable. # - Several of the models do not produce good results, and their AIC value # is set to NaN. This is not surprising, as Durbin and Koopman note # numerical problems with the high order models. import warnings aic_full = pd.DataFrame(np.zeros((6, 6), dtype=float)) aic_miss = pd.DataFrame(np.zeros((6, 6), dtype=float)) warnings.simplefilter('ignore') # Iterate over all ARMA(p,q) models with p,q in [0,6] for p in range(6): for q in range(6): if p == 0 and q == 0: continue # Estimate the model with no missing datapoints mod = sm.tsa.statespace.SARIMAX( dta_full, order=(p, 0, q), enforce_invertibility=False) try: res = mod.fit(disp=False) aic_full.iloc[p, q] = res.aic except: aic_full.iloc[p, q] = np.nan # Estimate the model with missing datapoints mod = sm.tsa.statespace.SARIMAX( dta_miss, order=(p, 0, q), enforce_invertibility=False) try: res = mod.fit(disp=False) aic_miss.iloc[p, q] = res.aic except: aic_miss.iloc[p, q] = np.nan # For the models estimated over the full (non-missing) dataset, the AIC # chooses ARMA(1,1) or ARMA(3,0). Durbin and Koopman suggest the ARMA(1,1) # specification is better due to parsimony. # # $$ # \text{Replication of:}\\ # \textbf{Table 8.1} ~~ \text{AIC for different ARMA models.}\\ # \newcommand{\r}[1]{{\color{red}{#1}}} # \begin{array}{lrrrrrr} # \hline # q & 0 & 1 & 2 & 3 & 4 & 5 \\ # \hline # p & {} & {} & {} & {} & {} & {} \\ # 0 & 0.00 & 549.81 & 519.87 & 520.27 & 519.38 & 518.86 \\ # 1 & 529.24 & \r{514.30} & 516.25 & 514.58 & 515.10 & 516.28 \\ # 2 & 522.18 & 516.29 & 517.16 & 515.77 & 513.24 & 514.73 \\ # 3 & \r{511.99} & 513.94 & 515.92 & 512.06 & 513.72 & 514.50 \\ # 4 & 513.93 & 512.89 & nan & nan & 514.81 & 516.08 \\ # 5 & 515.86 & 517.64 & nan & nan & nan & nan \\ # \hline # \end{array} # $$ # # For the models estimated over missing dataset, the AIC chooses ARMA(1,1) # # $$ # \text{Replication of:}\\ # \textbf{Table 8.2} ~~ \text{AIC for different ARMA models with missing # observations.}\\ # \begin{array}{lrrrrrr} # \hline # q & 0 & 1 & 2 & 3 & 4 & 5 \\ # \hline # p & {} & {} & {} & {} & {} & {} \\ # 0 & 0.00 & 488.93 & 464.01 & 463.86 & 462.63 & 463.62 \\ # 1 & 468.01 & \r{457.54} & 459.35 & 458.66 & 459.15 & 461.01 \\ # 2 & 469.68 & nan & 460.48 & 459.43 & 459.23 & 460.47 \\ # 3 & 467.10 & 458.44 & 459.64 & 456.66 & 459.54 & 460.05 \\ # 4 & 469.00 & 459.52 & nan & 463.04 & 459.35 & 460.96 \\ # 5 & 471.32 & 461.26 & nan & nan & 461.00 & 462.97 \\ # \hline # \end{array} # $$ # # **Note**: the AIC values are calculated differently than in Durbin and # Koopman, but show overall similar trends. # ### Postestimation # # Using the ARMA(1,1) specification selected above, we perform in-sample # prediction and out-of-sample forecasting. # Statespace mod = sm.tsa.statespace.SARIMAX(dta_miss, order=(1, 0, 1)) res = mod.fit(disp=False) print(res.summary()) # In-sample one-step-ahead predictions, and out-of-sample forecasts nforecast = 20 predict = res.get_prediction(end=mod.nobs + nforecast) idx = np.arange(len(predict.predicted_mean)) predict_ci = predict.conf_int(alpha=0.5) # Graph fig, ax = plt.subplots(figsize=(12, 6)) ax.xaxis.grid() ax.plot(dta_miss, 'k.') # Plot ax.plot(idx[:-nforecast], predict.predicted_mean[:-nforecast], 'gray') ax.plot( idx[-nforecast:], predict.predicted_mean[-nforecast:], 'k--', linestyle='--', linewidth=2) ax.fill_between(idx, predict_ci[:, 0], predict_ci[:, 1], alpha=0.15) ax.set(title='Figure 8.9 - Internet series') statsmodels-0.12.2/examples/python/statespace_sarimax_stata.py000066400000000000000000000472621400612667500247450ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook statespace_sarimax_stata.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # SARIMAX: Introduction # This notebook replicates examples from the Stata ARIMA time series # estimation and postestimation documentation. # # First, we replicate the four estimation examples # http://www.stata.com/manuals13/tsarima.pdf: # # 1. ARIMA(1,1,1) model on the U.S. Wholesale Price Index (WPI) dataset. # 2. Variation of example 1 which adds an MA(4) term to the ARIMA(1,1,1) # specification to allow for an additive seasonal effect. # 3. ARIMA(2,1,0) x (1,1,0,12) model of monthly airline data. This example # allows a multiplicative seasonal effect. # 4. ARMA(1,1) model with exogenous regressors; describes consumption as # an autoregressive process on which also the money supply is assumed to be # an explanatory variable. # # Second, we demonstrate postestimation capabilities to replicate # http://www.stata.com/manuals13/tsarimapostestimation.pdf. The model from # example 4 is used to demonstrate: # # 1. One-step-ahead in-sample prediction # 2. n-step-ahead out-of-sample forecasting # 3. n-step-ahead in-sample dynamic prediction import numpy as np import pandas as pd from scipy.stats import norm import statsmodels.api as sm import matplotlib.pyplot as plt from datetime import datetime import requests from io import BytesIO # ### ARIMA Example 1: Arima # # As can be seen in the graphs from Example 2, the Wholesale price index # (WPI) is growing over time (i.e. is not stationary). Therefore an ARMA # model is not a good specification. In this first example, we consider a # model where the original time series is assumed to be integrated of order # 1, so that the difference is assumed to be stationary, and fit a model # with one autoregressive lag and one moving average lag, as well as an # intercept term. # # The postulated data process is then: # # $$ # \Delta y_t = c + \phi_1 \Delta y_{t-1} + \theta_1 \epsilon_{t-1} + # \epsilon_{t} # $$ # # where $c$ is the intercept of the ARMA model, $\Delta$ is the first- # difference operator, and we assume $\epsilon_{t} \sim N(0, \sigma^2)$. # This can be rewritten to emphasize lag polynomials as (this will be useful # in example 2, below): # # $$ # (1 - \phi_1 L ) \Delta y_t = c + (1 + \theta_1 L) \epsilon_{t} # $$ # # where $L$ is the lag operator. # # Notice that one difference between the Stata output and the output below # is that Stata estimates the following model: # # $$ # (\Delta y_t - \beta_0) = \phi_1 ( \Delta y_{t-1} - \beta_0) + \theta_1 # \epsilon_{t-1} + \epsilon_{t} # $$ # # where $\beta_0$ is the mean of the process $y_t$. This model is # equivalent to the one estimated in the statsmodels SARIMAX class, but the # interpretation is different. To see the equivalence, note that: # # $$ # (\Delta y_t - \beta_0) = \phi_1 ( \Delta y_{t-1} - \beta_0) + \theta_1 # \epsilon_{t-1} + \epsilon_{t} \\ # \Delta y_t = (1 - \phi_1) \beta_0 + \phi_1 \Delta y_{t-1} + \theta_1 # \epsilon_{t-1} + \epsilon_{t} # $$ # # so that $c = (1 - \phi_1) \beta_0$. # Dataset wpi1 = requests.get('https://www.stata-press.com/data/r12/wpi1.dta').content data = pd.read_stata(BytesIO(wpi1)) data.index = data.t # Fit the model mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(1, 1, 1)) res = mod.fit(disp=False) print(res.summary()) # Thus the maximum likelihood estimates imply that for the process above, # we have: # # $$ # \Delta y_t = 0.1050 + 0.8740 \Delta y_{t-1} - 0.4206 \epsilon_{t-1} + # \epsilon_{t} # $$ # # where $\epsilon_{t} \sim N(0, 0.5226)$. Finally, recall that $c = (1 - # \phi_1) \beta_0$, and here $c = 0.1050$ and $\phi_1 = 0.8740$. To compare # with the output from Stata, we could calculate the mean: # # $$\beta_0 = \frac{c}{1 - \phi_1} = \frac{0.1050}{1 - 0.8740} = 0.83$$ # # **Note**: these values are slightly different from the values in the # Stata documentation because the optimizer in statsmodels has found # parameters here that yield a higher likelihood. Nonetheless, they are very # close. # ### ARIMA Example 2: Arima with additive seasonal effects # # This model is an extension of that from example 1. Here the data is # assumed to follow the process: # # $$ # \Delta y_t = c + \phi_1 \Delta y_{t-1} + \theta_1 \epsilon_{t-1} + # \theta_4 \epsilon_{t-4} + \epsilon_{t} # $$ # # The new part of this model is that there is allowed to be a annual # seasonal effect (it is annual even though the periodicity is 4 because the # dataset is quarterly). The second difference is that this model uses the # log of the data rather than the level. # # Before estimating the dataset, graphs showing: # # 1. The time series (in logs) # 2. The first difference of the time series (in logs) # 3. The autocorrelation function # 4. The partial autocorrelation function. # # From the first two graphs, we note that the original time series does # not appear to be stationary, whereas the first-difference does. This # supports either estimating an ARMA model on the first-difference of the # data, or estimating an ARIMA model with 1 order of integration (recall # that we are taking the latter approach). The last two graphs support the # use of an ARMA(1,1,1) model. # Dataset data = pd.read_stata(BytesIO(wpi1)) data.index = data.t data['ln_wpi'] = np.log(data['wpi']) data['D.ln_wpi'] = data['ln_wpi'].diff() # Graph data fig, axes = plt.subplots(1, 2, figsize=(15, 4)) # Levels axes[0].plot(data.index._mpl_repr(), data['wpi'], '-') axes[0].set(title='US Wholesale Price Index') # Log difference axes[1].plot(data.index._mpl_repr(), data['D.ln_wpi'], '-') axes[1].hlines(0, data.index[0], data.index[-1], 'r') axes[1].set(title='US Wholesale Price Index - difference of logs') # Graph data fig, axes = plt.subplots(1, 2, figsize=(15, 4)) fig = sm.graphics.tsa.plot_acf(data.iloc[1:]['D.ln_wpi'], lags=40, ax=axes[0]) fig = sm.graphics.tsa.plot_pacf(data.iloc[1:]['D.ln_wpi'], lags=40, ax=axes[1]) # To understand how to specify this model in statsmodels, first recall # that from example 1 we used the following code to specify the ARIMA(1,1,1) # model: # # ```python # mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(1,1,1)) # ``` # # The `order` argument is a tuple of the form `(AR specification, # Integration order, MA specification)`. The integration order must be an # integer (for example, here we assumed one order of integration, so it was # specified as 1. In a pure ARMA model where the underlying data is already # stationary, it would be 0). # # For the AR specification and MA specification components, there are two # possibilities. The first is to specify the **maximum degree** of the # corresponding lag polynomial, in which case the component is an integer. # For example, if we wanted to specify an ARIMA(1,1,4) process, we would # use: # # ```python # mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(1,1,4)) # ``` # # and the corresponding data process would be: # # $$ # y_t = c + \phi_1 y_{t-1} + \theta_1 \epsilon_{t-1} + \theta_2 # \epsilon_{t-2} + \theta_3 \epsilon_{t-3} + \theta_4 \epsilon_{t-4} + # \epsilon_{t} # $$ # # or # # $$ # (1 - \phi_1 L)\Delta y_t = c + (1 + \theta_1 L + \theta_2 L^2 + \theta_3 # L^3 + \theta_4 L^4) \epsilon_{t} # $$ # # When the specification parameter is given as a maximum degree of the lag # polynomial, it implies that all polynomial terms up to that degree are # included. Notice that this is *not* the model we want to use, because it # would include terms for $\epsilon_{t-2}$ and $\epsilon_{t-3}$, which we # do not want here. # # What we want is a polynomial that has terms for the 1st and 4th degrees, # but leaves out the 2nd and 3rd terms. To do that, we need to provide a # tuple for the specification parameter, where the tuple describes **the lag # polynomial itself**. In particular, here we would want to use: # # ```python # ar = 1 # this is the maximum degree specification # ma = (1,0,0,1) # this is the lag polynomial specification # mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', # order=(ar,1,ma))) # ``` # # This gives the following form for the process of the data: # # $$ # \Delta y_t = c + \phi_1 \Delta y_{t-1} + \theta_1 \epsilon_{t-1} + # \theta_4 \epsilon_{t-4} + \epsilon_{t} \\ # (1 - \phi_1 L)\Delta y_t = c + (1 + \theta_1 L + \theta_4 L^4) # \epsilon_{t} # $$ # # which is what we want. # Fit the model mod = sm.tsa.statespace.SARIMAX(data['ln_wpi'], trend='c', order=(1, 1, 1)) res = mod.fit(disp=False) print(res.summary()) # ### ARIMA Example 3: Airline Model # # In the previous example, we included a seasonal effect in an *additive* # way, meaning that we added a term allowing the process to depend on the # 4th MA lag. It may be instead that we want to model a seasonal effect in a # multiplicative way. We often write the model then as an ARIMA $(p,d,q) # \times (P,D,Q)_s$, where the lowercase letters indicate the specification # for the non-seasonal component, and the uppercase letters indicate the # specification for the seasonal component; $s$ is the periodicity of the # seasons (e.g. it is often 4 for quarterly data or 12 for monthly data). # The data process can be written generically as: # # $$ # \phi_p (L) \tilde \phi_P (L^s) \Delta^d \Delta_s^D y_t = A(t) + \theta_q # (L) \tilde \theta_Q (L^s) \epsilon_t # $$ # # where: # # - $\phi_p (L)$ is the non-seasonal autoregressive lag polynomial # - $\tilde \phi_P (L^s)$ is the seasonal autoregressive lag polynomial # - $\Delta^d \Delta_s^D y_t$ is the time series, differenced $d$ times, # and seasonally differenced $D$ times. # - $A(t)$ is the trend polynomial (including the intercept) # - $\theta_q (L)$ is the non-seasonal moving average lag polynomial # - $\tilde \theta_Q (L^s)$ is the seasonal moving average lag polynomial # # sometimes we rewrite this as: # # $$ # \phi_p (L) \tilde \phi_P (L^s) y_t^* = A(t) + \theta_q (L) \tilde # \theta_Q (L^s) \epsilon_t # $$ # # where $y_t^* = \Delta^d \Delta_s^D y_t$. This emphasizes that just as in # the simple case, after we take differences (here both non-seasonal and # seasonal) to make the data stationary, the resulting model is just an ARMA # model. # # As an example, consider the airline model ARIMA $(2,1,0) \times # (1,1,0)_{12}$, with an intercept. The data process can be written in the # form above as: # # $$ # (1 - \phi_1 L - \phi_2 L^2) (1 - \tilde \phi_1 L^{12}) \Delta # \Delta_{12} y_t = c + \epsilon_t # $$ # # Here, we have: # # - $\phi_p (L) = (1 - \phi_1 L - \phi_2 L^2)$ # - $\tilde \phi_P (L^s) = (1 - \phi_1 L^12)$ # - $d = 1, D = 1, s=12$ indicating that $y_t^*$ is derived from $y_t$ by # taking first-differences and then taking 12-th differences. # - $A(t) = c$ is the *constant* trend polynomial (i.e. just an intercept) # - $\theta_q (L) = \tilde \theta_Q (L^s) = 1$ (i.e. there is no moving # average effect) # # It may still be confusing to see the two lag polynomials in front of the # time-series variable, but notice that we can multiply the lag polynomials # together to get the following model: # # $$ # (1 - \phi_1 L - \phi_2 L^2 - \tilde \phi_1 L^{12} + \phi_1 \tilde \phi_1 # L^{13} + \phi_2 \tilde \phi_1 L^{14} ) y_t^* = c + \epsilon_t # $$ # # which can be rewritten as: # # $$ # y_t^* = c + \phi_1 y_{t-1}^* + \phi_2 y_{t-2}^* + \tilde \phi_1 # y_{t-12}^* - \phi_1 \tilde \phi_1 y_{t-13}^* - \phi_2 \tilde \phi_1 # y_{t-14}^* + \epsilon_t # $$ # # This is similar to the additively seasonal model from example 2, but the # coefficients in front of the autoregressive lags are actually combinations # of the underlying seasonal and non-seasonal parameters. # # Specifying the model in statsmodels is done simply by adding the # `seasonal_order` argument, which accepts a tuple of the form `(Seasonal AR # specification, Seasonal Integration order, Seasonal MA, Seasonal # periodicity)`. The seasonal AR and MA specifications, as before, can be # expressed as a maximum polynomial degree or as the lag polynomial itself. # Seasonal periodicity is an integer. # # For the airline model ARIMA $(2,1,0) \times (1,1,0)_{12}$ with an # intercept, the command is: # # ```python # mod = sm.tsa.statespace.SARIMAX(data['lnair'], order=(2,1,0), # seasonal_order=(1,1,0,12)) # ``` # Dataset air2 = requests.get('https://www.stata-press.com/data/r12/air2.dta').content data = pd.read_stata(BytesIO(air2)) data.index = pd.date_range( start=datetime(data.time[0], 1, 1), periods=len(data), freq='MS') data['lnair'] = np.log(data['air']) # Fit the model mod = sm.tsa.statespace.SARIMAX( data['lnair'], order=(2, 1, 0), seasonal_order=(1, 1, 0, 12), simple_differencing=True) res = mod.fit(disp=False) print(res.summary()) # Notice that here we used an additional argument # `simple_differencing=True`. This controls how the order of integration is # handled in ARIMA models. If `simple_differencing=True`, then the time # series provided as `endog` is literally differenced and an ARMA model is # fit to the resulting new time series. This implies that a number of # initial periods are lost to the differencing process, however it may be # necessary either to compare results to other packages (e.g. Stata's # `arima` always uses simple differencing) or if the seasonal periodicity # is large. # # The default is `simple_differencing=False`, in which case the # integration component is implemented as part of the state space # formulation, and all of the original data can be used in estimation. # ### ARIMA Example 4: ARMAX (Friedman) # # This model demonstrates the use of explanatory variables (the X part of # ARMAX). When exogenous regressors are included, the SARIMAX module uses # the concept of "regression with SARIMA errors" (see # http://robjhyndman.com/hyndsight/arimax/ for details of regression with # ARIMA errors versus alternative specifications), so that the model is # specified as: # # $$ # y_t = \beta_t x_t + u_t \\ # \phi_p (L) \tilde \phi_P (L^s) \Delta^d \Delta_s^D u_t = A(t) + # \theta_q (L) \tilde \theta_Q (L^s) \epsilon_t # $$ # # Notice that the first equation is just a linear regression, and the # second equation just describes the process followed by the error component # as SARIMA (as was described in example 3). One reason for this # specification is that the estimated parameters have their natural # interpretations. # # This specification nests many simpler specifications. For example, # regression with AR(2) errors is: # # $$ # y_t = \beta_t x_t + u_t \\ # (1 - \phi_1 L - \phi_2 L^2) u_t = A(t) + \epsilon_t # $$ # # The model considered in this example is regression with ARMA(1,1) # errors. The process is then written: # # $$ # \text{consump}_t = \beta_0 + \beta_1 \text{m2}_t + u_t \\ # (1 - \phi_1 L) u_t = (1 - \theta_1 L) \epsilon_t # $$ # # Notice that $\beta_0$ is, as described in example 1 above, *not* the # same thing as an intercept specified by `trend='c'`. Whereas in the # examples above we estimated the intercept of the model via the trend # polynomial, here, we demonstrate how to estimate $\beta_0$ itself by # adding a constant to the exogenous dataset. In the output, the $beta_0$ is # called `const`, whereas above the intercept $c$ was called `intercept` in # the output. # Dataset friedman2 = requests.get( 'https://www.stata-press.com/data/r12/friedman2.dta').content data = pd.read_stata(BytesIO(friedman2)) data.index = data.time # Variables endog = data.loc['1959':'1981', 'consump'] exog = sm.add_constant(data.loc['1959':'1981', 'm2']) # Fit the model mod = sm.tsa.statespace.SARIMAX(endog, exog, order=(1, 0, 1)) res = mod.fit(disp=False) print(res.summary()) # ### ARIMA Postestimation: Example 1 - Dynamic Forecasting # # Here we describe some of the post-estimation capabilities of # statsmodels' SARIMAX. # # First, using the model from example, we estimate the parameters using # data that *excludes the last few observations* (this is a little # artificial as an example, but it allows considering performance of out-of- # sample forecasting and facilitates comparison to Stata's documentation). # Dataset raw = pd.read_stata(BytesIO(friedman2)) raw.index = raw.time data = raw.loc[:'1981'] # Variables endog = data.loc['1959':, 'consump'] exog = sm.add_constant(data.loc['1959':, 'm2']) nobs = endog.shape[0] # Fit the model mod = sm.tsa.statespace.SARIMAX( endog.loc[:'1978-01-01'], exog=exog.loc[:'1978-01-01'], order=(1, 0, 1)) fit_res = mod.fit(disp=False) print(fit_res.summary()) # Next, we want to get results for the full dataset but using the # estimated parameters (on a subset of the data). mod = sm.tsa.statespace.SARIMAX(endog, exog=exog, order=(1, 0, 1)) res = mod.filter(fit_res.params) # The `predict` command is first applied here to get in-sample # predictions. We use the `full_results=True` argument to allow us to # calculate confidence intervals (the default output of `predict` is just # the predicted values). # # With no other arguments, `predict` returns the one-step-ahead in-sample # predictions for the entire sample. # In-sample one-step-ahead predictions predict = res.get_prediction() predict_ci = predict.conf_int() # We can also get *dynamic predictions*. One-step-ahead prediction uses # the true values of the endogenous values at each step to predict the next # in-sample value. Dynamic predictions use one-step-ahead prediction up to # some point in the dataset (specified by the `dynamic` argument); after # that, the previous *predicted* endogenous values are used in place of the # true endogenous values for each new predicted element. # # The `dynamic` argument is specified to be an *offset* relative to the # `start` argument. If `start` is not specified, it is assumed to be `0`. # # Here we perform dynamic prediction starting in the first quarter of # 1978. # Dynamic predictions predict_dy = res.get_prediction(dynamic='1978-01-01') predict_dy_ci = predict_dy.conf_int() # We can graph the one-step-ahead and dynamic predictions (and the # corresponding confidence intervals) to see their relative performance. # Notice that up to the point where dynamic prediction begins (1978:Q1), the # two are the same. # Graph fig, ax = plt.subplots(figsize=(9, 4)) npre = 4 ax.set( title='Personal consumption', xlabel='Date', ylabel='Billions of dollars') # Plot data points data.loc['1977-07-01':, 'consump'].plot(ax=ax, style='o', label='Observed') # Plot predictions predict.predicted_mean.loc['1977-07-01':].plot( ax=ax, style='r--', label='One-step-ahead forecast') ci = predict_ci.loc['1977-07-01':] ax.fill_between(ci.index, ci.iloc[:, 0], ci.iloc[:, 1], color='r', alpha=0.1) predict_dy.predicted_mean.loc['1977-07-01':].plot( ax=ax, style='g', label='Dynamic forecast (1978)') ci = predict_dy_ci.loc['1977-07-01':] ax.fill_between(ci.index, ci.iloc[:, 0], ci.iloc[:, 1], color='g', alpha=0.1) legend = ax.legend(loc='lower right') # Finally, graph the prediction *error*. It is obvious that, as one would # suspect, one-step-ahead prediction is considerably better. # Prediction error # Graph fig, ax = plt.subplots(figsize=(9, 4)) npre = 4 ax.set(title='Forecast error', xlabel='Date', ylabel='Forecast - Actual') # In-sample one-step-ahead predictions and 95% confidence intervals predict_error = predict.predicted_mean - endog predict_error.loc['1977-10-01':].plot(ax=ax, label='One-step-ahead forecast') ci = predict_ci.loc['1977-10-01':].copy() ci.iloc[:, 0] -= endog.loc['1977-10-01':] ci.iloc[:, 1] -= endog.loc['1977-10-01':] ax.fill_between(ci.index, ci.iloc[:, 0], ci.iloc[:, 1], alpha=0.1) # Dynamic predictions and 95% confidence intervals predict_dy_error = predict_dy.predicted_mean - endog predict_dy_error.loc['1977-10-01':].plot( ax=ax, style='r', label='Dynamic forecast (1978)') ci = predict_dy_ci.loc['1977-10-01':].copy() ci.iloc[:, 0] -= endog.loc['1977-10-01':] ci.iloc[:, 1] -= endog.loc['1977-10-01':] ax.fill_between(ci.index, ci.iloc[:, 0], ci.iloc[:, 1], color='r', alpha=0.1) legend = ax.legend(loc='lower left') legend.get_frame().set_facecolor('w') statsmodels-0.12.2/examples/python/statespace_seasonal.py000066400000000000000000000352221400612667500237030ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook statespace_seasonal.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Seasonality in time series data # # Consider the problem of modeling time series data with multiple seasonal # components with different periodicities. Let us take the time series # $y_t$ and decompose it explicitly to have a level component and two # seasonal components. # # $$ # y_t = \mu_t + \gamma^{(1)}_t + \gamma^{(2)}_t # $$ # # where $\mu_t$ represents the trend or level, $\gamma^{(1)}_t$ represents # a seasonal component with a relatively short period, and $\gamma^{(2)}_t$ # represents another seasonal component of longer period. We will have a # fixed intercept term for our level and consider both $\gamma^{(2)}_t$ and # $\gamma^{(2)}_t$ to be stochastic so that the seasonal patterns can vary # over time. # # In this notebook, we will generate synthetic data conforming to this # model and showcase modeling of the seasonal terms in a few different ways # under the unobserved components modeling framework. import numpy as np import pandas as pd import statsmodels.api as sm import matplotlib.pyplot as plt # ### Synthetic data creation # # We will create data with multiple seasonal patterns by following # equations (3.7) and (3.8) in Durbin and Koopman (2012). We will simulate # 300 periods and two seasonal terms parametrized in the frequency domain # having periods 10 and 100, respectively, and 3 and 2 number of harmonics, # respectively. Further, the variances of their stochastic parts are 4 and # 9, respectively. # First we'll simulate the synthetic data def simulate_seasonal_term(periodicity, total_cycles, noise_std=1., harmonics=None): duration = periodicity * total_cycles assert duration == int(duration) duration = int(duration) harmonics = harmonics if harmonics else int(np.floor(periodicity / 2)) lambda_p = 2 * np.pi / float(periodicity) gamma_jt = noise_std * np.random.randn((harmonics)) gamma_star_jt = noise_std * np.random.randn((harmonics)) total_timesteps = 100 * duration # Pad for burn in series = np.zeros(total_timesteps) for t in range(total_timesteps): gamma_jtp1 = np.zeros_like(gamma_jt) gamma_star_jtp1 = np.zeros_like(gamma_star_jt) for j in range(1, harmonics + 1): cos_j = np.cos(lambda_p * j) sin_j = np.sin(lambda_p * j) gamma_jtp1[j - 1] = ( gamma_jt[j - 1] * cos_j + gamma_star_jt[j - 1] * sin_j + noise_std * np.random.randn()) gamma_star_jtp1[j - 1] = ( -gamma_jt[j - 1] * sin_j + gamma_star_jt[j - 1] * cos_j + noise_std * np.random.randn()) series[t] = np.sum(gamma_jtp1) gamma_jt = gamma_jtp1 gamma_star_jt = gamma_star_jtp1 wanted_series = series[-duration:] # Discard burn in return wanted_series duration = 100 * 3 periodicities = [10, 100] num_harmonics = [3, 2] std = np.array([2, 3]) np.random.seed(8678309) terms = [] for ix, _ in enumerate(periodicities): s = simulate_seasonal_term( periodicities[ix], duration / periodicities[ix], harmonics=num_harmonics[ix], noise_std=std[ix]) terms.append(s) terms.append(np.ones_like(terms[0]) * 10.) series = pd.Series(np.sum(terms, axis=0)) df = pd.DataFrame(data={ 'total': series, '10(3)': terms[0], '100(2)': terms[1], 'level': terms[2] }) h1, = plt.plot(df['total']) h2, = plt.plot(df['10(3)']) h3, = plt.plot(df['100(2)']) h4, = plt.plot(df['level']) plt.legend(['total', '10(3)', '100(2)', 'level']) plt.show() # ### Unobserved components (frequency domain modeling) # # The next method is an unobserved components model, where the trend is # modeled as a fixed intercept and the seasonal components are modeled using # trigonometric functions with primary periodicities of 10 and 100, # respectively, and number of harmonics 3 and 2, respectively. Note that # this is the correct, generating model. The process for the time series can # be written as: # # $$ # \begin{align} # y_t & = \mu_t + \gamma^{(1)}_t + \gamma^{(2)}_t + \epsilon_t\\ # \mu_{t+1} & = \mu_t \\ # \gamma^{(1)}_{t} &= \sum_{j=1}^2 \gamma^{(1)}_{j, t} \\ # \gamma^{(2)}_{t} &= \sum_{j=1}^3 \gamma^{(2)}_{j, t}\\ # \gamma^{(1)}_{j, t+1} &= \gamma^{(1)}_{j, t}\cos(\lambda_j) + \gamma^{*, # (1)}_{j, t}\sin(\lambda_j) + \omega^{(1)}_{j,t}, ~j = 1, 2, 3\\ # \gamma^{*, (1)}_{j, t+1} &= -\gamma^{(1)}_{j, t}\sin(\lambda_j) + # \gamma^{*, (1)}_{j, t}\cos(\lambda_j) + \omega^{*, (1)}_{j, t}, ~j = 1, 2, # 3\\ # \gamma^{(2)}_{j, t+1} &= \gamma^{(2)}_{j, t}\cos(\lambda_j) + \gamma^{*, # (2)}_{j, t}\sin(\lambda_j) + \omega^{(2)}_{j,t}, ~j = 1, 2\\ # \gamma^{*, (2)}_{j, t+1} &= -\gamma^{(2)}_{j, t}\sin(\lambda_j) + # \gamma^{*, (2)}_{j, t}\cos(\lambda_j) + \omega^{*, (2)}_{j, t}, ~j = 1, # 2\\ # \end{align} # $$ # $$ # # where $\epsilon_t$ is white noise, $\omega^{(1)}_{j,t}$ are i.i.d. $N(0, # \sigma^2_1)$, and $\omega^{(2)}_{j,t}$ are i.i.d. $N(0, \sigma^2_2)$, # where $\sigma_1 = 2.$ model = sm.tsa.UnobservedComponents( series.values, level='fixed intercept', freq_seasonal=[{ 'period': 10, 'harmonics': 3 }, { 'period': 100, 'harmonics': 2 }]) res_f = model.fit(disp=False) print(res_f.summary()) # The first state variable holds our estimate of the intercept print("fixed intercept estimated as {0:.3f}".format( res_f.smoother_results.smoothed_state[0, -1:][0])) res_f.plot_components() plt.show() model.ssm.transition[:, :, 0] # Observe that the fitted variances are pretty close to the true variances # of 4 and 9. Further, the individual seasonal components look pretty close # to the true seasonal components. The smoothed level term is kind of close # to the true level of 10. Finally, our diagnostics look solid; the test # statistics are small enough to fail to reject our three tests. # ### Unobserved components (mixed time and frequency domain modeling) # # The second method is an unobserved components model, where the trend is # modeled as a fixed intercept and the seasonal components are modeled using # 10 constants summing to 0 and trigonometric functions with a primary # periodicities of 100 with 2 harmonics total. Note that this is not the # generating model, as it presupposes that there are more state errors for # the shorter seasonal component than in reality. The process for the time # series can be written as: # # $$ # \begin{align} # y_t & = \mu_t + \gamma^{(1)}_t + \gamma^{(2)}_t + \epsilon_t\\ # \mu_{t+1} & = \mu_t \\ # \gamma^{(1)}_{t + 1} &= - \sum_{j=1}^9 \gamma^{(1)}_{t + 1 - j} + # \omega^{(1)}_t\\ # \gamma^{(2)}_{j, t+1} &= \gamma^{(2)}_{j, t}\cos(\lambda_j) + \gamma^{*, # (2)}_{j, t}\sin(\lambda_j) + \omega^{(2)}_{j,t}, ~j = 1, 2\\ # \gamma^{*, (2)}_{j, t+1} &= -\gamma^{(2)}_{j, t}\sin(\lambda_j) + # \gamma^{*, (2)}_{j, t}\cos(\lambda_j) + \omega^{*, (2)}_{j, t}, ~j = 1, # 2\\ # \end{align} # $$ # # where $\epsilon_t$ is white noise, $\omega^{(1)}_{t}$ are i.i.d. $N(0, # \sigma^2_1)$, and $\omega^{(2)}_{j,t}$ are i.i.d. $N(0, \sigma^2_2)$. model = sm.tsa.UnobservedComponents( series, level='fixed intercept', seasonal=10, freq_seasonal=[{ 'period': 100, 'harmonics': 2 }]) res_tf = model.fit(disp=False) print(res_tf.summary()) # The first state variable holds our estimate of the intercept print("fixed intercept estimated as {0:.3f}".format( res_tf.smoother_results.smoothed_state[0, -1:][0])) res_tf.plot_components() plt.show() # The plotted components look good. However, the estimated variance of # the second seasonal term is inflated from reality. Additionally, we # reject the Ljung-Box statistic, indicating we may have remaining # autocorrelation after accounting for our components. # ### Unobserved components (lazy frequency domain modeling) # # The third method is an unobserved components model with a fixed # intercept and one seasonal component, which is modeled using trigonometric # functions with primary periodicity 100 and 50 harmonics. Note that this # is not the generating model, as it presupposes that there are more # harmonics then in reality. Because the variances are tied together, we # are not able to drive the estimated covariance of the non-existent # harmonics to 0. What is lazy about this model specification is that we # have not bothered to specify the two different seasonal components and # instead chosen to model them using a single component with enough # harmonics to cover both. We will not be able to capture any differences # in variances between the two true components. The process for the time # series can be written as: # # $$ # \begin{align} # y_t & = \mu_t + \gamma^{(1)}_t + \epsilon_t\\ # \mu_{t+1} &= \mu_t\\ # \gamma^{(1)}_{t} &= \sum_{j=1}^{50}\gamma^{(1)}_{j, t}\\ # \gamma^{(1)}_{j, t+1} &= \gamma^{(1)}_{j, t}\cos(\lambda_j) + \gamma^{*, # (1)}_{j, t}\sin(\lambda_j) + \omega^{(1}_{j,t}, ~j = 1, 2, \dots, 50\\ # \gamma^{*, (1)}_{j, t+1} &= -\gamma^{(1)}_{j, t}\sin(\lambda_j) + # \gamma^{*, (1)}_{j, t}\cos(\lambda_j) + \omega^{*, (1)}_{j, t}, ~j = 1, 2, # \dots, 50\\ # \end{align} # $$ # # where $\epsilon_t$ is white noise, $\omega^{(1)}_{t}$ are i.i.d. $N(0, # \sigma^2_1)$. model = sm.tsa.UnobservedComponents( series, level='fixed intercept', freq_seasonal=[{ 'period': 100 }]) res_lf = model.fit(disp=False) print(res_lf.summary()) # The first state variable holds our estimate of the intercept print("fixed intercept estimated as {0:.3f}".format( res_lf.smoother_results.smoothed_state[0, -1:][0])) res_lf.plot_components() plt.show() # Note that one of our diagnostic tests would be rejected at the .05 # level. # ### Unobserved components (lazy time domain seasonal modeling) # # The fourth method is an unobserved components model with a fixed # intercept and a single seasonal component modeled using a time-domain # seasonal model of 100 constants. The process for the time series can be # written as: # # $$ # \begin{align} # y_t & =\mu_t + \gamma^{(1)}_t + \epsilon_t\\ # \mu_{t+1} &= \mu_{t} \\ # \gamma^{(1)}_{t + 1} &= - \sum_{j=1}^{99} \gamma^{(1)}_{t + 1 - j} + # \omega^{(1)}_t\\ # \end{align} # $$ # # where $\epsilon_t$ is white noise, $\omega^{(1)}_{t}$ are i.i.d. $N(0, # \sigma^2_1)$. model = sm.tsa.UnobservedComponents( series, level='fixed intercept', seasonal=100) res_lt = model.fit(disp=False) print(res_lt.summary()) # The first state variable holds our estimate of the intercept print("fixed intercept estimated as {0:.3f}".format( res_lt.smoother_results.smoothed_state[0, -1:][0])) res_lt.plot_components() plt.show() # The seasonal component itself looks good--it is the primary signal. The # estimated variance of the seasonal term is very high ($>10^5$), leading to # a lot of uncertainty in our one-step-ahead predictions and slow # responsiveness to new data, as evidenced by large errors in one-step ahead # predictions and observations. Finally, all three of our diagnostic tests # were rejected. # ### Comparison of filtered estimates # # The plots below show that explicitly modeling the individual components # results in the filtered state being close to the true state within roughly # half a period. The lazy models took longer (almost a full period) to do # the same on the combined true state. # Assign better names for our seasonal terms true_seasonal_10_3 = terms[0] true_seasonal_100_2 = terms[1] true_sum = true_seasonal_10_3 + true_seasonal_100_2 time_s = np.s_[:50] # After this they basically agree fig1 = plt.figure() ax1 = fig1.add_subplot(111) h1, = ax1.plot( series.index[time_s], res_f.freq_seasonal[0].filtered[time_s], label='Double Freq. Seas') h2, = ax1.plot( series.index[time_s], res_tf.seasonal.filtered[time_s], label='Mixed Domain Seas') h3, = ax1.plot( series.index[time_s], true_seasonal_10_3[time_s], label='True Seasonal 10(3)') plt.legend( [h1, h2, h3], ['Double Freq. Seasonal', 'Mixed Domain Seasonal', 'Truth'], loc=2) plt.title('Seasonal 10(3) component') plt.show() time_s = np.s_[:50] # After this they basically agree fig2 = plt.figure() ax2 = fig2.add_subplot(111) h21, = ax2.plot( series.index[time_s], res_f.freq_seasonal[1].filtered[time_s], label='Double Freq. Seas') h22, = ax2.plot( series.index[time_s], res_tf.freq_seasonal[0].filtered[time_s], label='Mixed Domain Seas') h23, = ax2.plot( series.index[time_s], true_seasonal_100_2[time_s], label='True Seasonal 100(2)') plt.legend( [h21, h22, h23], ['Double Freq. Seasonal', 'Mixed Domain Seasonal', 'Truth'], loc=2) plt.title('Seasonal 100(2) component') plt.show() time_s = np.s_[:100] fig3 = plt.figure() ax3 = fig3.add_subplot(111) h31, = ax3.plot( series.index[time_s], res_f.freq_seasonal[1].filtered[time_s] + res_f.freq_seasonal[0].filtered[time_s], label='Double Freq. Seas') h32, = ax3.plot( series.index[time_s], res_tf.freq_seasonal[0].filtered[time_s] + res_tf.seasonal.filtered[time_s], label='Mixed Domain Seas') h33, = ax3.plot( series.index[time_s], true_sum[time_s], label='True Seasonal 100(2)') h34, = ax3.plot( series.index[time_s], res_lf.freq_seasonal[0].filtered[time_s], label='Lazy Freq. Seas') h35, = ax3.plot( series.index[time_s], res_lt.seasonal.filtered[time_s], label='Lazy Time Seas') plt.legend( [h31, h32, h33, h34, h35], [ 'Double Freq. Seasonal', 'Mixed Domain Seasonal', 'Truth', 'Lazy Freq. Seas', 'Lazy Time Seas' ], loc=1) plt.title('Seasonal components combined') plt.show() # ##### Conclusions # # In this notebook, we simulated a time series with two seasonal # components of different periods. We modeled them using structural time # series models with (a) two frequency domain components of correct periods # and numbers of harmonics, (b) time domain seasonal component for the # shorter term and a frequency domain term with correct period and number of # harmonics, (c) a single frequency domain term with the longer period and # full number of harmonics, and (d) a single time domain term with the # longer period. We saw a variety of diagnostic results, with only the # correct generating model, (a), failing to reject any of the tests. Thus, # more flexible seasonal modeling allowing for multiple components with # specifiable harmonics can be a useful tool for time series modeling. # Finally, we can represent seasonal components with fewer total states in # this way, allowing for the user to attempt to make the bias-variance # trade-off themselves instead of being forced to choose "lazy" models, which # use a large number of states and incur additional variance as a result. statsmodels-0.12.2/examples/python/statespace_structural_harvey_jaeger.py000066400000000000000000000350031400612667500271760ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook statespace_structural_harvey_jaeger.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Detrending, Stylized Facts and the Business Cycle # # In an influential article, Harvey and Jaeger (1993) described the use of # unobserved components models (also known as "structural time series # models") to derive stylized facts of the business cycle. # # Their paper begins: # # "Establishing the 'stylized facts' associated with a set of time # series is widely considered a crucial step # in macroeconomic research ... For such facts to be useful they # should (1) be consistent with the stochastic # properties of the data and (2) present meaningful information." # # In particular, they make the argument that these goals are often better # met using the unobserved components approach rather than the popular # Hodrick-Prescott filter or Box-Jenkins ARIMA modeling techniques. # # statsmodels has the ability to perform all three types of analysis, and # below we follow the steps of their paper, using a slightly updated # dataset. import numpy as np import pandas as pd import statsmodels.api as sm import matplotlib.pyplot as plt from IPython.display import display, Latex # ## Unobserved Components # # The unobserved components model available in statsmodels can be written # as: # # $$ # y_t = \underbrace{\mu_{t}}_{\text{trend}} + # \underbrace{\gamma_{t}}_{\text{seasonal}} + # \underbrace{c_{t}}_{\text{cycle}} + \sum_{j=1}^k \underbrace{\beta_j # x_{jt}}_{\text{explanatory}} + # \underbrace{\varepsilon_t}_{\text{irregular}} # $$ # # see Durbin and Koopman 2012, Chapter 3 for notation and additional # details. Notice that different specifications for the different individual # components can support a wide range of models. The specific models # considered in the paper and below are specializations of this general # equation. # # ### Trend # # The trend component is a dynamic extension of a regression model that # includes an intercept and linear time-trend. # # $$ # \begin{align} # \underbrace{\mu_{t+1}}_{\text{level}} & = \mu_t + \nu_t + \eta_{t+1} # \qquad & \eta_{t+1} \sim N(0, \sigma_\eta^2) \\\\ # \underbrace{\nu_{t+1}}_{\text{trend}} & = \nu_t + \zeta_{t+1} & # \zeta_{t+1} \sim N(0, \sigma_\zeta^2) \\ # \end{align} # $$ # # where the level is a generalization of the intercept term that can # dynamically vary across time, and the trend is a generalization of the # time-trend such that the slope can dynamically vary across time. # # For both elements (level and trend), we can consider models in which: # # - The element is included vs excluded (if the trend is included, there # must also be a level included). # - The element is deterministic vs stochastic (i.e. whether or not the # variance on the error term is confined to be zero or not) # # The only additional parameters to be estimated via MLE are the variances # of any included stochastic components. # # This leads to the following specifications: # # | | # Level | Trend | Stochastic Level | Stochastic Trend | # |----------------------------------------------------------------------| # -------|-------|------------------|------------------| # | Constant | # ✓ | | | | # | Local Level
(random walk) | # ✓ | | ✓ | | # | Deterministic trend | # ✓ | ✓ | | | # | Local level with deterministic trend
(random walk with drift) | # ✓ | ✓ | ✓ | | # | Local linear trend | # ✓ | ✓ | ✓ | ✓ | # | Smooth trend
(integrated random walk) | # ✓ | ✓ | | ✓ | # # ### Seasonal # # The seasonal component is written as: # # $$ # \gamma_t = - \sum_{j=1}^{s-1} \gamma_{t+1-j} + \omega_t \qquad \omega_t # \sim N(0, \sigma_\omega^2) # $$ # # The periodicity (number of seasons) is `s`, and the defining character # is that (without the error term), the seasonal components sum to zero # across one complete cycle. The inclusion of an error term allows the # seasonal effects to vary over time. # # The variants of this model are: # # - The periodicity `s` # - Whether or not to make the seasonal effects stochastic. # # If the seasonal effect is stochastic, then there is one additional # parameter to estimate via MLE (the variance of the error term). # # ### Cycle # # The cyclical component is intended to capture cyclical effects at time # frames much longer than captured by the seasonal component. For example, # in economics the cyclical term is often intended to capture the business # cycle, and is then expected to have a period between "1.5 and 12 years" # (see Durbin and Koopman). # # The cycle is written as: # # $$ # \begin{align} # c_{t+1} & = c_t \cos \lambda_c + c_t^* \sin \lambda_c + \tilde \omega_t # \qquad & \tilde \omega_t \sim N(0, \sigma_{\tilde \omega}^2) \\\\ # c_{t+1}^* & = -c_t \sin \lambda_c + c_t^* \cos \lambda_c + \tilde # \omega_t^* & \tilde \omega_t^* \sim N(0, \sigma_{\tilde \omega}^2) # \end{align} # $$ # # The parameter $\lambda_c$ (the frequency of the cycle) is an additional # parameter to be estimated by MLE. If the seasonal effect is stochastic, # then there is one another parameter to estimate (the variance of the error # term - note that both of the error terms here share the same variance, but # are assumed to have independent draws). # # ### Irregular # # The irregular component is assumed to be a white noise error term. Its # variance is a parameter to be estimated by MLE; i.e. # # $$ # \varepsilon_t \sim N(0, \sigma_\varepsilon^2) # $$ # # In some cases, we may want to generalize the irregular component to # allow for autoregressive effects: # # $$ # \varepsilon_t = \rho(L) \varepsilon_{t-1} + \epsilon_t, \qquad # \epsilon_t \sim N(0, \sigma_\epsilon^2) # $$ # # In this case, the autoregressive parameters would also be estimated via # MLE. # # ### Regression effects # # We may want to allow for explanatory variables by including additional # terms # # $$ # \sum_{j=1}^k \beta_j x_{jt} # $$ # # or for intervention effects by including # # $$ # \begin{align} # \delta w_t \qquad \text{where} \qquad w_t & = 0, \qquad t < \tau, \\\\ # & = 1, \qquad t \ge \tau # \end{align} # $$ # # These additional parameters could be estimated via MLE or by including # them as components of the state space formulation. # # ## Data # # Following Harvey and Jaeger, we will consider the following time series: # # - US real GNP, "output", # ([GNPC96](https://research.stlouisfed.org/fred2/series/GNPC96)) # - US GNP implicit price deflator, "prices", # ([GNPDEF](https://research.stlouisfed.org/fred2/series/GNPDEF)) # - US monetary base, "money", # ([AMBSL](https://research.stlouisfed.org/fred2/series/AMBSL)) # # The time frame in the original paper varied across series, but was # broadly 1954-1989. Below we use data from the period 1948-2008 for all # series. Although the unobserved components approach allows isolating a # seasonal component within the model, the series considered in the paper, # and here, are already seasonally adjusted. # # All data series considered here are taken from [Federal Reserve Economic # Data (FRED)](https://research.stlouisfed.org/fred2/). Conveniently, the # Python library [Pandas](http://pandas.pydata.org/) has the ability to # download data from FRED directly. # Datasets from pandas_datareader.data import DataReader # Get the raw data start = '1948-01' end = '2008-01' us_gnp = DataReader('GNPC96', 'fred', start=start, end=end) us_gnp_deflator = DataReader('GNPDEF', 'fred', start=start, end=end) us_monetary_base = DataReader( 'AMBSL', 'fred', start=start, end=end).resample('QS').mean() recessions = DataReader( 'USRECQ', 'fred', start=start, end=end).resample('QS').last().values[:, 0] # Construct the dataframe dta = pd.concat( map(np.log, (us_gnp, us_gnp_deflator, us_monetary_base)), axis=1) dta.columns = ['US GNP', 'US Prices', 'US monetary base'] dates = dta.index._mpl_repr() # To get a sense of these three variables over the timeframe, we can plot # them: # Plot the data ax = dta.plot(figsize=(13, 3)) ylim = ax.get_ylim() ax.xaxis.grid() ax.fill_between( dates, ylim[0] + 1e-5, ylim[1] - 1e-5, recessions, facecolor='k', alpha=0.1) # ## Model # # Since the data is already seasonally adjusted and there are no obvious # explanatory variables, the generic model considered is: # # $$ # y_t = \underbrace{\mu_{t}}_{\text{trend}} + # \underbrace{c_{t}}_{\text{cycle}} + # \underbrace{\varepsilon_t}_{\text{irregular}} # $$ # # The irregular will be assumed to be white noise, and the cycle will be # stochastic and damped. The final modeling choice is the specification to # use for the trend component. Harvey and Jaeger consider two models: # # 1. Local linear trend (the "unrestricted" model) # 2. Smooth trend (the "restricted" model, since we are forcing # $\sigma_\eta = 0$) # # Below, we construct `kwargs` dictionaries for each of these model types. # Notice that rather that there are two ways to specify the models. One way # is to specify components directly, as in the table above. The other way is # to use string names which map to various specifications. # Model specifications # Unrestricted model, using string specification unrestricted_model = { 'level': 'local linear trend', 'cycle': True, 'damped_cycle': True, 'stochastic_cycle': True } # Unrestricted model, setting components directly # This is an equivalent, but less convenient, way to specify a # local linear trend model with a stochastic damped cycle: # unrestricted_model = { # 'irregular': True, 'level': True, 'stochastic_level': True, 'trend': # True, 'stochastic_trend': True, # 'cycle': True, 'damped_cycle': True, 'stochastic_cycle': True # } # The restricted model forces a smooth trend restricted_model = { 'level': 'smooth trend', 'cycle': True, 'damped_cycle': True, 'stochastic_cycle': True } # Restricted model, setting components directly # This is an equivalent, but less convenient, way to specify a # smooth trend model with a stochastic damped cycle. Notice # that the difference from the local linear trend model is that # `stochastic_level=False` here. # unrestricted_model = { # 'irregular': True, 'level': True, 'stochastic_level': False, # 'trend': True, 'stochastic_trend': True, # 'cycle': True, 'damped_cycle': True, 'stochastic_cycle': True # } # We now fit the following models: # # 1. Output, unrestricted model # 2. Prices, unrestricted model # 3. Prices, restricted model # 4. Money, unrestricted model # 5. Money, restricted model # Output output_mod = sm.tsa.UnobservedComponents(dta['US GNP'], **unrestricted_model) output_res = output_mod.fit(method='powell', disp=False) # Prices prices_mod = sm.tsa.UnobservedComponents(dta['US Prices'], **unrestricted_model) prices_res = prices_mod.fit(method='powell', disp=False) prices_restricted_mod = sm.tsa.UnobservedComponents(dta['US Prices'], **restricted_model) prices_restricted_res = prices_restricted_mod.fit(method='powell', disp=False) # Money money_mod = sm.tsa.UnobservedComponents(dta['US monetary base'], **unrestricted_model) money_res = money_mod.fit(method='powell', disp=False) money_restricted_mod = sm.tsa.UnobservedComponents(dta['US monetary base'], **restricted_model) money_restricted_res = money_restricted_mod.fit(method='powell', disp=False) # Once we have fit these models, there are a variety of ways to display # the information. Looking at the model of US GNP, we can summarize the fit # of the model using the `summary` method on the fit object. print(output_res.summary()) # For unobserved components models, and in particular when exploring # stylized facts in line with point (2) from the introduction, it is often # more instructive to plot the estimated unobserved components (e.g. the # level, trend, and cycle) themselves to see if they provide a meaningful # description of the data. # # The `plot_components` method of the fit object can be used to show plots # and confidence intervals of each of the estimated states, as well as a # plot of the observed data versus the one-step-ahead predictions of the # model to assess fit. fig = output_res.plot_components( legend_loc='lower right', figsize=(15, 9)) # Finally, Harvey and Jaeger summarize the models in another way to # highlight the relative importances of the trend and cyclical components; # below we replicate their Table I. The values we find are broadly # consistent with, but different in the particulars from, the values from # their table. # Create Table I table_i = np.zeros((5, 6)) start = dta.index[0] end = dta.index[-1] time_range = '%d:%d-%d:%d' % (start.year, start.quarter, end.year, end.quarter) models = [ ('US GNP', time_range, 'None'), ('US Prices', time_range, 'None'), ('US Prices', time_range, r'$\sigma_\eta^2 = 0$'), ('US monetary base', time_range, 'None'), ('US monetary base', time_range, r'$\sigma_\eta^2 = 0$'), ] index = pd.MultiIndex.from_tuples( models, names=['Series', 'Time range', 'Restrictions']) parameter_symbols = [ r'$\sigma_\zeta^2$', r'$\sigma_\eta^2$', r'$\sigma_\kappa^2$', r'$\rho$', r'$2 \pi / \lambda_c$', r'$\sigma_\varepsilon^2$', ] i = 0 for res in (output_res, prices_res, prices_restricted_res, money_res, money_restricted_res): if res.model.stochastic_level: (sigma_irregular, sigma_level, sigma_trend, sigma_cycle, frequency_cycle, damping_cycle) = res.params else: (sigma_irregular, sigma_level, sigma_cycle, frequency_cycle, damping_cycle) = res.params sigma_trend = np.nan period_cycle = 2 * np.pi / frequency_cycle table_i[i, :] = [ sigma_level * 1e7, sigma_trend * 1e7, sigma_cycle * 1e7, damping_cycle, period_cycle, sigma_irregular * 1e7 ] i += 1 pd.set_option('float_format', lambda x: '%.4g' % np.round(x, 2) if not np.isnan(x) else '-') table_i = pd.DataFrame(table_i, index=index, columns=parameter_symbols) table_i statsmodels-0.12.2/examples/python/statespace_varmax.py000066400000000000000000000065371400612667500234030ustar00rootroot00000000000000# DO NOT EDIT # Autogenerated from the notebook statespace_varmax.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT #!/usr/bin/env python # coding: utf-8 # # VARMAX models # # This is a brief introduction notebook to VARMAX models in statsmodels. # The VARMAX model is generically specified as: # $$ # y_t = \nu + A_1 y_{t-1} + \dots + A_p y_{t-p} + B x_t + \epsilon_t + # M_1 \epsilon_{t-1} + \dots M_q \epsilon_{t-q} # $$ # # where $y_t$ is a $\text{k_endog} \times 1$ vector. import numpy as np import pandas as pd import statsmodels.api as sm import matplotlib.pyplot as plt dta = sm.datasets.webuse('lutkepohl2', 'https://www.stata-press.com/data/r12/') dta.index = dta.qtr endog = dta.loc['1960-04-01':'1978-10-01', ['dln_inv', 'dln_inc', 'dln_consump']] # ## Model specification # # The `VARMAX` class in statsmodels allows estimation of VAR, VMA, and # VARMA models (through the `order` argument), optionally with a constant # term (via the `trend` argument). Exogenous regressors may also be included # (as usual in statsmodels, by the `exog` argument), and in this way a time # trend may be added. Finally, the class allows measurement error (via the # `measurement_error` argument) and allows specifying either a diagonal or # unstructured innovation covariance matrix (via the `error_cov_type` # argument). # ## Example 1: VAR # # Below is a simple VARX(2) model in two endogenous variables and an # exogenous series, but no constant term. Notice that we needed to allow for # more iterations than the default (which is `maxiter=50`) in order for the # likelihood estimation to converge. This is not unusual in VAR models which # have to estimate a large number of parameters, often on a relatively small # number of time series: this model, for example, estimates 27 parameters # off of 75 observations of 3 variables. exog = endog['dln_consump'] mod = sm.tsa.VARMAX(endog[['dln_inv', 'dln_inc']], order=(2, 0), trend='n', exog=exog) res = mod.fit(maxiter=1000, disp=False) print(res.summary()) # From the estimated VAR model, we can plot the impulse response functions # of the endogenous variables. ax = res.impulse_responses(10, orthogonalized=True).plot(figsize=(13, 3)) ax.set(xlabel='t', title='Responses to a shock to `dln_inv`') # ## Example 2: VMA # # A vector moving average model can also be formulated. Below we show a # VMA(2) on the same data, but where the innovations to the process are # uncorrelated. In this example we leave out the exogenous regressor but now # include the constant term. mod = sm.tsa.VARMAX(endog[['dln_inv', 'dln_inc']], order=(0, 2), error_cov_type='diagonal') res = mod.fit(maxiter=1000, disp=False) print(res.summary()) # ## Caution: VARMA(p,q) specifications # # Although the model allows estimating VARMA(p,q) specifications, these # models are not identified without additional restrictions on the # representation matrices, which are not built-in. For this reason, it is # recommended that the user proceed with error (and indeed a warning is # issued when these models are specified). Nonetheless, they may in some # circumstances provide useful information. mod = sm.tsa.VARMAX(endog[['dln_inv', 'dln_inc']], order=(1, 1)) res = mod.fit(maxiter=1000, disp=False) print(res.summary()) statsmodels-0.12.2/examples/python/tsa_arma_0.py000066400000000000000000000107551400612667500216740ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook tsa_arma_0.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Autoregressive Moving Average (ARMA): Sunspots data import numpy as np from scipy import stats import pandas as pd import matplotlib.pyplot as plt import statsmodels.api as sm from statsmodels.graphics.api import qqplot # ## Sunspots Data print(sm.datasets.sunspots.NOTE) dta = sm.datasets.sunspots.load_pandas().data dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008')) del dta["YEAR"] dta.plot(figsize=(12, 8)) fig = plt.figure(figsize=(12, 8)) ax1 = fig.add_subplot(211) fig = sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40, ax=ax1) ax2 = fig.add_subplot(212) fig = sm.graphics.tsa.plot_pacf(dta, lags=40, ax=ax2) arma_mod20 = sm.tsa.ARMA(dta, (2, 0)).fit(disp=False) print(arma_mod20.params) arma_mod30 = sm.tsa.ARMA(dta, (3, 0)).fit(disp=False) print(arma_mod20.aic, arma_mod20.bic, arma_mod20.hqic) print(arma_mod30.params) print(arma_mod30.aic, arma_mod30.bic, arma_mod30.hqic) # * Does our model obey the theory? sm.stats.durbin_watson(arma_mod30.resid.values) fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111) ax = arma_mod30.resid.plot(ax=ax) resid = arma_mod30.resid stats.normaltest(resid) fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111) fig = qqplot(resid, line='q', ax=ax, fit=True) fig = plt.figure(figsize=(12, 8)) ax1 = fig.add_subplot(211) fig = sm.graphics.tsa.plot_acf(resid.values.squeeze(), lags=40, ax=ax1) ax2 = fig.add_subplot(212) fig = sm.graphics.tsa.plot_pacf(resid, lags=40, ax=ax2) r, q, p = sm.tsa.acf(resid.values.squeeze(), qstat=True) data = np.c_[range(1, 41), r[1:], q, p] table = pd.DataFrame(data, columns=['lag', "AC", "Q", "Prob(>Q)"]) print(table.set_index('lag')) # * This indicates a lack of fit. # * In-sample dynamic prediction. How good does our model do? predict_sunspots = arma_mod30.predict('1990', '2012', dynamic=True) print(predict_sunspots) fig, ax = plt.subplots(figsize=(12, 8)) ax = dta.loc['1950':].plot(ax=ax) fig = arma_mod30.plot_predict( '1990', '2012', dynamic=True, ax=ax, plot_insample=False) def mean_forecast_err(y, yhat): return y.sub(yhat).mean() mean_forecast_err(dta.SUNACTIVITY, predict_sunspots) # ### Exercise: Can you obtain a better fit for the Sunspots model? (Hint: # sm.tsa.AR has a method select_order) # ### Simulated ARMA(4,1): Model Identification is Difficult from statsmodels.tsa.arima_process import ArmaProcess np.random.seed(1234) # include zero-th lag arparams = np.array([1, .75, -.65, -.55, .9]) maparams = np.array([1, .65]) # Let's make sure this model is estimable. arma_t = ArmaProcess(arparams, maparams) arma_t.isinvertible arma_t.isstationary # * What does this mean? fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111) ax.plot(arma_t.generate_sample(nsample=50)) arparams = np.array([1, .35, -.15, .55, .1]) maparams = np.array([1, .65]) arma_t = ArmaProcess(arparams, maparams) arma_t.isstationary arma_rvs = arma_t.generate_sample(nsample=500, burnin=250, scale=2.5) fig = plt.figure(figsize=(12, 8)) ax1 = fig.add_subplot(211) fig = sm.graphics.tsa.plot_acf(arma_rvs, lags=40, ax=ax1) ax2 = fig.add_subplot(212) fig = sm.graphics.tsa.plot_pacf(arma_rvs, lags=40, ax=ax2) # * For mixed ARMA processes the Autocorrelation function is a mixture of # exponentials and damped sine waves after (q-p) lags. # * The partial autocorrelation function is a mixture of exponentials and # dampened sine waves after (p-q) lags. arma11 = sm.tsa.ARMA(arma_rvs, (1, 1)).fit(disp=False) resid = arma11.resid r, q, p = sm.tsa.acf(resid, qstat=True) data = np.c_[range(1, 41), r[1:], q, p] table = pd.DataFrame(data, columns=['lag', "AC", "Q", "Prob(>Q)"]) print(table.set_index('lag')) arma41 = sm.tsa.ARMA(arma_rvs, (4, 1)).fit(disp=False) resid = arma41.resid r, q, p = sm.tsa.acf(resid, qstat=True) data = np.c_[range(1, 41), r[1:], q, p] table = pd.DataFrame(data, columns=['lag', "AC", "Q", "Prob(>Q)"]) print(table.set_index('lag')) # ### Exercise: How good of in-sample prediction can you do for another # series, say, CPI macrodta = sm.datasets.macrodata.load_pandas().data macrodta.index = pd.Index( sm.tsa.datetools.dates_from_range('1959Q1', '2009Q3')) cpi = macrodta["cpi"] # #### Hint: fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111) ax = cpi.plot(ax=ax) ax.legend() # P-value of the unit-root test, resoundingly rejects the null of a unit- # root. print(sm.tsa.adfuller(cpi)[1]) statsmodels-0.12.2/examples/python/tsa_arma_1.py000066400000000000000000000024201400612667500216630ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook tsa_arma_1.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Autoregressive Moving Average (ARMA): Artificial data import numpy as np import statsmodels.api as sm import pandas as pd from statsmodels.tsa.arima_process import arma_generate_sample np.random.seed(12345) # Generate some data from an ARMA process: arparams = np.array([.75, -.25]) maparams = np.array([.65, .35]) # The conventions of the arma_generate function require that we specify a # 1 for the zero-lag of the AR and MA parameters and that the AR parameters # be negated. arparams = np.r_[1, -arparams] maparams = np.r_[1, maparams] nobs = 250 y = arma_generate_sample(arparams, maparams, nobs) # Now, optionally, we can add some dates information. For this example, # we'll use a pandas time series. dates = sm.tsa.datetools.dates_from_range('1980m1', length=nobs) y = pd.Series(y, index=dates) arma_mod = sm.tsa.ARMA(y, order=(2, 2)) arma_res = arma_mod.fit(trend='nc', disp=-1) print(arma_res.summary()) y.tail() import matplotlib.pyplot as plt fig, ax = plt.subplots(figsize=(10, 8)) fig = arma_res.plot_predict(start='1999-06-30', end='2001-05-31', ax=ax) legend = ax.legend(loc='upper left') statsmodels-0.12.2/examples/python/tsa_dates.py000066400000000000000000000025071400612667500216310ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook tsa_dates.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Dates in timeseries models import statsmodels.api as sm import numpy as np import pandas as pd # ## Getting started data = sm.datasets.sunspots.load() # Right now an annual date series must be datetimes at the end of the # year. from datetime import datetime dates = sm.tsa.datetools.dates_from_range('1700', length=len(data.endog)) # ## Using Pandas # # Make a pandas TimeSeries or DataFrame endog = pd.Series(data.endog, index=dates) # Instantiate the model ar_model = sm.tsa.AR(endog, freq='A') pandas_ar_res = ar_model.fit(maxlag=9, method='mle', disp=-1) # Out-of-sample prediction pred = pandas_ar_res.predict(start='2005', end='2015') print(pred) # ## Using explicit dates ar_model = sm.tsa.AR(data.endog, dates=dates, freq='A') ar_res = ar_model.fit(maxlag=9, method='mle', disp=-1) pred = ar_res.predict(start='2005', end='2015') print(pred) # This just returns a regular array, but since the model has date # information attached, you can get the prediction dates in a roundabout # way. print(ar_res.data.predict_dates) # Note: This attribute only exists if predict has been called. It holds # the dates associated with the last call to predict. statsmodels-0.12.2/examples/python/tsa_filters.py000066400000000000000000000112361400612667500222000ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook tsa_filters.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Time Series Filters import pandas as pd import matplotlib.pyplot as plt import statsmodels.api as sm dta = sm.datasets.macrodata.load_pandas().data index = pd.Index(sm.tsa.datetools.dates_from_range('1959Q1', '2009Q3')) print(index) dta.index = index del dta['year'] del dta['quarter'] print(sm.datasets.macrodata.NOTE) print(dta.head(10)) fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111) dta.realgdp.plot(ax=ax) legend = ax.legend(loc='upper left') legend.prop.set_size(20) # ### Hodrick-Prescott Filter # The Hodrick-Prescott filter separates a time-series $y_t$ into a trend # $\tau_t$ and a cyclical component $\zeta_t$ # # $$y_t = \tau_t + \zeta_t$$ # # The components are determined by minimizing the following quadratic loss # function # # $$\min_{\\{ \tau_{t}\\} }\sum_{t}^{T}\zeta_{t}^{2}+\lambda\sum_{t=1}^{T} # \left[\left(\tau_{t}-\tau_{t-1}\right)-\left(\tau_{t-1}-\tau_{t-2}\right)\ # right]^{2}$$ gdp_cycle, gdp_trend = sm.tsa.filters.hpfilter(dta.realgdp) gdp_decomp = dta[['realgdp']].copy() gdp_decomp["cycle"] = gdp_cycle gdp_decomp["trend"] = gdp_trend fig = plt.figure(figsize=(12, 8)) ax = fig.add_subplot(111) gdp_decomp[["realgdp", "trend"]]["2000-03-31":].plot( ax=ax, fontsize=16) legend = ax.get_legend() legend.prop.set_size(20) # ### Baxter-King approximate band-pass filter: Inflation and Unemployment # #### Explore the hypothesis that inflation and unemployment are counter- # cyclical. # The Baxter-King filter is intended to explicitly deal with the periodicity # of the business cycle. By applying their band-pass filter to a series, # they produce a new series that does not contain fluctuations at higher or # lower than those of the business cycle. Specifically, the BK filter takes # the form of a symmetric moving average # # $$y_{t}^{*}=\sum_{k=-K}^{k=K}a_ky_{t-k}$$ # # where $a_{-k}=a_k$ and $\sum_{k=-k}^{K}a_k=0$ to eliminate any trend in # the series and render it stationary if the series is I(1) or I(2). # # For completeness, the filter weights are determined as follows # # $$a_{j} = B_{j}+\theta\text{ for }j=0,\pm1,\pm2,\dots,\pm K$$ # # $$B_{0} = \frac{\left(\omega_{2}-\omega_{1}\right)}{\pi}$$ # $$B_{j} = \frac{1}{\pi j}\left(\sin\left(\omega_{2}j\right)-\sin\left(\o # mega_{1}j\right)\right)\text{ for }j=0,\pm1,\pm2,\dots,\pm K$$ # # where $\theta$ is a normalizing constant such that the weights sum to # zero. # # $$\theta=\frac{-\sum_{j=-K^{K}b_{j}}}{2K+1}$$ # # $$\omega_{1}=\frac{2\pi}{P_{H}}$$ # # $$\omega_{2}=\frac{2\pi}{P_{L}}$$ # # $P_L$ and $P_H$ are the periodicity of the low and high cut-off # frequencies. Following Burns and Mitchell's work on US business cycles # which suggests cycles last from 1.5 to 8 years, we use $P_L=6$ and # $P_H=32$ by default. bk_cycles = sm.tsa.filters.bkfilter(dta[["infl", "unemp"]]) # * We lose K observations on both ends. It is suggested to use K=12 for # quarterly data. fig = plt.figure(figsize=(12, 10)) ax = fig.add_subplot(111) bk_cycles.plot( ax=ax, style=['r--', 'b-']) # ### Christiano-Fitzgerald approximate band-pass filter: Inflation and # Unemployment # The Christiano-Fitzgerald filter is a generalization of BK and can thus # also be seen as weighted moving average. However, the CF filter is # asymmetric about $t$ as well as using the entire series. The # implementation of their filter involves the # calculations of the weights in # # $$y_{t}^{*}=B_{0}y_{t}+B_{1}y_{t+1}+\dots+B_{T-1-t}y_{T-1}+\tilde # B_{T-t}y_{T}+B_{1}y_{t-1}+\dots+B_{t-2}y_{2}+\tilde B_{t-1}y_{1}$$ # # for $t=3,4,...,T-2$, where # # $$B_{j} = \frac{\sin(jb)-\sin(ja)}{\pi j},j\geq1$$ # # $$B_{0} = \frac{b-a}{\pi},a=\frac{2\pi}{P_{u}},b=\frac{2\pi}{P_{L}}$$ # # $\tilde B_{T-t}$ and $\tilde B_{t-1}$ are linear functions of the # $B_{j}$'s, and the values for $t=1,2,T-1,$ and $T$ are also calculated in # much the same way. $P_{U}$ and $P_{L}$ are as described above with the # same interpretation. # The CF filter is appropriate for series that may follow a random walk. print(sm.tsa.stattools.adfuller(dta['unemp'])[:3]) print(sm.tsa.stattools.adfuller(dta['infl'])[:3]) cf_cycles, cf_trend = sm.tsa.filters.cffilter(dta[["infl", "unemp"]]) print(cf_cycles.head(10)) fig = plt.figure(figsize=(14, 10)) ax = fig.add_subplot(111) cf_cycles.plot( ax=ax, style=['r--', 'b-']) # Filtering assumes *a priori* that business cycles exist. Due to this # assumption, many macroeconomic models seek to create models that match the # shape of impulse response functions rather than replicating properties of # filtered series. See VAR notebook. statsmodels-0.12.2/examples/python/wls.py000066400000000000000000000060171400612667500204670ustar00rootroot00000000000000# coding: utf-8 # DO NOT EDIT # Autogenerated from the notebook wls.ipynb. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT # # Weighted Least Squares import numpy as np from scipy import stats import statsmodels.api as sm import matplotlib.pyplot as plt from statsmodels.sandbox.regression.predstd import wls_prediction_std from statsmodels.iolib.table import (SimpleTable, default_txt_fmt) np.random.seed(1024) # ## WLS Estimation # # ### Artificial data: Heteroscedasticity 2 groups # # Model assumptions: # # * Misspecification: true model is quadratic, estimate only linear # * Independent noise/error term # * Two groups for error variance, low and high variance groups nsample = 50 x = np.linspace(0, 20, nsample) X = np.column_stack((x, (x - 5)**2)) X = sm.add_constant(X) beta = [5., 0.5, -0.01] sig = 0.5 w = np.ones(nsample) w[nsample * 6 // 10:] = 3 y_true = np.dot(X, beta) e = np.random.normal(size=nsample) y = y_true + sig * w * e X = X[:, [0, 1]] # ### WLS knowing the true variance ratio of heteroscedasticity # # In this example, `w` is the standard deviation of the error. `WLS` # requires that the weights are proportional to the inverse of the error # variance. mod_wls = sm.WLS(y, X, weights=1. / (w**2)) res_wls = mod_wls.fit() print(res_wls.summary()) # ## OLS vs. WLS # # Estimate an OLS model for comparison: res_ols = sm.OLS(y, X).fit() print(res_ols.params) print(res_wls.params) # Compare the WLS standard errors to heteroscedasticity corrected OLS # standard errors: se = np.vstack([[res_wls.bse], [res_ols.bse], [res_ols.HC0_se], [res_ols.HC1_se], [res_ols.HC2_se], [res_ols.HC3_se]]) se = np.round(se, 4) colnames = ['x1', 'const'] rownames = ['WLS', 'OLS', 'OLS_HC0', 'OLS_HC1', 'OLS_HC3', 'OLS_HC3'] tabl = SimpleTable(se, colnames, rownames, txt_fmt=default_txt_fmt) print(tabl) # Calculate OLS prediction interval: covb = res_ols.cov_params() prediction_var = res_ols.mse_resid + (X * np.dot(covb, X.T).T).sum(1) prediction_std = np.sqrt(prediction_var) tppf = stats.t.ppf(0.975, res_ols.df_resid) prstd_ols, iv_l_ols, iv_u_ols = wls_prediction_std(res_ols) # Draw a plot to compare predicted values in WLS and OLS: prstd, iv_l, iv_u = wls_prediction_std(res_wls) fig, ax = plt.subplots(figsize=(8, 6)) ax.plot(x, y, 'o', label="Data") ax.plot(x, y_true, 'b-', label="True") # OLS ax.plot(x, res_ols.fittedvalues, 'r--') ax.plot(x, iv_u_ols, 'r--', label="OLS") ax.plot(x, iv_l_ols, 'r--') # WLS ax.plot(x, res_wls.fittedvalues, 'g--.') ax.plot(x, iv_u, 'g--', label="WLS") ax.plot(x, iv_l, 'g--') ax.legend(loc="best") # ## Feasible Weighted Least Squares (2-stage FWLS) # # Like ,`w`, `w_est` is proportional to the standard deviation, and so # must be squared. resid1 = res_ols.resid[w == 1.] var1 = resid1.var(ddof=int(res_ols.df_model) + 1) resid2 = res_ols.resid[w != 1.] var2 = resid2.var(ddof=int(res_ols.df_model) + 1) w_est = w.copy() w_est[w != 1.] = np.sqrt(var2) / np.sqrt(var1) res_fwls = sm.WLS(y, X, 1. / ((w_est**2))).fit() print(res_fwls.summary()) statsmodels-0.12.2/examples/run_all.py000066400000000000000000000031351400612667500177730ustar00rootroot00000000000000""" Run all python examples to make sure they do not raise """ import tempfile SHOW_PLOT = False BAD_FILES = ['robust_models_1'] def no_show(*args): pass if __name__ == '__main__': import glob import sys import matplotlib.pyplot as plt if not SHOW_PLOT: PLT_SHOW = plt.show plt.show = no_show SAVE_STDOUT = sys.stdout SAVE_STDERR = sys.stderr REDIRECT_STDOUT = tempfile.TemporaryFile('w') REDIRECT_STDERR = tempfile.TemporaryFile('w') EXAMPLE_FILES = glob.glob('python/*.py') for example in EXAMPLE_FILES: KNOWN_BAD_FILE = any([bf in example for bf in BAD_FILES]) with open(example, 'r') as pyfile: code = pyfile.read() try: sys.stdout = REDIRECT_STDOUT sys.stderr = REDIRECT_STDERR exec(code) except Exception as e: sys.stderr = SAVE_STDERR print('FAIL: {0}'.format(example), file=sys.stderr) if KNOWN_BAD_FILE: print('This FAIL is expected', file=sys.stderr) else: print('The last error was: ', file=sys.stderr) print(e.__class__.__name__, file=sys.stderr) print(e, file=sys.stderr) else: sys.stdout = SAVE_STDOUT print('SUCCESS: {0}'.format(example)) finally: plt.close('all') REDIRECT_STDOUT.close() REDIRECT_STDERR.close() sys.stdout = SAVE_STDOUT sys.stderr = SAVE_STDERR if not SHOW_PLOT: plt.show = PLT_SHOW statsmodels-0.12.2/github_deploy_key_statsmodels_statsmodels_github_io.enc000066400000000000000000000105441400612667500274430ustar00rootroot00000000000000gAAAAABbD1iyJdxfE21E38fK3bOZGE3-OwARYc7w9byx-2lWPszONeqmgD84evz73OmjkWMUYS4OmSQjVLOcgZKpS472dt7JGq_wYeo4lCX93ho02TWhtOnbbQpA8vdJ9aoy002WBOMHOi9AuosnH9mw52Qo6p1jNpBSqjeStSnVWEhEzIJynginRn7FODuocGf1kCJ91qc1sEPgT-7kxwuYPIqOkcSNRBZnap5E6L3kopI2fW9lL9rlCs9X4MDYygrua9PCVZRxMRvTSOW_Lx_5-6kbQgzP3HqrX1q_mKmnr2ZMGKrKwzv4OhY4YIJra-xZf2W-8dBbZbIhB76xwGCinOhY1EFI5oXvNngiILhBX-E_AfpQq8I5_dXsGhRD-Axxrzm5NCb-0-slouCUTo-R0IpO_eQTzpajkBkRXyxrzrr05xITeOfsDmzJHwYhKFTbChhriJqc2YnDLz_tjC9ApaekC8soPRXOOJmpmvtxFa_vQPFh9xQpNZvXU4zfVfYXRnTb1u97hxSBBX0vQqyix53qudMniCo2N45ILqsO4duTgmUHU09JxhgBw30Apa20Ry0qQ0suGwP9doSz3H43nHocjfANp4qM_XZhCC6SrgZDxZKEGBYcL3J8xUf4aykWUc29n6qKAOBv8p6IdPsAfjqkG45fHtyLmVBAkjVbQWZ-0YaJqafmrppU_L8s4_yEs-J5dTpficNwKFN9suKbR2d4ycxpvgxCL-t14lMA3-wKSyI6AvJ3kRkgj8OcXQXV3rQGo4F56-P0XBerghDtQyqTAZhl85eiFVg3VqnOTZL8UpqNsKlSWL47ed3LUsE3yNZE9Z3LdTZLZ2FFlCfRiJwnFu93nwcEY8Vej8aaJxjpCkluS6XIF_kbD001DYcuVKBf3LxSyApRouv8v2Tb2iVII_sbxWuRDtBeIiI27_Slv1LDOmu8NF0v-FB3C0uvWye08GvD5m4iPEtcY02hnBwkuwY8KbnixLd14NfdKErNaO9btSKwxu_yogtH2cLu_QHqy4SGo81q9QECnPtIQr16N0Pkeuo9Rx2z9nNKOYAaLRy9JSq4iE-AdfkwkQUuMcvkvPCwIXgKuq4ewroHWOUQND9LHWhpgMFT-3sELCw7Cx_y7wbfFJ8XtPVQDBhbd6jlOyu_D3t_Tty-FuKp2Cwhqv9bFn8jk8EbHc7jTvFEGDGckMJom3NY30BVucfe14PvideLHIMAT4a5zsS8skZ2F2mJEjGqmFfL8m4avrtb1BanPPur7XGeQKVhGumZ_yk4EwkQrCdTepCdFGG1A4078R7_pnqQ_yKyMUUwDbSUqVLBvRLhSGR9eLxQKFJQiQTzB-8CShGmkIoYqsOgd1WYVlC7SdOerTYZwaJ-1tPQ2tzy7anLh91IJJck-IlmlQbC_FP-c7Oj7oajRWFoDh6jT2lLhSu0UcnSTPAIvD8WJIfYeIFMqhO58_p78IRIc0eQccOPQZryQLB08x0iBOsv9fk4412jCLDZj-KnbEyG983MrQOYnMsJxgOfNb9Y9tPKads5PIpQGtoVMQshS89JJWxkyA_9HRJh40SIIT7nVcaLaZHYX-0dqiT7Q5CRFaSVat-AQSMercYkpr2gBvXEu6qyXKw6-I6LFfaaHvOuZwc6u_eUi5hjZ-bT79kfmBWBK-8AMLn9bqZzZgwAYg6_42WWzvXzUf03bqUjPg10M-xr_2BVhVPpgOa6p8RPzXweiJ1-NZ7G1nCLlv1nxq5BclwRmeLqRart0XvWHgB_ygKg972l3HXi0gUyVD0d7_Lfi2M7VK7rbR-bWlVdh65ZdGsztaDGiG07p4yh6wNKV1OpwZJgHVwYxIX1R2s7gIYcoVQD77KhwVKgfCjJ9ADJSIagrW_gOqa_Or5vxxu08scurGyqbpjOZ7wYAsdA_fU51SKS21zzlCiZqW8vVDtz6I03Dsbr30UxaRRihjuB_vybB8tUdkhSUAp8tD7n6GSLSMZs-88gSCaY3Epb7H-c9Xxi-q67jP36Hkjvgz3_gwbMi3ZReSh_pJSkj1qjq94mc4zVKP7e5DeKf279bl8z6-YkldExcX4jRnS72uTf6H8sjyEVvnIRpGts6BUZe8prwG2tVa2oXHKxK-gB7fWXFmJz0w6gfg1cRHVnh9chfIJHqkqJeV91RTrZbJdKNeUWNxe7CIGkaUxjoa0jXBVmbmXS2V3Cd-9TonLWffWbujUrFgc2Zi5eqmFHWdbfy-1KSOFcUF0ceT9X7fJvIOb6MVWZKu_JZ35_6vm_Fpeck1aZfJ1i6I-PXukxeOvq113StgfhbGFM2oUP502wKB_jlOppHO0cPzQ4cK_2gYaZ5auQL2n4LezEaJ1YrYZys-bQFAStJ6hFJqMbQQSqzI7pPsyLTthsQphuSAGuN9dbMLChx9W9VxeHJuWWVC3D64w9ETIX8GsW-Rv3qpnbx7ii_hCQJHRAjP6lFOBx4HkC7vv2Ya_KklegKzASqdJ1o9L1Q9DJDymKBcI-74OqcTJsFupB1qWbC3pRUoAsA2ohnt1GLPGw28uQrNl3gjiYPVenl8JlXK63cr94ydl3BdU8yjl_AMak7jTEq0AtxsdYwEK3FaweMf-0lETrEEN1kBaUp_rtTQv5cto4nBhaXTM5NEiQw-1KKZ3xLcyberJJUcxB9sXCeFvi0i2Edz2u20-yH0gJz4I9Fi5ky1wJDg7X9NJjRDIVE1IDq7TtEmJQPv0yhP4gkR_AWID5avxkEYiOd2YvMMqJWKDhsr3LFLo5qsgauMcylMjJVzI6nzJQsjdh6bJISrXdgJFnK9yNmW2C_WFsPwVjSueKUDKPPz5KzQ3zHlifZgZaEM2dDhMXMPF0m-FmZP4YRGmdc0jr4b15GzvErPcuLVifR4N5yiOlyRNW237ykFuo5TwDz5G-CJIS0AQSXA2AaQJcPuua8NiVZlaGEkaS0uJq1Y0Fxp3aShD-IQF6OOeG1DIJuc8joGB2nDCGndAK7N189DLSVQfYmqH8p5kIq-PybusN705xXASTJJWmmR2BiN1Y6WCnNUnxpEjnA7x555hBXq1lE5_72_uCJ6zx4eKVHKovVt_NE3bcjHmy2xfhjfK_ljQ4KwhmehfaqwcCApLZ_BoYxmdgvZereUhi7ttGylOmEFvRVyJfoH_Dp4sMFfWpSZUb8N3h1v83_ajAxTaH9BCP40UwOUr_DcM9tg-heAvemUVqa-CdbTvGYUK3WujzKnrXvkQNodjaGChR4f8swwjqV7rsbw1KTGFCbgq1xxhk_fs2-v0kc3btcPoPXejyRtJ0WONTzX9Eo8tBii-9xuT9VwKS9OzYlpiRHFFfKeQNWHD0zjgBTa9TTaFmFRXnzpWCv6pF64NuyLlB5KB1zKERJf9gMeeE8Lz8vxkMuQt_uKIco-ElGcwETn-bzyFpTJ8aPhgUo7WK1Ckz923qGnjurLQ_YPVrYOiq8ULbdWiraro6KNi1v-BrEaXuTCIoLI1S_PS7pS-NlN7YXII31pqSJ-mXCbV6iyIyim8rftVbGOK1DexnoOBqCTzsOF2A7A10Ma3qQX-Ded91MjjxWr34RYahME8mwlUYUsRamTgTV-ygPF6FOCMh_-B-HkzKTKKhtGtfM_hWp7nLoMQw2lIHdYumcB649HmiUcMoaxWsVyQdyhwLpEqcTtwh2dRbAS3Ttez4nL45sgaf8R5hHg-4S9Zj5YBVOfo1YyxcWpvZFkKzlM9doQxwbvM7_QmqXW1Eh-QtL8zqQrYm9D3VLx6A-bloH3VAOamExSwe5raEOrD2TaeQ2-kbSopFPWKoBe0ZE8VyIBZIoCzXFrAfp2gpPfOMA-KPHHAv-CVa3BqSZInZt9yzdGo-JPTE46lR6FoR4YD0AGwuoGai8ko94VEQqHaESmKkrKBtpH7AucEXSF0i5J71QvtWAxAOr5MbxjyIEqHqbXsAZg_D0m-eNW8IgiGy22EA2TbHahytLtVmL3im2iN0rNNQ0A5-PfojcsxAE15OyX5hILGXPSju6LIvztcFJxmBsQUmBObVoO6_KH4CkBS2lfgudtvkXpfJNnGFyb3l-aLEkTrfLtJuJlOQWGJLeDgV5MV41nH-qNUj7v3xWVJFiSrNBETlAlaIn0klbWGTjii-1s42LS9ReQv-fulXgbiiyzOQOPUYHwDQVINO4hxk5nId5Wzpd1jpczeC-6P5pQwlPV9lo98MTr6CydXARMYaplD0Y2Dg_3ekiWi5rHb364sO0q57RmmHMhN0rpohLzvUQOekvihXUycZ7aN7Rf1l2L09UjSp1hUH4cdiPbZxrL4wx3ZLs32KJsoxFOllZe9azBeBaH9841aywnJfylU_luMHhNy4XR3xx43NZnVRq9HvlQa34gu0JGNkZwCBp2ojewjfRGegA7F8M53mKA85Al5-Ts2RM-tdvqmM1JK8qw==statsmodels-0.12.2/lint.sh000077500000000000000000000261111400612667500154530ustar00rootroot00000000000000#!/bin/bash echo "inside $0" RET=0 if [ "$LINT" == true ]; then echo "Linting all files with limited rules" flake8 statsmodels if [ $? -ne "0" ]; then echo "Changed files failed linting using the required set of rules." echo "Additions and changes must conform to Python code style rules." RET=1 fi # Run with --isolated to ignore config files, the files included here # pass _all_ flake8 checks echo "Linting known clean files with strict rules" # Default flake8 rules plus the additional rules from setup.cfg flake8 --isolated --ignore=E121,E123,E126,E226,E24,E704,W503,W504,E741,E203 \ examples/ \ setup.py \ statsmodels/__init__.py \ statsmodels/_version.py \ statsmodels/api.py \ statsmodels/base/__init__.py \ statsmodels/base/distributed_estimation.py \ statsmodels/base/elastic_net.py \ statsmodels/base/tests/test_data.py \ statsmodels/base/tests/test_distributed_estimation.py \ statsmodels/base/tests/test_shrink_pickle.py \ statsmodels/base/tests/test_transform.py \ statsmodels/compat/ \ statsmodels/conftest.py \ statsmodels/datasets/__init__.py \ statsmodels/datasets/anes96/__init__.py \ statsmodels/datasets/cancer/__init__.py \ statsmodels/datasets/ccard/__init__.py \ statsmodels/datasets/china_smoking/__init__.py \ statsmodels/datasets/co2/__init__.py \ statsmodels/datasets/committee/__init__.py \ statsmodels/datasets/copper/__init__.py \ statsmodels/datasets/cpunish/__init__.py \ statsmodels/datasets/elec_equip/ \ statsmodels/datasets/elnino/__init__.py \ statsmodels/datasets/engel/__init__.py \ statsmodels/datasets/fair/__init__.py \ statsmodels/datasets/fertility/__init__.py \ statsmodels/datasets/grunfeld/__init__.py \ statsmodels/datasets/heart/__init__.py \ statsmodels/datasets/interest_inflation/__init__.py \ statsmodels/datasets/longley/__init__.py \ statsmodels/datasets/macrodata/__init__.py \ statsmodels/datasets/modechoice/__init__.py \ statsmodels/datasets/nile/__init__.py \ statsmodels/datasets/randhie/__init__.py \ statsmodels/datasets/scotland/__init__.py \ statsmodels/datasets/spector/__init__.py \ statsmodels/datasets/stackloss/__init__.py \ statsmodels/datasets/star98/__init__.py \ statsmodels/datasets/statecrime/__init__.py \ statsmodels/datasets/strikes/__init__.py \ statsmodels/datasets/sunspots/__init__.py \ statsmodels/datasets/tests/ \ statsmodels/discrete/__init__.py \ statsmodels/discrete/tests/results/ \ statsmodels/discrete/tests/test_constrained.py \ statsmodels/distributions/__init__.py \ statsmodels/duration/__init__.py \ statsmodels/duration/_kernel_estimates.py \ statsmodels/duration/api.py \ statsmodels/duration/tests/results/ \ statsmodels/duration/tests/test_survfunc.py \ statsmodels/emplike/__init__.py \ statsmodels/emplike/api.py \ statsmodels/emplike/tests/ \ statsmodels/examples/tests/ \ statsmodels/formula/ \ statsmodels/gam/ \ statsmodels/genmod/__init__.py \ statsmodels/genmod/_tweedie_compound_poisson.py \ statsmodels/genmod/api.py \ statsmodels/genmod/bayes_mixed_glm.py \ statsmodels/genmod/families/ \ statsmodels/genmod/generalized_estimating_equations.py \ statsmodels/genmod/qif.py \ statsmodels/genmod/tests/results/ \ statsmodels/genmod/tests/test_gee.py \ statsmodels/genmod/tests/test_qif.py \ statsmodels/graphics/__init__.py \ statsmodels/graphics/api.py \ statsmodels/graphics/functional.py \ statsmodels/graphics/tests/test_agreement.py \ statsmodels/graphics/tests/test_boxplots.py \ statsmodels/graphics/tests/test_correlation.py \ statsmodels/graphics/tests/test_functional.py \ statsmodels/graphics/tests/test_gofplots.py \ statsmodels/graphics/tsaplots.py \ statsmodels/imputation/__init__.py \ statsmodels/interface/ \ statsmodels/iolib/__init__.py \ statsmodels/iolib/api.py \ statsmodels/iolib/openfile.py \ statsmodels/iolib/smpickle.py \ statsmodels/iolib/summary2.py \ statsmodels/iolib/table.py \ statsmodels/iolib/tableformatting.py \ statsmodels/iolib/tests/results/ \ statsmodels/iolib/tests/test_pickle.py \ statsmodels/miscmodels/__init__.py \ statsmodels/miscmodels/tests/test_tarma.py \ statsmodels/multivariate/__init__.py \ statsmodels/multivariate/api.py \ statsmodels/multivariate/factor_rotation/_analytic_rotation.py \ statsmodels/multivariate/pca.py \ statsmodels/multivariate/tests/results/ \ statsmodels/nonparametric/__init__.py \ statsmodels/nonparametric/api.py \ statsmodels/nonparametric/kde.py \ statsmodels/nonparametric/tests/results/ \ statsmodels/regression/__init__.py \ statsmodels/regression/_prediction.py \ statsmodels/regression/_tools.py \ statsmodels/regression/dimred.py \ statsmodels/regression/mixed_linear_model.py \ statsmodels/regression/process_regression.py \ statsmodels/regression/recursive_ls.py \ statsmodels/regression/rolling.py \ statsmodels/regression/tests/results/ \ statsmodels/regression/tests/test_dimred.py \ statsmodels/regression/tests/test_lme.py \ statsmodels/regression/tests/test_processreg.py \ statsmodels/regression/tests/test_quantile_regression.py \ statsmodels/regression/tests/test_rolling.py \ statsmodels/regression/tests/test_tools.py \ statsmodels/robust/ \ statsmodels/sandbox/__init__.py \ statsmodels/sandbox/distributions/__init__.py \ statsmodels/sandbox/distributions/tests/test_gof_new.py \ statsmodels/sandbox/distributions/try_pot.py \ statsmodels/sandbox/nonparametric/__init__.py \ statsmodels/sandbox/panel/correlation_structures.py \ statsmodels/sandbox/regression/tests/results_gmm_griliches.py \ statsmodels/sandbox/regression/tests/results_gmm_griliches_iter.py \ statsmodels/sandbox/regression/tests/results_gmm_poisson.py \ statsmodels/sandbox/regression/tests/results_ivreg2_griliches.py \ statsmodels/sandbox/stats/__init__.py \ statsmodels/sandbox/stats/tests/ \ statsmodels/src/ \ statsmodels/stats/__init__.py \ statsmodels/stats/_knockoff.py \ statsmodels/stats/_lilliefors.py \ statsmodels/stats/_lilliefors_critical_values.py \ statsmodels/stats/api.py \ statsmodels/stats/base.py \ statsmodels/stats/contingency_tables.py \ statsmodels/stats/correlation_tools.py \ statsmodels/stats/diagnostic.py \ statsmodels/stats/dist_dependence_measures.py \ statsmodels/stats/knockoff_regeffects.py \ statsmodels/stats/libqsturng/__init__.py \ statsmodels/stats/moment_helpers.py \ statsmodels/stats/multicomp.py \ statsmodels/stats/oaxaca.py \ statsmodels/stats/regularized_covariance.py \ statsmodels/stats/stattools.py \ statsmodels/stats/tabledist.py \ statsmodels/stats/tests/results/ \ statsmodels/stats/tests/test_anova_rm.py \ statsmodels/stats/tests/test_correlation.py \ statsmodels/stats/tests/test_descriptivestats.py \ statsmodels/stats/tests/test_diagnostic.py \ statsmodels/stats/tests/test_dist_dependant_measures.py \ statsmodels/stats/tests/test_knockoff.py \ statsmodels/stats/tests/test_lilliefors.py \ statsmodels/stats/tests/test_moment_helpers.py \ statsmodels/stats/tests/test_multi.py \ statsmodels/stats/tests/test_oaxaca.py \ statsmodels/stats/tests/test_outliers_influence.py \ statsmodels/stats/tests/test_qsturng.py \ statsmodels/stats/tests/test_regularized_covariance.py \ statsmodels/stats/tests/test_tabledist.py \ statsmodels/tests/ \ statsmodels/tools/decorators.py \ statsmodels/tools/docstring.py \ statsmodels/tools/linalg.py \ statsmodels/tools/sm_exceptions.py \ statsmodels/tools/tests/test_decorators.py \ statsmodels/tools/tests/test_docstring.py \ statsmodels/tools/tests/test_linalg.py \ statsmodels/tools/validation/ \ statsmodels/tools/web.py \ statsmodels/tsa/__init__.py \ statsmodels/tsa/_bds.py \ statsmodels/tsa/adfvalues.py \ statsmodels/tsa/api.py \ statsmodels/tsa/ar_model.py \ statsmodels/tsa/arima/ \ statsmodels/tsa/arima_model.py \ statsmodels/tsa/base/__init__.py \ statsmodels/tsa/base/tests/test_datetools.py \ statsmodels/tsa/exponential_smoothing/ \ statsmodels/tsa/filters/__init__.py \ statsmodels/tsa/filters/api.py \ statsmodels/tsa/filters/bk_filter.py \ statsmodels/tsa/filters/hp_filter.py \ statsmodels/tsa/filters/tests/ \ statsmodels/tsa/innovations/ \ statsmodels/tsa/interp/__init__.py \ statsmodels/tsa/kalmanf/ \ statsmodels/tsa/regime_switching/ \ statsmodels/tsa/seasonal.py \ statsmodels/tsa/statespace/ \ statsmodels/tsa/tests/results/ \ statsmodels/tsa/tests/test_ar.py \ statsmodels/tsa/tests/test_arima.py \ statsmodels/tsa/tests/test_bds.py \ statsmodels/tsa/tests/test_seasonal.py \ statsmodels/tsa/tests/test_stl.py \ statsmodels/tsa/tests/test_x13.py \ statsmodels/tsa/vector_ar/__init__.py \ statsmodels/tsa/vector_ar/api.py \ statsmodels/tsa/vector_ar/hypothesis_test_results.py \ statsmodels/tsa/vector_ar/tests/JMulTi_results/ \ statsmodels/tsa/vector_ar/tests/Matlab_results/ \ statsmodels/tsa/vector_ar/tests/results/ \ statsmodels/tsa/x13.py \ tools/ if [ $? -ne "0" ]; then echo "Previously passing files failed linting." RET=1 fi # Tests any new python files if [ -f $(git rev-parse --git-dir)/shallow ]; then # Unshallow only when required, i.e., on CI echo "Repository is shallow" git fetch --unshallow --quiet fi git config remote.origin.fetch "+refs/heads/*:refs/remotes/origin/*" git fetch origin --quiet NEW_FILES=$(git diff origin/master --name-status -u -- "*.py" | grep ^A | cut -c 3- | paste -sd " " -) if [ -n "$NEW_FILES" ]; then echo "Linting newly added files with strict rules" echo "New files: $NEW_FILES" flake8 --isolated --ignore=E121,E123,E126,E226,E24,E704,W503,W504,E741,E203 $(eval echo $NEW_FILES) if [ $? -ne "0" ]; then echo "New files failed linting." RET=1 fi else echo "No new files to lint" fi fi exit "$RET" statsmodels-0.12.2/pyproject.toml000066400000000000000000000003521400612667500170610ustar00rootroot00000000000000[build-system] requires = [ "setuptools", "wheel", "cython>=0.29.14", "numpy==1.15.4; python_version=='3.6'", "numpy==1.15.4; python_version=='3.7'", "numpy==1.17.5; python_version>='3.8'", "scipy>=1.2", ] statsmodels-0.12.2/requirements-dev.txt000066400000000000000000000005721400612667500202110ustar00rootroot00000000000000# build cython>=0.29 # run matplotlib>=2.2 # Remove due to failures on azure CI # cvxopt; os_name != "win32" # test pytest pytest-randomly # Pin to 1.29 due to test discovery issues pytest-xdist==1.29 # code quality flake8 isort # doc sphinx sphinx-material; python_version > '3.5' jupyter notebook nbsphinx nbconvert pyyaml pandas-datareader simplegeneric seaborn numpydoc statsmodels-0.12.2/requirements.txt000066400000000000000000000000611400612667500174260ustar00rootroot00000000000000numpy>=1.15 scipy>=1.2 pandas>=0.23 patsy>=0.5.1 statsmodels-0.12.2/setup.cfg000066400000000000000000000237221400612667500157740ustar00rootroot00000000000000[metadata] license_file = LICENSE.txt [tool:pytest] # minversion = 3.6 testpaths = statsmodels xfail_strict = true addopts = --strict # Filter warnings generated by dependencies filterwarnings = ignore:pandas.core.common.is_categorical_dtype:DeprecationWarning:patsy ignore:Using or importing the ABCs:DeprecationWarning:patsy ignore:Using a non-tuple sequence:FutureWarning:mkl_fft ignore:Using a non-tuple:FutureWarning:scipy.signal ignore:Using a non-tuple:FutureWarning:scipy.stats.stats ignore:the matrix subclass is not the recommended:PendingDeprecationWarning: ignore:Method .ptp is deprecated:FutureWarning:numpy.core.fromnumeric ignore::DeprecationWarning:nbconvert.exporters.exporter_locator ignore:Using or importing the ABCs:DeprecationWarning:jinja2.utils ignore:Converting `np.integer`:DeprecationWarning:scipy.stats.morestats ignore:\nstatsmodels.tsa.arima_model.ARMA:FutureWarning error:genfromdta:FutureWarning error:StataReader:FutureWarning error:Estimation of VARMA:statsmodels.tools.sm_exceptions.EstimationWarning error:Care should be used:UserWarning error::statsmodels.tools.sm_exceptions.HypothesisTestWarning error::statsmodels.tools.sm_exceptions.SpecificationWarning error:load will return datasets:FutureWarning error:the 'lags' keyword is deprecated:FutureWarning error:nobs is deprecated in favor of lags:DeprecationWarning error:The default pvalmethod will change:FutureWarning error:Using an implicitly registered:FutureWarning error:An unsupported index:statsmodels.tools.sm_exceptions.ValueWarning error:No supported index is:statsmodels.tools.sm_exceptions.ValueWarning error:Anscombe residuals:FutureWarning error:Calling Family:DeprecationWarning error:SIR.fit_regularized did not:UserWarning error:the 'sigma' keyword:FutureWarning error:tight_layout:UserWarning error:statsmodels.tsa.AR has been deprecated:FutureWarning error:Using deprecated variance components:UserWarning error:recarray support has been deprecated:FutureWarning error:The value returned will change to a:FutureWarning error:The default value of lags:FutureWarning error::pandas.core.common.SettingWithCopyWarning error:non-integer arg n is deprecated:DeprecationWarning error:Creating an ndarray:numpy.VisibleDeprecationWarning error:The default number of lags:FutureWarning: error:fft=True will become the default:FutureWarning error:The parameter names will change:FutureWarning error:Only PeriodIndexes, DatetimeIndexes:UserWarning error:the 'unbiased'' keyword is deprecated:FutureWarning error:unbiased is deprecated in factor of adjusted:FutureWarning error:categorical is deprecated:FutureWarning error:After 0.13 initialization:FutureWarning error:The bic value:FutureWarning error:Setting initial values:FutureWarning error:Setting use_boxcox:FutureWarning error:``Describe`` has been deprecated:DeprecationWarning markers = example: mark a test that runs example code matplotlib: mark a test that requires matplotlib slow: mark a test as slow smoke: mark a test as a smoketest low_precision: mark a test as low precision todo: mark a test as incomplete junit_family = xunit2 [versioneer] VCS = git style = pep440 versionfile_source = statsmodels/_version.py versionfile_build = statsmodels/_version.py tag_prefix = v parentdir_prefix = statsmodels- [flake8] exclude=.git,build,docs,archive,versioneer.py ignore= W503, # W503: line break before binary operator W504, # W504: line break after binary operator E741, # E741: ambiguous variable name 'l' E203 # E203: Whitespace before ':' select= E101, # E101: indentation contains mixed spaces and tabs E124, # E124: closing bracket does not match visual indentation F811, # F811: redefinition of unused 'pytest' from line 10 F812, # F812: list comprehension redefines 'x' from line 199 F822, # F822: undefined name name in __all__ F823, # F823: local variable name ... referenced before assignment E129, # E129: visually indented line with same indent as next logical line E131, # E131: continuation line unaligned for hanging indent E125, # E125: continuation line with same indent as next logical line E111, # E111: Indentation is not a multiple of four E114, # E114: Indentation is not a multiple of four (comment) E117, # E117: over-indented E227, # E227: missing whitespace around bitwise or shift operator E228, # E228: missing whitespace around modulo operator E211, # E211: whitespace before '[' E112, # E112: expected an indented block E113, # E113: unexpected indentation E223, # E223: tab before operator E224, # E224: tab after operator E242, # E242: tab after ',' E304, # E304: blank lines found after function decorator F831, # F831: duplicate argument name in function definition E306, # E306: expected 1 blank line before a nested definition, found 0 W, # W191: indentation contains tabs # W291: trailing whitespace # W292: no newline at end of file # W293: blank line contains whitespace # W391: blank line at end of file # W601: .has_key() is deprecated, use 'in' # W602: deprecated form of raising exception # W603: '<>' is deprecated, use '!=' # W604: backticks are deprecated, use 'repr()' # W605: invalid escape sequence 'x' # W606: 'async' and 'await' are reserved keywords starting with Python 3.7 E70, # E701: multiple statements on one line (colon) # E702: multiple statements on one line (semicolon) # E703: statement ends with a semicolon # E704: multiple statements on one line (def) E71, # E711: comparison to None should be 'if cond is None:' # E712: comparison to True should be 'if cond is True:' or 'if cond:' # E713: test for membership should be 'not in' E721, # E721: do not compare types, use 'isinstance()' E74, # E741 ambiguous variable name 'l', 'O', or 'I' # E742: do not define classes named 'l', 'O', or 'I' # E743: do not define functions named 'l', 'O', or 'I' F4, # F401: 'foo.bar' imported but unused # F402: import 'assert_equal' from line 7 shadowed by loop variable # F403: 'from .data import *' used; unable to detect undefined names # F404: future import(s) name after other statements # F405: name may be undefined, or defined from star imports: module # F406: 'from module import *' only allowed at module level # F407: an undefined __future__ feature name was imported F6, # F601: dictionary key name repeated with different values # F602: dictionary key variable name repeated with different values # F621: too many expressions in an assignment with star-unpacking # F622: two or more starred expressions in an assignment (a, *b, *c = d) # F631: assertion test is a tuple, which are always True # F632: use ==/!= to compare str, bytes, and int literals F7, # F701: a break statement outside of a while or for loop # F702: a continue statement outside of a while or for loop # F703: a continue statement in a finally block in a loop # F704: a yield or yield from statement outside of a function # F705: a return statement with arguments inside a generator # F706: a return statement outside of a function/method # F707: an except: block as not the last exception handler # F721: doctest syntax error # F722: syntax error in forward type annotation F81, # F811: redefinition of unused 'pytest' from line 10 # F812: list comprehension redefines 'x' from line 199 F82, # F821: undefined name 'foo' # F822: undefined name name in __all__ # F823: local variable name ... referenced before assignment F9, # F901: raise NotImplemented should be raise NotImplementedError E27, # E271: multiple spaces after keyword # E272: multiple spaces before keyword # E273: tab after keyword # E274: tab before keyword # E275: missing whitespace after keyword E4, # E401: multiple imports on one line # E402: module level import not at top of file E9, # E901: SyntaxError or IndentationError # E902: IOError # E999: Syntax Error [coverage:run] source = statsmodels branch = True plugins = Cython.Coverage omit = # print_version is untestable */print_version.py # skip compatibility code */compat/* # Unused file */results/gee_generate_tests.py # Results for tests */tests/results/* # Simulation checks */tests/*_simulation_check.py # Misc non-test files in test directories */tests/_* */tests/e* */tests/c* */tests/d* */tests/g* */tests/m* */tests/p* */tests/r* */tests/s* # Versioneer */_version.py [coverage:report] show_missing = True ignore_errors = False # Regexes for lines to exclude from consideration exclude_lines = # Have to re-enable the standard pragma pragma: no cover # Do not complain about missing debug-only code: def __repr__ if self\.debug if pdf_output: # Do not complain if tests do not hit defensive assertion code: raise AssertionError raise NotImplementedError except NotImplementedError except ImportError except (HTTPError, URLError, SSLError, timeout) except IGNORED_EXCEPTIONS # Ignore pass pass # Do not complain if non-runnable code is not run: if 0: if __name__ == .__main__.: [coverage:html] directory = coverage_html_report [isort] sections=FUTURE,COMPAT,STDLIB,THIRDPARTY,FIRSTPARTY,LOCALFOLDER known_first_party=statsmodels known_third_party=Cython,numpy,matplotlib,pandas,patsy,pytest,cvxopt,cython multi_line_output=3 include_trailing_comma=True use_parentheses=True line_length=79 known_compat=statsmodels.compat.*,setuptools,setuptools.* force_grid_wrap=0 combine_as_imports=True force_sort_within_sections=True force_to_top=True statsmodels-0.12.2/setup.py000066400000000000000000000333251400612667500156650ustar00rootroot00000000000000""" To build with coverage of Cython files export SM_CYTHON_COVERAGE=1 python setup.py develop pytest --cov=statsmodels statsmodels coverage html """ from setuptools import Extension, find_packages, setup from setuptools.dist import Distribution from collections import defaultdict from distutils.command.clean import clean import fnmatch import os from os.path import abspath, join as pjoin, relpath, split import shutil import sys import pkg_resources import versioneer try: # SM_FORCE_C is a testing shim to force setup to use C source files FORCE_C = int(os.environ.get('SM_FORCE_C', 0)) if FORCE_C: raise ImportError('Force import error for testing') from Cython import Tempita from Cython.Build import cythonize from Cython.Distutils import build_ext HAS_CYTHON = True except ImportError: from setuptools.command.build_ext import build_ext HAS_CYTHON = False ############################################################################### # Key Values that Change Each Release ############################################################################### SETUP_REQUIREMENTS = {'numpy': '1.15', # released June 2018 'scipy': '1.1', # released May 2018 } REQ_NOT_MET_MSG = """ {0} is installed but older ({1}) than required ({2}). You must manually upgrade {0} before installing or install into a fresh virtualenv. """ for key in SETUP_REQUIREMENTS: from distutils.version import LooseVersion import importlib req_ver = LooseVersion(SETUP_REQUIREMENTS[key]) try: mod = importlib.import_module(key) ver = LooseVersion(mod.__version__) if ver < req_ver: raise RuntimeError(REQ_NOT_MET_MSG.format(key, ver, req_ver)) except ImportError: pass except AttributeError: raise RuntimeError(REQ_NOT_MET_MSG.format(key, ver, req_ver)) INSTALL_REQUIREMENTS = SETUP_REQUIREMENTS.copy() INSTALL_REQUIREMENTS.update({'pandas': '0.21', # released October 2017 'patsy': '0.5', # released January 2018 }) CYTHON_MIN_VER = '0.29' # released November 2018 SETUP_REQUIRES = [k + '>=' + v for k, v in SETUP_REQUIREMENTS.items()] INSTALL_REQUIRES = [k + '>=' + v for k, v in INSTALL_REQUIREMENTS.items()] EXTRAS_REQUIRE = {'build': ['cython>=' + CYTHON_MIN_VER], 'develop': ['cython>=' + CYTHON_MIN_VER], 'docs': ['sphinx', 'nbconvert', 'jupyter_client', 'ipykernel', 'matplotlib', 'nbformat', 'numpydoc', 'pandas-datareader']} ############################################################################### # Values that rarely change ############################################################################### DISTNAME = 'statsmodels' DESCRIPTION = 'Statistical computations and models for Python' SETUP_DIR = split(abspath(__file__))[0] with open(pjoin(SETUP_DIR, 'README.rst')) as readme: README = readme.read() LONG_DESCRIPTION = README MAINTAINER = 'statsmodels Developers' MAINTAINER_EMAIL = 'pystatsmodels@googlegroups.com' URL = 'https://www.statsmodels.org/' LICENSE = 'BSD License' DOWNLOAD_URL = '' PROJECT_URLS = { 'Bug Tracker': 'https://github.com/statsmodels/statsmodels/issues', 'Documentation': 'https://www.statsmodels.org/stable/index.html', 'Source Code': 'https://github.com/statsmodels/statsmodels' } CLASSIFIERS = ['Development Status :: 4 - Beta', 'Environment :: Console', 'Programming Language :: Cython', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7', 'Programming Language :: Python :: 3.8', 'Operating System :: OS Independent', 'Intended Audience :: End Users/Desktop', 'Intended Audience :: Developers', 'Intended Audience :: Science/Research', 'Natural Language :: English', 'License :: OSI Approved :: BSD License', 'Topic :: Office/Business :: Financial', 'Topic :: Scientific/Engineering'] FILES_TO_INCLUDE_IN_PACKAGE = ['LICENSE.txt', 'setup.cfg'] FILES_COPIED_TO_PACKAGE = [] for filename in FILES_TO_INCLUDE_IN_PACKAGE: if os.path.exists(filename): dest = os.path.join('statsmodels', filename) shutil.copy2(filename, dest) FILES_COPIED_TO_PACKAGE.append(dest) STATESPACE_RESULTS = "statsmodels.tsa.statespace.tests.results" ADDITIONAL_PACKAGE_DATA = { 'statsmodels': FILES_TO_INCLUDE_IN_PACKAGE, 'statsmodels.datasets.tests': ['*.zip'], 'statsmodels.iolib.tests.results': ['*.dta'], 'statsmodels.stats.tests.results': ['*.json'], 'statsmodels.tsa.vector_ar.tests.results': ['*.npz', '*.dat'], 'statsmodels.stats.tests': ['*.txt'], 'statsmodels.stats.libqsturng': ['*.r', '*.txt', '*.dat'], 'statsmodels.stats.libqsturng.tests': ['*.csv', '*.dat'], 'statsmodels.sandbox.regression.tests': ['*.dta', '*.csv'], STATESPACE_RESULTS: ['*.pkl', '*.csv'], STATESPACE_RESULTS + '.frbny_nowcast': ['test*.mat'], STATESPACE_RESULTS + '.frbny_nowcast.Nowcasting.data.US': ['*.csv'] } ############################################################################## # Extension Building ############################################################################## CYTHON_COVERAGE = os.environ.get('SM_CYTHON_COVERAGE', False) CYTHON_COVERAGE = CYTHON_COVERAGE in ('1', 'true', '"true"') CYTHON_TRACE_NOGIL = str(int(CYTHON_COVERAGE)) if CYTHON_COVERAGE: print('Building with coverage for Cython code') COMPILER_DIRECTIVES = {'linetrace': CYTHON_COVERAGE} DEFINE_MACROS = [('CYTHON_TRACE_NOGIL', CYTHON_TRACE_NOGIL)] exts = dict( _stl={'source': 'statsmodels/tsa/_stl.pyx'}, _exponential_smoothers={'source': 'statsmodels/tsa/holtwinters/_exponential_smoothers.pyx'}, # noqa: E501 _ets_smooth={'source': 'statsmodels/tsa/exponential_smoothing/_ets_smooth.pyx'}, # noqa: E501 _innovations={'source': 'statsmodels/tsa/_innovations.pyx'}, _hamilton_filter={'source': 'statsmodels/tsa/regime_switching/_hamilton_filter.pyx.in'}, # noqa: E501 _kim_smoother={'source': 'statsmodels/tsa/regime_switching/_kim_smoother.pyx.in'}, # noqa: E501 _arma_innovations={'source': 'statsmodels/tsa/innovations/_arma_innovations.pyx.in'}, # noqa: E501 linbin={'source': 'statsmodels/nonparametric/linbin.pyx'}, _qn={'source': 'statsmodels/robust/_qn.pyx'}, _smoothers_lowess={'source': 'statsmodels/nonparametric/_smoothers_lowess.pyx'}, # noqa: E501 kalman_loglike={'source': 'statsmodels/tsa/kalmanf/kalman_loglike.pyx', 'include_dirs': ['statsmodels/src'], 'depends': ['statsmodels/src/capsule.h']}) statespace_exts = [ 'statsmodels/tsa/statespace/_initialization.pyx.in', 'statsmodels/tsa/statespace/_representation.pyx.in', 'statsmodels/tsa/statespace/_kalman_filter.pyx.in', 'statsmodels/tsa/statespace/_filters/_conventional.pyx.in', 'statsmodels/tsa/statespace/_filters/_inversions.pyx.in', 'statsmodels/tsa/statespace/_filters/_univariate.pyx.in', 'statsmodels/tsa/statespace/_filters/_univariate_diffuse.pyx.in', 'statsmodels/tsa/statespace/_kalman_smoother.pyx.in', 'statsmodels/tsa/statespace/_smoothers/_alternative.pyx.in', 'statsmodels/tsa/statespace/_smoothers/_classical.pyx.in', 'statsmodels/tsa/statespace/_smoothers/_conventional.pyx.in', 'statsmodels/tsa/statespace/_smoothers/_univariate.pyx.in', 'statsmodels/tsa/statespace/_smoothers/_univariate_diffuse.pyx.in', 'statsmodels/tsa/statespace/_simulation_smoother.pyx.in', 'statsmodels/tsa/statespace/_cfa_simulation_smoother.pyx.in', 'statsmodels/tsa/statespace/_tools.pyx.in', ] class CleanCommand(clean): def run(self): msg = """ python setup.py clean is not supported. Use one of: * `git clean -xdf` to clean all untracked files * `git clean -Xdf` to clean untracked files ignored by .gitignore """ print(msg) sys.exit(1) class DeferredBuildExt(build_ext): """build_ext command for use when numpy headers are needed.""" def build_extensions(self): self._update_extensions() build_ext.build_extensions(self) def _update_extensions(self): import numpy from numpy.distutils.log import set_verbosity from numpy.distutils.misc_util import get_info set_verbosity(1) numpy_includes = [numpy.get_include()] extra_incl = pkg_resources.resource_filename('numpy', 'core/include') numpy_includes += [extra_incl] numpy_includes = list(set(numpy_includes)) numpy_math_libs = get_info('npymath') for extension in self.extensions: if not hasattr(extension, 'include_dirs'): continue extension.include_dirs = list(set(extension.include_dirs + numpy_includes)) if extension.name in EXT_REQUIRES_NUMPY_MATH_LIBS: extension.include_dirs += numpy_math_libs['include_dirs'] extension.libraries += numpy_math_libs['libraries'] extension.library_dirs += numpy_math_libs['library_dirs'] cmdclass = versioneer.get_cmdclass() cmdclass['build_ext'] = DeferredBuildExt cmdclass['clean'] = CleanCommand def check_source(source_name): """Chooses C or pyx source files, and raises if C is needed but missing""" source_ext = '.pyx' if not HAS_CYTHON: source_name = source_name.replace('.pyx.in', '.c') source_name = source_name.replace('.pyx', '.c') source_ext = '.c' if not os.path.exists(source_name): msg = 'C source not found. You must have Cython installed to ' \ 'build if the C source files have not been generated.' raise IOError(msg) return source_name, source_ext def process_tempita(source_name): """Runs pyx.in files through tempita is needed""" if source_name.endswith('pyx.in'): with open(source_name, 'r') as templated: pyx_template = templated.read() pyx = Tempita.sub(pyx_template) pyx_filename = source_name[:-3] with open(pyx_filename, 'w') as pyx_file: pyx_file.write(pyx) file_stats = os.stat(source_name) try: os.utime(pyx_filename, ns=(file_stats.st_atime_ns, file_stats.st_mtime_ns)) except AttributeError: os.utime(pyx_filename, (file_stats.st_atime, file_stats.st_mtime)) source_name = pyx_filename return source_name EXT_REQUIRES_NUMPY_MATH_LIBS = [] extensions = [] for config in exts.values(): uses_blas = True source, ext = check_source(config['source']) source = process_tempita(source) name = source.replace('/', '.').replace(ext, '') include_dirs = config.get('include_dirs', []) depends = config.get('depends', []) libraries = config.get('libraries', []) library_dirs = config.get('library_dirs', []) uses_numpy_libraries = config.get('numpy_libraries', False) if uses_blas or uses_numpy_libraries: EXT_REQUIRES_NUMPY_MATH_LIBS.append(name) ext = Extension(name, [source], include_dirs=include_dirs, depends=depends, libraries=libraries, library_dirs=library_dirs, define_macros=DEFINE_MACROS) extensions.append(ext) for source in statespace_exts: source, ext = check_source(source) source = process_tempita(source) name = source.replace('/', '.').replace(ext, '') EXT_REQUIRES_NUMPY_MATH_LIBS.append(name) ext = Extension(name, [source], include_dirs=['statsmodels/src'], depends=[], libraries=[], library_dirs=[], define_macros=DEFINE_MACROS) extensions.append(ext) if HAS_CYTHON: extensions = cythonize(extensions, compiler_directives=COMPILER_DIRECTIVES, language_level=3, force=CYTHON_COVERAGE) ############################################################################## # Construct package data ############################################################################## package_data = defaultdict(list) filetypes = ['*.csv', '*.txt', '*.dta'] for root, _, filenames in os.walk(pjoin(os.getcwd(), 'statsmodels', 'datasets')): # noqa: E501 matches = [] for filetype in filetypes: for filename in fnmatch.filter(filenames, filetype): matches.append(filename) if matches: package_data['.'.join(relpath(root).split(os.path.sep))] = filetypes for root, _, _ in os.walk(pjoin(os.getcwd(), 'statsmodels')): if root.endswith('results'): package_data['.'.join(relpath(root).split(os.path.sep))] = filetypes for path, filetypes in ADDITIONAL_PACKAGE_DATA.items(): package_data[path].extend(filetypes) if os.path.exists('MANIFEST'): os.unlink('MANIFEST') class BinaryDistribution(Distribution): def is_pure(self): return False setup(name=DISTNAME, version=versioneer.get_version(), maintainer=MAINTAINER, ext_modules=extensions, maintainer_email=MAINTAINER_EMAIL, description=DESCRIPTION, license=LICENSE, url=URL, download_url=DOWNLOAD_URL, project_urls=PROJECT_URLS, long_description=LONG_DESCRIPTION, classifiers=CLASSIFIERS, platforms='any', cmdclass=cmdclass, packages=find_packages(), package_data=package_data, distclass=BinaryDistribution, include_package_data=False, # True will install all files in repo setup_requires=SETUP_REQUIRES, install_requires=INSTALL_REQUIRES, extras_require=EXTRAS_REQUIRE, zip_safe=False, python_requires=">=3.6", ) # Clean-up copied files for copy in FILES_COPIED_TO_PACKAGE: os.unlink(copy) statsmodels-0.12.2/statsmodels/000077500000000000000000000000001400612667500165075ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/__init__.py000066400000000000000000000016671400612667500206320ustar00rootroot00000000000000 from statsmodels._version import get_versions debug_warnings = False if debug_warnings: import warnings warnings.simplefilter("default") # use the following to raise an exception for debugging specific warnings # warnings.filterwarnings("error", message=".*integer.*") def test(extra_args=None, exit=False): """ Run the test suite Parameters ---------- extra_args : list[str] List of argument to pass to pytest when running the test suite. The default is ['--tb=short', '--disable-pytest-warnings']. exit : bool Flag indicating whether the test runner should exist when finished. Returns ------- int The status code from the test run if exit is False. """ from .tools._testing import PytestTester tst = PytestTester(package_path=__file__) return tst(extra_args=extra_args, exit=exit) __version__ = get_versions()['version'] del get_versions statsmodels-0.12.2/statsmodels/_version.py000066400000000000000000000441471400612667500207170ustar00rootroot00000000000000 # This file helps to compute a version number in source trees obtained from # git-archive tarball (such as those provided by githubs download-from-tag # feature). Distribution tarballs (built by setup.py sdist) and build # directories (produced by setup.py build) will contain a much shorter file # that just contains the computed version number. # This file is released into the public domain. Generated by # versioneer-0.18 (https://github.com/warner/python-versioneer) """Git implementation of _version.py.""" import errno import os import re import subprocess import sys def get_keywords(): """Get the keywords needed to look up the version information.""" # these strings will be replaced by git during git-archive. # setup.py/versioneer.py will grep for the variable names, so they must # each be defined on a line of their own. _version.py will just call # get_keywords(). git_refnames = " (tag: v0.12.2, maintenance/0.12.x)" git_full = "cce93db5277ce2618dafdc84c42186bbafe2a6b6" git_date = "2021-02-01 20:41:17 -0500" keywords = {"refnames": git_refnames, "full": git_full, "date": git_date} return keywords class VersioneerConfig: """Container for Versioneer configuration parameters.""" def get_config(): """Create, populate and return the VersioneerConfig() object.""" # these strings are filled in when 'setup.py versioneer' creates # _version.py cfg = VersioneerConfig() cfg.VCS = "git" cfg.style = "pep440" cfg.tag_prefix = "" cfg.parentdir_prefix = "statsmodels-" cfg.versionfile_source = "statsmodels/_version.py" cfg.verbose = False return cfg class NotThisMethod(Exception): """Exception raised if a method is not valid for the current scenario.""" LONG_VERSION_PY = {} HANDLERS = {} def register_vcs_handler(vcs, method): # decorator """Decorator to mark a method as the handler for a particular VCS.""" def decorate(f): """Store f in HANDLERS[vcs][method].""" if vcs not in HANDLERS: HANDLERS[vcs] = {} HANDLERS[vcs][method] = f return f return decorate def run_command(commands, args, cwd=None, verbose=False, hide_stderr=False, env=None): """Call the given command(s).""" assert isinstance(commands, list) p = None for c in commands: try: dispcmd = str([c] + args) # remember shell=False, so use git.cmd on windows, not just git p = subprocess.Popen([c] + args, cwd=cwd, env=env, stdout=subprocess.PIPE, stderr=(subprocess.PIPE if hide_stderr else None)) break except EnvironmentError: e = sys.exc_info()[1] if e.errno == errno.ENOENT: continue if verbose: print("unable to run %s" % dispcmd) print(e) return None, None else: if verbose: print("unable to find command, tried %s" % (commands,)) return None, None stdout = p.communicate()[0].strip() if sys.version_info[0] >= 3: stdout = stdout.decode() if p.returncode != 0: if verbose: print("unable to run %s (error)" % dispcmd) print("stdout was %s" % stdout) return None, p.returncode return stdout, p.returncode def versions_from_parentdir(parentdir_prefix, root, verbose): """Try to determine the version from the parent directory name. Source tarballs conventionally unpack into a directory that includes both the project name and a version string. We will also support searching up two directory levels for an appropriately named parent directory """ rootdirs = [] for i in range(3): dirname = os.path.basename(root) if dirname.startswith(parentdir_prefix): return {"version": dirname[len(parentdir_prefix):], "full-revisionid": None, "dirty": False, "error": None, "date": None} else: rootdirs.append(root) root = os.path.dirname(root) # up a level if verbose: print("Tried directories %s but none started with prefix %s" % (str(rootdirs), parentdir_prefix)) raise NotThisMethod("rootdir does not start with parentdir_prefix") @register_vcs_handler("git", "get_keywords") def git_get_keywords(versionfile_abs): """Extract version information from the given file.""" # the code embedded in _version.py can just fetch the value of these # keywords. When used from setup.py, we do not want to import _version.py, # so we do it with a regexp instead. This function is not used from # _version.py. keywords = {} try: f = open(versionfile_abs, "r") for line in f.readlines(): if line.strip().startswith("git_refnames ="): mo = re.search(r'=\s*"(.*)"', line) if mo: keywords["refnames"] = mo.group(1) if line.strip().startswith("git_full ="): mo = re.search(r'=\s*"(.*)"', line) if mo: keywords["full"] = mo.group(1) if line.strip().startswith("git_date ="): mo = re.search(r'=\s*"(.*)"', line) if mo: keywords["date"] = mo.group(1) f.close() except EnvironmentError: pass return keywords @register_vcs_handler("git", "keywords") def git_versions_from_keywords(keywords, tag_prefix, verbose): """Get version information from git keywords.""" if not keywords: raise NotThisMethod("no keywords at all, weird") date = keywords.get("date") if date is not None: # git-2.2.0 added "%cI", which expands to an ISO-8601 -compliant # datestamp. However we prefer "%ci" (which expands to an "ISO-8601 # -like" string, which we must then edit to make compliant), because # it's been around since git-1.5.3, and it's too difficult to # discover which version we're using, or to work around using an # older one. date = date.strip().replace(" ", "T", 1).replace(" ", "", 1) refnames = keywords["refnames"].strip() if refnames.startswith("$Format"): if verbose: print("keywords are unexpanded, not using") raise NotThisMethod("unexpanded keywords, not a git-archive tarball") refs = set([r.strip() for r in refnames.strip("()").split(",")]) # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of # just "foo-1.0". If we see a "tag: " prefix, prefer those. TAG = "tag: " tags = set([r[len(TAG):] for r in refs if r.startswith(TAG)]) if not tags: # Either we're using git < 1.8.3, or there really are no tags. We use # a heuristic: assume all version tags have a digit. The old git %d # expansion behaves like git log --decorate=short and strips out the # refs/heads/ and refs/tags/ prefixes that would let us distinguish # between branches and tags. By ignoring refnames without digits, we # filter out many common branch names like "release" and # "stabilization", as well as "HEAD" and "master". tags = set([r for r in refs if re.search(r'\d', r)]) if verbose: print("discarding '%s', no digits" % ",".join(refs - tags)) if verbose: print("likely tags: %s" % ",".join(sorted(tags))) for ref in sorted(tags): # sorting will prefer e.g. "2.0" over "2.0rc1" if ref.startswith(tag_prefix): r = ref[len(tag_prefix):] if verbose: print("picking %s" % r) return {"version": r, "full-revisionid": keywords["full"].strip(), "dirty": False, "error": None, "date": date} # no suitable tags, so version is "0+unknown", but full hex is still there if verbose: print("no suitable tags, using unknown + full revision id") return {"version": "0+unknown", "full-revisionid": keywords["full"].strip(), "dirty": False, "error": "no suitable tags", "date": None} @register_vcs_handler("git", "pieces_from_vcs") def git_pieces_from_vcs(tag_prefix, root, verbose, run_command=run_command): """Get version from 'git describe' in the root of the source tree. This only gets called if the git-archive 'subst' keywords were *not* expanded, and _version.py has not already been rewritten with a short version string, meaning we're inside a checked out source tree. """ GITS = ["git"] if sys.platform == "win32": GITS = ["git.cmd", "git.exe"] out, rc = run_command(GITS, ["rev-parse", "--git-dir"], cwd=root, hide_stderr=True) if rc != 0: if verbose: print("Directory %s not under git control" % root) raise NotThisMethod("'git rev-parse --git-dir' returned error") # if there is a tag matching tag_prefix, this yields TAG-NUM-gHEX[-dirty] # if there is not one, this yields HEX[-dirty] (no NUM) describe_out, rc = run_command(GITS, ["describe", "--tags", "--dirty", "--always", "--long", "--match", "%s*" % tag_prefix], cwd=root) # --long was added in git-1.5.5 if describe_out is None: raise NotThisMethod("'git describe' failed") describe_out = describe_out.strip() full_out, rc = run_command(GITS, ["rev-parse", "HEAD"], cwd=root) if full_out is None: raise NotThisMethod("'git rev-parse' failed") full_out = full_out.strip() pieces = {} pieces["long"] = full_out pieces["short"] = full_out[:7] # maybe improved later pieces["error"] = None # parse describe_out. It will be like TAG-NUM-gHEX[-dirty] or HEX[-dirty] # TAG might have hyphens. git_describe = describe_out # look for -dirty suffix dirty = git_describe.endswith("-dirty") pieces["dirty"] = dirty if dirty: git_describe = git_describe[:git_describe.rindex("-dirty")] # now we have TAG-NUM-gHEX or HEX if "-" in git_describe: # TAG-NUM-gHEX mo = re.search(r'^(.+)-(\d+)-g([0-9a-f]+)$', git_describe) if not mo: # unparseable. Maybe git-describe is misbehaving? pieces["error"] = ("unable to parse git-describe output: '%s'" % describe_out) return pieces # tag full_tag = mo.group(1) if not full_tag.startswith(tag_prefix): if verbose: fmt = "tag '%s' does not start with prefix '%s'" print(fmt % (full_tag, tag_prefix)) pieces["error"] = ("tag '%s' does not start with prefix '%s'" % (full_tag, tag_prefix)) return pieces pieces["closest-tag"] = full_tag[len(tag_prefix):] # distance: number of commits since tag pieces["distance"] = int(mo.group(2)) # commit: short hex revision ID pieces["short"] = mo.group(3) else: # HEX: no tags pieces["closest-tag"] = None count_out, rc = run_command(GITS, ["rev-list", "HEAD", "--count"], cwd=root) pieces["distance"] = int(count_out) # total number of commits # commit date: see ISO-8601 comment in git_versions_from_keywords() date = run_command(GITS, ["show", "-s", "--format=%ci", "HEAD"], cwd=root)[0].strip() pieces["date"] = date.strip().replace(" ", "T", 1).replace(" ", "", 1) return pieces def plus_or_dot(pieces): """Return a + if we do not already have one, else return a .""" if "+" in pieces.get("closest-tag", ""): return "." return "+" def render_pep440(pieces): """Build up version string, with post-release "local version identifier". Our goal: TAG[+DISTANCE.gHEX[.dirty]] . Note that if you get a tagged build and then dirty it, you'll get TAG+0.gHEX.dirty Exceptions: 1: no tags. git_describe was just HEX. 0+untagged.DISTANCE.gHEX[.dirty] """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"] or pieces["dirty"]: rendered += plus_or_dot(pieces) rendered += "%d.g%s" % (pieces["distance"], pieces["short"]) if pieces["dirty"]: rendered += ".dirty" else: # exception #1 rendered = "0+untagged.%d.g%s" % (pieces["distance"], pieces["short"]) if pieces["dirty"]: rendered += ".dirty" return rendered def render_pep440_pre(pieces): """TAG[.post.devDISTANCE] -- No -dirty. Exceptions: 1: no tags. 0.post.devDISTANCE """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"]: rendered += ".post.dev%d" % pieces["distance"] else: # exception #1 rendered = "0.post.dev%d" % pieces["distance"] return rendered def render_pep440_post(pieces): """TAG[.postDISTANCE[.dev0]+gHEX] . The ".dev0" means dirty. Note that .dev0 sorts backwards (a dirty tree will appear "older" than the corresponding clean one), but you should not be releasing software with -dirty anyways. Exceptions: 1: no tags. 0.postDISTANCE[.dev0] """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"] or pieces["dirty"]: rendered += ".post%d" % pieces["distance"] if pieces["dirty"]: rendered += ".dev0" rendered += plus_or_dot(pieces) rendered += "g%s" % pieces["short"] else: # exception #1 rendered = "0.post%d" % pieces["distance"] if pieces["dirty"]: rendered += ".dev0" rendered += "+g%s" % pieces["short"] return rendered def render_pep440_old(pieces): """TAG[.postDISTANCE[.dev0]] . The ".dev0" means dirty. Eexceptions: 1: no tags. 0.postDISTANCE[.dev0] """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"] or pieces["dirty"]: rendered += ".post%d" % pieces["distance"] if pieces["dirty"]: rendered += ".dev0" else: # exception #1 rendered = "0.post%d" % pieces["distance"] if pieces["dirty"]: rendered += ".dev0" return rendered def render_git_describe(pieces): """TAG[-DISTANCE-gHEX][-dirty]. Like 'git describe --tags --dirty --always'. Exceptions: 1: no tags. HEX[-dirty] (note: no 'g' prefix) """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"]: rendered += "-%d-g%s" % (pieces["distance"], pieces["short"]) else: # exception #1 rendered = pieces["short"] if pieces["dirty"]: rendered += "-dirty" return rendered def render_git_describe_long(pieces): """TAG-DISTANCE-gHEX[-dirty]. Like 'git describe --tags --dirty --always -long'. The distance/hash is unconditional. Exceptions: 1: no tags. HEX[-dirty] (note: no 'g' prefix) """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] rendered += "-%d-g%s" % (pieces["distance"], pieces["short"]) else: # exception #1 rendered = pieces["short"] if pieces["dirty"]: rendered += "-dirty" return rendered def render(pieces, style): """Render the given version pieces into the requested style.""" if pieces["error"]: return {"version": "unknown", "full-revisionid": pieces.get("long"), "dirty": None, "error": pieces["error"], "date": None} if not style or style == "default": style = "pep440" # the default if style == "pep440": rendered = render_pep440(pieces) elif style == "pep440-pre": rendered = render_pep440_pre(pieces) elif style == "pep440-post": rendered = render_pep440_post(pieces) elif style == "pep440-old": rendered = render_pep440_old(pieces) elif style == "git-describe": rendered = render_git_describe(pieces) elif style == "git-describe-long": rendered = render_git_describe_long(pieces) else: raise ValueError("unknown style '%s'" % style) return {"version": rendered, "full-revisionid": pieces["long"], "dirty": pieces["dirty"], "error": None, "date": pieces.get("date")} def get_versions(): """Get version information or return default if unable to do so.""" # I am in _version.py, which lives at ROOT/VERSIONFILE_SOURCE. If we have # __file__, we can work backwards from there to the root. Some # py2exe/bbfreeze/non-CPython implementations do not do __file__, in which # case we can only use expanded keywords. cfg = get_config() verbose = cfg.verbose try: return git_versions_from_keywords(get_keywords(), cfg.tag_prefix, verbose) except NotThisMethod: pass try: root = os.path.realpath(__file__) # versionfile_source is the relative path from the top of the source # tree (where the .git directory might live) to this file. Invert # this to find the root from __file__. for i in cfg.versionfile_source.split('/'): root = os.path.dirname(root) except NameError: return {"version": "0+unknown", "full-revisionid": None, "dirty": None, "error": "unable to find root of source tree", "date": None} try: pieces = git_pieces_from_vcs(cfg.tag_prefix, root, verbose) return render(pieces, cfg.style) except NotThisMethod: pass try: if cfg.parentdir_prefix: return versions_from_parentdir(cfg.parentdir_prefix, root, verbose) except NotThisMethod: pass return {"version": "0+unknown", "full-revisionid": None, "dirty": None, "error": "unable to compute version", "date": None} statsmodels-0.12.2/statsmodels/api.py000066400000000000000000000041441400612667500176350ustar00rootroot00000000000000# -*- coding: utf-8 -*- # flake8: noqa import os from . import iolib from . import datasets from . import tools from .tools.tools import add_constant, categorical from . import regression from .regression.linear_model import OLS, GLS, WLS, GLSAR from .regression.recursive_ls import RecursiveLS from .regression.quantile_regression import QuantReg from .regression.mixed_linear_model import MixedLM from .genmod import api as genmod from .genmod.api import (GLM, GEE, OrdinalGEE, NominalGEE, families, cov_struct, BinomialBayesMixedGLM, PoissonBayesMixedGLM) from . import robust from .robust.robust_linear_model import RLM from .discrete.discrete_model import (Poisson, Logit, Probit, MNLogit, NegativeBinomial, GeneralizedPoisson, NegativeBinomialP) from .discrete.count_model import (ZeroInflatedPoisson, ZeroInflatedGeneralizedPoisson, ZeroInflatedNegativeBinomialP) from .tsa import api as tsa from .duration.survfunc import SurvfuncRight from .duration.hazard_regression import PHReg from .imputation.mice import MICE, MICEData from .imputation.bayes_mi import BayesGaussMI, MI from .nonparametric import api as nonparametric from . import distributions from .__init__ import test from .gam.generalized_additive_model import GLMGam from .gam import api as gam from .graphics.gofplots import qqplot, qqplot_2samples, qqline, ProbPlot from .graphics import api as graphics from .stats import api as stats from .emplike import api as emplike from .duration import api as duration from .multivariate.pca import PCA from .multivariate.manova import MANOVA from .multivariate.factor import Factor from .multivariate import api as multivariate from .formula import api as formula from .iolib.smpickle import load_pickle from .tools.print_version import show_versions from .tools.web import webdoc load = load_pickle from ._version import get_versions __version__ = get_versions()['version'] del get_versions statsmodels-0.12.2/statsmodels/base/000077500000000000000000000000001400612667500174215ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/base/__init__.py000066400000000000000000000001131400612667500215250ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/base/_constraints.py000066400000000000000000000316351400612667500225110ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Thu May 15 16:36:05 2014 Author: Josef Perktold License: BSD-3 """ import numpy as np class LinearConstraints(object): """Class to hold linear constraints information Affine constraints are defined as ``R b = q` where `R` is the constraints matrix and `q` are the constraints values and `b` are the parameters. This is in analogy to patsy's LinearConstraints class but can be pickled. Parameters ---------- constraint_matrix : ndarray R matrix, 2-dim with number of columns equal to the number of parameters. Each row defines one constraint. constraint_values : ndarray 1-dim array of constant values variable_names : list of strings parameter names, used only for display kwds : keyword arguments keywords are attached to the instance. """ def __init__(self, constraint_matrix, constraint_values, variable_names, **kwds): self.constraint_matrix = constraint_matrix self.constraint_values = constraint_values self.variable_names = variable_names # alias for patsy compatibility self.coefs = constraint_matrix self.constants = constraint_values self.__dict__.update(kwds) self.tuple = (self.constraint_matrix, self.constraint_values) def __iter__(self): yield from self.tuple def __getitem__(self, idx): return self.tuple[idx] def __str__(self): def prod_string(v, name): v = np.abs(v) if v != 1: ss = str(v) + " * " + name else: ss = name return ss constraints_strings = [] for r, q in zip(*self): ss = [] for v, name in zip(r, self.variable_names): if v != 0 and ss == []: ss += prod_string(v, name) elif v > 0: ss += " + " + prod_string(v, name) elif v < 0: ss += " - " + prod_string(np.abs(v), name) ss += " = " + str(q.item()) constraints_strings.append(''.join(ss)) return '\n'.join(constraints_strings) @classmethod def from_patsy(cls, lc): """class method to create instance from patsy instance Parameters ---------- lc : instance instance of patsy LinearConstraint, or other instances that have attributes ``lc.coefs, lc.constants, lc.variable_names`` Returns ------- instance of this class """ return cls(lc.coefs, lc.constants, lc.variable_names) class TransformRestriction(object): """Transformation for linear constraints `R params = q` Note, the transformation from the reduced to the full parameters is an affine and not a linear transformation if q is not zero. Parameters ---------- R : array_like Linear restriction matrix q : arraylike or None values of the linear restrictions Notes ----- The reduced parameters are not sorted with respect to constraints. TODO: error checking, eg. inconsistent constraints, how? Inconsistent constraints will raise an exception in the calculation of the constant or offset. However, homogeneous constraints, where q=0, will can have a solution where the relevant parameters are constraint to be zero, as in the following example:: b1 + b2 = 0 and b1 + 2*b2 = 0, implies that b2 = 0. The transformation applied from full to reduced parameter space does not raise and exception if the constraint does not hold. TODO: maybe change this, what's the behavior in this case? The `reduce` transform is applied to the array of explanatory variables, `exog`, when transforming a linear model to impose the constraints. """ def __init__(self, R, q=None): # The calculations are based on Stata manual for makecns R = self.R = np.atleast_2d(R) if q is not None: q = self.q = np.asarray(q) k_constr, k_vars = R.shape self.k_constr, self.k_vars = k_constr, k_vars self.k_unconstr = k_vars - k_constr m = np.eye(k_vars) - R.T.dot(np.linalg.pinv(R).T) evals, evecs = np.linalg.eigh(m) # This normalizes the transformation so the larges element is 1. # It makes it easier to interpret simple restrictions, e.g. b1 + b2 = 0 # TODO: make this work, there is something wrong, does not round-trip # need to adjust constant #evecs_maxabs = np.max(np.abs(evecs), 0) #evecs = evecs / evecs_maxabs self.evals = evals self.evecs = evecs # temporarily attach as attribute L = self.L = evecs[:, :k_constr] self.transf_mat = evecs[:, k_constr:] if q is not None: # use solve instead of inv #self.constant = q.T.dot(np.linalg.inv(L.T.dot(R.T)).dot(L.T)) try: self.constant = q.T.dot(np.linalg.solve(L.T.dot(R.T), L.T)) except np.linalg.linalg.LinAlgError as e: raise ValueError('possibly inconsistent constraints. error ' 'generated by\n%r' % (e, )) else: self.constant = 0 def expand(self, params_reduced): """transform from the reduced to the full parameter space Parameters ---------- params_reduced : array_like parameters in the transformed space Returns ------- params : array_like parameters in the original space Notes ----- If the restriction is not homogeneous, i.e. q is not equal to zero, then this is an affine transform. """ params_reduced = np.asarray(params_reduced) return self.transf_mat.dot(params_reduced.T).T + self.constant def reduce(self, params): """transform from the full to the reduced parameter space Parameters ---------- params : array_like parameters or data in the original space Returns ------- params_reduced : array_like parameters in the transformed space This transform can be applied to the original parameters as well as to the data. If params is 2-d, then each row is transformed. """ params = np.asarray(params) return params.dot(self.transf_mat) def transform_params_constraint(params, Sinv, R, q): """find the parameters that statisfy linear constraint from unconstrained The linear constraint R params = q is imposed. Parameters ---------- params : array_like unconstrained parameters Sinv : ndarray, 2d, symmetric covariance matrix of the parameter estimate R : ndarray, 2d constraint matrix q : ndarray, 1d values of the constraint Returns ------- params_constraint : ndarray parameters of the same length as params satisfying the constraint Notes ----- This is the exact formula for OLS and other linear models. It will be a local approximation for nonlinear models. TODO: Is Sinv always the covariance matrix? In the linear case it can be (X'X)^{-1} or sigmahat^2 (X'X)^{-1}. My guess is that this is the point in the subspace that satisfies the constraint that has minimum Mahalanobis distance. Proof ? """ rsr = R.dot(Sinv).dot(R.T) reduction = Sinv.dot(R.T).dot(np.linalg.solve(rsr, R.dot(params) - q)) return params - reduction def fit_constrained(model, constraint_matrix, constraint_values, start_params=None, fit_kwds=None): # note: self is model instance """fit model subject to linear equality constraints The constraints are of the form `R params = q` where R is the constraint_matrix and q is the vector of constraint_values. The estimation creates a new model with transformed design matrix, exog, and converts the results back to the original parameterization. Parameters ---------- model: model instance An instance of a model, see limitations in Notes section constraint_matrix : array_like, 2D This is R in the linear equality constraint `R params = q`. The number of columns needs to be the same as the number of columns in exog. constraint_values : This is `q` in the linear equality constraint `R params = q` If it is a tuple, then the constraint needs to be given by two arrays (constraint_matrix, constraint_value), i.e. (R, q). Otherwise, the constraints can be given as strings or list of strings. see t_test for details start_params : None or array_like starting values for the optimization. `start_params` needs to be given in the original parameter space and are internally transformed. **fit_kwds : keyword arguments fit_kwds are used in the optimization of the transformed model. Returns ------- params : ndarray ? estimated parameters (in the original parameterization cov_params : ndarray covariance matrix of the parameter estimates. This is a reverse transformation of the covariance matrix of the transformed model given by `cov_params()` Note: `fit_kwds` can affect the choice of covariance, e.g. by specifying `cov_type`, which will be reflected in the returned covariance. res_constr : results instance This is the results instance for the created transformed model. Notes ----- Limitations: Models where the number of parameters is different from the number of columns of exog are not yet supported. Requires a model that implement an offset option. """ self = model # internal alias, used for methods if fit_kwds is None: fit_kwds = {} R, q = constraint_matrix, constraint_values endog, exog = self.endog, self.exog transf = TransformRestriction(R, q) exogp_st = transf.reduce(exog) offset = exog.dot(transf.constant.squeeze()) if hasattr(self, 'offset'): offset += self.offset if start_params is not None: start_params = transf.reduce(start_params) #need copy, because we do not want to change it, we do not need deepcopy import copy init_kwds = copy.copy(self._get_init_kwds()) # TODO: refactor to combine with above or offset_all if 'offset' in init_kwds: del init_kwds['offset'] # using offset as keywords is not supported in all modules mod_constr = self.__class__(endog, exogp_st, offset=offset, **init_kwds) res_constr = mod_constr.fit(start_params=start_params, **fit_kwds) params_orig = transf.expand(res_constr.params).squeeze() cov_params = transf.transf_mat.dot(res_constr.cov_params()).dot(transf.transf_mat.T) return params_orig, cov_params, res_constr def fit_constrained_wrap(model, constraints, start_params=None, **fit_kwds): """fit_constraint that returns a results instance This is a development version for fit_constrained methods or fit_constrained as standalone function. It will not work correctly for all models because creating a new results instance is not standardized for use outside the `fit` methods, and might need adjustements for this. This is the prototype for the fit_constrained method that has been added to Poisson and GLM. """ self = model # alias for use as method #constraints = (R, q) # TODO: temporary trailing underscore to not overwrite the monkey # patched version # TODO: decide whether to move the imports from patsy import DesignInfo # we need this import if we copy it to a different module #from statsmodels.base._constraints import fit_constrained # same pattern as in base.LikelihoodModel.t_test lc = DesignInfo(self.exog_names).linear_constraint(constraints) R, q = lc.coefs, lc.constants # TODO: add start_params option, need access to tranformation # fit_constrained needs to do the transformation params, cov, res_constr = fit_constrained(self, R, q, start_params=start_params, fit_kwds=fit_kwds) #create dummy results Instance, TODO: wire up properly res = self.fit(start_params=params, maxiter=0, warn_convergence=False) # we get a wrapper back res._results.params = params res._results.cov_params_default = cov cov_type = fit_kwds.get('cov_type', 'nonrobust') if cov_type == 'nonrobust': res._results.normalized_cov_params = cov / res_constr.scale else: res._results.normalized_cov_params = None k_constr = len(q) res._results.df_resid += k_constr res._results.df_model -= k_constr res._results.constraints = LinearConstraints.from_patsy(lc) res._results.k_constr = k_constr res._results.results_constrained = res_constr return res statsmodels-0.12.2/statsmodels/base/_parameter_inference.py000066400000000000000000000237631400612667500241430ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed May 30 15:11:09 2018 @author: josef """ import numpy as np from scipy import stats # this is a copy from stats._diagnostic_other def _lm_robust(score, constraint_matrix, score_deriv_inv, cov_score, cov_params=None): '''general formula for score/LM test generalized score or lagrange multiplier test for implicit constraints `r(params) = 0`, with gradient `R = d r / d params` linear constraints are given by `R params - q = 0` It is assumed that all arrays are evaluated at the constrained estimates. Parameters ---------- score : ndarray, 1-D derivative of objective function at estimated parameters of constrained model constraint_matrix R : ndarray Linear restriction matrix or Jacobian of nonlinear constraints score_deriv_inv, Ainv : ndarray, symmetric, square inverse of second derivative of objective function TODO: could be inverse of OPG or any other estimator if information matrix equality holds cov_score B : ndarray, symmetric, square covariance matrix of the score. This is the inner part of a sandwich estimator. cov_params V : ndarray, symmetric, square covariance of full parameter vector evaluated at constrained parameter estimate. This can be specified instead of cov_score B. Returns ------- lm_stat : float score/lagrange multiplier statistic p-value : float p-value of the LM test based on chisquare distribution Notes ----- ''' # shorthand alias R, Ainv, B, V = constraint_matrix, score_deriv_inv, cov_score, cov_params k_constraints = np.linalg.matrix_rank(R) tmp = R.dot(Ainv) wscore = tmp.dot(score) # C Ainv score if B is None and V is None: # only Ainv is given, so we assume information matrix identity holds # computational short cut, should be same if Ainv == inv(B) lm_stat = score.dot(Ainv.dot(score)) else: # information matrix identity does not hold if V is None: inner = tmp.dot(B).dot(tmp.T) else: inner = R.dot(V).dot(R.T) #lm_stat2 = wscore.dot(np.linalg.pinv(inner).dot(wscore)) # Let's assume inner is invertible, TODO: check if usecase for pinv exists lm_stat = wscore.dot(np.linalg.solve(inner, wscore)) pval = stats.chi2.sf(lm_stat, k_constraints) return lm_stat, pval, k_constraints def score_test(self, exog_extra=None, params_constrained=None, hypothesis='joint', cov_type=None, cov_kwds=None, k_constraints=None, observed=True): """score test for restrictions or for omitted variables Null Hypothesis : constraints are satisfied Alternative Hypothesis : at least one of the constraints does not hold This allows to specify restricted and unrestricted model properties in three different ways - fit_constrained result: model contains score and hessian function for the full, unrestricted model, but the parameter estimate in the results instance is for the restricted model. This is the case if the model was estimated with fit_constrained. - restricted model with variable addition: If exog_extra is not None, then it is assumed that the current model is a model with zero restrictions and the unrestricted model is given by adding exog_extra as additional explanatory variables. - unrestricted model with restricted parameters explicitly provided. If params_constrained is not None, then the model is assumed to be for the unrestricted model, but the provided parameters are for the restricted model. TODO: This case will currently only work for `nonrobust` cov_type, otherwise we will also need the restriction matrix provided by the user. Parameters ---------- exog_extra : None or array_like Explanatory variables that are jointly tested for inclusion in the model, i.e. omitted variables. params_constrained : array_like estimated parameter of the restricted model. This can be the parameter estimate for the current when testing for omitted variables. hypothesis : str, 'joint' (default) or 'separate' If hypothesis is 'joint', then the chisquare test results for the joint hypothesis that all constraints hold is returned. If hypothesis is 'joint', then z-test results for each constraint is returned. This is currently only implemented for cov_type="nonrobust". cov_type : str Warning: only partially implemented so far, currently only "nonrobust" and "HC0" are supported. If cov_type is None, then the cov_type specified in fit for the Wald tests is used. If the cov_type argument is not None, then it will be used instead of the Wald cov_type given in fit. k_constraints : int or None Number of constraints that were used in the estimation of params restricted relative to the number of exog in the model. This must be provided if no exog_extra are given. If exog_extra is not None, then k_constraints is assumed to be zero if it is None. observed : bool If True, then the observed Hessian is used in calculating the covariance matrix of the score. If false then the expected information matrix is used. This currently only applies to GLM where EIM is available. Warning: This option might still change. Returns ------- chi2_stat : float chisquare statistic for the score test p-value : float P-value of the score test based on the chisquare distribution. df : int Degrees of freedom used in the p-value calculation. This is equal to the number of constraints. Notes ----- Status: experimental, several options are not implemented yet or are not verified yet. Currently available ptions might also still change. cov_type is 'nonrobust': The covariance matrix for the score is based on the Hessian, i.e. observed information matrix or optionally on the expected information matrix. cov_type is 'HC0' The covariance matrix of the score is the simple empirical covariance of score_obs without degrees of freedom correction. """ # TODO: we are computing unnecessary things for cov_type nonrobust model = self.model nobs = model.endog.shape[0] # model.nobs # discrete Poisson does not have nobs if params_constrained is None: params_constrained = self.params cov_type = cov_type if cov_type is not None else self.cov_type r_matrix = None if observed is False: hess_kwd = {'observed': False} else: hess_kwd = {} if exog_extra is None: if hasattr(self, 'constraints'): if isinstance(self.constraints, tuple): r_matrix = self.constraints[0] else: r_matrix = self.constraints.coefs k_constraints = r_matrix.shape[0] else: if k_constraints is None: raise ValueError('if exog_extra is None, then k_constraints' 'needs to be given') score = model.score(params_constrained) score_obs = model.score_obs(params_constrained) hessian = model.hessian(params_constrained, **hess_kwd) else: if cov_type == 'V': raise ValueError('if exog_extra is not None, then cov_type cannot ' 'be V') if hasattr(self, 'constraints'): raise NotImplementedError('if exog_extra is not None, then self' 'should not be a constrained fit result') exog_extra = np.asarray(exog_extra) k_constraints = 0 ex = np.column_stack((model.exog, exog_extra)) k_constraints += ex.shape[1] - model.exog.shape[1] # TODO use diag instead of full np.eye r_matrix = np.eye(len(self.params) + k_constraints)[-k_constraints:] score_factor = model.score_factor(params_constrained) score_obs = (score_factor[:, None] * ex) score = score_obs.sum(0) hessian_factor = model.hessian_factor(params_constrained, **hess_kwd) hessian = -np.dot(ex.T * hessian_factor, ex) if cov_type == 'nonrobust': cov_score_test = -hessian elif cov_type.upper() == 'HC0': hinv = -np.linalg.inv(hessian) cov_score = nobs * np.cov(score_obs.T) # temporary to try out lm = _lm_robust(score, r_matrix, hinv, cov_score, cov_params=None) return lm # alternative is to use only the center, but it is singular # https://github.com/statsmodels/statsmodels/pull/2096#issuecomment-393646205 # cov_score_test_inv = cov_lm_robust(score, r_matrix, hinv, # cov_score, cov_params=None) elif cov_type.upper() == 'V': # TODO: this does not work, V in fit_constrained results is singular # we need cov_params without the zeros in it hinv = -np.linalg.inv(hessian) cov_score = nobs * np.cov(score_obs.T) V = self.cov_params_default # temporary to try out chi2stat = _lm_robust(score, r_matrix, hinv, cov_score, cov_params=V) pval = stats.chi2.sf(chi2stat, k_constraints) return chi2stat, pval else: raise NotImplementedError('only cov_type "nonrobust" is available') if hypothesis == 'joint': chi2stat = score.dot(np.linalg.solve(cov_score_test, score[:, None])) pval = stats.chi2.sf(chi2stat, k_constraints) # return a stats results instance instead? Contrast? return chi2stat, pval, k_constraints elif hypothesis == 'separate': diff = score bse = np.sqrt(np.diag(cov_score_test)) stat = diff / bse pval = stats.norm.sf(np.abs(stat))*2 return stat, pval else: raise NotImplementedError('only hypothesis "joint" is available') statsmodels-0.12.2/statsmodels/base/_penalized.py000066400000000000000000000166261400612667500221200ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun May 10 08:23:48 2015 Author: Josef Perktold License: BSD-3 """ import numpy as np from ._penalties import NonePenalty from statsmodels.tools.numdiff import approx_fprime_cs, approx_fprime class PenalizedMixin(object): """Mixin class for Maximum Penalized Likelihood Parameters ---------- args and kwds for the model super class penal : None or instance of Penalized function class If penal is None, then NonePenalty is used. pen_weight : float or None factor for weighting the penalization term. If None, then pen_weight is set to nobs. TODO: missing **kwds or explicit keywords TODO: do we adjust the inherited docstrings? We would need templating to add the penalization parameters """ def __init__(self, *args, **kwds): # pop extra kwds before calling super self.penal = kwds.pop('penal', None) self.pen_weight = kwds.pop('pen_weight', None) super(PenalizedMixin, self).__init__(*args, **kwds) # TODO: define pen_weight as average pen_weight? i.e. per observation # I would have prefered len(self.endog) * kwds.get('pen_weight', 1) # or use pen_weight_factor in signature if self.pen_weight is None: self.pen_weight = len(self.endog) if self.penal is None: # unpenalized by default self.penal = NonePenalty() self.pen_weight = 0 self._init_keys.extend(['penal', 'pen_weight']) self._null_drop_keys = getattr(self, '_null_drop_keys', []) self._null_drop_keys.extend(['penal']) def _handle_scale(self, params, scale=None, **kwds): if scale is None: # special handling for GLM if hasattr(self, 'scaletype'): mu = self.predict(params) scale = self.estimate_scale(mu) else: scale = 1 return scale def loglike(self, params, pen_weight=None, **kwds): """ Log-likelihood of model at params """ if pen_weight is None: pen_weight = self.pen_weight llf = super(PenalizedMixin, self).loglike(params, **kwds) if pen_weight != 0: scale = self._handle_scale(params, **kwds) llf -= 1/scale * pen_weight * self.penal.func(params) return llf def loglikeobs(self, params, pen_weight=None, **kwds): """ Log-likelihood of model observations at params """ if pen_weight is None: pen_weight = self.pen_weight llf = super(PenalizedMixin, self).loglikeobs(params, **kwds) nobs_llf = float(llf.shape[0]) if pen_weight != 0: scale = self._handle_scale(params, **kwds) llf -= 1/scale * pen_weight / nobs_llf * self.penal.func(params) return llf def score_numdiff(self, params, pen_weight=None, method='fd', **kwds): """score based on finite difference derivative """ if pen_weight is None: pen_weight = self.pen_weight loglike = lambda p: self.loglike(p, pen_weight=pen_weight, **kwds) if method == 'cs': return approx_fprime_cs(params, loglike) elif method == 'fd': return approx_fprime(params, loglike, centered=True) else: raise ValueError('method not recognized, should be "fd" or "cs"') def score(self, params, pen_weight=None, **kwds): """ Gradient of model at params """ if pen_weight is None: pen_weight = self.pen_weight sc = super(PenalizedMixin, self).score(params, **kwds) if pen_weight != 0: scale = self._handle_scale(params, **kwds) sc -= 1/scale * pen_weight * self.penal.deriv(params) return sc def score_obs(self, params, pen_weight=None, **kwds): """ Gradient of model observations at params """ if pen_weight is None: pen_weight = self.pen_weight sc = super(PenalizedMixin, self).score_obs(params, **kwds) nobs_sc = float(sc.shape[0]) if pen_weight != 0: scale = self._handle_scale(params, **kwds) sc -= 1/scale * pen_weight / nobs_sc * self.penal.deriv(params) return sc def hessian_numdiff(self, params, pen_weight=None, **kwds): """hessian based on finite difference derivative """ if pen_weight is None: pen_weight = self.pen_weight loglike = lambda p: self.loglike(p, pen_weight=pen_weight, **kwds) from statsmodels.tools.numdiff import approx_hess return approx_hess(params, loglike) def hessian(self, params, pen_weight=None, **kwds): """ Hessian of model at params """ if pen_weight is None: pen_weight = self.pen_weight hess = super(PenalizedMixin, self).hessian(params, **kwds) if pen_weight != 0: scale = self._handle_scale(params, **kwds) h = self.penal.deriv2(params) if h.ndim == 1: hess -= 1/scale * np.diag(pen_weight * h) else: hess -= 1/scale * pen_weight * h return hess def fit(self, method=None, trim=None, **kwds): """minimize negative penalized log-likelihood Parameters ---------- method : None or str Method specifies the scipy optimizer as in nonlinear MLE models. trim : {bool, float} Default is False or None, which uses no trimming. If trim is True or a float, then small parameters are set to zero. If True, then a default threshold is used. If trim is a float, then it will be used as threshold. The default threshold is currently 1e-4, but it will change in future and become penalty function dependent. kwds : extra keyword arguments This keyword arguments are treated in the same way as in the fit method of the underlying model class. Specifically, additional optimizer keywords and cov_type related keywords can be added. """ # If method is None, then we choose a default method ourselves # TODO: temporary hack, need extra fit kwds # we need to rule out fit methods in a model that will not work with # penalization if hasattr(self, 'family'): # assume this identifies GLM kwds.update({'max_start_irls' : 0}) # currently we use `bfgs` by default if method is None: method = 'bfgs' if trim is None: trim = False res = super(PenalizedMixin, self).fit(method=method, **kwds) if trim is False: # note boolean check for "is False", not "False_like" return res else: if trim is True: trim = 1e-4 # trim threshold # TODO: make it penal function dependent # temporary standin, only checked for Poisson and GLM, # and is computationally inefficient drop_index = np.nonzero(np.abs(res.params) < trim)[0] keep_index = np.nonzero(np.abs(res.params) > trim)[0] if drop_index.any(): # TODO: do we need to add results attributes? res_aux = self._fit_zeros(keep_index, **kwds) return res_aux else: return res statsmodels-0.12.2/statsmodels/base/_penalties.py000066400000000000000000000423521400612667500221240ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ A collection of smooth penalty functions. Penalties on vectors take a vector argument and return a scalar penalty. The gradient of the penalty is a vector with the same shape as the input value. Penalties on covariance matrices take two arguments: the matrix and its inverse, both in unpacked (square) form. The returned penalty is a scalar, and the gradient is returned as a vector that contains the gradient with respect to the free elements in the lower triangle of the covariance matrix. All penalties are subtracted from the log-likelihood, so greater penalty values correspond to a greater degree of penalization. The penaties should be smooth so that they can be subtracted from log likelihood functions and optimized using standard methods (i.e. L1 penalties do not belong here). """ import numpy as np class Penalty(object): """ A class for representing a scalar-value penalty. Parameters ---------- weights : array_like A vector of weights that determines the weight of the penalty for each parameter. Notes ----- The class has a member called `alpha` that scales the weights. """ def __init__(self, weights=1.): self.weights = weights self.alpha = 1. def func(self, params): """ A penalty function on a vector of parameters. Parameters ---------- params : array_like A vector of parameters. Returns ------- A scalar penaty value; greater values imply greater penalization. """ raise NotImplementedError def deriv(self, params): """ The gradient of a penalty function. Parameters ---------- params : array_like A vector of parameters Returns ------- The gradient of the penalty with respect to each element in `params`. """ raise NotImplementedError def grad(self, params): import warnings warnings.warn('grad method is deprecated. Use `deriv` instead', DeprecationWarning) return self.deriv(params) def _null_weights(self, params): """work around for Null model This will not be needed anymore when we can use `self._null_drop_keys` as in DiscreteModels. TODO: check other models """ if np.size(self.weights) > 1: if len(params) == 1: raise # raise to identify models where this would be needed return 0. return self.weights class NonePenalty(Penalty): """ A penalty that does not penalize. """ def __init__(self, **kwds): super().__init__() if kwds: import warnings warnings.warn('keyword arguments are be ignored') def func(self, params): if params.ndim == 2: return np.zeros(params.shape[1:]) else: return 0 def deriv(self, params): return np.zeros(params.shape) def deriv2(self, params): # returns diagonal of hessian return np.zeros(params.shape[0]) class L2(Penalty): """ The L2 (ridge) penalty. """ def __init__(self, weights=1.): super().__init__(weights) def func(self, params): return np.sum(self.weights * self.alpha * params**2) def deriv(self, params): return 2 * self.weights * self.alpha * params def deriv2(self, params): return 2 * self.weights * self.alpha * np.ones(len(params)) class L2Univariate(Penalty): """ The L2 (ridge) penalty applied to each parameter. """ def __init__(self, weights=None): if weights is None: self.weights = 1. else: self.weights = weights def func(self, params): return self.weights * params**2 def deriv(self, params): return 2 * self.weights * params def deriv2(self, params): return 2 * self.weights * np.ones(len(params)) class PseudoHuber(Penalty): """ The pseudo-Huber penalty. """ def __init__(self, dlt, weights=1.): super().__init__(weights) self.dlt = dlt def func(self, params): v = np.sqrt(1 + (params / self.dlt)**2) v -= 1 v *= self.dlt**2 return np.sum(self.weights * self.alpha * v, 0) def deriv(self, params): v = np.sqrt(1 + (params / self.dlt)**2) return params * self.weights * self.alpha / v def deriv2(self, params): v = np.power(1 + (params / self.dlt)**2, -3/2) return self.weights * self.alpha * v class SCAD(Penalty): """ The SCAD penalty of Fan and Li. The SCAD penalty is linear around zero as a L1 penalty up to threshold tau. The SCAD penalty is constant for values larger than c*tau. The middle segment is quadratic and connect the two segments with a continuous derivative. The penalty is symmetric around zero. Parameterization follows Boo, Johnson, Li and Tan 2011. Fan and Li use lambda instead of tau, and a instead of c. Fan and Li recommend setting c=3.7. f(x) = { tau |x| if 0 <= |x| < tau { -(|x|^2 - 2 c tau |x| + tau^2) / (2 (c - 1)) if tau <= |x| < c tau { (c + 1) tau^2 / 2 if c tau <= |x| Parameters ---------- tau : float slope and threshold for linear segment c : float factor for second threshold which is c * tau weights : None or array weights for penalty of each parameter. If an entry is zero, then the corresponding parameter will not be penalized. References ---------- Buu, Anne, Norman J. Johnson, Runze Li, and Xianming Tan. "New variable selection methods for zeroâ€inflated count data with applications to the substance abuse field." Statistics in medicine 30, no. 18 (2011): 2326-2340. Fan, Jianqing, and Runze Li. "Variable selection via nonconcave penalized likelihood and its oracle properties." Journal of the American statistical Association 96, no. 456 (2001): 1348-1360. """ def __init__(self, tau, c=3.7, weights=1.): super().__init__(weights) self.tau = tau self.c = c def func(self, params): # 3 segments in absolute value tau = self.tau p_abs = np.atleast_1d(np.abs(params)) res = np.empty(p_abs.shape, p_abs.dtype) res.fill(np.nan) mask1 = p_abs < tau mask3 = p_abs >= self.c * tau res[mask1] = tau * p_abs[mask1] mask2 = ~mask1 & ~mask3 p_abs2 = p_abs[mask2] tmp = (p_abs2**2 - 2 * self.c * tau * p_abs2 + tau**2) res[mask2] = -tmp / (2 * (self.c - 1)) res[mask3] = (self.c + 1) * tau**2 / 2. return (self.weights * res).sum(0) def deriv(self, params): # 3 segments in absolute value tau = self.tau p = np.atleast_1d(params) p_abs = np.abs(p) p_sign = np.sign(p) res = np.empty(p_abs.shape) res.fill(np.nan) mask1 = p_abs < tau mask3 = p_abs >= self.c * tau mask2 = ~mask1 & ~mask3 res[mask1] = p_sign[mask1] * tau tmp = p_sign[mask2] * (p_abs[mask2] - self.c * tau) res[mask2] = -tmp / (self.c - 1) res[mask3] = 0 return self.weights * res def deriv2(self, params): """Second derivative of function This returns scalar or vector in same shape as params, not a square Hessian. If the return is 1 dimensional, then it is the diagonal of the Hessian. """ # 3 segments in absolute value tau = self.tau p = np.atleast_1d(params) p_abs = np.abs(p) res = np.zeros(p_abs.shape) mask1 = p_abs < tau mask3 = p_abs >= self.c * tau mask2 = ~mask1 & ~mask3 res[mask2] = -1 / (self.c - 1) return self.weights * res class SCADSmoothed(SCAD): """ The SCAD penalty of Fan and Li, quadratically smoothed around zero. This follows Fan and Li 2001 equation (3.7). Parameterization follows Boo, Johnson, Li and Tan 2011 see docstring of SCAD Parameters ---------- tau : float slope and threshold for linear segment c : float factor for second threshold c0 : float threshold for quadratically smoothed segment restriction : None or array linear constraints for Notes ----- TODO: Use delegation instead of subclassing, so smoothing can be added to all penalty classes. """ def __init__(self, tau, c=3.7, c0=None, weights=1., restriction=None): super().__init__(tau, c=c, weights=weights) self.tau = tau self.c = c self.c0 = c0 if c0 is not None else tau * 0.1 if self.c0 > tau: raise ValueError('c0 cannot be larger than tau') # get coefficients for quadratic approximation c0 = self.c0 # need to temporarily override weights for call to super weights = self.weights self.weights = 1. deriv_c0 = super(SCADSmoothed, self).deriv(c0) value_c0 = super(SCADSmoothed, self).func(c0) self.weights = weights self.aq1 = value_c0 - 0.5 * deriv_c0 * c0 self.aq2 = 0.5 * deriv_c0 / c0 self.restriction = restriction def func(self, params): # workaround for Null model weights = self._null_weights(params) # TODO: `and np.size(params) > 1` is hack for llnull, need better solution if self.restriction is not None and np.size(params) > 1: params = self.restriction.dot(params) # need to temporarily override weights for call to super # Note: we have the same problem with `restriction` self_weights = self.weights self.weights = 1. value = super(SCADSmoothed, self).func(params[None, ...]) self.weights = self_weights # shift down so func(0) == 0 value -= self.aq1 # change the segment corrsponding to quadratic approximation p_abs = np.atleast_1d(np.abs(params)) mask = p_abs < self.c0 p_abs_masked = p_abs[mask] value[mask] = self.aq2 * p_abs_masked**2 return (weights * value).sum(0) def deriv(self, params): # workaround for Null model weights = self._null_weights(params) if self.restriction is not None and np.size(params) > 1: params = self.restriction.dot(params) # need to temporarily override weights for call to super self_weights = self.weights self.weights = 1. value = super(SCADSmoothed, self).deriv(params) self.weights = self_weights #change the segment corrsponding to quadratic approximation p = np.atleast_1d(params) mask = np.abs(p) < self.c0 value[mask] = 2 * self.aq2 * p[mask] if self.restriction is not None and np.size(params) > 1: return weights * value.dot(self.restriction) else: return weights * value def deriv2(self, params): # workaround for Null model weights = self._null_weights(params) if self.restriction is not None and np.size(params) > 1: params = self.restriction.dot(params) # need to temporarily override weights for call to super self_weights = self.weights self.weights = 1. value = super(SCADSmoothed, self).deriv2(params) self.weights = self_weights # change the segment corrsponding to quadratic approximation p = np.atleast_1d(params) mask = np.abs(p) < self.c0 value[mask] = 2 * self.aq2 if self.restriction is not None and np.size(params) > 1: # note: super returns 1d array for diag, i.e. hessian_diag # TODO: weights are missing return (self.restriction.T * (weights * value) ).dot(self.restriction) else: return weights * value class ConstraintsPenalty(object): """ Penalty applied to linear transformation of parameters Parameters ---------- penalty: instance of penalty function currently this requires an instance of a univariate, vectorized penalty class weights : None or ndarray weights for adding penalties of transformed params restriction : None or ndarray If it is not None, then restriction defines a linear transformation of the parameters. The penalty function is applied to each transformed parameter independently. Notes ----- `restrictions` allows us to impose penalization on contrasts or stochastic constraints of the original parameters. Examples for these contrast are difference penalities or all pairs penalties. """ def __init__(self, penalty, weights=None, restriction=None): self.penalty = penalty if weights is None: self.weights = 1. else: self.weights = weights if restriction is not None: restriction = np.asarray(restriction) self.restriction = restriction def func(self, params): """evaluate penalty function at params Parameter --------- params : ndarray array of parameters at which derivative is evaluated Returns ------- deriv2 : ndarray value(s) of penalty function """ # TODO: `and np.size(params) > 1` is hack for llnull, need better solution # Is this still needed? it seems to work without if self.restriction is not None: params = self.restriction.dot(params) value = self.penalty.func(params) return (self.weights * value.T).T.sum(0) def deriv(self, params): """first derivative of penalty function w.r.t. params Parameter --------- params : ndarray array of parameters at which derivative is evaluated Returns ------- deriv2 : ndarray array of first partial derivatives """ if self.restriction is not None: params = self.restriction.dot(params) value = self.penalty.deriv(params) if self.restriction is not None: return self.weights * value.T.dot(self.restriction) else: return (self.weights * value.T) grad = deriv def deriv2(self, params): """second derivative of penalty function w.r.t. params Parameter --------- params : ndarray array of parameters at which derivative is evaluated Returns ------- deriv2 : ndarray, 2-D second derivative matrix """ if self.restriction is not None: params = self.restriction.dot(params) value = self.penalty.deriv2(params) if self.restriction is not None: # note: univariate penalty returns 1d array for diag, # i.e. hessian_diag v = (self.restriction.T * value * self.weights) value = v.dot(self.restriction) else: value = np.diag(self.weights * value) return value class L2ConstraintsPenalty(ConstraintsPenalty): """convenience class of ConstraintsPenalty with L2 penalization """ def __init__(self, weights=None, restriction=None, sigma_prior=None): if sigma_prior is not None: raise NotImplementedError('sigma_prior is not implemented yet') penalty = L2Univariate() super(L2ConstraintsPenalty, self).__init__(penalty, weights=weights, restriction=restriction) class CovariancePenalty(object): def __init__(self, weight): # weight should be scalar self.weight = weight def func(self, mat, mat_inv): """ Parameters ---------- mat : square matrix The matrix to be penalized. mat_inv : square matrix The inverse of `mat`. Returns ------- A scalar penalty value """ raise NotImplementedError def deriv(self, mat, mat_inv): """ Parameters ---------- mat : square matrix The matrix to be penalized. mat_inv : square matrix The inverse of `mat`. Returns ------- A vector containing the gradient of the penalty with respect to each element in the lower triangle of `mat`. """ raise NotImplementedError def grad(self, mat, mat_inv): import warnings warnings.warn('grad method is deprecated. Use `deriv` instead', DeprecationWarning) return self.deriv(mat, mat_inv) class PSD(CovariancePenalty): """ A penalty that converges to +infinity as the argument matrix approaches the boundary of the domain of symmetric, positive definite matrices. """ def func(self, mat, mat_inv): try: cy = np.linalg.cholesky(mat) except np.linalg.LinAlgError: return np.inf return -2 * self.weight * np.sum(np.log(np.diag(cy))) def deriv(self, mat, mat_inv): cy = mat_inv.copy() cy = 2*cy - np.diag(np.diag(cy)) i,j = np.tril_indices(mat.shape[0]) return -self.weight * cy[i,j] statsmodels-0.12.2/statsmodels/base/_screening.py000066400000000000000000000433641400612667500221210ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sat May 19 15:53:21 2018 Author: Josef Perktold License: BSD-3 """ from collections import defaultdict import numpy as np from statsmodels.base._penalties import SCADSmoothed class ScreeningResults(object): """Results for Variable Screening Note: Indices except for exog_idx and in the iterated case also idx_nonzero_batches are based on the combined [exog_keep, exog] array. Attributes ---------- results_final : instance Results instance returned by the final fit of the penalized model, i.e. after trimming exog with params below trimming threshold. results_pen : results instance Results instance of the penalized model before trimming. This includes variables from the last forward selection idx_nonzero index of exog columns in the final selection including exog_keep idx_exog index of exog columns in the final selection for exog candidates, i.e. without exog_keep idx_excl idx of excluded exog based on combined [exog_keep, exog] array. This is the complement of idx_nonzero converged : bool True if the iteration has converged and stopped before maxiter has been reached. False if maxiter has been reached. iterations : int number of iterations in the screening process. Each iteration consists of a forward selection step and a trimming step. history : dict of lists results collected for each iteration during the screening process 'idx_nonzero' 'params_keep'].append(start_params) history['idx_added'].append(idx) The ScreeningResults returned by `screen_exog_iterator` has additional attributes: idx_nonzero_batches : ndarray 2-D Two-dimensional array with batch index in the first column and variable index withing batch in the second column. They can be used jointly as index for the data in the exog_iterator. exog_final_names : list[str] 'var_' where `bidx` is the batch index and `idx` is the index of the selected column withing batch `bidx`. history_batches : dict of lists This provides information about the selected variables within each batch during the first round screening 'idx_nonzero' is based ond the array that includes exog_keep, while 'idx_exog' is the index based on the exog of the batch. """ def __init__(self, screener, **kwds): self.screener = screener self.__dict__.update(**kwds) class VariableScreening(object): """Ultra-high, conditional sure independence screening This is an adjusted version of Fan's sure independence screening. Parameters ---------- model : instance of penalizing model examples: GLMPenalized, PoissonPenalized and LogitPenalized. The attributes of the model instance `pen_weight` and `penal` will be ignored. pen_weight : None or float penalization weight use in SCAD penalized MLE k_add : int number of exog to add during expansion or forward selection see Notes section for tie handling k_max_add : int maximum number of variables to include during variable addition, i.e. forward selection. default is 30 threshold_trim : float threshold for trimming parameters to zero, default is 1e-4 k_max_included : int maximum total number of variables to include in model. ranking_attr : str This determines the result attribute or model method that is used for the ranking of exog to include. The availability of attributes depends on the model. Default is 'resid_pearson', 'model.score_factor' can be used in GLM. ranking_project : bool If ranking_project is True, then the exog candidates for inclusion are first projected on the already included exog before the computation of the ranking measure. This brings the ranking measure closer to the statistic of a score test for variable addition. Notes ----- Status: experimental, tested only on a limited set of models and with a limited set of model options. Tie handling: If there are ties at the decision threshold, then all those tied exog columns are treated in the same way. During forward selection all exog columns with the same boundary value are included. During elimination, the tied columns are not dropped. Consequently, if ties are present, then the number of included exog can be larger than specified by k_add, k_max_add and k_max_included. The screening algorithm works similar to step wise regression. Each iteration of the screening algorithm includes a forward selection step where variables are added to the model, and a backwards selection step where variables are removed. In contrast to step wise regression, we add a fixed number of variables at each forward selection step. The backwards selection step is based on SCAD penalized estimation and trimming of variables with estimated coefficients below a threshold. The tuning parameters can be used to adjust the number of variables to add and to include depending on the size of the dataset. There is currently no automatic tuning parameter selection. Candidate explanatory variables should be standardized or should be on a similar scale because penalization and trimming are based on the absolute values of the parameters. TODOs and current limitations: freq_weights are not supported in this. Candidate ranking uses moment condition with resid_pearson or others without freq_weights. pearson_resid: GLM resid_pearson does not include freq_weights. variable names: do we keep track of those? currently made-up names currently only supports numpy arrays, no exog type check or conversion currently only single columns are selected, no terms (multi column exog) """ def __init__(self, model, pen_weight=None, use_weights=True, k_add=30, k_max_add=30, threshold_trim=1e-4, k_max_included=20, ranking_attr='resid_pearson', ranking_project=True): self.model = model self.model_class = model.__class__ self.init_kwds = model._get_init_kwds() # pen_weight and penal are explicitly included # TODO: check what we want to do here self.init_kwds.pop('pen_weight', None) self.init_kwds.pop('penal', None) self.endog = model.endog self.exog_keep = model.exog self.k_keep = model.exog.shape[1] self.nobs = len(self.endog) self.penal = self._get_penal() if pen_weight is not None: self.pen_weight = pen_weight else: self.pen_weight = self.nobs * 10 # option for screening algorithm self.use_weights = use_weights self.k_add = k_add self.k_max_add = k_max_add self.threshold_trim = threshold_trim self.k_max_included = k_max_included self.ranking_attr = ranking_attr self.ranking_project = ranking_project def _get_penal(self, weights=None): """create new Penalty instance """ return SCADSmoothed(0.1, c0=0.0001, weights=weights) def ranking_measure(self, res_pen, exog, keep=None): """compute measure for ranking exog candidates for inclusion """ endog = self.endog if self.ranking_project: assert res_pen.model.exog.shape[1] == len(keep) ex_incl = res_pen.model.exog[:, keep] exog = exog - ex_incl.dot(np.linalg.pinv(ex_incl).dot(exog)) if self.ranking_attr == 'predicted_poisson': # I keep this for more experiments # TODO: does it really help to change/trim params # we are not reestimating with trimmed model p = res_pen.params.copy() if keep is not None: p[~keep] = 0 predicted = res_pen.model.predict(p) # this is currently hardcoded for Poisson resid_factor = (endog - predicted) / np.sqrt(predicted) elif self.ranking_attr[:6] == 'model.': # use model method, this is intended for score_factor attr = self.ranking_attr.split('.')[1] resid_factor = getattr(res_pen.model, attr)(res_pen.params) if resid_factor.ndim == 2: # for score_factor when extra params are in model resid_factor = resid_factor[:, 0] mom_cond = np.abs(resid_factor.dot(exog))**2 else: # use results attribute resid_factor = getattr(res_pen, self.ranking_attr) mom_cond = np.abs(resid_factor.dot(exog))**2 return mom_cond def screen_exog(self, exog, endog=None, maxiter=100, method='bfgs', disp=False, fit_kwds=None): """screen and select variables (columns) in exog Parameters ---------- exog : ndarray candidate explanatory variables that are screened for inclusion in the model endog : ndarray (optional) use a new endog in the screening model. This is not tested yet, and might not work correctly maxiter : int number of screening iterations method : str optimization method to use in fit, needs to be only of the gradient optimizers disp : bool display option for fit during optimization Returns ------- res_screen : instance of ScreeningResults The attribute `results_final` contains is the results instance with the final model selection. `idx_nonzero` contains the index of the selected exog in the full exog, combined exog that are always kept plust exog_candidates. see ScreeningResults for a full description """ model_class = self.model_class if endog is None: # allow a different endog than used in model endog = self.endog x0 = self.exog_keep k_keep = self.k_keep x1 = exog k_current = x0.shape[1] # TODO: remove the need for x, use x1 separately from x0 # needs change to idx to be based on x1 (candidate variables) x = np.column_stack((x0, x1)) nobs, k_vars = x.shape fkwds = fit_kwds if fit_kwds is not None else {} fit_kwds = {'maxiter': 200, 'disp': False} fit_kwds.update(fkwds) history = defaultdict(list) idx_nonzero = np.arange(k_keep, dtype=int) keep = np.ones(k_keep, np.bool_) idx_excl = np.arange(k_keep, k_vars) mod_pen = model_class(endog, x0, **self.init_kwds) # do not penalize initial estimate mod_pen.pen_weight = 0 res_pen = mod_pen.fit(**fit_kwds) start_params = res_pen.params converged = False idx_old = [] for it in range(maxiter): # candidates for inclusion in next iteration x1 = x[:, idx_excl] mom_cond = self.ranking_measure(res_pen, x1, keep=keep) assert len(mom_cond) == len(idx_excl) mcs = np.sort(mom_cond)[::-1] idx_thr = min((self.k_max_add, k_current + self.k_add, len(mcs))) threshold = mcs[idx_thr] # indices of exog in current expansion model idx = np.concatenate((idx_nonzero, idx_excl[mom_cond > threshold])) start_params2 = np.zeros(len(idx)) start_params2[:len(start_params)] = start_params if self.use_weights: weights = np.ones(len(idx)) weights[:k_keep] = 0 # modify Penalty instance attached to self # damgerous if res_pen is reused self.penal.weights = weights mod_pen = model_class(endog, x[:, idx], penal=self.penal, pen_weight=self.pen_weight, **self.init_kwds) res_pen = mod_pen.fit(method=method, start_params=start_params2, warn_convergence=False, skip_hessian=True, **fit_kwds) keep = np.abs(res_pen.params) > self.threshold_trim # use largest params to keep if keep.sum() > self.k_max_included: # TODO we can use now np.partition with partial sort thresh_params = np.sort(np.abs(res_pen.params))[ -self.k_max_included] keep2 = np.abs(res_pen.params) > thresh_params keep = np.logical_and(keep, keep2) # Note: idx and keep are for current expansion model # idx_nonzero has indices of selected variables in full exog keep[:k_keep] = True # always keep exog_keep idx_nonzero = idx[keep] if disp: print(keep) print(idx_nonzero) # x0 is exog of currently selected model, not used in iteration # x0 = x[:, idx_nonzero] k_current = len(idx_nonzero) start_params = res_pen.params[keep] # use mask to get excluded indices mask_excl = np.ones(k_vars, dtype=bool) mask_excl[idx_nonzero] = False idx_excl = np.nonzero(mask_excl)[0] history['idx_nonzero'].append(idx_nonzero) history['keep'].append(keep) history['params_keep'].append(start_params) history['idx_added'].append(idx) if (len(idx_nonzero) == len(idx_old) and (idx_nonzero == idx_old).all()): converged = True break idx_old = idx_nonzero # final esimate # check that we still have exog_keep assert np.all(idx_nonzero[:k_keep] == np.arange(k_keep)) if self.use_weights: weights = np.ones(len(idx_nonzero)) weights[:k_keep] = 0 # create new Penalty instance to avoide sharing attached penal penal = self._get_penal(weights=weights) else: penal = self.penal mod_final = model_class(endog, x[:, idx_nonzero], penal=penal, pen_weight=self.pen_weight, **self.init_kwds) res_final = mod_final.fit(method=method, start_params=start_params, warn_convergence=False, **fit_kwds) # set exog_names for final model xnames = ['var%4d' % ii for ii in idx_nonzero] res_final.model.exog_names[k_keep:] = xnames[k_keep:] res = ScreeningResults(self, results_pen = res_pen, results_final = res_final, idx_nonzero = idx_nonzero, idx_exog = idx_nonzero[k_keep:] - k_keep, idx_excl = idx_excl, history = history, converged = converged, iterations = it + 1 # it is 0-based ) return res def screen_exog_iterator(self, exog_iterator): """ batched version of screen exog This screens variables in a two step process: In the first step screen_exog is used on each element of the exog_iterator, and the batch winners are collected. In the second step all batch winners are combined into a new array of exog candidates and `screen_exog` is used to select a final model. Parameters ---------- exog_iterator : iterator over ndarrays Returns ------- res_screen_final : instance of ScreeningResults This is the instance returned by the second round call to `screen_exog`. Additional attributes are added to provide more information about the batched selection process. The index of final nonzero variables is `idx_nonzero_batches` which is a 2-dimensional array with batch index in the first column and variable index within batch in the second column. They can be used jointly as index for the data in the exog_iterator. see ScreeningResults for a full description """ k_keep = self.k_keep # res_batches = [] res_idx = [] exog_winner = [] exog_idx = [] for ex in exog_iterator: res_screen = self.screen_exog(ex, maxiter=20) # avoid storing res_screen, only for debugging # res_batches.append(res_screen) res_idx.append(res_screen.idx_nonzero) exog_winner.append(ex[:, res_screen.idx_nonzero[k_keep:] - k_keep]) exog_idx.append(res_screen.idx_nonzero[k_keep:] - k_keep) exog_winner = np.column_stack(exog_winner) res_screen_final = self.screen_exog(exog_winner, maxiter=20) exog_winner_names = ['var%d_%d' % (bidx, idx) for bidx, batch in enumerate(exog_idx) for idx in batch] idx_full = [(bidx, idx) for bidx, batch in enumerate(exog_idx) for idx in batch] ex_final_idx = res_screen_final.idx_nonzero[k_keep:] - k_keep final_names = np.array(exog_winner_names)[ex_final_idx] res_screen_final.idx_nonzero_batches = np.array(idx_full)[ex_final_idx] res_screen_final.exog_final_names = final_names history = {'idx_nonzero': res_idx, 'idx_exog': exog_idx} res_screen_final.history_batches = history return res_screen_final statsmodels-0.12.2/statsmodels/base/covtype.py000066400000000000000000000361471400612667500214770ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Mon Aug 04 08:00:16 2014 Author: Josef Perktold License: BSD-3 """ from statsmodels.compat.python import lzip import numpy as np descriptions = { 'HC0': 'Standard Errors are heteroscedasticity robust (HC0)', 'HC1': 'Standard Errors are heteroscedasticity robust (HC1)', 'HC2': 'Standard Errors are heteroscedasticity robust (HC2)', 'HC3': 'Standard Errors are heteroscedasticity robust (HC3)', 'HAC': 'Standard Errors are heteroscedasticity and autocorrelation ' 'robust (HAC) using {maxlags} lags and ' '{correction} small sample correction', 'fixed_scale': 'Standard Errors are based on fixed scale', 'cluster': 'Standard Errors are robust to cluster correlation (cluster)', 'HAC-Panel': 'Standard Errors are robust to ' 'cluster correlation (HAC-Panel)', 'HAC-Groupsum': 'Driscoll and Kraay Standard Errors are robust to ' 'cluster correlation (HAC-Groupsum)', 'none': 'Covariance matrix not calculated.', 'approx': 'Covariance matrix calculated using numerical ({approx_type}) ' 'differentiation.', 'OPG': 'Covariance matrix calculated using the outer product of ' 'gradients ({approx_type}).', 'OIM': 'Covariance matrix calculated using the observed information ' 'matrix ({approx_type}) described in Harvey (1989).', 'robust': 'Quasi-maximum likelihood covariance matrix used for ' 'robustness to some misspecifications; calculated using ' 'numerical ({approx_type}) differentiation.', 'robust-OIM': 'Quasi-maximum likelihood covariance matrix used for ' 'robustness to some misspecifications; calculated using the ' 'observed information matrix ({approx_type}) described in ' 'Harvey (1989).', 'robust-approx': 'Quasi-maximum likelihood covariance matrix used for ' 'robustness to some misspecifications; calculated using ' 'numerical ({approx_type}) differentiation.', } def normalize_cov_type(cov_type): """ Normalize the cov_type string to a canonical version Parameters ---------- cov_type : str Returns ------- normalized_cov_type : str """ if cov_type == 'nw-panel': cov_type = 'hac-panel' if cov_type == 'nw-groupsum': cov_type = 'hac-groupsum' return cov_type def get_robustcov_results(self, cov_type='HC1', use_t=None, **kwds): """create new results instance with robust covariance as default Parameters ---------- cov_type : str the type of robust sandwich estimator to use. see Notes below use_t : bool If true, then the t distribution is used for inference. If false, then the normal distribution is used. kwds : depends on cov_type Required or optional arguments for robust covariance calculation. see Notes below Returns ------- results : results instance This method creates a new results instance with the requested robust covariance as the default covariance of the parameters. Inferential statistics like p-values and hypothesis tests will be based on this covariance matrix. Notes ----- Warning: Some of the options and defaults in cov_kwds may be changed in a future version. The covariance keywords provide an option 'scaling_factor' to adjust the scaling of the covariance matrix, that is the covariance is multiplied by this factor if it is given and is not `None`. This allows the user to adjust the scaling of the covariance matrix to match other statistical packages. For example, `scaling_factor=(nobs - 1.) / (nobs - k_params)` provides a correction so that the robust covariance matrices match those of Stata in some models like GLM and discrete Models. The following covariance types and required or optional arguments are currently available: - 'HC0', 'HC1', 'HC2', 'HC3' and no keyword arguments: heteroscedasticity robust covariance - 'HAC' and keywords - `maxlag` integer (required) : number of lags to use - `kernel` callable or str (optional) : kernel currently available kernels are ['bartlett', 'uniform'], default is Bartlett - `use_correction` bool (optional) : If true, use small sample correction - 'cluster' and required keyword `groups`, integer group indicator - `groups` array_like, integer (required) : index of clusters or groups - `use_correction` bool (optional) : If True the sandwich covariance is calculated with a small sample correction. If False the the sandwich covariance is calculated without small sample correction. - `df_correction` bool (optional) If True (default), then the degrees of freedom for the inferential statistics and hypothesis tests, such as pvalues, f_pvalue, conf_int, and t_test and f_test, are based on the number of groups minus one instead of the total number of observations minus the number of explanatory variables. `df_resid` of the results instance is adjusted. If False, then `df_resid` of the results instance is not adjusted. - 'hac-groupsum' Driscoll and Kraay, heteroscedasticity and autocorrelation robust standard errors in panel data keywords - `time` array_like (required) : index of time periods - `maxlag` integer (required) : number of lags to use - `kernel` callable or str (optional) : kernel currently available kernels are ['bartlett', 'uniform'], default is Bartlett - `use_correction` False or string in ['hac', 'cluster'] (optional) : If False the the sandwich covariance is calculated without small sample correction. If `use_correction = 'cluster'` (default), then the same small sample correction as in the case of 'covtype='cluster'' is used. - `df_correction` bool (optional) adjustment to df_resid, see cov_type 'cluster' above #TODO: we need more options here - 'hac-panel' heteroscedasticity and autocorrelation robust standard errors in panel data. The data needs to be sorted in this case, the time series for each panel unit or cluster need to be stacked. The membership to a timeseries of an individual or group can be either specified by group indicators or by increasing time periods. keywords - either `groups` or `time` : array_like (required) `groups` : indicator for groups `time` : index of time periods - `maxlag` integer (required) : number of lags to use - `kernel` callable or str (optional) : kernel currently available kernels are ['bartlett', 'uniform'], default is Bartlett - `use_correction` False or string in ['hac', 'cluster'] (optional) : If False the the sandwich covariance is calculated without small sample correction. - `df_correction` bool (optional) adjustment to df_resid, see cov_type 'cluster' above #TODO: we need more options here Reminder: `use_correction` in "hac-groupsum" and "hac-panel" is not bool, needs to be in [False, 'hac', 'cluster'] TODO: Currently there is no check for extra or misspelled keywords, except in the case of cov_type `HCx` """ import statsmodels.stats.sandwich_covariance as sw cov_type = normalize_cov_type(cov_type) if 'kernel' in kwds: kwds['weights_func'] = kwds.pop('kernel') if 'weights_func' in kwds and not callable(kwds['weights_func']): kwds['weights_func'] = sw.kernel_dict[kwds['weights_func']] # pop because HCx raises if any kwds sc_factor = kwds.pop('scaling_factor', None) # TODO: make separate function that returns a robust cov plus info use_self = kwds.pop('use_self', False) if use_self: res = self else: # this does not work for most models, use raw instance instead from fit res = self.__class__(self.model, self.params, normalized_cov_params=self.normalized_cov_params, scale=self.scale) res.cov_type = cov_type # use_t might already be defined by the class, and already set if use_t is None: use_t = self.use_t res.cov_kwds = {'use_t':use_t} # store for information res.use_t = use_t adjust_df = False if cov_type in ['cluster', 'hac-panel', 'hac-groupsum']: df_correction = kwds.get('df_correction', None) # TODO: check also use_correction, do I need all combinations? if df_correction is not False: # i.e. in [None, True]: # user did not explicitely set it to False adjust_df = True res.cov_kwds['adjust_df'] = adjust_df # verify and set kwds, and calculate cov # TODO: this should be outsourced in a function so we can reuse it in # other models # TODO: make it DRYer repeated code for checking kwds if cov_type.upper() in ('HC0', 'HC1', 'HC2', 'HC3'): if kwds: raise ValueError('heteroscedasticity robust covariance ' 'does not use keywords') res.cov_kwds['description'] = descriptions[cov_type.upper()] res.cov_params_default = getattr(self, 'cov_' + cov_type.upper(), None) if res.cov_params_default is None: # results classes that do not have cov_HCx attribute res.cov_params_default = sw.cov_white_simple(self, use_correction=False) elif cov_type.lower() == 'hac': maxlags = kwds['maxlags'] # required?, default in cov_hac_simple res.cov_kwds['maxlags'] = maxlags weights_func = kwds.get('weights_func', sw.weights_bartlett) res.cov_kwds['weights_func'] = weights_func use_correction = kwds.get('use_correction', False) res.cov_kwds['use_correction'] = use_correction res.cov_kwds['description'] = descriptions['HAC'].format( maxlags=maxlags, correction=['without', 'with'][use_correction]) res.cov_params_default = sw.cov_hac_simple(self, nlags=maxlags, weights_func=weights_func, use_correction=use_correction) elif cov_type.lower() == 'cluster': #cluster robust standard errors, one- or two-way groups = kwds['groups'] if not hasattr(groups, 'shape'): groups = np.asarray(groups).T if groups.ndim >= 2: groups = groups.squeeze() res.cov_kwds['groups'] = groups use_correction = kwds.get('use_correction', True) res.cov_kwds['use_correction'] = use_correction if groups.ndim == 1: if adjust_df: # need to find number of groups # duplicate work self.n_groups = n_groups = len(np.unique(groups)) res.cov_params_default = sw.cov_cluster(self, groups, use_correction=use_correction) elif groups.ndim == 2: if hasattr(groups, 'values'): groups = groups.values if adjust_df: # need to find number of groups # duplicate work n_groups0 = len(np.unique(groups[:,0])) n_groups1 = len(np.unique(groups[:, 1])) self.n_groups = (n_groups0, n_groups1) n_groups = min(n_groups0, n_groups1) # use for adjust_df # Note: sw.cov_cluster_2groups has 3 returns res.cov_params_default = sw.cov_cluster_2groups(self, groups, use_correction=use_correction)[0] else: raise ValueError('only two groups are supported') res.cov_kwds['description'] = descriptions['cluster'] elif cov_type.lower() == 'hac-panel': #cluster robust standard errors res.cov_kwds['time'] = time = kwds.get('time', None) res.cov_kwds['groups'] = groups = kwds.get('groups', None) #TODO: nlags is currently required #nlags = kwds.get('nlags', True) #res.cov_kwds['nlags'] = nlags #TODO: `nlags` or `maxlags` res.cov_kwds['maxlags'] = maxlags = kwds['maxlags'] use_correction = kwds.get('use_correction', 'hac') res.cov_kwds['use_correction'] = use_correction weights_func = kwds.get('weights_func', sw.weights_bartlett) res.cov_kwds['weights_func'] = weights_func # TODO: clumsy time index in cov_nw_panel if groups is not None: groups = np.asarray(groups) tt = (np.nonzero(groups[:-1] != groups[1:])[0] + 1).tolist() nobs_ = len(groups) elif time is not None: # TODO: clumsy time index in cov_nw_panel time = np.asarray(time) tt = (np.nonzero(time[1:] < time[:-1])[0] + 1).tolist() nobs_ = len(time) else: raise ValueError('either time or groups needs to be given') groupidx = lzip([0] + tt, tt + [nobs_]) self.n_groups = n_groups = len(groupidx) res.cov_params_default = sw.cov_nw_panel(self, maxlags, groupidx, weights_func=weights_func, use_correction=use_correction) res.cov_kwds['description'] = descriptions['HAC-Panel'] elif cov_type.lower() == 'hac-groupsum': # Driscoll-Kraay standard errors res.cov_kwds['time'] = time = kwds['time'] #TODO: nlags is currently required #nlags = kwds.get('nlags', True) #res.cov_kwds['nlags'] = nlags #TODO: `nlags` or `maxlags` res.cov_kwds['maxlags'] = maxlags = kwds['maxlags'] use_correction = kwds.get('use_correction', 'cluster') res.cov_kwds['use_correction'] = use_correction weights_func = kwds.get('weights_func', sw.weights_bartlett) res.cov_kwds['weights_func'] = weights_func if adjust_df: # need to find number of groups tt = (np.nonzero(time[1:] < time[:-1])[0] + 1) self.n_groups = n_groups = len(tt) + 1 res.cov_params_default = sw.cov_nw_groupsum(self, maxlags, time, weights_func=weights_func, use_correction=use_correction) res.cov_kwds['description'] = descriptions['HAC-Groupsum'] else: raise ValueError('cov_type not recognized. See docstring for ' + 'available options and spelling') # generic optional factor to scale covariance res.cov_kwds['scaling_factor'] = sc_factor if sc_factor is not None: res.cov_params_default *= sc_factor if adjust_df: # Note: df_resid is used for scale and others, add new attribute res.df_resid_inference = n_groups - 1 return res statsmodels-0.12.2/statsmodels/base/data.py000066400000000000000000000575721400612667500207240ustar00rootroot00000000000000""" Base tools for handling various kinds of data structures, attaching metadata to results, and doing data cleaning """ from statsmodels.compat.python import lmap from functools import reduce import numpy as np from pandas import DataFrame, Series, isnull, MultiIndex import statsmodels.tools.data as data_util from statsmodels.tools.decorators import cache_readonly, cache_writable from statsmodels.tools.sm_exceptions import MissingDataError def _asarray_2dcolumns(x): if np.asarray(x).ndim > 1 and np.asarray(x).squeeze().ndim == 1: return def _asarray_2d_null_rows(x): """ Makes sure input is an array and is 2d. Makes sure output is 2d. True indicates a null in the rows of 2d x. """ #Have to have the asarrays because isnull does not account for array_like #input x = np.asarray(x) if x.ndim == 1: x = x[:, None] return np.any(isnull(x), axis=1)[:, None] def _nan_rows(*arrs): """ Returns a boolean array which is True where any of the rows in any of the _2d_ arrays in arrs are NaNs. Inputs can be any mixture of Series, DataFrames or array_like. """ if len(arrs) == 1: arrs += ([[False]],) def _nan_row_maybe_two_inputs(x, y): # check for dtype bc dataframe has dtypes x_is_boolean_array = hasattr(x, 'dtype') and x.dtype == bool and x return np.logical_or(_asarray_2d_null_rows(x), (x_is_boolean_array | _asarray_2d_null_rows(y))) return reduce(_nan_row_maybe_two_inputs, arrs).squeeze() class ModelData(object): """ Class responsible for handling input data and extracting metadata into the appropriate form """ _param_names = None _cov_names = None def __init__(self, endog, exog=None, missing='none', hasconst=None, **kwargs): if data_util._is_recarray(endog) or data_util._is_recarray(exog): import warnings from statsmodels.tools.sm_exceptions import recarray_warning warnings.warn(recarray_warning, FutureWarning) if 'design_info' in kwargs: self.design_info = kwargs.pop('design_info') if 'formula' in kwargs: self.formula = kwargs.pop('formula') if missing != 'none': arrays, nan_idx = self.handle_missing(endog, exog, missing, **kwargs) self.missing_row_idx = nan_idx self.__dict__.update(arrays) # attach all the data arrays self.orig_endog = self.endog self.orig_exog = self.exog self.endog, self.exog = self._convert_endog_exog(self.endog, self.exog) else: self.__dict__.update(kwargs) # attach the extra arrays anyway self.orig_endog = endog self.orig_exog = exog self.endog, self.exog = self._convert_endog_exog(endog, exog) self.const_idx = None self.k_constant = 0 self._handle_constant(hasconst) self._check_integrity() self._cache = {} def __getstate__(self): from copy import copy d = copy(self.__dict__) if "design_info" in d: del d["design_info"] d["restore_design_info"] = True return d def __setstate__(self, d): if "restore_design_info" in d: # NOTE: there may be a more performant way to do this from patsy import dmatrices, PatsyError exc = [] try: data = d['frame'] except KeyError: data = d['orig_endog'].join(d['orig_exog']) for depth in [2, 3, 1, 0, 4]: # sequence is a guess where to likely find it try: _, design = dmatrices(d['formula'], data, eval_env=depth, return_type='dataframe') break except (NameError, PatsyError) as e: exc.append(e) # why do I need a reference from outside except block pass else: raise exc[-1] self.design_info = design.design_info del d["restore_design_info"] self.__dict__.update(d) def _handle_constant(self, hasconst): if hasconst is False or self.exog is None: self.k_constant = 0 self.const_idx = None else: # detect where the constant is check_implicit = False exog_max = np.max(self.exog, axis=0) if not np.isfinite(exog_max).all(): raise MissingDataError('exog contains inf or nans') exog_min = np.min(self.exog, axis=0) const_idx = np.where(exog_max == exog_min)[0].squeeze() self.k_constant = const_idx.size if self.k_constant == 1: if self.exog[:, const_idx].mean() != 0: self.const_idx = int(const_idx) else: # we only have a zero column and no other constant check_implicit = True elif self.k_constant > 1: # we have more than one constant column # look for ones values = [] # keep values if we need != 0 for idx in const_idx: value = self.exog[:, idx].mean() if value == 1: self.k_constant = 1 self.const_idx = int(idx) break values.append(value) else: # we did not break, no column of ones pos = (np.array(values) != 0) if pos.any(): # take the first nonzero column self.k_constant = 1 self.const_idx = int(const_idx[pos.argmax()]) else: # only zero columns check_implicit = True elif self.k_constant == 0: check_implicit = True else: # should not be here pass if check_implicit and not hasconst: # look for implicit constant # Compute rank of augmented matrix augmented_exog = np.column_stack( (np.ones(self.exog.shape[0]), self.exog)) rank_augm = np.linalg.matrix_rank(augmented_exog) rank_orig = np.linalg.matrix_rank(self.exog) self.k_constant = int(rank_orig == rank_augm) self.const_idx = None elif hasconst: # Ensure k_constant is 1 any time hasconst is True # even if one is not found self.k_constant = 1 @classmethod def _drop_nans(cls, x, nan_mask): return x[nan_mask] @classmethod def _drop_nans_2d(cls, x, nan_mask): return x[nan_mask][:, nan_mask] @classmethod def handle_missing(cls, endog, exog, missing, **kwargs): """ This returns a dictionary with keys endog, exog and the keys of kwargs. It preserves Nones. """ none_array_names = [] # patsy's already dropped NaNs in y/X missing_idx = kwargs.pop('missing_idx', None) if missing_idx is not None: # y, X already handled by patsy. add back in later. combined = () combined_names = [] if exog is None: none_array_names += ['exog'] elif exog is not None: combined = (endog, exog) combined_names = ['endog', 'exog'] else: combined = (endog,) combined_names = ['endog'] none_array_names += ['exog'] # deal with other arrays combined_2d = () combined_2d_names = [] if len(kwargs): for key, value_array in kwargs.items(): if value_array is None or value_array.ndim == 0: none_array_names += [key] continue # grab 1d arrays if value_array.ndim == 1: combined += (np.asarray(value_array),) combined_names += [key] elif value_array.squeeze().ndim == 1: combined += (np.asarray(value_array),) combined_names += [key] # grab 2d arrays that are _assumed_ to be symmetric elif value_array.ndim == 2: combined_2d += (np.asarray(value_array),) combined_2d_names += [key] else: raise ValueError("Arrays with more than 2 dimensions " "are not yet handled") if missing_idx is not None: nan_mask = missing_idx updated_row_mask = None if combined: # there were extra arrays not handled by patsy combined_nans = _nan_rows(*combined) if combined_nans.shape[0] != nan_mask.shape[0]: raise ValueError("Shape mismatch between endog/exog " "and extra arrays given to model.") # for going back and updated endog/exog updated_row_mask = combined_nans[~nan_mask] nan_mask |= combined_nans # for updating extra arrays only if combined_2d: combined_2d_nans = _nan_rows(combined_2d) if combined_2d_nans.shape[0] != nan_mask.shape[0]: raise ValueError("Shape mismatch between endog/exog " "and extra 2d arrays given to model.") if updated_row_mask is not None: updated_row_mask |= combined_2d_nans[~nan_mask] else: updated_row_mask = combined_2d_nans[~nan_mask] nan_mask |= combined_2d_nans else: nan_mask = _nan_rows(*combined) if combined_2d: nan_mask = _nan_rows(*(nan_mask[:, None],) + combined_2d) if not np.any(nan_mask): # no missing do not do anything combined = dict(zip(combined_names, combined)) if combined_2d: combined.update(dict(zip(combined_2d_names, combined_2d))) if none_array_names: combined.update(dict(zip(none_array_names, [None] * len(none_array_names)))) if missing_idx is not None: combined.update({'endog': endog}) if exog is not None: combined.update({'exog': exog}) return combined, [] elif missing == 'raise': raise MissingDataError("NaNs were encountered in the data") elif missing == 'drop': nan_mask = ~nan_mask drop_nans = lambda x: cls._drop_nans(x, nan_mask) drop_nans_2d = lambda x: cls._drop_nans_2d(x, nan_mask) combined = dict(zip(combined_names, lmap(drop_nans, combined))) if missing_idx is not None: if updated_row_mask is not None: updated_row_mask = ~updated_row_mask # update endog/exog with this new information endog = cls._drop_nans(endog, updated_row_mask) if exog is not None: exog = cls._drop_nans(exog, updated_row_mask) combined.update({'endog': endog}) if exog is not None: combined.update({'exog': exog}) if combined_2d: combined.update(dict(zip(combined_2d_names, lmap(drop_nans_2d, combined_2d)))) if none_array_names: combined.update(dict(zip(none_array_names, [None] * len(none_array_names)))) return combined, np.where(~nan_mask)[0].tolist() else: raise ValueError("missing option %s not understood" % missing) def _convert_endog_exog(self, endog, exog): # for consistent outputs if endog is (n,1) yarr = self._get_yarr(endog) xarr = None if exog is not None: xarr = self._get_xarr(exog) if xarr.ndim == 1: xarr = xarr[:, None] if xarr.ndim != 2: raise ValueError("exog is not 1d or 2d") return yarr, xarr @cache_writable() def ynames(self): endog = self.orig_endog ynames = self._get_names(endog) if not ynames: ynames = _make_endog_names(self.endog) if len(ynames) == 1: return ynames[0] else: return list(ynames) @cache_writable() def xnames(self): exog = self.orig_exog if exog is not None: xnames = self._get_names(exog) if not xnames: xnames = _make_exog_names(self.exog) return list(xnames) return None @property def param_names(self): # for handling names of 'extra' parameters in summary, etc. return self._param_names or self.xnames @param_names.setter def param_names(self, values): self._param_names = values @property def cov_names(self): """ Labels for covariance matrices In multidimensional models, each dimension of a covariance matrix differs from the number of param_names. If not set, returns param_names """ # for handling names of covariance names in multidimensional models if self._cov_names is not None: return self._cov_names return self.param_names @cov_names.setter def cov_names(self, value): # for handling names of covariance names in multidimensional models self._cov_names = value @cache_readonly def row_labels(self): exog = self.orig_exog if exog is not None: row_labels = self._get_row_labels(exog) else: endog = self.orig_endog row_labels = self._get_row_labels(endog) return row_labels def _get_row_labels(self, arr): return None def _get_names(self, arr): if isinstance(arr, DataFrame): if isinstance(arr.columns, MultiIndex): # Flatten MultiIndexes into "simple" column names return ['_'.join((level for level in c if level)) for c in arr.columns] else: return list(arr.columns) elif isinstance(arr, Series): if arr.name: return [arr.name] else: return else: try: return arr.dtype.names except AttributeError: pass return None def _get_yarr(self, endog): if data_util._is_structured_ndarray(endog): endog = data_util.struct_to_ndarray(endog) endog = np.asarray(endog) if len(endog) == 1: # never squeeze to a scalar if endog.ndim == 1: return endog elif endog.ndim > 1: return np.asarray([endog.squeeze()]) return endog.squeeze() def _get_xarr(self, exog): if data_util._is_structured_ndarray(exog): exog = data_util.struct_to_ndarray(exog) return np.asarray(exog) def _check_integrity(self): if self.exog is not None: if len(self.exog) != len(self.endog): raise ValueError("endog and exog matrices are different sizes") def wrap_output(self, obj, how='columns', names=None): if how == 'columns': return self.attach_columns(obj) elif how == 'rows': return self.attach_rows(obj) elif how == 'cov': return self.attach_cov(obj) elif how == 'dates': return self.attach_dates(obj) elif how == 'columns_eq': return self.attach_columns_eq(obj) elif how == 'cov_eq': return self.attach_cov_eq(obj) elif how == 'generic_columns': return self.attach_generic_columns(obj, names) elif how == 'generic_columns_2d': return self.attach_generic_columns_2d(obj, names) elif how == 'ynames': return self.attach_ynames(obj) elif how == 'multivariate_confint': return self.attach_mv_confint(obj) else: return obj def attach_columns(self, result): return result def attach_columns_eq(self, result): return result def attach_cov(self, result): return result def attach_cov_eq(self, result): return result def attach_rows(self, result): return result def attach_dates(self, result): return result def attach_mv_confint(self, result): return result def attach_generic_columns(self, result, *args, **kwargs): return result def attach_generic_columns_2d(self, result, *args, **kwargs): return result def attach_ynames(self, result): return result class PatsyData(ModelData): def _get_names(self, arr): return arr.design_info.column_names class PandasData(ModelData): """ Data handling class which knows how to reattach pandas metadata to model results """ def _convert_endog_exog(self, endog, exog=None): #TODO: remove this when we handle dtype systematically endog = np.asarray(endog) exog = exog if exog is None else np.asarray(exog) if endog.dtype == object or exog is not None and exog.dtype == object: raise ValueError("Pandas data cast to numpy dtype of object. " "Check input data with np.asarray(data).") return super(PandasData, self)._convert_endog_exog(endog, exog) @classmethod def _drop_nans(cls, x, nan_mask): if isinstance(x, (Series, DataFrame)): return x.loc[nan_mask] else: # extra arguments could be plain ndarrays return super(PandasData, cls)._drop_nans(x, nan_mask) @classmethod def _drop_nans_2d(cls, x, nan_mask): if isinstance(x, (Series, DataFrame)): return x.loc[nan_mask].loc[:, nan_mask] else: # extra arguments could be plain ndarrays return super(PandasData, cls)._drop_nans_2d(x, nan_mask) def _check_integrity(self): endog, exog = self.orig_endog, self.orig_exog # exog can be None and we could be upcasting one or the other if (exog is not None and (hasattr(endog, 'index') and hasattr(exog, 'index')) and not self.orig_endog.index.equals(self.orig_exog.index)): raise ValueError("The indices for endog and exog are not aligned") super(PandasData, self)._check_integrity() def _get_row_labels(self, arr): try: return arr.index except AttributeError: # if we've gotten here it's because endog is pandas and # exog is not, so just return the row labels from endog return self.orig_endog.index def attach_generic_columns(self, result, names): # get the attribute to use column_names = getattr(self, names, None) return Series(result, index=column_names) def attach_generic_columns_2d(self, result, rownames, colnames=None): colnames = colnames or rownames rownames = getattr(self, rownames, None) colnames = getattr(self, colnames, None) return DataFrame(result, index=rownames, columns=colnames) def attach_columns(self, result): # this can either be a 1d array or a scalar # do not squeeze because it might be a 2d row array # if it needs a squeeze, the bug is elsewhere if result.ndim <= 1: return Series(result, index=self.param_names) else: # for e.g., confidence intervals return DataFrame(result, index=self.param_names) def attach_columns_eq(self, result): return DataFrame(result, index=self.xnames, columns=self.ynames) def attach_cov(self, result): return DataFrame(result, index=self.cov_names, columns=self.cov_names) def attach_cov_eq(self, result): return DataFrame(result, index=self.ynames, columns=self.ynames) def attach_rows(self, result): # assumes if len(row_labels) > len(result) it's bc it was truncated # at the front, for AR lags, for example squeezed = result.squeeze() k_endog = np.array(self.ynames, ndmin=1).shape[0] if k_endog > 1 and squeezed.shape == (k_endog,): squeezed = squeezed[None, :] # May be zero-dim, for example in the case of forecast one step in tsa if squeezed.ndim < 2: return Series(squeezed, index=self.row_labels[-len(result):]) else: return DataFrame(result, index=self.row_labels[-len(result):], columns=self.ynames) def attach_dates(self, result): squeezed = result.squeeze() k_endog = np.array(self.ynames, ndmin=1).shape[0] if k_endog > 1 and squeezed.shape == (k_endog,): squeezed = np.asarray(squeezed)[None, :] # May be zero-dim, for example in the case of forecast one step in tsa if squeezed.ndim < 2: return Series(squeezed, index=self.predict_dates) else: return DataFrame(np.asarray(result), index=self.predict_dates, columns=self.ynames) def attach_mv_confint(self, result): return DataFrame(result.reshape((-1, 2)), index=self.cov_names, columns=['lower', 'upper']) def attach_ynames(self, result): squeezed = result.squeeze() # May be zero-dim, for example in the case of forecast one step in tsa if squeezed.ndim < 2: return Series(squeezed, name=self.ynames) else: return DataFrame(result, columns=self.ynames) def _make_endog_names(endog): if endog.ndim == 1 or endog.shape[1] == 1: ynames = ['y'] else: # for VAR ynames = ['y%d' % (i+1) for i in range(endog.shape[1])] return ynames def _make_exog_names(exog): exog_var = exog.var(0) if (exog_var == 0).any(): # assumes one constant in first or last position # avoid exception if more than one constant const_idx = exog_var.argmin() exog_names = ['x%d' % i for i in range(1, exog.shape[1])] exog_names.insert(const_idx, 'const') else: exog_names = ['x%d' % i for i in range(1, exog.shape[1]+1)] return exog_names def handle_missing(endog, exog=None, missing='none', **kwargs): klass = handle_data_class_factory(endog, exog) if missing == 'none': ret_dict = dict(endog=endog, exog=exog) ret_dict.update(kwargs) return ret_dict, None return klass.handle_missing(endog, exog, missing=missing, **kwargs) def handle_data_class_factory(endog, exog): """ Given inputs """ if data_util._is_using_ndarray_type(endog, exog): klass = ModelData elif data_util._is_using_pandas(endog, exog): klass = PandasData elif data_util._is_using_patsy(endog, exog): klass = PatsyData # keep this check last elif data_util._is_using_ndarray(endog, exog): klass = ModelData else: raise ValueError('unrecognized data structures: %s / %s' % (type(endog), type(exog))) return klass def handle_data(endog, exog, missing='none', hasconst=None, **kwargs): # deal with lists and tuples up-front if isinstance(endog, (list, tuple)): endog = np.asarray(endog) if isinstance(exog, (list, tuple)): exog = np.asarray(exog) klass = handle_data_class_factory(endog, exog) return klass(endog, exog=exog, missing=missing, hasconst=hasconst, **kwargs) statsmodels-0.12.2/statsmodels/base/distributed_estimation.py000066400000000000000000000532521400612667500245600ustar00rootroot00000000000000from statsmodels.base.elastic_net import RegularizedResults from statsmodels.stats.regularized_covariance import _calc_nodewise_row, \ _calc_nodewise_weight, _calc_approx_inv_cov from statsmodels.base.model import LikelihoodModelResults from statsmodels.regression.linear_model import OLS import numpy as np """ Distributed estimation routines. Currently, we support several methods of distribution - sequential, has no extra dependencies - parallel - with joblib A variety of backends are supported through joblib This allows for different types of clusters besides standard local clusters. Some examples of backends supported by joblib are - dask.distributed - yarn - ipyparallel The framework is very general and allows for a variety of estimation methods. Currently, these include - debiased regularized estimation - simple coefficient averaging (naive) - regularized - unregularized Currently, the default is regularized estimation with debiasing which follows the methods outlined in Jason D. Lee, Qiang Liu, Yuekai Sun and Jonathan E. Taylor. "Communication-Efficient Sparse Regression: A One-Shot Approach." arXiv:1503.04337. 2015. https://arxiv.org/abs/1503.04337. There are several variables that are taken from the source paper for which the interpretation may not be directly clear from the code, these are mostly used to help form the estimate of the approximate inverse covariance matrix as part of the debiasing procedure. wexog A weighted design matrix used to perform the node-wise regression procedure. nodewise_row nodewise_row is produced as part of the node-wise regression procedure used to produce the approximate inverse covariance matrix. One is produced for each variable using the LASSO. nodewise_weight nodewise_weight is produced using the gamma_hat values for each p to produce weights to reweight the gamma_hat values which are ultimately used to form approx_inv_cov. approx_inv_cov This is the estimate of the approximate inverse covariance matrix. This is used to debiase the coefficient average along with the average gradient. For the OLS case, approx_inv_cov is an approximation for n * (X^T X)^{-1} formed by node-wise regression. """ def _est_regularized_naive(mod, pnum, partitions, fit_kwds=None): """estimates the regularized fitted parameters. Parameters ---------- mod : statsmodels model class instance The model for the current partition. pnum : scalar Index of current partition partitions : scalar Total number of partitions fit_kwds : dict-like or None Keyword arguments to be given to fit_regularized Returns ------- An array of the parameters for the regularized fit """ if fit_kwds is None: raise ValueError("_est_regularized_naive currently " + "requires that fit_kwds not be None.") return mod.fit_regularized(**fit_kwds).params def _est_unregularized_naive(mod, pnum, partitions, fit_kwds=None): """estimates the unregularized fitted parameters. Parameters ---------- mod : statsmodels model class instance The model for the current partition. pnum : scalar Index of current partition partitions : scalar Total number of partitions fit_kwds : dict-like or None Keyword arguments to be given to fit Returns ------- An array of the parameters for the fit """ if fit_kwds is None: raise ValueError("_est_unregularized_naive currently " + "requires that fit_kwds not be None.") return mod.fit(**fit_kwds).params def _join_naive(params_l, threshold=0): """joins the results from each run of _est__naive and returns the mean estimate of the coefficients Parameters ---------- params_l : list A list of arrays of coefficients. threshold : scalar The threshold at which the coefficients will be cut. """ p = len(params_l[0]) partitions = len(params_l) params_mn = np.zeros(p) for params in params_l: params_mn += params params_mn /= partitions params_mn[np.abs(params_mn) < threshold] = 0 return params_mn def _calc_grad(mod, params, alpha, L1_wt, score_kwds): """calculates the log-likelihood gradient for the debiasing Parameters ---------- mod : statsmodels model class instance The model for the current partition. params : array_like The estimated coefficients for the current partition. alpha : scalar or array_like The penalty weight. If a scalar, the same penalty weight applies to all variables in the model. If a vector, it must have the same length as `params`, and contains a penalty weight for each coefficient. L1_wt : scalar The fraction of the penalty given to the L1 penalty term. Must be between 0 and 1 (inclusive). If 0, the fit is a ridge fit, if 1 it is a lasso fit. score_kwds : dict-like or None Keyword arguments for the score function. Returns ------- An array-like object of the same dimension as params Notes ----- In general: gradient l_k(params) where k corresponds to the index of the partition For OLS: X^T(y - X^T params) """ grad = -mod.score(np.asarray(params), **score_kwds) grad += alpha * (1 - L1_wt) return grad def _calc_wdesign_mat(mod, params, hess_kwds): """calculates the weighted design matrix necessary to generate the approximate inverse covariance matrix Parameters ---------- mod : statsmodels model class instance The model for the current partition. params : array_like The estimated coefficients for the current partition. hess_kwds : dict-like or None Keyword arguments for the hessian function. Returns ------- An array-like object, updated design matrix, same dimension as mod.exog """ rhess = np.sqrt(mod.hessian_factor(np.asarray(params), **hess_kwds)) return rhess[:, None] * mod.exog def _est_regularized_debiased(mod, mnum, partitions, fit_kwds=None, score_kwds=None, hess_kwds=None): """estimates the regularized fitted parameters, is the default estimation_method for class DistributedModel. Parameters ---------- mod : statsmodels model class instance The model for the current partition. mnum : scalar Index of current partition. partitions : scalar Total number of partitions. fit_kwds : dict-like or None Keyword arguments to be given to fit_regularized score_kwds : dict-like or None Keyword arguments for the score function. hess_kwds : dict-like or None Keyword arguments for the Hessian function. Returns ------- A tuple of parameters for regularized fit An array-like object of the fitted parameters, params An array-like object for the gradient A list of array like objects for nodewise_row A list of array like objects for nodewise_weight """ score_kwds = {} if score_kwds is None else score_kwds hess_kwds = {} if hess_kwds is None else hess_kwds if fit_kwds is None: raise ValueError("_est_regularized_debiased currently " + "requires that fit_kwds not be None.") else: alpha = fit_kwds["alpha"] if "L1_wt" in fit_kwds: L1_wt = fit_kwds["L1_wt"] else: L1_wt = 1 nobs, p = mod.exog.shape p_part = int(np.ceil((1. * p) / partitions)) params = mod.fit_regularized(**fit_kwds).params grad = _calc_grad(mod, params, alpha, L1_wt, score_kwds) / nobs wexog = _calc_wdesign_mat(mod, params, hess_kwds) nodewise_row_l = [] nodewise_weight_l = [] for idx in range(mnum * p_part, min((mnum + 1) * p_part, p)): nodewise_row = _calc_nodewise_row(wexog, idx, alpha) nodewise_row_l.append(nodewise_row) nodewise_weight = _calc_nodewise_weight(wexog, nodewise_row, idx, alpha) nodewise_weight_l.append(nodewise_weight) return params, grad, nodewise_row_l, nodewise_weight_l def _join_debiased(results_l, threshold=0): """joins the results from each run of _est_regularized_debiased and returns the debiased estimate of the coefficients Parameters ---------- results_l : list A list of tuples each one containing the params, grad, nodewise_row and nodewise_weight values for each partition. threshold : scalar The threshold at which the coefficients will be cut. """ p = len(results_l[0][0]) partitions = len(results_l) params_mn = np.zeros(p) grad_mn = np.zeros(p) nodewise_row_l = [] nodewise_weight_l = [] for r in results_l: params_mn += r[0] grad_mn += r[1] nodewise_row_l.extend(r[2]) nodewise_weight_l.extend(r[3]) nodewise_row_l = np.array(nodewise_row_l) nodewise_weight_l = np.array(nodewise_weight_l) params_mn /= partitions grad_mn *= -1. / partitions approx_inv_cov = _calc_approx_inv_cov(nodewise_row_l, nodewise_weight_l) debiased_params = params_mn + approx_inv_cov.dot(grad_mn) debiased_params[np.abs(debiased_params) < threshold] = 0 return debiased_params def _helper_fit_partition(self, pnum, endog, exog, fit_kwds, init_kwds_e={}): """handles the model fitting for each machine. NOTE: this is primarily handled outside of DistributedModel because joblib cannot handle class methods. Parameters ---------- self : DistributedModel class instance An instance of DistributedModel. pnum : scalar index of current partition. endog : array_like endogenous data for current partition. exog : array_like exogenous data for current partition. fit_kwds : dict-like Keywords needed for the model fitting. init_kwds_e : dict-like Additional init_kwds to add for each partition. Returns ------- estimation_method result. For the default, _est_regularized_debiased, a tuple. """ temp_init_kwds = self.init_kwds.copy() temp_init_kwds.update(init_kwds_e) model = self.model_class(endog, exog, **temp_init_kwds) results = self.estimation_method(model, pnum, self.partitions, fit_kwds=fit_kwds, **self.estimation_kwds) return results class DistributedModel(object): __doc__ = """ Distributed model class Parameters ---------- partitions : scalar The number of partitions that the data will be split into. model_class : statsmodels model class The model class which will be used for estimation. If None this defaults to OLS. init_kwds : dict-like or None Keywords needed for initializing the model, in addition to endog and exog. init_kwds_generator : generator or None Additional keyword generator that produces model init_kwds that may vary based on data partition. The current usecase is for WLS and GLS estimation_method : function or None The method that performs the estimation for each partition. If None this defaults to _est_regularized_debiased. estimation_kwds : dict-like or None Keywords to be passed to estimation_method. join_method : function or None The method used to recombine the results from each partition. If None this defaults to _join_debiased. join_kwds : dict-like or None Keywords to be passed to join_method. results_class : results class or None The class of results that should be returned. If None this defaults to RegularizedResults. results_kwds : dict-like or None Keywords to be passed to results class. Attributes ---------- partitions : scalar See Parameters. model_class : statsmodels model class See Parameters. init_kwds : dict-like See Parameters. init_kwds_generator : generator or None See Parameters. estimation_method : function See Parameters. estimation_kwds : dict-like See Parameters. join_method : function See Parameters. join_kwds : dict-like See Parameters. results_class : results class See Parameters. results_kwds : dict-like See Parameters. Notes ----- Examples -------- """ def __init__(self, partitions, model_class=None, init_kwds=None, estimation_method=None, estimation_kwds=None, join_method=None, join_kwds=None, results_class=None, results_kwds=None): self.partitions = partitions if model_class is None: self.model_class = OLS else: self.model_class = model_class if init_kwds is None: self.init_kwds = {} else: self.init_kwds = init_kwds if estimation_method is None: self.estimation_method = _est_regularized_debiased else: self.estimation_method = estimation_method if estimation_kwds is None: self.estimation_kwds = {} else: self.estimation_kwds = estimation_kwds if join_method is None: self.join_method = _join_debiased else: self.join_method = join_method if join_kwds is None: self.join_kwds = {} else: self.join_kwds = join_kwds if results_class is None: self.results_class = RegularizedResults else: self.results_class = results_class if results_kwds is None: self.results_kwds = {} else: self.results_kwds = results_kwds def fit(self, data_generator, fit_kwds=None, parallel_method="sequential", parallel_backend=None, init_kwds_generator=None): """Performs the distributed estimation using the corresponding DistributedModel Parameters ---------- data_generator : generator A generator that produces a sequence of tuples where the first element in the tuple corresponds to an endog array and the element corresponds to an exog array. fit_kwds : dict-like or None Keywords needed for the model fitting. parallel_method : str type of distributed estimation to be used, currently "sequential", "joblib" and "dask" are supported. parallel_backend : None or joblib parallel_backend object used to allow support for more complicated backends, ex: dask.distributed init_kwds_generator : generator or None Additional keyword generator that produces model init_kwds that may vary based on data partition. The current usecase is for WLS and GLS Returns ------- join_method result. For the default, _join_debiased, it returns a p length array. """ if fit_kwds is None: fit_kwds = {} if parallel_method == "sequential": results_l = self.fit_sequential(data_generator, fit_kwds, init_kwds_generator) elif parallel_method == "joblib": results_l = self.fit_joblib(data_generator, fit_kwds, parallel_backend, init_kwds_generator) else: raise ValueError("parallel_method: %s is currently not supported" % parallel_method) params = self.join_method(results_l, **self.join_kwds) # NOTE that currently, the dummy result model that is initialized # here does not use any init_kwds from the init_kwds_generator event # if it is provided. It is possible to imagine an edge case where # this might be a problem but given that the results model instance # does not correspond to any data partition this seems reasonable. res_mod = self.model_class([0], [0], **self.init_kwds) return self.results_class(res_mod, params, **self.results_kwds) def fit_sequential(self, data_generator, fit_kwds, init_kwds_generator=None): """Sequentially performs the distributed estimation using the corresponding DistributedModel Parameters ---------- data_generator : generator A generator that produces a sequence of tuples where the first element in the tuple corresponds to an endog array and the element corresponds to an exog array. fit_kwds : dict-like Keywords needed for the model fitting. init_kwds_generator : generator or None Additional keyword generator that produces model init_kwds that may vary based on data partition. The current usecase is for WLS and GLS Returns ------- join_method result. For the default, _join_debiased, it returns a p length array. """ results_l = [] if init_kwds_generator is None: for pnum, (endog, exog) in enumerate(data_generator): results = _helper_fit_partition(self, pnum, endog, exog, fit_kwds) results_l.append(results) else: tup_gen = enumerate(zip(data_generator, init_kwds_generator)) for pnum, ((endog, exog), init_kwds_e) in tup_gen: results = _helper_fit_partition(self, pnum, endog, exog, fit_kwds, init_kwds_e) results_l.append(results) return results_l def fit_joblib(self, data_generator, fit_kwds, parallel_backend, init_kwds_generator=None): """Performs the distributed estimation in parallel using joblib Parameters ---------- data_generator : generator A generator that produces a sequence of tuples where the first element in the tuple corresponds to an endog array and the element corresponds to an exog array. fit_kwds : dict-like Keywords needed for the model fitting. parallel_backend : None or joblib parallel_backend object used to allow support for more complicated backends, ex: dask.distributed init_kwds_generator : generator or None Additional keyword generator that produces model init_kwds that may vary based on data partition. The current usecase is for WLS and GLS Returns ------- join_method result. For the default, _join_debiased, it returns a p length array. """ from statsmodels.tools.parallel import parallel_func par, f, n_jobs = parallel_func(_helper_fit_partition, self.partitions) if parallel_backend is None and init_kwds_generator is None: results_l = par(f(self, pnum, endog, exog, fit_kwds) for pnum, (endog, exog) in enumerate(data_generator)) elif parallel_backend is not None and init_kwds_generator is None: with parallel_backend: results_l = par(f(self, pnum, endog, exog, fit_kwds) for pnum, (endog, exog) in enumerate(data_generator)) elif parallel_backend is None and init_kwds_generator is not None: tup_gen = enumerate(zip(data_generator, init_kwds_generator)) results_l = par(f(self, pnum, endog, exog, fit_kwds, init_kwds) for pnum, ((endog, exog), init_kwds) in tup_gen) elif parallel_backend is not None and init_kwds_generator is not None: tup_gen = enumerate(zip(data_generator, init_kwds_generator)) with parallel_backend: results_l = par(f(self, pnum, endog, exog, fit_kwds, init_kwds) for pnum, ((endog, exog), init_kwds) in tup_gen) return results_l class DistributedResults(LikelihoodModelResults): """ Class to contain model results Parameters ---------- model : class instance Class instance for model used for distributed data, this particular instance uses fake data and is really only to allow use of methods like predict. params : ndarray Parameter estimates from the fit model. """ def __init__(self, model, params): super(DistributedResults, self).__init__(model, params) def predict(self, exog, *args, **kwargs): """Calls self.model.predict for the provided exog. See Results.predict. Parameters ---------- exog : array_like NOT optional The values for which we want to predict, unlike standard predict this is NOT optional since the data in self.model is fake. *args : Some models can take additional arguments. See the predict method of the model for the details. **kwargs : Some models can take additional keywords arguments. See the predict method of the model for the details. Returns ------- prediction : ndarray, pandas.Series or pandas.DataFrame See self.model.predict """ return self.model.predict(self.params, exog, *args, **kwargs) statsmodels-0.12.2/statsmodels/base/elastic_net.py000066400000000000000000000310411400612667500222640ustar00rootroot00000000000000import numpy as np from statsmodels.base.model import Results import statsmodels.base.wrapper as wrap from statsmodels.tools.decorators import cache_readonly """ Elastic net regularization. Routines for fitting regression models using elastic net regularization. The elastic net minimizes the objective function -llf / nobs + alpha((1 - L1_wt) * sum(params**2) / 2 + L1_wt * sum(abs(params))) The algorithm implemented here closely follows the implementation in the R glmnet package, documented here: http://cran.r-project.org/web/packages/glmnet/index.html and here: http://www.jstatsoft.org/v33/i01/paper This routine should work for any regression model that implements loglike, score, and hess. """ def _gen_npfuncs(k, L1_wt, alpha, loglike_kwds, score_kwds, hess_kwds): """ Negative penalized log-likelihood functions. Returns the negative penalized log-likelihood, its derivative, and its Hessian. The penalty only includes the smooth (L2) term. All three functions have argument signature (x, model), where ``x`` is a point in the parameter space and ``model`` is an arbitrary statsmodels regression model. """ def nploglike(params, model): nobs = model.nobs pen_llf = alpha[k] * (1 - L1_wt) * np.sum(params**2) / 2 llf = model.loglike(np.r_[params], **loglike_kwds) return - llf / nobs + pen_llf def npscore(params, model): nobs = model.nobs pen_grad = alpha[k] * (1 - L1_wt) * params gr = -model.score(np.r_[params], **score_kwds)[0] / nobs return gr + pen_grad def nphess(params, model): nobs = model.nobs pen_hess = alpha[k] * (1 - L1_wt) h = -model.hessian(np.r_[params], **hess_kwds)[0, 0] / nobs + pen_hess return h return nploglike, npscore, nphess def fit_elasticnet(model, method="coord_descent", maxiter=100, alpha=0., L1_wt=1., start_params=None, cnvrg_tol=1e-7, zero_tol=1e-8, refit=False, check_step=True, loglike_kwds=None, score_kwds=None, hess_kwds=None): """ Return an elastic net regularized fit to a regression model. Parameters ---------- model : model object A statsmodels object implementing ``loglike``, ``score``, and ``hessian``. method : {'coord_descent'} Only the coordinate descent algorithm is implemented. maxiter : int The maximum number of iteration cycles (an iteration cycle involves running coordinate descent on all variables). alpha : scalar or array_like The penalty weight. If a scalar, the same penalty weight applies to all variables in the model. If a vector, it must have the same length as `params`, and contains a penalty weight for each coefficient. L1_wt : scalar The fraction of the penalty given to the L1 penalty term. Must be between 0 and 1 (inclusive). If 0, the fit is a ridge fit, if 1 it is a lasso fit. start_params : array_like Starting values for `params`. cnvrg_tol : scalar If `params` changes by less than this amount (in sup-norm) in one iteration cycle, the algorithm terminates with convergence. zero_tol : scalar Any estimated coefficient smaller than this value is replaced with zero. refit : bool If True, the model is refit using only the variables that have non-zero coefficients in the regularized fit. The refitted model is not regularized. check_step : bool If True, confirm that the first step is an improvement and search further if it is not. loglike_kwds : dict-like or None Keyword arguments for the log-likelihood function. score_kwds : dict-like or None Keyword arguments for the score function. hess_kwds : dict-like or None Keyword arguments for the Hessian function. Returns ------- Results A results object. Notes ----- The ``elastic net`` penalty is a combination of L1 and L2 penalties. The function that is minimized is: -loglike/n + alpha*((1-L1_wt)*|params|_2^2/2 + L1_wt*|params|_1) where |*|_1 and |*|_2 are the L1 and L2 norms. The computational approach used here is to obtain a quadratic approximation to the smooth part of the target function: -loglike/n + alpha*(1-L1_wt)*|params|_2^2/2 then repeatedly optimize the L1 penalized version of this function along coordinate axes. """ k_exog = model.exog.shape[1] loglike_kwds = {} if loglike_kwds is None else loglike_kwds score_kwds = {} if score_kwds is None else score_kwds hess_kwds = {} if hess_kwds is None else hess_kwds if np.isscalar(alpha): alpha = alpha * np.ones(k_exog) # Define starting params if start_params is None: params = np.zeros(k_exog) else: params = start_params.copy() btol = 1e-4 params_zero = np.zeros(len(params), dtype=bool) init_args = model._get_init_kwds() # we do not need a copy of init_args b/c get_init_kwds provides new dict init_args['hasconst'] = False model_offset = init_args.pop('offset', None) if 'exposure' in init_args and init_args['exposure'] is not None: if model_offset is None: model_offset = np.log(init_args.pop('exposure')) else: model_offset += np.log(init_args.pop('exposure')) fgh_list = [ _gen_npfuncs(k, L1_wt, alpha, loglike_kwds, score_kwds, hess_kwds) for k in range(k_exog)] converged = False for itr in range(maxiter): # Sweep through the parameters params_save = params.copy() for k in range(k_exog): # Under the active set method, if a parameter becomes # zero we do not try to change it again. # TODO : give the user the option to switch this off if params_zero[k]: continue # Set the offset to account for the variables that are # being held fixed in the current coordinate # optimization. params0 = params.copy() params0[k] = 0 offset = np.dot(model.exog, params0) if model_offset is not None: offset += model_offset # Create a one-variable model for optimization. model_1var = model.__class__( model.endog, model.exog[:, k], offset=offset, **init_args) # Do the one-dimensional optimization. func, grad, hess = fgh_list[k] params[k] = _opt_1d( func, grad, hess, model_1var, params[k], alpha[k]*L1_wt, tol=btol, check_step=check_step) # Update the active set if itr > 0 and np.abs(params[k]) < zero_tol: params_zero[k] = True params[k] = 0. # Check for convergence pchange = np.max(np.abs(params - params_save)) if pchange < cnvrg_tol: converged = True break # Set approximate zero coefficients to be exactly zero params[np.abs(params) < zero_tol] = 0 if not refit: results = RegularizedResults(model, params) results.converged = converged return RegularizedResultsWrapper(results) # Fit the reduced model to get standard errors and other # post-estimation results. ii = np.flatnonzero(params) cov = np.zeros((k_exog, k_exog)) init_args = dict([(k, getattr(model, k, None)) for k in model._init_keys]) if len(ii) > 0: model1 = model.__class__( model.endog, model.exog[:, ii], **init_args) rslt = model1.fit() params[ii] = rslt.params cov[np.ix_(ii, ii)] = rslt.normalized_cov_params else: # Hack: no variables were selected but we need to run fit in # order to get the correct results class. So just fit a model # with one variable. model1 = model.__class__(model.endog, model.exog[:, 0], **init_args) rslt = model1.fit(maxiter=0) # fit may return a results or a results wrapper if issubclass(rslt.__class__, wrap.ResultsWrapper): klass = rslt._results.__class__ else: klass = rslt.__class__ # Not all models have a scale if hasattr(rslt, 'scale'): scale = rslt.scale else: scale = 1. # The degrees of freedom should reflect the number of parameters # in the refit model, not including the zeros that are displayed # to indicate which variables were dropped. See issue #1723 for # discussion about setting df parameters in model and results # classes. p, q = model.df_model, model.df_resid model.df_model = len(ii) model.df_resid = model.nobs - model.df_model # Assuming a standard signature for creating results classes. refit = klass(model, params, cov, scale=scale) refit.regularized = True refit.converged = converged refit.method = method refit.fit_history = {'iteration': itr + 1} # Restore df in model class, see issue #1723 for discussion. model.df_model, model.df_resid = p, q return refit def _opt_1d(func, grad, hess, model, start, L1_wt, tol, check_step=True): """ One-dimensional helper for elastic net. Parameters ---------- func : function A smooth function of a single variable to be optimized with L1 penaty. grad : function The gradient of `func`. hess : function The Hessian of `func`. model : statsmodels model The model being fit. start : real A starting value for the function argument L1_wt : non-negative real The weight for the L1 penalty function. tol : non-negative real A convergence threshold. check_step : bool If True, check that the first step is an improvement and use bisection if it is not. If False, return after the first step regardless. Notes ----- ``func``, ``grad``, and ``hess`` have argument signature (x, model), where ``x`` is a point in the parameter space and ``model`` is the model being fit. If the log-likelihood for the model is exactly quadratic, the global minimum is returned in one step. Otherwise numerical bisection is used. Returns ------- The argmin of the objective function. """ # Overview: # We want to minimize L(x) + L1_wt*abs(x), where L() is a smooth # loss function that includes the log-likelihood and L2 penalty. # This is a 1-dimensional optimization. If L(x) is exactly # quadratic we can solve for the argmin exactly. Otherwise we # approximate L(x) with a quadratic function Q(x) and try to use # the minimizer of Q(x) + L1_wt*abs(x). But if this yields an # uphill step for the actual target function L(x) + L1_wt*abs(x), # then we fall back to a expensive line search. The line search # is never needed for OLS. x = start f = func(x, model) b = grad(x, model) c = hess(x, model) d = b - c*x # The optimum is achieved by hard thresholding to zero if L1_wt > np.abs(d): return 0. # x + h is the minimizer of the Q(x) + L1_wt*abs(x) if d >= 0: h = (L1_wt - b) / c elif d < 0: h = -(L1_wt + b) / c else: return np.nan # If the new point is not uphill for the target function, take it # and return. This check is a bit expensive and un-necessary for # OLS if not check_step: return x + h f1 = func(x + h, model) + L1_wt*np.abs(x + h) if f1 <= f + L1_wt*np.abs(x) + 1e-10: return x + h # Fallback for models where the loss is not quadratic from scipy.optimize import brent x_opt = brent(func, args=(model,), brack=(x-1, x+1), tol=tol) return x_opt class RegularizedResults(Results): """ Results for models estimated using regularization Parameters ---------- model : Model The model instance used to estimate the parameters. params : ndarray The estimated (regularized) parameters. """ def __init__(self, model, params): super(RegularizedResults, self).__init__(model, params) @cache_readonly def fittedvalues(self): """ The predicted values from the model at the estimated parameters. """ return self.model.predict(self.params) class RegularizedResultsWrapper(wrap.ResultsWrapper): _attrs = { 'params': 'columns', 'resid': 'rows', 'fittedvalues': 'rows', } _wrap_attrs = _attrs wrap.populate_wrapper(RegularizedResultsWrapper, # noqa:E305 RegularizedResults) statsmodels-0.12.2/statsmodels/base/l1_cvxopt.py000066400000000000000000000146421400612667500217210ustar00rootroot00000000000000""" Holds files for l1 regularization of LikelihoodModel, using cvxopt. """ import numpy as np import statsmodels.base.l1_solvers_common as l1_solvers_common from cvxopt import solvers, matrix def fit_l1_cvxopt_cp( f, score, start_params, args, kwargs, disp=False, maxiter=100, callback=None, retall=False, full_output=False, hess=None): """ Solve the l1 regularized problem using cvxopt.solvers.cp Specifically: We convert the convex but non-smooth problem .. math:: \\min_\\beta f(\\beta) + \\sum_k\\alpha_k |\\beta_k| via the transformation to the smooth, convex, constrained problem in twice as many variables (adding the "added variables" :math:`u_k`) .. math:: \\min_{\\beta,u} f(\\beta) + \\sum_k\\alpha_k u_k, subject to .. math:: -u_k \\leq \\beta_k \\leq u_k. Parameters ---------- All the usual parameters from LikelhoodModel.fit alpha : non-negative scalar or numpy array (same size as parameters) The weight multiplying the l1 penalty term trim_mode : 'auto, 'size', or 'off' If not 'off', trim (set to zero) parameters that would have been zero if the solver reached the theoretical minimum. If 'auto', trim params using the Theory above. If 'size', trim params if they have very small absolute value size_trim_tol : float or 'auto' (default = 'auto') For use when trim_mode === 'size' auto_trim_tol : float For sue when trim_mode == 'auto'. Use qc_tol : float Print warning and do not allow auto trim when (ii) in "Theory" (above) is violated by this much. qc_verbose : bool If true, print out a full QC report upon failure abstol : float absolute accuracy (default: 1e-7). reltol : float relative accuracy (default: 1e-6). feastol : float tolerance for feasibility conditions (default: 1e-7). refinement : int number of iterative refinement steps when solving KKT equations (default: 1). """ start_params = np.array(start_params).ravel('F') ## Extract arguments # k_params is total number of covariates, possibly including a leading constant. k_params = len(start_params) # The start point x0 = np.append(start_params, np.fabs(start_params)) x0 = matrix(x0, (2 * k_params, 1)) # The regularization parameter alpha = np.array(kwargs['alpha_rescaled']).ravel('F') # Make sure it's a vector alpha = alpha * np.ones(k_params) assert alpha.min() >= 0 ## Wrap up functions for cvxopt f_0 = lambda x: _objective_func(f, x, k_params, alpha, *args) Df = lambda x: _fprime(score, x, k_params, alpha) G = _get_G(k_params) # Inequality constraint matrix, Gx \leq h h = matrix(0.0, (2 * k_params, 1)) # RHS in inequality constraint H = lambda x, z: _hessian_wrapper(hess, x, z, k_params) ## Define the optimization function def F(x=None, z=None): if x is None: return 0, x0 elif z is None: return f_0(x), Df(x) else: return f_0(x), Df(x), H(x, z) ## Convert optimization settings to cvxopt form solvers.options['show_progress'] = disp solvers.options['maxiters'] = maxiter if 'abstol' in kwargs: solvers.options['abstol'] = kwargs['abstol'] if 'reltol' in kwargs: solvers.options['reltol'] = kwargs['reltol'] if 'feastol' in kwargs: solvers.options['feastol'] = kwargs['feastol'] if 'refinement' in kwargs: solvers.options['refinement'] = kwargs['refinement'] ### Call the optimizer results = solvers.cp(F, G, h) x = np.asarray(results['x']).ravel() params = x[:k_params] ### Post-process # QC qc_tol = kwargs['qc_tol'] qc_verbose = kwargs['qc_verbose'] passed = l1_solvers_common.qc_results( params, alpha, score, qc_tol, qc_verbose) # Possibly trim trim_mode = kwargs['trim_mode'] size_trim_tol = kwargs['size_trim_tol'] auto_trim_tol = kwargs['auto_trim_tol'] params, trimmed = l1_solvers_common.do_trim_params( params, k_params, alpha, score, passed, trim_mode, size_trim_tol, auto_trim_tol) ### Pack up return values for statsmodels # TODO These retvals are returned as mle_retvals...but the fit was not ML if full_output: fopt = f_0(x) gopt = float('nan') # Objective is non-differentiable hopt = float('nan') iterations = float('nan') converged = (results['status'] == 'optimal') warnflag = results['status'] retvals = { 'fopt': fopt, 'converged': converged, 'iterations': iterations, 'gopt': gopt, 'hopt': hopt, 'trimmed': trimmed, 'warnflag': warnflag} else: x = np.array(results['x']).ravel() params = x[:k_params] ### Return results if full_output: return params, retvals else: return params def _objective_func(f, x, k_params, alpha, *args): """ The regularized objective function. """ x_arr = np.asarray(x) params = x_arr[:k_params].ravel() u = x_arr[k_params:] # Call the numpy version objective_func_arr = f(params, *args) + (alpha * u).sum() # Return return matrix(objective_func_arr) def _fprime(score, x, k_params, alpha): """ The regularized derivative. """ x_arr = np.asarray(x) params = x_arr[:k_params].ravel() # Call the numpy version # The derivative just appends a vector of constants fprime_arr = np.append(score(params), alpha) # Return return matrix(fprime_arr, (1, 2 * k_params)) def _get_G(k_params): """ The linear inequality constraint matrix. """ I = np.eye(k_params) # noqa:E741 A = np.concatenate((-I, -I), axis=1) B = np.concatenate((I, -I), axis=1) C = np.concatenate((A, B), axis=0) # Return return matrix(C) def _hessian_wrapper(hess, x, z, k_params): """ Wraps the hessian up in the form for cvxopt. cvxopt wants the hessian of the objective function and the constraints. Since our constraints are linear, this part is all zeros. """ x_arr = np.asarray(x) params = x_arr[:k_params].ravel() zh_x = np.asarray(z[0]) * hess(params) zero_mat = np.zeros(zh_x.shape) A = np.concatenate((zh_x, zero_mat), axis=1) B = np.concatenate((zero_mat, zero_mat), axis=1) zh_x_ext = np.concatenate((A, B), axis=0) return matrix(zh_x_ext, (2 * k_params, 2 * k_params)) statsmodels-0.12.2/statsmodels/base/l1_slsqp.py000066400000000000000000000127441400612667500215410ustar00rootroot00000000000000""" Holds files for l1 regularization of LikelihoodModel, using scipy.optimize.slsqp """ import numpy as np from scipy.optimize import fmin_slsqp import statsmodels.base.l1_solvers_common as l1_solvers_common def fit_l1_slsqp( f, score, start_params, args, kwargs, disp=False, maxiter=1000, callback=None, retall=False, full_output=False, hess=None): """ Solve the l1 regularized problem using scipy.optimize.fmin_slsqp(). Specifically: We convert the convex but non-smooth problem .. math:: \\min_\\beta f(\\beta) + \\sum_k\\alpha_k |\\beta_k| via the transformation to the smooth, convex, constrained problem in twice as many variables (adding the "added variables" :math:`u_k`) .. math:: \\min_{\\beta,u} f(\\beta) + \\sum_k\\alpha_k u_k, subject to .. math:: -u_k \\leq \\beta_k \\leq u_k. Parameters ---------- All the usual parameters from LikelhoodModel.fit alpha : non-negative scalar or numpy array (same size as parameters) The weight multiplying the l1 penalty term trim_mode : 'auto, 'size', or 'off' If not 'off', trim (set to zero) parameters that would have been zero if the solver reached the theoretical minimum. If 'auto', trim params using the Theory above. If 'size', trim params if they have very small absolute value size_trim_tol : float or 'auto' (default = 'auto') For use when trim_mode === 'size' auto_trim_tol : float For sue when trim_mode == 'auto'. Use qc_tol : float Print warning and do not allow auto trim when (ii) in "Theory" (above) is violated by this much. qc_verbose : bool If true, print out a full QC report upon failure acc : float (default 1e-6) Requested accuracy as used by slsqp """ start_params = np.array(start_params).ravel('F') ### Extract values # k_params is total number of covariates, # possibly including a leading constant. k_params = len(start_params) # The start point x0 = np.append(start_params, np.fabs(start_params)) # alpha is the regularization parameter alpha = np.array(kwargs['alpha_rescaled']).ravel('F') # Make sure it's a vector alpha = alpha * np.ones(k_params) assert alpha.min() >= 0 # Convert display parameters to scipy.optimize form disp_slsqp = _get_disp_slsqp(disp, retall) # Set/retrieve the desired accuracy acc = kwargs.setdefault('acc', 1e-10) ### Wrap up for use in fmin_slsqp func = lambda x_full: _objective_func(f, x_full, k_params, alpha, *args) f_ieqcons_wrap = lambda x_full: _f_ieqcons(x_full, k_params) fprime_wrap = lambda x_full: _fprime(score, x_full, k_params, alpha) fprime_ieqcons_wrap = lambda x_full: _fprime_ieqcons(x_full, k_params) ### Call the solver results = fmin_slsqp( func, x0, f_ieqcons=f_ieqcons_wrap, fprime=fprime_wrap, acc=acc, iter=maxiter, disp=disp_slsqp, full_output=full_output, fprime_ieqcons=fprime_ieqcons_wrap) params = np.asarray(results[0][:k_params]) ### Post-process # QC qc_tol = kwargs['qc_tol'] qc_verbose = kwargs['qc_verbose'] passed = l1_solvers_common.qc_results( params, alpha, score, qc_tol, qc_verbose) # Possibly trim trim_mode = kwargs['trim_mode'] size_trim_tol = kwargs['size_trim_tol'] auto_trim_tol = kwargs['auto_trim_tol'] params, trimmed = l1_solvers_common.do_trim_params( params, k_params, alpha, score, passed, trim_mode, size_trim_tol, auto_trim_tol) ### Pack up return values for statsmodels optimizers # TODO These retvals are returned as mle_retvals...but the fit was not ML. # This could be confusing someday. if full_output: x_full, fx, its, imode, smode = results fopt = func(np.asarray(x_full)) converged = (imode == 0) warnflag = str(imode) + ' ' + smode iterations = its gopt = float('nan') # Objective is non-differentiable hopt = float('nan') retvals = { 'fopt': fopt, 'converged': converged, 'iterations': iterations, 'gopt': gopt, 'hopt': hopt, 'trimmed': trimmed, 'warnflag': warnflag} ### Return if full_output: return params, retvals else: return params def _get_disp_slsqp(disp, retall): if disp or retall: if disp: disp_slsqp = 1 if retall: disp_slsqp = 2 else: disp_slsqp = 0 return disp_slsqp def _objective_func(f, x_full, k_params, alpha, *args): """ The regularized objective function """ x_params = x_full[:k_params] x_added = x_full[k_params:] ## Return return f(x_params, *args) + (alpha * x_added).sum() def _fprime(score, x_full, k_params, alpha): """ The regularized derivative """ x_params = x_full[:k_params] # The derivative just appends a vector of constants return np.append(score(x_params), alpha) def _f_ieqcons(x_full, k_params): """ The inequality constraints. """ x_params = x_full[:k_params] x_added = x_full[k_params:] # All entries in this vector must be \geq 0 in a feasible solution return np.append(x_params + x_added, x_added - x_params) def _fprime_ieqcons(x_full, k_params): """ Derivative of the inequality constraints """ I = np.eye(k_params) # noqa:E741 A = np.concatenate((I, I), axis=1) B = np.concatenate((-I, I), axis=1) C = np.concatenate((A, B), axis=0) ## Return return C statsmodels-0.12.2/statsmodels/base/l1_solvers_common.py000066400000000000000000000127161400612667500234430ustar00rootroot00000000000000""" Holds common functions for l1 solvers. """ import numpy as np from statsmodels.tools.sm_exceptions import ConvergenceWarning def qc_results(params, alpha, score, qc_tol, qc_verbose=False): """ Theory dictates that one of two conditions holds: i) abs(score[i]) == alpha[i] and params[i] != 0 ii) abs(score[i]) <= alpha[i] and params[i] == 0 qc_results checks to see that (ii) holds, within qc_tol qc_results also checks for nan or results of the wrong shape. Parameters ---------- params : ndarray model parameters. Not including the added variables x_added. alpha : ndarray regularization coefficients score : function Gradient of unregularized objective function qc_tol : float Tolerance to hold conditions (i) and (ii) to for QC check. qc_verbose : bool If true, print out a full QC report upon failure Returns ------- passed : bool True if QC check passed qc_dict : Dictionary Keys are fprime, alpha, params, passed_array Prints ------ Warning message if QC check fails. """ ## Check for fatal errors assert not np.isnan(params).max() assert (params == params.ravel('F')).min(), \ "params should have already been 1-d" ## Start the theory compliance check fprime = score(params) k_params = len(params) passed_array = np.array([True] * k_params) for i in range(k_params): if alpha[i] > 0: # If |fprime| is too big, then something went wrong if (abs(fprime[i]) - alpha[i]) / alpha[i] > qc_tol: passed_array[i] = False qc_dict = dict( fprime=fprime, alpha=alpha, params=params, passed_array=passed_array) passed = passed_array.min() if not passed: num_failed = (~passed_array).sum() message = 'QC check did not pass for %d out of %d parameters' % ( num_failed, k_params) message += '\nTry increasing solver accuracy or number of iterations'\ ', decreasing alpha, or switch solvers' if qc_verbose: message += _get_verbose_addon(qc_dict) import warnings warnings.warn(message, ConvergenceWarning) return passed def _get_verbose_addon(qc_dict): alpha = qc_dict['alpha'] params = qc_dict['params'] fprime = qc_dict['fprime'] passed_array = qc_dict['passed_array'] addon = '\n------ verbose QC printout -----------------' addon = '\n------ Recall the problem was rescaled by 1 / nobs ---' addon += '\n|%-10s|%-10s|%-10s|%-10s|' % ( 'passed', 'alpha', 'fprime', 'param') addon += '\n--------------------------------------------' for i in range(len(alpha)): addon += '\n|%-10s|%-10.3e|%-10.3e|%-10.3e|' % ( passed_array[i], alpha[i], fprime[i], params[i]) return addon def do_trim_params(params, k_params, alpha, score, passed, trim_mode, size_trim_tol, auto_trim_tol): """ Trims (set to zero) params that are zero at the theoretical minimum. Uses heuristics to account for the solver not actually finding the minimum. In all cases, if alpha[i] == 0, then do not trim the ith param. In all cases, do nothing with the added variables. Parameters ---------- params : ndarray model parameters. Not including added variables. k_params : Int Number of parameters alpha : ndarray regularization coefficients score : Function. score(params) should return a 1-d vector of derivatives of the unpenalized objective function. passed : bool True if the QC check passed trim_mode : 'auto, 'size', or 'off' If not 'off', trim (set to zero) parameters that would have been zero if the solver reached the theoretical minimum. If 'auto', trim params using the Theory above. If 'size', trim params if they have very small absolute value size_trim_tol : float or 'auto' (default = 'auto') For use when trim_mode === 'size' auto_trim_tol : float For sue when trim_mode == 'auto'. Use qc_tol : float Print warning and do not allow auto trim when (ii) in "Theory" (above) is violated by this much. Returns ------- params : ndarray Trimmed model parameters trimmed : ndarray of booleans trimmed[i] == True if the ith parameter was trimmed. """ ## Trim the small params trimmed = [False] * k_params if trim_mode == 'off': trimmed = np.array([False] * k_params) elif trim_mode == 'auto' and not passed: import warnings msg = "Could not trim params automatically due to failed QC check. " \ "Trimming using trim_mode == 'size' will still work." warnings.warn(msg, ConvergenceWarning) trimmed = np.array([False] * k_params) elif trim_mode == 'auto' and passed: fprime = score(params) for i in range(k_params): if alpha[i] != 0: if (alpha[i] - abs(fprime[i])) / alpha[i] > auto_trim_tol: params[i] = 0.0 trimmed[i] = True elif trim_mode == 'size': for i in range(k_params): if alpha[i] != 0: if abs(params[i]) < size_trim_tol: params[i] = 0.0 trimmed[i] = True else: raise ValueError( "trim_mode == %s, which is not recognized" % (trim_mode)) return params, np.asarray(trimmed) statsmodels-0.12.2/statsmodels/base/model.py000066400000000000000000003021741400612667500211020ustar00rootroot00000000000000from statsmodels.compat.python import lzip from functools import reduce import warnings import numpy as np from scipy import stats from statsmodels.base.data import handle_data from statsmodels.tools.data import _is_using_pandas from statsmodels.tools.tools import recipr, nan_dot from statsmodels.stats.contrast import (ContrastResults, WaldTestResults, t_test_pairwise) from statsmodels.tools.decorators import (cache_readonly, cached_value, cached_data) import statsmodels.base.wrapper as wrap from statsmodels.tools.numdiff import approx_fprime from statsmodels.tools.sm_exceptions import ValueWarning, \ HessianInversionWarning from statsmodels.formula import handle_formula_data from statsmodels.base.optimizer import Optimizer _model_params_doc = """Parameters ---------- endog : array_like A 1-d endogenous response variable. The dependent variable. exog : array_like A nobs x k array where `nobs` is the number of observations and `k` is the number of regressors. An intercept is not included by default and should be added by the user. See :func:`statsmodels.tools.add_constant`.""" _missing_param_doc = """\ missing : str Available options are 'none', 'drop', and 'raise'. If 'none', no nan checking is done. If 'drop', any observations with nans are dropped. If 'raise', an error is raised. Default is 'none'.""" _extra_param_doc = """ hasconst : None or bool Indicates whether the RHS includes a user-supplied constant. If True, a constant is not checked for and k_constant is set to 1 and all result statistics are calculated as if a constant is present. If False, a constant is not checked for and k_constant is set to 0. **kwargs Extra arguments that are used to set model properties when using the formula interface.""" class Model(object): __doc__ = """ A (predictive) statistical model. Intended to be subclassed not used. %(params_doc)s %(extra_params_doc)s Attributes ---------- exog_names endog_names Notes ----- `endog` and `exog` are references to any data provided. So if the data is already stored in numpy arrays and it is changed then `endog` and `exog` will change as well. """ % {'params_doc': _model_params_doc, 'extra_params_doc': _missing_param_doc + _extra_param_doc} # Maximum number of endogenous variables when using a formula # Default is 1, which is more common. Override in models when needed # Set to None to skip check _formula_max_endog = 1 def __init__(self, endog, exog=None, **kwargs): missing = kwargs.pop('missing', 'none') hasconst = kwargs.pop('hasconst', None) self.data = self._handle_data(endog, exog, missing, hasconst, **kwargs) self.k_constant = self.data.k_constant self.exog = self.data.exog self.endog = self.data.endog self._data_attr = [] self._data_attr.extend(['exog', 'endog', 'data.exog', 'data.endog']) if 'formula' not in kwargs: # will not be able to unpickle without these self._data_attr.extend(['data.orig_endog', 'data.orig_exog']) # store keys for extras if we need to recreate model instance # we do not need 'missing', maybe we need 'hasconst' self._init_keys = list(kwargs.keys()) if hasconst is not None: self._init_keys.append('hasconst') def _get_init_kwds(self): """return dictionary with extra keys used in model.__init__ """ kwds = dict(((key, getattr(self, key, None)) for key in self._init_keys)) return kwds def _handle_data(self, endog, exog, missing, hasconst, **kwargs): data = handle_data(endog, exog, missing, hasconst, **kwargs) # kwargs arrays could have changed, easier to just attach here for key in kwargs: if key in ['design_info', 'formula']: # leave attached to data continue # pop so we do not start keeping all these twice or references try: setattr(self, key, data.__dict__.pop(key)) except KeyError: # panel already pops keys in data handling pass return data @classmethod def from_formula(cls, formula, data, subset=None, drop_cols=None, *args, **kwargs): """ Create a Model from a formula and dataframe. Parameters ---------- formula : str or generic Formula object The formula specifying the model. data : array_like The data for the model. See Notes. subset : array_like An array-like object of booleans, integers, or index values that indicate the subset of df to use in the model. Assumes df is a `pandas.DataFrame`. drop_cols : array_like Columns to drop from the design matrix. Cannot be used to drop terms involving categoricals. *args Additional positional argument that are passed to the model. **kwargs These are passed to the model with one exception. The ``eval_env`` keyword is passed to patsy. It can be either a :class:`patsy:patsy.EvalEnvironment` object or an integer indicating the depth of the namespace to use. For example, the default ``eval_env=0`` uses the calling namespace. If you wish to use a "clean" environment set ``eval_env=-1``. Returns ------- model The model instance. Notes ----- data must define __getitem__ with the keys in the formula terms args and kwargs are passed on to the model instantiation. E.g., a numpy structured or rec array, a dictionary, or a pandas DataFrame. """ # TODO: provide a docs template for args/kwargs from child models # TODO: subset could use syntax. issue #469. if subset is not None: data = data.loc[subset] eval_env = kwargs.pop('eval_env', None) if eval_env is None: eval_env = 2 elif eval_env == -1: from patsy import EvalEnvironment eval_env = EvalEnvironment({}) elif isinstance(eval_env, int): eval_env += 1 # we're going down the stack again missing = kwargs.get('missing', 'drop') if missing == 'none': # with patsy it's drop or raise. let's raise. missing = 'raise' tmp = handle_formula_data(data, None, formula, depth=eval_env, missing=missing) ((endog, exog), missing_idx, design_info) = tmp max_endog = cls._formula_max_endog if (max_endog is not None and endog.ndim > 1 and endog.shape[1] > max_endog): raise ValueError('endog has evaluated to an array with multiple ' 'columns that has shape {0}. This occurs when ' 'the variable converted to endog is non-numeric' ' (e.g., bool or str).'.format(endog.shape)) if drop_cols is not None and len(drop_cols) > 0: cols = [x for x in exog.columns if x not in drop_cols] if len(cols) < len(exog.columns): exog = exog[cols] cols = list(design_info.term_names) for col in drop_cols: try: cols.remove(col) except ValueError: pass # OK if not present design_info = design_info.subset(cols) kwargs.update({'missing_idx': missing_idx, 'missing': missing, 'formula': formula, # attach formula for unpckling 'design_info': design_info}) mod = cls(endog, exog, *args, **kwargs) mod.formula = formula # since we got a dataframe, attach the original mod.data.frame = data return mod @property def endog_names(self): """ Names of endogenous variables. """ return self.data.ynames @property def exog_names(self): """ Names of exogenous variables. """ return self.data.xnames def fit(self): """ Fit a model to data. """ raise NotImplementedError def predict(self, params, exog=None, *args, **kwargs): """ After a model has been fit predict returns the fitted values. This is a placeholder intended to be overwritten by individual models. """ raise NotImplementedError class LikelihoodModel(Model): """ Likelihood model is a subclass of Model. """ def __init__(self, endog, exog=None, **kwargs): super(LikelihoodModel, self).__init__(endog, exog, **kwargs) self.initialize() def initialize(self): """ Initialize (possibly re-initialize) a Model instance. For example, if the the design matrix of a linear model changes then initialized can be used to recompute values using the modified design matrix. """ pass # TODO: if the intent is to re-initialize the model with new data then this # method needs to take inputs... def loglike(self, params): """ Log-likelihood of model. Parameters ---------- params : ndarray The model parameters used to compute the log-likelihood. Notes ----- Must be overridden by subclasses. """ raise NotImplementedError def score(self, params): """ Score vector of model. The gradient of logL with respect to each parameter. Parameters ---------- params : ndarray The parameters to use when evaluating the Hessian. Returns ------- ndarray The score vector evaluated at the parameters. """ raise NotImplementedError def information(self, params): """ Fisher information matrix of model. Returns -1 * Hessian of the log-likelihood evaluated at params. Parameters ---------- params : ndarray The model parameters. """ raise NotImplementedError def hessian(self, params): """ The Hessian matrix of the model. Parameters ---------- params : ndarray The parameters to use when evaluating the Hessian. Returns ------- ndarray The hessian evaluated at the parameters. """ raise NotImplementedError def fit(self, start_params=None, method='newton', maxiter=100, full_output=True, disp=True, fargs=(), callback=None, retall=False, skip_hessian=False, **kwargs): """ Fit method for likelihood based models Parameters ---------- start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. method : str, optional The `method` determines which solver from `scipy.optimize` is used, and it can be chosen from among the following strings: - 'newton' for Newton-Raphson, 'nm' for Nelder-Mead - 'bfgs' for Broyden-Fletcher-Goldfarb-Shanno (BFGS) - 'lbfgs' for limited-memory BFGS with optional box constraints - 'powell' for modified Powell's method - 'cg' for conjugate gradient - 'ncg' for Newton-conjugate gradient - 'basinhopping' for global basin-hopping solver - 'minimize' for generic wrapper of scipy minimize (BFGS by default) The explicit arguments in `fit` are passed to the solver, with the exception of the basin-hopping solver. Each solver has several optional arguments that are not the same across solvers. See the notes section below (or scipy.optimize) for the available arguments and for the list of explicit arguments that the basin-hopping solver supports. maxiter : int, optional The maximum number of iterations to perform. full_output : bool, optional Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. disp : bool, optional Set to True to print convergence messages. fargs : tuple, optional Extra arguments passed to the likelihood function, i.e., loglike(x,*args) callback : callable callback(xk), optional Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool, optional Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. skip_hessian : bool, optional If False (default), then the negative inverse hessian is calculated after the optimization. If True, then the hessian will not be calculated. However, it will be available in methods that use the hessian in the optimization (currently only with `"newton"`). kwargs : keywords All kwargs are passed to the chosen solver with one exception. The following keyword controls what happens after the fit:: warn_convergence : bool, optional If True, checks the model for the converged flag. If the converged flag is False, a ConvergenceWarning is issued. Notes ----- The 'basinhopping' solver ignores `maxiter`, `retall`, `full_output` explicit arguments. Optional arguments for solvers (see returned Results.mle_settings):: 'newton' tol : float Relative error in params acceptable for convergence. 'nm' -- Nelder Mead xtol : float Relative error in params acceptable for convergence ftol : float Relative error in loglike(params) acceptable for convergence maxfun : int Maximum number of function evaluations to make. 'bfgs' gtol : float Stop when norm of gradient is less than gtol. norm : float Order of norm (np.Inf is max, -np.Inf is min) epsilon If fprime is approximated, use this value for the step size. Only relevant if LikelihoodModel.score is None. 'lbfgs' m : int This many terms are used for the Hessian approximation. factr : float A stop condition that is a variant of relative error. pgtol : float A stop condition that uses the projected gradient. epsilon If fprime is approximated, use this value for the step size. Only relevant if LikelihoodModel.score is None. maxfun : int Maximum number of function evaluations to make. bounds : sequence (min, max) pairs for each element in x, defining the bounds on that parameter. Use None for one of min or max when there is no bound in that direction. 'cg' gtol : float Stop when norm of gradient is less than gtol. norm : float Order of norm (np.Inf is max, -np.Inf is min) epsilon : float If fprime is approximated, use this value for the step size. Can be scalar or vector. Only relevant if Likelihoodmodel.score is None. 'ncg' fhess_p : callable f'(x,*args) Function which computes the Hessian of f times an arbitrary vector, p. Should only be supplied if LikelihoodModel.hessian is None. avextol : float Stop when the average relative error in the minimizer falls below this amount. epsilon : float or ndarray If fhess is approximated, use this value for the step size. Only relevant if Likelihoodmodel.hessian is None. 'powell' xtol : float Line-search error tolerance ftol : float Relative error in loglike(params) for acceptable for convergence. maxfun : int Maximum number of function evaluations to make. start_direc : ndarray Initial direction set. 'basinhopping' niter : int The number of basin hopping iterations. niter_success : int Stop the run if the global minimum candidate remains the same for this number of iterations. T : float The "temperature" parameter for the accept or reject criterion. Higher "temperatures" mean that larger jumps in function value will be accepted. For best results `T` should be comparable to the separation (in function value) between local minima. stepsize : float Initial step size for use in the random displacement. interval : int The interval for how often to update the `stepsize`. minimizer : dict Extra keyword arguments to be passed to the minimizer `scipy.optimize.minimize()`, for example 'method' - the minimization method (e.g. 'L-BFGS-B'), or 'tol' - the tolerance for termination. Other arguments are mapped from explicit argument of `fit`: - `args` <- `fargs` - `jac` <- `score` - `hess` <- `hess` 'minimize' min_method : str, optional Name of minimization method to use. Any method specific arguments can be passed directly. For a list of methods and their arguments, see documentation of `scipy.optimize.minimize`. If no method is specified, then BFGS is used. """ Hinv = None # JP error if full_output=0, Hinv not defined if start_params is None: if hasattr(self, 'start_params'): start_params = self.start_params elif self.exog is not None: # fails for shape (K,)? start_params = [0] * self.exog.shape[1] else: raise ValueError("If exog is None, then start_params should " "be specified") # TODO: separate args from nonarg taking score and hessian, ie., # user-supplied and numerically evaluated estimate frprime does not take # args in most (any?) of the optimize function nobs = self.endog.shape[0] # f = lambda params, *args: -self.loglike(params, *args) / nobs def f(params, *args): return -self.loglike(params, *args) / nobs if method == 'newton': # TODO: why are score and hess positive? def score(params, *args): return self.score(params, *args) / nobs def hess(params, *args): return self.hessian(params, *args) / nobs else: def score(params, *args): return -self.score(params, *args) / nobs def hess(params, *args): return -self.hessian(params, *args) / nobs warn_convergence = kwargs.pop('warn_convergence', True) optimizer = Optimizer() xopt, retvals, optim_settings = optimizer._fit(f, score, start_params, fargs, kwargs, hessian=hess, method=method, disp=disp, maxiter=maxiter, callback=callback, retall=retall, full_output=full_output) # NOTE: this is for fit_regularized and should be generalized cov_params_func = kwargs.setdefault('cov_params_func', None) if cov_params_func: Hinv = cov_params_func(self, xopt, retvals) elif method == 'newton' and full_output: Hinv = np.linalg.inv(-retvals['Hessian']) / nobs elif not skip_hessian: H = -1 * self.hessian(xopt) invertible = False if np.all(np.isfinite(H)): eigvals, eigvecs = np.linalg.eigh(H) if np.min(eigvals) > 0: invertible = True if invertible: Hinv = eigvecs.dot(np.diag(1.0 / eigvals)).dot(eigvecs.T) Hinv = np.asfortranarray((Hinv + Hinv.T) / 2.0) else: warnings.warn('Inverting hessian failed, no bse or cov_params ' 'available', HessianInversionWarning) Hinv = None if 'cov_type' in kwargs: cov_kwds = kwargs.get('cov_kwds', {}) kwds = {'cov_type': kwargs['cov_type'], 'cov_kwds': cov_kwds} else: kwds = {} if 'use_t' in kwargs: kwds['use_t'] = kwargs['use_t'] # TODO: add Hessian approximation and change the above if needed mlefit = LikelihoodModelResults(self, xopt, Hinv, scale=1., **kwds) # TODO: hardcode scale? mlefit.mle_retvals = retvals if isinstance(retvals, dict): if warn_convergence and not retvals['converged']: from statsmodels.tools.sm_exceptions import ConvergenceWarning warnings.warn("Maximum Likelihood optimization failed to " "converge. Check mle_retvals", ConvergenceWarning) mlefit.mle_settings = optim_settings return mlefit def _fit_zeros(self, keep_index=None, start_params=None, return_auxiliary=False, k_params=None, **fit_kwds): """experimental, fit the model subject to zero constraints Intended for internal use cases until we know what we need. API will need to change to handle models with two exog. This is not yet supported by all model subclasses. This is essentially a simplified version of `fit_constrained`, and does not need to use `offset`. The estimation creates a new model with transformed design matrix, exog, and converts the results back to the original parameterization. Some subclasses could use a more efficient calculation than using a new model. Parameters ---------- keep_index : array_like (int or bool) or slice variables that should be dropped. start_params : None or array_like starting values for the optimization. `start_params` needs to be given in the original parameter space and are internally transformed. k_params : int or None If None, then we try to infer from start_params or model. **fit_kwds : keyword arguments fit_kwds are used in the optimization of the transformed model. Returns ------- results : Results instance """ # we need to append index of extra params to keep_index as in # NegativeBinomial if hasattr(self, 'k_extra') and self.k_extra > 0: # we cannot change the original, TODO: should we add keep_index_params? keep_index = np.array(keep_index, copy=True) k = self.exog.shape[1] extra_index = np.arange(k, k + self.k_extra) keep_index_p = np.concatenate((keep_index, extra_index)) else: keep_index_p = keep_index # not all models support start_params, drop if None, hide them in fit_kwds if start_params is not None: fit_kwds['start_params'] = start_params[keep_index_p] k_params = len(start_params) # ignore k_params in this case, or verify consisteny? # build auxiliary model and fit init_kwds = self._get_init_kwds() mod_constr = self.__class__(self.endog, self.exog[:, keep_index], **init_kwds) res_constr = mod_constr.fit(**fit_kwds) # switch name, only need keep_index for params below keep_index = keep_index_p if k_params is None: k_params = self.exog.shape[1] k_params += getattr(self, 'k_extra', 0) params_full = np.zeros(k_params) params_full[keep_index] = res_constr.params # create dummy results Instance, TODO: wire up properly # TODO: this could be moved into separate private method if needed # discrete L1 fit_regularized doens't reestimate AFAICS # RLM does not have method, disp nor warn_convergence keywords # OLS, WLS swallows extra kwds with **kwargs, but does not have method='nm' try: # Note: addding full_output=False causes exceptions res = self.fit(maxiter=0, disp=0, method='nm', skip_hessian=True, warn_convergence=False, start_params=params_full) # we get a wrapper back except (TypeError, ValueError): res = self.fit() # Warning: make sure we are not just changing the wrapper instead of # results #2400 # TODO: do we need to change res._results.scale in some models? if hasattr(res_constr.model, 'scale'): # Note: res.model is self # GLM problem, see #2399, # TODO: remove from model if not needed anymore res.model.scale = res._results.scale = res_constr.model.scale if hasattr(res_constr, 'mle_retvals'): res._results.mle_retvals = res_constr.mle_retvals # not available for not scipy optimization, e.g. glm irls # TODO: what retvals should be required? # res.mle_retvals['fcall'] = res_constr.mle_retvals.get('fcall', np.nan) # res.mle_retvals['iterations'] = res_constr.mle_retvals.get( # 'iterations', np.nan) # res.mle_retvals['converged'] = res_constr.mle_retvals['converged'] # overwrite all mle_settings if hasattr(res_constr, 'mle_settings'): res._results.mle_settings = res_constr.mle_settings res._results.params = params_full if (not hasattr(res._results, 'normalized_cov_params') or res._results.normalized_cov_params is None): res._results.normalized_cov_params = np.zeros((k_params, k_params)) else: res._results.normalized_cov_params[...] = 0 # fancy indexing requires integer array keep_index = np.array(keep_index) res._results.normalized_cov_params[keep_index[:, None], keep_index] = \ res_constr.normalized_cov_params k_constr = res_constr.df_resid - res._results.df_resid if hasattr(res_constr, 'cov_params_default'): res._results.cov_params_default = np.zeros((k_params, k_params)) res._results.cov_params_default[keep_index[:, None], keep_index] = \ res_constr.cov_params_default if hasattr(res_constr, 'cov_type'): res._results.cov_type = res_constr.cov_type res._results.cov_kwds = res_constr.cov_kwds res._results.keep_index = keep_index res._results.df_resid = res_constr.df_resid res._results.df_model = res_constr.df_model res._results.k_constr = k_constr res._results.results_constrained = res_constr # special temporary workaround for RLM # need to be able to override robust covariances if hasattr(res.model, 'M'): del res._results._cache['resid'] del res._results._cache['fittedvalues'] del res._results._cache['sresid'] cov = res._results._cache['bcov_scaled'] # inplace adjustment cov[...] = 0 cov[keep_index[:, None], keep_index] = res_constr.bcov_scaled res._results.cov_params_default = cov return res def _fit_collinear(self, atol=1e-14, rtol=1e-13, **kwds): """experimental, fit of the model without collinear variables This currently uses QR to drop variables based on the given sequence. Options will be added in future, when the supporting functions to identify collinear variables become available. """ # ------ copied from PR #2380 remove when merged x = self.exog tol = atol + rtol * x.var(0) r = np.linalg.qr(x, mode='r') mask = np.abs(r.diagonal()) < np.sqrt(tol) # TODO add to results instance # idx_collinear = np.where(mask)[0] idx_keep = np.where(~mask)[0] return self._fit_zeros(keep_index=idx_keep, **kwds) # TODO: the below is unfinished class GenericLikelihoodModel(LikelihoodModel): """ Allows the fitting of any likelihood function via maximum likelihood. A subclass needs to specify at least the log-likelihood If the log-likelihood is specified for each observation, then results that require the Jacobian will be available. (The other case is not tested yet.) Notes ----- Optimization methods that require only a likelihood function are 'nm' and 'powell' Optimization methods that require a likelihood function and a score/gradient are 'bfgs', 'cg', and 'ncg'. A function to compute the Hessian is optional for 'ncg'. Optimization method that require a likelihood function, a score/gradient, and a Hessian is 'newton' If they are not overwritten by a subclass, then numerical gradient, Jacobian and Hessian of the log-likelihood are calculated by numerical forward differentiation. This might results in some cases in precision problems, and the Hessian might not be positive definite. Even if the Hessian is not positive definite the covariance matrix of the parameter estimates based on the outer product of the Jacobian might still be valid. Examples -------- see also subclasses in directory miscmodels import statsmodels.api as sm data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog) # in this dir from model import GenericLikelihoodModel probit_mod = sm.Probit(data.endog, data.exog) probit_res = probit_mod.fit() loglike = probit_mod.loglike score = probit_mod.score mod = GenericLikelihoodModel(data.endog, data.exog, loglike, score) res = mod.fit(method="nm", maxiter = 500) import numpy as np np.allclose(res.params, probit_res.params) """ def __init__(self, endog, exog=None, loglike=None, score=None, hessian=None, missing='none', extra_params_names=None, **kwds): # let them be none in case user wants to use inheritance if loglike is not None: self.loglike = loglike if score is not None: self.score = score if hessian is not None: self.hessian = hessian self.__dict__.update(kwds) # TODO: data structures? # TODO temporary solution, force approx normal # self.df_model = 9999 # somewhere: CacheWriteWarning: 'df_model' cannot be overwritten super(GenericLikelihoodModel, self).__init__(endog, exog, missing=missing) # this will not work for ru2nmnl, maybe np.ndim of a dict? if exog is not None: self.nparams = (exog.shape[1] if np.ndim(exog) == 2 else 1) if extra_params_names is not None: self._set_extra_params_names(extra_params_names) def _set_extra_params_names(self, extra_params_names): # check param_names if extra_params_names is not None: if self.exog is not None: self.exog_names.extend(extra_params_names) else: self.data.xnames = extra_params_names self.nparams = len(self.exog_names) # this is redundant and not used when subclassing def initialize(self): """ Initialize (possibly re-initialize) a Model instance. For instance, the design matrix of a linear model may change and some things must be recomputed. """ if not self.score: # right now score is not optional self.score = lambda x: approx_fprime(x, self.loglike) if not self.hessian: pass else: # can use approx_hess_p if we have a gradient if not self.hessian: pass # Initialize is called by # statsmodels.model.LikelihoodModel.__init__ # and should contain any preprocessing that needs to be done for a model if self.exog is not None: # assume constant er = np.linalg.matrix_rank(self.exog) self.df_model = float(er - 1) self.df_resid = float(self.exog.shape[0] - er) else: self.df_model = np.nan self.df_resid = np.nan super(GenericLikelihoodModel, self).initialize() def expandparams(self, params): """ expand to full parameter array when some parameters are fixed Parameters ---------- params : ndarray reduced parameter array Returns ------- paramsfull : ndarray expanded parameter array where fixed parameters are included Notes ----- Calling this requires that self.fixed_params and self.fixed_paramsmask are defined. *developer notes:* This can be used in the log-likelihood to ... this could also be replaced by a more general parameter transformation. """ paramsfull = self.fixed_params.copy() paramsfull[self.fixed_paramsmask] = params return paramsfull def reduceparams(self, params): """Reduce parameters""" return params[self.fixed_paramsmask] def loglike(self, params): """Log-likelihood of model at params""" return self.loglikeobs(params).sum(0) def nloglike(self, params): """Negative log-likelihood of model at params""" return -self.loglikeobs(params).sum(0) def loglikeobs(self, params): """Log-likelihood of individual observations at params""" return -self.nloglikeobs(params) def score(self, params): """ Gradient of log-likelihood evaluated at params """ kwds = {} kwds.setdefault('centered', True) return approx_fprime(params, self.loglike, **kwds).ravel() def score_obs(self, params, **kwds): """ Jacobian/Gradient of log-likelihood evaluated at params for each observation. """ # kwds.setdefault('epsilon', 1e-4) kwds.setdefault('centered', True) return approx_fprime(params, self.loglikeobs, **kwds) def hessian(self, params): """ Hessian of log-likelihood evaluated at params """ from statsmodels.tools.numdiff import approx_hess # need options for hess (epsilon) return approx_hess(params, self.loglike) def hessian_factor(self, params, scale=None, observed=True): """Weights for calculating Hessian Parameters ---------- params : ndarray parameter at which Hessian is evaluated scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. observed : bool If True, then the observed Hessian is returned. If false then the expected information matrix is returned. Returns ------- hessian_factor : ndarray, 1d A 1d weight vector used in the calculation of the Hessian. The hessian is obtained by `(exog.T * hessian_factor).dot(exog)` """ raise NotImplementedError def fit(self, start_params=None, method='nm', maxiter=500, full_output=1, disp=1, callback=None, retall=0, **kwargs): """ Fit the model using maximum likelihood. See LikelihoodModel.fit for more information. """ if start_params is None: if hasattr(self, 'start_params'): start_params = self.start_params else: start_params = 0.1 * np.ones(self.nparams) fit_method = super(GenericLikelihoodModel, self).fit mlefit = fit_method(start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, **kwargs) genericmlefit = GenericLikelihoodModelResults(self, mlefit) # amend param names exog_names = [] if (self.exog_names is None) else self.exog_names k_miss = len(exog_names) - len(mlefit.params) if not k_miss == 0: if k_miss < 0: self._set_extra_params_names(['par%d' % i for i in range(-k_miss)]) else: # I do not want to raise after we have already fit() warnings.warn('more exog_names than parameters', ValueWarning) return genericmlefit class Results(object): """ Class to contain model results Parameters ---------- model : class instance the previously specified model instance params : ndarray parameter estimates from the fit model """ def __init__(self, model, params, **kwd): self.__dict__.update(kwd) self.initialize(model, params, **kwd) self._data_attr = [] # Variables to clear from cache self._data_in_cache = ['fittedvalues', 'resid', 'wresid'] def initialize(self, model, params, **kwargs): """ Initialize (possibly re-initialize) a Results instance. Parameters ---------- model : Model The model instance. params : ndarray The model parameters. **kwargs Any additional keyword arguments required to initialize the model. """ self.params = params self.model = model if hasattr(model, 'k_constant'): self.k_constant = model.k_constant def predict(self, exog=None, transform=True, *args, **kwargs): """ Call self.model.predict with self.params as the first argument. Parameters ---------- exog : array_like, optional The values for which you want to predict. see Notes below. transform : bool, optional If the model was fit via a formula, do you want to pass exog through the formula. Default is True. E.g., if you fit a model y ~ log(x1) + log(x2), and transform is True, then you can pass a data structure that contains x1 and x2 in their original form. Otherwise, you'd need to log the data first. *args Additional arguments to pass to the model, see the predict method of the model for the details. **kwargs Additional keywords arguments to pass to the model, see the predict method of the model for the details. Returns ------- array_like See self.model.predict. Notes ----- The types of exog that are supported depends on whether a formula was used in the specification of the model. If a formula was used, then exog is processed in the same way as the original data. This transformation needs to have key access to the same variable names, and can be a pandas DataFrame or a dict like object that contains numpy arrays. If no formula was used, then the provided exog needs to have the same number of columns as the original exog in the model. No transformation of the data is performed except converting it to a numpy array. Row indices as in pandas data frames are supported, and added to the returned prediction. """ import pandas as pd is_pandas = _is_using_pandas(exog, None) exog_index = exog.index if is_pandas else None if transform and hasattr(self.model, 'formula') and (exog is not None): design_info = self.model.data.design_info from patsy import dmatrix if isinstance(exog, pd.Series): # we are guessing whether it should be column or row if (hasattr(exog, 'name') and isinstance(exog.name, str) and exog.name in design_info.describe()): # assume we need one column exog = pd.DataFrame(exog) else: # assume we need a row exog = pd.DataFrame(exog).T orig_exog_len = len(exog) is_dict = isinstance(exog, dict) try: exog = dmatrix(design_info, exog, return_type="dataframe") except Exception as exc: msg = ('predict requires that you use a DataFrame when ' 'predicting from a model\nthat was created using the ' 'formula api.' '\n\nThe original error message returned by patsy is:\n' '{0}'.format(str(str(exc)))) raise exc.__class__(msg) if orig_exog_len > len(exog) and not is_dict: if exog_index is None: warnings.warn('nan values have been dropped', ValueWarning) else: exog = exog.reindex(exog_index) exog_index = exog.index if exog is not None: exog = np.asarray(exog) if exog.ndim == 1 and (self.model.exog.ndim == 1 or self.model.exog.shape[1] == 1): exog = exog[:, None] exog = np.atleast_2d(exog) # needed in count model shape[1] predict_results = self.model.predict(self.params, exog, *args, **kwargs) if exog_index is not None and not hasattr(predict_results, 'predicted_values'): if predict_results.ndim == 1: return pd.Series(predict_results, index=exog_index) else: return pd.DataFrame(predict_results, index=exog_index) else: return predict_results def summary(self): """ Summary Not implemented """ raise NotImplementedError # TODO: public method? class LikelihoodModelResults(Results): """ Class to contain results from likelihood models Parameters ---------- model : LikelihoodModel instance or subclass instance LikelihoodModelResults holds a reference to the model that is fit. params : 1d array_like parameter estimates from estimated model normalized_cov_params : 2d array Normalized (before scaling) covariance of params. (dot(X.T,X))**-1 scale : float For (some subset of models) scale will typically be the mean square error from the estimated model (sigma^2) Attributes ---------- mle_retvals : dict Contains the values returned from the chosen optimization method if full_output is True during the fit. Available only if the model is fit by maximum likelihood. See notes below for the output from the different methods. mle_settings : dict Contains the arguments passed to the chosen optimization method. Available if the model is fit by maximum likelihood. See LikelihoodModel.fit for more information. model : model instance LikelihoodResults contains a reference to the model that is fit. params : ndarray The parameters estimated for the model. scale : float The scaling factor of the model given during instantiation. tvalues : ndarray The t-values of the standard errors. Notes ----- The covariance of params is given by scale times normalized_cov_params. Return values by solver if full_output is True during fit: 'newton' fopt : float The value of the (negative) loglikelihood at its minimum. iterations : int Number of iterations performed. score : ndarray The score vector at the optimum. Hessian : ndarray The Hessian at the optimum. warnflag : int 1 if maxiter is exceeded. 0 if successful convergence. converged : bool True: converged. False: did not converge. allvecs : list List of solutions at each iteration. 'nm' fopt : float The value of the (negative) loglikelihood at its minimum. iterations : int Number of iterations performed. warnflag : int 1: Maximum number of function evaluations made. 2: Maximum number of iterations reached. converged : bool True: converged. False: did not converge. allvecs : list List of solutions at each iteration. 'bfgs' fopt : float Value of the (negative) loglikelihood at its minimum. gopt : float Value of gradient at minimum, which should be near 0. Hinv : ndarray value of the inverse Hessian matrix at minimum. Note that this is just an approximation and will often be different from the value of the analytic Hessian. fcalls : int Number of calls to loglike. gcalls : int Number of calls to gradient/score. warnflag : int 1: Maximum number of iterations exceeded. 2: Gradient and/or function calls are not changing. converged : bool True: converged. False: did not converge. allvecs : list Results at each iteration. 'lbfgs' fopt : float Value of the (negative) loglikelihood at its minimum. gopt : float Value of gradient at minimum, which should be near 0. fcalls : int Number of calls to loglike. warnflag : int Warning flag: - 0 if converged - 1 if too many function evaluations or too many iterations - 2 if stopped for another reason converged : bool True: converged. False: did not converge. 'powell' fopt : float Value of the (negative) loglikelihood at its minimum. direc : ndarray Current direction set. iterations : int Number of iterations performed. fcalls : int Number of calls to loglike. warnflag : int 1: Maximum number of function evaluations. 2: Maximum number of iterations. converged : bool True : converged. False: did not converge. allvecs : list Results at each iteration. 'cg' fopt : float Value of the (negative) loglikelihood at its minimum. fcalls : int Number of calls to loglike. gcalls : int Number of calls to gradient/score. warnflag : int 1: Maximum number of iterations exceeded. 2: Gradient and/ or function calls not changing. converged : bool True: converged. False: did not converge. allvecs : list Results at each iteration. 'ncg' fopt : float Value of the (negative) loglikelihood at its minimum. fcalls : int Number of calls to loglike. gcalls : int Number of calls to gradient/score. hcalls : int Number of calls to hessian. warnflag : int 1: Maximum number of iterations exceeded. converged : bool True: converged. False: did not converge. allvecs : list Results at each iteration. """ # by default we use normal distribution # can be overwritten by instances or subclasses def __init__(self, model, params, normalized_cov_params=None, scale=1., **kwargs): super(LikelihoodModelResults, self).__init__(model, params) self.normalized_cov_params = normalized_cov_params self.scale = scale self._use_t = False # robust covariance # We put cov_type in kwargs so subclasses can decide in fit whether to # use this generic implementation if 'use_t' in kwargs: use_t = kwargs['use_t'] self.use_t = use_t if use_t is not None else False if 'cov_type' in kwargs: cov_type = kwargs.get('cov_type', 'nonrobust') cov_kwds = kwargs.get('cov_kwds', {}) if cov_type == 'nonrobust': self.cov_type = 'nonrobust' self.cov_kwds = {'description': 'Standard Errors assume that the ' + 'covariance matrix of the errors is correctly ' + 'specified.'} else: from statsmodels.base.covtype import get_robustcov_results if cov_kwds is None: cov_kwds = {} use_t = self.use_t # TODO: we should not need use_t in get_robustcov_results get_robustcov_results(self, cov_type=cov_type, use_self=True, use_t=use_t, **cov_kwds) def normalized_cov_params(self): """See specific model class docstring""" raise NotImplementedError def _get_robustcov_results(self, cov_type='nonrobust', use_self=True, use_t=None, **cov_kwds): if use_self is False: raise ValueError("use_self should have been removed long ago. " "See GH#4401") from statsmodels.base.covtype import get_robustcov_results if cov_kwds is None: cov_kwds = {} if cov_type == 'nonrobust': self.cov_type = 'nonrobust' self.cov_kwds = {'description': 'Standard Errors assume that the ' + 'covariance matrix of the errors is correctly ' + 'specified.'} else: # TODO: we should not need use_t in get_robustcov_results get_robustcov_results(self, cov_type=cov_type, use_self=True, use_t=use_t, **cov_kwds) @property def use_t(self): """Flag indicating to use the Student's distribution in inference.""" return self._use_t @use_t.setter def use_t(self, value): self._use_t = bool(value) @cached_value def llf(self): """Log-likelihood of model""" return self.model.loglike(self.params) @cached_value def bse(self): """The standard errors of the parameter estimates.""" # Issue 3299 if ((not hasattr(self, 'cov_params_default')) and (self.normalized_cov_params is None)): bse_ = np.empty(len(self.params)) bse_[:] = np.nan else: with warnings.catch_warnings(): warnings.simplefilter("ignore", RuntimeWarning) bse_ = np.sqrt(np.diag(self.cov_params())) return bse_ @cached_value def tvalues(self): """ Return the t-statistic for a given parameter estimate. """ with warnings.catch_warnings(): warnings.simplefilter("ignore", RuntimeWarning) return self.params / self.bse @cached_value def pvalues(self): """The two-tailed p values for the t-stats of the params.""" with warnings.catch_warnings(): warnings.simplefilter("ignore", RuntimeWarning) if self.use_t: df_resid = getattr(self, 'df_resid_inference', self.df_resid) return stats.t.sf(np.abs(self.tvalues), df_resid) * 2 else: return stats.norm.sf(np.abs(self.tvalues)) * 2 def cov_params(self, r_matrix=None, column=None, scale=None, cov_p=None, other=None): """ Compute the variance/covariance matrix. The variance/covariance matrix can be of a linear contrast of the estimated parameters or all params multiplied by scale which will usually be an estimate of sigma^2. Scale is assumed to be a scalar. Parameters ---------- r_matrix : array_like Can be 1d, or 2d. Can be used alone or with other. column : array_like, optional Must be used on its own. Can be 0d or 1d see below. scale : float, optional Can be specified or not. Default is None, which means that the scale argument is taken from the model. cov_p : ndarray, optional The covariance of the parameters. If not provided, this value is read from `self.normalized_cov_params` or `self.cov_params_default`. other : array_like, optional Can be used when r_matrix is specified. Returns ------- ndarray The covariance matrix of the parameter estimates or of linear combination of parameter estimates. See Notes. Notes ----- (The below are assumed to be in matrix notation.) If no argument is specified returns the covariance matrix of a model ``(scale)*(X.T X)^(-1)`` If contrast is specified it pre and post-multiplies as follows ``(scale) * r_matrix (X.T X)^(-1) r_matrix.T`` If contrast and other are specified returns ``(scale) * r_matrix (X.T X)^(-1) other.T`` If column is specified returns ``(scale) * (X.T X)^(-1)[column,column]`` if column is 0d OR ``(scale) * (X.T X)^(-1)[column][:,column]`` if column is 1d """ if (hasattr(self, 'mle_settings') and self.mle_settings['optimizer'] in ['l1', 'l1_cvxopt_cp']): dot_fun = nan_dot else: dot_fun = np.dot if (cov_p is None and self.normalized_cov_params is None and not hasattr(self, 'cov_params_default')): raise ValueError('need covariance of parameters for computing ' '(unnormalized) covariances') if column is not None and (r_matrix is not None or other is not None): raise ValueError('Column should be specified without other ' 'arguments.') if other is not None and r_matrix is None: raise ValueError('other can only be specified with r_matrix') if cov_p is None: if hasattr(self, 'cov_params_default'): cov_p = self.cov_params_default else: if scale is None: scale = self.scale cov_p = self.normalized_cov_params * scale if column is not None: column = np.asarray(column) if column.shape == (): return cov_p[column, column] else: return cov_p[column[:, None], column] elif r_matrix is not None: r_matrix = np.asarray(r_matrix) if r_matrix.shape == (): raise ValueError("r_matrix should be 1d or 2d") if other is None: other = r_matrix else: other = np.asarray(other) tmp = dot_fun(r_matrix, dot_fun(cov_p, np.transpose(other))) return tmp else: # if r_matrix is None and column is None: return cov_p # TODO: make sure this works as needed for GLMs def t_test(self, r_matrix, cov_p=None, scale=None, use_t=None): """ Compute a t-test for a each linear hypothesis of the form Rb = q. Parameters ---------- r_matrix : {array_like, str, tuple} One of: - array : If an array is given, a p x k 2d array or length k 1d array specifying the linear restrictions. It is assumed that the linear combination is equal to zero. - str : The full hypotheses to test can be given as a string. See the examples. - tuple : A tuple of arrays in the form (R, q). If q is given, can be either a scalar or a length p row vector. cov_p : array_like, optional An alternative estimate for the parameter covariance matrix. If None is given, self.normalized_cov_params is used. scale : float, optional An optional `scale` to use. Default is the scale specified by the model fit. .. deprecated:: 0.10.0 use_t : bool, optional If use_t is None, then the default of the model is used. If use_t is True, then the p-values are based on the t distribution. If use_t is False, then the p-values are based on the normal distribution. Returns ------- ContrastResults The results for the test are attributes of this results instance. The available results have the same elements as the parameter table in `summary()`. See Also -------- tvalues : Individual t statistics for the estimated parameters. f_test : Perform an F tests on model parameters. patsy.DesignInfo.linear_constraint : Specify a linear constraint. Examples -------- >>> import numpy as np >>> import statsmodels.api as sm >>> data = sm.datasets.longley.load(as_pandas=False) >>> data.exog = sm.add_constant(data.exog) >>> results = sm.OLS(data.endog, data.exog).fit() >>> r = np.zeros_like(results.params) >>> r[5:] = [1,-1] >>> print(r) [ 0. 0. 0. 0. 0. 1. -1.] r tests that the coefficients on the 5th and 6th independent variable are the same. >>> T_test = results.t_test(r) >>> print(T_test) Test for Constraints ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ c0 -1829.2026 455.391 -4.017 0.003 -2859.368 -799.037 ============================================================================== >>> T_test.effect -1829.2025687192481 >>> T_test.sd 455.39079425193762 >>> T_test.tvalue -4.0167754636411717 >>> T_test.pvalue 0.0015163772380899498 Alternatively, you can specify the hypothesis tests using a string >>> from statsmodels.formula.api import ols >>> dta = sm.datasets.longley.load_pandas().data >>> formula = 'TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR' >>> results = ols(formula, dta).fit() >>> hypotheses = 'GNPDEFL = GNP, UNEMP = 2, YEAR/1829 = 1' >>> t_test = results.t_test(hypotheses) >>> print(t_test) Test for Constraints ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ c0 15.0977 84.937 0.178 0.863 -177.042 207.238 c1 -2.0202 0.488 -8.231 0.000 -3.125 -0.915 c2 1.0001 0.249 0.000 1.000 0.437 1.563 ============================================================================== """ if scale is not None: warnings.warn('scale is has no effect and is deprecated. It will' 'be removed in the next version.', DeprecationWarning) from patsy import DesignInfo names = self.model.data.cov_names LC = DesignInfo(names).linear_constraint(r_matrix) r_matrix, q_matrix = LC.coefs, LC.constants num_ttests = r_matrix.shape[0] num_params = r_matrix.shape[1] if (cov_p is None and self.normalized_cov_params is None and not hasattr(self, 'cov_params_default')): raise ValueError('Need covariance of parameters for computing ' 'T statistics') params = self.params.ravel() if num_params != params.shape[0]: raise ValueError('r_matrix and params are not aligned') if q_matrix is None: q_matrix = np.zeros(num_ttests) else: q_matrix = np.asarray(q_matrix) q_matrix = q_matrix.squeeze() if q_matrix.size > 1: if q_matrix.shape[0] != num_ttests: raise ValueError("r_matrix and q_matrix must have the same " "number of rows") if use_t is None: # switch to use_t false if undefined use_t = (hasattr(self, 'use_t') and self.use_t) _effect = np.dot(r_matrix, params) # Perform the test if num_ttests > 1: _sd = np.sqrt(np.diag(self.cov_params( r_matrix=r_matrix, cov_p=cov_p))) else: _sd = np.sqrt(self.cov_params(r_matrix=r_matrix, cov_p=cov_p)) _t = (_effect - q_matrix) * recipr(_sd) df_resid = getattr(self, 'df_resid_inference', self.df_resid) if use_t: return ContrastResults(effect=_effect, t=_t, sd=_sd, df_denom=df_resid) else: return ContrastResults(effect=_effect, statistic=_t, sd=_sd, df_denom=df_resid, distribution='norm') def f_test(self, r_matrix, cov_p=None, scale=1.0, invcov=None): """ Compute the F-test for a joint linear hypothesis. This is a special case of `wald_test` that always uses the F distribution. Parameters ---------- r_matrix : {array_like, str, tuple} One of: - array : An r x k array where r is the number of restrictions to test and k is the number of regressors. It is assumed that the linear combination is equal to zero. - str : The full hypotheses to test can be given as a string. See the examples. - tuple : A tuple of arrays in the form (R, q), ``q`` can be either a scalar or a length k row vector. cov_p : array_like, optional An alternative estimate for the parameter covariance matrix. If None is given, self.normalized_cov_params is used. scale : float, optional Default is 1.0 for no scaling. .. deprecated:: 0.10.0 invcov : array_like, optional A q x q array to specify an inverse covariance matrix based on a restrictions matrix. Returns ------- ContrastResults The results for the test are attributes of this results instance. See Also -------- t_test : Perform a single hypothesis test. wald_test : Perform a Wald-test using a quadratic form. statsmodels.stats.contrast.ContrastResults : Test results. patsy.DesignInfo.linear_constraint : Specify a linear constraint. Notes ----- The matrix `r_matrix` is assumed to be non-singular. More precisely, r_matrix (pX pX.T) r_matrix.T is assumed invertible. Here, pX is the generalized inverse of the design matrix of the model. There can be problems in non-OLS models where the rank of the covariance of the noise is not full. Examples -------- >>> import numpy as np >>> import statsmodels.api as sm >>> data = sm.datasets.longley.load(as_pandas=False) >>> data.exog = sm.add_constant(data.exog) >>> results = sm.OLS(data.endog, data.exog).fit() >>> A = np.identity(len(results.params)) >>> A = A[1:,:] This tests that each coefficient is jointly statistically significantly different from zero. >>> print(results.f_test(A)) Compare this to >>> results.fvalue 330.2853392346658 >>> results.f_pvalue 4.98403096572e-10 >>> B = np.array(([0,0,1,-1,0,0,0],[0,0,0,0,0,1,-1])) This tests that the coefficient on the 2nd and 3rd regressors are equal and jointly that the coefficient on the 5th and 6th regressors are equal. >>> print(results.f_test(B)) Alternatively, you can specify the hypothesis tests using a string >>> from statsmodels.datasets import longley >>> from statsmodels.formula.api import ols >>> dta = longley.load_pandas().data >>> formula = 'TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR' >>> results = ols(formula, dta).fit() >>> hypotheses = '(GNPDEFL = GNP), (UNEMP = 2), (YEAR/1829 = 1)' >>> f_test = results.f_test(hypotheses) >>> print(f_test) """ if scale != 1.0: warnings.warn('scale is has no effect and is deprecated. It will' 'be removed in the next version.', DeprecationWarning) res = self.wald_test(r_matrix, cov_p=cov_p, invcov=invcov, use_f=True) return res # TODO: untested for GLMs? def wald_test(self, r_matrix, cov_p=None, scale=1.0, invcov=None, use_f=None, df_constraints=None): """ Compute a Wald-test for a joint linear hypothesis. Parameters ---------- r_matrix : {array_like, str, tuple} One of: - array : An r x k array where r is the number of restrictions to test and k is the number of regressors. It is assumed that the linear combination is equal to zero. - str : The full hypotheses to test can be given as a string. See the examples. - tuple : A tuple of arrays in the form (R, q), ``q`` can be either a scalar or a length p row vector. cov_p : array_like, optional An alternative estimate for the parameter covariance matrix. If None is given, self.normalized_cov_params is used. scale : float, optional Default is 1.0 for no scaling. .. deprecated:: 0.10.0 invcov : array_like, optional A q x q array to specify an inverse covariance matrix based on a restrictions matrix. use_f : bool If True, then the F-distribution is used. If False, then the asymptotic distribution, chisquare is used. If use_f is None, then the F distribution is used if the model specifies that use_t is True. The test statistic is proportionally adjusted for the distribution by the number of constraints in the hypothesis. df_constraints : int, optional The number of constraints. If not provided the number of constraints is determined from r_matrix. Returns ------- ContrastResults The results for the test are attributes of this results instance. See Also -------- f_test : Perform an F tests on model parameters. t_test : Perform a single hypothesis test. statsmodels.stats.contrast.ContrastResults : Test results. patsy.DesignInfo.linear_constraint : Specify a linear constraint. Notes ----- The matrix `r_matrix` is assumed to be non-singular. More precisely, r_matrix (pX pX.T) r_matrix.T is assumed invertible. Here, pX is the generalized inverse of the design matrix of the model. There can be problems in non-OLS models where the rank of the covariance of the noise is not full. """ if scale != 1.0: warnings.warn('scale is has no effect and is deprecated. It will' 'be removed in the next version.', DeprecationWarning) if use_f is None: # switch to use_t false if undefined use_f = (hasattr(self, 'use_t') and self.use_t) from patsy import DesignInfo names = self.model.data.cov_names params = self.params.ravel() LC = DesignInfo(names).linear_constraint(r_matrix) r_matrix, q_matrix = LC.coefs, LC.constants if (self.normalized_cov_params is None and cov_p is None and invcov is None and not hasattr(self, 'cov_params_default')): raise ValueError('need covariance of parameters for computing ' 'F statistics') cparams = np.dot(r_matrix, params[:, None]) J = float(r_matrix.shape[0]) # number of restrictions if q_matrix is None: q_matrix = np.zeros(J) else: q_matrix = np.asarray(q_matrix) if q_matrix.ndim == 1: q_matrix = q_matrix[:, None] if q_matrix.shape[0] != J: raise ValueError("r_matrix and q_matrix must have the same " "number of rows") Rbq = cparams - q_matrix if invcov is None: cov_p = self.cov_params(r_matrix=r_matrix, cov_p=cov_p) if np.isnan(cov_p).max(): raise ValueError("r_matrix performs f_test for using " "dimensions that are asymptotically " "non-normal") invcov = np.linalg.pinv(cov_p) J_ = np.linalg.matrix_rank(cov_p) if J_ < J: warnings.warn('covariance of constraints does not have full ' 'rank. The number of constraints is %d, but ' 'rank is %d' % (J, J_), ValueWarning) J = J_ # TODO streamline computation, we do not need to compute J if given if df_constraints is not None: # let caller override J by df_constraint J = df_constraints if (hasattr(self, 'mle_settings') and self.mle_settings['optimizer'] in ['l1', 'l1_cvxopt_cp']): F = nan_dot(nan_dot(Rbq.T, invcov), Rbq) else: F = np.dot(np.dot(Rbq.T, invcov), Rbq) df_resid = getattr(self, 'df_resid_inference', self.df_resid) if use_f: F /= J return ContrastResults(F=F, df_denom=df_resid, df_num=J) #invcov.shape[0]) else: return ContrastResults(chi2=F, df_denom=J, statistic=F, distribution='chi2', distargs=(J,)) def wald_test_terms(self, skip_single=False, extra_constraints=None, combine_terms=None): """ Compute a sequence of Wald tests for terms over multiple columns. This computes joined Wald tests for the hypothesis that all coefficients corresponding to a `term` are zero. `Terms` are defined by the underlying formula or by string matching. Parameters ---------- skip_single : bool If true, then terms that consist only of a single column and, therefore, refers only to a single parameter is skipped. If false, then all terms are included. extra_constraints : ndarray Additional constraints to test. Note that this input has not been tested. combine_terms : {list[str], None} Each string in this list is matched to the name of the terms or the name of the exogenous variables. All columns whose name includes that string are combined in one joint test. Returns ------- WaldTestResults The result instance contains `table` which is a pandas DataFrame with the test results: test statistic, degrees of freedom and pvalues. Examples -------- >>> res_ols = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit() >>> res_ols.wald_test_terms() F P>F df constraint df denom Intercept 279.754525 2.37985521351e-22 1 51 C(Duration, Sum) 5.367071 0.0245738436636 1 51 C(Weight, Sum) 12.432445 3.99943118767e-05 2 51 C(Duration, Sum):C(Weight, Sum) 0.176002 0.83912310946 2 51 >>> res_poi = Poisson.from_formula("Days ~ C(Weight) * C(Duration)", \ data).fit(cov_type='HC0') >>> wt = res_poi.wald_test_terms(skip_single=False, \ combine_terms=['Duration', 'Weight']) >>> print(wt) chi2 P>chi2 df constraint Intercept 15.695625 7.43960374424e-05 1 C(Weight) 16.132616 0.000313940174705 2 C(Duration) 1.009147 0.315107378931 1 C(Weight):C(Duration) 0.216694 0.897315972824 2 Duration 11.187849 0.010752286833 3 Weight 30.263368 4.32586407145e-06 4 """ # lazy import from collections import defaultdict result = self if extra_constraints is None: extra_constraints = [] if combine_terms is None: combine_terms = [] design_info = getattr(result.model.data, 'design_info', None) if design_info is None and extra_constraints is None: raise ValueError('no constraints, nothing to do') identity = np.eye(len(result.params)) constraints = [] combined = defaultdict(list) if design_info is not None: for term in design_info.terms: cols = design_info.slice(term) name = term.name() constraint_matrix = identity[cols] # check if in combined for cname in combine_terms: if cname in name: combined[cname].append(constraint_matrix) k_constraint = constraint_matrix.shape[0] if skip_single: if k_constraint == 1: continue constraints.append((name, constraint_matrix)) combined_constraints = [] for cname in combine_terms: combined_constraints.append((cname, np.vstack(combined[cname]))) else: # check by exog/params names if there is no formula info for col, name in enumerate(result.model.exog_names): constraint_matrix = np.atleast_2d(identity[col]) # check if in combined for cname in combine_terms: if cname in name: combined[cname].append(constraint_matrix) if skip_single: continue constraints.append((name, constraint_matrix)) combined_constraints = [] for cname in combine_terms: combined_constraints.append((cname, np.vstack(combined[cname]))) use_t = result.use_t distribution = ['chi2', 'F'][use_t] res_wald = [] index = [] for name, constraint in constraints + combined_constraints + extra_constraints: wt = result.wald_test(constraint) row = [wt.statistic.item(), wt.pvalue.item(), constraint.shape[0]] if use_t: row.append(wt.df_denom) res_wald.append(row) index.append(name) # distribution nerutral names col_names = ['statistic', 'pvalue', 'df_constraint'] if use_t: col_names.append('df_denom') # TODO: maybe move DataFrame creation to results class from pandas import DataFrame table = DataFrame(res_wald, index=index, columns=col_names) res = WaldTestResults(None, distribution, None, table=table) # TODO: remove temp again, added for testing res.temp = constraints + combined_constraints + extra_constraints return res def t_test_pairwise(self, term_name, method='hs', alpha=0.05, factor_labels=None): """ Perform pairwise t_test with multiple testing corrected p-values. This uses the formula design_info encoding contrast matrix and should work for all encodings of a main effect. Parameters ---------- term_name : str The name of the term for which pairwise comparisons are computed. Term names for categorical effects are created by patsy and correspond to the main part of the exog names. method : {str, list[str]} The multiple testing p-value correction to apply. The default is 'hs'. See stats.multipletesting. alpha : float The significance level for multiple testing reject decision. factor_labels : {list[str], None} Labels for the factor levels used for pairwise labels. If not provided, then the labels from the formula design_info are used. Returns ------- MultiCompResult The results are stored as attributes, the main attributes are the following two. Other attributes are added for debugging purposes or as background information. - result_frame : pandas DataFrame with t_test results and multiple testing corrected p-values. - contrasts : matrix of constraints of the null hypothesis in the t_test. Notes ----- Status: experimental. Currently only checked for treatment coding with and without specified reference level. Currently there are no multiple testing corrected confidence intervals available. Examples -------- >>> res = ols("np.log(Days+1) ~ C(Weight) + C(Duration)", data).fit() >>> pw = res.t_test_pairwise("C(Weight)") >>> pw.result_frame coef std err t P>|t| Conf. Int. Low 2-1 0.632315 0.230003 2.749157 8.028083e-03 0.171563 3-1 1.302555 0.230003 5.663201 5.331513e-07 0.841803 3-2 0.670240 0.230003 2.914044 5.119126e-03 0.209488 Conf. Int. Upp. pvalue-hs reject-hs 2-1 1.093067 0.010212 True 3-1 1.763307 0.000002 True 3-2 1.130992 0.010212 True """ res = t_test_pairwise(self, term_name, method=method, alpha=alpha, factor_labels=factor_labels) return res def conf_int(self, alpha=.05, cols=None): """ Construct confidence interval for the fitted parameters. Parameters ---------- alpha : float, optional The significance level for the confidence interval. The default `alpha` = .05 returns a 95% confidence interval. cols : array_like, optional Specifies which confidence intervals to return. Returns ------- array_like Each row contains [lower, upper] limits of the confidence interval for the corresponding parameter. The first column contains all lower, the second column contains all upper limits. Notes ----- The confidence interval is based on the standard normal distribution if self.use_t is False. If self.use_t is True, then uses a Student's t with self.df_resid_inference (or self.df_resid if df_resid_inference is not defined) degrees of freedom. Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.longley.load(as_pandas=False) >>> data.exog = sm.add_constant(data.exog) >>> results = sm.OLS(data.endog, data.exog).fit() >>> results.conf_int() array([[-5496529.48322745, -1467987.78596704], [ -177.02903529, 207.15277984], [ -0.1115811 , 0.03994274], [ -3.12506664, -0.91539297], [ -1.5179487 , -0.54850503], [ -0.56251721, 0.460309 ], [ 798.7875153 , 2859.51541392]]) >>> results.conf_int(cols=(2,3)) array([[-0.1115811 , 0.03994274], [-3.12506664, -0.91539297]]) """ bse = self.bse if self.use_t: dist = stats.t df_resid = getattr(self, 'df_resid_inference', self.df_resid) q = dist.ppf(1 - alpha / 2, df_resid) else: dist = stats.norm q = dist.ppf(1 - alpha / 2) params = self.params lower = params - q * bse upper = params + q * bse if cols is not None: cols = np.asarray(cols) lower = lower[cols] upper = upper[cols] return np.asarray(lzip(lower, upper)) def save(self, fname, remove_data=False): """ Save a pickle of this instance. Parameters ---------- fname : {str, handle} A string filename or a file handle. remove_data : bool If False (default), then the instance is pickled without changes. If True, then all arrays with length nobs are set to None before pickling. See the remove_data method. In some cases not all arrays will be set to None. Notes ----- If remove_data is true and the model result does not implement a remove_data method then this will raise an exception. """ from statsmodels.iolib.smpickle import save_pickle if remove_data: self.remove_data() save_pickle(self, fname) @classmethod def load(cls, fname): """ Load a pickled results instance .. warning:: Loading pickled models is not secure against erroneous or maliciously constructed data. Never unpickle data received from an untrusted or unauthenticated source. Parameters ---------- fname : {str, handle} A string filename or a file handle. Returns ------- Results The unpickled results instance. """ from statsmodels.iolib.smpickle import load_pickle return load_pickle(fname) def remove_data(self): """ Remove data arrays, all nobs arrays from result and model. This reduces the size of the instance, so it can be pickled with less memory. Currently tested for use with predict from an unpickled results and model instance. .. warning:: Since data and some intermediate results have been removed calculating new statistics that require them will raise exceptions. The exception will occur the first time an attribute is accessed that has been set to None. Not fully tested for time series models, tsa, and might delete too much for prediction or not all that would be possible. The lists of arrays to delete are maintained as attributes of the result and model instance, except for cached values. These lists could be changed before calling remove_data. The attributes to remove are named in: model._data_attr : arrays attached to both the model instance and the results instance with the same attribute name. result._data_in_cache : arrays that may exist as values in result._cache result._data_attr_model : arrays attached to the model instance but not to the results instance """ cls = self.__class__ # Note: we cannot just use `getattr(cls, x)` or `getattr(self, x)` # because of redirection involved with property-like accessors cls_attrs = {} for name in dir(cls): try: attr = object.__getattribute__(cls, name) except AttributeError: pass else: cls_attrs[name] = attr data_attrs = [x for x in cls_attrs if isinstance(cls_attrs[x], cached_data)] value_attrs = [x for x in cls_attrs if isinstance(cls_attrs[x], cached_value)] # make sure the cached for value_attrs are evaluated; this needs to # occur _before_ any other attributes are removed. for name in value_attrs: getattr(self, name) for name in data_attrs: self._cache[name] = None def wipe(obj, att): # get to last element in attribute path p = att.split('.') att_ = p.pop(-1) try: obj_ = reduce(getattr, [obj] + p) if hasattr(obj_, att_): setattr(obj_, att_, None) except AttributeError: pass model_only = ['model.' + i for i in getattr(self, "_data_attr_model", [])] model_attr = ['model.' + i for i in self.model._data_attr] for att in self._data_attr + model_attr + model_only: if att in data_attrs: # these have been handled above, and trying to call wipe # would raise an Exception anyway, so skip these continue wipe(self, att) for key in self._data_in_cache: try: self._cache[key] = None except (AttributeError, KeyError): pass class LikelihoodResultsWrapper(wrap.ResultsWrapper): _attrs = { 'params': 'columns', 'bse': 'columns', 'pvalues': 'columns', 'tvalues': 'columns', 'resid': 'rows', 'fittedvalues': 'rows', 'normalized_cov_params': 'cov', } _wrap_attrs = _attrs _wrap_methods = { 'cov_params': 'cov', 'conf_int': 'columns' } wrap.populate_wrapper(LikelihoodResultsWrapper, # noqa:E305 LikelihoodModelResults) class ResultMixin(object): @cache_readonly def df_modelwc(self): """Model WC""" # collect different ways of defining the number of parameters, used for # aic, bic if hasattr(self, 'df_model'): if hasattr(self, 'hasconst'): hasconst = self.hasconst else: # default assumption hasconst = 1 return self.df_model + hasconst else: return self.params.size @cache_readonly def aic(self): """Akaike information criterion""" return -2 * self.llf + 2 * (self.df_modelwc) @cache_readonly def bic(self): """Bayesian information criterion""" return -2 * self.llf + np.log(self.nobs) * (self.df_modelwc) @cache_readonly def score_obsv(self): """cached Jacobian of log-likelihood """ return self.model.score_obs(self.params) @cache_readonly def hessv(self): """cached Hessian of log-likelihood """ return self.model.hessian(self.params) @cache_readonly def covjac(self): """ covariance of parameters based on outer product of jacobian of log-likelihood """ # if not hasattr(self, '_results'): # raise ValueError('need to call fit first') # #self.fit() # self.jacv = jacv = self.jac(self._results.params) jacv = self.score_obsv return np.linalg.inv(np.dot(jacv.T, jacv)) @cache_readonly def covjhj(self): """covariance of parameters based on HJJH dot product of Hessian, Jacobian, Jacobian, Hessian of likelihood name should be covhjh """ jacv = self.score_obsv hessv = self.hessv hessinv = np.linalg.inv(hessv) # self.hessinv = hessin = self.cov_params() return np.dot(hessinv, np.dot(np.dot(jacv.T, jacv), hessinv)) @cache_readonly def bsejhj(self): """standard deviation of parameter estimates based on covHJH """ return np.sqrt(np.diag(self.covjhj)) @cache_readonly def bsejac(self): """standard deviation of parameter estimates based on covjac """ return np.sqrt(np.diag(self.covjac)) def bootstrap(self, nrep=100, method='nm', disp=0, store=1): """simple bootstrap to get mean and variance of estimator see notes Parameters ---------- nrep : int number of bootstrap replications method : str optimization method to use disp : bool If true, then optimization prints results store : bool If true, then parameter estimates for all bootstrap iterations are attached in self.bootstrap_results Returns ------- mean : ndarray mean of parameter estimates over bootstrap replications std : ndarray standard deviation of parameter estimates over bootstrap replications Notes ----- This was mainly written to compare estimators of the standard errors of the parameter estimates. It uses independent random sampling from the original endog and exog, and therefore is only correct if observations are independently distributed. This will be moved to apply only to models with independently distributed observations. """ results = [] hascloneattr = True if hasattr(self.model, 'cloneattr') else False for i in range(nrep): rvsind = np.random.randint(self.nobs, size=self.nobs) # this needs to set startparam and get other defining attributes # need a clone method on model if self.exog is not None: exog_resamp = self.exog[rvsind, :] else: exog_resamp = None fitmod = self.model.__class__(self.endog[rvsind], exog=exog_resamp) if hascloneattr: for attr in self.model.cloneattr: setattr(fitmod, attr, getattr(self.model, attr)) fitres = fitmod.fit(method=method, disp=disp) results.append(fitres.params) results = np.array(results) if store: self.bootstrap_results = results return results.mean(0), results.std(0), results def get_nlfun(self, fun): """ get_nlfun This is not Implemented """ # I think this is supposed to get the delta method that is currently # in miscmodels count (as part of Poisson example) raise NotImplementedError class GenericLikelihoodModelResults(LikelihoodModelResults, ResultMixin): """ A results class for the discrete dependent variable models. ..Warning : The following description has not been updated to this version/class. Where are AIC, BIC, ....? docstring looks like copy from discretemod Parameters ---------- model : A DiscreteModel instance mlefit : instance of LikelihoodResults This contains the numerical optimization results as returned by LikelihoodModel.fit(), in a superclass of GnericLikelihoodModels Attributes ---------- aic : float Akaike information criterion. -2*(`llf` - p) where p is the number of regressors including the intercept. bic : float Bayesian information criterion. -2*`llf` + ln(`nobs`)*p where p is the number of regressors including the intercept. bse : ndarray The standard errors of the coefficients. df_resid : float See model definition. df_model : float See model definition. fitted_values : ndarray Linear predictor XB. llf : float Value of the loglikelihood llnull : float Value of the constant-only loglikelihood llr : float Likelihood ratio chi-squared statistic; -2*(`llnull` - `llf`) llr_pvalue : float The chi-squared probability of getting a log-likelihood ratio statistic greater than llr. llr has a chi-squared distribution with degrees of freedom `df_model`. prsquared : float McFadden's pseudo-R-squared. 1 - (`llf`/`llnull`) """ def __init__(self, model, mlefit): self.model = model self.endog = model.endog self.exog = model.exog self.nobs = model.endog.shape[0] # TODO: possibly move to model.fit() # and outsource together with patching names if hasattr(model, 'df_model'): self.df_model = model.df_model else: self.df_model = len(mlefit.params) # retrofitting the model, used in t_test TODO: check design self.model.df_model = self.df_model if hasattr(model, 'df_resid'): self.df_resid = model.df_resid else: self.df_resid = self.endog.shape[0] - self.df_model # retrofitting the model, used in t_test TODO: check design self.model.df_resid = self.df_resid self._cache = {} self.__dict__.update(mlefit.__dict__) def summary(self, yname=None, xname=None, title=None, alpha=.05): """Summarize the Regression Results Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Names for the exogenous variables, default is "var_xx". Must match the number of parameters in the model title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : class to hold summary results """ top_left = [('Dep. Variable:', None), ('Model:', None), ('Method:', ['Maximum Likelihood']), ('Date:', None), ('Time:', None), ('No. Observations:', None), ('Df Residuals:', None), ('Df Model:', None), ] top_right = [('Log-Likelihood:', None), ('AIC:', ["%#8.4g" % self.aic]), ('BIC:', ["%#8.4g" % self.bic]) ] if title is None: title = self.model.__class__.__name__ + ' ' + "Results" # create summary table instance from statsmodels.iolib.summary import Summary smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, yname=yname, xname=xname, title=title) smry.add_table_params(self, yname=yname, xname=xname, alpha=alpha, use_t=self.use_t) return smry statsmodels-0.12.2/statsmodels/base/optimizer.py000066400000000000000000001214201400612667500220150ustar00rootroot00000000000000""" Functions that are general enough to use for any model fitting. The idea is to untie these from LikelihoodModel so that they may be re-used generally. """ import numpy as np from scipy import optimize def _check_method(method, methods): if method not in methods: message = "Unknown fit method %s" % method raise ValueError(message) class Optimizer(object): def _fit(self, objective, gradient, start_params, fargs, kwargs, hessian=None, method='newton', maxiter=100, full_output=True, disp=True, callback=None, retall=False): """ Fit function for any model with an objective function. Parameters ---------- objective : function Objective function to be minimized. gradient : function The gradient of the objective function. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : tuple Extra keyworded arguments passed to the objective function, i.e. objective(x,**kwargs) hessian : str, optional Method for computing the Hessian matrix, if applicable. method : str {'newton','nm','bfgs','powell','cg','ncg','basinhopping', 'minimize'} Method can be 'newton' for Newton-Raphson, 'nm' for Nelder-Mead, 'bfgs' for Broyden-Fletcher-Goldfarb-Shanno, 'powell' for modified Powell's method, 'cg' for conjugate gradient, 'ncg' for Newton- conjugate gradient, 'basinhopping' for global basin-hopping solver, if available or a generic 'minimize' which is a wrapper for scipy.optimize.minimize. `method` determines which solver from scipy.optimize is used. The explicit arguments in `fit` are passed to the solver, with the exception of the basin-hopping solver. Each solver has several optional arguments that are not the same across solvers. See the notes section below (or scipy.optimize) for the available arguments and for the list of explicit arguments that the basin-hopping solver supports.. maxiter : int The maximum number of iterations to perform. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. disp : bool Set to True to print convergence messages. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. optim_settings : dict A dictionary that contains the parameters passed to the solver. Notes ----- The 'basinhopping' solver ignores `maxiter`, `retall`, `full_output` explicit arguments. Optional arguments for the solvers (available in Results.mle_settings):: 'newton' tol : float Relative error in params acceptable for convergence. 'nm' -- Nelder Mead xtol : float Relative error in params acceptable for convergence ftol : float Relative error in loglike(params) acceptable for convergence maxfun : int Maximum number of function evaluations to make. 'bfgs' gtol : float Stop when norm of gradient is less than gtol. norm : float Order of norm (np.Inf is max, -np.Inf is min) epsilon If fprime is approximated, use this value for the step size. Only relevant if LikelihoodModel.score is None. 'lbfgs' m : int The maximum number of variable metric corrections used to define the limited memory matrix. (The limited memory BFGS method does not store the full hessian but uses this many terms in an approximation to it.) pgtol : float The iteration will stop when ``max{|proj g_i | i = 1, ..., n} <= pgtol`` where pg_i is the i-th component of the projected gradient. factr : float The iteration stops when ``(f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr * eps``, where eps is the machine precision, which is automatically generated by the code. Typical values for factr are: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy. See Notes for relationship to ftol, which is exposed (instead of factr) by the scipy.optimize.minimize interface to L-BFGS-B. maxfun : int Maximum number of iterations. epsilon : float Step size used when approx_grad is True, for numerically calculating the gradient approx_grad : bool Whether to approximate the gradient numerically (in which case func returns only the function value). 'cg' gtol : float Stop when norm of gradient is less than gtol. norm : float Order of norm (np.Inf is max, -np.Inf is min) epsilon : float If fprime is approximated, use this value for the step size. Can be scalar or vector. Only relevant if Likelihoodmodel.score is None. 'ncg' fhess_p : callable f'(x,*args) Function which computes the Hessian of f times an arbitrary vector, p. Should only be supplied if LikelihoodModel.hessian is None. avextol : float Stop when the average relative error in the minimizer falls below this amount. epsilon : float or ndarray If fhess is approximated, use this value for the step size. Only relevant if Likelihoodmodel.hessian is None. 'powell' xtol : float Line-search error tolerance ftol : float Relative error in loglike(params) for acceptable for convergence. maxfun : int Maximum number of function evaluations to make. start_direc : ndarray Initial direction set. 'basinhopping' niter : int The number of basin hopping iterations. niter_success : int Stop the run if the global minimum candidate remains the same for this number of iterations. T : float The "temperature" parameter for the accept or reject criterion. Higher "temperatures" mean that larger jumps in function value will be accepted. For best results `T` should be comparable to the separation (in function value) between local minima. stepsize : float Initial step size for use in the random displacement. interval : int The interval for how often to update the `stepsize`. minimizer : dict Extra keyword arguments to be passed to the minimizer `scipy.optimize.minimize()`, for example 'method' - the minimization method (e.g. 'L-BFGS-B'), or 'tol' - the tolerance for termination. Other arguments are mapped from explicit argument of `fit`: - `args` <- `fargs` - `jac` <- `score` - `hess` <- `hess` 'minimize' min_method : str, optional Name of minimization method to use. Any method specific arguments can be passed directly. For a list of methods and their arguments, see documentation of `scipy.optimize.minimize`. If no method is specified, then BFGS is used. """ #TODO: generalize the regularization stuff # Extract kwargs specific to fit_regularized calling fit extra_fit_funcs = kwargs.setdefault('extra_fit_funcs', dict()) methods = ['newton', 'nm', 'bfgs', 'lbfgs', 'powell', 'cg', 'ncg', 'basinhopping', 'minimize'] methods += extra_fit_funcs.keys() method = method.lower() _check_method(method, methods) fit_funcs = { 'newton': _fit_newton, 'nm': _fit_nm, # Nelder-Mead 'bfgs': _fit_bfgs, 'lbfgs': _fit_lbfgs, 'cg': _fit_cg, 'ncg': _fit_ncg, 'powell': _fit_powell, 'basinhopping': _fit_basinhopping, 'minimize': _fit_minimize # wrapper for scipy.optimize.minimize } #NOTE: fit_regularized checks the methods for these but it should be # moved up probably if extra_fit_funcs: fit_funcs.update(extra_fit_funcs) func = fit_funcs[method] xopt, retvals = func(objective, gradient, start_params, fargs, kwargs, disp=disp, maxiter=maxiter, callback=callback, retall=retall, full_output=full_output, hess=hessian) optim_settings = {'optimizer': method, 'start_params': start_params, 'maxiter': maxiter, 'full_output': full_output, 'disp': disp, 'fargs': fargs, 'callback': callback, 'retall': retall} optim_settings.update(kwargs) # set as attributes or return? return xopt, retvals, optim_settings def _fit_constrained(self, params): """ TODO: how to add constraints? Something like sm.add_constraint(Model, func) or model_instance.add_constraint(func) model_instance.add_constraint("x1 + x2 = 2") result = model_instance.fit() """ raise NotImplementedError def _fit_regularized(self, params): # TODO: code will not necessarily be general here. 3 options. # 1) setup for scipy.optimize.fmin_sqlsqp # 2) setup for cvxopt # 3) setup for openopt raise NotImplementedError ######################################## # Helper functions to fit def _fit_minimize(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): """ Fit using scipy minimize, where kwarg `min_method` defines the algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : tuple Extra keyworded arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. """ kwargs.setdefault('min_method', 'BFGS') # prepare options dict for minimize filter_opts = ['extra_fit_funcs', 'niter', 'min_method', 'tol', 'bounds', 'constraints'] options = dict((k,v) for k,v in kwargs.items() if k not in filter_opts) options['disp'] = disp options['maxiter'] = maxiter # Use Hessian/Jacobian only if they're required by the method no_hess = ['Nelder-Mead', 'Powell', 'CG', 'BFGS', 'COBYLA', 'SLSQP'] no_jac = ['Nelder-Mead', 'Powell', 'COBYLA'] if kwargs['min_method'] in no_hess: hess = None if kwargs['min_method'] in no_jac: score = None # Use bounds/constraints only if they're allowed by the method has_bounds = ['L-BFGS-B', 'TNC', 'SLSQP', 'trust-constr'] has_constraints = ['COBYLA', 'SLSQP' , 'trust-constr'] if 'bounds' in kwargs.keys() and kwargs['min_method'] in has_bounds: bounds = kwargs['bounds'] else: bounds = None if 'constraints' in kwargs.keys() and kwargs['min_method'] in has_constraints: constraints = kwargs['constraints'] else: constraints = () res = optimize.minimize(f, start_params, args=fargs, method=kwargs['min_method'], jac=score, hess=hess, bounds=bounds, constraints=constraints, callback=callback, options=options) xopt = res.x retvals = None if full_output: nit = getattr(res, 'nit', np.nan) # scipy 0.14 compat retvals = {'fopt': res.fun, 'iterations': nit, 'fcalls': res.nfev, 'warnflag': res.status, 'converged': res.success} if retall: retvals.update({'allvecs': res.values()}) return xopt, retvals def _fit_newton(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None, ridge_factor=1e-10): """ Fit using Newton-Raphson algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : tuple Extra keyworded arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. ridge_factor : float Regularization factor for Hessian matrix. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. """ tol = kwargs.setdefault('tol', 1e-8) iterations = 0 oldparams = np.inf newparams = np.asarray(start_params) if retall: history = [oldparams, newparams] while (iterations < maxiter and np.any(np.abs(newparams - oldparams) > tol)): H = np.asarray(hess(newparams)) # regularize Hessian, not clear what ridge factor should be # keyword option with absolute default 1e-10, see #1847 if not np.all(ridge_factor == 0): H[np.diag_indices(H.shape[0])] += ridge_factor oldparams = newparams newparams = oldparams - np.dot(np.linalg.inv(H), score(oldparams)) if retall: history.append(newparams) if callback is not None: callback(newparams) iterations += 1 fval = f(newparams, *fargs) # this is the negative likelihood if iterations == maxiter: warnflag = 1 if disp: print("Warning: Maximum number of iterations has been " "exceeded.") print(" Current function value: %f" % fval) print(" Iterations: %d" % iterations) else: warnflag = 0 if disp: print("Optimization terminated successfully.") print(" Current function value: %f" % fval) print(" Iterations %d" % iterations) if full_output: (xopt, fopt, niter, gopt, hopt) = (newparams, f(newparams, *fargs), iterations, score(newparams), hess(newparams)) converged = not warnflag retvals = {'fopt': fopt, 'iterations': niter, 'score': gopt, 'Hessian': hopt, 'warnflag': warnflag, 'converged': converged} if retall: retvals.update({'allvecs': history}) else: xopt = newparams retvals = None return xopt, retvals def _fit_bfgs(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): """ Fit using Broyden-Fletcher-Goldfarb-Shannon algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : tuple Extra keyworded arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. """ gtol = kwargs.setdefault('gtol', 1.0000000000000001e-05) norm = kwargs.setdefault('norm', np.Inf) epsilon = kwargs.setdefault('epsilon', 1.4901161193847656e-08) retvals = optimize.fmin_bfgs(f, start_params, score, args=fargs, gtol=gtol, norm=norm, epsilon=epsilon, maxiter=maxiter, full_output=full_output, disp=disp, retall=retall, callback=callback) if full_output: if not retall: xopt, fopt, gopt, Hinv, fcalls, gcalls, warnflag = retvals else: (xopt, fopt, gopt, Hinv, fcalls, gcalls, warnflag, allvecs) = retvals converged = not warnflag retvals = {'fopt': fopt, 'gopt': gopt, 'Hinv': Hinv, 'fcalls': fcalls, 'gcalls': gcalls, 'warnflag': warnflag, 'converged': converged} if retall: retvals.update({'allvecs': allvecs}) else: xopt = retvals retvals = None return xopt, retvals def _fit_lbfgs(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): """ Fit using Limited-memory Broyden-Fletcher-Goldfarb-Shannon algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : tuple Extra keyworded arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. Notes ----- Within the mle part of statsmodels, the log likelihood function and its gradient with respect to the parameters do not have notationally consistent sign. """ # Use unconstrained optimization by default. bounds = kwargs.setdefault('bounds', [(None, None)] * len(start_params)) kwargs.setdefault('iprint', 0) # Pass the following keyword argument names through to fmin_l_bfgs_b # if they are present in kwargs, otherwise use the fmin_l_bfgs_b # default values. names = ('m', 'pgtol', 'factr', 'maxfun', 'epsilon', 'approx_grad') extra_kwargs = dict((x, kwargs[x]) for x in names if x in kwargs) # Extract values for the options related to the gradient. approx_grad = kwargs.get('approx_grad', False) loglike_and_score = kwargs.get('loglike_and_score', None) epsilon = kwargs.get('epsilon', None) # The approx_grad flag has superpowers nullifying the score function arg. if approx_grad: score = None # Choose among three options for dealing with the gradient (the gradient # of a log likelihood function with respect to its parameters # is more specifically called the score in statistics terminology). # The first option is to use the finite-differences # approximation that is built into the fmin_l_bfgs_b optimizer. # The second option is to use the provided score function. # The third option is to use the score component of a provided # function that simultaneously evaluates the log likelihood and score. if epsilon and not approx_grad: raise ValueError('a finite-differences epsilon was provided ' 'even though we are not using approx_grad') if approx_grad and loglike_and_score: raise ValueError('gradient approximation was requested ' 'even though an analytic loglike_and_score function ' 'was given') if loglike_and_score: func = lambda p, *a : tuple(-x for x in loglike_and_score(p, *a)) elif score: func = f extra_kwargs['fprime'] = score elif approx_grad: func = f retvals = optimize.fmin_l_bfgs_b(func, start_params, maxiter=maxiter, callback=callback, args=fargs, bounds=bounds, disp=disp, **extra_kwargs) if full_output: xopt, fopt, d = retvals # The warnflag is # 0 if converged # 1 if too many function evaluations or too many iterations # 2 if stopped for another reason, given in d['task'] warnflag = d['warnflag'] converged = (warnflag == 0) gopt = d['grad'] fcalls = d['funcalls'] iterations = d['nit'] retvals = {'fopt': fopt, 'gopt': gopt, 'fcalls': fcalls, 'warnflag': warnflag, 'converged': converged, 'iterations': iterations} else: xopt = retvals[0] retvals = None return xopt, retvals def _fit_nm(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): """ Fit using Nelder-Mead algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : tuple Extra keyworded arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. """ xtol = kwargs.setdefault('xtol', 0.0001) ftol = kwargs.setdefault('ftol', 0.0001) maxfun = kwargs.setdefault('maxfun', None) retvals = optimize.fmin(f, start_params, args=fargs, xtol=xtol, ftol=ftol, maxiter=maxiter, maxfun=maxfun, full_output=full_output, disp=disp, retall=retall, callback=callback) if full_output: if not retall: xopt, fopt, niter, fcalls, warnflag = retvals else: xopt, fopt, niter, fcalls, warnflag, allvecs = retvals converged = not warnflag retvals = {'fopt': fopt, 'iterations': niter, 'fcalls': fcalls, 'warnflag': warnflag, 'converged': converged} if retall: retvals.update({'allvecs': allvecs}) else: xopt = retvals retvals = None return xopt, retvals def _fit_cg(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): """ Fit using Conjugate Gradient algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : tuple Extra keyworded arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. """ gtol = kwargs.setdefault('gtol', 1.0000000000000001e-05) norm = kwargs.setdefault('norm', np.Inf) epsilon = kwargs.setdefault('epsilon', 1.4901161193847656e-08) retvals = optimize.fmin_cg(f, start_params, score, gtol=gtol, norm=norm, epsilon=epsilon, maxiter=maxiter, full_output=full_output, disp=disp, retall=retall, callback=callback) if full_output: if not retall: xopt, fopt, fcalls, gcalls, warnflag = retvals else: xopt, fopt, fcalls, gcalls, warnflag, allvecs = retvals converged = not warnflag retvals = {'fopt': fopt, 'fcalls': fcalls, 'gcalls': gcalls, 'warnflag': warnflag, 'converged': converged} if retall: retvals.update({'allvecs': allvecs}) else: xopt = retvals retvals = None return xopt, retvals def _fit_ncg(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): """ Fit using Newton Conjugate Gradient algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : tuple Extra keyworded arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. """ fhess_p = kwargs.setdefault('fhess_p', None) avextol = kwargs.setdefault('avextol', 1.0000000000000001e-05) epsilon = kwargs.setdefault('epsilon', 1.4901161193847656e-08) retvals = optimize.fmin_ncg(f, start_params, score, fhess_p=fhess_p, fhess=hess, args=fargs, avextol=avextol, epsilon=epsilon, maxiter=maxiter, full_output=full_output, disp=disp, retall=retall, callback=callback) if full_output: if not retall: xopt, fopt, fcalls, gcalls, hcalls, warnflag = retvals else: xopt, fopt, fcalls, gcalls, hcalls, warnflag, allvecs =\ retvals converged = not warnflag retvals = {'fopt': fopt, 'fcalls': fcalls, 'gcalls': gcalls, 'hcalls': hcalls, 'warnflag': warnflag, 'converged': converged} if retall: retvals.update({'allvecs': allvecs}) else: xopt = retvals retvals = None return xopt, retvals def _fit_powell(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): """ Fit using Powell's conjugate direction algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : tuple Extra keyworded arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. """ xtol = kwargs.setdefault('xtol', 0.0001) ftol = kwargs.setdefault('ftol', 0.0001) maxfun = kwargs.setdefault('maxfun', None) start_direc = kwargs.setdefault('start_direc', None) retvals = optimize.fmin_powell(f, start_params, args=fargs, xtol=xtol, ftol=ftol, maxiter=maxiter, maxfun=maxfun, full_output=full_output, disp=disp, retall=retall, callback=callback, direc=start_direc) if full_output: if not retall: xopt, fopt, direc, niter, fcalls, warnflag = retvals else: xopt, fopt, direc, niter, fcalls, warnflag, allvecs =\ retvals converged = not warnflag retvals = {'fopt': fopt, 'direc': direc, 'iterations': niter, 'fcalls': fcalls, 'warnflag': warnflag, 'converged': converged} if retall: retvals.update({'allvecs': allvecs}) else: xopt = retvals retvals = None return xopt, retvals def _fit_basinhopping(f, score, start_params, fargs, kwargs, disp=True, maxiter=100, callback=None, retall=False, full_output=True, hess=None): """ Fit using Basin-hopping algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : tuple Extra keyworded arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. """ from copy import copy kwargs = copy(kwargs) niter = kwargs.setdefault('niter', 100) niter_success = kwargs.setdefault('niter_success', None) T = kwargs.setdefault('T', 1.0) stepsize = kwargs.setdefault('stepsize', 0.5) interval = kwargs.setdefault('interval', 50) minimizer_kwargs = kwargs.get('minimizer', {}) minimizer_kwargs['args'] = fargs minimizer_kwargs['jac'] = score method = minimizer_kwargs.get('method', None) if method and method != 'L-BFGS-B': # l_bfgs_b does not take a hessian minimizer_kwargs['hess'] = hess retvals = optimize.basinhopping(f, start_params, minimizer_kwargs=minimizer_kwargs, niter=niter, niter_success=niter_success, T=T, stepsize=stepsize, disp=disp, callback=callback, interval=interval) if full_output: xopt, fopt, niter, fcalls = map(lambda x : getattr(retvals, x), ['x', 'fun', 'nit', 'nfev']) converged = 'completed successfully' in retvals.message[0] retvals = {'fopt': fopt, 'iterations': niter, 'fcalls': fcalls, 'converged': converged} else: xopt = retvals.x retvals = None return xopt, retvals statsmodels-0.12.2/statsmodels/base/tests/000077500000000000000000000000001400612667500205635ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/base/tests/__init__.py000066400000000000000000000000001400612667500226620ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/base/tests/test_data.py000066400000000000000000001061521400612667500231120ustar00rootroot00000000000000from statsmodels.compat.pandas import assert_series_equal, assert_frame_equal,\ make_dataframe import numpy as np from numpy.testing import assert_equal, assert_, assert_raises import pandas as pd import pytest from statsmodels.base import data as sm_data from statsmodels.formula import handle_formula_data from statsmodels.regression.linear_model import OLS from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod import families from statsmodels.discrete.discrete_model import Logit # FIXME: do not leave commented-out, enable or move/remove # class TestDates(object): # @classmethod # def setup_class(cls): # nrows = 10 # cls.dates_result = cls.dates_results = np.random.random(nrows) # # def test_dates(self): # np.testing.assert_equal(data.wrap_output(self.dates_input, 'dates'), # self.dates_result) class TestArrays(object): @classmethod def setup_class(cls): cls.endog = np.random.random(10) cls.exog = np.c_[np.ones(10), np.random.random((10, 2))] cls.data = sm_data.handle_data(cls.endog, cls.exog) nrows = 10 nvars = 3 cls.col_result = cls.col_input = np.random.random(nvars) cls.row_result = cls.row_input = np.random.random(nrows) cls.cov_result = cls.cov_input = np.random.random((nvars, nvars)) cls.xnames = ['const', 'x1', 'x2'] cls.ynames = 'y' cls.row_labels = None def test_orig(self): np.testing.assert_equal(self.data.orig_endog, self.endog) np.testing.assert_equal(self.data.orig_exog, self.exog) def test_endogexog(self): np.testing.assert_equal(self.data.endog, self.endog) np.testing.assert_equal(self.data.exog, self.exog) def test_attach(self): data = self.data # this makes sure what the wrappers need work but not the wrapped # results themselves np.testing.assert_equal(data.wrap_output(self.col_input, 'columns'), self.col_result) np.testing.assert_equal(data.wrap_output(self.row_input, 'rows'), self.row_result) np.testing.assert_equal(data.wrap_output(self.cov_input, 'cov'), self.cov_result) def test_names(self): data = self.data np.testing.assert_equal(data.xnames, self.xnames) np.testing.assert_equal(data.ynames, self.ynames) def test_labels(self): # HACK: because numpy master after NA stuff assert_equal fails on # pandas indices # FIXME: see if this can be de-hacked np.testing.assert_(np.all(self.data.row_labels == self.row_labels)) class TestArrays2dEndog(TestArrays): @classmethod def setup_class(cls): super(TestArrays2dEndog, cls).setup_class() cls.endog = np.random.random((10, 1)) cls.exog = np.c_[np.ones(10), np.random.random((10, 2))] cls.data = sm_data.handle_data(cls.endog, cls.exog) def test_endogexog(self): np.testing.assert_equal(self.data.endog, self.endog.squeeze()) np.testing.assert_equal(self.data.exog, self.exog) class TestArrays1dExog(TestArrays): @classmethod def setup_class(cls): super(TestArrays1dExog, cls).setup_class() cls.endog = np.random.random(10) exog = np.random.random(10) cls.data = sm_data.handle_data(cls.endog, exog) cls.exog = exog[:, None] cls.xnames = ['x1'] cls.ynames = 'y' def test_orig(self): np.testing.assert_equal(self.data.orig_endog, self.endog) np.testing.assert_equal(self.data.orig_exog, self.exog.squeeze()) class TestDataFrames(TestArrays): @classmethod def setup_class(cls): cls.endog = pd.DataFrame(np.random.random(10), columns=['y_1']) exog = pd.DataFrame(np.random.random((10, 2)), columns=['x_1', 'x_2']) exog.insert(0, 'const', 1) cls.exog = exog cls.data = sm_data.handle_data(cls.endog, cls.exog) nrows = 10 nvars = 3 cls.col_input = np.random.random(nvars) cls.col_result = pd.Series(cls.col_input, index=exog.columns) cls.row_input = np.random.random(nrows) cls.row_result = pd.Series(cls.row_input, index=exog.index) cls.cov_input = np.random.random((nvars, nvars)) cls.cov_result = pd.DataFrame(cls.cov_input, index=exog.columns, columns=exog.columns) cls.xnames = ['const', 'x_1', 'x_2'] cls.ynames = 'y_1' cls.row_labels = cls.exog.index def test_orig(self): assert_frame_equal(self.data.orig_endog, self.endog) assert_frame_equal(self.data.orig_exog, self.exog) def test_endogexog(self): np.testing.assert_equal(self.data.endog, self.endog.values.squeeze()) np.testing.assert_equal(self.data.exog, self.exog.values) def test_attach(self): data = self.data # this makes sure what the wrappers need work but not the wrapped # results themselves assert_series_equal(data.wrap_output(self.col_input, 'columns'), self.col_result) assert_series_equal(data.wrap_output(self.row_input, 'rows'), self.row_result) assert_frame_equal(data.wrap_output(self.cov_input, 'cov'), self.cov_result) class TestDataFramesWithMultiIndex(TestDataFrames): @classmethod def setup_class(cls): cls.endog = pd.DataFrame(np.random.random(10), columns=['y_1']) mi = pd.MultiIndex.from_product([['x'], ['1', '2']]) exog = pd.DataFrame(np.random.random((10, 2)), columns=mi) exog_flattened_idx = pd.Index(['const', 'x_1', 'x_2']) exog.insert(0, 'const', 1) cls.exog = exog cls.data = sm_data.handle_data(cls.endog, cls.exog) nrows = 10 nvars = 3 cls.col_input = np.random.random(nvars) cls.col_result = pd.Series(cls.col_input, index=exog_flattened_idx) cls.row_input = np.random.random(nrows) cls.row_result = pd.Series(cls.row_input, index=exog.index) cls.cov_input = np.random.random((nvars, nvars)) cls.cov_result = pd.DataFrame(cls.cov_input, index=exog_flattened_idx, columns=exog_flattened_idx) cls.xnames = ['const', 'x_1', 'x_2'] cls.ynames = 'y_1' cls.row_labels = cls.exog.index class TestLists(TestArrays): @classmethod def setup_class(cls): super(TestLists, cls).setup_class() cls.endog = np.random.random(10).tolist() cls.exog = np.c_[np.ones(10), np.random.random((10, 2))].tolist() cls.data = sm_data.handle_data(cls.endog, cls.exog) class TestRecarrays(TestArrays): @classmethod def setup_class(cls): super(TestRecarrays, cls).setup_class() cls.endog = np.random.random(9).view([('y_1', 'f8')]).view(np.recarray) exog = np.random.random(9*3).view([('const', 'f8'), ('x_1', 'f8'), ('x_2', 'f8')]).view(np.recarray) exog['const'] = 1 cls.exog = exog with pytest.warns(FutureWarning, match="recarray support"): cls.data = sm_data.handle_data(cls.endog, cls.exog) cls.xnames = ['const', 'x_1', 'x_2'] cls.ynames = 'y_1' def test_endogexog(self): np.testing.assert_equal(self.data.endog, self.endog.view(float, type=np.ndarray)) np.testing.assert_equal(self.data.exog, self.exog.view((float, 3), type=np.ndarray)) class TestStructarrays(TestArrays): @classmethod def setup_class(cls): super(TestStructarrays, cls).setup_class() cls.endog = np.random.random(9).view([('y_1', 'f8')]).view(np.recarray) exog = np.random.random(9*3).view([('const', 'f8'), ('x_1', 'f8'), ('x_2', 'f8')]).view(np.recarray) exog['const'] = 1 cls.exog = exog with pytest.warns(FutureWarning, match="recarray support"): cls.data = sm_data.handle_data(cls.endog, cls.exog) cls.xnames = ['const', 'x_1', 'x_2'] cls.ynames = 'y_1' def test_endogexog(self): np.testing.assert_equal(self.data.endog, self.endog.view(float, type=np.ndarray)) np.testing.assert_equal(self.data.exog, self.exog.view((float, 3), type=np.ndarray)) class TestListDataFrame(TestDataFrames): @classmethod def setup_class(cls): cls.endog = np.random.random(10).tolist() exog = pd.DataFrame(np.random.random((10, 2)), columns=['x_1', 'x_2']) exog.insert(0, 'const', 1) cls.exog = exog cls.data = sm_data.handle_data(cls.endog, cls.exog) nrows = 10 nvars = 3 cls.col_input = np.random.random(nvars) cls.col_result = pd.Series(cls.col_input, index=exog.columns) cls.row_input = np.random.random(nrows) cls.row_result = pd.Series(cls.row_input, index=exog.index) cls.cov_input = np.random.random((nvars, nvars)) cls.cov_result = pd.DataFrame(cls.cov_input, index=exog.columns, columns=exog.columns) cls.xnames = ['const', 'x_1', 'x_2'] cls.ynames = 'y' cls.row_labels = cls.exog.index def test_endogexog(self): np.testing.assert_equal(self.data.endog, self.endog) np.testing.assert_equal(self.data.exog, self.exog.values) def test_orig(self): np.testing.assert_equal(self.data.orig_endog, self.endog) assert_frame_equal(self.data.orig_exog, self.exog) class TestDataFrameList(TestDataFrames): @classmethod def setup_class(cls): cls.endog = pd.DataFrame(np.random.random(10), columns=['y_1']) exog = pd.DataFrame(np.random.random((10, 2)), columns=['x1', 'x2']) exog.insert(0, 'const', 1) cls.exog = exog.values.tolist() cls.data = sm_data.handle_data(cls.endog, cls.exog) nrows = 10 nvars = 3 cls.col_input = np.random.random(nvars) cls.col_result = pd.Series(cls.col_input, index=exog.columns) cls.row_input = np.random.random(nrows) cls.row_result = pd.Series(cls.row_input, index=exog.index) cls.cov_input = np.random.random((nvars, nvars)) cls.cov_result = pd.DataFrame(cls.cov_input, index=exog.columns, columns=exog.columns) cls.xnames = ['const', 'x1', 'x2'] cls.ynames = 'y_1' cls.row_labels = cls.endog.index def test_endogexog(self): np.testing.assert_equal(self.data.endog, self.endog.values.squeeze()) np.testing.assert_equal(self.data.exog, self.exog) def test_orig(self): assert_frame_equal(self.data.orig_endog, self.endog) np.testing.assert_equal(self.data.orig_exog, self.exog) class TestArrayDataFrame(TestDataFrames): @classmethod def setup_class(cls): cls.endog = np.random.random(10) exog = pd.DataFrame(np.random.random((10, 2)), columns=['x_1', 'x_2']) exog.insert(0, 'const', 1) cls.exog = exog cls.data = sm_data.handle_data(cls.endog, exog) nrows = 10 nvars = 3 cls.col_input = np.random.random(nvars) cls.col_result = pd.Series(cls.col_input, index=exog.columns) cls.row_input = np.random.random(nrows) cls.row_result = pd.Series(cls.row_input, index=exog.index) cls.cov_input = np.random.random((nvars, nvars)) cls.cov_result = pd.DataFrame(cls.cov_input, index=exog.columns, columns=exog.columns) cls.xnames = ['const', 'x_1', 'x_2'] cls.ynames = 'y' cls.row_labels = cls.exog.index def test_endogexog(self): np.testing.assert_equal(self.data.endog, self.endog) np.testing.assert_equal(self.data.exog, self.exog.values) def test_orig(self): np.testing.assert_equal(self.data.orig_endog, self.endog) assert_frame_equal(self.data.orig_exog, self.exog) class TestDataFrameArray(TestDataFrames): @classmethod def setup_class(cls): cls.endog = pd.DataFrame(np.random.random(10), columns=['y_1']) exog = pd.DataFrame(np.random.random((10, 2)), columns=['x1', 'x2']) # names mimic defaults exog.insert(0, 'const', 1) cls.exog = exog.values cls.data = sm_data.handle_data(cls.endog, cls.exog) nrows = 10 nvars = 3 cls.col_input = np.random.random(nvars) cls.col_result = pd.Series(cls.col_input, index=exog.columns) cls.row_input = np.random.random(nrows) cls.row_result = pd.Series(cls.row_input, index=exog.index) cls.cov_input = np.random.random((nvars, nvars)) cls.cov_result = pd.DataFrame(cls.cov_input, index=exog.columns, columns=exog.columns) cls.xnames = ['const', 'x1', 'x2'] cls.ynames = 'y_1' cls.row_labels = cls.endog.index def test_endogexog(self): np.testing.assert_equal(self.data.endog, self.endog.values.squeeze()) np.testing.assert_equal(self.data.exog, self.exog) def test_orig(self): assert_frame_equal(self.data.orig_endog, self.endog) np.testing.assert_equal(self.data.orig_exog, self.exog) class TestSeriesDataFrame(TestDataFrames): @classmethod def setup_class(cls): cls.endog = pd.Series(np.random.random(10), name='y_1') exog = pd.DataFrame(np.random.random((10, 2)), columns=['x_1', 'x_2']) exog.insert(0, 'const', 1) cls.exog = exog cls.data = sm_data.handle_data(cls.endog, cls.exog) nrows = 10 nvars = 3 cls.col_input = np.random.random(nvars) cls.col_result = pd.Series(cls.col_input, index=exog.columns) cls.row_input = np.random.random(nrows) cls.row_result = pd.Series(cls.row_input, index=exog.index) cls.cov_input = np.random.random((nvars, nvars)) cls.cov_result = pd.DataFrame(cls.cov_input, index=exog.columns, columns=exog.columns) cls.xnames = ['const', 'x_1', 'x_2'] cls.ynames = 'y_1' cls.row_labels = cls.exog.index def test_orig(self): assert_series_equal(self.data.orig_endog, self.endog) assert_frame_equal(self.data.orig_exog, self.exog) class TestSeriesSeries(TestDataFrames): @classmethod def setup_class(cls): cls.endog = pd.Series(np.random.random(10), name='y_1') exog = pd.Series(np.random.random(10), name='x_1') cls.exog = exog cls.data = sm_data.handle_data(cls.endog, cls.exog) nrows = 10 nvars = 1 cls.col_input = np.random.random(nvars) cls.col_result = pd.Series(cls.col_input, index=[exog.name]) cls.row_input = np.random.random(nrows) cls.row_result = pd.Series(cls.row_input, index=exog.index) cls.cov_input = np.random.random((nvars, nvars)) cls.cov_result = pd.DataFrame(cls.cov_input, index=[exog.name], columns=[exog.name]) cls.xnames = ['x_1'] cls.ynames = 'y_1' cls.row_labels = cls.exog.index def test_orig(self): assert_series_equal(self.data.orig_endog, self.endog) assert_series_equal(self.data.orig_exog, self.exog) def test_endogexog(self): np.testing.assert_equal(self.data.endog, self.endog.values.squeeze()) np.testing.assert_equal(self.data.exog, self.exog.values[:, None]) def test_alignment(): # Fix Issue GH#206 from statsmodels.datasets.macrodata import load_pandas d = load_pandas().data # growth rates gs_l_realinv = 400 * np.log(d['realinv']).diff().dropna() gs_l_realgdp = 400 * np.log(d['realgdp']).diff().dropna() lint = d['realint'][:-1] # incorrect indexing for test purposes endog = gs_l_realinv # re-index because they will not conform to lint realgdp = gs_l_realgdp.reindex(lint.index, method='bfill') data = dict(const=np.ones_like(lint), lrealgdp=realgdp, lint=lint) exog = pd.DataFrame(data) # TODO: which index do we get?? np.testing.assert_raises(ValueError, OLS, *(endog, exog)) class TestMultipleEqsArrays(TestArrays): @classmethod def setup_class(cls): cls.endog = np.random.random((10, 4)) cls.exog = np.c_[np.ones(10), np.random.random((10, 2))] cls.data = sm_data.handle_data(cls.endog, cls.exog) nrows = 10 nvars = 3 neqs = 4 cls.col_result = cls.col_input = np.random.random(nvars) cls.row_result = cls.row_input = np.random.random(nrows) cls.cov_result = cls.cov_input = np.random.random((nvars, nvars)) cls.cov_eq_result = cls.cov_eq_input = np.random.random((neqs, neqs)) cls.col_eq_result = cls.col_eq_input = np.array((neqs, nvars)) cls.xnames = ['const', 'x1', 'x2'] cls.ynames = ['y1', 'y2', 'y3', 'y4'] cls.row_labels = None def test_attach(self): data = self.data # this makes sure what the wrappers need work but not the wrapped # results themselves np.testing.assert_equal(data.wrap_output(self.col_input, 'columns'), self.col_result) np.testing.assert_equal(data.wrap_output(self.row_input, 'rows'), self.row_result) np.testing.assert_equal(data.wrap_output(self.cov_input, 'cov'), self.cov_result) np.testing.assert_equal(data.wrap_output(self.cov_eq_input, 'cov_eq'), self.cov_eq_result) np.testing.assert_equal(data.wrap_output(self.col_eq_input, 'columns_eq'), self.col_eq_result) class TestMultipleEqsDataFrames(TestDataFrames): @classmethod def setup_class(cls): cls.endog = endog = pd.DataFrame(np.random.random((10, 4)), columns=['y_1', 'y_2', 'y_3', 'y_4']) exog = pd.DataFrame(np.random.random((10, 2)), columns=['x_1', 'x_2']) exog.insert(0, 'const', 1) cls.exog = exog cls.data = sm_data.handle_data(cls.endog, cls.exog) nrows = 10 nvars = 3 neqs = 4 cls.col_input = np.random.random(nvars) cls.col_result = pd.Series(cls.col_input, index=exog.columns) cls.row_input = np.random.random(nrows) cls.row_result = pd.Series(cls.row_input, index=exog.index) cls.cov_input = np.random.random((nvars, nvars)) cls.cov_result = pd.DataFrame(cls.cov_input, index=exog.columns, columns=exog.columns) cls.cov_eq_input = np.random.random((neqs, neqs)) cls.cov_eq_result = pd.DataFrame(cls.cov_eq_input, index=endog.columns, columns=endog.columns) cls.col_eq_input = np.random.random((nvars, neqs)) cls.col_eq_result = pd.DataFrame(cls.col_eq_input, index=exog.columns, columns=endog.columns) cls.xnames = ['const', 'x_1', 'x_2'] cls.ynames = ['y_1', 'y_2', 'y_3', 'y_4'] cls.row_labels = cls.exog.index def test_attach(self): data = self.data assert_series_equal(data.wrap_output(self.col_input, 'columns'), self.col_result) assert_series_equal(data.wrap_output(self.row_input, 'rows'), self.row_result) assert_frame_equal(data.wrap_output(self.cov_input, 'cov'), self.cov_result) assert_frame_equal(data.wrap_output(self.cov_eq_input, 'cov_eq'), self.cov_eq_result) assert_frame_equal(data.wrap_output(self.col_eq_input, 'columns_eq'), self.col_eq_result) class TestMissingArray(object): @classmethod def setup_class(cls): X = np.random.random((25, 4)) y = np.random.random(25) y[10] = np.nan X[2, 3] = np.nan X[14, 2] = np.nan cls.y, cls.X = y, X @pytest.mark.smoke def test_raise_no_missing(self): # GH#1700 sm_data.handle_data(np.random.random(20), np.random.random((20, 2)), 'raise') def test_raise(self): with pytest.raises(Exception): # TODO: be more specific about exception sm_data.handle_data(self.y, self.X, 'raise') def test_drop(self): y = self.y X = self.X combined = np.c_[y, X] idx = ~np.isnan(combined).any(axis=1) y = y[idx] X = X[idx] data = sm_data.handle_data(self.y, self.X, 'drop') np.testing.assert_array_equal(data.endog, y) np.testing.assert_array_equal(data.exog, X) def test_none(self): data = sm_data.handle_data(self.y, self.X, 'none', hasconst=False) np.testing.assert_array_equal(data.endog, self.y) np.testing.assert_array_equal(data.exog, self.X) assert data.k_constant == 0 def test_endog_only_raise(self): with pytest.raises(Exception): # TODO: be more specific about exception sm_data.handle_data(self.y, None, 'raise') def test_endog_only_drop(self): y = self.y y = y[~np.isnan(y)] data = sm_data.handle_data(self.y, None, 'drop') np.testing.assert_array_equal(data.endog, y) def test_mv_endog(self): y = self.X y = y[~np.isnan(y).any(axis=1)] data = sm_data.handle_data(self.X, None, 'drop') np.testing.assert_array_equal(data.endog, y) def test_extra_kwargs_2d(self): sigma = np.random.random((25, 25)) sigma = sigma + sigma.T - np.diag(np.diag(sigma)) data = sm_data.handle_data(self.y, self.X, 'drop', sigma=sigma) idx = ~np.isnan(np.c_[self.y, self.X]).any(axis=1) sigma = sigma[idx][:, idx] np.testing.assert_array_equal(data.sigma, sigma) def test_extra_kwargs_1d(self): weights = np.random.random(25) data = sm_data.handle_data(self.y, self.X, 'drop', weights=weights) idx = ~np.isnan(np.c_[self.y, self.X]).any(axis=1) weights = weights[idx] np.testing.assert_array_equal(data.weights, weights) class TestMissingPandas(object): @classmethod def setup_class(cls): X = np.random.random((25, 4)) y = np.random.random(25) y[10] = np.nan X[2, 3] = np.nan X[14, 2] = np.nan cls.y = pd.Series(y) cls.X = pd.DataFrame(X) @pytest.mark.smoke def test_raise_no_missing(self): # GH#1700 sm_data.handle_data(pd.Series(np.random.random(20)), pd.DataFrame(np.random.random((20, 2))), 'raise') def test_raise(self): with pytest.raises(Exception): # TODO: be more specific about exception sm_data.handle_data(self.y, self.X, 'raise') def test_drop(self): y = self.y X = self.X combined = np.c_[y, X] idx = ~np.isnan(combined).any(axis=1) y = y.loc[idx] X = X.loc[idx] data = sm_data.handle_data(self.y, self.X, 'drop') np.testing.assert_array_equal(data.endog, y.values) assert_series_equal(data.orig_endog, self.y.loc[idx]) np.testing.assert_array_equal(data.exog, X.values) assert_frame_equal(data.orig_exog, self.X.loc[idx]) def test_none(self): data = sm_data.handle_data(self.y, self.X, 'none', hasconst=False) np.testing.assert_array_equal(data.endog, self.y.values) np.testing.assert_array_equal(data.exog, self.X.values) assert data.k_constant == 0 def test_endog_only_raise(self): with pytest.raises(Exception): # TODO: be more specific about exception sm_data.handle_data(self.y, None, 'raise') def test_endog_only_drop(self): y = self.y y = y.dropna() data = sm_data.handle_data(self.y, None, 'drop') np.testing.assert_array_equal(data.endog, y.values) def test_mv_endog(self): y = self.X y = y.loc[~np.isnan(y.values).any(axis=1)] data = sm_data.handle_data(self.X, None, 'drop') np.testing.assert_array_equal(data.endog, y.values) def test_labels(self): labels = pd.Index([0, 1, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]) data = sm_data.handle_data(self.y, self.X, 'drop') np.testing.assert_(data.row_labels.equals(labels)) class TestConstant(object): @classmethod def setup_class(cls): from statsmodels.datasets.longley import load_pandas cls.data = load_pandas() def test_array_constant(self): exog = self.data.exog.copy() exog['const'] = 1 data = sm_data.handle_data(self.data.endog.values, exog.values) np.testing.assert_equal(data.k_constant, 1) np.testing.assert_equal(data.const_idx, 6) def test_pandas_constant(self): exog = self.data.exog.copy() exog['const'] = 1 data = sm_data.handle_data(self.data.endog, exog) np.testing.assert_equal(data.k_constant, 1) np.testing.assert_equal(data.const_idx, 6) def test_pandas_noconstant(self): exog = self.data.exog.copy() data = sm_data.handle_data(self.data.endog, exog) np.testing.assert_equal(data.k_constant, 0) np.testing.assert_equal(data.const_idx, None) def test_array_noconstant(self): exog = self.data.exog.copy() data = sm_data.handle_data(self.data.endog.values, exog.values) np.testing.assert_equal(data.k_constant, 0) np.testing.assert_equal(data.const_idx, None) class TestHandleMissing(object): def test_pandas(self): df = make_dataframe() df.values[[2, 5, 10], [2, 3, 1]] = np.nan y, X = df[df.columns[0]], df[df.columns[1:]] data, _ = sm_data.handle_missing(y, X, missing='drop') df = df.dropna() y_exp, X_exp = df[df.columns[0]], df[df.columns[1:]] assert_frame_equal(data['exog'], X_exp) assert_series_equal(data['endog'], y_exp) def test_arrays(self): arr = np.random.randn(20, 4) arr[[2, 5, 10], [2, 3, 1]] = np.nan y, X = arr[:, 0], arr[:, 1:] data, _ = sm_data.handle_missing(y, X, missing='drop') bools_mask = np.ones(20, dtype=bool) bools_mask[[2, 5, 10]] = False y_exp = arr[bools_mask, 0] X_exp = arr[bools_mask, 1:] np.testing.assert_array_equal(data['endog'], y_exp) np.testing.assert_array_equal(data['exog'], X_exp) def test_pandas_array(self): df = make_dataframe() df.values[[2, 5, 10], [2, 3, 1]] = np.nan y, X = df[df.columns[0]], df[df.columns[1:]].values data, _ = sm_data.handle_missing(y, X, missing='drop') df = df.dropna() y_exp, X_exp = df[df.columns[0]], df[df.columns[1:]].values np.testing.assert_array_equal(data['exog'], X_exp) assert_series_equal(data['endog'], y_exp) def test_array_pandas(self): df = make_dataframe() df.values[[2, 5, 10], [2, 3, 1]] = np.nan y, X = df[df.columns[0]].values, df[df.columns[1:]] data, _ = sm_data.handle_missing(y, X, missing='drop') df = df.dropna() y_exp, X_exp = df[df.columns[0]].values, df[df.columns[1:]] assert_frame_equal(data['exog'], X_exp) np.testing.assert_array_equal(data['endog'], y_exp) def test_noop(self): df = make_dataframe() df.values[[2, 5, 10], [2, 3, 1]] = np.nan y, X = df[df.columns[0]], df[df.columns[1:]] data, _ = sm_data.handle_missing(y, X, missing='none') y_exp, X_exp = df[df.columns[0]], df[df.columns[1:]] assert_frame_equal(data['exog'], X_exp) assert_series_equal(data['endog'], y_exp) class CheckHasConstant(object): def test_hasconst(self): for x, result in zip(self.exogs, self.results): mod = self.mod(self.y, x) assert_equal(mod.k_constant, result[0]) assert_equal(mod.data.k_constant, result[0]) if result[1] is None: assert_(mod.data.const_idx is None) else: assert_equal(mod.data.const_idx, result[1]) # extra check after fit, some models raise on singular fit_kwds = getattr(self, 'fit_kwds', {}) try: res = mod.fit(**fit_kwds) except np.linalg.LinAlgError: pass else: assert_equal(res.model.k_constant, result[0]) assert_equal(res.model.data.k_constant, result[0]) @classmethod def setup_class(cls): # create data np.random.seed(0) cls.y_c = np.random.randn(20) cls.y_bin = (cls.y_c > 0).astype(int) x1 = np.column_stack((np.ones(20), np.zeros(20))) result1 = (1, 0) x2 = np.column_stack((np.arange(20) < 10.5, np.arange(20) > 10.5)).astype(float) result2 = (1, None) x3 = np.column_stack((np.arange(20), np.zeros(20))) result3 = (0, None) x4 = np.column_stack((np.arange(20), np.zeros((20, 2)))) result4 = (0, None) x5 = np.column_stack((np.zeros(20), 0.5 * np.ones(20))) result5 = (1, 1) x5b = np.column_stack((np.arange(20), np.ones((20, 3)))) result5b = (1, 1) x5c = np.column_stack((np.arange(20), np.ones((20, 3)) * [0.5, 1, 1])) result5c = (1, 2) # implicit and zero column x6 = np.column_stack((np.arange(20) < 10.5, np.arange(20) > 10.5, np.zeros(20))).astype(float) result6 = (1, None) x7 = np.column_stack((np.arange(20) < 10.5, np.arange(20) > 10.5, np.zeros((20, 2)))).astype(float) result7 = (1, None) cls.exogs = (x1, x2, x3, x4, x5, x5b, x5c, x6, x7) cls.results = (result1, result2, result3, result4, result5, result5b, result5c, result6, result7) cls._initialize() class TestHasConstantOLS(CheckHasConstant): @classmethod def _initialize(cls): cls.mod = OLS cls.y = cls.y_c class TestHasConstantGLM(CheckHasConstant): @staticmethod def mod(y, x): return GLM(y, x, family=families.Binomial()) @classmethod def _initialize(cls): cls.y = cls.y_bin class TestHasConstantLogit(CheckHasConstant): @classmethod def _initialize(cls): cls.mod = Logit cls.y = cls.y_bin cls.fit_kwds = {'disp': False} def test_dtype_object(): # see GH#880 X = np.random.random((40, 2)) df = pd.DataFrame(X) df[2] = np.random.randint(2, size=40).astype('object') df['constant'] = 1 y = pd.Series(np.random.randint(2, size=40)) np.testing.assert_raises(ValueError, sm_data.handle_data, y, df) def test_formula_missing_extra_arrays(): np.random.seed(1) # because patsy cannot turn off missing data-handling as of 0.3.0, we need # separate tests to make sure that missing values are handled correctly # when going through formulas # there is a handle_formula_data step # then there is the regular handle_data step # see GH#2083 # the untested cases are endog/exog have missing. extra has missing. # endog/exog are fine. extra has missing. # endog/exog do or do not have missing and extra has wrong dimension y = np.random.randn(10) y_missing = y.copy() y_missing[[2, 5]] = np.nan X = np.random.randn(10) X_missing = X.copy() X_missing[[1, 3]] = np.nan weights = np.random.uniform(size=10) weights_missing = weights.copy() weights_missing[[6]] = np.nan weights_wrong_size = np.random.randn(12) data = {'y': y, 'X': X, 'y_missing': y_missing, 'X_missing': X_missing, 'weights': weights, 'weights_missing': weights_missing} data = pd.DataFrame.from_dict(data) data['constant'] = 1 formula = 'y_missing ~ X_missing' ((endog, exog), missing_idx, design_info) = handle_formula_data(data, None, formula, depth=2, missing='drop') kwargs = {'missing_idx': missing_idx, 'missing': 'drop', 'weights': data['weights_missing']} model_data = sm_data.handle_data(endog, exog, **kwargs) data_nona = data.dropna() assert_equal(data_nona['y'].values, model_data.endog) assert_equal(data_nona[['constant', 'X']].values, model_data.exog) assert_equal(data_nona['weights'].values, model_data.weights) tmp = handle_formula_data(data, None, formula, depth=2, missing='drop') (endog, exog), missing_idx, design_info = tmp weights_2d = np.random.randn(10, 10) weights_2d[[8, 7], [7, 8]] = np.nan # symmetric missing values kwargs.update({'weights': weights_2d, 'missing_idx': missing_idx}) model_data2 = sm_data.handle_data(endog, exog, **kwargs) good_idx = [0, 4, 6, 9] assert_equal(data.loc[good_idx, 'y'], model_data2.endog) assert_equal(data.loc[good_idx, ['constant', 'X']], model_data2.exog) assert_equal(weights_2d[good_idx][:, good_idx], model_data2.weights) tmp = handle_formula_data(data, None, formula, depth=2, missing='drop') (endog, exog), missing_idx, design_info = tmp kwargs.update({'weights': weights_wrong_size, 'missing_idx': missing_idx}) assert_raises(ValueError, sm_data.handle_data, endog, exog, **kwargs) def test_raise_nonfinite_exog(): # we raise now in the has constant check before hitting the linear algebra from statsmodels.tools.sm_exceptions import MissingDataError x = np.arange(10)[:, None]**([0., 1.]) # random numbers for y y = np.array([-0.6, -0.1, 0., -0.7, -0.5, 0.5, 0.1, -0.8, -2., 1.1]) x[1, 1] = np.inf assert_raises(MissingDataError, OLS, y, x) x[1, 1] = np.nan assert_raises(MissingDataError, OLS, y, x) statsmodels-0.12.2/statsmodels/base/tests/test_distributed_estimation.py000066400000000000000000000372421400612667500267620ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_equal, assert_, assert_allclose from statsmodels.regression.linear_model import OLS from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod.families import Binomial from statsmodels.base.distributed_estimation import _calc_grad, \ _calc_wdesign_mat, _est_regularized_debiased, _join_debiased, \ _est_regularized_naive, _est_unregularized_naive, _join_naive, \ DistributedModel def _data_gen(endog, exog, partitions): """partitions data""" n_exog = exog.shape[0] n_part = np.ceil(n_exog / partitions) n_part = np.floor(n_exog / partitions) rem = n_exog - n_part * partitions stp = 0 while stp < (partitions - 1): ii = int(n_part * stp) jj = int(n_part * (stp + 1)) yield endog[ii:jj], exog[ii:jj, :] stp += 1 ii = int(n_part * stp) jj = int(n_part * (stp + 1) + rem) yield endog[ii:jj], exog[ii:jj, :] def test_calc_grad(): # separately tests that _calc_grad returns # sensible results # # regression test np.random.seed(435265) X = np.random.normal(size=(50, 3)) y = np.random.randint(0, 2, size=50) beta = np.random.normal(size=3) mod = OLS(y, X) grad = _calc_grad(mod, beta, 0.01, 1, {}) assert_allclose(grad, np.array([19.75816, -6.62307, 7.324644]), atol=1e-6, rtol=0) def test_calc_wdesign_mat(): # separately tests that _calc_wdesign_mat # returns sensible results # # regression test np.random.seed(435265) X = np.random.normal(size=(3, 3)) y = np.random.randint(0, 2, size=3) beta = np.random.normal(size=3) mod = OLS(y, X) dmat = _calc_wdesign_mat(mod, beta, {}) assert_allclose(dmat, np.array([[1.306314, -0.024897, 1.326498], [-0.539219, -0.483028, -0.703503], [-3.327987, 0.524541, -0.139761]]), atol=1e-6, rtol=0) mod = GLM(y, X, family=Binomial()) dmat = _calc_wdesign_mat(mod, beta, {}) assert_allclose(dmat, np.array([[0.408616, -0.007788, 0.41493], [-0.263292, -0.235854, -0.343509], [-0.11241, 0.017718, -0.004721]]), atol=1e-6, rtol=0) def test_est_regularized_debiased(): # tests that the shape of all the intermediate steps # remains correct for regularized debiased estimation, # does this for OLS and GLM np.random.seed(435265) X = np.random.normal(size=(50, 3)) y = np.random.randint(0, 2, size=50) beta = np.random.normal(size=3) mod = OLS(y, X) res = _est_regularized_debiased(mod, 0, 2, fit_kwds={"alpha": 0.5}) bhat = res[0] grad = res[1] ghat_l = res[2] that_l = res[3] assert_(isinstance(res, tuple)) assert_equal(bhat.shape, beta.shape) assert_equal(grad.shape, beta.shape) assert_(isinstance(ghat_l, list)) assert_(isinstance(that_l, list)) assert_equal(len(ghat_l), len(that_l)) assert_equal(ghat_l[0].shape, (2,)) assert_(isinstance(that_l[0], float)) mod = GLM(y, X, family=Binomial()) res = _est_regularized_debiased(mod, 0, 2, fit_kwds={"alpha": 0.5}) bhat = res[0] grad = res[1] ghat_l = res[2] that_l = res[3] assert_(isinstance(res, tuple)) assert_equal(bhat.shape, beta.shape) assert_equal(grad.shape, beta.shape) assert_(isinstance(ghat_l, list)) assert_(isinstance(that_l, list)) assert_equal(len(ghat_l), len(that_l)) assert_equal(ghat_l[0].shape, (2,)) assert_(isinstance(that_l[0], float)) def test_est_regularized_naive(): # tests that the shape of all the intermediate steps # remains correct for regularized naive estimation, # does this for OLS and GLM np.random.seed(435265) X = np.random.normal(size=(50, 3)) y = np.random.randint(0, 2, size=50) beta = np.random.normal(size=3) mod = OLS(y, X) res = _est_regularized_naive(mod, 0, 2, fit_kwds={"alpha": 0.5}) assert_equal(res.shape, beta.shape) mod = GLM(y, X, family=Binomial()) res = _est_regularized_naive(mod, 0, 2, fit_kwds={"alpha": 0.5}) assert_equal(res.shape, beta.shape) def test_est_unregularized_naive(): # tests that the shape of all the intermediate steps # remains correct for unregularized naive estimation, # does this for OLS and GLM np.random.seed(435265) X = np.random.normal(size=(50, 3)) y = np.random.randint(0, 2, size=50) beta = np.random.normal(size=3) mod = OLS(y, X) res = _est_unregularized_naive(mod, 0, 2, fit_kwds={"alpha": 0.5}) assert_equal(res.shape, beta.shape) mod = GLM(y, X, family=Binomial()) res = _est_unregularized_naive(mod, 0, 2, fit_kwds={"alpha": 0.5}) assert_equal(res.shape, beta.shape) def test_join_debiased(): # tests that the results of all the intermediate steps # remains correct for debiased join, does this for OLS and GLM # # regression test np.random.seed(435265) X = np.random.normal(size=(50, 3)) y = np.random.randint(0, 2, size=50) mod = OLS(y, X) res_l = [] for i in range(2): res = _est_regularized_debiased(mod, i, 2, fit_kwds={"alpha": 0.1}) res_l.append(res) joined = _join_debiased(res_l) assert_allclose(joined, np.array([-0.167548, -0.016567, -0.34414]), atol=1e-6, rtol=0) mod = GLM(y, X, family=Binomial()) res_l = [] for i in range(2): res = _est_regularized_debiased(mod, i, 2, fit_kwds={"alpha": 0.1}) res_l.append(res) joined = _join_debiased(res_l) assert_allclose(joined, np.array([-0.164515, -0.412854, -0.223955]), atol=1e-6, rtol=0) def test_join_naive(): # tests that the results of all the intermediate steps # remains correct for naive join, does this for OLS and GLM # # regression test np.random.seed(435265) X = np.random.normal(size=(50, 3)) y = np.random.randint(0, 2, size=50) mod = OLS(y, X) res_l = [] for i in range(2): res = _est_regularized_naive(mod, i, 2, fit_kwds={"alpha": 0.1}) res_l.append(res) joined = _join_naive(res_l) assert_allclose(joined, np.array([-0.020757, 0., 0.]), atol=1e-6, rtol=0) mod = GLM(y, X, family=Binomial()) res_l = [] for i in range(2): res = _est_regularized_naive(mod, i, 2, fit_kwds={"alpha": 0.1}) res_l.append(res) joined = _join_naive(res_l) assert_allclose(joined, np.array([0., 0., 0.]), atol=1e-6, rtol=0) def test_fit_sequential(): # tests that the results of all the intermediate steps # remains correct for sequential fit, does this for OLS and GLM # and a variety of model sizes # # regression test np.random.seed(435265) X = np.random.normal(size=(50, 3)) y = np.random.randint(0, 2, size=50) mod = DistributedModel(1, model_class=OLS) fit = mod.fit(_data_gen(y, X, 1), parallel_method="sequential", fit_kwds={"alpha": 0.5}) assert_allclose(fit.params, np.array([-0.191606, -0.012565, -0.351398]), atol=1e-6, rtol=0) mod = DistributedModel(2, model_class=OLS) fit = mod.fit(_data_gen(y, X, 2), parallel_method="sequential", fit_kwds={"alpha": 0.5}) assert_allclose(fit.params, np.array([-0.157416, -0.029643, -0.471653]), atol=1e-6, rtol=0) mod = DistributedModel(3, model_class=OLS) fit = mod.fit(_data_gen(y, X, 3), parallel_method="sequential", fit_kwds={"alpha": 0.5}) assert_allclose(fit.params, np.array([-0.124891, -0.050934, -0.403354]), atol=1e-6, rtol=0) mod = DistributedModel(1, model_class=GLM, init_kwds={"family": Binomial()}) fit = mod.fit(_data_gen(y, X, 1), parallel_method="sequential", fit_kwds={"alpha": 0.5}) assert_allclose(fit.params, np.array([-0.164515, -0.412854, -0.223955]), atol=1e-6, rtol=0) mod = DistributedModel(2, model_class=GLM, init_kwds={"family": Binomial()}) fit = mod.fit(_data_gen(y, X, 2), parallel_method="sequential", fit_kwds={"alpha": 0.5}) assert_allclose(fit.params, np.array([-0.142513, -0.360324, -0.295485]), atol=1e-6, rtol=0) mod = DistributedModel(3, model_class=GLM, init_kwds={"family": Binomial()}) fit = mod.fit(_data_gen(y, X, 3), parallel_method="sequential", fit_kwds={"alpha": 0.5}) assert_allclose(fit.params, np.array([-0.110487, -0.306431, -0.243921]), atol=1e-6, rtol=0) def test_fit_joblib(): # tests that the results of all the intermediate steps # remains correct for joblib fit, does this for OLS and GLM # and a variety of model sizes # # regression test np.random.seed(435265) X = np.random.normal(size=(50, 3)) y = np.random.randint(0, 2, size=50) mod = DistributedModel(1, model_class=OLS) fit = mod.fit(_data_gen(y, X, 1), parallel_method="joblib", fit_kwds={"alpha": 0.5}) assert_allclose(fit.params, np.array([-0.191606, -0.012565, -0.351398]), atol=1e-6, rtol=0) mod = DistributedModel(2, model_class=OLS) fit = mod.fit(_data_gen(y, X, 2), parallel_method="joblib", fit_kwds={"alpha": 0.5}) assert_allclose(fit.params, np.array([-0.157416, -0.029643, -0.471653]), atol=1e-6, rtol=0) mod = DistributedModel(3, model_class=OLS) fit = mod.fit(_data_gen(y, X, 3), parallel_method="joblib", fit_kwds={"alpha": 0.5}) assert_allclose(fit.params, np.array([-0.124891, -0.050934, -0.403354]), atol=1e-6, rtol=0) mod = DistributedModel(1, model_class=GLM, init_kwds={"family": Binomial()}) fit = mod.fit(_data_gen(y, X, 1), parallel_method="joblib", fit_kwds={"alpha": 0.5}) assert_allclose(fit.params, np.array([-0.164515, -0.412854, -0.223955]), atol=1e-6, rtol=0) mod = DistributedModel(2, model_class=GLM, init_kwds={"family": Binomial()}) fit = mod.fit(_data_gen(y, X, 2), parallel_method="joblib", fit_kwds={"alpha": 0.5}) assert_allclose(fit.params, np.array([-0.142513, -0.360324, -0.295485]), atol=1e-6, rtol=0) mod = DistributedModel(3, model_class=GLM, init_kwds={"family": Binomial()}) fit = mod.fit(_data_gen(y, X, 3), parallel_method="joblib", fit_kwds={"alpha": 0.5}) assert_allclose(fit.params, np.array([-0.110487, -0.306431, -0.243921]), atol=1e-6, rtol=0) def test_single_partition(): # tests that the results make sense if we have a single partition np.random.seed(435265) N = 200 p = 10 m = 1 beta = np.random.normal(size=p) beta = beta * np.random.randint(0, 2, p) X = np.random.normal(size=(N, p)) y = X.dot(beta) + np.random.normal(size=N) # test regularized OLS v. naive db_mod = DistributedModel(m) fitOLSdb = db_mod.fit(_data_gen(y, X, m), fit_kwds={"alpha": 0}) nv_mod = DistributedModel(m, estimation_method=_est_regularized_naive, join_method=_join_naive) fitOLSnv = nv_mod.fit(_data_gen(y, X, m), fit_kwds={"alpha": 0}) ols_mod = OLS(y, X) fitOLS = ols_mod.fit(alpha=0) assert_allclose(fitOLSdb.params, fitOLS.params) assert_allclose(fitOLSnv.params, fitOLS.params) # test regularized nv_mod = DistributedModel(m, estimation_method=_est_regularized_naive, join_method=_join_naive) fitOLSnv = nv_mod.fit(_data_gen(y, X, m), fit_kwds={"alpha": 0.1}) ols_mod = OLS(y, X) fitOLS = ols_mod.fit_regularized(alpha=0.1) assert_allclose(fitOLSnv.params, fitOLS.params) def test_larger_p(): # tests when p > N / m for the debiased and naive case np.random.seed(435265) N = 40 p = 40 m = 5 beta = np.random.normal(size=p) beta = beta * np.random.randint(0, 2, p) X = np.random.normal(size=(N, p)) y = X.dot(beta) + np.random.normal(size=N) db_mod = DistributedModel(m) fitOLSdb = db_mod.fit(_data_gen(y, X, m), fit_kwds={"alpha": 0.1}) assert_equal(np.sum(np.isnan(fitOLSdb.params)), 0) nv_mod = DistributedModel(m, estimation_method=_est_regularized_naive, join_method=_join_naive) fitOLSnv = nv_mod.fit(_data_gen(y, X, m), fit_kwds={"alpha": 0.1}) assert_equal(np.sum(np.isnan(fitOLSnv.params)), 0) def test_non_zero_params(): # tests that the thresholding does not cause any issues np.random.seed(435265) N = 200 p = 10 m = 5 beta = np.random.normal(size=p) beta = beta * np.random.randint(0, 2, p) X = np.random.normal(size=(N, p)) y = X.dot(beta) + np.random.normal(size=N) db_mod = DistributedModel(m, join_kwds={"threshold": 0.13}) fitOLSdb = db_mod.fit(_data_gen(y, X, m), fit_kwds={"alpha": 0.1}) ols_mod = OLS(y, X) fitOLS = ols_mod.fit_regularized(alpha=0.1) nz_params_db = 1 * (fitOLSdb.params != 0) nz_params_ols = 1 * (fitOLS.params != 0) assert_allclose(nz_params_db, nz_params_ols) def test_repeat_partition(): # tests that if we use identical partitions the average is the same # as the estimate for the full data np.random.seed(435265) N = 200 p = 10 m = 1 beta = np.random.normal(size=p) beta = beta * np.random.randint(0, 2, p) X = np.random.normal(size=(N, p)) y = X.dot(beta) + np.random.normal(size=N) def _rep_data_gen(endog, exog, partitions): """partitions data""" n_exog = exog.shape[0] n_part = np.ceil(n_exog / partitions) ii = 0 while ii < n_exog: yield endog, exog ii += int(n_part) nv_mod = DistributedModel(m, estimation_method=_est_regularized_naive, join_method=_join_naive) fitOLSnv = nv_mod.fit(_rep_data_gen(y, X, m), fit_kwds={"alpha": 0.1}) ols_mod = OLS(y, X) fitOLS = ols_mod.fit_regularized(alpha=0.1) assert_allclose(fitOLSnv.params, fitOLS.params) def test_debiased_v_average(): # tests that the debiased method performs better than the standard # average. Does this for both OLS and GLM. np.random.seed(435265) N = 200 p = 10 m = 4 beta = np.random.normal(size=p) beta = beta * np.random.randint(0, 2, p) X = np.random.normal(size=(N, p)) y = X.dot(beta) + np.random.normal(size=N) db_mod = DistributedModel(m) fitOLSdb = db_mod.fit(_data_gen(y, X, m), fit_kwds={"alpha": 0.2}) olsdb = np.linalg.norm(fitOLSdb.params - beta) n_mod = DistributedModel(m, estimation_method=_est_regularized_naive, join_method=_join_naive) fitOLSn = n_mod.fit(_data_gen(y, X, m), fit_kwds={"alpha": 0.2}) olsn = np.linalg.norm(fitOLSn.params - beta) assert_(olsdb < olsn) prob = 1 / (1 + np.exp(-X.dot(beta) + np.random.normal(size=N))) y = 1. * (prob > 0.5) db_mod = DistributedModel(m, model_class=GLM, init_kwds={"family": Binomial()}) fitGLMdb = db_mod.fit(_data_gen(y, X, m), fit_kwds={"alpha": 0.2}) glmdb = np.linalg.norm(fitGLMdb.params - beta) n_mod = DistributedModel(m, model_class=GLM, init_kwds={"family": Binomial()}, estimation_method=_est_regularized_naive, join_method=_join_naive) fitGLMn = n_mod.fit(_data_gen(y, X, m), fit_kwds={"alpha": 0.2}) glmn = np.linalg.norm(fitGLMn.params - beta) assert_(glmdb < glmn) statsmodels-0.12.2/statsmodels/base/tests/test_generic_methods.py000066400000000000000000000674761400612667500253570ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Tests that use cross-checks for generic methods Should be easy to check consistency across models Does not cover tsa Initial cases copied from test_shrink_pickle Created on Wed Oct 30 14:01:27 2013 Author: Josef Perktold """ from statsmodels.compat.pandas import assert_series_equal, assert_index_equal from statsmodels.compat.platform import (PLATFORM_OSX, PLATFORM_LINUX32, PLATFORM_WIN32) from statsmodels.compat.scipy import SCIPY_GT_14 import numpy as np import pandas as pd import pytest import statsmodels.api as sm from statsmodels.tools.sm_exceptions import HessianInversionWarning import statsmodels.tools._testing as smt from statsmodels.formula.api import ols, glm from numpy.testing import (assert_, assert_allclose, assert_equal, assert_array_equal) class CheckGenericMixin(object): @classmethod def setup_class(cls): nobs = 500 np.random.seed(987689) x = np.random.randn(nobs, 3) x = sm.add_constant(x) cls.exog = x cls.xf = 0.25 * np.ones((2, 4)) cls.predict_kwds = {} cls.transform_index = None def test_ttest_tvalues(self): # test that t_test has same results a params, bse, tvalues, ... smt.check_ttest_tvalues(self.results) res = self.results mat = np.eye(len(res.params)) tt = res.t_test(mat[0]) string_confint = lambda alpha: "[%4.3F %4.3F]" % ( alpha / 2, 1- alpha / 2) summ = tt.summary() # smoke test for #1323 assert_allclose(tt.pvalue, res.pvalues[0], rtol=5e-10) assert_(string_confint(0.05) in str(summ)) # issue #3116 alpha not used in column headers summ = tt.summary(alpha=0.1) ss = "[0.05 0.95]" # different formatting assert_(ss in str(summ)) summf = tt.summary_frame(alpha=0.1) pvstring_use_t = 'P>|z|' if res.use_t is False else 'P>|t|' tstring_use_t = 'z' if res.use_t is False else 't' cols = ['coef', 'std err', tstring_use_t, pvstring_use_t, 'Conf. Int. Low', 'Conf. Int. Upp.'] assert_array_equal(summf.columns.values, cols) def test_ftest_pvalues(self): smt.check_ftest_pvalues(self.results) def test_fitted(self): smt.check_fitted(self.results) def test_predict_types(self): smt.check_predict_types(self.results) def test_zero_constrained(self): # not completely generic yet if (isinstance(self.results.model, (sm.GEE))): # GEE does not subclass LikelihoodModel pytest.skip('GEE does not subclass LikelihoodModel') use_start_params = not isinstance(self.results.model, (sm.RLM, sm.OLS, sm.WLS)) self.use_start_params = use_start_params # attach for _get_constrained keep_index = list(range(self.results.model.exog.shape[1])) # index for params might include extra params keep_index_p = list(range(self.results.params.shape[0])) drop_index = [1] for i in drop_index: del keep_index[i] del keep_index_p[i] if use_start_params: res1 = self.results.model._fit_zeros(keep_index, maxiter=500, start_params=self.results.params) else: res1 = self.results.model._fit_zeros(keep_index, maxiter=500) res2 = self._get_constrained(keep_index, keep_index_p) assert_allclose(res1.params[keep_index_p], res2.params, rtol=1e-10, atol=1e-10) assert_equal(res1.params[drop_index], 0) assert_allclose(res1.bse[keep_index_p], res2.bse, rtol=1e-10, atol=1e-10) assert_equal(res1.bse[drop_index], 0) # OSX has many slight failures on this test tol = 1e-8 if PLATFORM_OSX else 1e-10 tvals1 = res1.tvalues[keep_index_p] assert_allclose(tvals1, res2.tvalues, rtol=tol, atol=tol) # See gh5993 if PLATFORM_LINUX32 or SCIPY_GT_14: pvals1 = res1.pvalues[keep_index_p] else: pvals1 = res1.pvalues[keep_index_p] assert_allclose(pvals1, res2.pvalues, rtol=tol, atol=tol) if hasattr(res1, 'resid'): # discrete models, Logit do not have `resid` yet # atol discussion at gh-5158 rtol = 1e-10 atol = 1e-12 if PLATFORM_OSX or PLATFORM_WIN32: # GH 5628 rtol = 1e-8 atol = 1e-10 assert_allclose(res1.resid, res2.resid, rtol=rtol, atol=atol) ex = self.results.model.exog.mean(0) predicted1 = res1.predict(ex, **self.predict_kwds) predicted2 = res2.predict(ex[keep_index], **self.predict_kwds) assert_allclose(predicted1, predicted2, rtol=1e-10) ex = self.results.model.exog[:5] predicted1 = res1.predict(ex, **self.predict_kwds) predicted2 = res2.predict(ex[:, keep_index], **self.predict_kwds) assert_allclose(predicted1, predicted2, rtol=1e-10) def _get_constrained(self, keep_index, keep_index_p): # override in some test classes, no fit_kwds yet, e.g. cov_type mod2 = self.results.model mod_cls = mod2.__class__ init_kwds = mod2._get_init_kwds() mod = mod_cls(mod2.endog, mod2.exog[:, keep_index], **init_kwds) if self.use_start_params: res = mod.fit(start_params=self.results.params[keep_index_p], maxiter=500) else: res = mod.fit(maxiter=500) return res def test_zero_collinear(self): # not completely generic yet if isinstance(self.results.model, (sm.GEE)): pytest.skip('Not completely generic yet') use_start_params = not isinstance(self.results.model, (sm.RLM, sm.OLS, sm.WLS, sm.GLM)) self.use_start_params = use_start_params # attach for _get_constrained keep_index = list(range(self.results.model.exog.shape[1])) # index for params might include extra params keep_index_p = list(range(self.results.params.shape[0])) drop_index = [] for i in drop_index: del keep_index[i] del keep_index_p[i] keep_index_p = list(range(self.results.params.shape[0])) # create collinear model mod2 = self.results.model mod_cls = mod2.__class__ init_kwds = mod2._get_init_kwds() ex = np.column_stack((mod2.exog, mod2.exog)) mod = mod_cls(mod2.endog, ex, **init_kwds) keep_index = list(range(self.results.model.exog.shape[1])) keep_index_p = list(range(self.results.model.exog.shape[1])) k_vars = ex.shape[1] k_extra = 0 if hasattr(mod, 'k_extra') and mod.k_extra > 0: keep_index_p += list(range(k_vars, k_vars + mod.k_extra)) k_extra = mod.k_extra # TODO: Can we choose a test case without this issue? # If not, should we be getting this warning for all # model subclasses? warn_cls = HessianInversionWarning if isinstance(mod, sm.GLM) else None cov_types = ['nonrobust', 'HC0'] for cov_type in cov_types: # Note: for RLM we only check default when cov_type is 'nonrobust' # cov_type is otherwise ignored if cov_type != 'nonrobust' and (isinstance(self.results.model, sm.RLM)): return if use_start_params: start_params = np.zeros(k_vars + k_extra) method = self.results.mle_settings['optimizer'] # string in `method` is not mutable, so no need for copy sp = self.results.mle_settings['start_params'].copy() if self.transform_index is not None: # work around internal transform_params, currently in NB sp[self.transform_index] = np.exp(sp[self.transform_index]) start_params[keep_index_p] = sp with pytest.warns(warn_cls): res1 = mod._fit_collinear(cov_type=cov_type, start_params=start_params, method=method, disp=0) if cov_type != 'nonrobust': # reestimate original model to get robust cov with pytest.warns(warn_cls): res2 = self.results.model.fit(cov_type=cov_type, start_params=sp, method=method, disp=0) else: with pytest.warns(warn_cls): # more special casing RLM if (isinstance(self.results.model, (sm.RLM))): res1 = mod._fit_collinear() else: res1 = mod._fit_collinear(cov_type=cov_type) if cov_type != 'nonrobust': # reestimate original model to get robust cov res2 = self.results.model.fit(cov_type=cov_type) if cov_type == 'nonrobust': res2 = self.results # check fit optimizer arguments, if mle_settings is available if hasattr(res2, 'mle_settings'): assert_equal(res1.results_constrained.mle_settings['optimizer'], res2.mle_settings['optimizer']) if 'start_params' in res2.mle_settings: spc = res1.results_constrained.mle_settings['start_params'] assert_allclose(spc, res2.mle_settings['start_params'], rtol=1e-10, atol=1e-20) assert_equal(res1.mle_settings['optimizer'], res2.mle_settings['optimizer']) assert_allclose(res1.mle_settings['start_params'], res2.mle_settings['start_params'], rtol=1e-10, atol=1e-20) # Poisson has reduced precision in params, difficult optimization? assert_allclose(res1.params[keep_index_p], res2.params, rtol=1e-6) assert_allclose(res1.params[drop_index], 0, rtol=1e-10) assert_allclose(res1.bse[keep_index_p], res2.bse, rtol=1e-8) assert_allclose(res1.bse[drop_index], 0, rtol=1e-10) tvals1 = res1.tvalues[keep_index_p] assert_allclose(tvals1, res2.tvalues, rtol=5e-8) # See gh5993 if PLATFORM_LINUX32 or SCIPY_GT_14: pvals1 = res1.pvalues[keep_index_p] else: pvals1 = res1.pvalues[keep_index_p] assert_allclose(pvals1, res2.pvalues, rtol=1e-6, atol=1e-30) if hasattr(res1, 'resid'): # discrete models, Logit do not have `resid` yet assert_allclose(res1.resid, res2.resid, rtol=1e-5, atol=1e-10) ex = res1.model.exog.mean(0) predicted1 = res1.predict(ex, **self.predict_kwds) predicted2 = res2.predict(ex[keep_index], **self.predict_kwds) assert_allclose(predicted1, predicted2, rtol=1e-8, atol=1e-11) ex = res1.model.exog[:5] kwds = getattr(self, 'predict_kwds_5', {}) predicted1 = res1.predict(ex, **kwds) predicted2 = res2.predict(ex[:, keep_index], **kwds) assert_allclose(predicted1, predicted2, rtol=1e-8, atol=1e-11) ######### subclasses for individual models, unchanged from test_shrink_pickle # TODO: check if setup_class is faster than setup class TestGenericOLS(CheckGenericMixin): def setup(self): #fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) y = x.sum(1) + np.random.randn(x.shape[0]) self.results = sm.OLS(y, self.exog).fit() class TestGenericOLSOneExog(CheckGenericMixin): # check with single regressor (no constant) def setup(self): #fit for each test, because results will be changed by test x = self.exog[:, 1] np.random.seed(987689) y = x + np.random.randn(x.shape[0]) self.results = sm.OLS(y, x).fit() def test_zero_constrained(self): # override, we cannot remove the only regressor pytest.skip('Override since cannot remove the only regressor') pass class TestGenericWLS(CheckGenericMixin): def setup(self): #fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) y = x.sum(1) + np.random.randn(x.shape[0]) self.results = sm.WLS(y, self.exog, weights=np.ones(len(y))).fit() class TestGenericPoisson(CheckGenericMixin): def setup(self): #fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) y_count = np.random.poisson(np.exp(x.sum(1) - x.mean())) model = sm.Poisson(y_count, x) # use start_params to converge faster start_params = np.array([0.75334818, 0.99425553, 1.00494724, 1.00247112]) self.results = model.fit(start_params=start_params, method='bfgs', disp=0) class TestGenericPoissonOffset(CheckGenericMixin): def setup(self): #fit for each test, because results will be changed by test x = self.exog nobs = x.shape[0] np.random.seed(987689) y_count = np.random.poisson(np.exp(x.sum(1) - x.mean())) model = sm.Poisson(y_count, x, offset=0.01 * np.ones(nobs), exposure=np.ones(nobs)) # bug with default # use start_params to converge faster start_params = np.array([0.75334818, 0.99425553, 1.00494724, 1.00247112]) self.results = model.fit(start_params=start_params, method='bfgs', disp=0) self.predict_kwds_5 = dict(exposure=0.01 * np.ones(5), offset=np.ones(5)) self.predict_kwds = dict(exposure=1, offset=0) class TestGenericNegativeBinomial(CheckGenericMixin): def setup(self): #fit for each test, because results will be changed by test np.random.seed(987689) data = sm.datasets.randhie.load(as_pandas=False) exog = sm.add_constant(data.exog, prepend=False) mod = sm.NegativeBinomial(data.endog, exog) start_params = np.array([-0.05783623, -0.26655806, 0.04109148, -0.03815837, 0.2685168 , 0.03811594, -0.04426238, 0.01614795, 0.17490962, 0.66461151, 1.2925957 ]) self.results = mod.fit(start_params=start_params, disp=0, maxiter=500) self.transform_index = -1 class TestGenericLogit(CheckGenericMixin): def setup(self): #fit for each test, because results will be changed by test x = self.exog nobs = x.shape[0] np.random.seed(987689) y_bin = (np.random.rand(nobs) < 1.0 / (1 + np.exp(x.sum(1) - x.mean()))).astype(int) model = sm.Logit(y_bin, x) #, exposure=np.ones(nobs), offset=np.zeros(nobs)) #bug with default # use start_params to converge faster start_params = np.array([-0.73403806, -1.00901514, -0.97754543, -0.95648212]) self.results = model.fit(start_params=start_params, method='bfgs', disp=0) class TestGenericRLM(CheckGenericMixin): def setup(self): #fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) y = x.sum(1) + np.random.randn(x.shape[0]) self.results = sm.RLM(y, self.exog).fit() class TestGenericGLM(CheckGenericMixin): def setup(self): #fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) y = x.sum(1) + np.random.randn(x.shape[0]) self.results = sm.GLM(y, self.exog).fit() class TestGenericGLMPoissonOffset(CheckGenericMixin): def setup(self): #fit for each test, because results will be changed by test x = self.exog nobs = x.shape[0] np.random.seed(987689) y_count = np.random.poisson(np.exp(x.sum(1) - x.mean())) model = sm.GLM(y_count, x, family=sm.families.Poisson(), offset=0.01 * np.ones(nobs), exposure=np.ones(nobs)) # use start_params to converge faster start_params = np.array([0.75334818, 0.99425553, 1.00494724, 1.00247112]) self.results = model.fit(start_params=start_params, method='bfgs', disp=0) self.predict_kwds_5 = dict(exposure=0.01 * np.ones(5), offset=np.ones(5)) self.predict_kwds = dict(exposure=1, offset=0) class TestGenericGEEPoisson(CheckGenericMixin): def setup(self): #fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) y_count = np.random.poisson(np.exp(x.sum(1) - x.mean())) groups = np.random.randint(0, 4, size=x.shape[0]) # use start_params to speed up test, difficult convergence not tested start_params = np.array([0., 1., 1., 1.]) vi = sm.cov_struct.Independence() family = sm.families.Poisson() self.results = sm.GEE(y_count, self.exog, groups, family=family, cov_struct=vi).fit(start_params=start_params) class TestGenericGEEPoissonNaive(CheckGenericMixin): def setup(self): #fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) #y_count = np.random.poisson(np.exp(x.sum(1) - x.mean())) y_count = np.random.poisson(np.exp(x.sum(1) - x.sum(1).mean(0))) groups = np.random.randint(0, 4, size=x.shape[0]) # use start_params to speed up test, difficult convergence not tested start_params = np.array([0., 1., 1., 1.]) vi = sm.cov_struct.Independence() family = sm.families.Poisson() self.results = sm.GEE(y_count, self.exog, groups, family=family, cov_struct=vi).fit(start_params=start_params, cov_type='naive') class TestGenericGEEPoissonBC(CheckGenericMixin): def setup(self): #fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) #y_count = np.random.poisson(np.exp(x.sum(1) - x.mean())) y_count = np.random.poisson(np.exp(x.sum(1) - x.sum(1).mean(0))) groups = np.random.randint(0, 4, size=x.shape[0]) # use start_params to speed up test, difficult convergence not tested start_params = np.array([0., 1., 1., 1.]) # params_est = np.array([-0.0063238 , 0.99463752, 1.02790201, 0.98080081]) vi = sm.cov_struct.Independence() family = sm.families.Poisson() mod = sm.GEE(y_count, self.exog, groups, family=family, cov_struct=vi) self.results = mod.fit(start_params=start_params, cov_type='bias_reduced') # Other test classes class CheckAnovaMixin(object): @classmethod def setup_class(cls): import statsmodels.stats.tests.test_anova as ttmod test = ttmod.TestAnova3() test.setup_class() cls.data = test.data.drop([0,1,2]) cls.initialize() def test_combined(self): res = self.res wa = res.wald_test_terms(skip_single=False, combine_terms=['Duration', 'Weight']) eye = np.eye(len(res.params)) c_const = eye[0] c_w = eye[[2,3]] c_d = eye[1] c_dw = eye[[4,5]] c_weight = eye[2:6] c_duration = eye[[1, 4, 5]] compare_waldres(res, wa, [c_const, c_d, c_w, c_dw, c_duration, c_weight]) def test_categories(self): # test only multicolumn terms res = self.res wa = res.wald_test_terms(skip_single=True) eye = np.eye(len(res.params)) c_w = eye[[2,3]] c_dw = eye[[4,5]] compare_waldres(res, wa, [c_w, c_dw]) def compare_waldres(res, wa, constrasts): for i, c in enumerate(constrasts): wt = res.wald_test(c) assert_allclose(wa.table.values[i, 0], wt.statistic) assert_allclose(wa.table.values[i, 1], wt.pvalue) df = c.shape[0] if c.ndim == 2 else 1 assert_equal(wa.table.values[i, 2], df) # attributes assert_allclose(wa.statistic[i], wt.statistic) assert_allclose(wa.pvalues[i], wt.pvalue) assert_equal(wa.df_constraints[i], df) if res.use_t: assert_equal(wa.df_denom[i], res.df_resid) col_names = wa.col_names if res.use_t: assert_equal(wa.distribution, 'F') assert_equal(col_names[0], 'F') assert_equal(col_names[1], 'P>F') else: assert_equal(wa.distribution, 'chi2') assert_equal(col_names[0], 'chi2') assert_equal(col_names[1], 'P>chi2') # SMOKETEST wa.summary_frame() class TestWaldAnovaOLS(CheckAnovaMixin): @classmethod def initialize(cls): mod = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", cls.data) cls.res = mod.fit(use_t=False) def test_noformula(self): # this verifies single and composite constraints against explicit # wald test endog = self.res.model.endog exog = self.res.model.data.orig_exog exog = pd.DataFrame(exog) res = sm.OLS(endog, exog).fit() wa = res.wald_test_terms(skip_single=False, combine_terms=['Duration', 'Weight']) eye = np.eye(len(res.params)) c_single = [row for row in eye] c_weight = eye[2:6] c_duration = eye[[1, 4, 5]] compare_waldres(res, wa, c_single + [c_duration, c_weight]) # assert correct df_constraints, see #5475 for bug in single constraint df_constraints = [1] * len(c_single) + [3, 4] assert_equal(wa.df_constraints, df_constraints) class TestWaldAnovaOLSF(CheckAnovaMixin): @classmethod def initialize(cls): mod = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", cls.data) cls.res = mod.fit() # default use_t=True def test_predict_missing(self): ex = self.data[:5].copy() ex.iloc[0, 1] = np.nan predicted1 = self.res.predict(ex) predicted2 = self.res.predict(ex[1:]) assert_index_equal(predicted1.index, ex.index) assert_series_equal(predicted1[1:], predicted2) assert_equal(predicted1.values[0], np.nan) class TestWaldAnovaGLM(CheckAnovaMixin): @classmethod def initialize(cls): mod = glm("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", cls.data) cls.res = mod.fit(use_t=False) class TestWaldAnovaPoisson(CheckAnovaMixin): @classmethod def initialize(cls): from statsmodels.discrete.discrete_model import Poisson mod = Poisson.from_formula("Days ~ C(Duration, Sum)*C(Weight, Sum)", cls.data) cls.res = mod.fit(cov_type='HC0') class TestWaldAnovaNegBin(CheckAnovaMixin): @classmethod def initialize(cls): from statsmodels.discrete.discrete_model import NegativeBinomial formula = "Days ~ C(Duration, Sum)*C(Weight, Sum)" mod = NegativeBinomial.from_formula(formula, cls.data, loglike_method='nb2') cls.res = mod.fit() class TestWaldAnovaNegBin1(CheckAnovaMixin): @classmethod def initialize(cls): from statsmodels.discrete.discrete_model import NegativeBinomial formula = "Days ~ C(Duration, Sum)*C(Weight, Sum)" mod = NegativeBinomial.from_formula(formula, cls.data, loglike_method='nb1') cls.res = mod.fit(cov_type='HC0') class CheckPairwise(object): def test_default(self): res = self.res tt = res.t_test(self.constraints) pw = res.t_test_pairwise(self.term_name) pw_frame = pw.result_frame assert_allclose(pw_frame.iloc[:, :6].values, tt.summary_frame().values) class TestTTestPairwiseOLS(CheckPairwise): @classmethod def setup_class(cls): from statsmodels.formula.api import ols import statsmodels.stats.tests.test_anova as ttmod test = ttmod.TestAnova3() test.setup_class() cls.data = test.data.drop([0,1,2]) mod = ols("np.log(Days+1) ~ C(Duration) + C(Weight)", cls.data) cls.res = mod.fit() cls.term_name = "C(Weight)" cls.constraints = ['C(Weight)[T.2]', 'C(Weight)[T.3]', 'C(Weight)[T.3] - C(Weight)[T.2]'] def test_alpha(self): pw1 = self.res.t_test_pairwise(self.term_name, method='hommel', factor_labels='A B C'.split()) pw2 = self.res.t_test_pairwise(self.term_name, method='hommel', alpha=0.01) assert_allclose(pw1.result_frame.iloc[:, :7].values, pw2.result_frame.iloc[:, :7].values, rtol=1e-10) assert_equal(pw1.result_frame.iloc[:, -1].values, [True]*3) assert_equal(pw2.result_frame.iloc[:, -1].values, [False, True, False]) assert_equal(pw1.result_frame.index.values, np.array(['B-A', 'C-A', 'C-B'], dtype=object)) class TestTTestPairwiseOLS2(CheckPairwise): @classmethod def setup_class(cls): from statsmodels.formula.api import ols import statsmodels.stats.tests.test_anova as ttmod test = ttmod.TestAnova3() test.setup_class() cls.data = test.data.drop([0,1,2]) mod = ols("np.log(Days+1) ~ C(Weight) + C(Duration)", cls.data) cls.res = mod.fit() cls.term_name = "C(Weight)" cls.constraints = ['C(Weight)[T.2]', 'C(Weight)[T.3]', 'C(Weight)[T.3] - C(Weight)[T.2]'] class TestTTestPairwiseOLS3(CheckPairwise): @classmethod def setup_class(cls): from statsmodels.formula.api import ols import statsmodels.stats.tests.test_anova as ttmod test = ttmod.TestAnova3() test.setup_class() cls.data = test.data.drop([0,1,2]) mod = ols("np.log(Days+1) ~ C(Weight) + C(Duration) - 1", cls.data) cls.res = mod.fit() cls.term_name = "C(Weight)" cls.constraints = ['C(Weight)[2] - C(Weight)[1]', 'C(Weight)[3] - C(Weight)[1]', 'C(Weight)[3] - C(Weight)[2]'] class TestTTestPairwiseOLS4(CheckPairwise): @classmethod def setup_class(cls): from statsmodels.formula.api import ols import statsmodels.stats.tests.test_anova as ttmod test = ttmod.TestAnova3() test.setup_class() cls.data = test.data.drop([0,1,2]) mod = ols("np.log(Days+1) ~ C(Weight, Treatment(2)) + C(Duration)", cls.data) cls.res = mod.fit() cls.term_name = "C(Weight, Treatment(2))" cls.constraints = ['-C(Weight, Treatment(2))[T.1]', 'C(Weight, Treatment(2))[T.3] - C(Weight, Treatment(2))[T.1]', 'C(Weight, Treatment(2))[T.3]',] class TestTTestPairwisePoisson(CheckPairwise): @classmethod def setup_class(cls): from statsmodels.discrete.discrete_model import Poisson import statsmodels.stats.tests.test_anova as ttmod test = ttmod.TestAnova3() test.setup_class() cls.data = test.data.drop([0,1,2]) mod = Poisson.from_formula("Days ~ C(Duration) + C(Weight)", cls.data) cls.res = mod.fit(cov_type='HC0') cls.term_name = "C(Weight)" cls.constraints = ['C(Weight)[T.2]', 'C(Weight)[T.3]', 'C(Weight)[T.3] - C(Weight)[T.2]'] statsmodels-0.12.2/statsmodels/base/tests/test_optimize.py000066400000000000000000000062761400612667500240470ustar00rootroot00000000000000from statsmodels.compat.scipy import SP_LT_15 import pytest from numpy.testing import assert_ from numpy.testing import assert_almost_equal from statsmodels.base.optimizer import ( _fit_newton, _fit_nm, _fit_bfgs, _fit_cg, _fit_ncg, _fit_powell, _fit_lbfgs, _fit_basinhopping, _fit_minimize, ) fit_funcs = { "newton": _fit_newton, "nm": _fit_nm, # Nelder-Mead "bfgs": _fit_bfgs, "cg": _fit_cg, "ncg": _fit_ncg, "powell": _fit_powell, "lbfgs": _fit_lbfgs, "basinhopping": _fit_basinhopping, "minimize": _fit_minimize, } def dummy_func(x): return x ** 2 def dummy_score(x): return 2.0 * x def dummy_hess(x): return [[2.0]] def dummy_bounds_constraint_func(x): return (x[0] - 1) ** 2 + (x[1] - 2.5) ** 2 def dummy_bounds(): return ((0, None), (0, None)) def dummy_constraints(): cons = ( {"type": "ineq", "fun": lambda x: x[0] - 2 * x[1] + 2}, {"type": "ineq", "fun": lambda x: -x[0] - 2 * x[1] + 6}, {"type": "ineq", "fun": lambda x: -x[0] + 2 * x[1] + 2}, ) return cons @pytest.mark.smoke def test_full_output_false(reset_randomstate): # newton needs f, score, start, fargs, kwargs # bfgs needs f, score start, fargs, kwargs # nm needs "" # cg "" # ncg "" # powell "" for method in fit_funcs: func = fit_funcs[method] if method == "newton": xopt, retvals = func( dummy_func, dummy_score, [1], (), {}, hess=dummy_hess, full_output=False, disp=0, ) else: xopt, retvals = func( dummy_func, dummy_score, [1], (), {}, full_output=False, disp=0 ) assert_(retvals is None) if method == "powell" and SP_LT_15: # Fixed in SP 1.5 assert_(xopt.shape == () and xopt.size == 1) else: assert_(len(xopt) == 1) def test_full_output(reset_randomstate): for method in fit_funcs: func = fit_funcs[method] if method == "newton": xopt, retvals = func( dummy_func, dummy_score, [1], (), {}, hess=dummy_hess, full_output=True, disp=0, ) else: xopt, retvals = func( dummy_func, dummy_score, [1], (), {}, full_output=True, disp=0 ) assert_(retvals is not None) assert_("converged" in retvals) if method == "powell" and SP_LT_15: # Fixed in SP 1.5 assert_(xopt.shape == () and xopt.size == 1) else: assert_(len(xopt) == 1) def test_minimize_scipy_slsqp(): func = fit_funcs["minimize"] xopt, _ = func( dummy_bounds_constraint_func, None, (2, 0), (), { "min_method": "SLSQP", "bounds": dummy_bounds(), "constraints": dummy_constraints(), }, hess=None, full_output=False, disp=0, ) assert_almost_equal(xopt, [1.4, 1.7], 4) statsmodels-0.12.2/statsmodels/base/tests/test_penalized.py000066400000000000000000000604141400612667500241540ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun May 10 12:39:33 2015 Author: Josef Perktold License: BSD-3 """ import warnings import pytest import numpy as np from numpy.testing import assert_allclose, assert_equal from statsmodels.discrete.discrete_model import Poisson, Logit, Probit from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod.families import family from statsmodels.sandbox.regression.penalized import TheilGLS from statsmodels.base._penalized import PenalizedMixin import statsmodels.base._penalties as smpen class PoissonPenalized(PenalizedMixin, Poisson): pass class LogitPenalized(PenalizedMixin, Logit): pass class ProbitPenalized(PenalizedMixin, Probit): pass class GLMPenalized(PenalizedMixin, GLM): pass class CheckPenalizedPoisson(object): @classmethod def setup_class(cls): # simulate data np.random.seed(987865) nobs, k_vars = 500, 10 k_nonzero = 4 x = ((np.random.rand(nobs, k_vars) + 0.5* (np.random.rand(nobs, 1) - 0.5)) * 2 - 1) x *= 1.2 x[:, 0] = 1 beta = np.zeros(k_vars) beta[:k_nonzero] = 1. / np.arange(1, k_nonzero + 1) linpred = x.dot(beta) y = cls._generate_endog(linpred) cls.k_nonzero = k_nonzero cls.x = x cls.y = y # defaults to be overwritten by subclasses cls.rtol = 1e-4 cls.atol = 1e-6 cls.exog_index = slice(None, None, None) cls.k_params = k_vars cls.skip_hessian = False # can be overwritten in _initialize cls.penalty = smpen.SCADSmoothed(0.1, c0=0.0001) # default for tests cls._initialize() @classmethod def _generate_endog(self, linpred): mu = np.exp(linpred) np.random.seed(999) y = np.random.poisson(mu) return y def test_params_table(self): res1 = self.res1 res2 = self.res2 assert_equal((res1.params != 0).sum(), self.k_params) assert_allclose(res1.params[self.exog_index], res2.params, rtol=self.rtol, atol=self.atol) assert_allclose(res1.bse[self.exog_index], res2.bse, rtol=self.rtol, atol=self.atol) with warnings.catch_warnings(): # silence scipy distribution warnigns becaus of zero bse warnings.simplefilter('ignore', RuntimeWarning) assert_allclose(res1.pvalues[self.exog_index], res2.pvalues, rtol=self.rtol, atol=self.atol) assert_allclose(res1.predict(), res2.predict(), rtol=0.05) @pytest.mark.smoke def test_summary(self): self.res1.summary() @pytest.mark.smoke def test_summary2(self): summ = self.res1.summary2() assert isinstance(summ.as_latex(), str) assert isinstance(summ.as_html(), str) assert isinstance(summ.as_text(), str) def test_numdiff(self): res1 = self.res1 # avoid checking score at MLE, score close to zero p = res1.params * 0.98 # GLM concentrates out scale which affects derivatives, see #4616 kwds = {'scale': 1} if isinstance(res1.model, GLM) else {} assert_allclose(res1.model.score(p, **kwds)[self.exog_index], res1.model.score_numdiff(p, **kwds)[self.exog_index], rtol=0.025) if not self.skip_hessian: if isinstance(self.exog_index, slice): idx1 = idx2 = self.exog_index else: idx1 = self.exog_index[:, None] idx2 = self.exog_index h1 = res1.model.hessian(res1.params, **kwds)[idx1, idx2] h2 = res1.model.hessian_numdiff(res1.params, **kwds)[idx1, idx2] assert_allclose(h1, h2, rtol=0.02) class TestPenalizedPoissonNonePenal(CheckPenalizedPoisson): @classmethod def _initialize(cls): y, x = cls.y, cls.x modp = Poisson(y, x) cls.res2 = modp.fit(disp=0) mod = PoissonPenalized(y, x) # default no penalty mod.pen_weight = 0 cls.res1 = mod.fit(method='bfgs', maxiter=100, disp=0) cls.atol = 5e-6 class TestPenalizedPoissonNoPenal(CheckPenalizedPoisson): # TODO: check, adjust cov_type @classmethod def _initialize(cls): y, x = cls.y, cls.x modp = Poisson(y, x) cls.res2 = modp.fit(disp=0) mod = PoissonPenalized(y, x) mod.pen_weight = 0 cls.res1 = mod.fit(method='bfgs', maxiter=100, disp=0) cls.atol = 5e-6 class TestPenalizedGLMPoissonNoPenal(CheckPenalizedPoisson): # TODO: check, adjust cov_type @classmethod def _initialize(cls): y, x = cls.y, cls.x modp = GLM(y, x, family=family.Poisson()) cls.res2 = modp.fit() mod = GLMPenalized(y, x, family=family.Poisson(), penal=cls.penalty) mod.pen_weight = 0 cls.res1 = mod.fit(method='bfgs', maxiter=100, disp=0) cls.atol = 5e-6 class TestPenalizedPoissonOracle(CheckPenalizedPoisson): @classmethod def _initialize(cls): y, x = cls.y, cls.x modp = Poisson(y, x[:, :cls.k_nonzero]) cls.res2 = modp.fit(disp=0) mod = PoissonPenalized(y, x, penal=cls.penalty) mod.pen_weight *= 1.5 mod.penal.tau = 0.05 cls.res1 = mod.fit(method='bfgs', maxiter=100, disp=0) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 5e-3 class TestPenalizedGLMPoissonOracle(CheckPenalizedPoisson): # TODO: check, adjust cov_type @classmethod def _initialize(cls): y, x = cls.y, cls.x modp = GLM(y, x[:, :cls.k_nonzero], family=family.Poisson()) cls.res2 = modp.fit() mod = GLMPenalized(y, x, family=family.Poisson(), penal=cls.penalty) mod.pen_weight *= 1.5 # same as discrete Poisson mod.penal.tau = 0.05 cls.res1 = mod.fit(method='bfgs', maxiter=100) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 5e-3 class TestPenalizedPoissonOracleHC(CheckPenalizedPoisson): @classmethod def _initialize(cls): y, x = cls.y, cls.x cov_type = 'HC0' modp = Poisson(y, x[:, :cls.k_nonzero]) cls.res2 = modp.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0) mod = PoissonPenalized(y, x, penal=cls.penalty) mod.pen_weight *= 1.5 mod.penal.tau = 0.05 cls.res1 = mod.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 5e-3 def test_cov_type(self): res1 = self.res1 res2 = self.res2 assert_equal(self.res1.cov_type, 'HC0') cov_kwds = {'description': 'Standard Errors are heteroscedasticity ' 'robust (HC0)', 'adjust_df': False, 'use_t': False, 'scaling_factor': None} assert_equal(self.res1.cov_kwds, cov_kwds) # numbers are regression test using bfgs params = np.array([0.96817787574701109, 0.43674374940137434, 0.33096260487556745, 0.27415680046693747]) bse = np.array([0.028126650444581985, 0.033099984564283147, 0.033184585514904545, 0.034282504130503301]) assert_allclose(res2.params[:self.k_nonzero], params, atol=1e-5) assert_allclose(res2.bse[:self.k_nonzero], bse, rtol=1e-6) assert_allclose(res1.params[:self.k_nonzero], params, atol=self.atol) assert_allclose(res1.bse[:self.k_nonzero], bse, rtol=0.02) class TestPenalizedGLMPoissonOracleHC(CheckPenalizedPoisson): @classmethod def _initialize(cls): y, x = cls.y, cls.x cov_type = 'HC0' modp = GLM(y, x[:, :cls.k_nonzero], family=family.Poisson()) cls.res2 = modp.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0) mod = GLMPenalized(y, x, family=family.Poisson(), penal=cls.penalty) mod.pen_weight *= 1.5 # same as ddiscrete Poisson mod.penal.tau = 0.05 cls.res1 = mod.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 5e-3 class TestPenalizedPoissonGLMOracleHC(CheckPenalizedPoisson): # compare discrete Poisson and GLM-Poisson @classmethod def _initialize(cls): y, x = cls.y, cls.x cov_type = 'HC0' modp = PoissonPenalized(y, x, penal=cls.penalty) modp.pen_weight *= 1.5 # same as discrete Poisson 1.5 modp.penal.tau = 0.05 cls.res2 = modp.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0) mod = GLMPenalized(y, x, family=family.Poisson(), penal=cls.penalty) mod.pen_weight *= 1.5 # same as discrete Poisson 1.5 mod.penal.tau = 0.05 cls.res1 = mod.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0) cls.exog_index = slice(None, None, None) cls.atol = 1e-4 class TestPenalizedPoissonOraclePenalized(CheckPenalizedPoisson): @classmethod def _initialize(cls): y, x = cls.y, cls.x modp = PoissonPenalized(y, x[:, :cls.k_nonzero], penal=cls.penalty) cls.res2 = modp.fit(method='bfgs', maxiter=100, disp=0) mod = PoissonPenalized(y, x, penal=cls.penalty) # mod.pen_weight *= 1.5 # mod.penal.tau = 0.05 cls.res1 = mod.fit(method='bfgs', maxiter=100, trim=False, disp=0) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 1e-3 class TestPenalizedPoissonOraclePenalized2(CheckPenalizedPoisson): @classmethod def _initialize(cls): y, x = cls.y, cls.x modp = PoissonPenalized(y, x[:, :cls.k_nonzero], penal=cls.penalty) modp.pen_weight *= 10 # need to penalize more to get oracle selection modp.penal.tau = 0.05 cls.res2 = modp.fit(method='bfgs', maxiter=100, disp=0) mod = PoissonPenalized(y, x, penal=cls.penalty) mod.pen_weight *= 10 # need to penalize more to get oracle selection mod.penal.tau = 0.05 cls.res1 = mod.fit(method='bfgs', maxiter=100, trim=True, disp=0) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 1e-8 cls.k_params = cls.k_nonzero def test_zeros(self): # first test for trimmed result assert_equal(self.res1.params[self.k_nonzero:], 0) # we also set bse to zero, TODO: check fit_regularized assert_equal(self.res1.bse[self.k_nonzero:], 0) class TestPenalizedPoissonOraclePenalized2HC(CheckPenalizedPoisson): @classmethod def _initialize(cls): y, x = cls.y, cls.x cov_type = 'HC0' modp = PoissonPenalized(y, x[:, :cls.k_nonzero], penal=cls.penalty) modp.pen_weight *= 10 # need to penalize more to get oracle selection modp.penal.tau = 0.05 cls.res2 = modp.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0) mod = PoissonPenalized(y, x, penal=cls.penalty) mod.pen_weight *= 10 # need to penalize more to get oracle selection mod.penal.tau = 0.05 cls.res1 = mod.fit(cov_type=cov_type, method='bfgs', maxiter=100, trim=True, disp=0) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 1e-12 cls.k_params = cls.k_nonzero def test_cov_type(self): res1 = self.res1 res2 = self.res2 assert_equal(self.res1.cov_type, 'HC0') assert_equal(self.res1.results_constrained.cov_type, 'HC0') cov_kwds = {'description': 'Standard Errors are heteroscedasticity ' 'robust (HC0)', 'adjust_df': False, 'use_t': False, 'scaling_factor': None} assert_equal(self.res1.cov_kwds, cov_kwds) assert_equal(self.res1.cov_kwds, self.res1.results_constrained.cov_kwds) # numbers are regression test using bfgs params = np.array([0.96817787574701109, 0.43674374940137434, 0.33096260487556745, 0.27415680046693747]) bse = np.array([0.028126650444581985, 0.033099984564283147, 0.033184585514904545, 0.034282504130503301]) assert_allclose(res2.params[:self.k_nonzero], params, atol=1e-5) assert_allclose(res2.bse[:self.k_nonzero], bse, rtol=5e-6) assert_allclose(res1.params[:self.k_nonzero], params, atol=1e-5) assert_allclose(res1.bse[:self.k_nonzero], bse, rtol=5e-6) # the following classes are copies of Poisson with model adjustments class CheckPenalizedLogit(CheckPenalizedPoisson): @classmethod def _generate_endog(self, linpred): mu = 1 / (1 + np.exp(-linpred + linpred.mean() - 0.5)) np.random.seed(999) y = np.random.rand(len(mu)) < mu return y class TestPenalizedLogitNoPenal(CheckPenalizedLogit): # TODO: check, adjust cov_type @classmethod def _initialize(cls): y, x = cls.y, cls.x modp = Logit(y, x) cls.res2 = modp.fit(disp=0) mod = LogitPenalized(y, x, penal=cls.penalty) mod.pen_weight = 0 cls.res1 = mod.fit(disp=0) cls.atol = 1e-4 # why not closer ? class TestPenalizedLogitOracle(CheckPenalizedLogit): # TODO: check, adjust cov_type @classmethod def _initialize(cls): y, x = cls.y, cls.x modp = Logit(y, x[:, :cls.k_nonzero]) cls.res2 = modp.fit(disp=0) mod = LogitPenalized(y, x, penal=cls.penalty) mod.pen_weight *= .5 mod.penal.tau = 0.05 cls.res1 = mod.fit(method='bfgs', maxiter=100, disp=0) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 5e-3 class TestPenalizedGLMLogitOracle(CheckPenalizedLogit): # TODO: check, adjust cov_type @classmethod def _initialize(cls): y, x = cls.y, cls.x modp = GLM(y, x[:, :cls.k_nonzero], family=family.Binomial()) cls.res2 = modp.fit(disp=0) mod = GLMPenalized(y, x, family=family.Binomial(), penal=cls.penalty) mod.pen_weight *= .5 mod.penal.tau = 0.05 cls.res1 = mod.fit(method='bfgs', maxiter=100, disp=0) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 5e-3 class TestPenalizedLogitOraclePenalized(CheckPenalizedLogit): # TODO: check, adjust cov_type @classmethod def _initialize(cls): y, x = cls.y, cls.x modp = LogitPenalized(y, x[:, :cls.k_nonzero], penal=cls.penalty) cls.res2 = modp.fit(method='bfgs', maxiter=100, disp=0) mod = LogitPenalized(y, x, penal=cls.penalty) # mod.pen_weight *= 1.5 # mod.penal.tau = 0.05 cls.res1 = mod.fit(method='bfgs', maxiter=100, trim=False, disp=0) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 1e-3 class TestPenalizedLogitOraclePenalized2(CheckPenalizedLogit): @classmethod def _initialize(cls): y, x = cls.y, cls.x modp = LogitPenalized(y, x[:, :cls.k_nonzero], penal=cls.penalty) modp.pen_weight *= 0.5 modp.penal.tau = 0.05 cls.res2 = modp.fit(method='bfgs', maxiter=100, disp=0) mod = LogitPenalized(y, x, penal=cls.penalty) mod.pen_weight *= 0.5 mod.penal.tau = 0.05 cls.res1 = mod.fit(method='bfgs', maxiter=100, trim=True, disp=0) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 1e-8 cls.k_params = cls.k_nonzero def test_zeros(self): # test for trimmed result assert_equal(self.res1.params[self.k_nonzero:], 0) # we also set bse to zero assert_equal(self.res1.bse[self.k_nonzero:], 0) # the following classes are copies of Poisson with model adjustments class CheckPenalizedBinomCount(CheckPenalizedPoisson): @classmethod def _generate_endog(self, linpred): mu = 1 / (1 + np.exp(-linpred + linpred.mean() - 0.5)) np.random.seed(999) n_trials = 5 * np.ones(len(mu), int) n_trials[:len(mu)//2] += 5 y = np.random.binomial(n_trials, mu) return np.column_stack((y, n_trials - y)) class TestPenalizedGLMBinomCountNoPenal(CheckPenalizedBinomCount): # TODO: check, adjust cov_type @classmethod def _initialize(cls): y, x = cls.y, cls.x x = x[:, :4] offset = -0.25 * np.ones(len(y)) # also check offset modp = GLM(y, x, family=family.Binomial(), offset=offset) cls.res2 = modp.fit(method='bfgs', max_start_irls=100) mod = GLMPenalized(y, x, family=family.Binomial(), offset=offset, penal=cls.penalty) mod.pen_weight = 0 cls.res1 = mod.fit(method='bfgs', max_start_irls=3, maxiter=100, disp=0, start_params=cls.res2.params*0.9) cls.atol = 1e-10 cls.k_params = 4 def test_deriv(self): res1 = self.res1 res2 = self.res2 assert_allclose(res1.model.score(res2.params * 0.98), res2.model.score(res2.params * 0.98), rtol=1e-10) assert_allclose(res1.model.score_obs(res2.params * 0.98), res2.model.score_obs(res2.params * 0.98), rtol=1e-10) class TestPenalizedGLMBinomCountOracleHC(CheckPenalizedBinomCount): # TODO: There are still problems with this case # using the standard optimization, I get convergence failures and # different estimates depending on details, e.g. small changes in pen_weight # most likely convexity fails with SCAD in this case @classmethod def _initialize(cls): y, x = cls.y, cls.x offset = -0.25 * np.ones(len(y)) # also check offset cov_type = 'HC0' modp = GLM(y, x[:, :cls.k_nonzero], family=family.Binomial(), offset=offset) cls.res2 = modp.fit(cov_type=cov_type, method='newton', maxiter=1000, disp=0) mod = GLMPenalized(y, x, family=family.Binomial(), offset=offset, penal=cls.penalty) mod.pen_weight *= 1 # lower than in other cases mod.penal.tau = 0.05 cls.res1 = mod.fit(cov_type=cov_type, method='bfgs', max_start_irls=0, maxiter=100, disp=0) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 1e-3 class TestPenalizedGLMBinomCountOracleHC2(CheckPenalizedBinomCount): # TODO: There are still problems with this case, see other class # with trimming of small parameters, needs larger trim threshold @classmethod def _initialize(cls): y, x = cls.y, cls.x offset = -0.25 * np.ones(len(y)) # also check offset cov_type = 'HC0' modp = GLM(y, x[:, :cls.k_nonzero], family=family.Binomial(), offset=offset) cls.res2 = modp.fit(cov_type=cov_type, method='newton', maxiter=1000, disp=0) mod = GLMPenalized(y, x, family=family.Binomial(), offset=offset, penal=cls.penalty) mod.pen_weight *= 1 # lower than in other cases mod.penal.tau = 0.05 cls.res1 = mod.fit(cov_type=cov_type, method='bfgs', max_start_irls=0, maxiter=100, disp=0, trim=0.001) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 1e-3 cls.k_params = cls.k_nonzero # the following classes are copies of Poisson with model adjustments class CheckPenalizedGaussian(CheckPenalizedPoisson): @classmethod def _generate_endog(self, linpred): sig_e = np.sqrt(0.1) np.random.seed(999) y = linpred + sig_e * np.random.rand(len(linpred)) return y class TestPenalizedGLMGaussianOracleHC(CheckPenalizedGaussian): @classmethod def _initialize(cls): y, x = cls.y, cls.x # adding 10 to avoid strict rtol at predicted values close to zero y = y + 10 cov_type = 'HC0' modp = GLM(y, x[:, :cls.k_nonzero], family=family.Gaussian()) cls.res2 = modp.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0) mod = GLMPenalized(y, x, family=family.Gaussian(), penal=cls.penalty) mod.pen_weight *= 1.5 # same as discrete Poisson mod.penal.tau = 0.05 cls.res1 = mod.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0) cls.exog_index = slice(None, cls.k_nonzero, None) cls.atol = 5e-6 cls.rtol = 1e-6 class TestPenalizedGLMGaussianOracleHC2(CheckPenalizedGaussian): # with trimming @classmethod def _initialize(cls): y, x = cls.y, cls.x # adding 10 to avoid strict rtol at predicted values close to zero y = y + 10 cov_type = 'HC0' modp = GLM(y, x[:, :cls.k_nonzero], family=family.Gaussian()) cls.res2 = modp.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0) mod = GLMPenalized(y, x, family=family.Gaussian(), penal=cls.penalty) mod.pen_weight *= 1.5 # same as discrete Poisson mod.penal.tau = 0.05 cls.res1 = mod.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0, trim=True) cls.exog_index = slice(None, cls.k_nonzero, None) cls.k_params = cls.k_nonzero cls.atol = 1e-5 cls.rtol = 1e-5 class TestPenalizedGLMGaussianL2(CheckPenalizedGaussian): # L2 penalty on redundant exog @classmethod def _initialize(cls): y, x = cls.y, cls.x # adding 10 to avoid strict rtol at predicted values close to zero y = y + 10 cov_type = 'HC0' modp = GLM(y, x[:, :cls.k_nonzero], family=family.Gaussian()) cls.res2 = modp.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0) weights = (np.arange(x.shape[1]) >= 4).astype(float) mod = GLMPenalized(y, x, family=family.Gaussian(), penal=smpen.L2ConstraintsPenalty(weights=weights)) # make pen_weight large to force redundant to close to zero mod.pen_weight *= 500 cls.res1 = mod.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0, trim=False) cls.exog_index = slice(None, cls.k_nonzero, None) cls.k_params = x.shape[1] cls.atol = 1e-5 cls.rtol = 1e-5 class TestPenalizedGLMGaussianL2Theil(CheckPenalizedGaussian): # L2 penalty on redundant exog @classmethod def _initialize(cls): y, x = cls.y, cls.x # adding 10 to avoid strict rtol at predicted values close to zero y = y + 10 k = x.shape[1] cov_type = 'HC0' restriction = np.eye(k)[2:] modp = TheilGLS(y, x, r_matrix=restriction) # the corresponding Theil penweight seems to be 2 * nobs / sigma2_e cls.res2 = modp.fit(pen_weight=120.74564413221599 * 1000, use_t=False) pen = smpen.L2ConstraintsPenalty(restriction=restriction) mod = GLMPenalized(y, x, family=family.Gaussian(), penal=pen) # use default weight for GLMPenalized mod.pen_weight *= 1 cls.res1 = mod.fit(cov_type=cov_type, method='bfgs', maxiter=100, disp=0, trim=False) cls.k_nonzero = k cls.exog_index = slice(None, cls.k_nonzero, None) cls.k_params = x.shape[1] cls.atol = 1e-5 cls.rtol = 1e-5 def test_params_table(self): # override inherited because match is not good except for params and predict # The cov_type in GLMPenalized and in TheilGLS are not the same # both use sandwiches but TheilGLS sandwich is not HC # relative difference in bse up to 7% res1 = self.res1 res2 = self.res2 assert_equal((res1.params != 0).sum(), self.k_params) assert_allclose(res1.params, res2.params, rtol=self.rtol, atol=self.atol) exog_index = slice(None, None, None) assert_allclose(res1.bse[exog_index], res2.bse[exog_index], rtol=0.1, atol=self.atol) assert_allclose(res1.tvalues[exog_index], res2.tvalues[exog_index], rtol=0.08, atol=5e-3) assert_allclose(res1.pvalues[exog_index], res2.pvalues[exog_index], rtol=0.1, atol=5e-3) assert_allclose(res1.predict(), res2.predict(), rtol=1e-5) statsmodels-0.12.2/statsmodels/base/tests/test_penalties.py000066400000000000000000000105571400612667500241700ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed May 16 22:21:26 2018 Author: Josef Perktold License: BSD-3 """ import numpy as np from numpy.testing import assert_allclose, assert_equal import statsmodels.base._penalties as smpen from statsmodels.tools.numdiff import approx_fprime, approx_hess class CheckPenalty(object): def test_symmetry(self): pen = self.pen x = self.params p = np.array([pen.func(np.atleast_1d(xi)) for xi in x]) assert_allclose(p, p[::-1], rtol=1e-10) # func(0) should be 0 assert_allclose(pen.func(0 * np.atleast_1d(x[0])), 0, rtol=1e-10) def test_derivatives(self): pen = self.pen x = self.params ps = np.array([pen.deriv(np.atleast_1d(xi)) for xi in x]) psn = np.array([approx_fprime(np.atleast_1d(xi), pen.func) for xi in x]) assert_allclose(ps, psn, rtol=1e-7, atol=1e-8) ph = np.array([pen.deriv2(np.atleast_1d(xi)) for xi in x]) phn = np.array([approx_hess(np.atleast_1d(xi), pen.func) for xi in x]) if ph.ndim == 2: # SmoothedSCAD returns only diagonal if hessian if independent # TODO should ww allow this also in L@? ph = np.array([np.diag(phi) for phi in ph]) assert_allclose(ph, phn, rtol=1e-7, atol=1e-8) class TestL2Constraints0(CheckPenalty): @classmethod def setup_class(cls): x0 = np.linspace(-0.2, 0.2, 11) cls.params = np.column_stack((x0, x0)) cls.pen = smpen.L2ConstraintsPenalty() def test_equivalence(self): # compare plain penalty with included weights or restriction pen = self.pen x = self.params k = x.shape[1] pen2 = smpen.L2ConstraintsPenalty(weights=np.ones(k)) pen3 = smpen.L2ConstraintsPenalty(restriction=np.eye(k)) f = pen.func(x.T) d = pen.deriv(x.T) d2 = np.array([pen.deriv2(np.atleast_1d(xi)) for xi in x]) for pen_ in [pen2, pen3]: assert_allclose(pen_.func(x.T), f, rtol=1e-7, atol=1e-8) assert_allclose(pen_.deriv(x.T), d, rtol=1e-7, atol=1e-8) d2_ = np.array([pen.deriv2(np.atleast_1d(xi)) for xi in x]) assert_allclose(d2_, d2, rtol=1e-10, atol=1e-8) class TestL2Constraints1(CheckPenalty): @classmethod def setup_class(cls): x0 = np.linspace(-0.2, 0.2, 11) cls.params = np.column_stack((x0, x0)) cls.pen = smpen.L2ConstraintsPenalty(restriction=[[1,0], [1, 1]]) def test_values(self): pen = self.pen x = self.params r = pen.restriction f = (r.dot(x.T)**2).sum(0) assert_allclose(pen.func(x.T), f, rtol=1e-7, atol=1e-8) class TestSmoothedSCAD(CheckPenalty): @classmethod def setup_class(cls): x0 = np.linspace(-0.2, 0.2, 11) cls.params = np.column_stack((x0, x0)) cls.pen = smpen.SCADSmoothed(tau=0.05, c0=0.05) class TestPseudoHuber(CheckPenalty): @classmethod def setup_class(cls): x0 = np.linspace(-0.2, 0.2, 11) cls.params = np.column_stack((x0, x0)) cls.pen = smpen.PseudoHuber(0.1) def test_backward_compatibility(self): wts = [0.5] pen = smpen.PseudoHuber(0.1, weights=wts) assert_equal(pen.weights, wts) def test_deprecated_priority(self): weights = [1.0] pen = smpen.PseudoHuber(0.1, weights=weights) assert_equal(pen.weights, weights) def test_weights_assignment(self): weights = [1.0, 2.0] pen = smpen.PseudoHuber(0.1, weights=weights) assert_equal(pen.weights, weights) class TestL2(CheckPenalty): @classmethod def setup_class(cls): x0 = np.linspace(-0.2, 0.2, 11) cls.params = np.column_stack((x0, x0)) cls.pen = smpen.L2() def test_backward_compatibility(self): wts = [0.5] pen = smpen.L2(weights=wts) assert_equal(pen.weights, wts) def test_deprecated_priority(self): weights = [1.0] pen = smpen.L2(weights=weights) assert_equal(pen.weights, weights) def test_weights_assignment(self): weights = [1.0, 2.0] pen = smpen.L2(weights=weights) assert_equal(pen.weights, weights) class TestNonePenalty(CheckPenalty): @classmethod def setup_class(cls): x0 = np.linspace(-0.2, 0.2, 11) cls.params = np.column_stack((x0, x0)) cls.pen = smpen.NonePenalty() statsmodels-0.12.2/statsmodels/base/tests/test_predict.py000066400000000000000000000123501400612667500236270ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Tests for Results.predict """ from statsmodels.compat.pandas import testing as pdt import numpy as np import pandas as pd from numpy.testing import assert_allclose, assert_equal from statsmodels.regression.linear_model import OLS from statsmodels.genmod.generalized_linear_model import GLM class CheckPredictReturns(object): def test_2d(self): res = self.res data = self.data fitted = res.fittedvalues.iloc[1:10:2] pred = res.predict(data.iloc[1:10:2]) pdt.assert_index_equal(pred.index, fitted.index) assert_allclose(pred.values, fitted.values, rtol=1e-13) # plain dict xd = dict(zip(data.columns, data.iloc[1:10:2].values.T)) pred = res.predict(xd) assert_equal(pred.index, np.arange(len(pred))) assert_allclose(pred.values, fitted.values, rtol=1e-13) def test_1d(self): # one observation res = self.res data = self.data pred = res.predict(data.iloc[:1]) pdt.assert_index_equal(pred.index, data.iloc[:1].index) assert_allclose(pred.values, res.fittedvalues[0], rtol=1e-13) fittedm = res.fittedvalues.mean() xmean = data.mean() pred = res.predict(xmean.to_frame().T) assert_equal(pred.index, np.arange(1)) assert_allclose(pred, fittedm, rtol=1e-13) # Series pred = res.predict(data.mean()) assert_equal(pred.index, np.arange(1)) assert_allclose(pred.values, fittedm, rtol=1e-13) # dict with scalar value (is plain dict) # Note: this warns about dropped nan, even though there are None -FIXED pred = res.predict(data.mean().to_dict()) assert_equal(pred.index, np.arange(1)) assert_allclose(pred.values, fittedm, rtol=1e-13) def test_nopatsy(self): res = self.res data = self.data fitted = res.fittedvalues.iloc[1:10:2] # plain numpy array pred = res.predict(res.model.exog[1:10:2], transform=False) assert_allclose(pred, fitted.values, rtol=1e-13) # pandas DataFrame x = pd.DataFrame(res.model.exog[1:10:2], index = data.index[1:10:2], columns=res.model.exog_names) pred = res.predict(x) pdt.assert_index_equal(pred.index, fitted.index) assert_allclose(pred.values, fitted.values, rtol=1e-13) # one observation - 1-D pred = res.predict(res.model.exog[1], transform=False) assert_allclose(pred, fitted.values[0], rtol=1e-13) # one observation - pd.Series pred = res.predict(x.iloc[0]) pdt.assert_index_equal(pred.index, fitted.index[:1]) assert_allclose(pred.values[0], fitted.values[0], rtol=1e-13) class TestPredictOLS(CheckPredictReturns): @classmethod def setup_class(cls): nobs = 30 np.random.seed(987128) x = np.random.randn(nobs, 3) y = x.sum(1) + np.random.randn(nobs) index = ['obs%02d' % i for i in range(nobs)] # add one extra column to check that it does not matter cls.data = pd.DataFrame(np.round(np.column_stack((y, x)), 4), columns='y var1 var2 var3'.split(), index=index) cls.res = OLS.from_formula('y ~ var1 + var2', data=cls.data).fit() class TestPredictGLM(CheckPredictReturns): @classmethod def setup_class(cls): nobs = 30 np.random.seed(987128) x = np.random.randn(nobs, 3) y = x.sum(1) + np.random.randn(nobs) index = ['obs%02d' % i for i in range(nobs)] # add one extra column to check that it does not matter cls.data = pd.DataFrame(np.round(np.column_stack((y, x)), 4), columns='y var1 var2 var3'.split(), index=index) cls.res = GLM.from_formula('y ~ var1 + var2', data=cls.data).fit() def test_predict_offset(self): res = self.res data = self.data fitted = res.fittedvalues.iloc[1:10:2] offset = np.arange(len(fitted)) fitted = fitted + offset pred = res.predict(data.iloc[1:10:2], offset=offset) pdt.assert_index_equal(pred.index, fitted.index) assert_allclose(pred.values, fitted.values, rtol=1e-13) # plain dict xd = dict(zip(data.columns, data.iloc[1:10:2].values.T)) pred = res.predict(xd, offset=offset) assert_equal(pred.index, np.arange(len(pred))) assert_allclose(pred.values, fitted.values, rtol=1e-13) # offset as pandas.Series data2 = data.iloc[1:10:2].copy() data2['offset'] = offset pred = res.predict(data2, offset=data2['offset']) pdt.assert_index_equal(pred.index, fitted.index) assert_allclose(pred.values, fitted.values, rtol=1e-13) # check nan in exog is ok, preserves index matching offset length data2 = data.iloc[1:10:2].copy() data2['offset'] = offset data2.iloc[0, 1] = np.nan pred = res.predict(data2, offset=data2['offset']) pdt.assert_index_equal(pred.index, fitted.index) fitted_nan = fitted.copy() fitted_nan[0] = np.nan assert_allclose(pred.values, fitted_nan.values, rtol=1e-13) statsmodels-0.12.2/statsmodels/base/tests/test_screening.py000066400000000000000000000266741400612667500241700ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed May 23 12:53:27 2018 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_allclose, assert_equal import pandas as pd from statsmodels.discrete.discrete_model import Poisson, Logit from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod.families import family from statsmodels.base._penalized import PenalizedMixin from statsmodels.base._screening import VariableScreening class PoissonPenalized(PenalizedMixin, Poisson): pass class LogitPenalized(PenalizedMixin, Logit): pass class GLMPenalized(PenalizedMixin, GLM): pass def _get_poisson_data(): np.random.seed(987865) nobs, k_vars = 100, 500 k_nonzero = 5 x = (np.random.rand(nobs, k_vars) + 1. * (np.random.rand(nobs, 1) - 0.5)) * 2 - 1 x *= 1.2 x = (x - x.mean(0)) / x.std(0) x[:, 0] = 1 beta = np.zeros(k_vars) idx_nonzero_true = [0, 100, 300, 400, 411] beta[idx_nonzero_true] = 1. / np.arange(1, k_nonzero + 1) beta = np.sqrt(beta) # make small coefficients larger linpred = x.dot(beta) mu = np.exp(linpred) y = np.random.poisson(mu) return y, x, idx_nonzero_true, beta def test_poisson_screening(): np.random.seed(987865) y, x, idx_nonzero_true, beta = _get_poisson_data() nobs = len(y) xnames_true = ['var%4d' % ii for ii in idx_nonzero_true] xnames_true[0] = 'const' parameters = pd.DataFrame(beta[idx_nonzero_true], index=xnames_true, columns=['true']) xframe_true = pd.DataFrame(x[:, idx_nonzero_true], columns=xnames_true) res_oracle = Poisson(y, xframe_true).fit() parameters['oracle'] = res_oracle.params mod_initial = PoissonPenalized(y, np.ones(nobs), pen_weight=nobs * 5) screener = VariableScreening(mod_initial) exog_candidates = x[:, 1:] res_screen = screener.screen_exog(exog_candidates, maxiter=10) assert_equal(np.sort(res_screen.idx_nonzero), idx_nonzero_true) xnames = ['var%4d' % ii for ii in res_screen.idx_nonzero] xnames[0] = 'const' # smoke test res_screen.results_final.summary(xname=xnames) res_screen.results_pen.summary() assert_equal(res_screen.results_final.mle_retvals['converged'], True) ps = pd.Series(res_screen.results_final.params, index=xnames, name='final') parameters = parameters.join(ps, how='outer') assert_allclose(parameters['oracle'], parameters['final'], atol=5e-6) def test_screen_iterated(): np.random.seed(987865) nobs, k_nonzero = 100, 5 x = (np.random.rand(nobs, k_nonzero - 1) + 1.* (np.random.rand(nobs, 1) - 0.5)) * 2 - 1 x *= 1.2 x = (x - x.mean(0)) / x.std(0) x = np.column_stack((np.ones(nobs), x)) beta = 1. / np.arange(1, k_nonzero + 1) beta = np.sqrt(beta) # make small coefficients larger linpred = x.dot(beta) mu = np.exp(linpred) y = np.random.poisson(mu) common = x[:, 1:].sum(1)[:, None] x_nonzero = x def exog_iterator(): k_vars = 100 n_batches = 6 for i in range(n_batches): x = (0.05 * common + np.random.rand(nobs, k_vars) + 1.* (np.random.rand(nobs, 1) - 0.5)) * 2 - 1 x *= 1.2 if i < k_nonzero - 1: # hide a nonezero x[:, 10] = x_nonzero[:, i + 1] x = (x - x.mean(0)) / x.std(0) yield x dummy = np.ones(nobs) dummy[:nobs // 2] = 0 exog_keep = np.column_stack((np.ones(nobs), dummy)) for k in [1, 2]: mod_initial = PoissonPenalized(y, exog_keep[:, :k], pen_weight=nobs * 500) screener = VariableScreening(mod_initial) screener.k_max_add = 30 final = screener.screen_exog_iterator(exog_iterator()) names = ['var0_10', 'var1_10', 'var2_10', 'var3_10'] assert_equal(final.exog_final_names, names) idx_full = np.array([[ 0, 10], [ 1, 10], [ 2, 10], [ 3, 10]], dtype=np.int64) assert_equal(final.idx_nonzero_batches, idx_full) def test_glmpoisson_screening(): y, x, idx_nonzero_true, beta = _get_poisson_data() nobs = len(y) xnames_true = ['var%4d' % ii for ii in idx_nonzero_true] xnames_true[0] = 'const' parameters = pd.DataFrame(beta[idx_nonzero_true], index=xnames_true, columns=['true']) xframe_true = pd.DataFrame(x[:, idx_nonzero_true], columns=xnames_true) res_oracle = GLMPenalized(y, xframe_true, family=family.Poisson()).fit() parameters['oracle'] = res_oracle.params mod_initial = GLMPenalized(y, np.ones(nobs), family=family.Poisson()) screener = VariableScreening(mod_initial) exog_candidates = x[:, 1:] res_screen = screener.screen_exog(exog_candidates, maxiter=10) assert_equal(np.sort(res_screen.idx_nonzero), idx_nonzero_true) xnames = ['var%4d' % ii for ii in res_screen.idx_nonzero] xnames[0] = 'const' # smoke test res_screen.results_final.summary(xname=xnames) res_screen.results_pen.summary() assert_equal(res_screen.results_final.mle_retvals['converged'], True) ps = pd.Series(res_screen.results_final.params, index=xnames, name='final') parameters = parameters.join(ps, how='outer') assert_allclose(parameters['oracle'], parameters['final'], atol=5e-6) def _get_logit_data(): np.random.seed(987865) nobs, k_vars = 300, 500 k_nonzero = 5 x = (np.random.rand(nobs, k_vars) + 0.01 * (np.random.rand(nobs, 1) - 0.5)) * 2 - 1 x *= 1.2 x = (x - x.mean(0)) / x.std(0) x[:, 0] = 1 beta = np.zeros(k_vars) idx_nonzero_true = [0, 100, 300, 400, 411] beta[idx_nonzero_true] = 1. / np.arange(1, k_nonzero + 1)**0.5 beta = np.sqrt(beta) # make small coefficients larger linpred = x.dot(beta) mu = 1 / (1 + np.exp(-linpred)) y = (np.random.rand(len(mu)) < mu).astype(int) return y, x, idx_nonzero_true, beta def test_logit_screening(): y, x, idx_nonzero_true, beta = _get_logit_data() nobs = len(y) # test uses screener_kwds = dict(pen_weight=nobs * 0.7, threshold_trim=1e-3) xnames_true = ['var%4d' % ii for ii in idx_nonzero_true] xnames_true[0] = 'const' parameters = pd.DataFrame(beta[idx_nonzero_true], index=xnames_true, columns=['true']) xframe_true = pd.DataFrame(x[:, idx_nonzero_true], columns=xnames_true) res_oracle = Logit(y, xframe_true).fit() parameters['oracle'] = res_oracle.params mod_initial = LogitPenalized(y, np.ones(nobs), pen_weight=nobs * 0.5) screener = VariableScreening(mod_initial, **screener_kwds) screener.k_max_add = 30 exog_candidates = x[:, 1:] res_screen = screener.screen_exog(exog_candidates, maxiter=30) # we have extra variables, check index for larger params mask = np.abs(res_screen.results_final.params) > 0.1 assert_equal(np.sort(res_screen.idx_nonzero[mask]), idx_nonzero_true) # regression test idx_r = np.array([0, 74, 100, 163, 300, 400, 411]) assert_equal(np.sort(res_screen.idx_nonzero), idx_r) xnames = ['var%4d' % ii for ii in res_screen.idx_nonzero] xnames[0] = 'const' # smoke test res_screen.results_final.summary(xname=xnames) res_screen.results_pen.summary() assert_equal(res_screen.results_final.mle_retvals['converged'], True) ps = pd.Series(res_screen.results_final.params, index=xnames, name='final') # changed the following to allow for some extra params # parameters = parameters.join(ps, how='outer') parameters['final'] = ps assert_allclose(parameters['oracle'], parameters['final'], atol=0.005) def test_glmlogit_screening(): y, x, idx_nonzero_true, beta = _get_logit_data() nobs = len(y) # test uses screener_kwds = dict(pen_weight=nobs * 0.75, threshold_trim=1e-3, ranking_attr='model.score_factor') xnames_true = ['var%4d' % ii for ii in idx_nonzero_true] xnames_true[0] = 'const' parameters = pd.DataFrame(beta[idx_nonzero_true], index=xnames_true, columns=['true']) xframe_true = pd.DataFrame(x[:, idx_nonzero_true], columns=xnames_true) res_oracle = GLMPenalized(y, xframe_true, family=family.Binomial()).fit() parameters['oracle'] = res_oracle.params #mod_initial = LogitPenalized(y, np.ones(nobs), pen_weight=nobs * 0.5) mod_initial = GLMPenalized(y, np.ones(nobs), family=family.Binomial()) screener = VariableScreening(mod_initial, **screener_kwds) screener.k_max_add = 10 exog_candidates = x[:, 1:] res_screen = screener.screen_exog(exog_candidates, maxiter=30) res_screen.idx_nonzero res_screen.results_final xnames = ['var%4d' % ii for ii in res_screen.idx_nonzero] xnames[0] = 'const' # smoke test res_screen.results_final.summary(xname=xnames) res_screen.results_pen.summary() assert_equal(res_screen.results_final.mle_retvals['converged'], True) ps = pd.Series(res_screen.results_final.params, index=xnames, name='final') # changed the following to allow for some extra params # parameters = parameters.join(ps, how='outer') parameters['final'] = ps assert_allclose(parameters['oracle'], parameters['final'], atol=0.005) def _get_gaussian_data(): np.random.seed(987865) nobs, k_vars = 100, 500 k_nonzero = 5 x = (np.random.rand(nobs, k_vars) + 0.01 * (np.random.rand(nobs, 1) - 0.5)) * 2 - 1 x *= 1.2 x = (x - x.mean(0)) / x.std(0) x[:, 0] = 1 # make first column into constant beta = np.zeros(k_vars) idx_nonzero_true = [0, 1, 300, 400, 411] beta[idx_nonzero_true] = 1. / np.arange(1, k_nonzero + 1) beta = np.sqrt(beta) # make small coefficients larger linpred = x.dot(beta) y = linpred + 0.1 * np.random.randn(len(linpred)) return y, x, idx_nonzero_true, beta def test_glmgaussian_screening(): y, x, idx_nonzero_true, beta = _get_gaussian_data() nobs = len(y) # demeaning makes constant zero, checks that exog_keep are not trimmed y = y - y.mean(0) # test uses screener_kwds = dict(pen_weight=nobs * 0.75, threshold_trim=1e-3, ranking_attr='model.score_factor') xnames_true = ['var%4d' % ii for ii in idx_nonzero_true] xnames_true[0] = 'const' parameters = pd.DataFrame(beta[idx_nonzero_true], index=xnames_true, columns=['true']) xframe_true = pd.DataFrame(x[:, idx_nonzero_true], columns=xnames_true) res_oracle = GLMPenalized(y, xframe_true, family=family.Gaussian()).fit() parameters['oracle'] = res_oracle.params for k_keep in [1, 2]: mod_initial = GLMPenalized(y, x[:, :k_keep], family=family.Gaussian()) screener = VariableScreening(mod_initial, **screener_kwds) exog_candidates = x[:, k_keep:] res_screen = screener.screen_exog(exog_candidates, maxiter=30) assert_equal(np.sort(res_screen.idx_nonzero), idx_nonzero_true) xnames = ['var%4d' % ii for ii in res_screen.idx_nonzero] xnames[0] = 'const' # smoke test res_screen.results_final.summary(xname=xnames) res_screen.results_pen.summary() assert_equal(res_screen.results_final.mle_retvals['converged'], True) ps = pd.Series(res_screen.results_final.params, index=xnames, name='final') parameters = parameters.join(ps, how='outer') assert_allclose(parameters['oracle'], parameters['final'], atol=1e-5) # we need to remove 'final' again for next iteration del parameters['final'] statsmodels-0.12.2/statsmodels/base/tests/test_shrink_pickle.py000066400000000000000000000255421400612667500250310ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Mar 09 16:00:27 2012 Author: Josef Perktold """ from statsmodels.compat.pandas import assert_series_equal import pickle from io import BytesIO import numpy as np import pandas as pd import pytest from numpy.testing import assert_ # we need log in module namespace for TestPickleFormula5 from numpy import log # noqa:F401 import statsmodels.api as sm import statsmodels.genmod.generalized_linear_model as glm def check_pickle(obj): fh = BytesIO() pickle.dump(obj, fh, protocol=pickle.HIGHEST_PROTOCOL) plen = fh.tell() fh.seek(0, 0) res = pickle.load(fh) fh.close() return res, plen class RemoveDataPickle(object): @classmethod def setup_class(cls): nobs = 1000 np.random.seed(987689) x = np.random.randn(nobs, 3) x = sm.add_constant(x) cls.exog = x cls.xf = 0.25 * np.ones((2, 4)) cls.predict_kwds = {} def test_remove_data_pickle(self): results = self.results xf = self.xf pred_kwds = self.predict_kwds pred1 = results.predict(xf, **pred_kwds) # create some cached attributes results.summary() results.summary2() # SMOKE test also summary2 # uncomment the following to check whether tests run (7 failures now) # np.testing.assert_equal(res, 1) # check pickle unpickle works on full results # TODO: drop of load save is tested res, orig_nbytes = check_pickle(results._results) # remove data arrays, check predict still works if isinstance(results, glm.GLMResultsWrapper): with pytest.warns(FutureWarning, match="Anscombe residuals"): results.remove_data() else: results.remove_data() pred2 = results.predict(xf, **pred_kwds) if isinstance(pred1, pd.Series) and isinstance(pred2, pd.Series): assert_series_equal(pred1, pred2) elif isinstance(pred1, pd.DataFrame) and isinstance(pred2, pd.DataFrame): assert_(pred1.equals(pred2)) else: np.testing.assert_equal(pred2, pred1) # pickle and unpickle reduced array res, nbytes = check_pickle(results._results) # for testing attach res self.res = res assert_(nbytes < orig_nbytes, msg='pickle length not %d < %d' % (nbytes, orig_nbytes)) pred3 = results.predict(xf, **pred_kwds) if isinstance(pred1, pd.Series) and isinstance(pred3, pd.Series): assert_series_equal(pred1, pred3) elif isinstance(pred1, pd.DataFrame) and isinstance(pred3, pd.DataFrame): assert_(pred1.equals(pred3)) else: np.testing.assert_equal(pred3, pred1) def test_remove_data_docstring(self): assert_(self.results.remove_data.__doc__ is not None) def test_pickle_wrapper(self): fh = BytesIO() # use pickle with binary content # test unwrapped results load save pickle self.results._results.save(fh) fh.seek(0, 0) res_unpickled = self.results._results.__class__.load(fh) assert type(res_unpickled) is type(self.results._results) # noqa: E721 # test wrapped results load save fh.seek(0, 0) self.results.save(fh) fh.seek(0, 0) res_unpickled = self.results.__class__.load(fh) fh.close() assert type(res_unpickled) is type(self.results) # noqa: E721 before = sorted(self.results.__dict__.keys()) after = sorted(res_unpickled.__dict__.keys()) assert_(before == after, msg='not equal %r and %r' % (before, after)) before = sorted(self.results._results.__dict__.keys()) after = sorted(res_unpickled._results.__dict__.keys()) assert_(before == after, msg='not equal %r and %r' % (before, after)) before = sorted(self.results.model.__dict__.keys()) after = sorted(res_unpickled.model.__dict__.keys()) assert_(before == after, msg='not equal %r and %r' % (before, after)) before = sorted(self.results._cache.keys()) after = sorted(res_unpickled._cache.keys()) assert_(before == after, msg='not equal %r and %r' % (before, after)) class TestRemoveDataPickleOLS(RemoveDataPickle): def setup(self): # fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) y = x.sum(1) + np.random.randn(x.shape[0]) self.results = sm.OLS(y, self.exog).fit() class TestRemoveDataPickleWLS(RemoveDataPickle): def setup(self): # fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) y = x.sum(1) + np.random.randn(x.shape[0]) self.results = sm.WLS(y, self.exog, weights=np.ones(len(y))).fit() class TestRemoveDataPicklePoisson(RemoveDataPickle): def setup(self): # fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) y_count = np.random.poisson(np.exp(x.sum(1) - x.mean())) # bug with default model = sm.Poisson(y_count, x) # use start_params to converge faster start_params = np.array( [0.75334818, 0.99425553, 1.00494724, 1.00247112]) self.results = model.fit(start_params=start_params, method='bfgs', disp=0) # TODO: temporary, fixed in master self.predict_kwds = dict(exposure=1, offset=0) class TestRemoveDataPickleNegativeBinomial(RemoveDataPickle): def setup(self): # fit for each test, because results will be changed by test np.random.seed(987689) data = sm.datasets.randhie.load(as_pandas=False) mod = sm.NegativeBinomial(data.endog, data.exog) self.results = mod.fit(disp=0) class TestRemoveDataPickleLogit(RemoveDataPickle): def setup(self): # fit for each test, because results will be changed by test x = self.exog nobs = x.shape[0] np.random.seed(987689) y_bin = (np.random.rand(nobs) < 1.0 / ( 1 + np.exp(x.sum(1) - x.mean()))).astype(int) # bug with default model = sm.Logit(y_bin, x) # use start_params to converge faster start_params = np.array( [-0.73403806, -1.00901514, -0.97754543, -0.95648212]) self.results = model.fit(start_params=start_params, method='bfgs', disp=0) class TestRemoveDataPickleRLM(RemoveDataPickle): def setup(self): # fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) y = x.sum(1) + np.random.randn(x.shape[0]) self.results = sm.RLM(y, self.exog).fit() class TestRemoveDataPickleGLM(RemoveDataPickle): def setup(self): # fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) y = x.sum(1) + np.random.randn(x.shape[0]) self.results = sm.GLM(y, self.exog).fit() def test_cached_data_removed(self): res = self.results # fill data-like members of the cache names = ['resid_response', 'resid_deviance', 'resid_pearson', 'resid_anscombe'] with pytest.warns(FutureWarning, match="Anscombe residuals"): for name in names: getattr(res, name) # check that the attributes are present before calling remove_data for name in names: assert name in res._cache assert res._cache[name] is not None import warnings with warnings.catch_warnings(): warnings.simplefilter("ignore", FutureWarning) # FutureWarning for BIC changes res.remove_data() for name in names: assert res._cache[name] is None def test_cached_values_evaluated(self): # check that value-like attributes are evaluated before data # is removed res = self.results assert res._cache == {} with pytest.warns(FutureWarning, match="Anscombe residuals"): res.remove_data() assert 'aic' in res._cache class TestRemoveDataPickleGLMConstrained(RemoveDataPickle): def setup(self): # fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) y = x.sum(1) + np.random.randn(x.shape[0]) self.results = sm.GLM(y, self.exog).fit_constrained("x1=x2") class TestPickleFormula(RemoveDataPickle): @classmethod def setup_class(cls): super(TestPickleFormula, cls).setup_class() nobs = 10000 np.random.seed(987689) x = np.random.randn(nobs, 3) cls.exog = pd.DataFrame(x, columns=["A", "B", "C"]) cls.xf = pd.DataFrame(0.25 * np.ones((2, 3)), columns=cls.exog.columns) def setup(self): x = self.exog np.random.seed(123) y = x.sum(1) + np.random.randn(x.shape[0]) y = pd.Series(y, name="Y") X = self.exog.copy() X["Y"] = y self.results = sm.OLS.from_formula("Y ~ A + B + C", data=X).fit() class TestPickleFormula2(RemoveDataPickle): @classmethod def setup_class(cls): super(TestPickleFormula2, cls).setup_class() nobs = 500 np.random.seed(987689) data = np.random.randn(nobs, 4) data[:, 0] = data[:, 1:].sum(1) cls.data = pd.DataFrame(data, columns=["Y", "A", "B", "C"]) cls.xf = pd.DataFrame(0.25 * np.ones((2, 3)), columns=cls.data.columns[1:]) def setup(self): self.results = sm.OLS.from_formula("Y ~ A + B + C", data=self.data).fit() class TestPickleFormula3(TestPickleFormula2): def setup(self): self.results = sm.OLS.from_formula("Y ~ A + B * C", data=self.data).fit() class TestPickleFormula4(TestPickleFormula2): def setup(self): self.results = sm.OLS.from_formula("Y ~ np.log(abs(A) + 1) + B * C", data=self.data).fit() # we need log in module namespace for TestPickleFormula5 class TestPickleFormula5(TestPickleFormula2): def setup(self): self.results = sm.OLS.from_formula("Y ~ log(abs(A) + 1) + B * C", data=self.data).fit() class TestRemoveDataPicklePoissonRegularized(RemoveDataPickle): def setup(self): # fit for each test, because results will be changed by test x = self.exog np.random.seed(987689) y_count = np.random.poisson(np.exp(x.sum(1) - x.mean())) model = sm.Poisson(y_count, x) self.results = model.fit_regularized(method='l1', disp=0, alpha=10) statsmodels-0.12.2/statsmodels/base/tests/test_transform.py000066400000000000000000000105651400612667500242160ustar00rootroot00000000000000import numpy as np from numpy.testing import (assert_almost_equal, assert_equal, assert_raises) from statsmodels.base.transform import (BoxCox) from statsmodels.datasets import macrodata class TestTransform: @classmethod def setup_class(cls): data = macrodata.load_pandas() cls.x = data.data['realgdp'].values cls.bc = BoxCox() def test_nonpositive(self): # Testing negative values y = [1, -1, 1] assert_raises(ValueError, self.bc.transform_boxcox, y) # Testing nonzero y = [1, 0, 1] assert_raises(ValueError, self.bc.transform_boxcox, y) def test_invalid_bounds(self): # more than two bounds assert_raises(ValueError, self.bc._est_lambda, self.x, (-3, 2, 3)) # upper bound <= lower bound assert_raises(ValueError, self.bc._est_lambda, self.x, (2, -1)) def test_unclear_methods(self): # Both _est_lambda and untransform have a method argument that should # be tested. assert_raises(ValueError, self.bc._est_lambda, self.x, (-1, 2), 'test') assert_raises(ValueError, self.bc.untransform_boxcox, self.x, 1, 'test') def test_unclear_scale_parameter(self): # bc.guerrero allows for 'mad' and 'sd', for the MAD and Standard # Deviation, respectively assert_raises(ValueError, self.bc._est_lambda, self.x, scale='test') # Next, check if mad/sd work: self.bc._est_lambda(self.x, scale='mad') self.bc._est_lambda(self.x, scale='MAD') self.bc._est_lambda(self.x, scale='sd') self.bc._est_lambda(self.x, scale='SD') def test_valid_guerrero(self): # `l <- BoxCox.lambda(x, method="guerrero")` on a ts object # with frequency 4 (BoxCox.lambda defaults to 2, but we use # Guerrero and Perera (2004) as a guideline) lmbda = self.bc._est_lambda(self.x, method='guerrero', window_length=4) assert_almost_equal(lmbda, 0.507624, 4) # `l <- BoxCox.lambda(x, method="guerrero")` with the default grouping # parameter (namely, window_length=2). lmbda = self.bc._est_lambda(self.x, method='guerrero', window_length=2) assert_almost_equal(lmbda, 0.513893, 4) def test_guerrero_robust_scale(self): # The lambda is derived from a manual check of the values for the MAD. # Compare also the result for the standard deviation on R=4: 0.5076, # i.e. almost the same value. lmbda = self.bc._est_lambda(self.x, scale='mad') assert_almost_equal(lmbda, 0.488621, 4) def test_loglik_lambda_estimation(self): # 0.2 is the value returned by `BoxCox.lambda(x, method="loglik")` lmbda = self.bc._est_lambda(self.x, method='loglik') assert_almost_equal(lmbda, 0.2, 1) def test_boxcox_transformation_methods(self): # testing estimated lambda vs. provided. Should result in almost # the same transformed data. Value taken from R. y_transformed_no_lambda = self.bc.transform_boxcox(self.x) y_transformed_lambda = self.bc.transform_boxcox(self.x, 0.507624) assert_almost_equal(y_transformed_no_lambda[0], y_transformed_lambda[0], 3) # a perfectly increasing set has a constant variance over the entire # series, hence stabilising should result in the same scale: lmbda = 1. y, lmbda = self.bc.transform_boxcox(np.arange(1, 100)) assert_almost_equal(lmbda, 1., 5) def test_zero_lambda(self): # zero lambda should be a log transform. y_transform_zero_lambda, lmbda = self.bc.transform_boxcox(self.x, 0.) assert_equal(lmbda, 0.) assert_almost_equal(y_transform_zero_lambda, np.log(self.x), 5) def test_naive_back_transformation(self): # test both transformations functions -> 0. and .5 y_zero_lambda = self.bc.transform_boxcox(self.x, 0.) y_half_lambda = self.bc.transform_boxcox(self.x, .5) y_zero_lambda_un = self.bc.untransform_boxcox(*y_zero_lambda, method='naive') y_half_lambda_un = self.bc.untransform_boxcox(*y_half_lambda, method='naive') assert_almost_equal(self.x, y_zero_lambda_un, 5) assert_almost_equal(self.x, y_half_lambda_un, 5) statsmodels-0.12.2/statsmodels/base/transform.py000066400000000000000000000200651400612667500220110ustar00rootroot00000000000000import numpy as np from statsmodels.robust import mad from scipy.optimize import minimize_scalar class BoxCox(object): """ Mixin class to allow for a Box-Cox transformation. """ def transform_boxcox(self, x, lmbda=None, method='guerrero', **kwargs): """ Performs a Box-Cox transformation on the data array x. If lmbda is None, the indicated method is used to estimate a suitable lambda parameter. Parameters ---------- x : array_like lmbda : float The lambda parameter for the Box-Cox transform. If None, a value will be estimated by means of the specified method. method : {'guerrero', 'loglik'} The method to estimate the lambda parameter. Will only be used if lmbda is None, and defaults to 'guerrero', detailed in Guerrero (1993). 'loglik' maximizes the profile likelihood. **kwargs Options for the specified method. * For 'guerrero', this entails window_length, the grouping parameter, scale, the dispersion measure, and options, to be passed to the optimizer. * For 'loglik': options, to be passed to the optimizer. Returns ------- y : array_like The transformed series. lmbda : float The lmbda parameter used to transform the series. References ---------- Guerrero, Victor M. 1993. "Time-series analysis supported by power transformations". `Journal of Forecasting`. 12 (1): 37-48. Guerrero, Victor M. and Perera, Rafael. 2004. "Variance Stabilizing Power Transformation for Time Series," `Journal of Modern Applied Statistical Methods`. 3 (2): 357-369. Box, G. E. P., and D. R. Cox. 1964. "An Analysis of Transformations". `Journal of the Royal Statistical Society`. 26 (2): 211-252. """ x = np.asarray(x) if np.any(x <= 0): raise ValueError("Non-positive x.") if lmbda is None: lmbda = self._est_lambda(x, method=method, **kwargs) # if less than 0.01, treat lambda as zero. if np.isclose(lmbda, 0.): y = np.log(x) else: y = (np.power(x, lmbda) - 1.) / lmbda return y, lmbda def untransform_boxcox(self, x, lmbda, method='naive'): """ Back-transforms the Box-Cox transformed data array, by means of the indicated method. The provided argument lmbda should be the lambda parameter that was used to initially transform the data. Parameters ---------- x : array_like The transformed series. lmbda : float The lambda parameter that was used to transform the series. method : {'naive'} Indicates the method to be used in the untransformation. Defaults to 'naive', which reverses the transformation. NOTE: 'naive' is implemented natively, while other methods may be available in subclasses! Returns ------- y : array_like The untransformed series. """ method = method.lower() x = np.asarray(x) if method == 'naive': if np.isclose(lmbda, 0.): y = np.exp(x) else: y = np.power(lmbda * x + 1, 1. / lmbda) else: raise ValueError("Method '{0}' not understood.".format(method)) return y def _est_lambda(self, x, bounds=(-1, 2), method='guerrero', **kwargs): """ Computes an estimate for the lambda parameter in the Box-Cox transformation using method. Parameters ---------- x : array_like The untransformed data. bounds : tuple Numeric 2-tuple, that indicate the solution space for the lambda parameter. Default (-1, 2). method : {'guerrero', 'loglik'} The method by which to estimate lambda. Defaults to 'guerrero', but the profile likelihood ('loglik') is also available. **kwargs Options for the specified method. * For 'guerrero': window_length (int), the seasonality/grouping parameter. Scale ({'mad', 'sd'}), the dispersion measure. Options (dict), to be passed to the optimizer. * For 'loglik': Options (dict), to be passed to the optimizer. Returns ------- lmbda : float The lambda parameter. """ method = method.lower() if len(bounds) != 2: raise ValueError("Bounds of length {0} not understood." .format(len(bounds))) elif bounds[0] >= bounds[1]: raise ValueError("Lower bound exceeds upper bound.") if method == 'guerrero': lmbda = self._guerrero_cv(x, bounds=bounds, **kwargs) elif method == 'loglik': lmbda = self._loglik_boxcox(x, bounds=bounds, **kwargs) else: raise ValueError("Method '{0}' not understood.".format(method)) return lmbda def _guerrero_cv(self, x, bounds, window_length=4, scale='sd', options={'maxiter': 25}): """ Computes lambda using guerrero's coefficient of variation. If no seasonality is present in the data, window_length is set to 4 (as per Guerrero and Perera, (2004)). NOTE: Seasonality-specific auxiliaries *should* provide their own seasonality parameter. Parameters ---------- x : array_like bounds : tuple Numeric 2-tuple, that indicate the solution space for the lambda parameter. window_length : int Seasonality/grouping parameter. Default 4, as per Guerrero and Perera (2004). NOTE: this indicates the length of the individual groups, not the total number of groups! scale : {'sd', 'mad'} The dispersion measure to be used. 'sd' indicates the sample standard deviation, but the more robust 'mad' is also available. options : dict The options (as a dict) to be passed to the optimizer. """ nobs = len(x) groups = int(nobs / window_length) # remove the first n < window_length observations from consideration. grouped_data = np.reshape(x[nobs - (groups * window_length): nobs], (groups, window_length)) mean = np.mean(grouped_data, 1) scale = scale.lower() if scale == 'sd': dispersion = np.std(grouped_data, 1, ddof=1) elif scale == 'mad': dispersion = mad(grouped_data, axis=1) else: raise ValueError("Scale '{0}' not understood.".format(scale)) def optim(lmbda): rat = np.divide(dispersion, np.power(mean, 1 - lmbda)) # eq 6, p 40 return np.std(rat, ddof=1) / np.mean(rat) res = minimize_scalar(optim, bounds=bounds, method='bounded', options=options) return res.x def _loglik_boxcox(self, x, bounds, options={'maxiter': 25}): """ Taken from the Stata manual on Box-Cox regressions, where this is the special case of 'lhs only'. As an estimator for the variance, the sample variance is used, by means of the well-known formula. Parameters ---------- x : array_like options : dict The options (as a dict) to be passed to the optimizer. """ sum_x = np.sum(np.log(x)) nobs = len(x) def optim(lmbda): y, lmbda = self.transform_boxcox(x, lmbda) return (1 - lmbda) * sum_x + (nobs / 2.) * np.log(np.var(y)) res = minimize_scalar(optim, bounds=bounds, method='bounded', options=options) return res.x statsmodels-0.12.2/statsmodels/base/wrapper.py000066400000000000000000000070121400612667500214530ustar00rootroot00000000000000import functools import inspect from textwrap import dedent class ResultsWrapper(object): """ Class which wraps a statsmodels estimation Results class and steps in to reattach metadata to results (if available) """ _wrap_attrs = {} _wrap_methods = {} def __init__(self, results): self._results = results self.__doc__ = results.__doc__ def __dir__(self): return [x for x in dir(self._results)] def __getattribute__(self, attr): get = lambda name: object.__getattribute__(self, name) try: results = get('_results') except AttributeError: pass try: return get(attr) except AttributeError: pass obj = getattr(results, attr) data = results.model.data how = self._wrap_attrs.get(attr) if how and isinstance(how, tuple): obj = data.wrap_output(obj, how[0], *how[1:]) elif how: obj = data.wrap_output(obj, how=how) return obj def __getstate__(self): # print 'pickling wrapper', self.__dict__ return self.__dict__ def __setstate__(self, dict_): # print 'unpickling wrapper', dict_ self.__dict__.update(dict_) def save(self, fname, remove_data=False): """ Save a pickle of this instance. Parameters ---------- fname : {str, handle} Either a filename or a valid file handle. remove_data : bool If False (default), then the instance is pickled without changes. If True, then all arrays with length nobs are set to None before pickling. See the remove_data method. In some cases not all arrays will be set to None. """ from statsmodels.iolib.smpickle import save_pickle if remove_data: self.remove_data() save_pickle(self, fname) @classmethod def load(cls, fname): """ Load a pickled results instance .. warning:: Loading pickled models is not secure against erroneous or maliciously constructed data. Never unpickle data received from an untrusted or unauthenticated source. Parameters ---------- fname : {str, handle} A string filename or a file handle. Returns ------- Results The unpickled results instance. """ from statsmodels.iolib.smpickle import load_pickle return load_pickle(fname) def union_dicts(*dicts): result = {} for d in dicts: result.update(d) return result def make_wrapper(func, how): @functools.wraps(func) def wrapper(self, *args, **kwargs): results = object.__getattribute__(self, '_results') data = results.model.data if how and isinstance(how, tuple): obj = data.wrap_output(func(results, *args, **kwargs), how[0], how[1:]) elif how: obj = data.wrap_output(func(results, *args, **kwargs), how) return obj sig = inspect.signature(func) formatted = str(sig) doc = dedent(wrapper.__doc__) if wrapper.__doc__ else '' wrapper.__doc__ = "\n%s%s\n%s" % (func.__name__, formatted, doc) return wrapper def populate_wrapper(klass, wrapping): for meth, how in klass._wrap_methods.items(): if not hasattr(wrapping, meth): continue func = getattr(wrapping, meth) wrapper = make_wrapper(func, how) setattr(klass, meth, wrapper) statsmodels-0.12.2/statsmodels/compat/000077500000000000000000000000001400612667500177725ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/compat/__init__.py000066400000000000000000000004611400612667500221040ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester from .python import ( PY37, asunicode, asbytes, asstr, lrange, lzip, lmap, lfilter, ) __all__ = ['PY37', 'asunicode', 'asbytes', 'asstr', 'lrange', 'lzip', 'lmap', 'lfilter', 'test'] test = PytestTester() statsmodels-0.12.2/statsmodels/compat/numpy.py000066400000000000000000000051151400612667500215160ustar00rootroot00000000000000"""Compatibility functions for numpy versions in lib np_new_unique ------------- Optionally provides the count of the number of occurrences of each unique element. Copied from Numpy source, under license: Copyright (c) 2005-2015, NumPy Developers. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the NumPy Developers nor the names of any contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. """ from distutils.version import LooseVersion import numpy as np NP_LT_114 = LooseVersion(np.__version__) < LooseVersion('1.14') np_matrix_rank = np.linalg.matrix_rank np_new_unique = np.unique def recarray_select(recarray, fields): """" Work-around for changes in NumPy 1.13 that return views for recarray multiple column selection """ from pandas import DataFrame fields = [fields] if not isinstance(fields, (tuple, list)) else fields if len(fields) == len(recarray.dtype): selection = recarray else: recarray = DataFrame.from_records(recarray) selection = recarray[fields].to_records(index=False) return selection def lstsq(a, b, rcond=None): """ Shim that allows modern rcond setting with backward compat for NumPY earlier than 1.14 """ if NP_LT_114 and rcond is None: rcond = -1 return np.linalg.lstsq(a, b, rcond=rcond) statsmodels-0.12.2/statsmodels/compat/pandas.py000066400000000000000000000105201400612667500216100ustar00rootroot00000000000000from distutils.version import LooseVersion import numpy as np import pandas as pd from pandas.util._decorators import deprecate_kwarg, Appender, Substitution __all__ = ['assert_frame_equal', 'assert_index_equal', 'assert_series_equal', 'data_klasses', 'frequencies', 'is_numeric_dtype', 'testing', 'cache_readonly', 'deprecate_kwarg', 'Appender', 'Substitution', 'make_dataframe', 'assert_equal', 'to_numpy', 'pandas_lt_1_0_0'] version = LooseVersion(pd.__version__) pandas_lt_1_0_0 = version < LooseVersion('1.0.0') pandas_lt_25_0 = version < LooseVersion('0.25.0') pandas_gte_23_0 = version >= LooseVersion('0.23.0') try: from pandas.api.types import is_numeric_dtype except ImportError: from pandas.core.common import is_numeric_dtype try: from pandas.tseries import offsets as frequencies except ImportError: from pandas.tseries import frequencies data_klasses = (pd.Series, pd.DataFrame) if pandas_lt_25_0: data_klasses += (pd.Panel,) try: import pandas.testing as testing except ImportError: import pandas.util.testing as testing assert_frame_equal = testing.assert_frame_equal assert_index_equal = testing.assert_index_equal assert_series_equal = testing.assert_series_equal try: from pandas.testing import assert_equal except ImportError: def assert_equal(left, right): """ pandas >= 0.24.0 has `pandas.testing.assert_equal` that works for any of Index, Series, and DataFrame inputs. Until statsmodels requirements catch up to that, we implement a version of that here. Parameters ---------- left : pd.Index, pd.Series, or pd.DataFrame right : object Raises ------ AssertionError """ if isinstance(left, pd.Index): assert_index_equal(left, right) elif isinstance(left, pd.Series): assert_series_equal(left, right) elif isinstance(left, pd.DataFrame): assert_frame_equal(left, right) else: raise TypeError(type(left)) if pandas_gte_23_0: from pandas.util._decorators import cache_readonly else: class CachedProperty(object): def __init__(self, func): self.func = func self.name = func.__name__ self.__doc__ = getattr(func, '__doc__', None) def __get__(self, obj, typ): if obj is None: # accessed on the class, not the instance return self # Get the cache or set a default one if needed cache = getattr(obj, '_cache', None) if cache is None: try: cache = obj._cache = {} except (AttributeError): return self if self.name in cache: # not necessary to Py_INCREF val = cache[self.name] else: val = self.func(obj) cache[self.name] = val return val def __set__(self, obj, value): raise AttributeError("Can't set attribute") cache_readonly = CachedProperty try: from pandas._testing import makeDataFrame as make_dataframe except ImportError: import string def rands_array(nchars, size, dtype="O"): """ Generate an array of byte strings. """ rands_chars = np.array(list(string.ascii_letters + string.digits), dtype=(np.str_, 1)) retval = (np.random.choice(rands_chars, size=nchars * np.prod(size)) .view((np.str_, nchars)) .reshape(size)) if dtype is None: return retval else: return retval.astype(dtype) def make_dataframe(): """ Simple verion of pandas._testing.makeDataFrame """ n = 30 k = 4 index = pd.Index(rands_array(nchars=10, size=n), name=None) data = {c: pd.Series(np.random.randn(n), index=index) for c in string.ascii_uppercase[:k]} return pd.DataFrame(data) def to_numpy(po: pd.DataFrame) -> np.ndarray: """ Workaround legacy pandas lacking to_numpy Parameters ---------- po : Pandas obkect Returns ------- ndarray A numpy array """ try: return po.to_numpy() except AttributeError: return po.values statsmodels-0.12.2/statsmodels/compat/platform.py000066400000000000000000000006731400612667500221760ustar00rootroot00000000000000import os import sys __all__ = ['PLATFORM_OSX', 'PLATFORM_WIN', 'PLATFORM_WIN32', 'PLATFORM_32', 'PLATFORM_LINUX', 'PLATFORM_LINUX32'] PLATFORM_OSX = sys.platform == 'darwin' PLATFORM_WIN = sys.platform in ('win32', 'cygwin') or os.name == 'nt' PLATFORM_WIN32 = PLATFORM_WIN and sys.maxsize < 2**33 PLATFORM_LINUX = sys.platform[:5] == 'linux' PLATFORM_32 = sys.maxsize < 2 ** 33 PLATFORM_LINUX32 = PLATFORM_32 and PLATFORM_LINUX statsmodels-0.12.2/statsmodels/compat/python.py000066400000000000000000000021601400612667500216640ustar00rootroot00000000000000""" Compatibility tools for differences between Python 2 and 3 """ import sys PY37 = (sys.version_info[:2] == (3, 7)) asunicode = lambda x, _: str(x) # noqa:E731 def asbytes(s): if isinstance(s, bytes): return s return s.encode('latin1') def asstr(s): if isinstance(s, str): return s return s.decode('latin1') # list-producing versions of the major Python iterating functions def lrange(*args, **kwargs): return list(range(*args, **kwargs)) def lzip(*args, **kwargs): return list(zip(*args, **kwargs)) def lmap(*args, **kwargs): return list(map(*args, **kwargs)) def lfilter(*args, **kwargs): return list(filter(*args, **kwargs)) def with_metaclass(meta, *bases): """Create a base class with a metaclass.""" # This requires a bit of explanation: the basic idea is to make a dummy # metaclass for one level of class instantiation that replaces itself with # the actual metaclass. class metaclass(meta): def __new__(cls, name, this_bases, d): return meta(name, bases, d) return type.__new__(metaclass, 'temporary_class', (), {}) statsmodels-0.12.2/statsmodels/compat/scipy.py000066400000000000000000000057761400612667500215120ustar00rootroot00000000000000from distutils.version import LooseVersion import numpy as np import scipy SP_VERSION = LooseVersion(scipy.__version__) SCIPY_11 = SP_VERSION < LooseVersion("1.2.0") SCIPY_11 = SCIPY_11 and SP_VERSION >= LooseVersion("1.1.0") SCIPY_GT_14 = SP_VERSION >= LooseVersion("1.5") SP_LT_15 = SP_VERSION < LooseVersion("1.5") def _next_regular(target): """ Find the next regular number greater than or equal to target. Regular numbers are composites of the prime factors 2, 3, and 5. Also known as 5-smooth numbers or Hamming numbers, these are the optimal size for inputs to FFTPACK. Target must be a positive integer. """ if target <= 6: return target # Quickly check if it's already a power of 2 if not (target & (target - 1)): return target match = float("inf") # Anything found will be smaller p5 = 1 while p5 < target: p35 = p5 while p35 < target: # Ceiling integer division, avoiding conversion to float # (quotient = ceil(target / p35)) quotient = -(-target // p35) # Quickly find next power of 2 >= quotient p2 = 2 ** ((quotient - 1).bit_length()) N = p2 * p35 if N == target: return N elif N < match: match = N p35 *= 3 if p35 == target: return p35 if p35 < match: match = p35 p5 *= 5 if p5 == target: return p5 if p5 < match: match = p5 return match def _valarray(shape, value=np.nan, typecode=None): """Return an array of all value. """ out = np.ones(shape, dtype=bool) * value if typecode is not None: out = out.astype(typecode) if not isinstance(out, np.ndarray): out = np.asarray(out) return out def _lazywhere(cond, arrays, f, fillvalue=None, f2=None): """ np.where(cond, x, fillvalue) always evaluates x even where cond is False. This one only evaluates f(arr1[cond], arr2[cond], ...). For example, >>> a, b = np.array([1, 2, 3, 4]), np.array([5, 6, 7, 8]) >>> def f(a, b): return a*b >>> _lazywhere(a > 2, (a, b), f, np.nan) array([ nan, nan, 21., 32.]) Notice it assumes that all `arrays` are of the same shape, or can be broadcasted together. """ if fillvalue is None: if f2 is None: raise ValueError("One of (fillvalue, f2) must be given.") else: fillvalue = np.nan else: if f2 is not None: raise ValueError("Only one of (fillvalue, f2) can be given.") arrays = np.broadcast_arrays(*arrays) temp = tuple(np.extract(cond, arr) for arr in arrays) tcode = np.mintypecode([a.dtype.char for a in arrays]) out = _valarray(np.shape(arrays[0]), value=fillvalue, typecode=tcode) np.place(out, cond, f(*temp)) if f2 is not None: temp = tuple(np.extract(~cond, arr) for arr in arrays) np.place(out, ~cond, f2(*temp)) return out statsmodels-0.12.2/statsmodels/compat/tests/000077500000000000000000000000001400612667500211345ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/compat/tests/__init__.py000066400000000000000000000000001400612667500232330ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/compat/tests/test_itercompat.py000066400000000000000000000022171400612667500247160ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Feb 29 10:34:00 2012 Author: Josef Perktold """ from statsmodels.compat import lrange from itertools import combinations, zip_longest from numpy.testing import assert_ def test_zip_longest(): lili = [['a0', 'b0', 'c0', 'd0'], ['a1', 'b1', 'c1'], ['a2', 'b2', 'c2', 'd2'], ['a3', 'b3', 'c3', 'd3'], ['a4', 'b4']] transposed = [('a0', 'a1', 'a2', 'a3', 'a4'), ('b0', 'b1', 'b2', 'b3', 'b4'), ('c0', 'c1', 'c2', 'c3', None), ('d0', None, 'd2', 'd3', None)] assert_(list(zip_longest(*lili)) == transposed, '%r not equal %r' % ( zip_longest(*lili), transposed)) def test_combinations(): actual = list(combinations('ABCD', 2)) desired = [('A', 'B'), ('A', 'C'), ('A', 'D'), ('B', 'C'), ('B', 'D'), ('C', 'D')] assert_(actual == desired, '%r not equal %r' % (actual, desired)) actual = list(combinations(lrange(4), 3)) desired = [(0, 1, 2), (0, 1, 3), (0, 2, 3), (1, 2, 3)] assert_(actual == desired, '%r not equal %r' % (actual, desired)) statsmodels-0.12.2/statsmodels/compat/tests/test_scipy_compat.py000066400000000000000000000067651400612667500252550ustar00rootroot00000000000000from numpy.testing import assert_equal from statsmodels.compat.scipy import _next_regular def test_next_regular(): hams = { 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 8, 8: 8, 14: 15, 15: 15, 16: 16, 17: 18, 1021: 1024, 1536: 1536, 51200000: 51200000, 510183360: 510183360, 510183360+1: 512000000, 511000000: 512000000, 854296875: 854296875, 854296875+1: 859963392, 196608000000: 196608000000, 196608000000+1: 196830000000, 8789062500000: 8789062500000, 8789062500000+1: 8796093022208, 206391214080000: 206391214080000, 206391214080000+1: 206624260800000, 470184984576000: 470184984576000, 470184984576000+1: 470715894135000, 7222041363087360: 7222041363087360, 7222041363087360+1: 7230196133913600, # power of 5 5**23 11920928955078125: 11920928955078125, 11920928955078125-1: 11920928955078125, # power of 3 3**34 16677181699666569: 16677181699666569, 16677181699666569-1: 16677181699666569, # power of 2 2**54 18014398509481984: 18014398509481984, 18014398509481984-1: 18014398509481984, # above this, int(ceil(n)) == int(ceil(n+1)) 19200000000000000: 19200000000000000, 19200000000000000+1: 19221679687500000, 288230376151711744: 288230376151711744, 288230376151711744+1: 288325195312500000, 288325195312500000-1: 288325195312500000, 288325195312500000: 288325195312500000, 288325195312500000+1: 288555831593533440, # power of 3 3**83 3990838394187339929534246675572349035227-1: 3990838394187339929534246675572349035227, 3990838394187339929534246675572349035227: 3990838394187339929534246675572349035227, # power of 2 2**135 43556142965880123323311949751266331066368-1: 43556142965880123323311949751266331066368, 43556142965880123323311949751266331066368: 43556142965880123323311949751266331066368, # power of 5 5**57 6938893903907228377647697925567626953125-1: 6938893903907228377647697925567626953125, 6938893903907228377647697925567626953125: 6938893903907228377647697925567626953125, # http://www.drdobbs.com/228700538 # 2**96 * 3**1 * 5**13 290142196707511001929482240000000000000-1: 290142196707511001929482240000000000000, 290142196707511001929482240000000000000: 290142196707511001929482240000000000000, 290142196707511001929482240000000000000+1: 290237644800000000000000000000000000000, # 2**36 * 3**69 * 5**7 4479571262811807241115438439905203543080960000000-1: 4479571262811807241115438439905203543080960000000, 4479571262811807241115438439905203543080960000000: 4479571262811807241115438439905203543080960000000, 4479571262811807241115438439905203543080960000000+1: 4480327901140333639941336854183943340032000000000, # 2**37 * 3**44 * 5**42 30774090693237851027531250000000000000000000000000000000000000-1: 30774090693237851027531250000000000000000000000000000000000000, 30774090693237851027531250000000000000000000000000000000000000: 30774090693237851027531250000000000000000000000000000000000000, 30774090693237851027531250000000000000000000000000000000000000+1: 30778180617309082445871527002041377406962596539492679680000000, } for x, y in hams.items(): assert_equal(_next_regular(x), y) statsmodels-0.12.2/statsmodels/conftest.py000066400000000000000000000066541400612667500207210ustar00rootroot00000000000000import numpy as np import pytest try: import matplotlib matplotlib.use('agg') HAVE_MATPLOTLIB = True except ImportError: HAVE_MATPLOTLIB = False def pytest_addoption(parser): parser.addoption("--skip-slow", action="store_true", help="skip slow tests") parser.addoption("--only-slow", action="store_true", help="run only slow tests") parser.addoption("--skip-examples", action="store_true", help="skip tests of examples") parser.addoption("--skip-matplotlib", action="store_true", help="skip tests that depend on matplotlib") parser.addoption("--skip-smoke", action="store_true", help="skip smoke tests") parser.addoption("--only-smoke", action="store_true", help="run only smoke tests") def pytest_runtest_setup(item): if 'slow' in item.keywords and item.config.getoption("--skip-slow"): pytest.skip("skipping due to --skip-slow") if 'slow' not in item.keywords and item.config.getoption("--only-slow"): pytest.skip("skipping due to --only-slow") if 'example' in item.keywords and item.config.getoption("--skip-examples"): pytest.skip("skipping due to --skip-examples") if 'matplotlib' in item.keywords and \ item.config.getoption("--skip-matplotlib"): pytest.skip("skipping due to --skip-matplotlib") if 'matplotlib' in item.keywords and not HAVE_MATPLOTLIB: pytest.skip("skipping since matplotlib is not intalled") if 'smoke' in item.keywords and item.config.getoption("--skip-smoke"): pytest.skip("skipping due to --skip-smoke") if 'smoke' not in item.keywords and item.config.getoption('--only-smoke'): pytest.skip("skipping due to --only-smoke") def pytest_configure(config): try: import matplotlib matplotlib.use('agg') try: from pandas.plotting import register_matplotlib_converters register_matplotlib_converters() except ImportError: pass except ImportError: pass @pytest.fixture() def close_figures(): """ Fixture that closes all figures after a test function has completed Returns ------- closer : callable Function that will close all figures when called. Notes ----- Used by passing as an argument to the function that produces a plot, for example def test_some_plot(close_figures): If a function creates many figures, then these can be destroyed within a test function by calling close_figures to ensure that the number of figures does not become too large. def test_many_plots(close_figures): for i in range(100000): plt.plot(x,y) close_figures() """ try: import matplotlib.pyplot def close(): matplotlib.pyplot.close('all') except ImportError: def close(): pass yield close close() @pytest.fixture() def reset_randomstate(): """ Fixture that set the global RandomState to the fixed seed 1 Notes ----- Used by passing as an argument to the function that uses the global RandomState def test_some_plot(reset_randomstate): Returns the state after the test function exits """ state = np.random.get_state() np.random.seed(1) yield np.random.set_state(state) statsmodels-0.12.2/statsmodels/datasets/000077500000000000000000000000001400612667500203175ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/__init__.py000066400000000000000000000017711400612667500224360ustar00rootroot00000000000000""" Datasets module """ from statsmodels.tools._testing import PytestTester from . import (anes96, cancer, committee, ccard, copper, cpunish, elnino, engel, grunfeld, interest_inflation, longley, macrodata, modechoice, nile, randhie, scotland, spector, stackloss, star98, strikes, sunspots, fair, heart, statecrime, co2, fertility, china_smoking) from .utils import (get_rdataset, get_data_home, clear_data_home, webuse, check_internet) __all__ = ['anes96', 'cancer', 'committee', 'ccard', 'copper', 'cpunish', 'elnino', 'engel', 'grunfeld', 'interest_inflation', 'longley', 'macrodata', 'modechoice', 'nile', 'randhie', 'scotland', 'spector', 'stackloss', 'star98', 'strikes', 'sunspots', 'fair', 'heart', 'statecrime', 'co2', 'fertility', 'china_smoking', 'get_rdataset', 'get_data_home', 'clear_data_home', 'webuse', 'check_internet', 'test'] test = PytestTester() statsmodels-0.12.2/statsmodels/datasets/anes96/000077500000000000000000000000001400612667500214245ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/anes96/__init__.py000066400000000000000000000003261400612667500235360ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/anes96/anes96.csv000066400000000000000000000521261400612667500232540ustar00rootroot00000000000000'popul' 'TVnews' 'selfLR' 'ClinLR' 'DoleLR' 'PID' 'age' 'educ' 'income' 'vote' 0 7 7 1 6 6 36 3 1 1 190 1 3 3 5 1 20 4 1 0 31 7 2 2 6 1 24 6 1 0 83 4 3 4 5 1 28 6 1 0 640 7 5 6 4 0 68 6 1 0 110 3 3 4 6 1 21 4 1 0 100 7 5 6 4 1 77 4 1 0 31 1 5 4 5 4 21 4 1 0 180 7 4 6 3 3 31 4 1 0 2800 0 3 3 7 0 39 3 1 0 1600 0 3 2 4 4 26 2 1 0 330 5 4 3 6 1 31 4 1 0 190 2 5 4 6 5 22 4 1 1 100 7 4 4 6 0 42 5 1 0 1000 7 5 7 4 0 74 1 1 0 0 7 6 7 5 0 62 3 1 0 130 7 4 4 5 1 58 3 1 0 5 5 3 3 6 1 24 6 1 0 33 7 6 2 6 5 51 4 1 1 19 2 2 1 4 0 36 3 2 0 74 7 4 4 7 2 88 2 2 0 190 0 2 4 6 2 20 4 2 0 12 3 4 6 3 2 27 3 2 0 0 7 6 1 6 6 44 4 2 1 19 0 4 2 2 1 45 3 2 0 0 2 4 3 6 1 21 4 2 0 390 5 3 4 7 1 40 5 2 0 40 7 4 3 4 0 40 6 2 0 3 3 5 5 4 1 48 3 2 0 450 3 4 7 1 0 34 3 2 0 350 0 3 4 7 2 26 2 2 0 64 3 4 4 2 1 60 2 3 0 3 0 4 4 3 0 32 3 3 0 0 1 4 3 7 1 31 3 3 0 640 7 7 5 7 4 33 3 3 1 0 7 3 4 6 0 57 3 3 0 12 7 4 3 6 1 84 3 3 0 62 6 7 2 7 5 75 3 3 1 31 2 7 2 6 6 19 4 3 1 0 1 3 2 6 1 47 6 3 0 180 6 5 5 5 0 51 2 3 0 640 3 6 4 4 5 40 3 3 0 110 0 2 3 6 1 22 6 3 0 100 1 7 7 5 6 35 2 3 0 100 7 4 4 7 2 43 5 3 0 11 3 6 6 3 2 76 6 3 0 0 7 4 3 1 6 45 3 3 1 4 7 4 6 6 0 88 2 3 0 35 6 4 4 2 1 46 3 4 0 0 1 3 4 5 2 22 6 4 0 0 7 5 1 6 5 68 3 4 1 0 2 5 2 6 5 38 3 4 1 33 7 4 3 6 3 69 2 4 0 270 2 5 4 3 0 67 3 4 0 45 7 2 4 6 0 88 4 4 0 40 3 6 2 5 5 68 3 4 1 6 1 5 2 4 2 76 3 4 1 2 7 4 4 6 0 72 2 4 0 0 0 6 2 6 6 37 6 4 1 35 3 4 2 6 0 69 3 4 0 83 0 2 4 6 0 33 6 4 0 3500 7 2 2 6 0 34 4 4 0 100 2 4 4 7 2 30 3 4 0 350 2 3 3 6 1 19 3 4 0 100 3 4 6 2 0 44 3 4 0 67 1 4 4 7 1 64 3 4 0 30 5 7 7 2 0 37 4 4 0 0 7 6 3 5 4 31 5 5 1 0 0 6 1 5 4 88 4 5 1 6 7 6 2 6 6 77 4 5 1 350 1 4 5 6 5 30 6 5 0 400 1 2 3 7 1 32 4 5 0 15 7 6 2 6 6 59 1 5 1 0 0 4 4 4 3 47 4 5 0 3 2 4 6 5 1 22 3 5 0 22 5 4 2 6 2 55 3 5 0 64 2 2 1 3 0 24 2 5 0 32 5 3 7 4 1 65 1 5 0 390 7 3 6 2 2 24 3 5 0 0 7 3 4 5 3 30 3 5 0 0 7 4 5 2 3 73 3 5 0 59 5 3 3 5 1 73 5 5 0 0 6 4 3 6 2 91 1 5 0 35 7 3 2 5 0 71 2 5 0 0 2 6 4 5 4 34 4 5 1 170 7 4 3 2 0 48 2 6 0 12 1 6 2 6 5 42 4 6 1 40 4 6 5 4 0 72 2 6 0 31 2 3 4 6 6 20 4 6 1 31 7 2 2 7 0 22 4 6 0 1600 1 3 3 6 1 24 6 6 0 1 1 4 2 7 2 39 6 6 0 4 7 6 1 6 6 83 5 6 1 190 0 6 2 6 6 39 3 6 1 53 3 5 3 6 1 33 5 6 0 31 7 4 3 6 1 53 3 6 1 16 7 5 3 6 5 82 3 6 1 33 5 4 3 5 6 82 3 6 1 0 3 5 3 6 5 47 6 7 1 0 3 4 2 7 4 68 3 7 0 0 7 4 3 5 0 84 6 7 0 27 2 6 1 6 5 35 5 7 1 84 7 4 5 6 1 67 2 7 0 22 3 5 3 5 4 33 2 7 1 0 3 3 3 5 0 49 7 7 0 3500 0 4 3 7 0 91 1 7 0 390 7 4 5 3 1 43 3 7 0 0 7 4 3 2 6 65 4 7 0 16 7 5 6 3 0 69 3 7 0 200 0 5 5 4 1 56 4 8 0 640 0 2 3 5 0 24 6 8 0 0 7 4 4 5 0 77 3 8 0 45 7 6 3 7 0 74 3 8 0 12 0 7 3 6 6 25 6 8 1 20 7 6 2 5 4 85 1 8 1 7300 5 7 7 6 3 21 2 8 0 64 7 6 3 1 0 24 4 8 0 13 7 5 4 7 4 73 4 8 0 190 0 4 5 3 2 37 3 8 0 9 4 4 5 1 2 35 4 8 0 0 7 4 4 7 0 47 3 8 0 170 2 4 2 6 6 21 3 8 1 640 7 3 6 4 0 55 5 8 0 9 4 6 3 6 6 30 6 8 1 0 4 5 3 6 4 76 7 8 1 7300 5 3 4 3 3 36 4 8 0 2800 0 1 1 7 0 38 3 9 0 0 7 2 3 5 0 67 3 9 0 30 7 7 3 7 6 70 2 9 1 44 7 5 3 7 2 78 4 9 0 7300 1 2 2 7 3 27 6 9 0 330 4 3 5 6 1 51 4 9 0 3 0 6 7 3 5 33 4 9 0 51 2 6 1 5 6 80 6 9 1 29 5 4 1 6 1 79 1 9 0 630 2 6 4 5 4 66 1 9 1 170 0 4 1 6 0 32 3 10 0 33 7 4 5 7 0 70 2 10 0 0 3 2 3 6 3 42 3 10 0 9 5 5 4 5 5 73 4 10 1 22 4 4 4 6 0 87 2 10 0 100 0 7 5 1 1 30 5 10 0 2 2 4 4 5 3 52 3 10 0 0 6 5 3 6 1 62 4 10 0 50 7 6 3 4 0 67 3 10 0 15 4 6 3 4 4 37 6 10 0 3 4 3 5 7 0 37 4 10 0 720 5 1 5 6 1 64 6 10 0 640 7 1 1 5 0 34 3 10 0 5 7 4 4 7 0 70 3 10 0 24 2 6 2 6 6 31 5 10 1 22 7 2 2 6 0 29 6 11 0 55 7 4 5 4 1 71 2 11 0 0 2 4 4 4 0 67 1 11 0 1600 5 4 4 6 0 41 7 11 0 170 6 1 2 6 0 49 6 11 0 1000 7 4 4 5 0 42 5 11 0 63 0 6 3 2 0 78 2 11 0 110 0 4 1 6 1 24 3 11 0 16 7 4 6 6 1 29 3 11 0 100 3 4 2 6 5 39 5 11 1 7300 3 5 3 6 1 19 4 11 0 22 2 4 2 7 1 32 5 11 0 71 3 4 2 6 5 69 3 11 1 900 4 5 2 5 5 83 3 11 1 35 7 4 1 5 4 76 2 11 1 2 7 7 1 2 0 62 2 11 0 83 2 3 3 6 0 47 7 11 0 370 5 6 7 4 0 35 3 11 0 12 0 4 5 3 4 23 3 11 0 370 7 4 4 1 1 79 4 11 0 100 7 6 2 6 5 64 5 11 1 470 7 6 2 4 5 70 4 11 1 22 7 6 1 6 6 87 5 11 1 2800 0 3 6 1 0 28 2 12 0 47 5 3 5 7 1 58 3 12 0 900 5 4 4 6 1 85 2 12 0 330 7 3 6 4 0 62 3 12 0 84 0 3 2 7 1 26 6 12 0 0 0 6 2 5 5 28 3 12 1 33 3 6 1 7 6 88 2 12 1 53 7 2 3 6 0 57 6 12 0 8 7 2 2 6 0 78 3 12 0 2 7 4 4 2 0 56 3 12 0 0 0 4 6 3 3 46 5 12 0 0 2 4 4 3 5 20 3 12 1 0 0 5 6 4 1 24 4 12 0 0 7 5 2 6 2 72 4 12 0 15 7 2 4 7 1 51 4 12 0 900 0 6 2 5 6 34 6 12 1 30 2 4 2 6 1 21 4 12 0 0 7 4 4 6 2 74 7 12 0 170 3 4 4 6 1 48 1 12 0 900 2 3 3 7 5 28 3 12 0 0 6 7 1 7 5 38 2 12 1 1600 7 4 6 1 0 70 3 12 0 0 7 4 5 4 0 72 2 12 0 2800 0 4 5 6 0 41 3 12 0 110 5 3 4 5 1 50 7 12 0 1 7 6 2 5 5 73 3 12 1 3 5 5 2 4 0 79 6 12 0 0 4 5 1 4 5 76 2 12 1 22 0 5 3 5 5 62 5 12 1 63 3 6 2 6 6 30 6 12 1 290 0 6 3 6 5 35 4 12 1 2 7 1 2 7 1 66 4 12 0 40 0 2 4 6 0 35 4 12 0 67 0 6 1 5 6 57 6 12 1 0 5 4 5 4 5 37 5 12 1 470 7 5 5 2 1 61 3 13 0 0 7 6 2 6 6 56 3 13 1 4 6 3 4 5 1 53 3 13 0 20 0 4 5 3 2 24 6 13 1 2800 7 4 1 6 5 74 3 13 1 0 0 4 4 3 1 36 3 13 0 1 0 6 2 4 5 30 5 13 1 640 0 4 7 4 1 55 2 13 0 170 3 3 2 7 2 35 6 13 0 270 2 3 4 6 0 26 4 13 0 390 0 3 4 6 2 25 4 13 0 16 2 6 7 4 3 27 3 13 0 11 7 4 1 6 5 66 3 13 1 0 1 5 2 6 2 39 2 13 0 270 7 1 1 2 2 58 5 13 0 170 2 4 4 4 0 53 3 13 1 900 7 6 7 4 0 76 3 13 0 270 7 5 2 7 1 51 3 13 0 0 7 4 2 7 0 70 2 13 0 350 3 6 3 6 6 68 4 13 1 0 0 5 4 5 2 32 3 13 1 6 0 5 4 5 5 55 3 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5 4 7 2 26 4 15 0 110 7 5 2 5 6 67 3 15 1 8 0 4 5 5 1 21 3 15 0 11 5 6 2 6 6 27 7 15 1 56 4 6 5 3 0 78 6 15 1 8 3 4 4 3 1 32 3 15 0 100 5 4 2 6 1 68 4 15 0 900 7 4 2 6 5 76 4 15 0 67 7 3 3 6 0 33 5 15 0 35 4 6 2 5 4 38 2 15 1 35 3 4 3 5 1 49 7 15 0 22 0 5 4 6 5 61 4 15 1 110 7 7 1 5 4 57 3 15 1 12 0 4 2 5 2 20 3 15 0 7300 7 4 2 4 4 63 6 15 1 0 0 4 1 5 4 53 3 15 1 19 5 4 2 6 5 35 4 15 1 470 3 4 4 7 0 39 3 15 0 4 3 3 5 3 4 48 3 15 1 640 4 6 2 5 4 62 3 15 1 640 2 4 2 3 1 30 5 15 0 200 7 7 1 4 6 26 6 15 1 0 7 3 2 4 5 74 6 15 1 29 4 3 4 6 2 37 5 15 0 330 2 4 5 5 1 43 5 15 0 19 5 5 1 4 6 68 3 15 1 1 7 5 3 4 5 73 5 15 1 110 5 6 1 6 6 60 7 15 1 0 7 5 4 6 1 35 3 15 0 350 4 3 4 6 0 29 6 15 0 2 5 3 3 5 1 25 6 15 0 0 7 2 2 6 0 25 7 15 0 7 4 2 4 5 0 70 6 15 0 71 1 6 2 5 6 41 3 15 1 53 0 4 2 6 1 37 6 15 0 0 0 6 1 6 6 39 5 15 1 2 6 3 4 6 0 35 4 15 0 190 4 2 3 6 0 62 7 15 0 31 0 3 2 6 1 30 7 15 0 16 7 4 2 6 0 74 4 15 0 22 7 3 3 4 5 47 3 15 0 3 4 4 5 3 1 43 6 15 0 0 6 5 3 6 5 64 2 15 1 0 7 4 3 5 2 75 4 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2 7 2 21 3 19 0 0 3 6 2 6 5 37 4 19 1 0 0 7 3 4 5 31 3 19 1 35 7 2 4 6 0 85 7 19 0 900 1 4 2 6 5 33 3 19 0 27 7 3 7 4 3 63 2 19 1 900 7 4 4 6 1 51 3 19 0 0 2 3 5 2 0 46 3 19 0 64 2 5 2 6 6 26 5 19 1 4 7 3 3 6 0 57 6 19 0 0 3 4 2 6 1 48 3 19 1 0 2 7 1 5 5 55 3 19 1 53 0 3 6 4 1 37 5 19 0 290 2 6 2 6 6 39 3 19 1 15 2 2 3 4 1 24 3 19 1 0 0 6 3 6 6 30 6 19 1 35 0 3 4 6 1 36 7 19 0 0 0 5 4 6 4 45 3 19 0 470 1 5 2 6 2 29 3 19 0 16 7 6 3 6 5 41 4 19 1 40 1 5 3 5 4 28 5 19 1 290 7 2 2 7 0 35 4 19 0 4 7 2 3 6 0 46 4 19 0 1 7 1 2 7 1 55 4 19 0 140 3 2 3 6 6 65 4 19 0 110 1 4 2 6 1 22 4 19 0 0 1 4 4 6 1 41 4 19 0 900 1 2 3 6 2 43 7 19 0 0 2 4 3 6 0 49 4 19 0 0 4 4 2 5 4 35 7 19 1 51 7 3 3 5 1 80 3 19 0 71 2 4 6 2 0 57 4 19 0 900 4 3 3 6 0 48 3 19 0 83 4 1 4 6 2 43 6 19 0 360 3 4 4 7 0 34 4 19 0 180 7 2 2 4 0 44 5 19 0 1 3 6 1 6 4 49 6 20 1 22 7 5 2 7 2 43 7 20 0 1 0 4 3 5 6 39 4 20 1 2 2 4 3 7 1 27 3 20 0 34 4 6 2 6 6 30 6 20 1 33 2 6 2 6 4 33 6 20 1 10 1 2 3 7 0 32 5 20 0 290 7 5 2 6 6 31 6 20 1 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21 0 2 1 2 2 5 0 43 4 21 0 0 7 4 3 6 5 59 3 21 1 0 3 6 1 6 6 40 5 21 1 310 0 5 2 7 0 35 4 21 0 470 5 2 3 5 1 48 4 21 0 0 4 6 1 6 6 40 3 21 1 270 3 3 2 7 0 48 3 21 0 110 0 2 4 6 0 47 7 21 0 50 3 6 4 1 1 23 3 21 0 0 0 6 1 6 6 38 3 21 1 3 7 6 2 6 6 81 7 21 1 31 5 3 3 6 1 48 6 21 0 22 7 5 6 2 4 52 3 21 0 83 2 4 1 6 3 24 6 21 1 9 0 4 2 6 1 21 5 21 0 5 7 5 2 6 5 70 6 21 1 0 7 7 1 7 6 24 6 21 1 0 7 4 3 5 1 57 7 21 0 0 6 3 5 6 4 37 6 21 0 27 1 3 5 3 5 25 5 21 0 110 1 6 5 1 1 33 3 21 0 0 7 4 6 3 0 45 3 22 0 0 3 5 2 7 5 42 6 22 0 350 3 3 3 6 2 47 6 22 0 0 7 6 1 6 6 51 7 22 1 5 7 5 4 6 5 85 2 22 0 15 4 3 3 6 2 32 7 22 0 35 7 3 3 6 2 31 7 22 0 0 2 4 3 6 2 23 6 22 0 75 3 3 3 6 0 42 6 22 0 0 5 6 2 5 5 55 6 22 1 16 7 6 2 6 6 45 6 22 1 0 1 6 2 5 6 35 7 22 1 0 0 2 4 6 0 45 6 22 0 0 0 3 3 5 2 42 3 22 0 4 1 6 2 6 5 37 4 22 1 62 0 4 4 4 5 38 3 22 1 0 3 2 2 6 1 47 7 22 0 4 7 4 2 6 2 32 6 22 0 56 2 5 2 6 5 35 6 22 1 2 6 4 2 6 5 38 4 22 1 0 0 4 4 4 3 40 3 22 0 75 7 6 2 5 6 62 6 22 1 10 2 2 2 6 1 28 7 22 0 0 6 6 2 5 6 59 5 22 1 0 2 1 2 6 0 25 6 22 0 220 2 4 2 6 6 31 6 22 1 0 1 7 2 6 6 45 4 22 1 75 0 5 2 7 5 42 6 22 0 0 3 2 2 5 1 56 7 22 0 140 5 3 3 6 1 47 7 22 0 290 1 6 2 5 5 38 6 22 1 350 7 4 3 7 2 47 6 22 0 55 1 5 2 6 6 49 4 22 1 31 3 3 3 6 2 29 7 22 0 17 7 2 2 6 0 57 6 22 0 51 4 6 3 5 6 68 3 22 1 140 7 2 2 4 0 76 6 22 0 9 4 6 2 6 5 66 6 22 1 0 7 5 1 6 4 59 4 22 1 640 7 5 3 6 4 37 7 22 0 32 2 5 2 6 6 38 6 22 1 5 7 6 2 6 5 47 7 22 1 8 1 5 2 4 5 36 7 22 1 18 0 5 4 6 0 45 7 22 0 0 6 5 2 6 5 39 7 22 1 0 1 3 2 6 1 34 6 22 0 0 3 6 6 4 0 49 4 22 0 31 2 6 2 6 5 36 6 22 1 350 7 6 1 6 6 81 5 22 1 20 1 5 2 6 4 29 4 22 1 70 3 5 3 4 0 45 6 22 0 31 3 5 2 6 5 21 4 22 1 3 7 2 4 3 6 33 6 22 1 9 7 4 4 2 2 44 3 23 0 59 1 2 2 6 4 52 7 23 0 27 2 3 5 7 1 38 4 23 0 51 4 2 3 6 2 44 5 23 0 9 7 6 2 6 6 87 7 23 1 0 2 7 2 6 5 22 3 23 1 88 0 3 3 5 2 32 6 23 1 67 0 4 5 6 4 69 3 23 0 29 2 6 2 5 6 49 6 23 1 5 0 6 2 6 6 53 3 23 1 0 0 6 1 6 5 44 6 23 1 900 1 6 2 7 5 34 6 23 1 18 1 6 1 5 5 55 7 23 1 190 2 3 3 6 0 35 6 23 0 2 7 4 5 5 3 55 3 23 0 5 3 6 3 5 5 27 6 23 1 56 3 4 4 5 1 26 6 23 0 75 7 4 2 6 5 54 6 23 0 56 0 5 2 6 5 42 4 23 1 0 5 6 1 6 6 57 7 23 1 0 0 7 1 4 6 54 6 23 1 75 6 6 3 6 6 55 6 23 1 1600 7 5 3 6 6 50 7 23 1 15 0 5 5 6 1 57 7 23 0 19 3 5 3 7 3 46 4 23 0 16 7 6 2 6 6 53 6 23 1 42 2 3 3 5 0 32 7 23 0 18 5 5 2 5 3 53 5 23 1 0 3 3 3 6 1 39 6 23 0 310 1 5 2 5 4 47 6 23 1 1600 7 5 2 4 2 57 4 23 0 23 5 6 3 6 6 49 6 23 1 20 1 5 4 6 5 31 5 23 0 51 5 5 3 5 5 43 6 23 1 0 2 5 2 5 4 44 6 23 1 0 4 4 3 6 0 39 6 23 0 0 2 6 1 6 5 49 4 23 1 18 7 5 4 6 4 72 6 23 1 7300 7 5 2 6 5 50 6 23 1 110 1 5 2 6 6 28 4 23 1 0 0 5 2 7 3 48 7 23 1 3500 1 3 4 7 1 32 6 23 0 720 7 5 5 5 1 63 4 23 0 9 4 4 5 6 5 36 4 23 1 47 7 6 3 6 6 36 6 23 1 350 7 3 2 7 2 53 3 23 0 0 5 2 2 6 2 44 7 23 0 0 0 4 2 6 6 41 7 24 1 83 0 2 3 6 1 56 7 24 0 1 4 4 4 6 2 63 7 24 0 190 7 2 4 6 0 52 6 24 0 0 7 3 3 7 2 43 7 24 0 12 7 4 3 6 2 40 3 24 0 9 5 5 1 7 4 69 4 24 1 23 7 2 2 6 0 49 7 24 0 9 1 3 3 6 2 65 7 24 0 18 5 6 1 6 5 53 7 24 1 0 5 5 3 5 6 50 4 24 1 12 3 2 4 6 0 27 5 24 0 0 6 5 3 5 5 44 6 24 1 170 2 2 3 5 0 54 7 24 0 0 7 4 2 6 4 33 5 24 1 9 0 4 4 6 3 48 7 24 0 23 3 5 2 6 5 54 5 24 1 0 0 6 2 5 6 56 3 24 1 9 1 2 4 7 2 34 7 24 0 290 7 6 4 7 6 41 6 24 0 1 0 5 1 5 6 40 6 24 1 350 1 7 2 6 6 55 6 24 1 20 0 4 3 5 5 38 6 24 1 0 3 6 2 6 6 40 6 24 1 23 1 6 1 6 6 46 4 24 1 150 4 3 3 4 0 26 6 24 0 31 0 5 2 7 3 49 6 24 0 0 7 4 1 5 6 51 5 24 1 9 2 5 2 6 4 46 6 24 0 47 0 3 4 6 2 40 7 24 0 900 0 3 4 7 2 30 5 24 0 83 3 2 3 6 2 45 5 24 0 18 7 5 4 6 4 52 7 24 1 0 0 6 1 5 6 36 6 24 1 20 0 4 3 5 3 49 6 24 0 24 7 3 4 5 1 38 7 24 0 18 0 2 4 6 1 51 7 24 0 9 3 3 2 5 1 47 6 24 0 0 1 6 1 5 6 52 7 24 1 9 0 6 2 6 6 33 6 24 1 0 4 4 2 6 6 50 4 24 1 18 7 6 2 5 4 48 7 24 1 19 3 2 2 6 0 36 6 24 0 31 3 2 3 6 1 35 7 24 0 3500 7 7 3 5 4 34 7 24 0 0 7 2 4 5 2 53 6 24 0 33 0 4 3 6 2 33 7 24 0 0 1 6 3 6 6 52 6 24 1 18 3 4 3 6 4 44 7 24 0 0 0 3 4 4 0 48 6 24 0 31 3 5 2 6 5 20 4 24 1 0 5 3 2 4 6 45 6 24 1 59 7 4 2 6 2 70 3 24 0 0 0 3 3 4 2 39 3 24 0 7300 7 3 3 5 1 40 7 24 1 75 4 5 2 7 5 62 6 24 1 0 7 5 2 6 4 46 6 24 1 27 7 4 4 7 2 46 3 24 0 1600 7 4 2 5 6 56 7 24 1 0 7 6 3 6 6 55 7 24 1 0 7 6 2 6 6 41 4 24 1 7300 1 2 3 6 0 43 7 24 0 16 7 7 1 7 6 34 3 24 1 0 7 7 1 6 4 73 6 24 1 0 7 5 2 6 6 50 6 24 1 0 3 6 2 7 5 43 6 24 1 0 6 6 2 5 6 46 7 24 1 18 7 4 2 6 3 61 7 24 1 statsmodels-0.12.2/statsmodels/datasets/anes96/data.py000066400000000000000000000075331400612667500227170ustar00rootroot00000000000000"""American National Election Survey 1996""" from numpy import log from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This is public domain.""" TITLE = __doc__ SOURCE = """ http://www.electionstudies.org/ The American National Election Studies. """ DESCRSHORT = """This data is a subset of the American National Election Studies of 1996.""" DESCRLONG = DESCRSHORT NOTE = """:: Number of observations - 944 Number of variables - 10 Variables name definitions:: popul - Census place population in 1000s TVnews - Number of times per week that respondent watches TV news. PID - Party identification of respondent. 0 - Strong Democrat 1 - Weak Democrat 2 - Independent-Democrat 3 - Independent-Indpendent 4 - Independent-Republican 5 - Weak Republican 6 - Strong Republican age : Age of respondent. educ - Education level of respondent 1 - 1-8 grades 2 - Some high school 3 - High school graduate 4 - Some college 5 - College degree 6 - Master's degree 7 - PhD income - Income of household 1 - None or less than $2,999 2 - $3,000-$4,999 3 - $5,000-$6,999 4 - $7,000-$8,999 5 - $9,000-$9,999 6 - $10,000-$10,999 7 - $11,000-$11,999 8 - $12,000-$12,999 9 - $13,000-$13,999 10 - $14,000-$14.999 11 - $15,000-$16,999 12 - $17,000-$19,999 13 - $20,000-$21,999 14 - $22,000-$24,999 15 - $25,000-$29,999 16 - $30,000-$34,999 17 - $35,000-$39,999 18 - $40,000-$44,999 19 - $45,000-$49,999 20 - $50,000-$59,999 21 - $60,000-$74,999 22 - $75,000-89,999 23 - $90,000-$104,999 24 - $105,000 and over vote - Expected vote 0 - Clinton 1 - Dole The following 3 variables all take the values: 1 - Extremely liberal 2 - Liberal 3 - Slightly liberal 4 - Moderate 5 - Slightly conservative 6 - Conservative 7 - Extremely Conservative selfLR - Respondent's self-reported political leanings from "Left" to "Right". ClinLR - Respondents impression of Bill Clinton's political leanings from "Left" to "Right". DoleLR - Respondents impression of Bob Dole's political leanings from "Left" to "Right". logpopul - log(popul + .1) """ def load_pandas(): """Load the anes96 data and returns a Dataset class. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ data = _get_data() return du.process_pandas(data, endog_idx=5, exog_idx=[10, 2, 6, 7, 8]) def load(as_pandas=None): """Load the anes96 data and returns a Dataset class. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def _get_data(): data = du.load_csv(__file__, 'anes96.csv', sep=r'\s') data = du.strip_column_names(data) data['logpopul'] = log(data['popul'] + .1) return data.astype(float) statsmodels-0.12.2/statsmodels/datasets/anes96/src/000077500000000000000000000000001400612667500222135ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/anes96/src/anes96.csv000066400000000000000000000565131400612667500240470ustar00rootroot00000000000000popul TVnews selfLR ClinLR DoleLR PID age educ income vote reldist 0 7 7 1 6 6 36 3 1 1 -5 190 1 3 3 5 1 20 4 1 0 2 31 7 2 2 6 1 24 6 1 0 4 83 4 3 4 5 1 28 6 1 0 1 640 7 5 6 4 0 68 6 1 0 0 110 3 3 4 6 1 21 4 1 0 2 100 7 5 6 4 1 77 4 1 0 0 31 1 5 4 5 4 21 4 1 0 -1 180 7 4 6 3 3 31 4 1 0 -1 2800 0 3 3 7 0 39 3 1 0 4 1600 0 3 2 4 4 26 2 1 0 0 330 5 4 3 6 1 31 4 1 0 1 190 2 5 4 6 5 22 4 1 1 0 100 7 4 4 6 0 42 5 1 0 2 1000 7 5 7 4 0 74 1 1 0 -1 0 7 6 7 5 0 62 3 1 0 0 130 7 4 4 5 1 58 3 1 0 1 5 5 3 3 6 1 24 6 1 0 3 33 7 6 2 6 5 51 4 1 1 -4 19 2 2 1 4 0 36 3 2 0 1 74 7 4 4 7 2 88 2 2 0 3 190 0 2 4 6 2 20 4 2 0 2 12 3 4 6 3 2 27 3 2 0 -1 0 7 6 1 6 6 44 4 2 1 -5 19 0 4 2 2 1 45 3 2 0 0 0 2 4 3 6 1 21 4 2 0 1 390 5 3 4 7 1 40 5 2 0 3 40 7 4 3 4 0 40 6 2 0 -1 3 3 5 5 4 1 48 3 2 0 1 450 3 4 7 1 0 34 3 2 0 0 350 0 3 4 7 2 26 2 2 0 3 64 3 4 4 2 1 60 2 3 0 2 3 0 4 4 3 0 32 3 3 0 1 0 1 4 3 7 1 31 3 3 0 2 640 7 7 5 7 4 33 3 3 1 -2 0 7 3 4 6 0 57 3 3 0 2 12 7 4 3 6 1 84 3 3 0 1 62 6 7 2 7 5 75 3 3 1 -5 31 2 7 2 6 6 19 4 3 1 -4 0 1 3 2 6 1 47 6 3 0 2 180 6 5 5 5 0 51 2 3 0 0 640 3 6 4 4 5 40 3 3 0 0 110 0 2 3 6 1 22 6 3 0 3 100 1 7 7 5 6 35 2 3 0 2 100 7 4 4 7 2 43 5 3 0 3 11 3 6 6 3 2 76 6 3 0 3 0 7 4 3 1 6 45 3 3 1 2 4 7 4 6 6 0 88 2 3 0 0 35 6 4 4 2 1 46 3 4 0 2 0 1 3 4 5 2 22 6 4 0 1 0 7 5 1 6 5 68 3 4 1 -3 0 2 5 2 6 5 38 3 4 1 -2 33 7 4 3 6 3 69 2 4 0 1 270 2 5 4 3 0 67 3 4 0 1 45 7 2 4 6 0 88 4 4 0 2 40 3 6 2 5 5 68 3 4 1 -3 6 1 5 2 4 2 76 3 4 1 -2 2 7 4 4 6 0 72 2 4 0 2 0 0 6 2 6 6 37 6 4 1 -4 35 3 4 2 6 0 69 3 4 0 0 83 0 2 4 6 0 33 6 4 0 2 3500 7 2 2 6 0 34 4 4 0 4 100 2 4 4 7 2 30 3 4 0 3 350 2 3 3 6 1 19 3 4 0 3 100 3 4 6 2 0 44 3 4 0 0 67 1 4 4 7 1 64 3 4 0 3 30 5 7 7 2 0 37 4 4 0 5 0 7 6 3 5 4 31 5 5 1 -2 0 0 6 1 5 4 88 4 5 1 -4 6 7 6 2 6 6 77 4 5 1 -4 350 1 4 5 6 5 30 6 5 0 1 400 1 2 3 7 1 32 4 5 0 4 15 7 6 2 6 6 59 1 5 1 -4 0 0 4 4 4 3 47 4 5 0 0 3 2 4 6 5 1 22 3 5 0 -1 22 5 4 2 6 2 55 3 5 0 0 64 2 2 1 3 0 24 2 5 0 0 32 5 3 7 4 1 65 1 5 0 -3 390 7 3 6 2 2 24 3 5 0 -2 0 7 3 4 5 3 30 3 5 0 1 0 7 4 5 2 3 73 3 5 0 1 59 5 3 3 5 1 73 5 5 0 2 0 6 4 3 6 2 91 1 5 0 1 35 7 3 2 5 0 71 2 5 0 1 0 2 6 4 5 4 34 4 5 1 -1 170 7 4 3 2 0 48 2 6 0 1 12 1 6 2 6 5 42 4 6 1 -4 40 4 6 5 4 0 72 2 6 0 1 31 2 3 4 6 6 20 4 6 1 2 31 7 2 2 7 0 22 4 6 0 5 1600 1 3 3 6 1 24 6 6 0 3 1 1 4 2 7 2 39 6 6 0 1 4 7 6 1 6 6 83 5 6 1 -5 190 0 6 2 6 6 39 3 6 1 -4 53 3 5 3 6 1 33 5 6 0 -1 31 7 4 3 6 1 53 3 6 1 1 16 7 5 3 6 5 82 3 6 1 -1 33 5 4 3 5 6 82 3 6 1 0 0 3 5 3 6 5 47 6 7 1 -1 0 3 4 2 7 4 68 3 7 0 1 0 7 4 3 5 0 84 6 7 0 0 27 2 6 1 6 5 35 5 7 1 -5 84 7 4 5 6 1 67 2 7 0 1 22 3 5 3 5 4 33 2 7 1 -2 0 3 3 3 5 0 49 7 7 0 2 3500 0 4 3 7 0 91 1 7 0 2 390 7 4 5 3 1 43 3 7 0 0 0 7 4 3 2 6 65 4 7 0 1 16 7 5 6 3 0 69 3 7 0 1 200 0 5 5 4 1 56 4 8 0 1 640 0 2 3 5 0 24 6 8 0 2 0 7 4 4 5 0 77 3 8 0 1 45 7 6 3 7 0 74 3 8 0 -2 12 0 7 3 6 6 25 6 8 1 -3 20 7 6 2 5 4 85 1 8 1 -3 7300 5 7 7 6 3 21 2 8 0 1 64 7 6 3 1 0 24 4 8 0 2 13 7 5 4 7 4 73 4 8 0 1 190 0 4 5 3 2 37 3 8 0 0 9 4 4 5 1 2 35 4 8 0 2 0 7 4 4 7 0 47 3 8 0 3 170 2 4 2 6 6 21 3 8 1 0 640 7 3 6 4 0 55 5 8 0 -2 9 4 6 3 6 6 30 6 8 1 -3 0 4 5 3 6 4 76 7 8 1 -1 7300 5 3 4 3 3 36 4 8 0 -1 2800 0 1 1 7 0 38 3 9 0 6 0 7 2 3 5 0 67 3 9 0 2 30 7 7 3 7 6 70 2 9 1 -4 44 7 5 3 7 2 78 4 9 0 0 7300 1 2 2 7 3 27 6 9 0 5 330 4 3 5 6 1 51 4 9 0 1 3 0 6 7 3 5 33 4 9 0 2 51 2 6 1 5 6 80 6 9 1 -4 29 5 4 1 6 1 79 1 9 0 -1 630 2 6 4 5 4 66 1 9 1 -1 170 0 4 1 6 0 32 3 10 0 -1 33 7 4 5 7 0 70 2 10 0 2 0 3 2 3 6 3 42 3 10 0 3 9 5 5 4 5 5 73 4 10 1 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12 0 3 0 0 6 2 5 5 28 3 12 1 -3 33 3 6 1 7 6 88 2 12 1 -4 53 7 2 3 6 0 57 6 12 0 3 8 7 2 2 6 0 78 3 12 0 4 2 7 4 4 2 0 56 3 12 0 2 0 0 4 6 3 3 46 5 12 0 -1 0 2 4 4 3 5 20 3 12 1 1 0 0 5 6 4 1 24 4 12 0 0 0 7 5 2 6 2 72 4 12 0 -2 15 7 2 4 7 1 51 4 12 0 3 900 0 6 2 5 6 34 6 12 1 -3 30 2 4 2 6 1 21 4 12 0 0 0 7 4 4 6 2 74 7 12 0 2 170 3 4 4 6 1 48 1 12 0 2 900 2 3 3 7 5 28 3 12 0 4 0 6 7 1 7 5 38 2 12 1 -6 1600 7 4 6 1 0 70 3 12 0 1 0 7 4 5 4 0 72 2 12 0 -1 2800 0 4 5 6 0 41 3 12 0 1 110 5 3 4 5 1 50 7 12 0 1 1 7 6 2 5 5 73 3 12 1 -3 3 5 5 2 4 0 79 6 12 0 -2 0 4 5 1 4 5 76 2 12 1 -3 22 0 5 3 5 5 62 5 12 1 -2 63 3 6 2 6 6 30 6 12 1 -4 290 0 6 3 6 5 35 4 12 1 -3 2 7 1 2 7 1 66 4 12 0 5 40 0 2 4 6 0 35 4 12 0 2 67 0 6 1 5 6 57 6 12 1 -4 0 5 4 5 4 5 37 5 12 1 -1 470 7 5 5 2 1 61 3 13 0 3 0 7 6 2 6 6 56 3 13 1 -4 4 6 3 4 5 1 53 3 13 0 1 20 0 4 5 3 2 24 6 13 1 0 2800 7 4 1 6 5 74 3 13 1 -1 0 0 4 4 3 1 36 3 13 0 1 1 0 6 2 4 5 30 5 13 1 -2 640 0 4 7 4 1 55 2 13 0 -3 170 3 3 2 7 2 35 6 13 0 3 270 2 3 4 6 0 26 4 13 0 2 390 0 3 4 6 2 25 4 13 0 2 16 2 6 7 4 3 27 3 13 0 1 11 7 4 1 6 5 66 3 13 1 -1 0 1 5 2 6 2 39 2 13 0 -2 270 7 1 1 2 2 58 5 13 0 1 170 2 4 4 4 0 53 3 13 1 0 900 7 6 7 4 0 76 3 13 0 1 270 7 5 2 7 1 51 3 13 0 -1 0 7 4 2 7 0 70 2 13 0 1 350 3 6 3 6 6 68 4 13 1 -3 0 0 5 4 5 2 32 3 13 1 -1 6 0 5 4 5 5 55 3 13 0 -1 290 7 2 2 6 0 52 4 13 0 4 630 7 6 4 6 4 73 2 13 1 -2 900 0 5 4 7 0 42 2 13 0 1 31 2 4 4 3 4 23 5 13 1 1 1600 5 2 3 6 0 30 7 14 0 3 71 7 2 2 7 0 68 4 14 0 5 200 7 5 2 3 2 68 3 14 0 -1 0 0 6 4 7 3 68 6 14 0 -1 30 5 2 3 6 0 38 5 14 0 3 10 1 4 3 6 2 74 3 14 0 1 0 7 5 6 3 0 59 2 14 0 1 900 2 5 2 5 2 73 2 14 0 -3 71 7 2 3 6 0 79 3 14 0 3 22 3 7 1 6 5 28 4 14 1 -5 0 7 6 2 6 6 50 3 14 1 -4 0 4 6 3 1 1 36 4 14 0 2 0 3 6 2 6 6 50 3 14 1 -4 0 1 6 2 6 6 61 3 14 1 -4 7300 3 2 2 6 0 37 4 14 0 4 83 0 3 4 7 0 29 6 14 0 3 93 7 2 3 7 0 39 4 14 0 4 0 7 4 5 4 2 83 6 14 1 -1 51 7 6 1 5 4 68 6 14 1 -4 31 2 6 1 5 6 25 4 14 1 -4 93 2 1 3 6 1 41 6 14 0 3 0 7 3 2 6 1 67 3 14 0 2 0 3 4 2 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2 3 5 0 54 7 24 0 2 0 7 4 2 6 4 33 5 24 1 0 9 0 4 4 6 3 48 7 24 0 2 23 3 5 2 6 5 54 5 24 1 -2 0 0 6 2 5 6 56 3 24 1 -3 9 1 2 4 7 2 34 7 24 0 3 290 7 6 4 7 6 41 6 24 0 -1 1 0 5 1 5 6 40 6 24 1 -4 350 1 7 2 6 6 55 6 24 1 -4 20 0 4 3 5 5 38 6 24 1 0 0 3 6 2 6 6 40 6 24 1 -4 23 1 6 1 6 6 46 4 24 1 -5 150 4 3 3 4 0 26 6 24 0 1 31 0 5 2 7 3 49 6 24 0 -1 0 7 4 1 5 6 51 5 24 1 -2 9 2 5 2 6 4 46 6 24 0 -2 47 0 3 4 6 2 40 7 24 0 2 900 0 3 4 7 2 30 5 24 0 3 83 3 2 3 6 2 45 5 24 0 3 18 7 5 4 6 4 52 7 24 1 0 0 0 6 1 5 6 36 6 24 1 -4 20 0 4 3 5 3 49 6 24 0 0 24 7 3 4 5 1 38 7 24 0 1 18 0 2 4 6 1 51 7 24 0 2 9 3 3 2 5 1 47 6 24 0 1 0 1 6 1 5 6 52 7 24 1 -4 9 0 6 2 6 6 33 6 24 1 -4 0 4 4 2 6 6 50 4 24 1 0 18 7 6 2 5 4 48 7 24 1 -3 19 3 2 2 6 0 36 6 24 0 4 31 3 2 3 6 1 35 7 24 0 3 3500 7 7 3 5 4 34 7 24 0 -2 0 7 2 4 5 2 53 6 24 0 1 33 0 4 3 6 2 33 7 24 0 1 0 1 6 3 6 6 52 6 24 1 -3 18 3 4 3 6 4 44 7 24 0 1 0 0 3 4 4 0 48 6 24 0 0 31 3 5 2 6 5 20 4 24 1 -2 0 5 3 2 4 6 45 6 24 1 0 59 7 4 2 6 2 70 3 24 0 0 0 0 3 3 4 2 39 3 24 0 1 7300 7 3 3 5 1 40 7 24 1 2 75 4 5 2 7 5 62 6 24 1 -1 0 7 5 2 6 4 46 6 24 1 -2 27 7 4 4 7 2 46 3 24 0 3 1600 7 4 2 5 6 56 7 24 1 -1 0 7 6 3 6 6 55 7 24 1 -3 0 7 6 2 6 6 41 4 24 1 -4 7300 1 2 3 6 0 43 7 24 0 3 16 7 7 1 7 6 34 3 24 1 -6 0 7 7 1 6 4 73 6 24 1 -5 0 7 5 2 6 6 50 6 24 1 -2 0 3 6 2 7 5 43 6 24 1 -3 0 6 6 2 5 6 46 7 24 1 -3 18 7 4 2 6 3 61 7 24 1 0 statsmodels-0.12.2/statsmodels/datasets/cancer/000077500000000000000000000000001400612667500215525ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/cancer/__init__.py000066400000000000000000000003261400612667500236640ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/cancer/cancer.csv000066400000000000000000000046621400612667500235320ustar00rootroot00000000000000cancer,population 1,445 0,559 3,677 4,681 3,746 4,869 1,950 5,976 5,1096 5,1098 5,1114 7,1125 5,1236 6,1285 3,1291 3,1318 2,1323 8,1327 9,1438 7,1479 4,1536 6,1598 6,1635 11,1667 4,1696 7,1792 7,1795 4,1808 6,1838 16,1838 3,1847 8,1933 8,1959 4,1990 9,2003 10,2070 7,2091 8,2099 5,2104 11,2147 4,2154 12,2163 11,2172 9,2174 13,2183 17,2193 11,2210 10,2212 4,2236 4,2245 8,2261 6,2317 8,2333 16,2393 10,2404 4,2419 11,2462 10,2476 11,2477 9,2483 11,2511 14,2591 6,2624 8,2690 12,2731 15,2735 9,2736 13,2747 18,2782 15,2783 12,2793 11,2891 12,2894 12,2906 14,2929 12,2935 3,2962 5,3054 7,3112 9,3118 11,3185 14,3217 18,3236 11,3290 11,3314 4,3316 13,3401 10,3409 10,3426 9,3470 11,3488 12,3511 4,3549 16,3571 20,3578 5,3620 15,3654 15,3680 12,3683 7,3688 7,3706 12,3733 21,3800 16,3802 13,3832 16,3863 8,3891 12,4008 20,4093 21,4149 15,4162 13,4223 13,4232 10,4312 22,4329 14,4331 16,4399 13,4470 24,4618 27,4669 16,4681 28,4737 11,4784 12,4829 14,4857 26,4918 27,4967 17,5041 20,5051 12,5077 20,5107 12,5108 24,5124 27,5156 25,5167 19,5211 21,5246 8,5743 15,5773 22,5932 21,5983 37,5989 23,5998 18,6021 25,6035 26,6074 17,6134 27,6175 13,6220 13,6296 15,6445 33,6624 24,6841 23,6868 18,6903 24,6904 21,6916 32,6934 23,6978 32,7014 16,7025 29,7031 33,7115 20,7256 19,7288 27,7304 10,7367 34,7376 36,7407 26,7408 33,7503 24,7599 37,7743 34,7760 37,7910 20,7917 28,7957 30,7984 27,8004 45,8208 39,8249 29,8289 22,8313 27,8377 19,8396 30,8468 34,8493 35,8531 21,8773 18,8866 41,9091 34,9215 51,9225 30,9243 32,9435 38,9445 18,9468 42,9563 60,9605 19,9841 29,9994 17,10033 29,10049 41,10144 31,10303 35,10416 27,10461 37,10670 18,10844 41,10875 39,10890 41,11105 61,11622 46,12038 47,12173 36,12181 43,12608 45,12775 46,12915 45,13021 49,13142 55,13206 64,13407 64,13647 66,13870 57,13989 53,14089 51,14197 36,14620 28,14816 59,14952 39,15039 73,15049 41,15179 48,15204 37,16161 72,16239 72,16427 48,16462 62,16793 51,16925 71,17027 60,17201 70,17526 59,17666 91,17692 52,17742 65,18482 77,18731 84,18835 51,19274 66,19818 53,19906 58,20065 75,20140 88,20268 83,20539 48,20639 69,20969 41,21353 73,21757 79,22811 63,23245 90,23258 92,24296 60,24351 63,24692 63,24896 75,25275 70,25405 90,25715 111,26245 103,26408 117,26691 118,28024 40,28270 83,28477 90,29254 97,29422 92,30125 104,30538 96,34109 142,35112 105,35876 145,36307 160,39023 127,40756 169,42997 104,47672 179,49126 152,53464 163,56529 167,59634 302,60161 246,62398 236,62652 250,62931 267,63476 244,66676 248,74005 360,88456 statsmodels-0.12.2/statsmodels/datasets/cancer/data.py000066400000000000000000000026151400612667500230410ustar00rootroot00000000000000"""Breast Cancer Data""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """???""" TITLE = """Breast Cancer Data""" SOURCE = """ This is the breast cancer data used in Owen's empirical likelihood. It is taken from Rice, J.A. Mathematical Statistics and Data Analysis. http://www.cengage.com/statistics/discipline_content/dataLibrary.html """ DESCRSHORT = """Breast Cancer and county population""" DESCRLONG = """The number of breast cancer observances in various counties""" #suggested notes NOTE = """:: Number of observations: 301 Number of variables: 2 Variable name definitions: cancer - The number of breast cancer observances population - The population of the county """ def load_pandas(): data = _get_data() return du.process_pandas(data, endog_idx=0, exog_idx=None) def load(as_pandas=None): """ Load the data and return a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def _get_data(): return du.load_csv(__file__, 'cancer.csv', convert_float=True) statsmodels-0.12.2/statsmodels/datasets/ccard/000077500000000000000000000000001400612667500213735ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/ccard/R_wls.s000066400000000000000000000005631400612667500226510ustar00rootroot00000000000000d <- read.csv('./ccard.csv') attach(d) m1 <- lm(AVGEXP ~ AGE + INCOME + INCOMESQ + OWNRENT, weights=1/INCOMESQ) results <- summary(m1) m2 <- lm(AVGEXP ~ AGE + INCOME + INCOMESQ + OWNRENT - 1, weights=1/INCOMESQ) results2 <- summary(m2) print('m1 has a constant, which theoretically should be INCOME') print('m2 include -1 for no constant') print('See ccard/R_wls.s') statsmodels-0.12.2/statsmodels/datasets/ccard/__init__.py000066400000000000000000000003261400612667500235050ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/ccard/ccard.csv000066400000000000000000000030431400612667500231640ustar00rootroot00000000000000"AVGEXP","AGE","INCOME","INCOMESQ","OWNRENT" 124.98,38,4.52,20.4304,1 9.85,33,2.42,5.8564,0 15,34,4.5,20.25,1 137.87,31,2.54,6.4516,0 546.5,32,9.79,95.8441,1 92,23,2.5,6.25,0 40.83,28,3.96,15.6816,0 150.79,29,2.37,5.6169,1 777.82,37,3.8,14.44,1 52.58,28,3.2,10.24,0 256.66,31,3.95,15.6025,1 78.87,29,2.45,6.0025,1 42.62,35,1.91,3.6481,1 335.43,41,3.2,10.24,1 248.72,40,4,16,1 548.03,40,10,100,1 43.34,35,2.35,5.5225,1 218.52,34,2,4,1 170.64,36,4,16,0 37.58,43,5.14,26.4196,1 502.2,30,4.51,20.3401,0 73.18,22,1.5,2.25,0 1532.77,40,5.5,30.25,1 42.69,22,2.03,4.1209,0 417.83,29,3.2,10.24,0 552.72,21,2.47,6.1009,1 222.54,24,3,9,0 541.3,43,3.54,12.5316,1 568.77,37,5.7,32.49,1 344.47,27,3.5,12.25,0 405.35,28,4.6,21.16,1 310.94,26,3,9,1 53.65,23,2.59,6.7081,0 63.92,30,1.51,2.2801,0 165.85,30,1.85,3.4225,0 9.58,38,2.6,6.76,0 319.49,36,2,4,0 83.08,26,2.35,5.5225,0 644.83,28,7,49,1 93.2,24,2,4,0 105.04,21,1.7,2.89,0 34.13,24,2.8,7.84,0 41.19,26,2.4,5.76,0 169.89,33,3,9,0 1898.03,34,4.8,23.04,0 810.39,33,3.18,10.1124,0 32.78,21,1.5,2.25,0 95.8,25,3,9,0 27.78,27,2.28,5.1984,0 215.07,26,2.8,7.84,0 79.51,22,2.7,7.29,0 306.03,41,6,36,0 104.54,42,3.9,15.21,0 642.47,25,3.07,9.4249,0 308.05,31,2.46,6.0516,1 186.35,27,2,4,0 56.15,33,3.25,10.5625,0 129.37,37,2.72,7.3984,0 93.11,27,2.2,4.84,0 292.66,24,3.75,14.0625,0 98.46,25,2.88,8.2944,0 258.55,36,3.05,9.3025,0 101.68,33,2.55,6.5025,0 65.25,55,2.64,6.9696,1 108.61,20,1.65,2.7225,0 49.56,29,2.4,5.76,0 235.57,41,7.24,52.4176,1 68.38,43,2.4,5.76,0 474.15,33,6,36,1 234.05,25,3.6,12.96,0 451.2,26,5,25,1 251.52,46,5.5,30.25,1 statsmodels-0.12.2/statsmodels/datasets/ccard/data.py000066400000000000000000000031011400612667500226510ustar00rootroot00000000000000"""Bill Greene's credit scoring data.""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """Used with express permission of the original author, who retains all rights.""" TITLE = __doc__ SOURCE = """ William Greene's `Econometric Analysis` More information can be found at the web site of the text: http://pages.stern.nyu.edu/~wgreene/Text/econometricanalysis.htm """ DESCRSHORT = """William Greene's credit scoring data""" DESCRLONG = """More information on this data can be found on the homepage for Greene's `Econometric Analysis`. See source. """ NOTE = """:: Number of observations - 72 Number of variables - 5 Variable name definitions - See Source for more information on the variables. """ def load_pandas(): """Load the credit card data and returns a Dataset class. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ data = _get_data() return du.process_pandas(data, endog_idx=0) def load(as_pandas=None): """Load the credit card data and returns a Dataset class. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def _get_data(): return du.load_csv(__file__, 'ccard.csv', convert_float=True) statsmodels-0.12.2/statsmodels/datasets/ccard/src/000077500000000000000000000000001400612667500221625ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/ccard/src/ccard.csv000066400000000000000000000040511400612667500237530ustar00rootroot00000000000000"MDR","Acc","Age","Income","Avgexp","Ownrent","Selfempl" 0,1,38,4.52,124.98,1,0 0,1,33,2.42,9.85,0,0 0,1,34,4.5,15,1,0 0,1,31,2.54,137.87,0,0 0,1,32,9.79,546.5,1,0 0,1,23,2.5,92,0,0 0,1,28,3.96,40.83,0,0 0,1,29,2.37,150.79,1,0 0,1,37,3.8,777.82,1,0 0,1,28,3.2,52.58,0,0 0,1,31,3.95,256.66,1,0 0,0,42,1.98,0,1,0 0,0,30,1.73,0,1,0 0,1,29,2.45,78.87,1,0 0,1,35,1.91,42.62,1,0 0,1,41,3.2,335.43,1,0 0,1,40,4,248.72,1,0 7,0,30,3,0,1,0 0,1,40,10,548.03,1,1 3,0,46,3.4,0,0,0 0,1,35,2.35,43.34,1,0 1,0,25,1.88,0,0,0 0,1,34,2,218.52,1,0 1,1,36,4,170.64,0,0 0,1,43,5.14,37.58,1,0 0,1,30,4.51,502.2,0,0 0,0,22,3.84,0,0,1 0,1,22,1.5,73.18,0,0 0,0,34,2.5,0,1,0 0,1,40,5.5,1532.77,1,0 0,1,22,2.03,42.69,0,0 1,1,29,3.2,417.83,0,0 1,0,25,3.15,0,1,0 0,1,21,2.47,552.72,1,0 0,1,24,3,222.54,0,0 0,1,43,3.54,541.3,1,0 0,0,43,2.28,0,0,0 0,1,37,5.7,568.77,1,0 0,1,27,3.5,344.47,0,0 0,1,28,4.6,405.35,1,0 0,1,26,3,310.94,1,0 0,1,23,2.59,53.65,0,0 0,1,30,1.51,63.92,0,0 0,1,30,1.85,165.85,0,0 0,1,38,2.6,9.58,0,0 0,0,28,1.8,0,0,1 0,1,36,2,319.49,0,0 0,0,38,3.26,0,0,0 0,1,26,2.35,83.08,0,0 0,1,28,7,644.83,1,0 0,0,50,3.6,0,0,0 0,1,24,2,93.2,0,0 0,1,21,1.7,105.04,0,0 0,1,24,2.8,34.13,0,0 0,1,26,2.4,41.19,0,0 1,1,33,3,169.89,0,0 0,1,34,4.8,1898.03,0,0 0,1,33,3.18,810.39,0,0 0,0,45,1.8,0,0,0 0,1,21,1.5,32.78,0,0 2,1,25,3,95.8,0,0 0,1,27,2.28,27.78,0,0 0,1,26,2.8,215.07,0,0 0,1,22,2.7,79.51,0,0 3,0,27,4.9,0,1,0 0,0,26,2.5,0,0,1 0,1,41,6,306.03,0,1 0,1,42,3.9,104.54,0,0 0,0,22,5.1,0,0,0 0,1,25,3.07,642.47,0,0 0,1,31,2.46,308.05,1,0 0,1,27,2,186.35,0,0 0,1,33,3.25,56.15,0,0 0,1,37,2.72,129.37,0,0 0,1,27,2.2,93.11,0,0 1,0,24,4.1,0,0,0 0,1,24,3.75,292.66,0,0 0,1,25,2.88,98.46,0,0 0,1,36,3.05,258.55,0,0 0,1,33,2.55,101.68,0,0 0,0,33,4,0,0,0 1,1,55,2.64,65.25,1,0 0,1,20,1.65,108.61,0,0 0,1,29,2.4,49.56,0,0 3,0,40,3.71,0,0,0 0,1,41,7.24,235.57,1,0 0,0,41,4.39,0,1,0 0,0,35,3.3,0,1,0 0,0,24,2.3,0,0,0 1,0,54,4.18,0,0,0 2,0,34,2.49,0,0,0 0,0,45,2.81,0,1,0 0,1,43,2.4,68.38,0,0 4,0,35,1.5,0,0,0 2,0,36,8.4,0,0,0 0,1,22,1.56,0,0,0 1,1,33,6,474.15,1,0 1,1,25,3.6,234.05,0,0 0,1,26,5,451.2,1,0 0,1,46,5.5,251.52,1,0 statsmodels-0.12.2/statsmodels/datasets/ccard/src/names.txt000066400000000000000000000004231400612667500240250ustar00rootroot00000000000000MDR = Number of derogator reports Acc = Credit card application accpeted (1=yes) Age = Age in years + 12ths of a year Income = Income divided by 10,000 Avgexp = Avg. monthly credit card expenditure Ownrent = Indiviual owns(1) or rents(0) home Selfempl = (1=yes, 0=no) statsmodels-0.12.2/statsmodels/datasets/china_smoking/000077500000000000000000000000001400612667500231305ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/china_smoking/__init__.py000066400000000000000000000003261400612667500252420ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/china_smoking/china_smoking.csv000066400000000000000000000004301400612667500264530ustar00rootroot00000000000000Location,smoking_yes_cancer_yes,smoking_yes_cancer_no,smoking_no_cancer_yes,smoking_no_cancer_no Beijing,126,100,35,61 Shanghai,908,688,497,807 Shenyang,913,747,336,598 Nanjng,235,172,58,121 Harbin,402,308,121,215 Zhengzhou,182,156,72,98 Taiyuan,60,99,11,43 Nanchang,104,89,21,36 statsmodels-0.12.2/statsmodels/datasets/china_smoking/data.py000066400000000000000000000034241400612667500244160ustar00rootroot00000000000000"""Smoking and lung cancer in eight cities in China.""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """Intern. J. Epidemiol. (1992)""" TITLE = __doc__ SOURCE = """ Transcribed from Z. Liu, Smoking and Lung Cancer Incidence in China, Intern. J. Epidemiol., 21:197-201, (1992). """ DESCRSHORT = """Co-occurrence of lung cancer and smoking in 8 Chinese cities.""" DESCRLONG = """This is a series of 8 2x2 contingency tables showing the co-occurrence of lung cancer and smoking in 8 Chinese cities. """ NOTE = """:: Number of Observations - 8 Number of Variables - 3 Variable name definitions:: city_name - name of the city smoking - yes or no, according to a person's smoking behavior lung_cancer - yes or no, according to a person's lung cancer status """ def load_pandas(): """ Load the China smoking/lung cancer data and return a Dataset class. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ raw_data = du.load_csv(__file__, 'china_smoking.csv') data = raw_data.set_index('Location') dset = du.Dataset(data=data, title="Smoking and lung cancer in Chinese regions") dset.raw_data = raw_data return dset def load(as_pandas=None): """ Load the China smoking/lung cancer data and return a Dataset class. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas, retain_index=True) statsmodels-0.12.2/statsmodels/datasets/co2/000077500000000000000000000000001400612667500210025ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/co2/__init__.py000066400000000000000000000003261400612667500231140ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/co2/co2.csv000066400000000000000000001022661400612667500222110ustar00rootroot00000000000000date,co2 19580329,316.1 19580405,317.3 19580412,317.6 19580419,317.5 19580426,316.4 19580503,316.9 19580510, 19580517,317.5 19580524,317.9 19580531, 19580607, 19580614, 19580621, 19580628, 19580705,315.8 19580712,315.8 19580719,315.4 19580726,315.5 19580802,315.6 19580809,315.1 19580816,315.0 19580823, 19580830,314.1 19580906,313.5 19580913, 19580920, 19580927, 19581004, 19581011, 19581018, 19581025, 19581101, 19581108,313.0 19581115,313.2 19581122,313.5 19581129,314.0 19581206,314.5 19581213,314.4 19581220,314.7 19581227,315.2 19590103,315.2 19590110,315.5 19590117,315.6 19590124,315.8 19590131,315.4 19590207, 19590214,316.9 19590221,316.6 19590228,316.6 19590307,316.8 19590314, 19590321,316.7 19590328,316.7 19590404,317.7 19590411,317.1 19590418,317.6 19590425,318.3 19590502,318.2 19590509,318.7 19590516,318.0 19590523,318.4 19590530, 19590606,318.5 19590613,318.1 19590620,317.8 19590627,317.7 19590704,316.8 19590711,316.8 19590718,316.4 19590725,316.1 19590801,315.6 19590808,314.9 19590815, 19590822,315.0 19590829,314.1 19590905,314.4 19590912,313.9 19590919,313.5 19590926,313.5 19591003,313.0 19591010,313.1 19591017,313.4 19591024,313.4 19591031,314.1 19591107,314.4 19591114,314.8 19591121,315.2 19591128,315.1 19591205,315.0 19591212,315.6 19591219,315.8 19591226,315.7 19600102,315.7 19600109,316.4 19600116,316.7 19600123,316.5 19600130,316.6 19600206,316.6 19600213,316.9 19600220,317.4 19600227,317.0 19600305,316.9 19600312,317.7 19600319,318.0 19600326,317.7 19600402,318.6 19600409,319.3 19600416,319.0 19600423,319.0 19600430,319.7 19600507,319.9 19600514,319.8 19600521,320.0 19600528,320.0 19600604,319.4 19600611,320.0 19600618,319.4 19600625,319.0 19600702,318.1 19600709,318.6 19600716,318.4 19600723,317.9 19600730,317.3 19600806,316.6 19600813,316.7 19600820,315.1 19600827,314.7 19600903,314.7 19600910,314.5 19600917,314.2 19600924,313.3 19601001,313.6 19601008,313.3 19601015,313.9 19601022,314.2 19601029,314.2 19601105,314.5 19601112,315.1 19601119,315.1 19601126,315.4 19601203,315.8 19601210,316.0 19601217,316.2 19601224,316.4 19601231,316.6 19610107,316.7 19610114,317.0 19610121,317.0 19610128,317.0 19610204,317.0 19610211,317.7 19610218,317.9 19610225,318.0 19610304,318.0 19610311,318.5 19610318,318.9 19610325,318.7 19610401,319.4 19610408,319.5 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19800712,339.7 19800719,338.5 19800726,338.9 19800802,337.9 19800809,337.7 19800816,337.7 19800823,337.7 19800830,337.0 19800906,336.6 19800913,335.7 19800920,335.2 19800927,336.0 19801004,335.8 19801011,335.8 19801018,336.1 19801025,336.4 19801101,336.6 19801108,336.9 19801115,337.1 19801122,337.3 19801129,337.4 19801206,337.7 19801213,338.1 19801220,338.3 19801227,338.7 19810103,338.9 19810110,339.1 19810117,339.3 19810124,339.3 19810131,339.5 19810207,340.5 19810214,340.0 19810221,340.2 19810228,341.1 19810307,340.7 19810314,341.0 19810321,341.8 19810328,342.1 19810404,342.4 19810411,342.4 19810418,342.7 19810425,342.3 19810502,342.9 19810509,343.0 19810516,342.8 19810523,342.7 19810530,342.7 19810606,342.6 19810613,342.5 19810620,341.8 19810627,341.6 19810704,341.0 19810711,340.8 19810718,339.7 19810725,340.2 19810801,339.5 19810808,338.9 19810815,338.4 19810822,337.5 19810829,337.7 19810905,337.2 19810912,337.0 19810919,336.7 19810926,335.9 19811003,336.3 19811010,336.6 19811017,337.1 19811024,337.2 19811031,337.5 19811107,337.8 19811114,338.1 19811121,338.5 19811128,339.3 19811205,339.2 19811212,339.4 19811219,339.6 19811226,340.2 19820102,340.2 19820109,340.3 19820116,340.7 19820123,341.1 19820130,341.2 19820206,341.9 19820213,341.1 19820220,341.1 19820227,342.1 19820306,342.6 19820313,342.6 19820320,342.7 19820327,342.8 19820403,342.9 19820410,343.3 19820417,343.5 19820424,344.2 19820501,343.8 19820508,343.6 19820515,344.2 19820522,344.1 19820529,344.1 19820605,343.4 19820612,343.5 19820619,343.4 19820626,342.9 19820703,342.5 19820710,342.0 19820717,342.0 19820724,341.8 19820731,341.3 19820807,340.5 19820814,340.0 19820821,339.7 19820828,338.3 19820904,338.8 19820911,338.6 19820918,337.8 19820925,336.9 19821002,337.3 19821009,338.0 19821016,337.6 19821023,337.9 19821030,338.7 19821106,338.4 19821113,339.2 19821120,339.7 19821127,339.8 19821204,339.8 19821211,340.4 19821218,340.7 19821225,340.8 19830101,340.9 19830108,341.4 19830115,341.5 19830122,341.2 19830129,341.7 19830205,342.0 19830212,342.7 19830219,342.5 19830226,342.8 19830305,342.3 19830312,342.5 19830319,344.0 19830326,343.8 19830402,344.0 19830409,344.8 19830416,345.0 19830423,345.3 19830430,345.4 19830507,345.4 19830514,345.7 19830521,345.8 19830528,345.7 19830604,345.6 19830611,345.6 19830618,345.0 19830625,344.9 19830702,344.7 19830709,344.5 19830716,343.7 19830723,343.6 19830730,342.6 19830806,343.0 19830813,341.7 19830820,342.1 19830827,341.8 19830903,339.9 19830910,339.9 19830917,339.8 19830924,339.9 19831001,339.8 19831008,339.7 19831015,340.1 19831022,340.2 19831029,340.3 19831105,340.8 19831112,341.0 19831119,341.1 19831126,341.7 19831203,341.8 19831210,342.8 19831217,343.3 19831224,343.6 19831231,343.4 19840107,343.7 19840114,343.4 19840121,343.5 19840128,344.1 19840204,344.3 19840211,344.5 19840218,344.3 19840225,344.6 19840303,344.8 19840310,344.9 19840317,345.4 19840324,345.6 19840331, 19840407, 19840414, 19840421, 19840428,347.4 19840505,347.4 19840512,347.7 19840519,347.3 19840526,347.0 19840602,347.0 19840609,347.0 19840616,346.8 19840623,346.3 19840630,346.2 19840707,345.8 19840714,345.4 19840721,345.2 19840728,344.4 19840804,344.0 19840811,344.1 19840818,343.1 19840825,342.0 19840901,341.6 19840908,340.6 19840915,341.3 19840922,341.3 19840929,340.8 19841006,341.1 19841013,341.3 19841020,341.9 19841027,341.6 19841103,342.0 19841110,342.6 19841117,343.1 19841124,343.7 19841201,343.6 19841208,343.9 19841215,344.2 19841222,344.5 19841229,344.5 19850105,344.7 19850112,345.0 19850119,345.0 19850126,345.0 19850202,345.9 19850209,345.5 19850216,345.8 19850223,346.3 19850302,346.7 19850309,347.1 19850316,347.5 19850323,347.7 19850330,348.2 19850406,348.0 19850413,348.0 19850420,348.5 19850427,348.8 19850504,348.8 19850511,349.3 19850518,349.1 19850525,348.1 19850601,349.0 19850608,348.4 19850615,348.2 19850622,347.9 19850629,347.4 19850706,346.9 19850713,346.8 19850720,346.4 19850727,345.7 19850803, 19850810,344.7 19850817,344.5 19850824,344.3 19850831,343.7 19850907,344.2 19850914,343.3 19850921,342.4 19850928,342.1 19851005,342.4 19851012,342.5 19851019,343.1 19851026,343.2 19851102,343.3 19851109,343.7 19851116,344.2 19851123,344.6 19851130,345.3 19851207,345.3 19851214,345.6 19851221,345.1 19851228,346.3 19860104,346.4 19860111,346.0 19860118,346.2 19860125,346.4 19860201,346.2 19860208,346.8 19860215,347.1 19860222,347.2 19860301,347.0 19860308,346.6 19860315,347.2 19860322,349.1 19860329,348.8 19860405,349.2 19860412,349.4 19860419,349.3 19860426,350.2 19860503,349.9 19860510,350.1 19860517,350.2 19860524,350.1 19860531,350.1 19860607,349.7 19860614,349.5 19860621,349.4 19860628,348.9 19860705,348.6 19860712,347.7 19860719,347.6 19860726,347.4 19860802,346.6 19860809,346.2 19860816,345.5 19860823,345.6 19860830,345.2 19860906,345.0 19860913,345.3 19860920,344.4 19860927,344.5 19861004,343.9 19861011,344.1 19861018,343.9 19861025,344.5 19861101,345.1 19861108,345.3 19861115,345.6 19861122,345.7 19861129,346.4 19861206,346.9 19861213,346.7 19861220,346.9 19861227,347.0 19870103,347.6 19870110,348.3 19870117,348.2 19870124,347.9 19870131,348.0 19870207,347.9 19870214,348.2 19870221,348.5 19870228,349.4 19870307,348.8 19870314,349.2 19870321,349.7 19870328,350.2 19870404,350.8 19870411,350.2 19870418,351.1 19870425,351.3 19870502,351.4 19870509,352.0 19870516,351.7 19870523,351.9 19870530,351.7 19870606,351.6 19870613,351.1 19870620,351.0 19870627,350.9 19870704,349.7 19870711,349.8 19870718,348.8 19870725,349.5 19870801,349.0 19870808,348.1 19870815,348.6 19870822,348.0 19870829,346.7 19870905,347.0 19870912,346.6 19870919,346.2 19870926,345.8 19871003,345.7 19871010,346.3 19871017,346.5 19871024,346.8 19871031,346.9 19871107,347.3 19871114,347.6 19871121,348.1 19871128,348.7 19871205,348.6 19871212,348.8 19871219,349.1 19871226,349.2 19880102,349.7 19880109,350.2 19880116,350.2 19880123,350.7 19880130,351.2 19880206,351.8 19880213,351.3 19880220,351.5 19880227,352.5 19880305,352.8 19880312,351.8 19880319,351.7 19880326,352.2 19880402,353.1 19880409,353.5 19880416,353.1 19880423,354.0 19880430,354.2 19880507,353.7 19880514,354.3 19880521,354.5 19880528,354.2 19880604,354.1 19880611,354.2 19880618,353.6 19880625,353.1 19880702,353.0 19880709,352.5 19880716,352.6 19880723,351.9 19880730,351.1 19880806,350.9 19880813,350.3 19880820,350.4 19880827,349.6 19880903,349.3 19880910,348.7 19880917,348.9 19880924,348.1 19881001,348.8 19881008,348.8 19881015,348.6 19881022,349.4 19881029,349.2 19881105,349.7 19881112,349.8 19881119,350.1 19881126,350.4 19881203,350.5 19881210,351.0 19881217,351.6 19881224,351.3 19881231,352.4 19890107,352.7 19890114,352.9 19890121,352.5 19890128,353.0 19890204,352.8 19890211,352.6 19890218,353.2 19890225,353.4 19890304,353.1 19890311,353.4 19890318,353.5 19890325,354.4 19890401,354.5 19890408,355.0 19890415,355.4 19890422,356.0 19890429,355.9 19890506,355.3 19890513,355.8 19890520,355.6 19890527,355.7 19890603,355.8 19890610,355.0 19890617,354.8 19890624,354.9 19890701,354.5 19890708,354.7 19890715,353.8 19890722,353.1 19890729,353.2 19890805,352.6 19890812,352.2 19890819,351.1 19890826,350.4 19890902,350.7 19890909,350.2 19890916,349.4 19890923,349.3 19890930,349.7 19891007,349.9 19891014,349.7 19891021,350.2 19891028,350.4 19891104,350.6 19891111,351.2 19891118,351.6 19891125,351.4 19891202,352.0 19891209,352.1 19891216,352.4 19891223,352.5 19891230,353.4 19900106,353.4 19900113,353.5 19900120,353.8 19900127,353.9 19900203,354.1 19900210,355.0 19900217,354.8 19900224,354.7 19900303,355.7 19900310,354.9 19900317,355.8 19900324,355.1 19900331,355.9 19900407,356.1 19900414,355.9 19900421,356.6 19900428,356.1 19900505,357.3 19900512,357.0 19900519,356.9 19900526,357.1 19900602,357.0 19900609,356.6 19900616,355.6 19900623,355.5 19900630,355.7 19900707,355.5 19900714,354.0 19900721,354.5 19900728,354.7 19900804,353.5 19900811,353.2 19900818,352.9 19900825,352.0 19900901,350.9 19900908,350.7 19900915,351.3 19900922,350.9 19900929,350.9 19901006,351.1 19901013,351.0 19901020,351.4 19901027,351.4 19901103,352.1 19901110,352.6 19901117,353.0 19901124,353.1 19901201,353.6 19901208,354.0 19901215,353.8 19901222,354.5 19901229,354.8 19910105,354.2 19910112,354.7 19910119,354.8 19910126,355.0 19910202,355.2 19910209,355.2 19910216,356.4 19910223,355.8 19910302,356.4 19910309,357.2 19910316,357.6 19910323,356.9 19910330,357.9 19910406,358.3 19910413,357.8 19910420,359.1 19910427,359.2 19910504,359.1 19910511,358.9 19910518,360.0 19910525,359.0 19910601,358.5 19910608,358.4 19910615,358.2 19910622,358.1 19910629,357.7 19910706,357.2 19910713,356.5 19910720,355.2 19910727,355.3 19910803,354.8 19910810,354.6 19910817,353.7 19910824,353.0 19910831,353.2 19910907,353.0 19910914,352.1 19910921,351.8 19910928,351.6 19911005,351.7 19911012,352.1 19911019,352.5 19911026,352.7 19911102,353.4 19911109,353.7 19911116,353.5 19911123,353.8 19911130,354.3 19911207,354.5 19911214,354.9 19911221,355.2 19911228,355.5 19920104,355.6 19920111,356.0 19920118,356.1 19920125,355.9 19920201,356.0 19920208,356.7 19920215,357.3 19920222,356.9 19920229,356.5 19920307,357.3 19920314,357.8 19920321,358.1 19920328,358.4 19920404,358.5 19920411,358.9 19920418,359.7 19920425,359.2 19920502,359.6 19920509,359.7 19920516,358.6 19920523,359.6 19920530,360.2 19920606,360.0 19920613,359.4 19920620,358.7 19920627,358.4 19920704,358.4 19920711,357.2 19920718,356.3 19920725,356.1 19920801,354.9 19920808,355.3 19920815,355.3 19920822,354.5 19920829,354.3 19920905,353.5 19920912,353.6 19920919,352.3 19920926,352.7 19921003,353.6 19921010,353.3 19921017,353.2 19921024,353.5 19921031,353.5 19921107,353.9 19921114,353.8 19921121,354.5 19921128,354.6 19921205,354.8 19921212,355.3 19921219,355.4 19921226,355.9 19930102,356.2 19930109,356.9 19930116,356.7 19930123,356.6 19930130,357.0 19930206,356.6 19930213,357.2 19930220,357.3 19930227,357.6 19930306,358.3 19930313,358.5 19930320,358.1 19930327,358.8 19930403,359.1 19930410,358.8 19930417,359.4 19930424,360.0 19930501,359.6 19930508,359.7 19930515,360.7 19930522,360.6 19930529,360.3 19930605,359.7 19930612,359.9 19930619,359.3 19930626,359.1 19930703,357.9 19930710,358.0 19930717,358.1 19930724,356.6 19930731,356.5 19930807,355.8 19930814,355.9 19930821,354.9 19930828,354.7 19930904,354.3 19930911,353.2 19930918,353.8 19930925,353.8 19931002,353.8 19931009,353.8 19931016,354.0 19931023,354.4 19931030,354.3 19931106,354.7 19931113,355.1 19931120,355.6 19931127,356.0 19931204,356.2 19931211,356.5 19931218,356.9 19931225,357.5 19940101,358.1 19940108,358.1 19940115,358.4 19940122,358.3 19940129,358.7 19940205,358.4 19940212,358.6 19940219,359.0 19940226,359.6 19940305,358.7 19940312,359.8 19940319,360.4 19940326,360.8 19940402,360.6 19940409,361.0 19940416,361.0 19940423,361.3 19940430,362.2 19940507,361.6 19940514,361.4 19940521,361.7 19940528,361.9 19940604,361.0 19940611,361.0 19940618,360.9 19940625,360.7 19940702,360.2 19940709,359.9 19940716,359.4 19940723,359.0 19940730,358.8 19940806,358.1 19940813,357.5 19940820,357.6 19940827,356.3 19940903,356.4 19940910,356.4 19940917,355.4 19940924,355.5 19941001,355.4 19941008,355.8 19941015,356.0 19941022,356.3 19941029,356.6 19941105,356.9 19941112,357.4 19941119,357.9 19941126,358.1 19941203,358.4 19941210,359.1 19941217,359.2 19941224,359.1 19941231,359.5 19950107,359.6 19950114,360.2 19950121,360.1 19950128,360.0 19950204,360.6 19950211,361.0 19950218,360.8 19950225,361.3 19950304,362.2 19950311,361.2 19950318,360.9 19950325,362.0 19950401,363.8 19950408,363.4 19950415,363.3 19950422,362.8 19950429,363.5 19950506,363.2 19950513,364.1 19950520,364.1 19950527,363.4 19950603,363.9 19950610,363.4 19950617,362.9 19950624,362.8 19950701,362.5 19950708,362.2 19950715,361.9 19950722,361.5 19950729,360.9 19950805,360.4 19950812,359.2 19950819,358.7 19950826,359.2 19950902,357.3 19950909,358.5 19950916,358.5 19950923,358.2 19950930,357.5 19951007,357.6 19951014,357.6 19951021,358.0 19951028,358.2 19951104,359.1 19951111,359.4 19951118,359.6 19951125,359.8 19951202,360.1 19951209,360.4 19951216,360.5 19951223,360.8 19951230,361.7 19960106,361.8 19960113,362.0 19960120,362.1 19960127,362.2 19960203,362.6 19960210,363.1 19960217,363.0 19960224,364.0 19960302,363.8 19960309,363.6 19960316,364.1 19960323,364.5 19960330,364.3 19960406,364.5 19960413,364.8 19960420,364.4 19960427,365.1 19960504,364.9 19960511,365.3 19960518,365.7 19960525,365.4 19960601,364.8 19960608,365.1 19960615,365.2 19960622,365.0 19960629,364.3 19960706,364.1 19960713,363.7 19960720,363.3 19960727,362.8 19960803,361.7 19960810,362.1 19960817,361.2 19960824,360.8 19960831,360.8 19960907,359.8 19960914,359.8 19960921,359.0 19960928,359.0 19961005,359.4 19961012,359.5 19961019,359.8 19961026,359.8 19961102,359.9 19961109,360.5 19961116,360.7 19961123,361.2 19961130,361.4 19961207,361.9 19961214,362.6 19961221,362.4 19961228,362.6 19970104,362.9 19970111,363.0 19970118,363.1 19970125,363.5 19970201,363.2 19970208,364.1 19970215,364.0 19970222,364.2 19970301,364.5 19970308,364.1 19970315,364.1 19970322,364.7 19970329,365.4 19970405,365.8 19970412,366.2 19970419,366.6 19970426,366.7 19970503,366.7 19970510,366.8 19970517,367.0 19970524,366.6 19970531,366.3 19970607,365.7 19970614,365.6 19970621,365.5 19970628,365.1 19970705,365.0 19970712,364.6 19970719,364.1 19970726,363.8 19970802,363.3 19970809,363.3 19970816,362.6 19970823,361.5 19970830,361.6 19970906,360.6 19970913,360.2 19970920,360.0 19970927,359.8 19971004,360.5 19971011,360.4 19971018,361.0 19971025,361.1 19971101,361.7 19971108,362.1 19971115,362.0 19971122,362.6 19971129,363.5 19971206,363.9 19971213,363.9 19971220,364.2 19971227,365.0 19980103,365.2 19980110,365.3 19980117,365.3 19980124,365.3 19980131,365.6 19980207,366.0 19980214,365.5 19980221,366.0 19980228,367.3 19980307,367.0 19980314,366.6 19980321,367.4 19980328,368.5 19980404,368.6 19980411,368.6 19980418,368.0 19980425,368.9 19980502,369.1 19980509,368.8 19980516,368.5 19980523,369.6 19980530,369.7 19980606,369.4 19980613,368.8 19980620,368.5 19980627,368.3 19980704,368.0 19980711,367.5 19980718,367.6 19980725,367.3 19980801,366.8 19980808,366.4 19980815,365.6 19980822,365.6 19980829,364.2 19980905,364.7 19980912,363.9 19980919,363.5 19980926,363.6 19981003,364.0 19981010,364.1 19981017,364.4 19981024,364.4 19981031,364.7 19981107,365.0 19981114,365.4 19981121,365.8 19981128,366.0 19981205,366.4 19981212,366.7 19981219,367.3 19981226,367.3 19990102,367.5 19990109,367.8 19990116,367.8 19990123,368.3 19990130,369.2 19990206,369.1 19990213,368.8 19990220,369.0 19990227,368.5 19990306,368.1 19990313,369.5 19990320,370.2 19990327,370.6 19990403,371.1 19990410,371.5 19990417,371.0 19990424,370.3 19990501,370.8 19990508,371.3 19990515,371.0 19990522,370.8 19990529,370.3 19990605,370.9 19990612,370.3 19990619,369.9 19990626,369.9 19990703,369.4 19990710,370.1 19990717,369.5 19990724,368.6 19990731,367.4 19990807,367.6 19990814,366.7 19990821,366.4 19990828,366.1 19990904,364.1 19990911,364.7 19990918,365.2 19990925,364.7 19991002,364.5 19991009,365.0 19991016,364.9 19991023,365.6 19991030,365.7 19991106,366.2 19991113,366.7 19991120,366.6 19991127,367.1 19991204,367.4 19991211,368.0 19991218,368.0 19991225,368.2 20000101,368.6 20000108,368.5 20000115,369.0 20000122,369.8 20000129,369.2 20000205,369.1 20000212,369.6 20000219,369.3 20000226,369.5 20000304,370.0 20000311,370.0 20000318,370.9 20000325,370.7 20000401,370.9 20000408,371.7 20000415,371.8 20000422,372.0 20000429,371.3 20000506,371.2 20000513,371.7 20000520,371.9 20000527,371.8 20000603,371.9 20000610,371.6 20000617,371.7 20000624,371.3 20000701,370.8 20000708,370.0 20000715,370.2 20000722,369.7 20000729,369.0 20000805,368.7 20000812,368.3 20000819,367.7 20000826,367.1 20000902,367.2 20000909,366.7 20000916,366.2 20000923,366.2 20000930,366.4 20001007,366.3 20001014,366.6 20001021,366.7 20001028,367.3 20001104,367.6 20001111,368.0 20001118,368.6 20001125,368.3 20001202,369.0 20001209,369.6 20001216,369.3 20001223,369.5 20001230,369.8 20010106,369.8 20010113,370.2 20010120,369.9 20010127,370.8 20010203,371.3 20010210,371.1 20010217,371.7 20010224,371.2 20010303,372.2 20010310,372.2 20010317,372.1 20010324,371.8 20010331,372.0 20010407,372.7 20010414,372.7 20010421,373.0 20010428,372.7 20010505,373.7 20010512,373.9 20010519,373.7 20010526,373.9 20010602,373.8 20010609,373.1 20010616,372.8 20010623,372.9 20010630,372.7 20010707,372.1 20010714,371.3 20010721,371.2 20010728,370.6 20010804,369.9 20010811,369.5 20010818,369.3 20010825,369.0 20010901,368.4 20010908,368.2 20010915,368.0 20010922,367.4 20010929,367.4 20011006,367.8 20011013,367.6 20011020,368.1 20011027,368.7 20011103,368.7 20011110,368.8 20011117,369.7 20011124,370.3 20011201,370.3 20011208,370.8 20011215,371.2 20011222,371.3 20011229,371.5 statsmodels-0.12.2/statsmodels/datasets/co2/data.py000066400000000000000000000050741400612667500222730ustar00rootroot00000000000000"""Mauna Loa Weekly Atmospheric CO2 Data""" import pandas as pd from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This is public domain.""" TITLE = """Mauna Loa Weekly Atmospheric CO2 Data""" SOURCE = """ Data obtained from http://cdiac.ornl.gov/trends/co2/sio-keel-flask/sio-keel-flaskmlo_c.html Obtained on 3/15/2014. Citation: Keeling, C.D. and T.P. Whorf. 2004. Atmospheric CO2 concentrations derived from flask air samples at sites in the SIO network. In Trends: A Compendium of Data on Global Change. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tennessee, U.S.A. """ DESCRSHORT = """Atmospheric CO2 from Continuous Air Samples at Mauna Loa Observatory, Hawaii, U.S.A.""" DESCRLONG = """ Atmospheric CO2 from Continuous Air Samples at Mauna Loa Observatory, Hawaii, U.S.A. Period of Record: March 1958 - December 2001 Methods: An Applied Physics Corporation (APC) nondispersive infrared gas analyzer was used to obtain atmospheric CO2 concentrations, based on continuous data (four measurements per hour) from atop intake lines on several towers. Steady data periods of not less than six hours per day are required; if no such six-hour periods are available on any given day, then no data are used that day. Weekly averages were calculated for most weeks throughout the approximately 44 years of record. The continuous data for year 2000 is compared with flask data from the same site in the graphics section.""" #suggested notes NOTE = """:: Number of observations: 2225 Number of variables: 2 Variable name definitions: date - sample date in YYMMDD format co2 - CO2 Concentration ppmv The data returned by load_pandas contains the dates as the index. """ def load_pandas(): data = _get_data() index = pd.date_range(start=str(data['date'][0]), periods=len(data), freq='W-SAT') dataset = data[['co2']] dataset.index = index return du.Dataset(data=dataset, names=list(data.columns)) def load(as_pandas=None): """ Load the data and return a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas, retain_index=True) def _get_data(): return du.load_csv(__file__, 'co2.csv') statsmodels-0.12.2/statsmodels/datasets/co2/src/000077500000000000000000000000001400612667500215715ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/co2/src/maunaloa_c.dat000066400000000000000000002501761400612667500243750ustar00rootroot00000000000000******************************************************************* *** Weekly averages derived from continuous air samples *** *** for the Mauna Loa Observatory, Hawaii, U.S.A. *** *** *** *** *** *** September 2004 *** *** *** *** Source: Carbon Dioxide Research Group *** *** Scripps Institution of Oceanography *** *** University of California, San Diego *** *** La Jolla, California, USA 92023-0444 *** ******************************************************************* These weekly averages are ultimately based on measurements of 4 air samples per hour taken atop intake lines on several towers during steady periods of CO2 concentration of not less than 6 hours per day; if no such periods are available on a given day, then no data are used for that day. The "Weight" column gives the number of days used in each weekly average. Flag codes are explained in the NDP writeup, available electronically from the home page of this data set. CO2 concentrations are in terms of the 1999 calibration scale (Keeling et al., 2002) available electronically from the references in the NDP writeup which can be accessed from the home page of this data set. Station Sample Weight Flag CO2 concentration code date code (ppmv) MLO 580329 4 0 316.10 MLO 580405 6 0 317.30 MLO 580412 4 0 317.60 MLO 580419 6 0 317.50 MLO 580426 2 0 316.40 MLO 580503 6 0 316.90 MLO 580517 1 0 317.50 MLO 580524 5 0 317.90 MLO 580705 2 0 315.80 MLO 580712 4 0 315.80 MLO 580719 4 0 315.40 MLO 580726 7 0 315.50 MLO 580802 3 0 315.60 MLO 580809 4 0 315.10 MLO 580816 3 0 315.00 MLO 580830 5 0 314.10 MLO 580906 1 0 313.50 MLO 581108 4 0 313.00 MLO 581115 7 0 313.20 MLO 581122 5 0 313.50 MLO 581129 7 0 314.00 MLO 581206 6 0 314.50 MLO 581213 7 0 314.40 MLO 581220 4 0 314.70 MLO 581227 2 0 315.20 MLO 590103 3 0 315.20 MLO 590110 7 0 315.50 MLO 590117 7 0 315.60 MLO 590124 5 0 315.80 MLO 590131 2 0 315.40 MLO 590214 1 0 316.90 MLO 590221 7 0 316.60 MLO 590228 3 0 316.60 MLO 590307 7 0 316.80 MLO 590321 4 0 316.70 MLO 590328 6 0 316.70 MLO 590404 7 0 317.70 MLO 590411 7 0 317.10 MLO 590418 6 0 317.60 MLO 590425 5 0 318.30 MLO 590502 3 0 318.20 MLO 590509 1 0 318.70 MLO 590516 7 0 318.00 MLO 590523 5 0 318.40 MLO 590606 7 0 318.50 MLO 590613 5 0 318.10 MLO 590620 5 0 317.80 MLO 590627 2 0 317.70 MLO 590704 7 0 316.80 MLO 590711 7 0 316.80 MLO 590718 5 0 316.40 MLO 590725 4 0 316.10 MLO 590801 7 0 315.60 MLO 590808 3 0 314.90 MLO 590822 1 0 315.00 MLO 590829 4 0 314.10 MLO 590905 5 0 314.40 MLO 590912 3 0 313.90 MLO 590919 5 0 313.50 MLO 590926 4 0 313.50 MLO 591003 6 0 313.00 MLO 591010 3 0 313.10 MLO 591017 7 0 313.40 MLO 591024 7 0 313.40 MLO 591031 7 0 314.10 MLO 591107 2 0 314.40 MLO 591114 5 0 314.80 MLO 591121 6 0 315.20 MLO 591128 5 0 315.10 MLO 591205 4 0 315.00 MLO 591212 5 0 315.60 MLO 591219 6 0 315.80 MLO 591226 6 0 315.70 MLO 600102 4 0 315.70 MLO 600109 5 0 316.40 MLO 600116 6 0 316.70 MLO 600123 5 0 316.50 MLO 600130 6 0 316.60 MLO 600206 2 0 316.60 MLO 600213 6 0 316.90 MLO 600220 4 0 317.40 MLO 600227 5 0 317.00 MLO 600305 7 0 316.90 MLO 600312 7 0 317.70 MLO 600319 4 0 318.00 MLO 600326 6 0 317.70 MLO 600402 5 0 318.60 MLO 600409 3 0 319.30 MLO 600416 7 0 319.00 MLO 600423 7 0 319.00 MLO 600430 1 0 319.70 MLO 600507 6 0 319.90 MLO 600514 5 0 319.80 MLO 600521 6 0 320.00 MLO 600528 7 0 320.00 MLO 600604 3 0 319.40 MLO 600611 5 0 320.00 MLO 600618 3 0 319.40 MLO 600625 2 0 319.00 MLO 600702 5 0 318.10 MLO 600709 4 0 318.60 MLO 600716 5 0 318.40 MLO 600723 6 0 317.90 MLO 600730 5 0 317.30 MLO 600806 3 0 316.60 MLO 600813 6 0 316.70 MLO 600820 5 0 315.10 MLO 600827 5 0 314.70 MLO 600903 7 0 314.70 MLO 600910 7 0 314.50 MLO 600917 6 0 314.20 MLO 600924 5 0 313.30 MLO 601001 2 0 313.60 MLO 601008 4 0 313.30 MLO 601015 5 0 313.90 MLO 601022 6 0 314.20 MLO 601029 3 0 314.20 MLO 601105 7 0 314.50 MLO 601112 6 0 315.10 MLO 601119 7 0 315.10 MLO 601126 7 0 315.40 MLO 601203 5 0 315.80 MLO 601210 7 0 316.00 MLO 601217 7 0 316.20 MLO 601224 5 0 316.40 MLO 601231 7 0 316.60 MLO 610107 6 0 316.70 MLO 610114 7 0 317.00 MLO 610121 7 0 317.00 MLO 610128 7 0 317.00 MLO 610204 6 0 317.00 MLO 610211 6 0 317.70 MLO 610218 7 0 317.90 MLO 610225 7 0 318.00 MLO 610304 5 0 318.00 MLO 610311 4 0 318.50 MLO 610318 6 0 318.90 MLO 610325 7 0 318.70 MLO 610401 7 0 319.40 MLO 610408 6 0 319.50 MLO 610415 7 0 318.90 MLO 610422 6 0 319.70 MLO 610429 6 0 319.60 MLO 610506 7 0 320.60 MLO 610513 3 0 320.40 MLO 610520 6 0 320.60 MLO 610527 7 0 320.30 MLO 610603 6 0 320.00 MLO 610610 5 0 320.00 MLO 610617 7 0 319.60 MLO 610624 6 0 319.40 MLO 610701 5 0 319.20 MLO 610708 6 0 319.00 MLO 610715 5 0 318.40 MLO 610722 1 0 317.10 MLO 610729 3 0 317.90 MLO 610805 7 0 317.90 MLO 610812 2 0 317.30 MLO 610819 5 0 316.70 MLO 610826 6 0 315.20 MLO 610902 5 0 315.20 MLO 610909 5 0 314.90 MLO 610916 5 0 314.50 MLO 610923 4 0 315.00 MLO 610930 4 0 315.60 MLO 611007 5 0 314.90 MLO 611014 7 0 315.40 MLO 611021 7 0 315.40 MLO 611028 6 0 315.70 MLO 611104 6 0 315.80 MLO 611111 5 0 315.70 MLO 611118 7 0 316.20 MLO 611125 6 0 316.50 MLO 611202 5 0 316.50 MLO 611209 5 0 317.00 MLO 611216 6 0 316.90 MLO 611223 3 0 317.10 MLO 611230 7 0 317.40 MLO 620106 5 0 317.90 MLO 620113 7 0 318.10 MLO 620120 5 0 318.00 MLO 620127 7 0 317.70 MLO 620203 7 0 318.00 MLO 620210 4 0 318.30 MLO 620217 4 0 318.90 MLO 620224 1 0 319.30 MLO 620303 6 0 319.20 MLO 620310 6 0 319.40 MLO 620317 7 0 319.90 MLO 620324 4 0 319.70 MLO 620331 5 0 320.20 MLO 620407 3 0 320.20 MLO 620414 6 0 321.00 MLO 620421 2 0 320.70 MLO 620428 5 0 320.30 MLO 620505 4 0 320.80 MLO 620512 5 0 320.70 MLO 620519 5 0 321.00 MLO 620526 5 0 321.10 MLO 620602 6 0 320.90 MLO 620609 5 0 320.80 MLO 620616 6 0 320.50 MLO 620623 6 0 320.10 MLO 620630 7 0 320.20 MLO 620707 6 0 320.10 MLO 620714 3 0 319.90 MLO 620721 2 0 319.00 MLO 620728 7 0 318.70 MLO 620804 3 0 318.60 MLO 620811 6 0 317.20 MLO 620818 3 0 317.40 MLO 620915 5 0 316.60 MLO 620922 4 0 315.70 MLO 620929 7 0 315.90 MLO 621006 5 0 315.10 MLO 621013 4 0 315.40 MLO 621020 5 0 315.70 MLO 621027 5 0 315.70 MLO 621103 5 0 315.90 MLO 621110 6 0 316.40 MLO 621117 7 0 316.90 MLO 621124 7 0 317.00 MLO 621201 7 0 317.10 MLO 621208 5 0 317.30 MLO 621215 7 0 317.60 MLO 621222 4 0 318.10 MLO 630105 5 0 318.50 MLO 630112 7 0 318.70 MLO 630119 7 0 318.90 MLO 630126 7 0 318.80 MLO 630202 7 0 318.70 MLO 630209 7 0 318.90 MLO 630223 2 0 319.30 MLO 630302 5 0 319.30 MLO 630309 6 0 319.70 MLO 630316 5 0 319.80 MLO 630323 7 0 320.30 MLO 630330 5 0 320.20 MLO 630406 3 0 320.30 MLO 630413 6 0 320.90 MLO 630420 6 0 322.00 MLO 630427 6 0 321.90 MLO 630511 3 0 321.90 MLO 630518 5 0 322.20 MLO 630525 6 0 322.20 MLO 630601 3 0 322.30 MLO 630608 2 0 322.00 MLO 630615 6 0 321.80 MLO 630622 4 0 320.80 MLO 630629 7 0 320.40 MLO 630706 7 0 320.10 MLO 630713 5 0 319.80 MLO 630720 7 0 319.50 MLO 630727 6 0 319.00 MLO 630803 3 0 318.60 MLO 630810 7 0 318.20 MLO 630817 3 0 317.70 MLO 630824 7 0 317.10 MLO 630831 3 0 316.40 MLO 630907 7 0 316.80 MLO 630914 7 0 315.90 MLO 630921 5 0 316.00 MLO 630928 4 0 315.90 MLO 631005 3 0 316.20 MLO 631012 7 0 315.60 MLO 631019 6 0 316.10 MLO 631026 7 0 316.30 MLO 631102 4 0 316.60 MLO 631109 6 0 316.80 MLO 631116 1 0 317.10 MLO 631130 5 0 317.50 MLO 631207 6 0 318.00 MLO 631214 4 0 318.20 MLO 631221 7 0 318.50 MLO 631228 7 0 318.70 MLO 640104 6 0 319.00 MLO 640111 6 0 319.40 MLO 640118 6 0 319.80 MLO 640530 2 0 322.00 MLO 640606 4 0 322.00 MLO 640627 3 0 321.50 MLO 640704 4 0 321.10 MLO 640711 2 0 319.90 MLO 640718 7 0 320.20 MLO 640725 5 0 320.00 MLO 640801 2 0 319.10 MLO 640815 4 0 318.60 MLO 640822 6 0 318.20 MLO 640829 5 0 318.10 MLO 640905 5 0 317.40 MLO 640912 4 0 316.50 MLO 640919 2 0 315.50 MLO 640926 2 0 317.00 MLO 641003 4 0 316.90 MLO 641010 7 0 316.50 MLO 641017 7 0 316.80 MLO 641024 2 0 317.00 MLO 641031 6 0 317.60 MLO 641107 7 0 317.70 MLO 641114 7 0 317.60 MLO 641121 6 0 317.50 MLO 641128 6 0 318.10 MLO 641205 6 0 318.40 MLO 641212 7 0 318.50 MLO 641219 7 0 318.90 MLO 641226 6 0 318.90 MLO 650102 5 0 319.00 MLO 650109 7 0 319.10 MLO 650116 7 0 319.10 MLO 650123 4 0 319.70 MLO 650130 7 0 320.10 MLO 650206 7 0 320.20 MLO 650213 7 0 320.10 MLO 650220 7 0 320.70 MLO 650227 6 0 320.80 MLO 650306 5 0 321.00 MLO 650313 7 0 320.90 MLO 650320 7 0 320.40 MLO 650327 7 0 321.40 MLO 650403 7 0 321.90 MLO 650410 4 0 322.20 MLO 650417 7 0 322.10 MLO 650424 5 0 321.80 MLO 650501 7 0 322.40 MLO 650508 6 0 322.20 MLO 650515 7 0 321.90 MLO 650522 7 0 321.60 MLO 650529 5 0 322.20 MLO 650605 7 0 321.80 MLO 650612 7 0 321.70 MLO 650619 7 0 321.70 MLO 650626 6 0 321.90 MLO 650703 7 0 321.90 MLO 650710 6 0 321.80 MLO 650717 3 0 321.70 MLO 650724 6 0 320.40 MLO 650731 5 0 319.40 MLO 650807 7 0 319.40 MLO 650814 5 0 318.00 MLO 650821 6 0 318.80 MLO 650828 3 0 318.70 MLO 650904 7 0 318.30 MLO 650911 4 0 318.00 MLO 650918 6 0 318.20 MLO 650925 6 0 316.80 MLO 651002 6 0 316.60 MLO 651009 7 0 317.20 MLO 651016 7 0 317.80 MLO 651023 7 0 317.50 MLO 651030 7 0 317.60 MLO 651106 7 0 318.30 MLO 651113 7 0 319.20 MLO 651120 7 0 318.90 MLO 651127 7 0 319.10 MLO 651204 7 0 319.00 MLO 651211 5 0 319.30 MLO 651218 6 0 319.30 MLO 651225 6 0 319.70 MLO 660101 7 0 319.60 MLO 660108 7 0 320.40 MLO 660115 7 0 320.60 MLO 660122 7 0 321.00 MLO 660129 7 0 321.10 MLO 660205 7 0 321.20 MLO 660212 6 0 321.70 MLO 660219 7 0 321.60 MLO 660226 7 0 321.80 MLO 660305 4 0 322.10 MLO 660312 5 0 322.10 MLO 660319 6 0 322.50 MLO 660326 5 0 322.80 MLO 660402 7 0 323.50 MLO 660409 3 0 323.60 MLO 660416 7 0 323.80 MLO 660423 4 0 323.90 MLO 660430 6 0 323.50 MLO 660507 6 0 324.00 MLO 660514 7 0 324.10 MLO 660521 7 0 323.70 MLO 660528 7 0 324.30 MLO 660604 7 0 324.00 MLO 660611 7 0 323.80 MLO 660618 7 0 323.70 MLO 660625 6 0 323.30 MLO 660702 5 0 322.80 MLO 660709 6 0 322.90 MLO 660806 4 0 321.30 MLO 660813 3 0 320.80 MLO 660820 3 0 319.10 MLO 660827 7 0 319.60 MLO 660903 4 0 319.90 MLO 660910 3 0 318.20 MLO 660917 7 0 318.40 MLO 660924 5 0 318.30 MLO 661001 6 0 317.90 MLO 661008 7 0 317.90 MLO 661015 4 0 318.20 MLO 661022 4 0 318.60 MLO 661029 6 0 318.30 MLO 661112 4 0 319.50 MLO 661119 5 0 320.00 MLO 661126 6 0 320.20 MLO 661203 3 0 320.80 MLO 661210 7 0 320.80 MLO 661217 5 0 321.10 MLO 661224 4 0 321.30 MLO 661231 7 0 321.30 MLO 670107 6 0 321.90 MLO 670114 2 0 322.90 MLO 670204 5 0 322.10 MLO 670211 5 0 322.20 MLO 670218 6 0 322.80 MLO 670225 4 0 322.60 MLO 670304 6 0 322.90 MLO 670311 6 0 322.60 MLO 670318 4 0 323.30 MLO 670325 2 0 323.20 MLO 670401 3 0 323.10 MLO 670408 7 0 324.20 MLO 670415 5 0 324.40 MLO 670422 3 0 324.60 MLO 670429 6 0 325.10 MLO 670506 1 0 325.20 MLO 670513 5 0 324.70 MLO 670520 5 0 325.00 MLO 670527 5 0 324.90 MLO 670603 4 0 324.90 MLO 670610 6 0 324.60 MLO 670617 4 0 323.30 MLO 670624 6 0 323.50 MLO 670701 6 0 322.80 MLO 670708 7 0 322.80 MLO 670715 5 0 322.40 MLO 670722 5 0 322.40 MLO 670729 6 0 322.00 MLO 670805 7 0 321.60 MLO 670812 5 0 321.40 MLO 670819 5 0 320.40 MLO 670826 5 0 320.00 MLO 670902 4 0 320.00 MLO 670909 6 0 319.40 MLO 670916 7 0 319.30 MLO 670923 7 0 319.00 MLO 670930 7 0 318.80 MLO 671007 7 0 318.80 MLO 671014 6 0 319.80 MLO 671021 7 0 319.40 MLO 671028 7 0 319.80 MLO 671104 7 0 320.00 MLO 671111 7 0 320.30 MLO 671118 7 0 320.90 MLO 671125 7 0 321.50 MLO 671202 7 0 321.40 MLO 671209 7 0 321.80 MLO 671216 7 0 322.20 MLO 671223 7 0 321.90 MLO 671230 7 0 322.30 MLO 680106 7 0 322.40 MLO 680113 7 0 322.50 MLO 680120 6 0 322.50 MLO 680127 7 0 322.80 MLO 680203 7 0 322.60 MLO 680210 7 0 323.10 MLO 680217 7 0 323.40 MLO 680224 7 0 323.10 MLO 680302 6 0 323.10 MLO 680309 4 0 323.80 MLO 680316 6 0 323.80 MLO 680323 6 0 324.20 MLO 680330 5 0 324.70 MLO 680406 7 0 324.70 MLO 680413 6 0 325.00 MLO 680420 5 0 324.80 MLO 680427 7 0 325.40 MLO 680504 7 0 325.60 MLO 680511 7 0 325.00 MLO 680518 6 0 325.50 MLO 680525 7 0 325.80 MLO 680601 5 0 325.60 MLO 680608 7 0 325.70 MLO 680615 4 0 325.50 MLO 680622 4 0 324.90 MLO 680629 5 0 324.60 MLO 680706 6 0 324.70 MLO 680713 7 0 324.10 MLO 680720 7 0 323.90 MLO 680727 7 0 323.40 MLO 680803 5 0 322.40 MLO 680810 5 0 322.20 MLO 680817 3 0 322.00 MLO 680824 6 0 321.70 MLO 680831 6 0 321.40 MLO 680907 7 0 320.40 MLO 680914 7 0 321.10 MLO 680921 7 0 319.70 MLO 680928 7 0 319.80 MLO 681005 7 0 320.50 MLO 681012 6 0 320.50 MLO 681019 7 0 320.20 MLO 681026 7 0 319.90 MLO 681102 5 0 320.70 MLO 681109 7 0 320.80 MLO 681116 7 0 321.40 MLO 681123 7 0 321.70 MLO 681130 6 0 322.00 MLO 681207 4 0 322.40 MLO 681214 7 0 322.90 MLO 681221 5 0 323.30 MLO 681228 6 0 323.10 MLO 690104 6 0 323.30 MLO 690111 6 0 324.00 MLO 690118 6 0 324.30 MLO 690125 7 0 324.10 MLO 690201 7 0 324.10 MLO 690208 5 0 323.90 MLO 690215 5 0 324.30 MLO 690222 5 0 324.80 MLO 690301 7 0 325.10 MLO 690308 7 0 325.50 MLO 690315 7 0 325.70 MLO 690322 6 0 325.90 MLO 690329 7 0 325.80 MLO 690405 7 0 326.20 MLO 690412 7 0 327.10 MLO 690419 6 0 326.50 MLO 690426 6 0 326.50 MLO 690503 7 0 327.50 MLO 690510 7 0 327.80 MLO 690517 6 0 326.80 MLO 690524 7 0 326.90 MLO 690531 5 0 327.40 MLO 690607 6 0 326.50 MLO 690614 4 0 326.70 MLO 690621 5 0 326.70 MLO 690628 7 0 326.30 MLO 690705 6 0 326.10 MLO 690712 7 0 326.00 MLO 690719 6 0 325.70 MLO 690726 4 0 325.40 MLO 690802 5 0 324.50 MLO 690809 7 0 324.50 MLO 690816 7 0 323.10 MLO 690823 5 0 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338.10 MLO 811121 4 0 338.50 MLO 811128 6 0 339.30 MLO 811205 5 0 339.20 MLO 811212 7 0 339.40 MLO 811219 6 0 339.60 MLO 811226 4 0 340.20 MLO 820102 5 0 340.20 MLO 820109 7 0 340.30 MLO 820116 5 0 340.70 MLO 820123 6 0 341.10 MLO 820130 7 0 341.20 MLO 820206 7 0 341.90 MLO 820213 6 0 341.10 MLO 820220 4 0 341.10 MLO 820227 5 0 342.10 MLO 820306 6 0 342.60 MLO 820313 4 0 342.60 MLO 820320 1 0 342.70 MLO 820327 4 0 342.80 MLO 820403 6 0 342.90 MLO 820410 6 0 343.30 MLO 820417 6 0 343.50 MLO 820424 5 0 344.20 MLO 820501 4 0 343.80 MLO 820508 1 0 343.60 MLO 820515 3 0 344.20 MLO 820522 6 0 344.10 MLO 820529 6 0 344.10 MLO 820605 6 0 343.40 MLO 820612 7 0 343.50 MLO 820619 3 0 343.40 MLO 820626 4 0 342.90 MLO 820703 7 0 342.50 MLO 820710 6 0 342.00 MLO 820717 5 0 342.00 MLO 820724 4 0 341.80 MLO 820731 6 0 341.30 MLO 820807 6 0 340.50 MLO 820814 6 0 340.00 MLO 820821 3 0 339.70 MLO 820828 5 0 338.30 MLO 820904 5 0 338.80 MLO 820911 6 0 338.60 MLO 820918 2 0 337.80 MLO 820925 6 0 336.90 MLO 821002 4 0 337.30 MLO 821009 5 0 338.00 MLO 821016 4 0 337.60 MLO 821023 4 0 337.90 MLO 821030 5 0 338.70 MLO 821106 5 0 338.40 MLO 821113 6 0 339.20 MLO 821120 6 0 339.70 MLO 821127 4 0 339.80 MLO 821204 6 0 339.80 MLO 821211 5 0 340.40 MLO 821218 7 0 340.70 MLO 821225 5 0 340.80 MLO 830101 5 0 340.90 MLO 830108 5 0 341.40 MLO 830115 6 0 341.50 MLO 830122 7 0 341.20 MLO 830129 7 0 341.70 MLO 830205 6 0 342.00 MLO 830212 7 0 342.70 MLO 830219 6 0 342.50 MLO 830226 6 0 342.80 MLO 830305 7 0 342.30 MLO 830312 7 0 342.50 MLO 830319 5 0 344.00 MLO 830326 5 0 343.80 MLO 830402 7 0 344.00 MLO 830409 6 0 344.80 MLO 830416 7 0 345.00 MLO 830423 7 0 345.30 MLO 830430 7 0 345.40 MLO 830507 5 0 345.40 MLO 830514 6 0 345.70 MLO 830521 6 0 345.80 MLO 830528 7 0 345.70 MLO 830604 5 0 345.60 MLO 830611 5 0 345.60 MLO 830618 7 0 345.00 MLO 830625 6 0 344.90 MLO 830702 6 0 344.70 MLO 830709 4 0 344.50 MLO 830716 3 0 343.70 MLO 830723 6 0 343.60 MLO 830730 4 0 342.60 MLO 830806 5 0 343.00 MLO 830813 2 0 341.70 MLO 830820 3 0 342.10 MLO 830827 6 0 341.80 MLO 830903 3 0 339.90 MLO 830910 5 0 339.90 MLO 830917 5 0 339.80 MLO 830924 4 0 339.90 MLO 831001 6 0 339.80 MLO 831008 7 0 339.70 MLO 831015 6 0 340.10 MLO 831022 6 0 340.20 MLO 831029 7 0 340.30 MLO 831105 7 0 340.80 MLO 831112 7 0 341.00 MLO 831119 6 0 341.10 MLO 831126 7 0 341.70 MLO 831203 6 0 341.80 MLO 831210 2 0 342.80 MLO 831217 7 0 343.30 MLO 831224 7 0 343.60 MLO 831231 7 0 343.40 MLO 840107 7 0 343.70 MLO 840114 5 0 343.40 MLO 840121 5 0 343.50 MLO 840128 5 0 344.10 MLO 840204 5 0 344.30 MLO 840211 7 0 344.50 MLO 840218 5 0 344.30 MLO 840225 6 0 344.60 MLO 840303 7 0 344.80 MLO 840310 6 0 344.90 MLO 840317 6 0 345.40 MLO 840324 5 0 345.60 MLO 840428 2 0 347.40 MLO 840505 6 0 347.40 MLO 840512 3 0 347.70 MLO 840519 5 0 347.30 MLO 840526 5 0 347.00 MLO 840602 5 0 347.00 MLO 840609 6 0 347.00 MLO 840616 3 0 346.80 MLO 840623 5 0 346.30 MLO 840630 6 0 346.20 MLO 840707 4 0 345.80 MLO 840714 5 0 345.40 MLO 840721 3 0 345.20 MLO 840728 6 0 344.40 MLO 840804 2 0 344.00 MLO 840811 2 0 344.10 MLO 840818 5 0 343.10 MLO 840825 3 0 342.00 MLO 840901 3 0 341.60 MLO 840908 6 0 340.60 MLO 840915 6 0 341.30 MLO 840922 6 0 341.30 MLO 840929 3 0 340.80 MLO 841006 5 0 341.10 MLO 841013 4 0 341.30 MLO 841020 1 0 341.90 MLO 841027 5 0 341.60 MLO 841103 5 0 342.00 MLO 841110 6 0 342.60 MLO 841117 6 0 343.10 MLO 841124 6 0 343.70 MLO 841201 4 0 343.60 MLO 841208 6 0 343.90 MLO 841215 4 0 344.20 MLO 841222 5 0 344.50 MLO 841229 3 0 344.50 MLO 850105 7 0 344.70 MLO 850112 6 0 345.00 MLO 850119 7 0 345.00 MLO 850126 5 0 345.00 MLO 850202 5 0 345.90 MLO 850209 4 0 345.50 MLO 850216 5 0 345.80 MLO 850223 5 0 346.30 MLO 850302 6 0 346.70 MLO 850309 6 0 347.10 MLO 850316 7 0 347.50 MLO 850323 4 0 347.70 MLO 850330 5 0 348.20 MLO 850406 7 0 348.00 MLO 850413 4 0 348.00 MLO 850420 5 0 348.50 MLO 850427 4 0 348.80 MLO 850504 5 0 348.80 MLO 850511 5 0 349.30 MLO 850518 7 0 349.10 MLO 850525 6 0 348.10 MLO 850601 4 0 349.00 MLO 850608 7 0 348.40 MLO 850615 3 0 348.20 MLO 850622 5 0 347.90 MLO 850629 6 0 347.40 MLO 850706 6 0 346.90 MLO 850713 5 0 346.80 MLO 850720 3 0 346.40 MLO 850727 6 0 345.70 MLO 850810 6 0 344.70 MLO 850817 3 0 344.50 MLO 850824 5 0 344.30 MLO 850831 5 0 343.70 MLO 850907 5 0 344.20 MLO 850914 6 0 343.30 MLO 850921 5 0 342.40 MLO 850928 5 0 342.10 MLO 851005 4 0 342.40 MLO 851012 4 0 342.50 MLO 851019 7 0 343.10 MLO 851026 6 0 343.20 MLO 851102 5 0 343.30 MLO 851109 5 0 343.70 MLO 851116 7 0 344.20 MLO 851123 6 0 344.60 MLO 851130 6 0 345.30 MLO 851207 5 0 345.30 MLO 851214 6 0 345.60 MLO 851221 6 0 345.10 MLO 851228 7 0 346.30 MLO 860104 4 0 346.40 MLO 860111 7 0 346.00 MLO 860118 4 0 346.20 MLO 860125 7 0 346.40 MLO 860201 6 0 346.20 MLO 860208 6 0 346.80 MLO 860215 7 0 347.10 MLO 860222 7 0 347.20 MLO 860301 7 0 347.00 MLO 860308 3 0 346.60 MLO 860315 6 0 347.20 MLO 860322 6 0 349.10 MLO 860329 6 0 348.80 MLO 860405 7 0 349.20 MLO 860412 4 0 349.40 MLO 860419 6 0 349.30 MLO 860426 6 0 350.20 MLO 860503 4 0 349.90 MLO 860510 5 0 350.10 MLO 860517 5 0 350.20 MLO 860524 6 0 350.10 MLO 860531 6 0 350.10 MLO 860607 4 0 349.70 MLO 860614 6 0 349.50 MLO 860621 7 0 349.40 MLO 860628 7 0 348.90 MLO 860705 7 0 348.60 MLO 860712 5 0 347.70 MLO 860719 6 0 347.60 MLO 860726 6 0 347.40 MLO 860802 3 0 346.60 MLO 860809 5 0 346.20 MLO 860816 7 0 345.50 MLO 860823 5 0 345.60 MLO 860830 4 0 345.20 MLO 860906 4 0 345.00 MLO 860913 7 0 345.30 MLO 860920 5 0 344.40 MLO 860927 6 0 344.50 MLO 861004 7 0 343.90 MLO 861011 7 0 344.10 MLO 861018 3 0 343.90 MLO 861025 7 0 344.50 MLO 861101 6 0 345.10 MLO 861108 5 0 345.30 MLO 861115 7 0 345.60 MLO 861122 6 0 345.70 MLO 861129 7 0 346.40 MLO 861206 7 0 346.90 MLO 861213 7 0 346.70 MLO 861220 7 0 346.90 MLO 861227 6 0 347.00 MLO 870103 6 0 347.60 MLO 870110 6 0 348.30 MLO 870117 7 0 348.20 MLO 870124 5 0 347.90 MLO 870131 6 0 348.00 MLO 870207 7 0 347.90 MLO 870214 6 0 348.20 MLO 870221 7 0 348.50 MLO 870228 7 0 349.40 MLO 870307 7 0 348.80 MLO 870314 7 0 349.20 MLO 870321 7 0 349.70 MLO 870328 7 0 350.20 MLO 870404 6 0 350.80 MLO 870411 5 0 350.20 MLO 870418 7 0 351.10 MLO 870425 7 0 351.30 MLO 870502 6 0 351.40 MLO 870509 7 0 352.00 MLO 870516 7 0 351.70 MLO 870523 7 0 351.90 MLO 870530 7 0 351.70 MLO 870606 6 0 351.60 MLO 870613 7 0 351.10 MLO 870620 6 0 351.00 MLO 870627 5 0 350.90 MLO 870704 7 0 349.70 MLO 870711 7 0 349.80 MLO 870718 3 0 348.80 MLO 870725 5 0 349.50 MLO 870801 4 0 349.00 MLO 870808 2 0 348.10 MLO 870815 3 0 348.60 MLO 870822 5 0 348.00 MLO 870829 5 0 346.70 MLO 870905 4 0 347.00 MLO 870912 6 0 346.60 MLO 870919 6 0 346.20 MLO 870926 3 0 345.80 MLO 871003 4 0 345.70 MLO 871010 5 0 346.30 MLO 871017 5 0 346.50 MLO 871024 7 0 346.80 MLO 871031 6 0 346.90 MLO 871107 4 0 347.30 MLO 871114 7 0 347.60 MLO 871121 3 0 348.10 MLO 871128 3 0 348.70 MLO 871205 5 0 348.60 MLO 871212 5 0 348.80 MLO 871219 5 0 349.10 MLO 871226 5 0 349.20 MLO 880102 6 0 349.70 MLO 880109 7 0 350.20 MLO 880116 5 0 350.20 MLO 880123 5 0 350.70 MLO 880130 5 0 351.20 MLO 880206 4 0 351.80 MLO 880213 7 0 351.30 MLO 880220 6 0 351.50 MLO 880227 7 0 352.50 MLO 880305 6 0 352.80 MLO 880312 7 0 351.80 MLO 880319 4 0 351.70 MLO 880326 5 0 352.20 MLO 880402 6 0 353.10 MLO 880409 7 0 353.50 MLO 880416 7 0 353.10 MLO 880423 5 0 354.00 MLO 880430 4 0 354.20 MLO 880507 7 0 353.70 MLO 880514 5 0 354.30 MLO 880521 6 0 354.50 MLO 880528 6 0 354.20 MLO 880604 5 0 354.10 MLO 880611 6 0 354.20 MLO 880618 6 0 353.60 MLO 880625 7 0 353.10 MLO 880702 4 0 353.00 MLO 880709 4 0 352.50 MLO 880716 4 0 352.60 MLO 880723 5 0 351.90 MLO 880730 3 0 351.10 MLO 880806 5 0 350.90 MLO 880813 3 0 350.30 MLO 880820 4 0 350.40 MLO 880827 6 0 349.60 MLO 880903 5 0 349.30 MLO 880910 5 0 348.70 MLO 880917 5 0 348.90 MLO 880924 4 0 348.10 MLO 881001 4 0 348.80 MLO 881008 3 0 348.80 MLO 881015 7 0 348.60 MLO 881022 3 0 349.40 MLO 881029 5 0 349.20 MLO 881105 7 0 349.70 MLO 881112 7 0 349.80 MLO 881119 5 0 350.10 MLO 881126 7 0 350.40 MLO 881203 5 0 350.50 MLO 881210 5 0 351.00 MLO 881217 4 0 351.60 MLO 881224 6 0 351.30 MLO 881231 7 0 352.40 MLO 890107 7 0 352.70 MLO 890114 6 0 352.90 MLO 890121 7 0 352.50 MLO 890128 7 0 353.00 MLO 890204 5 0 352.80 MLO 890211 5 0 352.60 MLO 890218 6 0 353.20 MLO 890225 7 0 353.40 MLO 890304 7 0 353.10 MLO 890311 6 0 353.40 MLO 890318 6 0 353.50 MLO 890325 7 0 354.40 MLO 890401 7 0 354.50 MLO 890408 7 0 355.00 MLO 890415 4 0 355.40 MLO 890422 7 0 356.00 MLO 890429 6 0 355.90 MLO 890506 6 0 355.30 MLO 890513 5 0 355.80 MLO 890520 6 0 355.60 MLO 890527 4 0 355.70 MLO 890603 6 0 355.80 MLO 890610 6 0 355.00 MLO 890617 7 0 354.80 MLO 890624 5 0 354.90 MLO 890701 6 0 354.50 MLO 890708 4 0 354.70 MLO 890715 7 0 353.80 MLO 890722 6 0 353.10 MLO 890729 6 0 353.20 MLO 890805 6 0 352.60 MLO 890812 6 0 352.20 MLO 890819 5 0 351.10 MLO 890826 5 0 350.40 MLO 890902 7 0 350.70 MLO 890909 5 0 350.20 MLO 890916 6 0 349.40 MLO 890923 7 0 349.30 MLO 890930 1 0 349.70 MLO 891007 6 0 349.90 MLO 891014 6 0 349.70 MLO 891021 6 0 350.20 MLO 891028 7 0 350.40 MLO 891104 7 0 350.60 MLO 891111 6 0 351.20 MLO 891118 7 0 351.60 MLO 891125 5 0 351.40 MLO 891202 6 0 352.00 MLO 891209 4 0 352.10 MLO 891216 6 0 352.40 MLO 891223 5 0 352.50 MLO 891230 4 0 353.40 MLO 900106 7 0 353.40 MLO 900113 7 0 353.50 MLO 900120 7 0 353.80 MLO 900127 7 0 353.90 MLO 900203 7 0 354.10 MLO 900210 5 0 355.00 MLO 900217 7 0 354.80 MLO 900224 7 0 354.70 MLO 900303 3 0 355.70 MLO 900310 5 0 354.90 MLO 900317 7 0 355.80 MLO 900324 6 0 355.10 MLO 900331 6 0 355.90 MLO 900407 7 0 356.10 MLO 900414 7 0 355.90 MLO 900421 6 0 356.60 MLO 900428 4 0 356.10 MLO 900505 5 0 357.30 MLO 900512 5 0 357.00 MLO 900519 7 0 356.90 MLO 900526 6 0 357.10 MLO 900602 6 0 357.00 MLO 900609 7 0 356.60 MLO 900616 5 0 355.60 MLO 900623 7 0 355.50 MLO 900630 7 0 355.70 MLO 900707 7 0 355.50 MLO 900714 7 0 354.00 MLO 900721 6 0 354.50 MLO 900728 5 0 354.70 MLO 900804 5 0 353.50 MLO 900811 5 0 353.20 MLO 900818 7 0 352.90 MLO 900825 5 0 352.00 MLO 900901 4 0 350.90 MLO 900908 3 0 350.70 MLO 900915 6 0 351.30 MLO 900922 6 0 350.90 MLO 900929 3 0 350.90 MLO 901006 2 0 351.10 MLO 901013 7 0 351.00 MLO 901020 4 0 351.40 MLO 901027 3 0 351.40 MLO 901103 5 0 352.10 MLO 901110 7 0 352.60 MLO 901117 6 0 353.00 MLO 901124 5 0 353.10 MLO 901201 7 0 353.60 MLO 901208 6 0 354.00 MLO 901215 6 0 353.80 MLO 901222 7 0 354.50 MLO 901229 6 0 354.80 MLO 910105 7 0 354.20 MLO 910112 7 0 354.70 MLO 910119 6 0 354.80 MLO 910126 7 0 355.00 MLO 910202 7 0 355.20 MLO 910209 6 0 355.20 MLO 910216 7 0 356.40 MLO 910223 6 0 355.80 MLO 910302 7 0 356.40 MLO 910309 7 0 357.20 MLO 910316 6 0 357.60 MLO 910323 7 0 356.90 MLO 910330 5 0 357.90 MLO 910406 7 0 358.30 MLO 910413 7 0 357.80 MLO 910420 6 0 359.10 MLO 910427 7 0 359.20 MLO 910504 7 0 359.10 MLO 910511 7 0 358.90 MLO 910518 7 0 360.00 MLO 910525 7 0 359.00 MLO 910601 7 0 358.50 MLO 910608 6 0 358.40 MLO 910615 6 0 358.20 MLO 910622 5 0 358.10 MLO 910629 5 0 357.70 MLO 910706 6 0 357.20 MLO 910713 5 0 356.50 MLO 910720 7 0 355.20 MLO 910727 5 0 355.30 MLO 910803 4 0 354.80 MLO 910810 5 0 354.60 MLO 910817 5 0 353.70 MLO 910824 7 0 353.00 MLO 910831 6 0 353.20 MLO 910907 4 0 353.00 MLO 910914 7 0 352.10 MLO 910921 6 0 351.80 MLO 910928 5 0 351.60 MLO 911005 7 0 351.70 MLO 911012 6 0 352.10 MLO 911019 6 0 352.50 MLO 911026 7 0 352.70 MLO 911102 6 0 353.40 MLO 911109 7 0 353.70 MLO 911116 7 0 353.50 MLO 911123 7 0 353.80 MLO 911130 7 0 354.30 MLO 911207 4 0 354.50 MLO 911214 7 0 354.90 MLO 911221 6 0 355.20 MLO 911228 6 0 355.50 MLO 920104 6 0 355.60 MLO 920111 7 0 356.00 MLO 920118 4 0 356.10 MLO 920125 7 0 355.90 MLO 920201 5 0 356.00 MLO 920208 7 0 356.70 MLO 920215 6 0 357.30 MLO 920222 4 0 356.90 MLO 920229 7 0 356.50 MLO 920307 7 0 357.30 MLO 920314 5 0 357.80 MLO 920321 6 0 358.10 MLO 920328 6 0 358.40 MLO 920404 7 0 358.50 MLO 920411 5 0 358.90 MLO 920418 5 0 359.70 MLO 920425 6 0 359.20 MLO 920502 7 0 359.60 MLO 920509 7 0 359.70 MLO 920516 7 0 358.60 MLO 920523 7 0 359.60 MLO 920530 7 0 360.20 MLO 920606 7 0 360.00 MLO 920613 4 0 359.40 MLO 920620 7 0 358.70 MLO 920627 7 0 358.40 MLO 920704 5 0 358.40 MLO 920711 5 0 357.20 MLO 920718 5 0 356.30 MLO 920725 5 0 356.10 MLO 920801 2 0 354.90 MLO 920808 6 0 355.30 MLO 920815 6 0 355.30 MLO 920822 4 0 354.50 MLO 920829 3 0 354.30 MLO 920905 5 0 353.50 MLO 920912 6 0 353.60 MLO 920919 7 0 352.30 MLO 920926 7 0 352.70 MLO 921003 6 0 353.60 MLO 921010 5 0 353.30 MLO 921017 7 0 353.20 MLO 921024 7 0 353.50 MLO 921031 7 0 353.50 MLO 921107 7 0 353.90 MLO 921114 6 0 353.80 MLO 921121 7 0 354.50 MLO 921128 7 0 354.60 MLO 921205 7 0 354.80 MLO 921212 7 0 355.30 MLO 921219 7 0 355.40 MLO 921226 6 0 355.90 MLO 930102 6 0 356.20 MLO 930109 5 0 356.90 MLO 930116 6 0 356.70 MLO 930123 6 0 356.60 MLO 930130 7 0 357.00 MLO 930206 7 0 356.60 MLO 930213 7 0 357.20 MLO 930220 7 0 357.30 MLO 930227 5 0 357.60 MLO 930306 6 0 358.30 MLO 930313 5 0 358.50 MLO 930320 7 0 358.10 MLO 930327 4 0 358.80 MLO 930403 7 0 359.10 MLO 930410 6 0 358.80 MLO 930417 7 0 359.40 MLO 930424 7 0 360.00 MLO 930501 6 0 359.60 MLO 930508 7 0 359.70 MLO 930515 6 0 360.70 MLO 930522 6 0 360.60 MLO 930529 7 0 360.30 MLO 930605 7 0 359.70 MLO 930612 7 0 359.90 MLO 930619 7 0 359.30 MLO 930626 6 0 359.10 MLO 930703 6 0 357.90 MLO 930710 7 0 358.00 MLO 930717 4 0 358.10 MLO 930724 5 0 356.60 MLO 930731 5 0 356.50 MLO 930807 6 0 355.80 MLO 930814 5 0 355.90 MLO 930821 4 0 354.90 MLO 930828 4 0 354.70 MLO 930904 1 0 354.30 MLO 930911 6 0 353.20 MLO 930918 6 0 353.80 MLO 930925 6 0 353.80 MLO 931002 5 0 353.80 MLO 931009 6 0 353.80 MLO 931016 6 0 354.00 MLO 931023 6 0 354.40 MLO 931030 7 0 354.30 MLO 931106 6 0 354.70 MLO 931113 7 0 355.10 MLO 931120 7 0 355.60 MLO 931127 7 0 356.00 MLO 931204 6 0 356.20 MLO 931211 7 0 356.50 MLO 931218 7 0 356.90 MLO 931225 2 0 357.50 MLO 940101 6 0 358.10 MLO 940108 6 0 358.10 MLO 940115 7 0 358.40 MLO 940122 7 0 358.30 MLO 940129 7 0 358.70 MLO 940205 5 0 358.40 MLO 940212 6 0 358.60 MLO 940219 7 0 359.00 MLO 940226 5 0 359.60 MLO 940305 6 0 358.70 MLO 940312 7 0 359.80 MLO 940319 7 0 360.40 MLO 940326 6 0 360.80 MLO 940402 7 0 360.60 MLO 940409 7 0 361.00 MLO 940416 7 0 361.00 MLO 940423 5 0 361.30 MLO 940430 6 0 362.20 MLO 940507 5 0 361.60 MLO 940514 6 0 361.40 MLO 940521 2 0 361.70 MLO 940528 4 0 361.90 MLO 940604 6 0 361.00 MLO 940611 6 0 361.00 MLO 940618 6 0 360.90 MLO 940625 6 0 360.70 MLO 940702 6 0 360.20 MLO 940709 7 0 359.90 MLO 940716 7 0 359.40 MLO 940723 7 0 359.00 MLO 940730 5 0 358.80 MLO 940806 6 0 358.10 MLO 940813 1 0 357.50 MLO 940820 4 0 357.60 MLO 940827 6 0 356.30 MLO 940903 7 0 356.40 MLO 940910 6 0 356.40 MLO 940917 7 0 355.40 MLO 940924 7 0 355.50 MLO 941001 7 0 355.40 MLO 941008 7 0 355.80 MLO 941015 7 0 356.00 MLO 941022 7 0 356.30 MLO 941029 7 0 356.60 MLO 941105 7 0 356.90 MLO 941112 5 0 357.40 MLO 941119 7 0 357.90 MLO 941126 7 0 358.10 MLO 941203 7 0 358.40 MLO 941210 7 0 359.10 MLO 941217 7 0 359.20 MLO 941224 7 0 359.10 MLO 941231 7 0 359.50 MLO 950107 4 0 359.60 MLO 950114 7 0 360.20 MLO 950121 6 0 360.10 MLO 950128 7 0 360.00 MLO 950204 6 0 360.60 MLO 950211 6 0 361.00 MLO 950218 7 0 360.80 MLO 950225 7 0 361.30 MLO 950304 6 0 362.20 MLO 950311 7 0 361.20 MLO 950318 5 0 360.90 MLO 950325 5 0 362.00 MLO 950401 7 0 363.80 MLO 950408 7 0 363.40 MLO 950415 7 0 363.30 MLO 950422 7 0 362.80 MLO 950429 6 0 363.50 MLO 950506 7 0 363.20 MLO 950513 7 0 364.10 MLO 950520 7 0 364.10 MLO 950527 7 0 363.40 MLO 950603 6 0 363.90 MLO 950610 7 0 363.40 MLO 950617 6 0 362.90 MLO 950624 7 0 362.80 MLO 950701 6 0 362.50 MLO 950708 5 0 362.20 MLO 950715 6 0 361.90 MLO 950722 6 0 361.50 MLO 950729 7 0 360.90 MLO 950805 7 0 360.40 MLO 950812 5 0 359.20 MLO 950819 7 0 358.70 MLO 950826 6 0 359.20 MLO 950902 4 0 357.30 MLO 950909 7 0 358.50 MLO 950916 6 0 358.50 MLO 950923 6 0 358.20 MLO 950930 7 0 357.50 MLO 951007 7 0 357.60 MLO 951014 7 0 357.60 MLO 951021 7 0 358.00 MLO 951028 6 0 358.20 MLO 951104 6 0 359.10 MLO 951111 6 0 359.40 MLO 951118 7 0 359.60 MLO 951125 7 0 359.80 MLO 951202 7 0 360.10 MLO 951209 7 0 360.40 MLO 951216 7 0 360.50 MLO 951223 6 0 360.80 MLO 951230 5 0 361.70 MLO 960106 7 0 361.80 MLO 960113 7 0 362.00 MLO 960120 7 0 362.10 MLO 960127 4 0 362.20 MLO 960203 7 0 362.60 MLO 960210 7 0 363.10 MLO 960217 7 0 363.00 MLO 960224 7 0 364.00 MLO 960302 6 0 363.80 MLO 960309 7 0 363.60 MLO 960316 7 0 364.10 MLO 960323 6 0 364.50 MLO 960330 7 0 364.30 MLO 960406 7 0 364.50 MLO 960413 7 0 364.80 MLO 960420 7 0 364.40 MLO 960427 7 0 365.10 MLO 960504 7 0 364.90 MLO 960511 6 0 365.30 MLO 960518 7 0 365.70 MLO 960525 7 0 365.40 MLO 960601 7 0 364.80 MLO 960608 5 0 365.10 MLO 960615 7 0 365.20 MLO 960622 7 0 365.00 MLO 960629 7 0 364.30 MLO 960706 7 0 364.10 MLO 960713 7 0 363.70 MLO 960720 7 0 363.30 MLO 960727 7 0 362.80 MLO 960803 7 0 361.70 MLO 960810 6 0 362.10 MLO 960817 7 0 361.20 MLO 960824 7 0 360.80 MLO 960831 7 0 360.80 MLO 960907 4 0 359.80 MLO 960914 6 0 359.80 MLO 960921 7 0 359.00 MLO 960928 6 0 359.00 MLO 961005 7 0 359.40 MLO 961012 5 0 359.50 MLO 961019 4 0 359.80 MLO 961026 6 0 359.80 MLO 961102 4 0 359.90 MLO 961109 7 0 360.50 MLO 961116 5 0 360.70 MLO 961123 7 0 361.20 MLO 961130 4 0 361.40 MLO 961207 6 0 361.90 MLO 961214 5 0 362.60 MLO 961221 7 0 362.40 MLO 961228 7 0 362.60 MLO 970104 7 0 362.90 MLO 970111 7 0 363.00 MLO 970118 5 0 363.10 MLO 970125 7 0 363.50 MLO 970201 7 0 363.20 MLO 970208 6 0 364.10 MLO 970215 6 0 364.00 MLO 970222 5 0 364.20 MLO 970301 4 0 364.50 MLO 970308 4 0 364.10 MLO 970315 7 0 364.10 MLO 970322 6 0 364.70 MLO 970329 7 0 365.40 MLO 970405 7 0 365.80 MLO 970412 6 0 366.20 MLO 970419 3 0 366.60 MLO 970426 6 0 366.70 MLO 970503 7 0 366.70 MLO 970510 7 0 366.80 MLO 970517 7 0 367.00 MLO 970524 6 0 366.60 MLO 970531 6 0 366.30 MLO 970607 7 0 365.70 MLO 970614 5 0 365.60 MLO 970621 7 0 365.50 MLO 970628 6 0 365.10 MLO 970705 7 0 365.00 MLO 970712 7 0 364.60 MLO 970719 6 0 364.10 MLO 970726 7 0 363.80 MLO 970802 5 0 363.30 MLO 970809 4 0 363.30 MLO 970816 4 0 362.60 MLO 970823 7 0 361.50 MLO 970830 6 0 361.60 MLO 970906 7 0 360.60 MLO 970913 7 0 360.20 MLO 970920 7 0 360.00 MLO 970927 7 0 359.80 MLO 971004 7 0 360.50 MLO 971011 7 0 360.40 MLO 971018 7 0 361.00 MLO 971025 6 0 361.10 MLO 971101 7 0 361.70 MLO 971108 7 0 362.10 MLO 971115 7 0 362.00 MLO 971122 6 0 362.60 MLO 971129 7 0 363.50 MLO 971206 7 0 363.90 MLO 971213 6 0 363.90 MLO 971220 7 0 364.20 MLO 971227 7 0 365.00 MLO 980103 6 0 365.20 MLO 980110 7 0 365.30 MLO 980117 7 0 365.30 MLO 980124 7 0 365.30 MLO 980131 7 0 365.60 MLO 980207 7 0 366.00 MLO 980214 7 0 365.50 MLO 980221 3 0 366.00 MLO 980228 5 0 367.30 MLO 980307 7 0 367.00 MLO 980314 7 0 366.60 MLO 980321 7 0 367.40 MLO 980328 7 0 368.50 MLO 980404 7 0 368.60 MLO 980411 6 0 368.60 MLO 980418 7 0 368.00 MLO 980425 7 0 368.90 MLO 980502 6 0 369.10 MLO 980509 4 0 368.80 MLO 980516 6 0 368.50 MLO 980523 7 0 369.60 MLO 980530 7 0 369.70 MLO 980606 6 0 369.40 MLO 980613 7 0 368.80 MLO 980620 6 0 368.50 MLO 980627 6 0 368.30 MLO 980704 6 0 368.00 MLO 980711 7 0 367.50 MLO 980718 5 0 367.60 MLO 980725 7 0 367.30 MLO 980801 7 0 366.80 MLO 980808 6 0 366.40 MLO 980815 6 0 365.60 MLO 980822 3 0 365.60 MLO 980829 4 0 364.20 MLO 980905 7 0 364.70 MLO 980912 7 0 363.90 MLO 980919 7 0 363.50 MLO 980926 7 0 363.60 MLO 981003 7 0 364.00 MLO 981010 7 0 364.10 MLO 981017 7 0 364.40 MLO 981024 7 0 364.40 MLO 981031 6 0 364.70 MLO 981107 7 0 365.00 MLO 981114 7 0 365.40 MLO 981121 7 0 365.80 MLO 981128 7 0 366.00 MLO 981205 7 0 366.40 MLO 981212 6 0 366.70 MLO 981219 7 0 367.30 MLO 981226 7 0 367.30 MLO 990102 7 0 367.50 MLO 990109 7 0 367.80 MLO 990116 7 0 367.80 MLO 990123 7 0 368.30 MLO 990130 7 0 369.20 MLO 990206 7 0 369.10 MLO 990213 7 0 368.80 MLO 990220 7 0 369.00 MLO 990227 7 0 368.50 MLO 990306 7 0 368.10 MLO 990313 7 0 369.50 MLO 990320 7 0 370.20 MLO 990327 7 0 370.60 MLO 990403 7 0 371.10 MLO 990410 7 0 371.50 MLO 990417 7 0 371.00 MLO 990424 6 0 370.30 MLO 990501 6 0 370.80 MLO 990508 7 0 371.30 MLO 990515 6 0 371.00 MLO 990522 4 0 370.80 MLO 990529 6 0 370.30 MLO 990605 6 0 370.90 MLO 990612 7 0 370.30 MLO 990619 7 0 369.90 MLO 990626 7 0 369.90 MLO 990703 5 0 369.40 MLO 990710 7 0 370.10 MLO 990717 7 0 369.50 MLO 990724 6 0 368.60 MLO 990731 6 0 367.40 MLO 990807 7 0 367.60 MLO 990814 6 0 366.70 MLO 990821 7 0 366.40 MLO 990828 7 0 366.10 MLO 990904 7 0 364.10 MLO 990911 7 0 364.70 MLO 990918 6 0 365.20 MLO 990925 7 0 364.70 MLO 991002 7 0 364.50 MLO 991009 6 0 365.00 MLO 991016 7 0 364.90 MLO 991023 7 0 365.60 MLO 991030 7 0 365.70 MLO 991106 7 0 366.20 MLO 991113 7 0 366.70 MLO 991120 5 0 366.60 MLO 991127 7 0 367.10 MLO 991204 7 0 367.40 MLO 991211 7 0 368.00 MLO 991218 7 0 368.00 MLO 991225 7 0 368.20 MLO 000101 7 0 368.60 MLO 000108 7 0 368.50 MLO 000115 6 0 369.00 MLO 000122 5 0 369.80 MLO 000129 6 0 369.20 MLO 000205 5 0 369.10 MLO 000212 7 0 369.60 MLO 000219 7 0 369.30 MLO 000226 7 0 369.50 MLO 000304 6 0 370.00 MLO 000311 7 0 370.00 MLO 000318 7 0 370.90 MLO 000325 7 0 370.70 MLO 000401 7 0 370.90 MLO 000408 6 0 371.70 MLO 000415 6 0 371.80 MLO 000422 7 0 372.00 MLO 000429 7 0 371.30 MLO 000506 7 0 371.20 MLO 000513 7 0 371.70 MLO 000520 7 0 371.90 MLO 000527 7 0 371.80 MLO 000603 6 0 371.90 MLO 000610 7 0 371.60 MLO 000617 7 0 371.70 MLO 000624 4 0 371.30 MLO 000701 7 0 370.80 MLO 000708 6 0 370.00 MLO 000715 7 0 370.20 MLO 000722 7 0 369.70 MLO 000729 6 0 369.00 MLO 000805 6 0 368.70 MLO 000812 7 0 368.30 MLO 000819 5 0 367.70 MLO 000826 6 0 367.10 MLO 000902 7 0 367.20 MLO 000909 4 0 366.70 MLO 000916 4 0 366.20 MLO 000923 7 0 366.20 MLO 000930 7 0 366.40 MLO 001007 7 0 366.30 MLO 001014 7 0 366.60 MLO 001021 7 0 366.70 MLO 001028 7 0 367.30 MLO 001104 6 0 367.60 MLO 001111 7 0 368.00 MLO 001118 7 0 368.60 MLO 001125 7 0 368.30 MLO 001202 5 0 369.00 MLO 001209 6 0 369.60 MLO 001216 6 0 369.30 MLO 001223 7 0 369.50 MLO 001230 7 0 369.80 MLO 010106 6 0 369.80 MLO 010113 4 0 370.20 MLO 010120 7 0 369.90 MLO 010127 7 0 370.80 MLO 010203 6 0 371.30 MLO 010210 7 0 371.10 MLO 010217 7 0 371.70 MLO 010224 7 0 371.20 MLO 010303 6 0 372.20 MLO 010310 7 0 372.20 MLO 010317 6 0 372.10 MLO 010324 6 0 371.80 MLO 010331 6 0 372.00 MLO 010407 7 0 372.70 MLO 010414 7 0 372.70 MLO 010421 7 0 373.00 MLO 010428 7 0 372.70 MLO 010505 5 0 373.70 MLO 010512 7 0 373.90 MLO 010519 5 0 373.70 MLO 010526 7 0 373.90 MLO 010602 6 0 373.80 MLO 010609 7 0 373.10 MLO 010616 7 0 372.80 MLO 010623 7 0 372.90 MLO 010630 6 0 372.70 MLO 010707 4 0 372.10 MLO 010714 7 0 371.30 MLO 010721 4 0 371.20 MLO 010728 6 0 370.60 MLO 010804 6 0 369.90 MLO 010811 7 0 369.50 MLO 010818 6 0 369.30 MLO 010825 7 0 369.00 MLO 010901 6 0 368.40 MLO 010908 7 0 368.20 MLO 010915 7 0 368.00 MLO 010922 7 0 367.40 MLO 010929 7 0 367.40 MLO 011006 7 0 367.80 MLO 011013 7 0 367.60 MLO 011020 7 0 368.10 MLO 011027 6 0 368.70 MLO 011103 7 0 368.70 MLO 011110 3 0 368.80 MLO 011117 7 0 369.70 MLO 011124 7 0 370.30 MLO 011201 7 0 370.30 MLO 011208 7 0 370.80 MLO 011215 7 0 371.20 MLO 011222 6 0 371.30 MLO 011229 6 0 371.50 statsmodels-0.12.2/statsmodels/datasets/committee/000077500000000000000000000000001400612667500223055ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/committee/R_committee.s000066400000000000000000000006151400612667500247420ustar00rootroot00000000000000### SETUP ### d <- read.table("./committee.csv",sep=",", header=T) attach(d) LNSTAFF <- log(STAFF) SUBS.LNSTAFF <- SUBS*LNSTAFF library(MASS) #m1 <- glm.nb(BILLS104 ~ SIZE + SUBS + LNSTAFF + PRESTIGE + BILLS103 + SUBS.LNSTAFF) m1 <- glm(BILLS104 ~ SIZE + SUBS + LNSTAFF + PRESTIGE + BILLS103 + SUBS.LNSTAFF, family=negative.binomial(1)) # Disp should be 1 by default results <- summary.glm(m1) statsmodels-0.12.2/statsmodels/datasets/committee/__init__.py000066400000000000000000000003261400612667500244170ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/committee/committee.csv000066400000000000000000000013101400612667500250030ustar00rootroot00000000000000"COMMITTEE","BILLS104","SIZE","SUBS","STAFF","PRESTIGE","BILLS103" "Appropriations",6,58,13,109,1,9 "Budget",23,42,0,39,1,101 "Rules",44,13,2,25,1,54 "Ways_and_Means",355,39,5,23,1,542 "Banking",125,51,5,61,0,101 "Economic_Educ_Oppor",131,43,5,69,0,158 "Commerce",271,49,4,79,0,196 "International_Relations",63,44,3,68,0,40 "Government_Reform",149,51,7,99,0,72 "Judiciary",253,35,5,56,0,168 "Agriculture",81,49,5,46,0,60 "National_Security",89,55,7,48,0,75 "Resources",142,44,5,58,0,98 "TransInfrastructure",155,61,6,74,0,69 "Science",27,50,4,58,0,25 "Small_Business",8,43,4,29,0,9 "Veterans_Affairs",28,33,3,36,0,41 "House_Oversight",68,12,0,24,0,233 "Stds_of_Conduct",1,10,0,9,0,0 "Intelligence",4,16,2,24,0,2 statsmodels-0.12.2/statsmodels/datasets/committee/data.py000066400000000000000000000050011400612667500235640ustar00rootroot00000000000000"""First 100 days of the US House of Representatives 1995""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """Used with express permission from the original author, who retains all rights.""" TITLE = __doc__ SOURCE = """ Jeff Gill's `Generalized Linear Models: A Unifited Approach` http://jgill.wustl.edu/research/books.html """ DESCRSHORT = """Number of bill assignments in the 104th House in 1995""" DESCRLONG = """The example in Gill, seeks to explain the number of bill assignments in the first 100 days of the US' 104th House of Representatives. The response variable is the number of bill assignments in the first 100 days over 20 Committees. The explanatory variables in the example are the number of assignments in the first 100 days of the 103rd House, the number of members on the committee, the number of subcommittees, the log of the number of staff assigned to the committee, a dummy variable indicating whether the committee is a high prestige committee, and an interaction term between the number of subcommittees and the log of the staff size. The data returned by load are not cleaned to represent the above example. """ NOTE = """:: Number of Observations - 20 Number of Variables - 6 Variable name definitions:: BILLS104 - Number of bill assignments in the first 100 days of the 104th House of Representatives. SIZE - Number of members on the committee. SUBS - Number of subcommittees. STAFF - Number of staff members assigned to the committee. PRESTIGE - PRESTIGE == 1 is a high prestige committee. BILLS103 - Number of bill assignments in the first 100 days of the 103rd House of Representatives. Committee names are included as a variable in the data file though not returned by load. """ def load_pandas(): data = _get_data() return du.process_pandas(data, endog_idx=0) def load(as_pandas=None): """Load the committee data and returns a data class. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def _get_data(): data = du.load_csv(__file__, 'committee.csv') data = data.iloc[:, 1:7].astype(float) return data statsmodels-0.12.2/statsmodels/datasets/committee/src/000077500000000000000000000000001400612667500230745ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/committee/src/committee.dat000066400000000000000000000026561400612667500255650ustar00rootroot00000000000000 SIZE SUBS STAFF PRESTIGE POLICY CONSTIT SERVICE BILLS103 BILLS104 Appropriations 58 13 109 1 0 0 0 9 6 Budget 42 0 39 1 0 0 0 101 23 Rules 13 2 25 1 0 0 0 54 44 Ways_and_Means 39 5 23 1 0 0 0 542 355 Banking 51 5 61 0 1 0 0 101 125 Economic_Educ_Oppor 43 5 69 0 1 0 0 158 131 Commerce 49 4 79 0 1 0 0 196 271 International_Relations 44 3 68 0 1 0 0 40 63 Government_Reform 51 7 99 0 1 0 0 72 149 Judiciary 35 5 56 0 1 0 0 168 253 Agriculture 49 5 46 0 0 1 0 60 81 National_Security 55 7 48 0 0 1 0 75 89 Resources 44 5 58 0 0 1 0 98 142 TransInfrastructure 61 6 74 0 0 1 0 69 155 Science 50 4 58 0 0 1 0 25 27 Small_Business 43 4 29 0 0 1 0 9 8 Veterans_Affairs 33 3 36 0 0 1 0 41 28 House_Oversight 12 0 24 0 0 0 1 233 68 Stds_of_Conduct 10 0 9 0 0 0 1 0 1 Intelligence 16 2 24 0 0 0 1 2 4 statsmodels-0.12.2/statsmodels/datasets/copper/000077500000000000000000000000001400612667500216075ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/copper/__init__.py000066400000000000000000000003261400612667500237210ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/copper/copper.csv000066400000000000000000000017261400612667500236220ustar00rootroot00000000000000"YEAR","WORLDCONSUMPTION","COPPERPRICE","INCOMEINDEX","ALUMPRICE","INVENTORYINDEX","TIME" 1951,3173,26.56,0.7,19.76,0.98,1 1952,3281.1,27.31,0.71,20.78,1.04,2 1953,3135.7,32.95,0.72,22.55,1.05,3 1954,3359.1,33.9,0.7,23.06,0.97,4 1955,3755.1,42.7,0.74,24.93,1.02,5 1956,3875.9,46.11,0.74,26.5,1.04,6 1957,3905.7,31.7,0.74,27.24,0.98,7 1958,3957.6,27.23,0.72,26.21,0.98,8 1959,4279.1,32.89,0.75,26.09,1.03,9 1960,4627.9,33.78,0.77,27.4,1.03,10 1961,4910.2,31.66,0.76,26.94,0.98,11 1962,4908.4,32.28,0.79,25.18,1,12 1963,5327.9,32.38,0.83,23.94,0.97,13 1964,5878.4,33.75,0.85,25.07,1.03,14 1965,6075.2,36.25,0.89,25.37,1.08,15 1966,6312.7,36.24,0.93,24.55,1.05,16 1967,6056.8,38.23,0.95,24.98,1.03,17 1968,6375.9,40.83,0.99,24.96,1.03,18 1969,6974.3,44.62,1,25.52,0.99,19 1970,7101.6,52.27,1,26.01,1,20 1971,7071.7,45.16,1.02,25.46,0.96,21 1972,7754.8,42.5,1.07,22.17,0.97,22 1973,8480.3,43.7,1.12,18.56,0.98,23 1974,8105.2,47.88,1.1,21.32,1.01,24 1975,7157.2,36.33,1.07,22.75,0.94,25 statsmodels-0.12.2/statsmodels/datasets/copper/data.py000066400000000000000000000043411400612667500230740ustar00rootroot00000000000000"""World Copper Prices 1951-1975 dataset.""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """Used with express permission from the original author, who retains all rights.""" TITLE = "World Copper Market 1951-1975 Dataset" SOURCE = """ Jeff Gill's `Generalized Linear Models: A Unified Approach` http://jgill.wustl.edu/research/books.html """ DESCRSHORT = """World Copper Market 1951-1975""" DESCRLONG = """This data describes the world copper market from 1951 through 1975. In an example, in Gill, the outcome variable (of a 2 stage estimation) is the world consumption of copper for the 25 years. The explanatory variables are the world consumption of copper in 1000 metric tons, the constant dollar adjusted price of copper, the price of a substitute, aluminum, an index of real per capita income base 1970, an annual measure of manufacturer inventory change, and a time trend. """ NOTE = """ Number of Observations - 25 Number of Variables - 6 Variable name definitions:: WORLDCONSUMPTION - World consumption of copper (in 1000 metric tons) COPPERPRICE - Constant dollar adjusted price of copper INCOMEINDEX - An index of real per capita income (base 1970) ALUMPRICE - The price of aluminum INVENTORYINDEX - A measure of annual manufacturer inventory trend TIME - A time trend Years are included in the data file though not returned by load. """ def _get_data(): data = du.load_csv(__file__, 'copper.csv') data = data.iloc[:, 1:7] return data.astype(float) def load_pandas(): """ Load the copper data and returns a Dataset class. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ data = _get_data() return du.process_pandas(data, endog_idx=0) def load(as_pandas=None): """ Load the copper data and returns a Dataset class. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) statsmodels-0.12.2/statsmodels/datasets/copper/src/000077500000000000000000000000001400612667500223765ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/copper/src/copper.dat000066400000000000000000000020531400612667500243600ustar00rootroot00000000000000YEAR WORLDCONSUMPTION COPPERPRICE INCOMEINDEX ALUMPRICE INVENTORYINDEX TIME 1951 3173.0 26.56 0.70 19.76 0.97679 1 1952 3281.1 27.31 0.71 20.78 1.03937 2 1953 3135.7 32.95 0.72 22.55 1.05153 3 1954 3359.1 33.90 0.70 23.06 0.97312 4 1955 3755.1 42.70 0.74 24.93 1.02349 5 1956 3875.9 46.11 0.74 26.50 1.04135 6 1957 3905.7 31.70 0.74 27.24 0.97686 7 1958 3957.6 27.23 0.72 26.21 0.98069 8 1959 4279.1 32.89 0.75 26.09 1.02888 9 1960 4627.9 33.78 0.77 27.40 1.03392 10 1961 4910.2 31.66 0.76 26.94 0.97922 11 1962 4908.4 32.28 0.79 25.18 0.99679 12 1963 5327.9 32.38 0.83 23.94 0.96630 13 1964 5878.4 33.75 0.85 25.07 1.02915 14 1965 6075.2 36.25 0.89 25.37 1.07950 15 1966 6312.7 36.24 0.93 24.55 1.05073 16 1967 6056.8 38.23 0.95 24.98 1.02788 17 1968 6375.9 40.83 0.99 24.96 1.02799 18 1969 6974.3 44.62 1.00 25.52 0.99151 19 1970 7101.6 52.27 1.00 26.01 1.00191 20 1971 7071.7 45.16 1.02 25.46 0.95644 21 1972 7754.8 42.50 1.07 22.17 0.96947 22 1973 8480.3 43.70 1.12 18.56 0.98220 23 1974 8105.2 47.88 1.10 21.32 1.00793 24 1975 7157.2 36.33 1.07 22.75 0.93810 25 statsmodels-0.12.2/statsmodels/datasets/cpunish/000077500000000000000000000000001400612667500217705ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/cpunish/R_cpunish.s000066400000000000000000000007411400612667500241100ustar00rootroot00000000000000### SETUP ### d <- read.table("./cpunish.csv",sep=",", header=T) attach(d) LN_VC100k96 = log(VC100k96) ### MODEL ### m1 <- glm(EXECUTIONS ~ INCOME + PERPOVERTY + PERBLACK + LN_VC100k96 + SOUTH + DEGREE, family=poisson) results <- summary.glm(m1) results results['coefficients'] # Model with exposure m2 <- glm(EXECUTIONS ~ INCOME + PERPOVERTY + PERBLACK + LN_VC100k96 + SOUTH + DEGREE, family=poisson, offset=rep(log(100), length(EXECUTIONS))) results2 <- summary.glm(m2) statsmodels-0.12.2/statsmodels/datasets/cpunish/__init__.py000066400000000000000000000003261400612667500241020ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/cpunish/cpunish.csv000066400000000000000000000013521400612667500241570ustar00rootroot00000000000000"STATE","EXECUTIONS","INCOME","PERPOVERTY","PERBLACK","VC100k96","SOUTH","DEGREE" "Texas",37,34453,16.7,12.2,644,1,0.16 "Virginia",9,41534,12.5,20,351,1,0.27 "Missouri",6,35802,10.6,11.2,591,0,0.21 "Arkansas",4,26954,18.4,16.1,524,1,0.16 "Alabama",3,31468,14.8,25.9,565,1,0.19 "Arizona",2,32552,18.8,3.5,632,0,0.25 "Illinois",2,40873,11.6,15.3,886,0,0.25 "South_Carolina",2,34861,13.1,30.1,997,1,0.21 "Colorado",1,42562,9.4,4.3,405,0,0.31 "Florida",1,31900,14.3,15.4,1051,1,0.24 "Indiana",1,37421,8.2,8.2,537,0,0.19 "Kentucky",1,33305,16.4,7.2,321,0,0.16 "Louisiana",1,32108,18.4,32.1,929,1,0.18 "Maryland",1,45844,9.3,27.4,931,0,0.29 "Nebraska",1,34743,10,4,435,0,0.24 "Oklahoma",1,29709,15.2,7.7,597,0,0.21 "Oregon",1,36777,11.7,1.8,463,0,0.25 statsmodels-0.12.2/statsmodels/datasets/cpunish/data.py000066400000000000000000000050041400612667500232520ustar00rootroot00000000000000"""US Capital Punishment dataset.""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """Used with express permission from the original author, who retains all rights.""" TITLE = __doc__ SOURCE = """ Jeff Gill's `Generalized Linear Models: A Unified Approach` http://jgill.wustl.edu/research/books.html """ DESCRSHORT = """Number of state executions in 1997""" DESCRLONG = """This data describes the number of times capital punishment is implemented at the state level for the year 1997. The outcome variable is the number of executions. There were executions in 17 states. Included in the data are explanatory variables for median per capita income in dollars, the percent of the population classified as living in poverty, the percent of Black citizens in the population, the rate of violent crimes per 100,000 residents for 1996, a dummy variable indicating whether the state is in the South, and (an estimate of) the proportion of the population with a college degree of some kind. """ NOTE = """:: Number of Observations - 17 Number of Variables - 7 Variable name definitions:: EXECUTIONS - Executions in 1996 INCOME - Median per capita income in 1996 dollars PERPOVERTY - Percent of the population classified as living in poverty PERBLACK - Percent of black citizens in the population VC100k96 - Rate of violent crimes per 100,00 residents for 1996 SOUTH - SOUTH == 1 indicates a state in the South DEGREE - An esimate of the proportion of the state population with a college degree of some kind State names are included in the data file, though not returned by load. """ def load_pandas(): """ Load the cpunish data and return a Dataset class. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ data = _get_data() return du.process_pandas(data, endog_idx=0) def load(as_pandas=None): """ Load the cpunish data and return a Dataset class. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def _get_data(): data = du.load_csv(__file__, 'cpunish.csv') data = data.iloc[:, 1:8].astype(float) return data statsmodels-0.12.2/statsmodels/datasets/cpunish/src/000077500000000000000000000000001400612667500225575ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/cpunish/src/cpunish.dat000066400000000000000000000037151400612667500247300ustar00rootroot00000000000000STATE EXECUTIONS INCOME PERPOVERTY PERBLACK VC100k96 SOUTH <9thGRADE 9thTO12th HSOREQUIV SOMECOLL AADEGREE BACHELORS GRAD/PROF Texas 37 34453 16.7 12.2 644 1 1492112 1924831 3153187 2777973 598956 530849 673250 Virginia 9 41534 12.5 20.0 351 1 461475 669851 1297714 969191 244488 676710 363602 Missouri 6 35802 10.6 11.2 591 0 391097 578440 1251550 785555 170146 420521 204294 Arkansas 4 26954 18.4 16.1 524 1 234071 328690 571252 323016 62246 143038 67144 Alabama 3 31468 14.8 25.9 565 1 362434 597455 875703 575123 146228 281466 142177 Arizona 2 32552 18.8 3.5 632 0 224662 368279 708340 724228 173801 325575 161560 Illinois 2 40873 11.6 15.3 886 0 786815 1203134 2531465 1817238 490791 1101193 552145 South_Carolina 2 34861 13.1 30.1 997 1 303694 479916 776053 466145 152671 267365 118811 Colorado 1 42562 9.4 4.3 405 0 124477 270560 654510 630445 161331 402917 190168 Florida 1 31900 14.3 15.4 1051 1 883820 1706839 3045682 2054574 682005 1133053 567453 Indiana 1 37421 8.2 8.2 537 0 310403 673362 1530741 775605 212379 360087 224057 Kentucky 1 33305 16.4 7.2 321 0 456107 467956 881795 476362 108409 209055 129994 Louisiana 1 32108 18.4 32.1 929 1 391630 534570 951832 586477 94409 288154 143624 Maryland 1 45844 9.3 27.4 931 0 257518 514788 1044976 744604 182465 532883 342012 Nebraska 1 34743 10.0 4.0 435 0 81690 124792 388540 272981 80956 141231 59008 Oklahoma 1 29709 15.2 7.7 597 0 201228 375155 706003 539511 113434 253635 119774 Oregon 1 36777 11.7 1.8 463 0 122513 283409 613983 561176 139269 267161 130403 statsmodels-0.12.2/statsmodels/datasets/elec_equip/000077500000000000000000000000001400612667500224325ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/elec_equip/__init__.py000066400000000000000000000003261400612667500245440ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/elec_equip/data.py000066400000000000000000000033431400612667500237200ustar00rootroot00000000000000"""Euro area 18 - Total Turnover Index, Manufacture of electrical equipment""" import os import pandas as pd from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This is public domain.""" TITLE = __doc__ SOURCE = """ Data are from the Statistical Office of the European Commission (Eurostat) """ DESCRSHORT = """EU Manufacture of electrical equipment""" DESCRLONG = DESCRSHORT NOTE = """:: Variable name definitions:: date - Date in format MMM-1-YYYY STS.M.I7.W.TOVT.NS0016.4.000 - Euro area 18 (fixed composition) - Total Turnover Index, NACE 26-27; Treatment and coating of metals; machining; Manufacture of electrical equipment - NACE Rev2; Eurostat; Working day adjusted, not seasonally adjusted """ def load_pandas(): data = _get_data() return du.Dataset(data=data, names=list(data.columns)) def load(as_pandas=None): """ Load the EU Electrical Equipment manufacturing data into a Dataset class Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. Notes ----- The Dataset instance does not contain endog and exog attributes. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def _get_data(): curr_dir = os.path.split(os.path.abspath(__file__))[0] data = pd.read_csv(os.path.join(curr_dir, 'elec_equip.csv')) data.index = pd.to_datetime(data.pop('DATE')) return data variable_names = ["elec_equip"] def __str__(): return "elec_equip" statsmodels-0.12.2/statsmodels/datasets/elec_equip/elec_equip.csv000066400000000000000000000106311400612667500252630ustar00rootroot00000000000000DATE,STS.M.I7.W.TOVT.NS0016.4.000 Jan-1-1995,66.19 Feb-1-1995,65.15 Mar-1-1995,74.48 Apr-1-1995,71.26 May-1-1995,67.63 Jun-1-1995,76.85 Jul-1-1995,68.62 Aug-1-1995,67.41 Sep-1-1995,90.18 Oct-1-1995,72.7 Nov-1-1995,77.97 Dec-1-1995,85.59 Jan-1-1996,68.06 Feb-1-1996,66.8 Mar-1-1996,77.88 Apr-1-1996,71.83 May-1-1996,69.73 Jun-1-1996,77.8 Jul-1-1996,70.26 Aug-1-1996,67.46 Sep-1-1996,92.5 Oct-1-1996,80.25 Nov-1-1996,82.81 Dec-1-1996,89.13 Jan-1-1997,71.03 Feb-1-1997,70.3 Mar-1-1997,83.68 Apr-1-1997,77.18 May-1-1997,72.83 Jun-1-1997,86.88 Jul-1-1997,78.67 Aug-1-1997,76.71 Sep-1-1997,98.31 Oct-1-1997,88.06 Nov-1-1997,93.12 Dec-1-1997,94.41 Jan-1-1998,76.69 Feb-1-1998,79.21 Mar-1-1998,92.74 Apr-1-1998,83.34 May-1-1998,82.08 Jun-1-1998,90.26 Jul-1-1998,83.15 Aug-1-1998,78.03 Sep-1-1998,102.73 Oct-1-1998,91.92 Nov-1-1998,91.33 Dec-1-1998,95.27 Jan-1-1999,85.21 Feb-1-1999,80.58 Mar-1-1999,99.85 Apr-1-1999,87.12 May-1-1999,83.33 Jun-1-1999,100.38 Jul-1-1999,91.13 Aug-1-1999,86.71 Sep-1-1999,112.68 Oct-1-1999,102.72 Nov-1-1999,103.37 Dec-1-1999,115.76 Jan-1-2000,97.69 Feb-1-2000,96.63 Mar-1-2000,114 Apr-1-2000,105.66 May-1-2000,102.84 Jun-1-2000,117.98 Jul-1-2000,108.66 Aug-1-2000,97.79 Sep-1-2000,131.65 Oct-1-2000,123.06 Nov-1-2000,126.82 Dec-1-2000,128.08 Jan-1-2001,107.71 Feb-1-2001,106.85 Mar-1-2001,127.59 Apr-1-2001,109.88 May-1-2001,106.02 Jun-1-2001,121.84 Jul-1-2001,107.75 Aug-1-2001,93.25 Sep-1-2001,121.47 Oct-1-2001,111.06 Nov-1-2001,114.99 Dec-1-2001,116.33 Jan-1-2002,97.58 Feb-1-2002,97.33 Mar-1-2002,117.34 Apr-1-2002,101.43 May-1-2002,97.56 Jun-1-2002,112.38 Jul-1-2002,98.4 Aug-1-2002,86.65 Sep-1-2002,116.4 Oct-1-2002,108.53 Nov-1-2002,112.88 Dec-1-2002,112.56 Jan-1-2003,93.65 Feb-1-2003,92.9 Mar-1-2003,108.07 Apr-1-2003,94.53 May-1-2003,92.38 Jun-1-2003,105.12 Jul-1-2003,98.2 Aug-1-2003,83.63 Sep-1-2003,112.8 Oct-1-2003,107.93 Nov-1-2003,112.78 Dec-1-2003,113.82 Jan-1-2004,95.34 Feb-1-2004,94.52 Mar-1-2004,110.97 Apr-1-2004,99.25 May-1-2004,97.58 Jun-1-2004,112.82 Jul-1-2004,102.9 Aug-1-2004,86.84 Sep-1-2004,115.9 Oct-1-2004,112.59 Nov-1-2004,113.71 Dec-1-2004,115.59 Jan-1-2005,101.28 Feb-1-2005,95.53 Mar-1-2005,114.22 Apr-1-2005,100.99 May-1-2005,97.65 Jun-1-2005,114.36 Jul-1-2005,104.38 Aug-1-2005,89.33 Sep-1-2005,122.23 Oct-1-2005,112.84 Nov-1-2005,121.37 Dec-1-2005,120.25 Jan-1-2006,105.1 Feb-1-2006,103.54 Mar-1-2006,123.16 Apr-1-2006,109.07 May-1-2006,109.89 Jun-1-2006,125.52 Jul-1-2006,113.67 Aug-1-2006,97.66 Sep-1-2006,133.79 Oct-1-2006,124.07 Nov-1-2006,130.19 Dec-1-2006,131.12 Jan-1-2007,110.17 Feb-1-2007,109.52 Mar-1-2007,130.82 Apr-1-2007,113.21 May-1-2007,113.85 Jun-1-2007,131.49 Jul-1-2007,119.74 Aug-1-2007,102.29 Sep-1-2007,133.88 Oct-1-2007,127.19 Nov-1-2007,133.39 Dec-1-2007,134.14 Jan-1-2008,115.79 Feb-1-2008,114.07 Mar-1-2008,130.05 Apr-1-2008,118.76 May-1-2008,114.88 Jun-1-2008,129.24 Jul-1-2008,118.54 Aug-1-2008,100.6 Sep-1-2008,132.86 Oct-1-2008,124.22 Nov-1-2008,125.03 Dec-1-2008,120.34 Jan-1-2009,87.05 Feb-1-2009,84.31 Mar-1-2009,99.01 Apr-1-2009,86.54 May-1-2009,84.3 Jun-1-2009,96.67 Jul-1-2009,87.68 Aug-1-2009,74.9 Sep-1-2009,99.16 Oct-1-2009,95.36 Nov-1-2009,101.02 Dec-1-2009,104.6 Jan-1-2010,83.35 Feb-1-2010,85.79 Mar-1-2010,102.24 Apr-1-2010,91.65 May-1-2010,94.78 Jun-1-2010,107.24 Jul-1-2010,99.29 Aug-1-2010,87.43 Sep-1-2010,111.55 Oct-1-2010,108.97 Nov-1-2010,114.45 Dec-1-2010,113.25 Jan-1-2011,94.27 Feb-1-2011,98.19 Mar-1-2011,113.95 Apr-1-2011,99.35 May-1-2011,100.32 Jun-1-2011,111.24 Jul-1-2011,104.05 Aug-1-2011,91.87 Sep-1-2011,113 Oct-1-2011,106.44 Nov-1-2011,111.47 Dec-1-2011,113.53 Jan-1-2012,90.55 Feb-1-2012,93.5 Mar-1-2012,108.49 Apr-1-2012,95.16 May-1-2012,97.78 Jun-1-2012,110.19 Jul-1-2012,100.34 Aug-1-2012,87.88 Sep-1-2012,107.78 Oct-1-2012,102 Nov-1-2012,103.97 Dec-1-2012,106.33 Jan-1-2013,87.09 Feb-1-2013,89.55 Mar-1-2013,106.49 Apr-1-2013,92.02 May-1-2013,92.74 Jun-1-2013,105.7 Jul-1-2013,95.99 Aug-1-2013,84.26 Sep-1-2013,106.43 Oct-1-2013,101.27 Nov-1-2013,103.1 Dec-1-2013,105.67 Jan-1-2014,86.99 Feb-1-2014,91.62 Mar-1-2014,104.65 Apr-1-2014,92.71 May-1-2014,91.51 Jun-1-2014,104.7 Jul-1-2014,98.86 Aug-1-2014,85.92 Sep-1-2014,106.46 Oct-1-2014,101.72 Nov-1-2014,104.51 Dec-1-2014,107.45 Jan-1-2015,89.89 Feb-1-2015,93.82 Mar-1-2015,109.12 Apr-1-2015,97.19 May-1-2015,97.35 Jun-1-2015,109.99 Jul-1-2015,102.13 Aug-1-2015,89.56 Sep-1-2015,111.03 Oct-1-2015,106.06 Nov-1-2015,108.1 Dec-1-2015,111.03 Jan-1-2016,92.73 Feb-1-2016,95.49 Mar-1-2016,110.57 Apr-1-2016,97.05 May-1-2016,97.86 statsmodels-0.12.2/statsmodels/datasets/elnino/000077500000000000000000000000001400612667500216035ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/elnino/__init__.py000066400000000000000000000003261400612667500237150ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/elnino/data.py000066400000000000000000000032541400612667500230720ustar00rootroot00000000000000"""El Nino dataset, 1950 - 2010""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This data is in the public domain.""" TITLE = """El Nino - Sea Surface Temperatures""" SOURCE = """ National Oceanic and Atmospheric Administration's National Weather Service ERSST.V3B dataset, Nino 1+2 http://www.cpc.ncep.noaa.gov/data/indices/ """ DESCRSHORT = """Averaged monthly sea surface temperature - Pacific Ocean.""" DESCRLONG = """This data contains the averaged monthly sea surface temperature in degrees Celcius of the Pacific Ocean, between 0-10 degrees South and 90-80 degrees West, from 1950 to 2010. This dataset was obtained from NOAA. """ NOTE = """:: Number of Observations - 61 x 12 Number of Variables - 1 Variable name definitions:: TEMPERATURE - average sea surface temperature in degrees Celcius (12 columns, one per month). """ def load_pandas(): data = _get_data() dataset = du.Dataset(data=data, names=list(data.columns)) return dataset def load(as_pandas=None): """ Load the El Nino data and return a Dataset class. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. Notes ----- The elnino Dataset instance does not contain endog and exog attributes. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def _get_data(): return du.load_csv(__file__, 'elnino.csv', convert_float=True) statsmodels-0.12.2/statsmodels/datasets/elnino/elnino.csv000066400000000000000000000126041400612667500236070ustar00rootroot00000000000000"YEAR","JAN","FEB","MAR","APR","MAY","JUN","JUL","AUG","SEP","OCT","NOV","DEC" 1950,23.110,24.200,25.370,23.860,23.030,21.570,20.630,20.150,19.670,20.030,20.020,21.800 1951,24.190,25.280,25.600,25.370,24.790,24.690,23.860,22.320,21.440,21.770,22.330,22.890 1952,24.520,26.210,26.370,24.730,23.710,22.340,20.890,20.020,19.630,20.400,20.770,22.390 1953,24.150,26.340,27.360,27.030,25.470,23.490,22.200,21.450,21.250,20.950,21.600,22.440 1954,23.020,25.000,25.330,22.970,21.730,20.770,19.520,19.330,18.950,19.110,20.270,21.300 1955,23.750,24.820,25.140,24.220,22.160,21.200,20.460,19.630,19.240,19.160,19.840,21.190 1956,23.240,24.710,25.900,24.660,23.140,22.040,21.470,20.550,19.890,19.690,20.570,21.580 1957,23.130,26.300,27.630,27.150,26.720,25.040,23.830,22.340,21.800,21.800,22.390,23.690 1958,24.890,26.550,27.090,26.370,24.710,23.230,22.310,20.720,20.620,21.050,21.520,22.500 1959,23.970,25.900,26.940,25.840,24.230,22.570,21.500,20.150,20.230,20.860,21.880,22.550 1960,24.400,25.590,26.010,24.660,23.530,21.830,20.730,20.100,20.560,20.270,20.930,22.740 1961,24.580,26.660,25.950,25.170,23.600,22.360,20.520,19.970,19.700,20.070,21.090,22.110 1962,24.020,25.350,24.470,23.430,23.030,21.810,20.600,20.170,20.020,20.140,20.990,21.820 1963,23.810,25.360,26.020,24.670,23.970,22.410,21.800,21.310,21.000,21.130,21.640,22.550 1964,24.150,25.080,25.300,24.610,21.930,21.440,20.250,19.480,19.670,19.790,20.880,21.830 1965,24.220,26.170,26.710,27.010,26.090,24.600,23.260,22.540,21.260,21.570,22.290,23.350 1966,25.150,25.880,25.350,24.260,22.920,21.800,20.850,20.170,20.040,20.510,21.030,22.250 1967,23.660,25.540,25.550,24.980,23.770,22.040,21.100,19.840,19.080,19.470,20.200,21.280 1968,23.190,24.880,25.110,23.970,22.440,21.700,21.250,20.970,21.230,21.120,21.680,23.200 1969,24.670,25.560,27.090,26.660,26.070,24.390,22.470,21.060,20.880,21.740,22.470,23.600 1970,25.020,25.760,25.530,24.760,22.940,21.270,19.690,19.270,19.500,20.160,20.610,21.770 1971,23.330,24.580,25.240,24.950,23.290,21.600,21.010,19.970,19.740,19.880,20.940,21.990 1972,24.510,26.660,27.090,26.250,25.470,25.010,24.110,23.420,22.120,22.580,23.320,24.890 1973,26.030,26.480,26.270,24.870,23.440,21.760,20.840,19.470,19.490,19.800,20.710,21.740 1974,23.290,24.870,25.690,25.280,24.350,22.480,21.580,20.730,20.150,19.880,20.680,21.410 1975,23.550,24.950,26.060,25.530,23.710,21.840,21.050,19.970,19.140,19.170,19.440,21.050 1976,23.510,25.360,25.880,25.720,25.110,24.460,23.300,21.910,21.560,21.690,22.140,23.290 1977,24.930,25.790,26.130,25.290,23.880,22.700,21.630,20.250,19.820,20.610,21.290,22.470 1978,24.320,25.770,25.390,24.730,23.150,21.890,21.010,19.660,19.980,20.220,21.620,22.940 1979,24.710,25.600,25.930,25.580,24.520,23.280,21.790,21.050,21.150,21.430,21.950,22.970 1980,24.350,25.730,26.460,25.710,24.460,22.880,21.260,20.570,20.450,20.430,21.230,22.340 1981,22.980,24.900,25.940,24.890,23.900,22.570,21.100,20.030,20.090,20.580,21.260,22.600 1982,24.360,25.420,25.400,24.960,24.210,23.350,22.500,21.890,22.040,22.880,24.570,25.890 1983,27.250,28.230,28.850,28.820,28.370,27.430,25.730,23.880,22.260,22.220,22.210,23.190 1984,24.320,25.120,25.750,25.400,23.580,22.300,21.530,20.640,20.730,20.620,21.700,22.470 1985,23.840,24.830,25.600,24.280,22.670,21.840,20.750,19.900,19.860,20.260,20.970,22.490 1986,24.310,25.900,25.780,24.860,23.350,22.030,21.640,21.070,21.130,21.460,22.170,23.530 1987,25.600,27.020,27.890,26.950,25.960,24.040,23.000,21.920,22.000,22.540,22.840,23.510 1988,24.760,25.740,25.710,24.680,23.180,21.660,20.590,19.630,19.440,19.830,20.960,22.250 1989,24.360,26.020,26.210,25.540,23.360,22.140,21.270,20.860,20.170,20.520,21.440,22.610 1990,24.220,26.170,26.150,25.150,24.140,22.760,21.360,20.700,20.280,20.400,21.190,22.290 1991,23.990,25.590,26.310,25.150,24.440,23.280,22.390,21.390,21.220,21.730,22.400,23.750 1992,25.020,26.620,27.720,27.580,26.440,23.860,21.840,20.870,20.850,21.150,21.840,22.790 1993,24.680,26.460,27.070,26.840,25.600,24.110,22.610,21.650,21.110,21.710,22.070,22.860 1994,24.560,25.890,25.750,24.490,23.520,22.310,21.170,20.220,20.650,22.040,22.270,23.750 1995,25.480,26.250,26.090,24.320,23.370,22.430,21.420,20.460,20.500,20.620,21.490,22.030 1996,23.810,25.520,26.280,24.000,23.110,21.660,20.720,20.230,20.430,20.520,20.770,21.680 1997,23.700,26.080,27.170,26.740,26.770,26.150,25.590,24.950,24.690,24.640,25.850,27.080 1998,28.120,28.820,29.240,28.450,27.360,25.190,23.610,22.270,21.310,21.370,21.600,22.810 1999,24.230,25.730,26.470,24.530,23.640,22.090,21.360,20.670,20.080,20.460,20.620,22.420 2000,24.010,25.380,25.670,25.530,24.270,22.930,21.470,20.070,20.640,20.900,20.670,22.080 2001,24.240,26.110,26.890,25.990,23.980,22.710,21.480,20.240,19.730,20.140,20.680,21.730 2002,24.090,26.230,27.390,26.440,25.290,23.280,21.640,21.320,21.420,21.850,22.850,24.050 2003,25.010,26.270,26.910,25.410,23.240,22.150,21.500,21.250,20.750,21.700,22.330,23.600 2004,25.090,26.470,26.120,25.270,23.440,22.540,21.260,20.790,20.830,21.560,22.880,23.390 2005,24.610,25.090,25.230,25.210,24.310,22.600,21.610,20.470,20.000,19.890,20.610,22.200 2006,24.760,26.520,26.220,24.290,23.840,22.820,22.200,21.890,21.930,22.460,22.610,24.150 2007,25.820,26.810,26.410,24.960,23.050,21.610,21.050,19.950,19.850,19.310,19.820,21.150 2008,24.240,26.390,26.910,25.680,24.430,23.190,23.020,22.140,21.600,21.390,21.540,22.730 2009,24.390,25.530,25.480,25.840,24.950,24.090,23.090,22.030,21.480,21.640,21.990,23.210 2010,24.700,26.160,26.540,26.040,24.750,23.260,21.110,19.490,19.280,19.730,20.440,22.070 statsmodels-0.12.2/statsmodels/datasets/elnino/src/000077500000000000000000000000001400612667500223725ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/elnino/src/elnino.dat000066400000000000000000001504051400612667500243550ustar00rootroot00000000000000 YR MON NINO1+2 ANOM NINO3 ANOM NINO4 ANOM NINO3.4 ANOM 1950 1 23.11 -1.42 23.74 -1.91 27.03 -1.12 24.83 -1.72 1950 2 24.20 -1.71 24.92 -1.45 27.15 -0.92 25.20 -1.53 1950 3 25.37 -1.00 26.33 -0.80 27.06 -1.11 26.03 -1.20 1950 4 23.86 -1.71 26.46 -0.97 27.29 -1.10 26.36 -1.30 1950 5 23.03 -1.39 25.72 -1.38 27.59 -1.10 26.19 -1.58 1950 6 21.57 -1.50 25.55 -0.92 27.97 -0.70 26.52 -1.01 1950 7 20.63 -1.34 24.97 -0.68 27.83 -0.78 26.42 -0.69 1950 8 20.15 -0.86 24.61 -0.45 27.72 -0.78 25.98 -0.77 1950 9 19.67 -1.10 24.22 -0.72 27.66 -0.85 25.78 -0.92 1950 10 20.03 -1.04 24.39 -0.56 27.44 -1.07 25.96 -0.68 1950 11 20.02 -1.72 24.00 -1.05 27.35 -1.11 25.64 -0.96 1950 12 21.80 -1.11 24.30 -0.91 27.30 -1.05 25.50 -1.07 1951 1 24.19 -0.35 25.00 -0.65 27.36 -0.79 25.46 -1.09 1951 2 25.28 -0.64 25.80 -0.57 27.27 -0.80 25.78 -0.96 1951 3 25.60 -0.78 26.91 -0.22 27.96 -0.21 26.72 -0.51 1951 4 25.37 -0.20 27.31 -0.11 28.49 0.09 27.24 -0.43 1951 5 24.79 0.37 27.08 -0.02 29.04 0.35 27.68 -0.09 1951 6 24.69 1.62 26.57 0.10 28.74 0.07 27.46 -0.07 1951 7 23.86 1.88 26.54 0.89 28.82 0.21 27.72 0.61 1951 8 22.32 1.31 25.67 0.62 28.53 0.04 27.36 0.61 1951 9 21.44 0.67 25.56 0.62 28.62 0.11 27.51 0.81 1951 10 21.77 0.70 25.85 0.90 28.71 0.20 27.43 0.78 1951 11 22.33 0.59 26.18 1.13 28.74 0.29 27.48 0.87 1951 12 22.89 -0.01 25.98 0.77 28.53 0.19 27.12 0.55 1952 1 24.52 -0.02 25.85 0.20 28.35 0.19 26.85 0.30 1952 2 26.21 0.29 26.46 0.08 28.08 0.00 26.79 0.06 1952 3 26.37 0.00 27.18 0.05 28.10 -0.07 27.32 0.09 1952 4 24.73 -0.84 27.41 -0.02 28.52 0.12 27.88 0.21 1952 5 23.71 -0.71 26.92 -0.18 28.69 -0.01 27.99 0.21 1952 6 22.34 -0.73 25.84 -0.63 28.47 -0.20 27.33 -0.20 1952 7 20.89 -1.09 24.92 -0.73 28.24 -0.37 26.72 -0.38 1952 8 20.02 -0.99 24.50 -0.56 28.09 -0.40 26.46 -0.29 1952 9 19.63 -1.14 24.43 -0.51 28.55 0.04 26.54 -0.17 1952 10 20.40 -0.67 24.52 -0.42 28.25 -0.26 26.54 -0.10 1952 11 20.77 -0.97 24.36 -0.69 28.28 -0.17 26.36 -0.24 1952 12 22.39 -0.52 24.88 -0.33 28.30 -0.04 26.53 -0.04 1953 1 24.15 -0.39 25.77 0.11 28.31 0.15 26.85 0.29 1953 2 26.34 0.42 26.74 0.36 28.26 0.18 27.19 0.45 1953 3 27.36 0.98 27.57 0.44 28.10 -0.07 27.68 0.45 1953 4 27.03 1.46 27.91 0.49 28.53 0.14 28.19 0.53 1953 5 25.47 1.05 27.39 0.28 28.92 0.23 28.29 0.52 1953 6 23.49 0.42 26.77 0.30 29.18 0.51 28.02 0.49 1953 7 22.20 0.23 25.81 0.16 29.02 0.41 27.52 0.42 1953 8 21.45 0.44 25.20 0.14 28.83 0.34 27.16 0.41 1953 9 21.25 0.49 25.17 0.24 28.61 0.09 27.13 0.43 1953 10 20.95 -0.12 25.07 0.13 28.91 0.41 27.02 0.38 1953 11 21.60 -0.14 25.25 0.19 28.91 0.46 26.96 0.36 1953 12 22.44 -0.47 25.55 0.34 28.74 0.40 26.99 0.42 1954 1 23.02 -1.52 25.73 0.07 28.30 0.14 27.03 0.47 1954 2 25.00 -0.92 26.43 0.05 28.16 0.08 27.22 0.48 1954 3 25.33 -1.05 26.85 -0.28 27.89 -0.28 27.21 -0.02 1954 4 22.97 -2.60 25.85 -1.57 28.20 -0.19 26.87 -0.80 1954 5 21.73 -2.69 25.67 -1.44 28.40 -0.30 27.06 -0.71 1954 6 20.77 -2.30 25.20 -1.27 28.32 -0.35 26.93 -0.60 1954 7 19.52 -2.46 24.47 -1.17 28.00 -0.61 26.37 -0.74 1954 8 19.33 -1.68 23.83 -1.23 27.76 -0.73 25.73 -1.02 1954 9 18.95 -1.82 23.51 -1.43 27.61 -0.90 25.38 -1.33 1954 10 19.11 -1.96 23.63 -1.31 27.54 -0.97 25.51 -1.13 1954 11 20.27 -1.47 23.86 -1.19 27.53 -0.92 25.67 -0.93 1954 12 21.30 -1.61 23.79 -1.42 27.61 -0.74 25.37 -1.20 1955 1 23.75 -0.79 24.79 -0.86 27.60 -0.56 25.54 -1.02 1955 2 24.82 -1.10 25.76 -0.62 27.30 -0.77 25.90 -0.84 1955 3 25.14 -1.23 26.35 -0.78 27.37 -0.81 26.37 -0.86 1955 4 24.22 -1.35 26.32 -1.11 27.82 -0.57 26.66 -1.01 1955 5 22.16 -2.26 25.52 -1.58 28.03 -0.66 26.66 -1.11 1955 6 21.20 -1.87 25.08 -1.39 28.08 -0.59 26.56 -0.97 1955 7 20.46 -1.52 24.55 -1.10 28.14 -0.47 26.31 -0.80 1955 8 19.63 -1.38 23.69 -1.37 27.94 -0.55 25.60 -1.15 1955 9 19.24 -1.53 23.36 -1.57 27.71 -0.81 25.63 -1.07 1955 10 19.16 -1.91 22.71 -2.24 27.22 -1.29 24.66 -1.98 1955 11 19.84 -1.90 22.66 -2.39 26.79 -1.66 24.29 -2.32 1955 12 21.19 -1.71 23.08 -2.13 27.20 -1.15 24.58 -1.99 1956 1 23.24 -1.30 24.47 -1.18 27.18 -0.97 25.28 -1.27 1956 2 24.71 -1.20 25.80 -0.57 27.27 -0.81 26.00 -0.73 1956 3 25.90 -0.47 26.84 -0.29 27.49 -0.68 26.62 -0.61 1956 4 24.66 -0.91 27.12 -0.30 27.72 -0.68 26.96 -0.70 1956 5 23.14 -1.28 26.63 -0.47 28.11 -0.58 27.23 -0.54 1956 6 22.04 -1.03 25.87 -0.60 28.22 -0.46 26.99 -0.54 1956 7 21.47 -0.51 24.82 -0.82 28.07 -0.54 26.37 -0.73 1956 8 20.55 -0.46 24.16 -0.90 27.67 -0.82 25.91 -0.84 1956 9 19.89 -0.88 23.97 -0.97 27.71 -0.80 25.91 -0.79 1956 10 19.69 -1.39 24.01 -0.94 27.92 -0.59 25.83 -0.81 1956 11 20.57 -1.17 23.91 -1.14 28.02 -0.43 25.64 -0.97 1956 12 21.58 -1.32 24.06 -1.15 28.09 -0.26 25.71 -0.86 1957 1 23.13 -1.40 25.05 -0.60 28.03 -0.12 26.09 -0.47 1957 2 26.30 0.38 26.23 -0.15 28.10 0.02 26.58 -0.16 1957 3 27.63 1.26 27.55 0.42 28.33 0.16 27.65 0.41 1957 4 27.15 1.59 27.94 0.51 28.86 0.47 28.34 0.68 1957 5 26.72 2.30 27.81 0.71 29.15 0.46 28.59 0.82 1957 6 25.04 1.97 27.30 0.84 28.83 0.16 28.28 0.75 1957 7 23.83 1.85 26.95 1.31 28.73 0.12 28.11 1.00 1957 8 22.34 1.33 26.14 1.08 28.91 0.41 27.75 1.00 1957 9 21.80 1.03 25.71 0.77 28.96 0.45 27.54 0.84 1957 10 21.80 0.73 25.68 0.74 29.12 0.61 27.49 0.85 1957 11 22.39 0.65 26.23 1.18 29.12 0.67 27.79 1.19 1957 12 23.69 0.78 26.64 1.43 29.08 0.74 28.08 1.51 1958 1 24.89 0.35 27.04 1.38 29.26 1.10 28.37 1.81 1958 2 26.55 0.63 27.57 1.20 29.28 1.21 28.41 1.68 1958 3 27.09 0.72 27.85 0.72 29.04 0.86 28.34 1.11 1958 4 26.37 0.80 27.86 0.44 29.04 0.65 28.35 0.69 1958 5 24.71 0.29 27.39 0.28 29.21 0.52 28.35 0.57 1958 6 23.23 0.16 26.70 0.23 29.13 0.46 28.05 0.52 1958 7 22.31 0.33 25.73 0.09 28.89 0.28 27.48 0.37 1958 8 20.72 -0.29 24.97 -0.08 28.53 0.04 26.90 0.15 1958 9 20.62 -0.14 24.45 -0.48 28.50 -0.02 26.50 -0.20 1958 10 21.05 -0.02 24.65 -0.30 28.68 0.17 26.61 -0.03 1958 11 21.52 -0.22 25.06 0.01 28.79 0.34 26.89 0.29 1958 12 22.50 -0.40 25.02 -0.19 28.76 0.41 26.77 0.20 1959 1 23.97 -0.57 25.75 0.10 28.63 0.48 27.14 0.58 1959 2 25.90 -0.01 26.50 0.13 28.38 0.31 27.25 0.51 1959 3 26.94 0.56 27.17 0.04 28.48 0.31 27.55 0.32 1959 4 25.84 0.27 27.56 0.14 28.75 0.36 27.93 0.27 1959 5 24.23 -0.19 26.94 -0.16 28.85 0.16 27.80 0.03 1959 6 22.57 -0.50 26.07 -0.39 28.39 -0.28 27.34 -0.19 1959 7 21.50 -0.47 24.94 -0.71 28.30 -0.31 26.56 -0.55 1959 8 20.15 -0.86 24.40 -0.66 28.27 -0.22 26.32 -0.43 1959 9 20.23 -0.54 24.37 -0.57 28.19 -0.32 26.17 -0.53 1959 10 20.86 -0.21 24.67 -0.28 28.21 -0.30 26.42 -0.22 1959 11 21.88 0.14 24.74 -0.31 28.12 -0.34 26.32 -0.28 1959 12 22.55 -0.36 24.94 -0.27 28.07 -0.27 26.44 -0.13 1960 1 24.40 -0.14 25.34 -0.32 27.77 -0.38 26.25 -0.31 1960 2 25.59 -0.32 25.87 -0.50 27.49 -0.58 26.27 -0.47 1960 3 26.01 -0.36 26.75 -0.38 27.77 -0.40 26.97 -0.26 1960 4 24.66 -0.91 27.03 -0.39 28.08 -0.31 27.51 -0.16 1960 5 23.53 -0.89 26.66 -0.45 28.52 -0.18 27.62 -0.16 1960 6 21.83 -1.24 25.95 -0.52 28.35 -0.32 27.24 -0.29 1960 7 20.73 -1.25 25.38 -0.26 28.31 -0.30 27.07 -0.04 1960 8 20.10 -0.91 24.95 -0.11 28.19 -0.30 26.85 0.10 1960 9 20.56 -0.20 24.70 -0.24 28.32 -0.20 26.60 -0.11 1960 10 20.27 -0.80 24.24 -0.71 28.33 -0.17 26.35 -0.29 1960 11 20.93 -0.81 24.31 -0.75 28.37 -0.09 26.34 -0.26 1960 12 22.74 -0.17 24.73 -0.48 28.36 0.02 26.41 -0.16 1961 1 24.58 0.04 25.19 -0.46 27.94 -0.21 26.38 -0.17 1961 2 26.66 0.75 26.25 -0.13 27.85 -0.23 26.61 -0.13 1961 3 25.95 -0.42 26.83 -0.30 27.92 -0.26 27.00 -0.24 1961 4 25.17 -0.40 27.40 -0.02 27.96 -0.43 27.50 -0.16 1961 5 23.60 -0.82 27.08 -0.02 28.38 -0.31 27.85 0.08 1961 6 22.36 -0.71 26.37 -0.10 28.49 -0.18 27.86 0.33 1961 7 20.52 -1.46 24.95 -0.70 28.33 -0.28 27.16 0.05 1961 8 19.97 -1.04 24.20 -0.86 28.12 -0.37 26.43 -0.32 1961 9 19.70 -1.07 23.65 -1.29 28.19 -0.33 25.97 -0.73 1961 10 20.07 -1.01 23.89 -1.06 28.09 -0.42 25.94 -0.71 1961 11 21.09 -0.65 24.38 -0.67 28.26 -0.19 26.20 -0.40 1961 12 22.11 -0.80 24.75 -0.46 28.06 -0.28 26.20 -0.37 1962 1 24.02 -0.52 25.23 -0.42 27.66 -0.49 26.12 -0.43 1962 2 25.35 -0.56 26.07 -0.31 27.57 -0.51 26.28 -0.46 1962 3 24.47 -1.90 26.49 -0.64 27.83 -0.34 26.80 -0.44 1962 4 23.43 -2.14 26.59 -0.83 28.19 -0.20 27.22 -0.44 1962 5 23.03 -1.39 26.28 -0.82 28.23 -0.47 27.23 -0.54 1962 6 21.81 -1.26 25.83 -0.64 28.30 -0.37 27.18 -0.35 1962 7 20.60 -1.37 25.21 -0.44 28.24 -0.37 26.93 -0.17 1962 8 20.17 -0.84 24.72 -0.33 28.15 -0.34 26.52 -0.23 1962 9 20.02 -0.75 24.20 -0.74 28.11 -0.40 26.07 -0.63 1962 10 20.14 -0.93 24.23 -0.72 28.10 -0.41 26.06 -0.58 1962 11 20.99 -0.75 24.10 -0.95 28.12 -0.33 25.88 -0.72 1962 12 21.82 -1.09 24.12 -1.09 27.96 -0.38 25.75 -0.82 1963 1 23.81 -0.73 24.96 -0.69 27.74 -0.41 25.86 -0.69 1963 2 25.36 -0.55 25.91 -0.47 27.70 -0.38 26.39 -0.35 1963 3 26.02 -0.36 27.06 -0.07 28.01 -0.16 27.31 0.08 1963 4 24.67 -0.90 27.66 0.23 28.28 -0.11 27.87 0.20 1963 5 23.97 -0.45 27.10 0.00 28.40 -0.30 27.71 -0.06 1963 6 22.41 -0.66 26.74 0.27 28.38 -0.29 27.69 0.16 1963 7 21.80 -0.18 26.36 0.71 28.72 0.11 27.91 0.80 1963 8 21.31 0.30 25.80 0.74 29.01 0.51 27.63 0.88 1963 9 21.00 0.23 25.41 0.48 29.03 0.52 27.47 0.76 1963 10 21.13 0.06 25.58 0.63 29.07 0.56 27.56 0.92 1963 11 21.64 -0.10 25.83 0.78 29.11 0.66 27.61 1.00 1963 12 22.55 -0.35 26.08 0.87 28.87 0.52 27.71 1.14 1964 1 24.15 -0.39 26.07 0.42 28.70 0.55 27.43 0.87 1964 2 25.08 -0.83 26.41 0.04 28.39 0.31 27.27 0.53 1964 3 25.30 -1.08 26.76 -0.37 28.08 -0.09 27.10 -0.13 1964 4 24.61 -0.96 26.34 -1.09 28.24 -0.15 27.06 -0.60 1964 5 21.93 -2.49 25.56 -1.54 28.39 -0.30 26.94 -0.84 1964 6 21.44 -1.63 25.10 -1.37 28.06 -0.61 26.66 -0.87 1964 7 20.25 -1.72 24.82 -0.82 27.87 -0.74 26.42 -0.69 1964 8 19.48 -1.53 23.73 -1.33 27.64 -0.85 25.74 -1.01 1964 9 19.67 -1.10 23.89 -1.04 27.38 -1.13 25.49 -1.22 1964 10 19.79 -1.28 23.95 -0.99 27.38 -1.13 25.53 -1.11 1964 11 20.88 -0.86 24.04 -1.02 27.34 -1.11 25.40 -1.20 1964 12 21.83 -1.08 23.86 -1.35 27.25 -1.10 25.42 -1.15 1965 1 24.22 -0.32 24.84 -0.81 27.57 -0.59 25.78 -0.77 1965 2 26.17 0.26 25.96 -0.41 27.77 -0.31 26.37 -0.37 1965 3 26.71 0.33 27.07 -0.06 27.93 -0.24 27.12 -0.11 1965 4 27.01 1.45 27.66 0.23 28.06 -0.33 27.62 -0.05 1965 5 26.09 1.67 27.68 0.57 28.70 0.01 28.07 0.29 1965 6 24.60 1.54 27.24 0.78 29.02 0.35 28.19 0.66 1965 7 23.26 1.29 26.64 0.99 29.08 0.47 28.02 0.91 1965 8 22.54 1.53 26.25 1.20 29.19 0.70 28.07 1.32 1965 9 21.26 0.49 26.07 1.13 29.11 0.60 28.03 1.32 1965 10 21.57 0.50 26.15 1.21 29.30 0.80 28.26 1.62 1965 11 22.29 0.55 26.50 1.45 29.17 0.72 28.29 1.69 1965 12 23.35 0.44 26.59 1.38 29.03 0.68 28.07 1.50 1966 1 25.15 0.62 26.70 1.05 28.87 0.71 27.75 1.19 1966 2 25.88 -0.03 26.86 0.49 28.85 0.78 27.66 0.92 1966 3 25.35 -1.02 27.26 0.13 29.18 1.01 28.22 0.99 1966 4 24.26 -1.31 27.40 -0.03 28.99 0.60 28.24 0.58 1966 5 22.92 -1.50 26.28 -0.82 29.08 0.39 27.67 -0.10 1966 6 21.80 -1.27 26.08 -0.39 29.13 0.46 27.77 0.24 1966 7 20.85 -1.13 25.42 -0.22 29.03 0.42 27.42 0.31 1966 8 20.17 -0.84 24.51 -0.55 28.76 0.27 26.65 -0.10 1966 9 20.04 -0.73 24.17 -0.77 28.71 0.20 26.49 -0.22 1966 10 20.51 -0.56 24.42 -0.53 28.57 0.06 26.40 -0.25 1966 11 21.03 -0.71 24.26 -0.79 28.65 0.20 26.42 -0.19 1966 12 22.25 -0.66 24.30 -0.91 28.27 -0.07 26.21 -0.36 1967 1 23.66 -0.88 25.09 -0.56 27.69 -0.46 26.18 -0.38 1967 2 25.54 -0.37 26.09 -0.28 27.48 -0.60 26.35 -0.39 1967 3 25.55 -0.83 26.46 -0.67 27.78 -0.39 26.67 -0.56 1967 4 24.98 -0.59 26.46 -0.96 28.40 0.01 26.91 -0.76 1967 5 23.77 -0.65 26.69 -0.41 28.80 0.11 27.49 -0.28 1967 6 22.04 -1.03 26.40 -0.07 28.69 0.02 27.62 0.09 1967 7 21.10 -0.88 25.32 -0.32 28.62 0.01 27.17 0.06 1967 8 19.84 -1.17 24.30 -0.76 28.42 -0.07 26.62 -0.13 1967 9 19.08 -1.68 23.69 -1.25 28.19 -0.32 26.10 -0.60 1967 10 19.47 -1.60 23.80 -1.14 28.32 -0.19 26.19 -0.45 1967 11 20.20 -1.54 24.01 -1.04 28.43 -0.02 26.26 -0.34 1967 12 21.28 -1.62 24.14 -1.07 28.27 -0.08 26.10 -0.47 1968 1 23.19 -1.35 24.40 -1.25 27.92 -0.24 25.78 -0.78 1968 2 24.88 -1.04 25.00 -1.38 27.80 -0.28 25.79 -0.95 1968 3 25.11 -1.27 25.86 -1.27 27.87 -0.30 26.38 -0.85 1968 4 23.97 -1.60 26.57 -0.85 28.16 -0.24 27.09 -0.58 1968 5 22.44 -1.98 26.19 -0.92 28.30 -0.40 27.15 -0.62 1968 6 21.70 -1.36 26.22 -0.25 28.90 0.23 27.69 0.16 1968 7 21.25 -0.72 26.00 0.35 28.70 0.09 27.61 0.51 1968 8 20.97 -0.04 25.28 0.22 28.68 0.19 27.12 0.37 1968 9 21.23 0.46 24.96 0.02 28.66 0.15 26.90 0.19 1968 10 21.12 0.05 25.17 0.22 28.77 0.26 26.99 0.34 1968 11 21.68 -0.06 25.35 0.29 29.17 0.72 27.38 0.78 1968 12 23.20 0.29 25.79 0.58 29.17 0.83 27.42 0.85 1969 1 24.67 0.13 26.27 0.62 29.11 0.95 27.55 0.99 1969 2 25.56 -0.36 26.92 0.54 29.28 1.20 27.95 1.21 1969 3 27.09 0.72 27.63 0.50 28.99 0.82 28.02 0.79 1969 4 26.66 1.10 27.94 0.52 29.03 0.64 28.39 0.73 1969 5 26.07 1.65 27.92 0.81 29.21 0.52 28.50 0.73 1969 6 24.39 1.32 27.05 0.58 29.09 0.42 27.99 0.46 1969 7 22.47 0.50 25.84 0.19 28.85 0.24 27.30 0.20 1969 8 21.06 0.05 25.41 0.35 28.93 0.44 27.16 0.41 1969 9 20.88 0.12 25.46 0.52 29.14 0.63 27.34 0.63 1969 10 21.74 0.67 25.69 0.75 29.20 0.69 27.50 0.86 1969 11 22.47 0.73 25.75 0.70 29.20 0.75 27.35 0.74 1969 12 23.60 0.69 26.16 0.95 28.87 0.52 27.30 0.73 1970 1 25.02 0.48 26.38 0.73 28.57 0.42 27.05 0.50 1970 2 25.76 -0.16 26.52 0.14 28.57 0.50 27.02 0.29 1970 3 25.53 -0.85 26.97 -0.16 28.52 0.35 27.35 0.12 1970 4 24.76 -0.81 27.20 -0.23 28.73 0.34 27.96 0.29 1970 5 22.94 -1.48 26.44 -0.66 28.97 0.28 27.77 0.00 1970 6 21.27 -1.80 25.30 -1.17 28.75 0.08 27.14 -0.39 1970 7 19.69 -2.28 24.18 -1.47 28.66 0.05 26.48 -0.63 1970 8 19.27 -1.74 23.69 -1.37 28.16 -0.34 25.86 -0.89 1970 9 19.50 -1.26 23.89 -1.05 27.88 -0.64 25.86 -0.84 1970 10 20.16 -0.91 23.80 -1.14 27.86 -0.65 25.79 -0.85 1970 11 20.61 -1.13 23.78 -1.28 27.91 -0.54 25.83 -0.77 1970 12 21.77 -1.13 24.01 -1.20 27.44 -0.91 25.47 -1.10 1971 1 23.33 -1.21 24.19 -1.47 26.94 -1.21 25.09 -1.46 1971 2 24.58 -1.34 24.91 -1.47 27.07 -1.00 25.40 -1.34 1971 3 25.24 -1.13 26.01 -1.11 27.25 -0.92 26.10 -1.13 1971 4 24.95 -0.62 26.61 -0.81 27.63 -0.76 26.78 -0.89 1971 5 23.29 -1.13 26.26 -0.85 28.02 -0.67 27.06 -0.71 1971 6 21.60 -1.47 25.44 -1.03 28.03 -0.64 26.70 -0.83 1971 7 21.01 -0.96 24.78 -0.86 27.93 -0.68 26.29 -0.82 1971 8 19.97 -1.04 23.90 -1.16 27.84 -0.66 25.99 -0.76 1971 9 19.74 -1.03 23.92 -1.02 27.75 -0.77 25.94 -0.76 1971 10 19.88 -1.19 23.73 -1.21 27.80 -0.71 25.65 -0.99 1971 11 20.94 -0.80 23.93 -1.12 27.87 -0.58 25.69 -0.91 1971 12 21.99 -0.92 23.92 -1.29 27.98 -0.36 25.55 -1.02 1972 1 24.51 -0.03 25.02 -0.63 27.97 -0.19 25.84 -0.72 1972 2 26.66 0.75 26.04 -0.34 28.15 0.07 26.42 -0.32 1972 3 27.09 0.72 27.12 -0.01 28.36 0.19 27.21 -0.02 1972 4 26.25 0.68 27.78 0.35 28.82 0.43 27.93 0.26 1972 5 25.47 1.05 27.62 0.52 29.21 0.52 28.27 0.49 1972 6 25.01 1.95 27.37 0.90 29.19 0.52 28.23 0.70 1972 7 24.11 2.13 27.14 1.49 29.09 0.48 28.18 1.07 1972 8 23.42 2.41 26.86 1.81 28.92 0.43 28.10 1.35 1972 9 22.12 1.35 26.48 1.54 29.10 0.58 28.10 1.40 1972 10 22.58 1.51 26.83 1.89 29.44 0.93 28.46 1.82 1972 11 23.32 1.58 27.17 2.11 29.48 1.03 28.69 2.09 1972 12 24.89 1.99 27.60 2.39 29.35 1.00 28.81 2.24 1973 1 26.03 1.49 27.52 1.86 29.03 0.88 28.44 1.88 1973 2 26.48 0.56 27.24 0.87 28.77 0.70 28.00 1.26 1973 3 26.27 -0.10 27.37 0.24 28.52 0.35 27.71 0.48 1973 4 24.87 -0.70 26.87 -0.55 28.39 0.00 27.39 -0.28 1973 5 23.44 -0.98 26.06 -1.04 28.51 -0.18 27.13 -0.65 1973 6 21.76 -1.31 25.34 -1.12 28.23 -0.44 26.74 -0.79 1973 7 20.84 -1.14 24.31 -1.34 28.01 -0.60 25.95 -1.16 1973 8 19.47 -1.54 23.69 -1.36 27.65 -0.84 25.46 -1.29 1973 9 19.49 -1.28 23.56 -1.38 27.53 -0.98 25.32 -1.39 1973 10 19.80 -1.27 23.49 -1.46 27.32 -1.19 25.03 -1.61 1973 11 20.71 -1.03 23.35 -1.71 26.97 -1.48 24.50 -2.11 1973 12 21.74 -1.17 23.40 -1.81 26.69 -1.65 24.43 -2.14 1974 1 23.29 -1.25 23.93 -1.72 26.50 -1.65 24.52 -2.04 1974 2 24.87 -1.04 25.11 -1.27 26.87 -1.21 25.12 -1.61 1974 3 25.69 -0.68 26.28 -0.85 27.21 -0.96 25.91 -1.32 1974 4 25.28 -0.29 26.84 -0.58 27.46 -0.93 26.63 -1.03 1974 5 24.35 -0.07 26.56 -0.54 27.94 -0.75 26.84 -0.93 1974 6 22.48 -0.58 25.91 -0.55 27.97 -0.70 26.71 -0.82 1974 7 21.58 -0.40 25.30 -0.35 27.83 -0.78 26.48 -0.63 1974 8 20.73 -0.28 24.82 -0.24 27.97 -0.52 26.37 -0.38 1974 9 20.15 -0.62 24.38 -0.56 27.91 -0.61 26.23 -0.47 1974 10 19.88 -1.19 24.14 -0.81 27.74 -0.77 25.92 -0.73 1974 11 20.68 -1.06 24.07 -0.98 27.72 -0.73 25.63 -0.97 1974 12 21.41 -1.50 24.31 -0.90 27.61 -0.74 25.70 -0.87 1975 1 23.55 -0.99 25.34 -0.31 27.86 -0.30 26.18 -0.37 1975 2 24.95 -0.97 25.74 -0.64 27.96 -0.12 26.22 -0.52 1975 3 26.06 -0.32 26.49 -0.64 27.76 -0.41 26.44 -0.79 1975 4 25.53 -0.04 27.08 -0.34 27.83 -0.56 26.99 -0.67 1975 5 23.71 -0.72 26.27 -0.83 27.95 -0.74 26.97 -0.80 1975 6 21.84 -1.22 25.29 -1.18 27.71 -0.96 26.29 -1.24 1975 7 21.05 -0.92 24.72 -0.93 27.57 -1.04 25.98 -1.12 1975 8 19.97 -1.04 24.15 -0.91 27.29 -1.21 25.47 -1.28 1975 9 19.14 -1.63 23.67 -1.27 26.91 -1.60 25.20 -1.50 1975 10 19.17 -1.90 23.40 -1.54 26.76 -1.75 24.87 -1.77 1975 11 19.44 -2.30 23.73 -1.33 26.80 -1.66 25.10 -1.50 1975 12 21.05 -1.85 23.39 -1.82 26.84 -1.50 24.76 -1.81 1976 1 23.51 -1.02 23.91 -1.74 26.92 -1.23 24.72 -1.84 1976 2 25.36 -0.56 25.31 -1.07 27.19 -0.89 25.58 -1.16 1976 3 25.88 -0.49 26.46 -0.66 27.56 -0.61 26.61 -0.62 1976 4 25.72 0.15 26.94 -0.49 27.98 -0.42 26.99 -0.67 1976 5 25.11 0.69 26.98 -0.12 28.32 -0.37 27.27 -0.50 1976 6 24.46 1.39 26.95 0.48 28.32 -0.35 27.34 -0.19 1976 7 23.30 1.33 26.29 0.65 28.42 -0.19 27.26 0.16 1976 8 21.91 0.90 25.87 0.81 28.34 -0.15 27.09 0.34 1976 9 21.56 0.79 25.76 0.83 28.50 -0.01 27.12 0.42 1976 10 21.69 0.62 25.97 1.03 28.82 0.31 27.48 0.84 1976 11 22.14 0.40 25.93 0.87 28.92 0.47 27.42 0.82 1976 12 23.29 0.39 25.91 0.70 28.45 0.10 27.17 0.60 1977 1 24.93 0.39 26.57 0.92 28.38 0.23 27.31 0.76 1977 2 25.79 -0.13 27.03 0.65 28.11 0.04 27.15 0.41 1977 3 26.13 -0.24 27.51 0.38 28.28 0.10 27.57 0.34 1977 4 25.29 -0.28 27.02 -0.41 28.50 0.10 27.61 -0.05 1977 5 23.88 -0.54 27.04 -0.06 28.78 0.09 27.97 0.19 1977 6 22.70 -0.37 26.56 0.09 28.97 0.30 27.96 0.43 1977 7 21.63 -0.34 25.70 0.05 29.13 0.52 27.56 0.45 1977 8 20.25 -0.76 24.81 -0.25 28.87 0.38 26.93 0.18 1977 9 19.82 -0.95 24.97 0.04 28.98 0.47 27.21 0.50 1977 10 20.61 -0.46 25.34 0.39 28.96 0.45 27.37 0.73 1977 11 21.29 -0.45 25.41 0.35 29.10 0.65 27.28 0.67 1977 12 22.47 -0.44 25.54 0.33 29.11 0.76 27.37 0.80 1978 1 24.32 -0.22 25.92 0.27 28.80 0.65 27.32 0.77 1978 2 25.77 -0.15 26.46 0.09 28.48 0.41 27.17 0.43 1978 3 25.39 -0.98 26.83 -0.30 28.26 0.09 27.24 0.01 1978 4 24.73 -0.84 26.66 -0.77 28.28 -0.11 27.26 -0.41 1978 5 23.15 -1.27 26.13 -0.97 28.72 0.03 27.36 -0.42 1978 6 21.89 -1.18 25.68 -0.79 28.56 -0.11 27.16 -0.37 1978 7 21.01 -0.96 25.08 -0.57 28.26 -0.35 26.81 -0.29 1978 8 19.66 -1.35 24.35 -0.71 28.25 -0.24 26.23 -0.52 1978 9 19.98 -0.79 24.33 -0.61 28.43 -0.08 26.20 -0.50 1978 10 20.22 -0.86 24.72 -0.22 28.35 -0.16 26.40 -0.24 1978 11 21.62 -0.12 24.94 -0.11 28.37 -0.09 26.43 -0.17 1978 12 22.94 0.03 25.34 0.13 28.27 -0.08 26.48 -0.09 1979 1 24.71 0.17 25.43 -0.23 28.40 0.25 26.45 -0.11 1979 2 25.60 -0.32 26.19 -0.19 28.22 0.14 26.60 -0.13 1979 3 25.93 -0.44 27.25 0.12 28.26 0.09 27.48 0.25 1979 4 25.58 0.01 27.66 0.23 28.35 -0.05 27.87 0.20 1979 5 24.52 0.10 27.26 0.16 28.70 0.01 27.74 -0.03 1979 6 23.28 0.22 26.54 0.08 28.74 0.07 27.55 0.02 1979 7 21.79 -0.19 25.56 -0.09 28.66 0.05 26.95 -0.15 1979 8 21.05 0.04 25.29 0.23 28.36 -0.13 26.77 0.02 1979 9 21.15 0.39 25.58 0.65 28.67 0.16 27.15 0.45 1979 10 21.43 0.36 25.54 0.60 28.81 0.31 27.01 0.36 1979 11 21.95 0.21 25.58 0.53 28.87 0.42 27.08 0.48 1979 12 22.97 0.07 25.68 0.47 28.79 0.45 27.09 0.52 1980 1 24.35 -0.18 26.12 0.47 28.62 0.47 27.10 0.54 1980 2 25.73 -0.18 26.52 0.15 28.47 0.39 27.03 0.29 1980 3 26.46 0.08 27.05 -0.07 28.51 0.34 27.38 0.15 1980 4 25.71 0.14 27.33 -0.10 28.70 0.30 27.78 0.12 1980 5 24.46 0.04 27.15 0.05 29.08 0.39 27.99 0.21 1980 6 22.88 -0.19 26.76 0.29 29.15 0.48 27.99 0.46 1980 7 21.26 -0.71 25.65 0.00 28.95 0.34 27.35 0.24 1980 8 20.57 -0.44 24.87 -0.19 28.47 -0.02 26.62 -0.13 1980 9 20.45 -0.32 24.86 -0.08 28.50 -0.01 26.57 -0.13 1980 10 20.43 -0.64 24.62 -0.32 28.66 0.15 26.51 -0.13 1980 11 21.23 -0.51 25.07 0.02 28.58 0.13 26.63 0.03 1980 12 22.34 -0.56 25.28 0.07 28.44 0.10 26.58 0.01 1981 1 22.98 -1.56 25.05 -0.61 28.08 -0.08 26.17 -0.39 1981 2 24.90 -1.01 25.63 -0.75 27.94 -0.14 26.13 -0.60 1981 3 25.94 -0.43 26.74 -0.39 28.08 -0.09 26.75 -0.48 1981 4 24.89 -0.68 27.10 -0.32 28.17 -0.22 27.32 -0.34 1981 5 23.90 -0.52 26.74 -0.37 28.34 -0.35 27.41 -0.36 1981 6 22.57 -0.50 26.26 -0.20 28.36 -0.31 27.35 -0.18 1981 7 21.10 -0.87 25.26 -0.39 28.29 -0.32 26.66 -0.44 1981 8 20.03 -0.98 24.43 -0.63 28.22 -0.28 26.25 -0.50 1981 9 20.09 -0.68 24.74 -0.20 28.30 -0.22 26.54 -0.17 1981 10 20.58 -0.49 24.92 -0.03 28.45 -0.06 26.52 -0.12 1981 11 21.26 -0.48 24.83 -0.22 28.47 0.02 26.41 -0.19 1981 12 22.60 -0.30 25.23 0.03 28.43 0.09 26.47 -0.10 1982 1 24.36 -0.18 25.96 0.30 28.19 0.03 26.69 0.14 1982 2 25.42 -0.49 26.55 0.17 28.04 -0.04 26.71 -0.02 1982 3 25.40 -0.98 27.06 -0.07 28.37 0.19 27.36 0.13 1982 4 24.96 -0.61 27.52 0.10 28.78 0.39 27.90 0.24 1982 5 24.21 -0.21 27.66 0.56 29.21 0.52 28.42 0.65 1982 6 23.35 0.29 27.31 0.84 29.20 0.53 28.32 0.79 1982 7 22.50 0.52 26.33 0.68 28.83 0.22 27.65 0.54 1982 8 21.89 0.88 26.21 1.15 28.81 0.32 27.64 0.89 1982 9 22.04 1.27 26.82 1.88 28.98 0.47 28.21 1.50 1982 10 22.88 1.81 27.31 2.37 29.37 0.86 28.68 2.04 1982 11 24.57 2.83 27.68 2.63 29.18 0.73 28.72 2.11 1982 12 25.89 2.98 28.23 3.02 29.13 0.79 28.94 2.37 1983 1 27.25 2.71 28.60 2.95 28.96 0.81 28.93 2.37 1983 2 28.23 2.32 28.63 2.26 28.80 0.73 28.75 2.01 1983 3 28.85 2.48 28.91 1.78 28.81 0.64 28.76 1.53 1983 4 28.82 3.25 29.06 1.63 28.81 0.42 28.74 1.07 1983 5 28.37 3.95 28.98 1.87 29.21 0.51 28.82 1.05 1983 6 27.43 4.36 28.19 1.72 28.98 0.31 28.27 0.74 1983 7 25.73 3.75 26.66 1.01 28.64 0.03 27.18 0.07 1983 8 23.88 2.87 25.78 0.72 28.35 -0.14 26.51 -0.24 1983 9 22.26 1.49 25.02 0.09 28.05 -0.46 26.18 -0.52 1983 10 22.22 1.15 24.48 -0.46 27.92 -0.59 25.75 -0.89 1983 11 22.21 0.47 24.19 -0.86 27.73 -0.73 25.54 -1.06 1983 12 23.19 0.29 24.58 -0.63 27.75 -0.59 25.82 -0.75 1984 1 24.32 -0.21 25.30 -0.35 27.64 -0.51 26.14 -0.42 1984 2 25.12 -0.79 26.43 0.05 27.60 -0.48 26.72 -0.02 1984 3 25.75 -0.63 27.14 0.01 27.59 -0.58 27.05 -0.19 1984 4 25.40 -0.17 27.24 -0.18 27.78 -0.61 27.30 -0.37 1984 5 23.58 -0.84 26.38 -0.72 28.19 -0.51 27.31 -0.47 1984 6 22.30 -0.77 25.50 -0.97 28.38 -0.29 26.95 -0.58 1984 7 21.53 -0.44 25.04 -0.60 28.47 -0.14 26.84 -0.26 1984 8 20.64 -0.37 24.81 -0.25 28.30 -0.19 26.67 -0.08 1984 9 20.73 -0.04 24.63 -0.30 28.26 -0.25 26.43 -0.27 1984 10 20.62 -0.45 24.34 -0.61 28.19 -0.32 26.15 -0.49 1984 11 21.70 -0.04 24.23 -0.83 27.92 -0.53 25.60 -1.00 1984 12 22.47 -0.44 24.10 -1.11 27.60 -0.74 25.38 -1.19 1985 1 23.84 -0.70 24.68 -0.97 27.55 -0.60 25.58 -0.98 1985 2 24.83 -1.08 25.65 -0.72 27.68 -0.39 26.11 -0.63 1985 3 25.60 -0.77 26.45 -0.68 27.59 -0.58 26.53 -0.71 1985 4 24.28 -1.29 26.63 -0.79 27.78 -0.61 26.93 -0.74 1985 5 22.67 -1.75 26.26 -0.84 27.99 -0.70 27.09 -0.68 1985 6 21.84 -1.23 25.66 -0.81 28.09 -0.58 26.92 -0.61 1985 7 20.75 -1.23 24.72 -0.93 28.32 -0.30 26.64 -0.46 1985 8 19.90 -1.11 24.12 -0.94 28.34 -0.16 26.28 -0.47 1985 9 19.86 -0.91 24.05 -0.88 28.32 -0.20 26.08 -0.62 1985 10 20.26 -0.81 24.23 -0.71 28.40 -0.11 26.22 -0.42 1985 11 20.97 -0.77 24.40 -0.65 28.48 0.03 26.39 -0.22 1985 12 22.49 -0.41 24.56 -0.65 28.39 0.05 26.19 -0.38 1986 1 24.31 -0.23 24.99 -0.67 27.96 -0.19 26.04 -0.52 1986 2 25.90 -0.02 26.04 -0.33 27.95 -0.13 26.26 -0.48 1986 3 25.78 -0.59 26.92 -0.21 28.11 -0.06 26.99 -0.24 1986 4 24.86 -0.71 27.30 -0.13 28.23 -0.17 27.65 -0.02 1986 5 23.35 -1.07 26.78 -0.32 28.53 -0.17 27.58 -0.20 1986 6 22.03 -1.04 26.27 -0.20 28.76 0.09 27.56 0.03 1986 7 21.64 -0.33 25.82 0.18 28.75 0.14 27.39 0.28 1986 8 21.07 0.06 25.38 0.33 28.95 0.46 27.21 0.46 1986 9 21.13 0.36 25.38 0.44 29.20 0.69 27.35 0.65 1986 10 21.46 0.39 25.65 0.70 29.27 0.76 27.60 0.95 1986 11 22.17 0.43 25.94 0.88 29.33 0.88 27.67 1.07 1986 12 23.53 0.63 26.26 1.05 28.97 0.63 27.75 1.18 1987 1 25.60 1.07 26.74 1.09 28.81 0.65 27.82 1.27 1987 2 27.02 1.10 27.60 1.23 28.82 0.74 28.02 1.29 1987 3 27.89 1.51 28.38 1.26 28.95 0.77 28.49 1.26 1987 4 26.95 1.38 28.63 1.20 28.97 0.58 28.68 1.02 1987 5 25.96 1.53 28.30 1.19 29.24 0.55 28.70 0.93 1987 6 24.04 0.97 27.51 1.04 29.44 0.77 28.67 1.14 1987 7 23.00 1.03 26.94 1.30 29.37 0.76 28.52 1.42 1987 8 21.92 0.91 26.59 1.53 29.40 0.91 28.48 1.73 1987 9 22.00 1.23 26.62 1.68 29.47 0.96 28.42 1.71 1987 10 22.54 1.47 26.19 1.25 29.67 1.17 28.08 1.43 1987 11 22.84 1.10 26.21 1.16 29.53 1.08 27.94 1.34 1987 12 23.51 0.60 26.33 1.12 29.25 0.90 27.60 1.03 1988 1 24.76 0.22 26.47 0.82 28.97 0.81 27.49 0.94 1988 2 25.74 -0.18 26.43 0.05 28.54 0.46 27.01 0.28 1988 3 25.71 -0.66 27.10 -0.03 28.46 0.29 27.45 0.22 1988 4 24.68 -0.89 27.01 -0.41 28.41 0.02 27.56 -0.10 1988 5 23.18 -1.24 25.88 -1.22 28.26 -0.43 26.97 -0.80 1988 6 21.66 -1.41 24.61 -1.86 28.00 -0.67 26.21 -1.32 1988 7 20.59 -1.38 23.79 -1.85 27.95 -0.67 25.66 -1.45 1988 8 19.63 -1.38 23.71 -1.35 28.07 -0.43 25.71 -1.04 1988 9 19.44 -1.32 23.88 -1.06 27.90 -0.61 25.72 -0.99 1988 10 19.83 -1.24 23.41 -1.53 27.12 -1.39 24.82 -1.82 1988 11 20.96 -0.78 23.45 -1.61 27.06 -1.39 24.73 -1.87 1988 12 22.25 -0.66 23.50 -1.71 26.85 -1.49 24.68 -1.89 1989 1 24.36 -0.18 24.27 -1.38 26.63 -1.52 24.70 -1.86 1989 2 26.02 0.10 25.49 -0.89 26.75 -1.33 25.34 -1.40 1989 3 26.21 -0.17 26.23 -0.90 27.25 -0.93 26.12 -1.12 1989 4 25.54 -0.03 26.85 -0.57 27.71 -0.68 26.83 -0.83 1989 5 23.36 -1.06 26.58 -0.53 28.24 -0.46 27.18 -0.60 1989 6 22.14 -0.93 26.42 -0.05 28.12 -0.55 27.23 -0.30 1989 7 21.27 -0.70 25.32 -0.32 28.23 -0.38 26.80 -0.31 1989 8 20.86 -0.15 24.73 -0.33 28.10 -0.39 26.43 -0.32 1989 9 20.17 -0.60 24.67 -0.27 28.37 -0.14 26.46 -0.24 1989 10 20.52 -0.55 24.61 -0.34 28.27 -0.24 26.31 -0.34 1989 11 21.44 -0.30 24.56 -0.49 28.10 -0.36 26.29 -0.31 1989 12 22.61 -0.30 24.92 -0.29 28.51 0.17 26.58 0.01 1990 1 24.22 -0.32 25.45 -0.20 28.49 0.33 26.63 0.07 1990 2 26.17 0.26 26.54 0.16 28.58 0.50 27.03 0.29 1990 3 26.15 -0.22 27.01 -0.12 28.69 0.51 27.39 0.16 1990 4 25.15 -0.42 27.56 0.14 28.83 0.44 27.94 0.27 1990 5 24.14 -0.29 27.42 0.32 28.93 0.23 28.08 0.30 1990 6 22.76 -0.31 26.55 0.08 28.97 0.30 27.63 0.10 1990 7 21.36 -0.61 25.82 0.18 29.01 0.40 27.42 0.31 1990 8 20.70 -0.31 25.32 0.26 28.99 0.49 27.16 0.41 1990 9 20.28 -0.49 25.15 0.21 28.92 0.41 26.96 0.25 1990 10 20.40 -0.67 24.96 0.02 29.10 0.59 27.01 0.37 1990 11 21.19 -0.55 25.00 -0.06 29.13 0.68 26.88 0.28 1990 12 22.29 -0.61 25.23 0.02 29.16 0.81 26.96 0.39 1991 1 23.99 -0.55 25.84 0.19 28.96 0.81 27.07 0.51 1991 2 25.59 -0.33 26.50 0.12 28.71 0.63 27.12 0.38 1991 3 26.31 -0.06 27.12 -0.01 28.58 0.40 27.38 0.15 1991 4 25.15 -0.42 27.65 0.22 28.94 0.55 28.10 0.44 1991 5 24.44 0.02 27.64 0.54 29.37 0.68 28.36 0.58 1991 6 23.28 0.21 27.43 0.96 29.28 0.61 28.41 0.88 1991 7 22.39 0.42 26.75 1.10 29.27 0.66 28.17 1.07 1991 8 21.39 0.38 25.71 0.65 29.23 0.74 27.73 0.98 1991 9 21.22 0.45 25.32 0.39 29.24 0.73 27.42 0.71 1991 10 21.73 0.66 25.63 0.69 29.44 0.93 27.62 0.98 1991 11 22.40 0.66 26.10 1.04 29.40 0.95 27.93 1.33 1991 12 23.75 0.85 26.42 1.21 29.46 1.12 28.32 1.75 1992 1 25.02 0.48 27.03 1.38 29.03 0.87 28.36 1.81 1992 2 26.62 0.71 27.61 1.23 29.00 0.92 28.43 1.69 1992 3 27.72 1.34 28.22 1.09 29.03 0.86 28.66 1.42 1992 4 27.58 2.01 28.79 1.37 29.16 0.77 29.05 1.39 1992 5 26.44 2.02 28.49 1.38 29.39 0.70 29.01 1.24 1992 6 23.86 0.79 27.28 0.82 29.28 0.60 28.35 0.82 1992 7 21.84 -0.14 25.84 0.19 29.15 0.54 27.56 0.45 1992 8 20.87 -0.14 25.11 0.06 28.92 0.43 26.96 0.21 1992 9 20.85 0.08 24.90 -0.03 28.83 0.32 26.66 -0.04 1992 10 21.15 0.08 24.65 -0.29 28.69 0.18 26.39 -0.25 1992 11 21.84 0.10 24.77 -0.29 28.67 0.21 26.60 0.00 1992 12 22.79 -0.12 24.97 -0.24 28.82 0.47 26.72 0.15 1993 1 24.68 0.15 25.79 0.14 28.71 0.56 26.87 0.31 1993 2 26.46 0.55 26.94 0.57 28.37 0.29 27.20 0.46 1993 3 27.07 0.69 27.64 0.51 28.50 0.32 27.71 0.48 1993 4 26.84 1.28 28.43 1.00 28.78 0.38 28.50 0.83 1993 5 25.60 1.18 28.33 1.23 29.03 0.34 28.70 0.93 1993 6 24.11 1.04 27.03 0.56 29.03 0.36 28.08 0.55 1993 7 22.61 0.64 26.19 0.54 29.01 0.40 27.59 0.49 1993 8 21.65 0.64 25.52 0.46 28.86 0.37 27.01 0.26 1993 9 21.11 0.34 25.25 0.31 29.02 0.51 27.14 0.43 1993 10 21.71 0.64 25.28 0.33 28.84 0.33 27.01 0.36 1993 11 22.07 0.33 25.20 0.14 28.88 0.43 26.92 0.32 1993 12 22.86 -0.05 25.30 0.09 28.85 0.50 26.79 0.22 1994 1 24.56 0.02 25.84 0.18 28.54 0.39 26.74 0.19 1994 2 25.89 -0.03 26.40 0.02 28.27 0.20 26.97 0.23 1994 3 25.75 -0.62 26.88 -0.24 28.46 0.28 27.52 0.29 1994 4 24.49 -1.08 27.15 -0.28 28.82 0.43 28.13 0.46 1994 5 23.52 -0.90 27.17 0.06 29.20 0.51 28.27 0.50 1994 6 22.31 -0.76 26.63 0.17 29.27 0.60 28.09 0.56 1994 7 21.17 -0.80 25.61 -0.04 29.49 0.88 27.68 0.57 1994 8 20.22 -0.79 24.93 -0.13 29.51 1.02 27.40 0.65 1994 9 20.65 -0.12 24.97 0.03 29.38 0.87 27.25 0.54 1994 10 22.04 0.97 25.65 0.70 29.51 1.00 27.53 0.89 1994 11 22.27 0.53 26.17 1.12 29.60 1.15 27.95 1.35 1994 12 23.75 0.85 26.23 1.02 29.56 1.22 28.02 1.45 1995 1 25.48 0.94 26.51 0.86 29.24 1.09 27.74 1.18 1995 2 26.25 0.33 26.90 0.52 29.16 1.09 27.67 0.94 1995 3 26.09 -0.28 27.26 0.13 29.23 1.05 27.91 0.68 1995 4 24.32 -1.25 27.20 -0.23 29.26 0.87 28.17 0.50 1995 5 23.37 -1.05 26.55 -0.55 29.36 0.67 27.87 0.10 1995 6 22.43 -0.64 26.30 -0.17 29.21 0.54 27.80 0.27 1995 7 21.42 -0.55 25.65 0.00 29.03 0.42 27.24 0.14 1995 8 20.46 -0.55 24.36 -0.70 28.81 0.32 26.42 -0.33 1995 9 20.50 -0.27 24.05 -0.89 28.59 0.08 26.20 -0.50 1995 10 20.62 -0.45 24.16 -0.78 28.52 0.01 26.08 -0.57 1995 11 21.49 -0.25 24.22 -0.84 28.32 -0.13 25.82 -0.78 1995 12 22.03 -0.87 24.45 -0.76 28.13 -0.22 25.86 -0.71 1996 1 23.81 -0.73 25.06 -0.59 27.89 -0.27 25.83 -0.73 1996 2 25.52 -0.40 25.84 -0.54 27.61 -0.46 25.98 -0.76 1996 3 26.28 -0.09 26.75 -0.38 27.91 -0.27 26.73 -0.50 1996 4 24.00 -1.57 26.83 -0.59 28.25 -0.15 27.42 -0.25 1996 5 23.11 -1.31 26.63 -0.47 28.62 -0.07 27.65 -0.12 1996 6 21.66 -1.41 26.10 -0.37 28.71 0.04 27.49 -0.04 1996 7 20.72 -1.26 25.29 -0.36 28.65 0.04 27.02 -0.09 1996 8 20.23 -0.78 24.78 -0.28 28.62 0.12 26.75 0.00 1996 9 20.43 -0.34 24.53 -0.41 28.57 0.05 26.44 -0.27 1996 10 20.52 -0.55 24.52 -0.42 28.62 0.11 26.49 -0.15 1996 11 20.77 -0.97 24.56 -0.49 28.62 0.17 26.43 -0.17 1996 12 21.68 -1.22 24.31 -0.90 28.52 0.18 26.13 -0.44 1997 1 23.70 -0.83 24.80 -0.85 28.42 0.26 26.09 -0.47 1997 2 26.08 0.16 25.78 -0.60 28.53 0.45 26.46 -0.28 1997 3 27.17 0.80 26.97 -0.16 28.73 0.56 27.13 -0.10 1997 4 26.74 1.17 27.50 0.07 29.33 0.94 27.97 0.31 1997 5 26.77 2.35 28.03 0.92 29.51 0.82 28.63 0.85 1997 6 26.15 3.08 28.23 1.76 29.37 0.70 28.86 1.33 1997 7 25.59 3.61 27.99 2.34 29.41 0.80 28.86 1.76 1997 8 24.95 3.94 27.75 2.69 29.31 0.82 28.69 1.94 1997 9 24.69 3.92 27.82 2.88 29.54 1.03 28.89 2.19 1997 10 24.64 3.57 28.09 3.15 29.51 1.00 29.14 2.50 1997 11 25.85 4.11 28.40 3.35 29.45 1.00 29.13 2.52 1997 12 27.08 4.18 28.53 3.32 29.27 0.93 29.04 2.48 1998 1 28.12 3.58 28.71 3.06 29.06 0.91 28.98 2.43 1998 2 28.82 2.90 28.86 2.48 28.90 0.82 28.71 1.97 1998 3 29.24 2.87 29.10 1.97 28.83 0.66 28.66 1.43 1998 4 28.45 2.88 29.16 1.74 28.77 0.38 28.64 0.98 1998 5 27.36 2.94 28.53 1.42 28.87 0.18 28.47 0.70 1998 6 25.19 2.12 27.04 0.57 28.46 -0.21 27.41 -0.12 1998 7 23.61 1.64 25.60 -0.05 28.30 -0.31 26.52 -0.59 1998 8 22.27 1.26 24.78 -0.28 27.99 -0.50 25.91 -0.84 1998 9 21.31 0.54 24.19 -0.75 27.83 -0.68 25.66 -1.05 1998 10 21.37 0.30 24.08 -0.86 27.51 -1.00 25.46 -1.19 1998 11 21.60 -0.14 24.40 -0.66 27.41 -1.04 25.48 -1.12 1998 12 22.81 -0.10 24.25 -0.96 27.19 -1.16 25.12 -1.45 1999 1 24.23 -0.31 24.41 -1.24 26.89 -1.26 24.96 -1.59 1999 2 25.73 -0.19 25.56 -0.82 26.90 -1.18 25.58 -1.16 1999 3 26.47 0.10 26.81 -0.32 27.14 -1.04 26.43 -0.80 1999 4 24.53 -1.04 26.90 -0.52 27.66 -0.73 26.92 -0.75 1999 5 23.64 -0.78 26.55 -0.56 28.14 -0.55 26.99 -0.78 1999 6 22.09 -0.98 25.89 -0.58 28.05 -0.62 26.66 -0.87 1999 7 21.36 -0.61 25.03 -0.62 27.89 -0.72 26.28 -0.83 1999 8 20.67 -0.34 24.36 -0.70 27.77 -0.73 25.82 -0.93 1999 9 20.08 -0.69 23.91 -1.03 27.96 -0.56 25.77 -0.94 1999 10 20.46 -0.61 23.77 -1.18 27.93 -0.58 25.62 -1.03 1999 11 20.62 -1.12 23.72 -1.34 27.54 -0.91 25.20 -1.40 1999 12 22.42 -0.48 23.76 -1.45 27.30 -1.05 24.97 -1.60 2000 1 24.01 -0.53 24.12 -1.53 27.17 -0.99 24.88 -1.68 2000 2 25.38 -0.54 25.35 -1.03 26.88 -1.20 25.23 -1.50 2000 3 25.67 -0.70 26.78 -0.35 26.95 -1.22 26.27 -0.96 2000 4 25.53 -0.04 27.46 0.04 27.40 -0.99 26.99 -0.68 2000 5 24.27 -0.15 26.85 -0.26 27.90 -0.79 27.10 -0.67 2000 6 22.93 -0.13 26.01 -0.46 28.25 -0.42 26.97 -0.56 2000 7 21.47 -0.50 25.24 -0.41 28.41 -0.20 26.69 -0.41 2000 8 20.07 -0.94 24.74 -0.31 28.28 -0.21 26.46 -0.29 2000 9 20.64 -0.13 24.73 -0.21 28.37 -0.14 26.32 -0.39 2000 10 20.90 -0.17 24.60 -0.34 28.27 -0.24 26.11 -0.53 2000 11 20.67 -1.07 24.43 -0.62 28.06 -0.39 26.01 -0.59 2000 12 22.08 -0.83 24.73 -0.48 27.66 -0.68 25.83 -0.74 2001 1 24.24 -0.29 25.37 -0.29 27.49 -0.66 25.93 -0.63 2001 2 26.11 0.20 26.38 0.01 27.38 -0.70 26.24 -0.49 2001 3 26.89 0.52 27.31 0.18 27.68 -0.50 26.89 -0.35 2001 4 25.99 0.42 27.52 0.09 28.16 -0.23 27.38 -0.28 2001 5 23.98 -0.44 27.21 0.11 28.65 -0.04 27.70 -0.08 2001 6 22.71 -0.36 26.44 -0.03 28.91 0.24 27.60 0.07 2001 7 21.48 -0.50 25.63 -0.02 29.12 0.51 27.37 0.26 2001 8 20.24 -0.77 25.03 -0.03 28.98 0.48 26.95 0.20 2001 9 19.73 -1.04 24.49 -0.45 29.11 0.60 26.74 0.04 2001 10 20.14 -0.93 24.59 -0.36 29.08 0.58 26.66 0.02 2001 11 20.68 -1.06 24.53 -0.53 28.93 0.48 26.47 -0.13 2001 12 21.73 -1.17 24.79 -0.42 28.77 0.42 26.32 -0.25 2002 1 24.09 -0.45 25.23 -0.42 28.84 0.69 26.49 -0.07 2002 2 26.23 0.31 26.22 -0.15 28.70 0.63 26.83 0.09 2002 3 27.39 1.01 27.51 0.38 28.62 0.44 27.48 0.25 2002 4 26.44 0.87 27.71 0.28 29.14 0.75 28.00 0.34 2002 5 25.29 0.87 27.68 0.58 29.61 0.92 28.44 0.66 2002 6 23.28 0.21 27.30 0.83 29.58 0.91 28.48 0.95 2002 7 21.64 -0.34 26.31 0.67 29.53 0.92 28.03 0.93 2002 8 21.32 0.31 25.62 0.56 29.41 0.92 27.67 0.92 2002 9 21.42 0.65 25.69 0.75 29.41 0.90 27.75 1.05 2002 10 21.85 0.78 25.94 1.00 29.52 1.01 27.95 1.31 2002 11 22.85 1.11 26.43 1.37 29.66 1.21 28.14 1.54 2002 12 24.05 1.15 26.62 1.41 29.57 1.23 28.08 1.52 2003 1 25.01 0.47 26.68 1.02 29.09 0.94 27.68 1.12 2003 2 26.27 0.35 27.01 0.63 28.94 0.86 27.63 0.89 2003 3 26.91 0.53 27.48 0.35 28.95 0.78 27.84 0.61 2003 4 25.41 -0.15 27.22 -0.20 28.94 0.55 27.75 0.08 2003 5 23.24 -1.18 26.44 -0.66 29.01 0.32 27.42 -0.36 2003 6 22.15 -0.91 26.20 -0.27 29.17 0.50 27.56 0.03 2003 7 21.50 -0.48 26.16 0.52 29.19 0.58 27.66 0.55 2003 8 21.25 0.24 25.65 0.59 29.09 0.59 27.32 0.57 2003 9 20.75 -0.02 25.20 0.26 29.05 0.54 27.10 0.40 2003 10 21.70 0.63 25.58 0.63 29.22 0.71 27.33 0.69 2003 11 22.33 0.59 25.85 0.80 29.08 0.62 27.13 0.53 2003 12 23.60 0.70 26.07 0.86 28.97 0.63 27.04 0.47 2004 1 25.09 0.55 26.23 0.58 28.71 0.56 26.90 0.35 2004 2 26.47 0.55 26.81 0.44 28.61 0.53 27.04 0.31 2004 3 26.12 -0.26 27.47 0.34 28.53 0.36 27.38 0.15 2004 4 25.27 -0.30 27.62 0.19 28.82 0.43 27.91 0.24 2004 5 23.44 -0.98 26.96 -0.14 29.18 0.49 28.02 0.24 2004 6 22.54 -0.53 26.55 0.08 29.24 0.57 27.93 0.40 2004 7 21.26 -0.72 25.94 0.30 29.36 0.75 27.86 0.75 2004 8 20.79 -0.22 25.47 0.41 29.47 0.98 27.67 0.92 2004 9 20.83 0.06 25.42 0.48 29.54 1.02 27.58 0.88 2004 10 21.56 0.49 25.64 0.70 29.53 1.03 27.53 0.89 2004 11 22.88 1.14 25.84 0.79 29.49 1.04 27.37 0.77 2004 12 23.39 0.49 25.95 0.74 29.41 1.07 27.38 0.81 2005 1 24.61 0.07 26.10 0.45 29.23 1.08 27.32 0.76 2005 2 25.09 -0.83 26.38 0.00 28.91 0.83 27.17 0.43 2005 3 25.23 -1.14 27.12 -0.01 28.89 0.71 27.63 0.40 2005 4 25.21 -0.36 27.62 0.20 29.03 0.64 28.02 0.36 2005 5 24.31 -0.11 27.56 0.46 29.24 0.55 28.30 0.52 2005 6 22.60 -0.47 26.86 0.39 29.20 0.53 27.99 0.46 2005 7 21.61 -0.37 26.07 0.42 28.93 0.32 27.45 0.34 2005 8 20.47 -0.54 25.44 0.38 28.78 0.29 27.11 0.36 2005 9 20.00 -0.77 24.88 -0.05 28.85 0.34 26.79 0.09 2005 10 19.89 -1.18 24.83 -0.12 28.85 0.34 26.70 0.06 2005 11 20.61 -1.13 23.92 -1.14 28.65 0.19 26.13 -0.48 2005 12 22.20 -0.70 24.01 -1.20 28.34 0.00 25.80 -0.77 2006 1 24.76 0.22 24.66 -0.99 27.91 -0.25 25.68 -0.87 2006 2 26.52 0.60 26.02 -0.35 27.58 -0.50 26.15 -0.59 2006 3 26.22 -0.15 26.83 -0.30 27.82 -0.35 26.80 -0.43 2006 4 24.29 -1.28 27.18 -0.24 28.36 -0.04 27.54 -0.13 2006 5 23.84 -0.58 27.30 0.19 28.91 0.21 27.91 0.13 2006 6 22.82 -0.24 26.73 0.27 29.15 0.48 27.82 0.29 2006 7 22.20 0.22 25.93 0.28 29.14 0.53 27.36 0.25 2006 8 21.89 0.88 25.68 0.62 29.20 0.71 27.25 0.50 2006 9 21.93 1.16 25.77 0.83 29.30 0.79 27.32 0.61 2006 10 22.46 1.39 26.00 1.06 29.43 0.92 27.47 0.83 2006 11 22.61 0.87 26.39 1.33 29.55 1.09 27.81 1.21 2006 12 24.15 1.24 26.63 1.42 29.45 1.11 27.86 1.29 2007 1 25.82 1.28 26.68 1.03 28.98 0.82 27.36 0.81 2007 2 26.81 0.90 26.56 0.18 28.69 0.61 26.98 0.24 2007 3 26.41 0.04 26.77 -0.36 28.81 0.64 27.25 0.02 2007 4 24.96 -0.61 26.93 -0.50 28.88 0.49 27.56 -0.10 2007 5 23.05 -1.37 26.40 -0.70 28.90 0.21 27.54 -0.23 2007 6 21.61 -1.46 26.11 -0.35 28.92 0.25 27.54 0.01 2007 7 21.05 -0.93 25.14 -0.51 28.80 0.19 26.99 -0.12 2007 8 19.95 -1.06 24.24 -0.82 28.57 0.08 26.41 -0.34 2007 9 19.85 -0.91 23.84 -1.10 28.21 -0.31 25.86 -0.84 2007 10 19.31 -1.76 23.85 -1.09 28.09 -0.42 25.73 -0.92 2007 11 19.82 -1.92 23.76 -1.30 27.90 -0.56 25.47 -1.14 2007 12 21.15 -1.76 23.91 -1.30 27.70 -0.64 25.40 -1.17 2008 1 24.24 -0.30 24.42 -1.23 27.18 -0.98 25.06 -1.50 2008 2 26.39 0.47 25.34 -1.04 26.79 -1.29 25.19 -1.55 2008 3 26.91 0.53 26.54 -0.59 27.22 -0.95 26.16 -1.07 2008 4 25.68 0.12 27.36 -0.07 27.53 -0.86 26.97 -0.70 2008 5 24.43 0.00 27.15 0.05 27.93 -0.76 27.19 -0.58 2008 6 23.19 0.12 26.49 0.02 28.10 -0.57 27.15 -0.38 2008 7 23.02 1.05 26.01 0.36 28.18 -0.43 27.00 -0.11 2008 8 22.14 1.13 25.56 0.51 28.27 -0.22 26.81 0.06 2008 9 21.60 0.84 25.36 0.42 28.25 -0.27 26.70 0.00 2008 10 21.39 0.32 25.48 0.53 28.23 -0.28 26.66 0.02 2008 11 21.54 -0.20 25.25 0.20 28.16 -0.29 26.52 -0.08 2008 12 22.73 -0.18 24.59 -0.62 27.83 -0.52 25.78 -0.79 2009 1 24.39 -0.15 25.26 -0.39 27.47 -0.69 25.69 -0.87 2009 2 25.53 -0.38 26.16 -0.22 27.34 -0.74 26.02 -0.71 2009 3 25.48 -0.89 26.62 -0.51 27.85 -0.32 26.66 -0.57 2009 4 25.84 0.27 27.38 -0.04 28.36 -0.03 27.53 -0.13 2009 5 24.95 0.52 27.57 0.47 29.09 0.40 28.10 0.33 2009 6 24.09 1.02 27.15 0.68 29.15 0.48 28.06 0.53 2009 7 23.09 1.12 26.56 0.91 29.13 0.52 27.88 0.78 2009 8 22.03 1.02 25.90 0.84 29.20 0.71 27.51 0.76 2009 9 21.48 0.71 25.74 0.80 29.24 0.73 27.48 0.78 2009 10 21.64 0.57 25.82 0.87 29.68 1.17 27.73 1.09 2009 11 21.99 0.25 26.13 1.07 29.90 1.44 28.17 1.57 2009 12 23.21 0.31 26.69 1.48 29.80 1.45 28.51 1.94 2010 1 24.70 0.17 26.86 1.21 29.58 1.42 28.32 1.76 2010 2 26.16 0.24 27.37 1.00 29.25 1.18 28.19 1.45 2010 3 26.54 0.16 28.04 0.91 29.18 1.01 28.46 1.23 2010 4 26.04 0.47 28.08 0.66 29.28 0.89 28.49 0.82 2010 5 24.75 0.33 27.34 0.24 29.27 0.57 28.13 0.36 2010 6 23.26 0.19 26.32 -0.15 28.76 0.09 27.35 -0.18 2010 7 21.11 -0.87 24.95 -0.70 28.33 -0.28 26.44 -0.67 2010 8 19.49 -1.52 24.21 -0.85 27.82 -0.68 25.70 -1.05 2010 9 19.28 -1.49 23.83 -1.11 27.47 -1.05 25.36 -1.34 2010 10 19.73 -1.34 23.67 -1.28 27.35 -1.16 25.25 -1.40 2010 11 20.44 -1.30 23.68 -1.37 27.47 -0.99 25.20 -1.41 2010 12 22.07 -0.83 24.00 -1.21 27.54 -0.81 25.29 -1.28 statsmodels-0.12.2/statsmodels/datasets/engel/000077500000000000000000000000001400612667500214115ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/engel/__init__.py000066400000000000000000000003261400612667500235230ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/engel/data.py000066400000000000000000000031171400612667500226760ustar00rootroot00000000000000"""Name of dataset.""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This is public domain.""" TITLE = """Engel (1857) food expenditure data""" SOURCE = """ This dataset was used in Koenker and Bassett (1982) and distributed alongside the ``quantreg`` package for R. Koenker, R. and Bassett, G (1982) Robust Tests of Heteroscedasticity based on Regression Quantiles; Econometrica 50, 43-61. Roger Koenker (2012). quantreg: Quantile Regression. R package version 4.94. http://CRAN.R-project.org/package=quantreg """ DESCRSHORT = """Engel food expenditure data.""" DESCRLONG = """Data on income and food expenditure for 235 working class households in 1857 Belgium.""" #suggested notes NOTE = """:: Number of observations: 235 Number of variables: 2 Variable name definitions: income - annual household income (Belgian francs) foodexp - annual household food expenditure (Belgian francs) """ def load(as_pandas=None): """ Load the data and return a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): data = _get_data() return du.process_pandas(data, endog_idx=0, exog_idx=None) def _get_data(): return du.load_csv(__file__, 'engel.csv') statsmodels-0.12.2/statsmodels/datasets/engel/engel.csv000066400000000000000000000174051400612667500232270ustar00rootroot00000000000000"income","foodexp" 420.157650843928,255.839424594576 541.411706721205,310.958667059145 901.157456651663,485.680014171085 639.08022868883,402.997355544163 750.875605828476,495.560774933776 945.7989310482,633.797815132393 829.397886847186,630.756567705217 979.164835837914,700.440904266032 1309.87894037831,830.95862150535 1492.39874437426,815.360217290461 502.838980218067,338.001387329587 616.71684724229,412.361338428638 790.922511291545,520.000617981121 555.878641643074,452.401472907332 713.44118368415,512.720057836885 838.756132722629,658.839530303595 535.076645900387,392.599496749012 596.440805359932,443.558633799595 924.561896582212,640.11637771341 487.758301817955,333.839386975747 692.639734238467,466.958318528848 997.876977824175,543.396904263231 506.999491179525,317.719843756484 654.158711401758,424.320896352573 933.919270183382,518.961656053407 433.681329252018,338.001387329587 587.596213341684,419.641174631375 896.474635643808,476.320048933563 454.478223782524,386.36016331012 584.998919370362,423.278349805554 800.799016617394,503.35717119023 502.436869899465,354.638868545299 713.519666530832,497.31816882899 906.000628725279,588.519463958722 880.596923786325,654.597144597117 796.828919368547,550.727427597965 854.87905261442,528.376976714303 1167.37159427026,640.481348055373 523.800035579844,401.320355546637 670.779185433114,435.999021900918 377.058368850099,276.560609645838 851.543001748297,588.348818059025 1121.09369365137,664.19780220393 625.517933400268,444.860166410776 805.537696174017,462.899514863823 558.581201465033,377.779238546012 884.400487319312,553.15043561635 1257.49886576834,810.896154761447 2051.17894099901,1067.95405614074 1466.33299214604,1049.87879168732 730.098896774438,522.701209676143 800.799016617394,572.080662617684 1245.69638760971,907.396944580766 1201.00021368196,811.57759369573 634.400209148622,427.797520201042 956.231463138833,649.998464123521 1148.60104702955,860.600154559902 1768.82364982203,1143.42108582835 2822.53303466609,2032.67919020832 922.354832141967,590.618327009967 2293.19197144236,1570.39113831708 627.472597042135,483.480024661708 889.980898378682,600.480399087121 1162.19995392922,696.202105745481 1197.07935707754,774.796179057776 530.797185462728,390.598430399482 1142.15259256708,612.56190089616 1088.00388697846,708.762151593178 484.661156316503,296.919185772441 1536.02010067662,1071.46269646941 678.897392141278,496.597580037315 671.880165854403,503.39744137471 690.468256477202,357.641110879089 860.694825783725,430.337592716917 873.309484596291,624.699041398883 894.459835214087,582.54125094185 1148.64699199033,580.221542246938 926.876192988813,543.88074278423 839.041358293354,588.637179622688 829.49742056551,627.99989545798 1264.00432957802,712.101174262357 1937.97714636527,968.394940061335 698.831741432851,482.581587621304 920.419919363967,593.169385581544 1897.57113999412,1033.56575426925 891.682386298282,693.679473449282 889.6783563083,693.679473449282 1221.48181114807,761.279065822776 544.599139402161,361.398056338879 1031.44911476975,628.452218199356 1462.94967217323,771.44856441849 830.435282442915,757.118666447887 975.04146665886,821.59699408795 1337.99833996025,1022.3201704203 867.64270523161,679.440727360101 725.745933703277,538.749115686801 989.005606041026,679.998097246959 1525.00047421177,977.003270959677 672.196023753147,561.201488176248 923.397682201603,728.399746623589 472.321548280698,372.318622584609 590.760092419618,361.52095256921 940.921768902254,517.919590751206 643.357141462033,459.817650989876 2551.66151377579,863.919851470995 1795.32258882792,831.440717300088 1165.77339020587,534.761043791083 815.62117431089,392.050242021584 1264.20658645087,934.975195444102 1095.40561684263,813.308096301318 447.447852411217,263.709996170628 1178.97417954918,769.083849021127 975.802295687602,630.586286420944 1017.85220007186,645.987400679307 423.879832013577,319.558386349475 558.776739102636,348.451830104442 943.248718270872,614.506803163417 1348.30024452767,662.009562038758 2340.61735387973,1504.37077491258 587.179168098792,406.218015716283 1540.97405699008,692.1688993212 1115.84807481956,588.137050604953 1044.68428590432,511.260885979623 1389.79286912095,700.559989341702 2497.78595383858,1301.14509754583 1585.38094296753,879.066017413729 1862.04383602348,912.885078250154 2008.8546243469,1509.7811718462 697.309947594492,484.060548936204 571.251746766114,399.670317095029 598.346489479165,444.100105563446 461.097722534667,248.810111222236 977.110747230569,527.801359578015 883.984916757004,500.631349055309 718.359399343153,436.810734740578 543.897059451262,374.799044124691 1587.34803468162,726.392135101241 4957.81302447901,1827.1999644396 969.68376220836,523.49108470832 419.998021268147,334.99982183865 561.998960360707,473.200883889103 689.598814337616,581.202945705675 1398.5202607169,929.75396743285 820.816847571835,591.197416678028 875.171616264683,637.548275219478 1392.44991016741,674.950935444337 1256.31737222348,776.758895179758 1362.85902988814,959.516968477919 1999.25521962472,1250.96433391432 1209.47299210597,737.820079380279 1125.0356465964,810.677242354166 1827.40096749065,983.000864895715 1014.15395295671,708.896829195949 880.394409783857,633.120014158391 2432.39099224122,1424.80465628899 1177.85468592228,830.95862150535 1222.5938655042,925.579474233555 1519.58112468928,1162.00239672989 687.663761691575,383.457962724518 953.11922427465,621.117329201764 953.11922427465,621.117329201764 953.11922427465,621.117329201764 939.04180595405,548.600231233027 1283.40245730726,745.235294456105 1511.57888086542,837.80049554801 1342.58212809281,795.34024163682 511.797991841133,418.597567936084 689.798826994207,508.797449887606 1532.30742618103,883.278011623353 1056.08082482784,742.527569034242 387.319525632704,242.32020192074 387.319525632704,242.32020192074 410.998678844171,266.00098186588 832.755431984518,614.75880260907 614.998605300573,385.318397885378 887.465812960725,515.619969025557 1024.81767735549,708.478703425954 1006.43533940422,734.235630810297 725.999989237198,433.000983776039 494.417350707113,327.418772037758 748.641327251627,429.039933638385 987.64171960278,619.640827692018 788.09607104789,400.798978053224 831.79831368624,620.800640126449 1139.49447493599,819.996440995918 507.516894491359,360.878017655466 576.197221195524,395.760804612775 696.59905406528,442.000052121661 650.817978373872,404.03843113149 949.580207412905,670.799309110531 497.119281341608,297.5701513364 570.167398903935,353.488163131684 724.730600295316,383.93758487932 408.339934376479,284.800803268761 638.671348198183,431.099964756245 1225.78900333424,801.351758612919 715.370077715236,448.451258996436 800.470756318541,577.911070749254 975.597398720442,570.521012300081 1613.75654835121,865.320535878418 608.501878790717,444.557764325978 958.663378279956,680.419826789901 835.942641428986,576.277894453487 873.737511101673,631.798175131743 951.44320976533,608.641850318947 473.002181248345,300.999920310599 601.003044352051,377.998414059123 713.99788489267,397.001476569931 829.29836507219,588.519463958722 959.795268750367,681.761575036767 1212.96129506839,807.360270100159 958.874307424532,696.801097085781 1129.44314702273,811.196241851397 1943.04187331083,1305.72014134299 539.638785503439,442.000052121661 463.599021125583,353.601297444411 562.640004501253,468.000797511221 736.758383070776,526.75734679978 1415.44606403432,890.239030266526 2208.78970565549,1318.80328223672 636.000913716338,331.000537750629 759.401026863119,416.401525383919 1078.83819961899,596.840554600565 499.751012804117,408.499218009175 1020.02253584507,775.020902533032 1595.1610788589,1138.16204602323 776.595792938105,485.519766208776 1230.92352504251,772.761142353133 1807.95201459536,993.96301727137 415.440747985411,305.438973730216 440.51742415637,306.519078570937 541.200597324592,299.199327967538 581.35989168777,468.000797511221 743.077242789534,522.601905880464 1057.67671146451,750.320163419201 statsmodels-0.12.2/statsmodels/datasets/fair/000077500000000000000000000000001400612667500212405ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/fair/__init__.py000066400000000000000000000003261400612667500233520ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/fair/data.py000066400000000000000000000052571400612667500225340ustar00rootroot00000000000000"""Fair's Extramarital Affairs Data""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """Included with permission of the author.""" TITLE = """Affairs dataset""" SOURCE = """ Fair, Ray. 1978. "A Theory of Extramarital Affairs," `Journal of Political Economy`, February, 45-61. The data is available at http://fairmodel.econ.yale.edu/rayfair/pdf/2011b.htm """ DESCRSHORT = """Extramarital affair data.""" DESCRLONG = """Extramarital affair data used to explain the allocation of an individual's time among work, time spent with a spouse, and time spent with a paramour. The data is used as an example of regression with censored data.""" #suggested notes NOTE = """:: Number of observations: 6366 Number of variables: 9 Variable name definitions: rate_marriage : How rate marriage, 1 = very poor, 2 = poor, 3 = fair, 4 = good, 5 = very good age : Age yrs_married : No. years married. Interval approximations. See original paper for detailed explanation. children : No. children religious : How relgious, 1 = not, 2 = mildly, 3 = fairly, 4 = strongly educ : Level of education, 9 = grade school, 12 = high school, 14 = some college, 16 = college graduate, 17 = some graduate school, 20 = advanced degree occupation : 1 = student, 2 = farming, agriculture; semi-skilled, or unskilled worker; 3 = white-colloar; 4 = teacher counselor social worker, nurse; artist, writers; technician, skilled worker, 5 = managerial, administrative, business, 6 = professional with advanced degree occupation_husb : Husband's occupation. Same as occupation. affairs : measure of time spent in extramarital affairs See the original paper for more details. """ def load(as_pandas=None): """ Load the data and return a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): data = _get_data() return du.process_pandas(data, endog_idx=8, exog_idx=None) def _get_data(): return du.load_csv(__file__, 'fair.csv', convert_float=True) statsmodels-0.12.2/statsmodels/datasets/fair/fair.csv000066400000000000000000004504101400612667500227020ustar00rootroot00000000000000"rate_marriage","age","yrs_married","children","religious","educ","occupation","occupation_husb","affairs" 3,32,9,3,3,17,2,5,0.1111111 3,27,13,3,1,14,3,4,3.2307692 4,22,2.5,0,1,16,3,5,1.3999996 4,37,16.5,4,3,16,5,5,0.7272727 5,27,9,1,1,14,3,4,4.666666 4,27,9,0,2,14,3,4,4.666666 5,37,23,5.5,2,12,5,4,0.8521735 5,37,23,5.5,2,12,2,3,1.826086 3,22,2.5,0,2,12,3,3,4.7999992 3,27,6,0,1,16,3,5,1.333333 2,27,6,2,1,16,3,5,3.2666645 5,27,6,2,3,14,3,5,2.041666 3,37,16.5,5.5,1,12,2,3,0.4848484 5,27,6,0,2,14,3,2,2 4,22,6,1,1,14,4,4,3.2666645 4,37,9,2,2,14,3,6,1.3611107 4,27,6,1,1,12,3,5,2 1,37,23,5.5,4,14,5,2,1.826086 2,42,23,2,2,20,4,4,1.826086 4,37,6,0,2,16,5,4,2.041666 5,22,2.5,0,2,14,3,4,7.8399963 3,37,16.5,5.5,2,9,3,2,2.545454 3,42,23,5.5,3,12,5,4,0.5326087 2,27,9,2,4,20,3,4,0.6222222 4,27,6,1,2,12,5,4,0.5833333 5,27,2.5,0,3,16,4,1,4.7999992 2,27,6,2,2,12,2,5,0.1666666 5,37,13,1,3,12,3,4,0.6153846 2,32,16.5,2,2,12,4,2,1.1878777 3,27,6,1,1,14,3,6,11.1999989 3,32,16.5,4,3,14,5,5,1.1878777 3,27,9,2,1,14,3,4,2.1777763 3,37,16.5,3,3,14,3,2,0.4848484 4,32,16.5,5.5,4,12,2,4,0.7272727 5,42,16.5,4,3,16,4,6,0.7272727 3,27,9,2,2,12,5,2,1.333333 3,17.5,0.5,0,1,12,3,2,7 4,42,23,5.5,2,20,3,2,0.5217391 5,37,16.5,3,3,12,3,5,0.2121212 4,22,2.5,1,2,14,3,5,0.4 4,27,2.5,0,2,16,4,1,1.3999996 4,22,2.5,0,2,14,3,6,3.1999998 4,37,13,3,2,16,4,5,1.5076914 4,22,2.5,0,2,16,3,4,7.8399963 4,22,2.5,0,1,14,1,2,7.8399963 5,22,2.5,0,3,12,3,2,0.4 5,22,2.5,0,3,16,4,5,4.8999996 3,42,23,4,3,16,5,5,0.0434783 5,32,13,3,3,14,4,4,0.0769231 5,22,6,2,2,14,3,4,0.5833333 3,27,2.5,1,4,17,4,6,4.7999992 2,42,23,3,3,14,3,5,0.8521735 4,22,2.5,0,1,17,6,6,4.7999992 2,42,23,3,3,14,3,5,2.9217386 4,42,23,2,2,14,4,4,0.5217391 4,42,23,3,3,12,5,4,0.5326087 4,37,16.5,2,3,14,3,4,0.4848484 4,27,2.5,0,2,20,4,5,7.8399963 2,32,9,2,2,12,2,2,1.333333 4,42,13,0,1,14,3,4,1.5076914 4,22,6,2,1,12,3,4,1.333333 5,32,16.5,3,3,14,2,4,1.1878777 4,42,13,0,2,12,3,2,1.5076914 5,27,9,1,3,14,5,5,1.333333 5,22,6,2,2,12,2,5,7 2,27,16.5,2,3,16,4,5,0.7272727 5,37,13,2,1,12,3,4,1.5076914 5,27,6,0,2,14,3,4,2.041666 2,27,2.5,1,1,12,2,3,26.8799896 5,42,23,5.5,4,20,5,4,0.5326087 5,27,6,0,2,16,5,2,2 5,37,16.5,3,2,14,3,5,0.2121212 2,32,9,2,2,16,3,5,1.333333 3,37,16.5,5.5,3,12,5,5,2.545454 5,27,6,2,2,12,3,4,0.1666666 5,32,16.5,3,1,12,4,4,0.4848484 5,27,9,2,1,14,5,1,1.333333 4,22,2.5,0,2,16,5,5,0.4 5,32,16.5,2,4,14,5,2,0.4848484 2,22,6,2,2,14,2,5,0.1666666 3,32,13,3,1,12,4,5,1.5076914 5,32,16.5,3,2,12,3,4,0.0606061 3,27,6,2,1,14,3,6,2.041666 5,22,2.5,0,1,20,4,4,0.4 3,32,9,2,3,14,3,5,0.8888888 3,22,2.5,1,2,14,3,2,4.7999992 3,22,2.5,0,2,16,3,4,4.7999992 5,27,9,2,1,16,4,6,1.333333 3,42,23,2,2,12,2,2,0.1521739 3,37,16.5,3,2,17,3,2,1.1878777 5,32,13,2,2,12,2,6,0.9423077 1,27,13,2,2,12,4,4,1.5076914 5,27,2.5,0,2,14,3,2,0.4 5,27,9,0,1,14,4,4,0.1111111 5,32,13,2,2,16,3,3,0.9423077 4,27,9,2,2,14,3,5,0.3888888 3,22,2.5,1,3,14,5,4,4.8999996 2,37,23,2,2,12,5,5,0.5326087 2,27,6,2,1,14,3,5,2.041666 4,27,2.5,1,2,12,5,2,4.8999996 3,37,13,5.5,2,12,5,5,5.1692305 5,37,16.5,4,1,12,3,6,1.696969 5,22,2.5,0,1,14,3,5,1.3999996 4,42,13,0,1,14,5,5,0.0769231 5,27,9,1,1,14,5,5,2.1777763 4,22,2.5,0,1,14,3,4,1.3999996 4,22,2.5,1,2,14,5,4,7.8399963 4,27,6,2,3,16,4,6,0.5833333 2,32,16.5,1,2,14,3,5,2.7151508 3,27,13,2,1,14,3,4,0.9423077 4,22,0.5,0,2,12,3,2,7 5,27,6,1,1,16,4,3,3.2666645 2,27,9,2,2,14,3,5,4.666666 3,27,9,2,2,12,3,4,2.1777763 4,32,16.5,3,3,12,2,3,0.4848484 5,22,2.5,0,1,12,3,3,1.3999996 4,22,2.5,1,2,14,4,4,3.1999998 1,22,2.5,0,2,9,2,4,11.1999998 3,32,13,2,1,20,6,6,1.5076914 5,32,9,1,2,14,3,5,1.333333 5,27,2.5,0,1,20,6,4,1.3999996 4,27,9,2,2,14,2,5,0.3888888 4,27,6,0,3,12,5,2,2 2,22,2.5,0,3,14,3,2,4.8999996 3,27,9,2,3,17,4,6,1.3611107 4,27,6,2,1,14,3,4,2.041666 5,22,2.5,1,1,12,2,2,1.3999996 4,27,16.5,4,3,12,2,6,0.2121212 2,27,6,1,2,14,4,3,3.2666645 2,32,6,1,1,17,4,4,7.4666672 5,27,6,2,2,16,4,3,0.5833333 4,42,23,3,3,17,4,4,0.5217391 4,32,9,2,1,16,4,6,0.1111111 3,42,23,4,3,14,4,3,0.5217391 5,27,6,2,1,12,5,2,2 2,42,23,4,4,20,4,5,0.1521739 3,32,6,0,2,20,4,5,4.666666 5,27,2.5,0,2,14,3,2,1.3999996 2,42,16.5,3,3,12,3,5,1.1878777 4,37,23,3,2,12,5,4,1.826086 3,27,2.5,0,2,17,4,4,1.3999996 3,32,13,3,3,20,4,6,3.2307692 3,27,2.5,0,2,14,3,4,4.7999992 3,42,16.5,2,1,16,3,5,1.1878777 4,22,2.5,0,2,14,5,5,0.4 5,27,6,0,3,14,3,5,0.5833333 3,22,2.5,0,1,12,2,4,7.8399963 4,27,6,0,3,14,2,4,11.1999989 3,27,9,2,2,16,3,4,1.3611107 2,27,9,1,2,14,2,2,4.9777775 3,22,2.5,0,3,12,3,3,4.7999992 4,32,16.5,4,4,14,3,5,2.7151508 5,32,2.5,2,2,14,3,4,0.4 4,27,2.5,0,2,14,3,5,0.4 5,32,9,3,3,16,4,4,0.1111111 3,32,13,2,2,12,3,5,0.2692307 3,32,16.5,3,3,12,3,2,0.7272727 5,42,23,2,2,14,5,5,0.5217391 3,27,16.5,4,3,14,4,2,0.7424242 3,32,16.5,4,2,20,4,4,0.7272727 4,22,2.5,2,2,14,5,2,4.7999992 5,27,6,0,1,12,3,4,7.4666672 4,37,16.5,3,4,16,5,5,0.2121212 3,22,2.5,0,2,12,3,5,1.3999996 4,32,13,2,2,14,3,5,1.5076914 5,42,23,5.5,3,17,4,4,0.5217391 2,27,6,2,3,12,2,2,1.333333 5,22,2.5,1,2,16,3,6,1.3999996 3,42,23,2,3,12,2,2,0.5326087 5,42,23,3,1,14,3,5,1.826086 4,22,2.5,0,3,12,3,4,4.8999996 3,27,9,1,4,14,5,5,0.1111111 2,37,23,3,3,12,2,4,4.173913 3,32,9,3,3,14,4,5,0.3888888 5,37,16.5,4,3,12,3,4,1.1878777 3,27,9,2,2,12,5,2,1.333333 3,27,6,1,2,17,2,2,1.333333 5,22,2.5,0,3,14,3,3,1.3999996 5,27,6,0,2,17,4,5,1.333333 4,22,2.5,0,2,12,4,2,4.8999996 4,27,6,0,2,12,3,4,4.666666 3,32,9,1,2,12,3,3,0.1111111 1,42,23,4,3,12,3,5,0.8521735 2,22,6,2,2,12,3,4,1.333333 4,32,16.5,2,2,12,2,2,0.4848484 4,32,13,3,3,14,2,2,0.9423077 5,27,9,2,1,12,3,3,0.3888888 3,42,23,3,2,12,3,2,0.5217391 3,37,16.5,1,3,20,6,6,2.7151508 5,32,13,2,1,12,5,2,0.9423077 4,27,13,3,1,12,4,2,3.4461536 2,37,13,0,2,14,3,5,0.9230769 3,27,9,1,1,12,2,2,3.1111107 5,27,6,0,1,14,5,5,3.2666645 2,42,23,2,3,12,5,2,0.8521735 5,27,6,0,2,16,3,4,0.5833333 4,22,2.5,0,4,16,5,4,7.8399963 5,22,2.5,0,2,16,4,4,1.3999996 5,42,13,0,3,12,3,2,1.5076914 4,22,2.5,1,1,16,3,4,1.3999996 4,32,9,1,3,16,3,5,1.3611107 4,27,9,2,2,12,4,2,0.3888888 5,27,6,0,1,16,5,2,2.041666 4,32,16.5,3,2,14,5,4,2.545454 2,42,2.5,0,4,20,6,5,4.7999992 2,42,23,5.5,4,14,3,6,0.3478261 4,42,23,4,2,12,3,2,0.3478261 3,22,2.5,0,3,16,5,5,4.7999992 2,22,2.5,0,3,14,3,5,1.3999996 4,22,2.5,0,3,14,3,3,4.7999992 4,32,16.5,4,3,14,4,4,0.2121212 5,32,13,2,4,17,4,5,0.9423077 4,32,13,3,4,12,3,5,1.5076914 5,27,9,2,1,14,4,4,1.3611107 4,27,6,1,4,16,3,4,0.5833333 4,27,9,2,3,12,2,4,1.333333 1,37,16.5,3,2,17,4,4,0.7424242 3,27,9,3,2,12,4,5,1.3611107 2,27,6,0,2,14,3,4,4.666666 3,22,2.5,1,2,14,2,2,25.5999908 4,22,2.5,1,3,12,3,4,4.8999996 4,27,2.5,0,2,14,4,4,1.3999996 1,42,23,2,3,12,3,5,0.5217391 5,27,6,2,4,14,5,5,3.2666645 5,27,6,0,1,12,4,2,0.5833333 4,37,23,2,3,12,3,5,0.1521739 4,22,6,2,2,12,3,4,0.1666666 1,32,13,1,3,14,3,1,0.9423077 5,22,6,1,1,16,3,5,0.5833333 5,27,6,0,1,14,3,5,2 5,27,6,1,1,17,4,5,3.2666645 4,37,16.5,1,2,14,2,5,1.1878777 4,27,9,2,2,12,2,2,2.1777763 4,42,23,4,1,12,3,4,0.1521739 4,32,13,0,3,12,2,2,2.1538458 5,32,13,2,3,12,2,2,0.9230769 4,42,23,4,1,17,4,4,0.8521735 4,37,23,4,2,14,4,3,0.5326087 4,32,16.5,2,2,14,3,6,1.1878777 4,27,13,4,3,12,2,4,3.2307692 5,37,23,3,2,12,3,2,0.1521739 2,32,13,0,3,9,6,2,0.0769231 5,32,13,2,1,14,4,6,3.4461536 4,27,6,1,2,14,4,2,0.1666666 5,27,2.5,0,3,20,4,5,4.7999992 2,42,23,3,3,14,4,2,0.5217391 3,27,6,0,1,14,3,2,0.5833333 4,27,6,1,2,12,3,4,2.041666 2,22,2.5,0,3,12,3,3,3.1999998 3,27,2.5,0,3,12,2,2,7.8399963 4,42,23,2,2,17,5,2,0.8521735 5,32,13,2,1,14,2,5,0.9230769 5,32,13,0,1,12,5,4,2.1538458 4,27,9,2,2,16,4,5,0.3888888 5,42,23,4,3,17,4,4,0.1521739 3,27,9,3,1,16,4,5,0.1111111 5,42,13,0,2,14,5,3,0.9230769 5,32,16.5,2,2,16,5,5,0.2121212 1,42,23,2,1,12,3,3,1.826086 4,27,6,0,1,12,3,4,0.5833333 5,42,23,3,2,12,5,4,1.9478254 4,27,9,2,3,16,4,5,1.333333 2,32,13,3,3,20,4,5,0.0769231 4,22,2.5,0,2,12,3,2,11.1999998 3,32,16.5,3,2,12,3,2,0.7272727 5,27,6,1,3,12,5,2,2 3,27,2.5,0,1,12,3,4,3.1999998 5,22,2.5,0,2,16,4,6,1.3999996 3,32,13,0,2,16,4,5,0.9230769 4,37,16.5,2,2,20,4,2,0.7424242 4,27,6,1,2,17,4,5,2.041666 4,37,23,4,2,12,3,2,0.1521739 4,22,2.5,2,2,14,3,5,4.8999996 3,27,6,1,3,17,4,4,1.333333 4,32,16.5,3,4,12,3,5,1.1878777 5,22,6,2,3,14,3,5,7.4666672 4,32,13,2,3,14,3,2,0.0769231 4,27,9,1,1,14,2,5,1.3611107 3,32,16.5,2,2,12,3,4,0.7272727 4,27,13,2,2,12,3,2,0.0769231 5,27,9,1,3,12,2,3,0.3888888 3,27,9,0,1,12,3,4,16 4,27,9,0,3,14,5,6,4.9777775 3,22,2.5,0,1,12,3,2,7.8399963 3,32,13,2,3,20,4,5,0.0769231 4,42,23,5.5,2,14,5,3,0.5326087 5,22,2.5,0,2,16,3,4,4.8999996 5,27,9,1,2,14,4,5,0.3888888 5,37,13,2,3,14,4,3,0.2692307 5,27,2.5,1,3,16,3,3,1.3999996 4,27,6,0,2,14,3,2,0.5833333 5,22,2.5,0,2,12,4,4,7.8399963 5,27,6,1,3,12,2,3,1.333333 4,32,9,2,2,16,5,5,1.333333 4,32,6,2,3,14,4,2,2.041666 2,22,2.5,1,2,17,2,2,11.1999998 5,27,2.5,0,2,17,5,5,4.7999992 5,37,16.5,3,2,14,4,4,1.1878777 3,27,2.5,1,3,14,5,3,4.7999992 4,27,6,1,1,14,3,4,0.1666666 5,27,6,2,3,12,2,4,3.2666645 4,42,23,3,2,12,3,2,1.217391 3,27,6,2,3,14,3,5,0.5833333 5,22,6,1,3,14,1,4,2 5,37,23,3,2,12,3,4,0.5326087 3,37,16.5,3,3,12,3,4,1.1878777 4,42,23,4,2,9,4,4,0.5217391 4,42,23,3,3,12,3,5,0.5217391 4,37,23,2,2,16,4,6,0.1521739 5,32,16.5,4,1,12,2,1,0.4848484 4,27,6,2,3,14,2,6,1.333333 3,32,16.5,2,2,12,2,2,1.1878777 2,27,6,1,2,12,3,2,0.5833333 4,22,2.5,0,1,14,3,4,4.7999992 3,22,6,1,2,14,3,2,0.5833333 2,27,6,0,3,12,3,3,0.1666666 4,27,6,1,2,12,2,5,3.2666645 3,22,2.5,1,1,12,5,5,4.8999996 2,37,16.5,3,2,14,3,5,1.1878777 5,32,13,2,2,16,4,2,3.2307692 5,22,2.5,0,1,12,3,2,1.3999996 4,22,6,1,3,14,4,1,0.5833333 4,22,0.5,0,2,12,5,2,2 3,27,2.5,0,2,20,4,4,1.3999996 5,27,2.5,0,3,12,2,2,1.3999996 4,22,2.5,0,3,14,3,2,1.3999996 4,42,16.5,2,1,16,4,5,2.7151508 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5,42,23,2,3,14,3,4,0.5217391 4,32,13,2,1,17,4,2,0.9230769 3,27,9,0,1,14,3,5,4.9777775 3,32,13,2,1,12,3,6,0.9423077 3,27,6,2,3,17,4,6,2.041666 2,37,16.5,3,2,12,2,4,0.7272727 2,22,6,2,1,14,3,4,0.1666666 3,17.5,2.5,1,3,12,4,2,4.8999996 3,27,6,3,2,14,2,2,0.1666666 3,22,2.5,0,1,12,2,5,1.3999996 4,42,23,3,2,14,3,5,1.826086 2,27,6,2,3,14,3,3,2 4,32,16.5,5.5,2,14,3,2,2.545454 4,27,2.5,0,3,12,3,5,0.4 4,27,6,2,3,12,3,2,2 4,27,2.5,0,3,16,4,5,4.7999992 5,27,6,0,1,16,4,5,4.666666 2,22,6,2,2,12,2,3,0.5833333 3,27,2.5,0,1,20,4,4,4.7999992 4,32,16.5,3,3,14,3,5,0.7272727 5,32,13,1,3,17,4,4,0.9423077 3,22,2.5,1,2,12,2,4,7.8399963 4,22,2.5,0,1,14,3,3,1.3999996 5,32,9,2,3,16,4,4,1.333333 5,32,2.5,0,3,14,5,4,0.4 5,27,9,2,1,14,2,4,1.333333 4,32,9,1,2,14,5,5,0.8888888 4,22,2.5,0,2,14,3,5,1.3999996 4,42,23,1,3,12,3,3,2.9217386 4,27,9,2,2,16,4,4,1.333333 4,32,16.5,3,2,17,4,2,0.4848484 4,27,6,2,2,16,4,5,7.4666672 4,37,16.5,2,2,14,4,5,0.7272727 5,27,6,1,3,16,4,4,4.666666 2,27,6,1,2,12,2,2,4.666666 4,22,2.5,1,1,12,2,2,3.1999998 3,37,13,1,2,12,3,2,0.9423077 4,42,23,2,2,14,3,5,0.1521739 5,22,2.5,0,1,14,3,2,0.4 3,42,23,2,1,17,4,6,4.173913 4,32,16.5,2,3,12,3,4,0.7272727 1,32,16.5,3,3,14,3,4,0.0606061 5,27,13,2,3,12,3,2,0.9230769 3,27,6,0,1,17,5,4,3.2666645 5,42,23,5.5,2,14,4,4,0.5326087 4,32,16.5,1,3,16,4,5,0.0606061 2,22,2.5,0,1,12,3,2,4.7999992 2,42,23,1,3,14,4,2,0.5326087 2,22,6,0,2,12,3,4,0.5833333 4,27,6,0,1,16,5,1,0.5833333 4,42,23,1,4,17,3,2,1.826086 5,42,23,2,1,12,3,2,0.3478261 4,27,6,2,2,16,4,2,2 3,22,2.5,0,1,12,3,2,1.3999996 3,27,13,3,2,14,5,5,3.4461536 4,32,13,2,2,14,4,5,2.1538458 4,27,9,3,3,14,4,3,0.3888888 3,32,9,1,2,14,3,4,0.3888888 3,27,9,2,1,14,4,2,1.333333 5,37,16.5,5.5,3,12,2,2,1.1878777 3,27,6,1,4,14,3,5,4.666666 2,27,9,1,1,14,5,3,4.666666 4,27,2.5,0,2,17,4,6,7.8399963 4,32,13,1,1,20,4,4,1.5076914 1,42,23,4,3,12,3,4,1.9478254 4,32,16.5,1,1,14,5,5,0.7424242 1,42,23,5.5,2,12,2,2,0.5217391 4,37,13,1,2,12,3,5,1.5076914 4,32,16.5,2,2,14,5,5,1.1878777 4,42,23,3,2,14,4,4,0.0434783 5,27,6,1,3,14,3,6,2.041666 3,37,16.5,4,3,12,3,2,0.7272727 3,37,23,3,3,9,4,2,0.1521739 4,37,16.5,2,2,12,3,4,2.545454 3,27,6,2,1,14,4,5,1.333333 4,37,13,0,3,12,3,2,1.5076914 2,27,2.5,1,3,16,4,4,4.8999996 4,42,23,5.5,3,12,5,5,0.5326087 3,32,16.5,3,2,12,2,2,0.7424242 4,37,16.5,3,2,12,5,2,0.2121212 3,42,13,0,3,12,4,4,0.9230769 4,37,13,4,3,14,4,2,0.6153846 2,32,16.5,4,2,14,5,4,1.1878777 3,27,13,2,1,14,4,4,2.1538458 5,22,2.5,0,2,14,4,5,0.4 4,22,2.5,1,2,14,4,5,0.4 3,32,2.5,0,1,16,4,5,17.9199982 5,27,6,2,3,14,3,5,3.2666645 5,32,16.5,3,4,12,2,3,0.0606061 2,42,23,2,3,16,4,5,0.5217391 5,22,6,2,3,14,2,4,0.5833333 5,42,23,2,1,14,4,5,0.0434783 4,22,6,0,2,14,3,3,0.5833333 3,32,16.5,4,3,14,3,4,0.7272727 3,32,16.5,2,2,14,3,5,0.7272727 4,42,16.5,1,3,17,4,5,0.7272727 1,37,16.5,3,2,12,3,5,0.2121212 3,32,13,1,3,20,4,4,0.0769231 3,27,2.5,0,3,14,5,5,1.3999996 5,22,2.5,2,1,14,5,4,16.7999878 3,42,23,5.5,3,12,3,2,0.5217391 4,27,9,2,3,12,2,2,0.3888888 3,32,16.5,2,3,12,2,4,1.1878777 4,32,16.5,3,2,14,3,4,2.545454 3,27,2.5,2,2,16,4,4,1.3999996 4,32,6,2,2,14,4,4,4.666666 1,42,23,2,1,12,2,3,1.9478254 4,22,2.5,0,2,16,5,1,3.1999998 3,22,6,0,2,12,3,4,2 2,42,23,5.5,3,17,4,4,2.9217386 3,27,13,2,2,12,2,4,3.2307692 4,27,9,2,3,12,2,2,0.3888888 5,32,16.5,3,3,17,4,4,2.545454 5,32,16.5,2,1,14,4,6,0.0606061 5,32,16.5,3,3,14,2,5,1.1878777 3,27,9,2,2,12,2,3,1.3611107 2,27,6,1,3,12,4,4,0.5833333 4,22,2.5,2,2,12,5,2,7.8399963 5,27,6,2,4,20,4,4,3.2666645 3,22,2.5,0,2,14,3,2,4.7999992 2,32,9,0,1,16,5,4,7.4666662 4,37,16.5,2,3,16,3,6,0.7272727 4,42,23,2,3,12,3,2,1.217391 5,22,2.5,0,3,14,3,4,7.8399963 5,32,9,1,2,14,2,4,1.333333 4,37,16.5,2,3,12,3,6,0.4848484 3,22,2.5,0,3,12,3,4,1.3999996 4,37,16.5,4,2,12,3,5,0.7272727 4,27,2.5,0,3,17,4,1,1.3999996 3,27,6,0,1,14,3,5,2.041666 5,32,16.5,2,2,20,4,4,0.7424242 2,22,2.5,1,2,12,5,5,0.4 4,42,16.5,2,1,14,5,4,0.7424242 5,42,13,3,4,14,2,2,1.5076914 5,32,13,1,3,16,6,6,0.2692307 5,37,13,0,1,14,4,5,0.0769231 2,22,6,0,1,20,6,4,3.2666645 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4,27,6,0,4,14,3,4,7.4666672 3,22,6,1,1,14,3,4,2.041666 5,22,2.5,0,2,14,3,5,1.3999996 3,27,2.5,4,2,14,3,2,16.7999878 4,27,6,3,2,14,2,4,2 3,32,16.5,2,3,14,3,5,1.696969 5,22,2.5,0,3,14,3,6,7.8399963 5,32,13,1,2,14,3,5,0.9230769 5,22,2.5,0,3,12,3,2,4.7999992 3,32,13,2,1,14,3,5,0.9230769 1,37,23,4,2,12,2,2,0.5217391 2,22,2.5,1,3,14,4,4,0.4 4,42,23,3,4,12,3,4,1.826086 4,27,6,2,2,14,5,5,2.041666 5,37,16.5,2,4,16,3,4,0.0606061 4,22,6,0,3,12,3,3,2.041666 3,32,16.5,3,2,14,5,3,0.2121212 4,27,9,3,3,12,3,4,2.1777763 5,27,6,0,1,16,4,4,0.1666666 2,22,6,3,3,12,3,2,3.2666645 5,22,2.5,0,1,16,4,5,0.4 5,42,23,4,4,14,1,6,0.8521735 4,32,9,1,1,16,4,5,2.1777763 4,22,2.5,2,3,12,2,2,11.1999998 3,42,23,5.5,3,14,3,5,0.8521735 3,22,2.5,1,1,12,5,4,4.7999992 5,27,9,2,2,17,2,2,2.1777763 3,22,2.5,0,1,12,2,4,3.1999998 4,32,13,1,2,12,3,3,0.2692307 4,37,16.5,1,2,12,3,4,4.0727262 5,32,9,3,2,17,4,6,0.1111111 4,27,9,1,2,12,2,3,1.333333 3,27,2.5,1,3,14,3,2,4.8999996 2,22,2.5,1,2,16,4,3,1.3999996 1,42,16.5,5.5,3,14,5,5,0.7424242 3,27,13,2,2,9,2,4,0.2692307 4,42,23,3,4,14,3,2,0.5217391 3,27,9,2,2,12,3,4,7.4666662 3,27,6,2,2,14,3,1,2.041666 5,27,2.5,0,3,14,3,2,0.4 3,27,2.5,0,3,16,3,5,3.1999998 3,22,2.5,0,3,16,4,2,0.4 3,42,23,3,1,12,3,3,2.9217386 5,42,23,2,2,12,2,5,0.1521739 4,27,2.5,0,1,17,4,4,4.8999996 5,27,6,0,2,14,3,5,0.1666666 4,32,16.5,4,2,14,4,4,0.7272727 4,27,6,0,3,12,3,2,3.2666645 4,32,9,2,2,14,3,4,2.1777763 3,27,9,2,1,14,3,4,0.8888888 3,27,2.5,1,2,16,2,2,1.3999996 5,27,13,2,2,9,2,4,0.9230769 2,27,13,2,2,12,3,4,1.5076914 3,42,16.5,4,2,14,3,5,0.2121212 3,32,9,2,1,14,3,2,1.3611107 5,32,13,0,2,12,3,5,0.2692307 1,27,9,2,2,12,2,4,2.1777763 3,32,13,3,2,12,3,2,0.9423077 5,27,2.5,0,3,14,5,5,1.3999996 4,32,6,1,1,16,4,4,0.1666666 5,27,13,3,1,14,3,4,3.4461536 5,27,2.5,0,3,20,6,6,1.3999996 5,32,16.5,4,2,12,2,4,1.1878777 4,37,13,0,2,12,3,3,1.5076914 3,22,2.5,0,3,16,4,4,0.4 5,37,13,2,4,17,4,6,0.9230769 4,22,2.5,2,1,12,3,4,0.4 1,42,16.5,2,4,16,5,2,0.2121212 3,37,16.5,3,3,17,4,4,2.7151508 4,22,2.5,0,3,17,3,4,0.4 5,32,13,2,2,20,4,2,1.5076914 3,37,16.5,2,3,17,4,5,2.545454 4,32,16.5,4,3,12,2,4,0.2121212 4,32,16.5,2,2,14,3,5,0.7272727 5,37,16.5,2,4,17,3,3,0.7272727 3,27,9,2,1,12,3,5,0.3888888 3,42,23,3,3,9,3,5,1.9478254 4,32,9,2,1,20,4,5,1.333333 4,22,6,2,2,12,3,3,0.5833333 1,32,13,2,2,16,6,5,1.5076914 4,22,2.5,0,1,12,2,2,4.7999992 4,27,9,2,1,12,3,4,0.3888888 3,27,6,0,2,14,4,5,2 4,32,13,4,2,12,3,5,0.0769231 5,42,23,3,4,12,2,4,1.217391 2,37,16.5,3,1,14,3,4,1.1878777 3,32,9,0,2,14,3,5,1.333333 4,37,16.5,2,3,14,3,6,0.7272727 1,32,16.5,4,3,12,3,5,1.1878777 3,37,16.5,1,3,14,3,5,1.1878777 4,22,2.5,0,3,14,4,5,1.3999996 4,22,6,2,2,12,2,2,0.5833333 3,22,2.5,1,3,12,3,2,3.1999998 5,27,6,1,3,16,4,1,0.1666666 5,27,9,2,2,20,6,5,0.3888888 4,22,6,1,2,12,5,4,4.666666 1,32,16.5,3,1,20,4,2,0.7272727 5,22,2.5,0,2,16,4,4,4.8999996 4,42,16.5,3,2,14,3,5,1.1878777 4,32,13,2,4,16,4,6,0.2692307 4,32,9,2,2,16,4,5,0.3888888 2,42,23,4,1,12,3,4,0.8521735 3,42,16.5,2,2,14,4,4,0.7272727 4,42,16.5,1,3,14,4,5,0.7272727 4,32,13,3,2,16,4,5,0.9230769 4,27,2.5,0,2,14,5,5,4.7999992 4,27,6,1,1,14,3,4,3.2666645 5,27,6,0,2,14,3,5,1.333333 4,27,6,0,3,20,6,6,2 5,27,6,0,2,14,3,4,3.2666645 4,27,6,2,2,12,4,4,2.041666 4,42,23,1,3,14,3,4,0.5217391 5,22,6,1,3,12,3,3,2 3,37,16.5,3,3,14,4,5,0.0606061 4,27,9,2,3,14,4,4,0.8888888 4,42,13,0,3,12,2,4,0.9423077 4,27,2.5,0,2,14,3,5,1.3999996 2,32,13,3,2,16,4,2,2.1538458 4,37,16.5,4,2,12,5,5,1.1878777 2,22,2.5,0,2,16,2,5,7.8399963 5,42,23,1,3,12,5,2,0.5217391 3,27,6,2,1,16,4,5,2 3,22,2.5,0,2,14,3,5,1.3999996 4,32,9,2,1,14,3,5,1.333333 4,27,9,1,1,14,3,5,0.8888888 5,27,6,0,3,12,3,4,0.5833333 4,37,13,2,3,17,4,6,0.2692307 3,42,23,2,2,14,3,4,0.8521735 5,22,2.5,0,1,17,5,1,0.4 2,37,23,5.5,2,14,3,5,0.1521739 4,32,2.5,0,2,12,3,2,4.7999992 4,27,2.5,0,3,12,3,3,1.3999996 2,27,2.5,0,2,14,3,5,1.3999996 3,22,2.5,0,3,14,3,6,3.1999998 3,42,23,5.5,2,12,4,2,1.9478254 3,37,16.5,3,3,14,3,3,8.727272 2,27,9,0,2,14,3,4,4.666666 2,37,16.5,3,1,12,3,2,2.545454 3,22,2.5,2,3,17,4,2,3.1999998 4,22,6,0,3,12,3,4,2.041666 4,37,16.5,4,1,14,5,4,0.7272727 4,27,9,3,3,14,3,2,0.1111111 4,22,2.5,0,1,14,2,5,0.4 2,42,23,4,2,14,3,5,0.8521735 5,27,6,0,2,14,5,2,0.5833333 2,27,6,1,1,12,3,5,0.5833333 3,32,16.5,2,2,12,3,2,0.7272727 4,37,23,5.5,2,12,4,2,0.5326087 4,17.5,2.5,0,1,12,4,2,17.9199982 5,22,2.5,1,1,14,3,5,57.5999908 4,22,2.5,0,2,14,5,4,1.3999996 3,27,9,2,2,14,3,5,4.666666 2,32,9,2,2,16,4,5,2.1777763 5,22,2.5,0,1,14,2,2,0.4 3,22,2.5,1,3,14,5,4,0.4 3,27,9,2,3,12,5,5,7.4666662 4,27,16.5,5.5,2,14,4,4,0.0606061 4,32,13,2,3,14,3,5,0.2692307 4,27,9,2,2,16,3,4,0.8888888 5,32,13,2,2,17,4,4,2.1538458 4,27,6,1,3,14,4,1,7.4666672 4,32,13,3,4,12,3,5,0.2692307 3,27,2.5,1,2,16,4,2,4.7999992 3,42,23,3,2,14,3,5,0.5326087 4,27,2.5,0,1,12,3,2,0.4 4,22,2.5,0,1,14,4,4,4.7999992 5,32,13,2,1,14,2,2,1.5076914 3,32,9,2,2,14,3,5,1.333333 3,37,16.5,2,2,12,3,4,0.7424242 2,42,23,3,3,14,3,4,0.8521735 5,32,16.5,2,4,17,4,4,0.2121212 4,22,2.5,1,3,12,5,3,4.8999996 5,27,9,2,2,14,3,4,0.1111111 4,32,16.5,3,2,16,5,6,0.7424242 5,32,16.5,4,3,12,3,5,0.0606061 3,32,16.5,3,2,12,5,5,0.7424242 4,42,23,2,3,20,4,4,0.0434783 4,37,16.5,4,1,14,4,5,0.2121212 5,27,2.5,0,2,12,3,3,0.4 3,22,2.5,0,2,14,3,5,0.4 5,37,23,5.5,2,12,2,4,0.1521739 4,42,23,2,2,12,3,5,1.217391 4,22,6,2,1,12,2,4,11.1999989 5,27,6,1,4,12,5,5,0.5833333 5,42,23,3,3,12,3,2,0.5326087 3,27,6,2,2,14,4,4,0.1666666 4,27,6,2,1,16,4,5,2 2,42,16.5,1,2,20,4,4,0.7272727 2,37,16.5,4,2,14,3,5,1.1878777 1,32,13,2,1,12,2,4,0.0769231 3,37,16.5,4,4,14,5,3,0.4848484 4,27,9,1,1,12,3,4,4.666666 2,27,2.5,0,3,14,5,4,4.7999992 3,32,16.5,5.5,4,12,3,2,0.2121212 4,22,2.5,0,2,14,2,2,3.1999998 4,27,6,0,3,17,4,4,3.2666645 5,32,9,0,3,20,6,4,0.1111111 3,22,6,0,2,17,4,3,4.666666 4,22,2.5,2,2,12,3,2,3.1999998 4,42,23,1,2,14,3,6,2.9217386 3,27,6,0,2,14,3,4,7 4,37,23,5.5,2,9,3,4,0.8521735 4,22,2.5,1,3,14,5,5,7.8399963 5,27,9,2,2,14,5,4,1.333333 4,22,2.5,0,2,12,3,4,4.8999996 3,27,9,2,3,14,3,5,1.333333 4,22,6,1,2,12,3,4,0.1666666 4,27,6,2,3,14,4,5,0.5833333 3,42,23,2,2,14,3,5,0.8521735 4,22,6,1,2,12,3,4,0.5833333 4,32,13,3,2,14,2,5,0.2692307 5,42,23,4,3,14,2,2,0.0434783 4,27,13,2,3,12,5,4,0.9230769 4,27,9,1,2,14,5,4,2.1777763 4,27,9,1,2,12,3,3,1.333333 5,22,2.5,0,3,14,3,4,1.3999996 3,32,13,2,3,12,3,5,0.6153846 3,42,23,4,2,12,3,4,0.8521735 3,27,6,0,2,16,4,4,0.1666666 5,42,23,2,2,14,3,3,0.1521739 3,37,16.5,5.5,3,12,2,2,0.4848484 4,22,2.5,0,2,14,3,4,17.9199982 5,42,23,2,2,12,3,2,0.5326087 5,27,2.5,0,1,16,5,2,1.3999996 4,32,23,3,4,12,2,2,0.5326087 5,22,2.5,0,2,17,4,6,7.8399963 4,37,16.5,5.5,2,14,2,3,1.1878777 4,22,2.5,1,3,12,2,2,4.8999996 2,27,6,2,2,12,3,2,2 5,32,16.5,3,3,16,2,4,0.2121212 3,27,6,1,3,14,3,2,3.2666645 3,27,2.5,2,1,14,3,5,1.3999996 5,42,23,5.5,3,16,4,4,0.5326087 3,17.5,2.5,0,1,12,3,4,7.8399963 3,37,23,3,2,12,3,5,0.8521735 5,27,6,0,3,17,3,1,0.1666666 4,37,16.5,1,2,12,3,5,2.7151508 3,32,16.5,2,2,12,3,6,0.7424242 3,27,2.5,0,1,17,4,6,4.7999992 4,32,16.5,4,3,12,2,4,0.7424242 3,32,16.5,2,2,12,3,4,1.1878777 4,17.5,2.5,1,1,12,3,2,4.7999992 3,22,2.5,1,2,12,5,2,7.8399963 5,37,16.5,2,2,16,4,4,0.7272727 5,37,16.5,2,3,12,3,2,0.7272727 5,22,2.5,0,4,14,3,3,0.4 4,27,2.5,0,1,14,3,2,4.8999996 4,22,2.5,1,2,14,4,2,0.4 4,37,16.5,3,3,12,2,4,0.7272727 3,22,6,1,3,16,4,4,3.2666645 4,27,6,1,1,14,3,5,0.5833333 1,42,23,3,3,12,3,4,1.826086 3,22,6,2,3,12,2,4,3.2666645 3,22,2.5,1,2,12,4,1,0.4 4,22,2.5,1,3,16,3,3,4.7999992 2,22,2.5,2,1,12,2,4,3.1999998 5,22,2.5,1,3,14,2,5,4.8999996 4,22,2.5,0,3,14,3,5,1.3999996 4,42,23,5.5,3,12,5,5,0.5217391 3,27,9,1,1,14,3,5,0.1111111 3,37,23,4,2,12,3,2,1.9478254 4,37,16.5,3,3,12,5,2,0.7424242 5,22,2.5,1,2,14,4,1,7.8399963 2,27,2.5,0,1,14,3,3,11.1999998 5,22,2.5,1,2,16,4,4,1.3999996 4,22,2.5,1,3,12,3,3,4.7999992 4,27,6,2,2,14,3,5,0.1666666 5,22,2.5,0,3,16,4,4,0.4 4,27,6,1,3,16,3,3,1.333333 5,42,23,3,2,17,5,5,0.0434783 5,37,16.5,4,2,12,3,2,1.696969 2,27,6,0,1,14,3,4,7 4,32,16.5,3,4,14,3,5,1.1878777 5,37,16.5,5.5,3,20,4,6,0.7424242 5,27,2.5,2,2,16,3,2,0.4 3,27,9,2,2,14,3,6,4.666666 4,32,13,4,3,12,3,4,0.2692307 5,27,9,1,3,12,3,4,2.1777763 5,32,6,3,1,14,3,2,4.666666 4,32,16.5,3,1,12,3,4,1.696969 3,27,9,0,1,12,3,5,7.4666662 4,32,13,1,3,14,3,5,1.5076914 3,42,23,2,3,9,2,2,0.5217391 3,22,6,1,2,12,3,2,1.333333 4,37,23,3,3,12,5,2,0.3478261 5,42,23,3,3,16,4,2,0.3478261 2,22,6,0,2,12,3,3,3.2666645 3,37,13,2,2,12,3,5,0.2692307 3,32,13,2,2,16,3,5,0.9230769 3,22,2.5,0,2,12,3,3,0.4 3,42,23,5.5,3,14,3,4,0.5326087 2,32,16.5,2,2,16,4,6,0.7424242 4,27,6,2,3,14,5,4,2 4,37,16.5,3,4,16,4,5,0.7424242 5,37,23,3,1,12,3,5,0.3478261 3,22,2.5,0,3,14,3,3,3.1999998 3,22,2.5,0,2,12,3,5,4.7999992 4,22,9,3,2,14,3,3,0.3888888 3,42,23,2,1,12,2,5,0.0434783 4,32,13,1,1,12,3,2,1.5076914 3,22,2.5,1,2,12,2,4,11.1999998 2,37,13,3,2,14,4,2,0.0769231 5,42,23,2,3,12,5,5,0.1521739 2,37,16.5,3,3,16,4,2,0.7272727 3,27,6,1,2,14,4,4,2 5,22,2.5,0,2,14,4,4,3.1999998 3,22,2.5,1,3,14,4,3,4.7999992 4,32,13,3,1,14,3,4,0.2692307 5,27,9,2,1,16,3,5,1.3611107 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4,27,16.5,2,3,9,2,4,0.7424242 4,32,13,1,3,20,2,2,0.9423077 4,37,16.5,2,2,12,3,3,1.1878777 3,27,6,0,4,12,3,5,1.333333 3,37,23,4,2,12,3,4,2.9217386 3,27,6,0,3,14,3,3,2 5,22,2.5,0,3,12,3,5,4.7999992 4,32,9,1,2,12,3,4,2.1777763 4,27,9,1,3,17,4,6,2.1777763 5,27,13,2,2,12,4,5,0.9230769 5,22,2.5,2,1,12,3,2,1.3999996 4,22,6,2,2,12,3,4,0.5833333 2,32,16.5,1,4,12,5,5,1.1878777 3,27,2.5,0,2,20,4,1,1.3999996 3,27,13,1,2,12,5,5,3.2307692 4,37,23,1,1,16,5,5,1.217391 4,27,6,0,3,16,2,1,2 4,22,6,0,2,14,3,5,4.666666 5,42,16.5,2,3,20,6,6,0.7272727 2,37,16.5,1,2,16,4,5,1.1878777 1,32,13,3,3,12,2,4,0.0769231 5,22,2.5,1,3,12,3,4,4.8999996 4,22,2.5,0,2,14,3,5,4.7999992 3,22,2.5,0,2,16,4,4,4.8999996 5,37,16.5,2,3,12,5,5,4.0727262 4,17.5,2.5,0,2,12,2,5,4.7999992 5,42,23,2,3,17,5,2,0.5326087 3,32,13,2,3,14,5,2,3.2307692 3,42,23,3,2,12,4,4,1.217391 4,27,2.5,0,3,14,3,4,1.3999996 5,42,13,0,2,12,5,5,0.9230769 2,32,9,2,4,16,4,4,2.1777763 3,27,6,1,3,14,3,4,3.2666645 2,27,9,3,3,12,5,4,2.1777763 3,27,6,2,3,14,4,6,0.5833333 5,27,9,2,1,14,3,4,4.9777775 2,27,13,1,3,12,3,2,0.0769231 4,27,13,2,2,12,3,4,0.0769231 5,22,2.5,0,3,12,3,4,4.7999992 4,27,9,0,3,12,2,4,4.666666 3,27,9,2,3,12,4,5,0.3888888 3,22,2.5,0,2,17,2,6,3.1999998 3,27,6,1,3,14,3,3,2.041666 4,27,6,0,2,14,5,3,2 4,32,16.5,3,3,14,5,5,0.0606061 4,32,16.5,2,3,12,5,5,0.7424242 3,42,16.5,2,4,16,5,5,0.2121212 3,32,6,2,3,14,3,4,2 3,37,23,4,4,9,5,5,0.5326087 1,42,16.5,1,2,12,3,5,1.1878777 2,42,23,5.5,3,14,2,2,0.5217391 5,37,16.5,4,4,14,3,3,0.0606061 5,42,23,1,3,14,3,5,0.8521735 3,22,2.5,1,2,12,2,2,7.8399963 5,22,2.5,0,2,16,5,4,4.8999996 2,27,6,1,2,14,3,4,0.1666666 1,32,13,2,2,16,4,6,0.0769231 3,32,16.5,2,2,16,4,2,1.1878777 5,27,9,1,3,14,3,5,2.1777763 3,22,6,1,1,12,3,2,3.2666645 4,27,6,2,3,12,3,2,1.333333 4,37,16.5,2,4,17,6,6,0.4848484 4,22,2.5,0,3,12,3,3,0.4 1,42,23,3,3,14,3,5,0.8521735 2,22,2.5,0,2,12,3,5,4.7999992 4,37,13,1,3,20,4,2,1.5076914 2,27,6,1,2,12,2,2,0.5833333 5,27,9,2,3,20,4,4,0.3888888 3,42,23,3,3,12,2,2,1.826086 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2,32,13,0,2,12,3,4,1.5076914 4,32,13,2,3,14,3,4,3.2307692 4,37,16.5,3,3,14,3,3,0.2121212 4,22,2.5,0,2,14,3,5,4.7999992 5,42,23,4,2,14,3,4,0.8521735 3,32,16.5,2,4,12,3,5,1.1878777 4,42,23,4,3,9,3,5,1.9478254 5,22,2.5,1,2,12,3,4,4.8999996 2,32,9,0,2,14,3,4,0.8888888 5,32,13,1,2,14,3,5,0.2692307 2,32,16.5,3,2,12,5,2,0.7424242 5,27,6,1,1,14,5,5,2 4,42,23,4,2,14,3,4,0.8521735 3,27,6,1,2,14,5,2,3.2666645 3,32,13,1,1,16,4,2,0.6153846 2,27,6,2,3,12,3,5,0.1666666 4,27,9,2,3,12,4,4,1.3611107 5,22,2.5,1,1,14,3,2,11.1999998 2,22,2.5,1,3,14,5,6,7.8399963 5,22,2.5,0,1,16,5,4,0.4 4,37,23,4,3,14,3,5,1.9478254 2,32,16.5,4,3,12,3,4,0.7424242 3,22,6,1,3,12,3,4,2.041666 3,32,9,2,3,12,3,4,16 1,27,2.5,0,2,12,4,3,4.8999996 5,42,23,2,3,14,3,4,0.5217391 4,27,13,1,2,12,3,4,0.0769231 4,32,9,2,3,17,3,4,1.3611107 5,42,23,4,4,14,5,4,0.5326087 4,27,6,2,3,12,2,2,2.041666 5,32,16.5,2,4,16,5,6,1.696969 5,27,9,2,1,16,2,5,0.3888888 4,22,6,1,2,12,2,1,2.041666 5,32,13,2,1,12,3,4,0.0769231 3,42,23,2,3,12,3,5,0.1521739 4,27,16.5,4,3,17,4,6,2.545454 3,37,16.5,2,3,12,3,4,0.7272727 5,27,6,2,3,14,4,2,3.2666645 2,17.5,2.5,1,3,12,3,2,1.3999996 4,22,2.5,1,2,14,3,5,1.3999996 5,27,6,1,3,14,3,3,2.041666 5,27,6,2,2,12,4,4,0.1666666 3,37,23,3,4,12,5,2,0.8521735 3,27,6,3,2,16,4,4,0.5833333 3,22,2.5,1,2,12,3,2,1.3999996 5,27,13,3,1,12,3,5,1.5076914 4,27,9,1,4,14,3,3,1.3611107 1,37,23,5.5,2,12,3,4,0.5217391 5,42,23,3,1,16,4,6,0.8521735 4,27,2.5,0,1,16,5,6,7.8399963 4,32,13,2,2,12,5,4,0.9423077 3,27,9,2,2,14,5,5,1.3611107 4,22,2.5,0,1,14,3,4,4.8999996 4,22,2.5,0,1,12,3,2,1.3999996 4,27,6,1,3,17,4,5,0.1666666 4,37,23,5.5,2,12,3,4,0.5217391 5,32,16.5,2,1,12,2,4,0.2121212 2,22,6,2,4,17,3,5,2 2,22,2.5,0,1,17,4,4,26.8799896 4,27,6,0,3,14,2,2,7.4666672 5,22,2.5,0,2,14,3,5,1.3999996 5,42,23,3,3,12,3,5,2.782608 5,32,13,2,2,14,5,4,0.9423077 5,32,13,2,2,14,5,4,1.5076914 3,42,23,5.5,3,20,6,4,2.9217386 5,22,2.5,1,1,12,3,5,1.3999996 2,22,2.5,0,1,16,3,5,17.9199982 3,42,23,2,3,16,4,5,0.1521739 3,27,6,0,2,12,3,4,4.666666 3,27,13,0,3,12,3,5,0.9423077 4,22,2.5,0,2,12,2,4,4.7999992 3,32,13,2,3,14,3,3,1.5076914 5,37,16.5,3,2,12,3,5,0.7272727 3,27,9,1,3,14,3,3,2.1777763 5,42,23,2,2,12,5,4,0.8521735 5,27,2.5,0,1,17,4,5,4.8999996 3,32,0.5,0,2,16,4,5,24.5 4,32,13,2,3,12,3,1,0.0769231 3,42,23,5.5,3,12,3,2,0.1521739 1,42,23,2,3,14,3,5,0.8521735 3,37,16.5,2,1,17,4,2,0.7272727 4,27,9,1,1,14,3,4,1.3611107 4,22,2.5,0,3,12,3,2,1.3999996 4,37,23,5.5,2,14,3,6,1.217391 5,32,9,3,2,14,2,6,0.3888888 4,37,9,3,3,16,4,2,2.1777763 5,37,16.5,3,3,16,3,4,1.696969 4,32,13,2,2,12,5,5,0.2692307 3,37,23,3,4,12,3,5,0.5217391 4,42,23,3,4,16,4,2,1.217391 3,27,6,1,2,12,3,4,0.5833333 5,42,23,2,3,16,3,5,0.5326087 5,27,6,1,3,20,5,6,1.333333 3,37,16.5,3,2,12,3,2,2.7151508 3,27,13,2,3,12,3,5,0.9230769 5,37,23,3,1,12,3,4,0.0434783 3,42,23,5.5,3,12,3,4,0.0434783 2,27,9,0,2,17,2,3,1.3611107 2,22,2.5,0,3,12,2,3,0.4 4,27,13,2,2,12,3,2,0.0769231 4,32,9,1,1,16,4,5,4.9777775 3,32,9,3,3,14,3,6,2.1777763 4,32,13,1,3,14,5,5,0.2692307 5,22,2.5,0,3,16,4,1,1.3999996 3,27,6,1,2,17,4,4,4.666666 4,27,2.5,0,2,16,4,2,7.8399963 3,27,6,0,1,16,4,4,1.333333 3,42,16.5,4,3,16,2,4,0.2121212 1,27,2.5,1,3,16,4,4,1.3999996 5,27,9,1,2,14,4,4,3.1111107 4,42,23,2,3,12,3,5,1.826086 4,27,13,2,2,12,3,4,0.9230769 5,32,13,1,1,14,4,4,0.9423077 4,22,2.5,1,2,14,3,4,7.8399963 2,27,9,2,2,14,5,5,4.666666 5,22,2.5,0,4,14,3,4,4.8999996 3,37,16.5,3,3,14,3,3,0.2121212 3,27,6,1,3,14,3,4,7 4,32,13,2,1,12,2,4,3.4461536 3,42,23,2,2,16,4,5,0.5217391 4,37,16.5,3,3,12,3,5,0.2121212 4,32,13,2,1,12,2,4,1.5076914 3,42,23,5.5,2,12,3,4,2.9217386 3,27,9,1,1,14,3,4,1.3611107 5,32,16.5,2,3,12,3,2,0.7424242 5,32,16.5,1,2,14,5,5,0.2121212 5,27,6,2,2,20,6,6,4.666666 4,27,6,2,3,12,3,2,0.1666666 3,22,6,1,3,14,5,4,0.5833333 5,27,16.5,3,3,14,5,5,0.2121212 5,22,2.5,0,2,14,5,6,4.8999996 3,42,23,5.5,3,14,3,5,0.5217391 4,37,23,3,2,12,3,3,0.5217391 1,42,16.5,3,4,17,4,4,1.1878777 3,27,2.5,0,2,16,4,2,4.7999992 2,27,6,2,2,12,5,1,0.1666666 5,27,9,3,2,16,4,4,0.1111111 5,27,6,2,2,12,5,3,0.5833333 3,32,16.5,3,1,14,2,2,0.4848484 4,27,6,2,2,14,3,4,0.5833333 4,27,0.5,0,3,17,4,6,7 4,22,6,1,2,12,3,3,3.2666645 5,42,23,2,1,14,6,6,2.9217386 4,27,6,2,4,14,5,4,0.1666666 5,27,6,1,2,16,4,5,2.041666 3,42,13,0,3,17,4,5,0.2692307 3,42,23,3,3,12,2,2,1.217391 5,27,6,1,1,16,4,4,2.041666 5,22,6,0,3,14,3,4,2.041666 3,42,23,3,2,14,3,4,0.8521735 4,22,6,0,2,16,4,5,0.5833333 5,32,13,2,1,14,3,5,3.2307692 3,22,6,2,3,14,2,2,11.1999989 5,27,2.5,0,2,14,3,2,1.3999996 2,42,23,5.5,2,14,3,2,0.0434783 4,37,23,3,1,14,3,4,0.8521735 5,22,2.5,0,1,14,3,4,7.8399963 5,27,2.5,0,1,17,4,5,0.4 4,27,9,1,2,16,3,5,0.3888888 4,27,9,3,3,14,3,4,1.3611107 4,42,23,4,2,16,4,5,0.8521735 4,37,16.5,4,3,14,3,2,0.7424242 4,32,9,0,2,12,3,3,1.333333 4,32,13,0,2,14,3,6,0.9423077 2,22,6,2,2,12,3,4,0.5833333 3,42,23,3,2,14,5,5,0.5326087 4,32,13,0,3,14,3,5,0.9230769 4,37,16.5,4,3,14,3,4,0.7424242 3,37,23,3,2,12,3,5,0.8521735 4,32,16.5,2,1,14,3,4,2.545454 4,27,6,1,2,16,3,5,2 4,22,2.5,0,2,16,4,5,3.1999998 2,22,2.5,0,3,12,3,2,1.3999996 4,27,6,1,2,14,3,3,1.333333 3,32,16.5,2,2,12,3,2,2.7151508 5,17.5,2.5,2,2,12,2,5,4.7999992 3,22,2.5,0,3,20,3,1,7.8399963 2,37,23,3,3,12,3,2,0.8521735 4,32,16.5,5.5,3,14,5,5,0.7424242 3,42,23,3,4,14,3,5,0.1521739 5,22,2.5,0,2,14,2,3,4.8999996 4,27,9,0,2,14,3,4,3.1111107 3,22,2.5,2,2,12,3,4,0.4 3,42,23,2,4,14,4,6,1.217391 5,42,23,5.5,2,14,3,2,0.5326087 4,27,6,0,3,14,6,6,2.041666 4,42,23,4,3,14,3,4,0.5217391 3,32,16.5,2,2,12,3,5,0.3393939 3,27,2.5,0,1,16,3,4,4.8999996 3,32,13,2,4,14,4,2,5.1692305 2,37,16.5,2,2,14,3,5,1.1878777 4,22,6,2,2,12,2,4,2 4,32,9,3,1,16,2,4,0.1111111 3,42,23,4,2,12,3,5,0.3478261 3,32,13,2,3,12,3,3,2.1538458 4,22,2.5,0,2,14,2,1,0.4 3,37,16.5,2,2,12,2,2,0.7272727 3,27,6,0,2,14,3,5,2 4,42,23,3,3,12,5,4,2.9217386 4,42,23,3,2,14,5,4,1.217391 2,42,23,5.5,4,14,2,5,0.1521739 5,27,6,0,2,12,5,4,0.5833333 4,32,16.5,1,2,14,3,4,0.7424242 4,37,16.5,3,3,12,4,2,1.696969 5,42,23,5.5,3,14,3,6,0.1521739 3,37,16.5,3,2,14,5,4,0.7272727 2,37,13,1,1,16,4,4,0.9423077 4,27,6,0,3,16,5,6,0.5833333 4,42,23,4,3,16,4,2,0.8521735 5,27,2.5,0,2,14,3,4,3.1999998 2,42,23,3,1,12,3,5,2.9217386 5,37,13,2,1,14,3,6,0.2692307 4,32,16.5,2,1,12,5,2,1.1878777 4,37,16.5,3,1,14,3,2,0.4848484 3,27,2.5,0,1,14,5,4,1.3999996 4,22,2.5,0,1,14,3,3,4.8999996 4,37,16.5,2,2,14,3,5,1.1878777 3,27,6,2,2,12,3,4,0.1666666 4,22,6,1,2,12,3,4,0.1666666 5,32,13,2,2,14,4,5,0.2692307 2,37,23,3,3,12,5,2,0.5326087 2,37,16.5,2,3,14,3,5,2.545454 4,32,16.5,2,2,14,5,4,0.7272727 5,37,16.5,5.5,4,20,4,6,0.7424242 3,32,16.5,3,2,12,3,2,1.1878777 3,27,9,4,3,14,3,5,2.1777763 3,37,13,0,1,14,5,4,3.2307692 2,27,2.5,2,2,14,4,5,4.8999996 4,27,9,2,1,14,3,4,0.8888888 4,42,23,2,3,14,3,4,0.3478261 5,42,23,2,1,14,5,5,0.8521735 4,42,23,4,2,12,3,3,0.5217391 4,37,16.5,4,3,14,3,5,0.2121212 4,32,16.5,3,2,12,2,2,1.1878777 2,37,23,2,2,12,4,4,0.0434783 4,42,23,1,3,20,4,4,0.5217391 4,22,2.5,1,2,14,4,4,4.8999996 1,32,13,2,2,14,4,4,2.1538458 3,42,23,3,2,14,3,5,1.826086 4,22,2.5,0,2,16,3,2,1.3999996 5,37,23,3,3,12,3,5,0.1521739 3,22,2.5,0,2,14,2,2,4.8999996 1,42,23,3,3,12,5,5,1.9478254 3,22,2.5,0,2,14,3,4,4.8999996 3,37,23,2,3,12,3,5,1.9478254 4,22,2.5,0,2,12,5,4,0.4 5,32,9,2,3,14,5,4,0.1111111 1,37,16.5,4,2,14,3,6,1.1878777 3,42,23,1,3,12,3,4,0.8521735 5,27,9,2,1,12,3,2,1.3611107 4,22,2.5,1,2,14,2,4,17.9199982 5,42,23,3,2,14,3,5,0.8521735 4,27,6,1,3,14,5,5,2 5,22,2.5,0,1,14,3,1,1.3999996 3,37,16.5,2,3,16,3,4,0.7272727 3,32,16.5,2,3,12,5,5,2.545454 5,37,16.5,3,3,14,2,5,0.7272727 3,27,6,2,1,16,4,3,0.5833333 4,27,9,1,2,20,4,4,0.1111111 4,27,6,0,2,14,3,4,2.041666 5,32,13,2,2,14,3,4,0.9423077 4,42,23,2,2,12,4,4,1.217391 2,37,16.5,2,2,12,5,4,0.4848484 4,27,2.5,0,2,17,5,5,0.4 4,37,16.5,2,2,17,4,5,0.2121212 4,32,13,2,2,12,3,3,0.9230769 4,32,9,2,1,14,3,4,1.3611107 4,32,9,2,2,14,3,5,0.1111111 4,32,13,2,3,12,5,5,0.9423077 4,32,13,3,2,14,3,2,2.1538458 4,22,2.5,1,1,14,2,2,1.3999996 5,27,16.5,2,3,12,5,4,0.2121212 4,32,2.5,0,3,14,2,6,4.8999996 3,32,16.5,1,2,14,2,4,0.2121212 3,37,16.5,3,2,16,4,3,1.1878777 5,42,23,4,2,12,5,5,0.8521735 5,27,6,2,3,14,3,4,3.2666645 4,22,2.5,1,3,12,3,2,1.3999996 4,42,23,3,1,20,6,6,1.217391 4,32,9,2,1,17,4,5,2.1777763 5,32,2.5,0,2,20,6,6,1.3999996 3,27,6,1,2,14,3,6,0.5833333 1,22,2.5,0,1,14,4,4,4.8999996 3,32,16.5,2,2,14,3,2,0.7424242 4,42,23,2,2,12,3,3,0.1521739 4,22,6,1,3,14,3,5,0.5833333 5,42,23,3,2,14,3,5,0.5326087 3,27,13,2,2,12,4,3,3.4461536 4,32,13,2,2,14,5,4,0.2692307 3,27,2.5,0,3,14,3,4,3.1999998 2,22,2.5,0,3,12,3,2,0.4 5,42,23,2,2,20,4,4,1.826086 3,27,6,1,2,14,2,2,0.5833333 5,42,23,2,2,20,3,6,0.5326087 3,37,23,4,1,12,3,2,0.3478261 5,42,23,4,4,20,6,6,6.260869 5,27,6,0,1,17,4,5,1.333333 3,32,13,2,1,17,4,6,0.2692307 2,27,2.5,0,1,14,5,5,1.3999996 4,27,9,3,2,12,3,6,1.333333 5,27,6,1,1,14,3,5,2 4,22,0.5,0,2,14,4,5,24.5 4,17.5,2.5,1,2,12,3,2,1.3999996 3,27,2.5,1,2,14,3,4,1.3999996 5,32,16.5,3,2,14,2,4,0.0606061 4,42,23,5.5,1,14,3,5,0.5326087 5,22,2.5,0,1,14,3,4,4.8999996 5,42,23,2,2,20,1,5,0.1521739 5,42,23,3,3,14,3,5,0.0434783 2,42,23,3,3,16,4,4,0.1521739 4,32,16.5,4,2,12,3,5,0.4848484 4,37,23,4,2,12,3,4,0.8521735 4,42,23,2,1,14,5,3,0.5326087 5,22,2.5,0,4,14,3,4,1.3999996 4,22,2.5,0,1,16,3,5,1.3999996 4,42,23,3,3,14,5,5,1.9478254 4,42,23,3,2,14,3,5,1.9478254 2,22,2.5,0,2,14,3,5,0.4 3,42,23,3,1,20,4,4,0.0434783 3,37,16.5,3,4,12,3,2,2.545454 4,27,16.5,2,1,12,3,2,0.2121212 3,27,6,1,1,16,4,1,3.2666645 5,32,13,2,2,14,4,4,0.9230769 4,32,13,3,2,12,2,4,0.6153846 5,42,13,0,1,16,3,6,1.5076914 4,32,9,2,3,14,3,4,2.1777763 3,42,16.5,1,3,17,3,3,0.7424242 4,42,23,3,1,14,3,5,0.8521735 1,32,13,3,3,14,3,4,1.5076914 4,27,6,2,2,14,3,5,1.333333 4,27,6,2,2,14,5,4,3.2666645 5,27,2.5,0,3,16,3,5,1.3999996 4,22,2.5,0,1,16,4,2,1.3999996 4,27,6,3,3,14,4,2,2.041666 4,42,23,2,1,16,4,5,0.1521739 3,27,6,1,4,14,5,4,0.5833333 3,32,13,0,2,16,3,6,0.9230769 1,27,6,2,3,14,3,2,3.2666645 3,32,13,2,2,14,3,2,2.1538458 3,37,16.5,4,2,14,4,4,0.7424242 4,37,16.5,3,4,14,4,4,0.2121212 4,32,16.5,4,3,14,3,5,0.2121212 5,27,2.5,0,1,14,3,5,4.7999992 3,22,2.5,0,2,14,3,1,0.4 5,32,23,2,3,14,5,6,0.5217391 3,27,9,1,3,14,3,2,1.333333 5,37,23,3,2,14,5,4,0.3478261 3,27,6,1,3,20,4,4,3.2666645 1,27,9,1,3,14,2,4,0.3888888 4,32,13,4,2,16,4,2,0.2692307 3,32,16.5,3,3,14,5,4,4.0727262 4,42,23,3,3,14,4,5,0.1521739 4,32,16.5,4,2,14,2,5,1.696969 3,27,9,4,4,14,4,4,0.3888888 4,27,6,1,2,12,2,4,0.1666666 2,22,6,1,3,14,3,5,2 4,22,2.5,1,2,14,3,5,1.3999996 3,22,2.5,1,3,14,3,4,3.1999998 5,22,2.5,0,1,14,3,2,1.3999996 5,37,23,3,1,12,5,2,1.826086 3,27,9,1,1,14,3,6,4.666666 4,27,2.5,0,1,14,5,5,7.8399963 5,27,2.5,0,1,16,4,2,1.3999996 3,22,6,2,3,12,3,2,0.5833333 4,37,23,2,2,12,3,2,0.1521739 3,22,2.5,0,2,14,3,4,4.7999992 5,27,2.5,0,2,17,4,5,1.3999996 4,22,2.5,0,1,14,5,2,4.8999996 4,27,6,1,2,14,3,3,7 4,27,6,2,2,14,4,4,0.5833333 4,32,13,0,2,12,3,3,3.2307692 4,27,9,2,2,12,2,4,1.3611107 3,22,2.5,0,1,14,3,2,7.8399963 5,27,2.5,0,1,14,2,4,7.8399963 3,37,23,4,2,14,3,4,1.9478254 5,27,9,3,2,16,4,4,1.333333 4,22,2.5,0,2,12,2,2,1.3999996 2,32,16.5,3,1,14,4,4,1.1878777 3,27,9,2,2,12,3,2,1.3611107 4,32,16.5,3,1,16,4,5,0.7272727 3,27,9,1,2,12,5,4,0.1111111 5,22,2.5,0,1,14,2,2,7.8399963 4,42,23,2,3,14,5,5,0.5326087 5,27,6,1,4,16,4,1,0.1666666 4,22,2.5,0,1,12,2,2,4.8999996 3,22,0.5,0,1,14,5,5,7 5,42,23,5.5,3,14,5,4,1.9478254 4,37,16.5,2,2,12,3,4,0.2121212 4,22,2.5,0,2,12,3,3,3.1999998 3,22,6,1,2,12,3,2,2.041666 4,42,23,4,3,17,6,3,2.782608 4,22,6,0,4,14,5,4,2.041666 2,27,9,3,3,14,4,4,0.1111111 3,27,6,1,1,14,5,4,7 5,42,23,5.5,3,16,4,6,0.0434783 4,37,13,3,1,12,4,4,0.6153846 4,37,16.5,2,3,12,5,5,0.7272727 4,37,13,3,3,16,3,4,0.2692307 5,22,6,2,2,12,2,4,4.666666 4,27,2.5,0,2,17,4,6,16.7999878 2,22,6,2,3,14,3,5,3.2666645 3,22,6,1,2,12,4,4,1.333333 5,32,9,2,2,14,4,4,0.1111111 3,27,9,3,2,12,3,2,0.3888888 3,32,13,2,3,14,3,5,0.2692307 2,27,9,1,2,16,4,5,4.9777775 4,27,6,1,1,17,3,5,0.5833333 4,32,2.5,0,2,20,6,6,16.7999878 5,32,13,2,1,12,3,5,0.9423077 4,32,16.5,1,1,14,5,5,1.696969 5,27,2.5,0,3,12,4,5,0.4 3,42,23,4,3,16,4,2,0.3478261 4,22,6,1,3,14,3,4,2.041666 4,27,6,0,3,14,3,4,0.1666666 4,17.5,2.5,0,2,12,3,4,7.8399963 4,22,2.5,0,1,12,3,4,0.4 1,37,13,3,1,17,5,6,0.0769231 2,32,16.5,2,1,12,5,2,2.7151508 3,37,23,3,3,12,3,5,0.1521739 5,27,9,1,3,12,3,5,1.3611107 4,27,6,1,1,12,3,3,3.2666645 3,37,23,4,2,12,3,2,1.826086 4,37,23,5.5,3,12,5,5,0.1521739 1,22,2.5,1,1,12,3,4,1.3999996 3,22,2.5,0,1,12,3,5,4.7999992 4,27,2.5,0,1,16,4,2,7.8399963 4,32,13,1,3,16,3,5,0.6153846 4,27,2.5,0,2,12,3,4,7.8399963 2,32,9,0,2,16,3,2,1.3611107 5,42,23,4,1,20,4,5,0.5217391 4,22,6,1,1,12,3,5,2 3,42,23,4,2,14,3,5,0.3478261 5,27,6,0,3,12,3,4,2.041666 4,42,16.5,2,2,12,3,4,0.2121212 5,22,2.5,0,2,16,4,1,3.1999998 4,42,23,5.5,4,20,4,2,0.1521739 5,27,9,2,3,14,4,5,0.3888888 4,27,2.5,1,3,16,6,5,4.7999992 3,27,9,0,3,16,5,5,1.333333 5,37,23,3,2,14,3,5,0.1521739 4,37,16.5,2,3,17,4,2,1.696969 3,27,6,1,1,17,4,5,2.041666 5,32,16.5,3,4,14,3,6,0.7272727 5,37,16.5,2,3,12,3,4,0.7424242 3,27,6,1,4,17,4,5,7 3,37,16.5,3,2,14,3,4,2.545454 5,27,9,1,1,14,3,4,0.3888888 3,32,9,3,2,14,5,5,1.3611107 2,42,23,3,2,12,3,5,0.8521735 4,32,13,2,1,14,3,5,1.5076914 4,22,2.5,1,2,14,3,2,4.7999992 5,27,9,2,2,12,3,6,0.3888888 5,32,16.5,2,1,12,3,6,0.0606061 4,32,16.5,2,2,12,2,4,1.696969 4,42,23,3,2,12,3,5,1.9478254 4,32,9,2,3,9,3,5,1.333333 2,27,6,2,3,12,3,4,2.041666 5,42,23,2,3,16,4,5,0.2434782 4,37,23,3,4,12,5,4,0.5326087 4,32,16.5,3,2,12,5,5,3.878787 3,27,9,1,2,12,3,4,7.1111107 2,37,13,2,3,14,3,4,0.9230769 4,32,16.5,3,3,14,4,3,0.2121212 3,32,16.5,4,3,12,2,2,1.1878777 3,42,23,4,2,12,4,4,1.826086 3,42,23,3,3,17,4,6,0.0434783 5,27,9,3,1,14,3,6,1.333333 4,27,6,1,3,14,4,5,0.5833333 3,22,2.5,0,2,12,3,5,1.3999996 3,22,2.5,0,2,14,5,4,0.4 4,32,16.5,3,3,9,5,5,0.2121212 4,27,2.5,0,3,16,4,6,4.8999996 3,27,6,1,2,12,3,5,0.5833333 3,32,16.5,2,3,16,4,4,0.7424242 5,42,23,3,3,12,4,2,1.217391 3,27,6,1,3,16,2,2,2 4,27,9,2,3,14,5,5,1.333333 4,27,9,1,4,12,3,2,3.1111107 3,37,13,2,3,16,2,4,1.5076914 4,22,6,1,2,14,3,5,0.5833333 5,37,13,2,3,14,5,5,0.6153846 3,22,2.5,0,1,14,3,1,4.8999996 4,37,16.5,3,3,12,5,5,0.2121212 1,32,13,2,2,17,4,6,3.2307692 3,22,2.5,0,3,14,5,4,3.1999998 3,22,6,1,3,12,4,2,2 4,22,2.5,1,3,14,2,2,16.7999878 2,42,23,2,1,14,3,5,0.1521739 1,42,23,3,1,17,4,5,1.826086 3,37,16.5,3,3,16,6,4,1.696969 4,27,6,0,2,12,3,4,7 3,37,16.5,4,1,12,3,6,0.7272727 4,27,6,2,2,12,3,2,0.1666666 3,32,9,0,1,16,4,5,7.4666662 5,22,2.5,0,3,14,4,4,0.4 2,37,16.5,2,4,12,3,3,0.2121212 3,22,2.5,0,3,12,3,2,1.3999996 4,27,6,2,1,14,2,2,2.041666 3,32,16.5,3,2,12,4,2,0.7424242 2,27,2.5,0,2,16,4,5,17.9199982 3,42,23,5.5,2,20,4,3,0.1521739 1,37,16.5,2,3,14,3,5,0.7272727 4,22,6,2,2,12,3,5,3.2666645 4,42,23,2,3,20,4,4,0.8521735 3,22,2.5,0,2,14,3,3,3.1999998 4,27,9,0,3,17,5,6,1.333333 5,27,2.5,0,2,16,3,2,11.1999998 5,27,9,2,3,14,3,3,0.3888888 2,27,6,1,1,16,4,5,2 3,42,23,2,2,14,3,5,0.5217391 4,27,9,2,3,12,3,5,1.3611107 3,37,23,5.5,2,12,2,5,0.3478261 4,27,6,1,2,14,3,4,3.2666645 3,27,2.5,0,3,12,3,5,4.7999992 1,27,2.5,0,2,14,3,2,4.8999996 3,27,6,1,3,16,5,4,2 4,27,6,2,3,16,4,2,3.2666645 4,27,13,3,4,14,2,4,1.5076914 3,27,9,2,3,16,4,5,4.666666 5,27,13,3,2,14,5,4,0.9423077 5,22,6,1,3,12,4,2,7 1,32,16.5,2,3,16,4,4,0.7272727 1,42,23,3,3,20,4,4,0.8521735 3,27,2.5,0,1,16,5,5,3.1999998 5,42,23,5.5,3,14,4,5,0.0434783 3,22,6,1,1,16,3,4,3.2666645 1,22,2.5,0,1,12,3,2,1.3999996 2,22,2.5,1,2,14,3,4,11.1999998 5,27,2.5,0,1,17,4,4,1.3999996 2,27,6,1,3,12,3,6,3.2666645 3,37,9,2,1,17,4,3,0.3888888 3,42,23,2,3,12,3,3,1.826086 4,37,16.5,4,3,17,4,2,1.1878777 4,32,13,2,2,14,5,5,0.2692307 5,27,9,2,3,14,4,4,1.333333 5,42,16.5,4,3,16,5,4,0.0606061 1,37,13,1,4,16,3,5,1.5076914 5,32,9,3,2,16,4,5,0.3888888 3,22,2.5,0,2,12,3,3,25.5999908 3,27,2.5,0,4,14,5,6,0.4 3,22,2.5,0,2,12,3,5,1.3999996 2,32,16.5,2,1,16,6,6,0.7272727 4,32,9,1,3,14,3,5,0.8888888 2,42,16.5,2,3,12,3,3,1.1878777 4,37,16.5,3,2,12,5,2,4.0727262 2,37,16.5,3,2,12,3,5,0.2121212 4,22,2.5,1,3,12,3,4,1.3999996 3,32,16.5,3,1,12,5,4,0.7272727 3,32,9,1,1,14,2,4,2.1777763 1,42,23,3,2,14,3,5,0.8521735 5,22,2.5,0,1,14,3,2,7.8399963 3,42,23,4,1,14,3,5,0.1521739 4,27,9,2,2,12,1,5,3.1111107 4,27,9,1,3,14,3,5,3.1111107 4,22,2.5,0,1,16,4,4,1.3999996 4,37,16.5,5.5,3,12,2,4,0.2121212 3,22,6,2,1,12,3,4,1.333333 1,42,16.5,5.5,2,12,2,5,0.2121212 3,32,9,2,4,17,4,2,2.1777763 4,32,13,2,2,12,3,5,0.9423077 3,37,16.5,2,2,16,4,5,1.1878777 3,37,16.5,3,3,17,4,6,0.7272727 4,32,13,2,2,14,5,4,1.5076914 3,42,23,3,1,14,4,4,1.217391 1,32,16.5,2,3,14,4,2,2.545454 1,42,23,2,3,12,3,4,0.8521735 5,37,6,2,3,17,4,4,0.5833333 5,22,2.5,0,3,16,3,5,16.7999878 3,32,16.5,2,1,12,3,4,0.7272727 1,27,6,2,2,12,2,2,0.5833333 3,42,23,4,2,12,3,5,0.8521735 5,27,6,2,1,14,4,4,2.041666 4,27,6,2,2,12,3,2,3.2666645 4,22,2.5,0,1,16,3,4,3.1999998 4,27,9,0,2,12,3,4,1.3611107 4,22,6,0,1,14,5,6,2 3,42,16.5,2,1,14,3,6,0.7272727 3,32,16.5,4,1,12,3,4,1.696969 1,22,2.5,1,1,12,3,4,7.8399963 4,37,16.5,3,2,12,3,5,2.545454 3,22,6,3,2,14,3,2,3.2666645 5,22,2.5,0,2,12,3,5,7.8399963 2,22,2.5,0,3,14,3,3,4.8999996 3,22,2.5,0,3,16,4,4,1.3999996 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5,42,23,3,3,12,3,5,1.217391 1,37,16.5,1,3,12,2,3,0.7424242 5,27,2.5,0,2,14,2,4,4.8999996 4,37,16.5,1,3,14,3,6,0.7424242 5,32,13,1,1,20,2,6,1.5076914 5,27,6,2,2,14,4,5,0.5833333 4,27,2.5,0,1,20,6,1,7.8399963 4,42,23,4,3,12,2,3,0.3478261 3,27,9,1,3,17,5,5,2.1777763 3,22,2.5,1,2,12,2,2,3.1999998 4,27,6,0,2,14,3,6,2.041666 4,32,13,2,1,12,3,5,3.4461536 2,32,9,1,2,16,3,3,0.1111111 2,27,6,1,1,14,4,6,2.041666 3,22,2.5,1,1,14,2,2,1.3999996 5,22,0.5,0,1,12,3,4,2 5,22,2.5,0,2,20,4,1,7.8399963 5,22,6,0,3,14,3,2,0.5833333 5,42,23,2,3,17,4,2,0.1521739 1,22,2.5,1,2,14,3,2,4.7999992 3,27,6,1,2,12,3,4,3.2666645 3,22,6,0,3,14,5,4,2 4,27,9,2,2,16,4,4,2.1777763 3,22,6,1,2,9,2,2,0.1666666 4,32,16.5,3,2,16,5,5,0.2121212 5,37,16.5,1,3,14,3,2,0.4848484 2,27,9,2,3,14,2,2,0.8888888 4,32,13,0,2,14,3,5,0.2692307 4,37,23,5.5,3,14,4,5,0.8521735 4,27,13,2,3,12,3,5,0.2692307 3,27,9,1,1,16,3,6,1.3611107 3,32,13,3,2,14,3,4,0.2692307 2,27,9,1,3,14,3,5,1.3611107 3,22,6,2,2,12,3,2,1.333333 3,32,16.5,2,2,12,3,5,0.0606061 3,42,23,2,3,12,2,3,2.9217386 4,27,6,1,3,14,3,3,2.041666 2,27,13,2,1,12,4,5,1.5076914 3,42,23,3,2,12,3,4,0.1521739 2,42,23,4,2,12,5,5,0.5217391 5,42,23,4,4,14,3,2,0.1521739 4,27,6,1,1,12,5,6,7 3,42,23,1,2,14,5,6,0.5326087 1,32,13,0,3,14,3,5,0.9423077 5,32,13,2,3,14,4,2,0.9230769 3,27,6,0,1,16,3,2,2.041666 3,27,9,2,3,14,5,5,1.333333 3,27,6,1,3,16,4,5,0.5833333 4,22,2.5,0,1,12,3,2,1.3999996 2,42,23,2,3,12,5,5,0.8521735 4,22,2.5,0,3,14,5,4,3.1999998 4,27,9,2,2,20,4,6,0.3888888 2,27,2.5,1,2,14,2,4,1.3999996 4,37,23,4,3,14,3,3,4.173913 3,27,9,1,2,14,3,4,1.333333 5,22,2.5,0,2,12,3,2,1.3999996 4,27,6,1,2,12,3,4,0.1666666 5,32,13,1,3,14,5,5,0.9230769 5,32,13,1,2,12,3,4,0.2692307 4,27,2.5,0,3,14,5,4,4.7999992 4,27,9,1,3,14,3,5,0.1111111 5,32,13,2,2,12,5,3,0.9423077 4,27,2.5,0,3,12,3,3,0.4 3,32,13,2,2,14,3,3,0.2692307 4,27,6,1,3,12,3,4,0.5833333 5,37,23,4,3,16,5,5,0.5217391 4,27,9,2,2,12,5,5,2.1777763 2,42,16.5,3,3,16,3,5,2.545454 4,27,6,0,2,14,3,5,2.041666 3,22,2.5,1,3,12,5,5,0.4 4,32,13,2,2,14,3,5,1.5076914 3,27,6,1,2,14,3,4,3.2666645 3,27,13,1,1,12,3,3,0.6153846 3,27,6,0,1,16,6,6,2.041666 3,32,16.5,3,2,14,3,4,1.1878777 5,42,23,3,3,14,3,4,0.8521735 4,22,6,0,3,12,3,5,0.5833333 4,32,16.5,2,3,12,3,4,0.2121212 1,37,16.5,3,2,14,4,4,0.2121212 3,22,2.5,0,3,16,3,4,4.8999996 3,27,6,0,3,17,5,5,3.2666645 3,37,16.5,2,3,16,5,3,0.0606061 2,32,13,3,2,12,3,2,0.9423077 4,37,23,2,3,14,5,2,0.1521739 4,27,9,2,4,17,4,4,1.3611107 4,27,9,1,2,14,3,5,0.1111111 2,42,16.5,5.5,2,16,3,5,2.545454 4,32,16.5,3,4,14,3,4,4.0727262 4,27,6,1,3,14,3,2,2 4,42,23,3,2,12,3,4,1.9478254 5,32,16.5,3,2,12,3,5,1.696969 5,32,16.5,3,1,14,2,4,0.0606061 4,37,16.5,2,2,14,3,2,0.7272727 2,22,6,2,3,12,3,4,2 4,32,16.5,3,4,14,3,3,0.0606061 2,37,23,3,3,12,3,2,0.1521739 5,27,6,2,2,12,4,4,0.5833333 5,32,16.5,2,2,17,4,3,0.0606061 3,32,16.5,2,2,12,4,4,1.1878777 4,27,9,2,3,12,3,4,0.8888888 4,32,16.5,1,3,14,5,2,1.696969 4,27,9,2,2,16,4,5,2.1777763 4,22,2.5,0,1,16,3,2,0.4 3,37,23,4,2,14,3,5,0.8521735 5,27,13,2,2,12,2,5,0.9423077 5,32,16.5,4,3,14,3,4,0.7272727 2,37,16.5,3,2,14,5,3,0.2121212 5,32,6,1,3,14,3,5,0.5833333 3,22,2.5,0,2,16,3,3,4.8999996 5,22,2.5,0,3,16,3,2,4.7999992 2,32,13,1,2,12,3,2,1.5076914 3,42,13,0,3,17,5,2,1.5076914 3,22,2.5,0,1,16,3,5,7.8399963 3,42,23,3,2,17,4,4,1.217391 2,27,13,2,1,14,3,5,4.9230766 4,22,2.5,1,1,14,3,1,1.3999996 5,22,2.5,1,3,14,4,5,0.4 4,42,23,1,3,14,3,2,0.1521739 5,32,9,2,1,17,6,6,2.1777763 4,32,16.5,3,2,12,3,2,2.545454 3,27,2.5,1,3,14,3,6,1.3999996 3,37,16.5,4,2,14,3,2,0.2121212 3,32,16.5,3,3,14,3,5,0.7424242 3,32,23,3,3,14,3,2,1.217391 5,22,2.5,0,1,12,2,2,1.3999996 3,32,16.5,3,2,12,5,5,4.0727262 4,27,2.5,0,1,17,4,3,1.3999996 3,27,6,0,2,20,6,6,3.2666645 5,27,13,0,3,14,3,4,0.0769231 5,37,16.5,3,4,14,5,5,0.2121212 4,37,16.5,3,1,14,3,3,0.7272727 5,32,13,1,3,14,5,2,3.2307692 4,27,6,0,2,14,3,6,2 3,27,0.5,0,1,14,3,3,24 3,22,2.5,2,3,14,2,2,4.8999996 4,37,23,4,4,12,3,3,0.1521739 5,32,16.5,2,3,14,4,5,1.1878777 5,32,13,3,3,14,3,6,0.9230769 4,32,13,3,1,20,5,5,1.5076914 3,27,6,0,1,12,3,4,0.5833333 5,22,2.5,0,3,14,3,2,1.3999996 4,32,23,3,2,9,4,5,1.217391 3,37,23,2,2,12,5,4,0.5217391 2,22,2.5,2,2,12,2,2,4.8999996 4,32,13,0,3,14,3,5,1.5076914 5,27,2.5,0,3,14,3,5,0.4 4,32,9,2,3,14,2,4,0 4,27,6,0,2,14,3,4,0 4,22,2.5,0,2,14,3,2,0 5,42,23,4,3,16,3,5,0 5,27,2.5,1,3,20,2,2,0 4,27,6,1,2,14,2,4,0 4,42,23,5.5,2,12,3,2,0 5,27,2.5,0,1,14,3,2,0 5,32,13,2,3,14,3,5,0 4,22,2.5,0,2,12,4,4,0 5,22,2.5,0,3,12,3,2,0 3,27,6,1,2,17,5,4,0 3,27,2.5,0,2,16,3,5,0 5,22,2.5,0,3,14,3,5,0 5,22,2.5,0,1,17,4,2,0 4,27,2.5,1,1,16,2,4,0 5,27,2.5,0,2,16,5,4,0 4,32,13,4,3,12,3,4,0 5,17.5,0.5,0,4,16,3,4,0 5,27,6,2,3,14,5,5,0 5,22,6,2,2,17,4,2,0 5,22,2.5,0,2,14,4,2,0 3,27,9,0,2,16,5,2,0 4,27,2.5,1,3,14,3,5,0 5,22,2.5,0,1,12,3,4,0 5,22,6,0,3,12,3,4,0 5,27,6,2,3,12,3,3,0 5,27,6,2,3,12,2,4,0 4,27,2.5,0,1,12,3,2,0 3,22,2.5,1,1,14,4,2,0 4,22,2.5,0,1,14,3,2,0 5,22,2.5,1,3,12,2,2,0 5,27,6,1,4,14,5,6,0 4,42,23,5.5,2,12,3,5,0 5,27,9,2,3,14,3,4,0 5,32,9,2,2,12,4,5,0 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4,37,9,0,3,20,4,4,0 4,22,2.5,0,1,16,3,5,0 4,37,13,2,2,16,4,4,0 5,37,16.5,3,4,17,4,4,0 4,27,6,0,1,20,6,6,0 4,27,6,0,3,16,4,5,0 5,37,16.5,3,1,17,4,6,0 5,27,6,2,3,14,3,4,0 5,37,16.5,3,3,12,3,4,0 5,42,23,1,4,12,3,4,0 5,27,9,2,3,12,5,5,0 5,27,13,2,2,14,2,4,0 5,42,23,2,4,14,5,5,0 5,42,23,5.5,4,14,5,4,0 4,22,6,0,1,17,4,1,0 4,27,2.5,0,4,16,3,1,0 4,17.5,2.5,0,1,12,5,2,0 3,27,9,0,2,16,4,4,0 5,22,2.5,0,2,12,3,5,0 4,27,9,2,3,12,3,2,0 4,22,6,0,2,16,5,5,0 4,22,0.5,0,1,14,1,1,0 5,22,2.5,1,2,12,3,1,0 5,27,9,2,3,12,5,5,0 5,27,6,0,2,14,3,5,0 4,22,2.5,0,3,14,2,2,0 4,22,6,1,2,12,3,4,0 5,22,2.5,1,3,14,3,4,0 3,27,6,1,1,12,3,5,0 5,37,16.5,4,3,20,4,2,0 4,22,2.5,0,2,14,3,5,0 4,32,13,2,3,14,5,5,0 5,22,2.5,0,1,14,3,4,0 5,27,2.5,0,2,14,3,4,0 4,27,9,1,2,12,2,2,0 5,22,2.5,0,2,14,3,4,0 3,37,13,1,3,17,5,3,0 5,42,23,3,4,12,2,2,0 5,27,6,0,4,16,4,5,0 2,27,6,0,2,14,3,4,0 5,32,13,2,4,14,4,5,0 5,22,2.5,0,1,17,4,4,0 5,27,9,2,3,12,3,5,0 5,27,6,0,2,16,6,6,0 5,27,6,1,3,16,4,2,0 4,22,9,1,1,12,2,2,0 4,32,13,3,3,20,4,5,0 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statsmodels-0.12.2/statsmodels/datasets/fair/src/000077500000000000000000000000001400612667500220275ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/fair/src/1978ADAT.asc000066400000000000000000015761621400612667500236030ustar00rootroot00000000000000PT data: 15 variables per line; they are: identifier, not used, constant, z1, z2, z3, z4, z5, z6, not used, z7, z8, yPT, not used, not used RB data: 14 variables per line; they are: identifier, constant, v1, v2, v3, v4, v5, v6, not used, v7, v8, yRB, not used, not used See Table 1 in the article for the notation. BEGIN PT data (601 observations): 4 0 1. 1 37.0 10.000 0 3 18. 40.0 7 4 0. 0. 1. 5 0 1. 0 27.0 4.000 0 4 14. 20.0 6 4 0. 0. 1. 11 0 1. 0 32.0 15.000 1 1 12. 12.5 1 4 0. 0. 1. 16 0 1. 1 57.0 15.000 1 5 18. 12.5 6 5 0. 0. 1. 23 0 1. 1 22.0 0.750 0 2 17. 7.5 6 3 0. 0. 1. 29 0 1. 0 32.0 1.500 0 2 17. 7.5 5 5 0. 0. 1. 44 0 1. 0 22.0 0.750 0 2 12. 12.5 1 3 0. 0. 1. 45 0 1. 1 57.0 15.000 1 2 14. 20.0 4 4 0. 0. 1. 47 0 1. 0 32.0 15.000 1 4 16. 20.0 1 2 0. 0. 1. 49 0 1. 1 22.0 1.500 0 4 14. 12.5 4 5 0. 0. 1. 50 0 1. 1 37.0 15.000 1 2 20. 20.0 7 2 0. 0. 1. 55 0 1. 1 27.0 4.000 1 4 18. 12.5 6 4 0. 0. 1. 64 0 1. 1 47.0 15.000 1 5 17. 12.5 6 4 0. 0. 1. 80 0 1. 0 22.0 1.500 0 2 17. 12.5 5 4 0. 0. 1. 86 0 1. 0 27.0 4.000 0 4 14. 7.5 5 4 0. 0. 1. 93 0 1. 0 37.0 15.000 1 1 17. 20.0 5 5 0. 0. 1. 108 0 1. 0 37.0 15.000 1 2 18. 20.0 4 3 0. 0. 1. 114 0 1. 0 22.0 0.750 0 3 16. 7.5 5 4 0. 0. 1. 115 0 1. 0 22.0 1.500 0 2 16. 7.5 5 5 0. 0. 1. 116 0 1. 0 27.0 10.000 1 2 14. 7.5 1 5 0. 0. 1. 123 0 1. 0 22.0 1.500 0 2 16. 12.5 5 5 0. 0. 1. 127 0 1. 0 22.0 1.500 0 2 16. 7.5 5 5 0. 0. 1. 129 0 1. 0 27.0 10.000 1 4 16. 20.0 5 4 0. 0. 1. 134 0 1. 0 32.0 10.000 1 3 14. 7.5 1 5 0. 0. 1. 137 0 1. 1 37.0 4.000 1 2 20. 20.0 6 4 0. 0. 1. 139 0 1. 0 22.0 1.500 0 2 18. 12.5 5 5 0. 0. 1. 147 0 1. 0 27.0 7.000 0 4 16. 12.5 1 5 0. 0. 1. 151 0 1. 1 42.0 15.000 1 5 20. 12.5 6 4 0. 0. 1. 153 0 1. 1 27.0 4.000 1 3 16. 12.5 5 5 0. 0. 1. 155 0 1. 0 27.0 4.000 1 3 17. 12.5 5 4 0. 0. 1. 162 0 1. 1 42.0 15.000 1 4 20. 20.0 6 3 0. 0. 1. 163 0 1. 0 22.0 1.500 0 3 16. 12.5 5 5 0. 0. 1. 165 0 1. 1 27.0 0.417 0 4 17. 7.5 6 4 0. 0. 1. 168 0 1. 0 42.0 15.000 1 5 14. 20.0 5 4 0. 0. 1. 170 0 1. 1 32.0 4.000 1 1 18. 20.0 6 4 0. 0. 1. 172 0 1. 0 22.0 1.500 0 4 16. 7.5 5 3 0. 0. 1. 184 0 1. 0 42.0 15.000 1 3 12. 20.0 1 4 0. 0. 1. 187 0 1. 0 22.0 4.000 0 4 17. 20.0 5 5 0. 0. 1. 192 0 1. 1 22.0 1.500 1 1 14. 7.5 3 5 0. 0. 1. 194 0 1. 0 22.0 0.750 0 3 16. 7.5 1 5 0. 0. 1. 210 0 1. 1 32.0 10.000 1 5 20. 12.5 6 5 0. 0. 1. 217 0 1. 1 52.0 15.000 1 5 18. 7.5 6 3 0. 0. 1. 220 0 1. 0 22.0 0.417 0 5 14. 12.5 1 4 0. 0. 1. 224 0 1. 0 27.0 4.000 1 2 18. 4.0 6 1 0. 0. 1. 227 0 1. 0 32.0 7.000 1 5 17. 12.5 5 3 0. 0. 1. 228 0 1. 1 22.0 4.000 0 3 16. 7.5 5 5 0. 0. 1. 239 0 1. 0 27.0 7.000 1 4 18. 40.0 6 5 0. 0. 1. 241 0 1. 0 42.0 15.000 1 2 18. 20.0 5 4 0. 0. 1. 245 0 1. 1 27.0 1.500 1 4 16. 7.5 3 5 0. 0. 1. 249 0 1. 1 42.0 15.000 1 2 20. 20.0 6 4 0. 0. 1. 262 0 1. 0 22.0 0.750 0 5 14. 20.0 3 5 0. 0. 1. 265 0 1. 1 32.0 7.000 1 2 20. 20.0 6 4 0. 0. 1. 267 0 1. 1 27.0 4.000 1 5 20. 7.5 6 5 0. 0. 1. 269 0 1. 1 27.0 10.000 1 4 20. 7.5 6 4 0. 0. 1. 271 0 1. 1 22.0 4.000 0 1 18. 20.0 5 5 0. 0. 1. 277 0 1. 0 37.0 15.000 1 4 14. 12.5 3 1 0. 0. 1. 290 0 1. 1 22.0 1.500 1 5 16. 20.0 4 4 0. 0. 1. 292 0 1. 0 37.0 15.000 1 4 17. 20.0 1 5 0. 0. 1. 293 0 1. 0 27.0 0.750 0 4 17. 12.5 5 4 0. 0. 1. 295 0 1. 1 32.0 10.000 1 4 20. 12.5 6 4 0. 0. 1. 299 0 1. 0 47.0 15.000 1 5 14. 40.0 7 2 0. 0. 1. 320 0 1. 1 37.0 10.000 1 3 20. 40.0 6 4 0. 0. 1. 321 0 1. 0 22.0 0.750 0 2 16. 7.5 5 5 0. 0. 1. 324 0 1. 1 27.0 4.000 0 2 18. 12.5 4 5 0. 0. 1. 334 0 1. 1 32.0 7.000 0 4 20. 7.5 6 4 0. 0. 1. 351 0 1. 1 42.0 15.000 1 2 17. 40.0 3 5 0. 0. 1. 355 0 1. 1 37.0 10.000 1 4 20. 7.5 6 4 0. 0. 1. 361 0 1. 0 47.0 15.000 1 3 17. 20.0 6 5 0. 0. 1. 362 0 1. 0 22.0 1.500 0 5 16. 7.5 5 5 0. 0. 1. 366 0 1. 0 27.0 1.500 0 2 16. 20.0 6 4 0. 0. 1. 370 0 1. 0 27.0 4.000 0 3 17. 7.5 5 5 0. 0. 1. 374 0 1. 0 32.0 10.000 1 5 14. 12.5 4 5 0. 0. 1. 378 0 1. 0 22.0 0.125 0 2 12. 7.5 5 5 0. 0. 1. 381 0 1. 1 47.0 15.000 1 4 14. 20.0 4 3 0. 0. 1. 382 0 1. 1 32.0 15.000 1 1 14. 40.0 5 5 0. 0. 1. 383 0 1. 1 27.0 7.000 1 4 16. 12.5 5 5 0. 0. 1. 384 0 1. 0 22.0 1.500 1 3 16. 7.5 5 5 0. 0. 1. 400 0 1. 1 27.0 4.000 1 3 17. 7.5 6 5 0. 0. 1. 403 0 1. 0 22.0 1.500 0 3 16. 7.5 5 5 0. 0. 1. 409 0 1. 1 57.0 15.000 1 2 14. 20.0 7 2 0. 0. 1. 412 0 1. 1 17.5 1.500 1 3 18. 20.0 6 5 0. 0. 1. 413 0 1. 1 57.0 15.000 1 4 20. 40.0 6 5 0. 0. 1. 416 0 1. 0 22.0 0.750 0 2 16. 20.0 3 4 0. 0. 1. 418 0 1. 1 42.0 4.000 0 4 17. 12.5 3 3 0. 0. 1. 422 0 1. 0 22.0 1.500 1 4 12. 12.5 1 5 0. 0. 1. 435 0 1. 0 22.0 0.417 0 1 17. 4.0 6 4 0. 0. 1. 439 0 1. 0 32.0 15.000 1 4 17. 12.5 5 5 0. 0. 1. 445 0 1. 0 27.0 1.500 0 3 18. 12.5 5 2 0. 0. 1. 447 0 1. 0 22.0 1.500 1 3 14. 7.5 1 5 0. 0. 1. 448 0 1. 0 37.0 15.000 1 3 14. 40.0 1 4 0. 0. 1. 449 0 1. 0 32.0 15.000 1 4 14. 20.0 3 4 0. 0. 1. 478 0 1. 1 37.0 10.000 1 2 14. 12.5 5 3 0. 0. 1. 482 0 1. 1 37.0 10.000 1 4 16. 12.5 5 4 0. 0. 1. 486 0 1. 1 57.0 15.000 1 5 20. 12.5 5 3 0. 0. 1. 489 0 1. 1 27.0 0.417 0 1 16. 7.5 3 4 0. 0. 1. 490 0 1. 0 42.0 15.000 1 5 14. 12.5 1 5 0. 0. 1. 491 0 1. 1 57.0 15.000 1 3 16. 20.0 6 1 0. 0. 1. 492 0 1. 1 37.0 10.000 1 1 16. 7.5 6 4 0. 0. 1. 503 0 1. 1 37.0 15.000 1 3 17. 40.0 5 5 0. 0. 1. 508 0 1. 1 37.0 15.000 1 4 20. 20.0 6 5 0. 0. 1. 509 0 1. 0 27.0 10.000 1 5 14. 12.5 1 5 0. 0. 1. 512 0 1. 1 37.0 10.000 1 2 18. 20.0 6 4 0. 0. 1. 515 0 1. 0 22.0 0.125 0 4 12. 12.5 4 5 0. 0. 1. 517 0 1. 1 57.0 15.000 1 5 20. 40.0 6 5 0. 0. 1. 532 0 1. 0 37.0 15.000 1 4 18. 40.0 6 4 0. 0. 1. 533 0 1. 1 22.0 4.000 1 4 14. 7.5 6 4 0. 0. 1. 535 0 1. 1 27.0 7.000 1 4 18. 7.5 5 4 0. 0. 1. 537 0 1. 1 57.0 15.000 1 4 20. 40.0 5 4 0. 0. 1. 538 0 1. 1 32.0 15.000 1 3 14. 12.5 6 3 0. 0. 1. 543 0 1. 0 22.0 1.500 0 2 14. 12.5 5 4 0. 0. 1. 547 0 1. 0 32.0 7.000 1 4 17. 40.0 1 5 0. 0. 1. 550 0 1. 0 37.0 15.000 1 4 17. 40.0 6 5 0. 0. 1. 558 0 1. 0 32.0 1.500 0 5 18. 40.0 5 5 0. 0. 1. 571 0 1. 1 42.0 10.000 1 5 20. 40.0 7 4 0. 0. 1. 578 0 1. 0 27.0 7.000 0 3 16. 12.5 5 4 0. 0. 1. 583 0 1. 1 37.0 15.000 0 4 20. 40.0 6 5 0. 0. 1. 586 0 1. 1 37.0 15.000 1 4 14. 12.5 3 2 0. 0. 1. 594 0 1. 1 32.0 10.000 0 5 18. 20.0 6 4 0. 0. 1. 597 0 1. 0 22.0 0.750 0 4 16. 7.5 1 5 0. 0. 1. 602 0 1. 0 27.0 7.000 1 4 12. 7.5 2 4 0. 0. 1. 603 0 1. 0 27.0 7.000 1 2 16. 12.5 2 5 0. 0. 1. 604 0 1. 0 42.0 15.000 1 5 18. 40.0 5 4 0. 0. 1. 612 0 1. 1 42.0 15.000 1 4 17. 20.0 5 3 0. 0. 1. 613 0 1. 0 27.0 7.000 1 2 16. 20.0 1 2 0. 0. 1. 621 0 1. 0 22.0 1.500 0 3 16. 12.5 5 5 0. 0. 1. 627 0 1. 1 37.0 15.000 1 5 20. 40.0 6 5 0. 0. 1. 630 0 1. 0 22.0 0.125 0 2 14. 12.5 4 5 0. 0. 1. 631 0 1. 1 27.0 1.500 0 4 16. 7.5 5 5 0. 0. 1. 632 0 1. 1 32.0 1.500 0 2 18. 20.0 6 5 0. 0. 1. 639 0 1. 1 27.0 1.500 0 2 17. 7.5 6 5 0. 0. 1. 645 0 1. 0 27.0 10.000 1 4 16. 12.5 1 3 0. 0. 1. 647 0 1. 1 42.0 15.000 1 4 18. 12.5 6 5 0. 0. 1. 648 0 1. 0 27.0 1.500 0 2 16. 7.5 6 5 0. 0. 1. 651 0 1. 1 27.0 4.000 0 2 18. 12.5 6 3 0. 0. 1. 655 0 1. 0 32.0 10.000 1 3 14. 7.5 5 3 0. 0. 1. 667 0 1. 0 32.0 15.000 1 3 18. 20.0 5 4 0. 0. 1. 670 0 1. 0 22.0 0.750 0 2 18. 4.0 6 5 0. 0. 1. 671 0 1. 0 37.0 15.000 1 2 16. 7.5 1 4 0. 0. 1. 673 0 1. 1 27.0 4.000 1 4 20. 12.5 5 5 0. 0. 1. 701 0 1. 1 27.0 4.000 0 1 20. 20.0 5 4 0. 0. 1. 705 0 1. 0 27.0 10.000 1 2 12. 7.5 1 4 0. 0. 1. 706 0 1. 0 32.0 15.000 1 5 18. 20.0 6 4 0. 0. 1. 709 0 1. 1 27.0 7.000 1 5 12. 7.5 5 3 0. 0. 1. 717 0 1. 1 52.0 15.000 1 2 18. 12.5 5 4 0. 0. 1. 719 0 1. 1 27.0 4.000 0 3 20. 12.5 6 3 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0. 0. 1. 1266 0 1. 0 37.0 15.000 1 2 18. 40.0 5 4 0. 0. 1. 1271 0 1. 0 37.0 7.000 1 3 14. 20.0 4 4 0. 0. 1. 1273 0 1. 1 22.0 1.500 0 2 16. 7.5 5 5 0. 0. 1. 1276 0 1. 1 37.0 15.000 1 5 20. 40.0 5 4 0. 0. 1. 1280 0 1. 0 22.0 1.500 0 4 16. 7.5 5 3 0. 0. 1. 1282 0 1. 0 32.0 10.000 1 4 16. 20.0 1 5 0. 0. 1. 1285 0 1. 1 27.0 4.000 0 2 17. 12.5 5 3 0. 0. 1. 1295 0 1. 0 22.0 0.417 0 4 14. 12.5 5 5 0. 0. 1. 1298 0 1. 0 27.0 4.000 0 2 18. 12.5 5 5 0. 0. 1. 1299 0 1. 1 37.0 15.000 1 4 18. 7.5 5 3 0. 0. 1. 1304 0 1. 1 37.0 10.000 1 5 20. 12.5 7 4 0. 0. 1. 1305 0 1. 0 27.0 7.000 1 2 14. 12.5 4 2 0. 0. 1. 1311 0 1. 1 32.0 4.000 1 2 16. 20.0 5 5 0. 0. 1. 1314 0 1. 1 32.0 4.000 1 2 16. 12.5 6 4 0. 0. 1. 1319 0 1. 1 22.0 1.500 0 3 18. 12.5 4 5 0. 0. 1. 1322 0 1. 0 22.0 4.000 1 4 14. 12.5 3 4 0. 0. 1. 1324 0 1. 0 17.5 0.750 0 2 18. 12.5 5 4 0. 0. 1. 1327 0 1. 1 32.0 10.000 1 4 20. 7.5 4 5 0. 0. 1. 1328 0 1. 0 32.0 0.750 0 5 14. 20.0 3 3 0. 0. 1. 1330 0 1. 1 37.0 15.000 1 4 17. 7.5 5 3 0. 0. 1. 1332 0 1. 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4 18. 7.5 5 3 0. 0. 1. 1417 0 1. 1 32.0 1.500 0 2 18. 12.5 4 4 0. 0. 1. 1418 0 1. 0 32.0 10.000 1 4 14. 12.5 1 4 0. 0. 1. 1419 0 1. 0 47.0 15.000 1 4 18. 20.0 5 4 0. 0. 1. 1420 0 1. 0 27.0 10.000 1 5 12. 7.5 1 5 0. 0. 1. 1423 0 1. 1 27.0 4.000 1 3 16. 12.5 4 5 0. 0. 1. 1424 0 1. 0 37.0 15.000 1 4 12. 12.5 4 2 0. 0. 1. 1432 0 1. 0 27.0 0.750 0 4 16. 12.5 5 5 0. 0. 1. 1433 0 1. 0 37.0 15.000 1 4 16. 7.5 1 5 0. 0. 1. 1437 0 1. 0 32.0 15.000 1 3 16. 12.5 1 5 0. 0. 1. 1438 0 1. 0 27.0 10.000 1 2 16. 7.5 1 5 0. 0. 1. 1439 0 1. 1 27.0 7.000 0 2 20. 20.0 6 5 0. 0. 1. 1446 0 1. 0 37.0 15.000 1 2 14. 20.0 1 3 0. 0. 1. 1450 0 1. 1 27.0 1.500 1 2 17. 7.5 4 4 0. 0. 1. 1451 0 1. 0 22.0 0.750 1 2 14. 12.5 1 5 0. 0. 1. 1452 0 1. 1 22.0 4.000 1 4 14. 7.5 2 4 0. 0. 1. 1453 0 1. 1 42.0 0.125 0 4 17. 12.5 6 4 0. 0. 1. 1456 0 1. 1 27.0 1.500 1 4 18. 7.5 6 5 0. 0. 1. 1464 0 1. 1 27.0 7.000 1 3 16. 12.5 6 3 0. 0. 1. 1469 0 1. 0 52.0 15.000 1 4 14. 7.5 1 3 0. 0. 1. 1473 0 1. 1 27.0 1.500 0 5 20. 7.5 5 2 0. 0. 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7.000 1 4 14. 7.5 3 2 0. 0. 1. 1595 0 1. 1 57.0 15.000 1 5 18. 20.0 5 2 0. 0. 1. 1603 0 1. 1 32.0 7.000 1 2 18. 7.5 5 5 0. 0. 1. 1608 0 1. 0 27.0 1.500 0 4 17. 7.5 1 3 0. 0. 1. 1609 0 1. 1 22.0 1.500 0 4 14. 7.5 5 5 0. 0. 1. 1615 0 1. 0 22.0 1.500 1 4 14. 4.0 5 4 0. 0. 1. 1616 0 1. 0 32.0 7.000 1 3 16. 12.5 1 5 0. 0. 1. 1617 0 1. 0 47.0 15.000 1 3 16. 20.0 5 4 0. 0. 1. 1620 0 1. 0 22.0 0.750 0 3 16. 40.0 1 5 0. 0. 1. 1621 0 1. 0 22.0 1.500 1 2 14. 7.5 5 5 0. 0. 1. 1637 0 1. 0 27.0 4.000 1 1 16. 7.5 5 5 0. 0. 1. 1638 0 1. 1 52.0 15.000 1 4 16. 20.0 5 5 0. 0. 1. 1650 0 1. 1 32.0 10.000 1 4 20. 40.0 6 5 0. 0. 1. 1654 0 1. 1 47.0 15.000 1 4 16. 20.0 6 4 0. 0. 1. 1665 0 1. 0 27.0 7.000 1 2 14. 7.5 1 2 0. 0. 1. 1670 0 1. 0 22.0 1.500 0 4 14. 20.0 4 5 0. 0. 1. 1671 0 1. 0 32.0 10.000 1 2 16. 20.0 5 4 0. 0. 1. 1675 0 1. 0 22.0 0.750 0 2 16. 12.5 5 4 0. 0. 1. 1688 0 1. 0 22.0 1.500 0 2 16. 12.5 5 5 0. 0. 1. 1691 0 1. 0 42.0 15.000 1 3 18. 20.0 6 4 0. 0. 1. 1695 0 1. 0 27.0 7.000 1 5 14. 20.0 4 5 0. 0. 1. 1698 0 1. 1 42.0 15.000 1 4 16. 20.0 4 4 0. 0. 1. 1704 0 1. 0 57.0 15.000 1 3 18. 20.0 5 2 0. 0. 1. 1705 0 1. 1 42.0 15.000 1 3 18. 12.5 6 2 0. 0. 1. 1711 0 1. 0 32.0 7.000 1 2 14. 7.5 1 2 0. 0. 1. 1719 0 1. 1 22.0 4.000 0 5 12. 7.5 4 5 0. 0. 1. 1723 0 1. 0 22.0 1.500 0 1 16. 7.5 6 5 0. 0. 1. 1726 0 1. 0 22.0 0.750 0 1 14. 7.5 4 5 0. 0. 1. 1749 0 1. 0 32.0 15.000 1 4 12. 20.0 1 5 0. 0. 1. 1752 0 1. 1 22.0 1.500 0 2 18. 12.5 5 3 0. 0. 1. 1754 0 1. 1 27.0 4.000 1 5 17. 7.5 2 5 0. 0. 1. 1758 0 1. 0 27.0 4.000 1 4 12. 7.5 1 5 0. 0. 1. 1761 0 1. 1 42.0 15.000 1 5 18. 7.5 5 4 0. 0. 1. 1773 0 1. 1 32.0 1.500 0 2 20. 20.0 7 3 0. 0. 1. 1775 0 1. 1 57.0 15.000 0 4 9. 7.5 3 1 0. 0. 1. 1786 0 1. 1 37.0 7.000 0 4 18. 12.5 5 5 0. 0. 1. 1793 0 1. 1 52.0 15.000 1 2 17. 20.0 5 4 0. 0. 1. 1799 0 1. 1 47.0 15.000 1 4 17. 20.0 6 5 0. 0. 1. 1803 0 1. 0 27.0 7.000 0 2 17. 20.0 5 4 0. 0. 1. 1806 0 1. 0 27.0 7.000 1 4 14. 40.0 5 5 0. 0. 1. 1807 0 1. 0 22.0 4.000 0 2 14. 12.5 3 3 0. 0. 1. 1808 0 1. 1 37.0 7.000 1 2 20. 40.0 6 5 0. 0. 1. 1814 0 1. 1 27.0 7.000 0 4 12. 7.5 4 3 0. 0. 1. 1815 0 1. 1 42.0 10.000 1 4 18. 40.0 6 4 0. 0. 1. 1818 0 1. 0 22.0 1.500 0 3 14. 7.5 1 5 0. 0. 1. 1827 0 1. 0 22.0 4.000 1 2 14. 12.5 1 3 0. 0. 1. 1834 0 1. 0 57.0 15.000 0 4 20. 20.0 6 5 0. 0. 1. 1835 0 1. 1 37.0 15.000 1 4 14. 12.5 4 3 0. 0. 1. 1843 0 1. 0 27.0 7.000 1 3 18. 12.5 5 5 0. 0. 1. 1846 0 1. 0 17.5 10.000 0 4 14. 20.0 4 5 0. 0. 1. 1850 0 1. 1 22.0 4.000 1 4 16. 12.5 5 5 0. 0. 1. 1851 0 1. 0 27.0 4.000 1 2 16. 12.5 1 4 0. 0. 1. 1854 0 1. 0 37.0 15.000 1 2 14. 12.5 5 1 0. 0. 1. 1859 0 1. 0 22.0 1.500 0 5 14. 4.0 1 4 0. 0. 1. 1861 0 1. 1 27.0 7.000 1 2 20. 7.5 5 4 0. 0. 1. 1866 0 1. 1 27.0 4.000 1 4 14. 7.5 5 5 0. 0. 1. 1873 0 1. 1 22.0 0.125 0 1 16. 7.5 3 5 0. 0. 1. 1875 0 1. 0 27.0 7.000 1 4 14. 20.0 1 4 0. 0. 1. 1885 0 1. 0 32.0 15.000 1 5 16. 12.5 5 3 0. 0. 1. 1892 0 1. 1 32.0 10.000 1 4 18. 12.5 5 4 0. 0. 1. 1895 0 1. 0 32.0 15.000 1 2 14. 7.5 3 4 0. 0. 1. 1896 0 1. 0 22.0 1.500 0 3 17. 7.5 5 5 0. 0. 1. 1897 0 1. 1 27.0 4.000 1 4 17. 7.5 4 4 0. 0. 1. 1899 0 1. 0 52.0 15.000 1 5 14. 12.5 1 5 0. 0. 1. 1904 0 1. 0 27.0 7.000 1 2 12. 20.0 1 2 0. 0. 1. 1905 0 1. 0 27.0 7.000 1 3 12. 12.5 1 4 0. 0. 1. 1908 0 1. 0 42.0 15.000 1 2 14. 20.0 1 4 0. 0. 1. 1916 0 1. 0 42.0 15.000 1 4 14. 20.0 5 4 0. 0. 1. 1918 0 1. 1 27.0 7.000 1 4 14. 7.5 3 3 0. 0. 1. 1920 0 1. 1 27.0 7.000 1 2 20. 20.0 6 2 0. 0. 1. 1930 0 1. 0 42.0 15.000 1 3 12. 20.0 3 3 0. 0. 1. 1940 0 1. 1 27.0 4.000 1 3 16. 7.5 3 5 0. 0. 1. 1947 0 1. 0 27.0 7.000 1 3 14. 40.0 1 4 0. 0. 1. 1949 0 1. 0 22.0 1.500 0 2 14. 12.5 4 5 0. 0. 1. 1951 0 1. 0 27.0 4.000 1 4 14. 12.5 1 4 0. 0. 1. 1952 0 1. 0 22.0 4.000 0 4 14. 4.0 5 5 0. 0. 1. 1960 0 1. 0 22.0 1.500 0 2 16. 20.0 4 5 0. 0. 1. 9001 0 1. 1 47.0 15.000 0 4 14. 12.5 5 4 0. 0. 1. 9012 0 1. 1 37.0 10.000 1 2 18. 12.5 6 2 0. 0. 1. 9023 0 1. 1 37.0 15.000 1 3 17. 40.0 5 4 0. 0. 1. 9029 0 1. 0 27.0 4.000 1 2 16. 7.5 1 4 0. 0. 1. 6 3 1. 1 27.0 1.500 0 3 18. 20.0 4 4 3. 0. 1. 12 3 1. 0 27.0 4.000 1 3 17. 12.5 1 5 3. 0. 1. 43 4 1. 1 37.0 15.000 1 5 18. 12.5 6 2 7. 0. 1. 53 6 1. 0 32.0 10.000 1 3 17. 40.0 5 2 12. 0. 1. 67 1 1. 1 22.0 0.125 0 4 16. 20.0 5 5 1. 0. 1. 79 1 1. 0 22.0 1.500 1 2 14. 4.0 1 5 1. 0. 1. 122 6 1. 1 37.0 15.000 1 4 14. 7.5 5 2 12. 0. 1. 126 4 1. 0 22.0 1.500 0 2 14. 4.0 3 4 7. 0. 1. 133 2 1. 1 37.0 15.000 1 2 18. 20.0 6 4 2. 0. 1. 138 3 1. 0 32.0 15.000 1 4 12. 12.5 3 2 3. 0. 1. 154 1 1. 0 37.0 15.000 1 4 14. 12.5 4 2 1. 0. 1. 159 4 1. 0 42.0 15.000 1 3 17. 40.0 1 4 7. 0. 1. 174 6 1. 0 42.0 15.000 1 5 9. 12.5 4 1 12. 0. 1. 176 5 1. 1 37.0 10.000 1 2 20. 40.0 6 2 12. 0. 1. 181 6 1. 0 32.0 15.000 1 3 14. 12.5 1 2 12. 0. 1. 182 3 1. 1 27.0 4.000 0 1 18. 7.5 6 5 3. 0. 1. 186 4 1. 1 37.0 10.000 1 2 18. 40.0 7 3 7. 0. 1. 189 4 1. 0 27.0 4.000 0 3 17. 7.5 5 5 7. 0. 1. 204 1 1. 1 42.0 15.000 1 4 16. 20.0 5 5 1. 0. 1. 215 1 1. 0 47.0 15.000 1 5 14. 12.5 4 5 1. 0. 1. 232 4 1. 0 27.0 4.000 1 3 18. 12.5 5 4 7. 0. 1. 233 1 1. 0 27.0 7.000 1 5 14. 4.0 1 4 1. 0. 1. 252 6 1. 1 27.0 1.500 1 3 17. 20.0 5 4 12. 0. 1. 253 5 1. 0 27.0 7.000 1 4 14. 12.5 6 2 12. 0. 1. 274 3 1. 0 42.0 15.000 1 4 16. 20.0 5 4 3. 0. 1. 275 4 1. 0 27.0 10.000 1 4 12. 12.5 7 3 7. 0. 1. 287 1 1. 1 27.0 1.500 0 2 18. 12.5 5 2 1. 0. 1. 288 1 1. 1 32.0 4.000 0 4 20. 20.0 6 4 1. 0. 1. 325 1 1. 0 27.0 7.000 1 3 14. 7.5 1 3 1. 0. 1. 328 3 1. 0 32.0 10.000 1 4 14. 7.5 1 4 3. 0. 1. 344 3 1. 1 27.0 4.000 1 2 18. 12.5 7 2 3. 0. 1. 353 1 1. 0 17.5 0.750 0 5 14. 7.5 4 5 1. 0. 1. 354 1 1. 0 32.0 10.000 1 4 18. 20.0 1 5 1. 0. 1. 367 4 1. 0 32.0 7.000 1 2 17. 20.0 6 4 7. 0. 1. 369 4 1. 1 37.0 15.000 1 2 20. 20.0 6 4 7. 0. 1. 390 4 1. 0 37.0 10.000 0 1 20. 20.0 5 3 7. 0. 1. 392 5 1. 0 32.0 10.000 1 2 16. 12.5 5 5 12. 0. 1. 423 4 1. 1 52.0 15.000 1 2 20. 40.0 6 4 7. 0. 1. 432 4 1. 0 42.0 15.000 1 1 12. 12.5 1 3 7. 0. 1. 436 1 1. 1 52.0 15.000 1 2 20. 40.0 6 3 1. 0. 1. 483 2 1. 1 37.0 15.000 1 3 18. 12.5 6 5 2. 0. 1. 513 5 1. 0 22.0 4.000 0 3 12. 12.5 3 4 12. 0. 1. 516 6 1. 1 27.0 7.000 1 1 18. 12.5 6 2 12. 0. 1. 518 1 1. 1 27.0 4.000 1 3 18. 12.5 5 5 1. 0. 1. 520 7 1. 1 47.0 15.000 1 4 17. 12.5 6 5 12. 0. 1. 526 6 1. 0 42.0 15.000 1 4 12. 20.0 1 1 12. 0. 1. 528 4 1. 1 27.0 4.000 0 3 14. 7.5 3 4 7. 0. 1. 553 4 1. 0 32.0 7.000 1 4 18. 12.5 4 5 7. 0. 1. 576 1 1. 1 32.0 0.417 1 3 12. 7.5 3 4 1. 0. 1. 611 3 1. 1 47.0 15.000 1 5 16. 12.5 5 4 3. 0. 1. 625 5 1. 1 37.0 15.000 1 2 20. 40.0 5 4 12. 0. 1. 635 4 1. 1 22.0 4.000 1 2 17. 7.5 6 4 7. 0. 1. 646 1 1. 1 27.0 4.000 0 2 14. 12.5 4 5 1. 0. 1. 657 4 1. 0 52.0 15.000 1 5 16. 12.5 1 3 7. 0. 1. 659 1 1. 1 27.0 4.000 0 3 14. 12.5 3 3 1. 0. 1. 666 1 1. 0 27.0 10.000 1 4 16. 12.5 1 4 1. 0. 1. 679 1 1. 1 32.0 7.000 1 3 14. 20.0 7 4 1. 0. 1. 729 4 1. 1 32.0 7.000 1 2 18. 20.0 4 1 7. 0. 1. 755 3 1. 1 22.0 1.500 0 1 14. 20.0 3 2 3. 0. 1. 758 4 1. 1 22.0 4.000 1 3 18. 12.5 6 4 7. 0. 1. 770 4 1. 1 42.0 15.000 1 4 20. 40.0 6 4 7. 0. 1. 786 2 1. 0 57.0 15.000 1 1 18. 40.0 5 4 2. 0. 1. 797 4 1. 0 32.0 4.000 1 3 18. 12.5 5 2 7. 0. 1. 811 1 1. 1 27.0 4.000 1 1 16. 20.0 4 4 1. 0. 1. 834 4 1. 1 32.0 7.000 1 4 16. 12.5 1 4 7. 0. 1. 858 2 1. 1 57.0 15.000 1 1 17. 20.0 4 4 2. 0. 1. 885 4 1. 0 42.0 15.000 1 4 14. 20.0 5 2 7. 0. 1. 893 4 1. 1 37.0 10.000 1 1 18. 12.5 5 3 7. 0. 1. 927 3 1. 1 42.0 15.000 1 3 17. 12.5 6 1 3. 0. 1. 928 1 1. 0 52.0 15.000 1 3 14. 12.5 4 4 1. 0. 1. 933 2 1. 0 27.0 7.000 1 3 17. 12.5 5 3 2. 0. 1. 951 6 1. 1 32.0 7.000 1 2 12. 20.0 4 2 12. 0. 1. 968 1 1. 1 22.0 4.000 0 4 14. 7.5 2 5 1. 0. 1. 972 3 1. 1 27.0 7.000 1 3 18. 12.5 6 4 3. 0. 1. 975 6 1. 0 37.0 15.000 1 1 18. 12.5 5 5 12. 0. 1. 977 4 1. 0 32.0 15.000 1 3 17. 20.0 1 3 7. 0. 1. 981 4 1. 0 27.0 7.000 0 2 17. 20.0 5 5 7. 0. 1. 986 1 1. 0 32.0 7.000 1 3 17. 12.5 5 3 1. 0. 1. 1002 1 1. 1 32.0 1.500 1 2 14. 7.5 2 4 1. 0. 1. 1007 6 1. 0 42.0 15.000 1 4 14. 12.5 1 2 12. 0. 1. 1011 4 1. 1 32.0 10.000 1 3 14. 20.0 5 4 7. 0. 1. 1035 4 1. 1 37.0 4.000 1 1 20. 20.0 6 3 7. 0. 1. 1050 1 1. 0 27.0 4.000 1 2 16. 12.5 5 3 1. 0. 1. 1056 5 1. 0 42.0 15.000 1 3 14. 20.0 4 3 12. 0. 1. 1057 1 1. 1 27.0 10.000 1 5 20. 20.0 6 5 1. 0. 1. 1075 6 1. 1 37.0 10.000 1 2 20. 40.0 6 2 12. 0. 1. 1080 6 1. 0 27.0 7.000 1 1 14. 12.5 3 3 12. 0. 1. 1125 3 1. 0 27.0 7.000 1 4 12. 7.5 1 2 3. 0. 1. 1131 3 1. 1 32.0 10.000 1 2 14. 12.5 4 4 3. 0. 1. 1138 7 1. 0 17.5 0.750 1 2 12. 7.5 1 3 12. 0. 1. 1150 5 1. 0 32.0 15.000 1 3 18. 40.0 5 4 12. 0. 1. 1163 2 1. 0 22.0 7.000 0 4 14. 20.0 4 3 2. 0. 1. 1169 1 1. 1 32.0 7.000 1 4 20. 20.0 6 5 1. 0. 1. 1198 4 1. 1 27.0 4.000 1 2 18. 12.5 6 2 7. 0. 1. 1204 1 1. 0 22.0 1.500 1 5 14. 7.5 5 3 1. 0. 1. 1218 7 1. 0 32.0 15.000 0 3 17. 7.5 5 1 12. 0. 1. 1230 5 1. 0 42.0 15.000 1 2 12. 20.0 1 2 12. 0. 1. 1236 4 1. 1 42.0 15.000 1 3 20. 40.0 5 4 7. 0. 1. 1247 6 1. 1 32.0 10.000 0 2 18. 20.0 4 2 12. 0. 1. 1259 5 1. 0 32.0 15.000 1 3 9. 12.5 1 1 12. 0. 1. 1294 4 1. 1 57.0 15.000 1 5 20. 12.5 4 5 7. 0. 1. 1353 5 1. 1 47.0 15.000 1 4 20. 40.0 6 4 12. 0. 1. 1370 2 1. 0 42.0 15.000 1 2 17. 20.0 6 3 2. 0. 1. 1427 6 1. 1 37.0 15.000 1 3 17. 40.0 6 3 12. 0. 1. 1445 5 1. 1 37.0 15.000 1 5 17. 12.5 5 2 12. 0. 1. 1460 4 1. 1 27.0 10.000 1 2 20. 12.5 6 4 7. 0. 1. 1480 2 1. 1 37.0 15.000 1 2 16. 20.0 5 4 2. 0. 1. 1505 6 1. 0 32.0 15.000 1 1 14. 20.0 5 2 12. 0. 1. 1543 4 1. 1 32.0 10.000 1 3 17. 7.5 6 3 7. 0. 1. 1548 2 1. 1 37.0 15.000 1 4 18. 12.5 5 1 2. 0. 1. 1550 4 1. 0 27.0 1.500 0 2 17. 12.5 5 5 7. 0. 1. 1561 3 1. 0 47.0 15.000 1 2 17. 20.0 5 2 3. 0. 1. 1564 6 1. 1 37.0 15.000 1 2 17. 20.0 5 4 12. 0. 1. 1573 5 1. 0 27.0 4.000 0 2 14. 20.0 5 5 12. 0. 1. 1575 2 1. 0 27.0 10.000 1 4 14. 12.5 1 5 2. 0. 1. 1599 1 1. 0 22.0 4.000 1 3 16. 12.5 1 3 1. 0. 1. 1622 6 1. 1 52.0 7.000 0 4 16. 7.5 5 5 12. 0. 1. 1629 2 1. 0 27.0 4.000 1 1 16. 7.5 3 5 2. 0. 1. 1664 4 1. 0 37.0 15.000 1 2 17. 40.0 6 4 7. 0. 1. 1669 2 1. 0 27.0 4.000 0 1 17. 4.0 3 1 2. 0. 1. 1674 7 1. 0 17.5 0.750 1 2 12. 7.5 3 5 12. 0. 1. 1682 4 1. 0 32.0 15.000 1 5 18. 12.5 5 4 7. 0. 1. 1685 4 1. 0 22.0 4.000 0 1 16. 7.5 3 5 7. 0. 1. 1697 2 1. 1 32.0 4.000 1 4 18. 20.0 6 4 2. 0. 1. 1716 1 1. 0 22.0 1.500 1 3 18. 20.0 5 2 1. 0. 1. 1730 3 1. 0 42.0 15.000 1 2 17. 40.0 5 4 3. 0. 1. 1731 1 1. 1 32.0 7.000 1 4 16. 12.5 4 4 1. 0. 1. 1732 5 1. 1 37.0 15.000 0 3 14. 20.0 6 2 12. 0. 1. 1743 1 1. 1 42.0 15.000 1 3 16. 40.0 6 3 1. 0. 1. 1751 1 1. 1 27.0 4.000 1 1 18. 7.5 5 4 1. 0. 1. 1757 2 1. 1 37.0 15.000 1 4 20. 40.0 7 3 2. 0. 1. 1763 4 1. 1 37.0 15.000 1 3 20. 40.0 6 4 7. 0. 1. 1766 3 1. 1 22.0 1.500 0 2 12. 12.5 3 3 3. 0. 1. 1772 3 1. 1 32.0 4.000 1 3 20. 20.0 6 2 3. 0. 1. 1776 2 1. 1 32.0 15.000 1 5 20. 20.0 6 5 2. 0. 1. 1782 5 1. 0 52.0 15.000 1 1 18. 40.0 5 5 12. 0. 1. 1784 5 1. 1 47.0 15.000 0 1 18. 40.0 6 5 12. 0. 1. 1791 3 1. 0 32.0 15.000 1 4 16. 12.5 4 4 3. 0. 1. 1831 4 1. 0 32.0 15.000 1 3 14. 12.5 3 2 7. 0. 1. 1840 4 1. 0 27.0 7.000 1 4 16. 20.0 1 2 7. 0. 1. 1844 5 1. 1 42.0 15.000 1 3 18. 12.5 6 2 12. 0. 1. 1856 4 1. 0 42.0 15.000 1 2 14. 12.5 3 2 7. 0. 1. 1876 5 1. 1 27.0 7.000 1 2 17. 12.5 5 4 12. 0. 1. 1929 3 1. 1 32.0 10.000 1 4 14. 7.5 4 3 3. 0. 1. 1935 4 1. 1 47.0 15.000 1 3 16. 20.0 4 2 7. 0. 1. 1938 1 1. 1 22.0 1.500 1 1 12. 7.5 2 5 1. 0. 1. 1941 4 1. 0 32.0 10.000 1 2 18. 7.5 5 4 7. 0. 1. 1954 2 1. 1 32.0 10.000 1 2 17. 20.0 6 5 2. 0. 1. 1959 2 1. 1 22.0 7.000 1 3 18. 20.0 6 2 2. 0. 1. 9010 1 1. 0 32.0 15.000 1 3 14. 40.0 1 5 1. 0. 1. END OF PT DATA BEGIN RB DATA (6366 observations): 3. 1. 3. 32.0 9.0 3.0 3. 17.0 40.0 2. 5. 0.1111111 0. 1. 12. 1. 3. 27.0 13.0 3.0 1. 14.0 20.0 3. 4. 3.2307692 0. 1. 51. 1. 4. 22.0 2.5 0.0 1. 16.0 11.5 3. 5. 1.3999996 0. 1. 53. 1. 4. 37.0 16.5 4.0 3. 16.0 20.0 5. 5. 0.7272727 0. 1. 54. 1. 5. 27.0 9.0 1.0 1. 14.0 14.0 3. 4. 4.6666660 0. 1. 74. 1. 4. 27.0 9.0 0.0 2. 14.0 20.0 3. 4. 4.6666660 0. 1. 81. 1. 5. 37.0 23.0 5.5 2. 12.0 20.0 5. 4. 0.8521735 0. 1. 83. 1. 5. 37.0 23.0 5.5 2. 12.0 20.0 2. 3. 1.8260860 0. 1. 89. 1. 3. 22.0 2.5 0.0 2. 12.0 11.5 3. 3. 4.7999992 0. 1. 102. 1. 3. 27.0 6.0 0.0 1. 16.0 20.0 3. 5. 1.3333330 0. 1. 135. 1. 2. 27.0 6.0 2.0 1. 16.0 20.0 3. 5. 3.2666645 0. 1. 137. 1. 5. 27.0 6.0 2.0 3. 14.0 14.0 3. 5. 2.0416660 0. 1. 144. 1. 3. 37.0 16.5 5.5 1. 12.0 11.5 2. 3. 0.4848484 0. 1. 160. 1. 5. 27.0 6.0 0.0 2. 14.0 20.0 3. 2. 2.0000000 0. 1. 168. 1. 4. 22.0 6.0 1.0 1. 14.0 14.0 4. 4. 3.2666645 0. 1. 182. 1. 4. 37.0 9.0 2.0 2. 14.0 40.0 3. 6. 1.3611107 0. 1. 202. 1. 4. 27.0 6.0 1.0 1. 12.0 20.0 3. 5. 2.0000000 0. 1. 228. 1. 1. 37.0 23.0 5.5 4. 14.0 14.0 5. 2. 1.8260860 0. 1. 239. 1. 2. 42.0 23.0 2.0 2. 20.0 20.0 4. 4. 1.8260860 0. 1. 243. 1. 4. 37.0 6.0 0.0 2. 16.0 20.0 5. 4. 2.0416660 0. 1. 248. 1. 5. 22.0 2.5 0.0 2. 14.0 20.0 3. 4. 7.8399963 0. 1. 251. 1. 3. 37.0 16.5 5.5 2. 9.0 40.0 3. 2. 2.5454540 0. 1. 264. 1. 3. 42.0 23.0 5.5 3. 12.0 14.0 5. 4. 0.5326087 0. 1. 266. 1. 2. 27.0 9.0 2.0 4. 20.0 20.0 3. 4. 0.6222222 0. 1. 280. 1. 4. 27.0 6.0 1.0 2. 12.0 11.5 5. 4. 0.5833333 0. 1. 284. 1. 5. 27.0 2.5 0.0 3. 16.0 14.0 4. 1. 4.7999992 0. 1. 286. 1. 2. 27.0 6.0 2.0 2. 12.0 11.5 2. 5. 0.1666666 0. 1. 289. 1. 5. 37.0 13.0 1.0 3. 12.0 11.5 3. 4. 0.6153846 0. 1. 293. 1. 2. 32.0 16.5 2.0 2. 12.0 14.0 4. 2. 1.1878777 0. 1. 296. 1. 3. 27.0 6.0 1.0 1. 14.0 14.0 3. 6. 11.1999989 0. 1. 297. 1. 3. 32.0 16.5 4.0 3. 14.0 20.0 5. 5. 1.1878777 0. 1. 300. 1. 3. 27.0 9.0 2.0 1. 14.0 20.0 3. 4. 2.1777763 0. 1. 308. 1. 3. 37.0 16.5 3.0 3. 14.0 14.0 3. 2. 0.4848484 0. 1. 312. 1. 4. 32.0 16.5 5.5 4. 12.0 14.0 2. 4. 0.7272727 0. 1. 320. 1. 5. 42.0 16.5 4.0 3. 16.0 40.0 4. 6. 0.7272727 0. 1. 322. 1. 3. 27.0 9.0 2.0 2. 12.0 14.0 5. 2. 1.3333330 0. 1. 332. 1. 3. 17.5 0.5 0.0 1. 12.0 11.5 3. 2. 7.0000000 0. 1. 339. 1. 4. 42.0 23.0 5.5 2. 20.0 4.0 3. 2. 0.5217391 0. 1. 354. 1. 5. 37.0 16.5 3.0 3. 12.0 20.0 3. 5. 0.2121212 0. 1. 359. 1. 4. 22.0 2.5 1.0 2. 14.0 20.0 3. 5. 0.4000000 0. 1. 361. 1. 4. 27.0 2.5 0.0 2. 16.0 20.0 4. 1. 1.3999996 0. 1. 368. 1. 4. 22.0 2.5 0.0 2. 14.0 14.0 3. 6. 3.1999998 0. 1. 370. 1. 4. 37.0 13.0 3.0 2. 16.0 40.0 4. 5. 1.5076914 0. 1. 373. 1. 4. 22.0 2.5 0.0 2. 16.0 14.0 3. 4. 7.8399963 0. 1. 386. 1. 4. 22.0 2.5 0.0 1. 14.0 11.5 1. 2. 7.8399963 0. 1. 387. 1. 5. 22.0 2.5 0.0 3. 12.0 14.0 3. 2. 0.4000000 0. 1. 410. 1. 5. 22.0 2.5 0.0 3. 16.0 20.0 4. 5. 4.8999996 0. 1. 411. 1. 3. 42.0 23.0 4.0 3. 16.0 40.0 5. 5. 0.0434783 0. 1. 425. 1. 5. 32.0 13.0 3.0 3. 14.0 14.0 4. 4. 0.0769231 0. 1. 431. 1. 5. 22.0 6.0 2.0 2. 14.0 14.0 3. 4. 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20.0 4. 5. 0.0 0. 1. 1841. 1. 2. 27.0 2.5 0.0 3. 14.0 11.5 4. 1. 0.0 0. 1. 1860. 1. 4. 27.0 6.0 0.0 2. 14.0 20.0 3. 6. 0.0 0. 1. 1866. 1. 5. 27.0 2.5 0.0 2. 17.0 20.0 3. 3. 0.0 0. 1. 1870. 1. 5. 32.0 13.0 2.0 2. 14.0 40.0 2. 4. 0.0 0. 1. 1875. 1. 5. 22.0 2.5 0.0 4. 12.0 6.5 2. 4. 0.0 0. 1. 1876. 1. 4. 42.0 16.5 2.0 2. 12.0 20.0 3. 2. 0.0 0. 1. 1879. 1. 5. 27.0 13.0 2.0 3. 12.0 11.5 3. 5. 0.0 0. 1. 1881. 1. 5. 22.0 2.5 1.0 2. 12.0 11.5 2. 2. 0.0 0. 1. 1887. 1. 5. 37.0 16.5 4.0 3. 12.0 40.0 2. 6. 0.0 0. 1. 1893. 1. 5. 27.0 2.5 0.0 2. 16.0 20.0 3. 4. 0.0 0. 1. 1902. 1. 4. 22.0 2.5 0.0 2. 14.0 9.0 3. 4. 0.0 0. 1. 1903. 1. 5. 22.0 2.5 0.0 3. 12.0 14.0 2. 5. 0.0 0. 1. 1905. 1. 5. 27.0 2.5 0.0 2. 17.0 20.0 4. 2. 0.0 0. 1. 1908. 1. 4. 27.0 2.5 0.0 2. 17.0 14.0 4. 4. 0.0 0. 1. 1913. 1. 4. 42.0 23.0 2.0 4. 12.0 20.0 4. 2. 0.0 0. 1. 1915. 1. 5. 27.0 2.5 0.0 2. 16.0 20.0 3. 5. 0.0 0. 1. 1919. 1. 4. 37.0 13.0 1.0 3. 12.0 40.0 2. 2. 0.0 0. 1. 1927. 1. 4. 27.0 6.0 2.0 3. 14.0 20.0 3. 5. 0.0 0. 1. 1929. 1. 5. 27.0 6.0 1.0 3. 12.0 14.0 3. 4. 0.0 0. 1. 1932. 1. 3. 42.0 23.0 5.5 2. 14.0 40.0 4. 5. 0.0 0. 1. 1943. 1. 5. 27.0 6.0 0.0 3. 20.0 40.0 4. 4. 0.0 0. 1. 1944. 1. 5. 22.0 2.5 0.0 2. 14.0 20.0 3. 2. 0.0 0. 1. 1945. 1. 4. 27.0 2.5 0.0 3. 12.0 20.0 3. 3. 0.0 0. 1. 1948. 1. 5. 22.0 2.5 0.0 3. 16.0 20.0 3. 5. 0.0 0. 1. 1949. 1. 2. 32.0 2.5 1.0 2. 12.0 14.0 5. 2. 0.0 0. 1. 1955. 1. 4. 27.0 2.5 1.0 2. 14.0 14.0 4. 4. 0.0 0. 1. 1956. 1. 4. 27.0 0.5 0.0 3. 14.0 14.0 3. 4. 0.0 0. 1. 1959. 1. 4. 32.0 9.0 1.0 3. 17.0 14.0 4. 4. 0.0 0. 1. 1962. 1. 4. 27.0 9.0 2.0 2. 17.0 20.0 4. 5. 0.0 0. 1. 1963. 1. 5. 22.0 2.5 0.0 4. 14.0 6.5 4. 4. 0.0 0. 1. 1985. 1. 4. 22.0 2.5 0.0 2. 12.0 14.0 2. 2. 0.0 0. 1. 1996. 1. 5. 27.0 6.0 2.0 2. 16.0 20.0 4. 1. 0.0 0. 1. 1997. 1. 4. 27.0 6.0 0.0 2. 12.0 14.0 3. 4. 0.0 0. 1. 1999. 1. 4. 32.0 13.0 2.0 2. 14.0 20.0 3. 5. 0.0 0. 1. 2009. 1. 4. 37.0 16.5 2.0 1. 20.0 40.0 4. 6. 0.0 0. 1. 2013. 1. 4. 42.0 23.0 3.0 2. 12.0 11.5 3. 5. 0.0 0. 1. 2017. 1. 1. 42.0 23.0 5.5 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17359. 1. 5. 27.0 6.0 1.0 4. 16.0 11.5 4. 4. 0.0 0. 1. 17362. 1. 3. 27.0 9.0 0.0 2. 14.0 20.0 3. 5. 0.0 0. 1. 17363. 1. 4. 42.0 23.0 3.0 4. 14.0 40.0 3. 3. 0.0 0. 1. 17364. 1. 4. 32.0 13.0 2.0 2. 12.0 20.0 5. 5. 0.0 0. 1. 17368. 1. 5. 27.0 6.0 0.0 4. 20.0 6.5 4. 1. 0.0 0. 1. 17370. 1. 5. 37.0 23.0 4.0 2. 14.0 20.0 3. 4. 0.0 0. 1. 17375. 1. 5. 22.0 2.5 0.0 2. 12.0 9.0 3. 4. 0.0 0. 1. 17382. 1. 5. 22.0 2.5 1.0 4. 14.0 11.5 3. 4. 0.0 0. 1. 17388. 1. 4. 22.0 2.5 0.0 3. 12.0 11.5 3. 4. 0.0 0. 1. 17393. 1. 4. 17.5 2.5 0.0 2. 12.0 6.5 3. 4. 0.0 0. 1. 17395. 1. 3. 22.0 2.5 1.0 3. 12.0 9.0 3. 4. 0.0 0. 1. 17396. 1. 5. 17.5 0.5 0.0 4. 12.0 6.5 3. 2. 0.0 0. 1. 17403. 1. 4. 37.0 23.0 3.0 4. 9.0 11.5 2. 2. 0.0 0. 1. 17408. 1. 5. 42.0 23.0 4.0 2. 14.0 14.0 5. 4. 0.0 0. 1. 17410. 1. 4. 32.0 16.5 2.0 3. 14.0 20.0 3. 4. 0.0 0. 1. 17412. 1. 4. 22.0 2.5 2.0 3. 14.0 11.5 5. 4. 0.0 0. 1. 17413. 1. 5. 17.5 0.5 0.0 2. 12.0 11.5 3. 4. 0.0 0. 1. 17415. 1. 5. 37.0 16.5 3.0 4. 14.0 11.5 3. 4. 0.0 0. 1. 17418. 1. 4. 27.0 9.0 1.0 3. 12.0 14.0 3. 3. 0.0 0. 1. 17426. 1. 5. 37.0 16.5 3.0 2. 14.0 11.5 3. 3. 0.0 0. 1. 17431. 1. 3. 42.0 13.0 2.0 3. 17.0 20.0 4. 4. 0.0 0. 1. 17433. 1. 5. 37.0 23.0 4.0 4. 16.0 20.0 4. 6. 0.0 0. 1. 17434. 1. 5. 37.0 23.0 1.0 3. 14.0 20.0 3. 5. 0.0 0. 1. 17445. 1. 4. 42.0 23.0 3.0 3. 17.0 40.0 4. 2. 0.0 0. 1. 17449. 1. 4. 27.0 6.0 1.0 3. 20.0 20.0 4. 4. 0.0 0. 1. 17450. 1. 5. 32.0 9.0 0.0 4. 20.0 20.0 4. 6. 0.0 0. 1. 17452. 1. 4. 27.0 2.5 0.0 4. 17.0 20.0 4. 4. 0.0 0. 1. 17454. 1. 3. 17.5 2.5 0.0 3. 12.0 6.5 4. 4. 0.0 0. 1. 17471. 1. 5. 22.0 2.5 0.0 3. 12.0 40.0 2. 2. 0.0 0. 1. 17472. 1. 5. 37.0 13.0 3.0 1. 20.0 20.0 4. 5. 0.0 0. 1. 17473. 1. 5. 27.0 16.5 2.0 3. 12.0 9.0 4. 4. 0.0 0. 1. 17474. 1. 4. 22.0 2.5 1.0 3. 14.0 11.5 3. 5. 0.0 0. 1. 17506. 1. 4. 42.0 16.5 4.0 3. 9.0 11.5 2. 2. 0.0 0. 1. 17508. 1. 4. 22.0 2.5 0.0 2. 14.0 9.0 3. 5. 0.0 0. 1. 17509. 1. 4. 42.0 23.0 2.0 3. 14.0 20.0 4. 2. 0.0 0. 1. 17517. 1. 5. 32.0 13.0 2.0 2. 14.0 20.0 2. 6. 0.0 0. 1. 17520. 1. 4. 32.0 13.0 2.0 3. 17.0 20.0 4. 5. 0.0 0. 1. 17523. 1. 5. 22.0 2.5 1.0 1. 12.0 9.0 5. 1. 0.0 0. 1. 17533. 1. 5. 22.0 2.5 0.0 4. 16.0 20.0 4. 2. 0.0 0. 1. 17544. 1. 5. 37.0 9.0 0.0 3. 20.0 40.0 4. 6. 0.0 0. 1. 17547. 1. 5. 42.0 23.0 2.0 3. 14.0 9.0 3. 5. 0.0 0. 1. 17551. 1. 5. 32.0 9.0 2.0 3. 16.0 11.5 4. 4. 0.0 0. 1. 17553. 1. 5. 22.0 6.0 0.0 1. 12.0 14.0 3. 2. 0.0 0. 1. 17558. 1. 4. 27.0 6.0 2.0 2. 12.0 9.0 2. 2. 0.0 0. 1. 17564. 1. 4. 22.0 2.5 0.0 2. 12.0 11.5 3. 4. 0.0 0. 1. 17569. 1. 5. 27.0 2.5 0.0 4. 16.0 6.5 4. 4. 0.0 0. 1. 17573. 1. 5. 32.0 16.5 3.0 4. 14.0 20.0 2. 4. 0.0 0. 1. 17574. 1. 4. 37.0 16.5 2.0 1. 12.0 20.0 3. 4. 0.0 0. 1. 17575. 1. 5. 22.0 2.5 0.0 3. 12.0 9.0 3. 3. 0.0 0. 1. 17578. 1. 4. 37.0 16.5 4.0 2. 12.0 11.5 2. 2. 0.0 0. 1. 17580. 1. 3. 27.0 9.0 1.0 3. 17.0 14.0 4. 1. 0.0 0. 1. 17585. 1. 5. 22.0 2.5 0.0 1. 17.0 9.0 2. 2. 0.0 0. 1. 17596. 1. 5. 22.0 2.5 0.0 1. 14.0 9.0 3. 4. 0.0 0. 1. 17598. 1. 5. 22.0 2.5 0.0 2. 16.0 14.0 4. 5. 0.0 0. 1. 17602. 1. 5. 27.0 6.0 0.0 2. 16.0 20.0 3. 5. 0.0 0. 1. 17608. 1. 4. 22.0 2.5 0.0 3. 14.0 11.5 5. 4. 0.0 0. 1. 17616. 1. 5. 27.0 2.5 0.0 1. 17.0 11.5 4. 6. 0.0 0. 1. 17620. 1. 5. 42.0 23.0 1.0 4. 20.0 40.0 4. 3. 0.0 0. 1. 17625. 1. 4. 17.5 0.5 0.0 2. 14.0 4.0 3. 1. 0.0 0. 1. 17627. 1. 5. 22.0 6.0 1.0 3. 12.0 11.5 2. 3. 0.0 0. 1. 17636. 1. 4. 22.0 6.0 2.0 2. 9.0 6.5 2. 3. 0.0 0. 1. 17643. 1. 5. 27.0 2.5 0.0 4. 16.0 20.0 5. 4. 0.0 0. 1. 17646. 1. 4. 22.0 2.5 1.0 2. 12.0 6.5 3. 2. 0.0 0. 1. 17651. 1. 3. 32.0 2.5 0.0 4. 17.0 14.0 6. 6. 0.0 0. 1. 17661. 1. 5. 37.0 16.5 3.0 4. 14.0 20.0 4. 6. 0.0 0. 1. 17668. 1. 5. 32.0 13.0 4.0 2. 12.0 11.5 5. 1. 0.0 0. 1. 17669. 1. 3. 42.0 23.0 3.0 4. 16.0 14.0 3. 5. 0.0 0. 1. 17673. 1. 5. 27.0 2.5 0.0 3. 12.0 20.0 3. 4. 0.0 0. 1. 17674. 1. 5. 32.0 2.5 1.0 3. 20.0 20.0 4. 4. 0.0 0. 1. 17676. 1. 5. 27.0 9.0 2.0 3. 12.0 9.0 2. 4. 0.0 0. 1. 17690. 1. 3. 27.0 2.5 0.0 2. 14.0 14.0 3. 3. 0.0 0. 1. 17691. 1. 5. 17.5 2.5 1.0 2. 12.0 6.5 5. 2. 0.0 0. 1. 17696. 1. 4. 37.0 16.5 3.0 2. 17.0 40.0 4. 5. 0.0 0. 1. 17700. 1. 4. 27.0 2.5 1.0 3. 16.0 40.0 4. 6. 0.0 0. 1. 17705. 1. 5. 22.0 2.5 1.0 3. 14.0 11.5 3. 5. 0.0 0. 1. 17706. 1. 4. 27.0 2.5 0.0 1. 20.0 40.0 5. 5. 0.0 0. 1. 17707. 1. 5. 22.0 2.5 0.0 3. 14.0 14.0 5. 5. 0.0 0. 1. 17716. 1. 5. 42.0 23.0 5.5 3. 14.0 14.0 4. 4. 0.0 0. 1. 17718. 1. 5. 42.0 23.0 4.0 3. 14.0 14.0 3. 2. 0.0 0. 1. 17721. 1. 5. 37.0 13.0 2.0 2. 20.0 40.0 6. 6. 0.0 0. 1. 17723. 1. 5. 27.0 13.0 2.0 3. 14.0 20.0 4. 5. 0.0 0. 1. 17726. 1. 4. 27.0 13.0 2.0 2. 12.0 6.5 2. 2. 0.0 0. 1. 17742. 1. 5. 37.0 23.0 3.0 2. 12.0 14.0 4. 4. 0.0 0. 1. 17748. 1. 5. 22.0 2.5 0.0 2. 17.0 11.5 5. 3. 0.0 0. 1. 17750. 1. 5. 27.0 6.0 1.0 2. 12.0 14.0 2. 4. 0.0 0. 1. 17752. 1. 5. 22.0 2.5 0.0 2. 14.0 11.5 3. 4. 0.0 0. 1. 17758. 1. 5. 37.0 13.0 2.0 3. 16.0 20.0 4. 4. 0.0 0. 1. 17780. 1. 5. 27.0 6.0 0.0 2. 17.0 20.0 5. 6. 0.0 0. 1. 17786. 1. 5. 27.0 0.5 0.0 3. 12.0 40.0 3. 4. 0.0 0. 1. 17796. 1. 2. 37.0 16.5 3.0 1. 14.0 14.0 3. 2. 0.0 0. 1. 17797. 1. 5. 37.0 23.0 2.0 3. 20.0 40.0 4. 4. 0.0 0. 1. 17802. 1. 2. 32.0 9.0 2.0 4. 14.0 14.0 3. 5. 0.0 0. 1. 17803. 1. 5. 32.0 13.0 2.0 4. 20.0 20.0 4. 5. 0.0 0. 1. 17805. 1. 5. 22.0 2.5 1.0 4. 16.0 11.5 4. 5. 0.0 0. 1. 17812. 1. 5. 22.0 2.5 0.0 3. 20.0 11.5 4. 4. 0.0 0. 1. 17813. 1. 3. 37.0 13.0 3.0 2. 16.0 11.5 4. 3. 0.0 0. 1. 17818. 1. 3. 17.5 2.5 1.0 1. 9.0 6.5 3. 3. 0.0 0. 1. 17820. 1. 4. 27.0 2.5 0.0 2. 14.0 11.5 3. 1. 0.0 0. 1. 17821. 1. 1. 27.0 6.0 1.0 3. 14.0 14.0 3. 4. 0.0 0. 1. 17824. 1. 4. 27.0 6.0 2.0 2. 14.0 40.0 4. 5. 0.0 0. 1. 17829. 1. 2. 42.0 23.0 2.0 2. 14.0 20.0 3. 4. 0.0 0. 1. 17832. 1. 5. 32.0 13.0 2.0 3. 14.0 20.0 4. 6. 0.0 0. 1. 17841. 1. 4. 22.0 2.5 1.0 3. 14.0 11.5 3. 4. 0.0 0. 1. 17866. 1. 4. 27.0 2.5 0.0 1. 14.0 9.0 2. 5. 0.0 0. 1. 17872. 1. 4. 22.0 2.5 0.0 3. 20.0 40.0 6. 6. 0.0 0. 1. 17873. 1. 3. 37.0 2.5 0.0 3. 12.0 11.5 3. 3. 0.0 0. 1. 17876. 1. 5. 27.0 2.5 0.0 3. 17.0 20.0 4. 4. 0.0 0. 1. 17878. 1. 5. 27.0 2.5 0.0 3. 16.0 20.0 3. 5. 0.0 0. 1. 17879. 1. 4. 27.0 6.0 1.0 2. 20.0 20.0 4. 2. 0.0 0. 1. 17880. 1. 4. 27.0 9.0 2.0 2. 14.0 20.0 4. 4. 0.0 0. 1. 17892. 1. 4. 27.0 2.5 0.0 3. 17.0 11.5 4. 4. 0.0 0. 1. 17895. 1. 5. 27.0 6.0 0.0 4. 16.0 14.0 4. 5. 0.0 0. 1. 17901. 1. 5. 42.0 23.0 5.5 3. 12.0 14.0 3. 2. 0.0 0. 1. 17905. 1. 5. 22.0 2.5 0.0 3. 16.0 9.0 4. 1. 0.0 0. 1. 17914. 1. 5. 22.0 0.5 0.0 3. 14.0 9.0 2. 2. 0.0 0. 1. 17916. 1. 4. 22.0 2.5 1.0 3. 14.0 9.0 2. 4. 0.0 0. 1. 17925. 1. 5. 22.0 2.5 1.0 4. 12.0 6.5 3. 4. 0.0 0. 1. 17928. 1. 5. 42.0 23.0 4.0 3. 14.0 14.0 5. 4. 0.0 0. 1. 17929. 1. 5. 27.0 6.0 0.0 4. 14.0 6.5 4. 4. 0.0 0. 1. 17934. 1. 5. 42.0 23.0 2.0 3. 12.0 40.0 2. 2. 0.0 0. 1. 17939. 1. 4. 32.0 13.0 3.0 3. 16.0 20.0 4. 2. 0.0 0. 1. 17940. 1. 5. 27.0 13.0 3.0 3. 16.0 14.0 4. 2. 0.0 0. 1. 17943. 1. 5. 27.0 9.0 1.0 2. 14.0 20.0 4. 5. 0.0 0. 1. 17946. 1. 4. 22.0 2.5 0.0 2. 16.0 6.5 4. 1. 0.0 0. 1. 17947. 1. 5. 17.5 2.5 0.0 4. 12.0 14.0 3. 5. 0.0 0. 1. 17952. 1. 4. 32.0 16.5 2.0 2. 12.0 20.0 3. 4. 0.0 0. 1. 17953. 1. 5. 27.0 9.0 1.0 3. 12.0 40.0 3. 5. 0.0 0. 1. 17960. 1. 4. 22.0 2.5 0.0 4. 14.0 11.5 4. 2. 0.0 0. 1. 17961. 1. 5. 22.0 2.5 1.0 2. 12.0 11.5 3. 2. 0.0 0. 1. 17962. 1. 5. 27.0 0.5 0.0 4. 20.0 20.0 4. 4. 0.0 0. 1. 17963. 1. 5. 37.0 16.5 3.0 3. 14.0 20.0 5. 5. 0.0 0. 1. 17967. 1. 5. 32.0 13.0 2.0 4. 14.0 20.0 3. 6. 0.0 0. 1. 17971. 1. 4. 22.0 0.5 0.0 2. 16.0 9.0 3. 1. 0.0 0. 1. 17973. 1. 5. 42.0 23.0 2.0 4. 12.0 20.0 3. 2. 0.0 0. 1. 17975. 1. 5. 22.0 2.5 2.0 2. 14.0 6.5 3. 5. 0.0 0. 1. 17978. 1. 5. 42.0 23.0 4.0 4. 12.0 20.0 3. 5. 0.0 0. 1. 17981. 1. 4. 27.0 6.0 0.0 3. 12.0 20.0 3. 4. 0.0 0. 1. 17982. 1. 5. 32.0 13.0 3.0 3. 12.0 20.0 3. 5. 0.0 0. 1. 17990. 1. 5. 32.0 13.0 4.0 2. 14.0 20.0 4. 4. 0.0 0. 1. 17997. 1. 3. 27.0 6.0 2.0 4. 14.0 6.5 3. 1. 0.0 0. 1. 17998. 1. 4. 22.0 2.5 0.0 3. 16.0 11.5 5. 5. 0.0 0. 1. 17999. 1. 5. 22.0 2.5 0.0 2. 14.0 20.0 3. 3. 0.0 0. 1. 19006. 1. 5. 32.0 13.0 2.0 3. 17.0 40.0 4. 3. 0.0 0. 1. 19009. 1. 4. 32.0 13.0 1.0 1. 16.0 40.0 5. 5. 0.0 0. 1. 19013. 1. 5. 22.0 2.5 0.0 2. 14.0 6.5 3. 1. 0.0 0. 1. 19015. 1. 5. 32.0 6.0 1.0 3. 14.0 20.0 3. 4. 0.0 0. 1. 19020. 1. 4. 22.0 2.5 0.0 2. 16.0 4.0 2. 4. 0.0 0. 1. END OF RB DATA statsmodels-0.12.2/statsmodels/datasets/fertility/000077500000000000000000000000001400612667500223325ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/fertility/__init__.py000066400000000000000000000003261400612667500244440ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/fertility/data.py000066400000000000000000000043461400612667500236240ustar00rootroot00000000000000"""World Bank Fertility Data.""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This data is distributed according to the World Bank terms of use. See SOURCE.""" TITLE = """World Bank Fertility Data""" SOURCE = """ This data has been acquired from The World Bank: Fertility rate, total (births per woman): World Development Indicators At the following URL: http://data.worldbank.org/indicator/SP.DYN.TFRT.IN The sources for these statistics are listed as (1) United Nations Population Division. World Population Prospects (2) United Nations Statistical Division. Population and Vital Statistics Repot (various years) (3) Census reports and other statistical publications from national statistical offices (4) Eurostat: Demographic Statistics (5) Secretariat of the Pacific Community: Statistics and Demography Programme (6) U.S. Census Bureau: International Database The World Bank Terms of Use can be found at the following URL http://go.worldbank.org/OJC02YMLA0 """ DESCRSHORT = """Total fertility rate represents the number of children that would be born to a woman if she were to live to the end of her childbearing years and bear children in accordance with current age-specific fertility rates.""" DESCRLONG = DESCRSHORT #suggested notes NOTE = """ :: This is panel data in wide-format Number of observations: 219 Number of variables: 58 Variable name definitions: Country Name Country Code Indicator Name - The World Bank Series indicator Indicator Code - The World Bank Series code 1960 - 2013 - The fertility rate for the given year """ def load(as_pandas=None): """ Load the data and return a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): data = _get_data() return du.Dataset(data=data) def _get_data(): return du.load_csv(__file__, 'fertility.csv') statsmodels-0.12.2/statsmodels/datasets/fertility/fertility.csv000066400000000000000000002703671400612667500251010ustar00rootroot00000000000000Country Name,Country Code,Indicator Name,Indicator Code,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013 Aruba,ABW,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.82,4.655,4.471,4.271,4.059,3.842,3.625,3.417,3.2260000000000004,3.054,2.908,2.7880000000000003,2.6910000000000003,2.613,2.552,2.506,2.472,2.446,2.425,2.408,2.392,2.377,2.364,2.353,2.342,2.332,2.32,2.307,2.291,2.272,2.249,2.221,2.187,2.149,2.108,2.064,2.021,1.979,1.94,1.905,1.874,1.848,1.825,1.805,1.786,1.769,1.754,1.739,1.726,1.713,1.7009999999999998,1.69,, Andorra,AND,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,1.24,1.18,1.25,1.19,1.22,,, Afghanistan,AFG,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.671,7.671,7.671,7.671,7.671,7.671,7.671,7.671,7.671,7.671,7.671,7.671,7.671,7.671,7.671,7.671,7.67,7.67,7.67,7.669,7.669,7.67,7.671,7.672999999999999,7.676,7.6789999999999985,7.681,7.682,7.682,7.682,7.687,7.7,7.725,7.757999999999999,7.796,7.832000000000002,7.859,7.869,7.854,7.809,7.733,7.622999999999997,7.484,7.3210000000000015,7.136,6.93,6.702000000000001,6.456,6.1960000000000015,5.928,5.659,5.395,, Angola,AGO,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.316,7.354,7.385,7.41,7.425,7.43,7.4220000000000015,7.403,7.375,7.338999999999999,7.301,7.2639999999999985,7.232,7.207999999999997,7.192,7.185,7.186,7.189,7.194,7.197,7.2,7.2010000000000005,7.2029999999999985,7.205,7.207000000000002,7.207999999999997,7.206,7.202000000000001,7.194,7.182,7.165,7.143,7.1160000000000005,7.0870000000000015,7.0539999999999985,7.019,6.984,6.949,6.9129999999999985,6.877999999999999,6.8439999999999985,6.811,6.778,6.7429999999999986,6.704,6.657,6.598,6.523,6.434,6.331,6.218,6.099,, Albania,ALB,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.186,6.0760000000000005,5.956,5.8329999999999975,5.711,5.5939999999999985,5.483,5.376,5.268,5.16,5.05,4.933,4.809,4.677,4.538,4.393,4.244,4.0939999999999985,3.947,3.807,3.678,3.562,3.46,3.372,3.297,3.233,3.177,3.1260000000000003,3.075,3.023,2.97,2.917,2.867,2.819,2.772,2.7230000000000003,2.67,2.611,2.543,2.467,2.383,2.291,2.195,2.097,2.004,1.919,1.849,1.796,1.761,1.744,1.741,1.7480000000000002,, United Arab Emirates,ARE,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.928,6.91,6.893,6.877000000000002,6.8610000000000015,6.841,6.816,6.783,6.738,6.6789999999999985,6.605,6.5120000000000005,6.402,6.279,6.146,6.009,5.8729999999999976,5.744,5.624,5.517,5.422999999999999,5.3439999999999985,5.274,5.209,5.141,5.065,4.973,4.86,4.724,4.566,4.388,4.1930000000000005,3.989,3.784,3.583,3.393,3.215,3.052,2.902,2.766,2.644,2.532,2.428,2.329,2.236,2.149,2.071,2.004,1.948,1.903,1.868,1.841,, Argentina,ARG,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.109,3.1,3.089,3.0780000000000003,3.068,3.0580000000000003,3.051,3.048,3.049,3.056,3.073,3.104,3.148,3.2030000000000003,3.264,3.321,3.366,3.391,3.391,3.3680000000000003,3.325,3.27,3.213,3.1630000000000003,3.123,3.093,3.073,3.056,3.037,3.016,2.989,2.9560000000000004,2.918,2.875,2.827,2.774,2.717,2.657,2.596,2.535,2.477,2.424,2.379,2.34,2.31,2.286,2.268,2.254,2.241,2.228,2.215,2.201,, Armenia,ARM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.55,4.512,4.435,4.317,4.1610000000000005,3.979,3.788,3.606,3.447,3.314,3.208,3.1180000000000003,3.032,2.942,2.846,2.745,2.6460000000000004,2.555,2.479,2.421,2.385,2.373,2.381,2.406,2.441,2.481,2.519,2.549,2.5660000000000003,2.565,2.5380000000000003,2.482,2.399,2.295,2.176,2.053,1.938,1.838,1.7619999999999998,1.712,1.6880000000000002,1.6840000000000002,1.692,1.704,1.715,1.724,1.7280000000000002,1.731,1.734,1.736,1.7380000000000002,1.7380000000000002,, American Samoa,ASM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Antigua and Barbuda,ATG,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.425,4.386,4.3439999999999985,4.299,4.25,4.1930000000000005,4.125,4.042,3.942,3.824,3.684,3.517,3.3280000000000003,3.122,2.908,2.701,2.514,2.358,2.239,2.1590000000000003,2.115,2.0980000000000003,2.096,2.0980000000000003,2.0980000000000003,2.092,2.082,2.07,2.062,2.0580000000000003,2.061,2.073,2.096,2.128,2.166,2.208,2.248,2.281,2.3040000000000003,2.316,2.316,2.305,2.2880000000000003,2.268,2.246,2.224,2.2030000000000003,2.1830000000000003,2.164,2.146,2.13,2.115,, Australia,AUS,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.4530000000000003,3.54,3.442,3.332,3.1460000000000004,2.977,2.881,2.8480000000000003,2.888,2.886,2.859,2.9610000000000003,2.744,2.491,2.397,2.148,2.06,2.007,1.949,1.907,1.891,1.935,1.929,1.924,1.84,1.923,1.868,1.845,1.831,1.838,1.902,1.849,1.888,1.859,1.842,1.822,1.796,1.778,1.7619999999999998,1.755,1.756,1.739,1.756,1.7480000000000002,1.768,1.807,1.883,1.931,1.933,1.857,1.87,1.87,, Austria,AUT,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.69,2.799,2.798,2.8110000000000004,2.77,2.685,2.662,2.63,2.591,2.496,2.29,2.202,2.102,1.97,1.95,1.82,1.6980000000000002,1.641,1.621,1.6,1.62,1.67,1.66,1.56,1.53,1.46,1.47,1.42,1.43,1.45,1.45,1.5,1.49,1.48,1.44,1.4,1.42,1.36,1.37,1.34,1.36,1.33,1.39,1.38,1.42,1.41,1.41,1.38,1.41,1.39,1.44,1.42,, Azerbaijan,AZE,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.5710000000000015,5.596,5.591,5.549,5.468,5.352,5.21,5.056,4.901,4.753,4.612,4.479,4.348,4.216,4.084,3.95,3.814,3.676,3.539,3.407,3.286,3.179,3.092,3.026,2.98,2.91,2.9,2.903,2.8,2.8,2.74,2.87,2.74,2.7,2.52,2.29,2.06,2.07,2.0,2.07,2.0,1.8,1.8,1.9,2.0540000000000003,2.0,1.97,1.97,1.9,1.82,1.92,1.92,, Burundi,BDI,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.9529999999999985,6.9979999999999976,7.045,7.0920000000000005,7.138,7.1789999999999985,7.216,7.247000000000001,7.272,7.292999999999997,7.311,7.329,7.348,7.37,7.395,7.419,7.439,7.452000000000001,7.457000000000002,7.455,7.45,7.449,7.454,7.4689999999999985,7.492000000000001,7.52,7.546,7.565,7.572,7.564,7.542000000000002,7.507999999999999,7.465,7.417999999999997,7.3679999999999986,7.318,7.267,7.217,7.165,7.112,7.057,7.0,6.939,6.8729999999999976,6.803,6.729,6.65,6.567,6.481,6.393,6.3039999999999985,6.214,, Belgium,BEL,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.575,2.644,2.592,2.68,2.712,2.613,2.53,2.42,2.313,2.245,2.2,2.208,2.09,1.95,1.83,1.736,1.725,1.705,1.6909999999999998,1.689,1.672,1.67,1.614,1.56,1.591,1.49,1.54,1.55,1.56,1.58,1.62,1.57,1.56,1.61,1.55,1.57,1.55,1.6,1.6,1.62,1.67,1.663,1.66,1.66,1.72,1.76,1.8,1.82,1.86,1.84,1.84,1.84,, Benin,BEN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.282,6.339,6.394,6.447,6.497000000000001,6.544,6.587999999999999,6.63,6.671,6.71,6.7479999999999976,6.7860000000000005,6.823,6.86,6.896,6.9289999999999985,6.959,6.984,7.004,7.018,7.025,7.025,7.021,7.01,6.994,6.972,6.942,6.904,6.858,6.805,6.744,6.6770000000000005,6.603,6.526,6.4460000000000015,6.365,6.284,6.205,6.127999999999999,6.051,5.975,5.898,5.818,5.733,5.645,5.553,5.459,5.365,5.273,5.182,5.095,5.01,, Burkina Faso,BFA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.291,6.316,6.3439999999999985,6.377000000000002,6.414,6.454,6.4929999999999986,6.53,6.563,6.593,6.6229999999999976,6.657,6.697,6.744,6.799,6.859,6.9220000000000015,6.984,7.041,7.09,7.127000000000002,7.152,7.165,7.1670000000000025,7.159,7.142,7.119,7.0920000000000005,7.064,7.0360000000000005,7.0070000000000014,6.979,6.95,6.9170000000000025,6.8820000000000014,6.8439999999999985,6.801,6.754,6.704,6.65,6.5920000000000005,6.5310000000000015,6.468,6.403,6.335,6.265,6.193,6.1160000000000005,6.037000000000001,5.954,5.869,5.7810000000000015,, Bangladesh,BGD,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.725,6.761,6.794,6.825,6.853,6.877999999999999,6.901,6.92,6.935,6.945,6.947,6.942,6.928,6.904,6.869,6.8210000000000015,6.757999999999999,6.68,6.5870000000000015,6.48,6.356,6.216,6.06,5.89,5.71,5.522,5.327000000000001,5.13,4.932,4.738,4.55,4.37,4.197,4.033,3.878,3.732,3.596,3.468,3.346,3.2310000000000003,3.12,3.011,2.905,2.802,2.702,2.607,2.52,2.443,2.377,2.322,2.277,2.24,, Bulgaria,BGR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.3080000000000003,2.29,2.24,2.21,2.19,2.09,2.03,2.02,2.27,2.27,2.17,2.1,2.03,2.15,2.29,2.23,2.24,2.2,2.15,2.15,2.05,2.01,2.02,2.0,1.99,1.95,1.99,1.96,1.97,1.9,1.81,1.65,1.54,1.45,1.37,1.23,1.24,1.09,1.11,1.23,1.26,1.21,1.21,1.23,1.29,1.32,1.38,1.42,1.48,1.57,1.49,1.51,, Bahrain,BHR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.09,7.1320000000000014,7.1679999999999975,7.19,7.192,7.165,7.101,6.9979999999999976,6.86,6.69,6.4979999999999976,6.2929999999999975,6.089,5.895,5.716,5.556,5.414,5.283,5.157,5.0360000000000005,4.917,4.802,4.69,4.581,4.472,4.362,4.248,4.128,4.002,3.872,3.738,3.6010000000000004,3.466,3.335,3.212,3.1,3.005,2.926,2.862,2.81,2.765,2.718,2.665,2.602,2.529,2.449,2.367,2.292,2.229,2.1790000000000003,2.142,2.115,, "Bahamas, The",BHS,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.495,4.496,4.45,4.356,4.22,4.057,3.893,3.75,3.641,3.571,3.531,3.504,3.469,3.411,3.33,3.234,3.139,3.062,3.012,2.99,2.989,2.994,2.989,2.965,2.919,2.857,2.789,2.728,2.6830000000000003,2.654,2.639,2.631,2.6210000000000004,2.6010000000000004,2.5660000000000003,2.514,2.443,2.357,2.263,2.165,2.071,1.989,1.924,1.88,1.857,1.853,1.862,1.876,1.889,1.898,1.901,1.898,, Bosnia and Herzegovina,BIH,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.052,3.954,3.849,3.737,3.619,3.495,3.367,3.239,3.114,2.994,2.881,2.775,2.675,2.5810000000000004,2.4930000000000003,2.412,2.336,2.267,2.202,2.144,2.092,2.05,2.017,1.992,1.973,1.953,1.925,1.887,1.836,1.775,1.7080000000000002,1.645,1.594,1.558,1.538,1.528,1.519,1.503,1.474,1.433,1.381,1.325,1.275,1.236,1.21,1.199,1.199,1.207,1.218,1.23,1.242,1.255,, Belarus,BLR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.67,2.59,2.5,2.4,2.31,2.27,2.29,2.26,2.22,2.26,2.31,2.31,2.28,2.25,2.21,2.17,2.12,2.08,2.06,2.05,2.03,2.02,2.05,2.11,2.11,2.09,2.09,2.03,2.04,2.03,1.91,1.8,1.75,1.61,1.51,1.386,1.31,1.23,1.27,1.31,1.31,1.27,1.22,1.21,1.2,1.21,1.287,1.37,1.42,1.42,1.44,1.51,, Belize,BLZ,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.5,6.48,6.46,6.44,6.42,6.4,6.379,6.358,6.3370000000000015,6.316,6.299,6.2879999999999985,6.284,6.285,6.2860000000000005,6.278,6.25,6.195,6.109,5.992000000000001,5.849,5.684,5.51,5.336,5.17,5.019,4.886,4.771,4.671,4.584,4.508,4.436,4.363,4.2860000000000005,4.2010000000000005,4.1080000000000005,4.008,3.905,3.8,3.696,3.594,3.4930000000000003,3.395,3.299,3.208,3.122,3.043,2.971,2.907,2.8510000000000004,2.801,2.756,, Bermuda,BMU,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,1.8,,,,,1.74,,,,,1.7519999999999998,1.754,1.757,1.759,1.7619999999999998,1.764,1.764,, Bolivia,BOL,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.6960000000000015,6.6720000000000015,6.648,6.627000000000002,6.607,6.593,6.586,6.585,6.5870000000000015,6.5870000000000015,6.5779999999999985,6.549,6.496,6.415,6.31,6.183,6.0429999999999975,5.899,5.761,5.634,5.521,5.422999999999999,5.3370000000000015,5.259,5.189,5.127000000000002,5.074,5.029,4.989,4.952,4.913,4.8660000000000005,4.81,4.742,4.663,4.575,4.482,4.39,4.302,4.2189999999999985,4.14,4.062,3.982,3.897,3.809,3.72,3.633,3.551,3.477,3.4130000000000003,3.357,3.3080000000000003,, Brazil,BRA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.21,6.19,6.143,6.063,5.9529999999999985,5.815,5.658,5.4910000000000005,5.3260000000000005,5.167999999999998,5.024,4.896,4.782,4.6789999999999985,4.585,4.499,4.418,4.339,4.256,4.169,4.073,3.966,3.848,3.721,3.587,3.449,3.3080000000000003,3.17,3.039,2.917,2.809,2.717,2.643,2.583,2.537,2.502,2.474,2.451,2.427,2.399,2.364,2.318,2.264,2.202,2.135,2.066,2.001,1.944,1.897,1.862,1.838,1.822,, Barbados,BRB,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.333,4.313,4.269,4.1960000000000015,4.0939999999999985,3.963,3.807,3.637,3.46,3.284,3.113,2.949,2.794,2.648,2.513,2.393,2.2880000000000003,2.198,2.121,2.057,2.004,1.96,1.922,1.889,1.858,1.83,1.805,1.7819999999999998,1.765,1.75,1.74,1.732,1.727,1.725,1.724,1.726,1.73,1.736,1.745,1.756,1.768,1.78,1.791,1.801,1.81,1.817,1.822,1.827,1.831,1.835,1.839,1.842,, Brunei Darussalam,BRN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.487,6.487,6.448,6.36,6.227,6.068,5.9179999999999975,5.8039999999999985,5.742000000000001,5.731,5.751,5.771,5.757999999999999,5.687,5.555,5.365,5.1320000000000014,4.884,4.645,4.4289999999999985,4.246,4.103,3.992,3.906,3.843,3.794,3.755,3.715,3.668,3.608,3.532,3.435,3.321,3.197,3.064,2.929,2.798,2.677,2.569,2.477,2.401,2.341,2.292,2.249,2.211,2.177,2.147,2.119,2.095,2.072,2.051,2.031,, Bhutan,BTN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.67,6.67,6.67,6.67,6.67,6.67,6.67,6.67,6.67,6.67,6.671,6.674,6.6789999999999985,6.685,6.69,6.692,6.685,6.6679999999999975,6.64,6.601,6.553,6.504,6.456,6.41,6.362,6.306,6.23,6.127000000000002,5.994,5.829,5.6389999999999985,5.431,5.216,5.003,4.796,4.597,4.401,4.205,4.006,3.806,3.608,3.417,3.237,3.071,2.923,2.793,2.682,2.587,2.506,2.436,2.375,2.322,, Botswana,BWA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.615,6.6320000000000014,6.649,6.666,6.681,6.693,6.698,6.6960000000000015,6.686,6.6670000000000025,6.641,6.6110000000000015,6.579,6.546,6.5120000000000005,6.477,6.44,6.399,6.35,6.291,6.2170000000000005,6.125,6.0120000000000005,5.88,5.731,5.567,5.393,5.214,5.0360000000000005,4.863,4.698,4.542,4.394,4.252,4.117,3.989,3.866,3.746,3.631,3.519,3.4130000000000003,3.3160000000000003,3.227,3.148,3.079,3.017,2.962,2.91,2.86,2.8110000000000004,2.761,2.712,, Sub-Saharan Africa (IFC classification),CAA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Central African Republic,CAF,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.84,5.867000000000001,5.891,5.91,5.925,5.937,5.945,5.95,5.9529999999999985,5.954,5.954,5.954,5.9529999999999985,5.952000000000001,5.9510000000000005,5.95,5.9510000000000005,5.952000000000001,5.9529999999999985,5.954,5.954,5.955,5.956,5.955,5.952000000000001,5.944,5.9270000000000005,5.902,5.8679999999999986,5.8260000000000005,5.78,5.734,5.691,5.653,5.622000000000001,5.596,5.573,5.55,5.522,5.488,5.4460000000000015,5.393,5.329,5.2570000000000014,5.176,5.089,4.997,4.9030000000000005,4.809,4.716,4.626,4.538,, Canada,CAN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.811,3.753,3.681,3.607,3.4560000000000004,3.115,2.749,2.528,2.386,2.334,2.258,2.141,1.98,1.89,1.837,1.824,1.796,1.7819999999999998,1.768,1.754,1.74,1.7,1.69,1.68,1.65,1.67,1.675,1.68,1.68,1.77,1.83,1.7,1.71,1.7,1.669,1.639,1.592,1.55,1.53,1.51,1.49,1.505,1.52,1.53,1.53,1.54,1.586,1.659,1.681,1.668,1.6269999999999998,1.6269999999999998,, Switzerland,CHE,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.336,2.484,2.464,2.68,2.852,2.568,2.472,2.374,2.287,2.123,2.087,2.033,1.923,1.823,1.731,1.598,1.531,1.521,1.493,1.505,1.55,1.55,1.56,1.51,1.52,1.51,1.52,1.55,1.57,1.56,1.59,1.58,1.58,1.51,1.49,1.47,1.5,1.48,1.47,1.48,1.5,1.38,1.39,1.39,1.42,1.42,1.44,1.46,1.48,1.5,1.52,1.52,, Channel Islands,CHI,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.421,2.481,2.525,2.55,2.551,2.526,2.475,2.404,2.318,2.222,2.121,2.019,1.918,1.822,1.735,1.659,1.596,1.546,1.505,1.475,1.454,1.4409999999999998,1.4340000000000002,1.433,1.4340000000000002,1.4369999999999998,1.4409999999999998,1.446,1.452,1.457,1.46,1.461,1.457,1.45,1.4409999999999998,1.43,1.42,1.411,1.405,1.402,1.402,1.404,1.408,1.411,1.413,1.415,1.4169999999999998,1.42,1.4240000000000002,1.43,1.436,1.444,, Chile,CHL,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.5820000000000025,5.5429999999999975,5.462999999999999,5.3420000000000005,5.185,5.0,4.799,4.593,4.392,4.202,4.023,3.851,3.679,3.504,3.33,3.1630000000000003,3.013,2.887,2.7880000000000003,2.718,2.675,2.656,2.65,2.651,2.655,2.657,2.656,2.653,2.649,2.64,2.624,2.597,2.559,2.51,2.4530000000000003,2.388,2.321,2.254,2.192,2.135,2.087,2.047,2.014,1.985,1.96,1.939,1.92,1.903,1.888,1.873,1.858,1.844,, China,CHN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.757999999999999,5.8870000000000005,6.007999999999999,6.103,6.157,6.1610000000000005,6.11,6.011,5.871,5.692,5.47,5.2,4.887,4.542,4.181,3.826,3.497,3.212,2.982,2.813,2.71,2.673,2.682,2.72,2.769,2.8110000000000004,2.826,2.806,2.745,2.644,2.506,2.342,2.171,2.009,1.865,1.746,1.656,1.591,1.546,1.52,1.51,1.514,1.527,1.546,1.5659999999999998,1.585,1.602,1.617,1.63,1.642,1.65,1.6569999999999998,, Cote d'Ivoire,CIV,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.351,7.427,7.501,7.572,7.6389999999999985,7.701,7.7570000000000014,7.806,7.849,7.882999999999999,7.907999999999999,7.927,7.937,7.94,7.934,7.916,7.883999999999999,7.8370000000000015,7.774,7.695,7.602,7.497000000000001,7.382999999999999,7.263,7.1389999999999985,7.013,6.884,6.752000000000002,6.619,6.4860000000000015,6.356,6.232,6.114,6.005,5.904,5.81,5.72,5.632999999999999,5.5470000000000015,5.46,5.375,5.289,5.207000000000002,5.13,5.06,5.0,4.956,4.928,4.913,4.909,4.91,4.907,, Cameroon,CMR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.647,5.705,5.766,5.8279999999999985,5.89,5.949,6.005,6.058,6.11,6.159,6.205,6.247000000000001,6.2860000000000005,6.322,6.356,6.391,6.4289999999999985,6.47,6.516,6.563,6.609,6.651,6.683,6.7029999999999985,6.7079999999999975,6.697,6.669,6.627000000000002,6.572,6.507999999999999,6.434,6.352,6.2639999999999985,6.172999999999999,6.08,5.989,5.903,5.823,5.749,5.682,5.621,5.567,5.515,5.464,5.4129999999999985,5.358,5.299,5.235,5.167000000000002,5.0939999999999985,5.017,4.939,, "Congo, Rep.",COG,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.88,5.9220000000000015,5.9670000000000005,6.0120000000000005,6.056,6.098,6.138,6.174,6.2070000000000025,6.235,6.259,6.28,6.2970000000000015,6.312,6.3210000000000015,6.325,6.318,6.301,6.273,6.231,6.178,6.112,6.0360000000000005,5.952000000000001,5.864,5.774,5.682,5.591,5.502999999999999,5.421,5.347,5.2860000000000005,5.2360000000000015,5.198,5.171,5.154,5.145,5.141,5.1389999999999985,5.1370000000000005,5.134,5.131,5.127999999999999,5.125,5.122000000000001,5.119,5.114,5.109,5.101,5.089,5.072,5.046,, Colombia,COL,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.807,6.8,6.776,6.731,6.6610000000000005,6.559,6.4220000000000015,6.25,6.05,5.83,5.599,5.37,5.153,4.956,4.782,4.631,4.497,4.372,4.247,4.121,3.993,3.867,3.744,3.63,3.525,3.43,3.347,3.275,3.2110000000000003,3.155,3.104,3.057,3.012,2.966,2.92,2.872,2.823,2.775,2.727,2.682,2.64,2.603,2.57,2.542,2.518,2.496,2.475,2.454,2.43,2.405,2.376,2.346,, Comoros,COM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.7920000000000025,6.849,6.897,6.939,6.975,7.004,7.027,7.044,7.055,7.06,7.061,7.06,7.058,7.055,7.0520000000000005,7.0539999999999985,7.065,7.084,7.106,7.126,7.129,7.102,7.033,6.921,6.766,6.5760000000000005,6.362,6.141,5.928,5.735,5.573,5.447,5.355,5.292999999999998,5.2570000000000014,5.246,5.252999999999999,5.27,5.289,5.306,5.315,5.313,5.303,5.283,5.254,5.216,5.167999999999998,5.112,5.051,4.9860000000000015,4.919,4.85,, Cabo Verde,CPV,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.885,6.9220000000000015,6.9529999999999985,6.976,6.989,6.9929999999999986,6.99,6.982,6.97,6.954,6.935,6.9129999999999985,6.8870000000000005,6.855,6.818,6.771,6.714,6.645,6.564,6.473,6.375,6.274,6.174,6.075,5.979,5.882999999999999,5.784,5.68,5.565,5.441,5.307,5.164,5.016,4.863,4.708,4.55,4.388,4.221,4.05,3.876,3.701,3.527,3.357,3.192,3.037,2.895,2.77,2.66,2.567,2.49,2.427,2.375,, Costa Rica,CRI,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.311,7.295,7.221,7.085,6.886,6.631,6.3279999999999985,5.997000000000001,5.657,5.324,5.012,4.7330000000000005,4.488,4.2780000000000005,4.105,3.968,3.864,3.784,3.719,3.665,3.618,3.577,3.544,3.517,3.491,3.463,3.427,3.38,3.323,3.254,3.175,3.09,3.002,2.917,2.835,2.758,2.6860000000000004,2.616,2.548,2.481,2.414,2.345,2.275,2.204,2.134,2.067,2.006,1.953,1.909,1.874,1.847,1.827,, Cuba,CUB,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.182,4.36,4.509,4.606,4.643,4.617,4.54,4.433,4.312,4.18,4.033,3.857,3.646,3.4,3.127,2.844,2.573,2.332,2.134,1.987,1.892,1.843,1.826,1.825,1.832,1.837,1.836,1.827,1.81,1.785,1.7519999999999998,1.715,1.68,1.65,1.628,1.614,1.609,1.61,1.615,1.621,1.626,1.626,1.621,1.61,1.592,1.57,1.545,1.52,1.4980000000000002,1.48,1.467,1.459,, Curacao,CUW,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,2.1,2.0,2.2,2.1,2.2,,, Cayman Islands,CYM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Cyprus,CYP,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.5,3.471,3.4210000000000003,3.346,3.249,3.133,3.01,2.889,2.779,2.6860000000000004,2.61,2.547,2.491,2.44,2.393,2.352,2.323,2.31,2.312,2.3280000000000003,2.354,2.385,2.415,2.438,2.4530000000000003,2.458,2.456,2.45,2.442,2.43,2.411,2.381,2.337,2.278,2.206,2.124,2.035,1.945,1.86,1.781,1.714,1.658,1.6130000000000002,1.577,1.5490000000000002,1.529,1.514,1.503,1.493,1.485,1.4780000000000002,1.47,, Czech Republic,CZE,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.075,2.11,2.12,2.31,2.34,2.165,2.02,1.9,1.84,1.87,1.929,1.99,2.09,2.31,2.46,2.43,2.39,2.34,2.33,2.27,2.07,2.0,2.02,1.97,1.97,1.95,1.94,1.91,1.94,1.874,1.893,1.86,1.72,1.67,1.44,1.278,1.185,1.17,1.16,1.13,1.14,1.14,1.17,1.18,1.23,1.28,1.33,1.44,1.5,1.49,1.49,1.43,, Germany,DEU,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.37,2.45,2.44,2.51,2.54,2.5,2.53,2.48,2.38,2.21,2.03,1.92,1.71,1.54,1.51,1.45,1.45,1.4,1.38,1.38,1.44,1.43,1.41,1.33,1.29,1.37,1.43,1.43,1.46,1.42,1.45,1.33,1.29,1.28,1.24,1.25,1.3,1.35,1.36,1.36,1.38,1.35,1.34,1.34,1.36,1.34,1.33,1.37,1.38,1.36,1.39,1.36,, Djibouti,DJI,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.461,6.4929999999999986,6.527,6.561,6.595,6.629,6.665,6.702000000000001,6.739,6.774,6.8039999999999985,6.8260000000000005,6.836,6.834,6.817,6.784,6.734,6.671,6.598,6.52,6.443,6.3729999999999976,6.316,6.271,6.239,6.218,6.205,6.193,6.174,6.142,6.0870000000000015,6.0,5.879,5.727,5.547999999999999,5.352,5.148,4.95,4.768,4.607,4.4689999999999985,4.353,4.253,4.16,4.074,3.991,3.911,3.832,3.755,3.679,3.604,3.53,, Dominica,DMA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,5.5,,,,,,,,,,3.52,,,,,3.0,,,,,2.5,,,,,1.9,,,,,1.9,1.9,,,,,,,,,, Denmark,DNK,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.57,2.547,2.544,2.642,2.602,2.61,2.615,2.35,2.117,2.0,1.95,2.043,2.029,1.917,1.897,1.919,1.747,1.66,1.668,1.602,1.546,1.4369999999999998,1.4269999999999998,1.3769999999999998,1.4,1.4469999999999998,1.48,1.5,1.56,1.62,1.67,1.68,1.76,1.75,1.806,1.807,1.747,1.7519999999999998,1.72,1.73,1.77,1.74,1.72,1.76,1.78,1.8,1.85,1.84,1.89,1.84,1.87,1.75,, Dominican Republic,DOM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.555,7.487999999999999,7.404,7.3039999999999985,7.187,7.0539999999999985,6.904,6.739,6.562,6.376,6.182,5.983,5.782,5.58,5.382999999999999,5.193,5.0139999999999985,4.848,4.6930000000000005,4.552,4.422,4.302,4.19,4.082,3.978,3.878,3.783,3.695,3.613,3.537,3.466,3.397,3.33,3.262,3.195,3.13,3.069,3.014,2.966,2.926,2.892,2.863,2.8360000000000003,2.809,2.781,2.7510000000000003,2.719,2.6860000000000004,2.652,2.6180000000000003,2.584,2.551,, Algeria,DZA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.648,7.649,7.65,7.652,7.653,7.655,7.657,7.657999999999999,7.657,7.652,7.641,7.622000000000001,7.591,7.547999999999999,7.492000000000001,7.4220000000000015,7.338999999999999,7.244,7.138,7.021,6.8889999999999985,6.7410000000000005,6.5760000000000005,6.392,6.192,5.976,5.747000000000001,5.507999999999999,5.263,5.0139999999999985,4.761,4.503,4.238,3.971,3.705,3.449,3.207,2.987,2.794,2.634,2.514,2.439,2.407,2.412,2.448,2.507,2.58,2.656,2.725,2.781,2.817,2.829,, Ecuador,ECU,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.689,6.6720000000000015,6.651,6.6229999999999976,6.589,6.545,6.488,6.4179999999999975,6.335,6.238,6.127999999999999,6.005,5.874,5.7360000000000015,5.593,5.449,5.3039999999999985,5.159,5.015,4.875,4.742,4.618,4.505,4.401,4.306,4.217,4.131,4.044,3.955,3.861,3.765,3.669,3.576,3.488,3.407,3.335,3.27,3.213,3.161,3.113,3.068,3.025,2.983,2.94,2.897,2.853,2.81,2.768,2.728,2.69,2.655,2.622,, "Egypt, Arab Rep.",EGY,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.63,6.605,6.57,6.526,6.471,6.405,6.327000000000001,6.238,6.141,6.04,5.94,5.846,5.763,5.692,5.632999999999999,5.585,5.545,5.5070000000000014,5.465,5.4179999999999975,5.3660000000000005,5.31,5.251,5.189,5.122999999999998,5.045,4.947,4.827,4.684,4.522,4.35,4.1789999999999985,4.018,3.876,3.757,3.659,3.579,3.508,3.44,3.372,3.306,3.242,3.184,3.134,3.091,3.053,3.02,2.987,2.954,2.919,2.883,2.845,, Eritrea,ERI,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.899,6.8679999999999986,6.8370000000000015,6.806,6.778,6.752000000000002,6.728,6.706,6.686,6.6670000000000025,6.65,6.6370000000000005,6.626,6.619,6.615,6.614,6.6160000000000005,6.619,6.6229999999999976,6.627000000000002,6.627999999999999,6.625,6.6179999999999986,6.607,6.591,6.572,6.553,6.535,6.519,6.504,6.488,6.4670000000000005,6.438,6.4,6.351,6.2929999999999975,6.228,6.159,6.087999999999999,6.015,5.94,5.86,5.774,5.681,5.5820000000000025,5.478,5.372000000000001,5.266,5.1629999999999985,5.063,4.968,4.875,, Spain,ESP,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.862,2.765,2.7960000000000003,2.875,3.011,2.937,2.912,2.939,2.87,2.858,2.8360000000000003,2.859,2.842,2.823,2.866,2.7880000000000003,2.786,2.649,2.524,2.341,2.217,2.031,1.936,1.7919999999999998,1.72,1.63,1.6,1.47,1.42,1.36,1.33,1.31,1.32,1.27,1.2,1.18,1.15,1.15,1.16,1.19,1.23,1.24,1.26,1.31,1.32,1.34,1.37,1.39,1.46,1.39,1.38,1.36,, Estonia,EST,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,1.96,1.97,1.96,1.94,1.94,1.93,1.92,1.95,2.03,2.11,2.16,2.18,2.16,2.13,2.1,2.08,2.09,2.08,2.04,2.009,2.02,2.07,2.08,2.16,2.17,2.12,2.17,2.26,2.26,2.21,2.04,1.77,1.69,1.45,1.37,1.32,1.335,1.24,1.28,1.32,1.38,1.34,1.37,1.37,1.47,1.5,1.55,1.63,1.65,1.62,1.63,1.52,, Ethiopia,ETH,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.88,6.877000000000002,6.875,6.872000000000001,6.867000000000001,6.864,6.867000000000001,6.88,6.903,6.937,6.978,7.02,7.06,7.0939999999999985,7.121,7.143,7.1670000000000025,7.195,7.23,7.271,7.316,7.36,7.397,7.423999999999999,7.437,7.435,7.417999999999997,7.387,7.347,7.297999999999999,7.246,7.193,7.143,7.0939999999999985,7.046,6.995,6.935,6.8610000000000015,6.769,6.659,6.529,6.38,6.218,6.046,5.87,5.693,5.52,5.353,5.193,5.043,4.902,4.769,, Finland,FIN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.714,2.689,2.637,2.637,2.533,2.398,2.324,2.24,2.068,1.851,1.828,1.703,1.5930000000000002,1.504,1.625,1.6880000000000002,1.72,1.69,1.652,1.642,1.63,1.65,1.72,1.74,1.7,1.64,1.6,1.59,1.7,1.71,1.78,1.8,1.85,1.81,1.85,1.81,1.76,1.75,1.7,1.73,1.73,1.73,1.72,1.76,1.8,1.8,1.84,1.83,1.85,1.86,1.87,1.83,, Fiji,FJI,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.461,6.2810000000000015,6.085,5.881,5.676,5.475,5.278,5.083,4.892,4.71,4.543,4.397,4.275,4.178,4.106,4.0539999999999985,4.018,3.992,3.968,3.941,3.907,3.864,3.813,3.755,3.693,3.629,3.568,3.512,3.465,3.427,3.398,3.374,3.352,3.33,3.305,3.276,3.244,3.209,3.1710000000000003,3.132,3.09,3.0460000000000003,3.0010000000000003,2.954,2.907,2.86,2.8160000000000003,2.774,2.736,2.701,2.67,2.641,, France,FRA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.85,2.87,2.89,2.89,2.87,2.84,2.8,2.75,2.69,2.62,2.55,2.47,2.38,2.28,2.18,2.09,2.01,1.94,1.89,1.87,1.85,1.85,1.86,1.86,1.86,1.86,1.85,1.83,1.81,1.79,1.77,1.75,1.74,1.73,1.73,1.74,1.75,1.77,1.78,1.81,1.89,1.9,1.88,1.89,1.92,1.94,2.0,1.98,2.01,2.0,2.03,2.03,, Faeroe Islands,FRO,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, "Micronesia, Fed. Sts.",FSM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.934,6.9170000000000025,6.905,6.897,6.893,6.894,6.9,6.9110000000000005,6.924,6.935,6.938,6.925,6.894,6.8420000000000005,6.77,6.682,6.586,6.49,6.398,6.311,6.223,6.129,6.02,5.894,5.752000000000002,5.6,5.4460000000000015,5.299,5.167000000000002,5.052,4.958,4.882,4.82,4.766,4.716,4.664,4.6080000000000005,4.544,4.471,4.39,4.3,4.204,4.105,4.007,3.912,3.823,3.739,3.661,3.589,3.522,3.46,3.402,, Gabon,GAB,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.384,4.462,4.541,4.619,4.694,4.766,4.834,4.899,4.961,5.021,5.081,5.143,5.207999999999998,5.275,5.343,5.412000000000001,5.48,5.5429999999999975,5.6,5.648,5.684,5.709,5.722,5.723,5.7120000000000015,5.689,5.654,5.609,5.5539999999999985,5.4910000000000005,5.421,5.343,5.259,5.17,5.078,4.987,4.898,4.814,4.735,4.664,4.6,4.544,4.494,4.449,4.408,4.37,4.335,4.3039999999999985,4.275,4.246,4.214,4.178,, United Kingdom,GBR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.692,2.784,2.859,2.881,2.934,2.863,2.783,2.679,2.604,2.507,2.437,2.408,2.204,2.036,1.92,1.81,1.74,1.69,1.75,1.86,1.89,1.81,1.78,1.77,1.77,1.8,1.78,1.82,1.83,1.8,1.83,1.82,1.79,1.82,1.74,1.71,1.72,1.72,1.71,1.68,1.64,1.63,1.64,1.71,1.77,1.78,1.84,1.9,1.96,1.94,1.98,1.98,, Georgia,GEO,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.964,2.965,2.95,2.915,2.864,2.801,2.737,2.68,2.637,2.609,2.595,2.588,2.579,2.563,2.537,2.502,2.461,2.419,2.379,2.343,2.315,2.296,2.2840000000000003,2.277,2.275,2.273,2.269,2.26,2.2430000000000003,2.217,2.18,2.132,2.076,2.013,1.946,1.879,1.812,1.749,1.692,1.643,1.609,1.592,1.5930000000000002,1.609,1.639,1.6780000000000002,1.719,1.758,1.788,1.809,1.82,1.822,, Ghana,GHA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.749,6.789,6.827000000000001,6.862,6.893,6.9179999999999975,6.937,6.95,6.9570000000000025,6.9570000000000025,6.95,6.936,6.915,6.888,6.855,6.815,6.771,6.721,6.665,6.605,6.539,6.468,6.392,6.31,6.223,6.131,6.035,5.935,5.831,5.725,5.6160000000000005,5.505,5.392,5.278,5.165,5.058,4.959,4.87,4.793,4.727,4.669,4.617,4.566,4.512,4.455,4.392,4.3260000000000005,4.257,4.188,4.119,4.052,3.985,, Guinea,GIN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.102,6.113,6.121,6.127000000000002,6.131,6.135,6.14,6.147,6.158,6.174,6.195,6.221,6.25,6.283,6.318,6.354,6.391,6.428,6.465,6.5,6.533,6.563,6.59,6.613,6.63,6.641,6.645,6.641,6.629,6.608,6.579,6.539,6.492000000000001,6.436,6.375,6.308,6.237,6.1629999999999985,6.089,6.0139999999999985,5.939,5.8660000000000005,5.794,5.722,5.649,5.5760000000000005,5.501,5.422999999999999,5.343,5.26,5.174,5.088,, "Gambia, The",GMB,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.573,5.621,5.6720000000000015,5.723,5.776,5.83,5.884,5.938,5.9910000000000005,6.0429999999999975,6.093,6.141,6.185,6.226,6.2620000000000005,6.2929999999999975,6.316,6.3329999999999975,6.3420000000000005,6.343,6.3370000000000015,6.323,6.303,6.277,6.2479999999999976,6.2189999999999985,6.19,6.164,6.141,6.1229999999999976,6.107,6.095,6.0829999999999975,6.07,6.056,6.039,6.018,5.995,5.97,5.944,5.9170000000000025,5.891,5.867000000000001,5.845,5.827000000000001,5.812,5.803,5.799,5.797999999999999,5.797999999999999,5.796,5.789,, Guinea-Bissau,GNB,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.8279999999999985,5.771,5.67,5.515,5.32,5.1389999999999985,5.045,5.091,5.296,5.643,6.0710000000000015,6.489,6.812,6.984,6.9929999999999986,6.8660000000000005,6.662000000000001,6.462999999999999,6.33,6.283,6.322,6.422999999999999,6.5420000000000025,6.642,6.71,6.7429999999999986,6.7429999999999986,6.728,6.706,6.68,6.649,6.608,6.5539999999999985,6.4860000000000015,6.404,6.311,6.214,6.115,6.019,5.9289999999999985,5.845,5.766,5.69,5.614,5.539,5.462999999999999,5.3889999999999985,5.317,5.247000000000001,5.18,5.115,5.052,, Equatorial Guinea,GNQ,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.505,5.515,5.529,5.547999999999999,5.57,5.595,5.619,5.64,5.658,5.671,5.678,5.681,5.68,5.6770000000000005,5.675,5.674,5.676,5.682,5.693,5.7079999999999975,5.728,5.751,5.776,5.8020000000000005,5.8260000000000005,5.848,5.8660000000000005,5.881,5.891,5.897,5.9,5.901,5.902,5.902,5.901,5.897,5.888,5.872000000000001,5.847,5.814,5.773,5.727,5.678,5.627000000000002,5.574,5.518,5.4570000000000025,5.39,5.314,5.231,5.14,5.044,, Greece,GRC,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.277,2.189,2.234,2.215,2.312,2.297,2.376,2.549,2.559,2.48,2.337,2.295,2.315,2.28,2.39,2.365,2.385,2.266,2.274,2.261,2.226,2.091,2.024,1.94,1.823,1.6769999999999998,1.615,1.5,1.5,1.41,1.4,1.38,1.38,1.34,1.36,1.32,1.3,1.31,1.26,1.24,1.26,1.25,1.27,1.28,1.3,1.33,1.4,1.41,1.51,1.52,1.51,1.43,, Grenada,GRD,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.7429999999999986,6.627000000000002,6.442,6.1960000000000015,5.9060000000000015,5.597,5.3,5.04,4.835,4.69,4.604,4.561,4.537,4.512,4.479,4.436,4.385,4.337,4.299,4.269,4.251,4.244,4.243,4.245,4.243,4.231,4.2,4.146,4.0680000000000005,3.966,3.842,3.701,3.551,3.401,3.254,3.116,2.988,2.87,2.762,2.6660000000000004,2.582,2.512,2.455,2.4090000000000003,2.373,2.344,2.321,2.301,2.282,2.262,2.24,2.217,, Greenland,GRL,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,2.44,2.41,2.53,2.57,2.47,2.53,2.49,2.6830000000000003,2.39,2.34,2.3080000000000003,2.451,2.489,2.361,2.42,2.3,2.26,2.23,2.247,2.359,2.2,2.1,, Guatemala,GTM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.534,6.5120000000000005,6.49,6.464,6.434,6.399,6.36,6.323,6.2879999999999985,6.259,6.235,6.2189999999999985,6.2079999999999975,6.2029999999999985,6.2010000000000005,6.2010000000000005,6.2029999999999985,6.204,6.2029999999999985,6.1960000000000015,6.18,6.152,6.109,6.0539999999999985,5.987,5.9129999999999985,5.8370000000000015,5.7639999999999985,5.697,5.636,5.58,5.525,5.465,5.397,5.32,5.237,5.148,5.058,4.97,4.884,4.801,4.718,4.634,4.547,4.459,4.371,4.283,4.199,4.119,4.044,3.974,3.908,, Guam,GUM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.0520000000000005,6.047999999999999,5.984,5.857,5.67,5.439,5.187,4.939,4.716,4.526,4.372,4.248,4.137,4.0280000000000005,3.917,3.801,3.681,3.5610000000000004,3.447,3.34,3.248,3.177,3.128,3.1,3.092,3.095,3.099,3.097,3.082,3.053,3.013,2.969,2.929,2.899,2.881,2.872,2.87,2.867,2.86,2.846,2.824,2.794,2.759,2.72,2.679,2.638,2.599,2.562,2.529,2.499,2.472,2.448,, Guyana,GUY,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.671,5.5779999999999985,5.485,5.401,5.329,5.272,5.228,5.19,5.152,5.112,5.0680000000000005,5.022,4.974,4.919,4.852,4.758,4.621,4.435,4.204,3.935,3.646,3.36,3.099,2.881,2.714,2.6,2.5340000000000003,2.499,2.48,2.471,2.467,2.465,2.467,2.4730000000000003,2.482,2.4930000000000003,2.505,2.521,2.54,2.5610000000000004,2.585,2.614,2.645,2.678,2.709,2.735,2.7510000000000003,2.754,2.7430000000000003,2.718,2.682,2.638,, "Hong Kong SAR, China",HKG,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.162000000000001,5.212999999999999,5.18,5.051,4.833,4.551,4.246,3.959,3.722,3.545,3.4210000000000003,3.459,3.315,3.177,2.967,2.6660000000000004,2.48,2.376,2.272,2.12,2.047,1.933,1.86,1.722,1.5590000000000002,1.491,1.367,1.311,1.4,1.296,1.272,1.281,1.347,1.342,1.355,1.295,1.1909999999999998,1.127,1.017,0.982,1.035,0.932,0.939,0.901,0.927,0.966,0.984,1.028,1.064,1.055,1.127,1.204,, Honduras,HND,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.457999999999997,7.447999999999999,7.443,7.441,7.443,7.442,7.435,7.417000000000002,7.382999999999999,7.334,7.27,7.195,7.1110000000000015,7.025,6.935,6.8439999999999985,6.749,6.649,6.5429999999999975,6.431,6.313,6.19,6.062,5.932,5.8020000000000005,5.675,5.5539999999999985,5.441,5.335,5.2360000000000015,5.142,5.048,4.95,4.846,4.735,4.617,4.493,4.3660000000000005,4.239,4.1160000000000005,3.996,3.883,3.775,3.674,3.579,3.492,3.4130000000000003,3.34,3.273,3.212,3.154,3.1010000000000004,, Croatia,HRV,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.332,2.302,2.273,2.2430000000000003,2.211,2.177,2.141,2.104,2.068,2.035,2.007,1.987,1.975,1.972,1.976,1.985,1.996,2.005,2.01,2.01,2.004,1.993,1.9,1.88,1.87,1.82,1.76,1.64,1.79,1.63,1.63,1.53,1.48,1.52,1.47,1.58,1.67,1.69,1.45,1.38,1.39,1.38,1.34,1.33,1.35,1.41,1.38,1.4,1.47,1.5,1.46,1.46,, Haiti,HTI,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.324,6.318,6.3020000000000005,6.274,6.233,6.1789999999999985,6.109,6.026,5.937,5.847,5.7620000000000005,5.693,5.643,5.6160000000000005,5.615,5.642,5.699,5.779,5.872000000000001,5.97,6.058,6.122000000000001,6.154,6.149,6.106,6.028,5.921,5.799,5.672999999999999,5.549,5.43,5.318,5.21,5.103,4.997,4.8889999999999985,4.779,4.665,4.547,4.426,4.303,4.182,4.065,3.953,3.849,3.753,3.664,3.58,3.5,3.424,3.35,3.28,, Hungary,HUN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.019,1.941,1.79,1.81,1.82,1.82,1.89,2.01,2.06,2.029,1.97,1.915,1.931,1.93,2.27,2.35,2.23,2.15,2.07,2.01,1.91,1.877,1.92,1.73,1.73,1.83,1.83,1.81,1.79,1.78,1.84,1.86,1.77,1.69,1.64,1.57,1.46,1.38,1.32,1.28,1.32,1.31,1.3,1.27,1.28,1.31,1.34,1.32,1.35,1.32,1.25,1.23,, Indonesia,IDN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.666,5.6560000000000015,5.645,5.634,5.6229999999999976,5.612,5.599,5.5820000000000025,5.556,5.521,5.474,5.4129999999999985,5.337999999999999,5.251,5.152,5.043,4.927,4.806,4.682,4.557,4.43,4.301,4.167,4.0280000000000005,3.887,3.745,3.606,3.472,3.346,3.229,3.122,3.023,2.931,2.844,2.764,2.6910000000000003,2.628,2.575,2.5340000000000003,2.503,2.484,2.475,2.474,2.479,2.486,2.4930000000000003,2.495,2.49,2.479,2.46,2.434,2.403,, Isle of Man,IMN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,2.707,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,1.8,,,,,,,,1.65,,,,,,,,,,, India,IND,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.87,5.856,5.8420000000000005,5.8260000000000005,5.807,5.7810000000000015,5.747000000000001,5.7010000000000005,5.642,5.573,5.494,5.41,5.323,5.238,5.1560000000000015,5.077,5.0,4.922,4.843,4.762,4.6789999999999985,4.597,4.515,4.436,4.3580000000000005,4.2810000000000015,4.203,4.125,4.044,3.961,3.878,3.793,3.709,3.628,3.549,3.4730000000000003,3.402,3.334,3.269,3.207,3.145,3.083,3.018,2.952,2.884,2.817,2.753,2.694,2.643,2.6,2.563,2.532,, Ireland,IRL,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.76,3.791,3.921,4.01,4.065,4.0310000000000015,3.954,3.842,3.778,3.845,3.93,3.975,3.874,3.74,3.617,3.3960000000000004,3.312,3.269,3.24,3.229,3.229,3.07,2.957,2.759,2.589,2.5,2.45,2.31,2.17,2.08,2.12,2.09,2.02,1.93,1.86,1.87,1.91,1.92,1.94,1.9,1.89,1.94,1.97,1.96,1.94,1.87,1.93,2.01,2.1,2.07,2.07,2.05,, "Iran, Islamic Rep.",IRN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.9270000000000005,6.924,6.914,6.896,6.8679999999999986,6.827000000000001,6.77,6.699,6.617000000000001,6.528,6.44,6.359,6.2920000000000025,6.2429999999999986,6.214,6.2120000000000015,6.238,6.289,6.354,6.4220000000000015,6.481,6.516,6.515,6.47,6.374,6.223,6.015,5.759,5.468,5.152,4.819,4.478,4.137,3.806,3.492,3.204,2.946,2.716,2.512,2.337,2.193,2.079,1.994,1.934,1.895,1.873,1.866,1.87,1.88,1.893,1.904,1.912,, Iraq,IRQ,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.252000000000002,6.364,6.5139999999999985,6.689,6.872000000000001,7.044,7.188,7.295,7.362,7.382999999999999,7.362,7.308,7.234,7.153,7.072,6.9929999999999986,6.915,6.834,6.7479999999999976,6.658,6.569,6.485,6.407,6.337999999999999,6.276,6.22,6.164,6.105,6.039,5.965,5.8820000000000014,5.7920000000000025,5.699,5.605,5.51,5.4170000000000025,5.324,5.233,5.142,5.053,4.965,4.879,4.795,4.713,4.634,4.557,4.4830000000000005,4.412,4.343,4.276,4.211,4.147,, Iceland,ISL,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.294,3.884,3.983,3.98,3.858,3.713,3.5780000000000003,3.282,3.0610000000000004,2.988,2.793,2.875,3.088,2.948,2.66,2.613,2.529,2.319,2.355,2.49,2.48,2.33,2.26,2.24,2.08,1.93,1.93,2.05,2.2,2.2,2.31,2.19,2.21,2.22,2.14,2.08,2.12,2.04,2.05,1.99,2.08,1.95,1.93,1.99,2.04,2.05,2.08,2.09,2.15,2.23,2.2,2.02,, Israel,ISR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.866,3.858,3.85,3.838,3.826,3.814,3.802,3.79,3.786,3.782,3.778,3.774,3.77,3.698,3.626,3.554,3.482,3.41,3.354,3.298,3.242,3.1860000000000004,3.13,3.1060000000000003,3.082,3.0580000000000003,3.034,3.01,2.948,2.886,2.824,2.762,2.7,2.8,2.9,2.9,2.9,2.94,2.98,2.965,2.95,2.92,2.89,2.95,2.9,2.84,2.88,2.9,2.96,2.96,3.03,3.0,, Italy,ITA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.406,2.407,2.463,2.547,2.701,2.665,2.625,2.535,2.4930000000000003,2.508,2.425,2.411,2.359,2.339,2.331,2.208,2.108,1.975,1.87,1.7619999999999998,1.64,1.617,1.592,1.52,1.462,1.39,1.34,1.28,1.32,1.28,1.26,1.27,1.3,1.25,1.22,1.18,1.21,1.22,1.21,1.23,1.26,1.25,1.27,1.29,1.33,1.32,1.35,1.37,1.42,1.41,1.41,1.41,, Jamaica,JAM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.419,5.529,5.627000000000002,5.711,5.775,5.815,5.8210000000000015,5.79,5.722,5.617000000000001,5.477,5.305,5.1080000000000005,4.899,4.685,4.478,4.2860000000000005,4.115,3.965,3.839,3.733,3.643,3.559,3.477,3.394,3.3080000000000003,3.224,3.143,3.07,3.005,2.948,2.899,2.855,2.815,2.778,2.744,2.712,2.6830000000000003,2.655,2.629,2.603,2.5780000000000003,2.552,2.525,2.498,2.47,2.442,2.414,2.387,2.36,2.334,2.309,, Jordan,JOR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.687,7.802,7.904,7.983,8.033999999999999,8.057,8.052999999999999,8.033,8.004,7.968,7.926,7.876,7.818,7.75,7.675,7.598,7.523,7.455,7.391,7.329,7.262,7.178,7.0710000000000015,6.935,6.771,6.581,6.3729999999999976,6.157,5.943,5.734,5.5360000000000005,5.349,5.169,4.997,4.832,4.677,4.5310000000000015,4.395,4.269,4.155,4.053,3.966,3.893,3.832,3.78,3.734,3.689,3.641,3.5860000000000003,3.526,3.458,3.386,, Japan,JPN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.001,2.05,2.01,2.02,2.05,2.139,1.58,2.02,2.13,2.13,2.135,2.16,2.14,2.14,2.05,1.909,1.85,1.8,1.79,1.77,1.75,1.74,1.77,1.8,1.81,1.76,1.72,1.69,1.66,1.57,1.54,1.53,1.5019999999999998,1.4580000000000002,1.5,1.422,1.425,1.388,1.384,1.342,1.359,1.33,1.32,1.29,1.29,1.26,1.32,1.34,1.37,1.37,1.39,1.39,, Kazakhstan,KAZ,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.563,4.5139999999999985,4.437,4.331,4.2010000000000005,4.059,3.918,3.79,3.683,3.6,3.5380000000000003,3.489,3.44,3.385,3.32,3.249,3.175,3.1060000000000003,3.048,3.019,2.9,2.95,3.0,3.04,3.08,3.08,3.135,3.19,3.13,2.82,2.72,2.61,2.5,2.3,2.28,2.26,2.13,2.0,1.8,1.7,1.8,1.9,2.0,2.03,2.21,2.22,2.36,2.5,2.7,2.6,2.59,2.59,, Kenya,KEN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.9460000000000015,7.997999999999997,8.042,8.078,8.103,8.119,8.126,8.125,8.117,8.103,8.081,8.051,8.012,7.962999999999999,7.905,7.84,7.769,7.695,7.6179999999999986,7.5379999999999985,7.455,7.366,7.27,7.165,7.049,6.9179999999999975,6.769,6.602,6.4220000000000015,6.231,6.037000000000001,5.847,5.6679999999999975,5.506,5.3660000000000005,5.251,5.165,5.102,5.059,5.03,5.012,5.001,4.99,4.976,4.955,4.923,4.879,4.824,4.761,4.691,4.6160000000000005,4.538,, Kyrgyz Republic,KGZ,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.166,5.255,5.314,5.335,5.317,5.266,5.193,5.112,5.034,4.961,4.892,4.815,4.724,4.615,4.492,4.365,4.247,4.15,4.082,4.044,4.035,4.046,4.0680000000000005,4.086,4.097,4.093,4.073,4.039,3.992,3.875,3.69,3.671,3.617,3.3,3.14,3.31,2.99,2.79,2.648,2.629,2.4,2.4,2.5,2.5,2.6,2.5,2.7,2.8,2.8,2.9,3.06,3.06,, Cambodia,KHM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.9670000000000005,6.964,6.955,6.937,6.909,6.8679999999999986,6.815,6.749,6.6720000000000015,6.5829999999999975,6.475,6.337999999999999,6.172999999999999,5.988,5.795,5.622000000000001,5.4979999999999976,5.441,5.459,5.545,5.685,5.85,6.007999999999999,6.13,6.2,6.21,6.16,6.065,5.941,5.7920000000000025,5.6229999999999976,5.438,5.24,5.033,4.825,4.62,4.423,4.2360000000000015,4.059,3.896,3.75,3.619,3.504,3.401,3.31,3.23,3.162,3.102,3.051,3.007,2.966,2.929,, Kiribati,KIR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.9529999999999985,7.0120000000000005,7.077000000000001,7.143,7.2010000000000005,7.221,7.165,7.013,6.763,6.431,6.051,5.674,5.346,5.103,4.957,4.904,4.925,4.978,5.029,5.064,5.073,5.053,5.015,4.967,4.912,4.855,4.799,4.748,4.704,4.666,4.632,4.601,4.5680000000000005,4.527,4.476,4.412,4.331,4.235,4.126,4.006,3.881,3.754,3.631,3.516,3.4130000000000003,3.324,3.249,3.1860000000000004,3.133,3.087,3.048,3.014,, St. Kitts and Nevis,KNA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,3.5,,,,,,,,,,3.3,,,,,2.8,,,,,2.6,,,,,2.4,,,,,2.107,,,,,,,,,,, "Korea, Rep.",KOR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.155,5.989,5.789,5.574,5.357,5.157,4.987,4.845,4.725,4.624,4.53,4.54,4.14,4.1,3.81,3.47,3.05,3.02,2.65,2.9,2.83,2.66,2.42,2.08,1.96,1.67,1.6,1.55,1.56,1.58,1.59,1.74,1.78,1.67,1.67,1.65,1.58,1.54,1.47,1.42,1.47,1.3,1.17,1.19,1.16,1.0759999999999998,1.123,1.25,1.192,1.149,1.226,1.244,, Kosovo,KSV,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,4.5760000000000005,4.884,4.476,4.82,4.564,4.466,4.43,4.263,3.922,3.903,3.584,2.958,2.84,2.7060000000000004,2.701,2.698,2.457,2.568,2.878,2.954,2.799,2.664,2.343,2.533,2.647,2.425,2.431,2.384,2.337,2.289,2.2,, Kuwait,KWT,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.251,7.279,7.312,7.348,7.381,7.407,7.419,7.4129999999999985,7.382999999999999,7.327000000000001,7.241,7.124,6.978,6.809,6.622000000000001,6.4270000000000005,6.234,6.05,5.874,5.7029999999999985,5.524,5.319,5.075,4.7860000000000005,4.456,4.092,3.704,3.313,2.944,2.615,2.358,2.2,2.144,2.182,2.3,2.467,2.642,2.7880000000000003,2.878,2.903,2.869,2.7960000000000003,2.718,2.66,2.63,2.628,2.645,2.667,2.681,2.6830000000000003,2.673,2.652,, Lao PDR,LAO,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.961,5.964,5.966,5.9689999999999985,5.971,5.973,5.974,5.973,5.973,5.972,5.974,5.979,5.99,6.006,6.029,6.059,6.096,6.1389999999999985,6.186,6.233,6.277,6.315,6.345,6.363,6.369,6.3610000000000015,6.3420000000000005,6.313,6.274,6.222,6.152,6.057,5.934,5.782,5.603,5.398,5.167999999999998,4.922,4.669,4.42,4.19,3.991,3.829,3.706,3.619,3.562,3.52,3.4810000000000003,3.432,3.3680000000000003,3.29,3.2,, Lebanon,LBN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.739,5.724,5.694,5.647,5.5829999999999975,5.501,5.403,5.295,5.181,5.064,4.948,4.836,4.73,4.629,4.534,4.444,4.357,4.271,4.182,4.092,3.997,3.898,3.796,3.692,3.587,3.482,3.379,3.279,3.182,3.09,3.002,2.919,2.841,2.765,2.6910000000000003,2.617,2.543,2.468,2.39,2.31,2.226,2.137,2.044,1.948,1.854,1.765,1.686,1.621,1.57,1.535,1.513,1.5019999999999998,, Liberia,LBR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.4060000000000015,6.4289999999999985,6.4529999999999985,6.476,6.5,6.524,6.5520000000000005,6.5829999999999975,6.617000000000001,6.655,6.695,6.7360000000000015,6.777,6.815,6.849,6.88,6.907,6.93,6.95,6.964,6.973,6.973,6.964,6.9460000000000015,6.9170000000000025,6.875,6.82,6.752000000000002,6.672999999999999,6.5870000000000015,6.499,6.414,6.336,6.267,6.2079999999999975,6.1560000000000015,6.109,6.061,6.007999999999999,5.948,5.88,5.8039999999999985,5.722,5.635,5.5470000000000015,5.456,5.3660000000000005,5.277,5.19,5.106,5.024,4.945,, Libya,LBY,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.536,7.5710000000000015,7.607,7.642,7.676,7.71,7.7429999999999986,7.776,7.808,7.837999999999999,7.867000000000001,7.898,7.9289999999999985,7.957000000000002,7.979,7.992000000000001,7.992000000000001,7.976,7.939,7.872999999999997,7.769,7.619,7.4220000000000015,7.1789999999999985,6.897,6.584,6.252000000000002,5.9129999999999985,5.581,5.263,4.966,4.688,4.426,4.178,3.945,3.732,3.544,3.383,3.248,3.139,3.052,2.984,2.929,2.882,2.8360000000000003,2.79,2.741,2.69,2.637,2.582,2.525,2.467,, St. Lucia,LCA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.9670000000000005,6.931,6.88,6.8210000000000015,6.757999999999999,6.688,6.607,6.507999999999999,6.3870000000000005,6.249,6.101,5.9529999999999985,5.813,5.686,5.5710000000000015,5.4620000000000015,5.347,5.216,5.064,4.891,4.703,4.512,4.328,4.1610000000000005,4.0139999999999985,3.888,3.78,3.683,3.589,3.495,3.398,3.298,3.195,3.09,2.983,2.873,2.76,2.644,2.528,2.416,2.313,2.224,2.152,2.0980000000000003,2.062,2.04,2.029,2.022,2.013,2.0,1.982,1.96,, Latin America & Caribbean (all income levels),LCN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.98,5.977,5.959,5.921,5.8660000000000005,5.7920000000000025,5.704,5.608,5.5070000000000014,5.405,5.301,5.197,5.091,4.982,4.871,4.759,4.646,4.533,4.419,4.307,4.1960000000000015,4.087,3.978,3.871,3.766,3.664,3.564,3.469,3.377,3.2910000000000004,3.209,3.134,3.065,3.0,2.9410000000000003,2.886,2.833,2.785,2.738,2.692,2.6460000000000004,2.597,2.549,2.5,2.452,2.405,2.361,2.32,2.285,2.254,2.228,2.205,, Liechtenstein,LIE,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,1.57,1.52,1.47,1.36,1.44,1.49,1.43,1.42,1.43,1.71,1.4,1.69,, Sri Lanka,LKA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.541,5.421,5.299,5.18,5.067,4.959,4.849,4.734,4.609,4.477,4.342,4.208,4.083,3.97,3.87,3.783,3.705,3.633,3.562,3.488,3.408,3.319,3.2230000000000003,3.12,3.012,2.904,2.8,2.7030000000000003,2.617,2.544,2.483,2.4330000000000003,2.39,2.353,2.32,2.291,2.268,2.251,2.24,2.236,2.237,2.2430000000000003,2.252,2.263,2.274,2.286,2.298,2.311,2.323,2.335,2.343,2.347,, Lesotho,LSO,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.839,5.829,5.82,5.812,5.806,5.8020000000000005,5.801,5.803,5.805,5.807,5.808,5.807,5.8020000000000005,5.794,5.78,5.761,5.7360000000000015,5.706,5.6720000000000015,5.632999999999999,5.589,5.5420000000000025,5.4910000000000005,5.436,5.377000000000002,5.313,5.244,5.169,5.088,5.004,4.919,4.837,4.759,4.686,4.617,4.548,4.475,4.394,4.302,4.2,4.089,3.975,3.862,3.754,3.654,3.562,3.48,3.405,3.335,3.269,3.207,3.148,, Lithuania,LTU,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.56,2.53,2.45,2.35,2.28,2.23,2.22,2.23,2.24,2.3,2.37,2.38,2.33,2.25,2.21,2.19,2.17,2.13,2.09,2.04,2.03,1.98,1.99,2.04,2.09,2.1,2.14,2.16,2.09,1.98,2.03,1.97,1.89,1.67,1.57,1.55,1.49,1.47,1.46,1.46,1.39,1.3,1.24,1.26,1.26,1.27,1.31,1.35,1.47,1.55,1.55,1.76,, Luxembourg,LUX,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.28,,2.369,,2.34,2.42,2.34,2.24,2.12,2.02,1.98,1.92,1.72,1.52,1.55,1.55,,1.45,1.49,1.48,1.5,1.55,1.49,1.44,1.43,1.38,1.44,1.4,1.51,1.52,1.62,1.6,1.67,1.69,1.72,1.68,1.76,1.71,1.68,1.74,1.76,1.66,1.63,1.62,1.66,1.63,1.65,1.61,1.61,1.59,1.63,1.52,, Latvia,LVA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,1.94,1.94,1.91,1.85,1.79,1.74,1.76,1.8,1.83,1.88,1.96,2.0,2.0,1.98,1.97,1.96,1.93,1.89,1.87,1.87,1.86,1.88,1.97,2.07,2.09,2.08,2.12,2.15,2.11,2.05,2.02,1.86,1.73,1.51,1.39,1.25,1.16,1.11,1.09,1.16,1.24,1.21,1.23,1.29,1.24,1.31,1.35,1.41,1.44,1.31,1.17,1.34,, "Macao SAR, China",MAC,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.945,4.763,4.525,4.242,3.926,3.594,3.261,2.942,2.647,2.388,2.166,1.98,1.821,1.683,1.568,1.484,1.44,1.4409999999999998,1.485,1.5630000000000002,1.665,1.777,1.882,1.966,2.021,2.04,2.019,1.966,1.891,1.798,1.694,1.589,1.487,1.394,1.3119999999999998,1.242,1.179,1.119,1.057,0.996,0.939,0.8909999999999999,0.856,0.838,0.836,0.8490000000000001,0.8740000000000001,0.906,0.939,0.973,1.003,1.031,, St. Martin (French part),MAF,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,2.4,2.4,2.3,2.2,2.1,2.1,2.1,2.2,2.1,2.1,1.9,1.8,1.8,1.8,1.8,1.8,1.8,1.8,1.8,1.8,1.8,1.8,1.8,1.8,1.8,1.8,1.8,1.8,1.8,1.8,, Morocco,MAR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.065,7.106,7.131,7.135,7.119,7.081,7.024,6.9529999999999985,6.871,6.7810000000000015,6.687,6.587999999999999,6.485,6.38,6.273,6.1679999999999975,6.067,5.97,5.876,5.782,5.682,5.57,5.439,5.29,5.122999999999998,4.942,4.754,4.567,4.387,4.217,4.058,3.905,3.755,3.606,3.457,3.31,3.167,3.033,2.909,2.797,2.698,2.611,2.535,2.47,2.418,2.385,2.377,2.398,2.443,2.509,2.583,2.652,, Monaco,MCO,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Moldova,MDA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.3280000000000003,3.259,3.178,3.0860000000000003,2.989,2.891,2.801,2.722,2.66,2.613,2.582,2.56,2.542,2.523,2.503,2.483,2.465,2.455,2.454,2.462,2.481,2.51,2.546,2.585,2.62,2.643,2.6460000000000004,2.625,2.5780000000000003,2.506,2.4130000000000003,2.305,2.191,2.079,1.975,1.882,1.801,1.73,1.6669999999999998,1.6130000000000002,1.568,1.535,1.511,1.497,1.489,1.487,1.487,1.4880000000000002,1.487,1.483,1.477,1.469,, Madagascar,MDG,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.3,7.3,7.3,7.3,7.3,7.301,7.3039999999999985,7.31,7.316,7.322,7.325,7.325,7.318,7.3,7.269,7.216,7.129,7.007999999999999,6.857,6.687,6.5139999999999985,6.359,6.24,6.165,6.135,6.146,6.182,6.225,6.256,6.268,6.257999999999999,6.225,6.1789999999999985,6.126,6.066,5.999,5.924,5.841,5.749,5.651,5.547999999999999,5.443,5.3370000000000015,5.233,5.132999999999999,5.039,4.952,4.87,4.794,4.722,4.654,4.59,, Maldives,MDV,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.021,7.075,7.1179999999999986,7.152,7.1789999999999985,7.2010000000000005,7.218,7.231,7.237,7.237,7.227,7.2010000000000005,7.159,7.103,7.04,6.981,6.941,6.931,6.9529999999999985,7.002000000000002,7.0710000000000015,7.146,7.21,7.245,7.24,7.183,7.064,6.888,6.664,6.397,6.099,5.783,5.461,5.146,4.845,4.56,4.289,4.024,3.763,3.51,3.2710000000000004,3.055,2.869,2.715,2.596,2.508,2.449,2.41,2.382,2.36,2.339,2.314,, Mexico,MEX,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.783,6.776,6.771,6.768,6.767,6.769,6.773,6.777,6.775,6.76,6.72,6.643,6.525,6.364,6.164,5.932,5.6789999999999985,5.4179999999999975,5.1629999999999985,4.924,4.705,4.51,4.334,4.174,4.029,3.898,3.778,3.669,3.5660000000000003,3.468,3.375,3.285,3.199,3.117,3.04,2.966,2.8960000000000004,2.8310000000000004,2.77,2.712,2.659,2.61,2.565,2.523,2.484,2.448,2.4130000000000003,2.379,2.346,2.313,2.281,2.248,, Marshall Islands,MHL,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,5.9,,,,,,,,,,,,5.71,,,,,,4.5,4.5,4.5,,,,,, "Macedonia, FYR",MKD,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.72,3.666,3.602,3.528,3.446,3.358,3.27,3.185,3.108,3.039,2.98,2.928,2.88,2.834,2.789,2.745,2.7030000000000003,2.665,2.629,2.597,2.567,2.537,2.507,2.474,2.44,2.404,2.369,2.336,2.305,2.275,2.244,2.208,2.164,2.113,2.0540000000000003,1.989,1.92,1.852,1.788,1.729,1.6780000000000002,1.635,1.598,1.567,1.54,1.519,1.501,1.486,1.473,1.462,1.452,1.443,, Mali,MLI,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.7029999999999985,6.725,6.747000000000001,6.77,6.7929999999999975,6.816,6.837999999999999,6.858,6.875,6.8889999999999985,6.901,6.9129999999999985,6.924,6.937,6.9510000000000005,6.966,6.982,6.999,7.016,7.0310000000000015,7.046,7.059,7.07,7.08,7.087999999999999,7.093,7.095,7.0920000000000005,7.086,7.0760000000000005,7.062,7.044,7.023,6.999,6.973,6.947,6.921,6.896,6.8729999999999976,6.853,6.836,6.822,6.811,6.803,6.7970000000000015,6.796,6.799,6.806,6.817,6.83,6.841,6.85,, Malta,MLT,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.62,3.274,3.237,2.904,2.79,2.52,2.326,2.236,2.12,2.019,2.025,2.06,2.007,1.649,1.64,2.274,2.205,2.18,2.1180000000000003,2.1,1.99,1.87,1.98,1.965,1.95,1.99,1.98,1.98,2.08,2.11,2.05,2.04,2.12,2.01,1.89,1.83,2.1,1.95,1.88,1.77,1.7,1.48,1.45,1.48,1.4,1.38,1.39,1.37,1.44,1.43,1.38,1.38,, Myanmar,MMR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.051,6.073,6.096,6.1160000000000005,6.13,6.136,6.129,6.109,6.074,6.024,5.959,5.881,5.791,5.694,5.5920000000000005,5.488,5.3870000000000005,5.289,5.194,5.1,5.001,4.891,4.7639999999999985,4.619,4.456,4.279,4.0939999999999985,3.909,3.732,3.5660000000000003,3.415,3.279,3.158,3.0460000000000003,2.945,2.8510000000000004,2.761,2.675,2.59,2.508,2.428,2.353,2.286,2.227,2.178,2.137,2.103,2.075,2.049,2.026,2.003,1.98,, Montenegro,MNE,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.5210000000000004,3.417,3.3080000000000003,3.199,3.093,2.994,2.906,2.833,2.773,2.7260000000000004,2.689,2.657,2.625,2.59,2.549,2.503,2.4530000000000003,2.402,2.354,2.309,2.266,2.225,2.185,2.145,2.104,2.063,2.022,1.98,1.94,1.902,1.869,1.843,1.825,1.815,1.813,1.815,1.82,1.824,1.826,1.823,1.815,1.804,1.7919999999999998,1.779,1.767,1.756,1.745,1.734,1.722,1.71,1.6980000000000002,1.6869999999999998,, Mongolia,MNG,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.9529999999999985,7.1679999999999975,7.347,7.477,7.558,7.593,7.599,7.591,7.584,7.5779999999999985,7.569,7.546,7.497000000000001,7.4129999999999985,7.294,7.144,6.9689999999999985,6.78,6.5870000000000015,6.395,6.209,6.033,5.864,5.6960000000000015,5.526,5.345,5.14,4.9060000000000015,4.644,4.356,4.052,3.746,3.451,3.18,2.9410000000000003,2.738,2.57,2.43,2.312,2.216,2.144,2.102,2.089,2.103,2.141,2.193,2.254,2.315,2.3680000000000003,2.41,2.437,2.447,, Northern Mariana Islands,MNP,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Mozambique,MOZ,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.6,6.6,6.601,6.601,6.602,6.602,6.602,6.601,6.599,6.596,6.591,6.586,6.58,6.572,6.564,6.5539999999999985,6.544,6.532,6.519,6.505,6.49,6.474,6.4570000000000025,6.439,6.42,6.398,6.3729999999999976,6.345,6.313,6.277,6.237,6.191,6.14,6.086,6.0310000000000015,5.976,5.925,5.88,5.84,5.808,5.782,5.76,5.7410000000000005,5.721,5.697,5.669,5.6320000000000014,5.587999999999999,5.5360000000000005,5.476,5.409,5.337999999999999,, Mauritania,MRT,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.775,6.787000000000001,6.794,6.797999999999999,6.799,6.799,6.797999999999999,6.797999999999999,6.795,6.791,6.784,6.774,6.759,6.739,6.712999999999999,6.681,6.641,6.5939999999999985,6.541,6.484,6.426,6.3679999999999986,6.314,6.2639999999999985,6.2189999999999985,6.178,6.141,6.104,6.065,6.023,5.978,5.928,5.875,5.818,5.757999999999999,5.6960000000000015,5.632999999999999,5.569,5.505,5.442,5.381,5.3210000000000015,5.263,5.205,5.15,5.095,5.042,4.99,4.939,4.888,4.837,4.783,, Mauritius,MUS,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.1670000000000025,6.178,6.124,5.9929999999999986,5.785,5.51,5.187,4.847,4.516,4.213,3.952,3.741,3.575,3.444,3.341,3.255,3.169,3.071,2.954,2.818,2.672,2.532,2.412,2.325,2.16,2.02,1.99,2.05,2.14,2.23,2.32,2.3,2.37,2.21,2.25,2.14,2.12,2.04,1.97,2.05,1.99,1.91,1.94,1.87,1.87,1.82,1.7,1.66,1.58,1.5,1.47,1.45,, Malawi,MWI,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.9129999999999985,6.9460000000000015,6.983,7.021,7.06,7.101,7.141,7.182,7.222,7.263,7.3039999999999985,7.346,7.3889999999999985,7.433,7.477,7.518,7.555,7.584,7.605,7.617000000000001,7.621,7.619,7.612999999999999,7.601,7.582999999999997,7.548999999999999,7.49,7.402,7.287000000000001,7.148,6.997000000000001,6.85,6.7189999999999985,6.614,6.5360000000000005,6.483,6.4460000000000015,6.4110000000000005,6.369,6.317,6.254,6.186,6.119,6.058,6.002000000000002,5.95,5.899,5.843,5.7810000000000015,5.7120000000000015,5.636,5.5539999999999985,, Malaysia,MYS,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.194,6.136,6.0520000000000005,5.942,5.808,5.655,5.492000000000001,5.3260000000000005,5.165,5.0139999999999985,4.872,4.737,4.603,4.4689999999999985,4.337,4.209,4.092,3.99,3.906,3.839,3.789,3.753,3.725,3.702,3.679,3.656,3.63,3.604,3.576,3.5460000000000003,3.515,3.485,3.454,3.422,3.385,3.339,3.275,3.19,3.085,2.9610000000000003,2.825,2.6830000000000003,2.544,2.418,2.307,2.216,2.146,2.093,2.052,2.023,2.002,1.986,, Namibia,NAM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.15,6.1670000000000025,6.184,6.199,6.216,6.2360000000000015,6.263,6.301,6.347,6.401,6.459,6.517,6.57,6.613,6.642,6.654,6.647,6.622000000000001,6.581,6.524,6.4510000000000005,6.362,6.259,6.145,6.022,5.893,5.76,5.625,5.4910000000000005,5.358,5.227,5.098,4.97,4.842,4.715,4.59,4.4689999999999985,4.351,4.24,4.134,4.033,3.938,3.847,3.759,3.674,3.591,3.512,3.4360000000000004,3.364,3.295,3.229,3.167,, New Caledonia,NCL,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.278,6.144,6.01,5.8729999999999976,5.737,5.6,5.385,5.17,4.88,4.59,4.3,4.176,4.051,3.927,3.803,3.679,3.554,3.43,3.372,3.314,3.256,3.198,3.14,3.093,3.047,3.0,3.025,3.05,3.097,3.143,3.19,3.02,2.85,2.763,2.677,2.59,2.645,2.7,2.677,2.653,2.63,2.47,2.37,2.3,2.18,2.2,2.29,2.2,2.166,2.2,2.193,2.172,, Niger,NER,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.0520000000000005,7.0829999999999975,7.1160000000000005,7.15,7.185,7.222,7.26,7.3,7.341,7.3820000000000014,7.4220000000000015,7.46,7.495,7.526,7.553,7.5779999999999985,7.603,7.627999999999999,7.654,7.681,7.707000000000002,7.731,7.751,7.7639999999999985,7.773,7.775,7.774,7.771,7.767,7.7639999999999985,7.763,7.7639999999999985,7.766,7.769,7.771,7.773,7.772,7.767,7.7570000000000014,7.7429999999999986,7.725,7.704,7.681,7.657999999999999,7.636,7.617000000000001,7.602,7.593,7.587999999999999,7.585,7.584,7.581,, Nigeria,NGA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.354,6.351,6.346,6.341,6.336,6.335,6.3420000000000005,6.359,6.3870000000000005,6.425,6.471,6.522,6.575,6.625,6.669,6.706,6.735,6.7570000000000014,6.772,6.7810000000000015,6.783,6.779,6.767,6.749,6.726,6.698,6.664,6.625,6.5820000000000025,6.537000000000001,6.49,6.443,6.395,6.348,6.303,6.261,6.222,6.187,6.154,6.125,6.099,6.077000000000001,6.058,6.0420000000000025,6.029,6.02,6.015,6.015,6.017,6.021,6.022,6.017,, Nicaragua,NIC,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.336,7.2570000000000014,7.1789999999999985,7.109,7.0520000000000005,7.01,6.981,6.961,6.941,6.919,6.892,6.855,6.807,6.7479999999999976,6.678,6.597,6.51,6.42,6.327000000000001,6.232,6.131,6.018,5.89,5.746,5.589,5.426,5.267,5.118,4.985,4.865,4.754,4.642,4.519,4.381,4.225,4.055,3.878,3.702,3.535,3.384,3.2510000000000003,3.139,3.0460000000000003,2.967,2.903,2.8480000000000003,2.802,2.759,2.717,2.675,2.631,2.585,, Netherlands,NLD,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.122,3.217,3.176,3.193,3.1660000000000004,3.039,2.903,2.814,2.716,2.748,2.572,2.362,2.151,1.904,1.773,1.664,1.632,1.579,1.5830000000000002,1.5630000000000002,1.602,1.5630000000000002,1.495,1.4680000000000002,1.491,1.511,1.5530000000000002,1.558,1.55,1.55,1.62,1.61,1.59,1.57,1.57,1.53,1.53,1.53,1.63,1.65,1.72,1.71,1.73,1.75,1.72,1.71,1.72,1.72,1.77,1.79,1.79,1.76,, Norway,NOR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.846,2.9130000000000003,2.887,2.906,2.964,2.932,2.893,2.8,2.75,2.699,2.503,2.498,2.372,2.238,2.137,1.991,1.871,1.76,1.775,1.755,1.72,1.7,1.69,1.66,1.66,1.68,1.71,1.8,1.84,1.88,1.93,1.92,1.88,1.86,1.87,1.87,1.89,1.86,1.81,1.85,1.85,1.78,1.75,1.8,1.83,1.84,1.9,1.9,1.96,1.98,1.95,1.88,, Nepal,NPL,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.9929999999999986,5.994,5.995,5.996,5.997000000000001,5.997000000000001,5.996,5.994,5.988,5.981,5.971,5.9579999999999975,5.945,5.9289999999999985,5.912000000000001,5.894,5.8729999999999976,5.85,5.824,5.795,5.76,5.721,5.676,5.625,5.569,5.507999999999999,5.444,5.377999999999999,5.31,5.239,5.165,5.088,5.004,4.914,4.817,4.711,4.596,4.473,4.343,4.208,4.0680000000000005,3.924,3.778,3.632,3.486,3.34,3.194,3.0460000000000003,2.899,2.755,2.619,2.496,, New Zealand,NZL,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.129,4.099,4.107,3.989,3.733,3.54,3.41,3.354,3.332,3.269,3.158,3.194,3.0,2.696,2.57,2.331,2.273,2.229,2.07,2.12,2.03,2.01,1.95,1.92,1.93,1.93,1.96,2.03,2.1,2.12,2.18,2.16,2.12,2.05,2.0,1.99,1.96,1.95,1.92,1.94,2.0,1.97,1.89,1.91,2.0,1.96,2.0,2.11,2.19,2.14,2.16,2.1,, OECD members,OED,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.247,3.252,3.208,3.1910000000000003,3.173,3.08,2.925,2.917,2.872,2.835,2.799,2.736,2.604,2.522,2.465,2.369,2.302,2.255,2.197,2.191,2.169,2.121,2.101,2.049,2.022,2.0,1.975,1.958,1.963,1.954,1.965,1.943,1.922,1.889,1.864,1.826,1.816,1.803,1.798,1.786,1.805,1.777,1.76,1.767,1.7719999999999998,1.766,1.796,1.817,1.824,1.79,1.78,1.759,, Oman,OMN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.247000000000001,7.247999999999997,7.251,7.256,7.263,7.271,7.277,7.282,7.286,7.292999999999997,7.311,7.35,7.414,7.504,7.617000000000001,7.747000000000001,7.885,8.017999999999999,8.137,8.232000000000001,8.299,8.338,8.352,8.34,8.299,8.222000000000001,8.101,7.933,7.7189999999999985,7.4620000000000015,7.164,6.831,6.472,6.098,5.72,5.346,4.982,4.631,4.298,3.992,3.72,3.488,3.297,3.144,3.029,2.951,2.906,2.887,2.886,2.894,2.901,2.899,, Other small states,OSS,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.841,5.849,5.847,5.8320000000000025,5.8039999999999985,5.768,5.733,5.7079999999999975,5.695,5.698,5.71,5.723,5.727,5.716,5.689,5.651,5.602,5.569,5.537000000000001,5.511,5.487,5.462999999999999,5.422999999999999,5.4,5.348,5.289,5.234,5.169,5.129,5.073,5.012,4.94,4.863,4.789,4.723,4.645,4.572,4.475,4.39,4.317,4.2360000000000015,4.158,4.097,4.033,3.968,3.902,3.834,3.777,3.733,3.691,3.646,3.604,, Pakistan,PAK,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.6,6.6,6.6,6.6,6.6,6.6,6.6,6.6,6.6,6.6,6.601,6.602,6.605,6.608,6.6110000000000015,6.612,6.608,6.599,6.5829999999999975,6.561,6.535,6.507999999999999,6.483,6.46,6.436,6.407,6.367000000000001,6.31,6.234,6.138,6.024,5.899,5.767,5.634,5.499,5.359,5.207999999999998,5.042,4.8610000000000015,4.669,4.474,4.29,4.125,3.986,3.873,3.785,3.713,3.648,3.5810000000000004,3.509,3.43,3.347,, Panama,PAN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.87,5.846,5.812,5.765,5.7070000000000025,5.638,5.559,5.472,5.377999999999999,5.279,5.172999999999999,5.06,4.939,4.81,4.675,4.537,4.398,4.26,4.128,4.002,3.884,3.775,3.673,3.579,3.492,3.41,3.334,3.262,3.195,3.132,3.075,3.024,2.982,2.948,2.9210000000000003,2.901,2.884,2.87,2.855,2.839,2.821,2.799,2.775,2.75,2.724,2.696,2.667,2.637,2.608,2.5780000000000003,2.549,2.521,, Peru,PER,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.876,6.872000000000001,6.86,6.836,6.8,6.75,6.684,6.605,6.515,6.415,6.307,6.192,6.073,5.952000000000001,5.8279999999999985,5.702000000000001,5.572,5.437,5.2970000000000015,5.153,5.009,4.8660000000000005,4.729,4.598,4.475,4.36,4.25,4.144,4.038,3.933,3.828,3.722,3.617,3.514,3.4130000000000003,3.317,3.2260000000000004,3.142,3.064,2.9930000000000003,2.929,2.872,2.82,2.773,2.73,2.689,2.65,2.614,2.579,2.545,2.511,2.479,, Philippines,PHL,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.148,7.0870000000000015,7.02,6.947,6.867000000000001,6.7810000000000015,6.689,6.589,6.485,6.376,6.2639999999999985,6.152,6.041,5.931,5.824,5.718,5.613,5.506,5.399,5.29,5.183,5.078,4.978,4.883,4.795,4.712,4.632,4.5539999999999985,4.476,4.397,4.32,4.246,4.177,4.113,4.056,4.006,3.962,3.923,3.888,3.852,3.813,3.766,3.709,3.642,3.5660000000000003,3.485,3.403,3.326,3.257,3.199,3.151,3.111,, Palau,PLW,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,2.757,,,,,2.861,,,,,1.535,,,,,,,,,,,,, Papua New Guinea,PNG,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.275,6.278,6.278,6.275,6.268,6.257999999999999,6.244,6.227,6.2079999999999975,6.187,6.1629999999999985,6.1370000000000005,6.108,6.077000000000001,6.041,6.0,5.954,5.9,5.839,5.771,5.694,5.609,5.515,5.415,5.312,5.21,5.11,5.018,4.934,4.8610000000000015,4.802,4.757,4.724,4.7010000000000005,4.685,4.671,4.654,4.631,4.599,4.557,4.507,4.4510000000000005,4.392,4.335,4.279,4.226,4.174,4.122,4.067,4.011,3.954,3.896,, Poland,POL,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.98,2.83,2.72,2.697,2.57,2.52,2.34,2.33,2.24,2.2,2.2,2.25,2.235,2.255,2.26,2.27,2.302,2.23,2.205,2.28,2.276,2.235,2.336,2.416,2.372,2.329,2.22,2.154,2.13,2.0780000000000003,2.04,2.05,1.93,1.85,1.798,1.61,1.58,1.513,1.44,1.37,1.35,1.31,1.25,1.22,1.23,1.24,1.27,1.31,1.39,1.4,1.38,1.3,, Puerto Rico,PRI,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.657,4.547,4.4110000000000005,4.252,4.075,3.888,3.703,3.53,3.377,3.248,3.1460000000000004,3.068,3.006,2.955,2.908,2.864,2.818,2.769,2.718,2.664,2.607,2.548,2.49,2.436,2.387,2.344,2.3080000000000003,2.279,2.256,2.236,2.219,2.201,2.18,2.154,2.124,2.088,1.94,1.9,1.9,1.974,2.049,1.935,1.832,1.7619999999999998,1.7819999999999998,1.77,1.712,1.651,1.652,1.653,1.664,1.653,, "Korea, Dem. Rep.",PRK,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,4.579,4.357,4.173,4.057,4.022,4.064,4.159,4.262,4.336,4.364,4.327,4.214,4.038,3.816,3.564,3.307,3.075,2.889,2.761,2.693,2.676,2.687,2.698,2.69,2.654,2.593,2.515,2.438,2.374,2.325,2.289,2.262,2.235,2.202,2.1630000000000003,2.121,2.079,2.042,2.015,1.999,1.991,1.992,1.996,2.0,2.004,2.005,2.006,2.005,2.005,2.004,2.003,2.0,, Portugal,PRT,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.006,3.1830000000000003,3.213,3.084,3.153,3.0780000000000003,3.052,2.9960000000000004,2.902,2.849,2.759,2.799,2.697,2.655,2.599,2.517,2.569,2.448,2.231,2.112,2.19,2.144,2.19,1.946,1.92,1.74,1.63,1.57,1.53,1.48,1.43,1.42,1.48,1.53,1.44,1.38,1.43,1.46,1.48,1.5,1.55,1.45,1.47,1.44,1.4,1.4,1.36,1.33,1.37,1.32,1.36,1.35,, Paraguay,PRY,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.5,6.489,6.472,6.447,6.41,6.356,6.276,6.17,6.041,5.894,5.739,5.589,5.456,5.347,5.267,5.2170000000000005,5.1960000000000015,5.195,5.2029999999999985,5.214,5.2189999999999985,5.212999999999999,5.191,5.151,5.0939999999999985,5.02,4.931,4.835,4.7360000000000015,4.637,4.541,4.448,4.356,4.266,4.177,4.09,4.005,3.921,3.839,3.758,3.677,3.595,3.512,3.429,3.346,3.266,3.1910000000000003,3.123,3.063,3.012,2.968,2.931,, Pacific island small states,PSS,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.774,6.6789999999999985,6.572,6.4570000000000025,6.336,6.214,6.091,5.9689999999999985,5.848,5.73,5.6160000000000005,5.51,5.4129999999999985,5.3279999999999985,5.257999999999999,5.202000000000001,5.158,5.122000000000001,5.085,5.042,4.99,4.927,4.855,4.7780000000000005,4.7010000000000005,4.627,4.56,4.501,4.449,4.402,4.357,4.312,4.2639999999999985,4.215,4.163,4.11,4.056,4.002,3.948,3.894,3.842,3.791,3.741,3.693,3.646,3.6010000000000004,3.557,3.514,3.472,3.43,3.389,3.349,, French Polynesia,PYF,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.658,5.577000000000001,5.5,5.43,5.3679999999999986,5.314,5.267,5.222,5.174,5.12,5.057,4.98,4.8889999999999985,4.785,4.67,4.548,4.423,4.301,4.185,4.08,3.989,3.916,3.858,3.812,3.774,3.738,3.697,3.645,3.579,3.497,3.4,3.2910000000000004,3.175,3.059,2.946,2.841,2.745,2.66,2.585,2.52,2.463,2.414,2.37,2.329,2.289,2.251,2.216,2.184,2.156,2.132,2.11,2.092,, Qatar,QAT,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.971,6.973,6.977,6.981,6.985,6.987,6.987,6.983,6.973,6.952000000000001,6.9179999999999975,6.8660000000000005,6.794,6.7029999999999985,6.595,6.474,6.3439999999999985,6.211,6.079,5.947,5.811,5.665,5.504,5.3260000000000005,5.1320000000000014,4.9289999999999985,4.722,4.521,4.333,4.163,4.016,3.894,3.796,3.715,3.648,3.59,3.534,3.477,3.411,3.334,3.241,3.127,2.9960000000000004,2.853,2.7030000000000003,2.555,2.418,2.299,2.2030000000000003,2.133,2.085,2.055,, Romania,ROU,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.34,2.173,2.04,2.008,1.963,1.907,1.9,3.66,3.63,3.19,2.886,2.67,2.548,2.439,2.71,2.6,2.55,2.57,2.52,2.48,2.43,2.36,2.166,2.06,2.26,2.31,2.386,2.313,2.306,2.2,1.84,1.57,1.52,1.44,1.41,1.3430000000000002,1.3,1.32,1.32,1.3,1.31,1.27,1.25,1.27,1.29,1.32,1.32,1.3,1.35,1.38,1.33,1.25,, Russian Federation,RUS,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.52,2.45,2.36,2.27,2.18,2.13,2.1,2.04,1.99,1.97,1.99,2.03,2.04,2.01,2.0,1.98,1.97,1.95,1.92,1.9,1.89,1.91,2.04,2.11,2.06,2.05,2.15,2.22,2.12,2.01,1.89,1.732,1.5519999999999998,1.385,1.4,1.34,1.277,1.23,1.24,1.17,1.21,1.25,1.3,1.31,1.33,1.29,1.3,1.41,1.49,1.54,1.54,1.54,, Rwanda,RWA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,8.187000000000001,8.193999999999999,8.197000000000001,8.198,8.198,8.198,8.198,8.201,8.207,8.217,8.231,8.252,8.277999999999999,8.307,8.339,8.37,8.399,8.423,8.441,8.449,8.448,8.439,8.423,8.397,8.355,8.283999999999999,8.169,8.004,7.792000000000002,7.541,7.271,7.005,6.766,6.568,6.416,6.307,6.229,6.16,6.085,5.9979999999999976,5.897,5.7860000000000005,5.674,5.566,5.462999999999999,5.365,5.267,5.167000000000002,5.062,4.954,4.841,4.728,, Saudi Arabia,SAU,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.216,7.23,7.2429999999999986,7.252000000000002,7.2570000000000014,7.26,7.262,7.2639999999999985,7.267,7.273,7.28,7.289,7.298999999999999,7.307,7.312,7.313,7.309,7.298999999999999,7.2810000000000015,7.252000000000002,7.206,7.14,7.05,6.939,6.806,6.6560000000000015,6.496,6.331,6.166,6.004,5.8439999999999985,5.685,5.522,5.352,5.174,4.989,4.795,4.5939999999999985,4.39,4.187,3.99,3.804,3.634,3.482,3.349,3.234,3.136,3.05,2.971,2.898,2.829,2.763,, Sudan,SDN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.691,6.712999999999999,6.737,6.7620000000000005,6.787000000000001,6.81,6.831,6.85,6.865,6.877999999999999,6.888,6.899,6.91,6.921,6.93,6.936,6.933,6.919,6.892,6.853,6.8020000000000005,6.7410000000000005,6.674,6.605,6.535,6.4670000000000005,6.401,6.337999999999999,6.275,6.214,6.153,6.0920000000000005,6.028,5.9620000000000015,5.893,5.8210000000000015,5.747000000000001,5.6720000000000015,5.596,5.52,5.444,5.3660000000000005,5.287000000000001,5.206,5.122999999999998,5.039,4.956,4.873,4.792,4.713,4.637,4.563,, Senegal,SEN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.9510000000000005,6.994,7.0360000000000005,7.075,7.114,7.152,7.189,7.227,7.266,7.303,7.338999999999999,7.374,7.405,7.432,7.452000000000001,7.465,7.468,7.461,7.445,7.417999999999997,7.3820000000000014,7.3370000000000015,7.284,7.225,7.16,7.087999999999999,7.01,6.925,6.8320000000000025,6.734,6.629,6.519,6.404,6.287000000000001,6.169,6.0539999999999985,5.943,5.8370000000000015,5.737,5.645,5.561,5.484,5.4129999999999985,5.346,5.285,5.229,5.181,5.14,5.107,5.078,5.05,5.019,, Singapore,SGP,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.454,5.256,5.2,5.007,4.853,4.698,4.498,3.946,3.562,3.2460000000000004,3.0860000000000003,3.0380000000000003,3.048,2.8,2.359,2.079,2.111,1.82,1.759,1.791,1.737,1.723,1.706,1.608,1.615,1.614,1.433,1.621,1.956,1.754,1.865,1.77,1.76,1.778,1.75,1.71,1.696,1.635,1.494,1.475,,1.41,1.37,1.27,1.26,1.26,1.28,1.29,1.28,1.22,1.15,1.2,, Solomon Islands,SLB,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.388,6.385,6.382999999999999,6.385,6.394,6.419,6.47,6.549,6.655,6.7810000000000015,6.914,7.04,7.145,7.216,7.247999999999997,7.2360000000000015,7.182,7.096,6.99,6.871,6.7479999999999976,6.6320000000000014,6.525,6.431,6.349,6.278,6.211,6.1389999999999985,6.056,5.961,5.851,5.728,5.596,5.461,5.3260000000000005,5.197,5.077,4.968,4.872,4.789,4.72,4.665,4.618,4.578,4.54,4.502,4.459,4.412,4.359,4.3,4.2360000000000015,4.168,, Sierra Leone,SLE,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.033,6.093,6.158,6.229,6.3020000000000005,6.376,6.449,6.519,6.5829999999999975,6.643,6.697,6.7479999999999976,6.797999999999999,6.847,6.894,6.938,6.979,7.013,7.0379999999999985,7.0539999999999985,7.058,7.047999999999999,7.025,6.99,6.945,6.8889999999999985,6.824,6.752999999999999,6.678,6.601,6.525,6.4529999999999985,6.385,6.32,6.26,6.204,6.15,6.098,6.0429999999999975,5.985,5.92,5.845,5.759,5.664,5.56,5.4510000000000005,5.34,5.232,5.127999999999999,5.032,4.9430000000000005,4.8610000000000015,, El Salvador,SLV,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.728,6.749,6.752000000000002,6.7360000000000015,6.699,6.643,6.5710000000000015,6.487,6.396,6.3,6.2029999999999985,6.106,6.01,5.914,5.817,5.718,5.615,5.506,5.3889999999999985,5.266,5.1370000000000005,5.004,4.87,4.738,4.609,4.485,4.367,4.255,4.148,4.047,3.951,3.862,3.777,3.695,3.614,3.529,3.432,3.323,3.201,3.07,2.934,2.803,2.6830000000000003,2.58,2.496,2.4330000000000003,2.386,2.35,2.319,2.291,2.263,2.236,, San Marino,SMR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Somalia,SOM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.25,7.252000000000002,7.255,7.257999999999999,7.261,7.261,7.2570000000000014,7.247999999999997,7.232,7.209,7.182,7.151,7.1179999999999986,7.086,7.057,7.033,7.016,7.005,7.0,7.002999999999999,7.013,7.03,7.053,7.08,7.112,7.149,7.19,7.237,7.2879999999999985,7.341,7.397,7.455,7.512,7.567,7.616,7.655,7.6789999999999985,7.687,7.678,7.651,7.61,7.556,7.495,7.4289999999999985,7.3610000000000015,7.292000000000002,7.2189999999999985,7.14,7.056,6.965,6.869,6.769,, Serbia,SRB,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,2.5,,,,,,,,,,2.3,,,,,,,,,,2.1,,,,,,,,,,1.8,,,,1.7,,1.6,,,1.48,1.58,1.57,1.59,1.57,1.45,1.43,1.38,1.4,1.44,1.4,1.36,, South Sudan,SSD,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.721,6.733,6.747000000000001,6.763,6.7810000000000015,6.8,6.819,6.837999999999999,6.855,6.869,6.881,6.892,6.903,6.912000000000001,6.92,6.924,6.9220000000000015,6.9129999999999985,6.897,6.874,6.85,6.829,6.813,6.806,6.806,6.811,6.817,6.819,6.813,6.796,6.769,6.729,6.682,6.627000000000002,6.567,6.502999999999999,6.435,6.364,6.289,6.2120000000000015,6.132999999999999,6.05,5.9620000000000015,5.871,5.777,5.68,5.5820000000000025,5.483,5.385,5.2879999999999985,5.194,5.101,, Sao Tome and Principe,STP,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.242000000000001,6.263,6.284,6.306,6.327000000000001,6.349,6.371,6.394,6.419,6.444,6.468,6.49,6.51,6.525,6.534,6.535,6.528,6.513,6.489,6.455,6.409,6.348,6.271,6.181,6.0779999999999985,5.9670000000000005,5.849,5.73,5.613,5.501,5.395,5.296,5.2029999999999985,5.115,5.032,4.956,4.887,4.8260000000000005,4.773,4.727,4.687,4.654,4.625,4.598,4.572,4.542,4.506,4.462,4.4110000000000005,4.352,4.287,4.217,, Suriname,SUR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.608,6.5939999999999985,6.558,6.497000000000001,6.412000000000001,6.3039999999999985,6.182,6.053,5.9220000000000015,5.79,5.653,5.504,5.336,5.148,4.945,4.735,4.5310000000000015,4.3439999999999985,4.18,4.041,3.922,3.815,3.708,3.594,3.471,3.338,3.2,3.063,2.9360000000000004,2.823,2.733,2.6710000000000003,2.639,2.634,2.651,2.682,2.717,2.7460000000000004,2.762,2.759,2.739,2.702,2.656,2.609,2.562,2.518,2.478,2.441,2.406,2.374,2.345,2.318,, Slovak Republic,SVK,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.04,2.96,2.83,2.92,2.89,2.78,2.66,2.48,2.39,2.43,2.41,2.43,2.49,2.56,2.61,2.55,2.55,2.49,2.47,2.45,2.32,2.29,2.28,2.28,2.26,2.26,2.2,2.14,2.13,2.07,2.09,2.05,1.93,1.87,1.67,1.52,1.47,1.43,1.37,1.33,1.3,1.2,1.19,1.2,1.24,1.25,1.24,1.25,1.32,1.41,1.4,1.45,, Slovenia,SVN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.324,2.325,2.33,2.336,2.34,2.341,2.336,2.326,2.312,2.294,2.273,2.255,2.239,2.227,2.218,2.209,2.195,2.172,2.138,2.093,2.039,1.978,1.93,1.81,1.74,1.71,1.67,1.65,1.63,1.52,1.46,1.42,1.33,1.33,1.32,1.29,1.28,1.25,1.23,1.21,1.26,1.21,1.21,1.2,1.25,1.26,1.31,1.38,1.53,1.53,1.57,1.56,, Sweden,SWE,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.174,2.213,2.246,2.3280000000000003,2.474,2.391,2.367,2.281,2.067,1.943,1.939,1.978,1.927,1.88,1.888,1.779,1.689,1.644,1.601,1.6569999999999998,1.68,1.63,1.65,1.61,1.66,1.74,1.79,1.9,1.975,2.02,2.13,2.11,2.09,2.0,1.88,1.73,1.6,1.52,1.5,1.5,1.54,1.57,1.65,1.71,1.75,1.77,1.85,1.88,1.91,1.94,1.98,1.9,, Swaziland,SWZ,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.7170000000000005,6.73,6.745,6.763,6.782,6.8020000000000005,6.822,6.841,6.857,6.869,6.875,6.876,6.87,6.858,6.84,6.817,6.79,6.761,6.729,6.695,6.658,6.6179999999999986,6.573,6.52,6.459,6.384,6.291,6.18,6.051,5.905,5.744,5.5710000000000015,5.392,5.211,5.035,4.8660000000000005,4.709,4.564,4.432,4.313,4.209,4.121,4.046,3.982,3.925,3.871,3.818,3.761,3.699,3.632,3.559,3.483,, Sint Maarten (Dutch part),SXM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,1.5,1.7,1.7,,,, Seychelles,SYC,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,4.5,,,,,,3.5,,,,,3.0,,,,,2.696,,,,,2.1,2.04,2.04,2.08,1.98,2.04,2.1,2.0,2.2,2.1,2.24,2.3,2.4,2.1,2.1,, Syrian Arab Republic,SYR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.467,7.497000000000001,7.522,7.541,7.555,7.564,7.569,7.572,7.574,7.574,7.572,7.566,7.556,7.537000000000001,7.51,7.472,7.4220000000000015,7.359,7.285,7.197,7.0939999999999985,6.976,6.843,6.695,6.534,6.359,6.1679999999999975,5.962999999999999,5.7479999999999976,5.529,5.313,5.11,4.925,4.76,4.618,4.495,4.386,4.282,4.178,4.07,3.958,3.841,3.724,3.61,3.5010000000000003,3.401,3.313,3.237,3.173,3.1210000000000004,3.0780000000000003,3.04,, Turks and Caicos Islands,TCA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Chad,TCD,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.25,6.268,6.285,6.301,6.318,6.3370000000000015,6.362,6.393,6.432,6.477,6.528,6.5820000000000025,6.636,6.688,6.7360000000000015,6.78,6.82,6.857,6.892,6.925,6.9579999999999975,6.99,7.023,7.056,7.089,7.124,7.1610000000000005,7.199,7.237999999999999,7.276,7.313,7.346,7.376,7.399,7.416,7.425,7.426,7.419,7.405,7.383999999999999,7.354,7.315,7.268,7.2120000000000015,7.147,7.074,6.992000000000001,6.902,6.805,6.702000000000001,6.596,6.4860000000000015,, Togo,TGO,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.521,6.57,6.622000000000001,6.6770000000000005,6.734,6.7920000000000025,6.851,6.9110000000000005,6.971,7.029,7.084,7.136,7.182,7.222,7.254,7.275,7.286,7.284,7.27,7.244,7.207000000000002,7.158,7.099,7.032,6.9570000000000025,6.874,6.7810000000000015,6.6789999999999985,6.569,6.452000000000001,6.331,6.206,6.081,5.9570000000000025,5.8370000000000015,5.725,5.62,5.524,5.437,5.359,5.2879999999999985,5.224,5.166,5.1110000000000015,5.059,5.009,4.962,4.918,4.876,4.835,4.792,4.746,, Thailand,THA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.147,6.151,6.155,6.157,6.151,6.129,6.084,6.009,5.903,5.7639999999999985,5.595,5.397,5.181,4.953,4.721,4.488,4.257,4.03,3.808,3.594,3.392,3.202,3.024,2.859,2.707,2.571,2.451,2.346,2.256,2.1790000000000003,2.113,2.055,2.003,1.956,1.911,1.867,1.824,1.784,1.745,1.709,1.676,1.644,1.615,1.588,1.5630000000000002,1.539,1.517,1.496,1.477,1.459,1.443,1.4269999999999998,, Tajikistan,TJK,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.235,6.266,6.308,6.365,6.433,6.513,6.602,6.693,6.775,6.841,6.877999999999999,6.87,6.814,6.712999999999999,6.572,6.402,6.22,6.0429999999999975,5.8870000000000005,5.759,5.6629999999999985,5.601,5.561,5.533,5.51,5.4860000000000015,5.4529999999999985,5.408,5.347,5.27,5.175,5.067,4.95,4.83,4.709,4.587,4.462,4.334,4.203,4.075,3.954,3.848,3.76,3.695,3.653,3.636,3.642,3.667,3.703,3.743,3.78,3.807,, Turkmenistan,TKM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.415,6.537000000000001,6.626,6.6679999999999975,6.6629999999999985,6.6160000000000005,6.545,6.4689999999999985,6.403,6.35,6.3020000000000005,6.249,6.175,6.0710000000000015,5.939,5.783,5.612,5.441,5.279,5.135,5.012,4.915,4.836,4.772,4.718,4.669,4.623,4.572,4.513,4.44,4.345,4.222,4.0710000000000015,3.898,3.707,3.512,3.325,3.159,3.0210000000000004,2.914,2.837,2.783,2.741,2.701,2.66,2.615,2.569,2.523,2.482,2.445,2.412,2.381,, Timor-Leste,TLS,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.3729999999999976,6.376,6.375,6.367000000000001,6.347,6.314,6.268,6.2070000000000025,6.1320000000000014,6.039,5.9170000000000025,5.751,5.541,5.297999999999999,5.037,4.794,4.6110000000000015,4.5139999999999985,4.513,4.606,4.767,4.956,5.13,5.256,5.324,5.336,5.308,5.271,5.256,5.273,5.34,5.4689999999999985,5.651,5.874,6.125,6.384,6.627000000000002,6.8320000000000025,6.9860000000000015,7.079,7.112,7.0920000000000005,7.037000000000001,6.965,6.649,6.3320000000000025,6.016,5.7,5.7,5.7,5.5779999999999985,5.4529999999999985,, Tonga,TON,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.362999999999999,7.346,7.302,7.226,7.117000000000001,6.974,6.795,6.59,6.371,6.15,5.941,5.761,5.6160000000000005,5.5120000000000005,5.449,5.426,5.438,5.471,5.509,5.541,5.553,5.532,5.475,5.385,5.266,5.127999999999999,4.989,4.864,4.763,4.691,4.644,4.612,4.583,4.547,4.501,4.447,4.391,4.34,4.3,4.27,4.25,4.2360000000000015,4.221,4.202,4.177,4.144,4.104,4.059,4.012,3.963,3.914,3.864,, Trinidad and Tobago,TTO,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.2639999999999985,5.1770000000000005,5.047,4.873,4.664,4.433,4.2,3.985,3.802,3.658,3.554,3.484,3.432,3.389,3.349,3.313,3.287,3.273,3.2710000000000004,3.278,3.284,3.281,3.261,3.218,3.151,3.06,2.949,2.827,2.7,2.574,2.4530000000000003,2.339,2.231,2.131,2.04,1.961,1.896,1.843,1.801,1.7719999999999998,1.753,1.744,1.744,1.749,1.758,1.769,1.779,1.788,1.796,1.8,1.802,1.801,, Tunisia,TUN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.0429999999999975,7.087999999999999,7.1179999999999986,7.125,7.107,7.059,6.978,6.869,6.737,6.59,6.438,6.2920000000000025,6.16,6.046,5.95,5.867000000000001,5.79,5.706,5.606,5.488,5.349,5.189,5.015,4.833,4.645,4.454,4.265,4.077,3.893,3.714,3.5380000000000003,3.363,3.188,3.013,2.9,2.67,2.51,2.38,2.23,2.09,2.08,2.05,2.0,2.06,2.02,2.04,2.03,2.04,2.06,2.05,2.13,2.13,, Turkey,TUR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.303,6.2410000000000005,6.175,6.104,6.029,5.9510000000000005,5.874,5.7970000000000015,5.721,5.644,5.563,5.475,5.375,5.263,5.14,5.008,4.872,4.738,4.6080000000000005,4.4830000000000005,4.3610000000000015,4.239,4.114,3.982,3.844,3.704,3.563,3.427,3.3,3.1830000000000003,3.0780000000000003,2.987,2.906,2.835,2.772,2.715,2.661,2.609,2.557,2.506,2.454,2.404,2.356,2.311,2.27,2.234,2.202,2.173,2.147,2.123,2.101,2.08,, Tuvalu,TUV,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, Tanzania,TZA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.806,6.806,6.8039999999999985,6.803,6.801,6.797999999999999,6.795,6.791,6.785,6.778,6.771,6.765,6.761,6.757999999999999,6.755,6.751,6.7429999999999986,6.73,6.711,6.685,6.653,6.6179999999999986,6.58,6.5420000000000025,6.504,6.465,6.424,6.379,6.3279999999999985,6.273,6.212999999999999,6.148,6.081,6.013,5.9460000000000015,5.882999999999999,5.8279999999999985,5.78,5.7410000000000005,5.711,5.689,5.675,5.666,5.659,5.651,5.638,5.6160000000000005,5.585,5.5429999999999975,5.49,5.428,5.359,, Uganda,UGA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.999,7.019,7.04,7.06,7.0779999999999985,7.0939999999999985,7.106,7.113,7.117000000000001,7.1179999999999986,7.115,7.1110000000000015,7.107,7.103,7.1,7.099,7.099,7.099,7.099,7.1,7.1,7.101,7.101,7.102,7.103,7.103,7.103,7.102,7.1,7.097,7.091,7.0820000000000025,7.0710000000000015,7.057,7.039,7.018,6.994,6.9670000000000005,6.937,6.903,6.865,6.822,6.772,6.716,6.653,6.5829999999999975,6.5070000000000014,6.425,6.337999999999999,6.2479999999999976,6.155,6.06,, Ukraine,UKR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.24,2.17,2.14,2.06,1.96,1.99,2.02,2.01,1.998,2.04,2.09,2.12,2.08,2.04,2.04,2.02,1.99,1.94,1.96,1.96,1.95,1.93,1.98,2.08,2.09,2.06,2.08,2.05,2.02,1.92,1.848,1.81,1.72,1.6,1.5,1.4,1.3,1.3,1.2,1.2,1.1,1.1,1.1,1.2,1.2,1.2,1.31,1.345,1.39,1.46,1.445,1.459,, Uruguay,URY,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,2.881,2.887,2.885,2.874,2.858,2.841,2.8310000000000004,2.8310000000000004,2.844,2.869,2.902,2.938,2.969,2.988,2.9930000000000003,2.9810000000000003,2.951,2.905,2.849,2.787,2.724,2.665,2.614,2.574,2.546,2.53,2.523,2.523,2.524,2.523,2.518,2.506,2.487,2.463,2.432,2.398,2.362,2.327,2.295,2.267,2.2430000000000003,2.2230000000000003,2.205,2.188,2.171,2.155,2.138,2.122,2.107,2.093,2.08,2.068,, United States,USA,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,3.654,3.62,3.4610000000000003,3.319,3.19,2.9130000000000003,2.721,2.5580000000000003,2.464,2.456,2.48,2.266,2.01,1.879,1.835,1.774,1.7380000000000002,1.79,1.76,1.808,1.839,1.812,1.827,1.7990000000000002,1.806,1.844,1.837,1.872,1.934,2.014,2.081,2.062,2.046,2.019,2.002,1.978,1.976,1.971,1.999,2.007,2.056,2.0340000000000003,2.013,2.042,2.045,2.0540000000000003,2.1,2.122,2.084,2.001,1.931,1.895,, Uzbekistan,UZB,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.7070000000000025,6.755,6.783,6.79,6.777,6.7479999999999976,6.7070000000000025,6.66,6.608,6.5520000000000005,6.492000000000001,6.4220000000000015,6.337999999999999,6.237,6.119,5.983,5.829,5.66,5.482,5.3020000000000005,5.127000000000002,4.968,4.829,4.711,4.6160000000000005,4.539,4.474,4.5,4.28,4.1789999999999985,4.072,4.199,4.004,3.8,3.537,3.596,3.32,3.082,2.815,2.72,2.58,2.46,2.52,2.36,2.46,2.36,2.39,2.55,2.64,2.53,2.499,2.499,, St. Vincent and the Grenadines,VCT,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.224,7.155,7.074,6.981,6.876,6.76,6.6320000000000014,6.494,6.345,6.185,6.0139999999999985,5.8279999999999985,5.629,5.4170000000000025,5.197,4.973,4.752,4.54,4.339,4.154,3.985,3.832,3.692,3.5610000000000004,3.439,3.3280000000000003,3.23,3.144,3.072,3.01,2.9560000000000004,2.907,2.86,2.8110000000000004,2.76,2.7030000000000003,2.641,2.576,2.509,2.442,2.379,2.321,2.271,2.229,2.196,2.17,2.149,2.131,2.112,2.092,2.07,2.046,, "Venezuela, RB",VEN,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.6160000000000005,6.6370000000000005,6.627999999999999,6.581,6.495,6.3679999999999986,6.2029999999999985,6.0139999999999985,5.811,5.605,5.404,5.2189999999999985,5.053,4.905,4.779,4.67,4.574,4.4830000000000005,4.391,4.296,4.199,4.104,4.0139999999999985,3.933,3.861,3.794,3.73,3.665,3.597,3.524,3.448,3.37,3.292,3.218,3.147,3.082,3.022,2.967,2.915,2.867,2.822,2.779,2.739,2.701,2.664,2.629,2.595,2.562,2.531,2.501,2.472,2.444,, Virgin Islands (U.S.),VIR,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,5.615,5.651,5.6789999999999985,5.6960000000000015,5.698,5.6789999999999985,5.634,5.561,5.459,5.3279999999999985,5.167000000000002,4.976,4.76,4.527,4.2860000000000005,4.047,3.818,3.607,3.42,3.261,3.138,3.053,3.0,2.9730000000000003,2.967,2.9730000000000003,2.986,2.997,2.999,2.987,2.954,2.895,2.813,2.712,2.599,2.481,2.367,2.265,2.184,2.128,2.055,1.9,2.113,2.006,2.068,2.111,1.95,1.915,1.88,1.845,1.8,1.8,, Vietnam,VNM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.348,6.392,6.425,6.448,6.464,6.475,6.485,6.4929999999999986,6.494,6.487,6.465,6.421,6.35,6.251,6.125,5.973,5.8,5.614,5.422999999999999,5.232,5.046,4.865,4.691,4.521,4.359,4.205,4.063,3.931,3.806,3.684,3.5580000000000003,3.4160000000000004,3.255,3.074,2.878,2.676,2.482,2.309,2.166,2.057,1.983,1.94,1.918,1.907,1.902,1.897,1.889,1.877,1.862,1.843,1.82,1.794,, Vanuatu,VUT,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.197,7.12,7.033,6.938,6.836,6.73,6.626,6.526,6.433,6.348,6.272,6.202000000000001,6.134,6.067,5.999,5.9289999999999985,5.858,5.787000000000001,5.716,5.645,5.575,5.502999999999999,5.43,5.356,5.282,5.209,5.141,5.078,5.022,4.971,4.927,4.887,4.85,4.814,4.775,4.73,4.677,4.614,4.542,4.459,4.368,4.268,4.162,4.056,3.95,3.851,3.76,3.679,3.608,3.549,3.499,3.4560000000000004,, West Bank and Gaza,PSE,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,6.532,6.547999999999999,6.539,6.4929999999999986,6.404,6.274,6.1110000000000015,5.931,5.7479999999999976,5.5710000000000015,5.404,5.247999999999998,5.1,4.958,4.823,4.697,4.581,4.476,4.381,4.295,4.216,4.144,, Samoa,WSM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.651,7.645,7.63,7.604,7.567,7.519,7.4620000000000015,7.4,7.334,7.265,7.194,7.119,7.039,6.952000000000001,6.859,6.761,6.6560000000000015,6.5470000000000015,6.434,6.32,6.2029999999999985,6.086,5.968,5.85,5.734,5.62,5.51,5.404,5.303,5.207999999999998,5.118,5.034,4.956,4.882,4.815,4.751,4.692,4.637,4.587,4.541,4.503,4.476,4.46,4.454,4.456,4.46,4.46,4.45,4.426,4.3889999999999985,4.338,4.277,, "Yemen, Rep.",YEM,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.292000000000002,7.308,7.3279999999999985,7.354,7.385,7.417999999999997,7.447,7.471,7.491,7.512,7.542000000000002,7.593,7.6720000000000015,7.782,7.9220000000000015,8.089,8.277000000000001,8.474,8.667,8.843,8.993,9.108,9.185,9.223,9.223,9.186,9.119,9.03,8.925,8.805,8.667,8.504,8.311,8.088,7.841,7.5779999999999985,7.31,7.049,6.8020000000000005,6.574,6.363,6.166,5.975,5.782,5.587999999999999,5.393,5.199,5.01,4.829,4.658,4.498,4.348,, South Africa,ZAF,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.172999999999999,6.144,6.103,6.049,5.984,5.9110000000000005,5.836,5.765,5.7,5.643,5.591,5.539,5.482,5.415,5.337999999999999,5.251,5.159,5.064,4.9689999999999985,4.877,4.7860000000000005,4.695,4.602,4.504,4.402,4.293,4.177,4.052,3.923,3.791,3.658,3.53,3.408,3.2960000000000003,3.196,3.11,3.04,2.983,2.937,2.899,2.866,2.834,2.801,2.763,2.721,2.675,2.627,2.58,2.5380000000000003,2.5,2.467,2.438,, "Congo, Dem. Rep.",COD,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,6.001,6.015,6.03,6.047999999999999,6.067,6.089,6.1110000000000015,6.135,6.1610000000000005,6.187,6.214,6.242000000000001,6.271,6.301,6.3329999999999975,6.3660000000000005,6.403,6.443,6.487,6.535,6.585,6.636,6.689,6.742000000000001,6.794,6.847,6.902,6.96,7.019,7.077000000000001,7.132999999999999,7.183,7.223,7.251,7.267,7.267,7.252999999999999,7.227,7.19,7.143,7.089,7.027,6.96,6.8870000000000005,6.809,6.728,6.642,6.55,6.454,6.354,6.251,6.146,, Zambia,ZMB,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.018,7.0710000000000015,7.127000000000002,7.184,7.24,7.292000000000002,7.337999999999999,7.376,7.405,7.425,7.437,7.443,7.4460000000000015,7.447,7.444,7.435,7.414,7.377999999999999,7.326,7.258999999999999,7.182,7.098,7.015,6.937,6.865,6.799,6.737,6.672999999999999,6.606,6.537000000000001,6.468,6.401,6.34,6.2879999999999985,6.245,6.209,6.1789999999999985,6.152,6.126,6.098,6.0710000000000015,6.044,6.018,5.995,5.974,5.954,5.932,5.908,5.881,5.849,5.813,5.773,, Zimbabwe,ZWE,"Fertility rate, total (births per woman)",SP.DYN.TFRT.IN,7.158,7.215,7.267,7.311,7.347,7.372999999999997,7.391,7.403,7.411,7.415,7.417000000000002,7.419,7.42,7.417000000000002,7.41,7.395,7.369,7.33,7.273,7.1960000000000015,7.095,6.9670000000000005,6.811,6.632999999999999,6.435,6.223,6.004,5.784,5.569,5.365,5.176,5.001,4.84,4.69,4.5539999999999985,4.432,4.328,4.24,4.169,4.112,4.069,4.039,4.018,4.002,3.987,3.969,3.941,3.903,3.853,3.792,3.721,3.643,,statsmodels-0.12.2/statsmodels/datasets/grunfeld/000077500000000000000000000000001400612667500221255ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/grunfeld/__init__.py000066400000000000000000000003261400612667500242370ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/grunfeld/data.py000066400000000000000000000047711400612667500234210ustar00rootroot00000000000000"""Grunfeld (1950) Investment Data""" import pandas as pd from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This is public domain.""" TITLE = __doc__ SOURCE = """This is the Grunfeld (1950) Investment Data. The source for the data was the original 11-firm data set from Grunfeld's Ph.D. thesis recreated by Kleiber and Zeileis (2008) "The Grunfeld Data at 50". The data can be found here. http://statmath.wu-wien.ac.at/~zeileis/grunfeld/ For a note on the many versions of the Grunfeld data circulating see: http://www.stanford.edu/~clint/bench/grunfeld.htm """ DESCRSHORT = """Grunfeld (1950) Investment Data for 11 U.S. Firms.""" DESCRLONG = DESCRSHORT NOTE = """:: Number of observations - 220 (20 years for 11 firms) Number of variables - 5 Variables name definitions:: invest - Gross investment in 1947 dollars value - Market value as of Dec. 31 in 1947 dollars capital - Stock of plant and equipment in 1947 dollars firm - General Motors, US Steel, General Electric, Chrysler, Atlantic Refining, IBM, Union Oil, Westinghouse, Goodyear, Diamond Match, American Steel year - 1935 - 1954 Note that raw_data has firm expanded to dummy variables, since it is a string categorical variable. """ def load(as_pandas=None): """ Loads the Grunfeld data and returns a Dataset class. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. Notes ----- raw_data has the firm variable expanded to dummy variables for each firm (ie., there is no reference dummy) """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): """ Loads the Grunfeld data and returns a Dataset class. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. Notes ----- raw_data has the firm variable expanded to dummy variables for each firm (ie., there is no reference dummy) """ data = _get_data() data.year = data.year.astype(float) raw_data = pd.get_dummies(data) ds = du.process_pandas(data, endog_idx=0) ds.raw_data = raw_data return ds def _get_data(): data = du.load_csv(__file__, 'grunfeld.csv') return data statsmodels-0.12.2/statsmodels/datasets/grunfeld/grunfeld.csv000066400000000000000000000167151400612667500244620ustar00rootroot00000000000000invest,value,capital,firm,year 317.6,3078.5,2.8,General Motors,1935 391.8,4661.7,52.6,General Motors,1936 410.6,5387.1,156.9,General Motors,1937 257.7,2792.2,209.2,General Motors,1938 330.8,4313.2,203.4,General Motors,1939 461.2,4643.9,207.2,General Motors,1940 512,4551.2,255.2,General Motors,1941 448,3244.1,303.7,General Motors,1942 499.6,4053.7,264.1,General Motors,1943 547.5,4379.3,201.6,General Motors,1944 561.2,4840.9,265,General Motors,1945 688.1,4900.9,402.2,General Motors,1946 568.9,3526.5,761.5,General Motors,1947 529.2,3254.7,922.4,General Motors,1948 555.1,3700.2,1020.1,General Motors,1949 642.9,3755.6,1099,General Motors,1950 755.9,4833,1207.7,General Motors,1951 891.2,4924.9,1430.5,General Motors,1952 1304.4,6241.7,1777.3,General Motors,1953 1486.7,5593.6,2226.3,General Motors,1954 209.9,1362.4,53.8,US Steel,1935 355.3,1807.1,50.5,US Steel,1936 469.9,2676.3,118.1,US Steel,1937 262.3,1801.9,260.2,US Steel,1938 230.4,1957.3,312.7,US Steel,1939 361.6,2202.9,254.2,US Steel,1940 472.8,2380.5,261.4,US Steel,1941 445.6,2168.6,298.7,US Steel,1942 361.6,1985.1,301.8,US Steel,1943 288.2,1813.9,279.1,US Steel,1944 258.7,1850.2,213.8,US Steel,1945 420.3,2067.7,132.6,US Steel,1946 420.5,1796.7,264.8,US Steel,1947 494.5,1625.8,306.9,US Steel,1948 405.1,1667,351.1,US Steel,1949 418.8,1677.4,357.8,US Steel,1950 588.2,2289.5,342.1,US Steel,1951 645.5,2159.4,444.2,US Steel,1952 641,2031.3,623.6,US Steel,1953 459.3,2115.5,669.7,US Steel,1954 33.1,1170.6,97.8,General Electric,1935 45,2015.8,104.4,General Electric,1936 77.2,2803.3,118,General Electric,1937 44.6,2039.7,156.2,General Electric,1938 48.1,2256.2,172.6,General Electric,1939 74.4,2132.2,186.6,General Electric,1940 113,1834.1,220.9,General Electric,1941 91.9,1588,287.8,General Electric,1942 61.3,1749.4,319.9,General Electric,1943 56.8,1687.2,321.3,General Electric,1944 93.6,2007.7,319.6,General Electric,1945 159.9,2208.3,346,General Electric,1946 147.2,1656.7,456.4,General Electric,1947 146.3,1604.4,543.4,General Electric,1948 98.3,1431.8,618.3,General Electric,1949 93.5,1610.5,647.4,General Electric,1950 135.2,1819.4,671.3,General Electric,1951 157.3,2079.7,726.1,General Electric,1952 179.5,2371.6,800.3,General Electric,1953 189.6,2759.9,888.9,General Electric,1954 40.29,417.5,10.5,Chrysler,1935 72.76,837.8,10.2,Chrysler,1936 66.26,883.9,34.7,Chrysler,1937 51.6,437.9,51.8,Chrysler,1938 52.41,679.7,64.3,Chrysler,1939 69.41,727.8,67.1,Chrysler,1940 68.35,643.6,75.2,Chrysler,1941 46.8,410.9,71.4,Chrysler,1942 47.4,588.4,67.1,Chrysler,1943 59.57,698.4,60.5,Chrysler,1944 88.78,846.4,54.6,Chrysler,1945 74.12,893.8,84.8,Chrysler,1946 62.68,579,96.8,Chrysler,1947 89.36,694.6,110.2,Chrysler,1948 78.98,590.3,147.4,Chrysler,1949 100.66,693.5,163.2,Chrysler,1950 160.62,809,203.5,Chrysler,1951 145,727,290.6,Chrysler,1952 174.93,1001.5,346.1,Chrysler,1953 172.49,703.2,414.9,Chrysler,1954 39.68,157.7,183.2,Atlantic Refining,1935 50.73,167.9,204,Atlantic Refining,1936 74.24,192.9,236,Atlantic Refining,1937 53.51,156.7,291.7,Atlantic Refining,1938 42.65,191.4,323.1,Atlantic Refining,1939 46.48,185.5,344,Atlantic Refining,1940 61.4,199.6,367.7,Atlantic Refining,1941 39.67,189.5,407.2,Atlantic Refining,1942 62.24,151.2,426.6,Atlantic Refining,1943 52.32,187.7,470,Atlantic Refining,1944 63.21,214.7,499.2,Atlantic Refining,1945 59.37,232.9,534.6,Atlantic Refining,1946 58.02,249,566.6,Atlantic Refining,1947 70.34,224.5,595.3,Atlantic Refining,1948 67.42,237.3,631.4,Atlantic Refining,1949 55.74,240.1,662.3,Atlantic Refining,1950 80.3,327.3,683.9,Atlantic Refining,1951 85.4,359.4,729.3,Atlantic Refining,1952 91.9,398.4,774.3,Atlantic Refining,1953 81.43,365.7,804.9,Atlantic Refining,1954 20.36,197,6.5,IBM,1935 25.98,210.3,15.8,IBM,1936 25.94,223.1,27.7,IBM,1937 27.53,216.7,39.2,IBM,1938 24.6,286.4,48.6,IBM,1939 28.54,298,52.5,IBM,1940 43.41,276.9,61.5,IBM,1941 42.81,272.6,80.5,IBM,1942 27.84,287.4,94.4,IBM,1943 32.6,330.3,92.6,IBM,1944 39.03,324.4,92.3,IBM,1945 50.17,401.9,94.2,IBM,1946 51.85,407.4,111.4,IBM,1947 64.03,409.2,127.4,IBM,1948 68.16,482.2,149.3,IBM,1949 77.34,673.8,164.4,IBM,1950 95.3,676.9,177.2,IBM,1951 99.49,702,200,IBM,1952 127.52,793.5,211.5,IBM,1953 135.72,927.3,238.7,IBM,1954 24.43,138,100.2,Union Oil,1935 23.21,200.1,125,Union Oil,1936 32.78,210.1,142.4,Union Oil,1937 32.54,161.2,165.1,Union Oil,1938 26.65,161.7,194.8,Union Oil,1939 33.71,145.1,222.9,Union Oil,1940 43.5,110.6,252.1,Union Oil,1941 34.46,98.1,276.3,Union Oil,1942 44.28,108.8,300.3,Union Oil,1943 70.8,118.2,318.2,Union Oil,1944 44.12,126.5,336.2,Union Oil,1945 48.98,156.7,351.2,Union Oil,1946 48.51,119.4,373.6,Union Oil,1947 50,129.1,389.4,Union Oil,1948 50.59,134.8,406.7,Union Oil,1949 42.53,140.8,429.5,Union Oil,1950 64.77,179,450.6,Union Oil,1951 72.68,178.1,466.9,Union Oil,1952 73.86,186.8,486.2,Union Oil,1953 89.51,192.7,511.3,Union Oil,1954 12.93,191.5,1.8,Westinghouse,1935 25.9,516,0.8,Westinghouse,1936 35.05,729,7.4,Westinghouse,1937 22.89,560.4,18.1,Westinghouse,1938 18.84,519.9,23.5,Westinghouse,1939 28.57,628.5,26.5,Westinghouse,1940 48.51,537.1,36.2,Westinghouse,1941 43.34,561.2,60.8,Westinghouse,1942 37.02,617.2,84.4,Westinghouse,1943 37.81,626.7,91.2,Westinghouse,1944 39.27,737.2,92.4,Westinghouse,1945 53.46,760.5,86,Westinghouse,1946 55.56,581.4,111.1,Westinghouse,1947 49.56,662.3,130.6,Westinghouse,1948 32.04,583.8,141.8,Westinghouse,1949 32.24,635.2,136.7,Westinghouse,1950 54.38,723.8,129.7,Westinghouse,1951 71.78,864.1,145.5,Westinghouse,1952 90.08,1193.5,174.8,Westinghouse,1953 68.6,1188.9,213.5,Westinghouse,1954 26.63,290.6,162,Goodyear,1935 23.39,291.1,174,Goodyear,1936 30.65,335,183,Goodyear,1937 20.89,246,198,Goodyear,1938 28.78,356.2,208,Goodyear,1939 26.93,289.8,223,Goodyear,1940 32.08,268.2,234,Goodyear,1941 32.21,213.3,248,Goodyear,1942 35.69,348.2,274,Goodyear,1943 62.47,374.2,282,Goodyear,1944 52.32,387.2,316,Goodyear,1945 56.95,347.4,302,Goodyear,1946 54.32,291.9,333,Goodyear,1947 40.53,297.2,359,Goodyear,1948 32.54,276.9,370,Goodyear,1949 43.48,274.6,376,Goodyear,1950 56.49,339.9,391,Goodyear,1951 65.98,474.8,414,Goodyear,1952 66.11,496,443,Goodyear,1953 49.34,474.5,468,Goodyear,1954 2.54,70.91,4.5,Diamond Match,1935 2,87.94,4.71,Diamond Match,1936 2.19,82.2,4.57,Diamond Match,1937 1.99,58.72,4.56,Diamond Match,1938 2.03,80.54,4.38,Diamond Match,1939 1.81,86.47,4.21,Diamond Match,1940 2.14,77.68,4.12,Diamond Match,1941 1.86,62.16,3.83,Diamond Match,1942 0.93,62.24,3.58,Diamond Match,1943 1.18,61.82,3.41,Diamond Match,1944 1.36,65.85,3.31,Diamond Match,1945 2.24,69.54,3.23,Diamond Match,1946 3.81,64.97,3.9,Diamond Match,1947 5.66,68,5.38,Diamond Match,1948 4.21,71.24,7.39,Diamond Match,1949 3.42,69.05,8.74,Diamond Match,1950 4.67,83.04,9.07,Diamond Match,1951 6,74.42,9.93,Diamond Match,1952 6.53,63.51,11.68,Diamond Match,1953 5.12,58.12,14.33,Diamond Match,1954 2.938,30.284,52.011,American Steel,1935 5.643,43.909,52.903,American Steel,1936 10.233,107.02,54.499,American Steel,1937 4.046,68.306,59.722,American Steel,1938 3.326,84.164,61.659,American Steel,1939 4.68,69.157,62.243,American Steel,1940 5.732,60.148,63.361,American Steel,1941 12.117,49.332,64.861,American Steel,1942 15.276,75.18,67.953,American Steel,1943 9.275,62.05,69.59,American Steel,1944 9.577,59.152,69.144,American Steel,1945 3.956,68.424,70.269,American Steel,1946 3.834,48.505,71.051,American Steel,1947 5.97,40.507,71.508,American Steel,1948 6.433,39.961,73.827,American Steel,1949 4.77,36.494,75.847,American Steel,1950 6.532,46.082,77.367,American Steel,1951 7.329,57.616,78.631,American Steel,1952 9.02,57.441,80.215,American Steel,1953 6.281,47.165,83.788,American Steel,1954 statsmodels-0.12.2/statsmodels/datasets/grunfeld/src/000077500000000000000000000000001400612667500227145ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/grunfeld/src/grunfeld.csv000066400000000000000000000167151400612667500252510ustar00rootroot00000000000000invest,value,capital,firm,year 317.6,3078.5,2.8,General Motors,1935 391.8,4661.7,52.6,General Motors,1936 410.6,5387.1,156.9,General Motors,1937 257.7,2792.2,209.2,General Motors,1938 330.8,4313.2,203.4,General Motors,1939 461.2,4643.9,207.2,General Motors,1940 512,4551.2,255.2,General Motors,1941 448,3244.1,303.7,General Motors,1942 499.6,4053.7,264.1,General Motors,1943 547.5,4379.3,201.6,General Motors,1944 561.2,4840.9,265,General Motors,1945 688.1,4900.9,402.2,General Motors,1946 568.9,3526.5,761.5,General Motors,1947 529.2,3254.7,922.4,General Motors,1948 555.1,3700.2,1020.1,General Motors,1949 642.9,3755.6,1099,General Motors,1950 755.9,4833,1207.7,General Motors,1951 891.2,4924.9,1430.5,General Motors,1952 1304.4,6241.7,1777.3,General Motors,1953 1486.7,5593.6,2226.3,General Motors,1954 209.9,1362.4,53.8,US Steel,1935 355.3,1807.1,50.5,US Steel,1936 469.9,2676.3,118.1,US Steel,1937 262.3,1801.9,260.2,US Steel,1938 230.4,1957.3,312.7,US Steel,1939 361.6,2202.9,254.2,US Steel,1940 472.8,2380.5,261.4,US Steel,1941 445.6,2168.6,298.7,US Steel,1942 361.6,1985.1,301.8,US Steel,1943 288.2,1813.9,279.1,US Steel,1944 258.7,1850.2,213.8,US Steel,1945 420.3,2067.7,132.6,US Steel,1946 420.5,1796.7,264.8,US Steel,1947 494.5,1625.8,306.9,US Steel,1948 405.1,1667,351.1,US Steel,1949 418.8,1677.4,357.8,US Steel,1950 588.2,2289.5,342.1,US Steel,1951 645.5,2159.4,444.2,US Steel,1952 641,2031.3,623.6,US Steel,1953 459.3,2115.5,669.7,US Steel,1954 33.1,1170.6,97.8,General Electric,1935 45,2015.8,104.4,General Electric,1936 77.2,2803.3,118,General Electric,1937 44.6,2039.7,156.2,General Electric,1938 48.1,2256.2,172.6,General Electric,1939 74.4,2132.2,186.6,General Electric,1940 113,1834.1,220.9,General Electric,1941 91.9,1588,287.8,General Electric,1942 61.3,1749.4,319.9,General Electric,1943 56.8,1687.2,321.3,General Electric,1944 93.6,2007.7,319.6,General Electric,1945 159.9,2208.3,346,General Electric,1946 147.2,1656.7,456.4,General Electric,1947 146.3,1604.4,543.4,General Electric,1948 98.3,1431.8,618.3,General Electric,1949 93.5,1610.5,647.4,General Electric,1950 135.2,1819.4,671.3,General Electric,1951 157.3,2079.7,726.1,General Electric,1952 179.5,2371.6,800.3,General Electric,1953 189.6,2759.9,888.9,General Electric,1954 40.29,417.5,10.5,Chrysler,1935 72.76,837.8,10.2,Chrysler,1936 66.26,883.9,34.7,Chrysler,1937 51.6,437.9,51.8,Chrysler,1938 52.41,679.7,64.3,Chrysler,1939 69.41,727.8,67.1,Chrysler,1940 68.35,643.6,75.2,Chrysler,1941 46.8,410.9,71.4,Chrysler,1942 47.4,588.4,67.1,Chrysler,1943 59.57,698.4,60.5,Chrysler,1944 88.78,846.4,54.6,Chrysler,1945 74.12,893.8,84.8,Chrysler,1946 62.68,579,96.8,Chrysler,1947 89.36,694.6,110.2,Chrysler,1948 78.98,590.3,147.4,Chrysler,1949 100.66,693.5,163.2,Chrysler,1950 160.62,809,203.5,Chrysler,1951 145,727,290.6,Chrysler,1952 174.93,1001.5,346.1,Chrysler,1953 172.49,703.2,414.9,Chrysler,1954 39.68,157.7,183.2,Atlantic Refining,1935 50.73,167.9,204,Atlantic Refining,1936 74.24,192.9,236,Atlantic Refining,1937 53.51,156.7,291.7,Atlantic Refining,1938 42.65,191.4,323.1,Atlantic Refining,1939 46.48,185.5,344,Atlantic Refining,1940 61.4,199.6,367.7,Atlantic Refining,1941 39.67,189.5,407.2,Atlantic Refining,1942 62.24,151.2,426.6,Atlantic Refining,1943 52.32,187.7,470,Atlantic Refining,1944 63.21,214.7,499.2,Atlantic Refining,1945 59.37,232.9,534.6,Atlantic Refining,1946 58.02,249,566.6,Atlantic Refining,1947 70.34,224.5,595.3,Atlantic Refining,1948 67.42,237.3,631.4,Atlantic Refining,1949 55.74,240.1,662.3,Atlantic Refining,1950 80.3,327.3,683.9,Atlantic Refining,1951 85.4,359.4,729.3,Atlantic Refining,1952 91.9,398.4,774.3,Atlantic Refining,1953 81.43,365.7,804.9,Atlantic Refining,1954 20.36,197,6.5,IBM,1935 25.98,210.3,15.8,IBM,1936 25.94,223.1,27.7,IBM,1937 27.53,216.7,39.2,IBM,1938 24.6,286.4,48.6,IBM,1939 28.54,298,52.5,IBM,1940 43.41,276.9,61.5,IBM,1941 42.81,272.6,80.5,IBM,1942 27.84,287.4,94.4,IBM,1943 32.6,330.3,92.6,IBM,1944 39.03,324.4,92.3,IBM,1945 50.17,401.9,94.2,IBM,1946 51.85,407.4,111.4,IBM,1947 64.03,409.2,127.4,IBM,1948 68.16,482.2,149.3,IBM,1949 77.34,673.8,164.4,IBM,1950 95.3,676.9,177.2,IBM,1951 99.49,702,200,IBM,1952 127.52,793.5,211.5,IBM,1953 135.72,927.3,238.7,IBM,1954 24.43,138,100.2,Union Oil,1935 23.21,200.1,125,Union Oil,1936 32.78,210.1,142.4,Union Oil,1937 32.54,161.2,165.1,Union Oil,1938 26.65,161.7,194.8,Union Oil,1939 33.71,145.1,222.9,Union Oil,1940 43.5,110.6,252.1,Union Oil,1941 34.46,98.1,276.3,Union Oil,1942 44.28,108.8,300.3,Union Oil,1943 70.8,118.2,318.2,Union Oil,1944 44.12,126.5,336.2,Union Oil,1945 48.98,156.7,351.2,Union Oil,1946 48.51,119.4,373.6,Union Oil,1947 50,129.1,389.4,Union Oil,1948 50.59,134.8,406.7,Union Oil,1949 42.53,140.8,429.5,Union Oil,1950 64.77,179,450.6,Union Oil,1951 72.68,178.1,466.9,Union Oil,1952 73.86,186.8,486.2,Union Oil,1953 89.51,192.7,511.3,Union Oil,1954 12.93,191.5,1.8,Westinghouse,1935 25.9,516,0.8,Westinghouse,1936 35.05,729,7.4,Westinghouse,1937 22.89,560.4,18.1,Westinghouse,1938 18.84,519.9,23.5,Westinghouse,1939 28.57,628.5,26.5,Westinghouse,1940 48.51,537.1,36.2,Westinghouse,1941 43.34,561.2,60.8,Westinghouse,1942 37.02,617.2,84.4,Westinghouse,1943 37.81,626.7,91.2,Westinghouse,1944 39.27,737.2,92.4,Westinghouse,1945 53.46,760.5,86,Westinghouse,1946 55.56,581.4,111.1,Westinghouse,1947 49.56,662.3,130.6,Westinghouse,1948 32.04,583.8,141.8,Westinghouse,1949 32.24,635.2,136.7,Westinghouse,1950 54.38,723.8,129.7,Westinghouse,1951 71.78,864.1,145.5,Westinghouse,1952 90.08,1193.5,174.8,Westinghouse,1953 68.6,1188.9,213.5,Westinghouse,1954 26.63,290.6,162,Goodyear,1935 23.39,291.1,174,Goodyear,1936 30.65,335,183,Goodyear,1937 20.89,246,198,Goodyear,1938 28.78,356.2,208,Goodyear,1939 26.93,289.8,223,Goodyear,1940 32.08,268.2,234,Goodyear,1941 32.21,213.3,248,Goodyear,1942 35.69,348.2,274,Goodyear,1943 62.47,374.2,282,Goodyear,1944 52.32,387.2,316,Goodyear,1945 56.95,347.4,302,Goodyear,1946 54.32,291.9,333,Goodyear,1947 40.53,297.2,359,Goodyear,1948 32.54,276.9,370,Goodyear,1949 43.48,274.6,376,Goodyear,1950 56.49,339.9,391,Goodyear,1951 65.98,474.8,414,Goodyear,1952 66.11,496,443,Goodyear,1953 49.34,474.5,468,Goodyear,1954 2.54,70.91,4.5,Diamond Match,1935 2,87.94,4.71,Diamond Match,1936 2.19,82.2,4.57,Diamond Match,1937 1.99,58.72,4.56,Diamond Match,1938 2.03,80.54,4.38,Diamond Match,1939 1.81,86.47,4.21,Diamond Match,1940 2.14,77.68,4.12,Diamond Match,1941 1.86,62.16,3.83,Diamond Match,1942 0.93,62.24,3.58,Diamond Match,1943 1.18,61.82,3.41,Diamond Match,1944 1.36,65.85,3.31,Diamond Match,1945 2.24,69.54,3.23,Diamond Match,1946 3.81,64.97,3.9,Diamond Match,1947 5.66,68,5.38,Diamond Match,1948 4.21,71.24,7.39,Diamond Match,1949 3.42,69.05,8.74,Diamond Match,1950 4.67,83.04,9.07,Diamond Match,1951 6,74.42,9.93,Diamond Match,1952 6.53,63.51,11.68,Diamond Match,1953 5.12,58.12,14.33,Diamond Match,1954 2.938,30.284,52.011,American Steel,1935 5.643,43.909,52.903,American Steel,1936 10.233,107.02,54.499,American Steel,1937 4.046,68.306,59.722,American Steel,1938 3.326,84.164,61.659,American Steel,1939 4.68,69.157,62.243,American Steel,1940 5.732,60.148,63.361,American Steel,1941 12.117,49.332,64.861,American Steel,1942 15.276,75.18,67.953,American Steel,1943 9.275,62.05,69.59,American Steel,1944 9.577,59.152,69.144,American Steel,1945 3.956,68.424,70.269,American Steel,1946 3.834,48.505,71.051,American Steel,1947 5.97,40.507,71.508,American Steel,1948 6.433,39.961,73.827,American Steel,1949 4.77,36.494,75.847,American Steel,1950 6.532,46.082,77.367,American Steel,1951 7.329,57.616,78.631,American Steel,1952 9.02,57.441,80.215,American Steel,1953 6.281,47.165,83.788,American Steel,1954 statsmodels-0.12.2/statsmodels/datasets/heart/000077500000000000000000000000001400612667500214225ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/heart/__init__.py000066400000000000000000000003261400612667500235340ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/heart/data.py000066400000000000000000000030241400612667500227040ustar00rootroot00000000000000"""Heart Transplant Data, Miller 1976""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """???""" TITLE = """Transplant Survival Data""" SOURCE = """Miller, R. (1976). Least squares regression with censored data. Biometrica, 63 (3). 449-464. """ DESCRSHORT = """Survival times after receiving a heart transplant""" DESCRLONG = """This data contains the survival time after receiving a heart transplant, the age of the patient and whether or not the survival time was censored. """ NOTE = """:: Number of Observations - 69 Number of Variables - 3 Variable name definitions:: death - Days after surgery until death age - age at the time of surgery censored - indicates if an observation is censored. 1 is uncensored """ def load(as_pandas=None): """ Load the data and return a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): data = _get_data() dataset = du.process_pandas(data, endog_idx=0, exog_idx=None) dataset.censors = dataset.exog.iloc[:, 0] dataset.exog = dataset.exog.iloc[:, 1] return dataset def _get_data(): return du.load_csv(__file__, 'heart.csv') statsmodels-0.12.2/statsmodels/datasets/heart/heart.csv000066400000000000000000000040201400612667500232360ustar00rootroot00000000000000survival,censors,age 15.000000,1.000000,54.300000 3.000000,1.000000,40.400000 624.000000,1.000000,51.000000 46.000000,1.000000,42.500000 127.000000,1.000000,48.000000 64.000000,1.000000,54.600000 1350.000000,1.000000,54.100000 280.000000,1.000000,49.500000 23.000000,1.000000,56.900000 10.000000,1.000000,55.300000 1024.000000,1.000000,43.400000 39.000000,1.000000,42.800000 730.000000,1.000000,58.400000 136.000000,1.000000,52.000000 1775.000000,0.000000,33.300000 1.000000,1.000000,54.200000 836.000000,1.000000,45.000000 60.000000,1.000000,64.500000 1536.000000,0.000000,49.000000 1549.000000,0.000000,40.600000 54.000000,1.000000,49.000000 47.000000,1.000000,61.500000 1.000000,1.000000,41.500000 51.000000,1.000000,50.500000 1367.000000,0.000000,48.600000 1264.000000,0.000000,45.500000 44.000000,1.000000,36.200000 994.000000,1.000000,48.600000 51.000000,1.000000,47.200000 1106.000000,0.000000,36.800000 897.000000,1.000000,46.100000 253.000000,1.000000,48.800000 147.000000,1.000000,47.500000 51.000000,1.000000,52.500000 875.000000,0.000000,38.900000 322.000000,1.000000,48.100000 838.000000,0.000000,41.600000 65.000000,1.000000,49.100000 815.000000,0.000000,32.700000 551.000000,1.000000,48.900000 66.000000,1.000000,51.300000 228.000000,1.000000,19.700000 65.000000,1.000000,45.200000 660.000000,0.000000,48.000000 25.000000,1.000000,53.000000 589.000000,0.000000,47.500000 592.000000,0.000000,26.700000 63.000000,1.000000,56.400000 12.000000,1.000000,29.200000 499.000000,0.000000,52.200000 305.000000,0.000000,49.300000 29.000000,1.000000,54.000000 456.000000,0.000000,46.500000 439.000000,0.000000,52.900000 48.000000,1.000000,53.400000 297.000000,1.000000,42.800000 389.000000,0.000000,48.900000 50.000000,1.000000,46.400000 339.000000,0.000000,54.400000 68.000000,1.000000,51.400000 26.000000,1.000000,52.500000 30.000000,0.000000,45.800000 237.000000,0.000000,47.800000 161.000000,1.000000,43.800000 14.000000,1.000000,40.300000 167.000000,0.000000,26.700000 110.000000,0.000000,23.700000 13.000000,0.000000,28.900000 1.000000,0.000000,35.200000 statsmodels-0.12.2/statsmodels/datasets/interest_inflation/000077500000000000000000000000001400612667500242175ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/interest_inflation/E6.csv000066400000000000000000000047461400612667500252210ustar00rootroot00000000000000"year","quarter","Dp","R" 1972,2,-0.00313258,0.083 1972,3,0.0188713,0.083 1972,4,0.0248036,0.087 1973,1,0.0162776,0.087 1973,2,0.000289679,0.102 1973,3,0.016829,0.098 1973,4,0.0385835,0.097 1974,1,-0.00144386,0.107 1974,2,0.0127239,0.109 1974,3,0.0238972,0.108 1974,4,0.0427728,0.099 1975,1,-0.0103779,0.089 1975,2,0.00558424,0.084 1975,3,0.00870609,0.087 1975,4,0.0389199,0.086 1976,1,-0.0196176,0.078 1976,2,0.00731993,0.083 1976,3,0.0180764,0.081 1976,4,0.0237775,0.074 1977,1,-0.0144377,0.07 1977,2,0.0110059,0.064 1977,3,0.0104017,0.06 1977,4,0.0354648,0.06 1978,1,-0.0157599,0.056 1978,2,0.0100193,0.06 1978,3,0.0180621,0.064 1978,4,0.0256915,0.066 1979,1,-0.0170689,0.071 1979,2,0.00350475,0.08 1979,3,0.0256438,0.078 1979,4,0.0315075,0.08 1980,1,-0.0132775,0.095 1980,2,0.0130968,0.083 1980,3,0.0151458,0.083 1980,4,0.0312119,0.091 1981,1,-0.0207896,0.104 1981,2,0.0104489,0.111 1981,3,0.018106,0.113 1981,4,0.0405002,0.099 1982,1,-0.0201483,0.096 1982,2,0.00380802,0.092 1982,3,0.0215569,0.088 1982,4,0.0327106,0.08 1983,1,-0.0201726,0.074 1983,2,-0.00333166,0.081 1983,3,0.0192871,0.084 1983,4,0.0345473,0.083 1984,1,-0.0262156,0.079 1984,2,-0.00519753,0.081 1984,3,0.0132318,0.077 1984,4,0.0374279,0.07 1985,1,-0.0291948,0.077 1985,2,-0.00261354,0.07 1985,3,0.0172353,0.064 1985,4,0.0376387,0.066 1986,1,-0.0204763,0.06 1986,2,0.000900269,0.06 1986,3,0.0125732,0.058 1986,4,0.0344677,0.06 1987,1,-0.0220394,0.056 1987,2,-0.00202703,0.055 1987,3,0.00173426,0.062 1987,4,0.0365901,0.058 1988,1,-0.0252557,0.056 1988,2,0.00092268,0.06 1988,3,0.00451374,0.063 1988,4,0.0383272,0.062 1989,1,-0.0211368,0.07 1989,2,-0.000533104,0.071 1989,3,0.00981092,0.071 1989,4,0.0373549,0.078 1990,1,-0.016232,0.09 1990,2,0.00197124,0.09 1990,3,0.00687361,0.091 1990,4,0.0274582,0.09 1991,1,-0.0140786,0.086 1991,2,0.0166497,0.086 1991,3,0.0144682,0.088 1991,4,0.043004,0.087 1992,1,-0.0127769,0.082 1992,2,0.00927353,0.084 1992,3,0.0179157,0.082 1992,4,0.030508,0.074 1993,1,-0.0105906,0.065 1993,2,0.00747108,0.067 1993,3,0.00467587,0.061 1993,4,0.0310678,0.056 1994,1,-0.0153685,0.062 1994,2,0.000810146,0.069 1994,3,0.00806475,0.074 1994,4,0.0287657,0.074 1995,1,-0.0183783,0.071 1995,2,0.00449467,0.064 1995,3,0.00988674,0.061 1995,4,0.0245948,0.055 1996,1,-0.0185189,0.058 1996,2,-0.00590181,0.059 1996,3,0.00581503,0.055 1996,4,0.0243654,0.051 1997,1,-0.0157485,0.051 1997,2,-0.00749254,0.05 1997,3,0.00388288,0.051 1997,4,0.0242448,0.051 1998,1,-0.014647,0.047 1998,2,-0.00204897,0.047 1998,3,0.00247526,0.041 1998,4,0.0239234,0.038 statsmodels-0.12.2/statsmodels/datasets/interest_inflation/E6_jmulti.csv000066400000000000000000000033371400612667500266000ustar00rootroot00000000000000-0.00313258 0.083 0.0188713 0.083 0.0248036 0.087 0.0162776 0.087 0.000289679 0.102 0.016829 0.098 0.0385835 0.097 -0.00144386 0.107 0.0127239 0.109 0.0238972 0.108 0.0427728 0.099 -0.0103779 0.089 0.00558424 0.084 0.00870609 0.087 0.0389199 0.086 -0.0196176 0.078 0.00731993 0.083 0.0180764 0.081 0.0237775 0.074 -0.0144377 0.07 0.0110059 0.064 0.0104017 0.06 0.0354648 0.06 -0.0157599 0.056 0.0100193 0.06 0.0180621 0.064 0.0256915 0.066 -0.0170689 0.071 0.00350475 0.08 0.0256438 0.078 0.0315075 0.08 -0.0132775 0.095 0.0130968 0.083 0.0151458 0.083 0.0312119 0.091 -0.0207896 0.104 0.0104489 0.111 0.018106 0.113 0.0405002 0.099 -0.0201483 0.096 0.00380802 0.092 0.0215569 0.088 0.0327106 0.08 -0.0201726 0.074 -0.00333166 0.081 0.0192871 0.084 0.0345473 0.083 -0.0262156 0.079 -0.00519753 0.081 0.0132318 0.077 0.0374279 0.07 -0.0291948 0.077 -0.00261354 0.07 0.0172353 0.064 0.0376387 0.066 -0.0204763 0.06 0.000900269 0.06 0.0125732 0.058 0.0344677 0.06 -0.0220394 0.056 -0.00202703 0.055 0.00173426 0.062 0.0365901 0.058 -0.0252557 0.056 0.00092268 0.06 0.00451374 0.063 0.0383272 0.062 -0.0211368 0.07 -0.000533104 0.071 0.00981092 0.071 0.0373549 0.078 -0.016232 0.09 0.00197124 0.09 0.00687361 0.091 0.0274582 0.09 -0.0140786 0.086 0.0166497 0.086 0.0144682 0.088 0.043004 0.087 -0.0127769 0.082 0.00927353 0.084 0.0179157 0.082 0.030508 0.074 -0.0105906 0.065 0.00747108 0.067 0.00467587 0.061 0.0310678 0.056 -0.0153685 0.062 0.000810146 0.069 0.00806475 0.074 0.0287657 0.074 -0.0183783 0.071 0.00449467 0.064 0.00988674 0.061 0.0245948 0.055 -0.0185189 0.058 -0.00590181 0.059 0.00581503 0.055 0.0243654 0.051 -0.0157485 0.051 -0.00749254 0.05 0.00388288 0.051 0.0242448 0.051 -0.014647 0.047 -0.00204897 0.047 0.00247526 0.041 0.0239234 0.038 statsmodels-0.12.2/statsmodels/datasets/interest_inflation/__init__.py000066400000000000000000000003261400612667500263310ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/interest_inflation/data.py000066400000000000000000000031561400612667500255070ustar00rootroot00000000000000"""(West) German interest and inflation rate 1972-1998""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """...""" # TODO TITLE = __doc__ SOURCE = """ http://www.jmulti.de/download/datasets/e6.dat """ DESCRSHORT = """(West) German interest and inflation rate 1972Q2 - 1998Q4""" DESCRLONG = """West German (until 1990) / German (afterwards) interest and inflation rate 1972Q2 - 1998Q4 """ NOTE = """:: Number of Observations - 107 Number of Variables - 2 Variable name definitions:: year - 1972q2 - 1998q4 quarter - 1-4 Dp - Delta log gdp deflator R - nominal long term interest rate """ variable_names = ["Dp", "R"] first_season = 1 # 1 stands for: first observation in Q2 (0 would mean Q1) def load(as_pandas=None): """ Load the West German interest/inflation data and return a Dataset class. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. Notes ----- The interest_inflation Dataset instance does not contain endog and exog attributes. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): data = _get_data() names = data.columns dataset = du.Dataset(data=data, names=names) return dataset def _get_data(): return du.load_csv(__file__, 'E6.csv', convert_float=True) def __str__(): return "e6" statsmodels-0.12.2/statsmodels/datasets/longley/000077500000000000000000000000001400612667500217705ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/longley/R_gls.s000066400000000000000000000021541400612667500232240ustar00rootroot00000000000000### GLS Example with Longley Data ### Done the long way... d <- read.table('./longley.csv', sep=',', header=T) attach(d) m1 <- lm(TOTEMP ~ GNP + POP) rho <- cor(m1$res[-1],m1$res[-16]) sigma <- diag(16) # diagonal matrix of ones sigma <- rho^abs(row(sigma)-col(sigma)) # row sigma is a matrix of the row index # col sigma is a matrix of the column index # this gives a upper-lower triangle with the # covariance structure of an AR1 process... sigma_inv <- solve(sigma) # inverse of sigma x <- model.matrix(m1) xPrimexInv <- solve(t(x) %*% sigma_inv %*% x) beta <- xPrimexInv %*% t(x) %*% sigma_inv %*% TOTEMP beta # residuals res <- TOTEMP - x %*% beta # whitened residuals, not sure if this is right # xPrimexInv is different than cholsigmainv obviously... wres = sigma_inv %*% TOTEMP - sigma_inv %*% x %*% beta sig <- sqrt(sum(res^2)/m1$df) wsig <- sqrt(sum(wres^2)/m1$df) wvc <- sqrt(diag(xPrimexInv))*wsig vc <- sqrt(diag(xPrimexInv))*sig vc ### Attempt to use a varFunc for GLS library(nlme) m1 <- gls(TOTEMP ~ GNP + POP, correlation=corAR1(value=rho, fixed=TRUE)) results <- summary(m1) bse <- sqrt(diag(vcov(m1))) statsmodels-0.12.2/statsmodels/datasets/longley/R_lm.s000066400000000000000000000002731400612667500230470ustar00rootroot00000000000000d <- read.table('./longley.csv', sep=',', header=T) attach(d) library(nlme) # to be able to get BIC m1 <- lm(TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR) results <-summary(m1) statsmodels-0.12.2/statsmodels/datasets/longley/__init__.py000066400000000000000000000003261400612667500241020ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/longley/data.py000066400000000000000000000036041400612667500232560ustar00rootroot00000000000000"""Longley dataset""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This is public domain.""" TITLE = __doc__ SOURCE = """ The classic 1967 Longley Data http://www.itl.nist.gov/div898/strd/lls/data/Longley.shtml :: Longley, J.W. (1967) "An Appraisal of Least Squares Programs for the Electronic Comptuer from the Point of View of the User." Journal of the American Statistical Association. 62.319, 819-41. """ DESCRSHORT = """""" DESCRLONG = """The Longley dataset contains various US macroeconomic variables that are known to be highly collinear. It has been used to appraise the accuracy of least squares routines.""" NOTE = """:: Number of Observations - 16 Number of Variables - 6 Variable name definitions:: TOTEMP - Total Employment GNPDEFL - GNP deflator GNP - GNP UNEMP - Number of unemployed ARMED - Size of armed forces POP - Population YEAR - Year (1947 - 1962) """ def load(as_pandas=None): """ Load the Longley data and return a Dataset class. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): """ Load the Longley data and return a Dataset class. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ data = _get_data() return du.process_pandas(data, endog_idx=0) def _get_data(): data = du.load_csv(__file__, 'longley.csv') data = data.iloc[:, [1, 2, 3, 4, 5, 6, 7]].astype(float) return data statsmodels-0.12.2/statsmodels/datasets/longley/longley.csv000066400000000000000000000013461400612667500241620ustar00rootroot00000000000000"Obs","TOTEMP","GNPDEFL","GNP","UNEMP","ARMED","POP","YEAR" 1,60323,83,234289,2356,1590,107608,1947 2,61122,88.5,259426,2325,1456,108632,1948 3,60171,88.2,258054,3682,1616,109773,1949 4,61187,89.5,284599,3351,1650,110929,1950 5,63221,96.2,328975,2099,3099,112075,1951 6,63639,98.1,346999,1932,3594,113270,1952 7,64989,99,365385,1870,3547,115094,1953 8,63761,100,363112,3578,3350,116219,1954 9,66019,101.2,397469,2904,3048,117388,1955 10,67857,104.6,419180,2822,2857,118734,1956 11,68169,108.4,442769,2936,2798,120445,1957 12,66513,110.8,444546,4681,2637,121950,1958 13,68655,112.6,482704,3813,2552,123366,1959 14,69564,114.2,502601,3931,2514,125368,1960 15,69331,115.7,518173,4806,2572,127852,1961 16,70551,116.9,554894,4007,2827,130081,1962 statsmodels-0.12.2/statsmodels/datasets/macrodata/000077500000000000000000000000001400612667500222525ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/macrodata/__init__.py000066400000000000000000000003261400612667500243640ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/macrodata/data.py000066400000000000000000000061571400612667500235460ustar00rootroot00000000000000"""United States Macroeconomic data""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This is public domain.""" TITLE = __doc__ SOURCE = """ Compiled by Skipper Seabold. All data are from the Federal Reserve Bank of St. Louis [1] except the unemployment rate which was taken from the National Bureau of Labor Statistics [2]. :: [1] Data Source: FRED, Federal Reserve Economic Data, Federal Reserve Bank of St. Louis; http://research.stlouisfed.org/fred2/; accessed December 15, 2009. [2] Data Source: Bureau of Labor Statistics, U.S. Department of Labor; http://www.bls.gov/data/; accessed December 15, 2009. """ DESCRSHORT = """US Macroeconomic Data for 1959Q1 - 2009Q3""" DESCRLONG = DESCRSHORT NOTE = """:: Number of Observations - 203 Number of Variables - 14 Variable name definitions:: year - 1959q1 - 2009q3 quarter - 1-4 realgdp - Real gross domestic product (Bil. of chained 2005 US$, seasonally adjusted annual rate) realcons - Real personal consumption expenditures (Bil. of chained 2005 US$, seasonally adjusted annual rate) realinv - Real gross private domestic investment (Bil. of chained 2005 US$, seasonally adjusted annual rate) realgovt - Real federal consumption expenditures & gross investment (Bil. of chained 2005 US$, seasonally adjusted annual rate) realdpi - Real private disposable income (Bil. of chained 2005 US$, seasonally adjusted annual rate) cpi - End of the quarter consumer price index for all urban consumers: all items (1982-84 = 100, seasonally adjusted). m1 - End of the quarter M1 nominal money stock (Seasonally adjusted) tbilrate - Quarterly monthly average of the monthly 3-month treasury bill: secondary market rate unemp - Seasonally adjusted unemployment rate (%) pop - End of the quarter total population: all ages incl. armed forces over seas infl - Inflation rate (ln(cpi_{t}/cpi_{t-1}) * 400) realint - Real interest rate (tbilrate - infl) """ def load_pandas(): data = _get_data() return du.Dataset(data=data, names=list(data.columns)) def load(as_pandas=None): """ Load the US macro data and return a Dataset class. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. Notes ----- The macrodata Dataset instance does not contain endog and exog attributes. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def _get_data(): return du.load_csv(__file__, 'macrodata.csv').astype(float) variable_names = ["realcons", "realgdp", "realinv"] def __str__(): return "macrodata" statsmodels-0.12.2/statsmodels/datasets/macrodata/macrodata.csv000066400000000000000000000426451400612667500247350ustar00rootroot00000000000000"year","quarter","realgdp","realcons","realinv","realgovt","realdpi","cpi","m1","tbilrate","unemp","pop","infl","realint" 1959,1,2710.349,1707.4,286.898,470.045,1886.9,28.980,139.7,2.82,5.8,177.146,0,0 1959,2,2778.801,1733.7,310.859,481.301,1919.7,29.150,141.7,3.08,5.1,177.830,2.34,0.74 1959,3,2775.488,1751.8,289.226,491.260,1916.4,29.350,140.5,3.82,5.3,178.657,2.74,1.09 1959,4,2785.204,1753.7,299.356,484.052,1931.3,29.370,140,4.33,5.6,179.386,0.27,4.06 1960,1,2847.699,1770.5,331.722,462.199,1955.5,29.540,139.6,3.50,5.2,180.007,2.31,1.19 1960,2,2834.390,1792.9,298.152,460.400,1966.1,29.550,140.2,2.68,5.2,180.671,0.14,2.55 1960,3,2839.022,1785.8,296.375,474.676,1967.8,29.750,140.9,2.36,5.6,181.528,2.7,-0.34 1960,4,2802.616,1788.2,259.764,476.434,1966.6,29.840,141.1,2.29,6.3,182.287,1.21,1.08 1961,1,2819.264,1787.7,266.405,475.854,1984.5,29.810,142.1,2.37,6.8,182.992,-0.4,2.77 1961,2,2872.005,1814.3,286.246,480.328,2014.4,29.920,142.9,2.29,7,183.691,1.47,0.81 1961,3,2918.419,1823.1,310.227,493.828,2041.9,29.980,144.1,2.32,6.8,184.524,0.8,1.52 1961,4,2977.830,1859.6,315.463,502.521,2082.0,30.040,145.2,2.60,6.2,185.242,0.8,1.8 1962,1,3031.241,1879.4,334.271,520.960,2101.7,30.210,146.4,2.73,5.6,185.874,2.26,0.47 1962,2,3064.709,1902.5,331.039,523.066,2125.2,30.220,146.5,2.78,5.5,186.538,0.13,2.65 1962,3,3093.047,1917.9,336.962,538.838,2137.0,30.380,146.7,2.78,5.6,187.323,2.11,0.67 1962,4,3100.563,1945.1,325.650,535.912,2154.6,30.440,148.3,2.87,5.5,188.013,0.79,2.08 1963,1,3141.087,1958.2,343.721,522.917,2172.5,30.480,149.7,2.90,5.8,188.580,0.53,2.38 1963,2,3180.447,1976.9,348.730,518.108,2193.1,30.690,151.3,3.03,5.7,189.242,2.75,0.29 1963,3,3240.332,2003.8,360.102,546.893,2217.9,30.750,152.6,3.38,5.5,190.028,0.78,2.6 1963,4,3264.967,2020.6,364.534,532.383,2254.6,30.940,153.7,3.52,5.6,190.668,2.46,1.06 1964,1,3338.246,2060.5,379.523,529.686,2299.6,30.950,154.8,3.51,5.5,191.245,0.13,3.38 1964,2,3376.587,2096.7,377.778,526.175,2362.1,31.020,156.8,3.47,5.2,191.889,0.9,2.57 1964,3,3422.469,2135.2,386.754,522.008,2392.7,31.120,159.2,3.53,5,192.631,1.29,2.25 1964,4,3431.957,2141.2,389.910,514.603,2420.4,31.280,160.7,3.76,5,193.223,2.05,1.71 1965,1,3516.251,2188.8,429.145,508.006,2447.4,31.380,162,3.93,4.9,193.709,1.28,2.65 1965,2,3563.960,2213.0,429.119,508.931,2474.5,31.580,163.1,3.84,4.7,194.303,2.54,1.3 1965,3,3636.285,2251.0,444.444,529.446,2542.6,31.650,166,3.93,4.4,194.997,0.89,3.04 1965,4,3724.014,2314.3,446.493,544.121,2594.1,31.880,169.1,4.35,4.1,195.539,2.9,1.46 1966,1,3815.423,2348.5,484.244,556.593,2618.4,32.280,171.8,4.62,3.9,195.999,4.99,-0.37 1966,2,3828.124,2354.5,475.408,571.371,2624.7,32.450,170.3,4.65,3.8,196.560,2.1,2.55 1966,3,3853.301,2381.5,470.697,594.514,2657.8,32.850,171.2,5.23,3.8,197.207,4.9,0.33 1966,4,3884.520,2391.4,472.957,599.528,2688.2,32.900,171.9,5.00,3.7,197.736,0.61,4.39 1967,1,3918.740,2405.3,460.007,640.682,2728.4,33.100,174.2,4.22,3.8,198.206,2.42,1.8 1967,2,3919.556,2438.1,440.393,631.430,2750.8,33.400,178.1,3.78,3.8,198.712,3.61,0.17 1967,3,3950.826,2450.6,453.033,641.504,2777.1,33.700,181.6,4.42,3.8,199.311,3.58,0.84 1967,4,3980.970,2465.7,462.834,640.234,2797.4,34.100,184.3,4.90,3.9,199.808,4.72,0.18 1968,1,4063.013,2524.6,472.907,651.378,2846.2,34.400,186.6,5.18,3.7,200.208,3.5,1.67 1968,2,4131.998,2563.3,492.026,646.145,2893.5,34.900,190.5,5.50,3.5,200.706,5.77,-0.28 1968,3,4160.267,2611.5,476.053,640.615,2899.3,35.300,194,5.21,3.5,201.290,4.56,0.65 1968,4,4178.293,2623.5,480.998,636.729,2918.4,35.700,198.7,5.85,3.4,201.760,4.51,1.34 1969,1,4244.100,2652.9,512.686,633.224,2923.4,36.300,200.7,6.08,3.4,202.161,6.67,-0.58 1969,2,4256.460,2669.8,508.601,623.160,2952.9,36.800,201.7,6.49,3.4,202.677,5.47,1.02 1969,3,4283.378,2682.7,520.360,623.613,3012.9,37.300,202.9,7.02,3.6,203.302,5.4,1.63 1969,4,4263.261,2704.1,492.334,606.900,3034.9,37.900,206.2,7.64,3.6,203.849,6.38,1.26 1970,1,4256.573,2720.7,476.925,594.888,3050.1,38.500,206.7,6.76,4.2,204.401,6.28,0.47 1970,2,4264.289,2733.2,478.419,576.257,3103.5,38.900,208,6.66,4.8,205.052,4.13,2.52 1970,3,4302.259,2757.1,486.594,567.743,3145.4,39.400,212.9,6.15,5.2,205.788,5.11,1.04 1970,4,4256.637,2749.6,458.406,564.666,3135.1,39.900,215.5,4.86,5.8,206.466,5.04,-0.18 1971,1,4374.016,2802.2,517.935,542.709,3197.3,40.100,220,3.65,5.9,207.065,2,1.65 1971,2,4398.829,2827.9,533.986,534.905,3245.3,40.600,224.9,4.76,5.9,207.661,4.96,-0.19 1971,3,4433.943,2850.4,541.010,532.646,3259.7,40.900,227.2,4.70,6,208.345,2.94,1.75 1971,4,4446.264,2897.8,524.085,516.140,3294.2,41.200,230.1,3.87,6,208.917,2.92,0.95 1972,1,4525.769,2936.5,561.147,518.192,3314.9,41.500,235.6,3.55,5.8,209.386,2.9,0.64 1972,2,4633.101,2992.6,595.495,526.473,3346.1,41.800,238.8,3.86,5.7,209.896,2.88,0.98 1972,3,4677.503,3038.8,603.970,498.116,3414.6,42.200,245,4.47,5.6,210.479,3.81,0.66 1972,4,4754.546,3110.1,607.104,496.540,3550.5,42.700,251.5,5.09,5.3,210.985,4.71,0.38 1973,1,4876.166,3167.0,645.654,504.838,3590.7,43.700,252.7,5.98,5,211.420,9.26,-3.28 1973,2,4932.571,3165.4,675.837,497.033,3626.2,44.200,257.5,7.19,4.9,211.909,4.55,2.64 1973,3,4906.252,3176.7,649.412,475.897,3644.4,45.600,259,8.06,4.8,212.475,12.47,-4.41 1973,4,4953.050,3167.4,674.253,476.174,3688.9,46.800,263.8,7.68,4.8,212.932,10.39,-2.71 1974,1,4909.617,3139.7,631.230,491.043,3632.3,48.100,267.2,7.80,5.1,213.361,10.96,-3.16 1974,2,4922.188,3150.6,628.102,490.177,3601.1,49.300,269.3,7.89,5.2,213.854,9.86,-1.96 1974,3,4873.520,3163.6,592.672,492.586,3612.4,51.000,272.3,8.16,5.6,214.451,13.56,-5.4 1974,4,4854.340,3117.3,598.306,496.176,3596.0,52.300,273.9,6.96,6.6,214.931,10.07,-3.11 1975,1,4795.295,3143.4,493.212,490.603,3581.9,53.000,276.2,5.53,8.2,215.353,5.32,0.22 1975,2,4831.942,3195.8,476.085,486.679,3749.3,54.000,283.7,5.57,8.9,215.973,7.48,-1.91 1975,3,4913.328,3241.4,516.402,498.836,3698.6,54.900,285.4,6.27,8.5,216.587,6.61,-0.34 1975,4,4977.511,3275.7,530.596,500.141,3736.0,55.800,288.4,5.26,8.3,217.095,6.5,-1.24 1976,1,5090.663,3341.2,585.541,495.568,3791.0,56.100,294.7,4.91,7.7,217.528,2.14,2.77 1976,2,5128.947,3371.8,610.513,494.532,3822.2,57.000,297.2,5.28,7.6,218.035,6.37,-1.09 1976,3,5154.072,3407.5,611.646,493.141,3856.7,57.900,302,5.05,7.7,218.644,6.27,-1.22 1976,4,5191.499,3451.8,615.898,494.415,3884.4,58.700,308.3,4.57,7.8,219.179,5.49,-0.92 1977,1,5251.762,3491.3,646.198,498.509,3887.5,60.000,316,4.60,7.5,219.684,8.76,-4.16 1977,2,5356.131,3510.6,696.141,506.695,3931.8,60.800,320.2,5.06,7.1,220.239,5.3,-0.24 1977,3,5451.921,3544.1,734.078,509.605,3990.8,61.600,326.4,5.82,6.9,220.904,5.23,0.59 1977,4,5450.793,3597.5,713.356,504.584,4071.2,62.700,334.4,6.20,6.6,221.477,7.08,-0.88 1978,1,5469.405,3618.5,727.504,506.314,4096.4,63.900,339.9,6.34,6.3,221.991,7.58,-1.24 1978,2,5684.569,3695.9,777.454,518.366,4143.4,65.500,347.6,6.72,6,222.585,9.89,-3.18 1978,3,5740.300,3711.4,801.452,520.199,4177.1,67.100,353.3,7.64,6,223.271,9.65,-2.01 1978,4,5816.222,3741.3,819.689,524.782,4209.8,68.500,358.6,9.02,5.9,223.865,8.26,0.76 1979,1,5825.949,3760.2,819.556,525.524,4255.9,70.600,368,9.42,5.9,224.438,12.08,-2.66 1979,2,5831.418,3758.0,817.660,532.040,4226.1,73.000,377.2,9.30,5.7,225.055,13.37,-4.07 1979,3,5873.335,3794.9,801.742,531.232,4250.3,75.200,380.8,10.49,5.9,225.801,11.88,-1.38 1979,4,5889.495,3805.0,786.817,531.126,4284.3,78.000,385.8,11.94,5.9,226.451,14.62,-2.68 1980,1,5908.467,3798.4,781.114,548.115,4296.2,80.900,383.8,13.75,6.3,227.061,14.6,-0.85 1980,2,5787.373,3712.2,710.640,561.895,4236.1,82.600,394,7.90,7.3,227.726,8.32,-0.42 1980,3,5776.617,3752.0,656.477,554.292,4279.7,84.700,409,10.34,7.7,228.417,10.04,0.3 1980,4,5883.460,3802.0,723.220,556.130,4368.1,87.200,411.3,14.75,7.4,228.937,11.64,3.11 1981,1,6005.717,3822.8,795.091,567.618,4358.1,89.100,427.4,13.95,7.4,229.403,8.62,5.32 1981,2,5957.795,3822.8,757.240,584.540,4358.6,91.500,426.9,15.33,7.4,229.966,10.63,4.69 1981,3,6030.184,3838.3,804.242,583.890,4455.4,93.400,428.4,14.58,7.4,230.641,8.22,6.36 1981,4,5955.062,3809.3,773.053,590.125,4464.4,94.400,442.7,11.33,8.2,231.157,4.26,7.07 1982,1,5857.333,3833.9,692.514,591.043,4469.6,95.000,447.1,12.95,8.8,231.645,2.53,10.42 1982,2,5889.074,3847.7,691.900,596.403,4500.8,97.500,448,11.97,9.4,232.188,10.39,1.58 1982,3,5866.370,3877.2,683.825,605.370,4520.6,98.100,464.5,8.10,9.9,232.816,2.45,5.65 1982,4,5871.001,3947.9,622.930,623.307,4536.4,97.900,477.2,7.96,10.7,233.322,-0.82,8.77 1983,1,5944.020,3986.6,645.110,630.873,4572.2,98.800,493.2,8.22,10.4,233.781,3.66,4.56 1983,2,6077.619,4065.7,707.372,644.322,4605.5,99.800,507.8,8.69,10.1,234.307,4.03,4.66 1983,3,6197.468,4137.6,754.937,662.412,4674.7,100.800,517.2,8.99,9.4,234.907,3.99,5.01 1983,4,6325.574,4203.2,834.427,639.197,4771.1,102.100,525.1,8.89,8.5,235.385,5.13,3.76 1984,1,6448.264,4239.2,921.763,644.635,4875.4,103.300,535,9.43,7.9,235.839,4.67,4.76 1984,2,6559.594,4299.9,952.841,664.839,4959.4,104.100,540.9,9.94,7.5,236.348,3.09,6.85 1984,3,6623.343,4333.0,974.989,662.294,5036.6,105.100,543.7,10.19,7.4,236.976,3.82,6.37 1984,4,6677.264,4390.1,958.993,684.282,5084.5,105.700,557,8.14,7.3,237.468,2.28,5.87 1985,1,6740.275,4464.6,927.375,691.613,5072.0,107.000,570.4,8.25,7.3,237.900,4.89,3.36 1985,2,6797.344,4505.2,943.383,708.524,5172.7,107.700,589.1,7.17,7.3,238.466,2.61,4.56 1985,3,6903.523,4590.8,932.959,732.305,5140.7,108.500,607.8,7.13,7.2,239.113,2.96,4.17 1985,4,6955.918,4600.9,969.434,732.026,5193.9,109.900,621.4,7.14,7,239.638,5.13,2.01 1986,1,7022.757,4639.3,967.442,728.125,5255.8,108.700,641,6.56,7,240.094,-4.39,10.95 1986,2,7050.969,4688.7,945.972,751.334,5315.5,109.500,670.3,6.06,7.2,240.651,2.93,3.13 1986,3,7118.950,4770.7,916.315,779.770,5343.3,110.200,694.9,5.31,7,241.274,2.55,2.76 1986,4,7153.359,4799.4,917.736,767.671,5346.5,111.400,730.2,5.44,6.8,241.784,4.33,1.1 1987,1,7193.019,4792.1,945.776,772.247,5379.4,112.700,743.9,5.61,6.6,242.252,4.64,0.97 1987,2,7269.510,4856.3,947.100,782.962,5321.0,113.800,743,5.67,6.3,242.804,3.89,1.79 1987,3,7332.558,4910.4,948.055,783.804,5416.2,115.000,756.2,6.19,6,243.446,4.2,1.99 1987,4,7458.022,4922.2,1021.980,795.467,5493.1,116.000,756.2,5.76,5.9,243.981,3.46,2.29 1988,1,7496.600,5004.4,964.398,773.851,5562.1,117.200,768.1,5.76,5.7,244.445,4.12,1.64 1988,2,7592.881,5040.8,987.858,765.980,5614.3,118.500,781.4,6.48,5.5,245.021,4.41,2.07 1988,3,7632.082,5080.6,994.204,760.245,5657.5,119.900,783.3,7.22,5.5,245.693,4.7,2.52 1988,4,7733.991,5140.4,1007.371,783.065,5708.5,121.200,785.7,8.03,5.3,246.224,4.31,3.72 1989,1,7806.603,5159.3,1045.975,767.024,5773.4,123.100,779.2,8.67,5.2,246.721,6.22,2.44 1989,2,7865.016,5182.4,1033.753,784.275,5749.8,124.500,777.8,8.15,5.2,247.342,4.52,3.63 1989,3,7927.393,5236.1,1021.604,791.819,5787.0,125.400,786.6,7.76,5.3,248.067,2.88,4.88 1989,4,7944.697,5261.7,1011.119,787.844,5831.3,127.500,795.4,7.65,5.4,248.659,6.64,1.01 1990,1,8027.693,5303.3,1021.070,799.681,5875.1,128.900,806.2,7.80,5.3,249.306,4.37,3.44 1990,2,8059.598,5320.8,1021.360,800.639,5913.9,130.500,810.1,7.70,5.3,250.132,4.93,2.76 1990,3,8059.476,5341.0,997.319,793.513,5918.1,133.400,819.8,7.33,5.7,251.057,8.79,-1.46 1990,4,7988.864,5299.5,934.248,800.525,5878.2,134.700,827.2,6.67,6.1,251.889,3.88,2.79 1991,1,7950.164,5284.4,896.210,806.775,5896.3,135.100,843.2,5.83,6.6,252.643,1.19,4.65 1991,2,8003.822,5324.7,891.704,809.081,5941.1,136.200,861.5,5.54,6.8,253.493,3.24,2.29 1991,3,8037.538,5345.0,913.904,793.987,5953.6,137.200,878,5.18,6.9,254.435,2.93,2.25 1991,4,8069.046,5342.6,948.891,778.378,5992.4,138.300,910.4,4.14,7.1,255.214,3.19,0.95 1992,1,8157.616,5434.5,927.796,778.568,6082.9,139.400,943.8,3.88,7.4,255.992,3.17,0.71 1992,2,8244.294,5466.7,988.912,777.762,6129.5,140.500,963.2,3.50,7.6,256.894,3.14,0.36 1992,3,8329.361,5527.1,999.135,786.639,6160.6,141.700,1003.8,2.97,7.6,257.861,3.4,-0.44 1992,4,8417.016,5594.6,1030.758,787.064,6248.2,142.800,1030.4,3.12,7.4,258.679,3.09,0.02 1993,1,8432.485,5617.2,1054.979,762.901,6156.5,143.800,1047.6,2.92,7.2,259.414,2.79,0.13 1993,2,8486.435,5671.1,1063.263,752.158,6252.3,144.500,1084.5,3.02,7.1,260.255,1.94,1.08 1993,3,8531.108,5732.7,1062.514,744.227,6265.7,145.600,1113,3.00,6.8,261.163,3.03,-0.04 1993,4,8643.769,5783.7,1118.583,748.102,6358.1,146.300,1131.6,3.05,6.6,261.919,1.92,1.13 1994,1,8727.919,5848.1,1166.845,721.288,6332.6,147.200,1141.1,3.48,6.6,262.631,2.45,1.02 1994,2,8847.303,5891.5,1234.855,717.197,6440.6,148.400,1150.5,4.20,6.2,263.436,3.25,0.96 1994,3,8904.289,5938.7,1212.655,736.890,6487.9,149.400,1150.1,4.68,6,264.301,2.69,2 1994,4,9003.180,5997.3,1269.190,716.702,6574.0,150.500,1151.4,5.53,5.6,265.044,2.93,2.6 1995,1,9025.267,6004.3,1282.090,715.326,6616.6,151.800,1149.3,5.72,5.5,265.755,3.44,2.28 1995,2,9044.668,6053.5,1247.610,712.492,6617.2,152.600,1145.4,5.52,5.7,266.557,2.1,3.42 1995,3,9120.684,6107.6,1235.601,707.649,6666.8,153.500,1137.3,5.32,5.7,267.456,2.35,2.97 1995,4,9184.275,6150.6,1270.392,681.081,6706.2,154.700,1123.5,5.17,5.6,268.151,3.11,2.05 1996,1,9247.188,6206.9,1287.128,695.265,6777.7,156.100,1124.8,4.91,5.5,268.853,3.6,1.31 1996,2,9407.052,6277.1,1353.795,705.172,6850.6,157.000,1112.4,5.09,5.5,269.667,2.3,2.79 1996,3,9488.879,6314.6,1422.059,692.741,6908.9,158.200,1086.1,5.04,5.3,270.581,3.05,2 1996,4,9592.458,6366.1,1418.193,690.744,6946.8,159.400,1081.5,4.99,5.3,271.360,3.02,1.97 1997,1,9666.235,6430.2,1451.304,681.445,7008.9,159.900,1063.8,5.10,5.2,272.083,1.25,3.85 1997,2,9809.551,6456.2,1543.976,693.525,7061.5,160.400,1066.2,5.01,5,272.912,1.25,3.76 1997,3,9932.672,6566.0,1571.426,691.261,7142.4,161.500,1065.5,5.02,4.9,273.852,2.73,2.29 1997,4,10008.874,6641.1,1596.523,690.311,7241.5,162.000,1074.4,5.11,4.7,274.626,1.24,3.88 1998,1,10103.425,6707.2,1672.732,668.783,7406.2,162.200,1076.1,5.02,4.6,275.304,0.49,4.53 1998,2,10194.277,6822.6,1652.716,687.184,7512.0,163.200,1075,4.98,4.4,276.115,2.46,2.52 1998,3,10328.787,6913.1,1700.071,681.472,7591.0,163.900,1086,4.49,4.5,277.003,1.71,2.78 1998,4,10507.575,7019.1,1754.743,688.147,7646.5,164.700,1097.8,4.38,4.4,277.790,1.95,2.43 1999,1,10601.179,7088.3,1809.993,683.601,7698.4,165.900,1101.9,4.39,4.3,278.451,2.9,1.49 1999,2,10684.049,7199.9,1803.674,683.594,7716.0,166.700,1098.7,4.54,4.3,279.295,1.92,2.62 1999,3,10819.914,7286.4,1848.949,697.936,7765.9,168.100,1102.3,4.75,4.2,280.203,3.35,1.41 1999,4,11014.254,7389.2,1914.567,713.445,7887.7,169.300,1121.9,5.20,4.1,280.976,2.85,2.35 2000,1,11043.044,7501.3,1887.836,685.216,8053.4,170.900,1113.5,5.63,4,281.653,3.76,1.87 2000,2,11258.454,7571.8,2018.529,712.641,8135.9,172.700,1103,5.81,3.9,282.385,4.19,1.62 2000,3,11267.867,7645.9,1986.956,698.827,8222.3,173.900,1098.7,6.07,4,283.190,2.77,3.3 2000,4,11334.544,7713.5,1987.845,695.597,8234.6,175.600,1097.7,5.70,3.9,283.900,3.89,1.81 2001,1,11297.171,7744.3,1882.691,710.403,8296.5,176.400,1114.9,4.39,4.2,284.550,1.82,2.57 2001,2,11371.251,7773.5,1876.650,725.623,8273.7,177.400,1139.7,3.54,4.4,285.267,2.26,1.28 2001,3,11340.075,7807.7,1837.074,730.493,8484.5,177.600,1166,2.72,4.8,286.047,0.45,2.27 2001,4,11380.128,7930.0,1731.189,739.318,8385.5,177.700,1190.9,1.74,5.5,286.728,0.23,1.51 2002,1,11477.868,7957.3,1789.327,756.915,8611.6,179.300,1185.9,1.75,5.7,287.328,3.59,-1.84 2002,2,11538.770,7997.8,1810.779,774.408,8658.9,180.000,1199.5,1.70,5.8,288.028,1.56,0.14 2002,3,11596.430,8052.0,1814.531,786.673,8629.2,181.200,1204,1.61,5.7,288.783,2.66,-1.05 2002,4,11598.824,8080.6,1813.219,799.967,8649.6,182.600,1226.8,1.20,5.8,289.421,3.08,-1.88 2003,1,11645.819,8122.3,1813.141,800.196,8681.3,183.200,1248.4,1.14,5.9,290.019,1.31,-0.17 2003,2,11738.706,8197.8,1823.698,838.775,8812.5,183.700,1287.9,0.96,6.2,290.704,1.09,-0.13 2003,3,11935.461,8312.1,1889.883,839.598,8935.4,184.900,1297.3,0.94,6.1,291.449,2.6,-1.67 2003,4,12042.817,8358.0,1959.783,845.722,8986.4,186.300,1306.1,0.90,5.8,292.057,3.02,-2.11 2004,1,12127.623,8437.6,1970.015,856.570,9025.9,187.400,1332.1,0.94,5.7,292.635,2.35,-1.42 2004,2,12213.818,8483.2,2055.580,861.440,9115.0,189.100,1340.5,1.21,5.6,293.310,3.61,-2.41 2004,3,12303.533,8555.8,2082.231,876.385,9175.9,190.800,1361,1.63,5.4,294.066,3.58,-1.95 2004,4,12410.282,8654.2,2125.152,865.596,9303.4,191.800,1366.6,2.20,5.4,294.741,2.09,0.11 2005,1,12534.113,8719.0,2170.299,869.204,9189.6,193.800,1357.8,2.69,5.3,295.308,4.15,-1.46 2005,2,12587.535,8802.9,2131.468,870.044,9253.0,194.700,1366.6,3.01,5.1,295.994,1.85,1.16 2005,3,12683.153,8865.6,2154.949,890.394,9308.0,199.200,1375,3.52,5,296.770,9.14,-5.62 2005,4,12748.699,8888.5,2232.193,875.557,9358.7,199.400,1380.6,4.00,4.9,297.435,0.4,3.6 2006,1,12915.938,8986.6,2264.721,900.511,9533.8,200.700,1380.5,4.51,4.7,298.061,2.6,1.91 2006,2,12962.462,9035.0,2261.247,892.839,9617.3,202.700,1369.2,4.82,4.7,298.766,3.97,0.85 2006,3,12965.916,9090.7,2229.636,892.002,9662.5,201.900,1369.4,4.90,4.7,299.593,-1.58,6.48 2006,4,13060.679,9181.6,2165.966,894.404,9788.8,203.574,1373.6,4.92,4.4,300.320,3.3,1.62 2007,1,13099.901,9265.1,2132.609,882.766,9830.2,205.920,1379.7,4.95,4.5,300.977,4.58,0.36 2007,2,13203.977,9291.5,2162.214,898.713,9842.7,207.338,1370,4.72,4.5,301.714,2.75,1.97 2007,3,13321.109,9335.6,2166.491,918.983,9883.9,209.133,1379.2,4.00,4.7,302.509,3.45,0.55 2007,4,13391.249,9363.6,2123.426,925.110,9886.2,212.495,1377.4,3.01,4.8,303.204,6.38,-3.37 2008,1,13366.865,9349.6,2082.886,943.372,9826.8,213.997,1384,1.56,4.9,303.803,2.82,-1.26 2008,2,13415.266,9351.0,2026.518,961.280,10059.0,218.610,1409.3,1.74,5.4,304.483,8.53,-6.79 2008,3,13324.600,9267.7,1990.693,991.551,9838.3,216.889,1474.7,1.17,6,305.270,-3.16,4.33 2008,4,13141.920,9195.3,1857.661,1007.273,9920.4,212.174,1576.5,0.12,6.9,305.952,-8.79,8.91 2009,1,12925.410,9209.2,1558.494,996.287,9926.4,212.671,1592.8,0.22,8.1,306.547,0.94,-0.71 2009,2,12901.504,9189.0,1456.678,1023.528,10077.5,214.469,1653.6,0.18,9.2,307.226,3.37,-3.19 2009,3,12990.341,9256.0,1486.398,1044.088,10040.6,216.385,1673.9,0.12,9.6,308.013,3.56,-3.44 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ÑþÿÿÿÒÓÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ l ÉBäREADME Monthly Quarterly=¼%r8X"1ÈÿArial1ÈÿArial1ÈÿArial1ÈÿArial1ÈÿArial1È Arial ¤ YYYY-MM-DD¥0.000¦0.0§0.00àõÿ À àõÿ À àõÿ À àõÿ À àõÿ À àõÿ À àõÿ À àõÿ À àõÿ À àõÿ À àõÿ À àõÿ À àõÿ À àõÿ À àõÿ À à À à À ठÀ à#À ॠÀ ঠÀ ॠÀ ॠÀ ॠÀ ঠÀ ঠÀ à À ৠÀ à¤!À à¤"À à"À à!À à#À “€ÿ’â8ÿÿÿÿÿÿÿÿÿÿÿÿ€€€€€€€€€ÀÀÀ€€€™™ÿ™3fÿÿÌÌÿÿffÿ€€fÌÌÌÿ€ÿÿÿÿÿÿ€€€€€ÿÌÿÌÿÿÌÿÌÿÿ™™Ìÿÿ™ÌÌ™ÿÿÌ™3fÿ3ÌÌ™ÌÿÌÿ™ÿfff™–––3f3™f333™3™3f33™333… ÛREADME…·#Monthly…F6 Quarterly l ÉU} ¸ } ¸ } ¸< Monthly Quarterly*+€‚Áƒ„&è?'è?(ð?)ð?¡"dXXà?à? Data List: macrodata Data Updated: 2009-12-11,$FRED (Federal Reserve Economic Data)2*Link: http://research.stlouisfed.org/fred2;3Help: http://research.stlouisfed.org/fred2/help-faq"Economic Research Division)!Federal Reserve Bank of St. Louis  Series ID: CPIAUCSL Title:? 7Consumer Price Index For All Urban Consumers: All ItemsSource:<4U.S. Department of Labor: Bureau of Labor StatisticsRelease:Consumer Price IndexUnits:Index 1982-84=100 Frequency:MonthlySeasonal Adjustment:Seasonally AdjustedNotes:Handbook of Methods -L D(http://stats.bls.gov:80/opub/hom/homch17_itc.htm) Understanding the)!!CPI: Frequently Asked Questions -0"((http://stats.bls.gov:80/cpi/cpifaq.htm)& Series ID:'DPIC96)Title:'*Real Disposable Personal Income,Source:@-8U.S. Department of Commerce: Bureau of Economic Analysis/Release:0Gross Domestic Product2Units:(3 Billions of Chained 2005 Dollars5 Frequency:6 Quarterly8Seasonal Adjustment:'9Seasonally Adjusted Annual Rate;Notes:I<AA Guide to the National Income and Product Accounts of the UnitedF=>States (NIPA) - (http://www.bea.gov/national/pdf/nipaguid.pdf)A Series ID:BFGCEC96DTitle:KECReal Federal Consumption Expenditures & Gross Investment, 3 DecimalGSource:@H8U.S. Department of Commerce: Bureau of Economic AnalysisJRelease:KGross Domestic ProductMUnits:(N Billions of Chained 2005 DollarsP Frequency:Q QuarterlySSeasonal Adjustment:'TSeasonally Adjusted Annual RateVNotes:GW?Data prior to 1990 for chained dollars were calculated by Haver1X)Analytics using chained quantity indexes.YIZAA Guide to the National Income and Product Accounts of the UnitedF[>States (NIPA) - (http://www.bea.gov/national/pdf/nipaguid.pdf)_ Series ID:`GDPC96bTitle:.c&Real Gross Domestic Product, 3 DecimaleSource:@f8U.S. Department of Commerce: Bureau of Economic AnalysishRelease:iGross Domestic ProductkUnits:(l Billions of Chained 2005 Dollarsn Frequency:o QuarterlyqSeasonal Adjustment:'rSeasonally Adjusted Annual RatetNotes:IuAA Guide to the National Income and Product Accounts of the UnitedFv>States (NIPA) - (http://www.bea.gov/national/pdf/nipaguid.pdf)z Series ID:{GPDIC96}Title:9~1Real Gross Private Domestic Investment, 3 Decimal€Source:@8U.S. Department of Commerce: Bureau of Economic AnalysisƒRelease:„Gross Domestic Product†Units:(‡ Billions of Chained 2005 Dollars‰ Frequency:Š QuarterlyŒSeasonal Adjustment:'Seasonally Adjusted Annual RateNotes:IAA Guide to the National Income and Product Accounts of the UnitedF‘>States (NIPA) - (http://www.bea.gov/national/pdf/nipaguid.pdf)• Series ID: –M1SL˜Title:™M1 Money Stock›Source:8œ0Board of Governors of the Federal Reserve SystemžRelease: ŸH.6 Money Stock Measures¡Units:¢Billions of Dollars¤ Frequency:¥Monthly§Seasonal Adjustment:¨Seasonally AdjustedªNotes:F«>Ml includes funds that are readily accessible for spending. M1L¬Dconsists of: (1) currency outside the U.S. Treasury, Federal ReserveH­@Banks, and the vaults of depository institutions; (2) traveler'sE®=checks of nonbank issuers; (3) demand deposits; and (4) otherN¯Fcheckable deposits (OCDs), which consist primarily of negotiable orderJ°Bof withdrawal (NOW) accounts at depository institutions and creditK±Cunion share draft accounts. Seasonally adjusted M1 is calculated byL²Dsumming currency, traveler's checks, demand deposits, and OCDs, each'³seasonally adjusted separately.· Series ID:¸PCECC96ºTitle:.»&Real Personal Consumption Expenditures½Source:@¾8U.S. Department of Commerce: Bureau of Economic AnalysisÀRelease:ÁGross Domestic ProductÃUnits:(Ä Billions of Chained 2005 DollarsÆ Frequency:Ç QuarterlyÉSeasonal Adjustment:'ÊSeasonally Adjusted Annual RateÌNotes:IÍAA Guide to the National Income and Product Accounts of the UnitedFÎ>States (NIPA) - (http://www.bea.gov/national/pdf/nipaguid.pdf)Ò Series ID: ÓPOPÕTitle:BÖ:Total Population: All Ages including Armed Forces OverseasØSource:2Ù*U.S. Department of Commerce: Census BureauÛRelease:-Ü%Monthly National Population EstimatesÞUnits:ß Thousandsá Frequency:âMonthlyäSeasonal Adjustment:åNot ApplicableçNotes:Eè=The intercensal estimates for 1990-2000 for the United StatesFé>population are produced by converting the 1990-2000 postcensalNêFestimates prepared previously for the U. S. to account for differencesLëDbetween the postcensal estimates in 2000 and census counts (error ofLìDclosure). The postcensal estimates for 1990 to 2000 were produced byIíAupdating the resident population enumerated in the 1990 census byNîFestimates of the components of population change between April 1, 1990IïAand April 1, 2000-- births to U.S. resident women, deaths to U.S.MðEresidents, net international migration (incl legal & residual foreignNñFborn), and net movement of the U.S. armed forces and civilian citizensJòBto the United States. Intercensal population estimates for 1990 toJóB2000 are derived from the postcensal estimates by distributing theJôBerror of closure over the decade by month. The method used for theMõE1990s for distributing the error of closure is the same that was usedHö@for the 1980s. This method produces an intercensal estimate as aI÷Afunction of time and the postcensal estimates,using the followingMøEformula: the population at time t is equal to the postcensal estimateMùEat time t multiplied by a function. The function is the April 1, 2000LúDcensus count divided by the April 1, 2000 postcensal estimate raised*û"to the power of t divided by 3653.ÿ Series ID: TB3MSTitle:4,3-Month Treasury Bill: Secondary Market RateSource:80Board of Governors of the Federal Reserve SystemRelease:$ H.15 Selected Interest Rates Units: Percent Frequency:MonthlySeasonal Adjustment:Not ApplicableNotes:1)Averages of Business Days, Discount Basis> ¶ l ÉU} ¸} ¸ } ¸ } ¸ } ¸ README Quarterly*+€‚Áƒ„&è?'è?(ð?)ð?¡"dXXà?à?  DATECPIAUCSL M1SL POP TB3MSBÈ@ ×£p= ç?€QÈ@×£p= ×ã?€_È@¸…ëQ¸Î?oÈ@333333Ã?~È@{®GázÄ?€È@333333Ã?€œÈ@333333Ã?¬È@R¸…ëQÈ? €»È@ áz®GáÊ? €ÊÈ@ Ház®GÑ? 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LNS14000000Q,2009,Q02,9.2 LNS14000000Q,2009,Q03,9.6 statsmodels-0.12.2/statsmodels/datasets/modechoice/000077500000000000000000000000001400612667500224165ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/modechoice/__init__.py000066400000000000000000000003261400612667500245300ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/modechoice/data.py000066400000000000000000000054751400612667500237140ustar00rootroot00000000000000"""Travel Mode Choice""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This is public domain.""" TITLE = __doc__ SOURCE = """ Greene, W.H. and D. Hensher (1997) Multinomial logit and discrete choice models in Greene, W. H. (1997) LIMDEP version 7.0 user's manual revised, Plainview, New York econometric software, Inc. Download from on-line complements to Greene, W.H. (2011) Econometric Analysis, Prentice Hall, 7th Edition (data table F18-2) http://people.stern.nyu.edu/wgreene/Text/Edition7/TableF18-2.csv """ DESCRSHORT = """Data used to study travel mode choice between Australian cities """ DESCRLONG = """The data, collected as part of a 1987 intercity mode choice study, are a sub-sample of 210 non-business trips between Sydney, Canberra and Melbourne in which the traveler chooses a mode from four alternatives (plane, car, bus and train). The sample, 840 observations, is choice based with over-sampling of the less popular modes (plane, train and bus) and under-sampling of the more popular mode, car. The level of service data was derived from highway and transport networks in Sydney, Melbourne, non-metropolitan N.S.W. and Victoria, including the Australian Capital Territory.""" NOTE = """:: Number of observations: 840 Observations On 4 Modes for 210 Individuals. Number of variables: 8 Variable name definitions:: individual = 1 to 210 mode = 1 - air 2 - train 3 - bus 4 - car choice = 0 - no 1 - yes ttme = terminal waiting time for plane, train and bus (minutes); 0 for car. invc = in vehicle cost for all stages (dollars). invt = travel time (in-vehicle time) for all stages (minutes). gc = generalized cost measure:invc+(invt*value of travel time savings) (dollars). hinc = household income ($1000s). psize = traveling group size in mode chosen (number).""" def load(as_pandas=None): """ Load the data modechoice data and return a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): """ Load the data modechoice data and return a Dataset class instance. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. 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1,60,111,205,133,70,1 0,34,97,888,193,70,1 0,35,52,878,147,70,1 0,0,49,855,142,70,1 1,60,70,95,93,40,2 0,44,31,360,85,40,2 0,53,25,405,86,40,2 0,0,7,335,58,40,2 1,45,74,70,85,35,3 0,44,26,361,81,35,3 0,53,21,406,82,35,3 0,0,4,315,52,35,3 1,75,165,180,192,60,2 0,44,98,967,245,60,2 0,53,53,922,193,60,2 0,0,26,947,170,60,2 1,30,93,175,112,60,1 0,34,96,1030,208,60,1 0,35,51,1020,162,60,1 0,0,54,967,159,60,1 1,90,71,115,89,50,2 0,44,31,385,89,50,2 0,53,25,430,90,50,2 0,0,7,332,57,50,2 1,45,75,75,96,40,3 0,44,33,418,96,40,3 0,53,28,463,98,40,3 0,0,5,291,49,40,3 1,60,81,70,89,60,1 0,34,32,341,69,60,1 0,35,26,386,68,60,1 0,0,13,307,46,60,1 1,75,94,95,104,20,1 0,34,33,367,73,20,1 0,35,27,412,72,20,1 0,0,14,314,48,20,1 0,64,70,158,93,50,3 0,44,61,778,179,50,3 0,53,34,772,151,50,3 1,0,11,470,82,50,3 0,64,65,145,87,70,4 0,44,54,674,156,70,4 0,53,33,668,135,70,4 1,0,8,560,93,70,4 0,64,71,133,91,50,3 0,44,59,625,153,50,3 0,53,32,619,126,50,3 1,0,8,510,85,50,3 0,69,81,139,96,26,1 0,34,71,698,147,26,1 0,35,32,692,107,26,1 1,0,33,600,98,26,1 0,64,65,154,89,45,4 0,44,53,621,147,45,4 0,53,32,615,125,45,4 1,0,9,535,90,45,4 0,64,58,148,80,45,6 0,44,48,646,145,45,6 0,53,32,640,129,45,6 1,0,5,470,76,45,6 0,69,81,95,91,30,1 0,34,70,610,136,30,1 0,35,31,604,96,30,1 1,0,30,440,78,30,1 0,64,71,145,93,40,3 0,44,59,658,159,40,3 0,53,32,652,131,40,3 1,0,10,590,100,40,3 0,64,82,159,106,50,2 0,44,71,765,187,50,2 0,53,32,759,147,50,2 1,0,13,490,87,50,2 0,69,61,73,69,35,1 0,34,33,350,71,35,1 1,50,26,227,51,35,1 0,0,14,314,48,35,1 0,69,60,133,74,34,1 0,34,31,397,74,34,1 1,15,21,240,47,34,1 0,0,14,351,52,34,1 0,64,81,129,101,8,2 0,44,35,677,138,8,2 1,15,31,565,117,8,2 0,0,12,588,101,8,2 0,69,59,117,72,30,1 0,34,32,397,75,30,1 0,35,26,442,74,30,1 1,0,17,180,37,30,1 0,69,111,276,141,32,1 0,34,93,1047,207,32,1 1,30,35,860,128,32,1 0,0,42,1008,151,32,1 0,69,59,88,68,26,1 0,34,30,361,70,26,1 1,15,21,295,53,26,1 0,0,13,299,45,26,1 0,69,59,114,71,42,1 0,34,31,389,73,42,1 1,15,21,243,47,42,1 0,0,13,334,49,42,1 1,90,55,115,72,50,1 0,44,72,602,163,50,1 0,53,33,596,123,50,1 0,0,24,589,113,50,1 1,15,87,110,104,70,2 0,44,31,348,84,70,2 0,53,25,393,85,70,2 0,0,7,320,56,70,2 0,69,62,76,71,30,1 0,34,39,377,80,30,1 0,35,33,422,79,30,1 1,0,12,300,45,30,1 0,69,59,121,72,26,1 0,34,31,386,73,26,1 0,35,25,431,72,26,1 1,0,14,270,43,26,1 0,64,51,90,64,26,3 1,20,61,350,114,26,3 0,53,22,405,83,26,3 0,0,6,327,56,26,3 0,64,64,215,97,18,2 1,50,41,420,104,18,2 0,53,15,385,73,18,2 0,0,9,321,58,18,2 0,64,58,74,69,35,2 1,30,21,295,66,35,2 0,53,24,389,83,35,2 0,0,7,315,55,35,2 0,64,71,119,89,50,3 0,44,58,617,152,50,3 1,15,35,615,128,50,3 0,0,11,586,100,50,3 1,15,50,75,58,4,1 0,34,15,361,55,4,1 0,35,12,406,56,4,1 0,0,13,315,47,4,1 1,10,61,80,73,30,4 0,44,24,350,77,30,4 0,53,19,395,79,30,4 0,0,4,314,52,30,4 0,69,59,100,70,45,1 0,34,31,372,71,45,1 0,35,25,417,70,45,1 1,0,13,210,36,45,1 0,69,58,73,66,60,1 0,34,31,324,66,60,1 0,35,25,334,61,60,1 1,0,18,240,44,60,1 0,69,62,184,82,4,1 0,34,19,454,68,4,1 0,35,16,464,66,4,1 1,0,18,225,42,4,1 1,30,93,85,102,30,1 0,34,33,365,72,30,1 0,35,27,410,71,30,1 0,0,13,308,46,30,1 1,20,76,95,86,60,1 0,34,33,344,70,60,1 0,35,27,389,69,60,1 0,0,13,315,47,60,1 0,64,100,190,129,4,2 0,44,49,678,152,4,2 1,30,48,430,113,4,2 0,0,14,629,109,4,2 0,64,48,63,58,18,3 1,10,21,255,60,18,3 0,53,13,397,73,18,3 0,0,4,324,53,18,3 0,64,58,93,72,15,2 1,10,30,315,78,15,2 0,53,13,346,65,15,2 0,0,6,316,54,15,2 0,69,59,94,69,26,1 0,34,30,361,70,26,1 0,35,24,406,68,26,1 1,0,10,270,39,26,1 1,30,111,105,122,40,1 0,34,71,596,136,40,1 0,35,32,590,96,40,1 0,0,27,577,90,40,1 1,5,64,80,76,70,2 0,44,30,348,83,70,2 0,53,24,393,84,70,2 0,0,7,291,51,70,2 1,5,60,85,73,45,4 0,44,24,379,81,45,4 0,53,19,424,83,45,4 0,0,3,337,54,45,4 0,64,97,188,125,26,3 0,44,76,825,201,26,3 1,16,38,810,161,26,3 0,0,15,803,137,26,3 0,69,91,117,104,35,1 0,34,77,630,145,35,1 0,35,38,624,106,35,1 1,0,29,540,88,35,1 0,69,59,114,72,4,1 0,34,16,378,57,4,1 1,5,14,370,54,4,1 0,0,17,335,53,4,1 0,69,60,66,67,20,1 0,34,34,352,72,20,1 1,10,37,250,64,20,1 0,0,13,307,46,20,1 0,69,107,144,123,45,1 0,34,89,879,184,45,1 1,30,35,775,119,45,1 0,0,37,868,131,45,1 0,69,81,124,94,40,1 0,34,69,605,135,40,1 0,35,30,599,95,40,1 1,0,30,720,108,40,1 1,45,126,135,141,40,1 0,34,70,596,135,40,1 0,35,31,590,95,40,1 0,0,32,577,95,40,1 0,69,59,86,68,2,1 0,34,15,360,54,2,1 1,50,29,265,57,2,1 0,0,13,300,46,2,1 0,69,81,124,94,20,1 0,34,35,605,100,20,1 0,35,31,599,96,20,1 1,0,27,510,82,20,1 0,64,66,140,87,70,4 0,44,54,670,156,70,4 0,53,33,664,134,70,4 1,0,12,540,94,70,4 statsmodels-0.12.2/statsmodels/datasets/nile/000077500000000000000000000000001400612667500212465ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/nile/__init__.py000066400000000000000000000003261400612667500233600ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/nile/data.py000066400000000000000000000031521400612667500225320ustar00rootroot00000000000000"""Nile River Flows.""" import pandas as pd from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This is public domain.""" TITLE = """Nile River flows at Ashwan 1871-1970""" SOURCE = """ This data is first analyzed in: Cobb, G. W. 1978. "The Problem of the Nile: Conditional Solution to a Changepoint Problem." *Biometrika*. 65.2, 243-51. """ DESCRSHORT = """This dataset contains measurements on the annual flow of the Nile as measured at Ashwan for 100 years from 1871-1970.""" DESCRLONG = DESCRSHORT + " There is an apparent changepoint near 1898." #suggested notes NOTE = """:: Number of observations: 100 Number of variables: 2 Variable name definitions: year - the year of the observations volumne - the discharge at Aswan in 10^8, m^3 """ def load(as_pandas=None): """ Load the Nile data and return a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): data = _get_data() # TODO: time series endog = pd.Series(data['volume'], index=data['year'].astype(int)) dataset = du.Dataset(data=data, names=list(data.columns), endog=endog, endog_name='volume') return dataset def _get_data(): return du.load_csv(__file__, 'nile.csv').astype(float) statsmodels-0.12.2/statsmodels/datasets/nile/nile.csv000066400000000000000000000016561400612667500227220ustar00rootroot00000000000000year,volume 1871,1120 1872,1160 1873,963 1874,1210 1875,1160 1876,1160 1877,813 1878,1230 1879,1370 1880,1140 1881,995 1882,935 1883,1110 1884,994 1885,1020 1886,960 1887,1180 1888,799 1889,958 1890,1140 1891,1100 1892,1210 1893,1150 1894,1250 1895,1260 1896,1220 1897,1030 1898,1100 1899,774 1900,840 1901,874 1902,694 1903,940 1904,833 1905,701 1906,916 1907,692 1908,1020 1909,1050 1910,969 1911,831 1912,726 1913,456 1914,824 1915,702 1916,1120 1917,1100 1918,832 1919,764 1920,821 1921,768 1922,845 1923,864 1924,862 1925,698 1926,845 1927,744 1928,796 1929,1040 1930,759 1931,781 1932,865 1933,845 1934,944 1935,984 1936,897 1937,822 1938,1010 1939,771 1940,676 1941,649 1942,846 1943,812 1944,742 1945,801 1946,1040 1947,860 1948,874 1949,848 1950,890 1951,744 1952,749 1953,838 1954,1050 1955,918 1956,986 1957,797 1958,923 1959,975 1960,815 1961,1020 1962,906 1963,901 1964,1170 1965,912 1966,746 1967,919 1968,718 1969,714 1970,740 statsmodels-0.12.2/statsmodels/datasets/randhie/000077500000000000000000000000001400612667500217315ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/randhie/__init__.py000066400000000000000000000003261400612667500240430ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/randhie/data.py000066400000000000000000000047631400612667500232260ustar00rootroot00000000000000"""RAND Health Insurance Experiment Data""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This is in the public domain.""" TITLE = __doc__ SOURCE = """ The data was collected by the RAND corporation as part of the Health Insurance Experiment (HIE). http://www.rand.org/health/projects/hie.html This data was used in:: Cameron, A.C. amd Trivedi, P.K. 2005. `Microeconometrics: Methods and Applications,` Cambridge: New York. And was obtained from: See randhie/src for the original data and description. The data included here contains only a subset of the original data. The data varies slightly compared to that reported in Cameron and Trivedi. """ DESCRSHORT = """The RAND Co. Health Insurance Experiment Data""" DESCRLONG = """""" NOTE = """:: Number of observations - 20,190 Number of variables - 10 Variable name definitions:: mdvis - Number of outpatient visits to an MD lncoins - ln(coinsurance + 1), 0 <= coninsurance <= 100 idp - 1 if individual deductible plan, 0 otherwise lpi - ln(max(1, annual participation incentive payment)) fmde - 0 if idp = 1; ln(max(1, MDE/(0.01 coinsurance))) otherwise physlm - 1 if the person has a physical limitation disea - number of chronic diseases hlthg - 1 if self-rated health is good hlthf - 1 if self-rated health is fair hlthp - 1 if self-rated health is poor (Omitted category is excellent self-rated health) """ def load(as_pandas=None): """ Loads the RAND HIE data and returns a Dataset class. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. Notes ----- endog - response variable, mdvis exog - design """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): """ Loads the RAND HIE data and returns a Dataset class. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. Notes ----- endog - response variable, mdvis exog - design """ return du.process_pandas(_get_data(), endog_idx=0) def _get_data(): return du.load_csv(__file__, 'randhie.csv') statsmodels-0.12.2/statsmodels/datasets/randhie/randhie.csv000066400000000000000000026652251400612667500241020ustar00rootroot00000000000000mdvis,lncoins,idp,lpi,fmde,physlm,disea,hlthg,hlthf,hlthp 0,4.61512,1,6.907755,0,0,13.73189,1,0,0 2,4.61512,1,6.907755,0,0,13.73189,1,0,0 0,4.61512,1,6.907755,0,0,13.73189,1,0,0 0,4.61512,1,6.907755,0,0,13.73189,1,0,0 0,4.61512,1,6.907755,0,0,13.73189,1,0,0 0,4.61512,1,6.907755,0,0,13.73189,0,0,0 0,4.61512,1,6.907755,0,0,13.73189,0,0,0 1,4.61512,1,6.907755,0,0,13.73189,0,0,0 0,4.61512,1,6.907755,0,0,13.73189,0,0,0 0,4.61512,1,6.907755,0,0,13.73189,0,0,0 0,4.61512,1,6.907755,0,0,13.73189,0,0,0 1,4.61512,1,6.907755,0,0,13.73189,0,0,0 0,4.61512,1,6.907755,0,0,13.73189,0,0,0 0,4.61512,1,6.907755,0,0,13.73189,0,0,0 0,4.61512,1,6.907755,0,0,13.73189,0,0,0 6,4.61512,1,6.907755,0,0,13.73189,1,0,0 2,4.61512,1,6.907755,0,0,13.73189,1,0,0 0,4.61512,1,6.907755,0,0,13.73189,1,0,0 0,4.61512,1,6.907755,0,0,13.73189,1,0,0 0,4.61512,1,6.907755,0,0,13.73189,1,0,0 1,0,1,6.109248,0,0,13.73189,1,0,0 0,0,1,6.109248,0,0,13.73189,1,0,0 0,0,1,6.109248,0,0,13.73189,1,0,0 0,0,1,6.109248,0,0,13.73189,1,0,0 0,0,1,6.109248,0,0,13.73189,1,0,0 1,0,1,6.109248,0,1,13,1,0,0 0,0,1,6.109248,0,1,13,1,0,0 1,0,1,6.109248,0,1,13,1,0,0 2,0,1,6.109248,0,1,13,1,0,0 4,0,1,6.109248,0,1,13,1,0,0 0,0,1,6.109248,0,0,17.4,1,0,0 0,0,1,6.109248,0,0,17.4,1,0,0 0,0,1,6.109248,0,0,17.4,1,0,0 0,0,1,6.109248,0,0,17.4,1,0,0 0,0,1,6.109248,0,0,17.4,1,0,0 0,0,1,0,0,0,4.3,0,0,0 0,0,1,0,0,0,4.3,0,0,0 0,0,1,0,0,0,4.3,0,0,0 0,0,0,6.006353,0,0,13,1,0,0 0,0,0,6.006353,0,0,13,1,0,0 0,0,0,6.006353,0,0,13,1,0,0 1,0,0,6.006353,0,0,4.3,1,0,0 0,0,0,6.006353,0,0,4.3,1,0,0 0,0,0,6.006353,0,0,4.3,1,0,0 0,0,0,6.006353,0,0,13,1,0,0 0,0,0,6.006353,0,0,13,1,0,0 0,0,0,6.006353,0,0,13,1,0,0 1,0,0,6.006353,0,0,13,1,0,0 0,0,0,6.006353,0,0,13,1,0,0 7,0,0,6.006353,0,0,13,1,0,0 1,0,0,0,0,0,4.3,0,0,0 0,0,0,0,0,0,4.3,0,0,0 2,0,0,0,0,0,4.3,0,0,0 8,0,0,0,0,0,0,0,0,0 1,0,0,0,0,0,0,0,0,0 2,0,0,0,0,0,0,0,0,0 1,0,0,0,0,0,8.7,0,0,0 1,0,0,0,0,0,8.7,0,0,0 0,0,0,0,0,0,8.7,0,0,0 4,4.61512,1,6.802395,0,0,17.4,1,0,0 5,4.61512,1,6.802395,0,0,17.4,1,0,0 14,4.61512,1,6.802395,0,0,17.4,1,0,0 3,4.61512,1,6.802395,0,0,13,1,0,0 3,4.61512,1,6.802395,0,0,13,1,0,0 5,4.61512,1,6.802395,0,0,13,1,0,0 1,3.258096,0,6.907755,8.294049,0,13.73189,0,0,0 0,3.258096,0,6.907755,8.294049,0,13.73189,0,0,0 5,3.258096,0,6.907755,8.294049,0,13.73189,0,0,0 0,3.258096,0,6.907755,8.294049,0,13.73189,0,0,0 1,3.258096,0,6.907755,8.294049,0,13.73189,0,0,0 0,3.258096,0,6.907755,8.294049,0,0,0,0,0 0,3.258096,0,6.907755,8.294049,0,0,0,0,0 2,3.258096,0,6.907755,8.294049,0,0,0,0,0 1,3.258096,0,6.907755,8.294049,0,0,0,0,0 0,3.258096,0,6.907755,8.294049,0,0,0,0,0 2,3.258096,0,6.907755,8.294049,1,26.1,0,0,0 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%9.0g black income float %9.0g income based on annual income r xage float %9.0g age that year female float %9.0g female educdec float %9.0g education of decision maker time float %9.0g time eligible during the year outpdol float %9.0g outpatient exp. excl. ment and drugdol float %9.0g drugs purchased, outpatient suppdol float %9.0g supplies purchased, outpatient mentdol float %9.0g psychotherapy exp., outpatient inpdol float %9.0g inpatient exp., facilities & md meddol float %9.0g medical exp excl outpatient men totadm float %9.0g number of hosp. admissions inpmis float %9.0g missing any inpatient charges mentvis float %9.0g number psychotherapy visits mdvis float %9.0g number face-to-fact md visits notmdvis float %9.0g number face-to-face, not-md vis num float %9.0g family size mhi float %9.0g mental health index -- baselin disea float %9.0g count of chronic diseases -- ba physlm float %9.0g physical limitations -- baselin ghindx float %9.0g general health index -- baselin mdeoff float %9.0g maximum expenditure offer pioff float %9.0g participation incentive child float %9.0g child fchild float %9.0g female child lfam float %9.0g log of family size lpi float %9.0g log participation incentive idp float %9.0g individual deductible plan logc float %9.0g log(coinsurance+1) fmde float %9.0g function of mdeoff hlthg float %9.0g good health hlthf float %9.0g fair health hlthp float %9.0g poor health xghindx float %9.0g ghi with imputation linc float %9.0g lnum float %9.0g lnmeddol float %9.0g binexp float %9.0g statsmodels-0.12.2/statsmodels/datasets/randhie/src/randhie.csv000066400000000000000000160742761400612667500246760ustar00rootroot00000000000000plan,site,coins,tookphys,year,zper,black,income,xage,female,educdec,time,outpdol,drugdol,suppdol,mentdol,inpdol,meddol,totadm,inpmis,mentvis,mdvis,notmdvis,num,mhi,disea,physlm,ghindx,mdeoff,pioff,child,fchild,lfam,lpi,idp,logc,fmde,hlthg,hlthf,hlthp,xghindx,linc,lnum,lnmeddol,binexp 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1,1,0,1,2,125057,1,5107.692,14.54962,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,450,450,1,1,1.098612,6.109248,1,0,0,1,0,0,80.28564,8.538699,1.098612,,0 1,1,0,1,3,125057,1,5107.692,15.54962,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,450,450,1,1,1.098612,6.109248,1,0,0,1,0,0,80.28564,8.538699,1.098612,,0 1,1,0,1,4,125057,1,5107.692,16.54962,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,450,450,1,1,1.098612,6.109248,1,0,0,1,0,0,80.28564,8.538699,1.098612,,0 1,1,0,1,5,125057,1,5107.692,17.54962,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,450,450,1,1,1.098612,6.109248,1,0,0,1,0,0,80.28564,8.538699,1.098612,,0 1,1,0,1,1,125058,1,5107.692,15.28268,1,12,1,18.4414,0,0,0,0,18.4414,0,0,0,1,0,3,61.1,13,1,,450,450,1,1,1.098612,6.109248,1,0,0,1,0,0,63.74599,8.538699,1.098612,2.914598,1 1,1,0,1,2,125058,1,5107.692,16.28268,1,12,1,0,2.39521,0,0,0,2.39521,0,0,0,0,0,3,61.1,13,1,,450,450,1,1,1.098612,6.109248,1,0,0,1,0,0,63.74599,8.538699,1.098612,.8734707,1 1,1,0,1,3,125058,1,5107.692,17.28268,1,12,1,4.955401,17.09613,0,0,0,22.05154,0,0,0,1,0,3,61.1,13,1,,450,450,1,1,1.098612,6.109248,1,0,0,1,0,0,63.74599,8.538699,1.098612,3.093382,1 1,1,0,1,4,125058,1,5107.692,18.28268,1,12,1,29.8302,25.7687,0,0,0,55.5989,0,0,0,2,0,3,61.1,13,1,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,63.74599,8.538699,1.098612,4.018163,1 1,1,0,1,5,125058,1,5107.692,19.28268,1,12,1,122.0025,11.75852,0,0,0,133.761,0,0,0,4,0,3,61.1,13,1,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,63.74599,8.538699,1.098612,4.896055,1 1,1,0,1,1,125059,1,5107.692,38.83094,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,81.1,17.4,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,68.12782,8.538699,1.098612,,0 1,1,0,1,2,125059,1,5107.692,39.83094,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,81.1,17.4,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,68.12782,8.538699,1.098612,,0 1,1,0,1,3,125059,1,5107.692,40.83094,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,81.1,17.4,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,68.12782,8.538699,1.098612,,0 1,1,0,1,4,125059,1,5107.692,41.83094,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,81.1,17.4,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,68.12782,8.538699,1.098612,,0 1,1,0,1,5,125059,1,5107.692,42.83094,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,81.1,17.4,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,68.12782,8.538699,1.098612,,0 1,1,0,0,1,125075,1,1,24.60233,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,80,4.3,0,,150,0,0,0,0,0,1,0,0,0,0,0,71.88312,.6931472,0,,0 1,1,0,0,2,125075,1,1,25.60233,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,80,4.3,0,,150,0,0,0,0,0,1,0,0,0,0,0,71.88312,.6931472,0,,0 1,1,0,0,3,125075,1,1,26.60233,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,80,4.3,0,,150,0,0,0,0,0,1,0,0,0,0,0,71.88312,.6931472,0,,0 11,1,0,0,1,125126,1,5899.918,15.74538,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,61.1,13,0,,0,406,1,1,1.386294,6.006353,0,0,0,1,0,0,59.67566,8.682863,1.386294,,0 11,1,0,0,2,125126,1,5899.918,16.74538,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,61.1,13,0,,0,406,1,1,1.386294,6.006353,0,0,0,1,0,0,59.67566,8.682863,1.386294,,0 11,1,0,0,3,125126,1,5899.918,17.74538,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,61.1,13,0,,0,406,1,1,1.386294,6.006353,0,0,0,1,0,0,59.67566,8.682863,1.386294,,0 11,1,0,1,1,125127,1,5899.918,60.48734,1,9,1,5.889281,0,0,0,0,5.889281,0,0,0,1,0,4,71.6,4.3,0,,0,406,0,0,1.386294,6.006353,0,0,0,1,0,0,63.0108,8.682863,1.386294,1.773134,1 11,1,0,1,2,125127,1,5899.918,61.48734,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,71.6,4.3,0,,0,406,0,0,1.386294,6.006353,0,0,0,1,0,0,63.0108,8.682863,1.386294,,0 11,1,0,1,3,125127,1,5899.918,62.48734,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,71.6,4.3,0,,0,406,0,0,1.386294,6.006353,0,0,0,1,0,0,63.0108,8.682863,1.386294,,0 11,1,0,0,1,125128,1,5899.918,14.59001,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,63.5,13,0,,0,406,1,1,1.386294,6.006353,0,0,0,1,0,0,59.67566,8.682863,1.386294,,0 11,1,0,0,2,125128,1,5899.918,15.59001,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,63.5,13,0,,0,406,1,1,1.386294,6.006353,0,0,0,1,0,0,59.67566,8.682863,1.386294,,0 11,1,0,0,3,125128,1,5899.918,16.59001,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,63.5,13,0,,0,406,1,1,1.386294,6.006353,0,0,0,1,0,0,59.67566,8.682863,1.386294,,0 11,1,0,1,1,125129,1,5899.918,59.27721,0,4,1,66.19553,67.13781,0,0,0,133.3333,0,0,0,1,0,4,71.6,13,0,,0,406,0,0,1.386294,6.006353,0,0,0,1,0,0,61.37119,8.682863,1.386294,4.892852,1 11,1,0,1,2,125129,1,5899.918,60.27721,0,4,1,0,61.45552,0,0,0,61.45552,0,0,0,0,0,4,71.6,13,0,,0,406,0,0,1.386294,6.006353,0,0,0,1,0,0,61.37119,8.682863,1.386294,4.118314,1 11,1,0,1,3,125129,1,5899.918,61.27721,0,4,1,695.5725,62.11302,5.405406,0,0,763.0909,0,0,0,7,32,4,71.6,13,0,,0,406,0,0,1.386294,6.006353,0,0,0,1,0,0,61.37119,8.682863,1.386294,6.637377,1 11,1,0,1,1,125133,1,3596.154,14.22313,0,12,1,11.99041,7.284173,0,0,0,19.27458,0,0,0,1,0,3,92.6,4.3,0,,0,0,1,0,1.098612,0,0,0,0,0,0,0,75.73199,8.187899,1.098612,2.958787,1 11,1,0,1,2,125133,1,3596.154,15.22313,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,92.6,4.3,0,,0,0,1,0,1.098612,0,0,0,0,0,0,0,75.73199,8.187899,1.098612,,0 11,1,0,1,3,125133,1,3596.154,16.22313,0,12,1,28.42893,0,0,0,0,28.42893,0,0,0,2,0,3,92.6,4.3,0,,0,0,1,0,1.098612,0,0,0,0,0,0,0,75.73199,8.187899,1.098612,3.347407,1 11,1,0,1,1,125134,1,3596.154,45.42916,0,7,1,455.9352,2.817746,0,0,0,458.753,0,0,0,8,0,3,83.2,0,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,67.10523,8.187899,1.098612,6.128512,1 11,1,0,1,2,125134,1,3596.154,46.42916,0,7,1,94.38663,0,40.40526,0,0,134.7919,0,0,0,1,1,3,83.2,0,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,67.10523,8.187899,1.098612,4.903732,1 11,1,0,1,3,125134,1,3596.154,47.42916,0,7,1,37.90524,0,0,0,1239.302,1277.207,1,0,0,2,0,3,83.2,0,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,67.10523,8.187899,1.098612,7.152431,1 11,1,0,1,1,125135,1,3596.154,37.11157,1,12,1,5.995204,4.586331,0,0,0,10.58153,0,0,0,1,0,3,68.4,8.7,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,74.57648,8.187899,1.098612,2.35911,1 11,1,0,1,2,125135,1,3596.154,38.11157,1,12,1,15.33406,14.0471,47.82585,0,0,77.20701,0,0,0,1,1,3,68.4,8.7,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,74.57648,8.187899,1.098612,4.34649,1 11,1,0,1,3,125135,1,3596.154,39.11157,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,68.4,8.7,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,74.57648,8.187899,1.098612,,0 2,1,100,0,1,125152,1,11468.98,55.32923,1,11,1,38.28033,11.23675,32.61484,0,0,82.13192,0,0,0,4,0,2,82.1,17.4,0,,900,900,0,0,.6931472,6.802395,1,0,0,1,0,0,60.89297,9.347488,.6931472,4.408327,1 2,1,100,0,2,125152,1,11468.98,56.32923,1,11,1,120.4852,17.69811,0,0,0,138.1833,0,0,0,5,0,2,82.1,17.4,0,,900,900,0,0,.6931472,6.802395,1,0,0,1,0,0,60.89297,9.347488,.6931472,4.928581,1 2,1,100,0,3,125152,1,11468.98,57.32923,1,11,1,126.5356,42.39312,52.37838,0,944.2113,1165.518,1,0,0,14,0,2,82.1,17.4,0,,900,900,0,0,.6931472,6.802395,1,0,0,1,0,0,60.89297,9.347488,.6931472,7.060921,1 2,1,100,0,1,125153,1,11468.98,59.01711,0,7,1,20.61249,5.624264,0,0,0,26.23675,0,0,0,3,0,2,87.4,13,0,,900,900,0,0,.6931472,6.802395,1,0,0,1,0,0,59.25336,9.347488,.6931472,3.267161,1 2,1,100,0,2,125153,1,11468.98,60.01711,0,7,1,18.86792,0,0,0,0,18.86792,0,0,0,3,0,2,87.4,13,0,,900,900,0,0,.6931472,6.802395,1,0,0,1,0,0,59.25336,9.347488,.6931472,2.937463,1 2,1,100,0,3,125153,1,11468.98,61.01711,0,7,1,80.09828,3.759214,45.18919,0,0,129.0467,0,0,0,5,0,2,87.4,13,0,,900,900,0,0,.6931472,6.802395,1,0,0,1,0,0,59.25336,9.347488,.6931472,4.860174,1 7,1,25,0,1,125159,0,7586.229,10.00411,1,12,1,4.711425,2.915194,0,0,0,7.626619,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,0,3.258096,8.294049,0,0,0,78.48192,8.934221,1.609438,2.031645,1 7,1,25,0,2,125159,0,7586.229,11.00411,1,12,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,0,3.258096,8.294049,0,0,0,78.48192,8.934221,1.609438,,0 7,1,25,0,3,125159,0,7586.229,12.00411,1,12,1,32.92383,28.55037,0,0,0,61.4742,0,0,0,5,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,0,3.258096,8.294049,0,0,0,78.48192,8.934221,1.609438,4.118618,1 7,1,25,0,4,125159,0,7586.229,13.00411,1,12,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,0,3.258096,8.294049,0,0,0,78.48192,8.934221,1.609438,,0 7,1,25,0,5,125159,0,7586.229,14.00411,1,12,1,10.42101,0,0,0,0,10.42101,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,0,3.258096,8.294049,0,0,0,78.48192,8.934221,1.609438,2.343824,1 7,1,25,0,1,125160,0,7586.229,32.61328,0,13,1,17.66784,0,0,191.4016,0,17.66784,0,0,16,0,0,5,60,0,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,0,0,0,77.5937,8.934221,1.609438,2.871746,1 7,1,25,0,2,125160,0,7586.229,33.61328,0,13,1,0,0,0,0,0,0,0,0,0,0,0,5,60,0,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,0,0,0,77.5937,8.934221,1.609438,,0 7,1,25,0,3,125160,0,7586.229,34.61328,0,13,1,9.336609,7.174447,0,0,0,16.51106,0,0,0,2,0,5,60,0,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,0,0,0,77.5937,8.934221,1.609438,2.80403,1 7,1,25,0,4,125160,0,7586.229,35.61328,0,13,1,5.469462,4.010939,0,0,0,9.480401,0,0,0,1,0,5,60,0,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,0,0,0,77.5937,8.934221,1.609438,2.249227,1 7,1,25,0,5,125160,0,7586.229,36.61328,0,13,1,0,0,0,0,0,0,0,0,0,0,0,5,60,0,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,0,0,0,77.5937,8.934221,1.609438,,0 7,1,25,0,1,125161,0,7586.229,32.50377,1,12,1,15.90106,51.88457,0,459.364,0,67.78563,0,0,30,2,0,5,40,26.1,1,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,0,0,0,79.16502,8.934221,1.609438,4.21635,1 7,1,25,0,2,125161,0,7586.229,33.50377,1,12,1,70.08086,50.88949,0,0,5875.984,5996.954,2,0,0,1,11,5,40,26.1,1,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,0,0,0,79.16502,8.934221,1.609438,8.699007,1 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7,1,25,0,2,125163,0,7586.229,9.309377,0,12,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,0,0,0,78.9959,8.934221,1.609438,,0 7,1,25,0,3,125163,0,7586.229,10.30938,0,12,1,22.60442,3.847666,0,0,0,26.45209,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,0,0,0,78.9959,8.934221,1.609438,3.275335,1 7,1,25,0,4,125163,0,7586.229,11.30938,0,12,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,0,0,0,78.9959,8.934221,1.609438,,0 7,1,25,0,5,125163,0,7586.229,12.30938,0,12,1,32.51355,0,0,0,0,32.51355,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,0,0,0,78.9959,8.934221,1.609438,3.481657,1 6,1,25,0,1,125164,0,7854.839,61.42642,0,13,1,15.90106,14.25206,62.77385,0,0,92.92697,0,0,0,1,1,3,85.3,30.4,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,77.34652,8.969012,1.098612,4.531814,1 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8,1,50,1,1,125183,0,14684.86,47.6961,0,9,1,5.995204,0,0,0,0,5.995204,0,0,0,1,0,3,87.4,13,0,,799,799,0,0,1.098612,6.683361,0,3.931826,7.376508,0,1,0,64.34435,9.594641,1.098612,1.79096,1 8,1,50,1,2,125183,0,14684.86,48.6961,0,9,1,21.90581,15.32311,26.90033,0,0,64.12924,0,0,0,1,2,3,87.4,13,0,,799,799,0,0,1.098612,6.683361,0,3.931826,7.376508,0,1,0,64.34435,9.594641,1.098612,4.160901,1 8,1,50,1,3,125183,0,14684.86,49.6961,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,87.4,13,0,,799,799,0,0,1.098612,6.683361,0,3.931826,7.376508,0,1,0,64.34435,9.594641,1.098612,,0 3,1,100,0,1,125184,0,12770.47,15.7755,0,12,1,2.944641,0,0,0,0,2.944641,0,0,0,1,0,6,88.4,0,0,,1000,1000,1,0,1.791759,6.907755,1,0,0,1,0,0,73.87741,9.454969,1.791759,1.079987,1 3,1,100,0,2,125184,0,12770.47,16.7755,0,12,1,33.42318,4.366577,0,0,0,37.78976,0,0,0,4,0,6,88.4,0,0,,1000,1000,1,0,1.791759,6.907755,1,0,0,1,0,0,73.87741,9.454969,1.791759,3.632038,1 3,1,100,0,3,125184,0,12770.47,17.7755,0,12,1,105.0369,0,0,0,0,105.0369,0,0,0,12,0,6,88.4,0,0,,1000,1000,1,0,1.791759,6.907755,1,0,0,1,0,0,73.87741,9.454969,1.791759,4.654311,1 3,1,100,0,1,125185,0,12770.47,43.87132,0,12,1,34.74676,20.81861,25.84806,0,0,81.41343,0,0,0,3,1,6,58.9,17.4,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,0,1,0,56.85956,9.454969,1.791759,4.39954,1 3,1,100,0,2,125185,0,12770.47,44.87132,0,12,1,22.64151,18.92183,42.81401,0,0,84.37736,0,0,0,2,1,6,58.9,17.4,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,0,1,0,56.85956,9.454969,1.791759,4.435299,1 3,1,100,0,3,125185,0,12770.47,45.87132,0,12,1,91.40049,6.388206,46.90909,0,0,144.6978,0,0,0,2,4,6,58.9,17.4,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,0,1,0,56.85956,9.454969,1.791759,4.974648,1 3,1,100,0,1,125186,0,12770.47,11.95072,1,12,1,2.944641,0,0,0,0,2.944641,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,1,0,0,1,0,0,78.63347,9.454969,1.791759,1.079987,1 3,1,100,0,2,125186,0,12770.47,12.95072,1,12,1,40.43127,0,11.10512,0,0,51.53639,0,0,0,3,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,1,0,0,1,0,0,78.63347,9.454969,1.791759,3.942288,1 3,1,100,0,3,125186,0,12770.47,13.95072,1,12,1,12.77641,4.078624,0,0,0,16.85504,0,0,0,2,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,1,0,0,1,0,0,78.63347,9.454969,1.791759,2.82465,1 3,1,100,0,1,125187,0,12770.47,14.44216,0,12,1,12.95642,8.36278,0,0,0,21.3192,0,0,0,2,0,6,77.9,8.7,0,,1000,1000,1,0,1.791759,6.907755,1,0,0,1,0,0,73.87741,9.454969,1.791759,3.059608,1 3,1,100,0,2,125187,0,12770.47,15.44216,0,12,1,11.32076,4.851752,0,0,0,16.17251,0,0,0,2,0,6,77.9,8.7,0,,1000,1000,1,0,1.791759,6.907755,1,0,0,1,0,0,73.87741,9.454969,1.791759,2.783313,1 3,1,100,0,3,125187,0,12770.47,16.44216,0,12,1,6.879607,6.388206,0,0,0,13.26781,0,0,0,1,0,6,77.9,8.7,0,,1000,1000,1,0,1.791759,6.907755,1,0,0,1,0,0,73.87741,9.454969,1.791759,2.585341,1 3,1,100,0,1,125188,0,12770.47,43.46064,1,12,1,27.38516,10.01178,0,0,0,37.39694,0,0,0,3,0,6,71.6,13,1,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,71.8888,9.454969,1.791759,3.621589,1 3,1,100,0,2,125188,0,12770.47,44.46064,1,12,1,24.25876,17.00809,58.59299,0,0,99.85984,0,0,0,1,1,6,71.6,13,1,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,71.8888,9.454969,1.791759,4.603767,1 3,1,100,0,3,125188,0,12770.47,45.46064,1,12,1,113.7592,0,0,0,785.9607,899.7199,1,0,0,4,0,6,71.6,13,1,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,71.8888,9.454969,1.791759,6.802083,1 3,1,100,0,1,125189,0,12770.47,17.13895,0,12,1,159.5995,8.863369,0,0,0,168.4629,0,0,0,20,0,6,71.6,21.7,0,,1000,1000,1,0,1.791759,6.907755,1,0,0,1,0,0,73.87741,9.454969,1.791759,5.126716,1 3,1,100,0,2,125189,0,12770.47,18.13895,0,12,1,81.9407,142.3989,44.86253,0,0,269.2021,0,0,0,15,1,6,71.6,21.7,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,73.87741,9.454969,1.791759,5.595463,1 3,1,100,0,3,125189,0,12770.47,19.13895,0,12,1,124.8157,139.9853,37.27273,0,0,302.0737,0,0,0,11,1,6,71.6,21.7,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,73.87741,9.454969,1.791759,5.710671,1 11,1,0,0,1,125214,0,6866.625,54.21492,1,10,1,588.0447,447.4853,0,0,1195.518,2231.048,1,0,0,69,0,2,76.3,13.73189,1,,0,598,0,0,.6931472,6.393591,0,0,0,0,1,0,50.56934,8.834574,.6931472,7.710227,1 11,1,0,0,2,125214,0,6866.625,55.21492,1,10,1,496.6146,343.035,25.33693,0,576.097,1441.084,1,0,0,58,1,2,76.3,13.73189,1,,0,598,0,0,.6931472,6.393591,0,0,0,0,1,0,50.56934,8.834574,.6931472,7.27315,1 11,1,0,0,3,125214,0,6866.625,56.21492,1,10,1,799.8133,335.2776,28.2457,0,41.27764,1204.614,0,0,0,63,1,2,76.3,13.73189,1,,0,598,0,0,.6931472,6.393591,0,0,0,0,1,0,50.56934,8.834574,.6931472,7.093915,1 11,1,0,0,1,125215,0,6866.625,49.56879,0,9,1,17.66784,0,0,0,0,17.66784,0,0,0,2,0,2,87.5,13.73189,1,,0,598,0,0,.6931472,6.393591,0,0,0,0,0,0,70.33569,8.834574,.6931472,2.871746,1 11,1,0,0,2,125215,0,6866.625,50.56879,0,9,1,74.93262,9.347709,28.57143,0,0,112.8518,0,0,0,3,1,2,87.5,13.73189,1,,0,598,0,0,.6931472,6.393591,0,0,0,0,0,0,70.33569,8.834574,.6931472,4.726075,1 11,1,0,0,3,125215,0,6866.625,51.56879,0,9,1,18.18182,8.255528,23.11057,0,0,49.54791,0,0,0,2,1,2,87.5,13.73189,1,,0,598,0,0,.6931472,6.393591,0,0,0,0,0,0,70.33569,8.834574,.6931472,3.90294,1 11,1,0,1,1,125216,0,9106.079,6.171116,0,12,1,80.01189,26.79952,0,0,286.8055,393.6169,1,0,0,11,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,0,0,0,84.24345,9.116807,1.386294,5.975378,1 11,1,0,1,2,125216,0,9106.079,7.171116,0,12,1,198.6935,16.08601,0,0,0,214.7795,0,0,0,9,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,0,0,0,84.24345,9.116807,1.386294,5.369612,1 11,1,0,1,3,125216,0,9106.079,8.171116,0,12,1,34.68781,16.16948,0,0,0,50.85728,0,0,0,5,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,0,0,0,84.24345,9.116807,1.386294,3.929023,1 11,1,0,1,4,125216,0,9106.079,9.171116,0,12,1,23.86416,7.755851,0,0,0,31.62001,0,0,0,3,0,3,74.36826,13.73189,0,,0,0,1,0,1.098612,0,0,0,0,0,0,0,84.24345,9.116807,1.098612,3.45379,1 11,1,0,1,5,125216,0,9106.079,10.17112,0,12,1,153.8704,35.07783,0,0,0,188.9483,0,0,0,8,0,3,74.36826,13.73189,0,,0,0,1,0,1.098612,0,0,0,0,0,0,0,84.24345,9.116807,1.098612,5.241473,1 11,1,0,1,1,125217,0,9106.079,10.39288,0,12,1,36.28793,4.46163,0,0,0,40.74955,0,0,0,6,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,74.06646,9.116807,1.386294,3.707445,1 11,1,0,1,2,125217,0,9106.079,11.39288,0,12,1,18.50844,5.960806,0,0,0,24.46924,0,0,0,3,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,74.06646,9.116807,1.386294,3.197417,1 11,1,0,1,3,125217,0,9106.079,12.39288,0,12,1,23.78593,6.665015,0,0,0,30.45094,0,0,0,4,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,74.06646,9.116807,1.386294,3.416117,1 11,1,0,1,4,125217,0,9106.079,13.39288,0,12,1,15.14456,8.926113,0,0,0,24.07067,0,0,0,3,0,3,74.36826,13.73189,0,,0,0,1,0,1.098612,0,0,0,0,1,0,0,74.06646,9.116807,1.098612,3.180994,1 11,1,0,1,5,125217,0,9106.079,14.39288,0,12,1,23.55911,1.262095,0,0,0,24.8212,0,0,0,2,0,3,74.36826,13.73189,0,,0,0,1,0,1.098612,0,0,0,0,1,0,0,74.06646,9.116807,1.098612,3.211698,1 11,1,0,1,1,125218,0,9106.079,44.80219,0,10,1,197.204,6.097561,0,0,0,203.3016,0,0,0,6,0,4,80,17.4,0,,0,0,0,0,1.386294,0,0,0,0,0,0,0,69.65557,9.116807,1.386294,5.314691,1 11,1,0,1,2,125218,0,9106.079,45.80219,0,10,1,166.0316,21.09418,0,0,7141.557,7328.683,2,0,0,10,0,4,80,17.4,0,,0,0,0,0,1.386294,0,0,0,0,0,0,0,69.65557,9.116807,1.386294,8.899551,1 11,1,0,1,3,125218,0,9106.079,46.80219,0,10,1,444.9951,90.65907,29.58375,0,0,565.2379,0,0,0,12,31,4,80,17.4,0,,0,0,0,0,1.386294,0,0,0,0,0,0,0,69.65557,9.116807,1.386294,6.337246,1 11,1,0,1,1,125219,0,9106.079,33.42916,1,12,1,249.8513,130.3093,3.777514,0,0,383.9381,0,0,0,35,0,4,55.8,13,0,,0,0,0,0,1.386294,0,0,0,0,0,0,0,78.52583,9.116807,1.386294,5.950481,1 11,1,0,1,2,125219,0,9106.079,34.42916,1,12,1,381.0561,177.006,4.899292,0,1644.339,2207.3,1,0,0,9,15,4,55.8,13,0,,0,0,0,0,1.386294,0,0,0,0,0,0,0,78.52583,9.116807,1.386294,7.699525,1 11,1,0,1,3,125219,0,9106.079,35.42916,1,12,1,98.11695,149.3062,170.9613,59.46482,0,418.3846,0,0,4,6,0,4,55.8,13,0,,0,0,0,0,1.386294,0,0,0,0,0,0,0,78.52583,9.116807,1.386294,6.036401,1 11,1,0,1,4,125219,0,9106.079,36.42916,1,12,1,54.61221,145.5484,0,80.31207,1999.358,2199.518,1,0,5,6,0,3,55.8,13,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,78.52583,9.116807,1.098612,7.695993,1 11,1,0,1,5,125219,0,9106.079,37.42916,1,12,1,110.223,271.9941,257.0467,117.7955,0,639.2638,0,0,8,14,0,3,55.8,13,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,78.52583,9.116807,1.098612,6.460317,1 2,1,100,0,1,125220,0,12213.6,35.87132,0,17,1,33.57314,10.8813,0,0,0,44.45444,0,0,0,5,0,5,77.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,72.73786,9.410387,1.609438,3.794465,1 2,1,100,0,2,125220,0,12213.6,36.87132,0,17,1,23.54874,7.338445,0,0,0,30.88719,0,0,0,4,0,5,77.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,72.73786,9.410387,1.609438,3.430341,1 2,1,100,0,3,125220,0,12213.6,37.87132,0,17,1,43.81047,4.189526,37.0773,0,0,85.07731,0,0,0,2,1,5,77.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,72.73786,9.410387,1.609438,4.44356,1 2,1,100,0,4,125220,0,12213.6,38.87132,0,17,1,0,0,0,0,0,0,0,0,0,0,0,5,77.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,72.73786,9.410387,1.609438,,0 2,1,100,0,5,125220,0,12213.6,39.87132,0,17,1,0,0,0,0,0,0,0,0,0,0,0,5,77.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,72.73786,9.410387,1.609438,,0 2,1,100,0,1,125221,0,12213.6,10.94045,0,16,1,42.86571,.5395684,0,0,0,43.40528,0,0,0,1,2,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,87.05311,9.410387,1.609438,3.770581,1 2,1,100,0,2,125221,0,12213.6,11.94045,0,16,1,29.84666,8.598028,26.85104,0,0,65.29573,0,0,0,2,1,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,87.05311,9.410387,1.609438,4.178926,1 2,1,100,0,3,125221,0,12213.6,12.94045,0,16,1,7.381546,8.254364,0,0,0,15.63591,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,87.05311,9.410387,1.609438,2.74957,1 2,1,100,0,4,125221,0,12213.6,13.94045,0,16,1,195.6893,3.665283,0,0,0,199.3545,0,0,0,5,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,87.05311,9.410387,1.609438,5.295085,1 2,1,100,0,5,125221,0,12213.6,14.94045,0,16,1,90.71096,0,0,0,0,90.71096,0,0,0,3,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,87.05311,9.410387,1.609438,4.507678,1 2,1,100,0,1,125222,0,12213.6,33.19096,1,16,1,45.20384,15.19784,0,0,0,60.40168,0,0,0,3,0,5,71.3,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,80.14037,9.410387,1.609438,4.101017,1 2,1,100,0,2,125222,0,12213.6,34.19096,1,16,1,21.35816,7.174151,0,0,0,28.53231,0,0,0,3,0,5,71.3,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,80.14037,9.410387,1.609438,3.351037,1 2,1,100,0,3,125222,0,12213.6,35.19096,1,16,1,23.94015,4.239401,0,0,0,28.17955,0,0,0,3,0,5,71.3,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,80.14037,9.410387,1.609438,3.338597,1 2,1,100,0,4,125222,0,12213.6,36.19096,1,16,1,6.915629,5.693868,0,0,0,12.6095,0,0,0,1,0,5,71.3,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,80.14037,9.410387,1.609438,2.53445,1 2,1,100,0,5,125222,0,12213.6,37.19096,1,16,1,49.93652,2.653407,0,0,0,52.58993,0,0,0,2,0,5,71.3,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,80.14037,9.410387,1.609438,3.962525,1 2,1,100,0,1,125223,0,12213.6,7.750855,0,16,1,34.77218,5.635491,0,0,0,40.40767,0,0,0,3,1,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,87.05311,9.410387,1.609438,3.69902,1 2,1,100,0,2,125223,0,12213.6,8.750855,0,16,1,13.96495,10.35049,0,0,0,24.31544,0,0,0,2,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,87.05311,9.410387,1.609438,3.191112,1 2,1,100,0,3,125223,0,12213.6,9.750855,0,16,1,29.55112,17.95511,0,0,0,47.50623,0,0,0,1,1,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,87.05311,9.410387,1.609438,3.860861,1 2,1,100,0,4,125223,0,12213.6,10.75086,0,16,1,15.3988,9.22084,0,0,0,24.61964,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,87.05311,9.410387,1.609438,3.203545,1 2,1,100,0,5,125223,0,12213.6,11.75086,0,16,1,11.84934,0,0,0,0,11.84934,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,87.05311,9.410387,1.609438,2.472273,1 2,1,100,0,1,125224,0,12213.6,6.606434,1,16,1,31.41487,10.52158,0,0,0,41.93645,0,0,0,2,1,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,86.53913,9.410387,1.609438,3.736156,1 2,1,100,0,2,125224,0,12213.6,7.606434,1,16,1,24.26068,11.22672,0,0,0,35.4874,0,0,0,3,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,86.53913,9.410387,1.609438,3.569178,1 2,1,100,0,3,125224,0,12213.6,8.606434,1,16,1,1.995013,0,0,0,0,1.995013,0,0,0,0,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,86.53913,9.410387,1.609438,.6906503,1 2,1,100,0,4,125224,0,12213.6,9.606434,1,16,1,14.01568,0,0,0,0,14.01568,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,86.53913,9.410387,1.609438,2.640176,1 2,1,100,0,5,125224,0,12213.6,10.60643,1,16,1,13.22471,0,0,0,0,13.22471,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,86.53913,9.410387,1.609438,2.582087,1 11,1,0,1,1,125229,0,22318.24,41.1143,1,12,1,151.6786,88.81295,26.6307,0,0,267.1223,0,0,0,16,0,8,74.7,21.7,1,,0,0,0,0,2.079442,0,0,0,0,1,0,0,68.03587,10.0132,2.079442,5.587707,1 11,1,0,1,2,125229,0,22318.24,42.1143,1,12,1,225.0822,26.31435,0,0,0,251.3965,0,0,0,16,0,8,74.7,21.7,1,,0,0,0,0,2.079442,0,0,0,0,1,0,0,68.03587,10.0132,2.079442,5.527031,1 11,1,0,1,3,125229,0,22318.24,43.1143,1,12,1,185.2868,61.14713,35.91022,0,0,282.3441,0,0,0,17,0,9,74.7,21.7,1,,0,0,0,0,2.197225,0,0,0,0,1,0,0,68.03587,10.0132,2.197225,5.643126,1 11,1,0,1,1,125230,0,22318.24,17.30869,0,12,1,5.395683,6.564748,0,0,0,11.96043,0,0,0,0,0,8,80,13,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,80.52389,10.0132,2.079442,2.481604,1 11,1,0,1,2,125230,0,22318.24,18.30869,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,80,13,0,,0,0,0,0,2.079442,0,0,0,0,0,0,0,80.52389,10.0132,2.079442,,0 11,1,0,1,3,125230,0,22318.24,19.30869,0,12,1,17.45636,9.077307,0,0,0,26.53367,0,0,0,3,0,9,80,13,0,,0,0,0,0,2.197225,0,0,0,0,0,0,0,80.52389,10.0132,2.197225,3.278414,1 11,1,0,1,1,125231,0,22318.24,18.41205,0,12,1,13.48921,5.749401,0,0,0,19.23861,0,0,0,2,0,8,52.6,0,0,,0,0,0,0,2.079442,0,0,0,0,0,0,0,78.67783,10.0132,2.079442,2.956919,1 11,1,0,1,2,125231,0,22318.24,19.41205,0,12,1,49.8357,15.33406,32.04819,0,0,97.21796,0,0,0,4,0,8,52.6,0,0,,0,0,0,0,2.079442,0,0,0,0,0,0,0,78.67783,10.0132,2.079442,4.576955,1 11,1,0,1,3,125231,0,22318.24,20.41205,0,12,1,32.91771,8.304239,0,0,700.02,741.2419,1,0,0,3,0,9,52.6,0,0,,0,0,0,0,2.197225,0,0,0,0,0,0,0,78.67783,10.0132,2.197225,6.608327,1 11,1,0,1,1,125232,0,22318.24,14.19576,0,12,1,59.95204,14.92806,0,0,0,74.8801,0,0,0,6,0,8,80,4.3,0,,0,0,1,0,2.079442,0,0,0,0,1,0,0,74.01256,10.0132,2.079442,4.315888,1 11,1,0,1,2,125232,0,22318.24,15.19576,0,12,1,21.90581,35.20263,0,0,0,57.10843,0,0,0,3,0,8,80,4.3,0,,0,0,1,0,2.079442,0,0,0,0,1,0,0,74.01256,10.0132,2.079442,4.044952,1 11,1,0,1,3,125232,0,22318.24,16.19576,0,12,1,19.95012,16.7581,0,0,0,36.70823,0,0,0,3,0,9,80,4.3,0,,0,0,1,0,2.197225,0,0,0,0,1,0,0,74.01256,10.0132,2.197225,3.603001,1 11,1,0,1,1,125233,0,22318.24,16.1807,1,12,1,90.22782,44.44844,27.56595,0,0,162.2422,0,0,0,7,0,8,75.8,0,0,,0,0,1,1,2.079442,0,0,0,0,0,0,0,74.24654,10.0132,2.079442,5.08909,1 11,1,0,1,2,125233,0,22318.24,17.1807,1,12,1,19.16758,27.40964,0,0,491.6375,538.2147,1,0,0,3,0,8,75.8,0,0,,0,0,1,1,2.079442,0,0,0,0,0,0,0,74.24654,10.0132,2.079442,6.288258,1 11,1,0,1,3,125233,0,22318.24,18.1807,1,12,1,334.2444,11.47132,0,0,11.97007,357.6858,0,0,0,7,0,9,75.8,0,0,,0,0,0,0,2.197225,0,0,0,0,0,0,0,74.24654,10.0132,2.197225,5.879655,1 11,1,0,1,1,125234,0,22318.24,43.61123,0,16,1,67.14629,178.0456,55.44365,0,0,300.6355,0,0,0,8,0,8,81.1,26.1,0,,0,0,0,0,2.079442,0,0,0,0,0,0,0,77.31422,10.0132,2.079442,5.705899,1 11,1,0,1,2,125234,0,22318.24,44.61123,0,16,1,65.71741,122.6451,0,0,0,188.3625,0,0,0,8,0,8,81.1,26.1,0,,0,0,0,0,2.079442,0,0,0,0,0,0,0,77.31422,10.0132,2.079442,5.238369,1 11,1,0,1,3,125234,0,22318.24,45.61123,0,16,1,70.82294,125.1122,46.90773,0,0,242.8429,0,0,0,4,0,9,81.1,26.1,0,,0,0,0,0,2.197225,0,0,0,0,0,0,0,77.31422,10.0132,2.197225,5.492415,1 11,1,0,1,1,125235,0,22318.24,10.42026,0,12,1,26.3789,21.07314,0,0,0,47.45204,0,0,0,4,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,84.64054,10.0132,2.079442,3.85972,1 11,1,0,1,2,125235,0,22318.24,11.42026,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,84.64054,10.0132,2.079442,,0 11,1,0,1,3,125235,0,22318.24,12.42026,0,12,1,41.39651,10.69825,0,0,0,52.09476,0,0,0,4,0,9,74.36826,13.73189,0,,0,0,1,0,2.197225,0,0,0,0,0,0,0,84.64054,10.0132,2.197225,3.953064,1 11,1,0,1,1,125236,0,22318.24,11.50445,0,12,1,59.95204,63.31535,64.04076,0,0,187.3082,0,0,0,8,0,8,74.36826,13.73189,1,,0,0,1,0,2.079442,0,0,0,0,1,0,0,74.46355,10.0132,2.079442,5.232755,1 11,1,0,1,2,125236,0,22318.24,12.50445,0,12,1,23.00109,41.15005,54.45783,0,0,118.609,0,0,0,4,0,8,74.36826,13.73189,1,,0,0,1,0,2.079442,0,0,0,0,1,0,0,74.46355,10.0132,2.079442,4.775832,1 11,1,0,1,3,125236,0,22318.24,13.50445,0,12,1,68.82793,62.04489,55.70075,0,0,186.5736,0,0,0,7,0,9,74.36826,13.73189,1,,0,0,1,0,2.197225,0,0,0,0,1,0,0,74.46355,10.0132,2.197225,5.228826,1 11,1,0,1,1,125258,0,7810.794,41.70842,0,12,1,78.61987,51.86199,7.703748,0,0,138.1856,0,0,0,7,0,5,77.9,13,1,,0,232,0,0,1.609438,5.446737,0,0,0,1,0,0,63.76923,8.96339,1.609438,4.928598,1 11,1,0,1,2,125258,0,7810.794,42.70842,0,12,1,192.1611,112.0577,87.09853,0,2911.241,3302.559,3,0,0,19,1,5,77.9,13,1,,0,232,0,0,1.609438,5.446737,0,0,0,1,0,0,63.76923,8.96339,1.609438,8.102453,1 11,1,0,1,3,125258,0,7810.794,43.70842,0,12,1,663.4787,111.7344,26.26363,0,1011.516,1812.993,1,0,0,0,2,5,77.9,13,1,,0,232,0,0,1.609438,5.446737,0,0,0,1,0,0,63.76923,8.96339,1.609438,7.502734,1 11,1,0,1,1,125259,0,7810.794,31.87406,1,10,1,101.7252,56.00238,0,0,0,157.7275,0,0,0,12,0,5,80,17.4,0,,0,232,0,0,1.609438,5.446737,0,0,0,0,0,0,76.00816,8.96339,1.609438,5.060869,1 11,1,0,1,2,125259,0,7810.794,32.87406,1,10,1,60.42461,36.89167,0,0,0,97.31628,0,0,0,7,0,5,80,17.4,0,,0,232,0,0,1.609438,5.446737,0,0,0,0,0,0,76.00816,8.96339,1.609438,4.577966,1 11,1,0,1,3,125259,0,7810.794,33.87406,1,10,1,26.75917,31.91774,0,0,0,58.67691,0,0,0,3,0,5,80,17.4,0,,0,232,0,0,1.609438,5.446737,0,0,0,0,0,0,76.00816,8.96339,1.609438,4.072046,1 11,1,0,1,1,125260,0,7810.794,10.96509,0,10,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,0,232,1,0,1.609438,5.446737,0,0,0,0,0,0,79.16512,8.96339,1.609438,,0 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4,1,100,1,1,125433,0,2454.715,17.00479,1,12,1,38.3693,.8693045,0,0,0,39.23861,0,0,0,1,0,4,76.8,13,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,64.73034,7.806173,1.386294,3.669661,1 4,1,100,1,2,125433,0,2454.715,18.00479,1,12,1,18.15444,2.102957,33.7678,0,0,54.02519,0,0,0,1,1,4,76.8,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,64.73034,7.806173,1.386294,3.98945,1 4,1,100,1,3,125433,0,2454.715,19.00479,1,12,1,22.44389,0,0,0,0,22.44389,0,0,0,3,0,4,76.8,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,64.73034,7.806173,1.386294,3.111018,1 4,1,100,1,1,125434,0,2454.715,9.601643,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,1,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,76.38216,7.806173,1.386294,,0 4,1,100,1,2,125434,0,2454.715,10.60164,1,12,1,52.35487,0,0,0,0,52.35487,0,0,0,3,1,4,74.36826,13.73189,1,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,76.38216,7.806173,1.386294,3.958045,1 4,1,100,1,3,125434,0,2454.715,11.60164,1,12,1,18.95262,0,0,0,0,18.95262,0,0,0,1,0,4,74.36826,13.73189,1,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,76.38216,7.806173,1.386294,2.941942,1 4,1,100,1,1,125435,0,2454.715,47.8987,1,12,1,53.95683,68.91487,0,0,0,122.8717,0,0,0,8,0,4,42.1,39.1,1,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,1,0,54.82101,7.806173,1.386294,4.811141,1 4,1,100,1,2,125435,0,2454.715,48.8987,1,12,1,60.78861,79.4414,30.33406,0,325.3012,495.8653,1,0,0,6,1,4,42.1,39.1,1,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,1,0,54.82101,7.806173,1.386294,6.206304,1 4,1,100,1,3,125435,0,2454.715,49.8987,1,12,1,22.44389,2.009975,0,0,0,24.45387,0,0,0,3,0,4,42.1,39.1,1,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,1,0,54.82101,7.806173,1.386294,3.196788,1 6,1,25,1,1,125454,0,1093.672,60.81862,1,6,1,32.71862,20.09518,0,0,0,52.8138,0,0,0,3,0,1,75.8,21.7,1,,226,226,0,0,0,5.420535,0,3.258096,6.806829,1,0,0,62.52559,6.99821,0,3.966773,1 6,1,25,1,2,125454,0,1093.672,61.81862,1,6,1,26.12956,15.77572,0,0,0,41.90528,0,0,0,3,1,1,75.8,21.7,1,,226,226,0,0,0,5.420535,0,3.258096,6.806829,1,0,0,62.52559,6.99821,0,3.735412,1 6,1,25,1,3,125454,0,1093.672,62.81862,1,6,1,16.84836,6.868186,0,0,0,23.71655,0,0,0,3,0,1,75.8,21.7,1,,226,226,0,0,0,5.420535,0,3.258096,6.806829,1,0,0,62.52559,6.99821,0,3.166173,1 6,1,25,1,1,125455,0,3467.742,21.80698,1,12,1,27.95955,0,41.047,0,0,69.00655,0,0,0,2,0,1,68.4,8.7,0,,530,530,0,0,0,6.272877,0,3.258096,7.659172,0,0,0,79.25372,8.151547,0,4.234201,1 6,1,25,1,2,125455,0,3467.742,22.80698,1,12,1,26.12956,9.450191,13.60915,0,0,49.1889,0,0,0,1,1,1,68.4,8.7,0,,530,530,0,0,0,6.272877,0,3.258096,7.659172,0,0,0,79.25372,8.151547,0,3.895668,1 6,1,25,1,3,125455,0,3467.742,23.80698,1,12,1,20.19326,0,0,0,0,20.19326,0,0,0,1,0,1,68.4,8.7,0,,530,530,0,0,0,6.272877,0,3.258096,7.659172,0,0,0,79.25372,8.151547,0,3.005349,1 3,1,100,0,1,125484,0,4986.759,33.18549,0,11,1,18.8457,2.915194,0,0,0,21.76089,0,0,0,3,0,3,77.9,0,0,,1000,1000,0,0,1.098612,6.907755,1,0,0,1,0,0,67.92956,8.514742,1.098612,3.080115,1 3,1,100,0,2,125484,0,4986.759,34.18549,0,11,1,21.56334,0,0,0,0,21.56334,0,0,0,1,0,3,77.9,0,0,,1000,1000,0,0,1.098612,6.907755,1,0,0,1,0,0,67.92956,8.514742,1.098612,3.070995,1 3,1,100,0,3,125484,0,4986.759,35.18549,0,11,1,0,0,0,0,0,0,0,0,0,0,0,3,77.9,0,0,,1000,1000,0,0,1.098612,6.907755,1,0,0,1,0,0,67.92956,8.514742,1.098612,,0 3,1,100,0,1,125485,0,4986.759,6.672143,0,12,1,12.36749,28.97527,9.234393,0,360.424,411.0012,1,0,0,3,0,3,74.36826,13.73189,0,,1000,1000,1,0,1.098612,6.907755,1,0,0,1,0,0,73.90472,8.514742,1.098612,6.018596,1 3,1,100,0,2,125485,0,4986.759,7.672143,0,12,1,138.7062,37.19677,0,0,0,175.903,0,0,0,17,0,3,74.36826,13.73189,0,,1000,1000,1,0,1.098612,6.907755,1,0,0,1,0,0,73.90472,8.514742,1.098612,5.169932,1 3,1,100,0,3,125485,0,4986.759,8.672142,0,12,1,80.09828,7.149877,0,0,0,87.24815,0,0,0,21,1,3,74.36826,13.73189,0,,1000,1000,1,0,1.098612,6.907755,1,0,0,1,0,0,73.90472,8.514742,1.098612,4.468756,1 3,1,100,0,1,125486,0,4986.759,29.27858,1,12,1,19.43463,5.859835,0,0,0,25.29446,0,0,0,5,0,3,44.2,39.1,1,,1000,1000,0,0,1.098612,6.907755,1,0,0,1,0,0,68.93575,8.514742,1.098612,3.230586,1 3,1,100,0,2,125486,0,4986.759,30.27858,1,12,1,62.53369,97.96765,53.36927,0,2370.226,2584.097,2,0,0,5,0,3,44.2,39.1,1,,1000,1000,0,0,1.098612,6.907755,1,0,0,1,0,0,68.93575,8.514742,1.098612,7.857131,1 3,1,100,0,3,125486,0,4986.759,31.27858,1,12,1,33.90664,87.46928,0,0,0,121.3759,0,0,0,3,0,3,44.2,39.1,1,,1000,1000,0,0,1.098612,6.907755,1,0,0,1,0,0,68.93575,8.514742,1.098612,4.798892,1 11,1,0,0,1,125501,1,9055.211,39.57837,1,12,1,348.0216,43.64508,0,0,0,391.6667,0,0,0,10,0,8,45,13.73189,1,,0,0,0,0,2.079442,0,0,0,0,0,0,1,66.24201,9.111206,2.079442,5.970411,1 11,1,0,0,2,125501,1,9055.211,40.57837,1,12,1,59.96714,7.721797,0,0,0,67.68893,0,0,0,1,0,8,45,13.73189,1,,0,0,0,0,2.079442,0,0,0,0,0,0,1,66.24201,9.111206,2.079442,4.214923,1 11,1,0,0,3,125501,1,9055.211,41.57837,1,12,1,3.990025,12.06983,0,0,0,16.05985,0,0,0,1,0,8,45,13.73189,1,,0,0,0,0,2.079442,0,0,0,0,0,0,1,66.24201,9.111206,2.079442,2.776322,1 11,1,0,0,4,125501,1,9055.211,42.57837,1,12,1,13.83126,21.96865,0,0,0,35.79991,0,0,0,2,0,8,45,13.73189,1,,0,0,0,0,2.079442,0,0,0,0,0,0,1,66.24201,9.111206,2.079442,3.577945,1 11,1,0,0,5,125501,1,9055.211,43.57837,1,12,1,26.02624,20.94795,3.537876,0,0,50.51206,0,0,0,1,0,8,45,13.73189,1,,0,0,0,0,2.079442,0,0,0,0,0,0,1,66.24201,9.111206,2.079442,3.922212,1 11,1,0,0,1,125502,1,9055.211,9.535934,1,12,1,64.7482,0,0,0,0,64.7482,0,0,0,2,0,8,74.36826,13.73189,0,,0,0,1,1,2.079442,0,0,0,0,0,0,0,78.46435,9.111206,2.079442,4.170506,1 11,1,0,0,2,125502,1,9055.211,10.53593,1,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,1,2.079442,0,0,0,0,0,0,0,78.46435,9.111206,2.079442,,0 11,1,0,0,3,125502,1,9055.211,11.53593,1,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,1,2.079442,0,0,0,0,0,0,0,78.46435,9.111206,2.079442,,0 11,1,0,0,4,125502,1,9055.211,12.53593,1,12,1,56.93868,0,0,0,0,56.93868,0,0,0,3,0,8,74.36826,13.73189,0,,0,0,1,1,2.079442,0,0,0,0,0,0,0,78.46435,9.111206,2.079442,4.041975,1 11,1,0,0,5,125502,1,9055.211,13.53593,1,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,1,2.079442,0,0,0,0,0,0,0,78.46435,9.111206,2.079442,,0 11,1,0,0,1,125503,1,9055.211,4.971937,0,12,1,35.3717,1.858513,0,0,0,37.23022,0,0,0,1,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,75.5467,9.111206,2.079442,3.617121,1 11,1,0,0,2,125503,1,9055.211,5.971937,0,12,1,0,2.135816,0,0,0,2.135816,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,75.5467,9.111206,2.079442,.7588488,1 11,1,0,0,3,125503,1,9055.211,6.971937,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,75.5467,9.111206,2.079442,,0 11,1,0,0,4,125503,1,9055.211,7.971937,0,12,1,45.50484,0,0,0,0,45.50484,0,0,0,2,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,75.5467,9.111206,2.079442,3.817819,1 11,1,0,0,5,125503,1,9055.211,8.971937,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,75.5467,9.111206,2.079442,,0 11,1,0,0,1,125504,1,9055.211,16.19986,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,63.8,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,75.33212,9.111206,2.079442,,0 11,1,0,0,2,125504,1,9055.211,17.19986,0,12,1,146.2486,0,0,0,0,146.2486,0,0,0,7,0,8,63.8,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,75.33212,9.111206,2.079442,4.985308,1 11,1,0,0,3,125504,1,9055.211,18.19986,0,12,1,52.36908,0,0,0,0,52.36908,0,0,0,5,0,8,63.8,13.73189,0,,0,0,0,0,2.079442,0,0,0,0,0,0,0,75.33212,9.111206,2.079442,3.958316,1 11,1,0,0,4,125504,1,9055.211,19.19986,0,12,1,0,5.928999,0,0,0,5.928999,0,0,0,0,0,8,63.8,13.73189,0,,0,0,0,0,2.079442,0,0,0,0,0,0,0,75.33212,9.111206,2.079442,1.779855,1 11,1,0,0,5,125504,1,9055.211,20.19986,0,12,1,45.2391,0,0,0,0,45.2391,0,0,0,1,0,8,63.8,13.73189,0,,0,0,0,0,2.079442,0,0,0,0,0,0,0,75.33212,9.111206,2.079442,3.811962,1 11,1,0,0,1,125505,1,9055.211,7.827516,0,12,1,25.77938,1.396883,0,0,0,27.17626,0,0,0,2,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,1,0,0,79.24362,9.111206,2.079442,3.302344,1 11,1,0,0,2,125505,1,9055.211,8.827516,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,1,0,0,79.24362,9.111206,2.079442,,0 11,1,0,0,3,125505,1,9055.211,9.827516,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,1,0,0,79.24362,9.111206,2.079442,,0 11,1,0,0,4,125505,1,9055.211,10.82752,0,12,1,5.532504,0,0,0,0,5.532504,0,0,0,1,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,1,0,0,79.24362,9.111206,2.079442,1.71064,1 11,1,0,0,5,125505,1,9055.211,11.82752,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,1,0,0,79.24362,9.111206,2.079442,,0 11,1,0,0,1,125506,1,9055.211,14.91307,0,12,1,31.65468,1.318945,0,0,0,32.97362,0,0,0,2,0,8,80,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,75.33212,9.111206,2.079442,3.495708,1 11,1,0,0,2,125506,1,9055.211,15.91307,0,12,1,190.0986,11.74699,0,0,0,201.8456,0,0,0,2,0,8,80,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,75.33212,9.111206,2.079442,5.307503,1 11,1,0,0,3,125506,1,9055.211,16.91307,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,80,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,75.33212,9.111206,2.079442,,0 11,1,0,0,4,125506,1,9055.211,17.91307,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,80,13.73189,0,,0,0,1,0,2.079442,0,0,0,0,0,0,0,75.33212,9.111206,2.079442,,0 11,1,0,0,5,125506,1,9055.211,18.91307,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,80,13.73189,0,,0,0,0,0,2.079442,0,0,0,0,0,0,0,75.33212,9.111206,2.079442,,0 11,1,0,0,1,125507,1,9055.211,37.17728,0,3,1,0,0,0,0,0,0,0,0,0,0,0,8,73.8,13.73189,0,,0,0,0,0,2.079442,0,0,0,0,1,0,0,62.82508,9.111206,2.079442,,0 11,1,0,0,2,125507,1,9055.211,38.17728,0,3,1,8.214677,4.791895,0,0,699.9124,712.9189,1,0,0,1,0,8,73.8,13.73189,0,,0,0,0,0,2.079442,0,0,0,0,1,0,0,62.82508,9.111206,2.079442,6.569368,1 11,1,0,0,3,125507,1,9055.211,39.17728,0,3,1,0,0,0,0,0,0,0,0,0,0,0,8,73.8,13.73189,0,,0,0,0,0,2.079442,0,0,0,0,1,0,0,62.82508,9.111206,2.079442,,0 11,1,0,0,4,125507,1,9055.211,40.17728,0,3,1,28.5846,5.048409,0,0,0,33.63301,0,0,0,6,0,8,73.8,13.73189,0,,0,0,0,0,2.079442,0,0,0,0,1,0,0,62.82508,9.111206,2.079442,3.515508,1 11,1,0,0,5,125507,1,9055.211,41.17728,0,3,1,0,0,0,0,0,0,0,0,0,0,0,8,73.8,13.73189,0,,0,0,0,0,2.079442,0,0,0,0,1,0,0,62.82508,9.111206,2.079442,,0 11,1,0,0,1,125520,1,9542.002,13.06776,1,8,1,23.79536,8.090423,0,0,0,31.88578,0,0,0,3,0,3,74.36826,13.73189,0,,0,0,1,1,1.098612,0,0,0,0,1,0,0,78.41846,9.163564,1.098612,3.46216,1 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5,1,25,0,4,125535,1,4560.794,57.19576,1,9,1,1629.986,87.47349,369.29,0,10612.44,12699.19,6,0,0,48,99,1,81.3,13.73189,0,,305,305,0,0,0,5.720312,0,3.258096,7.106606,0,1,0,62.11581,8.425471,0,9.449294,1 5,1,25,0,5,125535,1,4560.794,58.19576,1,9,.2684931,1913.957,74.28693,70.22429,0,445.6665,2504.135,1,0,0,8,78,1,81.3,13.73189,0,,305,305,0,0,0,5.720312,0,3.258096,7.106606,0,1,0,62.11581,8.425471,0,7.825698,1 3,1,100,1,1,125558,0,10174.32,14.47775,1,12,1,34.50327,47.81678,0,0,0,82.32005,0,0,0,5,0,5,40,4.3,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,73.93777,9.22772,1.609438,4.410614,1 3,1,100,1,2,125558,0,10174.32,15.47775,1,12,1,53.89222,16.84812,0,0,0,70.74034,0,0,0,8,0,5,40,4.3,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,73.93777,9.22772,1.609438,4.259016,1 3,1,100,1,3,125558,0,10174.32,16.47775,1,12,1,96.25867,20.9663,0,0,0,117.225,0,0,0,14,0,5,40,4.3,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,73.93777,9.22772,1.609438,4.764095,1 3,1,100,1,1,125559,0,10174.32,11.84668,1,12,1,45.50863,13.48602,0,0,0,58.99464,0,0,0,5,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,83.01885,9.22772,1.609438,4.077446,1 3,1,100,1,2,125559,0,10174.32,12.84668,1,12,1,113.337,22.43876,34.69788,0,0,170.4736,0,0,0,10,1,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,83.01885,9.22772,1.609438,5.13858,1 3,1,100,1,3,125559,0,10174.32,13.84668,1,12,1,36.05054,9.088206,11.72943,0,0,56.86819,0,0,0,4,1,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,83.01885,9.22772,1.609438,4.040736,1 3,1,100,1,1,125560,0,10174.32,4.596851,1,12,1,52.94468,21.56454,0,0,0,74.50922,0,0,0,7,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,79.58723,9.22772,1.609438,4.310923,1 3,1,100,1,2,125560,0,10174.32,5.596851,1,12,1,62.0577,19.53185,0,0,0,81.58955,0,0,0,6,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,79.58723,9.22772,1.609438,4.401701,1 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9,1,50,1,3,125567,0,10021.71,38.75565,1,17,1,120.4163,3.320119,1.48662,14.8662,0,125.223,0,0,3,3,0,4,62.1,13,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,79.82717,9.212609,1.386294,4.830096,1 9,1,50,1,1,125568,0,10021.71,6.329911,0,17,1,19.03629,2.825699,0,0,0,21.86199,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,85.78433,9.212609,1.386294,3.084749,1 9,1,50,1,2,125568,0,10021.71,7.329911,0,17,1,34.02286,0,0,0,0,34.02286,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,85.78433,9.212609,1.386294,3.527033,1 9,1,50,1,3,125568,0,10021.71,8.329911,0,17,1,12.3885,0,0,0,0,12.3885,0,0,0,0,1,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,85.78433,9.212609,1.386294,2.516769,1 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9,1,50,1,3,125570,0,10021.71,44.07529,0,10,1,90.68385,1.73439,0,14.8662,0,92.41824,0,0,3,7,0,4,74.7,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,69.59772,9.212609,1.386294,4.526324,1 2,1,100,1,1,125574,0,5724.566,27.76728,1,13,1,0,0,0,0,0,0,0,0,0,0,0,3,77.9,0,0,,359,359,0,0,1.098612,5.883322,1,0,0,1,0,0,72.43401,8.652697,1.098612,,0 2,1,100,1,2,125574,0,5724.566,28.76728,1,13,1,0,0,0,0,0,0,0,0,0,0,0,3,77.9,0,0,,359,359,0,0,1.098612,5.883322,1,0,0,1,0,0,72.43401,8.652697,1.098612,,0 2,1,100,1,3,125574,0,5724.566,29.76728,1,13,1,10.90188,0,0,0,0,10.90188,0,0,0,1,0,3,77.9,0,0,,359,359,0,0,1.098612,5.883322,1,0,0,1,0,0,72.43401,8.652697,1.098612,2.388936,1 2,1,100,1,1,125575,0,5724.566,8.008214,0,13,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,359,359,1,0,1.098612,5.883322,1,0,0,0,0,0,82.44528,8.652697,1.098612,,0 2,1,100,1,2,125575,0,5724.566,9.008214,0,13,1,34.86663,0,0,0,0,34.86663,0,0,0,0,1,3,74.36826,13.73189,0,,359,359,1,0,1.098612,5.883322,1,0,0,0,0,0,82.44528,8.652697,1.098612,3.55153,1 2,1,100,1,3,125575,0,5724.566,10.00821,0,13,1,9.910803,.9910803,0,0,0,10.90188,0,0,0,2,0,3,74.36826,13.73189,0,,359,359,1,0,1.098612,5.883322,1,0,0,0,0,0,82.44528,8.652697,1.098612,2.388936,1 2,1,100,1,1,125576,0,5724.566,27.1102,0,16,1,0,0,0,0,0,0,0,0,0,0,0,3,62.1,26.1,0,,359,359,0,0,1.098612,5.883322,1,0,0,0,0,0,69.46257,8.652697,1.098612,,0 2,1,100,1,2,125576,0,5724.566,28.1102,0,16,1,0,0,0,0,0,0,0,0,0,0,0,3,62.1,26.1,0,,359,359,0,0,1.098612,5.883322,1,0,0,0,0,0,69.46257,8.652697,1.098612,,0 2,1,100,1,3,125576,0,5724.566,29.1102,0,16,1,0,0,0,0,0,0,0,0,0,0,0,3,62.1,26.1,0,,359,359,0,0,1.098612,5.883322,1,0,0,0,0,0,69.46257,8.652697,1.098612,,0 2,1,100,1,1,125586,0,18062.99,17.12252,1,12,1,21.41582,4.491374,0,0,0,25.9072,0,0,0,2,1,6,56.8,8.7,0,,1000,1000,1,1,1.791759,6.907755,1,0,0,1,0,0,68.8233,9.801676,1.791759,3.254521,1 2,1,100,1,2,125586,0,18062.99,18.12252,1,12,1,53.62003,1.360915,.9526402,0,0,55.93359,0,0,0,2,0,6,56.8,8.7,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,68.8233,9.801676,1.791759,4.024165,1 2,1,100,1,1,125587,0,18062.99,19.14305,1,12,1,152.1594,51.43367,33.56931,0,1869.024,2106.187,2,0,0,7,1,6,45.3,26.1,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,0,1,0,57.79599,9.801676,1.791759,7.652634,1 2,1,100,1,2,125587,0,18062.99,20.14305,1,12,1,40.55525,24.81764,0,0,0,65.37289,0,0,0,4,0,6,45.3,26.1,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,0,1,0,57.79599,9.801676,1.791759,4.180108,1 2,1,100,1,3,125587,0,18062.99,21.14305,1,12,1,117.6908,39.4004,37.28444,0,0,194.3756,0,0,0,9,1,5,45.3,26.1,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,1,0,57.79599,9.801676,1.609438,5.269793,1 2,1,100,1,4,125587,0,18062.99,22.14305,1,12,1,80.771,33.29509,0,0,0,114.0661,0,0,0,10,0,5,45.3,26.1,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,1,0,57.79599,9.801676,1.609438,4.736778,1 2,1,100,1,5,125587,0,18062.99,23.14305,1,12,1,260.2019,164.2785,32.5326,0,732.0782,1189.091,1,0,0,9,1,5,45.3,26.1,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,1,0,57.79599,9.801676,1.609438,7.080945,1 2,1,100,1,1,125588,0,18062.99,43.6961,0,12,1,45.21119,45.09221,62.14753,0,0,152.4509,0,0,0,5,2,6,77.9,8.7,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,64.31509,9.801676,1.791759,5.026843,1 2,1,100,1,2,125588,0,18062.99,44.6961,0,12,1,117.583,71.36636,0,0,0,188.9494,0,0,0,9,6,6,77.9,8.7,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,64.31509,9.801676,1.791759,5.241479,1 2,1,100,1,3,125588,0,18062.99,45.6961,0,12,1,100.0991,27.70069,0,0,0,127.7998,0,0,0,7,0,5,77.9,8.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,64.31509,9.801676,1.609438,4.850465,1 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2,1,100,1,4,125591,0,18062.99,16.03765,1,12,1,39.23818,5.598898,0,0,0,44.83708,0,0,0,3,0,5,74.36826,13.73189,1,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,1,0,66.11668,9.801676,1.609438,3.803035,1 2,1,100,1,5,125591,0,18062.99,17.03765,1,12,1,31.55238,0,30.33656,0,0,61.88894,0,0,0,1,1,5,74.36826,13.73189,1,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,1,0,66.11668,9.801676,1.609438,4.125341,1 11,1,0,1,1,125613,0,1388.958,20.10404,0,9,1,20.5235,36.35931,0,0,0,56.88281,0,0,0,2,0,1,46.3,17.4,1,,0,0,0,0,0,0,0,0,0,1,0,0,68.92193,7.237029,0,4.040993,1 11,1,0,1,2,125613,0,1388.958,21.10404,0,9,1,34.38214,0,0,0,0,34.38214,0,0,0,1,0,1,46.3,17.4,1,,0,0,0,0,0,0,0,0,0,1,0,0,68.92193,7.237029,0,3.537537,1 11,1,0,1,3,125613,0,1388.958,22.10404,0,9,1,37.41328,5.649158,0,0,0,43.06244,0,0,0,3,0,1,46.3,17.4,1,,0,0,0,0,0,0,0,0,0,1,0,0,68.92193,7.237029,0,3.762651,1 11,1,0,1,4,125613,0,1388.958,23.10404,0,9,1,0,0,0,0,0,0,0,0,0,0,0,1,46.3,17.4,1,,0,0,0,0,0,0,0,0,0,1,0,0,68.92193,7.237029,0,,0 11,1,0,1,5,125613,0,1388.958,24.10404,0,9,1,21.03492,0,0,0,0,21.03492,0,0,0,1,0,1,46.3,17.4,1,,0,0,0,0,0,0,0,0,0,1,0,0,68.92193,7.237029,0,3.046184,1 11,1,0,1,1,125614,0,3273.573,57.48391,1,8,1,0,45.87745,0,26.76978,0,45.87745,0,0,3,0,0,1,83.2,13,0,,0,0,0,0,0,0,0,0,0,0,1,0,53.37024,8.093943,0,3.825974,1 11,1,0,1,2,125614,0,3273.573,58.48391,1,8,1,0,32.69461,0,32.66195,0,32.69461,0,0,4,0,0,1,83.2,13,0,,0,0,0,0,0,0,0,0,0,0,1,0,53.37024,8.093943,0,3.48721,1 11,1,0,1,3,125614,0,3273.573,59.48391,1,8,1,0,33.05748,0,22.29931,0,33.05748,0,0,3,0,0,1,83.2,13,0,,0,0,0,0,0,0,0,0,0,0,1,0,53.37024,8.093943,0,3.498248,1 11,1,0,1,4,125614,0,3273.573,60.48391,1,8,1,0,35.09867,0,22.94631,0,35.09867,0,0,3,0,0,1,83.2,13,0,,0,0,0,0,0,0,0,0,0,0,1,0,53.37024,8.093943,0,3.558163,1 11,1,0,1,5,125614,0,3273.573,61.48391,1,8,1,0,35.12411,0,33.65587,0,35.12411,0,0,4,0,0,1,83.2,13,0,,0,0,0,0,0,0,0,0,0,0,1,0,53.37024,8.093943,0,3.558888,1 6,1,25,1,1,125617,0,9542.002,6.817248,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,72.63244,9.163564,1.791759,,0 6,1,25,1,2,125617,0,9542.002,7.817248,0,12,1,2.695418,0,0,0,0,2.695418,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,72.63244,9.163564,1.791759,.9915532,1 6,1,25,1,3,125617,0,9542.002,8.817248,0,12,1,67.66585,0,4.570024,0,0,72.23587,0,0,0,3,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,72.63244,9.163564,1.791759,4.279937,1 6,1,25,1,4,125617,0,9542.002,9.817248,0,12,1,24.38469,0,0,0,782.0739,806.4585,1,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,72.63244,9.163564,1.791759,6.692652,1 6,1,25,1,5,125617,0,9542.002,10.81725,0,12,1,236.9737,0,0,0,0,236.9737,0,0,0,4,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,72.63244,9.163564,1.791759,5.467949,1 6,1,25,1,1,125618,0,9542.002,3.693361,1,12,1,45.78917,0,27.07892,0,0,72.86808,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.258096,8.294049,1,0,0,68.68684,9.163564,1.791759,4.288651,1 6,1,25,1,2,125618,0,9542.002,4.693361,1,12,1,2.695418,0,0,0,0,2.695418,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.258096,8.294049,1,0,0,68.68684,9.163564,1.791759,.9915532,1 6,1,25,1,3,125618,0,9542.002,5.693361,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.258096,8.294049,1,0,0,68.68684,9.163564,1.791759,,0 6,1,25,1,4,125618,0,9542.002,6.693361,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.258096,8.294049,1,0,0,68.68684,9.163564,1.791759,,0 6,1,25,1,5,125618,0,9542.002,7.693361,1,12,1,10.42101,0,0,0,0,10.42101,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.258096,8.294049,1,0,0,68.68684,9.163564,1.791759,2.343824,1 6,1,25,1,1,125619,0,9542.002,4.807666,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,69.20081,9.163564,1.791759,,0 6,1,25,1,2,125619,0,9542.002,5.807666,0,12,1,2.695418,0,0,0,0,2.695418,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,69.20081,9.163564,1.791759,.9915532,1 6,1,25,1,3,125619,0,9542.002,6.807666,0,12,1,14.74201,0,23.48894,0,0,38.23096,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,69.20081,9.163564,1.791759,3.643646,1 6,1,25,1,4,125619,0,9542.002,7.807666,0,12,1,60.28715,0,14.28897,0,0,74.57612,0,0,0,3,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,69.20081,9.163564,1.791759,4.311821,1 6,1,25,1,5,125619,0,9542.002,8.807666,0,12,1,10.42101,0,20.90871,0,0,31.32972,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,69.20081,9.163564,1.791759,3.444567,1 6,1,25,1,1,125620,0,9542.002,35.6961,0,10,1,0,0,33.23322,0,0,33.23322,0,0,0,0,0,6,58.9,21.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,67.52351,9.163564,1.791759,3.50355,1 6,1,25,1,2,125620,0,9542.002,36.6961,0,10,1,140.9704,7.385445,0,0,0,148.3558,0,0,0,3,0,6,58.9,21.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,67.52351,9.163564,1.791759,4.999613,1 6,1,25,1,3,125620,0,9542.002,37.6961,0,10,1,35.74939,0,0,0,0,35.74939,0,0,0,1,0,6,58.9,21.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,67.52351,9.163564,1.791759,3.576533,1 6,1,25,1,4,125620,0,9542.002,38.6961,0,10,1,31.9052,0,0,0,675.6426,707.5479,1,0,0,0,3,6,58.9,21.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,67.52351,9.163564,1.791759,6.561805,1 6,1,25,1,5,125620,0,9542.002,39.6961,0,10,1,0,0,0,0,0,0,0,0,0,0,0,6,58.9,21.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,67.52351,9.163564,1.791759,,0 6,1,25,1,1,125621,0,9542.002,26.33539,1,12,1,0,3.239105,0,0,0,3.239105,0,0,0,0,0,6,49.5,21.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,71.57712,9.163564,1.791759,1.175297,1 6,1,25,1,2,125621,0,9542.002,27.33539,1,12,1,77.35849,5.175202,0,0,0,82.53369,0,0,0,4,9,6,49.5,21.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,71.57712,9.163564,1.791759,4.413207,1 6,1,25,1,3,125621,0,9542.002,28.33539,1,12,1,78.50123,1.719902,0,0,1031.071,1111.292,1,0,0,2,0,6,49.5,21.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,71.57712,9.163564,1.791759,7.013279,1 6,1,25,1,4,125621,0,9542.002,29.33539,1,12,1,48.76937,0,0,0,0,48.76937,0,0,0,2,2,6,49.5,21.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,71.57712,9.163564,1.791759,3.887102,1 6,1,25,1,5,125621,0,9542.002,30.33539,1,12,1,10.42101,0,0,0,0,10.42101,0,0,0,0,0,6,49.5,21.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,71.57712,9.163564,1.791759,2.343824,1 2,1,100,0,1,125635,0,6916.232,46.73785,1,9,1,62.42638,12.60306,29.44641,0,0,104.4759,0,0,0,2,2,3,73.8,13.73189,0,,300,300,0,0,1.098612,5.703783,1,0,0,1,0,0,67.80335,8.841771,1.098612,4.648956,1 2,1,100,0,2,125635,0,6916.232,47.73785,1,9,1,8.625337,2.96496,0,0,0,11.5903,0,0,0,1,0,3,73.8,13.73189,0,,300,300,0,0,1.098612,5.703783,1,0,0,1,0,0,67.80335,8.841771,1.098612,2.450168,1 2,1,100,0,3,125635,0,6916.232,48.73785,1,9,1,8.845209,6.486486,0,0,0,15.3317,0,0,0,1,0,3,73.8,13.73189,0,,300,300,0,0,1.098612,5.703783,1,0,0,1,0,0,67.80335,8.841771,1.098612,2.729922,1 2,1,100,0,1,125636,0,6916.232,10.32717,0,9,1,1.766784,15.22379,0,0,0,16.99058,0,0,0,0,0,3,74.36826,13.73189,0,,300,300,1,0,1.098612,5.703783,1,0,0,1,0,0,75.82542,8.841771,1.098612,2.832659,1 2,1,100,0,2,125636,0,6916.232,11.32717,0,9,1,54.44744,14.76011,0,0,0,69.20755,0,0,0,5,0,3,74.36826,13.73189,0,,300,300,1,0,1.098612,5.703783,1,0,0,1,0,0,75.82542,8.841771,1.098612,4.23711,1 2,1,100,0,3,125636,0,6916.232,12.32717,0,9,1,4.422605,4.29484,0,0,0,8.717444,0,0,0,1,0,3,74.36826,13.73189,0,,300,300,1,0,1.098612,5.703783,1,0,0,1,0,0,75.82542,8.841771,1.098612,2.165326,1 2,1,100,0,1,125637,0,6916.232,53.96851,0,11,1,141.9317,27.04947,0,0,0,168.9812,0,0,0,6,3,3,85,13.73189,0,,300,300,0,0,1.098612,5.703783,1,0,0,0,0,0,72.67507,8.841771,1.098612,5.129787,1 2,1,100,0,2,125637,0,6916.232,54.96851,0,11,1,7.54717,0,0,0,0,7.54717,0,0,0,1,0,3,85,13.73189,0,,300,300,0,0,1.098612,5.703783,1,0,0,0,0,0,72.67507,8.841771,1.098612,2.021173,1 2,1,100,0,3,125637,0,6916.232,55.96851,0,11,1,7.371007,11.08108,0,0,0,18.45209,0,0,0,3,0,3,85,13.73189,0,,300,300,0,0,1.098612,5.703783,1,0,0,0,0,0,72.67507,8.841771,1.098612,2.915178,1 11,1,0,1,1,125658,0,9201.975,14.49144,1,12,1,32.97998,28.15077,0,0,0,61.13074,0,0,0,4,0,6,80,4.3,0,,0,0,1,1,1.791759,0,0,0,0,0,0,0,75.07128,9.127282,1.791759,4.113015,1 11,1,0,1,2,125658,0,9201.975,15.49144,1,12,1,18.86792,2.156334,0,0,0,21.02426,0,0,0,2,0,6,80,4.3,0,,0,0,1,1,1.791759,0,0,0,0,0,0,0,75.07128,9.127282,1.791759,3.045677,1 11,1,0,1,3,125658,0,9201.975,16.49144,1,12,1,19.53317,0,2.702703,0,0,22.23587,0,0,0,1,0,6,80,4.3,0,,0,0,1,1,1.791759,0,0,0,0,0,0,0,75.07128,9.127282,1.791759,3.101707,1 11,1,0,1,1,125659,0,9201.975,44.49829,0,12,1,0,3.239105,22.77385,0,0,26.01296,0,0,0,0,0,6,91.6,8.7,0,,0,0,0,0,1.791759,0,0,0,0,0,0,0,76.77976,9.127282,1.791759,3.258595,1 11,1,0,1,2,125659,0,9201.975,45.49829,0,12,1,5.390836,4.636118,0,0,0,10.02695,0,0,0,1,0,6,91.6,8.7,0,,0,0,0,0,1.791759,0,0,0,0,0,0,0,76.77976,9.127282,1.791759,2.305277,1 11,1,0,1,3,125659,0,9201.975,46.49829,0,12,1,12.28501,0,44.71745,0,0,57.00246,0,0,0,1,0,6,91.6,8.7,0,,0,0,0,0,1.791759,0,0,0,0,0,0,0,76.77976,9.127282,1.791759,4.043094,1 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11,1,0,0,4,125690,0,11982.63,16.87269,1,16,1,5.532504,28.13278,0,0,0,33.66528,0,0,0,1,0,3,74.36826,13.73189,0,,0,288,1,1,1.098612,5.662961,0,0,0,0,0,0,86.44971,9.391296,1.098612,3.516467,1 11,1,0,0,5,125690,0,11982.63,17.87269,1,16,1,28.98857,24.13457,24.96826,0,0,78.09141,0,0,0,2,1,3,74.36826,13.73189,0,,0,288,1,1,1.098612,5.662961,0,0,0,0,0,0,86.44971,9.391296,1.098612,4.35788,1 11,1,0,0,1,125691,0,11982.63,49.93292,1,16,1,121.7026,14.65827,32.3741,0,0,168.735,0,0,0,4,1,3,92.5,13.73189,0,,0,288,0,0,1.098612,5.662961,0,0,0,0,0,0,79.07426,9.391296,1.098612,5.12833,1 11,1,0,0,2,125691,0,11982.63,50.93292,1,16,1,31.76342,20.81051,17.25082,0,0,69.82475,0,0,0,4,1,3,92.5,13.73189,0,,0,288,0,0,1.098612,5.662961,0,0,0,0,0,0,79.07426,9.391296,1.098612,4.245988,1 11,1,0,0,3,125691,0,11982.63,51.93292,1,16,1,44.13965,12.74314,32.53865,0,0,89.42145,0,0,0,1,1,3,92.5,13.73189,0,,0,288,0,0,1.098612,5.662961,0,0,0,0,0,0,79.07426,9.391296,1.098612,4.493361,1 11,1,0,0,4,125691,0,11982.63,52.93292,1,16,1,8.759797,6.325496,0,0,0,15.08529,0,0,0,1,0,3,92.5,13.73189,0,,0,288,0,0,1.098612,5.662961,0,0,0,0,0,0,79.07426,9.391296,1.098612,2.71372,1 11,1,0,0,5,125691,0,11982.63,53.93292,1,16,1,38.51037,27.10538,32.16251,0,0,97.77825,0,0,0,2,1,3,92.5,13.73189,0,,0,288,0,0,1.098612,5.662961,0,0,0,0,0,0,79.07426,9.391296,1.098612,4.582702,1 11,1,0,0,1,125692,0,11982.63,54.93224,0,16,1,176.8585,98.89688,64.34652,0,0,340.1019,0,0,0,10,1,3,90,13.73189,0,,0,288,0,0,1.098612,5.662961,0,0,0,0,0,0,71.24387,9.391296,1.098612,5.829246,1 11,1,0,0,2,125692,0,11982.63,55.93224,0,16,1,73.38445,85.47098,19.49617,0,0,178.3516,0,0,0,7,2,3,90,13.73189,0,,0,288,0,0,1.098612,5.662961,0,0,0,0,0,0,71.24387,9.391296,1.098612,5.183757,1 11,1,0,0,3,125692,0,11982.63,56.93224,0,16,1,56.85786,81.89027,33.78554,0,0,172.5337,0,0,0,5,2,3,90,13.73189,0,,0,288,0,0,1.098612,5.662961,0,0,0,0,0,0,71.24387,9.391296,1.098612,5.150592,1 11,1,0,0,4,125692,0,11982.63,57.93224,0,16,1,39.18856,88.06824,23.6284,0,0,150.8852,0,0,0,4,2,3,90,13.73189,0,,0,288,0,0,1.098612,5.662961,0,0,0,0,0,0,71.24387,9.391296,1.098612,5.01652,1 11,1,0,0,5,125692,0,11982.63,58.93224,0,16,1,75.43377,56.97419,22.99619,0,0,155.4041,0,0,0,4,2,3,90,13.73189,0,,0,288,0,0,1.098612,5.662961,0,0,0,0,0,0,71.24387,9.391296,1.098612,5.046029,1 11,1,0,0,1,125782,0,7207.816,7.958932,1,12,1,6.6345,4.191797,0,0,0,10.8263,0,0,0,1,0,5,74.36826,13.73189,0,,0,0,1,1,1.609438,0,0,0,0,1,0,0,76.96274,8.88306,1.609438,2.381978,1 11,1,0,0,2,125782,0,7207.816,8.958932,1,12,1,5.506608,0,0,0,0,5.506608,0,0,0,1,0,5,74.36826,13.73189,0,,0,0,1,1,1.609438,0,0,0,0,1,0,0,76.96274,8.88306,1.609438,1.705949,1 11,1,0,0,3,125782,0,7207.816,9.958932,1,12,1,5.524862,0,0,0,0,5.524862,0,0,0,1,0,5,74.36826,13.73189,0,,0,0,1,1,1.609438,0,0,0,0,1,0,0,76.96274,8.88306,1.609438,1.709258,1 11,1,0,0,1,125783,0,7207.816,27.72895,1,12,1,30.75995,43.27503,0,0,0,74.03498,0,0,0,4,0,5,70,13.73189,0,,0,0,0,0,1.609438,0,0,0,0,1,0,0,71.7831,8.88306,1.609438,4.304538,1 11,1,0,0,2,125783,0,7207.816,28.72895,1,12,1,26.98238,34.0859,0,0,0,61.06828,0,0,0,4,1,5,70,13.73189,0,,0,0,0,0,1.609438,0,0,0,0,1,0,0,71.7831,8.88306,1.609438,4.111993,1 11,1,0,0,3,125783,0,7207.816,29.72895,1,12,1,43.69664,22.25013,17.96585,0,0,83.91261,0,0,0,4,1,5,70,13.73189,0,,0,0,0,0,1.609438,0,0,0,0,1,0,0,71.7831,8.88306,1.609438,4.429776,1 11,1,0,0,1,125784,0,7207.816,2.38193,1,12,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,0,0,1,1,1.609438,0,0,0,0,1,0,0,73.53111,8.88306,1.609438,,0 11,1,0,0,2,125784,0,7207.816,3.38193,1,12,1,25.3304,9.388766,0,0,0,34.71916,0,0,0,4,0,5,74.36826,13.73189,0,,0,0,1,1,1.609438,0,0,0,0,1,0,0,73.53111,8.88306,1.609438,3.547292,1 11,1,0,0,3,125784,0,7207.816,4.38193,1,12,1,16.57458,7.132094,0,0,0,23.70668,0,0,0,3,0,5,74.36826,13.73189,0,,0,0,1,1,1.609438,0,0,0,0,1,0,0,73.53111,8.88306,1.609438,3.165757,1 11,1,0,0,1,125785,0,7207.816,4.599589,0,12,1,21.10977,8.685163,0,0,0,29.79493,0,0,0,3,0,5,74.36826,13.73189,0,,0,0,1,0,1.609438,0,0,0,0,1,0,0,74.04509,8.88306,1.609438,3.394338,1 11,1,0,0,2,125785,0,7207.816,5.599589,0,12,1,23.67841,20.56718,0,0,0,44.24559,0,0,0,5,0,5,74.36826,13.73189,0,,0,0,1,0,1.609438,0,0,0,0,1,0,0,74.04509,8.88306,1.609438,3.789756,1 11,1,0,0,3,125785,0,7207.816,6.599589,0,12,1,24.10849,14.13862,0,0,0,38.24711,0,0,0,4,0,5,74.36826,13.73189,0,,0,0,1,0,1.609438,0,0,0,0,1,0,0,74.04509,8.88306,1.609438,3.644068,1 11,1,0,0,1,125786,0,7207.816,33.67009,0,12,1,10.58504,0,0,0,0,10.58504,0,0,0,0,0,5,92.5,13.73189,0,,0,0,0,0,1.609438,0,0,0,0,1,0,0,71.81962,8.88306,1.609438,2.359442,1 11,1,0,0,2,125786,0,7207.816,34.67009,0,12,1,16.51982,4.157489,20.14317,0,0,40.82048,0,0,0,2,1,5,92.5,13.73189,0,,0,0,0,0,1.609438,0,0,0,0,1,0,0,71.81962,8.88306,1.609438,3.709184,1 11,1,0,0,3,125786,0,7207.816,35.67009,0,12,1,27.12205,7.332998,0,0,0,34.45505,0,0,0,4,1,5,92.5,13.73189,0,,0,0,0,0,1.609438,0,0,0,0,1,0,0,71.81962,8.88306,1.609438,3.539655,1 8,1,50,0,1,125798,0,8419.976,3.496235,0,12,1,18.58513,5.785372,0,0,0,24.3705,0,0,0,3,0,4,74.36826,13.73189,0,,599,599,1,0,1.386294,6.395262,0,3.931826,7.088409,0,0,0,75.69691,9.038481,1.386294,3.193374,1 8,1,50,0,2,125798,0,8419.976,4.496235,0,12,1,32.85871,8.652793,0,0,0,41.5115,0,0,0,6,0,4,74.36826,13.73189,0,,599,599,1,0,1.386294,6.395262,0,3.931826,7.088409,0,0,0,75.69691,9.038481,1.386294,3.725971,1 8,1,50,0,3,125798,0,8419.976,5.496235,0,12,1,56.53366,2.493766,0,0,0,59.02743,0,0,0,4,0,4,74.36826,13.73189,0,,599,599,1,0,1.386294,6.395262,0,3.931826,7.088409,0,0,0,75.69691,9.038481,1.386294,4.078002,1 8,1,50,0,4,125798,0,8419.976,6.496235,0,12,1,28.12356,1.032734,0,0,0,29.15629,0,0,0,2,1,5,74.36826,13.73189,0,,599,599,1,0,1.609438,6.395262,0,3.931826,7.088409,0,0,0,75.69691,9.038481,1.609438,3.372671,1 8,1,50,0,5,125798,0,8419.976,7.496235,0,12,1,81.07914,16.08125,0,0,0,97.16039,0,0,0,7,0,5,74.36826,13.73189,0,,599,599,1,0,1.609438,6.395262,0,3.931826,7.088409,0,0,0,75.69691,9.038481,1.609438,4.576363,1 8,1,50,0,1,125799,0,8419.976,27.74812,1,12,1,41.36691,17.44005,0,0,0,58.80695,0,0,0,6,0,4,82.5,13.73189,0,,599,599,0,0,1.386294,6.395262,0,3.931826,7.088409,0,0,0,78.26785,9.038481,1.386294,4.07426,1 8,1,50,0,2,125799,0,8419.976,28.74812,1,12,1,30.12048,9.83023,0,0,0,39.95071,0,0,0,1,0,4,82.5,13.73189,0,,599,599,0,0,1.386294,6.395262,0,3.931826,7.088409,0,0,0,78.26785,9.038481,1.386294,3.687646,1 8,1,50,0,3,125799,0,8419.976,29.74812,1,12,1,8.977556,5.21197,35.41147,0,1465.092,1514.693,1,0,0,0,1,4,82.5,13.73189,0,,599,599,0,0,1.386294,6.395262,0,3.931826,7.088409,0,0,0,78.26785,9.038481,1.386294,7.322968,1 8,1,50,0,4,125799,0,8419.976,30.74812,1,12,1,24.2047,23.02905,0,0,0,47.23375,0,0,0,2,0,5,82.5,13.73189,0,,599,599,0,0,1.609438,6.395262,0,3.931826,7.088409,0,0,0,78.26785,9.038481,1.609438,3.855109,1 8,1,50,0,5,125799,0,8419.976,31.74812,1,12,1,0,0,13.26703,0,0,13.26703,0,0,0,0,0,5,82.5,13.73189,0,,599,599,0,0,1.609438,6.395262,0,3.931826,7.088409,0,0,0,78.26785,9.038481,1.609438,2.585282,1 8,1,50,0,1,125800,0,8419.976,32.05202,0,14,1,0,0,0,0,0,0,0,0,0,0,0,4,87.5,13.73189,0,,599,599,0,0,1.386294,6.395262,0,3.931826,7.088409,0,0,0,77.63718,9.038481,1.386294,,0 8,1,50,0,2,125800,0,8419.976,33.05202,0,14,1,55.31216,23.84447,0,0,0,79.15662,0,0,0,5,0,4,87.5,13.73189,0,,599,599,0,0,1.386294,6.395262,0,3.931826,7.088409,0,0,0,77.63718,9.038481,1.386294,4.371428,1 8,1,50,0,3,125800,0,8419.976,34.05202,0,14,1,46.90773,9.17207,27.9601,0,0,84.0399,0,0,0,3,0,4,87.5,13.73189,0,,599,599,0,0,1.386294,6.395262,0,3.931826,7.088409,0,0,0,77.63718,9.038481,1.386294,4.431292,1 8,1,50,0,4,125800,0,8419.976,35.05202,0,14,1,20.05532,6.851083,0,0,0,26.90641,0,0,0,0,0,5,87.5,13.73189,0,,599,599,0,0,1.609438,6.395262,0,3.931826,7.088409,0,0,0,77.63718,9.038481,1.609438,3.292365,1 8,1,50,0,5,125800,0,8419.976,36.05202,0,14,1,8.887008,0,0,0,0,8.887008,0,0,0,1,0,5,87.5,13.73189,0,,599,599,0,0,1.609438,6.395262,0,3.931826,7.088409,0,0,0,77.63718,9.038481,1.609438,2.18459,1 8,1,50,0,1,125801,0,8419.976,.5804244,1,12,1,65.94724,10.76139,0,0,0,76.70863,0,0,0,8,0,4,74.36826,13.73189,0,,599,599,1,1,1.386294,6.395262,0,3.931826,7.088409,0,0,0,79.42434,9.038481,1.386294,4.340014,1 8,1,50,0,2,125801,0,8419.976,1.580424,1,12,1,37.23987,19.82475,0,0,0,57.06462,0,0,0,7,0,4,74.36826,13.73189,0,,599,599,1,1,1.386294,6.395262,0,3.931826,7.088409,0,0,0,79.42434,9.038481,1.386294,4.044184,1 8,1,50,0,3,125801,0,8419.976,2.580424,1,12,1,7.98005,0,0,0,0,7.98005,0,0,0,1,0,4,74.36826,13.73189,0,,599,599,1,1,1.386294,6.395262,0,3.931826,7.088409,0,0,0,79.42434,9.038481,1.386294,2.076945,1 8,1,50,0,4,125801,0,8419.976,3.580424,1,12,1,27.66252,0,0,0,0,27.66252,0,0,0,3,0,5,74.36826,13.73189,0,,599,599,1,1,1.609438,6.395262,0,3.931826,7.088409,0,0,0,79.42434,9.038481,1.609438,3.320078,1 8,1,50,0,5,125801,0,8419.976,4.580424,1,12,1,49.09014,0,0,0,0,49.09014,0,0,0,2,1,5,74.36826,13.73189,0,,599,599,1,1,1.609438,6.395262,0,3.931826,7.088409,0,0,0,79.42434,9.038481,1.609438,3.893658,1 8,1,50,0,1,125806,0,14051.49,28.63244,1,12,1,8.833922,18.49823,0,0,0,27.33216,0,0,0,1,0,3,83.8,13.73189,0,,718,718,0,0,1.098612,6.576469,0,3.931826,7.269617,0,0,0,79.52938,9.550555,1.098612,3.308064,1 8,1,50,0,2,125806,0,14051.49,29.63244,1,12,1,38.27493,14.47978,0,0,0,52.75472,0,0,0,4,2,3,83.8,13.73189,0,,718,718,0,0,1.098612,6.576469,0,3.931826,7.269617,0,0,0,79.52938,9.550555,1.098612,3.965653,1 8,1,50,0,3,125806,0,14051.49,30.63244,1,12,1,8.845209,22.13268,0,0,0,30.97789,0,0,0,1,0,3,83.8,13.73189,0,,718,718,0,0,1.098612,6.576469,0,3.931826,7.269617,0,0,0,79.52938,9.550555,1.098612,3.433274,1 8,1,50,0,1,125807,0,14051.49,8.531143,1,12,1,47.93875,7.832745,14.77032,0,0,70.54182,0,0,0,5,1,3,74.36826,13.73189,0,,718,718,1,1,1.098612,6.576469,0,3.931826,7.269617,1,0,0,79.35551,9.550555,1.098612,4.256206,1 8,1,50,0,2,125807,0,14051.49,9.531143,1,12,1,16.17251,2.560647,21.04582,0,0,39.77898,0,0,0,1,1,3,74.36826,13.73189,0,,718,718,1,1,1.098612,6.576469,0,3.931826,7.269617,1,0,0,79.35551,9.550555,1.098612,3.683339,1 8,1,50,0,3,125807,0,14051.49,10.53114,1,12,1,23.09582,0,11.05651,0,0,34.15233,0,0,0,2,1,3,74.36826,13.73189,0,,718,718,1,1,1.098612,6.576469,0,3.931826,7.269617,1,0,0,79.35551,9.550555,1.098612,3.530831,1 8,1,50,0,1,125808,0,14051.49,8.531143,0,12,1,63.60424,18.22144,0,0,0,81.82568,0,0,0,13,0,3,74.36826,13.73189,0,,718,718,1,0,1.098612,6.576469,0,3.931826,7.269617,0,1,0,60.19517,9.550555,1.098612,4.404591,1 8,1,50,0,2,125808,0,14051.49,9.531143,0,12,1,77.08895,21.96766,18.88949,0,0,117.9461,0,0,0,12,1,3,74.36826,13.73189,0,,718,718,1,0,1.098612,6.576469,0,3.931826,7.269617,0,1,0,60.19517,9.550555,1.098612,4.770227,1 8,1,50,0,3,125808,0,14051.49,10.53114,0,12,1,72.72727,13.09582,8.039312,0,0,93.86241,0,0,0,13,1,3,74.36826,13.73189,0,,718,718,1,0,1.098612,6.576469,0,3.931826,7.269617,0,1,0,60.19517,9.550555,1.098612,4.54183,1 6,1,25,0,1,125810,0,10455.96,8.303902,1,12,1,10.25332,0,0,0,0,10.25332,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,84.24701,9.255023,1.386294,2.327601,1 6,1,25,0,2,125810,0,10455.96,9.303902,1,12,1,5.506608,0,0,0,0,5.506608,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,84.24701,9.255023,1.386294,1.705949,1 6,1,25,0,3,125810,0,10455.96,10.3039,1,12,1,11.04972,0,0,0,166.6449,177.6946,1,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,84.24701,9.255023,1.386294,5.180067,1 6,1,25,0,1,125811,0,10455.96,38.2642,1,12,1,138.1182,6.574186,0,0,0,144.6924,0,0,0,5,0,4,83.8,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.34193,9.255023,1.386294,4.97461,1 6,1,25,0,2,125811,0,10455.96,39.2642,1,12,1,29.18502,13.51872,0,0,0,42.70374,0,0,0,3,0,4,83.8,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.34193,9.255023,1.386294,3.754287,1 6,1,25,0,3,125811,0,10455.96,40.2642,1,12,1,8.538423,7.157207,0,0,0,15.69563,0,0,0,1,0,4,83.8,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.34193,9.255023,1.386294,2.753382,1 6,1,25,0,1,125812,0,10455.96,15.65777,0,12,1,53.49819,51.538,0,0,0,105.0362,0,0,0,2,4,4,77.5,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,80.2968,9.255023,1.386294,4.654305,1 6,1,25,0,2,125812,0,10455.96,16.65777,0,12,1,6.60793,36.17841,0,0,0,42.78634,0,0,0,1,0,4,77.5,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,80.2968,9.255023,1.386294,3.756219,1 6,1,25,0,3,125812,0,10455.96,17.65777,0,12,1,24.61075,33.24962,0,0,0,57.86037,0,0,0,1,0,4,77.5,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,80.2968,9.255023,1.386294,4.058033,1 6,1,25,0,1,125813,0,10455.96,42.66393,0,12,1,15.07841,0,38.76357,0,0,53.84198,0,0,0,1,0,4,82.5,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.66858,9.255023,1.386294,3.986053,1 6,1,25,0,2,125813,0,10455.96,43.66393,0,12,1,89.75771,3.276432,0,0,0,93.03414,0,0,0,5,0,4,82.5,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.66858,9.255023,1.386294,4.532967,1 6,1,25,0,3,125813,0,10455.96,44.66393,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,82.5,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.66858,9.255023,1.386294,,0 6,1,25,0,1,125817,0,7893.92,27.98905,0,14,1,17.38609,11.95444,0,0,0,29.34053,0,0,0,3,0,2,80,13.73189,0,,1000,1000,0,0,.6931472,6.907755,0,3.258096,8.294049,0,0,0,77.89652,8.973975,.6931472,3.37897,1 6,1,25,0,2,125817,0,7893.92,28.98905,0,14,1,68.45564,33.51041,0,0,0,101.966,0,0,0,6,0,3,80,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,77.89652,8.973975,1.098612,4.62464,1 6,1,25,0,3,125817,0,7893.92,29.98905,0,14,1,28.91771,24.4389,0,0,0,53.35661,0,0,0,3,0,3,80,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,77.89652,8.973975,1.098612,3.976998,1 6,1,25,0,1,125818,0,7893.92,24.09309,1,12,1,80.03597,20.73741,0,0,1351.439,1452.212,2,0,0,5,2,2,86.3,13.73189,0,,1000,1000,0,0,.6931472,6.907755,0,3.258096,8.294049,0,0,0,78.52718,8.973975,.6931472,7.280843,1 6,1,25,0,2,125818,0,7893.92,25.09309,1,12,1,174.5619,19.24973,0,0,947.6287,1141.44,1,0,0,6,0,3,86.3,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,78.52718,8.973975,1.098612,7.040046,1 6,1,25,0,3,125818,0,7893.92,26.09309,1,12,1,48.00499,42.1197,0,0,0,90.12469,0,0,0,0,0,3,86.3,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,78.52718,8.973975,1.098612,4.501194,1 1,1,0,1,1,125819,0,6789.702,59.02533,1,14,1,19.03629,33.78941,0,0,0,52.8257,0,0,0,0,0,1,82.1,13,0,,150,93,0,0,0,4.532599,1,0,0,0,0,0,78.15913,8.82331,0,3.966998,1 1,1,0,1,2,125819,0,6789.702,60.02533,1,14,1,145.3457,14.31682,52.62384,0,0,212.2863,0,0,0,4,0,1,82.1,13,0,,150,93,0,0,0,4.532599,1,0,0,0,0,0,78.15913,8.82331,0,5.357936,1 1,1,0,1,3,125819,0,6789.702,61.02533,1,14,1,0,14.79187,0,0,0,14.79187,0,0,0,0,0,1,82.1,13,0,,150,93,0,0,0,4.532599,1,0,0,0,0,0,78.15913,8.82331,0,2.694078,1 4,1,100,0,1,125825,0,5982.63,21.49213,0,12,1,0,0,0,0,0,0,0,0,0,0,0,2,74.7,0,0,,1000,1000,0,0,.6931472,6.907755,1,0,0,1,0,0,68.84245,8.696783,.6931472,,0 4,1,100,0,2,125825,0,5982.63,22.49213,0,12,1,4.043127,0,0,0,0,4.043127,0,0,0,1,0,2,74.7,0,0,,1000,1000,0,0,.6931472,6.907755,1,0,0,1,0,0,68.84245,8.696783,.6931472,1.397018,1 4,1,100,0,3,125825,0,5982.63,23.49213,0,12,1,7.371007,6.422605,0,0,0,13.79361,0,0,0,1,0,3,74.7,0,0,,1000,1000,0,0,1.098612,6.907755,1,0,0,1,0,0,68.84245,8.696783,1.098612,2.624206,1 4,1,100,0,4,125825,0,5982.63,24.49213,0,12,1,9.913401,2.402005,0,0,0,12.31541,0,0,0,2,0,4,74.7,0,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,68.84245,8.696783,1.386294,2.510851,1 4,1,100,0,5,125825,0,5982.63,25.49213,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.7,0,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,68.84245,8.696783,1.386294,,0 4,1,100,0,1,125826,0,5982.63,21.79055,1,13,1,0,8.551237,0,0,0,8.551237,0,0,0,0,0,2,92.6,0,0,,1000,1000,0,0,.6931472,6.907755,1,0,0,1,0,0,70.0071,8.696783,.6931472,2.146076,1 4,1,100,0,2,125826,0,5982.63,22.79055,1,13,1,195.1483,7.681941,0,0,249.3261,452.1563,2,1,0,1,0,2,92.6,0,0,,1000,1000,0,0,.6931472,6.907755,1,0,0,1,0,0,70.0071,8.696783,.6931472,6.114028,1 4,1,100,0,3,125826,0,5982.63,23.79055,1,13,1,2.457002,26.60442,0,0,504.5946,533.656,1,0,0,0,0,3,92.6,0,0,,1000,1000,0,0,1.098612,6.907755,1,0,0,1,0,0,70.0071,8.696783,1.098612,6.279751,1 4,1,100,0,4,125826,0,5982.63,24.79055,1,13,1,15.38286,6.536007,0,0,0,21.91887,0,0,0,1,0,4,92.6,0,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,70.0071,8.696783,1.386294,3.087348,1 4,1,100,0,5,125826,0,5982.63,25.79055,1,13,1,37.51563,1.350563,0,0,0,38.8662,0,0,0,0,1,4,92.6,0,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,70.0071,8.696783,1.386294,3.660125,1 11,1,0,0,1,125832,0,7975.186,2.302532,0,12,1,142.5513,5.500603,0,0,0,148.0519,0,0,0,4,0,4,74.36826,13.73189,0,,0,323,1,0,1.386294,5.777652,0,0,0,1,0,0,72.61372,8.984216,1.386294,4.997563,1 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6,1,25,1,2,125892,0,19523.22,39.18207,0,15,1,0,0,0,0,0,0,0,0,0,0,0,4,95.8,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.21307,9.879411,1.386294,,0 6,1,25,1,3,125892,0,19523.22,40.18207,0,15,1,17.19902,0,0,0,0,17.19902,0,0,0,1,0,4,95.8,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.21307,9.879411,1.386294,2.844852,1 6,1,25,1,1,125893,0,19523.22,16.64066,0,14,1,41.8139,16.0424,0,0,0,57.8563,0,0,0,6,0,4,86.3,0,1,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.05912,9.879411,1.386294,4.057962,1 6,1,25,1,2,125893,0,19523.22,17.64066,0,14,1,34.50135,1.617251,8.086253,0,0,44.20485,0,0,0,4,0,4,86.3,0,1,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.05912,9.879411,1.386294,3.788835,1 6,1,25,1,3,125893,0,19523.22,18.64066,0,14,1,0,2.432432,0,0,0,2.432432,0,0,0,0,0,4,86.3,0,1,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.05912,9.879411,1.386294,.8888918,1 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1,1,0,1,3,125907,0,18647.29,40.52703,0,8,1,43.58722,0,0,0,0,43.58722,0,0,0,1,0,3,93.7,0,0,,113,113,0,0,1.098612,4.727388,1,0,0,0,0,0,75.67756,9.83351,1.098612,3.774764,1 1,1,0,1,4,125907,0,18647.29,41.52703,0,8,1,10.93892,0,0,0,0,10.93892,0,0,0,2,0,3,93.7,0,0,,113,113,0,0,1.098612,4.727388,1,0,0,0,0,0,75.67756,9.83351,1.098612,2.392328,1 1,1,0,1,5,125907,0,18647.29,42.52703,0,8,1,19.17466,5.122968,29.18716,0,0,53.48479,0,0,0,2,0,3,93.7,0,0,,113,113,0,0,1.098612,4.727388,1,0,0,0,0,0,75.67756,9.83351,1.098612,3.979397,1 1,1,0,1,1,125908,0,18647.29,38.16564,1,11,1,21.20141,10.3298,0,0,0,31.53121,0,0,0,2,0,3,82.1,13,0,,113,113,0,0,1.098612,4.727388,1,0,0,0,0,0,76.56874,9.83351,1.098612,3.450978,1 1,1,0,1,2,125908,0,18647.29,39.16564,1,11,1,33.531,9.229111,0,0,0,42.76011,0,0,0,0,1,3,82.1,13,0,,113,113,0,0,1.098612,4.727388,1,0,0,0,0,0,76.56874,9.83351,1.098612,3.755606,1 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1,1,0,1,3,125909,0,18647.29,18.5421,1,11,1,17.69042,9.77887,0,0,0,27.46929,0,0,0,3,0,3,82.1,8.7,0,,113,113,0,0,1.098612,4.727388,1,0,0,0,0,0,72.18691,9.83351,1.098612,3.313069,1 1,1,0,1,4,125909,0,18647.29,19.5421,1,11,1,0,0,0,0,0,0,0,0,0,0,0,3,82.1,8.7,0,,113,113,0,0,1.098612,4.727388,1,0,0,0,0,0,72.18691,9.83351,1.098612,,0 1,1,0,1,5,125909,0,18647.29,20.5421,1,11,1,0,0,0,0,0,0,0,0,0,0,0,3,82.1,8.7,0,,113,113,0,0,1.098612,4.727388,1,0,0,0,0,0,72.18691,9.83351,1.098612,,0 1,1,0,0,1,125962,0,3588.089,15.34292,1,10,1,0,0,0,0,0,0,0,0,0,0,0,3,80,13.73189,0,,450,0,1,1,1.098612,0,1,0,0,0,0,0,70.76381,8.185654,1.098612,,0 1,1,0,0,2,125962,0,3588.089,16.34292,1,10,1,55.52561,0,1.886792,0,0,57.4124,0,0,0,2,2,3,80,13.73189,0,,450,0,1,1,1.098612,0,1,0,0,0,0,0,70.76381,8.185654,1.098612,4.05026,1 1,1,0,0,3,125962,0,3588.089,17.34292,1,10,1,126.7813,0,0,0,0,126.7813,0,0,0,4,0,3,80,13.73189,0,,450,0,1,1,1.098612,0,1,0,0,0,0,0,70.76381,8.185654,1.098612,4.842464,1 1,1,0,0,1,125963,0,3588.089,55.24162,1,10,1,0,0,0,0,0,0,0,0,0,0,0,3,83.8,13.73189,0,,450,0,0,0,1.098612,0,1,0,0,1,0,0,64.55314,8.185654,1.098612,,0 1,1,0,0,2,125963,0,3588.089,56.24162,1,10,1,15.09434,3.234501,0,0,0,18.32884,0,0,0,1,0,3,83.8,13.73189,0,,450,0,0,0,1.098612,0,1,0,0,1,0,0,64.55314,8.185654,1.098612,2.908476,1 1,1,0,0,3,125963,0,3588.089,57.24162,1,10,1,6.879607,0,0,0,0,6.879607,0,0,0,1,0,3,83.8,13.73189,0,,450,0,0,0,1.098612,0,1,0,0,1,0,0,64.55314,8.185654,1.098612,1.928561,1 1,1,0,0,1,125964,0,3588.089,58.2204,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,70,13.73189,1,,450,0,0,0,1.098612,0,1,0,0,0,0,1,47.8484,8.185654,1.098612,,0 1,1,0,0,2,125964,0,3588.089,59.2204,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,70,13.73189,1,,450,0,0,0,1.098612,0,1,0,0,0,0,1,47.8484,8.185654,1.098612,,0 1,1,0,0,3,125964,0,3588.089,60.2204,0,9,1,0,0,0,0,360.2555,360.2555,1,0,0,0,0,3,70,13.73189,1,,450,0,0,0,1.098612,0,1,0,0,0,0,1,47.8484,8.185654,1.098612,5.886814,1 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7,1,25,1,2,125968,1,1176.179,17.41615,1,5,1,0,0,0,0,0,0,0,0,0,0,0,6,75.8,4.3,0,,340,340,1,1,1.791759,5.828946,0,3.258096,7.21524,1,0,0,58.89369,7.070876,1.791759,,0 7,1,25,1,1,125969,1,1176.179,17.52225,1,5,1,136.8233,5.264723,0,0,0,142.088,0,0,0,3,0,6,85.3,4.3,0,,340,340,1,1,1.791759,5.828946,0,3.258096,7.21524,1,0,0,58.69306,7.070876,1.791759,4.956447,1 7,1,25,1,2,125969,1,1176.179,18.52225,1,5,1,41.3718,3.739793,0,0,253.4295,298.5411,1,0,0,2,0,6,85.3,4.3,0,,340,340,0,0,1.791759,5.828946,0,3.258096,7.21524,1,0,0,58.69306,7.070876,1.791759,5.698908,1 7,1,25,1,3,125969,1,1176.179,19.52225,1,5,1,9.415262,0,0,0,0,9.415262,0,0,0,0,0,1,85.3,4.3,0,,340,340,0,0,0,5.828946,0,3.258096,7.21524,1,0,0,58.69306,7.070876,0,2.242332,1 7,1,25,1,4,125969,1,1176.179,20.52225,1,5,1,0,0,0,0,0,0,0,0,0,0,0,1,85.3,4.3,0,,340,340,0,0,0,5.828946,0,3.258096,7.21524,1,0,0,58.69306,7.070876,0,,0 7,1,25,1,1,125970,1,1176.179,1.850787,0,5,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,340,340,1,0,1.791759,5.828946,0,3.258096,7.21524,1,0,0,73.69083,7.070876,1.791759,,0 7,1,25,1,2,125970,1,1176.179,2.850787,0,5,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,340,340,1,0,1.791759,5.828946,0,3.258096,7.21524,1,0,0,73.69083,7.070876,1.791759,,0 7,1,25,1,1,125971,1,1176.179,45.83984,1,5,1,0,0,0,0,0,0,0,0,0,0,0,6,63.3,8.7,0,,340,340,0,0,1.791759,5.828946,0,3.258096,7.21524,0,1,0,51.09576,7.070876,1.791759,,0 7,1,25,1,2,125971,1,1176.179,46.83984,1,5,1,54.98095,10.90365,0,0,0,65.8846,0,0,0,5,0,6,63.3,8.7,0,,340,340,0,0,1.791759,5.828946,0,3.258096,7.21524,0,1,0,51.09576,7.070876,1.791759,4.187905,1 1,1,0,0,1,125983,0,16303.07,27.41684,1,12,1,15.07841,8.455971,0,0,0,23.53438,0,0,0,2,0,2,35,13.73189,0,,300,300,0,0,.6931472,5.703783,1,0,0,1,0,0,72.96643,9.69917,.6931472,3.158462,1 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4,1,100,1,1,126152,0,8923.697,42.28337,1,12,1,10.79137,0,0,0,0,10.79137,0,0,0,1,0,2,90.5,4.3,0,,1000,1000,0,0,.6931472,6.907755,1,0,0,0,0,0,78.46137,9.096578,.6931472,2.378747,1 4,1,100,1,2,126152,0,8923.697,43.28337,1,12,1,0,0,0,0,0,0,0,0,0,0,0,2,90.5,4.3,0,,1000,1000,0,0,.6931472,6.907755,1,0,0,0,0,0,78.46137,9.096578,.6931472,,0 4,1,100,1,3,126152,0,8923.697,44.28337,1,12,1,5.985037,0,23.94015,0,0,29.92519,0,0,0,0,1,2,90.5,4.3,0,,1000,1000,0,0,.6931472,6.907755,1,0,0,0,0,0,78.46137,9.096578,.6931472,3.3987,1 5,1,25,0,1,126156,0,4841.812,46.5243,1,9,1,27.67962,3.898704,0,0,0,31.57833,0,0,0,4,0,1,85.6,13,0,,375,375,0,0,0,5.926926,0,3.258096,7.313221,1,0,0,68.95127,8.48525,0,3.452471,1 5,1,25,0,2,126156,0,4841.812,47.5243,1,9,1,0,0,0,0,0,0,0,0,0,0,0,1,85.6,13,0,,375,375,0,0,0,5.926926,0,3.258096,7.313221,1,0,0,68.95127,8.48525,0,,0 5,1,25,0,3,126156,0,4841.812,48.5243,1,9,1,0,0,0,0,0,0,0,0,0,0,0,1,85.6,13,0,,375,375,0,0,0,5.926926,0,3.258096,7.313221,1,0,0,68.95127,8.48525,0,,0 5,1,25,0,4,126156,0,4841.812,49.5243,1,9,1,10.93892,0,30.44212,0,0,41.38104,0,0,0,0,1,1,85.6,13,0,,375,375,0,0,0,5.926926,0,3.258096,7.313221,1,0,0,68.95127,8.48525,0,3.722823,1 5,1,25,0,5,126156,0,4841.812,50.5243,1,9,1,0,0,0,0,0,0,0,0,0,0,0,1,85.6,13,0,,375,375,0,0,0,5.926926,0,3.258096,7.313221,1,0,0,68.95127,8.48525,0,,0 4,1,100,0,1,126157,0,9122.829,38.24504,0,12,1,13.68233,10.35098,0,0,0,24.03331,0,0,0,2,0,4,58.8,13.73189,1,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,65.64435,9.118645,1.386294,3.179441,1 4,1,100,0,2,126157,0,9122.829,39.24504,0,12,1,381.6004,0,37.54491,0,0,419.1454,0,0,0,1,45,4,58.8,13.73189,1,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,65.64435,9.118645,1.386294,6.038218,1 4,1,100,0,3,126157,0,9122.829,40.24504,0,12,1,5.946482,0,0,0,0,5.946482,0,0,0,0,1,4,58.8,13.73189,1,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,65.64435,9.118645,1.386294,1.7828,1 4,1,100,0,1,126158,0,9122.829,35.38124,1,10,1,20.82094,21.14813,0,0,0,41.96907,0,0,0,1,1,4,56.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,68.66209,9.118645,1.386294,3.736933,1 4,1,100,0,2,126158,0,9122.829,36.38124,1,10,1,221.0125,22.37343,6.53239,0,0,249.9184,0,0,0,1,33,4,56.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,68.66209,9.118645,1.386294,5.521134,1 4,1,100,0,3,126158,0,9122.829,37.38124,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,56.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,68.66209,9.118645,1.386294,,0 4,1,100,0,1,126159,0,9122.829,14.94045,0,10,1,25.58001,0,0,0,0,25.58001,0,0,0,1,1,4,82.5,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,69.60401,9.118645,1.386294,3.241811,1 4,1,100,0,2,126159,0,9122.829,15.94045,0,10,1,8.165487,0,0,0,0,8.165487,0,0,0,0,1,4,82.5,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,69.60401,9.118645,1.386294,2.099916,1 4,1,100,0,3,126159,0,9122.829,16.94045,0,10,1,0,0,0,0,0,0,0,0,0,0,0,4,82.5,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,69.60401,9.118645,1.386294,,0 4,1,100,0,1,126160,0,9122.829,18.52156,1,12,1,21.49911,5.562165,0,0,0,27.06127,0,0,0,3,1,4,91.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,71.81157,9.118645,1.386294,3.298104,1 4,1,100,0,2,126160,0,9122.829,19.52156,1,12,1,305.4763,14.70332,0,0,0,320.1796,0,0,0,8,36,4,91.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,71.81157,9.118645,1.386294,5.768882,1 4,1,100,0,3,126160,0,9122.829,20.52156,1,12,1,9.142715,.6937562,0,0,0,9.836472,0,0,0,0,1,4,91.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,71.81157,9.118645,1.386294,2.286097,1 3,1,100,0,1,126177,0,10341.81,52.85695,0,12,1,75.97173,6.089517,0,0,0,82.06125,0,0,0,3,0,5,86.3,21.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,66.41367,9.244047,1.609438,4.407466,1 3,1,100,0,2,126177,0,10341.81,53.85695,0,12,1,361.5903,18.72776,50.42049,0,6563.558,6994.296,2,0,0,12,0,5,86.3,21.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,66.41367,9.244047,1.609438,8.85285,1 3,1,100,0,3,126177,0,10341.81,54.85695,0,12,1,565.1351,59.71008,9.085995,0,834.1572,1468.089,1,0,0,18,1,5,86.3,21.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,66.41367,9.244047,1.609438,7.291717,1 3,1,100,0,1,126178,0,10341.81,53.33333,1,12,1,110.7185,38.45701,0,0,0,149.1755,0,0,0,8,0,5,80,13,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,74.55164,9.244047,1.609438,5.005124,1 3,1,100,0,2,126178,0,10341.81,54.33333,1,12,1,69.00269,47.7035,40.56065,0,1090.016,1247.283,1,0,0,4,1,5,80,13,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,74.55164,9.244047,1.609438,7.128723,1 3,1,100,0,3,126178,0,10341.81,55.33333,1,12,1,105.774,65.58723,51.59705,0,0,222.9582,0,0,0,13,1,5,80,13,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,74.55164,9.244047,1.609438,5.406984,1 3,1,100,0,1,126179,0,10341.81,12.38877,0,12,1,18.8457,3.374558,0,0,0,22.22026,0,0,0,2,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,85.67059,9.244047,1.609438,3.101004,1 3,1,100,0,2,126179,0,10341.81,13.38877,0,12,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,85.67059,9.244047,1.609438,,0 3,1,100,0,3,126179,0,10341.81,14.38877,0,12,1,19.65602,1.503685,0,0,0,21.1597,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,85.67059,9.244047,1.609438,3.052099,1 3,1,100,0,1,126180,0,10341.81,16.52841,1,12,1,15.31213,2.479388,0,0,0,17.79152,0,0,0,2,0,5,72.6,13,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,75.20459,9.244047,1.609438,2.878722,1 3,1,100,0,2,126180,0,10341.81,17.52841,1,12,1,21.56334,11.21833,0,0,0,32.78167,0,0,0,2,1,5,72.6,13,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,75.20459,9.244047,1.609438,3.48987,1 3,1,100,0,3,126180,0,10341.81,18.52841,1,12,1,61.42506,14.27518,3.415233,0,0,79.11548,0,0,0,4,0,5,72.6,13,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,75.20459,9.244047,1.609438,4.370909,1 3,1,100,0,1,126181,0,10341.81,18.2423,0,12.32507,1,91.8728,8.60424,0,0,0,100.477,0,0,0,6,0,5,42.1,13,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,78.95576,9.244047,1.609438,4.609929,1 3,1,100,0,2,126181,0,10341.81,19.2423,0,12.32507,1,3.234501,1.078167,0,0,0,4.312668,0,0,0,0,0,5,42.1,13,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,78.95576,9.244047,1.609438,1.461557,1 3,1,100,0,3,126181,0,10341.81,20.2423,0,12.32507,1,193.4742,22.92383,0,0,0,216.398,0,0,0,8,0,5,42.1,13,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,78.95576,9.244047,1.609438,5.37712,1 3,1,100,0,1,126182,0,9542.002,21.45927,1,12,1,0,0,0,0,0,0,0,0,0,0,0,1,72.6,8.7,0,,1000,1000,0,0,0,6.907755,1,0,0,0,0,0,76.1736,9.163564,0,,0 3,1,100,0,2,126182,0,9542.002,22.45927,1,12,1,0,.6630728,0,0,0,.6630728,0,0,0,0,0,1,72.6,8.7,0,,1000,1000,0,0,0,6.907755,1,0,0,0,0,0,76.1736,9.163564,0,-.4108706,1 3,1,100,0,3,126182,0,9542.002,23.45927,1,12,1,115.7248,41.2973,30.02948,0,0,187.0516,0,0,0,7,4,1,72.6,8.7,0,,1000,1000,0,0,0,6.907755,1,0,0,0,0,0,76.1736,9.163564,0,5.231384,1 5,1,25,1,1,126192,0,7179.28,53.90007,0,10,1,20.98321,4.664268,0,0,0,25.64748,0,0,0,1,0,3,45.3,30.4,0,,799,799,0,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,63.23743,8.879094,1.098612,3.244445,1 5,1,25,1,2,126192,0,7179.28,54.90007,0,10,1,6.024096,3.450164,0,0,0,9.47426,0,0,0,1,0,3,45.3,30.4,0,,799,799,0,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,63.23743,8.879094,1.098612,2.248579,1 5,1,25,1,3,126192,0,7179.28,55.90007,0,10,1,61.7207,2.488778,0,0,0,64.20947,0,0,0,2,0,3,45.3,30.4,0,,799,799,0,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,63.23743,8.879094,1.098612,4.162151,1 5,1,25,1,4,126192,0,7179.28,56.90007,0,10,1,158.5293,29.65422,0,0,1485.177,1673.361,1,0,0,12,0,3,45.3,30.4,0,,799,799,0,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,63.23743,8.879094,1.098612,7.422589,1 5,1,25,1,5,126192,0,7179.28,57.90007,0,10,1,35.12484,21.30766,1.481168,125.8951,0,57.91367,0,0,15,3,1,3,45.3,30.4,0,,799,799,0,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,63.23743,8.879094,1.098612,4.058953,1 5,1,25,1,1,126193,0,7179.28,13.78782,0,12,1,61.15108,8.141487,0,0,0,69.29256,0,0,0,4,0,3,74.36826,13.73189,0,,799,799,1,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,78.66734,8.879094,1.098612,4.238338,1 5,1,25,1,2,126193,0,7179.28,14.78782,0,12,1,22.45345,2.924425,36.8839,0,0,62.26178,0,0,0,2,0,3,74.36826,13.73189,0,,799,799,1,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,78.66734,8.879094,1.098612,4.131348,1 5,1,25,1,3,126193,0,7179.28,15.78782,0,12,1,33.91521,11.08728,0,0,0,45.00249,0,0,0,3,0,3,74.36826,13.73189,0,,799,799,1,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,78.66734,8.879094,1.098612,3.806718,1 5,1,25,1,4,126193,0,7179.28,16.78782,0,12,1,19.59428,2.996773,27.18764,0,0,49.7787,0,0,0,2,0,3,74.36826,13.73189,0,,799,799,1,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,78.66734,8.879094,1.098612,3.907587,1 5,1,25,1,5,126193,0,7179.28,17.78782,0,12,1,35.89928,2.276767,0,0,0,38.17605,0,0,0,2,0,3,74.36826,13.73189,0,,799,799,1,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,78.66734,8.879094,1.098612,3.642208,1 5,1,25,1,1,126194,0,7179.28,34.96235,1,12,1,29.3765,17.90168,33.0036,0,0,80.28178,0,0,0,2,0,3,71.6,30.4,1,,799,799,0,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,69.07321,8.879094,1.098612,4.385543,1 5,1,25,1,2,126194,0,7179.28,35.96235,1,12,1,9.857613,11.45674,0,0,0,21.31435,0,0,0,1,0,3,71.6,30.4,1,,799,799,0,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,69.07321,8.879094,1.098612,3.059381,1 5,1,25,1,3,126194,0,7179.28,36.96235,1,12,1,25.93516,1.94015,0,0,0,27.87531,0,0,0,2,0,3,71.6,30.4,1,,799,799,0,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,69.07321,8.879094,1.098612,3.327741,1 5,1,25,1,4,126194,0,7179.28,37.96235,1,12,1,30.42877,15.09451,0,0,0,45.52328,0,0,0,3,0,3,71.6,30.4,1,,799,799,0,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,69.07321,8.879094,1.098612,3.818224,1 5,1,25,1,5,126194,0,7179.28,38.96235,1,12,1,121.4558,2.175201,0,276.6653,0,123.631,0,0,23,3,0,3,71.6,30.4,1,,799,799,0,0,1.098612,6.683361,0,3.258096,8.069655,1,0,0,69.07321,8.879094,1.098612,4.817301,1 5,1,25,1,1,126195,0,3355.459,19.83573,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,66.3,4.3,0,,259,259,0,0,0,5.556828,0,3.258096,6.943122,1,0,0,67.43752,8.118642,0,,0 5,1,25,1,2,126195,0,3355.459,20.83573,0,12,1,9.309967,0,36.05695,0,0,45.36692,0,0,0,0,1,1,66.3,4.3,0,,259,259,0,0,0,5.556828,0,3.258096,6.943122,1,0,0,67.43752,8.118642,0,3.814783,1 5,1,25,1,3,126195,0,3355.459,21.83573,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,66.3,4.3,0,,259,259,0,0,0,5.556828,0,3.258096,6.943122,1,0,0,67.43752,8.118642,0,,0 5,1,25,1,4,126195,0,3355.459,22.83573,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,66.3,4.3,0,,259,259,0,0,0,5.556828,0,3.258096,6.943122,1,0,0,67.43752,8.118642,0,,0 5,1,25,1,5,126195,0,3355.459,23.83573,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,66.3,4.3,0,,259,259,0,0,0,5.556828,0,3.258096,6.943122,1,0,0,67.43752,8.118642,0,,0 11,1,0,0,1,126198,0,11809.23,20.53388,0,13,1,61.24853,18.55124,34.06949,0,0,113.8693,0,0,0,7,0,3,85,13.73189,0,,0,464,0,0,1.098612,6.139884,0,0,0,0,0,0,79.07556,9.376721,1.098612,4.735051,1 11,1,0,0,2,126198,0,11809.23,21.53388,0,13,1,84.20485,23.42318,.4851752,0,0,108.1132,0,0,0,6,2,3,85,13.73189,0,,0,464,0,0,1.098612,6.139884,0,0,0,0,0,0,79.07556,9.376721,1.098612,4.683179,1 11,1,0,0,3,126198,0,11809.23,22.53388,0,13,1,217.1499,11.10565,32.33415,0,0,260.5897,0,0,0,12,1,3,85,13.73189,0,,0,464,0,0,1.098612,6.139884,0,0,0,0,0,0,79.07556,9.376721,1.098612,5.562947,1 11,1,0,0,1,126199,0,11809.23,48.39151,1,12,1,72.61484,5.270907,44.00471,0,0,121.8905,0,0,0,5,2,3,67.5,13.73189,0,,0,464,0,0,1.098612,6.139884,0,0,0,1,0,0,72.16116,9.376721,1.098612,4.803123,1 11,1,0,0,2,126199,0,11809.23,49.39151,1,12,1,212.3181,48.61995,.2695418,0,0,261.2076,0,0,0,10,0,3,67.5,13.73189,0,,0,464,0,0,1.098612,6.139884,0,0,0,1,0,0,72.16116,9.376721,1.098612,5.565315,1 11,1,0,0,3,126199,0,11809.23,50.39151,1,12,1,116.9533,11.7199,56.48649,0,0,185.1597,0,0,0,5,0,3,67.5,13.73189,0,,0,464,0,0,1.098612,6.139884,0,0,0,1,0,0,72.16116,9.376721,1.098612,5.221219,1 11,1,0,0,1,126200,0,11809.23,13.55236,0,12,1,20.61249,2.502945,0,0,0,23.11543,0,0,0,3,0,3,74.36826,13.73189,0,,0,464,1,0,1.098612,6.139884,0,0,0,0,0,0,87.52181,9.376721,1.098612,3.1405,1 11,1,0,0,2,126200,0,11809.23,14.55236,0,12,1,46.36119,10.08625,0,0,0,56.44744,0,0,0,7,0,3,74.36826,13.73189,0,,0,464,1,0,1.098612,6.139884,0,0,0,0,0,0,87.52181,9.376721,1.098612,4.03331,1 11,1,0,0,3,126200,0,11809.23,15.55236,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,0,464,1,0,1.098612,6.139884,0,0,0,0,0,0,87.52181,9.376721,1.098612,,0 7,1,25,1,1,126205,0,8393.3,6.31896,1,13,1,9.518144,2.647234,0,0,0,12.16538,0,0,0,1,0,3,74.36826,13.73189,0,,1000,1000,1,1,1.098612,6.907755,0,3.258096,8.294049,0,0,0,83.31136,9.035308,1.098612,2.498594,1 7,1,25,1,2,126205,0,8393.3,7.31896,1,13,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,1000,1000,1,1,1.098612,6.907755,0,3.258096,8.294049,0,0,0,83.31136,9.035308,1.098612,,0 7,1,25,1,3,126205,0,8393.3,8.318959,1,13,1,14.8662,7.433102,0,0,0,22.29931,0,0,0,3,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,83.31136,9.035308,1.386294,3.104556,1 7,1,25,1,1,126206,0,8393.3,30.34634,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,80,17.4,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,75.11373,9.035308,1.098612,,0 7,1,25,1,2,126206,0,8393.3,31.34634,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,80,17.4,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,75.11373,9.035308,1.098612,,0 7,1,25,1,3,126206,0,8393.3,32.34634,0,12,1,26.16452,0,39.99009,0,0,66.15461,0,0,0,1,1,4,80,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.11373,9.035308,1.386294,4.191995,1 7,1,25,1,1,126207,0,8393.3,28.46817,1,13,1,30.63653,18.38192,0,0,0,49.01844,0,0,0,1,0,3,41.1,21.7,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,76.69158,9.035308,1.098612,3.892197,1 7,1,25,1,2,126207,0,8393.3,29.46817,1,13,1,5.443658,4.327708,3.266195,0,933.2335,946.2711,2,0,0,1,0,3,41.1,21.7,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,76.69158,9.035308,1.098612,6.852529,1 7,1,25,1,3,126207,0,8393.3,30.46817,1,13,1,37.6115,14.14272,0,0,0,51.75421,0,0,0,3,0,4,41.1,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.69158,9.035308,1.386294,3.946506,1 9,1,50,1,1,126208,0,12392.06,54.0616,0,12,1,131.1719,20.19631,0,0,0,151.3682,0,0,0,8,0,3,95.8,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,77.03518,9.424891,1.098612,5.019715,1 9,1,50,1,2,126208,0,12392.06,55.0616,0,12,1,101.0343,13.28253,0,0,2096.51,2210.827,2,0,0,8,1,3,95.8,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,77.03518,9.424891,1.098612,7.701122,1 9,1,50,1,3,126208,0,12392.06,56.0616,0,12,1,72.74529,16.82359,0,0,0,89.56888,0,0,0,8,0,3,95.8,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,77.03518,9.424891,1.098612,4.495008,1 9,1,50,1,1,126209,0,12392.06,15.93155,0,16,1,39.26234,11.60024,28.59607,0,0,79.45866,0,0,0,5,1,3,77.9,4.3,0,,1000,1000,1,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,81.08195,9.424891,1.098612,4.375237,1 9,1,50,1,2,126209,0,12392.06,16.93155,0,16,1,10.77844,19.13446,0,0,0,29.9129,0,0,0,2,0,3,77.9,4.3,0,,1000,1000,1,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,81.08195,9.424891,1.098612,3.39829,1 9,1,50,1,3,126209,0,12392.06,17.93155,0,16,1,54.60852,4.286422,24.28147,0,0,83.17641,0,0,0,3,2,3,77.9,4.3,0,,1000,1000,1,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,81.08195,9.424891,1.098612,4.420964,1 9,1,50,1,1,126210,0,12392.06,50.22313,1,16,1,155.7406,39.29209,31.52885,0,0,226.5616,0,0,0,6,2,3,86.3,21.7,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,78.13973,9.424891,1.098612,5.423017,1 9,1,50,1,2,126210,0,12392.06,51.22313,1,16,1,50.08165,37.20741,31.85629,0,0,119.1453,0,0,0,4,1,3,86.3,21.7,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,78.13973,9.424891,1.098612,4.780344,1 9,1,50,1,3,126210,0,12392.06,52.22313,1,16,1,42.76511,39.51933,0,0,0,82.28444,0,0,0,5,0,3,86.3,21.7,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,78.13973,9.424891,1.098612,4.410182,1 10,1,50,0,1,126222,0,25825.28,54.11088,0,19,1,50.05889,0,0,38.86926,0,50.05889,0,0,3,0,0,2,81.3,13.73189,0,,1000,1000,0,0,.6931472,6.907755,0,3.931826,7.600903,0,0,0,77.43079,10.15915,.6931472,3.9132,1 10,1,50,0,2,126222,0,25825.28,55.11088,0,19,1,13.47709,0,0,266.8464,0,13.47709,0,0,15,0,0,2,81.3,13.73189,0,,1000,1000,0,0,.6931472,6.907755,0,3.931826,7.600903,0,0,0,77.43079,10.15915,.6931472,2.600991,1 10,1,50,0,3,126222,0,25825.28,56.11088,0,19,1,0,0,0,16.21622,0,0,0,0,1,0,0,2,81.3,13.73189,0,,1000,1000,0,0,.6931472,6.907755,0,3.931826,7.600903,0,0,0,77.43079,10.15915,.6931472,,0 10,1,50,0,1,126223,0,25825.28,52.73375,1,13,1,0,0,0,0,0,0,0,0,0,0,0,2,75,13.73189,0,,1000,1000,0,0,.6931472,6.907755,0,3.931826,7.600903,0,0,0,78.89941,10.15915,.6931472,,0 10,1,50,0,2,126223,0,25825.28,53.73375,1,13,1,0,0,0,0,0,0,0,0,0,0,0,2,75,13.73189,0,,1000,1000,0,0,.6931472,6.907755,0,3.931826,7.600903,0,0,0,78.89941,10.15915,.6931472,,0 10,1,50,0,3,126223,0,25825.28,54.73375,1,13,1,0,0,0,0,0,0,0,0,0,0,0,2,75,13.73189,0,,1000,1000,0,0,.6931472,6.907755,0,3.931826,7.600903,0,0,0,78.89941,10.15915,.6931472,,0 1,1,0,1,1,126231,0,3460.918,51.72895,1,12,1,128.9753,61.96113,17.85041,0,0,208.7868,0,0,0,7,0,1,85.3,13,0,,150,203,0,0,0,5.313206,1,0,0,0,0,0,79.21188,8.149578,0,5.341314,1 1,1,0,1,2,126231,0,3460.918,52.72895,1,12,1,170.8895,74.88949,44.60917,0,0,290.3882,0,0,0,9,2,1,85.3,13,0,,150,203,0,0,0,5.313206,1,0,0,0,0,0,79.21188,8.149578,0,5.671218,1 1,1,0,1,3,126231,0,3460.918,53.72895,1,12,1,47.66585,37.99509,62.63882,0,0,148.2998,0,0,0,5,0,1,85.3,13,0,,150,203,0,0,0,5.313206,1,0,0,0,0,0,79.21188,8.149578,0,4.999236,1 4,1,100,1,1,126240,0,9577.765,28.52019,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,52.6,17.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,1,0,59.58581,9.167304,1.386294,,0 4,1,100,1,2,126240,0,9577.765,29.52019,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,52.6,17.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,1,0,59.58581,9.167304,1.386294,,0 4,1,100,1,3,126240,0,9577.765,30.52019,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,52.6,17.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,1,0,59.58581,9.167304,1.386294,,0 4,1,100,1,1,126241,0,9577.765,32.32854,0,11,1,5.889281,0,0,0,0,5.889281,0,0,0,1,0,4,33.7,30.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,67.88706,9.167304,1.386294,1.773134,1 4,1,100,1,2,126241,0,9577.765,33.32854,0,11,1,0,0,0,0,0,0,0,0,0,0,0,4,33.7,30.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,67.88706,9.167304,1.386294,,0 4,1,100,1,3,126241,0,9577.765,34.32854,0,11,1,0,0,0,0,0,0,0,0,0,0,0,4,33.7,30.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,67.88706,9.167304,1.386294,,0 4,1,100,1,1,126242,0,9577.765,11.16222,0,9,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,81.2337,9.167304,1.386294,,0 4,1,100,1,2,126242,0,9577.765,12.16222,0,9,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,81.2337,9.167304,1.386294,,0 4,1,100,1,3,126242,0,9577.765,13.16222,0,9,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,81.2337,9.167304,1.386294,,0 4,1,100,1,1,126243,0,9577.765,12.92539,0,9,1,21.3192,0,0,0,0,21.3192,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,81.2337,9.167304,1.386294,3.059608,1 4,1,100,1,2,126243,0,9577.765,13.92539,0,9,1,8.086253,9.153639,0,0,0,17.23989,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,81.2337,9.167304,1.386294,2.847226,1 4,1,100,1,3,126243,0,9577.765,14.92539,0,9,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,81.2337,9.167304,1.386294,,0 10,1,50,1,1,126250,0,11668.83,45.38809,1,11,1,36.27098,36.3729,33.71103,0,0,106.3549,0,0,0,4,0,3,80,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,75.51671,9.364761,1.098612,4.666782,1 10,1,50,1,2,126250,0,11668.83,46.38809,1,11,1,71.08434,16.78532,8.105148,0,0,95.97481,0,0,0,6,0,3,80,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,75.51671,9.364761,1.098612,4.564086,1 10,1,50,1,3,126250,0,11668.83,47.38809,1,11,1,46.13466,14.3591,37.29177,0,0,97.78554,0,0,0,4,1,3,80,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,75.51671,9.364761,1.098612,4.582777,1 10,1,50,1,4,126250,0,11668.83,48.38809,1,11,1,35.96127,9.400645,0,0,0,45.36192,0,0,0,3,0,3,80,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,75.51671,9.364761,1.098612,3.814673,1 10,1,50,1,5,126250,0,11668.83,49.38809,1,11,1,125.6877,34.24884,0,0,0,159.9365,0,0,0,8,0,3,80,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,75.51671,9.364761,1.098612,5.074777,1 10,1,50,1,1,126251,0,11668.83,46.72416,0,11,1,138.1895,26.90648,31.03717,0,990.5935,1186.727,2,0,0,6,0,3,71.6,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,73.89005,9.364761,1.098612,7.078954,1 10,1,50,1,2,126251,0,11668.83,47.72416,0,11,1,13.14348,11.65936,0,0,0,24.80285,0,0,0,2,0,3,71.6,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,73.89005,9.364761,1.098612,3.210958,1 10,1,50,1,3,126251,0,11668.83,48.72416,0,11,1,43.01746,14.46883,33.99002,0,0,91.47631,0,0,0,3,0,3,71.6,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,73.89005,9.364761,1.098612,4.51608,1 10,1,50,1,4,126251,0,11668.83,49.72416,0,11,1,48.4094,4.319963,0,0,0,52.72937,0,0,0,6,0,3,71.6,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,73.89005,9.364761,1.098612,3.965173,1 10,1,50,1,5,126251,0,11668.83,50.72416,0,11,1,11.42615,0,29.67414,0,0,41.1003,0,0,0,0,1,3,71.6,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,73.89005,9.364761,1.098612,3.716015,1 10,1,50,1,1,126252,0,11668.83,18.41752,0,11,1,32.07434,11.66067,0,0,632.9616,676.6967,1,0,0,3,0,3,82.1,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,75.67222,9.364761,1.098612,6.517223,1 10,1,50,1,2,126252,0,11668.83,19.41752,0,11,1,5.476451,2.584885,0,0,0,8.061337,0,0,0,1,0,3,82.1,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,75.67222,9.364761,1.098612,2.087079,1 10,1,50,1,3,126252,0,11668.83,20.41752,0,11,1,16.70823,2.992519,0,0,0,19.70075,0,0,0,2,0,3,82.1,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,75.67222,9.364761,1.098612,2.980657,1 10,1,50,1,4,126252,0,11668.83,21.41752,0,11,1,82.98755,15.20055,0,0,2542.153,2640.341,2,0,0,6,0,3,82.1,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,75.67222,9.364761,1.098612,7.878664,1 10,1,50,1,5,126252,0,11668.83,22.41752,0,11,1,95.64114,21.17647,0,0,0,116.8176,0,0,0,11,0,3,82.1,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,75.67222,9.364761,1.098612,4.760614,1 5,1,25,1,1,126256,0,17812.88,41.86721,0,16,1,24.98513,8.893516,27.35277,0,0,61.23141,0,0,0,1,0,4,78.9,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,73.33533,9.787733,1.386294,4.11466,1 5,1,25,1,2,126256,0,17812.88,42.86721,0,16,1,26.21121,0,0,0,0,26.21121,0,0,0,1,0,4,78.9,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,73.33533,9.787733,1.386294,3.266187,1 5,1,25,1,3,126256,0,17812.88,43.86721,0,16,1,98.11695,6.243806,9.32111,0,0,113.6819,0,0,0,1,2,4,78.9,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,73.33533,9.787733,1.386294,4.733404,1 5,1,25,1,4,126256,0,17812.88,44.86721,0,16,1,15.14456,0,44.60303,0,0,59.74759,0,0,0,1,0,4,78.9,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,73.33533,9.787733,1.386294,4.090129,1 5,1,25,1,5,126256,0,17812.88,45.86721,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,78.9,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,73.33533,9.787733,1.386294,,0 5,1,25,1,1,126257,0,17812.88,17.46201,0,15,1,28.55443,6.216538,0,0,0,34.77097,0,0,0,4,0,4,82.1,8.7,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.80552,9.787733,1.386294,3.548783,1 5,1,25,1,2,126257,0,17812.88,18.46201,0,15,1,50.62602,1.986935,0,0,0,52.61296,0,0,0,3,0,4,82.1,8.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.80552,9.787733,1.386294,3.962962,1 5,1,25,1,3,126257,0,17812.88,19.46201,0,15,1,25.76809,4.212091,0,0,0,29.98018,0,0,0,2,0,4,82.1,8.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.80552,9.787733,1.386294,3.400537,1 5,1,25,1,4,126257,0,17812.88,20.46201,0,15,1,23.40523,0,0,0,0,23.40523,0,0,0,1,0,4,82.1,8.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.80552,9.787733,1.386294,3.15296,1 5,1,25,1,5,126257,0,17812.88,21.46201,0,15,1,4.417333,0,0,0,0,4.417333,0,0,0,0,0,4,82.1,8.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.80552,9.787733,1.386294,1.485536,1 5,1,25,1,1,126258,0,17812.88,9.459274,1,15,1,41.047,27.79298,0,0,0,68.83997,0,0,0,8,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.77095,9.787733,1.386294,4.231785,1 5,1,25,1,2,126258,0,17812.88,10.45927,1,15,1,22.319,3.810561,0,0,0,26.12956,0,0,0,4,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.77095,9.787733,1.386294,3.263067,1 5,1,25,1,3,126258,0,17812.88,11.45927,1,15,1,22.29931,4.831516,0,0,0,27.13082,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.77095,9.787733,1.386294,3.30067,1 5,1,25,1,4,126258,0,17812.88,12.45927,1,15,1,43.13905,12.09729,0,0,0,55.23635,0,0,0,3,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.77095,9.787733,1.386294,4.011621,1 5,1,25,1,5,126258,0,17812.88,13.45927,1,15,1,47.11822,11.42196,0,0,0,58.54018,0,0,0,6,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.77095,9.787733,1.386294,4.069713,1 5,1,25,1,1,126259,0,17812.88,39.07187,1,15,1,101.7252,0,0,0,0,101.7252,0,0,0,3,0,4,80,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.85065,9.787733,1.386294,4.622275,1 5,1,25,1,2,126259,0,17812.88,40.07187,1,15,1,126.0207,0,0,0,0,126.0207,0,0,0,3,0,4,80,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.85065,9.787733,1.386294,4.836446,1 5,1,25,1,3,126259,0,17812.88,41.07187,1,15,1,19.82161,2.750248,0,0,0,22.57185,0,0,0,2,0,4,80,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.85065,9.787733,1.386294,3.116704,1 5,1,25,1,4,126259,0,17812.88,42.07187,1,15,1,18.81597,0,0,0,0,18.81597,0,0,0,1,0,4,80,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.85065,9.787733,1.386294,2.934706,1 5,1,25,1,5,126259,0,17812.88,43.07187,1,15,1,109.8023,23.09634,3.407657,0,0,136.3063,0,0,0,4,0,4,80,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.85065,9.787733,1.386294,4.914905,1 7,1,25,0,1,126288,0,11939.83,4.073922,0,12,1,35.92462,0,0,0,0,35.92462,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.3802,9.387718,1.386294,3.581423,1 7,1,25,0,2,126288,0,11939.83,5.073922,0,12,1,28.84097,0,0,0,0,28.84097,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.3802,9.387718,1.386294,3.361797,1 7,1,25,0,3,126288,0,11939.83,6.073922,0,12,1,52.82555,0,4.511056,4.299754,0,57.33661,0,0,1,2,1,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.3802,9.387718,1.386294,4.048939,1 7,1,25,0,4,126288,0,11939.83,7.073922,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.3802,9.387718,1.386294,,0 7,1,25,0,5,126288,0,11939.83,8.073922,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.3802,9.387718,1.386294,,0 7,1,25,0,1,126289,0,11939.83,29.62628,0,11,1,0,0,0,0,0,0,0,0,0,0,0,4,91.6,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.3162,9.387718,1.386294,,0 7,1,25,0,2,126289,0,11939.83,30.62628,0,11,1,24.25876,0,0,0,0,24.25876,0,0,0,2,0,4,91.6,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.3162,9.387718,1.386294,3.188778,1 7,1,25,0,3,126289,0,11939.83,31.62628,0,11,1,0,0,0,19.04177,0,0,0,0,3,0,0,4,91.6,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.3162,9.387718,1.386294,,0 7,1,25,0,4,126289,0,11939.83,32.62628,0,11,1,87.39745,0,0,0,0,87.39745,0,0,0,3,0,4,91.6,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.3162,9.387718,1.386294,4.470466,1 7,1,25,0,5,126289,0,11939.83,33.62628,0,11,1,33.97249,0,0,0,0,33.97249,0,0,0,1,0,4,91.6,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.3162,9.387718,1.386294,3.525551,1 7,1,25,0,1,126290,0,11939.83,29.02943,1,12,1,438.1036,0,17.85041,0,0,455.9541,0,0,0,3,1,4,61.1,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.35686,9.387718,1.386294,6.122392,1 7,1,25,0,2,126290,0,11939.83,30.02943,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,61.1,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.35686,9.387718,1.386294,,0 7,1,25,0,3,126290,0,11939.83,31.02943,1,12,1,12.28501,0,32.40786,50.9828,0,44.69287,0,0,5,0,1,4,61.1,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.35686,9.387718,1.386294,3.799814,1 7,1,25,0,4,126290,0,11939.83,32.02943,1,12,1,458.7284,0,7.146764,0,1132.84,1598.715,1,0,0,3,0,4,61.1,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.35686,9.387718,1.386294,7.376956,1 7,1,25,0,5,126290,0,11939.83,33.02943,1,12,1,12.50521,0,0,0,0,12.50521,0,0,0,1,0,4,61.1,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.35686,9.387718,1.386294,2.526145,1 7,1,25,0,1,126291,0,11939.83,8.657084,1,12,1,75.97173,0,0,0,0,75.97173,0,0,0,2,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,78.36227,9.387718,1.386294,4.330361,1 7,1,25,0,2,126291,0,11939.83,9.657084,1,12,1,24.20485,0,0,0,0,24.20485,0,0,0,0,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,78.36227,9.387718,1.386294,3.186553,1 7,1,25,0,3,126291,0,11939.83,10.65708,1,12,1,20.63882,0,0,4.299754,0,20.63882,0,0,1,1,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,78.36227,9.387718,1.386294,3.027174,1 7,1,25,0,4,126291,0,11939.83,11.65708,1,12,1,116.4768,2.734731,0,0,0,119.2115,0,0,0,4,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,78.36227,9.387718,1.386294,4.780899,1 7,1,25,0,5,126291,0,11939.83,12.65708,1,12,1,91.9133,0,0,0,0,91.9133,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,78.36227,9.387718,1.386294,4.520846,1 5,1,25,1,1,126311,0,7136.477,35.90691,0,12,1,58.15348,2.93765,0,0,0,61.09113,0,0,0,2,0,3,85.3,8.7,0,,678,678,0,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,78.56193,8.873115,1.098612,4.112367,1 5,1,25,1,2,126311,0,7136.477,36.90691,0,12,1,44.35926,0,0,0,0,44.35926,0,0,0,3,0,3,85.3,8.7,0,,678,678,0,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,78.56193,8.873115,1.098612,3.792321,1 5,1,25,1,3,126311,0,7136.477,37.90691,0,12,1,444.1596,27.6808,0,0,0,471.8404,0,0,0,2,1,3,85.3,8.7,0,,678,678,0,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,78.56193,8.873115,1.098612,6.156641,1 5,1,25,1,4,126311,0,7136.477,38.90691,0,12,1,76.07192,6.339327,52.0332,0,0,134.4444,0,0,0,5,1,3,85.3,8.7,0,,678,678,0,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,78.56193,8.873115,1.098612,4.901151,1 5,1,25,1,5,126311,0,7136.477,39.90691,0,12,1,20.31316,8.78121,0,0,0,29.09437,0,0,0,5,0,3,85.3,8.7,0,,678,678,0,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,78.56193,8.873115,1.098612,3.370545,1 5,1,25,1,1,126312,0,7136.477,.6680356,0,7,1,35.3717,2.068345,0,0,0,37.44005,0,0,0,6,0,3,74.36826,13.73189,0,,678,678,1,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,80.9538,8.873115,1.098612,3.622741,1 5,1,25,1,2,126312,0,7136.477,1.668036,0,7,1,8.214677,2.382256,0,0,0,10.59693,0,0,0,1,0,3,74.36826,13.73189,0,,678,678,1,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,80.9538,8.873115,1.098612,2.360565,1 5,1,25,1,3,126312,0,7136.477,2.668036,0,7,1,4.987531,0,0,0,0,4.987531,0,0,0,1,0,3,74.36826,13.73189,0,,678,678,1,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,80.9538,8.873115,1.098612,1.606941,1 5,1,25,1,4,126312,0,7136.477,3.668036,0,7,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,678,678,1,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,80.9538,8.873115,1.098612,,0 5,1,25,1,5,126312,0,7136.477,4.668036,0,7,1,22.85231,0,0,0,0,22.85231,0,0,0,2,1,3,74.36826,13.73189,0,,678,678,1,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,80.9538,8.873115,1.098612,3.129052,1 5,1,25,1,1,126313,0,7136.477,36.23819,1,7,1,11.39089,21.94245,0,0,0,33.33333,0,0,0,0,0,3,64.2,17.4,0,,678,678,0,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,69.21714,8.873115,1.098612,3.506558,1 5,1,25,1,2,126313,0,7136.477,37.23819,1,7,1,43.81161,27.65608,0,0,0,71.46769,0,0,0,1,0,3,64.2,17.4,0,,678,678,0,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,69.21714,8.873115,1.098612,4.269246,1 5,1,25,1,3,126313,0,7136.477,38.23819,1,7,1,23.94015,34.0399,26.58354,0,0,84.56359,0,0,0,1,1,3,64.2,17.4,0,,678,678,0,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,69.21714,8.873115,1.098612,4.437504,1 5,1,25,1,4,126313,0,7136.477,39.23819,1,7,1,47.02628,47.30291,0,0,0,94.32919,0,0,0,3,0,3,64.2,17.4,0,,678,678,0,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,69.21714,8.873115,1.098612,4.546791,1 5,1,25,1,5,126313,0,7136.477,40.23819,1,7,1,121.5404,33.64367,56.60601,0,0,211.7901,0,0,0,5,1,3,64.2,17.4,0,,678,678,0,0,1.098612,6.519147,0,3.258096,7.905442,0,0,0,69.21714,8.873115,1.098612,5.355596,1 5,1,25,1,1,126314,0,2291.563,19.36208,0,12,1,8.992805,0,38.21943,0,0,47.21223,0,0,0,0,1,1,73.7,0,0,,179,0,0,0,0,0,0,3.258096,6.57368,0,0,0,77.80665,7.737426,0,3.854653,1 5,1,25,1,2,126314,0,2291.563,20.36208,0,12,1,0,0,39.49069,0,0,39.49069,0,0,0,0,0,1,73.7,0,0,,179,0,0,0,0,0,0,3.258096,6.57368,0,0,0,77.80665,7.737426,0,3.676065,1 5,1,25,1,3,126314,0,2291.563,21.36208,0,12,1,8.977556,1.9202,31.79551,0,0,42.69327,0,0,0,0,1,1,73.7,0,0,,179,0,0,0,0,0,0,3.258096,6.57368,0,0,0,77.80665,7.737426,0,3.754041,1 5,1,25,1,4,126314,0,2291.563,22.36208,0,12,1,49.80175,0,20.71922,0,0,70.52098,0,0,0,1,0,1,73.7,0,0,,179,0,0,0,0,0,0,3.258096,6.57368,0,0,0,77.80665,7.737426,0,4.25591,1 5,1,25,1,5,126314,0,2291.563,23.36208,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,73.7,0,0,,179,0,0,0,0,0,0,3.258096,6.57368,0,0,0,77.80665,7.737426,0,,0 8,1,50,0,1,126319,0,3717.07,6.833675,0,13,1,12.58993,10.61151,0,0,0,23.20144,0,0,0,2,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,3.931826,0,0,0,0,84.2508,8.22096,1.386294,3.144214,1 8,1,50,0,2,126319,0,3717.07,7.833675,0,13,1,34.50164,15.03286,0,0,0,49.5345,0,0,0,5,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,3.931826,0,0,0,0,84.2508,8.22096,1.386294,3.902669,1 8,1,50,0,3,126319,0,3717.07,8.833675,0,13,1,42.39402,16.28429,0,0,0,58.6783,0,0,0,7,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,3.931826,0,0,0,0,84.2508,8.22096,1.386294,4.07207,1 8,1,50,0,1,126320,0,3717.07,34.01232,0,17,1,111.8106,2.667866,0,0,0,114.4784,0,0,0,7,0,4,33.8,13.73189,0,,0,0,0,0,1.386294,0,0,3.931826,0,0,0,0,74.86721,8.22096,1.386294,4.740386,1 8,1,50,0,2,126320,0,3717.07,35.01232,0,17,1,30.66813,13.82804,37.48631,0,0,81.98248,0,0,0,4,0,4,33.8,13.73189,0,,0,0,0,0,1.386294,0,0,3.931826,0,0,0,0,74.86721,8.22096,1.386294,4.406506,1 8,1,50,0,3,126320,0,3717.07,36.01232,0,17,1,84.78803,16.70823,0,0,0,101.4963,0,0,0,1,0,4,33.8,13.73189,0,,0,0,0,0,1.386294,0,0,3.931826,0,0,0,0,74.86721,8.22096,1.386294,4.620022,1 8,1,50,0,1,126321,0,3717.07,32.33128,1,13,1,125,24.79017,102.0923,0,783.5432,1035.426,1,0,0,9,0,4,62.5,13.73189,1,,0,0,0,0,1.386294,0,0,3.931826,0,1,0,0,66.88633,8.22096,1.386294,6.942568,1 8,1,50,0,2,126321,0,3717.07,33.33128,1,13,1,77.76561,40.82694,328.5871,0,1728.598,2175.778,2,0,0,7,0,4,62.5,13.73189,1,,0,0,0,0,1.386294,0,0,3.931826,0,1,0,0,66.88633,8.22096,1.386294,7.685142,1 8,1,50,0,3,126321,0,3717.07,34.33128,1,13,1,483.5162,15.3616,249.3766,0,982.2244,1730.479,1,0,0,14,0,4,62.5,13.73189,1,,0,0,0,0,1.386294,0,0,3.931826,0,1,0,0,66.88633,8.22096,1.386294,7.456153,1 8,1,50,0,1,126322,0,3717.07,.6926762,1,13,1,90.52758,16.78657,0,0,0,107.3141,0,0,0,11,1,4,74.36826,13.73189,0,,0,0,1,1,1.386294,0,0,3.931826,0,0,0,0,80.3052,8.22096,1.386294,4.67576,1 8,1,50,0,2,126322,0,3717.07,1.692676,1,13,1,355.942,60.68456,0,0,0,416.6265,0,0,0,16,0,4,74.36826,13.73189,0,,0,0,1,1,1.386294,0,0,3.931826,0,0,0,0,80.3052,8.22096,1.386294,6.03219,1 8,1,50,0,3,126322,0,3717.07,2.692676,1,13,1,100.7481,32.74314,0,0,352.1596,485.6509,1,0,0,15,0,4,74.36826,13.73189,0,,0,0,1,1,1.386294,0,0,3.931826,0,0,0,0,80.3052,8.22096,1.386294,6.18549,1 1,1,0,0,1,126331,0,8401.985,1.689254,0,16,1,21.20141,21.2662,0,0,0,42.46761,0,0,0,4,0,3,74.36826,13.73189,0,,450,450,1,0,1.098612,6.109248,1,0,0,0,0,0,80.40897,9.036343,1.098612,3.748742,1 1,1,0,0,2,126331,0,8401.985,2.689254,0,16,1,20.48518,19.89757,0,0,0,40.38275,0,0,0,3,0,3,74.36826,13.73189,0,,450,450,1,0,1.098612,6.109248,1,0,0,0,0,0,80.40897,9.036343,1.098612,3.698403,1 1,1,0,0,3,126331,0,8401.985,3.689254,0,16,1,24.57002,20.2113,0,0,0,44.78133,0,0,0,3,0,4,74.36826,13.73189,0,,450,450,1,0,1.386294,6.109248,1,0,0,0,0,0,80.40897,9.036343,1.386294,3.801791,1 1,1,0,0,1,126332,0,8401.985,28.7447,0,16,1,21.49588,5.223793,0,0,0,26.71967,0,0,0,1,1,3,80,17.4,0,,450,450,0,0,1.098612,6.109248,1,0,0,0,0,0,78.62843,9.036343,1.098612,3.2854,1 1,1,0,0,2,126332,0,8401.985,29.7447,0,16,1,18.86792,0,0,0,0,18.86792,0,0,0,0,1,3,80,17.4,0,,450,450,0,0,1.098612,6.109248,1,0,0,0,0,0,78.62843,9.036343,1.098612,2.937463,1 1,1,0,0,3,126332,0,8401.985,30.7447,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,80,17.4,0,,450,450,0,0,1.386294,6.109248,1,0,0,0,0,0,78.62843,9.036343,1.386294,,0 1,1,0,0,1,126333,0,8401.985,29.08419,1,16,1,60.6596,27.34393,42.40283,0,0,130.4064,0,0,0,4,1,3,87.4,13,0,,450,450,0,0,1.098612,6.109248,1,0,0,0,0,0,79.51961,9.036343,1.098612,4.870656,1 1,1,0,0,2,126333,0,8401.985,30.08419,1,16,1,2.695418,27.78976,0,0,736.7925,767.2776,1,0,0,0,0,3,87.4,13,0,,450,450,0,0,1.098612,6.109248,1,0,0,0,0,0,79.51961,9.036343,1.098612,6.642848,1 1,1,0,0,3,126333,0,8401.985,31.08419,1,16,1,26.04423,24.44226,0,0,0,50.48649,0,0,0,3,0,4,87.4,13,0,,450,450,0,0,1.386294,6.109248,1,0,0,0,0,0,79.51961,9.036343,1.386294,3.921706,1 11,1,0,1,1,126340,0,6321.658,17.30048,1,14,1,132.0643,70.28555,42.75431,0,0,245.1041,0,0,0,19,0,3,92.6,13,0,,0,0,1,1,1.098612,0,0,0,0,0,0,0,74.41844,8.751895,1.098612,5.501683,1 11,1,0,1,2,126340,0,6321.658,18.30048,1,14,1,22.86336,70.44093,0,0,0,93.3043,0,0,0,3,0,3,92.6,13,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,74.41844,8.751895,1.098612,4.535866,1 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11,1,0,1,2,126342,0,6321.658,54.65366,0,14,1,97.44148,37.34349,0,0,0,134.785,0,0,0,10,5,3,52.6,13,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,76.12692,8.751895,1.098612,4.903681,1 11,1,0,1,3,126342,0,6321.658,55.65366,0,14,1,46.08523,23.14172,37.16551,0,0,106.3925,0,0,0,1,5,3,52.6,13,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,76.12692,8.751895,1.098612,4.667135,1 11,1,0,1,1,126343,0,5065.757,23.02259,0,12,1,46.84117,6.632957,34.19393,0,0,87.66805,0,0,0,6,0,1,62.1,4.3,0,,0,52,0,0,0,3.951244,0,0,0,0,0,0,77.42352,8.530457,0,4.473557,1 11,1,0,1,2,126343,0,5065.757,24.02259,0,12,1,20.6859,8.328797,0,0,0,29.0147,0,0,0,4,0,1,62.1,4.3,0,,0,52,0,0,0,3.951244,0,0,0,0,0,0,77.42352,8.530457,0,3.367803,1 11,1,0,1,3,126343,0,5065.757,25.02259,0,12,1,48.56293,12.31417,29.51933,0,0,90.39643,0,0,0,7,0,1,62.1,4.3,0,,0,52,0,0,0,3.951244,0,0,0,0,0,0,77.42352,8.530457,0,4.504205,1 5,1,25,0,1,126350,0,9707.816,61.90281,1,11,1,107.3322,87.77974,39.3934,0,0,234.5053,0,0,0,15,0,1,95,13.73189,0,,716,716,0,0,0,6.57368,0,3.258096,7.959975,0,0,0,76.49065,9.18079,0,5.457478,1 5,1,25,0,2,126350,0,9707.816,62.90281,1,11,1,165.2291,86.33962,46.47979,0,1636.14,1934.189,1,0,0,16,0,1,95,13.73189,0,,716,716,0,0,0,6.57368,0,3.258096,7.959975,0,0,0,76.49065,9.18079,0,7.567443,1 5,1,25,0,3,126350,0,9707.816,63.90281,1,11,1,29.48403,50.71253,0,0,0,80.19656,0,0,0,3,0,1,95,13.73189,0,,716,716,0,0,0,6.57368,0,3.258096,7.959975,0,0,0,76.49065,9.18079,0,4.38448,1 5,1,25,0,1,126359,0,6277.295,32.53114,1,9,1,6.478209,0,0,0,0,6.478209,0,0,0,1,0,4,95,13.73189,0,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,69.47372,8.744854,1.386294,1.868444,1 5,1,25,0,2,126359,0,6277.295,33.53114,1,9,1,25.87601,2.156334,0,0,0,28.03234,0,0,0,2,0,4,95,13.73189,0,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,69.47372,8.744854,1.386294,3.333359,1 5,1,25,0,3,126359,0,6277.295,34.53114,1,9,1,46.06879,6.314497,0,0,0,52.38329,0,0,0,3,0,4,95,13.73189,0,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,69.47372,8.744854,1.386294,3.958588,1 5,1,25,0,4,126359,0,6277.295,35.53114,1,9,1,26.89152,0,0,0,0,26.89152,0,0,0,2,0,4,95,13.73189,0,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,69.47372,8.744854,1.386294,3.291811,1 5,1,25,0,5,126359,0,6277.295,36.53114,1,9,1,350.3126,6.669446,196.0192,0,0,553.0012,0,0,0,9,0,4,95,13.73189,0,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,69.47372,8.744854,1.386294,6.31536,1 5,1,25,0,1,126360,0,6277.295,9.029432,1,9,1,19.43463,0,20.84806,0,0,40.28268,0,0,0,2,1,4,74.36826,13.73189,0,,500,500,1,1,1.386294,6.214608,0,3.258096,7.600903,1,0,0,76.85021,8.744854,1.386294,3.695922,1 5,1,25,0,2,126360,0,6277.295,10.02943,1,9,1,5.390836,2.495957,8.964959,0,0,16.85175,0,0,0,1,0,4,74.36826,13.73189,0,,500,500,1,1,1.386294,6.214608,0,3.258096,7.600903,1,0,0,76.85021,8.744854,1.386294,2.824455,1 5,1,25,0,3,126360,0,6277.295,11.02943,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,500,500,1,1,1.386294,6.214608,0,3.258096,7.600903,1,0,0,76.85021,8.744854,1.386294,,0 5,1,25,0,4,126360,0,6277.295,12.02943,1,9,1,46.03464,2.734731,0,0,0,48.76937,0,0,0,2,1,4,74.36826,13.73189,0,,500,500,1,1,1.386294,6.214608,0,3.258096,7.600903,1,0,0,76.85021,8.744854,1.386294,3.887102,1 5,1,25,0,5,126360,0,6277.295,13.02943,1,9,1,40.45436,5.360567,23.88495,0,492.0342,561.7341,1,0,0,2,0,4,74.36826,13.73189,0,,500,500,1,1,1.386294,6.214608,0,3.258096,7.600903,1,0,0,76.85021,8.744854,1.386294,6.331028,1 5,1,25,0,1,126361,0,6277.295,32.85695,0,12.32507,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,.12982,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,71.97958,8.744854,1.386294,,0 5,1,25,0,2,126361,0,6277.295,33.85695,0,12.32507,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,.12982,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,71.97958,8.744854,1.386294,,0 5,1,25,0,3,126361,0,6277.295,34.85695,0,12.32507,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,.12982,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,71.97958,8.744854,1.386294,,0 5,1,25,0,4,126361,0,6277.295,35.85695,0,12.32507,1,30.76572,0,0,0,0,30.76572,0,0,0,1,0,4,74.36826,13.73189,.12982,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,71.97958,8.744854,1.386294,3.426401,1 5,1,25,0,5,126361,0,6277.295,36.85695,0,12.32507,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,.12982,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,71.97958,8.744854,1.386294,,0 5,1,25,0,1,126362,0,6277.295,14.23956,0,9,1,104.2108,.8598351,0,0,0,105.0707,0,0,0,3,0,4,95,13.73189,0,,500,500,1,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,70.41564,8.744854,1.386294,4.654633,1 5,1,25,0,2,126362,0,6277.295,15.23956,0,9,1,0,0,0,0,0,0,0,0,0,0,0,4,95,13.73189,0,,500,500,1,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,70.41564,8.744854,1.386294,,0 5,1,25,0,3,126362,0,6277.295,16.23956,0,9,1,0,0,0,0,0,0,0,0,0,0,0,4,95,13.73189,0,,500,500,1,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,70.41564,8.744854,1.386294,,0 5,1,25,0,4,126362,0,6277.295,17.23956,0,9,1,0,0,0,0,0,0,0,0,0,0,0,4,95,13.73189,0,,500,500,1,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,70.41564,8.744854,1.386294,,0 5,1,25,0,5,126362,0,6277.295,18.23956,0,9,1,0,0,0,0,0,0,0,0,0,0,0,4,95,13.73189,0,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,1,0,0,70.41564,8.744854,1.386294,,0 4,1,100,1,1,126384,0,4298.431,62.02327,1,11,1,26.50177,11.16019,0,0,0,37.66196,0,0,0,3,0,1,81.1,17.4,0,,1000,1000,0,0,0,6.907755,1,0,0,1,0,0,68.18743,8.366238,0,3.62865,1 4,1,100,1,2,126384,0,4298.431,63.02327,1,11,1,202.4259,99.78436,431.1752,0,0,733.3854,0,0,0,7,1,1,81.1,17.4,0,,1000,1000,0,0,0,6.907755,1,0,0,1,0,0,68.18743,8.366238,0,6.597672,1 4,1,100,1,3,126384,0,4298.431,64.02327,1,11,1,351.8427,100.1228,107.4889,0,703.9951,1263.45,1,0,0,14,0,1,81.1,17.4,0,,1000,1000,0,0,0,6.907755,1,0,0,1,0,0,68.18743,8.366238,0,7.141601,1 5,1,25,1,1,126386,0,7500,31.64134,1,12,1,47.29328,14.6282,0,0,0,61.92147,0,0,0,5,0,4,74.7,13,0,,455,455,0,0,1.386294,6.120297,0,3.258096,7.506592,0,0,0,77.99498,8.922791,1.386294,4.125867,1 5,1,25,1,2,126386,0,7500,32.64134,1,12,1,51.44257,27.51769,0,0,0,78.96026,0,0,0,4,0,4,74.7,13,0,,455,455,0,0,1.386294,6.120297,0,3.258096,7.506592,0,0,0,77.99498,8.922791,1.386294,4.368945,1 5,1,25,1,3,126386,0,7500,33.64134,1,12,1,9.910803,0,0,0,0,9.910803,0,0,0,1,0,4,74.7,13,0,,455,455,0,0,1.386294,6.120297,0,3.258096,7.506592,0,0,0,77.99498,8.922791,1.386294,2.293625,1 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7,1,25,0,2,126461,0,6078.164,50.24572,1,14,1,0,0,0,0,0,0,0,0,0,0,0,1,82.5,13.73189,0,,843,843,0,0,0,6.736967,0,3.258096,8.123261,0,0,0,79.31465,8.712623,0,,0 7,1,25,0,3,126461,0,6078.164,51.24572,1,14,1,0,0,0,0,0,0,0,0,0,0,0,1,82.5,13.73189,0,,843,843,0,0,0,6.736967,0,3.258096,8.123261,0,0,0,79.31465,8.712623,0,,0 2,1,100,0,1,126465,0,9542.002,59.37577,1,8,1,77.73852,111.331,0,0,0,189.0695,0,0,0,14,0,1,93.7,26.1,1,,107,0,0,0,0,0,1,0,0,0,0,0,74.02026,9.163564,0,5.242115,1 2,1,100,0,2,126465,0,9542.002,60.37577,1,8,.4098361,33.42318,51.71429,0,0,0,85.13747,0,0,0,3,1,1,93.7,26.1,1,,107,0,0,0,0,0,1,0,0,0,0,0,74.02026,9.163564,0,4.444267,1 1,1,0,0,1,126467,0,9542.002,51.60301,0,13,1,59.48174,17.95642,0,0,0,77.43816,0,0,0,7,0,3,52.6,21.7,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,69.33797,9.163564,1.098612,4.34948,1 1,1,0,0,2,126467,0,9542.002,52.60301,0,13,1,17.78976,0,0,0,0,17.78976,0,0,0,3,0,3,52.6,21.7,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,69.33797,9.163564,1.098612,2.878623,1 1,1,0,0,3,126467,0,9542.002,53.60301,0,13,1,28.13268,0,0,0,0,28.13268,0,0,0,2,0,3,52.6,21.7,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,69.33797,9.163564,1.098612,3.336932,1 1,1,0,0,1,126468,0,9542.002,18.52704,1,12,1,30.62426,9.045937,0,0,0,39.6702,0,0,0,1,0,3,42.1,13,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,72.70441,9.163564,1.098612,3.6806,1 1,1,0,0,2,126468,0,9542.002,19.52704,1,12,1,40.97035,5.369272,26.41509,0,0,72.75471,0,0,0,3,0,3,42.1,13,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,72.70441,9.163564,1.098612,4.287094,1 1,1,0,0,3,126468,0,9542.002,20.52704,1,12,1,42.01474,11.95086,0,0,767.0762,821.0417,1,0,0,2,0,3,42.1,13,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,72.70441,9.163564,1.098612,6.710574,1 1,1,0,0,1,126469,0,9542.002,47.10199,1,12,1,89.28151,26.27797,0,0,992.2438,1107.803,1,0,0,8,0,3,51.6,8.7,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,71.65771,9.163564,1.098612,7.010134,1 1,1,0,0,2,126469,0,9542.002,48.10199,1,12,1,284.717,61.062,0,0,0,345.779,0,0,0,14,0,3,51.6,8.7,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,71.65771,9.163564,1.098612,5.8458,1 1,1,0,0,3,126469,0,9542.002,49.10199,1,12,1,51.30221,44.10811,0,0,0,95.41032,0,0,0,6,0,3,51.6,8.7,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,71.65771,9.163564,1.098612,4.558187,1 8,1,50,1,1,126486,0,1728.908,10.76797,0,11,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,163,450,1,0,1.098612,6.109248,0,3.931826,5.786897,1,0,0,76.10808,7.455823,1.098612,,0 8,1,50,1,2,126486,0,1728.908,11.76797,0,11,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,163,450,1,0,1.386294,6.109248,0,3.931826,5.786897,1,0,0,76.10808,7.455823,1.386294,,0 8,1,50,1,3,126486,0,1728.908,12.76797,0,11,1,16.35283,0,0,0,0,16.35283,0,0,0,2,0,4,74.36826,13.73189,0,,163,450,1,0,1.386294,6.109248,0,3.931826,5.786897,1,0,0,76.10808,7.455823,1.386294,2.794401,1 8,1,50,1,4,126486,0,1728.908,13.76797,0,11,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,163,450,1,0,1.386294,6.109248,0,3.931826,5.786897,1,0,0,76.10808,7.455823,1.386294,,0 8,1,50,1,5,126486,0,1728.908,14.76797,0,11,1,41.22844,4.585612,0,0,0,45.81405,0,0,0,5,0,4,74.36826,13.73189,0,,163,450,1,0,1.386294,6.109248,0,3.931826,5.786897,1,0,0,76.10808,7.455823,1.386294,3.824591,1 8,1,50,1,1,126488,0,1728.908,47.95893,1,11,1,98.15586,20.80904,39.78584,0,0,158.7507,0,0,0,4,1,3,64.2,26.1,0,,163,450,0,0,1.098612,6.109248,0,3.931826,5.786897,1,0,0,67.26075,7.455823,1.098612,5.067335,1 8,1,50,1,2,126488,0,1728.908,48.95893,1,11,1,0,0,0,0,0,0,0,0,0,0,0,4,64.2,26.1,0,,163,450,0,0,1.386294,6.109248,0,3.931826,5.786897,1,0,0,67.26075,7.455823,1.386294,,0 8,1,50,1,3,126488,0,1728.908,49.95893,1,11,1,81.26859,19.94053,54.89098,0,0,156.1001,0,0,0,9,1,4,64.2,26.1,0,,163,450,0,0,1.386294,6.109248,0,3.931826,5.786897,1,0,0,67.26075,7.455823,1.386294,5.050498,1 8,1,50,1,4,126488,0,1728.908,50.95893,1,11,1,19.73382,9.343736,0,0,0,29.07756,0,0,0,2,0,4,64.2,26.1,0,,163,450,0,0,1.386294,6.109248,0,3.931826,5.786897,1,0,0,67.26075,7.455823,1.386294,3.369967,1 8,1,50,1,5,126488,0,1728.908,51.95893,1,11,1,276.7144,45.35128,47.48002,0,470.8162,840.3618,1,0,0,7,1,4,64.2,26.1,0,,163,450,0,0,1.386294,6.109248,0,3.931826,5.786897,1,0,0,67.26075,7.455823,1.386294,6.733832,1 8,1,50,1,1,126489,0,1728.908,15.86858,1,11,1,95.18144,36.38311,0,0,25263.65,25395.21,1,0,0,9,0,3,75.8,13,0,,163,450,1,1,1.098612,6.109248,0,3.931826,5.786897,1,0,0,63.92562,7.455823,1.098612,10.14232,1 8,1,50,1,2,126489,0,1728.908,16.86858,1,11,1,27.21829,27.10942,0,0,0,54.32771,0,0,0,3,0,4,75.8,13,0,,163,450,1,1,1.386294,6.109248,0,3.931826,5.786897,1,0,0,63.92562,7.455823,1.386294,3.995034,1 8,1,50,1,3,126489,0,1728.908,17.86858,1,11,1,80.94153,38.60258,41.94747,0,0,161.4916,0,0,0,7,2,4,75.8,13,0,,163,450,1,1,1.386294,6.109248,0,3.931826,5.786897,1,0,0,63.92562,7.455823,1.386294,5.084453,1 8,1,50,1,4,126489,0,1728.908,18.86858,1,11,1,76.8793,25.69527,0,0,0,102.5746,0,0,0,4,0,4,75.8,13,0,,163,450,0,0,1.386294,6.109248,0,3.931826,5.786897,1,0,0,63.92562,7.455823,1.386294,4.63059,1 8,1,50,1,5,126489,0,1728.908,19.86858,1,11,1,134.8296,25.7257,0,0,223.8199,384.3753,1,0,0,5,1,4,75.8,13,0,,163,450,0,0,1.386294,6.109248,0,3.931826,5.786897,1,0,0,63.92562,7.455823,1.386294,5.951619,1 7,1,25,1,1,126497,0,5035.244,58.32717,0,8,1,143.735,43.96283,25.94125,0,558.5552,772.1943,1,0,0,10,0,2,65.3,21.7,0,,1000,1000,0,0,.6931472,6.907755,0,3.258096,8.294049,0,1,0,58.96577,8.524416,.6931472,6.649236,1 7,1,25,1,2,126497,0,5035.244,59.32717,0,8,1,15.88171,57.19058,30.77218,0,0,103.8445,0,0,0,2,1,2,65.3,21.7,0,,1000,1000,0,0,.6931472,6.907755,0,3.258096,8.294049,0,1,0,58.96577,8.524416,.6931472,4.642894,1 7,1,25,1,1,126498,0,5035.244,49.82888,1,8,1,285.8513,28.84892,0,0,0,314.7002,0,0,0,6,0,2,80,8.7,0,,1000,1000,0,0,.6931472,6.907755,0,3.258096,8.294049,1,0,0,63.43494,8.524416,.6931472,5.75162,1 7,1,25,1,2,126498,0,5035.244,50.82888,1,8,1,17.52464,11.33625,37.48083,0,448.7952,515.1369,1,0,0,2,1,2,80,8.7,0,,1000,1000,0,0,.6931472,6.907755,0,3.258096,8.294049,1,0,0,63.43494,8.524416,.6931472,6.244433,1 3,1,100,0,1,126516,0,17296.53,33.73032,1,16,1,16.65675,11.08864,0,0,0,27.74539,0,0,0,2,0,5,73.8,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,69.55659,9.758319,1.609438,3.32307,1 3,1,100,0,2,126516,0,17296.53,34.73032,1,16,1,371.8018,30.44638,0,0,0,402.2482,0,0,0,10,0,5,73.8,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,69.55659,9.758319,1.609438,5.997069,1 3,1,100,0,3,126516,0,17296.53,35.73032,1,16,1,10.15857,43.91972,0,0,0,54.0783,0,0,0,1,0,5,73.8,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,69.55659,9.758319,1.609438,3.990433,1 3,1,100,0,1,126517,0,17296.53,9.330595,0,16,1,20.22606,17.93575,0,0,0,38.16181,0,0,0,3,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,1,0,0,77.79649,9.758319,1.609438,3.641835,1 3,1,100,0,2,126517,0,17296.53,10.3306,0,16,1,29.9129,4.599891,0,0,0,34.51279,0,0,0,2,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,1,0,0,77.79649,9.758319,1.609438,3.54133,1 3,1,100,0,3,126517,0,17296.53,11.3306,0,16,1,22.79485,3.657086,0,0,0,26.45193,0,0,0,3,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,1,0,0,77.79649,9.758319,1.609438,3.275329,1 3,1,100,0,1,126518,0,17296.53,10.42026,1,16,1,24.39024,1.754908,0,0,0,26.14515,0,0,0,3,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,83.2181,9.758319,1.609438,3.263664,1 3,1,100,0,2,126518,0,17296.53,11.42026,1,16,1,77.81709,13.05389,0,0,182.5259,273.3969,1,0,0,2,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,83.2181,9.758319,1.609438,5.610924,1 3,1,100,0,3,126518,0,17296.53,12.42026,1,16,1,14.37066,0,0,0,0,14.37066,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,83.2181,9.758319,1.609438,2.665189,1 3,1,100,0,1,126519,0,17296.53,34.54894,0,18,1,35.09816,49.55384,0,0,0,84.65199,0,0,0,5,0,5,80,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,64.61339,9.758319,1.609438,4.438549,1 3,1,100,0,2,126519,0,17296.53,35.54894,0,18,1,159.4992,37.40882,0,0,0,196.908,0,0,0,7,0,5,80,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,64.61339,9.758319,1.609438,5.282737,1 3,1,100,0,3,126519,0,17296.53,36.54894,0,18,1,101.5857,55.32706,0,0,0,156.9128,0,0,0,10,0,5,80,13.73189,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,64.61339,9.758319,1.609438,5.05569,1 3,1,100,0,1,126520,0,17296.53,4.112252,1,16,1,39.26234,15.84176,0,0,0,55.1041,0,0,0,5,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,1,0,0,71.73346,9.758319,1.609438,4.009224,1 3,1,100,0,2,126520,0,17296.53,5.112252,1,16,1,89.82036,26.32553,0,0,0,116.1459,0,0,0,6,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,1,0,0,71.73346,9.758319,1.609438,4.754847,1 3,1,100,0,3,126520,0,17296.53,6.112252,1,16,1,8.919723,16.0555,0,0,0,24.97522,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,1,0,0,71.73346,9.758319,1.609438,3.217884,1 8,1,50,0,1,126544,0,13919.98,11.49076,1,12,1,28.85748,2.37338,0,0,0,31.23086,0,0,0,2,0,3,74.36826,13.73189,0,,1000,1000,1,1,1.098612,6.907755,0,3.931826,7.600903,0,0,0,84.23631,9.541152,1.098612,3.441407,1 8,1,50,0,2,126544,0,13919.98,12.49076,1,12,1,9.703504,0,0,0,0,9.703504,0,0,0,0,1,3,74.36826,13.73189,0,,1000,1000,1,1,1.098612,6.907755,0,3.931826,7.600903,0,0,0,84.23631,9.541152,1.098612,2.272487,1 8,1,50,0,3,126544,0,13919.98,13.49076,1,12,1,7.371007,1.941032,0,0,0,9.312039,0,0,0,1,0,3,74.36826,13.73189,0,,1000,1000,1,1,1.098612,6.907755,0,3.931826,7.600903,0,0,0,84.23631,9.541152,1.098612,2.231308,1 8,1,50,0,1,126545,0,13919.98,42.7269,1,12,1,283.5689,45.36514,0,0,0,328.9341,0,0,0,12,0,3,34.7,26.1,1,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,66.0592,9.541152,1.098612,5.795857,1 8,1,50,0,2,126545,0,13919.98,43.7269,1,12,1,264.469,92.54447,33.66038,0,0,390.6739,0,0,0,17,6,3,34.7,26.1,1,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,66.0592,9.541152,1.098612,5.967873,1 8,1,50,0,3,126545,0,13919.98,44.7269,1,12,1,0,47.2629,0,0,0,47.2629,0,0,0,0,0,3,34.7,26.1,1,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,66.0592,9.541152,1.098612,3.855726,1 8,1,50,0,1,126546,0,13919.98,43.47981,0,11,1,191.9906,6.861013,0,0,0,198.8516,0,0,0,2,0,3,74.7,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,61.27012,9.541152,1.098612,5.292559,1 8,1,50,0,2,126546,0,13919.98,44.47981,0,11,1,0,8.916442,0,0,0,8.916442,0,0,0,0,0,3,74.7,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,61.27012,9.541152,1.098612,2.187897,1 8,1,50,0,3,126546,0,13919.98,45.47981,0,11,1,32.43243,2.584767,53.40541,0,0,88.42261,0,0,0,1,0,3,74.7,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,61.27012,9.541152,1.098612,4.482128,1 3,1,100,1,1,126553,0,11575.06,3.471595,1,14,1,7.237636,0,0,0,0,7.237636,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,74.41945,9.356694,1.386294,1.979295,1 3,1,100,1,2,126553,0,11575.06,4.471595,1,14,1,18.72247,0,0,0,0,18.72247,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,74.41945,9.356694,1.386294,2.929724,1 3,1,100,1,3,126553,0,11575.06,5.471595,1,14,1,39.02562,2.556504,0,0,0,41.58212,0,0,0,3,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,74.41945,9.356694,1.386294,3.72767,1 3,1,100,1,4,126553,0,11575.06,6.471595,1,14,1,12.05378,0,0,0,0,12.05378,0,0,0,0,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,74.41945,9.356694,1.386294,2.489378,1 3,1,100,1,5,126553,0,11575.06,7.471595,1,14,1,16.58869,0,0,0,0,16.58869,0,0,0,1,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,74.41945,9.356694,1.386294,2.808721,1 3,1,100,1,1,126554,0,11575.06,32.55578,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,77.9,17.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,71.67448,9.356694,1.386294,,0 3,1,100,1,2,126554,0,11575.06,33.55578,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,77.9,17.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,71.67448,9.356694,1.386294,,0 3,1,100,1,3,126554,0,11575.06,34.55578,0,16,1,12.05424,0,14.1336,0,0,26.18785,0,0,0,0,1,4,77.9,17.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,71.67448,9.356694,1.386294,3.265295,1 3,1,100,1,4,126554,0,11575.06,35.55578,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,77.9,17.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,71.67448,9.356694,1.386294,,0 3,1,100,1,5,126554,0,11575.06,36.55578,0,16,1,11.90983,0,0,0,0,11.90983,0,0,0,0,1,4,77.9,17.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,71.67448,9.356694,1.386294,2.477364,1 3,1,100,1,1,126555,0,11575.06,6.401095,1,14,1,9.650181,8.27503,0,0,0,17.92521,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,77.85107,9.356694,1.386294,2.886208,1 3,1,100,1,2,126555,0,11575.06,7.401095,1,14,1,0,7.621145,0,0,0,7.621145,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,77.85107,9.356694,1.386294,2.030927,1 3,1,100,1,3,126555,0,11575.06,8.401095,1,14,1,15.57007,4.650929,0,0,0,20.22099,0,0,0,1,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,77.85107,9.356694,1.386294,3.006721,1 3,1,100,1,4,126555,0,11575.06,9.401095,1,14,1,12.05378,2.545202,20.34771,0,0,34.94669,0,0,0,0,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,77.85107,9.356694,1.386294,3.553824,1 3,1,100,1,5,126555,0,11575.06,10.4011,1,14,1,16.58869,0,12.44577,0,0,29.03445,0,0,0,1,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,1,0,0,77.85107,9.356694,1.386294,3.368483,1 3,1,100,1,1,126556,0,11575.06,31.86311,1,14,1,28.34741,0,25.84439,0,0,54.1918,0,0,0,2,1,4,86.3,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,72.42058,9.356694,1.386294,3.99253,1 3,1,100,1,2,126556,0,11575.06,32.86311,1,14,1,0,0,0,0,0,0,0,0,0,0,0,4,86.3,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,72.42058,9.356694,1.386294,,0 3,1,100,1,3,126556,0,11575.06,33.86311,1,14,1,10.54746,0,0,0,0,10.54746,0,0,0,1,0,4,86.3,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,72.42058,9.356694,1.386294,2.355886,1 3,1,100,1,4,126556,0,11575.06,34.86311,1,14,1,23.64395,1.687529,0,0,0,25.33148,0,0,0,1,1,4,86.3,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,72.42058,9.356694,1.386294,3.232048,1 3,1,100,1,5,126556,0,11575.06,35.86311,1,14,1,11.48448,0,0,0,0,11.48448,0,0,0,1,0,4,86.3,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,72.42058,9.356694,1.386294,2.440996,1 4,1,100,1,1,126566,0,8857.32,37.21561,0,13,1,80.33573,134.2626,0,0,0,214.5983,0,0,0,4,0,5,93.7,8.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,72.11638,9.089112,1.609438,5.368768,1 4,1,100,1,2,126566,0,8857.32,38.21561,0,13,1,108.4337,120.2026,22.32202,0,0,250.9584,0,0,0,3,0,5,93.7,8.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,72.11638,9.089112,1.609438,5.525287,1 4,1,100,1,3,126566,0,8857.32,39.21561,0,13,1,9.476309,0,0,0,0,9.476309,0,0,0,1,0,6,93.7,8.7,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,72.11638,9.089112,1.791759,2.248795,1 4,1,100,1,4,126566,0,8857.32,40.21561,0,13,1,9.22084,4.601199,0,0,0,13.82204,0,0,0,1,0,6,93.7,8.7,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,72.11638,9.089112,1.791759,2.626264,1 4,1,100,1,5,126566,0,8857.32,41.21561,0,13,1,.5289886,2.391028,0,0,0,2.920017,0,0,0,0,0,6,93.7,8.7,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,72.11638,9.089112,1.791759,1.071589,1 4,1,100,1,1,126567,0,8857.32,14.45311,0,12,1,29.3765,0,0,0,0,29.3765,0,0,0,0,0,5,95.8,0,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,79.27259,9.089112,1.609438,3.380195,1 4,1,100,1,2,126567,0,8857.32,15.45311,0,12,1,0,4.359255,0,0,0,4.359255,0,0,0,0,0,5,95.8,0,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,79.27259,9.089112,1.609438,1.472301,1 4,1,100,1,3,126567,0,8857.32,16.45311,0,12,1,26.18454,6.528678,0,0,0,32.71322,0,0,0,3,0,6,95.8,0,0,,1000,1000,1,0,1.791759,6.907755,1,0,0,0,0,0,79.27259,9.089112,1.791759,3.487779,1 4,1,100,1,4,126567,0,8857.32,17.45311,0,12,1,23.0521,0,0,0,0,23.0521,0,0,0,2,0,6,95.8,0,0,,1000,1000,1,0,1.791759,6.907755,1,0,0,0,0,0,79.27259,9.089112,1.791759,3.137757,1 4,1,100,1,5,126567,0,8857.32,18.45311,0,12,1,8.463818,0,0,0,0,8.463818,0,0,0,1,0,6,95.8,0,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,0,0,0,79.27259,9.089112,1.791759,2.1358,1 4,1,100,1,1,126568,0,8857.32,13.40178,1,12,1,14.98801,3.52518,0,0,0,18.51319,0,0,0,1,0,5,74.36826,13.73189,.0277778,,1000,1000,1,1,1.609438,6.907755,1,0,0,1,0,0,77.07726,9.089112,1.609438,2.918483,1 4,1,100,1,2,126568,0,8857.32,14.40178,1,12,1,6.024096,4.813801,16.59912,0,0,27.43702,0,0,0,1,0,5,74.36826,13.73189,.0277778,,1000,1000,1,1,1.609438,6.907755,1,0,0,1,0,0,77.07726,9.089112,1.609438,3.311893,1 4,1,100,1,3,126568,0,8857.32,15.40178,1,12,1,17.45636,2.024938,0,0,0,19.4813,0,0,0,2,0,6,74.36826,13.73189,.0277778,,1000,1000,1,1,1.791759,6.907755,1,0,0,1,0,0,77.07726,9.089112,1.791759,2.969455,1 4,1,100,1,4,126568,0,8857.32,16.40178,1,12,1,0,3.720608,0,0,0,3.720608,0,0,0,0,0,6,74.36826,13.73189,.0277778,,1000,1000,1,1,1.791759,6.907755,1,0,0,1,0,0,77.07726,9.089112,1.791759,1.313887,1 4,1,100,1,5,126568,0,8857.32,17.40178,1,12,1,74.1642,3.643673,28.67964,0,0,106.4875,0,0,0,2,1,6,74.36826,13.73189,.0277778,,1000,1000,1,1,1.791759,6.907755,1,0,0,1,0,0,77.07726,9.089112,1.791759,4.668028,1 4,1,100,1,1,126569,0,8857.32,6.075291,1,12,1,4.196643,12.58993,0,0,0,16.78657,0,0,0,0,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,83.01283,9.089112,1.609438,2.820579,1 4,1,100,1,2,126569,0,8857.32,7.075291,1,12,1,16.977,11.17196,0,0,0,28.14896,0,0,0,1,1,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,0,0,0,83.01283,9.089112,1.609438,3.33751,1 4,1,100,1,3,126569,0,8857.32,8.075291,1,12,1,0,3.690773,0,0,0,3.690773,0,0,0,0,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,1,0,0,0,0,0,83.01283,9.089112,1.791759,1.305836,1 4,1,100,1,4,126569,0,8857.32,9.075291,1,12,1,29.50669,6.325496,0,0,0,35.83218,0,0,0,1,3,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,1,0,0,0,0,0,83.01283,9.089112,1.791759,3.578846,1 4,1,100,1,5,126569,0,8857.32,10.07529,1,12,1,17.45662,1.447313,0,0,0,18.90394,0,0,0,0,3,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,1,0,0,0,0,0,83.01283,9.089112,1.791759,2.93937,1 4,1,100,1,1,126570,0,8857.32,32.82683,1,12,1,40.76739,2.392086,0,0,0,43.15947,0,0,0,2,0,5,88.4,8.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,66.55627,9.089112,1.609438,3.764902,1 4,1,100,1,2,126570,0,8857.32,33.82683,1,12,1,60.24096,11.12815,0,0,1100.181,1171.55,1,0,0,6,0,5,88.4,8.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,66.55627,9.089112,1.609438,7.066083,1 4,1,100,1,3,126570,0,8857.32,34.82683,1,12,1,2.992519,2.109726,0,0,0,5.102244,0,0,0,0,0,6,88.4,8.7,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,66.55627,9.089112,1.791759,1.629681,1 4,1,100,1,4,126570,0,8857.32,35.82683,1,12,1,62.24067,0,0,0,0,62.24067,0,0,0,1,1,6,88.4,8.7,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,66.55627,9.089112,1.791759,4.131009,1 4,1,100,1,5,126570,0,8857.32,36.82683,1,12,1,18.30301,2.835379,0,0,0,21.13838,0,0,0,1,0,6,88.4,8.7,0,,1000,1000,0,0,1.791759,6.907755,1,0,0,1,0,0,66.55627,9.089112,1.791759,3.05109,1 9,1,50,1,1,126596,0,14330.02,35.03354,1,20,1,106.0071,42.30271,0,0,696.6019,844.9117,1,0,0,12,0,4,67.4,21.7,1,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,64.92197,9.570182,1.386294,6.739232,1 9,1,50,1,2,126596,0,14330.02,36.03354,1,20,1,100.2695,26.14016,8.625337,0,1220.782,1355.817,1,0,0,9,0,4,67.4,21.7,1,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,64.92197,9.570182,1.386294,7.212159,1 9,1,50,1,3,126596,0,14330.02,37.03354,1,20,1,83.53809,47.91155,0,0,0,131.4496,0,0,0,7,0,4,67.4,21.7,1,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,64.92197,9.570182,1.386294,4.878624,1 9,1,50,1,1,126597,0,14330.02,42.59822,0,24,1,21.20141,5.683156,49.85277,0,0,76.73734,0,0,0,3,0,4,68.4,13,1,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,68.74699,9.570182,1.386294,4.340388,1 9,1,50,1,2,126597,0,14330.02,43.59822,0,24,1,1.617251,2.754717,0,0,0,4.371968,0,0,0,2,0,4,68.4,13,1,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,68.74699,9.570182,1.386294,1.475213,1 9,1,50,1,3,126597,0,14330.02,44.59822,0,24,1,26.53563,4.127764,48.27027,0,0,78.93366,0,0,0,3,0,4,68.4,13,1,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,68.74699,9.570182,1.386294,4.368608,1 9,1,50,1,1,126598,0,14330.02,2.023272,0,20,1,55.35925,13.26266,4.711425,0,0,73.33334,0,0,0,10,1,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,66.69353,9.570182,1.386294,4.295015,1 9,1,50,1,2,126598,0,14330.02,3.023272,0,20,1,51.21294,1.644205,0,0,0,52.85714,0,0,1,7,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,66.69353,9.570182,1.386294,3.967593,1 9,1,50,1,3,126598,0,14330.02,4.023272,0,20,1,24.57002,11.46929,0,0,0,36.03931,0,0,0,5,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,66.69353,9.570182,1.386294,3.58461,1 9,1,50,1,1,126599,0,14330.02,4.607803,0,20,1,324.7644,8.386337,0,0,0,333.1508,0,0,0,5,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,66.69353,9.570182,1.386294,5.808595,1 9,1,50,1,2,126599,0,14330.02,5.607803,0,20,1,24.25876,4.684636,0,0,0,28.9434,0,0,0,5,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,66.69353,9.570182,1.386294,3.365342,1 9,1,50,1,3,126599,0,14330.02,6.607803,0,20,1,15.23342,10.93366,0,0,0,26.16708,0,0,0,3,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,66.69353,9.570182,1.386294,3.264502,1 2,1,100,0,1,126609,0,9542.002,41.79603,1,12,1,45.34747,11.702,0,0,0,57.04947,0,0,0,4,0,4,90.5,8.7,0,,0,0,0,0,1.386294,0,1,0,0,1,0,0,72.1002,9.163564,1.386294,4.043919,1 2,1,100,0,2,126609,0,9542.002,42.79603,1,12,1,89.75742,4.911051,0,0,0,94.66846,0,0,0,3,0,4,90.5,8.7,0,,0,0,0,0,1.386294,0,1,0,0,1,0,0,72.1002,9.163564,1.386294,4.550381,1 2,1,100,0,3,126609,0,9542.002,43.79603,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,90.5,8.7,0,,0,0,0,0,1.386294,0,1,0,0,1,0,0,72.1002,9.163564,1.386294,,0 2,1,100,0,4,126609,0,9542.002,44.79603,1,12,1,13.67366,2.962625,0,0,0,16.63628,0,0,0,1,0,4,90.5,8.7,0,,0,0,0,0,1.386294,0,1,0,0,1,0,0,72.1002,9.163564,1.386294,2.811586,1 2,1,100,0,5,126609,0,9542.002,45.79603,1,12,1,38.76615,0,0,0,0,38.76615,0,0,0,1,0,4,90.5,8.7,0,,0,0,0,0,1.386294,0,1,0,0,1,0,0,72.1002,9.163564,1.386294,3.657547,1 2,1,100,0,1,126610,0,9542.002,14.57632,0,12,1,5.889281,0,0,0,0,5.889281,0,0,0,1,0,4,73.7,4.3,0,,0,0,1,0,1.386294,0,1,0,0,1,0,0,74.08881,9.163564,1.386294,1.773134,1 2,1,100,0,2,126610,0,9542.002,15.57632,0,12,1,13.47709,0,0,0,0,13.47709,0,0,0,1,0,4,73.7,4.3,0,,0,0,1,0,1.386294,0,1,0,0,1,0,0,74.08881,9.163564,1.386294,2.600991,1 2,1,100,0,3,126610,0,9542.002,16.57632,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,73.7,4.3,0,,0,0,1,0,1.386294,0,1,0,0,1,0,0,74.08881,9.163564,1.386294,,0 2,1,100,0,4,126610,0,9542.002,17.57632,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,73.7,4.3,0,,0,0,1,0,1.386294,0,1,0,0,1,0,0,74.08881,9.163564,1.386294,,0 2,1,100,0,5,126610,0,9542.002,18.57632,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,73.7,4.3,0,,0,0,0,0,1.386294,0,1,0,0,1,0,0,74.08881,9.163564,1.386294,,0 2,1,100,0,1,126611,0,9542.002,8.405202,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,0,0,1,1,1.386294,0,1,0,0,1,0,0,79.46868,9.163564,1.386294,,0 2,1,100,0,2,126611,0,9542.002,9.405202,1,12,1,4.851752,3.28841,0,0,0,8.140162,0,0,0,1,0,4,74.36826,13.73189,0,,0,0,1,1,1.386294,0,1,0,0,1,0,0,79.46868,9.163564,1.386294,2.09681,1 2,1,100,0,3,126611,0,9542.002,10.4052,1,12,1,118.6732,23.14496,0,0,0,141.8182,0,0,0,8,0,4,74.36826,13.73189,0,,0,0,1,1,1.386294,0,1,0,0,1,0,0,79.46868,9.163564,1.386294,4.954546,1 2,1,100,0,4,126611,0,9542.002,11.4052,1,12,1,34.43482,15.10939,0,0,0,49.54421,0,0,0,3,0,4,74.36826,13.73189,0,,0,0,1,1,1.386294,0,1,0,0,1,0,0,79.46868,9.163564,1.386294,3.902865,1 2,1,100,0,5,126611,0,9542.002,12.4052,1,12,1,22.50938,21.21717,0,0,0,43.72655,0,0,0,2,0,4,74.36826,13.73189,0,,0,0,1,1,1.386294,0,1,0,0,1,0,0,79.46868,9.163564,1.386294,3.777956,1 2,1,100,0,1,126612,0,9542.002,19.47433,1,13,1,48.29211,40.22968,21.49588,0,0,110.0177,0,0,0,7,0,1,78.9,17.4,0,,0,0,0,0,0,0,1,0,0,1,0,0,74.33247,9.163564,0,4.700641,1 2,1,100,0,2,126612,0,9542.002,20.47433,1,13,1,44.20485,29.82749,0,0,0,74.03235,0,0,0,5,0,1,78.9,17.4,0,,0,0,0,0,0,0,1,0,0,1,0,0,74.33247,9.163564,0,4.304502,1 2,1,100,0,3,126612,0,9542.002,21.47433,1,13,1,45.70024,17.79852,0,0,0,63.49877,0,0,0,4,0,1,78.9,17.4,0,,0,0,0,0,0,0,1,0,0,1,0,0,74.33247,9.163564,0,4.151021,1 2,1,100,0,4,126612,0,9542.002,22.47433,1,13,1,34.27985,5.556062,0,0,0,39.83591,0,0,0,2,0,1,78.9,17.4,0,,0,0,0,0,0,0,1,0,0,1,0,0,74.33247,9.163564,0,3.684769,1 2,1,100,0,5,126612,0,9542.002,23.47433,1,13,1,33.34723,8.724468,0,0,0,42.0717,0,0,0,4,0,1,78.9,17.4,0,,0,0,0,0,0,0,1,0,0,1,0,0,74.33247,9.163564,0,3.739375,1 2,1,100,0,1,126613,0,9542.002,42.00411,0,12,1,24.44052,8.763251,37.27915,0,0,70.48292,0,0,0,1,0,4,77.9,13,0,,0,0,0,0,1.386294,0,1,0,0,0,1,0,66.69038,9.163564,1.386294,4.255371,1 2,1,100,0,2,126613,0,9542.002,43.00411,0,12,1,379.2668,48.46361,0,0,0,427.7305,0,0,0,6,0,4,77.9,13,0,,0,0,0,0,1.386294,0,1,0,0,0,1,0,66.69038,9.163564,1.386294,6.058493,1 2,1,100,0,3,126613,0,9542.002,44.00411,0,12,1,15.47912,16.09337,0,0,0,31.57248,0,0,0,2,0,4,77.9,13,0,,0,0,0,0,1.386294,0,1,0,0,0,1,0,66.69038,9.163564,1.386294,3.452286,1 2,1,100,0,4,126613,0,9542.002,45.00411,0,12,1,29.62625,24.09754,37.09207,0,0,90.81586,0,0,0,4,0,4,77.9,13,0,,0,0,0,0,1.386294,0,1,0,0,0,1,0,66.69038,9.163564,1.386294,4.508834,1 2,1,100,0,5,126613,0,9542.002,46.00411,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,77.9,13,0,,0,0,0,0,1.386294,0,1,0,0,0,1,0,66.69038,9.163564,1.386294,,0 1,1,0,0,1,126635,0,9092.432,1.092402,0,19,1,47.59072,9.970256,0,0,0,57.56097,0,0,0,8,0,4,74.36826,13.73189,0,,450,450,1,0,1.386294,6.109248,1,0,0,0,0,0,79.71203,9.115308,1.386294,4.052845,1 1,1,0,0,2,126635,0,9092.432,2.092402,0,19,1,31.8454,3.712575,0,0,0,35.55798,0,0,0,4,0,4,74.36826,13.73189,0,,450,450,1,0,1.386294,6.109248,1,0,0,0,0,0,79.71203,9.115308,1.386294,3.571164,1 1,1,0,0,3,126635,0,9092.432,3.092402,0,19,1,66.15461,10.53023,18.58276,0,0,95.26759,0,0,0,6,0,4,74.36826,13.73189,0,,450,450,1,0,1.386294,6.109248,1,0,0,0,0,0,79.71203,9.115308,1.386294,4.55669,1 1,1,0,0,4,126635,0,9092.432,4.092402,0,19,1,33.73107,5.043598,0,0,0,38.77467,0,0,0,4,0,4,74.36826,13.73189,0,,450,450,1,0,1.386294,6.109248,1,0,0,0,0,0,79.71203,9.115308,1.386294,3.657767,1 1,1,0,0,5,126635,0,9092.432,5.092402,0,19,1,40.80774,7.942785,28.18679,0,0,76.93732,0,0,0,3,0,4,74.36826,13.73189,0,,450,450,1,0,1.386294,6.109248,1,0,0,0,0,0,79.71203,9.115308,1.386294,4.342991,1 1,1,0,0,1,126636,0,9092.432,3.92334,1,19,1,27.36466,5.591909,0,0,0,32.95657,0,0,0,4,0,4,74.36826,13.73189,0,,450,450,1,1,1.386294,6.109248,1,0,0,0,0,0,79.19805,9.115308,1.386294,3.495191,1 1,1,0,0,2,126636,0,9092.432,4.92334,1,19,1,31.02885,5.035384,0,0,0,36.06424,0,0,0,3,0,4,74.36826,13.73189,0,,450,450,1,1,1.386294,6.109248,1,0,0,0,0,0,79.19805,9.115308,1.386294,3.585302,1 1,1,0,0,3,126636,0,9092.432,5.92334,1,19,1,84.14272,0,0,0,0,84.14272,0,0,0,2,1,4,74.36826,13.73189,0,,450,450,1,1,1.386294,6.109248,1,0,0,0,0,0,79.19805,9.115308,1.386294,4.432514,1 1,1,0,0,4,126636,0,9092.432,6.92334,1,19,1,19.04543,10.11014,0,0,0,29.15558,0,0,0,3,0,4,74.36826,13.73189,0,,450,450,1,1,1.386294,6.109248,1,0,0,0,0,0,79.19805,9.115308,1.386294,3.372646,1 1,1,0,0,5,126636,0,9092.432,7.92334,1,19,1,66.91628,14.11022,0,0,0,81.0265,0,0,0,3,0,4,74.36826,13.73189,0,,450,450,1,1,1.386294,6.109248,1,0,0,0,0,0,79.19805,9.115308,1.386294,4.394776,1 1,1,0,0,1,126637,0,9092.432,32.19439,0,19,1,14.8721,0,35.12195,0,0,49.99405,0,0,0,1,0,4,57.5,13.73189,0,,450,450,0,0,1.386294,6.109248,1,0,0,1,0,0,68.50468,9.115308,1.386294,3.911904,1 1,1,0,0,2,126637,0,9092.432,33.19439,0,19,1,0,0,0,0,0,0,0,0,0,0,0,4,57.5,13.73189,0,,450,450,0,0,1.386294,6.109248,1,0,0,1,0,0,68.50468,9.115308,1.386294,,0 1,1,0,0,3,126637,0,9092.432,34.19439,0,19,1,51.53617,2.685827,25.76809,0,0,79.99009,0,0,0,4,0,4,57.5,13.73189,0,,450,450,0,0,1.386294,6.109248,1,0,0,1,0,0,68.50468,9.115308,1.386294,4.381903,1 1,1,0,0,4,126637,0,9092.432,35.19439,0,19,1,116.5672,6.094539,0,0,0,122.6618,0,0,0,3,0,4,57.5,13.73189,0,,450,450,0,0,1.386294,6.109248,1,0,0,1,0,0,68.50468,9.115308,1.386294,4.809431,1 1,1,0,0,5,126637,0,9092.432,36.19439,0,19,1,3.365587,0,0,0,0,3.365587,0,0,0,0,0,4,57.5,13.73189,0,,450,450,0,0,1.386294,6.109248,1,0,0,1,0,0,68.50468,9.115308,1.386294,1.213602,1 1,1,0,0,1,126638,0,9092.432,30.88022,1,19,1,33.3135,27.72159,27.35277,0,0,88.38786,0,0,0,3,0,4,62.5,13.73189,0,,450,450,0,0,1.386294,6.109248,1,0,0,1,0,0,67.19316,9.115308,1.386294,4.481735,1 1,1,0,0,2,126638,0,9092.432,31.88022,1,19,1,26.12956,11.24115,0,0,0,37.37071,0,0,0,2,0,4,62.5,13.73189,0,,450,450,0,0,1.386294,6.109248,1,0,0,1,0,0,67.19316,9.115308,1.386294,3.620887,1 1,1,0,0,3,126638,0,9092.432,32.88022,1,19,1,14.8662,9.781962,0,0,0,24.64817,0,0,0,1,0,4,62.5,13.73189,0,,450,450,0,0,1.386294,6.109248,1,0,0,1,0,0,67.19316,9.115308,1.386294,3.204703,1 1,1,0,0,4,126638,0,9092.432,33.88022,1,19,1,48.64617,2.505737,0,0,0,51.15191,0,0,0,2,0,4,62.5,13.73189,0,,450,450,0,0,1.386294,6.109248,1,0,0,1,0,0,67.19316,9.115308,1.386294,3.9348,1 1,1,0,0,5,126638,0,9092.432,34.88022,1,19,1,24.8212,0,0,0,0,24.8212,0,0,0,2,0,4,62.5,13.73189,0,,450,450,0,0,1.386294,6.109248,1,0,0,1,0,0,67.19316,9.115308,1.386294,3.211698,1 6,1,25,0,1,126650,0,9743.176,32.97467,0,14,1,0,2.338045,0,0,0,2.338045,0,0,0,0,0,4,91.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,78.79201,9.184425,1.386294,.8493149,1 6,1,25,0,2,126650,0,9743.176,33.97467,0,14,1,43.66577,6.080863,0,0,0,49.74663,0,0,0,2,0,4,91.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,78.79201,9.184425,1.386294,3.906943,1 6,1,25,0,3,126650,0,9743.176,34.97467,0,14,1,7.371007,7.208845,0,0,0,14.57985,0,0,0,1,0,5,91.3,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,0,0,0,78.79201,9.184425,1.609438,2.679641,1 6,1,25,0,1,126651,0,9743.176,6.130048,0,12,1,50.79505,3.274441,0,0,0,54.06949,0,0,0,4,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,85.04264,9.184425,1.386294,3.99027,1 6,1,25,0,2,126651,0,9743.176,7.130048,0,12,1,18.86792,8.722372,0,0,0,27.5903,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,85.04264,9.184425,1.386294,3.317464,1 6,1,25,0,3,126651,0,9743.176,8.130048,0,12,1,64.37347,9.7543,0,0,0,74.12776,0,0,0,3,1,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,0,0,0,85.04264,9.184425,1.609438,4.30579,1 6,1,25,0,1,126652,0,9743.176,31.21424,1,12,1,80.09423,51.60188,0,0,0,131.6961,0,0,0,9,0,4,86.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,1,0,56.3639,9.184425,1.386294,4.880497,1 6,1,25,0,2,126652,0,9743.176,32.21424,1,12,1,124.5283,109.504,35.76819,0,4801.725,5071.525,1,0,0,11,0,4,86.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,1,0,56.3639,9.184425,1.386294,8.531397,1 6,1,25,0,3,126652,0,9743.176,33.21424,1,12,1,6.633907,58.45209,0,0,0,65.086,0,0,0,1,0,5,86.3,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,0,1,0,56.3639,9.184425,1.609438,4.175709,1 6,1,25,0,1,126653,0,9743.176,8.919918,0,12,1,130.7421,58.75147,0,0,0,189.4935,0,0,0,7,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,73.90643,9.184425,1.386294,5.244355,1 6,1,25,0,2,126653,0,9743.176,9.919918,0,12,1,90.29649,40.14016,26.95418,0,0,157.3908,0,0,0,31,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,73.90643,9.184425,1.386294,5.058732,1 6,1,25,0,3,126653,0,9743.176,10.91992,0,12,1,7.371007,18.92875,0,0,0,26.29976,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,73.90643,9.184425,1.609438,3.26956,1 11,1,0,1,1,126665,0,5583.747,3.039014,0,11,1,51.56815,9.408926,0,0,255.5609,316.538,1,0,0,5,1,5,74.36826,13.73189,0,,0,458,1,0,1.609438,6.126869,0,0,0,0,0,0,79.08629,8.627794,1.609438,5.757443,1 11,1,0,1,2,126665,0,5583.747,4.039014,0,11,1,62.67621,0,0,0,0,62.67621,0,0,0,3,0,6,74.36826,13.73189,0,,0,458,1,0,1.791759,6.126869,0,0,0,0,0,0,79.08629,8.627794,1.791759,4.137982,1 11,1,0,1,3,126665,0,5583.747,5.039014,0,11,1,47.21246,14.21396,0,0,0,61.42642,0,0,0,6,0,6,74.36826,13.73189,0,,0,458,1,0,1.791759,6.126869,0,0,0,0,0,0,79.08629,8.627794,1.791759,4.11784,1 11,1,0,1,4,126665,0,5583.747,6.039014,0,11,1,25.96198,5.656003,0,0,0,31.61799,0,0,0,4,0,6,74.36826,13.73189,0,,0,458,1,0,1.791759,6.126869,0,0,0,0,0,0,79.08629,8.627794,1.791759,3.453726,1 11,1,0,1,5,126665,0,5583.747,7.039014,0,11,1,13.61123,2.105487,20.44662,0,0,36.16333,0,0,0,1,1,6,74.36826,13.73189,0,,0,458,1,0,1.791759,6.126869,0,0,0,0,0,0,79.08629,8.627794,1.791759,3.588046,1 11,1,0,1,1,126666,0,5583.747,22.5243,1,11,1,15.68154,12.14113,0,0,1307.382,1335.205,1,0,0,3,0,5,96.8,8.7,0,,0,458,0,0,1.609438,6.126869,0,0,0,0,0,0,75.68143,8.627794,1.609438,7.19684,1 11,1,0,1,2,126666,0,5583.747,23.5243,1,11,1,237.5991,13.05066,0,0,0,250.6498,0,0,0,9,0,6,96.8,8.7,0,,0,458,0,0,1.791759,6.126869,0,0,0,0,0,0,75.68143,8.627794,1.791759,5.524056,1 11,1,0,1,3,126666,0,5583.747,24.5243,1,11,1,47.40332,1.808137,0,0,1024.405,1073.616,1,0,0,1,0,6,96.8,8.7,0,,0,458,0,0,1.791759,6.126869,0,0,0,0,0,0,75.68143,8.627794,1.791759,6.978788,1 11,1,0,1,4,126666,0,5583.747,25.5243,1,11,1,25.49838,10.75568,0,0,0,36.25406,0,0,0,4,0,6,96.8,8.7,0,,0,458,0,0,1.791759,6.126869,0,0,0,0,0,0,75.68143,8.627794,1.791759,3.590551,1 11,1,0,1,5,126666,0,5583.747,26.5243,1,11,1,5.104211,9.506593,0,0,0,14.6108,0,0,0,1,0,6,96.8,8.7,0,,0,458,0,0,1.791759,6.126869,0,0,0,0,0,0,75.68143,8.627794,1.791759,2.681761,1 11,1,0,1,1,126667,0,5583.747,23.90144,0,11,1,1.809409,5.458384,0,0,0,7.267793,0,0,0,1,0,5,93.7,0,0,,0,458,0,0,1.609438,6.126869,0,0,0,0,0,0,74.79025,8.627794,1.609438,1.983453,1 11,1,0,1,2,126667,0,5583.747,24.90144,0,11,1,23.95374,7.075991,0,0,0,31.02974,0,0,0,3,0,6,93.7,0,0,,0,458,0,0,1.791759,6.126869,0,0,0,0,0,0,74.79025,8.627794,1.791759,3.434946,1 11,1,0,1,3,126667,0,5583.747,25.90144,0,11,1,0,0,0,0,0,0,0,0,0,0,0,6,93.7,0,0,,0,458,0,0,1.791759,6.126869,0,0,0,0,0,0,74.79025,8.627794,1.791759,,0 11,1,0,1,4,126667,0,5583.747,26.90144,0,11,1,10.19935,1.34446,0,0,0,11.54381,0,0,0,2,0,6,93.7,0,0,,0,458,0,0,1.791759,6.126869,0,0,0,0,0,0,74.79025,8.627794,1.791759,2.446149,1 11,1,0,1,5,126667,0,5583.747,27.90144,0,11,1,7.230966,5.338154,0,0,0,12.56912,0,0,0,1,0,6,93.7,0,0,,0,458,0,0,1.791759,6.126869,0,0,0,0,0,0,74.79025,8.627794,1.791759,2.531243,1 11,1,0,1,1,126668,0,5583.747,1.954826,1,11,1,24.12545,11.78528,0,0,0,35.91074,0,0,0,3,0,5,74.36826,13.73189,0,,0,458,1,1,1.609438,6.126869,0,0,0,0,0,0,78.57231,8.627794,1.609438,3.581036,1 11,1,0,1,2,126668,0,5583.747,2.954825,1,11,1,29.29515,14.17952,0,0,0,43.47467,0,0,0,5,0,6,74.36826,13.73189,0,,0,458,1,1,1.791759,6.126869,0,0,0,0,0,0,78.57231,8.627794,1.791759,3.772178,1 11,1,0,1,3,126668,0,5583.747,3.954825,1,11,1,42.69212,10.29633,0,0,0,52.98845,0,0,0,7,0,6,74.36826,13.73189,0,,0,458,1,1,1.791759,6.126869,0,0,0,0,0,0,78.57231,8.627794,1.791759,3.970074,1 11,1,0,1,4,126668,0,5583.747,4.954825,1,11,1,15.76263,0,0,0,0,15.76263,0,0,0,3,0,6,74.36826,13.73189,0,,0,458,1,1,1.791759,6.126869,0,0,0,0,0,0,78.57231,8.627794,1.791759,2.757642,1 11,1,0,1,5,126668,0,5583.747,5.954825,1,11,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,0,458,1,1,1.791759,6.126869,0,0,0,0,0,0,78.57231,8.627794,1.791759,,0 11,1,0,1,1,126669,0,5583.747,4.911705,0,11,1,6.6345,2.110977,0,0,0,8.745477,0,0,0,1,0,5,74.36826,13.73189,0,,0,458,1,0,1.609438,6.126869,0,0,0,0,0,0,79.08629,8.627794,1.609438,2.168537,1 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1,1,0,1,3,126674,0,3711.042,26.17796,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,34.7,4.3,0,,150,0,0,0,0,0,1,0,0,0,0,0,78.79221,8.219337,0,,0 1,1,0,1,4,126674,0,3711.042,27.17796,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,34.7,4.3,0,,150,0,0,0,0,0,1,0,0,0,0,0,78.79221,8.219337,0,,0 1,1,0,1,5,126674,0,3711.042,28.17796,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,34.7,4.3,0,,150,0,0,0,0,0,1,0,0,0,0,0,78.79221,8.219337,0,,0 4,1,100,0,1,126678,0,4242.556,11.52088,1,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,1,0,0,1,0,0,75.05559,8.353157,1.94591,,0 4,1,100,0,2,126678,0,4242.556,12.52088,1,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,1,0,0,1,0,0,75.05559,8.353157,1.94591,,0 4,1,100,0,3,126678,0,4242.556,13.52088,1,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,1,0,0,1,0,0,75.05559,8.353157,1.94591,,0 4,1,100,0,1,126679,0,4242.556,10.59274,1,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,1,0,0,0,0,0,80.99117,8.353157,1.94591,,0 4,1,100,0,2,126679,0,4242.556,11.59274,1,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,1,0,0,0,0,0,80.99117,8.353157,1.94591,,0 4,1,100,0,3,126679,0,4242.556,12.59274,1,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,1,0,0,0,0,0,80.99117,8.353157,1.94591,,0 4,1,100,0,1,126680,0,4242.556,2.778919,1,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,1,0,0,1,0,0,68.34178,8.353157,1.94591,,0 4,1,100,0,2,126680,0,4242.556,3.778919,1,10,1,0,1.518781,0,0,0,1.518781,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,1,0,0,1,0,0,68.34178,8.353157,1.94591,.4179078,1 4,1,100,0,3,126680,0,4242.556,4.778919,1,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,1,0,0,1,0,0,68.34178,8.353157,1.94591,,0 4,1,100,0,1,126681,0,4242.556,30.5681,0,8,1,38.66746,16.00238,0,0,0,54.66984,0,0,0,4,1,7,60,13.73189,1,,1000,1000,0,0,1.94591,6.907755,1,0,0,0,1,0,59.22386,8.353157,1.94591,4.001312,1 4,1,100,0,2,126681,0,4242.556,31.5681,0,8,1,0,0,0,0,0,0,0,0,0,0,0,7,60,13.73189,1,,1000,1000,0,0,1.94591,6.907755,1,0,0,0,1,0,59.22386,8.353157,1.94591,,0 4,1,100,0,3,126681,0,4242.556,32.5681,0,8,1,23.29039,0,0,0,0,23.29039,0,0,0,3,0,7,60,13.73189,1,,1000,1000,0,0,1.94591,6.907755,1,0,0,0,1,0,59.22386,8.353157,1.94591,3.148041,1 4,1,100,0,1,126682,0,4242.556,28.33402,1,10,1,0,0,0,0,0,0,0,0,0,0,0,7,72.5,13.73189,0,,1000,1000,0,0,1.94591,6.907755,1,0,0,1,0,0,69.16129,8.353157,1.94591,,0 4,1,100,0,2,126682,0,4242.556,29.33402,1,10,1,0,0,0,0,0,0,0,0,0,0,0,7,72.5,13.73189,0,,1000,1000,0,0,1.94591,6.907755,1,0,0,1,0,0,69.16129,8.353157,1.94591,,0 4,1,100,0,3,126682,0,4242.556,30.33402,1,10,1,0,0,0,0,0,0,0,0,0,0,0,7,72.5,13.73189,0,,1000,1000,0,0,1.94591,6.907755,1,0,0,1,0,0,69.16129,8.353157,1.94591,,0 4,1,100,0,1,126683,0,4242.556,7.980835,0,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,1,0,0,1,0,0,71.32816,8.353157,1.94591,,0 4,1,100,0,2,126683,0,4242.556,8.980835,0,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,1,0,0,1,0,0,71.32816,8.353157,1.94591,,0 4,1,100,0,3,126683,0,4242.556,9.980835,0,10,1,0,1.778989,0,0,0,1.778989,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,1,0,0,1,0,0,71.32816,8.353157,1.94591,.5760453,1 4,1,100,0,1,126684,0,4242.556,9.38809,0,10,1,5.94884,1.302796,0,0,0,7.251636,0,0,0,1,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,1,0,0,0,0,0,82.46437,8.353157,1.94591,1.981227,1 4,1,100,0,2,126684,0,4242.556,10.38809,0,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,1,0,0,0,0,0,82.46437,8.353157,1.94591,,0 4,1,100,0,3,126684,0,4242.556,11.38809,0,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,1,0,0,0,0,0,82.46437,8.353157,1.94591,,0 11,1,0,1,1,126755,0,4586.849,50.34086,1,12,1,39.26234,2.492564,0,0,0,41.75491,0,0,0,4,0,3,77.8,17.4,0,,0,0,0,0,1.098612,0,0,0,0,1,0,0,71.87788,8.431167,1.098612,3.731817,1 11,1,0,1,2,126755,0,4586.849,51.34086,1,12,1,50.08165,16.44529,0,0,0,66.52695,0,0,0,5,0,3,77.8,17.4,0,,0,0,0,0,1.098612,0,0,0,0,1,0,0,71.87788,8.431167,1.098612,4.197607,1 11,1,0,1,3,126755,0,4586.849,52.34086,1,12,1,0,7.41328,0,0,0,7.41328,0,0,0,0,0,3,77.8,17.4,0,,0,0,0,0,1.098612,0,0,0,0,1,0,0,71.87788,8.431167,1.098612,2.003273,1 11,1,0,1,4,126755,0,4586.849,53.34086,1,12,1,0,12.29004,0,0,0,12.29004,0,0,0,0,0,3,77.8,17.4,0,,0,0,0,0,1.098612,0,0,0,0,1,0,0,71.87788,8.431167,1.098612,2.508789,1 11,1,0,1,5,126755,0,4586.849,54.34086,1,12,1,19.77282,22.36853,0,0,0,42.14135,0,0,0,3,0,3,77.8,17.4,0,,0,0,0,0,1.098612,0,0,0,0,1,0,0,71.87788,8.431167,1.098612,3.74103,1 11,1,0,1,1,126756,0,4586.849,18.26694,1,11,1,39.26234,8.370018,0,0,342.0583,389.6907,1,0,0,4,0,3,85.3,4.3,0,,0,0,0,0,1.098612,0,0,0,0,1,0,0,69.7751,8.431167,1.098612,5.965353,1 11,1,0,1,2,126756,0,4586.849,19.26694,1,11,1,0,0,0,0,0,0,0,0,0,0,0,3,85.3,4.3,0,,0,0,0,0,1.098612,0,0,0,0,1,0,0,69.7751,8.431167,1.098612,,0 11,1,0,1,3,126756,0,4586.849,20.26694,1,11,1,0,0,0,0,0,0,0,0,0,0,0,3,85.3,4.3,0,,0,0,0,0,1.098612,0,0,0,0,1,0,0,69.7751,8.431167,1.098612,,0 11,1,0,1,4,126756,0,4586.849,21.26694,1,11,1,0,0,0,0,0,0,0,0,0,0,0,3,85.3,4.3,0,,0,0,0,0,1.098612,0,0,0,0,1,0,0,69.7751,8.431167,1.098612,,0 11,1,0,1,5,126756,0,4586.849,22.26694,1,11,1,12.62095,2.440051,0,0,0,15.061,0,0,0,2,0,3,85.3,4.3,0,,0,0,0,0,1.098612,0,0,0,0,1,0,0,69.7751,8.431167,1.098612,2.712109,1 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10,1,50,1,5,126765,0,13699.75,47.59753,1,12,1,45.01876,12.85536,0,0,0,57.87411,0,0,0,4,0,3,74.7,26.1,1,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,1,0,62.05545,9.525206,1.098612,4.05827,1 10,1,50,1,1,126766,0,13699.75,43.93977,0,8,1,10.60071,0,36.21908,0,0,46.81979,0,0,0,0,1,3,75.8,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,67.41241,9.525206,1.098612,3.846306,1 10,1,50,1,2,126766,0,13699.75,44.93977,0,8,1,0,0,0,0,0,0,0,0,0,0,0,3,75.8,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,67.41241,9.525206,1.098612,,0 10,1,50,1,3,126766,0,13699.75,45.93977,0,8,1,0,0,0,0,0,0,0,0,0,0,0,3,75.8,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,67.41241,9.525206,1.098612,,0 10,1,50,1,4,126766,0,13699.75,46.93977,0,8,1,15.49681,0,51.44029,0,0,66.9371,0,0,0,1,1,3,75.8,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,67.41241,9.525206,1.098612,4.203753,1 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11,1,0,1,3,126796,1,9542.002,23.71937,0,12,1,116.997,4.578791,0,0,0,121.5758,0,0,0,8,0,4,80,8.7,0,,0,0,0,0,1.386294,0,0,0,0,1,0,0,66.78163,9.163564,1.386294,4.800538,1 11,1,0,1,4,126796,1,9542.002,24.71937,0,12,1,5.96604,0,0,0,0,5.96604,0,0,0,1,0,4,80,8.7,0,,0,0,0,0,1.386294,0,0,0,0,1,0,0,66.78163,9.163564,1.386294,1.786083,1 11,1,0,1,5,126796,1,9542.002,25.71937,0,12,1,42.49054,.8413967,.3575936,0,0,43.68953,0,0,0,3,0,5,80,8.7,0,,0,0,0,0,1.609438,0,0,0,0,1,0,0,66.78163,9.163564,1.609438,3.777108,1 11,1,0,0,1,126797,1,9542.002,23.11294,1,12,1,24.98513,9.571684,21.94527,0,0,56.50208,0,0,0,4,0,1,78.9,0,0,,0,72,0,0,0,4.276666,0,0,0,1,0,0,63.49755,9.163564,0,4.034277,1 11,1,0,0,2,126797,1,9542.002,24.11294,1,12,1,617.534,13.03212,18.96026,0,0,649.5264,0,0,0,10,1,1,78.9,0,0,,0,72,0,0,0,4.276666,0,0,0,1,0,0,63.49755,9.163564,0,6.476243,1 11,1,0,0,3,126797,1,9542.002,25.11294,1,12,1,406.5857,28.15164,0,0,29.73241,464.4698,0,0,0,8,0,1,78.9,0,0,,0,72,0,0,0,4.276666,0,0,0,1,0,0,63.49755,9.163564,0,6.140896,1 11,1,0,0,4,126797,1,9542.002,26.11294,1,12,1,519.9404,51.39054,38.84809,0,2560.996,3171.175,1,0,0,3,1,1,78.9,0,0,,0,72,0,0,0,4.276666,0,0,0,1,0,0,63.49755,9.163564,0,8.061857,1 11,1,0,0,5,126797,1,9542.002,27.11294,1,12,1,648.3172,59.20909,16.48717,0,0,724.0135,0,0,0,2,3,1,78.9,0,0,,0,72,0,0,0,4.276666,0,0,0,1,0,0,63.49755,9.163564,0,6.58481,1 4,1,100,0,1,126800,1,2297.767,52.39699,1,8,1,189.4582,0,0,0,0,189.4582,0,0,0,8,0,1,35.8,21.7,0,,0,0,0,0,0,0,1,0,0,0,0,1,62.06791,7.740128,0,5.244168,1 4,1,100,0,2,126800,1,2297.767,53.39699,1,8,1,0,0,0,0,0,0,0,0,0,0,0,1,35.8,21.7,0,,0,0,0,0,0,0,1,0,0,0,0,1,62.06791,7.740128,0,,0 4,1,100,0,3,126800,1,2297.767,54.39699,1,8,1,0,0,0,0,0,0,0,0,0,0,0,1,35.8,21.7,0,,0,0,0,0,0,0,1,0,0,0,0,1,62.06791,7.740128,0,,0 5,1,25,0,1,126805,1,898.263,13.59617,0,9,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,101,101,1,0,1.609438,4.61512,0,3.258096,6.001415,0,0,0,75.72706,6.801576,1.609438,,0 5,1,25,0,2,126805,1,898.263,14.59617,0,9,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,101,101,1,0,1.609438,4.61512,0,3.258096,6.001415,0,0,0,75.72706,6.801576,1.609438,,0 5,1,25,0,1,126806,1,898.263,11.47159,0,9,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,101,101,1,0,1.609438,4.61512,0,3.258096,6.001415,0,0,0,75.72706,6.801576,1.609438,,0 5,1,25,0,2,126806,1,898.263,12.47159,0,9,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,101,101,1,0,1.609438,4.61512,0,3.258096,6.001415,0,0,0,75.72706,6.801576,1.609438,,0 5,1,25,0,1,126807,1,898.263,9.409993,1,9,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,101,101,1,1,1.609438,4.61512,0,3.258096,6.001415,0,0,0,75.21308,6.801576,1.609438,,0 5,1,25,0,2,126807,1,898.263,10.40999,1,9,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,101,101,1,1,1.609438,4.61512,0,3.258096,6.001415,0,0,0,75.21308,6.801576,1.609438,,0 5,1,25,0,1,126808,1,898.263,14.93224,1,9,1,0,0,0,0,0,0,0,0,0,0,0,5,75.8,8.7,0,,101,101,1,1,1.609438,4.61512,0,3.258096,6.001415,0,0,0,65.00531,6.801576,1.609438,,0 5,1,25,0,2,126808,1,898.263,15.93224,1,9,1,0,0,0,0,0,0,0,0,0,0,0,5,75.8,8.7,0,,101,101,1,1,1.609438,4.61512,0,3.258096,6.001415,0,0,0,65.00531,6.801576,1.609438,,0 5,1,25,0,1,126809,1,898.263,32.79945,1,9,1,0,0,0,0,0,0,0,0,0,0,0,5,62.1,21.7,0,,101,101,0,0,1.609438,4.61512,0,3.258096,6.001415,0,0,0,69.38714,6.801576,1.609438,,0 5,1,25,0,2,126809,1,898.263,33.79945,1,9,1,0,0,0,0,0,0,0,0,0,0,0,5,62.1,21.7,0,,101,101,0,0,1.609438,4.61512,0,3.258096,6.001415,0,0,0,69.38714,6.801576,1.609438,,0 11,1,0,0,1,126815,1,3944.789,51.42231,1,6,1,307.2278,0,0,0,0,307.2278,0,0,0,2,0,1,94.7,13,0,,0,0,0,0,0,0,0,0,0,0,0,0,67.9421,8.280404,0,5.72759,1 11,1,0,0,2,126815,1,3944.789,52.42231,1,6,1,133.914,5.307567,0,0,0,139.2216,0,0,0,5,0,1,94.7,13,0,,0,0,0,0,0,0,0,0,0,0,0,0,67.9421,8.280404,0,4.936067,1 11,1,0,0,3,126815,1,3944.789,53.42231,1,6,1,129.2121,0,34.14272,0,0,163.3548,0,0,0,5,1,1,94.7,13,0,,0,0,0,0,0,0,0,0,0,0,0,0,67.9421,8.280404,0,5.095924,1 11,1,0,0,4,126815,1,3944.789,54.42231,1,6,1,128.4993,0,0,0,0,128.4993,0,0,0,5,0,1,94.7,13,0,,0,0,0,0,0,0,0,0,0,0,0,0,67.9421,8.280404,0,4.855924,1 11,1,0,0,5,126815,1,3944.789,55.42231,1,6,1,138.1994,0,46.38199,0,749.2806,933.862,1,0,0,5,0,1,94.7,13,0,,0,0,0,0,0,0,0,0,0,0,0,0,67.9421,8.280404,0,6.839329,1 9,1,50,1,1,126822,0,14151.37,7.118412,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,81.68566,9.557637,1.791759,,0 9,1,50,1,2,126822,0,14151.37,8.118412,1,12,1,8.259912,0,0,0,0,8.259912,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,81.68566,9.557637,1.791759,2.111414,1 9,1,50,1,3,126822,0,14151.37,9.118412,1,12,1,2.009041,0,0,0,0,2.009041,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,81.68566,9.557637,1.791759,.6976573,1 9,1,50,1,4,126822,0,14151.37,10.11841,1,12,1,2.318034,0,0,0,0,2.318034,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,81.68566,9.557637,1.791759,.8407196,1 9,1,50,1,5,126822,0,14151.37,11.11841,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,81.68566,9.557637,1.791759,,0 9,1,50,1,1,126823,0,14151.37,8.678987,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,85.92707,9.557637,1.791759,,0 9,1,50,1,2,126823,0,14151.37,9.678987,1,12,1,46.25551,2.114537,28.19934,0,0,76.56938,0,0,0,6,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,85.92707,9.557637,1.791759,4.338197,1 9,1,50,1,3,126823,0,14151.37,10.67899,1,12,1,24.10849,0,0,0,0,24.10849,0,0,0,5,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,85.92707,9.557637,1.791759,3.182564,1 9,1,50,1,4,126823,0,14151.37,11.67899,1,12,1,49.95364,0,29.13305,0,0,79.08669,0,0,0,3,1,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,85.92707,9.557637,1.791759,4.370544,1 9,1,50,1,5,126823,0,14151.37,12.67899,1,12,1,14.88728,0,11.90983,0,0,26.79711,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,85.92707,9.557637,1.791759,3.288294,1 9,1,50,1,1,126824,0,14151.37,35.06092,1,12,1,3.015682,0,0,0,0,3.015682,0,0,0,0,0,6,72.6,0,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,69.27332,9.557637,1.791759,1.103826,1 9,1,50,1,2,126824,0,14151.37,36.06092,1,12,1,22.57709,0,0,0,0,22.57709,0,0,0,1,0,6,72.6,0,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,69.27332,9.557637,1.791759,3.116936,1 9,1,50,1,3,126824,0,14151.37,37.06092,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,72.6,0,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,69.27332,9.557637,1.791759,,0 9,1,50,1,4,126824,0,14151.37,38.06092,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,72.6,0,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,69.27332,9.557637,1.791759,,0 9,1,50,1,5,126824,0,14151.37,39.06092,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,72.6,0,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,69.27332,9.557637,1.791759,,0 9,1,50,1,1,126825,0,14151.37,13.82615,1,12,1,4.221954,1.206273,33.40772,0,0,38.83595,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,85.92707,9.557637,1.791759,3.659346,1 9,1,50,1,2,126825,0,14151.37,14.82615,1,12,1,13.76652,0,0,0,0,13.76652,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,85.92707,9.557637,1.791759,2.62224,1 9,1,50,1,3,126825,0,14151.37,15.82615,1,12,1,4.018081,0,95.42944,0,0,99.44752,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,85.92707,9.557637,1.791759,4.59963,1 9,1,50,1,4,126825,0,14151.37,16.82615,1,12,1,17.61706,0,24.22346,0,0,41.84052,0,0,0,2,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,85.92707,9.557637,1.791759,3.733865,1 9,1,50,1,5,126825,0,14151.37,17.82615,1,12,1,2.552105,0,6.682263,0,0,9.234368,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,85.92707,9.557637,1.791759,2.222932,1 9,1,50,1,1,126826,0,14151.37,41.97399,0,16,1,18.09409,0,0,0,0,18.09409,0,0,0,1,0,6,84.2,21.7,1,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,65.73057,9.557637,1.791759,2.895585,1 9,1,50,1,2,126826,0,14151.37,42.97399,0,16,1,0,0,17.84141,0,0,17.84141,0,0,0,0,0,6,84.2,21.7,1,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,65.73057,9.557637,1.791759,2.881522,1 9,1,50,1,3,126826,0,14151.37,43.97399,0,16,1,16.57458,0,0,0,0,16.57458,0,0,0,1,0,6,84.2,21.7,1,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,65.73057,9.557637,1.791759,2.80787,1 9,1,50,1,4,126826,0,14151.37,44.97399,0,16,1,13.90821,0,47.2879,0,0,61.19611,0,0,0,1,0,6,84.2,21.7,1,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,65.73057,9.557637,1.791759,4.114084,1 9,1,50,1,5,126826,0,14151.37,45.97399,0,16,1,11.48448,0,0,0,0,11.48448,0,0,0,2,0,6,84.2,21.7,1,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,65.73057,9.557637,1.791759,2.440996,1 9,1,50,1,1,126827,0,14151.37,12.54483,0,12,1,3.015682,0,0,0,0,3.015682,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,86.44105,9.557637,1.791759,1.103826,1 9,1,50,1,2,126827,0,14151.37,13.54483,0,12,1,98.01762,0,0,0,0,98.01762,0,0,0,4,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,86.44105,9.557637,1.791759,4.585147,1 9,1,50,1,3,126827,0,14151.37,14.54483,0,12,1,2.009041,0,0,0,0,2.009041,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,86.44105,9.557637,1.791759,.6976573,1 9,1,50,1,4,126827,0,14151.37,15.54483,0,12,1,115.9017,0,0,0,0,115.9017,0,0,0,3,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,86.44105,9.557637,1.791759,4.752743,1 9,1,50,1,5,126827,0,14151.37,16.54483,0,12,1,298.4688,33.93024,0,0,0,332.399,0,0,0,6,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,86.44105,9.557637,1.791759,5.806336,1 6,1,25,0,1,126835,0,12640.82,26.57084,1,8,1,14.13428,12.45583,0,0,0,26.59011,0,0,0,2,0,4,75.8,13,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,69.97394,9.444766,1.386294,3.280539,1 6,1,25,0,2,126835,0,12640.82,27.57084,1,8,1,16.17251,7.02965,0,0,0,23.20216,0,0,0,2,0,4,75.8,13,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,69.97394,9.444766,1.386294,3.144245,1 6,1,25,0,3,126835,0,12640.82,28.57084,1,8,1,8.845209,0,0,0,0,8.845209,0,0,0,1,0,4,75.8,13,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,69.97394,9.444766,1.386294,2.179876,1 6,1,25,0,4,126835,0,12640.82,29.57084,1,8,1,0,0,0,0,0,0,0,0,0,0,0,4,75.8,13,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,69.97394,9.444766,1.386294,,0 6,1,25,0,5,126835,0,12640.82,30.57084,1,8,1,42.93456,0,0,0,0,42.93456,0,0,0,4,0,4,75.8,13,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,69.97394,9.444766,1.386294,3.759677,1 6,1,25,0,1,126836,0,12640.82,30.97604,0,12,1,14.13428,11.42521,0,0,0,25.55948,0,0,0,2,0,4,72.6,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,72.21928,9.444766,1.386294,3.241008,1 6,1,25,0,2,126836,0,12640.82,31.97604,0,12,1,57.14286,8.533692,0,0,0,65.67655,0,0,0,9,0,4,72.6,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,72.21928,9.444766,1.386294,4.184742,1 6,1,25,0,3,126836,0,12640.82,32.97604,0,12,1,60.93366,10.4226,.7371007,0,0,72.09337,0,0,0,4,1,4,72.6,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,72.21928,9.444766,1.386294,4.277962,1 6,1,25,0,4,126836,0,12640.82,33.97604,0,12,1,5.925251,0,0,0,0,5.925251,0,0,0,1,0,4,72.6,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,72.21928,9.444766,1.386294,1.779223,1 6,1,25,0,5,126836,0,12640.82,34.97604,0,12,1,50.85452,0,0,0,0,50.85452,0,0,0,2,0,4,72.6,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,72.21928,9.444766,1.386294,3.928969,1 6,1,25,0,1,126837,0,12640.82,8.791239,0,8,1,154.1519,26.88457,0,0,0,181.0365,0,0,0,8,1,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,1,0,58.4809,9.444766,1.386294,5.198699,1 6,1,25,0,2,126837,0,12640.82,9.791239,0,8,1,72.29111,0,0,0,0,72.29111,0,0,0,5,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,1,0,58.4809,9.444766,1.386294,4.280701,1 6,1,25,0,3,126837,0,12640.82,10.79124,0,8,1,5.405406,3.552825,0,0,0,8.958231,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,1,0,58.4809,9.444766,1.386294,2.192573,1 6,1,25,0,4,126837,0,12640.82,11.79124,0,8,1,41.02097,0,0,0,0,41.02097,0,0,0,4,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,1,0,58.4809,9.444766,1.386294,3.714083,1 6,1,25,0,5,126837,0,12640.82,12.79124,0,8,1,29.28304,0,0,0,0,29.28304,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,1,0,58.4809,9.444766,1.386294,3.377008,1 6,1,25,0,1,126838,0,12640.82,11.44695,1,8,1,16.48999,7.232038,0,0,0,23.72203,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,78.60046,9.444766,1.386294,3.166404,1 6,1,25,0,2,126838,0,12640.82,12.44695,1,8,1,12.93801,4.819407,0,0,0,17.75741,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,78.60046,9.444766,1.386294,2.876803,1 6,1,25,0,3,126838,0,12640.82,13.44695,1,8,1,5.896806,6.943489,0,0,0,12.84029,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,78.60046,9.444766,1.386294,2.552588,1 6,1,25,0,4,126838,0,12640.82,14.44695,1,8,1,36.78213,0,.911577,0,0,37.69371,0,0,0,3,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,78.60046,9.444766,1.386294,3.629493,1 6,1,25,0,5,126838,0,12640.82,15.44695,1,8,1,31.88829,0,0,0,0,31.88829,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,78.60046,9.444766,1.386294,3.462239,1 5,1,25,0,1,126839,0,13224.14,26.36276,1,13,1,81.86102,31.21908,0,0,530.1649,643.245,1,0,0,7,0,4,71.6,13,0,,679,679,0,0,1.386294,6.520621,0,3.258096,7.906916,1,0,0,70.1928,9.489875,1.386294,6.466526,1 5,1,25,0,2,126839,0,13224.14,27.36276,1,13,1,119.6766,33.57412,0,0,0,153.2507,0,0,0,13,0,4,71.6,13,0,,679,679,0,0,1.386294,6.520621,0,3.258096,7.906916,1,0,0,70.1928,9.489875,1.386294,5.032075,1 5,1,25,0,3,126839,0,13224.14,28.36276,1,13,1,79.60688,13.03685,34.91892,0,0,127.5627,0,0,0,4,1,4,71.6,13,0,,679,679,0,0,1.386294,6.520621,0,3.258096,7.906916,1,0,0,70.1928,9.489875,1.386294,4.848608,1 5,1,25,0,1,126840,0,13224.14,28.4627,0,12,1,5.300354,5.683156,0,0,0,10.98351,0,0,0,1,0,4,83.2,8.7,0,,679,679,0,0,1.386294,6.520621,0,3.258096,7.906916,1,0,0,69.02815,9.489875,1.386294,2.396395,1 5,1,25,0,2,126840,0,13224.14,29.4627,0,12,1,4.851752,4.177897,0,0,0,9.02965,0,0,0,1,0,4,83.2,8.7,0,,679,679,0,0,1.386294,6.520621,0,3.258096,7.906916,1,0,0,69.02815,9.489875,1.386294,2.200514,1 5,1,25,0,3,126840,0,13224.14,30.4627,0,12,1,102.8256,24.99754,0,0,0,127.8231,0,0,0,7,2,4,83.2,8.7,0,,679,679,0,0,1.386294,6.520621,0,3.258096,7.906916,1,0,0,69.02815,9.489875,1.386294,4.850647,1 5,1,25,0,1,126841,0,13224.14,5.155373,0,13,1,26.79623,9.952886,0,0,320.3769,357.126,1,0,0,2,1,4,74.36826,13.73189,0,,679,679,1,0,1.386294,6.520621,0,3.258096,7.906916,1,0,0,73.48592,9.489875,1.386294,5.878089,1 5,1,25,0,2,126841,0,13224.14,6.155373,0,13,1,12.93801,4.716981,0,0,0,17.65499,0,0,0,1,0,4,74.36826,13.73189,0,,679,679,1,0,1.386294,6.520621,0,3.258096,7.906916,1,0,0,73.48592,9.489875,1.386294,2.871018,1 5,1,25,0,3,126841,0,13224.14,7.155373,0,13,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,679,679,1,0,1.386294,6.520621,0,3.258096,7.906916,1,0,0,73.48592,9.489875,1.386294,,0 5,1,25,0,1,126842,0,13224.14,6.63655,1,13,1,1.766784,5.918728,0,0,0,7.685513,0,0,0,0,0,4,74.36826,13.73189,0,,679,679,1,1,1.386294,6.520621,0,3.258096,7.906916,1,0,0,76.40357,9.489875,1.386294,2.039337,1 5,1,25,0,2,126842,0,13224.14,7.63655,1,13,1,5.390836,0,0,0,0,5.390836,0,0,0,1,0,4,74.36826,13.73189,0,,679,679,1,1,1.386294,6.520621,0,3.258096,7.906916,1,0,0,76.40357,9.489875,1.386294,1.6847,1 5,1,25,0,3,126842,0,13224.14,8.63655,1,13,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,679,679,1,1,1.386294,6.520621,0,3.258096,7.906916,1,0,0,76.40357,9.489875,1.386294,,0 1,1,0,0,1,126859,0,10039.08,30.91581,0,14,1,191.8433,11.21319,33.5689,0,0,236.6254,0,0,0,5,2,3,56.8,30.4,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,66.07695,9.21434,1.098612,5.466478,1 1,1,0,0,2,126859,0,10039.08,31.91581,0,14,1,70.08086,1.617251,0,0,0,71.69811,0,0,0,2,0,3,56.8,30.4,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,66.07695,9.21434,1.098612,4.272464,1 1,1,0,0,3,126859,0,10039.08,32.91581,0,14,1,0,0,0,0,0,0,0,0,0,0,0,3,56.8,30.4,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,66.07695,9.21434,1.098612,,0 1,1,0,0,4,126859,0,10039.08,33.91581,0,14,1,34.18414,9.553328,12.13765,0,0,55.87511,0,0,0,3,1,3,56.8,30.4,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,66.07695,9.21434,1.098612,4.023119,1 1,1,0,0,5,126859,0,10039.08,34.91581,0,14,1,36.68195,5.944143,0,0,0,42.62609,0,0,0,4,0,3,56.8,30.4,0,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,66.07695,9.21434,1.098612,3.752467,1 1,1,0,0,1,126860,0,10039.08,26.48871,1,9,1,58.33333,32.86808,24.73498,0,1244.411,1360.347,2,0,0,2,1,3,64.2,17.4,1,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,63.57109,9.21434,1.098612,7.215496,1 1,1,0,0,2,126860,0,10039.08,27.48871,1,9,1,21.56334,0,0,0,514.6092,536.1725,1,0,0,1,0,3,64.2,17.4,1,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,63.57109,9.21434,1.098612,6.284456,1 1,1,0,0,3,126860,0,10039.08,28.48871,1,9,1,15.23342,4.117936,0,0,0,19.35135,0,0,0,1,0,3,64.2,17.4,1,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,63.57109,9.21434,1.098612,2.962762,1 1,1,0,0,4,126860,0,10039.08,29.48871,1,9,1,24.15679,5.720146,29.17047,0,0,59.0474,0,0,0,1,1,3,64.2,17.4,1,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,63.57109,9.21434,1.098612,4.078341,1 1,1,0,0,5,126860,0,10039.08,30.48871,1,9,1,100.0417,6.335973,0,0,0,106.3777,0,0,0,1,1,3,64.2,17.4,1,,450,450,0,0,1.098612,6.109248,1,0,0,1,0,0,63.57109,9.21434,1.098612,4.666996,1 1,1,0,0,1,126861,0,10039.08,7.359343,1,9,1,58.89281,7.108363,0,0,0,66.00117,0,0,0,9,0,3,74.36826,13.73189,0,,450,450,1,1,1.098612,6.109248,1,0,0,1,0,0,72.6246,9.21434,1.098612,4.189672,1 1,1,0,0,2,126861,0,10039.08,8.359343,1,9,1,105.6604,21.6496,24.25876,0,0,151.5687,0,0,0,10,1,3,74.36826,13.73189,0,,450,450,1,1,1.098612,6.109248,1,0,0,1,0,0,72.6246,9.21434,1.098612,5.021039,1 1,1,0,0,3,126861,0,10039.08,9.359343,1,9,1,73.46437,13.72482,0,0,0,87.18919,0,0,0,8,0,3,74.36826,13.73189,0,,450,450,1,1,1.098612,6.109248,1,0,0,1,0,0,72.6246,9.21434,1.098612,4.468081,1 1,1,0,0,4,126861,0,10039.08,10.35934,1,9,1,56.06199,27.39289,20.4649,0,0,103.9198,0,0,0,6,1,3,74.36826,13.73189,0,,450,450,1,1,1.098612,6.109248,1,0,0,1,0,0,72.6246,9.21434,1.098612,4.64362,1 1,1,0,0,5,126861,0,10039.08,11.35934,1,9,1,130.471,21.85911,10.83785,0,0,163.168,0,0,0,8,1,3,74.36826,13.73189,0,,450,450,1,1,1.098612,6.109248,1,0,0,1,0,0,72.6246,9.21434,1.098612,5.09478,1 9,1,50,1,1,126862,0,10156.33,29.44832,0,13,1,0,0,0,0,0,0,0,0,0,0,0,3,84.2,0,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,72.47523,9.22595,1.098612,,0 9,1,50,1,2,126862,0,10156.33,30.44832,0,13,1,30.12048,16.57722,0,0,0,46.6977,0,0,0,3,0,3,84.2,0,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,72.47523,9.22595,1.098612,3.843695,1 9,1,50,1,3,126862,0,10156.33,31.44832,0,13,1,5.985037,0,37.08229,0,0,43.06733,0,0,0,0,1,3,84.2,0,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,72.47523,9.22595,1.098612,3.762765,1 9,1,50,1,4,126862,0,10156.33,32.44832,0,13,1,23.51314,17.75011,0,0,0,41.26326,0,0,0,2,1,3,84.2,0,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,72.47523,9.22595,1.098612,3.719972,1 9,1,50,1,5,126862,0,10156.33,33.44832,0,13,1,40.71096,1.531951,.6347863,0,0,42.8777,0,0,0,2,0,3,84.2,0,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,72.47523,9.22595,1.098612,3.758352,1 9,1,50,1,1,126863,0,10156.33,2.915811,1,12,1,4.796163,18.59712,0,0,0,23.39329,0,0,0,1,0,3,74.36826,13.73189,0,,1000,1000,1,1,1.098612,6.907755,0,3.931826,7.600903,0,0,0,80.70722,9.22595,1.098612,3.152449,1 9,1,50,1,2,126863,0,10156.33,3.915811,1,12,1,0,8.849945,0,0,0,8.849945,0,0,0,0,0,3,74.36826,13.73189,0,,1000,1000,1,1,1.098612,6.907755,0,3.931826,7.600903,0,0,0,80.70722,9.22595,1.098612,2.180411,1 9,1,50,1,3,126863,0,10156.33,4.915811,1,12,1,17.95511,1.915212,0,0,0,19.87033,0,0,0,2,0,3,74.36826,13.73189,0,,1000,1000,1,1,1.098612,6.907755,0,3.931826,7.600903,0,0,0,80.70722,9.22595,1.098612,2.989228,1 9,1,50,1,4,126863,0,10156.33,5.915811,1,12,1,5.532504,15.67543,0,0,0,21.20793,0,0,0,1,0,3,74.36826,13.73189,0,,1000,1000,1,1,1.098612,6.907755,0,3.931826,7.600903,0,0,0,80.70722,9.22595,1.098612,3.054375,1 9,1,50,1,5,126863,0,10156.33,6.915811,1,12,1,5.924672,12.91578,0,0,0,18.84046,0,0,0,1,0,3,74.36826,13.73189,0,,1000,1000,1,1,1.098612,6.907755,0,3.931826,7.600903,0,0,0,80.70722,9.22595,1.098612,2.936007,1 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9,1,50,1,1,126865,0,17723.95,18.58179,0,11,1,4.759072,0,0,0,0,4.759072,0,0,0,1,0,6,65.3,8.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,68.26189,9.782728,1.791759,1.560053,1 9,1,50,1,2,126865,0,17723.95,19.58179,0,11,1,0,0,0,0,0,0,0,0,0,0,0,6,65.3,8.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,68.26189,9.782728,1.791759,,0 9,1,50,1,3,126865,0,17723.95,20.58179,0,11,1,0,0,0,0,0,0,0,0,0,0,0,7,65.3,8.7,0,,1000,1000,0,0,1.94591,6.907755,0,3.931826,7.600903,1,0,0,68.26189,9.782728,1.94591,,0 9,1,50,1,1,126866,0,17723.95,15.44422,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,64.2,4.3,0,,1000,1000,1,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,73.25742,9.782728,1.791759,,0 9,1,50,1,2,126866,0,17723.95,16.44422,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,64.2,4.3,0,,1000,1000,1,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,73.25742,9.782728,1.791759,,0 9,1,50,1,3,126866,0,17723.95,17.44422,0,12,1,3.964321,0,0,0,0,3.964321,0,0,0,1,0,7,64.2,4.3,0,,1000,1000,1,0,1.94591,6.907755,0,3.931826,7.600903,1,0,0,73.25742,9.782728,1.94591,1.377335,1 9,1,50,1,1,126867,0,17723.95,17.24025,1,12,1,19.63117,5.205235,0,0,0,24.83641,0,0,0,2,0,6,46.3,0,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,1,0,0,67.93368,9.782728,1.791759,3.212311,1 9,1,50,1,2,126867,0,17723.95,18.24025,1,12,1,51.71475,4.148067,0,0,0,55.86282,0,0,0,2,1,6,46.3,0,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,67.93368,9.782728,1.791759,4.022899,1 9,1,50,1,3,126867,0,17723.95,19.24025,1,12,1,29.23687,6.778989,0,0,0,36.01586,0,0,0,6,0,7,46.3,0,0,,1000,1000,0,0,1.94591,6.907755,0,3.931826,7.600903,1,0,0,67.93368,9.782728,1.94591,3.583959,1 9,1,50,1,1,126868,0,17723.95,41.54415,0,12,1,7.733492,0,0,0,0,7.733492,0,0,0,1,0,6,73.7,21.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,69.6292,9.782728,1.791759,2.045561,1 9,1,50,1,2,126868,0,17723.95,42.54415,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,73.7,21.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,69.6292,9.782728,1.791759,,0 9,1,50,1,3,126868,0,17723.95,43.54415,0,12,1,12.3885,1.466799,0,0,0,13.8553,0,0,0,2,0,7,73.7,21.7,0,,1000,1000,0,0,1.94591,6.907755,0,3.931826,7.600903,1,0,0,69.6292,9.782728,1.94591,2.628668,1 9,1,50,1,1,126869,0,17723.95,40.38877,1,12,1,21.41582,0,0,0,0,21.41582,0,0,0,0,0,6,60,30.4,1,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,71.26881,9.782728,1.791759,3.06413,1 9,1,50,1,2,126869,0,17723.95,41.38877,1,12,1,22.86336,2.928688,0,0,0,25.79205,0,0,0,2,0,6,60,30.4,1,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,71.26881,9.782728,1.791759,3.250066,1 9,1,50,1,3,126869,0,17723.95,42.38877,1,12,1,69.87116,11.04063,54.50941,0,1599.336,1734.757,2,0,0,6,1,7,60,30.4,1,,1000,1000,0,0,1.94591,6.907755,0,3.931826,7.600903,1,0,0,71.26881,9.782728,1.94591,7.458623,1 9,1,50,1,1,126870,0,17723.95,10.39836,1,12,1,9.518144,1.778703,0,0,0,11.29685,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,1,0,0,79.00697,9.782728,1.791759,2.424524,1 9,1,50,1,2,126870,0,17723.95,11.39836,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,1,0,0,79.00697,9.782728,1.791759,,0 9,1,50,1,3,126870,0,17723.95,12.39836,1,12,1,50.54509,10.41625,0,0,0,60.96135,0,0,0,7,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,0,3.931826,7.600903,1,0,0,79.00697,9.782728,1.94591,4.11024,1 9,1,50,1,1,126871,0,4004.963,20.87064,1,12,1,15.46698,17.07317,0,0,0,32.54015,0,0,0,2,0,1,83.2,21.7,0,,580.31,580.31,0,0,0,6.363563,0,3.931826,7.05671,1,0,0,71.42945,8.295539,0,3.482475,1 9,1,50,1,2,126871,0,4004.963,21.87064,1,12,1,23.9521,16.66848,0,0,0,40.62058,0,0,0,2,0,1,83.2,21.7,0,,580.31,580.31,0,0,0,6.363563,0,3.931826,7.05671,1,0,0,71.42945,8.295539,0,3.704275,1 9,1,50,1,3,126871,0,4004.963,22.87064,1,12,1,12.3885,5.133796,36.76908,0,0,54.29138,0,0,0,1,1,1,83.2,21.7,0,,580.31,580.31,0,0,0,6.363563,0,3.931826,7.05671,1,0,0,71.42945,8.295539,0,3.994365,1 8,1,50,1,1,126894,0,8056.452,28.20808,1,13,1,41.64188,7.013682,0,0,0,48.65556,0,0,0,2,0,4,68.4,8.7,0,,525,525,0,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,79.3287,8.994352,1.386294,3.884766,1 8,1,50,1,2,126894,0,8056.452,29.20808,1,13,1,22.72727,0,0,0,0,22.72727,0,0,0,2,0,4,68.4,8.7,0,,525,525,0,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,79.3287,8.994352,1.386294,3.123566,1 8,1,50,1,3,126894,0,8056.452,30.20808,1,13,1,0,7.190288,0,0,0,7.190288,0,0,0,0,0,4,68.4,8.7,0,,525,525,0,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,79.3287,8.994352,1.386294,1.972731,1 8,1,50,1,4,126894,0,8056.452,31.20808,1,13,1,18.35704,9.307021,32.13401,0,0,59.79807,0,0,0,1,1,4,68.4,8.7,0,,525,525,0,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,79.3287,8.994352,1.386294,4.090973,1 8,1,50,1,5,126894,0,8056.452,32.20808,1,13,1,7.57257,2.086664,0,0,0,9.659234,0,0,0,1,0,4,68.4,8.7,0,,525,525,0,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,79.3287,8.994352,1.386294,2.267914,1 8,1,50,1,1,126895,0,8056.452,8.271048,1,13,1,13.08745,7.067222,0,0,0,20.15467,0,0,0,2,0,4,74.36826,13.73189,0,,525,525,1,1,1.386294,6.263398,0,3.931826,6.956545,0,0,0,77.73626,8.994352,1.386294,3.003436,1 8,1,50,1,2,126895,0,8056.452,9.271048,1,13,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,525,525,1,1,1.386294,6.263398,0,3.931826,6.956545,0,0,0,77.73626,8.994352,1.386294,,0 8,1,50,1,3,126895,0,8056.452,10.27105,1,13,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,525,525,1,1,1.386294,6.263398,0,3.931826,6.956545,0,0,0,77.73626,8.994352,1.386294,,0 8,1,50,1,4,126895,0,8056.452,11.27105,1,13,1,30.51859,0,22.54245,0,0,53.06104,0,0,0,2,1,4,74.36826,13.73189,0,,525,525,1,1,1.386294,6.263398,0,3.931826,6.956545,0,0,0,77.73626,8.994352,1.386294,3.971443,1 8,1,50,1,5,126895,0,8056.452,12.27105,1,13,1,33.65587,0,15.38494,0,0,49.04081,0,0,0,1,1,4,74.36826,13.73189,0,,525,525,1,1,1.386294,6.263398,0,3.931826,6.956545,0,0,0,77.73626,8.994352,1.386294,3.892653,1 8,1,50,1,1,126896,0,8056.452,5.842574,0,13,1,121.3563,8.596074,0,0,517.1624,647.1148,1,0,0,16,6,4,74.36826,13.73189,0,,525,525,1,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,83.45087,8.994352,1.386294,6.472524,1 8,1,50,1,2,126896,0,8056.452,6.842574,0,13,1,146.9788,2.280893,31.29015,0,0,180.5498,0,0,0,16,4,4,74.36826,13.73189,0,,525,525,1,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,83.45087,8.994352,1.386294,5.196007,1 8,1,50,1,3,126896,0,8056.452,7.842574,0,13,1,48.06739,0,37.80476,0,0,85.87215,0,0,0,7,0,4,74.36826,13.73189,0,,525,525,1,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,83.45087,8.994352,1.386294,4.452859,1 8,1,50,1,4,126896,0,8056.452,8.842573,0,13,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,525,525,1,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,83.45087,8.994352,1.386294,,0 8,1,50,1,5,126896,0,8056.452,9.842573,0,13,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,525,525,1,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,83.45087,8.994352,1.386294,,0 8,1,50,1,1,126897,0,8056.452,29.61533,0,14,1,37.47769,18.91731,0,0,0,56.395,0,0,0,4,0,4,75.8,17.4,0,,525,525,0,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,78.43752,8.994352,1.386294,4.032381,1 8,1,50,1,2,126897,0,8056.452,30.61533,0,14,1,9.798585,0,43.23353,0,0,53.03212,0,0,0,0,1,4,75.8,17.4,0,,525,525,0,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,78.43752,8.994352,1.386294,3.970898,1 8,1,50,1,3,126897,0,8056.452,31.61533,0,14,1,18.83052,2.552032,0,0,0,21.38256,0,0,0,3,0,4,75.8,17.4,0,,525,525,0,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,78.43752,8.994352,1.386294,3.062576,1 8,1,50,1,4,126897,0,8056.452,32.61533,0,14,1,3.212483,3.969711,0,0,0,7.182194,0,0,0,1,0,4,75.8,17.4,0,,525,525,0,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,78.43752,8.994352,1.386294,1.971605,1 8,1,50,1,5,126897,0,8056.452,33.61533,0,14,1,9.255363,8.140513,0,0,0,17.39588,0,0,0,2,0,4,75.8,17.4,0,,525,525,0,0,1.386294,6.263398,0,3.931826,6.956545,0,0,0,78.43752,8.994352,1.386294,2.856233,1 5,1,25,0,1,126899,1,1,6.8282,1,10,1,0,0,0,0,0,0,0,0,0,0,0,2,74.36826,13.73189,1,,72,72,1,1,.6931472,4.276666,0,3.258096,5.662961,0,1,0,63.00796,.6931472,.6931472,,0 5,1,25,0,2,126899,1,1,7.8282,1,10,1,0,0,0,0,0,0,0,0,0,0,0,2,74.36826,13.73189,1,,72,72,1,1,.6931472,4.276666,0,3.258096,5.662961,0,1,0,63.00796,.6931472,.6931472,,0 5,1,25,0,3,126899,1,1,8.828199,1,10,1,274.4472,29.65111,0,0,678.231,982.3292,1,0,0,29,4,2,74.36826,13.73189,1,,72,72,1,1,.6931472,4.276666,0,3.258096,5.662961,0,1,0,63.00796,.6931472,.6931472,6.889926,1 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4,1,100,1,3,126916,0,13328.78,16.84736,1,18,1,45.09415,12.63132,0,0,0,57.72547,0,0,0,7,0,4,68.4,8.7,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,0,0,0,75.75117,9.497756,1.386294,4.055698,1 4,1,100,1,4,126916,0,13328.78,17.84736,1,18,1,14.22671,13.24002,0,0,0,27.46673,0,0,0,2,0,4,68.4,8.7,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,0,0,0,75.75117,9.497756,1.386294,3.312975,1 4,1,100,1,5,126916,0,13328.78,18.84736,1,18,1,10.09676,5.889777,0,0,0,15.98654,0,0,0,1,0,4,68.4,8.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,75.75117,9.497756,1.386294,2.771747,1 4,1,100,1,1,126917,0,13328.78,45.85352,0,15,1,67.22189,2.135633,52.8376,0,0,122.1951,0,0,0,4,0,4,54.7,4.3,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,73.31355,9.497756,1.386294,4.805619,1 4,1,100,1,2,126917,0,13328.78,46.85352,0,15,1,0,0,0,0,0,0,0,0,0,0,0,4,54.7,4.3,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,73.31355,9.497756,1.386294,,0 4,1,100,1,3,126917,0,13328.78,47.85352,0,15,1,0,0,0,0,0,0,0,0,0,0,0,4,54.7,4.3,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,73.31355,9.497756,1.386294,,0 4,1,100,1,4,126917,0,13328.78,48.85352,0,15,1,0,0,0,0,0,0,0,0,0,0,0,4,54.7,4.3,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,73.31355,9.497756,1.386294,,0 4,1,100,1,5,126917,0,13328.78,49.85352,0,15,1,12.62095,0,40.44173,0,0,53.06268,0,0,0,1,0,4,54.7,4.3,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,73.31355,9.497756,1.386294,3.971474,1 4,1,100,1,1,126918,0,13328.78,16.09309,0,18,1,20.82094,0,0,0,0,20.82094,0,0,0,1,0,4,77.9,4.3,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,81.08788,9.497756,1.386294,3.035959,1 4,1,100,1,2,126918,0,13328.78,17.09309,0,18,1,35.38378,2.885139,28.16004,0,0,66.42896,0,0,0,3,0,4,77.9,4.3,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,81.08788,9.497756,1.386294,4.196133,1 4,1,100,1,3,126918,0,13328.78,18.09309,0,18,1,47.40833,0,0,0,0,47.40833,0,0,0,1,0,4,77.9,4.3,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,81.08788,9.497756,1.386294,3.858798,1 4,1,100,1,4,126918,0,13328.78,19.09309,0,18,1,16.06241,0,16.06241,0,0,32.12483,0,0,0,0,2,4,77.9,4.3,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,81.08788,9.497756,1.386294,3.469629,1 4,1,100,1,5,126918,0,13328.78,20.09309,0,18,1,80.77409,1.598654,0,0,0,82.37274,0,0,0,2,1,4,77.9,4.3,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,81.08788,9.497756,1.386294,4.411254,1 4,1,100,1,1,126919,0,13328.78,51.32923,1,18,1,66.27008,0,35.69304,0,0,101.9631,0,0,0,2,1,4,58.9,26.1,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,66.3842,9.497756,1.386294,4.624611,1 4,1,100,1,2,126919,0,13328.78,52.32923,1,18,1,48.44856,10.01633,0,0,0,58.46489,0,0,0,4,0,4,58.9,26.1,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,66.3842,9.497756,1.386294,4.068427,1 4,1,100,1,3,126919,0,13328.78,53.32923,1,18,1,16.35283,13.95441,0,0,0,30.30724,0,0,0,1,0,4,58.9,26.1,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,66.3842,9.497756,1.386294,3.411386,1 4,1,100,1,4,126919,0,13328.78,54.32923,1,18,1,80.31207,0,0,0,0,80.31207,0,0,0,4,0,4,58.9,26.1,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,66.3842,9.497756,1.386294,4.38592,1 4,1,100,1,5,126919,0,13328.78,55.32923,1,18,1,44.17333,0,0,250.3155,0,44.17333,0,0,17,6,0,4,58.9,26.1,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,66.3842,9.497756,1.386294,3.788121,1 4,1,100,1,1,126920,0,4392.68,1.919233,1,11,1,129.6231,0,0,0,0,129.6231,0,0,0,2,3,2,74.36826,13.73189,0,,75,75,1,1,.6931472,4.317488,1,0,0,0,0,0,75.32616,8.387922,.6931472,4.864631,1 4,1,100,1,2,126920,0,4392.68,2.919233,1,11,1,69.54178,11.37466,0,0,0,80.91644,0,0,0,8,0,2,74.36826,13.73189,0,,75,75,1,1,.6931472,4.317488,1,0,0,0,0,0,75.32616,8.387922,.6931472,4.393417,1 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1,1,0,0,2,127001,0,9542.002,3.102669,0,16,1,53.36927,12.67924,0,0,0,66.04852,0,0,0,7,0,4,74.36826,13.73189,0,,450,145,1,0,1.386294,4.976734,1,0,0,0,0,0,78.82387,9.163564,1.386294,4.19039,1 1,1,0,0,3,127001,0,9542.002,4.102669,0,16,1,7.862408,1.371007,0,0,0,9.233416,0,0,0,1,0,4,74.36826,13.73189,0,,450,145,1,0,1.386294,4.976734,1,0,0,0,0,0,78.82387,9.163564,1.386294,2.222829,1 1,1,0,0,1,127002,0,9542.002,31.37851,1,16,1,11.18964,34.65842,0,0,762.0789,807.927,1,0,0,0,0,3,67.5,13.73189,0,,450,145,0,0,1.098612,4.976734,1,0,0,1,0,0,72.19561,9.163564,1.098612,6.694472,1 1,1,0,0,2,127002,0,9542.002,32.37851,1,16,1,156.0647,8.743936,0,0,0,164.8086,0,0,0,7,0,4,67.5,13.73189,0,,450,145,0,0,1.386294,4.976734,1,0,0,1,0,0,72.19561,9.163564,1.386294,5.104785,1 1,1,0,0,3,127002,0,9542.002,33.37851,1,16,1,101.7199,15.31204,0,0,0,117.0319,0,0,0,6,0,4,67.5,13.73189,0,,450,145,0,0,1.386294,4.976734,1,0,0,1,0,0,72.19561,9.163564,1.386294,4.762447,1 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10,1,50,1,3,127059,0,9848.635,36.73785,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,95.8,0,0,,1000,1000,0,0,0,6.907755,0,3.931826,7.600903,0,0,0,78.73395,9.195189,0,,0 10,1,50,1,1,127060,0,9848.635,10.09993,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,1000,1000,1,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,79.89645,9.195189,1.098612,,0 10,1,50,1,2,127060,0,9848.635,11.09993,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,1000,1000,1,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,79.89645,9.195189,1.098612,,0 10,1,50,1,1,127061,0,9848.635,33.32786,1,12,1,28.55443,56.45449,0,0,0,85.00893,0,0,0,4,0,3,87.4,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,66.92303,9.195189,1.098612,4.442756,1 10,1,50,1,2,127061,0,9848.635,34.32786,1,12,1,21.77463,1.986935,0,0,0,23.76157,0,0,0,2,0,3,87.4,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,66.92303,9.195189,1.098612,3.16807,1 10,1,50,1,1,127074,0,11740.07,22.89391,0,13,1,0,1.6247,0,0,0,1.6247,0,0,0,0,0,1,75.8,0,0,,1000,1000,0,0,0,6.907755,0,3.931826,7.600903,1,0,0,66.68941,9.370849,0,.4853233,1 10,1,50,1,2,127074,0,11740.07,23.89391,0,13,1,12.04819,0,0,0,0,12.04819,0,0,0,1,0,1,75.8,0,0,,1000,1000,0,0,0,6.907755,0,3.931826,7.600903,1,0,0,66.68941,9.370849,0,2.488915,1 10,1,50,1,3,127074,0,11740.07,24.89391,0,13,1,4.987531,0,0,0,0,4.987531,0,0,0,1,0,1,75.8,0,0,,1000,1000,0,0,0,6.907755,0,3.931826,7.600903,1,0,0,66.68941,9.370849,0,1.606941,1 10,1,50,1,4,127074,0,11740.07,25.89391,0,13,1,5.532504,0,0,0,0,5.532504,0,0,0,1,0,1,75.8,0,0,,1000,1000,0,0,0,6.907755,0,3.931826,7.600903,1,0,0,66.68941,9.370849,0,1.71064,1 10,1,50,1,5,127074,0,11740.07,26.89391,0,13,1,0,0,0,0,0,0,0,0,0,0,0,1,75.8,0,0,,1000,1000,0,0,0,6.907755,0,3.931826,7.600903,1,0,0,66.68941,9.370849,0,,0 4,1,100,1,1,127075,0,7539.082,.8158795,0,12,1,20.38369,1.306954,0,0,0,21.69065,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,80.7198,8.927988,1.386294,3.076881,1 4,1,100,1,2,127075,0,7539.082,1.81588,0,12,1,20.26287,1.484118,0,0,0,21.74699,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,80.7198,8.927988,1.386294,3.079475,1 4,1,100,1,3,127075,0,7539.082,2.81588,0,12,1,7.98005,0,0,0,0,7.98005,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,80.7198,8.927988,1.386294,2.076945,1 4,1,100,1,4,127075,0,7539.082,3.81588,0,12,1,14.75334,0,0,0,0,14.75334,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,80.7198,8.927988,1.386294,2.69147,1 4,1,100,1,5,127075,0,7539.082,4.815879,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,80.7198,8.927988,1.386294,,0 4,1,100,1,1,127076,0,7539.082,25.78508,0,12,1,17.38609,0,0,0,0,17.38609,0,0,0,1,0,4,97.9,4.3,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,78.25877,8.927988,1.386294,2.85567,1 4,1,100,1,2,127076,0,7539.082,26.78508,0,12,1,2.190581,0,47.27273,0,0,49.46331,0,0,0,0,0,4,97.9,4.3,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,78.25877,8.927988,1.386294,3.901231,1 4,1,100,1,3,127076,0,7539.082,27.78508,0,12,1,9.476309,0,0,0,0,9.476309,0,0,0,1,0,4,97.9,4.3,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,78.25877,8.927988,1.386294,2.248795,1 4,1,100,1,4,127076,0,7539.082,28.78508,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,97.9,4.3,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,78.25877,8.927988,1.386294,,0 4,1,100,1,5,127076,0,7539.082,29.78508,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,97.9,4.3,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,78.25877,8.927988,1.386294,,0 4,1,100,1,1,127077,0,7539.082,3.531827,0,12,1,16.18705,1.306954,0,0,0,17.49401,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,70.5428,8.927988,1.386294,2.861858,1 4,1,100,1,2,127077,0,7539.082,4.531827,0,12,1,50.38335,15.73932,0,0,307.6396,373.7623,1,0,0,6,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,70.5428,8.927988,1.386294,5.92362,1 4,1,100,1,3,127077,0,7539.082,5.531827,0,12,1,19.95012,1.391521,0,0,0,21.34165,0,0,0,3,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,70.5428,8.927988,1.386294,3.06066,1 4,1,100,1,4,127077,0,7539.082,6.531827,0,12,1,18.44168,3.379437,0,0,191.9087,213.7298,1,1,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,70.5428,8.927988,1.386294,5.364713,1 4,1,100,1,5,127077,0,7539.082,7.531827,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,70.5428,8.927988,1.386294,,0 4,1,100,1,1,127078,0,7539.082,23.96715,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,83.2,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,79.14996,8.927988,1.386294,,0 4,1,100,1,2,127078,0,7539.082,24.96715,1,12,1,42.71632,4.83023,34.33735,0,0,81.8839,0,0,0,4,1,4,83.2,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,79.14996,8.927988,1.386294,4.405303,1 4,1,100,1,3,127078,0,7539.082,25.96715,1,12,1,34.91272,3.241895,0,0,0,38.15461,0,0,0,3,0,4,83.2,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,79.14996,8.927988,1.386294,3.641647,1 4,1,100,1,4,127078,0,7539.082,26.96715,1,12,1,7.376671,2.434302,0,0,0,9.810973,0,0,0,1,0,4,83.2,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,79.14996,8.927988,1.386294,2.283501,1 4,1,100,1,5,127078,0,7539.082,27.96715,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,83.2,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,79.14996,8.927988,1.386294,,0 5,1,25,1,1,127097,0,8867.866,.9089665,1,16,1,110.1296,20.01178,0,0,0,130.1413,0,0,0,15,0,4,74.36826,13.73189,0,,640,640,1,1,1.386294,6.461468,0,3.258096,7.847763,1,0,0,73.34382,9.090302,1.386294,4.868621,1 5,1,25,1,2,127097,0,8867.866,1.908966,1,16,1,21.02426,7.929919,0,0,0,28.95418,0,0,0,4,0,4,74.36826,13.73189,0,,640,640,1,1,1.386294,6.461468,0,3.258096,7.847763,1,0,0,73.34382,9.090302,1.386294,3.365715,1 5,1,25,1,3,127097,0,8867.866,2.908967,1,16,1,52.92383,6.240786,0,0,0,59.16462,0,0,0,6,1,4,74.36826,13.73189,0,,640,640,1,1,1.386294,6.461468,0,3.258096,7.847763,1,0,0,73.34382,9.090302,1.386294,4.080324,1 5,1,25,1,1,127098,0,8867.866,34.62286,0,16,1,125.4417,25.9364,0,0,0,151.3781,0,0,0,11,0,4,57.9,30.4,1,,640,640,0,0,1.386294,6.461468,0,3.258096,7.847763,0,1,0,63.20214,9.090302,1.386294,5.019781,1 5,1,25,1,2,127098,0,8867.866,35.62286,0,16,1,13.47709,1.061995,0,0,0,14.53908,0,0,0,1,0,4,57.9,30.4,1,,640,640,0,0,1.386294,6.461468,0,3.258096,7.847763,0,1,0,63.20214,9.090302,1.386294,2.676841,1 5,1,25,1,3,127098,0,8867.866,36.62286,0,16,1,133.1695,1.965602,50.84029,0,242.7568,428.7322,1,0,0,6,1,4,57.9,30.4,1,,640,640,0,0,1.386294,6.461468,0,3.258096,7.847763,0,1,0,63.20214,9.090302,1.386294,6.060833,1 5,1,25,1,1,127099,0,8867.866,3.931554,1,16,1,44.75854,15.00589,0,0,0,59.76443,0,0,0,7,0,4,74.36826,13.73189,0,,640,640,1,1,1.386294,6.461468,0,3.258096,7.847763,1,0,0,70.0731,9.090302,1.386294,4.090411,1 5,1,25,1,2,127099,0,8867.866,4.931554,1,16,1,32.8841,13.29919,0,0,0,46.18329,0,0,0,6,0,4,74.36826,13.73189,0,,640,640,1,1,1.386294,6.461468,0,3.258096,7.847763,1,0,0,70.0731,9.090302,1.386294,3.832618,1 5,1,25,1,3,127099,0,8867.866,5.931554,1,16,1,26.53563,4.825553,0,0,0,31.36118,0,0,0,5,0,4,74.36826,13.73189,0,,640,640,1,1,1.386294,6.461468,0,3.258096,7.847763,1,0,0,70.0731,9.090302,1.386294,3.445571,1 5,1,25,1,1,127100,0,8867.866,33.295,1,16,1,50.05889,18.32155,45.02356,0,0,113.404,0,0,0,2,1,4,83.2,26.1,0,,640,640,0,0,1.386294,6.461468,0,3.258096,7.847763,0,0,0,75.64986,9.090302,1.386294,4.730957,1 5,1,25,1,2,127100,0,8867.866,34.295,1,16,1,465.6334,18.71698,0,0,0,484.3504,0,0,0,9,0,4,83.2,26.1,0,,640,640,0,0,1.386294,6.461468,0,3.258096,7.847763,0,0,0,75.64986,9.090302,1.386294,6.182808,1 5,1,25,1,3,127100,0,8867.866,35.295,1,16,1,84.02949,13.94595,0,0,0,97.97543,0,0,0,4,0,4,83.2,26.1,0,,640,640,0,0,1.386294,6.461468,0,3.258096,7.847763,0,0,0,75.64986,9.090302,1.386294,4.584717,1 11,1,0,0,1,127104,0,14157.57,52,1,13,1,42.56595,58.15348,34.43045,0,0,135.1499,0,0,0,4,0,2,82.5,13.73189,0,,0,166,0,0,.6931472,5.111988,0,0,0,1,0,0,67.18981,9.558075,.6931472,4.906384,1 11,1,0,0,2,127104,0,14157.57,53,1,13,1,33.954,49.09639,0,0,0,83.05038,0,0,0,4,0,2,82.5,13.73189,0,,0,166,0,0,.6931472,5.111988,0,0,0,1,0,0,67.18981,9.558075,.6931472,4.419447,1 11,1,0,0,3,127104,0,14157.57,54,1,13,1,47.8803,35.03741,0,0,0,82.91771,0,0,0,6,0,2,82.5,13.73189,0,,0,166,0,0,.6931472,5.111988,0,0,0,1,0,0,67.18981,9.558075,.6931472,4.417849,1 11,1,0,0,1,127105,0,14157.57,51.43327,0,12,1,80.93525,9.106714,0,0,0,90.04197,0,0,0,2,0,2,68.8,13.73189,0,,0,166,0,0,.6931472,5.111988,0,0,0,0,0,0,70.86036,9.558075,.6931472,4.500276,1 11,1,0,0,2,127105,0,14157.57,52.43327,0,12,1,60.24096,3.444688,0,0,0,63.68565,0,0,0,1,0,2,68.8,13.73189,0,,0,166,0,0,.6931472,5.111988,0,0,0,0,0,0,70.86036,9.558075,.6931472,4.153959,1 11,1,0,0,3,127105,0,14157.57,53.43327,0,12,1,30.92269,7.047381,16.6783,0,0,54.64838,0,0,0,5,0,2,68.8,13.73189,0,,0,166,0,0,.6931472,5.111988,0,0,0,0,0,0,70.86036,9.558075,.6931472,4.000919,1 11,1,0,0,1,127106,0,7895.782,22.43669,1,16,1,111.5108,12.47602,42.44005,0,0,166.4269,0,0,0,5,0,1,71.3,13.73189,0,,0,166,0,0,0,5.111988,0,0,0,0,0,0,75.76809,8.974211,0,5.114556,1 11,1,0,0,2,127106,0,7895.782,23.43669,1,16,1,57.63965,14.15115,0,0,0,71.7908,0,0,0,5,0,1,71.3,13.73189,0,,0,166,0,0,0,5.111988,0,0,0,0,0,0,75.76809,8.974211,0,4.273757,1 11,1,0,0,3,127106,0,7895.782,24.43669,1,16,1,73.71571,0,0,0,0,73.71571,0,0,0,3,1,1,71.3,13.73189,0,,0,166,0,0,0,5.111988,0,0,0,0,0,0,75.76809,8.974211,0,4.300216,1 5,1,25,1,1,127107,0,8823.201,22.49966,0,11,1,0,0,0,0,0,0,0,0,0,0,0,4,80,0,0,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,0,0,0,74.03484,9.085254,1.386294,,0 5,1,25,1,2,127107,0,8823.201,23.49966,0,11,1,0,0,0,0,0,0,0,0,0,0,0,4,80,0,0,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,0,0,0,74.03484,9.085254,1.386294,,0 5,1,25,1,3,127107,0,8823.201,24.49966,0,11,1,0,0,0,0,0,0,0,0,0,0,0,4,80,0,0,,500,500,0,0,1.386294,6.214608,0,3.258096,7.600903,0,0,0,74.03484,9.085254,1.386294,,0 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3,1,100,1,4,127297,0,2896.791,9.773443,0,14,1,95.71559,15.01823,0,0,0,110.7338,0,0,0,6,1,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,82.37522,7.971704,1.386294,4.707129,1 3,1,100,1,5,127297,0,2896.791,10.77344,0,14,1,81.70071,46.26928,28.49104,0,0,156.461,0,0,0,23,1,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,82.37522,7.971704,1.386294,5.052807,1 3,1,100,1,1,127298,0,2896.791,41.39631,0,14,1,54.77032,90.02945,0,0,0,144.7998,0,0,0,23,0,5,62.1,21.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,73.19926,7.971704,1.609438,4.975352,1 3,1,100,1,2,127298,0,2896.791,42.39631,0,14,1,68.46362,0,0,0,0,68.46362,0,0,0,12,2,5,62.1,21.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,73.19926,7.971704,1.609438,4.226303,1 3,1,100,1,3,127298,0,2896.791,43.39631,0,14,1,61.42506,66.82064,0,0,0,128.2457,0,0,0,17,0,5,62.1,21.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,0,0,0,73.19926,7.971704,1.609438,4.853948,1 3,1,100,1,4,127298,0,2896.791,44.39631,0,14,1,72.47038,40,38.10392,0,0,150.5743,0,0,0,11,1,4,62.1,21.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,73.19926,7.971704,1.386294,5.014457,1 3,1,100,1,5,127298,0,2896.791,45.39631,0,14,1,98.79116,68.77866,12.08837,0,0,179.6582,0,0,0,13,0,4,62.1,21.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,73.19926,7.971704,1.386294,5.191056,1 3,1,100,1,1,127299,0,2896.791,36.58316,1,14,1,34.15783,4.652533,25.47703,0,0,64.2874,0,0,0,2,1,5,92.6,13,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,69.37424,7.971704,1.609438,4.163363,1 3,1,100,1,2,127299,0,2896.791,37.58316,1,14,1,12.39892,0,0,0,0,12.39892,0,0,0,2,0,5,92.6,13,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,69.37424,7.971704,1.609438,2.51761,1 3,1,100,1,3,127299,0,2896.791,38.58316,1,14,1,6.388206,0,0,0,0,6.388206,0,0,0,1,0,5,92.6,13,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,69.37424,7.971704,1.609438,1.854454,1 3,1,100,1,4,127299,0,2896.791,39.58316,1,14,1,345.0319,0,27.62534,0,0,372.6573,0,0,0,5,1,4,92.6,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,69.37424,7.971704,1.386294,5.920659,1 3,1,100,1,5,127299,0,2896.791,40.58316,1,14,1,16.67361,4.614423,0,0,0,21.28804,0,0,0,2,0,4,92.6,13,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,69.37424,7.971704,1.386294,3.058145,1 3,1,100,1,1,127300,0,2896.791,11.66324,0,14,1,9.422851,0,0,0,0,9.422851,0,0,0,2,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,82.37522,7.971704,1.609438,2.243138,1 3,1,100,1,2,127300,0,2896.791,12.66324,0,14,1,13.47709,0,15.21294,0,0,28.69003,0,0,0,2,1,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,82.37522,7.971704,1.609438,3.35655,1 3,1,100,1,3,127300,0,2896.791,13.66324,0,14,1,64.71745,2.432432,32.86486,0,0,100.0147,0,0,0,2,2,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,82.37522,7.971704,1.609438,4.605318,1 3,1,100,1,4,127300,0,2896.791,14.66324,0,14,1,27.34731,4.512306,0,0,0,31.85962,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,82.37522,7.971704,1.386294,3.461339,1 3,1,100,1,5,127300,0,2896.791,15.66324,0,14,1,47.10296,9.349729,29.62068,0,0,86.07336,0,0,0,5,1,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,82.37522,7.971704,1.386294,4.4552,1 3,1,100,1,1,127301,0,2896.791,14.59822,0,14,1,45.9364,13.69258,36.9258,0,0,96.55477,0,0,0,4,1,5,78.9,4.3,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,76.82748,7.971704,1.609438,4.57011,1 3,1,100,1,2,127301,0,2896.791,15.59822,0,14,1,18.32884,28.93262,0,0,0,47.26146,0,0,0,3,0,5,78.9,4.3,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,76.82748,7.971704,1.609438,3.855695,1 3,1,100,1,3,127301,0,2896.791,16.59822,0,14,1,63.88206,26.3145,31.32678,0,0,121.5233,0,0,0,5,1,5,78.9,4.3,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,0,0,0,76.82748,7.971704,1.609438,4.800107,1 5,1,25,1,1,127311,0,14820.32,42.91034,0,14,1,0,71.58273,0,0,0,71.58273,0,0,0,0,0,4,73.7,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,64.57561,9.603822,1.386294,4.270854,1 5,1,25,1,2,127311,0,14820.32,43.91034,0,14,1,13.69113,100.4107,39.32092,0,0,153.4228,0,0,0,0,1,4,73.7,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,64.57561,9.603822,1.386294,5.033197,1 5,1,25,1,3,127311,0,14820.32,44.91034,0,14,1,94.56359,112.9077,0,0,0,207.4713,0,0,0,5,0,4,73.7,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,64.57561,9.603822,1.386294,5.334993,1 5,1,25,1,4,127311,0,14820.32,45.91034,0,14,1,10.14292,77.39511,0,0,0,87.53803,0,0,0,1,0,4,73.7,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,64.57561,9.603822,1.386294,4.472074,1 5,1,25,1,5,127311,0,14820.32,46.91034,0,14,1,35.97122,47.20694,0,0,0,83.17816,0,0,0,5,0,4,73.7,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,64.57561,9.603822,1.386294,4.420985,1 5,1,25,1,1,127312,0,14820.32,17.10062,0,15,1,26.3789,1.798561,25.28177,0,0,53.45923,0,0,0,1,1,4,78.9,17.4,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.97823,9.603822,1.386294,3.978919,1 5,1,25,1,2,127312,0,14820.32,18.10062,0,15,1,41.07338,2.190581,0,0,0,43.26397,0,0,0,5,0,4,78.9,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.97823,9.603822,1.386294,3.76732,1 5,1,25,1,3,127312,0,14820.32,19.10062,0,15,1,0,0,0,0,0,0,0,0,0,0,0,4,78.9,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.97823,9.603822,1.386294,,0 5,1,25,1,4,127312,0,14820.32,20.10062,0,15,1,0,0,0,0,0,0,0,0,0,0,0,4,78.9,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.97823,9.603822,1.386294,,0 5,1,25,1,5,127312,0,14820.32,21.10062,0,15,1,0,0,0,0,0,0,0,0,0,0,0,4,78.9,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.97823,9.603822,1.386294,,0 5,1,25,1,1,127313,0,14820.32,7.244353,1,15,1,11.99041,0,0,0,0,11.99041,0,0,0,0,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.31068,9.603822,1.386294,2.484107,1 5,1,25,1,2,127313,0,14820.32,8.244353,1,15,1,24.09639,1.09529,31.68675,0,0,56.87842,0,0,0,2,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.31068,9.603822,1.386294,4.040916,1 5,1,25,1,3,127313,0,14820.32,9.244353,1,15,1,7.481297,0,0,0,0,7.481297,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.31068,9.603822,1.386294,2.012406,1 5,1,25,1,4,127313,0,14820.32,10.24435,1,15,1,25.81835,5.855233,31.51222,0,0,63.1858,0,0,0,3,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.31068,9.603822,1.386294,4.14608,1 5,1,25,1,5,127313,0,14820.32,11.24435,1,15,1,26.23783,0,3.377063,0,0,29.6149,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.31068,9.603822,1.386294,3.388278,1 5,1,25,1,1,127314,0,14820.32,42.61191,1,15,1,13.18945,0,0,0,0,13.18945,0,0,0,1,0,4,82.1,8.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,77.97667,9.603822,1.386294,2.579417,1 5,1,25,1,2,127314,0,14820.32,43.61191,1,15,1,72.8368,0,36.98248,0,0,109.8193,0,0,0,4,1,4,82.1,8.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,77.97667,9.603822,1.386294,4.698836,1 5,1,25,1,3,127314,0,14820.32,44.61191,1,15,1,128.5287,0,0,0,116.0898,244.6185,1,0,0,1,0,4,82.1,8.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,77.97667,9.603822,1.386294,5.4997,1 5,1,25,1,4,127314,0,14820.32,45.61191,1,15,1,87.59797,5.60166,0,0,0,93.19963,0,0,0,5,0,4,82.1,8.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,77.97667,9.603822,1.386294,4.534744,1 5,1,25,1,5,127314,0,14820.32,46.61191,1,15,1,135.8697,0,0,0,979.3737,1115.243,1,0,0,2,0,4,82.1,8.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,77.97667,9.603822,1.386294,7.016828,1 7,1,25,0,1,127315,0,9408.188,44.71458,0,16,1,8.833922,0,36.9258,0,0,45.75972,0,0,0,0,1,5,78.8,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,66.6989,9.149442,1.609438,3.823404,1 7,1,25,0,2,127315,0,9408.188,45.71458,0,16,1,6.469003,0,0,0,0,6.469003,0,0,0,1,0,5,78.8,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,66.6989,9.149442,1.609438,1.867022,1 7,1,25,0,3,127315,0,9408.188,46.71458,0,16,1,0,5.356266,0,0,0,5.356266,0,0,0,0,0,5,78.8,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,66.6989,9.149442,1.609438,1.678267,1 7,1,25,0,4,127315,0,9408.188,47.71458,0,16,1,9.11577,0,51.85506,0,0,60.97083,0,0,0,0,1,5,78.8,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,66.6989,9.149442,1.609438,4.110395,1 7,1,25,0,5,127315,0,9408.188,48.71458,0,16,1,5.418924,2.163401,0,0,0,7.582326,0,0,0,1,0,5,78.8,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,66.6989,9.149442,1.609438,2.02582,1 7,1,25,0,1,127316,0,9408.188,17.31143,0,12,1,24.14605,0,1.177856,0,0,25.32391,0,0,0,5,0,5,87.5,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,72.956,9.149442,1.609438,3.231749,1 7,1,25,0,2,127316,0,9408.188,18.31143,0,12,1,54.44744,6.134771,0,0,0,60.58221,0,0,0,3,3,5,87.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,72.956,9.149442,1.609438,4.104002,1 7,1,25,0,3,127316,0,9408.188,19.31143,0,12,1,168.7617,3.70516,0,0,0,172.4668,0,0,0,5,0,5,87.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,72.956,9.149442,1.609438,5.150205,1 7,1,25,0,4,127316,0,9408.188,20.31143,0,12,1,50.59253,0,0,0,0,50.59253,0,0,0,3,0,5,87.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,72.956,9.149442,1.609438,3.923804,1 7,1,25,0,5,127316,0,9408.188,21.31143,0,12,1,18.75782,.8336807,0,0,0,19.5915,0,0,0,2,0,5,87.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,72.956,9.149442,1.609438,2.975096,1 7,1,25,0,1,127317,0,9408.188,15.33744,0,12,1,32.39105,0,0,0,0,32.39105,0,0,0,3,0,5,76.3,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,72.956,9.149442,1.609438,3.477882,1 7,1,25,0,2,127317,0,9408.188,16.33744,0,12,1,29.11051,0,0,0,0,29.11051,0,0,0,1,2,5,76.3,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,72.956,9.149442,1.609438,3.371099,1 7,1,25,0,3,127317,0,9408.188,17.33744,0,12,1,30.95823,8.643735,0,0,0,39.60197,0,0,0,5,0,5,76.3,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,72.956,9.149442,1.609438,3.678879,1 7,1,25,0,4,127317,0,9408.188,18.33744,0,12,1,123.5187,2.39289,0,0,0,125.9116,0,0,0,2,13,5,76.3,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,72.956,9.149442,1.609438,4.83558,1 7,1,25,0,5,127317,0,9408.188,19.33744,0,12,1,265.5273,6.335973,32.23426,0,0,304.0975,0,0,0,33,3,5,76.3,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,72.956,9.149442,1.609438,5.717349,1 7,1,25,0,1,127318,0,9408.188,44.18617,1,12,1,24.14605,0,0,0,0,24.14605,0,0,0,3,0,5,82.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,67.91996,9.149442,1.609438,3.184121,1 7,1,25,0,2,127318,0,9408.188,45.18617,1,12,1,339.0836,0,0,0,0,339.0836,0,0,0,5,0,5,82.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,67.91996,9.149442,1.609438,5.826247,1 7,1,25,0,3,127318,0,9408.188,46.18617,1,12,1,16.21622,3.734644,0,0,0,19.95086,0,0,0,2,0,5,82.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,67.91996,9.149442,1.609438,2.993272,1 7,1,25,0,4,127318,0,9408.188,47.18617,1,12,1,76.11668,9.52598,33.16773,0,0,118.8104,0,0,0,8,0,5,82.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,67.91996,9.149442,1.609438,4.777529,1 7,1,25,0,5,127318,0,9408.188,48.18617,1,12,1,179.5248,30.37932,42.51772,0,0,252.4218,0,0,0,10,2,5,82.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,67.91996,9.149442,1.609438,5.531102,1 7,1,25,0,1,127319,0,9408.188,14.46133,1,12,1,30.3298,10.13545,0,0,0,40.46525,0,0,0,4,0,5,62.5,13.73189,0,,1000,1000,1,1,1.609438,6.907755,0,3.258096,8.294049,1,0,0,67.63226,9.149442,1.609438,3.700444,1 7,1,25,0,2,127319,0,9408.188,15.46133,1,12,1,361.3154,1.185984,0,0,0,362.5013,0,0,0,5,0,5,62.5,13.73189,0,,1000,1000,1,1,1.609438,6.907755,0,3.258096,8.294049,1,0,0,67.63226,9.149442,1.609438,5.893028,1 7,1,25,0,3,127319,0,9408.188,16.46133,1,12,1,76.90417,5.710074,0,0,0,82.61425,0,0,0,5,0,5,62.5,13.73189,0,,1000,1000,1,1,1.609438,6.907755,0,3.258096,8.294049,1,0,0,67.63226,9.149442,1.609438,4.414182,1 7,1,25,0,4,127319,0,9408.188,17.46133,1,12,1,36.46308,6.020966,0,0,667.0146,709.4987,1,0,0,5,0,5,62.5,13.73189,0,,1000,1000,1,1,1.609438,6.907755,0,3.258096,8.294049,1,0,0,67.63226,9.149442,1.609438,6.564559,1 7,1,25,0,5,127319,0,9408.188,18.46133,1,12,1,46.18591,23.84744,0,0,0,70.03335,0,0,0,4,0,5,62.5,13.73189,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,67.63226,9.149442,1.609438,4.248971,1 5,1,25,0,1,127345,0,9044.045,13.45927,0,12,1,29.59364,0,0,0,0,29.59364,0,0,0,0,1,7,74.36826,13.73189,0,,515,515,1,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,77.87675,9.109972,1.94591,3.387559,1 5,1,25,0,2,127345,0,9044.045,14.45927,0,12,1,26.95418,0,0,0,0,26.95418,0,0,0,2,0,7,74.36826,13.73189,0,,515,515,1,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,77.87675,9.109972,1.94591,3.294138,1 5,1,25,0,3,127345,0,9044.045,15.45927,0,12,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,515,515,1,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,77.87675,9.109972,1.94591,,0 5,1,25,0,1,127346,0,9044.045,11.54552,0,12,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,515,515,1,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,77.87675,9.109972,1.94591,,0 5,1,25,0,2,127346,0,9044.045,12.54552,0,12,1,72.2372,0,0,0,0,72.2372,0,0,0,4,0,7,74.36826,13.73189,0,,515,515,1,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,77.87675,9.109972,1.94591,4.279955,1 5,1,25,0,3,127346,0,9044.045,13.54552,0,12,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,515,515,1,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,77.87675,9.109972,1.94591,,0 5,1,25,0,1,127347,0,9044.045,14.51608,0,12,1,0,0,0,0,0,0,0,0,0,0,0,7,78.8,13.73189,0,,515,515,1,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,73.47551,9.109972,1.94591,,0 5,1,25,0,2,127347,0,9044.045,15.51608,0,12,1,13.47709,0,0,0,0,13.47709,0,0,0,1,0,7,78.8,13.73189,0,,515,515,1,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,73.47551,9.109972,1.94591,2.600991,1 5,1,25,0,3,127347,0,9044.045,16.51608,0,12,1,17.51843,5.061425,0,0,0,22.57985,0,0,0,1,0,7,78.8,13.73189,0,,515,515,1,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,73.47551,9.109972,1.94591,3.117058,1 5,1,25,0,1,127348,0,9044.045,6.55989,1,12,1,8.244994,0,0,0,0,8.244994,0,0,0,1,0,7,74.36826,13.73189,0,,515,515,1,1,1.94591,6.244167,0,3.258096,7.630461,1,0,0,77.36277,9.109972,1.94591,2.109606,1 5,1,25,0,2,127348,0,9044.045,7.55989,1,12,1,3.773585,0,15.77359,0,0,19.54717,0,0,0,0,1,7,74.36826,13.73189,0,,515,515,1,1,1.94591,6.244167,0,3.258096,7.630461,1,0,0,77.36277,9.109972,1.94591,2.972831,1 5,1,25,0,3,127348,0,9044.045,8.559891,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,515,515,1,1,1.94591,6.244167,0,3.258096,7.630461,1,0,0,77.36277,9.109972,1.94591,,0 5,1,25,0,1,127349,0,9044.045,10.0835,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,515,515,1,1,1.94591,6.244167,0,3.258096,7.630461,1,0,0,77.36277,9.109972,1.94591,,0 5,1,25,0,2,127349,0,9044.045,11.0835,1,12,1,5.390836,1.078167,0,0,0,6.469003,0,0,0,1,0,7,74.36826,13.73189,0,,515,515,1,1,1.94591,6.244167,0,3.258096,7.630461,1,0,0,77.36277,9.109972,1.94591,1.867022,1 5,1,25,0,3,127349,0,9044.045,12.0835,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,515,515,1,1,1.94591,6.244167,0,3.258096,7.630461,1,0,0,77.36277,9.109972,1.94591,,0 5,1,25,0,1,127350,0,9044.045,32.64887,1,12,1,25.32391,12.04947,0,0,0,37.37338,0,0,0,3,0,7,73.8,13.73189,0,,515,515,0,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,71.59294,9.109972,1.94591,3.620959,1 5,1,25,0,2,127350,0,9044.045,33.64887,1,12,1,17.25067,12.02695,16.33962,16.17251,0,45.61725,0,0,2,0,1,7,73.8,13.73189,0,,515,515,0,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,71.59294,9.109972,1.94591,3.820286,1 5,1,25,0,3,127350,0,9044.045,34.64887,1,12,1,4.914005,4.732187,0,0,0,9.646192,0,0,0,1,0,7,73.8,13.73189,0,,515,515,0,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,71.59294,9.109972,1.94591,2.266563,1 5,1,25,0,1,127351,0,9044.045,41.00479,0,12,1,0,0,0,0,0,0,0,0,0,0,0,7,72.5,13.73189,0,,515,515,0,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,68.90664,9.109972,1.94591,,0 5,1,25,0,2,127351,0,9044.045,42.00479,0,12,1,8.086253,3.962264,0,0,0,12.04852,0,0,0,1,0,7,72.5,13.73189,0,,515,515,0,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,68.90664,9.109972,1.94591,2.488942,1 5,1,25,0,3,127351,0,9044.045,43.00479,0,12,1,0,0,0,0,0,0,0,0,0,0,0,7,72.5,13.73189,0,,515,515,0,0,1.94591,6.244167,0,3.258096,7.630461,1,0,0,68.90664,9.109972,1.94591,,0 3,1,100,0,1,127361,0,9542.002,8.287475,0,10,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,283,283,1,0,1.791759,5.645447,1,0,0,1,0,0,73.43399,9.163564,1.791759,,0 3,1,100,0,2,127361,0,9542.002,9.287475,0,10,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,283,283,1,0,1.791759,5.645447,1,0,0,1,0,0,73.43399,9.163564,1.791759,,0 3,1,100,0,3,127361,0,9542.002,10.28747,0,10,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,283,283,1,0,1.791759,5.645447,1,0,0,1,0,0,73.43399,9.163564,1.791759,,0 3,1,100,0,1,127362,0,9542.002,7.074606,1,10,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,283,283,1,1,1.791759,5.645447,1,0,0,1,0,0,72.92001,9.163564,1.791759,,0 3,1,100,0,2,127362,0,9542.002,8.074607,1,10,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,283,283,1,1,1.791759,5.645447,1,0,0,1,0,0,72.92001,9.163564,1.791759,,0 3,1,100,0,3,127362,0,9542.002,9.074607,1,10,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,283,283,1,1,1.791759,5.645447,1,0,0,1,0,0,72.92001,9.163564,1.791759,,0 3,1,100,0,1,127363,0,9542.002,9.166325,1,10,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,283,283,1,1,1.791759,5.645447,1,0,0,1,0,0,69.64929,9.163564,1.791759,,0 3,1,100,0,2,127363,0,9542.002,10.16632,1,10,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,283,283,1,1,1.791759,5.645447,1,0,0,1,0,0,69.64929,9.163564,1.791759,,0 3,1,100,0,3,127363,0,9542.002,11.16632,1,10,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,283,283,1,1,1.791759,5.645447,1,0,0,1,0,0,69.64929,9.163564,1.791759,,0 3,1,100,0,1,127364,0,9542.002,27.91239,1,10,1,0,0,0,0,0,0,0,0,0,0,0,6,82.1,0,0,,283,283,0,0,1.791759,5.645447,1,0,0,1,0,0,63.48573,9.163564,1.791759,,0 3,1,100,0,2,127364,0,9542.002,28.91239,1,10,1,8.086253,6.134771,0,0,0,14.22102,0,0,0,0,0,6,82.1,0,0,,283,283,0,0,1.791759,5.645447,1,0,0,1,0,0,63.48573,9.163564,1.791759,2.654721,1 3,1,100,0,3,127364,0,9542.002,29.91239,1,10,1,0,0,0,0,0,0,0,0,0,0,0,6,82.1,0,0,,283,283,0,0,1.791759,5.645447,1,0,0,1,0,0,63.48573,9.163564,1.791759,,0 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6,1,25,1,3,127380,0,3809.553,26.06297,1,7,1,0,0,0,0,0,0,0,0,0,0,0,4,84.2,4.3,0,,700,700,0,0,1.386294,6.55108,0,3.258096,7.937375,0,0,0,75.53199,8.24553,1.386294,,0 6,1,25,1,1,127381,0,3809.553,9.500342,1,7,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,700,700,1,1,1.386294,6.55108,0,3.258096,7.937375,0,0,0,81.64835,8.24553,1.386294,,0 6,1,25,1,2,127381,0,3809.553,10.50034,1,7,1,16.98421,6.303756,0,0,0,23.28797,0,0,0,1,0,4,74.36826,13.73189,0,,700,700,1,1,1.386294,6.55108,0,3.258096,7.937375,0,0,0,81.64835,8.24553,1.386294,3.147937,1 6,1,25,1,3,127381,0,3809.553,11.50034,1,7,1,19.32607,0,0,0,0,19.32607,0,0,0,1,0,4,74.36826,13.73189,0,,700,700,1,1,1.386294,6.55108,0,3.258096,7.937375,0,0,0,81.64835,8.24553,1.386294,2.961455,1 11,1,0,1,1,127385,0,9658.188,13.39357,1,12,1,16.35931,0,0,0,0,16.35931,0,0,0,1,0,5,74.36826,13.73189,0,,0,0,1,1,1.609438,0,0,0,0,0,0,0,83.986,9.175665,1.609438,2.794797,1 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6,1,25,1,3,127470,0,9668.734,42.4846,0,13,1,17.45636,7.256858,32.83292,0,0,57.54613,0,0,0,2,1,5,58.9,13,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,70.47347,9.176756,1.609438,4.052587,1 6,1,25,1,4,127470,0,9668.734,43.4846,0,13,1,6.915629,3.457815,0,0,0,10.37344,0,0,0,1,0,5,58.9,13,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,70.47347,9.176756,1.609438,2.339249,1 6,1,25,1,5,127470,0,9668.734,44.4846,0,13,1,25.81464,0,24.32501,0,0,50.13965,0,0,0,1,1,5,58.9,13,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,70.47347,9.176756,1.609438,3.914812,1 6,1,25,1,1,127471,0,9668.734,7.422314,0,13,1,0,13.09352,0,0,0,13.09352,0,0,0,0,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,78.55493,9.176756,1.609438,2.572118,1 6,1,25,1,2,127471,0,9668.734,8.422314,0,13,1,9.309967,0,0,0,0,9.309967,0,0,0,0,1,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,78.55493,9.176756,1.609438,2.231086,1 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6,1,25,1,2,127472,0,9668.734,13.29295,0,13,1,19.71523,6.818182,17.16867,0,0,43.70208,0,0,0,2,1,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,78.55493,9.176756,1.609438,3.777396,1 6,1,25,1,3,127472,0,9668.734,14.29295,0,13,1,34.41396,2.119701,28.84289,14.96259,0,65.37656,0,0,1,3,1,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,78.55493,9.176756,1.609438,4.180164,1 6,1,25,1,4,127472,0,9668.734,15.29295,0,13,1,25.35731,2.581835,0,0,0,27.93914,0,0,0,2,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,78.55493,9.176756,1.609438,3.330029,1 6,1,25,1,5,127472,0,9668.734,16.29295,0,13,1,14.81168,0,23.7537,0,0,38.56538,0,0,0,1,1,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,78.55493,9.176756,1.609438,3.652355,1 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6,1,25,1,5,127473,0,9668.734,42.16564,1,13,1,42.31908,10.77021,25.6496,0,0,78.73889,0,0,0,4,1,5,58.9,26.1,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,0,1,0,56.59937,9.176756,1.609438,4.366137,1 6,1,25,1,1,127474,0,9668.734,14.28884,1,13,1,107.9137,82.73381,0,0,0,190.6475,0,0,0,34,0,5,74.7,4.3,0,,1000,1000,1,1,1.609438,6.907755,0,3.258096,8.294049,1,0,0,68.77795,9.176756,1.609438,5.250426,1 6,1,25,1,2,127474,0,9668.734,15.28884,1,13,1,75.02738,95.0712,0,0,0,170.0986,0,0,0,24,1,5,74.7,4.3,0,,1000,1000,1,1,1.609438,6.907755,0,3.258096,8.294049,1,0,0,68.77795,9.176756,1.609438,5.136378,1 6,1,25,1,3,127474,0,9668.734,16.28884,1,13,1,182.2943,45.40648,0,0,0,227.7007,0,0,0,28,1,5,74.7,4.3,0,,1000,1000,1,1,1.609438,6.907755,0,3.258096,8.294049,1,0,0,68.77795,9.176756,1.609438,5.428032,1 6,1,25,1,4,127474,0,9668.734,17.28884,1,13,1,108.1143,4.495159,24.09405,0,0,136.7036,0,0,0,22,1,5,74.7,4.3,0,,1000,1000,1,1,1.609438,6.907755,0,3.258096,8.294049,1,0,0,68.77795,9.176756,1.609438,4.917815,1 6,1,25,1,5,127474,0,9668.734,18.28884,1,13,1,94.79475,6.749894,0,0,535.1968,636.7415,1,0,0,24,0,5,74.7,4.3,0,,1000,1000,0,0,1.609438,6.907755,0,3.258096,8.294049,1,0,0,68.77795,9.176756,1.609438,6.456364,1 1,1,0,0,1,127486,0,10792.37,5.193703,1,12,1,7.733492,0,0,0,0,7.733492,0,0,0,1,0,5,74.36826,13.73189,0,,450,450,1,1,1.609438,6.109248,1,0,0,0,0,0,81.95454,9.286687,1.609438,2.045561,1 1,1,0,0,2,127486,0,10792.37,6.193703,1,12,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,450,450,1,1,1.609438,6.109248,1,0,0,0,0,0,81.95454,9.286687,1.609438,,0 1,1,0,0,3,127486,0,10792.37,7.193703,1,12,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,450,450,1,1,1.609438,6.109248,1,0,0,0,0,0,81.95454,9.286687,1.609438,,0 1,1,0,0,1,127487,0,10792.37,18.14374,0,12.32507,1,45.21119,0,0,0,0,45.21119,0,0,0,2,0,5,81.3,13.73189,0,,450,450,0,0,1.609438,6.109248,1,0,0,0,0,0,79.01041,9.286687,1.609438,3.811345,1 1,1,0,0,2,127487,0,10792.37,19.14374,0,12.32507,1,37.56124,0,0,0,0,37.56124,0,0,0,1,0,5,81.3,13.73189,0,,450,450,0,0,1.609438,6.109248,1,0,0,0,0,0,79.01041,9.286687,1.609438,3.625973,1 1,1,0,0,3,127487,0,10792.37,20.14374,0,12.32507,1,0,0,0,0,0,0,0,0,0,0,0,5,81.3,13.73189,0,,450,450,0,0,1.609438,6.109248,1,0,0,0,0,0,79.01041,9.286687,1.609438,,0 1,1,0,0,1,127488,0,10792.37,50.19849,1,12,1,33.3135,88.65556,2.379536,0,0,124.3486,0,0,0,2,0,5,55,13.73189,0,,450,450,0,0,1.609438,6.109248,1,0,0,0,0,0,77.65372,9.286687,1.609438,4.823089,1 1,1,0,0,2,127488,0,10792.37,51.19849,1,12,1,42.46053,63.02667,20.14153,0,0,125.6287,0,0,0,2,1,5,55,13.73189,0,,450,450,0,0,1.609438,6.109248,1,0,0,0,0,0,77.65372,9.286687,1.609438,4.833331,1 1,1,0,0,3,127488,0,10792.37,52.19849,1,12,1,20.81269,38.45887,0,0,0,59.27156,0,0,0,2,0,5,55,13.73189,0,,450,450,0,0,1.609438,6.109248,1,0,0,0,0,0,77.65372,9.286687,1.609438,4.082129,1 1,1,0,0,1,127489,0,10792.37,24.3039,1,12,1,48.1856,20.65437,0,0,0,68.83997,0,0,0,3,0,5,66.3,13.73189,0,,450,450,0,0,1.609438,6.109248,1,0,0,0,0,0,79.64108,9.286687,1.609438,4.231785,1 1,1,0,0,2,127489,0,10792.37,25.3039,1,12,1,0,0,0,0,0,0,0,0,0,0,0,5,66.3,13.73189,0,,450,450,0,0,1.609438,6.109248,1,0,0,0,0,0,79.64108,9.286687,1.609438,,0 1,1,0,0,3,127489,0,10792.37,26.3039,1,12,1,0,0,0,0,0,0,0,0,0,0,0,5,66.3,13.73189,0,,450,450,0,0,1.609438,6.109248,1,0,0,0,0,0,79.64108,9.286687,1.609438,,0 1,1,0,0,1,127490,0,10792.37,49.90281,0,10,1,0,0,0,0,0,0,0,0,0,0,0,5,68.8,13.73189,0,,450,450,0,0,1.609438,6.109248,1,0,0,0,0,0,73.81825,9.286687,1.609438,,0 1,1,0,0,2,127490,0,10792.37,50.90281,0,10,1,8.709853,0,20.14153,0,0,28.85139,0,0,0,0,1,5,68.8,13.73189,0,,450,450,0,0,1.609438,6.109248,1,0,0,0,0,0,73.81825,9.286687,1.609438,3.362158,1 1,1,0,0,3,127490,0,10792.37,51.90281,0,10,1,120.664,34.2666,0,0,0,154.9306,0,0,0,8,6,5,68.8,13.73189,0,,450,450,0,0,1.609438,6.109248,1,0,0,0,0,0,73.81825,9.286687,1.609438,5.042977,1 2,1,100,0,1,127496,0,4168.734,57.92471,0,12,1,0,2.255595,0,0,0,2.255595,0,0,0,0,0,1,74.7,17.4,0,,170,170,0,0,0,5.135798,1,0,0,0,1,0,65.84276,8.335608,0,.8134137,1 2,1,100,0,2,127496,0,4168.734,58.92471,0,12,1,57.68194,7.563342,0,0,0,65.24529,0,0,0,3,0,1,74.7,17.4,0,,170,170,0,0,0,5.135798,1,0,0,0,1,0,65.84276,8.335608,0,4.178154,1 2,1,100,0,3,127496,0,4168.734,59.92471,0,12,1,22.85012,32.3489,0,0,0,55.19902,0,0,0,2,0,1,74.7,17.4,0,,170,170,0,0,0,5.135798,1,0,0,0,1,0,65.84276,8.335608,0,4.010945,1 2,1,100,0,4,127496,0,4168.734,60.92471,0,12,1,0,22.1103,0,0,0,22.1103,0,0,0,0,0,1,74.7,17.4,0,,170,170,0,0,0,5.135798,1,0,0,0,1,0,65.84276,8.335608,0,3.096044,1 2,1,100,0,5,127496,0,4168.734,61.92471,0,12,1,93.58066,67.77824,27.44477,0,1607.753,1796.557,2,0,0,4,6,1,74.7,17.4,0,,170,170,0,0,0,5.135798,1,0,0,0,1,0,65.84276,8.335608,0,7.493627,1 5,1,25,1,1,127511,0,1191.067,53.73032,1,3,1,9.592326,0,34.77218,0,0,44.36451,0,0,0,0,1,1,71.6,30.4,1,,0,0,0,0,0,0,0,3.258096,0,0,1,0,52.28558,7.083444,0,3.79244,1 5,1,25,1,2,127511,0,1191.067,54.73032,1,3,1,0,0,0,0,0,0,0,0,0,0,0,1,71.6,30.4,1,,0,0,0,0,0,0,0,3.258096,0,0,1,0,52.28558,7.083444,0,,0 5,1,25,1,3,127511,0,1191.067,55.73032,1,3,1,0,0,0,0,0,0,0,0,0,0,0,1,71.6,30.4,1,,0,0,0,0,0,0,0,3.258096,0,0,1,0,52.28558,7.083444,0,,0 1,1,0,0,1,127513,0,7029.777,3.879534,1,9,1,0,14.46643,0,0,0,14.46643,0,0,0,0,0,4,74.36826,13.73189,0,,450,0,1,1,1.386294,0,1,0,0,0,1,0,57.77286,8.858052,1.386294,2.671831,1 1,1,0,0,2,127513,0,7029.777,4.879535,1,9,1,11.50055,8.209201,0,0,0,19.70975,0,0,0,2,0,4,74.36826,13.73189,0,,450,0,1,1,1.386294,0,1,0,0,0,1,0,57.77286,8.858052,1.386294,2.981113,1 1,1,0,0,3,127513,0,7029.777,5.879535,1,9,1,76.30923,11.42145,0,0,0,87.73067,0,0,0,4,0,4,74.36826,13.73189,0,,450,0,1,1,1.386294,0,1,0,0,0,1,0,57.77286,8.858052,1.386294,4.474272,1 1,1,0,0,4,127513,0,7029.777,6.879535,1,9,1,27.20148,20.72845,0,0,0,47.92992,0,0,0,4,0,4,74.36826,13.73189,0,,450,0,1,1,1.386294,0,1,0,0,0,1,0,57.77286,8.858052,1.386294,3.86974,1 1,1,0,0,5,127513,0,7029.777,7.879535,1,9,1,83.03004,9.983072,0,0,0,93.01312,0,0,0,5,0,4,74.36826,13.73189,0,,450,0,1,1,1.386294,0,1,0,0,0,1,0,57.77286,8.858052,1.386294,4.532741,1 1,1,0,0,1,127514,0,7029.777,27.0527,0,10,1,25.17986,27.96763,0,0,0,53.14748,0,0,0,0,2,4,73.8,13.73189,1,,450,0,0,0,1.386294,0,1,0,0,1,0,0,64.24998,8.858052,1.386294,3.973071,1 1,1,0,0,2,127514,0,7029.777,28.0527,0,10,1,0,0,0,0,0,0,0,0,0,0,0,4,73.8,13.73189,1,,450,0,0,0,1.386294,0,1,0,0,1,0,0,64.24998,8.858052,1.386294,,0 1,1,0,0,3,127514,0,7029.777,29.0527,0,10,1,4.488778,6.284289,0,0,0,10.77307,0,0,0,1,0,4,73.8,13.73189,1,,450,0,0,0,1.386294,0,1,0,0,1,0,0,64.24998,8.858052,1.386294,2.377049,1 1,1,0,0,4,127514,0,7029.777,30.0527,0,10,1,4.61042,4.633471,0,0,0,9.243891,0,0,0,1,0,4,73.8,13.73189,1,,450,0,0,0,1.386294,0,1,0,0,1,0,0,64.24998,8.858052,1.386294,2.223963,1 1,1,0,0,5,127514,0,7029.777,31.0527,0,10,1,5.924672,2.598392,0,0,0,8.523064,0,0,0,1,0,4,73.8,13.73189,1,,450,0,0,0,1.386294,0,1,0,0,1,0,0,64.24998,8.858052,1.386294,2.142776,1 1,1,0,0,1,127515,0,7029.777,2.767967,1,9,1,4.196643,10.71343,0,0,0,14.91007,0,0,0,1,0,4,74.36826,13.73189,0,,450,0,1,1,1.386294,0,1,0,0,1,0,0,69.64755,8.858052,1.386294,2.702037,1 1,1,0,0,2,127515,0,7029.777,3.767967,1,9,1,4.381161,8.187295,0,0,0,12.56846,0,0,0,1,0,4,74.36826,13.73189,0,,450,0,1,1,1.386294,0,1,0,0,1,0,0,69.64755,8.858052,1.386294,2.53119,1 1,1,0,0,3,127515,0,7029.777,4.767967,1,9,1,16.45885,9.002494,0,0,0,25.46135,0,0,0,3,0,4,74.36826,13.73189,0,,450,0,1,1,1.386294,0,1,0,0,1,0,0,69.64755,8.858052,1.386294,3.237162,1 1,1,0,0,4,127515,0,7029.777,5.767967,1,9,1,0,6.219456,0,0,0,6.219456,0,0,0,0,0,4,74.36826,13.73189,0,,450,0,1,1,1.386294,0,1,0,0,1,0,0,69.64755,8.858052,1.386294,1.827682,1 1,1,0,0,5,127515,0,7029.777,6.767967,1,9,1,19.04359,14.78206,0,0,0,33.82565,0,0,0,3,0,4,74.36826,13.73189,0,,450,0,1,1,1.386294,0,1,0,0,1,0,0,69.64755,8.858052,1.386294,3.521219,1 1,1,0,0,1,127516,0,7029.777,25.68652,1,9,1,16.18705,13.26739,0,0,0,29.45444,0,0,0,2,1,4,68.8,13.73189,0,,450,0,0,0,1.386294,0,1,0,0,1,0,0,65.15411,8.858052,1.386294,3.382845,1 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11,1,0,1,3,127598,0,10902.61,33.96441,0,12,1,175.3865,88.24937,34.399,0,0,298.0349,0,0,0,11,1,5,82.1,17.4,0,,0,291,0,0,1.609438,5.673323,0,0,0,0,0,1,53.44062,9.296849,1.609438,5.697211,1 11,1,0,1,1,127599,0,10902.61,10.11088,1,9,1,34.17266,0,0,0,0,34.17266,0,0,0,3,1,5,74.36826,13.73189,0,,0,291,1,1,1.609438,5.673323,0,0,0,1,0,0,75.8055,9.296849,1.609438,3.531426,1 11,1,0,1,2,127599,0,10902.61,11.11088,1,9,1,49.28806,6.440307,30.33406,0,0,86.06243,0,0,0,6,1,5,74.36826,13.73189,0,,0,291,1,1,1.609438,5.673323,0,0,0,1,0,0,75.8055,9.296849,1.609438,4.455073,1 11,1,0,1,3,127599,0,10902.61,12.11088,1,9,1,17.45636,4.82793,31.79551,0,0,54.0798,0,0,0,2,1,5,74.36826,13.73189,0,,0,291,1,1,1.609438,5.673323,0,0,0,1,0,0,75.8055,9.296849,1.609438,3.990461,1 6,1,25,1,1,127600,0,7676.799,21.86995,1,15,1,23.98082,6.294964,31.95444,0,0,62.23022,0,0,0,2,0,4,84.2,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.52619,8.946088,1.386294,4.130841,1 6,1,25,1,2,127600,0,7676.799,22.86995,1,15,1,38.8828,13.36254,0,0,0,52.24535,0,0,0,4,0,4,84.2,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.52619,8.946088,1.386294,3.955951,1 6,1,25,1,3,127600,0,7676.799,23.86995,1,15,1,23.4414,2.319202,38.04988,0,0,63.81047,0,0,0,2,0,4,84.2,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.52619,8.946088,1.386294,4.155917,1 6,1,25,1,1,127601,0,7676.799,17.16906,1,12,1,13.18945,11.1211,0,0,0,24.31055,0,0,0,2,0,4,78.9,0,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,74.88385,8.946088,1.386294,3.19091,1 6,1,25,1,2,127601,0,7676.799,18.16906,1,12,1,33.954,0,31.47864,0,0,65.43264,0,0,0,3,0,4,78.9,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,74.88385,8.946088,1.386294,4.181021,1 6,1,25,1,3,127601,0,7676.799,19.16906,1,12,1,50.87282,7.082294,0,0,0,57.95511,0,0,0,4,0,4,78.9,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,74.88385,8.946088,1.386294,4.059669,1 6,1,25,1,1,127602,0,7676.799,53.17728,0,12,1,19.78417,49.43045,0,0,0,69.21463,0,0,0,2,0,4,85.3,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,63.87726,8.946088,1.386294,4.237212,1 6,1,25,1,2,127602,0,7676.799,54.17728,0,12,1,57.41512,31.06791,33.19277,0,0,121.6758,0,0,0,5,0,4,85.3,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,63.87726,8.946088,1.386294,4.80136,1 6,1,25,1,3,127602,0,7676.799,55.17728,0,12,1,75.5611,48.17955,0,0,0,123.7406,0,0,0,5,0,4,85.3,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,63.87726,8.946088,1.386294,4.818188,1 6,1,25,1,1,127603,0,7676.799,53.577,1,12,1,68.95084,51.25899,230.8154,0,1179.568,1530.594,1,0,0,2,0,4,71.6,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,65.51687,8.946088,1.386294,7.333411,1 6,1,25,1,2,127603,0,7676.799,54.577,1,12,1,62.43155,65.4436,42.91895,0,0,170.7941,0,0,0,5,0,4,71.6,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,65.51687,8.946088,1.386294,5.140459,1 6,1,25,1,3,127603,0,7676.799,55.577,1,12,1,22.44389,51.94514,0,0,0,74.38903,0,0,0,2,0,4,71.6,21.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,1,0,0,65.51687,8.946088,1.386294,4.309309,1 4,1,100,1,1,127611,0,11610.42,11.06639,0,13,1,113.6631,22.9682,0,0,0,136.6313,0,0,0,10,1,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,1,0,0,79.12157,9.359744,1.609438,4.917286,1 4,1,100,1,2,127611,0,11610.42,12.06639,0,13,1,8.086253,0,0,0,0,8.086253,0,0,0,1,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,1,0,0,79.12157,9.359744,1.609438,2.090165,1 4,1,100,1,3,127611,0,11610.42,13.06639,0,13,1,123.8329,13.2973,0,71.04177,1380.973,1518.103,1,0,13,13,8,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,1,0,0,79.12157,9.359744,1.609438,7.325217,1 4,1,100,1,1,127612,0,11610.42,8.689939,0,13,1,50.05889,63.03298,0,0,887.8975,1000.989,1,0,0,5,0,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,1,0,0,74.88016,9.359744,1.609438,6.908744,1 4,1,100,1,2,127612,0,11610.42,9.689939,0,13,1,105.4771,32.70081,0,182.2102,0,138.1779,0,0,21,7,1,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,1,0,0,74.88016,9.359744,1.609438,4.928542,1 4,1,100,1,3,127612,0,11610.42,10.68994,0,13,1,55.03685,17.09091,0,194.5209,0,72.12776,0,0,21,4,1,5,74.36826,13.73189,0,,1000,1000,1,0,1.609438,6.907755,1,0,0,1,0,0,74.88016,9.359744,1.609438,4.278439,1 4,1,100,1,1,127613,0,11610.42,34.77618,0,12,1,106.0071,48.20966,0,0,204.9764,359.1932,1,0,0,8,1,5,53.7,17.4,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,64.79161,9.359744,1.609438,5.88386,1 4,1,100,1,2,127613,0,11610.42,35.77618,0,12,1,30.18868,22.73854,0,75.47169,0,52.92722,0,0,4,3,0,5,53.7,17.4,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,64.79161,9.359744,1.609438,3.968918,1 4,1,100,1,3,127613,0,11610.42,36.77618,0,12,1,74.69287,10.05405,0,171.9902,0,84.74693,0,0,7,5,1,5,53.7,17.4,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,64.79161,9.359744,1.609438,4.43967,1 4,1,100,1,1,127614,0,11610.42,35.45517,1,13,1,148.4099,50.30035,0,0,0,198.7103,0,0,0,15,0,5,38.9,21.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,67.10754,9.359744,1.609438,5.291848,1 4,1,100,1,2,127614,0,11610.42,36.45517,1,13,1,67.16982,43.47709,0,16.17251,0,110.6469,0,0,1,4,0,5,38.9,21.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,67.10754,9.359744,1.609438,4.706344,1 4,1,100,1,3,127614,0,11610.42,37.45517,1,13,1,187.715,87.88698,0,243.0319,0,275.602,0,0,24,9,4,5,38.9,21.7,0,,1000,1000,0,0,1.609438,6.907755,1,0,0,1,0,0,67.10754,9.359744,1.609438,5.618958,1 4,1,100,1,1,127615,0,11610.42,12.72005,1,13,1,130.7421,41.56655,30.62426,0,0,202.9329,0,0,0,22,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,1,0,0,78.60759,9.359744,1.609438,5.312875,1 4,1,100,1,2,127615,0,11610.42,13.72005,1,13,1,140.1617,31.34232,0,0,0,171.504,0,0,0,23,0,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,1,0,0,78.60759,9.359744,1.609438,5.144607,1 4,1,100,1,3,127615,0,11610.42,14.72005,1,13,1,110.5651,15.47912,26.04423,74.72236,0,152.0885,0,0,13,13,7,5,74.36826,13.73189,0,,1000,1000,1,1,1.609438,6.907755,1,0,0,1,0,0,78.60759,9.359744,1.609438,5.024462,1 2,1,100,0,1,127628,0,8910.67,15.91786,0,12,1,0,4.640095,14.30101,0,0,18.94111,0,0,0,0,0,6,76.3,13.73189,0,,624,624,1,0,1.791759,6.436151,1,0,0,0,0,0,80.20427,9.095117,1.791759,2.941334,1 2,1,100,0,2,127628,0,8910.67,16.91786,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,76.3,13.73189,0,,624,624,1,0,1.791759,6.436151,1,0,0,0,0,0,80.20427,9.095117,1.791759,,0 2,1,100,0,3,127628,0,8910.67,17.91786,0,12,1,12.3885,0,0,0,0,12.3885,0,0,0,1,0,6,76.3,13.73189,0,,624,624,1,0,1.791759,6.436151,1,0,0,0,0,0,80.20427,9.095117,1.791759,2.516769,1 2,1,100,0,4,127628,0,8910.67,18.91786,0,12,1,3.212483,2.349702,0,0,0,5.562184,0,0,0,1,0,6,76.3,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,0,0,0,80.20427,9.095117,1.791759,1.715991,1 2,1,100,0,5,127628,0,8910.67,19.91786,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,76.3,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,0,0,0,80.20427,9.095117,1.791759,,0 2,1,100,0,1,127629,0,8910.67,17.71389,0,12,1,19.54194,0,0,0,0,19.54194,0,0,0,0,0,6,92.5,13.73189,0,,624,624,1,0,1.791759,6.436151,1,0,0,0,0,0,80.20427,9.095117,1.791759,2.972563,1 2,1,100,0,2,127629,0,8910.67,18.71389,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,92.5,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,0,0,0,80.20427,9.095117,1.791759,,0 2,1,100,0,3,127629,0,8910.67,19.71389,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,92.5,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,0,0,0,80.20427,9.095117,1.791759,,0 2,1,100,0,4,127629,0,8910.67,20.71389,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,92.5,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,0,0,0,80.20427,9.095117,1.791759,,0 2,1,100,0,5,127629,0,8910.67,21.71389,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,92.5,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,0,0,0,80.20427,9.095117,1.791759,,0 2,1,100,0,1,127630,0,8910.67,47.63039,0,12,1,10.70791,0,43.27781,0,0,53.98572,0,0,0,0,1,6,90,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,1,0,0,66.07664,9.095117,1.791759,3.98872,1 2,1,100,0,2,127630,0,8910.67,48.63039,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,90,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,1,0,0,66.07664,9.095117,1.791759,,0 2,1,100,0,3,127630,0,8910.67,49.63039,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,90,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,1,0,0,66.07664,9.095117,1.791759,,0 2,1,100,0,4,127630,0,8910.67,50.63039,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,90,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,1,0,0,66.07664,9.095117,1.791759,,0 2,1,100,0,5,127630,0,8910.67,51.63039,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,90,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,1,0,0,66.07664,9.095117,1.791759,,0 2,1,100,0,1,127631,0,8910.67,9.270363,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,624,624,1,0,1.791759,6.436151,1,0,0,0,0,0,84.45741,9.095117,1.791759,,0 2,1,100,0,2,127631,0,8910.67,10.27036,0,12,1,26.12956,4.082744,0,0,0,30.2123,0,0,0,1,1,6,74.36826,13.73189,0,,624,624,1,0,1.791759,6.436151,1,0,0,0,0,0,84.45741,9.095117,1.791759,3.408249,1 2,1,100,0,3,127631,0,8910.67,11.27036,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,624,624,1,0,1.791759,6.436151,1,0,0,0,0,0,84.45741,9.095117,1.791759,,0 2,1,100,0,4,127631,0,8910.67,12.27036,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,624,624,1,0,1.791759,6.436151,1,0,0,0,0,0,84.45741,9.095117,1.791759,,0 2,1,100,0,5,127631,0,8910.67,13.27036,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,624,624,1,0,1.791759,6.436151,1,0,0,0,0,0,84.45741,9.095117,1.791759,,0 2,1,100,0,1,127632,0,8910.67,47.85216,1,12,1,19.63117,0,39.78584,0,0,59.41702,0,0,0,1,1,6,82.5,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,1,0,0,70.76368,9.095117,1.791759,4.08458,1 2,1,100,0,2,127632,0,8910.67,48.85216,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,82.5,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,1,0,0,70.76368,9.095117,1.791759,,0 2,1,100,0,3,127632,0,8910.67,49.85216,1,12,1,29.23687,11.11497,33.45391,0,0,73.80575,0,0,0,2,1,6,82.5,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,1,0,0,70.76368,9.095117,1.791759,4.301436,1 2,1,100,0,4,127632,0,8910.67,50.85216,1,12,1,0,11.7531,0,0,0,11.7531,0,0,0,0,0,6,82.5,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,1,0,0,70.76368,9.095117,1.791759,2.464117,1 2,1,100,0,5,127632,0,8910.67,51.85216,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,82.5,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,1,0,0,70.76368,9.095117,1.791759,,0 2,1,100,0,1,127633,0,8910.67,14.77071,1,12,1,41.19572,2.40928,0,0,0,43.605,0,0,0,1,1,6,85,13.73189,0,,624,624,1,1,1.791759,6.436151,1,0,0,0,0,0,74.86757,9.095117,1.791759,3.775172,1 2,1,100,0,2,127633,0,8910.67,15.77071,1,12,1,13.06478,4.082744,26.12956,0,0,43.27708,0,0,0,0,1,6,85,13.73189,0,,624,624,1,1,1.791759,6.436151,1,0,0,0,0,0,74.86757,9.095117,1.791759,3.767623,1 2,1,100,0,3,127633,0,8910.67,16.7707,1,12,1,3.468781,0,0,0,0,3.468781,0,0,0,1,0,6,85,13.73189,0,,624,624,1,1,1.791759,6.436151,1,0,0,0,0,0,74.86757,9.095117,1.791759,1.243803,1 2,1,100,0,4,127633,0,8910.67,17.7707,1,12,1,22.48738,0,0,0,0,22.48738,0,0,0,3,0,6,85,13.73189,0,,624,624,1,1,1.791759,6.436151,1,0,0,0,0,0,74.86757,9.095117,1.791759,3.112954,1 2,1,100,0,5,127633,0,8910.67,18.7707,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,85,13.73189,0,,624,624,0,0,1.791759,6.436151,1,0,0,0,0,0,74.86757,9.095117,1.791759,,0 4,1,100,1,1,127637,0,2199.752,48.90623,1,13,1,21.10977,0,43.80579,0,0,64.91556,0,0,0,2,0,1,61.1,21.7,0,,403,403,0,0,0,5.998937,1,0,0,1,0,0,69.50401,7.696554,0,4.173087,1 4,1,100,1,2,127637,0,2199.752,49.90623,1,13,1,0,0,0,0,0,0,0,0,0,0,0,1,61.1,21.7,0,,403,403,0,0,0,5.998937,1,0,0,1,0,0,69.50401,7.696554,0,,0 4,1,100,1,3,127637,0,2199.752,50.90623,1,13,1,0,0,0,0,0,0,0,0,0,0,0,1,61.1,21.7,0,,403,403,0,0,0,5.998937,1,0,0,1,0,0,69.50401,7.696554,0,,0 4,1,100,1,4,127637,0,2199.752,51.90623,1,13,1,23.18034,0,25.656,0,0,48.83635,0,0,0,3,0,1,61.1,21.7,0,,403,403,0,0,0,5.998937,1,0,0,1,0,0,69.50401,7.696554,0,3.888475,1 4,1,100,1,5,127637,0,2199.752,52.90623,1,13,1,380.5827,0,55.08294,0,1714.241,2149.906,1,0,0,2,0,1,61.1,21.7,0,,403,403,0,0,0,5.998937,1,0,0,1,0,0,69.50401,7.696554,0,7.67318,1 11,1,0,1,1,127641,0,9150.124,.6872005,0,12,1,101.3189,18.94484,0,0,0,120.2638,0,0,0,6,1,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,74.24259,9.121632,1.386294,4.789688,1 11,1,0,1,2,127641,0,9150.124,1.687201,0,12,1,79.68237,23.05586,0,0,0,102.7382,0,0,0,6,1,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,74.24259,9.121632,1.386294,4.632185,1 11,1,0,1,3,127641,0,9150.124,2.687201,0,12,1,57.4813,22.81796,0,0,236.813,317.1122,1,0,0,6,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,74.24259,9.121632,1.386294,5.759256,1 11,1,0,1,4,127641,0,9150.124,3.687201,0,12,1,89.5574,10.23513,0,0,0,99.79253,0,0,0,8,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,74.24259,9.121632,1.386294,4.603093,1 11,1,0,1,5,127641,0,9150.124,4.687201,0,12,1,45.70461,15.88235,0,0,0,61.58697,0,0,0,6,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,74.24259,9.121632,1.386294,4.12045,1 11,1,0,1,1,127642,0,9150.124,25.93566,1,12,1,98.32134,53.5012,0,0,0,151.8225,0,0,0,7,0,4,42.1,21.7,1,,0,0,0,0,1.386294,0,0,0,0,1,0,0,67.19587,9.121632,1.386294,5.022712,1 11,1,0,1,2,127642,0,9150.124,26.93566,1,12,1,63.52684,23.7678,0,0,0,87.29463,0,0,0,7,0,4,42.1,21.7,1,,0,0,0,0,1.386294,0,0,0,0,1,0,0,67.19587,9.121632,1.386294,4.469289,1 11,1,0,1,3,127642,0,9150.124,27.93566,1,12,1,44.88778,30.44888,0,0,0,75.33665,0,0,0,6,0,4,42.1,21.7,1,,0,0,0,0,1.386294,0,0,0,0,1,0,0,67.19587,9.121632,1.386294,4.321967,1 11,1,0,1,4,127642,0,9150.124,28.93566,1,12,1,117.1047,57.42278,0,0,0,174.5274,0,0,0,9,0,4,42.1,21.7,1,,0,0,0,0,1.386294,0,0,0,0,1,0,0,67.19587,9.121632,1.386294,5.162082,1 11,1,0,1,5,127642,0,9150.124,29.93566,1,12,1,118.2818,46.21244,0,0,724.4604,888.9547,1,0,0,6,0,4,42.1,21.7,1,,0,0,0,0,1.386294,0,0,0,0,1,0,0,67.19587,9.121632,1.386294,6.790046,1 11,1,0,1,1,127643,0,9150.124,4.982888,0,12,1,34.77218,1.199041,0,0,0,35.97122,0,0,0,3,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,74.24259,9.121632,1.386294,3.582719,1 11,1,0,1,2,127643,0,9150.124,5.982888,0,12,1,83.7897,1.09529,0,0,0,84.88499,0,0,0,5,1,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,74.24259,9.121632,1.386294,4.441298,1 11,1,0,1,3,127643,0,9150.124,6.982888,0,12,1,67.98504,0,0,0,0,67.98504,0,0,0,4,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,74.24259,9.121632,1.386294,4.219288,1 11,1,0,1,4,127643,0,9150.124,7.982888,0,12,1,26.74043,7.076994,0,0,0,33.81743,0,0,0,3,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,74.24259,9.121632,1.386294,3.520976,1 11,1,0,1,5,127643,0,9150.124,8.982888,0,12,1,10.57977,0,0,0,0,10.57977,0,0,0,1,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,74.24259,9.121632,1.386294,2.358944,1 11,1,0,1,1,127644,0,9150.124,26.34908,0,14,1,57.40408,6.792566,0,0,299.7602,363.9568,1,1,0,1,0,4,70.5,8.7,0,,0,0,0,0,1.386294,0,0,0,0,1,0,0,71.81533,9.121632,1.386294,5.897035,1 11,1,0,1,2,127644,0,9150.124,27.34908,0,14,1,107.667,2.88609,20.60241,0,0,131.1555,0,0,0,6,2,4,70.5,8.7,0,,0,0,0,0,1.386294,0,0,0,0,1,0,0,71.81533,9.121632,1.386294,4.876384,1 11,1,0,1,3,127644,0,9150.124,28.34908,0,14,1,0,4.927681,0,0,0,4.927681,0,0,0,0,0,4,70.5,8.7,0,,0,0,0,0,1.386294,0,0,0,0,1,0,0,71.81533,9.121632,1.386294,1.594869,1 11,1,0,1,4,127644,0,9150.124,29.34908,0,14,1,0,0,0,0,822.2914,822.2914,1,0,0,0,0,4,70.5,8.7,0,,0,0,0,0,1.386294,0,0,0,0,1,0,0,71.81533,9.121632,1.386294,6.712095,1 11,1,0,1,5,127644,0,9150.124,30.34908,0,14,1,11.00296,0,0,0,0,11.00296,0,0,0,1,0,4,70.5,8.7,0,,0,0,0,0,1.386294,0,0,0,0,1,0,0,71.81533,9.121632,1.386294,2.398165,1 6,1,25,0,1,127645,0,13521.71,39.54826,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,76.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,78.64024,9.512126,1.386294,,0 6,1,25,0,2,127645,0,13521.71,40.54826,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,76.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,78.64024,9.512126,1.386294,,0 6,1,25,0,3,127645,0,13521.71,41.54826,0,12,1,16.70762,0,0,0,0,16.70762,0,0,0,2,0,4,76.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,78.64024,9.512126,1.386294,2.815865,1 6,1,25,0,4,127645,0,13521.71,42.54826,0,12,1,30.08204,0,0,0,0,30.08204,0,0,0,1,0,3,76.3,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,78.64024,9.512126,1.098612,3.403929,1 6,1,25,0,5,127645,0,13521.71,43.54826,0,12,1,118.1117,3.980825,0,0,0,122.0925,0,0,0,3,0,3,76.3,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,78.64024,9.512126,1.098612,4.804779,1 6,1,25,0,1,127646,0,13521.71,36.74469,1,12,1,35.92462,15.04711,0,0,0,50.97173,0,0,0,4,0,4,78.8,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.53143,9.512126,1.386294,3.931271,1 6,1,25,0,2,127646,0,13521.71,37.74469,1,12,1,98.65229,17.70889,8.528302,0,1512.577,1637.466,1,0,0,6,0,4,78.8,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.53143,9.512126,1.386294,7.400906,1 6,1,25,0,3,127646,0,13521.71,38.74469,1,12,1,41.03194,0,0,0,0,41.03194,0,0,0,1,1,4,78.8,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.53143,9.512126,1.386294,3.714351,1 6,1,25,0,4,127646,0,13521.71,39.74469,1,12,1,164.0839,0,0,0,0,164.0839,0,0,0,5,0,3,78.8,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,79.53143,9.512126,1.098612,5.100378,1 6,1,25,0,5,127646,0,13521.71,40.74469,1,12,1,51.27136,1.538141,0,0,1592.955,1645.765,2,0,0,8,0,3,78.8,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,79.53143,9.512126,1.098612,7.405961,1 6,1,25,0,1,127647,0,13521.71,3.367557,0,12,1,34.15783,13.10365,0,0,0,47.26148,0,0,0,2,3,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.0187,9.512126,1.386294,3.855696,1 6,1,25,0,2,127647,0,13521.71,4.367557,0,12,1,57.14286,20.96496,0,0,0,78.10782,0,0,0,9,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.0187,9.512126,1.386294,4.35809,1 6,1,25,0,3,127647,0,13521.71,5.367557,0,12,1,75.18427,14.38329,0,0,0,89.56757,0,0,0,10,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.0187,9.512126,1.386294,4.494993,1 6,1,25,0,4,127647,0,13521.71,6.367557,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,1000,1000,1,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,82.0187,9.512126,1.098612,,0 6,1,25,0,5,127647,0,13521.71,7.367557,0,12,1,20.42518,0,0,0,0,20.42518,0,0,0,2,0,3,74.36826,13.73189,0,,1000,1000,1,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,82.0187,9.512126,1.098612,3.016768,1 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1,1,0,0,3,127956,0,2800.868,23.32238,1,13,1,0,0,0,0,0,0,0,0,0,0,0,1,67.5,13.73189,0,,300,300,0,0,0,5.703783,1,0,0,1,0,0,65.36804,7.938042,0,,0 11,1,0,1,1,127957,0,9542.002,4.867898,0,10,1,67.83274,5.647821,0,0,0,73.48057,0,0,0,4,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,70.7345,9.163564,1.386294,4.297021,1 11,1,0,1,2,127957,0,9542.002,5.867898,0,10,1,114.7439,24.42048,0,0,898.6685,1037.833,2,0,0,8,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,70.7345,9.163564,1.386294,6.94489,1 11,1,0,1,3,127957,0,9542.002,6.867898,0,10,1,35.87223,14.05405,0,0,0,49.92629,0,0,0,4,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,70.7345,9.163564,1.386294,3.910548,1 11,1,0,1,4,127957,0,9542.002,7.867898,0,10,1,37.16955,0,0,0,0,37.16955,0,0,0,1,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,1,0,0,70.7345,9.163564,1.386294,3.61549,1 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5,1,25,0,2,128077,0,12376.42,43.25051,1,17,1,178.6064,75.40011,0,0,0,254.0065,0,0,0,6,0,4,78.8,13.73189,1,,762,762,0,0,1.386294,6.635947,0,3.258096,8.022241,0,0,0,75.74407,9.423629,1.386294,5.53736,1 5,1,25,0,3,128077,0,12376.42,44.25051,1,17,1,69.87116,54.74232,0,0,0,124.6135,0,0,0,8,0,4,78.8,13.73189,1,,762,762,0,0,1.386294,6.635947,0,3.258096,8.022241,0,0,0,75.74407,9.423629,1.386294,4.825217,1 5,1,25,0,1,128078,0,12376.42,17.92197,0,17,1,88.10232,3.866746,32.69482,0,0,124.6639,0,0,0,3,1,4,82.5,13.73189,0,,762,762,1,0,1.386294,6.635947,0,3.258096,8.022241,0,0,0,77.74564,9.423629,1.386294,4.825621,1 5,1,25,0,2,128078,0,12376.42,18.92197,0,17,1,14.15351,3.756124,0,0,0,17.90964,0,0,0,2,0,4,82.5,13.73189,0,,762,762,0,0,1.386294,6.635947,0,3.258096,8.022241,0,0,0,77.74564,9.423629,1.386294,2.885339,1 5,1,25,0,3,128078,0,12376.42,19.92197,0,17,1,0,0,0,0,0,0,0,0,0,0,0,4,82.5,13.73189,0,,762,762,0,0,1.386294,6.635947,0,3.258096,8.022241,0,0,0,77.74564,9.423629,1.386294,,0 5,1,25,0,1,128079,0,12376.42,19.00616,0,12,1,41.047,0,33.28971,0,0,74.33671,0,0,0,3,1,4,35,13.73189,1,,762,762,0,0,1.386294,6.635947,0,3.258096,8.022241,0,0,0,75.48103,9.423629,1.386294,4.308605,1 5,1,25,0,2,128079,0,12376.42,20.00616,0,12,1,70.76756,8.633642,14.62167,0,0,94.02287,0,0,0,2,1,4,35,13.73189,1,,762,762,0,0,1.386294,6.635947,0,3.258096,8.022241,0,0,0,75.48103,9.423629,1.386294,4.543538,1 5,1,25,0,3,128079,0,12376.42,21.00616,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,35,13.73189,1,,762,762,0,0,1.386294,6.635947,0,3.258096,8.022241,0,0,0,75.48103,9.423629,1.386294,,0 11,1,0,0,1,128084,0,8041.563,4.835044,0,12,1,31.80212,5.57126,0,0,0,37.37338,0,0,0,3,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,0,0,0,78.92502,8.992503,1.386294,3.620959,1 11,1,0,0,2,128084,0,8041.563,5.835044,0,12,1,46.36119,11.26146,0,0,0,57.62264,0,0,0,5,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,0,0,0,78.92502,8.992503,1.386294,4.053916,1 11,1,0,0,3,128084,0,8041.563,6.835044,0,12,1,227.2727,82.0344,0,0,0,309.3071,0,0,0,23,2,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,0,0,0,78.92502,8.992503,1.386294,5.734335,1 11,1,0,0,1,128085,0,8041.563,1.716632,0,12,1,22.9682,7.043581,0,0,0,30.01178,0,0,0,4,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,0,0,0,78.92502,8.992503,1.386294,3.40159,1 11,1,0,0,2,128085,0,8041.563,2.716632,0,12,1,19.40701,0,0,0,0,19.40701,0,0,0,3,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,0,0,0,78.92502,8.992503,1.386294,2.965634,1 11,1,0,0,3,128085,0,8041.563,3.716632,0,12,1,19.16462,2.815725,0,0,0,21.98034,0,0,0,2,0,4,74.36826,13.73189,0,,0,0,1,0,1.386294,0,0,0,0,0,0,0,78.92502,8.992503,1.386294,3.090149,1 11,1,0,0,1,128086,0,8041.563,36.61602,0,9,1,88.33923,0,0,0,0,88.33923,0,0,0,1,0,4,78.8,13.73189,0,,0,0,0,0,1.386294,0,0,0,0,0,0,0,73.86172,8.992503,1.386294,4.481184,1 11,1,0,0,2,128086,0,8041.563,37.61602,0,9,1,53.36927,0,0,0,0,53.36927,0,0,0,1,0,4,78.8,13.73189,0,,0,0,0,0,1.386294,0,0,0,0,0,0,0,73.86172,8.992503,1.386294,3.977235,1 11,1,0,0,3,128086,0,8041.563,38.61602,0,9,1,20.63882,0,0,0,0,20.63882,0,0,0,2,1,4,78.8,13.73189,0,,0,0,0,0,1.386294,0,0,0,0,0,0,0,73.86172,8.992503,1.386294,3.027174,1 11,1,0,0,1,128087,0,8041.563,28.39699,1,12,1,146.7903,45.18846,0,0,0,191.9788,0,0,0,5,0,4,78.8,13.73189,0,,0,0,0,0,1.386294,0,0,0,0,0,0,0,77.90237,8.992503,1.386294,5.257385,1 11,1,0,0,2,128087,0,8041.563,29.39699,1,12,1,56.60378,7.202157,0,0,0,63.80593,0,0,0,1,0,4,78.8,13.73189,0,,0,0,0,0,1.386294,0,0,0,0,0,0,0,77.90237,8.992503,1.386294,4.155846,1 11,1,0,0,3,128087,0,8041.563,30.39699,1,12,1,62.89926,5.110565,0,0,0,68.00983,0,0,0,4,0,4,78.8,13.73189,0,,0,0,0,0,1.386294,0,0,0,0,0,0,0,77.90237,8.992503,1.386294,4.219652,1 11,1,0,0,1,128088,0,9542.002,27.37851,1,15,1,151.6786,141.9364,0,0,0,293.6151,0,0,0,11,0,3,28.8,13.73189,0,,0,258,0,0,1.098612,5.552959,0,0,0,1,0,0,73.3112,9.163564,1.098612,5.68227,1 11,1,0,0,2,128088,0,9542.002,28.37851,1,15,1,116.1008,116.5663,0,0,460.1259,692.793,1,0,0,3,0,3,28.8,13.73189,0,,0,258,0,0,1.098612,5.552959,0,0,0,1,0,0,73.3112,9.163564,1.098612,6.540731,1 11,1,0,0,3,128088,0,9542.002,29.37851,1,15,1,65.83541,142.0199,0,0,0,207.8554,0,0,0,6,0,3,28.8,13.73189,0,,0,258,0,0,1.098612,5.552959,0,0,0,1,0,0,73.3112,9.163564,1.098612,5.336843,1 11,1,0,0,4,128088,0,9542.002,30.37851,1,15,1,75.8414,85.0023,0,0,745.0945,905.9382,1,0,0,6,0,3,28.8,13.73189,0,,0,258,0,0,1.098612,5.552959,0,0,0,1,0,0,73.3112,9.163564,1.098612,6.808971,1 11,1,0,0,5,128088,0,9542.002,31.37851,1,15,1,410.8422,155.5438,24.41388,0,0,590.7998,0,0,0,2,1,4,28.8,13.73189,0,,0,258,0,0,1.386294,5.552959,0,0,0,1,0,0,73.3112,9.163564,1.386294,6.381477,1 11,1,0,0,1,128089,0,9542.002,3.017112,0,15,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,0,258,1,0,1.098612,5.552959,0,0,0,1,0,0,69.03037,9.163564,1.098612,,0 11,1,0,0,2,128089,0,9542.002,4.017112,0,15,1,9.857613,0,0,0,0,9.857613,0,0,0,1,0,3,74.36826,13.73189,0,,0,258,1,0,1.098612,5.552959,0,0,0,1,0,0,69.03037,9.163564,1.098612,2.288244,1 11,1,0,0,3,128089,0,9542.002,5.017112,0,15,1,136.2095,15.18703,.798005,0,0,152.1945,0,0,0,5,0,3,74.36826,13.73189,0,,0,258,1,0,1.098612,5.552959,0,0,0,1,0,0,69.03037,9.163564,1.098612,5.025159,1 11,1,0,0,4,128089,0,9542.002,6.017112,0,15,1,43.79898,18.55694,0,0,287.953,350.3089,1,0,0,6,0,3,74.36826,13.73189,0,,0,258,1,0,1.098612,5.552959,0,0,0,1,0,0,69.03037,9.163564,1.098612,5.858815,1 11,1,0,0,5,128089,0,9542.002,7.017112,0,15,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,0,258,1,0,1.386294,5.552959,0,0,0,1,0,0,69.03037,9.163564,1.386294,,0 11,1,0,0,1,128090,0,9542.002,5.481177,0,15,1,35.97122,11.90048,0,0,0,47.8717,0,0,0,1,0,3,74.36826,13.73189,0,,0,258,1,0,1.098612,5.552959,0,0,0,1,0,0,72.462,9.163564,1.098612,3.868525,1 11,1,0,0,2,128090,0,9542.002,6.481177,0,15,1,21.35816,14.23877,0,0,0,35.59693,0,0,0,1,1,3,74.36826,13.73189,0,,0,258,1,0,1.098612,5.552959,0,0,0,1,0,0,72.462,9.163564,1.098612,3.572259,1 11,1,0,0,3,128090,0,9542.002,7.481177,0,15,1,9.476309,40.52369,0,0,0,50,0,0,0,2,0,3,74.36826,13.73189,0,,0,258,1,0,1.098612,5.552959,0,0,0,1,0,0,72.462,9.163564,1.098612,3.912023,1 11,1,0,0,4,128090,0,9542.002,8.481177,0,15,1,261.2494,57.51498,7.607192,0,0,326.3716,0,0,0,11,0,3,74.36826,13.73189,0,,0,258,1,0,1.098612,5.552959,0,0,0,1,0,0,72.462,9.163564,1.098612,5.788037,1 11,1,0,0,5,128090,0,9542.002,9.481177,0,15,1,90.56284,34.84977,32.69996,410.4951,0,158.1126,0,0,26,5,1,4,74.36826,13.73189,0,,0,258,1,0,1.386294,5.552959,0,0,0,1,0,0,72.462,9.163564,1.386294,5.063307,1 4,1,100,0,1,128091,0,10933.62,27.28268,1,16,1,29.7442,10.61868,0,0,0,40.36288,0,0,0,4,0,1,70,13.73189,0,,1000,1000,0,0,0,6.907755,1,0,0,1,0,0,72.76367,9.299689,0,3.697911,1 4,1,100,0,2,128091,0,10933.62,28.28268,1,16,1,50.62602,11.66032,0,0,0,62.28633,0,0,0,2,1,1,70,13.73189,0,,1000,1000,0,0,0,6.907755,1,0,0,1,0,0,72.76367,9.299689,0,4.131742,1 4,1,100,0,3,128091,0,10933.62,29.28268,1,16,1,37.66105,11.61546,14.8662,0,0,64.14272,0,0,0,3,1,1,70,13.73189,0,,1000,1000,0,0,0,6.907755,1,0,0,1,0,0,72.76367,9.299689,0,4.16111,1 4,1,100,0,4,128091,0,10933.62,30.28268,1,16,1,20.19275,22.69849,0,0,0,42.89124,0,0,0,3,0,1,70,13.73189,0,,1000,1000,0,0,0,6.907755,1,0,0,1,0,0,72.76367,9.299689,0,3.758667,1 4,1,100,0,5,128091,0,10933.62,31.28268,1,16,1,10.93816,11.76693,0,0,0,22.70509,0,0,0,2,0,1,70,13.73189,0,,1000,1000,0,0,0,6.907755,1,0,0,1,0,0,72.76367,9.299689,0,3.122589,1 4,1,100,0,1,128092,0,5406.948,27.50445,1,16,1,24.98513,76.14515,0,0,0,101.1303,0,0,0,3,0,1,76.3,13.73189,0,,1000,1000,0,0,0,6.907755,1,0,0,0,0,0,76.18845,8.595625,0,4.61641,1 4,1,100,0,2,128092,0,5406.948,28.50445,1,16,1,29.94012,37.01688,0,0,0,66.95699,0,0,0,5,0,1,76.3,13.73189,0,,1000,1000,0,0,0,6.907755,1,0,0,0,0,0,76.18845,8.595625,0,4.204051,1 4,1,100,0,3,128092,0,5406.948,29.50445,1,16,1,23.98414,40.51041,0,0,0,64.49455,0,0,0,2,2,1,76.3,13.73189,0,,1000,1000,0,0,0,6.907755,1,0,0,0,0,0,76.18845,8.595625,0,4.166581,1 4,1,100,0,4,128092,0,5406.948,30.50445,1,16,1,11.47315,29.42175,0,0,0,40.89491,0,0,0,1,0,1,76.3,13.73189,0,,1000,1000,0,0,0,6.907755,1,0,0,0,0,0,76.18845,8.595625,0,3.711005,1 4,1,100,0,5,128092,0,5406.948,31.50445,1,16,1,7.57257,0,0,0,0,7.57257,0,0,0,1,0,1,76.3,13.73189,0,,1000,1000,0,0,0,6.907755,1,0,0,0,0,0,76.18845,8.595625,0,2.024533,1 3,1,100,0,1,128093,0,6576.303,24.33676,1,13,1,17.66784,15.23557,0,0,0,32.90342,0,0,0,2,0,2,92.5,13.73189,0,,1000,1000,0,0,.6931472,6.907755,1,0,0,0,0,0,79.71188,8.79138,.6931472,3.493577,1 3,1,100,0,2,128093,0,6576.303,25.33676,1,13,1,18.86792,16.08086,0,0,0,34.94879,0,0,0,2,0,2,92.5,13.73189,0,,1000,1000,0,0,.6931472,6.907755,1,0,0,0,0,0,79.71188,8.79138,.6931472,3.553884,1 3,1,100,0,3,128093,0,6576.303,26.33676,1,13,1,19.16462,21.88698,0,0,0,41.0516,0,0,0,2,0,2,92.5,13.73189,0,,1000,1000,0,0,.6931472,6.907755,1,0,0,0,0,0,79.71188,8.79138,.6931472,3.71483,1 3,1,100,0,1,128094,0,6576.303,37.62902,0,13,1,0,0,0,0,0,0,0,0,0,0,0,2,74.36826,13.73189,.12982,,1000,1000,0,0,.6931472,6.907755,1,0,0,0,0,0,78.8207,8.79138,.6931472,,0 3,1,100,0,2,128094,0,6576.303,38.62902,0,13,1,0,0,0,0,0,0,0,0,0,0,0,2,74.36826,13.73189,.12982,,1000,1000,0,0,.6931472,6.907755,1,0,0,0,0,0,78.8207,8.79138,.6931472,,0 3,1,100,0,3,128094,0,6576.303,39.62902,0,13,1,0,0,0,0,0,0,0,0,0,0,0,2,74.36826,13.73189,.12982,,1000,1000,0,0,.6931472,6.907755,1,0,0,0,0,0,78.8207,8.79138,.6931472,,0 6,1,25,0,1,128097,0,4321.96,26.02601,1,13,1,25.61837,18.10954,0,0,0,43.72792,0,0,0,2,0,1,65,13.73189,0,,700,700,0,0,0,6.55108,0,3.258096,7.937375,0,0,0,78.92638,8.371696,0,3.777987,1 6,1,25,0,2,128097,0,4321.96,27.02601,1,13,1,25.33693,19.94609,0,0,0,45.28302,0,0,0,3,0,1,65,13.73189,0,,700,700,0,0,0,6.55108,0,3.258096,7.937375,0,0,0,78.92638,8.371696,0,3.812932,1 6,1,25,0,3,128097,0,4321.96,28.02601,1,13,1,72.60442,19.31204,0,0,0,91.91646,0,0,0,3,1,1,65,13.73189,0,,700,700,0,0,0,6.55108,0,3.258096,7.937375,0,0,0,78.92638,8.371696,0,4.52088,1 6,1,25,0,4,128097,0,4321.96,29.02601,1,13,1,16.86418,14.75387,0,0,0,31.61805,0,0,0,2,0,1,65,13.73189,0,,700,700,0,0,0,6.55108,0,3.258096,7.937375,0,0,0,78.92638,8.371696,0,3.453728,1 6,1,25,0,5,128097,0,4321.96,30.02601,1,13,1,32.93039,0,0,0,0,32.93039,0,0,0,4,0,1,65,13.73189,0,,700,700,0,0,0,6.55108,0,3.258096,7.937375,0,0,0,78.92638,8.371696,0,3.494396,1 2,1,100,1,1,128103,0,7545.561,10.15195,1,13,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,399,399,1,1,1.609438,5.988961,1,0,0,0,0,0,82.314,8.928847,1.609438,,0 2,1,100,1,2,128103,0,7545.561,11.15195,1,13,1,138.0066,14.50712,29.02519,0,0,181.5389,0,0,0,6,0,5,74.36826,13.73189,0,,399,399,1,1,1.609438,5.988961,1,0,0,0,0,0,82.314,8.928847,1.609438,5.20147,1 2,1,100,1,3,128103,0,7545.561,12.15195,1,13,1,127.4314,3.266833,11.63092,0,0,142.3292,0,0,0,6,0,5,74.36826,13.73189,0,,399,399,1,1,1.609438,5.988961,1,0,0,0,0,0,82.314,8.928847,1.609438,4.958143,1 2,1,100,1,1,128104,0,7545.561,37.71115,0,18,1,68.94485,33.4952,0,0,0,102.44,0,0,0,3,0,5,62.1,21.7,0,,399,399,0,0,1.609438,5.988961,1,0,0,0,0,0,78.36037,8.928847,1.609438,4.629278,1 2,1,100,1,2,128104,0,7545.561,38.71115,0,18,1,26.28697,33.16539,9.56736,0,0,69.01971,0,0,0,1,0,5,62.1,21.7,0,,399,399,0,0,1.609438,5.988961,1,0,0,0,0,0,78.36037,8.928847,1.609438,4.234392,1 2,1,100,1,3,128104,0,7545.561,39.71115,0,18,1,89.2818,47.7606,33.46634,0,4.488778,174.9975,0,0,0,2,0,5,62.1,21.7,0,,399,399,0,0,1.609438,5.988961,1,0,0,0,0,0,78.36037,8.928847,1.609438,5.164772,1 2,1,100,1,1,128105,0,7545.561,36.46544,1,13,1,119.3046,8.051558,0,0,0,127.3561,0,0,0,2,0,5,63.2,17.4,0,,399,399,0,0,1.609438,5.988961,1,0,0,1,0,0,72.59515,8.928847,1.609438,4.846987,1 2,1,100,1,2,128105,0,7545.561,37.46544,1,13,1,68.45564,14.81928,0,0,229.6112,312.8861,1,0,0,2,0,5,63.2,17.4,0,,399,399,0,0,1.609438,5.988961,1,0,0,1,0,0,72.59515,8.928847,1.609438,5.745839,1 2,1,100,1,3,128105,0,7545.561,38.46544,1,13,1,31.9202,29.04239,26.59352,0,0,87.55611,0,0,0,3,0,5,63.2,17.4,0,,399,399,0,0,1.609438,5.988961,1,0,0,1,0,0,72.59515,8.928847,1.609438,4.47228,1 2,1,100,1,1,128106,0,7545.561,13.4757,0,13,1,86.03117,27.79976,93.04556,0,0,206.8765,0,0,0,8,1,5,74.36826,13.73189,0,,399,399,1,0,1.609438,5.988961,1,0,0,1,0,0,72.65098,8.928847,1.609438,5.332122,1 2,1,100,1,2,128106,0,7545.561,14.4757,0,13,1,37.23987,66.91676,62.15772,0,2215.767,2382.081,2,0,0,3,0,5,74.36826,13.73189,0,,399,399,1,0,1.609438,5.988961,1,0,0,1,0,0,72.65098,8.928847,1.609438,7.77573,1 2,1,100,1,3,128106,0,7545.561,15.4757,0,13,1,320.6384,147.2618,127.2668,0,1133.676,1728.843,3,0,0,20,0,5,74.36826,13.73189,0,,399,399,1,0,1.609438,5.988961,1,0,0,1,0,0,72.65098,8.928847,1.609438,7.455208,1 2,1,100,1,1,128107,0,7545.561,15.72074,1,13,1,139.6882,0,19.70024,0,0,159.3885,0,0,0,7,0,5,71.6,8.7,0,,399,399,1,1,1.609438,5.988961,1,0,0,0,0,0,74.71169,8.928847,1.609438,5.071344,1 2,1,100,1,2,128107,0,7545.561,16.72074,1,13,1,4.928806,2.749179,36.3253,0,0,44.00328,0,0,0,1,0,5,71.6,8.7,0,,399,399,1,1,1.609438,5.988961,1,0,0,0,0,0,74.71169,8.928847,1.609438,3.784264,1 2,1,100,1,3,128107,0,7545.561,17.72074,1,13,1,75.31172,12.41895,13.74564,0,210.8778,312.3541,1,0,0,5,0,5,71.6,8.7,0,,399,399,1,1,1.609438,5.988961,1,0,0,0,0,0,74.71169,8.928847,1.609438,5.744138,1 10,1,50,1,1,128124,0,8723.945,23.91786,1,16,1,153.777,66.43285,0,0,0,220.2098,0,0,0,15,1,1,75.8,8.7,0,,200,200,0,0,0,5.298317,0,3.931826,5.991465,1,0,0,67.59779,9.073941,0,5.394581,1 10,1,50,1,2,128124,0,8723.945,24.91786,1,16,1,56.65389,20.18072,11.24863,0,788.3351,876.4184,1,0,0,2,1,1,75.8,8.7,0,,200,200,0,0,0,5.298317,0,3.931826,5.991465,1,0,0,67.59779,9.073941,0,6.775844,1 10,1,50,1,3,128124,0,8723.945,25.91786,1,16,1,29.42643,13.62095,0,0,0,43.04738,0,0,0,1,2,2,75.8,8.7,0,,200,200,0,0,.6931472,5.298317,0,3.931826,5.991465,1,0,0,67.59779,9.073941,.6931472,3.762301,1 10,1,50,1,4,128124,0,8723.945,26.91786,1,16,1,418.7736,18.03596,0,0,0,436.8096,0,0,0,4,1,2,75.8,8.7,0,,200,200,0,0,.6931472,5.298317,0,3.931826,5.991465,1,0,0,67.59779,9.073941,.6931472,6.079497,1 10,1,50,1,5,128124,0,8723.945,27.91786,1,16,1,71.94244,49.97461,0,0,0,121.9171,0,0,0,2,1,2,75.8,8.7,0,,200,200,0,0,.6931472,5.298317,0,3.931826,5.991465,1,0,0,67.59779,9.073941,.6931472,4.803341,1 8,1,50,1,1,128125,0,4032.878,24.02738,1,16,1,9.422851,1.766784,0,0,0,11.18964,0,0,0,2,0,1,89.5,8.7,0,,115,115,0,0,0,4.744932,0,3.931826,5.438079,1,0,0,71.18497,8.302484,0,2.414988,1 8,1,50,1,2,128125,0,4032.878,25.02738,1,16,1,0,0,0,0,0,0,0,0,0,0,0,1,89.5,8.7,0,,115,115,0,0,0,4.744932,0,3.931826,5.438079,1,0,0,71.18497,8.302484,0,,0 8,1,50,1,3,128125,0,4032.878,26.02738,1,16,1,0,0,0,0,0,0,0,0,0,0,0,1,89.5,8.7,0,,115,115,0,0,0,4.744932,0,3.931826,5.438079,1,0,0,71.18497,8.302484,0,,0 8,1,50,1,4,128125,0,4032.878,27.02738,1,16,1,9.571559,1.458523,0,0,0,11.03008,0,0,0,2,0,1,89.5,8.7,0,,115,115,0,0,0,4.744932,0,3.931826,5.438079,1,0,0,71.18497,8.302484,0,2.400626,1 8,1,50,1,5,128125,0,4032.878,28.02738,1,16,1,130.9712,6.490204,0,0,0,137.4614,0,0,0,5,0,1,89.5,8.7,0,,115,115,0,0,0,4.744932,0,3.931826,5.438079,1,0,0,71.18497,8.302484,0,4.923344,1 9,1,50,0,1,128127,0,9204.095,31.49897,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,95,13.73189,0,,1000,1000,0,0,0,6.907755,0,3.931826,7.600903,0,0,0,79.2669,9.127512,0,,0 9,1,50,0,2,128127,0,9204.095,32.49897,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,95,13.73189,0,,1000,1000,0,0,0,6.907755,0,3.931826,7.600903,0,0,0,79.2669,9.127512,0,,0 9,1,50,0,3,128127,0,9204.095,33.49897,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,95,13.73189,0,,1000,1000,0,0,0,6.907755,0,3.931826,7.600903,0,0,0,79.2669,9.127512,0,,0 9,1,50,0,4,128127,0,9204.095,34.49897,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,95,13.73189,0,,1000,1000,0,0,0,6.907755,0,3.931826,7.600903,0,0,0,79.2669,9.127512,0,,0 9,1,50,0,5,128127,0,9204.095,35.49897,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,95,13.73189,0,,1000,1000,0,0,0,6.907755,0,3.931826,7.600903,0,0,0,79.2669,9.127512,0,,0 11,1,0,1,1,128129,0,11576.82,4.668036,0,12,1,26.1749,4.544914,0,0,0,30.71981,0,0,0,2,0,4,74.36826,13.73189,0,,0,291,1,0,1.386294,5.673323,0,0,0,0,0,0,82.35892,9.356847,1.386294,3.424908,1 11,1,0,1,2,128129,0,11576.82,5.668036,0,12,1,7.621121,3.162765,0,0,0,10.78389,0,0,0,1,0,4,74.36826,13.73189,0,,0,291,1,0,1.386294,5.673323,0,0,0,0,0,0,82.35892,9.356847,1.386294,2.378053,1 11,1,0,1,3,128129,0,11576.82,6.668036,0,12,1,90.68385,4.44004,0,0,0,95.12389,0,0,0,1,1,4,74.36826,13.73189,0,,0,291,1,0,1.386294,5.673323,0,0,0,0,0,0,82.35892,9.356847,1.386294,4.55518,1 11,1,0,1,4,128129,0,11576.82,7.668036,0,12,1,35.33731,6.883892,0,0,0,42.2212,0,0,0,3,0,4,74.36826,13.73189,0,,0,291,1,0,1.386294,5.673323,0,0,0,0,0,0,82.35892,9.356847,1.386294,3.742923,1 11,1,0,1,5,128129,0,11576.82,8.668036,0,12,1,12.62095,0,25.94026,0,0,38.56121,0,0,0,1,0,4,74.36826,13.73189,0,,0,291,1,0,1.386294,5.673323,0,0,0,0,0,0,82.35892,9.356847,1.386294,3.652247,1 11,1,0,1,1,128130,0,11576.82,26.73511,1,12,1,51.75491,17.40036,44.14039,0,0,113.2957,0,0,0,6,1,4,69.5,17.4,0,,0,291,0,0,1.386294,5.673323,0,0,0,1,0,0,66.9132,9.356847,1.386294,4.730001,1 11,1,0,1,2,128130,0,11576.82,27.73511,1,12,1,56.06968,3.511159,0,0,0,59.58084,0,0,0,3,0,4,69.5,17.4,0,,0,291,0,0,1.386294,5.673323,0,0,0,1,0,0,66.9132,9.356847,1.386294,4.087334,1 11,1,0,1,3,128130,0,11576.82,28.73511,1,12,1,258.3251,15.58969,0,0,0,273.9148,0,0,0,7,0,4,69.5,17.4,0,,0,291,0,0,1.386294,5.673323,0,0,0,1,0,0,66.9132,9.356847,1.386294,5.612817,1 11,1,0,1,4,128130,0,11576.82,29.73511,1,12,1,106.0119,6.810463,37.88894,0,837.9532,988.6646,1,0,0,8,1,4,69.5,17.4,0,,0,291,0,0,1.386294,5.673323,0,0,0,1,0,0,66.9132,9.356847,1.386294,6.896355,1 11,1,0,1,5,128130,0,11576.82,30.73511,1,12,1,21.03492,4.299537,0,0,0,25.33446,0,0,0,2,0,4,69.5,17.4,0,,0,291,0,0,1.386294,5.673323,0,0,0,1,0,0,66.9132,9.356847,1.386294,3.232165,1 11,1,0,1,1,128131,0,11576.82,9.839836,1,12,1,32.71862,6.061868,0,0,0,38.78049,0,0,0,1,2,4,74.36826,13.73189,0,,0,291,1,1,1.386294,5.673323,0,0,0,0,0,0,85.27657,9.356847,1.386294,3.657917,1 11,1,0,1,2,128131,0,11576.82,10.83984,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,0,291,1,1,1.386294,5.673323,0,0,0,0,0,0,85.27657,9.356847,1.386294,,0 11,1,0,1,3,128131,0,11576.82,11.83984,1,12,1,111.4965,1.655104,0,0,0,113.1516,0,0,0,3,2,4,74.36826,13.73189,0,,0,291,1,1,1.386294,5.673323,0,0,0,0,0,0,85.27657,9.356847,1.386294,4.728729,1 11,1,0,1,4,128131,0,11576.82,12.83984,1,12,1,61.95502,5.392382,0,0,0,67.3474,0,0,0,6,0,4,74.36826,13.73189,0,,0,291,1,1,1.386294,5.673323,0,0,0,0,0,0,85.27657,9.356847,1.386294,4.209864,1 11,1,0,1,5,128131,0,11576.82,13.83984,1,12,1,12.62095,0,0,0,0,12.62095,0,0,0,1,0,4,74.36826,13.73189,0,,0,291,1,1,1.386294,5.673323,0,0,0,0,0,0,85.27657,9.356847,1.386294,2.535358,1 11,1,0,1,1,128132,0,11576.82,30.79261,0,12,1,12.49256,2.325996,0,0,0,14.81856,0,0,0,2,0,4,100,8.7,0,,0,291,0,0,1.386294,5.673323,0,0,0,0,0,0,78.72413,9.356847,1.386294,2.69588,1 11,1,0,1,2,128132,0,11576.82,31.79261,0,12,1,10.88732,8.21448,0,0,143.3587,162.4605,1,0,0,2,0,4,100,8.7,0,,0,291,0,0,1.386294,5.673323,0,0,0,0,0,0,78.72413,9.356847,1.386294,5.090435,1 11,1,0,1,3,128132,0,11576.82,32.79261,0,12,1,393.9544,9.187314,0,0,0,403.1417,0,0,0,5,4,4,100,8.7,0,,0,291,0,0,1.386294,5.673323,0,0,0,0,0,0,78.72413,9.356847,1.386294,5.999288,1 11,1,0,1,4,128132,0,11576.82,33.79261,0,12,1,31.98715,0,43.64388,0,0,75.63102,0,0,0,3,0,4,100,8.7,0,,0,291,0,0,1.386294,5.673323,0,0,0,0,0,0,78.72413,9.356847,1.386294,4.325867,1 11,1,0,1,5,128132,0,11576.82,34.79261,0,12,1,33.44552,2.309634,0,0,0,35.75515,0,0,0,2,0,4,100,8.7,0,,0,291,0,0,1.386294,5.673323,0,0,0,0,0,0,78.72413,9.356847,1.386294,3.576694,1 2,1,100,0,1,128137,0,13813.28,5.229295,1,12,1,4.82509,4.282268,0,0,0,9.107358,0,0,0,1,0,4,74.36826,13.73189,0,,978,978,1,1,1.386294,6.885509,1,0,0,0,0,0,80.12564,9.533458,1.386294,2.209083,1 2,1,100,0,2,128137,0,13813.28,6.229295,1,12,1,40.7489,0,0,0,0,40.7489,0,0,0,3,0,4,74.36826,13.73189,0,,978,978,1,1,1.386294,6.885509,1,0,0,0,0,0,80.12564,9.533458,1.386294,3.707429,1 2,1,100,0,3,128137,0,13813.28,7.229295,1,12,1,7.533903,0,0,0,0,7.533903,0,0,0,1,0,4,74.36826,13.73189,0,,978,978,1,1,1.386294,6.885509,1,0,0,0,0,0,80.12564,9.533458,1.386294,2.019413,1 2,1,100,0,1,128138,0,13813.28,4.262834,1,12,1,14.47527,4.101327,0,0,0,18.5766,0,0,0,2,0,4,74.36826,13.73189,0,,978,978,1,1,1.386294,6.885509,1,0,0,0,0,0,80.93543,9.533458,1.386294,2.921903,1 2,1,100,0,2,128138,0,13813.28,5.262834,1,12,1,5.506608,0,0,0,0,5.506608,0,0,0,1,0,4,74.36826,13.73189,0,,978,978,1,1,1.386294,6.885509,1,0,0,0,0,0,80.93543,9.533458,1.386294,1.705949,1 2,1,100,0,3,128138,0,13813.28,6.262834,1,12,1,20.09041,0,0,0,0,20.09041,0,0,0,2,0,4,74.36826,13.73189,0,,978,978,1,1,1.386294,6.885509,1,0,0,0,0,0,80.93543,9.533458,1.386294,3.000242,1 2,1,100,0,1,128139,0,13813.28,34.96783,0,20,1,0,0,0,0,0,0,0,0,0,0,0,4,82.5,13.73189,0,,978,978,0,0,1.386294,6.885509,1,0,0,0,0,0,79.15443,9.533458,1.386294,,0 2,1,100,0,2,128139,0,13813.28,35.96783,0,20,1,90.80396,0,.5506608,0,0,91.35462,0,0,0,3,1,4,82.5,13.73189,0,,978,978,0,0,1.386294,6.885509,1,0,0,0,0,0,79.15443,9.533458,1.386294,4.514749,1 2,1,100,0,3,128139,0,13813.28,36.96783,0,20,1,0,0,0,0,0,0,0,0,0,0,0,4,82.5,13.73189,0,,978,978,0,0,1.386294,6.885509,1,0,0,0,0,0,79.15443,9.533458,1.386294,,0 2,1,100,0,1,128140,0,13813.28,24.83778,1,12,1,219.3004,28.75754,0,0,0,248.0579,0,0,0,22,0,4,68.8,13.73189,0,,978,978,0,0,1.386294,6.885509,1,0,0,1,0,0,66.92496,9.533458,1.386294,5.513662,1 2,1,100,0,2,128140,0,13813.28,25.83778,1,12,1,152.533,16.68502,36.82819,0,0,206.0462,0,0,0,19,0,4,68.8,13.73189,0,,978,978,0,0,1.386294,6.885509,1,0,0,1,0,0,66.92496,9.533458,1.386294,5.328101,1 2,1,100,0,3,128140,0,13813.28,26.83778,1,12,1,89.40231,14.68106,0,0,0,104.0834,0,0,0,14,0,4,68.8,13.73189,0,,978,978,0,0,1.386294,6.885509,1,0,0,1,0,0,66.92496,9.533458,1.386294,4.645192,1 2,1,100,1,1,128155,0,8172.457,16.1232,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,52.6,0,0,,0,0,1,1,1.94591,0,1,0,0,1,0,0,68.42788,9.008647,1.94591,,0 2,1,100,1,2,128155,0,8172.457,17.1232,1,12,1,0,0,0,0,0,0,0,0,0,0,0,8,52.6,0,0,,0,0,1,1,2.079442,0,1,0,0,1,0,0,68.42788,9.008647,2.079442,,0 2,1,100,1,3,128155,0,8172.457,18.1232,1,12,1,13.62735,8.657086,0,0,0,22.28444,0,0,0,1,0,8,52.6,0,0,,0,0,0,0,2.079442,0,1,0,0,1,0,0,68.42788,9.008647,2.079442,3.103889,1 2,1,100,1,4,128155,0,8172.457,19.1232,1,12,1,0,6.929784,0,0,340.1331,347.0629,1,0,0,0,0,8,52.6,0,0,,0,0,0,0,2.079442,0,1,0,0,1,0,0,68.42788,9.008647,2.079442,5.849506,1 2,1,100,1,5,128155,0,8172.457,20.1232,1,12,1,0,0,0,0,0,0,0,0,0,0,0,9,52.6,0,0,,0,0,0,0,2.197225,0,1,0,0,1,0,0,68.42788,9.008647,2.197225,,0 2,1,100,1,1,128156,0,8172.457,10.89938,1,12,1,4.759072,0,0,0,0,4.759072,0,0,0,1,0,7,74.36826,13.73189,0,,0,0,1,1,1.94591,0,1,0,0,1,0,0,78.19813,9.008647,1.94591,1.560053,1 2,1,100,1,2,128156,0,8172.457,11.89938,1,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,1,2.079442,0,1,0,0,1,0,0,78.19813,9.008647,2.079442,,0 2,1,100,1,3,128156,0,8172.457,12.89938,1,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,1,2.079442,0,1,0,0,1,0,0,78.19813,9.008647,2.079442,,0 2,1,100,1,4,128156,0,8172.457,13.89938,1,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,1,2.079442,0,1,0,0,1,0,0,78.19813,9.008647,2.079442,,0 2,1,100,1,5,128156,0,8172.457,14.89938,1,12,1,0,0,0,0,0,0,0,0,0,0,0,9,74.36826,13.73189,0,,0,0,1,1,2.197225,0,1,0,0,1,0,0,78.19813,9.008647,2.197225,,0 2,1,100,1,1,128157,0,8172.457,46.67214,0,9,1,9.518144,20.93992,0,0,0,30.45806,0,0,0,2,0,7,38.9,21.7,0,,0,0,0,0,1.94591,0,1,0,0,1,0,0,60.7702,9.008647,1.94591,3.416351,1 2,1,100,1,2,128157,0,8172.457,47.67214,0,9,1,0,0,0,0,0,0,0,0,0,0,0,8,38.9,21.7,0,,0,0,0,0,2.079442,0,1,0,0,1,0,0,60.7702,9.008647,2.079442,,0 2,1,100,1,3,128157,0,8172.457,48.67214,0,9,1,0,0,0,0,0,0,0,0,0,0,0,8,38.9,21.7,0,,0,0,0,0,2.079442,0,1,0,0,1,0,0,60.7702,9.008647,2.079442,,0 2,1,100,1,4,128157,0,8172.457,49.67214,0,9,1,0,0,0,0,0,0,0,0,0,0,0,8,38.9,21.7,0,,0,0,0,0,2.079442,0,1,0,0,1,0,0,60.7702,9.008647,2.079442,,0 2,1,100,1,5,128157,0,8172.457,50.67214,0,9,1,16.40724,0,0,0,350.0841,366.4914,1,0,0,1,0,9,38.9,21.7,0,,0,0,0,0,2.197225,0,1,0,0,1,0,0,60.7702,9.008647,2.197225,5.903975,1 2,1,100,1,1,128158,0,8172.457,14.77071,0,12,1,0,0,0,0,0,0,0,0,0,0,0,7,81.1,0,0,,0,0,1,0,1.94591,0,1,0,0,1,0,0,73.75163,9.008647,1.94591,,0 2,1,100,1,2,128158,0,8172.457,15.77071,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,81.1,0,0,,0,0,1,0,2.079442,0,1,0,0,1,0,0,73.75163,9.008647,2.079442,,0 2,1,100,1,3,128158,0,8172.457,16.7707,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,81.1,0,0,,0,0,1,0,2.079442,0,1,0,0,1,0,0,73.75163,9.008647,2.079442,,0 2,1,100,1,4,128158,0,8172.457,17.7707,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,81.1,0,0,,0,0,1,0,2.079442,0,1,0,0,1,0,0,73.75163,9.008647,2.079442,,0 2,1,100,1,5,128158,0,8172.457,18.7707,0,12,1,0,0,0,0,0,0,0,0,0,0,0,9,81.1,0,0,,0,0,0,0,2.197225,0,1,0,0,1,0,0,73.75163,9.008647,2.197225,,0 2,1,100,1,1,128159,0,8172.457,8.919918,0,12,1,4.759072,0,0,0,0,4.759072,0,0,0,1,0,7,74.36826,13.73189,0,,0,0,1,0,1.94591,0,1,0,0,1,0,0,78.7121,9.008647,1.94591,1.560053,1 2,1,100,1,2,128159,0,8172.457,9.919918,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,1,0,0,1,0,0,78.7121,9.008647,2.079442,,0 2,1,100,1,3,128159,0,8172.457,10.91992,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,1,0,0,1,0,0,78.7121,9.008647,2.079442,,0 2,1,100,1,4,128159,0,8172.457,11.91992,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,1,0,0,1,0,0,78.7121,9.008647,2.079442,,0 2,1,100,1,5,128159,0,8172.457,12.91992,0,12,1,0,0,0,0,0,0,0,0,0,0,0,9,74.36826,13.73189,0,,0,0,1,0,2.197225,0,1,0,0,1,0,0,78.7121,9.008647,2.197225,,0 2,1,100,1,1,128160,0,8172.457,40.27652,1,12,1,198.0964,6.30577,0,0,351.398,555.8001,1,1,0,5,0,7,44.2,21.7,0,,0,0,0,0,1.94591,0,1,0,0,1,0,0,65.55928,9.008647,1.94591,6.320409,1 2,1,100,1,2,128160,0,8172.457,41.27652,1,12,1,0,0,0,0,0,0,0,0,0,0,0,8,44.2,21.7,0,,0,0,0,0,2.079442,0,1,0,0,1,0,0,65.55928,9.008647,2.079442,,0 2,1,100,1,3,128160,0,8172.457,42.27652,1,12,1,0,0,0,0,0,0,0,0,0,0,0,8,44.2,21.7,0,,0,0,0,0,2.079442,0,1,0,0,1,0,0,65.55928,9.008647,2.079442,,0 2,1,100,1,4,128160,0,8172.457,43.27652,1,12,1,0,0,0,0,0,0,0,0,0,0,0,8,44.2,21.7,0,,0,0,0,0,2.079442,0,1,0,0,1,0,0,65.55928,9.008647,2.079442,,0 2,1,100,1,5,128160,0,8172.457,44.27652,1,12,1,0,0,0,0,0,0,0,0,0,0,0,9,44.2,21.7,0,,0,0,0,0,2.197225,0,1,0,0,1,0,0,65.55928,9.008647,2.197225,,0 2,1,100,1,1,128161,0,8172.457,12.79398,0,12,1,5.353956,0,0,0,0,5.353956,0,0,0,1,0,7,74.36826,13.73189,0,,0,0,1,0,1.94591,0,1,0,0,1,0,0,78.7121,9.008647,1.94591,1.677836,1 2,1,100,1,2,128161,0,8172.457,13.79398,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,1,0,0,1,0,0,78.7121,9.008647,2.079442,,0 2,1,100,1,3,128161,0,8172.457,14.79398,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,1,0,0,1,0,0,78.7121,9.008647,2.079442,,0 2,1,100,1,4,128161,0,8172.457,15.79398,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,0,1,0,2.079442,0,1,0,0,1,0,0,78.7121,9.008647,2.079442,,0 2,1,100,1,5,128161,0,8172.457,16.79398,0,12,1,0,0,0,0,0,0,0,0,0,0,0,9,74.36826,13.73189,0,,0,0,1,0,2.197225,0,1,0,0,1,0,0,78.7121,9.008647,2.197225,,0 11,1,0,0,1,128190,0,13406.87,19.57837,1,13,1,61.83746,23.351,36.00118,0,0,121.1896,0,0,0,3,0,5,82.5,13.73189,0,,0,165,0,0,1.609438,5.105946,0,0,0,0,0,0,79.76627,9.503597,1.609438,4.797357,1 11,1,0,0,2,128190,0,13406.87,20.57837,1,13,1,41.50943,20.78167,14.92722,0,0,77.21833,0,0,0,4,0,5,82.5,13.73189,0,,0,165,0,0,1.609438,5.105946,0,0,0,0,0,0,79.76627,9.503597,1.609438,4.346637,1 11,1,0,0,3,128190,0,13406.87,21.57837,1,13,1,10.81081,12.93366,0,0,0,23.74447,0,0,0,1,0,5,82.5,13.73189,0,,0,165,0,0,1.609438,5.105946,0,0,0,0,0,0,79.76627,9.503597,1.609438,3.16735,1 11,1,0,0,4,128190,0,13406.87,22.57837,1,13,1,59.25251,7.233364,0,0,0,66.48587,0,0,0,3,0,5,82.5,13.73189,0,,0,165,0,0,1.609438,5.105946,0,0,0,0,0,0,79.76627,9.503597,1.609438,4.19699,1 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10,1,50,0,3,128228,1,9542.002,20.73511,0,11,1,0,0,0,0,0,0,0,0,0,0,0,2,85.3,8.7,0,,179,179,0,0,.6931472,5.187386,0,3.931826,5.880533,1,0,0,60.33361,9.163564,.6931472,,0 11,1,0,0,1,128239,1,1191.067,4.043806,0,10,1,0,0,0,0,0,0,0,0,0,0,0,2,74.36826,13.73189,0,,0,0,1,0,.6931472,0,0,0,0,0,1,0,70.64633,7.083444,.6931472,,0 11,1,0,0,2,128239,1,1191.067,5.043806,0,10,1,0,0,0,0,0,0,0,0,0,0,0,2,74.36826,13.73189,0,,0,0,1,0,.6931472,0,0,0,0,0,1,0,70.64633,7.083444,.6931472,,0 11,1,0,0,1,128240,1,1191.067,32.15606,1,10,1,0,0,0,0,0,0,0,0,0,0,0,2,90,13.73189,0,,0,0,0,0,.6931472,0,0,0,0,0,0,0,69.84738,7.083444,.6931472,,0 11,1,0,0,2,128240,1,1191.067,33.15606,1,10,1,0,0,0,0,0,0,0,0,0,0,0,2,90,13.73189,0,,0,0,0,0,.6931472,0,0,0,0,0,0,0,69.84738,7.083444,.6931472,,0 6,1,25,0,1,128248,0,14105.46,11.19507,0,12,1,77.59129,2.679623,33.54535,0,0,113.8163,0,0,0,5,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.27783,9.554388,1.386294,4.734585,1 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6,1,25,0,1,128249,0,14105.46,44.66804,0,17,1,79.5053,0,0,0,0,79.5053,0,0,0,2,0,4,82.5,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.57204,9.554388,1.386294,4.375823,1 6,1,25,0,2,128249,0,14105.46,45.66804,0,17,1,120.7547,6.738544,32.95957,0,0,160.4528,0,0,0,5,0,4,82.5,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.57204,9.554388,1.386294,5.078,1 6,1,25,0,3,128249,0,14105.46,46.66804,0,17,1,83.78378,0,28.75676,0,0,112.5405,0,0,0,4,0,4,82.5,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.57204,9.554388,1.386294,4.723313,1 6,1,25,0,4,128249,0,14105.46,47.66804,0,17,1,91.3856,14.17502,0,0,0,105.5606,0,0,0,3,0,4,82.5,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.57204,9.554388,1.386294,4.659286,1 6,1,25,0,5,128249,0,14105.46,48.66804,0,17,1,12.50521,7.169654,23.95998,0,0,43.63485,0,0,0,1,0,4,82.5,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,76.57204,9.554388,1.386294,3.775856,1 6,1,25,0,1,128250,0,14105.46,14.05886,0,12,1,35.92462,15.34158,0,0,0,51.2662,0,0,0,5,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.23705,9.554388,1.386294,3.937032,1 6,1,25,0,2,128250,0,14105.46,15.05886,0,12,1,88.40971,15.06739,0,0,0,103.4771,0,0,0,4,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.23705,9.554388,1.386294,4.63935,1 6,1,25,0,3,128250,0,14105.46,16.05886,0,12,1,63.88206,18.69779,0,0,0,82.57985,0,0,0,8,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.23705,9.554388,1.386294,4.413766,1 6,1,25,0,4,128250,0,14105.46,17.05886,0,12,1,109.2753,16.45397,0,0,0,125.7293,0,0,0,6,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.23705,9.554388,1.386294,4.834131,1 6,1,25,0,5,128250,0,14105.46,18.05886,0,12,1,22.92622,3.480617,0,0,0,26.40684,0,0,0,3,0,4,74.36826,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.23705,9.554388,1.386294,3.273623,1 6,1,25,0,1,128251,0,14105.46,40.33675,1,12,1,107.7738,49.08716,0,0,0,156.861,0,0,0,8,0,4,82.5,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,77.78014,9.554388,1.386294,5.05536,1 6,1,25,0,2,128251,0,14105.46,41.33675,1,12,1,191.1051,40.67385,0,0,0,231.779,0,0,0,11,0,4,82.5,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,77.78014,9.554388,1.386294,5.445784,1 6,1,25,0,3,128251,0,14105.46,42.33675,1,12,1,206.8796,28.74693,0,0,0,235.6265,0,0,0,12,0,4,82.5,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,77.78014,9.554388,1.386294,5.462248,1 6,1,25,0,4,128251,0,14105.46,43.33675,1,12,1,112.3519,91.53601,0,0,0,203.8879,0,0,0,9,0,4,82.5,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,77.78014,9.554388,1.386294,5.31757,1 6,1,25,0,5,128251,0,14105.46,44.33675,1,12,1,66.27762,101.5006,24.55606,0,0,192.3343,0,0,0,8,0,4,82.5,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,77.78014,9.554388,1.386294,5.259235,1 7,1,25,0,1,128265,0,9542.002,53.15263,0,3,1,204.9529,40.71849,290.3416,0,2527.833,3063.846,2,0,0,2,1,1,63.8,13.73189,1,,0,0,0,0,0,0,0,3.258096,0,0,1,0,54.80615,9.163564,0,8.027426,1 7,1,25,0,2,128265,0,9542.002,54.15263,0,3,1,221.4286,32.41509,0,56.60378,640.6469,894.4905,1,0,3,2,1,1,63.8,13.73189,1,,0,0,0,0,0,0,0,3.258096,0,0,1,0,54.80615,9.163564,0,6.796254,1 7,1,25,0,3,128265,0,9542.002,55.15263,0,3,1,128.6978,18.28993,0,0,761.2678,908.2556,1,0,0,4,0,1,63.8,13.73189,1,,0,0,0,0,0,0,0,3.258096,0,0,1,0,54.80615,9.163564,0,6.811526,1 7,1,25,0,4,128265,0,9542.002,56.15263,0,3,1,373.6372,38.15406,0,0,1635.72,2047.511,1,0,0,4,0,1,63.8,13.73189,1,,0,0,0,0,0,0,0,3.258096,0,0,1,0,54.80615,9.163564,0,7.624381,1 7,1,25,0,5,128265,0,9542.002,57.15263,0,3,1,307.0488,142.8095,0,0,1835.511,2285.369,3,0,0,7,0,1,63.8,13.73189,1,,0,0,0,0,0,0,0,3.258096,0,0,1,0,54.80615,9.163564,0,7.734283,1 6,1,25,0,1,128267,1,9542.002,55.04996,1,13,1,333.3333,198.828,0,0,0,532.1614,0,0,0,20,0,1,81.3,13.73189,1,,182,259,0,0,0,5.556828,0,3.258096,6.590301,0,1,0,63.87963,9.163564,0,6.276947,1 3,1,100,0,1,128268,0,1094.293,59.8193,1,12,1,22.9682,0,22.50883,0,0,45.47703,0,0,0,2,0,1,92.5,13.73189,0,,127,127,0,0,0,4.844187,1,0,0,1,0,0,68.38589,6.998777,0,3.817207,1 3,1,100,0,2,128268,0,1094.293,60.8193,1,12,1,0,0,0,0,0,0,0,0,0,0,0,1,92.5,13.73189,0,,127,127,0,0,0,4.844187,1,0,0,1,0,0,68.38589,6.998777,0,,0 2,1,100,1,1,128302,1,9276.055,35.74812,0,12,1,0,5.936942,0,0,0,5.936942,0,0,0,0,0,5,75.8,8.7,0,,650,650,0,0,1.609438,6.476973,1,0,0,0,0,0,73.78603,9.1353,1.609438,1.781194,1 2,1,100,1,2,128302,1,9276.055,36.74812,0,12,1,87.6429,24.61622,0,0,0,112.2591,0,0,0,4,1,5,75.8,8.7,0,,650,650,0,0,1.609438,6.476973,1,0,0,0,0,0,73.78603,9.1353,1.609438,4.72081,1 2,1,100,1,3,128302,1,9276.055,37.74812,0,12,1,4.955401,0,0,0,0,4.955401,0,0,0,1,0,5,75.8,8.7,0,,650,650,0,0,1.609438,6.476973,1,0,0,0,0,0,73.78603,9.1353,1.609438,1.600478,1 2,1,100,1,4,128302,1,9276.055,38.74812,0,12,1,11.93208,9.325378,0,0,0,21.25746,0,0,0,2,0,5,75.8,8.7,0,,650,650,0,0,1.609438,6.476973,1,0,0,0,0,0,73.78603,9.1353,1.609438,3.056708,1 2,1,100,1,5,128302,1,9276.055,39.74812,0,12,1,126.7985,0,0,0,0,126.7985,0,0,0,3,0,5,75.8,8.7,0,,650,650,0,0,1.609438,6.476973,1,0,0,0,0,0,73.78603,9.1353,1.609438,4.842599,1 2,1,100,1,1,128303,1,9276.055,34.69131,1,12,1,57.10886,8.120167,0,0,0,65.22903,0,0,0,8,0,5,87.4,8.7,0,,650,650,0,0,1.609438,6.476973,1,0,0,0,0,0,73.93718,9.1353,1.609438,4.177905,1 2,1,100,1,2,128303,1,9276.055,35.69131,1,12,1,34.29505,15.73217,0,0,0,50.02722,0,0,0,5,0,5,87.4,8.7,0,,650,650,0,0,1.609438,6.476973,1,0,0,0,0,0,73.93718,9.1353,1.609438,3.912567,1 2,1,100,1,3,128303,1,9276.055,36.69131,1,12,1,81.88801,8.369673,0,0,0,90.25768,0,0,0,4,0,5,87.4,8.7,0,,650,650,0,0,1.609438,6.476973,1,0,0,0,0,0,73.93718,9.1353,1.609438,4.502669,1 2,1,100,1,4,128303,1,9276.055,37.69131,1,12,1,0,0,0,0,0,0,0,0,0,0,0,5,87.4,8.7,0,,650,650,0,0,1.609438,6.476973,1,0,0,0,0,0,73.93718,9.1353,1.609438,,0 2,1,100,1,5,128303,1,9276.055,38.69131,1,12,1,16.82793,5.982331,0,0,0,22.81026,0,0,0,2,0,5,87.4,8.7,0,,650,650,0,0,1.609438,6.476973,1,0,0,0,0,0,73.93718,9.1353,1.609438,3.127211,1 2,1,100,1,1,128304,1,9276.055,4.062971,0,12,1,53.21237,6.20464,0,0,0,59.41702,0,0,0,3,1,5,74.36826,13.73189,0,,650,650,1,0,1.609438,6.476973,1,0,0,0,0,0,76.88281,9.1353,1.609438,4.08458,1 2,1,100,1,2,128304,1,9276.055,5.062971,0,12,1,4.899292,0,0,0,222.4551,227.3544,1,0,0,1,0,5,74.36826,13.73189,0,,650,650,1,0,1.609438,6.476973,1,0,0,0,0,0,76.88281,9.1353,1.609438,5.42651,1 2,1,100,1,3,128304,1,9276.055,6.062971,0,12,1,6.442022,0,0,0,0,6.442022,0,0,0,1,0,5,74.36826,13.73189,0,,650,650,1,0,1.609438,6.476973,1,0,0,0,0,0,76.88281,9.1353,1.609438,1.862842,1 2,1,100,1,4,128304,1,9276.055,7.062971,0,12,1,0,3.822855,0,0,0,3.822855,0,0,0,0,0,5,74.36826,13.73189,0,,650,650,1,0,1.609438,6.476973,1,0,0,0,0,0,76.88281,9.1353,1.609438,1.340997,1 2,1,100,1,5,128304,1,9276.055,8.06297,0,12,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,650,650,1,0,1.609438,6.476973,1,0,0,0,0,0,76.88281,9.1353,1.609438,,0 2,1,100,1,1,128305,1,9276.055,11.26899,1,12,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,650,650,1,1,1.609438,6.476973,1,0,0,0,0,0,78.84123,9.1353,1.609438,,0 2,1,100,1,2,128305,1,9276.055,12.26899,1,12,1,14.15351,3.369624,0,0,0,17.52314,0,0,0,1,0,5,74.36826,13.73189,0,,650,650,1,1,1.609438,6.476973,1,0,0,0,0,0,78.84123,9.1353,1.609438,2.863522,1 2,1,100,1,3,128305,1,9276.055,13.26899,1,12,1,4.955401,0,0,0,0,4.955401,0,0,0,1,0,5,74.36826,13.73189,0,,650,650,1,1,1.609438,6.476973,1,0,0,0,0,0,78.84123,9.1353,1.609438,1.600478,1 2,1,100,1,4,128305,1,9276.055,14.26899,1,12,1,41.50987,0,0,0,0,41.50987,0,0,0,2,0,5,74.36826,13.73189,0,,650,650,1,1,1.609438,6.476973,1,0,0,0,0,0,78.84123,9.1353,1.609438,3.725931,1 2,1,100,1,5,128305,1,9276.055,15.26899,1,12,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,650,650,1,1,1.609438,6.476973,1,0,0,0,0,0,78.84123,9.1353,1.609438,,0 2,1,100,1,1,128306,1,9276.055,8.125941,1,12,1,23.20048,0,13.68233,0,0,36.88281,0,0,0,3,0,5,74.36826,13.73189,0,,650,650,1,1,1.609438,6.476973,1,0,0,0,0,0,78.84123,9.1353,1.609438,3.607746,1 2,1,100,1,2,128306,1,9276.055,9.125941,1,12,1,14.69788,0,32.99401,0,0,47.69189,0,0,0,2,0,5,74.36826,13.73189,0,,650,650,1,1,1.609438,6.476973,1,0,0,0,0,0,78.84123,9.1353,1.609438,3.864761,1 2,1,100,1,3,128306,1,9276.055,10.12594,1,12,1,7.928642,0,0,0,0,7.928642,0,0,0,1,0,5,74.36826,13.73189,0,,650,650,1,1,1.609438,6.476973,1,0,0,0,0,0,78.84123,9.1353,1.609438,2.070482,1 2,1,100,1,4,128306,1,9276.055,11.12594,1,12,1,37.76962,2.134007,28.75172,0,0,68.65535,0,0,0,4,0,5,74.36826,13.73189,0,,650,650,1,1,1.609438,6.476973,1,0,0,0,0,0,78.84123,9.1353,1.609438,4.229099,1 2,1,100,1,5,128306,1,9276.055,12.12594,1,12,1,5.04838,.8960875,0,0,0,5.944468,0,0,0,1,0,5,74.36826,13.73189,0,,650,650,1,1,1.609438,6.476973,1,0,0,0,0,0,78.84123,9.1353,1.609438,1.782461,1 1,1,0,1,1,128326,0,11965.26,35.28542,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,83.2,21.7,0,,450,120,0,0,1.386294,4.787492,1,0,0,0,0,0,78.30748,9.389847,1.386294,,0 1,1,0,1,2,128326,0,11965.26,36.28542,0,16,1,13.60915,0,0,0,0,13.60915,0,0,0,1,0,4,83.2,21.7,0,,450,120,0,0,1.386294,4.787492,1,0,0,0,0,0,78.30748,9.389847,1.386294,2.610742,1 1,1,0,1,3,128326,0,11965.26,37.28542,0,16,1,29.23687,0,0,0,0,29.23687,0,0,0,1,0,4,83.2,21.7,0,,450,120,0,0,1.386294,4.787492,1,0,0,0,0,0,78.30748,9.389847,1.386294,3.375431,1 1,1,0,1,4,128326,0,11965.26,38.28542,0,16,1,0,0,22.00551,0,0,22.00551,0,0,0,0,0,4,83.2,21.7,0,,450,120,0,0,1.386294,4.787492,1,0,0,0,0,0,78.30748,9.389847,1.386294,3.091293,1 1,1,0,1,5,128326,0,11965.26,39.28542,0,16,1,69.83593,5.107278,0,0,0,74.94321,0,0,0,2,0,5,83.2,21.7,0,,450,120,0,0,1.609438,4.787492,1,0,0,0,0,0,78.30748,9.389847,1.609438,4.31673,1 1,1,0,1,1,128327,0,11965.26,33.0924,1,15,1,0,0,0,0,0,0,0,0,0,0,0,4,72.6,0,0,,450,120,0,0,1.386294,4.787492,1,0,0,0,0,0,79.98129,9.389847,1.386294,,0 1,1,0,1,2,128327,0,11965.26,34.0924,1,15,1,0,0,0,0,0,0,0,0,0,0,0,4,72.6,0,0,,450,120,0,0,1.386294,4.787492,1,0,0,0,0,0,79.98129,9.389847,1.386294,,0 1,1,0,1,3,128327,0,11965.26,35.0924,1,15,1,0,0,0,0,0,0,0,0,0,0,0,4,72.6,0,0,,450,120,0,0,1.386294,4.787492,1,0,0,0,0,0,79.98129,9.389847,1.386294,,0 1,1,0,1,4,128327,0,11965.26,36.0924,1,15,1,17.66866,20.21569,0,0,1247.728,1285.613,1,0,0,0,0,4,72.6,0,0,,450,120,0,0,1.386294,4.787492,1,0,0,0,0,0,79.98129,9.389847,1.386294,7.158991,1 1,1,0,1,5,128327,0,11965.26,37.0924,1,15,1,9.570888,3.819941,0,0,0,13.39083,0,0,0,1,0,5,72.6,0,0,,450,120,0,0,1.609438,4.787492,1,0,0,0,0,0,79.98129,9.389847,1.609438,2.59457,1 1,1,0,1,1,128328,0,11965.26,3.115674,1,15,1,9.518144,0,0,0,0,9.518144,0,0,0,1,0,4,74.36826,13.73189,0,,450,120,1,1,1.386294,4.787492,1,0,0,0,0,0,81.84772,9.389847,1.386294,2.2532,1 1,1,0,1,2,128328,0,11965.26,4.115674,1,15,1,9.798585,0,0,0,0,9.798585,0,0,0,1,0,4,74.36826,13.73189,0,,450,120,1,1,1.386294,4.787492,1,0,0,0,0,0,81.84772,9.389847,1.386294,2.282238,1 1,1,0,1,3,128328,0,11965.26,5.115674,1,15,1,13.37958,0,0,0,0,13.37958,0,0,0,1,0,4,74.36826,13.73189,0,,450,120,1,1,1.386294,4.787492,1,0,0,0,0,0,81.84772,9.389847,1.386294,2.59373,1 1,1,0,1,4,128328,0,11965.26,6.115674,1,15,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,450,120,1,1,1.386294,4.787492,1,0,0,0,0,0,81.84772,9.389847,1.386294,,0 1,1,0,1,5,128328,0,11965.26,7.115674,1,15,1,55.88978,0,0,0,0,55.88978,0,0,0,3,0,5,74.36826,13.73189,0,,450,120,1,1,1.609438,4.787492,1,0,0,0,0,0,81.84772,9.389847,1.609438,4.023382,1 1,1,0,1,1,128329,0,11965.26,9.319644,0,15,1,50.2677,0,0,0,0,50.2677,0,0,0,2,1,4,74.36826,13.73189,0,,450,120,1,0,1.386294,4.787492,1,0,0,0,0,0,85.79333,9.389847,1.386294,3.917363,1 1,1,0,1,2,128329,0,11965.26,10.31964,0,15,1,14.15351,0,0,0,0,14.15351,0,0,0,1,0,4,74.36826,13.73189,0,,450,120,1,0,1.386294,4.787492,1,0,0,0,0,0,85.79333,9.389847,1.386294,2.649963,1 1,1,0,1,3,128329,0,11965.26,11.31964,0,15,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,450,120,1,0,1.386294,4.787492,1,0,0,0,0,0,85.79333,9.389847,1.386294,,0 1,1,0,1,4,128329,0,11965.26,12.31964,0,15,1,22.3497,0,1.032584,0,0,23.38229,0,0,0,1,0,4,74.36826,13.73189,0,,450,120,1,0,1.386294,4.787492,1,0,0,0,0,0,85.79333,9.389847,1.386294,3.151979,1 1,1,0,1,5,128329,0,11965.26,13.31964,0,15,1,99.01556,0,3.828355,0,0,102.8439,0,0,0,4,0,5,74.36826,13.73189,0,,450,120,1,0,1.609438,4.787492,1,0,0,0,0,0,85.79333,9.389847,1.609438,4.633213,1 5,1,25,1,1,128360,0,13322.58,33.62628,0,16,1,11.89768,0,15.27662,0,0,27.1743,0,0,0,0,1,7,89.5,4.3,0,,964,964,0,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,79.16077,9.497291,1.94591,3.302272,1 5,1,25,1,2,128360,0,13322.58,34.62628,0,16,1,0,0,0,0,0,0,0,0,0,0,0,7,89.5,4.3,0,,964,964,0,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,79.16077,9.497291,1.94591,,0 5,1,25,1,3,128360,0,13322.58,35.62628,0,16,1,47.57185,30.00496,0,0,0,77.57681,0,0,0,5,1,7,89.5,4.3,0,,964,964,0,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,79.16077,9.497291,1.94591,4.351268,1 5,1,25,1,1,128361,0,13322.58,7.008898,0,16,1,22.60559,8.774539,0,0,0,31.38013,0,0,0,4,0,7,74.36826,13.73189,0,,964,964,1,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,86.65917,9.497291,1.94591,3.446175,1 5,1,25,1,2,128361,0,13322.58,8.008898,0,16,1,9.254219,0,0,0,0,9.254219,0,0,0,2,0,7,74.36826,13.73189,0,,964,964,1,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,86.65917,9.497291,1.94591,2.22508,1 5,1,25,1,3,128361,0,13322.58,9.008898,0,16,1,11.39742,0,0,0,0,11.39742,0,0,0,1,0,7,74.36826,13.73189,0,,964,964,1,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,86.65917,9.497291,1.94591,2.433387,1 5,1,25,1,1,128362,0,13322.58,5.713894,0,16,1,14.8721,3.997621,0,0,0,18.86972,0,0,0,2,0,7,74.36826,13.73189,0,,964,964,1,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,86.65917,9.497291,1.94591,2.937559,1 5,1,25,1,2,128362,0,13322.58,6.713894,0,16,1,43.0049,0,0,0,0,43.0049,0,0,0,1,4,7,74.36826,13.73189,0,,964,964,1,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,86.65917,9.497291,1.94591,3.761314,1 5,1,25,1,3,128362,0,13322.58,7.713894,0,16,1,30.72349,3.528246,0,0,0,34.25174,0,0,0,2,3,7,74.36826,13.73189,0,,964,964,1,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,86.65917,9.497291,1.94591,3.533737,1 5,1,25,1,1,128363,0,13322.58,4.654346,0,16,1,35.99048,5.48483,0,0,293.8132,335.2885,1,0,0,1,1,7,74.36826,13.73189,1,,964,964,1,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,83.22755,9.497291,1.94591,5.814991,1 5,1,25,1,2,128363,0,13322.58,5.654346,0,16,1,13.06478,1.475231,0,0,0,14.54001,0,0,0,2,0,7,74.36826,13.73189,1,,964,964,1,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,83.22755,9.497291,1.94591,2.676904,1 5,1,25,1,3,128363,0,13322.58,6.654346,0,16,1,6.442022,0,0,0,0,6.442022,0,0,0,1,0,7,74.36826,13.73189,1,,964,964,1,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,83.22755,9.497291,1.94591,1.862842,1 5,1,25,1,1,128364,0,13322.58,30.62286,1,16,1,39.55978,5.841761,0,0,0,45.40155,0,0,0,2,0,7,87.4,13,0,,964,964,0,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,76.06387,9.497291,1.94591,3.815546,1 5,1,25,1,2,128364,0,13322.58,31.62286,1,16,1,13.60915,0,0,0,0,13.60915,0,0,0,1,0,7,87.4,13,0,,964,964,0,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,76.06387,9.497291,1.94591,2.610742,1 5,1,25,1,3,128364,0,13322.58,32.62286,1,16,1,12.3885,0,0,0,0,12.3885,0,0,0,1,0,7,87.4,13,0,,964,964,0,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,76.06387,9.497291,1.94591,2.516769,1 5,1,25,1,1,128365,0,13322.58,.9117043,1,16,1,39.85723,0,0,0,0,39.85723,0,0,0,6,0,7,74.36826,13.73189,0,,964,964,1,1,1.94591,6.871091,0,3.258096,8.257385,0,0,0,82.71357,9.497291,1.94591,3.685304,1 5,1,25,1,2,128365,0,13322.58,1.911704,1,16,1,9.254219,0,0,0,0,9.254219,0,0,0,1,0,7,74.36826,13.73189,0,,964,964,1,1,1.94591,6.871091,0,3.258096,8.257385,0,0,0,82.71357,9.497291,1.94591,2.22508,1 5,1,25,1,3,128365,0,13322.58,2.911704,1,16,1,7.928642,0,0,0,0,7.928642,0,0,0,1,0,7,74.36826,13.73189,0,,964,964,1,1,1.94591,6.871091,0,3.258096,8.257385,0,0,0,82.71357,9.497291,1.94591,2.070482,1 5,1,25,1,1,128366,0,13322.58,3.389459,0,16,1,116.2998,2.082094,0,0,143.0696,261.4515,1,0,0,4,1,7,74.36826,13.73189,0,,964,964,1,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,83.22755,9.497291,1.94591,5.566249,1 5,1,25,1,2,128366,0,13322.58,4.389459,0,16,1,7.076756,0,0,0,0,7.076756,0,0,0,1,0,7,74.36826,13.73189,0,,964,964,1,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,83.22755,9.497291,1.94591,1.956816,1 5,1,25,1,3,128366,0,13322.58,5.389459,0,16,1,8.424182,0,0,0,0,8.424182,0,0,0,1,0,7,74.36826,13.73189,0,,964,964,1,0,1.94591,6.871091,0,3.258096,8.257385,0,0,0,83.22755,9.497291,1.94591,2.131106,1 5,1,25,0,1,128383,0,16140.09,46.6256,1,13,1,7.067138,17.55006,0,0,0,24.6172,0,0,0,1,0,3,85.3,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,67.22846,9.689123,1.098612,3.203445,1 5,1,25,0,2,128383,0,16140.09,47.6256,1,13,1,6.469003,9.757412,0,0,0,16.22642,0,0,0,1,0,3,85.3,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,67.22846,9.689123,1.098612,2.78664,1 5,1,25,0,3,128383,0,16140.09,48.6256,1,13,1,21.62162,15.74939,33.89189,0,0,71.2629,0,0,0,2,0,3,85.3,13,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,67.22846,9.689123,1.098612,4.266376,1 5,1,25,0,1,128384,0,16140.09,18.68309,0,12,1,0,5.182568,30.59482,0,0,35.77739,0,0,0,0,0,3,73.7,17.4,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,78.88491,9.689123,1.098612,3.577316,1 5,1,25,0,2,128384,0,16140.09,19.68309,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,73.7,17.4,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,78.88491,9.689123,1.098612,,0 5,1,25,0,3,128384,0,16140.09,20.68309,0,12,1,22.11302,0,25.16462,0,0,47.27764,0,0,0,1,0,3,73.7,17.4,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,78.88491,9.689123,1.098612,3.856037,1 5,1,25,0,1,128385,0,16140.09,52.03012,0,12,1,51.23675,73.16843,0,0,0,124.4052,0,0,0,4,0,3,87.4,17.4,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,63.23641,9.689123,1.098612,4.823544,1 5,1,25,0,2,128385,0,16140.09,53.03012,0,12,1,45.8221,73.8814,39.40701,0,0,159.1105,0,0,0,3,0,3,87.4,17.4,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,63.23641,9.689123,1.098612,5.069599,1 5,1,25,0,3,128385,0,16140.09,54.03012,0,12,1,43.24324,103.0713,22.08354,0,0,168.398,0,0,0,2,0,3,87.4,17.4,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,63.23641,9.689123,1.098612,5.12633,1 11,1,0,1,1,128411,0,9645.161,10.0178,0,12,1,76.14515,9.613325,0,0,0,85.75848,0,0,0,3,1,4,74.36826,13.73189,0,,0,233,1,0,1.386294,5.451038,0,0,0,0,0,0,85.65124,9.174315,1.386294,4.451535,1 11,1,0,1,2,128411,0,9645.161,11.0178,0,12,1,44.638,3.135547,0,0,0,47.77354,0,0,0,6,1,4,74.36826,13.73189,0,,0,233,1,0,1.386294,5.451038,0,0,0,0,0,0,85.65124,9.174315,1.386294,3.866472,1 11,1,0,1,3,128411,0,9645.161,12.0178,0,12,1,27.75025,5.673934,0,0,0,33.42418,0,0,0,3,0,4,74.36826,13.73189,0,,0,233,1,0,1.386294,5.451038,0,0,0,0,0,0,85.65124,9.174315,1.386294,3.50928,1 11,1,0,1,4,128411,0,9645.161,13.0178,0,12,1,56.67738,0,0,0,0,56.67738,0,0,0,4,1,4,74.36826,13.73189,0,,0,233,1,0,1.386294,5.451038,0,0,0,0,0,0,85.65124,9.174315,1.386294,4.037375,1 11,1,0,1,5,128411,0,9645.161,14.0178,0,12,1,75.72571,12.25494,0,0,0,87.98064,0,0,0,6,0,4,74.36826,13.73189,0,,0,233,1,0,1.386294,5.451038,0,0,0,0,0,0,85.65124,9.174315,1.386294,4.477117,1 11,1,0,1,1,128412,0,9645.161,45.86448,1,12,1,75.49078,74.17014,11.8144,0,0,161.4753,0,0,0,4,0,4,76.8,13,0,,0,233,0,0,1.386294,5.451038,0,0,0,0,0,0,77.59435,9.174315,1.386294,5.084352,1 11,1,0,1,2,128412,0,9645.161,46.86448,1,12,1,109.4175,106.0425,31.29015,0,0,246.7501,0,0,0,10,1,4,76.8,13,0,,0,233,0,0,1.386294,5.451038,0,0,0,0,0,0,77.59435,9.174315,1.386294,5.508376,1 11,1,0,1,3,128412,0,9645.161,47.86448,1,12,1,103.0723,32.41328,0,0,0,135.4856,0,0,0,3,0,4,76.8,13,0,,0,233,0,0,1.386294,5.451038,0,0,0,0,0,0,77.59435,9.174315,1.386294,4.908865,1 11,1,0,1,4,128412,0,9645.161,48.86448,1,12,1,83.98348,39.02249,47.47591,0,0,170.4819,0,0,0,7,1,4,76.8,13,0,,0,233,0,0,1.386294,5.451038,0,0,0,0,0,0,77.59435,9.174315,1.386294,5.138629,1 11,1,0,1,5,128412,0,9645.161,49.86448,1,12,1,53.84939,105.7089,0,0,414.6992,574.2574,1,0,0,5,0,4,76.8,13,0,,0,233,0,0,1.386294,5.451038,0,0,0,0,0,0,77.59435,9.174315,1.386294,6.353078,1 11,1,0,1,1,128413,0,9645.161,8.123203,0,12,1,49.97026,49.26829,0,0,0,99.23855,0,0,0,5,0,4,74.36826,13.73189,0,,0,233,1,0,1.386294,5.451038,0,0,0,0,0,0,84.69201,9.174315,1.386294,4.597527,1 11,1,0,1,2,128413,0,9645.161,9.123203,0,12,1,53.34785,60.31573,28.44311,0,0,142.1067,0,0,0,3,4,4,74.36826,13.73189,0,,0,233,1,0,1.386294,5.451038,0,0,0,0,0,0,84.69201,9.174315,1.386294,4.956578,1 11,1,0,1,3,128413,0,9645.161,10.1232,0,12,1,58.47374,63.35976,0,0,0,121.8335,0,0,0,5,3,4,74.36826,13.73189,0,,0,233,1,0,1.386294,5.451038,0,0,0,0,0,0,84.69201,9.174315,1.386294,4.802655,1 11,1,0,1,4,128413,0,9645.161,11.1232,0,12,1,21.1106,29.25195,0,0,0,50.36255,0,0,0,2,1,4,74.36826,13.73189,0,,0,233,1,0,1.386294,5.451038,0,0,0,0,0,0,84.69201,9.174315,1.386294,3.919248,1 11,1,0,1,5,128413,0,9645.161,12.1232,0,12,1,34.91796,30.53008,0,0,0,65.44804,0,0,0,4,1,4,74.36826,13.73189,0,,0,233,1,0,1.386294,5.451038,0,0,0,0,0,0,84.69201,9.174315,1.386294,4.181257,1 11,1,0,1,1,128414,0,9645.161,43.7755,0,16,1,137.4182,34.33076,0,0,0,171.749,0,0,0,4,0,4,94.7,4.3,0,,0,233,0,0,1.386294,5.451038,0,0,0,0,0,0,77.32689,9.174315,1.386294,5.146034,1 11,1,0,1,2,128414,0,9645.161,44.7755,0,16,1,188.8949,33.78879,0,0,0,222.6837,0,0,0,7,0,4,94.7,4.3,0,,0,233,0,0,1.386294,5.451038,0,0,0,0,0,0,77.32689,9.174315,1.386294,5.405753,1 11,1,0,1,3,128414,0,9645.161,45.7755,0,16,1,282.4579,30.66402,21.23389,0,0,334.3558,0,0,0,6,1,4,94.7,4.3,0,,0,233,0,0,1.386294,5.451038,0,0,0,0,0,0,77.32689,9.174315,1.386294,5.812206,1 11,1,0,1,4,128414,0,9645.161,46.7755,0,16,1,293.2538,49.88527,0,0,0,343.1391,0,0,0,12,0,4,94.7,4.3,0,,0,233,0,0,1.386294,5.451038,0,0,0,0,0,0,77.32689,9.174315,1.386294,5.838136,1 11,1,0,1,5,128414,0,9645.161,47.7755,0,16,1,21.87631,31.66597,0,0,0,53.54228,0,0,0,1,0,4,94.7,4.3,0,,0,233,0,0,1.386294,5.451038,0,0,0,0,0,0,77.32689,9.174315,1.386294,3.980472,1 2,1,100,1,1,128431,0,5694.789,27.08008,1,7,1,92.92566,50.67746,32.57794,0,306.1631,482.3441,1,0,0,13,1,5,66.3,34.8,1,,594,594,0,0,1.609438,6.386879,1,0,0,0,1,0,52.32401,8.647483,1.609438,6.178658,1 2,1,100,1,2,128431,0,5694.789,28.08008,1,7,1,117.1961,28.75137,0,0,0,145.9474,0,0,0,5,0,5,66.3,34.8,1,,594,594,0,0,1.609438,6.386879,1,0,0,0,1,0,52.32401,8.647483,1.609438,4.983246,1 2,1,100,1,3,128431,0,5694.789,29.08008,1,7,1,17.45636,9.900249,26.58354,0,0,53.94015,0,0,0,1,1,5,66.3,34.8,1,,594,594,0,0,1.609438,6.386879,1,0,0,0,1,0,52.32401,8.647483,1.609438,3.987875,1 2,1,100,1,1,128432,0,5694.789,7.937029,0,7,1,10.79137,7.847722,0,0,0,18.63909,0,0,0,1,0,5,74.36826,13.73189,0,,594,594,1,0,1.609438,6.386879,1,0,0,0,1,0,59.21023,8.647483,1.609438,2.925261,1 2,1,100,1,2,128432,0,5694.789,8.93703,0,7,1,60.24096,4.156627,0,0,2155.75,2220.148,2,0,0,6,0,5,74.36826,13.73189,0,,594,594,1,0,1.609438,6.386879,1,0,0,0,1,0,59.21023,8.647483,1.609438,7.705329,1 2,1,100,1,3,128432,0,5694.789,9.93703,0,7,1,555.3616,7.845387,0,0,2160.798,2724.005,2,0,0,7,2,5,74.36826,13.73189,0,,594,594,1,0,1.609438,6.386879,1,0,0,0,1,0,59.21023,8.647483,1.609438,7.909858,1 2,1,100,1,1,128433,0,5694.789,10.80356,0,7,1,20.38369,1.193046,26.97842,0,0,48.55516,0,0,0,1,2,5,74.36826,13.73189,0,,594,594,1,0,1.609438,6.386879,1,0,0,0,1,0,63.0433,8.647483,1.609438,3.8827,1 2,1,100,1,2,128433,0,5694.789,11.80356,0,7,1,50.38335,3.214677,0,0,0,53.59803,0,0,0,3,0,5,74.36826,13.73189,0,,594,594,1,0,1.609438,6.386879,1,0,0,0,1,0,63.0433,8.647483,1.609438,3.981512,1 2,1,100,1,3,128433,0,5694.789,12.80356,0,7,1,30.1995,8.249376,0,0,358.9526,397.4015,1,0,0,2,0,5,74.36826,13.73189,0,,594,594,1,0,1.609438,6.386879,1,0,0,0,1,0,63.0433,8.647483,1.609438,5.984947,1 2,1,100,1,1,128434,0,5694.789,4.172484,0,7,1,49.46043,12.11031,0,0,0,61.57074,0,0,0,4,1,5,74.36826,13.73189,0,,594,594,1,0,1.609438,6.386879,1,0,0,0,0,0,75.11046,8.647483,1.609438,4.120187,1 2,1,100,1,2,128434,0,5694.789,5.172484,0,7,1,98.35706,5.219058,0,0,0,103.5761,0,0,0,6,0,5,74.36826,13.73189,0,,594,594,1,0,1.609438,6.386879,1,0,0,0,0,0,75.11046,8.647483,1.609438,4.640307,1 2,1,100,1,3,128434,0,5694.789,6.172484,0,7,1,20.94763,7.246883,0,0,0,28.19451,0,0,0,2,0,5,74.36826,13.73189,0,,594,594,1,0,1.609438,6.386879,1,0,0,0,0,0,75.11046,8.647483,1.609438,3.339127,1 2,1,100,1,1,128435,0,5694.789,32.46544,0,12,1,185.7014,3.219424,0,0,0,188.9209,0,0,0,2,0,5,65.3,17.4,0,,594,594,0,0,1.609438,6.386879,1,0,0,1,0,0,70.86124,8.647483,1.609438,5.241328,1 2,1,100,1,2,128435,0,5694.789,33.46544,0,12,1,0,0,0,0,0,0,0,0,0,0,0,5,65.3,17.4,0,,594,594,0,0,1.609438,6.386879,1,0,0,1,0,0,70.86124,8.647483,1.609438,,0 2,1,100,1,3,128435,0,5694.789,34.46544,0,12,1,18.95262,2.049875,0,0,0,21.00249,0,0,0,1,0,5,65.3,17.4,0,,594,594,0,0,1.609438,6.386879,1,0,0,1,0,0,70.86124,8.647483,1.609438,3.044641,1 11,1,0,1,1,128438,0,14655.34,47.23614,1,12,1,89.32854,307.9616,39.47842,0,0,436.7686,0,0,0,6,1,3,46.3,13,0,,0,329,0,0,1.098612,5.796058,0,0,0,0,0,0,78.72062,9.592628,1.098612,6.079403,1 11,1,0,1,2,128438,0,14655.34,48.23614,1,12,1,0,304.2169,0,0,0,304.2169,0,0,0,0,0,3,46.3,13,0,,0,329,0,0,1.098612,5.796058,0,0,0,0,0,0,78.72062,9.592628,1.098612,5.717741,1 11,1,0,1,3,128438,0,14655.34,49.23614,1,12,1,14.96259,64.68828,16.6783,0,0,96.32918,0,0,0,1,1,3,46.3,13,0,,0,329,0,0,1.098612,5.796058,0,0,0,0,0,0,78.72062,9.592628,1.098612,4.567771,1 11,1,0,1,4,128438,0,14655.34,50.23614,1,12,1,51.6367,44.92854,0,0,0,96.56524,0,0,0,3,1,3,46.3,13,0,,0,329,0,0,1.098612,5.796058,0,0,0,0,0,0,78.72062,9.592628,1.098612,4.570219,1 11,1,0,1,5,128438,0,14655.34,51.23614,1,12,1,101.1426,62.95387,25.20525,0,451.3161,640.6179,1,0,0,2,0,3,46.3,13,0,,0,329,0,0,1.098612,5.796058,0,0,0,0,0,0,78.72062,9.592628,1.098612,6.462433,1 11,1,0,1,1,128439,0,14655.34,18.45311,1,12,1,11.99041,0,29.73022,0,0,41.72062,0,0,0,0,1,3,65.3,4.3,0,,0,329,0,0,1.098612,5.796058,0,0,0,0,0,0,79.76731,9.592628,1.098612,3.730996,1 11,1,0,1,2,128439,0,14655.34,19.45311,1,12,1,31.21577,5.969332,0,0,0,37.1851,0,0,0,4,0,3,65.3,4.3,0,,0,329,0,0,1.098612,5.796058,0,0,0,0,0,0,79.76731,9.592628,1.098612,3.615908,1 11,1,0,1,3,128439,0,14655.34,20.45311,1,12,1,40.399,15.12219,24.0798,0,0,79.601,0,0,0,3,1,3,65.3,4.3,0,,0,329,0,0,1.098612,5.796058,0,0,0,0,0,0,79.76731,9.592628,1.098612,4.377027,1 11,1,0,1,4,128439,0,14655.34,21.45311,1,12,1,22.59105,57.13232,0,0,0,79.72337,0,0,0,3,0,3,65.3,4.3,0,,0,329,0,0,1.098612,5.796058,0,0,0,0,0,0,79.76731,9.592628,1.098612,4.378563,1 11,1,0,1,5,128439,0,14655.34,22.45311,1,12,1,28.35379,37.93906,27.08845,0,0,93.38129,0,0,0,2,1,3,65.3,4.3,0,,0,329,0,0,1.098612,5.796058,0,0,0,0,0,0,79.76731,9.592628,1.098612,4.536691,1 11,1,0,1,1,128440,0,14655.34,52.82409,0,12,1,39.56834,67.91367,16.91846,0,0,124.4005,0,0,0,4,1,3,66.3,17.4,0,,0,329,0,0,1.098612,5.796058,0,0,0,1,0,0,64.3789,9.592628,1.098612,4.823506,1 11,1,0,1,2,128440,0,14655.34,53.82409,0,12,1,83.24206,58.61446,0,0,3381.911,3523.768,1,0,0,11,0,3,66.3,17.4,0,,0,329,0,0,1.098612,5.796058,0,0,0,1,0,0,64.3789,9.592628,1.098612,8.167286,1 11,1,0,1,3,128440,0,14655.34,54.82409,0,12,1,70.07481,24.01496,18.95262,0,938.4589,1051.501,1,0,0,7,1,3,66.3,17.4,0,,0,329,0,0,1.098612,5.796058,0,0,0,1,0,0,64.3789,9.592628,1.098612,6.957974,1 11,1,0,1,4,128440,0,14655.34,55.82409,0,12,1,38.72752,27.70862,0,0,0,66.43614,0,0,0,3,0,3,66.3,17.4,0,,0,329,0,0,1.098612,5.796058,0,0,0,1,0,0,64.3789,9.592628,1.098612,4.196241,1 11,1,0,1,5,128440,0,14655.34,56.82409,0,12,1,69.4033,34.40542,0,0,0,103.8087,0,0,0,5,1,3,66.3,17.4,0,,0,329,0,0,1.098612,5.796058,0,0,0,1,0,0,64.3789,9.592628,1.098612,4.64255,1 2,1,100,0,1,128443,0,9138.338,3.674196,1,13,1,7.656066,0,0,0,0,7.656066,0,0,0,1,0,3,74.36826,13.73189,0,,890,890,1,1,1.098612,6.791222,1,0,0,0,0,0,78.11302,9.120343,1.098612,2.035498,1 2,1,100,0,2,128443,0,9138.338,4.674196,1,13,1,15.63342,2.12938,0,0,0,17.7628,0,0,0,2,0,4,74.36826,13.73189,0,,890,890,1,1,1.386294,6.791222,1,0,0,0,0,0,78.11302,9.120343,1.386294,2.877107,1 2,1,100,0,3,128443,0,9138.338,5.674196,1,13,1,13.26781,.982801,0,0,0,14.25061,0,0,0,1,0,4,74.36826,13.73189,0,,890,890,1,1,1.386294,6.791222,1,0,0,0,0,0,78.11302,9.120343,1.386294,2.6568,1 2,1,100,0,4,128443,0,9138.338,6.674196,1,13,1,15.04102,0,0,0,0,15.04102,0,0,0,1,0,4,74.36826,13.73189,0,,890,890,1,1,1.386294,6.791222,1,0,0,0,0,0,78.11302,9.120343,1.386294,2.710781,1 2,1,100,0,5,128443,0,9138.338,7.674196,1,13,1,22.50938,0,0,0,0,22.50938,0,0,0,3,0,4,74.36826,13.73189,0,,890,890,1,1,1.386294,6.791222,1,0,0,0,0,0,78.11302,9.120343,1.386294,3.113932,1 2,1,100,0,1,128444,0,9138.338,28.71184,0,14,1,337.1614,5.276796,21.66667,0,0,364.1048,0,0,0,4,1,3,50.5,0,0,,890,890,0,0,1.098612,6.791222,1,0,0,0,0,0,77.94995,9.120343,1.098612,5.897442,1 2,1,100,0,2,128444,0,9138.338,29.71184,0,14,1,41.53639,4.204852,0,0,0,45.74124,0,0,0,3,0,4,50.5,0,0,,890,890,0,0,1.386294,6.791222,1,0,0,0,0,0,77.94995,9.120343,1.386294,3.823,1 2,1,100,0,3,128444,0,9138.338,30.71184,0,14,1,9.82801,5.174447,0,0,0,15.00246,0,0,0,2,0,4,50.5,0,0,,890,890,0,0,1.386294,6.791222,1,0,0,0,0,0,77.94995,9.120343,1.386294,2.708214,1 2,1,100,0,4,128444,0,9138.338,31.71184,0,14,1,5.469462,0,0,0,0,5.469462,0,0,0,1,0,4,50.5,0,0,,890,890,0,0,1.386294,6.791222,1,0,0,0,0,0,77.94995,9.120343,1.386294,1.69918,1 2,1,100,0,5,128444,0,9138.338,32.71184,0,14,1,77.2822,2.917882,0,0,0,80.20008,0,0,0,4,0,4,50.5,0,0,,890,890,0,0,1.386294,6.791222,1,0,0,0,0,0,77.94995,9.120343,1.386294,4.384524,1 2,1,100,0,1,128445,0,9138.338,25.40452,1,13,1,85.39458,11.40754,0,0,665.3121,762.1143,1,0,0,2,0,3,84.2,8.7,0,,890,890,0,0,1.098612,6.791222,1,0,0,0,0,0,73.57805,9.120343,1.098612,6.636096,1 2,1,100,0,2,128445,0,9138.338,26.40452,1,13,1,21.02426,6.091644,0,0,0,27.1159,0,0,0,3,0,4,84.2,8.7,0,,890,890,0,0,1.386294,6.791222,1,0,0,0,0,0,73.57805,9.120343,1.386294,3.30012,1 2,1,100,0,3,128445,0,9138.338,27.40452,1,13,1,43.24324,3.439803,0,0,0,46.68305,0,0,0,6,0,4,84.2,8.7,0,,890,890,0,0,1.386294,6.791222,1,0,0,0,0,0,73.57805,9.120343,1.386294,3.843381,1 2,1,100,0,4,128445,0,9138.338,28.40452,1,13,1,0,0,0,0,0,0,0,0,0,0,0,4,84.2,8.7,0,,890,890,0,0,1.386294,6.791222,1,0,0,0,0,0,73.57805,9.120343,1.386294,,0 2,1,100,0,5,128445,0,9138.338,29.40452,1,13,1,19.17466,0,0,0,0,19.17466,0,0,0,2,0,4,84.2,8.7,0,,890,890,0,0,1.386294,6.791222,1,0,0,0,0,0,73.57805,9.120343,1.386294,2.953589,1 11,1,0,0,1,128468,0,10325.68,19.80561,0,12,1,32.97998,9.140165,41.54299,0,0,83.66313,0,0,0,2,1,4,78.9,4.3,0,,0,195,0,0,1.386294,5.273,0,0,0,0,0,0,78.46669,9.242486,1.386294,4.426798,1 11,1,0,0,2,128468,0,10325.68,20.80561,0,12,1,57.68194,0,0,0,0,57.68194,0,0,0,3,0,4,78.9,4.3,0,,0,195,0,0,1.386294,5.273,0,0,0,0,0,0,78.46669,9.242486,1.386294,4.054944,1 11,1,0,0,3,128468,0,10325.68,21.80561,0,12,1,253.0713,5.479115,0,0,0,258.5504,0,0,0,1,22,4,78.9,4.3,0,,0,195,0,0,1.386294,5.273,0,0,0,0,0,0,78.46669,9.242486,1.386294,5.55509,1 11,1,0,0,4,128468,0,10325.68,22.80561,0,12,.2684931,260.711,0,0,0,0,260.711,0,0,0,0,21,4,78.9,4.3,0,,0,195,0,0,1.386294,5.273,0,0,0,0,0,0,78.46669,9.242486,1.386294,5.563413,1 11,1,0,0,1,128469,0,10325.68,40.51472,1,12,1,11.77856,0,0,0,0,11.77856,0,0,0,0,0,4,84.2,4.3,0,,0,195,0,0,1.386294,5.273,0,0,0,0,0,0,78.31118,9.242486,1.386294,2.466281,1 11,1,0,0,2,128469,0,10325.68,41.51472,1,12,1,43.66577,2.156334,366.5768,0,0,412.3989,0,0,0,4,0,4,84.2,4.3,0,,0,195,0,0,1.386294,5.273,0,0,0,0,0,0,78.31118,9.242486,1.386294,6.021991,1 11,1,0,0,3,128469,0,10325.68,42.51472,1,12,1,14.74201,0,0,0,271.9754,286.7174,1,0,0,2,0,4,84.2,4.3,0,,0,195,0,0,1.386294,5.273,0,0,0,0,0,0,78.31118,9.242486,1.386294,5.658497,1 11,1,0,0,4,128469,0,10325.68,43.51472,1,12,1,15.9526,0,15.9526,0,0,31.9052,0,0,0,1,0,4,84.2,4.3,0,,0,195,0,0,1.386294,5.273,0,0,0,0,0,0,78.31118,9.242486,1.386294,3.462769,1 11,1,0,0,5,128469,0,10325.68,44.51472,1,12,1,45.85244,5.814923,0,0,0,51.66736,0,0,0,2,0,3,84.2,4.3,0,,0,195,0,0,1.098612,5.273,0,0,0,0,0,0,78.31118,9.242486,1.098612,3.944826,1 11,1,0,0,1,128470,0,10325.68,40.4627,0,11,1,98.0742,16.16608,0,0,0,114.2403,0,0,0,7,1,4,83.2,0,0,,0,195,0,0,1.386294,5.273,0,0,0,0,0,0,73.53505,9.242486,1.386294,4.738304,1 11,1,0,0,2,128470,0,10325.68,41.4627,0,11,1,5.390836,0,0,0,0,5.390836,0,0,0,1,0,4,83.2,0,0,,0,195,0,0,1.386294,5.273,0,0,0,0,0,0,73.53505,9.242486,1.386294,1.6847,1 11,1,0,0,3,128470,0,10325.68,42.4627,0,11,1,269.7789,1.891892,29.27273,0,0,300.9435,0,0,0,2,13,4,83.2,0,0,,0,195,0,0,1.386294,5.273,0,0,0,0,0,0,73.53505,9.242486,1.386294,5.706923,1 11,1,0,0,4,128470,0,10325.68,43.4627,0,11,1,209.6627,0,0,0,0,209.6627,0,0,0,1,18,4,83.2,0,0,,0,195,0,0,1.386294,5.273,0,0,0,0,0,0,73.53505,9.242486,1.386294,5.3455,1 11,1,0,0,5,128470,0,10325.68,44.4627,0,11,1,125.2188,.2084202,0,0,0,125.4273,0,0,0,4,0,3,83.2,0,0,,0,195,0,0,1.098612,5.273,0,0,0,0,0,0,73.53505,9.242486,1.098612,4.831726,1 11,1,0,0,1,128471,0,10325.68,15.37851,0,12,1,14.13428,4.240283,0,0,0,18.37456,0,0,0,2,0,4,83.2,0,0,,0,195,1,0,1.386294,5.273,0,0,0,0,0,0,80.31274,9.242486,1.386294,2.910967,1 11,1,0,0,2,128471,0,10325.68,16.37851,0,12,1,33.42318,2.156334,0,0,0,35.57951,0,0,0,3,0,4,83.2,0,0,,0,195,1,0,1.386294,5.273,0,0,0,0,0,0,80.31274,9.242486,1.386294,3.57177,1 11,1,0,0,3,128471,0,10325.68,17.37851,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,83.2,0,0,,0,195,1,0,1.386294,5.273,0,0,0,0,0,0,80.31274,9.242486,1.386294,,0 11,1,0,0,4,128471,0,10325.68,18.37851,0,12,1,25.06837,0,0,0,0,25.06837,0,0,0,4,0,4,83.2,0,0,,0,195,0,0,1.386294,5.273,0,0,0,0,0,0,80.31274,9.242486,1.386294,3.221607,1 11,1,0,0,5,128471,0,10325.68,19.37851,0,12,1,31.26303,0,0,0,0,31.26303,0,0,0,1,0,3,83.2,0,0,,0,195,0,0,1.098612,5.273,0,0,0,0,0,0,80.31274,9.242486,1.098612,3.442436,1 7,1,25,0,1,128493,0,11517.37,12.82957,1,12,1,17.07892,1.177856,0,0,0,18.25677,0,0,0,3,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,73.87948,9.351699,1.386294,2.904536,1 7,1,25,0,2,128493,0,11517.37,13.82957,1,12,1,33.96227,0,0,0,0,33.96227,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,73.87948,9.351699,1.386294,3.52525,1 7,1,25,0,3,128493,0,11517.37,14.82957,1,12,1,21.62162,.982801,0,0,0,22.60442,0,0,0,4,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,73.87948,9.351699,1.386294,3.118146,1 7,1,25,0,4,128493,0,11517.37,15.82957,1,12,1,37.60255,0,32.38833,0,0,69.99088,0,0,0,4,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,73.87948,9.351699,1.386294,4.248365,1 7,1,25,0,5,128493,0,11517.37,16.82957,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,73.87948,9.351699,1.386294,,0 7,1,25,0,1,128494,0,11517.37,38.95414,0,10,1,50.05889,1.177856,0,0,0,51.23675,0,0,0,2,0,4,82.5,13.73189,1,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,71.52279,9.351699,1.386294,3.936457,1 7,1,25,0,2,128494,0,11517.37,39.95414,0,10,1,0,0,0,0,0,0,0,0,0,0,0,4,82.5,13.73189,1,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,71.52279,9.351699,1.386294,,0 7,1,25,0,3,128494,0,11517.37,40.95414,0,10,1,12.28501,0,28.99263,0,0,41.27764,0,0,0,1,0,4,82.5,13.73189,1,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,71.52279,9.351699,1.386294,3.720321,1 7,1,25,0,4,128494,0,11517.37,41.95414,0,10,1,0,0,0,0,0,0,0,0,0,0,0,4,82.5,13.73189,1,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,71.52279,9.351699,1.386294,,0 7,1,25,0,5,128494,0,11517.37,42.95414,0,10,1,172.5719,0,37.09879,0,0,209.6707,0,0,0,4,4,4,82.5,13.73189,1,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,71.52279,9.351699,1.386294,5.345538,1 7,1,25,0,1,128495,0,11517.37,10.46133,1,12,1,9.422851,6.919906,0,0,0,16.34276,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,76.19097,9.351699,1.386294,2.793785,1 7,1,25,0,2,128495,0,11517.37,11.46133,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,76.19097,9.351699,1.386294,,0 7,1,25,0,3,128495,0,11517.37,12.46133,1,12,1,8.845209,0,0,0,0,8.845209,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,76.19097,9.351699,1.386294,2.179876,1 7,1,25,0,4,128495,0,11517.37,13.46133,1,12,1,10.25524,0,0,0,0,10.25524,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,76.19097,9.351699,1.386294,2.327789,1 7,1,25,0,5,128495,0,11517.37,14.46133,1,12,1,8.336807,0,0,0,0,8.336807,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,1,0,0,76.19097,9.351699,1.386294,2.12068,1 7,1,25,0,1,128496,0,11517.37,34.08624,1,12,1,283.2744,67.55595,27.67962,0,0,378.51,0,0,0,19,0,4,80,13.73189,1,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,1,0,56.49276,9.351699,1.386294,5.936243,1 7,1,25,0,2,128496,0,11517.37,35.08624,1,12,1,76.54987,32.19946,0,0,0,108.7493,0,0,0,11,0,4,80,13.73189,1,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,1,0,56.49276,9.351699,1.386294,4.689045,1 7,1,25,0,3,128496,0,11517.37,36.08624,1,12,1,40.29484,20.93366,0,0,0,61.2285,0,0,0,8,0,4,80,13.73189,1,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,1,0,56.49276,9.351699,1.386294,4.114613,1 7,1,25,0,4,128496,0,11517.37,37.08624,1,12,1,20.96627,0,0,0,0,20.96627,0,0,0,1,1,4,80,13.73189,1,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,1,0,56.49276,9.351699,1.386294,3.042915,1 7,1,25,0,5,128496,0,11517.37,38.08624,1,12,1,32.51355,4.997916,26.5694,0,0,64.08086,0,0,0,3,0,4,80,13.73189,1,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,1,0,56.49276,9.351699,1.386294,4.160146,1 10,1,50,0,1,128497,0,10301.49,7.545517,0,9,1,8.833922,0,0,0,0,8.833922,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,84.4333,9.240141,1.791759,2.178599,1 10,1,50,0,2,128497,0,10301.49,8.545517,0,9,1,90.02695,0,0,0,173.5094,263.5364,1,0,0,2,2,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,84.4333,9.240141,1.791759,5.574192,1 10,1,50,0,1,128498,0,10301.49,27.53183,1,9,1,30.03534,5.300354,0,0,0,35.33569,0,0,0,4,0,6,65,13.73189,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,63.61448,9.240141,1.791759,3.564893,1 10,1,50,0,2,128498,0,10301.49,28.53183,1,9,1,14.01617,1.617251,29.6496,0,0,45.28302,0,0,0,1,0,6,65,13.73189,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,63.61448,9.240141,1.791759,3.812932,1 10,1,50,0,1,128499,0,10301.49,10.04517,1,9,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,83.91933,9.240141,1.791759,,0 10,1,50,0,2,128499,0,10301.49,11.04517,1,9,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,83.91933,9.240141,1.791759,,0 10,1,50,0,1,128500,0,10301.49,11.32101,0,9,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,84.4333,9.240141,1.791759,,0 10,1,50,0,2,128500,0,10301.49,12.32101,0,9,1,7.008086,0,0,0,0,7.008086,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,84.4333,9.240141,1.791759,1.947065,1 10,1,50,0,1,128501,0,10301.49,4.911705,1,9,1,101.2956,0,0,0,0,101.2956,0,0,0,4,2,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,80.4877,9.240141,1.791759,4.618043,1 10,1,50,0,2,128501,0,10301.49,5.911705,1,9,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,1000,1000,1,1,1.791759,6.907755,0,3.931826,7.600903,0,0,0,80.4877,9.240141,1.791759,,0 10,1,50,0,1,128502,0,10301.49,31.90417,0,8,1,8.462897,16.66078,0,0,0,25.12367,0,0,0,0,0,6,90,13.73189,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,61.55907,9.240141,1.791759,3.223811,1 10,1,50,0,2,128502,0,10301.49,32.90417,0,8,1,229.3801,2.32345,0,0,0,231.7035,0,0,0,2,1,6,90,13.73189,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,1,0,0,61.55907,9.240141,1.791759,5.445458,1 11,1,0,1,1,128520,0,9861.166,15.50171,0,12,1,19.63117,0,36.68055,0,0,56.31172,0,0,0,1,1,6,98.9,13,0,,0,196,1,0,1.791759,5.278115,0,0,0,0,0,0,80.40273,9.196461,1.791759,4.030903,1 11,1,0,1,2,128520,0,9861.166,16.50171,0,12,1,9.798585,1.633097,0,0,0,11.43168,0,0,0,2,0,6,98.9,13,0,,0,196,1,0,1.791759,5.278115,0,0,0,0,0,0,80.40273,9.196461,1.791759,2.436388,1 11,1,0,1,3,128520,0,9861.166,17.50171,0,12,1,53.51833,14.49455,0,0,0,68.01289,0,0,0,5,0,6,98.9,13,0,,0,196,1,0,1.791759,5.278115,0,0,0,0,0,0,80.40273,9.196461,1.791759,4.219697,1 11,1,0,1,4,128520,0,9861.166,18.50171,0,12,1,219.0225,36.85177,19.66498,0,0,275.5392,0,0,0,3,1,6,98.9,13,0,,0,196,0,0,1.791759,5.278115,0,0,0,0,0,0,80.40273,9.196461,1.791759,5.61873,1 11,1,0,1,5,128520,0,9861.166,19.50171,0,12,1,33.65587,27.34539,0,0,0,61.00126,0,0,0,0,0,6,98.9,13,0,,0,196,0,0,1.791759,5.278115,0,0,0,0,0,0,80.40273,9.196461,1.791759,4.110895,1 11,1,0,1,1,128521,0,9861.166,8.960985,1,12,1,27.95955,7.346817,0,0,0,35.30637,0,0,0,4,0,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,0,0,0,84.62004,9.196461,1.791759,3.564063,1 11,1,0,1,2,128521,0,9861.166,9.960985,1,12,1,16.33097,3.701688,0,0,0,20.03266,0,0,0,3,0,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,0,0,0,84.62004,9.196461,1.791759,2.997364,1 11,1,0,1,3,128521,0,9861.166,10.96099,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,0,0,0,84.62004,9.196461,1.791759,,0 11,1,0,1,4,128521,0,9861.166,11.96099,1,12,1,11.93208,0,0,0,0,11.93208,0,0,0,1,1,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,0,0,0,84.62004,9.196461,1.791759,2.47923,1 11,1,0,1,5,128521,0,9861.166,12.96099,1,12,1,18.93143,0,0,0,0,18.93143,0,0,0,2,0,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,0,0,0,84.62004,9.196461,1.791759,2.940823,1 11,1,0,1,1,128522,0,9861.166,11.76454,1,12,1,224.0631,213.028,51.08864,0,0,488.1797,0,0,0,20,0,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,1,0,0,74.44305,9.196461,1.791759,6.190683,1 11,1,0,1,2,128522,0,9861.166,12.76454,1,12,1,44.09363,98.44855,0,0,319.4883,462.0305,1,0,0,9,0,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,1,0,0,74.44305,9.196461,1.791759,6.135631,1 11,1,0,1,3,128522,0,9861.166,13.76454,1,12,1,127.8494,71.67988,0,0,0,199.5292,0,0,0,26,0,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,1,0,0,74.44305,9.196461,1.791759,5.295961,1 11,1,0,1,4,128522,0,9861.166,14.76454,1,12,1,114.5021,82.07893,.6883892,0,407.8476,605.117,1,0,0,28,1,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,1,0,0,74.44305,9.196461,1.791759,6.405422,1 11,1,0,1,5,128522,0,9861.166,15.76454,1,12,1,225.6458,82.06563,0,0,0,307.7114,0,0,0,33,0,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,1,0,0,74.44305,9.196461,1.791759,5.729162,1 11,1,0,1,1,128523,0,9861.166,41.42368,0,12,1,151.6954,39.64902,36.68055,0,1444.325,1672.35,2,0,0,13,1,6,100,8.7,0,,0,196,0,0,1.791759,5.278115,0,0,0,0,0,0,76.77452,9.196461,1.791759,7.421985,1 11,1,0,1,2,128523,0,9861.166,42.42368,0,12,1,91.99783,33.043,0,0,0,125.0408,0,0,0,11,0,6,100,8.7,0,,0,196,0,0,1.791759,5.278115,0,0,0,0,0,0,76.77452,9.196461,1.791759,4.82864,1 11,1,0,1,3,128523,0,9861.166,43.42368,0,12,1,95.14371,26.53617,0,0,0,121.6799,0,0,0,12,0,6,100,8.7,0,,0,196,0,0,1.791759,5.278115,0,0,0,0,0,0,76.77452,9.196461,1.791759,4.801394,1 11,1,0,1,4,128523,0,9861.166,44.42368,0,12,1,55.98899,34.69481,0,0,0,90.6838,0,0,0,7,0,6,100,8.7,0,,0,196,0,0,1.791759,5.278115,0,0,0,0,0,0,76.77452,9.196461,1.791759,4.507379,1 11,1,0,1,5,128523,0,9861.166,45.42368,0,12,1,147.1435,32.96172,36.04544,0,0,216.1506,0,0,0,16,0,6,100,8.7,0,,0,196,0,0,1.791759,5.278115,0,0,0,0,0,0,76.77452,9.196461,1.791759,5.375976,1 11,1,0,1,1,128524,0,9861.166,39.96167,1,12,1,42.23676,22.57585,24.98513,0,0,89.79774,0,0,0,6,0,6,77.9,8.7,0,,0,196,0,0,1.791759,5.278115,0,0,0,0,0,0,79.44787,9.196461,1.791759,4.49756,1 11,1,0,1,2,128524,0,9861.166,40.96167,1,12,1,193.5493,5.770278,21.62221,0,0,220.9418,0,0,0,3,1,6,77.9,8.7,0,,0,196,0,0,1.791759,5.278115,0,0,0,0,0,0,79.44787,9.196461,1.791759,5.397899,1 11,1,0,1,3,128524,0,9861.166,41.96167,1,12,1,48.06739,8.671952,0,0,0,56.73935,0,0,0,6,0,6,77.9,8.7,0,,0,196,0,0,1.791759,5.278115,0,0,0,0,0,0,79.44787,9.196461,1.791759,4.038468,1 11,1,0,1,4,128524,0,9861.166,42.96167,1,12,1,64.70858,17.37035,53.7173,0,0,135.7962,0,0,0,7,1,6,77.9,8.7,0,,0,196,0,0,1.791759,5.278115,0,0,0,0,0,0,79.44787,9.196461,1.791759,4.911156,1 11,1,0,1,5,128524,0,9861.166,43.96167,1,12,1,251.6702,37.54733,31.15692,0,0,320.3744,0,0,0,6,0,6,77.9,8.7,0,,0,196,0,0,1.791759,5.278115,0,0,0,0,0,0,79.44787,9.196461,1.791759,5.76949,1 11,1,0,1,1,128525,0,9861.166,10.65571,1,12,1,19.63117,1.784652,0,0,0,21.41582,0,0,0,2,0,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,0,0,0,84.62004,9.196461,1.791759,3.06413,1 11,1,0,1,2,128525,0,9861.166,11.65571,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,0,0,0,84.62004,9.196461,1.791759,,0 11,1,0,1,3,128525,0,9861.166,12.65571,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,0,0,0,84.62004,9.196461,1.791759,,0 11,1,0,1,4,128525,0,9861.166,13.65571,1,12,1,35.79624,.9178522,0,0,0,36.71409,0,0,0,3,1,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,0,0,0,84.62004,9.196461,1.791759,3.603161,1 11,1,0,1,5,128525,0,9861.166,14.65571,1,12,1,22.71771,0,0,0,0,22.71771,0,0,0,3,0,6,74.36826,13.73189,0,,0,196,1,1,1.791759,5.278115,0,0,0,0,0,0,84.62004,9.196461,1.791759,3.123145,1 5,1,25,0,1,128550,1,5445.176,5.004791,1,14,1,100.2698,0,0,0,464.0707,564.3405,1,0,0,2,0,3,74.36826,13.73189,0,,359,359,1,1,1.098612,5.883322,0,3.258096,7.269617,1,0,0,76.07727,8.602669,1.098612,6.335658,1 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9,1,50,1,1,128759,0,11526.05,37.77139,1,12,1,11.99041,4.376499,27.56595,0,961.0971,1005.03,1,0,0,1,0,5,80,8.7,0,,1000,1000,0,0,1.609438,6.907755,0,3.931826,7.600903,0,0,0,78.54103,9.352452,1.609438,6.912773,1 9,1,50,1,2,128759,0,11526.05,38.77139,1,12,1,10.9529,0,0,0,0,10.9529,0,0,0,1,0,6,80,8.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,78.54103,9.352452,1.791759,2.393605,1 9,1,50,1,3,128759,0,11526.05,39.77139,1,12,1,18.70324,0,0,0,0,18.70324,0,0,0,2,0,6,80,8.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,78.54103,9.352452,1.791759,2.928697,1 9,1,50,1,4,128759,0,11526.05,40.77139,1,12,1,7.837713,0,0,0,0,7.837713,0,0,0,0,0,6,80,8.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,78.54103,9.352452,1.791759,2.058947,1 9,1,50,1,5,128759,0,11526.05,41.77139,1,12,1,194.2023,11.91282,35.01904,0,0,241.1342,0,0,0,4,9,6,80,8.7,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,78.54103,9.352452,1.791759,5.485353,1 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9,1,50,1,1,128761,0,11526.05,36.88706,0,18,1,57.85372,8.033573,38.21943,0,0,104.1067,0,0,0,3,0,5,71.6,0,0,,1000,1000,0,0,1.609438,6.907755,0,3.931826,7.600903,0,0,0,79.00905,9.352452,1.609438,4.645416,1 9,1,50,1,2,128761,0,11526.05,37.88706,0,18,1,41.07338,7.420591,0,0,0,48.49398,0,0,0,0,3,6,71.6,0,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,79.00905,9.352452,1.791759,3.88144,1 9,1,50,1,3,128761,0,11526.05,38.88706,0,18,1,47.38155,0,0,0,257.6559,305.0374,1,0,0,2,0,6,71.6,0,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,79.00905,9.352452,1.791759,5.720435,1 9,1,50,1,4,128761,0,11526.05,39.88706,0,18,1,0,0,0,0,0,0,0,0,0,0,0,6,71.6,0,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,79.00905,9.352452,1.791759,,0 9,1,50,1,5,128761,0,11526.05,40.88706,0,18,1,13.11892,0,27.74016,0,0,40.85908,0,0,0,1,0,6,71.6,0,0,,1000,1000,0,0,1.791759,6.907755,0,3.931826,7.600903,0,0,0,79.00905,9.352452,1.791759,3.710129,1 2,1,100,1,1,128767,0,9549.008,32.92539,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,80,13,0,,900,900,0,0,1.386294,6.802395,1,0,0,0,0,0,77.67306,9.164297,1.386294,,0 2,1,100,1,2,128767,0,9549.008,33.92539,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,80,13,0,,900,900,0,0,1.386294,6.802395,1,0,0,0,0,0,77.67306,9.164297,1.386294,,0 2,1,100,1,3,128767,0,9549.008,34.92539,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,80,13,0,,900,900,0,0,1.386294,6.802395,1,0,0,0,0,0,77.67306,9.164297,1.386294,,0 2,1,100,1,1,128768,0,9549.008,29.96852,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,84.2,13,0,,900,900,0,0,1.386294,6.802395,1,0,0,0,0,0,79.50489,9.164297,1.386294,,0 2,1,100,1,2,128768,0,9549.008,30.96852,1,12,1,24.49646,0,0,0,0,24.49646,0,0,0,1,0,4,84.2,13,0,,900,900,0,0,1.386294,6.802395,1,0,0,0,0,0,79.50489,9.164297,1.386294,3.198529,1 2,1,100,1,3,128768,0,9549.008,31.96852,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,84.2,13,0,,900,900,0,0,1.386294,6.802395,1,0,0,0,0,0,79.50489,9.164297,1.386294,,0 2,1,100,1,1,128769,0,9549.008,9.245722,0,12,1,35.69304,6.71624,0,0,0,42.40928,0,0,0,3,0,4,74.36826,13.73189,0,,900,900,1,0,1.386294,6.802395,1,0,0,0,0,0,85.34759,9.164297,1.386294,3.747367,1 2,1,100,1,2,128769,0,9549.008,10.24572,0,12,1,4.899292,1.061513,0,0,0,5.960806,0,0,0,1,0,4,74.36826,13.73189,0,,900,900,1,0,1.386294,6.802395,1,0,0,0,0,0,85.34759,9.164297,1.386294,1.785206,1 2,1,100,1,3,128769,0,9549.008,11.24572,0,12,1,7.433102,4.658077,0,0,0,12.09118,0,0,0,1,0,4,74.36826,13.73189,0,,900,900,1,0,1.386294,6.802395,1,0,0,0,0,0,85.34759,9.164297,1.386294,2.492476,1 2,1,100,1,1,128770,0,9549.008,12.4052,1,12,1,16.65675,.9518144,0,0,0,17.60857,0,0,0,1,0,4,74.36826,13.73189,0,,900,900,1,1,1.386294,6.802395,1,0,0,0,0,0,84.83361,9.164297,1.386294,2.868386,1 2,1,100,1,2,128770,0,9549.008,13.4052,1,12,1,6.53239,0,0,0,0,6.53239,0,0,0,1,0,4,74.36826,13.73189,0,,900,900,1,1,1.386294,6.802395,1,0,0,0,0,0,84.83361,9.164297,1.386294,1.876773,1 2,1,100,1,3,128770,0,9549.008,14.4052,1,12,1,22.29931,0,0,0,0,22.29931,0,0,0,1,0,4,74.36826,13.73189,0,,900,900,1,1,1.386294,6.802395,1,0,0,0,0,0,84.83361,9.164297,1.386294,3.104556,1 6,1,25,1,1,128771,0,17027.92,30.54346,0,17,1,35.09816,0,34.19393,0,0,69.29209,0,0,0,2,0,3,90.5,8.7,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,79.23241,9.742668,1.098612,4.238331,1 6,1,25,1,2,128771,0,17027.92,31.54346,0,17,1,6.53239,4.654328,0,0,0,11.18672,0,0,0,1,0,4,90.5,8.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.23241,9.742668,1.386294,2.414727,1 6,1,25,1,3,128771,0,17027.92,32.54346,0,17,1,19.32607,8.414271,28.99901,0,0,56.73935,0,0,0,2,0,4,90.5,8.7,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.23241,9.742668,1.386294,4.038468,1 6,1,25,1,1,128772,0,17027.92,3.126626,1,15,1,42.23676,34.17609,0,0,0,76.41285,0,0,0,5,0,3,74.36826,13.73189,0,,1000,1000,1,1,1.098612,6.907755,0,3.258096,8.294049,0,0,0,81.77524,9.742668,1.098612,4.336151,1 6,1,25,1,2,128772,0,17027.92,4.126626,1,15,1,268.6445,10.96897,0,0,0,279.6135,0,0,0,22,41,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.77524,9.742668,1.386294,5.633408,1 6,1,25,1,3,128772,0,17027.92,5.126626,1,15,1,280.9713,40.88206,0,0,0,321.8533,0,0,0,41,32,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.258096,8.294049,0,0,0,81.77524,9.742668,1.386294,5.774096,1 6,1,25,1,1,128773,0,17027.92,28.36413,1,15,1,48.1856,19.36347,0,0,731.7133,799.2623,1,0,0,2,0,3,96.8,4.3,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,79.96555,9.742668,1.098612,6.683689,1 6,1,25,1,2,128773,0,17027.92,29.36413,1,15,1,263.2009,17.17474,0,0,2118.759,2399.135,1,0,0,22,0,4,96.8,4.3,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.96555,9.742668,1.386294,7.782863,1 6,1,25,1,3,128773,0,17027.92,30.36413,1,15,1,622.3984,220.7978,0,0,0,843.1962,0,0,0,65,0,4,96.8,4.3,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,79.96555,9.742668,1.386294,6.7372,1 11,1,0,1,1,128808,0,9253.722,31.62218,0,17,1,0,29.71823,0,0,0,29.71823,0,0,0,0,0,3,55.8,8.7,0,,0,192,0,0,1.098612,5.257495,0,0,0,1,0,0,65.66811,9.132889,1.098612,3.391761,1 11,1,0,1,2,128808,0,9253.722,32.62218,0,17,1,113.6364,6.544359,0,21.90581,1063.527,1183.708,1,0,1,2,0,3,55.8,8.7,0,,0,192,0,0,1.098612,5.257495,0,0,0,1,0,0,65.66811,9.132889,1.098612,7.076407,1 11,1,0,1,3,128808,0,9253.722,33.62218,0,17,1,0,0,0,0,0,0,0,0,0,0,0,3,55.8,8.7,0,,0,192,0,0,1.098612,5.257495,0,0,0,1,0,0,65.66811,9.132889,1.098612,,0 11,1,0,1,1,128809,0,9253.722,28.39425,1,12,1,40.76739,3.657074,0,0,0,44.42446,0,0,0,2,1,3,71.6,17.4,0,,0,192,0,0,1.098612,5.257495,0,0,0,1,0,0,71.41678,9.132889,1.098612,3.79379,1 11,1,0,1,2,128809,0,9253.722,29.39425,1,12,1,127.5192,2.135816,0,0,950.0547,1079.71,1,0,0,3,1,3,71.6,17.4,0,,0,192,0,0,1.098612,5.257495,0,0,0,1,0,0,71.41678,9.132889,1.098612,6.984447,1 11,1,0,1,3,128809,0,9253.722,30.39425,1,12,1,29.92519,0,0,0,0,29.92519,0,0,0,1,0,3,71.6,17.4,0,,0,192,0,0,1.098612,5.257495,0,0,0,1,0,0,71.41678,9.132889,1.098612,3.3987,1 11,1,0,1,1,128810,0,9253.722,4.202601,1,12,1,44.96403,3.597122,0,0,0,48.56115,0,0,0,4,0,3,74.36826,13.73189,0,,0,192,1,1,1.098612,5.257495,0,0,0,0,0,0,79.40221,9.132889,1.098612,3.882824,1 11,1,0,1,2,128810,0,9253.722,5.202601,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,0,192,1,1,1.098612,5.257495,0,0,0,0,0,0,79.40221,9.132889,1.098612,,0 11,1,0,1,3,128810,0,9253.722,6.202601,1,12,1,18.95262,3.990025,0,0,0,22.94264,0,0,0,3,0,3,74.36826,13.73189,0,,0,192,1,1,1.098612,5.257495,0,0,0,0,0,0,79.40221,9.132889,1.098612,3.132997,1 11,1,0,1,1,128812,0,13159.43,13.07598,1,12,1,20.98321,3.357314,24.43645,0,0,48.77698,0,0,0,1,1,4,74.36826,13.73189,0,,0,60,1,1,1.386294,4.094345,0,0,0,0,0,0,83.29486,9.48497,1.386294,3.887259,1 11,1,0,1,2,128812,0,13159.43,14.07598,1,12,1,33.40635,8.871851,0,0,0,42.2782,0,0,0,2,0,4,74.36826,13.73189,0,,0,60,1,1,1.386294,4.094345,0,0,0,0,0,0,83.29486,9.48497,1.386294,3.744272,1 11,1,0,1,3,128812,0,13159.43,15.07598,1,12,1,12.46883,12.06983,23.69077,0,0,48.22943,0,0,0,1,0,4,74.36826,13.73189,0,,0,60,1,1,1.386294,4.094345,0,0,0,0,0,0,83.29486,9.48497,1.386294,3.875969,1 11,1,0,1,4,128812,0,13159.43,16.07598,1,12,1,46.10419,7.100046,0,0,0,53.20424,0,0,0,4,0,4,74.36826,13.73189,0,,0,60,1,1,1.386294,4.094345,0,0,0,0,0,0,83.29486,9.48497,1.386294,3.974138,1 11,1,0,1,5,128812,0,13159.43,17.07598,1,12,1,21.37114,6.157427,26.23783,0,0,53.7664,0,0,0,2,0,4,74.36826,13.73189,0,,0,60,1,1,1.386294,4.094345,0,0,0,0,0,0,83.29486,9.48497,1.386294,3.984649,1 11,1,0,1,1,128813,0,13159.43,9.453798,0,12,1,178.0576,62.73981,23.4952,0,534.982,799.2746,1,0,0,34,0,4,74.36826,13.73189,0,,0,60,1,0,1.386294,4.094345,0,0,0,1,0,0,74.60253,9.48497,1.386294,6.683704,1 11,1,0,1,2,128813,0,13159.43,10.4538,0,12,1,94.74261,19.27711,14.23877,0,0,128.2585,0,0,0,22,0,4,74.36826,13.73189,0,,0,60,1,0,1.386294,4.094345,0,0,0,1,0,0,74.60253,9.48497,1.386294,4.854048,1 11,1,0,1,3,128813,0,13159.43,11.4538,0,12,1,157.8554,16.68329,14.46384,0,0,189.0025,0,0,0,31,0,4,74.36826,13.73189,0,,0,60,1,0,1.386294,4.094345,0,0,0,1,0,0,74.60253,9.48497,1.386294,5.24176,1 11,1,0,1,4,128813,0,13159.43,12.4538,0,12,1,59.47441,5.532504,32.9645,0,0,97.97141,0,0,0,4,0,4,74.36826,13.73189,0,,0,60,1,0,1.386294,4.094345,0,0,0,1,0,0,74.60253,9.48497,1.386294,4.584676,1 11,1,0,1,5,128813,0,13159.43,13.4538,0,12,1,116.1659,9.331359,24.65087,0,0,150.1481,0,0,0,7,0,4,74.36826,13.73189,0,,0,60,1,0,1.386294,4.094345,0,0,0,1,0,0,74.60253,9.48497,1.386294,5.011622,1 11,1,0,1,1,128814,0,13159.43,37.65366,1,12,1,32.67386,216.0791,0,119.9041,0,248.753,0,0,5,2,0,4,36.8,17.4,0,,0,60,0,0,1.386294,4.094345,0,0,0,0,0,0,73.39919,9.48497,1.386294,5.51646,1 11,1,0,1,2,128814,0,13159.43,38.65366,1,12,1,48.19277,181.4841,30.66813,150.6024,0,260.345,0,0,6,4,0,4,36.8,17.4,0,,0,60,0,0,1.386294,4.094345,0,0,0,0,0,0,73.39919,9.48497,1.386294,5.562008,1 11,1,0,1,3,128814,0,13159.43,39.65366,1,12,1,48.37905,227.1571,38.65337,256.8578,0,314.1895,0,0,12,2,0,4,36.8,17.4,0,,0,60,0,0,1.386294,4.094345,0,0,0,0,0,0,73.39919,9.48497,1.386294,5.749996,1 11,1,0,1,4,128814,0,13159.43,40.65366,1,12,1,107.8838,207.2845,0,228.2158,2219.751,2534.919,1,0,10,10,0,4,36.8,17.4,0,,0,60,0,0,1.386294,4.094345,0,0,0,0,0,0,73.39919,9.48497,1.386294,7.837917,1 11,1,0,1,5,128814,0,13159.43,41.65366,1,12,1,178.375,130.1523,29.83496,152.3487,0,338.3622,0,0,6,12,0,4,36.8,17.4,0,,0,60,0,0,1.386294,4.094345,0,0,0,0,0,0,73.39919,9.48497,1.386294,5.824117,1 11,1,0,1,1,128815,0,13159.43,40.26831,0,16,1,189.7482,37.33213,31.17506,0,0,258.2554,0,0,0,28,0,4,66.3,13,0,,0,60,0,0,1.386294,4.094345,0,0,0,0,0,0,73.36005,9.48497,1.386294,5.553949,1 11,1,0,1,2,128815,0,13159.43,41.26831,0,16,1,47.64513,26.58817,18.07229,54.76451,0,92.30559,0,0,2,9,0,4,66.3,13,0,,0,60,0,0,1.386294,4.094345,0,0,0,0,0,0,73.36005,9.48497,1.386294,4.525105,1 11,1,0,1,3,128815,0,13159.43,42.26831,0,16,1,14.96259,7.306733,34.16459,296.7581,0,56.43391,0,0,13,1,0,4,66.3,13,0,,0,60,0,0,1.386294,4.094345,0,0,0,0,0,0,73.36005,9.48497,1.386294,4.03307,1 11,1,0,1,4,128815,0,13159.43,43.26831,0,16,1,65.00691,16.41309,23.0521,0,0,104.4721,0,0,0,9,0,4,66.3,13,0,,0,60,0,0,1.386294,4.094345,0,0,0,0,0,0,73.36005,9.48497,1.386294,4.64892,1 11,1,0,1,5,128815,0,13159.43,44.26831,0,16,1,139.5472,27.06306,45.28142,0,0,211.8917,0,0,0,24,0,4,66.3,13,0,,0,60,0,0,1.386294,4.094345,0,0,0,0,0,0,73.36005,9.48497,1.386294,5.356075,1 11,1,0,1,1,128840,0,4372.829,58.75154,1,16,1,46.76259,107.7998,0,0,0,154.5623,0,0,0,6,0,1,68.4,17.4,0,,0,258,0,0,0,5.552959,0,0,0,1,0,0,66.1049,8.383394,0,5.040597,1 11,1,0,1,2,128840,0,4372.829,59.75154,1,16,1,36.14458,49.2333,52.65608,0,0,138.034,0,0,0,5,0,1,68.4,17.4,0,,0,258,0,0,0,5.552959,0,0,0,1,0,0,66.1049,8.383394,0,4.9275,1 11,1,0,1,3,128840,0,4372.829,60.75154,1,16,1,68.82793,63.85536,0,0,0,132.6833,0,0,0,6,0,1,68.4,17.4,0,,0,258,0,0,0,5.552959,0,0,0,1,0,0,66.1049,8.383394,0,4.887965,1 11,1,0,1,4,128840,0,4372.829,61.75154,1,16,1,95.43568,64.47672,0,0,0,159.9124,0,0,0,11,0,1,68.4,17.4,0,,0,258,0,0,0,5.552959,0,0,0,1,0,0,66.1049,8.383394,0,5.074626,1 11,1,0,1,5,128840,0,4372.829,62.75154,1,16,1,477.8671,66.08125,4.159966,0,0,548.1083,0,0,0,10,0,1,68.4,17.4,0,,0,258,0,0,0,5.552959,0,0,0,1,0,0,66.1049,8.383394,0,6.306473,1 11,1,0,0,1,128865,0,15260.55,36.5421,1,17,1,38.57479,40.97173,0,0,0,79.54652,0,0,0,4,0,4,57.9,13,0,,0,84,0,0,1.386294,4.430817,0,0,0,0,0,0,79.29243,9.633092,1.386294,4.376342,1 11,1,0,0,2,128865,0,15260.55,37.5421,1,17,1,63.34232,40.48518,26.95418,0,0,130.7817,0,0,0,4,0,4,57.9,13,0,,0,84,0,0,1.386294,4.430817,0,0,0,0,0,0,79.29243,9.633092,1.386294,4.873529,1 11,1,0,0,3,128865,0,15260.55,38.5421,1,17,1,244.5946,27.64128,12.77641,0,0,285.0123,0,0,0,5,0,4,57.9,13,0,,0,84,0,0,1.386294,4.430817,0,0,0,0,0,0,79.29243,9.633092,1.386294,5.652532,1 11,1,0,0,4,128865,0,15260.55,39.5421,1,17,1,34.41203,18.79216,26.89152,0,0,80.09572,0,0,0,4,0,4,57.9,13,0,,0,84,0,0,1.386294,4.430817,0,0,0,0,0,0,79.29243,9.633092,1.386294,4.383223,1 11,1,0,0,5,128865,0,15260.55,40.5421,1,17,1,142.9762,77.84493,0,0,0,220.8212,0,0,0,10,0,4,57.9,13,0,,0,84,0,0,1.386294,4.430817,0,0,0,0,0,0,79.29243,9.633092,1.386294,5.397353,1 11,1,0,0,1,128866,0,15260.55,14.86379,0,17,1,135.8952,65.41814,30.62426,0,0,231.9376,0,0,0,16,0,4,49.5,13,0,,0,84,1,0,1.386294,4.430817,0,0,0,0,0,0,72.45129,9.633092,1.386294,5.446468,1 11,1,0,0,2,128866,0,15260.55,15.86379,0,17,1,38.81401,54.28571,0,0,0,93.09973,0,0,0,8,0,4,49.5,13,0,,0,84,1,0,1.386294,4.430817,0,0,0,0,0,0,72.45129,9.633092,1.386294,4.533671,1 11,1,0,0,3,128866,0,15260.55,16.86379,0,17,1,30.95823,73.34152,0,0,0,104.2998,0,0,0,7,0,4,49.5,13,0,,0,84,1,0,1.386294,4.430817,0,0,0,0,0,0,72.45129,9.633092,1.386294,4.647269,1 11,1,0,0,4,128866,0,15260.55,17.86379,0,17,1,26.89152,36.98724,0,0,0,63.87876,0,0,0,5,0,4,49.5,13,0,,0,84,1,0,1.386294,4.430817,0,0,0,0,0,0,72.45129,9.633092,1.386294,4.156987,1 11,1,0,0,5,128866,0,15260.55,18.86379,0,17,1,81.86327,33.38891,12.50521,0,0,127.7574,0,0,0,7,1,4,49.5,13,0,,0,84,0,0,1.386294,4.430817,0,0,0,0,0,0,72.45129,9.633092,1.386294,4.850133,1 11,1,0,0,1,128867,0,15260.55,42.35455,0,17,1,35.48292,13.82803,0,0,0,49.31096,0,0,0,4,0,4,71.6,13,0,,0,84,0,0,1.386294,4.430817,0,0,0,0,0,0,76.61908,9.633092,1.386294,3.898146,1 11,1,0,0,2,128867,0,15260.55,43.35455,0,17,1,13.47709,0,29.11051,0,0,42.5876,0,0,0,1,0,4,71.6,13,0,,0,84,0,0,1.386294,4.430817,0,0,0,0,0,0,76.61908,9.633092,1.386294,3.751563,1 11,1,0,0,3,128867,0,15260.55,44.35455,0,17,1,30.58968,24.00491,0,0,0,54.59459,0,0,0,4,0,4,71.6,13,0,,0,84,0,0,1.386294,4.430817,0,0,0,0,0,0,76.61908,9.633092,1.386294,3.999935,1 11,1,0,0,4,128867,0,15260.55,45.35455,0,17,1,55.6062,31.95078,36.00729,0,0,123.5643,0,0,0,4,0,4,71.6,13,0,,0,84,0,0,1.386294,4.430817,0,0,0,0,0,0,76.61908,9.633092,1.386294,4.816761,1 11,1,0,0,5,128867,0,15260.55,46.35455,0,17,1,87.11964,7.23218,0,0,0,94.35181,0,0,0,2,0,4,71.6,13,0,,0,84,0,0,1.386294,4.430817,0,0,0,0,0,0,76.61908,9.633092,1.386294,4.54703,1 11,1,0,0,1,128868,0,15260.55,11.75633,1,17,1,50.05889,5.65371,31.38987,0,0,87.10247,0,0,0,4,0,4,74.36826,13.73189,0,,0,84,1,1,1.386294,4.430817,0,0,0,1,0,0,80.09667,9.633092,1.386294,4.467085,1 11,1,0,0,2,128868,0,15260.55,12.75633,1,17,1,71.15903,83.95148,12.93801,0,0,168.0485,0,0,0,11,0,4,74.36826,13.73189,0,,0,84,1,1,1.386294,4.430817,0,0,0,1,0,0,80.09667,9.633092,1.386294,5.124253,1 11,1,0,0,3,128868,0,15260.55,13.75633,1,17,1,88.57494,168.7568,12.77641,0,0,270.1081,0,0,0,13,0,4,74.36826,13.73189,0,,0,84,1,1,1.386294,4.430817,0,0,0,1,0,0,80.09667,9.633092,1.386294,5.598822,1 11,1,0,0,4,128868,0,15260.55,14.75633,1,17,1,34.82224,135.8022,0,0,0,170.6244,0,0,0,6,0,4,74.36826,13.73189,0,,0,84,1,1,1.386294,4.430817,0,0,0,1,0,0,80.09667,9.633092,1.386294,5.139465,1 11,1,0,0,5,128868,0,15260.55,15.75633,1,17,1,57.31555,188.1617,23.34306,0,0,268.8203,0,0,0,9,0,4,74.36826,13.73189,0,,0,84,1,1,1.386294,4.430817,0,0,0,1,0,0,80.09667,9.633092,1.386294,5.594043,1 11,1,0,0,1,128869,0,18811.16,11.55647,0,12,1,57.71496,2.944641,0,0,0,60.6596,0,0,0,5,0,5,74.36826,13.73189,0,,0,0,1,0,1.609438,0,0,0,0,0,0,0,85.46126,9.842258,1.609438,4.105278,1 11,1,0,0,2,128869,0,18811.16,12.55647,0,12,1,37.19677,2.156334,0,0,0,39.3531,0,0,0,2,0,5,74.36826,13.73189,0,,0,0,1,0,1.609438,0,0,0,0,0,0,0,85.46126,9.842258,1.609438,3.672575,1 11,1,0,0,3,128869,0,18811.16,13.55647,0,12,1,95.15971,15.70025,0,0,0,110.8599,0,0,0,9,0,5,74.36826,13.73189,0,,0,0,1,0,1.609438,0,0,0,0,0,0,0,85.46126,9.842258,1.609438,4.708268,1 11,1,0,0,1,128870,0,18811.16,50.33812,1,12,1,247.3498,30.50648,0,0,0,277.8563,0,0,0,5,1,5,61.3,13.73189,0,,0,0,0,0,1.609438,0,0,0,0,1,0,0,71.26979,9.842258,1.609438,5.627104,1 11,1,0,0,2,128870,0,18811.16,51.33812,1,12,1,28.57143,28.32884,52.39353,0,0,109.2938,0,0,0,2,0,5,61.3,13.73189,0,,0,0,0,0,1.609438,0,0,0,0,1,0,0,71.26979,9.842258,1.609438,4.69404,1 11,1,0,0,3,128870,0,18811.16,52.33812,1,12,1,420.4423,83.63636,28.97789,0,0,533.0565,0,0,0,12,0,5,61.3,13.73189,0,,0,0,0,0,1.609438,0,0,0,0,1,0,0,71.26979,9.842258,1.609438,6.278627,1 11,1,0,0,1,128872,0,18811.16,16.14511,0,12,1,50.64782,14.28151,0,0,0,64.92933,0,0,0,3,0,5,66.3,13.73189,0,,0,0,1,0,1.609438,0,0,0,0,0,0,0,79.76973,9.842258,1.609438,4.173299,1 11,1,0,0,2,128872,0,18811.16,17.14511,0,12,1,53.63881,8.247978,30.42048,0,0,92.30727,0,0,0,8,0,5,66.3,13.73189,0,,0,0,1,0,1.609438,0,0,0,0,0,0,0,79.76973,9.842258,1.609438,4.525123,1 11,1,0,0,3,128872,0,18811.16,18.14511,0,12,1,66.09337,38.13268,12.32432,0,0,116.5504,0,0,0,18,0,5,66.3,13.73189,0,,0,0,0,0,1.609438,0,0,0,0,0,0,0,79.76973,9.842258,1.609438,4.758324,1 11,1,0,0,1,128873,0,18811.16,50.37098,0,16,1,14.7232,0,22.15548,0,0,36.87868,0,0,0,1,0,5,83.8,13.73189,0,,0,0,0,0,1.609438,0,0,0,0,0,0,0,76.56006,9.842258,1.609438,3.607634,1 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11,1,0,1,5,129074,1,9542.002,14.78987,0,13,1,0,0,0,0,0,0,0,0,0,0,0,10,74.36826,13.73189,0,,0,325,1,0,2.302585,5.783825,0,0,0,0,0,0,81.08335,9.163564,2.302585,,0 11,1,0,1,1,129075,1,9542.002,20.62149,1,13,1,32.97362,28.34532,0,0,0,61.31894,0,0,0,4,0,8,67.4,0,0,,0,325,0,0,2.079442,5.783825,0,0,0,0,0,0,72.91712,9.163564,2.079442,4.116089,1 11,1,0,1,2,129075,1,9542.002,21.62149,1,13,1,37.73275,6.900329,0,0,0,44.63308,0,0,0,4,1,8,67.4,0,0,,0,325,0,0,2.079442,5.783825,0,0,0,0,0,0,72.91712,9.163564,2.079442,3.798475,1 11,1,0,1,3,129075,1,9542.002,22.62149,1,13,1,499.7756,17.60599,0,0,0,517.3815,0,0,0,9,0,9,67.4,0,0,,0,325,0,0,2.197225,5.783825,0,0,0,0,0,0,72.91712,9.163564,2.197225,6.248781,1 11,1,0,1,4,129075,1,9542.002,23.62149,1,13,1,151.2218,14.56893,0,0,0,165.7907,0,0,0,4,0,10,67.4,0,0,,0,325,0,0,2.302585,5.783825,0,0,0,0,0,0,72.91712,9.163564,2.302585,5.110726,1 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11,1,0,1,1,129077,1,9542.002,9.492128,1,13,1,0,0,0,0,0,0,0,0,0,0,0,8,74.36826,13.73189,0,,0,325,1,1,2.079442,5.783825,0,0,0,0,0,0,80.56938,9.163564,2.079442,,0 11,1,0,1,2,129077,1,9542.002,10.49213,1,13,1,3.833516,0,0,0,0,3.833516,0,0,0,1,0,8,74.36826,13.73189,0,,0,325,1,1,2.079442,5.783825,0,0,0,0,0,0,80.56938,9.163564,2.079442,1.343782,1 11,1,0,1,3,129077,1,9542.002,11.49213,1,13,1,9.975062,0,0,0,0,9.975062,0,0,0,1,0,9,74.36826,13.73189,0,,0,325,1,1,2.197225,5.783825,0,0,0,0,0,0,80.56938,9.163564,2.197225,2.300088,1 11,1,0,1,4,129077,1,9542.002,12.49213,1,13,1,0,0,0,0,0,0,0,0,0,0,0,10,74.36826,13.73189,0,,0,325,1,1,2.302585,5.783825,0,0,0,0,0,0,80.56938,9.163564,2.302585,,0 11,1,0,1,5,129077,1,9542.002,13.49213,1,13,1,0,0,0,0,0,0,0,0,0,0,0,10,74.36826,13.73189,0,,0,325,1,1,2.302585,5.783825,0,0,0,0,0,0,80.56938,9.163564,2.302585,,0 11,1,0,1,1,129082,1,5959.057,50.58453,1,9,1,27.95955,31.66568,0,0,0,59.62522,0,0,0,3,1,3,84.2,26.1,1,,0,313,0,0,1.098612,5.746203,0,0,0,0,0,1,52.06449,8.692836,1.098612,4.088078,1 11,1,0,1,2,129082,1,5959.057,51.58453,1,9,1,228.0893,26.40174,0,0,0,254.491,0,0,0,7,10,3,84.2,26.1,1,,0,313,0,0,1.098612,5.746203,0,0,0,0,0,1,52.06449,8.692836,1.098612,5.539266,1 11,1,0,1,3,129082,1,5959.057,52.58453,1,9,1,122.3984,40.05946,26.92765,0,0,189.3855,0,0,0,6,6,3,84.2,26.1,1,,0,313,0,0,1.098612,5.746203,0,0,0,0,0,1,52.06449,8.692836,1.098612,5.243785,1 11,1,0,1,1,129083,1,5959.057,18.05613,1,12.32507,1,35.09816,.594884,0,0,0,35.69304,0,0,0,3,0,3,83.2,17.4,0,,0,313,0,0,1.098612,5.746203,0,0,0,0,1,0,62.13012,8.692836,1.098612,3.574956,1 11,1,0,1,2,129083,1,5959.057,19.05613,1,12.32507,1,69.67883,13.62003,0,0,0,83.29886,0,0,0,8,0,3,83.2,17.4,0,,0,313,0,0,1.098612,5.746203,0,0,0,0,1,0,62.13012,8.692836,1.098612,4.422435,1 11,1,0,1,3,129083,1,5959.057,20.05613,1,12.32507,1,0,0,0,0,0,0,0,0,0,0,0,3,83.2,17.4,0,,0,313,0,0,1.098612,5.746203,0,0,0,0,1,0,62.13012,8.692836,1.098612,,0 11,1,0,1,1,129084,1,5959.057,56,0,2,1,131.1719,67.55502,21.76086,0,1095.604,1316.092,1,0,0,9,1,3,75.8,34.8,1,,0,313,0,0,1.098612,5.746203,0,0,0,0,0,1,60.90429,8.692836,1.098612,7.182422,1 11,1,0,1,2,129084,1,5959.057,57,0,2,1,136.6358,50.28851,0,0,0,186.9243,0,0,0,8,6,3,75.8,34.8,1,,0,313,0,0,1.098612,5.746203,0,0,0,0,0,1,60.90429,8.692836,1.098612,5.230704,1 11,1,0,1,3,129084,1,5959.057,58,0,2,1,66.40238,43.68186,21.74926,0,0,131.8335,0,0,0,6,3,3,75.8,34.8,1,,0,313,0,0,1.098612,5.746203,0,0,0,0,0,1,60.90429,8.692836,1.098612,4.88154,1 11,1,0,0,1,129090,0,4912.531,49.28679,1,11,1,23.55713,55.73027,0,0,0,79.2874,0,0,0,2,0,1,87.5,13.73189,0,,0,0,0,0,0,0,0,0,0,0,0,0,75.54311,8.499748,0,4.373079,1 11,1,0,0,2,129090,0,4912.531,50.28679,1,11,1,80.86253,58.14016,0,0,0,139.0027,0,0,0,9,0,1,87.5,13.73189,0,,0,0,0,0,0,0,0,0,0,0,0,0,75.54311,8.499748,0,4.934494,1 11,1,0,0,3,129090,0,4912.531,51.28679,1,11,1,28.99263,28.7027,48.78624,0,0,106.4816,0,0,0,2,1,1,87.5,13.73189,0,,0,0,0,0,0,0,0,0,0,0,0,0,75.54311,8.499748,0,4.667972,1 11,1,0,0,4,129090,0,4912.531,52.28679,1,11,1,11.8505,29.98177,0,0,0,41.83227,0,0,0,1,0,1,87.5,13.73189,0,,0,0,0,0,0,0,0,0,0,0,0,0,75.54311,8.499748,0,3.733668,1 11,1,0,0,5,129090,0,4912.531,53.28679,1,11,1,27.09462,24.73948,45.30221,0,0,97.13631,0,0,0,4,1,1,87.5,13.73189,0,,0,0,0,0,0,0,0,0,0,0,0,0,75.54311,8.499748,0,4.576115,1 11,1,0,0,1,129091,0,7755.583,21.3963,0,11,1,0,0,0,0,0,0,0,0,0,0,0,1,83.8,13.73189,0,,0,204,0,0,0,5.31812,0,0,0,0,0,0,69.5586,8.956297,0,,0 11,1,0,0,2,129091,0,7755.583,22.3963,0,11,1,0,0,0,0,0,0,0,0,0,0,0,1,83.8,13.73189,0,,0,204,0,0,0,5.31812,0,0,0,0,0,0,69.5586,8.956297,0,,0 11,1,0,0,3,129091,0,7755.583,23.3963,0,11,1,0,0,0,0,0,0,0,0,0,0,0,2,83.8,13.73189,0,,0,204,0,0,.6931472,5.31812,0,0,0,0,0,0,69.5586,8.956297,.6931472,,0 11,1,0,0,4,129091,0,7755.583,24.3963,0,11,1,0,0,0,0,0,0,0,0,0,0,0,2,83.8,13.73189,0,,0,204,0,0,.6931472,5.31812,0,0,0,0,0,0,69.5586,8.956297,.6931472,,0 11,1,0,0,5,129091,0,7755.583,25.3963,0,11,1,14.58941,0,0,0,0,14.58941,0,0,0,1,0,2,83.8,13.73189,0,,0,204,0,0,.6931472,5.31812,0,0,0,0,0,0,69.5586,8.956297,.6931472,2.680296,1 7,1,25,1,1,129103,0,6910.05,5.472964,1,12,1,222.7218,12.71583,0,0,0,235.4377,0,0,0,12,1,4,74.36826,13.73189,0,,224,398,1,1,1.386294,5.986452,0,3.258096,6.79794,0,0,0,76.40307,8.840877,1.386294,5.461446,1 7,1,25,1,2,129103,0,6910.05,6.472964,1,12,1,127.0537,4.742607,0,0,0,131.7963,0,0,0,12,1,4,74.36826,13.73189,0,,224,398,1,1,1.386294,5.986452,0,3.258096,6.79794,0,0,0,76.40307,8.840877,1.386294,4.881258,1 7,1,25,1,3,129103,0,6910.05,7.472964,1,12,1,68.32918,14.43392,0,0,0,82.76309,0,0,0,7,1,4,74.36826,13.73189,0,,224,398,1,1,1.386294,5.986452,0,3.258096,6.79794,0,0,0,76.40307,8.840877,1.386294,4.415982,1 7,1,25,1,1,129104,0,6910.05,38.43943,0,8,1,329.7362,135.4736,28.19544,0,0,493.4053,0,0,0,21,1,4,87.4,30.4,1,,224,398,0,0,1.386294,5.986452,0,3.258096,6.79794,0,0,1,47.57713,8.840877,1.386294,6.201331,1 7,1,25,1,2,129104,0,6910.05,39.43943,0,8,1,134.7207,65.96385,0,0,2631.38,2832.065,1,0,0,10,0,4,87.4,30.4,1,,224,398,0,0,1.386294,5.986452,0,3.258096,6.79794,0,0,1,47.57713,8.840877,1.386294,7.948761,1 7,1,25,1,3,129104,0,6910.05,40.43943,0,8,1,143.8903,14.93766,0,0,0,158.8279,0,0,0,12,0,4,87.4,30.4,1,,224,398,0,0,1.386294,5.986452,0,3.258096,6.79794,0,0,1,47.57713,8.840877,1.386294,5.067822,1 7,1,25,1,1,129105,0,6910.05,33.98768,1,12,1,508.3933,79.76619,41.03717,0,0,629.1967,0,0,0,38,1,4,78.9,26.1,0,,224,398,0,0,1.386294,5.986452,0,3.258096,6.79794,1,0,0,70.62605,8.840877,1.386294,6.444444,1 7,1,25,1,2,129105,0,6910.05,34.98768,1,12,1,277.1084,22.51369,0,0,0,299.6221,0,0,0,13,1,4,78.9,26.1,0,,224,398,0,0,1.386294,5.986452,0,3.258096,6.79794,1,0,0,70.62605,8.840877,1.386294,5.702522,1 7,1,25,1,3,129105,0,6910.05,35.98768,1,12,1,261.3466,23.19701,34.00998,0,538.4988,857.0524,1,0,0,15,0,4,78.9,26.1,0,,224,398,0,0,1.386294,5.986452,0,3.258096,6.79794,1,0,0,70.62605,8.840877,1.386294,6.753499,1 7,1,25,1,1,129106,0,6910.05,8.221766,0,12,1,345.024,44.55635,0,0,210.3777,599.958,1,0,0,35,3,4,74.36826,13.73189,0,,224,398,1,0,1.386294,5.986452,0,3.258096,6.79794,0,0,0,81.70934,8.840877,1.386294,6.39686,1 7,1,25,1,2,129106,0,6910.05,9.221766,0,12,1,289.1566,50.91457,0,0,0,340.0712,0,0,0,46,0,4,74.36826,13.73189,0,,224,398,1,0,1.386294,5.986452,0,3.258096,6.79794,0,0,0,81.70934,8.840877,1.386294,5.829155,1 7,1,25,1,3,129106,0,6910.05,10.22177,0,12,1,253.4414,20.40898,4.912718,0,0,278.7631,0,0,0,31,0,4,74.36826,13.73189,0,,224,398,1,0,1.386294,5.986452,0,3.258096,6.79794,0,0,0,81.70934,8.840877,1.386294,5.630363,1 5,1,25,0,1,129128,0,9542.002,54.53799,1,13,1,79.13669,172.6859,0,0,0,251.8225,0,0,0,13,0,1,53.8,13.73189,1,,278,278,0,0,0,5.627621,0,3.258096,7.013916,0,0,0,71.19215,9.163564,0,5.528725,1 11,1,0,1,1,129131,0,7450.372,20.3039,0,11,1,5.353956,0,0,0,0,5.353956,0,0,0,1,0,3,61.1,8.7,0,,0,0,0,0,1.098612,0,0,0,0,1,0,0,68.49515,8.916154,1.098612,1.677836,1 11,1,0,1,2,129131,0,7450.372,21.3039,0,11,1,22.86336,.7185629,0,0,0,23.58193,0,0,0,2,0,3,61.1,8.7,0,,0,0,0,0,1.098612,0,0,0,0,1,0,0,68.49515,8.916154,1.098612,3.16048,1 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2,1,100,0,1,129419,0,5361.663,20.16153,0,11,1,0,0,0,0,0,0,0,0,0,0,0,3,69.5,8.7,0,,409,0,0,0,1.098612,0,1,0,0,0,0,0,73.19886,8.587215,1.098612,,0 2,1,100,0,2,129419,0,5361.663,21.16153,0,11,1,0,0,0,0,0,0,0,0,0,0,0,3,69.5,8.7,0,,409,0,0,0,1.098612,0,1,0,0,0,0,0,73.19886,8.587215,1.098612,,0 2,1,100,0,3,129419,0,5361.663,22.16153,0,11,1,134.8379,4.528678,24.97257,0,0,164.3392,0,0,0,7,1,3,69.5,8.7,0,,409,0,0,0,1.098612,0,1,0,0,0,0,0,73.19886,8.587215,1.098612,5.101933,1 2,1,100,0,4,129419,0,5361.663,23.16153,0,11,1,7.376671,0,0,0,0,7.376671,0,0,0,1,0,4,69.5,8.7,0,,409,0,0,0,1.386294,0,1,0,0,0,0,0,73.19886,8.587215,1.386294,1.998322,1 2,1,100,0,5,129419,0,5361.663,24.16153,0,11,1,116.8007,0,30.40626,0,0,147.2069,0,0,0,3,1,4,69.5,8.7,0,,409,0,0,0,1.386294,0,1,0,0,0,0,0,73.19886,8.587215,1.386294,4.991839,1 10,1,50,0,1,129425,0,13275.43,1.938398,0,17,1,32.97998,21.76678,0,0,0,54.74676,0,0,0,5,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,78.00792,9.493746,1.386294,4.002718,1 10,1,50,0,2,129425,0,13275.43,2.938398,0,17,1,61.2938,15.55256,0,0,0,76.84636,0,0,0,8,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,78.00792,9.493746,1.386294,4.341808,1 10,1,50,0,3,129425,0,13275.43,3.938398,0,17,1,78.86978,11.86732,0,0,0,90.7371,0,0,0,6,1,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,78.00792,9.493746,1.386294,4.507967,1 10,1,50,0,4,129425,0,13275.43,4.938398,0,17,1,100.7293,42.83956,0,0,393.938,537.5068,1,0,0,11,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,78.00792,9.493746,1.386294,6.286942,1 10,1,50,0,5,129425,0,13275.43,5.938398,0,17,1,33.76407,7.899125,0,0,0,41.66319,0,0,0,5,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,78.00792,9.493746,1.386294,3.729618,1 10,1,50,0,1,129426,0,13275.43,34.79261,0,20,1,7.067138,14.25206,0,0,0,21.3192,0,0,0,1,0,4,51.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,75.16824,9.493746,1.386294,3.059608,1 10,1,50,0,2,129426,0,13275.43,35.79261,0,20,1,11.32076,16.06469,0,0,0,27.38544,0,0,0,1,0,4,51.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,75.16824,9.493746,1.386294,3.310012,1 10,1,50,0,3,129426,0,13275.43,36.79261,0,20,1,7.862408,6.142506,0,0,0,14.00491,0,0,0,1,0,4,51.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,75.16824,9.493746,1.386294,2.639408,1 10,1,50,0,4,129426,0,13275.43,37.79261,0,20,1,95.03191,20.03191,0,0,0,115.0638,0,0,0,6,0,4,51.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,75.16824,9.493746,1.386294,4.745487,1 10,1,50,0,5,129426,0,13275.43,38.79261,0,20,1,48.77032,9.866611,0,0,0,58.63693,0,0,0,3,0,4,51.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,75.16824,9.493746,1.386294,4.071365,1 10,1,50,0,1,129427,0,13275.43,34.05339,1,17,1,230.2709,15.95995,0,0,0,246.2309,0,0,0,6,1,4,76.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,76.05943,9.493746,1.386294,5.506269,1 10,1,50,0,2,129427,0,13275.43,35.05339,1,17,1,243.6658,7.843666,0,0,0,251.5094,0,0,0,4,3,4,76.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,76.05943,9.493746,1.386294,5.527481,1 10,1,50,0,3,129427,0,13275.43,36.05339,1,17,1,31.94103,2.407862,16.21622,0,0,50.56511,0,0,0,2,1,4,76.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,76.05943,9.493746,1.386294,3.923262,1 10,1,50,0,4,129427,0,13275.43,37.05339,1,17,1,59.4804,21.28532,0,0,0,80.76572,0,0,0,3,1,4,76.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,76.05943,9.493746,1.386294,4.391552,1 10,1,50,0,5,129427,0,13275.43,38.05339,1,17,1,181.1171,16.87786,8.336807,0,0,206.3318,0,0,0,10,0,4,76.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,76.05943,9.493746,1.386294,5.329485,1 10,1,50,0,1,129428,0,13275.43,6.009583,1,17,1,162.2497,27.67962,0,0,0,189.9293,0,0,0,30,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.931826,7.600903,0,0,0,85.16698,9.493746,1.386294,5.246652,1 10,1,50,0,2,129428,0,13275.43,7.009583,1,17,1,97.57413,20.61995,0,0,0,118.1941,0,0,0,18,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.931826,7.600903,0,0,0,85.16698,9.493746,1.386294,4.772328,1 10,1,50,0,3,129428,0,13275.43,8.009583,1,17,1,96.21622,12.72727,1.228501,0,0,110.172,0,0,0,18,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.931826,7.600903,0,0,0,85.16698,9.493746,1.386294,4.702043,1 10,1,50,0,4,129428,0,13275.43,9.009583,1,17,1,123.0629,22.21969,0,0,0,145.2826,0,0,0,17,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.931826,7.600903,0,0,0,85.16698,9.493746,1.386294,4.978681,1 10,1,50,0,5,129428,0,13275.43,10.00958,1,17,1,89.9333,14.8812,20.03752,0,0,124.852,0,0,0,14,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.931826,7.600903,0,0,0,85.16698,9.493746,1.386294,4.827129,1 7,1,25,0,1,129436,0,15786.6,36.2026,0,20,1,173.7338,27.31449,43.69847,0,0,244.7468,0,0,0,19,0,7,44.2,26.1,1,,1000,1000,0,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,68.73036,9.66698,1.94591,5.500224,1 7,1,25,0,2,129436,0,15786.6,37.2026,0,20,1,167.1159,49.062,67.38544,261.4555,0,283.5634,0,0,20,23,0,7,44.2,26.1,1,,1000,1000,0,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,68.73036,9.66698,1.94591,5.647436,1 7,1,25,0,3,129436,0,15786.6,38.2026,0,20,1,223.5627,62.92875,37.06142,0,0,323.5528,0,0,0,29,0,7,44.2,26.1,1,,1000,1000,0,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,68.73036,9.66698,1.94591,5.779362,1 7,1,25,0,4,129436,0,15786.6,39.2026,0,20,1,208.5232,36.45396,1.189608,0,0,246.1668,0,0,0,27,0,7,44.2,26.1,1,,1000,1000,0,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,68.73036,9.66698,1.94591,5.50601,1 7,1,25,0,5,129436,0,15786.6,40.2026,0,20,1,127.97,55.42309,34.74364,0,0,218.1367,0,0,0,25,0,7,44.2,26.1,1,,1000,1000,0,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,68.73036,9.66698,1.94591,5.385122,1 7,1,25,0,1,129437,0,15786.6,12.64066,0,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,,0 7,1,25,0,2,129437,0,15786.6,13.64066,0,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,,0 7,1,25,0,3,129437,0,15786.6,14.64066,0,10,1,16.21622,.982801,0,0,0,17.19902,0,0,0,3,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,2.844852,1 7,1,25,0,4,129437,0,15786.6,15.64066,0,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,,0 7,1,25,0,5,129437,0,15786.6,16.64066,0,10,1,13.75573,2.551063,0,0,0,16.3068,0,0,0,2,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,2.791582,1 7,1,25,0,1,129438,0,15786.6,7.772758,0,10,1,5.300354,0,0,0,0,5.300354,0,0,0,1,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,1.667773,1 7,1,25,0,2,129438,0,15786.6,8.772758,0,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,,0 7,1,25,0,3,129438,0,15786.6,9.772758,0,10,1,20.14742,2.457002,0,0,0,22.60442,0,0,0,3,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,3.118146,1 7,1,25,0,4,129438,0,15786.6,10.77276,0,10,1,0,0,0,0,0,0,0,0,0,0,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,,0 7,1,25,0,5,129438,0,15786.6,11.77276,0,10,1,17.5073,8.520217,0,0,0,26.02751,0,0,0,2,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,3.259154,1 7,1,25,0,1,129439,0,15786.6,10.02327,0,10,1,9.422851,9.729093,0,0,0,19.15194,0,0,0,2,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,2.952404,1 7,1,25,0,2,129439,0,15786.6,11.02327,0,10,1,43.39622,8.25876,0,0,0,51.65499,0,0,0,6,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,3.944587,1 7,1,25,0,3,129439,0,15786.6,12.02327,0,10,1,44.22604,4.157248,0,0,0,48.38329,0,0,0,4,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,3.879155,1 7,1,25,0,4,129439,0,15786.6,13.02327,0,10,1,101.6408,3.646308,5.528715,0,0,110.8159,0,0,0,3,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,4.70787,1 7,1,25,0,5,129439,0,15786.6,14.02327,0,10,1,83.47228,4.172572,0,0,0,87.64485,0,0,0,7,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,4.473293,1 7,1,25,0,1,129440,0,15786.6,13.55784,1,10,1,20.02356,1.177856,41.23675,0,0,62.43816,0,0,0,2,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.06523,9.66698,1.94591,4.134177,1 7,1,25,0,2,129440,0,15786.6,14.55784,1,10,1,45.8221,8.334231,0,0,0,54.15633,0,0,0,4,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.06523,9.66698,1.94591,3.991875,1 7,1,25,0,3,129440,0,15786.6,15.55784,1,10,1,33.41523,6.914005,0,0,0,40.32924,0,0,0,5,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.06523,9.66698,1.94591,3.697077,1 7,1,25,0,4,129440,0,15786.6,16.55784,1,10,1,27.34731,1.823154,0,0,0,29.17047,0,0,0,4,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.06523,9.66698,1.94591,3.373157,1 7,1,25,0,5,129440,0,15786.6,17.55784,1,10,1,31.88829,5.060442,0,0,0,36.94873,0,0,0,2,0,7,74.36826,13.73189,0,,1000,1000,1,1,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.06523,9.66698,1.94591,3.609531,1 7,1,25,0,1,129441,0,15786.6,33.65914,1,10,1,99.52885,47.54417,0,0,0,147.073,0,0,0,4,0,7,24.2,21.7,0,,1000,1000,0,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,63.85081,9.66698,1.94591,4.990929,1 7,1,25,0,2,129441,0,15786.6,34.65914,1,10,1,115.903,50.22102,0,318.0593,0,166.124,0,0,23,6,0,7,24.2,21.7,0,,1000,1000,0,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,63.85081,9.66698,1.94591,5.112734,1 7,1,25,0,3,129441,0,15786.6,35.65914,1,10,1,56.01966,17.88206,0,0,0,73.90172,0,0,0,2,0,7,24.2,21.7,0,,1000,1000,0,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,63.85081,9.66698,1.94591,4.302736,1 7,1,25,0,4,129441,0,15786.6,36.65914,1,10,1,295.8067,4.922516,0,0,0,300.7292,0,0,0,1,0,7,24.2,21.7,0,,1000,1000,0,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,63.85081,9.66698,1.94591,5.70621,1 7,1,25,0,5,129441,0,15786.6,37.65914,1,10,1,75.4481,5.939975,0,0,0,81.38808,0,0,0,6,0,7,24.2,21.7,0,,1000,1000,0,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,63.85081,9.66698,1.94591,4.399229,1 7,1,25,0,1,129442,0,15786.6,11.68515,0,10,1,41.22497,4.658422,0,0,0,45.88339,0,0,0,5,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,3.826103,1 7,1,25,0,2,129442,0,15786.6,12.68515,0,10,1,17.25067,0,0,0,0,17.25067,0,0,0,2,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,2.847851,1 7,1,25,0,3,129442,0,15786.6,13.68515,0,10,1,12.28501,.982801,0,0,0,13.26781,0,0,0,3,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,2.585341,1 7,1,25,0,4,129442,0,15786.6,14.68515,0,10,1,33.52325,2.461258,0,0,641.6135,677.598,1,0,0,4,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,6.518554,1 7,1,25,0,5,129442,0,15786.6,15.68515,0,10,1,6.252605,0,0,0,0,6.252605,0,0,0,1,0,7,74.36826,13.73189,0,,1000,1000,1,0,1.94591,6.907755,0,3.258096,8.294049,1,0,0,76.57921,9.66698,1.94591,1.832998,1 2,1,100,0,1,129446,0,2588.71,4.533881,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,400,405.56,1,0,1.386294,6.005269,1,0,0,0,0,0,79.54541,7.859301,1.386294,,0 2,1,100,0,2,129446,0,2588.71,5.533881,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,400,405.56,1,0,1.386294,6.005269,1,0,0,0,0,0,79.54541,7.859301,1.386294,,0 2,1,100,0,3,129446,0,2588.71,6.533881,0,12,1,12.46883,0,31.27182,0,0,43.74065,0,0,0,0,1,4,74.36826,13.73189,0,,400,405.56,1,0,1.386294,6.005269,1,0,0,0,0,0,79.54541,7.859301,1.386294,3.778278,1 2,1,100,0,1,129447,0,2588.71,2.469541,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,400,405.56,1,1,1.386294,6.005269,1,0,0,0,0,0,79.03143,7.859301,1.386294,,0 2,1,100,0,2,129447,0,2588.71,3.469541,1,12,1,2.738226,4.441402,0,0,0,7.179627,0,0,0,1,0,4,74.36826,13.73189,0,,400,405.56,1,1,1.386294,6.005269,1,0,0,0,0,0,79.03143,7.859301,1.386294,1.971247,1 2,1,100,0,3,129447,0,2588.71,4.469542,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,400,405.56,1,1,1.386294,6.005269,1,0,0,0,0,0,79.03143,7.859301,1.386294,,0 2,1,100,0,1,129448,0,2588.71,24.95004,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,61.3,13.73189,0,,400,405.56,0,0,1.386294,6.005269,1,0,0,0,0,0,78.70184,7.859301,1.386294,,0 2,1,100,0,2,129448,0,2588.71,25.95004,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,61.3,13.73189,0,,400,405.56,0,0,1.386294,6.005269,1,0,0,0,0,0,78.70184,7.859301,1.386294,,0 2,1,100,0,3,129448,0,2588.71,26.95004,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,61.3,13.73189,0,,400,405.56,0,0,1.386294,6.005269,1,0,0,0,0,0,78.70184,7.859301,1.386294,,0 2,1,100,0,1,129449,0,2588.71,27.07734,0,15,1,0,0,0,0,0,0,0,0,0,0,0,4,77.5,13.73189,0,,400,405.56,0,0,1.386294,6.005269,1,0,0,0,0,0,78.07117,7.859301,1.386294,,0 2,1,100,0,2,129449,0,2588.71,28.07734,0,15,1,5.476451,7.738225,0,0,0,13.21468,0,0,0,0,1,4,77.5,13.73189,0,,400,405.56,0,0,1.386294,6.005269,1,0,0,0,0,0,78.07117,7.859301,1.386294,2.581328,1 2,1,100,0,3,129449,0,2588.71,29.07734,0,15,1,7.481297,2.523691,22.06983,0,0,32.07481,0,0,0,1,0,4,77.5,13.73189,0,,400,405.56,0,0,1.386294,6.005269,1,0,0,0,0,0,78.07117,7.859301,1.386294,3.468071,1 4,1,100,1,1,129458,0,8129.032,27.72622,0,12,1,14.98801,0,0,0,0,14.98801,0,0,0,1,0,4,76.8,8.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,77.82298,9.00332,1.386294,2.707251,1 4,1,100,1,2,129458,0,8129.032,28.72622,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,76.8,8.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,77.82298,9.00332,1.386294,,0 4,1,100,1,3,129458,0,8129.032,29.72622,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,76.8,8.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,77.82298,9.00332,1.386294,,0 4,1,100,1,1,129459,0,8129.032,7.104723,1,13,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,0,0,0,84.02346,9.00332,1.386294,,0 4,1,100,1,2,129459,0,8129.032,8.104723,1,13,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,0,0,0,84.02346,9.00332,1.386294,,0 4,1,100,1,3,129459,0,8129.032,9.104723,1,13,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,1,0,0,0,0,0,84.02346,9.00332,1.386294,,0 4,1,100,1,1,129460,0,8129.032,26.54894,1,13,1,0,0,0,0,0,0,0,0,0,0,0,4,78.9,8.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,78.97468,9.00332,1.386294,,0 4,1,100,1,2,129460,0,8129.032,27.54894,1,13,1,0,0,0,0,0,0,0,0,0,0,0,4,78.9,8.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,78.97468,9.00332,1.386294,,0 4,1,100,1,3,129460,0,8129.032,28.54894,1,13,1,0,0,0,0,0,0,0,0,0,0,0,4,78.9,8.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,0,0,0,78.97468,9.00332,1.386294,,0 4,1,100,1,1,129461,0,8129.032,6.162902,0,13,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,84.53744,9.00332,1.386294,,0 4,1,100,1,2,129461,0,8129.032,7.162902,0,13,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,84.53744,9.00332,1.386294,,0 4,1,100,1,3,129461,0,8129.032,8.162902,0,13,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,0,0,0,84.53744,9.00332,1.386294,,0 10,1,50,0,1,129466,0,4528.536,20.27105,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,85.3,4.3,0,,750,750,0,0,0,6.620073,0,3.931826,7.313221,0,0,0,77.9943,8.418375,0,,0 10,1,50,0,2,129466,0,4528.536,21.27105,0,12,1,33.82749,0,0,0,0,33.82749,0,0,0,0,1,1,85.3,4.3,0,,750,750,0,0,0,6.620073,0,3.931826,7.313221,0,0,0,77.9943,8.418375,0,3.521274,1 10,1,50,0,3,129466,0,4528.536,22.27105,0,12,1,0,0,0,0,0,0,0,0,0,0,0,1,85.3,4.3,0,,750,750,0,0,0,6.620073,0,3.931826,7.313221,0,0,0,77.9943,8.418375,0,,0 4,1,100,1,1,129467,1,7848.96,32.72827,0,16,1,5.94884,0,0,0,0,5.94884,0,0,0,1,0,4,91.6,17.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,66.55058,8.968264,1.386294,1.783196,1 4,1,100,1,2,129467,1,7848.96,33.72827,0,16,1,154.8775,1.796407,0,0,0,156.6739,0,0,0,5,0,4,91.6,17.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,66.55058,8.968264,1.386294,5.054167,1 4,1,100,1,3,129467,1,7848.96,34.72827,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,91.6,17.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,66.55058,8.968264,1.386294,,0 4,1,100,1,4,129467,1,7848.96,35.72827,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,91.6,17.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,66.55058,8.968264,1.386294,,0 4,1,100,1,5,129467,1,7848.96,36.72827,0,16,1,96.33151,1.262095,0,0,0,97.59361,0,0,0,6,0,4,91.6,17.4,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,66.55058,8.968264,1.386294,4.580812,1 4,1,100,1,1,129468,1,7848.96,30.68583,1,16,1,23.79536,3.569304,0,0,0,27.36466,0,0,0,3,0,4,92.6,21.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,67.45471,8.968264,1.386294,3.309253,1 4,1,100,1,2,129468,1,7848.96,31.68583,1,16,1,90.36472,4.899292,0,0,791.3609,886.6249,2,0,0,5,0,4,92.6,21.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,67.45471,8.968264,1.386294,6.787422,1 4,1,100,1,3,129468,1,7848.96,32.68583,1,16,1,4.955401,0,0,0,0,4.955401,0,0,0,1,0,4,92.6,21.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,67.45471,8.968264,1.386294,1.600478,1 4,1,100,1,4,129468,1,7848.96,33.68583,1,16,1,303.1804,.9178522,0,0,0,304.0982,0,0,0,4,0,4,92.6,21.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,67.45471,8.968264,1.386294,5.71735,1 4,1,100,1,5,129468,1,7848.96,34.68583,1,16,1,71.51872,10.53849,14.50989,0,1084.666,1181.233,1,0,0,1,1,4,92.6,21.7,0,,1000,1000,0,0,1.386294,6.907755,1,0,0,1,0,0,67.45471,8.968264,1.386294,7.074314,1 4,1,100,1,1,129469,1,7848.96,9.437371,0,16,1,21.41582,0,0,0,0,21.41582,0,0,0,0,1,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,82.78881,8.968264,1.386294,3.06413,1 4,1,100,1,2,129469,1,7848.96,10.43737,0,16,1,13.60915,0,0,0,0,13.60915,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,82.78881,8.968264,1.386294,2.610742,1 4,1,100,1,3,129469,1,7848.96,11.43737,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,82.78881,8.968264,1.386294,,0 4,1,100,1,4,129469,1,7848.96,12.43737,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,82.78881,8.968264,1.386294,,0 4,1,100,1,5,129469,1,7848.96,13.43737,0,16,1,49.81068,0,0,0,0,49.81068,0,0,0,3,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,82.78881,8.968264,1.386294,3.90823,1 4,1,100,1,1,129470,1,7848.96,7.318275,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,82.78881,8.968264,1.386294,,0 4,1,100,1,2,129470,1,7848.96,8.318275,0,16,1,13.60915,0,0,0,0,13.60915,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,82.78881,8.968264,1.386294,2.610742,1 4,1,100,1,3,129470,1,7848.96,9.318275,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,82.78881,8.968264,1.386294,,0 4,1,100,1,4,129470,1,7848.96,10.31828,0,16,1,17.89812,0,0,0,0,17.89812,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,82.78881,8.968264,1.386294,2.884696,1 4,1,100,1,5,129470,1,7848.96,11.31828,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,1,0,0,1,0,0,82.78881,8.968264,1.386294,,0 6,1,25,0,1,129474,0,10085.61,1.708419,0,14,1,48.78049,6.472338,0,0,0,55.25283,0,0,0,10,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.35837,9.218964,1.386294,4.011919,1 6,1,25,0,2,129474,0,10085.61,2.708419,0,14,1,16.33097,4.30049,0,0,0,20.63146,0,0,0,3,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.35837,9.218964,1.386294,3.026817,1 6,1,25,0,3,129474,0,10085.61,3.708419,0,14,1,8.424182,1.367691,0,0,0,9.791873,0,0,0,1,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.35837,9.218964,1.386294,2.281553,1 6,1,25,0,1,129475,0,10085.61,29.94114,0,16,1,0,0,0,0,0,0,0,0,0,0,0,4,86.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,74.78748,9.218964,1.386294,,0 6,1,25,0,2,129475,0,10085.61,30.94114,0,16,1,204.1372,16.46707,0,0,0,220.6042,0,0,0,6,0,4,86.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,74.78748,9.218964,1.386294,5.39637,1 6,1,25,0,3,129475,0,10085.61,31.94114,0,16,1,41.3776,11.12488,0,0,0,52.50248,0,0,0,3,0,4,86.3,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,74.78748,9.218964,1.386294,3.96086,1 6,1,25,0,1,129476,0,10085.61,29.64819,1,14,1,29.7442,7.911957,0,0,0,37.65616,0,0,0,3,0,4,80,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,78.56806,9.218964,1.386294,3.628496,1 6,1,25,0,2,129476,0,10085.61,30.64819,1,14,1,28.30702,8.628199,33.20631,0,0,70.14153,0,0,0,1,1,4,80,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,78.56806,9.218964,1.386294,4.250515,1 6,1,25,0,3,129476,0,10085.61,31.64819,1,14,1,165.3865,13.18137,12.42815,0,0,190.996,0,0,0,8,1,4,80,13.73189,0,,1000,1000,0,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,78.56806,9.218964,1.386294,5.252253,1 6,1,25,0,1,129477,0,10085.61,2.833676,0,14,1,45.80607,21.47531,0,0,0,67.28138,0,0,0,8,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.35837,9.218964,1.386294,4.208883,1 6,1,25,0,2,129477,0,10085.61,3.833676,0,14,1,14.15351,55.44366,0,0,0,69.59717,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.35837,9.218964,1.386294,4.242724,1 6,1,25,0,3,129477,0,10085.61,4.833675,0,14,1,81.26859,41.65015,0,0,0,122.9187,0,0,0,9,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,75.35837,9.218964,1.386294,4.811523,1 11,1,0,0,1,129481,0,1518.61,24.78576,1,11,1,31.6247,18.07554,0,0,0,49.70024,1,1,0,3,0,2,97.5,13.73189,0,,0,0,0,0,.6931472,0,0,0,0,0,0,0,74.46398,7.32621,.6931472,3.90601,1 11,1,0,0,2,129481,0,1518.61,25.78576,1,11,1,183.5433,12.49726,0,0,69.1402,265.1807,1,0,0,8,1,3,97.5,13.73189,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,74.46398,7.32621,1.098612,5.580411,1 11,1,0,0,3,129481,0,1518.61,26.78576,1,11,1,33.04239,12.74314,0,0,0,45.78554,0,0,0,0,0,3,97.5,13.73189,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,74.46398,7.32621,1.098612,3.823968,1 11,1,0,0,4,129481,0,1518.61,27.78576,1,11,1,120.2397,30.54403,0,0,633.4025,784.1863,1,0,0,1,2,3,97.5,13.73189,0,,0,0,0,0,1.098612,0,0,0,0,0,0,0,74.46398,7.32621,1.098612,6.664647,1 11,1,0,0,5,129481,0,1518.61,28.78576,1,11,1,36.56369,18.42996,.2539145,0,712.7592,768.0068,1,0,0,2,0,4,97.5,13.73189,0,,0,0,0,0,1.386294,0,0,0,0,0,0,0,74.46398,7.32621,1.386294,6.643798,1 11,1,0,0,1,129482,0,1518.61,3.811088,1,11,1,46.76259,7.07434,0,0,0,53.83693,0,0,0,8,0,2,74.36826,13.73189,0,,0,0,1,1,.6931472,0,0,0,0,0,0,0,76.44289,7.32621,.6931472,3.98596,1 11,1,0,0,2,129482,0,1518.61,4.811088,1,11,1,6.571742,2.628697,0,0,0,9.200438,0,0,0,1,0,3,74.36826,13.73189,0,,0,0,1,1,1.098612,0,0,0,0,0,0,0,76.44289,7.32621,1.098612,2.219251,1 11,1,0,0,3,129482,0,1518.61,5.811088,1,11,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,0,0,1,1,1.098612,0,0,0,0,0,0,0,76.44289,7.32621,1.098612,,0 11,1,0,0,4,129482,0,1518.61,6.811088,1,11,1,8.298756,0,0,0,0,8.298756,0,0,0,2,0,3,74.36826,13.73189,0,,0,0,1,1,1.098612,0,0,0,0,0,0,0,76.44289,7.32621,1.098612,2.116106,1 11,1,0,0,5,129482,0,1518.61,7.811088,1,11,1,4.655099,2.010157,0,0,0,6.665256,0,0,0,1,0,4,74.36826,13.73189,0,,0,0,1,1,1.386294,0,0,0,0,0,0,0,76.44289,7.32621,1.386294,1.896908,1 11,1,0,1,1,129489,0,7368.771,24.77207,0,14,1,14.8721,0,16.35931,0,0,31.23141,0,0,0,1,0,2,75.8,8.7,0,,0,0,0,0,.6931472,0,0,0,0,1,0,0,66.63726,8.905142,.6931472,3.441424,1 11,1,0,1,2,129489,0,7368.771,25.77207,0,14,1,16.33097,0,0,0,0,16.33097,0,0,0,0,0,2,75.8,8.7,0,,0,0,0,0,.6931472,0,0,0,0,1,0,0,66.63726,8.905142,.6931472,2.793064,1 11,1,0,1,3,129489,0,7368.771,26.77207,0,14,1,0,0,0,0,0,0,0,0,0,0,0,2,75.8,8.7,0,,0,0,0,0,.6931472,0,0,0,0,1,0,0,66.63726,8.905142,.6931472,,0 11,1,0,1,1,129490,0,7368.771,24.8898,1,13,1,26.76978,0,0,0,0,26.76978,0,0,0,2,0,2,67.4,21.7,0,,0,0,0,0,.6931472,0,0,0,0,1,0,0,68.8164,8.905142,.6931472,3.287274,1 11,1,0,1,2,129490,0,7368.771,25.8898,1,13,1,22.86336,0,0,0,0,22.86336,0,0,0,2,0,2,67.4,21.7,0,,0,0,0,0,.6931472,0,0,0,0,1,0,0,68.8164,8.905142,.6931472,3.129536,1 11,1,0,1,3,129490,0,7368.771,26.8898,1,13,1,27.75025,0,0,0,0,27.75025,0,0,0,1,0,2,67.4,21.7,0,,0,0,0,0,.6931472,0,0,0,0,1,0,0,68.8164,8.905142,.6931472,3.323245,1 5,1,25,0,1,129498,0,13740.69,27.41684,1,12,1,20.82094,4.521118,33.79536,0,0,59.13742,0,0,0,1,1,3,71.3,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,69.22522,9.52819,1.098612,4.079864,1 5,1,25,0,2,129498,0,13740.69,28.41684,1,12,1,43.54927,1.137725,14.62167,0,0,59.30865,0,0,0,2,1,3,71.3,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,69.22522,9.52819,1.098612,4.082755,1 5,1,25,0,3,129498,0,13740.69,29.41684,1,12,1,122.3984,3.409316,0,138.7512,1198.622,1324.43,1,0,8,2,2,3,71.3,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,69.22522,9.52819,1.098612,7.188737,1 5,1,25,0,4,129498,0,13740.69,30.41684,1,12,1,27.53557,0,0,13.76778,0,27.53557,0,0,1,3,0,3,71.3,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,69.22522,9.52819,1.098612,3.315479,1 5,1,25,0,5,129498,0,13740.69,31.41684,1,12,1,181.7417,3.878839,0,0,0,185.6205,0,0,0,6,0,3,71.3,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,69.22522,9.52819,1.098612,5.223704,1 5,1,25,0,1,129499,0,13740.69,7.29911,0,12,1,15.46698,0,0,0,0,15.46698,0,0,0,1,0,3,74.36826,13.73189,0,,1000,1000,1,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,77.38953,9.52819,1.098612,2.738708,1 5,1,25,0,2,129499,0,13740.69,8.29911,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,1000,1000,1,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,77.38953,9.52819,1.098612,,0 5,1,25,0,3,129499,0,13740.69,9.29911,0,12,1,51.53617,6.818632,0,0,0,58.3548,0,0,0,3,1,3,74.36826,13.73189,0,,1000,1000,1,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,77.38953,9.52819,1.098612,4.066542,1 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1,1,0,0,1,129682,0,9542.002,14.48597,1,4,1,71.26031,12.50294,0,0,0,83.76325,0,0,0,4,0,3,52.5,13.73189,0,,450,0,1,1,1.098612,0,1,0,0,1,0,0,63.93338,9.163564,1.098612,4.427994,1 1,1,0,0,2,129682,0,9542.002,15.48597,1,4,1,53.47709,27.09434,29.85984,0,1364.836,1475.267,2,0,0,7,0,3,52.5,13.73189,0,,450,0,1,1,1.098612,0,1,0,0,1,0,0,63.93338,9.163564,1.098612,7.296594,1 1,1,0,0,3,129682,0,9542.002,16.48597,1,4,1,49.45946,18.36364,0,0,0,67.8231,0,0,0,6,1,3,52.5,13.73189,0,,450,0,1,1,1.098612,0,1,0,0,1,0,0,63.93338,9.163564,1.098612,4.216903,1 1,1,0,0,1,129683,0,9542.002,61.5332,0,4,1,19.43463,11.1543,41.84924,0,0,72.43816,0,0,0,2,0,3,35,13.73189,1,,450,0,0,0,1.098612,0,1,0,0,0,1,0,55.00333,9.163564,1.098612,4.282733,1 1,1,0,0,2,129683,0,9542.002,62.5332,0,4,1,8.625337,13.19137,0,0,0,21.81671,0,0,0,2,0,3,35,13.73189,1,,450,0,0,0,1.098612,0,1,0,0,0,1,0,55.00333,9.163564,1.098612,3.082676,1 1,1,0,0,3,129683,0,9542.002,63.5332,0,4,1,134.8894,23.32187,0,0,0,158.2113,0,0,0,4,0,3,35,13.73189,1,,450,0,0,0,1.098612,0,1,0,0,0,1,0,55.00333,9.163564,1.098612,5.063931,1 10,1,50,1,1,129684,0,6771.712,4.120465,1,13,1,45.50863,3.491969,0,0,0,49.0006,0,0,0,2,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.931826,7.600903,0,0,0,79.02408,8.820657,1.386294,3.891832,1 10,1,50,1,2,129684,0,6771.712,5.120465,1,13,1,39.7387,3.739793,0,0,0,43.4785,0,0,0,4,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.931826,7.600903,0,0,0,79.02408,8.820657,1.386294,3.772266,1 10,1,50,1,3,129684,0,6771.712,6.120465,1,13,1,9.910803,0,23.20119,0,0,33.11199,0,0,0,0,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.931826,7.600903,0,0,0,79.02408,8.820657,1.386294,3.499896,1 10,1,50,1,1,129685,0,6771.712,5.207392,1,13,1,22.60559,10.5235,0,0,0,33.12909,0,0,0,2,0,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.931826,7.600903,0,0,0,79.02408,8.820657,1.386294,3.500412,1 10,1,50,1,2,129685,0,6771.712,6.207392,1,13,1,49.53729,1.62221,20.37017,0,0,71.52967,0,0,0,1,1,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.931826,7.600903,0,0,0,79.02408,8.820657,1.386294,4.270113,1 10,1,50,1,3,129685,0,6771.712,7.207392,1,13,1,27.25471,2.477701,36.43211,0,0,66.16452,0,0,0,1,2,4,74.36826,13.73189,0,,1000,1000,1,1,1.386294,6.907755,0,3.931826,7.600903,0,0,0,79.02408,8.820657,1.386294,4.192144,1 10,1,50,1,1,129686,0,6771.712,24.282,1,13,1,39.26234,13.38489,0,0,0,52.64723,0,0,0,3,0,4,78.9,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,67.72769,8.820657,1.386294,3.963614,1 10,1,50,1,2,129686,0,6771.712,25.282,1,13,1,95.80838,29.86391,0,0,0,125.6723,0,0,0,6,0,4,78.9,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,67.72769,8.820657,1.386294,4.833678,1 10,1,50,1,3,129686,0,6771.712,26.282,1,13,1,164.668,36.86819,13.46383,0,0,215,0,0,0,13,0,4,78.9,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,67.72769,8.820657,1.386294,5.370638,1 10,1,50,1,1,129687,0,6771.712,26.52704,0,14,1,0,0,0,0,0,0,0,0,0,0,0,4,76.8,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,78.59797,8.820657,1.386294,,0 10,1,50,1,2,129687,0,6771.712,27.52704,0,14,1,0,0,0,0,0,0,0,0,0,0,0,4,76.8,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,78.59797,8.820657,1.386294,,0 10,1,50,1,3,129687,0,6771.712,28.52704,0,14,1,0,0,0,0,0,0,0,0,0,0,0,4,76.8,0,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,78.59797,8.820657,1.386294,,0 10,1,50,0,1,129693,0,4394.988,27.54552,0,10,1,0,0,0,0,0,0,0,0,0,0,0,4,78.9,4.3,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,1,0,61.37853,8.388448,1.386294,,0 10,1,50,0,2,129693,0,4394.988,28.54552,0,10,1,5.390836,0,0,0,453.6604,459.0512,1,0,0,1,0,4,78.9,4.3,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,1,0,61.37853,8.388448,1.386294,6.129162,1 10,1,50,0,3,129693,0,4394.988,29.54552,0,10,1,0,0,0,0,0,0,0,0,0,0,0,4,78.9,4.3,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,1,0,61.37853,8.388448,1.386294,,0 10,1,50,0,4,129693,0,4394.988,30.54552,0,10,1,53.6691,0,6.836828,0,0,60.50592,0,0,0,2,0,4,78.9,4.3,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,1,0,61.37853,8.388448,1.386294,4.102741,1 10,1,50,0,5,129693,0,4394.988,31.54552,0,10,1,0,0,0,0,0,0,0,0,0,0,0,4,78.9,4.3,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,0,1,0,61.37853,8.388448,1.386294,,0 10,1,50,0,1,129694,0,4394.988,25.69199,1,11,1,0,0,0,0,0,0,0,0,0,0,0,4,74.7,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,68.15965,8.388448,1.386294,,0 10,1,50,0,2,129694,0,4394.988,26.69199,1,11,1,0,0,7.719676,0,0,7.719676,0,0,0,0,0,4,74.7,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,68.15965,8.388448,1.386294,2.043772,1 10,1,50,0,3,129694,0,4394.988,27.69199,1,11,1,0,5.208845,0,0,0,5.208845,0,0,0,0,0,4,74.7,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,68.15965,8.388448,1.386294,1.650358,1 10,1,50,0,4,129694,0,4394.988,28.69199,1,11,1,68.82407,11.54512,0,0,0,80.36919,0,0,0,6,0,4,74.7,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,68.15965,8.388448,1.386294,4.386631,1 10,1,50,0,5,129694,0,4394.988,29.69199,1,11,1,65.23551,0,0,0,0,65.23551,0,0,0,2,0,4,74.7,17.4,0,,1000,1000,0,0,1.386294,6.907755,0,3.931826,7.600903,1,0,0,68.15965,8.388448,1.386294,4.178004,1 10,1,50,0,1,129695,0,4394.988,4.676249,0,11,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,.0327869,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,78.88596,8.388448,1.386294,,0 10,1,50,0,2,129695,0,4394.988,5.676249,0,11,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,.0327869,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,78.88596,8.388448,1.386294,,0 10,1,50,0,3,129695,0,4394.988,6.676249,0,11,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,.0327869,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,78.88596,8.388448,1.386294,,0 10,1,50,0,4,129695,0,4394.988,7.676249,0,11,1,5.925251,1.937101,0,0,0,7.862352,0,0,0,1,0,4,74.36826,13.73189,.0327869,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,78.88596,8.388448,1.386294,2.062086,1 10,1,50,0,5,129695,0,4394.988,8.67625,0,11,1,0,0,0,0,0,0,0,0,0,0,0,4,74.36826,13.73189,.0327869,,1000,1000,1,0,1.386294,6.907755,0,3.931826,7.600903,0,0,0,78.88596,8.388448,1.386294,,0 2,1,100,0,1,129696,0,7392.06,21.99589,0,12,1,5.94884,0,0,0,0,5.94884,0,0,0,1,0,3,71.6,8.7,0,,599,599,0,0,1.098612,6.395262,1,0,0,1,0,0,68.6146,8.908297,1.098612,1.783196,1 2,1,100,0,2,129696,0,7392.06,22.99589,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,71.6,8.7,0,,599,599,0,0,1.098612,6.395262,1,0,0,1,0,0,68.6146,8.908297,1.098612,,0 2,1,100,0,3,129696,0,7392.06,23.99589,0,12,1,9.910803,0,0,0,0,9.910803,0,0,0,2,0,3,71.6,8.7,0,,599,599,0,0,1.098612,6.395262,1,0,0,1,0,0,68.6146,8.908297,1.098612,2.293625,1 2,1,100,0,1,129697,0,7392.06,20.45996,1,11,1,5.94884,0,0,0,0,5.94884,0,0,0,1,0,3,31.6,17.4,1,,599,599,0,0,1.098612,6.395262,1,0,0,0,1,0,54.00756,8.908297,1.098612,1.783196,1 2,1,100,0,2,129697,0,7392.06,21.45996,1,11,1,40.82743,11.5841,0,0,0,52.41154,0,0,0,0,0,3,31.6,17.4,1,,599,599,0,0,1.098612,6.395262,1,0,0,0,1,0,54.00756,8.908297,1.098612,3.959127,1 2,1,100,0,3,129697,0,7392.06,22.45996,1,11,1,15.36174,15.66898,0,0,762.1853,793.2161,1,0,0,2,0,3,31.6,17.4,1,,599,599,0,0,1.098612,6.395262,1,0,0,0,1,0,54.00756,8.908297,1.098612,6.676095,1 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3,1,100,1,4,129699,0,4174.593,21.51061,0,9,1,0,0,0,0,0,0,0,0,0,0,0,4,73.7,17.4,0,,513,0,0,0,1.386294,0,1,0,0,1,0,0,63.95783,8.337011,1.386294,,0 3,1,100,1,1,129700,0,4174.593,16.45448,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,61.1,8.7,0,,513,0,1,1,1.386294,0,1,0,0,1,0,0,60.48014,8.337011,1.386294,,0 3,1,100,1,2,129700,0,4174.593,17.45448,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,61.1,8.7,0,,513,0,1,1,1.386294,0,1,0,0,1,0,0,60.48014,8.337011,1.386294,,0 3,1,100,1,3,129700,0,4174.593,18.45448,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,61.1,8.7,0,,513,0,0,0,1.386294,0,1,0,0,1,0,0,60.48014,8.337011,1.386294,,0 3,1,100,1,4,129700,0,4174.593,19.45448,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,61.1,8.7,0,,513,0,0,0,1.386294,0,1,0,0,1,0,0,60.48014,8.337011,1.386294,,0 3,1,100,1,5,129700,0,4174.593,20.45448,1,9,1,0,0,0,0,0,0,0,0,0,0,0,3,61.1,8.7,0,,513,0,0,0,1.098612,0,1,0,0,1,0,0,60.48014,8.337011,1.098612,,0 3,1,100,1,1,129701,0,4174.593,51.77823,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,42.1,34.8,0,,513,0,0,0,1.386294,0,1,0,0,0,1,0,48.03789,8.337011,1.386294,,0 3,1,100,1,2,129701,0,4174.593,52.77823,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,42.1,34.8,0,,513,0,0,0,1.386294,0,1,0,0,0,1,0,48.03789,8.337011,1.386294,,0 3,1,100,1,3,129701,0,4174.593,53.77823,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,42.1,34.8,0,,513,0,0,0,1.386294,0,1,0,0,0,1,0,48.03789,8.337011,1.386294,,0 3,1,100,1,4,129701,0,4174.593,54.77823,1,9,1,0,0,0,0,0,0,0,0,0,0,0,4,42.1,34.8,0,,513,0,0,0,1.386294,0,1,0,0,0,1,0,48.03789,8.337011,1.386294,,0 3,1,100,1,5,129701,0,4174.593,55.77823,1,9,1,0,0,0,0,0,0,0,0,0,0,0,3,42.1,34.8,0,,513,0,0,0,1.098612,0,1,0,0,0,1,0,48.03789,8.337011,1.098612,,0 3,1,100,1,1,129702,0,4174.593,55.30732,0,9,1,0,0,0,0,0,0,0,0,0,0,0,4,96.8,4.3,0,,513,0,0,0,1.386294,0,1,0,0,0,0,0,72.67507,8.337011,1.386294,,0 3,1,100,1,2,129702,0,4174.593,56.30732,0,9,1,0,0,0,0,0,0,0,0,0,0,0,4,96.8,4.3,0,,513,0,0,0,1.386294,0,1,0,0,0,0,0,72.67507,8.337011,1.386294,,0 3,1,100,1,3,129702,0,4174.593,57.30732,0,9,1,0,0,0,0,0,0,0,0,0,0,0,4,96.8,4.3,0,,513,0,0,0,1.386294,0,1,0,0,0,0,0,72.67507,8.337011,1.386294,,0 3,1,100,1,4,129702,0,4174.593,58.30732,0,9,1,0,0,0,0,0,0,0,0,0,0,0,4,96.8,4.3,0,,513,0,0,0,1.386294,0,1,0,0,0,0,0,72.67507,8.337011,1.386294,,0 3,1,100,1,5,129702,0,4174.593,59.30732,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,96.8,4.3,0,,513,0,0,0,1.098612,0,1,0,0,0,0,0,72.67507,8.337011,1.098612,,0 4,1,100,0,1,129703,0,9542.002,21.23751,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,87.4,13,0,,1000,1000,0,0,1.098612,6.907755,1,0,0,0,0,0,72.72614,9.163564,1.098612,,0 4,1,100,0,1,129704,0,9542.002,23.34292,0,14,1,0,0,0,0,0,0,0,0,0,0,0,3,76.8,13,0,,1000,1000,0,0,1.098612,6.907755,1,0,0,0,0,0,72.09547,9.163564,1.098612,,0 4,1,100,0,1,129705,0,9542.002,.6652977,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,74.36826,13.73189,0,,1000,1000,1,1,1.098612,6.907755,1,0,0,1,0,0,69.41489,9.163564,1.098612,,0 5,1,25,1,1,129706,0,13354.84,54.72964,1,13,1,191.8917,231.4515,71.64188,0,0,494.9851,0,0,0,7,1,3,86.3,17.4,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,66.29183,9.499709,1.098612,6.204528,1 5,1,25,1,2,129706,0,13354.84,55.72964,1,13,1,313.865,226.3963,18.50844,0,0,558.7697,0,0,0,5,21,3,86.3,17.4,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,66.29183,9.499709,1.098612,6.325737,1 5,1,25,1,3,129706,0,13354.84,56.72964,1,13,1,183.3499,280.3023,50.54509,0,0,514.1972,0,0,0,4,25,3,86.3,17.4,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,1,0,0,66.29183,9.499709,1.098612,6.242607,1 5,1,25,1,1,129707,0,13354.84,53.22108,0,18,1,67.22189,3.099346,0,0,0,70.32124,0,0,0,2,7,3,71.6,26.1,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,76.58466,9.499709,1.098612,4.253074,1 5,1,25,1,2,129707,0,13354.84,54.22108,0,18,1,158.9548,27.13119,22.75449,0,0,208.8405,0,0,0,2,11,3,71.6,26.1,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,76.58466,9.499709,1.098612,5.341571,1 5,1,25,1,3,129707,0,13354.84,55.22108,0,18,1,220.2428,30.00496,34.1774,0,0,284.4252,0,0,0,15,15,3,71.6,26.1,0,,1000,1000,0,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,76.58466,9.499709,1.098612,5.65047,1 5,1,25,1,1,129708,0,13354.84,14.42574,0,13,1,0,0,0,0,0,0,0,0,0,0,0,3,63.2,4.3,0,,1000,1000,1,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,80.99551,9.499709,1.098612,,0 5,1,25,1,2,129708,0,13354.84,15.42574,0,13,1,22.319,10.37017,13.08655,0,0,45.77572,0,0,0,2,1,3,63.2,4.3,0,,1000,1000,1,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,80.99551,9.499709,1.098612,3.823754,1 5,1,25,1,3,129708,0,13354.84,16.42574,0,13,1,15.85728,0,25.46085,0,0,41.31814,0,0,0,1,1,3,63.2,4.3,0,,1000,1000,1,0,1.098612,6.907755,0,3.258096,8.294049,0,0,0,80.99551,9.499709,1.098612,3.721302,1 3,1,100,1,1,129711,0,6417.494,20.31759,1,13,1,39.85723,7.311124,41.12433,0,0,88.29269,0,0,0,3,0,2,86.3,8.7,0,,549,549,0,0,.6931472,6.308098,1,0,0,0,0,0,74.39403,8.766939,.6931472,4.480657,1 3,1,100,1,2,129711,0,6417.494,21.31759,1,13,1,12.52041,14.8503,12.1448,0,0,39.51551,0,0,0,1,0,2,86.3,8.7,0,,549,549,0,0,.6931472,6.308098,1,0,0,0,0,0,74.39403,8.766939,.6931472,3.676693,1 3,1,100,1,3,129711,0,6417.494,22.31759,1,13,1,39.39544,2.106045,1.555996,0,0,43.05748,0,0,0,3,0,2,86.3,8.7,0,,549,549,0,0,.6931472,6.308098,1,0,0,0,0,0,74.39403,8.766939,.6931472,3.762536,1 3,1,100,1,1,129712,0,6417.494,20.5859,0,12,1,33.3135,0,33.56931,0,0,66.8828,0,0,0,4,0,2,78.9,21.7,0,,549,549,0,0,.6931472,6.308098,1,0,0,0,0,0,76.28976,8.766939,.6931472,4.202942,1 3,1,100,1,2,129712,0,6417.494,21.5859,0,12,1,14.69788,9.031029,0,0,0,23.72891,0,0,0,3,0,2,78.9,21.7,0,,549,549,0,0,.6931472,6.308098,1,0,0,0,0,0,76.28976,8.766939,.6931472,3.166694,1 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6,1,25,1,4,129730,0,9542.002,3.520192,0,12,1,14.58523,0,0,0,0,14.58523,0,0,0,1,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,69.2646,9.163564,1.791759,2.68001,1 6,1,25,1,5,129730,0,9542.002,4.520192,0,12,1,45.85244,0,0,0,0,45.85244,0,0,0,3,0,6,74.36826,13.73189,0,,1000,1000,1,0,1.791759,6.907755,0,3.258096,8.294049,1,0,0,69.2646,9.163564,1.791759,3.825428,1 7,1,25,1,1,129732,1,1176.179,.4079398,0,5,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,340,340,1,0,1.791759,5.828946,0,3.258096,7.21524,0,1,0,76.96879,7.070876,1.791759,,0 7,1,25,1,2,129732,1,1176.179,1.40794,0,5,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,340,340,1,0,1.791759,5.828946,0,3.258096,7.21524,0,1,0,76.96879,7.070876,1.791759,,0 9,1,50,0,1,129733,0,9542.002,.3477071,1,10,1,20.82094,0,0,0,0,20.82094,0,0,0,3,0,5,74.36826,13.73189,0,,799,799,1,1,1.609438,6.683361,0,3.931826,7.376508,0,0,0,78.49355,9.163564,1.609438,3.035959,1 9,1,50,0,2,129733,0,9542.002,1.347707,1,10,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,799,799,1,1,1.609438,6.683361,0,3.931826,7.376508,0,0,0,78.49355,9.163564,1.609438,,0 9,1,50,0,3,129733,0,9542.002,2.347707,1,10,1,0,0,0,0,0,0,0,0,0,0,0,5,74.36826,13.73189,0,,799,799,1,1,1.609438,6.683361,0,3.931826,7.376508,0,0,0,78.49355,9.163564,1.609438,,0 11,1,0,0,1,129734,0,7262.407,.2628337,1,18,1,64.19317,6.990577,0,0,0,71.18375,0,0,0,8,0,3,74.36826,13.73189,0,,0,0,1,1,1.098612,0,0,0,0,0,0,0,79.03451,8.890604,1.098612,4.265265,1 11,1,0,0,2,129734,0,7262.407,1.262834,1,18,1,80.6469,14.57682,0,0,0,95.22372,0,0,0,9,0,3,74.36826,13.73189,0,,0,0,1,1,1.098612,0,0,0,0,0,0,0,79.03451,8.890604,1.098612,4.556229,1 11,1,0,0,3,129734,0,7262.407,2.262834,1,18,1,23.58722,14.57494,0,0,0,38.16216,0,0,0,3,0,3,74.36826,13.73189,0,,0,0,1,1,1.098612,0,0,0,0,0,0,0,79.03451,8.890604,1.098612,3.641845,1 11,1,0,0,4,129734,0,7262.407,3.262834,1,18,1,18.68733,14.7402,0,0,0,33.42753,0,0,0,2,0,3,74.36826,13.73189,0,,0,0,1,1,1.098612,0,0,0,0,0,0,0,79.03451,8.890604,1.098612,3.50938,1 11,1,0,0,5,129734,0,7262.407,4.262834,1,18,1,45.01876,11.32138,0,0,0,56.34014,0,0,0,6,0,3,74.36826,13.73189,0,,0,0,1,1,1.098612,0,0,0,0,0,0,0,79.03451,8.890604,1.098612,4.031407,1 9,1,50,0,1,129736,0,84.36725,20.80493,0,12.32507,1,19.43463,0,33.23911,0,0,52.67373,0,0,0,2,0,3,86.3,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,78.6664,4.446962,1.098612,3.964117,1 9,1,50,0,2,129736,0,84.36725,21.80493,0,12.32507,1,56.87331,3.22911,0,0,0,60.10242,0,0,0,4,0,3,86.3,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,78.6664,4.446962,1.098612,4.09605,1 9,1,50,0,3,129736,0,84.36725,22.80493,0,12.32507,1,45.70024,.972973,30.46683,0,0,77.14005,0,0,0,3,1,3,86.3,13.73189,0,,1000,1000,0,0,1.098612,6.907755,0,3.931826,7.600903,0,0,0,78.6664,4.446962,1.098612,4.345623,1 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1,1,0,1,4,129738,0,10474.57,3.145106,0,11,1,55.98899,16.12207,0,0,0,72.11106,0,0,0,9,0,8,74.36826,13.73189,1,,450,0,1,0,2.079442,0,1,0,0,0,0,0,79.9105,9.256801,2.079442,4.278207,1 1,1,0,1,5,129738,0,10474.57,4.145106,0,11,1,7.57257,2.141355,0,0,0,9.713925,0,0,0,1,0,8,74.36826,13.73189,1,,450,0,1,0,2.079442,0,1,0,0,0,0,0,79.9105,9.256801,2.079442,2.273561,1 3,1,100,0,1,129740,0,9542.002,.1670089,0,10,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,283,283,1,0,1.791759,5.645447,1,0,0,0,0,0,76.84648,9.163564,1.791759,,0 3,1,100,0,2,129740,0,9542.002,1.167009,0,10,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,283,283,1,0,1.791759,5.645447,1,0,0,0,0,0,76.84648,9.163564,1.791759,,0 3,1,100,0,3,129740,0,9542.002,2.167009,0,10,1,0,0,0,0,0,0,0,0,0,0,0,6,74.36826,13.73189,0,,283,283,1,0,1.791759,5.645447,1,0,0,0,0,0,76.84648,9.163564,1.791759,,0 10,1,50,0,1,129741,0,7948.511,.1560575,0,13,1,97.46761,54.91755,0,0,0,152.3852,0,0,0,16,0,3,74.36826,13.73189,0,,1000,1000,1,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,71.92097,8.980865,1.098612,5.026411,1 10,1,50,0,2,129741,0,7948.511,1.156057,0,13,1,44.74393,20.91105,0,0,0,65.65498,0,0,0,6,0,3,74.36826,13.73189,0,,1000,1000,1,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,71.92097,8.980865,1.098612,4.184413,1 10,1,50,0,3,129741,0,7948.511,2.156058,0,13,1,43.73464,23.56757,0,0,271.7445,339.0467,1,0,0,9,0,3,74.36826,13.73189,0,,1000,1000,1,0,1.098612,6.907755,0,3.931826,7.600903,1,0,0,71.92097,8.980865,1.098612,5.826138,1 6,1,25,1,1,129742,0,7717.122,.2956879,0,16,1,29.97602,0,0,0,0,29.97602,0,0,0,3,0,4,74.36826,13.73189,0,,1000,1000,1,0,1.386294,6.907755,0,3.258096,8.294049,0,0,0,82.4164,8.951326,1.386294,3.400398,1 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13,3,0,0,2,327892,0,9591.202,13.05202,0,11,1,0,0,0,0,0,0,0,0,0,0,0,3,88.3,9.967326,0,85.2,450,450,1,0,1.098612,6.109248,1,4.564348,6.160541,0,0,0,85.2,9.168706,1.098612,,0 13,3,0,0,3,327892,0,9591.202,14.05202,0,11,1,0,0,0,0,0,0,0,0,0,0,0,3,88.3,9.967326,0,85.2,450,450,1,0,1.098612,6.109248,1,4.564348,6.160541,0,0,0,85.2,9.168706,1.098612,,0 13,3,0,0,1,327893,0,9591.202,48.91171,0,11,1,0,0,0,0,0,0,0,0,0,0,0,4,81.4,0,0,86.4,450,450,0,0,1.386294,6.109248,1,4.564348,6.160541,0,0,0,86.4,9.168706,1.386294,,0 13,3,0,0,2,327893,0,9591.202,49.91171,0,11,1,0,0,0,0,0,0,0,0,0,0,0,3,81.4,0,0,86.4,450,450,0,0,1.098612,6.109248,1,4.564348,6.160541,0,0,0,86.4,9.168706,1.098612,,0 13,3,0,0,3,327893,0,9591.202,50.91171,0,11,1,0,0,0,0,0,0,0,0,0,0,0,3,81.4,0,0,86.4,450,450,0,0,1.098612,6.109248,1,4.564348,6.160541,0,0,0,86.4,9.168706,1.098612,,0 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14,4,95,1,3,429343,0,12450.44,11.73853,0,16,1,5.985464,0,0,0,0,5.985464,0,0,0,1,0,5,95,9.967326,0,66.7,1000,1000,1,0,1.609438,6.907755,0,4.564348,6.959049,0,0,0,66.7,9.429591,1.609438,1.789334,1 16,4,95,1,1,429344,0,234.6041,23.63039,1,12,1,36.1083,3.441296,0,0,0,39.54959,0,0,0,3,0,1,67.6,10.3,0,81.8,300,0,0,0,0,0,0,4.564348,5.755076,0,0,0,81.8,5.462153,0,3.677556,1 16,4,95,1,2,429344,0,234.6041,24.63039,1,12,1,0,0,0,0,0,0,0,0,0,0,0,1,67.6,10.3,0,81.8,300,0,0,0,0,0,0,4.564348,5.755076,0,0,0,81.8,5.462153,0,,0 13,4,0,1,1,429353,0,8326.687,34.10267,0,12,1,13.66397,44.28138,0,0,0,57.94534,0,0,0,2,0,4,77.1,3.4,0,75,450,425,0,0,1.386294,6.052089,1,4.564348,6.160541,1,0,0,75,9.027341,1.386294,4.0595,1 13,4,0,1,2,429353,0,8326.687,35.10267,0,12,1,41.02564,60.09324,0,0,0,101.1189,0,0,0,2,0,4,77.1,3.4,0,75,450,425,0,0,1.386294,6.052089,1,4.564348,6.160541,1,0,0,75,9.027341,1.386294,4.616297,1 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13,4,0,1,1,429396,0,8216.422,15.69062,1,9,1,34.1573,6.332993,0,0,0,40.4903,0,0,0,3,0,3,70.7,3.4,0,53.4,450,450,1,1,1.098612,6.109248,1,4.564348,6.160541,1,0,0,53.4,9.014011,1.098612,3.701062,1 13,4,0,1,2,429396,0,8216.422,16.69062,1,9,1,20.39381,1.80497,0,0,0,22.19878,0,0,0,1,0,3,70.7,3.4,0,53.4,450,450,1,1,1.098612,6.109248,1,4.564348,6.160541,1,0,0,53.4,9.014011,1.098612,3.100037,1 13,4,0,1,3,429396,0,8216.422,17.69062,1,9,1,0,0,0,0,0,0,0,0,0,0,0,3,70.7,3.4,0,53.4,450,450,1,1,1.098612,6.109248,1,4.564348,6.160541,1,0,0,53.4,9.014011,1.098612,,0 13,4,0,1,1,429397,0,8216.422,53.02122,1,9,1,167.4668,136.6701,43.92237,20.42901,0,348.0592,0,0,1,6,7,3,71.8,6.9,0,86.4,450,450,0,0,1.098612,6.109248,1,4.564348,6.160541,1,0,0,86.4,9.014011,1.098612,5.852373,1 13,4,0,1,2,429397,0,8216.422,54.02122,1,9,1,98.45288,31.80497,0,0,0,130.2579,0,0,0,0,17,3,71.8,6.9,0,86.4,450,450,0,0,1.098612,6.109248,1,4.564348,6.160541,1,0,0,86.4,9.014011,1.098612,4.869516,1 13,4,0,1,3,429397,0,8216.422,55.02122,1,9,1,32.99656,45.51161,0,0,0,78.50817,0,0,0,1,1,3,71.8,6.9,0,86.4,450,450,0,0,1.098612,6.109248,1,4.564348,6.160541,1,0,0,86.4,9.014011,1.098612,4.363203,1 13,4,0,1,1,429398,0,8216.422,54.99247,0,9,1,35.24004,49.33606,0,0,0,84.5761,0,0,0,6,0,3,79.3,24.1,0,43.2,450,450,0,0,1.098612,6.109248,1,4.564348,6.160541,1,0,0,43.2,9.014011,1.098612,4.437652,1 13,4,0,1,2,429398,0,8216.422,55.99247,0,9,1,7.032349,31.17675,0,0,0,38.2091,0,0,0,1,0,3,79.3,24.1,0,43.2,450,450,0,0,1.098612,6.109248,1,4.564348,6.160541,1,0,0,43.2,9.014011,1.098612,3.643074,1 13,4,0,1,3,429398,0,8216.422,56.99247,0,9,1,23.64574,49.49699,29.23474,0,0,102.3775,0,0,0,1,1,3,79.3,24.1,0,43.2,450,450,0,0,1.098612,6.109248,1,4.564348,6.160541,1,0,0,43.2,9.014011,1.098612,4.628667,1 13,4,0,1,1,429401,0,2856.892,59.66325,1,12,1,37.44939,35.32389,39.97976,0,0,112.753,0,0,0,6,0,1,62.8,31,0,53.4,150,150,0,0,0,5.010635,1,4.564348,5.061929,1,0,0,53.4,7.957839,0,4.7252,1 13,4,0,1,2,429401,0,2856.892,60.66325,1,12,1,11.18881,11.04895,0,0,0,22.23776,0,0,0,2,0,1,62.8,31,0,53.4,150,150,0,0,0,5.010635,1,4.564348,5.061929,1,0,0,53.4,7.957839,0,3.101792,1 13,4,0,1,3,429401,0,2856.892,61.66325,1,12,1,80.91064,10.66268,40.61565,0,0,132.189,0,0,0,6,0,1,62.8,31,0,53.4,150,150,0,0,0,5.010635,1,4.564348,5.061929,1,0,0,53.4,7.957839,0,4.884233,1 11,4,0,1,1,429463,0,4336.07,5.355236,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,88.3,9.967326,0,92.6,0,0,1,0,1.098612,0,0,0,0,0,0,0,92.6,8.374954,1.098612,,0 11,4,0,1,2,429463,0,4336.07,6.355236,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,88.3,9.967326,0,92.6,0,0,1,0,1.098612,0,0,0,0,0,0,0,92.6,8.374954,1.098612,,0 11,4,0,1,3,429463,0,4336.07,7.355236,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,88.3,9.967326,0,92.6,0,0,1,0,1.386294,0,0,0,0,0,0,0,92.6,8.374954,1.386294,,0 11,4,0,1,1,429464,0,4336.07,7.876797,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,85,9.967326,0,66.7,0,0,1,1,1.098612,0,0,0,0,0,0,0,66.7,8.374954,1.098612,,0 11,4,0,1,2,429464,0,4336.07,8.876797,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,85,9.967326,0,66.7,0,0,1,1,1.098612,0,0,0,0,0,0,0,66.7,8.374954,1.098612,,0 11,4,0,1,3,429464,0,4336.07,9.876797,1,12,1,5.803955,0,0,0,0,5.803955,0,0,0,2,0,4,85,9.967326,0,66.7,0,0,1,1,1.386294,0,0,0,0,0,0,0,66.7,8.374954,1.386294,1.75854,1 11,4,0,1,1,429465,0,4336.07,27.17591,1,12,1,15.32176,0,0,0,0,15.32176,0,0,0,1,0,3,78.7,0,0,84.1,0,0,0,0,1.098612,0,0,0,0,0,0,0,84.1,8.374954,1.098612,2.729274,1 11,4,0,1,2,429465,0,4336.07,28.17591,1,12,1,0,0,0,0,7.032349,7.032349,1,1,0,0,0,3,78.7,0,0,84.1,0,0,0,0,1.098612,0,0,0,0,0,0,0,84.1,8.374954,1.098612,1.950521,1 11,4,0,1,3,429465,0,4336.07,29.17591,1,12,1,36.04901,7.115219,0,0,0,43.16423,0,0,0,2,0,4,78.7,0,0,84.1,0,0,0,0,1.386294,0,0,0,0,0,0,0,84.1,8.374954,1.386294,3.765012,1 11,4,0,1,1,429466,0,1759.531,23.84668,0,11,1,61.21587,0,0,0,0,61.21587,0,0,0,3,0,1,81.9,0,0,88.6,0,0,0,0,0,0,0,0,0,0,0,0,88.6,7.473371,0,4.114407,1 11,4,0,1,2,429466,0,1759.531,24.84668,0,11,1,0,0,0,0,0,0,0,0,0,0,0,1,81.9,0,0,88.6,0,0,0,0,0,0,0,0,0,0,0,0,88.6,7.473371,0,,0 11,4,0,1,3,429466,0,1759.531,25.84668,0,11,1,34.78543,6.337234,0,0,0,41.12267,0,0,0,5,0,1,81.9,0,0,88.6,0,0,0,0,0,0,0,0,0,0,0,0,88.6,7.473371,0,3.71656,1 11,4,0,1,1,429534,0,4631.085,17.41821,0,12,1,0,0,0,0,0,0,0,0,0,0,0,8,78.7,0,0,92,0,492.84,1,0,2.079442,6.200184,0,0,0,0,0,0,92,8.440763,2.079442,,0 11,4,0,1,2,429534,0,4631.085,18.41821,0,12,1,37.74027,40.3188,0,0,0,78.05907,0,0,0,4,0,8,78.7,0,0,92,0,492.84,0,0,2.079442,6.200184,0,0,0,0,0,0,92,8.440763,2.079442,4.357466,1 11,4,0,1,3,429534,0,4631.085,19.41821,0,12,1,21.49613,52.38607,0,0,0,73.8822,0,0,0,5,0,7,78.7,0,0,92,0,492.84,0,0,1.94591,6.200184,0,0,0,0,0,0,92,8.440763,1.94591,4.302472,1 11,4,0,1,1,429535,0,4631.085,43.73717,0,12,1,10.2145,0,12.76813,0,0,22.98264,0,0,0,0,1,8,86.7,6.9,0,64.8,0,492.84,0,0,2.079442,6.200184,0,0,0,1,0,0,64.8,8.440763,2.079442,3.134739,1 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5,5,25,0,1,525405,1,5774.706,3.578371,1,12,1,58.3157,0,0,0,808.7177,867.0334,1,0,0,0,0,5,77.40034,10.57626,0,88.9,80.25,646.36,1,1,1.609438,6.471356,0,3.258096,5.771441,1,0,0,88.9,8.661416,1.609438,6.765078,1 5,5,25,0,2,525405,1,5774.706,4.578371,1,12,1,7.593014,0,0,0,0,7.593014,0,0,0,0,0,5,77.40034,10.57626,0,88.9,80.25,646.36,1,1,1.609438,6.471356,0,3.258096,5.771441,1,0,0,88.9,8.661416,1.609438,2.027229,1 5,5,25,0,3,525405,1,5774.706,5.578371,1,12,1,0,0,0,0,0,0,0,0,0,0,0,5,77.40034,10.57626,0,88.9,80.25,646.36,1,1,1.609438,6.471356,0,3.258096,5.771441,1,0,0,88.9,8.661416,1.609438,,0 5,5,25,0,1,525406,1,5774.706,28.00548,0,12,1,0,0,0,0,0,0,0,0,0,0,0,5,81.4,0,0,81.8,80.25,646.36,0,0,1.609438,6.471356,0,3.258096,5.771441,0,1,0,81.8,8.661416,1.609438,,0 5,5,25,0,2,525406,1,5774.706,29.00548,0,12,1,3.796507,0,0,0,0,3.796507,0,0,0,1,0,5,81.4,0,0,81.8,80.25,646.36,0,0,1.609438,6.471356,0,3.258096,5.771441,0,1,0,81.8,8.661416,1.609438,1.334081,1 5,5,25,0,3,525406,1,5774.706,30.00548,0,12,1,0,0,0,0,0,0,0,0,0,0,0,5,81.4,0,0,81.8,80.25,646.36,0,0,1.609438,6.471356,0,3.258096,5.771441,0,1,0,81.8,8.661416,1.609438,,0 5,5,25,0,1,525407,1,5774.706,25.17728,1,12,1,11.00296,3.554803,0,0,0,14.55777,0,0,0,0,0,5,77.7,3.4,0,69.3,80.25,646.36,0,0,1.609438,6.471356,0,3.258096,5.771441,1,0,0,69.3,8.661416,1.609438,2.678125,1 5,5,25,0,2,525407,1,5774.706,26.17728,1,12,1,0,0,0,0,326.4996,326.4996,1,0,0,0,0,5,77.7,3.4,0,69.3,80.25,646.36,0,0,1.609438,6.471356,0,3.258096,5.771441,1,0,0,69.3,8.661416,1.609438,5.788429,1 5,5,25,0,3,525407,1,5774.706,27.17728,1,12,1,0,0,0,0,0,0,0,0,0,0,0,5,77.7,3.4,0,69.3,80.25,646.36,0,0,1.609438,6.471356,0,3.258096,5.771441,1,0,0,69.3,8.661416,1.609438,,0 5,5,25,0,1,525408,1,5774.706,5.812457,1,12,1,15.42531,0,0,0,0,15.42531,0,0,0,0,0,5,86.7,10.57626,0,88.9,80.25,646.36,1,1,1.609438,6.471356,0,3.258096,5.771441,1,0,0,88.9,8.661416,1.609438,2.73601,1 5,5,25,0,2,525408,1,5774.706,6.812457,1,12,1,0,0,0,0,0,0,0,0,0,0,0,5,86.7,10.57626,0,88.9,80.25,646.36,1,1,1.609438,6.471356,0,3.258096,5.771441,1,0,0,88.9,8.661416,1.609438,,0 5,5,25,0,3,525408,1,5774.706,7.812457,1,12,1,13.84083,0,0,0,0,13.84083,0,0,0,0,0,5,86.7,10.57626,0,88.9,80.25,646.36,1,1,1.609438,6.471356,0,3.258096,5.771441,1,0,0,88.9,8.661416,1.609438,2.627623,1 13,5,0,0,1,525423,1,9648.745,16.99384,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,82.4,0,0,81.8,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,81.8,9.174686,1.791759,,0 13,5,0,0,2,525423,1,9648.745,17.99384,0,12,1,0,0,0,0,0,0,0,0,0,0,0,5,82.4,0,0,81.8,450,450,1,0,1.609438,6.109248,1,4.564348,6.160541,0,0,0,81.8,9.174686,1.609438,,0 13,5,0,0,3,525423,1,9648.745,18.99384,0,12,1,0,1.35506,0,0,0,1.35506,0,0,0,0,0,5,82.4,0,0,81.8,450,450,0,0,1.609438,6.109248,1,4.564348,6.160541,0,0,0,81.8,9.174686,1.609438,.3038457,1 13,5,0,0,1,525424,1,9648.745,20.0794,1,10,1,0,0,0,0,0,0,0,0,0,0,0,6,93.1,3.4,0,76.1,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,76.1,9.174686,1.791759,,0 13,5,0,0,2,525424,1,9648.745,21.0794,1,10,1,0,0,0,0,0,0,0,0,0,0,0,5,93.1,3.4,0,76.1,450,450,0,0,1.609438,6.109248,1,4.564348,6.160541,0,0,0,76.1,9.174686,1.609438,,0 13,5,0,0,3,525424,1,9648.745,22.0794,1,10,1,0,7.025729,0,0,0,7.025729,0,0,0,0,0,5,93.1,3.4,0,76.1,450,450,0,0,1.609438,6.109248,1,4.564348,6.160541,0,0,0,76.1,9.174686,1.609438,1.949579,1 13,5,0,0,1,525425,1,9648.745,13.80972,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,96.7,10.57626,.1442925,88.9,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,88.9,9.174686,1.791759,,0 13,5,0,0,1,525426,1,9648.745,36.27926,1,12,1,6.310475,0,0,0,0,6.310475,0,0,0,0,0,6,77.40034,10.57626,.1442925,,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,70.68995,9.174686,1.791759,1.842211,1 13,5,0,0,2,525426,1,9648.745,37.27926,1,12,1,3.777862,1.511145,0,0,812.9958,818.2849,1,0,0,1,0,5,77.40034,10.57626,.1442925,,450,450,0,0,1.609438,6.109248,1,4.564348,6.160541,0,0,0,70.68995,9.174686,1.609438,6.707211,1 13,5,0,0,3,525426,1,9648.745,38.27926,1,12,1,0,4.082333,0,0,0,4.082333,0,0,0,0,0,5,77.40034,10.57626,.1442925,,450,450,0,0,1.609438,6.109248,1,4.564348,6.160541,0,0,0,70.68995,9.174686,1.609438,1.406669,1 13,5,0,0,1,525427,1,9648.745,18.3436,0,10.96978,1,0,0,0,0,0,0,0,0,0,0,0,6,90.4,0,0,80.7,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,80.7,9.174686,1.791759,,0 13,5,0,0,2,525427,1,9648.745,19.3436,0,10.96978,1,0,0,0,0,0,0,0,0,0,0,0,5,90.4,0,0,80.7,450,450,0,0,1.609438,6.109248,1,4.564348,6.160541,0,0,0,80.7,9.174686,1.609438,,0 13,5,0,0,3,525427,1,9648.745,20.3436,0,10.96978,1,0,0,0,0,0,0,0,0,0,0,0,5,90.4,0,0,80.7,450,450,0,0,1.609438,6.109248,1,4.564348,6.160541,0,0,0,80.7,9.174686,1.609438,,0 13,5,0,0,1,525428,1,9648.745,43.84121,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,94.1,6.9,0,80.7,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,80.7,9.174686,1.791759,,0 13,5,0,0,2,525428,1,9648.745,44.84121,0,12,1,0,0,0,0,0,0,0,0,0,0,0,5,94.1,6.9,0,80.7,450,450,0,0,1.609438,6.109248,1,4.564348,6.160541,0,0,0,80.7,9.174686,1.609438,,0 13,5,0,0,3,525428,1,9648.745,45.84121,0,12,1,0,0,0,0,0,0,0,0,0,0,0,5,94.1,6.9,0,80.7,450,450,0,0,1.609438,6.109248,1,4.564348,6.160541,0,0,0,80.7,9.174686,1.609438,,0 13,5,0,0,1,525438,0,7237.583,30.45038,0,10,1,0,0,0,0,0,0,0,0,0,0,0,3,97.9,3.4,0,71.6,450,450,0,0,1.098612,6.109248,1,4.564348,6.160541,0,1,0,71.6,8.88718,1.098612,,0 13,5,0,0,2,525438,0,7237.583,31.45038,0,10,1,0,0,0,0,0,0,0,0,0,0,0,3,97.9,3.4,0,71.6,450,450,0,0,1.098612,6.109248,1,4.564348,6.160541,0,1,0,71.6,8.88718,1.098612,,0 13,5,0,0,3,525438,0,7237.583,32.45037,0,10,1,0,0,0,0,0,0,0,0,0,0,0,3,97.9,3.4,0,71.6,450,450,0,0,1.098612,6.109248,1,4.564348,6.160541,0,1,0,71.6,8.88718,1.098612,,0 13,5,0,1,1,525439,0,7237.583,11.00616,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,100,10.57626,0,92.6,450,450,1,0,1.098612,6.109248,1,4.564348,6.160541,0,0,0,92.6,8.88718,1.098612,,0 13,5,0,1,2,525439,0,7237.583,12.00616,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,100,10.57626,0,92.6,450,450,1,0,1.098612,6.109248,1,4.564348,6.160541,0,0,0,92.6,8.88718,1.098612,,0 13,5,0,1,3,525439,0,7237.583,13.00616,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,100,10.57626,0,92.6,450,450,1,0,1.098612,6.109248,1,4.564348,6.160541,0,0,0,92.6,8.88718,1.098612,,0 13,5,0,1,1,525440,0,7237.583,29.96852,1,9,1,0,5.469079,0,0,0,5.469079,0,0,0,0,0,3,96.3,3.4,0,77.4,450,450,0,0,1.098612,6.109248,1,4.564348,6.160541,0,0,0,77.4,8.88718,1.098612,1.69911,1 13,5,0,1,2,525440,0,7237.583,30.96852,1,9,1,0,0,0,0,0,0,0,0,0,0,0,3,96.3,3.4,0,77.4,450,450,0,0,1.098612,6.109248,1,4.564348,6.160541,0,0,0,77.4,8.88718,1.098612,,0 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18,5,25,0,3,525529,0,6674.895,41.48802,1,11,1,0,0,0,0,0,0,0,0,0,0,0,3,90.4,10.3,0,96.6,750,750,0,0,1.098612,6.620073,0,3.258096,8.006368,1,0,0,96.6,8.806258,1.098612,,0 18,5,25,0,1,525531,0,6674.895,40.53114,0,10,1,41.39651,0,0,0,0,41.39651,0,0,0,0,2,3,85.1,17.2,0,60.2,750,750,0,0,1.098612,6.620073,0,3.258096,8.006368,1,0,0,60.2,8.806258,1.098612,3.723197,1 18,5,25,0,2,525531,0,6674.895,41.53114,0,10,1,146.1503,0,0,0,0,146.1503,0,0,0,4,0,3,85.1,17.2,0,60.2,750,750,0,0,1.098612,6.620073,0,3.258096,8.006368,1,0,0,60.2,8.806258,1.098612,4.984635,1 18,5,25,0,3,525531,0,6674.895,42.53114,0,10,1,0,0,0,0,0,0,0,0,0,0,0,3,85.1,17.2,0,60.2,750,750,0,0,1.098612,6.620073,0,3.258096,8.006368,1,0,0,60.2,8.806258,1.098612,,0 18,5,25,0,1,525532,0,6674.895,16.89528,0,11,1,45.88529,0,0,0,0,45.88529,0,0,0,2,3,3,55.9,3.4,0,61.4,750,750,1,0,1.098612,6.620073,0,3.258096,8.006368,0,0,0,61.4,8.806258,1.098612,3.826144,1 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16,5,95,1,1,525534,1,1451.101,9.607119,0,11,1,0,0,0,0,702.0736,702.0736,1,0,0,0,0,5,98.3,10.57626,0,81.5,510.6,510.6,1,0,1.609438,6.235587,0,4.564348,6.28688,0,0,0,81.5,7.280766,1.609438,6.554038,1 16,5,95,1,2,525534,1,1451.101,10.60712,0,11,1,0,0,0,0,258.1625,258.1625,1,1,0,0,0,5,98.3,10.57626,0,81.5,510.6,510.6,1,0,1.609438,6.235587,0,4.564348,6.28688,0,0,0,81.5,7.280766,1.609438,5.553589,1 16,5,95,1,3,525534,1,1451.101,11.60712,0,11,1,93.07958,41.19723,0,0,996.8858,1131.163,1,0,0,6,0,5,98.3,10.57626,0,81.5,510.6,510.6,1,0,1.609438,6.235587,0,4.564348,6.28688,0,0,0,81.5,7.280766,1.609438,7.031001,1 16,5,95,1,1,525535,1,1451.101,18.88022,1,10.96978,1,0,0,0,0,0,0,0,0,0,0,0,5,70.2,0,0,61.4,510.6,510.6,0,0,1.609438,6.235587,0,4.564348,6.28688,0,0,0,61.4,7.280766,1.609438,,0 16,5,95,1,2,525535,1,1451.101,19.88022,1,10.96978,1,8.352316,0,0,0,0,8.352316,0,0,0,1,0,5,70.2,0,0,61.4,510.6,510.6,0,0,1.609438,6.235587,0,4.564348,6.28688,0,0,0,61.4,7.280766,1.609438,2.122539,1 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14,5,95,1,2,525553,1,3421.403,28.36756,1,12,1,0,4.652672,0,0,0,4.652672,0,0,0,0,0,3,26.1,6.9,1,34.1,142.55,142.55,0,0,1.098612,4.959693,0,4.564348,5.010986,1,0,0,34.1,8.138098,1.098612,1.537442,1 14,5,95,1,3,525553,1,3421.403,29.36756,1,12,1,0,0,0,0,453.6585,453.6585,1,0,0,0,0,3,26.1,6.9,1,34.1,142.55,142.55,0,0,1.098612,4.959693,0,4.564348,5.010986,1,0,0,34.1,8.138098,1.098612,6.117345,1 14,5,95,1,1,525554,1,3421.403,26.67488,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,63.8,13.8,1,52.3,142.55,142.55,0,0,1.098612,4.959693,0,4.564348,5.010986,0,0,0,52.3,8.138098,1.098612,,0 14,5,95,1,2,525554,1,3421.403,27.67488,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,63.8,13.8,1,52.3,142.55,142.55,0,0,1.098612,4.959693,0,4.564348,5.010986,0,0,0,52.3,8.138098,1.098612,,0 14,5,95,1,3,525554,1,3421.403,28.67488,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,63.8,13.8,1,52.3,142.55,142.55,0,0,1.098612,4.959693,0,4.564348,5.010986,0,0,0,52.3,8.138098,1.098612,,0 11,5,0,1,1,525555,1,769.5853,33.47844,1,12,1,8.081667,0,0,0,0,8.081667,0,0,0,0,0,6,63.3,10.3,0,83,0,0,0,0,1.791759,0,0,0,0,0,0,0,83,6.647151,1.791759,2.089598,1 11,5,0,1,2,525555,1,769.5853,34.47844,1,12,1,15.64886,.9770992,0,0,0,16.62595,0,0,0,2,0,6,63.3,10.3,0,83,0,0,0,0,1.791759,0,0,0,0,0,0,0,83,6.647151,1.791759,2.810965,1 11,5,0,1,3,525555,1,769.5853,35.47844,1,12,1,54.3554,10.79094,0,0,0,65.14634,0,0,0,4,0,6,63.3,10.3,0,83,0,0,0,0,1.791759,0,0,0,0,0,0,0,83,6.647151,1.791759,4.176636,1 11,5,0,1,1,525556,1,769.5853,12.44353,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,75,10.57626,0,77.8,0,0,1,0,1.791759,0,0,0,0,0,0,0,77.8,6.647151,1.791759,,0 11,5,0,1,2,525556,1,769.5853,13.44353,0,12,1,3.816794,0,0,0,0,3.816794,0,0,0,1,0,6,75,10.57626,0,77.8,0,0,1,0,1.791759,0,0,0,0,0,0,0,77.8,6.647151,1.791759,1.339411,1 11,5,0,1,3,525556,1,769.5853,14.44353,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,75,10.57626,0,77.8,0,0,1,0,1.791759,0,0,0,0,0,0,0,77.8,6.647151,1.791759,,0 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11,5,0,0,1,525586,0,4301.075,8.147844,0,8,1,7.993269,0,0,0,0,7.993269,0,0,0,0,0,4,85,10.57626,.1442925,74.1,0,147.36,1,0,1.386294,4.992878,0,0,0,0,0,0,74.1,8.366853,1.386294,2.0786,1 11,5,0,0,2,525586,0,4301.075,9.147844,0,8,1,11.33358,0,0,0,0,11.33358,0,0,0,0,1,4,85,10.57626,.1442925,74.1,0,147.36,1,0,1.386294,4.992878,0,0,0,0,0,0,74.1,8.366853,1.386294,2.42777,1 11,5,0,0,3,525586,0,4301.075,10.14784,0,8,1,0,0,0,0,0,0,0,0,0,0,0,4,85,10.57626,.1442925,74.1,0,147.36,1,0,1.386294,4.992878,0,0,0,0,0,0,74.1,8.366853,1.386294,,0 11,5,0,0,1,525587,0,4301.075,40.20534,0,13,1,0,8.93984,0,0,0,8.93984,0,0,0,0,0,4,64.9,6.9,1,60.2,0,147.36,0,0,1.386294,4.992878,0,0,0,1,0,0,60.2,8.366853,1.386294,2.190518,1 11,5,0,0,2,525587,0,4301.075,41.20534,0,13,1,0,0,0,0,0,0,0,0,0,0,0,4,64.9,6.9,1,60.2,0,147.36,0,0,1.386294,4.992878,0,0,0,1,0,0,60.2,8.366853,1.386294,,0 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11,5,0,0,2,525589,0,4301.075,26.8809,1,8,1,11.33358,0,0,0,0,11.33358,0,0,0,0,1,4,78.7,13.8,0,63.1,0,147.36,0,0,1.386294,4.992878,0,0,0,1,0,0,63.1,8.366853,1.386294,2.42777,1 11,5,0,0,3,525589,0,4301.075,27.8809,1,8,1,42.88165,9.73928,0,0,0,52.62093,0,0,0,0,0,4,78.7,13.8,0,63.1,0,147.36,0,0,1.386294,4.992878,0,0,0,1,0,0,63.1,8.366853,1.386294,3.963114,1 16,5,95,0,1,525593,1,6674.895,36.65435,1,9,1,0,0,0,0,0,0,0,0,0,0,0,3,63.3,10.3,0,76.1,176.4,176.4,0,0,1.098612,5.172754,0,4.564348,5.224048,1,0,0,76.1,8.806258,1.098612,,0 16,5,95,0,2,525593,1,6674.895,37.65435,1,9,1,11.62791,0,0,0,0,11.62791,0,0,0,0,0,3,63.3,10.3,0,76.1,176.4,176.4,0,0,1.098612,5.172754,0,4.564348,5.224048,1,0,0,76.1,8.806258,1.098612,2.453408,1 16,5,95,0,3,525593,1,6674.895,38.65435,1,9,1,0,0,0,0,0,0,0,0,0,0,0,3,63.3,10.3,0,76.1,176.4,176.4,0,0,1.098612,5.172754,0,4.564348,5.224048,1,0,0,76.1,8.806258,1.098612,,0 16,5,95,0,1,525595,1,6674.895,14.87748,0,9,1,7.919967,0,0,0,0,7.919967,0,0,0,0,0,3,77.40034,10.57626,.1442925,,176.4,176.4,1,0,1.098612,5.172754,0,4.564348,5.224048,1,0,0,70.68995,8.806258,1.098612,2.069387,1 16,5,95,0,2,525595,1,6674.895,15.87748,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,77.40034,10.57626,.1442925,,176.4,176.4,1,0,1.098612,5.172754,0,4.564348,5.224048,1,0,0,70.68995,8.806258,1.098612,,0 16,5,95,0,3,525595,1,6674.895,16.87748,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,77.40034,10.57626,.1442925,,176.4,176.4,1,0,1.098612,5.172754,0,4.564348,5.224048,1,0,0,70.68995,8.806258,1.098612,,0 16,5,95,0,1,525596,1,6674.895,6.913073,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,88.3,10.57626,.1442925,85.2,176.4,176.4,1,0,1.098612,5.172754,0,4.564348,5.224048,0,0,0,85.2,8.806258,1.098612,,0 16,5,95,0,2,525596,1,6674.895,7.913073,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,88.3,10.57626,.1442925,85.2,176.4,176.4,1,0,1.098612,5.172754,0,4.564348,5.224048,0,0,0,85.2,8.806258,1.098612,,0 16,5,95,0,3,525596,1,6674.895,8.913074,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,88.3,10.57626,.1442925,85.2,176.4,176.4,1,0,1.098612,5.172754,0,4.564348,5.224048,0,0,0,85.2,8.806258,1.098612,,0 11,5,0,1,1,525617,1,1426.523,12.2026,0,7,1,10.57977,0,23.69869,0,0,34.27846,0,0,0,0,1,7,90,10.57626,0,96.3,0,0,1,0,1.94591,0,0,0,0,1,0,0,96.3,7.263696,1.94591,3.534517,1 11,5,0,1,2,525617,1,1426.523,13.2026,0,7,1,0,0,0,0,0,0,0,0,0,0,0,7,90,10.57626,0,96.3,0,0,1,0,1.94591,0,0,0,0,1,0,0,96.3,7.263696,1.94591,,0 11,5,0,1,3,525617,1,1426.523,14.2026,0,7,1,0,0,0,0,0,0,0,0,0,0,0,7,90,10.57626,0,96.3,0,0,1,0,1.94591,0,0,0,0,1,0,0,96.3,7.263696,1.94591,,0 11,5,0,1,1,525618,1,1426.523,11.28542,0,7,1,0,0,0,0,0,0,0,0,0,0,0,7,95,10.57626,0,96.3,0,0,1,0,1.94591,0,0,0,0,0,0,0,96.3,7.263696,1.94591,,0 11,5,0,1,2,525618,1,1426.523,12.28542,0,7,1,13.09795,0,0,0,0,13.09795,0,0,0,0,0,7,95,10.57626,0,96.3,0,0,1,0,1.94591,0,0,0,0,0,0,0,96.3,7.263696,1.94591,2.572456,1 11,5,0,1,3,525618,1,1426.523,13.28542,0,7,1,62.28374,3.442907,23.87543,0,267.8201,357.4221,1,1,0,3,1,7,95,10.57626,0,96.3,0,0,1,0,1.94591,0,0,0,0,0,0,0,96.3,7.263696,1.94591,5.878918,1 11,5,0,1,1,525619,1,1426.523,20.0794,1,10,1,28.24799,1.815489,23.69869,0,0,53.76217,0,0,0,0,1,7,51.6,6.9,0,71.6,0,0,0,0,1.94591,0,0,0,0,0,0,0,71.6,7.263696,1.94591,3.98457,1 11,5,0,1,2,525619,1,1426.523,21.0794,1,10,1,7.213364,43.92559,0,0,2274.108,2325.247,1,0,0,0,0,7,51.6,6.9,0,71.6,0,0,0,0,1.94591,0,0,0,0,0,0,0,71.6,7.263696,1.94591,7.751582,1 11,5,0,1,3,525619,1,1426.523,22.0794,1,10,1,20.41522,10.34602,21.79931,0,0,52.56055,0,0,0,1,1,7,51.6,6.9,0,71.6,0,0,0,0,1.94591,0,0,0,0,0,0,0,71.6,7.263696,1.94591,3.961966,1 11,5,0,1,1,525620,1,1426.523,35.14305,1,7,1,10.57977,0,23.69869,0,0,34.27846,0,0,0,0,1,7,85.1,6.9,0,81.8,0,0,0,0,1.94591,0,0,0,0,1,0,0,81.8,7.263696,1.94591,3.534517,1 11,5,0,1,2,525620,1,1426.523,36.14305,1,7,1,0,0,0,0,0,0,0,0,0,0,0,7,85.1,6.9,0,81.8,0,0,0,0,1.94591,0,0,0,0,1,0,0,81.8,7.263696,1.94591,,0 11,5,0,1,3,525620,1,1426.523,37.14305,1,7,1,8.650519,0,22.14533,0,0,30.79585,0,0,0,0,1,7,85.1,6.9,0,81.8,0,0,0,0,1.94591,0,0,0,0,1,0,0,81.8,7.263696,1.94591,3.42738,1 11,5,0,1,1,525621,1,1426.523,14.09719,1,7,1,10.57977,0,23.69869,0,0,34.27846,0,0,0,0,1,7,100,10.57626,0,96.3,0,0,1,1,1.94591,0,0,0,0,1,0,0,96.3,7.263696,1.94591,3.534517,1 11,5,0,1,2,525621,1,1426.523,15.09719,1,7,1,0,0,0,0,0,0,0,0,0,0,0,7,100,10.57626,0,96.3,0,0,1,1,1.94591,0,0,0,0,1,0,0,96.3,7.263696,1.94591,,0 11,5,0,1,3,525621,1,1426.523,16.09719,1,7,1,14.87889,8.079585,20.41522,0,0,43.3737,0,0,0,1,1,7,100,10.57626,0,96.3,0,0,1,1,1.94591,0,0,0,0,1,0,0,96.3,7.263696,1.94591,3.769853,1 11,5,0,1,1,525622,1,1426.523,15.154,0,7,1,0,0,0,0,0,0,0,0,0,0,0,7,97.3,0,0,96.6,0,0,1,0,1.94591,0,0,0,0,1,0,0,96.6,7.263696,1.94591,,0 11,5,0,1,2,525622,1,1426.523,16.15401,0,7,1,0,0,0,0,0,0,0,0,0,0,0,7,97.3,0,0,96.6,0,0,1,0,1.94591,0,0,0,0,1,0,0,96.6,7.263696,1.94591,,0 11,5,0,1,1,525624,1,1426.523,14.09719,1,7,1,0,0,0,0,0,0,0,0,0,0,0,7,85,10.57626,0,96.3,0,0,1,1,1.94591,0,0,0,0,1,0,0,96.3,7.263696,1.94591,,0 11,5,0,1,2,525624,1,1426.523,15.09719,1,7,1,0,0,0,0,0,0,0,0,0,0,0,7,85,10.57626,0,96.3,0,0,1,1,1.94591,0,0,0,0,1,0,0,96.3,7.263696,1.94591,,0 11,5,0,1,3,525624,1,1426.523,16.09719,1,7,1,0,0,0,0,0,0,0,0,0,0,0,7,85,10.57626,0,96.3,0,0,1,1,1.94591,0,0,0,0,1,0,0,96.3,7.263696,1.94591,,0 11,5,0,1,1,525628,0,8880.185,34.78166,0,12,1,150.6559,39.1113,1.481168,0,0,191.2484,0,0,0,12,0,5,89.4,3.4,0,75,0,646.36,0,0,1.609438,6.471356,0,0,0,0,0,0,75,9.09169,1.609438,5.253573,1 11,5,0,1,2,525628,0,8880.185,35.78166,0,12,1,157.5551,22.35004,0,0,0,179.9051,0,0,0,10,0,5,89.4,3.4,0,75,0,646.36,0,0,1.609438,6.471356,0,0,0,0,0,0,75,9.09169,1.609438,5.19243,1 11,5,0,1,3,525628,0,8880.185,36.78166,0,12,1,87.88927,30.34256,0,0,0,118.2318,0,0,0,10,0,5,89.4,3.4,0,75,0,646.36,0,0,1.609438,6.471356,0,0,0,0,0,0,75,9.09169,1.609438,4.772647,1 11,5,0,1,1,525629,0,8880.185,31.92882,1,12,1,79.55988,48.15912,0,0,872.6196,1000.339,1,0,0,8,0,5,75.5,10.3,1,73.7,0,646.36,0,0,1.609438,6.471356,0,0,0,0,0,0,73.7,9.09169,1.609438,6.908094,1 11,5,0,1,2,525629,0,8880.185,32.92882,1,12,1,17.46393,17.73348,0,0,1247.912,1283.109,2,1,0,2,0,5,75.5,10.3,1,73.7,0,646.36,0,0,1.609438,6.471356,0,0,0,0,0,0,73.7,9.09169,1.609438,7.157042,1 11,5,0,1,3,525629,0,8880.185,33.92882,1,12,1,134.6021,21.53287,0,0,0,156.1349,0,0,0,7,0,5,75.5,10.3,1,73.7,0,646.36,0,0,1.609438,6.471356,0,0,0,0,0,0,73.7,9.09169,1.609438,5.050721,1 11,5,0,1,1,525630,0,8880.185,10.05339,1,12,1,0,2.06094,0,0,0,2.06094,0,0,0,0,0,5,93.3,10.57626,0,92.6,0,646.36,1,1,1.609438,6.471356,0,0,0,0,0,0,92.6,9.09169,1.609438,.723162,1 11,5,0,1,2,525630,0,8880.185,11.05339,1,12,1,5.694761,6.545178,0,0,0,12.23994,0,0,0,1,0,5,93.3,10.57626,0,92.6,0,646.36,1,1,1.609438,6.471356,0,0,0,0,0,0,92.6,9.09169,1.609438,2.504704,1 11,5,0,1,3,525630,0,8880.185,12.05339,1,12,1,32.17993,1.346021,0,0,0,33.52595,0,0,0,1,0,5,93.3,10.57626,0,92.6,0,646.36,1,1,1.609438,6.471356,0,0,0,0,0,0,92.6,9.09169,1.609438,3.51232,1 11,5,0,1,1,525631,0,8880.185,5.377139,0,12,1,19.46678,16.35209,0,0,0,35.81887,0,0,0,4,0,5,83.3,10.57626,0,51.9,0,646.36,1,0,1.609438,6.471356,0,0,0,0,0,0,51.9,9.09169,1.609438,3.578475,1 11,5,0,1,2,525631,0,8880.185,6.377139,0,12,1,11.38952,18.95976,0,0,0,30.34928,0,0,0,2,0,5,83.3,10.57626,0,51.9,0,646.36,1,0,1.609438,6.471356,0,0,0,0,0,0,51.9,9.09169,1.609438,3.412773,1 11,5,0,1,3,525631,0,8880.185,7.377139,0,12,1,25.95156,21.89619,0,0,0,47.84775,0,0,0,5,0,5,83.3,10.57626,0,51.9,0,646.36,1,0,1.609438,6.471356,0,0,0,0,0,0,51.9,9.09169,1.609438,3.868024,1 11,5,0,1,1,525632,0,8880.185,2.882957,0,12,1,60.51629,10.44012,0,0,0,70.95641,0,0,0,8,0,5,77.40034,10.57626,0,59.3,0,646.36,1,0,1.609438,6.471356,0,0,0,0,0,0,59.3,9.09169,1.609438,4.262066,1 11,5,0,1,2,525632,0,8880.185,3.882957,0,12,1,57.70691,3.02202,0,0,0,60.72893,0,0,0,3,0,5,77.40034,10.57626,0,59.3,0,646.36,1,0,1.609438,6.471356,0,0,0,0,0,0,59.3,9.09169,1.609438,4.10642,1 11,5,0,1,3,525632,0,8880.185,4.882957,0,12,1,23.18339,2.885813,0,0,537.7162,563.7855,1,0,0,2,0,5,77.40034,10.57626,0,59.3,0,646.36,1,0,1.609438,6.471356,0,0,0,0,0,0,59.3,9.09169,1.609438,6.334674,1 5,5,25,0,1,525656,1,0,39.29911,0,5,1,0,0,0,0,0,0,0,0,0,0,0,8,62.2,0,0,76.1,333.75,333.75,0,0,2.079442,5.810392,0,3.258096,7.196687,0,0,0,76.1,0,2.079442,,0 5,5,25,0,2,525656,1,0,40.29911,0,5,1,0,0,0,0,0,0,0,0,0,0,0,9,62.2,0,0,76.1,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,0,0,0,76.1,0,2.197225,,0 5,5,25,0,3,525656,1,0,41.29911,0,5,1,0,0,0,0,0,0,0,0,0,0,0,9,62.2,0,0,76.1,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,0,0,0,76.1,0,2.197225,,0 5,5,25,0,4,525656,1,0,42.29911,0,5,1,0,0,0,0,0,0,0,0,0,0,0,9,62.2,0,0,76.1,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,0,0,0,76.1,0,2.197225,,0 5,5,25,0,5,525656,1,0,43.29911,0,5,1,10.14885,0,0,0,0,10.14885,0,0,0,0,0,9,62.2,0,0,76.1,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,0,0,0,76.1,0,2.197225,2.31736,1 5,5,25,1,1,525657,1,0,10.00958,1,6,1,0,0,0,0,0,0,0,0,0,0,0,8,83.3,10.57626,0,63,333.75,333.75,1,1,2.079442,5.810392,0,3.258096,7.196687,0,1,0,63,0,2.079442,,0 5,5,25,1,2,525657,1,0,11.00958,1,6,1,0,0,0,0,0,0,0,0,0,0,0,9,83.3,10.57626,0,63,333.75,333.75,1,1,2.197225,5.810392,0,3.258096,7.196687,0,1,0,63,0,2.197225,,0 5,5,25,1,3,525657,1,0,12.00958,1,6,1,0,0,0,0,0,0,0,0,0,0,0,9,83.3,10.57626,0,63,333.75,333.75,1,1,2.197225,5.810392,0,3.258096,7.196687,0,1,0,63,0,2.197225,,0 5,5,25,1,4,525657,1,0,13.00958,1,6,1,0,0,0,0,0,0,0,0,0,0,0,9,83.3,10.57626,0,63,333.75,333.75,1,1,2.197225,5.810392,0,3.258096,7.196687,0,1,0,63,0,2.197225,,0 5,5,25,1,5,525657,1,0,14.00958,1,6,1,0,0,0,0,0,0,0,0,0,0,0,9,83.3,10.57626,0,63,333.75,333.75,1,1,2.197225,5.810392,0,3.258096,7.196687,0,1,0,63,0,2.197225,,0 5,5,25,1,1,525658,1,0,44.6872,1,6,1,8.599508,0,0,0,0,8.599508,0,0,0,0,0,8,63.3,6.9,0,50,333.75,333.75,0,0,2.079442,5.810392,0,3.258096,7.196687,0,1,0,50,0,2.079442,2.151705,1 5,5,25,1,2,525658,1,0,45.6872,1,6,1,0,0,0,0,0,0,0,0,0,0,0,9,63.3,6.9,0,50,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,0,1,0,50,0,2.197225,,0 5,5,25,1,3,525658,1,0,46.6872,1,6,1,17.5073,0,0,0,0,17.5073,0,0,0,0,0,9,63.3,6.9,0,50,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,0,1,0,50,0,2.197225,2.862618,1 5,5,25,1,4,525658,1,0,47.6872,1,6,1,0,0,0,0,0,0,0,0,0,0,0,9,63.3,6.9,0,50,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,0,1,0,50,0,2.197225,,0 5,5,25,1,5,525658,1,0,48.6872,1,6,1,44.99323,3.697564,35.53112,0,0,84.22192,0,0,0,0,2,9,63.3,6.9,0,50,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,0,1,0,50,0,2.197225,4.433455,1 5,5,25,1,1,525659,1,0,13.4757,0,6,1,8.599508,0,0,0,0,8.599508,0,0,0,0,0,8,98.3,10.57626,0,59.3,333.75,333.75,1,0,2.079442,5.810392,0,3.258096,7.196687,1,0,0,59.3,0,2.079442,2.151705,1 5,5,25,1,2,525659,1,0,14.4757,0,6,1,0,0,0,0,0,0,0,0,0,0,0,9,98.3,10.57626,0,59.3,333.75,333.75,1,0,2.197225,5.810392,0,3.258096,7.196687,1,0,0,59.3,0,2.197225,,0 5,5,25,1,3,525659,1,0,15.4757,0,6,1,0,0,0,0,0,0,0,0,0,0,0,9,98.3,10.57626,0,59.3,333.75,333.75,1,0,2.197225,5.810392,0,3.258096,7.196687,1,0,0,59.3,0,2.197225,,0 5,5,25,1,4,525659,1,0,16.4757,0,6,1,316.2978,0,0,0,0,316.2978,0,0,0,2,0,9,98.3,10.57626,0,59.3,333.75,333.75,1,0,2.197225,5.810392,0,3.258096,7.196687,1,0,0,59.3,0,2.197225,5.756684,1 5,5,25,1,5,525659,1,0,17.4757,0,6,1,0,0,0,0,0,0,0,0,0,0,0,9,98.3,10.57626,0,59.3,333.75,333.75,1,0,2.197225,5.810392,0,3.258096,7.196687,1,0,0,59.3,0,2.197225,,0 5,5,25,1,1,525660,1,0,11.77002,0,6,1,0,0,0,0,0,0,0,0,0,0,0,8,80,10.57626,0,77.8,333.75,333.75,1,0,2.079442,5.810392,0,3.258096,7.196687,1,0,0,77.8,0,2.079442,,0 5,5,25,1,2,525660,1,0,12.77002,0,6,1,0,0,0,0,0,0,0,0,0,0,0,9,80,10.57626,0,77.8,333.75,333.75,1,0,2.197225,5.810392,0,3.258096,7.196687,1,0,0,77.8,0,2.197225,,0 5,5,25,1,3,525660,1,0,13.77002,0,6,1,0,0,0,0,0,0,0,0,0,0,0,9,80,10.57626,0,77.8,333.75,333.75,1,0,2.197225,5.810392,0,3.258096,7.196687,1,0,0,77.8,0,2.197225,,0 5,5,25,1,4,525660,1,0,14.77002,0,6,1,0,0,0,0,0,0,0,0,0,0,0,9,80,10.57626,0,77.8,333.75,333.75,1,0,2.197225,5.810392,0,3.258096,7.196687,1,0,0,77.8,0,2.197225,,0 5,5,25,1,5,525660,1,0,15.77002,0,6,1,10.14885,2.405277,0,0,0,12.55413,0,0,0,0,0,9,80,10.57626,0,77.8,333.75,333.75,1,0,2.197225,5.810392,0,3.258096,7.196687,1,0,0,77.8,0,2.197225,2.530049,1 5,5,25,1,1,525661,1,0,16.75565,1,6,1,0,0,0,0,0,0,1,1,0,0,0,8,54.8,3.4,0,54.5,333.75,333.75,1,1,2.079442,5.810392,0,3.258096,7.196687,0,1,0,54.5,0,2.079442,,0 5,5,25,1,2,525661,1,0,17.75565,1,6,1,0,1.244303,0,0,0,1.244303,0,0,0,0,0,9,54.8,3.4,0,54.5,333.75,333.75,1,1,2.197225,5.810392,0,3.258096,7.196687,0,1,0,54.5,0,2.197225,.2185752,1 5,5,25,1,3,525661,1,0,18.75565,1,6,1,0,0,0,0,0,0,0,0,0,0,0,9,54.8,3.4,0,54.5,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,0,1,0,54.5,0,2.197225,,0 5,5,25,1,4,525661,1,0,19.75565,1,6,1,0,0,0,0,0,0,0,0,0,0,0,9,54.8,3.4,0,54.5,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,0,1,0,54.5,0,2.197225,,0 5,5,25,1,5,525661,1,0,20.75565,1,6,1,27.74019,1.589986,0,0,0,29.33018,0,0,0,1,0,9,54.8,3.4,0,54.5,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,0,1,0,54.5,0,2.197225,3.378617,1 5,5,25,0,1,525662,1,0,15.77002,0,6,1,0,0,0,0,0,0,0,0,0,0,0,8,58.5,0,0,76.1,333.75,333.75,1,0,2.079442,5.810392,0,3.258096,7.196687,0,1,0,76.1,0,2.079442,,0 5,5,25,0,2,525662,1,0,16.77002,0,6,1,6.836828,0,0,0,0,6.836828,0,0,0,1,0,9,58.5,0,0,76.1,333.75,333.75,1,0,2.197225,5.810392,0,3.258096,7.196687,0,1,0,76.1,0,2.197225,1.922324,1 5,5,25,0,3,525662,1,0,17.77002,0,6,1,0,0,0,0,0,0,0,0,0,0,0,9,58.5,0,0,76.1,333.75,333.75,1,0,2.197225,5.810392,0,3.258096,7.196687,0,1,0,76.1,0,2.197225,,0 5,5,25,0,4,525662,1,0,18.77002,0,6,1,0,0,0,0,0,0,0,0,0,0,0,9,58.5,0,0,76.1,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,0,1,0,76.1,0,2.197225,,0 5,5,25,0,5,525662,1,0,19.77002,0,6,1,0,0,0,0,0,0,0,0,0,0,0,9,58.5,0,0,76.1,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,0,1,0,76.1,0,2.197225,,0 5,5,25,0,1,525663,1,0,14.61465,1,6,1,0,0,0,0,0,0,0,0,0,0,0,8,60.1,3.4,0,59.1,333.75,333.75,1,1,2.079442,5.810392,0,3.258096,7.196687,1,0,0,59.1,0,2.079442,,0 5,5,25,0,2,525663,1,0,15.61465,1,6,1,0,0,0,0,0,0,0,0,0,0,0,9,60.1,3.4,0,59.1,333.75,333.75,1,1,2.197225,5.810392,0,3.258096,7.196687,1,0,0,59.1,0,2.197225,,0 5,5,25,0,3,525663,1,0,16.61465,1,6,1,0,0,0,0,0,0,0,0,0,0,0,9,60.1,3.4,0,59.1,333.75,333.75,1,1,2.197225,5.810392,0,3.258096,7.196687,1,0,0,59.1,0,2.197225,,0 5,5,25,0,4,525663,1,0,17.61465,1,6,1,0,0,0,0,0,0,0,0,0,0,0,9,60.1,3.4,0,59.1,333.75,333.75,1,1,2.197225,5.810392,0,3.258096,7.196687,1,0,0,59.1,0,2.197225,,0 5,5,25,0,5,525663,1,0,18.61465,1,6,1,0,0,0,0,0,0,0,0,0,0,0,9,60.1,3.4,0,59.1,333.75,333.75,0,0,2.197225,5.810392,0,3.258096,7.196687,1,0,0,59.1,0,2.197225,,0 11,5,0,1,1,525705,0,12350.23,36.18344,0,9,1,0,0,0,0,0,0,0,0,0,0,0,2,78.2,0,0,84.1,0,308.42,0,0,.6931472,5.731462,0,0,0,0,0,0,84.1,9.421511,.6931472,,0 11,5,0,1,2,525705,0,12350.23,37.18344,0,9,1,7.972665,8.363706,0,0,0,16.33637,0,0,0,1,0,2,78.2,0,0,84.1,0,308.42,0,0,.6931472,5.731462,0,0,0,0,0,0,84.1,9.421511,.6931472,2.793394,1 11,5,0,1,3,525705,0,12350.23,38.18344,0,9,1,366.436,37.78547,0,0,309.6886,713.91,1,0,0,4,0,2,78.2,0,0,84.1,0,308.42,0,0,.6931472,5.731462,0,0,0,0,0,0,84.1,9.421511,.6931472,6.570757,1 11,5,0,1,1,525706,0,12350.23,36.99384,1,12,1,19.46678,3.440542,0,0,0,22.90732,0,0,0,1,0,2,84,13.8,0,83,0,308.42,0,0,.6931472,5.731462,0,0,0,0,1,0,83,9.421511,.6931472,3.131457,1 11,5,0,1,2,525706,0,12350.23,37.99384,1,12,1,9.491268,8.986333,0,0,0,18.4776,0,0,0,1,0,2,84,13.8,0,83,0,308.42,0,0,.6931472,5.731462,0,0,0,0,1,0,83,9.421511,.6931472,2.916559,1 11,5,0,1,3,525706,0,12350.23,38.99384,1,12,1,36.33218,2.730104,0,0,0,39.06228,0,0,0,2,0,2,84,13.8,0,83,0,308.42,0,0,.6931472,5.731462,0,0,0,0,1,0,83,9.421511,.6931472,3.665157,1 11,5,0,0,1,525715,0,8507.937,45.06503,1,9,1,14.58941,0,47.93664,0,0,62.52605,0,0,0,0,1,5,75.5,10.3,0,67.9,0,1189.12,0,0,1.609438,7.080969,0,0,0,1,0,0,67.9,9.048872,1.609438,4.135583,1 11,5,0,0,2,525715,0,8507.937,46.06503,1,9,1,7.501875,2.985746,0,0,0,10.48762,0,0,0,1,0,5,75.5,10.3,0,67.9,0,1189.12,0,0,1.609438,7.080969,0,0,0,1,0,0,67.9,9.048872,1.609438,2.350196,1 11,5,0,0,3,525715,0,8507.937,47.06503,1,9,1,88.97158,0,0,0,0,88.97158,0,0,0,4,0,5,75.5,10.3,0,67.9,0,1189.12,0,0,1.609438,7.080969,0,0,0,1,0,0,67.9,9.048872,1.609438,4.488317,1 11,5,0,0,1,525716,0,8507.937,12.05476,0,9,1,0,0,0,0,0,0,0,0,0,0,0,5,91.7,10.57626,.1442925,96.3,0,1189.12,1,0,1.609438,7.080969,0,0,0,1,0,0,96.3,9.048872,1.609438,,0 11,5,0,0,2,525716,0,8507.937,13.05476,0,9,1,23.44336,0,0,0,0,23.44336,0,0,0,1,0,5,91.7,10.57626,.1442925,96.3,0,1189.12,1,0,1.609438,7.080969,0,0,0,1,0,0,96.3,9.048872,1.609438,3.154587,1 11,5,0,0,3,525716,0,8507.937,14.05476,0,9,1,48.71448,4.803789,0,0,0,53.51827,0,0,0,1,0,5,91.7,10.57626,.1442925,96.3,0,1189.12,1,0,1.609438,7.080969,0,0,0,1,0,0,96.3,9.048872,1.609438,3.980023,1 11,5,0,0,1,525717,0,8507.937,44.58043,0,3,1,0,0,0,0,0,0,0,0,0,0,0,5,70.2,0,0,67,0,1189.12,0,0,1.609438,7.080969,0,0,0,1,0,0,67,9.048872,1.609438,,0 11,5,0,0,2,525717,0,8507.937,45.58043,0,3,1,31.88297,0,0,0,0,31.88297,0,0,0,1,0,5,70.2,0,0,67,0,1189.12,0,0,1.609438,7.080969,0,0,0,1,0,0,67,9.048872,1.609438,3.462072,1 11,5,0,0,3,525717,0,8507.937,46.58043,0,3,1,0,0,0,0,0,0,0,0,0,0,0,5,70.2,0,0,67,0,1189.12,0,0,1.609438,7.080969,0,0,0,1,0,0,67,9.048872,1.609438,,0 11,5,0,0,1,525718,0,8507.937,16.09856,1,9,1,50.22926,9.983326,47.93664,0,513.1305,621.2797,1,0,0,4,1,5,88.3,3.4,0,84.1,0,1189.12,1,1,1.609438,7.080969,0,0,0,1,0,0,84.1,9.048872,1.609438,6.431781,1 11,5,0,0,2,525718,0,8507.937,17.09856,1,9,1,18.75469,.900225,0,0,0,19.65491,0,0,0,2,0,5,88.3,3.4,0,84.1,0,1189.12,1,1,1.609438,7.080969,0,0,0,1,0,0,84.1,9.048872,1.609438,2.978327,1 11,5,0,0,3,525718,0,8507.937,18.09856,1,9,1,21.98917,0,0,0,0,21.98917,0,0,0,3,0,5,88.3,3.4,0,84.1,0,1189.12,0,0,1.609438,7.080969,0,0,0,1,0,0,84.1,9.048872,1.609438,3.09055,1 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7,5,25,1,2,526187,0,15450.08,17.21082,0,12,1,3.777862,0,0,28.33396,0,3.777862,0,0,3,1,0,5,41.5,3.4,0,72.5,750,750,1,0,1.609438,6.620073,0,3.258096,8.006368,0,0,0,72.5,9.645434,1.609438,1.329158,1 7,5,25,1,3,526187,0,15450.08,18.21082,0,12,1,66.89537,0,0,0,0,66.89537,0,0,0,1,0,5,41.5,3.4,0,72.5,750,750,0,0,1.609438,6.620073,0,3.258096,8.006368,0,0,0,72.5,9.645434,1.609438,4.20313,1 11,5,0,1,1,526188,0,11392.73,34.33265,0,12,1,122.408,35.48032,0,0,177.7402,335.6284,1,0,0,5,0,4,75,20.7,0,60.2,0,0,0,0,1.386294,0,0,0,0,1,0,0,60.2,9.340818,1.386294,5.816005,1 11,5,0,1,2,526188,0,11392.73,35.33265,0,12,1,30.75171,9.335611,0,0,0,40.08732,0,0,0,1,1,4,75,20.7,0,60.2,0,0,0,0,1.386294,0,0,0,0,1,0,0,60.2,9.340818,1.386294,3.69106,1 11,5,0,1,3,526188,0,11392.73,36.33265,0,12,1,0,0,0,0,0,0,0,0,0,0,0,4,75,20.7,0,60.2,0,0,0,0,1.386294,0,0,0,0,1,0,0,60.2,9.340818,1.386294,,0 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11,5,0,0,1,526449,1,1998.976,17.57153,0,11,1,0,0,0,0,0,0,0,0,0,0,0,5,66.5,3.4,0,55.7,0,0,1,0,1.609438,0,0,0,0,0,0,0,55.7,7.600891,1.609438,,0 11,5,0,0,2,526449,1,1998.976,18.57153,0,11,1,0,0,0,0,0,0,0,0,0,0,0,5,66.5,3.4,0,55.7,0,0,0,0,1.609438,0,0,0,0,0,0,0,55.7,7.600891,1.609438,,0 11,5,0,0,3,526449,1,1998.976,19.57153,0,11,1,10.38062,0,0,0,0,10.38062,0,0,0,0,0,6,66.5,3.4,0,55.7,0,0,0,0,1.791759,0,0,0,0,0,0,0,55.7,7.600891,1.791759,2.339941,1 11,5,0,0,1,526450,1,1998.976,16.53114,1,11,1,0,0,0,0,0,0,0,0,0,0,0,5,73.4,3.4,0,81.8,0,0,1,1,1.609438,0,0,0,0,0,0,0,81.8,7.600891,1.609438,,0 11,5,0,0,2,526450,1,1998.976,17.53114,1,11,1,0,0,0,0,0,0,1,1,0,0,0,5,73.4,3.4,0,81.8,0,0,1,1,1.609438,0,0,0,0,0,0,0,81.8,7.600891,1.609438,,0 11,5,0,0,3,526450,1,1998.976,18.53114,1,11,1,92.04152,0,0,0,0,92.04152,0,0,0,5,0,6,73.4,3.4,0,81.8,0,0,0,0,1.791759,0,0,0,0,0,0,0,81.8,7.600891,1.791759,4.52224,1 11,5,0,0,1,526451,1,1998.976,45.02943,0,10,1,0,0,0,0,0,0,0,0,0,0,0,5,95.2,6.9,0,87.5,0,0,0,0,1.609438,0,0,0,0,0,0,0,87.5,7.600891,1.609438,,0 11,5,0,0,2,526451,1,1998.976,46.02943,0,10,1,0,0,0,0,0,0,0,0,0,0,0,5,95.2,6.9,0,87.5,0,0,0,0,1.609438,0,0,0,0,0,0,0,87.5,7.600891,1.609438,,0 11,5,0,0,3,526451,1,1998.976,47.02943,0,10,1,11.07266,0,0,0,0,11.07266,0,0,0,0,0,6,95.2,6.9,0,87.5,0,0,0,0,1.791759,0,0,0,0,0,0,0,87.5,7.600891,1.791759,2.40448,1 11,5,0,0,1,526452,1,1998.976,42.10267,1,11,1,0,0,0,0,0,0,0,0,0,0,0,5,80.3,13.8,0,72.7,0,0,0,0,1.609438,0,0,0,0,0,0,0,72.7,7.600891,1.609438,,0 11,5,0,0,2,526452,1,1998.976,43.10267,1,11,1,0,0,0,0,0,0,0,0,0,0,0,5,80.3,13.8,0,72.7,0,0,0,0,1.609438,0,0,0,0,0,0,0,72.7,7.600891,1.609438,,0 11,5,0,0,3,526452,1,1998.976,44.10267,1,11,1,0,0,0,0,0,0,0,0,0,0,0,6,80.3,13.8,0,72.7,0,0,0,0,1.791759,0,0,0,0,0,0,0,72.7,7.600891,1.791759,,0 6,5,25,0,1,526457,1,1484.895,48.95551,1,6,1,0,0,0,0,0,0,0,0,0,0,0,2,64.4,10.57626,1,62.5,190.4,0,0,0,.6931472,0,0,3.258096,6.635421,0,1,0,62.5,7.303772,.6931472,,0 6,5,25,0,2,526457,1,1484.895,49.95551,1,6,1,15.18603,0,0,0,0,15.18603,0,0,0,0,0,2,64.4,10.57626,1,62.5,190.4,0,0,0,.6931472,0,0,3.258096,6.635421,0,1,0,62.5,7.303772,.6931472,2.720376,1 6,5,25,0,3,526457,1,1484.895,50.95551,1,6,1,0,0,0,0,0,0,0,0,0,0,0,1,64.4,10.57626,1,62.5,190.4,0,0,0,0,0,0,3.258096,6.635421,0,1,0,62.5,7.303772,0,,0 10,5,50,0,1,526458,1,4537.243,40.77481,1,10,1,0,0,0,0,0,0,0,0,0,0,0,3,75.5,10.3,0,63.1,540,0,0,0,1.098612,0,0,3.931826,6.984716,1,0,0,63.1,8.420296,1.098612,,0 10,5,50,0,2,526458,1,4537.243,41.77481,1,10,1,0,0,0,0,0,0,0,0,0,0,0,3,75.5,10.3,0,63.1,540,0,0,0,1.098612,0,0,3.931826,6.984716,1,0,0,63.1,8.420296,1.098612,,0 10,5,50,0,3,526458,1,4537.243,42.77481,1,10,1,0,0,0,0,0,0,0,0,0,0,0,3,75.5,10.3,0,63.1,540,0,0,0,1.098612,0,0,3.931826,6.984716,1,0,0,63.1,8.420296,1.098612,,0 10,5,50,0,4,526458,1,4537.243,43.77481,1,10,1,0,0,0,0,0,0,0,0,0,0,0,3,75.5,10.3,0,63.1,540,0,0,0,1.098612,0,0,3.931826,6.984716,1,0,0,63.1,8.420296,1.098612,,0 10,5,50,0,5,526458,1,4537.243,44.77481,1,10,1,66.64411,0,0,0,2310.217,2376.861,1,0,0,1,0,3,75.5,10.3,0,63.1,540,0,0,0,1.098612,0,0,3.931826,6.984716,1,0,0,63.1,8.420296,1.098612,7.773536,1 10,5,50,0,1,526459,1,4537.243,13.32786,0,10,1,0,0,0,0,0,0,0,0,0,0,0,3,78.3,10.57626,0,74.1,540,0,1,0,1.098612,0,0,3.931826,6.984716,1,0,0,74.1,8.420296,1.098612,,0 10,5,50,0,2,526459,1,4537.243,14.32786,0,10,1,0,0,0,0,0,0,0,0,0,0,0,3,78.3,10.57626,0,74.1,540,0,1,0,1.098612,0,0,3.931826,6.984716,1,0,0,74.1,8.420296,1.098612,,0 10,5,50,0,3,526459,1,4537.243,15.32786,0,10,1,0,0,0,0,0,0,0,0,0,0,0,3,78.3,10.57626,0,74.1,540,0,1,0,1.098612,0,0,3.931826,6.984716,1,0,0,74.1,8.420296,1.098612,,0 10,5,50,0,4,526459,1,4537.243,16.32786,0,10,1,0,0,0,0,0,0,0,0,0,0,0,3,78.3,10.57626,0,74.1,540,0,1,0,1.098612,0,0,3.931826,6.984716,1,0,0,74.1,8.420296,1.098612,,0 10,5,50,0,5,526459,1,4537.243,17.32786,0,10,1,0,0,0,0,0,0,0,0,0,0,0,3,78.3,10.57626,0,74.1,540,0,1,0,1.098612,0,0,3.931826,6.984716,1,0,0,74.1,8.420296,1.098612,,0 10,5,50,0,1,526460,1,4537.243,11.78097,1,10,1,0,0,0,0,0,0,0,0,0,0,0,3,76.7,10.57626,0,88.9,540,0,1,1,1.098612,0,0,3.931826,6.984716,1,0,0,88.9,8.420296,1.098612,,0 10,5,50,0,2,526460,1,4537.243,12.78097,1,10,1,0,0,0,0,0,0,0,0,0,0,0,3,76.7,10.57626,0,88.9,540,0,1,1,1.098612,0,0,3.931826,6.984716,1,0,0,88.9,8.420296,1.098612,,0 10,5,50,0,3,526460,1,4537.243,13.78097,1,10,1,0,0,0,0,0,0,0,0,0,0,0,3,76.7,10.57626,0,88.9,540,0,1,1,1.098612,0,0,3.931826,6.984716,1,0,0,88.9,8.420296,1.098612,,0 10,5,50,0,4,526460,1,4537.243,14.78097,1,10,1,0,0,0,0,0,0,0,0,0,0,0,3,76.7,10.57626,0,88.9,540,0,1,1,1.098612,0,0,3.931826,6.984716,1,0,0,88.9,8.420296,1.098612,,0 10,5,50,0,5,526460,1,4537.243,15.78097,1,10,1,0,0,0,0,0,0,0,0,0,0,0,3,76.7,10.57626,0,88.9,540,0,1,1,1.098612,0,0,3.931826,6.984716,1,0,0,88.9,8.420296,1.098612,,0 13,5,0,0,1,526462,1,1185.868,14.36277,1,8,1,0,0,0,0,0,0,0,0,0,0,0,9,78.2,0,0,75,450,450,1,1,2.197225,6.109248,1,4.564348,6.160541,1,0,0,75,7.079073,2.197225,,0 13,5,0,0,2,526462,1,1185.868,15.36277,1,8,1,0,0,0,0,0,0,0,0,0,0,0,6,78.2,0,0,75,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,1,0,0,75,7.079073,1.791759,,0 13,5,0,0,3,526462,1,1185.868,16.36276,1,8,1,0,0,0,0,0,0,0,0,0,0,0,6,78.2,0,0,75,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,1,0,0,75,7.079073,1.791759,,0 13,5,0,0,1,526463,1,1185.868,40.42163,1,8,1,0,0,0,0,0,0,0,0,0,0,0,9,80.3,17.2,1,38.6,450,450,0,0,2.197225,6.109248,1,4.564348,6.160541,1,0,0,38.6,7.079073,2.197225,,0 13,5,0,0,2,526463,1,1185.868,41.42163,1,8,1,0,0,0,0,0,0,0,0,0,0,0,6,80.3,17.2,1,38.6,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,1,0,0,38.6,7.079073,1.791759,,0 13,5,0,0,3,526463,1,1185.868,42.42163,1,8,1,0,0,0,0,0,0,0,0,0,0,0,6,80.3,17.2,1,38.6,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,1,0,0,38.6,7.079073,1.791759,,0 13,5,0,0,1,526464,1,1185.868,9.995893,0,8,1,0,0,0,0,0,0,0,0,0,0,0,9,66.7,10.57626,0,70.4,450,450,1,0,2.197225,6.109248,1,4.564348,6.160541,1,0,0,70.4,7.079073,2.197225,,0 13,5,0,0,2,526464,1,1185.868,10.99589,0,8,1,0,0,0,0,0,0,0,0,0,0,0,6,66.7,10.57626,0,70.4,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,1,0,0,70.4,7.079073,1.791759,,0 13,5,0,0,3,526464,1,1185.868,11.99589,0,8,1,0,0,0,0,0,0,0,0,0,0,0,6,66.7,10.57626,0,70.4,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,1,0,0,70.4,7.079073,1.791759,,0 13,5,0,0,1,526465,1,1185.868,18.98973,1,9,1,0,0,0,0,0,0,0,0,0,0,0,9,61.7,6.9,0,63.6,450,450,0,0,2.197225,6.109248,1,4.564348,6.160541,1,0,0,63.6,7.079073,2.197225,,0 13,5,0,0,1,526466,1,1185.868,11.0883,1,8,1,0,0,0,0,0,0,0,0,0,0,0,9,85,10.57626,0,85.2,450,450,1,1,2.197225,6.109248,1,4.564348,6.160541,1,0,0,85.2,7.079073,2.197225,,0 13,5,0,0,2,526466,1,1185.868,12.0883,1,8,1,0,0,0,0,0,0,0,0,0,0,0,6,85,10.57626,0,85.2,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,1,0,0,85.2,7.079073,1.791759,,0 13,5,0,0,3,526466,1,1185.868,13.0883,1,8,1,0,0,0,0,0,0,0,0,0,0,0,6,85,10.57626,0,85.2,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,1,0,0,85.2,7.079073,1.791759,,0 13,5,0,0,1,526467,1,1185.868,15.44969,0,8,1,0,0,0,0,0,0,0,0,0,0,0,9,83,3.4,0,68.2,450,450,1,0,2.197225,6.109248,1,4.564348,6.160541,1,0,0,68.2,7.079073,2.197225,,0 13,5,0,0,2,526467,1,1185.868,16.44969,0,8,1,0,0,0,0,0,0,0,0,0,0,0,6,83,3.4,0,68.2,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,1,0,0,68.2,7.079073,1.791759,,0 13,5,0,0,3,526467,1,1185.868,17.44969,0,8,1,0,0,0,0,0,0,0,0,0,0,0,6,83,3.4,0,68.2,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,1,0,0,68.2,7.079073,1.791759,,0 13,5,0,0,1,526468,1,1185.868,12.8679,1,8,1,0,0,0,0,0,0,0,0,0,0,0,9,63.3,10.57626,0,81.5,450,450,1,1,2.197225,6.109248,1,4.564348,6.160541,1,0,0,81.5,7.079073,2.197225,,0 13,5,0,0,2,526468,1,1185.868,13.8679,1,8,1,2.250563,0,0,0,0,2.250563,0,0,0,1,0,6,63.3,10.57626,0,81.5,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,1,0,0,81.5,7.079073,1.791759,.8111802,1 13,5,0,0,3,526468,1,1185.868,14.8679,1,8,1,0,0,0,0,0,0,0,0,0,0,0,6,63.3,10.57626,0,81.5,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,1,0,0,81.5,7.079073,1.791759,,0 13,5,0,0,1,526469,1,1185.868,17.78234,1,8,1,0,0,0,0,0,0,0,0,0,0,0,9,59,3.4,0,43.8,450,450,1,1,2.197225,6.109248,1,4.564348,6.160541,1,0,0,43.8,7.079073,2.197225,,0 10,5,50,1,1,526470,1,4288.563,10.60643,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,83.3,10.57626,1,59.3,960.6,960.6,1,1,1.386294,6.867558,0,3.931826,7.560705,0,0,0,59.3,8.36394,1.386294,,0 10,5,50,1,2,526470,1,4288.563,11.60643,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,83.3,10.57626,1,59.3,960.6,960.6,1,1,1.386294,6.867558,0,3.931826,7.560705,0,0,0,59.3,8.36394,1.386294,,0 10,5,50,1,3,526470,1,4288.563,12.60643,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,83.3,10.57626,1,59.3,960.6,960.6,1,1,1.386294,6.867558,0,3.931826,7.560705,0,0,0,59.3,8.36394,1.386294,,0 10,5,50,1,4,526470,1,4288.563,13.60643,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,83.3,10.57626,1,59.3,960.6,960.6,1,1,1.386294,6.867558,0,3.931826,7.560705,0,0,0,59.3,8.36394,1.386294,,0 10,5,50,1,5,526470,1,4288.563,14.60643,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,83.3,10.57626,1,59.3,960.6,960.6,1,1,1.386294,6.867558,0,3.931826,7.560705,0,0,0,59.3,8.36394,1.386294,,0 10,5,50,1,1,526472,1,4288.563,8.013689,0,10,1,0,0,0,0,0,0,0,0,0,0,0,4,83.3,10.57626,0,70.4,960.6,960.6,1,0,1.386294,6.867558,0,3.931826,7.560705,0,0,0,70.4,8.36394,1.386294,,0 10,5,50,1,2,526472,1,4288.563,9.013689,0,10,1,0,0,0,0,0,0,0,0,0,0,0,4,83.3,10.57626,0,70.4,960.6,960.6,1,0,1.386294,6.867558,0,3.931826,7.560705,0,0,0,70.4,8.36394,1.386294,,0 10,5,50,1,3,526472,1,4288.563,10.01369,0,10,1,11.42615,0,0,0,0,11.42615,0,0,0,0,0,4,83.3,10.57626,0,70.4,960.6,960.6,1,0,1.386294,6.867558,0,3.931826,7.560705,0,0,0,70.4,8.36394,1.386294,2.435905,1 10,5,50,1,4,526472,1,4288.563,11.01369,0,10,1,0,0,0,0,0,0,0,0,0,0,0,4,83.3,10.57626,0,70.4,960.6,960.6,1,0,1.386294,6.867558,0,3.931826,7.560705,0,0,0,70.4,8.36394,1.386294,,0 10,5,50,1,5,526472,1,4288.563,12.01369,0,10,1,21.28028,0,0,0,0,21.28028,0,0,0,0,0,4,83.3,10.57626,0,70.4,960.6,960.6,1,0,1.386294,6.867558,0,3.931826,7.560705,0,0,0,70.4,8.36394,1.386294,3.057781,1 10,5,50,1,1,526473,1,4288.563,9.442847,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,73.3,10.57626,0,66.7,960.6,960.6,1,1,1.386294,6.867558,0,3.931826,7.560705,0,0,0,66.7,8.36394,1.386294,,0 10,5,50,1,2,526473,1,4288.563,10.44285,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,73.3,10.57626,0,66.7,960.6,960.6,1,1,1.386294,6.867558,0,3.931826,7.560705,0,0,0,66.7,8.36394,1.386294,,0 10,5,50,1,3,526473,1,4288.563,11.44285,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,73.3,10.57626,0,66.7,960.6,960.6,1,1,1.386294,6.867558,0,3.931826,7.560705,0,0,0,66.7,8.36394,1.386294,,0 10,5,50,1,4,526473,1,4288.563,12.44285,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,73.3,10.57626,0,66.7,960.6,960.6,1,1,1.386294,6.867558,0,3.931826,7.560705,0,0,0,66.7,8.36394,1.386294,,0 10,5,50,1,5,526473,1,4288.563,13.44285,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,73.3,10.57626,0,66.7,960.6,960.6,1,1,1.386294,6.867558,0,3.931826,7.560705,0,0,0,66.7,8.36394,1.386294,,0 10,5,50,1,1,526474,1,4288.563,30.08077,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,56.4,3.4,0,62.5,960.6,960.6,0,0,1.386294,6.867558,0,3.931826,7.560705,0,1,0,62.5,8.36394,1.386294,,0 10,5,50,1,2,526474,1,4288.563,31.08077,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,56.4,3.4,0,62.5,960.6,960.6,0,0,1.386294,6.867558,0,3.931826,7.560705,0,1,0,62.5,8.36394,1.386294,,0 10,5,50,1,3,526474,1,4288.563,32.08076,1,10,1,23.2755,0,0,0,0,23.2755,0,0,0,1,0,4,56.4,3.4,0,62.5,960.6,960.6,0,0,1.386294,6.867558,0,3.931826,7.560705,0,1,0,62.5,8.36394,1.386294,3.147401,1 10,5,50,1,4,526474,1,4288.563,33.08076,1,10,1,19.36219,0,0,0,0,19.36219,0,0,0,1,0,4,56.4,3.4,0,62.5,960.6,960.6,0,0,1.386294,6.867558,0,3.931826,7.560705,0,1,0,62.5,8.36394,1.386294,2.963322,1 10,5,50,1,5,526474,1,4288.563,34.08076,1,10,1,10.38062,0,0,0,0,10.38062,0,0,0,0,0,4,56.4,3.4,0,62.5,960.6,960.6,0,0,1.386294,6.867558,0,3.931826,7.560705,0,1,0,62.5,8.36394,1.386294,2.339941,1 11,5,0,1,1,526482,1,9806.964,59.19781,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,64.4,13.8,0,88.1,0,777.6,0,0,1.098612,6.656212,0,0,0,0,1,0,88.1,9.19095,1.098612,,0 11,5,0,1,2,526482,1,9806.964,60.19781,0,9,1,66.41222,0,0,0,0,66.41222,0,0,0,0,0,3,64.4,13.8,0,88.1,0,777.6,0,0,1.098612,6.656212,0,0,0,0,1,0,88.1,9.19095,1.098612,4.195881,1 11,5,0,1,3,526482,1,9806.964,61.19781,0,9,1,0,0,0,0,0,0,0,0,0,0,0,3,64.4,13.8,0,88.1,0,777.6,0,0,1.098612,6.656212,0,0,0,0,1,0,88.1,9.19095,1.098612,,0 11,5,0,0,1,526483,1,9806.964,32.15879,1,11,1,0,0,0,0,0,0,0,0,0,0,0,3,77.7,3.4,0,62.5,0,777.6,0,0,1.098612,6.656212,0,0,0,0,0,0,62.5,9.19095,1.098612,,0 11,5,0,0,2,526483,1,9806.964,33.15879,1,11,1,22.13741,6.240458,0,0,0,28.37786,0,0,0,3,0,3,77.7,3.4,0,62.5,0,777.6,0,0,1.098612,6.656212,0,0,0,0,0,0,62.5,9.19095,1.098612,3.345609,1 11,5,0,0,3,526483,1,9806.964,34.15879,1,11,1,26.82927,21.28223,0,0,0,48.1115,0,0,0,2,1,3,77.7,3.4,0,62.5,0,777.6,0,0,1.098612,6.656212,0,0,0,0,0,0,62.5,9.19095,1.098612,3.873521,1 11,5,0,0,1,526484,1,9806.964,50.9514,1,11,1,0,0,0,0,0,0,0,0,0,0,0,3,79.1,20.7,0,70.2,0,777.6,0,0,1.098612,6.656212,0,0,0,0,1,0,70.2,9.19095,1.098612,,0 11,5,0,0,2,526484,1,9806.964,51.9514,1,11,1,0,0,0,0,0,0,0,0,0,0,0,3,79.1,20.7,0,70.2,0,777.6,0,0,1.098612,6.656212,0,0,0,0,1,0,70.2,9.19095,1.098612,,0 11,5,0,0,3,526484,1,9806.964,52.9514,1,11,1,0,0,0,0,0,0,0,0,0,0,0,3,79.1,20.7,0,70.2,0,777.6,0,0,1.098612,6.656212,0,0,0,0,1,0,70.2,9.19095,1.098612,,0 13,5,0,1,1,526485,1,3130.205,18.55989,1,9,1,0,0,0,0,306.7393,306.7393,1,1,0,0,0,4,82.4,0,1,72.7,450,0,0,0,1.386294,0,1,4.564348,6.160541,1,0,0,72.7,8.049173,1.386294,5.725998,1 13,5,0,1,2,526485,1,3130.205,19.55989,1,9,1,0,0,0,0,0,0,0,0,0,0,0,5,82.4,0,1,72.7,450,0,0,0,1.609438,0,1,4.564348,6.160541,1,0,0,72.7,8.049173,1.609438,,0 13,5,0,1,3,526485,1,3130.205,20.55989,1,9,1,0,0,0,0,0,0,0,0,0,0,0,5,82.4,0,1,72.7,450,0,0,0,1.609438,0,1,4.564348,6.160541,1,0,0,72.7,8.049173,1.609438,,0 13,5,0,1,4,526485,1,3130.205,21.55989,1,9,1,10.9558,7.457499,0,0,208.538,226.9513,1,1,0,2,0,5,82.4,0,1,72.7,450,0,0,0,1.609438,0,1,4.564348,6.160541,1,0,0,72.7,8.049173,1.609438,5.424735,1 13,5,0,1,5,526485,1,3130.205,22.55989,1,9,1,167.6844,1.876501,0,0,855.9177,1025.479,1,0,0,7,0,7,82.4,0,1,72.7,450,0,0,0,1.94591,0,1,4.564348,6.160541,1,0,0,72.7,8.049173,1.94591,6.932915,1 13,5,0,1,1,526486,1,3130.205,48.23272,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,83.5,13.8,0,84.1,450,0,0,0,1.386294,0,1,4.564348,6.160541,1,0,0,84.1,8.049173,1.386294,,0 13,5,0,1,2,526486,1,3130.205,49.23272,1,10,1,0,0,0,0,0,0,0,0,0,0,0,5,83.5,13.8,0,84.1,450,0,0,0,1.609438,0,1,4.564348,6.160541,1,0,0,84.1,8.049173,1.609438,,0 13,5,0,1,3,526486,1,3130.205,50.23272,1,10,1,0,0,0,0,0,0,0,0,0,0,0,5,83.5,13.8,0,84.1,450,0,0,0,1.609438,0,1,4.564348,6.160541,1,0,0,84.1,8.049173,1.609438,,0 13,5,0,1,4,526486,1,3130.205,51.23272,1,10,1,11.33358,0,0,0,0,11.33358,0,0,0,1,0,5,83.5,13.8,0,84.1,450,0,0,0,1.609438,0,1,4.564348,6.160541,1,0,0,84.1,8.049173,1.609438,2.42777,1 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18,5,25,1,1,528015,1,7266.257,41.12526,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,73.4,10.3,1,47.7,362.31,362.31,0,0,1.386294,5.8925,0,3.258096,7.278795,0,1,0,47.7,8.891134,1.386294,,0 18,5,25,1,2,528015,1,7266.257,42.12526,1,10,1,34.35115,45.17176,0,0,0,79.5229,0,0,0,0,0,4,73.4,10.3,1,47.7,362.31,362.31,0,0,1.386294,5.8925,0,3.258096,7.278795,0,1,0,47.7,8.891134,1.386294,4.376045,1 18,5,25,1,3,528015,1,7266.257,43.12526,1,10,1,0,8.170732,0,0,0,8.170732,0,0,0,0,0,4,73.4,10.3,1,47.7,362.31,362.31,0,0,1.386294,5.8925,0,3.258096,7.278795,0,1,0,47.7,8.891134,1.386294,2.100559,1 18,5,25,1,1,528018,1,7266.257,10.8282,1,10,1,8.081667,0,0,0,0,8.081667,0,0,0,0,0,4,83.3,10.57626,0,63,362.31,362.31,1,1,1.386294,5.8925,0,3.258096,7.278795,1,0,0,63,8.891134,1.386294,2.089598,1 18,5,25,1,2,528018,1,7266.257,11.8282,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,83.3,10.57626,0,63,362.31,362.31,1,1,1.386294,5.8925,0,3.258096,7.278795,1,0,0,63,8.891134,1.386294,,0 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18,6,25,1,1,627228,0,1896.569,18.42574,1,9,1,37.66399,39.91536,0,0,0,77.57935,0,0,0,4,0,5,31.9,6.9,0,73.9,173.5,173.5,0,0,1.609438,5.156178,0,3.258096,6.542472,1,0,0,73.9,7.548329,1.609438,4.351301,1 18,6,25,1,2,627228,0,1896.569,19.42574,1,9,1,18.98254,10.44039,0,0,609.0699,638.4928,1,0,0,0,0,5,31.9,6.9,0,73.9,173.5,173.5,0,0,1.609438,5.156178,0,3.258096,6.542472,1,0,0,73.9,7.548329,1.609438,6.45911,1 18,6,25,1,3,627228,0,1896.569,20.42574,1,9,1,6.228374,22.97578,0,0,0,29.20415,0,0,0,1,0,6,31.9,6.9,0,73.9,173.5,173.5,0,0,1.791759,5.156178,0,3.258096,6.542472,1,0,0,73.9,7.548329,1.791759,3.374311,1 18,6,25,1,1,627229,0,1896.569,50.48323,0,16,1,9.310199,137.7148,0,0,0,147.025,0,0,0,1,0,5,91,17.2,1,75,173.5,173.5,0,0,1.609438,5.156178,0,3.258096,6.542472,0,0,0,75,7.548329,1.609438,4.990602,1 18,6,25,1,2,627229,0,1896.569,51.48323,0,16,1,5.31511,133.6447,0,0,0,138.9598,0,0,0,1,0,5,91,17.2,1,75,173.5,173.5,0,0,1.609438,5.156178,0,3.258096,6.542472,0,0,0,75,7.548329,1.609438,4.934185,1 18,6,25,1,3,627229,0,1896.569,52.48323,0,16,1,21.79931,143.474,39.66436,0,0,204.9377,0,0,0,2,0,6,91,17.2,1,75,173.5,173.5,0,0,1.791759,5.156178,0,3.258096,6.542472,0,0,0,75,7.548329,1.791759,5.322706,1 16,6,95,0,1,627239,1,1725.55,26.29706,0,5,1,0,0,0,0,0,0,0,0,0,0,0,3,54.3,6.9,0,57.5,756,0,0,0,1.098612,0,0,4.564348,6.679335,1,0,0,57.5,7.453881,1.098612,,0 16,6,95,0,2,627239,1,1725.55,27.29706,0,5,1,0,0,0,0,0,0,0,0,0,0,0,4,54.3,6.9,0,57.5,756,0,0,0,1.386294,0,0,4.564348,6.679335,1,0,0,57.5,7.453881,1.386294,,0 16,6,95,0,3,627239,1,1725.55,28.29706,0,5,1,0,0,0,0,0,0,0,0,0,0,0,4,54.3,6.9,0,57.5,756,0,0,0,1.386294,0,0,4.564348,6.679335,1,0,0,57.5,7.453881,1.386294,,0 16,6,95,0,1,627240,1,1725.55,24.30664,1,12,1,0,0,0,0,295.3872,295.3872,1,0,0,0,0,3,38.8,17.2,0,59.1,756,0,0,0,1.098612,0,0,4.564348,6.679335,0,1,0,59.1,7.453881,1.098612,5.688287,1 16,6,95,0,2,627240,1,1725.55,25.30664,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,38.8,17.2,0,59.1,756,0,0,0,1.386294,0,0,4.564348,6.679335,0,1,0,59.1,7.453881,1.386294,,0 16,6,95,0,3,627240,1,1725.55,26.30664,1,12,1,0,1.449827,0,0,0,1.449827,0,0,0,0,0,4,38.8,17.2,0,59.1,756,0,0,0,1.386294,0,0,4.564348,6.679335,0,1,0,59.1,7.453881,1.386294,.3714442,1 16,6,95,0,1,627241,1,1725.55,3.195072,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,77.40034,10.57626,0,64.8,756,0,1,1,1.098612,0,0,4.564348,6.679335,0,0,0,64.8,7.453881,1.098612,,0 16,6,95,0,2,627241,1,1725.55,4.195072,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,77.40034,10.57626,0,64.8,756,0,1,1,1.386294,0,0,4.564348,6.679335,0,0,0,64.8,7.453881,1.386294,,0 16,6,95,0,3,627241,1,1725.55,5.195072,1,12,1,0,0,0,0,0,0,0,0,0,0,0,4,77.40034,10.57626,0,64.8,756,0,1,1,1.386294,0,0,4.564348,6.679335,0,0,0,64.8,7.453881,1.386294,,0 15,6,95,1,1,627247,1,9989.247,34.69405,0,12,1,222.4585,4.147171,0,0,0,226.6057,0,0,0,2,28,4,65.4,3.4,0,90.9,350,350,0,0,1.386294,5.857933,0,4.564348,5.909226,1,0,0,90.9,9.209365,1.386294,5.423212,1 15,6,95,1,1,627248,1,9989.247,11.75086,1,12,1,9.783071,0,0,0,0,9.783071,0,0,0,1,0,4,68.3,10.57626,1,51.9,350,350,1,1,1.386294,5.857933,0,4.564348,5.909226,1,0,0,51.9,9.209365,1.386294,2.280653,1 15,6,95,1,1,627249,1,9989.247,3.986311,0,12,1,12.76053,6.061251,0,0,0,18.82178,0,0,0,2,0,4,77.40034,10.57626,0,70.4,350,350,1,0,1.386294,5.857933,0,4.564348,5.909226,1,0,0,70.4,9.209365,1.386294,2.935014,1 15,6,95,1,1,627250,1,9989.247,33.21287,1,12,1,45.51255,8.430455,0,0,0,53.943,0,0,0,3,0,4,64.9,10.3,1,69.3,350,350,0,0,1.386294,5.857933,0,4.564348,5.909226,1,0,0,69.3,9.209365,1.386294,3.987928,1 13,6,0,0,1,627265,1,6735.316,22.54073,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,70.2,0,0,95.5,450,150,0,0,1.098612,5.010635,1,4.564348,6.160541,0,0,0,95.5,8.815269,1.098612,,0 13,6,0,0,2,627265,1,6735.316,23.54073,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,70.2,0,0,95.5,450,150,0,0,1.098612,5.010635,1,4.564348,6.160541,0,0,0,95.5,8.815269,1.098612,,0 13,6,0,0,3,627265,1,6735.316,24.54073,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,70.2,0,0,95.5,450,150,0,0,1.098612,5.010635,1,4.564348,6.160541,0,0,0,95.5,8.815269,1.098612,,0 13,6,0,0,1,627266,1,213.5177,16.33402,0,10,1,0,0,0,0,0,0,0,0,0,0,0,7,78.2,0,0,82.1,450,450,1,0,1.94591,6.109248,1,4.564348,6.160541,0,0,0,82.1,5.368392,1.94591,,0 13,6,0,0,2,627266,1,213.5177,17.33402,0,10,1,0,0,0,0,0,0,0,0,0,0,0,8,78.2,0,0,82.1,450,450,1,0,2.079442,6.109248,1,4.564348,6.160541,0,0,0,82.1,5.368392,2.079442,,0 13,6,0,0,3,627266,1,213.5177,18.33402,0,10,1,0,0,0,0,0,0,0,0,0,0,0,8,78.2,0,0,82.1,450,450,0,0,2.079442,6.109248,1,4.564348,6.160541,0,0,0,82.1,5.368392,2.079442,,0 13,6,0,0,1,627267,1,213.5177,43.57837,0,10,1,0,0,0,0,0,0,0,0,0,0,0,7,89.9,10.3,0,84.1,450,450,0,0,1.94591,6.109248,1,4.564348,6.160541,1,0,0,84.1,5.368392,1.94591,,0 13,6,0,0,2,627267,1,213.5177,44.57837,0,10,1,0,0,0,0,0,0,0,0,0,0,0,8,89.9,10.3,0,84.1,450,450,0,0,2.079442,6.109248,1,4.564348,6.160541,1,0,0,84.1,5.368392,2.079442,,0 13,6,0,0,3,627267,1,213.5177,45.57837,0,10,1,0,0,0,0,0,0,0,0,0,0,0,8,89.9,10.3,0,84.1,450,450,0,0,2.079442,6.109248,1,4.564348,6.160541,1,0,0,84.1,5.368392,2.079442,,0 13,6,0,0,1,627268,1,213.5177,41.78234,1,10,1,19.46678,0,30.89293,0,0,50.35971,0,0,0,1,1,7,88.3,6.9,0,,450,450,0,0,1.94591,6.109248,1,4.564348,6.160541,1,0,0,86.4,5.368392,1.94591,3.919191,1 13,6,0,0,2,627268,1,213.5177,42.78234,1,10,1,7.213364,0,0,0,0,7.213364,0,0,0,0,0,8,88.3,6.9,0,,450,450,0,0,2.079442,6.109248,1,4.564348,6.160541,1,0,0,86.4,5.368392,2.079442,1.975935,1 13,6,0,0,3,627268,1,213.5177,43.78234,1,10,1,8.650519,0,32.87197,0,0,41.52249,0,0,0,0,1,8,88.3,6.9,0,,450,450,0,0,2.079442,6.109248,1,4.564348,6.160541,1,0,0,86.4,5.368392,2.079442,3.726235,1 13,6,0,0,1,627269,1,213.5177,14.69678,0,10,1,0,0,0,0,0,0,0,0,0,0,0,7,100,10.57626,0,81.5,450,450,1,0,1.94591,6.109248,1,4.564348,6.160541,0,0,0,81.5,5.368392,1.94591,,0 13,6,0,0,2,627269,1,213.5177,15.69678,0,10,1,0,0,0,0,0,0,0,0,0,0,0,8,100,10.57626,0,81.5,450,450,1,0,2.079442,6.109248,1,4.564348,6.160541,0,0,0,81.5,5.368392,2.079442,,0 13,6,0,0,3,627269,1,213.5177,16.69678,0,10,1,0,0,0,0,0,0,0,0,0,0,0,8,100,10.57626,0,81.5,450,450,1,0,2.079442,6.109248,1,4.564348,6.160541,0,0,0,81.5,5.368392,2.079442,,0 13,6,0,0,1,627270,1,213.5177,13.14168,1,10,1,0,0,0,0,0,0,0,0,0,0,0,7,86.7,10.57626,0,51.9,450,450,1,1,1.94591,6.109248,1,4.564348,6.160541,0,0,0,51.9,5.368392,1.94591,,0 13,6,0,0,2,627270,1,213.5177,14.14168,1,10,1,0,0,0,0,0,0,0,0,0,0,0,8,86.7,10.57626,0,51.9,450,450,1,1,2.079442,6.109248,1,4.564348,6.160541,0,0,0,51.9,5.368392,2.079442,,0 13,6,0,0,3,627270,1,213.5177,15.14168,1,10,1,0,0,0,0,0,0,0,0,0,0,0,8,86.7,10.57626,0,51.9,450,450,1,1,2.079442,6.109248,1,4.564348,6.160541,0,0,0,51.9,5.368392,2.079442,,0 13,6,0,0,1,627271,1,213.5177,17.83984,1,10,1,0,0,0,0,0,0,0,0,0,0,0,7,72.3,0,0,84.1,450,450,1,1,1.94591,6.109248,1,4.564348,6.160541,0,0,0,84.1,5.368392,1.94591,,0 13,6,0,0,2,627271,1,213.5177,18.83984,1,10,1,0,0,0,0,0,0,0,0,0,0,0,8,72.3,0,0,84.1,450,450,0,0,2.079442,6.109248,1,4.564348,6.160541,0,0,0,84.1,5.368392,2.079442,,0 13,6,0,0,3,627271,1,213.5177,19.83984,1,10,1,32.17993,0,0,0,428.3737,460.5536,1,0,0,0,0,8,72.3,0,0,84.1,450,450,0,0,2.079442,6.109248,1,4.564348,6.160541,0,0,0,84.1,5.368392,2.079442,6.132429,1 13,6,0,0,1,627272,1,213.5177,19.49897,1,10,1,8.463818,0,0,0,0,8.463818,1,1,0,0,0,7,71.3,0,0,73.9,450,450,0,0,1.94591,6.109248,1,4.564348,6.160541,0,0,0,73.9,5.368392,1.94591,2.1358,1 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15,6,95,1,3,629653,1,10112.13,30.44901,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,62.3,13.8,0,48.9,1000,1000,0,0,1.098612,6.907755,0,4.564348,6.959049,1,0,0,48.9,9.22159,1.098612,,0 15,6,95,1,1,629654,1,10112.13,24.59411,1,12,1,41.04951,21.4854,0,0,497.2493,559.7842,1,0,0,2,0,2,46.3,20.7,0,47.7,1000,1000,0,0,.6931472,6.907755,0,4.564348,6.959049,1,0,0,47.7,9.22159,.6931472,6.327551,1 15,6,95,1,2,629654,1,10112.13,25.59411,1,12,1,14.42673,0,0,0,0,14.42673,0,0,0,1,0,3,46.3,20.7,0,47.7,1000,1000,0,0,1.098612,6.907755,0,4.564348,6.959049,1,0,0,47.7,9.22159,1.098612,2.669083,1 15,6,95,1,3,629654,1,10112.13,26.59411,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,46.3,20.7,0,47.7,1000,1000,0,0,1.098612,6.907755,0,4.564348,6.959049,1,0,0,47.7,9.22159,1.098612,,0 13,6,0,1,1,629667,1,0,4.717317,1,3,1,0,2.052476,0,0,0,2.052476,0,0,0,0,0,6,77.40034,10.57626,1,63,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,0,0,1,63,0,1.791759,.7190467,1 13,6,0,1,2,629667,1,0,5.717317,1,3,1,7.593014,0,0,0,0,7.593014,0,0,0,2,0,6,77.40034,10.57626,1,63,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,0,0,1,63,0,1.791759,2.027229,1 13,6,0,1,3,629667,1,0,6.717317,1,3,1,0,0,0,0,0,0,0,0,0,0,0,6,77.40034,10.57626,1,63,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,0,0,1,63,0,1.791759,,0 13,6,0,1,1,629668,1,0,16.55031,1,3,1,0,0,0,0,0,0,0,0,0,0,0,6,60.6,6.9,1,47.7,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,1,0,0,47.7,0,1.791759,,0 13,6,0,1,2,629668,1,0,17.55031,1,3,1,0,0,0,0,0,0,0,0,0,0,0,6,60.6,6.9,1,47.7,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,1,0,0,47.7,0,1.791759,,0 13,6,0,1,3,629668,1,0,18.55031,1,3,1,63.3218,6.903114,33.78201,0,0,104.0069,0,0,0,3,1,6,60.6,6.9,1,47.7,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,1,0,0,47.7,0,1.791759,4.644457,1 13,6,0,1,1,629669,1,0,18.74607,1,8,1,0,0,0,0,0,0,0,0,0,0,0,6,75.5,13.8,0,53.4,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,1,53.4,0,1.791759,,0 13,6,0,1,2,629669,1,0,19.74607,1,8,1,0,0,0,0,0,0,0,0,0,0,0,6,75.5,13.8,0,53.4,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,1,53.4,0,1.791759,,0 13,6,0,1,3,629669,1,0,20.74607,1,8,1,14.53287,0,0,0,0,14.53287,0,0,0,0,0,6,75.5,13.8,0,53.4,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,1,53.4,0,1.791759,2.676413,1 13,6,0,1,1,629670,1,0,25.89186,1,10,1,0,0,0,0,0,0,0,0,0,0,0,6,63.8,6.9,0,47.7,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,1,0,47.7,0,1.791759,,0 13,6,0,1,2,629670,1,0,26.89186,1,10,1,0,0,0,0,0,0,0,0,0,0,0,6,63.8,6.9,0,47.7,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,1,0,47.7,0,1.791759,,0 13,6,0,1,3,629670,1,0,27.89186,1,10,1,0,0,0,0,0,0,0,0,0,0,0,6,63.8,6.9,0,47.7,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,1,0,47.7,0,1.791759,,0 13,6,0,1,1,629671,1,0,47.07734,1,3,1,13.54211,10.57977,35.97122,0,0,60.0931,0,0,0,1,1,6,63.8,6.9,0,47.7,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,1,47.7,0,1.791759,4.095895,1 13,6,0,1,2,629671,1,0,48.07734,1,3,1,2.657555,4.536826,0,0,0,7.194381,0,0,0,1,0,6,63.8,6.9,0,47.7,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,1,47.7,0,1.791759,1.9733,1 13,6,0,1,3,629671,1,0,49.07734,1,3,1,0,0,0,0,0,0,0,0,0,0,0,6,63.8,6.9,0,47.7,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,1,47.7,0,1.791759,,0 13,6,0,1,1,629672,1,0,12.44627,0,3,1,31.31612,0,0,0,0,31.31612,0,0,0,1,0,6,78.3,10.57626,0,59.3,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,0,0,1,59.3,0,1.791759,3.444133,1 13,6,0,1,2,629672,1,0,13.44627,0,3,1,0,0,0,0,0,0,0,0,0,0,0,6,78.3,10.57626,0,59.3,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,0,0,1,59.3,0,1.791759,,0 13,6,0,1,3,629672,1,0,14.44627,0,3,1,0,0,0,0,0,0,0,0,0,0,0,6,78.3,10.57626,0,59.3,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,0,0,1,59.3,0,1.791759,,0 13,6,0,0,1,629689,1,6735.316,60.1013,0,7,1,0,0,0,0,0,0,0,0,0,0,0,1,72.4,0,0,45.5,150,274.64,0,0,0,5.615461,1,4.564348,5.061929,0,1,0,45.5,8.815269,0,,0 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14,6,95,1,2,629910,0,3860.727,15.93498,0,13,1,0,0,0,0,0,0,0,0,0,0,0,4,85.6,3.4,0,79.8,357,377.4,1,0,1.386294,5.933306,0,4.564348,5.929029,0,0,0,79.8,8.25887,1.386294,,0 14,6,95,1,3,629910,0,3860.727,16.93498,0,13,1,0,0,0,0,0,0,0,0,0,0,0,4,85.6,3.4,0,79.8,357,377.4,1,0,1.386294,5.933306,0,4.564348,5.929029,0,0,0,79.8,8.25887,1.386294,,0 14,6,95,1,1,629911,0,3860.727,41.21561,1,13,1,17.92414,0,0,0,0,17.92414,0,0,0,0,0,4,58,6.9,0,63.6,357,377.4,0,0,1.386294,5.933306,0,4.564348,5.929029,0,0,0,63.6,8.25887,1.386294,2.886148,1 14,6,95,1,2,629911,0,3860.727,42.21561,1,13,1,0,0,0,0,0,0,0,0,0,0,0,4,58,6.9,0,63.6,357,377.4,0,0,1.386294,5.933306,0,4.564348,5.929029,0,0,0,63.6,8.25887,1.386294,,0 14,6,95,1,3,629911,0,3860.727,43.21561,1,13,1,0,0,0,0,0,0,0,0,0,0,0,4,58,6.9,0,63.6,357,377.4,0,0,1.386294,5.933306,0,4.564348,5.929029,0,0,0,63.6,8.25887,1.386294,,0 14,6,95,1,1,629912,0,3860.727,14.02875,0,13,1,0,0,0,0,0,0,0,0,0,0,0,4,76.7,10.57626,0,55.6,357,377.4,1,0,1.386294,5.933306,0,4.564348,5.929029,0,0,0,55.6,8.25887,1.386294,,0 14,6,95,1,2,629912,0,3860.727,15.02875,0,13,1,0,0,0,0,0,0,0,0,0,0,0,4,76.7,10.57626,0,55.6,357,377.4,1,0,1.386294,5.933306,0,4.564348,5.929029,0,0,0,55.6,8.25887,1.386294,,0 14,6,95,1,3,629912,0,3860.727,16.02875,0,13,1,0,0,0,0,0,0,0,0,0,0,0,4,76.7,10.57626,0,55.6,357,377.4,1,0,1.386294,5.933306,0,4.564348,5.929029,0,0,0,55.6,8.25887,1.386294,,0 16,6,95,0,1,629920,0,2548.899,7.126626,1,12,1,21.87631,0,0,0,0,21.87631,0,0,0,3,0,7,73.3,10.57626,0,92.6,1000,1000,1,1,1.94591,6.907755,0,4.564348,6.959049,0,0,0,92.6,7.843809,1.94591,3.085404,1 16,6,95,0,2,629920,0,2548.899,8.126626,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,73.3,10.57626,0,92.6,1000,1000,1,1,1.94591,6.907755,0,4.564348,6.959049,0,0,0,92.6,7.843809,1.94591,,0 16,6,95,0,3,629920,0,2548.899,9.126626,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,73.3,10.57626,0,92.6,1000,1000,1,1,1.94591,6.907755,0,4.564348,6.959049,0,0,0,92.6,7.843809,1.94591,,0 16,6,95,0,1,629921,0,2548.899,11.29637,0,12,1,75.72571,2.734539,0,0,530.5006,608.9609,2,0,0,5,0,7,78.3,10.57626,0,81.5,1000,1000,1,0,1.94591,6.907755,0,4.564348,6.959049,0,0,0,81.5,7.843809,1.94591,6.411754,1 16,6,95,0,2,629921,0,2548.899,12.29637,0,12,1,0,0,0,0,0,0,0,0,0,0,0,7,78.3,10.57626,0,81.5,1000,1000,1,0,1.94591,6.907755,0,4.564348,6.959049,0,0,0,81.5,7.843809,1.94591,,0 16,6,95,0,3,629921,0,2548.899,13.29637,0,12,1,0,0,0,0,0,0,0,0,0,0,0,7,78.3,10.57626,0,81.5,1000,1000,1,0,1.94591,6.907755,0,4.564348,6.959049,0,0,0,81.5,7.843809,1.94591,,0 16,6,95,0,1,629922,0,2548.899,40.10951,0,12,1,8.413967,9.676063,0,0,0,18.09003,0,0,0,1,0,7,71.3,6.9,1,75,1000,1000,0,0,1.94591,6.907755,0,4.564348,6.959049,0,0,1,75,7.843809,1.94591,2.895361,1 16,6,95,0,2,629922,0,2548.899,41.10951,0,12,1,0,0,0,0,0,0,0,0,0,0,0,7,71.3,6.9,1,75,1000,1000,0,0,1.94591,6.907755,0,4.564348,6.959049,0,0,1,75,7.843809,1.94591,,0 16,6,95,0,3,629922,0,2548.899,42.10951,0,12,1,43.2247,0,39.45111,0,0,82.67581,0,0,0,1,8,7,71.3,6.9,1,75,1000,1000,0,0,1.94591,6.907755,0,4.564348,6.959049,0,0,1,75,7.843809,1.94591,4.414927,1 16,6,95,0,1,629923,0,2548.899,9.130733,1,12,1,10.51746,0,25.2419,0,0,35.75936,0,0,0,1,0,7,86.7,10.57626,0,81.5,1000,1000,1,1,1.94591,6.907755,0,4.564348,6.959049,0,0,0,81.5,7.843809,1.94591,3.576812,1 16,6,95,0,2,629923,0,2548.899,10.13073,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,86.7,10.57626,0,81.5,1000,1000,1,1,1.94591,6.907755,0,4.564348,6.959049,0,0,0,81.5,7.843809,1.94591,,0 16,6,95,0,3,629923,0,2548.899,11.13073,1,12,1,10.2916,0,30.87479,0,0,41.16638,0,0,0,1,0,7,86.7,10.57626,0,81.5,1000,1000,1,1,1.94591,6.907755,0,4.564348,6.959049,0,0,0,81.5,7.843809,1.94591,3.717622,1 16,6,95,0,1,629924,0,2548.899,17.95756,1,12,1,16.82793,0,33.65587,0,0,50.4838,0,0,0,2,0,7,71.3,17.2,0,55.7,1000,1000,1,1,1.94591,6.907755,0,4.564348,6.959049,0,0,0,55.7,7.843809,1.94591,3.921653,1 16,6,95,0,2,629924,0,2548.899,18.95756,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,71.3,17.2,0,55.7,1000,1000,0,0,1.94591,6.907755,0,4.564348,6.959049,0,0,0,55.7,7.843809,1.94591,,0 16,6,95,0,3,629924,0,2548.899,19.95756,1,12,1,80.61749,0,23.46484,0,0,104.0823,0,0,0,7,0,7,71.3,17.2,0,55.7,1000,1000,0,0,1.94591,6.907755,0,4.564348,6.959049,0,0,0,55.7,7.843809,1.94591,4.645182,1 16,6,95,0,1,629925,0,2548.899,15.91239,1,12,1,10.51746,14.72444,27.34539,0,0,52.5873,0,0,0,1,0,7,55.3,3.4,0,56.8,1000,1000,1,1,1.94591,6.907755,0,4.564348,6.959049,0,0,0,56.8,7.843809,1.94591,3.962475,1 16,6,95,0,2,629925,0,2548.899,16.91239,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,55.3,3.4,0,56.8,1000,1000,1,1,1.94591,6.907755,0,4.564348,6.959049,0,0,0,56.8,7.843809,1.94591,,0 16,6,95,0,3,629925,0,2548.899,17.91239,1,12,1,0,5.780446,28.34648,0,0,34.12693,0,0,0,0,0,7,55.3,3.4,0,56.8,1000,1000,1,1,1.94591,6.907755,0,4.564348,6.959049,0,0,0,56.8,7.843809,1.94591,3.530087,1 16,6,95,0,1,629926,0,2548.899,37.50034,1,12,1,198.5696,79.5162,29.44888,0,0,307.5347,0,0,0,4,14,7,43.6,3.4,0,64.8,1000,1000,0,0,1.94591,6.907755,0,4.564348,6.959049,1,0,0,64.8,7.843809,1.94591,5.728588,1 16,6,95,0,2,629926,0,2548.899,38.50034,1,12,1,20.77824,0,0,0,0,20.77824,0,0,0,3,0,7,43.6,3.4,0,64.8,1000,1000,0,0,1.94591,6.907755,0,4.564348,6.959049,1,0,0,64.8,7.843809,1.94591,3.033906,1 16,6,95,0,3,629926,0,2548.899,39.50034,1,12,1,270.6689,21.44082,25.72899,0,734.4769,1052.316,1,0,0,3,10,7,43.6,3.4,0,64.8,1000,1000,0,0,1.94591,6.907755,0,4.564348,6.959049,1,0,0,64.8,7.843809,1.94591,6.958748,1 16,6,95,0,1,629932,0,13601.13,44.76386,1,13,1,0,0,0,0,0,0,0,0,0,0,0,3,94.7,6.9,0,88.6,1000,1000,0,0,1.098612,6.907755,0,4.564348,6.959049,0,0,0,88.6,9.517982,1.098612,,0 16,6,95,0,2,629932,0,13601.13,45.76386,1,13,1,0,29.56107,0,0,0,29.56107,0,0,0,0,0,3,94.7,6.9,0,88.6,1000,1000,0,0,1.098612,6.907755,0,4.564348,6.959049,0,0,0,88.6,9.517982,1.098612,3.386458,1 16,6,95,0,3,629932,0,13601.13,46.76386,1,13,1,12.19512,10.49129,0,0,0,22.68641,0,0,0,1,0,3,94.7,6.9,0,88.6,1000,1000,0,0,1.098612,6.907755,0,4.564348,6.959049,0,0,0,88.6,9.517982,1.098612,3.121766,1 16,6,95,0,1,629933,0,13601.13,47.36756,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,78.2,13.8,0,77.3,1000,1000,0,0,1.098612,6.907755,0,4.564348,6.959049,1,0,0,77.3,9.517982,1.098612,,0 16,6,95,0,2,629933,0,13601.13,48.36756,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,78.2,13.8,0,77.3,1000,1000,0,0,1.098612,6.907755,0,4.564348,6.959049,1,0,0,77.3,9.517982,1.098612,,0 16,6,95,0,3,629933,0,13601.13,49.36756,0,12,1,0,0,0,0,0,0,0,0,0,0,0,3,78.2,13.8,0,77.3,1000,1000,0,0,1.098612,6.907755,0,4.564348,6.959049,1,0,0,77.3,9.517982,1.098612,,0 16,6,95,0,1,629934,0,13601.13,16.60506,1,13,1,0,0,0,0,0,0,0,0,0,0,0,3,82.4,6.9,0,76.1,1000,1000,1,1,1.098612,6.907755,0,4.564348,6.959049,0,0,0,76.1,9.517982,1.098612,,0 16,6,95,0,2,629934,0,13601.13,17.60506,1,13,1,0,0,0,0,0,0,0,0,0,0,0,3,82.4,6.9,0,76.1,1000,1000,1,1,1.098612,6.907755,0,4.564348,6.959049,0,0,0,76.1,9.517982,1.098612,,0 16,6,95,0,3,629934,0,13601.13,18.60506,1,13,1,0,0,0,0,0,0,0,0,0,0,0,3,82.4,6.9,0,76.1,1000,1000,0,0,1.098612,6.907755,0,4.564348,6.959049,0,0,0,76.1,9.517982,1.098612,,0 11,6,0,1,1,629944,0,3328.213,9.14716,1,8,1,15.56584,2.52419,0,0,354.6487,372.7387,1,0,0,2,0,3,86.7,10.57626,0,85.2,0,0,1,1,1.098612,0,0,0,0,1,0,0,85.2,8.110491,1.098612,5.920878,1 11,6,0,1,2,629944,0,3328.213,10.14716,1,8,1,0,9.161315,0,0,0,9.161315,0,0,0,0,0,3,86.7,10.57626,0,85.2,0,0,1,1,1.098612,0,0,0,0,1,0,0,85.2,8.110491,1.098612,2.21499,1 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11,6,0,1,2,630608,1,10933.14,43.40657,1,7,1,0,0,0,0,0,0,0,0,0,0,0,6,77.40034,10.3,.1442925,,0,424.32,0,0,1.791759,6.050488,0,0,0,0,1,0,70.68995,9.299645,1.791759,,0 11,6,0,1,3,630608,1,10933.14,44.40657,1,7,1,10.42101,0,42.10088,0,0,52.52188,0,0,0,0,1,7,77.40034,10.3,.1442925,,0,424.32,0,0,1.94591,6.050488,0,0,0,0,1,0,70.68995,9.299645,1.94591,3.96123,1 11,6,0,1,4,630608,1,10933.14,45.40657,1,7,1,78.3946,33.21455,0,0,0,111.6092,0,0,0,9,0,8,77.40034,10.3,.1442925,,0,424.32,0,0,2.079442,6.050488,0,0,0,0,1,0,70.68995,9.299645,2.079442,4.715003,1 11,6,0,1,5,630608,1,10933.14,46.40657,1,7,1,29.43166,105.8999,0,0,0,135.3315,0,0,0,3,0,8,77.40034,10.3,.1442925,,0,424.32,0,0,2.079442,6.050488,0,0,0,0,1,0,70.68995,9.299645,2.079442,4.907728,1 11,6,0,1,1,630609,1,10933.14,49.30322,0,3,1,18.67322,16.22604,0,0,0,34.89926,0,0,0,5,0,4,75,10.3,0,45.5,0,424.32,0,0,1.386294,6.050488,0,0,0,1,0,0,45.5,9.299645,1.386294,3.552466,1 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11,6,0,1,2,631291,0,9949.82,4.405886,1,11,1,94.82433,6.664148,0,0,0,101.4885,0,0,0,3,11,5,77.40034,10.57626,0,88.9,0,0,1,1,1.609438,0,0,0,0,0,0,0,88.9,9.20541,1.609438,4.619946,1 11,6,0,1,3,631291,0,9949.82,5.405886,1,11,1,79.58833,1.554031,0,0,0,81.14236,0,0,0,1,13,5,77.40034,10.57626,0,88.9,0,0,1,1,1.609438,0,0,0,0,0,0,0,88.9,9.20541,1.609438,4.396205,1 11,6,0,1,1,631296,1,6278.034,15.37303,1,11,1,30.89293,0,28.35379,0,0,59.24672,0,0,0,1,1,8,74.3,13.8,0,54.5,0,0,1,1,2.079442,0,0,0,0,1,0,0,54.5,8.744971,2.079442,4.08171,1 11,6,0,1,2,631296,1,6278.034,16.37303,1,11,1,17.08428,0,0,0,0,17.08428,0,0,0,3,0,8,74.3,13.8,0,54.5,0,0,1,1,2.079442,0,0,0,0,1,0,0,54.5,8.744971,2.079442,2.838159,1 11,6,0,1,3,631296,1,6278.034,17.37303,1,11,1,30.44983,2.058824,29.41176,0,0,61.92041,0,0,0,4,1,8,74.3,13.8,0,54.5,0,0,1,1,2.079442,0,0,0,0,1,0,0,54.5,8.744971,2.079442,4.12585,1 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11,6,0,1,2,631300,1,6278.034,15.44216,1,11,1,134.3964,0,25.05695,0,0,159.4533,0,0,0,9,1,8,73.4,6.9,1,69.3,0,0,1,1,2.079442,0,0,0,0,1,0,0,69.3,8.744971,2.079442,5.071751,1 11,6,0,1,3,631300,1,6278.034,16.44216,1,11,1,84.08305,29.25606,13.84083,0,0,127.1799,0,0,0,8,1,8,73.4,6.9,1,69.3,0,0,1,1,2.079442,0,0,0,0,1,0,0,69.3,8.744971,2.079442,4.845603,1 11,6,0,1,1,631301,1,6278.034,34.15469,1,11,1,0,0,0,0,0,0,0,0,0,0,0,8,76.1,10.3,0,51.1,0,0,0,0,2.079442,0,0,0,0,1,0,0,51.1,8.744971,2.079442,,0 11,6,0,1,2,631301,1,6278.034,35.15469,1,11,1,31.89066,0,0,0,0,31.89066,0,0,0,6,0,8,76.1,10.3,0,51.1,0,0,0,0,2.079442,0,0,0,0,1,0,0,51.1,8.744971,2.079442,3.462313,1 11,6,0,1,3,631301,1,6278.034,36.15469,1,11,1,15.22491,43.96194,0,0,0,59.18685,0,0,0,3,0,8,76.1,10.3,0,51.1,0,0,0,0,2.079442,0,0,0,0,1,0,0,51.1,8.744971,2.079442,4.080699,1 11,6,0,1,1,631302,1,6278.034,12.5859,1,11,1,14.81168,4.731274,0,0,0,19.54295,0,0,0,1,0,8,61.7,10.57626,0,77.8,0,0,1,1,2.079442,0,0,0,0,1,0,0,77.8,8.744971,2.079442,2.972615,1 11,6,0,1,2,631302,1,6278.034,13.5859,1,11,1,7.593014,0,26.57555,0,0,34.16856,0,0,0,0,1,8,61.7,10.57626,0,77.8,0,0,1,1,2.079442,0,0,0,0,1,0,0,77.8,8.744971,2.079442,3.531306,1 11,6,0,1,3,631302,1,6278.034,14.5859,1,11,1,38.75433,1.730104,0,0,0,40.48443,0,0,0,2,0,8,61.7,10.57626,0,77.8,0,0,1,1,2.079442,0,0,0,0,1,0,0,77.8,8.744971,2.079442,3.700917,1 13,6,0,1,1,631308,1,1989.247,3.173169,1,12,1,0,4.020313,0,0,109.6064,113.6267,1,1,0,0,0,3,77.40034,10.57626,0,85.2,300,300,1,1,1.098612,5.703783,1,4.564348,5.755076,0,0,0,85.2,7.596014,1.098612,4.732919,1 13,6,0,1,2,631308,1,1989.247,4.173169,1,12,.1530055,0,0,0,0,0,0,0,0,0,0,0,3,77.40034,10.57626,0,85.2,300,300,1,1,1.098612,5.703783,1,4.564348,5.755076,0,0,0,85.2,7.596014,1.098612,,0 13,6,0,1,1,631309,1,1989.247,24.57221,1,12,1,70.24968,3.118917,0,0,0,73.3686,0,0,0,4,0,3,42,6.9,1,63.6,300,300,0,0,1.098612,5.703783,1,4.564348,5.755076,1,0,0,63.6,7.596014,1.098612,4.295496,1 13,6,0,1,2,631309,1,1989.247,25.57221,1,12,1,72.13364,5.550494,27.33485,0,857.631,962.65,1,0,0,5,0,3,42,6.9,1,63.6,300,300,0,0,1.098612,5.703783,1,4.564348,5.755076,1,0,0,63.6,7.596014,1.098612,6.86969,1 13,6,0,1,3,631309,1,1989.247,26.57221,1,12,1,36.33218,13.3391,0,0,191.6955,241.3668,1,0,0,3,0,1,42,6.9,1,63.6,300,300,0,0,0,5.703783,1,4.564348,5.755076,1,0,0,63.6,7.596014,0,5.486318,1 11,6,0,1,1,631310,1,6735.316,20.47091,0,9,1,50.7829,2.32755,0,0,0,53.11045,0,0,0,0,0,9,77.1,0,0,55.7,0,0,0,0,2.197225,0,0,0,0,1,0,0,55.7,8.815269,2.197225,3.972374,1 11,6,0,1,2,631310,1,6735.316,21.47091,0,9,1,0,1.708428,0,0,0,1.708428,0,0,0,0,0,9,77.1,0,0,55.7,0,0,0,0,2.197225,0,0,0,0,1,0,0,55.7,8.815269,2.197225,.5355738,1 11,6,0,1,3,631310,1,6735.316,22.47091,0,9,1,0,0,0,0,0,0,0,0,0,0,0,9,77.1,0,0,55.7,0,0,0,0,2.197225,0,0,0,0,1,0,0,55.7,8.815269,2.197225,,0 11,6,0,1,1,631311,1,6735.316,18.51335,1,8,1,0,0,0,0,0,0,0,0,0,0,0,9,77.1,0,0,55.7,0,0,0,0,2.197225,0,0,0,0,1,0,0,55.7,8.815269,2.197225,,0 11,6,0,1,1,631312,1,6735.316,17.59617,0,0,1,0,0,0,0,0,0,0,0,0,0,0,9,77.1,0,0,55.7,0,0,1,0,2.197225,0,0,0,0,1,0,0,55.7,8.815269,2.197225,,0 11,6,0,1,2,631312,1,6735.316,18.59617,0,0,1,0,0,0,0,0,0,0,0,0,0,0,9,77.1,0,0,55.7,0,0,0,0,2.197225,0,0,0,0,1,0,0,55.7,8.815269,2.197225,,0 11,6,0,1,3,631312,1,6735.316,19.59617,0,0,1,31.14187,0,0,0,0,31.14187,0,0,0,0,0,9,77.1,0,0,55.7,0,0,0,0,2.197225,0,0,0,0,1,0,0,55.7,8.815269,2.197225,3.438553,1 11,6,0,1,1,631313,1,6735.316,12.02464,1,0,1,0,0,0,0,0,0,0,0,0,0,0,9,58.3,10.57626,1,70.4,0,0,1,1,2.197225,0,0,0,0,1,0,0,70.4,8.815269,2.197225,,0 11,6,0,1,2,631313,1,6735.316,13.02464,1,0,1,0,0,0,0,0,0,0,0,0,0,0,9,58.3,10.57626,1,70.4,0,0,1,1,2.197225,0,0,0,0,1,0,0,70.4,8.815269,2.197225,,0 11,6,0,1,3,631313,1,6735.316,14.02464,1,0,1,0,0,0,0,0,0,0,0,0,0,0,9,58.3,10.57626,1,70.4,0,0,1,1,2.197225,0,0,0,0,1,0,0,70.4,8.815269,2.197225,,0 11,6,0,1,1,631314,1,6735.316,15.03901,0,0,1,12.69573,2.539145,0,0,0,15.23487,0,0,0,0,0,9,58.3,10.57626,1,70.4,0,0,1,0,2.197225,0,0,0,0,1,0,0,70.4,8.815269,2.197225,2.723587,1 11,6,0,1,2,631314,1,6735.316,16.03901,0,0,1,0,0,0,56.94761,0,0,0,0,1,0,0,9,58.3,10.57626,1,70.4,0,0,1,0,2.197225,0,0,0,0,1,0,0,70.4,8.815269,2.197225,,0 11,6,0,1,3,631314,1,6735.316,17.03901,0,0,1,0,0,0,0,0,0,0,0,0,0,0,9,58.3,10.57626,1,70.4,0,0,1,0,2.197225,0,0,0,0,1,0,0,70.4,8.815269,2.197225,,0 11,6,0,1,1,631315,1,6735.316,16.55852,1,0,1,50.35971,13.43631,0,0,315.7004,379.4964,1,0,0,0,0,9,77.1,3.4,0,51.1,0,0,1,1,2.197225,0,0,0,0,1,0,0,51.1,8.815269,2.197225,5.938845,1 11,6,0,1,2,631315,1,6735.316,17.55852,1,0,1,52.01215,0,32.64996,0,0,84.66211,0,0,0,0,1,9,77.1,3.4,0,51.1,0,0,1,1,2.197225,0,0,0,0,1,0,0,51.1,8.815269,2.197225,4.438668,1 11,6,0,1,3,631315,1,6735.316,18.55852,1,0,1,35.98616,2.49827,38.97232,0,0,77.45675,0,0,0,2,1,9,77.1,3.4,0,51.1,0,0,0,0,2.197225,0,0,0,0,1,0,0,51.1,8.815269,2.197225,4.34972,1 11,6,0,0,1,631316,.5112414,6735.316,29.59617,1,7,1,32.93039,5.210505,0,0,0,38.14089,0,0,0,4,0,4,79.8,10.3,0,83,0,0,0,0,1.386294,0,0,0,0,1,0,0,83,8.815269,1.386294,3.641287,1 11,6,0,0,2,631316,.5112414,6735.316,30.59617,1,7,1,9.752439,4.793698,0,0,0,14.54614,0,0,0,0,0,4,79.8,10.3,0,83,0,0,0,0,1.386294,0,0,0,0,1,0,0,83,8.815269,1.386294,2.677325,1 11,6,0,0,3,631316,.5112414,6735.316,31.59617,1,7,1,0,0,0,0,0,0,0,0,0,0,0,4,79.8,10.3,0,83,0,0,0,0,1.386294,0,0,0,0,1,0,0,83,8.815269,1.386294,,0 11,6,0,1,1,631317,1,6735.316,50.05065,1,0,1,64.7482,16.57639,0,0,0,81.32458,0,0,0,5,0,9,67.6,10.3,0,40.9,0,0,0,0,2.197225,0,0,0,0,1,0,0,40.9,8.815269,2.197225,4.398448,1 11,6,0,1,2,631317,1,6735.316,51.05065,1,0,1,137.0539,41.22627,36.44647,0,0,214.7267,0,0,0,4,1,9,67.6,10.3,0,40.9,0,0,0,0,2.197225,0,0,0,0,1,0,0,40.9,8.815269,2.197225,5.369366,1 11,6,0,1,3,631317,1,6735.316,52.05065,1,0,1,47.05882,82.61938,0,0,0,129.6782,0,0,0,3,0,9,67.6,10.3,0,40.9,0,0,0,0,2.197225,0,0,0,0,1,0,0,40.9,8.815269,2.197225,4.865056,1 11,6,0,1,1,631318,1,6735.316,19.5729,0,9,1,0,0,0,0,0,0,0,0,0,0,0,9,77.1,0,0,51.1,0,0,0,0,2.197225,0,0,0,0,1,0,0,51.1,8.815269,2.197225,,0 11,6,0,1,2,631318,1,6735.316,20.5729,0,9,1,0,14.2369,0,22.77904,1382.878,1397.115,3,0,1,0,0,9,77.1,0,0,51.1,0,0,0,0,2.197225,0,0,0,0,1,0,0,51.1,8.815269,2.197225,7.242165,1 11,6,0,1,3,631318,1,6735.316,21.5729,0,9,1,11.24568,0,0,51.90311,181.6609,192.9066,1,0,2,0,0,9,77.1,0,0,51.1,0,0,0,0,2.197225,0,0,0,0,1,0,0,51.1,8.815269,2.197225,5.262206,1 13,6,0,1,1,631319,0,6735.316,49.62628,1,12,1,1.965602,33.04668,0,0,0,35.01228,0,0,0,1,0,1,70.7,31,0,73.9,150,150,0,0,0,5.010635,1,4.564348,5.061929,1,0,0,73.9,8.815269,0,3.555699,1 13,6,0,1,2,631319,0,6735.316,50.62628,1,12,1,33.72835,55.35551,0,0,0,89.08386,0,0,0,16,0,1,70.7,31,0,73.9,150,150,0,0,0,5.010635,1,4.564348,5.061929,1,0,0,73.9,8.815269,0,4.489578,1 13,6,0,1,3,631319,0,6735.316,51.62628,1,12,1,410.5877,19.9875,0,0,0,430.5752,0,0,0,16,28,1,70.7,31,0,73.9,150,150,0,0,0,5.010635,1,4.564348,5.061929,1,0,0,73.9,8.815269,0,6.065122,1 13,6,0,1,4,631319,0,6735.316,52.62628,1,12,1,163.1658,160.2776,0,0,0,323.4434,0,0,0,17,8,1,70.7,31,0,73.9,150,150,0,0,0,5.010635,1,4.564348,5.061929,1,0,0,73.9,8.815269,0,5.779024,1 13,6,0,1,5,631319,0,6735.316,53.62628,1,12,1,305.4804,220.3112,35.39581,0,0,561.1874,0,0,0,11,25,1,70.7,31,0,73.9,150,150,0,0,0,5.010635,1,4.564348,5.061929,1,0,0,73.9,8.815269,0,6.330055,1 11,6,0,1,1,631331,1,5319.648,29.19644,1,12,1,69.28747,8.230958,27.02703,0,0,104.5455,0,0,0,3,1,7,55.9,20.7,0,40.9,0,206.44,0,0,1.94591,5.33001,0,0,0,1,0,0,40.9,8.57935,1.94591,4.649622,1 11,6,0,1,2,631331,1,5319.648,30.19644,1,12,1,96.17138,14.81313,0,0,11.39471,122.3792,1,1,0,2,0,7,55.9,20.7,0,40.9,0,206.44,0,0,1.94591,5.33001,0,0,0,1,0,0,40.9,8.57935,1.94591,4.807125,1 11,6,0,1,3,631331,1,5319.648,31.19644,1,12,1,66.27762,23.28053,0,0,0,89.55815,0,0,0,4,0,7,55.9,20.7,0,40.9,0,206.44,0,0,1.94591,5.33001,0,0,0,1,0,0,40.9,8.57935,1.94591,4.494888,1 11,6,0,1,4,631331,1,5319.648,32.19644,1,12,1,64.14104,14.79745,28.50713,0,0,107.4456,0,0,0,2,1,8,55.9,20.7,0,40.9,0,206.44,0,0,2.079442,5.33001,0,0,0,1,0,0,40.9,8.57935,2.079442,4.676985,1 11,6,0,1,5,631331,1,5319.648,33.19644,1,12,1,84.23545,21.88769,0,0,0,106.1231,0,0,0,3,0,8,55.9,20.7,0,40.9,0,206.44,0,0,2.079442,5.33001,0,0,0,1,0,0,40.9,8.57935,2.079442,4.6646,1 11,6,0,1,1,631332,1,5319.648,6.743327,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,75,10.57626,0,59.3,0,206.44,1,1,1.94591,5.33001,0,0,0,1,0,0,59.3,8.57935,1.94591,,0 11,6,0,1,2,631332,1,5319.648,7.743327,1,12,1,36.00729,3.988149,0,0,0,39.99544,0,0,0,1,0,7,75,10.57626,0,59.3,0,206.44,1,1,1.94591,5.33001,0,0,0,1,0,0,59.3,8.57935,1.94591,3.688766,1 11,6,0,1,3,631332,1,5319.648,8.743326,1,12,1,95.45644,8.107545,0,0,743.6432,847.2072,2,0,0,8,0,7,75,10.57626,0,59.3,0,206.44,1,1,1.94591,5.33001,0,0,0,1,0,0,59.3,8.57935,1.94591,6.741945,1 11,6,0,1,4,631332,1,5319.648,9.743326,1,12,1,0,0,0,0,0,0,0,0,0,0,0,8,75,10.57626,0,59.3,0,206.44,1,1,2.079442,5.33001,0,0,0,1,0,0,59.3,8.57935,2.079442,,0 11,6,0,1,5,631332,1,5319.648,10.74333,1,12,1,0,0,0,0,0,0,0,0,0,0,0,8,75,10.57626,0,59.3,0,206.44,1,1,2.079442,5.33001,0,0,0,1,0,0,59.3,8.57935,2.079442,,0 11,6,0,1,1,631333,1,5319.648,11.41136,1,12,1,9.82801,0,27.02703,0,0,36.85504,0,0,0,0,1,7,66.7,10.57626,0,63,0,206.44,1,1,1.94591,5.33001,0,0,0,1,0,0,63,8.57935,1.94591,3.606992,1 11,6,0,1,2,631333,1,5319.648,12.41136,1,12,1,48.76937,2.620784,0,0,0,51.39016,0,0,0,3,0,7,66.7,10.57626,0,63,0,206.44,1,1,1.94591,5.33001,0,0,0,1,0,0,63,8.57935,1.94591,3.939447,1 11,6,0,1,3,631333,1,5319.648,13.41136,1,12,1,132.9721,19.61234,30.84619,0,4315.131,4498.562,2,0,0,7,0,7,66.7,10.57626,0,63,0,206.44,1,1,1.94591,5.33001,0,0,0,1,0,0,63,8.57935,1.94591,8.411513,1 11,6,0,1,4,631333,1,5319.648,14.41136,1,12,1,67.14178,15.71643,0,0,0,82.85822,0,0,0,5,0,8,66.7,10.57626,0,63,0,206.44,1,1,2.079442,5.33001,0,0,0,1,0,0,63,8.57935,2.079442,4.417131,1 11,6,0,1,5,631333,1,5319.648,15.41136,1,12,1,100.1353,44.82409,25.71042,0,0,170.6698,0,0,0,4,0,8,66.7,10.57626,0,63,0,206.44,1,1,2.079442,5.33001,0,0,0,1,0,0,63,8.57935,2.079442,5.139731,1 11,6,0,1,1,631334,1,5319.648,9.382615,0,12,1,0,0,0,0,0,0,0,0,0,0,0,7,68.3,10.57626,0,63,0,206.44,1,0,1.94591,5.33001,0,0,0,1,0,0,63,8.57935,1.94591,,0 11,6,0,1,2,631334,1,5319.648,10.38262,0,12,1,70.19143,4.216044,0,0,0,74.40748,0,0,0,5,0,7,68.3,10.57626,0,63,0,206.44,1,0,1.94591,5.33001,0,0,0,1,0,0,63,8.57935,1.94591,4.309556,1 11,6,0,1,3,631334,1,5319.648,11.38262,0,12,1,0,0,0,0,0,0,0,0,0,0,0,7,68.3,10.57626,0,63,0,206.44,1,0,1.94591,5.33001,0,0,0,1,0,0,63,8.57935,1.94591,,0 11,6,0,1,4,631334,1,5319.648,12.38262,0,12,1,60.76519,4.782445,0,0,0,65.54764,0,0,0,2,0,8,68.3,10.57626,0,63,0,206.44,1,0,2.079442,5.33001,0,0,0,1,0,0,63,8.57935,2.079442,4.182777,1 11,6,0,1,5,631334,1,5319.648,13.38262,0,12,1,17.59134,0,0,0,0,17.59134,0,0,0,1,0,8,68.3,10.57626,0,63,0,206.44,1,0,2.079442,5.33001,0,0,0,1,0,0,63,8.57935,2.079442,2.867407,1 11,6,0,1,1,631335,1,5319.648,32.31211,0,9,1,35.38084,1.149877,0,0,0,36.53071,0,0,0,1,1,7,78.7,3.4,0,68.2,0,206.44,0,0,1.94591,5.33001,0,0,0,1,0,0,68.2,8.57935,1.94591,3.598153,1 11,6,0,1,2,631335,1,5319.648,33.31211,0,9,1,19.59891,0,0,0,356.4266,376.0255,1,0,0,1,0,7,78.7,3.4,0,68.2,0,206.44,0,0,1.94591,5.33001,0,0,0,1,0,0,68.2,8.57935,1.94591,5.929657,1 11,6,0,1,3,631335,1,5319.648,34.31211,0,9,1,0,0,0,0,0,0,0,0,0,0,0,7,78.7,3.4,0,68.2,0,206.44,0,0,1.94591,5.33001,0,0,0,1,0,0,68.2,8.57935,1.94591,,0 11,6,0,1,4,631335,1,5319.648,35.31211,0,9,1,84.3961,18.9985,0,0,0,103.3946,0,0,0,2,0,8,78.7,3.4,0,68.2,0,206.44,0,0,2.079442,5.33001,0,0,0,1,0,0,68.2,8.57935,2.079442,4.638553,1 11,6,0,1,5,631335,1,5319.648,36.31211,0,9,1,49.05277,4.634641,0,0,263.1935,316.8809,1,0,0,2,0,8,78.7,3.4,0,68.2,0,206.44,0,0,2.079442,5.33001,0,0,0,1,0,0,68.2,8.57935,2.079442,5.758526,1 11,6,0,1,1,631336,1,5319.648,8.221766,1,12,1,20.14742,2.810811,0,0,0,22.95823,0,0,0,1,0,7,71.7,10.57626,0,55.6,0,206.44,1,1,1.94591,5.33001,0,0,0,1,0,0,55.6,8.57935,1.94591,3.133677,1 11,6,0,1,2,631336,1,5319.648,9.221766,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,71.7,10.57626,0,55.6,0,206.44,1,1,1.94591,5.33001,0,0,0,1,0,0,55.6,8.57935,1.94591,,0 11,6,0,1,3,631336,1,5319.648,10.22177,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,71.7,10.57626,0,55.6,0,206.44,1,1,1.94591,5.33001,0,0,0,1,0,0,55.6,8.57935,1.94591,,0 11,6,0,1,4,631336,1,5319.648,11.22177,1,12,1,0,0,0,0,0,0,0,0,0,0,0,8,71.7,10.57626,0,55.6,0,206.44,1,1,2.079442,5.33001,0,0,0,1,0,0,55.6,8.57935,2.079442,,0 11,6,0,1,5,631336,1,5319.648,12.22177,1,12,1,17.59134,0,0,0,0,17.59134,0,0,0,1,0,8,71.7,10.57626,0,55.6,0,206.44,1,1,2.079442,5.33001,0,0,0,1,0,0,55.6,8.57935,2.079442,2.867407,1 11,6,0,1,1,631337,1,5319.648,5.497604,1,12,1,32.43243,1.405405,0,0,345.946,379.7838,1,0,0,0,0,7,75,10.57626,0,74.1,0,206.44,1,1,1.94591,5.33001,0,0,0,1,0,0,74.1,8.57935,1.94591,5.939602,1 11,6,0,1,2,631337,1,5319.648,6.497604,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,75,10.57626,0,74.1,0,206.44,1,1,1.94591,5.33001,0,0,0,1,0,0,74.1,8.57935,1.94591,,0 11,6,0,1,3,631337,1,5319.648,7.497604,1,12,1,0,0,0,0,0,0,0,0,0,0,0,7,75,10.57626,0,74.1,0,206.44,1,1,1.94591,5.33001,0,0,0,1,0,0,74.1,8.57935,1.94591,,0 11,6,0,1,4,631337,1,5319.648,8.497604,1,12,1,43.88597,3.938485,0,0,0,47.82446,0,0,0,3,0,8,75,10.57626,0,74.1,0,206.44,1,1,2.079442,5.33001,0,0,0,1,0,0,74.1,8.57935,2.079442,3.867537,1 11,6,0,1,5,631337,1,5319.648,9.497604,1,12,1,29.76996,6.529093,0,0,0,36.29905,0,0,0,1,0,8,75,10.57626,0,74.1,0,206.44,1,1,2.079442,5.33001,0,0,0,1,0,0,74.1,8.57935,2.079442,3.591792,1 13,6,0,0,1,631338,1,9940.604,5.629021,1,10,1,10.51746,0,0,0,0,10.51746,0,0,0,0,0,4,90,10.57626,0,74.1,450,450,1,1,1.386294,6.109248,1,4.564348,6.160541,1,0,0,74.1,9.204484,1.386294,2.353037,1 13,6,0,0,2,631338,1,9940.604,6.629021,1,10,1,49.86777,0,0,0,800.5289,850.3967,1,0,0,4,0,4,90,10.57626,0,74.1,450,450,1,1,1.386294,6.109248,1,4.564348,6.160541,1,0,0,74.1,9.204484,1.386294,6.745703,1 13,6,0,0,3,631338,1,9940.604,7.629021,1,10,1,0,0,0,0,0,0,0,0,0,0,0,4,90,10.57626,0,74.1,450,450,1,1,1.386294,6.109248,1,4.564348,6.160541,1,0,0,74.1,9.204484,1.386294,,0 13,6,0,0,1,631340,1,9940.604,27.73717,0,9,1,28.18679,0,0,0,0,28.18679,0,0,0,1,0,4,80.9,3.4,0,69.3,450,450,0,0,1.386294,6.109248,1,4.564348,6.160541,1,0,0,69.3,9.204484,1.386294,3.338853,1 13,6,0,0,2,631340,1,9940.604,28.73717,0,9,1,69.89044,0,0,0,0,69.89044,0,0,0,3,0,4,80.9,3.4,0,69.3,450,450,0,0,1.386294,6.109248,1,4.564348,6.160541,1,0,0,69.3,9.204484,1.386294,4.246929,1 13,6,0,0,3,631340,1,9940.604,29.73717,0,9,1,81.3036,0,0,0,0,81.3036,0,0,0,4,0,4,80.9,3.4,0,69.3,450,450,0,0,1.386294,6.109248,1,4.564348,6.160541,1,0,0,69.3,9.204484,1.386294,4.39819,1 13,6,0,0,1,631341,1,9940.604,28.77481,1,10,1,116.1127,21.30837,0,0,0,137.4211,0,0,0,6,0,4,82.4,3.4,0,63.6,450,450,0,0,1.386294,6.109248,1,4.564348,6.160541,1,0,0,63.6,9.204484,1.386294,4.92305,1 13,6,0,0,2,631341,1,9940.604,29.77481,1,10,1,91.36758,0,0,0,0,91.36758,0,0,0,5,0,4,82.4,3.4,0,63.6,450,450,0,0,1.386294,6.109248,1,4.564348,6.160541,1,0,0,63.6,9.204484,1.386294,4.514891,1 13,6,0,0,3,631341,1,9940.604,30.77481,1,10,1,24.5283,2.024014,0,0,0,26.55231,0,0,0,2,0,4,82.4,3.4,0,63.6,450,450,0,0,1.386294,6.109248,1,4.564348,6.160541,1,0,0,63.6,9.204484,1.386294,3.279117,1 11,6,0,1,1,631367,0,10634.41,41.39631,0,11,1,0,0,0,0,0,0,0,0,0,0,0,3,85.1,6.9,0,81.8,0,144.36,0,0,1.098612,4.97231,0,0,0,0,0,0,81.8,9.271944,1.098612,,0 11,6,0,1,2,631367,0,10634.41,42.39631,0,11,1,11.33358,16.40347,0,0,0,27.73706,0,0,0,3,0,3,85.1,6.9,0,81.8,0,144.36,0,0,1.098612,4.97231,0,0,0,0,0,0,81.8,9.271944,1.098612,3.322769,1 11,6,0,1,3,631367,0,10634.41,43.39631,0,11,1,30.18868,11.80789,24.01372,0,0,66.01029,0,0,0,5,0,3,85.1,6.9,0,81.8,0,144.36,0,0,1.098612,4.97231,0,0,0,0,0,0,81.8,9.271944,1.098612,4.189811,1 11,6,0,1,1,631368,0,10634.41,39.15127,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,88.8,24.1,0,56.8,0,144.36,0,0,1.098612,4.97231,0,0,0,0,0,0,56.8,9.271944,1.098612,,0 11,6,0,1,2,631368,0,10634.41,40.15127,1,12,1,0,0,0,0,0,0,0,0,0,0,0,3,88.8,24.1,0,56.8,0,144.36,0,0,1.098612,4.97231,0,0,0,0,0,0,56.8,9.271944,1.098612,,0 11,6,0,1,3,631368,0,10634.41,41.15127,1,12,1,33.61921,10.18868,40.01029,0,0,83.81818,0,0,0,4,0,3,88.8,24.1,0,56.8,0,144.36,0,0,1.098612,4.97231,0,0,0,0,0,0,56.8,9.271944,1.098612,4.42865,1 11,6,0,1,1,631370,0,10634.41,12.71732,0,12,1,27.34539,0,0,0,0,27.34539,0,0,0,2,0,3,91.7,10.57626,0,92.6,0,144.36,1,0,1.098612,4.97231,0,0,0,0,0,0,92.6,9.271944,1.098612,3.308548,1 11,6,0,1,2,631370,0,10634.41,13.71732,0,12,1,25.31167,4.998111,0,0,0,30.30978,0,0,0,4,0,3,91.7,10.57626,0,92.6,0,144.36,1,0,1.098612,4.97231,0,0,0,0,0,0,92.6,9.271944,1.098612,3.411471,1 11,6,0,1,3,631370,0,10634.41,14.71732,0,12,1,13.72213,4.425386,0,0,0,18.14751,0,0,0,3,0,3,91.7,10.57626,0,92.6,0,144.36,1,0,1.098612,4.97231,0,0,0,0,0,0,92.6,9.271944,1.098612,2.898534,1 13,6,0,1,1,631379,1,6906.158,14.16016,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,92,0,0,75,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,0,0,0,75,8.840314,1.791759,,0 13,6,0,1,2,631379,1,6906.158,15.16016,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,92,0,0,75,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,0,0,0,75,8.840314,1.791759,,0 13,6,0,1,3,631379,1,6906.158,16.16016,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,92,0,0,75,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,0,0,0,75,8.840314,1.791759,,0 13,6,0,1,4,631379,1,6906.158,17.16016,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,92,0,0,75,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,0,0,0,75,8.840314,1.791759,,0 13,6,0,1,5,631379,1,6906.158,18.16016,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,92,0,0,75,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,75,8.840314,1.791759,,0 13,6,0,1,1,631380,1,6906.158,16.70363,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,81.9,0,0,58,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,0,0,0,58,8.840314,1.791759,,0 13,6,0,1,2,631380,1,6906.158,17.70363,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,81.9,0,0,58,450,450,1,1,1.791759,6.109248,1,4.564348,6.160541,0,0,0,58,8.840314,1.791759,,0 13,6,0,1,3,631380,1,6906.158,18.70363,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,81.9,0,0,58,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,58,8.840314,1.791759,,0 13,6,0,1,4,631380,1,6906.158,19.70363,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,81.9,0,0,58,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,58,8.840314,1.791759,,0 13,6,0,1,5,631380,1,6906.158,20.70363,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,81.9,0,0,58,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,58,8.840314,1.791759,,0 13,6,0,1,1,631381,1,6906.158,50.141,0,4,1,0,0,0,0,0,0,0,0,0,0,0,6,70.7,10.3,1,59.1,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,59.1,8.840314,1.791759,,0 13,6,0,1,2,631381,1,6906.158,51.141,0,4,1,0,0,0,0,0,0,0,0,0,0,0,6,70.7,10.3,1,59.1,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,59.1,8.840314,1.791759,,0 13,6,0,1,3,631381,1,6906.158,52.141,0,4,1,0,0,0,0,0,0,0,0,0,0,0,6,70.7,10.3,1,59.1,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,59.1,8.840314,1.791759,,0 13,6,0,1,4,631381,1,6906.158,53.141,0,4,1,0,0,0,0,0,0,0,0,0,0,0,6,70.7,10.3,1,59.1,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,59.1,8.840314,1.791759,,0 13,6,0,1,5,631381,1,6906.158,54.141,0,4,1,0,0,0,0,0,0,0,0,0,0,0,6,70.7,10.3,1,59.1,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,59.1,8.840314,1.791759,,0 13,6,0,1,1,631382,1,6906.158,12.14784,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,88.3,10.57626,0,77.8,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,77.8,8.840314,1.791759,,0 13,6,0,1,2,631382,1,6906.158,13.14784,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,88.3,10.57626,0,77.8,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,77.8,8.840314,1.791759,,0 13,6,0,1,3,631382,1,6906.158,14.14784,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,88.3,10.57626,0,77.8,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,77.8,8.840314,1.791759,,0 13,6,0,1,4,631382,1,6906.158,15.14784,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,88.3,10.57626,0,77.8,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,77.8,8.840314,1.791759,,0 13,6,0,1,5,631382,1,6906.158,16.14784,0,12,1,0,0,0,0,0,0,0,0,0,0,0,6,88.3,10.57626,0,77.8,450,450,1,0,1.791759,6.109248,1,4.564348,6.160541,0,0,0,77.8,8.840314,1.791759,,0 13,6,0,1,1,631383,1,6906.158,43.71252,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,88.8,10.3,1,61.4,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,1,0,0,61.4,8.840314,1.791759,,0 13,6,0,1,2,631383,1,6906.158,44.71252,1,12,1,0,0,0,0,0,0,0,0,0,0,0,6,88.8,10.3,1,61.4,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,1,0,0,61.4,8.840314,1.791759,,0 13,6,0,1,3,631383,1,6906.158,45.71252,1,12,1,0,0,0,0,1636.932,1636.932,2,0,0,0,0,6,88.8,10.3,1,61.4,450,450,0,0,1.791759,6.109248,1,4.564348,6.160541,1,0,0,61.4,8.840314,1.791759,7.400579,1 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11,6,0,0,3,632031,0,7922.171,.5982204,1,15,1,54.32526,7.865052,0,0,0,62.19031,0,0,0,6,0,4,77.40034,10.57626,.1442925,,0,0,1,1,1.386294,0,0,0,0,0,0,0,70.68995,8.977547,1.386294,4.130199,1 11,6,0,0,3,632032,.5112414,6735.316,.4284737,0,12,1,92.68293,42.0662,0,0,0,134.7491,0,0,0,20,0,4,77.40034,10.57626,.1442925,,0,0,1,0,1.386294,0,0,0,0,0,0,0,70.68995,8.815269,1.386294,4.903415,1 19,6,25,0,3,632036,0,5479.263,.7734429,1,12,1,11.76471,0,0,0,0,11.76471,0,0,0,2,0,8,77.40034,10.57626,.1442925,,696.3,884,1,1,2.079442,6.784457,0,3.258096,7.932075,0,0,0,70.68995,8.608909,2.079442,2.465104,1 19,6,25,0,3,632037,0,5479.263,.6830938,0,12,1,5.882353,1.965398,0,0,0,7.847751,0,0,0,1,0,8,77.40034,10.57626,.1442925,,696.3,884,1,0,2.079442,6.784457,0,3.258096,7.932075,0,0,0,70.68995,8.608909,2.079442,2.060227,1 10,6,50,0,3,632038,1,1264.721,.6119096,0,10,1,36.70669,0,0,0,0,36.70669,0,0,0,3,0,7,77.40034,10.57626,.1442925,,795,0,1,0,1.94591,0,0,3.931826,7.37149,0,0,0,70.68995,7.143397,1.94591,3.602959,1 13,6,0,0,5,632045,1,6735.316,.3066393,0,11,1,0,0,0,0,0,0,0,0,0,0,0,7,77.40034,10.57626,.1442925,,450,450,1,0,1.94591,6.109248,1,4.564348,6.160541,0,0,0,70.68995,8.815269,1.94591,,0 17,6,25,0,5,632050,0,8273.9,.4544832,1,8,1,34.64837,0,0,0,0,34.64837,0,0,0,5,0,5,77.40034,10.57626,.1442925,,650,650,1,1,1.609438,6.476973,0,3.258096,7.863267,0,0,0,70.68995,9.020982,1.609438,3.545251,1 5,6,25,0,3,632051,0,8730.671,.275154,0,8,1,29.50257,4.51801,0,0,0,34.02058,0,0,0,0,0,5,77.40034,10.57626,.1442925,,670,670,1,0,1.609438,6.507277,0,3.258096,7.893572,0,0,0,70.68995,9.074712,1.609438,3.526966,1 14,6,95,0,3,632058,1,3400.922,.3737166,0,7,1,5.882353,0,0,0,0,5.882353,0,0,0,1,0,10,77.40034,10.57626,.1442925,,48.6,48.6,1,0,2.302585,3.883624,0,4.564348,3.934917,0,0,0,70.68995,8.132095,2.302585,1.771957,1 19,6,25,0,3,632064,1,6735.316,.5845311,1,8,1,0,0,0,0,0,0,0,0,0,0,0,4,77.40034,10.57626,.1442925,,524.7,524.7,1,1,1.386294,6.262826,0,3.258096,7.649121,0,0,0,70.68995,8.815269,1.386294,,0 11,6,0,0,2,632073,0,6735.316,.4031485,1,6,1,11.38952,7.517084,0,0,0,18.90661,0,0,0,2,0,7,77.40034,10.57626,.1442925,,0,216.48,1,1,1.94591,5.377498,0,0,0,0,0,0,70.68995,8.815269,1.94591,2.939512,1 11,6,0,0,3,632073,0,6735.316,1.403149,1,6,1,0,0,0,0,0,0,0,0,0,0,0,8,77.40034,10.57626,.1442925,,0,216.48,1,1,2.079442,5.377498,0,0,0,0,0,0,70.68995,8.815269,2.079442,,0 18,6,25,0,3,632075,0,7493.087,.3052704,0,12,1,98.96194,16.81661,0,0,467.4741,583.2526,1,0,0,8,0,5,77.40034,10.57626,.1442925,,750,967.6,1,0,1.609438,6.874819,0,3.258096,8.006368,0,0,0,70.68995,8.921869,1.609438,6.36862,1 18,6,25,0,3,632166,0,1896.569,.0561259,0,12,1,61.93772,4.865052,0,0,0,66.80276,0,0,0,8,0,6,77.40034,10.57626,.1442925,,173.5,173.5,1,0,1.791759,5.156178,0,3.258096,6.542472,0,0,0,70.68995,7.548329,1.791759,4.201745,1 6,6,25,0,3,632167,1,6735.316,.1054073,1,12,1,28.02768,6.813149,0,0,0,34.84083,0,0,0,6,0,4,77.40034,10.57626,.1442925,,750,750,1,1,1.386294,6.620073,0,3.258096,8.006368,0,0,0,70.68995,8.815269,1.386294,3.55079,1 statsmodels-0.12.2/statsmodels/datasets/scotland/000077500000000000000000000000001400612667500221265ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/scotland/R_scotvote.s000066400000000000000000000006611400612667500244440ustar00rootroot00000000000000### SETUP ### d <- read.table("./scotvote.csv",sep=",", header=T) attach(d) ### MODEL ### m1 <- glm(YES ~ COUTAX * UNEMPF + MOR + ACT + GDP + AGE, family=Gamma) results <- summary.glm(m1) results results['coefficients'] logLik(m1) scale <- results$disp Y <- YES mu <- m1$fitted llf <- -1/scale * sum(Y/mu+log(mu)+(scale-1)*log(Y)+log(scale)+scale*lgamma(1/scale)) print(llf) print("This is the llf calculated with the formula") statsmodels-0.12.2/statsmodels/datasets/scotland/__init__.py000066400000000000000000000003261400612667500242400ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/scotland/data.py000066400000000000000000000056321400612667500234170ustar00rootroot00000000000000"""Taxation Powers Vote for the Scottish Parliament 1997 dataset.""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """Used with express permission from the original author, who retains all rights.""" TITLE = "Taxation Powers Vote for the Scottish Parliament 1997" SOURCE = """ Jeff Gill's `Generalized Linear Models: A Unified Approach` http://jgill.wustl.edu/research/books.html """ DESCRSHORT = """Taxation Powers' Yes Vote for Scottish Parliamanet-1997""" DESCRLONG = """ This data is based on the example in Gill and describes the proportion of voters who voted Yes to grant the Scottish Parliament taxation powers. The data are divided into 32 council districts. This example's explanatory variables include the amount of council tax collected in pounds sterling as of April 1997 per two adults before adjustments, the female percentage of total claims for unemployment benefits as of January, 1998, the standardized mortality rate (UK is 100), the percentage of labor force participation, regional GDP, the percentage of children aged 5 to 15, and an interaction term between female unemployment and the council tax. The original source files and variable information are included in /scotland/src/ """ NOTE = """:: Number of Observations - 32 (1 for each Scottish district) Number of Variables - 8 Variable name definitions:: YES - Proportion voting yes to granting taxation powers to the Scottish parliament. COUTAX - Amount of council tax collected in pounds steling as of April '97 UNEMPF - Female percentage of total unemployment benefits claims as of January 1998 MOR - The standardized mortality rate (UK is 100) ACT - Labor force participation (Short for active) GDP - GDP per county AGE - Percentage of children aged 5 to 15 in the county COUTAX_FEMALEUNEMP - Interaction between COUTAX and UNEMPF Council district names are included in the data file, though are not returned by load. """ def load(as_pandas=None): """ Load the Scotvote data and returns a Dataset instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): """ Load the Scotvote data and returns a Dataset instance. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ data = _get_data() return du.process_pandas(data, endog_idx=0) def _get_data(): data = du.load_csv(__file__, 'scotvote.csv') data = data.iloc[:, 1:9] return data.astype(float) statsmodels-0.12.2/statsmodels/datasets/scotland/scotvote.csv000066400000000000000000000035421400612667500245150ustar00rootroot00000000000000"COUNCILDIST","YES","COUTAX","UNEMPF","MOR","ACT","GDP","AGE","COUTAX_FEMALEUNEMP" "Aberdeen_City",60.3,712,21,105,82.4,13566,12.3,14952 "Aberdeenshire",52.3,643,26.5,97,80.2,13566,15.3,17039.5 "Angus",53.4,679,28.3,113,86.3,9611,13.9,19215.7 "Argyll_and_Bute",57,801,27.1,109,80.4,9483,13.6,21707.1 "Clackmannanshire",68.7,753,22,115,64.7,9265,14.6,16566 "Dumfries_and_Galloway",48.8,714,24.3,107,79,9555,13.8,17350.2 "Dundee_City",65.5,920,21.2,118,72.2,9611,13.3,19504 "East_Ayrshire",70.5,779,20.5,114,75.2,9483,14.5,15969.5 "East_Dunbartonshire",59.1,771,23.2,102,81.1,9483,14.2,17887.2 "East_Lothian",62.7,724,20.5,112,80.3,12656,13.7,14842 "East_Renfrewshire",51.6,682,23.8,96,83,9483,14.6,16231.6 "Edinburgh_City",62,837,22.1,111,74.5,12656,11.6,18497.7 "Eilean_Siar_(Western_Isles)",68.4,599,19.9,117,83.8,8298,15.1,11920.1 "Falkirk",69.2,680,21.5,121,77.6,9265,13.7,14620 "Fife",64.7,747,22.5,109,77.9,8314,14.4,16807.5 "Glasgow_City",75,982,19.4,137,65.3,9483,13.3,19050.8 "Highland",62.1,719,25.9,109,80.9,8298,14.9,18622.1 "Inverclyde",67.2,831,18.5,138,80.2,9483,14.6,15373.5 "Midlothian",67.7,858,19.4,119,84.8,12656,14.3,16645.2 "Moray",52.7,652,27.2,108,86.4,13566,14.6,17734.4 "North_Ayrshire",65.7,718,23.7,115,73.5,9483,15,17016.6 "North_Lanarkshire",72.2,787,20.8,126,74.7,9483,14.9,16369.6 "Orkney_Islands",47.4,515,26.8,106,87.8,8298,15.3,13802 "Perth_and_Kinross",51.3,732,23,103,86.6,9611,13.8,16836 "Renfrewshire",63.6,783,20.5,125,78.5,9483,14.1,16051.5 "Scottish_Borders_The",50.7,612,23.7,100,80.6,9033,13.3,14504.4 "Shetland_Islands",51.6,486,23.2,117,84.8,8298,15.9,11275.2 "South_Ayrshire",56.2,765,23.6,105,79.2,9483,13.7,18054 "South_Lanarkshire",67.6,793,21.7,125,78.4,9483,14.5,17208.1 "Stirling",58.9,776,23,110,77.2,9265,13.6,17848 "West_Dunbartonshire",74.7,978,19.3,130,71.5,9483,15.3,18875.4 "West_Lothian",67.3,792,21.2,126,82.2,12656,15.1,16790.4 statsmodels-0.12.2/statsmodels/datasets/scotland/src/000077500000000000000000000000001400612667500227155ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/scotland/src/scotland.readme000066400000000000000000000026651400612667500257140ustar00rootroot00000000000000######################################################################################################### # # # This archive is part of the free distribution of data and statistical software code for # # "Generalized Linear Models: A Unified Approach", Jeff Gill, Sage QASS Series. You are # # free to use, modify, distribute, publish, etc. provided attribution. Please forward # # bugs, complaints, comments, and useful changes to: jgill@latte.harvard.edu. # # # ######################################################################################################### Electoral Politics in Scotland. These data are from the 1997 vote that established a Scottish Parliament with taxing powers. The data are culled from several different official UK documents provided by the Office for National Statistics, the General Register Office for Scotland, the Scottish Office: Education and Industry Department, the Scottish Department for Education and Employment, The Scottish Office Office: Development Department, and David Boothroyd (thank you). The files in this zip archive are: scotland.readme this file scotvote.dat the data file with a header indicating scotland_births.html scotland_changes.html scotland_devolution.html scotland_econ_summary.html scotland_economics.html scotland_education.html scotland_housing.html scotland_population.html these are html files with various details on the variables included. statsmodels-0.12.2/statsmodels/datasets/scotland/src/scotland_births.html000066400000000000000000000350371400612667500267750ustar00rootroot00000000000000 Cross-sectional dataset viewer v1.1
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Dataset Display - Cross-Sectional
Dataset Name: RT331602
Title: Vital and social statistics: Scotland
Description: Vital and social statistics: Scotland

This dataset has been compiled from data published in Regional Trends 33, 1998 edition published on 25 June 1998.
Source: Office for National Statistics; General Register Office for Scotland
Time Frame: 1996
Geographic Coverage: United Kingdom
Universe: UK live births
Measure: various
Units: See table
Scalar: various
Formula: none
Table Dimensions
Please select at least one item from each list and "Display Selection" or choose "Display All"
To select list items either hold down 'Ctrl' key and click each item required, or click the first item and hold down the mouse button whilst scrolling down the list.
Region 4 Measure
 
To change your selection, click in the appropriate box
Table
Live births per 1,000 population 19961Deaths per 1,000 population 19961Perinatal mortality rate, 3 year average, 1994-19962Infant mortality rate, 3 year average, 1994-19963Percentage of live births outside marriage 1996
United Kingdom12.510.98.86.136.0
Scotland11.611.89.36.236.0
Aberdeen City11.010.47.75.735.0
Aberdeenshire11.39.09.03.824.0
Angus311.013.25.63.233.0
Argyll and Bute10.513.88.67.033.0
Clackmannanshire12.311.310.46.340.0
Dumfries and Galloway10.912.88.87.834.0
Dundee City11.513.18.66.851.0
East Ayrshire311.411.612.36.540.0
East Dunbartonshire10.59.28.17.219.0
East Lothian12.312.67.65.229.0
East Renfrewshire11.59.57.46.219.0
Edinburgh, City of11.411.78.16.433.0
Eilean Siar (Western Isles)239.714.911.25.719.0
Falkirk11.711.77.94.834.0
Fife11.011.48.77.137.0
Glasgow City12.514.011.16.949.0
Highland11.411.48.36.534.0
Inverclyde11.714.511.58.045.0
Midlothian11.210.710.86.035.0
Moray12.411.09.87.426.0
North Ayrshire2311.311.811.66.942.0
North Lanarkshire12.511.111.68.538.0
Orkney Islands10.911.67.51.430.0
Perth and Kinross310.512.69.85.929.0
Renfrewshire311.911.68.04.539.0
Scottish Borders, The310.712.88.04.928.0
Shetland Islands2311.710.99.96.528.0
South Ayrshire10.112.76.24.333.0
South Lanarkshire11.511.39.25.133.0
Stirling11.111.87.74.933.0
West Dunbartonshire12.512.711.78.742.0
West Lothian13.19.58.74.633.0
Footnotes
1 -Births are on the basis of year of occurrence in England and Wales and year of registration in Scotland and Northern Ireland. Deaths relate to year of registration.
2 -Still births and deaths of infants under 1 week of age per 1,000 live and still births. Figures for some Council areas should be treated with caution as the perinatal mortality rate was based on fewer than 20 deaths.
3 -Deaths of infants under 1 year of age per 1,000 live births. Figures for some Council areas should be treated with caution as the infant mortality rate was based on fewer than 20 deaths.
4 -New Councils for Scotland
statsmodels-0.12.2/statsmodels/datasets/scotland/src/scotland_changes.html000066400000000000000000000265351400612667500271150ustar00rootroot00000000000000 GENUKI: Administrative Areas of Scotland

GENUKI Home page
Administrative Regions
of the British Isles		    Contents

Administrative Areas of Scotland

The first table below shows the historic counties and their administrative sub-divisions before the first round of changes and lists the successor regions for each, that is the post-change regions which contain some or all of the original county area. The second table shows the regions after the first round of changes and lists their successor unitary authorities. In all cases only the top-tier authority is shown - either the top-tier in a two-tier arrangement or a single tier authority (shown italicised).

The tables also show the Chapman County Codes (CCC) for each county and region. These are unique 3 letter codes.

For a brief description of the administrative changes in the United Kingdom see - Local Government Changes in the United Kingdom.

The following abbreviations are used in these tables:

Key
(C) County of a City
(U) Unitary Authority

Single-tier local authorities are shown italicised.

The links in the following table are to outline maps showing the location of each county.

Scotland - changes of 1975
Historic County CCC Administration until 1975 Successor Regions
Aberdeenshire ABD Aberdeenshire
Aberdeen (C)		 Grampian
Angus (1) ANS Angus
Dundee (C)		 Tayside
Argyllshire (2) ARL Argyllshire Strathclyde
Highland
Ayrshire AYR Ayrshire Strathclyde
Banffshire BAN Banffshire Grampian
Berwickshire BEW Berwickshire Borders
Bute (3) BUT Bute Strathclyde
Caithness CAI Caithness Highland
Clackmannanshire CLK Clackmannanshire Central
Dunbartonshire DNB Dunbartonshire Strathclyde
Dumfriesshire DFS Dumfriesshire Dumfries and Galloway
East Lothian ELN East Lothian Lothian
Fife FIF Fife Fife
Inverness-shire (4) INV Inverness-shire Highland
Western Isles
Kincardineshire KCD Kincardineshire Grampian
Kinross-shire KRS Kinross-shire Tayside
Kirkcudbrightshire KKD Kirkcudbrightshire Dumfries and Galloway
Lanarkshire LKS Lanarkshire
Glasgow (C)		 Strathclyde
Midlothian MLN Midlothian
Edinburgh (C)		 Lothian
Borders
Moray MOR Moray Grampian
Highland
Nairnshire NAI Nairnshire Highland
Orkney (5) OKI Orkney Orkney
Peeblesshire PEE Peeblesshire Borders
Perthshire PER Perthshire Tayside
Central
Renfrewshire RFW Renfrewshire Strathclyde
Ross and Cromarty (6) ROC Ross and Cromarty Highland
Western Isles
Roxburghshire ROX Roxburghshire Borders
Selkirkshire SEL Selkirkshire Borders
Shetland (7) SHI Shetland Shetland
Stirlingshire STI Stirlingshire Central
Strathclyde
Sutherland SUT Sutherland Highland
West Lothian WLN West Lothian Lothian
Central
Wigtownshire WIG Wigtownshire Dumfries and Galloway

The links in the following table are to maps provided by the Scottish Office.

Scotland - changes of 1996
Administration 1975-1996 CCC Successor Unitary Authorities
Borders BOR The Scottish Borders (U)
Central CEN Clackmannanshire (U)
Falkirk (U)
Stirling (U)
Dumfries and Galloway DGY Dumfries and Galloway (U)
Fife FIF Fife (U)
Grampian GMP Aberdeenshire (U)
Aberdeen City (U)
Moray (U)
Highland (8) HLD Highland (U)
Lothian LTN City of Edinburgh (U)
East Lothian (U)
Midlothian (U)
West Lothian (U)
Orkney (5) OKI Orkney Islands (U)
Shetland (7) SHI Shetland Islands (U)
Strathclyde (9) STD Argyll and Bute (U)
City of Glasgow (U)
East Ayrshire (U)
East Dunbartonshire (U)
East Renfrewshire (U)
Inverclyde (U)
North Ayrshire (U)
North Lanarkshire (U)
Renfrewshire (U)
South Ayrshire (U)
South Lanarkshire (U)
West Dunbartonshire (U)
Tayside TAY Angus (U)
Dundee City (U)
Perth and Kinross (U)
Western Isles (10) WIS Western Isles (U)

Notes

  1. An old name for Angus is "Forfarshire".
  2. Includes islands: Islay, Jura and Mull.
  3. Consists of islands Arran and Bute.
  4. Includes islands: Lewis (part), North Uist, South Uist, and Skye.
  5. Also "Orkney Isles", or "Orkney Islands", but NOT "The Orkneys"!
  6. Includes part of the island of Lewis.
  7. Also "Shetland Isles", or "Shetland Islands", but NOT "The Shetlands"! Originally known as "Zetland".
  8. Includes the island of Skye.
  9. Includes islands: Arran, Bute, Islay, Jura and Mull.
  10. Includes islands: Lewis, North Uist and South Uist.
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© GENUKI and Contributors 1993, 1997

Page created by Phil Lloyd in January 1993. Revised and updated in September 1997 by Brian Pears.

[Last updated: 13th February 1999 - Brian Pears]

statsmodels-0.12.2/statsmodels/datasets/scotland/src/scotland_devolution.html000066400000000000000000000321461400612667500276700ustar00rootroot00000000000000Devolution referendum 97 result

Devolution referendum 97 result

saltire shield'The reason we need a parliament in Scotland is partly so that we can repair some of the damage done by the last Government to, for example, the health service and our manufacturing industry, and partly to ensure that anti-democratic experiments like using Scotland to rehearse the poll tax can never happen again.'
The Duke of Hamilton & Brandon, whose ancestors resisted the 1707 Treaty of Union, 9 th September 1997. 		Lion Rampant

Devolution referendum 1997 - the results

(See the note below concerning the Fife count by David Boothroyd).

Ballot paper

Final votes

I agree that there should be a Scottish Parliament1,775,04574.3 %
I do not agree that there should be a Scottish Parliament614,40025.7 %

I agree that a Scottish Parliament should have tax-varying powers1,512,88963.5 %
I do not agree that a Scottish Parliament should have tax-varying powers870,26336.5 %

Votes by Unitary Authority

I agree that there should be a Scottish Parliament

AuthorityYes votesYes %No votesNo %
Orkney4,74957.3 %3,54142.7 %
Dumfries & Galloway44,61960.7 %28,86339.3 %
Perthshire & Kinross40,34461.7 %24,99838.3 %
East Renfrewshire28,25361.7 %17,57338.3 %
Shetland5,43062.4 %3,27537.6 %
Scottish Borders33,85562.8 %20,06037.2 %
Aberdeenshire61,62163.9 %34,87836.1 %
Angus33,57164.7 %18,35035.3 %
South Ayrshire40,16166.9 %19,90933.1 %
Moray24,82267.2 %12,12232.8 %
Argyll & Bute30,45267.3 %14,79632.7 %
Stirling29,19068.5 %13,44031.5 %
East Dunbartonshire40,91769.8 %17,72530.2 %
Aberdeen65,03571.8 %25,58028.2 %
Edinburgh155,90071.9 %60,83228.1 %
Highland72,55172.6 %27,43127.4 %
East Lothian33,52574.2 %11,66525.8 %
Dundee49,25276.0 %15,55324.0 %
Fife125,66876.1 %39,51723.9 %
North Ayrshire51,30476.3 %15,93123.7 %
South Lanarkshire114,90877.8 %32,76222.2 %
Inverclyde31,68078.0 %8,94522.0 %
Renfrewshire68,71179.0 %18,21321.0 %
Western Isles9,97779.4 %2,58920.6 %
West Lothian56,92379.6 %14,61420.4 %
Midlothian31,68179.9 %7,97920.1 %
Clackmannanshire18,79080.0 %4,70620.0 %
Falkirk55,64280.0 %13,95320.0 %
East Ayrshire49,13181.1 %11,42618.9 %
North Lanarkshire123,06382.6 %26,01017.4 %
Glasgow204,26983.6 %40,10616.4 %
West Dunbartonshire39,05184.7 %7,05815.3 %
Scotland1,775,04574.3 %614,40025.7 %

I agree that a Scottish Parliament should have tax-varying powers

AuthorityYes votesYes %No votesNo %
Orkney3,91747.4 %4,34452.6 %
Dumfries & Galloway35,73748.8 %37,49951.2 %
Scottish Borders27,28450.7 %26,49749.3 %
Perthshire & Kinross33,39851.3 %31,70948.7 %
East Renfrewshire23,58051.6 %22,15348.4 %
Shetland4,47851.6 %4,19848.4 %
Aberdeenshire50,29552.3 %45,92947.7 %
Moray19,32652.7 %17,34447.3 %
Angus27,64153.4 %24,08946.6 %
South Ayrshire33,67956.2 %26,21743.8 %
Argyll & Bute25,74657.0 %19,42943.0 %
Stirling25,04458.9 %17,48741.1 %
East Dunbartonshire34,57659.1 %23,91440.9 %
Aberdeen54,32060.3 %35,70939.7 %
Edinburgh133,84362.0 %82,18838.0 %
Highland61,35962.1 %37,52537.9 %
East Lothian28,15262.7 %16,76537.3 %
Renfrewshire55,07563.6 %31,53736.4 %
Fife108,02164.7 %58,98735.3 %
Dundee42,30465.5 %22,28034.5 %
North Ayrshire43,99065.7 %22,99134.3 %
Inverclyde27,19467.2 %13,27732.8 %
West Lothian47,99067.3 %23,35432.7 %
South Lanarkshire99,58767.6 %47,70832.4 %
Midlothian26,77667.7 %12,76232.3 %
Western Isles8,55768.4 %3,94731.6 %
Clackmannanshire16,11268.7 %7,35531.3 %
Falkirk48,06469.2 %21,40330.8
East Ayrshire42,55970.5 %17,82429.5 %
North Lanarkshire107,28872.2 %41,37227.8 %
West Dunbartonshire34,40874.7 %11,62825.3 %
Glasgow182,58975.0 %60,84225.0 %
Scotland1,512,88963.5 %870,26336.5 %

How Scotland voted, region by region, in 1979

Region/Islands areaYes Votes% votes% electorateNo Votes% votes% electorateTurnout
Shetland Islands 2,02027145,466733650
Orkney Islands2,1042815 5,439723954
Borders 20,7464027 30,780604067
Dumfries & Galloway 27,1624026 40,239603864
Grampian 94,9444828101,485523058
Tayside 91,482493193,325513263
Lothian 187,2215033186,421503366
Highland 44,9735133 43,274493265
Fife86,2525435 74,436463065
Strathclyde 596,5195434508,599462963
Central 71,2965536 59,105453066
Western Isles6,2185628 4,933442250
Scotland1,230,9375233*1,153,5024831*64*
*Percentage on register of 3,747,112 as adjusted by Secretary of State.

Note by David Boothroyd concerning the Fife count

I have been doing some work developing my website (which is now at http://www.election.demon.co.uk/election.html) and while preparing the results of the Scottish Parliament referendum I discovered a fairly big discrepancy in the count from Fife Council.

The Scottish Office press release giving the results of the referendum (no. 1269/97) says that 166,554 people voted in Fife, which I presume represents the number marked on registers as voting. On the first question, the total number of votes (Yes, No and spoilt ballot papers) is 166,025.

However on the second question, the total number of votes is 167,999 - 1,445 more than the number of ballot papers which should have been issued, and 1,974 more than the number of ballot papers counted on the first question.

All sources of results give the same figures and so I wrote to the Scottish Office to ask them how this discrepancy might have come about. Their reply suggests it may have resulted from voters demanding only the ballot paper for the second question, though presiding officers were instructed to give all voters both ballot papers, and such people would be marked as voting and therefore included anyway.

The Scottish Office verified that the results which were issued were those which were certified by the counting officer in Fife and so they represent the result of the referendum in spite of being inaccurate.

If anyone can shed any light on this please contact David Boothroyd at david@election.demon.co.uk


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statsmodels-0.12.2/statsmodels/datasets/scotland/src/scotland_econ_summary.html000066400000000000000000000751071400612667500302050ustar00rootroot00000000000000 Scottish Economic Bulletin: Economic Review
Scottish Economic Bulletin 

 

The Scottish Economy

Gross Domestic Product

Provisional estimates of GDP (income measure) for each UK Government Office Region/country are now available for 1996 with the publication of the Regional Accounts.7 Estimates for 1995 were also made available at county/former Scottish region level.

Scottish GDP in 1996 was £54.43 billion, 8.6 per cent of UK GDP. GDP per head was £10,614, 99.1 per cent of the UK average. This was the fourth highest of the 12 UK Government Office Regions/countries - below only London, South East and Eastern - for the fifth successive year.

GDP per head in Scotland relative to the UK increased strongly between 1989 and 1992, reflecting the stronger performance of the Scottish economy in the 1990-1992 UK recession. Since 1992, GDP per head has fluctuated around 99 per cent of UK GDP per head, reaching a peak of 100.2 per cent in 1995.

Table 2 shows GDP per head in the former Scottish regions in 1995.8 It is instructive to look at trends and, accordingly, Table 2 also provides data for 1989. GDP per head was well above the UK average in both Grampian (133 per cent) and Lothian (124 per cent) in 1995. Although Grampian showed the smallest increase in GDP per head over the 1993-1995 period (and fell slightly relative to the UK), the level of GDP per head was third only to London and Berkshire across the UK, followed by Lothian. All other Scottish regions were below the UK average and GDP per head in the Highlands and Islands and in Fife was amongst the lowest in the UK.

Table 2: GDP in the Scottish Regions, 1989 and 1995

 GDP per head 1995 (£)GDP per head, 1990=100
19891995
Borders9,00380.188.3
Central9,26589.190.8
Dumfries and Galloway9,55586.493.7
Fife8,31484.081.5
Grampian13,566119.4133.0
Highlands and Islands8,29880.481.4
Lothian12,656111.4124.1
Strathclyde9,48387.993.0
Tayside9,61188.894.2
Scotland10,24493.8100.2
UK10,199100.0100.0

Source: Office for National Statistics

The improvement in Scottish GDP per head, relative to the UK, from 1989 has been evident across most Scottish regions. Lothian, Borders and Grampian have seen particularly marked improvements and only Fife had a lower relative level of GDP per head in 1995 than in 1989. Relative GDP per head in the Highlands and Islands has increased slightly but levels have fallen since the peak (of 88.8 per cent ) in 1991.

Index of Production and Construction

The Scottish Office Education and Industry Department's quarterly Index of Production and Construction rose by 0.4 per cent in 1997 Q3. Excluding oil and gas, the Index rose by 0.5 per cent. At a broad sectoral level, output rose in manufacturing (0.9 per cent) and in electricity, gas and water supply (5.7 per cent), offset by falling output in construction (2.5 per cent) and mining and quarrying (1.8 per cent). The UK index (less oil and gas) rose by 0.7 per cent in 1997 Q3.

An indication of the underlying trend in industrial output is obtained by comparing the last 4 quarters for which data are available (to 1997 Q3) with the previous 4 quarters (to 1996 Q3). Excluding oil and gas, the Index rose by 6.0 per cent over this period, as increases were recorded in manufacturing (7.4 per cent), construction (1.8 per cent), electricity, gas and water supply (5.7 per cent) and mining and quarrying (3.3 per cent). By comparison, the UK Index (less oil and gas) rose by 2.0 per cent over the same period.

Since 1990, manufacturing output has increased by 25.6 per cent. Growth in UK manufacturing has been much more sluggish than in Scotland, growing by only 5.1 per cent over the same period. The influence of the electrical and instrument engineering sector (EIE) on Scottish manufacturing has been discussed in past editions of the Scottish Economic Bulletin and by outside commentators. Excluding EIE, manufacturing output in Scotland has declined by 7.7 per cent since 1990. UK manufacturing excluding EIE has increased by 1.8 per cent.

In the year to 1997 Q3, the EIE sector continued to grow strongly - by 18.4 per cent. However, growth was also evident in 6 of the other 10 manufacturing sectors over the period. This is the continuation of a trend over the last year in which growth in the manufacturing sector has become more broadly based. Indeed as Chart 3 shows, manufacturing output excluding EIE has been increasing year-on-year in each quarter since 1996 Q4, a trend not seen since 1990 Q3. In the year to 1997 Q3, manufacturing output excluding EIE grew by 1.4 per cent, only slightly below the 1.5 per cent growth in the UK as a whole.

CHART 3 HERE

Exports

The manufacturing sector accounts for most of Scotland's external trade with the rest of the world. Estimates from the 1994 Input-Output Tables99 indicate that around three quarters of trade is in manufacturing. The Scottish Council Development and Industry (SCDI) annual survey of Scottish Manufactured Exports for 1996 was published in December 1997. In current prices, the value of Scottish manufactured exports10 was estimated to have risen by 6.4 per cent in 1996 to £18.42 billion. This represents a slower rate of growth than in recent years (20.3 per cent in 1995 and 24.8 per cent in 1994) and can be compared with growth of 8.9 per cent in UK manufactured exports (to £155.18 billion) in 1996. For the first time since 1988, UK manufactured exports growth outpaced that of Scotland and Scotland's share of UK exports fell marginally from 12.1 per cent in 1995 to 11.9 per cent in 1996.

As shown in Table 3, four sectors - Office Machinery, Radio/TV/Communication Equipment, Whisky and Chemicals - continued to dominate Scottish manufactured exports in 1996, accounting for 75 per cent of the total. The electronics sector11 had a more mixed export performance in 1996 than in recent years. Exports grew by 6.9 per cent to £10.21 billion (55.5 per cent of total manufactured exports). This compares with growth of over 42 per cent in 1995. Exports from the Office Machinery sector - the largest exporting sector - rose by 14.3 per cent in 1996 to £6.83 billion (37.1 per cent of total manufactured exports). While this rate of growth was considerably lower than in 1995, the sector still contributed over 77 per cent to the total growth in manufactured exports in 1996. Exports from the other major element of Scotland's electronics industry - the Radio/TV/Communication Equipment sector - declined by 7.3 per cent to £3.00 billion.

Table 3: Top Exporting Sectors in Scotland, 1996

Sector (SIC92)Value at current prices (£ million)Per cent of TotalNominal increase in value 1995-96: per centContribution to total export growth: per cent
Office Machinery6,825.037.114.377.5
Radio, Television & Communication3,003.816.3-7.3-21.6
Equipment and Apparatus Whisky2,278.112.40.10.1
Chemicals and Chemical Products1,706.49.39.213.1
Machinery and Equipment nec802.24.418.411.4
Other Food Products & Beverages446.02.4-10.7-4.8
Fabricated Metal Products except Machinery and Equipment411.12.237.310.2
Pulp, Paper and Paper Products387.02.1-2.0-0.7
Coke, Refined Petroleum Products and Nuclear Fuel332.01.869.612.4
Other Transport Equipment326.81.8-22.4-8.6
Other sectors1,896.210.36.811.1
All Manufacturing Industries18,414.6100.06.3100.0

Source: Scottish Council Development and Industry

Note: 1. Under SIC 92 Whisky is normally incorporated in the Food Products & Beverages sector.

Exports from the whisky sector increased only marginally in 1996, up by 0.1 per cent to £2.28 billion (12.4 per cent of total manufactured exports). The Chemicals and Chemical Products sector experienced a further rise in exports in 1996, of 9.2 per cent to £1.71 billion (9.3 per cent of total manufactured exports). This follows growth of 9.0 per cent in 1995. An additional 19 industry sectors together represented 25 per cent of total manufactured exports in 1996. Export growth was recorded in 14 sectors.

Overall the latest figures record a positive - and better than expected - performance by Scottish manufacturing in export markets during 1996. The SCDI quarterly index based on a selected panel survey of large exporters had provisionally estimated a fall of 6.8 per cent in manufactured exports. The rapid growth rates of recent years have slowed but export levels in most sectors continue to rise. Initial estimates from the SCDI quarterly index for 1997 suggest further growth of 12.0 per cent to £20.61 billion.

Exports by Destination

As shown in Table 4, the EU remained Scotland's main trading area in 1996 with a 58 per cent share of Scotland's exports. However, exports grew more modestly - by 2.9 per cent - in 1996. Six of the top ten individual country markets were in the EU, the others being the USA, Japan, Switzerland and Norway. The latest survey results confirm France as Scotland's largest export market for the fourth successive year, despite a drop in the actual value of exports of 5.4 per cent to £2.80 billion. (15.2 per cent of total Scottish manufactured exports).

Table 4: Destination of Scottish Exports in 1996

 Value (£ million, current prices)Per cent of totalNominal percentage growth in 1996Contribution to overall growth: per cent
European Union10,75658.42.927.5
North America2,31812.636.856.8
Other Asia Pacific1,5568.4-14.2-23.5
EFTA1,0725.816.413.7
Japan8124.46.34.4
Middle East5132.823.38.8
Latin America5102.84.52.0
Eastern Europe3962.253.512.6
Africa3111.7-0.6-0.2
Australasia1710.9-11.9-2.1

Source: Scottish Council Development and Industry

Exports to the USA rose by 38.3 per cent in 1996 to £2.22 billion. The USA was responsible for nearly 50 per cent of the increase in total Scottish exports and overtook Germany as the second largest market. There was a strong upturn in sales across the Office Machinery, Radio/TV/Communication Equipment, Coke/Petroleum and Chemicals sectors; the strength of the US economy a causal factor. North America displaced Other Asia Pacific as Scotland's second largest trading area.

Exports to Japan continued to increase and remained the 7th largest country market for Scottish goods. Total exports to the Other Asia Pacific countries fell by 14.2 per cent in 1996, compared with strong growth of 30.9 per cent in 1995. However, this was almost entirely due to a large drop in exports to Malaysia; there were significant rises in exports to Hong Kong, Singapore and Taiwan. Elsewhere, exports to most other regions showed significant growth with sales to Eastern Europe up 53.5 per cent and exports to the Middle East up 23.3 per cent. Growth in sales were also recorded to the EFTA countries, while exports to Latin America continued to grow modestly. There was a marginal decline in sales to Africa following last year's significant increase, while exports to Australasia continued to decline.

The Sterling Exchange Rate and Exports

Inevitably, the strength of sterling has put pressure on Scottish exports. As one would expect, the exposure to exchange rate movements varies by sector in Scotland. This is illustrated in Table 5 which shows, at the broad sectoral level, the proportion of total domestic (i.e. Scottish) output dependent on exports outwith the UK (i.e. to the rest of the world, ROW) and the import content of that output from the same source. The table also shows the corresponding proportions for Scotland's trade with the rest of the UK (RUK).

Table 5: The External Orientation of Scottish Industry, 1994

IndustryProportion of domestic output dependent on :Components of gross domestic output
Exports to RUKExports to ROWImports from RUKImports from ROW
Agriculture, Forestry and Fishing19.712.97.41.4
Mining and Quarrying41.029.118.96.8
Energy and Water Supply6.41.07.87.7
Manufacturing26.741.818.818.2
Construction6.00.017.73.9
Transport and Communication20.08.48.92.5
Distribution and Catering14.10.05.71.0
Financial and Business Services12.35.810.81.9
Other Services4.12.74.11.2
Whole Economy16.516.312.07.3

Source: The Scottish Office

The manufacturing sector is clearly the most sensitive to the effects of exchange rate changes: over 40 per cent of output is exported to ROW and almost 20 per cent of inputs are imported from ROW. Within the sector (though not shown in the table), 2 industries - drink and electrical and instrument engineering - export more than two thirds of their output to ROW, while chemicals and electrical and instrument engineering also import more than a third of inputs. By contrast, the output of the service sector is much more dependent on the home market, relying less on exports to generate value added. The gross output of the service sector also embodies a lower import content.

For manufacturing, available evidence from the SCDI for 1997 suggests that the strength of sterling is causing difficulties in terms of reduced margins and some job losses. However, as described above, it appears that it has not yet impacted upon the level of export sales, only profitability.

Business survey evidence in Scotland does point to an adverse impact on exports resulting from sterling's strength but results are far from conclusive. The Scottish Chambers' Business Survey reported a decline in export orders and sales in 1997 Q4, as in Q3 and results from Scottish Engineering also revealed that export orders declined for the third successive quarter, falling in all sectors of the industry. By contrast, the CBI Industrial Trends Survey reported a return to growth in export orders and deliveries also increased significantly in the fourth quarter. However, optimism regarding export prospects fell markedly and, as one might expect, respondents continued to believe that prices would be the most important constraint on export orders over the coming months.

One particular area in which the exchange rate may have been expected to affect activity levels is travel and tourism both to and from overseas. International Passenger Survey (IPS) evidence for the 12 months to November 1997 shows that the number of visitors to the UK rose by 3 per cent, compared with the year to November 1996. The number of visits from North America increased by 14 per cent, while the number of visits from Western Europe was broadly static. Visits from Other Areas rose by 4 per cent. The total number of UK residents' visits abroad during the 12 months ending November 1997 rose by 11 per cent compared with a year earlier. Visits to Western Europe increased by 12 per cent, while visits to North America and Other Areas increased by 2 per cent and 10 per cent respectively. Overseas earnings rose by 2 per cent in current prices in the year to November and expenditure by UK residents rose by 6 per cent. This resulted in an increase in the deficit on the travel account of the balance of payments from £3.8 billion to £4.6 billion over the period.

The change in the composition of the tourism market appears to be consistent with the larger rise in sterling against the main European currencies over the last 18 months and has implications for Scotland. North America, Germany and France all account for higher proportions of overseas visits to Scotland than to the UK as a whole. However, a complicating factor is that US and French visitors tend to have a high propensity for travelling as part of a package holiday, paid for in advance with prices based on an exchange rate determined possibly months before the holiday is taken. Consequently, the impact of changes in exchange rates on visits from US and French residents may be delayed. By contrast, the principal types of Dutch and German holidaymakers to Scotland tend to travel independently and to holiday on an ad hoc basis at relatively short notice. The impact of the strength of sterling on these groups is likely to have been demonstrated relatively quickly.

Some IPS data for Scotland are available to the third quarter of 1997. The total number of overnight visits from overseas tourists was broadly unchanged in the first 3 quarters of the year, compared with the same period in 1996. However, the total from Western Europe fell by 6 per cent and overnight visits from North America were broadly unchanged. By contrast, visits from Other Areas rose by 12 per cent. Evidence for Scotland from the United Kingdom Tourism Survey, covering the first 3 quarters of 1997, reported a 3 per cent fall in the number of tourist trips to Scotland by UK residents compared with the same period in 1996. This compares with growth rates of around 15 per cent in each of the previous 2 years. The value of these trips increased by 7 per cent in current prices, broadly equal to growth in the UK over the same period but lower than growth in 1995 and 1996.

Labour Market

Unemployment

There are 2 main sources of unemployment data. An estimate of unemployment under the International Labour Office definition - ILO unemployment - is provided by the Labour Force Survey (LFS), a quarterly sample survey of households. The second measure of unemployment - the claimant count - is based on records of those claiming Jobseeker's Allowance and National Insurance Credits at Employment Service Offices. The Office for National Statistics announced on 3 February that (from April) its assessment of the labour market would give more weight than previously to the LFS, which is conducted according to internationally agreed definitions drawn up by the ILO.

ILO unemployment (not seasonally adjusted) in Scotland fell by 32,000 in the year to Autumn (September to November) 1997 to 185,000. The rate of unemployment fell by 1.4 percentage points to 7.4 per cent of the workforce. ILO unemployment in the UK fell by 379,000 in the year to Autumn 1997 to 1,919,000 or 6.6 per cent, 0.8 percentage points below the Scottish rate. Unemployment fell in every Government Office Region (GOR) of the UK. Four GORs - Merseyside, North East, London and Northern Ireland - have higher ILO unemployment rates than Scotland.

Claimant count unemployment (seasonally adjusted) in Scotland fell throughout 1997 but rose by 1,200 in January 1998 to 141,100, the first rise since April 1996. The rate of unemployment rose by 0.1 percentage point to 5.8 per cent of the workforce, 0.8 percentage points above the UK rate. Of the UK GORs, Merseyside, North East, and Northern Ireland have higher unemployment rates than Scotland, while London has the same rate.

The claimant count measure of unemployment in Scotland remains significantly lower than the ILO measure. The difference between the ILO measure and the claimant count measure12 in Autumn 1997 was 42,000, a rise of 7,000 on Autumn 1996.

In the July 1997 Budget, the Government set out a New Deal to help young people, the long term unemployed, lone parents and the disabled move from Welfare to Work. The New Deal for young claimants (aged 18-24) who have been unemployed for 6 months or more was launched in 12 "pathfinder" areas of the UK (including Tayside) in January and the programme will be launched nationally from April. The New Deal for long term unemployed adults (those aged 25 and over who have been unemployed for more than 2 years) will be launched in June.13

Table 6 summarises the eligibility for the New Deal for these two groups in January 1998. It can be seen that, in Scotland there were 11,300 youth unemployed of over 6 months duration and 17,100 aged 25 and over who had been unemployed for 2 years or more in January 1998 (7.4 per cent and 11.3 per cent of total claimant unemployed, respectively). The total number in these 2 groups has fallen significantly over the last year - by 17,800 (38.5 per cent).

Table 6: Claiment Count Unemployment for New Deal Target Groups

 Youth (18-24) Unemployment, over 6 months durationAdult (25+) Unemployment, over 2 years duration
January 1997January 1998Percentage changeJanuary 1997January 1998Percentage change
Scotland18,10011,300-37.728,10017,100-39.1
Per cent of claimant count9.87.4..15.211.3..
UK198,300118,400-40.3357,000216,300-39.4
Scotland as a percentage of the UK9.19.5..7.97.9..

Source: Office for National Statistics

Note: 1. Percentages calculated with reference to unrounded figures.

Employment

There are two main official sources of quarterly employment data: the Workforce in Employment series, which is a survey of employers, and the Labour Force Survey.

An increase of 43,000 in total employment (not seasonally adjusted) in Scotland was recorded by the LFS over the year to Autumn 1997 to reach a new (Autumn) peak of 2,305,000. This was due to increases of 24,000 in the number of employees, 14,000 in the number of self-employed and 5,000 in the number of people either on government supported training and employment programmes or who were unpaid family workers. Given the fall of 32,000 in the level of ILO unemployment, the number of people classed as economically active increased by 10,000 in the year to Autumn 1997. Increases in total employment were evident in most UK GORs, falling only in the North East, Merseyside and Wales. In the UK as a whole, total employment increased by 456,000.

An increase of 23,000 in the civilian workforce (not seasonally adjusted) was recorded by the Workforce in Employment series over the year to September 1997 to reach a new peak of 2,277,000, (7,000 higher than the 1991 peak and 202,000 above the trough in 1983). This comprised increases of 19,000 in the number of self-employed and 6,000 in the number of employees (comprising increases across the service sector (14,000) and decreases in manufacturing (5,000) and other sectors (3,000)) over the year, partly offset by a fall of 2,000 in the number on work-related government training programmes. Increases in the civilian workforce were evident in all GB regions, except East Anglia and Yorkshire and Humberside. In Great Britain as a whole, the civilian workforce increased by 349,000.

The growth in the number of employees has been due to the increase in part-time employment.14 In the year to September 1997, part-time employment rose by 32,000 (17,000 males and 15,000 females), offset by a fall of 26,000 in full-time employment (24,000 males and 2,000 females). This is a continuation of a trend over the past few years in which part-time employment has increased - in each year since 1992 (data are available from 1991) - to a level 104,000 higher (46,000 males and 58,000 females) in 1997 than 5 years earlier. By contrast, full-time employment has fallen consistently and in September 1997 was 90,000 lower than 1992 levels (86,000 males and 4,000 females).


 

7Published in Economic Trends, February 1998.
8GDP estimates of the Scottish regions measure the value of goods and services produced in an area; they do not measure the income of the residents in an area, as is the case for Government Office Regions/countries of the UK. There is a wide variation between areas in terms of size and population; in order to compare the economic performance of areas it is necessary to use an indicator such as GDP per head of population. Resident population is used as the denominator. The implication of using this in conjunction with the workplace-based GDP figures is that the productivity of urban areas into which workers commute will tend to be overstated by this indicator, while that of surrounding areas in which they live will be understated.
9Input -Output Tables and Multipliers for Scotland, 1994, The Stationery Office.
10It should be noted that the data presented by the SCDI for Scottish manufactured exports refer to gross output. They do not measure the level of (or changes in) the value-added component of Scottish manufactured exports (that is, the wages and profits accruing to domestic suppliers of labour and capital).
11Electronics is classified by the SCDI as consisting of 4 industry groupings: Office Machinery, Electrical Machinery and Apparatus nec, Radio/TV/Communication Equipment and Apparatus and Medical, Precision and Optical Instruments, Watches and Clocks.
12Average of September to November levels (not seasonally adjusted).
13The New Deal for young people provides a period of advice and guidance -'the Gateway' - to find unsubsidised jobs. Thereafter, four options will be available: a subsidised job with an employer; a place on an Environment Task Force; a job in the voluntary sector; or full-time education or training. The first 3 options involve at least one day a week training and options 2 and 3 include top-ups to existing benefits. Long term unemployed adults under the New Deal will be able to benefit from two options: a subsidised job with an employer; or opportunities to study for up to 12 months in full-time employment-related courses designed to reach an accredited qualification.
14Part-time employment is defined here as working less than 30 hours per week.
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Prepared 13 March 1998
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Dataset Name: RT331605
Title: Labour market statistics: Scotland
Description: Labour market statistics: Scotland

This dataset has been compiled from data published in Regional Trends 33, 1998 edition published on 25 June 1998.
Source: Office for National Statistics
Time Frame: 1996-1998
Geographic Coverage: United Kingdom
Universe: Various
Measure: Various
Units: See table
Scalar: none
Formula: various
Substitution Details:

Value Meaning
.. Not Available
Table Dimensions
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Region 7 Measure
 
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Table1
Economically active 1996-97 (percentages)23Total in employment: 1996-97 (thousands)34In employment 1996-97 Manufacturing (percentages)13ILO unemployment rate 1996-97 (percentages)13Total claimant count: January 1998 (thousands)Claimant count: of which females: January 1998 (percentage)Claimant count: of which long-term unemployed January 1998 (percentages)5Average gross weekly all persons full-time earnings, April 1997 (£)16
United Kingdom78.626462.019.18.01479.323.226.2366.3
Scotland77.12277.017.18.7152.222.022.4336.8
Aberdeen City82.4113.014.34.93.621.017.6404.8
Aberdeenshire80.2112.014.5..2.826.516.3330.9
Angus86.359.016.9..3.228.323.3320.0
Argyll and Bute80.441.0..11.92.927.122.8305.2
Clackmannanshire64.717.0....1.622.027.5..
Dumfries and Galloway79.067.017.7..4.424.323.4300.2
Dundee City72.260.014.69.36.221.226.3327.4
East Ayrshire75.250.023.114.24.520.528.9307.6
East Dunbartonshire81.153.0....2.223.217.3329.2
East Lothian80.341.0....1.720.516.3310.3
East Renfrewshire83.042.016.8..1.423.820.9..
Edinburgh, City of74.5207.010.36.611.122.120.4362.8
Eilean Siar (Western Isles)83.815.0....1.419.923.8..
Falkirk77.666.023.4..4.521.519.9335.6
Fife77.9147.021.79.311.122.522.7325.2
Glasgow City65.3210.014.215.226.919.429.5341.5
Highland80.9100.012.99.37.925.920.9296.2
Inverclyde80.239.026.5..2.518.512.7323.4
Midlothian84.839.0....1.619.413.7309.0
Moray86.443.014.3..2.227.215.4285.0
North Ayrshire73.558.027.49.15.123.719.2317.8
North Lanarkshire74.7133.021.212.410.720.820.1336.7
Orkney Islands87.810.0....0.426.824.4..
Perth and Kinross86.666.011.3..2.823.017.8..
Renfrewshire78.580.020.111.35.520.523.3336.1
Scottish Borders, The80.649.020.6..2.123.712.3303.5
Shetland Islands84.811.0....0.423.214.2..
South Ayrshire79.248.022.910.33.623.623.4346.2
South Lanarkshire78.4146.022.08.38.221.721.8319.1
Stirling77.237.0....2.123.019.5346.6
West Dunbartonshire71.536.0..13.64.219.327.3319.0
West Lothian82.278.032.6..3.521.210.2335.5
Footnotes
1 -In some cases sample sizes are too small to provide reliable estimates.
2 -Based on the population of working age.
3 -Data are from the Labour Force Survey and relate to the period March 1996 - February 1997.
4 -Includes those on government-supported employment and training programmes and unpaid family workers.
5 -Persons who have been claiming for more than 12 months as a percentage of all claimants.
6 -Average gross weekly earnings estimates have been derived from the New Earnings Survey and relate to full-time employees on adult rates whose pay for the survey pay-period was not affected by absence.
7 -New Councils for Scotland
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Dataset Name: RT331603
Title: Education and training: Scotland
Description: Education and training: Scotland

This dataset has been compiled from data published in Regional Trends 33, 1998 edition published on 25 June 1998.
Source: The Scottish Office Home Department; The Scottish Office Education and Industry Department; Department for Education and Employment
Time Frame: 1995-1997
Geographic Coverage: United Kingdom
Universe: various
Measure: various
Units: See table
Scalar: none
Formula: none
Substitution Details:

Value Meaning
- Negligible (less than half the final digit shown)
.. Not Available
Table Dimensions
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Region 8 Measure
 
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Table
Day nursery places per 1,000 population aged under 5 years Nov. 19961Children under 5 in education (percentages) Jan. 19972Pupil/teacher ratio: primary schools (numbers) 1996/97Pupil/teacher ratio: secondary schools (numbers) 1996/97Pupils and students participating in post-compulsory education, (percentages) 1995/963Percentage of pupils in last year of compulsory schooling with no graded results 1995/9645Percentage of pupils in last year of compulsory schooling with 5 or more Grades 1-3 SCE Standard Grade (or equivalent) 1995/9645Percentage of employees of working age receiving job-related training 1996-9767
United Kingdom..59.022.816.278.07.445.514.5
Scotland80.639.019.613.093.03.653.612.5
Aberdeen City126.050.019.912.9113.01.953.015.4
Aberdeenshire34.434.018.613.881.09.258.211.4
Angus70.238.019.113.089.0..62.0..
Argyll and Bute38.813.017.312.481.08.654.1..
Clackmannanshire90.947.021.213.478.0..63.6..
Dumfries and Galloway21.344.018.912.793.02.760.2..
Dundee City114.359.018.012.2117.00.646.9..
East Ayrshire43.443.021.013.589.06.450.2..
East Dunbartonshire76.211.022.213.994.0..71.2..
East Lothian48.656.020.613.466.012.746.0..
East Renfrewshire146.033.022.314.091.0..78.8..
Edinburgh, City of132.350.020.713.4109.02.356.714.7
Eilean Siar (Western Isles)12.6..13.09.5102.03.260.9..
Falkirk81.840.021.313.691.04.049.4..
Fife20.251.019.113.4106.05.352.113.5
Glasgow City99.853.019.312.488.012.741.915.3
Highland41.519.017.311.894.0..60.0..
Inverclyde105.827.021.413.695.0..56.2..
Midlothian49.054.019.913.677.03.853.0..
Moray21.631.018.912.291.08.054.3..
North Ayrshire115.323.021.213.472.010.545.6..
North Lanarkshire64.425.020.213.494.02.347.511.8
Orkney Islands31.852.015.110.997.0-69.3..
Perth and Kinross93.245.018.712.578.010.253.9..
Renfrewshire119.631.022.013.7103.0..55.915.5
Scottish Borders, The56.922.018.512.192.01.361.7..
Shetland Islands14.842.012.78.179.0..73.6..
South Ayrshire70.436.021.013.699.0..61.9..
South Lanarkshire103.915.020.713.792.03.651.513.7
Stirling200.546.019.513.381.02.961.4..
West Dunbartonshire81.947.020.314.0108.0..52.5..
West Lothian53.651.020.313.580.06.346.8..
Footnotes
1 -Social Work Provision only (local authority and registered); includes Day Nurseries, Childrens Centres, Family Centres and Private Nursery Schools. Population data used mid-1996 estimates.
2 -Figures relate to all pupils as a percentage of the three and four year old population.
3 -In Scotland pupils in S5 at September 1995. The figure for the United Kingdom relates to 16 year olds in education at the beginning of the academic year. Some students in Scotland participate on short courses. They are counted for each course; hence there is double counting which results in some percentages being greater that 100.
4 -Pupils in their last year of compulsory schooling as a percentage of the school population of the same age.
5 -Figures relate to all schools.
6 -Males aged 16-64 and females aged 16-59. Job-related education or training received in the four weeks before interview. In some cases sample sizes are too small to provide reliable estimates.
7 -Data relate to the period March 1996 to February 1997. Figure for United Kingdom relates to Great Britain.
8 -New Councils for Scotland
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Dataset Name: RT331604
Title: Housing and households: Scotland
Description: Housing and households: Scotland

This dataset has been compiled from data published in Regional Trends 33, 1998 edition published on 25 June 1998.
Source: The Scottish Office Development Department
Time Frame: 1996 and 1997
Geographic Coverage: United Kingdom
Universe: various
Measure: various
Units: See table
Scalar: various
Formula: none
Substitution Details:

Value Meaning
. Not applicable
.. Not available
Table Dimensions
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Region 5 Measure
 
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Table
Housing starts: private enterprise (numbers) 19961Housing starts: housing associations, local authorities etc (numbers) 19962Stock of dwellings (thousands) 19963Households (thousands) 1996Local authority tenants: average weekly unrebated rent per dwelling (£) April 1997Council Tax (£) April 19974
United Kingdom151826.031224.024607.024115.3...
Scotland15759.04768.02232.02136.233.6783.0
Aberdeen City1142.0136.0100.096.827.5712.0
Aberdeenshire533.090.092.087.129.7643.0
Angus272.0167.048.046.223.5679.0
Argyll and Bute300.0266.043.037.735.0801.0
Clackmannanshire125.037.021.020.029.6753.0
Dumfries and Galloway388.0159.066.062.332.7714.0
Dundee City182.0151.072.067.536.8920.0
East Ayrshire262.030.051.050.126.9779.0
East Dunbartonshire236.06.042.041.329.6771.0
East Lothian469.0165.038.036.328.8724.0
East Renfrewshire295.096.034.033.128.9682.0
Edinburgh, City of1496.0525.0206.0198.243.8837.0
Eilean Siar (Western Isles)75.010.013.011.636.5599.0
Falkirk651.066.061.059.129.8680.0
Fife202.0251.0152.0145.630.3747.0
Glasgow City1884.01056.0286.0271.940.4982.0
Highland664.0161.095.085.838.5719.0
Inverclyde291.0126.039.038.034.6831.0
Midlothian362.061.032.030.825.2858.0
Moray327.00.037.034.928.0652.0
North Ayrshire344.0157.060.057.730.2718.0
North Lanarkshire1557.0175.0130.0128.531.3787.0
Orkney Islands0.06.09.08.133.8515.0
Perth and Kinross448.0147.059.055.028.2732.0
Renfrewshire732.066.077.075.132.5783.0
Scottish Borders, The245.098.049.044.929.7612.0
Shetland Islands131.021.010.08.936.1486.0
South Ayrshire182.080.049.047.630.7765.0
South Lanarkshire488.098.0124.0122.335.3793.0
Stirling341.066.034.033.133.6776.0
West Dunbartonshire193.0139.042.040.433.4978.0
West Lothian942.0156.061.060.328.3792.0
Footnotes
1 -Includes estimates for outstanding returns.
2 -Based on incomplete returns.
3 -Number of residential dwellings from the Council Tax Register.
4 -Amounts shown for Council Tax are headline Council Tax for the area of each billing authority for B and D, 2 adults before transitional relief and benefit. The ratios of other bands are: A 6/9, B7/9, C 8/9, E 11/9, F 13/9, G 15/9 and H 18/9.
5 -New Councils for Scotland
statsmodels-0.12.2/statsmodels/datasets/scotland/src/scotland_population.csv000066400000000000000000000122631400612667500275170ustar00rootroot00000000000000Dataset Name:,"RT331601" Title:,"Area and population, 1996: Scotland" Description:,"Area and population, 1996: Scotland This dataset has been compiled from data published in Regional Trends 33, 1998 edition published on 25 June 1998. " Source:,"Office for National Statistics; General Register Office for Scotland" Time Frame:,"1996" Geographic Coverage:,"United Kingdom" Universe:,"UK population" Measure:,"various" Units:,"See table" Scalar:,"various" Formula:,"none" ==================================== Table ,"Area (sq km)","Persons per sq km","Population (thousands) Males","Population (thousands) Females","Population (thousands) Total","Total population percentage change 1981-1996","Total period fertility rate (TPFR)<1>","Standardised mortality ratio (UK=100) (SMR)<2>","Percentage of population aged under 5","Percentage of population aged 5-15","Percentage of population aged 16 up to pension age<3>","Percentage of population of pension age or over<4>", "United Kingdom","242910.00","242.00","28856.00","29946.00","58801.00","4.30","1.72","100.00","6.40","14.20","61.30","18.10", "Scotland","78133.00","66.00","2486.00","2642.00","5128.00","-1.00","1.55","116.00","6.10","13.90","63.10","17.80", "Aberdeen City","186.00","1169.00","106.00","111.00","217.00","2.20","1.35","105.00","5.80","12.30","65.80","17.10", "Aberdeenshire","6318.00","36.00","113.00","114.00","227.00","20.40","1.64","97.00","6.50","15.30","63.80","15.30", "Angus","2181.00","51.00","54.00","57.00","111.00","4.90","1.67","113.00","6.00","13.90","61.60","19.40", "Argyll and Bute","6930.00","13.00","45.00","46.00","91.00","-0.10","1.70","109.00","5.50","13.60","61.10","20.80", "Clackmannanshire","157.00","312.00","24.00","25.00","49.00","1.20","1.76","115.00","6.60","14.60","63.00","16.70", "Dumfries and Galloway","6439.00","23.00","72.00","76.00","148.00","1.40","1.78","107.00","5.90","13.80","60.30","21.20", "Dundee City","65.00","2306.00","72.00","79.00","150.00","-11.40","1.57","118.00","5.90","13.30","62.00","19.90", "East Ayrshire","1252.00","98.00","59.00","63.00","122.00","-3.90","1.64","114.00","6.30","14.50","61.90","18.30", "East Dunbartonshire","172.00","645.00","54.00","57.00","111.00","1.00","1.56","102.00","5.80","14.20","64.50","16.50", "East Lothian","678.00","130.00","43.00","45.00","88.00","9.20","1.77","112.00","6.40","13.70","61.50","19.50", "East Renfrewshire","173.00","510.00","43.00","45.00","88.00","9.80","1.67","96.00","6.20","14.60","63.00","17.10", "Edinburgh, City of","262.00","1711.00","217.00","232.00","449.00","0.60","1.34","111.00","5.70","11.60","65.80","17.90", "Eilean Siar (Western Isles)","3134.00","9.00","14.00","15.00","29.00","-8.50","1.65","117.00","5.50","15.10","59.80","20.70", "Falkirk","299.00","478.00","69.00","74.00","143.00","-1.50","1.58","121.00","6.20","13.70","63.80","17.40", "Fife","1323.00","264.00","169.00","180.00","349.00","2.30","1.55","109.00","6.00","14.40","62.30","18.30", "Glasgow City","175.00","3522.00","294.00","322.00","616.00","-13.50","1.48","137.00","6.30","13.30","63.20","18.10", "Highland","25784.00","8.00","102.00","106.00","209.00","7.10","1.77","109.00","6.20","14.90","61.80","18.10", "Inverclyde","162.00","538.00","42.00","45.00","87.00","-13.90","1.66","138.00","6.20","14.60","61.70","18.60", "Midlothian","356.00","225.00","39.00","41.00","80.00","-4.20","1.61","119.00","6.10","14.30","64.20","16.40", "Moray","2238.00","39.00","43.00","44.00","87.00","3.60","1.76","108.00","6.60","14.60","61.80","18.00", "North Ayrshire","884.00","158.00","67.00","72.00","140.00","1.60","1.63","115.00","6.20","15.00","62.20","17.60", "North Lanarkshire","474.00","688.00","158.00","168.00","326.00","-4.60","1.66","126.00","6.40","14.90","63.80","15.90", "Orkney Islands","992.00","20.00","10.00","10.00","20.00","3.20","1.78","106.00","6.00","15.30","61.20","18.50", "Perth and Kinross","5311.00","25.00","64.00","69.00","133.00","8.80","1.61","103.00","5.60","13.80","60.70","20.90", "Renfrewshire","261.00","683.00","86.00","92.00","179.00","-3.50","1.59","125.00","6.30","14.10","63.70","17.00", "Scottish Borders, The","4734.00","22.00","51.00","55.00","106.00","4.80","1.67","100.00","5.80","13.30","60.20","21.80", "Shetland Islands","1438.00","16.00","12.00","11.00","23.00","-12.60","1.77","117.00","7.00","15.90","62.90","14.90", "South Ayrshire","1202.00","95.00","55.00","60.00","115.00","1.30","1.55","105.00","5.50","13.70","61.10","20.90", "South Lanarkshire","1771.00","174.00","149.00","159.00","307.00","-0.80","1.55","125.00","6.30","14.50","63.80","16.50", "Stirling","2196.00","38.00","40.00","43.00","83.00","3.10","1.55","110.00","5.70","13.60","63.80","17.90", "West Dunbartonshire","162.00","590.00","46.00","50.00","96.00","-9.50","1.70","130.00","6.40","15.30","61.40","17.80", "West Lothian","425.00","355.00","74.00","77.00","151.00","8.30","1.63","126.00","6.80","15.10","65.80","13.20", ==================================== Footnotes "1 - The total period fertility rate (TPFR) is the average number of children which would be born to a woman if the current pattern of fertility persisted throughout her child-bearing years." "2 - Adjusted for the age structure of the population." "3 - Pension age is 65 for males and 60 for females." "4 - New Councils for Scotland" statsmodels-0.12.2/statsmodels/datasets/scotland/src/scotland_population.html000066400000000000000000000534171400612667500276760ustar00rootroot00000000000000 Cross-sectional dataset viewer v1.1
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Dataset Name: RT331601
Title: Area and population, 1996: Scotland
Description: Area and population, 1996: Scotland

This dataset has been compiled from data published in Regional Trends 33, 1998 edition published on 25 June 1998.
Source: Office for National Statistics; General Register Office for Scotland
Time Frame: 1996
Geographic Coverage: United Kingdom
Universe: UK population
Measure: various
Units: See table
Scalar: various
Formula: none
Table Dimensions
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To select list items either hold down 'Ctrl' key and click each item required, or click the first item and hold down the mouse button whilst scrolling down the list.
Region 4 Measure
 
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Table
Area (sq km)Persons per sq kmPopulation (thousands) MalesPopulation (thousands) FemalesPopulation (thousands) TotalTotal population percentage change 1981-1996Total period fertility rate (TPFR)1Standardised mortality ratio (UK=100) (SMR)2Percentage of population aged under 5Percentage of population aged 5-15Percentage of population aged 16 up to pension age3Percentage of population of pension age or over4
United Kingdom242910.00242.0028856.0029946.0058801.004.301.72100.006.4014.2061.3018.10
Scotland78133.0066.002486.002642.005128.00-1.001.55116.006.1013.9063.1017.80
Aberdeen City186.001169.00106.00111.00217.002.201.35105.005.8012.3065.8017.10
Aberdeenshire6318.0036.00113.00114.00227.0020.401.6497.006.5015.3063.8015.30
Angus2181.0051.0054.0057.00111.004.901.67113.006.0013.9061.6019.40
Argyll and Bute6930.0013.0045.0046.0091.00-0.101.70109.005.5013.6061.1020.80
Clackmannanshire157.00312.0024.0025.0049.001.201.76115.006.6014.6063.0016.70
Dumfries and Galloway6439.0023.0072.0076.00148.001.401.78107.005.9013.8060.3021.20
Dundee City65.002306.0072.0079.00150.00-11.401.57118.005.9013.3062.0019.90
East Ayrshire1252.0098.0059.0063.00122.00-3.901.64114.006.3014.5061.9018.30
East Dunbartonshire172.00645.0054.0057.00111.001.001.56102.005.8014.2064.5016.50
East Lothian678.00130.0043.0045.0088.009.201.77112.006.4013.7061.5019.50
East Renfrewshire173.00510.0043.0045.0088.009.801.6796.006.2014.6063.0017.10
Edinburgh, City of262.001711.00217.00232.00449.000.601.34111.005.7011.6065.8017.90
Eilean Siar (Western Isles)3134.009.0014.0015.0029.00-8.501.65117.005.5015.1059.8020.70
Falkirk299.00478.0069.0074.00143.00-1.501.58121.006.2013.7063.8017.40
Fife1323.00264.00169.00180.00349.002.301.55109.006.0014.4062.3018.30
Glasgow City175.003522.00294.00322.00616.00-13.501.48137.006.3013.3063.2018.10
Highland25784.008.00102.00106.00209.007.101.77109.006.2014.9061.8018.10
Inverclyde162.00538.0042.0045.0087.00-13.901.66138.006.2014.6061.7018.60
Midlothian356.00225.0039.0041.0080.00-4.201.61119.006.1014.3064.2016.40
Moray2238.0039.0043.0044.0087.003.601.76108.006.6014.6061.8018.00
North Ayrshire884.00158.0067.0072.00140.001.601.63115.006.2015.0062.2017.60
North Lanarkshire474.00688.00158.00168.00326.00-4.601.66126.006.4014.9063.8015.90
Orkney Islands992.0020.0010.0010.0020.003.201.78106.006.0015.3061.2018.50
Perth and Kinross5311.0025.0064.0069.00133.008.801.61103.005.6013.8060.7020.90
Renfrewshire261.00683.0086.0092.00179.00-3.501.59125.006.3014.1063.7017.00
Scottish Borders, The4734.0022.0051.0055.00106.004.801.67100.005.8013.3060.2021.80
Shetland Islands1438.0016.0012.0011.0023.00-12.601.77117.007.0015.9062.9014.90
South Ayrshire1202.0095.0055.0060.00115.001.301.55105.005.5013.7061.1020.90
South Lanarkshire1771.00174.00149.00159.00307.00-0.801.55125.006.3014.5063.8016.50
Stirling2196.0038.0040.0043.0083.003.101.55110.005.7013.6063.8017.90
West Dunbartonshire162.00590.0046.0050.0096.00-9.501.70130.006.4015.3061.4017.80
West Lothian425.00355.0074.0077.00151.008.301.63126.006.8015.1065.8013.20
Footnotes
1 -The total period fertility rate (TPFR) is the average number of children which would be born to a woman if the current pattern of fertility persisted throughout her child-bearing years.
2 -Adjusted for the age structure of the population.
3 -Pension age is 65 for males and 60 for females.
4 -New Councils for Scotland
statsmodels-0.12.2/statsmodels/datasets/scotland/src/scotvote.csv000066400000000000000000000153031400612667500253020ustar00rootroot00000000000000"PrivateHousingStarts" "PublicHousingStarts" "StockofDwellings" "Households" "LocalAuthorityRent" "CouncilTax" "Areas" "Density" "Males" "Females" "Population" "PopulationChange" "FertilityRate" "StdMortalityRatio" "PercentageUnder5" "Percentage5to15" "Percentage16topension" "PercentageOverPensionage" "InNursery" "InPreschool" "PrimaryPTRatio" "SecondaryPTRatio" "PostCompulsory" "NoGrade" "Grades" "InJobTraining" "Birthsper1000" "Deathsper1000" "PeriMortality" "InfantMortality" "PerBirthsOut" "Active" "TotalEmployment" "PerMfgEmployment" "PerUnemployment" "TotalClaimants" "PerClaimantFemale" "PerClaimLongT" "MeanWeekSal" "GDP" "Var.41" "Var.42" "Aberdeen_City" 1142 136 100 96.8 27.5 712 186 1169 106 111 217 2.2 1.35 105 5.8 12.3 65.8 17.1 126 50 19.9 12.9 113 1.9 53 15.4 11 10.4 7.7 5.7 35 82.4 113 14.3 4.9 3.6 21 17.6 404.8 13566 71.8 60.3 "Aberdeenshire" 533 90 92 87.1 29.7 643 6318 36 113 114 227 20.4 1.64 97 6.5 15.3 63.8 15.3 34.4 34 18.6 13.8 81 9.2 58.2 11.4 11.3 9 9 3.8 24 80.2 112 14.5 NA 2.8 26.5 16.3 330.9 13566 63.9 52.3 "Angus" 272 167 48 46.2 23.5 679 2181 51 54 57 111 4.9 1.67 113 6 13.9 61.6 19.4 70.2 38 19.1 13 89 NA 62 NA 11 13.2 5.6 3.2 33 86.3 59 16.9 NA 3.2 28.3 23.3 320 9611 64.7 53.4 "Argyll_and_Bute" 300 266 43 37.7 35 801 6930 13 45 46 91 -0.1 1.7 109 5.5 13.6 61.1 20.8 38.8 13 17.3 12.4 81 8.6 54.1 NA 10.5 13.8 8.6 7 33 80.4 41 NA 11.9 2.9 27.1 22.8 305.2 9483 67.3 57 "Clackmannanshire" 125 37 21 20 29.6 753 157 312 24 25 49 1.2 1.76 115 6.6 14.6 63 16.7 90.9 47 21.2 13.4 78 NA 63.6 NA 12.3 11.3 10.4 6.3 40 64.7 17 NA NA 1.6 22 27.5 NA 9265 80 68.7 "Dumfries_and_Galloway" 388 159 66 62.3 32.7 714 6439 23 72 76 148 1.4 1.78 107 5.9 13.8 60.3 21.2 21.3 44 18.9 12.7 93 2.7 60.2 NA 10.9 12.8 8.8 7.8 34 79 67 17.7 NA 4.4 24.3 23.4 300.2 9555 60.7 48.8 "Dundee_City" 182 151 72 67.5 36.8 920 65 2306 72 79 150 -11.4 1.57 118 5.9 13.3 62 19.9 114.3 59 18 12.2 117 0.6 46.9 NA 11.5 13.1 8.6 6.8 51 72.2 60 14.6 9.3 6.2 21.2 26.3 327.4 9611 76 65.5 "East_Ayrshire" 262 30 51 50.1 26.9 779 1252 98 59 63 122 -3.9 1.64 114 6.3 14.5 61.9 18.3 43.4 43 21 13.5 89 6.4 50.2 NA 11.4 11.6 12.3 6.5 40 75.2 50 23.1 14.2 4.5 20.5 28.9 307.6 9483 81.1 70.5 "East_Dunbartonshire" 236 6 42 41.3 29.6 771 172 645 54 57 111 1 1.56 102 5.8 14.2 64.5 16.5 76.2 11 22.2 13.9 94 NA 71.2 NA 10.5 9.2 8.1 7.2 19 81.1 53 NA NA 2.2 23.2 17.3 329.2 9483 69.8 59.1 "East_Lothian" 469 165 38 36.3 28.8 724 678 130 43 45 88 9.2 1.77 112 6.4 13.7 61.5 19.5 48.6 56 20.6 13.4 66 12.7 46 NA 12.3 12.6 7.6 5.2 29 80.3 41 NA NA 1.7 20.5 16.3 310.3 12656 74.2 62.7 "East_Renfrewshire" 295 96 34 33.1 28.9 682 173 510 43 45 88 9.8 1.67 96 6.2 14.6 63 17.1 146 33 22.3 14 91 NA 78.8 NA 11.5 9.5 7.4 6.2 19 83 42 16.8 NA 1.4 23.8 20.9 NA 9483 61.7 51.6 "Edinburgh_City" 1496 525 206 198.2 43.8 837 262 1711 217 232 449 0.6 1.34 111 5.7 11.6 65.8 17.9 132.3 50 20.7 13.4 109 2.3 56.7 14.7 11.4 11.7 8.1 6.4 33 74.5 207 10.3 6.6 11.1 22.1 20.4 362.8 12656 71.9 62 "Eilean_Siar_(Western_Isles)" 75 10 13 11.6 36.5 599 3134 9 14 15 29 -8.5 1.65 117 5.5 15.1 59.8 20.7 12.6 NA 13 9.5 102 3.2 60.9 NA 9.7 14.9 11.2 5.7 19 83.8 15 NA NA 1.4 19.9 23.8 NA 8298 79.4 68.4 "Falkirk" 651 66 61 59.1 29.8 680 299 478 69 74 143 -1.5 1.58 121 6.2 13.7 63.8 17.4 81.8 40 21.3 13.6 91 4 49.4 NA 11.7 11.7 7.9 4.8 34 77.6 66 23.4 NA 4.5 21.5 19.9 335.6 9265 80 69.2 "Fife" 202 251 152 145.6 30.3 747 1323 264 169 180 349 2.3 1.55 109 6 14.4 62.3 18.3 20.2 51 19.1 13.4 106 5.3 52.1 13.5 11 11.4 8.7 7.1 37 77.9 147 21.7 9.3 11.1 22.5 22.7 325.2 8314 76.1 64.7 "Glasgow_City" 1884 1056 286 271.9 40.4 982 175 3522 294 322 616 -13.5 1.48 137 6.3 13.3 63.2 18.1 99.8 53 19.3 12.4 88 12.7 41.9 15.3 12.5 14 11.1 6.9 49 65.3 210 14.2 15.2 26.9 19.4 29.5 341.5 9483 83.6 75 "Highland" 664 161 95 85.8 38.5 719 25784 8 102 106 209 7.1 1.77 109 6.2 14.9 61.8 18.1 41.5 19 17.3 11.8 94 NA 60 NA 11.4 11.4 8.3 6.5 34 80.9 100 12.9 9.3 7.9 25.9 20.9 296.2 8298 72.6 62.1 "Inverclyde" 291 126 39 38 34.6 831 162 538 42 45 87 -13.9 1.66 138 6.2 14.6 61.7 18.6 105.8 27 21.4 13.6 95 NA 56.2 NA 11.7 14.5 11.5 8 45 80.2 39 26.5 NA 2.5 18.5 12.7 323.4 9483 78 67.2 "Midlothian" 362 61 32 30.8 25.2 858 356 225 39 41 80 -4.2 1.61 119 6.1 14.3 64.2 16.4 49 54 19.9 13.6 77 3.8 53 NA 11.2 10.7 10.8 6 35 84.8 39 NA NA 1.6 19.4 13.7 309 12656 79.9 67.7 "Moray" 327 0 37 34.9 28 652 2238 39 43 44 87 3.6 1.76 108 6.6 14.6 61.8 18 21.6 31 18.9 12.2 91 8 54.3 NA 12.4 11 9.8 7.4 26 86.4 43 14.3 NA 2.2 27.2 15.4 285 13566 67.2 52.7 "North_Ayrshire" 344 157 60 57.7 30.2 718 884 158 67 72 140 1.6 1.63 115 6.2 15 62.2 17.6 115.3 23 21.2 13.4 72 10.5 45.6 NA 11.3 11.8 11.6 6.9 42 73.5 58 27.4 9.1 5.1 23.7 19.2 317.8 9483 76.3 65.7 "North_Lanarkshire" 1557 175 130 128.5 31.3 787 474 688 158 168 326 -4.6 1.66 126 6.4 14.9 63.8 15.9 64.4 25 20.2 13.4 94 2.3 47.5 11.8 12.5 11.1 11.6 8.5 38 74.7 133 21.2 12.4 10.7 20.8 20.1 336.7 9483 82.6 72.2 "Orkney_Islands" 0 6 9 8.1 33.8 515 992 20 10 10 20 3.2 1.78 106 6 15.3 61.2 18.5 31.8 52 15.1 10.9 97 0 69.3 NA 10.9 11.6 7.5 1.4 30 87.8 10 NA NA 0.4 26.8 24.4 NA 8298 57.3 47.4 "Perth_and_Kinross" 448 147 59 55 28.2 732 5311 25 64 69 133 8.8 1.61 103 5.6 13.8 60.7 20.9 93.2 45 18.7 12.5 78 10.2 53.9 NA 10.5 12.6 9.8 5.9 29 86.6 66 11.3 NA 2.8 23 17.8 NA 9611 61.7 51.3 "Renfrewshire" 732 66 77 75.1 32.5 783 261 683 86 92 179 -3.5 1.59 125 6.3 14.1 63.7 17 119.6 31 22 13.7 103 NA 55.9 15.5 11.9 11.6 8 4.5 39 78.5 80 20.1 11.3 5.5 20.5 23.3 336.1 9483 79 63.6 "Scottish_Borders_The" 245 98 49 44.9 29.7 612 4734 22 51 55 106 4.8 1.67 100 5.8 13.3 60.2 21.8 56.9 22 18.5 12.1 92 1.3 61.7 NA 10.7 12.8 8 4.9 28 80.6 49 20.6 NA 2.1 23.7 12.3 303.5 9033 62.8 50.7 "Shetland_Islands" 131 21 10 8.9 36.1 486 1438 16 12 11 23 -12.6 1.77 117 7 15.9 62.9 14.9 14.8 42 12.7 8.1 79 NA 73.6 NA 11.7 10.9 9.9 6.5 28 84.8 11 NA NA 0.4 23.2 14.2 NA 8298 62.4 51.6 "South_Ayrshire" 182 80 49 47.6 30.7 765 1202 95 55 60 115 1.3 1.55 105 5.5 13.7 61.1 20.9 70.4 36 21 13.6 99 NA 61.9 NA 10.1 12.7 6.2 4.3 33 79.2 48 22.9 10.3 3.6 23.6 23.4 346.2 9483 66.9 56.2 "South_Lanarkshire" 488 98 124 122.3 35.3 793 1771 174 149 159 307 -0.8 1.55 125 6.3 14.5 63.8 16.5 103.9 15 20.7 13.7 92 3.6 51.5 13.7 11.5 11.3 9.2 5.1 33 78.4 146 22 8.3 8.2 21.7 21.8 319.1 9483 77.8 67.6 "Stirling" 341 66 34 33.1 33.6 776 2196 38 40 43 83 3.1 1.55 110 5.7 13.6 63.8 17.9 200.5 46 19.5 13.3 81 2.9 61.4 NA 11.1 11.8 7.7 4.9 33 77.2 37 NA NA 2.1 23 19.5 346.6 9265 68.5 58.9 "West_Dunbartonshire" 193 139 42 40.4 33.4 978 162 590 46 50 96 -9.5 1.7 130 6.4 15.3 61.4 17.8 81.9 47 20.3 14 108 NA 52.5 NA 12.5 12.7 11.7 8.7 42 71.5 36 NA 13.6 4.2 19.3 27.3 319 9483 84.7 74.7 "West_Lothian" 942 156 61 60.3 28.3 792 425 355 74 77 151 8.3 1.63 126 6.8 15.1 65.8 13.2 53.6 51 20.3 13.5 80 6.3 46.8 NA 13.1 9.5 8.7 4.6 33 82.2 78 32.6 NA 3.5 21.2 10.2 335.5 12656 79.6 67.3 statsmodels-0.12.2/statsmodels/datasets/scotland/src/scotvote.dat000066400000000000000000000153031400612667500252570ustar00rootroot00000000000000"PrivateHousingStarts" "PublicHousingStarts" "StockofDwellings" "Households" "LocalAuthorityRent" "CouncilTax" "Areas" "Density" "Males" "Females" "Population" "PopulationChange" "FertilityRate" "StdMortalityRatio" "PercentageUnder5" "Percentage5to15" "Percentage16topension" "PercentageOverPensionage" "InNursery" "InPreschool" "PrimaryPTRatio" "SecondaryPTRatio" "PostCompulsory" "NoGrade" "Grades" "InJobTraining" "Birthsper1000" "Deathsper1000" "PeriMortality" "InfantMortality" "PerBirthsOut" "Active" "TotalEmployment" "PerMfgEmployment" "PerUnemployment" "TotalClaimants" "PerClaimantFemale" "PerClaimLongT" "MeanWeekSal" "GDP" "Var.41" "Var.42" "Aberdeen_City" 1142 136 100 96.8 27.5 712 186 1169 106 111 217 2.2 1.35 105 5.8 12.3 65.8 17.1 126 50 19.9 12.9 113 1.9 53 15.4 11 10.4 7.7 5.7 35 82.4 113 14.3 4.9 3.6 21 17.6 404.8 13566 71.8 60.3 "Aberdeenshire" 533 90 92 87.1 29.7 643 6318 36 113 114 227 20.4 1.64 97 6.5 15.3 63.8 15.3 34.4 34 18.6 13.8 81 9.2 58.2 11.4 11.3 9 9 3.8 24 80.2 112 14.5 NA 2.8 26.5 16.3 330.9 13566 63.9 52.3 "Angus" 272 167 48 46.2 23.5 679 2181 51 54 57 111 4.9 1.67 113 6 13.9 61.6 19.4 70.2 38 19.1 13 89 NA 62 NA 11 13.2 5.6 3.2 33 86.3 59 16.9 NA 3.2 28.3 23.3 320 9611 64.7 53.4 "Argyll_and_Bute" 300 266 43 37.7 35 801 6930 13 45 46 91 -0.1 1.7 109 5.5 13.6 61.1 20.8 38.8 13 17.3 12.4 81 8.6 54.1 NA 10.5 13.8 8.6 7 33 80.4 41 NA 11.9 2.9 27.1 22.8 305.2 9483 67.3 57 "Clackmannanshire" 125 37 21 20 29.6 753 157 312 24 25 49 1.2 1.76 115 6.6 14.6 63 16.7 90.9 47 21.2 13.4 78 NA 63.6 NA 12.3 11.3 10.4 6.3 40 64.7 17 NA NA 1.6 22 27.5 NA 9265 80 68.7 "Dumfries_and_Galloway" 388 159 66 62.3 32.7 714 6439 23 72 76 148 1.4 1.78 107 5.9 13.8 60.3 21.2 21.3 44 18.9 12.7 93 2.7 60.2 NA 10.9 12.8 8.8 7.8 34 79 67 17.7 NA 4.4 24.3 23.4 300.2 9555 60.7 48.8 "Dundee_City" 182 151 72 67.5 36.8 920 65 2306 72 79 150 -11.4 1.57 118 5.9 13.3 62 19.9 114.3 59 18 12.2 117 0.6 46.9 NA 11.5 13.1 8.6 6.8 51 72.2 60 14.6 9.3 6.2 21.2 26.3 327.4 9611 76 65.5 "East_Ayrshire" 262 30 51 50.1 26.9 779 1252 98 59 63 122 -3.9 1.64 114 6.3 14.5 61.9 18.3 43.4 43 21 13.5 89 6.4 50.2 NA 11.4 11.6 12.3 6.5 40 75.2 50 23.1 14.2 4.5 20.5 28.9 307.6 9483 81.1 70.5 "East_Dunbartonshire" 236 6 42 41.3 29.6 771 172 645 54 57 111 1 1.56 102 5.8 14.2 64.5 16.5 76.2 11 22.2 13.9 94 NA 71.2 NA 10.5 9.2 8.1 7.2 19 81.1 53 NA NA 2.2 23.2 17.3 329.2 9483 69.8 59.1 "East_Lothian" 469 165 38 36.3 28.8 724 678 130 43 45 88 9.2 1.77 112 6.4 13.7 61.5 19.5 48.6 56 20.6 13.4 66 12.7 46 NA 12.3 12.6 7.6 5.2 29 80.3 41 NA NA 1.7 20.5 16.3 310.3 12656 74.2 62.7 "East_Renfrewshire" 295 96 34 33.1 28.9 682 173 510 43 45 88 9.8 1.67 96 6.2 14.6 63 17.1 146 33 22.3 14 91 NA 78.8 NA 11.5 9.5 7.4 6.2 19 83 42 16.8 NA 1.4 23.8 20.9 NA 9483 61.7 51.6 "Edinburgh_City" 1496 525 206 198.2 43.8 837 262 1711 217 232 449 0.6 1.34 111 5.7 11.6 65.8 17.9 132.3 50 20.7 13.4 109 2.3 56.7 14.7 11.4 11.7 8.1 6.4 33 74.5 207 10.3 6.6 11.1 22.1 20.4 362.8 12656 71.9 62 "Eilean_Siar_(Western_Isles)" 75 10 13 11.6 36.5 599 3134 9 14 15 29 -8.5 1.65 117 5.5 15.1 59.8 20.7 12.6 NA 13 9.5 102 3.2 60.9 NA 9.7 14.9 11.2 5.7 19 83.8 15 NA NA 1.4 19.9 23.8 NA 8298 79.4 68.4 "Falkirk" 651 66 61 59.1 29.8 680 299 478 69 74 143 -1.5 1.58 121 6.2 13.7 63.8 17.4 81.8 40 21.3 13.6 91 4 49.4 NA 11.7 11.7 7.9 4.8 34 77.6 66 23.4 NA 4.5 21.5 19.9 335.6 9265 80 69.2 "Fife" 202 251 152 145.6 30.3 747 1323 264 169 180 349 2.3 1.55 109 6 14.4 62.3 18.3 20.2 51 19.1 13.4 106 5.3 52.1 13.5 11 11.4 8.7 7.1 37 77.9 147 21.7 9.3 11.1 22.5 22.7 325.2 8314 76.1 64.7 "Glasgow_City" 1884 1056 286 271.9 40.4 982 175 3522 294 322 616 -13.5 1.48 137 6.3 13.3 63.2 18.1 99.8 53 19.3 12.4 88 12.7 41.9 15.3 12.5 14 11.1 6.9 49 65.3 210 14.2 15.2 26.9 19.4 29.5 341.5 9483 83.6 75 "Highland" 664 161 95 85.8 38.5 719 25784 8 102 106 209 7.1 1.77 109 6.2 14.9 61.8 18.1 41.5 19 17.3 11.8 94 NA 60 NA 11.4 11.4 8.3 6.5 34 80.9 100 12.9 9.3 7.9 25.9 20.9 296.2 8298 72.6 62.1 "Inverclyde" 291 126 39 38 34.6 831 162 538 42 45 87 -13.9 1.66 138 6.2 14.6 61.7 18.6 105.8 27 21.4 13.6 95 NA 56.2 NA 11.7 14.5 11.5 8 45 80.2 39 26.5 NA 2.5 18.5 12.7 323.4 9483 78 67.2 "Midlothian" 362 61 32 30.8 25.2 858 356 225 39 41 80 -4.2 1.61 119 6.1 14.3 64.2 16.4 49 54 19.9 13.6 77 3.8 53 NA 11.2 10.7 10.8 6 35 84.8 39 NA NA 1.6 19.4 13.7 309 12656 79.9 67.7 "Moray" 327 0 37 34.9 28 652 2238 39 43 44 87 3.6 1.76 108 6.6 14.6 61.8 18 21.6 31 18.9 12.2 91 8 54.3 NA 12.4 11 9.8 7.4 26 86.4 43 14.3 NA 2.2 27.2 15.4 285 13566 67.2 52.7 "North_Ayrshire" 344 157 60 57.7 30.2 718 884 158 67 72 140 1.6 1.63 115 6.2 15 62.2 17.6 115.3 23 21.2 13.4 72 10.5 45.6 NA 11.3 11.8 11.6 6.9 42 73.5 58 27.4 9.1 5.1 23.7 19.2 317.8 9483 76.3 65.7 "North_Lanarkshire" 1557 175 130 128.5 31.3 787 474 688 158 168 326 -4.6 1.66 126 6.4 14.9 63.8 15.9 64.4 25 20.2 13.4 94 2.3 47.5 11.8 12.5 11.1 11.6 8.5 38 74.7 133 21.2 12.4 10.7 20.8 20.1 336.7 9483 82.6 72.2 "Orkney_Islands" 0 6 9 8.1 33.8 515 992 20 10 10 20 3.2 1.78 106 6 15.3 61.2 18.5 31.8 52 15.1 10.9 97 0 69.3 NA 10.9 11.6 7.5 1.4 30 87.8 10 NA NA 0.4 26.8 24.4 NA 8298 57.3 47.4 "Perth_and_Kinross" 448 147 59 55 28.2 732 5311 25 64 69 133 8.8 1.61 103 5.6 13.8 60.7 20.9 93.2 45 18.7 12.5 78 10.2 53.9 NA 10.5 12.6 9.8 5.9 29 86.6 66 11.3 NA 2.8 23 17.8 NA 9611 61.7 51.3 "Renfrewshire" 732 66 77 75.1 32.5 783 261 683 86 92 179 -3.5 1.59 125 6.3 14.1 63.7 17 119.6 31 22 13.7 103 NA 55.9 15.5 11.9 11.6 8 4.5 39 78.5 80 20.1 11.3 5.5 20.5 23.3 336.1 9483 79 63.6 "Scottish_Borders_The" 245 98 49 44.9 29.7 612 4734 22 51 55 106 4.8 1.67 100 5.8 13.3 60.2 21.8 56.9 22 18.5 12.1 92 1.3 61.7 NA 10.7 12.8 8 4.9 28 80.6 49 20.6 NA 2.1 23.7 12.3 303.5 9033 62.8 50.7 "Shetland_Islands" 131 21 10 8.9 36.1 486 1438 16 12 11 23 -12.6 1.77 117 7 15.9 62.9 14.9 14.8 42 12.7 8.1 79 NA 73.6 NA 11.7 10.9 9.9 6.5 28 84.8 11 NA NA 0.4 23.2 14.2 NA 8298 62.4 51.6 "South_Ayrshire" 182 80 49 47.6 30.7 765 1202 95 55 60 115 1.3 1.55 105 5.5 13.7 61.1 20.9 70.4 36 21 13.6 99 NA 61.9 NA 10.1 12.7 6.2 4.3 33 79.2 48 22.9 10.3 3.6 23.6 23.4 346.2 9483 66.9 56.2 "South_Lanarkshire" 488 98 124 122.3 35.3 793 1771 174 149 159 307 -0.8 1.55 125 6.3 14.5 63.8 16.5 103.9 15 20.7 13.7 92 3.6 51.5 13.7 11.5 11.3 9.2 5.1 33 78.4 146 22 8.3 8.2 21.7 21.8 319.1 9483 77.8 67.6 "Stirling" 341 66 34 33.1 33.6 776 2196 38 40 43 83 3.1 1.55 110 5.7 13.6 63.8 17.9 200.5 46 19.5 13.3 81 2.9 61.4 NA 11.1 11.8 7.7 4.9 33 77.2 37 NA NA 2.1 23 19.5 346.6 9265 68.5 58.9 "West_Dunbartonshire" 193 139 42 40.4 33.4 978 162 590 46 50 96 -9.5 1.7 130 6.4 15.3 61.4 17.8 81.9 47 20.3 14 108 NA 52.5 NA 12.5 12.7 11.7 8.7 42 71.5 36 NA 13.6 4.2 19.3 27.3 319 9483 84.7 74.7 "West_Lothian" 942 156 61 60.3 28.3 792 425 355 74 77 151 8.3 1.63 126 6.8 15.1 65.8 13.2 53.6 51 20.3 13.5 80 6.3 46.8 NA 13.1 9.5 8.7 4.6 33 82.2 78 32.6 NA 3.5 21.2 10.2 335.5 12656 79.6 67.3 statsmodels-0.12.2/statsmodels/datasets/spector/000077500000000000000000000000001400612667500217765ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/spector/__init__.py000066400000000000000000000003261400612667500241100ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/spector/data.py000066400000000000000000000037051400612667500232660ustar00rootroot00000000000000"""Spector and Mazzeo (1980) - Program Effectiveness Data""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """Used with express permission of the original author, who retains all rights. """ TITLE = __doc__ SOURCE = """ http://pages.stern.nyu.edu/~wgreene/Text/econometricanalysis.htm The raw data was downloaded from Bill Greene's Econometric Analysis web site, though permission was obtained from the original researcher, Dr. Lee Spector, Professor of Economics, Ball State University.""" DESCRSHORT = """Experimental data on the effectiveness of the personalized system of instruction (PSI) program""" DESCRLONG = DESCRSHORT NOTE = """:: Number of Observations - 32 Number of Variables - 4 Variable name definitions:: Grade - binary variable indicating whether or not a student's grade improved. 1 indicates an improvement. TUCE - Test score on economics test PSI - participation in program GPA - Student's grade point average """ def load(as_pandas=None): """ Load the Spector dataset and returns a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): """ Load the Spector dataset and returns a Dataset class instance. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ data = _get_data() return du.process_pandas(data, endog_idx=3) def _get_data(): data = du.load_csv(__file__, 'spector.csv', sep=r'\s') data = du.strip_column_names(data) data = data.iloc[:, [1, 2, 3, 4]] return data.astype(float) statsmodels-0.12.2/statsmodels/datasets/spector/spector.csv000066400000000000000000000007611400612667500241760ustar00rootroot00000000000000'OBS' 'GPA' 'TUCE' 'PSI' 'GRADE' 1 2.66 20 0 0 2 2.89 22 0 0 3 3.28 24 0 0 4 2.92 12 0 0 5 4 21 0 1 6 2.86 17 0 0 7 2.76 17 0 0 8 2.87 21 0 0 9 3.03 25 0 0 10 3.92 29 0 1 11 2.63 20 0 0 12 3.32 23 0 0 13 3.57 23 0 0 14 3.26 25 0 1 15 3.53 26 0 0 16 2.74 19 0 0 17 2.75 25 0 0 18 2.83 19 0 0 19 3.12 23 1 0 20 3.16 25 1 1 21 2.06 22 1 0 22 3.62 28 1 1 23 2.89 14 1 0 24 3.51 26 1 0 25 3.54 24 1 1 26 2.83 27 1 1 27 3.39 17 1 1 28 2.67 24 1 0 29 3.65 21 1 1 30 4 23 1 1 31 3.1 21 1 0 32 2.39 19 1 1 statsmodels-0.12.2/statsmodels/datasets/stackloss/000077500000000000000000000000001400612667500223255ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/stackloss/R_stackloss.s000066400000000000000000000014061400612667500250010ustar00rootroot00000000000000### SETUP ### d <- read.table("./stackloss.csv",sep=",", header=T) attach(d) library(MASS) m1 <- rlm(STACKLOSS ~ AIRFLOW + WATERTEMP + ACIDCONC) # psi.huber default m2 <- rlm(STACKLOSS ~ AIRFLOW + WATERTEMP + ACIDCONC, psi = psi.hampel, init = "lts") m3 <- rlm(STACKLOSS ~ AIRFLOW + WATERTEMP + ACIDCONC, psi = psi.bisquare) results1 <- summary(m1) results2 <- summary(m2) results3 <- summary(m3) m4 <- rlm(STACKLOSS ~ AIRFLOW + WATERTEMP + ACIDCONC, scale.est="Huber") # psi.huber default m5 <- rlm(STACKLOSS ~ AIRFLOW + WATERTEMP + ACIDCONC, scale.est="Huber", psi = psi.hampel, init = "lts") m6 <- rlm(STACKLOSS ~ AIRFLOW + WATERTEMP + ACIDCONC, scale.est="Huber", psi = psi.bisquare) results4 <- summary(m4) results5 <- summary(m5) results6 <- summary(m6) statsmodels-0.12.2/statsmodels/datasets/stackloss/__init__.py000066400000000000000000000003261400612667500244370ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/stackloss/data.py000066400000000000000000000034741400612667500236200ustar00rootroot00000000000000"""Stack loss data""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This is public domain. """ TITLE = __doc__ SOURCE = """ Brownlee, K. A. (1965), "Statistical Theory and Methodology in Science and Engineering", 2nd edition, New York:Wiley. """ DESCRSHORT = """Stack loss plant data of Brownlee (1965)""" DESCRLONG = """The stack loss plant data of Brownlee (1965) contains 21 days of measurements from a plant's oxidation of ammonia to nitric acid. The nitric oxide pollutants are captured in an absorption tower.""" NOTE = """:: Number of Observations - 21 Number of Variables - 4 Variable name definitions:: STACKLOSS - 10 times the percentage of ammonia going into the plant that escapes from the absoroption column AIRFLOW - Rate of operation of the plant WATERTEMP - Cooling water temperature in the absorption tower ACIDCONC - Acid concentration of circulating acid minus 50 times 10. """ def load(as_pandas=None): """ Load the stack loss data and returns a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): """ Load the stack loss data and returns a Dataset class instance. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ data = _get_data() return du.process_pandas(data, endog_idx=0) def _get_data(): return du.load_csv(__file__, 'stackloss.csv').astype(float) statsmodels-0.12.2/statsmodels/datasets/stackloss/stackloss.csv000066400000000000000000000004441400612667500250520ustar00rootroot00000000000000"STACKLOSS","AIRFLOW","WATERTEMP","ACIDCONC" 42,80,27,89 37,80,27,88 37,75,25,90 28,62,24,87 18,62,22,87 18,62,23,87 19,62,24,93 20,62,24,93 15,58,23,87 14,58,18,80 14,58,18,89 13,58,17,88 11,58,18,82 12,58,19,93 8,50,18,89 7,50,18,86 8,50,19,72 8,50,19,79 9,50,20,80 15,56,20,82 15,70,20,91 statsmodels-0.12.2/statsmodels/datasets/star98/000077500000000000000000000000001400612667500214515ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/star98/__init__.py000066400000000000000000000003261400612667500235630ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/star98/data.py000066400000000000000000000072351400612667500227430ustar00rootroot00000000000000"""Star98 Educational Testing dataset.""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """Used with express permission from the original author, who retains all rights.""" TITLE = "Star98 Educational Dataset" SOURCE = """ Jeff Gill's `Generalized Linear Models: A Unified Approach` http://jgill.wustl.edu/research/books.html """ DESCRSHORT = """Math scores for 303 student with 10 explanatory factors""" DESCRLONG = """ This data is on the California education policy and outcomes (STAR program results for 1998. The data measured standardized testing by the California Department of Education that required evaluation of 2nd - 11th grade students by the the Stanford 9 test on a variety of subjects. This dataset is at the level of the unified school district and consists of 303 cases. The binary response variable represents the number of 9th graders scoring over the national median value on the mathematics exam. The data used in this example is only a subset of the original source. """ NOTE = """:: Number of Observations - 303 (counties in California). Number of Variables - 13 and 8 interaction terms. Definition of variables names:: NABOVE - Total number of students above the national median for the math section. NBELOW - Total number of students below the national median for the math section. LOWINC - Percentage of low income students PERASIAN - Percentage of Asian student PERBLACK - Percentage of black students PERHISP - Percentage of Hispanic students PERMINTE - Percentage of minority teachers AVYRSEXP - Sum of teachers' years in educational service divided by the number of teachers. AVSALK - Total salary budget including benefits divided by the number of full-time teachers (in thousands) PERSPENK - Per-pupil spending (in thousands) PTRATIO - Pupil-teacher ratio. PCTAF - Percentage of students taking UC/CSU prep courses PCTCHRT - Percentage of charter schools PCTYRRND - Percentage of year-round schools The below variables are interaction terms of the variables defined above. PERMINTE_AVYRSEXP PEMINTE_AVSAL AVYRSEXP_AVSAL PERSPEN_PTRATIO PERSPEN_PCTAF PTRATIO_PCTAF PERMINTE_AVTRSEXP_AVSAL PERSPEN_PTRATIO_PCTAF """ def load(as_pandas=None): """ Load the star98 data and returns a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Load instance: a class of the data with array attrbutes 'endog' and 'exog' """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): data = _get_data() return du.process_pandas(data, endog_idx=['NABOVE', 'NBELOW']) def _get_data(): data = du.load_csv(__file__, 'star98.csv') names = ["NABOVE","NBELOW","LOWINC","PERASIAN","PERBLACK","PERHISP", "PERMINTE","AVYRSEXP","AVSALK","PERSPENK","PTRATIO","PCTAF", "PCTCHRT","PCTYRRND","PERMINTE_AVYRSEXP","PERMINTE_AVSAL", "AVYRSEXP_AVSAL","PERSPEN_PTRATIO","PERSPEN_PCTAF","PTRATIO_PCTAF", "PERMINTE_AVYRSEXP_AVSAL","PERSPEN_PTRATIO_PCTAF"] data.columns = names nabove = data['NABOVE'].copy() nbelow = data['NBELOW'].copy() data['NABOVE'] = nbelow # successes data['NBELOW'] = nabove - nbelow # now failures return data statsmodels-0.12.2/statsmodels/datasets/star98/r_glm.s000066400000000000000000000037041400612667500227410ustar00rootroot00000000000000### SETUP #star.data <- as.matrix(read.csv("./star98.csv",header=T)) #star.factors3 <- data.frame( LOWINC=star.data[,3], PERASIAN=star.data[,4], PERBLACK=star.data[,5], # PERHISP=star.data[,6], PERMINTE=star.data[,7], AVYRSEXP=star.data[,8], AVSAL=star.data[,9], # PERSPEN=star.data[,10], PTRATIO=star.data[,11], PCTAF=star.data[,12], PCTCHRT=star.data[,13], # PCTYRRND=star.data[,14], PERMINTE.AVYRSEXP=star.data[,15], PERMINTE.AVSAL=star.data[,16], # AVYRSEXP.AVSAL=star.data[,17], PERSPEN.PTRATIO=star.data[,18], PERSPEN.PCTAF=star.data[,19], # PTRATIO.PCTAF=star.data[,20], PERMINTE.AVYRSEXP.AVSAL=star.data[,21], # PERSPEN.PTRATIO.PCTAF=star.data[,22], MATHTOT=star.data[,1], PR50M=star.data[,2] ) d <- read.table("./star98.csv", sep=",", header=T) attach(d) #attach(star.factors3) ### MATH MODEL m1 <- glm(cbind(PR50M,MATHTOT-PR50M) ~ LOWINC + PERASIAN + PERBLACK + PERHISP + PERMINTE + AVYRSEXP + AVSALK + PERSPENK + PTRATIO + PCTAF + PCTCHRT + PCTYRRND + PERMINTE_AVYRSEXP + PERMINTE_AVSAL + AVYRSEXP_AVSAL + PERSPEN_PTRATIO + PERSPEN_PCTAF + PTRATIO_PCTAF + PERMINTE_AVYRSEXP_AVSAL + PERSPEN_PTRATIO_PCTAF, family=binomial) #as.numeric(m1$coef) #as.numeric(sqrt(diag(vcov(m1)))) results <- summary.glm(m1) #star.logit.fit3 <- glm(cbind(PR50M,MATHTOT-PR50M) ~ LOWINC + PERASIAN + PERBLACK + PERHISP + # PERMINTE + AVYRSEXP + AVSAL + PERSPEN + PTRATIO + PCTAF + PCTCHRT + PCTYRRND + # PERMINTE.AVYRSEXP + PERMINTE.AVSAL + AVYRSEXP.AVSAL + PERSPEN.PTRATIO + PERSPEN.PCTAF + # PTRATIO.PCTAF + PERMINTE.AVYRSEXP.AVSAL + PERSPEN.PTRATIO.PCTAF, # family = binomial(), data=star.factors3) #results <- summary.glm(star.logit.fit3) # WITH R STYLE INTERACTIONS #star.logit.fit4 <- glm(cbind(PR50M,MATHTOT-PR50M) ~ LOWINC + PERASIAN + PERBLACK + PERHISP + # PERMINTE + AVYRSEXP + AVSAL + PERSPEN + PTRATIO + PCTAF + PCTCHRT + PCTYRRND + # PERMINTE*AVYRSEXP*AVSAL + PERSPEN*PTRATIO*PCTAF, # family = binomial(), data=star.factors3) statsmodels-0.12.2/statsmodels/datasets/star98/src/000077500000000000000000000000001400612667500222405ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/star98/src/star.bi.dat000066400000000000000000001063551400612667500243060ustar00rootroot00000000000000161119 34.3973 23.29930 14.23528 11.41112 15.91837 14.70646 59157.32 4445.207 21.71025 57.03276 0 22.22222 805 467 807 452 161127 17.36507 29.32838 8.234897 9.314884 13.63636 16.08324 59503.97 5267.598 20.44278 64.62264 0 0 182 140 184 144 161143 32.64324 9.226386 42.40631 13.54372 28.83436 14.59559 60569.92 5482.922 18.95419 53.94191 0 0 566 357 571 337 161150 11.90953 13.88309 3.796973 11.44311 11.11111 14.38939 58334.11 4165.093 21.63539 49.06103 0 7.142857 573 424 573 395 161168 36.88889 12.1875 76.875 7.604167 43.58974 13.90568 63153.64 4324.902 18.77984 52.38095 0 0 62 15 65 8 161176 20.93149 28.02351 4.643221 13.80816 15.37849 14.97755 66970.55 3916.104 24.51914 44.91578 0 2.380952 2234 1452 2247 1348 161192 53.26898 8.447858 19.37483 37.90533 25.52553 14.67829 57621.95 4270.903 22.21278 32.28916 0 12.12121 1363 491 1364 477 161200 15.19009 3.665781 2.649680 13.09207 6.203008 13.66197 63447.4 4309.734 24.59026 30.45267 0 0 904 579 912 565 161234 28.21582 10.43042 6.786374 32.3343 13.46154 16.41760 57845.64 4527.603 21.74138 22.64574 0 0 519 218 525 205 161242 32.77897 17.17831 12.48493 28.32329 27.25989 12.51864 57801.41 4648.917 20.26010 26.07099 0 0 1071 514 1067 469 161259 59.97293 17.51736 50.94093 23.10134 52.34344 16.93283 57434.44 4693.069 21.31489 19.53216 3.296703 13.18681 2964 830 3016 784 161275 0 19.74886 1.864536 2.587519 7.407407 15.86979 52193.46 5248.693 18.51182 80.37975 0 0 235 204 235 209 161291 28.12111 12.69201 19.26582 26.84197 13.37209 14.42864 57240.45 3980.589 21.89844 31.65829 0 9.090909 547 241 556 195 161309 36.99047 10.03236 15.42302 30.74434 13.50763 13.29753 58413.74 4197.615 23.12943 31.15079 0 0 685 315 688 206 175093 12.92796 7.172996 4.825949 13.23840 6.185567 17.47108 65570.86 5382.009 20.68333 34.83146 0 0 259 179 252 136 175101 4.700895 8.736718 1.745657 6.932029 7.127883 16.18176 67367.55 4607.673 24.65106 39.63415 0 0 922 765 925 694 373981 20.25979 0.4857445 0.8025343 5.976769 2.439024 15.30949 51311.63 4025.593 24.82292 36.19403 0 91.66667 377 249 377 204 461408 42.66827 2.836879 0.9456265 23.87707 10.63830 11.83962 55990.32 5151.626 17.91209 24.44444 0 0 66 40 69 31 461424 33.12923 6.305412 2.766154 12.86616 6.17284 14.60144 58558.6 4004.401 22.73008 49.65517 4.347826 26.08696 1089 632 1092 601 461432 29.39297 1.071155 0.765111 9.716909 4.477612 14.04527 53772.3 4518.034 21.18506 51.02041 0 0 116 82 115 64 461473 52.99313 6.217371 0.3322259 38.72805 7.619048 14.17395 50695.12 4114.065 20.41136 23.27586 0 0 137 58 139 51 461531 35.08836 0.8292167 0.388144 4.622442 4.135338 14.30221 55278.74 4148.228 21.91947 25 23.07692 15.38462 439 241 449 220 561564 37.20441 0.5699482 1.113990 6.321244 5.357143 13.60247 50668.49 3975.448 24.86918 22.97872 0 8.333333 312 175 309 151 661598 54.26829 0.5497862 0.5497862 40.74527 7.407407 14.87105 52537 4205.362 19.44511 36.28319 0 0 115 46 116 36 661614 65.82397 0.2640845 3.873239 58.89085 6.557377 10.92652 46291.79 4469.798 19.52548 37.93103 0 0 80 29 81 15 661622 78.54077 1.282051 0 78.4188 20.83333 11.47788 49267.19 3893.337 21.12311 19.23077 0 0 66 7 66 5 761648 30.07553 3.626196 10.50386 20.94431 8.66575 13.69108 62341.2 4011.390 23.88905 23.85445 0 72.22222 1252 676 1259 541 761697 28.24601 6.893424 19.81859 16.78005 12.74510 15.91555 59176.53 4225.738 22.18379 18 0 0 188 94 190 86 761739 22.33375 2.523732 3.310952 14.03103 10.30928 16.15686 59230.72 4114.418 21.74332 34.42623 0 0 323 210 322 142 761754 22.62465 7.697888 4.902207 16.77688 9.421586 15.32368 57128.58 3928.696 22.14162 37.63838 0 0 2390 1482 2394 1365 761788 51.78493 4.598930 27.79679 35.10160 30.02481 15.97489 58788.93 4049.181 22.87300 85.11166 0 8.333333 646 239 648 201 761796 51.23848 13.02024 35.10118 25.52703 25.82688 17.18977 62664.1 4347.936 22.8705 36.5 0 8.474576 1909 668 1949 585 761804 1.895322 9.925228 1.633719 4.276349 4.503464 15.92369 59976.94 4035.189 23.34687 50.74503 0 0 1420 1235 1417 1247 861820 42.51143 6.252442 0.4103165 10.17976 8.076923 14.70948 58233.81 4733.28 20.67364 15.50388 0 0 396 210 403 165 961903 45.42344 1.501194 0.9041283 26.27090 5.338078 14.35703 55740.14 4323.754 21.53458 86.722 0 0 337 172 329 135 973783 30.16965 0.7973734 0.5159475 2.251407 1.904762 14.23233 51822.37 4030.978 21.47295 32.45614 0 0 188 132 193 106 1062117 23.43337 11.75065 2.871447 19.03101 15.94416 11.87890 53158.07 4242.702 22.70517 40.50633 0 0 2295 1584 2267 1496 1062125 57.9224 0.871731 0.6475716 68.74222 18.93491 11.19787 61085.44 4258.425 24.4786 14.83516 0 0 277 89 272 68 1062158 60.59908 7.196613 0.8466604 72.34243 24.76190 11.83632 51537.34 3807.79 21.07004 38.7931 0 0 146 50 144 55 1062166 62.01977 19.65177 11.31566 45.23962 23.40485 14.67996 61095.3 4685.643 22.25973 27.47559 0 31.11111 4973 1641 5018 1455 1062240 35.60339 2.518757 0.375134 67.73848 7.913669 15.34516 54702.22 6836.694 21.14435 41.57895 71.42857 0 195 109 196 84 1062265 63.17132 1.40625 0.6009615 71.35817 16.79198 14.46149 55184.78 4478.657 22.25652 16.78657 0 6.25 614 178 617 136 1062281 72.91667 1.238739 0.5630631 70.04505 3.921569 11.55763 39728.35 3899.132 18.23651 13.04348 0 0 62 12 64 6 1062364 91.60484 0.2143623 0.1071811 98.821 62.18487 11.92754 55527.29 4223.126 21.68654 13.38583 0 40 190 27 189 21 1062414 57.00249 4.322917 0.5859375 70.66406 23.48066 14.00443 52155.26 4382.061 21.71153 23.02326 0 0 550 198 552 132 1062430 69.6452 3.972303 1.020408 76.71283 27.6 13.01188 53531.64 4180.037 22.50103 14.69194 0 0 284 114 290 78 1073809 87.83718 0.4054054 1.216216 90.45045 32.40741 10.37561 51400.56 4317.728 20.49057 30.85106 0 0 143 26 146 16 1073965 49.25084 10.15299 7.874184 42.32374 16.53944 10.08090 54568.74 4006.118 22.59174 37.66667 0 76.92308 581 221 585 211 1073999 69.49807 5.350028 0.3130336 70.43256 22.64151 12.32314 54546.01 4283.101 22.15424 40 0 60 265 85 274 82 1075127 87.77725 0.5334627 0.5819593 97.76916 40 12.20753 60303.18 3933.777 25.6375 47.16981 0 0 151 14 155 16 1075234 86.54599 1.713710 0.2016129 92.2379 26.08696 14.58066 62758.26 5242.8 21.72113 19.17808 0 0 143 24 144 35 1075275 21.60468 0.5405405 0.2910603 7.484407 1.526718 17.11242 62522.82 5879.966 19.48512 26.37363 0 0 143 102 143 90 1075408 64.85075 0.6671114 3.068712 64.50967 14.92537 11.36918 47732.57 3511.9 21.48872 10.66667 0 0 67 24 67 23 1162661 53.125 21.75227 0.9063444 20.74522 4.651163 15.73608 60020.66 4325.154 24.48113 47.11538 0 0 138 68 138 76 1175481 44.97466 1.348412 0.8264463 33.18834 5.932203 16.25328 55653.8 4602.903 20.85538 49.19355 0 0 186 78 183 73 1262901 76.32121 0 0.6559767 2.842566 30 14.78554 65665.47 5770.566 19.64964 25.92593 0 0 90 37 88 38 1263040 33.91672 0.7147498 1.169591 2.988954 0 15.79261 56055.94 4427.872 21.31544 44.70588 0 0 114 67 109 23 1275374 11.71617 0.5 0 4.666667 0 15.51220 54645.67 4893.857 20.32154 34.14634 0 0 59 40 59 40 1363073 54.25667 0.5188067 0.2779322 80.21123 35.04274 14.95651 66530.25 4304.715 23.78075 33.89831 0 0 372 104 373 67 1363099 43.95482 1.432902 0.0551116 97.51998 70.09967 14.58775 67370.06 4266.618 23.57191 15.82569 0 0 495 89 506 91 1363107 74.30168 0.4219409 5.555556 71.58931 40.57971 12.21709 53519.74 4518.243 20.625 29.41176 0 0 99 32 98 36 1363123 62.10008 1.554243 2.9427 82.64429 33.41289 15.20630 66125.09 4453.164 23.32139 31.30288 0 0 560 162 578 133 1363149 63.91804 0.3990025 0.1496259 70.47382 26.88172 11.60701 56622.57 4245.811 21.68514 32.14286 0 0 158 41 162 19 1363164 39.94452 0.7492287 2.688409 60.77567 24.5283 9.224783 51167.03 3708.859 20.85687 34.92063 0 0 179 66 179 75 1363214 76.8279 0 3.005780 31.09827 20.40816 15.31852 60141.08 5355.161 18.99177 19.35484 0 0 49 14 50 4 1463255 25.58849 0.7623888 0.5082592 11.01228 5.454545 16.50992 59805.55 4349.222 23.45035 40.71856 0 0 171 106 170 126 1563404 68.64343 0.7808143 1.728946 76.8879 31.81818 12.21163 58861.69 3714.92 25.99096 14.03509 0 0 520 78 550 104 1563677 40.599 1.107011 14.87085 24.53875 7.627119 15.24427 63042.2 4572.615 24.41998 32.48408 0 37.5 190 63 187 45 1563685 31.86047 2.014723 12.43704 7.477722 9.848485 15.32667 63498 5767.594 20.30722 32.8 0 0 170 87 167 75 1563776 49.35103 1.697439 8.219178 31.98332 9.45946 13.08426 58159.2 4284.445 23.42700 15.49296 0 33.33333 216 97 219 68 1563800 51.46237 0.3612479 0.7553366 17.76683 2.739726 14.43697 62633.1 5763.701 21.05658 17.79141 0 0 195 80 193 58 1563826 24.99504 0.4204204 2.722723 17.39740 4.524887 14.79 60455.09 4308.128 22.87165 29.72973 0 0 322 213 324 156 1563842 65.89027 0.4718152 4.395332 78.91731 21.10092 14.93269 61803.9 4139.937 24.51174 14.01515 0 0 250 55 255 43 1573742 32.59873 2.233486 4.79962 10.89815 5.629139 14.35102 62453.15 4537.569 22.04157 38.66279 0 0 458 256 463 208 1573908 81.96457 0.3115265 0.2336449 92.01713 31.89655 13.13246 55369.86 4428.046 22.50856 23.68421 0 0 199 28 200 18 1575168 37.83202 0.3584229 0.860215 13.69176 8.333333 10.38143 55942.07 4098.994 24.92174 0 0 0 91 49 91 47 1663891 64.27918 0.4638219 4.050711 79.37539 17.36111 15.31545 66404.2 4605.861 22.67635 15.58442 0 0 191 61 197 45 1673932 86.49362 0 0.7340946 89.96737 15.59633 11.06066 57641.57 4543.492 21.75277 26.19048 0 0 153 28 161 14 1764014 45.57020 0.9541985 1.335878 22.08969 7.207207 14.75781 54040.6 4832.32 20.08333 50.9434 0 0 162 91 165 91 1764022 73.609 0.8296107 5.966816 9.60434 6.329114 13.7825 54439.95 4354.388 20.61290 10.60606 0 100 201 66 206 52 1764030 46.29523 0.6597031 1.869159 15.66795 3.448276 15.13131 58962.14 4361.361 21.41705 28.42105 0 0 146 88 147 85 1764055 26.79575 0.7237636 0.3618818 8.685163 1.204819 11.29516 50096.41 3932.39 19.15049 40.69767 0 0 120 76 116 77 1764063 52.91709 1.732926 2.854230 8.25688 6.25 14.98707 59995.4 5022.533 21.89956 37.70492 0 0 60 30 61 23 1864204 41.9708 0 0.5714286 9.142857 3.030303 17.90429 55176.85 5259.958 18.96552 18.18182 0 0 42 15 43 8 1964212 30.50552 32.46542 10.40141 32.65980 36.00406 15.25756 59289.09 4219.665 22.57679 49.73262 0 3.333333 1579 837 1599 879 1964261 8.362214 52.59396 1.213040 9.888444 8.900524 15.98201 64415.47 4166.218 24.27460 60.84011 0 27.27273 771 540 771 640 1964279 70.73827 0.9595613 3.152844 78.94106 25.95573 14.49885 64611.03 4379.243 23.98186 19.42446 0 11.11111 794 191 800 200 1964287 62.87168 4.72375 1.793829 85.46998 27.21202 15.06211 67839.96 3819.118 27.50542 26.77165 0 0 972 272 1029 268 1964295 79.6766 2.102924 2.102924 89.14344 45.6 14.39982 62084.61 4432.065 23.55966 20.98765 0 0 395 71 399 108 1964303 49.17215 5.575448 18.15857 38.48009 12.27437 13.04228 58550.52 3988.183 23.88522 17.99729 0 7.142857 927 287 927 260 1964311 9.733488 10.93985 3.571429 4.097744 10.81967 18.2 62455.76 6015.758 17.72469 61.88437 0 0 417 329 417 346 1964329 25.84395 5.866005 4.823821 27.58313 9.501188 16.89201 62021.76 4054.136 24.11424 51.76471 0 0 803 450 804 426 1964337 37.6798 5.688124 2.774695 36.95893 13.16667 14.46938 62400.43 4138.196 23.95766 32.4291 0 5.263158 995 517 992 436 1964378 23.94770 5.265554 4.871017 36.61608 11.76471 15.32254 61534.67 4024.875 24.12297 38.72549 0 0 459 271 464 209 1964394 20.80702 10.11185 12.00121 20.87364 11.70886 13.90775 61447.66 4401.148 21.54203 53.16973 0 0 482 323 483 338 1964436 37.64495 8.548446 5.798903 50.82998 14.25993 13.90046 62290.03 4265.807 24.2564 42.08443 0 0 955 458 958 450 1964444 33.51168 10.20237 17.91269 36.81218 18.65079 15.38502 62132.02 4282.612 22.95729 41.17647 0 0 386 174 388 144 1964451 42.84095 5.595576 4.80418 63.33705 14.59948 12.29348 64631.93 3979.219 25.14150 23.26733 0 0 1300 637 1312 538 1964469 61.40009 2.775971 13.20755 61.96053 30 16.06842 59303.74 4179.698 25.22527 15.01597 0 0 267 85 273 71 1964527 68.0851 0.683527 0.580998 94.48052 51.81452 16.27428 65653 4338.243 22.49503 33.67003 0 0 662 152 682 130 1964535 13.80008 6.320789 3.397881 14.87030 4.761905 11.92766 57362.05 4718.115 21.28874 38.99371 0 0 209 146 212 125 1964568 50.67402 12.12724 1.119947 23.8668 12.23958 13.22109 73039 4224.937 26.67020 26.38655 0 34.48276 2339 1123 2327 1326 1964576 14.82624 4.119138 1.292776 16.56527 6.329114 14.99266 63784.61 4130.35 24.90064 33.6 0 0 556 350 584 339 1964634 69.00829 0.1925546 43.09138 55.36819 63.43907 15.01983 63040.99 3748.33 27.40275 38.88889 0 57.89474 1095 296 1111 222 1964659 1.421801 26.20056 0.5414313 3.060264 8.205128 15.02579 63791.63 4705.506 21.59624 66.18182 0 0 326 293 326 287 1964683 2.971741 7.57133 1.366449 4.975937 7.024793 17.00701 64749.85 4414.05 24.23913 60.62323 0 0 825 693 828 671 1964725 64.2387 14.16632 20.33687 40.48983 29.10875 13.30980 59298.18 4210.309 22.98312 41.37823 2.325581 19.76744 5645 2145 5677 1930 1964733 73.18394 4.308746 13.79525 68.52417 45.46139 20.54574 73073.07 4365.276 23.42095 49.30618 2.321981 32.19814 38418 10373 38852 9324 1964774 59.29694 0.224649 12.05616 86.5273 52.48714 15.79301 67063.02 4064.954 27.05961 15.08475 0 50 951 171 939 113 1964790 56.89858 1.915122 14.06465 48.07722 17.54386 14.42588 57193.3 4017.302 22.55472 25.94752 0 11.11111 398 183 401 144 1964808 75.0343 4.879927 0.4471292 90.5185 59.52981 16.92341 67605.91 3810.285 27.99578 28.54167 0 25 2025 466 2093 377 1964840 44.02203 4.939493 5.01597 62.97629 29.22002 15.62108 60665.56 3616.505 25.62582 21.50866 0 7.142857 1425 513 1436 388 1964865 1.943602 30.02693 1.723209 3.941842 7.474227 18.94287 59821.21 3946.788 24.11441 89.13043 0 0 680 551 678 597 1964873 58.22835 1.783620 14.61458 75.7082 35.24845 11.80146 63190.71 4370.215 24.5058 5.430712 0 73.33333 1080 248 1088 185 1964881 61.8811 2.22193 32.00543 47.11193 42.18415 14.27299 64584.04 4443.599 23.86713 39.65517 0 0 1348 404 1352 365 1964907 73.5053 6.393463 11.23378 71.20447 48.69857 16.68337 65628.77 4007.186 26.04422 8.27719 0 23.68421 1986 616 1983 575 1964964 0.2653400 63.20234 0.4871712 3.345242 6.944444 15.90786 57543.38 4619.277 22.17736 78.1893 0 0 265 215 265 246 1964980 26.09065 5.531472 8.617999 27.07647 22.2664 15.87400 65963.43 5063.35 22.31528 65.10638 0 0 735 500 753 429 1965029 11.67883 32.08936 4.467806 18.21288 13.01775 16.19645 61169.62 4043.499 22.99094 64.07407 0 0 300 228 300 234 1965052 27.32198 38.10775 1.445466 20.36794 7.359307 13.7875 59417.3 4035.891 23.64895 31.56499 0 0 384 246 376 237 1965060 17.70193 28.47688 3.996755 15.83330 19.65726 13.31861 59555.29 3822.103 23.78323 45.95661 0 0 1726 1105 1732 1108 1965094 47.30717 9.43911 9.122654 58.16237 17.52022 13.90339 56841.37 3907.338 24.42266 29.06178 0 0 629 233 627 194 1973437 78.42391 0.05453864 35.72962 62.92736 80.17493 14.79315 58991.42 3743.125 28.09997 41.78905 0 2.564103 1810 308 1843 258 1973445 40.23607 16.39995 2.539347 67.97602 28.90365 17.39357 62325.3 4103.139 25.05607 38.67849 0 0 1636 622 1647 609 1973452 33.85063 18.78119 6.688608 55.35089 29.18239 16.1731 62277.31 4369.675 24.44574 30.26188 0 0 1204 554 1213 606 1973460 6.196674 42.31389 5.721689 18.18054 17.73649 14.82445 60555.24 3982.78 24.25086 57.78547 0 0 1162 802 1171 831 1975291 53.4557 36.40237 1.889589 43.47907 22.06573 14.12308 57663.26 3814.974 23.16667 0 11.11111 0 320 173 319 185 1975309 28.17235 1.443203 1.722533 11.91806 7.446809 11.72804 58880.17 3806.893 24.82222 0 0 0 191 124 192 109 1975333 7.197273 7.00382 1.819174 8.659269 7.936508 15.21719 64224.89 5093.928 21.58711 43.08943 0 0 296 263 299 242 1975341 25.63993 7.277444 5.188422 23.18405 10.24845 16.50521 68096.37 5006.776 22.47522 51.54062 0 0 488 303 489 298 2065193 59.28721 0.9413778 2.524604 41.63457 6.666667 12.20542 53265.82 3873.24 23.55149 25.40984 0 0 147 71 159 48 2065243 60.0239 1.152145 3.543626 67.3538 26.82927 14.05485 56274.59 4064.557 23.45833 31.99405 0 45 1101 374 1130 362 2165417 14.79229 4.893837 2.770585 11.10823 3.562341 16.62018 53794.99 4365.513 20.39636 48.08511 6.25 12.5 558 407 564 412 2165458 34.76768 7.884136 5.198542 36.17878 8.536585 15.19114 53336.38 4458.969 20.96682 53.59281 0 0 278 161 277 144 2173361 0 0.4801921 0.4801921 28.69148 7.407407 13.72615 60992.5 6459.384 16.40535 26 0 0 52 36 52 28 2265532 27.00072 0.5113221 0.2921841 6.208912 1.459854 15.59845 51692.82 4183.603 21.53846 29.80132 0 0 223 140 225 112 2365540 55.9322 0.8403361 1.344538 45.37815 0 12.756 48855.96 6406.862 14.31604 44.73684 0 0 38 23 38 21 2365565 37.29968 1.162791 0.4152824 19.68439 2.272727 17.13074 56336.78 4990.487 19.47287 25.89928 0 0 188 103 188 98 2365615 46.92754 0.969469 1.114166 22.81869 4.848485 17.4015 64535.71 4838.431 21.34488 33.33333 0 36.36364 492 241 489 240 2365623 46.53846 0.8461538 0.6923077 11.57692 2.985075 17.472 56568.13 4611.976 20.82808 26.38037 0 0 170 90 171 67 2373916 56.33117 0.5172414 0.6896552 3.965517 4.651163 12.49787 48867.6 6578.053 15.73298 34.21053 0 0 34 24 33 13 2465698 37.78899 1.586639 0.2922756 17.32777 11.71171 13.41706 58102.55 4361.619 22.78612 20.8 0 16.66667 181 63 183 60 2465722 41.43167 0.9155646 0 84.13021 25.58140 12.77143 55709.23 4140.527 22.18527 24.74227 0 0 46 4 48 14 2465755 50.92824 1.244953 4.862046 53.17968 12.1673 12.07816 55074.62 4075.188 21.77028 33.93502 0 50 454 141 455 123 2473619 52.40793 0.6143345 0.9556314 50.44369 8.333333 11.98961 53609.9 4080.966 21.15774 49.27536 0 0 106 29 108 23 2475317 60.91821 0.1568013 6.31125 61.70129 15.44118 11.49135 54802.7 4750.999 18.81218 19.59459 0 0 179 48 181 33 2573585 33.27773 0.75 0.75 10.41667 1.612903 11.68088 55854.74 4786.679 19.22953 32.78689 0 0 94 47 94 37 2573593 64.85084 0 0 52.38095 4.761905 12.95532 50840.07 4851.063 18.40095 45.71429 0 0 47 15 47 19 2673668 45.93373 0.3100775 0.7751938 14.10853 2.222222 14.03431 52320.31 6283.433 14.66970 76.92308 0 0 39 24 40 24 2673692 21.84007 0.5828476 0.08326395 21.81515 4.83871 14.98485 60159.44 4806.483 20.59423 42.85714 0 0 92 58 93 45 2765987 10.70682 2.977162 1.305057 7.544861 4.8 17.29423 69887.39 5676.651 20.67854 55.92105 0 0 202 156 201 149 2766092 40.13453 8.813424 15.63724 25.22573 17.65705 19.47192 61011.63 4496.243 20.60704 28.90792 0 95.2381 761 365 773 255 2766134 14.27955 4.711581 1.893439 7.089388 2.941176 17.54195 63909.55 4756.384 22.63210 48.17518 0 0 157 116 154 105 2773825 40.66667 1.844262 1.285395 49.23621 20.15810 14.68534 56619.21 4356.072 21.57957 60.59783 0 0 353 124 357 107 2775473 67.26937 0.2738788 0.4108182 86.51147 24.19355 11.88684 58893.12 4200.852 24.90864 11.30435 0 0 161 43 163 60 2866241 45.67023 0.6825939 0.3412969 47.09898 4.545455 13.51122 54344.89 4650.725 20.97387 50 0 0 62 31 61 21 2866266 32.70906 1.396074 1.776254 26.488 6.388527 15.47587 54785.13 3912.949 21.83841 29.25258 3.333333 0 1171 656 1198 587 2866290 34.43425 0.7380074 0.4305043 37.45387 14.63415 15.64778 51434.44 4386.959 21.20205 44.14414 0 0 113 62 112 58 3066449 16.15780 8.398994 2.179380 21.62615 4.897959 15.22727 57193.42 3825.952 25.22776 40.72022 0 0 449 323 455 300 3066464 17.33803 4.709514 1.580624 16.95375 9.391933 12.69992 60779.38 3802.974 23.00043 44.82558 0 10.52632 2686 1934 2692 1804 3066522 48.15608 28.71155 1.291070 44.05147 11.48612 15.67656 65184.42 3835.549 24.67322 20.3813 0 0 2986 1224 3007 1473 3066555 9.316273 1.883830 1.216641 9.22292 7.619048 16.90641 70274.37 4481.474 24.26357 74.28571 0 0 188 154 188 145 3066597 39.02544 4.683563 1.235117 34.12381 4.426788 16.00117 60202.04 4349.231 22.48276 42.87149 0 0 1186 759 1186 688 3066621 36.01998 10.88242 2.085541 36.82177 9.424084 16.81767 56415.11 3586.935 25.44882 47.33026 2.564103 12.82051 1989 1054 1991 1035 3066647 21.01388 8.124397 1.888460 25.92012 11.39742 15.15302 63101.53 4172.242 24.71715 36.56174 0 0 1873 1180 1875 1238 3066670 73.27723 4.408512 1.079825 90.79082 26.48752 14.97092 69824.54 4102.145 25.03219 21.72937 0 56.25 3331 666 3391 610 3073635 10.53450 8.401664 2.167491 14.81068 6.056435 14.97990 60372.2 3840.866 22.19101 53.79189 0 0 2363 1654 2363 1607 3073643 29.86897 8.276043 4.655274 41.6814 5.263158 13.01412 57831.15 3629.530 24.16947 39.59538 0 0 1053 569 1074 526 3073650 10.51650 25.16370 3.039764 7.41078 9.255725 16.09776 62550.98 4352.488 22.65816 0 0 9.67742 1795 1400 1799 1421 3073924 11.60025 8.99128 3.111006 11.53665 10.13333 15.09307 67284.94 4726.529 23.19879 49.59217 0 10 622 491 621 416 3166944 23.35644 0.627574 0.4314571 17.70935 6.617647 13.59359 49513.03 4638.098 19.67842 44.13146 0 0 357 243 358 204 3166951 28.66097 0.5628095 1.440792 17.42458 4.878049 13.33273 42658.39 3503.698 24.26859 27.46114 62.5 0 194 95 182 49 3175085 17.13624 3.538945 1.372581 6.664462 4.651163 11.19239 52654.82 3596.095 23.04330 0 0 0 438 346 445 276 3266969 36.66211 0.6635333 1.216478 6.856511 2.717391 16.15405 56500.12 4912.702 21.23209 33.19328 0 0 289 182 288 132 3366977 42.29029 4.021226 7.222877 47.15802 17.24138 13.00708 62390.7 3758.198 25.18195 41.66667 0 70.58824 1079 356 1078 280 3366985 75.52987 13.36851 13.85224 36.69745 20.29703 13.81733 60074.78 4456.322 21.89966 41.81818 0 12.5 316 95 335 54 3366993 58.74644 1.151316 3.426535 34.64912 9.027778 15.96616 59270.44 4070.74 24.75627 26.25 0 12.5 219 103 219 53 3367033 41.51139 3.604238 4.644538 41.77843 11.37321 13.54297 64063.46 4083.554 25.23114 34.63727 0 34.28571 2104 989 2122 849 3367058 55.99125 1.264684 2.467791 60.04168 15.80882 12.68737 64123.52 3937.206 25.2138 43.17181 4.347826 0 1428 486 1434 387 3367082 62.40778 1.435897 2.666667 29.23077 9.03328 15.50251 59735.05 3916.537 24.51756 21.42857 0 5.263158 1090 534 1085 456 3367090 50.21092 1.388811 5.304256 53.2545 23.78976 13.27531 62068.72 3826.458 24.66667 26.38353 0 4.166667 1177 424 1199 300 3367124 43.06891 3.265436 23.67600 35.35328 23.12358 14.01194 58401.16 4173.917 24.09220 25.59242 2.857143 22.85714 2269 885 2300 644 3367173 62.50497 1.157494 5.942876 53.49124 8.933333 13.07002 57242.97 4143.368 24.20104 13.75405 0 9.52381 1210 460 1226 319 3367181 55.91289 0.6329114 10.52215 52.08333 10.79545 14.11026 61885.48 4694.474 22.19581 20.93023 0 0 233 75 238 93 3367215 47.23435 3.598305 10.32666 40.11093 21.7477 10.97662 61445.65 4384.205 23.56853 33.77246 0 19.04762 2371 1091 2388 860 3367249 64.1791 1.007308 3.851471 50.81967 7.446809 13.11981 58040.66 3564.449 26.02162 11.93182 12.5 25 306 92 306 92 3373676 85.51459 0.1381215 0.2762431 96.16713 36.46532 11.92077 61385.59 4099.012 25.27964 13.54680 0 0 838 92 862 86 3375176 38.11647 1.790807 4.072428 30.11209 11.41869 13.05375 62326.66 3960.634 25.39694 25.38330 0 83.33333 994 457 990 307 3375192 18.16999 1.957028 3.825099 17.78432 8.097928 12.19485 64156.11 3664.265 25.5498 25.86806 6.25 81.25 1028 617 1029 587 3375200 18.21645 2.105698 3.437242 17.84682 15.19337 9.219296 59134.67 3774.601 25.86148 38.25666 0 100 669 408 674 290 3375242 54.84387 1.897597 23.57961 45.82304 21.23894 10.90779 58447.44 3799.078 25.54149 31.80212 0 0 647 214 656 177 3467314 36.94477 15.21258 19.09346 16.26987 17.40431 12.27789 58331.63 3762.583 23.11697 29.58015 0 33.33333 2805 1318 2817 1239 3467330 26.11432 5.308799 9.912578 8.671743 9.722222 14.26319 51104.65 3845.847 22.19777 27.70919 4.347826 30.43478 957 584 957 555 3467348 33.11538 1.770956 1.180638 35.72609 9.166667 11.77256 51742.2 4581.189 22.21333 23.98374 0 0 347 180 349 154 3467413 35.97884 1.407285 1.034768 36.92053 11.90476 14.73511 51080.37 4420.624 20.18018 45.3125 0 0 171 91 174 82 3467439 59.40643 23.87054 21.95251 23.50613 27.45747 14.0033 61997.03 4125.407 24.82678 38.74261 1.298701 10.38961 3322 1329 3398 1325 3467447 28.84975 4.59477 5.959822 8.972135 7.187223 12.61622 58872.75 4335.660 21.75074 39.28442 1.219512 6.097561 3282 2100 3310 1787 3473973 29.30606 7.97491 13.87097 10.28674 10.69959 13.23241 55944.13 3811.049 22.28951 78.96825 0 42.85714 388 244 391 266 3475283 37.95538 6.22615 29.74493 26.23017 12.23404 10.66611 57672.68 3312.515 22.42841 0 14.28571 14.28571 411 193 412 136 3575259 35.75375 2.109375 0.625 40.46875 16.66667 11.91818 61919.85 4272.916 22.22222 0 0 0 114 72 114 58 3667611 50.62411 1.101449 11.78261 38.13043 19.26910 14.40147 57100.62 4203.244 22.98675 12.98701 0 0 459 184 467 149 3667637 40.70337 0.449312 0.954788 11.42937 3.521127 13.88148 57824.88 3838.359 25.36429 35.42857 0 100 273 158 280 143 3667678 25.95567 6.023256 5.232558 38.20266 18.69852 15.21277 62270.05 3664.259 24.16969 29.01554 0 10 2137 1133 2132 1002 3667686 44.45212 2.019903 9.084639 63.68608 19.09425 11.89511 59625.26 3811.724 24.03023 34.44593 0 48 1302 430 1304 352 3667710 39.99806 1.101044 11.80547 65.77463 19.71081 12.96852 60468.72 3939.782 24.37131 18.2534 0 56.25 2213 575 2259 407 3667777 46.74229 1.503836 8.194373 13.34015 4.504505 13.40194 62286.07 4128.065 22.62928 13.5 5.882353 0 660 290 667 280 3667801 54.40152 1.161946 3.776325 17.28395 2.941176 16.79467 61234.99 4903.238 21.27721 40.35088 0 10 101 42 103 45 3667843 34.60404 8.123958 7.962554 30.9894 15.03356 14.84909 60477.27 3763.685 24.72111 24.77432 0 50 1262 681 1261 580 3667850 57.88502 2.875776 27.39844 51.59111 24.49393 12.17399 59096.31 3838.001 25.16211 13.23944 0 70.83333 1662 482 1750 368 3667868 24.70073 0.979605 1.268669 13.05605 10.27668 15.79196 62201.87 3995.416 24.43908 31.28655 0 0 457 279 488 229 3667876 70.23575 3.366044 19.61802 50.84942 25.21964 11.67938 61672.89 4147.682 23.98684 22.39521 0 42.62295 3036 911 3080 739 3667918 44.91996 1.618203 16.41763 36.17087 15.53398 10.97167 61492.85 4057.497 26.51144 13.97059 15 20 998 389 1011 354 3667959 27.57103 0.7626423 0.7743752 19.66444 6.060606 11.88049 63432.72 3784.39 25.07162 25 0 70 626 313 626 244 3673890 46.96416 2.107896 18.18507 12.04001 7.913669 11.09907 60618.41 5342.537 20.25289 18.34862 0 0 179 98 180 74 3673957 20.98413 0.8261886 2.088854 16.67966 4.054054 8.420029 53764.2 3823.18 22.52066 10.24845 9.090909 0 482 294 482 241 3675044 47.6781 0.955685 5.308634 31.19068 11.89711 12.19179 62220.1 3865.725 24.81302 13.34405 0 61.11111 1035 424 1057 328 3675051 62.31156 1.224847 2.274716 17.93526 5.263158 10.46923 59114.49 4587.305 20.48736 26.08696 0 0 81 32 81 17 3675069 30.64712 7.226302 11.49032 28.47964 11.45631 13.98121 59659.77 3922.567 23.51056 35.31353 6.666667 6.666667 905 507 910 473 3675077 43.73161 1.65699 17.27445 20.43186 5.168986 13.20700 62106.35 3058.089 24.52082 35.83916 13.33333 86.66667 889 471 880 352 3768031 12.89092 1.749271 2.587464 10.49563 8.661417 15.07955 59963.79 4346.546 22.36994 58.82353 0 0 199 163 200 152 3768098 43.17715 2.752435 1.797588 43.81089 8.999082 14.07094 58398.9 3882.451 23.42240 29.01186 4 44 1607 820 1610 757 3768114 49.18965 0.8987701 4.328288 36.21097 10.14085 16.56101 66966.72 4540.894 24.11054 22.46094 0 0 536 316 538 285 3768163 7.723036 0.1381215 0.6906077 9.254144 5 15.96932 62789.97 5092.907 19.09561 32.07547 0 0 54 48 54 40 3768213 48.69423 0.1632209 1.468988 25.29924 4.301075 12.16262 52084.4 4470.921 20.17877 40.86957 0 0 142 68 143 47 3768296 10.58816 8.755863 2.760139 7.792208 11.01512 14.19155 58198.62 3718.169 22.87571 46.68874 0 0 2347 1831 2349 1785 3768304 35.02365 0.7042254 0.8766887 19.61771 7.491857 13.51452 57168.13 3976.03 23.11592 39.73684 0 0 510 342 509 280 3768338 64.15235 9.492747 16.92434 35.27733 25.08497 12.29597 62782.7 4952.585 22.19313 31.24032 4.166667 28.57143 8470 3812 8479 3392 3768452 40.05977 2.53262 6.127555 37.38501 11.09091 12.81245 65164.45 4103.446 23.64449 34.33243 3.703704 81.48148 1691 846 1707 683 3773551 26.92308 2.594662 1.762880 26.13284 13.33333 15.28393 62997.11 4261.82 24.32617 43.44473 0 0 594 410 595 357 3773569 54.9774 1.804259 14.86001 41.52190 16.01344 13.17371 57811.14 3832.582 23.35025 44.7178 0 0 1303 573 1317 435 3773791 49.26504 2.389785 2.553705 44.13769 11.06472 13.66803 60657.16 4097.092 24.63998 29.65517 0 83.33333 734 338 749 330 3868478 64.55428 41.36902 16.19322 21.20412 43.73746 15.28547 52885.51 5230.051 17.93118 48.83066 2.654867 1.769912 3624 1740 3633 1925 3968502 36.41286 0.9198423 0.3285151 26.64258 5.673759 14.19245 53510.44 3846.512 23.32055 26.41509 0 0 197 126 200 114 3968569 44.12983 19.62769 10.69226 17.62653 14.7343 13.20137 53970.81 4022.264 21.56064 29.83539 0 0 629 327 634 279 3968577 40.58286 1.936027 0.3367003 34.21717 7.207207 16.12520 52198.86 3727.909 22.02652 39.28571 0 0 190 89 193 60 3968585 48.76863 19.79547 5.832491 23.64881 11.27119 15.08360 59465.23 4469.021 22.00292 30.33708 0 62.85714 1916 824 1932 638 3968593 35.13317 2.449629 4.936003 29.09547 11.32638 13.80978 56910.66 3589.197 24.38578 36.2426 0 0 1189 606 1207 591 3968650 13.77399 0.7308161 0.4872107 21.84328 2.564103 14.55039 51683 3786.43 20.59880 29.72973 0 0 173 119 173 130 3968676 68.72708 20.87249 13.34830 42.18544 33.74755 12.67768 66654.75 4527.226 22.94049 18.20926 0 21.95122 2218 554 2323 558 3975499 26.57033 4.436534 5.981941 26.72339 14.19624 10.59350 55631.9 3616.366 23.96260 26.28676 0 0 745 417 749 397 4068700 18.07366 1.065779 1.648626 9.342215 3.284672 14.97258 60464.24 4506.425 23.30425 45.45455 0 0 438 324 437 293 4068759 38.07467 1.538031 1.165175 30.20134 8.932039 13.48316 55684.26 3887.088 21.21927 25.90361 0 0 730 518 727 465 4068809 22.46579 2.346382 2.090835 12.61471 5.326877 16.19522 64397.68 4933.223 21.43327 25.63559 5.263158 0 669 482 676 453 4068841 17.99781 0.6178288 1.41218 9.223301 4.587156 11.08730 50372.47 3667.019 19.39394 35.95506 0 0 175 114 174 96 4075457 36.82691 1.330486 3.876478 27.18463 5.802048 14.22784 59653.03 4756.442 22.28147 39.81481 0 0 423 245 423 224 4075465 27.08779 1.005025 0.3015075 21.60804 9.23077 12.86419 46347.38 4792.461 17.37132 41.33333 0 0 65 45 66 34 4168890 19.30207 2.108511 0.5399846 25.09643 8.290155 13.32290 51768.27 4138.211 21.00933 48.80952 0 0 329 220 331 179 4169070 31.91489 8.753316 4.823657 34.79713 11.89931 17.10861 57489.22 3823.838 23.52320 38.95447 0 0 707 325 705 303 4269146 39.27727 1.385309 0.9664948 54.38144 21.32353 14.49774 60262.91 4158.069 22.21329 33.33333 0 0 232 123 235 108 4269229 35.70633 4.651992 8.920774 32.86695 9.057301 17.08317 53117.72 4325.819 21.67377 42.91498 0 13.33333 740 363 754 302 4369484 44.54203 2.308979 1.528165 62.94479 22.37197 15.48966 62890.81 4312.730 24.50787 20.19002 0 15.38462 562 242 590 171 4369583 23.6491 5.235658 2.399232 33.46129 11.25 17.79609 60283.85 4361.515 23.73711 37.80488 0 0 716 437 715 400 4369641 7.894435 17.389 4.916817 6.887782 13.52834 14.11575 66182.01 5970.823 18.74769 73.37526 0 0 598 514 605 538 4369666 42.80784 12.24502 3.270391 49.41048 22.36951 16.57729 80565.04 5038.4 28.21085 38.10758 0 0 2185 1071 2216 975 4369674 40.20545 18.39412 4.340957 25.20091 11.52 15.60997 65468.92 4317.319 23.7628 29.55112 0 0 898 476 908 463 4373387 28.89357 31.45988 5.952142 18.42952 20.22727 14.80637 60774.92 4090.016 22.11977 26.72065 0 0 710 426 713 399 4469799 56.34867 1.201376 0.587457 72.01376 19.71665 14.11421 59922.13 4282.146 22.53530 26.64756 4 20 1253 426 1269 393 4469807 14.50640 1.659053 1.226256 4.087521 3.333333 17.28916 58616.28 4262.088 24.33353 60.58091 14.28571 0 346 253 345 204 4569989 39.60894 0.7471264 0.2873563 8.908046 4.301075 16.49120 56131.94 4741.874 18.73638 28.82883 0 0 144 81 145 59 4575267 49.37712 0.8405323 1.074014 4.809713 4.090909 14.58583 55396.61 4509.515 20.73813 34.48276 0 0 338 169 335 131 4670177 32.10162 1.633166 0.6281407 8.354271 1.960784 14.40364 54122.02 2908.312 16.88889 43.24324 9.090909 0 121 88 121 80 4870524 11.44366 4.562111 7.805057 10.15024 10.16260 15.17562 61419.34 4303.057 22.27944 40.4908 0 0 433 359 435 326 4870532 40.81942 1.316920 1.774979 39.96565 12.64368 15.51333 57074.22 4262.563 20.02370 39.66480 0 16.66667 245 103 239 100 4870540 28.11086 6.548673 21.01071 18.01584 13.24153 15.96551 59268.99 3955.489 22.88891 26.11607 0 34.61538 1486 728 1496 688 4870565 22.71245 2.529475 15.34834 10.39657 18.22034 15.12085 62353.6 4900.856 20.22874 66.31016 0 0 320 189 323 155 4870573 23.01924 2.829361 8.373287 16.74657 9.129815 14.62274 53901.88 4110.539 22.38147 40.26144 5.263158 10.52632 1044 585 1052 515 4870581 35.46088 3.839582 35.21459 15.5493 23.87677 16.68085 68338.8 4364.927 25.67080 20.02275 0 56 1290 477 1324 450 4970656 39.70868 0.4294479 0.6748466 25.09202 6.329114 15.62941 56854.04 3942.010 20.42161 43.83562 0 0 117 67 120 55 4970953 30.76032 1.923440 0.7165755 22.40241 6.153846 15.85861 54122.34 4170.568 21.14767 23.37165 11.11111 11.11111 392 239 386 224 4973882 19.67584 3.863969 3.644564 12.84739 5.99455 15.71779 59484.68 4081.602 22.29298 14.45087 0 0 612 373 616 320 4975358 33.55805 1.379099 0.858106 26.50935 17.56757 11.02364 50731.47 3834.786 21.02305 0 0 0 236 132 234 108 4975390 21.46387 0.8783784 0.4391892 34.05405 14.28571 16.46453 56837.35 4968.968 20.91327 46.48438 0 0 231 136 232 151 5071043 51.20522 4.550344 3.431583 39.2642 10.04902 13.27732 56234.31 3767.504 23.17001 12.96703 0 41.66667 690 228 688 193 5071068 42.13075 0.7830854 0.2349256 25.92013 1.724138 13.38175 49550.74 3282.389 21.30662 29.87013 0 0 118 63 120 55 5071217 55.00726 0.673968 1.235608 64.5886 18.12081 13.32733 55535.15 4008.414 24.00409 13.07190 0 0 220 86 224 72 5071308 42.6007 4.702023 1.366867 32.55878 9.221311 14.96416 59645.21 3932.407 24.17863 21.40625 0 50 747 388 733 359 5073601 53.90428 1.221374 1.475827 53.43511 14.73684 12.70857 51297.37 4109.917 21.68662 28.86598 0 16.66667 120 44 120 31 5171399 72.2977 12.32356 0.597177 45.33116 6.521739 12.38267 52194.34 4350.793 21.44379 17.72152 0 0 131 43 135 39 5171464 49.25642 13.28312 2.939555 25.5282 14.10788 15.09745 57777.56 4165.932 23.06171 24.24242 0 25 767 360 776 303 5271498 49.15907 0.8762706 1.892744 29.75815 3.597122 13.24340 55372.46 3941.387 20.91108 36.42384 0 0 204 82 207 79 5271571 51.2931 0.1422475 0.56899 32.29018 2.564103 15.81222 53216.62 5045.576 19.64384 34.21053 0 0 40 18 41 19 5375028 60.14599 0.4807692 0 5.128205 5.555556 16.13205 63507.83 6482.47 17.90831 42.42424 0 0 41 25 43 23 5471860 84.09904 0.5628518 0.2412222 90.72635 18.78788 14.21739 58391.11 3952.910 22.75184 8.370044 0 0 258 46 259 91 5471878 74.57442 0.8955831 0.2442499 80.46 15.98174 12.97066 53304.9 3688.748 22.96475 16.46586 0 0 343 103 342 96 5471993 76.58037 1.721170 0.05737235 83.76363 23.68421 13.28494 58362.71 4115.279 22.61873 27.42857 0 0 243 51 250 40 5472256 44.83328 7.621228 1.954371 43.13517 12.71111 14.47325 58322.98 4057.255 22.31273 35.91731 3.125 28.125 1726 794 1750 578 5472272 72.66314 1.192504 0.2981261 79.25894 13.15789 14.81406 58001.31 4081.734 21.10603 36.13445 0 0 147 46 150 26 5475325 92.3345 0.933553 0.1098298 83.0313 17.10526 14.40238 61350.21 3792.456 22.91892 0 0 100 137 15 134 23 5575184 36.71642 0.4279601 0.8559201 4.707561 4.651163 13.26809 48160.47 4666.561 18.42667 70.27027 0 0 53 36 53 31 5672454 51.80654 0.5471956 0.4377565 76.90834 15.52795 15.02404 56925.98 3897.079 23.48475 30.60109 0 16.66667 264 82 266 59 5672520 23.28170 1.366251 0.8628955 18.64813 8.152174 14.22136 56808.01 3825.936 22.87717 35.54688 0 0 308 222 304 204 5672603 15.68154 5.522166 1.674629 17.43977 6.917476 15.00022 57203.55 3831.574 23.20986 37.68719 0 0 1328 837 1338 736 5672652 38.15821 2.905512 2.354871 33.44268 9.943978 15.35255 56413.61 3699.07 24.85112 34.36341 0 22.22222 1166 653 1170 526 5673759 12.32702 5.661354 1.485200 14.53115 5.405405 15.73222 62750.24 4265.133 23.81032 41.16638 0 0 1425 1126 1431 1088 5673874 1.247051 6.066291 1.000625 2.345216 4.72973 12.22485 55208.84 4079.327 20.98849 74.3421 0 0 249 212 248 186 5673940 23.45529 3.861647 1.819697 29.78191 10.36585 10.28723 54402.98 4155.084 21.65256 21.14094 0 0 510 332 516 284 5772678 17.89883 10.49096 3.372093 12.70026 14.92891 14.43766 49783.31 4254.717 20.06286 46.42032 0 0 583 461 591 455 5772686 49.23581 0.77951 1.670379 43.76392 4.166667 11.36091 50433.17 5039.203 19.54545 27.08333 0 0 51 24 59 17 5772694 62.23968 13.82086 3.956157 32.12879 15.88448 13.27089 52881.33 4324.174 20.98711 8 0 18.18182 331 116 342 96 5772702 46.16188 1.150575 0.8004002 45.62281 13.33333 11.80714 48426.15 3945.069 19.8583 53.77358 0 0 147 63 154 37 5772710 43.41431 3.648564 1.541204 46.31998 21.37767 14.40468 53796.16 3845.481 22.70884 29.89247 0 6.666667 593 255 595 208 5872736 70.62104 20.46172 2.989345 17.42305 11.03286 16.56420 61705.66 3970.984 24.88647 15.14286 0 13.63636 699 259 709 199 5872751 77.74827 5.998899 9.576225 11.11723 7.874016 16.91871 65099.57 6913.397 20.03252 23.52941 0 0 154 92 156 72 statsmodels-0.12.2/statsmodels/datasets/star98/src/star98.dat000066400000000000000000005412161400612667500240750ustar00rootroot00000000000000CDS_CODE COUNTY DISTRICT LOWINC PERASIAN PERBLACK PERHISP PERMINTE AVYRSEXP AVSAL PERPSPEN PTRATIO PCT_AF PCTCHRT PCTYRRND READ MATH LANGUAGE LANGNCE MATHNCE READNCE READM11 READNC11 MATHM11 MATHNC11 LANGM11 LANGNC11 READM10 READNC10 MATHM10 MATHNC10 LANGM10 LANGNC10 READM9 READNCE9 MATHM9 MATHNCE9 LANGM9 LANGNCE9 READM8 READMCE8 MATHM8 MATHNCE8 LANGM8 LANGNCE8 READM7 READNCE7 MATHM7 MATHNCE7 LANGM7 LANGNCE7 READM6 READNCE6 MATHM6 MATHNCE6 LANGM6 LANGNCE6 READM5 READNCE5 MATHM5 MATHNCE5 LANGM5 LANGNCE5 READM4 READNCE4 MATHM4 MATHNCE4 LANGM4 LANGNCE4 READM3 READNCE3 MATHM3 MATHNCE3 LANGM3 LANGNCE3 READM2 READNCE2 MATHM2 MATHNCE2 LANGM2 LANGNCE2 161119 ALAMEDA ALAMEDA CITY UNIFIED 34.397299903568 23.2993035015743 14.2352828928537 11.4111248926629 15.9183673469388 14.7064601769912 59157.3224489796 4445.20742295583 21.7102488401518 57.0327552986513 0 22.2222222222222 661.66460833221 654.852837393022 649.464497916387 54.1977416319398 53.2739960500329 49.0258864770123 700.8 40 702.9 50 683.6 49 688.9 31 696.5 49 671.2 39 689.8 40 695.2 57 674.8 54 694.4 55 685.1 54 670.4 56 680 52 674.2 53 664.9 59 665.1 53 661.7 55 649.6 54 656.3 53 647 53 646.4 57 643.7 57 622 52 634.9 59 616.7 55 598.9 54 613.1 57 581.2 53 570.5 55 590.9 57 161127 ALAMEDA ALBANY CITY UNIFIED 17.3650687227623 29.3283833952076 8.2348970637867 9.31488356395545 13.6363636363636 16.0832386363636 59503.9675324675 5267.59838002025 20.4427792915531 64.622641509434 0 0 686.821559860904 682.097784342688 669.959373446047 72.8915962207857 76.2717872968981 71.290611028316 715.6 56 727.3 71 693.8 60 712.3 55 726.7 75 694.4 62 707.6 57 720.5 78 687.7 65 715.2 73 714.9 80 691.7 74 714.4 81 712.5 84 692.2 83 693.4 80 693.1 80 671.7 75 690.2 82 672.7 76 674.2 80 676.7 81 647.5 71 655.4 74 649.5 76 626 74 636.3 75 607.7 70 596.8 73 616.2 77 161143 ALAMEDA BERKELEY UNIFIED 32.6432354357246 9.22638614946307 42.4063116370809 13.5437212360289 28.8343558282209 14.5955882352941 60569.9202453988 5482.92209072978 18.9541918755402 53.9419087136929 0 0 671.640665091155 661.550763788391 653.599950413223 56.2609917355372 56.6483357452967 56.1053342336259 717.7 58 720 66 692.6 58 707.9 51 716.1 67 689.7 57 707.8 58 710.6 70 688.9 67 702.3 62 690.3 59 678.1 63 685.7 57 672.8 50 667.3 61 673.6 61 664 57 655.8 60 661.1 58 651.7 56 643.1 53 648.3 60 623.1 52 630.9 55 612.9 50 589.3 43 604.8 48 574.9 47 559.5 42 577.1 40 161150 ALAMEDA CASTRO VALLEY UNIFIED 11.9095333524191 13.8830897703549 3.79697286012526 11.4431106471816 11.1111111111111 14.3893861892583 58334.1081871345 4165.09303235908 21.6353887399464 49.0610328638498 0 7.14285714285714 676.513967201032 668.812306006938 660.962304147466 64.1185253456221 64.2161767390907 61.975677169707 716.3 57 713.7 61 691.9 58 708.3 51 705.5 54 685.9 54 704.7 54 705.1 66 684.6 63 709.9 69 701.2 69 683.7 68 697.9 68 691.1 68 676.8 70 677.8 66 675.9 67 660.5 65 665.9 62 659.8 63 653.1 63 654.4 65 637.1 61 644.6 65 629.4 61 615.8 65 622.2 63 600.4 64 589 66 607.4 69 175093 ALAMEDA DUBLIN UNIFIED 12.927964941112 7.17299578059072 4.82594936708861 13.2383966244726 6.18556701030929 17.4710762331839 65570.8608247423 5382.00870253165 20.6833333333333 34.8314606741573 0 0 672.820427644139 662.700114372856 657.977207001522 62.6826484018265 60.5428898208159 60.2913325696831 711.7 52 707.9 55 690.3 56 703 45 706.1 55 685.4 53 701.4 50 706.8 69 682 60 705 64 688.2 57 681.1 66 694.6 64 679.7 58 671.9 66 676.5 64 673.8 65 660 63 668.8 65 660.3 64 655.3 66 659 69 639.6 63 646.7 67 635.8 66 613.5 63 623.2 64 593.7 59 579.7 57 601.4 63 161168 ALAMEDA EMERY UNIFIED 36.8888888888889 12.1875 76.875 7.60416666666667 43.5897435897436 13.9056818181818 63153.641025641 4324.90208333333 18.7798408488064 52.3809523809524 0 0 634.917397881997 629.553768115942 624.377661169415 26.7661169415292 24.4666666666667 21.2692889561271 677.8 19 680.2 25 660.3 26 667.4 14 676.1 23 650.5 19 663.9 18 669.3 30 652.4 31 663.9 25 653 23 644.5 30 651.3 24 648.2 26 640.8 32 636.4 24 635.3 28 625.9 28 621.8 21 614.4 19 612.3 23 606.2 22 597.6 24 604.3 29 573.5 17 560.4 16 570.6 18 560.7 30 547.2 26 569.3 28 161176 ALAMEDA FREMONT UNIFIED 20.9314901814986 28.0235116408892 4.64322070075198 13.8081633993367 15.3784860557769 14.9775459688826 66970.5521912351 3916.10429185959 24.5191372040221 44.9157829070493 0 2.38095238095238 672.231665367151 667.751934900543 659.896057692308 64.1000915750916 64.6254972875226 59.4770903086731 713.3 54 720.7 67 695.4 61 708.2 51 715.9 64 688.8 56 699.6 49 707.6 68 683.5 61 701.3 61 694.5 62 679.9 64 693.9 64 689.7 66 676.7 70 679.4 67 682.7 72 666.9 70 668 64 661.2 64 658.7 68 652.3 63 636.5 61 646.2 67 624 56 609.1 59 619.8 60 601 64 586.7 64 601.3 63 161192 ALAMEDA HAYWARD UNIFIED 53.2689776217639 8.44785772029103 19.3748315817839 37.9053265067816 25.5255255255255 14.6782859680284 57621.947947948 4270.90330548819 22.2127790292853 32.289156626506 0 12.1212121212121 642.626397690466 636.33247468834 633.291838901472 39.561013590034 36.7048694813692 33.3479791578651 689.8 29 694 39 670.5 35 681.7 24 688.6 36 664.2 31 678.2 29 685.2 46 665.1 43 677.4 37 670.3 39 657 42 664.3 35 660 37 652.2 45 653.2 40 650.1 42 641.5 44 638.6 35 630.2 33 631.9 42 620.5 34 603.4 29 615.8 39 595 32 580.1 32 592.2 35 566.9 35 559.4 37 578.5 37 161200 ALAMEDA LIVERMORE VALLEY JOINT UNIFIED 15.1900897052542 3.6657808347663 2.6496795372831 13.0920744098796 6.20300751879699 13.6619730185497 63447.3966165414 4309.73393778334 24.5902624724504 30.4526748971193 0 0 668.662054255087 658.826442204589 652.29882914137 57.2864267129228 57.3267209950676 56.071866112448 713.8 54 712.7 60 691.6 57 706.3 48 707.3 57 685.7 53 704.3 54 706.4 68 687.7 65 701 60 694.2 62 674.3 59 688.2 58 682.1 59 666.8 61 667.7 55 667.6 59 650.8 54 663 59 652.8 56 648.7 59 647.9 59 625.8 50 633.7 56 626 58 603.4 54 614.7 56 590.3 55 574.2 51 593.5 54 161242 ALAMEDA NEW HAVEN UNIFIED 32.7789739401589 17.1783055654023 12.4849344204183 28.3232896136122 27.2598870056497 12.5186375321337 57801.4124293785 4648.91669620702 20.26010286554 26.0709914320685 0 0 654.289313771888 652.417934527718 647.614495897388 49.6735829482222 46.7383922708939 39.4493137718883 700.4 40 705.4 52 685.8 51 690.2 32 695.7 44 673.7 41 683.8 34 686 47 672.4 50 686.8 46 677.3 46 666.1 51 671.9 42 670.7 48 660.6 54 656.5 43 657.5 50 647.2 50 639.2 35 639.5 42 639.3 49 631.4 44 621.9 47 633.5 56 603.3 39 594.8 45 604.2 46 573.7 41 570.1 47 588.6 49 161234 ALAMEDA NEWARK UNIFIED 28.2158234660926 10.4304198574069 6.78637443886982 32.3343015579614 13.4615384615385 16.4176039119804 57845.6401098901 4527.60324795353 21.7413793103448 22.6457399103139 0 0 651.806326987682 646.560586617782 642.048435474912 46.2571745972968 43.4252978918424 39.2136991414707 693.5 33 696.5 42 677.8 43 687.1 29 693.1 41 671.5 39 686.3 36 690.7 52 672.7 51 684 43 676.6 45 661.3 46 673.1 43 665.8 43 659.6 53 657.4 44 657.4 50 648.3 52 646.6 43 639.3 42 640.2 50 631.6 44 617.4 42 625.9 49 603.3 38 586.7 37 597.6 40 570.3 38 563.6 41 581 40 161259 ALAMEDA OAKLAND UNIFIED 59.9729276290704 17.5173624075872 50.9409304756926 23.1013367186917 52.3434423001182 16.9328347826087 57434.4423001182 4693.06937495333 21.3148871700821 19.5321637426901 3.2967032967033 13.1868131868132 624.563806995628 620.398091796817 616.567219733771 28.6828906693584 28.4544450085108 24.1449718925671 683.7 24 689.8 35 670.7 35 673.7 18 683.6 31 658.8 26 669.3 21 677.1 38 657.9 36 669 29 663.1 32 647.5 32 651.6 24 651.8 29 640.7 32 636.6 24 631.9 25 625.3 28 626.8 25 621.6 25 617.5 28 606.4 22 594 22 602.8 28 582.5 23 573.1 26 579.8 24 556.9 28 552.3 31 566.7 26 161275 ALAMEDA PIEDMONT CITY UNIFIED 0 19.7488584474886 1.86453576864536 2.58751902587519 7.40740740740741 15.8697860962567 52193.4567901235 5248.69292237443 18.5118219749652 80.379746835443 0 0 704.578132444021 695.271888310459 688.142389758179 83.8003793266951 82.8760056791292 82.5393044306813 743.2 81 743.9 85 720.1 82 733.1 76 734.1 80 712.2 79 738.6 83 733.2 87 714.2 85 724.5 80 724.8 85 700.6 81 719.3 85 712.6 85 700.6 88 702.2 85 701 85 680.2 81 695.1 85 684.9 84 689.1 88 683.2 85 658.4 79 666.2 81 667.2 86 643.9 85 656.1 87 619.5 78 593.9 71 629.1 86 175101 ALAMEDA PLEASANTON UNIFIED 4.70089495996232 8.73671782762692 1.74565694046214 6.93202900995109 7.12788259958072 16.1817604355717 67367.5492662474 4607.67330072525 24.6510600706714 39.6341463414634 0 0 683.838015568723 678.03443586493 671.316753082152 73.9103583362139 73.4222657600553 69.0648309515511 718.5 59 718.9 65 697.9 64 716.1 59 717.2 66 696.5 64 712.5 61 715.3 75 695.9 72 714.1 72 705.2 72 694.2 77 703.2 72 698.1 74 686.5 79 682.7 70 685.8 75 670 73 680.2 75 673.8 76 671.9 79 669 76 652.1 75 656.4 75 646.5 74 631.8 78 638.8 77 607.4 70 600.2 76 616.3 77 161291 ALAMEDA SAN LEANDRO UNIFIED 28.1211115719618 12.6920072897683 19.2658161936996 26.8419682374382 13.3720930232558 14.428640776699 57240.4481686047 3980.58939468888 21.8984351933865 31.6582914572864 0 9.09090909090909 651.912278410151 642.209956553223 639.349656069902 43.8430935118052 39.3631426502534 39.3356969583878 693.6 33 695.4 40 678.3 43 685.4 27 689.7 38 668.9 36 682.1 32 685.9 47 666.9 45 684.7 44 672 40 657.5 42 673.9 44 666 44 661.2 54 657.4 44 653.1 45 643.3 46 649.5 46 632.8 35 637.7 48 629.4 42 606.2 32 623.1 46 602.7 38 579.5 31 594.8 37 573.9 41 563.8 41 581.1 40 161309 ALAMEDA SAN LORENZO UNIFIED 36.9904684648144 10.0323624595469 15.4230235783634 30.7443365695793 13.5076252723312 13.2975345167653 58413.7385620915 4197.61525658807 23.1294326241135 31.1507936507937 0 0 650.559694592323 638.287041796294 639.202783519361 43.6724541821689 35.5612065467334 37.6273465956851 691.3 31 691.2 37 672.9 38 685.6 28 690.8 39 666.7 34 680.2 30 683.6 45 666.5 44 685.2 44 666.5 35 661.1 46 677.5 47 665.6 43 662.1 56 655.8 43 642.8 35 645.4 49 643.1 39 628.4 31 635.5 46 628.1 40 604.1 30 622.6 45 598.1 34 575.6 28 592.3 35 570.8 38 555.8 33 581.4 41 373981 AMADOR AMADOR COUNTY UNIFIED 20.2597946783993 .485744456177402 .802534318901795 5.97676874340021 2.4390243902439 15.3094936708861 51311.6292682927 4025.59281942978 24.8229166666667 36.1940298507463 0 91.6666666666667 670.250681818182 655.3 651.925882352941 54.4072829131653 51.1426197729161 54.4082386363636 712.8 53 704.7 53 694.3 60 703.9 47 695.3 48 679.2 47 702.3 52 696.4 58 678.3 57 701.6 61 682.3 52 672.7 58 690 61 675.3 54 667 61 670.6 58 659.7 53 647.7 52 656.6 53 640.8 46 640.9 51 638.2 51 613.9 43 627.9 52 619.7 57 594.7 49 605.6 50 579.8 51 570.9 54 591.9 57 461408 BUTTE BIGGS UNIFIED 42.6682692307692 2.83687943262411 .945626477541371 23.8770685579196 10.6382978723404 11.8396226415094 55990.3191489362 5151.62647754137 17.9120879120879 24.4444444444444 0 0 654.831493506493 646.170872274143 638.868238993711 41.8977987421384 42.0809968847352 40.1103896103896 685.3 26 688.8 34 665.3 30 690.7 32 690.7 39 662 30 695.9 45 696.1 58 671 49 695.3 54 674.7 44 665.8 51 677.4 47 671.7 49 658.9 52 656.2 43 655.6 48 639.5 42 647.1 43 635.9 38 632.3 42 624.1 36 609.1 34 627.8 50 601.7 37 582.9 34 588.4 31 558.5 28 560.2 37 573.5 32 461424 BUTTE CHICO UNIFIED 33.1292320991212 6.30541173132846 2.76615362791687 12.8661607206185 6.17283950617285 14.6014383561644 58558.5972222222 4004.40095042202 22.7300762863172 49.6551724137931 4.34782608695652 26.0869565217391 663.164911595194 653.503262518968 647.277658142665 50.4598154201115 49.4008915022762 48.6200058610921 710.2 50 714.3 62 690.3 56 706.1 48 707.8 57 685.2 53 699.7 49 702.3 64 680.9 59 695 54 684.3 53 671 56 683.1 53 675.8 54 664.7 59 664.4 52 658.3 50 647.2 50 651.4 47 637.7 40 635.9 46 638.2 50 612 37 622.8 46 608.1 42 590.3 41 598.5 41 573.6 40 561.1 38 579.6 38 461432 BUTTE DURHAM UNIFIED 29.3929712460064 1.07115531752104 .765110941086458 9.71690895179801 4.47761194029852 14.0452702702703 53772.2985074627 4518.03442999235 21.1850649350649 51.0204081632653 0 0 675.541104294479 661.864705882353 662.146998982706 62.5757884028484 54.0425963488844 57.4836400817996 714.6 55 709.1 57 703.3 67 714 57 713.7 63 695.7 63 706.8 56 707.9 69 691.3 68 706.7 66 683.5 53 682.4 67 688.7 59 676.6 54 670.8 65 671.3 59 666.7 59 655.8 60 662.9 59 650.5 54 652.7 63 647.5 58 615.3 40 638 60 617.1 50 590.8 42 608.1 50 586.3 52 564.9 42 596.6 58 461473 BUTTE GRIDLEY UNION 52.9931305201178 6.21737066919791 .332225913621263 38.7280493592786 7.61904761904762 14.1739495798319 50695.1238095238 4114.06454674893 20.411361410382 23.2758620689655 0 0 647.268098591549 643.146611909651 636.80674002751 40.9401650618982 40.8555783709788 34.6556338028169 694.8 34 697 43 675.4 40 688 30 697.1 46 668.2 35 687.6 37 691.6 54 675.5 54 678.5 38 670.8 39 653.4 38 668.2 38 653.9 32 654.1 46 649 36 653.3 46 641.8 44 640.6 37 635.5 38 634.7 44 613.9 28 602.9 29 614.6 38 590.8 28 591.1 42 589 32 573.2 40 562.8 40 579.5 38 461531 BUTTE PARADISE UNIFIED 35.0883585352523 .829216654904728 .388143966125618 4.62244177840508 4.13533834586465 14.3022108843537 55278.7443609023 4148.22776993649 21.9194683346364 25 23.0769230769231 15.3846153846154 666.75602871998 653.663746369797 646.168135095448 48.0907978463045 47.7294288480155 50.525129982669 707.9 48 706.1 53 679.2 44 702.1 44 701.2 50 671.6 39 694.4 44 694.4 56 670.1 48 693.1 52 680.5 49 666.7 52 681.5 51 672.5 50 659.1 52 666.4 54 654.5 47 645.9 49 657.3 54 636.9 40 636.8 47 642 53 613.8 39 622.8 46 617.8 51 596.4 47 607.2 49 589.6 55 568.8 47 595.2 56 561564 CALAVERAS CALAVERAS UNIFIED 37.2044140830268 .569948186528497 1.1139896373057 6.32124352331606 5.35714285714286 13.6024725274725 50668.494047619 3975.44792746114 24.8691767708998 22.9787234042553 0 8.33333333333333 662.25800647715 649.149032711924 643.041403757533 46.6157390996101 45.047836792121 47.6523929471033 699.5 39 700.3 47 679.4 45 694.4 36 699.8 49 668 35 694.9 44 693.2 55 669.7 48 693.9 53 680.3 49 664.3 50 686 56 669.5 47 661 54 666.8 54 663 55 650.1 54 655.8 52 635.2 38 639.1 50 641.1 53 609.8 35 624.7 47 610.9 45 582.5 34 598.2 41 576.7 43 562 39 581.4 41 661598 COLUSA COLUSA UNIFIED 54.2682926829268 .549786194257789 .549786194257789 40.7452657299939 7.40740740740741 14.8710526315789 52537 4205.36224801466 19.4451145958987 36.283185840708 0 0 653.225547445255 646.493309545049 638.67279344859 38.926296633303 38.5388046387154 35.7308394160584 691.1 30 688.9 34 670.2 35 678.1 22 685.6 33 655.4 23 686.8 36 696.7 58 668.9 47 679.1 39 666.5 35 653.7 38 673.1 43 663 41 650.2 42 654.6 41 650.9 43 640.6 43 639 35 624.4 27 627.9 38 626.3 39 603.9 30 619.1 42 599 35 588.9 40 594.3 37 574.5 41 568.1 45 588 47 661614 COLUSA PIERCE JOINT UNIFIED 65.8239700374532 .264084507042254 3.87323943661972 58.8908450704225 6.55737704918032 10.9265151515152 46291.7868852459 4469.79753521127 19.5254833040422 37.9310344827586 0 0 639.172727272727 633.277030162413 623.559159859977 25.7491248541424 27.4095127610209 24.9306220095694 687.1 27 683.2 28 660 26 678.2 22 682.8 30 656.2 24 663.6 18 672.8 34 649 28 669.4 30 655.6 25 642.8 28 659 30 644.5 23 635.4 27 634.6 23 629.6 23 621.9 24 624.1 23 624.8 28 620 30 616.2 30 602.1 28 608.7 33 581.8 22 573.9 26 573.3 20 557.4 27 549.5 28 560.4 19 661622 COLUSA WILLIAMS UNIFIED 78.5407725321888 1.28205128205128 0 78.4188034188034 20.8333333333333 11.4778846153846 49267.1922916667 3893.3372008547 21.1231101511879 19.2307692307692 0 0 623.801777777778 624.58059914408 615.708849557522 19.3126843657817 21.2339514978602 15.0103703703704 661.9 10 676.5 22 648.2 16 664.9 13 679 26 639.6 13 652.6 11 665 26 639.1 20 645.7 13 651.1 21 627.6 16 640.4 16 647.8 25 628.5 20 628.7 18 634.6 28 618 21 610.6 14 603.4 12 602.1 16 592.5 14 581.3 13 594.7 22 573.5 16 558.5 15 572.4 19 556.7 26 545.9 24 576.9 34 761648 CONTRA COSTA ANTIOCH UNIFIED 30.0755277257763 3.62619624120835 10.5038625619739 20.9443099273608 8.66574965612105 13.6910780669145 62341.1939477304 4011.39040701026 23.8890485771774 23.8544474393531 0 72.2222222222222 654.988955223881 642.419637634059 642.558945199835 48.5542645241038 42.4466200844979 44.2719734660033 699.6 39 698.4 46 680.8 46 696.1 38 697.2 47 675.8 43 690.9 41 691.8 54 675.9 54 690.9 51 674.4 44 665.3 50 677.4 48 661.8 40 660 54 658.4 46 650.5 44 645.1 49 650.8 47 636.5 40 640.1 50 632.9 46 609.1 36 626.3 50 605.2 42 582.9 36 598.9 42 573.1 43 559.2 40 584.2 47 761697 CONTRA COSTA JOHN SWETT UNIFIED 28.246013667426 6.89342403628118 19.8185941043084 16.7800453514739 12.7450980392157 15.9155462184874 59176.5294117647 4225.73832199546 22.1837944664032 18 0 0 655.849803664921 645.640405904059 641.369559668156 44.1640076579451 42.0817958179582 40.6603403141361 701.6 41 695.7 43 682.3 48 689.9 33 693.4 47 672.5 41 689.3 40 688 50 673.1 52 687.5 48 678.3 47 664.4 49 672.4 44 669.3 48 657.4 50 657.2 44 656.5 50 642.1 45 640.7 38 626.1 31 629 39 624.7 38 605.1 34 616.7 41 601.9 41 582.2 37 593.7 38 562 36 545.8 29 573.1 36 761739 CONTRA COSTA MARTINEZ UNIFIED 22.3337515683814 2.52373234545034 3.31095160916879 14.0310257003936 10.3092783505155 16.1568584070796 59230.7216494845 4114.41768927993 21.7433155080214 34.4262295081967 0 0 666.986131386861 653.039726027397 651.011405568601 54.859443139886 49.3724722765819 53.342402123424 709.8 50 712.9 58 687.6 53 700.2 42 703.5 53 678.1 46 696.5 46 700.1 62 676.8 55 700.2 59 677.4 46 673.6 59 687.8 58 668.9 47 667.1 61 668.3 56 652.1 44 648 51 659 55 642 45 644.5 55 645 56 619 44 636.1 58 623.2 56 594.9 45 609.7 51 589.3 55 574 51 598.4 60 761754 CONTRA COSTA MT. DIABLO UNIFIED 22.6246525611209 7.69788789375297 4.90220696967161 16.7768756452108 9.42158616577221 15.3236785904965 57128.5825879547 3928.69554420915 22.1416213544241 37.6383763837638 0 0 663.753803895455 655.29439179166 651.228181140823 57.5844026823413 56.8430443382232 53.913434326619 707 47 709 57 687.9 53 702 45 706.7 60 683.5 51 699.4 50 703.6 65 682.9 62 698.4 58 688.6 58 675.1 60 687.6 59 680 58 669.1 63 670.3 58 663.6 57 655.3 59 660.9 58 650.9 56 649.8 60 646.3 58 625.9 54 634.6 58 613.8 51 595.7 50 607.9 51 581.4 52 571.4 55 592.7 57 761788 CONTRA COSTA PITTSBURG UNIFIED 51.7849321068769 4.59893048128342 27.7967914438503 35.1016042780749 30.0248138957816 15.9748903508772 58788.9305210918 4049.18085561497 22.8729963008631 85.1116625310174 0 8.33333333333333 638.057359342254 630.487298832439 628.793177419355 35.1459677419355 31.2234143262859 29.0448170240206 692.7 32 690.8 36 674.7 40 680.8 23 685 33 663.4 30 674.1 25 678.2 39 662.9 41 678.1 38 666.2 35 656.2 41 659.9 31 654.5 32 648.7 40 645.5 33 639.5 32 631.6 34 632.1 29 623.2 26 623.8 34 615.7 29 601 27 615.5 39 585.1 24 575.2 27 584.3 28 556.6 26 552.6 30 569 27 761804 CONTRA COSTA SAN RAMON VALLEY UNIFIED 1.89532160557704 9.92522790125986 1.63371914370583 4.27634948274096 4.50346420323325 15.9236921529175 59976.9376443418 4035.18872272867 23.3468734613491 50.7450331125828 0 0 687.436196062002 681.264960300878 673.262666202576 75.288827010094 75.4876027301853 71.8017036726714 720.5 61 724.5 71 701.7 68 719.4 63 722.3 71 700.5 68 716.3 65 719.3 79 700.1 76 717.3 75 719.1 82 695.6 78 708 76 709.8 83 689.1 81 690.4 77 690.4 79 674.7 77 684.4 78 674.4 77 672.6 79 670.5 77 652.6 75 656.3 75 646.9 74 622.9 71 636.1 75 608.6 71 589.8 67 613.3 75 761796 CONTRA COSTA WEST CONTRA COSTA UNIFIED 51.2384774565749 13.0202355783751 35.1011778918756 25.5270311084265 25.8268824771288 17.1897748592871 62664.0950035187 4347.93612201752 22.8705015585152 36.5 0 8.47457627118644 639.248799428299 632.602881497267 628.976394317857 36.1087329583373 34.3111275826925 31.5787994282992 690.4 30 694.8 39 674.4 39 682.4 25 688.6 36 663 30 677.9 28 679.4 40 663.4 41 674.5 34 665.7 34 652.4 37 658 29 654.6 32 644.3 35 650.5 37 646.9 39 636.4 39 637.6 34 629.3 32 627.6 37 617.2 30 602.6 28 613.3 37 595.4 32 582.9 34 590.8 33 566.8 34 555.8 33 576.2 34 861820 DEL NORTE DEL NORTE COUNTY UNIFIED 42.5114329268293 6.25244236029699 .41031652989449 10.1797577178585 8.07692307692308 14.7094827586207 58233.8115384615 4733.28038296209 20.6736353077816 15.5038759689922 0 0 654.110813174002 643.545233380481 636.959429065744 41.8500576701269 41.4144271570014 42.1262022733897 699 39 700.6 46 673.5 38 691.8 33 695.3 44 667.2 34 685.2 35 687.1 48 666.6 44 690.5 50 672.9 41 661.1 46 675.6 45 665.7 43 655.1 47 656.8 44 650.1 42 640.2 43 647.2 44 634.3 37 632.2 42 632.4 44 610.5 35 619.1 42 609.2 44 591.2 42 598.5 41 572.4 39 562.4 39 579.5 38 973783 EL DORADO BLACK OAK MINE UNIFIED 30.1696469509399 .797373358348968 .515947467166979 2.25140712945591 1.90476190476191 14.2323275862069 51822.3714285714 4030.97842401501 21.4729458917836 32.4561403508772 0 0 671.052793471438 662.392478421702 654.1465625 56.355 57.1011097410604 55.08223477715 705.8 46 707.6 55 681.9 47 697.9 40 697.6 47 670.9 38 698.2 47 700.9 63 676.7 55 701.4 61 687.5 57 679.5 65 683.2 53 672.5 50 663.4 58 670.9 59 675.1 67 653.5 57 667.6 64 661.2 65 654.8 65 652.4 63 631.3 55 643.1 64 629 60 609.6 59 620.7 61 593.5 58 574.4 52 591.6 52 961903 EL DORADO LAKE TAHOE UNIFIED 45.4234388366125 1.50119413169567 .904128283862163 26.2708973046742 5.33807829181495 14.3570287539936 55740.1387900356 4323.75400887069 21.5345821325648 86.7219917012448 0 0 655.848036826428 645.356022041459 644.127473404255 49.6300531914894 44.7874573602729 43.96452748443 695.8 35 697.4 43 675.1 40 697.6 39 696.4 45 675.4 42 692.2 41 695.5 57 676.1 54 690.4 50 673.4 42 671.7 57 675.7 46 665.6 43 665.1 59 658.7 46 653.6 46 650.5 54 652.7 49 641.8 45 643.8 54 632.9 45 615 40 629.9 52 607.4 42 589.4 40 598.8 41 579 45 569.8 47 585.3 44 1073965 FRESNO CENTRAL UNIFIED 49.2508395763369 10.1529902642559 7.8741842302343 42.3237402375094 16.5394402035623 10.0809012875536 54568.7404580153 4006.11832673585 22.5917372337696 37.6666666666667 0 76.9230769230769 645.428 641.522896312638 634.864938828075 40.9228911783645 41.6585250551529 34.9438367346939 683.8 24 688.6 35 665.9 31 680.9 24 683.7 33 654.2 23 673.7 26 680 41 658 37 681.1 41 669.9 39 660.8 46 665.5 37 663.1 41 653.5 47 652.1 39 651.7 45 642.2 46 638.1 35 632.4 37 629.1 39 624.4 39 614.8 44 620.7 46 597.8 38 592.8 47 594.7 39 571.8 45 566.7 51 586.8 52 1062117 FRESNO CLOVIS UNIFIED 23.433371722783 11.750645994832 2.87144702842377 19.031007751938 15.9441587068332 11.8789028213166 53158.0705363703 4242.7020994832 22.7051671732523 40.5063291139241 0 0 670.829070946691 669.983691062632 660.175030880537 62.7089730015881 64.6854327938072 55.8729220865118 710.2 50 711.5 59 690.5 56 703.4 45 704.1 53 681 48 699.3 49 701.6 63 682.2 60 703.5 63 695.2 64 685 69 691.8 62 686.1 64 676 70 673.7 61 683.2 73 662.4 66 661.2 57 660.4 64 652.9 63 644.3 55 638.2 62 639.1 61 624.2 57 622 71 623.1 64 595.7 60 597.9 74 609.4 70 1062125 FRESNO COALINGA/HURON JOINT UNIFIED 57.9224030037547 .87173100871731 .647571606475716 68.7422166874222 18.9349112426035 11.1978723404255 61085.4437869823 4258.42515566625 24.4786015672092 14.8351648351648 0 0 634.785217079297 631.830958230958 622.751865266208 28.8927924664976 32.6072306072306 26.6347326874776 687.3 27 689.2 35 666.3 31 673 18 682.7 32 650 20 670 23 673.3 34 653.7 33 673.4 34 661 31 649.2 34 659.9 31 651.6 30 640.7 32 641.8 29 636.7 30 627.2 30 631 29 626.8 30 620.1 30 617.5 32 610.5 38 610.1 35 575.7 20 579.1 33 579 24 550.5 25 551.9 33 562 23 1073809 FRESNO FIREBAUGH-LAS DELTAS UNIFIED 87.8371750858264 .405405405405405 1.21621621621622 90.4504504504505 32.4074074074074 10.3756097560976 51400.5555555556 4317.72837837838 20.4905660377359 30.8510638297872 0 0 629.51695945946 626.268102372035 615.682792207792 21.3207792207792 24.5274656679151 19.7959459459459 672.2 16 674.1 20 651.7 19 667 14 676.9 24 645.1 16 662.5 17 661.3 23 647.8 27 660.3 22 649.8 21 634.4 21 648.8 21 644.5 23 636.4 28 627.5 18 630.1 24 619.2 22 619.9 20 614.3 19 606.9 19 616.1 30 613.7 39 600.9 27 581 21 570.9 24 571 18 544.5 18 550.4 29 555.4 15 1062158 FRESNO FOWLER UNIFIED 60.5990783410138 7.19661335841957 .846660395108184 72.3424270931326 24.7619047619048 11.8363247863248 51537.3428571429 3807.78974600188 21.0700389105058 38.7931034482759 0 0 635.323164218959 638.899266177452 627.946421404682 32.0481605351171 36.1320880587058 25.084779706275 690 30 694.6 41 673 38 679.1 22 692.2 40 658.5 26 670.9 23 683 44 660.7 39 673.1 33 669.2 38 650.8 35 655.5 27 659.5 37 643.9 35 641.9 29 647.4 40 635.7 38 622 21 624.6 28 622.9 33 611.6 26 607.5 33 606.9 32 577.2 19 576.6 29 575.6 21 549.8 21 556 33 567.3 25 1062166 FRESNO FRESNO UNIFIED 62.0197740112994 19.6517667528081 11.3156615408234 45.2396182483433 23.4048481471162 14.6799561082663 61095.3050989134 4685.64291379884 22.2597299444003 27.4755927475593 0 31.1111111111111 632.640383670421 630.72546997266 623.040624146675 30.5068851180027 32.4933723013105 26.0484501837766 692 31 696.6 42 673.8 39 678.8 22 688.7 36 658.9 26 672.3 24 677.4 38 658.2 36 673.5 33 666 34 651.1 36 656.7 28 657 34 643.9 35 643.9 31 645.8 38 631.6 34 626.4 25 623.9 28 618.6 29 607.2 23 597.4 25 602.9 29 579.6 21 574.3 28 577.9 23 551.9 25 549.2 29 564.5 24 1075234 FRESNO GOLDEN PLAINS UNIFIED 86.545988258317 1.71370967741935 .201612903225806 92.2379032258065 26.0869565217391 14.5806603773585 62758.2608695652 5242.80040322581 21.7211328976035 19.1780821917808 0 0 617.92496382055 623.329073033708 614.588491779843 21.0793423874196 22.8026685393258 13.6685962373372 665.8 12 677.7 23 655.7 22 657.7 9 674.1 22 640.4 13 655.1 12 664.7 26 646.3 26 661.1 23 660.5 30 641.8 27 635.3 13 646.6 24 632.4 24 623 15 628.4 23 620.5 23 610.4 14 611.4 17 610.3 22 591.2 13 589.4 18 597 24 565.3 12 566.6 21 569.3 17 535.7 13 544.2 23 552.1 13 1073999 FRESNO KERMAN UNIFIED 69.4980694980695 5.35002845759818 .313033579965851 70.4325554923165 22.6415094339623 12.3231382978723 54546.0125786164 4283.10130904952 22.1542383683875 40 0 60 639.117610619469 631.208603832616 625.959092783505 27.9550515463918 27.4974579585452 24.4261061946903 680.9 21 682.1 27 662.2 28 668.7 15 676.4 24 649.9 19 668.4 21 670.5 32 654.5 33 673.2 33 663.2 32 645.7 30 661.4 33 659.3 36 646.3 38 641.3 28 641.6 34 627.5 30 630.1 28 619.5 23 620.2 30 607 22 592.9 21 599 25 574.7 17 571.6 25 577 22 552.3 23 539.2 20 563.8 22 1062265 FRESNO KINGS CANYON JOINT UNIFIED 63.1713244228433 1.40625 .600961538461539 71.3581730769231 16.7919799498747 14.4614893617021 55184.7769423559 4478.65733173077 22.2565194252262 16.7865707434053 0 6.25 638.653324854651 636.555282685512 628.19417703263 34.4696232197584 37.1314487632509 30.5952034883721 692.9 32 695.3 40 672.6 37 684.6 27 691.6 40 665.6 33 679.7 30 686.8 47 666.2 44 670.6 31 660.9 30 647.2 32 661.2 32 655.8 33 647.7 39 646.9 34 648.6 41 636.3 39 633.2 30 633.4 36 625.3 35 615 29 609.3 35 609 33 590.3 28 585.9 37 586.3 30 563 32 558.1 36 568 26 1062240 FRESNO KINGSBURG UNION 35.6033874382498 2.51875669882101 .37513397642015 67.7384780278671 7.91366906474819 15.3451612903226 54702.2225899281 6836.69390675241 21.1443530291698 41.5789473684211 71.4285714285714 0 659.55601965602 655.824398460058 646.9376953125 50.0771484375 50.7348411934552 45.3916461916462 684.7 25 690.8 36 667.3 32 685.3 27 692.4 41 660.8 28 682.4 32 689 50 667.3 45 696 55 677.3 46 669.6 55 683.5 54 672.6 50 662.9 57 663.8 51 660.4 53 651.2 54 654.3 51 643.1 46 641.3 51 637.9 50 630.8 56 634.8 57 614 48 613.3 63 611.8 53 597.7 62 589.2 66 606.2 68 1062281 FRESNO LATON JOINT UNIFIED 72.9166666666667 1.23873873873874 .563063063063063 70.045045045045 3.92156862745098 11.5576271186441 39728.3529411765 3899.13175675676 18.2365145228216 13.0434782608696 0 0 635.926148409894 633.431208053691 626.668181818182 29.2020202020202 27.7852348993289 22.6678445229682 677.3 19 683.7 29 659 25 673.8 18 674.7 22 655 23 662.3 17 668 29 653.2 31 663.5 24 654 24 644.3 29 656.1 27 652.4 30 646.5 38 640.5 28 642.2 35 631.5 34 628.4 26 630.6 33 620.1 30 603.8 20 595.4 22 593.5 21 581.9 22 570.6 24 580.3 25 556.2 26 553.8 31 574.4 33 1075127 FRESNO MENDOTA UNIFIED 87.7772534214252 .533462657613967 .5819592628516 97.7691561590689 40 12.2075268817204 60303.175 3933.77740058196 25.6375 47.1698113207547 0 0 622.616214335421 621.331699346405 613.684299191375 18.4973045822102 18.9797385620915 13.7035490605428 676.5 18 671.5 18 653.9 20 669 15 680.7 28 648 18 656.4 13 666.4 27 646.8 26 649.9 15 650.4 21 631.7 19 635.5 13 637.7 17 624.5 17 625.1 16 621.4 18 616.4 20 608.7 13 604.1 13 604.2 18 591.1 13 582.4 14 589.8 19 556.6 9 553.9 13 559.5 11 532.3 11 539 19 554.7 15 1062364 FRESNO PARLIER UNIFIED 91.604841858649 .214362272240086 .107181136120043 98.8210075026795 62.1848739495798 11.9275362318841 55527.2941176471 4223.12647374062 21.6865417376491 13.3858267716535 0 40 616.066551893753 620.616848599905 610.251985922574 19.1895424836601 22.1860465116279 13.9183472700443 672.7 16 681.9 26 651.7 19 660.9 11 675.8 23 642.5 14 653.9 12 665.1 26 643.9 24 652.1 17 651.2 22 636.9 23 637.6 14 642 21 626.7 19 630.3 20 637.5 30 624.3 27 611 14 612.6 18 606.3 19 588.5 12 589 18 591.7 20 562.6 11 560.4 16 561.7 12 535.6 13 545.9 24 554 14 1075408 FRESNO RIVERDALE JOINT UNIFIED 64.8507462686567 .66711140760507 3.06871247498332 64.5096731154103 14.9253731343284 11.3691780821918 47732.5671641791 3511.89993328886 21.4887218045113 10.6666666666667 0 0 644.658088235294 648.756526207606 634.010914760915 35.5135135135135 41.5817060637205 29.9044117647059 684 25 689.7 35 664.1 29 675.3 19 679.3 27 659.5 27 672.4 24 682.7 44 664.4 42 677.7 37 673.2 42 650.2 34 670.9 41 673.7 52 651.6 44 639.5 27 642.1 34 622.4 25 628.7 26 628.3 31 615.2 26 613 27 610.8 35 603.4 29 600.8 36 612.2 62 608.1 50 577.5 44 582.1 59 590.2 50 1062414 FRESNO SANGER UNIFIED 57.0024891916678 4.32291666666667 .5859375 70.6640625 23.4806629834254 14.0044289044289 52155.2569060773 4382.06119791667 21.7115330121848 23.0232558139535 0 0 637.416965285554 632.764367398802 627.134107534748 31.840160936357 30.8818297331639 26.3355729749907 684.5 24 688.6 34 664.3 29 677.5 21 688.4 36 655.2 23 668.7 21 676.6 37 655.4 34 675.1 35 662.4 31 654.5 39 659.7 30 653.5 31 645.4 37 646.6 33 642.3 35 637.1 39 631.3 28 625 28 625.4 35 609.5 24 596.3 23 608.1 33 584.5 23 575.5 28 580.4 25 553.5 24 548.4 27 566.1 24 1062430 FRESNO SELMA UNIFIED 69.6452036793693 3.97230320699708 1.02040816326531 76.7128279883382 27.6 13.0118794326241 53531.636 4180.03662536443 22.5010266940452 14.6919431279621 0 0 642.379013030219 638.60592632141 633.074566630553 38.6977248104009 38.217031500267 31.5431106182423 687.3 27 691.2 36 671.4 36 677.8 21 689.4 37 655.7 24 674.4 25 680.4 41 660.7 39 683.9 43 663.5 32 662.4 47 667.4 37 663.1 41 653.3 46 647.6 34 646.6 39 637.3 40 636.9 33 634.5 37 633 43 622.5 35 616.3 41 622.6 45 591.5 29 590.1 41 592.6 35 564 32 558.3 35 574.1 32 1075275 FRESNO SIERRA UNIFIED 21.604680317593 .540540540540541 .291060291060291 7.48440748440749 1.52671755725191 17.1124161073826 62522.8244274809 5879.9659043659 19.4851166532582 26.3736263736264 0 0 680.277309941521 669.70080552359 658.152347417841 51.9900234741784 53.2784810126582 53.2520467836257 711.1 51 707.9 55 683.2 49 701.1 43 698.3 48 673 40 700.3 50 692.4 54 673.5 52 702.6 62 689.3 59 677.1 63 691.9 62 677.3 56 666.5 61 669.9 57 666.6 59 650.9 55 661.6 57 653.6 57 644.7 55 646.7 58 620.3 45 631 54 627.6 60 606.6 57 615.6 57 579.7 46 566.6 44 586.4 46 1175481 GLENN ORLAND JOINT UNIFIED 44.9746621621622 1.34841235319704 .826446280991736 33.1883427577208 5.93220338983051 16.2532846715328 55653.8050847458 4602.90343627664 20.8553791887125 49.1935483870968 0 0 653.154290822408 643.173529411765 642.387649880096 45.0239808153477 39.0258823529412 39.0673420738975 703.1 43 699.9 47 688 54 687.7 29 690.1 38 669.3 36 687.7 37 687.2 49 673.3 51 682.9 42 671.7 41 666.3 52 667.7 38 654.9 32 657 50 651.7 39 645.4 38 646.8 50 639.5 36 625 28 623.7 34 633.9 46 611.1 36 623.7 46 605.6 41 590.4 41 594 37 572.7 40 560.9 38 580.8 40 1162661 GLENN WILLOWS UNIFIED 53.125 21.7522658610272 .906344410876133 20.7452165156093 4.65116279069767 15.7360824742268 60020.6627906977 4325.15357502518 24.4811320754717 47.1153846153846 0 0 652.248719723183 650.23700947226 643.737198067633 45.9889579020014 45.4945872801083 37.9148788927336 691.8 31 693.1 39 677.2 42 690.2 32 692.1 41 674.5 42 679.5 30 683.6 45 669.9 48 689.5 49 685.6 54 667.6 53 664.5 35 666.6 44 654 46 654.8 42 651.3 44 643.3 47 640.5 37 637.8 40 636.3 46 630.1 42 620.4 45 621 44 601.9 37 602 53 601.8 44 578.9 45 572.6 50 587.4 47 1275374 HUMBOLDT FERNDALE UNIFIED 11.7161716171617 .5 0 4.66666666666667 0 15.5121951219512 54645.6666666667 4893.85666666667 20.3215434083601 34.1463414634146 0 0 671.044444444444 664.697085201794 654.729306487696 57.5212527964206 59.7757847533632 55.0657596371882 718.1 59 723.3 72 689.6 56 712.5 55 711.6 63 692.2 60 698.7 48 703.4 66 668.9 47 698.4 58 693 62 676.2 62 694 63 695.4 73 672.1 67 668.4 56 671.7 65 651 55 661.4 58 656.1 60 655.5 65 640.2 52 611.8 37 632.9 55 620 53 606.1 55 609.5 50 576.4 43 565.7 42 591.7 53 1262901 HUMBOLDT KLAMATH-TRINITY JOINT UNIFIED 76.3212079615649 0 .65597667638484 2.84256559766764 30 14.7855421686747 65665.4714285714 5770.56559766764 19.6496350364964 25.9259259259259 0 0 647.671180124224 637.66 628.449749373434 33.7769423558897 36.3312883435583 34.6608695652174 684.3 24 691.1 37 660.4 26 683.6 26 689.4 37 656.8 24 674.3 25 681.1 42 655.3 34 683.1 42 678.6 47 661.6 47 676.2 46 670.1 47 658.5 52 650 37 646.1 38 629.6 32 637.3 34 628.7 31 617.1 28 631.9 44 603.1 29 614.1 38 599.6 36 583.4 35 590.9 34 557.8 27 544.6 23 561.2 20 1263040 HUMBOLDT SOUTHERN HUMBOLDT JOINT UNIFIE 33.9167169583585 .714749837556855 1.16959064327485 2.98895386614685 0 15.7926136363636 56055.9350649351 4427.87199480182 21.3154362416107 44.7058823529412 0 0 666.911310782241 645.515704154002 646.715384615385 48.0945945945946 39.0536980749747 49.9746300211417 715.8 57 707 55 692.5 59 709.5 51 691.3 40 681.4 49 693.9 43 688.8 50 668.7 47 693.2 53 660.6 30 656.8 41 673.1 43 657.6 35 657.8 50 672.8 60 656.2 49 653.5 58 652.4 48 632 34 634 44 646.3 57 616.6 41 631.5 53 614.1 48 576.9 29 599.2 42 578.7 45 554.2 32 582.4 41 1363073 IMPERIAL BRAWLEY UNION 54.2566709021601 .518806744487678 .277932184546971 80.2112284602557 35.042735042735 14.9565055762082 66530.2478632479 4304.7152121549 23.78075097 33.89830508 0 0 640.308263570078 636.234013245033 632.318937957193 35.1953400162558 32.2733774834437 28.2425060761545 688 28 684.8 30 668.7 33 682.4 25 684 31 661.9 29 674.2 25 676.8 37 658.1 36 671.3 32 660.1 29 651.3 36 658.3 29 656.3 34 646.7 38 647.1 34 648.9 41 638.9 41 632.7 30 628 31 627.8 38 611.5 26 602.9 28 618.7 42 585.2 24 575.4 27 585.1 28 561 30 556.7 34 574.1 33 1363099 IMPERIAL CALEXICO UNIFIED 43.954818017013 1.43290162579223 .0551116009920088 97.5199779553596 70.0996677740864 14.5877492877493 67370.0564784053 4266.61848994213 23.5719063545151 15.8256880733945 0 0 637.58567839196 641.629704962003 627.686793737236 24.8838211935557 28.0435851586947 18.5349474645957 674.8 17 684.6 30 657 23 666.5 13 681.6 29 648 18 665.1 18 675.4 36 653.7 32 662.4 24 658.6 28 643.7 29 645.1 19 647.2 25 635.2 26 632.7 21 635.1 28 625.9 28 621.3 21 622.2 25 613.4 25 598.1 17 598.7 25 598 24 571.7 16 572.5 25 573.9 20 549.8 21 546.7 25 561.1 20 1363107 IMPERIAL CALIPATRIA UNIFIED 74.3016759776536 .421940928270042 5.55555555555556 71.5893108298172 40.5797101449275 12.2170886075949 53519.7391304348 4518.24331926864 20.625 29.4117647058824 0 0 636.260303030303 641.081281281281 629.831552419355 32.9153225806452 35.8938938938939 24.4060606060606 680.7 21 679.3 24 661.7 27 666.9 14 678.7 26 648.1 18 665.8 19 672.9 34 656.8 35 676.1 36 669.9 39 655.9 41 658 29 657.7 34 651.2 43 635.4 24 642.6 35 630.5 33 623.4 22 627.8 30 624.6 35 605.7 22 613.3 38 611.1 35 593.5 30 605.5 56 592.3 35 554.7 25 563.8 41 565.6 24 1363123 IMPERIAL EL CENTRO UNION 62.1000820344545 1.55424308361828 2.94270023831727 82.6442855662626 33.4128878281623 15.2063025210084 66125.0906921241 4453.16423168584 23.3213859020311 31.3028764805415 0 0 646.318279404999 642.181461988304 635.553651897777 35.138363828822 34.3980994152047 28.9796043551603 687.7 27 686.7 32 668.1 33 680.1 23 682.8 30 656.5 24 675 26 676.6 37 658.3 36 671.6 32 660.7 30 651.1 36 656.6 28 654.7 32 645.5 37 649.6 36 653.1 45 639.8 42 629 26 627.6 30 623.4 33 617 31 609.2 34 618.3 41 591.7 29 583.8 35 589.7 33 569 36 562.3 39 580.7 39 1363149 IMPERIAL HOLTVILLE UNIFIED 63.9180409795103 .399002493765586 .149625935162095 70.4738154613466 26.8817204301075 11.6070093457944 56622.5698924731 4245.81097256858 21.6851441241685 32.1428571428571 0 0 646.915160142349 641.476949860724 635.499860432659 37.3028611304955 36.0898328690808 32.202846975089 694.8 34 691.8 38 671.9 37 684.5 27 687.4 35 657.8 25 678.1 29 681 42 661.6 40 665.8 27 652.6 23 645.8 30 650.7 23 644.3 22 639.3 30 653.6 41 644.9 37 640.5 43 640.6 37 634.2 37 634.5 44 621.9 35 604.3 30 621.7 45 591.5 29 590.9 42 594.6 37 575.8 43 580.2 57 584.4 44 1363164 IMPERIAL IMPERIAL UNIFIED 39.9445214979196 .749228735125606 2.68840899074482 60.7756721022477 24.5283018867924 9.22478260869565 51167.0283018868 3708.85940943147 20.8568738229755 34.9206349206349 0 0 648.104784978801 648.614979277679 637.713325401547 42.3599048185604 46.6820603907638 36.3301029678982 697 36 695.4 41 671.5 36 686.6 28 690.7 39 661.4 29 681.9 32 685.4 47 667.4 46 677.5 37 673 42 656.5 41 661.1 32 664.1 41 645.8 37 661.1 48 662.6 55 650 53 641.7 38 644.6 48 638.6 49 628.3 41 631.8 57 628.9 51 597.2 33 604.2 55 597 40 571 39 564.1 41 581.2 41 1363214 IMPERIAL SAN PASQUAL VALLEY UNIFIED 76.8278965129359 0 3.00578034682081 31.0982658959538 20.4081632653061 15.3185185185185 60141.0816326531 5355.16069364162 18.9917695473251 19.3548387096774 0 0 629.748180242634 614.521440536013 615.989964788732 20.7411971830986 16.5175879396985 20.155979202773 681.4 22 672 18 660.3 25 669.6 15 673.2 21 650.2 19 660.3 15 664.1 25 646.1 25 666.9 28 648.2 19 638.2 24 662.7 33 644.4 23 637.3 28 623.7 15 607.4 10 608.4 15 615.7 17 597.9 9 603.2 17 605.6 22 576.9 11 591.5 20 571.5 15 557.5 15 568.9 17 553.9 25 530.3 14 559.7 19 1463255 INYO BISHOP UNION 25.588491717524 .762388818297332 .508259212198221 11.0122829309615 5.45454545454545 16.5099173553719 59805.5454545455 4349.22151630665 23.4503510531595 40.7185628742515 0 0 665.129026548673 659.893040501997 647.360979827089 49.4184438040346 54.1928123217342 48.5286135693215 707.3 47 701.4 48 687.5 53 698.4 40 701 48 683.1 51 693.4 43 691.8 53 676.7 55 698 57 698.7 67 670.8 56 681 51 692 69 659.3 52 661.5 49 676.1 67 643.4 46 657.3 54 651.5 55 643.5 54 635.1 47 609.2 34 622.7 45 615 49 599.1 49 599.6 42 584 50 573.6 51 580.5 39 1563404 KERN DELANO UNION 68.6434302908726 .780814277746793 1.72894590072504 76.8878973786949 31.8181818181818 12.2116310160428 58861.6878787879 3714.92013385388 25.9909638554217 14.0350877192982 0 0 628.471576763485 630.4126899577 619.339649525057 22.7148706190632 27.0755130816231 16.9576417704011 677.2 19 685.1 30 660.5 26 666.8 14 680.2 28 644.8 15 661.6 16 672.3 33 649.1 28 655.4 19 658.3 27 638 24 643 18 650.9 28 631.8 23 631.7 21 639.6 32 625.9 28 615.6 17 619.6 24 613.2 24 593.1 14 590.2 19 594.6 22 565.4 13 565.1 20 570.9 18 549.1 21 550.2 29 560 19 1575168 KERN EL TEJON UNIFIED 37.8320172290022 .3584229390681 .860215053763441 13.6917562724014 8.33333333333334 10.3814285714286 55942.0666666667 4098.99426523297 24.9217391304348 0 0 0 656.297061704212 648.630488974113 642.803458213257 46.7867435158501 45.2895493767977 42.8873653281097 707.9 47 705.7 53 686 52 698.9 40 700.2 49 679.6 47 694.8 44 697.2 59 675.1 54 693.1 53 684.1 53 661.9 47 676.8 47 671.8 50 658.3 51 650.5 37 646.7 39 638.7 41 645.3 41 637.5 40 636.6 46 629.3 41 604.9 30 622.5 45 602.6 38 584.6 36 592.8 36 575.2 43 569.9 47 589.5 50 1573908 KERN MCFARLAND UNIFIED 81.9645732689211 .311526479750779 .233644859813084 92.0171339563863 31.8965517241379 13.1324626865672 55369.8620689655 4428.04595015576 22.5085616438356 23.6842105263158 0 0 624.363516609393 624.61632196758 615.951785714286 21.5478110599078 22.5846841811068 16.9203894616266 669 13 672.7 18 651.7 19 669.7 15 674.8 22 645.5 16 663.4 17 668.3 29 651 30 653.2 18 651.9 22 634.3 21 638 15 642.5 21 625.4 18 632.8 21 631 25 624.7 27 615.8 17 616.2 20 608.2 20 603.5 20 598.5 25 601.3 27 568.4 14 565.9 20 571.7 19 543.9 18 544.5 23 558.9 18 1563677 KERN MOJAVE UNIFIED 40.5990016638935 1.1070110701107 14.8708487084871 24.5387453874539 7.62711864406779 15.2442748091603 63042.2033898305 4572.61512915129 24.419983065199 32.484076433121 0 37.5 640.803693644758 630.078511087645 628.075648491265 34.137638962414 30.8104540654699 31.2036936447583 687.6 27 688.2 33 669.8 35 685.8 28 687.2 35 660 27 683 33 684.2 45 664.8 43 676.1 36 660.7 30 649.2 34 667.4 37 654.7 32 650.2 42 649.8 37 644.8 37 635.4 38 635.3 32 624.6 28 623.3 33 618.3 32 602.3 28 612.7 36 587.4 26 576.4 28 586.3 30 552.6 23 535.8 17 567.4 25 1563685 KERN MUROC JOINT UNIFIED 31.8604651162791 2.01472297559086 12.4370399070128 7.47772181325068 9.84848484848484 15.3266666666667 63498 5767.59356838435 20.3072196620584 32.8 0 0 663.702340772999 654.100107469103 645.626877682404 53.1512875536481 56.0972595378829 54.5666848121938 711.2 51 703.1 50 686.6 52 699.3 41 696.1 45 667.9 35 700.7 50 694.8 56 672.3 50 693.2 53 680 49 658.7 43 685.7 56 674.6 52 661 54 673.7 61 670.5 63 656.7 61 658.1 54 651 55 647.2 57 648.5 59 630.2 55 636.4 58 624.5 57 613.3 63 616.1 57 593.6 58 588.4 65 595.2 57 1573742 KERN SIERRA SANDS UNIFIED 32.5987279988168 2.2334864565183 4.79961983209251 10.898146681451 5.62913907284768 14.3510174418605 62453.1456953642 4537.56914303818 22.0415688903788 38.6627906976744 0 0 662.506528451698 650.898504875406 647.242869565218 51.0482608695652 47.435752979415 49.0284516982797 704.5 44 708.1 54 685.5 51 701 43 699.9 49 680.9 48 695 44 694.2 56 675.8 54 692.7 52 678.2 47 661.1 46 683.2 54 668.7 46 665 58 661.3 48 651 43 644.1 47 656.3 53 638.7 41 641.8 52 639.9 51 618.4 43 628.6 51 616.6 50 599.3 50 608.6 50 585.1 51 569.4 46 593 54 1563776 KERN SOUTHERN KERN UNIFIED 49.3510324483776 1.697438951757 8.21917808219178 31.9833234067898 9.45945945945947 13.0842592592593 58159.2027027027 4284.44460988684 23.4270047978067 15.4929577464789 0 33.3333333333333 648.160764044944 638.358244680851 633.247085002225 39.1441922563418 38.2047872340426 38.645393258427 698.4 38 690.8 36 679.3 44 693.3 35 690.6 39 668.8 36 681.1 31 682.2 43 664.3 42 684 44 670.8 39 653.6 38 673 43 661.5 39 652.7 45 662 49 656.4 49 644.3 47 645.3 41 633.4 36 630.7 41 621.8 35 605 30 615.9 39 596.9 33 583.4 35 588.3 32 569.6 37 560.1 37 572.8 31 1563800 KERN TAFT UNION 51.4623726585606 .361247947454844 .755336617405583 17.7668308702791 2.73972602739725 14.4369696969697 62633.095890411 5763.70114942529 21.0565780504431 17.7914110429448 0 0 644.816746411483 636.865050784857 627.733364355514 32.1526291298278 34.4307479224377 32.4698564593301 689.6 29 688.6 34 664.6 30 684.7 27 686.6 34 659 26 678.6 29 680.4 41 655.6 34 678.4 38 667.5 36 653 38 667 37 657.6 35 644.8 36 647.2 34 641.7 34 629.8 32 637.3 34 623.8 27 623.7 34 620.5 34 605.5 31 607.7 32 595.2 32 587 38 591.3 34 563.9 32 557 34 569.8 28 1563826 KERN TEHACHAPI UNIFIED 24.9950445986125 .42042042042042 2.72272272272272 17.3973973973974 4.52488687782805 14.79 60455.0904977376 4308.12812812813 22.8716528162512 29.7297297297297 0 0 664.144418872267 649.835591306802 645.632324660634 50.2760180995475 47.4959074230878 51.5356731875719 704.6 44 696.8 43 679.8 45 702.7 44 695.4 44 675.3 42 692.5 42 689.5 51 671.1 49 700.8 60 683.8 52 671.2 57 691 61 676.9 55 666.3 61 671.3 59 669 61 653.1 57 659.5 56 646.1 49 643.4 54 639.3 51 613.2 38 626.2 49 612.9 47 592.7 43 602.5 44 584 50 562.5 40 586 45 1563842 KERN WASCO UNION 65.8902691511387 .471815247082195 4.39533151229203 78.9173081698535 21.1009174311927 14.93269231 61803.9024390244 4139.93667742737 24.5117428924598 14.0151515151515 0 0 633.587433561124 631.382788990826 624.948731343284 27.0694029850746 25.8278899082569 20.7463933181473 679.6 21 680.3 25 666.2 31 673.9 18 679.5 27 658.3 26 663.8 18 672.7 33 657.2 35 667.7 28 657.5 27 642.2 27 655.2 27 656.4 34 641.3 33 637 25 635.6 29 631.3 33 621.8 21 617.8 22 616.3 27 602 19 590.4 19 601.3 27 575.4 18 570.1 23 571.3 18 540.1 15 539.3 19 553 14 1663891 KINGS CORCORAN JOINT UNIFIED 64.279183175861 .463821892393321 4.05071119356834 79.3753865182437 17.3611111111111 15.3154545454545 66404.1944444444 4605.86147186147 22.6763485477178 15.5844155844156 0 0 638.988273615635 633.939674152356 626.044679891795 29.0036068530207 29.4297666226332 25.7328990228013 678.1 19 683 28 663.7 29 671.3 16 681.1 28 651.4 20 666.9 20 674.1 35 654.7 33 672.1 32 662.2 31 651.2 36 660.4 31 652.7 30 639.9 31 646.7 34 649.6 42 634 36 628.9 26 616.1 20 614 25 607.8 23 595 22 604.6 30 592.1 30 580.1 31 584.4 28 561.2 30 552.5 30 567.8 26 1673932 KINGS REEF-SUNSET UNIFIED 86.4936207655081 0 .734094616639478 89.9673735725938 15.5963302752294 11.0606557377049 57641.5688073395 4543.49225122349 21.7527675276753 26.1904761904762 0 0 628.006722054381 614.202327044025 615.965977175464 19.9144079885877 16.6194968553459 16.5672205438066 671.1 15 672.3 19 652.6 19 661.4 11 669.5 18 643.8 15 659.7 15 663.4 24 644.7 24 659.5 22 650.5 21 637.1 23 645.6 19 637.8 17 634.2 25 626.4 17 617.3 15 615.5 19 619 19 607 14 606.4 19 597 16 584.5 15 593.9 21 559.1 10 551.5 12 561.8 13 547.8 20 528.6 13 558.6 18 1764014 LAKE KELSEYVILLE UNIFIED 45.5701953657428 .954198473282443 1.33587786259542 22.0896946564885 7.20720720720721 14.7578125 54040.6036036036 4832.31965648855 20.0833333333333 50.9433962264151 0 0 661.984046164291 654.591859695566 646.073990734613 48.5221707478491 49.3653209794838 46.0855397148676 701.9 41 696.4 42 679.7 45 694.1 36 697.2 46 674.5 42 692 41 689.5 51 673.1 51 696.1 55 682.8 52 675.9 60 673.1 43 662.8 40 655.7 48 668.8 56 667.2 59 655.9 60 651.8 48 648 51 636.7 47 642.5 53 626.2 51 627.2 50 605.6 40 597.3 48 594.3 37 583.2 49 575.4 53 584.8 45 1764022 LAKE KONOCTI UNIFIED 73.6089996959562 .829610721123165 5.96681557115507 9.60433950223357 6.32911392405063 13.7825 54439.9493670886 4354.3876834716 20.6129032258065 10.6060606060606 0 100 638.266855791962 624.112023328847 621.180950205573 28.9310187300137 28.0960071781068 31.0657210401891 696.7 36 691.8 39 673 38 687.6 30 684.4 34 662.3 30 678.4 30 677.7 39 657.4 37 674.2 34 660.2 30 644.9 30 655.3 28 647.7 26 633.3 25 649.5 37 641.5 35 625.4 28 635.7 33 615.7 21 617.2 28 617.9 32 591.2 21 604.2 30 585.7 27 563.7 21 578.6 24 552.7 27 541.7 24 563.5 25 1764030 LAKE LAKEPORT UNIFIED 46.2952326249282 .659703133589885 1.86915887850467 15.6679494227598 3.44827586206897 15.1313131313131 58962.1379310345 4361.36118746564 21.4170506912442 28.4210526315789 0 0 658.686214953271 647.881014604151 644.126870229008 48.1656488549618 45.1775557263643 45.417445482866 707.7 47 699.9 47 683.6 49 694.7 36 697 46 668.8 36 703 52 699.2 61 680.4 58 694.9 54 691.5 60 669.6 55 683.4 52 676.7 54 666.4 59 662.4 49 656.7 48 647.5 50 647 42 632.2 34 636.4 47 626.6 38 609.2 34 624.3 46 611.3 44 591.8 41 603.4 44 574.7 40 553.3 30 580.4 39 1764055 LAKE MIDDLETOWN UNIFIED 26.7957526545909 .723763570566948 .361881785283474 8.68516284680338 1.20481927710844 11.2951612903226 50096.4096385542 3932.38962605549 19.1504854368932 40.6976744186047 0 0 663.322495755518 657.100756938604 648.737091222031 52.0542168674699 52.7628259041211 48.4261460101868 701.7 41 705.9 53 681.2 47 695.3 37 698.3 47 670.4 37 693.1 42 698.8 61 672.8 50 696.2 55 692.1 61 674.5 60 679.8 50 669.1 47 663.3 57 667.8 55 670.5 62 655.6 60 648.6 45 642.9 46 639.5 50 643.8 55 621 45 634.7 57 618.4 52 599.4 50 606.5 48 586.1 52 580.5 58 594.3 56 1764063 LAKE UPPER LAKE UNION 52.9170931422723 1.7329255861366 2.85423037716616 8.25688073394496 6.25 14.9870689655172 59995.3958333333 5022.53312945974 21.8995633187773 37.7049180327869 0 0 656.359604519774 651.16495132128 638.096332863188 37.3497884344147 41.8817802503477 37.9901129943503 705.2 45 696.9 44 684.8 50 698.5 40 696 44 673.7 41 682.6 33 683.8 45 665 43 689.6 49 671.7 40 656.7 41 660.3 31 649.2 27 636.2 27 648 35 651.7 42 632.1 34 646.9 43 643 46 629.4 39 620.2 33 609 34 612 36 608.1 43 602.7 53 586.7 30 559.6 29 561.6 39 568.6 27 1864204 LASSEN WESTWOOD UNIFIED 41.970802919708 0 .571428571428571 9.14285714285714 3.03030303030303 17.9042857142857 55176.8484848485 5259.9580952381 18.9655172413793 18.1818181818182 0 0 652.683421052632 641.202067183463 631.90182767624 34.4229765013055 36.3927648578811 38.3631578947368 701.6 41 695.7 41 675.2 40 690.8 32 692.5 41 664.6 31 676.3 27 675.3 36 657.4 35 681.2 41 662.2 31 653.5 38 669.5 40 665 42 648.2 40 659.2 46 655.3 48 634.9 37 639.1 35 630.4 33 622.4 32 627.1 40 600.7 27 608.6 33 598.9 35 577.9 30 584.1 28 580.6 47 560.4 38 572.6 31 1964212 LOS ANGELES ABC UNIFIED 30.5055227095651 32.4654190398698 10.4014103607269 32.6597956785101 36.0040567951318 15.2575630252101 59289.0862068966 4219.66476810415 22.576788291074 49.7326203208556 0 3.33333333333333 659.923843327729 663.76048998045 650.499602854484 52.5440273037543 57.6390518084067 44.8664923096083 705.6 45 717.5 63 688.2 54 697 39 712.7 61 678.8 46 691.2 41 703.8 64 677.2 55 691.7 51 693.7 61 671.3 56 682.4 53 689.5 65 668.6 62 663.8 51 670.7 61 653.7 57 650.4 47 650.8 54 643.9 54 632.2 44 623.3 47 627.7 50 603.7 38 600.8 51 605 47 574.9 41 572.3 49 586.4 45 1975309 LOS ANGELES ACTON-AGUA DULCE UNIFIED 28.1723484848485 1.44320297951583 1.72253258845438 11.9180633147114 7.44680851063831 11.7280373831776 58880.170212766 3806.89338919926 24.8222222222222 0 0 0 663.988473520249 652.433478802993 652.670828105395 58.8782936010038 52.9339152119701 53.6859813084112 702.1 41 692.8 38 687.4 53 697 39 689.3 38 681.1 49 688.2 38 689.1 50 672.5 50 700.6 60 683.6 53 679.8 65 692.5 62 674.7 53 677.9 72 671.8 59 674.6 66 657.7 62 659.5 56 650.6 54 646 56 645 56 628.8 54 635.7 58 622.1 55 608.8 59 615.8 57 591.4 57 574.6 52 597.1 59 1964261 LOS ANGELES ARCADIA UNIFIED 8.36221352711012 52.593956460522 1.21304018195603 9.88844362612369 8.90052356020942 15.9820135746606 64415.4659685864 4166.21780569696 24.2746044515956 60.840108401084 0 27.2727272727273 682.071046962516 691.294912131519 676.073383867277 73.9323512585812 77.8511904761905 62.3396524486572 717 58 740.3 82 706 71 710.2 53 725.7 73 700.4 68 704.6 54 727.1 83 700.6 76 705.7 65 719.7 82 688.2 72 694.3 64 712.9 83 684.2 76 681.7 69 701.8 85 674.4 76 673 68 678.1 79 671.8 79 658.6 68 643.9 67 658.6 76 632.3 63 622.9 71 635.7 74 604.3 67 594.5 71 613.1 74 1964279 LOS ANGELES AZUSA UNIFIED 70.7382666782337 .959561343385881 3.15284441398218 78.9410555174777 25.9557344064386 14.4988495575221 64611.0342052314 4379.24306031528 23.9818631492168 19.4244604316547 0 11.1111111111111 630.515060402685 627.717457773394 619.018762369706 25.7844042749703 29.3741832079892 22.5122147651007 679 20 682.9 28 659.9 25 670.8 16 678.6 26 650.7 20 668.8 21 671.4 32 653.6 32 666.7 27 661.6 30 639.9 25 653.1 25 654.4 32 636.1 27 638.8 26 637.2 30 623.3 26 625.7 24 625.9 29 616.9 28 604.6 21 600.2 26 599.9 26 578.3 20 575.9 28 577.1 22 552.8 23 554.4 32 567.9 26 1964287 LOS ANGELES BALDWIN PARK UNIFIED 62.871681687205 4.72375029897154 1.79382922745755 85.4699832575939 27.212020033389 15.062106017192 67839.958263773 3819.11803396317 27.5054157640393 26.7716535433071 0 0 627.079255415984 625.502389252614 620.852864742304 28.1941222638877 26.5887254485163 21.1458219552157 680 21 683.3 28 663.7 29 667.7 14 675.8 23 652.8 21 664.8 18 668.8 30 655.5 34 671 31 663.1 32 650 35 656.1 27 653 30 643.7 35 642.2 29 645.7 38 634.4 37 621.9 21 621.8 25 620.2 30 603.9 21 596.1 23 605.4 30 571.2 15 568.8 22 573.2 20 542.6 17 537.9 19 556.9 16 1964295 LOS ANGELES BASSETT UNIFIED 79.6765957446809 2.10292357667977 2.10292357667977 89.1434433236451 45.6 14.3998207885305 62084.608 4432.06496837066 23.5596625150663 20.9876543209877 0 0 625.112745604964 627.803804077573 616.408769269649 23.1238311852413 26.8254599701641 18.82316442606 673.1 16 675.6 21 657.1 23 663 12 675.2 23 646.5 17 659.5 15 670.5 31 647.6 27 662.1 24 661.8 31 638.2 24 645 19 651.5 29 631.1 23 636.6 24 638.3 31 625 27 618.6 19 622.2 25 612.7 24 602.1 19 598.8 25 600.2 26 575.8 18 574.6 27 574.1 20 546.3 19 545.7 24 559.9 19 1964303 LOS ANGELES BELLFLOWER UNIFIED 49.1721460825477 5.57544757033248 18.1585677749361 38.4800876872488 12.2743682310469 13.0422764227642 58550.5216606498 3988.18260869565 23.8852218555189 17.9972936400541 0 7.14285714285714 641.814845076401 641.600951888257 632.726298875201 38.4131762185324 41.0006207966891 32.1771010186757 686.5 27 686.6 32 668.3 33 679.8 23 683.6 31 659.3 27 678.5 29 678.8 40 661.4 39 670.8 31 664.6 33 650 34 661.9 32 662 39 653.5 46 651.9 39 657.3 49 640.7 43 637.8 34 637.7 41 630.3 40 623.9 37 620.1 45 621.7 45 596.9 33 595.5 46 594.4 37 566.6 34 570.3 48 580 38 1964311 LOS ANGELES BEVERLY HILLS UNIFIED 9.73348783314021 10.9398496240602 3.57142857142857 4.09774436090226 10.8196721311475 18.2 62455.7573770492 6015.75751879699 17.7246909455396 61.8843683083512 0 0 690.567250257466 694.90896250642 681.280658436214 76.3996913580247 79.1928608115049 67.2659629248198 720.3 61 735.6 80 706 71 714.3 57 729.2 77 703.7 71 711.4 61 723.6 81 703.3 78 712.5 71 714.3 80 699.6 81 704.1 73 711.3 84 694.6 85 683.8 71 689.9 78 669.6 73 677.2 72 676.5 78 670.5 78 669.1 76 654.5 77 659.4 77 641 70 632.6 78 637 75 611.2 72 603.4 77 616.6 77 1964329 LOS ANGELES BONITA UNIFIED 25.843945825753 5.86600496277916 4.82382133995037 27.5831265508685 9.50118764845605 16.8920124481328 62021.7553444181 4054.13568238213 24.1142443962401 51.764705882353 0 0 663.099746396156 658.021031171906 650.03186929488 52.8662521497553 53.0515585952913 48.306727175654 706 46 704.3 51 683.8 49 699.9 42 698.4 47 678.1 45 694.5 44 694 56 677.8 56 692 51 684.9 53 669.1 54 680 50 678.1 56 663.6 57 666.2 54 669.3 61 652.6 56 653.9 50 647.7 51 643.3 54 637.5 49 623.3 48 629.2 52 614.2 48 601.5 52 606.9 49 582.9 49 577.9 55 595.2 56 1964337 LOS ANGELES BURBANK UNIFIED 37.6797976147452 5.6881243063263 2.77469478357381 36.9589345172031 13.1666666666667 14.4693832599119 62400.435 4138.19589345172 23.9576629974598 32.4290998766954 0 5.26315789473684 655.695169224715 652.230417919131 645.026701161769 49.5026847603241 49.3065063512072 43.0069854388036 701.1 40 701.4 48 682.2 47 694.7 36 701.4 50 675.9 43 684.1 34 687.9 49 667.8 46 688.5 48 678.8 47 668.1 53 676.8 47 668.2 46 662.2 56 661.1 48 663.3 55 649.3 53 651.1 47 645.2 48 643.4 54 636.1 48 627.9 53 629.6 52 605 40 596.6 47 600 42 575.3 42 573.2 50 588.4 48 1964378 LOS ANGELES CHARTER OAK UNIFIED 23.9477040816327 5.26555386949924 4.87101669195751 36.6160849772382 11.7647058823529 15.3225396825397 61534.6654411765 4024.87496206373 24.1229724632214 38.7254901960784 0 0 655.798924731183 648.840342904359 640.007804980122 44.9202762084118 47.0877917785582 44.1773139363272 704.8 44 699.6 46 679 44 697.8 39 699.4 49 671 38 693.9 43 694.8 57 669.7 48 693.7 53 680.1 49 669.2 54 680.8 51 674.1 52 658.7 52 661.1 48 659.9 52 643.7 47 646.8 43 638.3 41 633.1 43 630.3 42 620.3 44 621.6 45 603.3 39 590.3 41 594.3 37 574.6 41 565.4 42 582.4 42 1964394 LOS ANGELES CLAREMONT UNIFIED 20.8070229477899 10.1118500604595 12.0012091898428 20.8736396614268 11.7088607594937 13.9077464788732 61447.6582278481 4401.14782345828 21.542025148908 53.1697341513292 0 0 676.104095197256 668.467728327357 659.145744680851 59.1142553191489 59.8346340434508 57.3855060034305 718.3 59 724.6 70 695.3 61 713.2 56 716.2 66 691.2 59 702.4 52 709.3 70 682.9 60 702.2 61 699.9 68 680.5 66 685.8 56 686.1 64 669.1 63 680 67 672.9 64 662 66 664.9 61 646.3 50 649.6 59 648.1 59 622.8 47 630.7 53 622.2 55 594.2 45 611.5 53 582.5 48 568.8 46 588.6 49 1973437 LOS ANGELES COMPTON UNIFIED 78.4239149752959 .0545386372158026 35.7296247060027 62.9273613525582 80.1749271137026 14.7931484502447 58991.4207968902 3743.12516617241 28.0999707687811 41.7890520694259 0 2.56410256410256 612.667656386702 613.706413351527 605.890224260388 19.7304401319837 22.4384906056471 16.2775590551181 667.5 13 672.3 19 651.7 19 660.6 11 671.3 20 642.6 14 653.1 12 660.1 22 643.7 23 659 21 651.7 22 635.9 22 638 15 640.9 20 627.9 20 625.4 16 627.8 22 617.2 21 614.7 16 617.3 21 606.2 19 594.6 15 590.3 19 593.5 21 570.1 15 570.7 24 573.2 20 550 22 551.7 30 558.5 17 1964436 LOS ANGELES COVINA-VALLEY UNIFIED 37.6449529146237 8.54844606946984 5.79890310786106 50.8299817184644 14.2599277978339 13.9004615384615 62290.0270758123 4265.80702010969 24.2564009442528 42.0844327176781 0 0 653.860152895591 650.312752021288 641.89274360033 45.409372419488 46.8560024562481 40.6060320452403 701.5 41 701.1 48 680.3 45 691.6 34 692.5 42 669.9 37 684.8 35 687.6 49 667.8 47 687.3 47 680.2 49 661.1 46 672.2 43 669.4 47 653.3 46 657.4 44 658.3 51 645.5 49 644.3 41 641.4 44 637.2 47 631.7 44 620.7 45 625.1 48 603 38 598.8 50 602.2 44 572.7 40 566.4 44 585 45 1964444 LOS ANGELES CULVER CITY UNIFIED 33.5116818262886 10.2023749790935 17.9126944305068 36.8121759491554 18.6507936507936 15.3850174216028 62132.0198412699 4282.61247700284 22.9572925060435 41.1764705882353 0 0 659.061115169223 649.806527353839 644.15641634981 46.8624049429658 44.7816388823668 44.1195519844169 706 46 702.8 49 685 50 694.6 36 695.1 43 672.5 39 684.4 34 687.6 49 668.8 47 688.1 47 673.5 41 663.6 48 682.6 52 669.4 46 664.7 58 665.5 53 649.4 42 648.3 52 654 50 647.1 50 641.8 52 636.8 48 617.9 42 625.4 48 607.1 42 592.2 43 598.2 40 570.8 38 565.6 43 579.2 37 1964451 LOS ANGELES DOWNEY UNIFIED 42.8409459021704 5.5955762987013 4.8041801948052 63.3370535714286 14.5994832041344 12.2934807256236 64631.9341085271 3979.21940949675 25.1415032249572 23.2673267326733 0 0 651.33894611136 648.686241487882 645.34675671664 49.2248775419326 45.3423152961851 38.2581728616211 698.1 37 698.8 45 678.8 44 685.8 28 692 40 668.1 35 678.9 29 683.5 45 665.7 44 687.9 47 676.4 45 668.5 54 672.8 43 667.4 45 665.5 59 656.3 43 656.3 48 653.9 57 646.4 43 646.2 49 647 57 627.9 40 619.3 44 629.8 52 600.1 36 593.8 44 601.3 43 570.9 38 571.1 48 587.3 47 1964469 LOS ANGELES DUARTE UNIFIED 61.4000866926745 2.77597050531338 13.2075471698113 61.9605291693776 30 16.0684210526316 59303.7388888889 4179.69811320755 25.2252747252747 15.0159744408946 0 0 634.506660104987 631.105498721228 626.154217262882 33.6727929110601 32.9437340153453 27.7286745406824 679.6 21 685.1 30 664.3 29 669.8 16 679.6 27 651.7 20 669.4 22 677.7 39 656.4 35 671.7 32 664.7 33 649.7 34 662.8 33 654.5 32 646.9 39 650.7 37 646 38 639.5 42 632.9 30 629.2 32 625 35 616.1 30 609.9 35 616.6 40 584.7 24 581.7 33 586.2 30 557.7 27 551.2 29 569.6 28 1964527 LOS ANGELES EL RANCHO UNIFIED 68.0851063829787 .683526999316473 .580997949419002 94.4805194805195 51.8145161290323 16.2742753623188 65653 4338.24307928913 22.4950337703615 33.6700336700337 0 0 636.533907380608 629.92565662151 624.336384276997 28.9841067120761 28.1802598838817 25.4157742402316 682.5 23 684.1 29 667.2 32 673.8 18 684.4 32 656 24 669.6 22 676.7 37 659.1 37 668.9 29 658.3 28 646.5 31 653.9 25 646.9 25 635.3 27 640.3 28 635.3 28 624.4 27 628.2 26 620.6 24 617.6 28 609.2 24 595.8 23 602.6 28 589.8 28 576.1 28 585 29 560.8 30 550.6 29 570.1 28 1964535 LOS ANGELES EL SEGUNDO UNIFIED 13.8000809388911 6.32078918523931 3.39788089148703 14.8702959444647 4.76190476190477 11.9276595744681 57362.0476190476 4718.11472415053 21.2887438825449 38.9937106918239 0 0 677.041884280594 669.538985579314 659.628335832084 62.2778610694653 64.9607160616609 60.9467485919099 710.2 50 710.8 59 689.9 56 711.2 54 707.5 59 690.9 59 707.1 57 708.1 69 689.6 68 702.7 62 689.7 59 674.6 60 688.8 59 682.9 61 661.5 55 674.7 62 680.5 71 653.3 57 664.6 61 660.4 66 653.1 64 662.9 72 643.4 71 645.3 68 631.9 67 609.9 63 623 66 601.8 69 589.1 72 605.9 70 1964568 LOS ANGELES GLENDALE UNIFIED 50.674017547988 12.1272365805169 1.11994698475812 23.8667992047714 12.2395833333333 13.2210855949896 73039.0052083333 4224.93667992048 26.6702033598585 26.3865546218487 0 34.4827586206897 654.253990819555 657.112164532538 649.081694134326 52.2113680666312 53.7901683915103 40.357190605642 695.7 35 706.9 54 683 48 689.8 32 701.5 54 676.9 44 684.7 35 695.4 57 680.3 59 687.2 47 688.7 57 669.8 55 675.2 47 679.9 58 664.9 59 658 45 667.3 60 654.4 58 645.4 42 645.8 51 644.8 55 631.1 44 619.6 48 629.8 54 598.4 37 592.5 46 598.2 42 567.6 39 569.5 52 583.9 47 1964576 LOS ANGELES GLENDORA UNIFIED 14.826244465316 4.1191381495564 1.29277566539924 16.5652724968314 6.32911392405063 14.9926553672316 63784.6075949367 4130.34993662864 24.900641025641 33.6 0 0 669.393686181076 664.820381845587 655.879660447134 58.4019162884518 59.4938871210853 53.6786929884275 704.3 44 712.6 59 687.7 54 698.2 40 705.6 55 678.2 45 693.5 43 700.1 62 678.9 57 700.3 59 689.1 58 673.6 59 691.2 61 680.9 59 671.1 65 673.1 61 668.8 61 656.8 61 663.4 59 653.1 57 650.6 61 649.8 61 635.1 60 639.1 61 624.5 57 611.1 61 616.7 58 588.1 54 585.3 63 602 64 1973445 LOS ANGELES HACIENDA LA PUENTE UNIFIED 40.2360661714442 16.3999470969448 2.53934664726888 67.9760172816647 28.9036544850498 17.3935658153242 62325.3034330011 4103.13891460565 25.056066382597 38.6784850926672 0 0 642.964292922922 641.584377276038 632.63471999011 36.6834590184201 38.4453143966982 31.0369622808124 690.4 30 696 41 673.7 39 682.7 25 694.4 42 664.8 32 678.5 29 685.9 46 666.3 44 677.9 37 675 43 654.9 39 665.3 35 664.5 41 649.3 41 650.1 37 646.5 38 636.6 39 634.6 31 630.9 33 626.8 37 616.4 30 605.7 31 612 36 585.6 24 579 30 585.4 29 563.2 32 563.5 41 573.9 32 1964634 LOS ANGELES INGLEWOOD UNIFIED 69.0082898372736 .192554557124519 43.0913758898355 55.3681876531684 63.4390651085142 15.0198263386397 63040.9899833055 3748.32979344148 27.4027459954233 38.8888888888889 0 57.8947368421053 634.693625077045 632.165754127812 627.247653302921 35.6359329765769 35.4114124390453 29.0958879985912 676.7 18 675 21 659.8 25 668.1 14 674.2 22 649.1 18 662.9 17 664 25 649.5 28 670.1 30 658.6 28 647.9 33 654.3 26 648.3 26 642.8 34 643.1 30 642.5 35 633.7 36 639.9 36 640.3 43 636 46 617.4 31 612.5 37 616.4 40 595.7 32 596.3 47 598.9 41 574.3 41 573.3 50 580.8 39 1964659 LOS ANGELES LA CANADA UNIFIED 1.4218009478673 26.2005649717514 .541431261770245 3.06026365348399 8.20512820512821 15.0257918552036 63791.6307692308 4705.50564971751 21.5962441314554 66.1818181818182 0 0 695.106828057108 694.118644067797 679.942095416277 79.1699407545993 82.4656394453005 76.5555555555556 730.6 71 743.4 83 707.6 73 727.2 70 737.4 81 711.8 77 723.5 71 731.8 85 708.9 81 723.5 79 721.1 83 705 84 712.6 80 717.6 86 694.3 85 694.9 80 706.8 88 671.9 75 688 81 685.5 84 673.3 80 674.9 80 656 78 659.6 77 651 77 633.7 80 641.4 78 617.2 77 600.6 76 622.3 82 1964683 LOS ANGELES LAS VIRGENES UNIFIED 2.97174111212397 7.57133035407357 1.36644895152974 4.97593674802338 7.02479338842976 17.0070127504554 64749.8450413223 4414.05010312822 24.2391304347826 60.6232294617564 0 0 684.553328569727 678.410719754977 672.994556044217 75.3633662189469 73.8972788314289 70.318566154579 722.7 64 725.1 72 711.1 76 720.2 64 719.3 71 705.2 72 714.6 65 718.2 78 699.3 76 714.3 73 710 77 695 78 707.4 77 707.9 82 691.4 83 687.8 75 693.7 82 674.1 77 681.9 76 672.3 75 670.8 78 668.3 76 646.9 71 655.8 75 639.7 70 624.1 73 632.9 72 595.7 61 578.9 57 604 66 1964725 LOS ANGELES LONG BEACH UNIFIED 64.2386984600099 14.166317455883 20.3368720026074 40.4898263258369 29.1087489779231 13.3097951495173 59298.1777050968 4210.30880709596 22.9831165236645 41.3782252989302 2.32558139534884 19.7674418604651 639.333896392546 637.248315019538 631.351391051242 37.6159378596087 37.9077018135667 30.8294580270132 693 32 695.4 41 674.2 39 684.9 27 691.7 40 668.3 35 679.6 30 687 48 668.5 47 677.2 37 668.7 37 654.8 39 661.8 32 658.1 35 649.4 41 645.6 33 645.7 38 635.1 37 634.1 31 632 35 627.8 38 615.1 29 605.9 31 613.1 37 589 27 586.7 38 590 33 562.2 31 561.8 39 574.3 33 1964733 LOS ANGELES LOS ANGELES UNIFIED 73.183943472326 4.30874594006731 13.7952471231427 68.5241685404818 45.4613868482351 20.5457412962458 73073.0746819566 4365.27608718017 23.4209491853797 49.3061754442912 2.32198142414861 32.1981424148607 632.955948121759 630.926125049489 624.165265009434 30.2164675932538 30.9511268824142 24.1795656528519 689.1 29 692 37 671.9 37 678.5 22 686.2 33 659.5 27 670.4 22 676.2 37 657.5 35 667.4 28 661.8 30 647.1 32 651.1 23 652 29 639.3 30 637.3 25 637.9 30 627.4 30 626.5 24 625.1 28 618.7 29 608 23 601.3 27 605.3 30 581.6 21 578.9 30 583.1 27 557.3 27 554.4 32 570.2 28 1964774 LOS ANGELES LYNWOOD UNIFIED 59.296941237853 .224648985959438 12.0561622464899 86.5273010920437 52.4871355060034 15.7930124223603 67063.0171526587 4064.95432137286 27.0596092836868 15.0847457627119 0 50 618.290844222037 621.509246177233 613.061156723226 23.0633096150338 25.8221407493517 17.7372810675563 678.6 20 678 23 659.8 25 667.6 14 674.2 22 648.2 18 659.9 15 665.9 27 649.5 28 658.3 21 652.3 22 640.6 26 642.8 18 642.4 21 632.6 24 635.1 23 639.5 32 624.5 27 615.5 17 618.6 22 610.5 22 595.7 15 597.6 24 598.1 24 569 14 572.8 25 573.1 19 548.5 21 557.4 35 561.8 20 1975333 LOS ANGELES MANHATTAN BEACH UNIFIED 7.19727345629511 7.00382026559942 1.81917409496089 8.65926869201383 7.93650793650794 15.2171875 64224.8888888889 5093.92796070584 21.5871073031416 43.089430894309 0 0 690.056717557252 683.397692112605 674.556118036123 74.1541592470109 74.6817144306366 71.3648854961832 717.6 58 717.5 65 695.5 62 712.9 56 709.6 59 691.1 59 713.9 63 709.9 71 692.9 70 721.8 78 714.1 78 707.1 85 711.8 80 706.7 81 691.1 83 696.8 82 708.4 88 680.3 81 689.6 81 681.9 83 673.7 80 677.6 82 661.2 81 661.8 79 648.3 75 632.5 79 640.4 77 613.9 74 598.3 74 617 78 1964790 LOS ANGELES MONROVIA UNIFIED 56.8985750209556 1.91512180174659 14.064654512027 48.0772177110464 17.5438596491228 14.4258785942492 57193.298245614 4017.30228282519 22.5547183351274 25.9475218658892 0 11.1111111111111 645.345761124122 639.929743822263 635.35638225256 40.8038680318544 38.6701428247563 34.7861826697892 687.4 27 687.8 32 669.6 34 684.2 26 688.8 36 665.6 32 677.9 28 679.2 40 665.8 44 683.9 43 673.1 41 661.4 46 670.2 40 661.5 39 653.5 46 654 41 646.7 39 645 48 644.7 41 637.4 40 639.6 50 622.1 35 610.6 36 617.4 41 595.8 33 588.2 39 590.8 34 563.2 33 565.1 43 575.4 34 1964808 LOS ANGELES MONTEBELLO UNIFIED 75.0342977348252 4.8799265642119 .447129193686891 90.5184921974475 59.5298068849706 16.9234065934066 67605.9101595298 3810.28506706938 27.995777027027 28.5416666666667 0 25 633.256956384986 628.919973223583 622.355320469712 25.1499663752522 24.3407546982695 20.808764940239 684.5 24 686.5 31 666.3 31 673.2 18 681.1 28 651.6 20 664.1 18 669.4 30 651.4 30 665.3 26 656.4 26 643.6 29 649.9 23 648.5 26 638.1 29 636.2 24 632.3 26 625 27 620.1 20 614.7 19 612.6 24 607.4 23 592.3 20 600.8 26 573.3 16 563.9 19 571.7 18 542.2 16 536.5 18 556.4 16 1964840 LOS ANGELES NORWALK-LA MIRADA UNIFIED 44.0220253770649 4.93949345449638 5.01597012911062 62.9762922308696 29.2200232828871 15.6210774058577 60665.5646100116 3616.50474605245 25.6258156364931 21.5086646279307 0 7.14285714285714 639.250212154394 632.607114624506 627.880085696797 33.7937155682514 32.4326086956522 29.8602518477963 686.6 26 686.8 32 667.5 32 678.5 22 684.3 32 655.7 24 673.9 25 677.5 38 658.1 36 678.6 38 665.1 34 653.7 38 662.4 33 654.9 32 646 37 647.4 34 641.2 34 635.1 37 636.3 33 627.2 30 627.5 37 616.2 30 603.6 29 611.3 35 588.4 26 578.2 30 586.6 30 561 30 556.5 34 572.8 31 1964865 LOS ANGELES PALOS VERDES PENINSULA UNIFIED 1.94360184248961 30.0269251480883 1.72320947765213 3.94184168012924 7.4742268041237 18.9428733031674 59821.2139175258 3946.78772213247 24.1144056678037 89.1304347826087 0 0 691.220889080708 696.583954688844 679.690504153538 78.8099398453165 84.1756524232865 73.5451014242555 730.5 71 745.9 85 715.6 79 720.6 64 737.4 81 711.4 77 720 68 732.5 86 703.7 78 717.1 75 727.8 86 698.5 80 706.1 75 721 88 694.2 83 690 76 704.6 87 671.2 74 683.5 77 682.9 82 674.3 80 671.9 78 665.7 84 661.1 78 648.8 76 635.8 81 642.1 79 617.4 77 608.7 82 619.8 80 1964873 LOS ANGELES PARAMOUNT UNIFIED 58.2283516774964 1.78362031722521 14.6145775473678 75.7082021847806 35.2484472049689 11.8014563106796 63190.7142857143 4370.21483675863 24.5058004640371 5.43071161048689 0 73.3333333333333 621.628153616147 619.038806631794 616.064499361663 25.0995805216123 23.4514584626297 18.6787516352084 678 19 681.7 27 663.4 28 668.5 15 678.8 26 649.9 19 664.3 18 670.6 31 655.6 34 665 26 657.9 27 643.7 29 645 19 642.5 21 634.9 26 633.4 22 627.3 22 624.7 27 619.8 19 615.4 20 618 29 596.8 16 590.1 19 597.9 24 572.5 16 571.9 25 576.5 22 542.9 17 541.4 21 557.8 17 1964881 LOS ANGELES PASADENA UNIFIED 61.8810986628117 2.22193005521956 32.0054343062495 47.1119291787186 42.1841541755889 14.2729885057471 64584.0385438972 4443.59943903936 23.867133609254 39.6551724137931 0 0 640.261998178379 638.447005395069 630.055227304324 35.4722647017934 37.419791026429 30.9504659146641 692.5 32 687.4 33 674.8 40 680.3 23 682.4 30 661.7 29 675.6 26 675.8 37 661.1 39 671 31 663.6 32 646.6 31 656.9 28 656.7 34 643.9 35 647.7 35 651.4 43 636.6 39 637 34 636.9 39 626.5 36 616.8 30 609.7 34 609.9 34 594.5 31 592.1 42 592.3 34 569.3 37 569.4 46 580.4 38 1964907 LOS ANGELES POMONA UNIFIED 73.505306122449 6.3934630738523 11.2337824351297 71.2044660678643 48.6985726280437 16.6833691756272 65628.7707808564 4007.18603418164 26.0442219440968 8.2771896053898 0 23.6842105263158 633.616609392898 631.103751065644 625.687406073083 33.2647967061246 32.3901007973522 27.1438092262835 680.8 21 681.2 26 662.8 28 668.9 15 675.5 23 649.9 19 669.8 22 673.5 34 657 35 672.8 33 665.8 34 652.5 37 658.2 29 655 32 645.3 37 643.6 31 644 36 634.6 37 630.8 28 629 32 625.7 35 612.5 27 605.3 30 609.4 34 588 26 582 33 586.1 29 560.9 30 559.8 37 574.5 33 1975341 LOS ANGELES REDONDO BEACH UNIFIED 25.6399317406143 7.27744401966139 5.18842162752594 23.1840524303659 10.2484472049689 16.5052083333333 68096.3695652174 5006.77607864555 22.4752168525403 51.5406162464986 0 0 662.997025878718 658.485319712448 650.223375639326 56.3864368251563 58.2854710556186 52.5876786404017 703.3 43 705.6 52 683.2 48 696.6 38 704 53 676 43 693.9 43 699.2 61 674.9 53 700 59 693 61 677.1 62 685.5 55 684.5 62 669.4 63 667.8 55 673.2 64 654.3 58 664.3 60 655.2 59 652.4 63 646.8 58 629.9 54 635.2 57 621.5 54 606.2 57 614.4 56 589 54 581.4 59 596 57 1973452 LOS ANGELES ROWLAND UNIFIED 33.8506304558681 18.7811869625226 6.68860813249814 55.3508865059985 29.1823899371069 16.1730984340045 62277.3119496855 4369.67459390593 24.4457424714434 30.2618816682832 0 0 647.043888420569 652.661347437917 639.480387685291 44.3539338654504 50.7873808987921 36.0793930569392 695.9 35 704.1 51 676.8 42 686.1 28 699.8 48 667.6 34 682 32 694.1 55 667.6 46 684.7 44 685.8 54 661.7 47 670.1 40 674.6 52 657.3 50 656.3 43 661.5 53 648.2 51 638.7 35 645.1 48 634.9 45 622.8 35 621.1 45 624.2 47 598.4 34 604.5 54 600.4 42 567.9 35 572.3 49 581.5 40 1975291 LOS ANGELES SAN GABRIEL UNIFIED 53.4556990709268 36.4023712486106 1.8895887365691 43.4790663208596 22.0657276995305 14.1230769230769 57663.2582159624 3814.97406446832 23.1666666666667 0 11.1111111111111 0 652.373269403656 651.826455658406 643.521950492097 50.5377274082911 54.3069573006868 43.7374887623614 693 32 704.7 52 676.6 42 687.9 30 698 50 668.8 36 690.4 41 693.5 56 679.2 58 691 51 687 57 673.3 59 678.3 50 679.5 58 666.9 61 660.2 48 670.4 63 649.9 54 648.6 45 647.8 52 643.1 53 631.4 45 624.7 53 626.8 51 604.3 42 598.6 52 602.9 46 580.9 51 570.1 52 584.8 48 1964964 LOS ANGELES SAN MARINO UNIFIED .265339966832504 63.2023384215654 .48717115946736 3.34524196167587 6.94444444444444 15.9078616352201 57543.375 4619.27671321858 22.1773612112473 78.1893004115226 0 0 690.843953394938 703.648538245895 680.914090726616 78.169409875552 85.3384060873048 70.9003615910004 724 65 758 90 715 79 719.2 62 749.5 87 709.3 75 715.7 65 742.2 89 710.1 82 717.7 75 739.1 91 695.7 78 707.7 76 726.4 90 695.6 84 686.9 74 705.3 87 672.9 76 677.4 72 679.4 80 665.6 74 673.9 79 656.4 78 661.9 79 641 70 635.3 81 636.9 75 613.1 74 602.8 77 618.2 79 1964980 LOS ANGELES SANTA MONICA-MALIBU UNIFIED 26.0906515580737 5.53147216923877 8.61799895959771 27.0764695682331 22.2664015904573 15.8740034662045 65963.4274353877 5063.35009537021 22.315280853634 65.1063829787234 0 0 672.518027812895 666.633357933579 658.063282423635 60.9182523785679 60.80036900369 57.6074589127687 709.8 50 713.6 60 690.5 56 701.5 44 705.5 53 682.4 50 696.5 46 699 60 680.7 59 703.3 63 688.3 56 679.5 64 691.2 61 683.9 61 673.6 68 676.7 64 673 64 658.3 62 670.2 66 666 69 659.3 69 654.4 64 637.8 62 638.5 60 628.4 60 612.4 62 619.6 60 593.9 59 584.1 61 599.3 61 1965029 LOS ANGELES SOUTH PASADENA UNIFIED 11.6788321167883 32.0893561103811 4.46780551905388 18.2128777923785 13.0177514792899 16.1964467005076 61169.6213017752 4043.49855453351 22.9909365558912 64.0740740740741 0 0 684.429470771359 685.287564588357 669.604545454546 69.6936155447606 74.7888391319325 66.0823244552058 722.2 63 738.9 80 700.9 67 714.7 57 727 73 697.2 65 708 57 718.1 76 691.5 69 711.8 70 712.7 77 689.8 73 694.2 64 696.8 72 672.8 67 682 70 688.2 76 661.6 66 679.8 74 679.3 80 666.7 75 662.2 71 644.1 68 650.6 70 644.1 72 626.7 74 637.3 75 604.3 67 595.8 72 610.6 72 1965052 LOS ANGELES TEMPLE CITY UNIFIED 27.3219814241486 38.107752956636 1.44546649145861 20.3679369250986 7.35930735930735 13.7875 59417.303030303 4035.89093298292 23.6489504242966 31.5649867374005 0 0 668.867083854819 672.304788029925 658.75127245509 60.2450099800399 64.9730673316708 52.4027534418023 704.9 45 718 64 685.4 51 695.5 37 715 62 681.4 49 694.9 44 711 71 685 63 701.7 61 697.2 65 680.4 65 685.4 55 691.4 69 673.3 67 676.1 64 683.3 73 663.5 66 657.3 54 651.7 55 649.9 60 643.7 55 635.7 60 639.5 61 621.2 54 617 66 618.6 60 595.1 60 587 64 601.4 63 1965060 LOS ANGELES TORRANCE UNIFIED 17.7019320040674 28.4768777488364 3.99675477176651 15.8332977496904 19.6572580645161 13.3186108637578 59555.2883064516 3822.10277979418 23.7832310838446 45.956607495069 0 0 669.838492706645 669.997700028678 656.603946302511 58.3625737761833 63.3968454258675 53.6345797638342 706.4 46 713.2 60 686.6 52 700.6 42 709 58 681.9 49 699.2 48 711.1 71 682.8 61 700.4 60 696.8 65 676.2 61 690.1 60 688 65 669.2 63 669.5 57 675.1 66 653.9 57 661.4 58 659 62 651.8 62 648.5 59 640.2 64 641.2 63 620.3 53 612.2 62 615 56 590.4 56 583.8 61 599.3 61 1973460 LOS ANGELES WALNUT VALLEY UNIFIED 6.19667389732466 42.3138875271378 5.72168919392114 18.1805448560824 17.7364864864865 14.8244477172312 60555.2364864865 3982.78030674417 24.2508591065292 57.7854671280277 0 0 675.635385172445 678.79409180563 664.452948625181 63.8897431259045 68.21642460104 56.1614012854169 714.1 54 729.9 75 696.3 62 706.7 49 720.5 69 691.2 59 700 49 714.1 74 689.7 67 704.2 63 703.8 71 683 68 694.5 64 700.6 76 677.8 72 675.5 63 683.7 73 662.9 67 661.9 58 661.1 65 655.5 66 645.6 57 633.6 58 641.2 63 616 50 608 58 612.6 54 591.8 57 578.4 56 597.6 59 1965094 LOS ANGELES WEST COVINA UNIFIED 47.3071656777727 9.43910955914448 9.12265386294195 58.1623745089481 17.5202156334232 13.9033898305085 56841.371967655 3907.33773461371 24.4226579520697 29.0617848970252 0 0 646.576221907905 644.418671371587 637.665678554886 42.1999382430137 42.0662779993863 34.8972182932579 690.9 30 690 35 673.2 38 684.5 26 687.3 35 663.5 30 682.3 32 683.1 44 668.5 47 677.6 37 668.2 37 658.2 43 666.1 36 662.4 39 654.3 47 650.8 38 651.6 44 644.4 47 642 38 645.3 48 634.4 45 623 36 617 41 620.5 44 600.2 36 596.6 47 598.9 41 570.9 38 570.6 48 580.5 39 2065193 MADERA CHOWCHILLA UNION 59.2872117400419 .94137783483098 2.52460419341036 41.6345742404793 6.66666666666667 12.2054166666667 53265.8190476191 3873.24005134788 23.5514918190568 25.4098360655738 0 0 642.458759783263 637.68853686636 630.755444964871 33.6891100702576 33.3064516129032 29.3991571342565 685.5 26 688.7 34 671.1 36 684.2 26 692.9 41 660 27 680.1 30 685.3 46 662.4 40 686.5 46 666.2 35 656 41 663.5 34 653.1 31 649.1 41 644.8 32 648.5 41 635.7 38 637.8 34 632.9 35 632.6 43 610.1 25 598.7 25 609.1 33 580.6 21 566.5 21 576 22 553.6 24 543.9 23 563 21 2065243 MADERA MADERA UNIFIED 60.0239038812355 1.15214548172137 3.54362583297004 67.3538020800897 26.8292682926829 14.0548488664987 56274.5882352941 4064.55738930062 23.4583272301157 31.9940476190476 0 45 634.873307579102 632.891376291368 622.640314369921 29.2889166741091 33.3825949921205 26.8529249448124 684 24 688.3 33 660.7 26 676.9 21 682.6 30 648.5 18 674.2 25 680.3 41 653.2 32 674 34 666.9 35 650.4 35 657.4 29 659.6 37 643 34 643.7 31 647.6 41 630.8 33 626.9 25 626.9 31 618.7 29 608.6 25 600.3 29 604.2 30 583.9 25 575 29 582.4 27 553.8 28 547.3 29 566.1 27 2165417 MARIN NOVATO UNIFIED 14.7922867865925 4.89383738995339 2.77058518902123 11.1082340756085 3.56234096692111 16.6201793721973 53794.9872773537 4365.51268772657 20.3963577932512 48.0851063829787 6.25 12.5 676.327673869621 670.308662832495 664.362228654125 67.1979015918958 65.5445722501797 61.5907027419648 717.7 58 718 65 699.3 65 709.2 52 707.6 57 689.2 57 708.1 57 706.3 68 688 65 706.9 66 703.2 71 685.3 70 697.1 67 698.7 75 683.9 77 676.7 65 685.2 75 666.6 70 670.1 66 664 68 661.8 71 655 65 637.4 62 644.9 66 629.8 61 605.8 56 621.1 62 593.5 58 579.7 57 606.4 68 2165458 MARIN SAN RAFAEL CITY UN 34.7676767676768 7.88413581431038 5.19854210627278 36.1787838097065 8.53658536585365 15.1911371237458 53336.3807692308 4458.96873201611 20.9668168783286 53.5928143712575 0 0 670.195434083601 661.617473035439 655.652214080918 58.6352341510035 57.6804314329738 55.5993569131833 713.1 53 710.2 57 694.1 60 705.9 49 702.6 51 680.1 47 707 56 704.7 66 684.9 63 698.5 58 683.3 52 668.9 54 685.3 55 675.3 53 670.6 64 674.1 62 664.1 56 664.1 67 663.7 60 654 58 651.3 61 651.4 62 639.2 63 640.6 62 614.8 48 607.7 58 608.5 50 590.5 55 582.9 60 600.7 60 2173361 MARIN SHORELINE UNIFIED 0 .480192076830732 .480192076830732 28.6914765906363 7.40740740740741 13.7261538461538 60992.5 6459.38415366147 16.4053537284895 26 0 0 670.308067542214 656.187862318841 650.405056179775 53.2621722846442 50.6322463768116 54.078799249531 709 49 699 45 688.7 54 703.3 45 699.4 47 681.9 50 692.1 41 686.7 48 671.9 50 701.2 61 683.1 52 677.2 63 692.9 63 670.3 48 666.8 61 683.6 71 677.5 69 660.9 65 672.5 68 656.8 60 655.6 65 648.5 60 611 36 620 43 625.8 57 601.8 52 606.5 48 578.1 44 577.5 55 585.2 45 2265532 MARIPOSA MARIPOSA COUNTY UNIFIED 27.0007209805335 .511322132943755 .29218407596786 6.20891161431702 1.45985401459853 15.5984472049689 51692.8248175182 4183.60336011687 21.5384615384615 29.8013245033113 0 0 664.224974619289 650.738696939783 646.636458852868 51.3226932668329 49.3326752221125 51.4238578680203 706.6 47 703 50 681.6 48 702.4 46 694.9 48 673.7 42 696.2 47 690 53 672.9 53 698.9 59 679.9 50 676.3 62 684 56 666.1 45 663 57 663.2 51 660.9 56 649 54 655.9 53 636.9 43 638.9 50 641.1 55 618.6 49 628.8 54 614 53 591.5 47 599.2 44 571.7 46 566.3 52 581.5 47 2365540 MENDOCINO ANDERSON VALLEY UNIFIED 55.9322033898305 .840336134453782 1.34453781512605 45.3781512605042 0 12.756 48855.9574468085 6406.86218487395 14.3160377358491 44.7368421052632 0 0 663.290476190476 663.766666666667 649.817894736842 48.6394736842105 53.8087855297158 42.7169312169312 704.5 44 716.5 61 692.3 56 694.5 36 703.4 51 677.1 45 676.1 27 681.5 42 667.6 46 694.9 54 683.4 53 673.8 58 680.9 52 675.8 51 664.9 58 652.5 39 660 53 641.2 44 664.6 60 663.7 67 648.9 59 630.4 43 629.7 54 617.3 41 594.6 30 601 52 589.7 32 580.9 47 582.7 60 582.2 43 2365565 MENDOCINO FORT BRAGG UNIFIED 37.2996794871795 1.16279069767442 .415282392026578 19.6843853820598 2.27272727272727 17.1307432432432 56336.7803030303 4990.48712624585 19.4728682170543 25.8992805755396 0 0 662.634256472005 649.819894675249 645.872770795931 48.7175344105326 45.9631363370392 47.8657435279952 705.6 45 698.1 44 682.3 47 694.2 36 695.8 45 673.4 40 695.6 45 697.8 59 676.6 54 692.9 52 682.5 51 671 56 678.8 49 667.8 46 659.1 52 662.5 50 666.9 59 648.1 52 662.3 58 648.3 51 650.3 60 637.6 49 610.4 35 628.6 51 610.1 44 581.8 33 597.1 39 585.9 51 559 36 577.6 36 2373916 MENDOCINO LAYTONVILLE UNIFIED 56.3311688311688 .517241379310345 .689655172413793 3.96551724137931 4.65116279069767 12.4978723404255 48867.6046511628 6578.05344827586 15.7329842931937 34.2105263157895 0 0 658.700571428571 644.085294117647 641.450287356322 43.1494252873563 36.9117647058824 42.5542857142857 693.1 33 687.5 32 672.8 38 699.4 41 689.9 38 669 36 688.6 38 680.9 42 654.4 33 702 61 672.2 41 679.4 65 673.6 43 661.9 39 652.5 45 658.8 46 650.6 44 647.3 51 654.8 51 638 39 638.3 49 630.7 43 605.8 31 619.6 43 602.6 38 586.8 38 589 32 562.2 30 548.2 26 578.9 36 2365615 MENDOCINO UKIAH UNIFIED 46.9275405445618 .969468962523513 1.11416582260165 22.8186948343221 4.84848484848484 17.4014986376022 64535.7121212121 4838.43134133989 21.3448818897638 33.3333333333333 0 36.3636363636364 652.817643378519 645.442461600647 637.560484873601 39.9751346871115 40.8148746968472 38.4404588112617 705.6 46 706.9 54 685.2 51 698 40 696.4 45 674.5 41 688.2 37 689.1 50 669.4 47 686 45 679.2 48 660.3 45 667.4 38 668.8 46 650 42 655 42 653.5 45 637.1 40 644.8 41 633.3 36 630 40 624.3 37 602.9 28 610.3 34 596.8 33 580 32 589 32 557.1 27 547 25 571 29 2365623 MENDOCINO WILLITS UNIFIED 46.5384615384615 .846153846153846 .692307692307692 11.5769230769231 2.98507462686567 17.472 56568.1268656716 4611.97576923077 20.8280757097792 26.3803680981595 0 0 658.926685714286 644.182815057283 640.649972451791 44.7129476584022 41.1047463175123 44.8982857142857 705.7 45 700 46 680.1 45 694.9 37 694.6 43 672.9 40 697.7 47 698.6 60 676.6 55 693.9 53 674.9 44 666.9 52 680.3 50 661.3 39 659.6 53 663.1 50 653.4 45 647.2 50 656.8 53 639.3 42 639.5 50 636.3 48 615 40 622.5 45 602.6 38 580.9 32 589.8 33 557.4 27 544.2 23 566.8 25 2475317 MERCED DOS PALOS ORO LOMA JT. UNIFIED 60.9182098765432 .156801254410035 6.31125049000392 61.7012936103489 15.4411764705882 11.4913461538462 54802.6985294118 4750.99882399059 18.8121752041574 19.5945945945946 0 0 631.770659722222 629.861754780653 621.061990950226 26.993778280543 29.0989876265467 22.5873842592593 680.9 21 688 34 662.5 28 670.6 16 681.7 29 646.8 17 673.6 25 678.7 40 654.3 33 667.7 28 658.7 28 642.4 28 649.8 22 650.1 28 636.1 27 640.2 28 646.4 39 629.9 32 627.7 25 620.9 24 618.3 29 599.9 18 596.3 23 602 27 578.9 20 571.2 24 576.8 22 551.8 23 548.2 26 568.9 27 2473619 MERCED GUSTINE UNIFIED 52.4079320113314 .614334470989761 .955631399317406 50.4436860068259 8.33333333333334 11.9896103896104 53609.9027777778 4080.96587030717 21.1577424023155 49.2753623188406 0 0 640.392330978809 634.424028906956 624.696633303003 28.8653321201092 31.8925022583559 26.6801210898083 686.5 26 690.3 36 665.9 31 685.9 28 689.4 38 658.6 26 673.2 24 676.8 38 655.1 33 672.8 33 662 31 648.5 33 670.7 41 661.2 38 651.3 43 640.7 28 640.9 34 627.9 30 629.8 27 626 29 622.8 33 599.8 18 596.6 23 595.4 23 569.2 14 568.8 22 572.8 19 560.7 30 554.5 32 563 21 2465698 MERCED HILMAR UNIFIED 37.7889869693148 1.5866388308977 .292275574112735 17.3277661795407 11.7117117117117 13.4170634920635 58102.5495495496 4361.61920668058 22.7861163227017 20.8 0 16.6666666666667 651.254748941319 640.575577367206 636.812100058173 38.4729493891798 34.8556581986143 35.0725952813067 685.4 25 684 30 667.7 33 679.3 22 679.5 27 659.4 27 680.8 31 679.3 41 665.1 43 680.7 40 668 37 653 38 675.5 46 665.5 43 652.2 44 655.1 42 650.1 43 644.8 48 646 42 634.7 37 635.4 45 628.9 41 602.6 28 616.9 40 599.5 35 586.1 37 594.7 37 559.1 28 546.9 25 571.8 30 2465722 MERCED LE GRAND UNION 41.4316702819957 .915564598168871 0 84.1302136317396 25.5813953488372 12.7714285714286 55709.2325581395 4140.52695829095 22.1852731591449 24.7422680412371 0 0 643.677083333333 645.689630681818 632.859677419355 25.2463343108504 27.5411931818182 18.0059523809524 682.2 23 686.4 32 663.1 28 665.9 13 681.8 29 650 19 668.9 21 672.1 33 654.2 33 657.9 21 664.3 33 646.7 32 642.9 18 652.2 30 636.3 27 632.1 21 630.5 24 625.9 28 610.4 14 607.6 14 610.7 22 588 11 584.5 15 589.9 19 569.7 15 568.2 22 572 20 547.5 20 550.8 28 551.7 13 2465755 MERCED LOS BANOS UNIFIED 50.9282399143163 1.24495289367429 4.86204576043069 53.1796769851952 12.1673003802281 12.078156996587 55074.6235741445 4075.18842530283 21.7702805155421 33.9350180505415 0 50 638.536482875881 629.930409090909 625.650664451827 29.1734693877551 27.6852272727273 25.195530726257 685.1 25 687.3 32 665.9 31 674.2 18 679.9 27 654 22 669.2 21 674.5 35 652.4 31 671.6 32 663.4 32 647.2 32 663.2 34 658.4 36 648.2 39 643.1 30 640.1 33 634.3 37 624.6 23 617.6 22 616.8 27 611.7 26 597.8 24 606.8 31 584.5 23 565.8 20 576.3 22 546.8 19 537 18 559.8 19 2573585 MODOC MODOC JOINT UNIFIED 33.2777314428691 .75 .75 10.4166666666667 1.61290322580645 11.6808823529412 55854.7419354839 4786.67916666667 19.2295345104334 32.7868852459016 0 0 659.431176470588 650.901276102088 639.167674418605 41.9476744186047 46.4164733178654 45.2776470588235 709.4 50 706.6 54 679.3 44 699.2 41 693.3 42 670.9 37 690.6 40 689 51 660.9 39 689.5 49 675.2 44 658 43 670.3 40 660.5 38 647.3 39 660 47 654.6 47 639.5 42 647.7 44 643.8 47 624.7 35 646.1 57 628.7 53 631.6 54 611.2 45 595 45 598 40 575.3 42 568.5 45 586.6 47 2573593 MODOC TULELAKE BASIN JOINT UNIFIED 64.8508430609598 0 0 52.3809523809524 4.76190476190477 12.9553191489362 50840.0714285714 4851.06302521008 18.4009546539379 45.7142857142857 0 0 640.7754601227 638.625294117647 630.765029469548 35.9548133595285 37.8666666666667 30.2024539877301 693.7 33 691.1 37 675.7 41 687 29 695.7 44 666.9 34 671.6 23 679.2 40 656.1 34 671.8 32 674.2 43 653.6 38 666.5 37 675.6 54 659.2 52 648.6 36 650.7 43 640 42 627.6 25 631.1 34 623.6 34 610 24 594.7 22 605.6 30 598.8 34 585.2 36 590.6 33 562 30 550 28 567.5 26 2673668 MONO EASTERN SIERRA UNIFIED 45.933734939759 .310077519379845 .775193798449613 14.1085271317829 2.22222222222223 14.0343137254902 52320.3111111111 6283.43255813954 14.6697038724374 76.9230769230769 0 0 664.066666666667 656.607675906184 644.631556503198 51.6183368869936 56.9424307036247 50.8013698630137 709.7 50 698.3 45 685.1 51 696.6 38 685.6 34 674.7 42 697.1 46 698 60 678.3 57 697.7 57 694.9 62 669.9 54 685.3 55 689.6 67 663.1 57 661.5 49 669.6 61 639.7 42 651.9 48 647 51 634 44 648.5 60 631.2 56 631.4 54 616.2 50 600 50 608.5 50 585.6 50 591.1 68 599.7 62 2673692 MONO MAMMOTH UNIFIED 21.8400687876182 .582847626977519 .0832639467110741 21.8151540383014 4.83870967741935 14.9848484848485 60159.435483871 4806.48293089092 20.5942275042445 42.8571428571429 0 0 668.114354066986 654.781134259259 655.868557919622 59.5957446808511 53.09375 54.9138755980861 705.7 46 693.8 40 686.2 51 709.7 51 693.3 42 685.9 54 705 54 692.3 55 686.9 65 700.4 60 680.1 49 675.5 61 689.1 59 667.9 46 671 65 673.5 61 665.2 58 657 61 662 58 664.1 68 656.6 67 653.5 64 631.4 56 646.9 67 613.5 47 597 48 610.4 52 579.4 46 585.9 63 589.4 50 2765987 MONTEREY CARMEL UNIFIED 10.706817231284 2.97716150081566 1.30505709624796 7.54486133768352 4.80000000000001 17.2942307692308 69887.392 5676.6513050571 20.6785411365564 55.921052631579 0 0 685.661973333333 677.989883474576 667.65821845175 69.2104984093319 71.0222457627119 68.8314666666667 724.7 66 721.3 67 694.2 60 718.2 61 719 68 690.1 58 709.7 59 708.5 70 681.8 60 709.8 69 702.2 69 689 73 697.5 67 694.5 71 682.4 76 681 69 684.2 74 668 71 682 76 670.8 73 667.2 75 673.7 79 646.5 70 649 70 644.1 72 634.1 80 636.1 74 607.6 70 591.5 68 612.5 74 2775473 MONTEREY GONZALES UNIFIED 67.2693726937269 .273878808627182 .410818212940774 86.5114686751113 24.1935483870968 11.8868421052632 58893.1209677419 4200.85210544334 24.9086378737542 11.304347826087 0 0 641.562837480148 644.002448979592 631.401393908105 27.6288074341766 29.0015306122449 20.4552673372155 675.7 18 674.1 20 659 24 669.9 16 676.1 24 651.4 20 664.7 18 668.7 30 653 31 666.6 27 668.1 37 652.9 37 651.5 24 661 38 650.3 42 634.7 23 644.5 37 626.1 28 622.7 22 626.5 29 617.5 28 604.7 21 604.7 30 604 29 578.8 20 574.8 27 578.8 24 553.8 24 547.7 26 559.9 19 2766092 MONTEREY MONTEREY PENINSULA UNIFIED 40.1345291479821 8.8134238913304 15.6372353176189 25.2257291250499 17.6570458404075 19.471915820029 61011.6332767402 4496.24306831802 20.6070396191124 28.9079229122056 0 95.2380952380952 653.881037456875 642.261085381784 639.283652789647 44.9874252228055 41.4812967581047 43.0559388861508 699.1 39 692.5 38 674.8 39 689.2 31 689.3 37 667.3 34 685.5 35 684.3 45 666.7 44 687.2 47 669.3 38 660.7 46 678.7 49 665.9 43 660 53 660.4 47 651.4 44 644.8 48 649.5 46 641 44 637 47 635.3 47 615.2 40 625.7 48 608.7 43 591.6 42 601.3 43 577.1 44 565.1 42 585.5 45 2773825 MONTEREY NORTH MONTEREY COUNTY UNIFIED 40.6666666666667 1.84426229508197 1.28539493293592 49.2362146050671 20.1581027667984 14.6853448275862 56619.2134387352 4356.07228017884 21.5795724465558 60.5978260869565 0 0 646.961362367393 637.964190837625 633.754023307436 34.9500554938957 32.8462998102467 31.5178671133445 692 31 691.3 37 672.3 37 684.4 26 685.9 34 660.3 27 679.1 29 680.7 42 662.1 40 674.8 35 665.1 34 653.5 38 663.1 33 656.3 34 645.7 37 645.6 33 638.4 31 632.5 35 638.3 35 623.5 27 626.1 36 621.1 34 600.8 27 611.9 36 596.9 33 580.8 32 590.8 34 559.3 28 552.2 30 573.4 31 2766134 MONTEREY PACIFIC GROVE UNIFIED 14.2795513373598 4.71158080140907 1.89343901365037 7.08938793483047 2.94117647058823 17.5419491525424 63909.5490196079 4756.38441215324 22.6321036889332 48.1751824817518 0 0 681.073791821561 669.929643296433 661.348655256724 64.1760391198044 64.9292742927429 65.1474597273854 719.7 60 716.7 64 692.9 59 715.5 58 706.7 56 694.4 63 712.2 61 707.9 70 690.3 68 709.7 69 702.2 70 684 69 698.6 68 693.7 71 672.1 66 677.8 66 682 72 657.1 61 670.1 66 662.1 66 657.1 67 663.5 72 640.9 65 651.9 72 637.5 68 609.6 60 620 61 599.4 63 576.7 54 593.1 55 2866241 NAPA CALISTOGA JOINT UNIFIED 45.6702253855279 .68259385665529 .341296928327645 47.098976109215 4.54545454545455 13.5112244897959 54344.8863636364 4650.72468714448 20.9738717339667 50 0 0 651.626136363636 644.014660493827 642.586842105263 46.3684210526316 40.8425925925926 38.8019480519481 693.2 33 696.4 41 676.4 41 688.6 31 688.3 36 666.8 34 685.5 35 684.8 46 673 51 686.2 46 671.7 40 665.3 50 680.9 51 673 51 668.1 62 658.1 45 652.9 45 643.9 47 645.8 41 642.3 44 636.7 47 625.1 37 603.9 30 627.6 50 599.1 35 592.8 43 593.1 36 566.4 33 556.5 34 590.4 49 2866266 NAPA NAPA VALLEY UNIFIED 32.7090648979061 1.39607354315986 1.77625428482393 26.4880024929885 6.38852672750979 15.4758720930233 54785.1342894394 3912.94858211281 21.8384091225143 29.2525773195876 3.33333333333333 0 661.755781448539 653.602858646089 645.835317212456 49.862496653877 50.1478428621536 47.9921038300962 707.6 48 708.2 55 683.5 49 696.7 38 697.8 46 674.5 41 695.8 45 694.6 56 675.6 54 693.2 53 681.2 50 666.8 52 680.3 50 672 50 660.1 54 665.4 53 663.8 56 650.3 54 654.2 50 642.8 46 642.1 52 639.2 51 620.4 45 627.3 50 614.1 47 599.4 50 604.9 47 577.6 44 571.1 48 585.4 45 2866290 NAPA ST. HELENA UNIFIED 34.434250764526 .738007380073801 .43050430504305 37.4538745387454 14.6341463414634 15.6477777777778 51434.4390243902 4386.9594095941 21.2020460358056 44.1441441441441 0 0 671.938825591586 667.352487135506 655.775432525952 54.4567474048443 57.0694682675815 51.5530236634531 707.1 47 708.5 56 690.8 57 696.4 38 705.9 54 677.7 45 700.1 50 709.1 71 682.9 61 688.9 49 685 54 660.5 45 683.1 53 677 54 665.6 59 669.7 57 659.8 52 649.1 52 661.4 58 647.6 51 645.9 56 655.5 66 628.5 53 638.8 61 618.3 51 614.5 64 615.5 57 585.9 52 579.5 57 589.6 49 3066449 ORANGE BREA-OLINDA UNIFIED 16.1578044596913 8.39899413243923 2.17937971500419 21.6261525565801 4.89795918367348 15.2272727272727 57193.4244897959 3825.95222129086 25.2277564921243 40.7202216066482 0 0 678.08792520838 676.768032786885 664.696648793566 65.8469615728329 69.0533894550288 60.8702410452805 709.9 50 724.2 70 690.5 56 709.4 52 718 67 688.1 56 698.5 48 712.1 72 682.2 60 705.4 65 698.5 66 680.5 65 698.1 67 688.6 66 680.9 74 679.1 67 683.1 73 670.2 73 669.1 65 669.9 73 658.5 68 653.2 64 645.8 69 646.9 68 633.9 65 619 68 626.6 67 606 69 589.7 67 610.8 73 3066464 ORANGE CAPISTRANO UNIFIED 17.3380285722466 4.70951361577139 1.58062428436302 16.9537511823568 9.39193257074051 12.6999165275459 60779.3835039133 3802.97418728531 23.0004288952883 44.8255813953488 0 10.5263157894737 671.50029010734 664.568939854735 656.9490234375 63.8142361111111 65.2306343697449 61.3329344357412 721.1 62 721.2 69 698.7 65 713.7 57 714.3 66 692.3 60 708 58 710.6 71 689.5 68 706.2 65 697.8 66 680.6 66 693.5 63 687.5 65 672.8 67 676.1 64 679.9 71 657.4 61 665.7 62 657.6 61 650.5 61 652.4 63 633.8 59 641.4 63 626.8 59 611.4 62 618.9 60 595.2 60 587.1 65 605 67 3066522 ORANGE GARDEN GROVE UNIFIED 48.1560822795015 28.7115519049283 1.29106955609927 44.0514680181755 11.4861186717474 15.6765557163531 65184.4246053348 3835.54895578469 24.6732224738965 20.3812982296868 0 0 644.83656906429 646.905817561278 637.042428705735 42.3321215919774 45.7674837108284 34.1665499681731 690.9 30 702.4 49 675.9 41 683.4 26 698.8 47 667.4 34 677.7 28 692.7 54 670.5 49 682.1 41 682.2 50 663.3 48 669.5 40 673.4 51 659.3 52 655.2 42 660.3 52 644.7 48 639.1 35 636.8 39 631.6 42 622.1 35 615.5 40 618.9 42 591.8 29 588.9 40 591 34 568.7 36 563 40 577.5 36 3073650 ORANGE IRVINE UNIFIED 10.5164960182025 25.1636962837691 3.03976410389836 7.41078010493907 9.2557251908397 16.0977599323753 62550.9770992366 4352.4882702398 22.6581642900181 0 0 9.67741935483871 684.851803374055 685.089444252277 671.314190288104 72.8213289962825 76.8866020984665 68.4994764397906 720.5 61 735.6 79 702.4 68 715.9 59 725.7 73 696.1 64 713.9 63 725.4 82 697.8 74 714.4 72 711.5 77 692.2 75 702.3 71 704.2 78 684.8 78 689 76 701.2 84 673.5 76 676.7 72 675.6 77 666.4 75 665.2 73 649.9 73 653.9 73 638 68 626.3 74 632.4 71 607.9 70 596.1 72 612.9 74 3066555 ORANGE LAGUNA BEACH UNIFIED 9.31627349060376 1.88383045525903 1.21664050235479 9.22291993720565 7.61904761904762 16.9064102564103 70274.3714285714 4481.47409733124 24.2635658914729 74.2857142857143 0 0 684.004074889868 677.346978021978 663.808360836084 67.2827282728273 72.2983516483517 69.2643171806167 727.2 68 724.5 71 705.3 71 719 62 710.9 61 693.6 62 719.2 68 716.5 77 695.5 72 714.8 73 704.7 71 685 70 703.5 72 694.7 72 676.1 71 680.1 68 685 75 651.8 55 677.4 72 674.9 77 659.4 69 660.8 70 643.3 67 641.9 63 638.8 69 632.2 79 627.7 68 607.1 70 597 73 609.1 71 3073924 ORANGE LOS ALAMITOS UNIFIED 11.6002452483139 8.99127975489041 3.11100636342211 11.5366485976903 10.1333333333333 15.0930715935335 67284.9401866667 4726.52929766675 23.1987918725975 49.5921696574225 0 10 683.151620147578 676.998132780083 669.268828685259 69.4602390438247 68.4106287902968 64.971767725377 717.8 58 718.3 65 697.9 64 712.7 55 716.3 65 693.9 61 707.3 57 714.9 75 694.8 71 713.9 72 698.7 67 686.3 71 700.9 70 690.6 68 679 73 682.5 70 681.5 72 663.6 68 669.3 65 655.7 60 657.3 67 658.2 68 638 62 648 69 639.6 69 625.9 74 634.2 73 606 69 601 76 619.4 80 3066597 ORANGE NEWPORT-MESA UNIFIED 39.0254420008624 4.68356306506596 1.23511684205326 34.1238081122474 4.42678774120317 16.0011663286004 60202.0374574347 4349.23086804012 22.4827586206897 42.8714859437751 0 0 662.048115315852 657.721892473118 652.410960005849 57.3834174161 56.1364157706093 49.8311978545888 702.7 42 701.3 47 682.3 47 700.4 42 699.9 48 680.6 48 693.6 43 694.4 56 676.8 55 699 58 691.1 59 679.2 64 683.9 54 679.7 57 670.3 64 668.3 56 672.3 63 661.3 64 653.6 50 655.2 58 647.9 58 640.1 51 630.8 55 636.2 58 616.1 49 610.3 60 614 55 588.1 53 579 56 598.8 59 3066621 ORANGE ORANGE UNIFIED 36.019976669583 10.8824233307122 2.08554138603029 36.821771684502 9.42408376963351 16.8176700547303 56415.1108202443 3586.93545078464 25.4488217305271 47.3302570863547 2.56410256410256 12.8205128205128 657.097121487969 653.340421234853 646.768285012285 51.7346437346437 51.4449413348721 45.6142793878856 707.4 47 708.8 54 688.1 54 702.3 44 703.8 52 682.2 50 695.4 45 701.6 63 679.6 57 690.5 50 685.1 53 671.2 56 676.7 47 674.8 52 665.7 59 666.6 54 666.2 58 653.9 57 648.7 45 643.3 46 640.2 50 633.8 45 621.7 46 628.3 51 605.5 40 595 45 599.4 41 574.6 41 571.3 48 585.8 45 3066647 ORANGE PLACENTIA-YORBA LINDA UNIFIED 21.0138794854435 8.12439729990357 1.88846030215365 25.9201221472195 11.3974231912785 15.153023465704 63101.5312190288 4172.24176309868 24.7171532846715 36.5617433414044 0 0 669.720971327595 666.268838856005 656.515978973547 60.006330544879 62.7434308790175 56.1279712705923 713.6 54 717.9 65 692.3 58 707.3 50 711 60 687.4 55 698.4 48 700.9 63 681.2 59 700.3 60 699.1 66 677.5 62 689.3 59 691 68 672.4 66 672.2 60 677.9 69 657.8 61 660.6 57 656.9 60 651.4 61 647 58 633.6 58 636.7 59 622.3 55 609.2 59 615.9 57 594 59 583.3 60 599.5 61 3073635 ORANGE SADDLEBACK VALLEY UNIFIED 10.5344975854998 8.40166405402147 2.16749065476908 14.8106837091523 6.05643496214728 14.9799044585987 60372.2057811425 3840.86554925841 22.1910073196236 53.7918871252205 0 0 674.518041730873 671.646055990119 662.072027826377 66.466383404149 69.0351996706464 62.0291949523135 713.1 54 722.3 69 695 61 710.8 54 713.6 63 690 58 706.2 56 712 73 687.8 65 703.8 63 698.7 67 682 67 695.3 65 694 71 678.1 72 678.3 66 684.3 74 665.4 69 669.9 66 664.4 68 658 68 655.6 66 641.1 65 646.3 67 633.1 64 621.5 70 627.6 67 600.8 64 593.8 70 607.8 69 3066670 ORANGE SANTA ANA UNIFIED 73.2772340256227 4.4085122200539 1.07982529504693 90.7908186971471 26.4875239923225 14.970924927416 69824.5398272553 4102.14481925472 25.0321867794005 21.729365524986 0 56.25 620.712644461482 623.755428773726 616.861563590674 26.7030852994555 29.2057133520329 19.6294119317375 679.8 21 686.3 32 664.6 30 668 15 682.5 32 651.4 21 659.5 15 670.2 31 651.4 31 663.1 25 656.6 26 645.4 30 645.5 20 650 28 638.2 30 632.4 21 635.4 29 626.7 30 620.4 21 623.5 28 616.7 28 599.5 19 596 27 601.1 28 571.1 18 572.6 28 572.8 20 542.4 21 548.7 32 559 22 3073643 ORANGE TUSTIN UNIFIED 29.8689696247767 8.27604268971387 4.65527401296405 41.6813985464545 5.26315789473685 13.0141193595342 57831.146381579 3629.52956197211 24.1694687289845 39.5953757225434 0 0 653.79774335437 650.860966858654 643.780960137984 49.8789766193944 50.3713530355963 43.5576592082616 695.7 35 702.1 48 679.9 45 695 37 703.2 51 675 42 687.8 37 691.4 53 672.1 50 692.4 52 681.1 49 669.4 55 679 49 673.1 50 661.8 55 660.5 48 661.8 54 646.1 49 644.2 40 641.7 44 638.5 48 632.2 44 621.6 46 628.7 51 609.5 43 604.3 55 608.7 50 580.5 47 575.8 53 591.2 51 3175085 PLACER ROCKLIN UNIFIED 17.136240833655 3.53894493137093 1.3725814453448 6.66446171655366 4.65116279069767 11.1923875432526 52654.8217054264 3596.09525384488 23.0433039294306 0 0 0 673.707947320618 662.480751278062 657.31606741573 62.7487640449438 60.8290731273616 61.4452770208901 716 57 715.2 63 695.3 62 713.2 56 709.2 60 688.7 57 705 54 708.1 70 686.7 65 710.1 69 692.4 61 683.7 69 696.8 66 679.4 58 674.4 69 678.7 67 670 62 660.2 65 664.7 61 654.9 59 651.8 62 652.5 63 629.8 54 639.1 61 630 62 609.6 60 615.2 57 592.3 57 584.8 62 597 59 3166944 PLACER TAHOE-TRUCKEE UNIFIED 23.3564377231674 .627574034124338 .431457148460482 17.7093547754462 6.61764705882352 13.5935897435897 49513.0257352941 4638.09786232595 19.6784192173576 44.131455399061 0 0 666.170820668693 655.992460533479 648.804707520891 54.0721448467967 54.4324986390855 53.8347609836972 707.3 47 712.2 60 682.6 48 705.3 48 710 59 678.3 46 696.2 45 700 62 675.2 53 701.4 61 687 56 677.2 62 688.8 59 680.2 58 667.8 62 669.5 57 663 55 653.3 57 660.9 57 647.8 51 648.4 59 646.3 57 616.3 41 631.5 54 615.8 49 597.5 48 606.5 48 592.1 57 580.6 58 590.1 51 3166951 PLACER WESTERN PLACER UNIFIED 28.6609686609687 .562809545249887 1.44079243583971 17.4245835209365 4.8780487804878 13.3327272727273 42658.3902439024 3503.69765871229 24.2685851318945 27.4611398963731 62.5 0 656.233281893004 645.500357507661 640.171112229492 44.5485656768999 42.8406537282942 43.2489711934156 698.9 38 695.1 41 679.6 45 691.5 33 698.9 48 670.6 38 689.2 39 694.3 56 669.5 48 688.7 48 668 36 659 44 676.9 47 676.4 54 656.5 50 661.5 49 655.6 48 651.3 55 648.5 45 630.4 33 630.5 41 635.9 48 614.6 39 626.5 49 611.6 46 590.5 41 598.9 41 572.5 40 559.2 36 579 37 3266969 PLUMAS PLUMAS UNIFIED 36.6621067031464 .663533314901852 1.21647774398673 6.85651092065247 2.71739130434783 16.1540476190476 56500.125 4912.70168648051 21.2320916905444 33.1932773109244 0 0 668.071468144044 656.273361934477 650.500313479624 52.3761755485893 50.1907176287052 51.4273842500989 706.4 46 700.2 47 685.8 51 699.4 41 694.7 43 673.5 40 697.7 47 694.3 56 674.3 52 696.1 56 679.4 48 668.6 54 683.3 53 672.8 50 663.1 57 667.4 55 658.6 51 648.5 52 660.8 57 651.2 55 644.4 55 643.8 54 621.2 46 632.3 54 620.3 53 601.5 52 609.5 51 587.6 53 576.9 54 596.5 58 3366977 RIVERSIDE ALVORD UNIFIED 42.2902910247004 4.02122641509434 7.22287735849057 47.1580188679245 17.2413793103448 13.0070779220779 62390.7051124438 3758.19761084906 25.181954887218 41.6666666666667 0 70.5882352941177 638.111402394775 630.693225584594 627.071274732972 34.6095254771494 33.3498968363136 30.1157474600871 687.5 27 687.6 33 667 32 678.2 21 684.7 32 655.2 23 676.4 27 681.1 42 660.5 38 674.4 34 662.9 32 655 40 660 31 656.5 34 649.7 42 649.6 37 648.7 42 636.3 39 636.4 34 627.3 31 626.3 36 616.8 31 601.7 30 611.6 37 583.6 25 573.6 28 582 27 559.1 32 550.6 32 569.9 31 3366985 RIVERSIDE BANNING UNIFIED 75.5298651252409 13.3685136323659 13.8522427440633 36.6974494283201 20.2970297029703 13.8173333333333 60074.7807425743 4456.32191292876 21.8996590355577 41.8181818181818 0 12.5 634.098734577665 628.219981640147 620.879110554338 25.6636392107736 25.7264381884945 23.4349889275546 677.9 19 684.4 29 658.6 24 672.1 17 680.3 27 648.2 18 666.3 19 671.9 33 651.9 30 670.3 30 654.3 24 645.2 30 655.6 27 645.9 24 639.7 31 639.8 27 629.3 23 625.6 28 627.6 25 623 26 612 23 609.6 25 598 24 602.2 28 581.8 22 574.5 27 580.2 25 551.7 23 541 21 561 20 3366993 RIVERSIDE BEAUMONT UNIFIED 58.7464387464387 1.15131578947368 3.4265350877193 34.6491228070176 9.02777777777779 15.9661585365854 59270.4442361111 4070.73959429825 24.7562674094708 26.25 0 12.5 645.879280347964 637.157724827056 633.962882603642 41.2026346377373 38.8439661798616 37.7323052589957 698.4 38 692.6 39 678.5 44 690.5 32 684.8 33 666.2 33 687.9 37 684.8 46 670.7 49 685.2 44 665.1 34 656.8 42 674.9 45 659.5 37 657.3 50 656 43 655.6 48 646.5 50 640.8 37 630.9 34 634.1 44 623.7 37 608.6 34 614.5 38 599.3 35 592.7 43 592.5 35 562.3 31 562.4 39 573 31 3373676 RIVERSIDE COACHELLA VALLEY UNIFIED 85.5145886105639 .138121546961326 .276243093922652 96.1671270718232 36.4653243847875 11.9207692307692 61385.5887024609 4099.01191902624 25.2796420581656 13.5467980295567 0 0 612.505972615675 616.307526637951 605.373097282673 15.8368427243854 19.4258671503061 12.4275259678942 670.5 14 676.1 21 652.3 19 661 11 675.8 23 640.5 13 653.8 12 664.4 26 641.4 22 651.2 16 649 20 632.6 19 632.1 12 639.1 18 623.3 16 622 14 625.5 21 613.2 18 608.6 13 611.1 17 600.4 15 586.8 11 585.9 16 585 16 557.9 9 559.9 16 560.2 12 535.4 13 538 19 549.1 11 3367033 RIVERSIDE CORONA-NORCO UNIFIED 41.5113871635611 3.60423802054992 4.64453762683653 41.7784321884703 11.3732097725358 13.5429739776952 64063.4574557709 4083.55417560257 25.2311373152183 34.6372688477952 0 34.2857142857143 649.575955248793 642.475290069264 639.372187638951 44.6634059582037 40.9677063572595 38.9997744394821 695 34 693.3 39 673.8 39 686.5 28 687.8 36 665.2 32 685.8 35 684.6 46 669 47 685.8 45 673.7 42 662.5 47 673.9 44 666 43 657.6 50 659.7 47 659.1 51 648.4 52 643.2 39 637.8 40 636.9 47 628 40 610.6 35 623.9 47 600.8 36 587.4 38 597.9 40 573 40 563.3 40 584.9 44 3367058 RIVERSIDE DESERT SANDS UNIFIED 55.9912521615299 1.2646835922698 2.4677908298598 60.0416824554756 15.8088235294118 12.6873655913979 64123.518125 3937.20569865479 25.2138016019717 43.1718061674009 4.34782608695652 0 642.625749337795 640.398884858256 630.882184459367 35.1719884884199 37.7696493349456 31.2600027882337 692.2 32 690.1 35 669.9 35 682.6 25 686.7 34 659.8 27 680.7 31 684.9 46 663 41 675.3 35 664.5 33 650.9 35 662.7 33 663.9 41 647.5 39 649.2 36 647.7 40 635.3 38 635 32 636.5 39 630.3 40 618.9 32 609.7 35 613.7 37 587.8 26 584 35 584.3 28 563 31 561.6 39 574.1 32 3367082 RIVERSIDE HEMET UNIFIED 62.4077800134138 1.43589743589744 2.66666666666667 29.2307692307692 9.03328050713154 15.5025143678161 59735.0526624406 3916.53708397436 24.517557734894 21.4285714285714 0 5.26315789473684 650.938309754281 645.971246796045 636.643406695025 41.9052154614389 44.9794031490297 40.3741623231571 703.7 43 701.6 48 678.6 43 692.4 34 691.6 40 667.1 34 686.7 36 688.1 50 665 43 687.6 47 675.5 44 663.3 48 674.6 44 664.1 41 659.5 53 659.6 47 659.5 51 643.8 47 648.5 45 645.5 49 635.1 45 625 38 616 41 615.9 39 600 36 592.5 43 591.1 34 567.7 35 566.7 44 575.7 34 3367090 RIVERSIDE JURUPA UNIFIED 50.2109216989309 1.38881142283451 5.30425567516314 53.2545038764014 23.789764868603 13.2753071253071 62068.7191286307 3826.45784650566 24.6666666666667 26.3835263835264 0 4.16666666666667 638.791092144514 630.901365487503 627.674335051968 34.6180538505606 32.1523596582289 30.0636393768644 690.5 30 689.5 35 669 34 680.6 23 683.8 31 657.1 25 676.1 27 679.6 41 659.9 38 677.3 37 663.2 32 653.3 38 661.1 32 654.6 32 649.4 41 648.5 35 648.2 41 637.4 40 633.9 31 627.4 30 625.1 35 616.9 30 598.3 25 610 34 586.6 25 576.1 28 586.3 30 561 30 552.7 30 572.5 31 3375176 RIVERSIDE LAKE ELSINORE UNIFIED 38.1164650109672 1.79080718975924 4.07242820189693 30.1120912648405 11.4186851211073 13.05374617737 62326.655449827 3960.63418584599 25.3969359331476 25.3833049403748 0 83.3333333333333 649.218096224461 642.148974546786 634.754570195195 41.2464339339339 42.5663797839224 39.5877977591564 696.1 35 694.7 40 670.8 36 689.4 31 692.9 41 666 33 686 35 688.6 50 668.6 47 684.1 44 667.9 36 656.3 41 674 44 665.4 43 655.4 48 657.1 44 656.1 48 644.4 47 645.2 41 639.6 43 632.3 42 630.3 42 615.9 41 619.7 43 601.5 37 590.9 42 593 35 573.3 40 564.2 41 580.4 39 3367124 RIVERSIDE MORENO VALLEY UNIFIED 43.0689140716757 3.26543602800764 23.676002546149 35.3532781667728 23.1235784685368 14.0119418132612 58401.1608491281 4173.91743189052 24.0922034941892 25.5924170616114 2.85714285714286 22.8571428571429 642.660522821957 634.998522406493 629.402435943703 34.4060357271743 33.1140613973183 31.6017030627661 692.3 32 694.2 39 670.6 35 687 29 692.5 40 662.4 30 676.9 27 680.2 41 657.9 36 678.6 38 664.4 33 652.4 37 665.4 35 656 33 647.4 39 649.1 36 643.6 36 635 37 634.6 31 624.4 27 622.6 33 618.9 32 602.9 28 612.9 37 589.8 27 576.4 28 585.2 29 559.8 29 552.9 30 572.7 31 3375200 RIVERSIDE MURRIETA VALLEY UNIFIED 18.2164543398024 2.10569777043765 3.43724194880264 17.8468208092486 15.1933701657459 9.21929611650485 59134.6718232044 3774.6010125929 25.86148169174 38.2566585956416 0 100 664.968239211877 655.571895604396 650.502999299229 56.3379117028732 54.6623626373626 53.4476203690856 706 46 701.7 48 682.7 48 702.5 44 698.8 48 680.6 48 699.1 48 702.4 64 678.3 57 695.8 55 676.8 46 671 56 683.9 54 672.8 51 662.9 57 667.3 55 671.7 63 651.2 55 662.3 58 653.8 58 649.6 60 651.1 62 633.2 58 643.2 65 621.3 54 601 52 614.2 56 589.5 55 578.8 56 596.9 58 3367173 RIVERSIDE PALM SPRINGS UNIFIED 62.5049747000967 1.15749423932265 5.94287551578158 53.4912384116607 8.93333333333334 13.0700234192038 57242.9728133333 4143.36832699212 24.2010412494994 13.7540453074434 0 9.52380952380952 638.104933204571 636.219372751447 626.655804398614 33.8860871666801 38.3268418582825 30.6045388701111 690.7 30 689.8 35 669.8 34 682.3 25 687.3 35 658.3 26 677.2 28 680.4 41 658.5 36 676.8 36 663.8 33 651 36 664.6 35 657 34 647.8 39 645.2 32 640.1 33 632.1 34 635.8 32 637.2 40 628.3 38 617 30 612.7 38 611.4 35 588.7 27 593.5 44 587.1 30 561.9 30 568 45 572 30 3367181 RIVERSIDE PALO VERDE UNIFIED 55.9128893390732 .632911392405063 10.5221518987342 52.0833333333333 10.7954545454545 14.1102564102564 61885.4805113636 4694.47362869198 22.1958121109225 20.9302325581395 0 0 642.057746478873 637.300819061802 629.136989409985 33.160363086233 34.7956068503351 30.516939474686 692.1 31 689.2 35 671.5 36 681.8 24 684.2 32 656.7 24 672.7 24 675.1 36 656.2 34 674.2 34 669.1 38 650 34 663.7 34 660.9 38 646.3 38 647.7 35 643.4 36 634.4 37 632 29 625.7 29 621.5 32 617.8 31 603.5 29 610.5 35 593.3 30 580.5 32 589.3 33 564.7 33 564.6 42 570.8 29 3367215 RIVERSIDE RIVERSIDE UNIFIED 47.2343460276708 3.59830536819221 10.3266625787391 40.1109314900496 21.7477003942181 10.9766241299304 61445.6489947438 4384.20497268521 23.5685282566731 33.7724550898204 0 19.047619047619 652.423640417888 645.365187645035 639.211258767073 42.8254788564866 42.4636712811075 39.2414419622579 701.5 41 701.3 47 680.3 45 695 37 694.8 43 671.5 38 684.7 34 684.6 46 666.3 44 685.6 45 671.4 40 661.1 46 672.7 43 664.2 41 655.9 48 657.6 45 658.4 50 645.2 48 645.9 42 642.3 45 636.4 46 627.4 40 613.6 38 618.7 42 595.2 32 585.9 37 591.8 34 567.2 35 562.1 39 579.3 38 3367249 RIVERSIDE SAN JACINTO UNIFIED 64.1791044776119 1.00730792020541 3.85147145960893 50.8196721311475 7.44680851063831 13.1198113207547 58040.6569680851 3564.44928500889 26.0216216216216 11.9318181818182 12.5 25 633.898633323641 630.169063926941 625.056898550725 32.6866666666667 32.3090753424658 27.9002617039837 686.4 26 687.1 32 673 37 685.5 27 685.8 33 670.4 37 677.5 28 678.3 39 663.5 42 674.5 34 669.2 38 651.1 36 659.4 30 653 30 645.8 37 648.3 35 642.9 35 635.6 38 630.7 28 625.4 28 617.1 28 611.4 26 597.2 24 604.5 29 587.6 26 585.4 36 583.5 27 549.8 21 553.3 31 566.2 24 3375192 RIVERSIDE TEMECULA VALLEY UNIFIED 18.1699877999187 1.95702750786917 3.8250992199261 17.784316408923 8.09792843691149 12.194847972973 64156.1068361582 3664.26510606268 25.5497985031664 25.8680555555556 6.25 81.25 664.46675821574 654.871055332649 652.040092513924 58.8132729160767 56.1685173089484 54.7503551472677 709.6 50 702.7 50 687.3 53 703 45 699.2 51 681.1 49 697.3 47 699.7 62 680.9 60 695.8 55 686.4 55 671.6 57 687.3 58 677.3 56 668.1 62 670.5 58 667.7 60 657.1 61 661.2 58 653 57 653.2 63 647.9 59 628.8 55 638.8 61 620.7 55 603.2 55 612.7 55 591.2 58 577.4 57 599.9 63 3375242 RIVERSIDE VAL VERDE UNIFIED 54.8438652569462 1.89759712553335 23.5796092521895 45.823040646755 21.2389380530973 10.9077922077922 58447.4374631269 3799.07750392993 25.5414949970571 31.8021201413428 0 0 637.066459230892 632.573991655077 627.424335378323 34.5670913953123 34.0865399474579 30.0086165629488 690.2 30 688.6 34 668.3 33 679.3 22 682.8 30 654 22 675.2 26 678.6 39 656.5 35 674.2 34 663.7 32 649.5 34 659.4 30 652.4 30 644.5 36 642.8 30 635.5 29 633.1 35 637.3 34 635.1 38 631.9 41 614.9 29 609.4 34 613.8 37 588.5 27 582.3 34 587.5 31 567.2 35 562 39 578.9 37 3473973 SACRAMENTO CENTER JOINT UNIFIED 29.3060600267635 7.97491039426523 13.8709677419355 10.2867383512545 10.6995884773662 13.2324074074074 55944.1275720165 3811.04928315412 22.2895064288677 78.968253968254 0 42.8571428571429 662.739604722793 655.475031525851 650.780858585859 57.0383838383838 56.1669609079445 51.7995379876797 703.4 43 706 53 681.1 47 695.9 37 696.9 46 672.5 39 686.6 36 690.8 52 669.2 47 700.1 59 696.1 65 676.1 61 686.1 56 689.8 68 671.9 66 670.3 58 667.8 62 662.7 67 656.7 54 649.3 55 650.2 61 641.1 54 625.1 54 640.9 64 617.1 55 599.6 54 611.8 56 593.4 62 568 52 592.9 58 3467314 SACRAMENTO ELK GROVE UNIFIED 36.9447663190421 15.2125780530885 19.0934646864194 16.269870885887 17.4043062200957 12.2778861360042 58331.6309808612 3762.5834017464 23.1169705126637 29.5801526717557 0 33.3333333333333 654.782969037773 648.209210391211 643.323938438074 47.4667059516794 45.1266043741657 42.0050387462209 692.9 32 697.5 43 675.4 40 688.4 30 693.9 42 667.9 35 686.8 36 692.7 54 671.3 49 685.7 45 677.4 46 660.8 46 674.5 44 668.2 45 655.9 48 661.5 49 657.8 50 649.5 53 648.3 44 638.2 41 641.1 51 630.8 43 612.8 37 626.7 49 609.6 44 592.9 44 605.1 47 584.7 50 571.4 49 593.7 54 3467330 SACRAMENTO FOLSOM-CORDOVA UNIFIED 26.1143156790771 5.3087986463621 9.91257755217146 8.67174280879865 9.72222222222221 14.2631906077348 51104.6527777778 3845.84679921038 22.1977666289044 27.7091906721536 4.34782608695652 30.4347826086957 663.980873539868 658.512398760124 649.557049411291 54.2888195632485 56.1346865313469 51.1814118842052 703 43 703.8 50 683.1 48 697.9 40 700.6 49 674.3 41 693.8 43 700 61 675.2 53 697.6 57 688 57 676.5 61 682.1 52 679.3 57 669.5 64 669.5 57 672.5 64 655 59 661 57 654.6 58 647.3 57 642.7 54 627.1 52 630.5 53 617.4 50 605 55 609.4 51 590.7 56 580.3 57 592.9 53 3467348 SACRAMENTO GALT JOINT UNION 33.1153765028475 1.77095631641086 1.18063754427391 35.7260920897285 9.16666666666667 11.7725563909774 51742.2041666667 4581.18913813459 22.2133333333333 23.9837398373984 0 0 656.585923753666 650.842329994729 644.455909694555 46.5211155378486 45.3125988402741 41.4806718208478 702.8 42 699.8 46 682.6 48 691.5 33 690.4 39 668.8 35 683.9 34 684.9 46 668.3 46 686.8 46 675.5 44 664.5 50 676.6 47 667.6 45 659.5 53 663.9 51 666.8 59 653.6 57 642.5 39 635.2 38 633.8 44 627.6 40 612.2 37 622.2 45 608.8 43 600.1 50 604.3 46 576.5 43 572.3 50 585.2 44 3475283 SACRAMENTO NATOMAS UNIFIED 37.9553798362045 6.22614982928299 29.7449287005423 26.2301667001406 12.2340425531915 10.6661137440758 57672.6808510638 3312.51496284394 22.4284140969163 0 14.2857142857143 14.2857142857143 654.991544666866 642.894449262793 641.367069121642 43.5976456383942 38.1156403584851 39.4711682103376 694.8 34 688.5 35 673.4 38 684.6 27 684.9 32 660.9 28 680.5 31 679.1 40 663.6 41 686.6 46 670.9 39 663 48 674 44 661.6 39 660.7 54 658.8 46 651.4 44 647.6 50 648 44 637.1 40 636.7 47 626.2 38 607.8 33 623.7 47 607.7 42 591.8 43 599.5 41 575.1 42 557.4 35 581.3 40 3467413 SACRAMENTO RIVER DELTA JOINT UNIFIED 35.978835978836 1.40728476821192 1.03476821192053 36.9205298013245 11.9047619047619 14.7351063829787 51080.373015873 4420.62417218543 20.1801801801802 45.3125 0 0 652.409325771897 645.858159509202 639.278937259923 41.1651728553137 42.3993865030675 38.5519848771267 697.9 37 698.6 45 680.1 45 688.8 30 692.1 40 669.4 36 681.4 31 689.3 51 667.8 46 691.1 50 680.4 49 659.2 44 676 46 671.1 49 657.4 50 654.3 41 654.5 47 640.6 43 641.3 38 633.5 36 628.4 38 630.5 43 612.6 37 616.7 40 594.6 31 580.1 32 591.1 34 569.6 37 560.6 38 576 34 3467439 SACRAMENTO SACRAMENTO CITY UNIFIED 59.4064346159987 23.8705379883233 21.9525096978959 23.5061322048509 27.4574669187146 14.0032991803279 61997.025047259 4125.40662591591 24.8267842434226 38.742611499194 1.2987012987013 10.3896103896104 642.590368715732 637.104240392201 631.379925928053 37.3836812035256 37.4236729403809 33.106930463288 694.4 34 697.5 43 676.9 42 684.5 27 691.4 39 666.1 33 677.7 28 683 44 664.6 43 680.8 40 675 43 658 42 664 34 664.9 42 650.5 42 651.5 38 651.5 43 637.5 40 636 33 631.7 34 625.3 35 620.1 33 606.4 32 614.3 38 591.8 29 578.2 30 588.5 32 567.1 35 552 30 572.2 30 3467447 SACRAMENTO SAN JUAN UNIFIED 28.8497509510099 4.59476973890503 5.95982189518574 8.97213454020946 7.18722271517302 12.6162215239592 58872.7457852706 4335.65953132512 21.750739140323 39.2844235634261 1.21951219512195 6.09756097560976 670.17213159824 662.936219245407 655.298383336865 58.550422330538 58.9531301507387 55.3249022482894 708 48 710.7 57 687.1 53 703.8 46 706.8 56 683.1 50 700.2 49 702.2 64 681.2 59 700.1 59 686.8 55 675.6 61 687.6 57 678.8 57 669.9 63 676.4 64 676.7 68 661.4 65 662.8 59 655.1 58 650.5 61 648.4 59 632.1 57 636.4 58 624.2 56 610.2 60 616.8 58 591.1 56 579.7 57 595.9 57 3575259 SAN BENITO AROMAS/SAN JUAN UNIFIED 35.7537490134175 2.109375 .625 40.46875 16.6666666666667 11.9181818181818 61919.85 4272.915625 22.2222222222222 0 0 0 657.229098805646 644.65762886598 639.917678381257 48.8051118210863 48.5010309278351 49.1226927252986 702.3 42 694.2 39 678.6 44 691.7 33 696.3 43 667.8 35 690.2 39 695.3 56 668.4 47 700.6 60 680 49 676.8 62 677.5 47 673.1 51 663.5 57 674 61 674 66 653.3 57 651.1 47 644.2 47 635.3 45 636.1 48 609.9 35 619.4 43 609.5 44 596.5 47 598.4 41 591.7 57 571.3 49 587.3 47 3675077 SAN BERNARDINO APPLE VALLEY UNIFIED 43.7316116377901 1.65699001891839 17.2744471263618 20.431861178159 5.16898608349901 13.2070035460993 62106.3459244533 3058.08872072542 24.5208208806535 35.8391608391608 13.3333333333333 86.6666666666667 652.699094870935 642.722250164006 639.455594713656 44.5601321585903 40.9465340039361 41.3233880880545 705.5 45 700.8 46 682.6 48 694.6 36 688.1 36 669.9 37 690.4 40 685.6 47 672.7 51 690.2 50 673.3 42 667 52 673.8 44 660 37 656.9 50 654.1 41 652.3 45 643.3 46 646 42 637.7 40 634.8 45 632.8 45 616.5 41 622.3 45 599.4 35 587 38 591.7 34 568.8 36 562.1 39 579.8 39 3667611 SAN BERNARDINO BARSTOW UNIFIED 50.6241134751773 1.10144927536232 11.7826086956522 38.1304347826087 19.2691029900332 14.4014662756598 57100.6212624585 4203.24405797101 22.9867549668874 12.987012987013 0 0 644.092824226465 638.257651547266 630.222731201383 34.9842264477096 35.8380669775329 33.0118499012508 693.2 33 693.1 39 671.2 36 685.7 28 686.9 34 656.4 24 675.6 26 678.3 39 655.8 34 681.4 41 670.1 39 655 40 671.1 41 662.7 40 648.6 41 652.9 40 645 37 636.5 39 636.7 33 632.5 35 627.1 37 614.1 28 602 28 608.1 33 595.2 32 584.4 35 591.7 34 559.9 29 556.4 34 575.1 33 3667637 SAN BERNARDINO BEAR VALLEY UNIFIED 40.7033727298933 .44931199101376 .954787980904241 11.4293737714125 3.52112676056338 13.8814814814815 57824.8802816902 3838.35888795282 25.3642857142857 35.4285714285714 0 100 662.867092034029 653.319750755287 647.145671412082 51.0623316660254 50.2843655589124 48.7935034802784 706.7 46 704.6 52 686.9 53 695 37 701.4 50 670.7 38 689.2 39 692.1 54 670.4 49 694.2 54 681.1 50 662.8 48 680 50 667.7 45 656.9 50 661.2 48 655.4 48 645.4 48 655.7 52 643.5 47 642.7 53 645 56 623.2 48 635.8 58 625 57 608.5 58 619.6 60 580.2 47 574.4 52 591.7 53 3667678 SAN BERNARDINO CHINO UNIFIED 25.955670898506 6.02325581395349 5.23255813953488 38.202657807309 18.6985172981878 15.2127715355805 62270.0461285008 3664.25887043189 24.169686985173 29.0155440414508 0 10 655.456794936477 649.093457228997 645.536307072925 50.6846006038979 47.2450164244251 43.8672659725726 694.7 34 695.2 41 680 45 689.7 32 693.4 41 675.4 43 687.2 37 688.5 50 676.9 55 690.3 50 680.8 49 669 54 678.9 49 671.7 49 663.3 57 663.2 50 662.1 54 651.3 54 650.6 47 644.4 47 640.8 51 637.3 49 623.6 48 630.9 53 605.6 40 593.2 44 600.5 42 580.5 47 570.9 48 591.3 52 3667686 SAN BERNARDINO COLTON JOINT UNIFIED 44.4521203103412 2.01990343876244 9.0846388806779 63.6860774460538 19.094247246022 11.8951140065147 59625.2607099143 3811.72376588827 24.0302328416433 34.4459279038718 0 48 634.139532950423 631.313346569601 626.092709725316 33.9203414996288 33.8149863960585 27.9621372430472 691.4 31 690.1 35 671.1 36 682.5 25 685.7 33 661.8 29 673 24 676.4 37 657.7 36 674 34 663.3 32 651.7 36 658.2 29 652.5 30 645.1 36 648.4 35 653.9 46 640.4 43 632.2 29 631.8 34 628 38 613.8 28 605.7 31 611.6 35 583.8 23 580.3 32 583.6 27 553.6 24 551.7 30 568.2 26 3667710 SAN BERNARDINO FONTANA UNIFIED 39.998063204106 1.10104404176167 11.8054722188888 65.7746309852394 19.7108066971081 12.9685172647258 60468.7168949772 3939.78189127565 24.3713073776701 18.2534001431639 0 56.25 627.433972790867 625.397574910601 618.264922374043 25.880959431448 27.0517489415923 21.4247886356809 681.2 22 686.3 31 664.7 30 670.7 16 682.4 30 654.1 22 667.5 20 673.4 34 656.3 34 668.1 29 657.4 27 642.5 28 651.2 23 648.7 26 637.3 28 636 24 634.1 27 622.3 25 624 22 621.3 25 616.1 27 604.8 21 596.5 23 601.5 27 575.9 18 574.2 27 574.8 21 547.9 20 545.7 24 561.2 20 3675044 SAN BERNARDINO HESPERIA UNIFIED 47.6781020421918 .955685016691759 5.30863389408915 31.1906787981934 11.8971061093248 12.1917877906977 62220.1045016077 3865.72474962362 24.8130160271977 13.3440514469453 0 61.1111111111111 645.811905419082 636.345861854387 632.887036026201 37.3387008733625 34.2974486621033 34.072499769988 697.9 37 693.7 39 674.4 39 690.1 32 688 36 666.6 34 683.1 33 681.5 43 664.7 43 678.8 38 667.3 36 654.8 39 668.8 39 659 36 651.9 44 651.1 38 644.5 37 637.8 40 634.5 31 625.7 29 625.6 35 619.3 33 600.6 27 612.5 36 593.9 31 579.3 31 589.5 32 561.4 30 552.3 30 573.6 32 3675051 SAN BERNARDINO LUCERNE VALLEY UNIFIED 62.3115577889447 1.22484689413823 2.27471566054243 17.9352580927384 5.26315789473685 10.4692307692308 59114.4912280702 4587.3053368329 20.4873646209386 26.0869565217391 0 0 646.713190954774 636.121039903265 631.081157635468 35.2697044334975 34.2660217654172 33.7110552763819 684.9 25 677.6 23 665.5 30 694.1 35 684.9 33 665.9 33 683.4 33 682.1 44 663.3 41 676.3 36 660.9 30 648.1 33 653.2 25 646.6 24 634.8 26 648 35 643.4 36 625 27 640.7 37 636.1 39 631.1 41 632.8 44 613.1 38 623.5 46 594.1 31 577 29 592.5 35 567.1 35 562.6 40 577.1 36 3667777 SAN BERNARDINO MORONGO UNIFIED 46.7422949503062 1.50383631713555 8.19437340153453 13.3401534526854 4.5045045045045 13.4019387755102 62286.0720720721 4128.06496163683 22.6292806251436 13.5 5.88235294117647 0 649.351451800232 645.395127543709 636.913963963964 43.5964835803546 46.3238750358269 40.457462253194 703.7 44 700.6 47 681.6 47 697.6 39 696.6 46 670.3 37 687.4 37 688.6 50 666.8 45 683.1 43 675.2 44 656.8 41 670.2 40 665.6 43 650 42 655.8 43 659.2 51 644.7 47 643.8 40 638.9 42 630.8 41 630.2 42 617.5 42 624.3 47 604.8 40 596.2 47 599.6 42 570.1 38 573.6 51 585.7 46 3667801 SAN BERNARDINO NEEDLES UNIFIED 54.401519949335 1.16194625998548 3.7763253449528 17.283950617284 2.94117647058823 16.7946666666667 61234.9852941177 4903.2381989833 21.2772133526851 40.3508771929825 0 10 648.882936918304 640.701925025329 637.151745379877 44.7659137577002 42.2958459979737 40.3660806618408 698.2 37 694.5 40 680 45 688.5 30 690.3 39 669.2 36 683.9 34 680.9 42 668.6 47 683.2 43 675 44 659 44 675.1 45 669.9 48 655.2 48 656.5 43 648.3 41 644.1 47 639.3 36 628.8 32 632.7 43 632.9 45 620.2 45 625.8 49 597.3 33 588.7 40 593.6 36 588.4 53 573.2 50 590.9 52 3667843 SAN BERNARDINO REDLANDS UNIFIED 34.6040390288178 8.12395760477753 7.96255447355679 30.9894011943832 15.0335570469799 14.8490898058252 60477.2657718121 3763.68477968473 24.7211127943809 24.7743229689067 0 50 656.081160748377 651.376363772792 643.838623810985 47.177124884934 47.9456741952427 42.7080565101184 694.5 34 701 47 675.2 40 694.7 37 699.9 49 675.2 42 688.4 38 694 56 673.9 52 691.8 51 680.7 49 667.5 52 678 48 673.2 50 662.2 55 659.3 46 658 50 645.8 49 650.6 47 642.1 45 638.5 48 631.3 43 614.7 39 622.3 45 604.8 39 594.5 45 600.6 43 576.9 43 572.3 50 585.8 45 3667850 SAN BERNARDINO RIALTO UNIFIED 57.88501888376 2.87577590948377 27.3984442523768 51.5911055236898 24.4939271255061 12.1739946380697 59096.3066801619 3838.00078573112 25.1621099705255 13.2394366197183 0 70.8333333333333 630.819776598716 626.145838751625 623.00284021703 29.9329531613332 27.4568162115301 24.1199664898073 686.7 26 684.5 30 667.6 32 676.5 20 681.2 29 656.7 24 669.3 21 673 34 656.2 34 670.7 31 660 29 645.9 31 656.7 28 650.9 28 643.2 34 640.4 28 640.5 33 632.1 34 627.5 25 621.1 24 622.6 33 607.6 23 596.1 23 607.8 32 579.2 20 571.1 24 579.3 24 550 21 545.3 24 565.1 23 3667868 SAN BERNARDINO RIM OF THE WORLD UNIFIED 24.7007250042151 .979604946202023 1.26866870081901 13.0560462502007 10.2766798418972 15.791958041958 62201.8656126482 3995.41560944275 24.4390832328106 31.2865497076023 0 0 663.493173758865 657.51976744186 651.892599080359 55.119115393037 53.1539621016365 48.792109929078 707.5 47 703.1 49 689.4 55 698.5 40 694.3 43 680.3 48 692.6 42 690.6 52 678.2 57 695 55 678.4 48 668.3 54 686.3 58 678.5 57 668.7 63 662.6 50 666.3 60 653 57 651.6 48 648.3 54 645.2 56 638.6 52 629.5 58 633.1 57 613 51 601.3 55 608.9 53 575 47 573 57 587.6 52 3667876 SAN BERNARDINO SAN BERNARDINO CITY UNIFIED 70.2357454924486 3.36604410678485 19.6180225809855 50.849424923499 25.2196382428941 11.6793846153846 61672.8863049096 4147.68156589638 23.9868434683518 22.3952095808383 0 42.6229508196721 629.083041804347 626.491443928802 621.690639289877 29.5900654532413 29.2053692063679 23.6404037954346 688.8 28 692.9 39 672.1 37 675.9 20 685.5 33 657.5 25 669 21 675.5 36 656.6 35 669.5 30 660.8 30 648.5 33 653.6 25 652.2 29 641.8 33 638.9 26 638.9 32 629.1 31 624.2 23 623.2 26 618.5 29 606.5 22 597.1 24 605.1 30 580.3 21 574.1 26 581 25 551.8 23 546.6 25 565.5 23 3673890 SAN BERNARDINO SILVER VALLEY UNIFIED 46.9641550841258 2.10789567702751 18.1850660950339 12.0400142908182 7.91366906474819 11.0990683229814 60618.4100719425 5342.53733476242 20.2528901734104 18.348623853211 0 0 650.362307692308 643.62908301682 635.705941143809 43.6912826207662 46.2045577862181 43.4203296703297 698.9 38 693 38 682 46 697.3 39 693.5 42 678.1 46 689.3 39 683.3 45 668.8 47 692.4 52 673.6 42 666.4 51 674.7 44 659.8 37 650.6 43 656.9 44 652.5 45 637.2 39 647.9 44 644 47 634.1 44 634.5 47 623.5 48 624.2 47 604.6 40 599.6 50 596.4 39 576.9 44 581 58 580 39 3673957 SAN BERNARDINO SNOWLINE JOINT UNIFIED 20.984126984127 .826188620420889 2.08885424785659 16.6796570537802 4.05405405405406 8.42002881844381 53764.1993243243 3823.18035853468 22.5206611570248 10.2484472049689 9.09090909090909 0 662.535723570191 655.407981119931 648.334442523768 51.4716940363008 51.1527569191161 48.2629982668977 701.2 41 702.5 49 680.8 46 694.3 36 700.8 50 675.1 42 691.4 41 696.7 59 673.3 51 696.9 56 682.8 52 671.8 57 679.7 50 668.3 46 660.6 54 664.6 52 662.8 55 648.8 52 658.5 55 651.9 56 644.2 54 641.6 53 618.4 43 628.5 51 612.5 47 598.8 49 606.7 48 584.2 50 575.7 53 596.6 58 3675069 SAN BERNARDINO UPLAND UNIFIED 30.647120055517 7.22630173564753 11.4903204272363 28.4796395193591 11.4563106796116 13.9812068965517 59659.7650485437 3922.56667222964 23.5105551211884 35.3135313531353 6.66666666666667 6.66666666666667 644.531339823829 632.309168925023 634.454106132436 50.2338278024163 44.4777175549533 46.7111729253593 677.6 19 674.3 19 653.2 20 677.6 21 677.1 24 655.7 24 682.2 32 677.1 38 669.7 48 692.3 52 683.8 52 669.1 54 683.2 53 674.4 52 664.8 59 664.5 52 663.2 55 651.6 55 649.7 46 639.2 42 637.7 48 634 46 613.3 38 628.1 50 605 40 586.7 38 600.1 42 576.2 43 561.5 39 588.5 49 3667918 SAN BERNARDINO VICTOR VALLEY 44.9199607971251 1.61820323640647 16.4176328352657 36.1708723417447 15.5339805825243 10.971671388102 61492.8507936508 4057.49705499411 26.5114405414115 13.9705882352941 15 20 648.337447048856 642.959543184761 636.856736065727 40.8697600597517 40.029221379693 36.1985314882801 693.3 32 689.7 35 671.5 36 687.8 30 686.3 34 664.1 31 681.1 31 679.3 40 662.3 40 679.9 39 670.3 39 653.4 38 667.9 38 660.1 37 651.9 44 657 44 660.9 53 647.4 50 643.8 40 637.7 40 632.8 43 627.1 39 614.4 39 622.1 45 600 36 591.1 42 598 40 564.5 33 562.5 40 581.1 40 3667959 SAN BERNARDINO YUCAIPA-CALIMESA JT. UNIFIED 27.5710334422932 .762642262114279 .77437521999296 19.6644374046697 6.06060606060606 11.880487804878 63432.7181818182 3784.39035550862 25.0716245047242 25 0 70 660.963865401208 653.070776566758 645.047559298728 47.8502921966311 48.70810626703 45.8515962036238 710 50 705.8 53 684.8 50 695 36 696.8 46 670.2 37 690.4 40 695.5 57 670.2 48 688.9 48 674.3 43 661.5 46 679.1 49 675.3 53 662.9 56 663.9 51 664.7 57 650 54 654.8 51 643.2 46 640.3 50 638.4 50 621.3 46 628.5 51 607.6 42 589 40 597.3 40 577 44 570.1 47 588.2 48 3773551 SAN DIEGO CARLSBAD UNIFIED 26.9230769230769 2.59466170080695 1.76288019863439 26.1328367473619 13.3333333333333 15.2839285714286 62997.1121212121 4261.82011173184 24.3261749144102 43.4447300771208 0 0 675.131481481482 670.382800941493 660.844547008547 63.8950427350427 65.6696368527236 60.6031260618417 711.9 52 708.8 56 693.3 59 705.9 48 702.6 51 688.3 56 700.2 50 698.9 61 683.5 61 704.1 63 692.2 60 684.5 68 696 66 690.3 68 678 71 678.2 66 687.2 76 660.2 64 671.2 66 672.1 74 659.2 68 658.6 68 646.5 70 644 65 631.4 62 618.5 67 622.8 63 601.5 65 597.6 73 603.9 64 3768031 SAN DIEGO CORONADO UNIFIED 12.8909229595728 1.74927113702624 2.58746355685131 10.4956268221574 8.66141732283464 15.0795454545455 59963.7874015748 4346.54555393586 22.3699421965318 58.8235294117647 0 0 685.812943528236 678.442246520875 668.551767048283 70.2528621204579 71.7176938369781 69.2713643178411 725 66 722.8 70 702.7 68 722 65 713.7 64 697 65 710.7 60 707.6 69 687 65 714.5 73 706.3 73 687.4 72 702.7 72 696.4 73 677.4 72 686.9 74 681.6 72 671.1 74 677.2 72 670.6 74 663.4 72 663.6 72 647.6 71 649 69 638 68 627.3 75 625.1 66 610 72 603.6 78 621.7 81 3768098 SAN DIEGO ESCONDIDO UNION 43.1771475544595 2.75243544147209 1.7975877532086 43.8108860368022 8.99908172635445 14.0709437086093 58398.8970798898 3882.45098422762 23.4224049331963 29.0118577075099 4 44 654.3185102935 648.733153018358 641.556212530857 46.9538027506759 47.8680439661622 42.2829361983074 706 46 699.7 46 683.9 49 699.7 41 695.6 45 677 44 694.7 44 692 54 675.7 54 689.5 49 678.5 47 666 51 676.6 47 669.8 47 659.3 52 656.4 43 661.2 53 647 50 644.2 40 644.3 47 637.8 47 628.1 40 621 45 622.9 46 599.5 35 595.6 46 596.4 39 573 40 570.7 48 581.3 40 3768114 SAN DIEGO FALLBROOK UNION 49.1896468311563 .898770104068117 4.3282876064333 36.2109744560076 10.1408450704225 16.5610126582279 66966.7211267606 4540.89427625355 24.1105354058722 22.4609375 0 0 658.178589678079 649.598358753316 644.485851117459 47.8462443286843 45.9941976127321 44.0805654913984 703.3 43 699.2 45 681.5 47 696.7 39 697.6 46 677 44 692.1 41 694.3 56 675.4 53 693.2 53 684.4 53 670.8 56 685 55 679.4 57 667 61 664.2 52 668.4 60 653.5 57 648.3 44 639.3 42 638.2 48 635.7 47 611.9 37 622.9 46 603.1 38 582.6 34 594.6 37 563.8 32 556.8 34 574.6 33 3768163 SAN DIEGO JULIAN UNION 7.72303595206391 .138121546961326 .69060773480663 9.25414364640884 5 15.9693181818182 62789.975 5092.90745856354 19.0956072351421 32.0754716981132 0 0 674.98523364486 667.565988909427 655.901663585952 55.1293900184843 57.9334565619224 54.8616822429907 706 46 702.5 49 682.9 48 696.3 38 699 48 666.4 33 686.2 35 686.4 48 664.4 42 719.1 76 700.6 69 687.2 72 694.8 65 692 70 681.4 76 678.8 66 678.1 70 659.4 63 665 61 647.6 52 650.2 60 657.1 67 638.1 62 640.8 61 620.4 54 605.2 56 606.9 49 588.7 54 585.4 63 596.3 58 3768213 SAN DIEGO MOUNTAIN EMPIRE UNIFIED 48.6942328618063 .163220892274211 1.4689880304679 25.2992383025027 4.3010752688172 12.1626213592233 52084.3978494624 4470.92056583243 20.1787709497207 40.8695652173913 0 0 655.573507462687 648.464296296296 641.53604826546 44.1809954751131 44.2 41.234328358209 692.9 33 687.6 33 669.6 34 691 33 693.3 41 670.5 37 683.4 33 690.3 52 662.7 41 687.5 47 669.8 38 660 45 673.3 43 663.5 41 657.1 50 660.4 47 658.5 51 642.3 45 645.9 42 638.3 41 636.9 46 637.8 49 614 39 626.5 49 602 37 593 44 600.1 42 582.4 48 580.2 58 591.2 51 3773569 SAN DIEGO OCEANSIDE CITY UNIFIED 54.9773988083008 1.80425939219909 14.8600143575018 41.5218951902369 16.013437849944 13.1737055837563 57811.1422172453 3832.5821009811 23.3502479529466 44.7178002894356 0 0 640.598977391304 634.624421296296 630.728302937491 39.543366281498 37.8617919389978 34.5817739130435 690.5 30 690.9 36 671 36 684.5 26 688.2 36 662.9 30 678.3 29 680.1 41 662.8 41 684.3 44 669.9 38 663.5 49 667.3 37 659.9 37 652.7 45 653 40 652.3 44 641.6 44 639.4 36 633.6 36 630.8 41 622.9 35 610.4 35 618.8 42 594.4 31 583.1 34 591 34 567.1 35 563.4 41 576.4 34 3768296 SAN DIEGO POWAY UNIFIED 10.5881569750025 8.75586330131785 2.76013912377549 7.79220779220779 11.0151187904968 14.1915538362347 58198.62275018 3718.16908644181 22.8757095906782 46.6887417218543 0 0 681.429950602305 677.907482088464 667.726259878223 70.3265967094183 72.5113475481574 66.1724152872866 716.6 57 721.2 69 698.6 65 711.9 54 713.2 63 693 61 706.7 56 713.1 74 691 68 711.1 70 704.7 72 687.3 71 701.8 71 696.1 73 682.1 76 684.5 72 687.1 76 667.1 71 678.7 73 674.4 76 666.8 75 667.2 75 648.9 72 653.8 73 638.2 68 629 76 632 71 602 66 598 74 610.5 72 3768304 SAN DIEGO RAMONA CITY UNIFIED 35.0236546422235 .704225352112676 .876688703650474 19.6177062374246 7.49185667752444 13.5145161290323 57168.1302931596 3976.02960620868 23.1159175397094 39.7368421052632 0 0 670.183532751977 661.177163940965 652.80687851971 55.8986323411102 56.5917431192661 55.3364429121882 707 47 701.4 48 684.7 50 702 44 697.5 46 678.8 46 694.1 43 693.2 55 672.9 51 701.8 61 684.7 53 672.1 57 685.8 56 672.1 50 661.1 55 674.9 63 676.6 68 658.1 62 662.7 59 657.9 61 646 56 653.6 64 633.7 58 640.3 62 626.2 58 609.9 60 619.3 60 592.9 58 586.4 64 597.3 59 3768338 SAN DIEGO SAN DIEGO CITY UNIFIED 64.1523473458116 9.49274671088837 16.9243412604654 35.2773273262256 25.0849652047257 12.2959692898273 62782.7030263797 4952.58531878518 22.193133902188 31.2403234130397 4.16666666666667 28.5714285714286 650.53792231777 646.218283229981 639.276522675464 45.5376015212436 46.3890985890177 40.3608356899636 699.9 39 700.5 47 682.1 47 691.5 33 694.8 43 671.8 39 686.7 36 689.2 50 670.9 49 684.1 44 674.6 43 662.2 47 671.1 41 667.8 45 657.2 50 656.6 44 656.5 49 644.7 48 645.9 42 641.8 46 636.7 47 628.2 41 616.1 43 621.9 46 602.2 39 595.1 47 597.9 40 573.3 43 570.6 50 581.7 43 3773791 SAN DIEGO SAN MARCOS UNIFIED 49.2650415411303 2.38978517815547 2.55370546113364 44.1376930377017 11.0647181628393 13.668029739777 60657.1607515658 4097.09248554913 24.6399825973461 29.6551724137931 0 83.3333333333333 653.268111815711 651.195564163439 642.022429078014 48.4894883485309 51.2722728976634 43.4528277468617 702.4 42 699.2 46 681.9 47 688.3 30 693.6 42 669.6 36 681.7 32 689.4 50 668 46 684.6 44 677.1 46 662.2 47 670.4 40 673.8 51 658.4 51 663.5 51 671.2 63 651.3 55 653.3 50 648.9 52 642.3 52 638.9 50 626.2 51 631.3 54 613.2 47 606.7 57 607.6 49 578.4 44 573.8 51 585.4 45 3768452 SAN DIEGO VISTA UNIFIED 40.0597659168258 2.53261999153227 6.12755475154921 37.3850121242446 11.0909090909091 12.812450748621 65164.4454545455 4103.44648012009 23.6444866920152 34.3324250681199 3.7037037037037 81.4814814814815 653.530254976898 645.181577922439 640.063129506615 45.9587804462613 45.2737439492572 43.5388739946381 701.8 41 698.1 44 678.7 44 694.3 36 693.3 42 668.6 35 690.3 40 690.6 52 671.1 49 688 48 673.6 43 664 49 678.9 50 668.2 46 659.4 53 659.8 47 655.6 48 643.4 47 647.3 44 639.6 44 637 47 632.1 45 614.6 43 623.3 47 602 41 589.2 43 596.9 41 570.2 42 564.7 47 583.3 46 3868478 SAN FRANCISCO SAN FRANCISCO UNIFIED 64.5542826673561 41.3690232268428 16.1932237284246 21.2041241169046 43.7374605904271 15.2854677206851 52885.5067354543 5230.05073188323 17.9311759878063 48.8306565229642 2.65486725663717 1.76991150442478 658.739665223665 661.291423925138 647.996224272947 50.8723181275654 56.3745114262075 43.9237806637807 704 44 717.9 64 689.9 56 695.9 37 707.5 56 678.6 46 692.4 42 703.8 65 679.5 57 688.1 47 688.1 56 667.1 52 676.5 47 680.5 57 662.5 56 656.4 43 664.2 56 644.8 48 649.3 45 651.7 55 640.3 50 633.7 46 625.1 50 628 50 604.2 39 601.1 51 602.4 44 584.9 51 579.2 56 590.4 51 3968502 SAN JOAQUIN ESCALON UNIFIED 36.4128595600677 .919842312746386 .328515111695138 26.6425755584757 5.67375886524822 14.1924528301887 53510.4397163121 3846.51215505913 23.3205521472393 26.4150943396226 0 0 661.910785749146 654.90570754717 649.375467177767 52.7709631049353 50.8150943396226 47.4553440702782 700.7 40 700.3 47 680.1 46 690.4 32 694.5 43 670 37 695.8 45 692.5 54 677.1 55 698.4 57 684.9 54 673.9 59 678 48 667.7 46 661.4 55 666.6 54 663.9 56 653.1 57 658.4 55 647.8 51 648.8 59 640.4 52 629.4 54 632.9 55 605.9 41 598.9 49 599.2 41 585.9 51 576.8 54 600.1 63 3968569 SAN JOAQUIN LINCOLN UNIFIED 44.1298342541436 19.6276905177429 10.6922629435718 17.6265270506108 14.7342995169082 13.2013742071882 53970.809178744 4022.26410703898 21.5606361829026 29.8353909465021 0 0 653.120987453153 648.215219123506 643.269463793941 46.5541875911226 43.7188844621514 39.3379501385042 693.6 33 699 44 681.3 47 686.2 28 695.7 44 672.1 39 680.5 31 688.7 50 673.6 52 690.7 50 676.9 46 667.6 53 672.9 43 668.6 46 658.2 51 661.5 49 658.3 51 645.3 48 650.1 46 639.1 42 637.8 48 628.1 40 613.3 38 623.8 47 602.9 38 588.3 39 597.7 40 567 35 560.3 37 581.9 41 3968577 SAN JOAQUIN LINDEN UNIFIED 40.5828621139626 1.93602693602694 .336700336700337 34.2171717171717 7.20720720720721 16.1252032520325 52198.8558558559 3727.90909090909 22.0265151515152 39.2857142857143 0 0 652.678872403561 644.666724237191 639.678812572759 40.9796274738068 38.2941853770869 36.4160237388724 692.7 32 694.7 40 672.1 37 690.1 32 687.3 35 666.3 33 683.1 33 685.2 47 664.4 42 682.6 42 666.9 36 658 42 675.1 45 663.4 41 656.3 49 651.5 38 649.1 41 640 42 638.8 35 630.9 33 635.2 45 629.3 41 609.9 35 622.7 46 597.9 34 582.7 34 593 36 560.9 30 563.5 41 578.1 37 3968585 SAN JOAQUIN LODI UNIFIED 48.7686274509804 19.7954739870908 5.83249086243098 23.6488062835368 11.271186440678 15.083598265896 59465.2338983051 4469.02146356637 22.0029152019206 30.3370786516854 0 62.8571428571429 646.503272085196 639.40676819852 635.370433124489 39.6596022882049 37.8718249108046 34.3092203277603 693 33 697 44 675.4 40 685.1 28 693.5 44 664.9 32 683.1 34 687.4 49 668.3 47 682.2 42 669.2 39 659.8 45 667.1 39 662 40 653.5 47 651.9 39 645.5 39 639.1 42 635.7 33 627.1 32 627.5 38 619.5 34 602.9 32 616 41 588 29 573 29 586.2 31 555.8 31 548.3 32 570.1 33 3968593 SAN JOAQUIN MANTECA UNIFIED 35.1331654962237 2.4496294935391 4.93600342948129 29.0954743095107 11.3263785394933 13.8097754293263 56910.6646795827 3589.19701145202 24.385775862069 36.2426035502959 0 0 653.420248760546 648.740296094614 639.964641555286 45.0128449921889 47.2959244448226 41.5854570757589 698.5 38 701.1 48 676.5 41 691.2 33 697.3 46 666.7 34 690.1 39 695.3 57 670.2 48 690.4 50 681.4 50 663.5 48 676.4 46 674.2 52 658.5 52 657.7 44 662.3 54 645.4 49 647.4 44 639.9 43 637.6 48 629.5 42 619.4 44 621.9 45 604.5 40 591.6 42 598.1 40 570.8 38 562.4 39 583.1 43 3968650 SAN JOAQUIN RIPON UNIFIED 13.773987206823 .730816077953715 .48721071863581 21.8432805521721 2.56410256410257 14.5503875968992 51683 3786.43036946813 20.5988023952096 29.7297297297297 0 0 665.134521880065 664.102466487936 654.637203023758 59.0599352051836 61.3678284182306 52.5834683954619 699.4 39 696.3 43 674.3 39 695.8 37 695 44 671.6 39 689.1 39 692 54 670.1 48 703.2 62 701.8 70 683.2 68 687.2 57 690.3 68 670.8 65 664.4 52 676.8 68 661.1 65 657.4 54 654.2 58 650.6 61 650.9 62 638.3 63 641.3 63 625 57 619.4 68 625.4 65 597.2 61 594.1 70 609.5 69 3968676 SAN JOAQUIN STOCKTON CITY UNIFIED 68.7270837543667 20.8724926357133 13.3482956936457 42.1854397531211 33.7475474166122 12.677675070028 66654.75147155 4527.22617477907 22.9404855129209 18.2092555331992 0 21.9512195121951 626.294401667588 625.040340654415 618.696566775791 27.7514060270293 29.0440487347704 22.2195516229208 683.5 24 686.3 31 666.9 32 674.3 18 683.1 30 655.5 23 668.5 21 677.4 38 657.9 36 664.5 26 660.9 30 642.7 28 647.7 21 650.1 27 636.5 28 638.3 26 638 31 628.6 31 620.6 20 618 23 615 26 603.1 20 595 23 602.9 29 575.9 19 573.8 28 577.2 23 554.5 27 552.7 33 565.1 25 3975499 SAN JOAQUIN TRACY JOINT UNIFIED 26.5703275529865 4.43653412050703 5.98194130925508 26.7233894773398 14.19624217119 10.5934981684982 55631.8997912317 3616.36638305261 23.96259626 26.2867647 0 0 657.620744108147 652.641071428571 645.445892687559 48.9863485280152 48.9051926691729 43.6359612393827 700.1 39 701.8 48 679.5 45 694.9 36 696.3 45 672.4 40 690 39 693.5 55 673.3 51 693.1 52 685.9 54 666.6 52 678.2 48 675.3 53 661.4 55 664.1 51 662.1 54 648.9 52 653 49 645.6 49 646.7 57 633.6 45 620.3 45 628.4 51 607 41 593.8 44 603 45 572.7 40 567.4 44 584.4 44 4068700 SAN LUIS OBISPO ATASCADERO UNIFIED 18.0736636245111 1.06577851790175 1.64862614487927 9.34221482098251 3.28467153284672 14.9725806451613 60464.2408759124 4506.42464612823 23.304248861912 45.4545454545455 0 0 678.001860465116 667.072236267525 661.377217835578 63.4382257315374 61.4366812227074 61.55 717.6 58 709.6 57 698.5 64 711.2 54 703.9 54 693.1 61 706.4 56 704.8 67 687.5 65 706.3 65 696.8 65 679.6 65 694.3 64 680.7 59 669.7 64 680 68 675.9 68 662.8 67 668.5 64 655.1 59 651.6 62 654.6 65 634.7 59 642.5 64 628.8 61 609.9 60 618.5 59 597 61 588.6 66 601.4 63 4075465 SAN LUIS OBISPO COAST UNIFIED 27.0877944325482 1.00502512562814 .301507537688442 21.608040201005 9.23076923076923 12.8641891891892 46347.3846153846 4792.46130653266 17.3713235294118 41.3333333333333 0 0 675.78129395218 659.928201634877 656.442441054092 53.619972260749 46.7506811989101 52.4669479606188 709.9 50 705.2 52 682.7 48 698.4 40 696 44 673.6 41 698.5 48 693.3 54 674.4 52 701.2 61 681.6 51 681.1 66 687.4 57 664.2 42 670.9 65 679.2 67 668.5 61 664.2 68 669.3 65 640.7 42 647.6 58 649.9 61 610.4 35 629.9 53 617.3 50 598 48 606.7 48 566.6 35 554.9 32 587.2 48 4068759 SAN LUIS OBISPO LUCIA MAR UNIFIED 38.0746712736347 1.53803131991051 1.16517524235645 30.2013422818792 8.93203883495146 13.4831597222222 55684.2582524272 3887.0884601044 21.2192704203014 25.9036144578313 0 0 668.336747668833 660.265566037736 653.880173742469 57.6306571388539 56.7943951165372 54.3489686352077 707.1 47 704.4 51 686.4 52 702.3 44 699.7 49 680.5 48 699.2 49 700.5 63 678.3 57 705.7 65 694 63 679 64 687.6 58 682.6 61 669.8 64 674.2 62 673.1 65 657.9 62 659.8 56 651.7 55 648.7 59 644 55 625.2 50 634.1 56 616.7 50 599.2 50 609.7 51 590.3 55 581.7 59 600.4 61 4075457 SAN LUIS OBISPO PASO ROBLES JUSD 36.8269067436725 1.33048620236531 3.87647831800263 27.1846254927727 5.80204778156997 14.2278425655977 59653.0341296928 4756.44152431012 22.2814653608995 39.8148148148148 0 0 660.040743405276 650.914003759399 646.067205208585 49.2531950807813 47.344219924812 45.636690647482 705.3 45 700.3 48 683.6 49 701.2 44 697.8 50 679.4 47 694.3 44 694.7 57 676 55 695 55 681.4 51 668 54 677.5 48 672.1 50 659.2 53 662.2 50 656.8 50 645.3 49 649.2 46 638.8 43 636.4 46 633.6 46 610.3 38 625.9 50 603.8 41 589.8 43 599.7 43 566 38 561 42 583.4 46 4068809 SAN LUIS OBISPO SAN LUIS COASTAL UNIFIED 22.4657866053046 2.34638169357649 2.0908351724939 12.6147055407132 5.32687651331719 16.19522417154 64397.6755447942 4933.22348704844 21.4332659251769 25.635593220339 5.26315789473684 0 683.558106585091 673.451621621622 664.669967373573 66.636541598695 67.3852146263911 66.9017871518274 725.5 66 722 69 698.4 65 718.1 61 712.2 62 690.7 59 710.2 59 711.6 72 688.4 66 707.2 66 695.1 64 683.8 68 693.4 63 689.3 67 674.7 69 685.6 73 686.4 76 667.8 71 678.7 73 661.7 65 660.1 70 664.6 73 642.7 67 646.1 67 638.3 68 612.8 63 622.5 63 605.6 68 591.8 68 606.8 68 4068841 SAN LUIS OBISPO TEMPLETON UNIFIED 17.9978118161926 .617828773168579 1.41218005295675 9.22330097087379 4.58715596330275 11.0872950819672 50372.4678899083 3667.01941747573 19.3939393939394 35.9550561797753 0 0 673.663157894737 660.333891213389 658.17453565009 60.5056920311564 54.7489539748954 57.9606775559589 709.6 50 697.2 44 682.5 48 708.7 51 699.4 48 680.4 48 706 55 700.4 63 680 58 701.5 61 684.9 54 678.4 64 691.1 61 685.3 63 672.2 67 683.5 71 670.3 62 665.1 69 662.6 59 650.1 54 657.7 68 655.3 66 628.5 53 647.6 68 615.7 49 595.5 46 611.8 54 593.7 59 583.1 61 599.9 62 4168890 SAN MATEO CABRILLO UNIFIED 19.3020719738277 2.1085111853947 .539984571869375 25.0964258164052 8.29015544041451 13.3228971962617 51768.2660621762 4138.21131653381 21.0093252879868 48.8095238095238 0 0 670.851140684411 658.191318803103 654.942991356633 58.6384817737693 54.8485408200961 56.5441064638783 717.4 58 716.1 63 695.1 61 700.3 42 698.2 47 677.9 45 705.5 55 700.2 62 685.8 63 701.8 61 684.9 53 682.4 67 693.7 64 684.3 62 670.4 65 673.8 61 665 57 654.8 59 659.7 56 652.6 56 647.2 57 649 60 624.5 49 638.8 60 621.9 54 603.7 54 611.6 53 583.7 49 569 46 591.1 52 4169070 SAN MATEO SOUTH SAN FRANCISCO UNIFIED 31.9148936170213 8.75331564986738 4.82365654779448 34.7971313488555 11.8993135011442 17.1086138613861 57489.2173455378 3823.83839375184 23.5231970601746 38.9544688026981 0 0 657.938155779629 651.254546756409 645.310129153969 49.4857059933246 48.261205785479 44.5271079935701 699.2 38 699.5 46 681.2 47 697 39 701.6 50 680.4 48 692.1 41 693.5 55 679.2 57 683.6 43 675.7 44 658.8 44 674.8 45 670 47 657.1 50 662.1 49 658.5 51 647.2 51 653.9 50 646.9 50 643.9 54 633.1 45 618.6 43 626 49 609.2 44 604.1 54 606.4 48 584.1 50 565.9 43 586.6 47 4269146 SANTA BARBARA CARPINTERIA UNIFIED 39.2772711921648 1.38530927835052 .966494845360825 54.3814432989691 21.3235294117647 14.4977419354839 60262.9117647059 4158.06894329897 22.2132943754565 33.3333333333333 0 0 657.955866983373 652.616290842154 647.817581395349 50.293023255814 47.7096180395766 42.8688836104513 696.3 35 694.9 40 679 44 692.5 34 692.8 41 679.9 47 679.9 30 690.1 51 671.4 49 689.5 49 679.8 48 671.4 56 669.7 40 668 45 658.4 50 658.7 46 654.8 47 646.3 49 652.3 48 644.3 47 640.7 51 643.5 55 629.1 54 635.9 58 601.5 37 597.9 48 596 39 587.3 53 577.1 54 596.5 57 4269229 SANTA BARBARA LOMPOC UNIFIED 35.7063300538333 4.65199180108725 8.92077354959451 32.8669459049996 9.0573012939002 17.0831674958541 53117.7153419593 4325.81900008912 21.6737698566447 42.914979757085 0 13.3333333333333 652.84358281893 640.795576875156 636.877135995956 42.2170121334682 39.9328432594069 41.5646862139918 700.8 40 702.2 48 679.7 45 693.2 35 692.1 40 669.9 37 683.4 33 687.1 49 666.5 44 688.6 48 673.9 42 661.6 46 679.5 50 665.9 43 657.5 50 660.6 48 650.1 42 641.2 44 648.2 44 637.4 40 633.7 44 631.3 43 611.2 36 619.5 43 603.4 38 584.3 35 594.3 37 569.2 37 551 29 575.5 34 4369484 SANTA CLARA GILROY UNIFIED 44.5420326223338 2.30897936419409 1.5281650864473 62.9447852760736 22.3719676549865 15.4896551724138 62890.8086253369 4312.72950362521 24.507874015748 20.1900237529691 0 15.3846153846154 650.112128626354 639.755846077948 637.302743902439 42.6212737127371 39.8852162473277 39.2345333799371 696.2 35 697.8 43 677.1 42 689.4 31 693 41 669.1 36 684.7 34 690.3 52 670.3 48 682.4 42 668.5 37 657.6 42 668.8 39 660.9 38 650.9 43 660.5 48 658.6 51 647.7 51 644.2 40 634.9 37 633.4 43 626.8 39 609 34 617.6 41 599.2 35 582.8 34 594.6 37 579.7 46 559.4 36 583.3 42 4373387 SANTA CLARA MILPITAS UNIFIED 28.8935721812434 31.4598833701991 5.95214156444802 18.4295194047858 20.2272727272727 14.806374501992 60774.9181818182 4090.01588578323 22.1197740112994 26.7206477732794 0 0 662.136157941437 661.338135961734 648.919647918842 53.8408175443831 58.4918104073054 49.6240757172434 696.3 36 706.9 54 680.7 46 693.2 35 702.6 51 675.2 42 688.1 38 697.6 59 674.4 52 696.1 55 688.9 57 669.2 54 690.5 60 691.5 68 672.6 67 672.2 60 674.4 66 660.3 64 658 54 656.5 60 649 59 641.3 53 630.7 55 633.3 56 613.6 47 605.7 56 607.3 49 588.8 54 581.3 58 587.2 48 4369583 SANTA CLARA MORGAN HILL UNIFIED 23.6490993995997 5.23565792279804 2.39923224568138 33.4612923864363 11.25 17.7960850111857 60283.845 4361.51503518874 23.7371134020619 37.8048780487805 0 0 666.216356483583 659.320322915124 649.390683043739 52.9802276812463 55.3657235965042 51.7793917385384 707.5 47 710.7 58 684.1 50 696.6 38 703.4 52 673.1 40 701 50 707 68 678.9 57 698.3 58 688.3 57 673.5 58 684.9 55 677.9 56 663.2 57 668.9 57 668.2 59 651.2 55 653.9 50 645.1 48 641.2 51 644.9 56 625.6 50 632.6 55 618 51 604.1 54 610.1 52 588.8 54 573.5 51 593 53 4369641 SANTA CLARA PALO ALTO UNIFIED 7.89443488238669 17.3890007417612 4.91681678499523 6.8877821341528 13.528336380256 14.1157512116317 66182.0091407678 5970.82324891385 18.7476866132017 73.3752620545074 0 0 698.751069604087 698.750649145028 682.214690885915 81.8879859783302 86.2845155161495 81.1083971902937 739.9 79 754.8 89 719.9 82 730.8 74 745.8 86 710.1 76 729.9 77 743.6 90 708.6 81 724.1 80 731 87 706.7 85 714.6 81 719.1 87 695.7 85 702 85 711.2 89 681 81 697.4 86 694.1 88 682.4 85 686 86 662.7 82 663.7 80 660.4 82 639.3 82 647.4 82 622.7 80 613.5 84 624.1 82 4369666 SANTA CLARA SAN JOSE UNIFIED 42.8078358208955 12.2450216712636 3.27039068893402 49.4104810111236 22.3695111847556 16.5772932330827 80565.0364540182 5038.39963022459 28.2108543235523 38.1075826312378 0 0 655.468175303962 647.038183888913 641.538434616608 45.6173810281351 45.3295807963555 42.4182885673339 704.3 44 706.1 52 685 50 694.2 36 699 47 675.4 42 688.9 38 695.1 56 673.3 51 687.1 47 680 48 662.9 47 674 44 669.5 46 657.1 49 657.6 45 653.9 46 641.8 44 649.3 45 640.3 43 639.3 49 631.9 44 614.4 39 623.1 46 606.8 41 590.8 41 600.2 42 574 40 561.4 39 580 38 4369674 SANTA CLARA SANTA CLARA UNIFIED 40.20545013554 18.3941204753074 4.34095748334364 25.2009066556769 11.52 15.6099728629579 65468.92 4317.31904663782 23.7628014535844 29.5511221945137 0 0 655.844454600853 649.07458432304 643.911948427254 51.5725241747249 50.1679532858274 45.9975624619135 696.6 36 701.6 49 680.5 46 690.4 33 696.9 49 673.8 41 686 36 691.1 53 676.8 56 689.4 49 683.1 52 663.4 48 679.8 51 676.6 54 661.9 56 661.9 49 656.6 50 647.5 51 654.6 51 644.4 49 646.2 56 638.6 51 618.5 46 631.9 55 612.9 51 595.7 49 607.1 50 578.2 49 567.8 51 589.2 53 4469799 SANTA CRUZ PAJARO VALLEY JOINT UNIFIED 56.3486693730266 1.20137602540355 .587456999206139 72.0137602540355 19.7166469893743 14.11421107628 59922.1286894923 4282.14601746494 22.5352977286679 26.647564469914 4 20 640.186193505742 639.3257624461 628.568499879217 32.5221837507046 37.3257546060368 28.6157151119557 690.3 30 690.3 35 668.8 33 682.8 25 689.1 37 660.8 28 677.9 28 682.3 43 661.3 39 676 36 668 36 653.8 38 660 31 660.2 37 645.9 37 644.4 31 647.1 39 633.4 35 631.4 28 634.5 37 622.7 33 611.3 26 608.3 33 605.8 30 585 24 586.2 37 583.8 27 557.8 27 561.9 39 567.2 25 4469807 SANTA CRUZ SAN LORENZO VALLEY UNIFIED 14.506396331161 1.65905265688868 1.22625631161337 4.08752103871123 3.33333333333333 17.2891625615764 58616.2833333333 4262.08776148113 24.3335290663535 60.5809128630705 14.2857142857143 0 676.616056910569 662.310665329321 658.5132996633 60.0437710437711 55.7355399531929 59.2906504065041 714.7 55 706.8 54 689.2 55 704.1 46 696.8 46 679.9 47 701 50 698.3 61 681.6 59 707 66 687.2 56 681.2 66 692.1 62 666.9 45 673.7 67 680.7 68 676.7 68 661 65 672.6 68 659.9 63 657.3 67 654.8 65 627 51 638.8 61 627.1 59 611 61 612.5 54 590.3 55 573.8 51 597 59 4569989 SHASTA FALL RIVER JOINT UNIFIED 39.608938547486 .747126436781609 .28735632183908 8.9080459770115 4.3010752688172 16.4912037037037 56131.9429032258 4741.87406896552 18.7363834422658 28.8288288288288 0 0 662.603135313531 651.091162420382 643.225383993533 44.8334680679062 45.3734076433121 45.9117161716172 701 40 700.6 47 675.5 41 696.1 37 693 42 667.9 35 690 39 690.6 52 667.7 46 692.3 52 674.4 43 667.2 52 673.7 44 665.6 43 650.2 42 659.4 47 664.9 57 646.5 50 658.9 55 643.7 47 637.2 47 647.9 59 621.4 46 633 55 611.3 45 584.7 36 598.3 40 577.1 44 564.2 41 579.8 39 4575267 SHASTA GATEWAY UNIFIED 49.3771234428086 .84053233714686 1.07401354190988 4.80971281811814 4.09090909090909 14.5858299595142 55396.6149090909 4509.5146509456 20.7381288199342 34.4827586206897 0 0 653.934816312774 639.410946555055 634.704659498208 38.2245030954708 35.9034127495171 38.7081226828446 686.8 27 689.2 34 664.7 30 689.2 31 694.1 41 663.2 30 687.6 37 682.7 44 665.4 44 688.8 48 672.6 41 660.2 45 670 40 656.4 34 652.9 45 658.1 45 652 44 640.7 44 645 41 627.9 31 629 39 630.8 43 604.7 30 618.4 41 606 41 583.4 35 591.9 35 561.9 30 547.5 26 570.3 28 4670177 SIERRA SIERRA-PLUMAS JOINT UNIFIED 32.1016166281755 1.63316582914573 .628140703517588 8.35427135678392 1.9607843137255 14.4036363636364 54122.0196078431 2908.31155778895 16.8888888888889 43.2432432432432 9.09090909090909 0 672.277259752617 658.577871939736 653.042403846154 54.8115384615385 52.5866290018832 55.6641294005709 705.5 45 694.5 41 680.2 45 707 49 697 46 680.6 47 697.2 47 690.7 53 675.4 54 706.7 65 692.3 61 678.7 63 688.6 59 676.7 55 662.8 55 673.1 61 662.3 55 653.7 57 662.3 58 652.3 55 648 58 644.7 56 627.2 52 637.4 59 625 57 604.6 54 613.3 55 590.3 56 574.4 52 592 54 4870524 SOLANO BENICIA UNIFIED 11.443661971831 4.56211066324661 7.80505679736167 10.1502381824844 10.1626016260163 15.1756183745583 61419.337398374 4303.05734701356 22.2794428028704 40.4907975460123 0 0 681.573438639125 671.828107718202 664.123567802756 66.4998791394731 66.8773743688387 65.7105710814095 715.6 55 713.5 61 691.8 58 708.5 51 709.3 58 683.5 51 708.4 58 707.6 69 687.6 65 714.7 73 701.7 70 689.3 73 700.2 70 692.2 70 679 73 681.3 69 671.1 63 660.9 64 676.2 71 669.6 72 666.3 74 667.5 75 645.9 70 649 69 638.2 67 617 66 625.5 66 605.4 68 592.8 69 610.6 71 4870532 SOLANO DIXON UNIFIED 40.8194233687405 1.3169195533925 1.77497852848554 39.965645576868 12.6436781609195 15.5133333333333 57074.224137931 4262.56283996565 20.0236966824645 39.6648044692738 0 16.6666666666667 655.642246903033 647.059762100082 639.990394295302 42.4987416107383 43.0689089417555 40.5057667663392 696.4 36 699.5 46 672.7 37 689.9 32 695.7 44 664 31 687 36 687.6 49 664.3 42 679.2 39 674.1 43 657 41 670.8 41 670.6 48 654.9 47 661.6 49 655.5 47 647.6 51 647.9 44 634.6 37 634.3 44 632.9 45 613.6 38 623.5 46 607.8 42 589 40 600.1 42 574.8 41 561 39 583.5 42 4870540 SOLANO FAIRFIELD-SUISUN UNIFIED 28.1108624220201 6.54867256637168 21.0107126222636 18.0158360503027 13.2415254237288 15.9655090390105 59268.9862288136 3955.48863530508 22.8889128791968 26.1160714285714 0 34.6153846153846 653.017221528645 645.545050167224 640.046989921003 46.3172160174339 46.2223411371238 43.3465806630601 696.2 36 696.8 44 676.9 42 691.1 33 695.3 47 672.1 40 686.4 37 686.7 48 671.9 51 687.3 47 678.3 47 662.4 47 673.7 45 668.6 47 658.6 52 660.7 48 657.3 50 645.1 49 651.9 49 640.9 46 637.2 47 634.1 47 619.1 48 624.3 49 604.4 43 586.7 41 596.9 41 570.5 43 561.1 44 580 43 4870565 SOLANO TRAVIS UNIFIED 22.7124538143882 2.52947481243301 15.3483386923901 10.3965702036442 18.2203389830508 15.1208487084871 62353.6016949153 4900.85551982851 20.2287440656021 66.3101604278075 0 0 666.224245224892 651.059872804361 649.958239070621 55.8654845612962 50.3058752271351 55.0418977202711 705.8 46 700.1 46 685 50 698.3 40 695 44 671.8 39 701 50 697.9 60 675.7 54 697.6 57 681.6 50 665.7 50 690.7 61 679.7 58 665.2 59 672 60 661.9 54 655.3 59 662.8 59 644.2 47 653.5 64 649.3 60 624.4 49 641.7 63 620.9 54 596.9 48 613.8 55 592.9 58 569 46 598.4 60 4870573 SOLANO VACAVILLE UNIFIED 23.0192416525184 2.82936052400567 8.37328651495712 16.7465730299142 9.12981455064194 14.6227443609023 53901.8758915835 4110.53933418867 22.3814655172414 40.2614379084967 5.26315789473684 10.5263157894737 663.389330329715 654.597166998012 649.498064321 52.7524952112108 50.7088469184891 49.3357567069425 706 46 704.7 52 685.1 51 698.1 40 700.1 49 676.1 43 695.9 45 696.9 59 676.4 54 694.6 54 680.2 49 665.8 51 678.7 49 668.6 46 659.2 52 667.8 55 666.9 59 656.3 60 658.2 54 647.8 51 647.5 58 643.1 54 621.2 46 633.9 56 617.5 51 600.4 51 610.9 53 577.3 44 567.5 45 589.1 49 4870581 SOLANO VALLEJO CITY UNIFIED 35.4608814127758 3.83958186752437 35.2145944316012 15.5493014373304 23.8767650834403 16.6808544303798 68338.8023106547 4364.92657553523 25.6707959936742 20.0227531285552 0 56 644.687722460014 638.51153312395 632.704359794658 38.5993601666543 38.9284931706961 34.8631073064504 693.7 33 693.7 40 675.2 40 687.1 29 691.8 41 666.1 33 680.4 31 687 48 665.6 44 677.6 37 668.4 37 653.5 38 661.2 32 656.4 34 648 40 654.3 41 654.6 47 639.4 43 640.5 38 631.1 35 629.4 40 623.1 37 609 37 616.1 41 594.9 34 581.4 35 588.8 33 563.3 36 555.2 37 573 35 4970656 SONOMA CLOVERDALE UNIFIED 39.7086763774541 .429447852760736 .674846625766871 25.0920245398773 6.32911392405063 15.6294117647059 56854.0379746836 3942.01042944785 20.4216073781291 43.8356164383562 0 0 657.034640522876 649.894646098004 639.369549218031 43.8408463661454 47.7223230490018 44.2362278244631 708.5 48 702.7 50 677 42 703.2 45 696 45 674.8 42 693.4 42 696.2 58 673.4 52 689.4 49 678.9 48 664.6 50 679.8 49 671.4 49 653.2 45 663.9 51 674.4 66 648.5 52 644.5 41 641.3 44 628.6 39 635.8 48 613.7 38 624.9 48 600.9 36 588.5 39 592.7 35 566.5 34 562.9 40 576.7 35 4973882 SONOMA COTATI-ROHNERT PARK UNIFIED 19.6758386732002 3.86396879570941 3.64456362749878 12.8473915163335 5.99455040871935 15.7177884615385 59484.6839237057 4081.60153583618 22.2929762230118 14.4508670520231 0 0 663.548165536429 651.999588053553 648.170283428969 53.6576247609112 50.8764160659114 51.4564423578508 705.4 45 704.9 52 687.3 53 698.6 40 699.4 48 677.2 44 694.3 44 694.2 56 676.1 54 698.3 57 684.1 53 672.6 58 688.9 59 676.1 54 667.8 61 666.4 54 664.4 57 649.7 53 661.9 58 652.3 56 650.5 61 646.2 57 623 47 632.8 55 614.4 48 594.8 46 604.6 47 581.1 47 562.6 40 587.9 48 4975390 SONOMA HEALDSBURG UNIFIED 21.4638665843113 .878378378378378 .439189189189189 34.0540540540541 14.2857142857143 16.4645251396648 56837.3506493507 4968.96756756757 20.9132720105125 46.484375 0 0 667.173062015504 657.896311858077 648.388740458015 46.6307251908397 48.2278244631186 45.6545542635659 701.9 42 698.7 46 682.4 48 693.4 36 696.6 48 675 43 689.7 40 691.1 53 668.2 47 693.8 54 690 59 665.6 51 683.8 55 670.5 49 662.4 56 664.9 53 658.1 52 646.5 50 656.2 53 645.6 50 637.8 48 635 47 616.1 44 622.4 46 598.7 37 584.7 38 593.2 37 571.2 42 557.4 38 573.5 35 4970953 SONOMA SONOMA VALLEY UNIFIED 30.7603241991509 1.92343956251179 .716575523288705 22.4024137280784 6.15384615384616 15.8586092715232 54122.3423076923 4170.56835753347 21.1476725521669 23.3716475095785 11.1111111111111 11.1111111111111 664.450211416491 653.566589625064 648.412269300754 52.0428905640759 50.2734976887519 50.3742071881607 708.2 48 706.5 53 684 49 700.7 43 697.5 46 677.4 44 700 49 698.2 60 678.3 56 694.3 54 685.6 54 671.9 57 682.4 52 675.5 54 664.9 59 667.8 55 666 58 653.7 58 661.1 57 649.1 53 646.2 56 644.5 56 616.9 41 629.7 52 609 43 591.9 43 599.6 41 577.9 44 564.1 41 587 46 4975358 SONOMA WINDSOR UNIFIED 33.5580524344569 1.37909898866074 .858106037388906 26.5093472264787 17.5675675675676 11.0236363636364 50731.472972973 3834.78639288998 21.0230547550432 0 0 0 654.652495621716 641.131451275617 638.921030756442 48.0448877805486 45.0380593893768 46.2504378283713 703.4 43 692.3 38 682.7 48 697.6 39 694.9 44 675.6 43 696.2 45 692.8 54 676.9 55 695.5 55 678.5 47 668.7 54 680.6 50 670 48 659.7 53 663.9 51 660.4 53 644.8 48 649.6 46 636.3 39 636.4 46 631.2 43 617 41 623.4 46 608.4 42 592.7 43 599.2 41 578.4 45 566.4 43 588.1 48 5071308 STANILAUS TURLOCK UNION 42.6006966151648 4.70202296336796 1.36686714051394 32.5587752870421 9.22131147540983 14.9641577060932 59645.2069672131 3932.406689 24.1786317567568 21.40625 0 50 653.922410473623 649.459038583175 642.323309224718 44.8226113437381 45.3544592030361 39.6056988833269 699.6 39 698.2 44 682.7 48 690.7 32 692.8 41 674.5 41 684 34 686 47 669.2 47 687.1 46 681.2 50 662.8 47 669.3 39 668.3 45 653.1 46 657.8 45 659.4 52 645 48 642.3 39 637.8 41 635.1 45 630.6 43 616.2 42 621.3 45 601.2 38 591.4 44 596.5 39 573.1 42 567.7 47 581.6 42 5071043 STANISLAUS CERES UNIFIED 51.2052189296771 4.55034423407917 3.4315834767642 39.2641996557659 10.0490196078431 13.2773218142549 56234.306372549 3767.50398020654 23.1700146986771 12.967032967033 0 41.6666666666667 641.917007005515 635.964696577509 629.076138701146 33.683661475169 34.3288754673569 30.8339543896259 687.6 27 688.2 34 668.5 33 681.2 24 685.7 33 659.1 26 677.2 28 680.9 42 661.3 39 674.6 34 664.5 33 649.9 34 662.9 33 656.6 34 646 37 651 38 648.3 41 637.7 40 637.6 34 629.7 32 625.6 36 618.5 32 607.1 32 613.4 37 590.1 28 579.4 31 582.2 26 560.3 29 554.8 32 571.1 29 5071068 STANISLAUS DENAIR UNIFIED 42.1307506053269 .783085356303837 .234925606891151 25.920125293657 1.72413793103449 13.381746031746 49550.7413793104 3282.38919342208 21.3066202090592 29.8701298701299 0 0 658.764412416851 647.720043103448 644.830065359477 47.6655773420479 41.9946120689655 43.8968957871397 692.4 32 688.9 35 672.3 37 683.3 25 678 26 664.3 32 683.1 33 680.6 42 668.5 47 692.2 51 679.4 48 664.7 50 670.6 41 665.1 43 650.1 42 658.6 46 649.5 42 649.2 53 654.6 51 637.5 40 639.2 50 634 46 605.9 31 623.3 46 616.3 50 597.1 48 614.6 56 592.6 58 584 61 596.5 58 5073601 STANISLAUS NEWMAN-CROWS LANDING UNIFIED 53.904282115869 1.22137404580153 1.47582697201018 53.4351145038168 14.7368421052632 12.7085714285714 51297.3684210526 4109.91704834606 21.6866158868335 28.8659793814433 0 16.6666666666667 646.867903103709 644.301789709172 636.501729323308 40.2315789473684 40.7166293810589 34.1241483724451 688.8 28 695.2 41 671.8 37 681.7 24 687.2 35 662.8 30 673.1 24 679 40 660.1 38 679.7 39 663.2 32 657.3 43 666.6 37 658 35 651.9 44 646.6 33 648.6 41 634.8 37 632.7 30 630 33 623.6 34 621.8 35 615.2 40 616.1 39 596.2 33 596.7 47 599.4 41 596.1 61 588.6 65 598.9 61 5071217 STANISLAUS PATTERSON JOINT UNIFIED 55.0072568940494 .67396798652064 1.23560797528784 64.588598708228 18.1208053691275 13.3273255813954 55535.1476510067 4008.41449031171 24.0040927694407 13.0718954248366 0 0 645.663875278396 636.918853820598 634.555903083701 37.1092511013216 34.749584717608 31.6178173719376 686.7 26 689.7 35 670 35 681.7 24 683.5 31 659.6 27 676.1 27 679.7 41 664 42 682.5 42 669.5 38 655 40 669.9 40 662.5 40 654.3 47 646.1 33 642.2 35 637.1 39 636.5 33 625 28 632.5 42 612.3 27 603 29 613.3 37 592.1 30 574.3 27 582.8 27 566.8 35 565.5 43 575.6 34 5171399 SUTTER LIVE OAK UNIFIED 72.2976963969285 12.3235613463626 .597176981541802 45.3311617806732 6.52173913043478 12.3826732673267 52194.3369565217 4350.79261672096 21.4437869822485 17.7215189873418 0 0 640.02026295437 633.549270072993 626.57022556391 31.9917293233083 32.7766423357664 29.245939675174 686.9 27 688.7 34 663.4 29 682.6 25 687.5 36 657.9 26 669.9 22 677.1 38 650.6 29 673.9 34 664.9 34 651.3 36 657.5 28 655.3 33 642.3 34 643.2 30 640.4 33 630.6 33 634.7 32 619.8 24 623.9 34 624.9 38 608.9 34 619.4 42 585.6 24 580 32 580.9 25 565.4 33 553.5 31 573.2 32 5171464 SUTTER YUBA CITY UNIFIED 49.2564175428626 13.2831159287158 2.93955539224692 25.5282013595444 14.1078838174274 15.0974452554745 57777.5580912863 4165.93174719824 23.0617071597506 24.2424242424242 0 25 646.224358074926 636.887817258883 634.064643050297 38.9446998377501 35.8145872294951 34.6318226462747 688.3 28 697.8 44 674.6 39 685.1 27 692.1 40 666.9 34 681.6 32 688.3 50 669.3 47 683.9 44 674.4 43 662.3 47 668.1 39 658.2 35 652.9 46 650.8 38 646.1 39 636.1 39 639.8 36 625.2 28 627.2 37 622.3 35 604.2 30 615.4 39 594.3 32 573.7 27 587.5 31 562.3 32 548.9 28 572.1 31 5271498 TAHAMA CORNING UNION 49.1590749824807 .876270592358921 1.89274447949527 29.7581493165089 3.59712230215827 13.2433962264151 55372.4604316547 3941.38696109359 20.9110787172012 36.4238410596026 0 0 651.470603813559 639.559671805072 634.103220936084 36.3935581278309 34.4878170064644 35.4078389830508 698.1 37 694.3 40 673 38 684.8 27 689.4 37 662.6 30 681.6 32 684.4 46 665.8 44 680.9 40 670.8 39 654 39 660 31 651 28 642.2 33 651.4 38 641.9 34 635.3 38 639.6 36 626.1 29 620 30 627.9 40 600.6 27 613.7 37 600 36 577.1 29 590.3 33 571 38 557.1 35 581.9 41 5271571 TEHAMA LOS MOLINOS UNIFIED 51.2931034482759 .142247510668563 .568990042674253 32.2901849217639 2.56410256410257 15.8122222222222 53216.6153846154 5045.57610241821 19.6438356164384 34.2105263157895 0 0 648.061303462322 639.214003944773 634.328427419355 33.5907258064516 31.3510848126233 30.3401221995927 683.6 24 686.5 32 662.8 28 686.3 28 686.2 34 664.4 31 676.2 27 684.1 45 664.6 43 685 44 672.9 42 656.7 41 656.6 28 650.8 28 649.3 41 651.6 39 646 39 627.9 30 636 33 616.8 21 621.6 32 612.7 27 600.8 26 608.5 33 592.2 30 564.2 19 589 32 557.3 26 547.9 26 570.4 28 5375028 TRINITY MOUNTAIN VALLEY UNIFIED 60.1459854014599 .480769230769231 0 5.12820512820513 5.55555555555556 16.1320512820513 63507.8333333333 6482.46955128205 17.9083094555874 42.4242424242424 0 0 662.37205882353 650.207582938389 644.749373433584 42.4912280701754 42.6255924170616 44.5490196078431 702.5 42 704.1 50 685 50 699.4 41 689.2 37 676.9 43 691.4 41 686.5 48 667.5 46 698.1 57 680.5 50 667.7 53 672.6 43 662.4 40 647.2 39 648.8 36 632.8 26 624.3 27 650 46 628.5 31 629.8 40 643 54 617.7 43 625.2 48 609.7 45 608.3 59 596.6 40 578.2 46 569 46 580.3 40 5471860 TULARE CUTLER-OROSI JOINT UNIFIED 84.0990371389271 .562851782363978 .241222192441705 90.7263468239078 18.7878787878788 14.2173913043478 58391.1082424242 3952.91040471723 22.7518427518428 8.37004405286344 0 0 625.407986243791 629.289962962963 619.331384383252 25.2493398717465 28.1814814814815 18.533053114253 677.3 19 678.9 24 661.7 27 668.2 14 677 24 648.9 18 663.6 18 673.9 35 650.4 29 661.9 24 667.6 36 649.1 34 648 21 651.6 29 639.9 31 631.9 21 637.1 30 621.6 24 614.4 16 621.7 25 611.2 23 599.6 18 595.7 23 599.2 25 571.2 15 578 30 577.7 23 545.9 19 546.6 25 559.7 19 5471878 TULARE DINUBA UNION 74.5744216499345 .895583146753511 .244249949114594 80.4600040708325 15.9817351598174 12.970656637 53304.9005022831 3688.74829025036 22.9647513278609 16.4658634538153 0 0 636.254840613932 636.677197488584 626.026167956435 29.743766122098 32.8926940639269 24.8474025974026 682.8 23 686.7 32 663.8 29 671.7 17 681.4 29 651.5 20 668.3 21 676.5 37 653.9 32 671.8 32 666.6 35 647.9 33 652.7 25 657.3 34 643 34 648.6 35 653.2 45 637.7 40 627.9 26 628.1 31 620 30 612.1 26 605.4 31 608.8 33 577.9 19 571.6 24 576.4 22 557.3 27 554.8 32 569.1 27 5475325 TULARE FARMERSVILLE UNIFIED 92.3344947735192 .933552992861065 .109829763866008 83.0313014827018 17.1052631578947 14.402380952381 61350.2075 3792.45582646897 22.9189189189189 0 0 100 611.61476793249 605.792740046838 600.900717131474 15.8725099601594 16.3692427790788 13.3316455696203 665.2 13 676 23 643.7 15 656.9 14 664.4 25 643.7 23 651.1 16 653.8 24 631.2 19 644 18 641.1 20 630.2 22 622.6 14 621.1 17 612.8 17 609.2 13 605.1 13 597.8 14 592.6 14 577.6 11 586.3 17 558.4 9 544.6 9 559.5 11 530 10 526.7 12 544.8 9 5471993 TULARE LINDSAY UNIFIED 76.580373269115 1.72117039586919 .057372346528973 83.7636259323006 23.6842105263158 13.2849431818182 58362.7059868421 4115.27855708549 22.6187335092348 27.4285714285714 0 0 640.388823181549 640.34366359447 626.193461762989 26.1938120256859 30.7523041474654 23.0821998817268 685.3 25 684.6 30 663.6 29 672.6 17 682.5 30 650.2 19 669.4 22 678.4 39 655.6 34 664.8 26 655.1 25 637.4 23 645.7 19 645.9 24 631.3 23 633.6 22 634.2 28 621 24 628.3 26 633.3 36 620.6 31 608 24 598.6 25 602.4 28 584.7 24 583.3 34 580.5 25 559.8 30 568 45 570.9 29 5472256 TULARE VISALIA UNIFIED 44.8332783096732 7.62122822798266 1.95437075803418 43.1351704963611 12.7111111111111 14.4732521602514 58322.98376 4057.25547877995 22.3127332301811 35.9173126614987 3.125 28.125 648.229390179976 640.968154273093 635.425015825517 38.9894688381194 37.4061278812935 35.2702545285107 694.4 34 695.9 41 673.8 39 689.7 32 693.1 41 667.4 34 682.5 32 685.3 46 667 45 684.5 44 667.9 36 660.4 45 668.3 39 660.6 38 653.8 46 656.5 44 651.9 44 640.5 43 638.5 35 629.5 32 626.5 37 619.3 32 603.9 29 611.6 35 590.9 28 581.3 33 588.5 32 564.4 32 557.7 35 575.7 34 5472272 TULARE WOODLAKE UNION 72.663139329806 1.19250425894378 .298126064735946 79.2589437819421 13.1578947368421 14.8140625 58001.3071929825 4081.73411839864 21.1060329067642 36.1344537815126 0 0 640.209791122715 631.617446270544 627.961022364217 29.2447284345048 25.3400758533502 24.7630548302872 694.1 33 686.9 32 671 36 673.4 18 679.3 26 654.2 22 673.9 25 675.1 36 656.5 35 674.5 34 658.8 28 650.5 35 651.7 24 646.7 25 641.1 32 639.1 27 637.9 31 636.2 39 618.8 19 606.7 14 609.1 21 606.5 22 588.7 18 601.9 27 581.1 22 567.3 21 577.3 23 556 26 538.7 19 562.1 21 5575184 TUOLUMNE BIG OAK FLAT-GROVELAND UNIFIED 36.7164179104478 .427960057061341 .855920114122682 4.70756062767475 4.65116279069767 13.268085106383 48160.4651162791 4666.56062767475 18.4266666666667 70.2702702702703 0 0 670.61387283237 659.356621880998 649.060931174089 48.2085020242915 47.8541266794626 49.4836223506744 701.6 41 694.6 41 679.9 45 694.7 36 687.4 35 670.5 38 684.2 34 683.5 45 659.2 38 702.6 62 691.7 59 667.1 51 682.2 52 670.3 48 667.7 62 656.5 43 645.5 38 642.1 45 661.6 58 656.3 60 648 59 650.7 61 629.5 54 634 56 619.6 53 597.4 48 597.5 40 610.5 72 587.7 65 593.5 56 5673759 VENTURA CONEJO VALLEY UNIFIED 12.3270160618018 5.66135375698613 1.48519975160422 14.5311529703995 5.4054054054054 15.7322185061316 62750.2407862408 4265.1333057338 23.810318275154 41.1663807890223 0 0 682.02413435621 677.544326362702 667.723709777441 69.9877351340178 71.6343503599589 66.211486626581 721.7 62 725.9 72 700.8 67 715.4 58 717.1 66 695.7 63 711 60 716.7 77 691.1 68 713.5 72 708 74 689.6 73 702.2 71 699.3 75 682.8 76 684.1 71 688.9 78 671.2 74 670.9 67 666 69 660.3 70 660.1 69 640.4 65 648 69 635.5 66 620.5 69 628.3 68 604.9 67 595 71 610.3 72 5672454 VENTURA FILLMORE UNIFIED 51.8065433854908 .547195622435021 .437756497948016 76.9083447332421 15.527950310559 15.024043715847 56925.9751552795 3897.07879616963 23.4847501622323 30.6010928961749 0 16.6666666666667 635.765689381933 628.433169996231 624.119392073875 28.9003462870335 26.434602336977 24.655705229794 684.6 25 680.1 26 665.4 30 678.8 22 677 24 653 22 663.3 17 667.6 29 649.8 29 670.7 31 659.4 29 644.4 29 654.5 26 648.5 26 639.9 31 644.6 32 637.2 30 637.1 39 626.9 25 619.8 23 621.2 31 609.2 24 593.1 21 603.7 29 585.1 24 574.7 27 578.9 24 551.2 22 549.7 28 565.3 24 5673940 VENTURA MOORPARK UNIFIED 23.4552907241536 3.86164745103487 1.81969718016391 29.7819141547437 10.3658536585366 10.2872311827957 54402.9817073171 4155.08362272538 21.6525556600815 21.1409395973154 0 0 661.607069359756 652.657776530039 650.1753724307 56.6239864227796 52.736664795059 51.3782393292683 706.8 47 705.7 52 685.6 51 696 38 697.7 46 674.7 41 697.5 47 700.2 62 681.6 60 698.9 58 686 55 678.8 63 688.9 59 675.7 54 670.8 65 669.6 57 661.3 54 657.2 61 661.2 57 651.1 54 648.9 59 642.9 54 624.6 49 634.8 57 611.6 45 599.7 50 609.5 51 583.1 49 574.4 52 594.6 55 5673874 VENTURA OAK PARK UNIFIED 1.24705089315807 6.06629143214509 1.00062539086929 2.34521575984991 4.72972972972973 12.2248502994012 55208.8378378378 4079.32739212008 20.988490182803 74.3421052631579 0 0 682.161725394897 670.000522088354 672.424153225806 76.9189516129032 69.8827309236948 70.796678817335 720.7 61 715.6 63 704.4 70 719.3 62 714.3 64 701.3 68 714.1 63 720.6 80 701.4 77 716.9 74 705.7 72 698.2 80 709.7 78 697.1 74 694.8 85 684.3 72 691.1 80 673.3 76 680.2 74 665.5 69 676.5 82 667.3 75 640.4 65 658.8 77 643.5 72 611.4 61 636.6 75 608.3 71 594.6 71 615.4 76 5672520 VENTURA OJAI UNIFIED 23.2817037754114 1.36625119846596 .862895493767977 18.6481303930968 8.15217391304348 14.221359223301 56808.0108695652 3825.93600191755 22.8771733034212 35.546875 0 0 671.676079734219 660.902526246719 656.370046388337 58.2614314115308 55.6719160104987 55.8066445182724 705.2 45 707.1 54 682.6 48 706 48 708.6 58 682.5 50 697.6 47 699.6 62 674.6 53 708.4 67 696 65 684.8 69 691.6 61 680 58 671.2 65 678 66 670.2 62 663 67 663.6 59 645.4 48 653 63 649.3 60 626.3 51 637.7 59 617.1 50 598.3 49 609.8 51 583.4 49 570.5 48 591.1 51 5672603 VENTURA SIMI VALLEY UNIFIED 15.6815375530144 5.52216571634047 1.67462885909488 17.4397698669543 6.91747572815534 15.0002183406114 57203.5497572816 3831.57374017568 23.2098614007114 37.6871880199667 0 0 667.169897138059 658.573027866352 653.045612437846 57.1392254359549 55.2870511576321 54.030788608215 710 50 711.9 58 689.4 55 704.6 47 703.9 53 682.6 50 700.5 50 701.6 63 682.9 61 698.4 58 684.7 54 672.7 58 688.3 58 676.4 54 668.2 62 672.3 60 671.6 63 656.4 60 660.6 57 652.1 55 650.4 61 645.7 57 627.6 52 634.7 57 621.8 55 602.4 53 613.9 55 583 49 571.4 49 592.4 53 5672652 VENTURA VENTURA UNIFIED 38.1582125603865 2.90551227227462 2.35487083357741 33.4426805693867 9.94397759103642 15.3525516403402 56413.6120448179 3699.07023607287 24.8511202830189 34.3634116192831 0 22.2222222222222 663.126722987995 651.066852966466 648.690125295716 52.2804696398843 47.5606190885641 48.7767007558915 703.4 43 700.9 47 686.5 52 697.3 39 695.5 44 676.8 44 692.4 42 690.8 52 678.5 57 695.3 55 678.2 47 669.1 54 684.7 55 672.1 50 664.8 59 665.4 53 659.6 52 648.9 52 655.2 51 645.7 49 644.6 55 642.1 53 618.1 43 630.4 53 611.9 46 594 45 602.3 44 584.7 50 568.5 46 591.7 52 5772678 YOLO DAVIS JOINT UNIFIED 17.8988326848249 10.4909560723514 3.37209302325581 12.7002583979328 14.9289099526066 14.4376582278481 49783.3127962085 4254.71718346253 20.062860136197 46.4203233256351 0 0 688.106229626947 680.838578317557 668.965033207683 71.1364207503141 74.2502232541525 71.5622962694676 722.8 64 728.6 74 697.7 64 718.2 61 724 71 693.5 61 718.6 67 728.8 84 697.9 74 714.9 73 711.8 77 691.7 74 703.3 72 700.2 76 684.8 77 695.3 81 698.3 84 673.2 76 683.6 77 671 74 668.6 76 672 78 645.7 69 651.3 71 644.8 73 617 66 629.9 69 605.7 68 589.9 67 605.1 67 5772686 YOLO ESPARTO UNIFIED 49.235807860262 .779510022271715 1.67037861915368 43.7639198218263 4.16666666666666 11.3609090909091 50433.1666666667 5039.20267260579 19.5454545454545 27.0833333333333 0 0 640.121894409938 635.382379518072 625.547792998478 29.2648401826484 31.7394578313253 27.9472049689441 682.3 22 686.1 33 660.8 26 673.4 18 680.4 30 653.2 22 673.8 26 678.4 39 660 39 682.5 43 662 32 650.9 35 651.3 24 650.8 29 635.1 27 652.2 39 649.3 43 641.5 45 626.1 25 621.4 25 616.5 27 616.3 31 605.2 33 608.1 33 597.5 36 576.4 31 579.2 25 549.2 24 545.9 28 558.2 20 5772694 YOLO WASHINGTON UNIFIED 62.2396784800877 13.8208597362562 3.95615687617743 32.1287891762288 15.884476534296 13.2708860759494 52881.3321299639 4324.17365987327 20.9871086556169 8 0 18.1818181818182 639.1435538262 633.124164397128 627.616834677419 32.3477822580645 31.2792770487745 27.7229571984436 686.6 26 693.3 38 668.6 33 682.4 25 688 35 661.6 29 675.2 26 677.4 38 661.5 40 676.5 36 665.4 34 652.1 37 659.5 30 653.6 31 642.7 34 638.4 26 637.7 30 627 29 626.6 24 620.5 24 620.8 31 615.3 29 600.1 26 609.9 34 589.8 27 578.6 30 585.5 29 559.5 29 552.1 30 570.2 28 5772702 YOLO WINTERS JOINT UNIFIED 46.1618798955614 1.15057528764382 .80040020010005 45.6228114057029 13.3333333333333 11.8071428571429 48426.1523809524 3945.06903451726 19.8582995951417 53.7735849056604 0 0 650.807236842105 640.076315789474 634.960070175439 36.5312280701754 33.7548476454294 34.6834795321637 695.8 35 691.8 38 675.6 41 685.7 28 686.8 34 670.5 38 678.4 29 680.1 41 667.9 46 681.1 41 663.3 32 654.5 39 665.3 35 656.4 34 644.3 36 655 41 644.5 37 640.7 44 633.9 30 619.1 23 615.4 26 636.7 48 609.7 35 614.2 38 596.1 32 580.5 32 587.4 30 558.1 27 553 30 565.9 24 5772710 YOLO WOODLAND JOINT UNIFIED 43.4143080008915 3.64856364017614 1.54120360662613 46.3199832249948 21.3776722090261 14.4046843177189 53796.1638954869 3845.48081358775 22.7088422081094 29.8924731182796 0 6.66666666666667 650.685780525502 642.281801889866 636.105199735887 41.0627269725982 40.8595633756924 38.3171904516572 694.7 34 701.1 47 674.4 39 689.2 31 696.2 44 668.7 36 687.9 37 692.5 54 671.3 49 681.7 41 670.2 39 658.5 43 669.1 39 660.8 38 653.4 46 655.4 42 650.2 43 641.4 44 646.4 43 634.6 37 630.8 41 629.1 41 609.4 34 617.7 41 598.3 34 585.6 37 591 34 572.1 39 562.9 40 578.3 37 5872736 YUBA MARYSVILLE JOINT UNIFIED 70.6210416863598 20.4617205998422 2.98934490923441 17.423046566693 11.0328638497653 16.5641975308642 61705.6596244131 3970.9843133386 24.8864711447493 15.1428571428571 0 13.6363636363636 639.085190097259 631.172371396269 625.858513396716 30.7783059636992 30.1215375918598 28.466254052461 688.6 28 687.9 33 670.3 35 686.7 29 687.6 35 664 31 677.4 28 681.1 42 661.6 40 675.9 36 664.5 33 649.7 34 656.3 28 652.6 30 639.9 31 643.3 30 637.8 31 629.2 31 632.7 30 626.6 29 621.8 32 614.9 29 599.6 26 605.9 30 585.8 24 571.1 24 581.3 26 551.9 23 541.5 21 561.5 20 5872751 YUBA WHEATLAND UNION 77.7482740308019 5.99889928453495 9.57622454595487 11.1172261970281 7.8740157480315 16.9187050359712 65099.5669291339 6913.39680792515 20.0325203252033 23.5294117647059 0 0 663.065659500291 648.575580736544 645.966781214204 52.1821305841924 48.9008498583569 52.2887855897734 706.7 46 699 46 683.1 49 701 43 703.5 53 678.3 45 694.1 43 699.9 62 676.9 55 694.7 54 676.2 45 666.7 52 690.7 61 675.3 53 671.1 66 669.9 57 664.4 57 651.2 55 655.3 51 643.6 47 638.3 48 647 58 619.6 44 632.6 55 619.2 52 590.2 41 603.9 46 587.6 53 566.7 44 589.2 50 statsmodels-0.12.2/statsmodels/datasets/star98/src/star98.names000066400000000000000000000170131400612667500244210ustar00rootroot00000000000000 18 variables and 303 cases Variable: CDS_CODE Type: Numeric County District Code Variable: COUNTY Type: String Variable: DISTRICT Type: String Variable: LOWINC Type: Numeric Percent Low Income Students This variable is the sum of students eligible for free or reduced lunch programs divided by the sum of students multiplied by 100. The district level percentages were aggregated from school level data Source: The National Center for Educational Statistics (NECS) Common Core of Data site, "http://nces.ed.gov/ccd/index.html" Variable: PERASIAN Type: Numeric Percent Asian Students This variable is the number of Asian Students divided by the the total number of students, multiplied by 100. Source: The California Department of Education Educational Demographics Unit site, file "ethdst97.exe" at "http://www.cde.ca.gov/ftpbranch/retdiv/demo/newcbeds/" Variable: PERBLACK Type: Numeric Percent Black Students This variable is the number of Black Students divided by the the total number of students, multiplied by 100. Source: The California Department of Education Educational Demographics Unit site, file "ethdst97.exe" at "http://www.cde.ca.gov/ftpbranch/retdiv/demo/newcbeds/" Variable: PERHISP Type: Numeric Percent Hispanic Students This variable is the number of Hispanic Students divided by the the total number of students, multiplied by 100. Source: The California Department of Education Educational Demographics Unit site, file "ethdst97.exe" at "http://www.cde.ca.gov/ftpbranch/retdiv/demo/newcbeds/" Variable: PERMINTE Type: Numeric Percent Minority Teachers This variable is the number of minority (American Indians, Asians, Pacific Islanders, Filipinos, Hispanics And Blacks) teachers divided by the total number of teachers, then multiplied by 100. Source: The California Department of Education Educational Demographics Unit site, file "teaeth96.exe" at "http://www.cde.ca.gov/ftpbranch/retdiv/demo/newcbeds/" Variable: AVYRSEXP Type: Numeric Teachers' Experience This variable is the sum of years in educational service divided by the sum of teachers. The district level averages were aggregated from school level data. Source: The California Department of Education Educational Demographics Unit site, file "prcert96.exe" at "http://www.cde.ca.gov/ftpbranch/retdiv/demo/newcbeds/" Variable: PTRATIO Type: Numeric Class Size This variable is enrollment divided By full-time equivalent teachers. Source: The California Department of Education Educational Demographics Unit site, file "cbeds96.exe" at "http://www.cde.ca.gov/ftpbranch/retdiv/demo/newcbeds/" Variable: AVSAL Type: Numeric Teacher Salary This variable is the total salary budget, including benefits, divided the number of full-time teachers. Source: School Business Services Division http://www.cde.ca.gov/ftpbranch/sbsdiv/ Variable: PERPSPEN Type: Numeric Per-pupil Spending This variable is the total spending divided by total number of students. Source: School Business Services Division "http://www.cde.ca.gov/ftpbranch/sbsdiv/" Variable: PCT_AF Type: Numeric Percent Students Taking UC/CSU Prep Courses This variable is the percentage of students taking courses that meet University of California and California State University entry requirements. Source: The California Department of Education Educational Demographics Unit site, file "cbeds96.exe" at "http://www.cde.ca.gov/ftpbranch/retdiv/demo/newcbeds/" Variable: PCTCHRT Type: Numeric Percent Charter Schools Source: The California Department of Education Educational Demographics Unit site, file "schlname.exe" at "http://www.cde.ca.gov/ftpbranch/retdiv/demo/newcbeds/" Variable: PCTYRRND Type: Numeric Percent Year-round Schools Source: The California Department of Education Educational Demographics Unit site, file "schlname.exe" at "http://www.cde.ca.gov/ftpbranch/retdiv/demo/newcbeds/" Variable: LANGUAGE Type: Numeric Mean Language Score, Grades 2-11 This variable is the sum score for each grade(mean * test takers) divided by the sum of test takers for all grades. Source: The State of California Standardized Testing and Reporting site, "http://star.cde.ca.gov/index_index.html" Variable: MATH Type: Numeric Mean Math Score, Grades 2-11 This variable is the sum score for each grade(mean * test takers) divided by the sum of test takers for all grades. Source: The State of California Standardized Testing and Reporting site, "http://star.cde.ca.gov/index_index.html" Variable: READ Type: Numeric Mean Reading Score, Grades 2-11 This variable is the sum score for each grade(mean * test takers) divided by the sum of test takers for all grades. Source: The State of California Standardized Testing and Reporting site, "http://star.cde.ca.gov/index_index.html" Variable: LANGNCE Type: Numeric National Percentile Rank, Language National Percentile Rank is based on the mean NCE score for each district. Variable: MATHNCE Type: Numeric National Percentile Rank, Language National Percentile Rank is based on the mean NCE score for each district. Variable: READNCE Type: Numeric National Percentile Rank, Language National Percentile Rank is based on the mean NCE score for each district. Variables: READM(2-11) Mean reading score for individual grades. The grades are the number at the end of each variable name. Variables: MATHM(2-11) Mean math score for individual grades. The grades are the number at the end of each variable name. Variables: LANGM(2-11) Mean language score for individual grades. The grades are the number at the end of each variable name. Variables: READNCE(2-11) NCE percentile ranking for individual grades. The grades are the number at the end of each variable name. Variables: MATHCE(2-11) NCE percentile ranking for individual grades. The grades are the number at the end of each variable name. Variables: LANGNCE(2-11) NCE percentile ranking for individual grades. The grades are the number at the end of each variable name. statsmodels-0.12.2/statsmodels/datasets/star98/star98.csv000066400000000000000000001773751400612667500233440ustar00rootroot00000000000000"MATHTOT","PR50M","LOWINC","PERASIAN","PERBLACK","PERHISP","PERMINTE","AVYRSEXP","AVSALK","PERSPENK","PTRATIO","PCTAF","PCTCHRT","PCTYRRND","PERMINTE_AVYRSEXP","PERMINTE_AVSAL","AVYRSEXP_AVSAL","PERSPEN_PTRATIO","PERSPEN_PCTAF","PTRATIO_PCTAF","PERMINTE_AVYRSEXP_AVSAL","PERSPEN_PTRATIO_PCTAF" 807.000000,452.000000,34.397300,23.299300,14.235280,11.411120,15.918370,14.706460,59.15732,4.445207,21.710250,57.032760,0.000000,22.222220,234.102872,941.68811,869.9948,96.50656,253.52242,1238.1955,13848.8985,5504.0352 184.000000,144.000000,17.365070,29.328380,8.234897,9.314884,13.636360,16.083240,59.50397,5.267598,20.442780,64.622640,0.000000,0.000000,219.316851,811.41756,957.0166,107.68435,340.40609,1321.0664,13050.2233,6958.8468 571.000000,337.000000,32.643240,9.226386,42.406310,13.543720,28.834360,14.595590,60.56992,5.482922,18.954190,53.941910,0.000000,0.000000,420.854496,1746.49488,884.0537,103.92435,295.75929,1022.4252,25491.1232,5605.8777 573.000000,395.000000,11.909530,13.883090,3.796973,11.443110,11.111110,14.389390,58.33411,4.165093,21.635390,49.061030,0.000000,7.142857,159.882095,648.15671,839.3923,90.11341,204.34375,1061.4545,9326.5797,4421.0568 65.000000,8.000000,36.888890,12.187500,76.875000,7.604167,43.589740,13.905680,63.15364,4.324902,18.779840,52.380950,0.000000,0.000000,606.144976,2752.85075,878.1943,81.22097,226.54248,983.7059,38280.2616,4254.4314 2247.000000,1348.000000,20.931490,28.023510,4.643221,13.808160,15.378490,14.977550,66.97055,3.916104,24.519140,44.915780,0.000000,2.380952,230.332103,1029.90593,1003.0548,96.01950,175.89487,1101.2963,15425.4676,4312.7908 1364.000000,477.000000,53.268980,8.447858,19.374830,37.905330,25.525530,14.678290,57.62195,4.270903,22.212780,32.289160,0.000000,12.121210,374.671132,1470.83081,845.7917,94.86863,137.90387,717.2320,21589.2812,3063.2283 912.000000,565.000000,15.190090,3.665781,2.649680,13.092070,6.203008,13.661970,63.44740,4.309734,24.590260,30.452670,0.000000,0.000000,84.745309,393.56473,866.8165,105.97748,131.24291,748.8391,5376.8695,3227.2972 525.000000,205.000000,28.215820,10.430420,6.786374,32.334300,13.461540,16.417600,57.84564,4.527603,21.741380,22.645740,0.000000,0.000000,221.006179,778.69140,949.6866,98.43634,102.53092,492.3496,12784.2439,2229.1637 1067.000000,469.000000,32.778970,17.178310,12.484930,28.323290,27.259890,12.518640,57.80141,4.648917,20.260100,26.070990,0.000000,0.000000,341.256749,1575.66008,723.5950,94.18752,121.20187,528.2009,19725.1213,2455.5620 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156.000000,72.000000,77.748270,5.998899,9.576225,11.117230,7.874016,16.918710,65.09957,6.913397,20.032520,23.529410,0.000000,0.000000,133.218193,512.59506,1101.4007,138.49276,162.66815,471.3534,8672.4471,3258.6530 statsmodels-0.12.2/statsmodels/datasets/statecrime/000077500000000000000000000000001400612667500224575ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/statecrime/__init__.py000066400000000000000000000003261400612667500245710ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/statecrime/data.py000066400000000000000000000053511400612667500237460ustar00rootroot00000000000000"""Statewide Crime Data""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """Public domain.""" TITLE = """Statewide Crime Data 2009""" SOURCE = """ All data is for 2009 and was obtained from the American Statistical Abstracts except as indicated below. """ DESCRSHORT = """State crime data 2009""" DESCRLONG = DESCRSHORT #suggested notes NOTE = """:: Number of observations: 51 Number of variables: 8 Variable name definitions: state All 50 states plus DC. violent Rate of violent crimes / 100,000 population. Includes murder, forcible rape, robbery, and aggravated assault. Numbers for Illinois and Minnesota do not include forcible rapes. Footnote included with the American Statistical Abstract table reads: "The data collection methodology for the offense of forcible rape used by the Illinois and the Minnesota state Uniform Crime Reporting (UCR) Programs (with the exception of Rockford, Illinois, and Minneapolis and St. Paul, Minnesota) does not comply with national UCR guidelines. Consequently, their state figures for forcible rape and violent crime (of which forcible rape is a part) are not published in this table." murder Rate of murders / 100,000 population. hs_grad Percent of population having graduated from high school or higher. poverty % of individuals below the poverty line white Percent of population that is one race - white only. From 2009 American Community Survey single Calculated from 2009 1-year American Community Survey obtained obtained from Census. Variable is Male householder, no wife present, family household combined with Female householder, no husband present, family household, divided by the total number of Family households. urban % of population in Urbanized Areas as of 2010 Census. Urbanized Areas are area of 50,000 or more people.""" def load(as_pandas=None): """ Load the statecrime data and return a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas, retain_index=True) def load_pandas(): data = _get_data() return du.process_pandas(data, endog_idx=2, exog_idx=[7, 4, 3, 5], index_idx=0) def _get_data(): return du.load_csv(__file__, 'statecrime.csv') statsmodels-0.12.2/statsmodels/datasets/statecrime/statecrime.csv000066400000000000000000000045011400612667500253340ustar00rootroot00000000000000state,violent,murder,hs_grad,poverty,single,white,urban Alabama,459.9,7.1,82.1,17.5,29.0,70,48.65 Alaska,632.6,3.2,91.4,9.0,25.5,68.3,44.46 Arizona,423.2,5.5,84.2,16.5,25.7,80,80.07 Arkansas,530.3,6.3,82.4,18.8,26.3,78.4,39.54 California,473.4,5.4,80.6,14.2,27.8,62.7,89.73 Colorado,340.9,3.2,89.3,12.9,21.4,84.6,76.86 Connecticut,300.5,3.0,88.6,9.4,25.0,79.1,84.83 Delaware,645.1,4.6,87.4,10.8,27.6,71.9,68.71 District of Columbia,1348.9,24.2,87.1,18.4,48.0,38.7,100 Florida,612.6,5.5,85.3,14.9,26.6,76.9,87.44 Georgia,432.6,6.0,83.9,16.5,29.3,61.9,65.38 Hawaii,274.1,1.8,90.4,10.4,26.3,26.9,71.46 Idaho,238.5,1.5,88.4,14.3,19.0,92.3,50.51 Illinois,618.2,8.4,86.4,13.3,26.0,72.5,79.97 Indiana,366.4,5.3,86.6,14.4,24.5,85.7,59.17 Iowa,294.5,1.3,90.5,11.8,20.3,92.3,41.66 Kansas ,412.0,4.7,89.7,13.4,22.8,86.3,50.17 Kentucky ,265.5,4.3,81.7,18.6,25.4,88.8,40.99 Louisiana,628.4,12.3,82.2,17.3,31.4,63.7,61.33 Maine,119.9,2.0,90.2,12.3,22.0,94.9,26.21 Maryland,590.0,7.7,88.2,9.1,27.3,60.2,83.53 Massachusetts,465.6,2.7,89.0,10.3,25.0,82.4,90.3 Michigan,504.4,6.3,87.9,16.2,25.6,79.9,66.37 Minnesota,214.2,1.5,91.5,11.0,20.2,87.4,58 Mississippi,306.7,6.9,80.4,21.9,32.8,59.6,27.62 Missouri,500.3,6.6,86.8,14.6,25.3,83.9,56.61 Montana ,283.9,3.2,90.8,15.1,20.3,89.4,26.49 Nebraska,305.5,2.5,89.8,12.3,20.9,88.1,53.78 Nevada,704.6,5.9,83.9,12.4,28.5,76.2,86.51 New Hampshire,169.5,0.9,91.3,8.5,19.5,94.5,47.34 New Jersey,311.3,3.7,87.4,9.4,25.8,70.7,92.24 New Mexico,652.8,10.0,82.8,18.0,29.1,72.5,53.75 New York,385.5,4.0,84.7,14.2,30.2,67.4,82.66 North Carolina,414.0,5.4,84.3,16.3,26.3,70.5,54.88 North Dakota,223.6,2.0,90.1,11.7,18.2,90.2,40 Ohio,358.1,5.0,87.6,15.2,26.3,84,65.31 Oklahoma,510.4,6.5,85.6,16.2,25.9,75.4,45.79 Oregon,261.2,2.3,89.1,14.3,22.7,85.6,62.47 Pennsylvania,388.9,5.4,87.9,12.5,24.5,83.5,70.68 Rhode Island,254.3,3.0,84.7,11.5,27.3,82.6,90.46 South Carolina,675.1,6.7,83.6,17.1,28.4,67.6,55.78 South Dakota,201.0,3.6,89.9,14.2,20.8,86.3,29.92 Tennessee,666.0,7.4,83.1,17.1,26.3,79.1,54.38 Texas,491.4,5.4,79.9,17.2,27.6,73.8,75.35 Utah,216.2,1.4,90.4,11.5,17.9,89.3,81.17 Vermont,135.1,1.3,91.0,11.4,21.3,95.8,17.38 Virginia,230.0,4.7,86.6,10.5,24.0,70.4,69.79 Washington,338.3,2.8,89.7,12.3,22.2,80.2,74.97 West Virginia,331.2,4.9,82.8,17.7,23.3,94.3,33.2 Wisconsin,259.7,2.6,89.8,12.4,22.2,88.4,55.8 Wyoming,219.3,2.0,91.8,9.8,18.9,91.3,24.51 statsmodels-0.12.2/statsmodels/datasets/strikes/000077500000000000000000000000001400612667500220035ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/strikes/__init__.py000066400000000000000000000003261400612667500241150ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/strikes/data.py000066400000000000000000000035231400612667500232710ustar00rootroot00000000000000"""U.S. Strike Duration Data""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This is public domain.""" TITLE = __doc__ SOURCE = """ This is a subset of the data used in Kennan (1985). It was originally published by the Bureau of Labor Statistics. :: Kennan, J. 1985. "The duration of contract strikes in US manufacturing. `Journal of Econometrics` 28.1, 5-28. """ DESCRSHORT = """Contains data on the length of strikes in US manufacturing and unanticipated industrial production.""" DESCRLONG = """Contains data on the length of strikes in US manufacturing and unanticipated industrial production. The data is a subset of the data originally used by Kennan. The data here is data for the months of June only to avoid seasonal issues.""" #suggested notes NOTE = """:: Number of observations - 62 Number of variables - 2 Variable name definitions:: duration - duration of the strike in days iprod - unanticipated industrial production """ def load_pandas(): """ Load the strikes data and return a Dataset class instance. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ data = _get_data() return du.process_pandas(data, endog_idx=0) def load(as_pandas=None): """ Load the strikes data and return a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def _get_data(): return du.load_csv(__file__,'strikes.csv').astype(float) statsmodels-0.12.2/statsmodels/datasets/strikes/strikes.csv000066400000000000000000000013161400612667500242050ustar00rootroot00000000000000duration,iprod 7, .01138 9, .01138 13, .01138 14, .01138 26, .01138 29, .01138 52, .01138 130, .01138 9, .02299 37, .02299 41, .02299 49, .02299 52, .02299 119, .02299 3, -.03957 17, -.03957 19, -.03957 28, -.03957 72, -.03957 99, -.03957 104, -.03957 114, -.03957 152, -.03957 153, -.03957 216, -.03957 15, -.05467 61, -.05467 98, -.05467 2, .00535 25, .00535 85, .00535 3, .07427 10, .07427 1, .06450 2, .06450 2, .06450 3, .06450 3, .06450 4, .06450 8, .06450 11, .06450 22, .06450 23, .06450 27, .06450 32, .06450 33, .06450 35, .06450 43, .06450 43, .06450 44, .06450 100, .06450 5, -.10443 49, -.10443 2, -.00700 12, -.00700 12, -.00700 21, -.00700 21, -.00700 27, -.00700 38, -.00700 42, -.00700 117, -.00700 statsmodels-0.12.2/statsmodels/datasets/sunspots/000077500000000000000000000000001400612667500222155ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/sunspots/R_sunspots.s000066400000000000000000000006141400612667500245610ustar00rootroot00000000000000d <- read.table('./sunspots.csv', sep=',', header=T) attach(d) mod_ols <- ar(SUNACTIVITY, aic=FALSE, order.max=9, method="ols", intercept=FALSE) mod_yw <- ar(SUNACTIVITY, aic=FALSE, order.max=9, method="yw") mod_burg <- ar(SUNACTIVITY, aic=FALSE, order.max=9, method="burg") mod_mle <- ar(SUNACTIVITY, aic=FALSE, order.max=9, method="mle") select_ols <- ar(SUNACTIVITY, aic=TRUE, method="ols") statsmodels-0.12.2/statsmodels/datasets/sunspots/__init__.py000066400000000000000000000003261400612667500243270ustar00rootroot00000000000000__all__ = ["load", "load_pandas", "COPYRIGHT", "TITLE", "SOURCE", "DESCRSHORT", "DESCRLONG", "NOTE"] from .data import ( load, load_pandas, COPYRIGHT, TITLE, SOURCE, DESCRSHORT, DESCRLONG, NOTE) statsmodels-0.12.2/statsmodels/datasets/sunspots/arima_mod.R000066400000000000000000000002021400612667500242620ustar00rootroot00000000000000dta <- read.csv('./sunspots.csv') attach(dta) arma_mod <- arima(SUNACTIVITY, order=c(9,0,0), xreg=rep(1,309), include.mean=FALSE) statsmodels-0.12.2/statsmodels/datasets/sunspots/data.py000066400000000000000000000033631400612667500235050ustar00rootroot00000000000000"""Yearly sunspots data 1700-2008""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """This data is public domain.""" TITLE = __doc__ SOURCE = """ http://www.ngdc.noaa.gov/stp/solar/solarda3.html The original dataset contains monthly data on sunspot activity in the file ./src/sunspots_yearly.dat. There is also sunspots_monthly.dat. """ DESCRSHORT = """Yearly (1700-2008) data on sunspots from the National Geophysical Data Center.""" DESCRLONG = DESCRSHORT NOTE = """:: Number of Observations - 309 (Annual 1700 - 2008) Number of Variables - 1 Variable name definitions:: SUNACTIVITY - Number of sunspots for each year The data file contains a 'YEAR' variable that is not returned by load. """ def load_pandas(): data = _get_data() # TODO: time series endog = data.set_index(data.YEAR).SUNACTIVITY dataset = du.Dataset(data=data, names=list(data.columns), endog=endog, endog_name='volume') return dataset def load(as_pandas=None): """ Load the yearly sunspot data and returns a data class. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. Notes ----- This dataset only contains data for one variable, so the attributes data, raw_data, and endog are all the same variable. There is no exog attribute defined. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def _get_data(): return du.load_csv(__file__, 'sunspots.csv').astype(float) statsmodels-0.12.2/statsmodels/datasets/sunspots/src/000077500000000000000000000000001400612667500230045ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/sunspots/src/sunspots_monthly.dat000066400000000000000000000513121400612667500271500ustar00rootroot00000000000000 MONTHLY MEAN SUNSPOT NUMBERS =============================================================================== Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec ------------------------------------------------------------------------------- 1749 58.0 62.6 70.0 55.7 85.0 83.5 94.8 66.3 75.9 75.5 158.6 85.2 1750 73.3 75.9 89.2 88.3 90.0 100.0 85.4 103.0 91.2 65.7 63.3 75.4 1751 70.0 43.5 45.3 56.4 60.7 50.7 66.3 59.8 23.5 23.2 28.5 44.0 1752 35.0 50.0 71.0 59.3 59.7 39.6 78.4 29.3 27.1 46.6 37.6 40.0 1753 44.0 32.0 45.7 38.0 36.0 31.7 22.0 39.0 28.0 25.0 20.0 6.7 1754 0.0 3.0 1.7 13.7 20.7 26.7 18.8 12.3 8.2 24.1 13.2 4.2 1755 10.2 11.2 6.8 6.5 0.0 0.0 8.6 3.2 17.8 23.7 6.8 20.0 1756 12.5 7.1 5.4 9.4 12.5 12.9 3.6 6.4 11.8 14.3 17.0 9.4 1757 14.1 21.2 26.2 30.0 38.1 12.8 25.0 51.3 39.7 32.5 64.7 33.5 1758 37.6 52.0 49.0 72.3 46.4 45.0 44.0 38.7 62.5 37.7 43.0 43.0 1759 48.3 44.0 46.8 47.0 49.0 50.0 51.0 71.3 77.2 59.7 46.3 57.0 1760 67.3 59.5 74.7 58.3 72.0 48.3 66.0 75.6 61.3 50.6 59.7 61.0 1761 70.0 91.0 80.7 71.7 107.2 99.3 94.1 91.1 100.7 88.7 89.7 46.0 1762 43.8 72.8 45.7 60.2 39.9 77.1 33.8 67.7 68.5 69.3 77.8 77.2 1763 56.5 31.9 34.2 32.9 32.7 35.8 54.2 26.5 68.1 46.3 60.9 61.4 1764 59.7 59.7 40.2 34.4 44.3 30.0 30.0 30.0 28.2 28.0 26.0 25.7 1765 24.0 26.0 25.0 22.0 20.2 20.0 27.0 29.7 16.0 14.0 14.0 13.0 1766 12.0 11.0 36.6 6.0 26.8 3.0 3.3 4.0 4.3 5.0 5.7 19.2 1767 27.4 30.0 43.0 32.9 29.8 33.3 21.9 40.8 42.7 44.1 54.7 53.3 1768 53.5 66.1 46.3 42.7 77.7 77.4 52.6 66.8 74.8 77.8 90.6 111.8 1769 73.9 64.2 64.3 96.7 73.6 94.4 118.6 120.3 148.8 158.2 148.1 112.0 1770 104.0 142.5 80.1 51.0 70.1 83.3 109.8 126.3 104.4 103.6 132.2 102.3 1771 36.0 46.2 46.7 64.9 152.7 119.5 67.7 58.5 101.4 90.0 99.7 95.7 1772 100.9 90.8 31.1 92.2 38.0 57.0 77.3 56.2 50.5 78.6 61.3 64.0 1773 54.6 29.0 51.2 32.9 41.1 28.4 27.7 12.7 29.3 26.3 40.9 43.2 1774 46.8 65.4 55.7 43.8 51.3 28.5 17.5 6.6 7.9 14.0 17.7 12.2 1775 4.4 0.0 11.6 11.2 3.9 12.3 1.0 7.9 3.2 5.6 15.1 7.9 1776 21.7 11.6 6.3 21.8 11.2 19.0 1.0 24.2 16.0 30.0 35.0 40.0 1777 45.0 36.5 39.0 95.5 80.3 80.7 95.0 112.0 116.2 106.5 146.0 157.3 1778 177.3 109.3 134.0 145.0 238.9 171.6 153.0 140.0 171.7 156.3 150.3 105.0 1779 114.7 165.7 118.0 145.0 140.0 113.7 143.0 112.0 111.0 124.0 114.0 110.0 1780 70.0 98.0 98.0 95.0 107.2 88.0 86.0 86.0 93.7 77.0 60.0 58.7 1781 98.7 74.7 53.0 68.3 104.7 97.7 73.5 66.0 51.0 27.3 67.0 35.2 1782 54.0 37.5 37.0 41.0 54.3 38.0 37.0 44.0 34.0 23.2 31.5 30.0 1783 28.0 38.7 26.7 28.3 23.0 25.2 32.2 20.0 18.0 8.0 15.0 10.5 1784 13.0 8.0 11.0 10.0 6.0 9.0 6.0 10.0 10.0 8.0 17.0 14.0 1785 6.5 8.0 9.0 15.7 20.7 26.3 36.3 20.0 32.0 47.2 40.2 27.3 1786 37.2 47.6 47.7 85.4 92.3 59.0 83.0 89.7 111.5 112.3 116.0 112.7 1787 134.7 106.0 87.4 127.2 134.8 99.2 128.0 137.2 157.3 157.0 141.5 174.0 1788 138.0 129.2 143.3 108.5 113.0 154.2 141.5 136.0 141.0 142.0 94.7 129.5 1789 114.0 125.3 120.0 123.3 123.5 120.0 117.0 103.0 112.0 89.7 134.0 135.5 1790 103.0 127.5 96.3 94.0 93.0 91.0 69.3 87.0 77.3 84.3 82.0 74.0 1791 72.7 62.0 74.0 77.2 73.7 64.2 71.0 43.0 66.5 61.7 67.0 66.0 1792 58.0 64.0 63.0 75.7 62.0 61.0 45.8 60.0 59.0 59.0 57.0 56.0 1793 56.0 55.0 55.5 53.0 52.3 51.0 50.0 29.3 24.0 47.0 44.0 45.7 1794 45.0 44.0 38.0 28.4 55.7 41.5 41.0 40.0 11.1 28.5 67.4 51.4 1795 21.4 39.9 12.6 18.6 31.0 17.1 12.9 25.7 13.5 19.5 25.0 18.0 1796 22.0 23.8 15.7 31.7 21.0 6.7 26.9 1.5 18.4 11.0 8.4 5.1 1797 14.4 4.2 4.0 4.0 7.3 11.1 4.3 6.0 5.7 6.9 5.8 3.0 1798 2.0 4.0 12.4 1.1 0.0 0.0 0.0 3.0 2.4 1.5 12.5 9.9 1799 1.6 12.6 21.7 8.4 8.2 10.6 2.1 0.0 0.0 4.6 2.7 8.6 1800 6.9 9.3 13.9 0.0 5.0 23.7 21.0 19.5 11.5 12.3 10.5 40.1 1801 27.0 29.0 30.0 31.0 32.0 31.2 35.0 38.7 33.5 32.6 39.8 48.2 1802 47.8 47.0 40.8 42.0 44.0 46.0 48.0 50.0 51.8 38.5 34.5 50.0 1803 50.0 50.8 29.5 25.0 44.3 36.0 48.3 34.1 45.3 54.3 51.0 48.0 1804 45.3 48.3 48.0 50.6 33.4 34.8 29.8 43.1 53.0 62.3 61.0 60.0 1805 61.0 44.1 51.4 37.5 39.0 40.5 37.6 42.7 44.4 29.4 41.0 38.3 1806 39.0 29.6 32.7 27.7 26.4 25.6 30.0 26.3 24.0 27.0 25.0 24.0 1807 12.0 12.2 9.6 23.8 10.0 12.0 12.7 12.0 5.7 8.0 2.6 0.0 1808 0.0 4.5 0.0 12.3 13.5 13.5 6.7 8.0 11.7 4.7 10.5 12.3 1809 7.2 9.2 0.9 2.5 2.0 7.7 0.3 0.2 0.4 0.0 0.0 0.0 1810 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1811 0.0 0.0 0.0 0.0 0.0 0.0 6.6 0.0 2.4 6.1 0.8 1.1 1812 11.3 1.9 0.7 0.0 1.0 1.3 0.5 15.6 5.2 3.9 7.9 10.1 1813 0.0 10.3 1.9 16.6 5.5 11.2 18.3 8.4 15.3 27.8 16.7 14.3 1814 22.2 12.0 5.7 23.8 5.8 14.9 18.5 2.3 8.1 19.3 14.5 20.1 1815 19.2 32.2 26.2 31.6 9.8 55.9 35.5 47.2 31.5 33.5 37.2 65.0 1816 26.3 68.8 73.7 58.8 44.3 43.6 38.8 23.2 47.8 56.4 38.1 29.9 1817 36.4 57.9 96.2 26.4 21.2 40.0 50.0 45.0 36.7 25.6 28.9 28.4 1818 34.9 22.4 25.4 34.5 53.1 36.4 28.0 31.5 26.1 31.6 10.9 25.8 1819 32.8 20.7 3.7 20.2 19.6 35.0 31.4 26.1 14.9 27.5 25.1 30.6 1820 19.2 26.6 4.5 19.4 29.3 10.8 20.6 25.9 5.2 8.9 7.9 9.1 1821 21.5 4.2 5.7 9.2 1.7 1.8 2.5 4.8 4.4 18.8 4.4 0.2 1822 0.0 0.9 16.1 13.5 1.5 5.6 7.9 2.1 0.0 0.4 0.0 0.0 1823 0.0 0.0 0.6 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 20.4 1824 21.7 10.8 0.0 19.4 2.8 0.0 0.0 1.4 20.5 25.2 0.0 0.8 1825 5.0 15.5 22.4 3.8 15.5 15.4 30.9 25.7 15.7 15.6 11.7 22.0 1826 17.7 18.2 36.7 24.0 32.4 37.1 52.5 39.6 18.9 50.6 39.5 68.1 1827 34.6 47.4 57.8 46.0 56.3 56.7 42.3 53.7 49.6 56.1 48.2 46.1 1828 52.8 64.4 65.0 61.1 89.1 98.0 54.2 76.4 50.4 54.7 57.0 46.9 1829 43.0 49.4 72.3 95.0 67.4 73.9 90.8 77.6 52.8 57.2 67.6 56.5 1830 52.2 72.1 84.6 106.3 66.3 65.1 43.9 50.7 62.1 84.4 81.2 82.1 1831 47.5 50.1 93.4 54.5 38.1 33.4 45.2 55.0 37.9 46.3 43.5 28.9 1832 30.9 55.6 55.1 26.9 41.3 26.7 14.0 8.9 8.2 21.1 14.3 27.5 1833 11.3 14.9 11.8 2.8 12.9 1.0 7.0 5.7 11.6 7.5 5.9 9.9 1834 4.9 18.1 3.9 1.4 8.8 7.8 8.7 4.0 11.5 24.8 30.5 34.5 1835 7.5 24.5 19.7 61.5 43.6 33.2 59.8 59.0 100.8 95.2 100.0 77.5 1836 88.6 107.6 98.2 142.9 111.4 124.7 116.7 107.8 95.1 137.4 120.9 206.2 1837 188.0 175.6 134.6 138.2 111.7 158.0 162.8 134.0 96.3 123.7 107.0 129.8 1838 144.9 84.8 140.8 126.6 137.6 94.5 108.2 78.8 73.6 90.8 77.4 79.8 1839 105.6 102.5 77.7 61.8 53.8 54.6 84.8 131.2 132.7 90.9 68.8 63.7 1840 81.2 87.7 67.8 65.9 69.2 48.5 60.7 57.8 74.0 55.0 54.3 53.7 1841 24.1 29.9 29.7 40.2 67.5 55.7 30.8 39.3 36.5 28.5 19.8 38.8 1842 20.4 22.1 21.7 26.9 24.9 20.5 12.6 26.6 18.4 38.1 40.5 17.6 1843 13.3 3.5 8.3 9.5 21.1 10.5 9.5 11.8 4.2 5.3 19.1 12.7 1844 9.4 14.7 13.6 20.8 11.6 3.7 21.2 23.9 7.0 21.5 10.7 21.6 1845 25.7 43.6 43.3 57.0 47.8 31.1 30.6 32.3 29.6 40.7 39.4 59.7 1846 38.7 51.0 63.9 69.3 59.9 65.1 46.5 54.8 107.1 55.9 60.4 65.5 1847 62.6 44.9 85.7 44.7 75.4 85.3 52.2 140.6 160.9 180.4 138.9 109.6 1848 159.1 111.8 108.6 107.1 102.2 129.0 139.2 132.6 100.3 132.4 114.6 159.5 1849 157.0 131.7 96.2 102.5 80.6 81.1 78.0 67.7 93.7 71.5 99.0 97.0 1850 78.0 89.4 82.6 44.1 61.6 70.0 39.1 61.6 86.2 71.0 54.8 61.0 1851 75.5 105.4 64.6 56.5 62.6 63.2 36.1 57.4 67.9 62.5 51.0 71.4 1852 68.4 66.4 61.2 65.4 54.9 46.9 42.1 39.7 37.5 67.3 54.3 45.4 1853 41.1 42.9 37.7 47.6 34.7 40.0 45.9 50.4 33.5 42.3 28.8 23.4 1854 15.4 20.0 20.7 26.5 24.0 21.1 18.7 15.8 22.4 12.6 28.2 21.6 1855 12.3 11.4 17.4 4.4 9.1 5.3 0.4 3.1 0.0 9.6 4.2 3.1 1856 0.5 4.9 0.4 6.5 0.0 5.2 4.6 5.9 4.4 4.5 7.7 7.2 1857 13.7 7.4 5.2 11.1 28.6 16.0 22.2 16.9 42.4 40.6 31.4 37.2 1858 39.0 34.9 57.5 38.3 41.4 44.5 56.7 55.3 80.1 91.2 51.9 66.9 1859 83.7 87.6 90.3 85.7 91.0 87.1 95.2 106.8 105.8 114.6 97.2 81.0 1860 82.4 88.3 98.9 71.4 107.1 108.6 116.7 100.3 92.2 90.1 97.9 95.6 1861 62.3 77.7 101.0 98.5 56.8 88.1 78.0 82.5 79.9 67.2 53.7 80.5 1862 63.1 64.5 43.6 53.7 64.4 84.0 73.4 62.5 66.6 41.9 50.6 40.9 1863 48.3 56.7 66.4 40.6 53.8 40.8 32.7 48.1 22.0 39.9 37.7 41.2 1864 57.7 47.1 66.3 35.8 40.6 57.8 54.7 54.8 28.5 33.9 57.6 28.6 1865 48.7 39.3 39.5 29.4 34.5 33.6 26.8 37.8 21.6 17.1 24.6 12.8 1866 31.6 38.4 24.6 17.6 12.9 16.5 9.3 12.7 7.3 14.1 9.0 1.5 1867 0.0 0.7 9.2 5.1 2.9 1.5 5.0 4.8 9.8 13.5 9.6 25.2 1868 15.6 15.7 26.5 36.6 26.7 31.1 29.0 34.4 47.2 61.6 59.1 67.6 1869 60.9 59.9 52.7 41.0 103.9 108.4 59.2 79.6 80.6 59.3 78.1 104.3 1870 77.3 114.9 157.6 160.0 176.0 135.6 132.4 153.8 136.0 146.4 147.5 130.0 1871 88.3 125.3 143.2 162.4 145.5 91.7 103.0 110.1 80.3 89.0 105.4 90.4 1872 79.5 120.1 88.4 102.1 107.6 109.9 105.5 92.9 114.6 102.6 112.0 83.9 1873 86.7 107.0 98.3 76.2 47.9 44.8 66.9 68.2 47.1 47.1 55.4 49.2 1874 60.8 64.2 46.4 32.0 44.6 38.2 67.8 61.3 28.0 34.3 28.9 29.3 1875 14.6 21.5 33.8 29.1 11.5 23.9 12.5 14.6 2.4 12.7 17.7 9.9 1876 14.3 15.0 30.6 2.3 5.1 1.6 15.2 8.8 9.9 14.3 9.9 8.2 1877 24.4 8.7 11.9 15.8 21.6 14.2 6.0 6.3 16.9 6.7 14.2 2.2 1878 3.3 6.6 7.8 0.1 5.9 6.4 0.1 0.0 5.3 1.1 4.1 0.5 1879 1.0 0.6 0.0 6.2 2.4 4.8 7.5 10.7 6.1 12.3 13.1 7.3 1880 24.0 27.2 19.3 19.5 23.5 34.1 21.9 48.1 66.0 43.0 30.7 29.6 1881 36.4 53.2 51.5 51.6 43.5 60.5 76.9 58.4 53.2 64.4 54.8 47.3 1882 45.0 69.5 66.8 95.8 64.1 45.2 45.4 40.4 57.7 59.2 84.4 41.8 1883 60.6 46.9 42.8 82.1 31.5 76.3 80.6 46.0 52.6 83.8 84.5 75.9 1884 91.5 86.9 87.5 76.1 66.5 51.2 53.1 55.8 61.9 47.8 36.6 47.2 1885 42.8 71.8 49.8 55.0 73.0 83.7 66.5 50.0 39.6 38.7 30.9 21.7 1886 29.9 25.9 57.3 43.7 30.7 27.1 30.3 16.9 21.4 8.6 0.3 13.0 1887 10.3 13.2 4.2 6.9 20.0 15.7 23.3 21.4 7.4 6.6 6.9 20.7 1888 12.7 7.1 7.8 5.1 7.0 7.1 3.1 2.8 8.8 2.1 10.7 6.7 1889 0.8 8.5 6.7 4.3 2.4 6.4 9.4 20.6 6.5 2.1 0.2 6.7 1890 5.3 0.6 5.1 1.6 4.8 1.3 11.6 8.5 17.2 11.2 9.6 7.8 1891 13.5 22.2 10.4 20.5 41.1 48.3 58.8 33.0 53.8 51.5 41.9 32.5 1892 69.1 75.6 49.9 69.6 79.6 76.3 76.5 101.4 62.8 70.5 65.4 78.6 1893 75.0 73.0 65.7 88.1 84.7 89.9 88.6 129.2 77.9 80.0 75.1 93.8 1894 83.2 84.6 52.3 81.6 101.2 98.9 106.0 70.3 65.9 75.5 56.6 60.0 1895 63.3 67.2 61.0 76.9 67.5 71.5 47.8 68.9 57.7 67.9 47.2 70.7 1896 29.0 57.4 52.0 43.8 27.7 49.0 45.0 27.2 61.3 28.7 38.0 42.6 1897 40.6 29.4 29.1 31.0 20.0 11.3 27.6 21.8 48.1 14.3 8.4 33.3 1898 30.2 36.4 38.3 14.5 25.8 22.3 9.0 31.4 34.8 34.4 30.9 12.6 1899 19.5 9.2 18.1 14.2 7.7 20.5 13.5 2.9 8.4 13.0 7.8 10.5 1900 9.4 13.6 8.6 16.0 15.2 12.1 8.3 4.3 8.3 12.9 4.5 0.3 1901 0.2 2.4 4.5 0.0 10.2 5.8 0.7 1.0 0.6 3.7 3.8 0.0 1902 5.5 0.0 12.4 0.0 2.8 1.4 0.9 2.3 7.6 16.3 10.3 1.1 1903 8.3 17.0 13.5 26.1 14.6 16.3 27.9 28.8 11.1 38.9 44.5 45.6 1904 31.6 24.5 37.2 43.0 39.5 41.9 50.6 58.2 30.1 54.2 38.0 54.6 1905 54.8 85.8 56.5 39.3 48.0 49.0 73.0 58.8 55.0 78.7 107.2 55.5 1906 45.5 31.3 64.5 55.3 57.7 63.2 103.6 47.7 56.1 17.8 38.9 64.7 1907 76.4 108.2 60.7 52.6 42.9 40.4 49.7 54.3 85.0 65.4 61.5 47.3 1908 39.2 33.9 28.7 57.6 40.8 48.1 39.5 90.5 86.9 32.3 45.5 39.5 1909 56.7 46.6 66.3 32.3 36.0 22.6 35.8 23.1 38.8 58.4 55.8 54.2 1910 26.4 31.5 21.4 8.4 22.2 12.3 14.1 11.5 26.2 38.3 4.9 5.8 1911 3.4 9.0 7.8 16.5 9.0 2.2 3.5 4.0 4.0 2.6 4.2 2.2 1912 0.3 0.0 4.9 4.5 4.4 4.1 3.0 0.3 9.5 4.6 1.1 6.4 1913 2.3 2.9 0.5 0.9 0.0 0.0 1.7 0.2 1.2 3.1 0.7 3.8 1914 2.8 2.6 3.1 17.3 5.2 11.4 5.4 7.7 12.7 8.2 16.4 22.3 1915 23.0 42.3 38.8 41.3 33.0 68.8 71.6 69.6 49.5 53.5 42.5 34.5 1916 45.3 55.4 67.0 71.8 74.5 67.7 53.5 35.2 45.1 50.7 65.6 53.0 1917 74.7 71.9 94.8 74.7 114.1 114.9 119.8 154.5 129.4 72.2 96.4 129.3 1918 96.0 65.3 72.2 80.5 76.7 59.4 107.6 101.7 79.9 85.0 83.4 59.2 1919 48.1 79.5 66.5 51.8 88.1 111.2 64.7 69.0 54.7 52.8 42.0 34.9 1920 51.1 53.9 70.2 14.8 33.3 38.7 27.5 19.2 36.3 49.6 27.2 29.9 1921 31.5 28.3 26.7 32.4 22.2 33.7 41.9 22.8 17.8 18.2 17.8 20.3 1922 11.8 26.4 54.7 11.0 8.0 5.8 10.9 6.5 4.7 6.2 7.4 17.5 1923 4.5 1.5 3.3 6.1 3.2 9.1 3.5 0.5 13.2 11.6 10.0 2.8 1924 0.5 5.1 1.8 11.3 20.8 24.0 28.1 19.3 25.1 25.6 22.5 16.5 1925 5.5 23.2 18.0 31.7 42.8 47.5 38.5 37.9 60.2 69.2 58.6 98.6 1926 71.8 69.9 62.5 38.5 64.3 73.5 52.3 61.6 60.8 71.5 60.5 79.4 1927 81.6 93.0 69.6 93.5 79.1 59.1 54.9 53.8 68.4 63.1 67.2 45.2 1928 83.5 73.5 85.4 80.6 77.0 91.4 98.0 83.8 89.7 61.4 50.3 59.0 1929 68.9 62.8 50.2 52.8 58.2 71.9 70.2 65.8 34.4 54.0 81.1 108.0 1930 65.3 49.9 35.0 38.2 36.8 28.8 21.9 24.9 32.1 34.4 35.6 25.8 1931 14.6 43.1 30.0 31.2 24.6 15.3 17.4 13.0 19.0 10.0 18.7 17.8 1932 12.1 10.6 11.2 11.2 17.9 22.2 9.6 6.8 4.0 8.9 8.2 11.0 1933 12.3 22.2 10.1 2.9 3.2 5.2 2.8 0.2 5.1 3.0 0.6 0.3 1934 3.4 7.8 4.3 11.3 19.7 6.7 9.3 8.3 4.0 5.7 8.7 15.4 1935 18.6 20.5 23.1 12.2 27.3 45.7 33.9 30.1 42.1 53.2 64.2 61.5 1936 62.8 74.3 77.1 74.9 54.6 70.0 52.3 87.0 76.0 89.0 115.4 123.4 1937 132.5 128.5 83.9 109.3 116.7 130.3 145.1 137.7 100.7 124.9 74.4 88.8 1938 98.4 119.2 86.5 101.0 127.4 97.5 165.3 115.7 89.6 99.1 122.2 92.7 1939 80.3 77.4 64.6 109.1 118.3 101.0 97.6 105.8 112.6 88.1 68.1 42.1 1940 50.5 59.4 83.3 60.7 54.4 83.9 67.5 105.5 66.5 55.0 58.4 68.3 1941 45.6 44.5 46.4 32.8 29.5 59.8 66.9 60.0 65.9 46.3 38.4 33.7 1942 35.6 52.8 54.2 60.7 25.0 11.4 17.7 20.2 17.2 19.2 30.7 22.5 1943 12.4 28.9 27.4 26.1 14.1 7.6 13.2 19.4 10.0 7.8 10.2 18.8 1944 3.7 0.5 11.0 0.3 2.5 5.0 5.0 16.7 14.3 16.9 10.8 28.4 1945 18.5 12.7 21.5 32.0 30.6 36.2 42.6 25.9 34.9 68.8 46.0 27.4 1946 47.6 86.2 76.6 75.7 84.9 73.5 116.2 107.2 94.4 102.3 123.8 121.7 1947 115.7 133.4 129.8 149.8 201.3 163.9 157.9 188.8 169.4 163.6 128.0 116.5 1948 108.5 86.1 94.8 189.7 174.0 167.8 142.2 157.9 143.3 136.3 95.8 138.0 1949 119.1 182.3 157.5 147.0 106.2 121.7 125.8 123.8 145.3 131.6 143.5 117.6 1950 101.6 94.8 109.7 113.4 106.2 83.6 91.0 85.2 51.3 61.4 54.8 54.1 1951 59.9 59.9 55.9 92.9 108.5 100.6 61.5 61.0 83.1 51.6 52.4 45.8 1952 40.7 22.7 22.0 29.1 23.4 36.4 39.3 54.9 28.2 23.8 22.1 34.3 1953 26.5 3.9 10.0 27.8 12.5 21.8 8.6 23.5 19.3 8.2 1.6 2.5 1954 0.2 0.5 10.9 1.8 0.8 0.2 4.8 8.4 1.5 7.0 9.2 7.6 1955 23.1 20.8 4.9 11.3 28.9 31.7 26.7 40.7 42.7 58.5 89.2 76.9 1956 73.6 124.0 118.4 110.7 136.6 116.6 129.1 169.6 173.2 155.3 201.3 192.1 1957 165.0 130.2 157.4 175.2 164.6 200.7 187.2 158.0 235.8 253.8 210.9 239.4 1958 202.5 164.9 190.7 196.0 175.3 171.5 191.4 200.2 201.2 181.5 152.3 187.6 1959 217.4 143.1 185.7 163.3 172.0 168.7 149.6 199.6 145.2 111.4 124.0 125.0 1960 146.3 106.0 102.2 122.0 119.6 110.2 121.7 134.1 127.2 82.8 89.6 85.6 1961 57.9 46.1 53.0 61.4 51.0 77.4 70.2 55.8 63.6 37.7 32.6 39.9 1962 38.7 50.3 45.6 46.4 43.7 42.0 21.8 21.8 51.3 39.5 26.9 23.2 1963 19.8 24.4 17.1 29.3 43.0 35.9 19.6 33.2 38.8 35.3 23.4 14.9 1964 15.3 17.7 16.5 8.6 9.5 9.1 3.1 9.3 4.7 6.1 7.4 15.1 1965 17.5 14.2 11.7 6.8 24.1 15.9 11.9 8.9 16.8 20.1 15.8 17.0 1966 28.2 24.4 25.3 48.7 45.3 47.7 56.7 51.2 50.2 57.2 57.2 70.4 1967 110.9 93.6 111.8 69.5 86.5 67.3 91.5 107.2 76.8 88.2 94.3 126.4 1968 121.8 111.9 92.2 81.2 127.2 110.3 96.1 109.3 117.2 107.7 86.0 109.8 1969 104.4 120.5 135.8 106.8 120.0 106.0 96.8 98.0 91.3 95.7 93.5 97.9 1970 111.5 127.8 102.9 109.5 127.5 106.8 112.5 93.0 99.5 86.6 95.2 83.5 1971 91.3 79.0 60.7 71.8 57.5 49.8 81.0 61.4 50.2 51.7 63.2 82.2 1972 61.5 88.4 80.1 63.2 80.5 88.0 76.5 76.8 64.0 61.3 41.6 45.3 1973 43.4 42.9 46.0 57.7 42.4 37.5 23.1 25.6 59.3 30.7 23.9 23.3 1974 27.6 26.0 21.3 40.3 39.5 36.0 55.8 33.6 40.2 47.1 25.0 20.5 1975 18.9 11.5 11.5 5.1 9.0 11.4 28.2 39.7 13.9 9.1 19.4 7.8 1976 8.1 4.3 21.9 18.8 12.4 12.2 1.9 16.4 13.5 20.6 5.2 15.3 1977 16.4 23.1 8.7 12.9 18.6 38.5 21.4 30.1 44.0 43.8 29.1 43.2 1978 51.9 93.6 76.5 99.7 82.7 95.1 70.4 58.1 138.2 125.1 97.9 122.7 1979 166.6 137.5 138.0 101.5 134.4 149.5 159.4 142.2 188.4 186.2 183.3 176.3 1980 159.6 155.0 126.2 164.1 179.9 157.3 136.3 135.4 155.0 164.7 147.9 174.4 1981 114.0 141.3 135.5 156.4 127.5 90.9 143.8 158.7 167.3 162.4 137.5 150.1 1982 111.2 163.6 153.8 122.0 82.2 110.4 106.1 107.6 118.8 94.7 98.1 127.0 1983 84.3 51.0 66.5 80.7 99.2 91.1 82.2 71.8 50.3 55.8 33.3 33.4 1984 57.0 85.4 83.5 69.7 76.4 46.1 37.4 25.5 15.7 12.0 22.8 18.7 1985 16.5 15.9 17.2 16.2 27.5 24.2 30.7 11.1 3.9 18.6 16.2 17.3 1986 2.5 23.2 15.1 18.5 13.7 1.1 18.1 7.4 3.8 35.4 15.2 6.8 1987 10.4 2.4 14.7 39.6 33.0 17.4 33.0 38.7 33.9 60.6 39.9 27.1 1988 59.0 40.0 76.2 88.0 60.1 101.8 113.8 111.6 120.1 125.1 125.1 179.2 1989 161.3 165.1 131.4 130.6 138.5 196.2 126.9 168.9 176.7 159.4 173.0 165.5 1990 177.3 130.5 140.3 140.3 132.2 105.4 149.4 200.3 125.2 145.5 131.4 129.7 1991 136.9 167.5 141.9 140.0 121.3 169.7 173.7 176.3 125.3 144.1 108.2 144.4 1992 150.0 161.1 106.7 99.8 73.8 65.2 85.7 64.5 63.9 88.7 91.8 82.6 1993 59.3 91.0 69.8 62.2 61.3 49.8 57.9 42.2 22.4 56.4 35.6 48.9 1994 57.8 35.5 31.7 16.1 17.8 28.0 35.1 22.5 25.7 44.0 18.0 26.2 1995 24.2 29.9 31.1 14.0 14.5 15.6 14.5 14.3 11.8 21.1 9.0 10.0 1996 11.5 4.4 9.2 4.8 5.5 11.8 8.2 14.4 1.6 0.9 17.9 13.3 1997 5.7 7.6 8.7 15.5 18.5 12.7 10.4 24.4 51.3 23.8 39.0 41.2 1998 31.9 40.3 54.8 53.4 56.3 70.7 66.6 92.2 92.9 55.5 74.0 81.9 1999 62.0 66.3 68.8 63.7 106.4 137.7 113.5 93.7 71.5 116.7 133.2 84.6 2000 90.1 112.9 138.5 125.5 121.6 124.9 170.1 130.5 109.7 99.4 106.8 104.4 2001 95.6 80.6 113.5 107.7 96.6 134.0 81.8 106.4 150.7 125.5 106.5 132.2 2002 114.1 107.4 98.4 120.7 120.8 88.3 99.6 116.4 109.6 97.5 95.5 80.8 2003 79.7 46.0 61.1 60.0 54.6 77.4 83.3 72.7 48.7 65.5 67.3 46.5 2004 37.3 45.8 49.1 39.3 41.5 43.2 51.1 40.9 27.7 48.0 43.5 17.9 2005 31.3 29.2 24.5 24.2 42.7 39.3 40.1 36.4 21.9 8.7 18.0 41.1 2006 15.3 4.9 10.6 30.2 22.3 13.9 12.2 12.9 14.4 10.5 21.4 13.6 2007 16.8 10.7 4.5 3.4 11.7 12.1 9.7 6.0 2.4 0.9 1.7 10.1 2008 3.3 2.1 9.3 2.9 3.2 3.4 0.8 0.5 1.1 2.9 4.1 0.8 2009 1.5 1.4 0.7 1.2 2.9 2.6 ------------------------------------------------------------------------------- No observations were available during February 1824. The value shown was interpolated from the January and March monthly means of that year. Note: Data are preliminary after Dec 08. statsmodels-0.12.2/statsmodels/datasets/sunspots/src/sunspots_yearly.dat000066400000000000000000000063451400612667500267710ustar00rootroot000000000000001700 5 1701 11 1702 16 1703 23 1704 36 1705 58 1706 29 1707 20 1708 10 1709 8 1710 3 1711 0 1712 0 1713 2 1714 11 1715 27 1716 47 1717 63 1718 60 1719 39 1720 28 1721 26 1722 22 1723 11 1724 21 1725 40 1726 78 1727 122 1728 103 1729 73 1730 47 1731 35 1732 11 1733 5 1734 16 1735 34 1736 70 1737 81 1738 111 1739 101 1740 73 1741 40 1742 20 1743 16 1744 5 1745 11 1746 22 1747 40 1748 60 1749 80.9 1750 83.4 1751 47.7 1752 47.8 1753 30.7 1754 12.2 1755 9.6 1756 10.2 1757 32.4 1758 47.6 1759 54.0 1760 62.9 1761 85.9 1762 61.2 1763 45.1 1764 36.4 1765 20.9 1766 11.4 1767 37.8 1768 69.8 1769 106.1 1770 100.8 1771 81.6 1772 66.5 1773 34.8 1774 30.6 1775 7.0 1776 19.8 1777 92.5 1778 154.4 1779 125.9 1780 84.8 1781 68.1 1782 38.5 1783 22.8 1784 10.2 1785 24.1 1786 82.9 1787 132.0 1788 130.9 1789 118.1 1790 89.9 1791 66.6 1792 60.0 1793 46.9 1794 41.0 1795 21.3 1796 16.0 1797 6.4 1798 4.1 1799 6.8 1800 14.5 1801 34.0 1802 45.0 1803 43.1 1804 47.5 1805 42.2 1806 28.1 1807 10.1 1808 8.1 1809 2.5 1810 0.0 1811 1.4 1812 5.0 1813 12.2 1814 13.9 1815 35.4 1816 45.8 1817 41.1 1818 30.1 1819 23.9 1820 15.6 1821 6.6 1822 4.0 1823 1.8 1824 8.5 1825 16.6 1826 36.3 1827 49.6 1828 64.2 1829 67.0 1830 70.9 1831 47.8 1832 27.5 1833 8.5 1834 13.2 1835 56.9 1836 121.5 1837 138.3 1838 103.2 1839 85.7 1840 64.6 1841 36.7 1842 24.2 1843 10.7 1844 15.0 1845 40.1 1846 61.5 1847 98.5 1848 124.7 1849 96.3 1850 66.6 1851 64.5 1852 54.1 1853 39.0 1854 20.6 1855 6.7 1856 4.3 1857 22.7 1858 54.8 1859 93.8 1860 95.8 1861 77.2 1862 59.1 1863 44.0 1864 47.0 1865 30.5 1866 16.3 1867 7.3 1868 37.6 1869 74.0 1870 139.0 1871 111.2 1872 101.6 1873 66.2 1874 44.7 1875 17.0 1876 11.3 1877 12.4 1878 3.4 1879 6.0 1880 32.3 1881 54.3 1882 59.7 1883 63.7 1884 63.5 1885 52.2 1886 25.4 1887 13.1 1888 6.8 1889 6.3 1890 7.1 1891 35.6 1892 73.0 1893 85.1 1894 78.0 1895 64.0 1896 41.8 1897 26.2 1898 26.7 1899 12.1 1900 9.5 1901 2.7 1902 5.0 1903 24.4 1904 42.0 1905 63.5 1906 53.8 1907 62.0 1908 48.5 1909 43.9 1910 18.6 1911 5.7 1912 3.6 1913 1.4 1914 9.6 1915 47.4 1916 57.1 1917 103.9 1918 80.6 1919 63.6 1920 37.6 1921 26.1 1922 14.2 1923 5.8 1924 16.7 1925 44.3 1926 63.9 1927 69.0 1928 77.8 1929 64.9 1930 35.7 1931 21.2 1932 11.1 1933 5.7 1934 8.7 1935 36.1 1936 79.7 1937 114.4 1938 109.6 1939 88.8 1940 67.8 1941 47.5 1942 30.6 1943 16.3 1944 9.6 1945 33.2 1946 92.6 1947 151.6 1948 136.3 1949 134.7 1950 83.9 1951 69.4 1952 31.5 1953 13.9 1954 4.4 1955 38.0 1956 141.7 1957 190.2 1958 184.8 1959 159.0 1960 112.3 1961 53.9 1962 37.6 1963 27.9 1964 10.2 1965 15.1 1966 47.0 1967 93.8 1968 105.9 1969 105.5 1970 104.5 1971 66.6 1972 68.9 1973 38.0 1974 34.5 1975 15.5 1976 12.6 1977 27.5 1978 92.5 1979 155.4 1980 154.6 1981 140.4 1982 115.9 1983 66.6 1984 45.9 1985 17.9 1986 13.4 1987 29.4 1988 100.2 1989 157.6 1990 142.6 1991 145.7 1992 94.3 1993 54.6 1994 29.9 1995 17.5 1996 8.6 1997 21.5 1998 64.3 1999 93.3 2000 119.6 2001 111.0 2002 104.0 2003 63.7 2004 40.4 2005 29.8 2006 15.2 2007 7.5 2008 2.9 statsmodels-0.12.2/statsmodels/datasets/sunspots/sunspots.csv000066400000000000000000000056001400612667500246310ustar00rootroot00000000000000"YEAR","SUNACTIVITY" 1700,5 1701,11 1702,16 1703,23 1704,36 1705,58 1706,29 1707,20 1708,10 1709,8 1710,3 1711,0 1712,0 1713,2 1714,11 1715,27 1716,47 1717,63 1718,60 1719,39 1720,28 1721,26 1722,22 1723,11 1724,21 1725,40 1726,78 1727,122 1728,103 1729,73 1730,47 1731,35 1732,11 1733,5 1734,16 1735,34 1736,70 1737,81 1738,111 1739,101 1740,73 1741,40 1742,20 1743,16 1744,5 1745,11 1746,22 1747,40 1748,60 1749,80.9 1750,83.4 1751,47.7 1752,47.8 1753,30.7 1754,12.2 1755,9.6 1756,10.2 1757,32.4 1758,47.6 1759,54 1760,62.9 1761,85.9 1762,61.2 1763,45.1 1764,36.4 1765,20.9 1766,11.4 1767,37.8 1768,69.8 1769,106.1 1770,100.8 1771,81.6 1772,66.5 1773,34.8 1774,30.6 1775,7 1776,19.8 1777,92.5 1778,154.4 1779,125.9 1780,84.8 1781,68.1 1782,38.5 1783,22.8 1784,10.2 1785,24.1 1786,82.9 1787,132 1788,130.9 1789,118.1 1790,89.9 1791,66.6 1792,60 1793,46.9 1794,41 1795,21.3 1796,16 1797,6.4 1798,4.1 1799,6.8 1800,14.5 1801,34 1802,45 1803,43.1 1804,47.5 1805,42.2 1806,28.1 1807,10.1 1808,8.1 1809,2.5 1810,0 1811,1.4 1812,5 1813,12.2 1814,13.9 1815,35.4 1816,45.8 1817,41.1 1818,30.1 1819,23.9 1820,15.6 1821,6.6 1822,4 1823,1.8 1824,8.5 1825,16.6 1826,36.3 1827,49.6 1828,64.2 1829,67 1830,70.9 1831,47.8 1832,27.5 1833,8.5 1834,13.2 1835,56.9 1836,121.5 1837,138.3 1838,103.2 1839,85.7 1840,64.6 1841,36.7 1842,24.2 1843,10.7 1844,15 1845,40.1 1846,61.5 1847,98.5 1848,124.7 1849,96.3 1850,66.6 1851,64.5 1852,54.1 1853,39 1854,20.6 1855,6.7 1856,4.3 1857,22.7 1858,54.8 1859,93.8 1860,95.8 1861,77.2 1862,59.1 1863,44 1864,47 1865,30.5 1866,16.3 1867,7.3 1868,37.6 1869,74 1870,139 1871,111.2 1872,101.6 1873,66.2 1874,44.7 1875,17 1876,11.3 1877,12.4 1878,3.4 1879,6 1880,32.3 1881,54.3 1882,59.7 1883,63.7 1884,63.5 1885,52.2 1886,25.4 1887,13.1 1888,6.8 1889,6.3 1890,7.1 1891,35.6 1892,73 1893,85.1 1894,78 1895,64 1896,41.8 1897,26.2 1898,26.7 1899,12.1 1900,9.5 1901,2.7 1902,5 1903,24.4 1904,42 1905,63.5 1906,53.8 1907,62 1908,48.5 1909,43.9 1910,18.6 1911,5.7 1912,3.6 1913,1.4 1914,9.6 1915,47.4 1916,57.1 1917,103.9 1918,80.6 1919,63.6 1920,37.6 1921,26.1 1922,14.2 1923,5.8 1924,16.7 1925,44.3 1926,63.9 1927,69 1928,77.8 1929,64.9 1930,35.7 1931,21.2 1932,11.1 1933,5.7 1934,8.7 1935,36.1 1936,79.7 1937,114.4 1938,109.6 1939,88.8 1940,67.8 1941,47.5 1942,30.6 1943,16.3 1944,9.6 1945,33.2 1946,92.6 1947,151.6 1948,136.3 1949,134.7 1950,83.9 1951,69.4 1952,31.5 1953,13.9 1954,4.4 1955,38 1956,141.7 1957,190.2 1958,184.8 1959,159 1960,112.3 1961,53.9 1962,37.6 1963,27.9 1964,10.2 1965,15.1 1966,47 1967,93.8 1968,105.9 1969,105.5 1970,104.5 1971,66.6 1972,68.9 1973,38 1974,34.5 1975,15.5 1976,12.6 1977,27.5 1978,92.5 1979,155.4 1980,154.6 1981,140.4 1982,115.9 1983,66.6 1984,45.9 1985,17.9 1986,13.4 1987,29.4 1988,100.2 1989,157.6 1990,142.6 1991,145.7 1992,94.3 1993,54.6 1994,29.9 1995,17.5 1996,8.6 1997,21.5 1998,64.3 1999,93.3 2000,119.6 2001,111 2002,104 2003,63.7 2004,40.4 2005,29.8 2006,15.2 2007,7.5 2008,2.9 statsmodels-0.12.2/statsmodels/datasets/template_data.py000066400000000000000000000026731400612667500235050ustar00rootroot00000000000000"""Name of dataset.""" from statsmodels.datasets import utils as du __docformat__ = 'restructuredtext' COPYRIGHT = """E.g., This is public domain.""" TITLE = """Title of the dataset""" SOURCE = """ This section should provide a link to the original dataset if possible and attribution and correspondance information for the dataset's original author if so desired. """ DESCRSHORT = """A short description.""" DESCRLONG = """A longer description of the dataset.""" #suggested notes NOTE = """ :: Number of observations: Number of variables: Variable name definitions: Any other useful information that does not fit into the above categories. """ def load(as_pandas=None): """ Load the data and return a Dataset class instance. Parameters ---------- as_pandas : bool Flag indicating whether to return pandas DataFrames and Series or numpy recarrays and arrays. If True, returns pandas. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ return du.as_numpy_dataset(load_pandas(), as_pandas=as_pandas) def load_pandas(): """ Load the strikes data and return a Dataset class instance. Returns ------- Dataset See DATASET_PROPOSAL.txt for more information. """ data = _get_data() return du.process_pandas(data, endog_idx=0) def _get_data(): return du.load_csv(__file__, 'DatasetName.csv') statsmodels-0.12.2/statsmodels/datasets/tests/000077500000000000000000000000001400612667500214615ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/tests/__init__.py000066400000000000000000000000001400612667500235600ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/datasets/tests/test_data.py000066400000000000000000000027201400612667500240040ustar00rootroot00000000000000import importlib import numpy as np import pandas as pd import pytest import statsmodels.datasets from statsmodels.datasets.utils import Dataset exclude = ['check_internet', 'clear_data_home', 'get_data_home', 'get_rdataset', 'tests', 'utils', 'webuse', 'PytestTester', 'test'] datasets = [] for dataset_name in dir(statsmodels.datasets): if not dataset_name.startswith('_') and dataset_name not in exclude: datasets.append(dataset_name) @pytest.mark.parametrize('dataset_name', datasets) def test_dataset(dataset_name): dataset = importlib.import_module('statsmodels.datasets.' + dataset_name) ds = dataset.load() assert isinstance(ds, Dataset) assert isinstance(ds.data, np.recarray) if hasattr(ds, 'exog'): assert isinstance(ds.exog, np.ndarray) if hasattr(ds, 'endog'): assert isinstance(ds.endog, np.ndarray) ds = dataset.load(as_pandas=True) assert isinstance(ds, Dataset) assert isinstance(ds.data, pd.DataFrame) if hasattr(ds, 'exog'): assert isinstance(ds.exog, (pd.DataFrame, pd.Series)) if hasattr(ds, 'endog'): assert isinstance(ds.endog, (pd.DataFrame, pd.Series)) ds = dataset.load_pandas() assert isinstance(ds, Dataset) assert isinstance(ds.data, pd.DataFrame) if hasattr(ds, 'exog'): assert isinstance(ds.exog, (pd.DataFrame, pd.Series)) if hasattr(ds, 'endog'): assert isinstance(ds.endog, (pd.DataFrame, pd.Series)) statsmodels-0.12.2/statsmodels/datasets/tests/test_utils.py000066400000000000000000000063611400612667500242400ustar00rootroot00000000000000import os from ssl import SSLError from socket import timeout from urllib.error import HTTPError, URLError import numpy as np from numpy.testing import assert_, assert_array_equal import pytest from statsmodels.datasets import get_rdataset, webuse, check_internet, utils cur_dir = os.path.dirname(os.path.abspath(__file__)) IGNORED_EXCEPTIONS = (HTTPError, URLError, SSLError, UnicodeEncodeError, timeout) @pytest.mark.smoke def test_get_rdataset(): test_url = "https://raw.githubusercontent.com/vincentarelbundock/" \ "Rdatasets/master/csv/datasets/cars.csv" internet_available = check_internet(test_url) if not internet_available: # pragma: no cover pytest.skip('Unable to retrieve file - skipping test') try: duncan = get_rdataset("Duncan", "carData", cache=cur_dir) except IGNORED_EXCEPTIONS: pytest.skip('Failed with HTTPError or URLError, these are random') assert_(isinstance(duncan, utils.Dataset)) duncan = get_rdataset("Duncan", "carData", cache=cur_dir) assert_(duncan.from_cache) @pytest.mark.smoke def test_get_rdataset_write_read_cache(): # test writing and reading cache try: guerry = get_rdataset("Guerry", "HistData", cache=cur_dir) except IGNORED_EXCEPTIONS: pytest.skip('Failed with HTTPError or URLError, these are random') assert_(guerry.from_cache is False) guerry2 = get_rdataset("Guerry", "HistData", cache=cur_dir) assert_(guerry2.from_cache is True) fn = "raw.githubusercontent.com,vincentarelbundock,Rdatasets,master,csv," \ "HistData,Guerry-v2.csv.zip" os.remove(os.path.join(cur_dir, fn)) fn = "raw.githubusercontent.com,vincentarelbundock,Rdatasets,master,doc," \ "HistData,rst,Guerry-v2.rst.zip" os.remove(os.path.join(cur_dir, fn)) def test_webuse(): # test copied and adjusted from iolib/tests/test_foreign from statsmodels.iolib.tests.results.macrodata import macrodata_result res2 = np.array([list(row) for row in macrodata_result]) base_gh = "https://github.com/statsmodels/statsmodels/raw/master/" \ "statsmodels/datasets/macrodata/" internet_available = check_internet(base_gh) if not internet_available: # pragma: no cover pytest.skip('Unable to retrieve file - skipping test') try: res1 = webuse('macrodata', baseurl=base_gh, as_df=False) except IGNORED_EXCEPTIONS: pytest.skip('Failed with HTTPError or URLError, these are random') assert_array_equal(res1, res2) def test_webuse_pandas(): # test copied and adjusted from iolib/tests/test_foreign from statsmodels.compat.pandas import assert_frame_equal from statsmodels.datasets import macrodata dta = macrodata.load_pandas().data base_gh = "https://github.com/statsmodels/statsmodels/raw/master/" \ "statsmodels/datasets/macrodata/" internet_available = check_internet(base_gh) if not internet_available: # pragma: no cover pytest.skip('Unable to retrieve file - skipping test') try: res1 = webuse('macrodata', baseurl=base_gh) except IGNORED_EXCEPTIONS: pytest.skip('Failed with HTTP Error, these are random') res1 = res1.astype(float) assert_frame_equal(res1, dta.astype(float)) statsmodels-0.12.2/statsmodels/datasets/utils.py000066400000000000000000000245011400612667500220330ustar00rootroot00000000000000from statsmodels.compat.python import lrange from io import StringIO import shutil from os import environ, makedirs from os.path import expanduser, exists, dirname, abspath, join from urllib.error import HTTPError, URLError from urllib.request import urlopen from urllib.parse import urljoin import numpy as np from pandas import read_stata, read_csv, DataFrame, Series, Index def webuse(data, baseurl='https://www.stata-press.com/data/r11/', as_df=True): """ Download and return an example dataset from Stata. Parameters ---------- data : str Name of dataset to fetch. baseurl : str The base URL to the stata datasets. as_df : bool Deprecated. Always returns a DataFrame Returns ------- dta : DataFrame A DataFrame containing the Stata dataset. Examples -------- >>> dta = webuse('auto') Notes ----- Make sure baseurl has trailing forward slash. Does not do any error checking in response URLs. """ url = urljoin(baseurl, data+'.dta') return read_stata(url) class Dataset(dict): def __init__(self, **kw): # define some default attributes, so pylint can find them self.endog = None self.exog = None self.data = None self.names = None dict.__init__(self, kw) self.__dict__ = self # Some datasets have string variables. If you want a raw_data # attribute you must create this in the dataset's load function. try: # some datasets have string variables self.raw_data = self.data.astype(float) except: pass def __repr__(self): return str(self.__class__) def process_pandas(data, endog_idx=0, exog_idx=None, index_idx=None): names = data.columns if isinstance(endog_idx, int): endog_name = names[endog_idx] endog = data[endog_name].copy() if exog_idx is None: exog = data.drop([endog_name], axis=1) else: exog = data[names[exog_idx]].copy() else: endog = data.loc[:, endog_idx].copy() endog_name = list(endog.columns) if exog_idx is None: exog = data.drop(endog_name, axis=1) elif isinstance(exog_idx, int): exog = data[names[exog_idx]].copy() else: exog = data[names[exog_idx]].copy() if index_idx is not None: # NOTE: will have to be improved for dates index = Index(data.iloc[:, index_idx]) endog.index = index exog.index = index.copy() data = data.set_index(names[index_idx]) exog_name = list(exog.columns) dataset = Dataset(data=data, names=list(names), endog=endog, exog=exog, endog_name=endog_name, exog_name=exog_name) return dataset def _maybe_reset_index(data): """ All the Rdatasets have the integer row.labels from R if there is no real index. Strip this for a zero-based index """ if data.index.equals(Index(lrange(1, len(data) + 1))): data = data.reset_index(drop=True) return data def _get_cache(cache): if cache is False: # do not do any caching or load from cache cache = None elif cache is True: # use default dir for cache cache = get_data_home(None) else: cache = get_data_home(cache) return cache def _cache_it(data, cache_path): import zlib open(cache_path, "wb").write(zlib.compress(data)) def _open_cache(cache_path): import zlib data = zlib.decompress(open(cache_path, 'rb').read()) # return as bytes object encoded in utf-8 for cross-compat of cached return data def _urlopen_cached(url, cache): """ Tries to load data from cache location otherwise downloads it. If it downloads the data and cache is not None then it will put the downloaded data in the cache path. """ from_cache = False if cache is not None: file_name = url.split("://")[-1].replace('/', ',') file_name = file_name.split('.') if len(file_name) > 1: file_name[-2] += '-v2' else: file_name[0] += '-v2' file_name = '.'.join(file_name) + ".zip" cache_path = join(cache, file_name) try: data = _open_cache(cache_path) from_cache = True except: pass # not using the cache or did not find it in cache if not from_cache: data = urlopen(url, timeout=3).read() if cache is not None: # then put it in the cache _cache_it(data, cache_path) return data, from_cache def _get_data(base_url, dataname, cache, extension="csv"): url = base_url + (dataname + ".%s") % extension try: data, from_cache = _urlopen_cached(url, cache) except HTTPError as err: if '404' in str(err): raise ValueError("Dataset %s was not found." % dataname) else: raise err data = data.decode('utf-8', 'strict') return StringIO(data), from_cache def _get_dataset_meta(dataname, package, cache): # get the index, you'll probably want this cached because you have # to download info about all the data to get info about any of the data... index_url = ("https://raw.githubusercontent.com/vincentarelbundock/" "Rdatasets/master/datasets.csv") data, _ = _urlopen_cached(index_url, cache) data = data.decode('utf-8', 'strict') index = read_csv(StringIO(data)) idx = np.logical_and(index.Item == dataname, index.Package == package) dataset_meta = index.loc[idx] return dataset_meta["Title"].iloc[0] def get_rdataset(dataname, package="datasets", cache=False): """download and return R dataset Parameters ---------- dataname : str The name of the dataset you want to download package : str The package in which the dataset is found. The default is the core 'datasets' package. cache : bool or str If True, will download this data into the STATSMODELS_DATA folder. The default location is a folder called statsmodels_data in the user home folder. Otherwise, you can specify a path to a folder to use for caching the data. If False, the data will not be cached. Returns ------- dataset : Dataset A `statsmodels.data.utils.Dataset` instance. This objects has attributes: * data - A pandas DataFrame containing the data * title - The dataset title * package - The package from which the data came * from_cache - Whether not cached data was retrieved * __doc__ - The verbatim R documentation. Notes ----- If the R dataset has an integer index. This is reset to be zero-based. Otherwise the index is preserved. The caching facilities are dumb. That is, no download dates, e-tags, or otherwise identifying information is checked to see if the data should be downloaded again or not. If the dataset is in the cache, it's used. """ # NOTE: use raw github bc html site might not be most up to date data_base_url = ("https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/" "master/csv/"+package+"/") docs_base_url = ("https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/" "master/doc/"+package+"/rst/") cache = _get_cache(cache) data, from_cache = _get_data(data_base_url, dataname, cache) data = read_csv(data, index_col=0) data = _maybe_reset_index(data) title = _get_dataset_meta(dataname, package, cache) doc, _ = _get_data(docs_base_url, dataname, cache, "rst") return Dataset(data=data, __doc__=doc.read(), package=package, title=title, from_cache=from_cache) # The below function were taken from sklearn def get_data_home(data_home=None): """Return the path of the statsmodels data dir. This folder is used by some large dataset loaders to avoid downloading the data several times. By default the data dir is set to a folder named 'statsmodels_data' in the user home folder. Alternatively, it can be set by the 'STATSMODELS_DATA' environment variable or programatically by giving an explicit folder path. The '~' symbol is expanded to the user home folder. If the folder does not already exist, it is automatically created. """ if data_home is None: data_home = environ.get('STATSMODELS_DATA', join('~', 'statsmodels_data')) data_home = expanduser(data_home) if not exists(data_home): makedirs(data_home) return data_home def clear_data_home(data_home=None): """Delete all the content of the data home cache.""" data_home = get_data_home(data_home) shutil.rmtree(data_home) def check_internet(url=None): """Check if internet is available""" url = "https://github.com" if url is None else url try: urlopen(url) except URLError as err: return False return True def strip_column_names(df): """ Remove leading and trailing single quotes Parameters ---------- df : DataFrame DataFrame to process Returns ------- df : DataFrame DataFrame with stripped column names Notes ----- In-place modification """ columns = [] for c in df: if c.startswith('\'') and c.endswith('\''): c = c[1:-1] elif c.startswith('\''): c = c[1:] elif c.endswith('\''): c = c[:-1] columns.append(c) df.columns = columns return df def load_csv(base_file, csv_name, sep=',', convert_float=False): """Standard simple csv loader""" filepath = dirname(abspath(base_file)) filename = join(filepath,csv_name) engine = 'python' if sep != ',' else 'c' float_precision = {} if engine == 'c': float_precision = {'float_precision': 'high'} data = read_csv(filename, sep=sep, engine=engine, **float_precision) if convert_float: data = data.astype(float) return data def as_numpy_dataset(ds, as_pandas=True, retain_index=False): """Convert a pandas dataset to a NumPy dataset""" if as_pandas: return ds ds.data = ds.data.to_records(index=retain_index) for d in dir(ds): if d.startswith('_'): continue attr = getattr(ds, d) if isinstance(attr, (Series, DataFrame)): setattr(ds, d, np.asarray(attr)) return ds statsmodels-0.12.2/statsmodels/discrete/000077500000000000000000000000001400612667500203115ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/discrete/__init__.py000066400000000000000000000001131400612667500224150ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/discrete/_diagnostics_count.py000066400000000000000000000236311400612667500245460ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Sep 15 12:53:45 2017 Author: Josef Perktold """ import numpy as np from scipy import stats from statsmodels.regression.linear_model import OLS from statsmodels.discrete.discrete_model import Poisson def _combine_bins(edge_index, x): """group columns into bins using sum This is mainly a helper function for combining probabilities into cells. It similar to `np.add.reduceat(x, edge_index, axis=-1)` except for the treatment of the last index and last cell. Parameters ---------- edge_index : array_like This defines the (zero-based) indices for the columns that are be combined. Each index in `edge_index` except the last is the starting index for a bin. The largest index in a bin is the next edge_index-1. x : 1d or 2d array array for which columns are combined. If x is 1-dimensional that it will be treated as a 2-d row vector. Returns ------- x_new : ndarray Examples -------- >>> dia.combine_bins([0,1,5], np.arange(4)) (array([0, 6]), array([1, 4])) this aggregates to two bins with the sum of 1 and 4 elements >>> np.arange(4)[0].sum() 0 >>> np.arange(4)[1:5].sum() 6 If the rightmost index is smaller than len(x)+1, then the remaining columns will not be included. >>> dia.combine_bins([0,1,3], np.arange(4)) (array([0, 3]), array([1, 2])) """ x = np.asarray(x) if x.ndim == 1: is_1d = True x = x[None, :] else: is_1d = False xli = [] kli = [] for bin_idx in range(len(edge_index) - 1): i, j = edge_index[bin_idx : bin_idx + 2] xli.append(x[:, i:j].sum(1)) kli.append(j - i) x_new = np.column_stack(xli) if is_1d: x_new = x_new.squeeze() return x_new, np.asarray(kli) def plot_probs(freq, probs_predicted, label='predicted', upp_xlim=None, fig=None): """diagnostic plots for comparing two lists of discrete probabilities Parameters ---------- freq, probs_predicted : nd_arrays two arrays of probabilites, this can be any probabilities for the same events, default is designed for comparing predicted and observed probabilities label : str or tuple If string, then it will be used as the label for probs_predicted and "freq" is used for the other probabilities. If label is a tuple of strings, then the first is they are used as label for both probabilities upp_xlim : None or int If it is not None, then the xlim of the first two plots are set to (0, upp_xlim), otherwise the matplotlib default is used fig : None or matplotlib figure instance If fig is provided, then the axes will be added to it in a (3,1) subplots, otherwise a matplotlib figure instance is created Returns ------- Figure The figure contains 3 subplot with probabilities, cumulative probabilities and a PP-plot """ if isinstance(label, list): label0, label1 = label else: label0, label1 = 'freq', label if fig is None: import matplotlib.pyplot as plt fig = plt.figure(figsize=(8,12)) ax1 = fig.add_subplot(311) ax1.plot(freq, '-o', label=label0) ax1.plot(probs_predicted, '-d', label=label1) if upp_xlim is not None: ax1.set_xlim(0, upp_xlim) ax1.legend() ax1.set_title('probabilities') ax2 = fig.add_subplot(312) ax2.plot(np.cumsum(freq), '-o', label=label0) ax2.plot(np.cumsum(probs_predicted), '-d', label=label1) if upp_xlim is not None: ax2.set_xlim(0, upp_xlim) ax2.legend() ax2.set_title('cumulative probabilities') ax3 = fig.add_subplot(313) ax3.plot(np.cumsum(probs_predicted), np.cumsum(freq), 'o') ax3.plot(np.arange(len(freq)) / len(freq), np.arange(len(freq)) / len(freq)) ax3.set_title('PP-plot') ax3.set_xlabel(label1) ax3.set_ylabel(label0) return fig def test_chisquare_prob(results, probs, bin_edges=None, method=None): """ chisquare test for predicted probabilities using cmt-opg Parameters ---------- results : results instance Instance of a count regression results probs : ndarray Array of predicted probabilities with observations in rows and event counts in columns bin_edges : None or array intervals to combine several counts into cells see combine_bins Returns ------- (api not stable, replace by test-results class) statistic : float chisquare statistic for tes p-value : float p-value of test df : int degrees of freedom for chisquare distribution extras : ??? currently returns a tuple with some intermediate results (diff, res_aux) Notes ----- Status : experimental, no verified unit tests, needs to be generalized currently only OPG version with auxiliary regression is implemented Assumes counts are np.arange(probs.shape[1]), i.e. consecutive integers starting at zero. Auxiliary regression drops the last column of binned probs to avoid that probabilities sum to 1. """ res = results score_obs = results.model.score_obs(results.params) d_ind = (res.model.endog[:, None] == np.arange(probs.shape[1])).astype(int) if bin_edges is not None: d_ind_bins, k_bins = _combine_bins(bin_edges, d_ind) probs_bins, k_bins = _combine_bins(bin_edges, probs) else: d_ind_bins, k_bins = d_ind, d_ind.shape[1] probs_bins = probs diff1 = d_ind_bins - probs_bins #diff2 = (1 - d_ind.sum(1)) - (1 - probs_bins.sum(1)) x_aux = np.column_stack((score_obs, diff1[:, :-1])) #, diff2)) nobs = x_aux.shape[0] res_aux = OLS(np.ones(nobs), x_aux).fit() chi2_stat = nobs * (1 - res_aux.ssr / res_aux.uncentered_tss) df = res_aux.model.rank - score_obs.shape[1] if df < k_bins - 1: # not a problem in general, but it can be for OPG version import warnings warnings.warn('auxiliary model is rank deficient') extras = (diff1, res_aux) return chi2_stat, stats.chi2.sf(chi2_stat, df), df, extras def test_poisson_zeroinflation(results_poisson, exog_infl=None): """score test for zero inflation or deflation in Poisson This implements Jansakul and Hinde 2009 score test for excess zeros against a zero modified Poisson alternative. They use a linear link function for the inflation model to allow for zero deflation. Parameters ---------- results_poisson: results instance The test is only valid if the results instance is a Poisson model. exog_infl : ndarray Explanatory variables for the zero inflated or zero modified alternative. I exog_infl is None, then the inflation probability is assumed to be constant. Returns ------- score test results based on chisquare distribution Notes ----- This is a score test based on the null hypothesis that the true model is Poisson. It will also reject for other deviations from a Poisson model if those affect the zero probabilities, e.g. in the direction of excess dispersion as in the Negative Binomial or Generalized Poisson model. Therefore, rejection in this test does not imply that zero-inflated Poisson is the appropriate model. Status: experimental, no verified unit tests, TODO: If the zero modification probability is assumed to be constant under the alternative, then we only have a scalar test score and we can use one-sided tests to distinguish zero inflation and deflation from the two-sided deviations. (The general one-sided case is difficult.) References ---------- Jansakul and Hinde 2009 """ if not isinstance(results_poisson.model, Poisson): # GLM Poisson would be also valid, not tried import warnings warnings.warn('Test is only valid if model is Poisson') nobs = results_poisson.model.endog.shape[0] if exog_infl is None: exog_infl = np.ones((nobs, 1)) endog = results_poisson.model.endog exog = results_poisson.model.exog mu = results_poisson.predict() prob_zero = np.exp(-mu) cov_poi = results_poisson.cov_params() cross_derivative = (exog_infl.T * (-mu)).dot(exog).T cov_infl = (exog_infl.T * ((1 - prob_zero) / prob_zero)).dot(exog_infl) score_obs_infl = exog_infl * (((endog == 0) - prob_zero) / prob_zero)[:,None] #score_obs_infl = exog_infl * ((endog == 0) * (1 - prob_zero) / prob_zero - (endog>0))[:,None] #same score_infl = score_obs_infl.sum(0) cov_score_infl = cov_infl - cross_derivative.T.dot(cov_poi).dot(cross_derivative) cov_score_infl_inv = np.linalg.pinv(cov_score_infl) statistic = score_infl.dot(cov_score_infl_inv).dot(score_infl) df2 = np.linalg.matrix_rank(cov_score_infl) # more general, maybe not needed df = exog_infl.shape[1] pvalue = stats.chi2.sf(statistic, df) return statistic, pvalue, df, df2 def test_poisson_zeroinflation_brock(results_poisson): """score test for zero modification in Poisson, special case This assumes that the Poisson model has a constant and that the zero modification probability is constant. This is a special case of test_poisson_zeroinflation derived by van den Brock 1995. The test reports two sided and one sided alternatives based on the normal distribution of the test statistic. """ mu = results_poisson.predict() prob_zero = np.exp(-mu) endog = results_poisson.model.endog nobs = len(endog) score = ((endog == 0) / prob_zero).sum() - nobs var_score = (1 / prob_zero).sum() - nobs - endog.sum() statistic = score / np.sqrt(var_score) pvalue_two = 2 * stats.norm.sf(np.abs(statistic)) pvalue_upp = stats.norm.sf(statistic) pvalue_low = stats.norm.cdf(statistic) return statistic, pvalue_two, pvalue_upp, pvalue_low, stats.chi2.sf(statistic**2, 1) statsmodels-0.12.2/statsmodels/discrete/conditional_models.py000066400000000000000000000446451400612667500245460ustar00rootroot00000000000000""" Conditional logistic, Poisson, and multinomial logit regression """ import numpy as np import statsmodels.base.model as base import statsmodels.regression.linear_model as lm import statsmodels.base.wrapper as wrap from statsmodels.discrete.discrete_model import (MultinomialResults, MultinomialResultsWrapper) import collections import warnings import itertools class _ConditionalModel(base.LikelihoodModel): def __init__(self, endog, exog, missing='none', **kwargs): if "groups" not in kwargs: raise ValueError("'groups' is a required argument") groups = kwargs["groups"] if groups.size != endog.size: msg = "'endog' and 'groups' should have the same dimensions" raise ValueError(msg) if exog.shape[0] != endog.size: msg = "The leading dimension of 'exog' should equal the length of 'endog'" raise ValueError(msg) super(_ConditionalModel, self).__init__( endog, exog, missing=missing, **kwargs) if self.data.const_idx is not None: msg = ("Conditional models should not have an intercept in the " + "design matrix") raise ValueError(msg) exog = self.exog self.k_params = exog.shape[1] # Get the row indices for each group row_ix = {} for i, g in enumerate(groups): if g not in row_ix: row_ix[g] = [] row_ix[g].append(i) # Split the data into groups and remove groups with no variation endog, exog = np.asarray(endog), np.asarray(exog) offset = kwargs.get("offset") self._endog_grp = [] self._exog_grp = [] self._groupsize = [] if offset is not None: offset = np.asarray(offset) self._offset_grp = [] self._offset = [] self._sumy = [] self.nobs = 0 drops = [0, 0] for g, ix in row_ix.items(): y = endog[ix].flat if np.std(y) == 0: drops[0] += 1 drops[1] += len(y) continue self.nobs += len(y) self._endog_grp.append(y) if offset is not None: self._offset_grp.append(offset[ix]) self._groupsize.append(len(y)) self._exog_grp.append(exog[ix, :]) self._sumy.append(np.sum(y)) if drops[0] > 0: msg = ("Dropped %d groups and %d observations for having " + "no within-group variance") % tuple(drops) warnings.warn(msg) # This can be pre-computed if offset is not None: self._endofs = [] for k, ofs in enumerate(self._offset_grp): self._endofs.append(np.dot(self._endog_grp[k], ofs)) # Number of groups self._n_groups = len(self._endog_grp) # These are the sufficient statistics self._xy = [] self._n1 = [] for g in range(self._n_groups): self._xy.append(np.dot(self._endog_grp[g], self._exog_grp[g])) self._n1.append(np.sum(self._endog_grp[g])) def hessian(self, params): from statsmodels.tools.numdiff import approx_fprime hess = approx_fprime(params, self.score) hess = np.atleast_2d(hess) return hess def fit(self, start_params=None, method='BFGS', maxiter=100, full_output=True, disp=False, fargs=(), callback=None, retall=False, skip_hessian=False, **kwargs): rslt = super(_ConditionalModel, self).fit( start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, skip_hessian=skip_hessian) crslt = ConditionalResults(self, rslt.params, rslt.cov_params(), 1) crslt.method = method crslt.nobs = self.nobs crslt.n_groups = self._n_groups crslt._group_stats = [ "%d" % min(self._groupsize), "%d" % max(self._groupsize), "%.1f" % np.mean(self._groupsize) ] rslt = ConditionalResultsWrapper(crslt) return rslt def fit_regularized(self, method="elastic_net", alpha=0., start_params=None, refit=False, **kwargs): """ Return a regularized fit to a linear regression model. Parameters ---------- method : {'elastic_net'} Only the `elastic_net` approach is currently implemented. alpha : scalar or array_like The penalty weight. If a scalar, the same penalty weight applies to all variables in the model. If a vector, it must have the same length as `params`, and contains a penalty weight for each coefficient. start_params : array_like Starting values for `params`. refit : bool If True, the model is refit using only the variables that have non-zero coefficients in the regularized fit. The refitted model is not regularized. **kwargs Additional keyword argument that are used when fitting the model. Returns ------- Results A results instance. """ from statsmodels.base.elastic_net import fit_elasticnet if method != "elastic_net": raise ValueError("method for fit_regularied must be elastic_net") defaults = {"maxiter": 50, "L1_wt": 1, "cnvrg_tol": 1e-10, "zero_tol": 1e-10} defaults.update(kwargs) return fit_elasticnet(self, method=method, alpha=alpha, start_params=start_params, refit=refit, **defaults) # Override to allow groups to be passed as a variable name. @classmethod def from_formula(cls, formula, data, subset=None, drop_cols=None, *args, **kwargs): try: groups = kwargs["groups"] del kwargs["groups"] except KeyError: raise ValueError("'groups' is a required argument") if isinstance(groups, str): groups = data[groups] if "0+" not in formula.replace(" ", ""): warnings.warn("Conditional models should not include an intercept") model = super(_ConditionalModel, cls).from_formula( formula, data=data, groups=groups, *args, **kwargs) return model class ConditionalLogit(_ConditionalModel): """ Fit a conditional logistic regression model to grouped data. Every group is implicitly given an intercept, but the model is fit using a conditional likelihood in which the intercepts are not present. Thus, intercept estimates are not given, but the other parameter estimates can be interpreted as being adjusted for any group-level confounders. Parameters ---------- endog : array_like The response variable, must contain only 0 and 1. exog : array_like The array of covariates. Do not include an intercept in this array. groups : array_like Codes defining the groups. This is a required keyword parameter. """ def __init__(self, endog, exog, missing='none', **kwargs): super(ConditionalLogit, self).__init__( endog, exog, missing=missing, **kwargs) if np.any(np.unique(self.endog) != np.r_[0, 1]): msg = "endog must be coded as 0, 1" raise ValueError(msg) self.K = self.exog.shape[1] # i.e. self.k_params, for compatibility with MNLogit def loglike(self, params): ll = 0 for g in range(len(self._endog_grp)): ll += self.loglike_grp(g, params) return ll def score(self, params): score = 0 for g in range(self._n_groups): score += self.score_grp(g, params) return score def _denom(self, grp, params, ofs=None): if ofs is None: ofs = 0 exb = np.exp(np.dot(self._exog_grp[grp], params) + ofs) # In the recursions, f may be called multiple times with the # same arguments, so we memoize the results. memo = {} def f(t, k): if t < k: return 0 if k == 0: return 1 try: return memo[(t, k)] except KeyError: pass v = f(t - 1, k) + f(t - 1, k - 1) * exb[t - 1] memo[(t, k)] = v return v return f(self._groupsize[grp], self._n1[grp]) def _denom_grad(self, grp, params, ofs=None): if ofs is None: ofs = 0 ex = self._exog_grp[grp] exb = np.exp(np.dot(ex, params) + ofs) # s may be called multiple times in the recursions with the # same arguments, so memoize the results. memo = {} def s(t, k): if t < k: return 0, np.zeros(self.k_params) if k == 0: return 1, 0 try: return memo[(t, k)] except KeyError: pass h = exb[t - 1] a, b = s(t - 1, k) c, e = s(t - 1, k - 1) d = c * h * ex[t - 1, :] u, v = a + c * h, b + d + e * h memo[(t, k)] = (u, v) return u, v return s(self._groupsize[grp], self._n1[grp]) def loglike_grp(self, grp, params): ofs = None if hasattr(self, 'offset'): ofs = self._offset_grp[grp] llg = np.dot(self._xy[grp], params) if ofs is not None: llg += self._endofs[grp] llg -= np.log(self._denom(grp, params, ofs)) return llg def score_grp(self, grp, params): ofs = 0 if hasattr(self, 'offset'): ofs = self._offset_grp[grp] d, h = self._denom_grad(grp, params, ofs) return self._xy[grp] - h / d class ConditionalPoisson(_ConditionalModel): """ Fit a conditional Poisson regression model to grouped data. Every group is implicitly given an intercept, but the model is fit using a conditional likelihood in which the intercepts are not present. Thus, intercept estimates are not given, but the other parameter estimates can be interpreted as being adjusted for any group-level confounders. Parameters ---------- endog : array_like The response variable exog : array_like The covariates groups : array_like Codes defining the groups. This is a required keyword parameter. """ def loglike(self, params): ofs = None if hasattr(self, 'offset'): ofs = self._offset_grp ll = 0.0 for i in range(len(self._endog_grp)): xb = np.dot(self._exog_grp[i], params) if ofs is not None: xb += ofs[i] exb = np.exp(xb) y = self._endog_grp[i] ll += np.dot(y, xb) s = exb.sum() ll -= self._sumy[i] * np.log(s) return ll def score(self, params): ofs = None if hasattr(self, 'offset'): ofs = self._offset_grp score = 0.0 for i in range(len(self._endog_grp)): x = self._exog_grp[i] xb = np.dot(x, params) if ofs is not None: xb += ofs[i] exb = np.exp(xb) s = exb.sum() y = self._endog_grp[i] score += np.dot(y, x) score -= self._sumy[i] * np.dot(exb, x) / s return score class ConditionalResults(base.LikelihoodModelResults): def __init__(self, model, params, normalized_cov_params, scale): super(ConditionalResults, self).__init__( model, params, normalized_cov_params=normalized_cov_params, scale=scale) def summary(self, yname=None, xname=None, title=None, alpha=.05): """ Summarize the fitted model. Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Names for the exogenous variables, default is "var_xx". Must match the number of parameters in the model title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float Significance level for the confidence intervals Returns ------- smry : Summary instance This holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : class to hold summary results """ top_left = [ ('Dep. Variable:', None), ('Model:', None), ('Log-Likelihood:', None), ('Method:', [self.method]), ('Date:', None), ('Time:', None), ] top_right = [ ('No. Observations:', None), ('No. groups:', [self.n_groups]), ('Min group size:', [self._group_stats[0]]), ('Max group size:', [self._group_stats[1]]), ('Mean group size:', [self._group_stats[2]]), ] if title is None: title = "Conditional Logit Model Regression Results" # create summary tables from statsmodels.iolib.summary import Summary smry = Summary() smry.add_table_2cols( self, gleft=top_left, gright=top_right, # [], yname=yname, xname=xname, title=title) smry.add_table_params( self, yname=yname, xname=xname, alpha=alpha, use_t=self.use_t) return smry class ConditionalMNLogit(_ConditionalModel): """ Fit a conditional multinomial logit model to grouped data. Parameters ---------- endog : array_like The dependent variable, must be integer-valued, coded 0, 1, ..., c-1, where c is the number of response categories. exog : array_like The independent variables. groups : array_like Codes defining the groups. This is a required keyword parameter. Notes ----- Equivalent to femlogit in Stata. References ---------- Gary Chamberlain (1980). Analysis of covariance with qualitative data. The Review of Economic Studies. Vol. 47, No. 1, pp. 225-238. """ def __init__(self, endog, exog, missing='none', **kwargs): super(ConditionalMNLogit, self).__init__( endog, exog, missing=missing, **kwargs) # endog must be integers self.endog = self.endog.astype(int) self.k_cat = self.endog.max() + 1 self.df_model = (self.k_cat - 1) * self.exog.shape[1] self.df_resid = self.nobs - self.df_model self._ynames_map = {j: str(j) for j in range(self.k_cat)} self.J = self.k_cat # Unfortunate name, needed for results self.K = self.exog.shape[1] # for compatibility with MNLogit if self.endog.min() < 0: msg = "endog may not contain negative values" raise ValueError(msg) grx = collections.defaultdict(list) for k, v in enumerate(self.groups): grx[v].append(k) self._group_labels = list(grx.keys()) self._group_labels.sort() self._grp_ix = [grx[k] for k in self._group_labels] def fit(self, start_params=None, method='BFGS', maxiter=100, full_output=True, disp=False, fargs=(), callback=None, retall=False, skip_hessian=False, **kwargs): if start_params is None: q = self.exog.shape[1] c = self.k_cat - 1 start_params = np.random.normal(size=q * c) # Do not call super(...).fit because it cannot handle the 2d-params. rslt = base.LikelihoodModel.fit( self, start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, skip_hessian=skip_hessian) rslt.params = rslt.params.reshape((self.exog.shape[1], -1)) rslt = MultinomialResults(self, rslt) # Not clear what the null likelihood should be, there is no intercept # so the null model is not clearly defined. This is needed for summary # to work. rslt.set_null_options(llnull=np.nan) return MultinomialResultsWrapper(rslt) def loglike(self, params): q = self.exog.shape[1] c = self.k_cat - 1 pmat = params.reshape((q, c)) pmat = np.concatenate((np.zeros((q, 1)), pmat), axis=1) lpr = np.dot(self.exog, pmat) ll = 0.0 for ii in self._grp_ix: x = lpr[ii, :] jj = np.arange(x.shape[0], dtype=int) y = self.endog[ii] denom = 0.0 for p in itertools.permutations(y): denom += np.exp(x[(jj, p)].sum()) ll += x[(jj, y)].sum() - np.log(denom) return ll def score(self, params): q = self.exog.shape[1] c = self.k_cat - 1 pmat = params.reshape((q, c)) pmat = np.concatenate((np.zeros((q, 1)), pmat), axis=1) lpr = np.dot(self.exog, pmat) grad = np.zeros((q, c)) for ii in self._grp_ix: x = lpr[ii, :] jj = np.arange(x.shape[0], dtype=int) y = self.endog[ii] denom = 0.0 denomg = np.zeros((q, c)) for p in itertools.permutations(y): v = np.exp(x[(jj, p)].sum()) denom += v for i, r in enumerate(p): if r != 0: denomg[:, r - 1] += v * self.exog[ii[i], :] for i, r in enumerate(y): if r != 0: grad[:, r - 1] += self.exog[ii[i], :] grad -= denomg / denom return grad.flatten() class ConditionalResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(ConditionalResultsWrapper, ConditionalResults) statsmodels-0.12.2/statsmodels/discrete/count_model.py000066400000000000000000000751161400612667500232050ustar00rootroot00000000000000__all__ = ["ZeroInflatedPoisson", "ZeroInflatedGeneralizedPoisson", "ZeroInflatedNegativeBinomialP"] import warnings import numpy as np import statsmodels.base.model as base import statsmodels.base.wrapper as wrap import statsmodels.regression.linear_model as lm from statsmodels.discrete.discrete_model import (DiscreteModel, CountModel, Poisson, Logit, CountResults, L1CountResults, Probit, _discrete_results_docs, _validate_l1_method, GeneralizedPoisson, NegativeBinomialP) from statsmodels.distributions import zipoisson, zigenpoisson, zinegbin from statsmodels.tools.numdiff import approx_fprime, approx_hess from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.sm_exceptions import ConvergenceWarning from statsmodels.compat.pandas import Appender _doc_zi_params = """ exog_infl : array_like or None Explanatory variables for the binary inflation model, i.e. for mixing probability model. If None, then a constant is used. offset : array_like Offset is added to the linear prediction with coefficient equal to 1. exposure : array_like Log(exposure) is added to the linear prediction with coefficient equal to 1. inflation : {'logit', 'probit'} The model for the zero inflation, either Logit (default) or Probit """ class GenericZeroInflated(CountModel): __doc__ = """ Generic Zero Inflated Model %(params)s %(extra_params)s Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. exog_infl : ndarray A reference to the zero-inflated exogenous design. """ % {'params' : base._model_params_doc, 'extra_params' : _doc_zi_params + base._missing_param_doc} def __init__(self, endog, exog, exog_infl=None, offset=None, inflation='logit', exposure=None, missing='none', **kwargs): super(GenericZeroInflated, self).__init__(endog, exog, offset=offset, exposure=exposure, missing=missing, **kwargs) if exog_infl is None: self.k_inflate = 1 self.exog_infl = np.ones((endog.size, self.k_inflate), dtype=np.float64) else: self.exog_infl = exog_infl self.k_inflate = exog_infl.shape[1] if len(exog.shape) == 1: self.k_exog = 1 else: self.k_exog = exog.shape[1] self.infl = inflation if inflation == 'logit': self.model_infl = Logit(np.zeros(self.exog_infl.shape[0]), self.exog_infl) self._hessian_inflate = self._hessian_logit elif inflation == 'probit': self.model_infl = Probit(np.zeros(self.exog_infl.shape[0]), self.exog_infl) self._hessian_inflate = self._hessian_probit else: raise ValueError("inflation == %s, which is not handled" % inflation) self.inflation = inflation self.k_extra = self.k_inflate if len(self.exog) != len(self.exog_infl): raise ValueError('exog and exog_infl have different number of' 'observation. `missing` handling is not supported') infl_names = ['inflate_%s' % i for i in self.model_infl.data.param_names] self.exog_names[:] = infl_names + list(self.exog_names) self.exog_infl = np.asarray(self.exog_infl, dtype=np.float64) self._init_keys.extend(['exog_infl', 'inflation']) self._null_drop_keys = ['exog_infl'] def loglike(self, params): """ Loglikelihood of Generic Zero Inflated model. Parameters ---------- params : array_like The parameters of the model. Returns ------- loglike : float The log-likelihood function of the model evaluated at `params`. See notes. Notes -------- .. math:: \\ln L=\\sum_{y_{i}=0}\\ln(w_{i}+(1-w_{i})*P_{main\\_model})+ \\sum_{y_{i}>0}(\\ln(1-w_{i})+L_{main\\_model}) where P - pdf of main model, L - loglike function of main model. """ return np.sum(self.loglikeobs(params)) def loglikeobs(self, params): """ Loglikelihood for observations of Generic Zero Inflated model. Parameters ---------- params : array_like The parameters of the model. Returns ------- loglike : ndarray The log likelihood for each observation of the model evaluated at `params`. See Notes for definition. Notes -------- .. math:: \\ln L=\\ln(w_{i}+(1-w_{i})*P_{main\\_model})+ \\ln(1-w_{i})+L_{main\\_model} where P - pdf of main model, L - loglike function of main model. for observations :math:`i=1,...,n` """ params_infl = params[:self.k_inflate] params_main = params[self.k_inflate:] y = self.endog w = self.model_infl.predict(params_infl) w = np.clip(w, np.finfo(float).eps, 1 - np.finfo(float).eps) llf_main = self.model_main.loglikeobs(params_main) zero_idx = np.nonzero(y == 0)[0] nonzero_idx = np.nonzero(y)[0] llf = np.zeros_like(y, dtype=np.float64) llf[zero_idx] = (np.log(w[zero_idx] + (1 - w[zero_idx]) * np.exp(llf_main[zero_idx]))) llf[nonzero_idx] = np.log(1 - w[nonzero_idx]) + llf_main[nonzero_idx] return llf @Appender(DiscreteModel.fit.__doc__) def fit(self, start_params=None, method='bfgs', maxiter=35, full_output=1, disp=1, callback=None, cov_type='nonrobust', cov_kwds=None, use_t=None, **kwargs): if start_params is None: offset = getattr(self, "offset", 0) + getattr(self, "exposure", 0) if np.size(offset) == 1 and offset == 0: offset = None start_params = self._get_start_params() if callback is None: # work around perfect separation callback #3895 callback = lambda *x: x mlefit = super(GenericZeroInflated, self).fit(start_params=start_params, maxiter=maxiter, disp=disp, method=method, full_output=full_output, callback=callback, **kwargs) zipfit = self.result_class(self, mlefit._results) result = self.result_class_wrapper(zipfit) if cov_kwds is None: cov_kwds = {} result._get_robustcov_results(cov_type=cov_type, use_self=True, use_t=use_t, **cov_kwds) return result @Appender(DiscreteModel.fit_regularized.__doc__) def fit_regularized(self, start_params=None, method='l1', maxiter='defined_by_method', full_output=1, disp=1, callback=None, alpha=0, trim_mode='auto', auto_trim_tol=0.01, size_trim_tol=1e-4, qc_tol=0.03, **kwargs): _validate_l1_method(method) if np.size(alpha) == 1 and alpha != 0: k_params = self.k_exog + self.k_inflate alpha = alpha * np.ones(k_params) extra = self.k_extra - self.k_inflate alpha_p = alpha[:-(self.k_extra - extra)] if (self.k_extra and np.size(alpha) > 1) else alpha if start_params is None: offset = getattr(self, "offset", 0) + getattr(self, "exposure", 0) if np.size(offset) == 1 and offset == 0: offset = None start_params = self.model_main.fit_regularized( start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=0, callback=callback, alpha=alpha_p, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol, size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs).params start_params = np.append(np.ones(self.k_inflate), start_params) cntfit = super(CountModel, self).fit_regularized( start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, alpha=alpha, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol, size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs) discretefit = self.result_class_reg(self, cntfit) return self.result_class_reg_wrapper(discretefit) def score_obs(self, params): """ Generic Zero Inflated model score (gradient) vector of the log-likelihood Parameters ---------- params : array_like The parameters of the model Returns ------- score : ndarray, 1-D The score vector of the model, i.e. the first derivative of the loglikelihood function, evaluated at `params` """ params_infl = params[:self.k_inflate] params_main = params[self.k_inflate:] y = self.endog w = self.model_infl.predict(params_infl) w = np.clip(w, np.finfo(float).eps, 1 - np.finfo(float).eps) score_main = self.model_main.score_obs(params_main) llf_main = self.model_main.loglikeobs(params_main) llf = self.loglikeobs(params) zero_idx = np.nonzero(y == 0)[0] nonzero_idx = np.nonzero(y)[0] mu = self.model_main.predict(params_main) dldp = np.zeros((self.exog.shape[0], self.k_exog), dtype=np.float64) dldw = np.zeros_like(self.exog_infl, dtype=np.float64) dldp[zero_idx,:] = (score_main[zero_idx].T * (1 - (w[zero_idx]) / np.exp(llf[zero_idx]))).T dldp[nonzero_idx,:] = score_main[nonzero_idx] if self.inflation == 'logit': dldw[zero_idx,:] = (self.exog_infl[zero_idx].T * w[zero_idx] * (1 - w[zero_idx]) * (1 - np.exp(llf_main[zero_idx])) / np.exp(llf[zero_idx])).T dldw[nonzero_idx,:] = -(self.exog_infl[nonzero_idx].T * w[nonzero_idx]).T elif self.inflation == 'probit': return approx_fprime(params, self.loglikeobs) return np.hstack((dldw, dldp)) def score(self, params): return self.score_obs(params).sum(0) def _hessian_main(self, params): pass def _hessian_logit(self, params): params_infl = params[:self.k_inflate] params_main = params[self.k_inflate:] y = self.endog w = self.model_infl.predict(params_infl) w = np.clip(w, np.finfo(float).eps, 1 - np.finfo(float).eps) score_main = self.model_main.score_obs(params_main) llf_main = self.model_main.loglikeobs(params_main) llf = self.loglikeobs(params) zero_idx = np.nonzero(y == 0)[0] nonzero_idx = np.nonzero(y)[0] hess_arr = np.zeros((self.k_inflate, self.k_exog + self.k_inflate)) pmf = np.exp(llf) #d2l/dw2 for i in range(self.k_inflate): for j in range(i, -1, -1): hess_arr[i, j] = (( self.exog_infl[zero_idx, i] * self.exog_infl[zero_idx, j] * (w[zero_idx] * (1 - w[zero_idx]) * ((1 - np.exp(llf_main[zero_idx])) * (1 - 2 * w[zero_idx]) * np.exp(llf[zero_idx]) - (w[zero_idx] - w[zero_idx]**2) * (1 - np.exp(llf_main[zero_idx]))**2) / pmf[zero_idx]**2)).sum() - (self.exog_infl[nonzero_idx, i] * self.exog_infl[nonzero_idx, j] * w[nonzero_idx] * (1 - w[nonzero_idx])).sum()) #d2l/dpdw for i in range(self.k_inflate): for j in range(self.k_exog): hess_arr[i, j + self.k_inflate] = -(score_main[zero_idx, j] * w[zero_idx] * (1 - w[zero_idx]) * self.exog_infl[zero_idx, i] / pmf[zero_idx]).sum() return hess_arr def _hessian_probit(self, params): pass def hessian(self, params): """ Generic Zero Inflated model Hessian matrix of the loglikelihood Parameters ---------- params : array_like The parameters of the model Returns ------- hess : ndarray, (k_vars, k_vars) The Hessian, second derivative of loglikelihood function, evaluated at `params` Notes ----- """ hess_arr_main = self._hessian_main(params) hess_arr_infl = self._hessian_inflate(params) if hess_arr_main is None or hess_arr_infl is None: return approx_hess(params, self.loglike) dim = self.k_exog + self.k_inflate hess_arr = np.zeros((dim, dim)) hess_arr[:self.k_inflate,:] = hess_arr_infl hess_arr[self.k_inflate:,self.k_inflate:] = hess_arr_main tri_idx = np.triu_indices(self.k_exog + self.k_inflate, k=1) hess_arr[tri_idx] = hess_arr.T[tri_idx] return hess_arr def predict(self, params, exog=None, exog_infl=None, exposure=None, offset=None, which='mean'): """ Predict response variable of a count model given exogenous variables. Parameters ---------- params : array_like The parameters of the model exog : ndarray, optional A reference to the exogenous design. If not assigned, will be used exog from fitting. exog_infl : ndarray, optional A reference to the zero-inflated exogenous design. If not assigned, will be used exog from fitting. offset : ndarray, optional Offset is added to the linear prediction with coefficient equal to 1. exposure : ndarray, optional Log(exposure) is added to the linear prediction with coefficient equal to 1. If exposure is specified, then it will be logged by the method. The user does not need to log it first. which : str, optional Define values that will be predicted. 'mean', 'mean-main', 'linear', 'mean-nonzero', 'prob-zero, 'prob', 'prob-main' Default is 'mean'. Notes ----- """ if exog is None: exog = self.exog if exog_infl is None: exog_infl = self.exog_infl if exposure is None: exposure = getattr(self, 'exposure', 0) else: exposure = np.log(exposure) if offset is None: offset = 0 params_infl = params[:self.k_inflate] params_main = params[self.k_inflate:] prob_main = 1 - self.model_infl.predict(params_infl, exog_infl) lin_pred = np.dot(exog, params_main[:self.exog.shape[1]]) + exposure + offset # Refactor: This is pretty hacky, # there should be an appropriate predict method in model_main # this is just prob(y=0 | model_main) tmp_exog = self.model_main.exog tmp_endog = self.model_main.endog tmp_offset = getattr(self.model_main, 'offset', ['no']) tmp_exposure = getattr(self.model_main, 'exposure', ['no']) self.model_main.exog = exog self.model_main.endog = np.zeros((exog.shape[0])) self.model_main.offset = offset self.model_main.exposure = exposure llf = self.model_main.loglikeobs(params_main) self.model_main.exog = tmp_exog self.model_main.endog = tmp_endog # tmp_offset might be an array with elementwise equality testing if len(tmp_offset) == 1 and tmp_offset[0] == 'no': del self.model_main.offset else: self.model_main.offset = tmp_offset if len(tmp_exposure) == 1 and tmp_exposure[0] == 'no': del self.model_main.exposure else: self.model_main.exposure = tmp_exposure # end hack prob_zero = (1 - prob_main) + prob_main * np.exp(llf) if which == 'mean': return prob_main * np.exp(lin_pred) elif which == 'mean-main': return np.exp(lin_pred) elif which == 'linear': return lin_pred elif which == 'mean-nonzero': return prob_main * np.exp(lin_pred) / (1 - prob_zero) elif which == 'prob-zero': return prob_zero elif which == 'prob-main': return prob_main elif which == 'prob': return self._predict_prob(params, exog, exog_infl, exposure, offset) else: raise ValueError('which = %s is not available' % which) class ZeroInflatedPoisson(GenericZeroInflated): __doc__ = """ Poisson Zero Inflated Model %(params)s %(extra_params)s Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. exog_infl : ndarray A reference to the zero-inflated exogenous design. """ % {'params' : base._model_params_doc, 'extra_params' : _doc_zi_params + base._missing_param_doc} def __init__(self, endog, exog, exog_infl=None, offset=None, exposure=None, inflation='logit', missing='none', **kwargs): super(ZeroInflatedPoisson, self).__init__(endog, exog, offset=offset, inflation=inflation, exog_infl=exog_infl, exposure=exposure, missing=missing, **kwargs) self.model_main = Poisson(self.endog, self.exog, offset=offset, exposure=exposure) self.distribution = zipoisson self.result_class = ZeroInflatedPoissonResults self.result_class_wrapper = ZeroInflatedPoissonResultsWrapper self.result_class_reg = L1ZeroInflatedPoissonResults self.result_class_reg_wrapper = L1ZeroInflatedPoissonResultsWrapper def _hessian_main(self, params): params_infl = params[:self.k_inflate] params_main = params[self.k_inflate:] y = self.endog w = self.model_infl.predict(params_infl) w = np.clip(w, np.finfo(float).eps, 1 - np.finfo(float).eps) score = self.score(params) zero_idx = np.nonzero(y == 0)[0] nonzero_idx = np.nonzero(y)[0] mu = self.model_main.predict(params_main) hess_arr = np.zeros((self.k_exog, self.k_exog)) coeff = (1 + w[zero_idx] * (np.exp(mu[zero_idx]) - 1)) #d2l/dp2 for i in range(self.k_exog): for j in range(i, -1, -1): hess_arr[i, j] = (( self.exog[zero_idx, i] * self.exog[zero_idx, j] * mu[zero_idx] * (w[zero_idx] - 1) * (1 / coeff - w[zero_idx] * mu[zero_idx] * np.exp(mu[zero_idx]) / coeff**2)).sum() - (mu[nonzero_idx] * self.exog[nonzero_idx, i] * self.exog[nonzero_idx, j]).sum()) return hess_arr def _predict_prob(self, params, exog, exog_infl, exposure, offset): params_infl = params[:self.k_inflate] params_main = params[self.k_inflate:] counts = np.atleast_2d(np.arange(0, np.max(self.endog)+1)) if len(exog_infl.shape) < 2: transform = True w = np.atleast_2d( self.model_infl.predict(params_infl, exog_infl))[:, None] else: transform = False w = self.model_infl.predict(params_infl, exog_infl)[:, None] w = np.clip(w, np.finfo(float).eps, 1 - np.finfo(float).eps) mu = self.model_main.predict(params_main, exog, offset=offset)[:, None] result = self.distribution.pmf(counts, mu, w) return result[0] if transform else result def _get_start_params(self): start_params = self.model_main.fit(disp=0, method="nm").params start_params = np.append(np.ones(self.k_inflate) * 0.1, start_params) return start_params class ZeroInflatedGeneralizedPoisson(GenericZeroInflated): __doc__ = """ Zero Inflated Generalized Poisson Model %(params)s %(extra_params)s Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. exog_infl : ndarray A reference to the zero-inflated exogenous design. p : scalar P denotes parametrizations for ZIGP regression. """ % {'params' : base._model_params_doc, 'extra_params' : _doc_zi_params + """p : float dispersion power parameter for the GeneralizedPoisson model. p=1 for ZIGP-1 and p=2 for ZIGP-2. Default is p=2 """ + base._missing_param_doc} def __init__(self, endog, exog, exog_infl=None, offset=None, exposure=None, inflation='logit', p=2, missing='none', **kwargs): super(ZeroInflatedGeneralizedPoisson, self).__init__(endog, exog, offset=offset, inflation=inflation, exog_infl=exog_infl, exposure=exposure, missing=missing, **kwargs) self.model_main = GeneralizedPoisson(self.endog, self.exog, offset=offset, exposure=exposure, p=p) self.distribution = zigenpoisson self.k_exog += 1 self.k_extra += 1 self.exog_names.append("alpha") self.result_class = ZeroInflatedGeneralizedPoissonResults self.result_class_wrapper = ZeroInflatedGeneralizedPoissonResultsWrapper self.result_class_reg = L1ZeroInflatedGeneralizedPoissonResults self.result_class_reg_wrapper = L1ZeroInflatedGeneralizedPoissonResultsWrapper def _get_init_kwds(self): kwds = super(ZeroInflatedGeneralizedPoisson, self)._get_init_kwds() kwds['p'] = self.model_main.parameterization + 1 return kwds def _predict_prob(self, params, exog, exog_infl, exposure, offset): params_infl = params[:self.k_inflate] params_main = params[self.k_inflate:] p = self.model_main.parameterization counts = np.atleast_2d(np.arange(0, np.max(self.endog)+1)) if len(exog_infl.shape) < 2: transform = True w = np.atleast_2d( self.model_infl.predict(params_infl, exog_infl))[:, None] else: transform = False w = self.model_infl.predict(params_infl, exog_infl)[:, None] w[w == 1.] = np.nextafter(1, 0) mu = self.model_main.predict(params_main, exog, exposure=exposure, offset=offset)[:, None] result = self.distribution.pmf(counts, mu, params_main[-1], p, w) return result[0] if transform else result def _get_start_params(self): with warnings.catch_warnings(): warnings.simplefilter("ignore", category=ConvergenceWarning) start_params = ZeroInflatedPoisson(self.endog, self.exog, exog_infl=self.exog_infl).fit(disp=0).params start_params = np.append(start_params, 0.1) return start_params class ZeroInflatedNegativeBinomialP(GenericZeroInflated): __doc__ = """ Zero Inflated Generalized Negative Binomial Model %(params)s %(extra_params)s Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. exog_infl : ndarray A reference to the zero-inflated exogenous design. p : scalar P denotes parametrizations for ZINB regression. p=1 for ZINB-1 and p=2 for ZINB-2. Default is p=2 """ % {'params' : base._model_params_doc, 'extra_params' : _doc_zi_params + """p : float dispersion power parameter for the NegativeBinomialP model. p=1 for ZINB-1 and p=2 for ZINM-2. Default is p=2 """ + base._missing_param_doc} def __init__(self, endog, exog, exog_infl=None, offset=None, exposure=None, inflation='logit', p=2, missing='none', **kwargs): super(ZeroInflatedNegativeBinomialP, self).__init__(endog, exog, offset=offset, inflation=inflation, exog_infl=exog_infl, exposure=exposure, missing=missing, **kwargs) self.model_main = NegativeBinomialP(self.endog, self.exog, offset=offset, exposure=exposure, p=p) self.distribution = zinegbin self.k_exog += 1 self.k_extra += 1 self.exog_names.append("alpha") self.result_class = ZeroInflatedNegativeBinomialResults self.result_class_wrapper = ZeroInflatedNegativeBinomialResultsWrapper self.result_class_reg = L1ZeroInflatedNegativeBinomialResults self.result_class_reg_wrapper = L1ZeroInflatedNegativeBinomialResultsWrapper def _get_init_kwds(self): kwds = super(ZeroInflatedNegativeBinomialP, self)._get_init_kwds() kwds['p'] = self.model_main.parameterization return kwds def _predict_prob(self, params, exog, exog_infl, exposure, offset): params_infl = params[:self.k_inflate] params_main = params[self.k_inflate:] p = self.model_main.parameterization counts = np.arange(0, np.max(self.endog)+1) if len(exog_infl.shape) < 2: transform = True w = np.atleast_2d( self.model_infl.predict(params_infl, exog_infl))[:, None] else: transform = False w = self.model_infl.predict(params_infl, exog_infl)[:, None] w = np.clip(w, np.finfo(float).eps, 1 - np.finfo(float).eps) mu = self.model_main.predict(params_main, exog, exposure=exposure, offset=offset)[:, None] result = self.distribution.pmf(counts, mu, params_main[-1], p, w) return result[0] if transform else result def _get_start_params(self): with warnings.catch_warnings(): warnings.simplefilter("ignore", category=ConvergenceWarning) start_params = self.model_main.fit(disp=0, method='nm').params start_params = np.append(np.zeros(self.k_inflate), start_params) return start_params class ZeroInflatedPoissonResults(CountResults): __doc__ = _discrete_results_docs % { "one_line_description": "A results class for Zero Inflated Poisson", "extra_attr": ""} @cache_readonly def _dispersion_factor(self): mu = self.predict(which='linear') w = 1 - self.predict() / np.exp(self.predict(which='linear')) return (1 + w * np.exp(mu)) def get_margeff(self, at='overall', method='dydx', atexog=None, dummy=False, count=False): """Get marginal effects of the fitted model. Not yet implemented for Zero Inflated Models """ raise NotImplementedError("not yet implemented for zero inflation") class L1ZeroInflatedPoissonResults(L1CountResults, ZeroInflatedPoissonResults): pass class ZeroInflatedPoissonResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(ZeroInflatedPoissonResultsWrapper, ZeroInflatedPoissonResults) class L1ZeroInflatedPoissonResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(L1ZeroInflatedPoissonResultsWrapper, L1ZeroInflatedPoissonResults) class ZeroInflatedGeneralizedPoissonResults(CountResults): __doc__ = _discrete_results_docs % { "one_line_description": "A results class for Zero Inflated Generalized Poisson", "extra_attr": ""} @cache_readonly def _dispersion_factor(self): p = self.model.model_main.parameterization alpha = self.params[self.model.k_inflate:][-1] mu = np.exp(self.predict(which='linear')) w = 1 - self.predict() / mu return ((1 + alpha * mu**p)**2 + w * mu) def get_margeff(self, at='overall', method='dydx', atexog=None, dummy=False, count=False): """Get marginal effects of the fitted model. Not yet implemented for Zero Inflated Models """ raise NotImplementedError("not yet implemented for zero inflation") class L1ZeroInflatedGeneralizedPoissonResults(L1CountResults, ZeroInflatedGeneralizedPoissonResults): pass class ZeroInflatedGeneralizedPoissonResultsWrapper( lm.RegressionResultsWrapper): pass wrap.populate_wrapper(ZeroInflatedGeneralizedPoissonResultsWrapper, ZeroInflatedGeneralizedPoissonResults) class L1ZeroInflatedGeneralizedPoissonResultsWrapper( lm.RegressionResultsWrapper): pass wrap.populate_wrapper(L1ZeroInflatedGeneralizedPoissonResultsWrapper, L1ZeroInflatedGeneralizedPoissonResults) class ZeroInflatedNegativeBinomialResults(CountResults): __doc__ = _discrete_results_docs % { "one_line_description": "A results class for Zero Inflated Generalized Negative Binomial", "extra_attr": ""} @cache_readonly def _dispersion_factor(self): p = self.model.model_main.parameterization alpha = self.params[self.model.k_inflate:][-1] mu = np.exp(self.predict(which='linear')) w = 1 - self.predict() / mu return (1 + alpha * mu**(p-1) + w * mu) def get_margeff(self, at='overall', method='dydx', atexog=None, dummy=False, count=False): """Get marginal effects of the fitted model. Not yet implemented for Zero Inflated Models """ raise NotImplementedError("not yet implemented for zero inflation") class L1ZeroInflatedNegativeBinomialResults(L1CountResults, ZeroInflatedNegativeBinomialResults): pass class ZeroInflatedNegativeBinomialResultsWrapper( lm.RegressionResultsWrapper): pass wrap.populate_wrapper(ZeroInflatedNegativeBinomialResultsWrapper, ZeroInflatedNegativeBinomialResults) class L1ZeroInflatedNegativeBinomialResultsWrapper( lm.RegressionResultsWrapper): pass wrap.populate_wrapper(L1ZeroInflatedNegativeBinomialResultsWrapper, L1ZeroInflatedNegativeBinomialResults) statsmodels-0.12.2/statsmodels/discrete/discrete_margins.py000066400000000000000000000640241400612667500242130ustar00rootroot00000000000000#Splitting out maringal effects to see if they can be generalized from statsmodels.compat.python import lzip import numpy as np from scipy.stats import norm from statsmodels.tools.decorators import cache_readonly #### margeff helper functions #### #NOTE: todo marginal effects for group 2 # group 2 oprobit, ologit, gologit, mlogit, biprobit def _check_margeff_args(at, method): """ Checks valid options for margeff """ if at not in ['overall','mean','median','zero','all']: raise ValueError("%s not a valid option for `at`." % at) if method not in ['dydx','eyex','dyex','eydx']: raise ValueError("method is not understood. Got %s" % method) def _check_discrete_args(at, method): """ Checks the arguments for margeff if the exogenous variables are discrete. """ if method in ['dyex','eyex']: raise ValueError("%s not allowed for discrete variables" % method) if at in ['median', 'zero']: raise ValueError("%s not allowed for discrete variables" % at) def _get_const_index(exog): """ Returns a boolean array of non-constant column indices in exog and an scalar array of where the constant is or None """ effects_idx = exog.var(0) != 0 if np.any(~effects_idx): const_idx = np.where(~effects_idx)[0] else: const_idx = None return effects_idx, const_idx def _isdummy(X): """ Given an array X, returns the column indices for the dummy variables. Parameters ---------- X : array_like A 1d or 2d array of numbers Examples -------- >>> X = np.random.randint(0, 2, size=(15,5)).astype(float) >>> X[:,1:3] = np.random.randn(15,2) >>> ind = _isdummy(X) >>> ind array([0, 3, 4]) """ X = np.asarray(X) if X.ndim > 1: ind = np.zeros(X.shape[1]).astype(bool) max = (np.max(X, axis=0) == 1) min = (np.min(X, axis=0) == 0) remainder = np.all(X % 1. == 0, axis=0) ind = min & max & remainder if X.ndim == 1: ind = np.asarray([ind]) return np.where(ind)[0] def _get_dummy_index(X, const_idx): dummy_ind = _isdummy(X) dummy = True if dummy_ind.size == 0: # do not waste your time dummy = False dummy_ind = None # this gets passed to stand err func return dummy_ind, dummy def _iscount(X): """ Given an array X, returns the column indices for count variables. Parameters ---------- X : array_like A 1d or 2d array of numbers Examples -------- >>> X = np.random.randint(0, 10, size=(15,5)).astype(float) >>> X[:,1:3] = np.random.randn(15,2) >>> ind = _iscount(X) >>> ind array([0, 3, 4]) """ X = np.asarray(X) remainder = np.logical_and(np.logical_and(np.all(X % 1. == 0, axis = 0), X.var(0) != 0), np.all(X >= 0, axis=0)) dummy = _isdummy(X) remainder = np.where(remainder)[0].tolist() for idx in dummy: remainder.remove(idx) return np.array(remainder) def _get_count_index(X, const_idx): count_ind = _iscount(X) count = True if count_ind.size == 0: # do not waste your time count = False count_ind = None # for stand err func return count_ind, count def _get_margeff_exog(exog, at, atexog, ind): if atexog is not None: # user supplied if isinstance(atexog, dict): # assumes values are singular or of len(exog) for key in atexog: exog[:,key] = atexog[key] elif isinstance(atexog, np.ndarray): #TODO: handle DataFrames if atexog.ndim == 1: k_vars = len(atexog) else: k_vars = atexog.shape[1] try: assert k_vars == exog.shape[1] except: raise ValueError("atexog does not have the same number " "of variables as exog") exog = atexog #NOTE: we should fill in atexog after we process at if at == 'mean': exog = np.atleast_2d(exog.mean(0)) elif at == 'median': exog = np.atleast_2d(np.median(exog, axis=0)) elif at == 'zero': exog = np.zeros((1,exog.shape[1])) exog[0,~ind] = 1 return exog def _get_count_effects(effects, exog, count_ind, method, model, params): """ If there's a count variable, the predicted difference is taken by subtracting one and adding one to exog then averaging the difference """ # this is the index for the effect and the index for count col in exog for i in count_ind: exog0 = exog.copy() exog0[:, i] -= 1 effect0 = model.predict(params, exog0) exog0[:, i] += 2 effect1 = model.predict(params, exog0) #NOTE: done by analogy with dummy effects but untested bc # stata does not handle both count and eydx anywhere if 'ey' in method: effect0 = np.log(effect0) effect1 = np.log(effect1) effects[:, i] = ((effect1 - effect0)/2) return effects def _get_dummy_effects(effects, exog, dummy_ind, method, model, params): """ If there's a dummy variable, the predicted difference is taken at 0 and 1 """ # this is the index for the effect and the index for dummy col in exog for i in dummy_ind: exog0 = exog.copy() # only copy once, can we avoid a copy? exog0[:,i] = 0 effect0 = model.predict(params, exog0) #fittedvalues0 = np.dot(exog0,params) exog0[:,i] = 1 effect1 = model.predict(params, exog0) if 'ey' in method: effect0 = np.log(effect0) effect1 = np.log(effect1) effects[:, i] = (effect1 - effect0) return effects def _effects_at(effects, at): if at == 'all': effects = effects elif at == 'overall': effects = effects.mean(0) else: effects = effects[0,:] return effects def _margeff_cov_params_dummy(model, cov_margins, params, exog, dummy_ind, method, J): r""" Returns the Jacobian for discrete regressors for use in margeff_cov_params. For discrete regressors the marginal effect is \Delta F = F(XB) | d = 1 - F(XB) | d = 0 The row of the Jacobian for this variable is given by f(XB)*X | d = 1 - f(XB)*X | d = 0 Where F is the default prediction of the model. """ for i in dummy_ind: exog0 = exog.copy() exog1 = exog.copy() exog0[:,i] = 0 exog1[:,i] = 1 dfdb0 = model._derivative_predict(params, exog0, method) dfdb1 = model._derivative_predict(params, exog1, method) dfdb = (dfdb1 - dfdb0) if dfdb.ndim >= 2: # for overall dfdb = dfdb.mean(0) if J > 1: K = dfdb.shape[1] // (J-1) cov_margins[i::K, :] = dfdb else: # dfdb could be too short if there are extra params, k_extra > 0 cov_margins[i, :len(dfdb)] = dfdb # how each F changes with change in B return cov_margins def _margeff_cov_params_count(model, cov_margins, params, exog, count_ind, method, J): r""" Returns the Jacobian for discrete regressors for use in margeff_cov_params. For discrete regressors the marginal effect is \Delta F = F(XB) | d += 1 - F(XB) | d -= 1 The row of the Jacobian for this variable is given by (f(XB)*X | d += 1 - f(XB)*X | d -= 1) / 2 where F is the default prediction for the model. """ for i in count_ind: exog0 = exog.copy() exog0[:,i] -= 1 dfdb0 = model._derivative_predict(params, exog0, method) exog0[:,i] += 2 dfdb1 = model._derivative_predict(params, exog0, method) dfdb = (dfdb1 - dfdb0) if dfdb.ndim >= 2: # for overall dfdb = dfdb.mean(0) / 2 if J > 1: K = dfdb.shape[1] / (J-1) cov_margins[i::K, :] = dfdb else: # dfdb could be too short if there are extra params, k_extra > 0 cov_margins[i, :len(dfdb)] = dfdb # how each F changes with change in B return cov_margins def margeff_cov_params(model, params, exog, cov_params, at, derivative, dummy_ind, count_ind, method, J): """ Computes the variance-covariance of marginal effects by the delta method. Parameters ---------- model : model instance The model that returned the fitted results. Its pdf method is used for computing the Jacobian of discrete variables in dummy_ind and count_ind params : array_like estimated model parameters exog : array_like exogenous variables at which to calculate the derivative cov_params : array_like The variance-covariance of the parameters at : str Options are: - 'overall', The average of the marginal effects at each observation. - 'mean', The marginal effects at the mean of each regressor. - 'median', The marginal effects at the median of each regressor. - 'zero', The marginal effects at zero for each regressor. - 'all', The marginal effects at each observation. Only overall has any effect here.you derivative : function or array_like If a function, it returns the marginal effects of the model with respect to the exogenous variables evaluated at exog. Expected to be called derivative(params, exog). This will be numerically differentiated. Otherwise, it can be the Jacobian of the marginal effects with respect to the parameters. dummy_ind : array_like Indices of the columns of exog that contain dummy variables count_ind : array_like Indices of the columns of exog that contain count variables Notes ----- For continuous regressors, the variance-covariance is given by Asy. Var[MargEff] = [d margeff / d params] V [d margeff / d params]' where V is the parameter variance-covariance. The outer Jacobians are computed via numerical differentiation if derivative is a function. """ if callable(derivative): from statsmodels.tools.numdiff import approx_fprime_cs params = params.ravel('F') # for Multinomial try: jacobian_mat = approx_fprime_cs(params, derivative, args=(exog,method)) except TypeError: # norm.cdf does not take complex values from statsmodels.tools.numdiff import approx_fprime jacobian_mat = approx_fprime(params, derivative, args=(exog,method)) if at == 'overall': jacobian_mat = np.mean(jacobian_mat, axis=1) else: jacobian_mat = jacobian_mat.squeeze() # exog was 2d row vector if dummy_ind is not None: jacobian_mat = _margeff_cov_params_dummy(model, jacobian_mat, params, exog, dummy_ind, method, J) if count_ind is not None: jacobian_mat = _margeff_cov_params_count(model, jacobian_mat, params, exog, count_ind, method, J) else: jacobian_mat = derivative #NOTE: this will not go through for at == 'all' return np.dot(np.dot(jacobian_mat, cov_params), jacobian_mat.T) def margeff_cov_with_se(model, params, exog, cov_params, at, derivative, dummy_ind, count_ind, method, J): """ See margeff_cov_params. Same function but returns both the covariance of the marginal effects and their standard errors. """ cov_me = margeff_cov_params(model, params, exog, cov_params, at, derivative, dummy_ind, count_ind, method, J) return cov_me, np.sqrt(np.diag(cov_me)) def margeff(): raise NotImplementedError def _check_at_is_all(method): if method['at'] == 'all': raise ValueError("Only margeff are available when `at` is " "'all'. Please input specific points if you would " "like to do inference.") _transform_names = dict(dydx='dy/dx', eyex='d(lny)/d(lnx)', dyex='dy/d(lnx)', eydx='d(lny)/dx') class Margins(object): """ Mostly a do nothing class. Lays out the methods expected of a sub-class. This is just a sketch of what we may want out of a general margins class. I (SS) need to look at details of other models. """ def __init__(self, results, get_margeff, derivative, dist=None, margeff_args=()): self._cache = {} self.results = results self.dist = dist self.get_margeff(margeff_args) def _reset(self): self._cache = {} def get_margeff(self, *args, **kwargs): self._reset() self.margeff = self.get_margeff(*args) @cache_readonly def tvalues(self): raise NotImplementedError @cache_readonly def cov_margins(self): raise NotImplementedError @cache_readonly def margins_se(self): raise NotImplementedError def summary_frame(self): raise NotImplementedError @cache_readonly def pvalues(self): raise NotImplementedError def conf_int(self, alpha=.05): raise NotImplementedError def summary(self, alpha=.05): raise NotImplementedError #class DiscreteMargins(Margins): class DiscreteMargins(object): """Get marginal effects of a Discrete Choice model. Parameters ---------- results : DiscreteResults instance The results instance of a fitted discrete choice model args : tuple Args are passed to `get_margeff`. This is the same as results.get_margeff. See there for more information. kwargs : dict Keyword args are passed to `get_margeff`. This is the same as results.get_margeff. See there for more information. """ def __init__(self, results, args, kwargs={}): self._cache = {} self.results = results self.get_margeff(*args, **kwargs) def _reset(self): self._cache = {} @cache_readonly def tvalues(self): _check_at_is_all(self.margeff_options) return self.margeff / self.margeff_se def summary_frame(self, alpha=.05): """ Returns a DataFrame summarizing the marginal effects. Parameters ---------- alpha : float Number between 0 and 1. The confidence intervals have the probability 1-alpha. Returns ------- frame : DataFrames A DataFrame summarizing the marginal effects. Notes ----- The dataframe is created on each call and not cached, as are the tables build in `summary()` """ _check_at_is_all(self.margeff_options) results = self.results model = self.results.model from pandas import DataFrame, MultiIndex names = [_transform_names[self.margeff_options['method']], 'Std. Err.', 'z', 'Pr(>|z|)', 'Conf. Int. Low', 'Cont. Int. Hi.'] ind = self.results.model.exog.var(0) != 0 # True if not a constant exog_names = self.results.model.exog_names k_extra = getattr(model, 'k_extra', 0) if k_extra > 0: exog_names = exog_names[:-k_extra] var_names = [name for i,name in enumerate(exog_names) if ind[i]] if self.margeff.ndim == 2: # MNLogit case ci = self.conf_int(alpha) table = np.column_stack([i.ravel("F") for i in [self.margeff, self.margeff_se, self.tvalues, self.pvalues, ci[:, 0, :], ci[:, 1, :]]]) _, yname_list = results._get_endog_name(model.endog_names, None, all=True) ynames = np.repeat(yname_list, len(var_names)) xnames = np.tile(var_names, len(yname_list)) index = MultiIndex.from_tuples(list(zip(ynames, xnames)), names=['endog', 'exog']) else: table = np.column_stack((self.margeff, self.margeff_se, self.tvalues, self.pvalues, self.conf_int(alpha))) index=var_names return DataFrame(table, columns=names, index=index) @cache_readonly def pvalues(self): _check_at_is_all(self.margeff_options) return norm.sf(np.abs(self.tvalues)) * 2 def conf_int(self, alpha=.05): """ Returns the confidence intervals of the marginal effects Parameters ---------- alpha : float Number between 0 and 1. The confidence intervals have the probability 1-alpha. Returns ------- conf_int : ndarray An array with lower, upper confidence intervals for the marginal effects. """ _check_at_is_all(self.margeff_options) me_se = self.margeff_se q = norm.ppf(1 - alpha / 2) lower = self.margeff - q * me_se upper = self.margeff + q * me_se return np.asarray(lzip(lower, upper)) def summary(self, alpha=.05): """ Returns a summary table for marginal effects Parameters ---------- alpha : float Number between 0 and 1. The confidence intervals have the probability 1-alpha. Returns ------- Summary : SummaryTable A SummaryTable instance """ _check_at_is_all(self.margeff_options) results = self.results model = results.model title = model.__class__.__name__ + " Marginal Effects" method = self.margeff_options['method'] top_left = [('Dep. Variable:', [model.endog_names]), ('Method:', [method]), ('At:', [self.margeff_options['at']]),] from statsmodels.iolib.summary import (Summary, summary_params, table_extend) exog_names = model.exog_names[:] # copy smry = Summary() # TODO: sigh, we really need to hold on to this in _data... _, const_idx = _get_const_index(model.exog) if const_idx is not None: exog_names.pop(const_idx[0]) if getattr(model, 'k_extra', 0) > 0: exog_names = exog_names[:-model.k_extra] J = int(getattr(model, "J", 1)) if J > 1: yname, yname_list = results._get_endog_name(model.endog_names, None, all=True) else: yname = model.endog_names yname_list = [yname] smry.add_table_2cols(self, gleft=top_left, gright=[], yname=yname, xname=exog_names, title=title) # NOTE: add_table_params is not general enough yet for margeff # could use a refactor with getattr instead of hard-coded params # tvalues etc. table = [] conf_int = self.conf_int(alpha) margeff = self.margeff margeff_se = self.margeff_se tvalues = self.tvalues pvalues = self.pvalues if J > 1: for eq in range(J): restup = (results, margeff[:,eq], margeff_se[:,eq], tvalues[:,eq], pvalues[:,eq], conf_int[:,:,eq]) tble = summary_params(restup, yname=yname_list[eq], xname=exog_names, alpha=alpha, use_t=False, skip_header=True) tble.title = yname_list[eq] # overwrite coef with method name header = ['', _transform_names[method], 'std err', 'z', 'P>|z|', '[' + str(alpha/2), str(1-alpha/2) + ']'] tble.insert_header_row(0, header) table.append(tble) table = table_extend(table, keep_headers=True) else: restup = (results, margeff, margeff_se, tvalues, pvalues, conf_int) table = summary_params(restup, yname=yname, xname=exog_names, alpha=alpha, use_t=False, skip_header=True) header = ['', _transform_names[method], 'std err', 'z', 'P>|z|', '[' + str(alpha/2), str(1-alpha/2) + ']'] table.insert_header_row(0, header) smry.tables.append(table) return smry def get_margeff(self, at='overall', method='dydx', atexog=None, dummy=False, count=False): """Get marginal effects of the fitted model. Parameters ---------- at : str, optional Options are: - 'overall', The average of the marginal effects at each observation. - 'mean', The marginal effects at the mean of each regressor. - 'median', The marginal effects at the median of each regressor. - 'zero', The marginal effects at zero for each regressor. - 'all', The marginal effects at each observation. If `at` is all only margeff will be available. Note that if `exog` is specified, then marginal effects for all variables not specified by `exog` are calculated using the `at` option. method : str, optional Options are: - 'dydx' - dy/dx - No transformation is made and marginal effects are returned. This is the default. - 'eyex' - estimate elasticities of variables in `exog` -- d(lny)/d(lnx) - 'dyex' - estimate semi-elasticity -- dy/d(lnx) - 'eydx' - estimate semi-elasticity -- d(lny)/dx Note that tranformations are done after each observation is calculated. Semi-elasticities for binary variables are computed using the midpoint method. 'dyex' and 'eyex' do not make sense for discrete variables. atexog : array_like, optional Optionally, you can provide the exogenous variables over which to get the marginal effects. This should be a dictionary with the key as the zero-indexed column number and the value of the dictionary. Default is None for all independent variables less the constant. dummy : bool, optional If False, treats binary variables (if present) as continuous. This is the default. Else if True, treats binary variables as changing from 0 to 1. Note that any variable that is either 0 or 1 is treated as binary. Each binary variable is treated separately for now. count : bool, optional If False, treats count variables (if present) as continuous. This is the default. Else if True, the marginal effect is the change in probabilities when each observation is increased by one. Returns ------- effects : ndarray the marginal effect corresponding to the input options Notes ----- When using after Poisson, returns the expected number of events per period, assuming that the model is loglinear. """ self._reset() # always reset the cache when this is called #TODO: if at is not all or overall, we can also put atexog values # in summary table head method = method.lower() at = at.lower() _check_margeff_args(at, method) self.margeff_options = dict(method=method, at=at) results = self.results model = results.model params = results.params exog = model.exog.copy() # copy because values are changed effects_idx, const_idx = _get_const_index(exog) if dummy: _check_discrete_args(at, method) dummy_idx, dummy = _get_dummy_index(exog, const_idx) else: dummy_idx = None if count: _check_discrete_args(at, method) count_idx, count = _get_count_index(exog, const_idx) else: count_idx = None # attach dummy_idx and cout_idx self.dummy_idx = dummy_idx self.count_idx = count_idx # get the exogenous variables exog = _get_margeff_exog(exog, at, atexog, effects_idx) # get base marginal effects, handled by sub-classes effects = model._derivative_exog(params, exog, method, dummy_idx, count_idx) J = getattr(model, 'J', 1) effects_idx = np.tile(effects_idx, J) # adjust for multi-equation. effects = _effects_at(effects, at) if at == 'all': if J > 1: K = model.K - np.any(~effects_idx) # subtract constant self.margeff = effects[:, effects_idx].reshape(-1, K, J, order='F') else: self.margeff = effects[:, effects_idx] else: # Set standard error of the marginal effects by Delta method. margeff_cov, margeff_se = margeff_cov_with_se(model, params, exog, results.cov_params(), at, model._derivative_exog, dummy_idx, count_idx, method, J) # reshape for multi-equation if J > 1: K = model.K - np.any(~effects_idx) # subtract constant self.margeff = effects[effects_idx].reshape(K, J, order='F') self.margeff_se = margeff_se[effects_idx].reshape(K, J, order='F') self.margeff_cov = margeff_cov[effects_idx][:, effects_idx] else: # do not care about at constant # hack truncate effects_idx again if necessary # if eyex, then effects is truncated to be without extra params effects_idx = effects_idx[:len(effects)] self.margeff_cov = margeff_cov[effects_idx][:, effects_idx] self.margeff_se = margeff_se[effects_idx] self.margeff = effects[effects_idx] statsmodels-0.12.2/statsmodels/discrete/discrete_model.py000066400000000000000000004631231400612667500236560ustar00rootroot00000000000000""" Limited dependent variable and qualitative variables. Includes binary outcomes, count data, (ordered) ordinal data and limited dependent variables. General References -------------------- A.C. Cameron and P.K. Trivedi. `Regression Analysis of Count Data`. Cambridge, 1998 G.S. Madalla. `Limited-Dependent and Qualitative Variables in Econometrics`. Cambridge, 1983. W. Greene. `Econometric Analysis`. Prentice Hall, 5th. edition. 2003. """ __all__ = ["Poisson", "Logit", "Probit", "MNLogit", "NegativeBinomial", "GeneralizedPoisson", "NegativeBinomialP", "CountModel"] from statsmodels.compat.pandas import Appender import warnings import numpy as np from pandas import MultiIndex, get_dummies from scipy import special, stats from scipy.special import digamma, gammaln, loggamma, polygamma from scipy.stats import nbinom from statsmodels.base.data import handle_data # for mnlogit from statsmodels.base.l1_slsqp import fit_l1_slsqp import statsmodels.base.model as base import statsmodels.base.wrapper as wrap from statsmodels.distributions import genpoisson_p import statsmodels.regression.linear_model as lm from statsmodels.tools import data as data_tools, tools from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.numdiff import approx_fprime_cs from statsmodels.tools.sm_exceptions import ( PerfectSeparationError, SpecificationWarning, ) try: import cvxopt # noqa:F401 have_cvxopt = True except ImportError: have_cvxopt = False # TODO: When we eventually get user-settable precision, we need to change # this FLOAT_EPS = np.finfo(float).eps # TODO: add options for the parameter covariance/variance # ie., OIM, EIM, and BHHH see Green 21.4 _discrete_models_docs = """ """ _discrete_results_docs = """ %(one_line_description)s Parameters ---------- model : A DiscreteModel instance params : array_like The parameters of a fitted model. hessian : array_like The hessian of the fitted model. scale : float A scale parameter for the covariance matrix. Attributes ---------- df_resid : float See model definition. df_model : float See model definition. llf : float Value of the loglikelihood %(extra_attr)s""" _l1_results_attr = """ nnz_params : int The number of nonzero parameters in the model. Train with trim_params == True or else numerical error will distort this. trimmed : bool array trimmed[i] == True if the ith parameter was trimmed from the model.""" _get_start_params_null_docs = """ Compute one-step moment estimator for null (constant-only) model This is a preliminary estimator used as start_params. Returns ------- params : ndarray parameter estimate based one one-step moment matching """ _check_rank_doc = """ check_rank : bool Check exog rank to determine model degrees of freedom. Default is True. Setting to False reduces model initialization time when exog.shape[1] is large. """ # helper for MNLogit (will be generally useful later) def _numpy_to_dummies(endog): if endog.ndim == 2 and endog.dtype.kind not in ["S", "O"]: endog_dummies = endog ynames = range(endog.shape[1]) else: dummies = get_dummies(endog, drop_first=False) ynames = {i: dummies.columns[i] for i in range(dummies.shape[1])} endog_dummies = np.asarray(dummies, dtype=float) return endog_dummies, ynames return endog_dummies, ynames def _pandas_to_dummies(endog): if endog.ndim == 2: if endog.shape[1] == 1: yname = endog.columns[0] endog_dummies = get_dummies(endog.iloc[:, 0]) else: # series yname = 'y' endog_dummies = endog else: yname = endog.name endog_dummies = get_dummies(endog) ynames = endog_dummies.columns.tolist() return endog_dummies, ynames, yname def _validate_l1_method(method): """ As of 0.10.0, the supported values for `method` in `fit_regularized` are "l1" and "l1_cvxopt_cp". If an invalid value is passed, raise with a helpful error message Parameters ---------- method : str Raises ------ ValueError """ if method not in ['l1', 'l1_cvxopt_cp']: raise ValueError('`method` = {method} is not supported, use either ' '"l1" or "l1_cvxopt_cp"'.format(method=method)) #### Private Model Classes #### class DiscreteModel(base.LikelihoodModel): """ Abstract class for discrete choice models. This class does not do anything itself but lays out the methods and call signature expected of child classes in addition to those of statsmodels.model.LikelihoodModel. """ def __init__(self, endog, exog, check_rank=True, **kwargs): self._check_rank = check_rank super().__init__(endog, exog, **kwargs) self.raise_on_perfect_prediction = True def initialize(self): """ Initialize is called by statsmodels.model.LikelihoodModel.__init__ and should contain any preprocessing that needs to be done for a model. """ if self._check_rank: # assumes constant rank = tools.matrix_rank(self.exog, method="qr") else: # If rank check is skipped, assume full rank = self.exog.shape[1] self.df_model = float(rank - 1) self.df_resid = float(self.exog.shape[0] - rank) def cdf(self, X): """ The cumulative distribution function of the model. """ raise NotImplementedError def pdf(self, X): """ The probability density (mass) function of the model. """ raise NotImplementedError def _check_perfect_pred(self, params, *args): endog = self.endog fittedvalues = self.cdf(np.dot(self.exog, params[:self.exog.shape[1]])) if (self.raise_on_perfect_prediction and np.allclose(fittedvalues - endog, 0)): msg = "Perfect separation detected, results not available" raise PerfectSeparationError(msg) @Appender(base.LikelihoodModel.fit.__doc__) def fit(self, start_params=None, method='newton', maxiter=35, full_output=1, disp=1, callback=None, **kwargs): """ Fit the model using maximum likelihood. The rest of the docstring is from statsmodels.base.model.LikelihoodModel.fit """ if callback is None: callback = self._check_perfect_pred else: pass # TODO: make a function factory to have multiple call-backs mlefit = super().fit(start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, **kwargs) return mlefit # It is up to subclasses to wrap results def fit_regularized(self, start_params=None, method='l1', maxiter='defined_by_method', full_output=1, disp=True, callback=None, alpha=0, trim_mode='auto', auto_trim_tol=0.01, size_trim_tol=1e-4, qc_tol=0.03, qc_verbose=False, **kwargs): """ Fit the model using a regularized maximum likelihood. The regularization method AND the solver used is determined by the argument method. Parameters ---------- start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. method : 'l1' or 'l1_cvxopt_cp' See notes for details. maxiter : {int, 'defined_by_method'} Maximum number of iterations to perform. If 'defined_by_method', then use method defaults (see notes). full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. disp : bool Set to True to print convergence messages. fargs : tuple Extra arguments passed to the likelihood function, i.e., loglike(x,*args). callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. alpha : non-negative scalar or numpy array (same size as parameters) The weight multiplying the l1 penalty term. trim_mode : 'auto, 'size', or 'off' If not 'off', trim (set to zero) parameters that would have been zero if the solver reached the theoretical minimum. If 'auto', trim params using the Theory above. If 'size', trim params if they have very small absolute value. size_trim_tol : float or 'auto' (default = 'auto') Tolerance used when trim_mode == 'size'. auto_trim_tol : float Tolerance used when trim_mode == 'auto'. qc_tol : float Print warning and do not allow auto trim when (ii) (above) is violated by this much. qc_verbose : bool If true, print out a full QC report upon failure. **kwargs Additional keyword arguments used when fitting the model. Returns ------- Results A results instance. Notes ----- Using 'l1_cvxopt_cp' requires the cvxopt module. Extra parameters are not penalized if alpha is given as a scalar. An example is the shape parameter in NegativeBinomial `nb1` and `nb2`. Optional arguments for the solvers (available in Results.mle_settings):: 'l1' acc : float (default 1e-6) Requested accuracy as used by slsqp 'l1_cvxopt_cp' abstol : float absolute accuracy (default: 1e-7). reltol : float relative accuracy (default: 1e-6). feastol : float tolerance for feasibility conditions (default: 1e-7). refinement : int number of iterative refinement steps when solving KKT equations (default: 1). Optimization methodology With :math:`L` the negative log likelihood, we solve the convex but non-smooth problem .. math:: \\min_\\beta L(\\beta) + \\sum_k\\alpha_k |\\beta_k| via the transformation to the smooth, convex, constrained problem in twice as many variables (adding the "added variables" :math:`u_k`) .. math:: \\min_{\\beta,u} L(\\beta) + \\sum_k\\alpha_k u_k, subject to .. math:: -u_k \\leq \\beta_k \\leq u_k. With :math:`\\partial_k L` the derivative of :math:`L` in the :math:`k^{th}` parameter direction, theory dictates that, at the minimum, exactly one of two conditions holds: (i) :math:`|\\partial_k L| = \\alpha_k` and :math:`\\beta_k \\neq 0` (ii) :math:`|\\partial_k L| \\leq \\alpha_k` and :math:`\\beta_k = 0` """ _validate_l1_method(method) # Set attributes based on method cov_params_func = self.cov_params_func_l1 ### Bundle up extra kwargs for the dictionary kwargs. These are ### passed through super(...).fit() as kwargs and unpacked at ### appropriate times alpha = np.array(alpha) assert alpha.min() >= 0 try: kwargs['alpha'] = alpha except TypeError: kwargs = dict(alpha=alpha) kwargs['alpha_rescaled'] = kwargs['alpha'] / float(self.endog.shape[0]) kwargs['trim_mode'] = trim_mode kwargs['size_trim_tol'] = size_trim_tol kwargs['auto_trim_tol'] = auto_trim_tol kwargs['qc_tol'] = qc_tol kwargs['qc_verbose'] = qc_verbose ### Define default keyword arguments to be passed to super(...).fit() if maxiter == 'defined_by_method': if method == 'l1': maxiter = 1000 elif method == 'l1_cvxopt_cp': maxiter = 70 ## Parameters to pass to super(...).fit() # For the 'extra' parameters, pass all that are available, # even if we know (at this point) we will only use one. extra_fit_funcs = {'l1': fit_l1_slsqp} if have_cvxopt and method == 'l1_cvxopt_cp': from statsmodels.base.l1_cvxopt import fit_l1_cvxopt_cp extra_fit_funcs['l1_cvxopt_cp'] = fit_l1_cvxopt_cp elif method.lower() == 'l1_cvxopt_cp': raise ValueError("Cannot use l1_cvxopt_cp as cvxopt " "was not found (install it, or use method='l1' instead)") if callback is None: callback = self._check_perfect_pred else: pass # make a function factory to have multiple call-backs mlefit = super().fit(start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, extra_fit_funcs=extra_fit_funcs, cov_params_func=cov_params_func, **kwargs) return mlefit # up to subclasses to wrap results def cov_params_func_l1(self, likelihood_model, xopt, retvals): """ Computes cov_params on a reduced parameter space corresponding to the nonzero parameters resulting from the l1 regularized fit. Returns a full cov_params matrix, with entries corresponding to zero'd values set to np.nan. """ H = likelihood_model.hessian(xopt) trimmed = retvals['trimmed'] nz_idx = np.nonzero(~trimmed)[0] nnz_params = (~trimmed).sum() if nnz_params > 0: H_restricted = H[nz_idx[:, None], nz_idx] # Covariance estimate for the nonzero params H_restricted_inv = np.linalg.inv(-H_restricted) else: H_restricted_inv = np.zeros(0) cov_params = np.nan * np.ones(H.shape) cov_params[nz_idx[:, None], nz_idx] = H_restricted_inv return cov_params def predict(self, params, exog=None, linear=False): """ Predict response variable of a model given exogenous variables. """ raise NotImplementedError def _derivative_exog(self, params, exog=None, dummy_idx=None, count_idx=None): """ This should implement the derivative of the non-linear function """ raise NotImplementedError def _derivative_exog_helper(self, margeff, params, exog, dummy_idx, count_idx, transform): """ Helper for _derivative_exog to wrap results appropriately """ from .discrete_margins import _get_count_effects, _get_dummy_effects if count_idx is not None: margeff = _get_count_effects(margeff, exog, count_idx, transform, self, params) if dummy_idx is not None: margeff = _get_dummy_effects(margeff, exog, dummy_idx, transform, self, params) return margeff class BinaryModel(DiscreteModel): _continuous_ok = False def __init__(self, endog, exog, check_rank=True, **kwargs): super().__init__(endog, exog, check_rank, **kwargs) if not issubclass(self.__class__, MultinomialModel): if not np.all((self.endog >= 0) & (self.endog <= 1)): raise ValueError("endog must be in the unit interval.") if (not self._continuous_ok and np.any(self.endog != np.round(self.endog))): raise ValueError("endog must be binary, either 0 or 1") def predict(self, params, exog=None, linear=False): """ Predict response variable of a model given exogenous variables. Parameters ---------- params : array_like Fitted parameters of the model. exog : array_like 1d or 2d array of exogenous values. If not supplied, the whole exog attribute of the model is used. linear : bool, optional If True, returns the linear predictor dot(exog,params). Else, returns the value of the cdf at the linear predictor. Returns ------- array Fitted values at exog. """ if exog is None: exog = self.exog if not linear: return self.cdf(np.dot(exog, params)) else: return np.dot(exog, params) @Appender(DiscreteModel.fit_regularized.__doc__) def fit_regularized(self, start_params=None, method='l1', maxiter='defined_by_method', full_output=1, disp=1, callback=None, alpha=0, trim_mode='auto', auto_trim_tol=0.01, size_trim_tol=1e-4, qc_tol=0.03, **kwargs): _validate_l1_method(method) bnryfit = super().fit_regularized(start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, alpha=alpha, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol, size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs) discretefit = L1BinaryResults(self, bnryfit) return L1BinaryResultsWrapper(discretefit) def _derivative_predict(self, params, exog=None, transform='dydx'): """ For computing marginal effects standard errors. This is used only in the case of discrete and count regressors to get the variance-covariance of the marginal effects. It returns [d F / d params] where F is the predict. Transform can be 'dydx' or 'eydx'. Checking is done in margeff computations for appropriate transform. """ if exog is None: exog = self.exog dF = self.pdf(np.dot(exog, params))[:,None] * exog if 'ey' in transform: dF /= self.predict(params, exog)[:,None] return dF def _derivative_exog(self, params, exog=None, transform='dydx', dummy_idx=None, count_idx=None): """ For computing marginal effects returns dF(XB) / dX where F(.) is the predicted probabilities transform can be 'dydx', 'dyex', 'eydx', or 'eyex'. Not all of these make sense in the presence of discrete regressors, but checks are done in the results in get_margeff. """ # Note: this form should be appropriate for # group 1 probit, logit, logistic, cloglog, heckprob, xtprobit if exog is None: exog = self.exog margeff = np.dot(self.pdf(np.dot(exog, params))[:, None], params[None, :]) if 'ex' in transform: margeff *= exog if 'ey' in transform: margeff /= self.predict(params, exog)[:, None] return self._derivative_exog_helper(margeff, params, exog, dummy_idx, count_idx, transform) class MultinomialModel(BinaryModel): def _handle_data(self, endog, exog, missing, hasconst, **kwargs): if data_tools._is_using_ndarray_type(endog, None): endog_dummies, ynames = _numpy_to_dummies(endog) yname = 'y' elif data_tools._is_using_pandas(endog, None): endog_dummies, ynames, yname = _pandas_to_dummies(endog) else: endog = np.asarray(endog) endog_dummies, ynames = _numpy_to_dummies(endog) yname = 'y' if not isinstance(ynames, dict): ynames = dict(zip(range(endog_dummies.shape[1]), ynames)) self._ynames_map = ynames data = handle_data(endog_dummies, exog, missing, hasconst, **kwargs) data.ynames = yname # overwrite this to single endog name data.orig_endog = endog self.wendog = data.endog # repeating from upstream... for key in kwargs: if key in ['design_info', 'formula']: # leave attached to data continue try: setattr(self, key, data.__dict__.pop(key)) except KeyError: pass return data def initialize(self): """ Preprocesses the data for MNLogit. """ super().initialize() # This is also a "whiten" method in other models (eg regression) self.endog = self.endog.argmax(1) # turn it into an array of col idx self.J = self.wendog.shape[1] self.K = self.exog.shape[1] self.df_model *= (self.J-1) # for each J - 1 equation. self.df_resid = self.exog.shape[0] - self.df_model - (self.J-1) def predict(self, params, exog=None, linear=False): """ Predict response variable of a model given exogenous variables. Parameters ---------- params : array_like 2d array of fitted parameters of the model. Should be in the order returned from the model. exog : array_like 1d or 2d array of exogenous values. If not supplied, the whole exog attribute of the model is used. If a 1d array is given it assumed to be 1 row of exogenous variables. If you only have one regressor and would like to do prediction, you must provide a 2d array with shape[1] == 1. linear : bool, optional If True, returns the linear predictor dot(exog,params). Else, returns the value of the cdf at the linear predictor. Notes ----- Column 0 is the base case, the rest conform to the rows of params shifted up one for the base case. """ if exog is None: # do here to accommodate user-given exog exog = self.exog if exog.ndim == 1: exog = exog[None] pred = super().predict(params, exog, linear) if linear: pred = np.column_stack((np.zeros(len(exog)), pred)) return pred @Appender(DiscreteModel.fit.__doc__) def fit(self, start_params=None, method='newton', maxiter=35, full_output=1, disp=1, callback=None, **kwargs): if start_params is None: start_params = np.zeros((self.K * (self.J-1))) else: start_params = np.asarray(start_params) callback = lambda x : None # placeholder until check_perfect_pred # skip calling super to handle results from LikelihoodModel mnfit = base.LikelihoodModel.fit(self, start_params = start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, **kwargs) mnfit.params = mnfit.params.reshape(self.K, -1, order='F') mnfit = MultinomialResults(self, mnfit) return MultinomialResultsWrapper(mnfit) @Appender(DiscreteModel.fit_regularized.__doc__) def fit_regularized(self, start_params=None, method='l1', maxiter='defined_by_method', full_output=1, disp=1, callback=None, alpha=0, trim_mode='auto', auto_trim_tol=0.01, size_trim_tol=1e-4, qc_tol=0.03, **kwargs): if start_params is None: start_params = np.zeros((self.K * (self.J-1))) else: start_params = np.asarray(start_params) mnfit = DiscreteModel.fit_regularized( self, start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, alpha=alpha, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol, size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs) mnfit.params = mnfit.params.reshape(self.K, -1, order='F') mnfit = L1MultinomialResults(self, mnfit) return L1MultinomialResultsWrapper(mnfit) def _derivative_predict(self, params, exog=None, transform='dydx'): """ For computing marginal effects standard errors. This is used only in the case of discrete and count regressors to get the variance-covariance of the marginal effects. It returns [d F / d params] where F is the predicted probabilities for each choice. dFdparams is of shape nobs x (J*K) x (J-1)*K. The zero derivatives for the base category are not included. Transform can be 'dydx' or 'eydx'. Checking is done in margeff computations for appropriate transform. """ if exog is None: exog = self.exog if params.ndim == 1: # will get flatted from approx_fprime params = params.reshape(self.K, self.J-1, order='F') eXB = np.exp(np.dot(exog, params)) sum_eXB = (1 + eXB.sum(1))[:,None] J = int(self.J) K = int(self.K) repeat_eXB = np.repeat(eXB, J, axis=1) X = np.tile(exog, J-1) # this is the derivative wrt the base level F0 = -repeat_eXB * X / sum_eXB ** 2 # this is the derivative wrt the other levels when # dF_j / dParams_j (ie., own equation) #NOTE: this computes too much, any easy way to cut down? F1 = eXB.T[:,:,None]*X * (sum_eXB - repeat_eXB) / (sum_eXB**2) F1 = F1.transpose((1,0,2)) # put the nobs index first # other equation index other_idx = ~np.kron(np.eye(J-1), np.ones(K)).astype(bool) F1[:, other_idx] = (-eXB.T[:,:,None]*X*repeat_eXB / \ (sum_eXB**2)).transpose((1,0,2))[:, other_idx] dFdX = np.concatenate((F0[:, None,:], F1), axis=1) if 'ey' in transform: dFdX /= self.predict(params, exog)[:, :, None] return dFdX def _derivative_exog(self, params, exog=None, transform='dydx', dummy_idx=None, count_idx=None): """ For computing marginal effects returns dF(XB) / dX where F(.) is the predicted probabilities transform can be 'dydx', 'dyex', 'eydx', or 'eyex'. Not all of these make sense in the presence of discrete regressors, but checks are done in the results in get_margeff. For Multinomial models the marginal effects are P[j] * (params[j] - sum_k P[k]*params[k]) It is returned unshaped, so that each row contains each of the J equations. This makes it easier to take derivatives of this for standard errors. If you want average marginal effects you can do margeff.reshape(nobs, K, J, order='F).mean(0) and the marginal effects for choice J are in column J """ J = int(self.J) # number of alternative choices K = int(self.K) # number of variables # Note: this form should be appropriate for # group 1 probit, logit, logistic, cloglog, heckprob, xtprobit if exog is None: exog = self.exog if params.ndim == 1: # will get flatted from approx_fprime params = params.reshape(K, J-1, order='F') zeroparams = np.c_[np.zeros(K), params] # add base in cdf = self.cdf(np.dot(exog, params)) # TODO: meaningful interpretation for `iterm`? iterm = np.array([cdf[:, [i]] * zeroparams[:, i] for i in range(int(J))]).sum(0) margeff = np.array([cdf[:, [j]] * (zeroparams[:, j] - iterm) for j in range(J)]) # swap the axes to make sure margeff are in order nobs, K, J margeff = np.transpose(margeff, (1, 2, 0)) if 'ex' in transform: margeff *= exog if 'ey' in transform: margeff /= self.predict(params, exog)[:,None,:] margeff = self._derivative_exog_helper(margeff, params, exog, dummy_idx, count_idx, transform) return margeff.reshape(len(exog), -1, order='F') class CountModel(DiscreteModel): def __init__(self, endog, exog, offset=None, exposure=None, missing='none', check_rank=True, **kwargs): super().__init__(endog, exog, check_rank, missing=missing, offset=offset, exposure=exposure, **kwargs) if exposure is not None: self.exposure = np.asarray(self.exposure) self.exposure = np.log(self.exposure) if offset is not None: self.offset = np.asarray(self.offset) self._check_inputs(self.offset, self.exposure, self.endog) if offset is None: delattr(self, 'offset') if exposure is None: delattr(self, 'exposure') # promote dtype to float64 if needed dt = np.promote_types(self.endog.dtype, np.float64) self.endog = np.asarray(self.endog, dt) dt = np.promote_types(self.exog.dtype, np.float64) self.exog = np.asarray(self.exog, dt) def _check_inputs(self, offset, exposure, endog): if offset is not None and offset.shape[0] != endog.shape[0]: raise ValueError("offset is not the same length as endog") if exposure is not None and exposure.shape[0] != endog.shape[0]: raise ValueError("exposure is not the same length as endog") def _get_init_kwds(self): # this is a temporary fixup because exposure has been transformed # see #1609 kwds = super()._get_init_kwds() if 'exposure' in kwds and kwds['exposure'] is not None: kwds['exposure'] = np.exp(kwds['exposure']) return kwds def predict(self, params, exog=None, exposure=None, offset=None, linear=False): """ Predict response variable of a count model given exogenous variables Parameters ---------- params : array_like Model parameters exog : array_like, optional Design / exogenous data. Is exog is None, model exog is used. exposure : array_like, optional Log(exposure) is added to the linear prediction with coefficient equal to 1. If exposure is not provided and exog is None, uses the model's exposure if present. If not, uses 0 as the default value. offset : array_like, optional Offset is added to the linear prediction with coefficient equal to 1. If offset is not provided and exog is None, uses the model's offset if present. If not, uses 0 as the default value. linear : bool If True, returns the linear predicted values. If False, returns the exponential of the linear predicted value. Notes ----- If exposure is specified, then it will be logged by the method. The user does not need to log it first. """ # the following is copied from GLM predict (without family/link check) # Use fit offset if appropriate if offset is None and exog is None and hasattr(self, 'offset'): offset = self.offset elif offset is None: offset = 0. # Use fit exposure if appropriate if exposure is None and exog is None and hasattr(self, 'exposure'): # Already logged exposure = self.exposure elif exposure is None: exposure = 0. else: exposure = np.log(exposure) if exog is None: exog = self.exog fitted = np.dot(exog, params[:exog.shape[1]]) linpred = fitted + exposure + offset if not linear: return np.exp(linpred) # not cdf else: return linpred def _derivative_predict(self, params, exog=None, transform='dydx'): """ For computing marginal effects standard errors. This is used only in the case of discrete and count regressors to get the variance-covariance of the marginal effects. It returns [d F / d params] where F is the predict. Transform can be 'dydx' or 'eydx'. Checking is done in margeff computations for appropriate transform. """ if exog is None: exog = self.exog #NOTE: this handles offset and exposure dF = self.predict(params, exog)[:,None] * exog if 'ey' in transform: dF /= self.predict(params, exog)[:,None] return dF def _derivative_exog(self, params, exog=None, transform="dydx", dummy_idx=None, count_idx=None): """ For computing marginal effects. These are the marginal effects d F(XB) / dX For the Poisson model F(XB) is the predicted counts rather than the probabilities. transform can be 'dydx', 'dyex', 'eydx', or 'eyex'. Not all of these make sense in the presence of discrete regressors, but checks are done in the results in get_margeff. """ # group 3 poisson, nbreg, zip, zinb if exog is None: exog = self.exog k_extra = getattr(self, 'k_extra', 0) params_exog = params if k_extra == 0 else params[:-k_extra] margeff = self.predict(params, exog)[:,None] * params_exog[None,:] if 'ex' in transform: margeff *= exog if 'ey' in transform: margeff /= self.predict(params, exog)[:,None] return self._derivative_exog_helper(margeff, params, exog, dummy_idx, count_idx, transform) @Appender(DiscreteModel.fit.__doc__) def fit(self, start_params=None, method='newton', maxiter=35, full_output=1, disp=1, callback=None, **kwargs): cntfit = super().fit(start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, **kwargs) discretefit = CountResults(self, cntfit) return CountResultsWrapper(discretefit) @Appender(DiscreteModel.fit_regularized.__doc__) def fit_regularized(self, start_params=None, method='l1', maxiter='defined_by_method', full_output=1, disp=1, callback=None, alpha=0, trim_mode='auto', auto_trim_tol=0.01, size_trim_tol=1e-4, qc_tol=0.03, **kwargs): _validate_l1_method(method) cntfit = super().fit_regularized(start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, alpha=alpha, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol, size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs) discretefit = L1CountResults(self, cntfit) return L1CountResultsWrapper(discretefit) class OrderedModel(DiscreteModel): pass # Public Model Classes class Poisson(CountModel): __doc__ = """ Poisson Model %(params)s %(extra_params)s Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. """ % {'params': base._model_params_doc, 'extra_params': """offset : array_like Offset is added to the linear prediction with coefficient equal to 1. exposure : array_like Log(exposure) is added to the linear prediction with coefficient equal to 1. """ + base._missing_param_doc + _check_rank_doc} @property def family(self): from statsmodels.genmod import families return families.Poisson() def cdf(self, X): """ Poisson model cumulative distribution function Parameters ---------- X : array_like `X` is the linear predictor of the model. See notes. Returns ------- The value of the Poisson CDF at each point. Notes ----- The CDF is defined as .. math:: \\exp\\left(-\\lambda\\right)\\sum_{i=0}^{y}\\frac{\\lambda^{i}}{i!} where :math:`\\lambda` assumes the loglinear model. I.e., .. math:: \\ln\\lambda_{i}=X\\beta The parameter `X` is :math:`X\\beta` in the above formula. """ y = self.endog return stats.poisson.cdf(y, np.exp(X)) def pdf(self, X): """ Poisson model probability mass function Parameters ---------- X : array_like `X` is the linear predictor of the model. See notes. Returns ------- pdf : ndarray The value of the Poisson probability mass function, PMF, for each point of X. Notes -------- The PMF is defined as .. math:: \\frac{e^{-\\lambda_{i}}\\lambda_{i}^{y_{i}}}{y_{i}!} where :math:`\\lambda` assumes the loglinear model. I.e., .. math:: \\ln\\lambda_{i}=x_{i}\\beta The parameter `X` is :math:`x_{i}\\beta` in the above formula. """ y = self.endog return np.exp(stats.poisson.logpmf(y, np.exp(X))) def loglike(self, params): """ Loglikelihood of Poisson model Parameters ---------- params : array_like The parameters of the model. Returns ------- loglike : float The log-likelihood function of the model evaluated at `params`. See notes. Notes -------- .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right] """ offset = getattr(self, "offset", 0) exposure = getattr(self, "exposure", 0) XB = np.dot(self.exog, params) + offset + exposure endog = self.endog return np.sum(-np.exp(XB) + endog*XB - gammaln(endog+1)) def loglikeobs(self, params): """ Loglikelihood for observations of Poisson model Parameters ---------- params : array_like The parameters of the model. Returns ------- loglike : array_like The log likelihood for each observation of the model evaluated at `params`. See Notes Notes -------- .. math:: \\ln L_{i}=\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right] for observations :math:`i=1,...,n` """ offset = getattr(self, "offset", 0) exposure = getattr(self, "exposure", 0) XB = np.dot(self.exog, params) + offset + exposure endog = self.endog #np.sum(stats.poisson.logpmf(endog, np.exp(XB))) return -np.exp(XB) + endog*XB - gammaln(endog+1) @Appender(_get_start_params_null_docs) def _get_start_params_null(self): offset = getattr(self, "offset", 0) exposure = getattr(self, "exposure", 0) const = (self.endog / np.exp(offset + exposure)).mean() params = [np.log(const)] return params @Appender(DiscreteModel.fit.__doc__) def fit(self, start_params=None, method='newton', maxiter=35, full_output=1, disp=1, callback=None, **kwargs): if start_params is None and self.data.const_idx is not None: # k_params or k_exog not available? start_params = 0.001 * np.ones(self.exog.shape[1]) start_params[self.data.const_idx] = self._get_start_params_null()[0] cntfit = super(CountModel, self).fit(start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, **kwargs) if 'cov_type' in kwargs: cov_kwds = kwargs.get('cov_kwds', {}) kwds = {'cov_type':kwargs['cov_type'], 'cov_kwds':cov_kwds} else: kwds = {} discretefit = PoissonResults(self, cntfit, **kwds) return PoissonResultsWrapper(discretefit) @Appender(DiscreteModel.fit_regularized.__doc__) def fit_regularized(self, start_params=None, method='l1', maxiter='defined_by_method', full_output=1, disp=1, callback=None, alpha=0, trim_mode='auto', auto_trim_tol=0.01, size_trim_tol=1e-4, qc_tol=0.03, **kwargs): _validate_l1_method(method) cntfit = super(CountModel, self).fit_regularized( start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, alpha=alpha, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol, size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs) discretefit = L1PoissonResults(self, cntfit) return L1PoissonResultsWrapper(discretefit) def fit_constrained(self, constraints, start_params=None, **fit_kwds): """fit the model subject to linear equality constraints The constraints are of the form `R params = q` where R is the constraint_matrix and q is the vector of constraint_values. The estimation creates a new model with transformed design matrix, exog, and converts the results back to the original parameterization. Parameters ---------- constraints : formula expression or tuple If it is a tuple, then the constraint needs to be given by two arrays (constraint_matrix, constraint_value), i.e. (R, q). Otherwise, the constraints can be given as strings or list of strings. see t_test for details start_params : None or array_like starting values for the optimization. `start_params` needs to be given in the original parameter space and are internally transformed. **fit_kwds : keyword arguments fit_kwds are used in the optimization of the transformed model. Returns ------- results : Results instance """ #constraints = (R, q) # TODO: temporary trailing underscore to not overwrite the monkey # patched version # TODO: decide whether to move the imports from patsy import DesignInfo from statsmodels.base._constraints import (fit_constrained, LinearConstraints) # same pattern as in base.LikelihoodModel.t_test lc = DesignInfo(self.exog_names).linear_constraint(constraints) R, q = lc.coefs, lc.constants # TODO: add start_params option, need access to tranformation # fit_constrained needs to do the transformation params, cov, res_constr = fit_constrained(self, R, q, start_params=start_params, fit_kwds=fit_kwds) #create dummy results Instance, TODO: wire up properly res = self.fit(maxiter=0, method='nm', disp=0, warn_convergence=False) # we get a wrapper back res.mle_retvals['fcall'] = res_constr.mle_retvals.get('fcall', np.nan) res.mle_retvals['iterations'] = res_constr.mle_retvals.get( 'iterations', np.nan) res.mle_retvals['converged'] = res_constr.mle_retvals['converged'] res._results.params = params res._results.cov_params_default = cov cov_type = fit_kwds.get('cov_type', 'nonrobust') if cov_type != 'nonrobust': res._results.normalized_cov_params = cov # assume scale=1 else: res._results.normalized_cov_params = None k_constr = len(q) res._results.df_resid += k_constr res._results.df_model -= k_constr res._results.constraints = LinearConstraints.from_patsy(lc) res._results.k_constr = k_constr res._results.results_constrained = res_constr return res def score(self, params): """ Poisson model score (gradient) vector of the log-likelihood Parameters ---------- params : array_like The parameters of the model Returns ------- score : ndarray, 1-D The score vector of the model, i.e. the first derivative of the loglikelihood function, evaluated at `params` Notes ----- .. math:: \\frac{\\partial\\ln L}{\\partial\\beta}=\\sum_{i=1}^{n}\\left(y_{i}-\\lambda_{i}\\right)x_{i} where the loglinear model is assumed .. math:: \\ln\\lambda_{i}=x_{i}\\beta """ offset = getattr(self, "offset", 0) exposure = getattr(self, "exposure", 0) X = self.exog L = np.exp(np.dot(X,params) + offset + exposure) return np.dot(self.endog - L, X) def score_obs(self, params): """ Poisson model Jacobian of the log-likelihood for each observation Parameters ---------- params : array_like The parameters of the model Returns ------- score : array_like The score vector (nobs, k_vars) of the model evaluated at `params` Notes ----- .. math:: \\frac{\\partial\\ln L_{i}}{\\partial\\beta}=\\left(y_{i}-\\lambda_{i}\\right)x_{i} for observations :math:`i=1,...,n` where the loglinear model is assumed .. math:: \\ln\\lambda_{i}=x_{i}\\beta """ offset = getattr(self, "offset", 0) exposure = getattr(self, "exposure", 0) X = self.exog L = np.exp(np.dot(X,params) + offset + exposure) return (self.endog - L)[:,None] * X def score_factor(self, params): """ Poisson model score_factor for each observation Parameters ---------- params : array_like The parameters of the model Returns ------- score : array_like The score factor (nobs, ) of the model evaluated at `params` Notes ----- .. math:: \\frac{\\partial\\ln L_{i}}{\\partial\\beta}=\\left(y_{i}-\\lambda_{i}\\right) for observations :math:`i=1,...,n` where the loglinear model is assumed .. math:: \\ln\\lambda_{i}=x_{i}\\beta """ offset = getattr(self, "offset", 0) exposure = getattr(self, "exposure", 0) X = self.exog L = np.exp(np.dot(X,params) + offset + exposure) return (self.endog - L) def hessian(self, params): """ Poisson model Hessian matrix of the loglikelihood Parameters ---------- params : array_like The parameters of the model Returns ------- hess : ndarray, (k_vars, k_vars) The Hessian, second derivative of loglikelihood function, evaluated at `params` Notes ----- .. math:: \\frac{\\partial^{2}\\ln L}{\\partial\\beta\\partial\\beta^{\\prime}}=-\\sum_{i=1}^{n}\\lambda_{i}x_{i}x_{i}^{\\prime} where the loglinear model is assumed .. math:: \\ln\\lambda_{i}=x_{i}\\beta """ offset = getattr(self, "offset", 0) exposure = getattr(self, "exposure", 0) X = self.exog L = np.exp(np.dot(X,params) + exposure + offset) return -np.dot(L*X.T, X) def hessian_factor(self, params): """ Poisson model Hessian factor Parameters ---------- params : array_like The parameters of the model Returns ------- hess : ndarray, (nobs,) The Hessian factor, second derivative of loglikelihood function with respect to the linear predictor evaluated at `params` Notes ----- .. math:: \\frac{\\partial^{2}\\ln L}{\\partial\\beta\\partial\\beta^{\\prime}}=-\\sum_{i=1}^{n}\\lambda_{i} where the loglinear model is assumed .. math:: \\ln\\lambda_{i}=x_{i}\\beta """ offset = getattr(self, "offset", 0) exposure = getattr(self, "exposure", 0) X = self.exog L = np.exp(np.dot(X,params) + exposure + offset) return L class GeneralizedPoisson(CountModel): __doc__ = """ Generalized Poisson Model %(params)s %(extra_params)s Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. """ % {'params': base._model_params_doc, 'extra_params': """ p : scalar P denotes parameterizations for GP regression. p=1 for GP-1 and p=2 for GP-2. Default is p=1. offset : array_like Offset is added to the linear prediction with coefficient equal to 1. exposure : array_like Log(exposure) is added to the linear prediction with coefficient equal to 1.""" + base._missing_param_doc + _check_rank_doc} def __init__(self, endog, exog, p=1, offset=None, exposure=None, missing='none', check_rank=True, **kwargs): super().__init__(endog, exog, offset=offset, exposure=exposure, missing=missing, check_rank=check_rank, **kwargs) self.parameterization = p - 1 self.exog_names.append('alpha') self.k_extra = 1 self._transparams = False def _get_init_kwds(self): kwds = super()._get_init_kwds() kwds['p'] = self.parameterization + 1 return kwds def loglike(self, params): """ Loglikelihood of Generalized Poisson model Parameters ---------- params : array_like The parameters of the model. Returns ------- loglike : float The log-likelihood function of the model evaluated at `params`. See notes. Notes -------- .. math:: \\ln L=\\sum_{i=1}^{n}\\left[\\mu_{i}+(y_{i}-1)*ln(\\mu_{i}+ \\alpha*\\mu_{i}^{p-1}*y_{i})-y_{i}*ln(1+\\alpha*\\mu_{i}^{p-1})- ln(y_{i}!)-\\frac{\\mu_{i}+\\alpha*\\mu_{i}^{p-1}*y_{i}}{1+\\alpha* \\mu_{i}^{p-1}}\\right] """ return np.sum(self.loglikeobs(params)) def loglikeobs(self, params): """ Loglikelihood for observations of Generalized Poisson model Parameters ---------- params : array_like The parameters of the model. Returns ------- loglike : ndarray The log likelihood for each observation of the model evaluated at `params`. See Notes Notes -------- .. math:: \\ln L=\\sum_{i=1}^{n}\\left[\\mu_{i}+(y_{i}-1)*ln(\\mu_{i}+ \\alpha*\\mu_{i}^{p-1}*y_{i})-y_{i}*ln(1+\\alpha*\\mu_{i}^{p-1})- ln(y_{i}!)-\\frac{\\mu_{i}+\\alpha*\\mu_{i}^{p-1}*y_{i}}{1+\\alpha* \\mu_{i}^{p-1}}\\right] for observations :math:`i=1,...,n` """ if self._transparams: alpha = np.exp(params[-1]) else: alpha = params[-1] params = params[:-1] p = self.parameterization endog = self.endog mu = self.predict(params) mu_p = np.power(mu, p) a1 = 1 + alpha * mu_p a2 = mu + (a1 - 1) * endog return (np.log(mu) + (endog - 1) * np.log(a2) - endog * np.log(a1) - gammaln(endog + 1) - a2 / a1) @Appender(_get_start_params_null_docs) def _get_start_params_null(self): offset = getattr(self, "offset", 0) exposure = getattr(self, "exposure", 0) const = (self.endog / np.exp(offset + exposure)).mean() params = [np.log(const)] mu = const * np.exp(offset + exposure) resid = self.endog - mu a = self._estimate_dispersion(mu, resid, df_resid=resid.shape[0] - 1) params.append(a) return np.array(params) def _estimate_dispersion(self, mu, resid, df_resid=None): q = self.parameterization if df_resid is None: df_resid = resid.shape[0] a = ((np.abs(resid) / np.sqrt(mu) - 1) * mu**(-q)).sum() / df_resid return a @Appender( """ use_transparams : bool This parameter enable internal transformation to impose non-negativity. True to enable. Default is False. use_transparams=True imposes the no underdispersion (alpha > 0) constraint. In case use_transparams=True and method="newton" or "ncg" transformation is ignored. """) @Appender(DiscreteModel.fit.__doc__) def fit(self, start_params=None, method='bfgs', maxiter=35, full_output=1, disp=1, callback=None, use_transparams=False, cov_type='nonrobust', cov_kwds=None, use_t=None, **kwargs): if use_transparams and method not in ['newton', 'ncg']: self._transparams = True else: if use_transparams: warnings.warn('Parameter "use_transparams" is ignored', RuntimeWarning) self._transparams = False if start_params is None: offset = getattr(self, "offset", 0) + getattr(self, "exposure", 0) if np.size(offset) == 1 and offset == 0: offset = None optim_kwds_prelim = {'disp': 0, 'skip_hessian': True, 'warn_convergence': False} optim_kwds_prelim.update(kwargs.get('optim_kwds_prelim', {})) mod_poi = Poisson(self.endog, self.exog, offset=offset) with warnings.catch_warnings(): warnings.simplefilter("always") res_poi = mod_poi.fit(**optim_kwds_prelim) start_params = res_poi.params a = self._estimate_dispersion(res_poi.predict(), res_poi.resid, df_resid=res_poi.df_resid) start_params = np.append(start_params, max(-0.1, a)) if callback is None: # work around perfect separation callback #3895 callback = lambda *x: x mlefit = super().fit(start_params=start_params, maxiter=maxiter, method=method, disp=disp, full_output=full_output, callback=callback, **kwargs) if use_transparams and method not in ["newton", "ncg"]: self._transparams = False mlefit._results.params[-1] = np.exp(mlefit._results.params[-1]) gpfit = GeneralizedPoissonResults(self, mlefit._results) result = GeneralizedPoissonResultsWrapper(gpfit) if cov_kwds is None: cov_kwds = {} result._get_robustcov_results(cov_type=cov_type, use_self=True, use_t=use_t, **cov_kwds) return result @Appender(DiscreteModel.fit_regularized.__doc__) def fit_regularized(self, start_params=None, method='l1', maxiter='defined_by_method', full_output=1, disp=1, callback=None, alpha=0, trim_mode='auto', auto_trim_tol=0.01, size_trim_tol=1e-4, qc_tol=0.03, **kwargs): _validate_l1_method(method) if np.size(alpha) == 1 and alpha != 0: k_params = self.exog.shape[1] + self.k_extra alpha = alpha * np.ones(k_params) alpha[-1] = 0 alpha_p = alpha[:-1] if (self.k_extra and np.size(alpha) > 1) else alpha self._transparams = False if start_params is None: offset = getattr(self, "offset", 0) + getattr(self, "exposure", 0) if np.size(offset) == 1 and offset == 0: offset = None mod_poi = Poisson(self.endog, self.exog, offset=offset) with warnings.catch_warnings(): warnings.simplefilter("always") start_params = mod_poi.fit_regularized( start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=0, callback=callback, alpha=alpha_p, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol, size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs).params start_params = np.append(start_params, 0.1) cntfit = super(CountModel, self).fit_regularized( start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, alpha=alpha, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol, size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs) discretefit = L1GeneralizedPoissonResults(self, cntfit) return L1GeneralizedPoissonResultsWrapper(discretefit) def score_obs(self, params): if self._transparams: alpha = np.exp(params[-1]) else: alpha = params[-1] params = params[:-1] p = self.parameterization exog = self.exog y = self.endog[:,None] mu = self.predict(params)[:,None] mu_p = np.power(mu, p) a1 = 1 + alpha * mu_p a2 = mu + alpha * mu_p * y a3 = alpha * p * mu ** (p - 1) a4 = a3 * y dmudb = mu * exog dalpha = (mu_p * (y * ((y - 1) / a2 - 2 / a1) + a2 / a1**2)) dparams = dmudb * (-a4 / a1 + a3 * a2 / (a1 ** 2) + (1 + a4) * ((y - 1) / a2 - 1 / a1) + 1 / mu) return np.concatenate((dparams, np.atleast_2d(dalpha)), axis=1) def score(self, params): score = np.sum(self.score_obs(params), axis=0) if self._transparams: score[-1] == score[-1] ** 2 return score else: return score def _score_p(self, params): """ Generalized Poisson model derivative of the log-likelihood by p-parameter Parameters ---------- params : array_like The parameters of the model Returns ------- dldp : float dldp is first derivative of the loglikelihood function, evaluated at `p-parameter`. """ if self._transparams: alpha = np.exp(params[-1]) else: alpha = params[-1] params = params[:-1] p = self.parameterization exog = self.exog y = self.endog[:,None] mu = self.predict(params)[:,None] mu_p = np.power(mu, p) a1 = 1 + alpha * mu_p a2 = mu + alpha * mu_p * y dp = np.sum((np.log(mu) * ((a2 - mu) * ((y - 1) / a2 - 2 / a1) + (a1 - 1) * a2 / a1 ** 2))) return dp def hessian(self, params): """ Generalized Poisson model Hessian matrix of the loglikelihood Parameters ---------- params : array_like The parameters of the model Returns ------- hess : ndarray, (k_vars, k_vars) The Hessian, second derivative of loglikelihood function, evaluated at `params` """ if self._transparams: alpha = np.exp(params[-1]) else: alpha = params[-1] params = params[:-1] p = self.parameterization exog = self.exog y = self.endog[:,None] mu = self.predict(params)[:,None] mu_p = np.power(mu, p) a1 = 1 + alpha * mu_p a2 = mu + alpha * mu_p * y a3 = alpha * p * mu ** (p - 1) a4 = a3 * y a5 = p * mu ** (p - 1) dmudb = mu * exog # for dl/dparams dparams dim = exog.shape[1] hess_arr = np.empty((dim+1,dim+1)) for i in range(dim): for j in range(i + 1): hess_arr[i,j] = np.sum(mu * exog[:,i,None] * exog[:,j,None] * (mu * (a3 * a4 / a1**2 - 2 * a3**2 * a2 / a1**3 + 2 * a3 * (a4 + 1) / a1**2 - a4 * p / (mu * a1) + a3 * p * a2 / (mu * a1**2) + (y - 1) * a4 * (p - 1) / (a2 * mu) - (y - 1) * (1 + a4)**2 / a2**2 - a4 * (p - 1) / (a1 * mu)) + ((y - 1) * (1 + a4) / a2 - (1 + a4) / a1)), axis=0) tri_idx = np.triu_indices(dim, k=1) hess_arr[tri_idx] = hess_arr.T[tri_idx] # for dl/dparams dalpha dldpda = np.sum((2 * a4 * mu_p / a1**2 - 2 * a3 * mu_p * a2 / a1**3 - mu_p * y * (y - 1) * (1 + a4) / a2**2 + mu_p * (1 + a4) / a1**2 + a5 * y * (y - 1) / a2 - 2 * a5 * y / a1 + a5 * a2 / a1**2) * dmudb, axis=0) hess_arr[-1,:-1] = dldpda hess_arr[:-1,-1] = dldpda # for dl/dalpha dalpha dldada = mu_p**2 * (3 * y / a1**2 - (y / a2)**2. * (y - 1) - 2 * a2 / a1**3) hess_arr[-1,-1] = dldada.sum() return hess_arr def predict(self, params, exog=None, exposure=None, offset=None, which='mean'): """ Predict response variable of a count model given exogenous variables. Notes ----- If exposure is specified, then it will be logged by the method. The user does not need to log it first. """ if exog is None: exog = self.exog if exposure is None: exposure = getattr(self, 'exposure', 0) elif exposure != 0: exposure = np.log(exposure) if offset is None: offset = getattr(self, 'offset', 0) fitted = np.dot(exog, params[:exog.shape[1]]) linpred = fitted + exposure + offset if which == 'mean': return np.exp(linpred) elif which == 'linear': return linpred elif which =='prob': counts = np.atleast_2d(np.arange(0, np.max(self.endog)+1)) mu = self.predict(params, exog=exog, exposure=exposure, offset=offset)[:,None] return genpoisson_p.pmf(counts, mu, params[-1], self.parameterization + 1) else: raise ValueError('keyword \'which\' not recognized') class Logit(BinaryModel): __doc__ = """ Logit Model %(params)s %(extra_params)s Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. """ % {'params': base._model_params_doc, 'extra_params': base._missing_param_doc + _check_rank_doc} _continuous_ok = True def cdf(self, X): """ The logistic cumulative distribution function Parameters ---------- X : array_like `X` is the linear predictor of the logit model. See notes. Returns ------- 1/(1 + exp(-X)) Notes ----- In the logit model, .. math:: \\Lambda\\left(x^{\\prime}\\beta\\right)= \\text{Prob}\\left(Y=1|x\\right)= \\frac{e^{x^{\\prime}\\beta}}{1+e^{x^{\\prime}\\beta}} """ X = np.asarray(X) return 1/(1+np.exp(-X)) def pdf(self, X): """ The logistic probability density function Parameters ---------- X : array_like `X` is the linear predictor of the logit model. See notes. Returns ------- pdf : ndarray The value of the Logit probability mass function, PMF, for each point of X. ``np.exp(-x)/(1+np.exp(-X))**2`` Notes ----- In the logit model, .. math:: \\lambda\\left(x^{\\prime}\\beta\\right)=\\frac{e^{-x^{\\prime}\\beta}}{\\left(1+e^{-x^{\\prime}\\beta}\\right)^{2}} """ X = np.asarray(X) return np.exp(-X)/(1+np.exp(-X))**2 def loglike(self, params): """ Log-likelihood of logit model. Parameters ---------- params : array_like The parameters of the logit model. Returns ------- loglike : float The log-likelihood function of the model evaluated at `params`. See notes. Notes ----- .. math:: \\ln L=\\sum_{i}\\ln\\Lambda \\left(q_{i}x_{i}^{\\prime}\\beta\\right) Where :math:`q=2y-1`. This simplification comes from the fact that the logistic distribution is symmetric. """ q = 2*self.endog - 1 X = self.exog return np.sum(np.log(self.cdf(q*np.dot(X,params)))) def loglikeobs(self, params): """ Log-likelihood of logit model for each observation. Parameters ---------- params : array_like The parameters of the logit model. Returns ------- loglike : ndarray The log likelihood for each observation of the model evaluated at `params`. See Notes Notes ----- .. math:: \\ln L=\\sum_{i}\\ln\\Lambda \\left(q_{i}x_{i}^{\\prime}\\beta\\right) for observations :math:`i=1,...,n` where :math:`q=2y-1`. This simplification comes from the fact that the logistic distribution is symmetric. """ q = 2*self.endog - 1 X = self.exog return np.log(self.cdf(q*np.dot(X,params))) def score(self, params): """ Logit model score (gradient) vector of the log-likelihood Parameters ---------- params : array_like The parameters of the model Returns ------- score : ndarray, 1-D The score vector of the model, i.e. the first derivative of the loglikelihood function, evaluated at `params` Notes ----- .. math:: \\frac{\\partial\\ln L}{\\partial\\beta}=\\sum_{i=1}^{n}\\left(y_{i}-\\Lambda_{i}\\right)x_{i} """ y = self.endog X = self.exog L = self.cdf(np.dot(X,params)) return np.dot(y - L,X) def score_obs(self, params): """ Logit model Jacobian of the log-likelihood for each observation Parameters ---------- params : array_like The parameters of the model Returns ------- jac : array_like The derivative of the loglikelihood for each observation evaluated at `params`. Notes ----- .. math:: \\frac{\\partial\\ln L_{i}}{\\partial\\beta}=\\left(y_{i}-\\Lambda_{i}\\right)x_{i} for observations :math:`i=1,...,n` """ y = self.endog X = self.exog L = self.cdf(np.dot(X, params)) return (y - L)[:,None] * X def hessian(self, params): """ Logit model Hessian matrix of the log-likelihood Parameters ---------- params : array_like The parameters of the model Returns ------- hess : ndarray, (k_vars, k_vars) The Hessian, second derivative of loglikelihood function, evaluated at `params` Notes ----- .. math:: \\frac{\\partial^{2}\\ln L}{\\partial\\beta\\partial\\beta^{\\prime}}=-\\sum_{i}\\Lambda_{i}\\left(1-\\Lambda_{i}\\right)x_{i}x_{i}^{\\prime} """ X = self.exog L = self.cdf(np.dot(X,params)) return -np.dot(L*(1-L)*X.T,X) @Appender(DiscreteModel.fit.__doc__) def fit(self, start_params=None, method='newton', maxiter=35, full_output=1, disp=1, callback=None, **kwargs): bnryfit = super().fit(start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, **kwargs) discretefit = LogitResults(self, bnryfit) return BinaryResultsWrapper(discretefit) class Probit(BinaryModel): __doc__ = """ Probit Model %(params)s %(extra_params)s Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. """ % {'params': base._model_params_doc, 'extra_params': base._missing_param_doc + _check_rank_doc} def cdf(self, X): """ Probit (Normal) cumulative distribution function Parameters ---------- X : array_like The linear predictor of the model (XB). Returns ------- cdf : ndarray The cdf evaluated at `X`. Notes ----- This function is just an alias for scipy.stats.norm.cdf """ return stats.norm._cdf(X) def pdf(self, X): """ Probit (Normal) probability density function Parameters ---------- X : array_like The linear predictor of the model (XB). Returns ------- pdf : ndarray The value of the normal density function for each point of X. Notes ----- This function is just an alias for scipy.stats.norm.pdf """ X = np.asarray(X) return stats.norm._pdf(X) def loglike(self, params): """ Log-likelihood of probit model (i.e., the normal distribution). Parameters ---------- params : array_like The parameters of the model. Returns ------- loglike : float The log-likelihood function of the model evaluated at `params`. See notes. Notes ----- .. math:: \\ln L=\\sum_{i}\\ln\\Phi\\left(q_{i}x_{i}^{\\prime}\\beta\\right) Where :math:`q=2y-1`. This simplification comes from the fact that the normal distribution is symmetric. """ q = 2*self.endog - 1 X = self.exog return np.sum(np.log(np.clip(self.cdf(q*np.dot(X,params)), FLOAT_EPS, 1))) def loglikeobs(self, params): """ Log-likelihood of probit model for each observation Parameters ---------- params : array_like The parameters of the model. Returns ------- loglike : array_like The log likelihood for each observation of the model evaluated at `params`. See Notes Notes ----- .. math:: \\ln L_{i}=\\ln\\Phi\\left(q_{i}x_{i}^{\\prime}\\beta\\right) for observations :math:`i=1,...,n` where :math:`q=2y-1`. This simplification comes from the fact that the normal distribution is symmetric. """ q = 2*self.endog - 1 X = self.exog return np.log(np.clip(self.cdf(q*np.dot(X,params)), FLOAT_EPS, 1)) def score(self, params): """ Probit model score (gradient) vector Parameters ---------- params : array_like The parameters of the model Returns ------- score : ndarray, 1-D The score vector of the model, i.e. the first derivative of the loglikelihood function, evaluated at `params` Notes ----- .. math:: \\frac{\\partial\\ln L}{\\partial\\beta}=\\sum_{i=1}^{n}\\left[\\frac{q_{i}\\phi\\left(q_{i}x_{i}^{\\prime}\\beta\\right)}{\\Phi\\left(q_{i}x_{i}^{\\prime}\\beta\\right)}\\right]x_{i} Where :math:`q=2y-1`. This simplification comes from the fact that the normal distribution is symmetric. """ y = self.endog X = self.exog XB = np.dot(X,params) q = 2*y - 1 # clip to get rid of invalid divide complaint L = q*self.pdf(q*XB)/np.clip(self.cdf(q*XB), FLOAT_EPS, 1 - FLOAT_EPS) return np.dot(L,X) def score_obs(self, params): """ Probit model Jacobian for each observation Parameters ---------- params : array_like The parameters of the model Returns ------- jac : array_like The derivative of the loglikelihood for each observation evaluated at `params`. Notes ----- .. math:: \\frac{\\partial\\ln L_{i}}{\\partial\\beta}=\\left[\\frac{q_{i}\\phi\\left(q_{i}x_{i}^{\\prime}\\beta\\right)}{\\Phi\\left(q_{i}x_{i}^{\\prime}\\beta\\right)}\\right]x_{i} for observations :math:`i=1,...,n` Where :math:`q=2y-1`. This simplification comes from the fact that the normal distribution is symmetric. """ y = self.endog X = self.exog XB = np.dot(X,params) q = 2*y - 1 # clip to get rid of invalid divide complaint L = q*self.pdf(q*XB)/np.clip(self.cdf(q*XB), FLOAT_EPS, 1 - FLOAT_EPS) return L[:,None] * X def hessian(self, params): """ Probit model Hessian matrix of the log-likelihood Parameters ---------- params : array_like The parameters of the model Returns ------- hess : ndarray, (k_vars, k_vars) The Hessian, second derivative of loglikelihood function, evaluated at `params` Notes ----- .. math:: \\frac{\\partial^{2}\\ln L}{\\partial\\beta\\partial\\beta^{\\prime}}=-\\lambda_{i}\\left(\\lambda_{i}+x_{i}^{\\prime}\\beta\\right)x_{i}x_{i}^{\\prime} where .. math:: \\lambda_{i}=\\frac{q_{i}\\phi\\left(q_{i}x_{i}^{\\prime}\\beta\\right)}{\\Phi\\left(q_{i}x_{i}^{\\prime}\\beta\\right)} and :math:`q=2y-1` """ X = self.exog XB = np.dot(X,params) q = 2*self.endog - 1 L = q*self.pdf(q*XB)/self.cdf(q*XB) return np.dot(-L*(L+XB)*X.T,X) @Appender(DiscreteModel.fit.__doc__) def fit(self, start_params=None, method='newton', maxiter=35, full_output=1, disp=1, callback=None, **kwargs): bnryfit = super().fit(start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, **kwargs) discretefit = ProbitResults(self, bnryfit) return BinaryResultsWrapper(discretefit) class MNLogit(MultinomialModel): __doc__ = """ Multinomial Logit Model Parameters ---------- endog : array_like `endog` is an 1-d vector of the endogenous response. `endog` can contain strings, ints, or floats or may be a pandas Categorical Series. Note that if it contains strings, every distinct string will be a category. No stripping of whitespace is done. exog : array_like A nobs x k array where `nobs` is the number of observations and `k` is the number of regressors. An intercept is not included by default and should be added by the user. See `statsmodels.tools.add_constant`. %(extra_params)s Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. J : float The number of choices for the endogenous variable. Note that this is zero-indexed. K : float The actual number of parameters for the exogenous design. Includes the constant if the design has one. names : dict A dictionary mapping the column number in `wendog` to the variables in `endog`. wendog : ndarray An n x j array where j is the number of unique categories in `endog`. Each column of j is a dummy variable indicating the category of each observation. See `names` for a dictionary mapping each column to its category. Notes ----- See developer notes for further information on `MNLogit` internals. """ % {'extra_params': base._missing_param_doc + _check_rank_doc} def __init__(self, endog, exog, check_rank=True, **kwargs): super().__init__(endog, exog, check_rank=check_rank, **kwargs) # Override cov_names since multivariate model yname = self.endog_names ynames = self._ynames_map ynames = MultinomialResults._maybe_convert_ynames_int(ynames) # use range below to ensure sortedness ynames = [ynames[key] for key in range(int(self.J))] idx = MultiIndex.from_product((ynames[1:], self.data.xnames), names=(yname, None)) self.data.cov_names = idx def pdf(self, eXB): """ NotImplemented """ raise NotImplementedError def cdf(self, X): """ Multinomial logit cumulative distribution function. Parameters ---------- X : ndarray The linear predictor of the model XB. Returns ------- cdf : ndarray The cdf evaluated at `X`. Notes ----- In the multinomial logit model. .. math:: \\frac{\\exp\\left(\\beta_{j}^{\\prime}x_{i}\\right)}{\\sum_{k=0}^{J}\\exp\\left(\\beta_{k}^{\\prime}x_{i}\\right)} """ eXB = np.column_stack((np.ones(len(X)), np.exp(X))) return eXB/eXB.sum(1)[:,None] def loglike(self, params): """ Log-likelihood of the multinomial logit model. Parameters ---------- params : array_like The parameters of the multinomial logit model. Returns ------- loglike : float The log-likelihood function of the model evaluated at `params`. See notes. Notes ----- .. math:: \\ln L=\\sum_{i=1}^{n}\\sum_{j=0}^{J}d_{ij}\\ln \\left(\\frac{\\exp\\left(\\beta_{j}^{\\prime}x_{i}\\right)} {\\sum_{k=0}^{J} \\exp\\left(\\beta_{k}^{\\prime}x_{i}\\right)}\\right) where :math:`d_{ij}=1` if individual `i` chose alternative `j` and 0 if not. """ params = params.reshape(self.K, -1, order='F') d = self.wendog logprob = np.log(self.cdf(np.dot(self.exog,params))) return np.sum(d * logprob) def loglikeobs(self, params): """ Log-likelihood of the multinomial logit model for each observation. Parameters ---------- params : array_like The parameters of the multinomial logit model. Returns ------- loglike : array_like The log likelihood for each observation of the model evaluated at `params`. See Notes Notes ----- .. math:: \\ln L_{i}=\\sum_{j=0}^{J}d_{ij}\\ln \\left(\\frac{\\exp\\left(\\beta_{j}^{\\prime}x_{i}\\right)} {\\sum_{k=0}^{J} \\exp\\left(\\beta_{k}^{\\prime}x_{i}\\right)}\\right) for observations :math:`i=1,...,n` where :math:`d_{ij}=1` if individual `i` chose alternative `j` and 0 if not. """ params = params.reshape(self.K, -1, order='F') d = self.wendog logprob = np.log(self.cdf(np.dot(self.exog,params))) return d * logprob def score(self, params): """ Score matrix for multinomial logit model log-likelihood Parameters ---------- params : ndarray The parameters of the multinomial logit model. Returns ------- score : ndarray, (K * (J-1),) The 2-d score vector, i.e. the first derivative of the loglikelihood function, of the multinomial logit model evaluated at `params`. Notes ----- .. math:: \\frac{\\partial\\ln L}{\\partial\\beta_{j}}=\\sum_{i}\\left(d_{ij}-\\frac{\\exp\\left(\\beta_{j}^{\\prime}x_{i}\\right)}{\\sum_{k=0}^{J}\\exp\\left(\\beta_{k}^{\\prime}x_{i}\\right)}\\right)x_{i} for :math:`j=1,...,J` In the multinomial model the score matrix is K x J-1 but is returned as a flattened array to work with the solvers. """ params = params.reshape(self.K, -1, order='F') firstterm = self.wendog[:,1:] - self.cdf(np.dot(self.exog, params))[:,1:] #NOTE: might need to switch terms if params is reshaped return np.dot(firstterm.T, self.exog).flatten() def loglike_and_score(self, params): """ Returns log likelihood and score, efficiently reusing calculations. Note that both of these returned quantities will need to be negated before being minimized by the maximum likelihood fitting machinery. """ params = params.reshape(self.K, -1, order='F') cdf_dot_exog_params = self.cdf(np.dot(self.exog, params)) loglike_value = np.sum(self.wendog * np.log(cdf_dot_exog_params)) firstterm = self.wendog[:, 1:] - cdf_dot_exog_params[:, 1:] score_array = np.dot(firstterm.T, self.exog).flatten() return loglike_value, score_array def score_obs(self, params): """ Jacobian matrix for multinomial logit model log-likelihood Parameters ---------- params : ndarray The parameters of the multinomial logit model. Returns ------- jac : array_like The derivative of the loglikelihood for each observation evaluated at `params` . Notes ----- .. math:: \\frac{\\partial\\ln L_{i}}{\\partial\\beta_{j}}=\\left(d_{ij}-\\frac{\\exp\\left(\\beta_{j}^{\\prime}x_{i}\\right)}{\\sum_{k=0}^{J}\\exp\\left(\\beta_{k}^{\\prime}x_{i}\\right)}\\right)x_{i} for :math:`j=1,...,J`, for observations :math:`i=1,...,n` In the multinomial model the score vector is K x (J-1) but is returned as a flattened array. The Jacobian has the observations in rows and the flattened array of derivatives in columns. """ params = params.reshape(self.K, -1, order='F') firstterm = self.wendog[:,1:] - self.cdf(np.dot(self.exog, params))[:,1:] #NOTE: might need to switch terms if params is reshaped return (firstterm[:,:,None] * self.exog[:,None,:]).reshape(self.exog.shape[0], -1) def hessian(self, params): """ Multinomial logit Hessian matrix of the log-likelihood Parameters ---------- params : array_like The parameters of the model Returns ------- hess : ndarray, (J*K, J*K) The Hessian, second derivative of loglikelihood function with respect to the flattened parameters, evaluated at `params` Notes ----- .. math:: \\frac{\\partial^{2}\\ln L}{\\partial\\beta_{j}\\partial\\beta_{l}}=-\\sum_{i=1}^{n}\\frac{\\exp\\left(\\beta_{j}^{\\prime}x_{i}\\right)}{\\sum_{k=0}^{J}\\exp\\left(\\beta_{k}^{\\prime}x_{i}\\right)}\\left[\\boldsymbol{1}\\left(j=l\\right)-\\frac{\\exp\\left(\\beta_{l}^{\\prime}x_{i}\\right)}{\\sum_{k=0}^{J}\\exp\\left(\\beta_{k}^{\\prime}x_{i}\\right)}\\right]x_{i}x_{l}^{\\prime} where :math:`\\boldsymbol{1}\\left(j=l\\right)` equals 1 if `j` = `l` and 0 otherwise. The actual Hessian matrix has J**2 * K x K elements. Our Hessian is reshaped to be square (J*K, J*K) so that the solvers can use it. This implementation does not take advantage of the symmetry of the Hessian and could probably be refactored for speed. """ params = params.reshape(self.K, -1, order='F') X = self.exog pr = self.cdf(np.dot(X,params)) partials = [] J = self.J K = self.K for i in range(J-1): for j in range(J-1): # this loop assumes we drop the first col. if i == j: partials.append(\ -np.dot(((pr[:,i+1]*(1-pr[:,j+1]))[:,None]*X).T,X)) else: partials.append(-np.dot(((pr[:,i+1]*-pr[:,j+1])[:,None]*X).T,X)) H = np.array(partials) # the developer's notes on multinomial should clear this math up H = np.transpose(H.reshape(J-1, J-1, K, K), (0, 2, 1, 3)).reshape((J-1)*K, (J-1)*K) return H #TODO: Weibull can replaced by a survival analsysis function # like stat's streg (The cox model as well) #class Weibull(DiscreteModel): # """ # Binary choice Weibull model # # Notes # ------ # This is unfinished and untested. # """ ##TODO: add analytic hessian for Weibull # def initialize(self): # pass # # def cdf(self, X): # """ # Gumbell (Log Weibull) cumulative distribution function # """ ## return np.exp(-np.exp(-X)) # return stats.gumbel_r.cdf(X) # # these two are equivalent. # # Greene table and discussion is incorrect. # # def pdf(self, X): # """ # Gumbell (LogWeibull) probability distribution function # """ # return stats.gumbel_r.pdf(X) # # def loglike(self, params): # """ # Loglikelihood of Weibull distribution # """ # X = self.exog # cdf = self.cdf(np.dot(X,params)) # y = self.endog # return np.sum(y*np.log(cdf) + (1-y)*np.log(1-cdf)) # # def score(self, params): # y = self.endog # X = self.exog # F = self.cdf(np.dot(X,params)) # f = self.pdf(np.dot(X,params)) # term = (y*f/F + (1 - y)*-f/(1-F)) # return np.dot(term,X) # # def hessian(self, params): # hess = nd.Jacobian(self.score) # return hess(params) # # def fit(self, start_params=None, method='newton', maxiter=35, tol=1e-08): ## The example had problems with all zero start values, Hessian = 0 # if start_params is None: # start_params = OLS(self.endog, self.exog).fit().params # mlefit = super(Weibull, self).fit(start_params=start_params, # method=method, maxiter=maxiter, tol=tol) # return mlefit # class NegativeBinomial(CountModel): __doc__ = """ Negative Binomial Model %(params)s %(extra_params)s Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. References ---------- Greene, W. 2008. "Functional forms for the negative binomial model for count data". Economics Letters. Volume 99, Number 3, pp.585-590. Hilbe, J.M. 2011. "Negative binomial regression". Cambridge University Press. """ % {'params': base._model_params_doc, 'extra_params': """loglike_method : str Log-likelihood type. 'nb2','nb1', or 'geometric'. Fitted value :math:`\\mu` Heterogeneity parameter :math:`\\alpha` - nb2: Variance equal to :math:`\\mu + \\alpha\\mu^2` (most common) - nb1: Variance equal to :math:`\\mu + \\alpha\\mu` - geometric: Variance equal to :math:`\\mu + \\mu^2` offset : array_like Offset is added to the linear prediction with coefficient equal to 1. exposure : array_like Log(exposure) is added to the linear prediction with coefficient equal to 1. """ + base._missing_param_doc + _check_rank_doc} def __init__(self, endog, exog, loglike_method='nb2', offset=None, exposure=None, missing='none', check_rank=True, **kwargs): super().__init__(endog, exog, offset=offset, exposure=exposure, missing=missing, check_rank=check_rank, **kwargs) self.loglike_method = loglike_method self._initialize() if loglike_method in ['nb2', 'nb1']: self.exog_names.append('alpha') self.k_extra = 1 else: self.k_extra = 0 # store keys for extras if we need to recreate model instance # we need to append keys that do not go to super self._init_keys.append('loglike_method') def _initialize(self): if self.loglike_method == 'nb2': self.hessian = self._hessian_nb2 self.score = self._score_nbin self.loglikeobs = self._ll_nb2 self._transparams = True # transform lnalpha -> alpha in fit elif self.loglike_method == 'nb1': self.hessian = self._hessian_nb1 self.score = self._score_nb1 self.loglikeobs = self._ll_nb1 self._transparams = True # transform lnalpha -> alpha in fit elif self.loglike_method == 'geometric': self.hessian = self._hessian_geom self.score = self._score_geom self.loglikeobs = self._ll_geometric else: raise ValueError('Likelihood type must "nb1", "nb2" ' 'or "geometric"') # Workaround to pickle instance methods def __getstate__(self): odict = self.__dict__.copy() # copy the dict since we change it del odict['hessian'] del odict['score'] del odict['loglikeobs'] return odict def __setstate__(self, indict): self.__dict__.update(indict) self._initialize() def _ll_nbin(self, params, alpha, Q=0): if np.any(np.iscomplex(params)) or np.iscomplex(alpha): gamma_ln = loggamma else: gamma_ln = gammaln endog = self.endog mu = self.predict(params) size = 1/alpha * mu**Q prob = size/(size+mu) coeff = (gamma_ln(size+endog) - gamma_ln(endog+1) - gamma_ln(size)) llf = coeff + size*np.log(prob) + endog*np.log(1-prob) return llf def _ll_nb2(self, params): if self._transparams: # got lnalpha during fit alpha = np.exp(params[-1]) else: alpha = params[-1] return self._ll_nbin(params[:-1], alpha, Q=0) def _ll_nb1(self, params): if self._transparams: # got lnalpha during fit alpha = np.exp(params[-1]) else: alpha = params[-1] return self._ll_nbin(params[:-1], alpha, Q=1) def _ll_geometric(self, params): # we give alpha of 1 because it's actually log(alpha) where alpha=0 return self._ll_nbin(params, 1, 0) def loglike(self, params): r""" Loglikelihood for negative binomial model Parameters ---------- params : array_like The parameters of the model. If `loglike_method` is nb1 or nb2, then the ancillary parameter is expected to be the last element. Returns ------- llf : float The loglikelihood value at `params` Notes ----- Following notation in Greene (2008), with negative binomial heterogeneity parameter :math:`\alpha`: .. math:: \lambda_i &= exp(X\beta) \\ \theta &= 1 / \alpha \\ g_i &= \theta \lambda_i^Q \\ w_i &= g_i/(g_i + \lambda_i) \\ r_i &= \theta / (\theta+\lambda_i) \\ ln \mathcal{L}_i &= ln \Gamma(y_i+g_i) - ln \Gamma(1+y_i) + g_iln (r_i) + y_i ln(1-r_i) where :math`Q=0` for NB2 and geometric and :math:`Q=1` for NB1. For the geometric, :math:`\alpha=0` as well. """ llf = np.sum(self.loglikeobs(params)) return llf def _score_geom(self, params): exog = self.exog y = self.endog[:, None] mu = self.predict(params)[:, None] dparams = exog * (y-mu)/(mu+1) return dparams.sum(0) def _score_nbin(self, params, Q=0): """ Score vector for NB2 model """ if self._transparams: # lnalpha came in during fit alpha = np.exp(params[-1]) else: alpha = params[-1] params = params[:-1] exog = self.exog y = self.endog[:,None] mu = self.predict(params)[:,None] a1 = 1/alpha * mu**Q prob = a1 / (a1 + mu) # a1 aka "size" in _ll_nbin if Q == 1: # nb1 # Q == 1 --> a1 = mu / alpha --> prob = 1 / (alpha + 1) dgpart = digamma(y + a1) - digamma(a1) dparams = exog * a1 * (np.log(prob) + dgpart) dalpha = ((alpha * (y - mu * np.log(prob) - mu*(dgpart + 1)) - mu * (np.log(prob) + dgpart))/ (alpha**2*(alpha + 1))).sum() elif Q == 0: # nb2 dgpart = digamma(y + a1) - digamma(a1) dparams = exog*a1 * (y-mu)/(mu+a1) da1 = -alpha**-2 dalpha = (dgpart + np.log(a1) - np.log(a1+mu) - (y-mu)/(a1+mu)).sum() * da1 #multiply above by constant outside sum to reduce rounding error if self._transparams: return np.r_[dparams.sum(0), dalpha*alpha] else: return np.r_[dparams.sum(0), dalpha] def _score_nb1(self, params): return self._score_nbin(params, Q=1) def _hessian_geom(self, params): exog = self.exog y = self.endog[:,None] mu = self.predict(params)[:,None] # for dl/dparams dparams dim = exog.shape[1] hess_arr = np.empty((dim, dim)) const_arr = mu*(1+y)/(mu+1)**2 for i in range(dim): for j in range(dim): if j > i: continue hess_arr[i,j] = np.sum(-exog[:,i,None] * exog[:,j,None] * const_arr, axis=0) tri_idx = np.triu_indices(dim, k=1) hess_arr[tri_idx] = hess_arr.T[tri_idx] return hess_arr def _hessian_nb1(self, params): """ Hessian of NB1 model. """ if self._transparams: # lnalpha came in during fit alpha = np.exp(params[-1]) else: alpha = params[-1] params = params[:-1] exog = self.exog y = self.endog[:,None] mu = self.predict(params)[:,None] a1 = mu/alpha dgpart = digamma(y + a1) - digamma(a1) prob = 1 / (1 + alpha) # equiv: a1 / (a1 + mu) # for dl/dparams dparams dim = exog.shape[1] hess_arr = np.empty((dim+1,dim+1)) #const_arr = a1*mu*(a1+y)/(mu+a1)**2 # not all of dparams dparams = exog / alpha * (np.log(prob) + dgpart) dmudb = exog*mu xmu_alpha = exog * a1 trigamma = (special.polygamma(1, a1 + y) - special.polygamma(1, a1)) for i in range(dim): for j in range(dim): if j > i: continue hess_arr[i,j] = np.sum(dparams[:,i,None] * dmudb[:,j,None] + xmu_alpha[:,i,None] * xmu_alpha[:,j,None] * trigamma, axis=0) tri_idx = np.triu_indices(dim, k=1) hess_arr[tri_idx] = hess_arr.T[tri_idx] # for dl/dparams dalpha da1 = -alpha**-2 dldpda = np.sum(-a1 * dparams + exog * a1 * (-trigamma*mu/alpha**2 - prob), axis=0) hess_arr[-1,:-1] = dldpda hess_arr[:-1,-1] = dldpda log_alpha = np.log(prob) alpha3 = alpha**3 alpha2 = alpha**2 mu2 = mu**2 dada = ((alpha3*mu*(2*log_alpha + 2*dgpart + 3) - 2*alpha3*y + 4*alpha2*mu*(log_alpha + dgpart) + alpha2 * (2*mu - y) + 2*alpha*mu2*trigamma + mu2 * trigamma + alpha2 * mu2 * trigamma + 2*alpha*mu*(log_alpha + dgpart) )/(alpha**4*(alpha2 + 2*alpha + 1))) hess_arr[-1,-1] = dada.sum() return hess_arr def _hessian_nb2(self, params): """ Hessian of NB2 model. """ if self._transparams: # lnalpha came in during fit alpha = np.exp(params[-1]) else: alpha = params[-1] a1 = 1/alpha params = params[:-1] exog = self.exog y = self.endog[:,None] mu = self.predict(params)[:,None] prob = a1 / (a1 + mu) dgpart = digamma(a1 + y) - digamma(a1) # for dl/dparams dparams dim = exog.shape[1] hess_arr = np.empty((dim+1,dim+1)) const_arr = a1*mu*(a1+y)/(mu+a1)**2 for i in range(dim): for j in range(dim): if j > i: continue hess_arr[i,j] = np.sum(-exog[:,i,None] * exog[:,j,None] * const_arr, axis=0) tri_idx = np.triu_indices(dim, k=1) hess_arr[tri_idx] = hess_arr.T[tri_idx] # for dl/dparams dalpha da1 = -alpha**-2 dldpda = -np.sum(mu*exog*(y-mu)*a1**2/(mu+a1)**2 , axis=0) hess_arr[-1,:-1] = dldpda hess_arr[:-1,-1] = dldpda # for dl/dalpha dalpha #NOTE: polygamma(1,x) is the trigamma function da2 = 2*alpha**-3 dalpha = da1 * (dgpart + np.log(prob) - (y - mu)/(a1+mu)) dada = (da2 * dalpha/da1 + da1**2 * (special.polygamma(1, a1+y) - special.polygamma(1, a1) + 1/a1 - 1/(a1 + mu) + (y - mu)/(mu + a1)**2)).sum() hess_arr[-1,-1] = dada return hess_arr #TODO: replace this with analytic where is it used? def score_obs(self, params): sc = approx_fprime_cs(params, self.loglikeobs) return sc @Appender(_get_start_params_null_docs) def _get_start_params_null(self): offset = getattr(self, "offset", 0) exposure = getattr(self, "exposure", 0) const = (self.endog / np.exp(offset + exposure)).mean() params = [np.log(const)] mu = const * np.exp(offset + exposure) resid = self.endog - mu a = self._estimate_dispersion(mu, resid, df_resid=resid.shape[0] - 1) params.append(a) return np.array(params) def _estimate_dispersion(self, mu, resid, df_resid=None): if df_resid is None: df_resid = resid.shape[0] if self.loglike_method == 'nb2': #params.append(np.linalg.pinv(mu[:,None]).dot(resid**2 / mu - 1)) a = ((resid**2 / mu - 1) / mu).sum() / df_resid else: #self.loglike_method == 'nb1': a = (resid**2 / mu - 1).sum() / df_resid return a def fit(self, start_params=None, method='bfgs', maxiter=35, full_output=1, disp=1, callback=None, cov_type='nonrobust', cov_kwds=None, use_t=None, **kwargs): # Note: do not let super handle robust covariance because it has # transformed params self._transparams = False # always define attribute if self.loglike_method.startswith('nb') and method not in ['newton', 'ncg']: self._transparams = True # in case same Model instance is refit elif self.loglike_method.startswith('nb'): # method is newton/ncg self._transparams = False # because we need to step in alpha space if start_params is None: # Use poisson fit as first guess. #TODO, Warning: this assumes exposure is logged offset = getattr(self, "offset", 0) + getattr(self, "exposure", 0) if np.size(offset) == 1 and offset == 0: offset = None optim_kwds_prelim = {'disp': 0, 'skip_hessian': True, 'warn_convergence': False} optim_kwds_prelim.update(kwargs.get('optim_kwds_prelim', {})) mod_poi = Poisson(self.endog, self.exog, offset=offset) with warnings.catch_warnings(): warnings.simplefilter("always") res_poi = mod_poi.fit(**optim_kwds_prelim) start_params = res_poi.params if self.loglike_method.startswith('nb'): a = self._estimate_dispersion(res_poi.predict(), res_poi.resid, df_resid=res_poi.df_resid) start_params = np.append(start_params, max(0.05, a)) else: if self._transparams is True: # transform user provided start_params dispersion, see #3918 start_params = np.array(start_params, copy=True) start_params[-1] = np.log(start_params[-1]) if callback is None: # work around perfect separation callback #3895 callback = lambda *x: x mlefit = super().fit(start_params=start_params, maxiter=maxiter, method=method, disp=disp, full_output=full_output, callback=callback, **kwargs) # TODO: Fix NBin _check_perfect_pred if self.loglike_method.startswith('nb'): # mlefit is a wrapped counts results self._transparams = False # do not need to transform anymore now # change from lnalpha to alpha if method not in ["newton", "ncg"]: mlefit._results.params[-1] = np.exp(mlefit._results.params[-1]) nbinfit = NegativeBinomialResults(self, mlefit._results) result = NegativeBinomialResultsWrapper(nbinfit) else: result = mlefit if cov_kwds is None: cov_kwds = {} #TODO: make this unnecessary ? result._get_robustcov_results(cov_type=cov_type, use_self=True, use_t=use_t, **cov_kwds) return result def fit_regularized(self, start_params=None, method='l1', maxiter='defined_by_method', full_output=1, disp=1, callback=None, alpha=0, trim_mode='auto', auto_trim_tol=0.01, size_trim_tol=1e-4, qc_tol=0.03, **kwargs): _validate_l1_method(method) if self.loglike_method.startswith('nb') and (np.size(alpha) == 1 and alpha != 0): # do not penalize alpha if alpha is scalar k_params = self.exog.shape[1] + self.k_extra alpha = alpha * np.ones(k_params) alpha[-1] = 0 # alpha for regularized poisson to get starting values alpha_p = alpha[:-1] if (self.k_extra and np.size(alpha) > 1) else alpha self._transparams = False if start_params is None: # Use poisson fit as first guess. #TODO, Warning: this assumes exposure is logged offset = getattr(self, "offset", 0) + getattr(self, "exposure", 0) if np.size(offset) == 1 and offset == 0: offset = None mod_poi = Poisson(self.endog, self.exog, offset=offset) with warnings.catch_warnings(): warnings.simplefilter("always") start_params = mod_poi.fit_regularized( start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=0, callback=callback, alpha=alpha_p, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol, size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs).params if self.loglike_method.startswith('nb'): start_params = np.append(start_params, 0.1) cntfit = super(CountModel, self).fit_regularized( start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, alpha=alpha, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol, size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs) discretefit = L1NegativeBinomialResults(self, cntfit) return L1NegativeBinomialResultsWrapper(discretefit) class NegativeBinomialP(CountModel): __doc__ = """ Generalized Negative Binomial (NB-P) Model %(params)s %(extra_params)s Attributes ---------- endog : ndarray A reference to the endogenous response variable exog : ndarray A reference to the exogenous design. p : scalar P denotes parameterizations for NB-P regression. p=1 for NB-1 and p=2 for NB-2. Default is p=1. """ % {'params': base._model_params_doc, 'extra_params': """p : scalar P denotes parameterizations for NB regression. p=1 for NB-1 and p=2 for NB-2. Default is p=2. offset : array_like Offset is added to the linear prediction with coefficient equal to 1. exposure : array_like Log(exposure) is added to the linear prediction with coefficient equal to 1. """ + base._missing_param_doc + _check_rank_doc} def __init__(self, endog, exog, p=2, offset=None, exposure=None, missing='none', check_rank=True, **kwargs): super().__init__(endog, exog, offset=offset, exposure=exposure, missing=missing, check_rank=check_rank, **kwargs) self.parameterization = p self.exog_names.append('alpha') self.k_extra = 1 self._transparams = False def _get_init_kwds(self): kwds = super()._get_init_kwds() kwds['p'] = self.parameterization return kwds def loglike(self, params): """ Loglikelihood of Generalized Negative Binomial (NB-P) model Parameters ---------- params : array_like The parameters of the model. Returns ------- loglike : float The log-likelihood function of the model evaluated at `params`. See notes. """ return np.sum(self.loglikeobs(params)) def loglikeobs(self, params): """ Loglikelihood for observations of Generalized Negative Binomial (NB-P) model Parameters ---------- params : array_like The parameters of the model. Returns ------- loglike : ndarray The log likelihood for each observation of the model evaluated at `params`. See Notes """ if self._transparams: alpha = np.exp(params[-1]) else: alpha = params[-1] params = params[:-1] p = self.parameterization y = self.endog mu = self.predict(params) mu_p = mu**(2 - p) a1 = mu_p / alpha a2 = mu + a1 llf = (gammaln(y + a1) - gammaln(y + 1) - gammaln(a1) + a1 * np.log(a1) + y * np.log(mu) - (y + a1) * np.log(a2)) return llf def score_obs(self, params): """ Generalized Negative Binomial (NB-P) model score (gradient) vector of the log-likelihood for each observations. Parameters ---------- params : array_like The parameters of the model Returns ------- score : ndarray, 1-D The score vector of the model, i.e. the first derivative of the loglikelihood function, evaluated at `params` """ if self._transparams: alpha = np.exp(params[-1]) else: alpha = params[-1] params = params[:-1] p = 2 - self.parameterization y = self.endog mu = self.predict(params) mu_p = mu**p a1 = mu_p / alpha a2 = mu + a1 a3 = y + a1 a4 = p * a1 / mu dgpart = digamma(a3) - digamma(a1) dgterm = dgpart + np.log(a1 / a2) + 1 - a3 / a2 # TODO: better name/interpretation for dgterm? dparams = (a4 * dgterm - a3 / a2 + y / mu) dparams = (self.exog.T * mu * dparams).T dalpha = -a1 / alpha * dgterm return np.concatenate((dparams, np.atleast_2d(dalpha).T), axis=1) def score(self, params): """ Generalized Negative Binomial (NB-P) model score (gradient) vector of the log-likelihood Parameters ---------- params : array_like The parameters of the model Returns ------- score : ndarray, 1-D The score vector of the model, i.e. the first derivative of the loglikelihood function, evaluated at `params` """ score = np.sum(self.score_obs(params), axis=0) if self._transparams: score[-1] == score[-1] ** 2 return score else: return score def hessian(self, params): """ Generalized Negative Binomial (NB-P) model hessian maxtrix of the log-likelihood Parameters ---------- params : array_like The parameters of the model Returns ------- hessian : ndarray, 2-D The hessian matrix of the model. """ if self._transparams: alpha = np.exp(params[-1]) else: alpha = params[-1] params = params[:-1] p = 2 - self.parameterization y = self.endog exog = self.exog mu = self.predict(params) mu_p = mu**p a1 = mu_p / alpha a2 = mu + a1 a3 = y + a1 a4 = p * a1 / mu prob = a1 / a2 lprob = np.log(prob) dgpart = digamma(a3) - digamma(a1) pgpart = polygamma(1, a3) - polygamma(1, a1) dim = exog.shape[1] hess_arr = np.zeros((dim + 1, dim + 1)) coeff = mu**2 * (((1 + a4)**2 * a3 / a2**2 - a3 / a2 * (p - 1) * a4 / mu - y / mu**2 - 2 * a4 * (1 + a4) / a2 + p * a4 / mu * (lprob + dgpart + 2) - a4 / mu * (lprob + dgpart + 1) + a4**2 * pgpart) + (-(1 + a4) * a3 / a2 + y / mu + a4 * (lprob + dgpart + 1)) / mu) for i in range(dim): hess_arr[i, :-1] = np.sum(self.exog[:, :].T * self.exog[:, i] * coeff, axis=1) hess_arr[-1,:-1] = (self.exog[:, :].T * mu * a1 * ((1 + a4) * (1 - a3 / a2) / a2 - p * (lprob + dgpart + 2) / mu + p / mu * (a3 + p * a1) / a2 - a4 * pgpart) / alpha).sum(axis=1) da2 = (a1 * (2 * lprob + 2 * dgpart + 3 - 2 * a3 / a2 + a1 * pgpart - 2 * prob + prob * a3 / a2) / alpha**2) hess_arr[-1, -1] = da2.sum() tri_idx = np.triu_indices(dim + 1, k=1) hess_arr[tri_idx] = hess_arr.T[tri_idx] return hess_arr @Appender(_get_start_params_null_docs) def _get_start_params_null(self): offset = getattr(self, "offset", 0) exposure = getattr(self, "exposure", 0) q = self.parameterization - 1 const = (self.endog / np.exp(offset + exposure)).mean() params = [np.log(const)] mu = const * np.exp(offset + exposure) resid = self.endog - mu a = self._estimate_dispersion(mu, resid, df_resid=resid.shape[0] - 1) params.append(a) return np.array(params) def _estimate_dispersion(self, mu, resid, df_resid=None): q = self.parameterization - 1 if df_resid is None: df_resid = resid.shape[0] a = ((resid**2 / mu - 1) * mu**(-q)).sum() / df_resid return a @Appender(DiscreteModel.fit.__doc__) def fit(self, start_params=None, method='bfgs', maxiter=35, full_output=1, disp=1, callback=None, use_transparams=False, cov_type='nonrobust', cov_kwds=None, use_t=None, **kwargs): # TODO: Fix doc string """ use_transparams : bool This parameter enable internal transformation to impose non-negativity. True to enable. Default is False. use_transparams=True imposes the no underdispersion (alpha > 0) constraint. In case use_transparams=True and method="newton" or "ncg" transformation is ignored. """ if use_transparams and method not in ['newton', 'ncg']: self._transparams = True else: if use_transparams: warnings.warn('Parameter "use_transparams" is ignored', RuntimeWarning) self._transparams = False if start_params is None: offset = getattr(self, "offset", 0) + getattr(self, "exposure", 0) if np.size(offset) == 1 and offset == 0: offset = None optim_kwds_prelim = {'disp': 0, 'skip_hessian': True, 'warn_convergence': False} optim_kwds_prelim.update(kwargs.get('optim_kwds_prelim', {})) mod_poi = Poisson(self.endog, self.exog, offset=offset) with warnings.catch_warnings(): warnings.simplefilter("always") res_poi = mod_poi.fit(**optim_kwds_prelim) start_params = res_poi.params a = self._estimate_dispersion(res_poi.predict(), res_poi.resid, df_resid=res_poi.df_resid) start_params = np.append(start_params, max(0.05, a)) if callback is None: # work around perfect separation callback #3895 callback = lambda *x: x mlefit = super(NegativeBinomialP, self).fit(start_params=start_params, maxiter=maxiter, method=method, disp=disp, full_output=full_output, callback=callback, **kwargs) if use_transparams and method not in ["newton", "ncg"]: self._transparams = False mlefit._results.params[-1] = np.exp(mlefit._results.params[-1]) nbinfit = NegativeBinomialResults(self, mlefit._results) result = NegativeBinomialResultsWrapper(nbinfit) if cov_kwds is None: cov_kwds = {} result._get_robustcov_results(cov_type=cov_type, use_self=True, use_t=use_t, **cov_kwds) return result @Appender(DiscreteModel.fit_regularized.__doc__) def fit_regularized(self, start_params=None, method='l1', maxiter='defined_by_method', full_output=1, disp=1, callback=None, alpha=0, trim_mode='auto', auto_trim_tol=0.01, size_trim_tol=1e-4, qc_tol=0.03, **kwargs): _validate_l1_method(method) if np.size(alpha) == 1 and alpha != 0: k_params = self.exog.shape[1] + self.k_extra alpha = alpha * np.ones(k_params) alpha[-1] = 0 alpha_p = alpha[:-1] if (self.k_extra and np.size(alpha) > 1) else alpha self._transparams = False if start_params is None: offset = getattr(self, "offset", 0) + getattr(self, "exposure", 0) if np.size(offset) == 1 and offset == 0: offset = None mod_poi = Poisson(self.endog, self.exog, offset=offset) with warnings.catch_warnings(): warnings.simplefilter("always") start_params = mod_poi.fit_regularized( start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=0, callback=callback, alpha=alpha_p, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol, size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs).params start_params = np.append(start_params, 0.1) cntfit = super(CountModel, self).fit_regularized( start_params=start_params, method=method, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, alpha=alpha, trim_mode=trim_mode, auto_trim_tol=auto_trim_tol, size_trim_tol=size_trim_tol, qc_tol=qc_tol, **kwargs) discretefit = L1NegativeBinomialResults(self, cntfit) return L1NegativeBinomialResultsWrapper(discretefit) def predict(self, params, exog=None, exposure=None, offset=None, which='mean'): """ Predict response variable of a model given exogenous variables. Parameters ---------- params : array_like 2d array of fitted parameters of the model. Should be in the order returned from the model. exog : array_like, optional 1d or 2d array of exogenous values. If not supplied, the whole exog attribute of the model is used. If a 1d array is given it assumed to be 1 row of exogenous variables. If you only have one regressor and would like to do prediction, you must provide a 2d array with shape[1] == 1. linear : bool, optional If True, returns the linear predictor dot(exog,params). Else, returns the value of the cdf at the linear predictor. offset : array_like, optional Offset is added to the linear prediction with coefficient equal to 1. exposure : array_like, optional Log(exposure) is added to the linear prediction with coefficient equal to 1. which : 'mean', 'linear', 'prob', optional. 'mean' returns the exp of linear predictor exp(dot(exog,params)). 'linear' returns the linear predictor dot(exog,params). 'prob' return probabilities for counts from 0 to max(endog). Default is 'mean'. Notes ----- """ if exog is None: exog = self.exog if exposure is None: exposure = getattr(self, 'exposure', 0) elif exposure != 0: exposure = np.log(exposure) if offset is None: offset = getattr(self, 'offset', 0) fitted = np.dot(exog, params[:exog.shape[1]]) linpred = fitted + exposure + offset if which == 'mean': return np.exp(linpred) elif which == 'linear': return linpred elif which =='prob': counts = np.atleast_2d(np.arange(0, np.max(self.endog)+1)) mu = self.predict(params, exog, exposure, offset) size, prob = self.convert_params(params, mu) return nbinom.pmf(counts, size[:,None], prob[:,None]) else: raise ValueError('keyword "which" = %s not recognized' % which) def convert_params(self, params, mu): alpha = params[-1] p = 2 - self.parameterization size = 1. / alpha * mu**p prob = size / (size + mu) return (size, prob) ### Results Class ### class DiscreteResults(base.LikelihoodModelResults): __doc__ = _discrete_results_docs % {"one_line_description" : "A results class for the discrete dependent variable models.", "extra_attr" : ""} def __init__(self, model, mlefit, cov_type='nonrobust', cov_kwds=None, use_t=None): #super(DiscreteResults, self).__init__(model, params, # np.linalg.inv(-hessian), scale=1.) self.model = model self.df_model = model.df_model self.df_resid = model.df_resid self._cache = {} self.nobs = model.exog.shape[0] self.__dict__.update(mlefit.__dict__) if not hasattr(self, 'cov_type'): # do this only if super, i.e. mlefit did not already add cov_type # robust covariance if use_t is not None: self.use_t = use_t if cov_type == 'nonrobust': self.cov_type = 'nonrobust' self.cov_kwds = {'description' : 'Standard Errors assume that the ' + 'covariance matrix of the errors is correctly ' + 'specified.'} else: if cov_kwds is None: cov_kwds = {} from statsmodels.base.covtype import get_robustcov_results get_robustcov_results(self, cov_type=cov_type, use_self=True, **cov_kwds) def __getstate__(self): # remove unpicklable methods mle_settings = getattr(self, 'mle_settings', None) if mle_settings is not None: if 'callback' in mle_settings: mle_settings['callback'] = None if 'cov_params_func' in mle_settings: mle_settings['cov_params_func'] = None return self.__dict__ @cache_readonly def prsquared(self): """ McFadden's pseudo-R-squared. `1 - (llf / llnull)` """ return 1 - self.llf/self.llnull @cache_readonly def llr(self): """ Likelihood ratio chi-squared statistic; `-2*(llnull - llf)` """ return -2*(self.llnull - self.llf) @cache_readonly def llr_pvalue(self): """ The chi-squared probability of getting a log-likelihood ratio statistic greater than llr. llr has a chi-squared distribution with degrees of freedom `df_model`. """ return stats.distributions.chi2.sf(self.llr, self.df_model) def set_null_options(self, llnull=None, attach_results=True, **kwargs): """ Set the fit options for the Null (constant-only) model. This resets the cache for related attributes which is potentially fragile. This only sets the option, the null model is estimated when llnull is accessed, if llnull is not yet in cache. Parameters ---------- llnull : {None, float} If llnull is not None, then the value will be directly assigned to the cached attribute "llnull". attach_results : bool Sets an internal flag whether the results instance of the null model should be attached. By default without calling this method, thenull model results are not attached and only the loglikelihood value llnull is stored. **kwargs Additional keyword arguments used as fit keyword arguments for the null model. The override and model default values. Notes ----- Modifies attributes of this instance, and so has no return. """ # reset cache, note we need to add here anything that depends on # llnullor the null model. If something is missing, then the attribute # might be incorrect. self._cache.pop('llnull', None) self._cache.pop('llr', None) self._cache.pop('llr_pvalue', None) self._cache.pop('prsquared', None) if hasattr(self, 'res_null'): del self.res_null if llnull is not None: self._cache['llnull'] = llnull self._attach_nullmodel = attach_results self._optim_kwds_null = kwargs @cache_readonly def llnull(self): """ Value of the constant-only loglikelihood """ model = self.model kwds = model._get_init_kwds().copy() for key in getattr(model, '_null_drop_keys', []): del kwds[key] # TODO: what parameters to pass to fit? mod_null = model.__class__(model.endog, np.ones(self.nobs), **kwds) # TODO: consider catching and warning on convergence failure? # in the meantime, try hard to converge. see # TestPoissonConstrained1a.test_smoke optim_kwds = getattr(self, '_optim_kwds_null', {}).copy() if 'start_params' in optim_kwds: # user provided sp_null = optim_kwds.pop('start_params') elif hasattr(model, '_get_start_params_null'): # get moment estimates if available sp_null = model._get_start_params_null() else: sp_null = None opt_kwds = dict(method='bfgs', warn_convergence=False, maxiter=10000, disp=0) opt_kwds.update(optim_kwds) if optim_kwds: res_null = mod_null.fit(start_params=sp_null, **opt_kwds) else: # this should be a reasonably method case across versions res_null = mod_null.fit(start_params=sp_null, method='nm', warn_convergence=False, maxiter=10000, disp=0) res_null = mod_null.fit(start_params=res_null.params, method='bfgs', warn_convergence=False, maxiter=10000, disp=0) if getattr(self, '_attach_nullmodel', False) is not False: self.res_null = res_null return res_null.llf @cache_readonly def fittedvalues(self): """ Linear predictor XB. """ return np.dot(self.model.exog, self.params[:self.model.exog.shape[1]]) @cache_readonly def resid_response(self): """ Respnose residuals. The response residuals are defined as `endog - fittedvalues` """ return self.model.endog - self.predict() @cache_readonly def aic(self): """ Akaike information criterion. `-2*(llf - p)` where `p` is the number of regressors including the intercept. """ return -2*(self.llf - (self.df_model+1)) @cache_readonly def bic(self): """ Bayesian information criterion. `-2*llf + ln(nobs)*p` where `p` is the number of regressors including the intercept. """ return -2*self.llf + np.log(self.nobs)*(self.df_model+1) def _get_endog_name(self, yname, yname_list): if yname is None: yname = self.model.endog_names if yname_list is None: yname_list = self.model.endog_names return yname, yname_list def get_margeff(self, at='overall', method='dydx', atexog=None, dummy=False, count=False): """Get marginal effects of the fitted model. Parameters ---------- at : str, optional Options are: - 'overall', The average of the marginal effects at each observation. - 'mean', The marginal effects at the mean of each regressor. - 'median', The marginal effects at the median of each regressor. - 'zero', The marginal effects at zero for each regressor. - 'all', The marginal effects at each observation. If `at` is all only margeff will be available from the returned object. Note that if `exog` is specified, then marginal effects for all variables not specified by `exog` are calculated using the `at` option. method : str, optional Options are: - 'dydx' - dy/dx - No transformation is made and marginal effects are returned. This is the default. - 'eyex' - estimate elasticities of variables in `exog` -- d(lny)/d(lnx) - 'dyex' - estimate semi-elasticity -- dy/d(lnx) - 'eydx' - estimate semi-elasticity -- d(lny)/dx Note that tranformations are done after each observation is calculated. Semi-elasticities for binary variables are computed using the midpoint method. 'dyex' and 'eyex' do not make sense for discrete variables. For interpretations of these methods see notes below. atexog : array_like, optional Optionally, you can provide the exogenous variables over which to get the marginal effects. This should be a dictionary with the key as the zero-indexed column number and the value of the dictionary. Default is None for all independent variables less the constant. dummy : bool, optional If False, treats binary variables (if present) as continuous. This is the default. Else if True, treats binary variables as changing from 0 to 1. Note that any variable that is either 0 or 1 is treated as binary. Each binary variable is treated separately for now. count : bool, optional If False, treats count variables (if present) as continuous. This is the default. Else if True, the marginal effect is the change in probabilities when each observation is increased by one. Returns ------- DiscreteMargins : marginal effects instance Returns an object that holds the marginal effects, standard errors, confidence intervals, etc. See `statsmodels.discrete.discrete_margins.DiscreteMargins` for more information. Notes ----- Interpretations of methods: - 'dydx' - change in `endog` for a change in `exog`. - 'eyex' - proportional change in `endog` for a proportional change in `exog`. - 'dyex' - change in `endog` for a proportional change in `exog`. - 'eydx' - proportional change in `endog` for a change in `exog`. When using after Poisson, returns the expected number of events per period, assuming that the model is loglinear. """ from statsmodels.discrete.discrete_margins import DiscreteMargins return DiscreteMargins(self, (at, method, atexog, dummy, count)) def summary(self, yname=None, xname=None, title=None, alpha=.05, yname_list=None): """ Summarize the Regression Results. Parameters ---------- yname : str, optional The name of the endog variable in the tables. The default is `y`. xname : list[str], optional The names for the exogenous variables, default is "var_xx". Must match the number of parameters in the model. title : str, optional Title for the top table. If not None, then this replaces the default title. alpha : float The significance level for the confidence intervals. Returns ------- Summary Class that holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : Class that hold summary results. """ top_left = [('Dep. Variable:', None), ('Model:', [self.model.__class__.__name__]), ('Method:', ['MLE']), ('Date:', None), ('Time:', None), ('converged:', ["%s" % self.mle_retvals['converged']]), ] top_right = [('No. Observations:', None), ('Df Residuals:', None), ('Df Model:', None), ('Pseudo R-squ.:', ["%#6.4g" % self.prsquared]), ('Log-Likelihood:', None), ('LL-Null:', ["%#8.5g" % self.llnull]), ('LLR p-value:', ["%#6.4g" % self.llr_pvalue]) ] if hasattr(self, 'cov_type'): top_left.append(('Covariance Type:', [self.cov_type])) if title is None: title = self.model.__class__.__name__ + ' ' + "Regression Results" # boiler plate from statsmodels.iolib.summary import Summary smry = Summary() yname, yname_list = self._get_endog_name(yname, yname_list) # for top of table smry.add_table_2cols(self, gleft=top_left, gright=top_right, yname=yname, xname=xname, title=title) # for parameters, etc smry.add_table_params(self, yname=yname_list, xname=xname, alpha=alpha, use_t=self.use_t) if hasattr(self, 'constraints'): smry.add_extra_txt(['Model has been estimated subject to linear ' 'equality constraints.']) return smry def summary2(self, yname=None, xname=None, title=None, alpha=.05, float_format="%.4f"): """ Experimental function to summarize regression results. Parameters ---------- yname : str Name of the dependent variable (optional). xname : list[str], optional List of strings of length equal to the number of parameters Names of the independent variables (optional). title : str, optional Title for the top table. If not None, then this replaces the default title. alpha : float The significance level for the confidence intervals. float_format : str The print format for floats in parameters summary. Returns ------- Summary Instance that contains the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary2.Summary : Class that holds summary results. """ from statsmodels.iolib import summary2 smry = summary2.Summary() smry.add_base(results=self, alpha=alpha, float_format=float_format, xname=xname, yname=yname, title=title) if hasattr(self, 'constraints'): smry.add_text('Model has been estimated subject to linear ' 'equality constraints.') return smry class CountResults(DiscreteResults): __doc__ = _discrete_results_docs % { "one_line_description": "A results class for count data", "extra_attr": ""} @cache_readonly def resid(self): """ Residuals Notes ----- The residuals for Count models are defined as .. math:: y - p where :math:`p = \\exp(X\\beta)`. Any exposure and offset variables are also handled. """ return self.model.endog - self.predict() class NegativeBinomialResults(CountResults): __doc__ = _discrete_results_docs % { "one_line_description": "A results class for NegativeBinomial 1 and 2", "extra_attr": ""} @cache_readonly def lnalpha(self): """Natural log of alpha""" return np.log(self.params[-1]) @cache_readonly def lnalpha_std_err(self): """Natural log of standardized error""" return self.bse[-1] / self.params[-1] @cache_readonly def aic(self): # + 1 because we estimate alpha k_extra = getattr(self.model, 'k_extra', 0) return -2*(self.llf - (self.df_model + self.k_constant + k_extra)) @cache_readonly def bic(self): # + 1 because we estimate alpha k_extra = getattr(self.model, 'k_extra', 0) return -2*self.llf + np.log(self.nobs)*(self.df_model + self.k_constant + k_extra) class GeneralizedPoissonResults(NegativeBinomialResults): __doc__ = _discrete_results_docs % { "one_line_description": "A results class for Generalized Poisson", "extra_attr": ""} @cache_readonly def _dispersion_factor(self): p = getattr(self.model, 'parameterization', 0) mu = self.predict() return (1 + self.params[-1] * mu**p)**2 class L1CountResults(DiscreteResults): __doc__ = _discrete_results_docs % {"one_line_description" : "A results class for count data fit by l1 regularization", "extra_attr" : _l1_results_attr} def __init__(self, model, cntfit): super(L1CountResults, self).__init__(model, cntfit) # self.trimmed is a boolean array with T/F telling whether or not that # entry in params has been set zero'd out. self.trimmed = cntfit.mle_retvals['trimmed'] self.nnz_params = (~self.trimmed).sum() # Set degrees of freedom. In doing so, # adjust for extra parameter in NegativeBinomial nb1 and nb2 # extra parameter is not included in df_model k_extra = getattr(self.model, 'k_extra', 0) self.df_model = self.nnz_params - 1 - k_extra self.df_resid = float(self.model.endog.shape[0] - self.nnz_params) + k_extra class PoissonResults(CountResults): def predict_prob(self, n=None, exog=None, exposure=None, offset=None, transform=True): """ Return predicted probability of each count level for each observation Parameters ---------- n : array_like or int The counts for which you want the probabilities. If n is None then the probabilities for each count from 0 to max(y) are given. Returns ------- ndarray A nobs x n array where len(`n`) columns are indexed by the count n. If n is None, then column 0 is the probability that each observation is 0, column 1 is the probability that each observation is 1, etc. """ if n is not None: counts = np.atleast_2d(n) else: counts = np.atleast_2d(np.arange(0, np.max(self.model.endog)+1)) mu = self.predict(exog=exog, exposure=exposure, offset=offset, transform=transform, linear=False)[:,None] # uses broadcasting return stats.poisson.pmf(counts, mu) @property def resid_pearson(self): """ Pearson residuals Notes ----- Pearson residuals are defined to be .. math:: r_j = \\frac{(y - M_jp_j)}{\\sqrt{M_jp_j(1-p_j)}} where :math:`p_j=cdf(X\\beta)` and :math:`M_j` is the total number of observations sharing the covariate pattern :math:`j`. For now :math:`M_j` is always set to 1. """ # Pearson residuals p = self.predict() # fittedvalues is still linear return (self.model.endog - p)/np.sqrt(p) class L1PoissonResults(L1CountResults, PoissonResults): pass class L1NegativeBinomialResults(L1CountResults, NegativeBinomialResults): pass class L1GeneralizedPoissonResults(L1CountResults, GeneralizedPoissonResults): pass class OrderedResults(DiscreteResults): __doc__ = _discrete_results_docs % {"one_line_description" : "A results class for ordered discrete data." , "extra_attr" : ""} pass class BinaryResults(DiscreteResults): __doc__ = _discrete_results_docs % {"one_line_description" : "A results class for binary data", "extra_attr" : ""} def pred_table(self, threshold=.5): """ Prediction table Parameters ---------- threshold : scalar Number between 0 and 1. Threshold above which a prediction is considered 1 and below which a prediction is considered 0. Notes ----- pred_table[i,j] refers to the number of times "i" was observed and the model predicted "j". Correct predictions are along the diagonal. """ model = self.model actual = model.endog pred = np.array(self.predict() > threshold, dtype=float) bins = np.array([0, 0.5, 1]) return np.histogram2d(actual, pred, bins=bins)[0] @Appender(DiscreteResults.summary.__doc__) def summary(self, yname=None, xname=None, title=None, alpha=.05, yname_list=None): smry = super(BinaryResults, self).summary(yname, xname, title, alpha, yname_list) fittedvalues = self.model.cdf(self.fittedvalues) absprederror = np.abs(self.model.endog - fittedvalues) predclose_sum = (absprederror < 1e-4).sum() predclose_frac = predclose_sum / len(fittedvalues) # add warnings/notes etext = [] if predclose_sum == len(fittedvalues): # TODO: nobs? wstr = "Complete Separation: The results show that there is" wstr += "complete separation.\n" wstr += "In this case the Maximum Likelihood Estimator does " wstr += "not exist and the parameters\n" wstr += "are not identified." etext.append(wstr) elif predclose_frac > 0.1: # TODO: get better diagnosis wstr = "Possibly complete quasi-separation: A fraction " wstr += "%4.2f of observations can be\n" % predclose_frac wstr += "perfectly predicted. This might indicate that there " wstr += "is complete\nquasi-separation. In this case some " wstr += "parameters will not be identified." etext.append(wstr) if etext: smry.add_extra_txt(etext) return smry @cache_readonly def resid_dev(self): """ Deviance residuals Notes ----- Deviance residuals are defined .. math:: d_j = \\pm\\left(2\\left[Y_j\\ln\\left(\\frac{Y_j}{M_jp_j}\\right) + (M_j - Y_j\\ln\\left(\\frac{M_j-Y_j}{M_j(1-p_j)} \\right) \\right] \\right)^{1/2} where :math:`p_j = cdf(X\\beta)` and :math:`M_j` is the total number of observations sharing the covariate pattern :math:`j`. For now :math:`M_j` is always set to 1. """ #These are the deviance residuals #model = self.model endog = self.model.endog #exog = model.exog # M = # of individuals that share a covariate pattern # so M[i] = 2 for i = two share a covariate pattern M = 1 p = self.predict() #Y_0 = np.where(exog == 0) #Y_M = np.where(exog == M) #NOTE: Common covariate patterns are not yet handled res = -(1-endog)*np.sqrt(2*M*np.abs(np.log(1-p))) + \ endog*np.sqrt(2*M*np.abs(np.log(p))) return res @cache_readonly def resid_pearson(self): """ Pearson residuals Notes ----- Pearson residuals are defined to be .. math:: r_j = \\frac{(y - M_jp_j)}{\\sqrt{M_jp_j(1-p_j)}} where :math:`p_j=cdf(X\\beta)` and :math:`M_j` is the total number of observations sharing the covariate pattern :math:`j`. For now :math:`M_j` is always set to 1. """ # Pearson residuals #model = self.model endog = self.model.endog #exog = model.exog # M = # of individuals that share a covariate pattern # so M[i] = 2 for i = two share a covariate pattern # use unique row pattern? M = 1 p = self.predict() return (endog - M*p)/np.sqrt(M*p*(1-p)) @cache_readonly def resid_response(self): """ The response residuals Notes ----- Response residuals are defined to be .. math:: y - p where :math:`p=cdf(X\\beta)`. """ return self.model.endog - self.predict() class LogitResults(BinaryResults): __doc__ = _discrete_results_docs % { "one_line_description": "A results class for Logit Model", "extra_attr": ""} @cache_readonly def resid_generalized(self): """ Generalized residuals Notes ----- The generalized residuals for the Logit model are defined .. math:: y - p where :math:`p=cdf(X\\beta)`. This is the same as the `resid_response` for the Logit model. """ # Generalized residuals return self.model.endog - self.predict() class ProbitResults(BinaryResults): __doc__ = _discrete_results_docs % { "one_line_description": "A results class for Probit Model", "extra_attr": ""} @cache_readonly def resid_generalized(self): """ Generalized residuals Notes ----- The generalized residuals for the Probit model are defined .. math:: y\\frac{\\phi(X\\beta)}{\\Phi(X\\beta)}-(1-y)\\frac{\\phi(X\\beta)}{1-\\Phi(X\\beta)} """ # generalized residuals model = self.model endog = model.endog XB = self.predict(linear=True) pdf = model.pdf(XB) cdf = model.cdf(XB) return endog * pdf/cdf - (1-endog)*pdf/(1-cdf) class L1BinaryResults(BinaryResults): __doc__ = _discrete_results_docs % {"one_line_description" : "Results instance for binary data fit by l1 regularization", "extra_attr" : _l1_results_attr} def __init__(self, model, bnryfit): super(L1BinaryResults, self).__init__(model, bnryfit) # self.trimmed is a boolean array with T/F telling whether or not that # entry in params has been set zero'd out. self.trimmed = bnryfit.mle_retvals['trimmed'] self.nnz_params = (~self.trimmed).sum() self.df_model = self.nnz_params - 1 self.df_resid = float(self.model.endog.shape[0] - self.nnz_params) class MultinomialResults(DiscreteResults): __doc__ = _discrete_results_docs % {"one_line_description" : "A results class for multinomial data", "extra_attr" : ""} def __init__(self, model, mlefit): super(MultinomialResults, self).__init__(model, mlefit) self.J = model.J self.K = model.K @staticmethod def _maybe_convert_ynames_int(ynames): # see if they're integers issue_warning = False msg = ('endog contains values are that not int-like. Uses string ' 'representation of value. Use integer-valued endog to ' 'suppress this warning.') for i in ynames: try: if ynames[i] % 1 == 0: ynames[i] = str(int(ynames[i])) else: issue_warning = True ynames[i] = str(ynames[i]) except TypeError: ynames[i] = str(ynames[i]) if issue_warning: import warnings warnings.warn(msg, SpecificationWarning) return ynames def _get_endog_name(self, yname, yname_list, all=False): """ If all is False, the first variable name is dropped """ model = self.model if yname is None: yname = model.endog_names if yname_list is None: ynames = model._ynames_map ynames = self._maybe_convert_ynames_int(ynames) # use range below to ensure sortedness ynames = [ynames[key] for key in range(int(model.J))] ynames = ['='.join([yname, name]) for name in ynames] if not all: yname_list = ynames[1:] # assumes first variable is dropped else: yname_list = ynames return yname, yname_list def pred_table(self): """ Returns the J x J prediction table. Notes ----- pred_table[i,j] refers to the number of times "i" was observed and the model predicted "j". Correct predictions are along the diagonal. """ ju = self.model.J - 1 # highest index # these are the actual, predicted indices #idx = lzip(self.model.endog, self.predict().argmax(1)) bins = np.concatenate(([0], np.linspace(0.5, ju - 0.5, ju), [ju])) return np.histogram2d(self.model.endog, self.predict().argmax(1), bins=bins)[0] @cache_readonly def bse(self): bse = np.sqrt(np.diag(self.cov_params())) return bse.reshape(self.params.shape, order='F') @cache_readonly def aic(self): return -2*(self.llf - (self.df_model+self.model.J-1)) @cache_readonly def bic(self): return -2*self.llf + np.log(self.nobs)*(self.df_model+self.model.J-1) def conf_int(self, alpha=.05, cols=None): confint = super(DiscreteResults, self).conf_int(alpha=alpha, cols=cols) return confint.transpose(2,0,1) def margeff(self): raise NotImplementedError("Use get_margeff instead") @cache_readonly def resid_misclassified(self): """ Residuals indicating which observations are misclassified. Notes ----- The residuals for the multinomial model are defined as .. math:: argmax(y_i) \\neq argmax(p_i) where :math:`argmax(y_i)` is the index of the category for the endogenous variable and :math:`argmax(p_i)` is the index of the predicted probabilities for each category. That is, the residual is a binary indicator that is 0 if the category with the highest predicted probability is the same as that of the observed variable and 1 otherwise. """ # it's 0 or 1 - 0 for correct prediction and 1 for a missed one return (self.model.wendog.argmax(1) != self.predict().argmax(1)).astype(float) def summary2(self, alpha=0.05, float_format="%.4f"): """Experimental function to summarize regression results Parameters ---------- alpha : float significance level for the confidence intervals float_format : str print format for floats in parameters summary Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary2.Summary : class to hold summary results """ from statsmodels.iolib import summary2 smry = summary2.Summary() smry.add_dict(summary2.summary_model(self)) # One data frame per value of endog eqn = self.params.shape[1] confint = self.conf_int(alpha) for i in range(eqn): coefs = summary2.summary_params((self, self.params[:, i], self.bse[:, i], self.tvalues[:, i], self.pvalues[:, i], confint[i]), alpha=alpha) # Header must show value of endog level_str = self.model.endog_names + ' = ' + str(i) coefs[level_str] = coefs.index coefs = coefs.iloc[:, [-1, 0, 1, 2, 3, 4, 5]] smry.add_df(coefs, index=False, header=True, float_format=float_format) smry.add_title(results=self) return smry class L1MultinomialResults(MultinomialResults): __doc__ = _discrete_results_docs % {"one_line_description" : "A results class for multinomial data fit by l1 regularization", "extra_attr" : _l1_results_attr} def __init__(self, model, mlefit): super(L1MultinomialResults, self).__init__(model, mlefit) # self.trimmed is a boolean array with T/F telling whether or not that # entry in params has been set zero'd out. self.trimmed = mlefit.mle_retvals['trimmed'] self.nnz_params = (~self.trimmed).sum() # Note: J-1 constants self.df_model = self.nnz_params - (self.model.J - 1) self.df_resid = float(self.model.endog.shape[0] - self.nnz_params) #### Results Wrappers #### class OrderedResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(OrderedResultsWrapper, OrderedResults) class CountResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(CountResultsWrapper, CountResults) class NegativeBinomialResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(NegativeBinomialResultsWrapper, NegativeBinomialResults) class GeneralizedPoissonResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(GeneralizedPoissonResultsWrapper, GeneralizedPoissonResults) class PoissonResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(PoissonResultsWrapper, PoissonResults) class L1CountResultsWrapper(lm.RegressionResultsWrapper): pass class L1PoissonResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(L1PoissonResultsWrapper, L1PoissonResults) class L1NegativeBinomialResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(L1NegativeBinomialResultsWrapper, L1NegativeBinomialResults) class L1GeneralizedPoissonResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(L1GeneralizedPoissonResultsWrapper, L1GeneralizedPoissonResults) class BinaryResultsWrapper(lm.RegressionResultsWrapper): _attrs = {"resid_dev": "rows", "resid_generalized": "rows", "resid_pearson": "rows", "resid_response": "rows" } _wrap_attrs = wrap.union_dicts(lm.RegressionResultsWrapper._wrap_attrs, _attrs) wrap.populate_wrapper(BinaryResultsWrapper, BinaryResults) class L1BinaryResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(L1BinaryResultsWrapper, L1BinaryResults) class MultinomialResultsWrapper(lm.RegressionResultsWrapper): _attrs = {"resid_misclassified": "rows"} _wrap_attrs = wrap.union_dicts(lm.RegressionResultsWrapper._wrap_attrs, _attrs) _methods = {'conf_int': 'multivariate_confint'} _wrap_methods = wrap.union_dicts(lm.RegressionResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(MultinomialResultsWrapper, MultinomialResults) class L1MultinomialResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(L1MultinomialResultsWrapper, L1MultinomialResults) statsmodels-0.12.2/statsmodels/discrete/tests/000077500000000000000000000000001400612667500214535ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/discrete/tests/__init__.py000066400000000000000000000000001400612667500235520ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/discrete/tests/results/000077500000000000000000000000001400612667500231545ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/discrete/tests/results/__init__.py000066400000000000000000000000001400612667500252530ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/discrete/tests/results/mn_logit_summary.txt000066400000000000000000000074371400612667500273150ustar00rootroot00000000000000============================================================================== y=1 coef std err z P>|z| [0.025 0.975] ------------------------------------------------------------------------------ const -0.2794 0.612 -0.457 0.648 -1.479 0.920 x1 -0.0119 0.034 -0.350 0.727 -0.079 0.055 x2 0.2946 0.093 3.152 0.002 0.111 0.478 x3 -0.0257 0.007 -3.873 0.000 -0.039 -0.013 x4 0.0897 0.069 1.297 0.195 -0.046 0.225 ------------------------------------------------------------------------------ y=2 coef std err z P>|z| [0.025 0.975] ------------------------------------------------------------------------------ const -1.7392 0.720 -2.414 0.016 -3.151 -0.327 x1 -0.0941 0.039 -2.415 0.016 -0.170 -0.018 x2 0.3838 0.108 3.559 0.000 0.172 0.595 x3 -0.0230 0.008 -2.914 0.004 -0.038 -0.008 x4 0.2451 0.080 3.053 0.002 0.088 0.402 ------------------------------------------------------------------------------ y=3 coef std err z P>|z| [0.025 0.975] ------------------------------------------------------------------------------ const -3.0091 1.069 -2.815 0.005 -5.104 -0.914 x1 -0.1115 0.057 -1.965 0.049 -0.223 -0.000 x2 0.5641 0.159 3.557 0.000 0.253 0.875 x3 -0.0156 0.011 -1.391 0.164 -0.038 0.006 x4 0.0687 0.119 0.577 0.564 -0.165 0.302 ------------------------------------------------------------------------------ y=4 coef std err z P>|z| [0.025 0.975] ------------------------------------------------------------------------------ const -6.5607 0.870 -7.540 0.000 -8.266 -4.855 x1 -0.0949 0.043 -2.183 0.029 -0.180 -0.010 x2 1.2668 0.128 9.897 0.000 1.016 1.518 x3 -0.0109 0.008 -1.315 0.189 -0.027 0.005 x4 0.3067 0.088 3.475 0.001 0.134 0.480 ------------------------------------------------------------------------------ y=5 coef std err z P>|z| [0.025 0.975] ------------------------------------------------------------------------------ const -6.0760 0.774 -7.851 0.000 -7.593 -4.559 x1 -0.0967 0.039 -2.479 0.013 -0.173 -0.020 x2 1.3377 0.116 11.493 0.000 1.110 1.566 x3 -0.0198 0.008 -2.631 0.009 -0.035 -0.005 x4 0.3193 0.080 4.001 0.000 0.163 0.476 ------------------------------------------------------------------------------ y=6 coef std err z P>|z| [0.025 0.975] ------------------------------------------------------------------------------ const -10.5973 0.957 -11.076 0.000 -12.473 -8.722 x1 -0.1447 0.042 -3.475 0.001 -0.226 -0.063 x2 2.0395 0.141 14.479 0.000 1.763 2.316 x3 -0.0129 0.008 -1.612 0.107 -0.029 0.003 x4 0.4576 0.085 5.352 0.000 0.290 0.625 ============================================================================== 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3.667351615308579726e-02,1.212316575714769973e-01,2.003777703803729937e-01,2.207962929096410065e-01,1.824715992825579891e-01,1.206392882995020038e-01,6.646622423541169444e-02,3.138820357814629813e-02,1.296999969980200049e-02,4.763881487983540053e-03,1.574796501245009960e-03,4.732550407189550171e-04,1.303699487138589898e-04,3.315107642951420157e-05,7.827680508214350635e-06,1.725064447033169917e-06,3.564091411675569944e-07,6.930481446548139533e-08,1.272783077494139934e-08,2.214441867179409974e-09,3.660140699806459851e-10,5.761585062275659759e-11,8.657306423710390639e-12,1.244280932119739982e-12,1.713841664101940064e-13,2.266178840194519972e-14,2.881272435687100149e-15,3.527638328425570177e-16,4.164755530964130263e-17,4.747391064695470094e-18,5.231150871113779640e-19,5.578263743948540178e-20,5.762521491895889849e-21,5.772475663014290469e-22,5.612375057513309809e-23,5.300808730708199855e-24,4.867468228227479547e-25,4.348754525047629747e-26,3.783073589142530035e-27,3.206591777971869826e-28,2.650007942897260126e-29,2.136617648031550055e-30,1.681670915730689959e-31,1.292814010288440116e-32,9.712854114760189782e-34,7.135063528721190440e-35,5.127474449752560247e-36,3.606360514278259923e-37,2.483655718573480080e-38,1.675555457127449910e-39,1.107776874039400082e-40,7.180349945846680275e-42,4.564631883991050156e-43,2.847038776192090106e-44,1.742862456360189996e-45,1.047523844636680038e-46,6.183571442986500031e-48,3.586146436150379708e-49,2.043918234947270067e-50,1.145183280975199929e-51,6.309388078863389840e-53,3.419171605164850077e-54,1.823025321707859995e-55,9.565675496443530379e-57,4.940821478058910104e-58,2.512750094014659800e-59,1.258545307408900032e-60,6.209513052476710105e-62,3.018645569899840204e-63,1.446193900513559966e-64,6.829548253262870211e-66,3.179780351542369957e-67,1.459916837237680094e-68,6.611024239602200641e-70,2.953252104496869993e-71,1.301675561041950024e-72,5.661775582235429918e-74,2.430666739293579759e-75 statsmodels-0.12.2/statsmodels/discrete/tests/results/results_count_margins.py000066400000000000000000000413431400612667500301640ustar00rootroot00000000000000import numpy as np from statsmodels.tools.testing import MarginTableTestBunch est = dict( rank=7, N=17, ic=6, k=7, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=0, ll=-28.46285727296058, k_eq_model=1, ll_0=-101.6359341820935, df_m=6, chi2=146.3461538182658, p=4.58013206701e-29, r2_p=.719952814897477, properties="b V", depvar="sexecutions", which="max", technique="nr", singularHmethod="m-marquardt", ml_method="e2", crittype="log likelihood", user="poiss_lf", title="Poisson regression", vce="oim", opt="moptimize", chi2type="LR", gof="poiss_g", estat_cmd="poisson_estat", predict="poisso_p", cmd="poisson", cmdline="poisson sexecutions sincome sperpoverty sperblack LN_VC100k96 south sdegree", # noqa:E501 ) margins_table = np.array([ 47.514189267677, 12.722695157081, 3.7346009380122, .000188013074, 22.578164973516, 72.450213561838, np.nan, 1.9599639845401, 0, 2.3754103372885, 7.6314378245266, .31126642081184, .75559809249357, -12.58193294904, 17.332753623617, np.nan, 1.9599639845401, 0, -11.583732327397, 3.8511214886273, -3.007885459237, .00263072269737, -19.131791745195, -4.0356729095995, np.nan, 1.9599639845401, 0, -1.807106397978, 14.19277372084, -.12732580914219, .89868253380624, -29.624431731551, 26.010218935595, np.nan, 1.9599639845401, 0, 10.852916363139, 2.6197368291491, 4.1427506161617, .00003431650408, 5.7183265290336, 15.987506197244, np.nan, 1.9599639845401, 0, -26.588397789444, 7.6315578612519, -3.4840065780596, .00049396734722, -41.545976343431, -11.630819235457, np.nan, 1.9599639845401, 0]).reshape(6, 9) margins_table_colnames = 'b se z pvalue ll ul df crit eform'.split() margins_table_rownames = ['sincome', 'sperpoverty', 'sperblack', 'LN_VC100k96', 'south', 'sdegree'] margins_cov = np.array([ 10.87507957467, 3.4816608831283, .87483487811437, 3.1229403520191, -.87306122632875, -2.2870394487277, -12.321063650937, 3.4816608831283, 5.1715652306254, .27473956091394, 1.7908952063684, -.92880259796684, 1.8964947971413, -9.0063087868006, .87483487811437, .27473956091394, 1.1098392181639, -.99390727840297, -.34477731736542, -.98869834020742, .41772084541889, 3.1229403520191, 1.7908952063684, -.99390727840297, 17.912620004361, -.30763138390107, 2.8490197200257, -21.269786576194, -.87306122632875, -.92880259796684, -.34477731736542, -.30763138390107, .42666000427673, .05265352402592, 1.461997775289, -2.2870394487277, 1.8964947971413, -.98869834020742, 2.8490197200257, .05265352402592, 4.0773252373088, -4.46154120848, -12.321063650937, -9.0063087868006, .41772084541889, -21.269786576194, 1.461997775289, -4.46154120848, 37.559994394326]).reshape(7, 7) margins_cov_colnames = ['sincome', 'sperpoverty', 'sperblack', 'LN_VC100k96', 'south', 'sdegree', '_cons'] margins_cov_rownames = ['sincome', 'sperpoverty', 'sperblack', 'LN_VC100k96', 'south', 'sdegree', '_cons'] results_poisson_margins_cont = MarginTableTestBunch( margins_table=margins_table, margins_table_colnames=margins_table_colnames, margins_table_rownames=margins_table_rownames, margins_cov=margins_cov, margins_cov_colnames=margins_cov_colnames, margins_cov_rownames=margins_cov_rownames, **est ) est = dict( alpha=1.1399915663048, rank=8, N=17, ic=6, k=8, k_eq=2, k_dv=1, converged=1, rc=0, k_autoCns=0, ll=-27.58269157281191, k_eq_model=1, ll_0=-32.87628220135203, rank0=2, df_m=6, chi2=10.58718125708024, p=.1020042170100994, ll_c=-28.46285727296058, chi2_c=1.760331400297339, r2_p=.1610154881905236, k_aux=1, properties="b V", depvar="sexecutions", which="max", technique="nr", singularHmethod="m-marquardt", ml_method="e2", crittype="log likelihood", user="nbreg_lf", diparm1="lnalpha, exp label(", title="Negative binomial regression", vce="oim", opt="moptimize", chi2type="LR", chi2_ct="LR", diparm_opt2="noprob", dispers="mean", predict="nbreg_p", cmd="nbreg", cmdline="nbreg sexecutions sincome sperpoverty sperblack LN_VC100k96 south sdegree", # noqa:E501 ) margins_table = np.array([ 38.76996449636, 35.863089953808, 1.0810547709719, .27967275079666, -31.520400187424, 109.06032918014, np.nan, 1.9599639845401, 0, 2.5208248279391, 11.710699937092, .21525825454332, .82956597472339, -20.431725282518, 25.473374938396, np.nan, 1.9599639845401, 0, -8.225606184332, 9.557721280021, -.86062419517573, .38944505570119, -26.958395667445, 10.507183298781, np.nan, 1.9599639845401, 0, -4.4150939806524, 28.010544627225, -.15762256819387, .87475421903252, -59.314752637366, 50.484564676062, np.nan, 1.9599639845401, 0, 7.0049476220304, 6.3399264323903, 1.1048941492826, .26920545789466, -5.4210798500881, 19.430975094149, np.nan, 1.9599639845401, 0, -25.128303596214, 23.247820190364, -1.0808885904335, .279746674501, -70.693193888391, 20.436586695964, np.nan, 1.9599639845401, 0]).reshape(6, 9) margins_table_colnames = 'b se z pvalue ll ul df crit eform'.split() margins_table_rownames = ['sincome', 'sperpoverty', 'sperblack', 'LN_VC100k96', 'south', 'sdegree'] margins_cov = np.array([ 44.468037032422, 13.291812805254, .84306554343753, -.38095027773819, -2.1265212254924, -18.06714825989, -30.427077474507, .36347806905257, 13.291812805254, 15.093124820143, 3.3717840254072, -7.6860995498613, -3.3867901970823, -1.4200645173727, -12.979849717094, .51706617429388, .84306554343753, 3.3717840254072, 5.6928040093481, -12.140553562993, -2.5831646721297, -1.8071496111137, 7.961664784177, .27439267406128, -.38095027773819, -7.6860995498613, -12.140553562993, 91.950706114029, 6.6107070350689, 9.5470604840407, -82.665769963947, -1.1433180909155, -2.1265212254924, -3.3867901970823, -2.5831646721297, 6.6107070350689, 2.0499053083335, 1.7094543055869, -3.029543334606, -.34297224102579, -18.06714825989, -1.4200645173727, -1.8071496111137, 9.5470604840407, 1.7094543055869, 18.442703265156, -6.5839965105886, -.61952491151176, -30.427077474507, -12.979849717094, 7.961664784177, -82.665769963947, -3.029543334606, -6.5839965105886, 111.12618806587, .88600743091011, .36347806905257, .51706617429388, .27439267406128, -1.1433180909155, -.34297224102579, -.61952491151176, .88600743091011, .71851239110057 ]).reshape(8, 8) margins_cov_colnames = ['sincome', 'sperpoverty', 'sperblack', 'LN_VC100k96', 'south', 'sdegree', '_cons', '_cons'] margins_cov_rownames = ['sincome', 'sperpoverty', 'sperblack', 'LN_VC100k96', 'south', 'sdegree', '_cons', '_cons'] results_negbin_margins_cont = MarginTableTestBunch( margins_table=margins_table, margins_table_colnames=margins_table_colnames, margins_table_rownames=margins_table_rownames, margins_cov=margins_cov, margins_cov_colnames=margins_cov_colnames, margins_cov_rownames=margins_cov_rownames, **est ) est = dict( rank=7, N=17, ic=6, k=8, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=1, ll=-28.46285727296058, k_eq_model=1, ll_0=-101.6359341820935, df_m=6, chi2=146.3461538182658, p=4.58013206701e-29, r2_p=.719952814897477, properties="b V", depvar="sexecutions", which="max", technique="nr", singularHmethod="m-marquardt", ml_method="e2", crittype="log likelihood", user="poiss_lf", title="Poisson regression", vce="oim", opt="moptimize", chi2type="LR", gof="poiss_g", estat_cmd="poisson_estat", predict="poisso_p", cmd="poisson", cmdline="poisson sexecutions sincome sperpoverty sperblack LN_VC100k96 i.south sdegree", # noqa:E501 ) margins_table = np.array([ 47.514189267677, 12.72269515678, 3.7346009381004, .00018801307393, 22.578164974105, 72.450213561249, np.nan, 1.9599639845401, 0, 2.3754103372885, 7.6314378245485, .31126642081095, .75559809249425, -12.581932949083, 17.33275362366, np.nan, 1.9599639845401, 0, -11.583732327397, 3.8511214887188, -3.0078854591656, .00263072269799, -19.131791745374, -4.0356729094203, np.nan, 1.9599639845401, 0, -1.807106397978, 14.192773720841, -.12732580914219, .89868253380624, -29.624431731552, 26.010218935596, np.nan, 1.9599639845401, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, 1.9599639845401, 0, 12.894515685772, 5.7673506886042, 2.2357779822979, .02536631788468, 1.5907160498956, 24.198315321648, np.nan, 1.9599639845401, 0, -26.588397789444, 7.6315578608763, -3.4840065782311, .00049396734691, -41.545976342695, -11.630819236193, np.nan, 1.9599639845401, 0]).reshape(7, 9) margins_table_colnames = 'b se z pvalue ll ul df crit eform'.split() margins_table_rownames = ['sincome', 'sperpoverty', 'sperblack', 'LN_VC100k96', '0b.south', '1.south', 'sdegree'] margins_cov = np.array([ 10.875079574674, 3.4816608831298, .87483487811447, 3.1229403520208, 0, -.873061226329, -2.2870394487282, -12.321063650942, 3.4816608831298, 5.1715652306252, .27473956091396, 1.7908952063684, 0, -.92880259796679, 1.8964947971405, -9.0063087868012, .87483487811447, .27473956091396, 1.109839218164, -.9939072784041, 0, -.34477731736544, -.98869834020768, .41772084541996, 3.1229403520208, 1.7908952063684, -.9939072784041, 17.912620004373, 0, -.30763138390086, 2.8490197200274, -21.269786576207, 0, 0, 0, 0, 0, 0, 0, 0, -.873061226329, -.92880259796679, -.34477731736544, -.30763138390086, 0, .42666000427672, .05265352402609, 1.4619977752889, -2.2870394487282, 1.8964947971405, -.98869834020768, 2.8490197200274, 0, .05265352402609, 4.0773252373089, -4.4615412084808, -12.321063650942, -9.0063087868012, .41772084541996, -21.269786576207, 0, 1.4619977752889, -4.4615412084808, 37.559994394343 ]).reshape(8, 8) margins_cov_colnames = ['sincome', 'sperpoverty', 'sperblack', 'LN_VC100k96', '0b.south', '1.south', 'sdegree', '_cons'] margins_cov_rownames = ['sincome', 'sperpoverty', 'sperblack', 'LN_VC100k96', '0b.south', '1.south', 'sdegree', '_cons'] results_poisson_margins_dummy = MarginTableTestBunch( margins_table=margins_table, margins_table_colnames=margins_table_colnames, margins_table_rownames=margins_table_rownames, margins_cov=margins_cov, margins_cov_colnames=margins_cov_colnames, margins_cov_rownames=margins_cov_rownames, **est ) est = dict( alpha=1.139991566304804, rank=8, N=17, ic=6, k=9, k_eq=2, k_dv=1, converged=1, rc=0, k_autoCns=1, ll=-27.58269157281191, k_eq_model=1, ll_0=-32.87628220135203, rank0=2, df_m=6, chi2=10.58718125708025, p=.1020042170100991, ll_c=-28.46285727296058, chi2_c=1.760331400297339, r2_p=.1610154881905237, k_aux=1, properties="b V", depvar="sexecutions", which="max", technique="nr", singularHmethod="m-marquardt", ml_method="e2", crittype="log likelihood", user="nbreg_lf", diparm1="lnalpha, exp label(", title="Negative binomial regression", vce="oim", opt="moptimize", chi2type="LR", chi2_ct="LR", diparm_opt2="noprob", dispers="mean", predict="nbreg_p", cmd="nbreg", cmdline="nbreg sexecutions sincome sperpoverty sperblack LN_VC100k96 i.south sdegree", # noqa:E501 ) margins_table = np.array([ 38.769964496355, 35.863089979665, 1.0810547701924, .27967275114341, -31.520400238107, 109.06032923082, np.nan, 1.9599639845401, 0, 2.5208248279388, 11.710699937639, .21525825453324, .82956597473124, -20.43172528359, 25.473374939467, np.nan, 1.9599639845401, 0, -8.2256061843309, 9.5577212853699, -.86062419469397, .38944505596662, -26.958395677928, 10.507183309266, np.nan, 1.9599639845401, 0, -4.4150939806521, 28.010544626815, -.15762256819618, .87475421903071, -59.314752636561, 50.484564675257, np.nan, 1.9599639845401, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, 1.9599639845401, 0, 8.0380552593041, 8.8634487485248, .90687671214231, .36447199739385, -9.3339850666211, 25.410095585229, np.nan, 1.9599639845401, 0, -25.12830359621, 23.247820207656, -1.0808885896294, .27974667485873, -70.693193922279, 20.436586729858, np.nan, 1.9599639845401, 0]).reshape(7, 9) margins_table_colnames = 'b se z pvalue ll ul df crit eform'.split() margins_table_rownames = ['sincome', 'sperpoverty', 'sperblack', 'LN_VC100k96', '0b.south', '1.south', 'sdegree'] margins_cov = np.array([ 44.468037032424, 13.291812805256, .84306554343906, -.38095027774827, 0, -2.1265212254934, -18.067148259892, -30.427077474499, .36347806905277, 13.291812805256, 15.093124820144, 3.3717840254072, -7.6860995498609, 0, -3.3867901970823, -1.4200645173736, -12.979849717095, .51706617429393, .84306554343906, 3.3717840254072, 5.6928040093478, -12.14055356299, 0, -2.5831646721296, -1.8071496111144, 7.9616647841741, .27439267406129, -.38095027774827, -7.6860995498609, -12.14055356299, 91.950706114005, 0, 6.6107070350678, 9.5470604840447, -82.665769963921, -1.1433180909154, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2.1265212254934, -3.3867901970823, -2.5831646721296, 6.6107070350678, 0, 2.0499053083335, 1.7094543055874, -3.0295433346046, -.34297224102581, -18.067148259892, -1.4200645173736, -1.8071496111144, 9.5470604840447, 0, 1.7094543055874, 18.442703265157, -6.5839965105912, -.61952491151187, -30.427077474499, -12.979849717095, 7.9616647841741, -82.665769963921, 0, -3.0295433346046, -6.5839965105912, 111.12618806584, .88600743090998, .36347806905277, .51706617429393, .27439267406129, -1.1433180909154, 0, -.34297224102581, -.61952491151187, .88600743090998, .71851239110059]).reshape(9, 9) margins_cov_colnames = ['sincome', 'sperpoverty', 'sperblack', 'LN_VC100k96', '0b.south', '1.south', 'sdegree', '_cons', '_cons'] margins_cov_rownames = ['sincome', 'sperpoverty', 'sperblack', 'LN_VC100k96', '0b.south', '1.south', 'sdegree', '_cons', '_cons'] results_negbin_margins_dummy = MarginTableTestBunch( margins_table=margins_table, margins_table_colnames=margins_table_colnames, margins_table_rownames=margins_table_rownames, margins_cov=margins_cov, margins_cov_colnames=margins_cov_colnames, margins_cov_rownames=margins_cov_rownames, **est ) statsmodels-0.12.2/statsmodels/discrete/tests/results/results_count_robust_cluster.py000066400000000000000000000555771400612667500316210ustar00rootroot00000000000000import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch est = dict( rank=3, N=34, ic=1, k=3, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=0, N_clust=5, ll=-354.2436413025559, k_eq_model=1, ll_0=-356.2029100704882, df_m=2, chi2=5.204189583786304, p=.0741181533729996, r2_p=.0055004288638308, cmdline="poisson accident yr_con op_75_79, vce(cluster ship)", cmd="poisson", predict="poisso_p", estat_cmd="poisson_estat", gof="poiss_g", chi2type="Wald", opt="moptimize", vcetype="Robust", clustvar="ship", vce="cluster", title="Poisson regression", user="poiss_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="accident", properties="b V", ) params_table = np.array([ -.02172061893549, .19933709357097, -.10896426022065, .91323083771076, -.41241414311748, .36897290524649, np.nan, 1.9599639845401, 0, .22148585072024, .11093628220713, 1.9965140918162, .04587799343723, .00405473301549, .43891696842499, np.nan, 1.9599639845401, 0, 2.2697077143215, 1.1048569901548, 2.054299999499, .03994666479943, .10422780555076, 4.4351876230922, np.nan, 1.9599639845401, 0]).reshape(3, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'yr_con op_75_79 _cons'.split() cov = np.array([ .03973527687332, .00976206273414, -.21171095768584, .00976206273414, .01230685870994, -.06297293767114, -.21171095768584, -.06297293767114, 1.2207089686939]).reshape(3, 3) cov_colnames = 'yr_con op_75_79 _cons'.split() cov_rownames = 'yr_con op_75_79 _cons'.split() results_poisson_clu = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=3, N=34, ic=1, k=3, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=0, ll=-354.2436413025559, k_eq_model=1, ll_0=-356.2029100704882, df_m=2, chi2=.1635672212515404, p=.9214713337295277, r2_p=.0055004288638308, cmdline="poisson accident yr_con op_75_79, vce(robust)", cmd="poisson", predict="poisso_p", estat_cmd="poisson_estat", gof="poiss_g", chi2type="Wald", opt="moptimize", vcetype="Robust", vce="robust", title="Poisson regression", user="poiss_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="accident", properties="b V", ) params_table = np.array([ -.02172061893549, .19233713248134, -.11292993014545, .91008610728406, -.39869447148862, .35525323361764, np.nan, 1.9599639845401, 0, .22148585072024, .55301404772037, .400506735106, .68878332380143, -.8624017657564, 1.3053734671969, np.nan, 1.9599639845401, 0, 2.2697077143215, .66532523368388, 3.4114258702533, .00064624070669, .96569421829539, 3.5737212103476, np.nan, 1.9599639845401, 0]).reshape(3, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'yr_con op_75_79 _cons'.split() cov = np.array([ .03699357253114, -.01521223175214, -.09585501859714, -.01521223175214, .30582453697607, -.1649339692102, -.09585501859714, -.1649339692102, .44265766657651]).reshape(3, 3) cov_colnames = 'yr_con op_75_79 _cons'.split() cov_rownames = 'yr_con op_75_79 _cons'.split() results_poisson_hc1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=3, N=34, ic=4, k=3, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=0, ll=-91.28727940081573, k_eq_model=1, ll_0=-122.0974139280415, df_m=2, chi2=61.62026905445154, p=4.16225408420e-14, r2_p=.2523405986746273, cmdline="poisson accident yr_con op_75_79, exposure(service)", cmd="poisson", predict="poisso_p", estat_cmd="poisson_estat", offset="ln(service)", gof="poiss_g", chi2type="LR", opt="moptimize", vce="oim", title="Poisson regression", user="poiss_lf", crittype="log likelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="accident", properties="b V", ) params_table = np.array([ .30633819450439, .05790831365493, 5.290055523458, 1.222792336e-07, .19283998533528, .4198364036735, np.nan, 1.9599639845401, 0, .35592229608495, .12151759298719, 2.9289775030556, .00340079035234, .11775219034206, .59409240182785, np.nan, 1.9599639845401, 0, -6.974712802772, .13252425018256, -52.629709605328, 0, -7.234455560208, -6.714970045336, np.nan, 1.9599639845401, 0]).reshape(3, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'yr_con op_75_79 _cons'.split() cov = np.array([ .00335337279036, -.00315267340017, -.00589654294427, -.00315267340017, .0147665254054, -.00165060980569, -.00589654294427, -.00165060980569, .01756267688645]).reshape(3, 3) cov_colnames = 'yr_con op_75_79 _cons'.split() cov_rownames = 'yr_con op_75_79 _cons'.split() results_poisson_exposure_nonrobust = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=3, N=34, ic=4, k=3, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=0, ll=-91.28727940081573, k_eq_model=1, ll_0=-122.0974139280415, df_m=2, chi2=15.1822804640621, p=.0005049050167458, r2_p=.2523405986746273, cmdline="poisson accident yr_con op_75_79, exposure(service) vce(robust)", # noqa:E501 cmd="poisson", predict="poisso_p", estat_cmd="poisson_estat", offset="ln(service)", gof="poiss_g", chi2type="Wald", opt="moptimize", vcetype="Robust", vce="robust", title="Poisson regression", user="poiss_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="accident", properties="b V", ) params_table = np.array([ .30633819450439, .09144457613957, 3.3499875819514, .00080815183366, .12711011868929, .48556627031949, np.nan, 1.9599639845401, 0, .35592229608495, .16103531267836, 2.2102127177276, .02709040275274, .04029888299621, .67154570917369, np.nan, 1.9599639845401, 0, -6.974712802772, .2558675415017, -27.259076168227, 1.29723387e-163, -7.4762039689282, -6.4732216366159, np.nan, 1.9599639845401, 0]).reshape(3, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'yr_con op_75_79 _cons'.split() cov = np.array([ .00836211050535, .00098797681063, -.01860743122756, .00098797681063, .02593237192942, -.02395236210603, -.01860743122756, -.02395236210603, .06546819879413]).reshape(3, 3) cov_colnames = 'yr_con op_75_79 _cons'.split() cov_rownames = 'yr_con op_75_79 _cons'.split() results_poisson_exposure_hc1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=3, N=34, ic=4, k=3, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=0, N_clust=5, ll=-91.28727940081573, k_eq_model=1, ll_0=-122.0974139280415, df_m=2, chi2=340.7343047354823, p=1.02443835269e-74, r2_p=.2523405986746273, cmdline="poisson accident yr_con op_75_79, exposure(service) vce(cluster ship)", # noqa:E501 cmd="poisson", predict="poisso_p", estat_cmd="poisson_estat", offset="ln(service)", gof="poiss_g", chi2type="Wald", opt="moptimize", vcetype="Robust", clustvar="ship", vce="cluster", title="Poisson regression", user="poiss_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="accident", properties="b V", ) params_table = np.array([ .30633819450439, .03817694295902, 8.0241677504982, 1.022165435e-15, .23151276126487, .38116362774391, np.nan, 1.9599639845401, 0, .35592229608495, .09213163536669, 3.8631930787765, .00011191448109, .17534760892947, .53649698324044, np.nan, 1.9599639845401, 0, -6.974712802772, .0968656626603, -72.003975518463, 0, -7.1645660129248, -6.7848595926192, np.nan, 1.9599639845401, 0]).reshape(3, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'yr_con op_75_79 _cons'.split() cov = np.array([ .0014574789737, -.00277745275086, .00108765624666, -.00277745275086, .00848823823534, -.00469929607507, .00108765624666, -.00469929607507, .00938295660262]).reshape(3, 3) cov_colnames = 'yr_con op_75_79 _cons'.split() cov_rownames = 'yr_con op_75_79 _cons'.split() results_poisson_exposure_clu = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=4, N=34, ic=2, k=4, k_eq=2, k_dv=1, converged=1, rc=0, k_autoCns=0, N_clust=5, ll=-109.0877965183258, k_eq_model=1, ll_0=-109.1684720604314, rank0=2, df_m=2, chi2=5.472439553195301, p=.0648148991694882, k_aux=1, alpha=2.330298308905143, cmdline="nbreg accident yr_con op_75_79, vce(cluster ship)", cmd="nbreg", predict="nbreg_p", dispers="mean", diparm_opt2="noprob", chi2type="Wald", opt="moptimize", vcetype="Robust", clustvar="ship", vce="cluster", title="Negative binomial regression", diparm1="lnalpha, exp label(", user="nbreg_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="accident", properties="b V", ) params_table = np.array([ -.03536709401845, .27216090050938, -.12994921001605, .89660661037787, -.56879265701682, .49805846897992, np.nan, 1.9599639845401, 0, .23211570238882, .09972456245386, 2.3275680201277, .01993505322091, .03665915160525, .42757225317239, np.nan, 1.9599639845401, 0, 2.2952623989519, 1.2335785495143, 1.8606536242509, .06279310688494, -.12250713019722, 4.7130319281011, np.nan, 1.9599639845401, 0, .84599628895555, .22483100011931, np.nan, np.nan, .40533562611357, 1.2866569517975, np.nan, 1.9599639845401, 0, 2.3302983089051, .52392329936749, np.nan, np.nan, 1.4998057895818, 3.6206622525444, np.nan, 1.9599639845401, 0]).reshape(5, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'yr_con op_75_79 _cons _cons alpha'.split() cov = np.array([ .07407155576607, -.00421355148283, -.32663130963457, .02015715724983, -.00421355148283, .00994498835661, .00992613461881, -.00714955450361, -.32663130963457, .00992613461881, 1.5217160378218, -.09288283512096, .02015715724983, -.00714955450361, -.09288283512096, .05054897861465 ]).reshape(4, 4) cov_colnames = 'yr_con op_75_79 _cons _cons'.split() cov_rownames = 'yr_con op_75_79 _cons _cons'.split() results_negbin_clu = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=4, N=34, ic=2, k=4, k_eq=2, k_dv=1, converged=1, rc=0, k_autoCns=0, ll=-109.0877965183258, k_eq_model=1, ll_0=-109.1684720604314, rank0=2, df_m=2, chi2=.1711221347493475, p=.9179970816706797, r2_p=.0007390003778831, k_aux=1, alpha=2.330298308905143, cmdline="nbreg accident yr_con op_75_79, vce(robust)", cmd="nbreg", predict="nbreg_p", dispers="mean", diparm_opt2="noprob", chi2type="Wald", opt="moptimize", vcetype="Robust", vce="robust", title="Negative binomial regression", diparm1="lnalpha, exp label(", user="nbreg_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="accident", properties="b V", ) params_table = np.array([ -.03536709401845, .26106873337039, -.13547043172065, .89223994079058, -.5470524089139, .476318220877, np.nan, 1.9599639845401, 0, .23211570238882, .56245325203342, .41268443475019, .67983783029986, -.87027241458412, 1.3345038193618, np.nan, 1.9599639845401, 0, 2.2952623989519, .76040210713867, 3.0184850586341, .00254041928465, .80490165519179, 3.7856231427121, np.nan, 1.9599639845401, 0, .84599628895555, .24005700345444, np.nan, np.nan, .37549320794823, 1.3164993699629, np.nan, 1.9599639845401, 0, 2.3302983089051, .55940442919073, np.nan, np.nan, 1.4557092049439, 3.7303399539165, np.nan, 1.9599639845401, 0]).reshape(5, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'yr_con op_75_79 _cons _cons alpha'.split() cov = np.array([ .06815688354362, -.03840590969835, -.16217402790798, .02098165591138, -.03840590969835, .31635366072297, -.11049674936104, -.02643483668568, -.16217402790798, -.11049674936104, .57821136454093, -.03915049342584, .02098165591138, -.02643483668568, -.03915049342584, .05762736490753 ]).reshape(4, 4) cov_colnames = 'yr_con op_75_79 _cons _cons'.split() cov_rownames = 'yr_con op_75_79 _cons _cons'.split() results_negbin_hc1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=4, N=34, ic=4, k=4, k_eq=2, k_dv=1, converged=1, rc=0, k_autoCns=0, ll=-82.49115612464289, k_eq_model=1, ll_0=-84.68893065247886, rank0=2, df_m=2, chi2=4.39554905567195, p=.1110500222994781, ll_c=-91.28727940081573, chi2_c=17.5922465523457, r2_p=.0259511427397111, k_aux=1, alpha=.2457422083490335, cmdline="nbreg accident yr_con op_75_79, exposure(service)", cmd="nbreg", predict="nbreg_p", offset="ln(service)", dispers="mean", diparm_opt2="noprob", chi2_ct="LR", chi2type="LR", opt="moptimize", vce="oim", title="Negative binomial regression", diparm1="lnalpha, exp label(", user="nbreg_lf", crittype="log likelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="accident", properties="b V", ) params_table = np.array([ .28503762550355, .14983643534827, 1.9023251910727, .05712865433138, -.00863639135093, .57871164235802, np.nan, 1.9599639845401, 0, .17127003537767, .27580549562862, .62098122804736, .53461197443513, -.36929880279264, .71183887354798, np.nan, 1.9599639845401, 0, -6.5908639033905, .40391814231008, -16.31732574748, 7.432080344e-60, -7.3825289150206, -5.7991988917604, np.nan, 1.9599639845401, 0, -1.4034722260565, .51305874839271, np.nan, np.nan, -2.4090488948595, -.39789555725363, np.nan, 1.9599639845401, 0, .24574220834903, .12608018984282, np.nan, np.nan, .089900758997, .67173218155228, np.nan, 1.9599639845401, 0]).reshape(5, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'yr_con op_75_79 _cons _cons alpha'.split() cov = np.array([ .02245095735788, -.01097939549632, -.05127649084781, .00045725833006, -.01097939549632, .07606867141895, -.0197375670989, -.00926008351523, -.05127649084781, -.0197375670989, .16314986568722, .02198323898312, .00045725833006, -.00926008351523, .02198323898312, .26322927930229 ]).reshape(4, 4) cov_colnames = 'yr_con op_75_79 _cons _cons'.split() cov_rownames = 'yr_con op_75_79 _cons _cons'.split() results_negbin_exposure_nonrobust = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=4, N=34, ic=4, k=4, k_eq=2, k_dv=1, converged=1, rc=0, k_autoCns=0, N_clust=5, ll=-82.49115612464289, k_eq_model=1, ll_0=-84.68893065247886, rank0=2, df_m=2, chi2=5.473741859983782, p=.0647727084656973, k_aux=1, alpha=.2457422083490335, cmdline="nbreg accident yr_con op_75_79, exposure(service) vce(cluster ship)", # noqa:E501 cmd="nbreg", predict="nbreg_p", offset="ln(service)", dispers="mean", diparm_opt2="noprob", chi2type="Wald", opt="moptimize", vcetype="Robust", clustvar="ship", vce="cluster", title="Negative binomial regression", diparm1="lnalpha, exp label(", user="nbreg_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="accident", properties="b V", ) params_table = np.array([ .28503762550355, .14270989695062, 1.9973220610073, .04579020833966, .00533136724292, .56474388376418, np.nan, 1.9599639845401, 0, .17127003537767, .17997186802799, .95164892854829, .34127505843023, -.18146834418759, .52400841494293, np.nan, 1.9599639845401, 0, -6.5908639033905, .62542746996715, -10.538174640357, 5.760612980e-26, -7.8166792194681, -5.3650485873129, np.nan, 1.9599639845401, 0, -1.4034722260565, .86579403765571, np.nan, np.nan, -3.1003973578913, .29345290577817, np.nan, 1.9599639845401, 0, .24574220834903, .21276213878894, np.nan, np.nan, .0450313052935, 1.3410500222158, np.nan, 1.9599639845401, 0]).reshape(5, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'yr_con op_75_79 _cons _cons alpha'.split() cov = np.array([ .02036611468766, -.00330004038514, -.08114367170947, -.07133030733881, -.00330004038514, .03238987328148, -.03020509748676, -.09492663454187, -.08114367170947, -.03020509748676, .39115952018952, .43276143586693, -.07133030733881, -.09492663454187, .43276143586693, .74959931564018 ]).reshape(4, 4) cov_colnames = 'yr_con op_75_79 _cons _cons'.split() cov_rownames = 'yr_con op_75_79 _cons _cons'.split() results_negbin_exposure_clu = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) statsmodels-0.12.2/statsmodels/discrete/tests/results/results_discrete.py000066400000000000000000001436571400612667500271310ustar00rootroot00000000000000""" Test Results for discrete models from Stata """ import os import numpy as np class Namespace(object): pass # Discrete Model Tests # Note that there is a slight refactor of the classes, so that one dataset # might be used for more than one model cur_dir = os.path.abspath(os.path.dirname(__file__)) class Anes(object): def __init__(self): """r Results are from Stata 11 (checked vs R nnet package). """ self.nobs = 944 def mnlogit_basezero(): obj = Namespace() obj.nobs = 944 params = [ -.01153598, .29771435, -.024945, .08249144, .00519655, -.37340167, -.08875065, .39166864, -.02289784, .18104276, .04787398, -2.2509132, -.1059667, .57345051, -.01485121, -.00715242, .05757516, -3.6655835, -.0915567, 1.2787718, -.00868135, .19982796, .08449838, -7.6138431, -.0932846, 1.3469616, -.01790407, .21693885, .08095841, -7.0604782, -.14088069, 2.0700801, -.00943265, .3219257, .10889408, -12.105751] obj.params = np.reshape(params, (6, -1), order='F') bse = [ .0342823657, .093626795, .0065248584, .0735865799, .0176336937, .6298376313, .0391615553, .1082386919, .0079144618, .0852893563, .0222809297, .7631899491, .0570382292, .1585481337, .0113313133, .1262913234, .0336142088, 1.156541492, .0437902764, .1288965854, .0084187486, .0941250559, .0261963632, .9575809602, .0393516553, .1171860107, .0076110152, .0850070091, .0229760791, .8443638283, .042138047, .1434089089, .0081338625, .0910979921, .025300888, 1.059954821] obj.bse = np.reshape(bse, (6, -1), order='F') obj.yhat = np.loadtxt(os.path.join(cur_dir, 'yhat_mnlogit.csv')) obj.phat = np.loadtxt(os.path.join(cur_dir, 'phat_mnlogit.csv')) obj.cov_params = None obj.llf = -1461.922747312 obj.llnull = -1750.34670999 obj.llr = 576.8479253554 obj.llr_pvalue = 1.8223179e-102 obj.prsquared = .1647810465387 obj.df_model = 30 obj.df_resid = 944 - 36 obj.J = 7 obj.K = 6 obj.aic = 2995.84549462 obj.bic = 3170.45003661 z = [ -.3364988051, 3.179798597, -3.823070772, 1.121012042, .2946945327, -.5928538661, -2.266269864, 3.618564069, -2.893164162, 2.122688754, 2.148652536, -2.949348555, -1.857818873, 3.616885888, -1.310634214, -.0566342868, 1.712822091, -3.169435381, -2.090799808, 9.920912816, -1.031191864, 2.123004903, 3.225576554, -7.951122047, -2.370538224, 11.49421878, -2.352389066, 2.552011323, 3.523595639, -8.361890935, -3.34331327, 14.43480847, -1.159676452, 3.533839715, 4.303962885, -11.42100649] obj.z = np.reshape(z, (6, -1), order='F') pvalues = [ 0.7364947525, 0.0014737744, 0.0001317999, 0.2622827367, 0.7682272401, 0.5532789548, 0.0234348654, 0.0002962422, 0.0038138191, 0.0337799420, 0.0316619538, 0.0031844460, 0.0631947400, 0.0002981687, 0.1899813744, 0.9548365214, 0.0867452747, 0.0015273542, 0.0365460134, 3.37654e-23, 0.3024508550, 0.0337534410, 0.0012571921, 1.84830e-15, 0.0177622072, 1.41051e-30, 0.0186532528, 0.0107103038, 0.0004257334, 6.17209e-17, 0.0008278439, 3.12513e-47, 0.2461805610, 0.0004095694, 0.0000167770, 3.28408e-30] obj.pvalues = np.reshape(pvalues, (6, -1), order='F') conf_int = [ [[-0.0787282, 0.0556562], [0.1142092, 0.4812195], [-0.0377335, -0.0121565], [-0.0617356, 0.2267185], [-0.0293649, 0.0397580], [-1.6078610, 0.8610574]], [[-0.1655059, -0.0119954], [0.1795247, 0.6038126], [-0.0384099, -0.0073858], [0.0138787, 0.3482068], [0.0042042, 0.0915438], [-3.7467380, -0.7550884]], [[-0.2177596, 0.0058262], [0.2627019, 0.8841991], [-0.0370602, 0.0073578], [-0.2546789, 0.2403740], [-0.0083075, 0.1234578], [-5.9323630, -1.3988040]], [[-0.1773841, -0.0057293], [1.0261390, 1.5314040], [-0.0251818, 0.0078191], [0.0153462, 0.3843097], [0.0331544, 0.1358423], [-9.4906670, -5.7370190]], [[-0.1704124, -0.0161568], [1.1172810, 1.5766420], [-0.0328214, -0.0029868], [0.0503282, 0.3835495], [0.0359261, 0.1259907], [-8.7154010, -5.4055560]], [[-0.2234697, -0.0582916], [1.7890040, 2.3511560], [-0.0253747, 0.0065094], [0.1433769, 0.5004745], [0.0593053, 0.1584829], [-14.1832200, -10.0282800]]] obj.conf_int = np.asarray(conf_int) # margins, dydx(*) predict(outcome(#)) obj.margeff_dydx_overall = np.array([ [0.00868085993550, -0.09779854015456, 0.00272556969847, -0.01992376579372, -0.00603133322764], [0.00699386733148, -0.05022430802614, -0.00211003909752, -0.00536980000265, -0.00554366741814], [-0.00391040848820, -0.02824717135857, -0.00100551299310, 0.00664337806861, 0.00097987356999], [-0.00182580888015, -0.00573744730031, -0.00004249256428, -0.00546669558488, 0.00054101121854], [-0.00098558129923, 0.01985550937033, 0.00047972250012, 0.00172605778905, 0.00211291403209], [-0.00153469551647, 0.03755346502013, -0.00068531143399, 0.00472471794347, 0.00254733486106], [-0.00741820702809, 0.12459834487569, 0.00063806819375, 0.01766610701188, 0.00539385283759] ]).T obj.margeff_dydx_overall_se = np.array([ [.0038581061, .0080471125, .0007068488, .0082318967, .0020261706], [.003904378, .0073600286, .000756431, .0084381578, .0020482238], [.003137126, .0056813182, .0006601377, .0068932588, .0018481806], [.0019427783, .0031904763, .0003865411, .004361789, .0011523221], [.0029863227, .0054076092, .0005886612, .0064426365, .0018886818], [.0035806552, .0069497362, .000722511, .0078287717, .0022352393], [.0033641608, .008376629, .0006774697, .0073505286, .0021660086] ]).T obj.margeff_dydx_mean = np.array([ [0.01149887431225, -0.13784207091973, 0.00273313385873, -0.02542974260540, -0.00855346837482], [0.01114846831102, -0.09864273512889, -0.00222435063712, -0.01214617126321, -0.00903581444579], [-0.00381702868421, -0.05132297961269, -0.00116763216994, 0.00624203027060, 0.00021912081810], [-0.00233455327258, -0.00928554037343, -0.00000206561214, -0.00775415690571, 0.00060004460394], [-0.00352579921274, 0.06412187169362, 0.00073938948643, 0.00747778063206, 0.00459965010365], [-0.00574308219449, 0.11126535089794, -0.00057337915464, 0.01467424346725, 0.00641760846097], [-0.00722687818452, 0.12170608820238, 0.00049490419675, 0.01693601418978, 0.00575285798725]]).T obj.margeff_dydx_mean_se = np.array([ [.0043729758, .0110343353, .0008149907, .0092551389, .0023752071], [.004875051, .0124746358, .0009613152, .0105665812, .0026524426], [.0040718954, .0103613938, .0008554615, .0089931297, .0024374625], [.0026430804, .0070845916, .0005364369, .0057654258, .0015988838], [.0037798151, .0103849291, .0007393481, .0082021938, .0023489261], [.0045654631, .0130329403, .0009128134, .0100053262, .0028048602], [.0027682389, .0113292677, .0005325113, .0061289353, .0017330763] ]).T obj.margeff_dydx_dummy_overall = np.array([ [0.00549149574321, -0.05348235321783, 0.00298963549049, -0.01479461677951, -0.00332167981255, -0.26502967041815], [0.00345677928276, -0.00950322030929, -0.00189456107189, 0.00033893662061, -0.00314690167350, -0.21040878091828], [-0.00645089013284, 0.00401746940204, -0.00083948249351, 0.01114202556889, 0.00277069841472, -0.15967397659686], [-0.00215436802341, -0.00366545199370, -0.00000002297812, -0.00457368049644, 0.00065303026027, -0.00094772782001], [0.00058038428936, -0.00369080100124, 0.00035948233235, -0.00018863693013, 0.00079351293461, 0.12640653743480], [0.00217597030999, -0.01279456622853, -0.00091882392767, 0.00001651192759, -0.00037998290789, 0.27175070356670], [-0.00309932483642, 0.07911868907484, 0.00030378521102, 0.00805941631677, 0.00263129901425, 0.23790291475181]]).T obj.margeff_dydx_dummy_overall_se = np.array([ [.0037314453, .0094102332, .000688838, .0079744554, .0019365971, .0243914836], [.0038215262, .0095938828, .0007410885, .008259353, .0019984087, .0317628806], [.0031045718, .00785814, .0006504353, .0067892866, .0018060332, 0.0262803561], [.0019756086, .0051031194, .0003862449, .0043621673, .0011796953, .0219999601], [.0029714074, .0081732018, .0005715192, .0064742872, .0019130195, .0331694192], [.0034443743, .0097296187, .0006774867, .0075996454, .0021993881, .038600835], [.0032003518, .0098741227, .0006335772, .0070902078, .0021003227, .0255727127]]).T obj.margeff_eydx_dummy_overall = np.array([ [.03939188, -.65758371, .01750922, -.12131806, -.03613241, -3.2132513], [.02752366, -.383165, -.00830021, -.03652935, -.03286046, -1.8741853], [-.05006681, -.2719659, -.00626481, .06525323, .01012554, -2.0058029], [-.05239558, -.22549142, .00025015, -.13104416, .01114517, -.27052009], [-.00296374, .25627809, .00140513, .03358712, .02296041, 1.3302701], [.00328283, .2800168, -.0083912, .04332782, .01575863, 1.8441023], [-.03257068, .98346111, -.00122118, .10847807, .0406456, 2.9119099]]).T obj.margeff_eydx_dummy_overall_se = np.array([ [.0272085605, .0777760394, .0052427952, .0584011446, .0148618012, .5796921383], [.0262290023, .0724479385, .005174736, .0567743614, .0144447083, .3015738731], [.0321415498, .0895589422, .0067480662, .0701460193, .0190451865, .3904138447], [.0511305319, .1420904068, .0102342163, .1129912244, .0308618233, .3693799595], [.0340186217, .0991711703, .0065812158, .0737441012, .0212966336, .2346982385], [.0289250212, .0840662279, .0056743561, .0631772185, .0177278895, .2089516714], [.0318251305, .1085637405, .0062400589, .0699123044, .0201045606, .3727166284]]).T # taken from gretl obj.resid = np.loadtxt(os.path.join(cur_dir, 'mnlogit_resid.csv'), delimiter=",") return obj mnlogit_basezero = mnlogit_basezero() class DiscreteL1(object): def __init__(self): """ Special results for L1 models Uses the Spector data and a script to generate the baseline results """ pass def logit(): """ Results generated with: data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=True) alpha = 3 * np.array([0, 1, 1, 1]) res2 = sm.Logit(data.endog, data.exog).fit_regularized( method="l1", alpha=alpha, disp=0, trim_mode='size', size_trim_tol=1e-5, acc=1e-10, maxiter=1000) """ obj = Namespace() nan = np.nan obj.params = [-4.10271595, 0., 0.15493781, 0.] obj.conf_int = [ [-9.15205122, 0.94661932], [nan, nan], [-0.06539482, 0.37527044], [nan, nan]] obj.bse = [2.5762388, nan, 0.11241668, nan] obj.nnz_params = 2 obj.aic = 42.091439368583671 obj.bic = 45.022911174183122 obj.cov_params = [ [6.63700638, nan, -0.28636261, nan], [nan, nan, nan, nan], [-0.28636261, nan, 0.01263751, nan], [nan, nan, nan, nan]] return obj logit = logit() def sweep(): """ Results generated with params = np.zeros((3, 4)) alphas = np.array( [[0.1, 0.1, 0.1, 0.1], [0.4, 0.4, 0.5, 0.5], [0.5, 0.5, 1, 1]]) model = sm.Logit(data.endog, data.exog) for i in range(3): alpha = alphas[i, :] res2 = model.fit_regularized(method="l1", alpha=alpha, disp=0, acc=1e-10, maxiter=1000, trim_mode='off') params[i, :] = res2.params print(params) """ obj = Namespace() obj.params = [ [-10.37593611, 2.27080968, 0.06670638, 2.05723691], [-5.32670811, 1.18216019, 0.01402395, 1.45178712], [-3.92630318, 0.90126958, -0., 1.09498178]] return obj sweep = sweep() def probit(): """ Results generated with data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=True) alpha = np.array([0.1, 0.2, 0.3, 10]) res2 = sm.Probit(data.endog, data.exog).fit_regularized( method="l1", alpha=alpha, disp=0, trim_mode='auto', auto_trim_tol=0.02, acc=1e-10, maxiter=1000) """ obj = Namespace() nan = np.nan obj.params = [-5.40476992, 1.25018458, 0.04744558, 0.] obj.conf_int = [ [-9.44077951, -1.36876033], [0.03716721, 2.46320194], [-0.09727571, 0.19216687], [np.nan, np.nan]] obj.bse = [2.05922641, 0.61889778, 0.07383875, np.nan] obj.nnz_params = 3 obj.aic = 38.399773877542927 obj.bic = 42.796981585942106 obj.cov_params = [ [4.24041339, -0.83432592, -0.06827915, nan], [-0.83432592, 0.38303447, -0.01700249, nan], [-0.06827915, -0.01700249, 0.00545216, nan], [nan, nan, nan, nan]] return obj probit = probit() def mnlogit(): """ Results generated with anes_data = sm.datasets.anes96.load(as_pandas=False) anes_exog = anes_data.exog anes_exog = sm.add_constant(anes_exog, prepend=False) mlogit_mod = sm.MNLogit(anes_data.endog, anes_exog) alpha = 10 * np.ones((mlogit_mod.J - 1, mlogit_mod.K)) alpha[-1, :] = 0 mlogit_l1_res = mlogit_mod.fit_regularized( method='l1', alpha=alpha, trim_mode='auto', auto_trim_tol=0.02, acc=1e-10) """ obj = Namespace() obj.params = [ [0.00100163, -0.05864195, -0.06147822, -0.04769671, -0.05222987, -0.09522432], [0., 0.03186139, 0.12048999, 0.83211915, 0.92330292, 1.5680646], [-0.0218185, -0.01988066, -0.00808564, -0.00487463, -0.01400173, -0.00562079], [0., 0.03306875, 0., 0.02362861, 0.05486435, 0.14656966], [0., 0.04448213, 0.03252651, 0.07661761, 0.07265266, 0.0967758], [0.90993803, -0.50081247, -2.08285102, -5.26132955, -4.86783179, -9.31537963]] obj.conf_int = [ [[-0.0646223, 0.06662556], [np.nan, np.nan], [-0.03405931, -0.00957768], [np.nan, np.nan], [np.nan, np.nan], [0.26697895, 1.55289711]], [[-0.1337913, 0.01650741], [-0.14477255, 0.20849532], [-0.03500303, -0.00475829], [-0.11406121, 0.18019871], [0.00479741, 0.08416684], [-1.84626136, 0.84463642]], [[-0.17237962, 0.04942317], [-0.15146029, 0.39244026], [-0.02947379, 0.01330252], [np.nan, np.nan], [-0.02501483, 0.09006785], [-3.90379391, -0.26190812]], [[-0.12938296, 0.03398954], [0.62612955, 1.03810876], [-0.02046322, 0.01071395], [-0.13738534, 0.18464256], [0.03017236, 0.12306286], [-6.91227465, -3.61038444]], [[-0.12469773, 0.02023799], [0.742564, 1.10404183], [-0.02791975, -0.00008371], [-0.08491561, 0.19464431], [0.0332926, 0.11201273], [-6.29331126, -3.44235233]], [[-0.17165567, -0.01879296], [1.33994079, 1.79618841], [-0.02027503, 0.00903345], [-0.00267819, 0.29581751], [0.05343135, 0.14012026], [-11.10419107, -7.52656819]]] obj.bse = [ [0.03348221, 0.03834221, 0.05658338, 0.04167742, 0.03697408, 0.03899631], [np.nan, 0.09012101, 0.13875269, 0.10509867, 0.09221543, 0.11639184], [0.00624543, 0.00771564, 0.01091253, 0.00795351, 0.00710116, 0.00747679], [np.nan, 0.07506769, np.nan, 0.08215148, 0.07131762, 0.07614826], [np.nan, 0.02024768, 0.02935837, 0.02369699, 0.02008204, 0.02211492], [0.32804638, 0.68646613, 0.92906957, 0.84233441, 0.72729881, 0.91267567]] obj.nnz_params = 32 obj.aic = 3019.4391360294126 obj.bic = 3174.6431733460686 return obj mnlogit = mnlogit() class Spector(object): """ Results are from Stata 11 """ def __init__(self): self.nobs = 32 def logit(): obj = Namespace() obj.nobs = 32 obj.params = [2.82611297201, .0951576702557, 2.37868772835, -13.0213483201] obj.cov_params = [ [1.59502033639, -.036920566629, .427615725153, -4.57347950298], [-.036920566629, .0200375937069, .0149126464275, -.346255757562], [.427615725153, .0149126464275, 1.13329715236, -2.35916128427], [-4.57347950298, -.346255757562, -2.35916128427, 24.3179625937]] obj.bse = [1.26294114526, .141554207662, 1.06456430165, 4.93132462871] obj.resid_pearson = [ -.1652382, -.2515266, -.4800059, -.1630655, .8687437, -.1900454, -.165002, -.2331563, -.3535812, .6647838, -.1583799, -.4843181, -.689527, 2.043449, -.7516119, -.1764176, -.2380445, -.2003426, -1.199277, .7164842, -.255713, .3242821, -.5646816, -2.400189, .4392082, 1.038473, .75747, -.6659256, .4336657, .2404583, -1.060033, 2.829577] obj.resid_dev = [ -.2321102, -.3502712, -.6439626, -.2290982, 1.060478, -.2663844, -.2317827, -.3253788, -.4853875, .8555557, -.2225972, -.6491808, -.8819993, 1.813269, -.9463985, -.247583, -.3320177, -.2805444, -1.335131, .9103027, -.3559217, .4471892, -.744005, -1.955074, .5939538, 1.209638, .952332, -.8567857, .5870719, .335292, -1.227311, 2.096639] # from gretl obj.resid_generalized = [ -0.026578, -0.059501, -0.187260, -0.025902, 0.430107, -0.034858, -0.026504, -0.051559, -0.111127, 0.306489, -0.024470, -0.189997, -0.322240, 0.806789, -0.360990, -0.030184, -0.053626, -0.038588, -0.589872, 0.339214, -0.061376, 0.095153, -0.241772, -0.852091, 0.161709, 0.518867, 0.364579, -0.307219, 0.158296, 0.054660, -0.529117, 0.888969] obj.phat = np.array([ .02657799236476, .05950126051903, .18725991249084, .02590163610876, .56989300251007, .03485824912786, .02650404907763, .05155897513032, .11112663894892, .69351142644882, .02447037212551, .18999740481377, .32223951816559, .1932111531496, .36098992824554, .03018374741077, .05362640321255, .03858831897378, .58987241983414, .66078591346741, .06137581542134, .90484726428986, .24177247285843, .85209089517593, .8382905125618, .48113295435905, .63542068004608, .30721867084503, .84170418977737, .94534027576447, .52911710739136, .1110308393836]) obj.yhat = np.array([ -3.6007342338562, -2.7604126930237, -1.4679137468338, -3.6272060871124, .28141465783119, -3.3209850788116, -3.6035962104797, -2.9120934009552, -2.0792844295502, .81658720970154, -3.6855175495148, -1.4500269889832, -.74349880218506, -1.429278254509, -.57107019424438, -3.4698030948639, -2.8705959320068, -3.2154531478882, .36343798041344, .66679841279984, -2.7273993492126, 2.2522828578949, -1.1429864168167, 1.7510952949524, 1.6455633640289, -.07550399750471, .55554306507111, -.81315463781357, 1.6709630489349, 2.8504176139832, .11660042405128, -2.0802545547485]) obj.llf = -12.8896334653335 obj.llnull = -20.5917296966173 obj.df_model = 3 obj.df_resid = 32 - 4 # TODO: is this right? not reported in stata obj.llr = 15.4041924625676 obj.prsquared = .374038332124624 obj.llr_pvalue = .00150187761112892 obj.aic = 33.779266930667 obj.bic = 39.642210541866 obj.z = [2.237723415, 0.6722348408, 2.234423721, -2.640537645] obj.conf_int = [ [.3507938, 5.301432], [-.1822835, .3725988], [.29218, 4.465195], [-22.68657, -3.35613]] obj.pvalues = [.0252390974, .5014342039, .0254552063, .0082774596] # taken from margins command obj.margeff_nodummy_dydx = [ .36258084688424, .01220841099085, .30517768382304] obj.margeff_nodummy_dydx_se = [.1094412, .0177942, .0923796] obj.margeff_nodummy_dydxmean = [ .53385885781692, .01797548988961, .44933926079386] obj.margeff_nodummy_dydxmean_se = [.237038, .0262369, .1967626] obj.margeff_nodummy_dydxmedian = [ .25009492465091, .00842091261329, .2105003352955] obj.margeff_nodummy_dydxmedian_se = [.1546708, .0134314, .0928183] obj.margeff_nodummy_dydxzero = [ 6.252993785e-06, 2.105437138e-07, 5.263030788e-06] obj.margeff_nodummy_dydxzero_se = [.0000288, 9.24e-07, .000025] obj.margeff_nodummy_dyex = [ 1.1774000792198, .27896245178384, .16960002159996] obj.margeff_nodummy_dyex_se = [.3616481, .4090679, .0635583] obj.margeff_nodummy_dyexmean = [ 1.6641381583512, .39433730945339, .19658592659731] obj.margeff_nodummy_dyexmean_se = [.7388917, .5755722, .0860836] # NOTE: PSI at median should be a NaN or 'omitted' obj.margeff_nodummy_dyexmedian = [.76654095836557, .18947053379898, 0] obj.margeff_nodummy_dyexmedian_se = [.4740659, .302207, 0] # NOTE: all should be NaN # TODO: re above Note, since the values below are *not* NaN, # should something be done about this? obj.margeff_nodummy_dyexzero = [0, 0, 0] obj.margeff_nodummy_dyexzero_se = [0, 0, 0] obj.margeff_nodummy_eydx = [ 1.8546366266779, .06244722072812, 1.5610138123033] obj.margeff_nodummy_eydx_se = [.847903, .0930901, .7146715] obj.margeff_nodummy_eydxmean = [ 2.1116143062702, .0710998816585, 1.7773072368626] obj.margeff_nodummy_eydxmean_se = [1.076109, .1081501, .9120842] obj.margeff_nodummy_eydxmedian = [ 2.5488082240624, .0858205793373, 2.1452853812126] obj.margeff_nodummy_eydxmedian_se = [1.255377, .1283771, 1.106872] obj.margeff_nodummy_eydxzero = [ 2.8261067189993, .0951574597115, 2.3786824653103] obj.margeff_nodummy_eydxzero_se = [1.262961, .1415544, 1.064574] obj.margeff_nodummy_eyex = [ 5.4747106798973, 1.3173389907576, .44600395466634] obj.margeff_nodummy_eyex_se = [2.44682, 1.943525, .1567618] obj.margeff_nodummy_eyexmean = [ 6.5822977203268, 1.5597536538833, .77757191612739] obj.margeff_nodummy_eyexmean_se = [3.354433, 2.372543, .3990368] obj.margeff_nodummy_eyexmedian = [7.8120973525952, 1.9309630350892, 0] obj.margeff_nodummy_eyexmedian_se = [3.847731951, 2.888485089, 0] obj.margeff_nodummy_eyexzero = [0, 0, 0] obj.margeff_nodummy_eyexzero_se = [0, 0, 0] # for below GPA = 2.0, psi = 1 obj.margeff_nodummy_atexog1 = [ .1456333017086, .00490359933927, .12257689308426] obj.margeff_nodummy_atexog1_se = [.145633, .0111226, .1777101] # for below GPA at mean, tuce = 21, psi = 0 obj.margeff_nodummy_atexog2 = [ .25105129214546, .00845311433473, .2113052923675] obj.margeff_nodummy_atexog2_se = [.1735778, .012017, .0971515] # must get this from older margeff or i.psi then margins obj.margeff_dummy_dydx = [ .36258084688424, .01220841099085, .35751515254729] obj.margeff_dummy_dydx_se = [.1094412, .0177942, .1420034] obj.margeff_dummy_dydxmean = [ .53385885781692, .01797548988961, .4564984096959] obj.margeff_dummy_dydxmean_se = [.237038, .0262369, .1810537] # from margeff obj.margeff_dummy_count_dydx_median = [ 0.250110487483923, 0.008426867847905, 0.441897738279663] obj.margeff_dummy_count_dydx_median_se = [ .1546736661, .0134551951, .1792363708] # estimate with i.psi for the below then use margins obj.margeff_dummy_eydx = [ 1.8546366266779, .06244722072812, 1.5549034398832] obj.margeff_dummy_eydx_se = [.847903, .0930901, .7283702] # ie # margins, eydx(*) at((mean) _all) obj.margeff_dummy_eydxmean = [ 2.1116143062702, .0710998816585, 1.6631775707188] obj.margeff_dummy_eydxmean_se = [1.076109, .1081501, .801205] # TODO: Should we remove the commented-out code below? # Factor variables not allowed in below # test raises # obj.margeff_dummy_dydxzero # obj.margeff_dummy_eydxmedian # obj.margeff_dummy_eydxzero # obj.margeff_dummy_dyex # obj.margeff_dummy_dyexmean # obj.margeff_dummy_dyexmedian # obj.margeff_dummy_dyexzero # obj.margeff_dummy_eyex # obj.margeff_count_dummy_dydx_median # obj.margeff_count_dummy_dydx_median_se # NOTE: need old version of margeff for nodisc but at option is broken # stata command is margeff, count nodisc # this can be replicated with the new results by margeff # and then using margins for the last value obj.margeff_count_dydx = [.3625767598018, .0122068569914, .3051777] obj.margeff_count_dydx_se = [.1094379569, .0177869773, .0923796] # middle value taken from margeff rest from margins obj.margeff_count_dydxmean = [ .5338588, 0.01797186545386, .4493393] obj.margeff_count_dydxmean_se = [.237038, .0262211, .1967626] # with new version of margeff this is just a call to # margeff # mat list e(margeff_b), nonames format(%17.16g) obj.margeff_count_dummy_dydxoverall = [.362576759801767, .012206856991439, .357515163621704] # AFAICT, an easy way to get se is # mata # V = st_matrix("e(margeff_V)") # se = diagonal(cholesky(diag(V))) # last SE taken from margins with i.psi, do not know how they # do not know why margeff is different, but trust official results obj.margeff_count_dummy_dydxoverall_se = [.1094379569, .0177869773, .1420034] # from new margeff obj.margeff_count_dummy_dydxmean = [0.533849340033768, 0.017971865453858, 0.456498405282412] obj.margeff_count_dummy_dydxmean_se = [.2370202503, .0262210796, .1810536852] # for below GPA = 2.0, psi = 1 obj.margeff_dummy_atexog1 = [ .1456333017086, .00490359933927, .0494715429937] obj.margeff_dummy_atexog1_se = [.145633, .0111226, .0731368] # for below GPA at mean, tuce = 21, psi = 0 obj.margeff_dummy_atexog2 = [.25105129214546, .00845311433473, .44265645632553] obj.margeff_dummy_atexog2_se = [.1735778, .012017, .1811925] # The test for the prediction table was taken from Gretl # Gretl Output matched the Stata output here for params and SE obj.pred_table = np.array([[18, 3], [3, 8]]) return obj logit = logit() def probit(): obj = Namespace() obj.nobs = 32 obj.params = [ 1.62581025407, .051728948442, 1.42633236818, -7.45232041607] obj.cov_params = [ [.481472955383, -.01891350017, .105439226234, -1.1696681354], [-.01891350017, .00703757594, .002471864882, -.101172838897], [.105439226234, .002471864882, .354070126802, -.594791776765], [-1.1696681354, -.101172838897, -.594791776765, 6.46416639958]] obj.bse = [.693882522754, .083890261293, .595037920474, 2.54247249731] obj.llf = -12.8188033249334 obj.llnull = -20.5917296966173 obj.df_model = 3 obj.df_resid = 32 - 4 obj.llr = 15.5458527433678 obj.prsquared = .377478069409622 obj.llr_pvalue = .00140489496775855 obj.aic = 33.637606649867 obj.bic = 39.500550261066 obj.z = [2.343062695, .6166263836, 2.397044489, -2.931131182] obj.conf_int = [ [.2658255, 2.985795], [-.1126929, .2161508], [.2600795, 2.592585], [-12.43547, -2.469166]] obj.pvalues = [.0191261688, .537481188, .0165279168, .0033773013] obj.phat = [ .0181707, .0530805, .1899263, .0185707, .5545748, .0272331, .0185033, .0445714, .1088081, .6631207, .0161024, .1935566, .3233282, .1951826, .3563406, .0219654, .0456943, .0308513, .5934023, .6571863, .0619288, .9045388, .2731908, .8474501, .8341947, .488726, .6424073, .3286732, .8400168, .9522446, .5399595, .123544] obj.yhat = np.array([ -2.0930860042572, -1.615691781044, -.87816804647446, -2.0842070579529, .13722851872444, -1.9231110811234, -2.0856919288635, -1.6999372243881, -1.2328916788101, .42099541425705, -2.1418602466583, -.86486464738846, -.45841211080551, -.85895526409149, -.36825761198997, -2.0147502422333, -1.6881184577942, -1.8684275150299, .23630557954311, .40479621291161, -1.538782119751, 1.3078554868698, -.60319095849991, 1.025558590889, .97087496519089, -.02826354466379, .36490100622177, -.44357979297638, .99452745914459, 1.6670187711716, .10033150017262, -1.1574513912201]) obj.resid_dev = [ -.191509, -.3302762, -.6490455, -.1936247, 1.085867, -.2349926, -.1932698, -.3019776, -.4799906, .9064196, -.1801855, -.6559291, -.8838201, 1.807661, -.9387071, -.2107617, -.3058469, -.2503485, -1.341589, .9162835, -.3575735, .447951, -.7988633, -1.939208, .6021435, 1.196623, .9407793, -.8927477, .59048, .3128364, -1.246147, 2.045071] # Stata does not have it, but I think it's just oversight obj.resid_pearson = None # generalized residuals from gretl obj.resid_generalized = [ -0.045452, -0.114220, -0.334908, -0.046321, 0.712624, -0.064538, -0.046175, -0.098447, -0.209349, 0.550593, -0.040906, -0.340339, -0.530763, 1.413373, -0.579170, -0.053593, -0.100556, -0.071855, -0.954156, 0.559294, -0.130167, 0.187523, -0.457597, -1.545643, 0.298511, 0.815964, 0.581013, -0.538579, 0.289631, 0.104405, -0.862836, 1.652638] obj.pred_table = np.array([[18, 3], [3, 8]]) return obj probit = probit() class RandHIE(object): """ Results obtained from Stata 11 """ def __init__(self): self.nobs = 20190 def poisson(): obj = Namespace() obj.nobs = 20190 obj.params = [ -.052535114675, -.247086797633, .035290201794, -.03457750643, .271713973711, .033941474461, -.012635035534, .054056326828, .206115121809, .700352877227] obj.cov_params = None obj.bse = [ .00288398915279, .01061725196728, .00182833684966, .00161284852954, .01223913844387, .00056476496963, .00925061122826, .01530987068312, .02627928267502, .01116266712362] predict = np.loadtxt(os.path.join(cur_dir, 'yhat_poisson.csv'), delimiter=",") obj.phat = predict[:, 0] obj.yhat = predict[:, 1] obj.llf = -62419.588535018 obj.llnull = -66647.181687959 obj.df_model = 9 obj.df_resid = obj.nobs - obj.df_model - 1 obj.llr = 8455.186305881856 obj.prsquared = .0634324369893758 obj.llr_pvalue = 0 obj.aic = 124859.17707 obj.bic = 124938.306497 obj.z = [-18.21612769, -23.27219872, 19.30180524, -21.43878101, 22.20041672, 60.09840604, -1.36585953, 3.53081538, 7.84325525, 62.74063980] obj.conf_int = [ [-.0581876, -.0468826], [-0.2678962, -0.2262774], [0.0317067, 0.0388737], [-0.0377386, -0.0314164], [0.2477257, 0.2957022], [0.0328346, 0.0350484], [-0.0307659, 0.0054958], [0.0240495, 0.0840631], [0.1546087, 0.2576216], [0.6784745, 0.7222313]] obj.pvalues = [ 3.84415e-74, 8.4800e-120, 5.18652e-83, 5.8116e-102, 3.4028e-109, 0, .1719830562, .0004142808, 4.39014e-15, 0] # from stata # use margins and put i. in front of dummies obj.margeff_dummy_overall = [ -0.15027280560599, -0.66568074771099, 0.10094500919706, -0.09890639687842, 0.77721770295360, 0.09708707452600, -0.03608195237609, 0.15804581481115, 0.65104087597053] obj.margeff_dummy_overall_se = [ .008273103, .0269856266, .0052466639, .0046317555, .0351582169, .0016652181, .0263736472, .0457480115, .0913901155] # just use margins obj.margeff_nodummy_overall = [ -0.15027280560599, -0.70677348928158, 0.10094500919705, -0.09890639687842, 0.77721770295359, 0.09708707452600, -0.03614158359367, 0.15462412033340, 0.58957704430148] obj.margeff_nodummy_overall_se = [ .008273103, .0305119343, .0052466639, .0046317555, .0351582168, .0016652181, .0264611158, .0437974779, .0752099666] # taken from gretl obj.resid = np.loadtxt(os.path.join(cur_dir, 'poisson_resid.csv'), delimiter=",") return obj poisson = poisson() def negativebinomial_nb2_bfgs(): # R 2.15.1 MASS 7.3-22 glm.nb() obj = Namespace() obj.nobs = 20190 obj.params = [ -0.0579469537244314, -0.267787718814838, 0.0412060770911646, -0.0381376804392121, 0.268915772213171, 0.0381637446219235, -0.0441338846217674, 0.0172521803400544, 0.177960787443151, 0.663556087183864, # lnalpha from stata 1.292953339909746] # alpha and stderr from stata obj.lnalpha_std_err = .0143932 obj.lnalpha = 0.256929012449 obj.bse = [ 0.00607085853920512, 0.0226125368090765, 0.00405542008282773, 0.00344455937127785, 0.0298855063286547, 0.00142421904710063, 0.0199374393307107, 0.0358416931939136, 0.0741013728607101, 0.0250354082637892, # from stata .0186098] obj.z = [ -9.54510030998327, -11.8424447940467, 10.1607419822296, -11.071860382846, 8.99820030672628, 26.7962605187844, -2.21361850384595, 0.481343898758222, 2.40158556546135, 26.5047040652267] obj.pvalues = [ 1.35975947860026e-21, 2.35486776488278e-32, 2.96808970292151e-24, 1.71796558863781e-28, 2.2944789508802e-19, 3.57231639404726e-158, 0.0268550333379416, 0.630272102021494, 0.0163241908407114, 8.55476622951356e-155] obj.fittedvalues = [ 0.892904166867786, 0.892904166867786, 0.892904166867786, 0.892904166867786, 0.892904166867786, 0.937038051489553, 0.937038051489553, 0.937038051489553, 0.937038051489553, 0.937038051489553] # obj.aic = 86789.3241530713 # This is what R reports obj.aic = 86789.32415307125484 # from Stata obj.df_resid = 20180 obj.df_model = 9 # R conf_int: 1.96 * bse, not profile likelihood via R's confint() obj.conf_int = [ # from Stata [-.0698826, -.0460113], [-.3122654, -.2233101], [.0330781, .049334], [-.0448006, -.0314748], [.2102246, .3276069], [.0352959, .0410316], [-.0834356, -.0048321], [-.0535908, .0880951], [.0324115, .3235101], [.6150055, .7121067], # from Stata [1.256989, 1.329947] ] obj.bic = 86876.36652289562335 # stata obj.llnull = -44199.27443563430279 # stata obj.llr = 1631.224718197351 # stata obj.llf = -43383.66207653563 # stata obj.df_model = 9.0 obj.llr_pvalue = 0.0 return obj negativebinomial_nb2_bfgs = negativebinomial_nb2_bfgs() def negativebinomial_nb1_bfgs(): # Unpublished implementation intended for R's COUNT package. Sent by # J.Hilbe (of Cambridge UP NBin book) and Andrew Robinson to Vincent # Arel-Bundock on 2012-12-06. # TODO: Does the from Stata comment below apply to the # commented-out obj.params here or to everything below? If the # latter, then where do the commented-out version come from? # obj.params = [-0.065309744899923, -0.296016207412261, # 0.0411724098925173, -0.0320460533573259, 0.19083354227553, # 0.0318566232844115, -0.0331972813313092, -0.0484691550721231, # 0.111971860837541, 0.757560143822609, # 3.73086958562569] # from Stata obj = Namespace() obj.nobs = 20190 obj.params = [-.065317260803762961, -.296023807893893376, .041187021258044826, -.032028789543547605, .19065933246421754, .031871625115758778, -.033250849053302826, -.04850769174426571, .111813637465757343, .757277086555503409, 3.731151380800305] # lnalpha and lnalpha_std_err are from stata obj.lnalpha = 1.316716867203 obj.lnalpha_std_err = .0168876692 obj.bse = [ 0.00536019929563678, 0.0196998350459769, 0.00335779098766272, 0.00301145915122889, 0.0237984097096245, 0.00107360844112751, 0.0167174614755359, 0.0298037989274781, 0.0546838603596457, 0.0214703279904911, 0.0630011409376052] obj.z = [ -12.1842008660173, -15.0263292419148, 12.2617548393554, -10.6413707601675, 8.0187518663633, 29.6724784046551, -1.98578482623631, -1.62627439508848, 2.04762173155154, 35.2840508145997, # From R, this is alpha/bse(alpha) 59.2190796881069 # taken from Stata even though they do not report it # lnalpha/bse(lnalpha) # 77.968995 ] obj.conf_int = [ [-0.075815736, -0.0548037543], [-0.334627884, -0.2574045307], [0.034591140, 0.0477536802], [-0.037948513, -0.0261435934], [0.144188659, 0.2374784253], [0.029752351, 0.0339608958], [-0.065963506, -0.0004310568], [-0.106884601, 0.0099462908], [0.004791495, 0.2191522271], [3.607387349, 3.8543518219], [0.715478301, 0.7996419867]] # from Stata obj.llf = -43278.75612911823 obj.llnull = -44199.2744356343 obj.llr = 1841.036613032149 obj.aic = 86579.51225823645655 obj.bic = 86666.55462806082505 obj.llr_pvalue = 0.0 obj.df_model = 9.0 obj.df_resid = 20180.0 # Smoke tests TODO: check against other stats package obj.pvalues = [ 3.65557865e-034, 5.24431864e-051, 1.42921171e-034, 2.09797259e-026, 1.15949461e-015, 1.56785415e-193, 4.71746349e-002, 1.04731854e-001, 4.07534831e-002, 1.95504975e-272, 0.00000000e+000] obj.conf_int = [ [-.0758236, -.054811], [-.3346363, -.2574113], [.0346053, .0477687], [-.0379314, -.0261261], [.1440119, .2373067], [.0297667, .0339766], [-.0660178, -.0004839], [-.1069241, .0099087], [.0046266, .2190007], [.7151889, .7993652], # from stata for alpha no lnalpha [3.609675, 3.856716]] # [1.28360034e+00, 1.34979803e+00]] obj.fittedvalues = [ 0.8487497, 0.8487497, 0.8487497, 0.8487497, 0.8487497, 0.88201746, 0.88201746, 0.88201746, 0.88201746, 0.88201746] return obj negativebinomial_nb1_bfgs = negativebinomial_nb1_bfgs() def negativebinomial_geometric_bfgs(): # Smoke tests TODO: Cross check with other stats package obj = Namespace() obj.nobs = 20190 obj.params = [ -0.05768894, -0.26646696, 0.04088528, -0.03795503, 0.26885821, 0.03802523, -0.04308456, 0.01931675, 0.18051684, 0.66469896] obj.bse = [ 0.00553867, 0.02061988, 0.00375937, 0.0030924, 0.02701658, 0.00132201, 0.01821646, 0.03271784, 0.06666231, 0.02250053] obj.pvalues = [ 2.10310916e-025, 3.34666368e-038, 1.50697768e-027, 1.25468406e-034, 2.48155744e-023, 6.18745348e-182, 1.80230194e-002, 5.54919603e-001, 6.77044178e-003, 8.44913440e-192] obj.z = [-10.41567024, -12.92281571, 10.8755779, -12.27364916, 9.95160202, 28.76323587, -2.36514487, 0.59040434, 2.70792943, 29.54148082] obj.aic = 87101.159433012392 # old value 87101.160011780419 obj.bic = 87180.288860125467 # old value 87180.289438893495 obj.df_model = 9.0 obj.df_resid = 20180.0 obj.llf = -43540.58000589021 obj.llnull = -44586.650971362695 # old value -44199.27443567125 obj.llr = 2092.1425097129977 # old value 1317.3888595620811 obj.llr_pvalue = 0 # old value 5.4288002863296022e-278 obj.fittedvalues = [ 0.89348994, 0.89348994, 0.89348994, 0.89348994, 0.89348994, 0.9365745, 0.9365745, 0.9365745, 0.9365745, 0.9365745] obj.conf_int = [ [-0.06854453, -0.04683335], [-0.30688118, -0.22605273], [0.03351706, 0.04825351], [-0.04401602, -0.03189404], [0.21590669, 0.32180972], [0.03543415, 0.04061632], [-0.07878816, -0.00738096], [-0.04480903, 0.08344253], [0.04986111, 0.31117258], [0.62059873, 0.70879919]] return obj negativebinomial_geometric_bfgs = negativebinomial_geometric_bfgs() def generalizedpoisson_gp2(): # Stata gnpoisson function obj = Namespace() obj.nobs = 20190 obj.llf = -43326.42720093228 obj.params = [-0.0604495342, -0.277717228, 0.0438136144, -0.0395811744, 0.273044906, 0.0399108677, -0.0552626543, -0.001227569488, 0.151980519, 0.651125316, 0.448085318] obj.lnalpha_std_err = 0.0125607 obj.lnalpha = -0.8027716 obj.bse = [0.00634704, 0.02381906, 0.00443871, 0.00355094, 0.0334247, 0.00166303, 0.02102142, 0.0390845, 0.087821, 0.02626823, 0.00562825] obj.df_model = 9 obj.aic = 86674.854401865 obj.conf_int = [ [-0.07288951, -0.04800956], [-0.32440173, -0.23103272], [0.03511389, 0.05251333], [-0.04654088, -0.03262147], [0.20753371, 0.33855610], [0.03665139, 0.04317034], [-0.09646387, -0.01406144], [-0.07783191, 0.07537652], [-0.02014548, 0.32410651], [0.59964053, 0.70261011], [0.43718883, 0.45925338] ] obj.bic = 86761.896771689 obj.wald_pvalue = 4.8795019354e-254 obj.wald_statistic = 1206.46339591254 return obj generalizedpoisson_gp2 = generalizedpoisson_gp2() def zero_inflated_poisson_logit(): obj = Namespace() obj.nobs = 20190 obj.params = [.1033783, -1.045983, -.0821979, .0085692, -.0267957, 1.482363] obj.llf = -57005.72199826186 obj.bse = [0.0079912, 0.02235510, .0107145, 0.0018697, 0.0014121, 0.0085915] obj.conf_int = [ [0.0877159, 0.1190408], [-1.089798, -1.002167], [-0.1031979, -0.061198], [0.0049045, 0.0122338], [-0.0295635, -0.024028], [1.465524, 1.499202]] obj.aic = 114023.444 obj.bic = 114070.9 return obj zero_inflated_poisson_logit = zero_inflated_poisson_logit() def zero_inflated_poisson_probit(): obj = Namespace() obj.nobs = 20190 obj.params = [.0622534, -.6429324, -.0821788, .0085673, -.0267952, 1.482369] obj.llf = -57006.05 obj.bse = [.0048228, .0132516, .0107142, .0018697, .0014121, .0085913] obj.conf_int = [ [0.0528009, .0717058], [-0.6689051, -.6169597], [-0.1031783, -.0611793], [0.0049027, .0122319], [-0.0295629, -.0240275], [1.46553, 1.499208]] obj.aic = 114024.1 obj.bic = 114071.6 return obj zero_inflated_poisson_probit = zero_inflated_poisson_probit() def zero_inflated_poisson_offset(): obj = Namespace() obj.nobs = 20190 obj.params = [.1052014, -1.082434, -.0922822, .0115868, -.0283842, 1.347514] obj.llf = -58207.67 obj.bse = [.0081836, .0230043, .0107788, .0018687, .0014162, .0086309] obj.conf_int = [ [.0891619, .1212409], [-1.127522, -1.037347], [-.1134082, -.0711561], [.0079242, .0152494], [-.0311599, -.0256085], [1.330598, 1.36443]] obj.aic = 116427.3 obj.bic = 116474.8 return obj zero_inflated_poisson_offset = zero_inflated_poisson_offset() def zero_inflated_generalized_poisson(): obj = Namespace() obj.nobs = 20190 obj.params = [3.57337, -17.95797, -0.21380, 0.03847, -0.05348, 1.15666, 1.36468] obj.llf = -43630.6 obj.bse = [1.66109, 7.62052, 0.02066, 0.00339, 0.00289, 0.01680, 0.01606] obj.aic = 87275 return obj zero_inflated_generalized_poisson = zero_inflated_generalized_poisson() def zero_inflated_negative_binomial(): obj = Namespace() obj.params = [1.883859, -10.280888, -0.204769, 1.137985, 1.344457] obj.llf = -44077.91 obj.bse = [0.3653, 1.6694, 0.02178, 0.01163, 0.0217496] obj.aic = 88165.81 return obj zero_inflated_negative_binomial = zero_inflated_negative_binomial() statsmodels-0.12.2/statsmodels/discrete/tests/results/results_glm_logit_constrained.py000066400000000000000000000577431400612667500316750ustar00rootroot00000000000000import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch est = dict( k_eq_model=0, phi=1, vf=1, df=28, df_m=3, power=0, canonical=1, rank=4, aic=1.055602138883215, rc=0, p=.0388431588742135, chi2=8.376256383189103, ll=-12.88963422213144, k_autoCns=0, converged=1, k_dv=1, k_eq=1, k=4, ic=3, N=32, nbml=0, bic=-71.26133683412948, dispers_ps=.9734684585933382, deviance_ps=27.25711684061347, dispers_p=.9734684585933382, deviance_p=27.25711684061347, dispers_s=.920688158723674, deviance_s=25.77926844426287, dispers=.920688158723674, deviance=25.77926844426287, cmdline="glm grade gpa tuce psi, family(binomial)", cmd="glm", predict="glim_p", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 marginsok="default", hac_lag="30", vcetype="OIM", vce="oim", linkt="Logit", linkf="ln(u/(1-u))", varfunct="Bernoulli", varfuncf="u*(1-u)", opt1="ML", oim="oim", a="1", m="1", varfunc="glim_v2", link="glim_l02", chi2type="Wald", opt="moptimize", title="Generalized linear models", user="glim_lf", crittype="log likelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="grade", properties="b V", ) params_table = np.array([ 2.8261124216999, 1.2629410221647, 2.2377231969675, .02523911156938, .35079350365878, 5.301431339741, np.nan, 1.9599639845401, 0, .09515765001172, .141554201358, .67223472774972, .50143427587633, -.18228348651028, .37259878653373, np.nan, 1.9599639845401, 0, 2.3786875040587, 1.0645642078703, 2.2344237073472, .02545520725424, .29217999740245, 4.4651950107149, np.nan, 1.9599639845401, 0, -13.021345912635, 4.931323890811, -2.6405375515688, .00827746189686, -22.686563134726, -3.3561286905433, np.nan, 1.9599639845401, 0 ]).reshape(4, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'gpa tuce psi _cons'.split() cov = np.array([ 1.5950200254665, -.03692058012179, .42761557297075, -4.5734780841711, -.03692058012179, .0200375919221, .01491263753083, -.34625566662867, .42761557297075, .01491263753083, 1.1332969526786, -2.3591604492672, -4.5734780841711, -.34625566662867, -2.3591604492672, 24.317955316083 ]).reshape(4, 4) cov_colnames = 'gpa tuce psi _cons'.split() cov_rownames = 'gpa tuce psi _cons'.split() infocrit = np.array([ 32, np.nan, -12.889634222131, 4, 33.779268444263, 39.642212055462]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() results_noconstraint = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, **est ) est = dict( k_eq_model=0, phi=1, vf=1, df=28, df_m=3, power=0, canonical=1, rank=4, aic=1.055602138883215, rc=0, p=.0248623136764981, chi2=9.360530997638559, ll=-12.88963422213144, k_autoCns=0, converged=1, k_dv=1, k_eq=1, k=4, ic=3, N=32, nbml=0, bic=-71.26133683412948, dispers_ps=.9734684585933382, deviance_ps=27.25711684061347, dispers_p=.9734684585933382, deviance_p=27.25711684061347, dispers_s=.920688158723674, deviance_s=25.77926844426287, dispers=.920688158723674, deviance=25.77926844426287, cmdline="glm grade gpa tuce psi, family(binomial) vce(robust)", cmd="glm", predict="glim_p", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 marginsok="default", hac_lag="30", vcetype="Robust", vce="robust", linkt="Logit", linkf="ln(u/(1-u))", varfunct="Bernoulli", varfuncf="u*(1-u)", opt1="ML", oim="oim", a="1", m="1", varfunc="glim_v2", link="glim_l02", chi2type="Wald", opt="moptimize", title="Generalized linear models", user="glim_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="grade", properties="b V", ) params_table = np.array([ 2.8261124216999, 1.287827879216, 2.1944799202672, .02820092594159, .30201616014984, 5.3502086832499, np.nan, 1.9599639845401, 0, .09515765001172, .1198091371814, .79424367999287, .42705358424294, -.13966394388263, .32997924390608, np.nan, 1.9599639845401, 0, 2.3786875040587, .97985082470462, 2.4276016757712, .01519902587997, .45821517741577, 4.2991598307016, np.nan, 1.9599639845401, 0, -13.021345912635, 5.2807513766642, -2.4658130981467, .01367026437574, -23.371428422207, -2.6712634030626, np.nan, 1.9599639845401, 0 ]).reshape(4, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'gpa tuce psi _cons'.split() cov = np.array([ 1.6585006464861, .00630184631279, .20368998146717, -5.7738061195745, .00630184631279, .01435422935215, .01997066738212, -.34768562593344, .20368998146717, .01997066738212, .96010763867432, -1.5315997267117, -5.7738061195745, -.34768562593344, -1.5315997267117, 27.886335102141 ]).reshape(4, 4) cov_colnames = 'gpa tuce psi _cons'.split() cov_rownames = 'gpa tuce psi _cons'.split() infocrit = np.array([ 32, np.nan, -12.889634222131, 4, 33.779268444263, 39.642212055462]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() results_noconstraint_robust = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, **est ) est = dict( k_eq_model=0, phi=1, vf=1, df=29, df_m=2, power=0, canonical=1, rank=3, aic=.993115540206396, rc=0, p=.0600760311411508, chi2=5.624288666552698, ll=-12.88984864330234, k_autoCns=0, converged=1, k_dv=1, k_eq=1, k=4, ic=3, N=32, nbml=0, bic=-74.7266438945874, dispers_ps=.9340711710496038, deviance_ps=27.08806396043851, dispers_p=.9340711710496038, deviance_p=27.08806396043851, dispers_s=.8889550788484368, deviance_s=25.77969728660467, dispers=.8889550788484368, deviance=25.77969728660467, cmdline="glm grade gpa tuce psi, family(binomial) constraints(1)", cmd="glm", predict="glim_p", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 marginsok="default", hac_lag="30", vcetype="OIM", vce="oim", linkt="Logit", linkf="ln(u/(1-u))", varfunct="Bernoulli", varfuncf="u*(1-u)", opt1="ML", oim="oim", a="1", m="1", varfunc="glim_v2", link="glim_l02", chi2type="Wald", opt="moptimize", title="Generalized linear models", user="glim_lf", crittype="log likelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="grade", properties="b V", ) params_table = np.array([ 2.8, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, 1.9599639845401, 0, .09576464077943, .13824841412912, .69269974185736, .48849800113543, -.17519727183342, .36672655339228, np.nan, 1.9599639845401, 0, 2.3717067235827, 1.0071435928909, 2.3548843882081, .01852846934254, .39774155425619, 4.3456718929091, np.nan, 1.9599639845401, 0, -12.946549758905, 3.3404275889275, -3.8757163309928, .00010631147941, -19.493667526167, -6.3994319916434, np.nan, 1.9599639845401, 0 ]).reshape(4, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'gpa tuce psi _cons'.split() cov = np.array([ 0, 0, 0, 0, 0, .01911262400922, .02461998233256, -.45036648979107, 0, .02461998233256, 1.0143382167012, -1.126241119498, 0, -.45036648979107, -1.126241119498, 11.158456476868 ]).reshape(4, 4) cov_colnames = 'gpa tuce psi _cons'.split() cov_rownames = 'gpa tuce psi _cons'.split() infocrit = np.array([ 32, np.nan, -12.889848643302, 3, 31.779697286605, 36.176904995004]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() results_constraint1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, **est ) est = dict( k_eq_model=0, phi=1, vf=1, df=29, df_m=2, power=0, canonical=1, rank=3, aic=.9965088127779717, rc=0, p=.0151376593316312, chi2=8.381139289068923, ll=-12.94414100444755, k_autoCns=0, converged=1, k_dv=1, k_eq=1, k=4, ic=3, N=32, nbml=0, bic=-74.61805917229698, dispers_ps=.9101961406899989, deviance_ps=26.39568808000997, dispers_p=.9101961406899989, deviance_p=26.39568808000997, dispers_s=.892699379617072, deviance_s=25.88828200889509, dispers=.892699379617072, deviance=25.88828200889509, cmdline="glm grade gpa tuce psi, family(binomial) constraints(2)", cmd="glm", predict="glim_p", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 marginsok="default", hac_lag="30", vcetype="OIM", vce="oim", linkt="Logit", linkf="ln(u/(1-u))", varfunct="Bernoulli", varfuncf="u*(1-u)", opt1="ML", oim="oim", a="1", m="1", varfunc="glim_v2", link="glim_l02", chi2type="Wald", opt="moptimize", title="Generalized linear models", user="glim_lf", crittype="log likelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="grade", properties="b V", ) params_table = np.array([ 2.5537914524884, .92662050289421, 2.7560273537138, .00585081038138, .73764863947939, 4.3699342654975, np.nan, 1.9599639845401, 0, .10791139824293, .13554656123081, .79612051580696, .42596199070477, -.15775497999771, .37357777648357, np.nan, 1.9599639845401, 0, 2.5537914524884, .92662050289421, 2.7560273537138, .00585081038138, .73764863947939, 4.3699342654975, np.nan, 1.9599639845401, 0, -12.527922070831, 4.6393777844052, -2.7003453163357, .00692675392223, -21.62093543894, -3.4349087027211, np.nan, 1.9599639845401, 0 ]).reshape(4, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'gpa tuce psi _cons'.split() cov = np.array([ .85862555638391, -.00408642741742, .85862555638391, -3.1725052764862, -.00408642741742, .0183728702615, -.00408642741742, -.40376368789892, .85862555638391, -.00408642741742, .85862555638391, -3.1725052764862, -3.1725052764862, -.40376368789892, -3.1725052764862, 21.523826226433 ]).reshape(4, 4) cov_colnames = 'gpa tuce psi _cons'.split() cov_rownames = 'gpa tuce psi _cons'.split() infocrit = np.array([ 32, np.nan, -12.944141004448, 3, 31.888282008895, 36.285489717294]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predict_mu = np.array([ .02720933393726, .05877785527304, .17341537851768, .02240274574181, .48834788561471, .03262255746648, .02545734725406, .05057489993471, .10986224061161, .64848146294279, .02525325609066, .17259131542841, .28314297612096, .18171413480391, .33018645131295, .02988039105483, .05693576903037, .03731338966779, .61672273095571, .68861137241716, .08792248035539, .90822178043053, .25295501355621, .85758484919326, .83972248507748, .54158048311843, .62661357692624, .36224489285202, .83387563062407, .93837010344092, .55200183830167, .13940358008872 ]) predict_mu_colnames = 'predict_mu'.split() predict_mu_rownames = ['r'+str(n) for n in range(1, 33)] predict_linpred_std = np.array([ 1.2186852972383, .98250143329647, .71300625338041, 1.7281112031272, .58278126610648, 1.2588643933597, 1.323097466817, 1.0187451680624, .92583226681839, .97445803529749, 1.2426520057509, .66674211884633, .53877733839827, .77006015103931, .70670367147137, 1.2036701125873, 1.1407798755705, 1.1376397495763, .57331962577752, .65764380198652, .85122884445037, 1.1282943138296, 1.2981327331615, .91561885084703, .8524827403359, .75030433039358, 1.0902299962647, .53350768600347, .96511132361274, 1.2127047415358, .61923877005984, .80300912367498 ]) predict_linpred_std_colnames = 'predict_linpred_std'.split() predict_linpred_std_rownames = ['r'+str(n) for n in range(1, 33)] predict_hat = np.array([ .03931157544567, .05340381182541, .07287215399916, .06540404284993, .0848623883214, .0500117280211, .04343078449564, .04983412818394, .08382437063813, .21645722203914, .03801090644315, .06348261316195, .05891921860299, .08817451110282, .11045563375857, .04199779738721, .06987634275981, .04648995770552, .0776956378885, .09273814423054, .05810645039404, .10611489289649, .31844046474321, .10239122636412, .09780916971071, .13976583081559, .27809589396914, .06575633167064, .12902962938834, .08505028097419, .09482722348113, .07735963673184 ]) predict_hat_colnames = 'predict_hat'.split() predict_hat_rownames = ['r'+str(n) for n in range(1, 33)] results_constraint2 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predict_mu=predict_mu, predict_mu_colnames=predict_mu_colnames, predict_mu_rownames=predict_mu_rownames, predict_linpred_std=predict_linpred_std, predict_linpred_std_colnames=predict_linpred_std_colnames, predict_linpred_std_rownames=predict_linpred_std_rownames, predict_hat=predict_hat, predict_hat_colnames=predict_hat_colnames, predict_hat_rownames=predict_hat_rownames, **est ) est = dict( k_eq_model=0, phi=1, vf=1, df=29, df_m=2, power=0, canonical=1, rank=3, aic=.9965088127779717, rc=0, p=.0085760854232441, chi2=9.517555427941099, ll=-12.94414100444755, k_autoCns=0, converged=1, k_dv=1, k_eq=1, k=4, ic=3, N=32, nbml=0, bic=-74.61805917229698, dispers_ps=.9101961406899989, deviance_ps=26.39568808000997, dispers_p=.9101961406899989, deviance_p=26.39568808000997, dispers_s=.892699379617072, deviance_s=25.88828200889509, dispers=.892699379617072, deviance=25.88828200889509, cmdline="glm grade gpa tuce psi, family(binomial) constraints(2) vce(robust)", # noqa:E501 cmd="glm", predict="glim_p", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 marginsok="default", hac_lag="30", vcetype="Robust", vce="robust", linkt="Logit", linkf="ln(u/(1-u))", varfunct="Bernoulli", varfuncf="u*(1-u)", opt1="ML", oim="oim", a="1", m="1", varfunc="glim_v2", link="glim_l02", chi2type="Wald", opt="moptimize", title="Generalized linear models", user="glim_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="grade", properties="b V", ) params_table = np.array([ 2.5537914524884, .83609404798719, 3.0544308485827, .00225487991353, .91507723074524, 4.1925056742316, np.nan, 1.9599639845401, 0, .10791139824293, .12275592600281, .8790728216287, .37936179287834, -.13268579561143, .3485085920973, np.nan, 1.9599639845401, 0, 2.5537914524884, .83609404798719, 3.0544308485827, .00225487991353, .91507723074524, 4.1925056742316, np.nan, 1.9599639845401, 0, -12.527922070831, 4.510414281113, -2.7775546302454, .00547696322683, -21.368171617167, -3.6876725244938, np.nan, 1.9599639845401, 0 ]).reshape(4, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'gpa tuce psi _cons'.split() cov = np.array([ .6990532570796, .01512804251258, .6990532570796, -2.9662622048441, .01512804251258, .01506901736881, .01512804251258, -.3968065659911, .6990532570796, .01512804251258, .6990532570796, -2.9662622048441, -2.9662622048441, -.3968065659911, -2.9662622048441, 20.343836987269 ]).reshape(4, 4) cov_colnames = 'gpa tuce psi _cons'.split() cov_rownames = 'gpa tuce psi _cons'.split() infocrit = np.array([ 32, np.nan, -12.944141004448, 3, 31.888282008895, 36.285489717294]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() results_constraint2_robust = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, **est ) est = dict( N_cds=0, N_cdf=0, p=.0151376589433054, chi2=8.381139340374848, df_m=2, k_eq_model=1, ll=-12.94414100444751, k_autoCns=0, rc=0, converged=1, k_dv=1, k_eq=1, k=4, ic=5, N=32, rank=3, cmdline="logit grade gpa tuce psi, constraints(2)", cmd="logit", estat_cmd="logit_estat", predict="logit_p", marginsnotok="stdp DBeta DEviance DX2 DDeviance Hat Number Residuals RStandard SCore", # noqa:E501 title="Logistic regression", chi2type="Wald", opt="moptimize", vce="oim", user="mopt__logit_d2()", crittype="log likelihood", ml_method="d2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="grade", properties="b V", ) params_table = np.array([ 2.5537916456996, .92662056628814, 2.7560273736742, .00585081002433, .73764870844071, 4.3699345829585, np.nan, 1.9599639845401, 0, .10791141442743, .13554656655573, .79612060393329, .42596193948753, -.15775497424986, .37357780310472, np.nan, 1.9599639845401, 0, 2.5537916456996, .92662056628814, 2.7560273736742, .00585081002433, .73764870844071, 4.3699345829585, np.nan, 1.9599639845401, 0, -12.527923225554, 4.6393781670436, -2.7003453425175, .00692675337706, -21.62093734362, -3.4349091074867, np.nan, 1.9599639845401, 0 ]).reshape(4, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'gpa tuce psi _cons'.split() cov = np.array([ .85862567386816, -.00408642236043, .85862567386816, -3.172505858545, -.00408642236043, .01837287170505, -.00408642236043, -.40376374127778, .85862567386816, -.00408642236043, .85862567386816, -3.172505858545, -3.172505858545, -.40376374127778, -3.172505858545, 21.523829776841 ]).reshape(4, 4) cov_colnames = 'gpa tuce psi _cons'.split() cov_rownames = 'gpa tuce psi _cons'.split() infocrit = np.array([ 32, np.nan, -12.944141004448, 3, 31.888282008895, 36.285489717294]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() results_logit_constraint2 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, **est ) statsmodels-0.12.2/statsmodels/discrete/tests/results/results_poisson_constrained.py000066400000000000000000000664221400612667500314040ustar00rootroot00000000000000import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch est = dict( rank=7, N=10, ic=3, k=8, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=1, ll=-33.45804471711131, k_eq_model=1, ll_0=-349.6684656479622, df_m=6, chi2=632.4208418617018, p=2.3617193197e-133, r2_p=.9043149497192691, cmdline="poisson deaths lnpyears smokes i.agecat", cmd="poisson", predict="poisso_p", estat_cmd="poisson_estat", gof="poiss_g", chi2type="LR", opt="moptimize", vce="oim", title="Poisson regression", user="poiss_lf", crittype="log likelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="deaths", properties="b V", ) params_table = np.array([ .66308184237808, .63593388706566, 1.0426899019923, .29709193621918, -.58332567281917, 1.9094893575753, np.nan, 1.9599639845401, 0, .84966723812924, .94279599903649, .90122066597395, .36747100512904, -.99817896475073, 2.6975134410092, np.nan, 1.9599639845401, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, 1.9599639845401, 0, 1.3944392032504, .25613243411925, 5.4442117338454, 5.203529593e-08, .8924288571041, 1.8964495493967, np.nan, 1.9599639845401, 0, 2.389284381366, .48305517266329, 4.9461935542328, 7.567871319e-07, 1.4425136404002, 3.3360551223318, np.nan, 1.9599639845401, 0, 2.8385093615484, .98099727008295, 2.8934936397003, .00380982006764, .91579004325369, 4.7612286798431, np.nan, 1.9599639845401, 0, 2.9103531988515, 1.500316321385, 1.9398263935201, .05240079188831, -.03021275648066, 5.8509191541838, np.nan, 1.9599639845401, 0, -4.724924181641, 6.0276019460727, -.78388125558284, .43310978942119, -16.538806909087, 7.088958545805, np.nan, 1.9599639845401, 0 ]).reshape(8, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['lnpyears', 'smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov = np.array([ .40441190871844, -.59566294916097, 0, .1055698685775, .28413388045122, .61269322798077, .94624135329227, -3.8311942353131, -.59566294916097, .88886429579921, 0, -.15587944298625, -.4190789999425, -.90299843943229, -1.3940094688194, 5.6335527795822, 0, 0, 0, 0, 0, 0, 0, 0, .1055698685775, -.15587944298625, 0, .06560382380785, .10360281461667, .18937107288073, .27643306166968, -1.029211453947, .28413388045122, -.4190789999425, 0, .10360281461667, .23334229983676, .45990880867889, .69424104947043, -2.7206801001387, .61269322798077, -.90299843943229, 0, .18937107288073, .45990880867889, .96235564391021, 1.4630024143274, -5.8333014154113, .94624135329227, -1.3940094688194, 0, .27643306166968, .69424104947043, 1.4630024143274, 2.2509490642142, -8.993394678922, -3.8311942353131, 5.6335527795822, 0, -1.029211453947, -2.7206801001387, -5.8333014154113, -8.993394678922, 36.331985220299 ]).reshape(8, 8) cov_colnames = ['lnpyears', 'smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov_rownames = ['lnpyears', 'smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] results_noexposure_noconstraint = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=6, N=10, ic=3, k=7, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=1, ll=-33.6001534405213, k_eq_model=1, ll_0=-495.0676356770329, df_m=5, chi2=922.9349644730232, p=2.8920463572e-197, r2_p=.9321301757191799, cmdline="poisson deaths smokes i.agecat, exposure(pyears)", cmd="poisson", predict="poisso_p", estat_cmd="poisson_estat", offset="ln(pyears)", gof="poiss_g", chi2type="LR", opt="moptimize", vce="oim", title="Poisson regression", user="poiss_lf", crittype="log likelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="deaths", properties="b V", ) params_table = np.array([ .35453563725291, .10737411818853, 3.3018723993653, .00096041750265, .14408623273163, .56498504177418, np.nan, 1.9599639845401, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, 1.9599639845401, 0, 1.4840070063099, .19510337263434, 7.606260139291, 2.821411159e-14, 1.1016114226842, 1.8664025899355, np.nan, 1.9599639845401, 0, 2.6275051184579, .18372726944827, 14.301116684248, 2.153264398e-46, 2.2674062873614, 2.9876039495544, np.nan, 1.9599639845401, 0, 3.350492785161, .18479918093323, 18.130452571495, 1.832448146e-73, 2.9882930461593, 3.7126925241626, np.nan, 1.9599639845401, 0, 3.7000964518246, .19221951212105, 19.24932807807, 1.430055953e-82, 3.3233531309415, 4.0768397727077, np.nan, 1.9599639845401, 0, -7.919325711822, .19176181876223, -41.297719029467, 0, -8.2951719702059, -7.5434794534381, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov = np.array([ .01152920125677, 0, -.00061561668833, -.00090117889461, -.00087280941113, -.00045274641397, -.00921219275997, 0, 0, 0, 0, 0, 0, 0, -.00061561668833, 0, .0380653260133, .02945988432334, .02945836949789, .0294359396881, -.0289198676971, -.00090117889461, 0, .02945988432334, .03375570953892, .0294799877675, .02944715358419, -.02869169455392, -.00087280941113, 0, .02945836949789, .0294799877675, .03415073727359, .02944603952766, -.02871436265941, -.00045274641397, 0, .0294359396881, .02944715358419, .02944603952766, .03694834084006, -.02905000614546, -.00921219275997, 0, -.0289198676971, -.02869169455392, -.02871436265941, -.02905000614546, .036772595135]).reshape(7, 7) cov_colnames = ['smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov_rownames = ['smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] results_exposure_noconstraint = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=6, N=10, ic=4, k=8, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=1, ll=-33.46699798755848, k_eq_model=1, df_m=5, chi2=452.5895246742914, p=1.35732711092e-95, r2_p=np.nan, cmdline="poisson deaths lnpyears smokes i.agecat, constraints(1)", cmd="poisson", predict="poisso_p", estat_cmd="poisson_estat", gof="poiss_g", chi2type="Wald", opt="moptimize", vce="oim", title="Poisson regression", user="poiss_lf", crittype="log likelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="deaths", properties="b V", ) params_table = np.array([ .57966535352347, .13107152221057, 4.4225117992619, 9.756001957e-06, .32276989059191, .83656081645503, np.nan, 1.9599639845401, 0, .97254074124891, .22289894431919, 4.3631464663029, .00001282050472, .5356668381913, 1.4094146443065, np.nan, 1.9599639845401, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, 1.9599639845401, 0, 1.3727621378494, .19798042377276, 6.9338276567436, 4.096036246e-12, .98472763761078, 1.760796638088, np.nan, 1.9599639845401, 0, 2.3307703209845, .20530981936838, 11.352454199, 7.210981748e-30, 1.92837046935, 2.7331701726189, np.nan, 1.9599639845401, 0, 2.71338890728, .29962471107816, 9.0559583604312, 1.353737255e-19, 2.1261352646886, 3.3006425498714, np.nan, 1.9599639845401, 0, 2.71338890728, .29962471107816, 9.0559583604312, 1.353737255e-19, 2.1261352646886, 3.3006425498714, np.nan, 1.9599639845401, 0, -3.9347864312059, 1.2543868840549, -3.1368204508696, .00170790683415, -6.3933395466329, -1.476233315779, np.nan, 1.9599639845401, 0 ]).reshape(8, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['lnpyears', 'smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov = np.array([ .0171797439346, -.02561346650005, 0, .00445310785396, .01204526460873, .03142116278001, .03142116278001, -.16245493266167, -.02561346650005, .04968393937861, 0, -.0069699735991, -.01845598801461, -.04723465558226, -.04723465558226, .2326939064726, 0, 0, 0, 0, 0, 0, 0, 0, .00445310785396, -.0069699735991, 0, .03919624819724, .03254829669461, .03756752462584, .03756752462584, -.07124751761252, .01204526460873, -.01845598801461, 0, .03254829669461, .04215212192908, .05145895528528, .05145895528528, -.14290240509701, .03142116278001, -.04723465558226, 0, .03756752462584, .05145895528528, .08977496748867, .08977496748867, -.32621483141938, .03142116278001, -.04723465558226, 0, .03756752462584, .05145895528528, .08977496748867, .08977496748867, -.32621483141938, -.16245493266167, .2326939064726, 0, -.07124751761252, -.14290240509701, -.32621483141938, -.32621483141938, 1.5734864548889 ]).reshape(8, 8) cov_colnames = ['lnpyears', 'smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov_rownames = ['lnpyears', 'smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] results_noexposure_constraint = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=5, N=10, ic=3, k=7, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=1, ll=-38.45090497564205, k_eq_model=1, df_m=4, chi2=641.6446542589836, p=1.5005477751e-137, r2_p=np.nan, cmdline=("poisson deaths smokes i.agecat, " "exposure(pyears) constraints(1)"), cmd="poisson", predict="poisso_p", estat_cmd="poisson_estat", offset="ln(pyears)", gof="poiss_g", chi2type="Wald", opt="moptimize", vce="oim", title="Poisson regression", user="poiss_lf", crittype="log likelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="deaths", properties="b V", ) params_table = np.array([ .34304077058284, .1073083520206, 3.196776058186, .00138972774083, .13272026538212, .55336127578356, np.nan, 1.9599639845401, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, 1.9599639845401, 0, 1.4846230896448, .19510453584194, 7.6093724999174, 2.754298692e-14, 1.1022252261742, 1.8670209531154, np.nan, 1.9599639845401, 0, 2.6284071093765, .18373002757074, 14.305811326156, 2.012766793e-46, 2.2683028724593, 2.9885113462937, np.nan, 1.9599639845401, 0, 3.4712405808805, .17983994458502, 19.301833020969, 5.183735658e-83, 3.1187607665121, 3.8237203952488, np.nan, 1.9599639845401, 0, 3.4712405808805, .17983994458502, 19.301833020969, 5.183735658e-83, 3.1187607665121, 3.8237203952488, np.nan, 1.9599639845401, 0, -7.9101515866812, .19164951521841, -41.274049546467, 0, -8.2857777341639, -7.5345254391986, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov = np.array([ .01151508241338, 0, -.00061947268694, -.00090708285562, -.00074959767622, -.00074959767622, -.00917958318314, 0, 0, 0, 0, 0, 0, 0, -.00061947268694, 0, .0380657799061, .02946056271023, .0294520905375, .0294520905375, -.02891793401778, -.00090708285562, 0, .02946056271023, .03375672303114, .02947081310555, .02947081310555, -.02868865719866, -.00074959767622, 0, .0294520905375, .02947081310555, .03234240566834, .03234240566834, -.02881420109427, -.00074959767622, 0, .0294520905375, .02947081310555, .03234240566834, .03234240566834, -.02881420109427, -.00917958318314, 0, -.02891793401778, -.02868865719866, -.02881420109427, -.02881420109427, .03672953668345]).reshape(7, 7) cov_colnames = ['smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov_rownames = ['smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] results_exposure_constraint = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=6, N=10, ic=3, k=8, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=1, ll=-33.78306559091298, k_eq_model=1, df_m=5, chi2=526.719430888018, p=1.3614066522e-111, r2_p=np.nan, cmdline="poisson deaths lnpyears smokes i.agecat, constraints(2)", cmd="poisson", predict="poisso_p", estat_cmd="poisson_estat", gof="poiss_g", chi2type="Wald", opt="moptimize", vce="oim", title="Poisson regression", user="poiss_lf", crittype="log likelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="deaths", properties="b V", ) params_table = np.array([ 1.1598786864273, .13082965708054, 8.8655639119598, 7.611783820e-19, .90345727043975, 1.4163001024149, np.nan, 1.9599639845401, 0, .12111539473831, .22317899375276, .54268277090847, .58734823873758, -.31630739512299, .55853818459962, np.nan, 1.9599639845401, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, 1.9599639845401, 0, 1.5276244194375, .19848759770871, 7.6963217705896, 1.400389019e-14, 1.1385958765506, 1.9166529623245, np.nan, 1.9599639845401, 0, 2.7415571106656, .20647039325801, 13.278209371354, 3.097119459e-40, 2.3368825760061, 3.1462316453252, np.nan, 1.9599639845401, 0, 3.587300073596, .30160673316211, 11.893965482753, 1.272196529e-32, 2.9961617391034, 4.1784384080885, np.nan, 1.9599639845401, 0, 4.087300073596, .30160673316211, 13.551753406643, 7.735990122e-42, 3.4961617391034, 4.6784384080885, np.nan, 1.9599639845401, 0, -9.4376201542802, 1.2537557101599, -7.5274792990385, 5.172920628e-14, -11.894936191605, -6.9803041169553, np.nan, 1.9599639845401, 0 ]).reshape(8, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['lnpyears', 'smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov = np.array([ .01711639917181, -.02559852137367, 0, .00475026273828, .012305588195, .03167368550108, .03167368550108, -.16210959536359, -.02559852137367, .0498088632525, 0, -.00783669874902, -.01946551099054, -.0482099128044, -.0482099128044, .23336630265161, 0, 0, 0, 0, 0, 0, 0, 0, .00475026273828, -.00783669874902, 0, .03939732644417, .0328943776068, .0382554606876, .0382554606876, -.07382466315002, .012305588195, -.01946551099054, 0, .0328943776068, .04263002329212, .05226051095238, .05226051095238, -.14512177326509, .03167368550108, -.0482099128044, 0, .0382554606876, .05226051095238, .09096662148872, .09096662148872, -.32873181469848, .03167368550108, -.0482099128044, 0, .0382554606876, .05226051095238, .09096662148872, .09096662148872, -.32873181469848, -.16210959536359, .23336630265161, 0, -.07382466315002, -.14512177326509, -.32873181469848, -.32873181469848, 1.5719033807586 ]).reshape(8, 8) cov_colnames = ['lnpyears', 'smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov_rownames = ['lnpyears', 'smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] results_noexposure_constraint2 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=5, N=10, ic=3, k=7, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=1, ll=-34.5367006700131, k_eq_model=1, df_m=4, chi2=554.4168921897579, p=1.1331093797e-118, r2_p=np.nan, cmdline=("poisson deaths smokes i.agecat, " "exposure(pyears) constraints(2)"), cmd="poisson", predict="poisso_p", estat_cmd="poisson_estat", offset="ln(pyears)", gof="poiss_g", chi2type="Wald", opt="moptimize", vce="oim", title="Poisson regression", user="poiss_lf", crittype="log likelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="deaths", properties="b V", ) params_table = np.array([ .35978347114582, .10730668667519, 3.3528522992687, .00079983377167, .14946622996212, .57010071232952, np.nan, 1.9599639845401, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, 1.9599639845401, 0, 1.4837272702102, .19510269288329, 7.6048528509946, 2.852282383e-14, 1.1013330188722, 1.8661215215483, np.nan, 1.9599639845401, 0, 2.6270956495127, .18372567328363, 14.299012231442, 2.219372691e-46, 2.2669999468414, 2.987191352184, np.nan, 1.9599639845401, 0, 3.2898291023835, .17982035319735, 18.295087535352, 9.055555257e-75, 2.9373876864294, 3.6422705183376, np.nan, 1.9599639845401, 0, 3.7898291023835, .17982035319735, 21.075640409983, 1.330935038e-98, 3.4373876864294, 4.1422705183376, np.nan, 1.9599639845401, 0, -7.9235211042587, .19177810950798, -41.316087245761, 0, -8.2993992919175, -7.5476429165999, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov = np.array([ .01151472500521, 0, -.00061274288972, -.00089685568608, -.00069335681347, -.00069335681347, -.00921031399899, 0, 0, 0, 0, 0, 0, 0, -.00061274288972, 0, .03806506077031, .02945948985187, .02944866089267, .02944866089267, -.02892164840477, -.00089685568608, 0, .02945948985187, .03375512302352, .02946576868665, .02946576868665, -.0286943943397, -.00069335681347, 0, .02944866089267, .02946576868665, .03233535942402, .03233535942402, -.02885716752919, -.00069335681347, 0, .02944866089267, .02946576868665, .03233535942402, .03233535942402, -.02885716752919, -.00921031399899, 0, -.02892164840477, -.0286943943397, -.02885716752919, -.02885716752919, .03677884328645]).reshape(7, 7) cov_colnames = ['smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov_rownames = ['smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] results_exposure_constraint2 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=5, N=10, ic=3, k=7, k_eq=1, k_dv=1, converged=1, rc=0, k_autoCns=1, ll=-34.5367006700131, k_eq_model=1, df_m=4, chi2=582.5215805315736, p=9.3932644024e-125, r2_p=np.nan, cmdline=("poisson deaths smokes i.agecat," "exposure(pyears) constraints(2) vce(robust)"), cmd="poisson", predict="poisso_p", estat_cmd="poisson_estat", offset="ln(pyears)", gof="poiss_g", chi2type="Wald", opt="moptimize", vcetype="Robust", vce="robust", title="Poisson regression", user="poiss_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="deaths", properties="b V", ) params_table = np.array([ .35978347114582, .1172393358046, 3.0687948603312, .00214924117257, .1299985953974, .58956834689424, np.nan, 1.9599639845401, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, 1.9599639845401, 0, 1.4837272702102, .21969092615175, 6.7537030145039, 1.441186055e-11, 1.0531409672225, 1.9143135731979, np.nan, 1.9599639845401, 0, 2.6270956495127, .20894895542061, 12.572906355164, 2.975796525e-36, 2.217563222281, 3.0366280767443, np.nan, 1.9599639845401, 0, 3.2898291023835, .2211846822073, 14.873675109654, 4.885611722e-50, 2.8563150913252, 3.7233431134417, np.nan, 1.9599639845401, 0, 3.7898291023835, .2211846822073, 17.134229479922, 8.243780087e-66, 3.3563150913252, 4.2233431134417, np.nan, 1.9599639845401, 0, -7.9235211042587, .2479876721169, -31.951270144281, 5.18748229e-224, -8.4095680102177, -7.4374741982996, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov = np.array([ .0137450618599, 0, .00249770233028, .00412347653263, .00486142402447, .00486142402447, -.01620342093134, 0, 0, 0, 0, 0, 0, 0, .00249770233028, 0, .04826410303341, .04389964215014, .04391744129373, .04391744129373, -.04609122424924, .00412347653263, 0, .04389964215014, .04365966597136, .04367917402468, .04367917402468, -.04726310745444, .00486142402447, 0, .04391744129373, .04367917402468, .04892266364314, .04892266364314, -.04794543190806, .00486142402447, 0, .04391744129373, .04367917402468, .04892266364314, .04892266364314, -.04794543190806, -.01620342093134, 0, -.04609122424924, -.04726310745444, -.04794543190806, -.04794543190806, .06149788552196]).reshape(7, 7) cov_colnames = ['smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] cov_rownames = ['smokes', '1b.agecat', '2.agecat', '3.agecat', '4.agecat', '5.agecat', '_cons'] results_exposure_constraint2_robust = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) statsmodels-0.12.2/statsmodels/discrete/tests/results/ships.csv000066400000000000000000000015571400612667500250270ustar00rootroot00000000000000ship,yr_con,yr_op,service,accident,op_75_79,co_65_69,co_70_74,co_75_79 1,1,1,127,0,0,0,0,0 1,1,2,63,0,1,0,0,0 1,2,1,1095,3,0,1,0,0 1,2,2,1095,4,1,1,0,0 1,3,1,1512,6,0,0,1,0 1,3,2,3353,18,1,0,1,0 1,4,1,,,0,0,0,1 1,4,2,2244,11,1,0,0,1 2,1,1,44882,39,0,0,0,0 2,1,2,17176,29,1,0,0,0 2,2,1,28609,58,0,1,0,0 2,2,2,20370,53,1,1,0,0 2,3,1,7064,12,0,0,1,0 2,3,2,13099,44,1,0,1,0 2,4,1,,,0,0,0,1 2,4,2,7117,18,1,0,0,1 3,1,1,1179,1,0,0,0,0 3,1,2,552,1,1,0,0,0 3,2,1,781,0,0,1,0,0 3,2,2,676,1,1,1,0,0 3,3,1,783,6,0,0,1,0 3,3,2,1948,2,1,0,1,0 3,4,1,,,0,0,0,1 3,4,2,274,1,1,0,0,1 4,1,1,251,0,0,0,0,0 4,1,2,105,0,1,0,0,0 4,2,1,288,0,0,1,0,0 4,2,2,192,0,1,1,0,0 4,3,1,349,2,0,0,1,0 4,3,2,1208,11,1,0,1,0 4,4,1,,,0,0,0,1 4,4,2,2051,4,1,0,0,1 5,1,1,45,0,0,0,0,0 5,1,2,,,1,0,0,0 5,2,1,789,7,0,1,0,0 5,2,2,437,7,1,1,0,0 5,3,1,1157,5,0,0,1,0 5,3,2,2161,12,1,0,1,0 5,4,1,,,0,0,0,1 5,4,2,542,1,1,0,0,1 statsmodels-0.12.2/statsmodels/discrete/tests/results/sm3533.csv000066400000000000000000000146111400612667500246310ustar00rootroot00000000000000pp,num 10.171795655804711,1.0 10.501472042414694,1742.0 11.282291429896768,1.0 11.43695113687264,0.0 10.995897311894359,3071.0 11.259593288117415,4829.0 11.7913901878724,3.0 10.89529383688643,284.0 11.399319941347034,3558.0 11.142513744919452,2907.0 10.016101696905263,1.0 11.134749595299702,1.0 11.460178482911612,618.0 10.332962113104644,0.0 13.182255495711443,260.0 9.873234509365107,101.0 9.662243674190131,1.0 11.31757945705352,3196.0 11.17871067839023,1132.0 10.605321890243529,1072.0 10.849667129269148,17.0 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statsmodels-0.12.2/statsmodels/discrete/tests/test_conditional.py000066400000000000000000000226241400612667500253750ustar00rootroot00000000000000import numpy as np from statsmodels.discrete.conditional_models import ( ConditionalLogit, ConditionalPoisson, ConditionalMNLogit) from statsmodels.tools.numdiff import approx_fprime from numpy.testing import assert_allclose import pandas as pd def test_logit_1d(): y = np.r_[0, 1, 0, 1, 0, 1, 0, 1, 1, 1] g = np.r_[0, 0, 0, 1, 1, 1, 2, 2, 2, 2] x = np.r_[0, 1, 0, 0, 1, 1, 0, 0, 1, 0] x = x[:, None] model = ConditionalLogit(y, x, groups=g) # Check the gradient for the denominator of the partial likelihood for x in -1, 0, 1, 2: params = np.r_[x, ] _, grad = model._denom_grad(0, params) ngrad = approx_fprime(params, lambda x: model._denom(0, x)) assert_allclose(grad, ngrad) # Check the gradient for the loglikelihood for x in -1, 0, 1, 2: grad = approx_fprime(np.r_[x, ], model.loglike) score = model.score(np.r_[x, ]) assert_allclose(grad, score, rtol=1e-4) result = model.fit() # From Stata assert_allclose(result.params, np.r_[0.9272407], rtol=1e-5) assert_allclose(result.bse, np.r_[1.295155], rtol=1e-5) def test_logit_2d(): y = np.r_[0, 1, 0, 1, 0, 1, 0, 1, 1, 1] g = np.r_[0, 0, 0, 1, 1, 1, 2, 2, 2, 2] x1 = np.r_[0, 1, 0, 0, 1, 1, 0, 0, 1, 0] x2 = np.r_[0, 0, 1, 0, 0, 1, 0, 1, 1, 1] x = np.empty((10, 2)) x[:, 0] = x1 x[:, 1] = x2 model = ConditionalLogit(y, x, groups=g) # Check the gradient for the denominator of the partial likelihood for x in -1, 0, 1, 2: params = np.r_[x, -1.5*x] _, grad = model._denom_grad(0, params) ngrad = approx_fprime(params, lambda x: model._denom(0, x)) assert_allclose(grad, ngrad, rtol=1e-5) # Check the gradient for the loglikelihood for x in -1, 0, 1, 2: params = np.r_[-0.5*x, 0.5*x] grad = approx_fprime(params, model.loglike) score = model.score(params) assert_allclose(grad, score, rtol=1e-4) result = model.fit() # From Stata assert_allclose(result.params, np.r_[1.011074, 1.236758], rtol=1e-3) assert_allclose(result.bse, np.r_[1.420784, 1.361738], rtol=1e-5) result.summary() def test_formula(): for j in 0, 1: np.random.seed(34234) n = 200 y = np.random.randint(0, 2, size=n) x1 = np.random.normal(size=n) x2 = np.random.normal(size=n) g = np.random.randint(0, 25, size=n) x = np.hstack((x1[:, None], x2[:, None])) if j == 0: model1 = ConditionalLogit(y, x, groups=g) else: model1 = ConditionalPoisson(y, x, groups=g) result1 = model1.fit() df = pd.DataFrame({"y": y, "x1": x1, "x2": x2, "g": g}) if j == 0: model2 = ConditionalLogit.from_formula( "y ~ 0 + x1 + x2", groups="g", data=df) else: model2 = ConditionalPoisson.from_formula( "y ~ 0 + x1 + x2", groups="g", data=df) result2 = model2.fit() assert_allclose(result1.params, result2.params, rtol=1e-5) assert_allclose(result1.bse, result2.bse, rtol=1e-5) assert_allclose(result1.cov_params(), result2.cov_params(), rtol=1e-5) assert_allclose(result1.tvalues, result2.tvalues, rtol=1e-5) def test_poisson_1d(): y = np.r_[3, 1, 1, 4, 5, 2, 0, 1, 6, 2] g = np.r_[0, 0, 0, 0, 1, 1, 1, 1, 1, 1] x = np.r_[0, 1, 0, 0, 1, 1, 0, 0, 1, 0] x = x[:, None] model = ConditionalPoisson(y, x, groups=g) # Check the gradient for the loglikelihood for x in -1, 0, 1, 2: grad = approx_fprime(np.r_[x, ], model.loglike) score = model.score(np.r_[x, ]) assert_allclose(grad, score, rtol=1e-4) result = model.fit() # From Stata assert_allclose(result.params, np.r_[0.6466272], rtol=1e-4) assert_allclose(result.bse, np.r_[0.4170918], rtol=1e-5) def test_poisson_2d(): y = np.r_[3, 1, 4, 8, 2, 5, 4, 7, 2, 6] g = np.r_[0, 0, 0, 1, 1, 1, 2, 2, 2, 2] x1 = np.r_[0, 1, 0, 0, 1, 1, 0, 0, 1, 0] x2 = np.r_[2, 1, 0, 0, 1, 2, 3, 2, 0, 1] x = np.empty((10, 2)) x[:, 0] = x1 x[:, 1] = x2 model = ConditionalPoisson(y, x, groups=g) # Check the gradient for the loglikelihood for x in -1, 0, 1, 2: params = np.r_[-0.5*x, 0.5*x] grad = approx_fprime(params, model.loglike) score = model.score(params) assert_allclose(grad, score, rtol=1e-4) result = model.fit() # From Stata assert_allclose(result.params, np.r_[-.9478957, -.0134279], rtol=1e-3) assert_allclose(result.bse, np.r_[.3874942, .1686712], rtol=1e-5) result.summary() def test_lasso_logistic(): np.random.seed(3423948) n = 200 groups = np.arange(10) groups = np.kron(groups, np.ones(n // 10)) group_effects = np.random.normal(size=10) group_effects = np.kron(group_effects, np.ones(n // 10)) x = np.random.normal(size=(n, 4)) params = np.r_[0, 0, 1, 0] lin_pred = np.dot(x, params) + group_effects mean = 1 / (1 + np.exp(-lin_pred)) y = (np.random.uniform(size=n) < mean).astype(int) model0 = ConditionalLogit(y, x, groups=groups) result0 = model0.fit() # Should be the same as model0 model1 = ConditionalLogit(y, x, groups=groups) result1 = model1.fit_regularized(L1_wt=0, alpha=0) assert_allclose(result0.params, result1.params, rtol=1e-3) model2 = ConditionalLogit(y, x, groups=groups) result2 = model2.fit_regularized(L1_wt=1, alpha=0.05) # Rxegression test assert_allclose(result2.params, np.r_[0, 0, 0.55235152, 0], rtol=1e-4) # Test with formula df = pd.DataFrame({"y": y, "x1": x[:, 0], "x2": x[:, 1], "x3": x[:, 2], "x4": x[:, 3], "groups": groups}) fml = "y ~ 0 + x1 + x2 + x3 + x4" model3 = ConditionalLogit.from_formula(fml, groups="groups", data=df) result3 = model3.fit_regularized(L1_wt=1, alpha=0.05) assert_allclose(result2.params, result3.params) def test_lasso_poisson(): np.random.seed(342394) n = 200 groups = np.arange(10) groups = np.kron(groups, np.ones(n // 10)) group_effects = np.random.normal(size=10) group_effects = np.kron(group_effects, np.ones(n // 10)) x = np.random.normal(size=(n, 4)) params = np.r_[0, 0, 1, 0] lin_pred = np.dot(x, params) + group_effects mean = np.exp(lin_pred) y = np.random.poisson(mean) model0 = ConditionalPoisson(y, x, groups=groups) result0 = model0.fit() # Should be the same as model0 model1 = ConditionalPoisson(y, x, groups=groups) result1 = model1.fit_regularized(L1_wt=0, alpha=0) assert_allclose(result0.params, result1.params, rtol=1e-3) model2 = ConditionalPoisson(y, x, groups=groups) result2 = model2.fit_regularized(L1_wt=1, alpha=0.2) # Regression test assert_allclose(result2.params, np.r_[0, 0, 0.91697508, 0], rtol=1e-4) # Test with formula df = pd.DataFrame({"y": y, "x1": x[:, 0], "x2": x[:, 1], "x3": x[:, 2], "x4": x[:, 3], "groups": groups}) fml = "y ~ 0 + x1 + x2 + x3 + x4" model3 = ConditionalPoisson.from_formula(fml, groups="groups", data=df) result3 = model3.fit_regularized(L1_wt=1, alpha=0.2) assert_allclose(result2.params, result3.params) def gen_mnlogit(n): np.random.seed(235) g = np.kron(np.ones(5), np.arange(n//5)) x1 = np.random.normal(size=n) x2 = np.random.normal(size=n) xm = np.concatenate((x1[:, None], x2[:, None]), axis=1) pa = np.array([[0, 1, -1], [0, 2, -1]]) lpr = np.dot(xm, pa) pr = np.exp(lpr) pr /= pr.sum(1)[:, None] cpr = pr.cumsum(1) y = 2 * np.ones(n) u = np.random.uniform(size=n) y[u < cpr[:, 2]] = 2 y[u < cpr[:, 1]] = 1 y[u < cpr[:, 0]] = 0 df = pd.DataFrame({"y": y, "x1": x1, "x2": x2, "g": g}) return df def test_conditional_mnlogit_grad(): df = gen_mnlogit(90) model = ConditionalMNLogit.from_formula( "y ~ 0 + x1 + x2", groups="g", data=df) # Compare the gradients to numeric gradients for _ in range(5): za = np.random.normal(size=4) grad = model.score(za) ngrad = approx_fprime(za, model.loglike) assert_allclose(grad, ngrad, rtol=1e-5, atol=1e-3) def test_conditional_mnlogit_2d(): df = gen_mnlogit(90) model = ConditionalMNLogit.from_formula( "y ~ 0 + x1 + x2", groups="g", data=df) result = model.fit() # Regression tests assert_allclose( result.params, np.asarray([[0.75592035, -1.58565494], [1.82919869, -1.32594231]]), rtol=1e-5, atol=1e-5) assert_allclose( result.bse, np.asarray([[0.68099698, 0.70142727], [0.65190315, 0.59653771]]), rtol=1e-5, atol=1e-5) def test_conditional_mnlogit_3d(): df = gen_mnlogit(90) df["x3"] = np.random.normal(size=df.shape[0]) model = ConditionalMNLogit.from_formula( "y ~ 0 + x1 + x2 + x3", groups="g", data=df) result = model.fit() # Regression tests assert_allclose( result.params, np.asarray([[ 0.729629, -1.633673], [ 1.879019, -1.327163], [-0.114124, -0.109378]]), atol=1e-5, rtol=1e-5) assert_allclose( result.bse, np.asarray([[0.682965, 0.60472], [0.672947, 0.42401], [0.722631, 0.33663]]), atol=1e-5, rtol=1e-5) # Smoke test result.summary() statsmodels-0.12.2/statsmodels/discrete/tests/test_constrained.py000066400000000000000000000505301400612667500254000ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri May 30 16:22:29 2014 Author: Josef Perktold License: BSD-3 """ from io import StringIO import numpy as np from numpy.testing import assert_allclose, assert_equal, assert_ import pandas as pd import patsy import pytest from statsmodels.discrete.discrete_model import Poisson from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod import families from statsmodels.base._constraints import fit_constrained from statsmodels.tools.tools import add_constant from statsmodels import datasets from .results import results_poisson_constrained as results from .results import results_glm_logit_constrained as reslogit spector_data = datasets.spector.load(as_pandas=False) spector_data.exog = add_constant(spector_data.exog, prepend=False) DEBUG = False ss = '''\ agecat smokes deaths pyears 1 1 32 52407 2 1 104 43248 3 1 206 28612 4 1 186 12663 5 1 102 5317 1 0 2 18790 2 0 12 10673 3 0 28 5710 4 0 28 2585 5 0 31 1462''' data = pd.read_csv(StringIO(ss), delimiter='\t') data = data.astype(int) data['logpyears'] = np.log(data['pyears']) class CheckPoissonConstrainedMixin(object): def test_basic(self): res1 = self.res1 res2 = self.res2 assert_allclose(res1[0], res2.params[self.idx], rtol=1e-6) # see below Stata has nan, we have zero bse1 = np.sqrt(np.diag(res1[1])) mask = (bse1 == 0) & np.isnan(res2.bse[self.idx]) assert_allclose(bse1[~mask], res2.bse[self.idx][~mask], rtol=1e-6) def test_basic_method(self): if hasattr(self, 'res1m'): res1 = (self.res1m if not hasattr(self.res1m, '_results') else self.res1m._results) res2 = self.res2 assert_allclose(res1.params, res2.params[self.idx], rtol=1e-6) # when a parameter is fixed, the Stata has bse=nan, we have bse=0 mask = (res1.bse == 0) & np.isnan(res2.bse[self.idx]) assert_allclose(res1.bse[~mask], res2.bse[self.idx][~mask], rtol=1e-6) tvalues = res2.params_table[self.idx, 2] # when a parameter is fixed, the Stata has tvalue=nan, # we have tvalue=inf mask = np.isinf(res1.tvalues) & np.isnan(tvalues) assert_allclose(res1.tvalues[~mask], tvalues[~mask], rtol=1e-6) pvalues = res2.params_table[self.idx, 3] # note most pvalues are very small # examples so far agree at 8 or more decimal, but rtol is stricter # see above mask = (res1.pvalues == 0) & np.isnan(pvalues) assert_allclose(res1.pvalues[~mask], pvalues[~mask], rtol=5e-5) ci_low = res2.params_table[self.idx, 4] ci_upp = res2.params_table[self.idx, 5] ci = np.column_stack((ci_low, ci_upp)) # note most pvalues are very small # examples so far agree at 8 or more decimal, but rtol is stricter # see above: nan versus value assert_allclose(res1.conf_int()[~np.isnan(ci)], ci[~np.isnan(ci)], rtol=5e-5) # other assert_allclose(res1.llf, res2.ll, rtol=1e-6) assert_equal(res1.df_model, res2.df_m) # Stata does not have df_resid df_r = res2.N - res2.df_m - 1 assert_equal(res1.df_resid, df_r) else: pytest.skip("not available yet") def test_other(self): # some results may not be valid or available for all models if hasattr(self, 'res1m'): res1 = self.res1m res2 = self.res2 if hasattr(res2, 'll_0'): assert_allclose(res1.llnull, res2.ll_0, rtol=1e-6) else: if DEBUG: import warnings message = ('test: ll_0 not available, llnull=%6.4F' % res1.llnull) warnings.warn(message) else: pytest.skip("not available yet") class TestPoissonConstrained1a(CheckPoissonConstrainedMixin): @classmethod def setup_class(cls): cls.res2 = results.results_noexposure_constraint # 2 is dropped baseline for categorical cls.idx = [7, 3, 4, 5, 6, 0, 1] # example without offset formula = 'deaths ~ logpyears + smokes + C(agecat)' mod = Poisson.from_formula(formula, data=data) # get start_params, example fails to converge on one py TravisCI k_vars = len(mod.exog_names) start_params = np.zeros(k_vars) start_params[0] = np.log(mod.endog.mean()) # if we need it, this is desired params # p = np.array([-3.93478643, 1.37276214, 2.33077032, 2.71338891, # 2.71338891, 0.57966535, 0.97254074]) constr = 'C(agecat)[T.4] = C(agecat)[T.5]' lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr) cls.res1 = fit_constrained(mod, lc.coefs, lc.constants, start_params=start_params, fit_kwds={'method': 'bfgs', 'disp': 0}) # TODO: Newton fails # test method of Poisson, not monkey patched cls.res1m = mod.fit_constrained(constr, start_params=start_params, method='bfgs', disp=0) @pytest.mark.smoke def test_summary(self): # trailing text in summary, assumes it's the first extra string # NOTE: see comment about convergence in llnull for self.res1m summ = self.res1m.summary() assert_('linear equality constraints' in summ.extra_txt) @pytest.mark.smoke def test_summary2(self): # trailing text in summary, assumes it's the first extra string # NOTE: see comment about convergence in llnull for self.res1m summ = self.res1m.summary2() assert_('linear equality constraints' in summ.extra_txt[0]) class TestPoissonConstrained1b(CheckPoissonConstrainedMixin): @classmethod def setup_class(cls): cls.res2 = results.results_exposure_constraint cls.idx = [6, 2, 3, 4, 5, 0] # 2 is dropped baseline for categorical # example without offset formula = 'deaths ~ smokes + C(agecat)' mod = Poisson.from_formula(formula, data=data, exposure=data['pyears'].values) constr = 'C(agecat)[T.4] = C(agecat)[T.5]' lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr) cls.res1 = fit_constrained(mod, lc.coefs, lc.constants, fit_kwds={'method': 'newton', 'disp': 0}) cls.constraints = lc # TODO: bfgs fails # test method of Poisson, not monkey patched cls.res1m = mod.fit_constrained(constr, method='newton', disp=0) class TestPoissonConstrained1c(CheckPoissonConstrainedMixin): @classmethod def setup_class(cls): cls.res2 = results.results_exposure_constraint cls.idx = [6, 2, 3, 4, 5, 0] # 2 is dropped baseline for categorical # example without offset formula = 'deaths ~ smokes + C(agecat)' mod = Poisson.from_formula(formula, data=data, offset=np.log(data['pyears'].values)) constr = 'C(agecat)[T.4] = C(agecat)[T.5]' lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr) cls.res1 = fit_constrained(mod, lc.coefs, lc.constants, fit_kwds={'method': 'newton', 'disp': 0}) cls.constraints = lc # TODO: bfgs fails # test method of Poisson, not monkey patched cls.res1m = mod.fit_constrained(constr, method='newton', disp=0) class TestPoissonNoConstrained(CheckPoissonConstrainedMixin): @classmethod def setup_class(cls): cls.res2 = results.results_exposure_noconstraint cls.idx = [6, 2, 3, 4, 5, 0] # 1 is dropped baseline for categorical # example without offset formula = 'deaths ~ smokes + C(agecat)' mod = Poisson.from_formula(formula, data=data, offset=np.log(data['pyears'].values)) res1 = mod.fit(disp=0)._results # res1 is duplicate check, so we can follow the same pattern cls.res1 = (res1.params, res1.cov_params()) cls.res1m = res1 class TestPoissonConstrained2a(CheckPoissonConstrainedMixin): @classmethod def setup_class(cls): cls.res2 = results.results_noexposure_constraint2 # 2 is dropped baseline for categorical cls.idx = [7, 3, 4, 5, 6, 0, 1] # example without offset formula = 'deaths ~ logpyears + smokes + C(agecat)' mod = Poisson.from_formula(formula, data=data) # get start_params, example fails to converge on one py TravisCI k_vars = len(mod.exog_names) start_params = np.zeros(k_vars) start_params[0] = np.log(mod.endog.mean()) # if we need it, this is desired params # p = np.array([-9.43762015, 1.52762442, 2.74155711, 3.58730007, # 4.08730007, 1.15987869, 0.12111539]) constr = 'C(agecat)[T.5] - C(agecat)[T.4] = 0.5' lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr) cls.res1 = fit_constrained(mod, lc.coefs, lc.constants, start_params=start_params, fit_kwds={'method': 'bfgs', 'disp': 0}) # TODO: Newton fails # test method of Poisson, not monkey patched cls.res1m = mod.fit_constrained(constr, start_params=start_params, method='bfgs', disp=0) class TestPoissonConstrained2b(CheckPoissonConstrainedMixin): @classmethod def setup_class(cls): cls.res2 = results.results_exposure_constraint2 cls.idx = [6, 2, 3, 4, 5, 0] # 2 is dropped baseline for categorical # example without offset formula = 'deaths ~ smokes + C(agecat)' mod = Poisson.from_formula(formula, data=data, exposure=data['pyears'].values) constr = 'C(agecat)[T.5] - C(agecat)[T.4] = 0.5' lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr) cls.res1 = fit_constrained(mod, lc.coefs, lc.constants, fit_kwds={'method': 'newton', 'disp': 0}) cls.constraints = lc # TODO: bfgs fails to converge. overflow somewhere? # test method of Poisson, not monkey patched cls.res1m = mod.fit_constrained(constr, method='bfgs', disp=0, start_params=cls.res1[0]) class TestPoissonConstrained2c(CheckPoissonConstrainedMixin): @classmethod def setup_class(cls): cls.res2 = results.results_exposure_constraint2 cls.idx = [6, 2, 3, 4, 5, 0] # 2 is dropped baseline for categorical # example without offset formula = 'deaths ~ smokes + C(agecat)' mod = Poisson.from_formula(formula, data=data, offset=np.log(data['pyears'].values)) constr = 'C(agecat)[T.5] - C(agecat)[T.4] = 0.5' lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr) cls.res1 = fit_constrained(mod, lc.coefs, lc.constants, fit_kwds={'method': 'newton', 'disp': 0}) cls.constraints = lc # TODO: bfgs fails # test method of Poisson, not monkey patched cls.res1m = mod.fit_constrained(constr, method='bfgs', disp=0, start_params=cls.res1[0]) class TestGLMPoissonConstrained1a(CheckPoissonConstrainedMixin): @classmethod def setup_class(cls): from statsmodels.base._constraints import fit_constrained cls.res2 = results.results_noexposure_constraint # 2 is dropped baseline for categorical cls.idx = [7, 3, 4, 5, 6, 0, 1] # example without offset formula = 'deaths ~ logpyears + smokes + C(agecat)' mod = GLM.from_formula(formula, data=data, family=families.Poisson()) constr = 'C(agecat)[T.4] = C(agecat)[T.5]' lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr) cls.res1 = fit_constrained(mod, lc.coefs, lc.constants, fit_kwds={'atol': 1e-10}) cls.constraints = lc cls.res1m = mod.fit_constrained(constr, atol=1e-10) class TestGLMPoissonConstrained1b(CheckPoissonConstrainedMixin): @classmethod def setup_class(cls): from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod import families from statsmodels.base._constraints import fit_constrained cls.res2 = results.results_exposure_constraint cls.idx = [6, 2, 3, 4, 5, 0] # 2 is dropped baseline for categorical # example with offset formula = 'deaths ~ smokes + C(agecat)' mod = GLM.from_formula(formula, data=data, family=families.Poisson(), offset=np.log(data['pyears'].values)) constr = 'C(agecat)[T.4] = C(agecat)[T.5]' lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constr) cls.res1 = fit_constrained(mod, lc.coefs, lc.constants, fit_kwds={'atol': 1e-10}) cls.constraints = lc cls.res1m = mod.fit_constrained(constr, atol=1e-10)._results def test_compare_glm_poisson(self): res1 = self.res1m res2 = self.res2 formula = 'deaths ~ smokes + C(agecat)' mod = Poisson.from_formula(formula, data=data, exposure=data['pyears'].values) constr = 'C(agecat)[T.4] = C(agecat)[T.5]' res2 = mod.fit_constrained(constr, start_params=self.res1m.params, method='newton', warn_convergence=False, disp=0) # we get high precision because we use the params as start_params # basic, just as check that we have the same model assert_allclose(res1.params, res2.params, rtol=1e-12) assert_allclose(res1.bse, res2.bse, rtol=1e-11) # check predict, fitted, ... predicted = res1.predict() assert_allclose(predicted, res2.predict(), rtol=1e-10) assert_allclose(res1.mu, predicted, rtol=1e-10) assert_allclose(res1.fittedvalues, predicted, rtol=1e-10) assert_allclose(res2.predict(linear=True), res2.predict(linear=True), rtol=1e-10) class CheckGLMConstrainedMixin(CheckPoissonConstrainedMixin): # add tests for some GLM specific attributes def test_glm(self): res2 = self.res2 # reference results res1 = self.res1m # FIXME: dont leave commented-out # assert_allclose(res1.aic, res2.aic, rtol=1e-10) # far away # Stata aic in ereturn and in estat ic are very different # we have the same as estat ic # see issue GH#1733 assert_allclose(res1.aic, res2.infocrit[4], rtol=1e-10) import warnings with warnings.catch_warnings(): warnings.simplefilter("ignore", FutureWarning) # FutureWarning for BIC changes assert_allclose(res1.bic, res2.bic, rtol=1e-10) # bic is deviance based # FIXME: dont leave commented-out # assert_allclose(res1.bic, res2.infocrit[5], rtol=1e-10) assert_allclose(res1.deviance, res2.deviance, rtol=1e-10) # FIXME: dont leave commented-out # TODO: which chi2 are these # assert_allclose(res1.pearson_chi2, res2.chi2, rtol=1e-10) class TestGLMLogitConstrained1(CheckGLMConstrainedMixin): @classmethod def setup_class(cls): cls.idx = slice(None) # params sequence same as Stata, but Stata reports param = nan # and we have param = value = 0 cls.res2 = reslogit.results_constraint1 mod1 = GLM(spector_data.endog, spector_data.exog, family=families.Binomial()) constr = 'x1 = 2.8' cls.res1m = mod1.fit_constrained(constr) R, q = cls.res1m.constraints cls.res1 = fit_constrained(mod1, R, q) class TestGLMLogitConstrained2(CheckGLMConstrainedMixin): @classmethod def setup_class(cls): cls.idx = slice(None) # params sequence same as Stata cls.res2 = reslogit.results_constraint2 mod1 = GLM(spector_data.endog, spector_data.exog, family=families.Binomial()) constr = 'x1 - x3 = 0' cls.res1m = mod1.fit_constrained(constr, atol=1e-10) # patsy compatible constraints R, q = cls.res1m.constraints.coefs, cls.res1m.constraints.constants cls.res1 = fit_constrained(mod1, R, q, fit_kwds={'atol': 1e-10}) cls.constraints_rq = (R, q) def test_predict(self): # results only available for this case res2 = self.res2 # reference results res1 = self.res1m predicted = res1.predict() assert_allclose(predicted, res2.predict_mu, atol=1e-7) assert_allclose(res1.mu, predicted, rtol=1e-10) assert_allclose(res1.fittedvalues, predicted, rtol=1e-10) @pytest.mark.smoke def test_summary(self): # trailing text in summary, assumes it's the first extra string summ = self.res1m.summary() assert_('linear equality constraints' in summ.extra_txt) lc_string = str(self.res1m.constraints) assert lc_string == "x1 - x3 = 0.0" @pytest.mark.smoke def test_summary2(self): # trailing text in summary, assumes it's the first extra string import warnings with warnings.catch_warnings(): warnings.simplefilter("ignore", FutureWarning) # FutureWarning for BIC changes summ = self.res1m.summary2() assert_('linear equality constraints' in summ.extra_txt[0]) def test_fit_constrained_wrap(self): # minimal test res2 = self.res2 # reference results from statsmodels.base._constraints import fit_constrained_wrap res_wrap = fit_constrained_wrap(self.res1m.model, self.constraints_rq) assert_allclose(res_wrap.params, res2.params, rtol=1e-6) assert_allclose(res_wrap.params, res2.params, rtol=1e-6) class TestGLMLogitConstrained2HC(CheckGLMConstrainedMixin): @classmethod def setup_class(cls): cls.idx = slice(None) # params sequence same as Stata cls.res2 = reslogit.results_constraint2_robust mod1 = GLM(spector_data.endog, spector_data.exog, family=families.Binomial()) # not used to match Stata for HC # nobs, k_params = mod1.exog.shape # k_params -= 1 # one constraint cov_type = 'HC0' cov_kwds = {'scaling_factor': 32/31} # looks like nobs / (nobs - 1) and not (nobs - 1.) / (nobs - k_params)} constr = 'x1 - x3 = 0' cls.res1m = mod1.fit_constrained(constr, cov_type=cov_type, cov_kwds=cov_kwds, atol=1e-10) R, q = cls.res1m.constraints cls.res1 = fit_constrained(mod1, R, q, fit_kwds={'atol': 1e-10, 'cov_type': cov_type, 'cov_kwds': cov_kwds}) cls.constraints_rq = (R, q) def junk(): # FIXME: make this into a test, or move/remove # Singular Matrix in mod1a.fit() # same as Stata default formula2 = 'deaths ~ C(agecat) + C(smokes) : C(agecat)' mod = Poisson.from_formula(formula2, data=data, exposure=data['pyears'].values) mod.fit() constraints = 'C(smokes)[T.1]:C(agecat)[3] = C(smokes)[T.1]:C(agec`at)[4]' import patsy lc = patsy.DesignInfo(mod.exog_names).linear_constraint(constraints) R, q = lc.coefs, lc.constants mod.fit_constrained(R, q, fit_kwds={'method': 'bfgs'}) # example without offset formula1a = 'deaths ~ logpyears + smokes + C(agecat)' mod1a = Poisson.from_formula(formula1a, data=data) mod1a.fit() lc_1a = patsy.DesignInfo(mod1a.exog_names).linear_constraint( 'C(agecat)[T.4] = C(agecat)[T.5]') mod1a.fit_constrained(lc_1a.coefs, lc_1a.constants, fit_kwds={'method': 'newton'}) statsmodels-0.12.2/statsmodels/discrete/tests/test_count_model.py000066400000000000000000000662311400612667500254040ustar00rootroot00000000000000from statsmodels.compat.platform import PLATFORM_LINUX32 import numpy as np from numpy.testing import (assert_, assert_equal, assert_array_equal, assert_allclose) import pytest import pandas as pd import statsmodels.api as sm from .results.results_discrete import RandHIE from .test_discrete import CheckModelMixin class CheckGeneric(CheckModelMixin): def test_params(self): assert_allclose(self.res1.params, self.res2.params, atol=1e-5, rtol=1e-5) def test_llf(self): assert_allclose(self.res1.llf, self.res2.llf, atol=1e-5, rtol=1e-5) def test_conf_int(self): assert_allclose(self.res1.conf_int(), self.res2.conf_int, atol=1e-3, rtol=1e-5) def test_bse(self): assert_allclose(self.res1.bse, self.res2.bse, atol=1e-3, rtol=1e-3) def test_aic(self): assert_allclose(self.res1.aic, self.res2.aic, atol=1e-2, rtol=1e-2) def test_bic(self): assert_allclose(self.res1.aic, self.res2.aic, atol=1e-1, rtol=1e-1) def test_t(self): unit_matrix = np.identity(self.res1.params.size) t_test = self.res1.t_test(unit_matrix) assert_allclose(self.res1.tvalues, t_test.tvalue) def test_fit_regularized(self): model = self.res1.model alpha = np.ones(len(self.res1.params)) alpha[-2:] = 0 res_reg = model.fit_regularized(alpha=alpha*0.01, disp=0, maxiter=500) assert_allclose(res_reg.params[2:], self.res1.params[2:], atol=5e-2, rtol=5e-2) def test_init_keys(self): init_kwds = self.res1.model._get_init_kwds() assert_equal(set(init_kwds.keys()), set(self.init_keys)) for key, value in self.init_kwds.items(): assert_equal(init_kwds[key], value) def test_null(self): # call llnull, so null model is attached, side effect of cached attribute self.res1.llnull # check model instead of value exog_null = self.res1.res_null.model.exog exog_infl_null = self.res1.res_null.model.exog_infl assert_array_equal(exog_infl_null.shape, (len(self.res1.model.exog), 1)) assert_equal(np.ptp(exog_null), 0) assert_equal(np.ptp(exog_infl_null), 0) @pytest.mark.smoke def test_summary(self): summ = self.res1.summary() # GH 4581 assert 'Covariance Type:' in str(summ) class TestZeroInflatedModel_logit(CheckGeneric): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) cls.endog = data.endog exog = sm.add_constant(data.exog[:,1:4], prepend=False) exog_infl = sm.add_constant(data.exog[:,0], prepend=False) cls.res1 = sm.ZeroInflatedPoisson(data.endog, exog, exog_infl=exog_infl, inflation='logit').fit(method='newton', maxiter=500, disp=0) # for llnull test cls.res1._results._attach_nullmodel = True cls.init_keys = ['exog_infl', 'exposure', 'inflation', 'offset'] cls.init_kwds = {'inflation': 'logit'} res2 = RandHIE.zero_inflated_poisson_logit cls.res2 = res2 class TestZeroInflatedModel_probit(CheckGeneric): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) cls.endog = data.endog exog = sm.add_constant(data.exog[:,1:4], prepend=False) exog_infl = sm.add_constant(data.exog[:,0], prepend=False) cls.res1 = sm.ZeroInflatedPoisson(data.endog, exog, exog_infl=exog_infl, inflation='probit').fit(method='newton', maxiter=500, disp=0) # for llnull test cls.res1._results._attach_nullmodel = True cls.init_keys = ['exog_infl', 'exposure', 'inflation', 'offset'] cls.init_kwds = {'inflation': 'probit'} res2 = RandHIE.zero_inflated_poisson_probit cls.res2 = res2 @pytest.mark.skipif(PLATFORM_LINUX32, reason="Fails on 32-bit Linux") def test_fit_regularized(self): super().test_fit_regularized() class TestZeroInflatedModel_offset(CheckGeneric): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) cls.endog = data.endog exog = sm.add_constant(data.exog[:,1:4], prepend=False) exog_infl = sm.add_constant(data.exog[:,0], prepend=False) cls.res1 = sm.ZeroInflatedPoisson(data.endog, exog, exog_infl=exog_infl, offset=data.exog[:,7]).fit(method='newton', maxiter=500, disp=0) # for llnull test cls.res1._results._attach_nullmodel = True cls.init_keys = ['exog_infl', 'exposure', 'inflation', 'offset'] cls.init_kwds = {'inflation': 'logit'} res2 = RandHIE.zero_inflated_poisson_offset cls.res2 = res2 def test_exposure(self): # This test mostly the equivalence of offset and exposure = exp(offset) # use data arrays from class model model1 = self.res1.model offset = model1.offset model3 = sm.ZeroInflatedPoisson(model1.endog, model1.exog, exog_infl=model1.exog_infl, exposure=np.exp(offset)) res3 = model3.fit(start_params=self.res1.params, method='newton', maxiter=500, disp=0) assert_allclose(res3.params, self.res1.params, atol=1e-6, rtol=1e-6) fitted1 = self.res1.predict() fitted3 = self.res1.predict() assert_allclose(fitted3, fitted1, atol=1e-6, rtol=1e-6) ex = model1.exog ex_infl = model1.exog_infl offset = model1.offset fitted1_0 = self.res1.predict(exog=ex, exog_infl=ex_infl, offset=offset) fitted3_0 = res3.predict(exog=ex, exog_infl=ex_infl, exposure=np.exp(offset)) assert_allclose(fitted3_0, fitted1_0, atol=1e-6, rtol=1e-6) ex = model1.exog[:10:2] ex_infl = model1.exog_infl[:10:2] offset = offset[:10:2] # # TODO: this raises with shape mismatch, # # i.e. uses offset or exposure from model -> fix it or not? # GLM.predict to setting offset and exposure to zero # fitted1_1 = self.res1.predict(exog=ex, exog_infl=ex_infl) # fitted3_1 = res3.predict(exog=ex, exog_infl=ex_infl) # assert_allclose(fitted3_1, fitted1_1, atol=1e-6, rtol=1e-6) fitted1_2 = self.res1.predict(exog=ex, exog_infl=ex_infl, offset=offset) fitted3_2 = res3.predict(exog=ex, exog_infl=ex_infl, exposure=np.exp(offset)) assert_allclose(fitted3_2, fitted1_2, atol=1e-6, rtol=1e-6) assert_allclose(fitted1_2, fitted1[:10:2], atol=1e-6, rtol=1e-6) assert_allclose(fitted3_2, fitted1[:10:2], atol=1e-6, rtol=1e-6) class TestZeroInflatedModelPandas(CheckGeneric): @classmethod def setup_class(cls): data = sm.datasets.randhie.load_pandas() cls.endog = data.endog cls.data = data exog = sm.add_constant(data.exog.iloc[:,1:4], prepend=False) exog_infl = sm.add_constant(data.exog.iloc[:,0], prepend=False) # we do not need to verify convergence here start_params = np.asarray([0.10337834587498942, -1.0459825102508549, -0.08219794475894268, 0.00856917434709146, -0.026795737379474334, 1.4823632430107334]) model = sm.ZeroInflatedPoisson(data.endog, exog, exog_infl=exog_infl, inflation='logit') cls.res1 = model.fit(start_params=start_params, method='newton', maxiter=500, disp=0) # for llnull test cls.res1._results._attach_nullmodel = True cls.init_keys = ['exog_infl', 'exposure', 'inflation', 'offset'] cls.init_kwds = {'inflation': 'logit'} res2 = RandHIE.zero_inflated_poisson_logit cls.res2 = res2 def test_names(self): param_names = ['inflate_lncoins', 'inflate_const', 'idp', 'lpi', 'fmde', 'const'] assert_array_equal(self.res1.model.exog_names, param_names) assert_array_equal(self.res1.params.index.tolist(), param_names) assert_array_equal(self.res1.bse.index.tolist(), param_names) exog = sm.add_constant(self.data.exog.iloc[:,1:4], prepend=True) exog_infl = sm.add_constant(self.data.exog.iloc[:,0], prepend=True) param_names = ['inflate_const', 'inflate_lncoins', 'const', 'idp', 'lpi', 'fmde'] model = sm.ZeroInflatedPoisson(self.data.endog, exog, exog_infl=exog_infl, inflation='logit') assert_array_equal(model.exog_names, param_names) class TestZeroInflatedPoisson_predict(object): @classmethod def setup_class(cls): expected_params = [1, 0.5] np.random.seed(999) nobs = 2000 exog = np.ones((nobs, 2)) exog[:nobs//2, 1] = 2 mu_true = exog.dot(expected_params) cls.endog = sm.distributions.zipoisson.rvs(mu_true, 0.05, size=mu_true.shape) model = sm.ZeroInflatedPoisson(cls.endog, exog) cls.res = model.fit(method='bfgs', maxiter=5000, maxfun=5000, disp=0) cls.params_true = [mu_true, 0.05, nobs] def test_mean(self): def compute_conf_interval_95(mu, prob_infl, nobs): dispersion_factor = 1 + prob_infl * mu # scalar variance of the mixture of zip var = (dispersion_factor*(1-prob_infl)*mu).mean() var += (((1-prob_infl)*mu)**2).mean() var -= (((1-prob_infl)*mu).mean())**2 std = np.sqrt(var) # Central limit theorem conf_intv_95 = 2 * std / np.sqrt(nobs) return conf_intv_95 conf_interval_95 = compute_conf_interval_95(*self.params_true) assert_allclose(self.res.predict().mean(), self.endog.mean(), atol=conf_interval_95, rtol=0) def test_var(self): def compute_mixture_var(dispersion_factor, prob_main, mu): # the variance of the mixture is the mixture of the variances plus # a non-negative term accounting for the (weighted) # dispersion of the means, see stats.stackexchange #16609 and # Casella & Berger's Statistical Inference (Example 10.2.1) prob_infl = 1-prob_main var = (dispersion_factor*(1-prob_infl)*mu).mean() var += (((1-prob_infl)*mu)**2).mean() var -= (((1-prob_infl)*mu).mean())**2 return var res = self.res var_fitted = compute_mixture_var(res._dispersion_factor, res.predict(which='prob-main'), res.predict(which='mean-main')) assert_allclose(var_fitted.mean(), self.endog.var(), atol=5e-2, rtol=5e-2) def test_predict_prob(self): res = self.res pr = res.predict(which='prob') pr2 = sm.distributions.zipoisson.pmf(np.arange(pr.shape[1])[:, None], res.predict(), 0.05).T assert_allclose(pr, pr2, rtol=0.05, atol=0.05) @pytest.mark.slow class TestZeroInflatedGeneralizedPoisson(CheckGeneric): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) cls.endog = data.endog exog = sm.add_constant(data.exog[:,1:4], prepend=False) exog_infl = sm.add_constant(data.exog[:,0], prepend=False) cls.res1 = sm.ZeroInflatedGeneralizedPoisson(data.endog, exog, exog_infl=exog_infl, p=1).fit(method='newton', maxiter=500, disp=0) # for llnull test cls.res1._results._attach_nullmodel = True cls.init_keys = ['exog_infl', 'exposure', 'inflation', 'offset', 'p'] cls.init_kwds = {'inflation': 'logit', 'p': 1} res2 = RandHIE.zero_inflated_generalized_poisson cls.res2 = res2 def test_bse(self): pass def test_conf_int(self): pass def test_bic(self): pass def test_t(self): unit_matrix = np.identity(self.res1.params.size) t_test = self.res1.t_test(unit_matrix) assert_allclose(self.res1.tvalues, t_test.tvalue) def test_minimize(self, reset_randomstate): # check additional optimizers using the `minimize` option model = self.res1.model # use the same start_params, but avoid recomputing start_params = self.res1.mle_settings['start_params'] res_ncg = model.fit(start_params=start_params, method='minimize', min_method="trust-ncg", maxiter=500, disp=0) assert_allclose(res_ncg.params, self.res2.params, atol=1e-3, rtol=0.04) assert_allclose(res_ncg.bse, self.res2.bse, atol=1e-3, rtol=0.6) assert_(res_ncg.mle_retvals['converged'] is True) res_dog = model.fit(start_params=start_params, method='minimize', min_method="dogleg", maxiter=500, disp=0) assert_allclose(res_dog.params, self.res2.params, atol=1e-3, rtol=3e-3) assert_allclose(res_dog.bse, self.res2.bse, atol=1e-3, rtol=0.6) assert_(res_dog.mle_retvals['converged'] is True) # Ser random_state here to improve reproducibility random_state = np.random.RandomState(1) seed = {'seed': random_state} res_bh = model.fit(start_params=start_params, method='basinhopping', niter=500, stepsize=0.1, niter_success=None, disp=0, interval=1, **seed) assert_allclose(res_bh.params, self.res2.params, atol=1e-4, rtol=1e-4) assert_allclose(res_bh.bse, self.res2.bse, atol=1e-3, rtol=0.6) # skip, res_bh reports converged is false but params agree #assert_(res_bh.mle_retvals['converged'] is True) class TestZeroInflatedGeneralizedPoisson_predict(object): @classmethod def setup_class(cls): expected_params = [1, 0.5, 0.5] np.random.seed(999) nobs = 2000 exog = np.ones((nobs, 2)) exog[:nobs//2, 1] = 2 mu_true = exog.dot(expected_params[:-1]) cls.endog = sm.distributions.zigenpoisson.rvs(mu_true, expected_params[-1], 2, 0.5, size=mu_true.shape) model = sm.ZeroInflatedGeneralizedPoisson(cls.endog, exog, p=2) cls.res = model.fit(method='bfgs', maxiter=5000, maxfun=5000, disp=0) cls.params_true = [mu_true, expected_params[-1], 2, 0.5, nobs] def test_mean(self): def compute_conf_interval_95(mu, alpha, p, prob_infl, nobs): p = p-1 dispersion_factor = (1 + alpha * mu**p)**2 + prob_infl * mu # scalar variance of the mixture of zip var = (dispersion_factor*(1-prob_infl)*mu).mean() var += (((1-prob_infl)*mu)**2).mean() var -= (((1-prob_infl)*mu).mean())**2 std = np.sqrt(var) # Central limit theorem conf_intv_95 = 2 * std / np.sqrt(nobs) return conf_intv_95 conf_interval_95 = compute_conf_interval_95(*self.params_true) assert_allclose(self.res.predict().mean(), self.endog.mean(), atol=conf_interval_95, rtol=0) def test_var(self): def compute_mixture_var(dispersion_factor, prob_main, mu): prob_infl = 1-prob_main var = (dispersion_factor*(1-prob_infl)*mu).mean() var += (((1-prob_infl)*mu)**2).mean() var -= (((1-prob_infl)*mu).mean())**2 return var res = self.res var_fitted = compute_mixture_var(res._dispersion_factor, res.predict(which='prob-main'), res.predict(which='mean-main')) assert_allclose(var_fitted.mean(), self.endog.var(), atol=0.05, rtol=0.1) def test_predict_prob(self): res = self.res pr = res.predict(which='prob') pr2 = sm.distributions.zinegbin.pmf(np.arange(pr.shape[1])[:, None], res.predict(), 0.5, 2, 0.5).T assert_allclose(pr, pr2, rtol=0.08, atol=0.05) class TestZeroInflatedNegativeBinomialP(CheckGeneric): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) cls.endog = data.endog exog = sm.add_constant(data.exog[:,1], prepend=False) exog_infl = sm.add_constant(data.exog[:,0], prepend=False) # cheating for now, parameters are not well identified in this dataset # see https://github.com/statsmodels/statsmodels/pull/3928#issuecomment-331724022 sp = np.array([1.88, -10.28, -0.20, 1.14, 1.34]) cls.res1 = sm.ZeroInflatedNegativeBinomialP(data.endog, exog, exog_infl=exog_infl, p=2).fit(start_params=sp, method='nm', xtol=1e-6, maxiter=5000, disp=0) # for llnull test cls.res1._results._attach_nullmodel = True cls.init_keys = ['exog_infl', 'exposure', 'inflation', 'offset', 'p'] cls.init_kwds = {'inflation': 'logit', 'p': 2} res2 = RandHIE.zero_inflated_negative_binomial cls.res2 = res2 def test_params(self): assert_allclose(self.res1.params, self.res2.params, atol=1e-3, rtol=1e-3) def test_conf_int(self): pass def test_bic(self): pass def test_fit_regularized(self): model = self.res1.model alpha = np.ones(len(self.res1.params)) alpha[-2:] = 0 res_reg = model.fit_regularized(alpha=alpha*0.01, disp=0, maxiter=500) assert_allclose(res_reg.params[2:], self.res1.params[2:], atol=1e-1, rtol=1e-1) # possibly slow, adds 25 seconds def test_minimize(self, reset_randomstate): # check additional optimizers using the `minimize` option model = self.res1.model # use the same start_params, but avoid recomputing start_params = self.res1.mle_settings['start_params'] res_ncg = model.fit(start_params=start_params, method='minimize', min_method="trust-ncg", maxiter=500, disp=0) assert_allclose(res_ncg.params, self.res2.params, atol=1e-3, rtol=0.03) assert_allclose(res_ncg.bse, self.res2.bse, atol=1e-3, rtol=0.06) assert_(res_ncg.mle_retvals['converged'] is True) res_dog = model.fit(start_params=start_params, method='minimize', min_method="dogleg", maxiter=500, disp=0) assert_allclose(res_dog.params, self.res2.params, atol=1e-3, rtol=3e-3) assert_allclose(res_dog.bse, self.res2.bse, atol=1e-3, rtol=7e-3) assert_(res_dog.mle_retvals['converged'] is True) res_bh = model.fit(start_params=start_params, method='basinhopping', maxiter=500, niter_success=3, disp=0) assert_allclose(res_bh.params, self.res2.params, atol=1e-4, rtol=3e-4) assert_allclose(res_bh.bse, self.res2.bse, atol=1e-3, rtol=1e-3) # skip, res_bh reports converged is false but params agree #assert_(res_bh.mle_retvals['converged'] is True) class TestZeroInflatedNegativeBinomialP_predict(object): @classmethod def setup_class(cls): expected_params = [1, 1, 0.5] np.random.seed(999) nobs = 5000 exog = np.ones((nobs, 2)) exog[:nobs//2, 1] = 0 prob_infl = 0.15 mu_true = np.exp(exog.dot(expected_params[:-1])) cls.endog = sm.distributions.zinegbin.rvs(mu_true, expected_params[-1], 2, prob_infl, size=mu_true.shape) model = sm.ZeroInflatedNegativeBinomialP(cls.endog, exog, p=2) cls.res = model.fit(method='bfgs', maxiter=5000, maxfun=5000, disp=0) # attach others cls.prob_infl = prob_infl cls.params_true = [mu_true, expected_params[-1], 2, prob_infl, nobs] def test_mean(self): def compute_conf_interval_95(mu, alpha, p, prob_infl, nobs): dispersion_factor = 1 + alpha * mu**(p-1) + prob_infl * mu # scalar variance of the mixture of zip var = (dispersion_factor*(1-prob_infl)*mu).mean() var += (((1-prob_infl)*mu)**2).mean() var -= (((1-prob_infl)*mu).mean())**2 std = np.sqrt(var) # Central limit theorem conf_intv_95 = 2 * std / np.sqrt(nobs) return conf_intv_95 conf_interval_95 = compute_conf_interval_95(*self.params_true) mean_true = ((1-self.prob_infl)*self.params_true[0]).mean() assert_allclose(self.res.predict().mean(), mean_true, atol=conf_interval_95, rtol=0) def test_var(self): # todo check precision def compute_mixture_var(dispersion_factor, prob_main, mu): prob_infl = 1 - prob_main var = (dispersion_factor * (1 - prob_infl) * mu).mean() var += (((1 - prob_infl) * mu) ** 2).mean() var -= (((1 - prob_infl) * mu).mean()) ** 2 return var res = self.res var_fitted = compute_mixture_var(res._dispersion_factor, res.predict(which='prob-main'), res.predict(which='mean-main')) assert_allclose(var_fitted.mean(), self.endog.var(), rtol=0.2) def test_predict_prob(self): res = self.res endog = res.model.endog pr = res.predict(which='prob') pr2 = sm.distributions.zinegbin.pmf(np.arange(pr.shape[1])[:,None], res.predict(), 0.5, 2, self.prob_infl).T assert_allclose(pr, pr2, rtol=0.1, atol=0.1) prm = pr.mean(0) pr2m = pr2.mean(0) freq = np.bincount(endog.astype(int)) / len(endog) assert_allclose(((pr2m - prm)**2).mean(), 0, rtol=1e-10, atol=5e-4) assert_allclose(((prm - freq)**2).mean(), 0, rtol=1e-10, atol=1e-4) def test_predict_generic_zi(self): # These tests do not use numbers from other packages. # Tests are on closeness of estimated to true/DGP values # and theoretical relationship between quantities res = self.res endog = self.endog exog = self.res.model.exog prob_infl = self.prob_infl nobs = len(endog) freq = np.bincount(endog.astype(int)) / len(endog) probs = res.predict(which='prob') probsm = probs.mean(0) assert_allclose(freq, probsm, atol=0.02) probs_unique = res.predict(exog=[[1, 0], [1, 1]], exog_infl=np.asarray([[1], [1]]), which='prob') # no default for exog_infl yet #probs_unique = res.predict(exog=[[1, 0], [1, 1]], which='prob') probs_unique2 = probs[[1, nobs-1]] assert_allclose(probs_unique, probs_unique2, atol=1e-10) probs0_unique = res.predict(exog=[[1, 0], [1, 1]], exog_infl=np.asarray([[1], [1]]), which='prob-zero') assert_allclose(probs0_unique, probs_unique2[:, 0], rtol=1e-10) probs_main_unique = res.predict(exog=[[1, 0], [1, 1]], exog_infl=np.asarray([[1], [1]]), which='prob-main') probs_main = res.predict(which='prob-main') probs_main[[0,-1]] assert_allclose(probs_main_unique, probs_main[[0,-1]], rtol=1e-10) assert_allclose(probs_main_unique, 1 - prob_infl, atol=0.01) pred = res.predict(exog=[[1, 0], [1, 1]], exog_infl=np.asarray([[1], [1]])) pred1 = endog[exog[:, 1] == 0].mean(), endog[exog[:, 1] == 1].mean() assert_allclose(pred, pred1, rtol=0.05) pred_main_unique = res.predict(exog=[[1, 0], [1, 1]], exog_infl=np.asarray([[1], [1]]), which='mean-main') assert_allclose(pred_main_unique, np.exp(np.cumsum(res.params[1:3])), rtol=1e-10) # TODO: why does the following fail, params are not close enough to DGP # but results are close statistics of simulated data # what is mu_true in DGP sm.distributions.zinegbin.rvs # assert_allclose(pred_main_unique, mu_true[[1, -1]] * (1 - prob_infl), rtol=0.01) # mean-nonzero mean_nz = (endog[(exog[:, 1] == 0) & (endog > 0)].mean(), endog[(exog[:, 1] == 1) & (endog > 0)].mean()) pred_nonzero_unique = res.predict(exog=[[1, 0], [1, 1]], exog_infl=np.asarray([[1], [1]]), which='mean-nonzero') assert_allclose(pred_nonzero_unique, mean_nz, rtol=0.05) pred_lin_unique = res.predict(exog=[[1, 0], [1, 1]], exog_infl=np.asarray([[1], [1]]), which='linear') assert_allclose(pred_lin_unique, np.cumsum(res.params[1:3]), rtol=1e-10) class TestZeroInflatedNegativeBinomialP_predict2(object): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) cls.endog = data.endog exog = data.exog start_params = np.array([ -2.83983767, -2.31595924, -3.9263248, -4.01816431, -5.52251843, -2.4351714, -4.61636366, -4.17959785, -0.12960256, -0.05653484, -0.21206673, 0.08782572, -0.02991995, 0.22901208, 0.0620983, 0.06809681, 0.0841814, 0.185506, 1.36527888]) mod = sm.ZeroInflatedNegativeBinomialP( cls.endog, exog, exog_infl=exog, p=2) res = mod.fit(start_params=start_params, method="bfgs", maxiter=1000, disp=0) cls.res = res def test_mean(self): assert_allclose(self.res.predict().mean(), self.endog.mean(), atol=0.02) def test_zero_nonzero_mean(self): mean1 = self.endog.mean() mean2 = ((1 - self.res.predict(which='prob-zero').mean()) * self.res.predict(which='mean-nonzero').mean()) assert_allclose(mean1, mean2, atol=0.2) class TestPandasOffset: def test_pd_offset_exposure(self): endog = pd.DataFrame({'F': [0.0, 0.0, 0.0, 0.0, 1.0]}) exog = pd.DataFrame({'I': [1.0, 1.0, 1.0, 1.0, 1.0], 'C': [0.0, 1.0, 0.0, 1.0, 0.0]}) exposure = pd.Series([1., 1, 1, 2, 1]) offset = pd.Series([1, 1, 1, 2, 1]) sm.Poisson(endog=endog, exog=exog, offset=offset).fit() inflations = ['logit', 'probit'] for inflation in inflations: sm.ZeroInflatedPoisson(endog=endog, exog=exog["I"], exposure=exposure, inflation=inflation).fit() statsmodels-0.12.2/statsmodels/discrete/tests/test_diagnostic.py000066400000000000000000000042401400612667500252100ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Sep 15 13:38:13 2017 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_allclose import pytest from statsmodels.discrete.discrete_model import Poisson import statsmodels.discrete._diagnostics_count as dia class TestCountDiagnostic(object): @classmethod def setup_class(cls): expected_params = [1, 1, 0.5] np.random.seed(987123) nobs = 500 exog = np.ones((nobs, 2)) exog[:nobs//2, 1] = 0 # offset is used to create misspecification of the model # for predicted probabilities conditional moment test #offset = 0.5 * np.random.randn(nobs) #range_mix = 0.5 #offset = -range_mix / 2 + range_mix * np.random.rand(nobs) offset = 0 mu_true = np.exp(exog.dot(expected_params[:-1]) + offset) endog_poi = np.random.poisson(mu_true / 5) # endog3 = distr.zigenpoisson.rvs(mu_true, 0, # 2, 0.01, size=mu_true.shape) model_poi = Poisson(endog_poi, exog) res_poi = model_poi.fit(method='bfgs', maxiter=5000, maxfun=5000) cls.exog = exog cls.endog = endog_poi cls.res = res_poi cls.nobs = nobs def test_count(self): # partially smoke tzi1 = dia.test_poisson_zeroinflation(self.res) tzi2 = dia.test_poisson_zeroinflation_brock(self.res) # compare two implementation in special case assert_allclose(tzi1[:2], (tzi2[0]**2, tzi2[1]), rtol=1e-5) tzi3 = dia.test_poisson_zeroinflation(self.res, self.exog) # regression test tzi3_1 = (0.79863597832443878, 0.67077736750318928, 2, 2) assert_allclose(tzi3, tzi3_1, rtol=5e-4) @pytest.mark.matplotlib def test_probs(self, close_figures): nobs = self.nobs probs = self.res.predict_prob() freq = np.bincount(self.endog) / nobs tzi = dia.test_chisquare_prob(self.res, probs[:, :2]) # regression numbers tzi1 = (0.387770845, 0.5334734738) assert_allclose(tzi[:2], tzi1, rtol=5e-5) # smoke test for plot dia.plot_probs(freq, probs.mean(0)) statsmodels-0.12.2/statsmodels/discrete/tests/test_discrete.py000066400000000000000000002706461400612667500247050ustar00rootroot00000000000000""" Tests for discrete models Notes ----- DECIMAL_3 is used because it seems that there is a loss of precision in the Stata *.dta -> *.csv output, NOT the estimator for the Poisson tests. """ # pylint: disable-msg=E1101 from statsmodels.compat.pandas import assert_index_equal import os import warnings import numpy as np from numpy.testing import (assert_, assert_raises, assert_almost_equal, assert_equal, assert_array_equal, assert_allclose, assert_array_less) import pandas as pd import pytest from scipy import stats from statsmodels.discrete.discrete_model import (Logit, Probit, MNLogit, Poisson, NegativeBinomial, CountModel, GeneralizedPoisson, NegativeBinomialP) from statsmodels.discrete.discrete_margins import _iscount, _isdummy import statsmodels.api as sm import statsmodels.formula.api as smf from .results.results_discrete import Spector, DiscreteL1, RandHIE, Anes from statsmodels.tools.sm_exceptions import (PerfectSeparationError, SpecificationWarning, ConvergenceWarning) from scipy.stats import nbinom try: import cvxopt # noqa:F401 has_cvxopt = True except ImportError: has_cvxopt = False DECIMAL_14 = 14 DECIMAL_10 = 10 DECIMAL_9 = 9 DECIMAL_4 = 4 DECIMAL_3 = 3 DECIMAL_2 = 2 DECIMAL_1 = 1 DECIMAL_0 = 0 class CheckModelMixin(object): # Assertions about the Model object, as opposed to the Results # Assumes that mixed-in class implements: # res1 def test_fit_regularized_invalid_method(self): # GH#5224 check we get ValueError when passing invalid "method" arg model = self.res1.model with pytest.raises(ValueError, match=r'is not supported, use either'): model.fit_regularized(method="foo") class CheckModelResults(CheckModelMixin): """ res2 should be the test results from RModelWrap or the results as defined in model_results_data """ def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, DECIMAL_4) def test_conf_int(self): assert_allclose(self.res1.conf_int(), self.res2.conf_int, rtol=8e-5) def test_zstat(self): assert_almost_equal(self.res1.tvalues, self.res2.z, DECIMAL_4) def test_pvalues(self): assert_almost_equal(self.res1.pvalues, self.res2.pvalues, DECIMAL_4) def test_cov_params(self): if not hasattr(self.res2, "cov_params"): raise pytest.skip("TODO: implement res2.cov_params") assert_almost_equal(self.res1.cov_params(), self.res2.cov_params, DECIMAL_4) def test_llf(self): assert_almost_equal(self.res1.llf, self.res2.llf, DECIMAL_4) def test_llnull(self): assert_almost_equal(self.res1.llnull, self.res2.llnull, DECIMAL_4) def test_llr(self): assert_almost_equal(self.res1.llr, self.res2.llr, DECIMAL_3) def test_llr_pvalue(self): assert_almost_equal(self.res1.llr_pvalue, self.res2.llr_pvalue, DECIMAL_4) @pytest.mark.xfail(reason="Test has not been implemented for this class.", strict=True, raises=NotImplementedError) def test_normalized_cov_params(self): raise NotImplementedError def test_bse(self): assert_almost_equal(self.res1.bse, self.res2.bse, DECIMAL_4) def test_dof(self): assert_equal(self.res1.df_model, self.res2.df_model) assert_equal(self.res1.df_resid, self.res2.df_resid) def test_aic(self): assert_almost_equal(self.res1.aic, self.res2.aic, DECIMAL_3) def test_bic(self): assert_almost_equal(self.res1.bic, self.res2.bic, DECIMAL_3) def test_predict(self): assert_almost_equal(self.res1.model.predict(self.res1.params), self.res2.phat, DECIMAL_4) def test_predict_xb(self): assert_almost_equal(self.res1.model.predict(self.res1.params, linear=True), self.res2.yhat, DECIMAL_4) def test_loglikeobs(self): #basic cross check llobssum = self.res1.model.loglikeobs(self.res1.params).sum() assert_almost_equal(llobssum, self.res1.llf, DECIMAL_14) def test_jac(self): #basic cross check jacsum = self.res1.model.score_obs(self.res1.params).sum(0) score = self.res1.model.score(self.res1.params) assert_almost_equal(jacsum, score, DECIMAL_9) #Poisson has low precision ? class CheckBinaryResults(CheckModelResults): def test_pred_table(self): assert_array_equal(self.res1.pred_table(), self.res2.pred_table) def test_resid_dev(self): assert_almost_equal(self.res1.resid_dev, self.res2.resid_dev, DECIMAL_4) def test_resid_generalized(self): assert_almost_equal(self.res1.resid_generalized, self.res2.resid_generalized, DECIMAL_4) @pytest.mark.smoke def test_resid_response(self): self.res1.resid_response class CheckMargEff(object): """ Test marginal effects (margeff) and its options """ def test_nodummy_dydxoverall(self): me = self.res1.get_margeff() assert_almost_equal(me.margeff, self.res2.margeff_nodummy_dydx, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_dydx_se, DECIMAL_4) me_frame = me.summary_frame() eff = me_frame["dy/dx"].values assert_allclose(eff, me.margeff, rtol=1e-13) assert_equal(me_frame.shape, (me.margeff.size, 6)) def test_nodummy_dydxmean(self): me = self.res1.get_margeff(at='mean') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_dydxmean, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_dydxmean_se, DECIMAL_4) def test_nodummy_dydxmedian(self): me = self.res1.get_margeff(at='median') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_dydxmedian, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_dydxmedian_se, DECIMAL_4) def test_nodummy_dydxzero(self): me = self.res1.get_margeff(at='zero') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_dydxzero, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_dydxzero, DECIMAL_4) def test_nodummy_dyexoverall(self): me = self.res1.get_margeff(method='dyex') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_dyex, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_dyex_se, DECIMAL_4) def test_nodummy_dyexmean(self): me = self.res1.get_margeff(at='mean', method='dyex') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_dyexmean, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_dyexmean_se, DECIMAL_4) def test_nodummy_dyexmedian(self): me = self.res1.get_margeff(at='median', method='dyex') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_dyexmedian, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_dyexmedian_se, DECIMAL_4) def test_nodummy_dyexzero(self): me = self.res1.get_margeff(at='zero', method='dyex') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_dyexzero, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_dyexzero_se, DECIMAL_4) def test_nodummy_eydxoverall(self): me = self.res1.get_margeff(method='eydx') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_eydx, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_eydx_se, DECIMAL_4) def test_nodummy_eydxmean(self): me = self.res1.get_margeff(at='mean', method='eydx') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_eydxmean, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_eydxmean_se, DECIMAL_4) def test_nodummy_eydxmedian(self): me = self.res1.get_margeff(at='median', method='eydx') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_eydxmedian, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_eydxmedian_se, DECIMAL_4) def test_nodummy_eydxzero(self): me = self.res1.get_margeff(at='zero', method='eydx') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_eydxzero, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_eydxzero_se, DECIMAL_4) def test_nodummy_eyexoverall(self): me = self.res1.get_margeff(method='eyex') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_eyex, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_eyex_se, DECIMAL_4) def test_nodummy_eyexmean(self): me = self.res1.get_margeff(at='mean', method='eyex') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_eyexmean, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_eyexmean_se, DECIMAL_4) def test_nodummy_eyexmedian(self): me = self.res1.get_margeff(at='median', method='eyex') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_eyexmedian, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_eyexmedian_se, DECIMAL_4) def test_nodummy_eyexzero(self): me = self.res1.get_margeff(at='zero', method='eyex') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_eyexzero, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_eyexzero_se, DECIMAL_4) def test_dummy_dydxoverall(self): me = self.res1.get_margeff(dummy=True) assert_almost_equal(me.margeff, self.res2.margeff_dummy_dydx, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_dummy_dydx_se, DECIMAL_4) def test_dummy_dydxmean(self): me = self.res1.get_margeff(at='mean', dummy=True) assert_almost_equal(me.margeff, self.res2.margeff_dummy_dydxmean, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_dummy_dydxmean_se, DECIMAL_4) def test_dummy_eydxoverall(self): me = self.res1.get_margeff(method='eydx', dummy=True) assert_almost_equal(me.margeff, self.res2.margeff_dummy_eydx, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_dummy_eydx_se, DECIMAL_4) def test_dummy_eydxmean(self): me = self.res1.get_margeff(at='mean', method='eydx', dummy=True) assert_almost_equal(me.margeff, self.res2.margeff_dummy_eydxmean, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_dummy_eydxmean_se, DECIMAL_4) def test_count_dydxoverall(self): me = self.res1.get_margeff(count=True) assert_almost_equal(me.margeff, self.res2.margeff_count_dydx, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_count_dydx_se, DECIMAL_4) def test_count_dydxmean(self): me = self.res1.get_margeff(count=True, at='mean') assert_almost_equal(me.margeff, self.res2.margeff_count_dydxmean, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_count_dydxmean_se, DECIMAL_4) def test_count_dummy_dydxoverall(self): me = self.res1.get_margeff(count=True, dummy=True) assert_almost_equal(me.margeff, self.res2.margeff_count_dummy_dydxoverall, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_count_dummy_dydxoverall_se, DECIMAL_4) def test_count_dummy_dydxmean(self): me = self.res1.get_margeff(count=True, dummy=True, at='mean') assert_almost_equal(me.margeff, self.res2.margeff_count_dummy_dydxmean, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_count_dummy_dydxmean_se, DECIMAL_4) class TestProbitNewton(CheckBinaryResults): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) cls.res1 = Probit(data.endog, data.exog).fit(method="newton", disp=0) res2 = Spector.probit cls.res2 = res2 @pytest.mark.xfail(reason="res2 has no predict attribute", raises=AttributeError, strict=True) def test_predict(self): assert_almost_equal(self.res1.model.predict(self.res1.params), self.res2.predict, DECIMAL_4) class TestProbitBFGS(CheckBinaryResults): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) cls.res1 = Probit(data.endog, data.exog).fit(method="bfgs", disp=0) res2 = Spector.probit cls.res2 = res2 class TestProbitNM(CheckBinaryResults): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) res2 = Spector.probit cls.res2 = res2 cls.res1 = Probit(data.endog, data.exog).fit(method="nm", disp=0, maxiter=500) class TestProbitPowell(CheckBinaryResults): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) res2 = Spector.probit cls.res2 = res2 cls.res1 = Probit(data.endog, data.exog).fit(method="powell", disp=0, ftol=1e-8) class TestProbitCG(CheckBinaryResults): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) res2 = Spector.probit cls.res2 = res2 # fmin_cg fails to converge on some machines - reparameterize from statsmodels.tools.transform_model import StandardizeTransform transf = StandardizeTransform(data.exog) exog_st = transf(data.exog) res1_st = Probit(data.endog, exog_st).fit(method="cg", disp=0, maxiter=1000, gtol=1e-08) start_params = transf.transform_params(res1_st.params) assert_allclose(start_params, res2.params, rtol=1e-5, atol=1e-6) cls.res1 = Probit(data.endog, data.exog).fit(start_params=start_params, method="cg", maxiter=1000, gtol=1e-05, disp=0) assert_array_less(cls.res1.mle_retvals['fcalls'], 100) class TestProbitNCG(CheckBinaryResults): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) res2 = Spector.probit cls.res2 = res2 cls.res1 = Probit(data.endog, data.exog).fit(method="ncg", disp=0, avextol=1e-8, warn_convergence=False) # converges close enough but warnflag is 2 for precision loss class TestProbitBasinhopping(CheckBinaryResults): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) res2 = Spector.probit cls.res2 = res2 fit = Probit(data.endog, data.exog).fit np.random.seed(1) cls.res1 = fit(method="basinhopping", disp=0, niter=5, minimizer={'method' : 'L-BFGS-B', 'tol' : 1e-8}) class TestProbitMinimizeDefault(CheckBinaryResults): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) res2 = Spector.probit cls.res2 = res2 fit = Probit(data.endog, data.exog).fit cls.res1 = fit(method="minimize", disp=0, niter=5, tol = 1e-8) class TestProbitMinimizeDogleg(CheckBinaryResults): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) res2 = Spector.probit cls.res2 = res2 fit = Probit(data.endog, data.exog).fit cls.res1 = fit(method="minimize", disp=0, niter=5, tol = 1e-8, min_method = 'dogleg') class TestProbitMinimizeAdditionalOptions(CheckBinaryResults): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) res2 = Spector.probit cls.res2 = res2 cls.res1 = Probit(data.endog, data.exog).fit(method="minimize", disp=0, maxiter=500, min_method='Nelder-Mead', xatol=1e-4, fatol=1e-4) class CheckLikelihoodModelL1(object): """ For testing results generated with L1 regularization """ def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, DECIMAL_4) def test_conf_int(self): assert_almost_equal( self.res1.conf_int(), self.res2.conf_int, DECIMAL_4) def test_bse(self): assert_almost_equal(self.res1.bse, self.res2.bse, DECIMAL_4) def test_nnz_params(self): assert_almost_equal( self.res1.nnz_params, self.res2.nnz_params, DECIMAL_4) def test_aic(self): assert_almost_equal( self.res1.aic, self.res2.aic, DECIMAL_3) def test_bic(self): assert_almost_equal( self.res1.bic, self.res2.bic, DECIMAL_3) class TestProbitL1(CheckLikelihoodModelL1): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=True) alpha = np.array([0.1, 0.2, 0.3, 10]) #/ data.exog.shape[0] cls.res1 = Probit(data.endog, data.exog).fit_regularized( method="l1", alpha=alpha, disp=0, trim_mode='auto', auto_trim_tol=0.02, acc=1e-10, maxiter=1000) res2 = DiscreteL1.probit cls.res2 = res2 def test_cov_params(self): assert_almost_equal( self.res1.cov_params(), self.res2.cov_params, DECIMAL_4) class TestMNLogitL1(CheckLikelihoodModelL1): @classmethod def setup_class(cls): anes_data = sm.datasets.anes96.load(as_pandas=False) anes_exog = anes_data.exog anes_exog = sm.add_constant(anes_exog, prepend=False) mlogit_mod = sm.MNLogit(anes_data.endog, anes_exog) alpha = 10. * np.ones((mlogit_mod.J - 1, mlogit_mod.K)) #/ anes_exog.shape[0] alpha[-1,:] = 0 cls.res1 = mlogit_mod.fit_regularized( method='l1', alpha=alpha, trim_mode='auto', auto_trim_tol=0.02, acc=1e-10, disp=0) res2 = DiscreteL1.mnlogit cls.res2 = res2 class TestLogitL1(CheckLikelihoodModelL1): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=True) cls.alpha = 3 * np.array([0., 1., 1., 1.]) #/ data.exog.shape[0] cls.res1 = Logit(data.endog, data.exog).fit_regularized( method="l1", alpha=cls.alpha, disp=0, trim_mode='size', size_trim_tol=1e-5, acc=1e-10, maxiter=1000) res2 = DiscreteL1.logit cls.res2 = res2 def test_cov_params(self): assert_almost_equal( self.res1.cov_params(), self.res2.cov_params, DECIMAL_4) @pytest.mark.skipif(not has_cvxopt, reason='Skipped test_cvxopt since cvxopt ' 'is not available') class TestCVXOPT(object): @classmethod def setup_class(cls): if not has_cvxopt: pytest.skip('Skipped test_cvxopt since cvxopt is not available') cls.data = sm.datasets.spector.load(as_pandas=False) cls.data.exog = sm.add_constant(cls.data.exog, prepend=True) def test_cvxopt_versus_slsqp(self): # Compares results from cvxopt to the standard slsqp self.alpha = 3. * np.array([0, 1, 1, 1.]) #/ self.data.endog.shape[0] res_slsqp = Logit(self.data.endog, self.data.exog).fit_regularized( method="l1", alpha=self.alpha, disp=0, acc=1e-10, maxiter=1000, trim_mode='auto') res_cvxopt = Logit(self.data.endog, self.data.exog).fit_regularized( method="l1_cvxopt_cp", alpha=self.alpha, disp=0, abstol=1e-10, trim_mode='auto', auto_trim_tol=0.01, maxiter=1000) assert_almost_equal(res_slsqp.params, res_cvxopt.params, DECIMAL_4) class TestSweepAlphaL1(object): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=True) cls.model = Logit(data.endog, data.exog) cls.alphas = np.array( [[0.1, 0.1, 0.1, 0.1], [0.4, 0.4, 0.5, 0.5], [0.5, 0.5, 1, 1]]) #/ data.exog.shape[0] cls.res1 = DiscreteL1.sweep def test_sweep_alpha(self): for i in range(3): alpha = self.alphas[i, :] res2 = self.model.fit_regularized( method="l1", alpha=alpha, disp=0, acc=1e-10, trim_mode='off', maxiter=1000) assert_almost_equal(res2.params, self.res1.params[i], DECIMAL_4) class CheckL1Compatability(object): """ Tests compatability between l1 and unregularized by setting alpha such that certain parameters should be effectively unregularized, and others should be ignored by the model. """ def test_params(self): m = self.m assert_almost_equal( self.res_unreg.params[:m], self.res_reg.params[:m], DECIMAL_4) # The last entry should be close to zero # handle extra parameter of NegativeBinomial kvars = self.res_reg.model.exog.shape[1] assert_almost_equal(0, self.res_reg.params[m:kvars], DECIMAL_4) def test_cov_params(self): m = self.m # The restricted cov_params should be equal assert_almost_equal( self.res_unreg.cov_params()[:m, :m], self.res_reg.cov_params()[:m, :m], DECIMAL_1) def test_df(self): assert_equal(self.res_unreg.df_model, self.res_reg.df_model) assert_equal(self.res_unreg.df_resid, self.res_reg.df_resid) def test_t_test(self): m = self.m kvars = self.kvars # handle extra parameter of NegativeBinomial extra = getattr(self, 'k_extra', 0) t_unreg = self.res_unreg.t_test(np.eye(len(self.res_unreg.params))) t_reg = self.res_reg.t_test(np.eye(kvars + extra)) assert_almost_equal(t_unreg.effect[:m], t_reg.effect[:m], DECIMAL_3) assert_almost_equal(t_unreg.sd[:m], t_reg.sd[:m], DECIMAL_3) assert_almost_equal(np.nan, t_reg.sd[m]) assert_allclose(t_unreg.tvalue[:m], t_reg.tvalue[:m], atol=3e-3) assert_almost_equal(np.nan, t_reg.tvalue[m]) def test_f_test(self): m = self.m kvars = self.kvars # handle extra parameter of NegativeBinomial extra = getattr(self, 'k_extra', 0) f_unreg = self.res_unreg.f_test(np.eye(len(self.res_unreg.params))[:m]) f_reg = self.res_reg.f_test(np.eye(kvars + extra)[:m]) assert_allclose(f_unreg.fvalue, f_reg.fvalue, rtol=3e-5, atol=1e-3) assert_almost_equal(f_unreg.pvalue, f_reg.pvalue, DECIMAL_3) def test_bad_r_matrix(self): kvars = self.kvars assert_raises(ValueError, self.res_reg.f_test, np.eye(kvars) ) class TestPoissonL1Compatability(CheckL1Compatability): @classmethod def setup_class(cls): cls.kvars = 10 # Number of variables cls.m = 7 # Number of unregularized parameters rand_data = sm.datasets.randhie.load(as_pandas=False) rand_exog = rand_data.exog.view(float).reshape(len(rand_data.exog), -1) rand_exog = sm.add_constant(rand_exog, prepend=True) # Drop some columns and do an unregularized fit exog_no_PSI = rand_exog[:, :cls.m] mod_unreg = sm.Poisson(rand_data.endog, exog_no_PSI) cls.res_unreg = mod_unreg.fit(method="newton", disp=False) # Do a regularized fit with alpha, effectively dropping the last column alpha = 10 * len(rand_data.endog) * np.ones(cls.kvars) alpha[:cls.m] = 0 cls.res_reg = sm.Poisson(rand_data.endog, rand_exog).fit_regularized( method='l1', alpha=alpha, disp=False, acc=1e-10, maxiter=2000, trim_mode='auto') class TestNegativeBinomialL1Compatability(CheckL1Compatability): @classmethod def setup_class(cls): cls.kvars = 10 # Number of variables cls.m = 7 # Number of unregularized parameters rand_data = sm.datasets.randhie.load(as_pandas=False) rand_exog = rand_data.exog.view(float).reshape(len(rand_data.exog), -1) rand_exog_st = (rand_exog - rand_exog.mean(0)) / rand_exog.std(0) rand_exog = sm.add_constant(rand_exog_st, prepend=True) # Drop some columns and do an unregularized fit exog_no_PSI = rand_exog[:, :cls.m] mod_unreg = sm.NegativeBinomial(rand_data.endog, exog_no_PSI) cls.res_unreg = mod_unreg.fit(method="newton", disp=False) # Do a regularized fit with alpha, effectively dropping the last column alpha = 10 * len(rand_data.endog) * np.ones(cls.kvars + 1) alpha[:cls.m] = 0 alpha[-1] = 0 # do not penalize alpha mod_reg = sm.NegativeBinomial(rand_data.endog, rand_exog) cls.res_reg = mod_reg.fit_regularized( method='l1', alpha=alpha, disp=False, acc=1e-10, maxiter=2000, trim_mode='auto') cls.k_extra = 1 # 1 extra parameter in nb2 class TestNegativeBinomialGeoL1Compatability(CheckL1Compatability): @classmethod def setup_class(cls): cls.kvars = 10 # Number of variables cls.m = 7 # Number of unregularized parameters rand_data = sm.datasets.randhie.load(as_pandas=False) rand_exog = rand_data.exog.view(float).reshape(len(rand_data.exog), -1) rand_exog = sm.add_constant(rand_exog, prepend=True) # Drop some columns and do an unregularized fit exog_no_PSI = rand_exog[:, :cls.m] mod_unreg = sm.NegativeBinomial(rand_data.endog, exog_no_PSI, loglike_method='geometric') cls.res_unreg = mod_unreg.fit(method="newton", disp=False) # Do a regularized fit with alpha, effectively dropping the last columns alpha = 10 * len(rand_data.endog) * np.ones(cls.kvars) alpha[:cls.m] = 0 mod_reg = sm.NegativeBinomial(rand_data.endog, rand_exog, loglike_method='geometric') cls.res_reg = mod_reg.fit_regularized( method='l1', alpha=alpha, disp=False, acc=1e-10, maxiter=2000, trim_mode='auto') assert_equal(mod_reg.loglike_method, 'geometric') class TestLogitL1Compatability(CheckL1Compatability): @classmethod def setup_class(cls): cls.kvars = 4 # Number of variables cls.m = 3 # Number of unregularized parameters data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=True) # Do a regularized fit with alpha, effectively dropping the last column alpha = np.array([0, 0, 0, 10]) cls.res_reg = Logit(data.endog, data.exog).fit_regularized( method="l1", alpha=alpha, disp=0, acc=1e-15, maxiter=2000, trim_mode='auto') # Actually drop the last columnand do an unregularized fit exog_no_PSI = data.exog[:, :cls.m] cls.res_unreg = Logit(data.endog, exog_no_PSI).fit(disp=0, tol=1e-15) class TestMNLogitL1Compatability(CheckL1Compatability): @classmethod def setup_class(cls): cls.kvars = 4 # Number of variables cls.m = 3 # Number of unregularized parameters data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=True) alpha = np.array([0, 0, 0, 10]) cls.res_reg = MNLogit(data.endog, data.exog).fit_regularized( method="l1", alpha=alpha, disp=0, acc=1e-15, maxiter=2000, trim_mode='auto') # Actually drop the last columnand do an unregularized fit exog_no_PSI = data.exog[:, :cls.m] cls.res_unreg = MNLogit(data.endog, exog_no_PSI).fit( disp=0, tol=1e-15, method='bfgs', maxiter=1000) def test_t_test(self): m = self.m kvars = self.kvars t_unreg = self.res_unreg.t_test(np.eye(m)) t_reg = self.res_reg.t_test(np.eye(kvars)) assert_almost_equal(t_unreg.effect, t_reg.effect[:m], DECIMAL_3) assert_almost_equal(t_unreg.sd, t_reg.sd[:m], DECIMAL_3) assert_almost_equal(np.nan, t_reg.sd[m]) assert_almost_equal(t_unreg.tvalue, t_reg.tvalue[:m], DECIMAL_3) @pytest.mark.skip("Skipped test_f_test for MNLogit") def test_f_test(self): pass class TestProbitL1Compatability(CheckL1Compatability): @classmethod def setup_class(cls): cls.kvars = 4 # Number of variables cls.m = 3 # Number of unregularized parameters data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=True) alpha = np.array([0, 0, 0, 10]) cls.res_reg = Probit(data.endog, data.exog).fit_regularized( method="l1", alpha=alpha, disp=0, acc=1e-15, maxiter=2000, trim_mode='auto') # Actually drop the last columnand do an unregularized fit exog_no_PSI = data.exog[:, :cls.m] cls.res_unreg = Probit(data.endog, exog_no_PSI).fit(disp=0, tol=1e-15) class CompareL1(object): """ For checking results for l1 regularization. Assumes self.res1 and self.res2 are two legitimate models to be compared. """ def test_basic_results(self): assert_almost_equal(self.res1.params, self.res2.params, DECIMAL_4) assert_almost_equal(self.res1.cov_params(), self.res2.cov_params(), DECIMAL_4) assert_almost_equal(self.res1.conf_int(), self.res2.conf_int(), DECIMAL_4) assert_almost_equal(self.res1.pvalues, self.res2.pvalues, DECIMAL_4) assert_almost_equal(self.res1.pred_table(), self.res2.pred_table(), DECIMAL_4) assert_almost_equal(self.res1.bse, self.res2.bse, DECIMAL_4) assert_almost_equal(self.res1.llf, self.res2.llf, DECIMAL_4) assert_almost_equal(self.res1.aic, self.res2.aic, DECIMAL_4) assert_almost_equal(self.res1.bic, self.res2.bic, DECIMAL_4) assert_almost_equal(self.res1.pvalues, self.res2.pvalues, DECIMAL_4) assert_(self.res1.mle_retvals['converged'] is True) class CompareL11D(CompareL1): """ Check t and f tests. This only works for 1-d results """ def test_tests(self): restrictmat = np.eye(len(self.res1.params.ravel())) assert_almost_equal(self.res1.t_test(restrictmat).pvalue, self.res2.t_test(restrictmat).pvalue, DECIMAL_4) assert_almost_equal(self.res1.f_test(restrictmat).pvalue, self.res2.f_test(restrictmat).pvalue, DECIMAL_4) class TestL1AlphaZeroLogit(CompareL11D): # Compares l1 model with alpha = 0 to the unregularized model. @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=True) cls.res1 = Logit(data.endog, data.exog).fit_regularized( method="l1", alpha=0, disp=0, acc=1e-15, maxiter=1000, trim_mode='auto', auto_trim_tol=0.01) cls.res2 = Logit(data.endog, data.exog).fit(disp=0, tol=1e-15) def test_converged(self): res = self.res1.model.fit_regularized( method="l1", alpha=0, disp=0, acc=1e-15, maxiter=1, trim_mode='auto', auto_trim_tol=0.01) # see #2857 assert_(res.mle_retvals['converged'] is False) class TestL1AlphaZeroProbit(CompareL11D): # Compares l1 model with alpha = 0 to the unregularized model. @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=True) cls.res1 = Probit(data.endog, data.exog).fit_regularized( method="l1", alpha=0, disp=0, acc=1e-15, maxiter=1000, trim_mode='auto', auto_trim_tol=0.01) cls.res2 = Probit(data.endog, data.exog).fit(disp=0, tol=1e-15) class TestL1AlphaZeroMNLogit(CompareL1): @classmethod def setup_class(cls): data = sm.datasets.anes96.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) cls.res1 = MNLogit(data.endog, data.exog).fit_regularized( method="l1", alpha=0, disp=0, acc=1e-15, maxiter=1000, trim_mode='auto', auto_trim_tol=0.01) cls.res2 = MNLogit(data.endog, data.exog).fit(disp=0, tol=1e-15, method='bfgs', maxiter=1000) class TestLogitNewton(CheckBinaryResults, CheckMargEff): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) cls.res1 = Logit(data.endog, data.exog).fit(method="newton", disp=0) res2 = Spector.logit cls.res2 = res2 def test_resid_pearson(self): assert_almost_equal(self.res1.resid_pearson, self.res2.resid_pearson, 5) def test_nodummy_exog1(self): me = self.res1.get_margeff(atexog={0 : 2.0, 2 : 1.}) assert_almost_equal(me.margeff, self.res2.margeff_nodummy_atexog1, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_atexog1_se, DECIMAL_4) def test_nodummy_exog2(self): me = self.res1.get_margeff(atexog={1 : 21., 2 : 0}, at='mean') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_atexog2, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_atexog2_se, DECIMAL_4) def test_dummy_exog1(self): me = self.res1.get_margeff(atexog={0 : 2.0, 2 : 1.}, dummy=True) assert_almost_equal(me.margeff, self.res2.margeff_dummy_atexog1, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_dummy_atexog1_se, DECIMAL_4) def test_dummy_exog2(self): me = self.res1.get_margeff(atexog={1 : 21., 2 : 0}, at='mean', dummy=True) assert_almost_equal(me.margeff, self.res2.margeff_dummy_atexog2, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_dummy_atexog2_se, DECIMAL_4) class TestLogitNewtonPrepend(CheckMargEff): # same as previous version but adjusted for add_constant prepend=True # bug #3695 @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=True) cls.res1 = Logit(data.endog, data.exog).fit(method="newton", disp=0) res2 = Spector.logit cls.res2 = res2 cls.slice = np.roll(np.arange(len(cls.res1.params)), 1) #.astype(int) def test_resid_pearson(self): assert_almost_equal(self.res1.resid_pearson, self.res2.resid_pearson, 5) def test_nodummy_exog1(self): me = self.res1.get_margeff(atexog={1 : 2.0, 3 : 1.}) assert_almost_equal(me.margeff, self.res2.margeff_nodummy_atexog1, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_atexog1_se, DECIMAL_4) def test_nodummy_exog2(self): me = self.res1.get_margeff(atexog={2 : 21., 3 : 0}, at='mean') assert_almost_equal(me.margeff, self.res2.margeff_nodummy_atexog2, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_atexog2_se, DECIMAL_4) def test_dummy_exog1(self): me = self.res1.get_margeff(atexog={1 : 2.0, 3 : 1.}, dummy=True) assert_almost_equal(me.margeff, self.res2.margeff_dummy_atexog1, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_dummy_atexog1_se, DECIMAL_4) def test_dummy_exog2(self): me = self.res1.get_margeff(atexog={2 : 21., 3 : 0}, at='mean', dummy=True) assert_almost_equal(me.margeff, self.res2.margeff_dummy_atexog2, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_dummy_atexog2_se, DECIMAL_4) class TestLogitBFGS(CheckBinaryResults, CheckMargEff): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) res2 = Spector.logit cls.res2 = res2 cls.res1 = Logit(data.endog, data.exog).fit(method="bfgs", disp=0) class TestPoissonNewton(CheckModelResults): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) exog = sm.add_constant(data.exog, prepend=False) cls.res1 = Poisson(data.endog, exog).fit(method='newton', disp=0) res2 = RandHIE.poisson cls.res2 = res2 def test_margeff_overall(self): me = self.res1.get_margeff() assert_almost_equal(me.margeff, self.res2.margeff_nodummy_overall, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_nodummy_overall_se, DECIMAL_4) def test_margeff_dummy_overall(self): me = self.res1.get_margeff(dummy=True) assert_almost_equal(me.margeff, self.res2.margeff_dummy_overall, DECIMAL_4) assert_almost_equal(me.margeff_se, self.res2.margeff_dummy_overall_se, DECIMAL_4) def test_resid(self): assert_almost_equal(self.res1.resid, self.res2.resid, 2) def test_predict_prob(self): cur_dir = os.path.dirname(os.path.abspath(__file__)) path = os.path.join(cur_dir, "results", "predict_prob_poisson.csv") probs_res = np.loadtxt(path, delimiter=",") # just check the first 100 obs. vs R to save memory probs = self.res1.predict_prob()[:100] assert_almost_equal(probs, probs_res, 8) @pytest.mark.xfail(reason="res2.cov_params is a zero-dim array of None", strict=True) def test_cov_params(self): super(TestPoissonNewton, self).test_cov_params() class CheckNegBinMixin(object): # Test methods shared by TestNegativeBinomialXYZ classes @pytest.mark.xfail(reason="pvalues do not match, in some cases wrong size", strict=True, raises=AssertionError) def test_pvalues(self): assert_almost_equal(self.res1.pvalues, self.res2.pvalues, DECIMAL_4) class TestNegativeBinomialNB2Newton(CheckNegBinMixin, CheckModelResults): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) exog = sm.add_constant(data.exog, prepend=False) cls.res1 = NegativeBinomial(data.endog, exog, 'nb2').fit(method='newton', disp=0) res2 = RandHIE.negativebinomial_nb2_bfgs cls.res2 = res2 #NOTE: The bse is much closer precitions to stata def test_bse(self): assert_almost_equal(self.res1.bse, self.res2.bse, DECIMAL_3) def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, DECIMAL_4) def test_alpha(self): self.res1.bse # attaches alpha_std_err assert_almost_equal(self.res1.lnalpha, self.res2.lnalpha, DECIMAL_4) assert_almost_equal(self.res1.lnalpha_std_err, self.res2.lnalpha_std_err, DECIMAL_4) def test_conf_int(self): assert_almost_equal(self.res1.conf_int(), self.res2.conf_int, DECIMAL_3) def test_zstat(self): # Low precision because Z vs. t assert_almost_equal(self.res1.pvalues[:-1], self.res2.pvalues, DECIMAL_2) def test_fittedvalues(self): assert_almost_equal(self.res1.fittedvalues[:10], self.res2.fittedvalues[:10], DECIMAL_3) def test_predict(self): assert_almost_equal(self.res1.predict()[:10], np.exp(self.res2.fittedvalues[:10]), DECIMAL_3) def test_predict_xb(self): assert_almost_equal(self.res1.predict(linear=True)[:10], self.res2.fittedvalues[:10], DECIMAL_3) class TestNegativeBinomialNB1Newton(CheckNegBinMixin, CheckModelResults): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) exog = sm.add_constant(data.exog, prepend=False) model = NegativeBinomial(data.endog, exog, 'nb1') cls.res1 = model.fit(method="newton", maxiter=100, disp=0) res2 = RandHIE.negativebinomial_nb1_bfgs cls.res2 = res2 def test_zstat(self): assert_almost_equal(self.res1.tvalues, self.res2.z, DECIMAL_1) def test_lnalpha(self): self.res1.bse # attaches alpha_std_err assert_almost_equal(self.res1.lnalpha, self.res2.lnalpha, 3) assert_almost_equal(self.res1.lnalpha_std_err, self.res2.lnalpha_std_err, DECIMAL_4) def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, DECIMAL_4) def test_conf_int(self): # the bse for alpha is not high precision from the hessian # approximation assert_almost_equal(self.res1.conf_int(), self.res2.conf_int, DECIMAL_2) @pytest.mark.xfail(reason="Test has not been implemented for this class.", strict=True, raises=NotImplementedError) def test_predict(self): raise NotImplementedError @pytest.mark.xfail(reason="Test has not been implemented for this class.", strict=True, raises=NotImplementedError) def test_predict_xb(self): raise NotImplementedError class TestNegativeBinomialNB2BFGS(CheckNegBinMixin, CheckModelResults): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) exog = sm.add_constant(data.exog, prepend=False) cls.res1 = NegativeBinomial(data.endog, exog, 'nb2').fit( method='bfgs', disp=0, maxiter=1000) res2 = RandHIE.negativebinomial_nb2_bfgs cls.res2 = res2 #NOTE: The bse is much closer precitions to stata def test_bse(self): assert_almost_equal(self.res1.bse, self.res2.bse, DECIMAL_3) def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, DECIMAL_4) def test_alpha(self): self.res1.bse # attaches alpha_std_err assert_almost_equal(self.res1.lnalpha, self.res2.lnalpha, DECIMAL_4) assert_almost_equal(self.res1.lnalpha_std_err, self.res2.lnalpha_std_err, DECIMAL_4) def test_conf_int(self): assert_almost_equal(self.res1.conf_int(), self.res2.conf_int, DECIMAL_3) def test_zstat(self): # Low precision because Z vs. t assert_almost_equal(self.res1.pvalues[:-1], self.res2.pvalues, DECIMAL_2) def test_fittedvalues(self): assert_almost_equal(self.res1.fittedvalues[:10], self.res2.fittedvalues[:10], DECIMAL_3) def test_predict(self): assert_almost_equal(self.res1.predict()[:10], np.exp(self.res2.fittedvalues[:10]), DECIMAL_3) def test_predict_xb(self): assert_almost_equal(self.res1.predict(linear=True)[:10], self.res2.fittedvalues[:10], DECIMAL_3) class TestNegativeBinomialNB1BFGS(CheckNegBinMixin, CheckModelResults): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) exog = sm.add_constant(data.exog, prepend=False) cls.res1 = NegativeBinomial(data.endog, exog, 'nb1').fit(method="bfgs", maxiter=100, disp=0) res2 = RandHIE.negativebinomial_nb1_bfgs cls.res2 = res2 def test_zstat(self): assert_almost_equal(self.res1.tvalues, self.res2.z, DECIMAL_1) def test_lnalpha(self): self.res1.bse # attaches alpha_std_err assert_almost_equal(self.res1.lnalpha, self.res2.lnalpha, 3) assert_almost_equal(self.res1.lnalpha_std_err, self.res2.lnalpha_std_err, DECIMAL_4) def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, DECIMAL_4) def test_conf_int(self): # the bse for alpha is not high precision from the hessian # approximation assert_almost_equal(self.res1.conf_int(), self.res2.conf_int, DECIMAL_2) @pytest.mark.xfail(reason="Test has not been implemented for this class.", strict=True, raises=NotImplementedError) def test_predict(self): raise NotImplementedError @pytest.mark.xfail(reason="Test has not been implemented for this class.", strict=True, raises=NotImplementedError) def test_predict_xb(self): raise NotImplementedError class TestNegativeBinomialGeometricBFGS(CheckNegBinMixin, CheckModelResults): # Cannot find another implementation of the geometric to cross-check results # we only test fitted values because geometric has fewer parameters # than nb1 and nb2 # and we want to make sure that predict() np.dot(exog, params) works @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) exog = sm.add_constant(data.exog, prepend=False) mod = NegativeBinomial(data.endog, exog, 'geometric') cls.res1 = mod.fit(method='bfgs', disp=0) res2 = RandHIE.negativebinomial_geometric_bfgs cls.res2 = res2 # the following are regression tests, could be inherited instead def test_aic(self): assert_almost_equal(self.res1.aic, self.res2.aic, DECIMAL_3) def test_bic(self): assert_almost_equal(self.res1.bic, self.res2.bic, DECIMAL_3) def test_conf_int(self): assert_almost_equal(self.res1.conf_int(), self.res2.conf_int, DECIMAL_3) def test_fittedvalues(self): assert_almost_equal(self.res1.fittedvalues[:10], self.res2.fittedvalues[:10], DECIMAL_3) def test_predict(self): assert_almost_equal(self.res1.predict()[:10], np.exp(self.res2.fittedvalues[:10]), DECIMAL_3) def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, DECIMAL_3) def test_predict_xb(self): assert_almost_equal(self.res1.predict(linear=True)[:10], self.res2.fittedvalues[:10], DECIMAL_3) def test_zstat(self): # Low precision because Z vs. t assert_almost_equal(self.res1.tvalues, self.res2.z, DECIMAL_1) def test_llf(self): assert_almost_equal(self.res1.llf, self.res2.llf, DECIMAL_1) def test_llr(self): assert_almost_equal(self.res1.llr, self.res2.llr, DECIMAL_2) def test_bse(self): assert_almost_equal(self.res1.bse, self.res2.bse, DECIMAL_3) class CheckMNLogitBaseZero(CheckModelResults): def test_margeff_overall(self): me = self.res1.get_margeff() assert_almost_equal(me.margeff, self.res2.margeff_dydx_overall, 6) assert_almost_equal(me.margeff_se, self.res2.margeff_dydx_overall_se, 6) me_frame = me.summary_frame() eff = me_frame["dy/dx"].values.reshape(me.margeff.shape, order="F") assert_allclose(eff, me.margeff, rtol=1e-13) assert_equal(me_frame.shape, (np.size(me.margeff), 6)) def test_margeff_mean(self): me = self.res1.get_margeff(at='mean') assert_almost_equal(me.margeff, self.res2.margeff_dydx_mean, 7) assert_almost_equal(me.margeff_se, self.res2.margeff_dydx_mean_se, 7) def test_margeff_dummy(self): data = self.data vote = data.data['vote'] exog = np.column_stack((data.exog, vote)) exog = sm.add_constant(exog, prepend=False) res = MNLogit(data.endog, exog).fit(method="newton", disp=0) me = res.get_margeff(dummy=True) assert_almost_equal(me.margeff, self.res2.margeff_dydx_dummy_overall, 6) assert_almost_equal(me.margeff_se, self.res2.margeff_dydx_dummy_overall_se, 6) me = res.get_margeff(dummy=True, method="eydx") assert_almost_equal(me.margeff, self.res2.margeff_eydx_dummy_overall, 5) assert_almost_equal(me.margeff_se, self.res2.margeff_eydx_dummy_overall_se, 6) def test_j(self): assert_equal(self.res1.model.J, self.res2.J) def test_k(self): assert_equal(self.res1.model.K, self.res2.K) def test_endog_names(self): assert_equal(self.res1._get_endog_name(None,None)[1], ['y=1', 'y=2', 'y=3', 'y=4', 'y=5', 'y=6']) def test_pred_table(self): # fitted results taken from gretl pred = [6, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 6, 0, 1, 6, 0, 0, 1, 1, 6, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 6, 0, 0, 6, 6, 0, 0, 1, 1, 6, 1, 6, 0, 0, 0, 1, 0, 1, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 1, 1, 0, 0, 6, 6, 6, 6, 1, 0, 5, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 6, 0, 6, 6, 1, 0, 1, 1, 6, 5, 1, 0, 0, 0, 5, 0, 0, 6, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 6, 6, 6, 6, 5, 0, 1, 1, 0, 1, 0, 6, 6, 0, 0, 0, 6, 0, 0, 0, 6, 6, 0, 5, 1, 0, 0, 0, 0, 6, 0, 5, 6, 6, 0, 0, 0, 0, 6, 1, 0, 0, 1, 0, 1, 6, 1, 1, 1, 1, 1, 0, 0, 0, 6, 0, 5, 1, 0, 6, 6, 6, 0, 0, 0, 0, 1, 6, 6, 0, 0, 0, 1, 1, 5, 6, 0, 6, 1, 0, 0, 1, 6, 0, 0, 1, 0, 6, 6, 0, 5, 6, 6, 0, 0, 6, 1, 0, 6, 0, 1, 0, 1, 6, 0, 1, 1, 1, 6, 0, 5, 0, 0, 6, 1, 0, 6, 5, 5, 0, 6, 1, 1, 1, 0, 0, 6, 0, 0, 5, 0, 0, 6, 6, 6, 6, 6, 0, 1, 0, 0, 6, 6, 0, 0, 1, 6, 0, 0, 6, 1, 6, 1, 1, 1, 0, 1, 6, 5, 0, 0, 1, 5, 0, 1, 6, 6, 1, 0, 0, 1, 6, 1, 5, 6, 1, 0, 0, 1, 1, 0, 6, 1, 6, 0, 1, 1, 5, 6, 6, 5, 1, 1, 1, 0, 6, 1, 6, 1, 0, 1, 0, 0, 1, 5, 0, 1, 1, 0, 5, 6, 0, 5, 1, 1, 6, 5, 0, 6, 0, 0, 0, 0, 0, 0, 1, 6, 1, 0, 5, 1, 0, 0, 1, 6, 0, 0, 6, 6, 6, 0, 2, 1, 6, 5, 6, 1, 1, 0, 5, 1, 1, 1, 6, 1, 6, 6, 5, 6, 0, 1, 0, 1, 6, 0, 6, 1, 6, 0, 0, 6, 1, 0, 6, 1, 0, 0, 0, 0, 6, 6, 6, 6, 5, 6, 6, 0, 0, 6, 1, 1, 6, 0, 0, 6, 6, 0, 6, 6, 0, 0, 6, 0, 0, 6, 6, 6, 1, 0, 6, 0, 0, 0, 6, 1, 1, 0, 1, 5, 0, 0, 5, 0, 0, 0, 1, 1, 6, 1, 0, 0, 0, 6, 6, 1, 1, 6, 5, 5, 0, 6, 6, 0, 1, 1, 0, 6, 6, 0, 6, 5, 5, 6, 5, 1, 0, 6, 0, 6, 1, 0, 1, 6, 6, 6, 1, 0, 6, 0, 5, 6, 6, 5, 0, 5, 1, 0, 6, 0, 6, 1, 5, 5, 0, 1, 5, 5, 2, 6, 6, 6, 5, 0, 0, 1, 6, 1, 0, 1, 6, 1, 0, 0, 1, 5, 6, 6, 0, 0, 0, 5, 6, 6, 6, 1, 5, 6, 1, 0, 0, 6, 5, 0, 1, 1, 1, 6, 6, 0, 1, 0, 0, 0, 5, 0, 0, 6, 1, 6, 0, 6, 1, 5, 5, 6, 5, 0, 0, 0, 0, 1, 1, 0, 5, 5, 0, 0, 0, 0, 1, 0, 6, 6, 1, 1, 6, 6, 0, 5, 5, 0, 0, 0, 6, 6, 1, 6, 0, 0, 5, 0, 1, 6, 5, 6, 6, 5, 5, 6, 6, 1, 0, 1, 6, 6, 1, 6, 0, 6, 0, 6, 5, 0, 6, 6, 0, 5, 6, 0, 6, 6, 5, 0, 1, 6, 6, 1, 0, 1, 0, 6, 6, 1, 0, 6, 6, 6, 0, 1, 6, 0, 1, 5, 1, 1, 5, 6, 6, 0, 1, 6, 6, 1, 5, 0, 5, 0, 6, 0, 1, 6, 1, 0, 6, 1, 6, 0, 6, 1, 0, 0, 0, 6, 6, 0, 1, 1, 6, 6, 6, 1, 6, 0, 5, 6, 0, 5, 6, 6, 5, 5, 5, 6, 0, 6, 0, 0, 0, 5, 0, 6, 1, 2, 6, 6, 6, 5, 1, 6, 0, 6, 0, 0, 0, 0, 6, 5, 0, 5, 1, 6, 5, 1, 6, 5, 1, 1, 0, 0, 6, 1, 1, 5, 6, 6, 0, 5, 2, 5, 5, 0, 5, 5, 5, 6, 5, 6, 6, 5, 2, 6, 5, 6, 0, 0, 6, 5, 0, 6, 0, 0, 6, 6, 6, 0, 5, 1, 1, 6, 6, 5, 2, 1, 6, 5, 6, 0, 6, 6, 1, 1, 5, 1, 6, 6, 6, 0, 0, 6, 1, 0, 5, 5, 1, 5, 6, 1, 6, 0, 1, 6, 5, 0, 0, 6, 1, 5, 1, 0, 6, 0, 6, 6, 5, 5, 6, 6, 6, 6, 2, 6, 6, 6, 5, 5, 5, 0, 1, 0, 0, 0, 6, 6, 1, 0, 6, 6, 6, 6, 6, 1, 0, 6, 1, 5, 5, 6, 6, 6, 6, 6, 5, 6, 1, 6, 2, 5, 5, 6, 5, 6, 6, 5, 6, 6, 5, 5, 6, 1, 5, 1, 6, 0, 2, 5, 0, 5, 0, 2, 1, 6, 0, 0, 6, 6, 1, 6, 0, 5, 5, 6, 6, 1, 6, 6, 6, 5, 6, 6, 1, 6, 5, 6, 1, 1, 0, 6, 6, 5, 1, 0, 0, 6, 6, 5, 6, 0, 1, 6, 0, 5, 6, 5, 2, 5, 2, 0, 0, 1, 6, 6, 1, 5, 6, 6, 0, 6, 6, 6, 6, 6, 5] assert_array_equal(self.res1.predict().argmax(1), pred) # the rows should add up for pred table assert_array_equal(self.res1.pred_table().sum(0), np.bincount(pred)) # note this is just a regression test, gretl does not have a prediction # table pred = [[ 126., 41., 2., 0., 0., 12., 19.], [ 77., 73., 3., 0., 0., 15., 12.], [ 37., 43., 2., 0., 0., 19., 7.], [ 12., 9., 1., 0., 0., 9., 6.], [ 19., 10., 2., 0., 0., 20., 43.], [ 22., 25., 1., 0., 0., 31., 71.], [ 9., 7., 1., 0., 0., 18., 140.]] assert_array_equal(self.res1.pred_table(), pred) def test_resid(self): assert_array_equal(self.res1.resid_misclassified, self.res2.resid) @pytest.mark.xfail(reason="res2.cov_params is a zero-dim array of None", strict=True) def test_cov_params(self): super(CheckMNLogitBaseZero, self).test_cov_params() class TestMNLogitNewtonBaseZero(CheckMNLogitBaseZero): @classmethod def setup_class(cls): data = sm.datasets.anes96.load(as_pandas=False) cls.data = data exog = data.exog exog = sm.add_constant(exog, prepend=False) cls.res1 = MNLogit(data.endog, exog).fit(method="newton", disp=0) res2 = Anes.mnlogit_basezero cls.res2 = res2 class TestMNLogitLBFGSBaseZero(CheckMNLogitBaseZero): @classmethod def setup_class(cls): data = sm.datasets.anes96.load(as_pandas=False) cls.data = data exog = data.exog exog = sm.add_constant(exog, prepend=False) mymodel = MNLogit(data.endog, exog) cls.res1 = mymodel.fit(method="lbfgs", disp=0, maxiter=50000, #m=12, pgtol=1e-7, factr=1e3, # 5 failures #m=20, pgtol=1e-8, factr=1e2, # 3 failures #m=30, pgtol=1e-9, factr=1e1, # 1 failure m=40, pgtol=1e-10, factr=5e0, loglike_and_score=mymodel.loglike_and_score) res2 = Anes.mnlogit_basezero cls.res2 = res2 def test_perfect_prediction(): cur_dir = os.path.dirname(os.path.abspath(__file__)) iris_dir = os.path.join(cur_dir, '..', '..', 'genmod', 'tests', 'results') iris_dir = os.path.abspath(iris_dir) iris = np.genfromtxt(os.path.join(iris_dir, 'iris.csv'), delimiter=",", skip_header=1) y = iris[:,-1] X = iris[:,:-1] X = X[y != 2] y = y[y != 2] X = sm.add_constant(X, prepend=True) mod = Logit(y,X) assert_raises(PerfectSeparationError, mod.fit, maxiter=1000) #turn off raise PerfectSeparationError mod.raise_on_perfect_prediction = False # this will raise if you set maxiter high enough with a singular matrix with pytest.warns(ConvergenceWarning): res = mod.fit(disp=False, maxiter=50) # should not raise but does warn assert_(not res.mle_retvals['converged']) def test_poisson_predict(): #GH: 175, make sure poisson predict works without offset and exposure data = sm.datasets.randhie.load(as_pandas=False) exog = sm.add_constant(data.exog, prepend=True) res = sm.Poisson(data.endog, exog).fit(method='newton', disp=0) pred1 = res.predict() pred2 = res.predict(exog) assert_almost_equal(pred1, pred2) #exta options pred3 = res.predict(exog, offset=0, exposure=1) assert_almost_equal(pred1, pred3) pred3 = res.predict(exog, offset=0, exposure=2) assert_almost_equal(2*pred1, pred3) pred3 = res.predict(exog, offset=np.log(2), exposure=1) assert_almost_equal(2*pred1, pred3) def test_poisson_newton(): #GH: 24, Newton does not work well sometimes nobs = 10000 np.random.seed(987689) x = np.random.randn(nobs, 3) x = sm.add_constant(x, prepend=True) y_count = np.random.poisson(np.exp(x.sum(1))) mod = sm.Poisson(y_count, x) # this is not thread-safe with pytest.warns(ConvergenceWarning): res = mod.fit(start_params=-np.ones(4), method='newton', disp=0) assert_(not res.mle_retvals['converged']) def test_issue_339(): # make sure MNLogit summary works for J != K. data = sm.datasets.anes96.load(as_pandas=False) exog = data.exog # leave out last exog column exog = exog[:,:-1] exog = sm.add_constant(exog, prepend=True) res1 = sm.MNLogit(data.endog, exog).fit(method="newton", disp=0) # strip the header from the test smry = "\n".join(res1.summary().as_text().split('\n')[9:]) cur_dir = os.path.dirname(os.path.abspath(__file__)) test_case_file = os.path.join(cur_dir, 'results', 'mn_logit_summary.txt') with open(test_case_file, 'r') as fd: test_case = fd.read() np.testing.assert_equal(smry, test_case[:-1]) # smoke test for summary2 res1.summary2() # see #3651 def test_issue_341(): data = sm.datasets.anes96.load(as_pandas=False) exog = data.exog # leave out last exog column exog = exog[:,:-1] exog = sm.add_constant(exog, prepend=True) res1 = sm.MNLogit(data.endog, exog).fit(method="newton", disp=0) x = exog[0] np.testing.assert_equal(res1.predict(x).shape, (1,7)) np.testing.assert_equal(res1.predict(x[None]).shape, (1,7)) def test_iscount(): X = np.random.random((50, 10)) X[:,2] = np.random.randint(1, 10, size=50) X[:,6] = np.random.randint(1, 10, size=50) X[:,4] = np.random.randint(0, 2, size=50) X[:,1] = np.random.randint(-10, 10, size=50) # not integers count_ind = _iscount(X) assert_equal(count_ind, [2, 6]) def test_isdummy(): X = np.random.random((50, 10)) X[:,2] = np.random.randint(1, 10, size=50) X[:,6] = np.random.randint(0, 2, size=50) X[:,4] = np.random.randint(0, 2, size=50) X[:,1] = np.random.randint(-10, 10, size=50) # not integers count_ind = _isdummy(X) assert_equal(count_ind, [4, 6]) def test_non_binary(): y = [1, 2, 1, 2, 1, 2] X = np.random.randn(6, 2) assert_raises(ValueError, Logit, y, X) y = [0, 1, 0, 0, 1, 0.5] assert_raises(ValueError, Probit, y, X) def test_mnlogit_factor(): dta = sm.datasets.anes96.load_pandas() dta['endog'] = dta.endog.replace(dict(zip(range(7), 'ABCDEFG'))) exog = sm.add_constant(dta.exog, prepend=True) mod = sm.MNLogit(dta.endog, exog) res = mod.fit(disp=0) # smoke tests params = res.params summary = res.summary() predicted = res.predict(exog.iloc[:5, :]) # with patsy mod = smf.mnlogit('PID ~ ' + ' + '.join(dta.exog.columns), dta.data) res2 = mod.fit(disp=0) params_f = res2.params summary = res2.summary() assert_allclose(params_f, params, rtol=1e-10) predicted_f = res2.predict(dta.exog.iloc[:5, :]) assert_allclose(predicted_f, predicted, rtol=1e-10) def test_mnlogit_factor_categorical(): dta = sm.datasets.anes96.load_pandas() dta['endog'] = dta.endog.replace(dict(zip(range(7), 'ABCDEFG'))) exog = sm.add_constant(dta.exog, prepend=True) mod = sm.MNLogit(dta.endog, exog) res = mod.fit(disp=0) dta['endog'] = dta['endog'].astype('category') mod = sm.MNLogit(dta.endog, exog) res_cat = mod.fit(disp=0) assert_allclose(res.params, res_cat.params) def test_formula_missing_exposure(): # see 2083 d = {'Foo': [1, 2, 10, 149], 'Bar': [1, 2, 3, np.nan], 'constant': [1] * 4, 'exposure' : np.random.uniform(size=4), 'x': [1, 3, 2, 1.5]} df = pd.DataFrame(d) # should work mod1 = smf.poisson('Foo ~ Bar', data=df, exposure=df['exposure']) assert_(type(mod1.exposure) is np.ndarray, msg='Exposure is not ndarray') # make sure this raises exposure = pd.Series(np.random.uniform(size=5)) df.loc[3, 'Bar'] = 4 # nan not relevant for ValueError for shape mismatch assert_raises(ValueError, sm.Poisson, df.Foo, df[['constant', 'Bar']], exposure=exposure) def test_predict_with_exposure(): # Case where CountModel.predict is called with exog = None and exposure # or offset not-None # See 3565 # Setup copied from test_formula_missing_exposure import pandas as pd d = {'Foo': [1, 2, 10, 149], 'Bar': [1, 2, 3, 4], 'constant': [1] * 4, 'exposure' : [np.exp(1)]*4, 'x': [1, 3, 2, 1.5]} df = pd.DataFrame(d) mod1 = CountModel.from_formula('Foo ~ Bar', data=df, exposure=df['exposure']) params = np.array([1, .4]) pred = mod1.predict(params, linear=True) # No exposure is passed, so default to using mod1.exposure, which # should have been logged X = df[['constant', 'Bar']].values # mod1.exog expected = np.dot(X, params) + 1 assert_allclose(pred, expected) # The above should have passed without the current patch. The next # test would fail under the old code pred2 = mod1.predict(params, exposure=[np.exp(2)]*4, linear=True) expected2 = expected + 1 assert_allclose(pred2, expected2) def test_binary_pred_table_zeros(): # see 2968 nobs = 10 y = np.zeros(nobs) y[[1,3]] = 1 res = Logit(y, np.ones(nobs)).fit(disp=0) expected = np.array([[ 8., 0.], [ 2., 0.]]) assert_equal(res.pred_table(), expected) res = MNLogit(y, np.ones(nobs)).fit(disp=0) expected = np.array([[ 8., 0.], [ 2., 0.]]) assert_equal(res.pred_table(), expected) class TestGeneralizedPoisson_p2(object): # Test Generalized Poisson model @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) mod = GeneralizedPoisson(data.endog, data.exog, p=2) cls.res1 = mod.fit(method='newton', disp=0) res2 = RandHIE.generalizedpoisson_gp2 cls.res2 = res2 def test_bse(self): assert_allclose(self.res1.bse, self.res2.bse, atol=1e-5) def test_params(self): assert_allclose(self.res1.params, self.res2.params, atol=1e-5) def test_alpha(self): assert_allclose(self.res1.lnalpha, self.res2.lnalpha) assert_allclose(self.res1.lnalpha_std_err, self.res2.lnalpha_std_err, atol=1e-5) def test_conf_int(self): assert_allclose(self.res1.conf_int(), self.res2.conf_int, atol=1e-3) def test_aic(self): assert_allclose(self.res1.aic, self.res2.aic) def test_bic(self): assert_allclose(self.res1.bic, self.res2.bic) def test_df(self): assert_equal(self.res1.df_model, self.res2.df_model) def test_llf(self): assert_allclose(self.res1.llf, self.res2.llf) def test_wald(self): result = self.res1.wald_test(np.eye(len(self.res1.params))[:-2]) assert_allclose(result.statistic, self.res2.wald_statistic) assert_allclose(result.pvalue, self.res2.wald_pvalue, atol=1e-15) def test_t(self): unit_matrix = np.identity(self.res1.params.size) t_test = self.res1.t_test(unit_matrix) assert_allclose(self.res1.tvalues, t_test.tvalue) class TestGeneralizedPoisson_transparams(object): # Test Generalized Poisson model @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) cls.res1 = GeneralizedPoisson(data.endog, data.exog, p=2).fit( method='newton', disp=0) res2 = RandHIE.generalizedpoisson_gp2 cls.res2 = res2 def test_bse(self): assert_allclose(self.res1.bse, self.res2.bse, atol=1e-5) def test_params(self): assert_allclose(self.res1.params, self.res2.params, atol=1e-5) def test_alpha(self): assert_allclose(self.res1.lnalpha, self.res2.lnalpha) assert_allclose(self.res1.lnalpha_std_err, self.res2.lnalpha_std_err, atol=1e-5) def test_conf_int(self): assert_allclose(self.res1.conf_int(), self.res2.conf_int, atol=1e-3) def test_aic(self): assert_allclose(self.res1.aic, self.res2.aic) def test_bic(self): assert_allclose(self.res1.bic, self.res2.bic) def test_df(self): assert_equal(self.res1.df_model, self.res2.df_model) def test_llf(self): assert_allclose(self.res1.llf, self.res2.llf) class TestGeneralizedPoisson_p1(object): # Test Generalized Poisson model @classmethod def setup_class(cls): cls.data = sm.datasets.randhie.load(as_pandas=False) cls.data.exog = sm.add_constant(cls.data.exog, prepend=False) cls.res1 = GeneralizedPoisson( cls.data.endog, cls.data.exog, p=1).fit(method='newton', disp=0) def test_llf(self): poisson_llf = sm.Poisson( self.data.endog, self.data.exog).loglike( self.res1.params[:-1]) genpoisson_llf = sm.GeneralizedPoisson( self.data.endog, self.data.exog, p=1).loglike( list(self.res1.params[:-1]) + [0]) assert_allclose(genpoisson_llf, poisson_llf) def test_score(self): poisson_score = sm.Poisson( self.data.endog, self.data.exog).score( self.res1.params[:-1]) genpoisson_score = sm.GeneralizedPoisson( self.data.endog, self.data.exog, p=1).score( list(self.res1.params[:-1]) + [0]) assert_allclose(genpoisson_score[:-1], poisson_score, atol=1e-9) def test_hessian(self): poisson_score = sm.Poisson( self.data.endog, self.data.exog).hessian( self.res1.params[:-1]) genpoisson_score = sm.GeneralizedPoisson( self.data.endog, self.data.exog, p=1).hessian( list(self.res1.params[:-1]) + [0]) assert_allclose(genpoisson_score[:-1,:-1], poisson_score, atol=1e-10) def test_t(self): unit_matrix = np.identity(self.res1.params.size) t_test = self.res1.t_test(unit_matrix) assert_allclose(self.res1.tvalues, t_test.tvalue) def test_fit_regularized(self): model = self.res1.model # do not penalize constant and dispersion parameter alpha = np.ones(len(self.res1.params)) alpha[-2:] = 0 # the first prints currently a warning, irrelevant here res_reg1 = model.fit_regularized(alpha=alpha*0.01, disp=0) res_reg2 = model.fit_regularized(alpha=alpha*100, disp=0) res_reg3 = model.fit_regularized(alpha=alpha*1000, disp=0) assert_allclose(res_reg1.params, self.res1.params, atol=5e-5) assert_allclose(res_reg1.bse, self.res1.bse, atol=1e-5) # check shrinkage, regression numbers assert_allclose((self.res1.params[:-2]**2).mean(), 0.016580955543320779) assert_allclose((res_reg1.params[:-2]**2).mean(), 0.016580734975068664) assert_allclose((res_reg2.params[:-2]**2).mean(), 0.010672558641545994) assert_allclose((res_reg3.params[:-2]**2).mean(), 0.00035544919793048415) def test_init_kwds(self): kwds = self.res1.model._get_init_kwds() assert_('p' in kwds) assert_equal(kwds['p'], 1) class TestGeneralizedPoisson_underdispersion(object): @classmethod def setup_class(cls): cls.expected_params = [1, -0.5, -0.05] np.random.seed(1234) nobs = 200 exog = np.ones((nobs, 2)) exog[:nobs//2, 1] = 2 mu_true = np.exp(exog.dot(cls.expected_params[:-1])) cls.endog = sm.distributions.genpoisson_p.rvs(mu_true, cls.expected_params[-1], 1, size=len(mu_true)) model_gp = sm.GeneralizedPoisson(cls.endog, exog, p=1) cls.res = model_gp.fit(method='nm', xtol=1e-6, maxiter=5000, maxfun=5000, disp=0) def test_basic(self): res = self.res endog = res.model.endog # check random data generation, regression test assert_allclose(endog.mean(), 1.42, rtol=1e-3) assert_allclose(endog.var(), 1.2836, rtol=1e-3) # check estimation assert_allclose(res.params, self.expected_params, atol=0.07, rtol=0.1) assert_(res.mle_retvals['converged'] is True) assert_allclose(res.mle_retvals['fopt'], 1.418753161722015, rtol=0.01) def test_newton(self): # check newton optimization with start_params res = self.res res2 = res.model.fit(start_params=res.params, method='newton', disp=0) assert_allclose(res.model.score(res.params), np.zeros(len(res2.params)), atol=0.01) assert_allclose(res.model.score(res2.params), np.zeros(len(res2.params)), atol=1e-10) assert_allclose(res.params, res2.params, atol=1e-4) def test_mean_var(self): assert_allclose(self.res.predict().mean(), self.endog.mean(), atol=1e-1, rtol=1e-1) assert_allclose( self.res.predict().mean() * self.res._dispersion_factor.mean(), self.endog.var(), atol=2e-1, rtol=2e-1) def test_predict_prob(self): res = self.res endog = res.model.endog freq = np.bincount(endog.astype(int)) pr = res.predict(which='prob') pr2 = sm.distributions.genpoisson_p.pmf(np.arange(6)[:, None], res.predict(), res.params[-1], 1).T assert_allclose(pr, pr2, rtol=1e-10, atol=1e-10) expected = pr.sum(0) # add expected obs from right tail to last bin expected[-1] += pr.shape[0] - expected.sum() # scipy requires observed and expected add to the same at rtol=1e-8 assert_allclose(freq.sum(), expected.sum(), rtol=1e-13) from scipy import stats chi2 = stats.chisquare(freq, expected) # numbers are regression test, we should not reject assert_allclose(chi2[:], (0.5511787456691261, 0.9901293016678583), rtol=0.01) class TestNegativeBinomialPNB2Newton(CheckNegBinMixin, CheckModelResults): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) exog = sm.add_constant(data.exog, prepend=False) mod = NegativeBinomialP(data.endog, exog, p=2) cls.res1 = mod.fit(method='newton', disp=0) res2 = RandHIE.negativebinomial_nb2_bfgs cls.res2 = res2 #NOTE: The bse is much closer precitions to stata def test_bse(self): assert_allclose(self.res1.bse, self.res2.bse, atol=1e-3, rtol=1e-3) def test_params(self): assert_allclose(self.res1.params, self.res2.params, atol=1e-7) def test_alpha(self): self.res1.bse # attaches alpha_std_err assert_allclose(self.res1.lnalpha, self.res2.lnalpha) assert_allclose(self.res1.lnalpha_std_err, self.res2.lnalpha_std_err, atol=1e-7) def test_conf_int(self): assert_allclose(self.res1.conf_int(), self.res2.conf_int, atol=1e-3, rtol=1e-3) def test_zstat(self): # Low precision because Z vs. t assert_allclose(self.res1.pvalues[:-1], self.res2.pvalues, atol=5e-3, rtol=5e-3) def test_fittedvalues(self): assert_allclose(self.res1.fittedvalues[:10], self.res2.fittedvalues[:10]) def test_predict(self): assert_allclose(self.res1.predict()[:10], np.exp(self.res2.fittedvalues[:10])) def test_predict_xb(self): assert_allclose(self.res1.predict(which='linear')[:10], self.res2.fittedvalues[:10]) class TestNegativeBinomialPNB1Newton(CheckNegBinMixin, CheckModelResults): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) exog = sm.add_constant(data.exog, prepend=False) mod = NegativeBinomialP(data.endog, exog, p=1) cls.res1 = mod.fit(method="newton", maxiter=100, disp=0) res2 = RandHIE.negativebinomial_nb1_bfgs cls.res2 = res2 def test_zstat(self): assert_allclose(self.res1.tvalues, self.res2.z, atol=5e-3, rtol=5e-3) def test_lnalpha(self): self.res1.bse # attaches alpha_std_err assert_allclose(self.res1.lnalpha, self.res2.lnalpha) assert_allclose(self.res1.lnalpha_std_err, self.res2.lnalpha_std_err) def test_params(self): assert_allclose(self.res1.params, self.res2.params) def test_conf_int(self): # the bse for alpha is not high precision from the hessian # approximation assert_allclose(self.res1.conf_int(), self.res2.conf_int, atol=1e-3, rtol=1e-3) def test_predict(self): assert_allclose(self.res1.predict()[:10], np.exp(self.res2.fittedvalues[:10]), atol=1e-3, rtol=1e-3) def test_predict_xb(self): assert_allclose(self.res1.predict(which='linear')[:10], self.res2.fittedvalues[:10], atol=1e-3, rtol=1e-3) class TestNegativeBinomialPNB2BFGS(CheckNegBinMixin, CheckModelResults): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) exog = sm.add_constant(data.exog, prepend=False) cls.res1 = NegativeBinomialP(data.endog, exog, p=2).fit( method='bfgs', disp=0, maxiter=1000) res2 = RandHIE.negativebinomial_nb2_bfgs cls.res2 = res2 #NOTE: The bse is much closer precitions to stata def test_bse(self): assert_allclose(self.res1.bse, self.res2.bse, atol=1e-3, rtol=1e-3) def test_params(self): assert_allclose(self.res1.params, self.res2.params, atol=1e-3, rtol=1e-3) def test_alpha(self): self.res1.bse # attaches alpha_std_err assert_allclose(self.res1.lnalpha, self.res2.lnalpha, atol=1e-5, rtol=1e-5) assert_allclose(self.res1.lnalpha_std_err, self.res2.lnalpha_std_err, atol=1e-5, rtol=1e-5) def test_conf_int(self): assert_allclose(self.res1.conf_int(), self.res2.conf_int, atol=1e-3, rtol=1e-3) def test_zstat(self): # Low precision because Z vs. t assert_allclose(self.res1.pvalues[:-1], self.res2.pvalues, atol=5e-3, rtol=5e-3) def test_fittedvalues(self): assert_allclose(self.res1.fittedvalues[:10], self.res2.fittedvalues[:10], atol=1e-4, rtol=1e-4) def test_predict(self): assert_allclose(self.res1.predict()[:10], np.exp(self.res2.fittedvalues[:10]), atol=1e-3, rtol=1e-3) def test_predict_xb(self): assert_allclose(self.res1.predict(which='linear')[:10], self.res2.fittedvalues[:10], atol=1e-3, rtol=1e-3) class TestNegativeBinomialPNB1BFGS(CheckNegBinMixin, CheckModelResults): @classmethod def setup_class(cls): data = sm.datasets.randhie.load(as_pandas=False) exog = sm.add_constant(data.exog, prepend=False) cls.res1 = NegativeBinomialP(data.endog, exog, p=1).fit(method="bfgs", maxiter=100, disp=0) res2 = RandHIE.negativebinomial_nb1_bfgs cls.res2 = res2 def test_bse(self): assert_allclose(self.res1.bse, self.res2.bse, atol=5e-3, rtol=5e-3) def test_aic(self): assert_allclose(self.res1.aic, self.res2.aic, atol=0.5, rtol=0.5) def test_bic(self): assert_allclose(self.res1.bic, self.res2.bic, atol=0.5, rtol=0.5) def test_llf(self): assert_allclose(self.res1.llf, self.res2.llf, atol=1e-3, rtol=1e-3) def test_llr(self): assert_allclose(self.res1.llf, self.res2.llf, atol=1e-3, rtol=1e-3) def test_zstat(self): assert_allclose(self.res1.tvalues, self.res2.z, atol=0.5, rtol=0.5) def test_lnalpha(self): assert_allclose(self.res1.lnalpha, self.res2.lnalpha, atol=1e-3, rtol=1e-3) assert_allclose(self.res1.lnalpha_std_err, self.res2.lnalpha_std_err, atol=1e-3, rtol=1e-3) def test_params(self): assert_allclose(self.res1.params, self.res2.params, atol=5e-2, rtol=5e-2) def test_conf_int(self): # the bse for alpha is not high precision from the hessian # approximation assert_allclose(self.res1.conf_int(), self.res2.conf_int, atol=5e-2, rtol=5e-2) def test_predict(self): assert_allclose(self.res1.predict()[:10], np.exp(self.res2.fittedvalues[:10]), atol=5e-3, rtol=5e-3) def test_predict_xb(self): assert_allclose(self.res1.predict(which='linear')[:10], self.res2.fittedvalues[:10], atol=5e-3, rtol=5e-3) def test_init_kwds(self): kwds = self.res1.model._get_init_kwds() assert_('p' in kwds) assert_equal(kwds['p'], 1) class TestNegativeBinomialPL1Compatability(CheckL1Compatability): @classmethod def setup_class(cls): cls.kvars = 10 # Number of variables cls.m = 7 # Number of unregularized parameters rand_data = sm.datasets.randhie.load(as_pandas=False) rand_exog = rand_data.exog.view(float).reshape(len(rand_data.exog), -1) rand_exog_st = (rand_exog - rand_exog.mean(0)) / rand_exog.std(0) rand_exog = sm.add_constant(rand_exog_st, prepend=True) # Drop some columns and do an unregularized fit exog_no_PSI = rand_exog[:, :cls.m] mod_unreg = sm.NegativeBinomialP(rand_data.endog, exog_no_PSI) cls.res_unreg = mod_unreg.fit(method="newton", disp=0) # Do a regularized fit with alpha, effectively dropping the last column alpha = 10 * len(rand_data.endog) * np.ones(cls.kvars + 1) alpha[:cls.m] = 0 alpha[-1] = 0 # do not penalize alpha mod_reg = sm.NegativeBinomialP(rand_data.endog, rand_exog) cls.res_reg = mod_reg.fit_regularized( method='l1', alpha=alpha, disp=False, acc=1e-10, maxiter=2000, trim_mode='auto') cls.k_extra = 1 # 1 extra parameter in nb2 class TestNegativeBinomialPPredictProb(object): def test_predict_prob_p1(self): expected_params = [1, -0.5] np.random.seed(1234) nobs = 200 exog = np.ones((nobs, 2)) exog[:nobs//2, 1] = 2 mu_true = np.exp(exog.dot(expected_params)) alpha = 0.05 size = 1. / alpha * mu_true prob = size / (size + mu_true) endog = nbinom.rvs(size, prob, size=len(mu_true)) res = sm.NegativeBinomialP(endog, exog).fit(disp=0) mu = res.predict() size = 1. / alpha * mu prob = size / (size + mu) probs = res.predict(which='prob') assert_allclose(probs, nbinom.pmf(np.arange(8)[:,None], size, prob).T, atol=1e-2, rtol=1e-2) probs_ex = res.predict(exog=exog[[0, -1]], which='prob') assert_allclose(probs_ex, probs[[0, -1]], rtol=1e-10, atol=1e-15) def test_predict_prob_p2(self): expected_params = [1, -0.5] np.random.seed(1234) nobs = 200 exog = np.ones((nobs, 2)) exog[:nobs//2, 1] = 2 mu_true = np.exp(exog.dot(expected_params)) alpha = 0.05 size = 1. / alpha prob = size / (size + mu_true) endog = nbinom.rvs(size, prob, size=len(mu_true)) res = sm.NegativeBinomialP(endog, exog, p=2).fit(disp=0) mu = res.predict() size = 1. / alpha prob = size / (size + mu) assert_allclose(res.predict(which='prob'), nbinom.pmf(np.arange(8)[:,None], size, prob).T, atol=1e-2, rtol=1e-2) class CheckNull(object): @classmethod def _get_data(cls): x = np.array([ 20., 25., 30., 35., 40., 45., 50.]) nobs = len(x) exog = np.column_stack((np.ones(nobs), x)) endog = np.array([ 469, 5516, 6854, 6837, 5952, 4066, 3242]) return endog, exog def test_llnull(self): res = self.model.fit(start_params=self.start_params, disp=0) res._results._attach_nullmodel = True llf0 = res.llnull res_null0 = res.res_null assert_allclose(llf0, res_null0.llf, rtol=1e-6) res_null1 = self.res_null assert_allclose(llf0, res_null1.llf, rtol=1e-6) # Note default convergence tolerance does not get lower rtol # from different starting values (using bfgs) assert_allclose(res_null0.params, res_null1.params, rtol=5e-5) class TestPoissonNull(CheckNull): @classmethod def setup_class(cls): endog, exog = cls._get_data() cls.model = Poisson(endog, exog) cls.res_null = Poisson(endog, exog[:, 0]).fit(start_params=[8.5], disp=0) # use start params to avoid warnings cls.start_params = [8.5, 0] class TestNegativeBinomialNB1Null(CheckNull): @classmethod def setup_class(cls): endog, exog = cls._get_data() cls.model = NegativeBinomial(endog, exog, loglike_method='nb1') cls.model_null = NegativeBinomial(endog, exog[:, 0], loglike_method='nb1') cls.res_null = cls.model_null.fit(start_params=[8, 1000], method='bfgs', gtol=1e-08, maxiter=300, disp=0) # for convergence with bfgs, I needed to round down alpha start_params cls.start_params = np.array([7.730452, 2.01633068e-02, 1763.0]) class TestNegativeBinomialNB2Null(CheckNull): @classmethod def setup_class(cls): endog, exog = cls._get_data() cls.model = NegativeBinomial(endog, exog, loglike_method='nb2') cls.model_null = NegativeBinomial(endog, exog[:, 0], loglike_method='nb2') cls.res_null = cls.model_null.fit(start_params=[8, 0.5], method='bfgs', gtol=1e-06, maxiter=300, disp=0) cls.start_params = np.array([8.07216448, 0.01087238, 0.44024134]) class TestNegativeBinomialNBP2Null(CheckNull): @classmethod def setup_class(cls): endog, exog = cls._get_data() cls.model = NegativeBinomialP(endog, exog, p=2) cls.model_null = NegativeBinomialP(endog, exog[:, 0], p=2) cls.res_null = cls.model_null.fit(start_params=[8, 1], method='bfgs', gtol=1e-06, maxiter=300, disp=0) cls.start_params = np.array([8.07216448, 0.01087238, 0.44024134]) def test_start_null(self): endog, exog = self.model.endog, self.model.exog model_nb2 = NegativeBinomial(endog, exog, loglike_method='nb2') sp1 = model_nb2._get_start_params_null() sp0 = self.model._get_start_params_null() assert_allclose(sp0, sp1, rtol=1e-12) class TestNegativeBinomialNBP1Null(CheckNull): @classmethod def setup_class(cls): endog, exog = cls._get_data() cls.model = NegativeBinomialP(endog, exog, p=1.) cls.model_null = NegativeBinomialP(endog, exog[:, 0], p=1) cls.res_null = cls.model_null.fit(start_params=[8, 1], method='bfgs', gtol=1e-06, maxiter=300, disp=0) cls.start_params = np.array([7.730452, 2.01633068e-02, 1763.0]) def test_start_null(self): endog, exog = self.model.endog, self.model.exog model_nb2 = NegativeBinomial(endog, exog, loglike_method='nb1') sp1 = model_nb2._get_start_params_null() sp0 = self.model._get_start_params_null() assert_allclose(sp0, sp1, rtol=1e-12) class TestGeneralizedPoissonNull(CheckNull): @classmethod def setup_class(cls): endog, exog = cls._get_data() cls.model = GeneralizedPoisson(endog, exog, p=1.5) cls.model_null = GeneralizedPoisson(endog, exog[:, 0], p=1.5) cls.res_null = cls.model_null.fit(start_params=[8.4, 1], method='bfgs', gtol=1e-08, maxiter=300, disp=0) cls.start_params = np.array([6.91127148, 0.04501334, 0.88393736]) def test_null_options(): # this is a "nice" case because we only check that options are used # correctly nobs = 10 exog = np.ones((20, 2)) exog[:nobs // 2, 1] = 0 mu = np.exp(exog.sum(1)) endog = np.random.poisson(mu) # Note no size=nobs in np.random res = Poisson(endog, exog).fit(start_params=np.log([1, 1]), disp=0) llnull0 = res.llnull assert_(hasattr(res, 'res_llnull') is False) res.set_null_options(attach_results=True) # default optimization lln = res.llnull # access to trigger computation assert_allclose(res.res_null.mle_settings['start_params'], np.log(endog.mean()), rtol=1e-10) assert_equal(res.res_null.mle_settings['optimizer'], 'bfgs') assert_allclose(lln, llnull0) res.set_null_options(attach_results=True, start_params=[0.5], method='nm') lln = res.llnull # access to trigger computation assert_allclose(res.res_null.mle_settings['start_params'], [0.5], rtol=1e-10) assert_equal(res.res_null.mle_settings['optimizer'], 'nm') res.summary() # call to fill cache assert_('prsquared' in res._cache) assert_equal(res._cache['llnull'], lln) assert_('prsquared' in res._cache) assert_equal(res._cache['llnull'], lln) # check setting cache res.set_null_options(llnull=999) assert_('prsquared' not in res._cache) assert_equal(res._cache['llnull'], 999) def test_optim_kwds_prelim(): # test that fit options for preliminary fit is correctly transmitted cur_dir = os.path.dirname(os.path.abspath(__file__)) filepath = os.path.join(cur_dir, "results", "sm3533.csv") df = pd.read_csv(filepath) features = ['pp'] X = (df[features] - df[features].mean())/df[features].std() y = df['num'].values exog = sm.add_constant(X[features].copy()) # offset=np.log(df['population'].values + 1) # offset currently not used offset = None # we use "nm", "bfgs" does not work for Poisson/exp with older scipy optim_kwds_prelim = dict(method='nm', maxiter=5000) model = Poisson(y, exog, offset=offset) # res_poi = model.fit(disp=0, **optim_kwds_prelim) model = NegativeBinomial(y, exog, offset=offset) res = model.fit(disp=0, optim_kwds_prelim=optim_kwds_prelim) assert_allclose(res.mle_settings['start_params'][:-1], res_poi.params, rtol=1e-4) assert_equal(res.mle_settings['optim_kwds_prelim'], optim_kwds_prelim) assert_allclose(res.predict().mean(), y.mean(), rtol=0.1) # NBP22 and GPP p=1.5 also fail on older scipy with bfgs, use nm instead optim_kwds_prelim = dict(method='nm', maxiter=5000) model = NegativeBinomialP(y, exog, offset=offset, p=2) res = model.fit(disp=0, optim_kwds_prelim=optim_kwds_prelim) assert_allclose(res.mle_settings['start_params'][:-1], res_poi.params, rtol=1e-4) assert_equal(res.mle_settings['optim_kwds_prelim'], optim_kwds_prelim) assert_allclose(res.predict().mean(), y.mean(), rtol=0.1) # GPP with p=1.5 converges correctly, # GPP fails when p=2 even with good start_params model = GeneralizedPoisson(y, exog, offset=offset, p=1.5) res = model.fit(disp=0, maxiter=200, optim_kwds_prelim=optim_kwds_prelim ) assert_allclose(res.mle_settings['start_params'][:-1], res_poi.params, rtol=1e-4) assert_equal(res.mle_settings['optim_kwds_prelim'], optim_kwds_prelim) # rough check that convergence makes sense assert_allclose(res.predict().mean(), y.mean(), rtol=0.1) def test_unchanging_degrees_of_freedom(): data = sm.datasets.randhie.load(as_pandas=False) # see GH3734 warnings.simplefilter('error') model = sm.NegativeBinomial(data.endog, data.exog, loglike_method='nb2') params = np.array([-0.05654134, -0.21213734, 0.08783102, -0.02991825, 0.22902315, 0.06210253, 0.06799444, 0.08406794, 0.18530092, 1.36645186]) res1 = model.fit(start_params=params, disp=0) assert_equal(res1.df_model, 8) reg_params = np.array([-0.04854 , -0.15019404, 0.08363671, -0.03032834, 0.17592454, 0.06440753, 0.01584555, 0. , 0. , 1.36984628]) res2 = model.fit_regularized(alpha=100, start_params=reg_params, disp=0) assert_(res2.df_model != 8) # If res2.df_model == res1.df_model, then this test is invalid. res3 = model.fit(start_params=params, disp=0) # Test that the call to `fit_regularized` did not # modify model.df_model inplace. assert_equal(res3.df_model, res1.df_model) assert_equal(res3.df_resid, res1.df_resid) def test_mnlogit_float_name(): df = pd.DataFrame({"A": [0., 1.1, 0, 0, 1.1], "B": [0, 1, 0, 1, 1]}) with pytest.warns(SpecificationWarning, match='endog contains values are that not int-like'): result = smf.mnlogit(formula="A ~ B", data=df).fit() summ = result.summary().as_text() assert 'A=1.1' in summ def test_cov_confint_pandas(): data = sm.datasets.anes96.load(as_pandas=True) exog = sm.add_constant(data.exog, prepend=False) res1 = sm.MNLogit(data.endog, exog).fit(method="newton", disp=0) cov = res1.cov_params() ci = res1.conf_int() se = np.sqrt(np.diag(cov)) se2 = (ci.iloc[:, 1] - ci.iloc[:, 0]) / (2 * stats.norm.ppf(0.975)) assert_allclose(se, se2) assert_index_equal(ci.index, cov.index) assert_index_equal(cov.index, cov.columns) assert isinstance(ci.index, pd.MultiIndex) def test_t_test(): # GH669, check t_test works in multivariate model data = sm.datasets.anes96.load(as_pandas=True) exog = sm.add_constant(data.exog, prepend=False) res1 = sm.MNLogit(data.endog, exog).fit(disp=0) r = np.ones(res1.cov_params().shape[0]) t1 = res1.t_test(r) f1 = res1.f_test(r) data = sm.datasets.anes96.load(as_pandas=True) exog = sm.add_constant(data.exog, prepend=False) endog, exog = np.asarray(data.endog), np.asarray(exog) res2 = sm.MNLogit(endog, exog).fit(disp=0) t2 = res2.t_test(r) f2 = res2.f_test(r) assert_allclose(t1.effect, t2.effect) assert_allclose(f1.statistic, f2.statistic) statsmodels-0.12.2/statsmodels/discrete/tests/test_margins.py000066400000000000000000000110031400612667500245170ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Thu Aug 3 21:08:49 2017 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_allclose from statsmodels.discrete.discrete_model import (Poisson, NegativeBinomial, NegativeBinomialP) from statsmodels.tools.tools import add_constant import statsmodels.discrete.tests.results.results_count_margins as res_stata # load data into module namespace from statsmodels.datasets.cpunish import load cpunish_data = load(as_pandas=False) cpunish_data.exog[:,3] = np.log(cpunish_data.exog[:,3]) exog = add_constant(cpunish_data.exog, prepend=False) endog = cpunish_data.endog - 1 # avoid zero-truncation exog /= np.round(exog.max(0), 3) class CheckMarginMixin(object): rtol_fac = 1 def test_margins_table(self): res1 = self.res1 sl = self.res1_slice rf = self.rtol_fac assert_allclose(self.margeff.margeff, self.res1.params[sl], rtol=1e-5 * rf) assert_allclose(self.margeff.margeff_se, self.res1.bse[sl], rtol=1e-6 * rf) assert_allclose(self.margeff.pvalues, self.res1.pvalues[sl], rtol=5e-6 * rf) assert_allclose(self.margeff.conf_int(), res1.margins_table[sl, 4:6], rtol=1e-6 * rf) class TestPoissonMargin(CheckMarginMixin): @classmethod def setup_class(cls): # here we do not need to check convergence from default start_params start_params = [14.1709, 0.7085, -3.4548, -0.539, 3.2368, -7.9299, -5.0529] mod_poi = Poisson(endog, exog) res_poi = mod_poi.fit(start_params=start_params) #res_poi = mod_poi.fit(maxiter=100) marge_poi = res_poi.get_margeff() cls.res = res_poi cls.margeff = marge_poi cls.rtol_fac = 1 cls.res1_slice = slice(None, None, None) cls.res1 = res_stata.results_poisson_margins_cont class TestPoissonMarginDummy(CheckMarginMixin): @classmethod def setup_class(cls): # here we do not need to check convergence from default start_params start_params = [14.1709, 0.7085, -3.4548, -0.539, 3.2368, -7.9299, -5.0529] mod_poi = Poisson(endog, exog) res_poi = mod_poi.fit(start_params=start_params) marge_poi = res_poi.get_margeff(dummy=True) cls.res = res_poi cls.margeff = marge_poi cls.res1_slice = [0, 1, 2, 3, 5, 6] cls.res1 = res_stata.results_poisson_margins_dummy class TestNegBinMargin(CheckMarginMixin): @classmethod def setup_class(cls): # here we do not need to check convergence from default start_params start_params = [13.1996, 0.8582, -2.8005, -1.5031, 2.3849, -8.5552, -2.88, 1.14] mod = NegativeBinomial(endog, exog) res = mod.fit(start_params=start_params, method='nm', maxiter=2000) marge = res.get_margeff() cls.res = res cls.margeff = marge cls.res1_slice = slice(None, None, None) cls.res1 = res_stata.results_negbin_margins_cont cls.rtol_fac = 5e1 # negbin has lower agreement with Stata in this case class TestNegBinMarginDummy(CheckMarginMixin): @classmethod def setup_class(cls): # here we do not need to check convergence from default start_params start_params = [13.1996, 0.8582, -2.8005, -1.5031, 2.3849, -8.5552, -2.88, 1.14] mod = NegativeBinomial(endog, exog) res = mod.fit(start_params=start_params, method='nm', maxiter=2000) marge = res.get_margeff(dummy=True) cls.res = res cls.margeff = marge cls.res1_slice = cls.res1_slice = [0, 1, 2, 3, 5, 6] cls.res1 = res_stata.results_negbin_margins_dummy cls.rtol_fac = 5e1 class TestNegBinPMargin(CheckMarginMixin): # this is the same as the nb2 version above for NB-P, p=2 @classmethod def setup_class(cls): # here we do not need to check convergence from default start_params start_params = [13.1996, 0.8582, -2.8005, -1.5031, 2.3849, -8.5552, -2.88, 1.14] mod = NegativeBinomialP(endog, exog) # checks also that default p=2 res = mod.fit(start_params=start_params, method='nm', maxiter=2000) marge = res.get_margeff() cls.res = res cls.margeff = marge cls.res1_slice = slice(None, None, None) cls.res1 = res_stata.results_negbin_margins_cont cls.rtol_fac = 5e1 # negbin has lower agreement with Stata in this case statsmodels-0.12.2/statsmodels/discrete/tests/test_sandwich_cov.py000066400000000000000000000547031400612667500255440ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Mon Dec 09 21:29:20 2013 Author: Josef Perktold """ import os import numpy as np import pandas as pd import statsmodels.discrete.discrete_model as smd from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod import families from statsmodels.genmod.families import links from statsmodels.regression.linear_model import OLS from statsmodels.base.covtype import get_robustcov_results import statsmodels.stats.sandwich_covariance as sw from statsmodels.tools.tools import add_constant from numpy.testing import assert_allclose, assert_equal, assert_ import statsmodels.tools._testing as smt # get data and results as module global for now, TODO: move to class from .results import results_count_robust_cluster as results_st cur_dir = os.path.dirname(os.path.abspath(__file__)) filepath = os.path.join(cur_dir, "results", "ships.csv") data_raw = pd.read_csv(filepath, index_col=False) data = data_raw.dropna() #mod = smd.Poisson.from_formula('accident ~ yr_con + op_75_79', data=dat) # Do not use formula for tests against Stata because intercept needs to be last endog = data['accident'] exog_data = data['yr_con op_75_79'.split()] exog = add_constant(exog_data, prepend=False) group = np.asarray(data['ship'], int) exposure = np.asarray(data['service']) # TODO get the test methods from regression/tests class CheckCountRobustMixin(object): def test_basic(self): res1 = self.res1 res2 = self.res2 if len(res1.params) == (len(res2.params) - 1): # Stata includes lnalpha in table for NegativeBinomial mask = np.ones(len(res2.params), np.bool_) mask[-2] = False res2_params = res2.params[mask] res2_bse = res2.bse[mask] else: res2_params = res2.params res2_bse = res2.bse assert_allclose(res1._results.params, res2_params, 1e-4) assert_allclose(self.bse_rob / self.corr_fact, res2_bse, 6e-5) @classmethod def get_robust_clu(cls): res1 = cls.res1 cov_clu = sw.cov_cluster(res1, group) cls.bse_rob = sw.se_cov(cov_clu) cls.corr_fact = cls.get_correction_factor(res1) @classmethod def get_correction_factor(cls, results, sub_kparams=True): mod = results.model nobs, k_vars = mod.exog.shape if sub_kparams: # TODO: document why we adjust by k_params for some classes # but not others. k_params = len(results.params) else: k_params = 0 corr_fact = (nobs - 1.) / float(nobs - k_params) # for bse we need sqrt of correction factor return np.sqrt(corr_fact) def test_oth(self): res1 = self.res1 res2 = self.res2 assert_allclose(res1._results.llf, res2.ll, 1e-4) assert_allclose(res1._results.llnull, res2.ll_0, 1e-4) def test_ttest(self): smt.check_ttest_tvalues(self.res1) def test_waldtest(self): smt.check_ftest_pvalues(self.res1) class TestPoissonClu(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_poisson_clu mod = smd.Poisson(endog, exog) cls.res1 = mod.fit(disp=False) cls.get_robust_clu() class TestPoissonCluGeneric(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_poisson_clu mod = smd.Poisson(endog, exog) cls.res1 = res1 = mod.fit(disp=False) debug = False if debug: # for debugging cls.bse_nonrobust = cls.res1.bse.copy() cls.res1 = res1 = mod.fit(disp=False) cls.get_robust_clu() cls.res3 = cls.res1 cls.bse_rob3 = cls.bse_rob.copy() cls.res1 = res1 = mod.fit(disp=False) from statsmodels.base.covtype import get_robustcov_results #res_hc0_ = cls.res1.get_robustcov_results('HC1') get_robustcov_results(cls.res1._results, 'cluster', groups=group, use_correction=True, df_correction=True, #TODO has no effect use_t=False, #True, use_self=True) cls.bse_rob = cls.res1.bse cls.corr_fact = cls.get_correction_factor(cls.res1) class TestPoissonHC1Generic(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_poisson_hc1 mod = smd.Poisson(endog, exog) cls.res1 = mod.fit(disp=False) from statsmodels.base.covtype import get_robustcov_results #res_hc0_ = cls.res1.get_robustcov_results('HC1') get_robustcov_results(cls.res1._results, 'HC1', use_self=True) cls.bse_rob = cls.res1.bse cls.corr_fact = cls.get_correction_factor(cls.res1, sub_kparams=False) # TODO: refactor xxxFit to full testing results class TestPoissonCluFit(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_poisson_clu mod = smd.Poisson(endog, exog) # scaling of cov_params_default to match Stata # TODO should the default be changed? nobs, k_params = mod.exog.shape # TODO: this is similar but not identical to logic in # get_correction_factor; can we de-duplicate? sc_fact = (nobs-1.) / float(nobs - k_params) cls.res1 = mod.fit(disp=False, cov_type='cluster', cov_kwds=dict(groups=group, use_correction=True, scaling_factor=1. / sc_fact, df_correction=True), #TODO has no effect use_t=False, #True, ) # The model results, t_test, ... should also work without # normalized_cov_params, see #2209 # Note: we cannot set on the wrapper res1, we need res1._results cls.res1._results.normalized_cov_params = None cls.bse_rob = cls.res1.bse # backwards compatibility with inherited test methods cls.corr_fact = 1 def test_basic_inference(self): res1 = self.res1 res2 = self.res2 rtol = 1e-7 assert_allclose(res1.params, res2.params, rtol=1e-8) assert_allclose(res1.bse, res2.bse, rtol=rtol) assert_allclose(res1.tvalues, res2.tvalues, rtol=rtol, atol=1e-8) assert_allclose(res1.pvalues, res2.pvalues, rtol=rtol, atol=1e-20) ci = res2.params_table[:, 4:6] assert_allclose(res1.conf_int(), ci, rtol=5e-7, atol=1e-20) class TestPoissonHC1Fit(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_poisson_hc1 mod = smd.Poisson(endog, exog) cls.res1 = mod.fit(disp=False, cov_type='HC1') cls.bse_rob = cls.res1.bse cls.corr_fact = cls.get_correction_factor(cls.res1, sub_kparams=False) class TestPoissonHC1FitExposure(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_poisson_exposure_hc1 mod = smd.Poisson(endog, exog, exposure=exposure) cls.res1 = mod.fit(disp=False, cov_type='HC1') cls.bse_rob = cls.res1.bse cls.corr_fact = cls.get_correction_factor(cls.res1, sub_kparams=False) class TestPoissonCluExposure(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_poisson_exposure_clu #nonrobust mod = smd.Poisson(endog, exog, exposure=exposure) cls.res1 = mod.fit(disp=False) cls.get_robust_clu() class TestPoissonCluExposureGeneric(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_poisson_exposure_clu #nonrobust mod = smd.Poisson(endog, exog, exposure=exposure) cls.res1 = res1 = mod.fit(disp=False) from statsmodels.base.covtype import get_robustcov_results #res_hc0_ = cls.res1.get_robustcov_results('HC1') get_robustcov_results(cls.res1._results, 'cluster', groups=group, use_correction=True, df_correction=True, #TODO has no effect use_t=False, #True, use_self=True) cls.bse_rob = cls.res1.bse #sw.se_cov(cov_clu) cls.corr_fact = cls.get_correction_factor(cls.res1) class TestGLMPoissonClu(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_poisson_clu mod = smd.Poisson(endog, exog) mod = GLM(endog, exog, family=families.Poisson()) cls.res1 = mod.fit() cls.get_robust_clu() class TestGLMPoissonCluGeneric(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_poisson_clu mod = GLM(endog, exog, family=families.Poisson()) cls.res1 = res1 = mod.fit() get_robustcov_results(cls.res1._results, 'cluster', groups=group, use_correction=True, df_correction=True, #TODO has no effect use_t=False, #True, use_self=True) cls.bse_rob = cls.res1.bse cls.corr_fact = cls.get_correction_factor(cls.res1) class TestGLMPoissonHC1Generic(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_poisson_hc1 mod = GLM(endog, exog, family=families.Poisson()) cls.res1 = mod.fit() #res_hc0_ = cls.res1.get_robustcov_results('HC1') get_robustcov_results(cls.res1._results, 'HC1', use_self=True) cls.bse_rob = cls.res1.bse cls.corr_fact = cls.get_correction_factor(cls.res1, sub_kparams=False) # TODO: refactor xxxFit to full testing results class TestGLMPoissonCluFit(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_poisson_clu mod = GLM(endog, exog, family=families.Poisson()) cls.res1 = res1 = mod.fit(cov_type='cluster', cov_kwds=dict(groups=group, use_correction=True, df_correction=True), #TODO has no effect use_t=False, #True, ) # The model results, t_test, ... should also work without # normalized_cov_params, see #2209 # Note: we cannot set on the wrapper res1, we need res1._results cls.res1._results.normalized_cov_params = None cls.bse_rob = cls.res1.bse cls.corr_fact = cls.get_correction_factor(cls.res1) class TestGLMPoissonHC1Fit(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_poisson_hc1 mod = GLM(endog, exog, family=families.Poisson()) cls.res1 = mod.fit(cov_type='HC1') cls.bse_rob = cls.res1.bse cls.corr_fact = cls.get_correction_factor(cls.res1, sub_kparams=False) class TestNegbinClu(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_negbin_clu mod = smd.NegativeBinomial(endog, exog) cls.res1 = mod.fit(disp=False, gtol=1e-7) cls.get_robust_clu() class TestNegbinCluExposure(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_negbin_exposure_clu #nonrobust mod = smd.NegativeBinomial(endog, exog, exposure=exposure) cls.res1 = mod.fit(disp=False) cls.get_robust_clu() # mod_nbe = smd.NegativeBinomial(endog, exog, exposure=data['service']) # res_nbe = mod_nbe.fit() # mod_nb = smd.NegativeBinomial(endog, exog) # res_nb = mod_nb.fit() # # cov_clu_nb = sw.cov_cluster(res_nb, group) # k_params = k_vars + 1 # print sw.se_cov(cov_clu_nb / ((nobs-1.) / float(nobs - k_params))) # # wt = res_nb.wald_test(np.eye(len(res_nb.params))[1:3], cov_p=cov_clu_nb/((nobs-1.) / float(nobs - k_params))) # print wt # # print dir(results_st) class TestNegbinCluGeneric(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_negbin_clu mod = smd.NegativeBinomial(endog, exog) cls.res1 = res1 = mod.fit(disp=False, gtol=1e-7) get_robustcov_results(cls.res1._results, 'cluster', groups=group, use_correction=True, df_correction=True, #TODO has no effect use_t=False, #True, use_self=True) cls.bse_rob = cls.res1.bse cls.corr_fact = cls.get_correction_factor(cls.res1) class TestNegbinCluFit(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_negbin_clu mod = smd.NegativeBinomial(endog, exog) cls.res1 = res1 = mod.fit(disp=False, cov_type='cluster', cov_kwds=dict(groups=group, use_correction=True, df_correction=True), #TODO has no effect use_t=False, #True, gtol=1e-7) cls.bse_rob = cls.res1.bse cls.corr_fact = cls.get_correction_factor(cls.res1) class TestNegbinCluExposureFit(CheckCountRobustMixin): @classmethod def setup_class(cls): cls.res2 = results_st.results_negbin_exposure_clu #nonrobust mod = smd.NegativeBinomial(endog, exog, exposure=exposure) cls.res1 = res1 = mod.fit(disp=False, cov_type='cluster', cov_kwds=dict(groups=group, use_correction=True, df_correction=True), #TODO has no effect use_t=False, #True, ) cls.bse_rob = cls.res1.bse cls.corr_fact = cls.get_correction_factor(cls.res1) class CheckDiscreteGLM(object): # compare GLM with other models, no verified reference results def test_basic(self): res1 = self.res1 res2 = self.res2 assert_equal(res1.cov_type, self.cov_type) assert_equal(res2.cov_type, self.cov_type) rtol = getattr(res1, 'rtol', 1e-13) assert_allclose(res1.params, res2.params, rtol=rtol) assert_allclose(res1.bse, res2.bse, rtol=1e-10) class TestGLMLogit(CheckDiscreteGLM): @classmethod def setup_class(cls): endog_bin = (endog > endog.mean()).astype(int) cls.cov_type = 'cluster' mod1 = GLM(endog_bin, exog, family=families.Binomial()) cls.res1 = mod1.fit(cov_type='cluster', cov_kwds=dict(groups=group)) mod1 = smd.Logit(endog_bin, exog) cls.res2 = mod1.fit(cov_type='cluster', cov_kwds=dict(groups=group)) class TestGLMProbit(CheckDiscreteGLM): @classmethod def setup_class(cls): endog_bin = (endog > endog.mean()).astype(int) cls.cov_type = 'cluster' mod1 = GLM(endog_bin, exog, family=families.Binomial(link=links.probit())) cls.res1 = mod1.fit(method='newton', cov_type='cluster', cov_kwds=dict(groups=group)) mod1 = smd.Probit(endog_bin, exog) cls.res2 = mod1.fit(cov_type='cluster', cov_kwds=dict(groups=group)) cls.rtol = 1e-6 def test_score_hessian(self): res1 = self.res1 res2 = self.res2 # Note scale is fixed at 1, so we do not need to fix it explicitly score1 = res1.model.score(res1.params * 0.98) score2 = res2.model.score(res1.params * 0.98) assert_allclose(score1, score2, rtol=1e-13) hess1 = res1.model.hessian(res1.params) hess2 = res2.model.hessian(res1.params) assert_allclose(hess1, hess2, rtol=1e-13) class TestGLMGaussNonRobust(CheckDiscreteGLM): @classmethod def setup_class(cls): cls.cov_type = 'nonrobust' mod1 = GLM(endog, exog, family=families.Gaussian()) cls.res1 = mod1.fit() mod2 = OLS(endog, exog) cls.res2 = mod2.fit() class TestGLMGaussClu(CheckDiscreteGLM): @classmethod def setup_class(cls): cls.cov_type = 'cluster' mod1 = GLM(endog, exog, family=families.Gaussian()) cls.res1 = mod1.fit(cov_type='cluster', cov_kwds=dict(groups=group)) mod2 = OLS(endog, exog) cls.res2 = mod2.fit(cov_type='cluster', cov_kwds=dict(groups=group)) class TestGLMGaussHC(CheckDiscreteGLM): @classmethod def setup_class(cls): cls.cov_type = 'HC0' mod1 = GLM(endog, exog, family=families.Gaussian()) cls.res1 = mod1.fit(cov_type='HC0') mod2 = OLS(endog, exog) cls.res2 = mod2.fit(cov_type='HC0') class TestGLMGaussHAC(CheckDiscreteGLM): @classmethod def setup_class(cls): cls.cov_type = 'HAC' kwds={'maxlags':2} mod1 = GLM(endog, exog, family=families.Gaussian()) cls.res1 = mod1.fit(cov_type='HAC', cov_kwds=kwds) mod2 = OLS(endog, exog) cls.res2 = mod2.fit(cov_type='HAC', cov_kwds=kwds) class TestGLMGaussHAC2(CheckDiscreteGLM): @classmethod def setup_class(cls): cls.cov_type = 'HAC' # check kernel specified as string kwds = {'kernel': 'bartlett', 'maxlags': 2} mod1 = GLM(endog, exog, family=families.Gaussian()) cls.res1 = mod1.fit(cov_type='HAC', cov_kwds=kwds) mod2 = OLS(endog, exog) kwds2 = {'maxlags': 2} cls.res2 = mod2.fit(cov_type='HAC', cov_kwds=kwds2) class TestGLMGaussHACUniform(CheckDiscreteGLM): @classmethod def setup_class(cls): cls.cov_type = 'HAC' kwds={'kernel':sw.weights_uniform, 'maxlags':2} mod1 = GLM(endog, exog, family=families.Gaussian()) cls.res1 = mod1.fit(cov_type='HAC', cov_kwds=kwds) mod2 = OLS(endog, exog) cls.res2 = mod2.fit(cov_type='HAC', cov_kwds=kwds) #for debugging cls.res3 = mod2.fit(cov_type='HAC', cov_kwds={'maxlags':2}) def test_cov_options(self): # check keyword `weights_func kwdsa = {'weights_func': sw.weights_uniform, 'maxlags': 2} res1a = self.res1.model.fit(cov_type='HAC', cov_kwds=kwdsa) res2a = self.res2.model.fit(cov_type='HAC', cov_kwds=kwdsa) assert_allclose(res1a.bse, self.res1.bse, rtol=1e-12) assert_allclose(res2a.bse, self.res2.bse, rtol=1e-12) # regression test for bse values bse = np.array([ 2.82203924, 4.60199596, 11.01275064]) assert_allclose(res1a.bse, bse, rtol=1e-6) assert_(res1a.cov_kwds['weights_func'] is sw.weights_uniform) kwdsb = {'kernel': sw.weights_bartlett, 'maxlags': 2} res1a = self.res1.model.fit(cov_type='HAC', cov_kwds=kwdsb) res2a = self.res2.model.fit(cov_type='HAC', cov_kwds=kwdsb) assert_allclose(res1a.bse, res2a.bse, rtol=1e-12) # regression test for bse values bse = np.array([ 2.502264, 3.697807, 9.193303]) assert_allclose(res1a.bse, bse, rtol=1e-6) class TestGLMGaussHACUniform2(TestGLMGaussHACUniform): @classmethod def setup_class(cls): cls.cov_type = 'HAC' kwds={'kernel': sw.weights_uniform, 'maxlags': 2} mod1 = GLM(endog, exog, family=families.Gaussian()) cls.res1 = mod1.fit(cov_type='HAC', cov_kwds=kwds) # check kernel as string mod2 = OLS(endog, exog) kwds2 = {'kernel': 'uniform', 'maxlags': 2} cls.res2 = mod2.fit(cov_type='HAC', cov_kwds=kwds) class TestGLMGaussHACPanel(CheckDiscreteGLM): @classmethod def setup_class(cls): cls.cov_type = 'hac-panel' # time index is just made up to have a test case time = np.tile(np.arange(7), 5)[:-1] mod1 = GLM(endog.copy(), exog.copy(), family=families.Gaussian()) kwds = dict(time=time, maxlags=2, kernel=sw.weights_uniform, use_correction='hac', df_correction=False) cls.res1 = mod1.fit(cov_type='hac-panel', cov_kwds=kwds) cls.res1b = mod1.fit(cov_type='nw-panel', cov_kwds=kwds) mod2 = OLS(endog, exog) cls.res2 = mod2.fit(cov_type='hac-panel', cov_kwds=kwds) def test_kwd(self): # test corrected keyword name assert_allclose(self.res1b.bse, self.res1.bse, rtol=1e-12) class TestGLMGaussHACPanelGroups(CheckDiscreteGLM): @classmethod def setup_class(cls): cls.cov_type = 'hac-panel' # time index is just made up to have a test case groups = np.repeat(np.arange(5), 7)[:-1] mod1 = GLM(endog.copy(), exog.copy(), family=families.Gaussian()) kwds = dict(groups=pd.Series(groups), # check for #3606 maxlags=2, kernel=sw.weights_uniform, use_correction='hac', df_correction=False) cls.res1 = mod1.fit(cov_type='hac-panel', cov_kwds=kwds) mod2 = OLS(endog, exog) cls.res2 = mod2.fit(cov_type='hac-panel', cov_kwds=kwds) class TestGLMGaussHACGroupsum(CheckDiscreteGLM): @classmethod def setup_class(cls): cls.cov_type = 'hac-groupsum' # time index is just made up to have a test case time = np.tile(np.arange(7), 5)[:-1] mod1 = GLM(endog, exog, family=families.Gaussian()) kwds = dict(time=pd.Series(time), # check for #3606 maxlags=2, use_correction='hac', df_correction=False) cls.res1 = mod1.fit(cov_type='hac-groupsum', cov_kwds=kwds) cls.res1b = mod1.fit(cov_type='nw-groupsum', cov_kwds=kwds) mod2 = OLS(endog, exog) cls.res2 = mod2.fit(cov_type='hac-groupsum', cov_kwds=kwds) def test_kwd(self): # test corrected keyword name assert_allclose(self.res1b.bse, self.res1.bse, rtol=1e-12) statsmodels-0.12.2/statsmodels/distributions/000077500000000000000000000000001400612667500214115ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/distributions/__init__.py000066400000000000000000000006511400612667500235240ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester from .empirical_distribution import ECDF, monotone_fn_inverter, StepFunction from .edgeworth import ExpandedNormal from .discrete import genpoisson_p, zipoisson, zigenpoisson, zinegbin __all__ = ['test', 'ECDF', 'monotone_fn_inverter', 'StepFunction', 'ExpandedNormal', 'genpoisson_p', 'zigenpoisson', 'zinegbin', 'zipoisson'] test = PytestTester() statsmodels-0.12.2/statsmodels/distributions/discrete.py000066400000000000000000000116451400612667500235740ustar00rootroot00000000000000import numpy as np from scipy.stats import rv_discrete, nbinom, poisson from scipy.special import gammaln from statsmodels.compat.scipy import _lazywhere class genpoisson_p_gen(rv_discrete): '''Generalized Poisson distribution ''' def _argcheck(self, mu, alpha, p): return (mu >= 0) & (alpha==alpha) & (p > 0) def _logpmf(self, x, mu, alpha, p): mu_p = mu ** (p - 1.) a1 = np.maximum(np.nextafter(0, 1), 1 + alpha * mu_p) a2 = np.maximum(np.nextafter(0, 1), mu + (a1 - 1.) * x) logpmf_ = np.log(mu) + (x - 1.) * np.log(a2) logpmf_ -= x * np.log(a1) + gammaln(x + 1.) + a2 / a1 return logpmf_ def _pmf(self, x, mu, alpha, p): return np.exp(self._logpmf(x, mu, alpha, p)) genpoisson_p = genpoisson_p_gen(name='genpoisson_p', longname='Generalized Poisson') class zipoisson_gen(rv_discrete): '''Zero Inflated Poisson distribution ''' def _argcheck(self, mu, w): return (mu > 0) & (w >= 0) & (w<=1) def _logpmf(self, x, mu, w): return _lazywhere(x != 0, (x, mu, w), (lambda x, mu, w: np.log(1. - w) + x * np.log(mu) - gammaln(x + 1.) - mu), np.log(w + (1. - w) * np.exp(-mu))) def _pmf(self, x, mu, w): return np.exp(self._logpmf(x, mu, w)) def _cdf(self, x, mu, w): # construct cdf from standard poisson's cdf and the w inflation of zero return w + poisson(mu=mu).cdf(x) * (1 - w) def _ppf(self, q, mu, w): # we just translated and stretched q to remove zi q_mod = (q - w) / (1 - w) x = poisson(mu=mu).ppf(q_mod) # set to zero if in the zi range x[q < w] = 0 return x def _mean(self, mu, w): return (1 - w) * mu def _var(self, mu, w): dispersion_factor = 1 + w * mu var = (dispersion_factor * self._mean(mu, w)) return var def _moment(self, n, mu, w): return (1 - w) * poisson.moment(n, mu) zipoisson = zipoisson_gen(name='zipoisson', longname='Zero Inflated Poisson') class zigeneralizedpoisson_gen(rv_discrete): '''Zero Inflated Generalized Poisson distribution ''' def _argcheck(self, mu, alpha, p, w): return (mu > 0) & (w >= 0) & (w<=1) def _logpmf(self, x, mu, alpha, p, w): return _lazywhere(x != 0, (x, mu, alpha, p, w), (lambda x, mu, alpha, p, w: np.log(1. - w) + genpoisson_p.logpmf(x, mu, alpha, p)), np.log(w + (1. - w) * genpoisson_p.pmf(x, mu, alpha, p))) def _pmf(self, x, mu, alpha, p, w): return np.exp(self._logpmf(x, mu, alpha, p, w)) def _mean(self, mu, alpha, p, w): return (1 - w) * mu def _var(self, mu, alpha, p, w): p = p - 1 dispersion_factor = (1 + alpha * mu ** p) ** 2 + w * mu var = (dispersion_factor * self._mean(mu, alpha, p, w)) return var zigenpoisson = zigeneralizedpoisson_gen( name='zigenpoisson', longname='Zero Inflated Generalized Poisson') class zinegativebinomial_gen(rv_discrete): '''Zero Inflated Generalized Negative Binomial distribution ''' def _argcheck(self, mu, alpha, p, w): return (mu > 0) & (w >= 0) & (w<=1) def _logpmf(self, x, mu, alpha, p, w): s, p = self.convert_params(mu, alpha, p) return _lazywhere(x != 0, (x, s, p, w), (lambda x, s, p, w: np.log(1. - w) + nbinom.logpmf(x, s, p)), np.log(w + (1. - w) * nbinom.pmf(x, s, p))) def _pmf(self, x, mu, alpha, p, w): return np.exp(self._logpmf(x, mu, alpha, p, w)) def _cdf(self, x, mu, alpha, p, w): s, p = self.convert_params(mu, alpha, p) # construct cdf from standard negative binomial cdf # and the w inflation of zero return w + nbinom.cdf(x, s, p) * (1 - w) def _ppf(self, q, mu, alpha, p, w): s, p = self.convert_params(mu, alpha, p) # we just translated and stretched q to remove zi q_mod = (q - w) / (1 - w) x = nbinom.ppf(q_mod, s, p) # set to zero if in the zi range x[q < w] = 0 return x def _mean(self, mu, alpha, p, w): return (1 - w) * mu def _var(self, mu, alpha, p, w): dispersion_factor = 1 + alpha * mu ** (p - 1) + w * mu var = (dispersion_factor * self._mean(mu, alpha, p, w)) return var def _moment(self, n, mu, alpha, p, w): s, p = self.convert_params(mu, alpha, p) return (1 - w) * nbinom.moment(n, s, p) def convert_params(self, mu, alpha, p): size = 1. / alpha * mu**(2-p) prob = size / (size + mu) return (size, prob) zinegbin = zinegativebinomial_gen(name='zinegbin', longname='Zero Inflated Generalized Negative Binomial') statsmodels-0.12.2/statsmodels/distributions/edgeworth.py000066400000000000000000000150261400612667500237570ustar00rootroot00000000000000 import warnings import numpy as np from numpy.polynomial.hermite_e import HermiteE from scipy.special import factorial from scipy.stats import rv_continuous import scipy.special as special # TODO: # * actually solve (31) of Blinnikov & Moessner # * numerical stability: multiply factorials in logspace? # * ppf & friends: Cornish & Fisher series, or tabulate/solve _faa_di_bruno_cache = { 1: [[(1, 1)]], 2: [[(1, 2)], [(2, 1)]], 3: [[(1, 3)], [(2, 1), (1, 1)], [(3, 1)]], 4: [[(1, 4)], [(1, 2), (2, 1)], [(2, 2)], [(3, 1), (1, 1)], [(4, 1)]]} def _faa_di_bruno_partitions(n): """ Return all non-negative integer solutions of the diophantine equation n*k_n + ... + 2*k_2 + 1*k_1 = n (1) Parameters ---------- n : int the r.h.s. of Eq. (1) Returns ------- partitions : list Each solution is itself a list of the form `[(m, k_m), ...]` for non-zero `k_m`. Notice that the index `m` is 1-based. Examples: --------- >>> _faa_di_bruno_partitions(2) [[(1, 2)], [(2, 1)]] >>> for p in _faa_di_bruno_partitions(4): ... assert 4 == sum(m * k for (m, k) in p) """ if n < 1: raise ValueError("Expected a positive integer; got %s instead" % n) try: return _faa_di_bruno_cache[n] except KeyError: # TODO: higher order terms # solve Eq. (31) from Blinninkov & Moessner here raise NotImplementedError('Higher order terms not yet implemented.') def cumulant_from_moments(momt, n): """Compute n-th cumulant given moments. Parameters ---------- momt : array_like `momt[j]` contains `(j+1)`-th moment. These can be raw moments around zero, or central moments (in which case, `momt[0]` == 0). n : int which cumulant to calculate (must be >1) Returns ------- kappa : float n-th cumulant. """ if n < 1: raise ValueError("Expected a positive integer. Got %s instead." % n) if len(momt) < n: raise ValueError("%s-th cumulant requires %s moments, " "only got %s." % (n, n, len(momt))) kappa = 0. for p in _faa_di_bruno_partitions(n): r = sum(k for (m, k) in p) term = (-1)**(r - 1) * factorial(r - 1) for (m, k) in p: term *= np.power(momt[m - 1] / factorial(m), k) / factorial(k) kappa += term kappa *= factorial(n) return kappa ## copied from scipy.stats.distributions to avoid the overhead of ## the public methods _norm_pdf_C = np.sqrt(2*np.pi) def _norm_pdf(x): return np.exp(-x**2/2.0) / _norm_pdf_C def _norm_cdf(x): return special.ndtr(x) def _norm_sf(x): return special.ndtr(-x) class ExpandedNormal(rv_continuous): """Construct the Edgeworth expansion pdf given cumulants. Parameters ---------- cum : array_like `cum[j]` contains `(j+1)`-th cumulant: cum[0] is the mean, cum[1] is the variance and so on. Notes ----- This is actually an asymptotic rather than convergent series, hence higher orders of the expansion may or may not improve the result. In a strongly non-Gaussian case, it is possible that the density becomes negative, especially far out in the tails. Examples -------- Construct the 4th order expansion for the chi-square distribution using the known values of the cumulants: >>> import matplotlib.pyplot as plt >>> from scipy import stats >>> from scipy.special import factorial >>> df = 12 >>> chi2_c = [2**(j-1) * factorial(j-1) * df for j in range(1, 5)] >>> edgw_chi2 = ExpandedNormal(chi2_c, name='edgw_chi2', momtype=0) Calculate several moments: >>> m, v = edgw_chi2.stats(moments='mv') >>> np.allclose([m, v], [df, 2 * df]) True Plot the density function: >>> mu, sigma = df, np.sqrt(2*df) >>> x = np.linspace(mu - 3*sigma, mu + 3*sigma) >>> fig1 = plt.plot(x, stats.chi2.pdf(x, df=df), 'g-', lw=4, alpha=0.5) >>> fig2 = plt.plot(x, stats.norm.pdf(x, mu, sigma), 'b--', lw=4, alpha=0.5) >>> fig3 = plt.plot(x, edgw_chi2.pdf(x), 'r-', lw=2) >>> plt.show() References ---------- .. [*] E.A. Cornish and R.A. Fisher, Moments and cumulants in the specification of distributions, Revue de l'Institut Internat. de Statistique. 5: 307 (1938), reprinted in R.A. Fisher, Contributions to Mathematical Statistics. Wiley, 1950. .. [*] https://en.wikipedia.org/wiki/Edgeworth_series .. [*] S. Blinnikov and R. Moessner, Expansions for nearly Gaussian distributions, Astron. Astrophys. Suppl. Ser. 130, 193 (1998) """ def __init__(self, cum, name='Edgeworth expanded normal', **kwds): if len(cum) < 2: raise ValueError("At least two cumulants are needed.") self._coef, self._mu, self._sigma = self._compute_coefs_pdf(cum) self._herm_pdf = HermiteE(self._coef) if self._coef.size > 2: self._herm_cdf = HermiteE(-self._coef[1:]) else: self._herm_cdf = lambda x: 0. # warn if pdf(x) < 0 for some values of x within 4 sigma r = np.real_if_close(self._herm_pdf.roots()) r = (r - self._mu) / self._sigma if r[(np.imag(r) == 0) & (np.abs(r) < 4)].any(): mesg = 'PDF has zeros at %s ' % r warnings.warn(mesg, RuntimeWarning) kwds.update({'name': name, 'momtype': 0}) # use pdf, not ppf in self.moment() super(ExpandedNormal, self).__init__(**kwds) def _pdf(self, x): y = (x - self._mu) / self._sigma return self._herm_pdf(y) * _norm_pdf(y) / self._sigma def _cdf(self, x): y = (x - self._mu) / self._sigma return (_norm_cdf(y) + self._herm_cdf(y) * _norm_pdf(y)) def _sf(self, x): y = (x - self._mu) / self._sigma return (_norm_sf(y) - self._herm_cdf(y) * _norm_pdf(y)) def _compute_coefs_pdf(self, cum): # scale cumulants by \sigma mu, sigma = cum[0], np.sqrt(cum[1]) lam = np.asarray(cum) for j, l in enumerate(lam): lam[j] /= cum[1]**j coef = np.zeros(lam.size * 3 - 5) coef[0] = 1. for s in range(lam.size - 2): for p in _faa_di_bruno_partitions(s+1): term = sigma**(s+1) for (m, k) in p: term *= np.power(lam[m+1] / factorial(m+2), k) / factorial(k) r = sum(k for (m, k) in p) coef[s + 1 + 2*r] += term return coef, mu, sigma statsmodels-0.12.2/statsmodels/distributions/empirical_distribution.py000066400000000000000000000121641400612667500265330ustar00rootroot00000000000000""" Empirical CDF Functions """ import numpy as np from scipy.interpolate import interp1d def _conf_set(F, alpha=.05): r""" Constructs a Dvoretzky-Kiefer-Wolfowitz confidence band for the eCDF. Parameters ---------- F : array_like The empirical distributions alpha : float Set alpha for a (1 - alpha) % confidence band. Notes ----- Based on the DKW inequality. .. math:: P \left( \sup_x \left| F(x) - \hat(F)_n(X) \right| > \epsilon \right) \leq 2e^{-2n\epsilon^2} References ---------- Wasserman, L. 2006. `All of Nonparametric Statistics`. Springer. """ nobs = len(F) epsilon = np.sqrt(np.log(2./alpha) / (2 * nobs)) lower = np.clip(F - epsilon, 0, 1) upper = np.clip(F + epsilon, 0, 1) return lower, upper class StepFunction(object): """ A basic step function. Values at the ends are handled in the simplest way possible: everything to the left of x[0] is set to ival; everything to the right of x[-1] is set to y[-1]. Parameters ---------- x : array_like y : array_like ival : float ival is the value given to the values to the left of x[0]. Default is 0. sorted : bool Default is False. side : {'left', 'right'}, optional Default is 'left'. Defines the shape of the intervals constituting the steps. 'right' correspond to [a, b) intervals and 'left' to (a, b]. Examples -------- >>> import numpy as np >>> from statsmodels.distributions.empirical_distribution import StepFunction >>> >>> x = np.arange(20) >>> y = np.arange(20) >>> f = StepFunction(x, y) >>> >>> print(f(3.2)) 3.0 >>> print(f([[3.2,4.5],[24,-3.1]])) [[ 3. 4.] [ 19. 0.]] >>> f2 = StepFunction(x, y, side='right') >>> >>> print(f(3.0)) 2.0 >>> print(f2(3.0)) 3.0 """ def __init__(self, x, y, ival=0., sorted=False, side='left'): if side.lower() not in ['right', 'left']: msg = "side can take the values 'right' or 'left'" raise ValueError(msg) self.side = side _x = np.asarray(x) _y = np.asarray(y) if _x.shape != _y.shape: msg = "x and y do not have the same shape" raise ValueError(msg) if len(_x.shape) != 1: msg = 'x and y must be 1-dimensional' raise ValueError(msg) self.x = np.r_[-np.inf, _x] self.y = np.r_[ival, _y] if not sorted: asort = np.argsort(self.x) self.x = np.take(self.x, asort, 0) self.y = np.take(self.y, asort, 0) self.n = self.x.shape[0] def __call__(self, time): tind = np.searchsorted(self.x, time, self.side) - 1 return self.y[tind] class ECDF(StepFunction): """ Return the Empirical CDF of an array as a step function. Parameters ---------- x : array_like Observations side : {'left', 'right'}, optional Default is 'right'. Defines the shape of the intervals constituting the steps. 'right' correspond to [a, b) intervals and 'left' to (a, b]. Returns ------- Empirical CDF as a step function. Examples -------- >>> import numpy as np >>> from statsmodels.distributions.empirical_distribution import ECDF >>> >>> ecdf = ECDF([3, 3, 1, 4]) >>> >>> ecdf([3, 55, 0.5, 1.5]) array([ 0.75, 1. , 0. , 0.25]) """ def __init__(self, x, side='right'): x = np.array(x, copy=True) x.sort() nobs = len(x) y = np.linspace(1./nobs,1,nobs) super(ECDF, self).__init__(x, y, side=side, sorted=True) # TODO: make `step` an arg and have a linear interpolation option? # This is the path with `step` is True # If `step` is False, a previous version of the code read # `return interp1d(x,y,drop_errors=False,fill_values=ival)` # which would have raised a NameError if hit, so would need to be # fixed. See GH#5701. def monotone_fn_inverter(fn, x, vectorized=True, **keywords): """ Given a monotone function fn (no checking is done to verify monotonicity) and a set of x values, return an linearly interpolated approximation to its inverse from its values on x. """ x = np.asarray(x) if vectorized: y = fn(x, **keywords) else: y = [] for _x in x: y.append(fn(_x, **keywords)) y = np.array(y) a = np.argsort(y) return interp1d(y[a], x[a]) if __name__ == "__main__": #TODO: Make sure everything is correctly aligned and make a plotting # function from urllib.request import urlopen import matplotlib.pyplot as plt nerve_data = urlopen('http://www.statsci.org/data/general/nerve.txt') nerve_data = np.loadtxt(nerve_data) x = nerve_data / 50. # was in 1/50 seconds cdf = ECDF(x) x.sort() F = cdf(x) plt.step(x, F, where='post') lower, upper = _conf_set(F) plt.step(x, lower, 'r', where='post') plt.step(x, upper, 'r', where='post') plt.xlim(0, 1.5) plt.ylim(0, 1.05) plt.vlines(x, 0, .05) plt.show() statsmodels-0.12.2/statsmodels/distributions/mixture_rvs.py000066400000000000000000000236621400612667500243630ustar00rootroot00000000000000import numpy as np def _make_index(prob,size): """ Returns a boolean index for given probabilities. Notes --------- prob = [.75,.25] means that there is a 75% chance of the first column being True and a 25% chance of the second column being True. The columns are mutually exclusive. """ rv = np.random.uniform(size=(size,1)) cumprob = np.cumsum(prob) return np.logical_and(np.r_[0,cumprob[:-1]] <= rv, rv < cumprob) def mixture_rvs(prob, size, dist, kwargs=None): """ Sample from a mixture of distributions. Parameters ---------- prob : array_like Probability of sampling from each distribution in dist size : int The length of the returned sample. dist : array_like An iterable of distributions objects from scipy.stats. kwargs : tuple of dicts, optional A tuple of dicts. Each dict in kwargs can have keys loc, scale, and args to be passed to the respective distribution in dist. If not provided, the distribution defaults are used. Examples -------- Say we want 5000 random variables from mixture of normals with two distributions norm(-1,.5) and norm(1,.5) and we want to sample from the first with probability .75 and the second with probability .25. >>> from scipy import stats >>> prob = [.75,.25] >>> Y = mixture_rvs(prob, 5000, dist=[stats.norm, stats.norm], ... kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.5))) """ if len(prob) != len(dist): raise ValueError("You must provide as many probabilities as distributions") if not np.allclose(np.sum(prob), 1): raise ValueError("prob does not sum to 1") if kwargs is None: kwargs = ({},)*len(prob) idx = _make_index(prob,size) sample = np.empty(size) for i in range(len(prob)): sample_idx = idx[...,i] sample_size = sample_idx.sum() loc = kwargs[i].get('loc',0) scale = kwargs[i].get('scale',1) args = kwargs[i].get('args',()) sample[sample_idx] = dist[i].rvs(*args, **dict(loc=loc,scale=scale, size=sample_size)) return sample class MixtureDistribution(object): '''univariate mixture distribution for simple case for now (unbound support) does not yet inherit from scipy.stats.distributions adding pdf to mixture_rvs, some restrictions on broadcasting Currently it does not hold any state, all arguments included in each method. ''' #def __init__(self, prob, size, dist, kwargs=None): def rvs(self, prob, size, dist, kwargs=None): return mixture_rvs(prob, size, dist, kwargs=kwargs) def pdf(self, x, prob, dist, kwargs=None): """ pdf a mixture of distributions. Parameters ---------- x : array_like Array containing locations where the PDF should be evaluated prob : array_like Probability of sampling from each distribution in dist dist : array_like An iterable of distributions objects from scipy.stats. kwargs : tuple of dicts, optional A tuple of dicts. Each dict in kwargs can have keys loc, scale, and args to be passed to the respective distribution in dist. If not provided, the distribution defaults are used. Examples -------- Say we want 5000 random variables from mixture of normals with two distributions norm(-1,.5) and norm(1,.5) and we want to sample from the first with probability .75 and the second with probability .25. >>> import numpy as np >>> from scipy import stats >>> from statsmodels.distributions.mixture_rvs import MixtureDistribution >>> x = np.arange(-4.0, 4.0, 0.01) >>> prob = [.75,.25] >>> mixture = MixtureDistribution() >>> Y = mixture.pdf(x, prob, dist=[stats.norm, stats.norm], ... kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.5))) """ if len(prob) != len(dist): raise ValueError("You must provide as many probabilities as distributions") if not np.allclose(np.sum(prob), 1): raise ValueError("prob does not sum to 1") if kwargs is None: kwargs = ({},)*len(prob) for i in range(len(prob)): loc = kwargs[i].get('loc',0) scale = kwargs[i].get('scale',1) args = kwargs[i].get('args',()) if i == 0: #assume all broadcast the same as the first dist pdf_ = prob[i] * dist[i].pdf(x, *args, loc=loc, scale=scale) else: pdf_ += prob[i] * dist[i].pdf(x, *args, loc=loc, scale=scale) return pdf_ def cdf(self, x, prob, dist, kwargs=None): """ cdf of a mixture of distributions. Parameters ---------- x : array_like Array containing locations where the CDF should be evaluated prob : array_like Probability of sampling from each distribution in dist size : int The length of the returned sample. dist : array_like An iterable of distributions objects from scipy.stats. kwargs : tuple of dicts, optional A tuple of dicts. Each dict in kwargs can have keys loc, scale, and args to be passed to the respective distribution in dist. If not provided, the distribution defaults are used. Examples -------- Say we want 5000 random variables from mixture of normals with two distributions norm(-1,.5) and norm(1,.5) and we want to sample from the first with probability .75 and the second with probability .25. >>> import numpy as np >>> from scipy import stats >>> from statsmodels.distributions.mixture_rvs import MixtureDistribution >>> x = np.arange(-4.0, 4.0, 0.01) >>> prob = [.75,.25] >>> mixture = MixtureDistribution() >>> Y = mixture.pdf(x, prob, dist=[stats.norm, stats.norm], ... kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.5))) """ if len(prob) != len(dist): raise ValueError("You must provide as many probabilities as distributions") if not np.allclose(np.sum(prob), 1): raise ValueError("prob does not sum to 1") if kwargs is None: kwargs = ({},)*len(prob) for i in range(len(prob)): loc = kwargs[i].get('loc',0) scale = kwargs[i].get('scale',1) args = kwargs[i].get('args',()) if i == 0: #assume all broadcast the same as the first dist cdf_ = prob[i] * dist[i].cdf(x, *args, loc=loc, scale=scale) else: cdf_ += prob[i] * dist[i].cdf(x, *args, loc=loc, scale=scale) return cdf_ def mv_mixture_rvs(prob, size, dist, nvars, **kwargs): """ Sample from a mixture of multivariate distributions. Parameters ---------- prob : array_like Probability of sampling from each distribution in dist size : int The length of the returned sample. dist : array_like An iterable of distributions instances with callable method rvs. nvargs : int dimension of the multivariate distribution, could be inferred instead kwargs : tuple of dicts, optional ignored Examples -------- Say we want 2000 random variables from mixture of normals with two multivariate normal distributions, and we want to sample from the first with probability .4 and the second with probability .6. import statsmodels.sandbox.distributions.mv_normal as mvd cov3 = np.array([[ 1. , 0.5 , 0.75], [ 0.5 , 1.5 , 0.6 ], [ 0.75, 0.6 , 2. ]]) mu = np.array([-1, 0.0, 2.0]) mu2 = np.array([4, 2.0, 2.0]) mvn3 = mvd.MVNormal(mu, cov3) mvn32 = mvd.MVNormal(mu2, cov3/2., 4) rvs = mix.mv_mixture_rvs([0.4, 0.6], 2000, [mvn3, mvn32], 3) """ if len(prob) != len(dist): raise ValueError("You must provide as many probabilities as distributions") if not np.allclose(np.sum(prob), 1): raise ValueError("prob does not sum to 1") if kwargs is None: kwargs = ({},)*len(prob) idx = _make_index(prob,size) sample = np.empty((size, nvars)) for i in range(len(prob)): sample_idx = idx[...,i] sample_size = sample_idx.sum() #loc = kwargs[i].get('loc',0) #scale = kwargs[i].get('scale',1) #args = kwargs[i].get('args',()) # use int to avoid numpy bug with np.random.multivariate_normal sample[sample_idx] = dist[i].rvs(size=int(sample_size)) return sample if __name__ == '__main__': from scipy import stats obs_dist = mixture_rvs([.25,.75], size=10000, dist=[stats.norm, stats.beta], kwargs=(dict(loc=-1,scale=.5),dict(loc=1,scale=1,args=(1,.5)))) nobs = 10000 mix = MixtureDistribution() ## mrvs = mixture_rvs([1/3.,2/3.], size=nobs, dist=[stats.norm, stats.norm], ## kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.75))) mix_kwds = (dict(loc=-1,scale=.25),dict(loc=1,scale=.75)) mrvs = mix.rvs([1/3.,2/3.], size=nobs, dist=[stats.norm, stats.norm], kwargs=mix_kwds) grid = np.linspace(-4,4, 100) mpdf = mix.pdf(grid, [1/3.,2/3.], dist=[stats.norm, stats.norm], kwargs=mix_kwds) mcdf = mix.cdf(grid, [1/3.,2/3.], dist=[stats.norm, stats.norm], kwargs=mix_kwds) doplot = 1 if doplot: import matplotlib.pyplot as plt plt.figure() plt.hist(mrvs, bins=50, normed=True, color='red') plt.title('histogram of sample and pdf') plt.plot(grid, mpdf, lw=2, color='black') plt.figure() plt.hist(mrvs, bins=50, normed=True, cumulative=True, color='red') plt.title('histogram of sample and pdf') plt.plot(grid, mcdf, lw=2, color='black') plt.show() statsmodels-0.12.2/statsmodels/distributions/tests/000077500000000000000000000000001400612667500225535ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/distributions/tests/__init__.py000066400000000000000000000000001400612667500246520ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/distributions/tests/test_discrete.py000066400000000000000000000231241400612667500257700ustar00rootroot00000000000000 import numpy as np import statsmodels.api as sm from scipy.stats import poisson, nbinom from numpy.testing import assert_allclose class TestGenpoisson_p(object): # Test Generalized Poisson Destribution def test_pmf_p1(self): poisson_pmf = poisson.pmf(1, 1) genpoisson_pmf = sm.distributions.genpoisson_p.pmf(1, 1, 0, 1) assert_allclose(poisson_pmf, genpoisson_pmf, rtol=1e-15) def test_pmf_p2(self): poisson_pmf = poisson.pmf(2, 2) genpoisson_pmf = sm.distributions.genpoisson_p.pmf(2, 2, 0, 2) assert_allclose(poisson_pmf, genpoisson_pmf, rtol=1e-15) def test_pmf_p5(self): poisson_pmf = poisson.pmf(10, 2) genpoisson_pmf_5 = sm.distributions.genpoisson_p.pmf(10, 2, 1e-25, 5) assert_allclose(poisson_pmf, genpoisson_pmf_5, rtol=1e-12) def test_logpmf_p1(self): poisson_pmf = poisson.logpmf(5, 2) genpoisson_pmf = sm.distributions.genpoisson_p.logpmf(5, 2, 0, 1) assert_allclose(poisson_pmf, genpoisson_pmf, rtol=1e-15) def test_logpmf_p2(self): poisson_pmf = poisson.logpmf(6, 1) genpoisson_pmf = sm.distributions.genpoisson_p.logpmf(6, 1, 0, 2) assert_allclose(poisson_pmf, genpoisson_pmf, rtol=1e-15) class TestZIPoisson(object): def test_pmf_zero(self): poisson_pmf = poisson.pmf(3, 2) zipoisson_pmf = sm.distributions.zipoisson.pmf(3, 2, 0) assert_allclose(poisson_pmf, zipoisson_pmf, rtol=1e-12) def test_logpmf_zero(self): poisson_logpmf = poisson.logpmf(5, 1) zipoisson_logpmf = sm.distributions.zipoisson.logpmf(5, 1, 0) assert_allclose(poisson_logpmf, zipoisson_logpmf, rtol=1e-12) def test_pmf(self): poisson_pmf = poisson.pmf(2, 2) zipoisson_pmf = sm.distributions.zipoisson.pmf(2, 2, 0.1) assert_allclose(poisson_pmf, zipoisson_pmf, rtol=5e-2, atol=5e-2) def test_logpmf(self): poisson_logpmf = poisson.logpmf(7, 3) zipoisson_logpmf = sm.distributions.zipoisson.logpmf(7, 3, 0.1) assert_allclose(poisson_logpmf, zipoisson_logpmf, rtol=5e-2, atol=5e-2) def test_cdf_zero(self): poisson_cdf = poisson.cdf(3, 2) zipoisson_cdf = sm.distributions.zipoisson.cdf(3, 2, 0) assert_allclose(poisson_cdf, zipoisson_cdf, rtol=1e-12) def test_ppf_zero(self): poisson_ppf = poisson.ppf(5, 1) zipoisson_ppf = sm.distributions.zipoisson.ppf(5, 1, 0) assert_allclose(poisson_ppf, zipoisson_ppf, rtol=1e-12) def test_mean_var(self): poisson_mean, poisson_var = poisson.mean(12), poisson.var(12) zipoisson_mean = sm.distributions.zipoisson.mean(12, 0) zipoisson_var = sm.distributions.zipoisson.var(12, 0) assert_allclose(poisson_mean, zipoisson_mean, rtol=1e-10) assert_allclose(poisson_var, zipoisson_var, rtol=1e-10) m = np.array([1, 5, 10]) poisson_mean, poisson_var = poisson.mean(m), poisson.var(m) zipoisson_mean = sm.distributions.zipoisson._mean(m, 0) zipoisson_var = sm.distributions.zipoisson._var(m, 0.0) assert_allclose(poisson_mean, zipoisson_mean, rtol=1e-10) assert_allclose(poisson_var, zipoisson_var, rtol=1e-10) def test_moments(self): poisson_m1, poisson_m2 = poisson.moment(1, 12), poisson.moment(2, 12) zip_m0 = sm.distributions.zipoisson.moment(0, 12, 0) zip_m1 = sm.distributions.zipoisson.moment(1, 12, 0) zip_m2 = sm.distributions.zipoisson.moment(2, 12, 0) assert_allclose(1, zip_m0, rtol=1e-10) assert_allclose(poisson_m1, zip_m1, rtol=1e-10) assert_allclose(poisson_m2, zip_m2, rtol=1e-10) class TestZIGeneralizedPoisson(object): def test_pmf_zero(self): gp_pmf = sm.distributions.genpoisson_p.pmf(3, 2, 1, 1) zigp_pmf = sm.distributions.zigenpoisson.pmf(3, 2, 1, 1, 0) assert_allclose(gp_pmf, zigp_pmf, rtol=1e-12) def test_logpmf_zero(self): gp_logpmf = sm.distributions.genpoisson_p.logpmf(7, 3, 1, 1) zigp_logpmf = sm.distributions.zigenpoisson.logpmf(7, 3, 1, 1, 0) assert_allclose(gp_logpmf, zigp_logpmf, rtol=1e-12) def test_pmf(self): gp_pmf = sm.distributions.genpoisson_p.pmf(3, 2, 2, 2) zigp_pmf = sm.distributions.zigenpoisson.pmf(3, 2, 2, 2, 0.1) assert_allclose(gp_pmf, zigp_pmf, rtol=5e-2, atol=5e-2) def test_logpmf(self): gp_logpmf = sm.distributions.genpoisson_p.logpmf(2, 3, 0, 2) zigp_logpmf = sm.distributions.zigenpoisson.logpmf(2, 3, 0, 2, 0.1) assert_allclose(gp_logpmf, zigp_logpmf, rtol=5e-2, atol=5e-2) def test_mean_var(self): # compare with Poisson special case m = np.array([1, 5, 10]) poisson_mean, poisson_var = poisson.mean(m), poisson.var(m) zigenpoisson_mean = sm.distributions.zigenpoisson._mean(m, 0, 1, 0) zigenpoisson_var = sm.distributions.zigenpoisson._var(m, 0.0, 1, 0) assert_allclose(poisson_mean, zigenpoisson_mean, rtol=1e-10) assert_allclose(poisson_var, zigenpoisson_var, rtol=1e-10) class TestZiNBP(object): def test_pmf_p2(self): n, p = sm.distributions.zinegbin.convert_params(30, 0.1, 2) nb_pmf = nbinom.pmf(100, n, p) tnb_pmf = sm.distributions.zinegbin.pmf(100, 30, 0.1, 2, 0.01) assert_allclose(nb_pmf, tnb_pmf, rtol=1e-5, atol=1e-5) def test_logpmf_p2(self): n, p = sm.distributions.zinegbin.convert_params(10, 1, 2) nb_logpmf = nbinom.logpmf(200, n, p) tnb_logpmf = sm.distributions.zinegbin.logpmf(200, 10, 1, 2, 0.01) assert_allclose(nb_logpmf, tnb_logpmf, rtol=1e-2, atol=1e-2) def test_cdf_p2(self): n, p = sm.distributions.zinegbin.convert_params(30, 0.1, 2) nbinom_cdf = nbinom.cdf(10, n, p) zinbinom_cdf = sm.distributions.zinegbin.cdf(10, 30, 0.1, 2, 0) assert_allclose(nbinom_cdf, zinbinom_cdf, rtol=1e-12, atol=1e-12) def test_ppf_p2(self): n, p = sm.distributions.zinegbin.convert_params(100, 1, 2) nbinom_ppf = nbinom.ppf(0.27, n, p) zinbinom_ppf = sm.distributions.zinegbin.ppf(0.27, 100, 1, 2, 0) assert_allclose(nbinom_ppf, zinbinom_ppf, rtol=1e-12, atol=1e-12) def test_mran_var_p2(self): n, p = sm.distributions.zinegbin.convert_params(7, 1, 2) nbinom_mean, nbinom_var = nbinom.mean(n, p), nbinom.var(n, p) zinb_mean = sm.distributions.zinegbin.mean(7, 1, 2, 0) zinb_var = sm.distributions.zinegbin.var(7, 1, 2, 0) assert_allclose(nbinom_mean, zinb_mean, rtol=1e-10) assert_allclose(nbinom_var, zinb_var, rtol=1e-10) def test_moments_p2(self): n, p = sm.distributions.zinegbin.convert_params(7, 1, 2) nb_m1, nb_m2 = nbinom.moment(1, n, p), nbinom.moment(2, n, p) zinb_m0 = sm.distributions.zinegbin.moment(0, 7, 1, 2, 0) zinb_m1 = sm.distributions.zinegbin.moment(1, 7, 1, 2, 0) zinb_m2 = sm.distributions.zinegbin.moment(2, 7, 1, 2, 0) assert_allclose(1, zinb_m0, rtol=1e-10) assert_allclose(nb_m1, zinb_m1, rtol=1e-10) assert_allclose(nb_m2, zinb_m2, rtol=1e-10) def test_pmf(self): n, p = sm.distributions.zinegbin.convert_params(1, 0.9, 1) nb_logpmf = nbinom.pmf(2, n, p) tnb_pmf = sm.distributions.zinegbin.pmf(2, 1, 0.9, 2, 0.5) assert_allclose(nb_logpmf, tnb_pmf * 2, rtol=1e-7) def test_logpmf(self): n, p = sm.distributions.zinegbin.convert_params(5, 1, 1) nb_logpmf = nbinom.logpmf(2, n, p) tnb_logpmf = sm.distributions.zinegbin.logpmf(2, 5, 1, 1, 0.005) assert_allclose(nb_logpmf, tnb_logpmf, rtol=1e-2, atol=1e-2) def test_cdf(self): n, p = sm.distributions.zinegbin.convert_params(1, 0.9, 1) nbinom_cdf = nbinom.cdf(2, n, p) zinbinom_cdf = sm.distributions.zinegbin.cdf(2, 1, 0.9, 2, 0) assert_allclose(nbinom_cdf, zinbinom_cdf, rtol=1e-12, atol=1e-12) def test_ppf(self): n, p = sm.distributions.zinegbin.convert_params(5, 1, 1) nbinom_ppf = nbinom.ppf(0.71, n, p) zinbinom_ppf = sm.distributions.zinegbin.ppf(0.71, 5, 1, 1, 0) assert_allclose(nbinom_ppf, zinbinom_ppf, rtol=1e-12, atol=1e-12) def test_convert(self): n, p = sm.distributions.zinegbin.convert_params(25, 0.85, 2) n_true, p_true = 1.1764705882352942, 0.04494382022471911 assert_allclose(n, n_true, rtol=1e-12, atol=1e-12) assert_allclose(p, p_true, rtol=1e-12, atol=1e-12) n, p = sm.distributions.zinegbin.convert_params(7, 0.17, 1) n_true, p_true = 41.17647058823529, 0.8547008547008547 assert_allclose(n, n_true, rtol=1e-12, atol=1e-12) assert_allclose(p, p_true, rtol=1e-12, atol=1e-12) def test_mean_var(self): for m in [9, np.array([1, 5, 10])]: n, p = sm.distributions.zinegbin.convert_params(m, 1, 1) nbinom_mean, nbinom_var = nbinom.mean(n, p), nbinom.var(n, p) zinb_mean = sm.distributions.zinegbin._mean(m, 1, 1, 0) zinb_var = sm.distributions.zinegbin._var(m, 1, 1, 0) assert_allclose(nbinom_mean, zinb_mean, rtol=1e-10) assert_allclose(nbinom_var, zinb_var, rtol=1e-10) def test_moments(self): n, p = sm.distributions.zinegbin.convert_params(9, 1, 1) nb_m1, nb_m2 = nbinom.moment(1, n, p), nbinom.moment(2, n, p) zinb_m0 = sm.distributions.zinegbin.moment(0, 9, 1, 1, 0) zinb_m1 = sm.distributions.zinegbin.moment(1, 9, 1, 1, 0) zinb_m2 = sm.distributions.zinegbin.moment(2, 9, 1, 1, 0) assert_allclose(1, zinb_m0, rtol=1e-10) assert_allclose(nb_m1, zinb_m1, rtol=1e-10) assert_allclose(nb_m2, zinb_m2, rtol=1e-10) statsmodels-0.12.2/statsmodels/distributions/tests/test_ecdf.py000066400000000000000000000032011400612667500250610ustar00rootroot00000000000000import numpy as np import numpy.testing as npt from numpy.testing import assert_raises from statsmodels.distributions import StepFunction, monotone_fn_inverter class TestDistributions(object): def test_StepFunction(self): x = np.arange(20) y = np.arange(20) f = StepFunction(x, y) npt.assert_almost_equal(f( np.array([[3.2,4.5],[24,-3.1],[3.0, 4.0]])), [[ 3, 4], [19, 0], [2, 3]]) def test_StepFunctionBadShape(self): x = np.arange(20) y = np.arange(21) assert_raises(ValueError, StepFunction, x, y) x = np.zeros((2, 2)) y = np.zeros((2, 2)) assert_raises(ValueError, StepFunction, x, y) def test_StepFunctionValueSideRight(self): x = np.arange(20) y = np.arange(20) f = StepFunction(x, y, side='right') npt.assert_almost_equal(f( np.array([[3.2,4.5],[24,-3.1],[3.0, 4.0]])), [[ 3, 4], [19, 0], [3, 4]]) def test_StepFunctionRepeatedValues(self): x = [1, 1, 2, 2, 2, 3, 3, 3, 4, 5] y = [6, 7, 8, 9, 10, 11, 12, 13, 14, 15] f = StepFunction(x, y) npt.assert_almost_equal(f([1, 2, 3, 4, 5]), [0, 7, 10, 13, 14]) f2 = StepFunction(x, y, side='right') npt.assert_almost_equal(f2([1, 2, 3, 4, 5]), [7, 10, 13, 14, 15]) def test_monotone_fn_inverter(self): x = [6, 7, 8, 9, 10, 11, 12, 13, 14, 15] fn = lambda x : 1./x y = fn(np.array(x)) f = monotone_fn_inverter(fn, x) npt.assert_array_equal(f.y, x[::-1]) npt.assert_array_equal(f.x, y[::-1]) statsmodels-0.12.2/statsmodels/distributions/tests/test_edgeworth.py000066400000000000000000000144501400612667500261600ustar00rootroot00000000000000 import warnings import numpy as np from numpy.testing import (assert_equal, assert_raises, assert_allclose) import numpy.testing as npt from scipy.special import gamma, factorial, factorial2 import scipy.stats as stats from statsmodels.distributions.edgeworth import (_faa_di_bruno_partitions, cumulant_from_moments, ExpandedNormal) class TestFaaDiBruno(object): def test_neg_arg(self): assert_raises(ValueError, _faa_di_bruno_partitions, -1) assert_raises(ValueError, _faa_di_bruno_partitions, 0) def test_small_vals(self): for n in range(1, 5): for ks in _faa_di_bruno_partitions(n): lhs = sum(m * k for (m, k) in ks) assert_equal(lhs, n) def _norm_moment(n): # moments of N(0, 1) return (1 - n % 2) * factorial2(n - 1) def _norm_cumulant(n): # cumulants of N(0, 1) try: return {1: 0, 2: 1}[n] except KeyError: return 0 def _chi2_moment(n, df): # (raw) moments of \chi^2(df) return (2**n) * gamma(n + df/2.) / gamma(df/2.) def _chi2_cumulant(n, df): assert n > 0 return 2**(n-1) * factorial(n - 1) * df class TestCumulants(object): def test_badvalues(self): assert_raises(ValueError, cumulant_from_moments, [1, 2, 3], 0) assert_raises(ValueError, cumulant_from_moments, [1, 2, 3], 4) def test_norm(self): N = 4 momt = [_norm_moment(j+1) for j in range(N)] for n in range(1, N+1): kappa = cumulant_from_moments(momt, n) assert_allclose(kappa, _norm_cumulant(n), atol=1e-12) def test_chi2(self): N = 4 df = 8 momt = [_chi2_moment(j+1, df) for j in range(N)] for n in range(1, N+1): kappa = cumulant_from_moments(momt, n) assert_allclose(kappa, _chi2_cumulant(n, df)) class TestExpandedNormal(object): def test_too_few_cumulants(self): assert_raises(ValueError, ExpandedNormal, [1]) def test_coefficients(self): with warnings.catch_warnings(): warnings.simplefilter('ignore', RuntimeWarning) # 3rd order in n**(1/2) ne3 = ExpandedNormal([0., 1., 1.]) assert_allclose(ne3._coef, [1., 0., 0., 1./6]) # 4th order in n**(1/2) ne4 = ExpandedNormal([0., 1., 1., 1.]) assert_allclose(ne4._coef, [1., 0., 0., 1./6, 1./24, 0., 1./72]) # 5th order ne5 = ExpandedNormal([0., 1., 1., 1., 1.]) assert_allclose(ne5._coef, [1., 0., 0., 1./6, 1./24, 1./120, 1./72, 1./144, 0., 1./1296]) # adding trailing zeroes increases the order ne33 = ExpandedNormal([0., 1., 1., 0.]) assert_allclose(ne33._coef, [1., 0., 0., 1./6, 0., 0., 1./72]) def test_normal(self): # with two cumulants, it's just a gaussian ne2 = ExpandedNormal([3, 4]) x = np.linspace(-2., 2., 100) assert_allclose(ne2.pdf(x), stats.norm.pdf(x, loc=3, scale=2)) def test_chi2_moments(self): # construct the expansion for \chi^2 N, df = 6, 15 cum = [_chi2_cumulant(n+1, df) for n in range(N)] with warnings.catch_warnings(): warnings.simplefilter("ignore", RuntimeWarning) ne = ExpandedNormal(cum, name='edgw_chi2') # compare the moments assert_allclose([_chi2_moment(n, df) for n in range(N)], [ne.moment(n) for n in range(N)]) # compare the pdf [fragile!] # this one is actually not a very good test: there is, strictly # speaking, no guarantee that the pdfs match point-by-point # m, s = df, np.sqrt(df) # x = np.linspace(m - s, m + s, 10) # assert_allclose(ne.pdf(x), stats.chi2.pdf(x, df), # atol=1e-4, rtol=1e-5) # pdf-cdf roundtrip check_pdf(ne, arg=(), msg='') # cdf-ppf roundtrip check_cdf_ppf(ne, arg=(), msg='') # cdf + sf == 1 check_cdf_sf(ne, arg=(), msg='') # generate rvs & run a KS test np.random.seed(765456) rvs = ne.rvs(size=500) check_distribution_rvs(ne, args=(), alpha=0.01, rvs=rvs) def test_pdf_no_roots(self): with warnings.catch_warnings(): warnings.simplefilter("error", RuntimeWarning) ne = ExpandedNormal([0, 1]) ne = ExpandedNormal([0, 1, 0.1, 0.1]) def test_pdf_has_roots(self): with warnings.catch_warnings(): warnings.simplefilter("error", RuntimeWarning) assert_raises(RuntimeWarning, ExpandedNormal, [0, 1, 101]) ## stolen verbatim from scipy/stats/tests/test_continuous_extra.py DECIMAL = 8 def check_pdf(distfn, arg, msg): # compares pdf at median with numerical derivative of cdf median = distfn.ppf(0.5, *arg) eps = 1e-6 pdfv = distfn.pdf(median, *arg) if (pdfv < 1e-4) or (pdfv > 1e4): # avoid checking a case where pdf is close to zero # or huge (singularity) median = median + 0.1 pdfv = distfn.pdf(median, *arg) cdfdiff = (distfn.cdf(median + eps, *arg) - distfn.cdf(median - eps, *arg))/eps/2.0 # replace with better diff and better test (more points), # actually, this works pretty well npt.assert_almost_equal(pdfv, cdfdiff, decimal=DECIMAL, err_msg=msg + ' - cdf-pdf relationship') def check_cdf_ppf(distfn, arg, msg): values = [0.001, 0.5, 0.999] npt.assert_almost_equal(distfn.cdf(distfn.ppf(values, *arg), *arg), values, decimal=DECIMAL, err_msg=msg + ' - cdf-ppf roundtrip') def check_cdf_sf(distfn, arg, msg): values = [0.001, 0.5, 0.999] npt.assert_almost_equal(distfn.cdf(values, *arg), 1. - distfn.sf(values, *arg), decimal=DECIMAL, err_msg=msg +' - sf+cdf == 1') def check_distribution_rvs(distfn, args, alpha, rvs): ## signature changed to avoid calling a distribution by name # test from scipy.stats.tests # this version reuses existing random variables D,pval = stats.kstest(rvs, distfn.cdf, args=args, N=1000) if (pval < alpha): D,pval = stats.kstest(distfn.rvs, distfn.cdf, args=args, N=1000) npt.assert_(pval > alpha, "D = " + str(D) + "; pval = " + str(pval) + "; alpha = " + str(alpha) + "\nargs = " + str(args)) statsmodels-0.12.2/statsmodels/distributions/tests/test_mixture.py000066400000000000000000000117171400612667500256700ustar00rootroot00000000000000# Copyright (c) 2013 Ana Martinez Pardo # License: BSD-3 [see LICENSE.txt] import numpy as np import numpy.testing as npt from statsmodels.distributions.mixture_rvs import (mv_mixture_rvs, MixtureDistribution) import statsmodels.sandbox.distributions.mv_normal as mvd from scipy import stats class TestMixtureDistributions(object): def test_mixture_rvs_random(self): # Test only medium small sample at 1 decimal np.random.seed(0) mix = MixtureDistribution() res = mix.rvs([.75,.25], 1000, dist=[stats.norm, stats.norm], kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.5))) npt.assert_almost_equal( np.array([res.std(),res.mean(),res.var()]), np.array([1,-0.5,1]), decimal=1) def test_mv_mixture_rvs_random(self): cov3 = np.array([[ 1. , 0.5 , 0.75], [ 0.5 , 1.5 , 0.6 ], [ 0.75, 0.6 , 2. ]]) mu = np.array([-1, 0.0, 2.0]) mu2 = np.array([4, 2.0, 2.0]) mvn3 = mvd.MVNormal(mu, cov3) mvn32 = mvd.MVNormal(mu2, cov3/2.) np.random.seed(0) res = mv_mixture_rvs([0.4, 0.6], 5000, [mvn3, mvn32], 3) npt.assert_almost_equal( np.array([res.std(),res.mean(),res.var()]), np.array([1.874,1.733,3.512]), decimal=1) def test_mixture_pdf(self): mix = MixtureDistribution() grid = np.linspace(-4,4, 10) res = mix.pdf(grid, [1/3.,2/3.], dist=[stats.norm, stats.norm], kwargs= (dict(loc=-1,scale=.25),dict(loc=1,scale=.75))) npt.assert_almost_equal( res, np.array([ 7.92080017e-11, 1.05977272e-07, 3.82368500e-05, 2.21485447e-01, 1.00534607e-01, 2.69531536e-01, 3.21265627e-01, 9.39899015e-02, 6.74932493e-03, 1.18960201e-04])) def test_mixture_cdf(self): mix = MixtureDistribution() grid = np.linspace(-4,4, 10) res = mix.cdf(grid, [1/3.,2/3.], dist=[stats.norm, stats.norm], kwargs= (dict(loc=-1,scale=.25),dict(loc=1,scale=.75))) npt.assert_almost_equal( res, np.array([ 8.72261646e-12, 1.40592960e-08, 5.95819161e-06, 3.10250226e-02, 3.46993159e-01, 4.86283549e-01, 7.81092904e-01, 9.65606734e-01, 9.98373155e-01, 9.99978886e-01])) def test_mixture_rvs_fixed(self): mix = MixtureDistribution() np.random.seed(1234) res = mix.rvs([.15,.85], 50, dist=[stats.norm, stats.norm], kwargs = (dict(loc=1,scale=.5),dict(loc=-1,scale=.5))) npt.assert_almost_equal( res, np.array([-0.5794956 , -1.72290504, -1.70098664, -1.0504591 , -1.27412122,-1.07230975, -0.82298983, -1.01775651, -0.71713085,-0.2271706 ,-1.48711817, -1.03517244, -0.84601557, -1.10424938, -0.48309963,-2.20022682, 0.01530181, 1.1238961 , -1.57131564, -0.89405831, -0.64763969, -1.39271761, 0.55142161, -0.76897013, -0.64788589,-0.73824602, -1.46312716, 0.00392148, -0.88651873, -1.57632955,-0.68401028, -0.98024366, -0.76780384, 0.93160258,-2.78175833,-0.33944719, -0.92368472, -0.91773523, -1.21504785, -0.61631563, 1.0091446 , -0.50754008, 1.37770699, -0.86458208, -0.3040069 ,-0.96007884, 1.10763429, -1.19998229, -1.51392528, -1.29235911])) def test_mv_mixture_rvs_fixed(self): np.random.seed(1234) cov3 = np.array([[ 1. , 0.5 , 0.75], [ 0.5 , 1.5 , 0.6 ], [ 0.75, 0.6 , 2. ]]) mu = np.array([-1, 0.0, 2.0]) mu2 = np.array([4, 2.0, 2.0]) mvn3 = mvd.MVNormal(mu, cov3) mvn32 = mvd.MVNormal(mu2, cov3/2) res = mv_mixture_rvs([0.2, 0.8], 10, [mvn3, mvn32], 3) npt.assert_almost_equal( res, np.array([[-0.23955497, 1.73426482, 0.36100243], [ 2.52063189, 1.0832677 , 1.89947131], [ 4.36755379, 2.14480498, 2.22003966], [ 3.1141545 , 1.21250505, 2.58511199], [ 4.1980202 , 2.50017561, 1.87324933], [ 3.48717503, 0.91847424, 2.14004598], [ 3.55904133, 2.74367622, 0.68619582], [ 3.60521933, 1.57316531, 0.82784584], [ 3.86102275, 0.6211812 , 1.33016426], [ 3.91074761, 2.037155 , 2.22247051]])) statsmodels-0.12.2/statsmodels/duration/000077500000000000000000000000001400612667500203345ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/duration/__init__.py000066400000000000000000000001131400612667500224400ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/duration/_kernel_estimates.py000066400000000000000000000141201400612667500244010ustar00rootroot00000000000000import numpy as np from statsmodels.duration.hazard_regression import PHReg def _kernel_cumincidence(time, status, exog, kfunc, freq_weights, dimred=True): """ Calculates cumulative incidence functions using kernels. Parameters ---------- time : array_like The observed time values status : array_like The status values. status == 0 indicates censoring, status == 1, 2, ... are the events. exog : array_like Covariates such that censoring becomes independent of outcome times conditioned on the covariate values. kfunc : function A kernel function freq_weights : array_like Optional frequency weights dimred : bool If True, proportional hazards regression models are used to reduce exog to two columns by predicting overall events and censoring in two separate models. If False, exog is used directly for calculating kernel weights without dimension reduction. """ # Reorder so time is ascending ii = np.argsort(time) time = time[ii] status = status[ii] exog = exog[ii, :] nobs = len(time) # Convert the unique times to ranks (0, 1, 2, ...) utime, rtime = np.unique(time, return_inverse=True) # Last index where each unique time occurs. ie = np.searchsorted(time, utime, side='right') - 1 ngrp = int(status.max()) # All-cause status statusa = (status >= 1).astype(np.float64) if freq_weights is not None: freq_weights = freq_weights / freq_weights.sum() ip = [] sp = [None] * nobs n_risk = [None] * nobs kd = [None] * nobs for k in range(ngrp): status0 = (status == k + 1).astype(np.float64) # Dimension reduction step if dimred: sfe = PHReg(time, exog, status0).fit() fitval_e = sfe.predict().predicted_values sfc = PHReg(time, exog, 1 - status0).fit() fitval_c = sfc.predict().predicted_values exog2d = np.hstack((fitval_e[:, None], fitval_c[:, None])) exog2d -= exog2d.mean(0) exog2d /= exog2d.std(0) else: exog2d = exog ip0 = 0 for i in range(nobs): if k == 0: kd1 = exog2d - exog2d[i, :] kd1 = kfunc(kd1) kd[i] = kd1 # Get the local all-causes survival function if k == 0: denom = np.cumsum(kd[i][::-1])[::-1] num = kd[i] * statusa rat = num / denom tr = 1e-15 ii = np.flatnonzero((denom < tr) & (num < tr)) rat[ii] = 0 ratc = 1 - rat ratc = np.clip(ratc, 1e-10, np.inf) lrat = np.log(ratc) prat = np.cumsum(lrat)[ie] sf = np.exp(prat) sp[i] = np.r_[1, sf[:-1]] n_risk[i] = denom[ie] # Number of cause-specific deaths at each unique time. d0 = np.bincount(rtime, weights=status0*kd[i], minlength=len(utime)) # The cumulative incidence function probabilities. Carry # forward once the effective sample size drops below 1. ip1 = np.cumsum(sp[i] * d0 / n_risk[i]) jj = len(ip1) - np.searchsorted(n_risk[i][::-1], 1) if jj < len(ip1): ip1[jj:] = ip1[jj - 1] if freq_weights is None: ip0 += ip1 else: ip0 += freq_weights[i] * ip1 if freq_weights is None: ip0 /= nobs ip.append(ip0) return utime, ip def _kernel_survfunc(time, status, exog, kfunc, freq_weights): """ Estimate the marginal survival function under dependent censoring. Parameters ---------- time : array_like The observed times for each subject status : array_like The status for each subject (1 indicates event, 0 indicates censoring) exog : array_like Covariates such that censoring is independent conditional on exog kfunc : function Kernel function freq_weights : array_like Optional frequency weights Returns ------- probs : array_like The estimated survival probabilities times : array_like The times at which the survival probabilities are estimated References ---------- Zeng, Donglin 2004. Estimating Marginal Survival Function by Adjusting for Dependent Censoring Using Many Covariates. The Annals of Statistics 32 (4): 1533 55. doi:10.1214/009053604000000508. https://arxiv.org/pdf/math/0409180.pdf """ # Dimension reduction step sfe = PHReg(time, exog, status).fit() fitval_e = sfe.predict().predicted_values sfc = PHReg(time, exog, 1 - status).fit() fitval_c = sfc.predict().predicted_values exog2d = np.hstack((fitval_e[:, None], fitval_c[:, None])) n = len(time) ixd = np.flatnonzero(status == 1) # For consistency with standard KM, only compute the survival # function at the times of observed events. utime = np.unique(time[ixd]) # Reorder everything so time is ascending ii = np.argsort(time) time = time[ii] status = status[ii] exog2d = exog2d[ii, :] # Last index where each evaluation time occurs. ie = np.searchsorted(time, utime, side='right') - 1 if freq_weights is not None: freq_weights = freq_weights / freq_weights.sum() sprob = 0. for i in range(n): kd = exog2d - exog2d[i, :] kd = kfunc(kd) denom = np.cumsum(kd[::-1])[::-1] num = kd * status rat = num / denom tr = 1e-15 ii = np.flatnonzero((denom < tr) & (num < tr)) rat[ii] = 0 ratc = 1 - rat ratc = np.clip(ratc, 1e-12, np.inf) lrat = np.log(ratc) prat = np.cumsum(lrat)[ie] prat = np.exp(prat) if freq_weights is None: sprob += prat else: sprob += prat * freq_weights[i] if freq_weights is None: sprob /= n return sprob, utime statsmodels-0.12.2/statsmodels/duration/api.py000066400000000000000000000003051400612667500214550ustar00rootroot00000000000000__all__ = ["PHReg", "SurvfuncRight", "survdiff", "CumIncidenceRight"] from .hazard_regression import PHReg from .survfunc import (SurvfuncRight, survdiff, CumIncidenceRight) statsmodels-0.12.2/statsmodels/duration/hazard_regression.py000066400000000000000000001623221400612667500244250ustar00rootroot00000000000000""" Implementation of proportional hazards regression models for duration data that may be censored ("Cox models"). References ---------- T Therneau (1996). Extending the Cox model. Technical report. http://www.mayo.edu/research/documents/biostat-58pdf/DOC-10027288 G Rodriguez (2005). Non-parametric estimation in survival models. http://data.princeton.edu/pop509/NonParametricSurvival.pdf B Gillespie (2006). Checking the assumptions in the Cox proportional hazards model. http://www.mwsug.org/proceedings/2006/stats/MWSUG-2006-SD08.pdf """ import numpy as np from statsmodels.base import model import statsmodels.base.model as base from statsmodels.tools.decorators import cache_readonly from statsmodels.compat.pandas import Appender _predict_docstring = """ Returns predicted values from the proportional hazards regression model. Parameters ----------%(params_doc)s exog : array_like Data to use as `exog` in forming predictions. If not provided, the `exog` values from the model used to fit the data are used.%(cov_params_doc)s endog : array_like Duration (time) values at which the predictions are made. Only used if pred_type is either 'cumhaz' or 'surv'. If using model `exog`, defaults to model `endog` (time), but may be provided explicitly to make predictions at alternative times. strata : array_like A vector of stratum values used to form the predictions. Not used (may be 'None') if pred_type is 'lhr' or 'hr'. If `exog` is None, the model stratum values are used. If `exog` is not None and pred_type is 'surv' or 'cumhaz', stratum values must be provided (unless there is only one stratum). offset : array_like Offset values used to create the predicted values. pred_type : str If 'lhr', returns log hazard ratios, if 'hr' returns hazard ratios, if 'surv' returns the survival function, if 'cumhaz' returns the cumulative hazard function. pred_only : bool If True, returns only an array of predicted values. Otherwise returns a bunch containing the predicted values and standard errors. Returns ------- A bunch containing two fields: `predicted_values` and `standard_errors`. Notes ----- Standard errors are only returned when predicting the log hazard ratio (pred_type is 'lhr'). Types `surv` and `cumhaz` require estimation of the cumulative hazard function. """ _predict_params_doc = """ params : array_like The proportional hazards model parameters.""" _predict_cov_params_docstring = """ cov_params : array_like The covariance matrix of the estimated `params` vector, used to obtain prediction errors if pred_type='lhr', otherwise optional.""" class PHSurvivalTime(object): def __init__(self, time, status, exog, strata=None, entry=None, offset=None): """ Represent a collection of survival times with possible stratification and left truncation. Parameters ---------- time : array_like The times at which either the event (failure) occurs or the observation is censored. status : array_like Indicates whether the event (failure) occurs at `time` (`status` is 1), or if `time` is a censoring time (`status` is 0). exog : array_like The exogeneous (covariate) data matrix, cases are rows and variables are columns. strata : array_like Grouping variable defining the strata. If None, all observations are in a single stratum. entry : array_like Entry (left truncation) times. The observation is not part of the risk set for times before the entry time. If None, the entry time is treated as being zero, which gives no left truncation. The entry time must be less than or equal to `time`. offset : array_like An optional array of offsets """ # Default strata if strata is None: strata = np.zeros(len(time), dtype=np.int32) # Default entry times if entry is None: entry = np.zeros(len(time)) # Parameter validity checks. self._check(time, status, strata, entry) # Get the row indices for the cases in each stratum stu = np.unique(strata) sth = {x: [] for x in stu} for i,k in enumerate(strata): sth[k].append(i) stratum_rows = [np.asarray(sth[k], dtype=np.int32) for k in stu] stratum_names = stu # Remove strata with no events ix = [i for i,ix in enumerate(stratum_rows) if status[ix].sum() > 0] self.nstrat_orig = len(stratum_rows) stratum_rows = [stratum_rows[i] for i in ix] stratum_names = [stratum_names[i] for i in ix] # The number of strata nstrat = len(stratum_rows) self.nstrat = nstrat # Remove subjects whose entry time occurs after the last event # in their stratum. for stx,ix in enumerate(stratum_rows): last_failure = max(time[ix][status[ix] == 1]) # Stata uses < here, R uses <= ii = [i for i,t in enumerate(entry[ix]) if t <= last_failure] stratum_rows[stx] = stratum_rows[stx][ii] # Remove subjects who are censored before the first event in # their stratum. for stx,ix in enumerate(stratum_rows): first_failure = min(time[ix][status[ix] == 1]) ii = [i for i,t in enumerate(time[ix]) if t >= first_failure] stratum_rows[stx] = stratum_rows[stx][ii] # Order by time within each stratum for stx,ix in enumerate(stratum_rows): ii = np.argsort(time[ix]) stratum_rows[stx] = stratum_rows[stx][ii] if offset is not None: self.offset_s = [] for stx in range(nstrat): self.offset_s.append(offset[stratum_rows[stx]]) else: self.offset_s = None # Number of informative subjects self.n_obs = sum([len(ix) for ix in stratum_rows]) self.stratum_rows = stratum_rows self.stratum_names = stratum_names # Split everything by stratum self.time_s = self._split(time) self.exog_s = self._split(exog) self.status_s = self._split(status) self.entry_s = self._split(entry) # Precalculate some indices needed to fit Cox models. # Distinct failure times within a stratum are always taken to # be sorted in ascending order. # # ufailt_ix[stx][k] is a list of indices for subjects who fail # at the k^th sorted unique failure time in stratum stx # # risk_enter[stx][k] is a list of indices for subjects who # enter the risk set at the k^th sorted unique failure time in # stratum stx # # risk_exit[stx][k] is a list of indices for subjects who exit # the risk set at the k^th sorted unique failure time in # stratum stx self.ufailt_ix, self.risk_enter, self.risk_exit, self.ufailt =\ [], [], [], [] for stx in range(self.nstrat): # All failure times ift = np.flatnonzero(self.status_s[stx] == 1) ft = self.time_s[stx][ift] # Unique failure times uft = np.unique(ft) nuft = len(uft) # Indices of cases that fail at each unique failure time #uft_map = {x:i for i,x in enumerate(uft)} # requires >=2.7 uft_map = dict([(x, i) for i,x in enumerate(uft)]) # 2.6 uft_ix = [[] for k in range(nuft)] for ix,ti in zip(ift,ft): uft_ix[uft_map[ti]].append(ix) # Indices of cases (failed or censored) that enter the # risk set at each unique failure time. risk_enter1 = [[] for k in range(nuft)] for i,t in enumerate(self.time_s[stx]): ix = np.searchsorted(uft, t, "right") - 1 if ix >= 0: risk_enter1[ix].append(i) # Indices of cases (failed or censored) that exit the # risk set at each unique failure time. risk_exit1 = [[] for k in range(nuft)] for i,t in enumerate(self.entry_s[stx]): ix = np.searchsorted(uft, t) risk_exit1[ix].append(i) self.ufailt.append(uft) self.ufailt_ix.append([np.asarray(x, dtype=np.int32) for x in uft_ix]) self.risk_enter.append([np.asarray(x, dtype=np.int32) for x in risk_enter1]) self.risk_exit.append([np.asarray(x, dtype=np.int32) for x in risk_exit1]) def _split(self, x): v = [] if x.ndim == 1: for ix in self.stratum_rows: v.append(x[ix]) else: for ix in self.stratum_rows: v.append(x[ix, :]) return v def _check(self, time, status, strata, entry): n1, n2, n3, n4 = len(time), len(status), len(strata),\ len(entry) nv = [n1, n2, n3, n4] if max(nv) != min(nv): raise ValueError("endog, status, strata, and " + "entry must all have the same length") if min(time) < 0: raise ValueError("endog must be non-negative") if min(entry) < 0: raise ValueError("entry time must be non-negative") # In Stata, this is entry >= time, in R it is >. if np.any(entry > time): raise ValueError("entry times may not occur " + "after event or censoring times") class PHReg(model.LikelihoodModel): """ Cox Proportional Hazards Regression Model The Cox PH Model is for right censored data. Parameters ---------- endog : array_like The observed times (event or censoring) exog : 2D array_like The covariates or exogeneous variables status : array_like The censoring status values; status=1 indicates that an event occurred (e.g. failure or death), status=0 indicates that the observation was right censored. If None, defaults to status=1 for all cases. entry : array_like The entry times, if left truncation occurs strata : array_like Stratum labels. If None, all observations are taken to be in a single stratum. ties : str The method used to handle tied times, must be either 'breslow' or 'efron'. offset : array_like Array of offset values missing : str The method used to handle missing data Notes ----- Proportional hazards regression models should not include an explicit or implicit intercept. The effect of an intercept is not identified using the partial likelihood approach. `endog`, `event`, `strata`, `entry`, and the first dimension of `exog` all must have the same length """ def __init__(self, endog, exog, status=None, entry=None, strata=None, offset=None, ties='breslow', missing='drop', **kwargs): # Default is no censoring if status is None: status = np.ones(len(endog)) super(PHReg, self).__init__(endog, exog, status=status, entry=entry, strata=strata, offset=offset, missing=missing, **kwargs) # endog and exog are automatically converted, but these are # not if self.status is not None: self.status = np.asarray(self.status) if self.entry is not None: self.entry = np.asarray(self.entry) if self.strata is not None: self.strata = np.asarray(self.strata) if self.offset is not None: self.offset = np.asarray(self.offset) self.surv = PHSurvivalTime(self.endog, self.status, self.exog, self.strata, self.entry, self.offset) self.nobs = len(self.endog) self.groups = None # TODO: not used? self.missing = missing self.df_resid = float(self.exog.shape[0] - np.linalg.matrix_rank(self.exog)) self.df_model = float(np.linalg.matrix_rank(self.exog)) ties = ties.lower() if ties not in ("efron", "breslow"): raise ValueError("`ties` must be either `efron` or " + "`breslow`") self.ties = ties @classmethod def from_formula(cls, formula, data, status=None, entry=None, strata=None, offset=None, subset=None, ties='breslow', missing='drop', *args, **kwargs): """ Create a proportional hazards regression model from a formula and dataframe. Parameters ---------- formula : str or generic Formula object The formula specifying the model data : array_like The data for the model. See Notes. status : array_like The censoring status values; status=1 indicates that an event occurred (e.g. failure or death), status=0 indicates that the observation was right censored. If None, defaults to status=1 for all cases. entry : array_like The entry times, if left truncation occurs strata : array_like Stratum labels. If None, all observations are taken to be in a single stratum. offset : array_like Array of offset values subset : array_like An array-like object of booleans, integers, or index values that indicate the subset of df to use in the model. Assumes df is a `pandas.DataFrame` ties : str The method used to handle tied times, must be either 'breslow' or 'efron'. missing : str The method used to handle missing data args : extra arguments These are passed to the model kwargs : extra keyword arguments These are passed to the model with one exception. The ``eval_env`` keyword is passed to patsy. It can be either a :class:`patsy:patsy.EvalEnvironment` object or an integer indicating the depth of the namespace to use. For example, the default ``eval_env=0`` uses the calling namespace. If you wish to use a "clean" environment set ``eval_env=-1``. Returns ------- model : PHReg model instance """ # Allow array arguments to be passed by column name. if isinstance(status, str): status = data[status] if isinstance(entry, str): entry = data[entry] if isinstance(strata, str): strata = data[strata] if isinstance(offset, str): offset = data[offset] import re terms = re.split(r"[+\-~]", formula) for term in terms: term = term.strip() if term in ("0", "1"): import warnings warnings.warn("PHReg formulas should not include any '0' or '1' terms") mod = super(PHReg, cls).from_formula(formula, data, status=status, entry=entry, strata=strata, offset=offset, subset=subset, ties=ties, missing=missing, drop_cols=["Intercept"], *args, **kwargs) return mod def fit(self, groups=None, **args): """ Fit a proportional hazards regression model. Parameters ---------- groups : array_like Labels indicating groups of observations that may be dependent. If present, the standard errors account for this dependence. Does not affect fitted values. Returns ------- PHRegResults Returns a results instance. """ # TODO process for missing values if groups is not None: if len(groups) != len(self.endog): msg = ("len(groups) = %d and len(endog) = %d differ" % (len(groups), len(self.endog))) raise ValueError(msg) self.groups = np.asarray(groups) else: self.groups = None if 'disp' not in args: args['disp'] = False fit_rslts = super(PHReg, self).fit(**args) if self.groups is None: cov_params = fit_rslts.cov_params() else: cov_params = self.robust_covariance(fit_rslts.params) results = PHRegResults(self, fit_rslts.params, cov_params) return results def fit_regularized(self, method="elastic_net", alpha=0., start_params=None, refit=False, **kwargs): r""" Return a regularized fit to a linear regression model. Parameters ---------- method : {'elastic_net'} Only the `elastic_net` approach is currently implemented. alpha : scalar or array_like The penalty weight. If a scalar, the same penalty weight applies to all variables in the model. If a vector, it must have the same length as `params`, and contains a penalty weight for each coefficient. start_params : array_like Starting values for `params`. refit : bool If True, the model is refit using only the variables that have non-zero coefficients in the regularized fit. The refitted model is not regularized. **kwargs Additional keyword arguments used to fit the model. Returns ------- PHRegResults Returns a results instance. Notes ----- The penalty is the ``elastic net`` penalty, which is a combination of L1 and L2 penalties. The function that is minimized is: .. math:: -loglike/n + alpha*((1-L1\_wt)*|params|_2^2/2 + L1\_wt*|params|_1) where :math:`|*|_1` and :math:`|*|_2` are the L1 and L2 norms. Post-estimation results are based on the same data used to select variables, hence may be subject to overfitting biases. The elastic_net method uses the following keyword arguments: maxiter : int Maximum number of iterations L1_wt : float Must be in [0, 1]. The L1 penalty has weight L1_wt and the L2 penalty has weight 1 - L1_wt. cnvrg_tol : float Convergence threshold for line searches zero_tol : float Coefficients below this threshold are treated as zero. """ from statsmodels.base.elastic_net import fit_elasticnet if method != "elastic_net": raise ValueError("method for fit_regularied must be elastic_net") defaults = {"maxiter" : 50, "L1_wt" : 1, "cnvrg_tol" : 1e-10, "zero_tol" : 1e-10} defaults.update(kwargs) return fit_elasticnet(self, method=method, alpha=alpha, start_params=start_params, refit=refit, **defaults) def loglike(self, params): """ Returns the log partial likelihood function evaluated at `params`. """ if self.ties == "breslow": return self.breslow_loglike(params) elif self.ties == "efron": return self.efron_loglike(params) def score(self, params): """ Returns the score function evaluated at `params`. """ if self.ties == "breslow": return self.breslow_gradient(params) elif self.ties == "efron": return self.efron_gradient(params) def hessian(self, params): """ Returns the Hessian matrix of the log partial likelihood function evaluated at `params`. """ if self.ties == "breslow": return self.breslow_hessian(params) else: return self.efron_hessian(params) def breslow_loglike(self, params): """ Returns the value of the log partial likelihood function evaluated at `params`, using the Breslow method to handle tied times. """ surv = self.surv like = 0. # Loop over strata for stx in range(surv.nstrat): uft_ix = surv.ufailt_ix[stx] exog_s = surv.exog_s[stx] nuft = len(uft_ix) linpred = np.dot(exog_s, params) if surv.offset_s is not None: linpred += surv.offset_s[stx] linpred -= linpred.max() e_linpred = np.exp(linpred) xp0 = 0. # Iterate backward through the unique failure times. for i in range(nuft)[::-1]: # Update for new cases entering the risk set. ix = surv.risk_enter[stx][i] xp0 += e_linpred[ix].sum() # Account for all cases that fail at this point. ix = uft_ix[i] like += (linpred[ix] - np.log(xp0)).sum() # Update for cases leaving the risk set. ix = surv.risk_exit[stx][i] xp0 -= e_linpred[ix].sum() return like def efron_loglike(self, params): """ Returns the value of the log partial likelihood function evaluated at `params`, using the Efron method to handle tied times. """ surv = self.surv like = 0. # Loop over strata for stx in range(surv.nstrat): # exog and linear predictor for this stratum exog_s = surv.exog_s[stx] linpred = np.dot(exog_s, params) if surv.offset_s is not None: linpred += surv.offset_s[stx] linpred -= linpred.max() e_linpred = np.exp(linpred) xp0 = 0. # Iterate backward through the unique failure times. uft_ix = surv.ufailt_ix[stx] nuft = len(uft_ix) for i in range(nuft)[::-1]: # Update for new cases entering the risk set. ix = surv.risk_enter[stx][i] xp0 += e_linpred[ix].sum() xp0f = e_linpred[uft_ix[i]].sum() # Account for all cases that fail at this point. ix = uft_ix[i] like += linpred[ix].sum() m = len(ix) J = np.arange(m, dtype=np.float64) / m like -= np.log(xp0 - J*xp0f).sum() # Update for cases leaving the risk set. ix = surv.risk_exit[stx][i] xp0 -= e_linpred[ix].sum() return like def breslow_gradient(self, params): """ Returns the gradient of the log partial likelihood, using the Breslow method to handle tied times. """ surv = self.surv grad = 0. # Loop over strata for stx in range(surv.nstrat): # Indices of subjects in the stratum strat_ix = surv.stratum_rows[stx] # Unique failure times in the stratum uft_ix = surv.ufailt_ix[stx] nuft = len(uft_ix) # exog and linear predictor for the stratum exog_s = surv.exog_s[stx] linpred = np.dot(exog_s, params) if surv.offset_s is not None: linpred += surv.offset_s[stx] linpred -= linpred.max() e_linpred = np.exp(linpred) xp0, xp1 = 0., 0. # Iterate backward through the unique failure times. for i in range(nuft)[::-1]: # Update for new cases entering the risk set. ix = surv.risk_enter[stx][i] if len(ix) > 0: v = exog_s[ix,:] xp0 += e_linpred[ix].sum() xp1 += (e_linpred[ix][:,None] * v).sum(0) # Account for all cases that fail at this point. ix = uft_ix[i] grad += (exog_s[ix,:] - xp1 / xp0).sum(0) # Update for cases leaving the risk set. ix = surv.risk_exit[stx][i] if len(ix) > 0: v = exog_s[ix,:] xp0 -= e_linpred[ix].sum() xp1 -= (e_linpred[ix][:,None] * v).sum(0) return grad def efron_gradient(self, params): """ Returns the gradient of the log partial likelihood evaluated at `params`, using the Efron method to handle tied times. """ surv = self.surv grad = 0. # Loop over strata for stx in range(surv.nstrat): # Indices of cases in the stratum strat_ix = surv.stratum_rows[stx] # exog and linear predictor of the stratum exog_s = surv.exog_s[stx] linpred = np.dot(exog_s, params) if surv.offset_s is not None: linpred += surv.offset_s[stx] linpred -= linpred.max() e_linpred = np.exp(linpred) xp0, xp1 = 0., 0. # Iterate backward through the unique failure times. uft_ix = surv.ufailt_ix[stx] nuft = len(uft_ix) for i in range(nuft)[::-1]: # Update for new cases entering the risk set. ix = surv.risk_enter[stx][i] if len(ix) > 0: v = exog_s[ix,:] xp0 += e_linpred[ix].sum() xp1 += (e_linpred[ix][:,None] * v).sum(0) ixf = uft_ix[i] if len(ixf) > 0: v = exog_s[ixf,:] xp0f = e_linpred[ixf].sum() xp1f = (e_linpred[ixf][:,None] * v).sum(0) # Consider all cases that fail at this point. grad += v.sum(0) m = len(ixf) J = np.arange(m, dtype=np.float64) / m numer = xp1 - np.outer(J, xp1f) denom = xp0 - np.outer(J, xp0f) ratio = numer / denom rsum = ratio.sum(0) grad -= rsum # Update for cases leaving the risk set. ix = surv.risk_exit[stx][i] if len(ix) > 0: v = exog_s[ix,:] xp0 -= e_linpred[ix].sum() xp1 -= (e_linpred[ix][:,None] * v).sum(0) return grad def breslow_hessian(self, params): """ Returns the Hessian of the log partial likelihood evaluated at `params`, using the Breslow method to handle tied times. """ surv = self.surv hess = 0. # Loop over strata for stx in range(surv.nstrat): uft_ix = surv.ufailt_ix[stx] nuft = len(uft_ix) exog_s = surv.exog_s[stx] linpred = np.dot(exog_s, params) if surv.offset_s is not None: linpred += surv.offset_s[stx] linpred -= linpred.max() e_linpred = np.exp(linpred) xp0, xp1, xp2 = 0., 0., 0. # Iterate backward through the unique failure times. for i in range(nuft)[::-1]: # Update for new cases entering the risk set. ix = surv.risk_enter[stx][i] if len(ix) > 0: xp0 += e_linpred[ix].sum() v = exog_s[ix,:] xp1 += (e_linpred[ix][:,None] * v).sum(0) elx = e_linpred[ix] xp2 += np.einsum("ij,ik,i->jk", v, v, elx) # Account for all cases that fail at this point. m = len(uft_ix[i]) hess += m*(xp2 / xp0 - np.outer(xp1, xp1) / xp0**2) # Update for new cases entering the risk set. ix = surv.risk_exit[stx][i] if len(ix) > 0: xp0 -= e_linpred[ix].sum() v = exog_s[ix,:] xp1 -= (e_linpred[ix][:,None] * v).sum(0) elx = e_linpred[ix] xp2 -= np.einsum("ij,ik,i->jk", v, v, elx) return -hess def efron_hessian(self, params): """ Returns the Hessian matrix of the partial log-likelihood evaluated at `params`, using the Efron method to handle tied times. """ surv = self.surv hess = 0. # Loop over strata for stx in range(surv.nstrat): exog_s = surv.exog_s[stx] linpred = np.dot(exog_s, params) if surv.offset_s is not None: linpred += surv.offset_s[stx] linpred -= linpred.max() e_linpred = np.exp(linpred) xp0, xp1, xp2 = 0., 0., 0. # Iterate backward through the unique failure times. uft_ix = surv.ufailt_ix[stx] nuft = len(uft_ix) for i in range(nuft)[::-1]: # Update for new cases entering the risk set. ix = surv.risk_enter[stx][i] if len(ix) > 0: xp0 += e_linpred[ix].sum() v = exog_s[ix,:] xp1 += (e_linpred[ix][:,None] * v).sum(0) elx = e_linpred[ix] xp2 += np.einsum("ij,ik,i->jk", v, v, elx) ixf = uft_ix[i] if len(ixf) > 0: v = exog_s[ixf,:] xp0f = e_linpred[ixf].sum() xp1f = (e_linpred[ixf][:,None] * v).sum(0) elx = e_linpred[ixf] xp2f = np.einsum("ij,ik,i->jk", v, v, elx) # Account for all cases that fail at this point. m = len(uft_ix[i]) J = np.arange(m, dtype=np.float64) / m c0 = xp0 - J*xp0f hess += xp2 * np.sum(1 / c0) hess -= xp2f * np.sum(J / c0) mat = (xp1[None, :] - np.outer(J, xp1f)) / c0[:, None] hess -= np.einsum("ij,ik->jk", mat, mat) # Update for new cases entering the risk set. ix = surv.risk_exit[stx][i] if len(ix) > 0: xp0 -= e_linpred[ix].sum() v = exog_s[ix,:] xp1 -= (e_linpred[ix][:,None] * v).sum(0) elx = e_linpred[ix] xp2 -= np.einsum("ij,ik,i->jk", v, v, elx) return -hess def robust_covariance(self, params): """ Returns a covariance matrix for the proportional hazards model regresion coefficient estimates that is robust to certain forms of model misspecification. Parameters ---------- params : ndarray The parameter vector at which the covariance matrix is calculated. Returns ------- The robust covariance matrix as a square ndarray. Notes ----- This function uses the `groups` argument to determine groups within which observations may be dependent. The covariance matrix is calculated using the Huber-White "sandwich" approach. """ if self.groups is None: raise ValueError("`groups` must be specified to calculate the robust covariance matrix") hess = self.hessian(params) score_obs = self.score_residuals(params) # Collapse grads = {} for i,g in enumerate(self.groups): if g not in grads: grads[g] = 0. grads[g] += score_obs[i, :] grads = np.asarray(list(grads.values())) mat = grads[None, :, :] mat = mat.T * mat mat = mat.sum(1) hess_inv = np.linalg.inv(hess) cmat = np.dot(hess_inv, np.dot(mat, hess_inv)) return cmat def score_residuals(self, params): """ Returns the score residuals calculated at a given vector of parameters. Parameters ---------- params : ndarray The parameter vector at which the score residuals are calculated. Returns ------- The score residuals, returned as a ndarray having the same shape as `exog`. Notes ----- Observations in a stratum with no observed events have undefined score residuals, and contain NaN in the returned matrix. """ surv = self.surv score_resid = np.zeros(self.exog.shape, dtype=np.float64) # Use to set undefined values to NaN. mask = np.zeros(self.exog.shape[0], dtype=np.int32) w_avg = self.weighted_covariate_averages(params) # Loop over strata for stx in range(surv.nstrat): uft_ix = surv.ufailt_ix[stx] exog_s = surv.exog_s[stx] nuft = len(uft_ix) strat_ix = surv.stratum_rows[stx] xp0 = 0. linpred = np.dot(exog_s, params) if surv.offset_s is not None: linpred += surv.offset_s[stx] linpred -= linpred.max() e_linpred = np.exp(linpred) at_risk_ix = set([]) # Iterate backward through the unique failure times. for i in range(nuft)[::-1]: # Update for new cases entering the risk set. ix = surv.risk_enter[stx][i] at_risk_ix |= set(ix) xp0 += e_linpred[ix].sum() atr_ix = list(at_risk_ix) leverage = exog_s[atr_ix, :] - w_avg[stx][i, :] # Event indicators d = np.zeros(exog_s.shape[0]) d[uft_ix[i]] = 1 # The increment in the cumulative hazard dchaz = len(uft_ix[i]) / xp0 # Piece of the martingale residual mrp = d[atr_ix] - e_linpred[atr_ix] * dchaz # Update the score residuals ii = strat_ix[atr_ix] score_resid[ii,:] += leverage * mrp[:, None] mask[ii] = 1 # Update for cases leaving the risk set. ix = surv.risk_exit[stx][i] at_risk_ix -= set(ix) xp0 -= e_linpred[ix].sum() jj = np.flatnonzero(mask == 0) if len(jj) > 0: score_resid[jj, :] = np.nan return score_resid def weighted_covariate_averages(self, params): """ Returns the hazard-weighted average of covariate values for subjects who are at-risk at a particular time. Parameters ---------- params : ndarray Parameter vector Returns ------- averages : list of ndarrays averages[stx][i,:] is a row vector containing the weighted average values (for all the covariates) of at-risk subjects a the i^th largest observed failure time in stratum `stx`, using the hazard multipliers as weights. Notes ----- Used to calculate leverages and score residuals. """ surv = self.surv averages = [] xp0, xp1 = 0., 0. # Loop over strata for stx in range(surv.nstrat): uft_ix = surv.ufailt_ix[stx] exog_s = surv.exog_s[stx] nuft = len(uft_ix) average_s = np.zeros((len(uft_ix), exog_s.shape[1]), dtype=np.float64) linpred = np.dot(exog_s, params) if surv.offset_s is not None: linpred += surv.offset_s[stx] linpred -= linpred.max() e_linpred = np.exp(linpred) # Iterate backward through the unique failure times. for i in range(nuft)[::-1]: # Update for new cases entering the risk set. ix = surv.risk_enter[stx][i] xp0 += e_linpred[ix].sum() xp1 += np.dot(e_linpred[ix], exog_s[ix, :]) average_s[i, :] = xp1 / xp0 # Update for cases leaving the risk set. ix = surv.risk_exit[stx][i] xp0 -= e_linpred[ix].sum() xp1 -= np.dot(e_linpred[ix], exog_s[ix, :]) averages.append(average_s) return averages def baseline_cumulative_hazard(self, params): """ Estimate the baseline cumulative hazard and survival functions. Parameters ---------- params : ndarray The model parameters. Returns ------- A list of triples (time, hazard, survival) containing the time values and corresponding cumulative hazard and survival function values for each stratum. Notes ----- Uses the Nelson-Aalen estimator. """ # TODO: some disagreements with R, not the same algorithm but # hard to deduce what R is doing. Our results are reasonable. surv = self.surv rslt = [] # Loop over strata for stx in range(surv.nstrat): uft = surv.ufailt[stx] uft_ix = surv.ufailt_ix[stx] exog_s = surv.exog_s[stx] nuft = len(uft_ix) linpred = np.dot(exog_s, params) if surv.offset_s is not None: linpred += surv.offset_s[stx] e_linpred = np.exp(linpred) xp0 = 0. h0 = np.zeros(nuft, dtype=np.float64) # Iterate backward through the unique failure times. for i in range(nuft)[::-1]: # Update for new cases entering the risk set. ix = surv.risk_enter[stx][i] xp0 += e_linpred[ix].sum() # Account for all cases that fail at this point. ix = uft_ix[i] h0[i] = len(ix) / xp0 # Update for cases leaving the risk set. ix = surv.risk_exit[stx][i] xp0 -= e_linpred[ix].sum() cumhaz = np.cumsum(h0) - h0 current_strata_surv = np.exp(-cumhaz) rslt.append([uft, cumhaz, current_strata_surv]) return rslt def baseline_cumulative_hazard_function(self, params): """ Returns a function that calculates the baseline cumulative hazard function for each stratum. Parameters ---------- params : ndarray The model parameters. Returns ------- A dict mapping stratum names to the estimated baseline cumulative hazard function. """ from scipy.interpolate import interp1d surv = self.surv base = self.baseline_cumulative_hazard(params) cumhaz_f = {} for stx in range(surv.nstrat): time_h = base[stx][0] cumhaz = base[stx][1] time_h = np.r_[-np.inf, time_h, np.inf] cumhaz = np.r_[cumhaz[0], cumhaz, cumhaz[-1]] func = interp1d(time_h, cumhaz, kind='zero') cumhaz_f[self.surv.stratum_names[stx]] = func return cumhaz_f @Appender(_predict_docstring % { 'params_doc': _predict_params_doc, 'cov_params_doc': _predict_cov_params_docstring}) def predict(self, params, exog=None, cov_params=None, endog=None, strata=None, offset=None, pred_type="lhr", pred_only=False): # This function breaks mediation, because it does not simply # return the predicted values as an array. pred_type = pred_type.lower() if pred_type not in ["lhr", "hr", "surv", "cumhaz"]: msg = "Type %s not allowed for prediction" % pred_type raise ValueError(msg) class bunch: predicted_values = None standard_errors = None ret_val = bunch() # Do not do anything with offset here because we want to allow # different offsets to be specified even if exog is the model # exog. exog_provided = True if exog is None: exog = self.exog exog_provided = False lhr = np.dot(exog, params) if offset is not None: lhr += offset # Never use self.offset unless we are also using self.exog elif self.offset is not None and not exog_provided: lhr += self.offset # Handle lhr and hr prediction first, since they do not make # use of the hazard function. if pred_type == "lhr": ret_val.predicted_values = lhr if cov_params is not None: mat = np.dot(exog, cov_params) va = (mat * exog).sum(1) ret_val.standard_errors = np.sqrt(va) if pred_only: return ret_val.predicted_values return ret_val hr = np.exp(lhr) if pred_type == "hr": ret_val.predicted_values = hr if pred_only: return ret_val.predicted_values return ret_val # Makes sure endog is defined if endog is None and exog_provided: msg = "If `exog` is provided `endog` must be provided." raise ValueError(msg) # Use model endog if using model exog elif endog is None and not exog_provided: endog = self.endog # Make sure strata is defined if strata is None: if exog_provided and self.surv.nstrat > 1: raise ValueError("`strata` must be provided") if self.strata is None: strata = [self.surv.stratum_names[0],] * len(endog) else: strata = self.strata cumhaz = np.nan * np.ones(len(endog), dtype=np.float64) stv = np.unique(strata) bhaz = self.baseline_cumulative_hazard_function(params) for stx in stv: ix = np.flatnonzero(strata == stx) func = bhaz[stx] cumhaz[ix] = func(endog[ix]) * hr[ix] if pred_type == "cumhaz": ret_val.predicted_values = cumhaz elif pred_type == "surv": ret_val.predicted_values = np.exp(-cumhaz) if pred_only: return ret_val.predicted_values return ret_val def get_distribution(self, params, scale=1.0, exog=None): """ Returns a scipy distribution object corresponding to the distribution of uncensored endog (duration) values for each case. Parameters ---------- params : array_like The proportional hazards model parameters. scale : float Present for compatibility, not used. exog : array_like A design matrix, defaults to model.exog. Returns ------- A list of objects of type scipy.stats.distributions.rv_discrete Notes ----- The distributions are obtained from a simple discrete estimate of the survivor function that puts all mass on the observed failure times within a stratum. """ surv = self.surv bhaz = self.baseline_cumulative_hazard(params) # The arguments to rv_discrete_float, first obtained by # stratum pk, xk = [], [] if exog is None: exog_split = surv.exog_s else: exog_split = self.surv._split(exog) for stx in range(self.surv.nstrat): exog_s = exog_split[stx] linpred = np.dot(exog_s, params) if surv.offset_s is not None: linpred += surv.offset_s[stx] e_linpred = np.exp(linpred) # The unique failure times for this stratum (the support # of the distribution). pts = bhaz[stx][0] # The individual cumulative hazards for everyone in this # stratum. ichaz = np.outer(e_linpred, bhaz[stx][1]) # The individual survival functions. usurv = np.exp(-ichaz) z = np.zeros((usurv.shape[0], 1)) usurv = np.concatenate((usurv, z), axis=1) # The individual survival probability masses. probs = -np.diff(usurv, 1) pk.append(probs) xk.append(np.outer(np.ones(probs.shape[0]), pts)) # Pad to make all strata have the same shape mxc = max([x.shape[1] for x in xk]) for k in range(self.surv.nstrat): if xk[k].shape[1] < mxc: xk1 = np.zeros((xk[k].shape[0], mxc)) pk1 = np.zeros((pk[k].shape[0], mxc)) xk1[:, 0:xk[k].shape[1]] = xk[k] pk1[:, 0:pk[k].shape[1]] = pk[k] xk[k], pk[k] = xk1, pk1 # Put the support points and probabilities into single matrices xka = np.nan * np.ones((len(self.endog), mxc)) pka = np.ones((len(self.endog), mxc), dtype=np.float64) / mxc for stx in range(self.surv.nstrat): ix = self.surv.stratum_rows[stx] xka[ix, :] = xk[stx] pka[ix, :] = pk[stx] dist = rv_discrete_float(xka, pka) return dist class PHRegResults(base.LikelihoodModelResults): ''' Class to contain results of fitting a Cox proportional hazards survival model. PHregResults inherits from statsmodels.LikelihoodModelResults Parameters ---------- See statsmodels.LikelihoodModelResults Attributes ---------- model : class instance PHreg model instance that called fit. normalized_cov_params : ndarray The sampling covariance matrix of the estimates params : ndarray The coefficients of the fitted model. Each coefficient is the log hazard ratio corresponding to a 1 unit difference in a single covariate while holding the other covariates fixed. bse : ndarray The standard errors of the fitted parameters. See Also -------- statsmodels.LikelihoodModelResults ''' def __init__(self, model, params, cov_params, scale=1., covariance_type="naive"): # There is no scale parameter, but we need it for # meta-procedures that work with results. self.covariance_type = covariance_type self.df_resid = model.df_resid self.df_model = model.df_model super(PHRegResults, self).__init__(model, params, scale=1., normalized_cov_params=cov_params) @cache_readonly def standard_errors(self): """ Returns the standard errors of the parameter estimates. """ return np.sqrt(np.diag(self.cov_params())) @cache_readonly def bse(self): """ Returns the standard errors of the parameter estimates. """ return self.standard_errors def get_distribution(self): """ Returns a scipy distribution object corresponding to the distribution of uncensored endog (duration) values for each case. Returns ------- A list of objects of type scipy.stats.distributions.rv_discrete Notes ----- The distributions are obtained from a simple discrete estimate of the survivor function that puts all mass on the observed failure times within a stratum. """ return self.model.get_distribution(self.params) @Appender(_predict_docstring % {'params_doc': '', 'cov_params_doc': ''}) def predict(self, endog=None, exog=None, strata=None, offset=None, transform=True, pred_type="lhr"): return super(PHRegResults, self).predict(exog=exog, transform=transform, cov_params=self.cov_params(), endog=endog, strata=strata, offset=offset, pred_type=pred_type) def _group_stats(self, groups): """ Descriptive statistics of the groups. """ gsizes = np.unique(groups, return_counts=True) gsizes = gsizes[1] return gsizes.min(), gsizes.max(), gsizes.mean(), len(gsizes) @cache_readonly def weighted_covariate_averages(self): """ The average covariate values within the at-risk set at each event time point, weighted by hazard. """ return self.model.weighted_covariate_averages(self.params) @cache_readonly def score_residuals(self): """ A matrix containing the score residuals. """ return self.model.score_residuals(self.params) @cache_readonly def baseline_cumulative_hazard(self): """ A list (corresponding to the strata) containing the baseline cumulative hazard function evaluated at the event points. """ return self.model.baseline_cumulative_hazard(self.params) @cache_readonly def baseline_cumulative_hazard_function(self): """ A list (corresponding to the strata) containing function objects that calculate the cumulative hazard function. """ return self.model.baseline_cumulative_hazard_function(self.params) @cache_readonly def schoenfeld_residuals(self): """ A matrix containing the Schoenfeld residuals. Notes ----- Schoenfeld residuals for censored observations are set to zero. """ surv = self.model.surv w_avg = self.weighted_covariate_averages # Initialize at NaN since rows that belong to strata with no # events have undefined residuals. sch_resid = np.nan*np.ones(self.model.exog.shape, dtype=np.float64) # Loop over strata for stx in range(surv.nstrat): uft = surv.ufailt[stx] exog_s = surv.exog_s[stx] time_s = surv.time_s[stx] strat_ix = surv.stratum_rows[stx] ii = np.searchsorted(uft, time_s) # These subjects are censored after the last event in # their stratum, so have empty risk sets and undefined # residuals. jj = np.flatnonzero(ii < len(uft)) sch_resid[strat_ix[jj], :] = exog_s[jj, :] - w_avg[stx][ii[jj], :] jj = np.flatnonzero(self.model.status == 0) sch_resid[jj, :] = np.nan return sch_resid @cache_readonly def martingale_residuals(self): """ The martingale residuals. """ surv = self.model.surv # Initialize at NaN since rows that belong to strata with no # events have undefined residuals. mart_resid = np.nan*np.ones(len(self.model.endog), dtype=np.float64) cumhaz_f_list = self.baseline_cumulative_hazard_function # Loop over strata for stx in range(surv.nstrat): cumhaz_f = cumhaz_f_list[stx] exog_s = surv.exog_s[stx] time_s = surv.time_s[stx] linpred = np.dot(exog_s, self.params) if surv.offset_s is not None: linpred += surv.offset_s[stx] e_linpred = np.exp(linpred) ii = surv.stratum_rows[stx] chaz = cumhaz_f(time_s) mart_resid[ii] = self.model.status[ii] - e_linpred * chaz return mart_resid def summary(self, yname=None, xname=None, title=None, alpha=.05): """ Summarize the proportional hazards regression results. Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Names for the exogenous variables, default is `x#` for ## in p the number of regressors. Must match the number of parameters in the model title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary2.Summary : class to hold summary results """ from statsmodels.iolib import summary2 smry = summary2.Summary() float_format = "%8.3f" info = {} info["Model:"] = "PH Reg" if yname is None: yname = self.model.endog_names info["Dependent variable:"] = yname info["Ties:"] = self.model.ties.capitalize() info["Sample size:"] = str(self.model.surv.n_obs) info["Num. events:"] = str(int(sum(self.model.status))) if self.model.groups is not None: mn, mx, avg, num = self._group_stats(self.model.groups) info["Num groups:"] = "%.0f" % num info["Min group size:"] = "%.0f" % mn info["Max group size:"] = "%.0f" % mx info["Avg group size:"] = "%.1f" % avg if self.model.strata is not None: mn, mx, avg, num = self._group_stats(self.model.strata) info["Num strata:"] = "%.0f" % num info["Min stratum size:"] = "%.0f" % mn info["Max stratum size:"] = "%.0f" % mx info["Avg stratum size:"] = "%.1f" % avg smry.add_dict(info, align='l', float_format=float_format) param = summary2.summary_params(self, alpha=alpha) param = param.rename(columns={"Coef.": "log HR", "Std.Err.": "log HR SE"}) param.insert(2, "HR", np.exp(param["log HR"])) a = "[%.3f" % (alpha / 2) param.loc[:, a] = np.exp(param.loc[:, a]) a = "%.3f]" % (1 - alpha / 2) param.loc[:, a] = np.exp(param.loc[:, a]) if xname is not None: param.index = xname smry.add_df(param, float_format=float_format) smry.add_title(title=title, results=self) smry.add_text("Confidence intervals are for the hazard ratios") dstrat = self.model.surv.nstrat_orig - self.model.surv.nstrat if dstrat > 0: if dstrat == 1: smry.add_text("1 stratum dropped for having no events") else: smry.add_text("%d strata dropped for having no events" % dstrat) if self.model.entry is not None: n_entry = sum(self.model.entry != 0) if n_entry == 1: smry.add_text("1 observation has a positive entry time") else: smry.add_text("%d observations have positive entry times" % n_entry) if self.model.groups is not None: smry.add_text("Standard errors account for dependence within groups") if hasattr(self, "regularized"): smry.add_text("Standard errors do not account for the regularization") return smry class rv_discrete_float(object): """ A class representing a collection of discrete distributions. Parameters ---------- xk : 2d array_like The support points, should be non-decreasing within each row. pk : 2d array_like The probabilities, should sum to one within each row. Notes ----- Each row of `xk`, and the corresponding row of `pk` describe a discrete distribution. `xk` and `pk` should both be two-dimensional ndarrays. Each row of `pk` should sum to 1. This class is used as a substitute for scipy.distributions. rv_discrete, since that class does not allow non-integer support points, or vectorized operations. Only a limited number of methods are implemented here compared to the other scipy distribution classes. """ def __init__(self, xk, pk): self.xk = xk self.pk = pk self.cpk = np.cumsum(self.pk, axis=1) def rvs(self, n=None): """ Returns a random sample from the discrete distribution. A vector is returned containing a single draw from each row of `xk`, using the probabilities of the corresponding row of `pk` Parameters ---------- n : not used Present for signature compatibility """ n = self.xk.shape[0] u = np.random.uniform(size=n) ix = (self.cpk < u[:, None]).sum(1) ii = np.arange(n, dtype=np.int32) return self.xk[(ii,ix)] def mean(self): """ Returns a vector containing the mean values of the discrete distributions. A vector is returned containing the mean value of each row of `xk`, using the probabilities in the corresponding row of `pk`. """ return (self.xk * self.pk).sum(1) def var(self): """ Returns a vector containing the variances of the discrete distributions. A vector is returned containing the variance for each row of `xk`, using the probabilities in the corresponding row of `pk`. """ mn = self.mean() xkc = self.xk - mn[:, None] return (self.pk * (self.xk - xkc)**2).sum(1) def std(self): """ Returns a vector containing the standard deviations of the discrete distributions. A vector is returned containing the standard deviation for each row of `xk`, using the probabilities in the corresponding row of `pk`. """ return np.sqrt(self.var()) statsmodels-0.12.2/statsmodels/duration/survfunc.py000066400000000000000000000651651400612667500225760ustar00rootroot00000000000000import numpy as np import pandas as pd from scipy.stats.distributions import chi2, norm from statsmodels.graphics import utils def _calc_survfunc_right(time, status, weights=None, entry=None, compress=True, retall=True): """ Calculate the survival function and its standard error for a single group. """ # Convert the unique times to ranks (0, 1, 2, ...) if entry is None: utime, rtime = np.unique(time, return_inverse=True) else: tx = np.concatenate((time, entry)) utime, rtime = np.unique(tx, return_inverse=True) rtime = rtime[0:len(time)] # Number of deaths at each unique time. ml = len(utime) if weights is None: d = np.bincount(rtime, weights=status, minlength=ml) else: d = np.bincount(rtime, weights=status*weights, minlength=ml) # Size of risk set just prior to each event time. if weights is None: n = np.bincount(rtime, minlength=ml) else: n = np.bincount(rtime, weights=weights, minlength=ml) if entry is not None: n = np.cumsum(n) - n rentry = np.searchsorted(utime, entry, side='left') if weights is None: n0 = np.bincount(rentry, minlength=ml) else: n0 = np.bincount(rentry, weights=weights, minlength=ml) n0 = np.cumsum(n0) - n0 n = n0 - n else: n = np.cumsum(n[::-1])[::-1] # Only retain times where an event occurred. if compress: ii = np.flatnonzero(d > 0) d = d[ii] n = n[ii] utime = utime[ii] # The survival function probabilities. sp = 1 - d / n.astype(np.float64) ii = sp < 1e-16 sp[ii] = 1e-16 sp = np.log(sp) sp = np.cumsum(sp) sp = np.exp(sp) sp[ii] = 0 if not retall: return sp, utime, rtime, n, d # Standard errors if weights is None: # Greenwood's formula denom = n * (n - d) denom = np.clip(denom, 1e-12, np.inf) se = d / denom.astype(np.float64) se[(n == d) | (n == 0)] = np.nan se = np.cumsum(se) se = np.sqrt(se) locs = np.isfinite(se) | (sp != 0) se[locs] *= sp[locs] se[~locs] = np.nan else: # Tsiatis' (1981) formula se = d / (n * n).astype(np.float64) se = np.cumsum(se) se = np.sqrt(se) return sp, se, utime, rtime, n, d def _calc_incidence_right(time, status, weights=None): """ Calculate the cumulative incidence function and its standard error. """ # Calculate the all-cause survival function. status0 = (status >= 1).astype(np.float64) sp, utime, rtime, n, d = _calc_survfunc_right(time, status0, weights, compress=False, retall=False) ngrp = int(status.max()) # Number of cause-specific deaths at each unique time. d = [] for k in range(ngrp): status0 = (status == k + 1).astype(np.float64) if weights is None: d0 = np.bincount(rtime, weights=status0, minlength=len(utime)) else: d0 = np.bincount(rtime, weights=status0*weights, minlength=len(utime)) d.append(d0) # The cumulative incidence function probabilities. ip = [] sp0 = np.r_[1, sp[:-1]] / n for k in range(ngrp): ip0 = np.cumsum(sp0 * d[k]) ip.append(ip0) # The standard error of the cumulative incidence function. if weights is not None: return ip, None, utime se = [] da = sum(d) for k in range(ngrp): ra = da / (n * (n - da)) v = ip[k]**2 * np.cumsum(ra) v -= 2 * ip[k] * np.cumsum(ip[k] * ra) v += np.cumsum(ip[k]**2 * ra) ra = (n - d[k]) * d[k] / n v += np.cumsum(sp0**2 * ra) ra = sp0 * d[k] / n v -= 2 * ip[k] * np.cumsum(ra) v += 2 * np.cumsum(ip[k] * ra) se.append(np.sqrt(v)) return ip, se, utime def _checkargs(time, status, entry, freq_weights, exog): if len(time) != len(status): raise ValueError("time and status must have the same length") if entry is not None and (len(entry) != len(time)): msg = "entry times and event times must have the same length" raise ValueError(msg) if entry is not None and np.any(entry >= time): msg = "Entry times must not occur on or after event times" raise ValueError(msg) if freq_weights is not None and (len(freq_weights) != len(time)): raise ValueError("weights, time and status must have the same length") if exog is not None and (exog.shape[0] != len(time)): raise ValueError("the rows of exog should align with time") class CumIncidenceRight(object): """ Estimation and inference for a cumulative incidence function. If J = 1, 2, ... indicates the event type, the cumulative incidence function for cause j is: I(t, j) = P(T <= t and J=j) Only right censoring is supported. If frequency weights are provided, the point estimate is returned without a standard error. Parameters ---------- time : array_like An array of times (censoring times or event times) status : array_like If status >= 1 indicates which event occurred at time t. If status = 0, the subject was censored at time t. title : str Optional title used for plots and summary output. freq_weights : array_like Optional frequency weights exog : array_like Optional, if present used to account for violation of independent censoring. bw_factor : float Band-width multiplier for kernel-based estimation. Only used if exog is provided. dimred : bool If True, proportional hazards regression models are used to reduce exog to two columns by predicting overall events and censoring in two separate models. If False, exog is used directly for calculating kernel weights without dimension reduction. Attributes ---------- times : array_like The distinct times at which the incidence rates are estimated cinc : list of arrays cinc[k-1] contains the estimated cumulative incidence rates for outcome k=1,2,... cinc_se : list of arrays The standard errors for the values in `cinc`. Not available when exog and/or frequency weights are provided. Notes ----- When exog is provided, a local estimate of the cumulative incidence rate around each point is provided, and these are averaged to produce an estimate of the marginal cumulative incidence functions. The procedure is analogous to that described in Zeng (2004) for estimation of the marginal survival function. The approach removes bias resulting from dependent censoring when the censoring becomes independent conditioned on the columns of exog. References ---------- The Stata stcompet procedure: http://www.stata-journal.com/sjpdf.html?articlenum=st0059 Dinse, G. E. and M. G. Larson. 1986. A note on semi-Markov models for partially censored data. Biometrika 73: 379-386. Marubini, E. and M. G. Valsecchi. 1995. Analysing Survival Data from Clinical Trials and Observational Studies. Chichester, UK: John Wiley & Sons. D. Zeng (2004). Estimating marginal survival function by adjusting for dependent censoring using many covariates. Annals of Statistics 32:4. https://arxiv.org/pdf/math/0409180.pdf """ def __init__(self, time, status, title=None, freq_weights=None, exog=None, bw_factor=1., dimred=True): _checkargs(time, status, None, freq_weights, None) time = self.time = np.asarray(time) status = self.status = np.asarray(status) if freq_weights is not None: freq_weights = self.freq_weights = np.asarray(freq_weights) if exog is not None: from ._kernel_estimates import _kernel_cumincidence exog = self.exog = np.asarray(exog) nobs = exog.shape[0] kw = nobs**(-1/3.0) * bw_factor kfunc = lambda x: np.exp(-x**2 / kw**2).sum(1) x = _kernel_cumincidence(time, status, exog, kfunc, freq_weights, dimred) self.times = x[0] self.cinc = x[1] return x = _calc_incidence_right(time, status, freq_weights) self.cinc = x[0] self.cinc_se = x[1] self.times = x[2] self.title = "" if not title else title class SurvfuncRight(object): """ Estimation and inference for a survival function. The survival function S(t) = P(T > t) is the probability that an event time T is greater than t. This class currently only supports right censoring. Parameters ---------- time : array_like An array of times (censoring times or event times) status : array_like Status at the event time, status==1 is the 'event' (e.g. death, failure), meaning that the event occurs at the given value in `time`; status==0 indicates that censoring has occurred, meaning that the event occurs after the given value in `time`. entry : array_like, optional An array of entry times for handling left truncation (the subject is not in the risk set on or before the entry time) title : str Optional title used for plots and summary output. freq_weights : array_like Optional frequency weights exog : array_like Optional, if present used to account for violation of independent censoring. bw_factor : float Band-width multiplier for kernel-based estimation. Only used if exog is provided. Attributes ---------- surv_prob : array_like The estimated value of the survivor function at each time point in `surv_times`. surv_prob_se : array_like The standard errors for the values in `surv_prob`. Not available if exog is provided. surv_times : array_like The points where the survival function changes. n_risk : array_like The number of subjects at risk just before each time value in `surv_times`. Not available if exog is provided. n_events : array_like The number of events (e.g. deaths) that occur at each point in `surv_times`. Not available if exog is provided. Notes ----- If exog is None, the standard Kaplan-Meier estimator is used. If exog is not None, a local estimate of the marginal survival function around each point is constructed, and these are then averaged. This procedure gives an estimate of the marginal survival function that accounts for dependent censoring as long as the censoring becomes independent when conditioning on the covariates in exog. See Zeng et al. (2004) for details. References ---------- D. Zeng (2004). Estimating marginal survival function by adjusting for dependent censoring using many covariates. Annals of Statistics 32:4. https://arxiv.org/pdf/math/0409180.pdf """ def __init__(self, time, status, entry=None, title=None, freq_weights=None, exog=None, bw_factor=1.): _checkargs(time, status, entry, freq_weights, exog) time = self.time = np.asarray(time) status = self.status = np.asarray(status) if freq_weights is not None: freq_weights = self.freq_weights = np.asarray(freq_weights) if entry is not None: entry = self.entry = np.asarray(entry) if exog is not None: if entry is not None: raise ValueError("exog and entry cannot both be present") from ._kernel_estimates import _kernel_survfunc exog = self.exog = np.asarray(exog) nobs = exog.shape[0] kw = nobs**(-1/3.0) * bw_factor kfunc = lambda x: np.exp(-x**2 / kw**2).sum(1) x = _kernel_survfunc(time, status, exog, kfunc, freq_weights) self.surv_prob = x[0] self.surv_times = x[1] return x = _calc_survfunc_right(time, status, weights=freq_weights, entry=entry) self.surv_prob = x[0] self.surv_prob_se = x[1] self.surv_times = x[2] self.n_risk = x[4] self.n_events = x[5] self.title = "" if not title else title def plot(self, ax=None): """ Plot the survival function. Examples -------- Change the line color: >>> import statsmodels.api as sm >>> data = sm.datasets.get_rdataset("flchain", "survival").data >>> df = data.loc[data.sex == "F", :] >>> sf = sm.SurvfuncRight(df["futime"], df["death"]) >>> fig = sf.plot() >>> ax = fig.get_axes()[0] >>> li = ax.get_lines() >>> li[0].set_color('purple') >>> li[1].set_color('purple') Do not show the censoring points: >>> fig = sf.plot() >>> ax = fig.get_axes()[0] >>> li = ax.get_lines() >>> li[1].set_visible(False) """ return plot_survfunc(self, ax) def quantile(self, p): """ Estimated quantile of a survival distribution. Parameters ---------- p : float The probability point at which the quantile is determined. Returns the estimated quantile. """ # SAS uses a strict inequality here. ii = np.flatnonzero(self.surv_prob < 1 - p) if len(ii) == 0: return np.nan return self.surv_times[ii[0]] def quantile_ci(self, p, alpha=0.05, method='cloglog'): """ Returns a confidence interval for a survival quantile. Parameters ---------- p : float The probability point for which a confidence interval is determined. alpha : float The confidence interval has nominal coverage probability 1 - `alpha`. method : str Function to use for g-transformation, must be ... Returns ------- lb : float The lower confidence limit. ub : float The upper confidence limit. Notes ----- The confidence interval is obtained by inverting Z-tests. The limits of the confidence interval will always be observed event times. References ---------- The method is based on the approach used in SAS, documented here: http://support.sas.com/documentation/cdl/en/statug/68162/HTML/default/viewer.htm#statug_lifetest_details03.htm """ tr = norm.ppf(1 - alpha / 2) method = method.lower() if method == "cloglog": g = lambda x: np.log(-np.log(x)) gprime = lambda x: -1 / (x * np.log(x)) elif method == "linear": g = lambda x: x gprime = lambda x: 1 elif method == "log": g = lambda x: np.log(x) gprime = lambda x: 1 / x elif method == "logit": g = lambda x: np.log(x / (1 - x)) gprime = lambda x: 1 / (x * (1 - x)) elif method == "asinsqrt": g = lambda x: np.arcsin(np.sqrt(x)) gprime = lambda x: 1 / (2 * np.sqrt(x) * np.sqrt(1 - x)) else: raise ValueError("unknown method") r = g(self.surv_prob) - g(1 - p) r /= (gprime(self.surv_prob) * self.surv_prob_se) ii = np.flatnonzero(np.abs(r) <= tr) if len(ii) == 0: return np.nan, np.nan lb = self.surv_times[ii[0]] if ii[-1] == len(self.surv_times) - 1: ub = np.inf else: ub = self.surv_times[ii[-1] + 1] return lb, ub def summary(self): """ Return a summary of the estimated survival function. The summary is a dataframe containing the unique event times, estimated survival function values, and related quantities. """ df = pd.DataFrame(index=self.surv_times) df.index.name = "Time" df["Surv prob"] = self.surv_prob df["Surv prob SE"] = self.surv_prob_se df["num at risk"] = self.n_risk df["num events"] = self.n_events return df def simultaneous_cb(self, alpha=0.05, method="hw", transform="log"): """ Returns a simultaneous confidence band for the survival function. Parameters ---------- alpha : float `1 - alpha` is the desired simultaneous coverage probability for the confidence region. Currently alpha must be set to 0.05, giving 95% simultaneous intervals. method : str The method used to produce the simultaneous confidence band. Only the Hall-Wellner (hw) method is currently implemented. transform : str The used to produce the interval (note that the returned interval is on the survival probability scale regardless of which transform is used). Only `log` and `arcsin` are implemented. Returns ------- lcb : array_like The lower confidence limits corresponding to the points in `surv_times`. ucb : array_like The upper confidence limits corresponding to the points in `surv_times`. """ method = method.lower() if method != "hw": msg = "only the Hall-Wellner (hw) method is implemented" raise ValueError(msg) if alpha != 0.05: raise ValueError("alpha must be set to 0.05") transform = transform.lower() s2 = self.surv_prob_se**2 / self.surv_prob**2 nn = self.n_risk if transform == "log": denom = np.sqrt(nn) * np.log(self.surv_prob) theta = 1.3581 * (1 + nn * s2) / denom theta = np.exp(theta) lcb = self.surv_prob**(1/theta) ucb = self.surv_prob**theta elif transform == "arcsin": k = 1.3581 k *= (1 + nn * s2) / (2 * np.sqrt(nn)) k *= np.sqrt(self.surv_prob / (1 - self.surv_prob)) f = np.arcsin(np.sqrt(self.surv_prob)) v = np.clip(f - k, 0, np.inf) lcb = np.sin(v)**2 v = np.clip(f + k, -np.inf, np.pi/2) ucb = np.sin(v)**2 else: raise ValueError("Unknown transform") return lcb, ucb def survdiff(time, status, group, weight_type=None, strata=None, entry=None, **kwargs): """ Test for the equality of two survival distributions. Parameters ---------- time : array_like The event or censoring times. status : array_like The censoring status variable, status=1 indicates that the event occurred, status=0 indicates that the observation was censored. group : array_like Indicators of the two groups weight_type : str The following weight types are implemented: None (default) : logrank test fh : Fleming-Harrington, weights by S^(fh_p), requires exponent fh_p to be provided as keyword argument; the weights are derived from S defined at the previous event time, and the first weight is always 1. gb : Gehan-Breslow, weights by the number at risk tw : Tarone-Ware, weights by the square root of the number at risk strata : array_like Optional stratum indicators for a stratified test entry : array_like Entry times to handle left truncation. The subject is not in the risk set on or before the entry time. Returns ------- chisq : The chi-square (1 degree of freedom) distributed test statistic value pvalue : The p-value for the chi^2 test """ time = np.asarray(time) status = np.asarray(status) group = np.asarray(group) gr = np.unique(group) if strata is None: obs, var = _survdiff(time, status, group, weight_type, gr, entry, **kwargs) else: strata = np.asarray(strata) stu = np.unique(strata) obs, var = 0., 0. for st in stu: # could be more efficient? ii = (strata == st) obs1, var1 = _survdiff(time[ii], status[ii], group[ii], weight_type, gr, entry, **kwargs) obs += obs1 var += var1 chisq = obs.dot(np.linalg.solve(var, obs)) # (O - E).T * V^(-1) * (O - E) pvalue = 1 - chi2.cdf(chisq, len(gr)-1) return chisq, pvalue def _survdiff(time, status, group, weight_type, gr, entry=None, **kwargs): # logrank test for one stratum # calculations based on https://web.stanford.edu/~lutian/coursepdf/unit6.pdf # formula for variance better to take from https://web.stanford.edu/~lutian/coursepdf/survweek3.pdf # Get the unique times. if entry is None: utimes, rtimes = np.unique(time, return_inverse=True) else: utimes, rtimes = np.unique(np.concatenate((time, entry)), return_inverse=True) rtimes = rtimes[0:len(time)] # Split entry times by group if present (should use pandas groupby) tse = [(gr_i, None) for gr_i in gr] if entry is not None: for k, _ in enumerate(gr): ii = (group == gr[k]) entry1 = entry[ii] tse[k] = (gr[k], entry1) # Event count and risk set size at each time point, per group and overall. # TODO: should use Pandas groupby nrisk, obsv = [], [] ml = len(utimes) for g, entry0 in tse: mk = (group == g) n = np.bincount(rtimes, weights=mk, minlength=ml) ob = np.bincount(rtimes, weights=status*mk, minlength=ml) obsv.append(ob) if entry is not None: n = np.cumsum(n) - n rentry = np.searchsorted(utimes, entry0, side='left') n0 = np.bincount(rentry, minlength=ml) n0 = np.cumsum(n0) - n0 nr = n0 - n else: nr = np.cumsum(n[::-1])[::-1] nrisk.append(nr) obs = sum(obsv) nrisk_tot = sum(nrisk) ix = np.flatnonzero(nrisk_tot > 1) weights = None if weight_type is not None: weight_type = weight_type.lower() if weight_type == "gb": weights = nrisk_tot elif weight_type == "tw": weights = np.sqrt(nrisk_tot) elif weight_type == "fh": if "fh_p" not in kwargs: msg = "weight_type type 'fh' requires specification of fh_p" raise ValueError(msg) fh_p = kwargs["fh_p"] # Calculate the survivor function directly to avoid the # overhead of creating a SurvfuncRight object sp = 1 - obs / nrisk_tot.astype(np.float64) sp = np.log(sp) sp = np.cumsum(sp) sp = np.exp(sp) weights = sp**fh_p weights = np.roll(weights, 1) weights[0] = 1 else: raise ValueError("weight_type not implemented") dfs = len(gr) - 1 r = np.vstack(nrisk) / np.clip(nrisk_tot, 1e-10, np.inf)[None, :] # each line is timeseries of r's. line per group # The variance of event counts in each group. groups_oe = [] groups_var = [] var_denom = nrisk_tot - 1 var_denom = np.clip(var_denom, 1e-10, np.inf) # use the first group as a reference for g in range(1, dfs+1): # Difference between observed and expected number of events in the group #g oe = obsv[g] - r[g]*obs # build one row of the dfs x dfs variance matrix var_tensor_part = r[1:, :].T * (np.eye(1, dfs, g-1).ravel() - r[g, :, None]) # r*(1 - r) in multidim var_scalar_part = obs * (nrisk_tot - obs) / var_denom var = var_tensor_part * var_scalar_part[:, None] if weights is not None: oe = weights * oe var = (weights**2)[:, None] * var # sum over times and store groups_oe.append(oe[ix].sum()) groups_var.append(var[ix].sum(axis=0)) obs_vec = np.hstack(groups_oe) var_mat = np.vstack(groups_var) return obs_vec, var_mat def plot_survfunc(survfuncs, ax=None): """ Plot one or more survivor functions. Parameters ---------- survfuncs : object or array_like A single SurvfuncRight object, or a list or SurvfuncRight objects that are plotted together. Returns ------- A figure instance on which the plot was drawn. Examples -------- Add a legend: >>> import statsmodels.api as sm >>> from statsmodels.duration.survfunc import plot_survfunc >>> data = sm.datasets.get_rdataset("flchain", "survival").data >>> df = data.loc[data.sex == "F", :] >>> sf0 = sm.SurvfuncRight(df["futime"], df["death"]) >>> sf1 = sm.SurvfuncRight(3.0 * df["futime"], df["death"]) >>> fig = plot_survfunc([sf0, sf1]) >>> ax = fig.get_axes()[0] >>> ax.set_position([0.1, 0.1, 0.64, 0.8]) >>> ha, lb = ax.get_legend_handles_labels() >>> leg = fig.legend((ha[0], ha[1]), (lb[0], lb[1]), 'center right') Change the line colors: >>> fig = plot_survfunc([sf0, sf1]) >>> ax = fig.get_axes()[0] >>> ax.set_position([0.1, 0.1, 0.64, 0.8]) >>> ha, lb = ax.get_legend_handles_labels() >>> ha[0].set_color('purple') >>> ha[1].set_color('orange') """ fig, ax = utils.create_mpl_ax(ax) # If we have only a single survival function to plot, put it into # a list. try: assert(type(survfuncs[0]) is SurvfuncRight) except: survfuncs = [survfuncs] for gx, sf in enumerate(survfuncs): # The estimated survival function does not include a point at # time 0, include it here for plotting. surv_times = np.concatenate(([0], sf.surv_times)) surv_prob = np.concatenate(([1], sf.surv_prob)) # If the final times are censoring times they are not included # in the survival function so we add them here mxt = max(sf.time) if mxt > surv_times[-1]: surv_times = np.concatenate((surv_times, [mxt])) surv_prob = np.concatenate((surv_prob, [surv_prob[-1]])) label = getattr(sf, "title", "Group %d" % (gx + 1)) li, = ax.step(surv_times, surv_prob, '-', label=label, lw=2, where='post') # Plot the censored points. ii = np.flatnonzero(np.logical_not(sf.status)) ti = np.unique(sf.time[ii]) jj = np.searchsorted(surv_times, ti) - 1 sp = surv_prob[jj] ax.plot(ti, sp, '+', ms=12, color=li.get_color(), label=label + " points") ax.set_ylim(0, 1.01) return fig statsmodels-0.12.2/statsmodels/duration/tests/000077500000000000000000000000001400612667500214765ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/duration/tests/__init__.py000066400000000000000000000000001400612667500235750ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/duration/tests/results/000077500000000000000000000000001400612667500231775ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/duration/tests/results/__init__.py000066400000000000000000000000001400612667500252760ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/duration/tests/results/bmt.csv000066400000000000000000000044501400612667500245010ustar00rootroot00000000000000Group,T,Status ALL,2081,0 ALL,1602,0 ALL,1496,0 ALL,1462,0 ALL,1433,0 ALL,1377,0 ALL,1330,0 ALL,996,0 ALL,226,0 ALL,1199,0 ALL,1111,0 ALL,530,0 ALL,1182,0 ALL,1167,0 ALL,418,1 ALL,383,1 ALL,276,1 ALL,104,1 ALL,609,1 ALL,172,1 ALL,487,1 ALL,662,1 ALL,194,1 ALL,230,1 ALL,526,1 ALL,122,1 ALL,129,1 ALL,74,1 ALL,122,1 ALL,86,1 ALL,466,1 ALL,192,1 ALL,109,1 ALL,55,1 ALL,1,1 ALL,107,1 ALL,110,1 ALL,332,1 AML-Low Risk,2569,0 AML-Low Risk,2506,0 AML-Low Risk,2409,0 AML-Low Risk,2218,0 AML-Low Risk,1857,0 AML-Low Risk,1829,0 AML-Low Risk,1562,0 AML-Low Risk,1470,0 AML-Low Risk,1363,0 AML-Low Risk,1030,0 AML-Low Risk,860,0 AML-Low Risk,1258,0 AML-Low Risk,2246,0 AML-Low Risk,1870,0 AML-Low Risk,1799,0 AML-Low Risk,1709,0 AML-Low Risk,1674,0 AML-Low Risk,1568,0 AML-Low Risk,1527,0 AML-Low Risk,1324,0 AML-Low Risk,957,0 AML-Low Risk,932,0 AML-Low Risk,847,0 AML-Low Risk,848,0 AML-Low Risk,1850,0 AML-Low Risk,1843,0 AML-Low Risk,1535,0 AML-Low Risk,1447,0 AML-Low Risk,1384,0 AML-Low Risk,414,1 AML-Low Risk,2204,1 AML-Low Risk,1063,1 AML-Low Risk,481,1 AML-Low Risk,105,1 AML-Low Risk,641,1 AML-Low Risk,390,1 AML-Low Risk,288,1 AML-Low Risk,421,1 AML-Low Risk,79,1 AML-Low Risk,748,1 AML-Low Risk,486,1 AML-Low Risk,48,1 AML-Low Risk,272,1 AML-Low Risk,1074,1 AML-Low Risk,381,1 AML-Low Risk,10,1 AML-Low Risk,53,1 AML-Low Risk,80,1 AML-Low Risk,35,1 AML-Low Risk,248,1 AML-Low Risk,704,1 AML-Low Risk,211,1 AML-Low Risk,219,1 AML-Low Risk,606,1 AML-High Risk,2640,0 AML-High Risk,2430,0 AML-High Risk,2252,0 AML-High Risk,2140,0 AML-High Risk,2133,0 AML-High Risk,1238,0 AML-High Risk,1631,0 AML-High Risk,2024,0 AML-High Risk,1345,0 AML-High Risk,1136,0 AML-High Risk,845,0 AML-High Risk,422,1 AML-High Risk,162,1 AML-High Risk,84,1 AML-High Risk,100,1 AML-High Risk,2,1 AML-High Risk,47,1 AML-High Risk,242,1 AML-High Risk,456,1 AML-High Risk,268,1 AML-High Risk,318,1 AML-High Risk,32,1 AML-High Risk,467,1 AML-High Risk,47,1 AML-High Risk,390,1 AML-High Risk,183,1 AML-High Risk,105,1 AML-High Risk,115,1 AML-High Risk,164,1 AML-High Risk,93,1 AML-High Risk,120,1 AML-High Risk,80,1 AML-High Risk,677,1 AML-High Risk,64,1 AML-High Risk,168,1 AML-High Risk,74,1 AML-High Risk,16,1 AML-High Risk,157,1 AML-High Risk,625,1 AML-High Risk,48,1 AML-High Risk,273,1 AML-High Risk,63,1 AML-High Risk,76,1 AML-High Risk,113,1 AML-High Risk,363,1 statsmodels-0.12.2/statsmodels/duration/tests/results/bmt_results.csv000066400000000000000000000031211400612667500262540ustar00rootroot00000000000000t,s,se,linear,loglog,log,asinsqrt,logit 1,0.97368,0.025967,8.6141,2.37831,9.7871,4.44648,2.47903 55,0.94737,0.036224,5.4486,2.36375,6.1098,3.60151,2.46635 74,0.92105,0.043744,3.9103,2.16833,4.3257,2.94398,2.25757 86,0.89474,0.049784,2.9073,1.89961,3.1713,2.38164,1.97023 104,0.86842,0.054836,2.1595,1.59196,2.3217,1.87884,1.64297 107,0.84211,0.059153,1.5571,1.26050,1.6490,1.41733,1.29331 109,0.81579,0.062886,1.0462,0.91307,1.0908,0.98624,0.93069 110,0.78947,0.066135,0.5969,0.55415,0.6123,0.57846,0.56079 122,0.73684,0.071434,–0.1842,–0.18808,–0.1826,–0.18573,–0.18728 129,0.71053,0.073570,–0.5365,–0.56842,–0.5222,–0.54859,–0.56101 172,0.68421,0.075405,–0.8725,–0.95372,–0.8330,–0.90178,–0.93247 192,0.65789,0.076960,–1.1968,–1.34341,–1.1201,–1.24712,–1.30048 194,0.63158,0.078252,–1.5133,–1.73709,–1.3870,–1.58613,–1.66406 230,0.60412,0.079522,–1.8345,–2.14672,–1.6432,–1.92995,–2.03291 276,0.57666,0.080509,–2.1531,–2.55898,–1.8825,–2.26871,–2.39408 332,0.54920,0.081223,–2.4722,–2.97389,–2.1070,–2.60380,–2.74691 383,0.52174,0.081672,–2.7948,–3.39146,–2.3183,–2.93646,–3.09068 418,0.49428,0.081860,–3.1239,–3.81166,–2.5177,–3.26782,–3.42460 466,0.46682,0.081788,–3.4624,–4.23445,–2.7062,–3.59898,–3.74781 487,0.43936,0.081457,–3.8136,–4.65971,–2.8844,–3.93103,–4.05931 526,0.41190,0.080862,–4.1812,–5.08726,–3.0527,–4.26507,–4.35795 609,0.38248,0.080260,–4.5791,–5.52446,–3.2091,–4.60719,–4.64271 662,0.35306,0.079296,–5.0059,–5.96222,–3.3546,–4.95358,–4.90900 statsmodels-0.12.2/statsmodels/duration/tests/results/km_cox1.do000066400000000000000000000041531400612667500250670ustar00rootroot00000000000000/* Run Survival models and save results Author: Josef Perktold based on example from Stata help */ clear *basic Kaplan-Meier capture use "E:\Josef\statawork\stan3.dta", clear if _rc != 0 webuse stan3 capture save "E:\Josef\statawork\stan3.dta" capture erase surf.dta sts list, saving("surf") use "E:\Josef\statawork\surf.dta", clear outsheet using "surv_km.csv", comma replace * Kaplan-Meier with by use "E:\Josef\statawork\stan3.dta", clear capture erase surf2.dta sts list, by(posttran) saving("surf2") use "E:\Josef\statawork\surf2.dta", clear outsheet using "surv_km2.csv", comma replace * Cox Proportional Hazard use "E:\Josef\statawork\stan3.dta", clear stcox age posttran , estimate norobust ereturn list, matlist e(V) matlist e(p) * the next does not work * predict predictall, hr xb stdp basesurv basechazard basehc mgale csnell deviance ldisplace lmax effects /* generate in python: >>> for i in 'hr xb stdp basesurv basechazard basehc mgale csnell deviance ldisplace lmax effects'.split(): print 'predict %s, %s' % (i,i) */ predict hr, hr predict xb, xb predict stdp, stdp predict basesurv, basesurv predict basechazard, basechazard predict basehc, basehc predict mgale, mgale predict csnell, csnell predict deviance, deviance predict ldisplace, ldisplace predict lmax, lmax *capture predict effects, effects outsheet hr xb stdp basesurv basechazard basehc mgale csnell deviance ldisplace lmax using "surv_coxph.csv", comma replace * replay stcox matrix cov = e(V) svmat cov, names(cov) * get the colnames and rownames capture drop nacol narow matrix params_table = r(table)' gen nacol = "`: colnames params_table'" gen narow = "`: rownames params_table'" di nacol di narow *2nd version capture drop rown2 local colnms: coln params_table gen str rown2 = "`colnms'" di rown2 svmat params_table, names(params_table) estmat2nparray params_table cov, saving("results_coxphrobust.py") format("%16.0g") append * other options, no matrices or no est results *estmat2nparray params_table cov, saving("results_coxphrobust_2.py") format("%16.0g") append noest *estmat2nparray , saving("results_coxphrobust_2.py") format("%16.0g") append statsmodels-0.12.2/statsmodels/duration/tests/results/phreg_gentests.py000066400000000000000000000036211400612667500265740ustar00rootroot00000000000000import numpy as np """ Generate data sets for testing Cox proportional hazards regression models. After updating the test data sets, use R to run the survival.R script to update the R results. """ # The current data may not reflect this seed np.random.seed(5234) # Loop over pairs containing (sample size, number of variables). for (n, p) in (20, 1), (50, 1), (50, 2), (100, 5), (1000, 10): exog = np.random.normal(size=(5*n, p)) coef = np.linspace(-0.5, 0.5, p) lpred = np.dot(exog, coef) expected_survival_time = np.exp(-lpred) # Survival times are exponential survival_time = -np.log(np.random.uniform(size=5*n)) survival_time *= expected_survival_time # Set this to get a reasonable amount of censoring expected_censoring_time = np.mean(expected_survival_time) # Theses are the observation times. censoring_time = -np.log(np.random.uniform(size=5*n)) censoring_time *= expected_censoring_time # Entry times entry_time = -np.log(np.random.uniform(size=5*n)) entry_time *= 0.5*expected_censoring_time # 1=failure (death), 0=no failure (no death) status = 1*(survival_time <= censoring_time) # The censoring time of the failure time, whichever comes first time = np.where(status == 1, survival_time, censoring_time) # Round time so that we have ties time = np.around(time, decimals=1) # Only take cases where the entry time is before the failure or # censoring time. Take exactly n such cases. ii = np.flatnonzero(entry_time < time) ii = ii[np.random.permutation(len(ii))[0:n]] status = status[ii] time = time[ii] exog = exog[ii, :] entry_time = entry_time[ii] data = np.concatenate((time[:, None], status[:, None], entry_time[:, None], exog), axis=1) fname = "results/survival_data_%d_%d.csv" % (n, p) np.savetxt(fname, data, fmt="%.5f") statsmodels-0.12.2/statsmodels/duration/tests/results/survival.R000066400000000000000000000042541400612667500252020ustar00rootroot00000000000000library(survival) library(R2nparray) ixd = list(c(20,1), c(50,1), c(50,2), c(100,5), c(1000,10)) res = list() for (ix in ixd) { fname = sprintf("results/survival_data_%d_%d.csv", ix[1], ix[2]) data = read.table(fname) time = data[,1] status = data[,2] entry = data[,3] exog = data[,4:dim(data)[2]] exog = as.matrix(exog) n = dim(exog)[1] p = dim(exog)[2] # Needs to match the kronecker statement in test_phreg.py strata = kronecker(seq(5), array(1, n/5)) for (ties in c("breslow", "efron")) { ti = substr(ties, 1, 3) # Base model surv = Surv(time, status) md = coxph(surv ~ exog, ties=ties) tag = sprintf("%d_%d_%s", n, p, ti) res[[sprintf("coef_%s", tag)]] = md$coef res[[sprintf("se_%s", tag)]] = sqrt(diag(md$var)) #bhaz = basehaz(md) bhaz = survfit(md, type="aalen") #bhaz = survfit(md, type="efron") res[[sprintf("time_%s", tag)]] = bhaz$time res[[sprintf("hazard_%s", tag)]] = -log(bhaz$surv) # With entry time surv = Surv(entry, time, status) md = coxph(surv ~ exog, ties=ties) tag = sprintf("%d_%d_et_%s", n, p, ti) res[[sprintf("coef_%s", tag)]] = md$coef res[[sprintf("se_%s", tag)]] = sqrt(diag(md$var)) res[[sprintf("time_%s", tag)]] = c(0) res[[sprintf("hazard_%s", tag)]] = c(0) # With strata surv = Surv(time, status) md = coxph(surv ~ exog + strata(strata), ties=ties) tag = sprintf("%d_%d_st_%s", n, p, ti) res[[sprintf("coef_%s", tag)]] = md$coef res[[sprintf("se_%s", tag)]] = sqrt(diag(md$var)) res[[sprintf("time_%s", tag)]] = c(0) res[[sprintf("hazard_%s", tag)]] = c(0) # With entry time and strata surv = Surv(entry, time, status) md = coxph(surv ~ exog + strata(strata), ties=ties) tag = sprintf("%d_%d_et_st_%s", n, p, ti) res[[sprintf("coef_%s", tag)]] = md$coef res[[sprintf("se_%s", tag)]] = sqrt(diag(md$var)) res[[sprintf("time_%s", tag)]] = c(0) res[[sprintf("hazard_%s", tag)]] = c(0) } } R2nparray(res, fname="survival_r_results.py") statsmodels-0.12.2/statsmodels/duration/tests/results/survival_data_1000_10.csv000066400000000000000000003247271400612667500275370ustar00rootroot000000000000002.20000 1.00000 0.61724 -0.55769 0.53610 0.36943 1.27222 1.50100 -0.12360 -1.96969 0.19446 0.51010 0.02451 4.00000 0.00000 0.07211 0.25464 -0.35689 -0.65315 1.29070 2.10784 -1.08015 -1.10013 0.51913 -1.35782 0.14478 1.40000 1.00000 0.44822 0.58003 -0.44211 2.40188 -0.64420 1.06588 0.01564 -0.20484 1.17820 -0.05933 -0.20595 0.50000 1.00000 0.00636 1.21382 0.09781 0.46914 -0.49769 0.52211 -0.20400 -0.35330 1.52768 -0.55526 1.94335 2.40000 0.00000 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0.26199 0.80000 0.00000 0.10030 0.85841 0.88421 0.80000 1.00000 0.63120 -0.36353 0.26827 0.70000 1.00000 0.55604 -1.95990 -0.44759 1.10000 0.00000 0.40564 0.88427 -1.96625 0.20000 1.00000 0.03342 0.64777 -0.36391 0.10000 1.00000 0.06233 -0.64523 0.51863 1.10000 1.00000 0.04864 2.43561 0.44143 1.00000 0.00000 0.14794 1.51211 -1.71867 1.30000 1.00000 0.16023 -0.49040 -0.02378 0.40000 1.00000 0.24862 0.08828 -0.70830 0.50000 0.00000 0.12510 1.64139 -0.07560 1.90000 1.00000 0.57775 0.22910 -0.06035 0.60000 0.00000 0.21988 -0.61760 -0.84216 1.50000 0.00000 0.73572 -0.31742 -0.50461 0.20000 0.00000 0.09880 0.01778 -0.61300 2.70000 1.00000 0.68267 0.46799 -1.20130 0.20000 0.00000 0.00640 -0.57452 0.07641 1.00000 0.00000 0.53120 0.10882 -1.29716 1.40000 0.00000 0.39915 1.78210 -0.98747 0.30000 1.00000 0.24249 -0.52481 -0.00631 1.50000 0.00000 0.90297 -0.15558 -0.41401 0.60000 0.00000 0.11513 1.91513 0.84025 2.90000 0.00000 1.22897 0.83216 0.05158 0.20000 1.00000 0.14026 -0.15508 2.57765 0.20000 1.00000 0.02342 -0.43017 -0.19378 0.10000 1.00000 0.01043 -2.09826 1.82889 1.00000 0.00000 0.12414 -0.15255 -0.78868 0.10000 0.00000 0.08182 2.05096 -0.00273 0.70000 0.00000 0.50106 -1.11553 -0.37599 0.70000 0.00000 0.04540 0.20011 -1.63279 0.70000 1.00000 0.41003 1.04118 0.07873 0.40000 1.00000 0.33584 -1.70869 -0.94676 1.20000 0.00000 0.59698 0.21795 -2.65967 1.10000 0.00000 0.90747 1.10303 2.21828 0.20000 0.00000 0.15655 1.50321 0.88795 statsmodels-0.12.2/statsmodels/duration/tests/results/survival_enet_r_results.py000066400000000000000000000004211400612667500305360ustar00rootroot00000000000000import numpy as np coef_50_2_0 = np.array([-0.6748149, 0.5219471]) coef_50_2_1 = np.array([-0.3464841, 0.211115]) coef_100_5_0 = np.array([ -0.4839566, -0.3130558, -0.1239565, 0.3466049, 0.5827503]) coef_100_5_1 = np.array([-0.1314948, 0, 0, 0.0324285, 0.2364489]) statsmodels-0.12.2/statsmodels/duration/tests/results/survival_r_results.py000066400000000000000000000316641400612667500275400ustar00rootroot00000000000000import numpy as np coef_20_1_bre = np.array([-0.9185611]) se_20_1_bre = np.array([0.4706831]) time_20_1_bre = np.array([ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 1.1, 1.2, 1.3, 1.4, 1.5]) hazard_20_1_bre = np.array([ 0, 0, 0.04139181, 0.1755379, 0.3121216, 0.3121216, 0.4263121, 0.6196358, 0.6196358, 0.6196358, 0.909556, 1.31083, 1.31083]) coef_20_1_et_bre = np.array([-0.8907007]) se_20_1_et_bre = np.array([0.4683384]) time_20_1_et_bre = np.array([0]) hazard_20_1_et_bre = np.array([0]) coef_20_1_st_bre = np.array([-0.5766809]) se_20_1_st_bre = np.array([0.4418918]) time_20_1_st_bre = np.array([0]) hazard_20_1_st_bre = np.array([0]) coef_20_1_et_st_bre = np.array([-0.5785683]) se_20_1_et_st_bre = np.array([0.4388437]) time_20_1_et_st_bre = np.array([0]) hazard_20_1_et_st_bre = np.array([0]) coef_20_1_efr = np.array([-0.9975319]) se_20_1_efr = np.array([0.4792421]) time_20_1_efr = np.array([ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 1.1, 1.2, 1.3, 1.4, 1.5]) hazard_20_1_efr = np.array([ 0, 0, 0.03934634, 0.1663316, 0.2986427, 0.2986427, 0.4119189, 0.6077373, 0.6077373, 0.6077373, 0.8933041, 1.285732, 1.285732]) coef_20_1_et_efr = np.array([-0.9679541]) se_20_1_et_efr = np.array([0.4766406]) time_20_1_et_efr = np.array([0]) hazard_20_1_et_efr = np.array([0]) coef_20_1_st_efr = np.array([-0.6345294]) se_20_1_st_efr = np.array([0.4455952]) time_20_1_st_efr = np.array([0]) hazard_20_1_st_efr = np.array([0]) coef_20_1_et_st_efr = np.array([-0.6355622]) se_20_1_et_st_efr = np.array([0.4423104]) time_20_1_et_st_efr = np.array([0]) hazard_20_1_et_st_efr = np.array([0]) coef_50_1_bre = np.array([-0.6761247]) se_50_1_bre = np.array([0.25133]) time_50_1_bre = np.array([ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.5, 1.6, 1.7, 1.8, 1.9, 2.4, 2.8]) hazard_50_1_bre = np.array([ 0, 0.04895521, 0.08457461, 0.2073863, 0.2382473, 0.2793018, 0.3271622, 0.3842953, 0.3842953, 0.5310807, 0.6360276, 0.7648251, 0.7648251, 0.9294298, 0.9294298, 0.9294298, 1.206438, 1.555569, 1.555569]) coef_50_1_et_bre = np.array([-0.6492871]) se_50_1_et_bre = np.array([0.2542493]) time_50_1_et_bre = np.array([0]) hazard_50_1_et_bre = np.array([0]) coef_50_1_st_bre = np.array([-0.7051135]) se_50_1_st_bre = np.array([0.2852093]) time_50_1_st_bre = np.array([0]) hazard_50_1_st_bre = np.array([0]) coef_50_1_et_st_bre = np.array([-0.8672546]) se_50_1_et_st_bre = np.array([0.3443235]) time_50_1_et_st_bre = np.array([0]) hazard_50_1_et_st_bre = np.array([0]) coef_50_1_efr = np.array([-0.7119322]) se_50_1_efr = np.array([0.2533563]) time_50_1_efr = np.array([ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.5, 1.6, 1.7, 1.8, 1.9, 2.4, 2.8]) hazard_50_1_efr = np.array([ 0, 0.04773902, 0.08238731, 0.2022993, 0.2327053, 0.2736316, 0.3215519, 0.3787123, 0.3787123, 0.526184, 0.6323073, 0.7627338, 0.7627338, 0.9288858, 0.9288858, 0.9288858, 1.206835, 1.556054, 1.556054]) coef_50_1_et_efr = np.array([-0.7103063]) se_50_1_et_efr = np.array([0.2598129]) time_50_1_et_efr = np.array([0]) hazard_50_1_et_efr = np.array([0]) coef_50_1_st_efr = np.array([-0.7417904]) se_50_1_st_efr = np.array([0.2846437]) time_50_1_st_efr = np.array([0]) hazard_50_1_st_efr = np.array([0]) coef_50_1_et_st_efr = np.array([-0.9276112]) se_50_1_et_st_efr = np.array([0.3462638]) time_50_1_et_st_efr = np.array([0]) hazard_50_1_et_st_efr = np.array([0]) coef_50_2_bre = np.array([-0.5935189, 0.5035724]) se_50_2_bre = np.array([0.2172841, 0.2399933]) time_50_2_bre = np.array([ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.9, 2.7, 2.9]) hazard_50_2_bre = np.array([ 0.02695812, 0.09162381, 0.1309537, 0.1768423, 0.2033353, 0.2033353, 0.3083449, 0.3547287, 0.4076453, 0.4761318, 0.5579718, 0.7610905, 0.918962, 0.918962, 1.136173, 1.605757, 2.457676, 2.457676]) coef_50_2_et_bre = np.array([-0.4001465, 0.4415933]) se_50_2_et_bre = np.array([0.1992302, 0.2525949]) time_50_2_et_bre = np.array([0]) hazard_50_2_et_bre = np.array([0]) coef_50_2_st_bre = np.array([-0.6574891, 0.4416079]) se_50_2_st_bre = np.array([0.2753398, 0.269458]) time_50_2_st_bre = np.array([0]) hazard_50_2_st_bre = np.array([0]) coef_50_2_et_st_bre = np.array([-0.3607069, 0.2731982]) se_50_2_et_st_bre = np.array([0.255415, 0.306942]) time_50_2_et_st_bre = np.array([0]) hazard_50_2_et_st_bre = np.array([0]) coef_50_2_efr = np.array([-0.6107485, 0.5309737]) se_50_2_efr = np.array([0.2177713, 0.2440535]) time_50_2_efr = np.array([ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.9, 2.7, 2.9]) hazard_50_2_efr = np.array([ 0.02610571, 0.08933637, 0.1279094, 0.1731699, 0.19933, 0.19933, 0.303598, 0.3497025, 0.4023939, 0.4706978, 0.5519237, 0.7545023, 0.9129989, 0.9129989, 1.13186, 1.60574, 2.472615, 2.472615]) coef_50_2_et_efr = np.array([-0.4092002, 0.4871344]) se_50_2_et_efr = np.array([0.1968905, 0.2608527]) time_50_2_et_efr = np.array([0]) hazard_50_2_et_efr = np.array([0]) coef_50_2_st_efr = np.array([-0.6631286, 0.4663285]) se_50_2_st_efr = np.array([0.2748224, 0.273603]) time_50_2_st_efr = np.array([0]) hazard_50_2_st_efr = np.array([0]) coef_50_2_et_st_efr = np.array([-0.3656059, 0.2943912]) se_50_2_et_st_efr = np.array([0.2540752, 0.3124632]) time_50_2_et_st_efr = np.array([0]) hazard_50_2_et_st_efr = np.array([0]) coef_100_5_bre = np.array([ -0.529776, -0.2916374, -0.1205425, 0.3493476, 0.6034305]) se_100_5_bre = np.array([ 0.1789305, 0.1482505, 0.1347422, 0.1528205, 0.1647927]) time_100_5_bre = np.array([ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2, 2.1, 2.5, 2.8, 3.2, 3.3]) hazard_100_5_bre = np.array([ 0.02558588, 0.05608812, 0.1087773, 0.1451098, 0.1896703, 0.2235791, 0.3127521, 0.3355107, 0.439452, 0.504983, 0.5431706, 0.5841462, 0.5841462, 0.5841462, 0.6916466, 0.7540191, 0.8298704, 1.027876, 1.170335, 1.379306, 1.648758, 1.943177, 1.943177, 1.943177, 4.727101]) coef_100_5_et_bre = np.array([ -0.4000784, -0.1790941, -0.1378969, 0.3288529, 0.533246]) se_100_5_et_bre = np.array([ 0.1745655, 0.1513545, 0.1393968, 0.1487803, 0.1686992]) time_100_5_et_bre = np.array([0]) hazard_100_5_et_bre = np.array([0]) coef_100_5_st_bre = np.array([ -0.53019, -0.3225739, -0.1241568, 0.3246598, 0.6196859]) se_100_5_st_bre = np.array([ 0.1954581, 0.1602811, 0.1470644, 0.17121, 0.1784115]) time_100_5_st_bre = np.array([0]) hazard_100_5_st_bre = np.array([0]) coef_100_5_et_st_bre = np.array([ -0.3977171, -0.2166136, -0.1387623, 0.3251726, 0.5664705]) se_100_5_et_st_bre = np.array([ 0.1951054, 0.1707925, 0.1501968, 0.1699932, 0.1843428]) time_100_5_et_st_bre = np.array([0]) hazard_100_5_et_st_bre = np.array([0]) coef_100_5_efr = np.array([ -0.5641909, -0.3233021, -0.1234858, 0.3712328, 0.6421963]) se_100_5_efr = np.array([ 0.1804027, 0.1496253, 0.1338531, 0.1529832, 0.1670848]) time_100_5_efr = np.array([ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2, 2.1, 2.5, 2.8, 3.2, 3.3]) hazard_100_5_efr = np.array([ 0.02393412, 0.05276399, 0.1028432, 0.1383859, 0.1823461, 0.2158107, 0.3037825, 0.3264864, 0.4306648, 0.4964367, 0.5348595, 0.5760305, 0.5760305, 0.5760305, 0.6842238, 0.7468135, 0.8228841, 1.023195, 1.166635, 1.379361, 1.652898, 1.950119, 1.950119, 1.950119, 4.910635]) coef_100_5_et_efr = np.array([ -0.4338666, -0.2140139, -0.1397387, 0.3535993, 0.5768645]) se_100_5_et_efr = np.array([ 0.1756485, 0.1527244, 0.138298, 0.1488427, 0.1716654]) time_100_5_et_efr = np.array([0]) hazard_100_5_et_efr = np.array([0]) coef_100_5_st_efr = np.array([ -0.5530876, -0.3331652, -0.128381, 0.3503472, 0.6397813]) se_100_5_st_efr = np.array([ 0.1969338, 0.1614976, 0.1464088, 0.171299, 0.1800787]) time_100_5_st_efr = np.array([0]) hazard_100_5_st_efr = np.array([0]) coef_100_5_et_st_efr = np.array([ -0.421153, -0.2350069, -0.1433638, 0.3538863, 0.5934568]) se_100_5_et_st_efr = np.array([ 0.1961729, 0.1724719, 0.1492979, 0.170464, 0.1861849]) time_100_5_et_st_efr = np.array([0]) hazard_100_5_et_st_efr = np.array([0]) coef_1000_10_bre = np.array([ -0.4699279, -0.464557, -0.308411, -0.2158298, -0.09048563, 0.09359662, 0.112588, 0.3343705, 0.3480601, 0.5634985]) se_1000_10_bre = np.array([ 0.04722914, 0.04785291, 0.04503528, 0.04586872, 0.04429793, 0.0446141, 0.04139944, 0.04464292, 0.04559903, 0.04864393]) time_1000_10_bre = np.array([ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4, 4.1, 4.2, 4.3, 4.4, 4.6, 4.8, 4.9, 5, 5.1, 5.2, 5.7, 5.8, 5.9, 6.9]) hazard_1000_10_bre = np.array([ 0.01610374, 0.04853538, 0.08984849, 0.1311329, 0.168397, 0.2230488, 0.2755388, 0.3312606, 0.3668702, 0.4146558, 0.477935, 0.5290705, 0.5831775, 0.6503129, 0.7113068, 0.7830385, 0.8361717, 0.8910061, 0.9615944, 1.024011, 1.113399, 1.165349, 1.239827, 1.352902, 1.409548, 1.53197, 1.601843, 1.682158, 1.714907, 1.751564, 1.790898, 1.790898, 1.83393, 1.83393, 1.936055, 1.992303, 2.050778, 2.118776, 2.263056, 2.504999, 2.739343, 2.895514, 3.090349, 3.090349, 3.391772, 3.728142, 4.152769, 4.152769, 4.152769, 4.725957, 4.725957, 5.69653, 5.69653, 5.69653]) coef_1000_10_et_bre = np.array([ -0.410889, -0.3929442, -0.2975845, -0.1851533, -0.0918359, 0.1011997, 0.106735, 0.2899179, 0.3220672, 0.5069589]) se_1000_10_et_bre = np.array([ 0.04696754, 0.04732169, 0.04537707, 0.04605371, 0.04365232, 0.04450021, 0.04252475, 0.04482007, 0.04562374, 0.04859727]) time_1000_10_et_bre = np.array([0]) hazard_1000_10_et_bre = np.array([0]) coef_1000_10_st_bre = np.array([ -0.471015, -0.4766859, -0.3070839, -0.2091938, -0.09190845, 0.0964942, 0.1138269, 0.3307131, 0.3543551, 0.562492]) se_1000_10_st_bre = np.array([ 0.04814778, 0.04841938, 0.04572291, 0.04641227, 0.04502525, 0.04517603, 0.04203737, 0.04524356, 0.04635037, 0.04920866]) time_1000_10_st_bre = np.array([0]) hazard_1000_10_st_bre = np.array([0]) coef_1000_10_et_st_bre = np.array([ -0.4165849, -0.4073504, -0.2980959, -0.1765194, -0.09152798, 0.1013213, 0.1009838, 0.2859668, 0.3247608, 0.5044448]) se_1000_10_et_st_bre = np.array([ 0.04809818, 0.04809499, 0.0460829, 0.04679922, 0.0445294, 0.04514045, 0.04339298, 0.04580591, 0.04652447, 0.04920744]) time_1000_10_et_st_bre = np.array([0]) hazard_1000_10_et_st_bre = np.array([0]) coef_1000_10_efr = np.array([ -0.4894399, -0.4839746, -0.3227769, -0.2261293, -0.09318482, 0.09767154, 0.1173205, 0.3493732, 0.3640146, 0.5879749]) se_1000_10_efr = np.array([ 0.0474181, 0.04811855, 0.04507655, 0.04603044, 0.04440409, 0.04478202, 0.04136728, 0.04473343, 0.045768, 0.04891375]) time_1000_10_efr = np.array([ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4, 4.1, 4.2, 4.3, 4.4, 4.6, 4.8, 4.9, 5, 5.1, 5.2, 5.7, 5.8, 5.9, 6.9]) hazard_1000_10_efr = np.array([ 0.01549698, 0.04680035, 0.08682564, 0.1269429, 0.1632388, 0.2167291, 0.2682311, 0.3231316, 0.3582936, 0.4054892, 0.4681098, 0.5188697, 0.5727059, 0.639571, 0.7003012, 0.7718979, 0.825053, 0.880063, 0.950935, 1.013828, 1.103903, 1.156314, 1.231707, 1.346235, 1.40359, 1.527475, 1.598231, 1.6795, 1.712779, 1.750227, 1.790455, 1.790455, 1.834455, 1.834455, 1.938997, 1.996804, 2.056859, 2.126816, 2.275217, 2.524027, 2.76669, 2.929268, 3.13247, 3.13247, 3.448515, 3.80143, 4.249649, 4.249649, 4.249649, 4.851365, 4.851365, 5.877307, 5.877307, 5.877307]) coef_1000_10_et_efr = np.array([ -0.4373066, -0.4131901, -0.3177637, -0.1978493, -0.09679451, 0.1092037, 0.1136069, 0.3088907, 0.3442007, 0.5394121]) se_1000_10_et_efr = np.array([ 0.04716041, 0.04755342, 0.04546713, 0.04627802, 0.04376583, 0.04474868, 0.04259991, 0.04491564, 0.04589027, 0.04890847]) time_1000_10_et_efr = np.array([0]) hazard_1000_10_et_efr = np.array([0]) coef_1000_10_st_efr = np.array([ -0.4911117, -0.4960756, -0.3226152, -0.220949, -0.09478141, 0.1015735, 0.1195524, 0.3446977, 0.3695904, 0.5878576]) se_1000_10_st_efr = np.array([ 0.04833676, 0.04868554, 0.04578407, 0.04661755, 0.04518267, 0.04537135, 0.04202183, 0.04531266, 0.0464931, 0.04949831]) time_1000_10_st_efr = np.array([0]) hazard_1000_10_st_efr = np.array([0]) coef_1000_10_et_st_efr = np.array([ -0.444355, -0.4283278, -0.3198815, -0.1901781, -0.09727039, 0.1106191, 0.1092104, 0.3034778, 0.3451699, 0.5382381]) se_1000_10_et_st_efr = np.array([ 0.04830664, 0.04833619, 0.04617371, 0.04706401, 0.04472699, 0.0454208, 0.04350539, 0.04588588, 0.04675675, 0.04950987]) time_1000_10_et_st_efr = np.array([0]) hazard_1000_10_et_st_efr = np.array([0]) statsmodels-0.12.2/statsmodels/duration/tests/results/survival_regularized.R000066400000000000000000000015721400612667500275770ustar00rootroot00000000000000library(glmnet) library(survival) library(R2nparray) # List containing (sample size, # covariates) for each data set ixd = list(c(50,2), c(100,5)) res = list() for (ix in ixd) { fname = sprintf("results/survival_data_%d_%d.csv", ix[1], ix[2]) data = read.table(fname) time = data[,1] status = data[,2] entry = data[,3] exog = data[,4:dim(data)[2]] exog = as.matrix(exog) n = dim(exog)[1] p = dim(exog)[2] for (k in 1:p) { exog[,k] = (exog[,k] - mean(exog[,k])) / sd(exog[,k]) } surv = Surv(time, status) md = glmnet(exog, surv, family="cox", lambda=c(0, 0.1)) #md1 = coxph(surv ~ exog, ties="breslow") tag = sprintf("%d_%d", n, p) res[[sprintf("coef_%s_0", tag)]] = as.vector(coef(md, s=0)) res[[sprintf("coef_%s_1", tag)]] = as.vector(coef(md, s=0.1)) } R2nparray(res, fname="survival_enet_r_results.py") statsmodels-0.12.2/statsmodels/duration/tests/test_phreg.py000066400000000000000000000352331400612667500242220ustar00rootroot00000000000000import itertools import os import numpy as np from statsmodels.duration.hazard_regression import PHReg from numpy.testing import (assert_allclose, assert_equal, assert_) import pandas as pd import pytest # TODO: Include some corner cases: data sets with empty strata, strata # with no events, entry times after censoring times, etc. # All the R results from .results import survival_r_results from .results import survival_enet_r_results """ Tests of PHReg against R coxph. Tests include entry times and stratification. phreg_gentests.py generates the test data sets and puts them into the results folder. survival.R runs R on all the test data sets and constructs the survival_r_results module. """ # Arguments passed to the PHReg fit method. args = {"method": "bfgs", "disp": 0} def get_results(n, p, ext, ties): if ext is None: coef_name = "coef_%d_%d_%s" % (n, p, ties) se_name = "se_%d_%d_%s" % (n, p, ties) time_name = "time_%d_%d_%s" % (n, p, ties) hazard_name = "hazard_%d_%d_%s" % (n, p, ties) else: coef_name = "coef_%d_%d_%s_%s" % (n, p, ext, ties) se_name = "se_%d_%d_%s_%s" % (n, p, ext, ties) time_name = "time_%d_%d_%s_%s" % (n, p, ext, ties) hazard_name = "hazard_%d_%d_%s_%s" % (n, p, ext, ties) coef = getattr(survival_r_results, coef_name) se = getattr(survival_r_results, se_name) time = getattr(survival_r_results, time_name) hazard = getattr(survival_r_results, hazard_name) return coef, se, time, hazard class TestPHReg(object): # Load a data file from the results directory @staticmethod def load_file(fname): cur_dir = os.path.dirname(os.path.abspath(__file__)) data = np.genfromtxt(os.path.join(cur_dir, 'results', fname), delimiter=" ") time = data[:,0] status = data[:,1] entry = data[:,2] exog = data[:,3:] return time, status, entry, exog # Run a single test against R output @staticmethod def do1(fname, ties, entry_f, strata_f): # Read the test data. time, status, entry, exog = TestPHReg.load_file(fname) n = len(time) vs = fname.split("_") n = int(vs[2]) p = int(vs[3].split(".")[0]) ties1 = ties[0:3] # Needs to match the kronecker statement in survival.R strata = np.kron(range(5), np.ones(n // 5)) # No stratification or entry times mod = PHReg(time, exog, status, ties=ties) phrb = mod.fit(**args) coef_r, se_r, time_r, hazard_r = get_results(n, p, None, ties1) assert_allclose(phrb.params, coef_r, rtol=1e-3) assert_allclose(phrb.bse, se_r, rtol=1e-4) time_h, cumhaz, surv = phrb.baseline_cumulative_hazard[0] # Entry times but no stratification phrb = PHReg(time, exog, status, entry=entry, ties=ties).fit(**args) coef, se, time_r, hazard_r = get_results(n, p, "et", ties1) assert_allclose(phrb.params, coef, rtol=1e-3) assert_allclose(phrb.bse, se, rtol=1e-3) # Stratification but no entry times phrb = PHReg(time, exog, status, strata=strata, ties=ties).fit(**args) coef, se, time_r, hazard_r = get_results(n, p, "st", ties1) assert_allclose(phrb.params, coef, rtol=1e-4) assert_allclose(phrb.bse, se, rtol=1e-4) # Stratification and entry times phrb = PHReg(time, exog, status, entry=entry, strata=strata, ties=ties).fit(**args) coef, se, time_r, hazard_r = get_results(n, p, "et_st", ties1) assert_allclose(phrb.params, coef, rtol=1e-3) assert_allclose(phrb.bse, se, rtol=1e-4) #smoke test time_h, cumhaz, surv = phrb.baseline_cumulative_hazard[0] def test_missing(self): np.random.seed(34234) time = 50 * np.random.uniform(size=200) status = np.random.randint(0, 2, 200).astype(np.float64) exog = np.random.normal(size=(200,4)) time[0:5] = np.nan status[5:10] = np.nan exog[10:15,:] = np.nan md = PHReg(time, exog, status, missing='drop') assert_allclose(len(md.endog), 185) assert_allclose(len(md.status), 185) assert_allclose(md.exog.shape, np.r_[185,4]) def test_formula(self): np.random.seed(34234) time = 50 * np.random.uniform(size=200) status = np.random.randint(0, 2, 200).astype(np.float64) exog = np.random.normal(size=(200,4)) entry = np.zeros_like(time) entry[0:10] = time[0:10] / 2 df = pd.DataFrame({"time": time, "status": status, "exog1": exog[:, 0], "exog2": exog[:, 1], "exog3": exog[:, 2], "exog4": exog[:, 3], "entry": entry}) mod1 = PHReg(time, exog, status, entry=entry) rslt1 = mod1.fit() # works with "0 +" on RHS but issues warning fml = "time ~ exog1 + exog2 + exog3 + exog4" mod2 = PHReg.from_formula(fml, df, status=status, entry=entry) rslt2 = mod2.fit() mod3 = PHReg.from_formula(fml, df, status="status", entry="entry") rslt3 = mod3.fit() assert_allclose(rslt1.params, rslt2.params) assert_allclose(rslt1.params, rslt3.params) assert_allclose(rslt1.bse, rslt2.bse) assert_allclose(rslt1.bse, rslt3.bse) def test_formula_cat_interactions(self): time = np.r_[1, 2, 3, 4, 5, 6, 7, 8, 9] status = np.r_[1, 1, 0, 0, 1, 0, 1, 1, 1] x1 = np.r_[1, 1, 1, 2, 2, 2, 3, 3, 3] x2 = np.r_[1, 2, 3, 1, 2, 3, 1, 2, 3] df = pd.DataFrame({"time": time, "status": status, "x1": x1, "x2": x2}) model1 = PHReg.from_formula("time ~ C(x1) + C(x2) + C(x1)*C(x2)", status="status", data=df) assert_equal(model1.exog.shape, [9, 8]) def test_predict_formula(self): n = 100 np.random.seed(34234) time = 50 * np.random.uniform(size=n) status = np.random.randint(0, 2, n).astype(np.float64) exog = np.random.uniform(1, 2, size=(n, 2)) df = pd.DataFrame({"time": time, "status": status, "exog1": exog[:, 0], "exog2": exog[:, 1]}) # Works with "0 +" on RHS but issues warning fml = "time ~ exog1 + np.log(exog2) + exog1*exog2" model1 = PHReg.from_formula(fml, df, status=status) result1 = model1.fit() from patsy import dmatrix dfp = dmatrix(model1.data.design_info, df) pr1 = result1.predict() pr2 = result1.predict(exog=df) pr3 = model1.predict(result1.params, exog=dfp) # No standard errors pr4 = model1.predict(result1.params, cov_params=result1.cov_params(), exog=dfp) prl = (pr1, pr2, pr3, pr4) for i in range(4): for j in range(i): assert_allclose(prl[i].predicted_values, prl[j].predicted_values) prl = (pr1, pr2, pr4) for i in range(3): for j in range(i): assert_allclose(prl[i].standard_errors, prl[j].standard_errors) def test_formula_args(self): np.random.seed(34234) n = 200 time = 50 * np.random.uniform(size=n) status = np.random.randint(0, 2, size=n).astype(np.float64) exog = np.random.normal(size=(200, 2)) offset = np.random.uniform(size=n) entry = np.random.uniform(0, 1, size=n) * time df = pd.DataFrame({"time": time, "status": status, "x1": exog[:, 0], "x2": exog[:, 1], "offset": offset, "entry": entry}) model1 = PHReg.from_formula("time ~ x1 + x2", status="status", offset="offset", entry="entry", data=df) result1 = model1.fit() model2 = PHReg.from_formula("time ~ x1 + x2", status=df.status, offset=df.offset, entry=df.entry, data=df) result2 = model2.fit() assert_allclose(result1.params, result2.params) assert_allclose(result1.bse, result2.bse) def test_offset(self): np.random.seed(34234) time = 50 * np.random.uniform(size=200) status = np.random.randint(0, 2, 200).astype(np.float64) exog = np.random.normal(size=(200,4)) for ties in "breslow", "efron": mod1 = PHReg(time, exog, status) rslt1 = mod1.fit() offset = exog[:,0] * rslt1.params[0] exog = exog[:, 1:] mod2 = PHReg(time, exog, status, offset=offset, ties=ties) rslt2 = mod2.fit() assert_allclose(rslt2.params, rslt1.params[1:]) def test_post_estimation(self): # All regression tests np.random.seed(34234) time = 50 * np.random.uniform(size=200) status = np.random.randint(0, 2, 200).astype(np.float64) exog = np.random.normal(size=(200,4)) mod = PHReg(time, exog, status) rslt = mod.fit() mart_resid = rslt.martingale_residuals assert_allclose(np.abs(mart_resid).sum(), 120.72475743348433) w_avg = rslt.weighted_covariate_averages assert_allclose(np.abs(w_avg[0]).sum(0), np.r_[7.31008415, 9.77608674,10.89515885, 13.1106801]) bc_haz = rslt.baseline_cumulative_hazard v = [np.mean(np.abs(x)) for x in bc_haz[0]] w = np.r_[23.482841556421608, 0.44149255358417017, 0.68660114081275281] assert_allclose(v, w) score_resid = rslt.score_residuals v = np.r_[ 0.50924792, 0.4533952, 0.4876718, 0.5441128] w = np.abs(score_resid).mean(0) assert_allclose(v, w) groups = np.random.randint(0, 3, 200) mod = PHReg(time, exog, status) rslt = mod.fit(groups=groups) robust_cov = rslt.cov_params() v = [0.00513432, 0.01278423, 0.00810427, 0.00293147] w = np.abs(robust_cov).mean(0) assert_allclose(v, w, rtol=1e-6) s_resid = rslt.schoenfeld_residuals ii = np.flatnonzero(np.isfinite(s_resid).all(1)) s_resid = s_resid[ii, :] v = np.r_[0.85154336, 0.72993748, 0.73758071, 0.78599333] assert_allclose(np.abs(s_resid).mean(0), v) @pytest.mark.smoke def test_summary(self): np.random.seed(34234) time = 50 * np.random.uniform(size=200) status = np.random.randint(0, 2, 200).astype(np.float64) exog = np.random.normal(size=(200,4)) mod = PHReg(time, exog, status) rslt = mod.fit() smry = rslt.summary() strata = np.kron(np.arange(50), np.ones(4)) mod = PHReg(time, exog, status, strata=strata) rslt = mod.fit() smry = rslt.summary() msg = "3 strata dropped for having no events" assert_(msg in str(smry)) groups = np.kron(np.arange(25), np.ones(8)) mod = PHReg(time, exog, status) rslt = mod.fit(groups=groups) smry = rslt.summary() entry = np.random.uniform(0.1, 0.8, 200) * time mod = PHReg(time, exog, status, entry=entry) rslt = mod.fit() smry = rslt.summary() msg = "200 observations have positive entry times" assert_(msg in str(smry)) @pytest.mark.smoke def test_predict(self): # All smoke tests. We should be able to convert the lhr and hr # tests into real tests against R. There are many options to # this function that may interact in complicated ways. Only a # few key combinations are tested here. np.random.seed(34234) endog = 50 * np.random.uniform(size=200) status = np.random.randint(0, 2, 200).astype(np.float64) exog = np.random.normal(size=(200,4)) mod = PHReg(endog, exog, status) rslt = mod.fit() rslt.predict() for pred_type in 'lhr', 'hr', 'cumhaz', 'surv': rslt.predict(pred_type=pred_type) rslt.predict(endog=endog[0:10], pred_type=pred_type) rslt.predict(endog=endog[0:10], exog=exog[0:10,:], pred_type=pred_type) @pytest.mark.smoke def test_get_distribution(self): np.random.seed(34234) n = 200 exog = np.random.normal(size=(n, 2)) lin_pred = exog.sum(1) elin_pred = np.exp(-lin_pred) time = -elin_pred * np.log(np.random.uniform(size=n)) status = np.ones(n) status[0:20] = 0 strata = np.kron(range(5), np.ones(n // 5)) mod = PHReg(time, exog, status=status, strata=strata) rslt = mod.fit() dist = rslt.get_distribution() fitted_means = dist.mean() true_means = elin_pred fitted_var = dist.var() fitted_sd = dist.std() sample = dist.rvs() def test_fit_regularized(self): # Data set sizes for n,p in (50,2),(100,5): # Penalty weights for js,s in enumerate([0,0.1]): coef_name = "coef_%d_%d_%d" % (n, p, js) params = getattr(survival_enet_r_results, coef_name) fname = "survival_data_%d_%d.csv" % (n, p) time, status, entry, exog = self.load_file(fname) exog -= exog.mean(0) exog /= exog.std(0, ddof=1) model = PHReg(time, exog, status=status, ties='breslow') sm_result = model.fit_regularized(alpha=s) # The agreement is not very high, the issue may be on # the R side. See below for further checks. assert_allclose(sm_result.params, params, rtol=0.3) # The penalized log-likelihood that we are maximizing. def plf(params): llf = model.loglike(params) / len(time) L1_wt = 1 llf = llf - s * ((1 - L1_wt)*np.sum(params**2) / 2 + L1_wt*np.sum(np.abs(params))) return llf # Confirm that we are doing better than glmnet. llf_r = plf(params) llf_sm = plf(sm_result.params) assert_equal(np.sign(llf_sm - llf_r), 1) cur_dir = os.path.dirname(os.path.abspath(__file__)) rdir = os.path.join(cur_dir, 'results') fnames = os.listdir(rdir) fnames = [x for x in fnames if x.startswith("survival") and x.endswith(".csv")] ties = ("breslow", "efron") entry_f = (False, True) strata_f = (False, True) @pytest.mark.parametrize('fname,ties,entry_f,strata_f', list(itertools.product(fnames, ties, entry_f, strata_f))) def test_r(fname, ties, entry_f, strata_f): TestPHReg.do1(fname, ties, entry_f, strata_f) statsmodels-0.12.2/statsmodels/duration/tests/test_survfunc.py000066400000000000000000000455211400612667500247710ustar00rootroot00000000000000import os import numpy as np from statsmodels.duration.survfunc import ( SurvfuncRight, survdiff, plot_survfunc, CumIncidenceRight) from numpy.testing import assert_allclose import pandas as pd import pytest # If true, the output is written to a multi-page pdf file. pdf_output = False try: import matplotlib.pyplot as plt except ImportError: pass def close_or_save(pdf, fig): if pdf_output: pdf.savefig(fig) """ library(survival) ti1 = c(3, 1, 2, 3, 2, 1, 5, 3) st1 = c(0, 1, 1, 1, 0, 0, 1, 0) ti2 = c(1, 1, 2, 3, 7, 1, 5, 3, 9) st2 = c(0, 1, 0, 0, 1, 0, 1, 0, 1) ti = c(ti1, ti2) st = c(st1, st2) ix = c(rep(1, length(ti1)), rep(2, length(ti2))) sd = survdiff(Surv(ti, st) ~ ix) """ ti1 = np.r_[3, 1, 2, 3, 2, 1, 5, 3] st1 = np.r_[0, 1, 1, 1, 0, 0, 1, 0] times1 = np.r_[1, 2, 3, 5] surv_prob1 = np.r_[0.8750000, 0.7291667, 0.5468750, 0.0000000] surv_prob_se1 = np.r_[0.1169268, 0.1649762, 0.2005800, np.nan] n_risk1 = np.r_[8, 6, 4, 1] n_events1 = np.r_[1., 1., 1., 1.] ti2 = np.r_[1, 1, 2, 3, 7, 1, 5, 3, 9] st2 = np.r_[0, 1, 0, 0, 1, 0, 1, 0, 1] times2 = np.r_[1, 5, 7, 9] surv_prob2 = np.r_[0.8888889, 0.5925926, 0.2962963, 0.0000000] surv_prob_se2 = np.r_[0.1047566, 0.2518034, 0.2444320, np.nan] n_risk2 = np.r_[9, 3, 2, 1] n_events2 = np.r_[1., 1., 1., 1.] cur_dir = os.path.dirname(os.path.abspath(__file__)) fp = os.path.join(cur_dir, 'results', 'bmt.csv') bmt = pd.read_csv(fp) def test_survfunc1(): # Test where all times have at least 1 event. sr = SurvfuncRight(ti1, st1) assert_allclose(sr.surv_prob, surv_prob1, atol=1e-5, rtol=1e-5) assert_allclose(sr.surv_prob_se, surv_prob_se1, atol=1e-5, rtol=1e-5) assert_allclose(sr.surv_times, times1) assert_allclose(sr.n_risk, n_risk1) assert_allclose(sr.n_events, n_events1) def test_survfunc2(): # Test where some times have no events. sr = SurvfuncRight(ti2, st2) assert_allclose(sr.surv_prob, surv_prob2, atol=1e-5, rtol=1e-5) assert_allclose(sr.surv_prob_se, surv_prob_se2, atol=1e-5, rtol=1e-5) assert_allclose(sr.surv_times, times2) assert_allclose(sr.n_risk, n_risk2) assert_allclose(sr.n_events, n_events2) def test_survdiff_basic(): # Constants taken from R, code above ti = np.concatenate((ti1, ti2)) st = np.concatenate((st1, st2)) groups = np.ones(len(ti)) groups[0:len(ti1)] = 0 z, p = survdiff(ti, st, groups) assert_allclose(z, 2.14673, atol=1e-4, rtol=1e-4) assert_allclose(p, 0.14287, atol=1e-4, rtol=1e-4) def test_simultaneous_cb(): # The exact numbers here are regression tests, but they are close # to page 103 of Klein and Moeschberger. df = bmt.loc[bmt["Group"] == "ALL", :] sf = SurvfuncRight(df["T"], df["Status"]) lcb1, ucb1 = sf.simultaneous_cb(transform="log") lcb2, ucb2 = sf.simultaneous_cb(transform="arcsin") ti = sf.surv_times.tolist() ix = [ti.index(x) for x in (110, 122, 129, 172)] assert_allclose(lcb1[ix], np.r_[0.43590582, 0.42115592, 0.4035897, 0.38785927]) assert_allclose(ucb1[ix], np.r_[0.93491636, 0.89776803, 0.87922239, 0.85894181]) assert_allclose(lcb2[ix], np.r_[0.52115708, 0.48079378, 0.45595321, 0.43341115]) assert_allclose(ucb2[ix], np.r_[0.96465636, 0.92745068, 0.90885428, 0.88796708]) def test_bmt(): # All tests against SAS # Results taken from here: # http://support.sas.com/documentation/cdl/en/statug/68162/HTML/default/viewer.htm#statug_lifetest_details03.htm # Confidence intervals for 25% percentile of the survival # distribution (for "ALL" subjects), taken from the SAS web site cb = {"linear": [107, 276], "cloglog": [86, 230], "log": [107, 332], "asinsqrt": [104, 276], "logit": [104, 230]} dfa = bmt[bmt.Group == "ALL"] cur_dir = os.path.dirname(os.path.abspath(__file__)) fp = os.path.join(cur_dir, 'results', 'bmt_results.csv') rslt = pd.read_csv(fp) sf = SurvfuncRight(dfa["T"].values, dfa.Status.values) assert_allclose(sf.surv_times, rslt.t) assert_allclose(sf.surv_prob, rslt.s, atol=1e-4, rtol=1e-4) assert_allclose(sf.surv_prob_se, rslt.se, atol=1e-4, rtol=1e-4) for method in "linear", "cloglog", "log", "logit", "asinsqrt": lcb, ucb = sf.quantile_ci(0.25, method=method) assert_allclose(cb[method], np.r_[lcb, ucb]) def test_survdiff(): # Results come from R survival and survMisc packages (survMisc is # used for non G-rho family tests but does not seem to support # stratification) full_df = bmt.copy() df = bmt[bmt.Group != "ALL"].copy() # Not stratified stat, p = survdiff(df["T"], df.Status, df.Group) assert_allclose(stat, 13.44556, atol=1e-4, rtol=1e-4) stat, p = survdiff(df["T"], df.Status, df.Group, weight_type="gb") assert_allclose(stat, 15.38787, atol=1e-4, rtol=1e-4) stat, p = survdiff(df["T"], df.Status, df.Group, weight_type="tw") assert_allclose(stat, 14.98382, atol=1e-4, rtol=1e-4) stat, p = survdiff(df["T"], df.Status, df.Group, weight_type="fh", fh_p=0.5) assert_allclose(stat, 14.46866, atol=1e-4, rtol=1e-4) stat, p = survdiff(df["T"], df.Status, df.Group, weight_type="fh", fh_p=1) assert_allclose(stat, 14.84500, atol=1e-4, rtol=1e-4) # Not stratified, >2 groups stat, p = survdiff(full_df["T"], full_df.Status, full_df.Group, weight_type="fh", fh_p=1) assert_allclose(stat, 15.67247, atol=1e-4, rtol=1e-4) # 5 strata strata = np.arange(df.shape[0]) % 5 df["strata"] = strata stat, p = survdiff(df["T"], df.Status, df.Group, strata=df.strata) assert_allclose(stat, 11.97799, atol=1e-4, rtol=1e-4) stat, p = survdiff(df["T"], df.Status, df.Group, strata=df.strata, weight_type="fh", fh_p=0.5) assert_allclose(stat, 12.6257, atol=1e-4, rtol=1e-4) stat, p = survdiff(df["T"], df.Status, df.Group, strata=df.strata, weight_type="fh", fh_p=1) assert_allclose(stat, 12.73565, atol=1e-4, rtol=1e-4) # 5 strata, >2 groups full_strata = np.arange(full_df.shape[0]) % 5 full_df["strata"] = full_strata stat, p = survdiff(full_df["T"], full_df.Status, full_df.Group, strata=full_df.strata, weight_type="fh", fh_p=0.5) assert_allclose(stat, 13.56793, atol=1e-4, rtol=1e-4) # 8 strata df["strata"] = np.arange(df.shape[0]) % 8 stat, p = survdiff(df["T"], df.Status, df.Group, strata=df.strata) assert_allclose(stat, 12.12631, atol=1e-4, rtol=1e-4) stat, p = survdiff(df["T"], df.Status, df.Group, strata=df.strata, weight_type="fh", fh_p=0.5) assert_allclose(stat, 12.9633, atol=1e-4, rtol=1e-4) stat, p = survdiff(df["T"], df.Status, df.Group, strata=df.strata, weight_type="fh", fh_p=1) assert_allclose(stat, 13.35259, atol=1e-4, rtol=1e-4) @pytest.mark.matplotlib def test_plot_km(close_figures): if pdf_output: from matplotlib.backends.backend_pdf import PdfPages pdf = PdfPages("test_survfunc.pdf") else: pdf = None sr1 = SurvfuncRight(ti1, st1) sr2 = SurvfuncRight(ti2, st2) fig = plot_survfunc(sr1) close_or_save(pdf, fig) fig = plot_survfunc(sr2) close_or_save(pdf, fig) fig = plot_survfunc([sr1, sr2]) close_or_save(pdf, fig) # Plot the SAS BMT data gb = bmt.groupby("Group") sv = [] for g in gb: s0 = SurvfuncRight(g[1]["T"], g[1]["Status"], title=g[0]) sv.append(s0) fig = plot_survfunc(sv) ax = fig.get_axes()[0] ax.set_position([0.1, 0.1, 0.64, 0.8]) ha, lb = ax.get_legend_handles_labels() fig.legend([ha[k] for k in (0, 2, 4)], [lb[k] for k in (0, 2, 4)], 'center right') close_or_save(pdf, fig) # Simultaneous CB for BMT data ii = bmt.Group == "ALL" sf = SurvfuncRight(bmt.loc[ii, "T"], bmt.loc[ii, "Status"]) fig = sf.plot() ax = fig.get_axes()[0] ax.set_position([0.1, 0.1, 0.64, 0.8]) ha, lb = ax.get_legend_handles_labels() lcb, ucb = sf.simultaneous_cb(transform="log") plt.fill_between(sf.surv_times, lcb, ucb, color="lightgrey") lcb, ucb = sf.simultaneous_cb(transform="arcsin") plt.plot(sf.surv_times, lcb, color="darkgrey") plt.plot(sf.surv_times, ucb, color="darkgrey") plt.plot(sf.surv_times, sf.surv_prob - 2*sf.surv_prob_se, color="red") plt.plot(sf.surv_times, sf.surv_prob + 2*sf.surv_prob_se, color="red") plt.xlim(100, 600) close_or_save(pdf, fig) if pdf_output: pdf.close() def test_weights1(): # tm = c(1, 3, 5, 6, 7, 8, 8, 9, 3, 4, 1, 3, 2) # st = c(1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0) # wt = c(1, 2, 3, 2, 3, 1, 2, 1, 1, 2, 2, 3, 1) # library(survival) # sf = survfit(Surv(tm, st) ~ 1, weights=wt, err='tsiatis') tm = np.r_[1, 3, 5, 6, 7, 8, 8, 9, 3, 4, 1, 3, 2] st = np.r_[1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0] wt = np.r_[1, 2, 3, 2, 3, 1, 2, 1, 1, 2, 2, 3, 1] sf = SurvfuncRight(tm, st, freq_weights=wt) assert_allclose(sf.surv_times, np.r_[1, 3, 6, 7, 9]) assert_allclose(sf.surv_prob, np.r_[0.875, 0.65625, 0.51041667, 0.29166667, 0.]) assert_allclose(sf.surv_prob_se, np.r_[0.07216878, 0.13307266, 0.20591185, 0.3219071, 1.05053519]) def test_weights2(): # tm = c(1, 3, 5, 6, 7, 2, 4, 6, 8, 10) # st = c(1, 1, 0, 1, 1, 1, 1, 0, 1, 1) # wt = c(1, 1, 1, 1, 1, 2, 2, 2, 2, 2) # library(survival) # sf =s urvfit(Surv(tm, st) ~ 1, weights=wt, err='tsiatis') tm = np.r_[1, 3, 5, 6, 7, 2, 4, 6, 8, 10] st = np.r_[1, 1, 0, 1, 1, 1, 1, 0, 1, 1] wt = np.r_[1, 1, 1, 1, 1, 2, 2, 2, 2, 2] tm0 = np.r_[1, 3, 5, 6, 7, 2, 4, 6, 8, 10, 2, 4, 6, 8, 10] st0 = np.r_[1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1] sf0 = SurvfuncRight(tm, st, freq_weights=wt) sf1 = SurvfuncRight(tm0, st0) assert_allclose(sf0.surv_times, sf1.surv_times) assert_allclose(sf0.surv_prob, sf1.surv_prob) assert_allclose(sf0.surv_prob_se, np.r_[0.06666667, 0.1210311, 0.14694547, 0.19524829, 0.23183377, 0.30618115, 0.46770386, 0.84778942]) def test_incidence(): # Check estimates in R: # ftime = c(1, 1, 2, 4, 4, 4, 6, 6, 7, 8, 9, 9, 9, 1, 2, 2, 4, 4) # fstat = c(1, 1, 1, 2, 2, 2, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0) # cuminc(ftime, fstat) # # The standard errors agree with Stata, not with R (cmprisk # package), which uses a different SE formula from Aalen (1978) # # To check with Stata: # stset ftime failure(fstat==1) # stcompet ci=ci, compet1(2) ftime = np.r_[1, 1, 2, 4, 4, 4, 6, 6, 7, 8, 9, 9, 9, 1, 2, 2, 4, 4] fstat = np.r_[1, 1, 1, 2, 2, 2, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0] ci = CumIncidenceRight(ftime, fstat) cinc = [np.array([0.11111111, 0.17037037, 0.17037037, 0.17037037, 0.17037037, 0.17037037, 0.17037037]), np.array([0., 0., 0.20740741, 0.20740741, 0.20740741, 0.20740741, 0.20740741]), np.array([0., 0., 0., 0.17777778, 0.26666667, 0.26666667, 0.26666667])] assert_allclose(cinc[0], ci.cinc[0]) assert_allclose(cinc[1], ci.cinc[1]) assert_allclose(cinc[2], ci.cinc[2]) cinc_se = [np.array([0.07407407, 0.08976251, 0.08976251, 0.08976251, 0.08976251, 0.08976251, 0.08976251]), np.array([0., 0., 0.10610391, 0.10610391, 0.10610391, 0.10610391, 0.10610391]), np.array([0., 0., 0., 0.11196147, 0.12787781, 0.12787781, 0.12787781])] assert_allclose(cinc_se[0], ci.cinc_se[0]) assert_allclose(cinc_se[1], ci.cinc_se[1]) assert_allclose(cinc_se[2], ci.cinc_se[2]) # Simple check for frequency weights weights = np.ones(len(ftime)) ciw = CumIncidenceRight(ftime, fstat, freq_weights=weights) assert_allclose(ci.cinc[0], ciw.cinc[0]) assert_allclose(ci.cinc[1], ciw.cinc[1]) assert_allclose(ci.cinc[2], ciw.cinc[2]) def test_survfunc_entry_1(): # times = c(1, 3, 3, 5, 5, 7, 7, 8, 8, 9, 10, 10) # status = c(1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1) # entry = c(0, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 0) # sv = Surv(entry, times, event=status) # sdf = survfit(coxph(sv ~ 1), type='kaplan-meier') times = np.r_[1, 3, 3, 5, 5, 7, 7, 8, 8, 9, 10, 10] status = np.r_[1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1] entry = np.r_[0, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 0] sf = SurvfuncRight(times, status, entry=entry) assert_allclose(sf.n_risk, np.r_[2, 6, 9, 7, 5, 3, 2]) assert_allclose(sf.surv_times, np.r_[1, 3, 5, 7, 8, 9, 10]) assert_allclose(sf.surv_prob, np.r_[ 0.5000, 0.4167, 0.3241, 0.2778, 0.2222, 0.1481, 0.0741], atol=1e-4) assert_allclose(sf.surv_prob_se, np.r_[ 0.3536, 0.3043, 0.2436, 0.2132, 0.1776, 0.1330, 0.0846], atol=1e-4) def test_survfunc_entry_2(): # entry = 0 is equivalent to no entry time times = np.r_[1, 3, 3, 5, 5, 7, 7, 8, 8, 9, 10, 10] status = np.r_[1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1] entry = np.r_[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] sf = SurvfuncRight(times, status, entry=entry) sf0 = SurvfuncRight(times, status) assert_allclose(sf.n_risk, sf0.n_risk) assert_allclose(sf.surv_times, sf0.surv_times) assert_allclose(sf.surv_prob, sf0.surv_prob) assert_allclose(sf.surv_prob_se, sf0.surv_prob_se) def test_survfunc_entry_3(): # times = c(1, 2, 5, 6, 6, 6, 6, 6, 9) # status = c(0, 0, 1, 1, 1, 0, 1, 1, 0) # entry = c(0, 1, 1, 2, 2, 2, 3, 4, 4) # sv = Surv(entry, times, event=status) # sdf = survfit(coxph(sv ~ 1), type='kaplan-meier') times = np.r_[1, 2, 5, 6, 6, 6, 6, 6, 9] status = np.r_[0, 0, 1, 1, 1, 0, 1, 1, 0] entry = np.r_[0, 1, 1, 2, 2, 2, 3, 4, 4] sf = SurvfuncRight(times, status, entry=entry) assert_allclose(sf.n_risk, np.r_[7, 6]) assert_allclose(sf.surv_times, np.r_[5, 6]) assert_allclose(sf.surv_prob, np.r_[0.857143, 0.285714], atol=1e-5) assert_allclose(sf.surv_prob_se, np.r_[0.13226, 0.170747], atol=1e-5) def test_survdiff_entry_1(): # entry times = 0 is equivalent to no entry times ti = np.r_[1, 3, 4, 2, 5, 4, 6, 7, 5, 9] st = np.r_[1, 1, 0, 1, 1, 0, 1, 1, 0, 0] gr = np.r_[0, 0, 0, 0, 0, 1, 1, 1, 1, 1] entry = np.r_[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] z1, p1 = survdiff(ti, st, gr, entry=entry) z2, p2 = survdiff(ti, st, gr) assert_allclose(z1, z2) assert_allclose(p1, p2) def test_survdiff_entry_2(): # Tests against Stata: # # stset time, failure(status) entry(entry) # sts test group, logrank ti = np.r_[5, 3, 4, 2, 5, 4, 6, 7, 5, 9] st = np.r_[1, 1, 0, 1, 1, 0, 1, 1, 0, 0] gr = np.r_[0, 0, 0, 0, 0, 1, 1, 1, 1, 1] entry = np.r_[1, 2, 2, 1, 3, 3, 5, 4, 2, 5] # Check with no entry times z, p = survdiff(ti, st, gr) assert_allclose(z, 6.694424) assert_allclose(p, 0.00967149) # Check with entry times z, p = survdiff(ti, st, gr, entry=entry) assert_allclose(z, 3.0) assert_allclose(p, 0.083264516) def test_survdiff_entry_3(): # Tests against Stata: # # stset time, failure(status) entry(entry) # sts test group, logrank ti = np.r_[2, 1, 5, 8, 7, 8, 8, 9, 4, 9] st = np.r_[1, 1, 1, 1, 1, 0, 1, 0, 0, 0] gr = np.r_[0, 0, 0, 0, 0, 1, 1, 1, 1, 1] entry = np.r_[1, 1, 2, 2, 3, 3, 2, 1, 2, 0] # Check with no entry times z, p = survdiff(ti, st, gr) assert_allclose(z, 6.9543024) assert_allclose(p, 0.008361789) # Check with entry times z, p = survdiff(ti, st, gr, entry=entry) assert_allclose(z, 6.75082959) assert_allclose(p, 0.00937041) def test_incidence2(): # Check that the cumulative incidence functions for all competing # risks sum to the complementary survival function. np.random.seed(2423) n = 200 time = -np.log(np.random.uniform(size=n)) status = np.random.randint(0, 3, size=n) ii = np.argsort(time) time = time[ii] status = status[ii] ci = CumIncidenceRight(time, status) statusa = 1*(status >= 1) sf = SurvfuncRight(time, statusa) x = 1 - sf.surv_prob y = (ci.cinc[0] + ci.cinc[1])[np.flatnonzero(statusa)] assert_allclose(x, y) def test_kernel_survfunc1(): # Regression test n = 100 np.random.seed(3434) x = np.random.normal(size=(n, 3)) time = np.random.uniform(size=n) status = np.random.randint(0, 2, size=n) result = SurvfuncRight(time, status, exog=x) timex = np.r_[0.30721103, 0.0515439, 0.69246897, 0.16446079, 0.31308528] sprob = np.r_[0.98948277, 0.98162275, 0.97129237, 0.96044668, 0.95030368] assert_allclose(result.time[0:5], timex) assert_allclose(result.surv_prob[0:5], sprob) def test_kernel_survfunc2(): # Check that when bandwidth is very large, the kernel procedure # agrees with standard KM. (Note: the results do not agree # perfectly when there are tied times). n = 100 np.random.seed(3434) x = np.random.normal(size=(n, 3)) time = np.random.uniform(0, 10, size=n) status = np.random.randint(0, 2, size=n) resultkm = SurvfuncRight(time, status) result = SurvfuncRight(time, status, exog=x, bw_factor=10000) assert_allclose(resultkm.surv_times, result.surv_times) assert_allclose(resultkm.surv_prob, result.surv_prob, rtol=1e-6, atol=1e-6) @pytest.mark.smoke def test_kernel_survfunc3(): # cases with tied times n = 100 np.random.seed(3434) x = np.random.normal(size=(n, 3)) time = np.random.randint(0, 10, size=n) status = np.random.randint(0, 2, size=n) SurvfuncRight(time, status, exog=x, bw_factor=10000) SurvfuncRight(time, status, exog=x, bw_factor=np.r_[10000, 10000]) def test_kernel_cumincidence1(): # Check that when the bandwidth is very large, the kernel # procedure agrees with standard cumulative incidence # calculations. (Note: the results do not agree perfectly when # there are tied times). n = 100 np.random.seed(3434) x = np.random.normal(size=(n, 3)) time = np.random.uniform(0, 10, size=n) status = np.random.randint(0, 3, size=n) result1 = CumIncidenceRight(time, status) for dimred in False, True: result2 = CumIncidenceRight(time, status, exog=x, bw_factor=10000, dimred=dimred) assert_allclose(result1.times, result2.times) for k in 0, 1: assert_allclose(result1.cinc[k], result2.cinc[k], rtol=1e-5) @pytest.mark.smoke def test_kernel_cumincidence2(): # cases with tied times n = 100 np.random.seed(3434) x = np.random.normal(size=(n, 3)) time = np.random.randint(0, 10, size=n) status = np.random.randint(0, 3, size=n) CumIncidenceRight(time, status, exog=x, bw_factor=10000) statsmodels-0.12.2/statsmodels/emplike/000077500000000000000000000000001400612667500201355ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/emplike/__init__.py000066400000000000000000000001131400612667500222410ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/emplike/aft_el.py000066400000000000000000000434001400612667500217420ustar00rootroot00000000000000""" Accelerated Failure Time (AFT) Model with empirical likelihood inference. AFT regression analysis is applicable when the researcher has access to a randomly right censored dependent variable, a matrix of exogenous variables and an indicatior variable (delta) that takes a value of 0 if the observation is censored and 1 otherwise. AFT References -------------- Stute, W. (1993). "Consistent Estimation Under Random Censorship when Covariables are Present." Journal of Multivariate Analysis. Vol. 45. Iss. 1. 89-103 EL and AFT References --------------------- Zhou, Kim And Bathke. "Empirical Likelihood Analysis for the Heteroskedastic Accelerated Failure Time Model." Manuscript: URL: www.ms.uky.edu/~mai/research/CasewiseEL20080724.pdf Zhou, M. (2005). Empirical Likelihood Ratio with Arbitrarily Censored/ Truncated Data by EM Algorithm. Journal of Computational and Graphical Statistics. 14:3, 643-656. """ import numpy as np from statsmodels.regression.linear_model import OLS, WLS from statsmodels.tools import add_constant #from elregress import ElReg from scipy import optimize from scipy.stats import chi2 from .descriptive import _OptFuncts import warnings from statsmodels.tools.sm_exceptions import IterationLimitWarning class OptAFT(_OptFuncts): """ Provides optimization functions used in estimating and conducting inference in an AFT model. Methods ------ _opt_wtd_nuis_regress: Function optimized over nuisance parameters to compute the profile likelihood _EM_test: Uses the modified Em algorithm of Zhou 2005 to maximize the likelihood of a parameter vector. """ def __init__(self): pass def _opt_wtd_nuis_regress(self, test_vals): """ A function that is optimized over nuisance parameters to conduct a hypothesis test for the parameters of interest Parameters ---------- params: 1d array The regression coefficients of the model. This includes the nuisance and parameters of interests. Returns ------- llr : float -2 times the log likelihood of the nuisance parameters and the hypothesized value of the parameter(s) of interest. """ test_params = test_vals.reshape(self.model.nvar, 1) est_vect = self.model.uncens_exog * (self.model.uncens_endog - np.dot(self.model.uncens_exog, test_params)) eta_star = self._modif_newton(np.zeros(self.model.nvar), est_vect, self.model._fit_weights) denom = np.sum(self.model._fit_weights) + np.dot(eta_star, est_vect.T) self.new_weights = self.model._fit_weights / denom return -1 * np.sum(np.log(self.new_weights)) def _EM_test(self, nuisance_params, params=None, param_nums=None, b0_vals=None, F=None, survidx=None, uncens_nobs=None, numcensbelow=None, km=None, uncensored=None, censored=None, maxiter=None, ftol=None): """ Uses EM algorithm to compute the maximum likelihood of a test Parameters ---------- nuisance_params : ndarray Vector of values to be used as nuisance params. maxiter : int Number of iterations in the EM algorithm for a parameter vector Returns ------- -2 ''*'' log likelihood ratio at hypothesized values and nuisance params Notes ----- Optional parameters are provided by the test_beta function. """ iters = 0 params[param_nums] = b0_vals nuis_param_index = np.int_(np.delete(np.arange(self.model.nvar), param_nums)) params[nuis_param_index] = nuisance_params to_test = params.reshape(self.model.nvar, 1) opt_res = np.inf diff = np.inf while iters < maxiter and diff > ftol: F = F.flatten() death = np.cumsum(F[::-1]) survivalprob = death[::-1] surv_point_mat = np.dot(F.reshape(-1, 1), 1. / survivalprob[survidx].reshape(1, - 1)) surv_point_mat = add_constant(surv_point_mat) summed_wts = np.cumsum(surv_point_mat, axis=1) wts = summed_wts[np.int_(np.arange(uncens_nobs)), numcensbelow[uncensored]] # ^E step # See Zhou 2005, section 3. self.model._fit_weights = wts new_opt_res = self._opt_wtd_nuis_regress(to_test) # ^ Uncensored weights' contribution to likelihood value. F = self.new_weights # ^ M step diff = np.abs(new_opt_res - opt_res) opt_res = new_opt_res iters = iters + 1 death = np.cumsum(F.flatten()[::-1]) survivalprob = death[::-1] llike = -opt_res + np.sum(np.log(survivalprob[survidx])) wtd_km = km.flatten() / np.sum(km) survivalmax = np.cumsum(wtd_km[::-1])[::-1] llikemax = np.sum(np.log(wtd_km[uncensored])) + \ np.sum(np.log(survivalmax[censored])) if iters == maxiter: warnings.warn('The EM reached the maximum number of iterations', IterationLimitWarning) return -2 * (llike - llikemax) def _ci_limits_beta(self, b0, param_num=None): """ Returns the difference between the log likelihood for a parameter and some critical value. Parameters ---------- b0: float Value of a regression parameter param_num : int Parameter index of b0 """ return self.test_beta([b0], [param_num])[0] - self.r0 class emplikeAFT(object): """ Class for estimating and conducting inference in an AFT model. Parameters ---------- endog: nx1 array Response variables that are subject to random censoring exog: nxk array Matrix of covariates censors: nx1 array array with entries 0 or 1. 0 indicates a response was censored. Attributes ---------- nobs : float Number of observations endog : ndarray Endog attay exog : ndarray Exogenous variable matrix censors Censors array but sets the max(endog) to uncensored nvar : float Number of exogenous variables uncens_nobs : float Number of uncensored observations uncens_endog : ndarray Uncensored response variables uncens_exog : ndarray Exogenous variables of the uncensored observations Methods ------- params: Fits model parameters test_beta: Tests if beta = b0 for any vector b0. Notes ----- The data is immediately sorted in order of increasing endogenous variables The last observation is assumed to be uncensored which makes estimation and inference possible. """ def __init__(self, endog, exog, censors): self.nobs = np.shape(exog)[0] self.endog = endog.reshape(self.nobs, 1) self.exog = exog.reshape(self.nobs, -1) self.censors = censors.reshape(self.nobs, 1) self.nvar = self.exog.shape[1] idx = np.lexsort((-self.censors[:, 0], self.endog[:, 0])) self.endog = self.endog[idx] self.exog = self.exog[idx] self.censors = self.censors[idx] self.censors[-1] = 1 # Sort in init, not in function self.uncens_nobs = int(np.sum(self.censors)) mask = self.censors.ravel().astype(bool) self.uncens_endog = self.endog[mask, :].reshape(-1, 1) self.uncens_exog = self.exog[mask, :] def _is_tied(self, endog, censors): """ Indicated if an observation takes the same value as the next ordered observation. Parameters ---------- endog : ndarray Models endogenous variable censors : ndarray arrat indicating a censored array Returns ------- indic_ties : ndarray ties[i]=1 if endog[i]==endog[i+1] and censors[i]=censors[i+1] """ nobs = int(self.nobs) endog_idx = endog[np.arange(nobs - 1)] == ( endog[np.arange(nobs - 1) + 1]) censors_idx = censors[np.arange(nobs - 1)] == ( censors[np.arange(nobs - 1) + 1]) indic_ties = endog_idx * censors_idx # Both true return np.int_(indic_ties) def _km_w_ties(self, tie_indic, untied_km): """ Computes KM estimator value at each observation, taking into acocunt ties in the data. Parameters ---------- tie_indic: 1d array Indicates if the i'th observation is the same as the ith +1 untied_km: 1d array Km estimates at each observation assuming no ties. """ # TODO: Vectorize, even though it is only 1 pass through for any # function call num_same = 1 idx_nums = [] for obs_num in np.arange(int(self.nobs - 1))[::-1]: if tie_indic[obs_num] == 1: idx_nums.append(obs_num) num_same = num_same + 1 untied_km[obs_num] = untied_km[obs_num + 1] elif tie_indic[obs_num] == 0 and num_same > 1: idx_nums.append(max(idx_nums) + 1) idx_nums = np.asarray(idx_nums) untied_km[idx_nums] = untied_km[idx_nums] num_same = 1 idx_nums = [] return untied_km.reshape(self.nobs, 1) def _make_km(self, endog, censors): """ Computes the Kaplan-Meier estimate for the weights in the AFT model Parameters ---------- endog: nx1 array Array of response variables censors: nx1 array Censor-indicating variable Returns ------- Kaplan Meier estimate for each observation Notes ----- This function makes calls to _is_tied and km_w_ties to handle ties in the data.If a censored observation and an uncensored observation has the same value, it is assumed that the uncensored happened first. """ nobs = self.nobs num = (nobs - (np.arange(nobs) + 1.)) denom = ((nobs - (np.arange(nobs) + 1.) + 1.)) km = (num / denom).reshape(nobs, 1) km = km ** np.abs(censors - 1.) km = np.cumprod(km) # If no ties, this is kaplan-meier tied = self._is_tied(endog, censors) wtd_km = self._km_w_ties(tied, km) return (censors / wtd_km).reshape(nobs, 1) def fit(self): """ Fits an AFT model and returns results instance Parameters ---------- None Returns ------- Results instance. Notes ----- To avoid dividing by zero, max(endog) is assumed to be uncensored. """ return AFTResults(self) def predict(self, params, endog=None): if endog is None: endog = self.endog return np.dot(endog, params) class AFTResults(OptAFT): def __init__(self, model): self.model = model def params(self): """ Fits an AFT model and returns parameters. Parameters ---------- None Returns ------- Fitted params Notes ----- To avoid dividing by zero, max(endog) is assumed to be uncensored. """ self.model.modif_censors = np.copy(self.model.censors) self.model.modif_censors[-1] = 1 wts = self.model._make_km(self.model.endog, self.model.modif_censors) res = WLS(self.model.endog, self.model.exog, wts).fit() params = res.params return params def test_beta(self, b0_vals, param_nums, ftol=10 ** - 5, maxiter=30, print_weights=1): """ Returns the profile log likelihood for regression parameters 'param_num' at 'b0_vals.' Parameters ---------- b0_vals : list The value of parameters to be tested param_num : list Which parameters to be tested maxiter : int, optional How many iterations to use in the EM algorithm. Default is 30 ftol : float, optional The function tolerance for the EM optimization. Default is 10''**''-5 print_weights : bool If true, returns the weights tate maximize the profile log likelihood. Default is False Returns ------- test_results : tuple The log-likelihood and p-pvalue of the test. Notes ----- The function will warn if the EM reaches the maxiter. However, when optimizing over nuisance parameters, it is possible to reach a maximum number of inner iterations for a specific value for the nuisance parameters while the resultsof the function are still valid. This usually occurs when the optimization over the nuisance parameters selects parameter values that yield a log-likihood ratio close to infinity. Examples -------- >>> import statsmodels.api as sm >>> import numpy as np # Test parameter is .05 in one regressor no intercept model >>> data=sm.datasets.heart.load(as_pandas=False) >>> y = np.log10(data.endog) >>> x = data.exog >>> cens = data.censors >>> model = sm.emplike.emplikeAFT(y, x, cens) >>> res=model.test_beta([0], [0]) >>> res (1.4657739632606308, 0.22601365256959183) #Test slope is 0 in model with intercept >>> data=sm.datasets.heart.load(as_pandas=False) >>> y = np.log10(data.endog) >>> x = data.exog >>> cens = data.censors >>> model = sm.emplike.emplikeAFT(y, sm.add_constant(x), cens) >>> res = model.test_beta([0], [1]) >>> res (4.623487775078047, 0.031537049752572731) """ censors = self.model.censors endog = self.model.endog exog = self.model.exog uncensored = (censors == 1).flatten() censored = (censors == 0).flatten() uncens_endog = endog[uncensored] uncens_exog = exog[uncensored, :] reg_model = OLS(uncens_endog, uncens_exog).fit() llr, pval, new_weights = reg_model.el_test(b0_vals, param_nums, return_weights=True) # Needs to be changed km = self.model._make_km(endog, censors).flatten() # when merged uncens_nobs = self.model.uncens_nobs F = np.asarray(new_weights).reshape(uncens_nobs) # Step 0 ^ params = self.params() survidx = np.where(censors == 0) survidx = survidx[0] - np.arange(len(survidx[0])) numcensbelow = np.int_(np.cumsum(1 - censors)) if len(param_nums) == len(params): llr = self._EM_test([], F=F, params=params, param_nums=param_nums, b0_vals=b0_vals, survidx=survidx, uncens_nobs=uncens_nobs, numcensbelow=numcensbelow, km=km, uncensored=uncensored, censored=censored, ftol=ftol, maxiter=25) return llr, chi2.sf(llr, self.model.nvar) else: x0 = np.delete(params, param_nums) try: res = optimize.fmin(self._EM_test, x0, (params, param_nums, b0_vals, F, survidx, uncens_nobs, numcensbelow, km, uncensored, censored, maxiter, ftol), full_output=1, disp=0) llr = res[1] return llr, chi2.sf(llr, len(param_nums)) except np.linalg.linalg.LinAlgError: return np.inf, 0 def ci_beta(self, param_num, beta_high, beta_low, sig=.05): """ Returns the confidence interval for a regression parameter in the AFT model. Parameters ---------- param_num : int Parameter number of interest beta_high : float Upper bound for the confidence interval beta_low : float Lower bound for the confidence interval sig : float, optional Significance level. Default is .05 Notes ----- If the function returns f(a) and f(b) must have different signs, consider widening the search area by adjusting beta_low and beta_high. Also note that this process is computational intensive. There are 4 levels of optimization/solving. From outer to inner: 1) Solving so that llr-critical value = 0 2) maximizing over nuisance parameters 3) Using EM at each value of nuisamce parameters 4) Using the _modified_Newton optimizer at each iteration of the EM algorithm. Also, for very unlikely nuisance parameters, it is possible for the EM algorithm to not converge. This is not an indicator that the solver did not find the correct solution. It just means for a specific iteration of the nuisance parameters, the optimizer was unable to converge. If the user desires to verify the success of the optimization, it is recommended to test the limits using test_beta. """ params = self.params() self.r0 = chi2.ppf(1 - sig, 1) ll = optimize.brentq(self._ci_limits_beta, beta_low, params[param_num], (param_num)) ul = optimize.brentq(self._ci_limits_beta, params[param_num], beta_high, (param_num)) return ll, ul statsmodels-0.12.2/statsmodels/emplike/api.py000066400000000000000000000005061400612667500212610ustar00rootroot00000000000000""" API for empirical likelihood """ __all__ = [ "DescStat", "DescStatUV", "DescStatMV", "ELOriginRegress", "ANOVA", "emplikeAFT" ] # pylint: disable=W0611 from .descriptive import DescStat, DescStatUV, DescStatMV from .originregress import ELOriginRegress from .elanova import ANOVA from .aft_el import emplikeAFT statsmodels-0.12.2/statsmodels/emplike/descriptive.py000066400000000000000000001140531400612667500230340ustar00rootroot00000000000000""" Empirical likelihood inference on descriptive statistics This module conducts hypothesis tests and constructs confidence intervals for the mean, variance, skewness, kurtosis and correlation. If matplotlib is installed, this module can also generate multivariate confidence region plots as well as mean-variance contour plots. See _OptFuncts docstring for technical details and optimization variable definitions. General References: ------------------ Owen, A. (2001). "Empirical Likelihood." Chapman and Hall """ import numpy as np from scipy import optimize from scipy.stats import chi2, skew, kurtosis from statsmodels.base.optimizer import _fit_newton import itertools from statsmodels.graphics import utils def DescStat(endog): """ Returns an instance to conduct inference on descriptive statistics via empirical likelihood. See DescStatUV and DescStatMV for more information. Parameters ---------- endog : ndarray Array of data Returns : DescStat instance If k=1, the function returns a univariate instance, DescStatUV. If k>1, the function returns a multivariate instance, DescStatMV. """ if endog.ndim == 1: endog = endog.reshape(len(endog), 1) if endog.shape[1] == 1: return DescStatUV(endog) if endog.shape[1] > 1: return DescStatMV(endog) class _OptFuncts(object): """ A class that holds functions that are optimized/solved. The general setup of the class is simple. Any method that starts with _opt_ creates a vector of estimating equations named est_vect such that np.dot(p, (est_vect))=0 where p is the weight on each observation as a 1 x n array and est_vect is n x k. Then _modif_Newton is called to determine the optimal p by solving for the Lagrange multiplier (eta) in the profile likelihood maximization problem. In the presence of nuisance parameters, _opt_ functions are optimized over to profile out the nuisance parameters. Any method starting with _ci_limits calculates the log likelihood ratio for a specific value of a parameter and then subtracts a pre-specified critical value. This is solved so that llr - crit = 0. """ def __init__(self, endog): pass def _log_star(self, eta, est_vect, weights, nobs): """ Transforms the log of observation probabilities in terms of the Lagrange multiplier to the log 'star' of the probabilities. Parameters ---------- eta : float Lagrange multiplier est_vect : ndarray (n,k) Estimating equations vector wts : nx1 array Observation weights Returns ------ data_star : ndarray The weighted logstar of the estimting equations Notes ----- This function is only a placeholder for the _fit_Newton. The function value is not used in optimization and the optimal value is disregarded when computing the log likelihood ratio. """ data_star = np.log(weights) + (np.sum(weights) +\ np.dot(est_vect, eta)) idx = data_star < 1. / nobs not_idx = ~idx nx = nobs * data_star[idx] data_star[idx] = np.log(1. / nobs) - 1.5 + nx * (2. - nx / 2) data_star[not_idx] = np.log(data_star[not_idx]) return data_star def _hess(self, eta, est_vect, weights, nobs): """ Calculates the hessian of a weighted empirical likelihood problem. Parameters ---------- eta : ndarray, (1,m) Lagrange multiplier in the profile likelihood maximization est_vect : ndarray (n,k) Estimating equations vector weights : 1darray Observation weights Returns ------- hess : m x m array Weighted hessian used in _wtd_modif_newton """ #eta = np.squeeze(eta) data_star_doub_prime = np.sum(weights) + np.dot(est_vect, eta) idx = data_star_doub_prime < 1. / nobs not_idx = ~idx data_star_doub_prime[idx] = - nobs ** 2 data_star_doub_prime[not_idx] = - (data_star_doub_prime[not_idx]) ** -2 wtd_dsdp = weights * data_star_doub_prime return np.dot(est_vect.T, wtd_dsdp[:, None] * est_vect) def _grad(self, eta, est_vect, weights, nobs): """ Calculates the gradient of a weighted empirical likelihood problem Parameters ---------- eta : ndarray, (1,m) Lagrange multiplier in the profile likelihood maximization est_vect : ndarray, (n,k) Estimating equations vector weights : 1darray Observation weights Returns ------- gradient : ndarray (m,1) The gradient used in _wtd_modif_newton """ #eta = np.squeeze(eta) data_star_prime = np.sum(weights) + np.dot(est_vect, eta) idx = data_star_prime < 1. / nobs not_idx = ~idx data_star_prime[idx] = nobs * (2 - nobs * data_star_prime[idx]) data_star_prime[not_idx] = 1. / data_star_prime[not_idx] return np.dot(weights * data_star_prime, est_vect) def _modif_newton(self, eta, est_vect, weights): """ Modified Newton's method for maximizing the log 'star' equation. This function calls _fit_newton to find the optimal values of eta. Parameters ---------- eta : ndarray, (1,m) Lagrange multiplier in the profile likelihood maximization est_vect : ndarray, (n,k) Estimating equations vector weights : 1darray Observation weights Returns ------- params : 1xm array Lagrange multiplier that maximizes the log-likelihood """ nobs = len(est_vect) f = lambda x0: - np.sum(self._log_star(x0, est_vect, weights, nobs)) grad = lambda x0: - self._grad(x0, est_vect, weights, nobs) hess = lambda x0: - self._hess(x0, est_vect, weights, nobs) kwds = {'tol': 1e-8} eta = eta.squeeze() res = _fit_newton(f, grad, eta, (), kwds, hess=hess, maxiter=50, \ disp=0) return res[0] def _find_eta(self, eta): """ Finding the root of sum(xi-h0)/(1+eta(xi-mu)) solves for eta when computing ELR for univariate mean. Parameters ---------- eta : float Lagrange multiplier in the empirical likelihood maximization Returns ------- llr : float n times the log likelihood value for a given value of eta """ return np.sum((self.endog - self.mu0) / \ (1. + eta * (self.endog - self.mu0))) def _ci_limits_mu(self, mu): """ Calculates the difference between the log likelihood of mu_test and a specified critical value. Parameters ---------- mu : float Hypothesized value of the mean. Returns ------- diff : float The difference between the log likelihood value of mu0 and a specified value. """ return self.test_mean(mu)[0] - self.r0 def _find_gamma(self, gamma): """ Finds gamma that satisfies sum(log(n * w(gamma))) - log(r0) = 0 Used for confidence intervals for the mean Parameters ---------- gamma : float Lagrange multiplier when computing confidence interval Returns ------- diff : float The difference between the log-liklihood when the Lagrange multiplier is gamma and a pre-specified value """ denom = np.sum((self.endog - gamma) ** -1) new_weights = (self.endog - gamma) ** -1 / denom return -2 * np.sum(np.log(self.nobs * new_weights)) - \ self.r0 def _opt_var(self, nuisance_mu, pval=False): """ This is the function to be optimized over a nuisance mean parameter to determine the likelihood ratio for the variance Parameters ---------- nuisance_mu : float Value of a nuisance mean parameter Returns ------- llr : float Log likelihood of a pre-specified variance holding the nuisance parameter constant """ endog = self.endog nobs = self.nobs sig_data = ((endog - nuisance_mu) ** 2 \ - self.sig2_0) mu_data = (endog - nuisance_mu) est_vect = np.column_stack((mu_data, sig_data)) eta_star = self._modif_newton(np.array([1. / nobs, 1. / nobs]), est_vect, np.ones(nobs) * (1. / nobs)) denom = 1 + np.dot(eta_star, est_vect.T) self.new_weights = 1. / nobs * 1. / denom llr = np.sum(np.log(nobs * self.new_weights)) if pval: # Used for contour plotting return chi2.sf(-2 * llr, 1) return -2 * llr def _ci_limits_var(self, var): """ Used to determine the confidence intervals for the variance. It calls test_var and when called by an optimizer, finds the value of sig2_0 that is chi2.ppf(significance-level) Parameters ---------- var_test : float Hypothesized value of the variance Returns ------- diff : float The difference between the log likelihood ratio at var_test and a pre-specified value. """ return self.test_var(var)[0] - self.r0 def _opt_skew(self, nuis_params): """ Called by test_skew. This function is optimized over nuisance parameters mu and sigma Parameters ---------- nuis_params : 1darray An array with a nuisance mean and variance parameter Returns ------- llr : float The log likelihood ratio of a pre-specified skewness holding the nuisance parameters constant. """ endog = self.endog nobs = self.nobs mu_data = endog - nuis_params[0] sig_data = ((endog - nuis_params[0]) ** 2) - nuis_params[1] skew_data = ((((endog - nuis_params[0]) ** 3) / (nuis_params[1] ** 1.5))) - self.skew0 est_vect = np.column_stack((mu_data, sig_data, skew_data)) eta_star = self._modif_newton(np.array([1. / nobs, 1. / nobs, 1. / nobs]), est_vect, np.ones(nobs) * (1. / nobs)) denom = 1. + np.dot(eta_star, est_vect.T) self.new_weights = 1. / nobs * 1. / denom llr = np.sum(np.log(nobs * self.new_weights)) return -2 * llr def _opt_kurt(self, nuis_params): """ Called by test_kurt. This function is optimized over nuisance parameters mu and sigma Parameters ---------- nuis_params : 1darray An array with a nuisance mean and variance parameter Returns ------- llr : float The log likelihood ratio of a pre-speified kurtosis holding the nuisance parameters constant """ endog = self.endog nobs = self.nobs mu_data = endog - nuis_params[0] sig_data = ((endog - nuis_params[0]) ** 2) - nuis_params[1] kurt_data = (((((endog - nuis_params[0]) ** 4) / \ (nuis_params[1] ** 2))) - 3) - self.kurt0 est_vect = np.column_stack((mu_data, sig_data, kurt_data)) eta_star = self._modif_newton(np.array([1. / nobs, 1. / nobs, 1. / nobs]), est_vect, np.ones(nobs) * (1. / nobs)) denom = 1 + np.dot(eta_star, est_vect.T) self.new_weights = 1. / nobs * 1. / denom llr = np.sum(np.log(nobs * self.new_weights)) return -2 * llr def _opt_skew_kurt(self, nuis_params): """ Called by test_joint_skew_kurt. This function is optimized over nuisance parameters mu and sigma Parameters ---------- nuis_params : 1darray An array with a nuisance mean and variance parameter Returns ------ llr : float The log likelihood ratio of a pre-speified skewness and kurtosis holding the nuisance parameters constant. """ endog = self.endog nobs = self.nobs mu_data = endog - nuis_params[0] sig_data = ((endog - nuis_params[0]) ** 2) - nuis_params[1] skew_data = ((((endog - nuis_params[0]) ** 3) / \ (nuis_params[1] ** 1.5))) - self.skew0 kurt_data = (((((endog - nuis_params[0]) ** 4) / \ (nuis_params[1] ** 2))) - 3) - self.kurt0 est_vect = np.column_stack((mu_data, sig_data, skew_data, kurt_data)) eta_star = self._modif_newton(np.array([1. / nobs, 1. / nobs, 1. / nobs, 1. / nobs]), est_vect, np.ones(nobs) * (1. / nobs)) denom = 1. + np.dot(eta_star, est_vect.T) self.new_weights = 1. / nobs * 1. / denom llr = np.sum(np.log(nobs * self.new_weights)) return -2 * llr def _ci_limits_skew(self, skew): """ Parameters ---------- skew0 : float Hypothesized value of skewness Returns ------- diff : float The difference between the log likelihood ratio at skew and a pre-specified value. """ return self.test_skew(skew)[0] - self.r0 def _ci_limits_kurt(self, kurt): """ Parameters ---------- skew0 : float Hypothesized value of kurtosis Returns ------- diff : float The difference between the log likelihood ratio at kurt and a pre-specified value. """ return self.test_kurt(kurt)[0] - self.r0 def _opt_correl(self, nuis_params, corr0, endog, nobs, x0, weights0): """ Parameters ---------- nuis_params : 1darray Array containing two nuisance means and two nuisance variances Returns ------- llr : float The log-likelihood of the correlation coefficient holding nuisance parameters constant """ mu1_data, mu2_data = (endog - nuis_params[::2]).T sig1_data = mu1_data ** 2 - nuis_params[1] sig2_data = mu2_data ** 2 - nuis_params[3] correl_data = ((mu1_data * mu2_data) - corr0 * (nuis_params[1] * nuis_params[3]) ** .5) est_vect = np.column_stack((mu1_data, sig1_data, mu2_data, sig2_data, correl_data)) eta_star = self._modif_newton(x0, est_vect, weights0) denom = 1. + np.dot(est_vect, eta_star) self.new_weights = 1. / nobs * 1. / denom llr = np.sum(np.log(nobs * self.new_weights)) return -2 * llr def _ci_limits_corr(self, corr): return self.test_corr(corr)[0] - self.r0 class DescStatUV(_OptFuncts): """ A class to compute confidence intervals and hypothesis tests involving mean, variance, kurtosis and skewness of a univariate random variable. Parameters ---------- endog : 1darray Data to be analyzed Attributes ---------- endog : 1darray Data to be analyzed nobs : float Number of observations """ def __init__(self, endog): self.endog = np.squeeze(endog) self.nobs = endog.shape[0] def test_mean(self, mu0, return_weights=False): """ Returns - 2 x log-likelihood ratio, p-value and weights for a hypothesis test of the mean. Parameters ---------- mu0 : float Mean value to be tested return_weights : bool If return_weights is True the function returns the weights of the observations under the null hypothesis. Default is False Returns ------- test_results : tuple The log-likelihood ratio and p-value of mu0 """ self.mu0 = mu0 endog = self.endog nobs = self.nobs eta_min = (1. - (1. / nobs)) / (self.mu0 - max(endog)) eta_max = (1. - (1. / nobs)) / (self.mu0 - min(endog)) eta_star = optimize.brentq(self._find_eta, eta_min, eta_max) new_weights = (1. / nobs) * 1. / (1. + eta_star * (endog - self.mu0)) llr = -2 * np.sum(np.log(nobs * new_weights)) if return_weights: return llr, chi2.sf(llr, 1), new_weights else: return llr, chi2.sf(llr, 1) def ci_mean(self, sig=.05, method='gamma', epsilon=10 ** -8, gamma_low=-10 ** 10, gamma_high=10 ** 10): """ Returns the confidence interval for the mean. Parameters ---------- sig : float significance level. Default is .05 method : str Root finding method, Can be 'nested-brent' or 'gamma'. Default is 'gamma' 'gamma' Tries to solve for the gamma parameter in the Lagrange (see Owen pg 22) and then determine the weights. 'nested brent' uses brents method to find the confidence intervals but must maximize the likelihood ratio on every iteration. gamma is generally much faster. If the optimizations does not converge, try expanding the gamma_high and gamma_low variable. gamma_low : float Lower bound for gamma when finding lower limit. If function returns f(a) and f(b) must have different signs, consider lowering gamma_low. gamma_high : float Upper bound for gamma when finding upper limit. If function returns f(a) and f(b) must have different signs, consider raising gamma_high. epsilon : float When using 'nested-brent', amount to decrease (increase) from the maximum (minimum) of the data when starting the search. This is to protect against the likelihood ratio being zero at the maximum (minimum) value of the data. If data is very small in absolute value (<10 ``**`` -6) consider shrinking epsilon When using 'gamma', amount to decrease (increase) the minimum (maximum) by to start the search for gamma. If function returns f(a) and f(b) must have different signs, consider lowering epsilon. Returns ------- Interval : tuple Confidence interval for the mean """ endog = self.endog sig = 1 - sig if method == 'nested-brent': self.r0 = chi2.ppf(sig, 1) middle = np.mean(endog) epsilon_u = (max(endog) - np.mean(endog)) * epsilon epsilon_l = (np.mean(endog) - min(endog)) * epsilon ulim = optimize.brentq(self._ci_limits_mu, middle, max(endog) - epsilon_u) llim = optimize.brentq(self._ci_limits_mu, middle, min(endog) + epsilon_l) return llim, ulim if method == 'gamma': self.r0 = chi2.ppf(sig, 1) gamma_star_l = optimize.brentq(self._find_gamma, gamma_low, min(endog) - epsilon) gamma_star_u = optimize.brentq(self._find_gamma, \ max(endog) + epsilon, gamma_high) weights_low = ((endog - gamma_star_l) ** -1) / \ np.sum((endog - gamma_star_l) ** -1) weights_high = ((endog - gamma_star_u) ** -1) / \ np.sum((endog - gamma_star_u) ** -1) mu_low = np.sum(weights_low * endog) mu_high = np.sum(weights_high * endog) return mu_low, mu_high def test_var(self, sig2_0, return_weights=False): """ Returns -2 x log-likelihood ratio and the p-value for the hypothesized variance Parameters ---------- sig2_0 : float Hypothesized variance to be tested return_weights : bool If True, returns the weights that maximize the likelihood of observing sig2_0. Default is False Returns ------- test_results : tuple The log-likelihood ratio and the p_value of sig2_0 Examples -------- >>> import numpy as np >>> import statsmodels.api as sm >>> random_numbers = np.random.standard_normal(1000)*100 >>> el_analysis = sm.emplike.DescStat(random_numbers) >>> hyp_test = el_analysis.test_var(9500) """ self.sig2_0 = sig2_0 mu_max = max(self.endog) mu_min = min(self.endog) llr = optimize.fminbound(self._opt_var, mu_min, mu_max, \ full_output=1)[1] p_val = chi2.sf(llr, 1) if return_weights: return llr, p_val, self.new_weights.T else: return llr, p_val def ci_var(self, lower_bound=None, upper_bound=None, sig=.05): """ Returns the confidence interval for the variance. Parameters ---------- lower_bound : float The minimum value the lower confidence interval can take. The p-value from test_var(lower_bound) must be lower than 1 - significance level. Default is .99 confidence limit assuming normality upper_bound : float The maximum value the upper confidence interval can take. The p-value from test_var(upper_bound) must be lower than 1 - significance level. Default is .99 confidence limit assuming normality sig : float The significance level. Default is .05 Returns ------- Interval : tuple Confidence interval for the variance Examples -------- >>> import numpy as np >>> import statsmodels.api as sm >>> random_numbers = np.random.standard_normal(100) >>> el_analysis = sm.emplike.DescStat(random_numbers) >>> el_analysis.ci_var() (0.7539322567470305, 1.229998852496268) >>> el_analysis.ci_var(.5, 2) (0.7539322567469926, 1.2299988524962664) Notes ----- If the function returns the error f(a) and f(b) must have different signs, consider lowering lower_bound and raising upper_bound. """ endog = self.endog if upper_bound is None: upper_bound = ((self.nobs - 1) * endog.var()) / \ (chi2.ppf(.0001, self.nobs - 1)) if lower_bound is None: lower_bound = ((self.nobs - 1) * endog.var()) / \ (chi2.ppf(.9999, self.nobs - 1)) self.r0 = chi2.ppf(1 - sig, 1) llim = optimize.brentq(self._ci_limits_var, lower_bound, endog.var()) ulim = optimize.brentq(self._ci_limits_var, endog.var(), upper_bound) return llim, ulim def plot_contour(self, mu_low, mu_high, var_low, var_high, mu_step, var_step, levs=[.2, .1, .05, .01, .001]): """ Returns a plot of the confidence region for a univariate mean and variance. Parameters ---------- mu_low : float Lowest value of the mean to plot mu_high : float Highest value of the mean to plot var_low : float Lowest value of the variance to plot var_high : float Highest value of the variance to plot mu_step : float Increments to evaluate the mean var_step : float Increments to evaluate the mean levs : list Which values of significance the contour lines will be drawn. Default is [.2, .1, .05, .01, .001] Returns ------- Figure The contour plot """ fig, ax = utils.create_mpl_ax() ax.set_ylabel('Variance') ax.set_xlabel('Mean') mu_vect = list(np.arange(mu_low, mu_high, mu_step)) var_vect = list(np.arange(var_low, var_high, var_step)) z = [] for sig0 in var_vect: self.sig2_0 = sig0 for mu0 in mu_vect: z.append(self._opt_var(mu0, pval=True)) z = np.asarray(z).reshape(len(var_vect), len(mu_vect)) ax.contour(mu_vect, var_vect, z, levels=levs) return fig def test_skew(self, skew0, return_weights=False): """ Returns -2 x log-likelihood and p-value for the hypothesized skewness. Parameters ---------- skew0 : float Skewness value to be tested return_weights : bool If True, function also returns the weights that maximize the likelihood ratio. Default is False. Returns ------- test_results : tuple The log-likelihood ratio and p_value of skew0 """ self.skew0 = skew0 start_nuisance = np.array([self.endog.mean(), self.endog.var()]) llr = optimize.fmin_powell(self._opt_skew, start_nuisance, full_output=1, disp=0)[1] p_val = chi2.sf(llr, 1) if return_weights: return llr, p_val, self.new_weights.T return llr, p_val def test_kurt(self, kurt0, return_weights=False): """ Returns -2 x log-likelihood and the p-value for the hypothesized kurtosis. Parameters ---------- kurt0 : float Kurtosis value to be tested return_weights : bool If True, function also returns the weights that maximize the likelihood ratio. Default is False. Returns ------- test_results : tuple The log-likelihood ratio and p-value of kurt0 """ self.kurt0 = kurt0 start_nuisance = np.array([self.endog.mean(), self.endog.var()]) llr = optimize.fmin_powell(self._opt_kurt, start_nuisance, full_output=1, disp=0)[1] p_val = chi2.sf(llr, 1) if return_weights: return llr, p_val, self.new_weights.T return llr, p_val def test_joint_skew_kurt(self, skew0, kurt0, return_weights=False): """ Returns - 2 x log-likelihood and the p-value for the joint hypothesis test for skewness and kurtosis Parameters ---------- skew0 : float Skewness value to be tested kurt0 : float Kurtosis value to be tested return_weights : bool If True, function also returns the weights that maximize the likelihood ratio. Default is False. Returns ------- test_results : tuple The log-likelihood ratio and p-value of the joint hypothesis test. """ self.skew0 = skew0 self.kurt0 = kurt0 start_nuisance = np.array([self.endog.mean(), self.endog.var()]) llr = optimize.fmin_powell(self._opt_skew_kurt, start_nuisance, full_output=1, disp=0)[1] p_val = chi2.sf(llr, 2) if return_weights: return llr, p_val, self.new_weights.T return llr, p_val def ci_skew(self, sig=.05, upper_bound=None, lower_bound=None): """ Returns the confidence interval for skewness. Parameters ---------- sig : float The significance level. Default is .05 upper_bound : float Maximum value of skewness the upper limit can be. Default is .99 confidence limit assuming normality. lower_bound : float Minimum value of skewness the lower limit can be. Default is .99 confidence level assuming normality. Returns ------- Interval : tuple Confidence interval for the skewness Notes ----- If function returns f(a) and f(b) must have different signs, consider expanding lower and upper bounds """ nobs = self.nobs endog = self.endog if upper_bound is None: upper_bound = skew(endog) + \ 2.5 * ((6. * nobs * (nobs - 1.)) / \ ((nobs - 2.) * (nobs + 1.) * \ (nobs + 3.))) ** .5 if lower_bound is None: lower_bound = skew(endog) - \ 2.5 * ((6. * nobs * (nobs - 1.)) / \ ((nobs - 2.) * (nobs + 1.) * \ (nobs + 3.))) ** .5 self.r0 = chi2.ppf(1 - sig, 1) llim = optimize.brentq(self._ci_limits_skew, lower_bound, skew(endog)) ulim = optimize.brentq(self._ci_limits_skew, skew(endog), upper_bound) return llim, ulim def ci_kurt(self, sig=.05, upper_bound=None, lower_bound=None): """ Returns the confidence interval for kurtosis. Parameters ---------- sig : float The significance level. Default is .05 upper_bound : float Maximum value of kurtosis the upper limit can be. Default is .99 confidence limit assuming normality. lower_bound : float Minimum value of kurtosis the lower limit can be. Default is .99 confidence limit assuming normality. Returns ------- Interval : tuple Lower and upper confidence limit Notes ----- For small n, upper_bound and lower_bound may have to be provided by the user. Consider using test_kurt to find values close to the desired significance level. If function returns f(a) and f(b) must have different signs, consider expanding the bounds. """ endog = self.endog nobs = self.nobs if upper_bound is None: upper_bound = kurtosis(endog) + \ (2.5 * (2. * ((6. * nobs * (nobs - 1.)) / \ ((nobs - 2.) * (nobs + 1.) * \ (nobs + 3.))) ** .5) * \ (((nobs ** 2.) - 1.) / ((nobs - 3.) *\ (nobs + 5.))) ** .5) if lower_bound is None: lower_bound = kurtosis(endog) - \ (2.5 * (2. * ((6. * nobs * (nobs - 1.)) / \ ((nobs - 2.) * (nobs + 1.) * \ (nobs + 3.))) ** .5) * \ (((nobs ** 2.) - 1.) / ((nobs - 3.) *\ (nobs + 5.))) ** .5) self.r0 = chi2.ppf(1 - sig, 1) llim = optimize.brentq(self._ci_limits_kurt, lower_bound, \ kurtosis(endog)) ulim = optimize.brentq(self._ci_limits_kurt, kurtosis(endog), \ upper_bound) return llim, ulim class DescStatMV(_OptFuncts): """ A class for conducting inference on multivariate means and correlation. Parameters ---------- endog : ndarray Data to be analyzed Attributes ---------- endog : ndarray Data to be analyzed nobs : float Number of observations """ def __init__(self, endog): self.endog = endog self.nobs = endog.shape[0] def mv_test_mean(self, mu_array, return_weights=False): """ Returns -2 x log likelihood and the p-value for a multivariate hypothesis test of the mean Parameters ---------- mu_array : 1d array Hypothesized values for the mean. Must have same number of elements as columns in endog return_weights : bool If True, returns the weights that maximize the likelihood of mu_array. Default is False. Returns ------- test_results : tuple The log-likelihood ratio and p-value for mu_array """ endog = self.endog nobs = self.nobs if len(mu_array) != endog.shape[1]: raise ValueError('mu_array must have the same number of ' 'elements as the columns of the data.') mu_array = mu_array.reshape(1, endog.shape[1]) means = np.ones((endog.shape[0], endog.shape[1])) means = mu_array * means est_vect = endog - means start_vals = 1. / nobs * np.ones(endog.shape[1]) eta_star = self._modif_newton(start_vals, est_vect, np.ones(nobs) * (1. / nobs)) denom = 1 + np.dot(eta_star, est_vect.T) self.new_weights = 1 / nobs * 1 / denom llr = -2 * np.sum(np.log(nobs * self.new_weights)) p_val = chi2.sf(llr, mu_array.shape[1]) if return_weights: return llr, p_val, self.new_weights.T else: return llr, p_val def mv_mean_contour(self, mu1_low, mu1_upp, mu2_low, mu2_upp, step1, step2, levs=(.001, .01, .05, .1, .2), var1_name=None, var2_name=None, plot_dta=False): """ Creates a confidence region plot for the mean of bivariate data Parameters ---------- m1_low : float Minimum value of the mean for variable 1 m1_upp : float Maximum value of the mean for variable 1 mu2_low : float Minimum value of the mean for variable 2 mu2_upp : float Maximum value of the mean for variable 2 step1 : float Increment of evaluations for variable 1 step2 : float Increment of evaluations for variable 2 levs : list Levels to be drawn on the contour plot. Default = (.001, .01, .05, .1, .2) plot_dta : bool If True, makes a scatter plot of the data on top of the contour plot. Defaultis False. var1_name : str Name of variable 1 to be plotted on the x-axis var2_name : str Name of variable 2 to be plotted on the y-axis Notes ----- The smaller the step size, the more accurate the intervals will be If the function returns optimization failed, consider narrowing the boundaries of the plot Examples -------- >>> import statsmodels.api as sm >>> two_rvs = np.random.standard_normal((20,2)) >>> el_analysis = sm.emplike.DescStat(two_rvs) >>> contourp = el_analysis.mv_mean_contour(-2, 2, -2, 2, .1, .1) >>> contourp.show() """ if self.endog.shape[1] != 2: raise ValueError('Data must contain exactly two variables') fig, ax = utils.create_mpl_ax() if var2_name is None: ax.set_ylabel('Variable 2') else: ax.set_ylabel(var2_name) if var1_name is None: ax.set_xlabel('Variable 1') else: ax.set_xlabel(var1_name) x = np.arange(mu1_low, mu1_upp, step1) y = np.arange(mu2_low, mu2_upp, step2) pairs = itertools.product(x, y) z = [] for i in pairs: z.append(self.mv_test_mean(np.asarray(i))[0]) X, Y = np.meshgrid(x, y) z = np.asarray(z) z = z.reshape(X.shape[1], Y.shape[0]) ax.contour(x, y, z.T, levels=levs) if plot_dta: ax.plot(self.endog[:, 0], self.endog[:, 1], 'bo') return fig def test_corr(self, corr0, return_weights=0): """ Returns -2 x log-likelihood ratio and p-value for the correlation coefficient between 2 variables Parameters ---------- corr0 : float Hypothesized value to be tested return_weights : bool If true, returns the weights that maximize the log-likelihood at the hypothesized value """ nobs = self.nobs endog = self.endog if endog.shape[1] != 2: raise NotImplementedError('Correlation matrix not yet implemented') nuis0 = np.array([endog[:, 0].mean(), endog[:, 0].var(), endog[:, 1].mean(), endog[:, 1].var()]) x0 = np.zeros(5) weights0 = np.array([1. / nobs] * int(nobs)) args = (corr0, endog, nobs, x0, weights0) llr = optimize.fmin(self._opt_correl, nuis0, args=args, full_output=1, disp=0)[1] p_val = chi2.sf(llr, 1) if return_weights: return llr, p_val, self.new_weights.T return llr, p_val def ci_corr(self, sig=.05, upper_bound=None, lower_bound=None): """ Returns the confidence intervals for the correlation coefficient Parameters ---------- sig : float The significance level. Default is .05 upper_bound : float Maximum value the upper confidence limit can be. Default is 99% confidence limit assuming normality. lower_bound : float Minimum value the lower confidence limit can be. Default is 99% confidence limit assuming normality. Returns ------- interval : tuple Confidence interval for the correlation """ endog = self.endog nobs = self.nobs self.r0 = chi2.ppf(1 - sig, 1) point_est = np.corrcoef(endog[:, 0], endog[:, 1])[0, 1] if upper_bound is None: upper_bound = min(.999, point_est + \ 2.5 * ((1. - point_est ** 2.) / \ (nobs - 2.)) ** .5) if lower_bound is None: lower_bound = max(- .999, point_est - \ 2.5 * (np.sqrt((1. - point_est ** 2.) / \ (nobs - 2.)))) llim = optimize.brenth(self._ci_limits_corr, lower_bound, point_est) ulim = optimize.brenth(self._ci_limits_corr, point_est, upper_bound) return llim, ulim statsmodels-0.12.2/statsmodels/emplike/elanova.py000066400000000000000000000071161400612667500221410ustar00rootroot00000000000000""" This script contains empirical likelihood ANOVA. Currently the script only contains one feature that allows the user to compare means of multiple groups. General References ------------------ Owen, A. B. (2001). Empirical Likelihood. Chapman and Hall. """ import numpy as np from .descriptive import _OptFuncts from scipy import optimize from scipy.stats import chi2 class _ANOVAOpt(_OptFuncts): """ Class containing functions that are optimized over when conducting ANOVA. """ def _opt_common_mu(self, mu): """ Optimizes the likelihood under the null hypothesis that all groups have mean mu. Parameters ---------- mu : float The common mean. Returns ------- llr : float -2 times the llr ratio, which is the test statistic. """ nobs = self.nobs endog = self.endog num_groups = self.num_groups endog_asarray = np.zeros((nobs, num_groups)) obs_num = 0 for arr_num in range(len(endog)): new_obs_num = obs_num + len(endog[arr_num]) endog_asarray[obs_num: new_obs_num, arr_num] = endog[arr_num] - \ mu obs_num = new_obs_num est_vect = endog_asarray wts = np.ones(est_vect.shape[0]) * (1. / (est_vect.shape[0])) eta_star = self._modif_newton(np.zeros(num_groups), est_vect, wts) denom = 1. + np.dot(eta_star, est_vect.T) self.new_weights = 1. / nobs * 1. / denom llr = np.sum(np.log(nobs * self.new_weights)) return -2 * llr class ANOVA(_ANOVAOpt): """ A class for ANOVA and comparing means. Parameters ---------- endog : list of arrays endog should be a list containing 1 dimensional arrays. Each array is the data collected from a certain group. """ def __init__(self, endog): self.endog = endog self.num_groups = len(self.endog) self.nobs = 0 for i in self.endog: self.nobs = self.nobs + len(i) def compute_ANOVA(self, mu=None, mu_start=0, return_weights=0): """ Returns -2 log likelihood, the pvalue and the maximum likelihood estimate for a common mean. Parameters ---------- mu : float If a mu is specified, ANOVA is conducted with mu as the common mean. Otherwise, the common mean is the maximum empirical likelihood estimate of the common mean. Default is None. mu_start : float Starting value for commean mean if specific mu is not specified. Default = 0. return_weights : bool if TRUE, returns the weights on observations that maximize the likelihood. Default is FALSE. Returns ------- res: tuple The log-likelihood, p-value and estimate for the common mean. """ if mu is not None: llr = self._opt_common_mu(mu) pval = 1 - chi2.cdf(llr, self.num_groups - 1) if return_weights: return llr, pval, mu, self.new_weights else: return llr, pval, mu else: res = optimize.fmin_powell(self._opt_common_mu, mu_start, full_output=1, disp=False) llr = res[1] mu_common = float(res[0]) pval = 1 - chi2.cdf(llr, self.num_groups - 1) if return_weights: return llr, pval, mu_common, self.new_weights else: return llr, pval, mu_common statsmodels-0.12.2/statsmodels/emplike/elregress.py000066400000000000000000000060341400612667500225050ustar00rootroot00000000000000""" Empirical Likelihood Linear Regression Inference The script contains the function that is optimized over nuisance parameters to conduct inference on linear regression parameters. It is called by eltest in OLSResults. General References ----------------- Owen, A.B.(2001). Empirical Likelihood. Chapman and Hall """ import numpy as np from statsmodels.emplike.descriptive import _OptFuncts class _ELRegOpts(_OptFuncts): """ A class that holds functions to be optimized over when conducting hypothesis tests and calculating confidence intervals. Parameters ---------- OLSResults : Results instance A fitted OLS result. """ def __init__(self): pass def _opt_nuis_regress(self, nuisance_params, param_nums=None, endog=None, exog=None, nobs=None, nvar=None, params=None, b0_vals=None, stochastic_exog=None): """ A function that is optimized over nuisance parameters to conduct a hypothesis test for the parameters of interest. Parameters ---------- nuisance_params: 1darray Parameters to be optimized over. Returns ------- llr : float -2 x the log-likelihood of the nuisance parameters and the hypothesized value of the parameter(s) of interest. """ params[param_nums] = b0_vals nuis_param_index = np.int_(np.delete(np.arange(nvar), param_nums)) params[nuis_param_index] = nuisance_params new_params = params.reshape(nvar, 1) self.new_params = new_params est_vect = exog * \ (endog - np.squeeze(np.dot(exog, new_params))).reshape(int(nobs), 1) if not stochastic_exog: exog_means = np.mean(exog, axis=0)[1:] exog_mom2 = (np.sum(exog * exog, axis=0))[1:]\ / nobs mean_est_vect = exog[:, 1:] - exog_means mom2_est_vect = (exog * exog)[:, 1:] - exog_mom2 regressor_est_vect = np.concatenate((mean_est_vect, mom2_est_vect), axis=1) est_vect = np.concatenate((est_vect, regressor_est_vect), axis=1) wts = np.ones(int(nobs)) * (1. / nobs) x0 = np.zeros(est_vect.shape[1]).reshape(-1, 1) try: eta_star = self._modif_newton(x0, est_vect, wts) denom = 1. + np.dot(eta_star, est_vect.T) self.new_weights = 1. / nobs * 1. / denom # the following commented out code is to verify weights # see open issue #1845 #self.new_weights /= self.new_weights.sum() #if not np.allclose(self.new_weights.sum(), 1., rtol=0, atol=1e-10): # raise RuntimeError('weights do not sum to 1') llr = np.sum(np.log(nobs * self.new_weights)) return -2 * llr except np.linalg.linalg.LinAlgError: return np.inf statsmodels-0.12.2/statsmodels/emplike/originregress.py000066400000000000000000000212431400612667500233730ustar00rootroot00000000000000""" This module implements empirical likelihood regression that is forced through the origin. This is different than regression not forced through the origin because the maximum empirical likelihood estimate is calculated with a vector of ones in the exogenous matrix but restricts the intercept parameter to be 0. This results in significantly more narrow confidence intervals and different parameter estimates. For notes on regression not forced through the origin, see empirical likelihood methods in the OLSResults class. General References ------------------ Owen, A.B. (2001). Empirical Likelihood. Chapman and Hall. p. 82. """ import numpy as np from scipy.stats import chi2 from scipy import optimize # When descriptive merged, this will be changed from statsmodels.tools.tools import add_constant from statsmodels.regression.linear_model import OLS, RegressionResults class ELOriginRegress(object): """ Empirical Likelihood inference and estimation for linear regression through the origin. Parameters ---------- endog: nx1 array Array of response variables. exog: nxk array Array of exogenous variables. Assumes no array of ones Attributes ---------- endog : nx1 array Array of response variables exog : nxk array Array of exogenous variables. Assumes no array of ones. nobs : float Number of observations. nvar : float Number of exogenous regressors. """ def __init__(self, endog, exog): self.endog = endog self.exog = exog self.nobs = self.exog.shape[0] try: self.nvar = float(exog.shape[1]) except IndexError: self.nvar = 1. def fit(self): """ Fits the model and provides regression results. Returns ------- Results : class Empirical likelihood regression class. """ exog_with = add_constant(self.exog, prepend=True) restricted_model = OLS(self.endog, exog_with) restricted_fit = restricted_model.fit() restricted_el = restricted_fit.el_test( np.array([0]), np.array([0]), ret_params=1) params = np.squeeze(restricted_el[3]) beta_hat_llr = restricted_el[0] llf = np.sum(np.log(restricted_el[2])) return OriginResults(restricted_model, params, beta_hat_llr, llf) def predict(self, params, exog=None): if exog is None: exog = self.exog return np.dot(add_constant(exog, prepend=True), params) class OriginResults(RegressionResults): """ A Results class for empirical likelihood regression through the origin. Parameters ---------- model : class An OLS model with an intercept. params : 1darray Fitted parameters. est_llr : float The log likelihood ratio of the model with the intercept restricted to 0 at the maximum likelihood estimates of the parameters. llr_restricted/llr_unrestricted llf_el : float The log likelihood of the fitted model with the intercept restricted to 0. Attributes ---------- model : class An OLS model with an intercept. params : 1darray Fitted parameter. llr : float The log likelihood ratio of the maximum empirical likelihood estimate. llf_el : float The log likelihood of the fitted model with the intercept restricted to 0. Notes ----- IMPORTANT. Since EL estimation does not drop the intercept parameter but instead estimates the slope parameters conditional on the slope parameter being 0, the first element for params will be the intercept, which is restricted to 0. IMPORTANT. This class inherits from RegressionResults but inference is conducted via empirical likelihood. Therefore, any methods that require an estimate of the covariance matrix will not function. Instead use el_test and conf_int_el to conduct inference. Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.bc.load(as_pandas=False) >>> model = sm.emplike.ELOriginRegress(data.endog, data.exog) >>> fitted = model.fit() >>> fitted.params # 0 is the intercept term. array([ 0. , 0.00351813]) >>> fitted.el_test(np.array([.0034]), np.array([1])) (3.6696503297979302, 0.055411808127497755) >>> fitted.conf_int_el(1) (0.0033971871114706867, 0.0036373150174892847) # No covariance matrix so normal inference is not valid >>> fitted.conf_int() TypeError: unsupported operand type(s) for *: 'instancemethod' and 'float' """ def __init__(self, model, params, est_llr, llf_el): self.model = model self.params = np.squeeze(params) self.llr = est_llr self.llf_el = llf_el def el_test(self, b0_vals, param_nums, method='nm', stochastic_exog=1, return_weights=0): """ Returns the llr and p-value for a hypothesized parameter value for a regression that goes through the origin. Parameters ---------- b0_vals : 1darray The hypothesized value to be tested. param_num : 1darray Which parameters to test. Note this uses python indexing but the '0' parameter refers to the intercept term, which is assumed 0. Therefore, param_num should be > 0. return_weights : bool If true, returns the weights that optimize the likelihood ratio at b0_vals. Default is False. method : str Can either be 'nm' for Nelder-Mead or 'powell' for Powell. The optimization method that optimizes over nuisance parameters. Default is 'nm'. stochastic_exog : bool When TRUE, the exogenous variables are assumed to be stochastic. When the regressors are nonstochastic, moment conditions are placed on the exogenous variables. Confidence intervals for stochastic regressors are at least as large as non-stochastic regressors. Default is TRUE. Returns ------- res : tuple pvalue and likelihood ratio. """ b0_vals = np.hstack((0, b0_vals)) param_nums = np.hstack((0, param_nums)) test_res = self.model.fit().el_test(b0_vals, param_nums, method=method, stochastic_exog=stochastic_exog, return_weights=return_weights) llr_test = test_res[0] llr_res = llr_test - self.llr pval = chi2.sf(llr_res, self.model.exog.shape[1] - 1) if return_weights: return llr_res, pval, test_res[2] else: return llr_res, pval def conf_int_el(self, param_num, upper_bound=None, lower_bound=None, sig=.05, method='nm', stochastic_exog=1): """ Returns the confidence interval for a regression parameter when the regression is forced through the origin. Parameters ---------- param_num : int The parameter number to be tested. Note this uses python indexing but the '0' parameter refers to the intercept term. upper_bound : float The maximum value the upper confidence limit can be. The closer this is to the confidence limit, the quicker the computation. Default is .00001 confidence limit under normality. lower_bound : float The minimum value the lower confidence limit can be. Default is .00001 confidence limit under normality. sig : float, optional The significance level. Default .05. method : str, optional Algorithm to optimize of nuisance params. Can be 'nm' or 'powell'. Default is 'nm'. Returns ------- ci: tuple The confidence interval for the parameter 'param_num'. """ r0 = chi2.ppf(1 - sig, 1) param_num = np.array([param_num]) if upper_bound is None: upper_bound = (np.squeeze(self.model.fit(). conf_int(.0001)[param_num])[1]) if lower_bound is None: lower_bound = (np.squeeze(self.model.fit().conf_int(.00001) [param_num])[0]) f = lambda b0: self.el_test(np.array([b0]), param_num, method=method, stochastic_exog=stochastic_exog)[0] - r0 lowerl = optimize.brentq(f, lower_bound, self.params[param_num]) upperl = optimize.brentq(f, self.params[param_num], upper_bound) return (lowerl, upperl) statsmodels-0.12.2/statsmodels/emplike/tests/000077500000000000000000000000001400612667500212775ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/emplike/tests/__init__.py000066400000000000000000000000001400612667500233760ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/emplike/tests/results/000077500000000000000000000000001400612667500230005ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/emplike/tests/results/__init__.py000066400000000000000000000000231400612667500251040ustar00rootroot00000000000000# Init for results statsmodels-0.12.2/statsmodels/emplike/tests/results/el_results.py000066400000000000000000000440431400612667500255400ustar00rootroot00000000000000""" Results from Matlab and R """ import numpy as np class DescStatRes(object): """ The results were generated from Bruce Hansen's MATLAb package: Bruce E. Hansen Department of Economics Social Science Building University of Wisconsin Madison, WI 53706-1393 bhansen@ssc.wisc.edu http://www.ssc.wisc.edu/~bhansen/ The R results are from Mai Zhou's emplik package """ def __init__(self): self.ci_mean = (13.556709, 14.559394) self.test_mean_14 = (.080675, .776385) self.test_mean_weights = np.array([[0.01969213], [0.01911859], [0.01973982], [0.01982913], [0.02004183], [0.0195765], [0.01970423], [0.02015074], [0.01898431], [0.02067787], [0.01878104], [0.01920531], [0.01981207], [0.02031582], [0.01857329], [0.01907883], [0.01943674], [0.0210042], [0.0197373], [0.01997998], [0.0199233], [0.01986713], [0.02017751], [0.01962176], [0.0214596], [0.02118228], [0.02013767], [0.01918665], [0.01908886], [0.01943081], [0.01916251], [0.01868129], [0.01918334], [0.01969084], [0.01984322], [0.0198977], [0.02098504], [0.02132222], [0.02100581], [0.01970351], [0.01942184], [0.01979781], [0.02114276], [0.02096136], [0.01999804], [0.02044712], [0.02174404], [0.02189933], [0.02077078], [0.02082612]]).squeeze() self.test_var_3 = (.199385, .655218) self.ci_var = (2.290077, 4.423634) self.test_var_weights = np.array([[0.020965], [0.019686], [0.021011], [0.021073], [0.021089], [0.020813], [0.020977], [0.021028], [0.019213], [0.02017], [0.018397], [0.01996], [0.021064], [0.020854], [0.017463], [0.019552], [0.020555], [0.019283], [0.021009], [0.021103], [0.021102], [0.021089], [0.021007], [0.020879], [0.017796], [0.018726], [0.021038], [0.019903], [0.019587], [0.020543], [0.019828], [0.017959], [0.019893], [0.020963], [0.02108], [0.021098], [0.01934], [0.018264], [0.019278], [0.020977], [0.020523], [0.021055], [0.018853], [0.019411], [0.0211], [0.02065], [0.016803], [0.016259], [0.019939], [0.019793]]).squeeze() self.mv_test_mean = (.7002663, .7045943) self.mv_test_mean_wts = np.array([[0.01877015], [0.01895746], [0.01817092], [0.01904308], [0.01707106], [0.01602806], [0.0194296], [0.01692204], [0.01978322], [0.01881313], [0.02011785], [0.0226274], [0.01953733], [0.01874346], [0.01694224], [0.01611816], [0.02297437], [0.01943187], [0.01899873], [0.02113375], [0.02295293], [0.02043509], [0.02276583], [0.02208274], [0.02466621], [0.02287983], [0.0173136], [0.01905693], [0.01909335], [0.01982534], [0.01924093], [0.0179352], [0.01871907], [0.01916633], [0.02022359], [0.02228696], [0.02080555], [0.01725214], [0.02166185], [0.01798537], [0.02103582], [0.02052757], [0.03096074], [0.01966538], [0.02201629], [0.02094854], [0.02127771], [0.01961964], [0.02023756], [0.01774807]]).squeeze() self.test_skew = (2.498418, .113961) self.test_skew_wts = np.array([[0.016698], [0.01564], [0.01701], [0.017675], [0.019673], [0.016071], [0.016774], [0.020902], [0.016397], [0.027359], [0.019136], [0.015419], [0.01754], [0.022965], [0.027203], [0.015805], [0.015565], [0.028518], [0.016992], [0.019034], [0.018489], [0.01799], [0.021222], [0.016294], [0.022725], [0.027133], [0.020748], [0.015452], [0.015759], [0.01555], [0.015506], [0.021863], [0.015459], [0.01669], [0.017789], [0.018257], [0.028578], [0.025151], [0.028512], [0.01677], [0.015529], [0.01743], [0.027563], [0.028629], [0.019216], [0.024677], [0.017376], [0.014739], [0.028112], [0.02842]]).squeeze() self.test_kurt_0 = (1.904269, .167601) self.test_corr = (.012025, .912680,) self.test_corr_weights = np.array([[0.020037], [0.020108], [0.020024], [0.02001], [0.019766], [0.019971], [0.020013], [0.019663], [0.019944], [0.01982], [0.01983], [0.019436], [0.020005], [0.019897], [0.020768], [0.020468], [0.019521], [0.019891], [0.020024], [0.01997], [0.019824], [0.019976], [0.019979], [0.019753], [0.020814], [0.020474], [0.019751], [0.020085], [0.020087], [0.019977], [0.020057], [0.020435], [0.020137], [0.020025], [0.019982], [0.019866], [0.020151], [0.019046], [0.020272], [0.020034], [0.019813], [0.01996], [0.020657], [0.019947], [0.019931], [0.02008], [0.02035], [0.019823], [0.02005], [0.019497]]).squeeze() self.test_joint_skew_kurt = (8.753952, .012563) class RegressionResults(object): """ Results for EL Regression """ def __init__(self): self.source = 'Matlab' self.test_beta0 = (1.758104, .184961, np.array([ 0.04326392, 0.04736749, 0.03573865, 0.04770535, 0.04721684, 0.04718301, 0.07088816, 0.05631242, 0.04865098, 0.06572099, 0.04016013, 0.04438627, 0.04042288, 0.03938043, 0.04006474, 0.04845233, 0.01991985, 0.03623254, 0.03617999, 0.05607242, 0.0886806])) self.test_beta1 = (1.932529, .164482, np.array([ 0.033328, 0.051412, 0.03395, 0.071695, 0.046433, 0.041303, 0.033329, 0.036413, 0.03246, 0.037776, 0.043872, 0.037507, 0.04762, 0.04881, 0.05874, 0.049553, 0.048898, 0.04512, 0.041142, 0.048121, 0.11252])) self.test_beta2 = (.494593, .481866, np.array([ 0.046287, 0.048632, 0.048772, 0.034769, 0.048416, 0.052447, 0.053336, 0.050112, 0.056053, 0.049318, 0.053609, 0.055634, 0.042188, 0.046519, 0.048415, 0.047897, 0.048673, 0.047695, 0.047503, 0.047447, 0.026279])) self.test_beta3 = (3.537250, .060005, np.array([ 0.036327, 0.070483, 0.048965, 0.087399, 0.041685, 0.036221, 0.016752, 0.019585, 0.027467, 0.02957, 0.069204, 0.060167, 0.060189, 0.030007, 0.067371, 0.046862, 0.069814, 0.053041, 0.053362, 0.041585, 0.033943])) self.test_ci_beta0 = (-52.77128837058528, -24.11607348661947) self.test_ci_beta1 = (0.41969831751229664, 0.9857167306604057) self.test_ci_beta2 = (0.6012045929381431, 2.1847079367275692) self.test_ci_beta3 = (-0.3804313225443794, 0.006934528877337928) class ANOVAResults(object): """ Results for ANOVA """ def __init__(self): self.source = 'Matlab' self.compute_ANOVA = (.426163, .51387, np.array([9.582371]), np.array([ 0.018494, 0.01943, 0.016624, 0.0172, 0.016985, 0.01922, 0.016532, 0.015985, 0.016769, 0.017631, 0.017677, 0.017984, 0.017049, 0.016721, 0.016382, 0.016566, 0.015642, 0.015894, 0.016282, 0.015704, 0.016272, 0.015678, 0.015651, 0.015648, 0.015618, 0.015726, 0.015981, 0.01635, 0.01586, 0.016443, 0.016126, 0.01683, 0.01348, 0.017391, 0.011225, 0.017282, 0.015568, 0.017543, 0.017009, 0.016325, 0.012841, 0.017648, 0.01558, 0.015994, 0.017258, 0.017664, 0.017792, 0.017772, 0.017527, 0.017797, 0.017856, 0.017849, 0.017749, 0.017827, 0.017381, 0.017902, 0.016557, 0.015522, 0.017455, 0.017248])) class AFTRes(object): """ Results for the AFT model from package emplik in R written by Mai Zhou """ def __init__(self): self.test_params = np.array([3.77710799, -0.03281745]) self.test_beta0 = (.132511, 0.7158323) self.test_beta1 = (.297951, .5851693) self.test_joint = (11.8068, 0.002730147) class OriginResults(object): """ These results are from Bruce Hansen's Matlab package. To replicate the results, the exogenous variables were scaled down by 10**-2 and the results were then rescaled. These tests must also test likelihood functions because the llr when conducting hypothesis tests is the MLE while restricting the intercept to 0. Matlab's generic package always uses the unrestricted MLE. """ def __init__(self): self.test_params = np.array([0, .00351861]) self.test_llf = -1719.793173 # llf when testing param = .0034 self.test_llf_hat = -1717.95833 # llf when origin=0 self.test_llf_hypoth = -2*(self.test_llf-self.test_llf_hat) self.test_llf_conf = -1719.879077 # The likelihood func at conf_vals statsmodels-0.12.2/statsmodels/emplike/tests/test_aft.py000066400000000000000000000027751400612667500234750ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_almost_equal import pytest from statsmodels.datasets import heart from statsmodels.tools import add_constant from statsmodels.emplike.aft_el import emplikeAFT from .results.el_results import AFTRes class GenRes(object): @classmethod def setup_class(cls): data = heart.load(as_pandas=False) endog = np.log10(data.endog) exog = add_constant(data.exog) cls.mod1 = emplikeAFT(endog, exog, data.censors) cls.res1 = cls.mod1.fit() cls.res2 = AFTRes() class Test_AFTModel(GenRes): def test_params(self): assert_almost_equal(self.res1.params(), self.res2.test_params, decimal=4) def test_beta0(self): assert_almost_equal(self.res1.test_beta([4], [0]), self.res2.test_beta0, decimal=4) def test_beta1(self): assert_almost_equal(self.res1.test_beta([-.04], [1]), self.res2.test_beta1, decimal=4) def test_beta_vect(self): assert_almost_equal(self.res1.test_beta([3.5, -.035], [0, 1]), self.res2.test_joint, decimal=4) @pytest.mark.slow def test_betaci(self): ci = self.res1.ci_beta(1, -.06, 0) ll = ci[0] ul = ci[1] ll_pval = self.res1.test_beta([ll], [1])[1] ul_pval = self.res1.test_beta([ul], [1])[1] assert_almost_equal(ul_pval, .050000, decimal=4) assert_almost_equal(ll_pval, .05000, decimal=4) statsmodels-0.12.2/statsmodels/emplike/tests/test_anova.py000066400000000000000000000015241400612667500240160ustar00rootroot00000000000000from numpy.testing import assert_almost_equal from statsmodels.datasets import star98 from statsmodels.emplike.elanova import ANOVA from .results.el_results import ANOVAResults class TestANOVA(object): """ Tests ANOVA difference in means """ @classmethod def setup_class(cls): cls.data = star98.load(as_pandas=False).exog[:30, 1:3] cls.res1 = ANOVA([cls.data[:, 0], cls.data[:, 1]]) cls.res2 = ANOVAResults() def test_anova(self): assert_almost_equal(self.res1.compute_ANOVA()[:2], self.res2.compute_ANOVA[:2], 4) assert_almost_equal(self.res1.compute_ANOVA()[2], self.res2.compute_ANOVA[2], 4) assert_almost_equal(self.res1.compute_ANOVA(return_weights=1)[3], self.res2.compute_ANOVA[3], 4) statsmodels-0.12.2/statsmodels/emplike/tests/test_descriptive.py000066400000000000000000000103431400612667500252320ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_almost_equal from statsmodels.datasets import star98 from statsmodels.emplike.descriptive import DescStat from .results.el_results import DescStatRes class GenRes(object): """ Reads in the data and creates class instance to be tested """ @classmethod def setup_class(cls): data = star98.load(as_pandas=False) desc_stat_data = data.exog[:50, 5] mv_desc_stat_data = data.exog[:50, 5:7] # mv = multivariate cls.res1 = DescStat(desc_stat_data) cls.res2 = DescStatRes() cls.mvres1 = DescStat(mv_desc_stat_data) class TestDescriptiveStatistics(GenRes): @classmethod def setup_class(cls): super(TestDescriptiveStatistics, cls).setup_class() def test_test_mean(self): assert_almost_equal(self.res1.test_mean(14), self.res2.test_mean_14, 4) def test_test_mean_weights(self): assert_almost_equal(self.res1.test_mean(14, return_weights=1)[2], self.res2.test_mean_weights, 4) def test_ci_mean(self): assert_almost_equal(self.res1.ci_mean(), self.res2.ci_mean, 4) def test_test_var(self): assert_almost_equal(self.res1.test_var(3), self.res2.test_var_3, 4) def test_test_var_weights(self): assert_almost_equal(self.res1.test_var(3, return_weights=1)[2], self.res2.test_var_weights, 4) def test_ci_var(self): assert_almost_equal(self.res1.ci_var(), self.res2.ci_var, 4) def test_mv_test_mean(self): assert_almost_equal(self.mvres1.mv_test_mean(np.array([14, 56])), self.res2.mv_test_mean, 4) def test_mv_test_mean_weights(self): assert_almost_equal(self.mvres1.mv_test_mean(np.array([14, 56]), return_weights=1)[2], self.res2.mv_test_mean_wts, 4) def test_test_skew(self): assert_almost_equal(self.res1.test_skew(0), self.res2.test_skew, 4) def test_ci_skew(self): # This will be tested in a round about way since MATLAB fails when # computing CI with multiple nuisance parameters. The process is: # # (1) Get CI for skewness from ci.skew() # (2) In MATLAB test the hypotheis that skew=results of test_skew. # (3) If p-value approx .05, test confirmed skew_ci = self.res1.ci_skew() lower_lim = skew_ci[0] upper_lim = skew_ci[1] ul_pval = self.res1.test_skew(lower_lim)[1] ll_pval = self.res1.test_skew(upper_lim)[1] assert_almost_equal(ul_pval, .050000, 4) assert_almost_equal(ll_pval, .050000, 4) def test_ci_skew_weights(self): assert_almost_equal(self.res1.test_skew(0, return_weights=1)[2], self.res2.test_skew_wts, 4) def test_test_kurt(self): assert_almost_equal(self.res1.test_kurt(0), self.res2.test_kurt_0, 4) def test_ci_kurt(self): # Same strategy for skewness CI kurt_ci = self.res1.ci_kurt(upper_bound=.5, lower_bound=-1.5) lower_lim = kurt_ci[0] upper_lim = kurt_ci[1] ul_pval = self.res1.test_kurt(upper_lim)[1] ll_pval = self.res1.test_kurt(lower_lim)[1] assert_almost_equal(ul_pval, .050000, 4) assert_almost_equal(ll_pval, .050000, 4) def test_joint_skew_kurt(self): assert_almost_equal(self.res1.test_joint_skew_kurt(0, 0), self.res2.test_joint_skew_kurt, 4) def test_test_corr(self): assert_almost_equal(self.mvres1.test_corr(.5), self.res2.test_corr, 4) def test_ci_corr(self): corr_ci = self.mvres1.ci_corr() lower_lim = corr_ci[0] upper_lim = corr_ci[1] ul_pval = self.mvres1.test_corr(upper_lim)[1] ll_pval = self.mvres1.test_corr(lower_lim)[1] assert_almost_equal(ul_pval, .050000, 4) assert_almost_equal(ll_pval, .050000, 4) def test_test_corr_weights(self): assert_almost_equal(self.mvres1.test_corr(.5, return_weights=1)[2], self.res2.test_corr_weights, 4) statsmodels-0.12.2/statsmodels/emplike/tests/test_origin.py000066400000000000000000000026671400612667500242120ustar00rootroot00000000000000from numpy.testing import assert_almost_equal from statsmodels.emplike.originregress import ELOriginRegress from statsmodels.datasets import cancer from .results.el_results import OriginResults import numpy as np class GenRes(object): """ Loads data and creates class instance ot be tested. """ @classmethod def setup_class(cls): data = cancer.load(as_pandas=False) cls.res1 = ELOriginRegress(data.endog, data.exog).fit() cls.res2 = OriginResults() class TestOrigin(GenRes): """ See OriginResults for details on how tests were computed """ def test_params(self): assert_almost_equal(self.res1.params, self.res2.test_params, 4) def test_llf(self): assert_almost_equal(self.res1.llf_el, self.res2.test_llf_hat, 4) def test_hypothesis_beta1(self): assert_almost_equal(self.res1.el_test([.0034], [1])[0], self.res2.test_llf_hypoth, 4) def test_ci_beta(self): ci = self.res1.conf_int_el(1) ll = ci[0] ul = ci[1] llf_low = np.sum(np.log(self.res1.el_test([ll], [1], return_weights=1)[2])) llf_high = np.sum(np.log(self.res1.el_test([ul], [1], return_weights=1)[2])) assert_almost_equal(llf_low, self.res2.test_llf_conf, 4) assert_almost_equal(llf_high, self.res2.test_llf_conf, 4) statsmodels-0.12.2/statsmodels/emplike/tests/test_regression.py000066400000000000000000000132331400612667500250720ustar00rootroot00000000000000from numpy.testing import assert_almost_equal import pytest from statsmodels.regression.linear_model import OLS from statsmodels.tools import add_constant from .results.el_results import RegressionResults from statsmodels.datasets import stackloss class GenRes(object): """ Loads data and creates class instance ot be tested """ @classmethod def setup_class(cls): data = stackloss.load(as_pandas=False) data.exog = add_constant(data.exog) cls.res1 = OLS(data.endog, data.exog).fit() cls.res2 = RegressionResults() @pytest.mark.slow class TestRegressionPowell(GenRes): """ All confidence intervals are tested by conducting a hypothesis tests at the confidence interval values. See Also -------- test_descriptive.py, test_ci_skew """ @pytest.mark.slow def test_hypothesis_beta0(self): beta0res = self.res1.el_test([-30], [0], return_weights=1, method='powell') assert_almost_equal(beta0res[:2], self.res2.test_beta0[:2], 4) assert_almost_equal(beta0res[2], self.res2.test_beta0[2], 4) @pytest.mark.slow def test_hypothesis_beta1(self): beta1res = self.res1.el_test([.5], [1], return_weights=1, method='powell') assert_almost_equal(beta1res[:2], self.res2.test_beta1[:2], 4) assert_almost_equal(beta1res[2], self.res2.test_beta1[2], 4) def test_hypothesis_beta2(self): beta2res = self.res1.el_test([1], [2], return_weights=1, method='powell') assert_almost_equal(beta2res[:2], self.res2.test_beta2[:2], 4) assert_almost_equal(beta2res[2], self.res2.test_beta2[2], 4) def test_hypothesis_beta3(self): beta3res = self.res1.el_test([0], [3], return_weights=1, method='powell') assert_almost_equal(beta3res[:2], self.res2.test_beta3[:2], 4) assert_almost_equal(beta3res[2], self.res2.test_beta3[2], 4) # Confidence interval results obtained through hypothesis testing in Matlab @pytest.mark.slow def test_ci_beta0(self): beta0ci = self.res1.conf_int_el(0, lower_bound=-52.9, upper_bound=-24.1, method='powell') assert_almost_equal(beta0ci, self.res2.test_ci_beta0, 3) # Slightly lower precision. CI was obtained from nm method. @pytest.mark.slow def test_ci_beta1(self): beta1ci = self.res1.conf_int_el(1, lower_bound=.418, upper_bound=.986, method='powell') assert_almost_equal(beta1ci, self.res2.test_ci_beta1, 4) @pytest.mark.slow def test_ci_beta2(self): beta2ci = self.res1.conf_int_el(2, lower_bound=.59, upper_bound=2.2, method='powell') assert_almost_equal(beta2ci, self.res2.test_ci_beta2, 5) @pytest.mark.slow def test_ci_beta3(self): beta3ci = self.res1.conf_int_el(3, lower_bound=-.39, upper_bound=.01, method='powell') assert_almost_equal(beta3ci, self.res2.test_ci_beta3, 6) class TestRegressionNM(GenRes): """ All confidence intervals are tested by conducting a hypothesis tests at the confidence interval values. See Also -------- test_descriptive.py, test_ci_skew """ def test_hypothesis_beta0(self): beta0res = self.res1.el_test([-30], [0], return_weights=1, method='nm') assert_almost_equal(beta0res[:2], self.res2.test_beta0[:2], 4) assert_almost_equal(beta0res[2], self.res2.test_beta0[2], 4) def test_hypothesis_beta1(self): beta1res = self.res1.el_test([.5], [1], return_weights=1, method='nm') assert_almost_equal(beta1res[:2], self.res2.test_beta1[:2], 4) assert_almost_equal(beta1res[2], self.res2.test_beta1[2], 4) @pytest.mark.slow def test_hypothesis_beta2(self): beta2res = self.res1.el_test([1], [2], return_weights=1, method='nm') assert_almost_equal(beta2res[:2], self.res2.test_beta2[:2], 4) assert_almost_equal(beta2res[2], self.res2.test_beta2[2], 4) @pytest.mark.slow def test_hypothesis_beta3(self): beta3res = self.res1.el_test([0], [3], return_weights=1, method='nm') assert_almost_equal(beta3res[:2], self.res2.test_beta3[:2], 4) assert_almost_equal(beta3res[2], self.res2.test_beta3[2], 4) # Confidence interval results obtained through hyp testing in Matlab @pytest.mark.slow def test_ci_beta0(self): # All confidence intervals are tested by conducting a hypothesis # tests at the confidence interval values since el_test # is already tested against Matlab # # See Also # -------- # # test_descriptive.py, test_ci_skew beta0ci = self.res1.conf_int_el(0, method='nm') assert_almost_equal(beta0ci, self.res2.test_ci_beta0, 6) @pytest.mark.slow def test_ci_beta1(self): beta1ci = self.res1.conf_int_el(1, method='nm') assert_almost_equal(beta1ci, self.res2.test_ci_beta1, 6) @pytest.mark.slow def test_ci_beta2(self): beta2ci = self.res1.conf_int_el(2, lower_bound=.59, upper_bound=2.2, method='nm') assert_almost_equal(beta2ci, self.res2.test_ci_beta2, 6) @pytest.mark.slow def test_ci_beta3(self): beta3ci = self.res1.conf_int_el(3, method='nm') assert_almost_equal(beta3ci, self.res2.test_ci_beta3, 6) statsmodels-0.12.2/statsmodels/examples/000077500000000000000000000000001400612667500203255ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/examples/es_misc_poisson2.py000066400000000000000000000035571400612667500241670ustar00rootroot00000000000000 import numpy as np import statsmodels.api as sm from statsmodels.miscmodels.count import (PoissonGMLE, PoissonOffsetGMLE, PoissonZiGMLE) from statsmodels.discrete.discrete_model import Poisson DEC = 3 class Dummy(object): pass self = Dummy() # generate artificial data np.random.seed(98765678) nobs = 200 rvs = np.random.randn(nobs,6) data_exog = rvs data_exog = sm.add_constant(data_exog, prepend=False) xbeta = 1 + 0.1*rvs.sum(1) data_endog = np.random.poisson(np.exp(xbeta)) #estimate discretemod.Poisson as benchmark res_discrete = Poisson(data_endog, data_exog).fit() mod_glm = sm.GLM(data_endog, data_exog, family=sm.families.Poisson()) res_glm = mod_glm.fit() #estimate generic MLE self.mod = PoissonGMLE(data_endog, data_exog) res = self.mod.fit() offset = res.params[0] * data_exog[:,0] #1d ??? mod1 = PoissonOffsetGMLE(data_endog, data_exog[:,1:], offset=offset) start_params = np.ones(6)/2. start_params = res.params[1:] res1 = mod1.fit(start_params=start_params, method='nm', maxiter=1000, maxfun=1000) print('mod2') mod2 = PoissonZiGMLE(data_endog, data_exog[:,1:], offset=offset) start_params = np.r_[np.ones(6)/2.,10] start_params = np.r_[res.params[1:], 20.] #-100] res2 = mod2.fit(start_params=start_params, method='bfgs', maxiter=1000, maxfun=2000) print('mod3') mod3 = PoissonZiGMLE(data_endog, data_exog, offset=None) start_params = np.r_[np.ones(7)/2.,10] start_params = np.r_[res.params, 20.] res3 = mod3.fit(start_params=start_params, method='nm', maxiter=1000, maxfun=2000) print('mod4') data_endog2 = np.r_[data_endog, np.zeros(nobs)] data_exog2 = np.r_[data_exog, data_exog] mod4 = PoissonZiGMLE(data_endog2, data_exog2, offset=None) start_params = np.r_[np.ones(7)/2.,10] start_params = np.r_[res.params, 0.] res4 = mod4.fit(start_params=start_params, method='nm', maxiter=1000, maxfun=1000) print(res4.summary()) statsmodels-0.12.2/statsmodels/examples/ex_arch_canada.py000066400000000000000000000207041400612667500236020ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sat Dec 24 07:31:47 2011 Author: Josef Perktold """ import numpy as np import statsmodels.stats.diagnostic as dia canada_raw = '''\ 405.36646642737 929.610513893698 7.52999999999884 386.136109062605 404.639833965913 929.803984550587 7.69999999999709 388.135759111711 403.814883043744 930.318387567177 7.47000000000116 390.540112911955 404.215773188006 931.427687420772 7.2699999999968 393.963817246136 405.046713585284 932.662005594273 7.37000000000262 396.764690917547 404.416738673847 933.550939726636 7.12999999999738 400.021701616327 402.81912737043 933.531526191785 7.40000000000146 400.751498688807 401.977334663103 933.076879439814 8.33000000000175 405.733473658807 402.089724946428 932.12375320915 8.83000000000175 409.05038628366 401.306688373207 930.635939140315 10.429999999993 411.398377747425 401.630171263522 929.097059933419 12.1999999999971 413.019421511595 401.56375463175 928.563335601161 12.7700000000041 415.166962884156 402.815698906973 929.069380060201 12.429999999993 414.662070678749 403.142107624713 930.265516098198 12.2299999999959 415.731936138368 403.078619166324 931.677031559203 11.6999999999971 416.231468866173 403.718785733801 932.138967575148 11.1999999999971 418.14392690728 404.866799027579 932.276686471608 11.2700000000041 419.735231229658 405.636186735378 932.832783118083 11.4700000000012 420.484186198549 405.136285378794 933.733419116009 11.3000000000029 420.930881402259 406.024639922986 934.177206176622 11.1699999999983 422.112404525291 406.412269729241 934.592839827856 11 423.627805811063 406.300932644569 935.606709830033 10.6300000000047 423.988686751336 406.335351723382 936.511085968336 10.2700000000041 424.190212657915 406.773695329549 937.420090112655 10.1999999999971 426.127043353785 405.152547649247 938.415921627889 9.66999999999825 426.857794216679 404.929830809648 938.999170021426 9.60000000000582 426.745717993024 404.576546350926 939.235354789206 9.60000000000582 426.885793656802 404.199492630983 939.679504234357 9.5 428.840253264144 405.94985619596 940.249674139969 9.5 430.122322107039 405.82209202516 941.435818685214 9.02999999999884 430.230679154048 406.446282537108 942.29809597644 8.69999999999709 430.392994893689 407.051247525876 943.532223256403 8.13000000000466 432.028420083791 407.946023990985 944.34896981513 7.87000000000262 433.388625934544 408.179584663105 944.821488789039 7.66999999999825 433.964091817787 408.599812740441 945.067136927327 7.80000000000291 434.484384354647 409.090560656008 945.80672616174 7.7300000000032 436.156879277168 408.704215141145 946.869661504613 7.56999999999971 438.265143944308 408.980275213206 946.876612143542 7.56999999999971 438.763587343863 408.328690037174 947.249692256472 7.33000000000175 439.949811558539 407.885696563307 947.651276093962 7.56999999999971 441.835856392131 407.260532233258 948.183970741596 7.62999999999738 443.176872656863 406.775150765526 948.349239264364 7.59999999999854 444.359199033223 406.179413590339 948.032170661406 8.16999999999825 444.523614807208 405.439793348166 947.106483115935 9.19999999999709 446.969404642587 403.279970790458 946.079554231134 10.1699999999983 450.158586973168 403.364855995771 946.183811678692 10.3300000000017 451.546427290378 403.380680430043 946.22579516585 10.3999999999942 452.298351499968 404.003182812546 945.997783938785 10.3699999999953 453.120066578834 404.47739841708 945.518279080208 10.6000000000058 453.999145996277 404.786782762866 945.351397570438 11 454.955176222477 405.271003921828 945.291785517556 11.3999999999942 455.482381155116 405.382993140508 945.400785900878 11.7299999999959 456.100929020225 405.156416006566 945.905809840959 11.070000000007 457.202696739531 406.470043094757 945.90347041344 11.6699999999983 457.388589594786 406.229308967752 946.319028746014 11.4700000000012 457.779898919191 406.726483850871 946.579621275764 11.3000000000029 457.553538085846 408.578504884277 946.780032223884 10.9700000000012 458.80240271533 409.67671010704 947.628284240641 10.6300000000047 459.05640335985 410.385763295936 948.622057553611 10.1000000000058 459.15782324686 410.539523677181 949.399183241404 9.66999999999825 459.703720275789 410.445258303139 949.948137966398 9.52999999999884 459.703720275789 410.625605270832 949.794494142446 9.47000000000116 460.025814162716 410.867239714014 949.953380175189 9.5 461.025722503696 411.235917829196 950.250239444989 9.27000000000407 461.30391443673 410.663655285725 950.538030883093 9.5 461.4030814421 410.808508412624 950.787128498243 9.42999999999302 462.927726133156 412.115961520089 950.869528648471 9.69999999999709 464.688777934061 412.999407129539 950.928132469716 9.89999999999418 465.071700094375 412.955056755303 951.845722481401 9.42999999999302 464.285125295526 412.82413309368 952.6004761952 9.30000000000291 464.034426099541 413.048874899 953.597552755418 8.86999999999534 463.453479461824 413.611017876145 954.143388344158 8.77000000000407 465.071700094375 413.604781916778 954.542593332134 8.60000000000582 466.088867474481 412.968388225217 955.263136106029 8.33000000000175 466.617120754625 412.265886525002 956.056052852469 8.16999999999825 465.747796561181 412.910594097915 956.79658640007 8.02999999999884 465.899527268299 413.829416419695 957.386480451857 7.90000000000146 466.409925351738 414.22415210314 958.06341570725 7.87000000000262 466.955244491812 415.1677707968 958.716592187518 7.52999999999884 467.628081344681 415.701580225863 959.488142422254 6.93000000000029 467.70256230891 416.867407108435 960.362493080892 6.80000000000291 469.134788222928 417.610399060359 960.783379042937 6.69999999999709 469.336419672322 418.002980476361 961.029029939624 6.93000000000029 470.011666329664 417.266680178544 961.765709811429 6.87000000000262 469.647234439539''' canada = np.array(canada_raw.split(), float).reshape(-1,4) k=2 resarch2 = dia.acorr_lm((canada[:,k]-canada[:,k].mean())**2, maxlag=2, autolag=None, store=1) print(resarch2) resarch5 = dia.acorr_lm(canada[:,k]**2, maxlag=12, autolag=None, store=1) ss = '''\ ARCH LM-test; Null hypothesis: no ARCH effects Chi-squared = %(chi)-8.4f df = %(df)-4d p-value = %(pval)8.4g ''' resarch = resarch5 print() print(ss % dict(chi=resarch[2], df=resarch[-1].resols.df_model, pval=resarch[3])) #R:FinTS: ArchTest(as.vector(Canada[,3]), lag=5) ''' ARCH LM-test; Null hypothesis: no ARCH effects data: as.vector(Canada[, 3]) Chi-squared = 78.878, df = 5, p-value = 1.443e-15 ''' #from ss above ''' ARCH LM-test; Null hypothesis: no ARCH effects Chi-squared = 78.849 df = 5 p-value = 1.461e-15 ''' #k=2 #R ''' ARCH LM-test; Null hypothesis: no ARCH effects data: as.vector(Canada[, 4]) Chi-squared = 74.6028, df = 5, p-value = 1.121e-14 ''' #mine ''' ARCH LM-test; Null hypothesis: no ARCH effects Chi-squared = 74.6028 df = 5 p-value = 1.126e-14 ''' ''' > ArchTest(as.vector(Canada[,4]), lag=12) ARCH LM-test; Null hypothesis: no ARCH effects data: as.vector(Canada[, 4]) Chi-squared = 69.6359, df = 12, p-value = 3.747e-10 ''' #mine: ''' ARCH LM-test; Null hypothesis: no ARCH effects Chi-squared = 69.6359 df = 12 p-value = 3.747e-10 ''' statsmodels-0.12.2/statsmodels/examples/ex_emplike_1.py000066400000000000000000000070741400612667500232510ustar00rootroot00000000000000""" This is a basic tutorial on how to conduct basic empirical likelihood inference for descriptive statistics. If matplotlib is installed it also generates plots. """ import numpy as np import statsmodels.api as sm print('Welcome to El') np.random.seed(634) # No significance of the seed. # Let's first generate some univariate data. univariate = np.random.standard_normal(30) # Now let's play with it # Initiate an empirical likelihood descriptive statistics instance eldescriptive = sm.emplike.DescStat(univariate) # Empirical likelihood is (typically) a method of inference, # not estimation. Therefore, there is no attribute eldescriptive.mean # However, we can check the mean: eldescriptive_mean = eldescriptive.endog.mean() #.42 #Let's conduct a hypothesis test to see if the mean is 0 print('Hypothesis test results for the mean:') print(eldescriptive.test_mean(0)) # The first value is is -2 *log-likelihood ratio, which is distributed #chi2. The second value is the p-value. # Let's see what the variance is: eldescriptive_var = eldescriptive.endog.var() # 1.01 #Let's test if the variance is 1: print('Hypothesis test results for the variance:') print(eldescriptive.test_var(1)) # Let's test if Skewness and Kurtosis are 0 print('Hypothesis test results for Skewness:') print(eldescriptive.test_skew(0)) print('Hypothesis test results for the Kurtosis:') print(eldescriptive.test_kurt(0)) # Note that the skewness and Kurtosis take longer. This is because # we have to optimize over the nuisance parameters (mean, variance). # We can also test for the joint skewness and kurtosis print(' Joint Skewness-Kurtosis test') eldescriptive.test_joint_skew_kurt(0, 0) # Let's try and get some confidence intervals print('Confidence interval for the mean') print(eldescriptive.ci_mean()) print('Confidence interval for the variance') print(eldescriptive.ci_var()) print('Confidence interval for skewness') print(eldescriptive.ci_skew()) print('Confidence interval for kurtosis') print(eldescriptive.ci_kurt()) # if matplotlib is installed, we can get a contour plot for the mean # and variance. mean_variance_contour = eldescriptive.plot_contour(-.5, 1.2, .2, 2.5, .05, .05) # This returns a figure instance. Just type mean_var_contour.show() # to see the plot. # Once you close the plot, we can start some multivariate analysis. x1 = np.random.exponential(2, (30, 1)) x2 = 2 * x1 + np.random.chisquare(4, (30, 1)) mv_data = np.concatenate((x1, x2), axis=1) mv_elmodel = sm.emplike.DescStat(mv_data) # For multivariate data, the only methods are mv_test_mean, # mv mean contour and ci_corr and test_corr. # Let's test the hypthesis that x1 has a mean of 2 and x2 has a mean of 7 print('Multivaraite mean hypothesis test') print(mv_elmodel.mv_test_mean(np.array([2, 7]))) # Now let's get the confidence interval for correlation print('Correlation Coefficient CI') print(mv_elmodel.ci_corr()) # Note how this took much longer than previous functions. That is # because the function is optimizing over 4 nuisance parameters. # We can also do a hypothesis test for correlation print('Hypothesis test for correlation') print(mv_elmodel.test_corr(.7)) # Finally, let's create a contour plot for the means of the data means_contour = mv_elmodel.mv_mean_contour(1, 3, 6,9, .15,.15, plot_dta=1) # This also returns a fig so we can type mean_contour.show() to see the figure # Sometimes, the data is very dispersed and we would like to see the confidence # intervals without the plotted data. Let's see the difference when we set # plot_dta=0 means_contour2 = mv_elmodel.mv_mean_contour(1, 3, 6,9, .05,.05, plot_dta=0) statsmodels-0.12.2/statsmodels/examples/ex_emplike_2.py000066400000000000000000000047441400612667500232530ustar00rootroot00000000000000""" This script is a basic tutorial on how to conduct empirical likelihood estimation and inference in linear regression models. """ import numpy as np import statsmodels.api as sm # Let's generate some regression data np.random.seed(100) # no significance of the seed X = np.random.standard_normal((40, 3)) X = sm.add_constant(X) beta = np.arange(1,5) y = np.dot(X, beta) + np.random.standard_normal(40) # There are no distributional assumptions on the error. I just chose # normal errors to demonstrate. print('Lets play with EL Regression') # In a model with an intercept, access EL inference through OLS results. elmodel = sm.OLS(y, X) fitted = elmodel.fit() # Let's test if the intercept is 0 print('Intercept test') test0_1 = fitted.el_test(np.array([0]), np.array([0])) print(test0_1) # Let's test if beta3 is 4 print('beta3 test') test1 = fitted.el_test(np.array([4]), np.array([3])) print(test1) # Lets test the hypothesis that beta3=4 and beta2=3 print('joint beta test') test2 = fitted.el_test(np.array([3, 4]), np.array([2, 3])) print(test2) # Let's get the confidence intervals for the parameters print('Confidence Interval for Beta1') ci_beta1 = fitted.conf_int_el(1) print(ci_beta1) # Of course, we can still see the rest of the RegressionResults print('R-squared') print(fitted.rsquared) print('Params') print(fitted.params) # Now lets check out regression through the origin print('Origin Regression') originx = np.random.standard_normal((30, 3)) originbeta = np.array([[1], [2], [3]]) originy = np.dot(originx, originbeta) + np.random.standard_normal((30, 1)) originmodel = sm.emplike.ELOriginRegress(originy, originx) # Since in this case, parameter estimates are different then in OLS, # we need to fit the model. originfit = originmodel.fit() print('The fitted parameters') print(originfit.params) print('The MSE') print(originfit.mse_model) print('The R-squared') print(originfit.rsquared) # Note that the first element of param is 0 and there are 4 params. That is # because the first param is the intercept term. This is noted in the # documentation. # Now that the model is fitted, we can do some inference. print('Test beta1 =1') test_beta1 = originfit.el_test([1], [1]) print(test_beta1) # A confidence interval for Beta1. print('confidence interval for beta1') ci_beta2 = originfit.conf_int_el(1) print(ci_beta2) # Finally, since we initiated an EL model, normal inference is not available try: originfit.conf_int() except: print('No normal inference available') statsmodels-0.12.2/statsmodels/examples/ex_emplike_3.py000066400000000000000000000015151400612667500232450ustar00rootroot00000000000000""" This script provides a tutorial on how to use estimate and conduct inference in an accelerated failure time model using empirical likelihood. We will be using the Stanford Heart Transplant data """ import statsmodels.api as sm import numpy as np data = sm.datasets.heart.load(as_pandas=False) # Note this data has endog, exog and censors # We will take the log (base 10) of the endogenous survival times model = sm.emplike.emplikeAFT(np.log10(data.endog), sm.add_constant(data.exog), data.censors) # We need to fit the model to get the parameters fitted = model.fit() print(fitted.params()) test1 = fitted.test_beta([4],[0]) # Test that the intercept is 4 print(test1) test2 = fitted.test_beta([-.05], [1]) # Test that the slope is -.05 print(test2) ci_beta1 = fitted.ci_beta(1, .1, -.1) print(ci_beta1) statsmodels-0.12.2/statsmodels/examples/ex_feasible_gls_het.py000066400000000000000000000101741400612667500246550ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Examples for linear model with heteroscedasticity estimated by feasible GLS These are examples to check the results during development. The assumptions: We have a linear model y = X*beta where the variance of an observation depends on some explanatory variable Z (`exog_var`). linear_model.WLS estimated the model for a given weight matrix here we want to estimate also the weight matrix by two step or iterative WLS Created on Wed Dec 21 12:28:17 2011 Author: Josef Perktold There might be something fishy with the example, but I do not see it. Or maybe it's supposed to be this way because in the first case I do not include a constant and in the second case I include some of the same regressors as in the main equation. """ import numpy as np from numpy.testing import assert_almost_equal from statsmodels.regression.linear_model import OLS from statsmodels.regression.feasible_gls import GLSHet, GLSHet2 examples = ['ex1'] if 'ex1' in examples: #from tut_ols_wls nsample = 1000 sig = 0.5 x1 = np.linspace(0, 20, nsample) X = np.c_[x1, (x1-5)**2, np.ones(nsample)] np.random.seed(0)#9876789) #9876543) beta = [0.5, -0.015, 1.] y_true2 = np.dot(X, beta) w = np.ones(nsample) w[nsample*6//10:] = 4 #Note this is the squared value #y2[:nsample*6/10] = y_true2[:nsample*6/10] + sig*1. * np.random.normal(size=nsample*6/10) #y2[nsample*6/10:] = y_true2[nsample*6/10:] + sig*4. * np.random.normal(size=nsample*4/10) y2 = y_true2 + sig*np.sqrt(w)* np.random.normal(size=nsample) X2 = X[:,[0,2]] X2 = X res_ols = OLS(y2, X2).fit() print('OLS beta estimates') print(res_ols.params) print('OLS stddev of beta') print(res_ols.bse) print('\nWLS') mod0 = GLSHet2(y2, X2, exog_var=w) res0 = mod0.fit() print('new version') mod1 = GLSHet(y2, X2, exog_var=w) res1 = mod1.iterative_fit(2) print('WLS beta estimates') print(res1.params) print(res0.params) print('WLS stddev of beta') print(res1.bse) #compare with previous version GLSHet2, refactoring check #assert_almost_equal(res1.params, np.array([ 0.37642521, 1.51447662])) #this fails ??? more iterations? different starting weights? print(res1.model.weights/res1.model.weights.max()) #why is the error so small in the estimated weights ? assert_almost_equal(res1.model.weights/res1.model.weights.max(), 1./w, 14) print('residual regression params') print(res1.results_residual_regression.params) print('scale of model ?') print(res1.scale) print('unweighted residual variance, note unweighted mean is not zero') print(res1.resid.var()) #Note weighted mean is zero: #(res1.model.weights * res1.resid).mean() doplots = False if doplots: import matplotlib.pyplot as plt plt.figure() plt.plot(x1, y2, 'o') plt.plot(x1, y_true2, 'b-', label='true') plt.plot(x1, res1.fittedvalues, 'r-', label='fwls') plt.plot(x1, res_ols.fittedvalues, '--', label='ols') plt.legend() #z = (w[:,None] == [1,4]).astype(float) #dummy variable z = (w[:,None] == np.unique(w)).astype(float) #dummy variable mod2 = GLSHet(y2, X2, exog_var=z) res2 = mod2.iterative_fit(2) print(res2.params) import statsmodels.api as sm z = sm.add_constant(w) mod3 = GLSHet(y2, X2, exog_var=z) res3 = mod3.iterative_fit(8) print(res3.params) print("np.array(res3.model.history['ols_params'])") print(np.array(res3.model.history['ols_params'])) print("np.array(res3.model.history['self_params'])") print(np.array(res3.model.history['self_params'])) print(np.unique(res2.model.weights)) #for discrete z only, only a few uniques print(np.unique(res3.model.weights)) if doplots: plt.figure() plt.plot(x1, y2, 'o') plt.plot(x1, y_true2, 'b-', label='true') plt.plot(x1, res1.fittedvalues, '-', label='fwls1') plt.plot(x1, res2.fittedvalues, '-', label='fwls2') plt.plot(x1, res3.fittedvalues, '-', label='fwls3') plt.plot(x1, res_ols.fittedvalues, '--', label='ols') plt.legend() plt.show() statsmodels-0.12.2/statsmodels/examples/ex_feasible_gls_het_0.py000066400000000000000000000144051400612667500250750ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Examples for linear model with heteroscedasticity estimated by feasible GLS These are examples to check the results during development. The assumptions: We have a linear model y = X*beta where the variance of an observation depends on some explanatory variable Z (`exog_var`). linear_model.WLS estimated the model for a given weight matrix here we want to estimate also the weight matrix by two step or iterative WLS Created on Wed Dec 21 12:28:17 2011 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_almost_equal from statsmodels.regression.linear_model import OLS from statsmodels.regression.feasible_gls import GLSHet, GLSHet2 from statsmodels.tools.tools import add_constant examples = ['ex1'] if 'ex1' in examples: nsample = 300 #different pattern last graph with 100 or 200 or 500 sig = 0.5 np.random.seed(9876789) #9876543) X = np.random.randn(nsample, 3) X = np.column_stack((np.ones((nsample,1)), X)) beta = [1, 0.5, -0.5, 1.] y_true2 = np.dot(X, beta) x1 = np.linspace(0, 1, nsample) gamma = np.array([1, 3.]) #with slope 3 instead of two, I get negative weights, Not correct # - was misspecified, but the negative weights are still possible with identity link #gamma /= gamma.sum() #normalize assuming x1.max is 1 z_true = add_constant(x1) winv = np.dot(z_true, gamma) het_params = sig**2 * np.array([1, 3.]) # for squared sig2_het = sig**2 * winv weights_dgp = 1/winv weights_dgp /= weights_dgp.max() #should be already normalized - NOT check normalization #y2[:nsample*6/10] = y_true2[:nsample*6/10] + sig*1. * np.random.normal(size=nsample*6/10) z0 = np.zeros(nsample) z0[(nsample * 5)//10:] = 1 #dummy for 2 halfs of sample z0 = add_constant(z0) z1 = add_constant(x1) noise = np.sqrt(sig2_het) * np.random.normal(size=nsample) y2 = y_true2 + noise X2 = X[:,[0,2]] #misspecified, missing regressor in main equation X2 = X #correctly specigied res_ols = OLS(y2, X2).fit() print('OLS beta estimates') print(res_ols.params) print('OLS stddev of beta') print(res_ols.bse) print('\nWLS') mod0 = GLSHet2(y2, X2, exog_var=winv) res0 = mod0.fit() print('new version') mod1 = GLSHet(y2, X2, exog_var=winv) res1 = mod1.iterative_fit(2) print('WLS beta estimates') print(res1.params) print(res0.params) print('WLS stddev of beta') print(res1.bse) #compare with previous version GLSHet2, refactoring check #assert_almost_equal(res1.params, np.array([ 0.37642521, 1.51447662])) #this fails ??? more iterations? different starting weights? print(res1.model.weights/res1.model.weights.max()) #why is the error so small in the estimated weights ? assert_almost_equal(res1.model.weights/res1.model.weights.max(), weights_dgp, 14) print('residual regression params') print(res1.results_residual_regression.params) print('scale of model ?') print(res1.scale) print('unweighted residual variance, note unweighted mean is not zero') print(res1.resid.var()) #Note weighted mean is zero: #(res1.model.weights * res1.resid).mean() doplots = True #False if doplots: import matplotlib.pyplot as plt plt.figure() plt.plot(x1, y2, 'o') plt.plot(x1, y_true2, 'b-', label='true') plt.plot(x1, res1.fittedvalues, 'r-', label='fwls') plt.plot(x1, res_ols.fittedvalues, '--', label='ols') plt.legend() #the next only works if w has finite support, discrete/categorical #z = (w[:,None] == [1,4]).astype(float) #dummy variable #z = (w0[:,None] == np.unique(w0)).astype(float) #dummy variable #changed z0 contains dummy and constant mod2 = GLSHet(y2, X2, exog_var=z0) res2 = mod2.iterative_fit(3) print(res2.params) import statsmodels.api as sm #z = sm.add_constant(w, prepend=True) z = sm.add_constant(x1/x1.max()) mod3 = GLSHet(y2, X2, exog_var=z1)#, link=sm.families.links.log()) res3 = mod3.iterative_fit(20) error_var_3 = res3.mse_resid/res3.model.weights print(res3.params) print("np.array(res3.model.history['ols_params'])") print(np.array(res3.model.history['ols_params'])) print("np.array(res3.model.history['self_params'])") print(np.array(res3.model.history['self_params'])) #Models 2 and 3 are equivalent with different parameterization of Z print(np.unique(res2.model.weights)) #for discrete z only, only a few uniques print(np.unique(res3.model.weights)) print(res3.summary()) print('\n\nResults of estimation of weights') print('--------------------------------') print(res3.results_residual_regression.summary()) if doplots: plt.figure() plt.plot(x1, y2, 'o') plt.plot(x1, y_true2, 'b-', label='true') plt.plot(x1, res1.fittedvalues, '-', label='fwls1') plt.plot(x1, res2.fittedvalues, '-', label='fwls2') plt.plot(x1, res3.fittedvalues, '-', label='fwls3') plt.plot(x1, res_ols.fittedvalues, '--', label='ols') plt.legend() plt.figure() plt.ylim(0, 5) res_e2 = OLS(noise**2, z).fit() plt.plot(noise**2, 'bo', alpha=0.5, label='dgp error**2') plt.plot(res_e2.fittedvalues, lw=2, label='ols for noise**2') #plt.plot(res3.model.weights, label='GLSHet weights') plt.plot(error_var_3, lw=2, label='GLSHet error var') plt.plot(res3.resid**2, 'ro', alpha=0.5, label='resid squared') #plt.plot(weights_dgp, label='DGP weights') plt.plot(sig**2 * winv, lw=2, label='DGP error var') plt.legend() plt.show() '''Note these are close but maybe biased because of skewed distribution >>> res3.mse_resid/res3.model.weights[-10:] array([ 1.03115871, 1.03268209, 1.03420547, 1.03572885, 1.03725223, 1.03877561, 1.04029899, 1.04182237, 1.04334575, 1.04486913]) >>> res_e2.fittedvalues[-10:] array([ 1.0401953 , 1.04171386, 1.04323242, 1.04475098, 1.04626954, 1.0477881 , 1.04930666, 1.05082521, 1.05234377, 1.05386233]) >>> sig**2 * w[-10:] array([ 0.98647295, 0.98797595, 0.98947896, 0.99098196, 0.99248497, 0.99398798, 0.99549098, 0.99699399, 0.99849699, 1. ]) ''' statsmodels-0.12.2/statsmodels/examples/ex_generic_mle.py000066400000000000000000000351241400612667500236510ustar00rootroot00000000000000 from functools import partial import numpy as np from scipy import stats import statsmodels.api as sm from statsmodels.base.model import GenericLikelihoodModel from statsmodels.tools.numdiff import approx_fprime, approx_hess data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) # in this dir probit_mod = sm.Probit(data.endog, data.exog) probit_res = probit_mod.fit() loglike = probit_mod.loglike score = probit_mod.score mod = GenericLikelihoodModel(data.endog, data.exog*2, loglike, score) res = mod.fit(method="nm", maxiter = 500) def probitloglike(params, endog, exog): """ Log likelihood for the probit """ q = 2*endog - 1 X = exog return np.add.reduce(stats.norm.logcdf(q*np.dot(X,params))) model_loglike = partial(probitloglike, endog=data.endog, exog=data.exog) mod = GenericLikelihoodModel(data.endog, data.exog, loglike=model_loglike) res = mod.fit(method="nm", maxiter=500) print(res) np.allclose(res.params, probit_res.params, rtol=1e-4) print(res.params, probit_res.params) #datal = sm.datasets.longley.load(as_pandas=False) datal = sm.datasets.ccard.load(as_pandas=False) datal.exog = sm.add_constant(datal.exog, prepend=False) # Instance of GenericLikelihood model does not work directly, because loglike # cannot get access to data in self.endog, self.exog nobs = 5000 rvs = np.random.randn(nobs,6) datal.exog = rvs[:,:-1] datal.exog = sm.add_constant(datal.exog, prepend=False) datal.endog = 1 + rvs.sum(1) show_error = False show_error2 = 1#False if show_error: def loglike_norm_xb(self, params): beta = params[:-1] sigma = params[-1] xb = np.dot(self.exog, beta) return stats.norm.logpdf(self.endog, loc=xb, scale=sigma) mod_norm = GenericLikelihoodModel(datal.endog, datal.exog, loglike_norm_xb) res_norm = mod_norm.fit(method="nm", maxiter = 500) print(res_norm.params) if show_error2: def loglike_norm_xb(params, endog, exog): beta = params[:-1] sigma = params[-1] #print exog.shape, beta.shape xb = np.dot(exog, beta) #print xb.shape, stats.norm.logpdf(endog, loc=xb, scale=sigma).shape return stats.norm.logpdf(endog, loc=xb, scale=sigma).sum() model_loglike3 = partial(loglike_norm_xb, endog=datal.endog, exog=datal.exog) mod_norm = GenericLikelihoodModel(datal.endog, datal.exog, model_loglike3) res_norm = mod_norm.fit(start_params=np.ones(datal.exog.shape[1]+1), method="nm", maxiter = 5000) print(res_norm.params) class MygMLE(GenericLikelihoodModel): # just for testing def loglike(self, params): beta = params[:-1] sigma = params[-1] xb = np.dot(self.exog, beta) return stats.norm.logpdf(self.endog, loc=xb, scale=sigma).sum() def loglikeobs(self, params): beta = params[:-1] sigma = params[-1] xb = np.dot(self.exog, beta) return stats.norm.logpdf(self.endog, loc=xb, scale=sigma) mod_norm2 = MygMLE(datal.endog, datal.exog) #res_norm = mod_norm.fit(start_params=np.ones(datal.exog.shape[1]+1), method="nm", maxiter = 500) res_norm2 = mod_norm2.fit(start_params=[1.]*datal.exog.shape[1]+[1], method="nm", maxiter = 500) np.allclose(res_norm.params, res_norm2.params) print(res_norm2.params) res2 = sm.OLS(datal.endog, datal.exog).fit() start_params = np.hstack((res2.params, np.sqrt(res2.mse_resid))) res_norm3 = mod_norm2.fit(start_params=start_params, method="nm", maxiter = 500, retall=0) print(start_params) print(res_norm3.params) print(res2.bse) print(res_norm3.bse) print('llf', res2.llf, res_norm3.llf) bse = np.sqrt(np.diag(np.linalg.inv(res_norm3.model.hessian(res_norm3.params)))) res_norm3.model.score(res_norm3.params) #fprime in fit option cannot be overwritten, set to None, when score is defined # exception is fixed, but I do not think score was supposed to be called res_bfgs = mod_norm2.fit(start_params=start_params, method="bfgs", fprime=None, maxiter=500, retall=0) hb=-approx_hess(res_norm3.params, mod_norm2.loglike, epsilon=-1e-4) hf=-approx_hess(res_norm3.params, mod_norm2.loglike, epsilon=1e-4) hh = (hf+hb)/2. print(np.linalg.eigh(hh)) grad = -approx_fprime(res_norm3.params, mod_norm2.loglike, epsilon=-1e-4) print(grad) gradb = -approx_fprime(res_norm3.params, mod_norm2.loglike, epsilon=-1e-4) gradf = -approx_fprime(res_norm3.params, mod_norm2.loglike, epsilon=1e-4) print((gradb+gradf)/2.) print(res_norm3.model.score(res_norm3.params)) print(res_norm3.model.score(start_params)) mod_norm2.loglike(start_params/2.) print(np.linalg.inv(-1*mod_norm2.hessian(res_norm3.params))) print(np.sqrt(np.diag(res_bfgs.cov_params()))) print(res_norm3.bse) print("MLE - OLS parameter estimates") print(res_norm3.params[:-1] - res2.params) print("bse diff in percent") print((res_norm3.bse[:-1] / res2.bse)*100. - 100) ''' Optimization terminated successfully. Current function value: 12.818804 Iterations 6 Optimization terminated successfully. Current function value: 12.818804 Iterations: 439 Function evaluations: 735 Optimization terminated successfully. Current function value: 12.818804 Iterations: 439 Function evaluations: 735 [ 1.6258006 0.05172931 1.42632252 -7.45229732] [ 1.62581004 0.05172895 1.42633234 -7.45231965] Warning: Maximum number of function evaluations has been exceeded. [ -1.18109149 246.94438535 -16.21235536 24.05282629 -324.80867176 274.07378453] Warning: Maximum number of iterations has been exceeded [ 17.57107 -149.87528787 19.89079376 -72.49810777 -50.06067953 306.14170418] Optimization terminated successfully. Current function value: 506.488765 Iterations: 339 Function evaluations: 550 [ -3.08181404 234.34702702 -14.99684418 27.94090839 -237.1465136 284.75079529] [ -3.08181304 234.34701361 -14.99684381 27.94088692 -237.14649571 274.6857294 ] [ 5.51471653 80.36595035 7.46933695 82.92232357 199.35166485] llf -506.488764864 -506.488764864 Optimization terminated successfully. Current function value: 506.488765 Iterations: 9 Function evaluations: 13 Gradient evaluations: 13 (array([ 2.41772580e-05, 1.62492628e-04, 2.79438138e-04, 1.90996240e-03, 2.07117946e-01, 1.28747174e+00]), array([[ 1.52225754e-02, 2.01838216e-02, 6.90127235e-02, -2.57002471e-04, -5.25941060e-01, -8.47339404e-01], [ 2.39797491e-01, -2.32325602e-01, -9.36235262e-01, 3.02434938e-03, 3.95614029e-02, -1.02035585e-01], [ -2.11381471e-02, 3.01074776e-02, 7.97208277e-02, -2.94955832e-04, 8.49402362e-01, -5.20391053e-01], [ -1.55821981e-01, -9.66926643e-01, 2.01517298e-01, 1.52397702e-03, 4.13805882e-03, -1.19878714e-02], [ -9.57881586e-01, 9.87911166e-02, -2.67819451e-01, 1.55192932e-03, -1.78717579e-02, -2.55757014e-02], [ -9.96486655e-04, -2.03697290e-03, -2.98130314e-03, -9.99992985e-01, -1.71500426e-05, 4.70854949e-06]])) [[ -4.91007768e-05 -7.28732630e-07 -2.51941401e-05 -2.50111043e-08 -4.77484718e-08 -9.72022463e-08]] [[ -1.64845915e-08 -2.87059265e-08 -2.88764568e-07 -6.82121026e-09 2.84217094e-10 -1.70530257e-09]] [ -4.90678076e-05 -6.71320777e-07 -2.46166110e-05 -1.13686838e-08 -4.83169060e-08 -9.37916411e-08] [ -4.56753924e-05 -6.50857146e-07 -2.31756303e-05 -1.70530257e-08 -4.43378667e-08 -1.75592936e-02] [[ 2.99386348e+01 -1.24442928e+02 9.67254672e+00 -1.58968536e+02 -5.91960010e+02 -2.48738183e+00] [ -1.24442928e+02 5.62972166e+03 -5.00079203e+02 -7.13057475e+02 -7.82440674e+03 -1.05126925e+01] [ 9.67254672e+00 -5.00079203e+02 4.87472259e+01 3.37373299e+00 6.96960872e+02 7.69866589e-01] [ -1.58968536e+02 -7.13057475e+02 3.37373299e+00 6.82417837e+03 4.84485862e+03 3.21440021e+01] [ -5.91960010e+02 -7.82440674e+03 6.96960872e+02 4.84485862e+03 3.43753691e+04 9.37524459e+01] [ -2.48738183e+00 -1.05126925e+01 7.69866589e-01 3.21440021e+01 9.37524459e+01 5.23915258e+02]] >>> res_norm3.bse array([ 5.47162086, 75.03147114, 6.98192136, 82.60858536, 185.40595756, 22.88919522]) >>> print res_norm3.model.score(res_norm3.params) [ -4.90678076e-05 -6.71320777e-07 -2.46166110e-05 -1.13686838e-08 -4.83169060e-08 -9.37916411e-08] >>> print res_norm3.model.score(start_params) [ -4.56753924e-05 -6.50857146e-07 -2.31756303e-05 -1.70530257e-08 -4.43378667e-08 -1.75592936e-02] >>> mod_norm2.loglike(start_params/2.) -598.56178102781314 >>> print np.linalg.inv(-1*mod_norm2.hessian(res_norm3.params)) [[ 2.99386348e+01 -1.24442928e+02 9.67254672e+00 -1.58968536e+02 -5.91960010e+02 -2.48738183e+00] [ -1.24442928e+02 5.62972166e+03 -5.00079203e+02 -7.13057475e+02 -7.82440674e+03 -1.05126925e+01] [ 9.67254672e+00 -5.00079203e+02 4.87472259e+01 3.37373299e+00 6.96960872e+02 7.69866589e-01] [ -1.58968536e+02 -7.13057475e+02 3.37373299e+00 6.82417837e+03 4.84485862e+03 3.21440021e+01] [ -5.91960010e+02 -7.82440674e+03 6.96960872e+02 4.84485862e+03 3.43753691e+04 9.37524459e+01] [ -2.48738183e+00 -1.05126925e+01 7.69866589e-01 3.21440021e+01 9.37524459e+01 5.23915258e+02]] >>> print np.sqrt(np.diag(res_bfgs.cov_params())) [ 5.10032831 74.34988912 6.96522122 76.7091604 169.8117832 22.91695494] >>> print res_norm3.bse [ 5.47162086 75.03147114 6.98192136 82.60858536 185.40595756 22.88919522] >>> res_norm3.conf_int > >>> res_norm3.conf_int() array([[0.96421437, 1.01999835], [0.99251725, 1.04863332], [0.95721328, 1.01246222], [0.97134549, 1.02695393], [0.97050081, 1.02660988], [0.97773434, 1.03290028], [0.97529207, 1.01428874]]) >>> res_norm3.params array([ -3.08181304, 234.34701361, -14.99684381, 27.94088692, -237.14649571, 274.6857294 ]) >>> res2.params array([ -3.08181404, 234.34702702, -14.99684418, 27.94090839, -237.1465136 ]) >>> >>> res_norm3.params - res2.params Traceback (most recent call last): File "", line 1, in ValueError: shape mismatch: objects cannot be broadcast to a single shape >>> res_norm3.params[:-1] - res2.params array([ 9.96859735e-07, -1.34122981e-05, 3.72278400e-07, -2.14645839e-05, 1.78919019e-05]) >>> >>> res_norm3.bse[:-1] - res2.bse array([ -0.04309567, -5.33447922, -0.48741559, -0.31373822, -13.94570729]) >>> (res_norm3.bse[:-1] / res2.bse) - 1 array([-0.00781467, -0.06637735, -0.06525554, -0.00378352, -0.06995531]) >>> (res_norm3.bse[:-1] / res2.bse)*100. - 100 array([-0.7814667 , -6.6377355 , -6.52555369, -0.37835193, -6.99553089]) >>> np.sqrt(np.diag(np.linalg.inv(res_norm3.model.hessian(res_bfgs.params)))) array([ NaN, NaN, NaN, NaN, NaN, NaN]) >>> np.sqrt(np.diag(np.linalg.inv(-res_norm3.model.hessian(res_bfgs.params)))) array([ 5.10032831, 74.34988912, 6.96522122, 76.7091604 , 169.8117832 , 22.91695494]) >>> res_norm3.bse array([ 5.47162086, 75.03147114, 6.98192136, 82.60858536, 185.40595756, 22.88919522]) >>> res2.bse array([ 5.51471653, 80.36595035, 7.46933695, 82.92232357, 199.35166485]) >>> >>> bse_bfgs = np.sqrt(np.diag(np.linalg.inv(-res_norm3.model.hessian(res_bfgs.params)))) >>> (bse_bfgs[:-1] / res2.bse)*100. - 100 array([ -7.51422527, -7.4858335 , -6.74913633, -7.49275094, -14.8179759 ]) >>> hb=-approx_hess(res_bfgs.params, mod_norm2.loglike, epsilon=-1e-4) >>> hf=-approx_hess(res_bfgs.params, mod_norm2.loglike, epsilon=1e-4) >>> hh = (hf+hb)/2. >>> bse_bfgs = np.sqrt(np.diag(np.linalg.inv(-hh))) >>> bse_bfgs array([ NaN, NaN, NaN, NaN, NaN, NaN]) >>> bse_bfgs = np.sqrt(np.diag(np.linalg.inv(hh))) >>> np.diag(hh) array([ 9.81680159e-01, 1.39920076e-02, 4.98101826e-01, 3.60955710e-04, 9.57811608e-04, 1.90709670e-03]) >>> np.diag(np.inv(hh)) Traceback (most recent call last): File "", line 1, in AttributeError: 'module' object has no attribute 'inv' >>> np.diag(np.linalg.inv(hh)) array([ 2.64875153e+01, 5.91578496e+03, 5.13279911e+01, 6.11533345e+03, 3.33775960e+04, 5.24357391e+02]) >>> res2.bse**2 array([ 3.04120984e+01, 6.45868598e+03, 5.57909945e+01, 6.87611175e+03, 3.97410863e+04]) >>> bse_bfgs array([ 5.14660231, 76.91414015, 7.1643556 , 78.20059751, 182.69536402, 22.89885131]) >>> bse_bfgs - res_norm3.bse array([-0.32501855, 1.88266901, 0.18243424, -4.40798785, -2.71059354, 0.00965609]) >>> (bse_bfgs[:-1] / res2.bse)*100. - 100 array([-6.67512508, -4.29511526, -4.0831115 , -5.69415552, -8.35523538]) >>> (res_norm3.bse[:-1] / res2.bse)*100. - 100 array([-0.7814667 , -6.6377355 , -6.52555369, -0.37835193, -6.99553089]) >>> (bse_bfgs / res_norm3.bse)*100. - 100 array([-5.94007812, 2.50917247, 2.61295176, -5.33599242, -1.46197759, 0.04218624]) >>> bse_bfgs array([ 5.14660231, 76.91414015, 7.1643556 , 78.20059751, 182.69536402, 22.89885131]) >>> res_norm3.bse array([ 5.47162086, 75.03147114, 6.98192136, 82.60858536, 185.40595756, 22.88919522]) >>> res2.bse array([ 5.51471653, 80.36595035, 7.46933695, 82.92232357, 199.35166485]) >>> dir(res_bfgs) ['__class__', '__delattr__', '__dict__', '__doc__', '__getattribute__', '__hash__', '__init__', '__module__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__str__', '__weakref__', 'bse', 'conf_int', 'cov_params', 'f_test', 'initialize', 'llf', 'mle_retvals', 'mle_settings', 'model', 'normalized_cov_params', 'params', 'scale', 't', 't_test'] >>> res_bfgs.scale 1.0 >>> res2.scale 81083.015420213851 >>> res2.mse_resid 81083.015420213851 >>> print np.sqrt(np.diag(np.linalg.inv(-1*mod_norm2.hessian(res_bfgs.params)))) [ 5.10032831 74.34988912 6.96522122 76.7091604 169.8117832 22.91695494] >>> print np.sqrt(np.diag(np.linalg.inv(-1*res_bfgs.model.hessian(res_bfgs.params)))) [ 5.10032831 74.34988912 6.96522122 76.7091604 169.8117832 22.91695494] Is scale a misnomer, actually scale squared, i.e. variance of error term ? ''' print(res_norm3.model.score_obs(res_norm3.params).shape) jac = res_norm3.model.score_obs(res_norm3.params) print(np.sqrt(np.diag(np.dot(jac.T, jac)))/start_params) jac2 = res_norm3.model.score_obs(res_norm3.params, centered=True) print(np.sqrt(np.diag(np.linalg.inv(np.dot(jac.T, jac))))) print(res_norm3.bse) print(res2.bse) statsmodels-0.12.2/statsmodels/examples/ex_generic_mle_t.py000066400000000000000000000235141400612667500241740ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Jul 28 08:28:04 2010 Author: josef-pktd """ import numpy as np from scipy import special import statsmodels.api as sm from statsmodels.base.model import GenericLikelihoodModel from statsmodels.tools.numdiff import approx_hess #redefine some shortcuts np_log = np.log np_pi = np.pi sps_gamln = special.gammaln def maxabs(arr1, arr2): return np.max(np.abs(arr1 - arr2)) def maxabsrel(arr1, arr2): return np.max(np.abs(arr2 / arr1 - 1)) class MyT(GenericLikelihoodModel): '''Maximum Likelihood Estimation of Poisson Model This is an example for generic MLE which has the same statistical model as discretemod.Poisson. Except for defining the negative log-likelihood method, all methods and results are generic. Gradients and Hessian and all resulting statistics are based on numerical differentiation. ''' def loglike(self, params): return -self.nloglikeobs(params).sum(0) # copied from discretemod.Poisson def nloglikeobs(self, params): """ Loglikelihood of Poisson model Parameters ---------- params : array_like The parameters of the model. Returns ------- The log likelihood of the model evaluated at `params` Notes -------- .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right] """ #print len(params), beta = params[:-2] df = params[-2] scale = params[-1] loc = np.dot(self.exog, beta) endog = self.endog x = (endog - loc)/scale #next part is stats.t._logpdf lPx = sps_gamln((df+1)/2) - sps_gamln(df/2.) lPx -= 0.5*np_log(df*np_pi) + (df+1)/2.*np_log(1+(x**2)/df) lPx -= np_log(scale) # correction for scale return -lPx #Example: np.random.seed(98765678) nobs = 1000 rvs = np.random.randn(nobs,5) data_exog = sm.add_constant(rvs, prepend=False) xbeta = 0.9 + 0.1*rvs.sum(1) data_endog = xbeta + 0.1*np.random.standard_t(5, size=nobs) #print data_endog modp = MyT(data_endog, data_exog) modp.start_value = np.ones(data_exog.shape[1]+2) modp.start_value[-2] = 10 modp.start_params = modp.start_value resp = modp.fit(start_params = modp.start_value) print(resp.params) print(resp.bse) hb=-approx_hess(modp.start_value, modp.loglike, epsilon=-1e-4) tmp = modp.loglike(modp.start_value) print(tmp.shape) ''' >>> tmp = modp.loglike(modp.start_value) 8 >>> tmp.shape (100,) >>> tmp.sum(0) -24220.877108016182 >>> tmp = modp.nloglikeobs(modp.start_value) 8 >>> tmp.shape (100, 100) >>> params = modp.start_value >>> beta = params[:-2] >>> beta.shape (6,) >>> np.dot(modp.exog, beta).shape (100,) >>> modp.endog.shape (100, 100) >>> xbeta.shape (100,) >>> ''' ''' repr(start_params) array([ 1., 1., 1., 1., 1., 1., 1., 1.]) Optimization terminated successfully. Current function value: 91.897859 Iterations: 108 Function evaluations: 173 Gradient evaluations: 173 [ 1.58253308e-01 1.73188603e-01 1.77357447e-01 2.06707494e-02 -1.31174789e-01 8.79915580e-01 6.47663840e+03 6.73457641e+02] [ NaN NaN NaN NaN NaN 28.26906182 NaN NaN] () >>> resp.params array([ 1.58253308e-01, 1.73188603e-01, 1.77357447e-01, 2.06707494e-02, -1.31174789e-01, 8.79915580e-01, 6.47663840e+03, 6.73457641e+02]) >>> resp.bse array([ NaN, NaN, NaN, NaN, NaN, 28.26906182, NaN, NaN]) >>> resp.jac Traceback (most recent call last): File "", line 1, in AttributeError: 'GenericLikelihoodModelResults' object has no attribute 'jac' >>> resp.bsejac array([ 45243.35919908, 51997.80776897, 41418.33021984, 42763.46575168, 50101.91631612, 42804.92083525, 3005625.35649203, 13826948.68708931]) >>> resp.bsejhj array([ 1.51643931, 0.80229636, 0.27720185, 0.4711138 , 0.9028682 , 0.31673747, 0.00524426, 0.69729368]) >>> resp.covjac array([[ 2.04696155e+09, 1.46643494e+08, 7.59932781e+06, -2.39993397e+08, 5.62644255e+08, 2.34300598e+08, -3.07824799e+09, -1.93425470e+10], [ 1.46643494e+08, 2.70377201e+09, 1.06005712e+08, 3.76824011e+08, -1.21778986e+08, 5.38612723e+08, -2.12575784e+10, -1.69503271e+11], [ 7.59932781e+06, 1.06005712e+08, 1.71547808e+09, -5.94451158e+07, -1.44586401e+08, -5.41830441e+06, 1.25899515e+10, 1.06372065e+11], [ -2.39993397e+08, 3.76824011e+08, -5.94451158e+07, 1.82871400e+09, -5.66930891e+08, 3.75061111e+08, -6.84681772e+09, -7.29993789e+10], [ 5.62644255e+08, -1.21778986e+08, -1.44586401e+08, -5.66930891e+08, 2.51020202e+09, -4.67886982e+08, 1.78890380e+10, 1.75428694e+11], [ 2.34300598e+08, 5.38612723e+08, -5.41830441e+06, 3.75061111e+08, -4.67886982e+08, 1.83226125e+09, -1.27484996e+10, -1.12550321e+11], [ -3.07824799e+09, -2.12575784e+10, 1.25899515e+10, -6.84681772e+09, 1.78890380e+10, -1.27484996e+10, 9.03378378e+12, 2.15188047e+13], [ -1.93425470e+10, -1.69503271e+11, 1.06372065e+11, -7.29993789e+10, 1.75428694e+11, -1.12550321e+11, 2.15188047e+13, 1.91184510e+14]]) >>> hb array([[ 33.68732564, -2.33209221, -13.51255321, -1.60840159, -13.03920385, -9.3506543 , 4.86239173, -9.30409101], [ -2.33209221, 3.12512611, -6.08530968, -6.79232244, 3.66804898, 1.26497071, 5.10113409, -2.53482995], [ -13.51255321, -6.08530968, 31.14883498, -5.01514705, -10.48819911, -2.62533035, 3.82241581, -12.51046342], [ -1.60840159, -6.79232244, -5.01514705, 28.40141917, -8.72489636, -8.82449456, 5.47584023, -18.20500017], [ -13.03920385, 3.66804898, -10.48819911, -8.72489636, 9.03650914, 3.65206176, 6.55926726, -1.8233635 ], [ -9.3506543 , 1.26497071, -2.62533035, -8.82449456, 3.65206176, 21.41825348, -1.28610793, 4.28101146], [ 4.86239173, 5.10113409, 3.82241581, 5.47584023, 6.55926726, -1.28610793, 46.52354448, -32.23861427], [ -9.30409101, -2.53482995, -12.51046342, -18.20500017, -1.8233635 , 4.28101146, -32.23861427, 178.61978279]]) >>> np.linalg.eigh(hb) (array([ -10.50373649, 0.7460258 , 14.73131793, 29.72453087, 36.24103832, 41.98042979, 48.99815223, 190.04303734]), array([[-0.40303259, 0.10181305, 0.18164206, 0.48201456, 0.03916688, 0.00903695, 0.74620692, 0.05853619], [-0.3201713 , -0.88444855, -0.19867642, 0.02828812, 0.16733946, -0.21440765, -0.02927317, 0.01176904], [-0.41847094, 0.00170161, 0.04973298, 0.43276118, -0.55894304, 0.26454728, -0.49745582, 0.07251685], [-0.3508729 , -0.08302723, 0.25004884, -0.73495077, -0.38936448, 0.20677082, 0.24464779, 0.11448238], [-0.62065653, 0.44662675, -0.37388565, -0.19453047, 0.29084735, -0.34151809, -0.19088978, 0.00342713], [-0.15119802, -0.01099165, 0.84377273, 0.00554863, 0.37332324, -0.17917015, -0.30371283, -0.03635211], [ 0.15813581, 0.0293601 , 0.09882271, 0.03515962, -0.48768565, -0.81960996, 0.05248464, 0.22533642], [-0.06118044, -0.00549223, 0.03205047, -0.01782649, -0.21128588, -0.14391393, 0.05973658, -0.96226835]])) >>> np.linalg.eigh(np.linalg.inv(hb)) (array([-0.09520422, 0.00526197, 0.02040893, 0.02382062, 0.02759303, 0.03364225, 0.06788259, 1.34043621]), array([[-0.40303259, 0.05853619, 0.74620692, -0.00903695, -0.03916688, 0.48201456, 0.18164206, 0.10181305], [-0.3201713 , 0.01176904, -0.02927317, 0.21440765, -0.16733946, 0.02828812, -0.19867642, -0.88444855], [-0.41847094, 0.07251685, -0.49745582, -0.26454728, 0.55894304, 0.43276118, 0.04973298, 0.00170161], [-0.3508729 , 0.11448238, 0.24464779, -0.20677082, 0.38936448, -0.73495077, 0.25004884, -0.08302723], [-0.62065653, 0.00342713, -0.19088978, 0.34151809, -0.29084735, -0.19453047, -0.37388565, 0.44662675], [-0.15119802, -0.03635211, -0.30371283, 0.17917015, -0.37332324, 0.00554863, 0.84377273, -0.01099165], [ 0.15813581, 0.22533642, 0.05248464, 0.81960996, 0.48768565, 0.03515962, 0.09882271, 0.0293601 ], [-0.06118044, -0.96226835, 0.05973658, 0.14391393, 0.21128588, -0.01782649, 0.03205047, -0.00549223]])) >>> np.diag(np.linalg.inv(hb)) array([ 0.01991288, 1.0433882 , 0.00516616, 0.02642799, 0.24732871, 0.05281555, 0.02236704, 0.00643486]) >>> np.sqrt(np.diag(np.linalg.inv(hb))) array([ 0.14111302, 1.02146375, 0.07187597, 0.16256686, 0.49732154, 0.22981633, 0.14955616, 0.08021756]) >>> hess = modp.hessian(resp.params) >>> np.sqrt(np.diag(np.linalg.inv(hess))) array([ 231.3823423 , 117.79508218, 31.46595143, 53.44753106, 132.4855704 , NaN, 5.47881705, 90.75332693]) >>> hb=-approx_hess(resp.params, modp.loglike, epsilon=-1e-4) >>> np.sqrt(np.diag(np.linalg.inv(hb))) array([ 31.93524822, 22.0333515 , NaN, 29.90198792, 38.82615785, NaN, NaN, NaN]) >>> hb=-approx_hess(resp.params, modp.loglike, epsilon=-1e-8) >>> np.sqrt(np.diag(np.linalg.inv(hb))) Traceback (most recent call last): [...] raise LinAlgError, 'Singular matrix' numpy.linalg.linalg.LinAlgError: Singular matrix >>> resp.params array([ 1.58253308e-01, 1.73188603e-01, 1.77357447e-01, 2.06707494e-02, -1.31174789e-01, 8.79915580e-01, 6.47663840e+03, 6.73457641e+02]) >>> ''' statsmodels-0.12.2/statsmodels/examples/ex_generic_mle_tdist.py000066400000000000000000000665301400612667500250650ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Jul 28 08:28:04 2010 Author: josef-pktd """ import numpy as np from scipy import stats, special, optimize import statsmodels.api as sm from statsmodels.base.model import GenericLikelihoodModel from statsmodels.tools.numdiff import approx_hess #import for kstest based estimation #should be replace # FIXME: importing these patches scipy distribution classes in-place. # Do not do this. import statsmodels.sandbox.distributions.sppatch # noqa:F401 #redefine some shortcuts np_log = np.log np_pi = np.pi sps_gamln = special.gammaln def maxabs(arr1, arr2): return np.max(np.abs(arr1 - arr2)) def maxabsrel(arr1, arr2): return np.max(np.abs(arr2 / arr1 - 1)) #global store_params = [] class MyT(GenericLikelihoodModel): '''Maximum Likelihood Estimation of Linear Model with t-distributed errors This is an example for generic MLE which has the same statistical model as discretemod.Poisson. Except for defining the negative log-likelihood method, all methods and results are generic. Gradients and Hessian and all resulting statistics are based on numerical differentiation. ''' def loglike(self, params): return -self.nloglikeobs(params).sum(0) # copied from discretemod.Poisson def nloglikeobs(self, params): """ Loglikelihood of Poisson model Parameters ---------- params : array_like The parameters of the model. Returns ------- The log likelihood of the model evaluated at `params` Notes -------- .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right] """ #print len(params), store_params.append(params) if self.fixed_params is not None: #print 'using fixed' params = self.expandparams(params) beta = params[:-2] df = params[-2] scale = params[-1] loc = np.dot(self.exog, beta) endog = self.endog x = (endog - loc)/scale #next part is stats.t._logpdf lPx = sps_gamln((df+1)/2) - sps_gamln(df/2.) lPx -= 0.5*np_log(df*np_pi) + (df+1)/2.*np_log(1+(x**2)/df) lPx -= np_log(scale) # correction for scale return -lPx #Example: np.random.seed(98765678) nobs = 1000 nvars = 6 df = 5 rvs = np.random.randn(nobs, nvars-1) data_exog = sm.add_constant(rvs, prepend=False) xbeta = 0.9 + 0.1*rvs.sum(1) data_endog = xbeta + 0.1*np.random.standard_t(df, size=nobs) print(data_endog.var()) res_ols = sm.OLS(data_endog, data_exog).fit() print(res_ols.scale) print(np.sqrt(res_ols.scale)) print(res_ols.params) kurt = stats.kurtosis(res_ols.resid) df_fromkurt = 6./kurt + 4 print(stats.t.stats(df_fromkurt, moments='mvsk')) print(stats.t.stats(df, moments='mvsk')) modp = MyT(data_endog, data_exog) start_value = 0.1*np.ones(data_exog.shape[1]+2) #start_value = np.zeros(data_exog.shape[1]+2) #start_value[:nvars] = sm.OLS(data_endog, data_exog).fit().params start_value[:nvars] = res_ols.params start_value[-2] = df_fromkurt #10 start_value[-1] = np.sqrt(res_ols.scale) #0.5 modp.start_params = start_value #adding fixed parameters fixdf = np.nan * np.zeros(modp.start_params.shape) fixdf[-2] = 100 fixone = 0 if fixone: modp.fixed_params = fixdf modp.fixed_paramsmask = np.isnan(fixdf) modp.start_params = modp.start_params[modp.fixed_paramsmask] else: modp.fixed_params = None modp.fixed_paramsmask = None resp = modp.fit(start_params = modp.start_params, disp=1, method='nm')#'newton') #resp = modp.fit(start_params = modp.start_params, disp=1, method='newton') print('\nestimation results t-dist') print(resp.params) print(resp.bse) resp2 = modp.fit(start_params = resp.params, method='Newton') print('using Newton') print(resp2.params) print(resp2.bse) hb=-approx_hess(modp.start_params, modp.loglike, epsilon=-1e-4) tmp = modp.loglike(modp.start_params) print(tmp.shape) #np.linalg.eigh(np.linalg.inv(hb))[0] pp=np.array(store_params) print(pp.min(0)) print(pp.max(0)) ##################### Example: Pareto # estimating scale does not work yet, a bug somewhere ? # fit_ks works well, but no bse or other result statistics yet class MyPareto(GenericLikelihoodModel): '''Maximum Likelihood Estimation pareto distribution first version: iid case, with constant parameters ''' #copied from stats.distribution def pdf(self, x, b): return b * x**(-b-1) def loglike(self, params): return -self.nloglikeobs(params).sum(0) def nloglikeobs(self, params): #print params.shape if self.fixed_params is not None: #print 'using fixed' params = self.expandparams(params) b = params[0] loc = params[1] scale = params[2] #loc = np.dot(self.exog, beta) endog = self.endog x = (endog - loc)/scale logpdf = np_log(b) - (b+1.)*np_log(x) #use np_log(1 + x) for Pareto II logpdf -= np.log(scale) #lb = loc + scale #logpdf[endog>> res_par.params array([ 7.42705803e+152, 2.17339053e+153]) >>> mod_par.loglike(mod_par.start_params) -1085.1993430947232 >>> np.log(mod_par.pdf(*mod_par.start_params)) 0.69314718055994529 >>> mod_par.loglike(mod_par.start_params) -1085.1993430947232 >>> np.log(stats.pareto.pdf(y[0],*mod_par.start_params)) -4.6414308627431353 >>> mod_par.loglike(mod_par.start_params) -1085.1993430947232 >>> mod_par.nloglikeobs(mod_par.start_params)[0] 0.29377232943845044 >>> mod_par.start_params array([ 1., 2.]) >>> np.log(stats.pareto.pdf(y[0],1,9.5,2)) -1.2806918394368461 >>> mod_par.fixed_params= None >>> mod_par.nloglikeobs(np.array([1., 10., 2.]))[0] 0.087533156771285828 >>> y[0] 12.182956907488885 >>> mod_par.endog[0] 12.182956907488885 >>> np.log(stats.pareto.pdf(y[0],1,10,2)) -0.86821349410251702 >>> np.log(stats.pareto.pdf(y[0],1.,10.,2.)) -0.86821349410251702 >>> stats.pareto.pdf(y[0],1.,10.,2.) 0.41970067762301644 >>> mod_par.loglikeobs(np.array([1., 10., 2.]))[0] -0.087533156771285828 >>> ''' ''' >>> mod_par.nloglikeobs(np.array([1., 10., 2.]))[0] 0.86821349410251691 >>> np.log(stats.pareto.pdf(y,1.,10.,2.)).sum() -2627.9403758026938 ''' #''' #0.0686702747648 #0.0164150896481 #0.128121386381 #[ 0.10370428 0.09921315 0.09676723 0.10457413 0.10201618 0.89964496] #(array(0.0), array(1.4552599885729827), array(0.0), array(2.5072143354058203)) #(array(0.0), array(1.6666666666666667), array(0.0), array(6.0)) #repr(start_params) array([ 0.10370428, 0.09921315, 0.09676723, 0.10457413, 0.10201618, # 0.89964496, 6.39309417, 0.12812139]) #Optimization terminated successfully. # Current function value: -679.951339 # Iterations: 398 # Function evaluations: 609 # #estimation results t-dist #[ 0.10400826 0.10111893 0.09725133 0.10507788 0.10086163 0.8996041 # 4.72131318 0.09825355] #[ 0.00365493 0.00356149 0.00349329 0.00362333 0.003732 0.00362716 # 0.72325227 0.00388822] #repr(start_params) array([ 0.10400826, 0.10111893, 0.09725133, 0.10507788, 0.10086163, # 0.8996041 , 4.72131318, 0.09825355]) #Optimization terminated successfully. # Current function value: -679.950443 # Iterations 3 #using Newton #[ 0.10395383 0.10106762 0.09720665 0.10503384 0.10080599 0.89954546 # 4.70918964 0.09815885] #[ 0.00365299 0.00355968 0.00349147 0.00362166 0.00373015 0.00362533 # 0.72014669 0.00388436] #() #[ 0.09992709 0.09786601 0.09387356 0.10229919 0.09756623 0.85466272 # 4.60459182 0.09661986] #[ 0.11308292 0.10828401 0.1028508 0.11268895 0.10934726 0.94462721 # 7.15412655 0.13452746] #repr(start_params) array([ 1., 2.]) #Warning: Maximum number of function evaluations has been exceeded. #repr(start_params) array([ 3.06504406e+302, 3.29325579e+303]) # #>>> mod_par.fixed_params #array([ NaN, 10., NaN]) #>>> mod_par.start_params #array([ 1., 2.]) # # #>>> stats.pareto.fit_fr(y, 1., frozen=[np.nan, 10., np.nan]) #array([ 1.0346268 , 2.00184808]) # #>>> stats.pareto.fit_fr(y, frozen=[np.nan, 10., np.nan]) #array([ 1.03463526, 2.00184809]) #>>> stats.pareto.pdf(y, 1.03463526, 10, 2.00184809).sum() #173.33947284555239 # #>>> mod_par.loglike((1.03463526, 10, 2.00184809)) #-962.21623668859741 #>>> np.log(stats.pareto.pdf(y, 1.03463526, 10, 2.00184809)).sum() #-inf #>>> np.log(stats.pareto.pdf(y, 1.03463526, 9, 2.00184809)).sum() #-3074.5947476137271 #>>> np.log(stats.pareto.pdf(y, 1.03463526, 10., 2.00184809)).sum() #-inf #>>> np.log(stats.pareto.pdf(y, 1.03463526, 9.9, 2.00184809)).sum() #-2677.3867091635661 #>>> y.min() #12.001848089426717 #>>> np.log(stats.pareto.pdf(y, 1.03463526, loc=9.9, scale=2.00184809)).sum() #-2677.3867091635661 #>>> np.log(stats.pareto.pdf(y, 1.03463526, loc=10., scale=2.00184809)).sum() #-inf #>>> stats.pareto.logpdf(y, 1.03463526, loc=10., scale=2.00184809).sum() #-inf #>>> stats.pareto.logpdf(y, 1.03463526, loc=9.99, scale=2.00184809).sum() #-2631.6120098202355 #>>> mod_par.loglike((1.03463526, 9.99, 2.00184809)) #-963.2513896113644 #>>> maxabs(y, mod_par.endog) #0.0 # #>>> stats.pareto.a #1.0 # #>>> b, loc, scale = (1.03463526, 9.99, 2.00184809) #>>> (1-loc)/scale #-4.4908502522786327 # #>>> lb = scale + loc #>>> lb #11.991848090000001 #>>> (lb-loc)/scale == 1 #False #>>> (lb-loc)/scale #1.0000000000000004 #>>> #''' ''' repr(start_params) array([ 1., 10., 2.]) Optimization terminated successfully. Current function value: 2626.436870 Iterations: 102 Function evaluations: 210 Optimization terminated successfully. Current function value: 0.016555 Iterations: 16 Function evaluations: 35 [ 1.03482659 10.00737039 1.9944777 ] (1.0596088578825995, 9.9043376069230007, 2.0975104813987118) >>> 9.9043376069230007 + 2.0975104813987118 12.001848088321712 >>> y.min() 12.001848089426717 ''' ''' 0.0686702747648 0.0164150896481 0.128121386381 [ 0.10370428 0.09921315 0.09676723 0.10457413 0.10201618 0.89964496] (array(0.0), array(1.4552599885729829), array(0.0), array(2.5072143354058221)) (array(0.0), array(1.6666666666666667), array(0.0), array(6.0)) repr(start_params) array([ 0.10370428, 0.09921315, 0.09676723, 0.10457413, 0.10201618, 0.89964496, 6.39309417, 0.12812139]) Optimization terminated successfully. Current function value: -679.951339 Iterations: 398 Function evaluations: 609 estimation results t-dist [ 0.10400826 0.10111893 0.09725133 0.10507788 0.10086163 0.8996041 4.72131318 0.09825355] [ 0.00365493 0.00356149 0.00349329 0.00362333 0.003732 0.00362716 0.72329352 0.00388832] repr(start_params) array([ 0.10400826, 0.10111893, 0.09725133, 0.10507788, 0.10086163, 0.8996041 , 4.72131318, 0.09825355]) Optimization terminated successfully. Current function value: -679.950443 Iterations 3 using Newton [ 0.10395383 0.10106762 0.09720665 0.10503384 0.10080599 0.89954546 4.70918964 0.09815885] [ 0.00365299 0.00355968 0.00349147 0.00362166 0.00373015 0.00362533 0.7201488 0.00388437] () [ 0.09992709 0.09786601 0.09387356 0.10229919 0.09756623 0.85466272 4.60459182 0.09661986] [ 0.11308292 0.10828401 0.1028508 0.11268895 0.10934726 0.94462721 7.15412655 0.13452746] repr(start_params) array([ 1., 9., 2.]) Optimization terminated successfully. Current function value: 2636.129089 Iterations: 147 Function evaluations: 279 Optimization terminated successfully. Current function value: 0.016555 Iterations: 16 Function evaluations: 35 [ 0.84856418 10.2197801 1.78206799] (1.0596088578825995, 9.9043376069230007, 2.0975104813987118) 12.0018480891 12.0018480883 12.0018480894 repr(start_params) array([ 1., 2.]) Warning: Desired error not necessarily achieveddue to precision loss Current function value: 2643.549907 Iterations: 2 Function evaluations: 13 Gradient evaluations: 12 >>> res_parks2 = mod_par.fit_ks() repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2642.465273 Iterations: 92 Function evaluations: 172 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2636.639863 Iterations: 73 Function evaluations: 136 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2631.568778 Iterations: 75 Function evaluations: 133 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2627.821044 Iterations: 75 Function evaluations: 135 repr(start_params) array([ 1., 2.]) Warning: Maximum number of function evaluations has been exceeded. repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2631.568778 Iterations: 75 Function evaluations: 133 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.431596 Iterations: 58 Function evaluations: 109 repr(start_params) array([ 1., 2.]) Warning: Maximum number of function evaluations has been exceeded. repr(start_params) array([ 1., 2.]) Warning: Maximum number of function evaluations has been exceeded. repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.737426 Iterations: 60 Function evaluations: 109 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2627.821044 Iterations: 75 Function evaluations: 135 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.471666 Iterations: 48 Function evaluations: 94 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2627.196314 Iterations: 66 Function evaluations: 119 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.578538 Iterations: 56 Function evaluations: 103 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.471666 Iterations: 48 Function evaluations: 94 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.651702 Iterations: 67 Function evaluations: 122 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.737426 Iterations: 60 Function evaluations: 109 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.613505 Iterations: 73 Function evaluations: 141 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.578538 Iterations: 56 Function evaluations: 103 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.632218 Iterations: 64 Function evaluations: 119 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.651702 Iterations: 67 Function evaluations: 122 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.622789 Iterations: 63 Function evaluations: 114 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.613505 Iterations: 73 Function evaluations: 141 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.627465 Iterations: 59 Function evaluations: 109 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.632218 Iterations: 64 Function evaluations: 119 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.625104 Iterations: 59 Function evaluations: 108 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.629829 Iterations: 66 Function evaluations: 118 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.632218 Iterations: 64 Function evaluations: 119 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.632218 Iterations: 64 Function evaluations: 119 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.628642 Iterations: 67 Function evaluations: 122 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.631023 Iterations: 68 Function evaluations: 129 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.630430 Iterations: 57 Function evaluations: 108 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.629598 Iterations: 60 Function evaluations: 112 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.630430 Iterations: 57 Function evaluations: 108 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.630130 Iterations: 65 Function evaluations: 122 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.629536 Iterations: 62 Function evaluations: 111 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.630130 Iterations: 65 Function evaluations: 122 repr(start_params) array([ 1., 2.]) Optimization terminated successfully. Current function value: 2626.629984 Iterations: 67 Function evaluations: 123 Optimization terminated successfully. Current function value: 0.016560 Iterations: 18 Function evaluations: 38 >>> res_parks2 (1.0592352626264809, 9.9051580457572399, 2.0966900385041591) >>> res_parks (1.0596088578825995, 9.9043376069230007, 2.0975104813987118) >>> res_par.params array([ 0.84856418, 10.2197801 , 1.78206799]) >>> np.sqrt(np.diag(mod_par.hessian(res_par.params))) array([ NaN, NaN, NaN]) >>> mod_par.hessian(res_par.params ... ) array([[ NaN, NaN, NaN], [ NaN, NaN, NaN], [ NaN, NaN, NaN]]) >>> mod_par.hessian(res_parks) array([[ NaN, NaN, NaN], [ NaN, NaN, NaN], [ NaN, NaN, NaN]]) >>> mod_par.hessian(np.array(res_parks)) array([[ NaN, NaN, NaN], [ NaN, NaN, NaN], [ NaN, NaN, NaN]]) >>> mod_par.fixed_params array([ NaN, 9.90510677, NaN]) >>> mod_par.fixed_params=None >>> mod_par.hessian(np.array(res_parks)) array([[-890.48553491, NaN, NaN], [ NaN, NaN, NaN], [ NaN, NaN, NaN]]) >>> mod_par.loglike(np.array(res_parks)) -2626.6322080820569 >>> mod_par.bsejac Traceback (most recent call last): [...] AttributeError: 'MyPareto' object has no attribute 'bsejac' >>> hasattr(mod_par, 'start_params') True >>> mod_par.start_params array([ 1., 2.]) >>> stats.pareto.stats(1., 9., 2., moments='mvsk') (array(1.#INF), array(1.#INF), array(1.#QNAN), array(1.#QNAN)) >>> stats.pareto.stats(1., 8., 2., moments='mvsk') (array(1.#INF), array(1.#INF), array(1.#QNAN), array(1.#QNAN)) >>> stats.pareto.stats(1., 8., 1., moments='mvsk') (array(1.#INF), array(1.#INF), array(1.#QNAN), array(1.#QNAN)) >>> stats.pareto.stats(1., moments='mvsk') (array(1.#INF), array(1.#INF), array(1.#QNAN), array(1.#QNAN)) >>> stats.pareto.stats(0.5, moments='mvsk') (array(1.#INF), array(1.#INF), array(1.#QNAN), array(1.#QNAN)) >>> stats.pareto.stats(2, moments='mvsk') (array(2.0), array(1.#INF), array(1.#QNAN), array(1.#QNAN)) >>> stats.pareto.stats(10, moments='mvsk') (array(1.1111111111111112), array(0.015432098765432098), array(2.8110568859997356), array(14.828571428571429)) >>> stats.pareto.rvs(10, size=10) array([ 1.07716265, 1.18977526, 1.07093 , 1.05157081, 1.15991232, 1.31015589, 1.06675107, 1.08082475, 1.19501243, 1.34967158]) >>> r = stats.pareto.rvs(10, size=1000) >>> import matplotlib.pyplot as plt >>> plt.hist(r) (array([962, 32, 3, 2, 0, 0, 0, 0, 0, 1]), array([ 1.00013046, 1.3968991 , 1.79366773, 2.19043637, 2.587205 , 2.98397364, 3.38074227, 3.77751091, 4.17427955, 4.57104818, 4.96781682]), ) >>> plt.show() ''' statsmodels-0.12.2/statsmodels/examples/ex_grangercausality.py000066400000000000000000000021441400612667500247400ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sat Jul 06 15:44:57 2013 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_almost_equal from statsmodels.datasets import macrodata import statsmodels.tsa.stattools as tsa_stats # some example data mdata = macrodata.load_pandas().data mdata = mdata[['realgdp','realcons']].values data = mdata data = np.diff(np.log(data), axis=0) #R: lmtest:grangertest r_result = [0.243097, 0.7844328, 195, 2] #f_test gr = tsa_stats.grangercausalitytests(data[:,1::-1], 2, verbose=False) assert_almost_equal(r_result, gr[2][0]['ssr_ftest'], decimal=7) assert_almost_equal(gr[2][0]['params_ftest'], gr[2][0]['ssr_ftest'], decimal=7) lag = 2 print('\nTest Results for %d lags' % lag) print() print('\n'.join(['%-20s statistic: %f6.4 p-value: %f6.4' % (k, res[0], res[1]) for k, res in gr[lag][0].items()])) print('\n Results for auxiliary restricted regression with two lags') print() print(gr[lag][1][0].summary()) print('\n Results for auxiliary unrestricted regression with two lags') print() print(gr[lag][1][1].summary()) statsmodels-0.12.2/statsmodels/examples/ex_inter_rater.py000066400000000000000000000061121400612667500237110ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Mon Dec 10 08:54:02 2012 Author: Josef Perktold """ import numpy as np from statsmodels.stats.inter_rater import fleiss_kappa, cohens_kappa table0 = np.asarray('''\ 1 0 0 0 0 14 1.000 2 0 2 6 4 2 0.253 3 0 0 3 5 6 0.308 4 0 3 9 2 0 0.440 5 2 2 8 1 1 0.330 6 7 7 0 0 0 0.462 7 3 2 6 3 0 0.242 8 2 5 3 2 2 0.176 9 6 5 2 1 0 0.286 10 0 2 2 3 7 0.286'''.split(), float).reshape(10,-1) Total = np.asarray("20 28 39 21 32".split('\t'), int) Pj = np.asarray("0.143 0.200 0.279 0.150 0.229".split('\t'), float) kappa_wp = 0.210 table1 = table0[:, 1:-1] print(fleiss_kappa(table1)) table4 = np.array([[20,5], [10, 15]]) print('res', cohens_kappa(table4), 0.4) #wikipedia table5 = np.array([[45, 15], [25, 15]]) print('res', cohens_kappa(table5), 0.1304) #wikipedia table6 = np.array([[25, 35], [5, 35]]) print('res', cohens_kappa(table6), 0.2593) #wikipedia print('res', cohens_kappa(table6, weights=np.arange(2)), 0.2593) #wikipedia t7 = np.array([[16, 18, 28], [10, 27, 13], [28, 20, 24]]) print(cohens_kappa(t7, weights=[0, 1, 2])) table8 = np.array([[25, 35], [5, 35]]) print('res', cohens_kappa(table8)) #SAS example from http://www.john-uebersax.com/stat/saskappa.htm ''' Statistic Value ASE 95% Confidence Limits ------------------------------------------------------------ Simple Kappa 0.3333 0.0814 0.1738 0.4929 Weighted Kappa 0.2895 0.0756 0.1414 0.4376 ''' t9 = [[0, 0, 0], [5, 16, 3], [8, 12, 28]] res9 = cohens_kappa(t9) print('res', res9) print('res', cohens_kappa(t9, weights=[0, 1, 2])) #check max kappa, constructed by hand, same marginals table6a = np.array([[30, 30], [0, 40]]) res = cohens_kappa(table6a) assert res.kappa == res.kappa_max #print np.divide(*cohens_kappa(table6)[:2]) print(res.kappa / res.kappa_max) table10 = [[0, 4, 1], [0, 8, 0], [0, 1, 5]] res10 = cohens_kappa(table10) print('res10', res10) '''SAS result for table10 Simple Kappa Coefficient -------------------------------- Kappa 0.4842 ASE 0.1380 95% Lower Conf Limit 0.2137 95% Upper Conf Limit 0.7547 Test of H0: Kappa = 0 ASE under H0 0.1484 Z 3.2626 One-sided Pr > Z 0.0006 Two-sided Pr > |Z| 0.0011 Weighted Kappa Coefficient -------------------------------- Weighted Kappa 0.4701 ASE 0.1457 95% Lower Conf Limit 0.1845 95% Upper Conf Limit 0.7558 Test of H0: Weighted Kappa = 0 ASE under H0 0.1426 Z 3.2971 One-sided Pr > Z 0.0005 Two-sided Pr > |Z| 0.0010 ''' statsmodels-0.12.2/statsmodels/examples/ex_kde_confint.py000066400000000000000000000042631400612667500236630ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Mon Dec 16 11:02:59 2013 Author: Josef Perktold """ import numpy as np from scipy import stats import matplotlib.pyplot as plt import statsmodels.nonparametric.api as npar from statsmodels.sandbox.nonparametric import kernels from statsmodels.distributions.mixture_rvs import mixture_rvs # example from test_kde.py mixture of two normal distributions np.random.seed(12345) x = mixture_rvs([.25,.75], size=200, dist=[stats.norm, stats.norm], kwargs = (dict(loc=-1, scale=.5),dict(loc=1, scale=.5))) x.sort() # not needed kde = npar.KDEUnivariate(x) kde.fit('gau') ci = kde.kernel.density_confint(kde.density, len(x)) fig = plt.figure() ax = fig.add_subplot(1, 1, 1) # gh5792. Remove except after matplotlib>2.1 required try: ax.hist(x, bins=15, density=True, alpha=0.25) except AttributeError: ax.hist(x, bins=15, normed=True, alpha=0.25) ax.plot(kde.support, kde.density, lw=2, color='red') ax.fill_between(kde.support, ci[:,0], ci[:,1], color='grey', alpha='0.7') ax.set_title('Kernel Density Gaussian (bw = %4.2f)' % kde.bw) # use all kernels directly x_grid = np.linspace(np.min(x), np.max(x), 51) x_grid = np.linspace(-3, 3, 51) kernel_names = ['Biweight', 'Cosine', 'Epanechnikov', 'Gaussian', 'Triangular', 'Triweight', #'Uniform', ] fig = plt.figure() for ii, kn in enumerate(kernel_names): ax = fig.add_subplot(2, 3, ii+1) # without uniform # gh5792. Remove except after matplotlib>2.1 required try: ax.hist(x, bins=10, density=True, alpha=0.25) except AttributeError: ax.hist(x, bins=10, normed=True, alpha=0.25) #reduce bandwidth for Gaussian and Uniform which are to large in example if kn in ['Gaussian', 'Uniform']: args = (0.5,) else: args = () kernel = getattr(kernels, kn)(*args) kde_grid = [kernel.density(x, xi) for xi in x_grid] confint_grid = kernel.density_confint(kde_grid, len(x)) ax.plot(x_grid, kde_grid, lw=2, color='red', label=kn) ax.fill_between(x_grid, confint_grid[:,0], confint_grid[:,1], color='grey', alpha='0.7') ax.legend(loc='upper left') plt.show() statsmodels-0.12.2/statsmodels/examples/ex_kde_normalreference.py000066400000000000000000000033451400612667500253720ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Author: Padarn Wilson Performance of normal reference plug-in estimator vs silverman. Sample is drawn from a mixture of gaussians. Distribution has been chosen to be reasoanbly close to normal. """ import numpy as np from scipy import stats import matplotlib.pyplot as plt import statsmodels.nonparametric.api as npar from statsmodels.distributions.mixture_rvs import mixture_rvs # example from test_kde.py mixture of two normal distributions np.random.seed(12345) x = mixture_rvs([.1, .9], size=200, dist=[stats.norm, stats.norm], kwargs=(dict(loc=0, scale=.5), dict(loc=1, scale=.5))) kde = npar.KDEUnivariate(x) kernel_names = ['Gaussian', 'Epanechnikov', 'Biweight', 'Triangular', 'Triweight', 'Cosine' ] kernel_switch = ['gau', 'epa', 'tri', 'biw', 'triw', 'cos' ] def true_pdf(x): pdf = 0.1 * stats.norm.pdf(x, loc=0, scale=0.5) pdf += 0.9 * stats.norm.pdf(x, loc=1, scale=0.5) return pdf fig = plt.figure() for ii, kn in enumerate(kernel_switch): ax = fig.add_subplot(2, 3, ii + 1) # without uniform # gh5792. Remove except after matplotlib>2.1 required try: ax.hist(x, bins=20, density=True, alpha=0.25) except AttributeError: ax.hist(x, bins=20, normed=True, alpha=0.25) kde.fit(kernel=kn, bw='silverman', fft=False) ax.plot(kde.support, kde.density) kde.fit(kernel=kn, bw='normal_reference', fft=False) ax.plot(kde.support, kde.density) ax.plot(kde.support, true_pdf(kde.support), color='black', linestyle='--') ax.set_title(kernel_names[ii]) ax.legend(['silverman', 'normal reference', 'true pdf'], loc='lower right') ax.set_title('200 points') plt.show() statsmodels-0.12.2/statsmodels/examples/ex_kernel_regression.py000066400000000000000000000033231400612667500251140ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Jan 02 09:17:40 2013 Author: Josef Perktold based on test file by George Panterov """ import numpy as np import numpy.testing as npt import matplotlib.pyplot as plt import statsmodels.nonparametric.api as nparam #import statsmodels.api as sm #nparam = sm.nonparametric italy_gdp = \ [8.556, 12.262, 9.587, 8.119, 5.537, 6.796, 8.638, 6.483, 6.212, 5.111, 6.001, 7.027, 4.616, 3.922, 4.688, 3.957, 3.159, 3.763, 3.829, 5.242, 6.275, 8.518, 11.542, 9.348, 8.02, 5.527, 6.865, 8.666, 6.672, 6.289, 5.286, 6.271, 7.94, 4.72, 4.357, 4.672, 3.883, 3.065, 3.489, 3.635, 5.443, 6.302, 9.054, 12.485, 9.896, 8.33, 6.161, 7.055, 8.717, 6.95] italy_year = \ [1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1953, 1953, 1953, 1953, 1953, 1953, 1953, 1953] italy_year = np.asarray(italy_year, float) model = nparam.KernelReg(endog=[italy_gdp], exog=[italy_year], reg_type='lc', var_type='o', bw='cv_ls') sm_bw = model.bw R_bw = 0.1390096 sm_mean, sm_mfx = model.fit() sm_mean2 = sm_mean[0:5] sm_mfx = sm_mfx[0:5] R_mean = 6.190486 sm_R2 = model.r_squared() R_R2 = 0.1435323 npt.assert_allclose(sm_bw, R_bw, atol=1e-2) npt.assert_allclose(sm_mean2, R_mean, atol=1e-2) npt.assert_allclose(sm_R2, R_R2, atol=1e-2) fig = plt.figure() ax = fig.add_subplot(1,1,1) ax.plot(italy_year, italy_gdp, 'o') ax.plot(italy_year, sm_mean, '-') plt.show() statsmodels-0.12.2/statsmodels/examples/ex_kernel_regression2.py000066400000000000000000000026451400612667500252040ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Jan 02 13:43:44 2013 Author: Josef Perktold """ import numpy as np import statsmodels.nonparametric.api as nparam if __name__ == '__main__': np.random.seed(500) nobs = [250, 1000][0] sig_fac = 1 x = np.random.uniform(-2, 2, size=nobs) x.sort() y_true = np.sin(x*5)/x + 2*x y = y_true + sig_fac * (np.sqrt(np.abs(3+x))) * np.random.normal(size=nobs) model = nparam.KernelReg(endog=[y], exog=[x], reg_type='lc', var_type='c', bw='cv_ls', defaults=nparam.EstimatorSettings(efficient=True)) sm_bw = model.bw sm_mean, sm_mfx = model.fit() model1 = nparam.KernelReg(endog=[y], exog=[x], reg_type='lc', var_type='c', bw='cv_ls') mean1, mfx1 = model1.fit() model2 = nparam.KernelReg(endog=[y], exog=[x], reg_type='ll', var_type='c', bw='cv_ls') mean2, mfx2 = model2.fit() print(model.bw) print(model1.bw) print(model2.bw) import matplotlib.pyplot as plt fig = plt.figure() ax = fig.add_subplot(1,1,1) ax.plot(x, y, 'o', alpha=0.5) ax.plot(x, y_true, lw=2, label='DGP mean') ax.plot(x, sm_mean, lw=2, label='kernel mean') ax.plot(x, mean2, lw=2, label='kernel mean') ax.legend() plt.show() statsmodels-0.12.2/statsmodels/examples/ex_kernel_regression3.py000066400000000000000000000044711400612667500252040ustar00rootroot00000000000000# -*- coding: utf-8 -*- """script to try out Censored kernel regression Created on Wed Jan 02 13:43:44 2013 Author: Josef Perktold """ import numpy as np import statsmodels.nonparametric.api as nparam if __name__ == '__main__': np.random.seed(500) nobs = [250, 1000][0] sig_fac = 1 x = np.random.uniform(-2, 2, size=nobs) x.sort() x2 = x**2 + 0.02 * np.random.normal(size=nobs) y_true = np.sin(x*5)/x + 2*x - 3 * x2 y = y_true + sig_fac * (np.sqrt(np.abs(3+x))) * np.random.normal(size=nobs) cens_side = ['left', 'right', 'random'][2] if cens_side == 'left': c_val = 0.5 y_cens = np.clip(y, c_val, 100) elif cens_side == 'right': c_val = 3.5 y_cens = np.clip(y, -100, c_val) elif cens_side == 'random': c_val = 3.5 + 3 * np.random.randn(nobs) y_cens = np.minimum(y, c_val) model = nparam.KernelCensoredReg(endog=[y_cens], #exog=[np.column_stack((x, x**2))], reg_type='lc', exog=[x, x2], reg_type='ll', var_type='cc', bw='aic', #'cv_ls', #[0.23, 434697.22], #'cv_ls', censor_val=c_val[:,None] #defaults=nparam.EstimatorSettings(efficient=True) ) sm_bw = model.bw sm_mean, sm_mfx = model.fit() # model1 = nparam.KernelReg(endog=[y], # exog=[x], reg_type='lc', # var_type='c', bw='cv_ls') # mean1, mfx1 = model1.fit() model2 = nparam.KernelReg(endog=[y_cens], exog=[x, x2], reg_type='ll', var_type='cc', bw='aic')#, 'cv_ls' mean2, mfx2 = model2.fit() print(model.bw) #print model1.bw print(model2.bw) ix = np.argsort(y_cens) ix_rev = np.zeros(nobs, int) ix_rev[ix] = np.arange(nobs) ix_rev = model.sortix_rev import matplotlib.pyplot as plt fig = plt.figure() ax = fig.add_subplot(1,1,1) ax.plot(x, y, 'o', alpha=0.5) ax.plot(x, y_cens, 'o', alpha=0.5) ax.plot(x, y_true, lw=2, label='DGP mean') ax.plot(x, sm_mean[ix_rev], lw=2, label='model 0 mean') ax.plot(x, mean2, lw=2, label='model 2 mean') ax.legend() plt.show() statsmodels-0.12.2/statsmodels/examples/ex_kernel_regression_censored2.py000066400000000000000000000021611400612667500270570ustar00rootroot00000000000000# -*- coding: utf-8 -*- """script to check KernelCensoredReg based on test file Created on Thu Jan 03 20:20:47 2013 Author: Josef Perktold """ import numpy as np import statsmodels.nonparametric.api as nparam if __name__ == '__main__': #example from test file nobs = 200 np.random.seed(1234) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) noise = 0.1 * np.random.normal(size=(nobs, )) y = 0.3 +1.2 * C1 - 0.9 * C2 + noise y[y>0] = 0 # censor the data model = nparam.KernelCensoredReg(endog=[y], exog=[C1, C2], reg_type='ll', var_type='cc', bw='cv_ls', censor_val=0) sm_mean, sm_mfx = model.fit() import matplotlib.pyplot as plt fig = plt.figure() ax = fig.add_subplot(1,1,1) sortidx = np.argsort(y) ax.plot(y[sortidx], 'o', alpha=0.5) #ax.plot(x, y_cens, 'o', alpha=0.5) #ax.plot(x, y_true, lw=2, label='DGP mean') ax.plot(sm_mean[sortidx], lw=2, label='model 0 mean') #ax.plot(x, mean2, lw=2, label='model 2 mean') ax.legend() plt.show() statsmodels-0.12.2/statsmodels/examples/ex_kernel_regression_dgp.py000066400000000000000000000022141400612667500257440ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Jan 06 09:50:54 2013 Author: Josef Perktold """ if __name__ == '__main__': import numpy as np import matplotlib.pyplot as plt from statsmodels.nonparametric.api import KernelReg import statsmodels.sandbox.nonparametric.dgp_examples as dgp seed = np.random.randint(999999) seed = 430973 print(seed) np.random.seed(seed) funcs = [dgp.UnivariateFanGijbels1(), dgp.UnivariateFanGijbels2(), dgp.UnivariateFanGijbels1EU(), #dgp.UnivariateFanGijbels2(distr_x=stats.uniform(-2, 4)) dgp.UnivariateFunc1() ] res = [] fig = plt.figure() for i,func in enumerate(funcs): #f = func() f = func model = KernelReg(endog=[f.y], exog=[f.x], reg_type='ll', var_type='c', bw='cv_ls') mean, mfx = model.fit() ax = fig.add_subplot(2, 2, i+1) f.plot(ax=ax) ax.plot(f.x, mean, color='r', lw=2, label='est. mean') ax.legend(loc='upper left') res.append((model, mean, mfx)) fig.suptitle('Kernel Regression') fig.show() statsmodels-0.12.2/statsmodels/examples/ex_kernel_regression_sigtest.py000066400000000000000000000061031400612667500266550ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Kernel Regression and Significance Test Warning: SLOW, 11 minutes on my computer Created on Thu Jan 03 20:20:47 2013 Author: Josef Perktold results - this version ---------------------- >>> exec(open('ex_kernel_regression_censored1.py').read()) bw [ 0.3987821 0.50933458] [0.39878209999999997, 0.50933457999999998] sig_test - default Not Significant pvalue 0.11 test statistic 0.000434305313291 bootstrap critical values [ 0.00043875 0.00046808 0.0005064 0.00054151] sig_test - pivot=True, nboot=200, nested_res=50 pvalue 0.01 test statistic 6.17877171579 bootstrap critical values [ 5.5658345 5.74761076 5.87386858 6.46012041] times: 8.34599995613 20.6909999847 666.373999834 """ import time import numpy as np import statsmodels.nonparametric.api as nparam import statsmodels.nonparametric.kernel_regression as smkr if __name__ == '__main__': t0 = time.time() #example from test file nobs = 200 np.random.seed(1234) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) noise = np.random.normal(size=(nobs, )) Y = 0.3 +1.2 * C1 - 0.9 * C2 + noise #self.write2file('RegData.csv', (Y, C1, C2)) #CODE TO PRODUCE BANDWIDTH ESTIMATION IN R #library(np) #data <- read.csv('RegData.csv', header=FALSE) #bw <- npregbw(formula=data$V1 ~ data$V2 + data$V3, # bwmethod='cv.aic', regtype='lc') model = nparam.KernelReg(endog=[Y], exog=[C1, C2], reg_type='lc', var_type='cc', bw='aic') mean, marg = model.fit() #R_bw = [0.4017893, 0.4943397] # Bandwidth obtained in R bw_expected = [0.3987821, 0.50933458] #npt.assert_allclose(model.bw, bw_expected, rtol=1e-3) print('bw') print(model.bw) print(bw_expected) print('\nsig_test - default') print(model.sig_test([1], nboot=100)) t1 = time.time() res0 = smkr.TestRegCoefC(model, [1]) print('pvalue') print((res0.t_dist >= res0.test_stat).mean()) print('test statistic', res0.test_stat) print('bootstrap critical values') probs = np.array([0.9, 0.95, 0.975, 0.99]) bsort0 = np.sort(res0.t_dist) nrep0 = len(bsort0) print(bsort0[(probs * nrep0).astype(int)]) t2 = time.time() print('\nsig_test - pivot=True, nboot=200, nested_res=50') res1 = smkr.TestRegCoefC(model, [1], pivot=True, nboot=200, nested_res=50) print('pvalue') print((res1.t_dist >= res1.test_stat).mean()) print('test statistic', res1.test_stat) print('bootstrap critical values') probs = np.array([0.9, 0.95, 0.975, 0.99]) bsort1 = np.sort(res1.t_dist) nrep1 = len(bsort1) print(bsort1[(probs * nrep1).astype(int)]) t3 = time.time() print('times:', t1-t0, t2-t1, t3-t2) # import matplotlib.pyplot as plt # fig = plt.figure() # ax = fig.add_subplot(1,1,1) # ax.plot(x, y, 'o', alpha=0.5) # ax.plot(x, y_cens, 'o', alpha=0.5) # ax.plot(x, y_true, lw=2, label='DGP mean') # ax.plot(x, sm_mean, lw=2, label='model 0 mean') # ax.plot(x, mean2, lw=2, label='model 2 mean') # ax.legend() # # plt.show() statsmodels-0.12.2/statsmodels/examples/ex_kernel_semilinear_dgp.py000066400000000000000000000115001400612667500257120ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Jan 06 09:50:54 2013 Author: Josef Perktold """ if __name__ == '__main__': import numpy as np import matplotlib.pyplot as plt #from statsmodels.nonparametric.api import KernelReg import statsmodels.sandbox.nonparametric.kernel_extras as smke import statsmodels.sandbox.nonparametric.dgp_examples as dgp class UnivariateFunc1a(dgp.UnivariateFunc1): def het_scale(self, x): return 0.5 seed = np.random.randint(999999) #seed = 430973 #seed = 47829 seed = 648456 #good seed for het_scale = 0.5 print(seed) np.random.seed(seed) nobs, k_vars = 300, 3 x = np.random.uniform(-2, 2, size=(nobs, k_vars)) xb = x.sum(1) / 3 #beta = [1,1,1] k_vars_lin = 2 x2 = np.random.uniform(-2, 2, size=(nobs, k_vars_lin)) funcs = [#dgp.UnivariateFanGijbels1(), #dgp.UnivariateFanGijbels2(), #dgp.UnivariateFanGijbels1EU(), #dgp.UnivariateFanGijbels2(distr_x=stats.uniform(-2, 4)) UnivariateFunc1a(x=xb) ] res = [] fig = plt.figure() for i,func in enumerate(funcs): #f = func() f = func y = f.y + x2.sum(1) model = smke.SemiLinear(y, x2, x, 'ccc', k_vars_lin) mean, mfx = model.fit() ax = fig.add_subplot(1, 1, i+1) f.plot(ax=ax) xb_est = np.dot(model.exog, model.b) sortidx = np.argsort(xb_est) #f.x) ax.plot(f.x[sortidx], mean[sortidx], 'o', color='r', lw=2, label='est. mean') # ax.plot(f.x, mean0, color='g', lw=2, label='est. mean') ax.legend(loc='upper left') res.append((model, mean, mfx)) print('beta', model.b) print('scale - est', (y - (xb_est+mean)).std()) print('scale - dgp realised, true', (y - (f.y_true + x2.sum(1))).std(), \ 2 * f.het_scale(1)) fittedvalues = xb_est + mean resid = np.squeeze(model.endog) - fittedvalues print('corrcoef(fittedvalues, resid)', np.corrcoef(fittedvalues, resid)[0,1]) print('variance of components, var and as fraction of var(y)') print('fitted values', fittedvalues.var(), fittedvalues.var() / y.var()) print('linear ', xb_est.var(), xb_est.var() / y.var()) print('nonparametric', mean.var(), mean.var() / y.var()) print('residual ', resid.var(), resid.var() / y.var()) print('\ncovariance decomposition fraction of var(y)') print(np.cov(fittedvalues, resid) / model.endog.var(ddof=1)) print('sum', (np.cov(fittedvalues, resid) / model.endog.var(ddof=1)).sum()) print('\ncovariance decomposition, xb, m, resid as fraction of var(y)') print(np.cov(np.column_stack((xb_est, mean, resid)), rowvar=False) / model.endog.var(ddof=1)) fig.suptitle('Kernel Regression') fig.show() alpha = 0.7 fig = plt.figure() ax = fig.add_subplot(1, 1, 1) ax.plot(f.x[sortidx], f.y[sortidx], 'o', color='b', lw=2, alpha=alpha, label='observed') ax.plot(f.x[sortidx], f.y_true[sortidx], 'o', color='g', lw=2, alpha=alpha, label='dgp. mean') ax.plot(f.x[sortidx], mean[sortidx], 'o', color='r', lw=2, alpha=alpha, label='est. mean') ax.legend(loc='upper left') sortidx = np.argsort(xb_est + mean) fig = plt.figure() ax = fig.add_subplot(1, 1, 1) ax.plot(f.x[sortidx], y[sortidx], 'o', color='b', lw=2, alpha=alpha, label='observed') ax.plot(f.x[sortidx], f.y_true[sortidx], 'o', color='g', lw=2, alpha=alpha, label='dgp. mean') ax.plot(f.x[sortidx], (xb_est + mean)[sortidx], 'o', color='r', lw=2, alpha=alpha, label='est. mean') ax.legend(loc='upper left') ax.set_title('Semilinear Model - observed and total fitted') fig = plt.figure() # ax = fig.add_subplot(1, 2, 1) # ax.plot(f.x, f.y, 'o', color='b', lw=2, alpha=alpha, label='observed') # ax.plot(f.x, f.y_true, 'o', color='g', lw=2, alpha=alpha, label='dgp. mean') # ax.plot(f.x, mean, 'o', color='r', lw=2, alpha=alpha, label='est. mean') # ax.legend(loc='upper left') sortidx0 = np.argsort(xb) ax = fig.add_subplot(1, 2, 1) ax.plot(f.y[sortidx0], 'o', color='b', lw=2, alpha=alpha, label='observed') ax.plot(f.y_true[sortidx0], 'o', color='g', lw=2, alpha=alpha, label='dgp. mean') ax.plot(mean[sortidx0], 'o', color='r', lw=2, alpha=alpha, label='est. mean') ax.legend(loc='upper left') ax.set_title('Single Index Model (sorted by true xb)') ax = fig.add_subplot(1, 2, 2) ax.plot(y - xb_est, 'o', color='b', lw=2, alpha=alpha, label='observed') ax.plot(f.y_true, 'o', color='g', lw=2, alpha=alpha, label='dgp. mean') ax.plot(mean, 'o', color='r', lw=2, alpha=alpha, label='est. mean') ax.legend(loc='upper left') ax.set_title('Single Index Model (nonparametric)') plt.figure() plt.plot(y, xb_est+mean, '.') plt.title('observed versus fitted values') plt.show() statsmodels-0.12.2/statsmodels/examples/ex_kernel_singleindex_dgp.py000066400000000000000000000065101400612667500261000ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Jan 06 09:50:54 2013 Author: Josef Perktold """ if __name__ == '__main__': import numpy as np import matplotlib.pyplot as plt #from statsmodels.nonparametric.api import KernelReg import statsmodels.sandbox.nonparametric.kernel_extras as smke import statsmodels.sandbox.nonparametric.dgp_examples as dgp class UnivariateFunc1a(dgp.UnivariateFunc1): def het_scale(self, x): return 0.5 seed = np.random.randint(999999) #seed = 430973 #seed = 47829 seed = 648456 #good seed for het_scale = 0.5 print(seed) np.random.seed(seed) nobs, k_vars = 300, 3 x = np.random.uniform(-2, 2, size=(nobs, k_vars)) xb = x.sum(1) / 3 #beta = [1,1,1] funcs = [#dgp.UnivariateFanGijbels1(), #dgp.UnivariateFanGijbels2(), #dgp.UnivariateFanGijbels1EU(), #dgp.UnivariateFanGijbels2(distr_x=stats.uniform(-2, 4)) UnivariateFunc1a(x=xb) ] res = [] fig = plt.figure() for i,func in enumerate(funcs): #f = func() f = func # mod0 = smke.SingleIndexModel(endog=[f.y], exog=[xb], #reg_type='ll', # var_type='c')#, bw='cv_ls') # mean0, mfx0 = mod0.fit() model = smke.SingleIndexModel(endog=[f.y], exog=x, #reg_type='ll', var_type='ccc')#, bw='cv_ls') mean, mfx = model.fit() ax = fig.add_subplot(1, 1, i+1) f.plot(ax=ax) xb_est = np.dot(model.exog, model.b) sortidx = np.argsort(xb_est) #f.x) ax.plot(f.x[sortidx], mean[sortidx], 'o', color='r', lw=2, label='est. mean') # ax.plot(f.x, mean0, color='g', lw=2, label='est. mean') ax.legend(loc='upper left') res.append((model, mean, mfx)) fig.suptitle('Kernel Regression') fig.show() alpha = 0.7 fig = plt.figure() ax = fig.add_subplot(1, 1, 1) ax.plot(f.x[sortidx], f.y[sortidx], 'o', color='b', lw=2, alpha=alpha, label='observed') ax.plot(f.x[sortidx], f.y_true[sortidx], 'o', color='g', lw=2, alpha=alpha, label='dgp. mean') ax.plot(f.x[sortidx], mean[sortidx], 'o', color='r', lw=2, alpha=alpha, label='est. mean') ax.legend(loc='upper left') fig = plt.figure() # ax = fig.add_subplot(1, 2, 1) # ax.plot(f.x, f.y, 'o', color='b', lw=2, alpha=alpha, label='observed') # ax.plot(f.x, f.y_true, 'o', color='g', lw=2, alpha=alpha, label='dgp. mean') # ax.plot(f.x, mean, 'o', color='r', lw=2, alpha=alpha, label='est. mean') # ax.legend(loc='upper left') sortidx0 = np.argsort(xb) ax = fig.add_subplot(1, 2, 1) ax.plot(f.y[sortidx0], 'o', color='b', lw=2, alpha=alpha, label='observed') ax.plot(f.y_true[sortidx0], 'o', color='g', lw=2, alpha=alpha, label='dgp. mean') ax.plot(mean[sortidx0], 'o', color='r', lw=2, alpha=alpha, label='est. mean') ax.legend(loc='upper left') ax.set_title('Single Index Model (sorted by true xb)') ax = fig.add_subplot(1, 2, 2) ax.plot(f.y[sortidx], 'o', color='b', lw=2, alpha=alpha, label='observed') ax.plot(f.y_true[sortidx], 'o', color='g', lw=2, alpha=alpha, label='dgp. mean') ax.plot(mean[sortidx], 'o', color='r', lw=2, alpha=alpha, label='est. mean') ax.legend(loc='upper left') ax.set_title('Single Index Model (sorted by estimated xb)') plt.show() statsmodels-0.12.2/statsmodels/examples/ex_kernel_test_functional.py000066400000000000000000000042401400612667500261340ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Tue Jan 08 19:03:20 2013 Author: Josef Perktold """ if __name__ == '__main__': import numpy as np from statsmodels.regression.linear_model import OLS #from statsmodels.nonparametric.api import KernelReg import statsmodels.sandbox.nonparametric.kernel_extras as smke seed = np.random.randint(999999) #seed = 661176 print(seed) np.random.seed(seed) sig_e = 0.5 #0.1 nobs, k_vars = 200, 1 x = np.random.uniform(-2, 2, size=(nobs, k_vars)) x.sort() order = 3 exog = x**np.arange(order + 1) beta = np.array([1, 1, 0.1, 0.0])[:order+1] # 1. / np.arange(1, order + 2) y_true = np.dot(exog, beta) y = y_true + sig_e * np.random.normal(size=nobs) endog = y print('DGP') print('nobs=%d, beta=%r, sig_e=%3.1f' % (nobs, beta, sig_e)) mod_ols = OLS(endog, exog[:,:2]) res_ols = mod_ols.fit() #'cv_ls'[1000, 0.5][0.01, 0.45] tst = smke.TestFForm(endog, exog[:,:2], bw=[0.01, 0.45], var_type='cc', fform=lambda x,p: mod_ols.predict(p,x), estimator=lambda y,x: OLS(y,x).fit().params, nboot=1000) print('bw', tst.bw) print('tst.test_stat', tst.test_stat) print(tst.sig) print('tst.boots_results mean, min, max', (tst.boots_results.mean(), tst.boots_results.min(), tst.boots_results.max())) print('lower tail bootstrap p-value', (tst.boots_results < tst.test_stat).mean()) print('upper tail bootstrap p-value', (tst.boots_results >= tst.test_stat).mean()) from scipy import stats print('aymp.normal p-value (2-sided)', stats.norm.sf(np.abs(tst.test_stat))*2) print('aymp.normal p-value (upper)', stats.norm.sf(tst.test_stat)) do_plot=True if do_plot: import matplotlib.pyplot as plt plt.figure() plt.plot(x, y, '.') plt.plot(x, res_ols.fittedvalues) plt.title('OLS fit') plt.figure() plt.hist(tst.boots_results.ravel(), bins=20) plt.title('bootstrap histogram or test statistic') plt.show() statsmodels-0.12.2/statsmodels/examples/ex_kernel_test_functional_li_wang.py000066400000000000000000000100341400612667500276320ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Example TestFForm with Li Wang DGP1 Created on Tue Jan 08 19:03:20 2013 Author: Josef Perktold trying to replicate some examples in Li, Q., and Suojin Wang. 1998. "A Simple Consistent Bootstrap Test for a Parametric Regression Function." Journal of Econometrics 87 (1) (November): 145-165. doi:10.1016/S0304-4076(98)00011-6. currently DGP1 Monte Carlo with 100 replications --------------------------------- results 598948 time 11.1642833312 [-0.72505981 0.26514944 0.45681704] [ 0.74884796 0.22005569 0.3004892 ] reject at [0.2, 0.1, 0.05] (row 1: normal, row 2: bootstrap) [[ 0.55 0.24 0.01] [ 0.29 0.16 0.06]] bw [ 0.11492364 0.11492364] tst.test_stat -1.40274609515 Not Significant tst.boots_results min, max -2.03386582198 2.32562183511 lower tail bootstrap p-value 0.077694235589 aymp.normal p-value (2-sided) 0.160692566481 mean and std in Li and Wang for n=1 are -0.764 and 0.621 results look reasonable now Power ----- true model: quadratic, estimated model: linear 498198 time 8.4588166674 [ 0.50374364 0.3991975 0.25373434] [ 1.21353172 0.28669981 0.25461368] reject at [0.2, 0.1, 0.05] (row 1: normal, row 2: bootstrap) [[ 0.66 0.78 0.82] [ 0.46 0.61 0.74]] bw [ 0.11492364 0.11492364] tst.test_stat 0.505426717024 Not Significant tst.boots_results min, max -1.67050998463 3.39835350718 lower tail bootstrap p-value 0.892230576441 upper tail bootstrap p-value 0.107769423559 aymp.normal p-value (2-sided) 0.613259157709 aymp.normal p-value (upper) 0.306629578855 """ if __name__ == '__main__': import time import numpy as np from scipy import stats from statsmodels.regression.linear_model import OLS #from statsmodels.nonparametric.api import KernelReg import statsmodels.sandbox.nonparametric.kernel_extras as smke seed = np.random.randint(999999) #seed = 661176 print(seed) np.random.seed(seed) sig_e = 0.1 #0.5 #0.1 nobs, k_vars = 100, 1 t0 = time.time() b_res = [] for i in range(100): x = np.random.uniform(0, 1, size=(nobs, k_vars)) x.sort(0) order = 2 exog = x**np.arange(1, order + 1) beta = np.array([2, -0.2])[:order+1-1] # 1. / np.arange(1, order + 2) y_true = np.dot(exog, beta) y = y_true + sig_e * np.random.normal(size=nobs) endog = y mod_ols = OLS(endog, exog[:,:1]) #res_ols = mod_ols.fit() #'cv_ls'[1000, 0.5] bw_lw = [1./np.sqrt(12.) * nobs**(-0.2)]*2 #(-1. / 5.) tst = smke.TestFForm(endog, exog[:,:1], bw=bw_lw, var_type='c', fform=lambda x,p: mod_ols.predict(p,x), estimator=lambda y,x: OLS(y,x).fit().params, nboot=399) b_res.append([tst.test_stat, stats.norm.sf(tst.test_stat), (tst.boots_results > tst.test_stat).mean()]) t1 = time.time() b_res = np.asarray(b_res) print('time', (t1 - t0) / 60.) print(b_res.mean(0)) print(b_res.std(0)) print('reject at [0.2, 0.1, 0.05] (row 1: normal, row 2: bootstrap)') print((b_res[:,1:,None] >= [0.2, 0.1, 0.05]).mean(0)) print('bw', tst.bw) print('tst.test_stat', tst.test_stat) print(tst.sig) print('tst.boots_results min, max', tst.boots_results.min(), tst.boots_results.max()) print('lower tail bootstrap p-value', (tst.boots_results < tst.test_stat).mean()) print('upper tail bootstrap p-value', (tst.boots_results >= tst.test_stat).mean()) from scipy import stats print('aymp.normal p-value (2-sided)', stats.norm.sf(np.abs(tst.test_stat))*2) print('aymp.normal p-value (upper)', stats.norm.sf(tst.test_stat)) res_ols = mod_ols.fit() do_plot=True if do_plot: import matplotlib.pyplot as plt plt.figure() plt.plot(x, y, '.') plt.plot(x, res_ols.fittedvalues) plt.title('OLS fit') plt.figure() plt.hist(tst.boots_results.ravel(), bins=20) plt.title('bootstrap histogram or test statistic') plt.show() statsmodels-0.12.2/statsmodels/examples/ex_lowess.py000066400000000000000000000053411400612667500227120ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Mon Oct 31 15:26:06 2011 Author: Chris Jordan Squire extracted from test suite by josef-pktd """ import os import numpy as np import matplotlib.pyplot as plt import statsmodels.api as sm import statsmodels.nonparametric.tests.results # this is just to check direct import import statsmodels.nonparametric.smoothers_lowess statsmodels.nonparametric.smoothers_lowess.lowess lowess = sm.nonparametric.lowess x = np.arange(20.) #standard normal noise noise = np.array([-0.76741118, -0.30754369, 0.39950921, -0.46352422, -1.67081778, 0.6595567 , 0.66367639, -2.04388585, 0.8123281 , 1.45977518, 1.21428038, 1.29296866, 0.78028477, -0.2402853 , -0.21721302, 0.24549405, 0.25987014, -0.90709034, -1.45688216, -0.31780505]) y = x + noise expected_lowess = np.array([[ 0. , -0.58337912], [ 1. , 0.61951246], [ 2. , 1.82221628], [ 3. , 3.02536876], [ 4. , 4.22667951], [ 5. , 5.42387723], [ 6. , 6.60834945], [ 7. , 7.7797691 ], [ 8. , 8.91824348], [ 9. , 9.94997506], [ 10. , 10.89697569], [ 11. , 11.78746276], [ 12. , 12.62356492], [ 13. , 13.41538492], [ 14. , 14.15745254], [ 15. , 14.92343948], [ 16. , 15.70019862], [ 17. , 16.48167846], [ 18. , 17.26380699], [ 19. , 18.0466769 ]]) actual_lowess = lowess(y, x) print(actual_lowess) print(np.max(np.abs(actual_lowess-expected_lowess))) plt.plot(y, 'o') plt.plot(actual_lowess[:,1]) plt.plot(expected_lowess[:,1]) rpath = os.path.split(statsmodels.nonparametric.tests.results.__file__)[0] rfile = os.path.join(rpath, 'test_lowess_frac.csv') test_data = np.genfromtxt(open(rfile, 'rb'), delimiter = ',', names = True) expected_lowess_23 = np.array([test_data['x'], test_data['out_2_3']]).T expected_lowess_15 = np.array([test_data['x'], test_data['out_1_5']]).T actual_lowess_23 = lowess(test_data['y'], test_data['x'] ,frac = 2./3) actual_lowess_15 = lowess(test_data['y'], test_data['x'] ,frac = 1./5) #plt.show() statsmodels-0.12.2/statsmodels/examples/ex_misc_tarma.py000066400000000000000000000034551400612667500235210ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Jul 03 23:01:44 2013 Author: Josef Perktold """ import numpy as np import matplotlib.pyplot as plt from statsmodels.tsa.arima_process import arma_generate_sample, ArmaProcess from statsmodels.miscmodels.tmodel import TArma from statsmodels.tsa.arima_model import ARMA from statsmodels.tsa.arma_mle import Arma nobs = 500 ar = [1, -0.6, -0.1] ma = [1, 0.7] dist = lambda n: np.random.standard_t(3, size=n) np.random.seed(8659567) x = arma_generate_sample(ar, ma, nobs, scale=1, distrvs=dist, burnin=500) mod = TArma(x) order = (2, 1) res = mod.fit(order=order) res2 = mod.fit_mle(order=order, start_params=np.r_[res[0], 5, 1], method='nm') print(res[0]) proc = ArmaProcess.from_coeffs(res[0][:order[0]], res[0][:order[1]]) print(ar, ma) proc.nobs = nobs # TODO: bug nobs is None, not needed ?, used in ArmaProcess.__repr__ print(proc.ar, proc.ma) print(proc.ar_roots(), proc.ma_roots()) modn = Arma(x) resn = modn.fit_mle(order=order) moda = ARMA(x, order=order) resa = moda.fit( trend='nc') print('\nparameter estimates') print('ls ', res[0]) print('norm', resn.params) print('t ', res2.params) print('A ', resa.params) print('\nstandard deviation of parameter estimates') #print 'ls ', res[0] #TODO: not available yet print('norm', resn.bse) print('t ', res2.bse) print('A ', resa.bse) print('A/t-1', resa.bse / res2.bse[:3] - 1) print('other bse') print(resn.bsejac) print(resn.bsejhj) print(res2.bsejac) print(res2.bsejhj) print(res2.t_test(np.eye(len(res2.params)))) # TArma has no fittedvalues and resid # TODO: check if lag is correct or if fitted `x-resid` is shifted resid = res2.model.geterrors(res2.params) fv = res[2]['fvec'] #resid returned from leastsq? plt.plot(x, 'o', alpha=0.5) plt.plot(x-resid) plt.plot(x-fv) #plt.show() statsmodels-0.12.2/statsmodels/examples/ex_misc_tmodel.py000066400000000000000000000044761400612667500237050ustar00rootroot00000000000000 import numpy as np from scipy import stats import statsmodels.api as sm from statsmodels.miscmodels import TLinearModel from statsmodels.tools.numdiff import approx_hess #Example: #np.random.seed(98765678) nobs = 50 nvars = 6 df = 3 rvs = np.random.randn(nobs, nvars-1) data_exog = sm.add_constant(rvs, prepend=False) xbeta = 0.9 + 0.1*rvs.sum(1) data_endog = xbeta + 0.1*np.random.standard_t(df, size=nobs) print('variance of endog:', data_endog.var()) print('true parameters:', [0.1]*nvars + [0.9]) res_ols = sm.OLS(data_endog, data_exog).fit() print('\nResults with ols') print('----------------') print(res_ols.scale) print(np.sqrt(res_ols.scale)) print(res_ols.params) print(res_ols.bse) kurt = stats.kurtosis(res_ols.resid) df_fromkurt = 6./kurt + 4 print('df_fromkurt from ols residuals', df_fromkurt) print(stats.t.stats(df_fromkurt, moments='mvsk')) print(stats.t.stats(df, moments='mvsk')) modp = TLinearModel(data_endog, data_exog) start_value = 0.1*np.ones(data_exog.shape[1]+2) #start_value = np.zeros(data_exog.shape[1]+2) #start_value[:nvars] = sm.OLS(data_endog, data_exog).fit().params start_value[:nvars] = res_ols.params start_value[-2] = df_fromkurt #10 start_value[-1] = np.sqrt(res_ols.scale) #0.5 modp.start_params = start_value #adding fixed parameters fixdf = np.nan * np.zeros(modp.start_params.shape) fixdf[-2] = 5 fixone = 0 if fixone: modp.fixed_params = fixdf modp.fixed_paramsmask = np.isnan(fixdf) modp.start_params = modp.start_params[modp.fixed_paramsmask] else: modp.fixed_params = None modp.fixed_paramsmask = None print('\nResults with TLinearModel') print('-------------------------') resp = modp.fit(start_params = modp.start_params, disp=1, method='nm', maxfun=10000, maxiter=5000)#'newton') #resp = modp.fit(start_params = modp.start_params, disp=1, method='newton') print('using Nelder-Mead') print(resp.params) print(resp.bse) resp2 = modp.fit(start_params = resp.params, method='Newton') print('using Newton') print(resp2.params) print(resp2.bse) hb=-approx_hess(modp.start_params, modp.loglike, epsilon=-1e-4) tmp = modp.loglike(modp.start_params) print(tmp.shape) print('eigenvalues of numerical Hessian') print(np.linalg.eigh(np.linalg.inv(hb))[0]) #store_params is only available in original test script ##pp=np.array(store_params) ##print pp.min(0) ##print pp.max(0) statsmodels-0.12.2/statsmodels/examples/ex_multivar_kde.py000066400000000000000000000026211400612667500240620ustar00rootroot00000000000000""" This example illustrates the nonparametric estimation of a bivariate bi-modal distribution that is a mixture of two normal distributions. author: George Panterov """ import numpy as np import matplotlib.pyplot as plt from matplotlib import cm import statsmodels.api as sm if __name__ == '__main__': np.random.seed(123456) # generate the data nobs = 500 BW = 'cv_ml' mu1 = [3, 4] mu2 = [6, 1] cov1 = np.asarray([[1, 0.7], [0.7, 1]]) cov2 = np.asarray([[1, -0.7], [-0.7, 1]]) ix = np.random.uniform(size=nobs) > 0.5 V = np.random.multivariate_normal(mu1, cov1, size=nobs) V[ix, :] = np.random.multivariate_normal(mu2, cov2, size=nobs)[ix, :] x = V[:, 0] y = V[:, 1] dens = sm.nonparametric.KDEMultivariate(data=[x, y], var_type='cc', bw=BW, defaults=sm.nonparametric.EstimatorSettings(efficient=True)) supportx = np.linspace(min(x), max(x), 60) supporty = np.linspace(min(y), max(y), 60) X, Y = np.meshgrid(supportx, supporty) edat = np.column_stack([X.ravel(), Y.ravel()]) Z = dens.pdf(edat).reshape(X.shape) # plot fig = plt.figure(1) ax = fig.gca(projection='3d') surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.jet, linewidth=0, antialiased=False) fig.colorbar(surf, shrink=0.5, aspect=5) plt.figure(2) plt.imshow(Z) plt.show() statsmodels-0.12.2/statsmodels/examples/ex_nearest_corr.py000066400000000000000000000064111400612667500240630ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Find near positive definite correlation and covariance matrices Created on Sun Aug 19 15:25:07 2012 Author: Josef Perktold TODO: add examples for cov_nearest from script log Notes ----- We are looking at eigenvalues before and after the conversion to psd matrix. As distance measure for how close the change in the matrix is, we consider the sum of squared differences (Frobenious norm without taking the square root) """ import numpy as np from statsmodels.stats.correlation_tools import ( corr_nearest, corr_clipped) examples = ['all'] if 'all' in examples: # x0 is positive definite x0 = np.array([[1, -0.2, -0.9], [-0.2, 1, -0.2], [-0.9, -0.2, 1]]) # x has negative eigenvalues, not definite x = np.array([[1, -0.9, -0.9], [-0.9, 1, -0.9], [-0.9, -0.9, 1]]) #x = np.array([[1, 0.2, 0.2], [0.2, 1, 0.2], [0.2, 0.2, 1]]) n_fact = 2 print('evals original', np.linalg.eigvalsh(x)) y = corr_nearest(x, n_fact=100) print('evals nearest', np.linalg.eigvalsh(y)) print(y) y = corr_nearest(x, n_fact=100, threshold=1e-16) print('evals nearest', np.linalg.eigvalsh(y)) print(y) y = corr_clipped(x, threshold=1e-16) print('evals clipped', np.linalg.eigvalsh(y)) print(y) np.set_printoptions(precision=4) print('\nMini Monte Carlo') # we are simulating a uniformly distributed symmetric matrix # and find close positive definite matrix # original can be far away from positive definite, # then original and converted matrices can be far apart in norm # results are printed for visual inspection of different cases k_vars = 5 diag_idx = np.arange(k_vars) for ii in range(10): print() x = np.random.uniform(-1, 1, size=(k_vars, k_vars)) x = (x + x.T) * 0.5 x[diag_idx, diag_idx] = 1 #x_std = np.sqrt(np.diag(x)) #x = x / x_std / x_std[:,None] print() print(np.sort(np.linalg.eigvals(x)), 'original') yn = corr_nearest(x, threshold=1e-12, n_fact=200) print(np.sort(np.linalg.eigvals(yn)), ((yn - x)**2).sum(), 'nearest') yc = corr_clipped(x, threshold=1e-12) print(np.sort(np.linalg.eigvals(yc)), ((yc - x)**2).sum(), 'clipped') import time t0 = time.time() for _ in range(100): corr_nearest(x, threshold=1e-15, n_fact=100) t1 = time.time() for _ in range(1000): corr_clipped(x, threshold=1e-15) t2 = time.time() print('\ntime (nearest, clipped):', t1 - t0, t2 - t1) if 'all' in examples: # example for test case against R x2 = np.array([ 1, 0.477, 0.644, 0.478, 0.651, 0.826, 0.477, 1, 0.516, 0.233, 0.682, 0.75, 0.644, 0.516, 1, 0.599, 0.581, 0.742, 0.478, 0.233, 0.599, 1, 0.741, 0.8, 0.651, 0.682, 0.581, 0.741, 1, 0.798, 0.826, 0.75, 0.742, 0.8, 0.798, 1]).reshape(6,6) y1 = corr_nearest(x2, threshold=1e-15, n_fact=200) y2 = corr_clipped(x2, threshold=1e-15) print('\nmatrix 2') print(np.sort(np.linalg.eigvals(x2)), 'original') print(np.sort(np.linalg.eigvals(y1)), ((y1 - x2)**2).sum(), 'nearest') print(np.sort(np.linalg.eigvals(y1)), ((y2 - x2)**2).sum(), 'clipped') statsmodels-0.12.2/statsmodels/examples/ex_ols_robustcov.py000066400000000000000000000033561400612667500243050ustar00rootroot00000000000000 import numpy as np from statsmodels.regression.linear_model import OLS from statsmodels.tools.tools import add_constant from statsmodels.datasets import macrodata d2 = macrodata.load(as_pandas=False).data g_gdp = 400*np.diff(np.log(d2['realgdp'])) g_inv = 400*np.diff(np.log(d2['realinv'])) exogg = add_constant(np.c_[g_gdp, d2['realint'][:-1]], prepend=False) res_olsg = OLS(g_inv, exogg).fit() print(res_olsg.summary()) res_hc0 = res_olsg.get_robustcov_results('HC1') print('\n\n') print(res_hc0.summary()) print('\n\n') res_hac4 = res_olsg.get_robustcov_results('HAC', maxlags=4, use_correction=True) print(res_hac4.summary()) print('\n\n') tt = res_hac4.t_test(np.eye(len(res_hac4.params))) print(tt.summary()) print('\n\n') print(tt.summary_frame()) res_hac4.use_t = False print('\n\n') tt = res_hac4.t_test(np.eye(len(res_hac4.params))) print(tt.summary()) print('\n\n') print(tt.summary_frame()) print(vars(res_hac4.f_test(np.eye(len(res_hac4.params))[:-1]))) print(vars(res_hac4.wald_test(np.eye(len(res_hac4.params))[:-1], use_f=True))) print(vars(res_hac4.wald_test(np.eye(len(res_hac4.params))[:-1], use_f=False))) # new cov_type can be set in fit method of model mod_olsg = OLS(g_inv, exogg) res_hac4b = mod_olsg.fit(cov_type='HAC', cov_kwds=dict(maxlags=4, use_correction=True)) print(res_hac4b.summary()) res_hc1b = mod_olsg.fit(cov_type='HC1') print(res_hc1b.summary()) # force t-distribution res_hc1c = mod_olsg.fit(cov_type='HC1', cov_kwds={'use_t':True}) print(res_hc1c.summary()) # force t-distribution decade = (d2['year'][1:] // 10).astype(int) # just make up a group variable res_clu = mod_olsg.fit(cov_type='cluster', cov_kwds={'groups':decade, 'use_t':True}) print(res_clu.summary()) statsmodels-0.12.2/statsmodels/examples/ex_outliers_influence.py000066400000000000000000000074341400612667500253010ustar00rootroot00000000000000 import numpy as np import statsmodels.stats.outliers_influence as oi if __name__ == '__main__': import statsmodels.api as sm data = np.array('''\ 64 57 8 71 59 10 53 49 6 67 62 11 55 51 8 58 50 7 77 55 10 57 48 9 56 42 10 51 42 6 76 61 12 68 57 9'''.split(), float).reshape(-1,3) varnames = 'weight height age'.split() endog = data[:,0] exog = sm.add_constant(data[:,2]) res_ols = sm.OLS(endog, exog).fit() hh = (res_ols.model.exog * res_ols.model.pinv_wexog.T).sum(1) x = res_ols.model.exog hh_check = np.diag(np.dot(x, np.dot(res_ols.model.normalized_cov_params, x.T))) from numpy.testing import assert_almost_equal assert_almost_equal(hh, hh_check, decimal=13) res = res_ols #alias #http://en.wikipedia.org/wiki/PRESS_statistic #predicted residuals, leave one out predicted residuals resid_press = res.resid / (1-hh) ess_press = np.dot(resid_press, resid_press) sigma2_est = np.sqrt(res.mse_resid) #can be replace by different estimators of sigma sigma_est = np.sqrt(sigma2_est) resid_studentized = res.resid / sigma_est / np.sqrt(1 - hh) #http://en.wikipedia.org/wiki/DFFITS: dffits = resid_studentized * np.sqrt(hh / (1 - hh)) nobs, k_vars = res.model.exog.shape #Belsley, Kuh and Welsch (1980) suggest a threshold for abs(DFFITS) dffits_threshold = 2 * np.sqrt(k_vars/nobs) res_ols.df_modelwc = res_ols.df_model + 1 n_params = res.model.exog.shape[1] #http://en.wikipedia.org/wiki/Cook%27s_distance cooks_d = res.resid**2 / sigma2_est / res_ols.df_modelwc * hh / (1 - hh)**2 #or #Eubank p.93, 94 cooks_d2 = resid_studentized**2 / res_ols.df_modelwc * hh / (1 - hh) #threshold if normal, also Wikipedia from scipy import stats alpha = 0.1 #df looks wrong print(stats.f.isf(1-alpha, n_params, res.df_resid)) print(stats.f.sf(cooks_d, n_params, res.df_resid)) print('Cooks Distance') print(cooks_d) print(cooks_d2) doplot = 0 if doplot: import matplotlib.pyplot as plt fig = plt.figure() # ax = fig.add_subplot(3,1,1) # plt.plot(andrew_results.weights, 'o', label='rlm weights') # plt.legend(loc='lower left') ax = fig.add_subplot(3,1,2) plt.plot(cooks_d, 'o', label="Cook's distance") plt.legend(loc='upper left') ax2 = fig.add_subplot(3,1,3) plt.plot(resid_studentized, 'o', label='studentized_resid') plt.plot(dffits, 'o', label='DFFITS') leg = plt.legend(loc='lower left', fancybox=True) leg.get_frame().set_alpha(0.5) #, fontsize='small') ltext = leg.get_texts() # all the text.Text instance in the legend plt.setp(ltext, fontsize='small') # the legend text fontsize print(oi.reset_ramsey(res, degree=3)) #note, constant in last column for i in range(1): print(oi.variance_inflation_factor(res.model.exog, i)) infl = oi.OLSInfluence(res_ols) print(infl.resid_studentized_external) print(infl.resid_studentized_internal) print(infl.summary_table()) print(oi.summary_table(res, alpha=0.05)[0]) ''' >>> res.resid array([ 4.28571429, 4. , 0.57142857, -3.64285714, -4.71428571, 1.92857143, 10. , -6.35714286, -11. , -1.42857143, 1.71428571, 4.64285714]) >>> infl.hat_matrix_diag array([ 0.10084034, 0.11764706, 0.28571429, 0.20168067, 0.10084034, 0.16806723, 0.11764706, 0.08403361, 0.11764706, 0.28571429, 0.33613445, 0.08403361]) >>> infl.resid_press array([ 4.76635514, 4.53333333, 0.8 , -4.56315789, -5.24299065, 2.31818182, 11.33333333, -6.94036697, -12.46666667, -2. , 2.58227848, 5.06880734]) >>> infl.ess_press 465.98646628086374 ''' statsmodels-0.12.2/statsmodels/examples/ex_pandas.py000066400000000000000000000057461400612667500226550ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Examples using Pandas """ from statsmodels.compat.pandas import frequencies from datetime import datetime import numpy as np import matplotlib.pyplot as plt import matplotlib as mpl from pandas import DataFrame, Series import statsmodels.api as sm import statsmodels.tsa.api as tsa from statsmodels.tsa.arima_process import arma_generate_sample data = sm.datasets.stackloss.load(as_pandas=False) X = DataFrame(data.exog, columns=data.exog_name) X['intercept'] = 1. Y = Series(data.endog) #Example: OLS model = sm.OLS(Y, X) results = model.fit() print(results.summary()) print(results.params) print(results.cov_params()) infl = results.get_influence() print(infl.summary_table()) #raise #Example RLM huber_t = sm.RLM(Y, X, M=sm.robust.norms.HuberT()) hub_results = huber_t.fit() print(hub_results.params) print(hub_results.bcov_scaled) print(hub_results.summary()) def plot_acf_multiple(ys, lags=20): """ """ from statsmodels.tsa.stattools import acf # hack old_size = mpl.rcParams['font.size'] mpl.rcParams['font.size'] = 8 plt.figure(figsize=(10, 10)) xs = np.arange(lags + 1) acorr = np.apply_along_axis(lambda x: acf(x, nlags=lags), 0, ys) k = acorr.shape[1] for i in range(k): ax = plt.subplot(k, 1, i + 1) ax.vlines(xs, [0], acorr[:, i]) ax.axhline(0, color='k') ax.set_ylim([-1, 1]) # hack? ax.set_xlim([-1, xs[-1] + 1]) mpl.rcParams['font.size'] = old_size #Example TSA descriptive data = sm.datasets.macrodata.load(as_pandas=False) mdata = data.data df = DataFrame.from_records(mdata) quarter_end = frequencies.BQuarterEnd() df.index = [quarter_end.rollforward(datetime(int(y), int(q) * 3, 1)) for y, q in zip(df.pop('year'), df.pop('quarter'))] logged = np.log(df.loc[:, ['m1', 'realgdp', 'cpi']]) logged.plot(subplots=True) log_difference = logged.diff().dropna() plot_acf_multiple(log_difference.values) #Example TSA VAR model = tsa.VAR(log_difference, freq='BQ') print(model.select_order()) res = model.fit(2) print(res.summary()) print(res.is_stable()) irf = res.irf(20) irf.plot() fevd = res.fevd() fevd.plot() print(res.test_whiteness()) print(res.test_causality('m1', 'realgdp')) print(res.test_normality()) #Example TSA ARMA # Generate some data from an ARMA process arparams = np.array([.75, -.25]) maparams = np.array([.65, .35]) # The conventions of the arma_generate function require that we specify a # 1 for the zero-lag of the AR and MA parameters and that the AR parameters # be negated. arparams = np.r_[1, -arparams] maparam = np.r_[1, maparams] nobs = 250 y = arma_generate_sample(arparams, maparams, nobs) plt.figure() plt.plot(y) # Now, optionally, we can add some dates information. For this example, # we'll use a pandas time series. dates = sm.tsa.datetools.dates_from_range('1980m1', length=nobs) y = Series(y, index=dates) arma_mod = sm.tsa.ARMA(y, order=(2, 2), freq='M') arma_res = arma_mod.fit(trend='nc', disp=-1) print(arma_res.params) plt.show() statsmodels-0.12.2/statsmodels/examples/ex_pareto_plot.py000066400000000000000000000014201400612667500237200ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Aug 01 19:20:16 2010 Author: josef-pktd """ import numpy as np from scipy import stats import matplotlib.pyplot as plt nobs = 1000 r = stats.pareto.rvs(1, size=nobs) #rhisto = np.histogram(r, bins=20) rhisto, e = np.histogram(np.clip(r, 0 , 1000), bins=50) plt.figure() plt.loglog(e[:-1]+np.diff(e)/2, rhisto, '-o') plt.figure() plt.loglog(e[:-1]+np.diff(e)/2, nobs-rhisto.cumsum(), '-o') ##plt.figure() ##plt.plot(e[:-1]+np.diff(e)/2, rhisto.cumsum(), '-o') ##plt.figure() ##plt.semilogx(e[:-1]+np.diff(e)/2, nobs-rhisto.cumsum(), '-o') rsind = np.argsort(r) rs = r[rsind] rsf = nobs-rsind.argsort() plt.figure() plt.loglog(rs, nobs-np.arange(nobs), '-o') print(stats.linregress(np.log(rs), np.log(nobs-np.arange(nobs)))) plt.show() statsmodels-0.12.2/statsmodels/examples/ex_predict_results.py000066400000000000000000000051461400612667500246140ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sat Dec 20 12:01:13 2014 Author: Josef Perktold License: BSD-3 """ import numpy as np from numpy.testing import assert_allclose from statsmodels.regression.linear_model import WLS from statsmodels.tools.tools import add_constant from statsmodels.sandbox.regression.predstd import wls_prediction_std from statsmodels.regression._prediction import get_prediction from statsmodels.genmod._prediction import params_transform_univariate from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod.families import links # from example wls.py nsample = 50 x = np.linspace(0, 20, nsample) X = np.column_stack((x, (x - 5)**2)) X = add_constant(X) beta = [5., 0.5, -0.01] sig = 0.5 w = np.ones(nsample) w[nsample * 6/10:] = 3 y_true = np.dot(X, beta) e = np.random.normal(size=nsample) y = y_true + sig * w * e X = X[:,[0,1]] # ### WLS knowing the true variance ratio of heteroscedasticity mod_wls = WLS(y, X, weights=1./w) res_wls = mod_wls.fit() prstd, iv_l, iv_u = wls_prediction_std(res_wls) pred_res = get_prediction(res_wls) ci = pred_res.conf_int(obs=True) assert_allclose(pred_res.se_obs, prstd, rtol=1e-13) assert_allclose(ci, np.column_stack((iv_l, iv_u)), rtol=1e-13) print(pred_res.summary_frame().head()) pred_res2 = res_wls.get_prediction() ci2 = pred_res2.conf_int(obs=True) assert_allclose(pred_res2.se_obs, prstd, rtol=1e-13) assert_allclose(ci2, np.column_stack((iv_l, iv_u)), rtol=1e-13) print(pred_res2.summary_frame().head()) res_wls_n = mod_wls.fit(use_t=False) pred_wls_n = res_wls_n.get_prediction() print(pred_wls_n.summary_frame().head()) w_sqrt = np.sqrt(w) mod_glm = GLM(y/w_sqrt, X/w_sqrt[:,None]) res_glm = mod_glm.fit() pred_glm = res_glm.get_prediction() print(pred_glm.summary_frame().head()) res_glm_t = mod_glm.fit(use_t=True) pred_glm_t = res_glm_t.get_prediction() print(pred_glm_t.summary_frame().head()) rates = params_transform_univariate(res_glm.params, res_glm.cov_params()) print('\nRates exp(params)') print(rates.summary_frame()) rates2 = np.column_stack((np.exp(res_glm.params), res_glm.bse * np.exp(res_glm.params), np.exp(res_glm.conf_int()))) assert_allclose(rates.summary_frame().values, rates2, rtol=1e-13) # with identity transform pt = params_transform_univariate(res_glm.params, res_glm.cov_params(), link=links.identity()) print(pt.tvalues) assert_allclose(pt.tvalues, res_glm.tvalues, rtol=1e-13) assert_allclose(pt.se_mean, res_glm.bse, rtol=1e-13) ptt = pt.t_test() assert_allclose(ptt[0], res_glm.tvalues, rtol=1e-13) assert_allclose(ptt[1], res_glm.pvalues, rtol=1e-13) statsmodels-0.12.2/statsmodels/examples/ex_proportion.py000066400000000000000000000035301400612667500236070ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Apr 21 07:59:26 2013 Author: Josef Perktold """ from statsmodels.compat.python import lmap import numpy as np import matplotlib.pyplot as plt import statsmodels.stats.proportion as sms import statsmodels.stats.weightstats as smw from numpy.testing import assert_almost_equal # Region, Eyes, Hair, Count ss = '''\ 1 blue fair 23 1 blue red 7 1 blue medium 24 1 blue dark 11 1 green fair 19 1 green red 7 1 green medium 18 1 green dark 14 1 brown fair 34 1 brown red 5 1 brown medium 41 1 brown dark 40 1 brown black 3 2 blue fair 46 2 blue red 21 2 blue medium 44 2 blue dark 40 2 blue black 6 2 green fair 50 2 green red 31 2 green medium 37 2 green dark 23 2 brown fair 56 2 brown red 42 2 brown medium 53 2 brown dark 54 2 brown black 13''' dta0 = np.array(ss.split()).reshape(-1,4) dta = np.array(lmap(tuple, dta0.tolist()), dtype=[('Region', int), ('Eyes', 'S6'), ('Hair', 'S6'), ('Count', int)]) xfair = np.repeat([1,0], [228, 762-228]) # comparing to SAS last output at # http://support.sas.com/documentation/cdl/en/procstat/63104/HTML/default/viewer.htm#procstat_freq_sect028.htm # confidence interval for tost ci01 = smw.confint_ztest(xfair, alpha=0.1) assert_almost_equal(ci01, [0.2719, 0.3265], 4) res = smw.ztost(xfair, 0.18, 0.38) assert_almost_equal(res[1][0], 7.1865, 4) assert_almost_equal(res[2][0], -4.8701, 4) nn = np.arange(200, 351) pow_z = sms.power_ztost_prop(0.5, 0.72, nn, 0.6, alpha=0.05) pow_bin = sms.power_ztost_prop(0.5, 0.72, nn, 0.6, alpha=0.05, dist='binom') plt.plot(nn, pow_z[0], label='normal') plt.plot(nn, pow_bin[0], label='binomial') plt.legend(loc='lower right') plt.title('Proportion Equivalence Test: Power as function of sample size') plt.xlabel('Number of Observations') plt.ylabel('Power') plt.show() statsmodels-0.12.2/statsmodels/examples/ex_regressionplots.py000066400000000000000000000105031400612667500246340ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Examples for Regression Plots Author: Josef Perktold """ import numpy as np import statsmodels.api as sm import matplotlib.pyplot as plt from statsmodels.sandbox.regression.predstd import wls_prediction_std import statsmodels.graphics.regressionplots as smrp from statsmodels.graphics.tests.test_regressionplots import TestPlot #example from tut.ols with changes #fix a seed for these examples np.random.seed(9876789) # OLS non-linear curve but linear in parameters # --------------------------------------------- nsample = 100 sig = 0.5 x1 = np.linspace(0, 20, nsample) x2 = 5 + 3* np.random.randn(nsample) X = np.c_[x1, x2, np.sin(0.5*x1), (x2-5)**2, np.ones(nsample)] beta = [0.5, 0.5, 1, -0.04, 5.] y_true = np.dot(X, beta) y = y_true + sig * np.random.normal(size=nsample) #estimate only linear function, misspecified because of non-linear terms exog0 = sm.add_constant(np.c_[x1, x2], prepend=False) # plt.figure() # plt.plot(x1, y, 'o', x1, y_true, 'b-') res = sm.OLS(y, exog0).fit() #print res.params #print res.bse plot_old = 0 #True if plot_old: #current bug predict requires call to model.results #print res.model.predict prstd, iv_l, iv_u = wls_prediction_std(res) plt.plot(x1, res.fittedvalues, 'r-o') plt.plot(x1, iv_u, 'r--') plt.plot(x1, iv_l, 'r--') plt.title('blue: true, red: OLS') plt.figure() plt.plot(res.resid, 'o') plt.title('Residuals') fig2 = plt.figure() ax = fig2.add_subplot(2,1,1) #namestr = ' for %s' % self.name if self.name else '' plt.plot(x1, res.resid, 'o') ax.set_title('residuals versus exog')# + namestr) ax = fig2.add_subplot(2,1,2) plt.plot(x2, res.resid, 'o') fig3 = plt.figure() ax = fig3.add_subplot(2,1,1) #namestr = ' for %s' % self.name if self.name else '' plt.plot(x1, res.fittedvalues, 'o') ax.set_title('Fitted values versus exog')# + namestr) ax = fig3.add_subplot(2,1,2) plt.plot(x2, res.fittedvalues, 'o') fig4 = plt.figure() ax = fig4.add_subplot(2,1,1) #namestr = ' for %s' % self.name if self.name else '' plt.plot(x1, res.fittedvalues + res.resid, 'o') ax.set_title('Fitted values plus residuals versus exog')# + namestr) ax = fig4.add_subplot(2,1,2) plt.plot(x2, res.fittedvalues + res.resid, 'o') # see http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partregr.htm fig5 = plt.figure() ax = fig5.add_subplot(2,1,1) #namestr = ' for %s' % self.name if self.name else '' res1a = sm.OLS(y, exog0[:,[0,2]]).fit() res1b = sm.OLS(x1, exog0[:,[0,2]]).fit() plt.plot(res1b.resid, res1a.resid, 'o') res1c = sm.OLS(res1a.resid, res1b.resid).fit() plt.plot(res1b.resid, res1c.fittedvalues, '-') ax.set_title('Partial Regression plot')# + namestr) ax = fig5.add_subplot(2,1,2) #plt.plot(x2, res.fittedvalues + res.resid, 'o') res2a = sm.OLS(y, exog0[:,[0,1]]).fit() res2b = sm.OLS(x2, exog0[:,[0,1]]).fit() plt.plot(res2b.resid, res2a.resid, 'o') res2c = sm.OLS(res2a.resid, res2b.resid).fit() plt.plot(res2b.resid, res2c.fittedvalues, '-') # see http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm fig6 = plt.figure() ax = fig6.add_subplot(2,1,1) #namestr = ' for %s' % self.name if self.name else '' x1beta = x1*res.params[1] x2beta = x2*res.params[2] plt.plot(x1, x1beta + res.resid, 'o') plt.plot(x1, x1beta, '-') ax.set_title('X_i beta_i plus residuals versus exog (CCPR)')# + namestr) ax = fig6.add_subplot(2,1,2) plt.plot(x2, x2beta + res.resid, 'o') plt.plot(x2, x2beta, '-') #print res.summary() doplots = 1 if doplots: fig1 = smrp.plot_fit(res, 0, y_true=None) smrp.plot_fit(res, 1, y_true=None) smrp.plot_partregress_grid(res, exog_idx=[0,1]) smrp.plot_regress_exog(res, exog_idx=0) smrp.plot_ccpr(res, exog_idx=0) smrp.plot_ccpr_grid(res, exog_idx=[0,1]) tp = TestPlot() tp.test_plot_fit() fig1 = smrp.plot_partregress_grid(res, exog_idx=[0,1]) #add lowess ax = fig1.axes[0] y0 = ax.get_lines()[0]._y x0 = ax.get_lines()[0]._x lres = sm.nonparametric.lowess(y0, x0, frac=0.2) ax.plot(lres[:,0], lres[:,1], 'r', lw=1.5) ax = fig1.axes[1] y0 = ax.get_lines()[0]._y x0 = ax.get_lines()[0]._x lres = sm.nonparametric.lowess(y0, x0, frac=0.2) ax.plot(lres[:,0], lres[:,1], 'r', lw=1.5) #plt.show() statsmodels-0.12.2/statsmodels/examples/ex_rootfinding.py000066400000000000000000000061241400612667500237200ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sat Mar 23 13:35:51 2013 Author: Josef Perktold """ import numpy as np from statsmodels.tools.rootfinding import brentq_expanding # Warning: module.global, changing this will affect everyone #import statsmodels.tools.rootfinding as smroots #smroots.DEBUG = True DEBUG = False #True def func(x, a): f = (x - a)**3 if DEBUG: print('evaluating at %g, fval = %f' % (x, f)) return f def func_nan(x, a, b): x = np.atleast_1d(x) f = (x - 1.*a)**3 f[x < b] = np.nan if DEBUG: print('evaluating at %f, fval = %f' % (x, f)) return f def funcn(x, a): f = -(x - a)**3 if DEBUG: print('evaluating at %g, fval = %g' % (x, f)) return f def func2(x, a): f = (x - a)**3 print('evaluating at %g, fval = %f' % (x, f)) return f if __name__ == '__main__': run_all = False if run_all: print(brentq_expanding(func, args=(0,), increasing=True)) print(brentq_expanding(funcn, args=(0,), increasing=False)) print(brentq_expanding(funcn, args=(-50,), increasing=False)) print(brentq_expanding(func, args=(20,))) print(brentq_expanding(funcn, args=(20,))) print(brentq_expanding(func, args=(500000,))) # one bound print(brentq_expanding(func, args=(500000,), low=10000)) print(brentq_expanding(func, args=(-50000,), upp=-1000)) print(brentq_expanding(funcn, args=(500000,), low=10000)) print(brentq_expanding(funcn, args=(-50000,), upp=-1000)) # both bounds # hits maxiter in brentq if bounds too wide print(brentq_expanding(func, args=(500000,), low=300000, upp=700000)) print(brentq_expanding(func, args=(-50000,), low= -70000, upp=-1000)) print(brentq_expanding(funcn, args=(500000,), low=300000, upp=700000)) print(brentq_expanding(funcn, args=(-50000,), low= -70000, upp=-10000)) print(brentq_expanding(func, args=(1.234e30,), xtol=1e10, increasing=True, maxiter_bq=200)) print(brentq_expanding(func, args=(-50000,), start_low=-10000)) try: print(brentq_expanding(func, args=(-500,), start_upp=-100)) except ValueError: print('raised ValueError start_upp needs to be positive') ''' it still works raise ValueError('start_upp needs to be positive') -499.999996336 ''' ''' this does not work >>> print(brentq_expanding(func, args=(-500,), start_upp=-1000) raise ValueError('start_upp needs to be positive') OverflowError: (34, 'Result too large') ''' try: print(brentq_expanding(funcn, args=(-50000,), low= -40000, upp=-10000)) except Exception as e: print(e) val, info = brentq_expanding(func, args=(500,), full_output=True) print(val) print(vars(info)) # print(brentq_expanding(func_nan, args=(20,0), increasing=True)) print(brentq_expanding(func_nan, args=(20,0))) # In the next point 0 is minumum, below is nan print(brentq_expanding(func_nan, args=(-20,0), increasing=True)) print(brentq_expanding(func_nan, args=(-20,0))) statsmodels-0.12.2/statsmodels/examples/ex_sandwich.py000066400000000000000000000051541400612667500232000ustar00rootroot00000000000000# -*- coding: utf-8 -*- """examples for sandwich estimators of covariance Author: Josef Perktold """ from statsmodels.compat.python import lzip import numpy as np from numpy.testing import assert_almost_equal import statsmodels.api as sm import statsmodels.stats.sandwich_covariance as sw nobs = 100 kvars = 4 #including constant x = np.random.randn(nobs, kvars-1) exog = sm.add_constant(x) params_true = np.ones(kvars) y_true = np.dot(exog, params_true) sigma = 0.1 + np.exp(exog[:,-1]) endog = y_true + sigma * np.random.randn(nobs) self = sm.OLS(endog, exog).fit() print(self.HC3_se) print(sw.se_cov(sw.cov_hc3(self))) #test standalone refactoring assert_almost_equal(sw.se_cov(sw.cov_hc0(self)), self.HC0_se, 15) assert_almost_equal(sw.se_cov(sw.cov_hc1(self)), self.HC1_se, 15) assert_almost_equal(sw.se_cov(sw.cov_hc2(self)), self.HC2_se, 15) assert_almost_equal(sw.se_cov(sw.cov_hc3(self)), self.HC3_se, 15) print(self.HC0_se) print(sw.se_cov(sw.cov_hac_simple(self, nlags=0, use_correction=False))) #test White as HAC with nlags=0, same as nlags=1 ? bse_hac0 = sw.se_cov(sw.cov_hac_simple(self, nlags=0, use_correction=False)) assert_almost_equal(bse_hac0, self.HC0_se, 15) print(bse_hac0) #test White as HAC with nlags=0, same as nlags=1 ? bse_hac0c = sw.se_cov(sw.cov_hac_simple(self, nlags=0, use_correction=True)) assert_almost_equal(bse_hac0c, self.HC1_se, 15) bse_w = sw.se_cov(sw.cov_white_simple(self, use_correction=False)) print(bse_w) #test White assert_almost_equal(bse_w, self.HC0_se, 15) bse_wc = sw.se_cov(sw.cov_white_simple(self, use_correction=True)) print(bse_wc) #test White assert_almost_equal(bse_wc, self.HC1_se, 15) groups = np.repeat(np.arange(5), 20) idx = np.nonzero(np.diff(groups))[0].tolist() groupidx = lzip([0]+idx, idx+[len(groups)]) ngroups = len(groupidx) print(sw.se_cov(sw.cov_cluster(self, groups))) #two strange looking corner cases BUG? print(sw.se_cov(sw.cov_cluster(self, np.ones(len(endog), int), use_correction=False))) print(sw.se_cov(sw.cov_crosssection_0(self, np.arange(len(endog))))) #these results are close to simple (no group) white, 50 groups 2 obs each groups = np.repeat(np.arange(50), 100//50) print(sw.se_cov(sw.cov_cluster(self, groups))) #2 groups with 50 obs each, what was the interpretation again? groups = np.repeat(np.arange(2), 100//2) print(sw.se_cov(sw.cov_cluster(self, groups))) "http://www.kellogg.northwestern.edu/faculty/petersen/htm/papers/se/test_data.txt" ''' test <- read.table( url(paste("http://www.kellogg.northwestern.edu/", "faculty/petersen/htm/papers/se/", "test_data.txt",sep="")), col.names=c("firmid", "year", "x", "y")) ''' statsmodels-0.12.2/statsmodels/examples/ex_sandwich2.py000066400000000000000000000050171400612667500232600ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Cluster robust standard errors for OLS Created on Fri Dec 16 12:52:13 2011 Author: Josef Perktold """ from urllib.request import urlretrieve import numpy as np from numpy.testing import assert_almost_equal import statsmodels.api as sm import statsmodels.stats.sandwich_covariance as sw #http://www.ats.ucla.edu/stat/stata/seminars/svy_stata_intro/srs.dta import statsmodels.iolib.foreign as dta try: srs = dta.genfromdta("srs.dta") print('using local file') except IOError: urlretrieve('http://www.ats.ucla.edu/stat/stata/seminars/svy_stata_intro/srs.dta', 'srs.dta') print('downloading file') srs = dta.genfromdta("srs.dta") # from statsmodels.datasets import webuse # srs = webuse('srs', 'http://www.ats.ucla.edu/stat/stata/seminars/svy_stata_intro/') # #does currently not cache file y = srs['api00'] #older numpy do not reorder #x = srs[['growth', 'emer', 'yr_rnd']].view(float).reshape(len(y), -1) #force sequence x = np.column_stack([srs[ii] for ii in ['growth', 'emer', 'yr_rnd']]) group = srs['dnum'] #xx = sm.add_constant(x, prepend=True) xx = sm.add_constant(x, prepend=False) #const at end for Stata compatibility #remove nan observation mask = (xx!=-999.0).all(1) #nan code in dta file mask.shape y = y[mask] xx = xx[mask] group = group[mask] #run OLS res_srs = sm.OLS(y, xx).fit() print('params ', res_srs.params) print('bse_OLS ', res_srs.bse) #get cluster robust standard errors and compare with STATA cov_cr = sw.cov_cluster(res_srs, group.astype(int)) bse_cr = sw.se_cov(cov_cr) print('bse_rob ', bse_cr) res_stata = np.rec.array( [('growth', '|', -0.1027121, 0.22917029999999999, -0.45000000000000001, 0.65500000000000003, -0.55483519999999997, 0.34941109999999997), ('emer', '|', -5.4449319999999997, 0.72939690000000001, -7.46, 0.0, -6.8839379999999997, -4.0059269999999998), ('yr_rnd', '|', -51.075690000000002, 22.83615, -2.2400000000000002, 0.027, -96.128439999999998, -6.0229350000000004), ('_cons', '|', 740.3981, 13.460760000000001, 55.0, 0.0, 713.84180000000003, 766.95439999999996)], dtype=[('exogname', '|S6'), ('del', '|S1'), ('params', 'float'), ('bse', 'float'), ('tvalues', 'float'), ('pvalues', 'float'), ('cilow', 'float'), ('ciupp', 'float')]) print('diff Stata', bse_cr - res_stata.bse) assert_almost_equal(bse_cr, res_stata.bse, decimal=6) #We see that in this case the robust standard errors of the parameter estimates #are larger than those of OLS by 8 to 35 % print('reldiff to OLS', bse_cr/res_srs.bse - 1) statsmodels-0.12.2/statsmodels/examples/ex_sandwich3.py000066400000000000000000000036451400612667500232660ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Cluster Robust Standard Errors with Two Clusters Created on Sat Dec 17 08:39:16 2011 Author: Josef Perktold """ from urllib.request import urlretrieve import numpy as np from numpy.testing import assert_almost_equal import statsmodels.api as sm import statsmodels.stats.sandwich_covariance as sw #requires Petersen's test_data #http://www.kellogg.northwestern.edu/faculty/petersen/htm/papers/se/test_data.txt try: pet = np.genfromtxt("test_data.txt") print('using local file') except IOError: urlretrieve('http://www.kellogg.northwestern.edu/faculty/petersen/htm/papers/se/test_data.txt', 'test_data.txt') print('downloading file') pet = np.genfromtxt("test_data.txt") endog = pet[:,-1] group = pet[:,0].astype(int) time = pet[:,1].astype(int) exog = sm.add_constant(pet[:,2]) res = sm.OLS(endog, exog).fit() cov01, covg, covt = sw.cov_cluster_2groups(res, group, group2=time) #Reference number from Petersen #http://www.kellogg.northwestern.edu/faculty/petersen/htm/papers/se/test_data.htm bse_petw = [0.0284, 0.0284] bse_pet0 = [0.0670, 0.0506] bse_pet1 = [0.0234, 0.0334] #year bse_pet01 = [0.0651, 0.0536] #firm and year bse_0 = sw.se_cov(covg) bse_1 = sw.se_cov(covt) bse_01 = sw.se_cov(cov01) print('OLS ', res.bse) print('het HC0 ', res.HC0_se, bse_petw - res.HC0_se) print('het firm ', bse_0, bse_0 - bse_pet0) print('het year ', bse_1, bse_1 - bse_pet1) print('het firm & year', bse_01, bse_01 - bse_pet01) print('relative difference standard error het firm & year to OLS') print(' ', bse_01 / res.bse) #From the last line we see that the cluster and year robust standard errors #are approximately twice those of OLS assert_almost_equal(bse_petw, res.HC0_se, decimal=4) assert_almost_equal(bse_0, bse_pet0, decimal=4) assert_almost_equal(bse_1, bse_pet1, decimal=4) assert_almost_equal(bse_01, bse_pet01, decimal=4) statsmodels-0.12.2/statsmodels/examples/ex_scatter_ellipse.py000066400000000000000000000025271400612667500245630ustar00rootroot00000000000000'''example for grid of scatter plots with probability ellipses Author: Josef Perktold License: BSD-3 ''' from statsmodels.compat.python import lrange import numpy as np import matplotlib.pyplot as plt from statsmodels.graphics.plot_grids import scatter_ellipse nvars = 6 mmean = np.arange(1.,nvars+1)/nvars * 1.5 rho = 0.5 #dcorr = rho*np.ones((nvars, nvars)) + (1-rho)*np.eye(nvars) r = np.random.uniform(-0.99, 0.99, size=(nvars, nvars)) ##from scipy import stats ##r = stats.rdist.rvs(1, size=(nvars, nvars)) r = (r + r.T) / 2. assert np.allclose(r, r.T) mcorr = r mcorr[lrange(nvars), lrange(nvars)] = 1 #dcorr = np.array([[1, 0.5, 0.1],[0.5, 1, -0.2], [0.1, -0.2, 1]]) mstd = np.arange(1.,nvars+1)/nvars mcov = mcorr * np.outer(mstd, mstd) evals = np.linalg.eigvalsh(mcov) assert evals.min > 0 #assert positive definite nobs = 100 data = np.random.multivariate_normal(mmean, mcov, size=nobs) dmean = data.mean(0) dcov = np.cov(data, rowvar=0) print(dmean) print(dcov) dcorr = np.corrcoef(data, rowvar=0) dcorr[np.triu_indices(nvars)] = 0 print(dcorr) #default #fig = scatter_ellipse(data, level=[0.5, 0.75, 0.95]) #used for checking #fig = scatter_ellipse(data, level=[0.5, 0.75, 0.95], add_titles=True, keep_ticks=True) #check varnames varnames = ['var%d' % i for i in range(nvars)] fig = scatter_ellipse(data, level=0.9, varnames=varnames) plt.show() statsmodels-0.12.2/statsmodels/examples/ex_univar_kde.py000066400000000000000000000117411400612667500235260ustar00rootroot00000000000000""" This example tests the nonparametric estimator for several popular univariate distributions with the different bandwidth selction methods - CV-ML; CV-LS; Scott's rule of thumb. Produces six different plots for each distribution 1) Beta 2) f 3) Pareto 4) Laplace 5) Weibull 6) Poisson """ import numpy as np import scipy.stats as stats import matplotlib.pyplot as plt import statsmodels.api as sm KDEMultivariate = sm.nonparametric.KDEMultivariate np.random.seed(123456) # Beta distribution # Parameters a = 2 b = 5 nobs = 250 support = np.random.beta(a, b, size=nobs) rv = stats.beta(a, b) ix = np.argsort(support) dens_normal = KDEMultivariate(data=[support], var_type='c', bw='normal_reference') dens_cvls = KDEMultivariate(data=[support], var_type='c', bw='cv_ls') dens_cvml = KDEMultivariate(data=[support], var_type='c', bw='cv_ml') plt.figure(1) plt.plot(support[ix], rv.pdf(support[ix]), label='Actual') plt.plot(support[ix], dens_normal.pdf()[ix], label='Scott') plt.plot(support[ix], dens_cvls.pdf()[ix], label='CV_LS') plt.plot(support[ix], dens_cvml.pdf()[ix], label='CV_ML') plt.title("Nonparametric Estimation of the Density of Beta Distributed " \ "Random Variable") plt.legend(('Actual', 'Scott', 'CV_LS', 'CV_ML')) # f distribution df = 100 dn = 100 nobs = 250 support = np.random.f(dn, df, size=nobs) rv = stats.f(df, dn) ix = np.argsort(support) dens_normal = KDEMultivariate(data=[support], var_type='c', bw='normal_reference') dens_cvls = KDEMultivariate(data=[support], var_type='c', bw='cv_ls') dens_cvml = KDEMultivariate(data=[support], var_type='c', bw='cv_ml') plt.figure(2) plt.plot(support[ix], rv.pdf(support[ix]), label='Actual') plt.plot(support[ix], dens_normal.pdf()[ix], label='Scott') plt.plot(support[ix], dens_cvls.pdf()[ix], label='CV_LS') plt.plot(support[ix], dens_cvml.pdf()[ix], label='CV_ML') plt.title("Nonparametric Estimation of the Density of f Distributed " \ "Random Variable") plt.legend(('Actual', 'Scott', 'CV_LS', 'CV_ML')) # Pareto distribution a = 2 nobs = 150 support = np.random.pareto(a, size=nobs) rv = stats.pareto(a) ix = np.argsort(support) dens_normal = KDEMultivariate(data=[support], var_type='c', bw='normal_reference') dens_cvls = KDEMultivariate(data=[support], var_type='c', bw='cv_ls') dens_cvml = KDEMultivariate(data=[support], var_type='c', bw='cv_ml') plt.figure(3) plt.plot(support[ix], rv.pdf(support[ix]), label='Actual') plt.plot(support[ix], dens_normal.pdf()[ix], label='Scott') plt.plot(support[ix], dens_cvls.pdf()[ix], label='CV_LS') plt.plot(support[ix], dens_cvml.pdf()[ix], label='CV_ML') plt.title("Nonparametric Estimation of the Density of Pareto " \ "Distributed Random Variable") plt.legend(('Actual', 'Scott', 'CV_LS', 'CV_ML')) # Laplace Distribution mu = 0 s = 1 nobs = 250 support = np.random.laplace(mu, s, size=nobs) rv = stats.laplace(mu, s) ix = np.argsort(support) dens_normal = KDEMultivariate(data=[support], var_type='c', bw='normal_reference') dens_cvls = KDEMultivariate(data=[support], var_type='c', bw='cv_ls') dens_cvml = KDEMultivariate(data=[support], var_type='c', bw='cv_ml') plt.figure(4) plt.plot(support[ix], rv.pdf(support[ix]), label='Actual') plt.plot(support[ix], dens_normal.pdf()[ix], label='Scott') plt.plot(support[ix], dens_cvls.pdf()[ix], label='CV_LS') plt.plot(support[ix], dens_cvml.pdf()[ix], label='CV_ML') plt.title("Nonparametric Estimation of the Density of Laplace " \ "Distributed Random Variable") plt.legend(('Actual', 'Scott', 'CV_LS', 'CV_ML')) # Weibull Distribution a = 1 nobs = 250 support = np.random.weibull(a, size=nobs) rv = stats.weibull_min(a) ix = np.argsort(support) dens_normal = KDEMultivariate(data=[support], var_type='c', bw='normal_reference') dens_cvls = KDEMultivariate(data=[support], var_type='c', bw='cv_ls') dens_cvml = KDEMultivariate(data=[support], var_type='c', bw='cv_ml') plt.figure(5) plt.plot(support[ix], rv.pdf(support[ix]), label='Actual') plt.plot(support[ix], dens_normal.pdf()[ix], label='Scott') plt.plot(support[ix], dens_cvls.pdf()[ix], label='CV_LS') plt.plot(support[ix], dens_cvml.pdf()[ix], label='CV_ML') plt.title("Nonparametric Estimation of the Density of Weibull " \ "Distributed Random Variable") plt.legend(('Actual', 'Scott', 'CV_LS', 'CV_ML')) # Poisson Distribution a = 2 nobs = 250 support = np.random.poisson(a, size=nobs) rv = stats.poisson(a) ix = np.argsort(support) dens_normal = KDEMultivariate(data=[support], var_type='o', bw='normal_reference') dens_cvls = KDEMultivariate(data=[support], var_type='o', bw='cv_ls') dens_cvml = KDEMultivariate(data=[support], var_type='o', bw='cv_ml') plt.figure(6) plt.plot(support[ix], rv.pmf(support[ix]), label='Actual') plt.plot(support[ix], dens_normal.pdf()[ix], label='Scott') plt.plot(support[ix], dens_cvls.pdf()[ix], label='CV_LS') plt.plot(support[ix], dens_cvml.pdf()[ix], label='CV_ML') plt.title("Nonparametric Estimation of the Density of Poisson " \ "Distributed Random Variable") plt.legend(('Actual', 'Scott', 'CV_LS', 'CV_ML')) plt.show() statsmodels-0.12.2/statsmodels/examples/ex_wald_anova.py000066400000000000000000000031361400612667500235110ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Example for wald_test for terms - `wald_anova` Created on Mon Dec 15 11:19:23 2014 Author: Josef Perktold License: BSD-3 """ import numpy as np # noqa:F401 --> needed for patsy from statsmodels.formula.api import ols, glm, poisson from statsmodels.discrete.discrete_model import Poisson import statsmodels.stats.tests.test_anova as ttmod from statsmodels.discrete.discrete_model import NegativeBinomial test = ttmod.TestAnova3() test.setup_class() data = test.data.drop([0,1,2]) res_ols = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit(use_t=False) res_glm = glm("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit() res_poi = Poisson.from_formula("Days ~ C(Weight) * C(Duration)", data).fit(cov_type='HC0') res_poi_2 = poisson("Days ~ C(Weight) + C(Duration)", data).fit(cov_type='HC0') print('\nOLS') print(res_ols.wald_test_terms()) print('\nGLM') print(res_glm.wald_test_terms(skip_single=False, combine_terms=['Duration', 'Weight'])) print('\nPoisson 1') print(res_poi.wald_test_terms(skip_single=False, combine_terms=['Duration', 'Weight'])) print('\nPoisson 2') print(res_poi_2.wald_test_terms(skip_single=False)) res_nb2 = NegativeBinomial.from_formula("Days ~ C(Weight) * C(Duration)", data).fit() print('\nNegative Binomial nb2') print(res_nb2.wald_test_terms(skip_single=False)) res_nb1 = NegativeBinomial.from_formula("Days ~ C(Weight) * C(Duration)", data, loglike_method='nb1').fit(cov_type='HC0') print('\nNegative Binomial nb2') print(res_nb1.wald_test_terms(skip_single=False)) statsmodels-0.12.2/statsmodels/examples/example_discrete_mnl.py000066400000000000000000000046071400612667500250710ustar00rootroot00000000000000"""Example: statsmodels.discretemod """ from statsmodels.compat.python import lrange import numpy as np import statsmodels.api as sm from statsmodels.iolib.summary import ( table_extend, summary_params_2d, summary_params_2dflat) anes_data = sm.datasets.anes96.load(as_pandas=False) anes_exog = anes_data.exog anes_exog = sm.add_constant(anes_exog, prepend=False) mlogit_mod = sm.MNLogit(anes_data.endog, anes_exog) mlogit_res = mlogit_mod.fit() # The default method for the fit is Newton-Raphson # However, you can use other solvers mlogit_res = mlogit_mod.fit(method='bfgs', maxiter=100) # The below needs a lot of iterations to get it right? #TODO: Add a technical note on algorithms #mlogit_res = mlogit_mod.fit(method='ncg') # this takes forever exog_names = [anes_data.exog_name[i] for i in [0, 2]+lrange(5,8)] + ['const'] endog_names = [anes_data.endog_name+'_%d' % i for i in np.unique(mlogit_res.model.endog)[1:]] print('\n\nMultinomial') print(summary_params_2d(mlogit_res, extras=['bse','tvalues'], endog_names=endog_names, exog_names=exog_names)) tables, table_all = summary_params_2dflat(mlogit_res, endog_names=endog_names, exog_names=exog_names, keep_headers=True) tables, table_all = summary_params_2dflat(mlogit_res, endog_names=endog_names, exog_names=exog_names, keep_headers=False) print('\n\n') print(table_all) print('\n\n') print('\n'.join((str(t) for t in tables))) at = table_extend(tables) print(at) print('\n\n') print(mlogit_res.summary()) print(mlogit_res.summary(yname='PID')) #the following is supposed to raise ValueError #mlogit_res.summary(yname=['PID']) endog_names = [anes_data.endog_name+'=%d' % i for i in np.unique(mlogit_res.model.endog)[1:]] print(mlogit_res.summary(yname='PID', yname_list=endog_names, xname=exog_names)) ''' #trying pickle import pickle #copy.deepcopy(mlogit_res) #raises exception: AttributeError: 'ResettableCache' object has no attribute '_resetdict' mnl_res = mlogit_mod.fit(method='bfgs', maxiter=100) mnl_res.cov_params() #mnl_res.model.endog = None #mnl_res.model.exog = None pickle.dump(mnl_res, open('mnl_res.dump', 'w')) mnl_res_l = pickle.load(open('mnl_res.dump', 'r')) ''' statsmodels-0.12.2/statsmodels/examples/example_enhanced_boxplots.py000066400000000000000000000061061400612667500261140ustar00rootroot00000000000000 import numpy as np import matplotlib.pyplot as plt import statsmodels.api as sm # Necessary to make horizontal axis labels fit plt.rcParams['figure.subplot.bottom'] = 0.23 data = sm.datasets.anes96.load_pandas() party_ID = np.arange(7) labels = ["Strong Democrat", "Weak Democrat", "Independent-Democrat", "Independent-Independent", "Independent-Republican", "Weak Republican", "Strong Republican"] # Group age by party ID. age = [data.exog['age'][data.endog == id] for id in party_ID] # Create a violin plot. fig = plt.figure() ax = fig.add_subplot(111) sm.graphics.violinplot(age, ax=ax, labels=labels, plot_opts={'cutoff_val':5, 'cutoff_type':'abs', 'label_fontsize':'small', 'label_rotation':30}) ax.set_xlabel("Party identification of respondent.") ax.set_ylabel("Age") ax.set_title("US national election '96 - Age & Party Identification") # Create a bean plot. fig2 = plt.figure() ax = fig2.add_subplot(111) sm.graphics.beanplot(age, ax=ax, labels=labels, plot_opts={'cutoff_val':5, 'cutoff_type':'abs', 'label_fontsize':'small', 'label_rotation':30}) ax.set_xlabel("Party identification of respondent.") ax.set_ylabel("Age") ax.set_title("US national election '96 - Age & Party Identification") # Create a jitter plot. fig3 = plt.figure() ax = fig3.add_subplot(111) plot_opts={'cutoff_val':5, 'cutoff_type':'abs', 'label_fontsize':'small', 'label_rotation':30, 'violin_fc':(0.8, 0.8, 0.8), 'jitter_marker':'.', 'jitter_marker_size':3, 'bean_color':'#FF6F00', 'bean_mean_color':'#009D91'} sm.graphics.beanplot(age, ax=ax, labels=labels, jitter=True, plot_opts=plot_opts) ax.set_xlabel("Party identification of respondent.") ax.set_ylabel("Age") ax.set_title("US national election '96 - Age & Party Identification") # Create an asymmetrical jitter plot. ix = data.exog['income'] < 16 # incomes < $30k age = data.exog['age'][ix] endog = data.endog[ix] age_lower_income = [age[endog == id] for id in party_ID] ix = data.exog['income'] >= 20 # incomes > $50k age = data.exog['age'][ix] endog = data.endog[ix] age_higher_income = [age[endog == id] for id in party_ID] fig = plt.figure() ax = fig.add_subplot(111) plot_opts['violin_fc'] = (0.5, 0.5, 0.5) plot_opts['bean_show_mean'] = False plot_opts['bean_show_median'] = False plot_opts['bean_legend_text'] = r'Income < \$30k' plot_opts['cutoff_val'] = 10 sm.graphics.beanplot(age_lower_income, ax=ax, labels=labels, side='left', jitter=True, plot_opts=plot_opts) plot_opts['violin_fc'] = (0.7, 0.7, 0.7) plot_opts['bean_color'] = '#009D91' plot_opts['bean_legend_text'] = r'Income > \$50k' sm.graphics.beanplot(age_higher_income, ax=ax, labels=labels, side='right', jitter=True, plot_opts=plot_opts) ax.set_xlabel("Party identification of respondent.") ax.set_ylabel("Age") ax.set_title("US national election '96 - Age & Party Identification") # Show all plots. plt.show() statsmodels-0.12.2/statsmodels/examples/example_functional_plots.py000066400000000000000000000025001400612667500257720ustar00rootroot00000000000000'''Functional boxplots and rainbow plots see docstrings for an explanation Author: Ralf Gommers ''' import numpy as np import matplotlib.pyplot as plt import statsmodels.api as sm #Load the El Nino dataset. Consists of 60 years worth of Pacific Ocean sea #surface temperature data. data = sm.datasets.elnino.load(as_pandas=False) #Create a functional boxplot: #We see that the years 1982-83 and 1997-98 are outliers; these are #the years where El Nino (a climate pattern characterized by warming #up of the sea surface and higher air pressures) occurred with unusual #intensity. fig = plt.figure() ax = fig.add_subplot(111) res = sm.graphics.fboxplot(data.raw_data[:, 1:], wfactor=2.58, labels=data.raw_data[:, 0].astype(int), ax=ax) ax.set_xlabel("Month of the year") ax.set_ylabel("Sea surface temperature (C)") ax.set_xticks(np.arange(13, step=3) - 1) ax.set_xticklabels(["", "Mar", "Jun", "Sep", "Dec"]) ax.set_xlim([-0.2, 11.2]) #Create a rainbow plot: fig = plt.figure() ax = fig.add_subplot(111) res = sm.graphics.rainbowplot(data.raw_data[:, 1:], ax=ax) ax.set_xlabel("Month of the year") ax.set_ylabel("Sea surface temperature (C)") ax.set_xticks(np.arange(13, step=3) - 1) ax.set_xticklabels(["", "Mar", "Jun", "Sep", "Dec"]) ax.set_xlim([-0.2, 11.2]) plt.show() statsmodels-0.12.2/statsmodels/examples/example_kde.py000066400000000000000000000020041400612667500231510ustar00rootroot00000000000000 import numpy as np from scipy import stats from statsmodels.distributions.mixture_rvs import mixture_rvs from statsmodels.nonparametric.kde import kdensityfft from statsmodels.nonparametric import bandwidths import matplotlib.pyplot as plt np.random.seed(12345) obs_dist = mixture_rvs([.25,.75], size=10000, dist=[stats.norm, stats.norm], kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.5))) #.. obs_dist = mixture_rvs([.25,.75], size=10000, dist=[stats.norm, stats.beta], #.. kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=1,args=(1,.5)))) f_hat, grid, bw = kdensityfft(obs_dist, kernel="gauss", bw="scott") # Check the plot plt.figure() plt.hist(obs_dist, bins=50, normed=True, color='red') plt.plot(grid, f_hat, lw=2, color='black') plt.show() # do some timings # get bw first because they're not streamlined bw = bandwidths.bw_scott(obs_dist) #.. timeit kdensity(obs_dist, kernel="gauss", bw=bw, gridsize=2**10) #.. timeit kdensityfft(obs_dist, kernel="gauss", bw=bw, gridsize=2**10) statsmodels-0.12.2/statsmodels/examples/example_ols_minimal_comp.py000066400000000000000000000012621400612667500257340ustar00rootroot00000000000000"""Example: minimal OLS add example for new compare methods """ import numpy as np import statsmodels.api as sm np.random.seed(765367) nsample = 100 x = np.linspace(0,10, 100) X = sm.add_constant(np.column_stack((x, x**2))) beta = np.array([10, 1, 0.01]) y = np.dot(X, beta) + np.random.normal(size=nsample) results = sm.OLS(y, X).fit() print(results.summary()) results2 = sm.OLS(y, X[:,:2]).fit() print(results.compare_f_test(results2)) print(results.f_test([0,0,1])) print(results.compare_lr_test(results2)) ''' (1.841903749875428, 0.1778775592033047) (1.8810663357027693, 0.17021300121753191, 1.0) ''' statsmodels-0.12.2/statsmodels/examples/example_rpy.py000066400000000000000000000033031400612667500232230ustar00rootroot00000000000000'''Just two examples for using rpy These examples are mainly for developers. # example 1: OLS using LM # example 2: GLM with binomial family The second results is not exactly correct since it assumes that each obvervation has the same number of trials see datasets/longley for an R script with the correct syntax. See rmodelwrap.py in the tests folder for a convenience wrapper to make rpy more like statsmodels. Note, however, that rmodelwrap was created in a very ad hoc manner and due to the idiosyncracies in R it does not work for all types of R models. There are also R scripts included with most of the datasets to run some basic models for comparisons of results to statsmodels. ''' from rpy import r import statsmodels.api as sm examples = [1, 2] if 1 in examples: data = sm.datasets.longley.load(as_pandas=False) y,x = data.endog, sm.add_constant(data.exog, prepend=False) des_cols = ['x.%d' % (i+1) for i in range(x.shape[1])] formula = r('y~%s-1' % '+'.join(des_cols)) frame = r.data_frame(y=y, x=x) results = r.lm(formula, data=frame) print(list(results.keys())) print(results['coefficients']) if 2 in examples: data2 = sm.datasets.star98.load(as_pandas=False) y2,x2 = data2.endog, sm.add_constant(data2.exog, prepend=False) y2 = y2[:,0]/y2.sum(axis=1) des_cols2 = ['x.%d' % (i+1) for i in range(x2.shape[1])] formula2 = r('y~%s-1' % '+'.join(des_cols2)) frame2 = r.data_frame(y=y2, x=x2) results2 = r.glm(formula2, data=frame2, family='binomial') params_est = [results2['coefficients'][k] for k in sorted(results2['coefficients'])] print(params_est) print(', '.join(['%13.10f']*21) % tuple(params_est)) statsmodels-0.12.2/statsmodels/examples/koul_and_mc.py000066400000000000000000000021721400612667500231540ustar00rootroot00000000000000import statsmodels.api as sm import numpy as np ################## #Monte Carlo test# ################## modrand1 = np.random.RandomState(5676576) modrand2 = np.random.RandomState(1543543) modrand3 = np.random.RandomState(5738276) X = modrand1.uniform(0, 5, (1000, 4)) X = sm.add_constant(X) beta = np.array([[10], [2], [3], [4], [5]]) y = np.dot(X, beta) params = [] for i in range(10000): yhat = y + modrand2.standard_normal((1000, 1)) cens_times = 50 + (modrand3.standard_normal((1000, 1)) * 5) yhat_observed = np.minimum(yhat, cens_times) censors = np.int_(yhat < cens_times) model = sm.emplike.emplikeAFT(yhat_observed, X, censors) new_params = model.fit().params params.append(new_params) mc_est = np.mean(params, axis=0) # Gives MC parameter estimate ################## #Koul replication# ################## koul_data = np.genfromtxt('/home/justin/rverify.csv', delimiter=';') # ^ Change path to where file is located. koul_y = np.log10(koul_data[:, 0]) koul_x = sm.add_constant(koul_data[:, 2]) koul_censors = koul_data[:, 1] koul_params = sm.emplike.emplikeAFT(koul_y, koul_x, koul_censors).fit().params statsmodels-0.12.2/statsmodels/examples/l1_demo/000077500000000000000000000000001400612667500216455ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/examples/l1_demo/demo.py000066400000000000000000000322361400612667500231510ustar00rootroot00000000000000from optparse import OptionParser import statsmodels.api as sm import scipy as sp from scipy import linalg from scipy import stats docstr = """ Demonstrates l1 regularization for likelihood models. Use different models by setting mode = mnlogit, logit, or probit. Examples ------- $ python demo.py --get_l1_slsqp_results logit >>> import demo >>> demo.run_demo('logit') The Story --------- The maximum likelihood (ML) solution works well when the number of data points is large and the noise is small. When the ML solution starts "breaking", the regularized solution should do better. The l1 Solvers -------------- The solvers are slower than standard Newton, and sometimes have convergence issues Nonetheless, the final solution makes sense and is often better than the ML solution. The standard l1 solver is fmin_slsqp and is included with scipy. It sometimes has trouble verifying convergence when the data size is large. The l1_cvxopt_cp solver is part of CVXOPT and this package needs to be installed separately. It works well even for larger data sizes. """ def main(): """ Provides a CLI for the demo. """ usage = "usage: %prog [options] mode" usage += '\n'+docstr parser = OptionParser(usage=usage) # base_alpha parser.add_option("-a", "--base_alpha", help="Size of regularization param (the param actully used will "\ "automatically scale with data size in this demo) "\ "[default: %default]", dest='base_alpha', action='store', type='float', default=0.01) # num_samples parser.add_option("-N", "--num_samples", help="Number of data points to generate for fit "\ "[default: %default]", dest='N', action='store', type='int', default=500) # get_l1_slsqp_results parser.add_option("--get_l1_slsqp_results", help="Do an l1 fit using slsqp. [default: %default]", \ action="store_true",dest='get_l1_slsqp_results', default=False) # get_l1_cvxopt_results parser.add_option("--get_l1_cvxopt_results", help="Do an l1 fit using cvxopt. [default: %default]", \ action="store_true",dest='get_l1_cvxopt_results', default=False) # num_nonconst_covariates parser.add_option("--num_nonconst_covariates", help="Number of covariates that are not constant "\ "(a constant will be prepended) [default: %default]", dest='num_nonconst_covariates', action='store', type='int', default=10) # noise_level parser.add_option("--noise_level", help="Level of the noise relative to signal [default: %default]", dest='noise_level', action='store', type='float', default=0.2) # cor_length parser.add_option("--cor_length", help="Correlation length of the (Gaussian) independent variables"\ "[default: %default]", dest='cor_length', action='store', type='float', default=2) # num_zero_params parser.add_option("--num_zero_params", help="Number of parameters equal to zero for every target in "\ "logistic regression examples. [default: %default]", dest='num_zero_params', action='store', type='int', default=8) # num_targets parser.add_option("-J", "--num_targets", help="Number of choices for the endogenous response in "\ "multinomial logit example [default: %default]", dest='num_targets', action='store', type='int', default=3) # print_summaries parser.add_option("-s", "--print_summaries", help="Print the full fit summary. [default: %default]", \ action="store_true",dest='print_summaries', default=False) # save_arrays parser.add_option("--save_arrays", help="Save exog/endog/true_params to disk for future use. "\ "[default: %default]", action="store_true",dest='save_arrays', default=False) # load_old_arrays parser.add_option("--load_old_arrays", help="Load exog/endog/true_params arrays from disk. "\ "[default: %default]", action="store_true",dest='load_old_arrays', default=False) (options, args) = parser.parse_args() assert len(args) == 1 mode = args[0].lower() run_demo(mode, **options.__dict__) def run_demo(mode, base_alpha=0.01, N=500, get_l1_slsqp_results=False, get_l1_cvxopt_results=False, num_nonconst_covariates=10, noise_level=0.2, cor_length=2, num_zero_params=8, num_targets=3, print_summaries=False, save_arrays=False, load_old_arrays=False): """ Run the demo and print results. Parameters ---------- mode : str either 'logit', 'mnlogit', or 'probit' base_alpha : Float Size of regularization param (the param actually used will automatically scale with data size in this demo) N : int Number of data points to generate for fit get_l1_slsqp_results : bool, Do an l1 fit using slsqp. get_l1_cvxopt_results : bool Do an l1 fit using cvxopt num_nonconst_covariates : int Number of covariates that are not constant (a constant will be prepended) noise_level : float (non-negative) Level of the noise relative to signal cor_length : float (non-negative) Correlation length of the (Gaussian) independent variables num_zero_params : int Number of parameters equal to zero for every target in logistic regression examples. num_targets : int Number of choices for the endogenous response in multinomial logit example print_summaries : bool print the full fit summary. save_arrays : bool Save exog/endog/true_params to disk for future use. load_old_arrays Load exog/endog/true_params arrays from disk. """ if mode != 'mnlogit': print("Setting num_targets to 2 since mode != 'mnlogit'") num_targets = 2 models = { 'logit': sm.Logit, 'mnlogit': sm.MNLogit, 'probit': sm.Probit} endog_funcs = { 'logit': get_logit_endog, 'mnlogit': get_logit_endog, 'probit': get_probit_endog} # The regularization parameter # Here we scale it with N for simplicity. In practice, you should # use cross validation to pick alpha alpha = base_alpha * N * sp.ones((num_nonconst_covariates+1, num_targets-1)) alpha[0,:] = 0 # Do not regularize the intercept #### Make the data and model exog = get_exog(N, num_nonconst_covariates, cor_length) exog = sm.add_constant(exog) true_params = sp.rand(num_nonconst_covariates+1, num_targets-1) if num_zero_params: true_params[-num_zero_params:, :] = 0 endog = endog_funcs[mode](true_params, exog, noise_level) endog, exog, true_params = save_andor_load_arrays( endog, exog, true_params, save_arrays, load_old_arrays) model = models[mode](endog, exog) #### Get the results and print results = run_solvers(model, true_params, alpha, get_l1_slsqp_results, get_l1_cvxopt_results, print_summaries) summary_str = get_summary_str(results, true_params, get_l1_slsqp_results, get_l1_cvxopt_results, print_summaries) print(summary_str) def run_solvers(model, true_params, alpha, get_l1_slsqp_results, get_l1_cvxopt_results, print_summaries): """ Runs the solvers using the specified settings and returns a result string. Works the same for any l1 penalized likelihood model. """ results = {} #### Train the models # Get ML results results['results_ML'] = model.fit(method='newton') # Get l1 results start_params = results['results_ML'].params.ravel(order='F') if get_l1_slsqp_results: results['results_l1_slsqp'] = model.fit_regularized( method='l1', alpha=alpha, maxiter=1000, start_params=start_params, retall=True) if get_l1_cvxopt_results: results['results_l1_cvxopt_cp'] = model.fit_regularized( method='l1_cvxopt_cp', alpha=alpha, maxiter=50, start_params=start_params, retall=True, feastol=1e-5) return results def get_summary_str(results, true_params, get_l1_slsqp_results, get_l1_cvxopt_results, print_summaries): """ Gets a string summarizing the results. """ #### Extract specific results results_ML = results['results_ML'] RMSE_ML = get_RMSE(results_ML, true_params) if get_l1_slsqp_results: results_l1_slsqp = results['results_l1_slsqp'] if get_l1_cvxopt_results: results_l1_cvxopt_cp = results['results_l1_cvxopt_cp'] #### Format summaries # Short summary print_str = '\n\n=========== Short Error Summary ============' print_str += '\n\n The maximum likelihood fit RMS error = %.4f' % RMSE_ML if get_l1_slsqp_results: RMSE_l1_slsqp = get_RMSE(results_l1_slsqp, true_params) print_str += '\n The l1_slsqp fit RMS error = %.4f' % RMSE_l1_slsqp if get_l1_cvxopt_results: RMSE_l1_cvxopt_cp = get_RMSE(results_l1_cvxopt_cp, true_params) print_str += '\n The l1_cvxopt_cp fit RMS error = %.4f' % RMSE_l1_cvxopt_cp # Parameters print_str += '\n\n\n============== Parameters =================' print_str += "\n\nTrue parameters: \n%s" % true_params # Full summary if print_summaries: print_str += '\n' + results_ML.summary().as_text() if get_l1_slsqp_results: print_str += '\n' + results_l1_slsqp.summary().as_text() if get_l1_cvxopt_results: print_str += '\n' + results_l1_cvxopt_cp.summary().as_text() else: print_str += '\n\nThe maximum likelihood params are \n%s' % results_ML.params if get_l1_slsqp_results: print_str += '\n\nThe l1_slsqp params are \n%s' % results_l1_slsqp.params if get_l1_cvxopt_results: print_str += '\n\nThe l1_cvxopt_cp params are \n%s' % \ results_l1_cvxopt_cp.params # Return return print_str def save_andor_load_arrays( endog, exog, true_params, save_arrays, load_old_arrays): if save_arrays: sp.save('endog.npy', endog) sp.save('exog.npy', exog) sp.save('true_params.npy', true_params) if load_old_arrays: endog = sp.load('endog.npy') exog = sp.load('exog.npy') true_params = sp.load('true_params.npy') return endog, exog, true_params def get_RMSE(results, true_params): """ Gets the (normalized) root mean square error. """ diff = results.params.reshape(true_params.shape) - true_params raw_RMSE = sp.sqrt(((diff)**2).sum()) param_norm = sp.sqrt((true_params**2).sum()) return raw_RMSE / param_norm def get_logit_endog(true_params, exog, noise_level): """ Gets an endogenous response that is consistent with the true_params, perturbed by noise at noise_level. """ N = exog.shape[0] ### Create the probability of entering the different classes, ### given exog and true_params Xdotparams = sp.dot(exog, true_params) noise = noise_level * sp.randn(*Xdotparams.shape) eXB = sp.column_stack((sp.ones(len(Xdotparams)), sp.exp(Xdotparams))) class_probabilities = eXB / eXB.sum(1)[:, None] ### Create the endog cdf = class_probabilities.cumsum(axis=1) endog = sp.zeros(N) for i in range(N): endog[i] = sp.searchsorted(cdf[i, :], sp.rand()) return endog def get_probit_endog(true_params, exog, noise_level): """ Gets an endogenous response that is consistent with the true_params, perturbed by noise at noise_level. """ N = exog.shape[0] ### Create the probability of entering the different classes, ### given exog and true_params Xdotparams = sp.dot(exog, true_params) noise = noise_level * sp.randn(*Xdotparams.shape) ### Create the endog cdf = stats.norm._cdf(-Xdotparams) endog = sp.zeros(N) for i in range(N): endog[i] = sp.searchsorted(cdf[i, :], sp.rand()) return endog def get_exog(N, num_nonconst_covariates, cor_length): """ Returns an exog array with correlations determined by cor_length. The covariance matrix of exog will have (asymptotically, as :math:'N\\to\\inf') .. math:: Cov[i,j] = \\exp(-|i-j| / cor_length) Higher cor_length makes the problem more ill-posed, and easier to screw up with noise. BEWARE: With very long correlation lengths, you often get a singular KKT matrix (during the l1_cvxopt_cp fit) """ ## Create the noiseless exog uncorrelated_exog = sp.randn(N, num_nonconst_covariates) if cor_length == 0: exog = uncorrelated_exog else: cov_matrix = sp.zeros((num_nonconst_covariates, num_nonconst_covariates)) j = sp.arange(num_nonconst_covariates) for i in range(num_nonconst_covariates): cov_matrix[i,:] = sp.exp(-sp.fabs(i-j) / cor_length) chol = linalg.cholesky(cov_matrix) # cov_matrix = sp.dot(chol.T, chol) exog = sp.dot(uncorrelated_exog, chol) ## Return return exog if __name__ == '__main__': main() statsmodels-0.12.2/statsmodels/examples/l1_demo/short_demo.py000066400000000000000000000071261400612667500243700ustar00rootroot00000000000000""" You can fit your LikelihoodModel using l1 regularization by changing the method argument and adding an argument alpha. See code for details. The Story --------- The maximum likelihood (ML) solution works well when the number of data points is large and the noise is small. When the ML solution starts "breaking", the regularized solution should do better. The l1 Solvers -------------- The standard l1 solver is fmin_slsqp and is included with scipy. It sometimes has trouble verifying convergence when the data size is large. The l1_cvxopt_cp solver is part of CVXOPT and this package needs to be installed separately. It works well even for larger data sizes. """ import statsmodels.api as sm import matplotlib.pyplot as plt import numpy as np ## Load the data from Spector and Mazzeo (1980) spector_data = sm.datasets.spector.load(as_pandas=False) spector_data.exog = sm.add_constant(spector_data.exog) N = len(spector_data.endog) K = spector_data.exog.shape[1] ### Logit Model logit_mod = sm.Logit(spector_data.endog, spector_data.exog) ## Standard logistic regression logit_res = logit_mod.fit() ## Regularized regression # Set the reularization parameter to something reasonable alpha = 0.05 * N * np.ones(K) # Use l1, which solves via a built-in (scipy.optimize) solver logit_l1_res = logit_mod.fit_regularized(method='l1', alpha=alpha, acc=1e-6) # Use l1_cvxopt_cp, which solves with a CVXOPT solver logit_l1_cvxopt_res = logit_mod.fit_regularized( method='l1_cvxopt_cp', alpha=alpha) ## Print results print("============ Results for Logit =================") print("ML results") print(logit_res.summary()) print("l1 results") print(logit_l1_res.summary()) print(logit_l1_cvxopt_res.summary()) ### Multinomial Logit Example using American National Election Studies Data anes_data = sm.datasets.anes96.load(as_pandas=False) anes_exog = anes_data.exog anes_exog = sm.add_constant(anes_exog, prepend=False) mlogit_mod = sm.MNLogit(anes_data.endog, anes_exog) mlogit_res = mlogit_mod.fit() ## Set the regularization parameter. alpha = 10 * np.ones((mlogit_mod.J - 1, mlogit_mod.K)) # Do not regularize the constant alpha[-1,:] = 0 mlogit_l1_res = mlogit_mod.fit_regularized(method='l1', alpha=alpha) print(mlogit_l1_res.params) #mlogit_l1_res = mlogit_mod.fit_regularized( # method='l1_cvxopt_cp', alpha=alpha, abstol=1e-10, trim_tol=1e-6) #print mlogit_l1_res.params ## Print results print("============ Results for MNLogit =================") print("ML results") print(mlogit_res.summary()) print("l1 results") print(mlogit_l1_res.summary()) # # #### Logit example with many params, sweeping alpha spector_data = sm.datasets.spector.load(as_pandas=False) X = spector_data.exog Y = spector_data.endog ## Fit N = 50 # number of points to solve at K = X.shape[1] logit_mod = sm.Logit(Y, X) coeff = np.zeros((N, K)) # Holds the coefficients alphas = 1 / np.logspace(-0.5, 2, N) ## Sweep alpha and store the coefficients # QC check does not always pass with the default options. # Use the options QC_verbose=True and disp=True # to to see what is happening. It just barely does not pass, so I decreased # acc and increased QC_tol to make it pass for n, alpha in enumerate(alphas): logit_res = logit_mod.fit_regularized( method='l1', alpha=alpha, trim_mode='off', QC_tol=0.1, disp=False, QC_verbose=True, acc=1e-15) coeff[n,:] = logit_res.params ## Plot plt.figure(1) plt.clf() plt.grid() plt.title('Regularization Path') plt.xlabel('alpha') plt.ylabel('Parameter value') for i in range(K): plt.plot(alphas, coeff[:,i], label='X'+str(i), lw=3) plt.legend(loc='best') plt.show() statsmodels-0.12.2/statsmodels/examples/l1_demo/sklearn_compare.py000066400000000000000000000070351400612667500253710ustar00rootroot00000000000000""" For comparison with sklearn.linear_model.LogisticRegression Computes a regularzation path with both packages. The coefficient values in either path are related by a "constant" in the sense that for any fixed value of the constraint C and log likelihood, there exists an l1 regularization constant alpha such that the optimal solutions should be the same. Note that alpha(C) is a nonlinear function in general. Here we find alpha(C) by finding a reparameterization of the statsmodels path that makes the paths match up. An equation is available, but to use it I would need to hack the sklearn code to extract the gradient of the log likelihood. The results "prove" that the regularization paths are the same. Note that finding the reparameterization is non-trivial since the coefficient paths are NOT monotonic. As a result, the paths do not match up perfectly. """ from statsmodels.compat.python import lrange from sklearn import linear_model import statsmodels.api as sm import numpy as np import matplotlib.pyplot as plt ## Decide which dataset to use # Use either spector or anes96 use_spector = False #### Load data ## The Spector and Mazzeo (1980) data from statsmodels if use_spector: spector_data = sm.datasets.spector.load(as_pandas=False) X = spector_data.exog Y = spector_data.endog else: raise Exception( "The anes96 dataset is now loaded in as a short version that cannot "\ "be used here") anes96_data = sm.datasets.anes96.load_pandas() Y = anes96_data.exog.vote #### Fit and plot results N = 200 # number of points to solve at K = X.shape[1] ## statsmodels logit_mod = sm.Logit(Y, X) sm_coeff = np.zeros((N, K)) # Holds the coefficients if use_spector: alphas = 1 / np.logspace(-1, 2, N) # for spector_data else: alphas = 1 / np.logspace(-3, 2, N) # for anes96_data for n, alpha in enumerate(alphas): logit_res = logit_mod.fit_regularized( method='l1', alpha=alpha, disp=False, trim_mode='off') sm_coeff[n,:] = logit_res.params ## Sklearn sk_coeff = np.zeros((N, K)) if use_spector: Cs = np.logspace(-0.45, 2, N) else: Cs = np.logspace(-2.6, 0, N) for n, C in enumerate(Cs): clf = linear_model.LogisticRegression( C=C, penalty='l1', fit_intercept=False) clf.fit(X, Y) sk_coeff[n, :] = clf.coef_ ## Get the reparametrization of sm_coeff that makes the paths equal # Do this by finding one single re-parameterization of the second coefficient # that makes the path for the second coefficient (almost) identical. This # same parameterization will work for the other two coefficients since the # the regularization coefficients (in sk and sm) are related by a constant. # # special_X is chosen since this coefficient becomes non-zero before the # other two...and is relatively monotonic...with both datasets. sk_special_X = np.fabs(sk_coeff[:,2]) sm_special_X = np.fabs(sm_coeff[:,2]) s = np.zeros(N) # Note that sk_special_X will not always be perfectly sorted... s = np.searchsorted(sk_special_X, sm_special_X) ## Plot plt.figure(2) plt.clf() plt.grid() plt.xlabel('Index in sklearn simulation') plt.ylabel('Coefficient value') plt.title('Regularization Paths') colors = ['b', 'r', 'k', 'g', 'm', 'c', 'y'] for coeff, name in [(sm_coeff, 'sm'), (sk_coeff, 'sk')]: if name == 'sk': ltype = 'x' # linetype t = lrange(N) # The 'time' parameter else: ltype = 'o' t = s for i in range(K): plt.plot(t, coeff[:,i], ltype+colors[i], label=name+'-X'+str(i)) plt.legend(loc='best') plt.show() statsmodels-0.12.2/statsmodels/examples/run_all.py000066400000000000000000000036331400612667500223400ustar00rootroot00000000000000'''run all examples to make sure we do not get an exception Note: If an example contaings plt.show(), then all plot windows have to be closed manually, at least in my setup. uncomment plt.show() to show all plot windows ''' from statsmodels.compat.python import lzip, input import matplotlib.pyplot as plt #matplotlib is required for many examples stop_on_error = True filelist = ['example_glsar.py', 'example_wls.py', 'example_gls.py', 'example_glm.py', 'example_ols_tftest.py', #'example_rpy.py', 'example_ols.py', 'example_ols_minimal.py', 'example_rlm.py', 'example_discrete.py', 'example_predict.py', 'example_ols_table.py', 'tut_ols.py', 'tut_ols_rlm.py', 'tut_ols_wls.py'] use_glob = True if use_glob: import glob filelist = glob.glob('*.py') print(lzip(range(len(filelist)), filelist)) for fname in ['run_all.py', 'example_rpy.py']: filelist.remove(fname) #filelist = filelist[15:] #temporarily disable show plt_show = plt.show def noop(*args): pass plt.show = noop cont = input("""Are you sure you want to run all of the examples? This is done mainly to check that they are up to date. (y/n) >>> """) has_errors = [] if 'y' in cont.lower(): for run_all_f in filelist: try: print("\n\nExecuting example file", run_all_f) print("-----------------------" + "-"*len(run_all_f)) exec(open(run_all_f).read()) except: #f might be overwritten in the executed file print("**********************" + "*"*len(run_all_f)) print("ERROR in example file", run_all_f) print("**********************" + "*"*len(run_all_f)) has_errors.append(run_all_f) if stop_on_error: raise print('\nModules that raised exception:') print(has_errors) #reenable show after closing windows plt.close('all') plt.show = plt_show plt.show() statsmodels-0.12.2/statsmodels/examples/tests/000077500000000000000000000000001400612667500214675ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/examples/tests/__init__.py000066400000000000000000000000001400612667500235660ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/examples/tests/test_notebooks.py000066400000000000000000000036601400612667500251100ustar00rootroot00000000000000import glob import io import os import sys import pytest try: import jupyter_client # noqa: F401 import nbformat from nbconvert.preprocessors import ExecutePreprocessor except ImportError: pytestmark = pytest.mark.skip(reason='Required packages not available') try: import rpy2 # noqa: F401 HAS_RPY2 = True except ImportError: HAS_RPY2 = False try: import joblib # noqa: F401 HAS_JOBLIB = True except ImportError: HAS_JOBLIB = False KNOWN_FAILURES = [] JOBLIB_NOTEBOOKS = ['distributed_estimation'] RPY2_NOTEBOOKS = ['mixed_lm_example', 'robust_models_1'] kernel_name = 'python%s' % sys.version_info.major head, _ = os.path.split(__file__) NOTEBOOK_DIR = os.path.join(head, '..', '..', '..', 'examples', 'notebooks') NOTEBOOK_DIR = os.path.abspath(NOTEBOOK_DIR) nbs = sorted(glob.glob(os.path.join(NOTEBOOK_DIR, '*.ipynb'))) ids = list(map(lambda p: os.path.split(p)[-1], nbs)) @pytest.fixture(params=nbs, ids=ids) def notebook(request): return request.param if not nbs: pytestmark = pytest.mark.skip(reason='No notebooks found so no tests run') @pytest.mark.slow @pytest.mark.example def test_notebook(notebook): fullfile = os.path.abspath(notebook) _, filename = os.path.split(fullfile) filename, _ = os.path.splitext(filename) if filename in KNOWN_FAILURES: pytest.skip('{0} is known to fail'.format(filename)) if filename in RPY2_NOTEBOOKS and not HAS_RPY2: pytest.skip('{0} since rpy2 is not installed'.format(filename)) if filename in JOBLIB_NOTEBOOKS and not JOBLIB_NOTEBOOKS: pytest.skip('{0} since joblib is not installed'.format(filename)) with io.open(fullfile, encoding='utf-8') as fp: nb = nbformat.read(fp, as_version=4) ep = ExecutePreprocessor(allow_errors=False, timeout=20, kernel_name=kernel_name) ep.preprocess(nb, {'metadata': {'path': NOTEBOOK_DIR}}) statsmodels-0.12.2/statsmodels/examples/try_2regress.py000066400000000000000000000035201400612667500233310ustar00rootroot00000000000000# -*- coding: utf-8 -*- """F test for null hypothesis that coefficients in two regressions are the same see discussion in http://mail.scipy.org/pipermail/scipy-user/2010-March/024851.html Created on Thu Mar 25 22:56:45 2010 Author: josef-pktd """ import numpy as np from numpy.testing import assert_almost_equal import statsmodels.api as sm np.random.seed(87654589) nobs = 10 #100 x1 = np.random.randn(nobs) y1 = 10 + 15*x1 + 2*np.random.randn(nobs) x1 = sm.add_constant(x1, prepend=False) assert_almost_equal(x1, np.vander(x1[:,0],2), 16) res1 = sm.OLS(y1, x1).fit() print(res1.params) print(np.polyfit(x1[:,0], y1, 1)) assert_almost_equal(res1.params, np.polyfit(x1[:,0], y1, 1), 14) print(res1.summary(xname=['x1','const1'])) #regression 2 x2 = np.random.randn(nobs) y2 = 19 + 17*x2 + 2*np.random.randn(nobs) #y2 = 10 + 15*x2 + 2*np.random.randn(nobs) # if H0 is true x2 = sm.add_constant(x2, prepend=False) assert_almost_equal(x2, np.vander(x2[:,0],2), 16) res2 = sm.OLS(y2, x2).fit() print(res2.params) print(np.polyfit(x2[:,0], y2, 1)) assert_almost_equal(res2.params, np.polyfit(x2[:,0], y2, 1), 14) print(res2.summary(xname=['x2','const2'])) # joint regression x = np.concatenate((x1,x2),0) y = np.concatenate((y1,y2)) dummy = np.arange(2*nobs)>nobs-1 x = np.column_stack((x,x*dummy[:,None])) res = sm.OLS(y, x).fit() print(res.summary(xname=['x','const','x2','const2'])) print('\nF test for equal coefficients in 2 regression equations') #effect of dummy times second regression is zero #is equivalent to 3rd and 4th coefficient are both zero print(res.f_test([[0,0,1,0],[0,0,0,1]])) print('\nchecking coefficients individual versus joint') print(res1.params, res2.params) print(res.params[:2], res.params[:2]+res.params[2:]) assert_almost_equal(res1.params, res.params[:2], 13) assert_almost_equal(res2.params, res.params[:2]+res.params[2:], 13) statsmodels-0.12.2/statsmodels/examples/try_fit_constrained.py000066400000000000000000000155521400612667500247600ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri May 30 22:56:57 2014 Author: Josef Perktold License: BSD-3 """ import numpy as np from numpy.testing import assert_allclose, assert_raises from statsmodels.base._constraints import (TransformRestriction, transform_params_constraint, fit_constrained) if __name__ == '__main__': R = np.array([[1, 1, 0, 0, 0], [0, 0, 1, -1, 0]]) k_constr, k_vars = R.shape m = np.eye(k_vars) - R.T.dot(np.linalg.pinv(R).T) evals, evecs = np.linalg.eigh(m) L = evecs[:, :k_constr] T = evecs[:, k_constr:] print(T.T.dot(np.eye(k_vars))) tr = np.column_stack((T, R.T)) q = [2, 0] tr0 = TransformRestriction(R, q) p_reduced = [1,1,1] #round trip test assert_allclose(tr0.reduce(tr0.expand(p_reduced)), p_reduced, rtol=1e-14) p = tr0.expand(p_reduced) assert_allclose(R.dot(p), q, rtol=1e-14) # inconsistent restrictions #Ri = np.array([[1, 1, 0, 0, 0], [0, 0, 1, -1, 0], [0, 0, 1, -2, 0]]) R = np.array([[1, 1, 0, 0, 0], [0, 0, 1, -1, 0], [0, 0, 1, 0, -1]]) q = np.zeros(R.shape[0]) tr1 = TransformRestriction(R, q) # bug raises error with q p = tr1.expand([1,1]) # inconsistent restrictions that has a solution with p3=0 Ri = np.array([[1, 1, 0, 0, 0], [0, 0, 1, -1, 0], [0, 0, 1, -2, 0]]) tri = TransformRestriction(Ri, [0, 1, 1]) # Note: the only way this can hold is if variable 3 is zero p = tri.expand([1,1]) print(p[[2,3]]) #array([ 1.00000000e+00, -1.34692639e-17]) # inconsistent without any possible solution Ri2 = np.array([[0, 0, 0, 1, 0], [0, 0, 1, -1, 0], [0, 0, 1, -2, 0]]) q = [1, 1] #tri2 = TransformRestriction(Ri2, q) #p = tri.expand([1,1]) assert_raises(ValueError, TransformRestriction, Ri2, q) # L does not have full row rank, calculating constant fails with Singular Matrix # transform data xr = T x np.random.seed(1) x = np.random.randn(10, 5) xr = tr1.reduce(x) # roundtrip x2 = tr1.expand(xr) # this does not hold ? do not use constant? do not need it anyway ? #assert_allclose(x2, x, rtol=1e-14) from patsy import DesignInfo names = 'a b c d'.split() LC = DesignInfo(names).linear_constraint('a + b = 0') LC = DesignInfo(names).linear_constraint(['a + b = 0', 'a + 2*c = 1', 'b-a', 'c-a', 'd-a']) #LC = DesignInfo(self.model.exog_names).linear_constraint(r_matrix) r_matrix, q_matrix = LC.coefs, LC.constants np.random.seed(123) nobs = 20 x = 1 + np.random.randn(nobs, 4) exog = np.column_stack((np.ones(nobs), x)) endog = exog.sum(1) + np.random.randn(nobs) from statsmodels.regression.linear_model import OLS res2 = OLS(endog, exog).fit() #transf = TransformRestriction(np.eye(exog.shape[1])[:2], res2.params[:2] / 2) transf = TransformRestriction([[0, 0, 0,1,1]], res2.params[-2:].sum()) exog_st = transf.reduce(exog) res1 = OLS(endog, exog_st).fit() # need to correct for constant/offset in the optimization res1 = OLS(endog - exog.dot(transf.constant.squeeze()), exog_st).fit() params = transf.expand(res1.params).squeeze() assert_allclose(params, res2.params, rtol=1e-13) print(res2.params) print(params) print(res1.params) res3_ols = OLS(endog - exog[:, -1], exog[:, :-2]).fit() #transf = TransformRestriction(np.eye(exog.shape[1])[:2], res2.params[:2] / 2) transf3 = TransformRestriction([[0, 0, 0, 1, 0],[0, 0, 0, 0, 1]], [0, 1]) exog3_st = transf3.reduce(exog) res3 = OLS(endog, exog3_st).fit() # need to correct for constant/offset in the optimization res3 = OLS(endog - exog.dot(transf3.constant.squeeze()), exog3_st).fit() params = transf3.expand(res3.params).squeeze() assert_allclose(params[:-2], res3_ols.params, rtol=1e-13) print(res3.params) print(params) print(res3_ols.params) print(res3_ols.bse) # the following raises `ValueError: cannot test a constant constraint` #tt = res3.t_test(transf3.transf_mat, transf3.constant.squeeze()) #print tt.sd cov_params3 = transf3.transf_mat.dot(res3.cov_params()).dot(transf3.transf_mat.T) bse3 = np.sqrt(np.diag(cov_params3)) print(bse3) tp = transform_params_constraint(res2.params, res2.normalized_cov_params, transf3.R, transf3.q) tp = transform_params_constraint(res2.params, res2.cov_params(), transf3.R, transf3.q) import statsmodels.api as sm rand_data = sm.datasets.randhie.load(as_pandas=False) rand_exog = rand_data.exog.view(float).reshape(len(rand_data.exog), -1) rand_exog = sm.add_constant(rand_exog, prepend=False) # Fit Poisson model: poisson_mod0 = sm.Poisson(rand_data.endog, rand_exog) poisson_res0 = poisson_mod0.fit(method="newton") R = np.zeros((2, 10)) R[0, -2] = 1 R[1, -1] = 1 transfp = TransformRestriction(R, [0, 1]) poisson_mod = sm.Poisson(rand_data.endog, rand_exog[:, :-2]) # note wrong offset, why did I put offset in fit ? it's ignored poisson_res = poisson_mod.fit(method="newton", offset=rand_exog.dot(transfp.constant.squeeze())) exogp_st = transfp.reduce(rand_exog) poisson_modr = sm.Poisson(rand_data.endog, exogp_st) poisson_resr = poisson_modr.fit(method="newton") paramsp = transfp.expand(poisson_resr.params).squeeze() print('\nPoisson') print(paramsp) print(poisson_res.params) # error because I do not use the unconstrained basic model # tp = transform_params_constraint(poisson_res.params, poisson_res.cov_params(), transfp.R, transfp.q) # cov_params3 = transf3.transf_mat.dot(res3.cov_params()).dot(transf3.transf_mat.T) # bse3 = np.sqrt(np.diag(cov_params3)) poisson_mod0 = sm.Poisson(rand_data.endog, rand_exog) poisson_res0 = poisson_mod0.fit(method="newton") tp = transform_params_constraint(poisson_res0.params, poisson_res0.cov_params(), transfp.R, transfp.q) cov_params3 = transf3.transf_mat.dot(res3.cov_params()).dot(transf3.transf_mat.T) bse3 = np.sqrt(np.diag(cov_params3)) # try again same example as it was intended poisson_mod = sm.Poisson(rand_data.endog, rand_exog[:, :-2], offset=rand_exog[:, -1]) poisson_res = poisson_mod.fit(method="newton") exogp_st = transfp.reduce(rand_exog) poisson_modr = sm.Poisson(rand_data.endog, exogp_st, offset=rand_exog.dot(transfp.constant.squeeze())) poisson_resr = poisson_modr.fit(method="newton") paramsp = transfp.expand(poisson_resr.params).squeeze() print('\nPoisson') print(paramsp) print(poisson_resr.params) tp = transform_params_constraint(poisson_res0.params, poisson_res0.cov_params(), transfp.R, transfp.q) cov_paramsp = transfp.transf_mat.dot(poisson_resr.cov_params()).dot(transfp.transf_mat.T) bsep = np.sqrt(np.diag(cov_paramsp)) print(bsep) p, cov, res_r = fit_constrained(poisson_mod0, transfp.R, transfp.q) se = np.sqrt(np.diag(cov)) print(p) print(se) statsmodels-0.12.2/statsmodels/examples/try_gee.py000066400000000000000000000041471400612667500223430ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Thu Jul 18 14:57:46 2013 Author: Josef Perktold """ import numpy as np from statsmodels.genmod.generalized_estimating_equations import GEE, GEEMargins from statsmodels.genmod.families import Gaussian from statsmodels.genmod.tests import gee_gaussian_simulation_check as gees da,va = gees.gen_gendat_ar0(0.6)() ga = Gaussian() lhs = np.array([[0., 1, 1, 0, 0],]) rhs = np.r_[0.,] example = [] if 'constraint' in example: md = GEE(da.endog, da.exog, da.group, da.time, ga, va, constraint=(lhs, rhs)) mdf = md.fit() print(mdf.summary()) md2 = GEE(da.endog, da.exog, da.group, da.time, ga, va, constraint=None) mdf2 = md2.fit() print('\n\n') print(mdf2.summary()) mdf2.use_t = False mdf2.df_resid = np.diff(mdf2.model.exog.shape) tt2 = mdf2.t_test(np.eye(len(mdf2.params))) # need master to get wald_test #print mdf2.wald_test(np.eye(len(mdf2.params))[1:]) mdf2.predict(da.exog.mean(0), offset=0) # -0.10867809062890971 marg2 = GEEMargins(mdf2, ()) print(marg2.summary()) mdf_nc = md2.fit(cov_type='naive') mdf_bc = md2.fit(cov_type='bias_reduced') mdf_nc.use_t = False mdf_nc.df_resid = np.diff(mdf2.model.exog.shape) mdf_bc.use_t = False mdf_bc.df_resid = np.diff(mdf2.model.exog.shape) tt_nc = mdf_nc.t_test(np.eye(len(mdf2.params))) tt_bc = mdf_bc.t_test(np.eye(len(mdf2.params))) print('\nttest robust') print(tt2) print('\nttest naive') print(tt_nc) print('\nttest bias corrected') print(tt_bc) print("\nbse after fit option ") bse = np.column_stack((mdf2.bse, mdf2.bse, mdf_nc.bse, mdf_bc.bse)) print(bse) print("\nimplemented `standard_errors`") bse2 = np.column_stack((mdf2.bse, mdf2.standard_errors(), mdf2.standard_errors(covariance_type='naive'), mdf2.standard_errors(covariance_type='bias_reduced'))) print(bse2) print("bse and `standard_errors` agree:", np.allclose(bse, bse2)) print("\nimplied standard errors in t_test") bse1 = np.column_stack((mdf2.bse, tt2.sd, tt_nc.sd, tt_bc.sd)) print(bse1) print("t_test uses correct cov_params:", np.allclose(bse1, bse2)) statsmodels-0.12.2/statsmodels/examples/try_gof_chisquare.py000066400000000000000000000063001400612667500244130ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Thu Feb 28 15:37:53 2013 Author: Josef Perktold """ import numpy as np from scipy import stats from statsmodels.stats.gof import (chisquare, chisquare_power, chisquare_effectsize) from numpy.testing import assert_almost_equal nobs = 30000 n_bins = 5 probs = 1./np.arange(2, n_bins + 2) probs /= probs.sum() #nicer probs = np.round(probs, 2) probs[-1] = 1 - probs[:-1].sum() print("probs", probs) probs_d = probs.copy() delta = 0.01 probs_d[0] += delta probs_d[1] -= delta probs_cs = probs.cumsum() #rvs = np.random.multinomial(n_bins, probs, size=10) #rvs = np.round(np.random.randn(10), 2) rvs = np.argmax(np.random.rand(nobs,1) < probs_cs, 1) print(probs) print(np.bincount(rvs) * (1. / nobs)) freq = np.bincount(rvs) print(stats.chisquare(freq, nobs*probs)) print('null', chisquare(freq, nobs*probs)) print('delta', chisquare(freq, nobs*probs_d)) chisq_null, pval_null = chisquare(freq, nobs*probs) # effect size ? d_null = ((freq / float(nobs) - probs)**2 / probs).sum() print(d_null) d_delta = ((freq / float(nobs) - probs_d)**2 / probs_d).sum() print(d_delta) d_null_alt = ((probs - probs_d)**2 / probs_d).sum() print(d_null_alt) print('\nchisquare with value') chisq, pval = chisquare(freq, nobs*probs_d) print(stats.ncx2.sf(chisq_null, n_bins, 0.001 * nobs)) print(stats.ncx2.sf(chisq, n_bins, 0.001 * nobs)) print(stats.ncx2.sf(chisq, n_bins, d_delta * nobs)) print(chisquare(freq, nobs*probs_d, value=np.sqrt(d_delta))) print(chisquare(freq, nobs*probs_d, value=np.sqrt(chisq / nobs))) print() assert_almost_equal(stats.chi2.sf(d_delta * nobs, n_bins - 1), chisquare(freq, nobs*probs_d)[1], decimal=13) crit = stats.chi2.isf(0.05, n_bins - 1) power = stats.ncx2.sf(crit, n_bins-1, 0.001**2 * nobs) #> library(pwr) #> tr = pwr.chisq.test(w =0.001, N =30000 , df = 5-1, sig.level = 0.05, power = NULL) assert_almost_equal(power, 0.05147563, decimal=7) effect_size = 0.001 power = chisquare_power(effect_size, nobs, n_bins, alpha=0.05) assert_almost_equal(power, 0.05147563, decimal=7) print(chisquare(freq, nobs*probs, value=0, ddof=0)) d_null_alt = ((probs - probs_d)**2 / probs).sum() print(chisquare(freq, nobs*probs, value=np.sqrt(d_null_alt), ddof=0)) #Monte Carlo to check correct size and power of test d_delta_r = chisquare_effectsize(probs, probs_d) n_rep = 10000 nobs = 3000 res_boots = np.zeros((n_rep, 6)) for i in range(n_rep): rvs = np.argmax(np.random.rand(nobs,1) < probs_cs, 1) freq = np.bincount(rvs) res1 = chisquare(freq, nobs*probs) res2 = chisquare(freq, nobs*probs_d) res3 = chisquare(freq, nobs*probs_d, value=d_delta_r) res_boots[i] = [res1[0], res2[0], res3[0], res1[1], res2[1], res3[1]] alpha = np.array([0.01, 0.05, 0.1, 0.25, 0.5]) chi2_power = chisquare_power(chisquare_effectsize(probs, probs_d), 3000, n_bins, alpha=[0.01, 0.05, 0.1, 0.25, 0.5]) print((res_boots[:, 3:] < 0.05).mean(0)) reject_freq = (res_boots[:, 3:, None] < alpha).mean(0) reject = (res_boots[:, 3:, None] < alpha).sum(0) desired = np.column_stack((alpha, chi2_power, alpha)).T print('relative difference Monte Carlo rejection and expected (in %)') print((reject_freq / desired - 1) * 100) statsmodels-0.12.2/statsmodels/examples/try_polytrend.py000066400000000000000000000025661400612667500236260ustar00rootroot00000000000000 import numpy as np import matplotlib.pyplot as plt #import statsmodels.linear_model.regression as smreg from scipy import special import statsmodels.api as sm from statsmodels.datasets.macrodata import data dta = data.load(as_pandas=False) gdp = np.log(dta.data['realgdp']) maxorder = 20 polybase = special.chebyt polybase = special.legendre t = np.linspace(-1,1,len(gdp)) exog = np.column_stack([polybase(i)(t) for i in range(maxorder)]) fitted = [sm.OLS(gdp, exog[:, :maxr]).fit().fittedvalues for maxr in range(2,maxorder)] print((np.corrcoef(exog[:,1:6], rowvar=0)*10000).astype(int)) plt.figure() plt.plot(gdp, 'o') for i in range(maxorder-2): plt.plot(fitted[i]) plt.figure() #plt.plot(gdp, 'o') for i in range(maxorder-4, maxorder-2): #plt.figure() plt.plot(gdp - fitted[i]) plt.title(str(i+2)) plt.figure() plt.plot(gdp, '.') plt.plot(fitted[-1], lw=2, color='r') plt.plot(fitted[0], lw=2, color='g') plt.title('GDP and Polynomial Trend') plt.figure() plt.plot(gdp - fitted[-1], lw=2, color='r') plt.plot(gdp - fitted[0], lw=2, color='g') plt.title('Residual GDP minus Polynomial Trend (green: linear, red: legendre(20))') #orthonormalize an exog using QR ex2 = t[:,None]**np.arange(6) #np.vander has columns reversed q2,r2 = np.linalg.qr(ex2, mode='full') np.max(np.abs(np.dot(q2.T, q2)-np.eye(6))) plt.figure() plt.plot(q2, lw=2) plt.show() statsmodels-0.12.2/statsmodels/examples/try_power.py000066400000000000000000000046141400612667500227360ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sat Mar 02 14:38:17 2013 Author: Josef Perktold """ import statsmodels.stats.power as smp sigma=1 d=0.3 nobs=80 alpha=0.05 print(smp.normal_power(d, nobs/2, 0.05)) print(smp.NormalIndPower().power(d, nobs, 0.05)) print(smp.NormalIndPower().solve_power(effect_size=0.3, nobs1=80, alpha=0.05, power=None)) print(0.475100870572638, 'R') norm_pow = smp.normal_power(-0.01, nobs/2, 0.05) norm_pow_R = 0.05045832927039234 #value from R: >pwr.2p.test(h=0.01,n=80,sig.level=0.05,alternative="two.sided") print('norm_pow', norm_pow, norm_pow - norm_pow_R) norm_pow = smp.NormalIndPower().power(0.01, nobs, 0.05, alternative="larger") norm_pow_R = 0.056869534873146124 #value from R: >pwr.2p.test(h=0.01,n=80,sig.level=0.05,alternative="greater") print('norm_pow', norm_pow, norm_pow - norm_pow_R) # Note: negative effect size is same as switching one-sided alternative # TODO: should I switch to larger/smaller instead of "one-sided" options norm_pow = smp.NormalIndPower().power(-0.01, nobs, 0.05, alternative="larger") norm_pow_R = 0.0438089705093578 #value from R: >pwr.2p.test(h=0.01,n=80,sig.level=0.05,alternative="less") print('norm_pow', norm_pow, norm_pow - norm_pow_R) #Note: I use n_bins and ddof instead of df # pwr.chisq.test(w=0.289,df=(4-1),N=100,sig.level=0.05) chi2_pow = smp.GofChisquarePower().power(0.289, 100, 4, 0.05) chi2_pow_R = 0.675077657003721 print('chi2_pow', chi2_pow, chi2_pow - chi2_pow_R) chi2_pow = smp.GofChisquarePower().power(0.01, 100, 4, 0.05) chi2_pow_R = 0.0505845519208533 print('chi2_pow', chi2_pow, chi2_pow - chi2_pow_R) chi2_pow = smp.GofChisquarePower().power(2, 100, 4, 0.05) chi2_pow_R = 1 print('chi2_pow', chi2_pow, chi2_pow - chi2_pow_R) chi2_pow = smp.GofChisquarePower().power(0.9, 100, 4, 0.05) chi2_pow_R = 0.999999999919477 print('chi2_pow', chi2_pow, chi2_pow - chi2_pow_R, 'lower precision ?') chi2_pow = smp.GofChisquarePower().power(0.8, 100, 4, 0.05) chi2_pow_R = 0.999999968205591 print('chi2_pow', chi2_pow, chi2_pow - chi2_pow_R) def cohen_es(*args, **kwds): print("You better check what's a meaningful effect size for your question.") #BUG: after fixing 2.sided option, 2 rejection areas tt_pow = smp.TTestPower().power(effect_size=0.01, nobs=nobs, alpha=0.05) tt_pow_R = 0.05089485285965 # value from> pwr.t.test(d=0.01,n=80,sig.level=0.05,type="one.sample",alternative="two.sided") print('tt_pow', tt_pow, tt_pow - tt_pow_R) statsmodels-0.12.2/statsmodels/examples/try_power2.py000066400000000000000000000057331400612667500230230ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Mar 13 13:06:14 2013 Author: Josef Perktold """ from statsmodels.stats.power import TTestPower, TTestIndPower, tt_solve_power if __name__ == '__main__': effect_size, alpha, power = 0.5, 0.05, 0.8 ttest_pow = TTestPower() print('\nroundtrip - root with respect to all variables') print('\n calculated, desired') nobs_p = ttest_pow.solve_power(effect_size=effect_size, nobs=None, alpha=alpha, power=power) print('nobs ', nobs_p) print('effect', ttest_pow.solve_power(effect_size=None, nobs=nobs_p, alpha=alpha, power=power), effect_size) print('alpha ', ttest_pow.solve_power(effect_size=effect_size, nobs=nobs_p, alpha=None, power=power), alpha) print('power ', ttest_pow.solve_power(effect_size=effect_size, nobs=nobs_p, alpha=alpha, power=None), power) print('\nroundtrip - root with respect to all variables') print('\n calculated, desired') print('nobs ', tt_solve_power(effect_size=effect_size, nobs=None, alpha=alpha, power=power), nobs_p) print('effect', tt_solve_power(effect_size=None, nobs=nobs_p, alpha=alpha, power=power), effect_size) print('alpha ', tt_solve_power(effect_size=effect_size, nobs=nobs_p, alpha=None, power=power), alpha) print('power ', tt_solve_power(effect_size=effect_size, nobs=nobs_p, alpha=alpha, power=None), power) print('\none sided') nobs_p1 = tt_solve_power(effect_size=effect_size, nobs=None, alpha=alpha, power=power, alternative='larger') print('nobs ', nobs_p1) print('effect', tt_solve_power(effect_size=None, nobs=nobs_p1, alpha=alpha, power=power, alternative='larger'), effect_size) print('alpha ', tt_solve_power(effect_size=effect_size, nobs=nobs_p1, alpha=None, power=power, alternative='larger'), alpha) print('power ', tt_solve_power(effect_size=effect_size, nobs=nobs_p1, alpha=alpha, power=None, alternative='larger'), power) #start_ttp = dict(effect_size=0.01, nobs1=10., alpha=0.15, power=0.6) ttind_solve_power = TTestIndPower().solve_power print('\nroundtrip - root with respect to all variables') print('\n calculated, desired') nobs_p2 = ttind_solve_power(effect_size=effect_size, nobs1=None, alpha=alpha, power=power) print('nobs ', nobs_p2) print('effect', ttind_solve_power(effect_size=None, nobs1=nobs_p2, alpha=alpha, power=power), effect_size) print('alpha ', ttind_solve_power(effect_size=effect_size, nobs1=nobs_p2, alpha=None, power=power), alpha) print('power ', ttind_solve_power(effect_size=effect_size, nobs1=nobs_p2, alpha=alpha, power=None), power) print('ratio ', ttind_solve_power(effect_size=effect_size, nobs1=nobs_p2, alpha=alpha, power=power, ratio=None), 1) print('\ncheck ratio') print('smaller power', ttind_solve_power(effect_size=effect_size, nobs1=nobs_p2, alpha=alpha, power=0.7, ratio=None), '< 1') print('larger power ', ttind_solve_power(effect_size=effect_size, nobs1=nobs_p2, alpha=alpha, power=0.9, ratio=None), '> 1') statsmodels-0.12.2/statsmodels/examples/try_tukey_hsd.py000066400000000000000000000146011400612667500235760ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Mar 28 15:34:18 2012 Author: Josef Perktold """ from io import StringIO import numpy as np from numpy.testing import assert_almost_equal, assert_equal from scipy import stats from statsmodels.stats.libqsturng import qsturng from statsmodels.stats.multicomp import tukeyhsd import statsmodels.stats.multicomp as multi ss = '''\ 43.9 1 1 39.0 1 2 46.7 1 3 43.8 1 4 44.2 1 5 47.7 1 6 43.6 1 7 38.9 1 8 43.6 1 9 40.0 1 10 89.8 2 1 87.1 2 2 92.7 2 3 90.6 2 4 87.7 2 5 92.4 2 6 86.1 2 7 88.1 2 8 90.8 2 9 89.1 2 10 68.4 3 1 69.3 3 2 68.5 3 3 66.4 3 4 70.0 3 5 68.1 3 6 70.6 3 7 65.2 3 8 63.8 3 9 69.2 3 10 36.2 4 1 45.2 4 2 40.7 4 3 40.5 4 4 39.3 4 5 40.3 4 6 43.2 4 7 38.7 4 8 40.9 4 9 39.7 4 10''' #idx Treatment StressReduction ss2 = '''\ 1 mental 2 2 mental 2 3 mental 3 4 mental 4 5 mental 4 6 mental 5 7 mental 3 8 mental 4 9 mental 4 10 mental 4 11 physical 4 12 physical 4 13 physical 3 14 physical 5 15 physical 4 16 physical 1 17 physical 1 18 physical 2 19 physical 3 20 physical 3 21 medical 1 22 medical 2 23 medical 2 24 medical 2 25 medical 3 26 medical 2 27 medical 3 28 medical 1 29 medical 3 30 medical 1''' ss3 = '''\ 1 24.5 1 23.5 1 26.4 1 27.1 1 29.9 2 28.4 2 34.2 2 29.5 2 32.2 2 30.1 3 26.1 3 28.3 3 24.3 3 26.2 3 27.8''' cylinders = np.array([8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 8, 8, 8, 8, 4, 4, 4, 4, 8, 8, 8, 8, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 4, 4, 8, 4, 6, 6, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4]) cyl_labels = np.array(['USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'France', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'Japan', 'USA', 'USA', 'USA', 'Japan', 'Germany', 'France', 'Germany', 'Sweden', 'Germany', 'USA', 'USA', 'USA', 'USA', 'USA', 'Germany', 'USA', 'USA', 'France', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'Germany', 'Japan', 'USA', 'USA', 'USA', 'USA', 'Germany', 'Japan', 'Japan', 'USA', 'Sweden', 'USA', 'France', 'Japan', 'Germany', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'Germany', 'Japan', 'Japan', 'USA', 'USA', 'Japan', 'Japan', 'Japan', 'Japan', 'Japan', 'Japan', 'USA', 'USA', 'USA', 'USA', 'Japan', 'USA', 'USA', 'USA', 'Germany', 'USA', 'USA', 'USA']) dta = np.recfromtxt(StringIO(ss), names=("Rust","Brand","Replication")) dta2 = np.recfromtxt(StringIO(ss2), names = ("idx", "Treatment", "StressReduction")) dta3 = np.recfromtxt(StringIO(ss3), names = ("Brand", "Relief")) #print tukeyhsd(dta['Brand'], dta['Rust']) def get_thsd(mci): var_ = np.var(mci.groupstats.groupdemean(), ddof=len(mci.groupsunique)) means = mci.groupstats.groupmean nobs = mci.groupstats.groupnobs resi = tukeyhsd(means, nobs, var_, df=None, alpha=0.05, q_crit=qsturng(0.95, len(means), (nobs-1).sum())) print(resi[4]) var2 = (mci.groupstats.groupvarwithin() * (nobs - 1)).sum() \ / (nobs - 1).sum() assert_almost_equal(var_, var2, decimal=14) return resi mc = multi.MultiComparison(dta['Rust'], dta['Brand']) res = mc.tukeyhsd() print(res) mc2 = multi.MultiComparison(dta2['StressReduction'], dta2['Treatment']) res2 = mc2.tukeyhsd() print(res2) mc2s = multi.MultiComparison(dta2['StressReduction'][3:29], dta2['Treatment'][3:29]) res2s = mc2s.tukeyhsd() print(res2s) res2s_001 = mc2s.tukeyhsd(alpha=0.01) #R result tukeyhsd2s = np.array([1.888889,0.8888889,-1,0.2658549,-0.5908785,-2.587133,3.511923,2.368656,0.5871331,0.002837638,0.150456,0.1266072]).reshape(3,4, order='F') assert_almost_equal(res2s_001.confint, tukeyhsd2s[:,1:3], decimal=3) mc3 = multi.MultiComparison(dta3['Relief'], dta3['Brand']) res3 = mc3.tukeyhsd() print(res3) tukeyhsd4 = multi.MultiComparison(cylinders, cyl_labels, group_order=["Sweden", "Japan", "Germany", "France", "USA"]) res4 = tukeyhsd4.tukeyhsd() print(res4) try: import matplotlib.pyplot as plt fig = res4.plot_simultaneous("USA") plt.show() except Exception as e: print(e) for mci in [mc, mc2, mc3]: get_thsd(mci) print(mc2.allpairtest(stats.ttest_ind, method='b')[0]) '''same as SAS: >>> np.var(mci.groupstats.groupdemean(), ddof=3) 4.6773333333333351 >>> var_ = np.var(mci.groupstats.groupdemean(), ddof=3) >>> tukeyhsd(means, nobs, var_, df=None, alpha=0.05, q_crit=qsturng(0.95, 3, 12))[4] array([[ 0.95263648, 8.24736352], [-3.38736352, 3.90736352], [-7.98736352, -0.69263648]]) >>> tukeyhsd(means, nobs, var_, df=None, alpha=0.05, q_crit=3.77278)[4] array([[ 0.95098508, 8.24901492], [-3.38901492, 3.90901492], [-7.98901492, -0.69098508]]) ''' ss5 = '''\ Comparisons significant at the 0.05 level are indicated by ***. BRAND Comparison Difference Between Means Simultaneous 95% Confidence Limits Sign. 2 - 3 4.340 0.691 7.989 *** 2 - 1 4.600 0.951 8.249 *** 3 - 2 -4.340 -7.989 -0.691 *** 3 - 1 0.260 -3.389 3.909 - 1 - 2 -4.600 -8.249 -0.951 *** 1 - 3 -0.260 -3.909 3.389 ''' ss5 = '''\ 2 - 3 4.340 0.691 7.989 *** 2 - 1 4.600 0.951 8.249 *** 3 - 2 -4.340 -7.989 -0.691 *** 3 - 1 0.260 -3.389 3.909 - 1 - 2 -4.600 -8.249 -0.951 *** 1 - 3 -0.260 -3.909 3.389 ''' dta5 = np.recfromtxt(StringIO(ss5), names = ('pair', 'mean', 'lower', 'upper', 'sig'), delimiter='\t') sas_ = dta5[[1,3,2]] confint1 = res3.confint confint2 = sas_[['lower','upper']].view(float).reshape((3,2)) assert_almost_equal(confint1, confint2, decimal=2) reject1 = res3.reject reject2 = sas_['sig'] == '***' assert_equal(reject1, reject2) meandiff1 = res3.meandiffs meandiff2 = sas_['mean'] assert_almost_equal(meandiff1, meandiff2, decimal=14) statsmodels-0.12.2/statsmodels/examples/tsa/000077500000000000000000000000001400612667500211145ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/examples/tsa/ar1cholesky.py000066400000000000000000000020211400612667500237060ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Thu Oct 21 15:42:18 2010 Author: josef-pktd """ import numpy as np from scipy import linalg def tiny2zero(x, eps = 1e-15): '''replace abs values smaller than eps by zero, makes copy ''' mask = np.abs(x.copy()) < eps x[mask] = 0 return x nobs = 5 autocov = 0.8**np.arange(nobs) #from statsmodels.tsa import arima_process as ap #autocov = ap.arma_acf([1, -0.8, 0.2], [1])[:10] autocov = np.array([ 3., 2., 1., 0.4, 0.12, 0.016, -0.0112, 0.016 , -0.0112 , -0.01216 , -0.007488 , -0.0035584])/3. autocov = autocov[:nobs] sigma = linalg.toeplitz(autocov) sigmainv = linalg.inv(sigma) c = linalg.cholesky(sigma, lower=True) ci = linalg.cholesky(sigmainv, lower=True) print(sigma) print(tiny2zero(ci/ci.max())) "this is the text book transformation" print('coefficient for first observation', np.sqrt(1-autocov[1]**2)) ci2 = ci[::-1,::-1].T print(tiny2zero(ci2/ci2.max())) print(np.dot(ci/ci.max(), np.ones(nobs))) print(np.dot(ci2/ci2.max(), np.ones(nobs))) statsmodels-0.12.2/statsmodels/examples/tsa/arma_plots.py000066400000000000000000000046141400612667500236340ustar00rootroot00000000000000'''Plot acf and pacf for some ARMA(1,1) ''' import numpy as np import matplotlib.pyplot as plt import matplotlib.ticker as mticker import statsmodels.tsa.arima_process as tsp from statsmodels.graphics.tsaplots import plotacf np.set_printoptions(precision=2) arcoefs = [0.9, 0., -0.5] #[0.9, 0.5, 0.1, 0., -0.5] macoefs = [0.9, 0., -0.5] #[0.9, 0.5, 0.1, 0., -0.5] nsample = 1000 nburnin = 1000 sig = 1 fig = plt.figure(figsize=(8, 13)) fig.suptitle('ARMA: Autocorrelation (left) and Partial Autocorrelation (right)') subplotcount = 1 nrows = 4 for arcoef in arcoefs[:-1]: for macoef in macoefs[:-1]: ar = np.r_[1., -arcoef] ma = np.r_[1., macoef] #from statsmodels.sandbox.tsa.fftarma import ArmaFft as FftArmaProcess #y = tsp.arma_generate_sample(ar,ma,nsample, sig, burnin) #armaprocess = FftArmaProcess(ar, ma, nsample) #TODO: make n optional #armaprocess.plot4() armaprocess = tsp.ArmaProcess(ar, ma) acf = armaprocess.acf(20)[:20] pacf = armaprocess.pacf(20)[:20] ax = fig.add_subplot(nrows, 2, subplotcount) plotacf(acf, ax=ax) ## ax.set_title('Autocorrelation \nar=%s, ma=%rs' % (ar, ma), ## size='xx-small') ax.text(0.7, 0.6, 'ar =%s \nma=%s' % (ar, ma), transform=ax.transAxes, horizontalalignment='left', #'right', size='xx-small') ax.set_xlim(-1,20) subplotcount +=1 ax = fig.add_subplot(nrows, 2, subplotcount) plotacf(pacf, ax=ax) ## ax.set_title('Partial Autocorrelation \nar=%s, ma=%rs' % (ar, ma), ## size='xx-small') ax.text(0.7, 0.6, 'ar =%s \nma=%s' % (ar, ma), transform=ax.transAxes, horizontalalignment='left', #'right', size='xx-small') ax.set_xlim(-1,20) subplotcount +=1 axs = fig.axes ### turn of the 2nd column y tick labels ##for ax in axs[1::2]:#[:,1].flat: ## for label in ax.get_yticklabels(): label.set_visible(False) # turn off all but the bottom xtick labels for ax in axs[:-2]: for label in ax.get_xticklabels(): label.set_visible(False) # use a MaxNLocator on the first column y axis if you have a bunch of # rows to avoid bunching; example below uses at most 3 ticks for ax in axs: #[::2]:#[:,1].flat: ax.yaxis.set_major_locator( mticker.MaxNLocator(3 )) plt.show() statsmodels-0.12.2/statsmodels/examples/tsa/compare_arma.py000066400000000000000000000042501400612667500241150ustar00rootroot00000000000000from time import time from statsmodels.tsa.arma_mle import Arma from statsmodels.tsa.api import ARMA import numpy as np print("Battle of the dueling ARMAs") y_arma22 = np.loadtxt(r'C:\Josef\eclipsegworkspace\statsmodels-josef-experimental-gsoc\scikits\statsmodels\tsa\y_arma22.txt') arma1 = Arma(y_arma22) arma2 = ARMA(y_arma22) print("The actual results from gretl exact mle are") params_mle = np.array([.826990, -.333986, .0362419, -.792825]) sigma_mle = 1.094011 llf_mle = -1510.233 print("params: ", params_mle) print("sigma: ", sigma_mle) print("llf: ", llf_mle) print("The actual results from gretl css are") params_css = np.array([.824810, -.337077, .0407222, -.789792]) sigma_css = 1.095688 llf_css = -1507.301 results = [] results += ["gretl exact mle", params_mle, sigma_mle, llf_mle] results += ["gretl css", params_css, sigma_css, llf_css] t0 = time() print("Exact MLE - Kalman filter version using l_bfgs_b") arma2.fit(order=(2,2), trend='nc') t1 = time() print("params: ", arma2.params) print("sigma: ", arma2.sigma2**.5) arma2.llf = arma2.loglike(arma2._invtransparams(arma2.params)) results += ["exact mle kalmanf", arma2.params, arma2.sigma2**.5, arma2.llf] print('time used:', t1-t0) t1=time() print("CSS MLE - ARMA Class") arma2.fit(order=(2,2), trend='nc', method="css") t2=time() arma2.llf = arma2.loglike_css(arma2._invtransparams(arma2.params)) print("params: ", arma2.params) print("sigma: ", arma2.sigma2**.5) results += ["css kalmanf", arma2.params, arma2.sigma2**.5, arma2.llf] print('time used:', t2-t1) print("Arma.fit_mle results") # have to set nar and nma manually arma1.nar = 2 arma1.nma = 2 t2=time() ret = arma1.fit_mle() t3=time() print("params, first 4, sigma, last 1 ", ret.params) results += ["Arma.fit_mle ", ret.params[:4], ret.params[-1], ret.llf] print('time used:', t3-t2) print("Arma.fit method = \"ls\"") t3=time() ret2 = arma1.fit(order=(2,0,2), method="ls") t4=time() print(ret2[0]) results += ["Arma.fit ls", ret2[0]] print('time used:', t4-t3) print("Arma.fit method = \"CLS\"") t4=time() ret3 = arma1.fit(order=(2,0,2), method="None") t5=time() print(ret3) results += ["Arma.fit other", ret3[0]] print('time used:', t5-t4) for i in results: print(i) statsmodels-0.12.2/statsmodels/examples/tsa/ex_arma_all.py000066400000000000000000000036321400612667500237360ustar00rootroot00000000000000 import numpy as np from numpy.testing import assert_almost_equal import matplotlib.pyplot as plt import statsmodels.sandbox.tsa.fftarma as fa from statsmodels.tsa.descriptivestats import TsaDescriptive from statsmodels.tsa.arma_mle import Arma from statsmodels.tsa.arima_model import ARMA from statsmodels.tsa.arima_process import arma_generate_sample from statsmodels.miscmodels.tmodel import TArma x = fa.ArmaFft([1, -0.5], [1., 0.4], 40).generate_sample(size=200, burnin=1000) d = TsaDescriptive(x) d.plot4() #d.fit(order=(1,1)) d.fit((1,1), trend='nc') print(d.res.params) modc = Arma(x) resls = modc.fit(order=(1,1)) print(resls[0]) rescm = modc.fit_mle(order=(1,1), start_params=[-0.4,0.4, 1.]) print(rescm.params) #decimal 1 corresponds to threshold of 5% difference assert_almost_equal(resls[0] / d.res.params, 1, decimal=1) assert_almost_equal(rescm.params[:-1] / d.res.params, 1, decimal=1) #copied to tsa.tests plt.figure() plt.plot(x, 'b-o') plt.plot(modc.predicted(), 'r-') plt.figure() plt.plot(modc.error_estimate) #plt.show() modct = TArma(x) reslst = modc.fit(order=(1,1)) print(reslst[0]) rescmt = modct.fit_mle(order=(1,1), start_params=[-0.4,0.4, 10, 1.],maxiter=500, maxfun=500) print(rescmt.params) mkf = ARMA(x) ##rkf = mkf.fit((1,1)) ##rkf.params rkf = mkf.fit((1,1), trend='nc') print(rkf.params) np.random.seed(12345) y_arma22 = arma_generate_sample([1.,-.85,.35, -0.1],[1,.25,-.7], nsample=1000) ##arma22 = ARMA(y_arma22) ##res22 = arma22.fit(trend = 'nc', order=(2,2)) ##print 'kf ',res22.params ##res22css = arma22.fit(method='css',trend = 'nc', order=(2,2)) ##print 'css', res22css.params mod22 = Arma(y_arma22) resls22 = mod22.fit(order=(2,2)) print('ls ', resls22[0]) resmle22 = mod22.fit_mle(order=(2,2), maxfun=2000) print('mle', resmle22.params) f = mod22.forecast() f3 = mod22.forecast3(start=900)[-20:] print(y_arma22[-10:]) print(f[-20:]) print(f3[-109:-90]) plt.show() statsmodels-0.12.2/statsmodels/examples/tsa/ex_coint.py000066400000000000000000000002621400612667500232760ustar00rootroot00000000000000 from statsmodels.tsa.tests.test_stattools import TestCoint_t #test whether t-test for cointegration equals that produced by Stata tst = TestCoint_t() print(tst.test_tstat()) statsmodels-0.12.2/statsmodels/examples/tsa/ex_var.py000066400000000000000000000023521400612667500227540ustar00rootroot00000000000000 import numpy as np import statsmodels.api as sm from statsmodels.tsa.api import VAR # some example data mdata = sm.datasets.macrodata.load(as_pandas=False).data mdata = mdata[['realgdp','realcons','realinv']] names = mdata.dtype.names data = mdata.view((float,3)) use_growthrate = False #True #False if use_growthrate: data = 100 * 4 * np.diff(np.log(data), axis=0) model = VAR(data, names=names) res = model.fit(4) nobs_all = data.shape[0] #in-sample 1-step ahead forecasts fc_in = np.array([np.squeeze(res.forecast(model.y[t-20:t], 1)) for t in range(nobs_all-6,nobs_all)]) print(fc_in - res.fittedvalues[-6:]) #out-of-sample 1-step ahead forecasts fc_out = np.array([np.squeeze(VAR(data[:t]).fit(2).forecast(data[t-20:t], 1)) for t in range(nobs_all-6,nobs_all)]) print(fc_out - data[nobs_all-6:nobs_all]) print(fc_out - res.fittedvalues[-6:]) #out-of-sample h-step ahead forecasts h = 2 fc_out = np.array([VAR(data[:t]).fit(2).forecast(data[t-20:t], h)[-1] for t in range(nobs_all-6-h+1,nobs_all-h+1)]) print(fc_out - data[nobs_all-6:nobs_all]) #out-of-sample forecast error print(fc_out - res.fittedvalues[-6:]) #import matplotlib.pyplot as plt res.plot_forecast(20) #plt.show() statsmodels-0.12.2/statsmodels/examples/tsa/ex_var_reorder.py000066400000000000000000000001721400612667500244740ustar00rootroot00000000000000 from statsmodels.tsa.vector_ar.tests.test_var import TestVARResults test_VAR = TestVARResults() test_VAR.test_reorder() statsmodels-0.12.2/statsmodels/examples/tsa/lagpolynomial.py000066400000000000000000000020631400612667500243360ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Oct 22 08:13:38 2010 Author: josef-pktd License: BSD (3-clause) """ import numpy as np from numpy import polynomial as npp class LagPolynomial(npp.Polynomial): #def __init__(self, maxlag): def pad(self, maxlag): return LagPolynomial(np.r_[self.coef, np.zeros(maxlag-len(self.coef))]) def padflip(self, maxlag): return LagPolynomial(np.r_[self.coef, np.zeros(maxlag-len(self.coef))][::-1]) def flip(self): '''reverse polynomial coefficients ''' return LagPolynomial(self.coef[::-1]) def div(self, other, maxlag=None): '''padded division, pads numerator with zeros to maxlag ''' if maxlag is None: maxlag = max(len(self.coef), len(other.coef)) + 1 return (self.padflip(maxlag) / other.flip()).flip() def filter(self, arr): return (self * arr).coef[:-len(self.coef)] #trim to end ar = LagPolynomial([1, -0.8]) arpad = ar.pad(10) ma = LagPolynomial([1, 0.1]) mapad = ma.pad(10) unit = LagPolynomial([1]) statsmodels-0.12.2/statsmodels/examples/tsa/try_ar.py000066400000000000000000000047371400612667500230010ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Thu Oct 21 21:45:24 2010 Author: josef-pktd """ import numpy as np from scipy import signal def armaloop(arcoefs, macoefs, x): '''get arma recursion in simple loop for simplicity assumes that ma polynomial is not longer than the ar-polynomial Parameters ---------- arcoefs : array_like autoregressive coefficients in right hand side parameterization macoefs : array_like moving average coefficients, without leading 1 Returns ------- y : ndarray predicted values, initial values are the same as the observed values e : ndarray predicted residuals, zero for initial observations Notes ----- Except for the treatment of initial observations this is the same as using scipy.signal.lfilter, which is much faster. Written for testing only ''' arcoefs_r = np.asarray(arcoefs) macoefs_r = np.asarray(macoefs) x = np.asarray(x) nobs = x.shape[0] #assume ar longer than ma arlag = arcoefs_r.shape[0] malag = macoefs_r.shape[0] maxlag = max(arlag, malag) print(maxlag) y = np.zeros(x.shape, float) e = np.zeros(x.shape, float) y[:maxlag] = x[:maxlag] #if malag > arlaga: for t in range(arlag, maxlag): y[t] = (x[t-arlag:t] * arcoefs_r).sum(0) + (e[:t] * macoefs_r[:t]).sum(0) e[t] = x[t] - y[t] for t in range(maxlag, nobs): #wrong broadcasting, 1d only y[t] = (x[t-arlag:t] * arcoefs_r).sum(0) + (e[t-malag:t] * macoefs_r).sum(0) e[t] = x[t] - y[t] return y, e arcoefs, macoefs = -np.array([1, -0.8, 0.2])[1:], np.array([1., 0.5, 0.1])[1:] print(armaloop(arcoefs, macoefs, np.ones(10))) print(armaloop([0.8], [], np.ones(10))) print(armaloop([0.8], [], np.arange(2,10))) y, e = armaloop([0.1], [0.8], np.arange(2,10)) print(e) print(signal.lfilter(np.array([1, -0.1]), np.array([1., 0.8]), np.arange(2,10))) y, e = armaloop([], [0.8], np.ones(10)) print(e) print(signal.lfilter(np.array([1, -0.]), np.array([1., 0.8]), np.ones(10))) ic=signal.lfiltic(np.array([1, -0.1]), np.array([1., 0.8]), np.ones([0]), np.array([1])) print(signal.lfilter(np.array([1, -0.1]), np.array([1., 0.8]), np.ones(10), zi=ic)) zi = signal.lfilter_zi(np.array([1, -0.8, 0.2]), np.array([1., 0, 0])) print(signal.lfilter(np.array([1, -0.1]), np.array([1., 0.8]), np.ones(10), zi=zi)) print(signal.filtfilt(np.array([1, -0.8]), np.array([1.]), np.ones(10))) #todo write examples/test across different versions statsmodels-0.12.2/statsmodels/examples/tut_ols_ancova.py000066400000000000000000000045551400612667500237300ustar00rootroot00000000000000'''Examples OLS Note: uncomment plt.show() to display graphs Summary: ======== Relevant part of construction of design matrix xg includes group numbers/labels, x1 is continuous explanatory variable >>> dummy = (xg[:,None] == np.unique(xg)).astype(float) >>> X = np.c_[x1, dummy[:,1:], np.ones(nsample)] Estimate the model >>> res2 = sm.OLS(y, X).fit() >>> print res2.params [ 1.00901524 3.08466166 -2.84716135 9.94655423] >>> print res2.bse [ 0.07499873 0.71217506 1.16037215 0.38826843] >>> prstd, iv_l, iv_u = wls_prediction_std(res2) "Test hypothesis that all groups have same intercept" >>> R = [[0, 1, 0, 0], ... [0, 0, 1, 0]] >>> print res2.f_test(R) strongly rejected because differences in intercept are very large ''' import numpy as np import statsmodels.api as sm import matplotlib.pyplot as plt from statsmodels.sandbox.regression.predstd import wls_prediction_std #fix a seed for these examples np.random.seed(98765789) #OLS with dummy variables, similar to ANCOVA #------------------------------------------- #construct simulated example: #3 groups common slope but different intercepts nsample = 50 x1 = np.linspace(0, 20, nsample) sig = 1. #suppose observations from 3 groups xg = np.zeros(nsample, int) xg[20:40] = 1 xg[40:] = 2 #print xg dummy = (xg[:,None] == np.unique(xg)).astype(float) #use group 0 as benchmark X = np.c_[x1, dummy[:,1:], np.ones(nsample)] beta = [1., 3, -3, 10] y_true = np.dot(X, beta) y = y_true + sig * np.random.normal(size=nsample) #estimate #~~~~~~~~ res2 = sm.OLS(y, X).fit() #print "estimated parameters: x d1-d0 d2-d0 constant" print(res2.params) #print "standard deviation of parameter estimates" print(res2.bse) prstd, iv_l, iv_u = wls_prediction_std(res2) #print res.summary() #plot #~~~~ plt.figure() plt.plot(x1, y, 'o', x1, y_true, 'b-') plt.plot(x1, res2.fittedvalues, 'r--.') plt.plot(x1, iv_u, 'r--') plt.plot(x1, iv_l, 'r--') plt.title('3 groups: different intercepts, common slope; blue: true, red: OLS') plt.show() #Test hypothesis that all groups have same intercept #~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ R = [[0, 1, 0, 0], [0, 0, 1, 0]] # F test joint hypothesis R * beta = 0 # i.e. coefficient on both dummy variables equal zero print("Test hypothesis that all groups have same intercept") print(res2.f_test(R)) statsmodels-0.12.2/statsmodels/examples/tut_ols_rlm_short.py000066400000000000000000000031131400612667500244570ustar00rootroot00000000000000'''Examples: comparing OLS and RLM robust estimators and outliers RLM is less influenced by outliers than OLS and has estimated slope closer to true slope and not tilted like OLS. Note: uncomment plt.show() to display graphs ''' import numpy as np #from scipy import stats import statsmodels.api as sm import matplotlib.pyplot as plt from statsmodels.sandbox.regression.predstd import wls_prediction_std #fix a seed for these examples np.random.seed(98765789) nsample = 50 x1 = np.linspace(0, 20, nsample) X = np.c_[x1, np.ones(nsample)] sig = 0.3 # smaller error variance makes OLS<->RLM contrast bigger beta = [0.5, 5.] y_true2 = np.dot(X, beta) y2 = y_true2 + sig*1. * np.random.normal(size=nsample) y2[[39,41,43,45,48]] -= 5 # add some outliers (10% of nsample) # Example: estimate linear function (true is linear) plt.figure() plt.plot(x1, y2, 'o', x1, y_true2, 'b-') res2 = sm.OLS(y2, X).fit() print("OLS: parameter estimates: slope, constant") print(res2.params) print("standard deviation of parameter estimates") print(res2.bse) prstd, iv_l, iv_u = wls_prediction_std(res2) plt.plot(x1, res2.fittedvalues, 'r-') plt.plot(x1, iv_u, 'r--') plt.plot(x1, iv_l, 'r--') #compare with robust estimator resrlm2 = sm.RLM(y2, X).fit() print("\nRLM: parameter estimates: slope, constant") print(resrlm2.params) print("standard deviation of parameter estimates") print(resrlm2.bse) plt.plot(x1, resrlm2.fittedvalues, 'g.-') plt.title('Data with Outliers; blue: true, red: OLS, green: RLM') # see also help(sm.RLM.fit) for more options and # module sm.robust.scale for scale options plt.show() statsmodels-0.12.2/statsmodels/formula/000077500000000000000000000000001400612667500201545ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/formula/__init__.py000066400000000000000000000002441400612667500222650ustar00rootroot00000000000000__all__ = ['handle_formula_data', 'test'] from .formulatools import handle_formula_data from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/formula/api.py000066400000000000000000000022251400612667500213000ustar00rootroot00000000000000import statsmodels.regression.linear_model as lm_ import statsmodels.discrete.discrete_model as dm_ import statsmodels.regression.mixed_linear_model as mlm_ import statsmodels.genmod.generalized_linear_model as glm_ import statsmodels.robust.robust_linear_model as roblm_ import statsmodels.regression.quantile_regression as qr_ import statsmodels.duration.hazard_regression as hr_ import statsmodels.genmod.generalized_estimating_equations as gee_ import statsmodels.gam.generalized_additive_model as gam_ gls = lm_.GLS.from_formula wls = lm_.WLS.from_formula ols = lm_.OLS.from_formula glsar = lm_.GLSAR.from_formula mixedlm = mlm_.MixedLM.from_formula glm = glm_.GLM.from_formula rlm = roblm_.RLM.from_formula mnlogit = dm_.MNLogit.from_formula logit = dm_.Logit.from_formula probit = dm_.Probit.from_formula poisson = dm_.Poisson.from_formula negativebinomial = dm_.NegativeBinomial.from_formula quantreg = qr_.QuantReg.from_formula phreg = hr_.PHReg.from_formula ordinal_gee = gee_.OrdinalGEE.from_formula nominal_gee = gee_.NominalGEE.from_formula gee = gee_.GEE.from_formula glmgam = gam_.GLMGam.from_formula del lm_, dm_, mlm_, glm_, roblm_, qr_, hr_, gee_, gam_ statsmodels-0.12.2/statsmodels/formula/formulatools.py000066400000000000000000000073331400612667500232620ustar00rootroot00000000000000import statsmodels.tools.data as data_util from patsy import dmatrices, NAAction import numpy as np # if users want to pass in a different formula framework, they can # add their handler here. how to do it interactively? # this is a mutable object, so editing it should show up in the below formula_handler = {} class NAAction(NAAction): # monkey-patch so we can handle missing values in 'extra' arrays later def _handle_NA_drop(self, values, is_NAs, origins): total_mask = np.zeros(is_NAs[0].shape[0], dtype=bool) for is_NA in is_NAs: total_mask |= is_NA good_mask = ~total_mask self.missing_mask = total_mask # "..." to handle 1- versus 2-dim indexing return [v[good_mask, ...] for v in values] def handle_formula_data(Y, X, formula, depth=0, missing='drop'): """ Returns endog, exog, and the model specification from arrays and formula. Parameters ---------- Y : array_like Either endog (the LHS) of a model specification or all of the data. Y must define __getitem__ for now. X : array_like Either exog or None. If all the data for the formula is provided in Y then you must explicitly set X to None. formula : str or patsy.model_desc You can pass a handler by import formula_handler and adding a key-value pair where the key is the formula object class and the value is a function that returns endog, exog, formula object. Returns ------- endog : array_like Should preserve the input type of Y,X. exog : array_like Should preserve the input type of Y,X. Could be None. """ # half ass attempt to handle other formula objects if isinstance(formula, tuple(formula_handler.keys())): return formula_handler[type(formula)] na_action = NAAction(on_NA=missing) if X is not None: if data_util._is_using_pandas(Y, X): result = dmatrices(formula, (Y, X), depth, return_type='dataframe', NA_action=na_action) else: result = dmatrices(formula, (Y, X), depth, return_type='dataframe', NA_action=na_action) else: if data_util._is_using_pandas(Y, None): result = dmatrices(formula, Y, depth, return_type='dataframe', NA_action=na_action) else: result = dmatrices(formula, Y, depth, return_type='dataframe', NA_action=na_action) # if missing == 'raise' there's not missing_mask missing_mask = getattr(na_action, 'missing_mask', None) if not np.any(missing_mask): missing_mask = None if len(result) > 1: # have RHS design design_info = result[1].design_info # detach it from DataFrame else: design_info = None # NOTE: is there ever a case where we'd need LHS design_info? return result, missing_mask, design_info def _remove_intercept_patsy(terms): """ Remove intercept from Patsy terms. """ from patsy.desc import INTERCEPT if INTERCEPT in terms: terms.remove(INTERCEPT) return terms def _has_intercept(design_info): from patsy.desc import INTERCEPT return INTERCEPT in design_info.terms def _intercept_idx(design_info): """ Returns boolean array index indicating which column holds the intercept. """ from patsy.desc import INTERCEPT from numpy import array return array([INTERCEPT == i for i in design_info.terms]) def make_hypotheses_matrices(model_results, test_formula): """ """ from patsy.constraint import linear_constraint exog_names = model_results.model.exog_names LC = linear_constraint(test_formula, exog_names) return LC statsmodels-0.12.2/statsmodels/formula/tests/000077500000000000000000000000001400612667500213165ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/formula/tests/__init__.py000066400000000000000000000000001400612667500234150ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/formula/tests/test_formula.py000066400000000000000000000210561400612667500244000ustar00rootroot00000000000000from statsmodels.compat.pandas import assert_series_equal from io import StringIO import warnings from statsmodels.formula.api import ols from statsmodels.formula.formulatools import make_hypotheses_matrices from statsmodels.tools import add_constant from statsmodels.datasets.longley import load, load_pandas from statsmodels.datasets import cpunish import numpy.testing as npt from statsmodels.tools.testing import assert_equal import numpy as np import pandas as pd import patsy import pytest longley_formula = 'TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR' class CheckFormulaOLS(object): @classmethod def setup_class(cls): cls.data = load(as_pandas=False) def test_endog_names(self): assert self.model.endog_names == 'TOTEMP' def test_exog_names(self): assert self.model.exog_names == ['Intercept', 'GNPDEFL', 'GNP', 'UNEMP', 'ARMED', 'POP', 'YEAR'] def test_design(self): npt.assert_equal(self.model.exog, add_constant(self.data.exog, prepend=True)) def test_endog(self): npt.assert_equal(self.model.endog, self.data.endog) @pytest.mark.smoke def test_summary(self): with warnings.catch_warnings(): warnings.filterwarnings("ignore", "kurtosistest only valid for n>=20") self.model.fit().summary() class TestFormulaPandas(CheckFormulaOLS): @classmethod def setup_class(cls): data = load_pandas().data cls.model = ols(longley_formula, data) super(TestFormulaPandas, cls).setup_class() class TestFormulaDict(CheckFormulaOLS): @classmethod def setup_class(cls): data = dict((k, v.tolist()) for k, v in load_pandas().data.items()) cls.model = ols(longley_formula, data) super(TestFormulaDict, cls).setup_class() def test_tests(): formula = 'TOTEMP ~ GNPDEFL + GNP + UNEMP + ARMED + POP + YEAR' dta = load_pandas().data results = ols(formula, dta).fit() test_formula = '(GNPDEFL = GNP), (UNEMP = 2), (YEAR/1829 = 1)' LC = make_hypotheses_matrices(results, test_formula) R = LC.coefs Q = LC.constants npt.assert_almost_equal(R, [[0, 1, -1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1./1829]], 8) npt.assert_array_equal(Q, [[0], [2], [1]]) def test_formula_labels(): # make sure labels pass through patsy as expected # data(Duncan) from car in R dta = StringIO('"type","income","education","prestige"\n' '"accountant","prof",62,86,82\n' '"pilot","prof",72,76,83\n' '"architect","prof",75,92,90\n' '"author","prof",55,90,76\n' '"chemist","prof",64,86,90\n' '"minister","prof",21,84,87\n' '"professor","prof",64,93,93\n' '"dentist","prof",80,100,90\n' '"reporter","wc",67,87,52\n' '"engineer","prof",72,86,88\n' '"undertaker","prof",42,74,57\n' '"lawyer","prof",76,98,89\n' '"physician","prof",76,97,97\n' '"welfare.worker","prof",41,84,59\n' '"teacher","prof",48,91,73\n' '"conductor","wc",76,34,38\n' '"contractor","prof",53,45,76\n' '"factory.owner","prof",60,56,81\n' '"store.manager","prof",42,44,45\n' '"banker","prof",78,82,92\n' '"bookkeeper","wc",29,72,39\n' '"mail.carrier","wc",48,55,34\n' '"insurance.agent","wc",55,71,41\n' '"store.clerk","wc",29,50,16\n' '"carpenter","bc",21,23,33\n' '"electrician","bc",47,39,53\n' '"RR.engineer","bc",81,28,67\n' '"machinist","bc",36,32,57\n' '"auto.repairman","bc",22,22,26\n' '"plumber","bc",44,25,29\n' '"gas.stn.attendant","bc",15,29,10\n' '"coal.miner","bc",7,7,15\n' '"streetcar.motorman","bc",42,26,19\n' '"taxi.driver","bc",9,19,10\n' '"truck.driver","bc",21,15,13\n' '"machine.operator","bc",21,20,24\n' '"barber","bc",16,26,20\n' '"bartender","bc",16,28,7\n' '"shoe.shiner","bc",9,17,3\n' '"cook","bc",14,22,16\n' '"soda.clerk","bc",12,30,6\n' '"watchman","bc",17,25,11\n' '"janitor","bc",7,20,8\n' '"policeman","bc",34,47,41\n' '"waiter","bc",8,32,10') from pandas import read_csv dta = read_csv(dta) model = ols("prestige ~ income + education", dta).fit() assert_equal(model.fittedvalues.index, dta.index) def test_formula_predict(): # `log` is needed in the namespace for patsy to find from numpy import log # noqa:F401 formula = """TOTEMP ~ log(GNPDEFL) + log(GNP) + UNEMP + ARMED + POP + YEAR""" data = load_pandas() dta = load_pandas().data results = ols(formula, dta).fit() npt.assert_almost_equal(results.fittedvalues.values, results.predict(data.exog), 8) def test_formula_predict_series(): data = pd.DataFrame({"y": [1, 2, 3], "x": [1, 2, 3]}, index=[5, 3, 1]) results = ols('y ~ x', data).fit() result = results.predict(data) expected = pd.Series([1., 2., 3.], index=[5, 3, 1]) assert_series_equal(result, expected) result = results.predict(data.x) assert_series_equal(result, expected) result = results.predict(pd.Series([1, 2, 3], index=[1, 2, 3], name='x')) expected = pd.Series([1., 2., 3.], index=[1, 2, 3]) assert_series_equal(result, expected) result = results.predict({"x": [1, 2, 3]}) expected = pd.Series([1., 2., 3.], index=[0, 1, 2]) assert_series_equal(result, expected) def test_patsy_lazy_dict(): class LazyDict(dict): def __init__(self, data): self.data = data def __missing__(self, key): return np.array(self.data[key]) data = cpunish.load_pandas().data data = LazyDict(data) res = ols('EXECUTIONS ~ SOUTH + INCOME', data=data).fit() res2 = res.predict(data) npt.assert_allclose(res.fittedvalues, res2) data = cpunish.load_pandas().data data['INCOME'].loc[0] = None data = LazyDict(data) data.index = cpunish.load_pandas().data.index res = ols('EXECUTIONS ~ SOUTH + INCOME', data=data).fit() res2 = res.predict(data) assert_equal(res.fittedvalues, res2) # Should lose a record assert_equal(len(res2) + 1, len(cpunish.load_pandas().data)) def test_patsy_missing_data(): # Test pandas-style first data = cpunish.load_pandas().data data['INCOME'].loc[0] = None res = ols('EXECUTIONS ~ SOUTH + INCOME', data=data).fit() res2 = res.predict(data) # First record will be dropped during fit, but not during predict assert_equal(res.fittedvalues, res2[1:]) # Non-pandas version data = cpunish.load_pandas().data data['INCOME'].loc[0] = None data = data.to_records(index=False) with warnings.catch_warnings(record=True) as w: warnings.simplefilter("always") res2 = res.predict(data) assert 'ValueWarning' in repr(w[-1].message) assert 'nan values have been dropped' in repr(w[-1].message) # Frist record will be dropped in both cases assert_equal(res.fittedvalues, res2) def test_predict_nondataframe(): df = pd.DataFrame([[3, 0.030], [10, 0.060], [20, 0.120]], columns=['BSA', 'Absorbance']) model = ols('Absorbance ~ BSA', data=df) fit = model.fit() error = patsy.PatsyError with pytest.raises(error): fit.predict([0.25]) def test_formula_environment(): df = pd.DataFrame({'x': [1, 2, 3], 'y': [2, 4, 6]}) env = patsy.EvalEnvironment([{'z': [3, 6, 9]}]) model = ols('y ~ x + z', eval_env=env, data=df) assert 'z' in model.exog_names with pytest.raises(TypeError): ols('y ~ x', eval_env='env', data=df) def test_formula_predict_series_exog(): # GH-6509 x = np.random.standard_normal((1000, 2)) data_full = pd.DataFrame(x, columns=["y", "x"]) data = data_full.iloc[:500] res = ols(formula='y ~ x', data=data).fit() oos = data_full.iloc[500:]["x"] prediction = res.get_prediction(oos) assert prediction.predicted_mean.shape[0] == 500 statsmodels-0.12.2/statsmodels/gam/000077500000000000000000000000001400612667500172535ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/gam/__init__.py000066400000000000000000000001131400612667500213570ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/gam/api.py000066400000000000000000000003401400612667500203730ustar00rootroot00000000000000 from .generalized_additive_model import GLMGam # noqa:F401 from .gam_cross_validation.gam_cross_validation import MultivariateGAMCVPath # noqa:F401,E501 from .smooth_basis import BSplines, CyclicCubicSplines # noqa:F401 statsmodels-0.12.2/statsmodels/gam/gam_cross_validation/000077500000000000000000000000001400612667500234425ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/gam/gam_cross_validation/__init__.py000066400000000000000000000000621400612667500255510ustar00rootroot00000000000000__author__ = 'luca puggini: lucapuggio@gmail.com' statsmodels-0.12.2/statsmodels/gam/gam_cross_validation/cross_validators.py000066400000000000000000000031741400612667500274020ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Cross-validation iterators for GAM Author: Luca Puggini """ from abc import ABCMeta, abstractmethod from statsmodels.compat.python import with_metaclass import numpy as np class BaseCrossValidator(with_metaclass(ABCMeta)): """ The BaseCrossValidator class is a base class for all the iterators that split the data in train and test as for example KFolds or LeavePOut """ def __init__(self): pass @abstractmethod def split(self): pass class KFold(BaseCrossValidator): """ K-Folds cross validation iterator: Provides train/test indexes to split data in train test sets Parameters ---------- k: int number of folds shuffle : bool If true, then the index is shuffled before splitting into train and test indices. Notes ----- All folds except for last fold have size trunc(n/k), the last fold has the remainder. """ def __init__(self, k_folds, shuffle=False): self.nobs = None self.k_folds = k_folds self.shuffle = shuffle def split(self, X, y=None, label=None): """yield index split into train and test sets """ # TODO: X and y are redundant, we only need nobs nobs = X.shape[0] index = np.array(range(nobs)) if self.shuffle: np.random.shuffle(index) folds = np.array_split(index, self.k_folds) for fold in folds: test_index = np.zeros(nobs, dtype=bool) test_index[fold] = True train_index = np.logical_not(test_index) yield train_index, test_index statsmodels-0.12.2/statsmodels/gam/gam_cross_validation/gam_cross_validation.py000066400000000000000000000171141400612667500302070ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Cross-validation classes for GAM Author: Luca Puggini """ from abc import ABCMeta, abstractmethod from statsmodels.compat.python import with_metaclass import itertools import numpy as np from statsmodels.gam.smooth_basis import (GenericSmoothers, UnivariateGenericSmoother) class BaseCV(with_metaclass(ABCMeta)): """ BaseCV class. It computes the cross validation error of a given model. All the cross validation classes can be derived by this one (e.g. GamCV, LassoCV,...) """ def __init__(self, cv_iterator, endog, exog): self.cv_iterator = cv_iterator self.exog = exog self.endog = endog # TODO: cv_iterator.split only needs nobs from endog or exog self.train_test_cv_indices = self.cv_iterator.split(self.exog, self.endog, label=None) def fit(self, **kwargs): # kwargs are the input values for the fit method of the # cross-validated object cv_err = [] for train_index, test_index in self.train_test_cv_indices: cv_err.append(self._error(train_index, test_index, **kwargs)) return np.array(cv_err) @abstractmethod def _error(self, train_index, test_index, **kwargs): # train the model on the train set # and returns the error on the test set pass def _split_train_test_smoothers(x, smoother, train_index, test_index): """split smoothers in test and train sets and create GenericSmoothers Note: this does not take exog_linear into account """ train_smoothers = [] test_smoothers = [] for smoother in smoother.smoothers: train_basis = smoother.basis[train_index] train_der_basis = smoother.der_basis[train_index] train_der2_basis = smoother.der2_basis[train_index] train_cov_der2 = smoother.cov_der2 # TODO: Double check this part. cov_der2 is calculated with all data train_x = smoother.x[train_index] train_smoothers.append( UnivariateGenericSmoother( train_x, train_basis, train_der_basis, train_der2_basis, train_cov_der2, smoother.variable_name + ' train')) test_basis = smoother.basis[test_index] test_der_basis = smoother.der_basis[test_index] test_cov_der2 = smoother.cov_der2 # TODO: Double check this part. cov_der2 is calculated with all data test_x = smoother.x[test_index] test_smoothers.append( UnivariateGenericSmoother( test_x, test_basis, test_der_basis, train_der2_basis, test_cov_der2, smoother.variable_name + ' test')) train_multivariate_smoothers = GenericSmoothers(x[train_index], train_smoothers) test_multivariate_smoothers = GenericSmoothers(x[test_index], test_smoothers) return train_multivariate_smoothers, test_multivariate_smoothers class MultivariateGAMCV(BaseCV): def __init__(self, smoother, alphas, gam, cost, endog, exog, cv_iterator): self.cost = cost self.gam = gam self.smoother = smoother self.exog_linear = exog self.alphas = alphas self.cv_iterator = cv_iterator # TODO: super does not do anything with endog, exog, except get nobs # refactor to clean up what where `exog` and `exog_linear` is attached super(MultivariateGAMCV, self).__init__(cv_iterator, endog, # exog, # not used in super self.smoother.basis) def _error(self, train_index, test_index, **kwargs): train_smoother, test_smoother = _split_train_test_smoothers( self.smoother.x, self.smoother, train_index, test_index) endog_train = self.endog[train_index] endog_test = self.endog[test_index] if self.exog_linear is not None: exog_linear_train = self.exog_linear[train_index] exog_linear_test = self.exog_linear[test_index] else: exog_linear_train = None exog_linear_test = None gam = self.gam(endog_train, exog=exog_linear_train, smoother=train_smoother, alpha=self.alphas) gam_res = gam.fit(**kwargs) # exog_linear_test and test_smoother.basis will be column_stacked # but not transformed in predict endog_est = gam_res.predict(exog_linear_test, test_smoother.basis, transform=False) return self.cost(endog_test, endog_est) class BasePenaltiesPathCV(with_metaclass(ABCMeta)): """ Base class for cross validation over a grid of parameters. The best parameter is saved in alpha_cv This class is currently not used """ def __init__(self, alphas): self.alphas = alphas self.alpha_cv = None self.cv_error = None self.cv_std = None def plot_path(self): from statsmodels.graphics.utils import _import_mpl plt = _import_mpl() plt.plot(self.alphas, self.cv_error, c='black') plt.plot(self.alphas, self.cv_error + 1.96 * self.cv_std, c='blue') plt.plot(self.alphas, self.cv_error - 1.96 * self.cv_std, c='blue') plt.plot(self.alphas, self.cv_error, 'o', c='black') plt.plot(self.alphas, self.cv_error + 1.96 * self.cv_std, 'o', c='blue') plt.plot(self.alphas, self.cv_error - 1.96 * self.cv_std, 'o', c='blue') return # TODO add return class MultivariateGAMCVPath(object): """k-fold cross-validation for GAM Warning: The API of this class is preliminary and will change. Parameters ---------- smoother : additive smoother instance alphas : list of iteratables list of alpha for smooths. The product space will be used as alpha grid for cross-validation gam : model class model class for creating a model with k-fole training data cost : function cost function for the prediction error endog : ndarray dependent (response) variable of the model cv_iterator : instance of cross-validation iterator """ def __init__(self, smoother, alphas, gam, cost, endog, exog, cv_iterator): self.cost = cost self.smoother = smoother self.gam = gam self.alphas = alphas self.alphas_grid = list(itertools.product(*self.alphas)) self.endog = endog self.exog = exog self.cv_iterator = cv_iterator self.cv_error = np.zeros(shape=(len(self.alphas_grid, ))) self.cv_std = np.zeros(shape=(len(self.alphas_grid, ))) self.alpha_cv = None def fit(self, **kwargs): for i, alphas_i in enumerate(self.alphas_grid): gam_cv = MultivariateGAMCV(smoother=self.smoother, alphas=alphas_i, gam=self.gam, cost=self.cost, endog=self.endog, exog=self.exog, cv_iterator=self.cv_iterator) cv_err = gam_cv.fit(**kwargs) self.cv_error[i] = cv_err.mean() self.cv_std[i] = cv_err.std() self.alpha_cv = self.alphas_grid[np.argmin(self.cv_error)] return self statsmodels-0.12.2/statsmodels/gam/gam_penalties.py000066400000000000000000000230511400612667500224360ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Penalty classes for Generalized Additive Models Author: Luca Puggini Author: Josef Perktold """ import numpy as np from scipy.linalg import block_diag from statsmodels.base._penalties import Penalty class UnivariateGamPenalty(Penalty): """ Penalty for smooth term in Generalized Additive Models Parameters ---------- univariate_smoother : instance instance of univariate smoother or spline class alpha : float default penalty weight, alpha can be provided to each method weights: TODO: not used and verified, might be removed Attributes ---------- Parameters are stored, additionally nob s: The number of samples used during the estimation n_columns : number of columns in smoother basis """ def __init__(self, univariate_smoother, alpha=1, weights=1): self.weights = weights self.alpha = alpha self.univariate_smoother = univariate_smoother self.nobs = self.univariate_smoother.nobs self.n_columns = self.univariate_smoother.dim_basis def func(self, params, alpha=None): """evaluate penalization at params Parameters ---------- params : ndarray coefficients for the spline basis in the regression model alpha : float default penalty weight Returns ------- func : float value of the penalty evaluated at params """ if alpha is None: alpha = self.alpha f = params.dot(self.univariate_smoother.cov_der2.dot(params)) return alpha * f / self.nobs def deriv(self, params, alpha=None): """evaluate derivative of penalty with respect to params Parameters ---------- params : ndarray coefficients for the spline basis in the regression model alpha : float default penalty weight Returns ------- deriv : ndarray derivative, gradient of the penalty with respect to params """ if alpha is None: alpha = self.alpha d = 2 * alpha * np.dot(self.univariate_smoother.cov_der2, params) d /= self.nobs return d def deriv2(self, params, alpha=None): """evaluate second derivative of penalty with respect to params Parameters ---------- params : ndarray coefficients for the spline basis in the regression model alpha : float default penalty weight Returns ------- deriv2 : ndarray, 2-Dim second derivative, hessian of the penalty with respect to params """ if alpha is None: alpha = self.alpha d2 = 2 * alpha * self.univariate_smoother.cov_der2 d2 /= self.nobs return d2 def penalty_matrix(self, alpha=None): """penalty matrix for the smooth term of a GAM Parameters ---------- alpha : list of floats or None penalty weights Returns ------- penalty matrix square penalty matrix for quadratic penalization. The number of rows and columns are equal to the number of columns in the smooth terms, i.e. the number of parameters for this smooth term in the regression model """ if alpha is None: alpha = self.alpha return alpha * self.univariate_smoother.cov_der2 class MultivariateGamPenalty(Penalty): """ Penalty for Generalized Additive Models Parameters ---------- multivariate_smoother : instance instance of additive smoother or spline class alpha : list of float default penalty weight, list with length equal to the number of smooth terms. ``alpha`` can also be provided to each method. weights : array_like currently not used is a list of doubles of the same length as alpha or a list of ndarrays where each component has the length equal to the number of columns in that component start_idx : int number of parameters that come before the smooth terms. If the model has a linear component, then the parameters for the smooth components start at ``start_index``. Attributes ---------- Parameters are stored, additionally nob s: The number of samples used during the estimation dim_basis : number of columns of additive smoother. Number of columns in all smoothers. k_variables : number of smooth terms k_params : total number of parameters in the regression model """ def __init__(self, multivariate_smoother, alpha, weights=None, start_idx=0): if len(multivariate_smoother.smoothers) != len(alpha): msg = ('all the input values should be of the same length.' ' len(smoothers)=%d, len(alphas)=%d') % ( len(multivariate_smoother.smoothers), len(alpha)) raise ValueError(msg) self.multivariate_smoother = multivariate_smoother self.dim_basis = self.multivariate_smoother.dim_basis self.k_variables = self.multivariate_smoother.k_variables self.nobs = self.multivariate_smoother.nobs self.alpha = alpha self.start_idx = start_idx self.k_params = start_idx + self.dim_basis # TODO: Review this, if weights is None: # weights should have total length as params # but it can also be scalar in individual component self.weights = [1. for _ in range(self.k_variables)] else: import warnings warnings.warn('weights is currently ignored') self.weights = weights self.mask = [np.zeros(self.k_params, dtype=bool) for _ in range(self.k_variables)] param_count = start_idx for i, smoother in enumerate(self.multivariate_smoother.smoothers): # the mask[i] contains a vector of length k_columns. The index # corresponding to the i-th input variable are set to True. self.mask[i][param_count: param_count + smoother.dim_basis] = True param_count += smoother.dim_basis self.gp = [] for i in range(self.k_variables): gp = UnivariateGamPenalty(self.multivariate_smoother.smoothers[i], weights=self.weights[i], alpha=self.alpha[i]) self.gp.append(gp) def func(self, params, alpha=None): """evaluate penalization at params Parameters ---------- params : ndarray coefficients in the regression model alpha : float or list of floats penalty weights Returns ------- func : float value of the penalty evaluated at params """ if alpha is None: alpha = [None] * self.k_variables cost = 0 for i in range(self.k_variables): params_i = params[self.mask[i]] cost += self.gp[i].func(params_i, alpha=alpha[i]) return cost def deriv(self, params, alpha=None): """evaluate derivative of penalty with respect to params Parameters ---------- params : ndarray coefficients in the regression model alpha : list of floats or None penalty weights Returns ------- deriv : ndarray derivative, gradient of the penalty with respect to params """ if alpha is None: alpha = [None] * self.k_variables grad = [np.zeros(self.start_idx)] for i in range(self.k_variables): params_i = params[self.mask[i]] grad.append(self.gp[i].deriv(params_i, alpha=alpha[i])) return np.concatenate(grad) def deriv2(self, params, alpha=None): """evaluate second derivative of penalty with respect to params Parameters ---------- params : ndarray coefficients in the regression model alpha : list of floats or None penalty weights Returns ------- deriv2 : ndarray, 2-Dim second derivative, hessian of the penalty with respect to params """ if alpha is None: alpha = [None] * self.k_variables deriv2 = [np.zeros((self.start_idx, self.start_idx))] for i in range(self.k_variables): params_i = params[self.mask[i]] deriv2.append(self.gp[i].deriv2(params_i, alpha=alpha[i])) return block_diag(*deriv2) def penalty_matrix(self, alpha=None): """penalty matrix for generalized additive model Parameters ---------- alpha : list of floats or None penalty weights Returns ------- penalty matrix block diagonal, square penalty matrix for quadratic penalization. The number of rows and columns are equal to the number of parameters in the regression model ``k_params``. Notes ----- statsmodels does not support backwards compatibility when keywords are used as positional arguments. The order of keywords might change. We might need to add a ``params`` keyword if the need arises. """ if alpha is None: alpha = self.alpha s_all = [np.zeros((self.start_idx, self.start_idx))] for i in range(self.k_variables): s_all.append(self.gp[i].penalty_matrix(alpha=alpha[i])) return block_diag(*s_all) statsmodels-0.12.2/statsmodels/gam/generalized_additive_model.py000066400000000000000000001134441400612667500251560ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Generalized Additive Models Author: Luca Puggini Author: Josef Perktold created on 08/07/2015 """ from collections.abc import Iterable import copy # check if needed when dropping python 2.7 import numpy as np from scipy import optimize import pandas as pd import statsmodels.base.wrapper as wrap from statsmodels.discrete.discrete_model import Logit from statsmodels.genmod.generalized_linear_model import ( GLM, GLMResults, GLMResultsWrapper, _check_convergence) import statsmodels.regression.linear_model as lm # import statsmodels.regression._tools as reg_tools # TODO: use this for pirls from statsmodels.tools.sm_exceptions import (PerfectSeparationError, ValueWarning) from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.data import _is_using_pandas from statsmodels.tools.linalg import matrix_sqrt from statsmodels.base._penalized import PenalizedMixin from statsmodels.gam.gam_penalties import MultivariateGamPenalty from statsmodels.gam.gam_cross_validation.gam_cross_validation import ( MultivariateGAMCVPath) from statsmodels.gam.gam_cross_validation.cross_validators import KFold def _transform_predict_exog(model, exog, design_info=None): """transform exog for predict using design_info Note: this is copied from base.model.Results.predict and converted to standalone function with additional options. """ is_pandas = _is_using_pandas(exog, None) exog_index = exog.index if is_pandas else None if design_info is None: design_info = getattr(model.data, 'design_info', None) if design_info is not None and (exog is not None): from patsy import dmatrix if isinstance(exog, pd.Series): # we are guessing whether it should be column or row if (hasattr(exog, 'name') and isinstance(exog.name, str) and exog.name in design_info.describe()): # assume we need one column exog = pd.DataFrame(exog) else: # assume we need a row exog = pd.DataFrame(exog).T orig_exog_len = len(exog) is_dict = isinstance(exog, dict) exog = dmatrix(design_info, exog, return_type="dataframe") if orig_exog_len > len(exog) and not is_dict: import warnings if exog_index is None: warnings.warn('nan values have been dropped', ValueWarning) else: exog = exog.reindex(exog_index) exog_index = exog.index if exog is not None: exog = np.asarray(exog) if exog.ndim == 1 and (model.exog.ndim == 1 or model.exog.shape[1] == 1): exog = exog[:, None] exog = np.atleast_2d(exog) # needed in count model shape[1] return exog, exog_index class GLMGamResults(GLMResults): """Results class for generalized additive models, GAM. This inherits from GLMResults. Warning: some inherited methods might not correctly take account of the penalization GLMGamResults inherits from GLMResults All methods related to the loglikelihood function return the penalized values. Attributes ---------- edf list of effective degrees of freedom for each column of the design matrix. hat_matrix_diag diagonal of hat matrix gcv generalized cross-validation criterion computed as ``gcv = scale / (1. - hat_matrix_trace / self.nobs)**2`` cv cross-validation criterion computed as ``cv = ((resid_pearson / (1 - hat_matrix_diag))**2).sum() / nobs`` Notes ----- status: experimental """ def __init__(self, model, params, normalized_cov_params, scale, **kwds): # this is a messy way to compute edf and update scale # need several attributes to compute edf self.model = model self.params = params self.normalized_cov_params = normalized_cov_params self.scale = scale edf = self.edf.sum() self.df_model = edf - 1 # assume constant # need to use nobs or wnobs attribute self.df_resid = self.model.endog.shape[0] - edf # we are setting the model df for the case when super is using it # df in model will be incorrect state when alpha/pen_weight changes self.model.df_model = self.df_model self.model.df_resid = self.df_resid mu = self.fittedvalues self.scale = scale = self.model.estimate_scale(mu) super(GLMGamResults, self).__init__(model, params, normalized_cov_params, scale, **kwds) def _tranform_predict_exog(self, exog=None, exog_smooth=None, transform=True): """Transform original explanatory variables for prediction Parameters ---------- exog : array_like, optional The values for the linear explanatory variables. exog_smooth : array_like values for the variables in the smooth terms transform : bool, optional If transform is False, then ``exog`` is returned unchanged and ``x`` is ignored. It is assumed that exog contains the full design matrix for the predict observations. If transform is True, then the basis representation of the smooth term will be constructed from the provided ``x``. Returns ------- exog_transformed : ndarray design matrix for the prediction """ if exog_smooth is not None: exog_smooth = np.asarray(exog_smooth) exog_index = None if transform is False: # the following allows that either or both exog are not None if exog_smooth is None: # exog could be None or array ex = exog else: if exog is None: ex = exog_smooth else: ex = np.column_stack((exog, exog_smooth)) else: # transform exog_linear if needed if exog is not None and hasattr(self.model, 'design_info_linear'): exog, exog_index = _transform_predict_exog( self.model, exog, self.model.design_info_linear) # create smooth basis if exog_smooth is not None: ex_smooth = self.model.smoother.transform(exog_smooth) if exog is None: ex = ex_smooth else: # TODO: there might be problems is exog_smooth is 1-D ex = np.column_stack((exog, ex_smooth)) else: ex = exog return ex, exog_index def predict(self, exog=None, exog_smooth=None, transform=True, **kwargs): """" compute prediction Parameters ---------- exog : array_like, optional The values for the linear explanatory variables exog_smooth : array_like values for the variables in the smooth terms transform : bool, optional If transform is True, then the basis representation of the smooth term will be constructed from the provided ``exog``. kwargs : Some models can take additional arguments or keywords, see the predict method of the model for the details. Returns ------- prediction : ndarray, pandas.Series or pandas.DataFrame predicted values """ ex, exog_index = self._tranform_predict_exog(exog=exog, exog_smooth=exog_smooth, transform=transform) predict_results = super(GLMGamResults, self).predict(ex, transform=False, **kwargs) if exog_index is not None and not hasattr( predict_results, 'predicted_values'): if predict_results.ndim == 1: return pd.Series(predict_results, index=exog_index) else: return pd.DataFrame(predict_results, index=exog_index) else: return predict_results def get_prediction(self, exog=None, exog_smooth=None, transform=True, **kwargs): """compute prediction results Parameters ---------- exog : array_like, optional The values for which you want to predict. exog_smooth : array_like values for the variables in the smooth terms transform : bool, optional If transform is True, then the basis representation of the smooth term will be constructed from the provided ``x``. kwargs : Some models can take additional arguments or keywords, see the predict method of the model for the details. Returns ------- prediction_results : generalized_linear_model.PredictionResults The prediction results instance contains prediction and prediction variance and can on demand calculate confidence intervals and summary tables for the prediction of the mean and of new observations. """ ex, exog_index = self._tranform_predict_exog(exog=exog, exog_smooth=exog_smooth, transform=transform) return super(GLMGamResults, self).get_prediction(ex, transform=False, **kwargs) def partial_values(self, smooth_index, include_constant=True): """contribution of a smooth term to the linear prediction Warning: This will be replaced by a predict method Parameters ---------- smooth_index : int index of the smooth term within list of smooth terms include_constant : bool If true, then the estimated intercept is added to the prediction and its standard errors. This avoids that the confidence interval has zero width at the imposed identification constraint, e.g. either at a reference point or at the mean. Returns ------- predicted : nd_array predicted value of linear term. This is not the expected response if the link function is not linear. se_pred : nd_array standard error of linear prediction """ variable = smooth_index smoother = self.model.smoother mask = smoother.mask[variable] start_idx = self.model.k_exog_linear idx = start_idx + np.nonzero(mask)[0] # smoother has only smooth parts, not exog_linear exog_part = smoother.basis[:, mask] const_idx = self.model.data.const_idx if include_constant and const_idx is not None: idx = np.concatenate(([const_idx], idx)) exog_part = self.model.exog[:, idx] linpred = np.dot(exog_part, self.params[idx]) # select the submatrix corresponding to a single variable partial_cov_params = self.cov_params(column=idx) covb = partial_cov_params var = (exog_part * np.dot(covb, exog_part.T).T).sum(1) se = np.sqrt(var) return linpred, se def plot_partial(self, smooth_index, plot_se=True, cpr=False, include_constant=True, ax=None): """plot the contribution of a smooth term to the linear prediction Parameters ---------- smooth_index : int index of the smooth term within list of smooth terms plot_se : bool If plot_se is true, then the confidence interval for the linear prediction will be added to the plot. cpr : bool If cpr (component plus residual) is true, the a scatter plot of the partial working residuals will be added to the plot. include_constant : bool If true, then the estimated intercept is added to the prediction and its standard errors. This avoids that the confidence interval has zero width at the imposed identification constraint, e.g. either at a reference point or at the mean. ax : None or matplotlib axis instance If ax is not None, then the plot will be added to it. Returns ------- Figure If `ax` is None, the created figure. Otherwise the Figure to which `ax` is connected. """ from statsmodels.graphics.utils import _import_mpl, create_mpl_ax _import_mpl() variable = smooth_index y_est, se = self.partial_values(variable, include_constant=include_constant) smoother = self.model.smoother x = smoother.smoothers[variable].x sort_index = np.argsort(x) x = x[sort_index] y_est = y_est[sort_index] se = se[sort_index] fig, ax = create_mpl_ax(ax) ax.plot(x, y_est, c='blue', lw=2) if plot_se: ax.plot(x, y_est + 1.96 * se, '-', c='blue') ax.plot(x, y_est - 1.96 * se, '-', c='blue') if cpr: # TODO: resid_response does not make sense with nonlinear link # use resid_working ? cpr_ = y_est + self.resid_working ax.plot(x, cpr_, '.', lw=2) ax.set_xlabel(smoother.smoothers[variable].variable_name) return fig def test_significance(self, smooth_index): """hypothesis test that a smooth component is zero. This calls `wald_test` to compute the hypothesis test, but uses effective degrees of freedom. Parameters ---------- smooth_index : int index of the smooth term within list of smooth terms Returns ------- wald_test : ContrastResults instance the results instance created by `wald_test` """ variable = smooth_index smoother = self.model.smoother start_idx = self.model.k_exog_linear k_params = len(self.params) # a bit messy, we need first index plus length of smooth term mask = smoother.mask[variable] k_constraints = mask.sum() idx = start_idx + np.nonzero(mask)[0][0] constraints = np.eye(k_constraints, k_params, idx) df_constraints = self.edf[idx: idx + k_constraints].sum() return self.wald_test(constraints, df_constraints=df_constraints) def get_hat_matrix_diag(self, observed=True, _axis=1): """ Compute the diagonal of the hat matrix Parameters ---------- observed : bool If true, then observed hessian is used in the hat matrix computation. If false, then the expected hessian is used. In the case of a canonical link function both are the same. This is only relevant for models that implement both observed and expected Hessian, which is currently only GLM. Other models only use the observed Hessian. _axis : int This is mainly for internal use. By default it returns the usual diagonal of the hat matrix. If _axis is zero, then the result corresponds to the effective degrees of freedom, ``edf`` for each column of exog. Returns ------- hat_matrix_diag : ndarray The diagonal of the hat matrix computed from the observed or expected hessian. """ weights = self.model.hessian_factor(self.params, scale=self.scale, observed=observed) wexog = np.sqrt(weights)[:, None] * self.model.exog # we can use inverse hessian directly instead of computing it from # WLS/IRLS as in GLM # TODO: does `normalized_cov_params * scale` work in all cases? # this avoids recomputing hessian, check when used for other models. hess_inv = self.normalized_cov_params * self.scale # this is in GLM equivalent to the more generic and direct # hess_inv = np.linalg.inv(-self.model.hessian(self.params)) hd = (wexog * hess_inv.dot(wexog.T).T).sum(axis=_axis) return hd @cache_readonly def edf(self): return self.get_hat_matrix_diag(_axis=0) @cache_readonly def hat_matrix_trace(self): return self.hat_matrix_diag.sum() @cache_readonly def hat_matrix_diag(self): return self.get_hat_matrix_diag(observed=True) @cache_readonly def gcv(self): return self.scale / (1. - self.hat_matrix_trace / self.nobs)**2 @cache_readonly def cv(self): cv_ = ((self.resid_pearson / (1. - self.hat_matrix_diag))**2).sum() cv_ /= self.nobs return cv_ class GLMGamResultsWrapper(GLMResultsWrapper): pass wrap.populate_wrapper(GLMGamResultsWrapper, GLMGamResults) class GLMGam(PenalizedMixin, GLM): """ Generalized Additive Models (GAM) This inherits from `GLM`. Warning: Not all inherited methods might take correctly account of the penalization. Not all options including offset and exposure have been verified yet. Parameters ---------- endog : array_like The response variable. exog : array_like or None This explanatory variables are treated as linear. The model in this case is a partial linear model. smoother : instance of additive smoother class Examples of smoother instances include Bsplines or CyclicCubicSplines. alpha : float or list of floats Penalization weights for smooth terms. The length of the list needs to be the same as the number of smooth terms in the ``smoother``. family : instance of GLM family See GLM. offset : None or array_like See GLM. exposure : None or array_like See GLM. missing : 'none' Missing value handling is not supported in this class. **kwargs Extra keywords are used in call to the super classes. Notes ----- Status: experimental. This has full unit test coverage for the core results with Gaussian and Poisson (without offset and exposure). Other options and additional results might not be correctly supported yet. (Binomial with counts, i.e. with n_trials, is most likely wrong in pirls. User specified var or freq weights are most likely also not correct for all results.) """ _results_class = GLMGamResults _results_class_wrapper = GLMGamResultsWrapper def __init__(self, endog, exog=None, smoother=None, alpha=0, family=None, offset=None, exposure=None, missing='none', **kwargs): # TODO: check usage of hasconst hasconst = kwargs.get('hasconst', None) xnames_linear = None if hasattr(exog, 'design_info'): self.design_info_linear = exog.design_info xnames_linear = self.design_info_linear.column_names is_pandas = _is_using_pandas(exog, None) # TODO: handle data is experimental, see #5469 # This is a bit wasteful because we need to `handle_data twice` self.data_linear = self._handle_data(endog, exog, missing, hasconst) if xnames_linear is None: xnames_linear = self.data_linear.xnames if exog is not None: exog_linear = self.data_linear.exog k_exog_linear = exog_linear.shape[1] else: exog_linear = None k_exog_linear = 0 self.k_exog_linear = k_exog_linear # We need exog_linear for k-fold cross validation # TODO: alternative is to take columns from combined exog self.exog_linear = exog_linear self.smoother = smoother self.k_smooths = smoother.k_variables self.alpha = self._check_alpha(alpha) penal = MultivariateGamPenalty(smoother, alpha=self.alpha, start_idx=k_exog_linear) kwargs.pop('penal', None) if exog_linear is not None: exog = np.column_stack((exog_linear, smoother.basis)) else: exog = smoother.basis # TODO: check: xnames_linear will be None instead of empty list # if no exog_linear # can smoother be empty ? I guess not allowed. if xnames_linear is None: xnames_linear = [] xnames = xnames_linear + self.smoother.col_names if is_pandas and exog_linear is not None: # we a dataframe so we can get a PandasData instance for wrapping exog = pd.DataFrame(exog, index=self.data_linear.row_labels, columns=xnames) super(GLMGam, self).__init__(endog, exog=exog, family=family, offset=offset, exposure=exposure, penal=penal, missing=missing, **kwargs) if not is_pandas: # set exog nanmes if not given by pandas DataFrame self.exog_names[:] = xnames # TODO: the generic data handling might attach the design_info from the # linear part, but this is incorrect for the full model and # causes problems in wald_test_terms if hasattr(self.data, 'design_info'): del self.data.design_info # formula also might be attached which causes problems in predict if hasattr(self, 'formula'): self.formula_linear = self.formula self.formula = None del self.formula def _check_alpha(self, alpha): """check and convert alpha to required list format Parameters ---------- alpha : scalar, list or array_like penalization weight Returns ------- alpha : list penalization weight, list with length equal to the number of smooth terms """ if not isinstance(alpha, Iterable): alpha = [alpha] * len(self.smoother.smoothers) elif not isinstance(alpha, list): # we want alpha to be a list alpha = list(alpha) return alpha def fit(self, start_params=None, maxiter=1000, method='pirls', tol=1e-8, scale=None, cov_type='nonrobust', cov_kwds=None, use_t=None, full_output=True, disp=False, max_start_irls=3, **kwargs): """estimate parameters and create instance of GLMGamResults class Parameters ---------- most parameters are the same as for GLM method : optimization method The special optimization method is "pirls" which uses a penalized version of IRLS. Other methods are gradient optimizers as used in base.model.LikelihoodModel. Returns ------- res : instance of wrapped GLMGamResults """ # TODO: temporary hack to remove attribute # formula also might be attached which in inherited from_formula # causes problems in predict if hasattr(self, 'formula'): self.formula_linear = self.formula del self.formula # TODO: alpha not allowed yet, but is in `_fit_pirls` # alpha = self._check_alpha() if method.lower() in ['pirls', 'irls']: res = self._fit_pirls(self.alpha, start_params=start_params, maxiter=maxiter, tol=tol, scale=scale, cov_type=cov_type, cov_kwds=cov_kwds, use_t=use_t, **kwargs) else: if max_start_irls > 0 and (start_params is None): res = self._fit_pirls(self.alpha, start_params=start_params, maxiter=max_start_irls, tol=tol, scale=scale, cov_type=cov_type, cov_kwds=cov_kwds, use_t=use_t, **kwargs) start_params = res.params del res res = super(GLMGam, self).fit(start_params=start_params, maxiter=maxiter, method=method, tol=tol, scale=scale, cov_type=cov_type, cov_kwds=cov_kwds, use_t=use_t, full_output=full_output, disp=disp, max_start_irls=0, **kwargs) return res # pag 165 4.3 # pag 136 PIRLS def _fit_pirls(self, alpha, start_params=None, maxiter=100, tol=1e-8, scale=None, cov_type='nonrobust', cov_kwds=None, use_t=None, weights=None): """fit model with penalized reweighted least squares """ # TODO: this currently modifies several attributes # self.scale, self.scaletype, self.mu, self.weights # self.data_weights, # and possibly self._offset_exposure # several of those might not be necessary, e.g. mu and weights # alpha = alpha * len(y) * self.scale / 100 # TODO: we need to rescale alpha endog = self.endog wlsexog = self.exog # smoother.basis spl_s = self.penal.penalty_matrix(alpha=alpha) nobs, n_columns = wlsexog.shape # TODO what are these values? if weights is None: self.data_weights = np.array([1.] * nobs) else: self.data_weights = weights if not hasattr(self, '_offset_exposure'): self._offset_exposure = 0 self.scaletype = scale # TODO: check default scale types # self.scaletype = 'dev' # during iteration self.scale = 1 if start_params is None: mu = self.family.starting_mu(endog) lin_pred = self.family.predict(mu) else: lin_pred = np.dot(wlsexog, start_params) + self._offset_exposure mu = self.family.fitted(lin_pred) dev = self.family.deviance(endog, mu) history = dict(params=[None, start_params], deviance=[np.inf, dev]) converged = False criterion = history['deviance'] # This special case is used to get the likelihood for a specific # params vector. if maxiter == 0: mu = self.family.fitted(lin_pred) self.scale = self.estimate_scale(mu) wls_results = lm.RegressionResults(self, start_params, None) iteration = 0 for iteration in range(maxiter): # TODO: is this equivalent to point 1 of page 136: # w = 1 / (V(mu) * g'(mu)) ? self.weights = self.data_weights * self.family.weights(mu) # TODO: is this equivalent to point 1 of page 136: # z = g(mu)(y - mu) + X beta ? wlsendog = (lin_pred + self.family.link.deriv(mu) * (endog - mu) - self._offset_exposure) # this defines the augmented matrix point 2a on page 136 wls_results = penalized_wls(wlsendog, wlsexog, spl_s, self.weights) lin_pred = np.dot(wlsexog, wls_results.params).ravel() lin_pred += self._offset_exposure mu = self.family.fitted(lin_pred) # We do not need to update scale in GLM/LEF models # We might need it in dispersion models. # self.scale = self.estimate_scale(mu) history = self._update_history(wls_results, mu, history) if endog.squeeze().ndim == 1 and np.allclose(mu - endog, 0): msg = "Perfect separation detected, results not available" raise PerfectSeparationError(msg) # TODO need atol, rtol # args of _check_convergence: (criterion, iteration, atol, rtol) converged = _check_convergence(criterion, iteration, tol, 0) if converged: break self.mu = mu self.scale = self.estimate_scale(mu) glm_results = GLMGamResults(self, wls_results.params, wls_results.normalized_cov_params, self.scale, cov_type=cov_type, cov_kwds=cov_kwds, use_t=use_t) glm_results.method = "PIRLS" history['iteration'] = iteration + 1 glm_results.fit_history = history glm_results.converged = converged return GLMGamResultsWrapper(glm_results) def select_penweight(self, criterion='aic', start_params=None, start_model_params=None, method='basinhopping', **fit_kwds): """find alpha by minimizing results criterion The objective for the minimization can be results attributes like ``gcv``, ``aic`` or ``bic`` where the latter are based on effective degrees of freedom. Warning: In many case the optimization might converge to a local optimum or near optimum. Different start_params or using a global optimizer is recommended, default is basinhopping. Parameters ---------- criterion='aic' name of results attribute to be minimized. Default is 'aic', other options are 'gcv', 'cv' or 'bic'. start_params : None or array starting parameters for alpha in the penalization weight minimization. The parameters are internally exponentiated and the minimization is with respect to ``exp(alpha)`` start_model_params : None or array starting parameter for the ``model._fit_pirls``. method : 'basinhopping', 'nm' or 'minimize' 'basinhopping' and 'nm' directly use the underlying scipy.optimize functions `basinhopping` and `fmin`. 'minimize' provides access to the high level interface, `scipy.optimize.minimize`. fit_kwds : keyword arguments additional keyword arguments will be used in the call to the scipy optimizer. Which keywords are supported depends on the scipy optimization function. Returns ------- alpha : ndarray penalization parameter found by minimizing the criterion. Note that this can be only a local (near) optimum. fit_res : tuple results returned by the scipy optimization routine. The parameters in the optimization problem are `log(alpha)` history : dict history of calls to pirls and contains alpha, the fit criterion and the parameters to which pirls converged to for the given alpha. Notes ----- In the test cases Nelder-Mead and bfgs often converge to local optima, see also https://github.com/statsmodels/statsmodels/issues/5381. This does not use any analytical derivatives for the criterion minimization. Status: experimental, It is possible that defaults change if there is a better way to find a global optimum. API (e.g. type of return) might also change. """ # copy attributes that are changed, so we can reset them scale_keep = self.scale scaletype_keep = self.scaletype # TODO: use .copy() method when available for all types alpha_keep = copy.copy(self.alpha) if start_params is None: start_params = np.zeros(self.k_smooths) else: start_params = np.log(1e-20 + start_params) history = {} history['alpha'] = [] history['params'] = [start_model_params] history['criterion'] = [] def fun(p): a = np.exp(p) res_ = self._fit_pirls(start_params=history['params'][-1], alpha=a) history['alpha'].append(a) history['params'].append(np.asarray(res_.params)) return getattr(res_, criterion) if method == 'nm': kwds = dict(full_output=True, maxiter=1000, maxfun=2000) kwds.update(fit_kwds) fit_res = optimize.fmin(fun, start_params, **kwds) opt = fit_res[0] elif method == 'basinhopping': kwds = dict(minimizer_kwargs={'method': 'Nelder-Mead', 'options': {'maxiter': 100, 'maxfev': 500}}, niter=10) kwds.update(fit_kwds) fit_res = optimize.basinhopping(fun, start_params, **kwds) opt = fit_res.x elif method == 'minimize': fit_res = optimize.minimize(fun, start_params, **fit_kwds) opt = fit_res.x else: raise ValueError('method not recognized') del history['params'][0] # remove the model start_params alpha = np.exp(opt) # reset attributes that have or might have changed self.scale = scale_keep self.scaletype = scaletype_keep self.alpha = alpha_keep return alpha, fit_res, history def select_penweight_kfold(self, alphas=None, cv_iterator=None, cost=None, k_folds=5, k_grid=11): """find alphas by k-fold cross-validation Warning: This estimates ``k_folds`` models for each point in the grid of alphas. Parameters ---------- alphas : None or list of arrays cv_iterator : instance instance of a cross-validation iterator, by default this is a KFold instance cost : function default is mean squared error. The cost function to evaluate the prediction error for the left out sample. This should take two arrays as argument and return one float. k_folds : int number of folds if default Kfold iterator is used. This is ignored if ``cv_iterator`` is not None. Returns ------- alpha_cv : list of float Best alpha in grid according to cross-validation res_cv : instance of MultivariateGAMCVPath The instance was used for cross-validation and holds the results Notes ----- The default alphas are defined as ``alphas = [np.logspace(0, 7, k_grid) for _ in range(k_smooths)]`` """ if cost is None: def cost(x1, x2): return np.linalg.norm(x1 - x2) / len(x1) if alphas is None: alphas = [np.logspace(0, 7, k_grid) for _ in range(self.k_smooths)] if cv_iterator is None: cv_iterator = KFold(k_folds=k_folds, shuffle=True) gam_cv = MultivariateGAMCVPath(smoother=self.smoother, alphas=alphas, gam=GLMGam, cost=cost, endog=self.endog, exog=self.exog_linear, cv_iterator=cv_iterator) gam_cv_res = gam_cv.fit() return gam_cv_res.alpha_cv, gam_cv_res class LogitGam(PenalizedMixin, Logit): """Generalized Additive model for discrete Logit This subclasses discrete_model Logit. Warning: not all inherited methods might take correctly account of the penalization not verified yet. """ def __init__(self, endog, smoother, alpha, *args, **kwargs): if not isinstance(alpha, Iterable): alpha = np.array([alpha] * len(smoother.smoothers)) self.smoother = smoother self.alpha = alpha self.pen_weight = 1 # TODO: pen weight should not be defined here!! penal = MultivariateGamPenalty(smoother, alpha=alpha) super(LogitGam, self).__init__(endog, smoother.basis, penal=penal, *args, **kwargs) def penalized_wls(endog, exog, penalty_matrix, weights): """weighted least squares with quadratic penalty Parameters ---------- endog : ndarray response or endogenous variable exog : ndarray design matrix, matrix of exogenous or explanatory variables penalty_matrix : ndarray, 2-Dim square penality matrix for quadratic penalization. Note, the penalty_matrix is multiplied by two to match non-pirls fitting methods. weights : ndarray weights for WLS Returns ------- results : Results instance of WLS """ y, x, s = endog, exog, penalty_matrix # TODO: I do not understand why I need 2 * s aug_y, aug_x, aug_weights = make_augmented_matrix(y, x, 2 * s, weights) wls_results = lm.WLS(aug_y, aug_x, aug_weights).fit() # TODO: use MinimalWLS during iterations, less overhead # However, MinimalWLS does not return normalized_cov_params # which we need at the end of the iterations # call would be # wls_results = reg_tools._MinimalWLS(aug_y, aug_x, aug_weights).fit() wls_results.params = wls_results.params.ravel() return wls_results def make_augmented_matrix(endog, exog, penalty_matrix, weights): """augment endog, exog and weights with stochastic restriction matrix Parameters ---------- endog : ndarray response or endogenous variable exog : ndarray design matrix, matrix of exogenous or explanatory variables penalty_matrix : ndarray, 2-Dim square penality matrix for quadratic penalization weights : ndarray weights for WLS Returns ------- endog_aug : ndarray augmented response variable exog_aug : ndarray augmented design matrix weights_aug : ndarray augmented weights for WLS """ y, x, s, = endog, exog, penalty_matrix nobs = x.shape[0] # TODO: needs full because of broadcasting with weights # check what weights should be doing rs = matrix_sqrt(s) x1 = np.vstack([x, rs]) # augmented x n_samp1es_x1 = x1.shape[0] y1 = np.array([0.] * n_samp1es_x1) # augmented y y1[:nobs] = y id1 = np.array([1.] * rs.shape[0]) w1 = np.concatenate([weights, id1]) return y1, x1, w1 statsmodels-0.12.2/statsmodels/gam/smooth_basis.py000066400000000000000000001147761400612667500223370ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Spline and other smoother classes for Generalized Additive Models Author: Luca Puggini Author: Josef Perktold Created on Fri Jun 5 16:32:00 2015 """ # import useful only for development from abc import ABCMeta, abstractmethod from statsmodels.compat.python import with_metaclass import numpy as np import pandas as pd from patsy import dmatrix from patsy.mgcv_cubic_splines import _get_all_sorted_knots from statsmodels.tools.linalg import transf_constraints # Obtain b splines from patsy def _equally_spaced_knots(x, df): n_knots = df - 2 x_min = x.min() x_max = x.max() knots = np.linspace(x_min, x_max, n_knots) return knots def _R_compat_quantile(x, probs): # return np.percentile(x, 100 * np.asarray(probs)) probs = np.asarray(probs) quantiles = np.asarray([np.percentile(x, 100 * prob) for prob in probs.ravel(order="C")]) return quantiles.reshape(probs.shape, order="C") # FIXME: is this copy/pasted? If so, why do we need it? If not, get # rid of the try/except for scipy import # from patsy splines.py def _eval_bspline_basis(x, knots, degree, deriv='all', include_intercept=True): try: from scipy.interpolate import splev except ImportError: raise ImportError("spline functionality requires scipy") # 'knots' are assumed to be already pre-processed. E.g. usually you # want to include duplicate copies of boundary knots; you should do # that *before* calling this constructor. knots = np.atleast_1d(np.asarray(knots, dtype=float)) assert knots.ndim == 1 knots.sort() degree = int(degree) x = np.atleast_1d(x) if x.ndim == 2 and x.shape[1] == 1: x = x[:, 0] assert x.ndim == 1 # XX FIXME: when points fall outside of the boundaries, splev and R seem # to handle them differently. I do not know why yet. So until we understand # this and decide what to do with it, I'm going to play it safe and # disallow such points. if np.min(x) < np.min(knots) or np.max(x) > np.max(knots): raise NotImplementedError("some data points fall outside the " "outermost knots, and I'm not sure how " "to handle them. (Patches accepted!)") # Thanks to Charles Harris for explaining splev. It's not well # documented, but basically it computes an arbitrary b-spline basis # given knots and degree on some specificed points (or derivatives # thereof, but we do not use that functionality), and then returns some # linear combination of these basis functions. To get out the basis # functions themselves, we use linear combinations like [1, 0, 0], [0, # 1, 0], [0, 0, 1]. # NB: This probably makes it rather inefficient (though I have not checked # to be sure -- maybe the fortran code actually skips computing the basis # function for coefficients that are zero). # Note: the order of a spline is the same as its degree + 1. # Note: there are (len(knots) - order) basis functions. k_const = 1 - int(include_intercept) n_bases = len(knots) - (degree + 1) - k_const if deriv in ['all', 0]: basis = np.empty((x.shape[0], n_bases), dtype=float) ret = basis if deriv in ['all', 1]: der1_basis = np.empty((x.shape[0], n_bases), dtype=float) ret = der1_basis if deriv in ['all', 2]: der2_basis = np.empty((x.shape[0], n_bases), dtype=float) ret = der2_basis for i in range(n_bases): coefs = np.zeros((n_bases + k_const,)) # we are skipping the first column of the basis to drop constant coefs[i + k_const] = 1 ii = i if deriv in ['all', 0]: basis[:, ii] = splev(x, (knots, coefs, degree)) if deriv in ['all', 1]: der1_basis[:, ii] = splev(x, (knots, coefs, degree), der=1) if deriv in ['all', 2]: der2_basis[:, ii] = splev(x, (knots, coefs, degree), der=2) if deriv == 'all': return basis, der1_basis, der2_basis else: return ret def compute_all_knots(x, df, degree): order = degree + 1 n_inner_knots = df - order lower_bound = np.min(x) upper_bound = np.max(x) knot_quantiles = np.linspace(0, 1, n_inner_knots + 2)[1:-1] inner_knots = _R_compat_quantile(x, knot_quantiles) all_knots = np.concatenate(([lower_bound, upper_bound] * order, inner_knots)) return all_knots, lower_bound, upper_bound, inner_knots def make_bsplines_basis(x, df, degree): ''' make a spline basis for x ''' all_knots, _, _, _ = compute_all_knots(x, df, degree) basis, der_basis, der2_basis = _eval_bspline_basis(x, all_knots, degree) return basis, der_basis, der2_basis def get_knots_bsplines(x=None, df=None, knots=None, degree=3, spacing='quantile', lower_bound=None, upper_bound=None, all_knots=None): """knots for use in B-splines There are two main options for the knot placement - quantile spacing with multiplicity of boundary knots - equal spacing extended to boundary or exterior knots The first corresponds to splines as used by patsy. the second is the knot spacing for P-Splines. """ # based on patsy memorize_finish if all_knots is not None: return all_knots x_min = x.min() x_max = x.max() if degree < 0: raise ValueError("degree must be greater than 0 (not %r)" % (degree,)) if int(degree) != degree: raise ValueError("degree must be an integer (not %r)" % (degree,)) # These are guaranteed to all be 1d vectors by the code above # x = np.concatenate(tmp["xs"]) if df is None and knots is None: raise ValueError("must specify either df or knots") order = degree + 1 if df is not None: n_inner_knots = df - order if n_inner_knots < 0: raise ValueError("df=%r is too small for degree=%r; must be >= %s" % (df, degree, # We know that n_inner_knots is negative; # if df were that much larger, it would # have been zero, and things would work. df - n_inner_knots)) if knots is not None: if len(knots) != n_inner_knots: raise ValueError("df=%s with degree=%r implies %s knots, " "but %s knots were provided" % (df, degree, n_inner_knots, len(knots))) elif spacing == 'quantile': # Need to compute inner knots knot_quantiles = np.linspace(0, 1, n_inner_knots + 2)[1:-1] inner_knots = _R_compat_quantile(x, knot_quantiles) elif spacing == 'equal': # Need to compute inner knots grid = np.linspace(0, 1, n_inner_knots + 2)[1:-1] inner_knots = x_min + grid * (x_max - x_min) diff_knots = inner_knots[1] - inner_knots[0] else: raise ValueError("incorrect option for spacing") if knots is not None: inner_knots = knots if lower_bound is None: lower_bound = np.min(x) if upper_bound is None: upper_bound = np.max(x) if lower_bound > upper_bound: raise ValueError("lower_bound > upper_bound (%r > %r)" % (lower_bound, upper_bound)) inner_knots = np.asarray(inner_knots) if inner_knots.ndim > 1: raise ValueError("knots must be 1 dimensional") if np.any(inner_knots < lower_bound): raise ValueError("some knot values (%s) fall below lower bound " "(%r)" % (inner_knots[inner_knots < lower_bound], lower_bound)) if np.any(inner_knots > upper_bound): raise ValueError("some knot values (%s) fall above upper bound " "(%r)" % (inner_knots[inner_knots > upper_bound], upper_bound)) if spacing == "equal": diffs = np.arange(1, order + 1) * diff_knots lower_knots = inner_knots[0] - diffs[::-1] upper_knots = inner_knots[-1] + diffs all_knots = np.concatenate((lower_knots, inner_knots, upper_knots)) else: all_knots = np.concatenate(([lower_bound, upper_bound] * order, inner_knots)) all_knots.sort() return all_knots def _get_integration_points(knots, k_points=3): """add points to each subinterval defined by knots inserts k_points between each two consecutive knots """ k_points = k_points + 1 knots = np.unique(knots) dxi = np.arange(k_points) / k_points dxk = np.diff(knots) dx = dxk[:, None] * dxi x = np.concatenate(((knots[:-1, None] + dx).ravel(), [knots[-1]])) return x def get_covder2(smoother, k_points=4, integration_points=None, skip_ctransf=False, deriv=2): """ Approximate integral of cross product of second derivative of smoother This uses scipy.integrate simps to compute an approximation to the integral of the smoother derivative cross-product at knots plus k_points in between knots. """ from scipy.integrate import simps knots = smoother.knots x = _get_integration_points(knots, k_points=3) if integration_points is None: d2 = smoother.transform(x, deriv=deriv, skip_ctransf=skip_ctransf) else: x = integration_points covd2 = simps(d2[:, :, None] * d2[:, None, :], x, axis=0) return covd2 # TODO: this function should be deleted def make_poly_basis(x, degree, intercept=True): ''' given a vector x returns poly=(1, x, x^2, ..., x^degree) and its first and second derivative ''' if intercept: start = 0 else: start = 1 nobs = len(x) basis = np.zeros(shape=(nobs, degree + 1 - start)) der_basis = np.zeros(shape=(nobs, degree + 1 - start)) der2_basis = np.zeros(shape=(nobs, degree + 1 - start)) for i in range(start, degree + 1): basis[:, i - start] = x ** i der_basis[:, i - start] = i * x ** (i - 1) der2_basis[:, i - start] = i * (i - 1) * x ** (i - 2) return basis, der_basis, der2_basis # TODO: try to include other kinds of splines from patsy # x = np.linspace(0, 1, 30) # df = 10 # degree = 3 # from patsy.mgcv_cubic_splines import cc, cr, te # all_knots, lower, upper, inner = compute_all_knots(x, df, degree) # result = cc(x, df=df, knots=all_knots, lower_bound=lower, upper_bound=upper, # constraints=None) # # import matplotlib.pyplot as plt # # result = np.array(result) # print(result.shape) # plt.plot(result.T) # plt.show() class UnivariateGamSmoother(with_metaclass(ABCMeta)): """Base Class for single smooth component """ def __init__(self, x, constraints=None, variable_name='x'): self.x = x self.constraints = constraints self.variable_name = variable_name self.nobs, self.k_variables = len(x), 1 base4 = self._smooth_basis_for_single_variable() if constraints == 'center': constraints = base4[0].mean(0)[None, :] if constraints is not None and not isinstance(constraints, str): ctransf = transf_constraints(constraints) self.ctransf = ctransf else: # subclasses might set ctransf directly # only used if constraints is None if not hasattr(self, 'ctransf'): self.ctransf = None self.basis, self.der_basis, self.der2_basis, self.cov_der2 = base4 if self.ctransf is not None: ctransf = self.ctransf # transform attributes that are not None if base4[0] is not None: self.basis = base4[0].dot(ctransf) if base4[1] is not None: self.der_basis = base4[1].dot(ctransf) if base4[2] is not None: self.der2_basis = base4[2].dot(ctransf) if base4[3] is not None: self.cov_der2 = ctransf.T.dot(base4[3]).dot(ctransf) self.dim_basis = self.basis.shape[1] self.col_names = [self.variable_name + "_s" + str(i) for i in range(self.dim_basis)] @abstractmethod def _smooth_basis_for_single_variable(self): return class UnivariateGenericSmoother(UnivariateGamSmoother): """Generic single smooth component """ def __init__(self, x, basis, der_basis, der2_basis, cov_der2, variable_name='x'): self.basis = basis self.der_basis = der_basis self.der2_basis = der2_basis self.cov_der2 = cov_der2 super(UnivariateGenericSmoother, self).__init__( x, variable_name=variable_name) def _smooth_basis_for_single_variable(self): return self.basis, self.der_basis, self.der2_basis, self.cov_der2 class UnivariatePolynomialSmoother(UnivariateGamSmoother): """polynomial single smooth component """ def __init__(self, x, degree, variable_name='x'): self.degree = degree super(UnivariatePolynomialSmoother, self).__init__( x, variable_name=variable_name) def _smooth_basis_for_single_variable(self): # TODO: unclear description """ given a vector x returns poly=(1, x, x^2, ..., x^degree) and its first and second derivative """ basis = np.zeros(shape=(self.nobs, self.degree)) der_basis = np.zeros(shape=(self.nobs, self.degree)) der2_basis = np.zeros(shape=(self.nobs, self.degree)) for i in range(self.degree): dg = i + 1 basis[:, i] = self.x ** dg der_basis[:, i] = dg * self.x ** (dg - 1) if dg > 1: der2_basis[:, i] = dg * (dg - 1) * self.x ** (dg - 2) else: der2_basis[:, i] = 0 cov_der2 = np.dot(der2_basis.T, der2_basis) return basis, der_basis, der2_basis, cov_der2 class UnivariateBSplines(UnivariateGamSmoother): """B-Spline single smooth component This creates and holds the B-Spline basis function for one component. Parameters ---------- x : ndarray, 1-D underlying explanatory variable for smooth terms. df : int numer of basis functions or degrees of freedom degree : int degree of the spline include_intercept : bool If False, then the basis functions are transformed so that they do not include a constant. This avoids perfect collinearity if a constant or several components are included in the model. constraints : {None, str, array} Constraints are used to transform the basis functions to satisfy those constraints. `constraints = 'center'` applies a linear transform to remove the constant and center the basis functions. variable_name : {None, str} The name for the underlying explanatory variable, x, used in for creating the column and parameter names for the basis functions. covder2_kwds : {None, dict} options for computing the penalty matrix from the second derivative of the spline. knot_kwds : {None, list[dict]} option for the knot selection. By default knots are selected in the same way as in patsy, however the number of knots is independent of keeping or removing the constant. Interior knot selection is based on quantiles of the data and is the same in patsy and mgcv. Boundary points are at the limits of the data range. The available options use with `get_knots_bsplines` are - knots : None or array interior knots - spacing : 'quantile' or 'equal' - lower_bound : None or float location of lower boundary knots, all boundary knots are at the same point - upper_bound : None or float location of upper boundary knots, all boundary knots are at the same point - all_knots : None or array If all knots are provided, then those will be taken as given and all other options will be ignored. """ def __init__(self, x, df, degree=3, include_intercept=False, constraints=None, variable_name='x', covder2_kwds=None, **knot_kwds): self.degree = degree self.df = df self.include_intercept = include_intercept self.knots = get_knots_bsplines(x, degree=degree, df=df, **knot_kwds) self.covder2_kwds = (covder2_kwds if covder2_kwds is not None else {}) super(UnivariateBSplines, self).__init__( x, constraints=constraints, variable_name=variable_name) def _smooth_basis_for_single_variable(self): basis, der_basis, der2_basis = _eval_bspline_basis( self.x, self.knots, self.degree, include_intercept=self.include_intercept) # cov_der2 = np.dot(der2_basis.T, der2_basis) cov_der2 = get_covder2(self, skip_ctransf=True, **self.covder2_kwds) return basis, der_basis, der2_basis, cov_der2 def transform(self, x_new, deriv=0, skip_ctransf=False): """create the spline basis for new observations The main use of this stateful transformation is for prediction using the same specification of the spline basis. Parameters ---------- x_new : ndarray observations of the underlying explanatory variable deriv : int which derivative of the spline basis to compute This is an options for internal computation. skip_ctransf : bool whether to skip the constraint transform This is an options for internal computation. Returns ------- basis : ndarray design matrix for the spline basis for given ``x_new`` """ if x_new is None: x_new = self.x exog = _eval_bspline_basis(x_new, self.knots, self.degree, deriv=deriv, include_intercept=self.include_intercept) # ctransf does not exist yet when cov_der2 is computed ctransf = getattr(self, 'ctransf', None) if ctransf is not None and not skip_ctransf: exog = exog.dot(self.ctransf) return exog class UnivariateCubicSplines(UnivariateGamSmoother): """Cubic Spline single smooth component Cubic splines as described in the wood's book in chapter 3 """ def __init__(self, x, df, constraints=None, transform='domain', variable_name='x'): self.degree = 3 self.df = df self.transform_data_method = transform self.x = x = self.transform_data(x, initialize=True) self.knots = _equally_spaced_knots(x, df) super(UnivariateCubicSplines, self).__init__( x, constraints=constraints, variable_name=variable_name) def transform_data(self, x, initialize=False): tm = self.transform_data_method if tm is None: return x if initialize is True: if tm == 'domain': self.domain_low = x.min(0) self.domain_upp = x.max(0) elif isinstance(tm, tuple): self.domain_low = tm[0] self.domain_upp = tm[1] self.transform_data_method = 'domain' else: raise ValueError("transform should be None, 'domain' " "or a tuple") self.domain_diff = self.domain_upp - self.domain_low if self.transform_data_method == 'domain': x = (x - self.domain_low) / self.domain_diff return x else: raise ValueError("incorrect transform_data_method") def _smooth_basis_for_single_variable(self): basis = self._splines_x()[:, :-1] # demean except for constant, does not affect derivatives if not self.constraints == 'none': self.transf_mean = basis[:, 1:].mean(0) basis[:, 1:] -= self.transf_mean else: self.transf_mean = np.zeros(basis.shape[1]) s = self._splines_s()[:-1, :-1] if not self.constraints == 'none': ctransf = np.diag(1/np.max(np.abs(basis), axis=0)) else: ctransf = np.eye(basis.shape[1]) # use np.eye to avoid rescaling # ctransf = np.eye(basis.shape[1]) if self.constraints == 'no-const': ctransf = ctransf[1:] self.ctransf = ctransf return basis, None, None, s def _rk(self, x, z): p1 = ((z - 1 / 2) ** 2 - 1 / 12) * ((x - 1 / 2) ** 2 - 1 / 12) / 4 p2 = ((np.abs(z - x) - 1 / 2) ** 4 - 1 / 2 * (np.abs(z - x) - 1 / 2) ** 2 + 7 / 240) / 24. return p1 - p2 def _splines_x(self, x=None): if x is None: x = self.x n_columns = len(self.knots) + 2 nobs = x.shape[0] basis = np.ones(shape=(nobs, n_columns)) basis[:, 1] = x # for loop equivalent to outer(x, xk, fun=rk) for i, xi in enumerate(x): for j, xkj in enumerate(self.knots): s_ij = self._rk(xi, xkj) basis[i, j + 2] = s_ij return basis def _splines_s(self): q = len(self.knots) + 2 s = np.zeros(shape=(q, q)) for i, x1 in enumerate(self.knots): for j, x2 in enumerate(self.knots): s[i + 2, j + 2] = self._rk(x1, x2) return s def transform(self, x_new): x_new = self.transform_data(x_new, initialize=False) exog = self._splines_x(x_new) exog[:, 1:] -= self.transf_mean if self.ctransf is not None: exog = exog.dot(self.ctransf) return exog class UnivariateCubicCyclicSplines(UnivariateGamSmoother): """cyclic cubic regression spline single smooth component This creates and holds the Cyclic CubicSpline basis function for one component. Parameters ---------- x : ndarray, 1-D underlying explanatory variable for smooth terms. df : int number of basis functions or degrees of freedom degree : int degree of the spline include_intercept : bool If False, then the basis functions are transformed so that they do not include a constant. This avoids perfect collinearity if a constant or several components are included in the model. constraints : {None, str, array} Constraints are used to transform the basis functions to satisfy those constraints. `constraints = 'center'` applies a linear transform to remove the constant and center the basis functions. variable_name : None or str The name for the underlying explanatory variable, x, used in for creating the column and parameter names for the basis functions. """ def __init__(self, x, df, constraints=None, variable_name='x'): self.degree = 3 self.df = df self.x = x self.knots = _equally_spaced_knots(x, df) super(UnivariateCubicCyclicSplines, self).__init__( x, constraints=constraints, variable_name=variable_name) def _smooth_basis_for_single_variable(self): basis = dmatrix("cc(x, df=" + str(self.df) + ") - 1", {"x": self.x}) self.design_info = basis.design_info n_inner_knots = self.df - 2 + 1 # +n_constraints # TODO: from CubicRegressionSplines class all_knots = _get_all_sorted_knots(self.x, n_inner_knots=n_inner_knots, inner_knots=None, lower_bound=None, upper_bound=None) b, d = self._get_b_and_d(all_knots) s = self._get_s(b, d) return basis, None, None, s def _get_b_and_d(self, knots): """Returns mapping of cyclic cubic spline values to 2nd derivatives. .. note:: See 'Generalized Additive Models', Simon N. Wood, 2006, pp 146-147 Parameters ---------- knots : ndarray The 1-d array knots used for cubic spline parametrization, must be sorted in ascending order. Returns ------- b : ndarray Array for mapping cyclic cubic spline values at knots to second derivatives. d : ndarray Array for mapping cyclic cubic spline values at knots to second derivatives. Notes ----- The penalty matrix is equal to ``s = d.T.dot(b^-1).dot(d)`` """ h = knots[1:] - knots[:-1] n = knots.size - 1 # b and d are defined such that the penalty matrix is equivalent to: # s = d.T.dot(b^-1).dot(d) # reference in particular to pag 146 of Wood's book b = np.zeros((n, n)) # the b matrix on page 146 of Wood's book d = np.zeros((n, n)) # the d matrix on page 146 of Wood's book b[0, 0] = (h[n - 1] + h[0]) / 3. b[0, n - 1] = h[n - 1] / 6. b[n - 1, 0] = h[n - 1] / 6. d[0, 0] = -1. / h[0] - 1. / h[n - 1] d[0, n - 1] = 1. / h[n - 1] d[n - 1, 0] = 1. / h[n - 1] for i in range(1, n): b[i, i] = (h[i - 1] + h[i]) / 3. b[i, i - 1] = h[i - 1] / 6. b[i - 1, i] = h[i - 1] / 6. d[i, i] = -1. / h[i - 1] - 1. / h[i] d[i, i - 1] = 1. / h[i - 1] d[i - 1, i] = 1. / h[i - 1] return b, d def _get_s(self, b, d): return d.T.dot(np.linalg.inv(b)).dot(d) def transform(self, x_new): exog = dmatrix(self.design_info, {"x": x_new}) if self.ctransf is not None: exog = exog.dot(self.ctransf) return exog class AdditiveGamSmoother(with_metaclass(ABCMeta)): """Base class for additive smooth components """ def __init__(self, x, variable_names=None, include_intercept=False, **kwargs): # get pandas names before using asarray if isinstance(x, pd.DataFrame): data_names = x.columns.tolist() elif isinstance(x, pd.Series): data_names = [x.name] else: data_names = None x = np.asarray(x) if x.ndim == 1: self.x = x.copy() self.x.shape = (len(x), 1) else: self.x = x self.nobs, self.k_variables = self.x.shape if isinstance(include_intercept, bool): self.include_intercept = [include_intercept] * self.k_variables else: self.include_intercept = include_intercept if variable_names is None: if data_names is not None: self.variable_names = data_names else: self.variable_names = ['x' + str(i) for i in range(self.k_variables)] else: self.variable_names = variable_names self.smoothers = self._make_smoothers_list() self.basis = np.hstack(list(smoother.basis for smoother in self.smoothers)) self.dim_basis = self.basis.shape[1] self.penalty_matrices = [smoother.cov_der2 for smoother in self.smoothers] self.col_names = [] for smoother in self.smoothers: self.col_names.extend(smoother.col_names) self.mask = [] last_column = 0 for smoother in self.smoothers: mask = np.array([False] * self.dim_basis) mask[last_column:smoother.dim_basis + last_column] = True last_column = last_column + smoother.dim_basis self.mask.append(mask) @abstractmethod def _make_smoothers_list(self): pass def transform(self, x_new): """create the spline basis for new observations The main use of this stateful transformation is for prediction using the same specification of the spline basis. Parameters ---------- x_new: ndarray observations of the underlying explanatory variable Returns ------- basis : ndarray design matrix for the spline basis for given ``x_new``. """ if x_new.ndim == 1 and self.k_variables == 1: x_new = x_new.reshape(-1, 1) exog = np.hstack(list(self.smoothers[i].transform(x_new[:, i]) for i in range(self.k_variables))) return exog class GenericSmoothers(AdditiveGamSmoother): """generic class for additive smooth components for GAM """ def __init__(self, x, smoothers): self.smoothers = smoothers super(GenericSmoothers, self).__init__(x, variable_names=None) def _make_smoothers_list(self): return self.smoothers class PolynomialSmoother(AdditiveGamSmoother): """additive polynomial components for GAM """ def __init__(self, x, degrees, variable_names=None): self.degrees = degrees super(PolynomialSmoother, self).__init__(x, variable_names=variable_names) def _make_smoothers_list(self): smoothers = [] for v in range(self.k_variables): uv_smoother = UnivariatePolynomialSmoother( self.x[:, v], degree=self.degrees[v], variable_name=self.variable_names[v]) smoothers.append(uv_smoother) return smoothers class BSplines(AdditiveGamSmoother): """additive smooth components using B-Splines This creates and holds the B-Spline basis function for several components. Parameters ---------- x : array_like, 1-D or 2-D underlying explanatory variable for smooth terms. If 2-dimensional, then observations should be in rows and explanatory variables in columns. df : {int, array_like[int]} number of basis functions or degrees of freedom; should be equal in length to the number of columns of `x`; may be an integer if `x` has one column or is 1-D. degree : {int, array_like[int]} degree(s) of the spline; the same length and type rules apply as to `df` include_intercept : bool If False, then the basis functions are transformed so that they do not include a constant. This avoids perfect collinearity if a constant or several components are included in the model. constraints : {None, str, array} Constraints are used to transform the basis functions to satisfy those constraints. `constraints = 'center'` applies a linear transform to remove the constant and center the basis functions. variable_names : {list[str], None} The names for the underlying explanatory variables, x used in for creating the column and parameter names for the basis functions. If ``x`` is a pandas object, then the names will be taken from it. knot_kwds : None or list of dict option for the knot selection. By default knots are selected in the same way as in patsy, however the number of knots is independent of keeping or removing the constant. Interior knot selection is based on quantiles of the data and is the same in patsy and mgcv. Boundary points are at the limits of the data range. The available options use with `get_knots_bsplines` are - knots : None or array interior knots - spacing : 'quantile' or 'equal' - lower_bound : None or float location of lower boundary knots, all boundary knots are at the same point - upper_bound : None or float location of upper boundary knots, all boundary knots are at the same point - all_knots : None or array If all knots are provided, then those will be taken as given and all other options will be ignored. Attributes ---------- smoothers : list of univariate smooth component instances basis : design matrix, array of spline bases columns for all components penalty_matrices : list of penalty matrices, one for each smooth term dim_basis : number of columns in the basis k_variables : number of smooth components col_names : created names for the basis columns There are additional attributes about the specification of the splines and some attributes mainly for internal use. Notes ----- A constant in the spline basis function can be removed in two different ways. The first is by dropping one basis column and normalizing the remaining columns. This is obtained by the default ``include_intercept=False, constraints=None`` The second option is by using the centering transform which is a linear transformation of all basis functions. As a consequence of the transformation, the B-spline basis functions do not have locally bounded support anymore. This is obtained ``constraints='center'``. In this case ``include_intercept`` will be automatically set to True to avoid dropping an additional column. """ def __init__(self, x, df, degree, include_intercept=False, constraints=None, variable_names=None, knot_kwds=None): if isinstance(degree, int): self.degrees = np.array([degree], dtype=int) else: self.degrees = degree if isinstance(df, int): self.dfs = np.array([df], dtype=int) else: self.dfs = df self.knot_kwds = knot_kwds # TODO: move attaching constraints to super call self.constraints = constraints if constraints == 'center': include_intercept = True super(BSplines, self).__init__(x, include_intercept=include_intercept, variable_names=variable_names) def _make_smoothers_list(self): smoothers = [] for v in range(self.k_variables): kwds = self.knot_kwds[v] if self.knot_kwds else {} uv_smoother = UnivariateBSplines( self.x[:, v], df=self.dfs[v], degree=self.degrees[v], include_intercept=self.include_intercept[v], constraints=self.constraints, variable_name=self.variable_names[v], **kwds) smoothers.append(uv_smoother) return smoothers class CubicSplines(AdditiveGamSmoother): """additive smooth components using cubic splines as in Wood 2006. Note, these splines do NOT use the same spline basis as ``Cubic Regression Splines``. """ def __init__(self, x, df, constraints='center', transform='domain', variable_names=None): self.dfs = df self.constraints = constraints self.transform = transform super(CubicSplines, self).__init__(x, constraints=constraints, variable_names=variable_names) def _make_smoothers_list(self): smoothers = [] for v in range(self.k_variables): uv_smoother = UnivariateCubicSplines( self.x[:, v], df=self.dfs[v], constraints=self.constraints, transform=self.transform, variable_name=self.variable_names[v]) smoothers.append(uv_smoother) return smoothers class CyclicCubicSplines(AdditiveGamSmoother): """additive smooth components using cyclic cubic regression splines This spline basis is the same as in patsy. Parameters ---------- x : array_like, 1-D or 2-D underlying explanatory variable for smooth terms. If 2-dimensional, then observations should be in rows and explanatory variables in columns. df : int numer of basis functions or degrees of freedom constraints : {None, str, array} Constraints are used to transform the basis functions to satisfy those constraints. variable_names : {list[str], None} The names for the underlying explanatory variables, x used in for creating the column and parameter names for the basis functions. If ``x`` is a pandas object, then the names will be taken from it. """ def __init__(self, x, df, constraints=None, variable_names=None): self.dfs = df # TODO: move attaching constraints to super call self.constraints = constraints super(CyclicCubicSplines, self).__init__(x, variable_names=variable_names) def _make_smoothers_list(self): smoothers = [] for v in range(self.k_variables): uv_smoother = UnivariateCubicCyclicSplines( self.x[:, v], df=self.dfs[v], constraints=self.constraints, variable_name=self.variable_names[v]) smoothers.append(uv_smoother) return smoothers # class CubicRegressionSplines(BaseCubicSplines): # # TODO: this class is still not tested # # def __init__(self, x, df=10): # import warnings # warnings.warn("This class is still not tested and it is probably" # " not working properly. " # "I suggest to use another smoother", Warning) # # super(CubicRegressionSplines, self).__init__(x, df) # # self.basis = dmatrix("cc(x, df=" + str(df) + ") - 1", {"x": x}) # n_inner_knots = df - 2 + 1 # +n_constraints # # TODO: ACcording to CubicRegressionSplines class this should be # # n_inner_knots = df - 2 # all_knots = _get_all_sorted_knots(x, n_inner_knots=n_inner_knots, # inner_knots=None, # lower_bound=None, upper_bound=None) # # b, d = self._get_b_and_d(all_knots) # self.s = self._get_s(b, d) # # self.dim_basis = self.basis.shape[1] # # def _get_b_and_d(self, knots): # # h = knots[1:] - knots[:-1] # n = knots.size - 1 # # # b and d are defined such that the penalty matrix is equivalent to: # # s = d.T.dot(b^-1).dot(d) # # reference in particular to pag 146 of Wood's book # b = np.zeros((n, n)) # the b matrix on page 146 of Wood's book # d = np.zeros((n, n)) # the d matrix on page 146 of Wood's book # # for i in range(n-2): # d[i, i] = 1/h[i] # d[i, i+1] = -1/h[i] - 1/h[i+1] # d[i, i+2] = 1/h[i+1] # # b[i, i] = (h[i] + h[i+1])/3 # # for i in range(n-3): # b[i, i+1] = h[i+1]/6 # b[i+1, i] = h[i+1]/6 # # return b, d # # def _get_s(self, b, d): # # return d.T.dot(np.linalg.pinv(b)).dot(d) 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"987",-0.120844419500681,-0.0445435177534819,0.0453778047952835,0.0664389325737422,0.0490895206580431,0,0.533497822659153 "988",-0.00845831203633671,0.0884680454619229,-0.0926164233343757,0.0718851489499701,-0.0945715526946103,0,-1.84324384297505 "989",0.36835273786989,-0.343684038612992,0.254924125529185,0.0687078056313837,0.260633186037081,1,4.94632681051919 "990",0.925439563107405,0.999861187301576,0.800234924422307,0.134618206480845,0.942924088291598,1,9.27872791866588 "991",-0.0691058332654721,0.0555636719800532,-0.0591495405499159,0.0710285871836794,-0.0598886973371698,0,-1.27551667844689 "992",-0.195611274619547,-0.732530983630568,-0.108247929347823,0.0707573238491324,-0.0634292813981925,0,-0.683519537094062 "993",0.206060931295594,-0.122919864486903,0.122470490014625,0.067235586626507,0.127992802909461,1,1.97022787594347 "994",-0.375886414575821,0.241587879601866,-0.222499533804098,0.0699347108359535,-0.228232759589956,0,-4.03342133295782 "995",0.188951394100895,-0.594175175763667,0.126680312970918,0.0712498850337396,0.17054304007204,1,2.92694767998707 "996",0.0193531991613668,-0.731660454533994,-0.106452963906501,0.0707263655059849,-0.0614464550299414,1,-0.657724039375207 "997",-0.219763089272701,0.55366799607873,-0.188258602637155,0.0716822837340163,-0.221662255102467,0,-3.45467613783501 "998",-0.21451558934989,0.271899697370827,-0.240274594161269,0.0707337966998637,-0.246883662751375,0,-4.33005832558093 "999",0.206364433507704,-0.435727406758815,0.25044084280166,0.0681881919449853,0.266983666951987,1,4.97530104613227 "1000",0.0803400626266812,-0.617481087800115,0.0947807616264508,0.0703452236366206,0.141950486563733,1,2.40957013901761 statsmodels-0.12.2/statsmodels/gam/tests/results/results_mpg_bs.py000066400000000000000000002253131400612667500255260ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch mpg_bs = Bunch() mpg_bs.smooth0 = Bunch() mpg_bs.smooth0.term = 'weight' mpg_bs.smooth0.bs_dim = 12 mpg_bs.smooth0.dim = 1 mpg_bs.smooth0.p_order = np.array([ 3, 2 ]) mpg_bs.smooth0.by = 'NA' mpg_bs.smooth0.label = 's(weight)' mpg_bs.smooth0.sp = -1 mpg_bs.smooth0.m = np.array([ 3, 2 ]) mpg_bs.smooth0.knots = np.array([ 1488, 1488, 1488, 1488, 1953.22222222, 2118.77777778, 2275, 2383.88888889, 2515.55555556, 2757.33333333, 3016.44444444, 3208.11111111, 4066, 4066, 4066, 4066 ]) mpg_bs.smooth0.rank = 10 mpg_bs.smooth0.null_space_dim = 1 mpg_bs.smooth0.df = 11 mpg_bs.smooth0.S_scale = 2.44395544177397e-06 mpg_bs.smooth0.vn = 'weight' mpg_bs.smooth0.first_para = 5 mpg_bs.smooth0.last_para = 15 mpg_bs.smooth0.S = np.array([ 0.130569121544375, -0.0191732921244136, 0.0202548028417763, 0.0393112950002946, 0.032061392663319, 0.0241651485426007, 0.0238771778381105, 0.0389406835250852, 0.0171569521441248, 0.00680570834700402, 0.00541920498010491, -0.0191732921244136, 0.0631473273216884, -0.0592997810399249, 0.0178641542128365, 0.00461438941034586, 0.00793912465273829, 0.00408821971418319, -0.000681869049168392, 0.00213834646721613, 0.000935846814259467, 0.000163463753965317, 0.0202548028417763, -0.0592997810399249, 0.201022514824508, -0.186241322892132, 0.00284878067469136, 0.0287314367063779, 0.00263260805442764, -0.00708846456492193, 0.00065385484055723, 0.000395067932117418, -0.000586348849229599, 0.0393112950002947, 0.0178641542128365, -0.186241322892132, 0.479322071007576, -0.286380917395105, 0.0563704638942206, 0.0348887744557148, 0.0255203052273876, 0.0138979985789615, 0.00560832050247454, 0.00383270204450356, 0.032061392663319, 0.00461438941034587, 0.00284878067469137, -0.286380917395105, 0.414581586658592, -0.181289913269406, -0.00412646444222532, -0.00354719180127285, -0.00206283566879658, -0.000685858743449883, -0.00142523589453221, 0.0241651485426007, 0.00793912465273829, 0.0287314367063779, 0.0563704638942206, -0.181289913269406, 0.213321319885371, -0.0483506678191679, 0.0110304252072989, 0.0122299348640366, 0.00357726593043956, 0.00234383478372281, 0.0238771778381105, 0.00408821971418319, 0.00263260805442764, 0.0348887744557148, -0.00412646444222533, -0.0483506678191679, 0.0999220996092033, -0.0356092452156359, 0.00921547832469341, 0.00389860712399989, 0.00147745030481206, 0.0389406835250852, -0.000681869049168392, -0.00708846456492192, 0.0255203052273876, -0.00354719180127286, 0.0110304252072989, -0.0356092452156359, 0.0574427000604467, -0.0102653399490586, -0.000311188772793241, 0.00285258581655637, 0.0171569521441248, 0.00213834646721613, 0.000653854840557233, 0.0138979985789615, -0.00206283566879658, 0.0122299348640366, 0.00921547832469341, -0.0102653399490586, 0.0189789273643945, -0.0062453384832703, 0.00255839876648785, 0.00680570834700402, 0.000935846814259467, 0.000395067932117419, 0.00560832050247454, -0.000685858743449884, 0.00357726593043956, 0.00389860712399989, -0.000311188772793241, -0.0062453384832703, 0.0211496391608495, -0.0111654555301857, 0.00541920498010491, 0.000163463753965317, -0.000586348849229599, 0.00383270204450356, -0.00142523589453221, 0.00234383478372281, 0.00147745030481206, 0.00285258581655637, 0.00255839876648785, -0.0111654555301857, 0.00794139033444708 ]).reshape(11, 11, order='F') mpg_bs.coefficients = np.array([ 29.6272774569595, -6.21365498504518, 1.43986598470837, 1.01128095138012, 20.1053719083286, -1.26007449980292, -5.26871981200625, -4.544036357677, -7.60063071956733, -5.01036711884368, -6.96226144900638, -9.06722069409647, -8.81829781369916, -7.9145836553663, -6.28068941724657, 5.09307848346347, 1.90848821039499, -0.646225516186639, -1.50240395085899, -4.19244286007642, -5.72993924243941, -6.83323296859843, -5.77088950575513, -4.29112523442438 ]) mpg_bs.fitted_values = np.array([ 21.9396113442978, 21.9396113442978, 18.7594768791121, 23.978775547494, 19.6605284085114, 22.5415570425591, 21.4364029092864, 21.5001397125411, 19.345544773382, 17.3284985371825, 23.0829354555269, 23.0829354555269, 20.5257074462847, 20.350418275392, 20.0920273672739, 16.3475493433762, 15.2683918200041, 14.6016645854518, 48.1414677548395, 34.6770647570973, 33.3220963193152, 34.9078179723597, 34.9078179723597, 25.7413956426768, 31.8998747894453, 31.4406608644666, 31.4406608644666, 25.4076816004152, 24.637322541799, 19.5423694752458, 43.7120662014648, 36.1794319009933, 37.8600814894106, 31.3973345386248, 30.9527603762328, 29.8740452948944, 29.6825700516209, 26.8853631419929, 26.3600803699054, 26.1773024038522, 25.3856227340742, 23.3020193188726, 24.7100852851954, 26.4172597325081, 34.6770647570973, 33.3220963193152, 23.0296498930938, 14.7476201253168, 14.7476201253168, 14.0557212409125, 34.34782143196, 33.965299405798, 33.7800699350403, 32.4689563918131, 32.329358068477, 23.1906404151376, 23.1906404151376, 23.1512875039068, 20.6941238423555, 25.5363151316018, 25.3886549365523, 25.5363151316018, 25.3886549365523, 34.4607486893619, 25.3326646650999, 20.7768158749875, 31.8441811103844, 23.0217104934054, 22.4301358955383, 23.1106217353394, 22.4200843547568, 14.7491664060278, 14.8191667947128, 14.012803756677, 13.9581303982076, 18.1760880728356, 33.3190101477328, 32.4975851853098, 31.1829311245072, 25.6555703896226, 22.6046524037776, 25.6230700315092, 19.5479517982215, 19.6165588348237, 19.6186479966108, 25.1994604891903, 24.8987688972877, 22.3628638356355, 22.3628638356355, 34.2300125601631, 39.2885271153262, 33.1621106074804, 32.5172901213345, 30.742747639841, 32.1452590079292, 30.6934785442198, 31.6517339944659, 30.5907093672281, 30.9641455088909, 24.6266167464042, 24.9022880874316, 18.78153275305, 17.1521355867311, 19.0141306741668, 18.231718904575, 16.8216593127165, 17.7202420891745, 22.0561680452922, 27.2153336488053, 20.5096211586017, 25.567299743712, 21.9831410020533, 26.7629956266796, 20.2961667790902, 25.2853678595518, 21.7669720922915, 26.7629956266796, 18.4910047689371, 33.3190101477328, 25.7413956426768, 31.8998747894453, 31.4406608644666, 29.7789375739066, 24.637322541799, 19.1142432042937, 19.2193336362723, 17.6365280620964, 17.6365280620964, 17.579806089837, 15.8168257322192, 21.8960566915, 21.7074289198647, 21.6525958338155, 21.4785952775663, 18.9756522798894, 18.9897722666541, 30.4602645168316, 29.3805961723331, 27.2238321670602, 27.9694092954432, 27.7274373142384, 24.7585135497211, 24.3629123288499, 21.0288767895242, 26.8745904429808, 24.038604652806, 24.1756501080763, 20.4312780252146, 32.4709598995115, 31.6700176166953, 31.9735144592214, 30.0023513412019, 28.4464554097632, 25.3419682258173, 30.061904278659, 29.8978667285749, 37.2387365989938, 37.2387365989938, 29.9813024611395, 29.8303048561215, 29.7392162621016, 29.1611058213974, 28.9573381148783, 23.6489155519235, 23.2515846177326, 21.6472193877583, 21.6596390100383, 21.6094248571684, 20.9701064457552, 20.8066296061343, 20.6663348110776, 25.161054576378, 33.0089371917933, 24.3712852430277, 24.3712852430277, 24.2659916432858, 18.5704777306123, 18.4763039586984, 17.9248313386425, 17.7576418795043, 38.0290768582748, 27.2115396047694, 37.9994882599177, 27.1914558802737, 26.6487573286281, 34.7866136817861, 24.6246815506878, 26.2295193582235, 26.4988154777346, 21.8800181352396, 33.5183981701922, 24.5373651901876, 20.8017272859603, 20.6222748754003, 20.8111189208126, 20.5838532565161, 18.3170655814092, 17.5023519244001, 20.8093138226564, 18.3617172827568, 19.5919656568361, 26.0100107405061, 20.4732985733418 ]) mpg_bs.linear_predictors = mpg_bs.fitted_values mpg_bs.deviance = 871.169775911354 mpg_bs.null_deviance = 8721.1724137931 mpg_bs.iter = 1 mpg_bs.weights = np.array([ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]) mpg_bs.prior_weights = np.array([ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]) mpg_bs.df_null = 202 mpg_bs.y = np.array([ 21, 21, 19, 24, 18, 19, 19, 19, 17, 16, 23, 23, 21, 21, 20, 16, 16, 15, 47, 38, 38, 37, 31, 24, 31, 31, 31, 24, 24, 19, 49, 31, 38, 30, 30, 30, 30, 27, 27, 27, 27, 24, 25, 24, 38, 38, 24, 15, 15, 13, 30, 31, 31, 31, 31, 17, 17, 17, 16, 26, 26, 26, 26, 36, 26, 19, 31, 22, 22, 22, 22, 16, 16, 14, 14, 19, 37, 31, 31, 24, 23, 25, 19, 19, 19, 25, 25, 23, 23, 31, 45, 31, 31, 31, 31, 31, 31, 31, 31, 27, 27, 17, 17, 19, 19, 17, 19, 19, 28, 19, 25, 19, 28, 19, 25, 19, 28, 18, 37, 24, 31, 31, 31, 24, 19, 19, 17, 17, 17, 17, 21, 21, 21, 21, 19, 19, 31, 26, 26, 32, 28, 26, 24, 24, 28, 25, 23, 23, 35, 31, 31, 31, 27, 27, 30, 30, 34, 38, 38, 28, 28, 29, 29, 26, 26, 24, 24, 24, 24, 24, 24, 29, 30, 27, 27, 27, 20, 19, 20, 19, 37, 27, 37, 27, 27, 37, 26, 24, 24, 19, 33, 25, 23, 23, 24, 24, 17, 17, 23, 19, 18, 26, 19 ]) mpg_bs.residuals = mpg_bs.y - mpg_bs.fitted_values mpg_bs.sig2 = 4.70648213227865 mpg_bs.edf_all = np.array([ 0.999999999999898, 1.00000000000005, 1.00000000000003, 1.00000000000002, 0.715182726327133, 0.945523457125076, 0.933952133938362, 0.910787981046657, 0.918439669310707, 0.936922915439925, 0.967620005020078, 0.978502846618072, 0.979593620228742, 0.973114724412765, 0.993928896515985, 0.206529848573726, 0.134722764346217, 0.130032558435079, 0.214058208629181, 0.428628830751172, 0.480753053928721, 0.728730191076721, 0.464984912297227, 0.858004843431828 ]) mpg_bs.edf1 = np.array([ 0.999999999999765, 1.00000000000012, 1.00000000000008, 1.00000000000005, 0.895328939039617, 0.985281018312391, 0.980485303917254, 0.985115307594987, 0.979973329752608, 0.991029113855046, 0.996293301947028, 0.996456521529546, 0.997881056094132, 0.998369079216076, 0.999638164901435, 0.263857404503542, 0.167489975859197, 0.241183045516588, 0.33714799512247, 0.51312433111897, 0.537892914498989, 0.811390270624644, 0.600430783273412, 0.922162336898961 ]) mpg_bs.hat = np.array([ 0.078074509536494, 0.078074509536494, 0.065030323239247, 0.0401345230539626, 0.168187944335173, 0.0664399958506056, 0.0736573430018038, 0.0780134136835909, 0.070154483540544, 0.180767093886445, 0.0664593954539867, 0.0664593954539867, 0.0594553974001933, 0.0675038468082751, 0.0536944450768444, 0.0970468595627894, 0.125358300385429, 0.125631704260218, 0.944302622125637, 0.0519142263263012, 0.0379831848669348, 0.0493844279965059, 0.0493844279965059, 0.0949083347321329, 0.0309819618026538, 0.029589102491272, 0.029589102491272, 0.0670447385890157, 0.0842123937662785, 0.0687733897932081, 0.422927507867707, 0.1328199698695, 0.096736475340286, 0.0419915413707043, 0.0396238084435642, 0.0346918436236485, 0.0363065585955308, 0.0491064279890273, 0.0441863897171056, 0.0388360718854439, 0.0414457600258062, 0.0451305758954266, 0.0505018876352514, 0.0744589274009074, 0.0519142263263012, 0.0379831848669348, 0.101629248471346, 0.436525380451652, 0.436525380451652, 0.410550032148353, 0.0425422548236529, 0.039274955616929, 0.0380389889031733, 0.0330421266803994, 0.0325988284653424, 0.066244431441902, 0.066244431441902, 0.0666221560337819, 0.0952529331187707, 0.046598430925228, 0.0484713995290722, 0.046598430925228, 0.0484713995290722, 0.11544865825422, 0.0480259855055657, 0.0566600271329405, 0.137824712103277, 0.112620492286817, 0.182195648532627, 0.11200306230358, 0.188335501134619, 0.169514959934583, 0.158055134563875, 0.160687809078496, 0.168998857825895, 0.0681007619372312, 0.0357408884807467, 0.0331290501952606, 0.0300353569162307, 0.0866855568546318, 0.0663539796978426, 0.0330200310685004, 0.0646249177791591, 0.0586792000782014, 0.0592011499253728, 0.0382030583658832, 0.0445521201486119, 0.067008407725231, 0.067008407725231, 0.0432898262619123, 0.12461566211325, 0.0358742808101827, 0.03362714942096, 0.0325446423810936, 0.0323846714084075, 0.0335509666038901, 0.0303353227561161, 0.0362607404205336, 0.0298241376272862, 0.0362837776795306, 0.0432688893651977, 0.0709252762463711, 0.147397446518277, 0.0723900341977973, 0.0517894283747262, 0.106665126964701, 0.0503219409131233, 0.0834357951937577, 0.100818501015755, 0.105292582127573, 0.104194456647628, 0.0762380011365815, 0.105895524421508, 0.131464943163143, 0.105727045973233, 0.0727635750299144, 0.105895524421508, 0.0437337708748914, 0.0357408884807467, 0.0949083347321329, 0.0309819618026538, 0.029589102491272, 0.0529778772840967, 0.0842123937662785, 0.0607153181824941, 0.0672240685836559, 0.144807911379215, 0.144807911379215, 0.141129878619691, 0.688420146600013, 0.0609351365077056, 0.0626297831888101, 0.0648027622574709, 0.0759997034218865, 0.0782103847541935, 0.0707477713155958, 0.0410921970518355, 0.0589697594313821, 0.152256577677227, 0.056765876958851, 0.0440206300688631, 0.0331810206918762, 0.145634415508243, 0.171438771769591, 0.045261532361592, 0.041840944187868, 0.143150260376584, 0.156242430028033, 0.0410741399980494, 0.0522187899853102, 0.0442706334210004, 0.0971923907649902, 0.165585071470526, 0.238054218005531, 0.0532738449881275, 0.0604428830039113, 0.111392476904907, 0.111392476904907, 0.057580243342699, 0.0605291866378679, 0.0573770911039481, 0.0885019494515106, 0.0862447970676653, 0.0955397769716847, 0.081739783220223, 0.0812965346829218, 0.0809796720150843, 0.0813844390983633, 0.0553602073413133, 0.0595903222287986, 0.0580738296478883, 0.0331472062547294, 0.117186329269605, 0.0421565210307805, 0.0421565210307805, 0.0431360897292105, 0.0601728243619919, 0.0608147839961041, 0.0469900387599093, 0.0511099791683115, 0.133968859142191, 0.0454828817219972, 0.134269192729732, 0.045677409250904, 0.0484924110945302, 0.0915494575563987, 0.0473953480872363, 0.0521826902889385, 0.0499074879741539, 0.0607510996298348, 0.138895050565221, 0.0906618240478993, 0.0545651794730959, 0.0588322152774606, 0.0555824719807064, 0.0578268424764083, 0.0579806773332134, 0.0555747554696179, 0.0570504628526928, 0.0556475846732603, 0.0510369790482531, 0.105422478219541, 0.0549738873644795 ]) mpg_bs.R = np.array([ -14.247806848775, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12.8440820360878, 0.373532783001862, -4.2296607322892, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8.28197639485442, 7.02914411540082, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5.33415428821132, -6.28488179729956, 0.275366266013156, 0.350799946868301, -0.320832128978794, -0.400140439924557, -2.75411074826349, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6.93889390390723e-18, 0.232054372832382, -0.059045600449299, 0.180812355115842, 0.128163547439293, 0.144886567744466, -0.0269730574249025, -0.184599966726543, 0.118427787192217, 0.122053978888216, -0.0642672707517637, 0.0681043144407656, -0.060071867550458, -0.150958262500398, 0.0229223735842404, 0.0444276150539449, -0.348767846881924, 0.400671529738335, -0.0077479495898858, -0.0233519344455665, -0.0016530657606304, 0.252520737261296, -0.0010134977318948, -0.440010476997986, -2.77555756156289e-17, 1.09497230004704, -0.214931983948417, 0.930799141411998, 0.550394857028419, 0.709391063166251, -0.109782318058198, -0.842294484569631, 0.695883635886005, 0.497451233152266, -0.43887148186347, 0.581743977285481, -0.402315830184767, -0.709015800353095, 0.0516077442049284, 0.028185898732357, -0.352543779422061, 1.27839021341958, 0, 0, 0, 0, 0, 0, -1.38777878078145e-16, 1.46496369379118, -0.201247454925983, 1.35850779046971, 0.280404550518566, 1.0970677381965, -0.0446546144567612, 0.111447137155272, 1.10339850569991, 0.314461688316244, -0.822981973569381, 0.910711177150427, -0.465095093337983, -0.492817626024387, -0.0302680940522306, -0.250587565379533, 1.36321225401071, 0, 0, 0, 0, 0, 0, 0, -5.55111512312578e-17, 0.636539976078798, 0.334849603625203, -0.801543168266999, -0.153261416776597, 0.590531348112483, 0.179469236924221, 2.6920602822558, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.52655665885959e-16, 0.386544461276061, 0.0617187417679946, -3.3375034414008, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2.22044604925031e-16, -0.268086271294675, 0.0357997911433628, -0.811541848512822, -0.417713567994733, -0.549046879404324, 0.191376270418331, 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0.951128380630708, 0, 0, 0, 0, -1.35308431126191e-16, -0.465120271023632, 0.406195493272399, 0.070203506724658, 0.112046096976311, -0.200096302157889, -0.152715842062604, 0.0104383470658289, 0.342550835873512, -0.273815544285267, -0.401207001497804, -0.040780018432021, -0.303740748176209, -0.0609839545858858, 0.319068530448539, -0.260734203657871, -0.260132352451617, -0.0932586655435074, 0.203432578212413, 0.317497529276374, -0.83938821954848, 0, 0, 0, -4.85722573273506e-17, -0.390650961425867, 0.0330907911134603, 0.00733620315637045, 0.228118285854502, -0.0868790621492882, -0.191943985560395, 0.0744153770730219, 0.343145769098306, -0.095185581001596, -0.223303572468095, -0.150287745525581, -0.158778635381907, 0.0110735369943658, 1.59565825328421, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.11022302462516e-16, 0.274167363775303, 0.474667692897905, 0.106124488726352, 0.284328629467105, 0.186661254435535, 0.187571744571793, 0.20413327819365, -0.0397206127231053, 0.383068904117848, 0.0739013097506463, -0.570930211792512, 0.0925572774037632, -0.322045428454689, -0.0206704824306383, 0.138827717514351, 0.305979392429139, 0.329598188006108, 0.056917317683023, 0.166351113868783, -0.0429579563012386, 0.698123470574497, 0, 0, 2.77555756156289e-17, 1.28869031811426, 0.159462695223405, 0.94874511527323, 1.22041060990194, 1.23041883682224, 0.214295232212795, -0.421272049466657, 0.484873150940021, 1.22340399746876, -0.126213059047102, 0.586508858858053, 0.0387247897517475, -1.73048932450117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.33066907387547e-16, 1.38101651269374, -0.161333143580265, 0.26879941823133, 1.5843908766769, 1.56675922898707, 0.130712348793346, -0.15459448409081, 0.322441342868708, 0.032841704236906, -0.040628028706388, 1.95780421180254, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4.71844785465692e-16, 0.547361386973655, -0.0560623687491847, -1.42773410582977, -0.319295075080351, 1.10930671785576, -0.249435864270354, 0.376460682854174, -0.859698359693027, -2.22778539317977, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.16573417585641e-15, -0.680782403896811, -0.0829421876833989, -1.06575902669119, -3.08847910097662, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3.05311331771918e-16, -1.73716924091107, -0.427903820099444, 0.508003939493925, 0.0674537346537795, -3.01780655906657, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8.32667268468867e-17, -0.907178653618356, -0.442910523756854, 0.50555822069335, 0.912713271576068, -0.893880669315821, -0.303415799851323, 0.00713986966174707, -0.565052960394418, -0.0893598475014228, 0.1719971566722, -0.455461128044599, -0.0927359754631413, 0.109881340577719, 0.546762409477948, -1.42658278966991, 0, 0, 0, 0, 0, 0, 0, 0, -5.89805981832114e-17, -0.358468733615153, -0.156326542139889, 0.124611476610136, 0.261720342968014, 0.0035504239879391, -0.178906878260252, -0.00818092652923195, -0.0665839339476971, 0.00890831066007731, 0.21700219401572, -0.192545410574642, -0.0251881401918565, 0.0596236111422667, 0.356927030887266, -0.559501871586496, 0.00939356269184223, 0.00808635023879492, 0.174506073397661, -0.00768811220727605, -0.0824771518664715, 0.00281995201714263, 0.552896914606241, 0, -8.15320033709099e-17, -0.153937258650552, -0.0600660535926754, 0.0307742140033325, 0.0538665072365687, 0.107288075694366, -0.0951443583796005, -0.0122161530644771, 0.00205111921342145, 0.00850795594637679, 0.0131768142662108, -0.0351898170323615, -0.00506295245698965, 0.000521970211206223, 0.172268163286512, 0.0600225535087082, -0.0453855401632395, -0.0806877659326075, 1.10081916052039, 0, 0, 0, 0, 0 ]).reshape(24, 24, order='F') mpg_bs.sp = np.array([ 0.830689464223685, 425.361212061649 ]) mpg_bs.nsdf = 4 mpg_bs.Ve = np.array([ 1.18849578741713, -0.569737725624008, -0.680858316482058, -0.683616810254248, 0.377412685416274, 0.162104128449963, 0.0284282197471564, -0.170886673387626, -0.194448131082813, -0.235607054710811, -0.334637151301396, -0.298355349820224, -0.598813240305989, -0.484066776146491, -0.222539433922648, 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0.0242576056241561, 0.0557321652408447, 0.162137334893874, 0.217365341750675, 0.0816311056865962, -0.0596536181056574, -0.0310250346933758, -0.0258598033359973, 1.57157757262447, -0.551846529931971, 0.178630089646898, -0.121940697227273, -0.025984796272873, -0.0676047713589873, -0.0647127382787066, -0.0818438736871805, -0.0939009139216642, -0.0902348993636832, -0.0508630584433755, -0.0609219372551081, -0.013009064200119, 0.0192798284833754, 0.0264362938415028, 0.0497024606324435, 0.0643121575768081, 0.0663163083142627, 0.0640123302445087, 0.0750880869238639 ]).reshape(24, 24, order='F') mpg_bs.gcv_ubre = 5.16162045425616 mpg_bs.aic = 909.585145453506 mpg_bs.rank = 24 mpg_bs.gcv_ubre_dev = 5.16162045425363 mpg_bs.method = 'GCV' mpg_bs.cmX = np.array([ 1, 0.901477832512315, 0.58128078817734, 0.374384236453202, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]) mpg_bs.assign = np.array([ 0, 1, 2, 2 ]) mpg_bs.offset = np.array([ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]) mpg_bs.df_residual = 185.099985812547 mpg_bs.min_edf = 6 mpg_bs.optimizer = 'magic' mpg_bs.p_coeff = np.array([ 29.6272774569595, -6.21365498504518, 1.43986598470837, 1.01128095138012 ]) mpg_bs.se = np.array([ 1.10736522428059, 0.730964352033962, 0.802742257532199, 0.82715120287436, 3.45934930908735, 1.72348162068993, 1.34626504738022, 1.128648591521, 1.23820355203725, 1.25079638223793, 1.32555503230954, 1.46276521490991, 2.08682079164069, 2.44820576733618, 1.57664310132803, 0.706341710395395, 0.340307783146933, 0.439430720698385, 0.475893350342798, 0.681557125789893, 0.862789472579143, 1.29715423972101, 2.01034871279469, 1.89702020234941 ]) mpg_bs.p_t = np.array([ 26.7547479434413, -8.50062655963349, 1.7936840513851, 1.22260712172806 ]) mpg_bs.p_pv = np.array([ 1.61958620027156e-65, 6.17307801841172e-15, 0.0744959485685591, 0.223032563883354 ]) mpg_bs.residual_df = 185.099985812547 mpg_bs.m = 2 mpg_bs.chi_sq = np.array([ 132.00007563458, 69.3539925351537 ]) mpg_bs.s_pv = np.array([ 4.72304400617769e-18, 6.21718617954453e-12 ]) mpg_bs.scale = 4.70648213227865 mpg_bs.r_sq = 0.890988350463498 mpg_bs.n = 203 mpg_bs.dev_expl = 0.900108639690056 mpg_bs.edf = np.array([ 10.2535689759835, 3.64644521146987 ]) mpg_bs.dispersion = 4.70648213227865 mpg_bs.pTerms_pv = np.array([ 6.1730780184117e-15, 0.175815884801339 ]) mpg_bs.pTerms_chi_sq = np.array([ 72.2606519063463, 3.50949117352962 ]) mpg_bs.pTerms_df = np.array([ 1, 2 ]) mpg_bs.cov_unscaled = np.array([ 0.260546562269068, -0.127261644910421, -0.147454452733496, -0.147400601308703, 0.0858934363413853, 0.0324027409627562, 0.001951459420489, -0.0444711495173745, -0.051050382403525, -0.0558058242079355, -0.0776843093730959, -0.0696248432860819, -0.143873948165499, -0.102565827833482, -0.0504628003799288, -0.0838215012227384, -0.0264331690405809, 0.0189063712819891, 0.0354335965549041, 0.0710226222907629, 0.086637653107266, 0.101618191765279, 0.081840238740399, 0.0953496710685112, -0.127261644910421, 0.11352616857503, 0.025864159966478, 0.026405976204483, -0.0647092342623571, -0.0194747421679251, 0.0013822670878288, 0.0319763850603683, 0.034430423334006, 0.0345203757451707, 0.0608821466756475, 0.0407664667130339, 0.130282891645105, 0.0851176416918229, 0.0400522748720902, 0.0629753993433594, 0.0181263443541013, -0.0160778765682171, -0.0267074236912963, -0.0523474645302372, -0.0639429975967239, -0.0786117565174105, -0.063904170832196, 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-0.0374137141732135, -0.00831843730650562, -0.111064756608917, -0.0196286635230926, -0.105907217560377, -0.0757024271527446, -0.144246293596641, -0.0721417252895369, -0.0272696852211407, 0.00594206245237508, 0.0172406430026829, 0.0510213739757127, 0.0878449503315404, -0.122181710723627, 0.858709718521459, 0.158673552049344, 0.0953496710685112, -0.077928384358563, -0.022334457938622, -0.0323634585859656, 0.0602549766706101, 0.0312444446552389, -0.000842958258748316, -0.0170673905077609, -0.03621185498621, -0.0139208013344843, -0.0921425296807421, -0.0172844920058013, -0.198551268786848, -0.0684075332800308, -0.121800944620384, -0.0729173883583565, -0.0275284441796622, 0.00694057449961806, 0.0190854917034619, 0.0513114624886664, 0.072216656566408, 0.0529625804413154, 0.158673552049344, 0.764623246615722 ]).reshape(24, 24, order='F') mpg_bs.cov_scaled = mpg_bs.cov_unscaled * mpg_bs.scale mpg_bs.p_table = np.array([ 29.6272774569595, -6.21365498504518, 1.43986598470837, 1.01128095138012, 1.10736522428059, 0.730964352033962, 0.802742257532199, 0.82715120287436, 26.7547479434413, -8.50062655963349, 1.7936840513851, 1.22260712172806, 1.61958620027156e-65, 6.17307801841172e-15, 0.0744959485685591, 0.223032563883354 ]).reshape(4, 4, order='F') mpg_bs.pTerms_table = np.array([ 1, 2, 72.2606519063463, 1.75474558676481, 6.1730780184117e-15, 0.175815884801339 ]).reshape(2, 3, order='F') mpg_bs.s_table = np.array([ 10.2535689759835, 3.64644521146987, 10.8058511361601, 4.39467905741677, 12.2156111509682, 15.7813555049275, 4.72304400617769e-18, 6.21718617954453e-12 ]).reshape(2, 4, order='F') mpg_bs.method = 'GCV' mpg_bs.sp_criterion = 5.16162045425616 mpg_bs.rank = 24 mpg_bs.np = 24 mpg_bs.params = np.array([ 29.6272774569595, -6.21365498504518, 1.43986598470837, 1.01128095138012, 20.1053719083286, -1.26007449980292, -5.26871981200625, -4.544036357677, -7.60063071956733, -5.01036711884368, -6.96226144900638, -9.06722069409647, -8.81829781369916, -7.9145836553663, -6.28068941724657, 5.09307848346347, 1.90848821039499, -0.646225516186639, -1.50240395085899, -4.19244286007642, -5.72993924243941, -6.83323296859843, -5.77088950575513, -4.29112523442438 ]) statsmodels-0.12.2/statsmodels/gam/tests/results/results_mpg_bs_poisson.py000066400000000000000000003141101400612667500272720ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch mpg_bs_poisson = Bunch() mpg_bs_poisson.smooth0 = Bunch() mpg_bs_poisson.smooth0.term = 'weight' mpg_bs_poisson.smooth0.bs_dim = 12 mpg_bs_poisson.smooth0.dim = 1 mpg_bs_poisson.smooth0.p_order = np.array([ 3, 2 ]) mpg_bs_poisson.smooth0.by = 'NA' mpg_bs_poisson.smooth0.label = 's(weight)' mpg_bs_poisson.smooth0.sp = -1 mpg_bs_poisson.smooth0.m = np.array([ 3, 2 ]) mpg_bs_poisson.smooth0.knots = np.array([ 1488, 1488, 1488, 1488, 1953.22222222, 2118.77777778, 2275, 2383.88888889, 2515.55555556, 2757.33333333, 3016.44444444, 3208.11111111, 4066, 4066, 4066, 4066 ]) mpg_bs_poisson.smooth0.rank = 10 mpg_bs_poisson.smooth0.null_space_dim = 1 mpg_bs_poisson.smooth0.df = 11 mpg_bs_poisson.smooth0.S_scale = 2.44395544177397e-06 mpg_bs_poisson.smooth0.vn = 'weight' mpg_bs_poisson.smooth0.first_para = 5 mpg_bs_poisson.smooth0.last_para = 15 mpg_bs_poisson.smooth0.S = np.array([ 0.130569121544375, -0.0191732921244136, 0.0202548028417763, 0.0393112950002946, 0.032061392663319, 0.0241651485426007, 0.0238771778381105, 0.0389406835250852, 0.0171569521441248, 0.00680570834700402, 0.00541920498010491, -0.0191732921244136, 0.0631473273216884, -0.0592997810399249, 0.0178641542128365, 0.00461438941034586, 0.00793912465273829, 0.00408821971418319, -0.000681869049168392, 0.00213834646721613, 0.000935846814259467, 0.000163463753965317, 0.0202548028417763, -0.0592997810399249, 0.201022514824508, -0.186241322892132, 0.00284878067469136, 0.0287314367063779, 0.00263260805442764, -0.00708846456492193, 0.00065385484055723, 0.000395067932117418, -0.000586348849229599, 0.0393112950002947, 0.0178641542128365, -0.186241322892132, 0.479322071007576, -0.286380917395105, 0.0563704638942206, 0.0348887744557148, 0.0255203052273876, 0.0138979985789615, 0.00560832050247454, 0.00383270204450356, 0.032061392663319, 0.00461438941034587, 0.00284878067469137, -0.286380917395105, 0.414581586658592, -0.181289913269406, -0.00412646444222532, -0.00354719180127285, -0.00206283566879658, -0.000685858743449883, -0.00142523589453221, 0.0241651485426007, 0.00793912465273829, 0.0287314367063779, 0.0563704638942206, -0.181289913269406, 0.213321319885371, -0.0483506678191679, 0.0110304252072989, 0.0122299348640366, 0.00357726593043956, 0.00234383478372281, 0.0238771778381105, 0.00408821971418319, 0.00263260805442764, 0.0348887744557148, -0.00412646444222533, -0.0483506678191679, 0.0999220996092033, -0.0356092452156359, 0.00921547832469341, 0.00389860712399989, 0.00147745030481206, 0.0389406835250852, -0.000681869049168392, -0.00708846456492192, 0.0255203052273876, -0.00354719180127286, 0.0110304252072989, -0.0356092452156359, 0.0574427000604467, -0.0102653399490586, -0.000311188772793241, 0.00285258581655637, 0.0171569521441248, 0.00213834646721613, 0.000653854840557233, 0.0138979985789615, -0.00206283566879658, 0.0122299348640366, 0.00921547832469341, -0.0102653399490586, 0.0189789273643945, -0.0062453384832703, 0.00255839876648785, 0.00680570834700402, 0.000935846814259467, 0.000395067932117419, 0.00560832050247454, -0.000685858743449884, 0.00357726593043956, 0.00389860712399989, -0.000311188772793241, -0.0062453384832703, 0.0211496391608495, -0.0111654555301857, 0.00541920498010491, 0.000163463753965317, -0.000586348849229599, 0.00383270204450356, -0.00142523589453221, 0.00234383478372281, 0.00147745030481206, 0.00285258581655637, 0.00255839876648785, -0.0111654555301857, 0.00794139033444708 ]).reshape(11, 11, order='F') mpg_bs_poisson.coefficients = np.array([ 3.38155196812657, -0.2398057983025, 0.0385574655971876, 0.0308789097162079, 0.322087207070371, 0.114222640046661, -0.0703319473834318, -0.0932993942273026, -0.164529819124519, -0.150860338924587, -0.19827414261489, -0.318132823476157, -0.277920321049033, -0.291752287584618, -0.335850782440607, 0.147266917321495, 0.0655746640077953, 0.00329634588440575, -0.0178203244735351, -0.0949069908870388, -0.162736107333124, -0.267760412623755, -0.31426029441775, -0.36537967845964 ]) mpg_bs_poisson.residuals = np.array([ -0.0597164611104715, -0.0597164611104715, 0.0070681780740447, -0.0244130279937029, -0.109459035981563, -0.167042459441988, -0.105640645333752, -0.0887544418878843, -0.0954712805695528, -0.0784623437350325, -0.0430169241934606, -0.0430169241934606, 0.0030916078609633, 0.0137773951290736, 0.0148539285398903, -0.0370396919392229, -0.0112736908607727, -0.052100214301857, 0.05696516521011, 0.132586599766586, 0.152452919091744, 0.0958117450422904, -0.0818874568564589, -0.0996285128088896, -0.039947957328768, -0.0297876572186078, -0.0297876572186078, -0.0757627215899457, -0.0131089324697808, -0.0233738731200743, 0.286760172557162, -0.0814957361302606, 0.0714671532989226, -0.0558415218265038, -0.0484787948859533, -0.0236434176492324, -0.0172259149323173, 0.00318143181414277, 0.0231117802042631, 0.0285924230117791, 0.0524599141234474, 0.0116354361716793, -0.00558296033674166, -0.0940825558878515, 0.132586599766586, 0.152452919091744, 0.0461585732431811, 0.036440559843717, 0.036440559843717, 0.00758219423801565, -0.105282911203192, -0.0708600665943635, -0.0685585970304921, -0.0501105407364437, -0.0478013558335348, -0.295992218769999, -0.295992218769999, -0.294876506179699, -0.243930144705301, 0.010594364536701, 0.0184495378782166, 0.010594364536701, 0.0184495378782166, 0.0421491667369525, 0.0230515193544041, -0.102317831424696, -0.00921877268202032, -0.04273337969419, -0.00119636037327275, -0.0461713804461907, 0.00242207736643074, -0.00206774027200307, -0.0119510982296829, -0.0463162166023352, -0.0776191103317818, 0.0686101070886802, 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-0.0146135261048062, -0.0264261656715257, -0.0145337592605999, -0.0145337592605999, -0.0064905487190714, 0.226809817977968, -0.0459953733057028, -0.0386603873101858, -0.0363408944476897, -0.0267731783454677, 0.00999638170999839, 0.0169931451495056, 0.00192444906825173, -0.120308776123272, -0.0400164322133238, 0.130247697154032, 0.00746981127430812, 0.0306709674011021, -0.0372819368771609, 0.0976557161110208, 0.0465873287478877, 0.0269883944212412, -0.0674146853454123, 0.0873341779571093, 0.0693951026504345, -0.0280641297469413, -0.0392924504624044, 0.0735437039091389, -0.0247046596041458, 0.171463552666685, -0.013091147087648, -0.000813946803385424, -0.0956269920449824, 0.0107698324203134, 0.25732769645148, -0.0621561621420588, -0.0549179845713752, -0.00160856625504557, 0.0126062678583092, 0.0705449231002744, 0.0842095493097967, 0.0883081440038147, 0.0872170109597095, 0.0912812221820642, 0.123175492931149, 0.131142517763956, 0.184711504210098, 0.136459914352958, -0.0929831907336212, 0.0885449049874016, 0.0885449049874016, 0.102638885670704, 0.104987186006888, 0.0567660298014965, 0.121868643941937, 0.0694291967778775, -0.0353205301526058, -0.0107460163888975, -0.0342456641975604, -0.00957686458378415, 0.0143852426645283, 0.0450346063721021, 0.0367753899157743, -0.0896986969406739, -0.101104390140708, -0.136305098940538, 0.00460226286555798, 0.0351388253204785, 0.116934978569832, 0.13995662419881, 0.170013018072364, 0.191118649321067, -0.0478214884195327, -0.0295329898984451, 0.124455798890416, 0.0603367500448151, -0.0610962381564639, 0.0212222309861203, -0.0538512733755478 ]) mpg_bs_poisson.fitted_values = np.array([ 22.3336888624052, 22.3336888624052, 18.8666471780851, 24.6005745142783, 20.2124334840001, 22.8102863289666, 21.2442570213741, 20.8505817458946, 18.7943175653995, 17.3622856225417, 24.0338628565774, 24.0338628565774, 20.9352763351109, 20.7146066788422, 19.7072696252699, 16.6154304243557, 16.1824357783393, 15.8244576339389, 44.4669337713292, 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25.0777557539364, 26.3648968966003, 26.6994295408305, 21.998508937234, 32.8488210905178, 24.1513499334353, 20.5920670775752, 20.1762062799231, 20.5125922782815, 20.1491262131442, 17.8537950533904, 17.5173394077775, 20.4543389101606, 17.9188356898853, 19.171293940347, 25.4596886075362, 20.0814094711999 ]) mpg_bs_poisson.linear_predictors = np.array([ 3.10609624980832, 3.10609624980832, 2.93739566357681, 3.20276979690456, 3.00629793406294, 3.12721158899991, 3.05608660102651, 3.03738184933733, 2.9335545669874, 2.85430036085041, 3.17946378824737, 3.17946378824737, 3.04143559905492, 3.03083908808588, 2.98098758418526, 2.81033180724024, 2.78392644284256, 2.76155669470604, 3.79474585164685, 3.51308211648978, 3.4956935157856, 3.51942250434414, 3.51942250434414, 3.28300166762353, 3.4747549893589, 3.46422752584326, 3.46422752584326, 3.25684027583847, 3.19124944323147, 2.96809035398114, 3.63969273297066, 3.51899593661304, 3.56855727914211, 3.45865862916789, 3.45089068817213, 3.42512479018631, 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3.05176522361415, 3.48825489749758, 3.46245265828934, 3.47407243971087, 3.36302215537105, 3.32085180663105, 3.13758299920276, 3.41437497308165, 3.4020116599001, 3.62687390889084, 3.62687390889084, 3.40859756683735, 3.39637633817112, 3.38868807661617, 3.36890569137327, 3.35476835958596, 3.18992874525813, 3.17724534251483, 3.09342950142183, 3.09443260003746, 3.09070139119307, 3.06189389526813, 3.05482563075123, 3.00855454176395, 3.23937773743491, 3.49879167788239, 3.21099501115507, 3.21099501115507, 3.19813057220198, 2.89589853502537, 2.88922564985387, 2.88073654644261, 2.8773139339888, 3.64687730106182, 3.30664103782876, 3.64576370051983, 3.30545988365993, 3.28155410925581, 3.56686791163023, 3.22198122826548, 3.27203346235845, 3.28464219966599, 3.09097467548117, 3.49191585663117, 3.18434027640117, 3.02490590830647, 3.00450400319504, 3.0210389550426, 3.00316092334049, 2.88221609366084, 2.86319121368963, 3.01819503162959, 2.88585243277332, 2.95341405297199, 3.23709636239996, 2.99979448514897 ]) mpg_bs_poisson.deviance = 37.5688885982924 mpg_bs_poisson.null_deviance = 337.261844954099 mpg_bs_poisson.iter = 2 mpg_bs_poisson.weights = np.array([ 22.3336888624052, 22.3336888624052, 18.8666471780852, 24.6005745142783, 20.2124334840002, 22.8102863289666, 21.2442570213741, 20.8505817458947, 18.7943175653996, 17.3622856225417, 24.0338628565775, 24.0338628565775, 20.935276335111, 20.7146066788423, 19.70726962527, 16.6154304243558, 16.1824357783394, 15.8244576339389, 44.4669337713293, 33.5515182749217, 32.9731474236259, 33.7649237356661, 33.7649237356661, 26.6556641802073, 32.2899161942786, 31.9517683223135, 31.9517683223135, 25.9673576911838, 24.3187934206986, 19.4547324478204, 38.0801341578851, 33.7505237802537, 35.4653895670087, 31.7743267613674, 31.5284618343365, 30.7264789753035, 30.5258354446068, 26.9143737550779, 26.3900783105142, 26.249464215323, 25.6541837248854, 23.7239613618351, 25.1403576194409, 26.4924802541157, 33.5515182749217, 32.9731474236259, 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37.5951069978099, 30.2228290263918, 29.8557167725842, 29.6270583323937, 29.0467235793695, 28.6389694795549, 24.2866968391243, 23.9806041337226, 22.0525777852821, 22.0747097939672, 21.9924979117766, 21.3679875950349, 21.2174855273262, 20.2580965194577, 25.5178380106008, 33.0754619909028, 24.8037539620955, 24.8037539620955, 24.4867112441593, 18.0997574028658, 17.9793818727964, 17.8273990524644, 17.7664870729599, 38.3547086431239, 27.2932941866367, 38.312020591921, 27.2610756297141, 26.6171064644809, 35.4055260700387, 25.0777557539365, 26.3648968966003, 26.6994295408305, 21.9985089372341, 32.8488210905178, 24.1513499334354, 20.5920670775753, 20.1762062799232, 20.5125922782816, 20.1491262131442, 17.8537950533905, 17.5173394077776, 20.4543389101607, 17.9188356898853, 19.1712939403471, 25.4596886075362, 20.0814094712 ]) mpg_bs_poisson.working_weights = np.array([ 22.3336888624052, 22.3336888624052, 18.8666471780852, 24.6005745142783, 20.2124334840002, 22.8102863289666, 21.2442570213741, 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33.0691112648596, 26.6556641802073, 32.2899161942786, 31.9517683223135, 29.2236217839984, 24.3187934206986, 19.2817747181913, 19.5157258032775, 17.2507177792766, 17.2507177792766, 17.1110601696662, 13.8570785388883, 22.0124718606101, 21.8445175074419, 21.7919385382284, 21.5777037097057, 18.8119485812728, 18.6825251385612, 30.940456666996, 29.5558251512618, 27.0837969236757, 28.3123779686313, 27.7923960466706, 25.2262854221659, 24.9294169490801, 21.8647793180832, 26.7536202960709, 24.343020949218, 24.6626229671211, 21.1526506443609, 32.7287827606977, 31.8951084621753, 32.2678842431507, 28.87632789156, 27.6839218662126, 23.048092224925, 30.3979439554834, 30.0244382955742, 37.5951069978099, 37.5951069978099, 30.2228290263918, 29.8557167725842, 29.6270583323937, 29.0467235793695, 28.6389694795549, 24.2866968391243, 23.9806041337226, 22.0525777852821, 22.0747097939672, 21.9924979117766, 21.3679875950349, 21.2174855273262, 20.2580965194577, 25.5178380106008, 33.0754619909028, 24.8037539620955, 24.8037539620955, 24.4867112441593, 18.0997574028658, 17.9793818727964, 17.8273990524644, 17.7664870729599, 38.3547086431239, 27.2932941866367, 38.312020591921, 27.2610756297141, 26.6171064644809, 35.4055260700387, 25.0777557539365, 26.3648968966003, 26.6994295408305, 21.9985089372341, 32.8488210905178, 24.1513499334354, 20.5920670775753, 20.1762062799232, 20.5125922782816, 20.1491262131442, 17.8537950533905, 17.5173394077776, 20.4543389101607, 17.9188356898853, 19.1712939403471, 25.4596886075362, 20.0814094712 ]) mpg_bs_poisson.prior_weights = np.array([ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]) mpg_bs_poisson.df_null = 202 mpg_bs_poisson.y = np.array([ 21, 21, 19, 24, 18, 19, 19, 19, 17, 16, 23, 23, 21, 21, 20, 16, 16, 15, 47, 38, 38, 37, 31, 24, 31, 31, 31, 24, 24, 19, 49, 31, 38, 30, 30, 30, 30, 27, 27, 27, 27, 24, 25, 24, 38, 38, 24, 15, 15, 13, 30, 31, 31, 31, 31, 17, 17, 17, 16, 26, 26, 26, 26, 36, 26, 19, 31, 22, 22, 22, 22, 16, 16, 14, 14, 19, 37, 31, 31, 24, 23, 25, 19, 19, 19, 25, 25, 23, 23, 31, 45, 31, 31, 31, 31, 31, 31, 31, 31, 27, 27, 17, 17, 19, 19, 17, 19, 19, 28, 19, 25, 19, 28, 19, 25, 19, 28, 18, 37, 24, 31, 31, 31, 24, 19, 19, 17, 17, 17, 17, 21, 21, 21, 21, 19, 19, 31, 26, 26, 32, 28, 26, 24, 24, 28, 25, 23, 23, 35, 31, 31, 31, 27, 27, 30, 30, 34, 38, 38, 28, 28, 29, 29, 26, 26, 24, 24, 24, 24, 24, 24, 29, 30, 27, 27, 27, 20, 19, 20, 19, 37, 27, 37, 27, 27, 37, 26, 24, 24, 19, 33, 25, 23, 23, 24, 24, 17, 17, 23, 19, 18, 26, 19 ]) mpg_bs_poisson.rV = np.array([ 0, 0, 0, 0, -8.9130297985463e-05, -0.000176684273823698, 0.0011584583691732, -0.00390049177471793, 0.00344010782379437, -0.00135790861015704, -0.000111385074008239, -0.000176972060004861, -9.86203908496754e-05, -3.64890558944375e-05, -3.08026950210881e-05, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.00732908209018e-08, -1.9968429523216e-08, 1.3092616450685e-07, -4.40824151599687e-07, 3.88792670366615e-07, -1.53467548605631e-07, -1.25884718098402e-08, -2.00009544217366e-08, -1.11458381757212e-08, -4.12390489107036e-09, -3.48124613097974e-09, 0.000484189713776837, 0.00176326319300196, -0.00213289729840957, 0.00171891163782342, 0.000158871132568822, 0.000404028755237099, 0.000172315861842303, 4.89726562858341e-05, 1.83249073133473e-05, 0, 0, 0, 0, -0.000254544577467626, -0.001035854174059, 0.0046293795015643, -0.00326301657903083, -0.00369019497478088, 0.00424113890068213, -0.00111478223779753, 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-0.00253188718079104, -0.000653429116975908, 0.0011620482733327, 0.00211589034759339, 0.00367778201322326, 0.0040677604350883, -0.00507376363738053, -0.00223095373191136, 0.00206213937427957, 0, 0, 0, 0, 0.00873021053727884, 0.00788912587315529, 0.00315035854914982, 0.000729499906725857, -0.00328134349842095, -0.00644376475504463, -0.0116331903146275, -0.015288226128054, -0.00792058428914374, 0.00838656968634575, 0.0196142787782849, -0.0222070071311449, -0.0085523948160152, 0.00197984349190124, 0.00552409581369225, 0.0173231753198411, 0.0269502786230045, 0.0444699184443161, -0.00195308066417439, -0.0363223282917489, 0, 0, 0, 0, 0.00169163794738931, -0.00383399031151375, -0.00585177655081489, -0.00499725225479528, -0.00415592538210646, -0.00148907462126999, 0.00173577250006001, 0.00294429784532539, 0.00458477957640236, -0.000484638769799792, -0.00384943847580776, 0.00842349237381884, 0.00485500145690797, 0.00281845357221204, 0.00271275264035418, -0.000438520740299198, 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0.0172500599680547, 0.018005707666409, 0.0201741350091917, 0.0401636589575239, -0.0318988645890763, -0.01850999070435, -0.00394626508026133, 0.0551382157508856, 0.0217807180807445, -0.00622899826733438, -0.00923850673879829, -0.0212137461370569, -0.020091132050748, -0.0314646112389824, -0.0563797107234094, -0.0618781724522286, -0.0809883829460941, -0.101451533937108, -0.0294660248157941, -0.0129461041972885, -0.000317118828092305, 0.00404893245763359, 0.0193119490827826, 0.0326887256219942, 0.0524397613334577, 0.0599889895213543, 0.0707562479561827, -0.00014417166463547, 0.000112486137657318, 2.93195506570937e-05, 7.11989286865333e-05, 0.000298020443190303, 7.43500900776159e-05, -0.000123025591619351, -0.000150144864483587, -0.000213602220981072, -0.000182287600073906, -0.000196294549615607, -0.000273238798774471, -0.000134016463849165, -5.87892574426707e-05, -3.61576064062375e-05, 0.00212707138394515, -0.000435955193172209, 0.000604997293885961, 0.000392867571322303, 0.000561225223337066, 0.00056952076942879, 0.000186965781647446, 2.43190236830834e-05, -1.49153748573756e-05 ]).reshape(24, 24, order='F') mpg_bs_poisson.db_drho = np.array([ -0.00955607829508903, 0.00430986949109399, 0.00462834751450597, 0.00835107524076425, -0.0333302515945607, 0.00139610358751732, 0.0263076303556022, 0.0268343416489505, 0.0314648272214792, 0.0226413860328889, 0.0162437421056309, 0.0181827810783155, 0.000275213760239914, 0.00115455787426117, 0.00197111543707827, 0.00493118340740466, 0.00145534674747094, -0.00147150121604032, -0.00260852436899397, -0.00515405425200522, -0.00625733949412647, -0.00215131919228267, 0.000695879282559118, 0.00245613544165302, 0.0165502705938555, -0.0120739288987487, -0.00539618833686599, -0.00676715282188502, 0.0196760486043603, 0.00772600754507691, -0.00364486556122667, -0.00558444320663137, -0.0105223419591228, -0.0104699677543541, -0.0139344474571075, -0.0207299030874315, -0.0154990384672306, -0.0114599389957355, -0.0101038003601939, -0.020380893865003, -0.00665329046642183, 0.00475504810058412, 0.00904455059277683, 0.0203739259385563, 0.026657106982953, 0.0214205189927133, -0.0170394753092789, -0.0478344361350309 ]).reshape(24, 2, order='F') mpg_bs_poisson.dw_drho = np.array([ 0.198451577496262, 0.198451577496262, 0.0211323116265804, 0.176795914312368, -0.158842940220042, 0.136552595840399, -0.0788956246522186, -0.145800287459428, -0.18078320916676, -0.227604968605315, 0.270528113197353, 0.270528113197353, 0.0871931177612735, 0.0488040223227676, -0.11212062083582, -0.0921466191935143, -0.0872523607945422, -0.0726475180150896, -2.03674569674128, -0.399858629869372, -0.294145790144752, -0.384037673792421, -0.384037673792421, 0.0374542295773345, -0.126689730715761, -0.0732225659783105, -0.0732225659783105, 0.103260641535857, 0.179088091909104, -0.0488091379129944, -0.947578113843131, -0.606019988745503, -0.473334587346908, -0.236955919521633, -0.195526007765597, -0.0688010780860252, -0.0392834493026195, 0.189928469830611, 0.21717147287679, 0.222511836808396, 0.234040644079886, 0.168755657511205, 0.169728133790599, 0.366698379522312, -0.399858629869372, -0.294145790144752, 0.121380760680706, 0.00910595279608145, 0.00910595279608145, 0.0340607755348701, -0.340709976973792, -0.310583848151182, -0.295779107765152, -0.18359861595662, -0.170364313792911, 0.271469840167182, 0.271469840167182, 0.271257913696808, 0.204605902971062, 0.242930319240712, 0.240554295492994, 0.242930319240712, 0.240554295492994, 0.290076687028269, 0.237905640625681, 0.114993524063036, 0.152699599788878, -0.24062847407969, -0.177222382324359, -0.245297972873039, -0.1716897049522, -0.0498413922857943, -0.0602427120173084, -0.00606488931871212, -0.0365248804113624, -0.0161146042525035, -0.258096696454203, -0.186266616268125, -0.0387572286849415, 0.0575914455113098, 0.157609243121204, 0.220346301053061, -0.0626777547324119, -0.113851702484695, -0.116475605634303, 0.22526164753013, 0.223826799079261, 0.156828878422261, 0.156828878422261, -0.348685874833428, -0.0903521318069049, -0.263248163466929, -0.207718489967913, -0.00114280263869193, -0.173123855988071, 0.00717472807613134, -0.122226134658981, 0.025464920617837, -0.0355698249808467, 0.187431184982238, 0.181218694001414, -0.170463957448774, -0.182265636600245, -0.162639928396832, -0.08984634445544, -0.0728162435542022, -0.102375349892814, -0.083518458576145, -0.26562651277574, -0.124224763801435, -0.247398017325716, -0.0987361747211609, -0.267357057917193, -0.121190412683788, -0.235390425297552, -0.102224269330431, -0.267357057917193, -0.11647321800326, -0.258096696454203, 0.0374542295773345, -0.126689730715761, -0.0732225659783105, 0.25371891049452, 0.179088091909104, 0.0189353803356997, 0.0439242698170608, 0.0885475465440703, 0.0885475465440703, 0.0627230661721545, -0.0267785017213478, 0.0513972263582553, 0.0260420185827092, 0.0176322762568806, -0.0186260827562727, -0.0357699577049284, -0.0594521157329645, 0.0508444244300699, 0.142346989140971, 0.125278734192754, 0.126468071771089, 0.17321276456908, 0.200109710036431, 0.127527720685718, 0.0276890383196247, 0.23637704520406, 0.191366461532249, 0.124763311559562, -0.0443449571558454, -0.0475135961354155, 0.074234409804811, 0.0216623623678642, 0.352213438519467, 0.21463189015559, -0.189097828932044, 0.100405735385079, 0.144407665462729, 0.336395360175917, 0.336395360175917, 0.12155167143745, 0.16287496031754, 0.18641467013746, 0.32607579411487, 0.357175125935867, 0.224343769580642, 0.237299332647382, 0.196244695452164, 0.198230836612474, 0.190617207491118, 0.111580641946218, 0.0872289438148001, -0.0809563578119795, 0.204355413307292, 0.209639717051386, 0.207342466515434, 0.207342466515434, 0.197169181872743, -0.0572474800374093, -0.0728827033179431, -0.10460003726393, -0.107196252644019, 0.361813401969034, 0.175102284300755, 0.363949986843691, 0.177442308769387, 0.215769343564575, 0.261298864778967, 0.172202480804323, 0.184076703337005, 0.163188602303023, 0.0493811888871374, 0.175827850286979, 0.163383083228185, -0.0462305614889876, -0.10500182436349, -0.0595021447805033, -0.107718395073629, -0.081368118853961, -0.10288400064567, -0.0687391241662543, -0.0840863186508532, -0.0922241572577749, -0.279777090829456, -0.113889925777426, 0.0930136922441679, 0.0930136922441679, 0.0582604661375774, 0.181541045905811, 0.160535840342632, 0.138401158506572, 0.0244932126510834, 0.00542933620282285, 0.0633164368215588, 0.128659554552638, 0.101233497721208, 0.101233497721208, 0.0760249394180194, 0.0608979020662987, 0.012262059474567, -0.0816046841286946, -0.0831343394498383, -0.0814694950097439, -0.109232145394468, 0.0770377761224491, 0.041925391053174, 0.0274589171017179, 0.0274589171017179, 0.347617575580373, -0.0596237774820829, -0.0794752848265101, -0.0794752848265101, 0.2925962616859, -0.0887185089091997, 0.101775115170702, -0.0645242547362925, 0.27126368025602, -0.137133999832565, 0.1427646918224, 0.12693641285656, 0.0754012256843574, 0.0625093748503227, 0.0612182250236711, 0.022647781585492, 0.0122598524089968, -0.031821546967195, 0.0950948808259056, 0.194301250561357, -0.176407422753569, 0.0770377761224491, 0.041925391053174, -0.162369831909575, -0.0320855187783016, -0.0320855187783016, -0.553307949537856, 0.0135199811625741, 0.00368762745876068, -0.00119025497296702, -0.0393155997407192, -0.0439714980600599, 0.110325691275902, 0.110325691275902, 0.107266760517285, 0.18135826013452, -0.070138627603902, -0.084586374173829, -0.070138627603902, -0.084586374173829, -0.18934706121959, -0.0929298188222547, 0.0852655356749052, -0.179394458894588, 0.279166751287957, 0.275139241012056, 0.279948761371457, 0.275155694583494, 0.0121935242055421, 0.0105151849876446, -0.0734774746915535, -0.0830825997308687, -0.0261494773912439, -0.0137546788196909, -0.0383815439915174, -0.092751399768813, 0.332355694092576, 0.245345164899538, 0.0254896012212449, 0.0970805551002128, 0.0811025946105638, 0.0803177348400819, 0.00164450882011678, -0.0224311131933797, 0.224672875336535, 0.224672875336535, 0.0383303142014232, -0.0317090718898804, 0.0098303983136882, -0.00933161038990583, -0.0873586528394907, -0.0215767942260494, -0.0908195449342244, -0.040099049184707, -0.0985530505261142, -0.0733677092344781, 0.141756395019668, 0.157166003405932, 0.0508331038597551, 0.0390688659098563, 0.0540369357658138, 0.0099459590057849, -0.177557776337536, 0.00493496128474215, -0.130643486152668, 0.113817128307549, -0.142574086775631, 0.100786016919189, -0.15587973038, 0.109227489252925, -0.163440665982954, 0.099878533303345, -0.135287923148148, 0.109227489252925, 0.0333059944181948, -0.0137546788196909, 0.347617575580373, -0.0596237774820829, -0.0794752848265101, -0.241561147836771, -0.0887185089091997, 0.0730471534751108, 0.0835002138786142, -0.189280927404009, -0.189280927404009, -0.19628855825041, -0.837484070977975, 0.0753082580083826, 0.0630294638001513, 0.0592929776175618, 0.0447029449409758, 0.0723308379811164, 0.0645975264797624, -0.109593771541039, -0.0811243820180713, -0.0188474302547651, 0.0685021880400987, 0.0321368032444232, 0.0966486930237446, 0.0363801672252788, 0.255050941838437, -0.0415198183216256, 0.0275908041907373, 0.0158480616637525, 0.194606530344896, -0.220059902653218, -0.265372977366032, -0.245100901081693, -0.434187429432454, -0.274154387736992, -0.498079277975881, -0.113234390595495, -0.13592301549537, -0.27298841850198, -0.27298841850198, -0.123853386260785, -0.146226945009001, -0.160255725328499, -0.220696627341507, -0.245525340689894, 0.265599932544055, 0.240132044079803, 0.12044536185896, 0.122242899082191, 0.11558414739394, 0.0672807026649379, 0.0565215464236424, 0.00320786060661828, 0.0811815737084521, 0.00442292020833086, 0.0259650355832699, 0.0259650355832699, 0.00159130624929899, 0.0167237159821922, 0.0123103421759687, 0.0151464759374235, 0.0138398492897789, -0.378259152221767, 0.0663775142988527, -0.380910748552257, 0.0640455341462561, 0.0171809160567121, 0.0133244698759663, 0.189239788364039, 0.105896755907438, 0.131163117931394, 0.0742692098161327, -0.17392768225168, -0.100700445594839, 0.0036126603654632, -0.0123831512006035, 5.23650575074128e-05, -0.0132043382182284, 0.00660287534316686, -0.00167186752805072, -0.00240546718672251, 0.0118803438893343, 0.0424368089424911, 0.219430516658537, -0.0151485147157889 ]).reshape(203, 2, order='F') mpg_bs_poisson.aic = 1077.25052939687 mpg_bs_poisson.rank = 24 mpg_bs_poisson.sp = np.array([ 40491.3940640059, 232455.530262537 ]) mpg_bs_poisson.gcv_ubre = -0.733688545240377 mpg_bs_poisson.scale = 1 mpg_bs_poisson.method = 'UBRE' mpg_bs_poisson.Vp = np.array([ 0.00909877938596195, -0.0036458463607326, -0.00588941030822462, -0.00591326964084843, 0.00270235043019556, 0.00119384910564329, -0.000286097332788069, -0.000538328684681065, -0.00118730774061063, -0.00118703780057675, -0.00172055345918883, -0.00282973019584382, -0.00279619972795585, -0.00289060805206229, -0.00320325258490701, -0.00198704716570621, -0.000847222204131792, 2.70515273679747e-05, 0.000326844162490547, 0.00135256413351957, 0.0022188465918784, 0.00337126604512471, 0.00374620280538731, 0.00434814343158575, -0.0036458463607326, 0.00322561886385797, 0.000818643340518427, 0.00081636578104383, -0.00190437247620751, -0.000863343934846812, 0.000139109866047115, 0.000296579927149878, 0.000740568197543185, 0.000742005374071472, 0.00114977928877198, 0.00200530841336703, 0.00222811101992064, 0.0024818042434364, 0.00282650455393769, 0.00146020870965775, 0.000618887019138287, -2.43124025263358e-05, -0.000241178336099445, -0.000991378139936192, -0.00162708135143005, -0.00248332970180653, -0.00275966775911108, -0.00320503008932793, -0.00588941030822462, 0.000818643340518427, 0.00565989642595176, 0.00495199955352287, -0.00137264214791527, -0.000624245731910545, 0.000134212108893823, 0.000277278672318982, 0.000624575880555572, 0.00064780126403512, 0.000935707806932052, 0.00148449349573531, 0.00132234065473106, 0.00121308059577345, 0.00127960812345634, 0.000598575017370257, 0.000255298927663316, -1.05348849084324e-05, -0.000105109656554569, -0.000413488381353818, -0.000668742250888912, -0.00101475517128789, -0.00106390221980279, -0.00121570767202619, -0.00591326964084843, 0.00081636578104383, 0.00495199955352287, 0.00612031056002729, -0.000638697385813232, -0.000200756794681808, 0.000234092062788641, 0.000317400792863984, 0.000474734639710034, 0.000434320019657147, 0.000459443487096387, 0.000570251932991725, 0.000195546004426462, 2.72052297316331e-05, -3.78499050833033e-05, 0.000783804355084115, 0.000338266801002889, -5.98980579055969e-06, -0.00012832043843202, -0.000542743279532203, -0.000890014730820339, -0.00128430664220486, -0.00146322120108432, -0.00169190306471577, 0.00270235043019556, -0.00190437247620751, -0.00137264214791527, -0.000638697385813232, 0.00467632009472188, 0.00125238169504067, -0.00129877704188898, -0.0015159828401994, -0.00244941224999582, -0.00216501742563322, -0.00281375885789835, -0.00449408146252495, -0.00364816304284394, -0.00343278843606667, -0.0037656405854337, -0.0019530192987073, -0.000823926841909847, 5.56765347348377e-05, 0.000369977630385713, 0.00139228419735132, 0.00223783577417036, 0.00315107722344203, 0.00316419340408527, 0.00352917384733862, 0.00119384910564329, -0.000863343934846812, -0.000624245731910545, -0.000200756794681808, 0.00125238169504067, 0.00114727766243173, 0.000242162647776926, 4.77172748392219e-06, -0.00037150498020405, -0.000523254030404203, -0.000886617935612452, -0.00140688678525427, -0.00151777207774812, -0.00163789857683012, -0.0018417095344788, -0.000869233941992018, -0.000381264599266638, -2.19177180982826e-06, 0.000134563688210397, 0.000592929102356622, 0.000989340528530486, 0.00149625051966445, 0.00155348190492993, 0.00176000748685542, -0.000286097332788069, 0.000139109866047115, 0.000134212108893823, 0.000234092062788641, -0.00129877704188898, 0.000242162647776926, 0.0011787952545672, 0.00103397353567405, 0.00113707718574448, 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-0.533797950669129, -1.2242088732616, -0.292185501092755, 0.653783193502416, -0.203012833152524, -0.233292506440238, -0.257179556553545, 0.701886900587847, 0.180875662130529, -2.78710370715732, 0.501821705771827, 0.199861513010874, 0.0705449671051595, 0.65845009000007, 0.271741081238087, 0.0296247577347264, 2.29204423094291, 0.295179535981046, -0.498021301042363, -0.191083976072719, 0.10022620819189, 0.149938173134123, -0.000647738071340076, 0.0932506134932401, -0.255992650247112, -0.173965873880064, 0.0746464264713858, -0.0438028632249015, -0.161854602228138, -0.0578372113962488, 0.157297649723395, 0.195127506637709, -0.126981325801707, -0.201542068281104, 0.633451731139413, 1.23686433543792, 0.0741286829376448, 3.93651436085439, 0, 0, 0 ]).reshape(24, 24, order='F') mpg_bs_poisson.nsdf = 4 mpg_bs_poisson.sig2 = 1 mpg_bs_poisson.cmX = np.array([ 1, 0.901477832512315, 0.58128078817734, 0.374384236453202, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]) mpg_bs_poisson.assign = np.array([ 0, 1, 2, 2 ]) mpg_bs_poisson.offset = np.array([ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]) mpg_bs_poisson.df_residual = 194.753831641044 mpg_bs_poisson.min_edf = 6 mpg_bs_poisson.optimizer = np.array([ 'outer', 'newton' ]) mpg_bs_poisson.p_coeff = np.array([ 3.38155196812657, -0.2398057983025, 0.0385574655971876, 0.0308789097162079 ]) mpg_bs_poisson.se = np.array([ 0.0953875221712041, 0.0567945319890742, 0.0752322831366413, 0.0782324137428169, 0.0683836244631848, 0.0338714874552585, 0.0343335878487408, 0.0327660488124372, 0.0419264132225423, 0.036884405501987, 0.0465922758083723, 0.0708176444724415, 0.0738292412039099, 0.0885015393163463, 0.116977237674529, 0.0436765043288013, 0.0191231267976919, 0.0122089069890121, 0.0159907519222515, 0.0342192166136885, 0.0515106100154504, 0.0817203372793118, 0.116254024441009, 0.164262927556978 ]) mpg_bs_poisson.p_t = np.array([ 35.4506741673956, -4.22233954403625, 0.512512235301397, 0.394707362829427 ]) mpg_bs_poisson.p_pv = np.array([ 2.83211381163377e-275, 2.41779512472801e-05, 0.608292559428079, 0.693058868325634 ]) mpg_bs_poisson.residual_df = 194.753831641044 mpg_bs_poisson.m = 2 mpg_bs_poisson.chi_sq = np.array([ 24.0890023854214, 12.9900133623474 ]) mpg_bs_poisson.s_pv = np.array([ 4.50054787026542e-05, 0.0019804834204652 ]) mpg_bs_poisson.scale = 1 mpg_bs_poisson.r_sq = 0.88083178283537 mpg_bs_poisson.n = 203 mpg_bs_poisson.dev_expl = 0.888606170071194 mpg_bs_poisson.edf = np.array([ 2.53986871460058, 1.70629964435497 ]) mpg_bs_poisson.dispersion = 1 mpg_bs_poisson.pTerms_pv = np.array([ 2.41779512472801e-05, 0.874926047858207 ]) mpg_bs_poisson.pTerms_chi_sq = np.array([ 17.8281512251323, 0.267231825859481 ]) mpg_bs_poisson.pTerms_df = np.array([ 1, 2 ]) mpg_bs_poisson.cov_unscaled = np.array([ 0.00909877938596195, -0.0036458463607326, -0.00588941030822462, -0.00591326964084843, 0.00270235043019556, 0.00119384910564329, -0.000286097332788069, -0.000538328684681065, -0.00118730774061063, -0.00118703780057675, -0.00172055345918883, -0.00282973019584382, -0.00279619972795585, -0.00289060805206229, -0.00320325258490701, -0.00198704716570621, -0.000847222204131792, 2.70515273679747e-05, 0.000326844162490547, 0.00135256413351957, 0.0022188465918784, 0.00337126604512471, 0.00374620280538731, 0.00434814343158575, -0.0036458463607326, 0.00322561886385797, 0.000818643340518427, 0.00081636578104383, 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0.00143202572023981, 0.00283652481021948, 0.00566170373323159, 0.0166147008644102, 0.0269823093695889 ]).reshape(24, 24, order='F') mpg_bs_poisson.cov_scaled = mpg_bs_poisson.cov_unscaled mpg_bs_poisson.p_table = np.array([ 3.38155196812657, -0.2398057983025, 0.0385574655971876, 0.0308789097162079, 0.0953875221712041, 0.0567945319890742, 0.0752322831366413, 0.0782324137428169, 35.4506741673956, -4.22233954403625, 0.512512235301397, 0.394707362829427, 2.83211381163377e-275, 2.41779512472801e-05, 0.608292559428079, 0.693058868325634 ]).reshape(4, 4, order='F') mpg_bs_poisson.pTerms_table = np.array([ 1, 2, 17.8281512251323, 0.267231825859481, 2.41779512472801e-05, 0.874926047858207 ]).reshape(2, 3, order='F') mpg_bs_poisson.s_table = np.array([ 2.53986871460058, 1.70629964435497, 3.20982914795608, 2.15301685267905, 24.0890023854214, 12.9900133623474, 4.50054787026542e-05, 0.0019804834204652 ]).reshape(2, 4, order='F') mpg_bs_poisson.method = 'UBRE' mpg_bs_poisson.sp_criterion = -0.733688545240377 mpg_bs_poisson.rank = 24 mpg_bs_poisson.np = 24 mpg_bs_poisson.params = np.array([ 3.38155196812657, -0.2398057983025, 0.0385574655971876, 0.0308789097162079, 0.322087207070371, 0.114222640046661, -0.0703319473834318, -0.0932993942273026, -0.164529819124519, -0.150860338924587, -0.19827414261489, -0.318132823476157, -0.277920321049033, -0.291752287584618, -0.335850782440607, 0.147266917321495, 0.0655746640077953, 0.00329634588440575, -0.0178203244735351, -0.0949069908870388, -0.162736107333124, -0.267760412623755, -0.31426029441775, -0.36537967845964 ]) statsmodels-0.12.2/statsmodels/gam/tests/results/results_mpg_bs_poisson.r000066400000000000000000000032421400612667500271040ustar00rootroot00000000000000 source("M:\\josef_new\\eclipse_ws\\statsmodels\\statsmodels_py34_pr\\tools\\R2nparray\\R\\R2nparray.R") library('mgcv') library('gamair') d = data(mpg) #gam_a = gam(city.mpg ~ fuel + drive + s(weight,bs="cc",k=7) + s(hp,bs="cc",k=6), data = mpg, # sp = c(6.46225497484073, 0.81532465890585)) #gam_a = gam(city.mpg ~ fuel + drive + s(weight,bs="bs",k=7) + s(hp,bs="bs",k=6), data = mpg) sm_knots_w = c(1488., 1488., 1488., 1488., 1953.22222222, 2118.77777778, 2275., 2383.88888889, 2515.55555556, 2757.33333333, 3016.44444444, 3208.11111111, 4066., 4066., 4066., 4066.) sm_knots_hp = c(48.0, 48.0, 48.0, 48.0, 68.0, 73.0, 88.0, 101.0, 116.0, 152.28571428571428, 288.0, 288.0, 288.0, 288.0) knots_w <- data.frame(weight=sm_knots_w) knots_h <- data.frame(hp=sm_knots_hp) gam_a = gam(city.mpg ~ fuel + drive + s(weight,bs="bs",k=12) + s(hp,bs="bs",k=10), data = mpg, knots=c(knots_w, knots_h), family=poisson) pls = gam_a fname = "results_mpg_bs_poisson.py" append = FALSE #TRUE #redirect output to file sink(file=fname, append=append) write_header() mod_name = "mpg_bs_poisson." cat("\nmpg_bs_poisson = Bunch()\n") cat(paste("\n", mod_name, "smooth0 = Bunch()\n", sep="")) sm1 <- gam_a$smooth[[1]] cat_items(sm1, prefix=paste(mod_name, "smooth0.", sep="")) #, blacklist=c()) cat("\n") cat(convert.numeric(pls$smooth[[1]]$S[[1]], name=paste(mod_name, "smooth0.S", sep=""))) cat("\n") cat_items(pls, prefix=mod_name, blacklist=c("eq", "control")) cat("\n") pls_summ = summary(pls) cat_items(pls_summ, prefix=mod_name, blacklist=c("eq", "control")) params = coef(pls) cat("\n") cat(convert.numeric(params, name=paste(mod_name, "params", sep=""))) # stop redirecting output sink() statsmodels-0.12.2/statsmodels/gam/tests/results/results_pls.py000066400000000000000000000523331400612667500250550ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch pls5 = Bunch() pls5.smooth = Bunch() pls5.smooth.term = 'times' pls5.smooth.bs_dim = 7 pls5.smooth.dim = 1 pls5.smooth.by = 'NA' pls5.smooth.label = 's(times)' pls5.smooth.sp = 1 pls5.smooth.BD = np.array([ -0.0322305472050642, 0.0332895629742452, -0.00907144581575865, 0.00386174436551668, -0.00624916066961505, 0.0181385348730838, 0.0292384327901831, -0.0717740723184547, 0.054914261809955, -0.0158383049768667, 0.00626042823599089, -0.0103543594891998, -0.011074996356557, 0.0526128870346165, -0.0930190975208449, 0.0595200902721069, -0.0135721686724522, 0.00600098849448633, 0.00625687187895293, -0.0145166841858048, 0.0594020303618183, -0.0946831790103269, 0.0511018949689336, -0.0114519440129956, -0.00994300967116444, 0.00619931821053046, -0.0156728054209229, 0.0550549724656574, -0.0669161912708059, 0.0271416199423184, 0.0177532485636497, -0.00581101171513275, 0.00344705658575325, -0.00791532311608746, 0.0293751974079486, -0.0294748398076931 ]).reshape(6, 6, order='F') pls5.smooth.xp = np.array([ 2.4, 11.2, 17.8, 24.8, 31.2, 41, 57.6 ]) pls5.smooth.rank = 5 pls5.smooth.df = 5 pls5.smooth.null_space_dim = 0 pls5.smooth.S_scale = 0.0263073404164214 pls5.smooth.vn = 'times' pls5.smooth.first_para = 1 pls5.smooth.last_para = 5 pls5.smooth.S = np.array([ 1.63230340200229, -0.830028815742871, 0.901802118895566, -0.00398686659390206, 0.518361615576888, -0.830028815742871, 1.06825930315182, -1.16452750566645, 0.27022513792646, -0.156140353580413, 0.901802118895566, -1.16452750566645, 1.99828270457965, -1.0130803218067, 0.537502835084835, -0.00398686659390202, 0.27022513792646, -1.0130803218067, 1.00336165100886, -0.42156685405732, 0.518361615576888, -0.156140353580413, 0.537502835084835, -0.42156685405732, 0.53026887882367 ]).reshape(5, 5, order='F') pls5.coefficients = np.array([ 20.036025308233, -62.6817097954891, -51.0985219408637, 42.0072653496657, 22.0294169083686 ]) pls5.residuals = np.array([ -27.9959461270327, -29.9873153013088, -33.4871658551864, -32.1806279683964, -36.2429080803179, -42.1809749693548, -42.7967018255375, -41.6315122829302, -43.3634717352437, -43.0512160670889, -40.6362776289091, -42.0362776289091, -39.5456492135197, -37.7626842421689, -39.4270272919089, -34.3534190712615, -34.2581579025003, -25.620485822405, -9.20474188594053, -4.25666047069376, 0.973620269858165, -1.98289744771254, 5.91710255228746, 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-22.6274495550672, -9.22744955506716, -23.7435355032739, -17.2959461270327 ]) pls5.fitted_values = np.array([ 27.9959461270327, 28.6873153013088, 30.7871658551864, 32.1806279683964, 33.5429080803179, 39.4809749693548, 40.0967018255375, 40.3315122829302, 40.6634717352437, 40.3512160670889, 39.3362776289091, 39.3362776289091, 36.8456492135197, 35.0626842421689, 34.0270272919089, 31.6534190712615, 28.8581579025003, 25.620485822405, 6.50474188594053, 1.55666047069376, -0.973620269858165, -11.3171025522875, -11.3171025522875, -11.3171025522875, -11.3171025522875, -11.3171025522875, -11.3171025522875, -13.9258684745284, -21.7024927542218, -21.7024927542218, -21.7024927542218, -21.7024927542218, -24.2563466994954, -24.2563466994954, -26.7801254113161, -26.7801254113161, -29.2672899939997, -29.2672899939997, -31.7113015518619, -31.7113015518619, -31.7113015518619, -34.1056211892181, -34.1056211892181, -36.4437100103842, -38.7190291196756, -38.7190291196756, -38.7190291196756, -47.0618305244081, -47.0618305244081, -47.0618305244081, -47.0618305244081, -48.9252176390611, -48.9252176390611, -55.3533972598403, -55.3533972598403, -59.0684985904528, -60.0913440540408, -60.0913440540408, -61.0049135002874, -63.0808745707767, -63.5482487834561, -64.2704384755527, -64.1596135268211, -63.5819529683103, -63.113299125691, -57.7265718484138, -56.3911648453531, -51.6165572960303, -49.7658622114755, -49.7658622114755, -45.6702784916742, -41.0447144402178, -41.0447144402178, -35.9220214153642, -35.9220214153642, -33.1964294858495, -27.4623645725674, -24.4721355007692, -24.4721355007692, -21.4119379601788, -11.902754085501, -8.65390222958812, -8.65390222958812, -8.65390222958812, -2.0922444071392, 7.77329826332311, 11.0314729126827, 11.0314729126827, 14.2592745150041, 26.6843113342156, 37.8936229220499, 47.303404095494, 49.3062580917222, 55.784830576711, 55.784830576711, 59.9853931943938, 61.7920300180993, 62.4154499346668, 62.5575969312418, 62.1695120512782, 61.4317921021069, 61.4317921021069, 60.9416344853907, 60.3758467119592, 60.3758467119592, 58.2639644866625, 58.2639644866625, 49.1163792915167, 49.1163792915167, 41.7347820148442, 40.4779999343159, 36.740721990024, 34.3160223101961, 27.6891170362285, 27.6891170362285, 23.9302944205558, 22.2450916690901, 22.2450916690901, 21.4499728420109, 17.9369803024212, 16.7419595489538, 15.1669773395835, 12.1850445709859, 11.0385180985158, 11.0385180985158, 10.7434946415046, 11.5970529121364, 13.3718934319111, 15.5794900717192, 19.9274495550672, 19.9274495550672, 21.0435355032739, 27.9959461270327 ]) pls5.linear_predictors = np.array([ 27.9959461270327, 28.6873153013088, 30.7871658551864, 32.1806279683964, 33.5429080803179, 39.4809749693548, 40.0967018255375, 40.3315122829302, 40.6634717352437, 40.3512160670889, 39.3362776289091, 39.3362776289091, 36.8456492135197, 35.0626842421689, 34.0270272919089, 31.6534190712615, 28.8581579025003, 25.620485822405, 6.50474188594053, 1.55666047069376, -0.973620269858165, -11.3171025522875, -11.3171025522875, -11.3171025522875, -11.3171025522875, -11.3171025522875, -11.3171025522875, -13.9258684745284, -21.7024927542218, -21.7024927542218, -21.7024927542218, -21.7024927542218, -24.2563466994954, -24.2563466994954, -26.7801254113161, -26.7801254113161, -29.2672899939997, -29.2672899939997, -31.7113015518619, -31.7113015518619, -31.7113015518619, -34.1056211892181, -34.1056211892181, -36.4437100103842, -38.7190291196756, -38.7190291196756, -38.7190291196756, -47.0618305244081, -47.0618305244081, -47.0618305244081, -47.0618305244081, -48.9252176390611, -48.9252176390611, -55.3533972598403, -55.3533972598403, -59.0684985904528, -60.0913440540408, -60.0913440540408, -61.0049135002874, -63.0808745707767, -63.5482487834561, -64.2704384755527, -64.1596135268211, -63.5819529683103, -63.113299125691, -57.7265718484138, -56.3911648453531, -51.6165572960303, -49.7658622114755, -49.7658622114755, -45.6702784916742, -41.0447144402178, -41.0447144402178, -35.9220214153642, -35.9220214153642, -33.1964294858495, -27.4623645725674, -24.4721355007692, -24.4721355007692, -21.4119379601788, -11.902754085501, -8.65390222958812, -8.65390222958812, -8.65390222958812, -2.0922444071392, 7.77329826332311, 11.0314729126827, 11.0314729126827, 14.2592745150041, 26.6843113342156, 37.8936229220499, 47.303404095494, 49.3062580917222, 55.784830576711, 55.784830576711, 59.9853931943938, 61.7920300180993, 62.4154499346668, 62.5575969312418, 62.1695120512782, 61.4317921021069, 61.4317921021069, 60.9416344853907, 60.3758467119592, 60.3758467119592, 58.2639644866625, 58.2639644866625, 49.1163792915167, 49.1163792915167, 41.7347820148442, 40.4779999343159, 36.740721990024, 34.3160223101961, 27.6891170362285, 27.6891170362285, 23.9302944205558, 22.2450916690901, 22.2450916690901, 21.4499728420109, 17.9369803024212, 16.7419595489538, 15.1669773395835, 12.1850445709859, 11.0385180985158, 11.0385180985158, 10.7434946415046, 11.5970529121364, 13.3718934319111, 15.5794900717192, 19.9274495550672, 19.9274495550672, 21.0435355032739, 27.9959461270327 ]) pls5.deviance = 180391.104352065 pls5.null_deviance = 395017.34 pls5.iter = 1 pls5.weights = np.array([ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]) pls5.prior_weights = np.array([ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]) pls5.df_null = 133 pls5.y = np.array([ 0, -1.3, -2.7, 0, -2.7, -2.7, -2.7, -1.3, -2.7, -2.7, -1.3, -2.7, -2.7, -2.7, -5.4, -2.7, -5.4, 0, -2.7, -2.7, 0, -13.3, -5.4, -5.4, -9.3, -16, -22.8, -2.7, -22.8, -32.1, -53.5, -54.9, -40.2, -21.5, -21.5, -50.8, -42.9, -26.8, -21.5, -50.8, -61.7, -5.4, -80.4, -59, -71, -91.1, -77.7, -37.5, -85.6, -123.1, -101.9, -99.1, -104.4, -112.5, -50.8, -123.1, -85.6, -72.3, -127.2, -123.1, -117.9, -134, -101.9, -108.4, -123.1, -123.1, -128.5, -112.5, -95.1, -81.8, -53.5, -64.4, -57.6, -72.3, -44.3, -26.8, -5.4, -107.1, -21.5, -65.6, -16, -45.6, -24.2, 9.5, 4, 12, -21.5, 37.5, 46.9, -17.4, 36.2, 75, 8.1, 54.9, 48.2, 46.9, 16, 45.6, 1.3, 75, -16, -54.9, 69.6, 34.8, 32.1, -37.5, 22.8, 46.9, 10.7, 5.4, -1.3, -21.5, -13.3, 30.8, -10.7, 29.4, 0, -10.7, 14.7, -1.3, 0, 10.7, 10.7, -26.8, -14.7, -13.3, 0, 10.7, -14.7, -2.7, 10.7, -2.7, 10.7 ]) pls5.sig2 = 1405.72589061551 pls5.edf = np.array([ 0.893973446261888, 0.964904681210716, 0.910197466057859, 0.951689945168155, 0.953288730104318 ]) pls5.edf1 = np.array([ 0.981711944544246, 0.996264240571943, 0.982938111847731, 0.994003453703398, 0.993140527833467 ]) pls5.hat = np.array([ 0.0648926406262456, 0.0631966900584761, 0.0577531173208777, 0.054095436609033, 0.050646403216983, 0.0414030519922767, 0.0419393714799485, 0.0424407004729246, 0.0466884028411439, 0.0488322930145467, 0.0519315914083648, 0.0519315914083648, 0.0547480920171652, 0.0551378158184696, 0.055000499312335, 0.0539763060097797, 0.0518779851195461, 0.0486811707669425, 0.0278002106937094, 0.0236664981666194, 0.0218678587405494, 0.0168702076728429, 0.0168702076728429, 0.0168702076728429, 0.0168702076728429, 0.0168702076728429, 0.0168702076728429, 0.0162099114442375, 0.0155969292014215, 0.0155969292014215, 0.0155969292014215, 0.0155969292014215, 0.0158045134149012, 0.0158045134149012, 0.0161857205884225, 0.0161857205884225, 0.016715730291764, 0.016715730291764, 0.0173667434517008, 0.0173667434517008, 0.0173667434517008, 0.0181085269560167, 0.0181085269560167, 0.01890902644145, 0.0197350472655703, 0.0197350472655703, 0.0197350472655703, 0.0226344032048916, 0.0226344032048916, 0.0226344032048916, 0.0226344032048916, 0.0231064605220144, 0.0231064605220144, 0.0236010474476975, 0.0236010474476975, 0.0229362836765587, 0.0226341946832984, 0.0226341946832984, 0.022331993508414, 0.0216507968090011, 0.0215654072946402, 0.022307353392817, 0.0227976525538385, 0.0241408042749582, 0.0249779152827976, 0.0312910194327127, 0.0323419434967748, 0.0349400511510723, 0.0355272516690269, 0.0355272516690269, 0.0361324218251331, 0.0358606650811796, 0.0358606650811796, 0.0347553939582878, 0.0347553939582878, 0.0339600300427633, 0.0320525342614235, 0.0310119683533198, 0.0310119683533198, 0.0299615237560085, 0.0270931967217139, 0.0263353031813311, 0.0263353031813311, 0.0263353031813311, 0.0252733837531764, 0.0250806228807981, 0.0254302543661375, 0.0254302543661375, 0.0259902742331093, 0.0301636177707758, 0.0364915828338694, 0.0429804641044596, 0.044338813283762, 0.0478470725808693, 0.0478470725808693, 0.0481431076555552, 0.0465422084456883, 0.0448254504760713, 0.0416389240869886, 0.0393309802887003, 0.0370523590709184, 0.0370523590709184, 0.0359684768956268, 0.0349434963301099, 0.0349434963301099, 0.0323665679080144, 0.0323665679080144, 0.0312847023217674, 0.0312847023217674, 0.0364198732168461, 0.037600534161656, 0.0414170598382483, 0.0440177673095073, 0.0505139848525673, 0.0505139848525673, 0.0529266400408666, 0.0535167237447347, 0.0535167237447347, 0.0536669701648488, 0.0531784414477218, 0.0525292698619672, 0.0512621693606931, 0.0477153739370841, 0.04661692338803, 0.04661692338803, 0.0475945362276516, 0.054093097958197, 0.0620671413133406, 0.0689518115696408, 0.0748549607794503, 0.0748549607794503, 0.0749105486240515, 0.0648926406262456 ]) pls5.R = np.array([ 0.419812589435278, -0.402017675646454, 0.488999441150794, 3.98552866496736, 0, 4.86284047828201, 0, 0, 0, 0, -0.642048459345638, 4.51912765154044, 0, 0, 0, -0.287016774143419, 0.0590176744049711, 4.48152596952222, 0, 0, -0.881192283208667, -0.721748467517155, 0.141530733755857, -0.975518963486962, 3.68675964176163 ]).reshape(5, 5, order='F') pls5.sp = None pls5.nsdf = 0 pls5.Ve = np.array([ 72.3041357618152, 1.66913532916499, 0.502555357170923, -6.08025176950849, 12.003156582929, 1.66913532916499, 60.8548565958852, 15.0519202741408, 3.17016170151452, 18.3724060596875, 0.502555357170922, 15.0519202741408, 59.9017269122546, 5.31826437849191, 9.33171431050043, -6.08025176950849, 3.17016170151452, 5.31826437849191, 64.066598433814, 0.697025995194202, 12.003156582929, 18.3724060596875, 9.33171431050043, 0.697025995194202, 90.4171907271362 ]).reshape(5, 5, order='F') pls5.Vp = np.array([ 82.3434717904795, -0.200148537531833, 5.72440590880333, -8.16239095841476, 17.8905796109278, -0.200148537531833, 62.7551455396847, 13.6184531397824, 3.34367783462779, 18.6689815079065, 5.72440590880333, 13.6184531397824, 65.7343350358227, 1.64716527529062, 13.483565756752, -8.16239095841476, 3.34367783462779, 1.64716527529062, 67.4465665922581, -2.30098498787076, 17.8905796109278, 18.6689815079065, 13.483565756752, -2.30098498787076, 96.3416133118078 ]).reshape(5, 5, order='F') pls5.rV = np.array([ -0.0392296145497642, -0.148679582608057, 0.0918117471236096, 0.00695938411477142, 0.0468995189236096, -0.00179994351487469, 0.056193728117226, 0.144936306168724, -0.104973822562831, -0.0915159363023183, -0.112299188421777, 0.00531211090361532, -0.0656150416863762, -0.150002132732638, 0.073614883684395, 0.168793284880097, -0.101999375560153, -0.0661656482881794, -0.11825783453015, -0.035090842164745, 0.126224824188388, 0.0945889794789336, 0.0929660567115005, -0.020649293225403, 0.226516853583393 ]).reshape(5, 5, order='F') pls5.gcv_ubre = 1456.9270648002 pls5.aic = 1348.0527067527 pls5.rank = 5 pls5.gcv_ubre_dev = 1456.92706480021 pls5.method = 'GCV' pls5.full_sp = 1 pls5.cmX = np.array([ 0, 0, 0, 0, 0 ]) pls5.model = np.array([ 0, -1.3, -2.7, 0, -2.7, -2.7, -2.7, -1.3, -2.7, -2.7, -1.3, -2.7, -2.7, -2.7, -5.4, -2.7, -5.4, 0, -2.7, -2.7, 0, -13.3, -5.4, -5.4, -9.3, -16, -22.8, -2.7, -22.8, -32.1, -53.5, -54.9, -40.2, -21.5, -21.5, -50.8, -42.9, -26.8, -21.5, -50.8, -61.7, -5.4, -80.4, -59, -71, -91.1, -77.7, -37.5, -85.6, -123.1, -101.9, -99.1, -104.4, -112.5, -50.8, -123.1, -85.6, -72.3, -127.2, -123.1, -117.9, -134, -101.9, -108.4, -123.1, -123.1, -128.5, -112.5, -95.1, -81.8, -53.5, -64.4, -57.6, -72.3, -44.3, -26.8, -5.4, -107.1, -21.5, -65.6, -16, -45.6, -24.2, 9.5, 4, 12, -21.5, 37.5, 46.9, -17.4, 36.2, 75, 8.1, 54.9, 48.2, 46.9, 16, 45.6, 1.3, 75, -16, -54.9, 69.6, 34.8, 32.1, -37.5, 22.8, 46.9, 10.7, 5.4, -1.3, -21.5, -13.3, 30.8, -10.7, 29.4, 0, -10.7, 14.7, -1.3, 0, 10.7, 10.7, -26.8, -14.7, -13.3, 0, 10.7, -14.7, -2.7, 10.7, -2.7, 10.7, 2.4, 2.6, 3.2, 3.6, 4, 6.2, 6.6, 6.8, 7.8, 8.2, 8.8, 8.8, 9.6, 10, 10.2, 10.6, 11, 11.4, 13.2, 13.6, 13.8, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.8, 15.4, 15.4, 15.4, 15.4, 15.6, 15.6, 15.8, 15.8, 16, 16, 16.2, 16.2, 16.2, 16.4, 16.4, 16.6, 16.8, 16.8, 16.8, 17.6, 17.6, 17.6, 17.6, 17.8, 17.8, 18.6, 18.6, 19.2, 19.4, 19.4, 19.6, 20.2, 20.4, 21.2, 21.4, 21.8, 22, 23.2, 23.4, 24, 24.2, 24.2, 24.6, 25, 25, 25.4, 25.4, 25.6, 26, 26.2, 26.2, 26.4, 27, 27.2, 27.2, 27.2, 27.6, 28.2, 28.4, 28.4, 28.6, 29.4, 30.2, 31, 31.2, 32, 32, 32.8, 33.4, 33.8, 34.4, 34.8, 35.2, 35.2, 35.4, 35.6, 35.6, 36.2, 36.2, 38, 38, 39.2, 39.4, 40, 40.4, 41.6, 41.6, 42.4, 42.8, 42.8, 43, 44, 44.4, 45, 46.6, 47.8, 47.8, 48.8, 50.6, 52, 53.2, 55, 55, 55.4, 57.6 ]).reshape(133, 2, order='F') pls5.assign = None pls5.offset = np.array([ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]) pls5.df_residual = 128.325945731197 pls5.min_edf = 0 pls5.optimizer = 'magic' pls5.p_coeff = None pls5.se = np.array([ 9.07433037697435, 7.92181453580458, 8.10767136950078, 8.21258586513761, 9.81537637137811 ]) pls5.p_t = None pls5.p_pv = None pls5.residual_df = 128.325945731197 pls5.m = 1 pls5.chi_sq = 147.917821150898 pls5.s_pv = 8.54761661656479e-25 pls5.scale = 1405.72589061551 pls5.r_sq = 0.687640791604775 pls5.n = 133 pls5.dev_expl = 0.543333706940396 pls5.edf = 4.67405426880294 pls5.dispersion = 1405.72589061551 pls5.pTerms_pv = None pls5.pTerms_chi_sq = None pls5.pTerms_df = None pls5.cov_unscaled = np.array([ 0.0585771894365725, -0.000142380914279238, 0.00407220635759709, -0.0058065309979037, 0.0127269332736656, -0.000142380914279238, 0.0446425195399984, 0.00968784400337069, 0.00237861296924945, 0.0132806698891575, 0.00407220635759709, 0.00968784400337069, 0.0467618441651097, 0.00117175424190942, 0.00959188832386668, -0.0058065309979037, 0.00237861296924945, 0.00117175424190942, 0.0479798850135184, -0.00163686605136315, 0.0127269332736656, 0.0132806698891575, 0.00959188832386668, -0.00163686605136315, 0.0685351347335742 ]).reshape(5, 5, order='F') pls5.cov_scaled = np.array([ 82.3434717904795, -0.200148537531833, 5.72440590880333, -8.16239095841476, 17.8905796109278, -0.200148537531833, 62.7551455396847, 13.6184531397824, 3.34367783462779, 18.6689815079065, 5.72440590880333, 13.6184531397824, 65.7343350358227, 1.64716527529062, 13.483565756752, -8.16239095841476, 3.34367783462779, 1.64716527529062, 67.4465665922581, -2.30098498787076, 17.8905796109278, 18.6689815079065, 13.483565756752, -2.30098498787076, 96.3416133118078 ]).reshape(5, 5, order='F') pls5.s_table = np.array([ 4.67405426880294, 5, 29.5835642301796, 8.54761661656479e-25 ]).reshape(1, 4, order='F') pls5.method = 'GCV' pls5.sp_criterion = 1456.9270648002 pls5.rank = 5 pls5.np = 5 pls5.params = np.array([ 20.036025308233, -62.6817097954891, -51.0985219408637, 42.0072653496657, 22.0294169083686 ]) statsmodels-0.12.2/statsmodels/gam/tests/test_gam.py000066400000000000000000000631631400612667500226030ustar00rootroot00000000000000# pylint: disable=F841 """ unit test for GAM Author: Luca Puggini Created on 08/07/2015 """ import os import numpy as np from numpy.testing import assert_allclose import pandas as pd from scipy.linalg import block_diag import pytest from statsmodels.tools.linalg import matrix_sqrt from statsmodels.gam.smooth_basis import ( UnivariatePolynomialSmoother, PolynomialSmoother, BSplines, GenericSmoothers, UnivariateCubicSplines, CyclicCubicSplines) from statsmodels.gam.generalized_additive_model import ( GLMGam, LogitGam, make_augmented_matrix, penalized_wls) from statsmodels.gam.gam_cross_validation.gam_cross_validation import ( MultivariateGAMCV, MultivariateGAMCVPath, _split_train_test_smoothers) from statsmodels.gam.gam_penalties import (UnivariateGamPenalty, MultivariateGamPenalty) from statsmodels.gam.gam_cross_validation.cross_validators import KFold from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod.families.family import Gaussian from statsmodels.genmod.generalized_linear_model import lm sigmoid = np.vectorize(lambda x: 1.0 / (1.0 + np.exp(-x))) def polynomial_sample_data(): """A polynomial of degree 4 poly = ax^4 + bx^3 + cx^2 + dx + e second der = 12ax^2 + 6bx + 2c integral from -1 to 1 of second der^2 is (288 a^2)/5 + 32 a c + 8 (3 b^2 + c^2) the gradient of the integral is der [576*a/5 + 32 * c, 48*b, 32*a + 16*c, 0, 0] Returns ------- poly : smoother instance y : ndarray generated function values, demeaned """ n = 10000 x = np.linspace(-1, 1, n) y = 2 * x ** 3 - x y -= y.mean() degree = [4] pol = PolynomialSmoother(x, degree) return pol, y def integral(params): d, c, b, a = params itg = (288 * a ** 2) / 5 + (32 * a * c) + 8 * (3 * b ** 2 + c ** 2) itg /= 2 return itg def grad(params): d, c, b, a = params grd = np.array([576 * a / 5 + 32 * c, 48 * b, 32 * a + 16 * c, 0]) grd = grd[::-1] return grd / 2 def hessian(params): hess = np.array([[576 / 5, 0, 32, 0], [0, 48, 0, 0], [32, 0, 16, 0], [0, 0, 0, 0] ]) return hess / 2 def cost_function(params, pol, y, alpha): # this should be the MSE or log likelihood value lin_pred = np.dot(pol.basis, params) gaussian = Gaussian() expval = gaussian.link.inverse(lin_pred) loglike = gaussian.loglike(y, expval) # this is the vale of the GAM penalty. For the example polynomial itg = integral(params) # return the cost function of the GAM for the given polynomial return loglike - alpha * itg, loglike, itg def test_gam_penalty(): """ test the func method of the gam penalty :return: """ pol, y = polynomial_sample_data() univ_pol = pol.smoothers[0] alpha = 1 gp = UnivariateGamPenalty(alpha=alpha, univariate_smoother=univ_pol) for _ in range(10): params = np.random.randint(-2, 2, 4) gp_score = gp.func(params) itg = integral(params) assert_allclose(gp_score, itg, atol=1.e-1) def test_gam_gradient(): # test the gam gradient for the example polynomial np.random.seed(1) pol, y = polynomial_sample_data() alpha = 1 smoother = pol.smoothers[0] gp = UnivariateGamPenalty(alpha=alpha, univariate_smoother=smoother) for _ in range(10): params = np.random.uniform(-2, 2, 4) params = np.array([1, 1, 1, 1]) gam_grad = gp.deriv(params) grd = grad(params) assert_allclose(gam_grad, grd, rtol=1.e-2, atol=1.e-2) def test_gam_hessian(): # test the deriv2 method of the gam penalty np.random.seed(1) pol, y = polynomial_sample_data() univ_pol = pol.smoothers[0] alpha = 1 gp = UnivariateGamPenalty(alpha=alpha, univariate_smoother=univ_pol) for _ in range(10): params = np.random.randint(-2, 2, 5) gam_der2 = gp.deriv2(params) hess = hessian(params) hess = np.flipud(hess) hess = np.fliplr(hess) assert_allclose(gam_der2, hess, atol=1.e-13, rtol=1.e-3) def test_approximation(): np.random.seed(1) poly, y = polynomial_sample_data() alpha = 1 for _ in range(10): params = np.random.uniform(-1, 1, 4) cost, err, itg = cost_function(params, poly, y, alpha) glm_gam = GLMGam(y, smoother=poly, alpha=alpha) # TODO: why do we need pen_weight=1 gam_loglike = glm_gam.loglike(params, scale=1, pen_weight=1) assert_allclose(err - itg, cost, rtol=1e-10) assert_allclose(gam_loglike, cost, rtol=0.1) def test_gam_glm(): cur_dir = os.path.dirname(os.path.abspath(__file__)) file_path = os.path.join(cur_dir, "results", "prediction_from_mgcv.csv") data_from_r = pd.read_csv(file_path) # dataset used to train the R model x = data_from_r.x.values y = data_from_r.y.values df = [10] degree = [3] bsplines = BSplines(x, degree=degree, df=df, include_intercept=True) # y_mgcv is obtained from R with the following code # g = gam(y~s(x, k = 10, bs = "cr"), data = data, scale = 80) y_mgcv = np.asarray(data_from_r.y_est) alpha = 0.1 # chosen by trial and error glm_gam = GLMGam(y, smoother=bsplines, alpha=alpha) res_glm_gam = glm_gam.fit(method='bfgs', max_start_irls=0, disp=1, maxiter=10000, maxfun=5000) y_gam0 = np.dot(bsplines.basis, res_glm_gam.params) y_gam = np.asarray(res_glm_gam.fittedvalues) assert_allclose(y_gam, y_gam0, rtol=1e-10) # plt.plot(x, y_gam, '.', label='gam') # plt.plot(x, y_mgcv, '.', label='mgcv') # plt.plot(x, y, '.', label='y') # plt.legend() # plt.show() assert_allclose(y_gam, y_mgcv, atol=1.e-2) def test_gam_discrete(): cur_dir = os.path.dirname(os.path.abspath(__file__)) file_path = os.path.join(cur_dir, "results", "prediction_from_mgcv.csv") data_from_r = pd.read_csv(file_path) # dataset used to train the R model x = data_from_r.x.values y = data_from_r.ybin.values df = [10] degree = [5] bsplines = BSplines(x, degree=degree, df=df, include_intercept=True) # y_mgcv is obtained from R with the following code # g = gam(y~s(x, k = 10, bs = "cr"), data = data, scale = 80) y_mgcv = data_from_r.ybin_est alpha = 0.00002 # gp = UnivariateGamPenalty(alpha=alpha, univariate_smoother=bsplines) # lg_gam = LogitGam(y, bsplines.basis, penal=gp) # lg_gam = LogitGam(y, bsplines, alpha=alpha) res_lg_gam = lg_gam.fit(maxiter=10000) y_gam = np.dot(bsplines.basis, res_lg_gam.params) y_gam = sigmoid(y_gam) y_mgcv = sigmoid(y_mgcv) # plt.plot(x, y_gam, label='gam') # plt.plot(x, y_mgcv, label='mgcv') # plt.plot(x, y, '.', label='y') # plt.ylim(-0.4, 1.4) # plt.legend() # plt.show() assert_allclose(y_gam, y_mgcv, rtol=1.e-10, atol=1.e-1) def multivariate_sample_data(seed=1): n = 1000 x1 = np.linspace(-1, 1, n) x2 = np.linspace(-10, 10, n) x = np.vstack([x1, x2]).T np.random.seed(seed) y = x1 * x1 * x1 + x2 + np.random.normal(0, 0.01, n) degree1 = 4 degree2 = 3 degrees = [degree1, degree2] pol = PolynomialSmoother(x, degrees) return x, y, pol def test_multivariate_penalty(): alphas = [1, 2] weights = [1, 1] np.random.seed(1) x, y, pol = multivariate_sample_data() univ_pol1 = UnivariatePolynomialSmoother(x[:, 0], degree=pol.degrees[0]) univ_pol2 = UnivariatePolynomialSmoother(x[:, 1], degree=pol.degrees[1]) gp1 = UnivariateGamPenalty(alpha=alphas[0], univariate_smoother=univ_pol1) gp2 = UnivariateGamPenalty(alpha=alphas[1], univariate_smoother=univ_pol2) with pytest.warns(UserWarning, match="weights is currently ignored"): mgp = MultivariateGamPenalty(multivariate_smoother=pol, alpha=alphas, weights=weights) for i in range(10): params1 = np.random.randint(-3, 3, pol.smoothers[0].dim_basis) params2 = np.random.randint(-3, 3, pol.smoothers[1].dim_basis) params = np.concatenate([params1, params2]) c1 = gp1.func(params1) c2 = gp2.func(params2) c = mgp.func(params) assert_allclose(c, c1 + c2, atol=1.e-10, rtol=1.e-10) d1 = gp1.deriv(params1) d2 = gp2.deriv(params2) d12 = np.concatenate([d1, d2]) d = mgp.deriv(params) assert_allclose(d, d12) h1 = gp1.deriv2(params1) h2 = gp2.deriv2(params2) h12 = block_diag(h1, h2) h = mgp.deriv2(params) assert_allclose(h, h12) def test_generic_smoother(): x, y, poly = multivariate_sample_data() alphas = [0.4, 0.7] weights = [1, 1] # noqa: F841 gs = GenericSmoothers(poly.x, poly.smoothers) gam_gs = GLMGam(y, smoother=gs, alpha=alphas) gam_gs_res = gam_gs.fit() gam_poly = GLMGam(y, smoother=poly, alpha=alphas) gam_poly_res = gam_poly.fit() assert_allclose(gam_gs_res.params, gam_poly_res.params) def test_multivariate_gam_1d_data(): cur_dir = os.path.dirname(os.path.abspath(__file__)) file_path = os.path.join(cur_dir, "results", "prediction_from_mgcv.csv") data_from_r = pd.read_csv(file_path) # dataset used to train the R model x = data_from_r.x.values y = data_from_r.y df = [10] degree = [3] bsplines = BSplines(x, degree=degree, df=df) # y_mgcv is obtained from R with the following code # g = gam(y~s(x, k = 10, bs = "cr"), data = data, scale = 80) y_mgcv = data_from_r.y_est # alpha is by manually adjustment to reduce discrepancy in fittedvalues alpha = [0.0168 * 0.0251 / 2 * 500] gp = MultivariateGamPenalty(bsplines, alpha=alpha) # noqa: F841 glm_gam = GLMGam(y, exog=np.ones((len(y), 1)), smoother=bsplines, alpha=alpha) # "nm" converges to a different params, "bfgs" params are close to pirls # res_glm_gam = glm_gam.fit(method='nm', max_start_irls=0, # disp=1, maxiter=10000, maxfun=5000) res_glm_gam = glm_gam.fit(method='pirls', max_start_irls=0, disp=1, maxiter=10000) y_gam = res_glm_gam.fittedvalues # plt.plot(x, y_gam, '.', label='gam') # plt.plot(x, y_mgcv, '.', label='mgcv') # plt.plot(x, y, '.', label='y') # plt.legend() # plt.show() assert_allclose(y_gam, y_mgcv, atol=0.01) def test_multivariate_gam_cv(): # SMOKE test # no test is performed. It only checks that there is not any runtime error def cost(x1, x2): return np.linalg.norm(x1 - x2) / len(x1) cur_dir = os.path.dirname(os.path.abspath(__file__)) file_path = os.path.join(cur_dir, "results", "prediction_from_mgcv.csv") data_from_r = pd.read_csv(file_path) # dataset used to train the R model x = data_from_r.x.values y = data_from_r.y.values df = [10] degree = [5] bsplines = BSplines(x, degree=degree, df=df) # y_mgcv is obtained from R with the following code # g = gam(y~s(x, k = 10, bs = "cr"), data = data, scale = 80) alphas = [0.0251] alphas = [2] cv = KFold(3) gp = MultivariateGamPenalty(bsplines, alpha=alphas) # noqa: F841 gam_cv = MultivariateGAMCV(smoother=bsplines, alphas=alphas, gam=GLMGam, cost=cost, endog=y, exog=None, cv_iterator=cv) gam_cv_res = gam_cv.fit() # noqa: F841 def test_multivariate_gam_cv_path(): def sample_metric(y1, y2): return np.linalg.norm(y1 - y2) / len(y1) cur_dir = os.path.dirname(os.path.abspath(__file__)) file_path = os.path.join(cur_dir, "results", "prediction_from_mgcv.csv") data_from_r = pd.read_csv(file_path) # dataset used to train the R model x = data_from_r.x.values y = data_from_r.y.values se_from_mgcv = data_from_r.y_est_se # noqa: F841 y_mgcv = data_from_r.y_mgcv_gcv # noqa: F841 df = [10] degree = [6] bsplines = BSplines(x, degree=degree, df=df, include_intercept=True) gam = GLMGam alphas = [np.linspace(0, 2, 10)] k = 3 cv = KFold(k_folds=k, shuffle=True) # Note: kfold cv uses random shuffle np.random.seed(123) gam_cv = MultivariateGAMCVPath(smoother=bsplines, alphas=alphas, gam=gam, cost=sample_metric, endog=y, exog=None, cv_iterator=cv) gam_cv_res = gam_cv.fit() # noqa: F841 glm_gam = GLMGam(y, smoother=bsplines, alpha=gam_cv.alpha_cv) res_glm_gam = glm_gam.fit(method='irls', max_start_irls=0, disp=1, maxiter=10000) y_est = res_glm_gam.predict(bsplines.basis) # plt.plot(x, y, '.', label='y') # plt.plot(x, y_est, '.', label='y est') # plt.plot(x, y_mgcv, '.', label='y mgcv') # plt.legend() # plt.show() # The test compares to result obtained with GCV and not KFOLDS CV. # This is because MGCV does not support KFOLD CV assert_allclose(data_from_r.y_mgcv_gcv, y_est, atol=1.e-1, rtol=1.e-1) # Note: kfold cv uses random shuffle np.random.seed(123) alpha_cv, res_cv = glm_gam.select_penweight_kfold(alphas=alphas, k_folds=3) assert_allclose(alpha_cv, gam_cv.alpha_cv, rtol=1e-12) def test_train_test_smoothers(): n = 6 x = np.zeros(shape=(n, 2)) x[:, 0] = range(6) x[:, 1] = range(6, 12) poly = PolynomialSmoother(x, degrees=[3, 3]) train_index = list(range(3)) test_index = list(range(3, 6)) train_smoother, test_smoother = _split_train_test_smoothers(poly.x, poly, train_index, test_index) expected_train_basis = [[0., 0., 0., 6., 36., 216.], [1., 1., 1., 7., 49., 343.], [2., 4., 8., 8., 64., 512.]] assert_allclose(train_smoother.basis, expected_train_basis) expected_test_basis = [[3., 9., 27., 9., 81., 729.], [4., 16., 64., 10., 100., 1000.], [5., 25., 125., 11., 121., 1331.]] assert_allclose(test_smoother.basis, expected_test_basis) def test_get_sqrt(): n = 1000 np.random.seed(1) x = np.random.normal(0, 1, (n, 3)) x2 = np.dot(x.T, x) sqrt_x2 = matrix_sqrt(x2) x2_reconstruction = np.dot(sqrt_x2.T, sqrt_x2) assert_allclose(x2_reconstruction, x2) def test_make_augmented_matrix(): np.random.seed(1) n = 500 x = np.random.uniform(-1, 1, (n, 3)) s = np.dot(x.T, x) y = np.array(list(range(n))) w = np.random.uniform(0, 1, n) nobs, n_columns = x.shape # matrix_sqrt removes redundant rows, # if alpha is zero, then no augmentation is needed alpha = 0 aug_y, aug_x, aug_w = make_augmented_matrix(y, x, alpha * s, w) expected_aug_x = x assert_allclose(aug_x, expected_aug_x) expected_aug_y = y expected_aug_y[:nobs] = y assert_allclose(aug_y, expected_aug_y) expected_aug_w = w assert_allclose(aug_w, expected_aug_w) alpha = 1 aug_y, aug_x, aug_w = make_augmented_matrix(y, x, s, w) rs = matrix_sqrt(alpha * s) # alternative version to matrix_sqrt using cholesky is not available # rs = sp.linalg.cholesky(alpha * s) assert_allclose(np.dot(rs.T, rs), alpha * s) expected_aug_x = np.vstack([x, rs]) assert_allclose(aug_x, expected_aug_x) expected_aug_y = np.zeros(shape=(nobs + n_columns,)) expected_aug_y[:nobs] = y assert_allclose(aug_y, expected_aug_y) expected_aug_w = np.concatenate((w, [1] * n_columns), axis=0) assert_allclose(aug_w, expected_aug_w) def test_penalized_wls(): np.random.seed(1) n = 20 p = 3 x = np.random.normal(0, 1, (n, 3)) y = x[:, 1] - x[:, 2] + np.random.normal(0, .1, n) y -= y.mean() weights = np.ones(shape=(n,)) s = np.random.normal(0, 1, (p, p)) pen_wls_res = penalized_wls(y, x, 0 * s, weights) ls_res = lm.OLS(y, x).fit() assert_allclose(ls_res.params, pen_wls_res.params) def test_cyclic_cubic_splines(): cur_dir = os.path.dirname(os.path.abspath(__file__)) file_path = os.path.join(cur_dir, "results", "cubic_cyclic_splines_from_mgcv.csv") data_from_r = pd.read_csv(file_path) x = data_from_r[['x0', 'x2']].values y = data_from_r['y'].values y_est_mgcv = data_from_r[['y_est']].values # noqa: F841 s_mgcv = data_from_r[['s(x0)', 's(x2)']].values dfs = [10, 10] ccs = CyclicCubicSplines(x, df=dfs) alpha = [0.05 / 2, 0.0005 / 2] # TODO: if alpha changes in pirls this should be updated gam = GLMGam(y, smoother=ccs, alpha=alpha) gam_res = gam.fit(method='pirls') s0 = np.dot(ccs.basis[:, ccs.mask[0]], gam_res.params[ccs.mask[0]]) # TODO: Mean has to be removed # removing mean could be replaced by options for intercept handling s0 -= s0.mean() s1 = np.dot(ccs.basis[:, ccs.mask[1]], gam_res.params[ccs.mask[1]]) s1 -= s1.mean() # TODO: Mean has to be removed # plt.subplot(2, 1, 1) # plt.plot(x[:, 0], s0, '.', label='s0') # plt.plot(x[:, 0], s_mgcv[:, 0], '.', label='s0_mgcv') # plt.legend(loc='best') # # plt.subplot(2, 1, 2) # plt.plot(x[:, 1], s1, '.', label='s1_est') # plt.plot(x[:, 1], s_mgcv[:, 1], '.', label='s1_mgcv') # plt.legend(loc='best') # plt.show() assert_allclose(s0, s_mgcv[:, 0], atol=0.02) assert_allclose(s1, s_mgcv[:, 1], atol=0.33) def test_multivariate_cubic_splines(): np.random.seed(0) from statsmodels.gam.smooth_basis import CubicSplines n = 500 x1 = np.linspace(-3, 3, n) x2 = np.linspace(0, 1, n)**2 x = np.vstack([x1, x2]).T y1 = np.sin(x1) / x1 y2 = x2 * x2 y0 = y1 + y2 # need small enough noise variance to get good estimate for this test y = y0 + np.random.normal(0, .3 / 2, n) y -= y.mean() y0 -= y0.mean() alphas = [1e-3, 1e-3] cs = CubicSplines(x, df=[10, 10], constraints='center') gam = GLMGam(y, exog=np.ones((n, 1)), smoother=cs, alpha=alphas) gam_res = gam.fit(method='pirls') y_est = gam_res.fittedvalues y_est -= y_est.mean() # cut the tails index = list(range(50, n - 50)) y_est = y_est[index] y0 = y0[index] y = y[index] # plt.plot(y_est, label='y est') # plt.plot(y0, label='y0') # plt.plot(y, '.', label='y') # plt.legend(loc='best') # plt.show() assert_allclose(y_est, y0, atol=0.04) def test_glm_pirls_compatibility(): np.random.seed(0) n = 500 x1 = np.linspace(-3, 3, n) x2 = np.random.rand(n) x = np.vstack([x1, x2]).T y1 = np.sin(x1) / x1 y2 = x2 * x2 y0 = y1 + y2 y = y0 + np.random.normal(0, .3, n) y -= y.mean() y0 -= y0.mean() # TODO: we have now alphas == alphas_glm alphas = [5.75] * 2 alphas_glm = [1.2] * 2 # noqa: F841 # using constraints avoids singular exog. cs = BSplines(x, df=[10, 10], degree=[3, 3], constraints='center') gam_pirls = GLMGam(y, smoother=cs, alpha=alphas) gam_glm = GLMGam(y, smoother=cs, alpha=alphas) gam_res_glm = gam_glm.fit(method='nm', max_start_irls=0, disp=1, maxiter=20000, maxfun=10000) gam_res_glm = gam_glm.fit(start_params=gam_res_glm.params, method='bfgs', max_start_irls=0, disp=1, maxiter=20000, maxfun=10000) gam_res_pirls = gam_pirls.fit() y_est_glm = np.dot(cs.basis, gam_res_glm.params) y_est_glm -= y_est_glm.mean() y_est_pirls = np.dot(cs.basis, gam_res_pirls.params) y_est_pirls -= y_est_pirls.mean() # plt.plot(y_est_pirls) # plt.plot(y_est_glm) # plt.plot(y, '.') # plt.show() assert_allclose(gam_res_glm.params, gam_res_pirls.params, atol=5e-5, rtol=5e-5) assert_allclose(y_est_glm, y_est_pirls, atol=5e-5) def test_zero_penalty(): x, y, poly = multivariate_sample_data() alphas = [0, 0] gam_gs = GLMGam(y, smoother=poly, alpha=alphas) gam_gs_res = gam_gs.fit() y_est_gam = gam_gs_res.predict() glm = GLM(y, poly.basis).fit() y_est = glm.predict() assert_allclose(y_est, y_est_gam) def test_spl_s(): # matrix from R spl_s_R = [[0, 0, 0.000000000, 0.000000000, 0.000000000, 0.000000000], [0, 0, 0.000000000, 0.000000000, 0.000000000, 0.000000000], [0, 0, 0.001400000, 0.000200000, -0.001133333, -0.001000000], [0, 0, 0.000200000, 0.002733333, 0.001666667, -0.001133333], [0, 0, -0.001133333, 0.001666667, 0.002733333, 0.000200000], [0, 0, -0.001000000, -0.001133333, 0.000200000, 0.001400000]] np.random.seed(1) x = np.random.normal(0, 1, 10) xk = np.array([0.2, .4, .6, .8]) cs = UnivariateCubicSplines(x, df=4) cs.knots = xk spl_s = cs._splines_s() assert_allclose(spl_s_R, spl_s, atol=4.e-10) def test_partial_values2(): np.random.seed(0) n = 1000 x = np.random.uniform(0, 1, (n, 2)) x = x - x.mean() y = x[:, 0] * x[:, 0] + np.random.normal(0, .01, n) y -= y.mean() alpha = 0.0 # BUG: mask is incorrect if exog is not None, start_idx missing # bsplines = BSplines(x, degree=[3] * 2, df=[10] * 2) # glm_gam = GLMGam(y, exog=np.ones((len(y), 1)), smoother=bsplines, # alpha=alpha) bsplines = BSplines(x, degree=[3] * 2, df=[10] * 2, include_intercept=[True, False]) glm_gam = GLMGam(y, smoother=bsplines, alpha=alpha) res_glm_gam = glm_gam.fit(method='pirls', max_start_irls=0, disp=0, maxiter=5000) glm = GLM(y, bsplines.basis) # noqa: F841 # case with constant column in exog is currently wrong # ex = np.column_stack((np.zeros((len(y), 1)), bsplines.smoothers[0].basis, # np.zeros_like(bsplines.smoothers[1].basis) )) ex = np.column_stack((bsplines.smoothers[0].basis, np.zeros_like(bsplines.smoothers[1].basis))) y_est = res_glm_gam.predict(ex, transform=False) y_partial_est, se = res_glm_gam.partial_values(0) assert_allclose(y_est, y_partial_est, atol=0.05) assert se.min() < 100 # TODO: sometimes the SE reported by partial_values is very large. # This should be double checked def test_partial_values(): # this test is only approximate because we do not use the same spline # basis functions (knots) as mgcv cur_dir = os.path.dirname(os.path.abspath(__file__)) file_path = os.path.join(cur_dir, "results", "prediction_from_mgcv.csv") data_from_r = pd.read_csv(file_path) # dataset used to train the R model x = data_from_r.x.values y = data_from_r.y.values se_from_mgcv = data_from_r.y_est_se df = [10] degree = [6] bsplines = BSplines(x, degree=degree, df=df, include_intercept=True) # TODO: alpha found by trial and error to pass assert alpha = 0.025 / 115 * 500 glm_gam = GLMGam(y, smoother=bsplines, alpha=alpha) res_glm_gam = glm_gam.fit(maxiter=10000, method='bfgs') # TODO: if IRLS is used res_glm_gam has not partial_values. univ_bsplines = bsplines.smoothers[0] # noqa: F841 hat_y, se = res_glm_gam.partial_values(0) assert_allclose(hat_y, data_from_r["y_est"], rtol=0, atol=0.008) # TODO: bug missing scale bug_fact = np.sqrt(res_glm_gam.scale) * 0.976 # this is = 0.106 assert_allclose(se, se_from_mgcv * bug_fact, rtol=0, atol=0.008) @pytest.mark.matplotlib def test_partial_plot(): # verify that plot and partial_values method agree # the model only has one component so partial values is the same as # fittedvalues # Generate a plot to visualize analyze the result. cur_dir = os.path.dirname(os.path.abspath(__file__)) file_path = os.path.join(cur_dir, "results", "prediction_from_mgcv.csv") data_from_r = pd.read_csv(file_path) # dataset used to train the R model x = data_from_r.x.values y = data_from_r.y.values se_from_mgcv = data_from_r.y_est_se # noqa: F841 df = [10] degree = [6] bsplines = BSplines(x, degree=degree, df=df) alpha = 0.03 glm_gam = GLMGam(y, smoother=bsplines, alpha=alpha) res_glm_gam = glm_gam.fit(maxiter=10000, method='bfgs') fig = res_glm_gam.plot_partial(0) xp, yp = fig.axes[0].get_children()[0].get_data() # Note xp and yp are sorted by x sort_idx = np.argsort(x) hat_y, se = res_glm_gam.partial_values(0) # assert that main plot line is the prediction assert_allclose(xp, x[sort_idx]) assert_allclose(yp, hat_y[sort_idx]) # Uncomment to visualize the plot # import matplotlib.pyplot as plt # res_glm_gam.plot_partial(0) # plt.plot(x, y, '.') # plt.show() def test_cov_params(): np.random.seed(0) n = 1000 x = np.random.uniform(0, 1, (n, 2)) x = x - x.mean() y = x[:, 0] * x[:, 0] + np.random.normal(0, .01, n) y -= y.mean() bsplines = BSplines(x, degree=[3] * 2, df=[10] * 2, constraints='center') alpha = [0, 0] glm_gam = GLMGam(y, smoother=bsplines, alpha=alpha) res_glm_gam = glm_gam.fit(method='pirls', max_start_irls=0, disp=0, maxiter=5000) glm = GLM(y, bsplines.basis) res_glm = glm.fit() assert_allclose(res_glm.cov_params(), res_glm_gam.cov_params(), rtol=0.0025) alpha = 1e-13 glm_gam = GLMGam(y, smoother=bsplines, alpha=alpha) res_glm_gam = glm_gam.fit(method='pirls', max_start_irls=0, disp=0, maxiter=5000) assert_allclose(res_glm.cov_params(), res_glm_gam.cov_params(), atol=1e-10) res_glm_gam = glm_gam.fit(method='bfgs', max_start_irls=0, disp=0, maxiter=5000, maxfun=5000) assert_allclose(res_glm.cov_params(), res_glm_gam.cov_params(), rtol=1e-4, atol=1e-8) statsmodels-0.12.2/statsmodels/gam/tests/test_penalized.py000066400000000000000000000577141400612667500240170ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ unit test for GAM Author: Josef Perktold """ import os import numpy as np from numpy.testing import assert_allclose, assert_equal, assert_ import pandas as pd import patsy from statsmodels.discrete.discrete_model import Poisson, Logit, Probit from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod.families import family from statsmodels.sandbox.regression.penalized import TheilGLS from statsmodels.base._penalized import PenalizedMixin import statsmodels.base._penalties as smpen from statsmodels.gam.smooth_basis import (BSplines, CyclicCubicSplines) from statsmodels.gam.generalized_additive_model import ( GLMGam, GLMGamResults, GLMGamResultsWrapper) from statsmodels.tools.linalg import matrix_sqrt, transf_constraints from .results import results_pls, results_mpg_bs, results_mpg_bs_poisson class PoissonPenalized(PenalizedMixin, Poisson): pass class LogitPenalized(PenalizedMixin, Logit): pass class ProbitPenalized(PenalizedMixin, Probit): pass class GLMPenalized(PenalizedMixin, GLM): pass cur_dir = os.path.dirname(os.path.abspath(__file__)) file_path = os.path.join(cur_dir, "results", "motorcycle.csv") data_mcycle = pd.read_csv(file_path) file_path = os.path.join(cur_dir, "results", "autos.csv") df_autos_ = pd.read_csv(file_path) df_autos = df_autos_[['city_mpg', 'fuel', 'drive', 'weight', 'hp']].dropna() class CheckGAMMixin(object): @classmethod def _init(cls): # TODO: CyclicCubicSplines raises when using pandas cc_h = CyclicCubicSplines(np.asarray(data_mcycle['times']), df=[6]) constraints = np.atleast_2d(cc_h.basis.mean(0)) transf = transf_constraints(constraints) exog = cc_h.basis.dot(transf) penalty_matrix = transf.T.dot(cc_h.penalty_matrices[0]).dot(transf) restriction = matrix_sqrt(penalty_matrix) return exog, penalty_matrix, restriction def test_params(self): res1 = self.res1 res2 = self.res2 assert_allclose(res1.params, res2.params, rtol=1e-5) assert_allclose(np.asarray(res1.cov_params()), res2.Vp * self.covp_corrfact, rtol=1e-6, atol=1e-9) assert_allclose(res1.scale, res2.scale * self.covp_corrfact, rtol=1e-8) assert_allclose(np.asarray(res1.bse), res2.se * np.sqrt(self.covp_corrfact), rtol=1e-6, atol=1e-9) def test_fitted(self): res1 = self.res1 res2 = self.res2 assert_allclose(res1.fittedvalues, res2.fitted_values, rtol=self.rtol_fitted) class TestTheilPLS5(CheckGAMMixin): cov_type = 'data-prior' @classmethod def setup_class(cls): exog, penalty_matrix, restriction = cls._init() endog = data_mcycle['accel'] modp = TheilGLS(endog, exog, r_matrix=restriction) # scaling of penweith in R mgcv s_scale_r = 0.02630734 # Theil penweight uses preliminary sigma2_e to scale penweight sigma_e = 1405.7950179165323 cls.pw = pw = 1 / sigma_e / s_scale_r cls.res1 = modp.fit(pen_weight=pw, cov_type=cls.cov_type) cls.res2 = results_pls.pls5 cls.rtol_fitted = 1e-7 cls.covp_corrfact = 0.99786932844203202 def test_cov_robust(self): res1 = self.res1 res2 = self.res2 pw = res1.penalization_factor res1 = res1.model.fit(pen_weight=pw, cov_type='sandwich') assert_allclose(np.asarray(res1.cov_params()), res2.Ve * self.covp_corrfact, rtol=1e-4) class TestGLMPenalizedPLS5(CheckGAMMixin): cov_type = 'nonrobust' @classmethod def setup_class(cls): exog, penalty_matrix, restriction = cls._init() endog = data_mcycle['accel'] pen = smpen.L2ConstraintsPenalty(restriction=restriction) mod = GLMPenalized(endog, exog, family=family.Gaussian(), penal=pen) # scaling of penweight in R mgcv s_scale_r = 0.02630734 # set pen_weight to correspond to R mgcv example cls.pw = mod.pen_weight = 1 / s_scale_r / 2 cls.res1 = mod.fit(cov_type=cls.cov_type, method='bfgs', maxiter=100, disp=0, trim=False, scale='x2') cls.res2 = results_pls.pls5 cls.rtol_fitted = 1e-5 # edf is currently not available with PenalizedMixin # need correction for difference in scale denominator cls.covp_corrfact = 1.0025464444310588 def _test_cov_robust(self): # TODO: HC0 differs from Theil sandwich, difference is large res1 = self.res1 res2 = self.res2 pw = res1.model.pen_weight res1 = res1.model.fit(pen_weight=pw, cov_type='HC0') assert_allclose(np.asarray(res1.cov_params()), res2.Ve * self.covp_corrfact, rtol=1e-4) class TestGAM5Pirls(CheckGAMMixin): cov_type = 'nonrobust' @classmethod def setup_class(cls): s_scale = 0.0263073404164214 x = data_mcycle['times'].values endog = data_mcycle['accel'] cc = CyclicCubicSplines(x, df=[6], constraints='center') gam_cc = GLMGam(endog, smoother=cc, alpha=1 / s_scale / 2) cls.res1 = gam_cc.fit() cls.res2 = results_pls.pls5 cls.rtol_fitted = 1e-12 # cls.covp_corrfact = 1.0025464444310588 # without edf # edf is implemented cls.covp_corrfact = 1 class TestGAM5Bfgs(CheckGAMMixin): cov_type = 'nonrobust' @classmethod def setup_class(cls): s_scale = 0.0263073404164214 x = data_mcycle['times'].values endog = data_mcycle['accel'] cc = CyclicCubicSplines(x, df=[6], constraints='center') gam_cc = GLMGam(endog, smoother=cc, alpha=1 / s_scale / 2) cls.res1 = gam_cc.fit(method='bfgs') cls.res2 = results_pls.pls5 cls.rtol_fitted = 1e-5 # cls.covp_corrfact = 1.0025464444310588 # without edf # edf is implemented cls.covp_corrfact = 1 def test_predict(self): res1 = self.res1 res2 = self.res2 predicted = res1.predict(None, res1.model.smoother.x[2:4]) assert_allclose(predicted, res1.fittedvalues[2:4], rtol=1e-13) assert_allclose(predicted, res2.fitted_values[2:4], rtol=self.rtol_fitted) class TestGAM6Pirls(object): @classmethod def setup_class(cls): s_scale = 0.0263073404164214 cc = CyclicCubicSplines(data_mcycle['times'].values, df=[6]) gam_cc = GLMGam(data_mcycle['accel'], smoother=cc, alpha=1 / s_scale / 2) cls.res1 = gam_cc.fit() def test_fitted(self): res1 = self.res1 pred = res1.get_prediction() self.rtol_fitted = 1e-7 pls6_fittedvalues = np.array([ 2.45008146537851, 3.14145063965465, 5.24130119353225, 6.63476330674223, 7.99704341866374, 13.9351103077006, 14.5508371638833, 14.785647621276, 15.1176070735895, 14.8053514054347, 13.790412967255, 13.790412967255, 11.2997845518655, 9.51681958051473, 8.4811626302547]) assert_allclose(res1.fittedvalues[:15], pls6_fittedvalues, rtol=self.rtol_fitted) assert_allclose(pred.predicted_mean[:15], pls6_fittedvalues, rtol=self.rtol_fitted) predicted = res1.predict(None, res1.model.smoother.x[2:4]) assert_allclose(predicted, pls6_fittedvalues[2:4], rtol=self.rtol_fitted) class TestGAM6Bfgs(object): @classmethod def setup_class(cls): s_scale = 0.0263073404164214 cc = CyclicCubicSplines(data_mcycle['times'].values, df=[6]) gam_cc = GLMGam(data_mcycle['accel'], smoother=cc, alpha=1 / s_scale / 2) cls.res1 = gam_cc.fit(method='bfgs') def test_fitted(self): res1 = self.res1 pred = res1.get_prediction() self.rtol_fitted = 1e-5 pls6_fittedvalues = np.array([ 2.45008146537851, 3.14145063965465, 5.24130119353225, 6.63476330674223, 7.99704341866374, 13.9351103077006, 14.5508371638833, 14.785647621276, 15.1176070735895, 14.8053514054347, 13.790412967255, 13.790412967255, 11.2997845518655, 9.51681958051473, 8.4811626302547]) assert_allclose(res1.fittedvalues[:15], pls6_fittedvalues, rtol=self.rtol_fitted) assert_allclose(pred.predicted_mean[:15], pls6_fittedvalues, rtol=self.rtol_fitted) class TestGAM6Bfgs0(object): @classmethod def setup_class(cls): s_scale = 0.0263073404164214 # noqa: F841 cc = CyclicCubicSplines(data_mcycle['times'].values, df=[6]) gam_cc = GLMGam(data_mcycle['accel'], smoother=cc, alpha=0) cls.res1 = gam_cc.fit(method='bfgs') def test_fitted(self): res1 = self.res1 pred = res1.get_prediction() self.rtol_fitted = 1e-5 pls6_fittedvalues = np.array([ 2.63203377595747, 3.41285892739456, 5.78168657308338, 7.35344779586831, 8.89178704316853, 15.7035642157176, 16.4510219628328, 16.7474993878412, 17.3397025587698, 17.1062522298643, 16.1786066072489, 16.1786066072489, 13.7402485937614, 11.9531909618517, 10.9073964111009]) assert_allclose(res1.fittedvalues[:15], pls6_fittedvalues, rtol=self.rtol_fitted) assert_allclose(pred.predicted_mean[:15], pls6_fittedvalues, rtol=self.rtol_fitted) pls6_fittedvalues = np.array([ 2.45008146537851, 3.14145063965465, 5.24130119353225, 6.63476330674223, 7.99704341866374, 13.9351103077006, 14.5508371638833, 14.785647621276, 15.1176070735895, 14.8053514054347, 13.790412967255, 13.790412967255, 11.2997845518655, 9.51681958051473, 8.4811626302547]) pls6_exog = np.array([ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -0.334312615555276, -0.302733562622373, -0.200049479196403, -0.12607681525989, -0.0487229716135211, 0.397628373646056, 0.475396222437879, 0.51311526571058, 0.685638355361239, 0.745083051531164, -0.633518318499726, -0.634362488928233, -0.635472088268483, -0.634802453890957, -0.632796625534419, -0.589886140629009, -0.574834708734556, -0.566315983948608, -0.51289784236512, -0.486061743835595, -0.353449234316442, -0.348107090921062, -0.328814083307981, -0.313617048982477, -0.296913301955505, -0.191949693921079, -0.173001127145111, -0.163813487426548, -0.12229019995063, -0.108463798212062, -0.33613551740577, -0.327911471033406, -0.303620832999443, -0.287786799373968, -0.272279566127816, -0.194325957984873, -0.18175817334823, -0.175688807660186, -0.147654475500976, -0.137597948224942, -0.406564043706154, -0.409594429953082, -0.412391645561287, -0.409453786864986, -0.403086590828732, -0.322579243114146, -0.302545882788086, -0.29221622484174, -0.239207291311699, -0.218194346676734 ]).reshape(10, 6, order='F') class TestGAM6ExogBfgs(object): @classmethod def setup_class(cls): s_scale = 0.0263073404164214 nobs = data_mcycle['times'].shape[0] cc = CyclicCubicSplines(data_mcycle['times'].values, df=[6], constraints='center') gam_cc = GLMGam(data_mcycle['accel'], np.ones(nobs), smoother=cc, alpha=1 / s_scale / 2) cls.res1 = gam_cc.fit(method='bfgs') def test_fitted(self): res1 = self.res1 pred = res1.get_prediction() self.rtol_fitted = 1e-5 assert_allclose(res1.fittedvalues[:15], pls6_fittedvalues, rtol=self.rtol_fitted) assert_allclose(pred.predicted_mean[:15], pls6_fittedvalues, rtol=self.rtol_fitted) def test_exog(self): exog = self.res1.model.exog assert_allclose(exog[:10], pls6_exog, rtol=1e-13) class TestGAM6ExogPirls(object): @classmethod def setup_class(cls): s_scale = 0.0263073404164214 nobs = data_mcycle['times'].shape[0] cc = CyclicCubicSplines(data_mcycle['times'].values, df=[6], constraints='center') gam_cc = GLMGam(data_mcycle['accel'], np.ones((nobs, 1)), smoother=cc, alpha=1 / s_scale / 2) cls.res1 = gam_cc.fit(method='pirls') def test_fitted(self): res1 = self.res1 pred = res1.get_prediction() self.rtol_fitted = 1e-5 assert_allclose(res1.fittedvalues[:15], pls6_fittedvalues, rtol=self.rtol_fitted) assert_allclose(pred.predicted_mean[:15], pls6_fittedvalues, rtol=self.rtol_fitted) def test_exog(self): exog = self.res1.model.exog assert_allclose(exog[:10], pls6_exog, rtol=1e-13) class TestGAMMPG(object): @classmethod def setup_class(cls): sp = np.array([6.46225497484073, 0.81532465890585]) s_scale = np.array([2.95973613706629e-07, 0.000126203730141359]) x_spline = df_autos[['weight', 'hp']].values exog = patsy.dmatrix('fuel + drive', data=df_autos) cc = CyclicCubicSplines(x_spline, df=[6, 5], constraints='center') # TODO alpha needs to be list gam_cc = GLMGam(df_autos['city_mpg'], exog=exog, smoother=cc, alpha=(1 / s_scale * sp / 2).tolist()) cls.res1a = gam_cc.fit() gam_cc = GLMGam(df_autos['city_mpg'], exog=exog, smoother=cc, alpha=(1 / s_scale * sp / 2).tolist()) cls.res1b = gam_cc.fit(method='newton') def test_exog(self): file_path = os.path.join(cur_dir, "results", "autos_exog.csv") df_exog = pd.read_csv(file_path) res2_exog = df_exog.values for res1 in [self.res1a, self.res1b]: exog = res1.model.exog # exog contains zeros assert_allclose(exog, res2_exog, atol=1e-14) def test_fitted(self): file_path = os.path.join(cur_dir, "results", "autos_predict.csv") df_pred = pd.read_csv(file_path, index_col="Row.names") df_pred.index = df_pred.index - 1 res2_fittedvalues = df_pred["fit"].values res2_se_mean = df_pred["se_fit"].values for res1 in [self.res1a, self.res1b]: pred = res1.get_prediction() self.rtol_fitted = 1e-5 assert_allclose(res1.fittedvalues, res2_fittedvalues, rtol=1e-10) assert_allclose(pred.predicted_mean, res2_fittedvalues, rtol=1e-10) # TODO: no edf, edf corrected df_resid # scale estimate differs # corr_fact = np.sqrt(191.669417019567 / 190) # without edf # edf is implemented corr_fact = 1 assert_allclose(pred.se_mean, res2_se_mean * corr_fact, rtol=1e-10) class TestGAMMPGBS(CheckGAMMixin): # This has matching results from mgcv @classmethod def setup_class(cls): sp = np.array([0.830689464223685, 425.361212061649]) cls.s_scale = s_scale = np.array([2.443955e-06, 0.007945455]) x_spline = df_autos[['weight', 'hp']].values # We need asarray to remove the design_info # If design_info is attached, # then exog_linear will also be transformed in predict. cls.exog = np.asarray(patsy.dmatrix('fuel + drive', data=df_autos)) bs = BSplines(x_spline, df=[12, 10], degree=[3, 3], variable_names=['weight', 'hp'], constraints='center', include_intercept=True) # TODO alpha needs to be list alpha0 = 1 / s_scale * sp / 2 gam_bs = GLMGam(df_autos['city_mpg'], exog=cls.exog, smoother=bs, alpha=(alpha0).tolist()) cls.res1a = gam_bs.fit(use_t=True) cls.res1b = gam_bs.fit(method='newton', use_t=True) cls.res1 = cls.res1a._results cls.res2 = results_mpg_bs.mpg_bs cls.rtol_fitted = 1e-8 cls.covp_corrfact = 1 # not needed # for checking that alpha model attribute is unchanged, same as alpha0 cls.alpha = [169947.78222669504, 26767.58046340008] @classmethod def _init(cls): pass def test_edf(self): res1 = self.res1 res2 = self.res2 assert_allclose(res1.edf, res2.edf_all, rtol=1e-6) hat = res1.get_hat_matrix_diag() assert_allclose(hat, res2.hat, rtol=1e-6) def test_smooth(self): res1 = self.res1 res2 = self.res2 smoothers = res1.model.smoother.smoothers pen_matrix0 = smoothers[0].cov_der2 assert_allclose(pen_matrix0, res2.smooth0.S * res2.smooth0.S_scale, rtol=1e-6) def test_predict(self): res1 = self.res1 res2 = self.res2 predicted = res1.predict(self.exog[2:4], res1.model.smoother.x[2:4]) assert_allclose(predicted, res1.fittedvalues[2:4], rtol=1e-13) assert_allclose(predicted, res2.fitted_values[2:4], rtol=self.rtol_fitted) def test_crossval(self): # includes some checks that penalization in the model is unchanged mod = self.res1.model assert_equal(mod.alpha, self.alpha) # assert unchanged assert_allclose(self.res1.scale, 4.7064821354391118, rtol=1e-13) alpha_aic = mod.select_penweight()[0] # regression number, but in the right ball park assert_allclose(alpha_aic, [112487.81362014, 129.89155677], rtol=1e-3) assert_equal(mod.alpha, self.alpha) # assert unchanged assert_equal(mod.penal.start_idx, 4) pm = mod.penal.penalty_matrix() assert_equal(pm[:, :4], 0) assert_equal(pm[:4, :], 0) assert_allclose(self.res1.scale, 4.7064821354391118, rtol=1e-13) np.random.seed(987125) alpha_cv, _ = mod.select_penweight_kfold(k_folds=3, k_grid=6) # regression number, but in the right ball park assert_allclose(alpha_cv, [10000000.0, 630.957344480193], rtol=1e-5) assert_equal(mod.alpha, self.alpha) # assert unchanged assert_equal(mod.penal.start_idx, 4) pm = mod.penal.penalty_matrix() assert_equal(pm[:, :4], 0) assert_equal(pm[:4, :], 0) assert_allclose(self.res1.scale, 4.7064821354391118, rtol=1e-13) class TestGAMMPGBSPoisson(CheckGAMMixin): # This has matching results from mgcv @classmethod def setup_class(cls): sp = np.array([40491.3940640059, 232455.530262537]) # s_scale is same as before cls.s_scale = s_scale = np.array([2.443955e-06, 0.007945455]) x_spline = df_autos[['weight', 'hp']].values cls.exog = patsy.dmatrix('fuel + drive', data=df_autos) bs = BSplines(x_spline, df=[12, 10], degree=[3, 3], variable_names=['weight', 'hp'], constraints='center', include_intercept=True) # TODO alpha needs to be list alpha0 = 1 / s_scale * sp / 2 gam_bs = GLMGam(df_autos['city_mpg'], exog=cls.exog, smoother=bs, family=family.Poisson(), alpha=alpha0) xnames = cls.exog.design_info.column_names + gam_bs.smoother.col_names gam_bs.exog_names[:] = xnames cls.res1a = gam_bs.fit(use_t=False) cls.res1b = gam_bs.fit(method='newton', use_t=True) cls.res1 = cls.res1a._results cls.res2 = results_mpg_bs_poisson.mpg_bs_poisson cls.rtol_fitted = 1e-8 cls.covp_corrfact = 1 # not needed @classmethod def _init(cls): pass def test_edf(self): res1 = self.res1 res2 = self.res2 assert_allclose(res1.edf, res2.edf_all, rtol=1e-6) hat = res1.get_hat_matrix_diag() assert_allclose(hat, res2.hat, rtol=1e-6) assert_allclose(res1.aic, res2.aic, rtol=1e-8) assert_allclose(res1.deviance, res2.deviance, rtol=1e-8) assert_allclose(res1.df_resid, res2.residual_df, rtol=1e-8) def test_smooth(self): res1 = self.res1 res2 = self.res2 smoothers = res1.model.smoother.smoothers pen_matrix0 = smoothers[0].cov_der2 assert_allclose(pen_matrix0, res2.smooth0.S * res2.smooth0.S_scale, rtol=1e-6) def test_predict(self): res1 = self.res1 res2 = self.res2 # this uses transform also for exog_linear # predicted = res1.predict(self.exog[2:4], res1.model.smoother.x[2:4]) predicted = res1.predict(df_autos.iloc[2:4], res1.model.smoother.x[2:4]) assert_allclose(predicted, res1.fittedvalues[2:4], rtol=1e-13) assert_allclose(predicted, res2.fitted_values[2:4], rtol=self.rtol_fitted) # linpred = res1.predict(self.exog[2:4], res1.model.smoother.x[2:4], # linear=True) xp = pd.DataFrame(res1.model.smoother.x[2:4]) linpred = res1.predict(df_autos.iloc[2:4], xp, linear=True) assert_allclose(linpred, res2.linear_predictors[2:4], rtol=self.rtol_fitted) assert_equal(predicted.index.values, [2, 3]) assert_equal(linpred.index.values, [2, 3]) def test_wald(self): res1 = self.res1 res2 = self.res2 wtt = res1.wald_test_terms(skip_single=True, combine_terms=['fuel', 'drive', 'weight', 'hp']) # mgcv has term test for linear part assert_allclose(wtt.statistic[:2], res2.pTerms_chi_sq, rtol=1e-7) assert_allclose(wtt.pvalues[:2], res2.pTerms_pv, rtol=1e-6) assert_equal(wtt.df_constraints[:2], res2.pTerms_df) def test_select_alpha(self): res1 = self.res1 alpha_mgcv = res1.model.alpha res_s = res1.model.select_penweight() assert_allclose(res_s[0], alpha_mgcv, rtol=5e-5) class TestGAMMPGBSPoissonFormula(TestGAMMPGBSPoisson): # This is the same as the previous but with from_formula @classmethod def setup_class(cls): sp = np.array([40491.3940640059, 232455.530262537]) # s_scale is same as before cls.s_scale = s_scale = np.array([2.443955e-06, 0.007945455]) cls.exog = patsy.dmatrix('fuel + drive', data=df_autos) x_spline = df_autos[['weight', 'hp']].values bs = BSplines(x_spline, df=[12, 10], degree=[3, 3], variable_names=['weight', 'hp'], constraints='center', include_intercept=True) alpha0 = 1 / s_scale * sp / 2 gam_bs = GLMGam.from_formula('city_mpg ~ fuel + drive', df_autos, smoother=bs, family=family.Poisson(), alpha=alpha0) cls.res1a = gam_bs.fit(use_t=False) cls.res1b = gam_bs.fit(method='newton', use_t=True) cls.res1 = cls.res1a._results cls.res2 = results_mpg_bs_poisson.mpg_bs_poisson cls.rtol_fitted = 1e-8 cls.covp_corrfact = 1 # not needed def test_names_wrapper(self): res1a = self.res1a xnames = ['Intercept', 'fuel[T.gas]', 'drive[T.fwd]', 'drive[T.rwd]', 'weight_s0', 'weight_s1', 'weight_s2', 'weight_s3', 'weight_s4', 'weight_s5', 'weight_s6', 'weight_s7', 'weight_s8', 'weight_s9', 'weight_s10', 'hp_s0', 'hp_s1', 'hp_s2', 'hp_s3', 'hp_s4', 'hp_s5', 'hp_s6', 'hp_s7', 'hp_s8'] assert_equal(res1a.model.exog_names, xnames) assert_equal(res1a.model.design_info_linear.column_names, xnames[:4]) assert_equal(res1a.fittedvalues[2:4].index.values, [2, 3]) assert_equal(res1a.params.index.values, xnames) assert_(isinstance(res1a.params, pd.Series)) assert_(isinstance(res1a, GLMGamResultsWrapper)) assert_(isinstance(res1a._results, GLMGamResults)) statsmodels-0.12.2/statsmodels/gam/tests/test_smooth_basis.py000066400000000000000000000023631400612667500245240ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ unit test for spline and other smoother classes Author: Luca Puggini """ import pytest import numpy as np from numpy.testing import assert_allclose, assert_equal from statsmodels.gam.smooth_basis import (UnivariatePolynomialSmoother, PolynomialSmoother, BSplines) def test_univariate_polynomial_smoother(): x = np.linspace(0, 1, 5) pol = UnivariatePolynomialSmoother(x, degree=3) assert_equal(pol.basis.shape, (5, 3)) assert_allclose(pol.basis[:, 2], x.ravel() ** 3) def test_multivariate_polynomial_basis(): np.random.seed(1) x = np.random.normal(0, 1, (10, 2)) degrees = [3, 4] mps = PolynomialSmoother(x, degrees) for i, deg in enumerate(degrees): uv_basis = UnivariatePolynomialSmoother(x[:, i], degree=deg).basis assert_allclose(mps.smoothers[i].basis, uv_basis) @pytest.mark.parametrize( "x, df, degree", [ ( np.c_[np.linspace(0, 1, 100), np.linspace(0, 10, 100)], [5, 6], [3, 5] ), (np.linspace(0, 1, 100), 6, 3), ] ) def test_bsplines(x, df, degree): bspline = BSplines(x, df, degree) bspline.transform(x) statsmodels-0.12.2/statsmodels/genmod/000077500000000000000000000000001400612667500177605ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/genmod/__init__.py000066400000000000000000000001131400612667500220640ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/genmod/_prediction.py000066400000000000000000000225011400612667500226310ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Dec 19 11:29:18 2014 Author: Josef Perktold License: BSD-3 """ import numpy as np from scipy import stats import pandas as pd # this is similar to ContrastResults after t_test, partially copied and adjusted class PredictionResults(object): def __init__(self, predicted_mean, var_pred_mean, var_resid=None, df=None, dist=None, row_labels=None, linpred=None, link=None): # TODO: is var_resid used? drop from arguments? self.predicted_mean = predicted_mean self.var_pred_mean = var_pred_mean self.df = df self.var_resid = var_resid self.row_labels = row_labels self.linpred = linpred self.link = link if dist is None or dist == 'norm': self.dist = stats.norm self.dist_args = () elif dist == 't': self.dist = stats.t self.dist_args = (self.df,) else: self.dist = dist self.dist_args = () @property def se_obs(self): raise NotImplementedError return np.sqrt(self.var_pred_mean + self.var_resid) @property def se_mean(self): return np.sqrt(self.var_pred_mean) @property def tvalues(self): return self.predicted_mean / self.se_mean def t_test(self, value=0, alternative='two-sided'): '''z- or t-test for hypothesis that mean is equal to value Parameters ---------- value : array_like value under the null hypothesis alternative : str 'two-sided', 'larger', 'smaller' Returns ------- stat : ndarray test statistic pvalue : ndarray p-value of the hypothesis test, the distribution is given by the attribute of the instance, specified in `__init__`. Default if not specified is the normal distribution. ''' # assumes symmetric distribution stat = (self.predicted_mean - value) / self.se_mean if alternative in ['two-sided', '2-sided', '2s']: pvalue = self.dist.sf(np.abs(stat), *self.dist_args)*2 elif alternative in ['larger', 'l']: pvalue = self.dist.sf(stat, *self.dist_args) elif alternative in ['smaller', 's']: pvalue = self.dist.cdf(stat, *self.dist_args) else: raise ValueError('invalid alternative') return stat, pvalue def conf_int(self, method='endpoint', alpha=0.05, **kwds): """ Returns the confidence interval of the value, `effect` of the constraint. This is currently only available for t and z tests. Parameters ---------- alpha : float, optional The significance level for the confidence interval. ie., The default `alpha` = .05 returns a 95% confidence interval. kwds : extra keyword arguments currently ignored, only for compatibility, consistent signature Returns ------- ci : ndarray, (k_constraints, 2) The array has the lower and the upper limit of the confidence interval in the columns. """ tmp = np.linspace(0, 1, 6) is_linear = (self.link.inverse(tmp) == tmp).all() if method == 'endpoint' and not is_linear: ci_linear = self.linpred.conf_int(alpha=alpha, obs=False) ci = self.link.inverse(ci_linear) elif method == 'delta' or is_linear: se = self.se_mean q = self.dist.ppf(1 - alpha / 2., *self.dist_args) lower = self.predicted_mean - q * se upper = self.predicted_mean + q * se ci = np.column_stack((lower, upper)) # if we want to stack at a new last axis, for lower.ndim > 1 # np.concatenate((lower[..., None], upper[..., None]), axis=-1) return ci def summary_frame(self, alpha=0.05): """Summary frame""" # TODO: finish and cleanup #ci_obs = self.conf_int(alpha=alpha, obs=True) # need to split ci_mean = self.conf_int(alpha=alpha) to_include = {} to_include['mean'] = self.predicted_mean to_include['mean_se'] = self.se_mean to_include['mean_ci_lower'] = ci_mean[:, 0] to_include['mean_ci_upper'] = ci_mean[:, 1] self.table = to_include # pandas dict does not handle 2d_array #data = np.column_stack(list(to_include.values())) #names = .... res = pd.DataFrame(to_include, index=self.row_labels, columns=to_include.keys()) return res def get_prediction_glm(self, exog=None, transform=True, weights=None, row_labels=None, linpred=None, link=None, pred_kwds=None): """ compute prediction results Parameters ---------- exog : array_like, optional The values for which you want to predict. transform : bool, optional If the model was fit via a formula, do you want to pass exog through the formula. Default is True. E.g., if you fit a model y ~ log(x1) + log(x2), and transform is True, then you can pass a data structure that contains x1 and x2 in their original form. Otherwise, you'd need to log the data first. weights : array_like, optional Weights interpreted as in WLS, used for the variance of the predicted residual. *args : Some models can take additional arguments. See the predict method of the model for the details. **kwargs : Some models can take additional keyword arguments. See the predict method of the model for the details. Returns ------- prediction_results : generalized_linear_model.PredictionResults The prediction results instance contains prediction and prediction variance and can on demand calculate confidence intervals and summary tables for the prediction of the mean and of new observations. """ # prepare exog and row_labels, based on base Results.predict if transform and hasattr(self.model, 'formula') and exog is not None: from patsy import dmatrix if isinstance(exog, pd.Series): exog = pd.DataFrame(exog) exog = dmatrix(self.model.data.design_info, exog) if exog is not None: if row_labels is None: row_labels = getattr(exog, 'index', None) if callable(row_labels): row_labels = None exog = np.asarray(exog) if exog.ndim == 1 and (self.model.exog.ndim == 1 or self.model.exog.shape[1] == 1): exog = exog[:, None] exog = np.atleast_2d(exog) # needed in count model shape[1] else: exog = self.model.exog if weights is None: weights = getattr(self.model, 'weights', None) if row_labels is None: row_labels = getattr(self.model.data, 'row_labels', None) # need to handle other arrays, TODO: is delegating to model possible ? if weights is not None: weights = np.asarray(weights) if (weights.size > 1 and (weights.ndim != 1 or weights.shape[0] == exog.shape[1])): raise ValueError('weights has wrong shape') ### end pred_kwds['linear'] = False predicted_mean = self.model.predict(self.params, exog, **pred_kwds) covb = self.cov_params() link_deriv = self.model.family.link.inverse_deriv(linpred.predicted_mean) var_pred_mean = link_deriv**2 * (exog * np.dot(covb, exog.T).T).sum(1) var_resid = self.scale # self.mse_resid / weights # TODO: check that we have correct scale, Refactor scale #??? # special case for now: if self.cov_type == 'fixed scale': var_resid = self.cov_kwds['scale'] if weights is not None: var_resid /= weights dist = ['norm', 't'][self.use_t] return PredictionResults(predicted_mean, var_pred_mean, var_resid, df=self.df_resid, dist=dist, row_labels=row_labels, linpred=linpred, link=link) def params_transform_univariate(params, cov_params, link=None, transform=None, row_labels=None): """ results for univariate, nonlinear, monotonicaly transformed parameters This provides transformed values, standard errors and confidence interval for transformations of parameters, for example in calculating rates with `exp(params)` in the case of Poisson or other models with exponential mean function. """ from statsmodels.genmod.families import links if link is None and transform is None: link = links.Log() if row_labels is None and hasattr(params, 'index'): row_labels = params.index params = np.asarray(params) predicted_mean = link.inverse(params) link_deriv = link.inverse_deriv(params) var_pred_mean = link_deriv**2 * np.diag(cov_params) # TODO: do we want covariance also, or just var/se dist = stats.norm # TODO: need ci for linear prediction, method of `lin_pred linpred = PredictionResults(params, np.diag(cov_params), dist=dist, row_labels=row_labels, link=links.identity()) res = PredictionResults(predicted_mean, var_pred_mean, dist=dist, row_labels=row_labels, linpred=linpred, link=link) return res statsmodels-0.12.2/statsmodels/genmod/_tweedie_compound_poisson.py000066400000000000000000000054501400612667500256010ustar00rootroot00000000000000""" Private experimental module for miscellaneous Tweedie functions. References ---------- Dunn, Peter K. and Smyth, Gordon K. 2001. Tweedie family densities: methods of evaluation. In Proceedings of the 16th International Workshop on Statistical Modelling, Odense, Denmark, 2–6 July. Jørgensen, B., Demétrio, C.G.B., Kristensen, E., Banta, G.T., Petersen, H.C., Delefosse, M.: Bias-corrected Pearson estimating functions for Taylor’s power law applied to benthic macrofauna data. Stat. Probab. Lett. 81, 749–758 (2011) Smyth G.K. and Jørgensen B. 2002. Fitting Tweedie's compound Poisson model to insurance claims data: dispersion modelling. ASTIN Bulletin 32: 143–157 """ import numpy as np from scipy._lib._util import _lazywhere as lazywhere from scipy.special import gammaln def _theta(mu, p): return np.where(p == 1, np.log(mu), mu ** (1 - p) / (1 - p)) def _alpha(p): return (2 - p) / (1 - p) def _logWj(y, j, p, phi): alpha = _alpha(p) logz = (-alpha * np.log(y) + alpha * np.log(p - 1) - (1 - alpha) * np.log(phi) - np.log(2 - p)) return (j * logz - gammaln(1 + j) - gammaln(-alpha * j)) def kappa(mu, p): return mu ** (2 - p) / (2 - p) @np.vectorize def _sumw(y, j_l, j_u, logWmax, p, phi): j = np.arange(j_l, j_u + 1) sumw = np.sum(np.exp(_logWj(y, j, p, phi) - logWmax)) return sumw def logW(y, p, phi): alpha = _alpha(p) jmax = y ** (2 - p) / ((2 - p) * phi) logWmax = np.array((1 - alpha) * jmax) tol = logWmax - 37 # Machine accuracy for 64 bit. j = np.ceil(jmax) while (_logWj(y, np.ceil(j), p, phi) > tol).any(): j = np.where(_logWj(y, j, p, phi) > tol, j + 1, j) j_u = j j = np.floor(jmax) j = np.where(j > 1, j, 1) while (_logWj(y, j, p, phi) > tol).any() and (j > 1).any(): j = np.where(_logWj(y, j, p, phi) > tol, j - 1, 1) j_l = j sumw = _sumw(y, j_l, j_u, logWmax, p, phi) return logWmax + np.log(sumw) def density_at_zero(y, mu, p, phi): return np.exp(-(mu ** (2 - p)) / (phi * (2 - p))) def density_otherwise(y, mu, p, phi): theta = _theta(mu, p) logd = logW(y, p, phi) - np.log(y) + (1 / phi * (y * theta - kappa(mu, p))) return np.exp(logd) def series_density(y, mu, p, phi): density = lazywhere(np.array(y) > 0, (y, mu, p, phi), f=density_otherwise, f2=density_at_zero) return density if __name__ == '__main__': from scipy import stats n = stats.poisson.rvs(.1, size=10000000) y = stats.gamma.rvs(.1, scale=30000, size=10000000) y = n * y mu = stats.gamma.rvs(10, scale=30, size=10000000) import time t = time.time() out = series_density(y=y, mu=mu, p=1.5, phi=20) print('That took {} seconds'.format(time.time() - t)) statsmodels-0.12.2/statsmodels/genmod/api.py000066400000000000000000000005731400612667500211100ustar00rootroot00000000000000__all__ = [ "GLM", "GEE", "OrdinalGEE", "NominalGEE", "BinomialBayesMixedGLM", "PoissonBayesMixedGLM", "families", "cov_struct" ] from .generalized_linear_model import GLM from .generalized_estimating_equations import GEE, OrdinalGEE, NominalGEE from .bayes_mixed_glm import BinomialBayesMixedGLM, PoissonBayesMixedGLM from . import families from . import cov_struct statsmodels-0.12.2/statsmodels/genmod/bayes_mixed_glm.py000066400000000000000000001137471400612667500234770ustar00rootroot00000000000000r""" Bayesian inference for generalized linear mixed models. Currently only families without additional scale or shape parameters are supported (binomial and Poisson). Two estimation approaches are supported: Laplace approximation ('maximum a posteriori'), and variational Bayes (mean field approximation to the posterior distribution). All realizations of random effects are modeled to be mutually independent in this implementation. The `exog_vc` matrix is the design matrix for the random effects. Every column of `exog_vc` corresponds to an independent realization of a random effect. These random effects have mean zero and an unknown standard deviation. The standard deviation parameters are constrained to be equal within subsets of the columns. When not using formulas, these subsets are specified through the parameter `ident`. `ident` must have the same length as the number of columns of `exog_vc`, and two columns whose `ident` values are equal have the same standard deviation. When formulas are used, the columns of `exog_vc` derived from a common formula are constrained to have the same standard deviation. In many applications, `exog_vc` will be sparse. A sparse matrix may be passed when constructing a model class. If a dense matrix is passed, it will be converted internally to a sparse matrix. There currently is no way to avoid creating a temporary dense version of `exog_vc` when using formulas. Model and parameterization -------------------------- The joint density of data and parameters factors as: .. math:: p(y | vc, fep) p(vc | vcp) p(vcp) p(fe) The terms :math:`p(vcp)` and :math:`p(fe)` are prior distributions that are taken to be Gaussian (the :math:`vcp` parameters are log standard deviations so the standard deviations have log-normal distributions). The random effects distribution :math:`p(vc | vcp)` is independent Gaussian (random effect realizations are independent within and between values of the `ident` array). The model :math:`p(y | vc, fep)` depends on the specific GLM being fit. """ import numpy as np from scipy.optimize import minimize from scipy import sparse import statsmodels.base.model as base from statsmodels.iolib import summary2 from statsmodels.genmod import families import pandas as pd import warnings import patsy # Gauss-Legendre weights glw = [ [0.2955242247147529, -0.1488743389816312], [0.2955242247147529, 0.1488743389816312], [0.2692667193099963, -0.4333953941292472], [0.2692667193099963, 0.4333953941292472], [0.2190863625159820, -0.6794095682990244], [0.2190863625159820, 0.6794095682990244], [0.1494513491505806, -0.8650633666889845], [0.1494513491505806, 0.8650633666889845], [0.0666713443086881, -0.9739065285171717], [0.0666713443086881, 0.9739065285171717], ] _init_doc = r""" Generalized Linear Mixed Model with Bayesian estimation The class implements the Laplace approximation to the posterior distribution (`fit_map`) and a variational Bayes approximation to the posterior (`fit_vb`). See the two fit method docstrings for more information about the fitting approaches. Parameters ---------- endog : array_like Vector of response values. exog : array_like Array of covariates for the fixed effects part of the mean structure. exog_vc : array_like Array of covariates for the random part of the model. A scipy.sparse array may be provided, or else the passed array will be converted to sparse internally. ident : array_like Array of integer labels showing which random terms (columns of `exog_vc`) have a common variance. vcp_p : float Prior standard deviation for variance component parameters (the prior standard deviation of log(s) is vcp_p, where s is the standard deviation of a random effect). fe_p : float Prior standard deviation for fixed effects parameters. family : statsmodels.genmod.families instance The GLM family. fep_names : list[str] The names of the fixed effects parameters (corresponding to columns of exog). If None, default names are constructed. vcp_names : list[str] The names of the variance component parameters (corresponding to distinct labels in ident). If None, default names are constructed. vc_names : list[str] The names of the random effect realizations. Returns ------- MixedGLMResults object Notes ----- There are three types of values in the posterior distribution: fixed effects parameters (fep), corresponding to the columns of `exog`, random effects realizations (vc), corresponding to the columns of `exog_vc`, and the standard deviations of the random effects realizations (vcp), corresponding to the unique integer labels in `ident`. All random effects are modeled as being independent Gaussian values (given the variance structure parameters). Every column of `exog_vc` has a distinct realized random effect that is used to form the linear predictors. The elements of `ident` determine the distinct variance structure parameters. Two random effect realizations that have the same value in `ident` have the same variance. When fitting with a formula, `ident` is constructed internally (each element of `vc_formulas` yields a distinct label in `ident`). The random effect standard deviation parameters (`vcp`) have log-normal prior distributions with mean 0 and standard deviation `vcp_p`. Note that for some families, e.g. Binomial, the posterior mode may be difficult to find numerically if `vcp_p` is set to too large of a value. Setting `vcp_p` to 0.5 seems to work well. The prior for the fixed effects parameters is Gaussian with mean 0 and standard deviation `fe_p`. Examples --------{example} References ---------- Introduction to generalized linear mixed models: https://stats.idre.ucla.edu/other/mult-pkg/introduction-to-generalized-linear-mixed-models SAS documentation: https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_intromix_a0000000215.htm An assessment of estimation methods for generalized linear mixed models with binary outcomes https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3866838/ """ # The code in the example should be identical to what appears in # the test_doc_examples unit test _logit_example = """ A binomial (logistic) random effects model with random intercepts for villages and random slopes for each year within each village: >>> random = {"a": '0 + C(Village)', "b": '0 + C(Village)*year_cen'} >>> model = BinomialBayesMixedGLM.from_formula( 'y ~ year_cen', random, data) >>> result = model.fit_vb() """ # The code in the example should be identical to what appears in # the test_doc_examples unit test _poisson_example = """ A Poisson random effects model with random intercepts for villages and random slopes for each year within each village: >>> random = {"a": '0 + C(Village)', "b": '0 + C(Village)*year_cen'} >>> model = PoissonBayesMixedGLM.from_formula( 'y ~ year_cen', random, data) >>> result = model.fit_vb() """ class _BayesMixedGLM(base.Model): def __init__(self, endog, exog, exog_vc=None, ident=None, family=None, vcp_p=1, fe_p=2, fep_names=None, vcp_names=None, vc_names=None, **kwargs): if exog.ndim == 1: if isinstance(exog, np.ndarray): exog = exog[:, None] else: exog = pd.DataFrame(exog) if exog.ndim != 2: msg = "'exog' must have one or two columns" raise ValueError(msg) if exog_vc.ndim == 1: if isinstance(exog_vc, np.ndarray): exog_vc = exog_vc[:, None] else: exog_vc = pd.DataFrame(exog_vc) if exog_vc.ndim != 2: msg = "'exog_vc' must have one or two columns" raise ValueError(msg) ident = np.asarray(ident) if ident.ndim != 1: msg = "ident must be a one-dimensional array" raise ValueError(msg) if len(ident) != exog_vc.shape[1]: msg = "len(ident) should match the number of columns of exog_vc" raise ValueError(msg) if not np.issubdtype(ident.dtype, np.integer): msg = "ident must have an integer dtype" raise ValueError(msg) # Get the fixed effects parameter names if fep_names is None: if hasattr(exog, "columns"): fep_names = exog.columns.tolist() else: fep_names = ["FE_%d" % (k + 1) for k in range(exog.shape[1])] # Get the variance parameter names if vcp_names is None: vcp_names = ["VC_%d" % (k + 1) for k in range(int(max(ident)) + 1)] else: if len(vcp_names) != len(set(ident)): msg = "The lengths of vcp_names and ident should be the same" raise ValueError(msg) if not sparse.issparse(exog_vc): exog_vc = sparse.csr_matrix(exog_vc) ident = ident.astype(int) vcp_p = float(vcp_p) fe_p = float(fe_p) # Number of fixed effects parameters if exog is None: k_fep = 0 else: k_fep = exog.shape[1] # Number of variance component structure parameters and # variance component realizations. if exog_vc is None: k_vc = 0 k_vcp = 0 else: k_vc = exog_vc.shape[1] k_vcp = max(ident) + 1 # power might be better but not available in older scipy exog_vc2 = exog_vc.multiply(exog_vc) super(_BayesMixedGLM, self).__init__(endog, exog, **kwargs) self.exog_vc = exog_vc self.exog_vc2 = exog_vc2 self.ident = ident self.family = family self.k_fep = k_fep self.k_vc = k_vc self.k_vcp = k_vcp self.fep_names = fep_names self.vcp_names = vcp_names self.vc_names = vc_names self.fe_p = fe_p self.vcp_p = vcp_p self.names = fep_names + vcp_names if vc_names is not None: self.names += vc_names def _unpack(self, vec): ii = 0 # Fixed effects parameters fep = vec[:ii + self.k_fep] ii += self.k_fep # Variance component structure parameters (standard # deviations). These are on the log scale. The standard # deviation for random effect j is exp(vcp[ident[j]]). vcp = vec[ii:ii + self.k_vcp] ii += self.k_vcp # Random effect realizations vc = vec[ii:] return fep, vcp, vc def logposterior(self, params): """ The overall log-density: log p(y, fe, vc, vcp). This differs by an additive constant from the log posterior log p(fe, vc, vcp | y). """ fep, vcp, vc = self._unpack(params) # Contributions from p(y | x, vc) lp = 0 if self.k_fep > 0: lp += np.dot(self.exog, fep) if self.k_vc > 0: lp += self.exog_vc.dot(vc) mu = self.family.link.inverse(lp) ll = self.family.loglike(self.endog, mu) if self.k_vc > 0: # Contributions from p(vc | vcp) vcp0 = vcp[self.ident] s = np.exp(vcp0) ll -= 0.5 * np.sum(vc**2 / s**2) + np.sum(vcp0) # Contributions from p(vc) ll -= 0.5 * np.sum(vcp**2 / self.vcp_p**2) # Contributions from p(fep) if self.k_fep > 0: ll -= 0.5 * np.sum(fep**2 / self.fe_p**2) return ll def logposterior_grad(self, params): """ The gradient of the log posterior. """ fep, vcp, vc = self._unpack(params) lp = 0 if self.k_fep > 0: lp += np.dot(self.exog, fep) if self.k_vc > 0: lp += self.exog_vc.dot(vc) mu = self.family.link.inverse(lp) score_factor = (self.endog - mu) / self.family.link.deriv(mu) score_factor /= self.family.variance(mu) te = [None, None, None] # Contributions from p(y | x, z, vc) if self.k_fep > 0: te[0] = np.dot(score_factor, self.exog) if self.k_vc > 0: te[2] = self.exog_vc.transpose().dot(score_factor) if self.k_vc > 0: # Contributions from p(vc | vcp) # vcp0 = vcp[self.ident] # s = np.exp(vcp0) # ll -= 0.5 * np.sum(vc**2 / s**2) + np.sum(vcp0) vcp0 = vcp[self.ident] s = np.exp(vcp0) u = vc**2 / s**2 - 1 te[1] = np.bincount(self.ident, weights=u) te[2] -= vc / s**2 # Contributions from p(vcp) # ll -= 0.5 * np.sum(vcp**2 / self.vcp_p**2) te[1] -= vcp / self.vcp_p**2 # Contributions from p(fep) if self.k_fep > 0: te[0] -= fep / self.fe_p**2 te = [x for x in te if x is not None] return np.concatenate(te) def _get_start(self): start_fep = np.zeros(self.k_fep) start_vcp = np.ones(self.k_vcp) start_vc = np.random.normal(size=self.k_vc) start = np.concatenate((start_fep, start_vcp, start_vc)) return start @classmethod def from_formula(cls, formula, vc_formulas, data, family=None, vcp_p=1, fe_p=2): """ Fit a BayesMixedGLM using a formula. Parameters ---------- formula : str Formula for the endog and fixed effects terms (use ~ to separate dependent and independent expressions). vc_formulas : dictionary vc_formulas[name] is a one-sided formula that creates one collection of random effects with a common variance parameter. If using categorical (factor) variables to produce variance components, note that generally `0 + ...` should be used so that an intercept is not included. data : data frame The data to which the formulas are applied. family : genmod.families instance A GLM family. vcp_p : float The prior standard deviation for the logarithms of the standard deviations of the random effects. fe_p : float The prior standard deviation for the fixed effects parameters. """ ident = [] exog_vc = [] vcp_names = [] j = 0 for na, fml in vc_formulas.items(): mat = patsy.dmatrix(fml, data, return_type='dataframe') exog_vc.append(mat) vcp_names.append(na) ident.append(j * np.ones(mat.shape[1], dtype=np.int_)) j += 1 exog_vc = pd.concat(exog_vc, axis=1) vc_names = exog_vc.columns.tolist() ident = np.concatenate(ident) model = super(_BayesMixedGLM, cls).from_formula( formula, data=data, family=family, subset=None, exog_vc=exog_vc, ident=ident, vc_names=vc_names, vcp_names=vcp_names, fe_p=fe_p, vcp_p=vcp_p) return model def fit(self, method="BFGS", minim_opts=None): """ fit is equivalent to fit_map. See fit_map for parameter information. Use `fit_vb` to fit the model using variational Bayes. """ self.fit_map(method, minim_opts) def fit_map(self, method="BFGS", minim_opts=None, scale_fe=False): """ Construct the Laplace approximation to the posterior distribution. Parameters ---------- method : str Optimization method for finding the posterior mode. minim_opts : dict Options passed to scipy.minimize. scale_fe : bool If True, the columns of the fixed effects design matrix are centered and scaled to unit variance before fitting the model. The results are back-transformed so that the results are presented on the original scale. Returns ------- BayesMixedGLMResults instance. """ if scale_fe: mn = self.exog.mean(0) sc = self.exog.std(0) self._exog_save = self.exog self.exog = self.exog.copy() ixs = np.flatnonzero(sc > 1e-8) self.exog[:, ixs] -= mn[ixs] self.exog[:, ixs] /= sc[ixs] def fun(params): return -self.logposterior(params) def grad(params): return -self.logposterior_grad(params) start = self._get_start() r = minimize(fun, start, method=method, jac=grad, options=minim_opts) if not r.success: msg = ("Laplace fitting did not converge, |gradient|=%.6f" % np.sqrt(np.sum(r.jac**2))) warnings.warn(msg) from statsmodels.tools.numdiff import approx_fprime hess = approx_fprime(r.x, grad) cov = np.linalg.inv(hess) params = r.x if scale_fe: self.exog = self._exog_save del self._exog_save params[ixs] /= sc[ixs] cov[ixs, :][:, ixs] /= np.outer(sc[ixs], sc[ixs]) return BayesMixedGLMResults(self, params, cov, optim_retvals=r) def predict(self, params, exog=None, linear=False): """ Return the fitted mean structure. Parameters ---------- params : array_like The parameter vector, may be the full parameter vector, or may be truncated to include only the mean parameters. exog : array_like The design matrix for the mean structure. If omitted, use the model's design matrix. linear : bool If True, return the linear predictor without passing through the link function. Returns ------- A 1-dimensional array of predicted values """ if exog is None: exog = self.exog q = exog.shape[1] pr = np.dot(exog, params[0:q]) if not linear: pr = self.family.link.inverse(pr) return pr class _VariationalBayesMixedGLM(object): """ A mixin providing generic (not family-specific) methods for variational Bayes mean field fitting. """ # Integration range (from -rng to +rng). The integrals are with # respect to a standard Gaussian distribution so (-5, 5) will be # sufficient in many cases. rng = 5 verbose = False # Returns the mean and variance of the linear predictor under the # given distribution parameters. def _lp_stats(self, fep_mean, fep_sd, vc_mean, vc_sd): tm = np.dot(self.exog, fep_mean) tv = np.dot(self.exog**2, fep_sd**2) tm += self.exog_vc.dot(vc_mean) tv += self.exog_vc2.dot(vc_sd**2) return tm, tv def vb_elbo_base(self, h, tm, fep_mean, vcp_mean, vc_mean, fep_sd, vcp_sd, vc_sd): """ Returns the evidence lower bound (ELBO) for the model. This function calculates the family-specific ELBO function based on information provided from a subclass. Parameters ---------- h : function mapping 1d vector to 1d vector The contribution of the model to the ELBO function can be expressed as y_i*lp_i + Eh_i(z), where y_i and lp_i are the response and linear predictor for observation i, and z is a standard normal random variable. This formulation can be achieved for any GLM with a canonical link function. """ # p(y | vc) contributions iv = 0 for w in glw: z = self.rng * w[1] iv += w[0] * h(z) * np.exp(-z**2 / 2) iv /= np.sqrt(2 * np.pi) iv *= self.rng iv += self.endog * tm iv = iv.sum() # p(vc | vcp) * p(vcp) * p(fep) contributions iv += self._elbo_common(fep_mean, fep_sd, vcp_mean, vcp_sd, vc_mean, vc_sd) r = (iv + np.sum(np.log(fep_sd)) + np.sum(np.log(vcp_sd)) + np.sum( np.log(vc_sd))) return r def vb_elbo_grad_base(self, h, tm, tv, fep_mean, vcp_mean, vc_mean, fep_sd, vcp_sd, vc_sd): """ Return the gradient of the ELBO function. See vb_elbo_base for parameters. """ fep_mean_grad = 0. fep_sd_grad = 0. vcp_mean_grad = 0. vcp_sd_grad = 0. vc_mean_grad = 0. vc_sd_grad = 0. # p(y | vc) contributions for w in glw: z = self.rng * w[1] u = h(z) * np.exp(-z**2 / 2) / np.sqrt(2 * np.pi) r = u / np.sqrt(tv) fep_mean_grad += w[0] * np.dot(u, self.exog) vc_mean_grad += w[0] * self.exog_vc.transpose().dot(u) fep_sd_grad += w[0] * z * np.dot(r, self.exog**2 * fep_sd) v = self.exog_vc2.multiply(vc_sd).transpose().dot(r) v = np.squeeze(np.asarray(v)) vc_sd_grad += w[0] * z * v fep_mean_grad *= self.rng vc_mean_grad *= self.rng fep_sd_grad *= self.rng vc_sd_grad *= self.rng fep_mean_grad += np.dot(self.endog, self.exog) vc_mean_grad += self.exog_vc.transpose().dot(self.endog) (fep_mean_grad_i, fep_sd_grad_i, vcp_mean_grad_i, vcp_sd_grad_i, vc_mean_grad_i, vc_sd_grad_i) = self._elbo_grad_common( fep_mean, fep_sd, vcp_mean, vcp_sd, vc_mean, vc_sd) fep_mean_grad += fep_mean_grad_i fep_sd_grad += fep_sd_grad_i vcp_mean_grad += vcp_mean_grad_i vcp_sd_grad += vcp_sd_grad_i vc_mean_grad += vc_mean_grad_i vc_sd_grad += vc_sd_grad_i fep_sd_grad += 1 / fep_sd vcp_sd_grad += 1 / vcp_sd vc_sd_grad += 1 / vc_sd mean_grad = np.concatenate((fep_mean_grad, vcp_mean_grad, vc_mean_grad)) sd_grad = np.concatenate((fep_sd_grad, vcp_sd_grad, vc_sd_grad)) if self.verbose: print( "|G|=%f" % np.sqrt(np.sum(mean_grad**2) + np.sum(sd_grad**2))) return mean_grad, sd_grad def fit_vb(self, mean=None, sd=None, fit_method="BFGS", minim_opts=None, scale_fe=False, verbose=False): """ Fit a model using the variational Bayes mean field approximation. Parameters ---------- mean : array_like Starting value for VB mean vector sd : array_like Starting value for VB standard deviation vector fit_method : str Algorithm for scipy.minimize minim_opts : dict Options passed to scipy.minimize scale_fe : bool If true, the columns of the fixed effects design matrix are centered and scaled to unit variance before fitting the model. The results are back-transformed so that the results are presented on the original scale. verbose : bool If True, print the gradient norm to the screen each time it is calculated. Notes ----- The goal is to find a factored Gaussian approximation q1*q2*... to the posterior distribution, approximately minimizing the KL divergence from the factored approximation to the actual posterior. The KL divergence, or ELBO function has the form E* log p(y, fe, vcp, vc) - E* log q where E* is expectation with respect to the product of qj. References ---------- Blei, Kucukelbir, McAuliffe (2017). Variational Inference: A review for Statisticians https://arxiv.org/pdf/1601.00670.pdf """ self.verbose = verbose if scale_fe: mn = self.exog.mean(0) sc = self.exog.std(0) self._exog_save = self.exog self.exog = self.exog.copy() ixs = np.flatnonzero(sc > 1e-8) self.exog[:, ixs] -= mn[ixs] self.exog[:, ixs] /= sc[ixs] n = self.k_fep + self.k_vcp + self.k_vc ml = self.k_fep + self.k_vcp + self.k_vc if mean is None: m = np.zeros(n) else: if len(mean) != ml: raise ValueError( "mean has incorrect length, %d != %d" % (len(mean), ml)) m = mean.copy() if sd is None: s = -0.5 + 0.1 * np.random.normal(size=n) else: if len(sd) != ml: raise ValueError( "sd has incorrect length, %d != %d" % (len(sd), ml)) # s is parametrized on the log-scale internally when # optimizing the ELBO function (this is transparent to the # caller) s = np.log(sd) # Do not allow the variance parameter starting mean values to # be too small. i1, i2 = self.k_fep, self.k_fep + self.k_vcp m[i1:i2] = np.where(m[i1:i2] < -1, -1, m[i1:i2]) # Do not allow the posterior standard deviation starting values # to be too small. s = np.where(s < -1, -1, s) def elbo(x): n = len(x) // 2 return -self.vb_elbo(x[:n], np.exp(x[n:])) def elbo_grad(x): n = len(x) // 2 gm, gs = self.vb_elbo_grad(x[:n], np.exp(x[n:])) gs *= np.exp(x[n:]) return -np.concatenate((gm, gs)) start = np.concatenate((m, s)) mm = minimize( elbo, start, jac=elbo_grad, method=fit_method, options=minim_opts) if not mm.success: warnings.warn("VB fitting did not converge") n = len(mm.x) // 2 params = mm.x[0:n] va = np.exp(2 * mm.x[n:]) if scale_fe: self.exog = self._exog_save del self._exog_save params[ixs] /= sc[ixs] va[ixs] /= sc[ixs]**2 return BayesMixedGLMResults(self, params, va, mm) # Handle terms in the ELBO that are common to all models. def _elbo_common(self, fep_mean, fep_sd, vcp_mean, vcp_sd, vc_mean, vc_sd): iv = 0 # p(vc | vcp) contributions m = vcp_mean[self.ident] s = vcp_sd[self.ident] iv -= np.sum((vc_mean**2 + vc_sd**2) * np.exp(2 * (s**2 - m))) / 2 iv -= np.sum(m) # p(vcp) contributions iv -= 0.5 * (vcp_mean**2 + vcp_sd**2).sum() / self.vcp_p**2 # p(b) contributions iv -= 0.5 * (fep_mean**2 + fep_sd**2).sum() / self.fe_p**2 return iv def _elbo_grad_common(self, fep_mean, fep_sd, vcp_mean, vcp_sd, vc_mean, vc_sd): # p(vc | vcp) contributions m = vcp_mean[self.ident] s = vcp_sd[self.ident] u = vc_mean**2 + vc_sd**2 ve = np.exp(2 * (s**2 - m)) dm = u * ve - 1 ds = -2 * u * ve * s vcp_mean_grad = np.bincount(self.ident, weights=dm) vcp_sd_grad = np.bincount(self.ident, weights=ds) vc_mean_grad = -vc_mean.copy() * ve vc_sd_grad = -vc_sd.copy() * ve # p(vcp) contributions vcp_mean_grad -= vcp_mean / self.vcp_p**2 vcp_sd_grad -= vcp_sd / self.vcp_p**2 # p(b) contributions fep_mean_grad = -fep_mean.copy() / self.fe_p**2 fep_sd_grad = -fep_sd.copy() / self.fe_p**2 return (fep_mean_grad, fep_sd_grad, vcp_mean_grad, vcp_sd_grad, vc_mean_grad, vc_sd_grad) class BayesMixedGLMResults(object): """ Class to hold results from a Bayesian estimation of a Mixed GLM model. Attributes ---------- fe_mean : array_like Posterior mean of the fixed effects coefficients. fe_sd : array_like Posterior standard deviation of the fixed effects coefficients vcp_mean : array_like Posterior mean of the logged variance component standard deviations. vcp_sd : array_like Posterior standard deviation of the logged variance component standard deviations. vc_mean : array_like Posterior mean of the random coefficients vc_sd : array_like Posterior standard deviation of the random coefficients """ def __init__(self, model, params, cov_params, optim_retvals=None): self.model = model self.params = params self._cov_params = cov_params self.optim_retvals = optim_retvals self.fe_mean, self.vcp_mean, self.vc_mean = (model._unpack(params)) if cov_params.ndim == 2: cp = np.diag(cov_params) else: cp = cov_params self.fe_sd, self.vcp_sd, self.vc_sd = model._unpack(cp) self.fe_sd = np.sqrt(self.fe_sd) self.vcp_sd = np.sqrt(self.vcp_sd) self.vc_sd = np.sqrt(self.vc_sd) def cov_params(self): if hasattr(self.model.data, "frame"): # Return the covariance matrix as a dataframe or series na = (self.model.fep_names + self.model.vcp_names + self.model.vc_names) if self._cov_params.ndim == 2: return pd.DataFrame(self._cov_params, index=na, columns=na) else: return pd.Series(self._cov_params, index=na) # Return the covariance matrix as a ndarray return self._cov_params def summary(self): df = pd.DataFrame() m = self.model.k_fep + self.model.k_vcp df["Type"] = (["M" for k in range(self.model.k_fep)] + ["V" for k in range(self.model.k_vcp)]) df["Post. Mean"] = self.params[0:m] if self._cov_params.ndim == 2: v = np.diag(self._cov_params)[0:m] df["Post. SD"] = np.sqrt(v) else: df["Post. SD"] = np.sqrt(self._cov_params[0:m]) # Convert variance parameters to natural scale df["SD"] = np.exp(df["Post. Mean"]) df["SD (LB)"] = np.exp(df["Post. Mean"] - 2 * df["Post. SD"]) df["SD (UB)"] = np.exp(df["Post. Mean"] + 2 * df["Post. SD"]) df["SD"] = ["%.3f" % x for x in df.SD] df["SD (LB)"] = ["%.3f" % x for x in df["SD (LB)"]] df["SD (UB)"] = ["%.3f" % x for x in df["SD (UB)"]] df.loc[df.index < self.model.k_fep, "SD"] = "" df.loc[df.index < self.model.k_fep, "SD (LB)"] = "" df.loc[df.index < self.model.k_fep, "SD (UB)"] = "" df.index = self.model.fep_names + self.model.vcp_names summ = summary2.Summary() summ.add_title(self.model.family.__class__.__name__ + " Mixed GLM Results") summ.add_df(df) summ.add_text("Parameter types are mean structure (M) and " "variance structure (V)") summ.add_text("Variance parameters are modeled as log " "standard deviations") return summ def random_effects(self, term=None): """ Posterior mean and standard deviation of random effects. Parameters ---------- term : int or None If None, results for all random effects are returned. If an integer, returns results for a given set of random effects. The value of `term` refers to an element of the `ident` vector, or to a position in the `vc_formulas` list. Returns ------- Data frame of posterior means and posterior standard deviations of random effects. """ z = self.vc_mean s = self.vc_sd na = self.model.vc_names if term is not None: termix = self.model.vcp_names.index(term) ii = np.flatnonzero(self.model.ident == termix) z = z[ii] s = s[ii] na = [na[i] for i in ii] x = pd.DataFrame({"Mean": z, "SD": s}) if na is not None: x.index = na return x def predict(self, exog=None, linear=False): """ Return predicted values for the mean structure. Parameters ---------- exog : array_like The design matrix for the mean structure. If None, use the model's design matrix. linear : bool If True, returns the linear predictor, otherwise transform the linear predictor using the link function. Returns ------- A one-dimensional array of fitted values. """ return self.model.predict(self.params, exog, linear) class BinomialBayesMixedGLM(_VariationalBayesMixedGLM, _BayesMixedGLM): __doc__ = _init_doc.format(example=_logit_example) def __init__(self, endog, exog, exog_vc, ident, vcp_p=1, fe_p=2, fep_names=None, vcp_names=None, vc_names=None): super(BinomialBayesMixedGLM, self).__init__( endog, exog, exog_vc=exog_vc, ident=ident, vcp_p=vcp_p, fe_p=fe_p, family=families.Binomial(), fep_names=fep_names, vcp_names=vcp_names, vc_names=vc_names) if not np.all(np.unique(endog) == np.r_[0, 1]): msg = "endog values must be 0 and 1, and not all identical" raise ValueError(msg) @classmethod def from_formula(cls, formula, vc_formulas, data, vcp_p=1, fe_p=2): fam = families.Binomial() x = _BayesMixedGLM.from_formula( formula, vc_formulas, data, family=fam, vcp_p=vcp_p, fe_p=fe_p) # Copy over to the intended class structure mod = BinomialBayesMixedGLM( x.endog, x.exog, exog_vc=x.exog_vc, ident=x.ident, vcp_p=x.vcp_p, fe_p=x.fe_p, fep_names=x.fep_names, vcp_names=x.vcp_names, vc_names=x.vc_names) mod.data = x.data return mod def vb_elbo(self, vb_mean, vb_sd): """ Returns the evidence lower bound (ELBO) for the model. """ fep_mean, vcp_mean, vc_mean = self._unpack(vb_mean) fep_sd, vcp_sd, vc_sd = self._unpack(vb_sd) tm, tv = self._lp_stats(fep_mean, fep_sd, vc_mean, vc_sd) def h(z): return -np.log(1 + np.exp(tm + np.sqrt(tv) * z)) return self.vb_elbo_base(h, tm, fep_mean, vcp_mean, vc_mean, fep_sd, vcp_sd, vc_sd) def vb_elbo_grad(self, vb_mean, vb_sd): """ Returns the gradient of the model's evidence lower bound (ELBO). """ fep_mean, vcp_mean, vc_mean = self._unpack(vb_mean) fep_sd, vcp_sd, vc_sd = self._unpack(vb_sd) tm, tv = self._lp_stats(fep_mean, fep_sd, vc_mean, vc_sd) def h(z): u = tm + np.sqrt(tv) * z x = np.zeros_like(u) ii = np.flatnonzero(u > 0) uu = u[ii] x[ii] = 1 / (1 + np.exp(-uu)) ii = np.flatnonzero(u <= 0) uu = u[ii] x[ii] = np.exp(uu) / (1 + np.exp(uu)) return -x return self.vb_elbo_grad_base(h, tm, tv, fep_mean, vcp_mean, vc_mean, fep_sd, vcp_sd, vc_sd) class PoissonBayesMixedGLM(_VariationalBayesMixedGLM, _BayesMixedGLM): __doc__ = _init_doc.format(example=_poisson_example) def __init__(self, endog, exog, exog_vc, ident, vcp_p=1, fe_p=2, fep_names=None, vcp_names=None, vc_names=None): super(PoissonBayesMixedGLM, self).__init__( endog=endog, exog=exog, exog_vc=exog_vc, ident=ident, vcp_p=vcp_p, fe_p=fe_p, family=families.Poisson(), fep_names=fep_names, vcp_names=vcp_names, vc_names=vc_names) @classmethod def from_formula(cls, formula, vc_formulas, data, vcp_p=1, fe_p=2, vcp_names=None, vc_names=None): fam = families.Poisson() x = _BayesMixedGLM.from_formula( formula, vc_formulas, data, family=fam, vcp_p=vcp_p, fe_p=fe_p) # Copy over to the intended class structure mod = PoissonBayesMixedGLM( endog=x.endog, exog=x.exog, exog_vc=x.exog_vc, ident=x.ident, vcp_p=x.vcp_p, fe_p=x.fe_p, fep_names=x.fep_names, vcp_names=x.vcp_names, vc_names=x.vc_names) mod.data = x.data return mod def vb_elbo(self, vb_mean, vb_sd): """ Returns the evidence lower bound (ELBO) for the model. """ fep_mean, vcp_mean, vc_mean = self._unpack(vb_mean) fep_sd, vcp_sd, vc_sd = self._unpack(vb_sd) tm, tv = self._lp_stats(fep_mean, fep_sd, vc_mean, vc_sd) def h(z): return -np.exp(tm + np.sqrt(tv) * z) return self.vb_elbo_base(h, tm, fep_mean, vcp_mean, vc_mean, fep_sd, vcp_sd, vc_sd) def vb_elbo_grad(self, vb_mean, vb_sd): """ Returns the gradient of the model's evidence lower bound (ELBO). """ fep_mean, vcp_mean, vc_mean = self._unpack(vb_mean) fep_sd, vcp_sd, vc_sd = self._unpack(vb_sd) tm, tv = self._lp_stats(fep_mean, fep_sd, vc_mean, vc_sd) def h(z): y = -np.exp(tm + np.sqrt(tv) * z) return y return self.vb_elbo_grad_base(h, tm, tv, fep_mean, vcp_mean, vc_mean, fep_sd, vcp_sd, vc_sd) statsmodels-0.12.2/statsmodels/genmod/cov_struct.py000066400000000000000000001362571400612667500225430ustar00rootroot00000000000000""" Covariance models and estimators for GEE. Some details for the covariance calculations can be found in the Stata docs: http://www.stata.com/manuals13/xtxtgee.pdf """ from statsmodels.compat.pandas import Appender from statsmodels.stats.correlation_tools import cov_nearest import numpy as np import pandas as pd from scipy import linalg as spl from collections import defaultdict from statsmodels.tools.sm_exceptions import (ConvergenceWarning, OutputWarning, NotImplementedWarning) import warnings class CovStruct(object): """ Base class for correlation and covariance structures. An implementation of this class takes the residuals from a regression model that has been fit to grouped data, and uses them to estimate the within-group dependence structure of the random errors in the model. The current state of the covariance structure is represented through the value of the `dep_params` attribute. The default state of a newly-created instance should always be the identity correlation matrix. """ def __init__(self, cov_nearest_method="clipped"): # Parameters describing the dependency structure self.dep_params = None # Keep track of the number of times that the covariance was # adjusted. self.cov_adjust = [] # Method for projecting the covariance matrix if it is not # PSD. self.cov_nearest_method = cov_nearest_method def initialize(self, model): """ Called by GEE, used by implementations that need additional setup prior to running `fit`. Parameters ---------- model : GEE class A reference to the parent GEE class instance. """ self.model = model def update(self, params): """ Update the association parameter values based on the current regression coefficients. Parameters ---------- params : array_like Working values for the regression parameters. """ raise NotImplementedError def covariance_matrix(self, endog_expval, index): """ Returns the working covariance or correlation matrix for a given cluster of data. Parameters ---------- endog_expval : array_like The expected values of endog for the cluster for which the covariance or correlation matrix will be returned index : int The index of the cluster for which the covariance or correlation matrix will be returned Returns ------- M : matrix The covariance or correlation matrix of endog is_cor : bool True if M is a correlation matrix, False if M is a covariance matrix """ raise NotImplementedError def covariance_matrix_solve(self, expval, index, stdev, rhs): """ Solves matrix equations of the form `covmat * soln = rhs` and returns the values of `soln`, where `covmat` is the covariance matrix represented by this class. Parameters ---------- expval : array_like The expected value of endog for each observed value in the group. index : int The group index. stdev : array_like The standard deviation of endog for each observation in the group. rhs : list/tuple of array_like A set of right-hand sides; each defines a matrix equation to be solved. Returns ------- soln : list/tuple of array_like The solutions to the matrix equations. Notes ----- Returns None if the solver fails. Some dependence structures do not use `expval` and/or `index` to determine the correlation matrix. Some families (e.g. binomial) do not use the `stdev` parameter when forming the covariance matrix. If the covariance matrix is singular or not SPD, it is projected to the nearest such matrix. These projection events are recorded in the fit_history attribute of the GEE model. Systems of linear equations with the covariance matrix as the left hand side (LHS) are solved for different right hand sides (RHS); the LHS is only factorized once to save time. This is a default implementation, it can be reimplemented in subclasses to optimize the linear algebra according to the structure of the covariance matrix. """ vmat, is_cor = self.covariance_matrix(expval, index) if is_cor: vmat *= np.outer(stdev, stdev) # Factor the covariance matrix. If the factorization fails, # attempt to condition it into a factorizable matrix. threshold = 1e-2 success = False cov_adjust = 0 for itr in range(20): try: vco = spl.cho_factor(vmat) success = True break except np.linalg.LinAlgError: vmat = cov_nearest(vmat, method=self.cov_nearest_method, threshold=threshold) threshold *= 2 cov_adjust += 1 msg = "At least one covariance matrix was not PSD " msg += "and required projection." warnings.warn(msg) self.cov_adjust.append(cov_adjust) # Last resort if we still cannot factor the covariance matrix. if not success: warnings.warn( "Unable to condition covariance matrix to an SPD " "matrix using cov_nearest", ConvergenceWarning) vmat = np.diag(np.diag(vmat)) vco = spl.cho_factor(vmat) soln = [spl.cho_solve(vco, x) for x in rhs] return soln def summary(self): """ Returns a text summary of the current estimate of the dependence structure. """ raise NotImplementedError class Independence(CovStruct): """ An independence working dependence structure. """ @Appender(CovStruct.update.__doc__) def update(self, params): # Nothing to update return @Appender(CovStruct.covariance_matrix.__doc__) def covariance_matrix(self, expval, index): dim = len(expval) return np.eye(dim, dtype=np.float64), True @Appender(CovStruct.covariance_matrix_solve.__doc__) def covariance_matrix_solve(self, expval, index, stdev, rhs): v = stdev ** 2 rslt = [] for x in rhs: if x.ndim == 1: rslt.append(x / v) else: rslt.append(x / v[:, None]) return rslt def summary(self): return ("Observations within a cluster are modeled " "as being independent.") class Exchangeable(CovStruct): """ An exchangeable working dependence structure. """ def __init__(self): super(Exchangeable, self).__init__() # The correlation between any two values in the same cluster self.dep_params = 0. @Appender(CovStruct.update.__doc__) def update(self, params): endog = self.model.endog_li nobs = self.model.nobs varfunc = self.model.family.variance cached_means = self.model.cached_means has_weights = self.model.weights is not None weights_li = self.model.weights residsq_sum, scale = 0, 0 fsum1, fsum2, n_pairs = 0., 0., 0. for i in range(self.model.num_group): expval, _ = cached_means[i] stdev = np.sqrt(varfunc(expval)) resid = (endog[i] - expval) / stdev f = weights_li[i] if has_weights else 1. ssr = np.sum(resid * resid) scale += f * ssr fsum1 += f * len(endog[i]) residsq_sum += f * (resid.sum() ** 2 - ssr) / 2 ngrp = len(resid) npr = 0.5 * ngrp * (ngrp - 1) fsum2 += f * npr n_pairs += npr ddof = self.model.ddof_scale scale /= (fsum1 * (nobs - ddof) / float(nobs)) residsq_sum /= scale self.dep_params = residsq_sum / \ (fsum2 * (n_pairs - ddof) / float(n_pairs)) @Appender(CovStruct.covariance_matrix.__doc__) def covariance_matrix(self, expval, index): dim = len(expval) dp = self.dep_params * np.ones((dim, dim), dtype=np.float64) np.fill_diagonal(dp, 1) return dp, True @Appender(CovStruct.covariance_matrix_solve.__doc__) def covariance_matrix_solve(self, expval, index, stdev, rhs): k = len(expval) c = self.dep_params / (1. - self.dep_params) c /= 1. + self.dep_params * (k - 1) rslt = [] for x in rhs: if x.ndim == 1: x1 = x / stdev y = x1 / (1. - self.dep_params) y -= c * sum(x1) y /= stdev else: x1 = x / stdev[:, None] y = x1 / (1. - self.dep_params) y -= c * x1.sum(0) y /= stdev[:, None] rslt.append(y) return rslt def summary(self): return ("The correlation between two observations in the " + "same cluster is %.3f" % self.dep_params) class Nested(CovStruct): """ A nested working dependence structure. A nested working dependence structure captures unique variance associated with each level in a hierarchy of partitions of the cases. For each level of the hierarchy, there is a set of iid random effects with mean zero, and with variance that is specific to the level. These variance parameters are estimated from the data using the method of moments. The top level of the hierarchy is always defined by the required `groups` argument to GEE. The `dep_data` argument used to create the GEE defines the remaining levels of the hierarchy. it should be either an array, or if using the formula interface, a string that contains a formula. If an array, it should contain a `n_obs x k` matrix of labels, corresponding to the k levels of partitioning that are nested under the top-level `groups` of the GEE instance. These subgroups should be nested from left to right, so that two observations with the same label for column j of `dep_data` should also have the same label for all columns j' < j (this only applies to observations in the same top-level cluster given by the `groups` argument to GEE). If `dep_data` is a formula, it should usually be of the form `0 + a + b + ...`, where `a`, `b`, etc. contain labels defining group membership. The `0 + ` should be included to prevent creation of an intercept. The variable values are interpreted as labels for group membership, but the variables should not be explicitly coded as categorical, i.e. use `0 + a` not `0 + C(a)`. Notes ----- The calculations for the nested structure involve all pairs of observations within the top level `group` passed to GEE. Large group sizes will result in slow iterations. """ def initialize(self, model): """ Called on the first call to update `ilabels` is a list of n_i x n_i matrices containing integer labels that correspond to specific correlation parameters. Two elements of ilabels[i] with the same label share identical variance components. `designx` is a matrix, with each row containing dummy variables indicating which variance components are associated with the corresponding element of QY. """ super(Nested, self).initialize(model) if self.model.weights is not None: warnings.warn("weights not implemented for nested cov_struct, " "using unweighted covariance estimate", NotImplementedWarning) # A bit of processing of the nest data id_matrix = np.asarray(self.model.dep_data) if id_matrix.ndim == 1: id_matrix = id_matrix[:, None] self.id_matrix = id_matrix endog = self.model.endog_li designx, ilabels = [], [] # The number of layers of nesting n_nest = self.id_matrix.shape[1] for i in range(self.model.num_group): ngrp = len(endog[i]) glab = self.model.group_labels[i] rix = self.model.group_indices[glab] # Determine the number of common variance components # shared by each pair of observations. ix1, ix2 = np.tril_indices(ngrp, -1) ncm = (self.id_matrix[rix[ix1], :] == self.id_matrix[rix[ix2], :]).sum(1) # This is used to construct the working correlation # matrix. ilabel = np.zeros((ngrp, ngrp), dtype=np.int32) ilabel[(ix1, ix2)] = ncm + 1 ilabel[(ix2, ix1)] = ncm + 1 ilabels.append(ilabel) # This is used to estimate the variance components. dsx = np.zeros((len(ix1), n_nest + 1), dtype=np.float64) dsx[:, 0] = 1 for k in np.unique(ncm): ii = np.flatnonzero(ncm == k) dsx[ii, 1:k + 1] = 1 designx.append(dsx) self.designx = np.concatenate(designx, axis=0) self.ilabels = ilabels svd = np.linalg.svd(self.designx, 0) self.designx_u = svd[0] self.designx_s = svd[1] self.designx_v = svd[2].T @Appender(CovStruct.update.__doc__) def update(self, params): endog = self.model.endog_li nobs = self.model.nobs dim = len(params) if self.designx is None: self._compute_design(self.model) cached_means = self.model.cached_means varfunc = self.model.family.variance dvmat = [] scale = 0. for i in range(self.model.num_group): expval, _ = cached_means[i] stdev = np.sqrt(varfunc(expval)) resid = (endog[i] - expval) / stdev ix1, ix2 = np.tril_indices(len(resid), -1) dvmat.append(resid[ix1] * resid[ix2]) scale += np.sum(resid ** 2) dvmat = np.concatenate(dvmat) scale /= (nobs - dim) # Use least squares regression to estimate the variance # components vcomp_coeff = np.dot(self.designx_v, np.dot(self.designx_u.T, dvmat) / self.designx_s) self.vcomp_coeff = np.clip(vcomp_coeff, 0, np.inf) self.scale = scale self.dep_params = self.vcomp_coeff.copy() @Appender(CovStruct.covariance_matrix.__doc__) def covariance_matrix(self, expval, index): dim = len(expval) # First iteration if self.dep_params is None: return np.eye(dim, dtype=np.float64), True ilabel = self.ilabels[index] c = np.r_[self.scale, np.cumsum(self.vcomp_coeff)] vmat = c[ilabel] vmat /= self.scale return vmat, True def summary(self): """ Returns a summary string describing the state of the dependence structure. """ dep_names = ["Groups"] if hasattr(self.model, "_dep_data_names"): dep_names.extend(self.model._dep_data_names) else: dep_names.extend(["Component %d:" % (k + 1) for k in range(len(self.vcomp_coeff) - 1)]) if hasattr(self.model, "_groups_name"): dep_names[0] = self.model._groups_name dep_names.append("Residual") vc = self.vcomp_coeff.tolist() vc.append(self.scale - np.sum(vc)) smry = pd.DataFrame({"Variance": vc}, index=dep_names) return smry class Stationary(CovStruct): """ A stationary covariance structure. The correlation between two observations is an arbitrary function of the distance between them. Distances up to a given maximum value are included in the covariance model. Parameters ---------- max_lag : float The largest distance that is included in the covariance model. grid : bool If True, the index positions in the data (after dropping missing values) are used to define distances, and the `time` variable is ignored. """ def __init__(self, max_lag=1, grid=False): super(Stationary, self).__init__() self.max_lag = max_lag self.grid = grid self.dep_params = np.zeros(max_lag + 1) def initialize(self, model): super(Stationary, self).initialize(model) # Time used as an index needs to be integer type. if not self.grid: time = self.model.time[:, 0].astype(np.int32) self.time = self.model.cluster_list(time) @Appender(CovStruct.update.__doc__) def update(self, params): if self.grid: self.update_grid(params) else: self.update_nogrid(params) def update_grid(self, params): endog = self.model.endog_li cached_means = self.model.cached_means varfunc = self.model.family.variance dep_params = np.zeros(self.max_lag + 1) for i in range(self.model.num_group): expval, _ = cached_means[i] stdev = np.sqrt(varfunc(expval)) resid = (endog[i] - expval) / stdev dep_params[0] += np.sum(resid * resid) / len(resid) for j in range(1, self.max_lag + 1): v = resid[j:] dep_params[j] += np.sum(resid[0:-j] * v) / len(v) dep_params /= dep_params[0] self.dep_params = dep_params def update_nogrid(self, params): endog = self.model.endog_li cached_means = self.model.cached_means varfunc = self.model.family.variance dep_params = np.zeros(self.max_lag + 1) dn = np.zeros(self.max_lag + 1) resid_ssq = 0 resid_ssq_n = 0 for i in range(self.model.num_group): expval, _ = cached_means[i] stdev = np.sqrt(varfunc(expval)) resid = (endog[i] - expval) / stdev j1, j2 = np.tril_indices(len(expval), -1) dx = np.abs(self.time[i][j1] - self.time[i][j2]) ii = np.flatnonzero(dx <= self.max_lag) j1 = j1[ii] j2 = j2[ii] dx = dx[ii] vs = np.bincount(dx, weights=resid[j1] * resid[j2], minlength=self.max_lag + 1) vd = np.bincount(dx, minlength=self.max_lag + 1) resid_ssq += np.sum(resid**2) resid_ssq_n += len(resid) ii = np.flatnonzero(vd > 0) if len(ii) > 0: dn[ii] += 1 dep_params[ii] += vs[ii] / vd[ii] i0 = np.flatnonzero(dn > 0) dep_params[i0] /= dn[i0] resid_msq = resid_ssq / resid_ssq_n dep_params /= resid_msq self.dep_params = dep_params @Appender(CovStruct.covariance_matrix.__doc__) def covariance_matrix(self, endog_expval, index): if self.grid: return self.covariance_matrix_grid(endog_expval, index) j1, j2 = np.tril_indices(len(endog_expval), -1) dx = np.abs(self.time[index][j1] - self.time[index][j2]) ii = np.flatnonzero(dx <= self.max_lag) j1 = j1[ii] j2 = j2[ii] dx = dx[ii] cmat = np.eye(len(endog_expval)) cmat[j1, j2] = self.dep_params[dx] cmat[j2, j1] = self.dep_params[dx] return cmat, True def covariance_matrix_grid(self, endog_expval, index): from scipy.linalg import toeplitz r = np.zeros(len(endog_expval)) r[0] = 1 r[1:self.max_lag + 1] = self.dep_params[1:] return toeplitz(r), True @Appender(CovStruct.covariance_matrix_solve.__doc__) def covariance_matrix_solve(self, expval, index, stdev, rhs): if not self.grid: return super(Stationary, self).covariance_matrix_solve( expval, index, stdev, rhs) from statsmodels.tools.linalg import stationary_solve r = np.zeros(len(expval)) r[0:self.max_lag] = self.dep_params[1:] return [stationary_solve(r, x) for x in rhs] def summary(self): lag = np.arange(self.max_lag + 1) return pd.DataFrame({"Lag": lag, "Cov": self.dep_params}) class Autoregressive(CovStruct): """ A first-order autoregressive working dependence structure. The dependence is defined in terms of the `time` component of the parent GEE class, which defaults to the index position of each value within its cluster, based on the order of values in the input data set. Time represents a potentially multidimensional index from which distances between pairs of observations can be determined. The correlation between two observations in the same cluster is dep_params^distance, where `dep_params` contains the (scalar) autocorrelation parameter to be estimated, and `distance` is the distance between the two observations, calculated from their corresponding time values. `time` is stored as an n_obs x k matrix, where `k` represents the number of dimensions in the time index. The autocorrelation parameter is estimated using weighted nonlinear least squares, regressing each value within a cluster on each preceding value in the same cluster. Parameters ---------- dist_func : function from R^k x R^k to R^+, optional A function that computes the distance between the two observations based on their `time` values. References ---------- B Rosner, A Munoz. Autoregressive modeling for the analysis of longitudinal data with unequally spaced examinations. Statistics in medicine. Vol 7, 59-71, 1988. """ def __init__(self, dist_func=None, grid=False): super(Autoregressive, self).__init__() # The function for determining distances based on time if dist_func is None: self.dist_func = lambda x, y: np.abs(x - y).sum() else: self.dist_func = dist_func self.grid = grid if not grid: self.designx = None # The autocorrelation parameter self.dep_params = 0. @Appender(CovStruct.update.__doc__) def update(self, params): if self.model.weights is not None: warnings.warn("weights not implemented for autoregressive " "cov_struct, using unweighted covariance estimate", NotImplementedWarning) if self.grid: self._update_grid(params) else: self._update_nogrid(params) def _update_grid(self, params): cached_means = self.model.cached_means scale = self.model.estimate_scale() varfunc = self.model.family.variance endog = self.model.endog_li lag0, lag1 = 0.0, 0.0 for i in range(self.model.num_group): expval, _ = cached_means[i] stdev = np.sqrt(scale * varfunc(expval)) resid = (endog[i] - expval) / stdev n = len(resid) if n > 1: lag1 += np.sum(resid[0:-1] * resid[1:]) / (n - 1) lag0 += np.sum(resid**2) / n self.dep_params = lag1 / lag0 def _update_nogrid(self, params): endog = self.model.endog_li time = self.model.time_li # Only need to compute this once if self.designx is not None: designx = self.designx else: designx = [] for i in range(self.model.num_group): ngrp = len(endog[i]) if ngrp == 0: continue # Loop over pairs of observations within a cluster for j1 in range(ngrp): for j2 in range(j1): designx.append(self.dist_func(time[i][j1, :], time[i][j2, :])) designx = np.array(designx) self.designx = designx scale = self.model.estimate_scale() varfunc = self.model.family.variance cached_means = self.model.cached_means # Weights var = 1. - self.dep_params ** (2 * designx) var /= 1. - self.dep_params ** 2 wts = 1. / var wts /= wts.sum() residmat = [] for i in range(self.model.num_group): expval, _ = cached_means[i] stdev = np.sqrt(scale * varfunc(expval)) resid = (endog[i] - expval) / stdev ngrp = len(resid) for j1 in range(ngrp): for j2 in range(j1): residmat.append([resid[j1], resid[j2]]) residmat = np.array(residmat) # Need to minimize this def fitfunc(a): dif = residmat[:, 0] - (a ** designx) * residmat[:, 1] return np.dot(dif ** 2, wts) # Left bracket point b_lft, f_lft = 0., fitfunc(0.) # Center bracket point b_ctr, f_ctr = 0.5, fitfunc(0.5) while f_ctr > f_lft: b_ctr /= 2 f_ctr = fitfunc(b_ctr) if b_ctr < 1e-8: self.dep_params = 0 return # Right bracket point b_rgt, f_rgt = 0.75, fitfunc(0.75) while f_rgt < f_ctr: b_rgt = b_rgt + (1. - b_rgt) / 2 f_rgt = fitfunc(b_rgt) if b_rgt > 1. - 1e-6: raise ValueError( "Autoregressive: unable to find right bracket") from scipy.optimize import brent self.dep_params = brent(fitfunc, brack=[b_lft, b_ctr, b_rgt]) @Appender(CovStruct.covariance_matrix.__doc__) def covariance_matrix(self, endog_expval, index): ngrp = len(endog_expval) if self.dep_params == 0: return np.eye(ngrp, dtype=np.float64), True idx = np.arange(ngrp) cmat = self.dep_params ** np.abs(idx[:, None] - idx[None, :]) return cmat, True @Appender(CovStruct.covariance_matrix_solve.__doc__) def covariance_matrix_solve(self, expval, index, stdev, rhs): # The inverse of an AR(1) covariance matrix is tri-diagonal. k = len(expval) soln = [] # LHS has 1 column if k == 1: return [x / stdev ** 2 for x in rhs] # LHS has 2 columns if k == 2: mat = np.array([[1, -self.dep_params], [-self.dep_params, 1]]) mat /= (1. - self.dep_params ** 2) for x in rhs: if x.ndim == 1: x1 = x / stdev else: x1 = x / stdev[:, None] x1 = np.dot(mat, x1) if x.ndim == 1: x1 /= stdev else: x1 /= stdev[:, None] soln.append(x1) return soln # LHS has >= 3 columns: values c0, c1, c2 defined below give # the inverse. c0 is on the diagonal, except for the first # and last position. c1 is on the first and last position of # the diagonal. c2 is on the sub/super diagonal. c0 = (1. + self.dep_params ** 2) / (1. - self.dep_params ** 2) c1 = 1. / (1. - self.dep_params ** 2) c2 = -self.dep_params / (1. - self.dep_params ** 2) soln = [] for x in rhs: flatten = False if x.ndim == 1: x = x[:, None] flatten = True x1 = x / stdev[:, None] z0 = np.zeros((1, x.shape[1])) rhs1 = np.concatenate((x[1:, :], z0), axis=0) rhs2 = np.concatenate((z0, x[0:-1, :]), axis=0) y = c0 * x + c2 * rhs1 + c2 * rhs2 y[0, :] = c1 * x[0, :] + c2 * x[1, :] y[-1, :] = c1 * x[-1, :] + c2 * x[-2, :] y /= stdev[:, None] if flatten: y = np.squeeze(y) soln.append(y) return soln def summary(self): return ("Autoregressive(1) dependence parameter: %.3f\n" % self.dep_params) class CategoricalCovStruct(CovStruct): """ Parent class for covariance structure for categorical data models. Attributes ---------- nlevel : int The number of distinct levels for the outcome variable. ibd : list A list whose i^th element ibd[i] is an array whose rows contain integer pairs (a,b), where endog_li[i][a:b] is the subvector of binary indicators derived from the same ordinal value. """ def initialize(self, model): super(CategoricalCovStruct, self).initialize(model) self.nlevel = len(model.endog_values) self._ncut = self.nlevel - 1 from numpy.lib.stride_tricks import as_strided b = np.dtype(np.int64).itemsize ibd = [] for v in model.endog_li: jj = np.arange(0, len(v) + 1, self._ncut, dtype=np.int64) jj = as_strided(jj, shape=(len(jj) - 1, 2), strides=(b, b)) ibd.append(jj) self.ibd = ibd class GlobalOddsRatio(CategoricalCovStruct): """ Estimate the global odds ratio for a GEE with ordinal or nominal data. References ---------- PJ Heagerty and S Zeger. "Marginal Regression Models for Clustered Ordinal Measurements". Journal of the American Statistical Association Vol. 91, Issue 435 (1996). Thomas Lumley. Generalized Estimating Equations for Ordinal Data: A Note on Working Correlation Structures. Biometrics Vol. 52, No. 1 (Mar., 1996), pp. 354-361 http://www.jstor.org/stable/2533173 Notes ----- The following data structures are calculated in the class: 'ibd' is a list whose i^th element ibd[i] is a sequence of integer pairs (a,b), where endog_li[i][a:b] is the subvector of binary indicators derived from the same ordinal value. `cpp` is a dictionary where cpp[group] is a map from cut-point pairs (c,c') to the indices of all between-subject pairs derived from the given cut points. """ def __init__(self, endog_type): super(GlobalOddsRatio, self).__init__() self.endog_type = endog_type self.dep_params = 0. def initialize(self, model): super(GlobalOddsRatio, self).initialize(model) if self.model.weights is not None: warnings.warn("weights not implemented for GlobalOddsRatio " "cov_struct, using unweighted covariance estimate", NotImplementedWarning) # Need to restrict to between-subject pairs cpp = [] for v in model.endog_li: # Number of subjects in this group m = int(len(v) / self._ncut) i1, i2 = np.tril_indices(m, -1) cpp1 = {} for k1 in range(self._ncut): for k2 in range(k1 + 1): jj = np.zeros((len(i1), 2), dtype=np.int64) jj[:, 0] = i1 * self._ncut + k1 jj[:, 1] = i2 * self._ncut + k2 cpp1[(k2, k1)] = jj cpp.append(cpp1) self.cpp = cpp # Initialize the dependence parameters self.crude_or = self.observed_crude_oddsratio() if self.model.update_dep: self.dep_params = self.crude_or def pooled_odds_ratio(self, tables): """ Returns the pooled odds ratio for a list of 2x2 tables. The pooled odds ratio is the inverse variance weighted average of the sample odds ratios of the tables. """ if len(tables) == 0: return 1. # Get the sampled odds ratios and variances log_oddsratio, var = [], [] for table in tables: lor = np.log(table[1, 1]) + np.log(table[0, 0]) -\ np.log(table[0, 1]) - np.log(table[1, 0]) log_oddsratio.append(lor) var.append((1 / table.astype(np.float64)).sum()) # Calculate the inverse variance weighted average wts = [1 / v for v in var] wtsum = sum(wts) wts = [w / wtsum for w in wts] log_pooled_or = sum([w * e for w, e in zip(wts, log_oddsratio)]) return np.exp(log_pooled_or) @Appender(CovStruct.covariance_matrix.__doc__) def covariance_matrix(self, expected_value, index): vmat = self.get_eyy(expected_value, index) vmat -= np.outer(expected_value, expected_value) return vmat, False def observed_crude_oddsratio(self): """ To obtain the crude (global) odds ratio, first pool all binary indicators corresponding to a given pair of cut points (c,c'), then calculate the odds ratio for this 2x2 table. The crude odds ratio is the inverse variance weighted average of these odds ratios. Since the covariate effects are ignored, this OR will generally be greater than the stratified OR. """ cpp = self.cpp endog = self.model.endog_li # Storage for the contingency tables for each (c,c') tables = {} for ii in cpp[0].keys(): tables[ii] = np.zeros((2, 2), dtype=np.float64) # Get the observed crude OR for i in range(len(endog)): # The observed joint values for the current cluster yvec = endog[i] endog_11 = np.outer(yvec, yvec) endog_10 = np.outer(yvec, 1. - yvec) endog_01 = np.outer(1. - yvec, yvec) endog_00 = np.outer(1. - yvec, 1. - yvec) cpp1 = cpp[i] for ky in cpp1.keys(): ix = cpp1[ky] tables[ky][1, 1] += endog_11[ix[:, 0], ix[:, 1]].sum() tables[ky][1, 0] += endog_10[ix[:, 0], ix[:, 1]].sum() tables[ky][0, 1] += endog_01[ix[:, 0], ix[:, 1]].sum() tables[ky][0, 0] += endog_00[ix[:, 0], ix[:, 1]].sum() return self.pooled_odds_ratio(list(tables.values())) def get_eyy(self, endog_expval, index): """ Returns a matrix V such that V[i,j] is the joint probability that endog[i] = 1 and endog[j] = 1, based on the marginal probabilities of endog and the global odds ratio `current_or`. """ current_or = self.dep_params ibd = self.ibd[index] # The between-observation joint probabilities if current_or == 1.0: vmat = np.outer(endog_expval, endog_expval) else: psum = endog_expval[:, None] + endog_expval[None, :] pprod = endog_expval[:, None] * endog_expval[None, :] pfac = np.sqrt((1. + psum * (current_or - 1.)) ** 2 + 4 * current_or * (1. - current_or) * pprod) vmat = 1. + psum * (current_or - 1.) - pfac vmat /= 2. * (current_or - 1) # Fix E[YY'] for elements that belong to same observation for bdl in ibd: evy = endog_expval[bdl[0]:bdl[1]] if self.endog_type == "ordinal": vmat[bdl[0]:bdl[1], bdl[0]:bdl[1]] =\ np.minimum.outer(evy, evy) else: vmat[bdl[0]:bdl[1], bdl[0]:bdl[1]] = np.diag(evy) return vmat @Appender(CovStruct.update.__doc__) def update(self, params): """ Update the global odds ratio based on the current value of params. """ cpp = self.cpp cached_means = self.model.cached_means # This will happen if all the clusters have only # one observation if len(cpp[0]) == 0: return tables = {} for ii in cpp[0]: tables[ii] = np.zeros((2, 2), dtype=np.float64) for i in range(self.model.num_group): endog_expval, _ = cached_means[i] emat_11 = self.get_eyy(endog_expval, i) emat_10 = endog_expval[:, None] - emat_11 emat_01 = -emat_11 + endog_expval emat_00 = 1. - (emat_11 + emat_10 + emat_01) cpp1 = cpp[i] for ky in cpp1.keys(): ix = cpp1[ky] tables[ky][1, 1] += emat_11[ix[:, 0], ix[:, 1]].sum() tables[ky][1, 0] += emat_10[ix[:, 0], ix[:, 1]].sum() tables[ky][0, 1] += emat_01[ix[:, 0], ix[:, 1]].sum() tables[ky][0, 0] += emat_00[ix[:, 0], ix[:, 1]].sum() cor_expval = self.pooled_odds_ratio(list(tables.values())) self.dep_params *= self.crude_or / cor_expval if not np.isfinite(self.dep_params): self.dep_params = 1. warnings.warn("dep_params became inf, resetting to 1", ConvergenceWarning) def summary(self): return "Global odds ratio: %.3f\n" % self.dep_params class OrdinalIndependence(CategoricalCovStruct): """ An independence covariance structure for ordinal models. The working covariance between indicators derived from different observations is zero. The working covariance between indicators derived form a common observation is determined from their current mean values. There are no parameters to estimate in this covariance structure. """ def covariance_matrix(self, expected_value, index): ibd = self.ibd[index] n = len(expected_value) vmat = np.zeros((n, n)) for bdl in ibd: ev = expected_value[bdl[0]:bdl[1]] vmat[bdl[0]:bdl[1], bdl[0]:bdl[1]] =\ np.minimum.outer(ev, ev) - np.outer(ev, ev) return vmat, False # Nothing to update def update(self, params): pass class NominalIndependence(CategoricalCovStruct): """ An independence covariance structure for nominal models. The working covariance between indicators derived from different observations is zero. The working covariance between indicators derived form a common observation is determined from their current mean values. There are no parameters to estimate in this covariance structure. """ def covariance_matrix(self, expected_value, index): ibd = self.ibd[index] n = len(expected_value) vmat = np.zeros((n, n)) for bdl in ibd: ev = expected_value[bdl[0]:bdl[1]] vmat[bdl[0]:bdl[1], bdl[0]:bdl[1]] =\ np.diag(ev) - np.outer(ev, ev) return vmat, False # Nothing to update def update(self, params): pass class Equivalence(CovStruct): """ A covariance structure defined in terms of equivalence classes. An 'equivalence class' is a set of pairs of observations such that the covariance of every pair within the equivalence class has a common value. Parameters ---------- pairs : dict-like A dictionary of dictionaries, where `pairs[group][label]` provides the indices of all pairs of observations in the group that have the same covariance value. Specifically, `pairs[group][label]` is a tuple `(j1, j2)`, where `j1` and `j2` are integer arrays of the same length. `j1[i], j2[i]` is one index pair that belongs to the `label` equivalence class. Only one triangle of each covariance matrix should be included. Positions where j1 and j2 have the same value are variance parameters. labels : array_like An array of labels such that every distinct pair of labels defines an equivalence class. Either `labels` or `pairs` must be provided. When the two labels in a pair are equal two equivalence classes are defined: one for the diagonal elements (corresponding to variances) and one for the off-diagonal elements (corresponding to covariances). return_cov : bool If True, `covariance_matrix` returns an estimate of the covariance matrix, otherwise returns an estimate of the correlation matrix. Notes ----- Using `labels` to define the class is much easier than using `pairs`, but is less general. Any pair of values not contained in `pairs` will be assigned zero covariance. The index values in `pairs` are row indices into the `exog` matrix. They are not updated if missing data are present. When using this covariance structure, missing data should be removed before constructing the model. If using `labels`, after a model is defined using the covariance structure it is possible to remove a label pair from the second level of the `pairs` dictionary to force the corresponding covariance to be zero. Examples -------- The following sets up the `pairs` dictionary for a model with two groups, equal variance for all observations, and constant covariance for all pairs of observations within each group. >> pairs = {0: {}, 1: {}} >> pairs[0][0] = (np.r_[0, 1, 2], np.r_[0, 1, 2]) >> pairs[0][1] = np.tril_indices(3, -1) >> pairs[1][0] = (np.r_[3, 4, 5], np.r_[3, 4, 5]) >> pairs[1][2] = 3 + np.tril_indices(3, -1) """ def __init__(self, pairs=None, labels=None, return_cov=False): super(Equivalence, self).__init__() if (pairs is None) and (labels is None): raise ValueError( "Equivalence cov_struct requires either `pairs` or `labels`") if (pairs is not None) and (labels is not None): raise ValueError( "Equivalence cov_struct accepts only one of `pairs` " "and `labels`") if pairs is not None: import copy self.pairs = copy.deepcopy(pairs) if labels is not None: self.labels = np.asarray(labels) self.return_cov = return_cov def _make_pairs(self, i, j): """ Create arrays containing all unique ordered pairs of i, j. The arrays i and j must be one-dimensional containing non-negative integers. """ mat = np.zeros((len(i) * len(j), 2), dtype=np.int32) # Create the pairs and order them f = np.ones(len(j)) mat[:, 0] = np.kron(f, i).astype(np.int32) f = np.ones(len(i)) mat[:, 1] = np.kron(j, f).astype(np.int32) mat.sort(1) # Remove repeated rows try: dtype = np.dtype((np.void, mat.dtype.itemsize * mat.shape[1])) bmat = np.ascontiguousarray(mat).view(dtype) _, idx = np.unique(bmat, return_index=True) except TypeError: # workaround for old numpy that cannot call unique with complex # dtypes rs = np.random.RandomState(4234) bmat = np.dot(mat, rs.uniform(size=mat.shape[1])) _, idx = np.unique(bmat, return_index=True) mat = mat[idx, :] return mat[:, 0], mat[:, 1] def _pairs_from_labels(self): from collections import defaultdict pairs = defaultdict(lambda: defaultdict(lambda: None)) model = self.model df = pd.DataFrame({"labels": self.labels, "groups": model.groups}) gb = df.groupby(["groups", "labels"]) ulabels = np.unique(self.labels) for g_ix, g_lb in enumerate(model.group_labels): # Loop over label pairs for lx1 in range(len(ulabels)): for lx2 in range(lx1 + 1): lb1 = ulabels[lx1] lb2 = ulabels[lx2] try: i1 = gb.groups[(g_lb, lb1)] i2 = gb.groups[(g_lb, lb2)] except KeyError: continue i1, i2 = self._make_pairs(i1, i2) clabel = str(lb1) + "/" + str(lb2) # Variance parameters belong in their own equiv class. jj = np.flatnonzero(i1 == i2) if len(jj) > 0: clabelv = clabel + "/v" pairs[g_lb][clabelv] = (i1[jj], i2[jj]) # Covariance parameters jj = np.flatnonzero(i1 != i2) if len(jj) > 0: i1 = i1[jj] i2 = i2[jj] pairs[g_lb][clabel] = (i1, i2) self.pairs = pairs def initialize(self, model): super(Equivalence, self).initialize(model) if self.model.weights is not None: warnings.warn("weights not implemented for equalence cov_struct, " "using unweighted covariance estimate", NotImplementedWarning) if not hasattr(self, 'pairs'): self._pairs_from_labels() # Initialize so that any equivalence class containing a # variance parameter has value 1. self.dep_params = defaultdict(lambda: 0.) self._var_classes = set([]) for gp in self.model.group_labels: for lb in self.pairs[gp]: j1, j2 = self.pairs[gp][lb] if np.any(j1 == j2): if not np.all(j1 == j2): warnings.warn( "equivalence class contains both variance " "and covariance parameters", OutputWarning) self._var_classes.add(lb) self.dep_params[lb] = 1 # Need to start indexing at 0 within each group. # rx maps olds indices to new indices rx = -1 * np.ones(len(self.model.endog), dtype=np.int32) for g_ix, g_lb in enumerate(self.model.group_labels): ii = self.model.group_indices[g_lb] rx[ii] = np.arange(len(ii), dtype=np.int32) # Reindex for gp in self.model.group_labels: for lb in self.pairs[gp].keys(): a, b = self.pairs[gp][lb] self.pairs[gp][lb] = (rx[a], rx[b]) @Appender(CovStruct.update.__doc__) def update(self, params): endog = self.model.endog_li varfunc = self.model.family.variance cached_means = self.model.cached_means dep_params = defaultdict(lambda: [0., 0., 0.]) n_pairs = defaultdict(lambda: 0) dim = len(params) for k, gp in enumerate(self.model.group_labels): expval, _ = cached_means[k] stdev = np.sqrt(varfunc(expval)) resid = (endog[k] - expval) / stdev for lb in self.pairs[gp].keys(): if (not self.return_cov) and lb in self._var_classes: continue jj = self.pairs[gp][lb] dep_params[lb][0] += np.sum(resid[jj[0]] * resid[jj[1]]) if not self.return_cov: dep_params[lb][1] += np.sum(resid[jj[0]] ** 2) dep_params[lb][2] += np.sum(resid[jj[1]] ** 2) n_pairs[lb] += len(jj[0]) if self.return_cov: for lb in dep_params.keys(): dep_params[lb] = dep_params[lb][0] / (n_pairs[lb] - dim) else: for lb in dep_params.keys(): den = np.sqrt(dep_params[lb][1] * dep_params[lb][2]) dep_params[lb] = dep_params[lb][0] / den for lb in self._var_classes: dep_params[lb] = 1. self.dep_params = dep_params self.n_pairs = n_pairs @Appender(CovStruct.covariance_matrix.__doc__) def covariance_matrix(self, expval, index): dim = len(expval) cmat = np.zeros((dim, dim)) g_lb = self.model.group_labels[index] for lb in self.pairs[g_lb].keys(): j1, j2 = self.pairs[g_lb][lb] cmat[j1, j2] = self.dep_params[lb] cmat = cmat + cmat.T np.fill_diagonal(cmat, cmat.diagonal() / 2) return cmat, not self.return_cov statsmodels-0.12.2/statsmodels/genmod/families/000077500000000000000000000000001400612667500215515ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/genmod/families/__init__.py000066400000000000000000000012301400612667500236560ustar00rootroot00000000000000""" This module contains the one-parameter exponential families used for fitting GLMs and GAMs. These families are described in P. McCullagh and J. A. Nelder. "Generalized linear models." Monographs on Statistics and Applied Probability. Chapman & Hall, London, 1983. """ from statsmodels.genmod.families import links from .family import Gaussian, Family, Poisson, Gamma, \ InverseGaussian, Binomial, NegativeBinomial, Tweedie from statsmodels.tools._testing import PytestTester __all__ = ['test', 'links', 'Family', 'Gamma', 'Gaussian', 'Poisson', 'InverseGaussian', 'Binomial', 'NegativeBinomial', 'Tweedie'] test = PytestTester() statsmodels-0.12.2/statsmodels/genmod/families/family.py000066400000000000000000001414611400612667500234130ustar00rootroot00000000000000''' The one parameter exponential family distributions used by GLM. ''' # TODO: quasi, quasibinomial, quasipoisson # see # http://www.biostat.jhsph.edu/~qli/biostatistics_r_doc/library/stats/html/family.html # for comparison to R, and McCullagh and Nelder import warnings import inspect import numpy as np from scipy import special from . import links as L from . import varfuncs as V FLOAT_EPS = np.finfo(float).eps class Family(object): """ The parent class for one-parameter exponential families. Parameters ---------- link : a link function instance Link is the linear transformation function. See the individual families for available links. variance : a variance function Measures the variance as a function of the mean probabilities. See the individual families for the default variance function. See Also -------- :ref:`links` : Further details on links. """ # TODO: change these class attributes, use valid somewhere... valid = [-np.inf, np.inf] links = [] def _setlink(self, link): """ Helper method to set the link for a family. Raises a ``ValueError`` exception if the link is not available. Note that the error message might not be that informative because it tells you that the link should be in the base class for the link function. See statsmodels.genmod.generalized_linear_model.GLM for a list of appropriate links for each family but note that not all of these are currently available. """ # TODO: change the links class attribute in the families to hold # meaningful information instead of a list of links instances such as # [, # , # ] # for Poisson... self._link = link if not isinstance(link, L.Link): raise TypeError("The input should be a valid Link object.") if hasattr(self, "links"): validlink = max([isinstance(link, _) for _ in self.links]) if not validlink: errmsg = "Invalid link for family, should be in %s. (got %s)" raise ValueError(errmsg % (repr(self.links), link)) def _getlink(self): """ Helper method to get the link for a family. """ return self._link # link property for each family is a pointer to link instance link = property(_getlink, _setlink, doc="Link function for family") def __init__(self, link, variance): if inspect.isclass(link): warnmssg = "Calling Family(..) with a link class as argument " warnmssg += "is deprecated.\n" warnmssg += "Use an instance of a link class instead." lvl = 2 if type(self) is Family else 3 warnings.warn(warnmssg, category=DeprecationWarning, stacklevel=lvl) self.link = link() else: self.link = link self.variance = variance def starting_mu(self, y): r""" Starting value for mu in the IRLS algorithm. Parameters ---------- y : ndarray The untransformed response variable. Returns ------- mu_0 : ndarray The first guess on the transformed response variable. Notes ----- .. math:: \mu_0 = (Y + \overline{Y})/2 Only the Binomial family takes a different initial value. """ return (y + y.mean())/2. def weights(self, mu): r""" Weights for IRLS steps Parameters ---------- mu : array_like The transformed mean response variable in the exponential family Returns ------- w : ndarray The weights for the IRLS steps Notes ----- .. math:: w = 1 / (g'(\mu)^2 * Var(\mu)) """ return 1. / (self.link.deriv(mu)**2 * self.variance(mu)) def deviance(self, endog, mu, var_weights=1., freq_weights=1., scale=1.): r""" The deviance function evaluated at (endog, mu, var_weights, freq_weights, scale) for the distribution. Deviance is usually defined as twice the loglikelihood ratio. Parameters ---------- endog : array_like The endogenous response variable mu : array_like The inverse of the link function at the linear predicted values. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. freq_weights : array_like 1d array of frequency weights. The default is 1. scale : float, optional An optional scale argument. The default is 1. Returns ------- Deviance : ndarray The value of deviance function defined below. Notes ----- Deviance is defined .. math:: D = 2\sum_i (freq\_weights_i * var\_weights * (llf(endog_i, endog_i) - llf(endog_i, \mu_i))) where y is the endogenous variable. The deviance functions are analytically defined for each family. Internally, we calculate deviance as: .. math:: D = \sum_i freq\_weights_i * var\_weights * resid\_dev_i / scale """ resid_dev = self._resid_dev(endog, mu) return np.sum(resid_dev * freq_weights * var_weights / scale) def resid_dev(self, endog, mu, var_weights=1., scale=1.): r""" The deviance residuals Parameters ---------- endog : array_like The endogenous response variable mu : array_like The inverse of the link function at the linear predicted values. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float, optional An optional scale argument. The default is 1. Returns ------- resid_dev : float Deviance residuals as defined below. Notes ----- The deviance residuals are defined by the contribution D_i of observation i to the deviance as .. math:: resid\_dev_i = sign(y_i-\mu_i) \sqrt{D_i} D_i is calculated from the _resid_dev method in each family. Distribution-specific documentation of the calculation is available there. """ resid_dev = self._resid_dev(endog, mu) resid_dev *= var_weights / scale return np.sign(endog - mu) * np.sqrt(np.clip(resid_dev, 0., np.inf)) def fitted(self, lin_pred): r""" Fitted values based on linear predictors lin_pred. Parameters ---------- lin_pred : ndarray Values of the linear predictor of the model. :math:`X \cdot \beta` in a classical linear model. Returns ------- mu : ndarray The mean response variables given by the inverse of the link function. """ fits = self.link.inverse(lin_pred) return fits def predict(self, mu): """ Linear predictors based on given mu values. Parameters ---------- mu : ndarray The mean response variables Returns ------- lin_pred : ndarray Linear predictors based on the mean response variables. The value of the link function at the given mu. """ return self.link(mu) def loglike_obs(self, endog, mu, var_weights=1., scale=1.): r""" The log-likelihood function for each observation in terms of the fitted mean response for the distribution. Parameters ---------- endog : ndarray Usually the endogenous response variable. mu : ndarray Usually but not always the fitted mean response variable. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float The scale parameter. The default is 1. Returns ------- ll_i : float The value of the loglikelihood evaluated at (endog, mu, var_weights, scale) as defined below. Notes ----- This is defined for each family. endog and mu are not restricted to ``endog`` and ``mu`` respectively. For instance, you could call both ``loglike(endog, endog)`` and ``loglike(endog, mu)`` to get the log-likelihood ratio. """ raise NotImplementedError def loglike(self, endog, mu, var_weights=1., freq_weights=1., scale=1.): r""" The log-likelihood function in terms of the fitted mean response. Parameters ---------- endog : ndarray Usually the endogenous response variable. mu : ndarray Usually but not always the fitted mean response variable. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. freq_weights : array_like 1d array of frequency weights. The default is 1. scale : float The scale parameter. The default is 1. Returns ------- ll : float The value of the loglikelihood evaluated at (endog, mu, var_weights, freq_weights, scale) as defined below. Notes ----- Where :math:`ll_i` is the by-observation log-likelihood: .. math:: ll = \sum(ll_i * freq\_weights_i) ``ll_i`` is defined for each family. endog and mu are not restricted to ``endog`` and ``mu`` respectively. For instance, you could call both ``loglike(endog, endog)`` and ``loglike(endog, mu)`` to get the log-likelihood ratio. """ ll_obs = self.loglike_obs(endog, mu, var_weights, scale) return np.sum(ll_obs * freq_weights) def resid_anscombe(self, endog, mu, var_weights=1., scale=1.): r""" The Anscombe residuals Parameters ---------- endog : ndarray The endogenous response variable mu : ndarray The inverse of the link function at the linear predicted values. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float, optional An optional argument to divide the residuals by sqrt(scale). The default is 1. See Also -------- statsmodels.genmod.families.family.Family : `resid_anscombe` for the individual families for more information Notes ----- Anscombe residuals are defined by .. math:: resid\_anscombe_i = \frac{A(y)-A(\mu)}{A'(\mu)\sqrt{Var[\mu]}} * \sqrt(var\_weights) where :math:`A'(y)=v(y)^{-\frac{1}{3}}` and :math:`v(\mu)` is the variance function :math:`Var[y]=\frac{\phi}{w}v(mu)`. The transformation :math:`A(y)` makes the residuals more normal distributed. """ raise NotImplementedError def _clean(self, x): """ Helper function to trim the data so that it is in (0,inf) Notes ----- The need for this function was discovered through usage and its possible that other families might need a check for validity of the domain. """ return np.clip(x, FLOAT_EPS, np.inf) class Poisson(Family): """ Poisson exponential family. Parameters ---------- link : a link instance, optional The default link for the Poisson family is the log link. Available links are log, identity, and sqrt. See statsmodels.families.links for more information. Attributes ---------- Poisson.link : a link instance The link function of the Poisson instance. Poisson.variance : varfuncs instance ``variance`` is an instance of statsmodels.genmod.families.varfuncs.mu See Also -------- statsmodels.genmod.families.family.Family : Parent class for all links. :ref:`links` : Further details on links. """ links = [L.log, L.identity, L.sqrt] variance = V.mu valid = [0, np.inf] safe_links = [L.Log, ] def __init__(self, link=None): if link is None: link = L.log() super(Poisson, self).__init__(link=link, variance=Poisson.variance) def _resid_dev(self, endog, mu): r""" Poisson deviance residuals Parameters ---------- endog : ndarray The endogenous response variable. mu : ndarray The inverse of the link function at the linear predicted values. Returns ------- resid_dev : float Deviance residuals as defined below. Notes ----- .. math:: resid\_dev_i = 2 * (endog_i * \ln(endog_i / \mu_i) - (endog_i - \mu_i)) """ endog_mu = self._clean(endog / mu) resid_dev = endog * np.log(endog_mu) - (endog - mu) return 2 * resid_dev def loglike_obs(self, endog, mu, var_weights=1., scale=1.): r""" The log-likelihood function for each observation in terms of the fitted mean response for the Poisson distribution. Parameters ---------- endog : ndarray Usually the endogenous response variable. mu : ndarray Usually but not always the fitted mean response variable. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float The scale parameter. The default is 1. Returns ------- ll_i : float The value of the loglikelihood evaluated at (endog, mu, var_weights, scale) as defined below. Notes ----- .. math:: ll_i = var\_weights_i / scale * (endog_i * \ln(\mu_i) - \mu_i - \ln \Gamma(endog_i + 1)) """ return var_weights / scale * (endog * np.log(mu) - mu - special.gammaln(endog + 1)) def resid_anscombe(self, endog, mu, var_weights=1., scale=1.): r""" The Anscombe residuals Parameters ---------- endog : ndarray The endogenous response variable mu : ndarray The inverse of the link function at the linear predicted values. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float, optional An optional argument to divide the residuals by sqrt(scale). The default is 1. Returns ------- resid_anscombe : ndarray The Anscombe residuals for the Poisson family defined below Notes ----- .. math:: resid\_anscombe_i = (3/2) * (endog_i^{2/3} - \mu_i^{2/3}) / \mu_i^{1/6} * \sqrt(var\_weights) """ resid = ((3 / 2.) * (endog**(2 / 3.) - mu**(2 / 3.)) / (mu ** (1 / 6.) * scale ** 0.5)) resid *= np.sqrt(var_weights) return resid class Gaussian(Family): """ Gaussian exponential family distribution. Parameters ---------- link : a link instance, optional The default link for the Gaussian family is the identity link. Available links are log, identity, and inverse. See statsmodels.genmod.families.links for more information. Attributes ---------- Gaussian.link : a link instance The link function of the Gaussian instance Gaussian.variance : varfunc instance ``variance`` is an instance of statsmodels.genmod.families.varfuncs.constant See Also -------- statsmodels.genmod.families.family.Family : Parent class for all links. :ref:`links` : Further details on links. """ links = [L.log, L.identity, L.inverse_power] variance = V.constant safe_links = links def __init__(self, link=None): if link is None: link = L.identity() super(Gaussian, self).__init__(link=link, variance=Gaussian.variance) def _resid_dev(self, endog, mu): r""" Gaussian deviance residuals Parameters ---------- endog : ndarray The endogenous response variable. mu : ndarray The inverse of the link function at the linear predicted values. Returns ------- resid_dev : float Deviance residuals as defined below. Notes -------- .. math:: resid\_dev_i = (endog_i - \mu_i) ** 2 """ return (endog - mu) ** 2 def loglike_obs(self, endog, mu, var_weights=1., scale=1.): r""" The log-likelihood function for each observation in terms of the fitted mean response for the Gaussian distribution. Parameters ---------- endog : ndarray Usually the endogenous response variable. mu : ndarray Usually but not always the fitted mean response variable. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float The scale parameter. The default is 1. Returns ------- ll_i : float The value of the loglikelihood evaluated at (endog, mu, var_weights, scale) as defined below. Notes ----- If the link is the identity link function then the loglikelihood function is the same as the classical OLS model. .. math:: llf = -nobs / 2 * (\log(SSR) + (1 + \log(2 \pi / nobs))) where .. math:: SSR = \sum_i (Y_i - g^{-1}(\mu_i))^2 If the links is not the identity link then the loglikelihood function is defined as .. math:: ll_i = -1 / 2 \sum_i * var\_weights * ((Y_i - mu_i)^2 / scale + \log(2 * \pi * scale)) """ ll_obs = -var_weights * (endog - mu) ** 2 / scale ll_obs += -np.log(scale / var_weights) - np.log(2 * np.pi) ll_obs /= 2 return ll_obs def resid_anscombe(self, endog, mu, var_weights=1., scale=1.): r""" The Anscombe residuals Parameters ---------- endog : ndarray The endogenous response variable mu : ndarray The inverse of the link function at the linear predicted values. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float, optional An optional argument to divide the residuals by sqrt(scale). The default is 1. Returns ------- resid_anscombe : ndarray The Anscombe residuals for the Gaussian family defined below Notes ----- For the Gaussian distribution, Anscombe residuals are the same as deviance residuals. .. math:: resid\_anscombe_i = (Y_i - \mu_i) / \sqrt{scale} * \sqrt(var\_weights) """ resid = (endog - mu) / scale ** 0.5 resid *= np.sqrt(var_weights) return resid class Gamma(Family): """ Gamma exponential family distribution. Parameters ---------- link : a link instance, optional The default link for the Gamma family is the inverse link. Available links are log, identity, and inverse. See statsmodels.genmod.families.links for more information. Attributes ---------- Gamma.link : a link instance The link function of the Gamma instance Gamma.variance : varfunc instance ``variance`` is an instance of statsmodels.genmod.family.varfuncs.mu_squared See Also -------- statsmodels.genmod.families.family.Family : Parent class for all links. :ref:`links` : Further details on links. """ links = [L.log, L.identity, L.inverse_power] variance = V.mu_squared safe_links = [L.Log, ] def __init__(self, link=None): if link is None: link = L.inverse_power() super(Gamma, self).__init__(link=link, variance=Gamma.variance) def _resid_dev(self, endog, mu): r""" Gamma deviance residuals Parameters ---------- endog : ndarray The endogenous response variable. mu : ndarray The inverse of the link function at the linear predicted values. Returns ------- resid_dev : float Deviance residuals as defined below. Notes ----- .. math:: resid\_dev_i = 2 * ((endog_i - \mu_i) / \mu_i - \log(endog_i / \mu_i)) """ endog_mu = self._clean(endog / mu) resid_dev = -np.log(endog_mu) + (endog - mu) / mu return 2 * resid_dev def loglike_obs(self, endog, mu, var_weights=1., scale=1.): r""" The log-likelihood function for each observation in terms of the fitted mean response for the Gamma distribution. Parameters ---------- endog : ndarray Usually the endogenous response variable. mu : ndarray Usually but not always the fitted mean response variable. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float The scale parameter. The default is 1. Returns ------- ll_i : float The value of the loglikelihood evaluated at (endog, mu, var_weights, scale) as defined below. Notes ----- .. math:: ll_i = var\_weights_i / scale * (\ln(var\_weights_i * endog_i / (scale * \mu_i)) - (var\_weights_i * endog_i) / (scale * \mu_i)) - \ln \Gamma(var\_weights_i / scale) - \ln(\mu_i) """ endog_mu = self._clean(endog / mu) weight_scale = var_weights / scale ll_obs = weight_scale * np.log(weight_scale * endog_mu) ll_obs -= weight_scale * endog_mu ll_obs -= special.gammaln(weight_scale) + np.log(endog) return ll_obs # in Stata scale is set to equal 1 for reporting llf # in R it's the dispersion, though there is a loss of precision vs. # our results due to an assumed difference in implementation def resid_anscombe(self, endog, mu, var_weights=1., scale=1.): r""" The Anscombe residuals Parameters ---------- endog : ndarray The endogenous response variable mu : ndarray The inverse of the link function at the linear predicted values. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float, optional An optional argument to divide the residuals by sqrt(scale). The default is 1. Returns ------- resid_anscombe : ndarray The Anscombe residuals for the Gamma family defined below Notes ----- .. math:: resid\_anscombe_i = 3 * (endog_i^{1/3} - \mu_i^{1/3}) / \mu_i^{1/3} / \sqrt{scale} * \sqrt(var\_weights) """ resid = 3 * (endog**(1/3.) - mu**(1/3.)) / mu**(1/3.) / scale ** 0.5 resid *= np.sqrt(var_weights) return resid class Binomial(Family): """ Binomial exponential family distribution. Parameters ---------- link : a link instance, optional The default link for the Binomial family is the logit link. Available links are logit, probit, cauchy, log, and cloglog. See statsmodels.genmod.families.links for more information. Attributes ---------- Binomial.link : a link instance The link function of the Binomial instance Binomial.variance : varfunc instance ``variance`` is an instance of statsmodels.genmod.families.varfuncs.binary See Also -------- statsmodels.genmod.families.family.Family : Parent class for all links. :ref:`links` : Further details on links. Notes ----- endog for Binomial can be specified in one of three ways: A 1d array of 0 or 1 values, indicating failure or success respectively. A 2d array, with two columns. The first column represents the success count and the second column represents the failure count. A 1d array of proportions, indicating the proportion of successes, with parameter `var_weights` containing the number of trials for each row. """ links = [L.logit, L.probit, L.cauchy, L.log, L.cloglog, L.identity] variance = V.binary # this is not used below in an effort to include n # Other safe links, e.g. cloglog and probit are subclasses safe_links = [L.Logit, L.CDFLink] def __init__(self, link=None): # , n=1.): if link is None: link = L.logit() # TODO: it *should* work for a constant n>1 actually, if freq_weights # is equal to n self.n = 1 # overwritten by initialize if needed but always used to initialize # variance since endog is assumed/forced to be (0,1) super(Binomial, self).__init__(link=link, variance=V.Binomial(n=self.n)) def starting_mu(self, y): r""" The starting values for the IRLS algorithm for the Binomial family. A good choice for the binomial family is :math:`\mu_0 = (Y_i + 0.5)/2` """ return (y + .5)/2 def initialize(self, endog, freq_weights): ''' Initialize the response variable. Parameters ---------- endog : ndarray Endogenous response variable freq_weights : ndarray 1d array of frequency weights Returns ------- If `endog` is binary, returns `endog` If `endog` is a 2d array, then the input is assumed to be in the format (successes, failures) and successes/(success + failures) is returned. And n is set to successes + failures. ''' # if not np.all(np.asarray(freq_weights) == 1): # self.variance = V.Binomial(n=freq_weights) if endog.ndim > 1 and endog.shape[1] > 2: raise ValueError('endog has more than 2 columns. The Binomial ' 'link supports either a single response variable ' 'or a paired response variable.') elif endog.ndim > 1 and endog.shape[1] > 1: y = endog[:, 0] # overwrite self.freq_weights for deviance below self.n = endog.sum(1) return y*1./self.n, self.n else: return endog, np.ones(endog.shape[0]) def _resid_dev(self, endog, mu): r""" Binomial deviance residuals Parameters ---------- endog : ndarray The endogenous response variable. mu : ndarray The inverse of the link function at the linear predicted values. Returns ------- resid_dev : float Deviance residuals as defined below. Notes ----- .. math:: resid\_dev_i = 2 * n * (endog_i * \ln(endog_i /\mu_i) + (1 - endog_i) * \ln((1 - endog_i) / (1 - \mu_i))) """ endog_mu = self._clean(endog / (mu + 1e-20)) n_endog_mu = self._clean((1. - endog) / (1. - mu + 1e-20)) resid_dev = endog * np.log(endog_mu) + (1 - endog) * np.log(n_endog_mu) return 2 * self.n * resid_dev def loglike_obs(self, endog, mu, var_weights=1., scale=1.): r""" The log-likelihood function for each observation in terms of the fitted mean response for the Binomial distribution. Parameters ---------- endog : ndarray Usually the endogenous response variable. mu : ndarray Usually but not always the fitted mean response variable. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float The scale parameter. The default is 1. Returns ------- ll_i : float The value of the loglikelihood evaluated at (endog, mu, var_weights, scale) as defined below. Notes ----- If the endogenous variable is binary: .. math:: ll_i = \sum_i (y_i * \log(\mu_i/(1-\mu_i)) + \log(1-\mu_i)) * var\_weights_i If the endogenous variable is binomial: .. math:: ll_i = \sum_i var\_weights_i * (\ln \Gamma(n+1) - \ln \Gamma(y_i + 1) - \ln \Gamma(n_i - y_i +1) + y_i * \log(\mu_i / (n_i - \mu_i)) + n * \log(1 - \mu_i/n_i)) where :math:`y_i = Y_i * n_i` with :math:`Y_i` and :math:`n_i` as defined in Binomial initialize. This simply makes :math:`y_i` the original number of successes. """ n = self.n # Number of trials y = endog * n # Number of successes # note that mu is still in (0,1), i.e. not converted back return (special.gammaln(n + 1) - special.gammaln(y + 1) - special.gammaln(n - y + 1) + y * np.log(mu / (1 - mu + 1e-20)) + n * np.log(1 - mu + 1e-20)) * var_weights def resid_anscombe(self, endog, mu, var_weights=1., scale=1.): r''' The Anscombe residuals Parameters ---------- endog : ndarray The endogenous response variable mu : ndarray The inverse of the link function at the linear predicted values. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float, optional An optional argument to divide the residuals by sqrt(scale). The default is 1. Returns ------- resid_anscombe : ndarray The Anscombe residuals as defined below. Notes ----- .. math:: n^{2/3}*(cox\_snell(endog)-cox\_snell(mu)) / (mu*(1-mu/n)*scale^3)^{1/6} * \sqrt(var\_weights) where cox_snell is defined as cox_snell(x) = betainc(2/3., 2/3., x)*betainc(2/3.,2/3.) where betainc is the incomplete beta function as defined in scipy, which uses a regularized version (with the unregularized version, one would just have :math:`cox_snell(x) = Betainc(2/3., 2/3., x)`). The name 'cox_snell' is idiosyncratic and is simply used for convenience following the approach suggested in Cox and Snell (1968). Further note that :math:`cox\_snell(x) = \frac{3}{2}*x^{2/3} * hyp2f1(2/3.,1/3.,5/3.,x)` where hyp2f1 is the hypergeometric 2f1 function. The Anscombe residuals are sometimes defined in the literature using the hyp2f1 formulation. Both betainc and hyp2f1 can be found in scipy. References ---------- Anscombe, FJ. (1953) "Contribution to the discussion of H. Hotelling's paper." Journal of the Royal Statistical Society B. 15, 229-30. Cox, DR and Snell, EJ. (1968) "A General Definition of Residuals." Journal of the Royal Statistical Society B. 30, 248-75. ''' endog = endog * self.n # convert back to successes mu = mu * self.n # convert back to successes def cox_snell(x): return special.betainc(2/3., 2/3., x) * special.beta(2/3., 2/3.) resid = (self.n ** (2/3.) * (cox_snell(endog * 1. / self.n) - cox_snell(mu * 1. / self.n)) / (mu * (1 - mu * 1. / self.n) * scale ** 3) ** (1 / 6.)) resid *= np.sqrt(var_weights) return resid class InverseGaussian(Family): """ InverseGaussian exponential family. Parameters ---------- link : a link instance, optional The default link for the inverse Gaussian family is the inverse squared link. Available links are inverse_squared, inverse, log, and identity. See statsmodels.genmod.families.links for more information. Attributes ---------- InverseGaussian.link : a link instance The link function of the inverse Gaussian instance InverseGaussian.variance : varfunc instance ``variance`` is an instance of statsmodels.genmod.families.varfuncs.mu_cubed See Also -------- statsmodels.genmod.families.family.Family : Parent class for all links. :ref:`links` : Further details on links. Notes ----- The inverse Gaussian distribution is sometimes referred to in the literature as the Wald distribution. """ links = [L.inverse_squared, L.inverse_power, L.identity, L.log] variance = V.mu_cubed safe_links = [L.inverse_squared, L.Log, ] def __init__(self, link=None): if link is None: link = L.inverse_squared() super(InverseGaussian, self).__init__( link=link, variance=InverseGaussian.variance) def _resid_dev(self, endog, mu): r""" Inverse Gaussian deviance residuals Parameters ---------- endog : ndarray The endogenous response variable. mu : ndarray The inverse of the link function at the linear predicted values. Returns ------- resid_dev : float Deviance residuals as defined below. Notes ----- .. math:: resid\_dev_i = 1 / (endog_i * \mu_i^2) * (endog_i - \mu_i)^2 """ return 1. / (endog * mu ** 2) * (endog - mu) ** 2 def loglike_obs(self, endog, mu, var_weights=1., scale=1.): r""" The log-likelihood function for each observation in terms of the fitted mean response for the Inverse Gaussian distribution. Parameters ---------- endog : ndarray Usually the endogenous response variable. mu : ndarray Usually but not always the fitted mean response variable. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float The scale parameter. The default is 1. Returns ------- ll_i : float The value of the loglikelihood evaluated at (endog, mu, var_weights, scale) as defined below. Notes ----- .. math:: ll_i = -1/2 * (var\_weights_i * (endog_i - \mu_i)^2 / (scale * endog_i * \mu_i^2) + \ln(scale * \endog_i^3 / var\_weights_i) - \ln(2 * \pi)) """ ll_obs = -var_weights * (endog - mu) ** 2 / (scale * endog * mu ** 2) ll_obs += -np.log(scale * endog ** 3 / var_weights) - np.log(2 * np.pi) ll_obs /= 2 return ll_obs def resid_anscombe(self, endog, mu, var_weights=1., scale=1.): r""" The Anscombe residuals Parameters ---------- endog : ndarray The endogenous response variable mu : ndarray The inverse of the link function at the linear predicted values. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float, optional An optional argument to divide the residuals by sqrt(scale). The default is 1. Returns ------- resid_anscombe : ndarray The Anscombe residuals for the inverse Gaussian distribution as defined below Notes ----- .. math:: resid\_anscombe_i = \log(Y_i / \mu_i) / \sqrt{\mu_i * scale} * \sqrt(var\_weights) """ resid = np.log(endog / mu) / np.sqrt(mu * scale) resid *= np.sqrt(var_weights) return resid class NegativeBinomial(Family): r""" Negative Binomial exponential family. Parameters ---------- link : a link instance, optional The default link for the negative binomial family is the log link. Available links are log, cloglog, identity, nbinom and power. See statsmodels.genmod.families.links for more information. alpha : float, optional The ancillary parameter for the negative binomial distribution. For now ``alpha`` is assumed to be nonstochastic. The default value is 1. Permissible values are usually assumed to be between .01 and 2. Attributes ---------- NegativeBinomial.link : a link instance The link function of the negative binomial instance NegativeBinomial.variance : varfunc instance ``variance`` is an instance of statsmodels.genmod.families.varfuncs.nbinom See Also -------- statsmodels.genmod.families.family.Family : Parent class for all links. :ref:`links` : Further details on links. Notes ----- Power link functions are not yet supported. Parameterization for :math:`y=0, 1, 2, \ldots` is .. math:: f(y) = \frac{\Gamma(y+\frac{1}{\alpha})}{y!\Gamma(\frac{1}{\alpha})} \left(\frac{1}{1+\alpha\mu}\right)^{\frac{1}{\alpha}} \left(\frac{\alpha\mu}{1+\alpha\mu}\right)^y with :math:`E[Y]=\mu\,` and :math:`Var[Y]=\mu+\alpha\mu^2`. """ links = [L.log, L.cloglog, L.identity, L.nbinom, L.Power] # TODO: add the ability to use the power links with an if test # similar to below variance = V.nbinom safe_links = [L.Log, ] def __init__(self, link=None, alpha=1.): self.alpha = 1. * alpha # make it at least float if link is None: link = L.log() super(NegativeBinomial, self).__init__( link=link, variance=V.NegativeBinomial(alpha=self.alpha)) def _resid_dev(self, endog, mu): r""" Negative Binomial deviance residuals Parameters ---------- endog : ndarray The endogenous response variable. mu : ndarray The inverse of the link function at the linear predicted values. Returns ------- resid_dev : float Deviance residuals as defined below. Notes ----- .. math:: resid_dev_i = 2 * (endog_i * \ln(endog_i / \mu_i) - (endog_i + 1 / \alpha) * \ln((endog_i + 1 / \alpha) / (\mu_i + 1 / \alpha))) """ endog_mu = self._clean(endog / mu) endog_alpha = endog + 1 / self.alpha mu_alpha = mu + 1 / self.alpha resid_dev = endog * np.log(endog_mu) resid_dev -= endog_alpha * np.log(endog_alpha / mu_alpha) return 2 * resid_dev def loglike_obs(self, endog, mu, var_weights=1., scale=1.): r""" The log-likelihood function for each observation in terms of the fitted mean response for the Negative Binomial distribution. Parameters ---------- endog : ndarray Usually the endogenous response variable. mu : ndarray Usually but not always the fitted mean response variable. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float The scale parameter. The default is 1. Returns ------- ll_i : float The value of the loglikelihood evaluated at (endog, mu, var_weights, scale) as defined below. Notes ----- Defined as: .. math:: llf = \sum_i var\_weights_i / scale * (Y_i * \log{(\alpha * \mu_i / (1 + \alpha * \mu_i))} - \log{(1 + \alpha * \mu_i)}/ \alpha + Constant) where :math:`Constant` is defined as: .. math:: Constant = \ln \Gamma{(Y_i + 1/ \alpha )} - \ln \Gamma(Y_i + 1) - \ln \Gamma{(1/ \alpha )} constant = (special.gammaln(endog + 1 / self.alpha) - special.gammaln(endog+1)-special.gammaln(1/self.alpha)) return (endog * np.log(self.alpha * mu / (1 + self.alpha * mu)) - np.log(1 + self.alpha * mu) / self.alpha + constant) * var_weights / scale """ ll_obs = endog * np.log(self.alpha * mu) ll_obs -= (endog + 1 / self.alpha) * np.log(1 + self.alpha * mu) ll_obs += special.gammaln(endog + 1 / self.alpha) ll_obs -= special.gammaln(1 / self.alpha) ll_obs -= special.gammaln(endog + 1) return var_weights / scale * ll_obs def resid_anscombe(self, endog, mu, var_weights=1., scale=1.): r""" The Anscombe residuals Parameters ---------- endog : ndarray The endogenous response variable mu : ndarray The inverse of the link function at the linear predicted values. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float, optional An optional argument to divide the residuals by sqrt(scale). The default is 1. Returns ------- resid_anscombe : ndarray The Anscombe residuals as defined below. Notes ----- Anscombe residuals for Negative Binomial are the same as for Binomial upon setting :math:`n=-\frac{1}{\alpha}`. Due to the negative value of :math:`-\alpha*Y` the representation with the hypergeometric function :math:`H2F1(x) = hyp2f1(2/3.,1/3.,5/3.,x)` is advantageous .. math:: resid\_anscombe_i = \frac{3}{2} * (Y_i^(2/3)*H2F1(-\alpha*Y_i) - \mu_i^(2/3)*H2F1(-\alpha*\mu_i)) / (\mu_i * (1+\alpha*\mu_i) * scale^3)^(1/6) * \sqrt(var\_weights) Note that for the (unregularized) Beta function, one has :math:`Beta(z,a,b) = z^a/a * H2F1(a,1-b,a+1,z)` """ def hyp2f1(x): return special.hyp2f1(2 / 3., 1 / 3., 5 / 3., x) resid = (3 / 2. * (endog ** (2 / 3.) * hyp2f1(-self.alpha * endog) - mu ** (2 / 3.) * hyp2f1(-self.alpha * mu)) / (mu * (1 + self.alpha * mu) * scale ** 3) ** (1 / 6.)) resid *= np.sqrt(var_weights) return resid class Tweedie(Family): """ Tweedie family. Parameters ---------- link : a link instance, optional The default link for the Tweedie family is the log link. Available links are log and Power. See statsmodels.genmod.families.links for more information. var_power : float, optional The variance power. The default is 1. eql : bool If True, the Extended Quasi-Likelihood is used, else the likelihood is used (however the latter is not implemented). If eql is True, var_power must be between 1 and 2. Attributes ---------- Tweedie.link : a link instance The link function of the Tweedie instance Tweedie.variance : varfunc instance ``variance`` is an instance of statsmodels.genmod.families.varfuncs.Power Tweedie.var_power : float The power of the variance function. See Also -------- statsmodels.genmod.families.family.Family : Parent class for all links. :ref:`links` : Further details on links. Notes ----- Loglikelihood function not implemented because of the complexity of calculating an infinite series of summations. The variance power can be estimated using the ``estimate_tweedie_power`` function that is part of the statsmodels.genmod.generalized_linear_model.GLM class. """ links = [L.log, L.Power] variance = V.Power(power=1.5) safe_links = [L.log, L.Power] def __init__(self, link=None, var_power=1., eql=False): self.var_power = var_power self.eql = eql if eql and (var_power < 1 or var_power > 2): raise ValueError("Tweedie: if EQL=True then var_power must fall " "between 1 and 2") if link is None: link = L.log() super(Tweedie, self).__init__( link=link, variance=V.Power(power=var_power * 1.)) def _resid_dev(self, endog, mu): r""" Tweedie deviance residuals Parameters ---------- endog : ndarray The endogenous response variable. mu : ndarray The inverse of the link function at the linear predicted values. Returns ------- resid_dev : float Deviance residuals as defined below. Notes ----- When :math:`p = 1`, .. math:: dev_i = \mu_i when :math:`endog_i = 0` and .. math:: dev_i = endog_i * \log(endog_i / \mu_i) + (\mu_i - endog_i) otherwise. When :math:`p = 2`, .. math:: dev_i = (endog_i - \mu_i) / \mu_i - \log(endog_i / \mu_i) For all other p, .. math:: dev_i = endog_i^{2 - p} / ((1 - p) * (2 - p)) - endog_i * \mu_i^{1 - p} / (1 - p) + \mu_i^{2 - p} / (2 - p) The deviance residual is then .. math:: resid\_dev_i = 2 * dev_i """ p = self.var_power if p == 1: dev = np.where(endog == 0, mu, endog * np.log(endog / mu) + (mu - endog)) elif p == 2: endog1 = self._clean(endog) dev = ((endog - mu) / mu) - np.log(endog1 / mu) else: dev = (endog ** (2 - p) / ((1 - p) * (2 - p)) - endog * mu ** (1-p) / (1 - p) + mu ** (2 - p) / (2 - p)) return 2 * dev def loglike_obs(self, endog, mu, var_weights=1., scale=1.): r""" The log-likelihood function for each observation in terms of the fitted mean response for the Tweedie distribution. Parameters ---------- endog : ndarray Usually the endogenous response variable. mu : ndarray Usually but not always the fitted mean response variable. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float The scale parameter. The default is 1. Returns ------- ll_i : float The value of the loglikelihood evaluated at (endog, mu, var_weights, scale) as defined below. Notes ----- If eql is True, the Extended Quasi-Likelihood is used. At present, this method returns NaN if eql is False. When the actual likelihood is implemented, it will be accessible by setting eql to False. References ---------- JA Nelder, D Pregibon (1987). An extended quasi-likelihood function. Biometrika 74:2, pp 221-232. https://www.jstor.org/stable/2336136 """ if not self.eql: # We have not yet implemented the actual likelihood return np.nan # Equations 9-10 or Nelder and Pregibon p = self.var_power llf = np.log(2 * np.pi * scale) + p * np.log(mu) - np.log(var_weights) llf /= -2 if p == 1: u = endog * np.log(endog / mu) - (endog - mu) u *= var_weights / scale elif p == 2: yr = endog / mu u = yr - np.log(yr) - 1 u *= var_weights / scale else: u = (endog ** (2 - p) - (2 - p) * endog * mu ** (1 - p) + (1 - p) * mu ** (2 - p)) u *= var_weights / (scale * (1 - p) * (2 - p)) llf -= u return llf def resid_anscombe(self, endog, mu, var_weights=1., scale=1.): r""" The Anscombe residuals Parameters ---------- endog : ndarray The endogenous response variable mu : ndarray The inverse of the link function at the linear predicted values. var_weights : array_like 1d array of variance (analytic) weights. The default is 1. scale : float, optional An optional argument to divide the residuals by sqrt(scale). The default is 1. Returns ------- resid_anscombe : ndarray The Anscombe residuals as defined below. Notes ----- When :math:`p = 3`, then .. math:: resid\_anscombe_i = \log(endog_i / \mu_i) / \sqrt{\mu_i * scale} * \sqrt(var\_weights) Otherwise, .. math:: c = (3 - p) / 3 .. math:: resid\_anscombe_i = (1 / c) * (endog_i^c - \mu_i^c) / \mu_i^{p / 6} / \sqrt{scale} * \sqrt(var\_weights) """ if self.var_power == 3: resid = np.log(endog / mu) / np.sqrt(mu * scale) else: c = (3. - self.var_power) / 3. resid = ((1. / c) * (endog ** c - mu ** c) / mu ** (self.var_power / 6.)) / scale ** 0.5 resid *= np.sqrt(var_weights) return resid statsmodels-0.12.2/statsmodels/genmod/families/links.py000066400000000000000000000534631400612667500232560ustar00rootroot00000000000000''' Defines the link functions to be used with GLM and GEE families. ''' import numpy as np import scipy.stats FLOAT_EPS = np.finfo(float).eps class Link(object): """ A generic link function for one-parameter exponential family. `Link` does nothing, but lays out the methods expected of any subclass. """ def __call__(self, p): """ Return the value of the link function. This is just a placeholder. Parameters ---------- p : array_like Probabilities Returns ------- g(p) : array_like The value of the link function g(p) = z """ return NotImplementedError def inverse(self, z): """ Inverse of the link function. Just a placeholder. Parameters ---------- z : array_like `z` is usually the linear predictor of the transformed variable in the IRLS algorithm for GLM. Returns ------- g^(-1)(z) : ndarray The value of the inverse of the link function g^(-1)(z) = p """ return NotImplementedError def deriv(self, p): """ Derivative of the link function g'(p). Just a placeholder. Parameters ---------- p : array_like Returns ------- g'(p) : ndarray The value of the derivative of the link function g'(p) """ return NotImplementedError def deriv2(self, p): """Second derivative of the link function g''(p) implemented through numerical differentiation """ from statsmodels.tools.numdiff import approx_fprime_cs # TODO: workaround proplem with numdiff for 1d return np.diag(approx_fprime_cs(p, self.deriv)) def inverse_deriv(self, z): """ Derivative of the inverse link function g^(-1)(z). Parameters ---------- z : array_like `z` is usually the linear predictor for a GLM or GEE model. Returns ------- g'^(-1)(z) : ndarray The value of the derivative of the inverse of the link function Notes ----- This reference implementation gives the correct result but is inefficient, so it can be overridden in subclasses. """ return 1 / self.deriv(self.inverse(z)) def inverse_deriv2(self, z): """ Second derivative of the inverse link function g^(-1)(z). Parameters ---------- z : array_like `z` is usually the linear predictor for a GLM or GEE model. Returns ------- g'^(-1)(z) : ndarray The value of the second derivative of the inverse of the link function Notes ----- This reference implementation gives the correct result but is inefficient, so it can be overridden in subclasses. """ iz = self.inverse(z) return -self.deriv2(iz) / self.deriv(iz)**3 class Logit(Link): """ The logit transform Notes ----- call and derivative use a private method _clean to make trim p by machine epsilon so that p is in (0,1) Alias of Logit: logit = Logit() """ def _clean(self, p): """ Clip logistic values to range (eps, 1-eps) Parameters ---------- p : array_like Probabilities Returns ------- pclip : ndarray Clipped probabilities """ return np.clip(p, FLOAT_EPS, 1. - FLOAT_EPS) def __call__(self, p): """ The logit transform Parameters ---------- p : array_like Probabilities Returns ------- z : ndarray Logit transform of `p` Notes ----- g(p) = log(p / (1 - p)) """ p = self._clean(p) return np.log(p / (1. - p)) def inverse(self, z): """ Inverse of the logit transform Parameters ---------- z : array_like The value of the logit transform at `p` Returns ------- p : ndarray Probabilities Notes ----- g^(-1)(z) = exp(z)/(1+exp(z)) """ z = np.asarray(z) t = np.exp(-z) return 1. / (1. + t) def deriv(self, p): """ Derivative of the logit transform Parameters ---------- p : array_like Probabilities Returns ------- g'(p) : ndarray Value of the derivative of logit transform at `p` Notes ----- g'(p) = 1 / (p * (1 - p)) Alias for `Logit`: logit = Logit() """ p = self._clean(p) return 1. / (p * (1 - p)) def inverse_deriv(self, z): """ Derivative of the inverse of the logit transform Parameters ---------- z : array_like `z` is usually the linear predictor for a GLM or GEE model. Returns ------- g'^(-1)(z) : ndarray The value of the derivative of the inverse of the logit function """ t = np.exp(z) return t/(1 + t)**2 def deriv2(self, p): """ Second derivative of the logit function. Parameters ---------- p : array_like probabilities Returns ------- g''(z) : ndarray The value of the second derivative of the logit function """ v = p * (1 - p) return (2*p - 1) / v**2 class logit(Logit): pass class Power(Link): """ The power transform Parameters ---------- power : float The exponent of the power transform Notes ----- Aliases of Power: inverse = Power(power=-1) sqrt = Power(power=.5) inverse_squared = Power(power=-2.) identity = Power(power=1.) """ def __init__(self, power=1.): self.power = power def __call__(self, p): """ Power transform link function Parameters ---------- p : array_like Mean parameters Returns ------- z : array_like Power transform of x Notes ----- g(p) = x**self.power """ if self.power == 1: return p else: return np.power(p, self.power) def inverse(self, z): """ Inverse of the power transform link function Parameters ---------- `z` : array_like Value of the transformed mean parameters at `p` Returns ------- `p` : ndarray Mean parameters Notes ----- g^(-1)(z`) = `z`**(1/`power`) """ if self.power == 1: return z else: return np.power(z, 1. / self.power) def deriv(self, p): """ Derivative of the power transform Parameters ---------- p : array_like Mean parameters Returns ------- g'(p) : ndarray Derivative of power transform of `p` Notes ----- g'(`p`) = `power` * `p`**(`power` - 1) """ if self.power == 1: return np.ones_like(p) else: return self.power * np.power(p, self.power - 1) def deriv2(self, p): """ Second derivative of the power transform Parameters ---------- p : array_like Mean parameters Returns ------- g''(p) : ndarray Second derivative of the power transform of `p` Notes ----- g''(`p`) = `power` * (`power` - 1) * `p`**(`power` - 2) """ if self.power == 1: return np.zeros_like(p) else: return self.power * (self.power - 1) * np.power(p, self.power - 2) def inverse_deriv(self, z): """ Derivative of the inverse of the power transform Parameters ---------- z : array_like `z` is usually the linear predictor for a GLM or GEE model. Returns ------- g^(-1)'(z) : ndarray The value of the derivative of the inverse of the power transform function """ if self.power == 1: return np.ones_like(z) else: return np.power(z, (1 - self.power)/self.power) / self.power def inverse_deriv2(self, z): """ Second derivative of the inverse of the power transform Parameters ---------- z : array_like `z` is usually the linear predictor for a GLM or GEE model. Returns ------- g^(-1)'(z) : ndarray The value of the derivative of the inverse of the power transform function """ if self.power == 1: return np.zeros_like(z) else: return ((1 - self.power) * np.power(z, (1 - 2*self.power)/self.power) / self.power**2) class inverse_power(Power): """ The inverse transform Notes ----- g(p) = 1/p Alias of statsmodels.family.links.Power(power=-1.) """ def __init__(self): super(inverse_power, self).__init__(power=-1.) class sqrt(Power): """ The square-root transform Notes ----- g(`p`) = sqrt(`p`) Alias of statsmodels.family.links.Power(power=.5) """ def __init__(self): super(sqrt, self).__init__(power=.5) class inverse_squared(Power): r""" The inverse squared transform Notes ----- g(`p`) = 1/(`p`\*\*2) Alias of statsmodels.family.links.Power(power=2.) """ def __init__(self): super(inverse_squared, self).__init__(power=-2.) class identity(Power): """ The identity transform Notes ----- g(`p`) = `p` Alias of statsmodels.family.links.Power(power=1.) """ def __init__(self): super(identity, self).__init__(power=1.) class Log(Link): """ The log transform Notes ----- call and derivative call a private method _clean to trim the data by machine epsilon so that p is in (0,1). log is an alias of Log. """ def _clean(self, x): return np.clip(x, FLOAT_EPS, np.inf) def __call__(self, p, **extra): """ Log transform link function Parameters ---------- x : array_like Mean parameters Returns ------- z : ndarray log(x) Notes ----- g(p) = log(p) """ x = self._clean(p) return np.log(x) def inverse(self, z): """ Inverse of log transform link function Parameters ---------- z : ndarray The inverse of the link function at `p` Returns ------- p : ndarray The mean probabilities given the value of the inverse `z` Notes ----- g^{-1}(z) = exp(z) """ return np.exp(z) def deriv(self, p): """ Derivative of log transform link function Parameters ---------- p : array_like Mean parameters Returns ------- g'(p) : ndarray derivative of log transform of x Notes ----- g'(x) = 1/x """ p = self._clean(p) return 1. / p def deriv2(self, p): """ Second derivative of the log transform link function Parameters ---------- p : array_like Mean parameters Returns ------- g''(p) : ndarray Second derivative of log transform of x Notes ----- g''(x) = -1/x^2 """ p = self._clean(p) return -1. / p**2 def inverse_deriv(self, z): """ Derivative of the inverse of the log transform link function Parameters ---------- z : ndarray The inverse of the link function at `p` Returns ------- g^(-1)'(z) : ndarray The value of the derivative of the inverse of the log function, the exponential function """ return np.exp(z) class log(Log): """ The log transform Notes ----- log is a an alias of Log. """ pass # TODO: the CDFLink is untested class CDFLink(Logit): """ The use the CDF of a scipy.stats distribution CDFLink is a subclass of logit in order to use its _clean method for the link and its derivative. Parameters ---------- dbn : scipy.stats distribution Default is dbn=scipy.stats.norm Notes ----- The CDF link is untested. """ def __init__(self, dbn=scipy.stats.norm): self.dbn = dbn def __call__(self, p): """ CDF link function Parameters ---------- p : array_like Mean parameters Returns ------- z : ndarray (ppf) inverse of CDF transform of p Notes ----- g(`p`) = `dbn`.ppf(`p`) """ p = self._clean(p) return self.dbn.ppf(p) def inverse(self, z): """ The inverse of the CDF link Parameters ---------- z : array_like The value of the inverse of the link function at `p` Returns ------- p : ndarray Mean probabilities. The value of the inverse of CDF link of `z` Notes ----- g^(-1)(`z`) = `dbn`.cdf(`z`) """ return self.dbn.cdf(z) def deriv(self, p): """ Derivative of CDF link Parameters ---------- p : array_like mean parameters Returns ------- g'(p) : ndarray The derivative of CDF transform at `p` Notes ----- g'(`p`) = 1./ `dbn`.pdf(`dbn`.ppf(`p`)) """ p = self._clean(p) return 1. / self.dbn.pdf(self.dbn.ppf(p)) def deriv2(self, p): """ Second derivative of the link function g''(p) implemented through numerical differentiation """ from statsmodels.tools.numdiff import approx_fprime p = np.atleast_1d(p) # Note: special function for norm.ppf does not support complex return np.diag(approx_fprime(p, self.deriv, centered=True)) def inverse_deriv(self, z): """ Derivative of the inverse of the CDF transformation link function Parameters ---------- z : ndarray The inverse of the link function at `p` Returns ------- g^(-1)'(z) : ndarray The value of the derivative of the inverse of the logit function """ return 1/self.deriv(self.inverse(z)) class probit(CDFLink): """ The probit (standard normal CDF) transform Notes ----- g(p) = scipy.stats.norm.ppf(p) probit is an alias of CDFLink. """ def inverse_deriv2(self, z): """ Second derivative of the inverse link function This is the derivative of the pdf in a CDFLink """ return - z * self.dbn.pdf(z) def deriv2(self, p): """ Second derivative of the link function g''(p) """ p = self._clean(p) linpred = self.dbn.ppf(p) return linpred / self.dbn.pdf(linpred)**2 class cauchy(CDFLink): """ The Cauchy (standard Cauchy CDF) transform Notes ----- g(p) = scipy.stats.cauchy.ppf(p) cauchy is an alias of CDFLink with dbn=scipy.stats.cauchy """ def __init__(self): super(cauchy, self).__init__(dbn=scipy.stats.cauchy) def deriv2(self, p): """ Second derivative of the Cauchy link function. Parameters ---------- p : array_like Probabilities Returns ------- g''(p) : ndarray Value of the second derivative of Cauchy link function at `p` """ p = self._clean(p) a = np.pi * (p - 0.5) d2 = 2 * np.pi**2 * np.sin(a) / np.cos(a)**3 return d2 def inverse_deriv2(self, z): return - 2 * z / (np.pi * (z**2 + 1)**2) class CLogLog(Logit): """ The complementary log-log transform CLogLog inherits from Logit in order to have access to its _clean method for the link and its derivative. Notes ----- CLogLog is untested. """ def __call__(self, p): """ C-Log-Log transform link function Parameters ---------- p : ndarray Mean parameters Returns ------- z : ndarray The CLogLog transform of `p` Notes ----- g(p) = log(-log(1-p)) """ p = self._clean(p) return np.log(-np.log(1 - p)) def inverse(self, z): """ Inverse of C-Log-Log transform link function Parameters ---------- z : array_like The value of the inverse of the CLogLog link function at `p` Returns ------- p : ndarray Mean parameters Notes ----- g^(-1)(`z`) = 1-exp(-exp(`z`)) """ return 1 - np.exp(-np.exp(z)) def deriv(self, p): """ Derivative of C-Log-Log transform link function Parameters ---------- p : array_like Mean parameters Returns ------- g'(p) : ndarray The derivative of the CLogLog transform link function Notes ----- g'(p) = - 1 / ((p-1)*log(1-p)) """ p = self._clean(p) return 1. / ((p - 1) * (np.log(1 - p))) def deriv2(self, p): """ Second derivative of the C-Log-Log ink function Parameters ---------- p : array_like Mean parameters Returns ------- g''(p) : ndarray The second derivative of the CLogLog link function """ p = self._clean(p) fl = np.log(1 - p) d2 = -1 / ((1 - p)**2 * fl) d2 *= 1 + 1 / fl return d2 def inverse_deriv(self, z): """ Derivative of the inverse of the C-Log-Log transform link function Parameters ---------- z : array_like The value of the inverse of the CLogLog link function at `p` Returns ------- g^(-1)'(z) : ndarray The derivative of the inverse of the CLogLog link function """ return np.exp(z - np.exp(z)) class cloglog(CLogLog): """ The CLogLog transform link function. Notes ----- g(`p`) = log(-log(1-`p`)) cloglog is an alias for CLogLog cloglog = CLogLog() """ pass class NegativeBinomial(Link): ''' The negative binomial link function Parameters ---------- alpha : float, optional Alpha is the ancillary parameter of the Negative Binomial link function. It is assumed to be nonstochastic. The default value is 1. Permissible values are usually assumed to be in (.01, 2). ''' def __init__(self, alpha=1.): self.alpha = alpha def _clean(self, x): return np.clip(x, FLOAT_EPS, np.inf) def __call__(self, p): ''' Negative Binomial transform link function Parameters ---------- p : array_like Mean parameters Returns ------- z : ndarray The negative binomial transform of `p` Notes ----- g(p) = log(p/(p + 1/alpha)) ''' p = self._clean(p) return np.log(p/(p + 1/self.alpha)) def inverse(self, z): ''' Inverse of the negative binomial transform Parameters ---------- z : array_like The value of the inverse of the negative binomial link at `p`. Returns ------- p : ndarray Mean parameters Notes ----- g^(-1)(z) = exp(z)/(alpha*(1-exp(z))) ''' return -1/(self.alpha * (1 - np.exp(-z))) def deriv(self, p): ''' Derivative of the negative binomial transform Parameters ---------- p : array_like Mean parameters Returns ------- g'(p) : ndarray The derivative of the negative binomial transform link function Notes ----- g'(x) = 1/(x+alpha*x^2) ''' return 1/(p + self.alpha * p**2) def deriv2(self, p): ''' Second derivative of the negative binomial link function. Parameters ---------- p : array_like Mean parameters Returns ------- g''(p) : ndarray The second derivative of the negative binomial transform link function Notes ----- g''(x) = -(1+2*alpha*x)/(x+alpha*x^2)^2 ''' numer = -(1 + 2 * self.alpha * p) denom = (p + self.alpha * p**2)**2 return numer / denom def inverse_deriv(self, z): ''' Derivative of the inverse of the negative binomial transform Parameters ---------- z : array_like Usually the linear predictor for a GLM or GEE model Returns ------- g^(-1)'(z) : ndarray The value of the derivative of the inverse of the negative binomial link ''' t = np.exp(z) return t / (self.alpha * (1-t)**2) class nbinom(NegativeBinomial): """ The negative binomial link function. Notes ----- g(p) = log(p/(p + 1/alpha)) nbinom is an alias of NegativeBinomial. nbinom = NegativeBinomial(alpha=1.) """ pass statsmodels-0.12.2/statsmodels/genmod/families/tests/000077500000000000000000000000001400612667500227135ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/genmod/families/tests/__init__.py000066400000000000000000000000001400612667500250120ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/genmod/families/tests/test_link.py000066400000000000000000000074041400612667500252660ustar00rootroot00000000000000""" Test functions for genmod.families.links """ import numpy as np from numpy.testing import assert_allclose, assert_equal import statsmodels.genmod.families as families from statsmodels.tools import numdiff as nd # Family instances links = families.links logit = links.Logit() inverse_power = links.inverse_power() sqrt = links.sqrt() inverse_squared = links.inverse_squared() identity = links.identity() log = links.log() probit = links.probit() cauchy = links.cauchy() cloglog = links.CLogLog() negbinom = links.NegativeBinomial() # TODO: parametrize all these tess Links = [logit, inverse_power, sqrt, inverse_squared, identity, log, probit, cauchy, cloglog, negbinom] def get_domainvalue(link): """ Get a value in the domain for a given family. """ z = -np.log(np.random.uniform(0, 1)) if isinstance(link, links.CLogLog): # prone to overflow z = min(z, 3) elif isinstance(link, links.NegativeBinomial): # domain is negative numbers z = -z return z def test_inverse(): # Logic check that link.inverse(link) and link(link.inverse) # are the identity. np.random.seed(3285) for link in Links: for k in range(10): p = np.random.uniform(0, 1) # In domain for all families d = link.inverse(link(p)) assert_allclose(d, p, atol=1e-8, err_msg=str(link)) z = get_domainvalue(link) d = link(link.inverse(z)) assert_allclose(d, z, atol=1e-8, err_msg=str(link)) def test_deriv(): # Check link function derivatives using numeric differentiation. np.random.seed(24235) for link in Links: for k in range(10): p = np.random.uniform(0, 1) d = link.deriv(p) da = nd.approx_fprime(np.r_[p], link) assert_allclose(d, da, rtol=1e-6, atol=1e-6, err_msg=str(link)) def test_deriv2(): # Check link function second derivatives using numeric differentiation. np.random.seed(24235) for link in Links: for k in range(10): p = np.random.uniform(0, 1) p = np.clip(p, 0.01, 0.99) if isinstance(link, links.cauchy): p = np.clip(p, 0.03, 0.97) d = link.deriv2(p) da = nd.approx_fprime(np.r_[p], link.deriv) assert_allclose(d, da, rtol=5e-6, atol=1e-6, err_msg=str(link)) def test_inverse_deriv(): # Logic check that inverse_deriv equals 1/link.deriv(link.inverse) np.random.seed(24235) for link in Links: for k in range(10): z = -np.log(np.random.uniform()) # In domain for all families d = link.inverse_deriv(z) f = 1 / link.deriv(link.inverse(z)) assert_allclose(d, f, rtol=1e-8, atol=1e-10, err_msg=str(link)) def test_invlogit_stability(): z = [1123.4910007309222, 1483.952316802719, 1344.86033748641, 706.339159002542, 1167.9986375146532, 663.8345826933115, 1496.3691686913917, 1563.0763842182257, 1587.4309332296314, 697.1173174974248, 1333.7256198289665, 1388.7667560586933, 819.7605431778434, 1479.9204150555015, 1078.5642245164856, 480.10338454985896, 1112.691659145772, 534.1061908007274, 918.2011296406588, 1280.8808515887802, 758.3890788775948, 673.503699841035, 1556.7043357878208, 819.5269028006679, 1262.5711060356423, 1098.7271535253608, 1482.811928490097, 796.198809756532, 893.7946963941745, 470.3304989319786, 1427.77079226037, 1365.2050226373822, 1492.4193201661922, 871.9922191949931, 768.4735925445908, 732.9222777654679, 812.2382651982667, 495.06449978924525] zinv = logit.inverse(z) assert_equal(zinv, np.ones_like(z)) statsmodels-0.12.2/statsmodels/genmod/families/varfuncs.py000066400000000000000000000124411400612667500237540ustar00rootroot00000000000000""" Variance functions for use with the link functions in statsmodels.family.links """ import numpy as np FLOAT_EPS = np.finfo(float).eps class VarianceFunction(object): """ Relates the variance of a random variable to its mean. Defaults to 1. Methods ------- call Returns an array of ones that is the same shape as `mu` Notes ----- After a variance function is initialized, its call method can be used. Alias for VarianceFunction: constant = VarianceFunction() See Also -------- statsmodels.genmod.families.family """ def __call__(self, mu): """ Default variance function Parameters ---------- mu : array_like mean parameters Returns ------- v : ndarray ones(mu.shape) """ mu = np.asarray(mu) return np.ones(mu.shape, np.float64) def deriv(self, mu): """ Derivative of the variance function v'(mu) """ return np.zeros_like(mu) constant = VarianceFunction() constant.__doc__ = """ The call method of constant returns a constant variance, i.e., a vector of ones. constant is an alias of VarianceFunction() """ class Power(object): """ Power variance function Parameters ---------- power : float exponent used in power variance function Methods ------- call Returns the power variance Notes ----- Formulas V(mu) = numpy.fabs(mu)**power Aliases for Power: mu = Power() mu_squared = Power(power=2) mu_cubed = Power(power=3) """ def __init__(self, power=1.): self.power = power def __call__(self, mu): """ Power variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray numpy.fabs(mu)**self.power """ return np.power(np.fabs(mu), self.power) def deriv(self, mu): """ Derivative of the variance function v'(mu) May be undefined at zero. """ der = self.power * np.fabs(mu) ** (self.power - 1) ii = np.flatnonzero(mu < 0) der[ii] *= -1 return der mu = Power() mu.__doc__ = """ Returns np.fabs(mu) Notes ----- This is an alias of Power() """ mu_squared = Power(power=2) mu_squared.__doc__ = """ Returns np.fabs(mu)**2 Notes ----- This is an alias of statsmodels.family.links.Power(power=2) """ mu_cubed = Power(power=3) mu_cubed.__doc__ = """ Returns np.fabs(mu)**3 Notes ----- This is an alias of statsmodels.family.links.Power(power=3) """ class Binomial(object): """ Binomial variance function Parameters ---------- n : int, optional The number of trials for a binomial variable. The default is 1 for p in (0,1) Methods ------- call Returns the binomial variance Notes ----- Formulas : V(mu) = p * (1 - p) * n where p = mu / n Alias for Binomial: binary = Binomial() A private method _clean trims the data by machine epsilon so that p is in (0,1) """ def __init__(self, n=1): self.n = n def _clean(self, p): return np.clip(p, FLOAT_EPS, 1 - FLOAT_EPS) def __call__(self, mu): """ Binomial variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray variance = mu/n * (1 - mu/n) * self.n """ p = self._clean(mu / self.n) return p * (1 - p) * self.n # TODO: inherit from super def deriv(self, mu): """ Derivative of the variance function v'(mu) """ return 1 - 2*mu binary = Binomial() binary.__doc__ = """ The binomial variance function for n = 1 Notes ----- This is an alias of Binomial(n=1) """ class NegativeBinomial(object): ''' Negative binomial variance function Parameters ---------- alpha : float The ancillary parameter for the negative binomial variance function. `alpha` is assumed to be nonstochastic. The default is 1. Methods ------- call Returns the negative binomial variance Notes ----- Formulas : V(mu) = mu + alpha*mu**2 Alias for NegativeBinomial: nbinom = NegativeBinomial() A private method _clean trims the data by machine epsilon so that p is in (0,inf) ''' def __init__(self, alpha=1.): self.alpha = alpha def _clean(self, p): return np.clip(p, FLOAT_EPS, np.inf) def __call__(self, mu): """ Negative binomial variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray variance = mu + alpha*mu**2 """ p = self._clean(mu) return p + self.alpha*p**2 def deriv(self, mu): """ Derivative of the negative binomial variance function. """ p = self._clean(mu) return 1 + 2 * self.alpha * p nbinom = NegativeBinomial() nbinom.__doc__ = """ Negative Binomial variance function. Notes ----- This is an alias of NegativeBinomial(alpha=1.) """ statsmodels-0.12.2/statsmodels/genmod/generalized_estimating_equations.py000066400000000000000000003373141400612667500271520ustar00rootroot00000000000000""" Procedures for fitting marginal regression models to dependent data using Generalized Estimating Equations. References ---------- KY Liang and S Zeger. "Longitudinal data analysis using generalized linear models". Biometrika (1986) 73 (1): 13-22. S Zeger and KY Liang. "Longitudinal Data Analysis for Discrete and Continuous Outcomes". Biometrics Vol. 42, No. 1 (Mar., 1986), pp. 121-130 A Rotnitzky and NP Jewell (1990). "Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster correlated data", Biometrika, 77, 485-497. Xu Guo and Wei Pan (2002). "Small sample performance of the score test in GEE". http://www.sph.umn.edu/faculty1/wp-content/uploads/2012/11/rr2002-013.pdf LA Mancl LA, TA DeRouen (2001). A covariance estimator for GEE with improved small-sample properties. Biometrics. 2001 Mar;57(1):126-34. """ from statsmodels.compat.python import lzip from statsmodels.compat.pandas import Appender import numpy as np from scipy import stats import pandas as pd import patsy from collections import defaultdict from statsmodels.tools.decorators import cache_readonly import statsmodels.base.model as base # used for wrapper: import statsmodels.regression.linear_model as lm import statsmodels.base.wrapper as wrap from statsmodels.genmod import families from statsmodels.genmod.generalized_linear_model import GLM, GLMResults from statsmodels.genmod import cov_struct as cov_structs import statsmodels.genmod.families.varfuncs as varfuncs from statsmodels.genmod.families.links import Link from statsmodels.tools.sm_exceptions import (ConvergenceWarning, DomainWarning, IterationLimitWarning, ValueWarning) import warnings from statsmodels.graphics._regressionplots_doc import ( _plot_added_variable_doc, _plot_partial_residuals_doc, _plot_ceres_residuals_doc) from statsmodels.discrete.discrete_margins import ( _get_margeff_exog, _check_margeff_args, _effects_at, margeff_cov_with_se, _check_at_is_all, _transform_names, _check_discrete_args, _get_dummy_index, _get_count_index) class ParameterConstraint(object): """ A class for managing linear equality constraints for a parameter vector. """ def __init__(self, lhs, rhs, exog): """ Parameters ---------- lhs : ndarray A q x p matrix which is the left hand side of the constraint lhs * param = rhs. The number of constraints is q >= 1 and p is the dimension of the parameter vector. rhs : ndarray A 1-dimensional vector of length q which is the right hand side of the constraint equation. exog : ndarray The n x p exognenous data for the full model. """ # In case a row or column vector is passed (patsy linear # constraints passes a column vector). rhs = np.atleast_1d(rhs.squeeze()) if rhs.ndim > 1: raise ValueError("The right hand side of the constraint " "must be a vector.") if len(rhs) != lhs.shape[0]: raise ValueError("The number of rows of the left hand " "side constraint matrix L must equal " "the length of the right hand side " "constraint vector R.") self.lhs = lhs self.rhs = rhs # The columns of lhs0 are an orthogonal basis for the # orthogonal complement to row(lhs), the columns of lhs1 are # an orthogonal basis for row(lhs). The columns of lhsf = # [lhs0, lhs1] are mutually orthogonal. lhs_u, lhs_s, lhs_vt = np.linalg.svd(lhs.T, full_matrices=1) self.lhs0 = lhs_u[:, len(lhs_s):] self.lhs1 = lhs_u[:, 0:len(lhs_s)] self.lhsf = np.hstack((self.lhs0, self.lhs1)) # param0 is one solution to the underdetermined system # L * param = R. self.param0 = np.dot(self.lhs1, np.dot(lhs_vt, self.rhs) / lhs_s) self._offset_increment = np.dot(exog, self.param0) self.orig_exog = exog self.exog_fulltrans = np.dot(exog, self.lhsf) def offset_increment(self): """ Returns a vector that should be added to the offset vector to accommodate the constraint. Parameters ---------- exog : array_like The exogeneous data for the model. """ return self._offset_increment def reduced_exog(self): """ Returns a linearly transformed exog matrix whose columns span the constrained model space. Parameters ---------- exog : array_like The exogeneous data for the model. """ return self.exog_fulltrans[:, 0:self.lhs0.shape[1]] def restore_exog(self): """ Returns the full exog matrix before it was reduced to satisfy the constraint. """ return self.orig_exog def unpack_param(self, params): """ Converts the parameter vector `params` from reduced to full coordinates. """ return self.param0 + np.dot(self.lhs0, params) def unpack_cov(self, bcov): """ Converts the covariance matrix `bcov` from reduced to full coordinates. """ return np.dot(self.lhs0, np.dot(bcov, self.lhs0.T)) _gee_init_doc = """ Marginal regression model fit using Generalized Estimating Equations. GEE can be used to fit Generalized Linear Models (GLMs) when the data have a grouped structure, and the observations are possibly correlated within groups but not between groups. Parameters ---------- endog : array_like 1d array of endogenous values (i.e. responses, outcomes, dependent variables, or 'Y' values). exog : array_like 2d array of exogeneous values (i.e. covariates, predictors, independent variables, regressors, or 'X' values). A `nobs x k` array where `nobs` is the number of observations and `k` is the number of regressors. An intercept is not included by default and should be added by the user. See `statsmodels.tools.add_constant`. groups : array_like A 1d array of length `nobs` containing the group labels. time : array_like A 2d array of time (or other index) values, used by some dependence structures to define similarity relationships among observations within a cluster. family : family class instance %(family_doc)s cov_struct : CovStruct class instance The default is Independence. To specify an exchangeable structure use cov_struct = Exchangeable(). See statsmodels.genmod.cov_struct.CovStruct for more information. offset : array_like An offset to be included in the fit. If provided, must be an array whose length is the number of rows in exog. dep_data : array_like Additional data passed to the dependence structure. constraint : (ndarray, ndarray) If provided, the constraint is a tuple (L, R) such that the model parameters are estimated under the constraint L * param = R, where L is a q x p matrix and R is a q-dimensional vector. If constraint is provided, a score test is performed to compare the constrained model to the unconstrained model. update_dep : bool If true, the dependence parameters are optimized, otherwise they are held fixed at their starting values. weights : array_like An array of case weights to use in the analysis. %(extra_params)s See Also -------- statsmodels.genmod.families.family :ref:`families` :ref:`links` Notes ----- Only the following combinations make sense for family and link :: + ident log logit probit cloglog pow opow nbinom loglog logc Gaussian | x x x inv Gaussian | x x x binomial | x x x x x x x x x Poisson | x x x neg binomial | x x x x gamma | x x x Not all of these link functions are currently available. Endog and exog are references so that if the data they refer to are already arrays and these arrays are changed, endog and exog will change. The "robust" covariance type is the standard "sandwich estimator" (e.g. Liang and Zeger (1986)). It is the default here and in most other packages. The "naive" estimator gives smaller standard errors, but is only correct if the working correlation structure is correctly specified. The "bias reduced" estimator of Mancl and DeRouen (Biometrics, 2001) reduces the downward bias of the robust estimator. The robust covariance provided here follows Liang and Zeger (1986) and agrees with R's gee implementation. To obtain the robust standard errors reported in Stata, multiply by sqrt(N / (N - g)), where N is the total sample size, and g is the average group size. Examples -------- %(example)s """ _gee_family_doc = """\ The default is Gaussian. To specify the binomial distribution use `family=sm.families.Binomial()`. Each family can take a link instance as an argument. See statsmodels.genmod.families.family for more information.""" _gee_ordinal_family_doc = """\ The only family supported is `Binomial`. The default `Logit` link may be replaced with `probit` if desired.""" _gee_nominal_family_doc = """\ The default value `None` uses a multinomial logit family specifically designed for use with GEE. Setting this argument to a non-default value is not currently supported.""" _gee_fit_doc = """ Fits a marginal regression model using generalized estimating equations (GEE). Parameters ---------- maxiter : int The maximum number of iterations ctol : float The convergence criterion for stopping the Gauss-Seidel iterations start_params : array_like A vector of starting values for the regression coefficients. If None, a default is chosen. params_niter : int The number of Gauss-Seidel updates of the mean structure parameters that take place prior to each update of the dependence structure. first_dep_update : int No dependence structure updates occur before this iteration number. cov_type : str One of "robust", "naive", or "bias_reduced". ddof_scale : scalar or None The scale parameter is estimated as the sum of squared Pearson residuals divided by `N - ddof_scale`, where N is the total sample size. If `ddof_scale` is None, the number of covariates (including an intercept if present) is used. scaling_factor : scalar The estimated covariance of the parameter estimates is scaled by this value. Default is 1, Stata uses N / (N - g), where N is the total sample size and g is the average group size. scale : str or float, optional `scale` can be None, 'X2', or a float If a float, its value is used as the scale parameter. The default value is None, which uses `X2` (Pearson's chi-square) for Gamma, Gaussian, and Inverse Gaussian. The default is 1 for the Binomial and Poisson families. Returns ------- An instance of the GEEResults class or subclass Notes ----- If convergence difficulties occur, increase the values of `first_dep_update` and/or `params_niter`. Setting `first_dep_update` to a greater value (e.g. ~10-20) causes the algorithm to move close to the GLM solution before attempting to identify the dependence structure. For the Gaussian family, there is no benefit to setting `params_niter` to a value greater than 1, since the mean structure parameters converge in one step. """ _gee_results_doc = """ Attributes ---------- cov_params_default : ndarray default covariance of the parameter estimates. Is chosen among one of the following three based on `cov_type` cov_robust : ndarray covariance of the parameter estimates that is robust cov_naive : ndarray covariance of the parameter estimates that is not robust to correlation or variance misspecification cov_robust_bc : ndarray covariance of the parameter estimates that is robust and bias reduced converged : bool indicator for convergence of the optimization. True if the norm of the score is smaller than a threshold cov_type : str string indicating whether a "robust", "naive" or "bias_reduced" covariance is used as default fit_history : dict Contains information about the iterations. fittedvalues : ndarray Linear predicted values for the fitted model. dot(exog, params) model : class instance Pointer to GEE model instance that called `fit`. normalized_cov_params : ndarray See GEE docstring params : ndarray The coefficients of the fitted model. Note that interpretation of the coefficients often depends on the distribution family and the data. scale : float The estimate of the scale / dispersion for the model fit. See GEE.fit for more information. score_norm : float norm of the score at the end of the iterative estimation. bse : ndarray The standard errors of the fitted GEE parameters. """ _gee_example = """ Logistic regression with autoregressive working dependence: >>> import statsmodels.api as sm >>> family = sm.families.Binomial() >>> va = sm.cov_struct.Autoregressive() >>> model = sm.GEE(endog, exog, group, family=family, cov_struct=va) >>> result = model.fit() >>> print(result.summary()) Use formulas to fit a Poisson GLM with independent working dependence: >>> import statsmodels.api as sm >>> fam = sm.families.Poisson() >>> ind = sm.cov_struct.Independence() >>> model = sm.GEE.from_formula("y ~ age + trt + base", "subject", \ data, cov_struct=ind, family=fam) >>> result = model.fit() >>> print(result.summary()) Equivalent, using the formula API: >>> import statsmodels.api as sm >>> import statsmodels.formula.api as smf >>> fam = sm.families.Poisson() >>> ind = sm.cov_struct.Independence() >>> model = smf.gee("y ~ age + trt + base", "subject", \ data, cov_struct=ind, family=fam) >>> result = model.fit() >>> print(result.summary()) """ _gee_ordinal_example = """ Fit an ordinal regression model using GEE, with "global odds ratio" dependence: >>> import statsmodels.api as sm >>> gor = sm.cov_struct.GlobalOddsRatio("ordinal") >>> model = sm.OrdinalGEE(endog, exog, groups, cov_struct=gor) >>> result = model.fit() >>> print(result.summary()) Using formulas: >>> import statsmodels.formula.api as smf >>> model = smf.ordinal_gee("y ~ x1 + x2", groups, data, cov_struct=gor) >>> result = model.fit() >>> print(result.summary()) """ _gee_nominal_example = """ Fit a nominal regression model using GEE: >>> import statsmodels.api as sm >>> import statsmodels.formula.api as smf >>> gor = sm.cov_struct.GlobalOddsRatio("nominal") >>> model = sm.NominalGEE(endog, exog, groups, cov_struct=gor) >>> result = model.fit() >>> print(result.summary()) Using formulas: >>> import statsmodels.api as sm >>> model = sm.NominalGEE.from_formula("y ~ x1 + x2", groups, data, cov_struct=gor) >>> result = model.fit() >>> print(result.summary()) Using the formula API: >>> import statsmodels.formula.api as smf >>> model = smf.nominal_gee("y ~ x1 + x2", groups, data, cov_struct=gor) >>> result = model.fit() >>> print(result.summary()) """ def _check_args(endog, exog, groups, time, offset, exposure): if endog.size != exog.shape[0]: raise ValueError("Leading dimension of 'exog' should match " "length of 'endog'") if groups.size != endog.size: raise ValueError("'groups' and 'endog' should have the same size") if time is not None and (time.size != endog.size): raise ValueError("'time' and 'endog' should have the same size") if offset is not None and (offset.size != endog.size): raise ValueError("'offset and 'endog' should have the same size") if exposure is not None and (exposure.size != endog.size): raise ValueError("'exposure' and 'endog' should have the same size") class GEE(GLM): __doc__ = ( " Marginal Regression Model using Generalized Estimating " "Equations.\n" + _gee_init_doc % {'extra_params': base._missing_param_doc, 'family_doc': _gee_family_doc, 'example': _gee_example}) cached_means = None def __init__(self, endog, exog, groups, time=None, family=None, cov_struct=None, missing='none', offset=None, exposure=None, dep_data=None, constraint=None, update_dep=True, weights=None, **kwargs): if family is not None: if not isinstance(family.link, tuple(family.safe_links)): import warnings msg = ("The {0} link function does not respect the " "domain of the {1} family.") warnings.warn(msg.format(family.link.__class__.__name__, family.__class__.__name__), DomainWarning) groups = np.asarray(groups) # in case groups is pandas if "missing_idx" in kwargs and kwargs["missing_idx"] is not None: # If here, we are entering from super.from_formula; missing # has already been dropped from endog and exog, but not from # the other variables. ii = ~kwargs["missing_idx"] groups = groups[ii] if time is not None: time = time[ii] if offset is not None: offset = offset[ii] if exposure is not None: exposure = exposure[ii] del kwargs["missing_idx"] _check_args(endog, exog, groups, time, offset, exposure) self.missing = missing self.dep_data = dep_data self.constraint = constraint self.update_dep = update_dep self._fit_history = defaultdict(list) # Pass groups, time, offset, and dep_data so they are # processed for missing data along with endog and exog. # Calling super creates self.exog, self.endog, etc. as # ndarrays and the original exog, endog, etc. are # self.data.endog, etc. super(GEE, self).__init__(endog, exog, groups=groups, time=time, offset=offset, exposure=exposure, weights=weights, dep_data=dep_data, missing=missing, family=family, **kwargs) self._init_keys.extend(["update_dep", "constraint", "family", "cov_struct"]) # Handle the family argument if family is None: family = families.Gaussian() else: if not issubclass(family.__class__, families.Family): raise ValueError("GEE: `family` must be a genmod " "family instance") self.family = family # Handle the cov_struct argument if cov_struct is None: cov_struct = cov_structs.Independence() else: if not issubclass(cov_struct.__class__, cov_structs.CovStruct): raise ValueError("GEE: `cov_struct` must be a genmod " "cov_struct instance") self.cov_struct = cov_struct # Handle the constraint self.constraint = None if constraint is not None: if len(constraint) != 2: raise ValueError("GEE: `constraint` must be a 2-tuple.") if constraint[0].shape[1] != self.exog.shape[1]: raise ValueError( "GEE: the left hand side of the constraint must have " "the same number of columns as the exog matrix.") self.constraint = ParameterConstraint(constraint[0], constraint[1], self.exog) if self._offset_exposure is not None: self._offset_exposure += self.constraint.offset_increment() else: self._offset_exposure = ( self.constraint.offset_increment().copy()) self.exog = self.constraint.reduced_exog() # Create list of row indices for each group group_labels, ix = np.unique(self.groups, return_inverse=True) se = pd.Series(index=np.arange(len(ix)), dtype="int") gb = se.groupby(ix).groups dk = [(lb, np.asarray(gb[k])) for k, lb in enumerate(group_labels)] self.group_indices = dict(dk) self.group_labels = group_labels # Convert the data to the internal representation, which is a # list of arrays, corresponding to the groups. self.endog_li = self.cluster_list(self.endog) self.exog_li = self.cluster_list(self.exog) if self.weights is not None: self.weights_li = self.cluster_list(self.weights) self.num_group = len(self.endog_li) # Time defaults to a 1d grid with equal spacing if self.time is not None: self.time = np.asarray(self.time, np.float64) if self.time.ndim == 1: self.time = self.time[:, None] self.time_li = self.cluster_list(self.time) else: self.time_li = \ [np.arange(len(y), dtype=np.float64)[:, None] for y in self.endog_li] self.time = np.concatenate(self.time_li) if (self._offset_exposure is None or (np.isscalar(self._offset_exposure) and self._offset_exposure == 0.)): self.offset_li = None else: self.offset_li = self.cluster_list(self._offset_exposure) if constraint is not None: self.constraint.exog_fulltrans_li = \ self.cluster_list(self.constraint.exog_fulltrans) self.family = family self.cov_struct.initialize(self) # Total sample size group_ns = [len(y) for y in self.endog_li] self.nobs = sum(group_ns) # The following are column based, not on rank see #1928 self.df_model = self.exog.shape[1] - 1 # assumes constant self.df_resid = self.nobs - self.exog.shape[1] # Skip the covariance updates if all groups have a single # observation (reduces to fitting a GLM). maxgroup = max([len(x) for x in self.endog_li]) if maxgroup == 1: self.update_dep = False # Override to allow groups and time to be passed as variable # names. @classmethod def from_formula(cls, formula, groups, data, subset=None, time=None, offset=None, exposure=None, *args, **kwargs): """ Create a GEE model instance from a formula and dataframe. Parameters ---------- formula : str or generic Formula object The formula specifying the model groups : array_like or string Array of grouping labels. If a string, this is the name of a variable in `data` that contains the grouping labels. data : array_like The data for the model. subset : array_like An array-like object of booleans, integers, or index values that indicate the subset of the data to used when fitting the model. time : array_like or string The time values, used for dependence structures involving distances between observations. If a string, this is the name of a variable in `data` that contains the time values. offset : array_like or string The offset values, added to the linear predictor. If a string, this is the name of a variable in `data` that contains the offset values. exposure : array_like or string The exposure values, only used if the link function is the logarithm function, in which case the log of `exposure` is added to the offset (if any). If a string, this is the name of a variable in `data` that contains the offset values. %(missing_param_doc)s args : extra arguments These are passed to the model kwargs : extra keyword arguments These are passed to the model with two exceptions. `dep_data` is processed as described below. The ``eval_env`` keyword is passed to patsy. It can be either a :class:`patsy:patsy.EvalEnvironment` object or an integer indicating the depth of the namespace to use. For example, the default ``eval_env=0`` uses the calling namespace. If you wish to use a "clean" environment set ``eval_env=-1``. Optional arguments ------------------ dep_data : str or array_like Data used for estimating the dependence structure. See specific dependence structure classes (e.g. Nested) for details. If `dep_data` is a string, it is interpreted as a formula that is applied to `data`. If it is an array, it must be an array of strings corresponding to column names in `data`. Otherwise it must be an array-like with the same number of rows as data. Returns ------- model : GEE model instance Notes ----- `data` must define __getitem__ with the keys in the formula terms args and kwargs are passed on to the model instantiation. E.g., a numpy structured or rec array, a dictionary, or a pandas DataFrame. """ % {'missing_param_doc': base._missing_param_doc} groups_name = "Groups" if isinstance(groups, str): groups_name = groups groups = data[groups] if isinstance(time, str): time = data[time] if isinstance(offset, str): offset = data[offset] if isinstance(exposure, str): exposure = data[exposure] dep_data = kwargs.get("dep_data") dep_data_names = None if dep_data is not None: if isinstance(dep_data, str): dep_data = patsy.dmatrix(dep_data, data, return_type='dataframe') dep_data_names = dep_data.columns.tolist() else: dep_data_names = list(dep_data) dep_data = data[dep_data] kwargs["dep_data"] = np.asarray(dep_data) family = None if "family" in kwargs: family = kwargs["family"] del kwargs["family"] model = super(GEE, cls).from_formula(formula, data=data, subset=subset, groups=groups, time=time, offset=offset, exposure=exposure, family=family, *args, **kwargs) if dep_data_names is not None: model._dep_data_names = dep_data_names model._groups_name = groups_name return model def cluster_list(self, array): """ Returns `array` split into subarrays corresponding to the cluster structure. """ if array.ndim == 1: return [np.array(array[self.group_indices[k]]) for k in self.group_labels] else: return [np.array(array[self.group_indices[k], :]) for k in self.group_labels] def compare_score_test(self, submodel): """ Perform a score test for the given submodel against this model. Parameters ---------- submodel : GEEResults instance A fitted GEE model that is a submodel of this model. Returns ------- A dictionary with keys "statistic", "p-value", and "df", containing the score test statistic, its chi^2 p-value, and the degrees of freedom used to compute the p-value. Notes ----- The score test can be performed without calling 'fit' on the larger model. The provided submodel must be obtained from a fitted GEE. This method performs the same score test as can be obtained by fitting the GEE with a linear constraint and calling `score_test` on the results. References ---------- Xu Guo and Wei Pan (2002). "Small sample performance of the score test in GEE". http://www.sph.umn.edu/faculty1/wp-content/uploads/2012/11/rr2002-013.pdf """ # Since the model has not been fit, its scaletype has not been # set. So give it the scaletype of the submodel. self.scaletype = submodel.model.scaletype # Check consistency between model and submodel (not a comprehensive # check) submod = submodel.model if self.exog.shape[0] != submod.exog.shape[0]: msg = "Model and submodel have different numbers of cases." raise ValueError(msg) if self.exog.shape[1] == submod.exog.shape[1]: msg = "Model and submodel have the same number of variables" warnings.warn(msg) if not isinstance(self.family, type(submod.family)): msg = "Model and submodel have different GLM families." warnings.warn(msg) if not isinstance(self.cov_struct, type(submod.cov_struct)): warnings.warn("Model and submodel have different GEE covariance " "structures.") if not np.equal(self.weights, submod.weights).all(): msg = "Model and submodel should have the same weights." warnings.warn(msg) # Get the positions of the submodel variables in the # parent model qm, qc = _score_test_submodel(self, submodel.model) if qm is None: msg = "The provided model is not a submodel." raise ValueError(msg) # Embed the submodel params into a params vector for the # parent model params_ex = np.dot(qm, submodel.params) # Attempt to preserve the state of the parent model cov_struct_save = self.cov_struct import copy cached_means_save = copy.deepcopy(self.cached_means) # Get the score vector of the submodel params in # the parent model self.cov_struct = submodel.cov_struct self.update_cached_means(params_ex) _, score = self._update_mean_params() if score is None: msg = "Singular matrix encountered in GEE score test" warnings.warn(msg, ConvergenceWarning) return None if not hasattr(self, "ddof_scale"): self.ddof_scale = self.exog.shape[1] if not hasattr(self, "scaling_factor"): self.scaling_factor = 1 _, ncov1, cmat = self._covmat() scale = self.estimate_scale() cmat = cmat / scale ** 2 score2 = np.dot(qc.T, score) / scale amat = np.linalg.inv(ncov1) bmat_11 = np.dot(qm.T, np.dot(cmat, qm)) bmat_22 = np.dot(qc.T, np.dot(cmat, qc)) bmat_12 = np.dot(qm.T, np.dot(cmat, qc)) amat_11 = np.dot(qm.T, np.dot(amat, qm)) amat_12 = np.dot(qm.T, np.dot(amat, qc)) score_cov = bmat_22 - np.dot(amat_12.T, np.linalg.solve(amat_11, bmat_12)) score_cov -= np.dot(bmat_12.T, np.linalg.solve(amat_11, amat_12)) score_cov += np.dot(amat_12.T, np.dot(np.linalg.solve(amat_11, bmat_11), np.linalg.solve(amat_11, amat_12))) # Attempt to restore state self.cov_struct = cov_struct_save self.cached_means = cached_means_save from scipy.stats.distributions import chi2 score_statistic = np.dot(score2, np.linalg.solve(score_cov, score2)) score_df = len(score2) score_pvalue = 1 - chi2.cdf(score_statistic, score_df) return {"statistic": score_statistic, "df": score_df, "p-value": score_pvalue} def estimate_scale(self): """ Estimate the dispersion/scale. """ if self.scaletype is None: if isinstance(self.family, (families.Binomial, families.Poisson, families.NegativeBinomial, _Multinomial)): return 1. elif isinstance(self.scaletype, float): return np.array(self.scaletype) endog = self.endog_li cached_means = self.cached_means nobs = self.nobs varfunc = self.family.variance scale = 0. fsum = 0. for i in range(self.num_group): if len(endog[i]) == 0: continue expval, _ = cached_means[i] sdev = np.sqrt(varfunc(expval)) resid = (endog[i] - expval) / sdev if self.weights is not None: f = self.weights_li[i] scale += np.sum(f * (resid ** 2)) fsum += f.sum() else: scale += np.sum(resid ** 2) fsum += len(resid) scale /= (fsum * (nobs - self.ddof_scale) / float(nobs)) return scale def mean_deriv(self, exog, lin_pred): """ Derivative of the expected endog with respect to the parameters. Parameters ---------- exog : array_like The exogeneous data at which the derivative is computed. lin_pred : array_like The values of the linear predictor. Returns ------- The value of the derivative of the expected endog with respect to the parameter vector. Notes ----- If there is an offset or exposure, it should be added to `lin_pred` prior to calling this function. """ idl = self.family.link.inverse_deriv(lin_pred) dmat = exog * idl[:, None] return dmat def mean_deriv_exog(self, exog, params, offset_exposure=None): """ Derivative of the expected endog with respect to exog. Parameters ---------- exog : array_like Values of the independent variables at which the derivative is calculated. params : array_like Parameter values at which the derivative is calculated. offset_exposure : array_like, optional Combined offset and exposure. Returns ------- The derivative of the expected endog with respect to exog. """ lin_pred = np.dot(exog, params) if offset_exposure is not None: lin_pred += offset_exposure idl = self.family.link.inverse_deriv(lin_pred) dmat = np.outer(idl, params) return dmat def _update_mean_params(self): """ Returns ------- update : array_like The update vector such that params + update is the next iterate when solving the score equations. score : array_like The current value of the score equations, not incorporating the scale parameter. If desired, multiply this vector by the scale parameter to incorporate the scale. """ endog = self.endog_li exog = self.exog_li weights = getattr(self, "weights_li", None) cached_means = self.cached_means varfunc = self.family.variance bmat, score = 0, 0 for i in range(self.num_group): expval, lpr = cached_means[i] resid = endog[i] - expval dmat = self.mean_deriv(exog[i], lpr) sdev = np.sqrt(varfunc(expval)) if weights is not None: w = weights[i] wresid = resid * w wdmat = dmat * w[:, None] else: wresid = resid wdmat = dmat rslt = self.cov_struct.covariance_matrix_solve( expval, i, sdev, (wdmat, wresid)) if rslt is None: return None, None vinv_d, vinv_resid = tuple(rslt) bmat += np.dot(dmat.T, vinv_d) score += np.dot(dmat.T, vinv_resid) update = np.linalg.solve(bmat, score) self._fit_history["cov_adjust"].append( self.cov_struct.cov_adjust) return update, score def update_cached_means(self, mean_params): """ cached_means should always contain the most recent calculation of the group-wise mean vectors. This function should be called every time the regression parameters are changed, to keep the cached means up to date. """ endog = self.endog_li exog = self.exog_li offset = self.offset_li linkinv = self.family.link.inverse self.cached_means = [] for i in range(self.num_group): if len(endog[i]) == 0: continue lpr = np.dot(exog[i], mean_params) if offset is not None: lpr += offset[i] expval = linkinv(lpr) self.cached_means.append((expval, lpr)) def _covmat(self): """ Returns the sampling covariance matrix of the regression parameters and related quantities. Returns ------- cov_robust : array_like The robust, or sandwich estimate of the covariance, which is meaningful even if the working covariance structure is incorrectly specified. cov_naive : array_like The model-based estimate of the covariance, which is meaningful if the covariance structure is correctly specified. cmat : array_like The center matrix of the sandwich expression, used in obtaining score test results. """ endog = self.endog_li exog = self.exog_li weights = getattr(self, "weights_li", None) varfunc = self.family.variance cached_means = self.cached_means # Calculate the naive (model-based) and robust (sandwich) # covariances. bmat, cmat = 0, 0 for i in range(self.num_group): expval, lpr = cached_means[i] resid = endog[i] - expval dmat = self.mean_deriv(exog[i], lpr) sdev = np.sqrt(varfunc(expval)) if weights is not None: w = weights[i] wresid = resid * w wdmat = dmat * w[:, None] else: wresid = resid wdmat = dmat rslt = self.cov_struct.covariance_matrix_solve( expval, i, sdev, (wdmat, wresid)) if rslt is None: return None, None, None, None vinv_d, vinv_resid = tuple(rslt) bmat += np.dot(dmat.T, vinv_d) dvinv_resid = np.dot(dmat.T, vinv_resid) cmat += np.outer(dvinv_resid, dvinv_resid) scale = self.estimate_scale() bmati = np.linalg.inv(bmat) cov_naive = bmati * scale cov_robust = np.dot(bmati, np.dot(cmat, bmati)) cov_naive *= self.scaling_factor cov_robust *= self.scaling_factor return cov_robust, cov_naive, cmat # Calculate the bias-corrected sandwich estimate of Mancl and # DeRouen. def _bc_covmat(self, cov_naive): cov_naive = cov_naive / self.scaling_factor endog = self.endog_li exog = self.exog_li varfunc = self.family.variance cached_means = self.cached_means scale = self.estimate_scale() bcm = 0 for i in range(self.num_group): expval, lpr = cached_means[i] resid = endog[i] - expval dmat = self.mean_deriv(exog[i], lpr) sdev = np.sqrt(varfunc(expval)) rslt = self.cov_struct.covariance_matrix_solve( expval, i, sdev, (dmat,)) if rslt is None: return None vinv_d = rslt[0] vinv_d /= scale hmat = np.dot(vinv_d, cov_naive) hmat = np.dot(hmat, dmat.T).T f = self.weights_li[i] if self.weights is not None else 1. aresid = np.linalg.solve(np.eye(len(resid)) - hmat, resid) rslt = self.cov_struct.covariance_matrix_solve( expval, i, sdev, (aresid,)) if rslt is None: return None srt = rslt[0] srt = f * np.dot(dmat.T, srt) / scale bcm += np.outer(srt, srt) cov_robust_bc = np.dot(cov_naive, np.dot(bcm, cov_naive)) cov_robust_bc *= self.scaling_factor return cov_robust_bc def _starting_params(self): if np.isscalar(self._offset_exposure): offset = None else: offset = self._offset_exposure model = GLM(self.endog, self.exog, family=self.family, offset=offset, freq_weights=self.weights) result = model.fit() return result.params @Appender(_gee_fit_doc) def fit(self, maxiter=60, ctol=1e-6, start_params=None, params_niter=1, first_dep_update=0, cov_type='robust', ddof_scale=None, scaling_factor=1., scale=None): self.scaletype = scale # Subtract this number from the total sample size when # normalizing the scale parameter estimate. if ddof_scale is None: self.ddof_scale = self.exog.shape[1] else: if not ddof_scale >= 0: raise ValueError( "ddof_scale must be a non-negative number or None") self.ddof_scale = ddof_scale self.scaling_factor = scaling_factor self._fit_history = defaultdict(list) if self.weights is not None and cov_type == 'naive': raise ValueError("when using weights, cov_type may not be naive") if start_params is None: mean_params = self._starting_params() else: start_params = np.asarray(start_params) mean_params = start_params.copy() self.update_cached_means(mean_params) del_params = -1. num_assoc_updates = 0 for itr in range(maxiter): update, score = self._update_mean_params() if update is None: warnings.warn("Singular matrix encountered in GEE update", ConvergenceWarning) break mean_params += update self.update_cached_means(mean_params) # L2 norm of the change in mean structure parameters at # this iteration. del_params = np.sqrt(np.sum(score ** 2)) self._fit_history['params'].append(mean_params.copy()) self._fit_history['score'].append(score) self._fit_history['dep_params'].append( self.cov_struct.dep_params) # Do not exit until the association parameters have been # updated at least once. if (del_params < ctol and (num_assoc_updates > 0 or self.update_dep is False)): break # Update the dependence structure if (self.update_dep and (itr % params_niter) == 0 and (itr >= first_dep_update)): self._update_assoc(mean_params) num_assoc_updates += 1 if del_params >= ctol: warnings.warn("Iteration limit reached prior to convergence", IterationLimitWarning) if mean_params is None: warnings.warn("Unable to estimate GEE parameters.", ConvergenceWarning) return None bcov, ncov, _ = self._covmat() if bcov is None: warnings.warn("Estimated covariance structure for GEE " "estimates is singular", ConvergenceWarning) return None bc_cov = None if cov_type == "bias_reduced": bc_cov = self._bc_covmat(ncov) if self.constraint is not None: x = mean_params.copy() mean_params, bcov = self._handle_constraint(mean_params, bcov) if mean_params is None: warnings.warn("Unable to estimate constrained GEE " "parameters.", ConvergenceWarning) return None y, ncov = self._handle_constraint(x, ncov) if y is None: warnings.warn("Unable to estimate constrained GEE " "parameters.", ConvergenceWarning) return None if bc_cov is not None: y, bc_cov = self._handle_constraint(x, bc_cov) if x is None: warnings.warn("Unable to estimate constrained GEE " "parameters.", ConvergenceWarning) return None scale = self.estimate_scale() # kwargs to add to results instance, need to be available in __init__ res_kwds = dict(cov_type=cov_type, cov_robust=bcov, cov_naive=ncov, cov_robust_bc=bc_cov) # The superclass constructor will multiply the covariance # matrix argument bcov by scale, which we do not want, so we # divide bcov by the scale parameter here results = GEEResults(self, mean_params, bcov / scale, scale, cov_type=cov_type, use_t=False, attr_kwds=res_kwds) # attributes not needed during results__init__ results.fit_history = self._fit_history self.fit_history = defaultdict(list) results.score_norm = del_params results.converged = (del_params < ctol) results.cov_struct = self.cov_struct results.params_niter = params_niter results.first_dep_update = first_dep_update results.ctol = ctol results.maxiter = maxiter # These will be copied over to subclasses when upgrading. results._props = ["cov_type", "use_t", "cov_params_default", "cov_robust", "cov_naive", "cov_robust_bc", "fit_history", "score_norm", "converged", "cov_struct", "params_niter", "first_dep_update", "ctol", "maxiter"] return GEEResultsWrapper(results) def _update_regularized(self, params, pen_wt, scad_param, eps): sn, hm = 0, 0 for i in range(self.num_group): expval, _ = self.cached_means[i] resid = self.endog_li[i] - expval sdev = np.sqrt(self.family.variance(expval)) ex = self.exog_li[i] * sdev[:, None]**2 rslt = self.cov_struct.covariance_matrix_solve( expval, i, sdev, (resid, ex)) sn0 = rslt[0] sn += np.dot(ex.T, sn0) hm0 = rslt[1] hm += np.dot(ex.T, hm0) # Wang et al. divide sn here by num_group, but that # seems to be incorrect ap = np.abs(params) clipped = np.clip(scad_param * pen_wt - ap, 0, np.inf) en = pen_wt * clipped * (ap > pen_wt) en /= (scad_param - 1) * pen_wt en += pen_wt * (ap <= pen_wt) en /= eps + ap hm.flat[::hm.shape[0] + 1] += self.num_group * en sn -= self.num_group * en * params update = np.linalg.solve(hm, sn) hm *= self.estimate_scale() return update, hm def _regularized_covmat(self, mean_params): self.update_cached_means(mean_params) ma = 0 for i in range(self.num_group): expval, _ = self.cached_means[i] resid = self.endog_li[i] - expval sdev = np.sqrt(self.family.variance(expval)) ex = self.exog_li[i] * sdev[:, None]**2 rslt = self.cov_struct.covariance_matrix_solve( expval, i, sdev, (resid,)) ma0 = np.dot(ex.T, rslt[0]) ma += np.outer(ma0, ma0) return ma def fit_regularized(self, pen_wt, scad_param=3.7, maxiter=100, ddof_scale=None, update_assoc=5, ctol=1e-5, ztol=1e-3, eps=1e-6, scale=None): """ Regularized estimation for GEE. Parameters ---------- pen_wt : float The penalty weight (a non-negative scalar). scad_param : float Non-negative scalar determining the shape of the Scad penalty. maxiter : int The maximum number of iterations. ddof_scale : int Value to subtract from `nobs` when calculating the denominator degrees of freedom for t-statistics, defaults to the number of columns in `exog`. update_assoc : int The dependence parameters are updated every `update_assoc` iterations of the mean structure parameter updates. ctol : float Convergence criterion, default is one order of magnitude smaller than proposed in section 3.1 of Wang et al. ztol : float Coefficients smaller than this value are treated as being zero, default is based on section 5 of Wang et al. eps : non-negative scalar Numerical constant, see section 3.2 of Wang et al. scale : float or string If a float, this value is used as the scale parameter. If "X2", the scale parameter is always estimated using Pearson's chi-square method (e.g. as in a quasi-Poisson analysis). If None, the default approach for the family is used to estimate the scale parameter. Returns ------- GEEResults instance. Note that not all methods of the results class make sense when the model has been fit with regularization. Notes ----- This implementation assumes that the link is canonical. References ---------- Wang L, Zhou J, Qu A. (2012). Penalized generalized estimating equations for high-dimensional longitudinal data analysis. Biometrics. 2012 Jun;68(2):353-60. doi: 10.1111/j.1541-0420.2011.01678.x. https://www.ncbi.nlm.nih.gov/pubmed/21955051 http://users.stat.umn.edu/~wangx346/research/GEE_selection.pdf """ self.scaletype = scale mean_params = np.zeros(self.exog.shape[1]) self.update_cached_means(mean_params) converged = False fit_history = defaultdict(list) # Subtract this number from the total sample size when # normalizing the scale parameter estimate. if ddof_scale is None: self.ddof_scale = self.exog.shape[1] else: if not ddof_scale >= 0: raise ValueError( "ddof_scale must be a non-negative number or None") self.ddof_scale = ddof_scale # Keep this private for now. In some cases the early steps are # very small so it seems necessary to ensure a certain minimum # number of iterations before testing for convergence. miniter = 20 for itr in range(maxiter): update, hm = self._update_regularized( mean_params, pen_wt, scad_param, eps) if update is None: msg = "Singular matrix encountered in regularized GEE update", warnings.warn(msg, ConvergenceWarning) break if itr > miniter and np.sqrt(np.sum(update**2)) < ctol: converged = True break mean_params += update fit_history['params'].append(mean_params.copy()) self.update_cached_means(mean_params) if itr != 0 and (itr % update_assoc == 0): self._update_assoc(mean_params) if not converged: msg = "GEE.fit_regularized did not converge" warnings.warn(msg) mean_params[np.abs(mean_params) < ztol] = 0 self._update_assoc(mean_params) ma = self._regularized_covmat(mean_params) cov = np.linalg.solve(hm, ma) cov = np.linalg.solve(hm, cov.T) # kwargs to add to results instance, need to be available in __init__ res_kwds = dict(cov_type="robust", cov_robust=cov) scale = self.estimate_scale() rslt = GEEResults(self, mean_params, cov, scale, regularized=True, attr_kwds=res_kwds) rslt.fit_history = fit_history return GEEResultsWrapper(rslt) def _handle_constraint(self, mean_params, bcov): """ Expand the parameter estimate `mean_params` and covariance matrix `bcov` to the coordinate system of the unconstrained model. Parameters ---------- mean_params : array_like A parameter vector estimate for the reduced model. bcov : array_like The covariance matrix of mean_params. Returns ------- mean_params : array_like The input parameter vector mean_params, expanded to the coordinate system of the full model bcov : array_like The input covariance matrix bcov, expanded to the coordinate system of the full model """ # The number of variables in the full model red_p = len(mean_params) full_p = self.constraint.lhs.shape[1] mean_params0 = np.r_[mean_params, np.zeros(full_p - red_p)] # Get the score vector under the full model. save_exog_li = self.exog_li self.exog_li = self.constraint.exog_fulltrans_li import copy save_cached_means = copy.deepcopy(self.cached_means) self.update_cached_means(mean_params0) _, score = self._update_mean_params() if score is None: warnings.warn("Singular matrix encountered in GEE score test", ConvergenceWarning) return None, None _, ncov1, cmat = self._covmat() scale = self.estimate_scale() cmat = cmat / scale ** 2 score2 = score[red_p:] / scale amat = np.linalg.inv(ncov1) bmat_11 = cmat[0:red_p, 0:red_p] bmat_22 = cmat[red_p:, red_p:] bmat_12 = cmat[0:red_p, red_p:] amat_11 = amat[0:red_p, 0:red_p] amat_12 = amat[0:red_p, red_p:] score_cov = bmat_22 - np.dot(amat_12.T, np.linalg.solve(amat_11, bmat_12)) score_cov -= np.dot(bmat_12.T, np.linalg.solve(amat_11, amat_12)) score_cov += np.dot(amat_12.T, np.dot(np.linalg.solve(amat_11, bmat_11), np.linalg.solve(amat_11, amat_12))) from scipy.stats.distributions import chi2 score_statistic = np.dot(score2, np.linalg.solve(score_cov, score2)) score_df = len(score2) score_pvalue = 1 - chi2.cdf(score_statistic, score_df) self.score_test_results = {"statistic": score_statistic, "df": score_df, "p-value": score_pvalue} mean_params = self.constraint.unpack_param(mean_params) bcov = self.constraint.unpack_cov(bcov) self.exog_li = save_exog_li self.cached_means = save_cached_means self.exog = self.constraint.restore_exog() return mean_params, bcov def _update_assoc(self, params): """ Update the association parameters """ self.cov_struct.update(params) def _derivative_exog(self, params, exog=None, transform='dydx', dummy_idx=None, count_idx=None): """ For computing marginal effects, returns dF(XB) / dX where F(.) is the fitted mean. transform can be 'dydx', 'dyex', 'eydx', or 'eyex'. Not all of these make sense in the presence of discrete regressors, but checks are done in the results in get_margeff. """ # This form should be appropriate for group 1 probit, logit, # logistic, cloglog, heckprob, xtprobit. offset_exposure = None if exog is None: exog = self.exog offset_exposure = self._offset_exposure margeff = self.mean_deriv_exog(exog, params, offset_exposure) if 'ex' in transform: margeff *= exog if 'ey' in transform: margeff /= self.predict(params, exog)[:, None] if count_idx is not None: from statsmodels.discrete.discrete_margins import ( _get_count_effects) margeff = _get_count_effects(margeff, exog, count_idx, transform, self, params) if dummy_idx is not None: from statsmodels.discrete.discrete_margins import ( _get_dummy_effects) margeff = _get_dummy_effects(margeff, exog, dummy_idx, transform, self, params) return margeff def qic(self, params, scale, cov_params): """ Returns quasi-information criteria and quasi-likelihood values. Parameters ---------- params : array_like The GEE estimates of the regression parameters. scale : scalar Estimated scale parameter cov_params : array_like An estimate of the covariance matrix for the model parameters. Conventionally this is the robust covariance matrix. Returns ------- ql : scalar The quasi-likelihood value qic : scalar A QIC that can be used to compare the mean and covariance structures of the model. qicu : scalar A simplified QIC that can be used to compare mean structures but not covariance structures Notes ----- The quasi-likelihood used here is obtained by numerically evaluating Wedderburn's integral representation of the quasi-likelihood function. This approach is valid for all families and links. Many other packages use analytical expressions for quasi-likelihoods that are valid in special cases where the link function is canonical. These analytical expressions may omit additive constants that only depend on the data. Therefore, the numerical values of our QL and QIC values will differ from the values reported by other packages. However only the differences between two QIC values calculated for different models using the same data are meaningful. Our QIC should produce the same QIC differences as other software. When using the QIC for models with unknown scale parameter, use a common estimate of the scale parameter for all models being compared. References ---------- .. [*] W. Pan (2001). Akaike's information criterion in generalized estimating equations. Biometrics (57) 1. """ varfunc = self.family.variance means = [] omega = 0.0 # omega^-1 is the model-based covariance assuming independence for i in range(self.num_group): expval, lpr = self.cached_means[i] means.append(expval) dmat = self.mean_deriv(self.exog_li[i], lpr) omega += np.dot(dmat.T, dmat) / scale means = np.concatenate(means) # The quasi-likelihood, use change of variables so the integration is # from -1 to 1. du = means - self.endog nstep = 10000 qv = np.empty(nstep) xv = np.linspace(-0.99999, 1, nstep) for i, g in enumerate(xv): u = self.endog + (g + 1) * du / 2.0 vu = varfunc(u) qv[i] = -np.sum(du**2 * (g + 1) / vu) qv /= (4 * scale) from scipy.integrate import trapz ql = trapz(qv, dx=xv[1] - xv[0]) qicu = -2 * ql + 2 * self.exog.shape[1] qic = -2 * ql + 2 * np.trace(np.dot(omega, cov_params)) return ql, qic, qicu class GEEResults(GLMResults): __doc__ = ( "This class summarizes the fit of a marginal regression model " "using GEE.\n" + _gee_results_doc) def __init__(self, model, params, cov_params, scale, cov_type='robust', use_t=False, regularized=False, **kwds): super(GEEResults, self).__init__( model, params, normalized_cov_params=cov_params, scale=scale) # not added by super self.df_resid = model.df_resid self.df_model = model.df_model self.family = model.family attr_kwds = kwds.pop('attr_kwds', {}) self.__dict__.update(attr_kwds) # we do not do this if the cov_type has already been set # subclasses can set it through attr_kwds if not (hasattr(self, 'cov_type') and hasattr(self, 'cov_params_default')): self.cov_type = cov_type # keep alias covariance_type = self.cov_type.lower() allowed_covariances = ["robust", "naive", "bias_reduced"] if covariance_type not in allowed_covariances: msg = ("GEE: `cov_type` must be one of " + ", ".join(allowed_covariances)) raise ValueError(msg) if cov_type == "robust": cov = self.cov_robust elif cov_type == "naive": cov = self.cov_naive elif cov_type == "bias_reduced": cov = self.cov_robust_bc self.cov_params_default = cov else: if self.cov_type != cov_type: raise ValueError('cov_type in argument is different from ' 'already attached cov_type') @cache_readonly def resid(self): """ The response residuals. """ return self.resid_response def standard_errors(self, cov_type="robust"): """ This is a convenience function that returns the standard errors for any covariance type. The value of `bse` is the standard errors for whichever covariance type is specified as an argument to `fit` (defaults to "robust"). Parameters ---------- cov_type : str One of "robust", "naive", or "bias_reduced". Determines the covariance used to compute standard errors. Defaults to "robust". """ # Check covariance_type covariance_type = cov_type.lower() allowed_covariances = ["robust", "naive", "bias_reduced"] if covariance_type not in allowed_covariances: msg = ("GEE: `covariance_type` must be one of " + ", ".join(allowed_covariances)) raise ValueError(msg) if covariance_type == "robust": return np.sqrt(np.diag(self.cov_robust)) elif covariance_type == "naive": return np.sqrt(np.diag(self.cov_naive)) elif covariance_type == "bias_reduced": if self.cov_robust_bc is None: raise ValueError( "GEE: `bias_reduced` covariance not available") return np.sqrt(np.diag(self.cov_robust_bc)) # Need to override to allow for different covariance types. @cache_readonly def bse(self): return self.standard_errors(self.cov_type) def score_test(self): """ Return the results of a score test for a linear constraint. Returns ------- Adictionary containing the p-value, the test statistic, and the degrees of freedom for the score test. Notes ----- See also GEE.compare_score_test for an alternative way to perform a score test. GEEResults.score_test is more general, in that it supports testing arbitrary linear equality constraints. However GEE.compare_score_test might be easier to use when comparing two explicit models. References ---------- Xu Guo and Wei Pan (2002). "Small sample performance of the score test in GEE". http://www.sph.umn.edu/faculty1/wp-content/uploads/2012/11/rr2002-013.pdf """ if not hasattr(self.model, "score_test_results"): msg = "score_test on results instance only available when " msg += " model was fit with constraints" raise ValueError(msg) return self.model.score_test_results @cache_readonly def resid_split(self): """ Returns the residuals, the endogeneous data minus the fitted values from the model. The residuals are returned as a list of arrays containing the residuals for each cluster. """ sresid = [] for v in self.model.group_labels: ii = self.model.group_indices[v] sresid.append(self.resid[ii]) return sresid @cache_readonly def resid_centered(self): """ Returns the residuals centered within each group. """ cresid = self.resid.copy() for v in self.model.group_labels: ii = self.model.group_indices[v] cresid[ii] -= cresid[ii].mean() return cresid @cache_readonly def resid_centered_split(self): """ Returns the residuals centered within each group. The residuals are returned as a list of arrays containing the centered residuals for each cluster. """ sresid = [] for v in self.model.group_labels: ii = self.model.group_indices[v] sresid.append(self.centered_resid[ii]) return sresid def qic(self, scale=None): """ Returns the QIC and QICu information criteria. For families with a scale parameter (e.g. Gaussian), provide as the scale argument the estimated scale from the largest model under consideration. If the scale parameter is not provided, the estimated scale parameter is used. Doing this does not allow comparisons of QIC values between models. """ # It is easy to forget to set the scale parameter. Sometimes # this is intentional, so we warn. if scale is None: warnings.warn("QIC values obtained using scale=None are not " "appropriate for comparing models") if scale is None: scale = self.scale _, qic, qicu = self.model.qic(self.params, scale, self.cov_params()) return qic, qicu # FIXME: alias to be removed, temporary backwards compatibility split_resid = resid_split centered_resid = resid_centered split_centered_resid = resid_centered_split @Appender(_plot_added_variable_doc % {'extra_params_doc': ''}) def plot_added_variable(self, focus_exog, resid_type=None, use_glm_weights=True, fit_kwargs=None, ax=None): from statsmodels.graphics.regressionplots import plot_added_variable fig = plot_added_variable(self, focus_exog, resid_type=resid_type, use_glm_weights=use_glm_weights, fit_kwargs=fit_kwargs, ax=ax) return fig @Appender(_plot_partial_residuals_doc % {'extra_params_doc': ''}) def plot_partial_residuals(self, focus_exog, ax=None): from statsmodels.graphics.regressionplots import plot_partial_residuals return plot_partial_residuals(self, focus_exog, ax=ax) @Appender(_plot_ceres_residuals_doc % {'extra_params_doc': ''}) def plot_ceres_residuals(self, focus_exog, frac=0.66, cond_means=None, ax=None): from statsmodels.graphics.regressionplots import plot_ceres_residuals return plot_ceres_residuals(self, focus_exog, frac, cond_means=cond_means, ax=ax) def conf_int(self, alpha=.05, cols=None, cov_type=None): """ Returns confidence intervals for the fitted parameters. Parameters ---------- alpha : float, optional The `alpha` level for the confidence interval. i.e., The default `alpha` = .05 returns a 95% confidence interval. cols : array_like, optional `cols` specifies which confidence intervals to return cov_type : str The covariance type used for computing standard errors; must be one of 'robust', 'naive', and 'bias reduced'. See `GEE` for details. Notes ----- The confidence interval is based on the Gaussian distribution. """ # super does not allow to specify cov_type and method is not # implemented, # FIXME: remove this method here if cov_type is None: bse = self.bse else: bse = self.standard_errors(cov_type=cov_type) params = self.params dist = stats.norm q = dist.ppf(1 - alpha / 2) if cols is None: lower = self.params - q * bse upper = self.params + q * bse else: cols = np.asarray(cols) lower = params[cols] - q * bse[cols] upper = params[cols] + q * bse[cols] return np.asarray(lzip(lower, upper)) def summary(self, yname=None, xname=None, title=None, alpha=.05): """ Summarize the GEE regression results Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Names for the exogenous variables, default is `var_#` for ## in the number of regressors. Must match the number of parameters in the model title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals cov_type : str The covariance type used to compute the standard errors; one of 'robust' (the usual robust sandwich-type covariance estimate), 'naive' (ignores dependence), and 'bias reduced' (the Mancl/DeRouen estimate). Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : class to hold summary results """ top_left = [('Dep. Variable:', None), ('Model:', None), ('Method:', ['Generalized']), ('', ['Estimating Equations']), ('Family:', [self.model.family.__class__.__name__]), ('Dependence structure:', [self.model.cov_struct.__class__.__name__]), ('Date:', None), ('Covariance type: ', [self.cov_type, ]) ] NY = [len(y) for y in self.model.endog_li] top_right = [('No. Observations:', [sum(NY)]), ('No. clusters:', [len(self.model.endog_li)]), ('Min. cluster size:', [min(NY)]), ('Max. cluster size:', [max(NY)]), ('Mean cluster size:', ["%.1f" % np.mean(NY)]), ('Num. iterations:', ['%d' % len(self.fit_history['params'])]), ('Scale:', ["%.3f" % self.scale]), ('Time:', None), ] # The skew of the residuals skew1 = stats.skew(self.resid) kurt1 = stats.kurtosis(self.resid) skew2 = stats.skew(self.centered_resid) kurt2 = stats.kurtosis(self.centered_resid) diagn_left = [('Skew:', ["%12.4f" % skew1]), ('Centered skew:', ["%12.4f" % skew2])] diagn_right = [('Kurtosis:', ["%12.4f" % kurt1]), ('Centered kurtosis:', ["%12.4f" % kurt2]) ] if title is None: title = self.model.__class__.__name__ + ' ' +\ "Regression Results" # Override the exog variable names if xname is provided as an # argument. if xname is None: xname = self.model.exog_names if yname is None: yname = self.model.endog_names # Create summary table instance from statsmodels.iolib.summary import Summary smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, yname=yname, xname=xname, title=title) smry.add_table_params(self, yname=yname, xname=xname, alpha=alpha, use_t=False) smry.add_table_2cols(self, gleft=diagn_left, gright=diagn_right, yname=yname, xname=xname, title="") return smry def get_margeff(self, at='overall', method='dydx', atexog=None, dummy=False, count=False): """Get marginal effects of the fitted model. Parameters ---------- at : str, optional Options are: - 'overall', The average of the marginal effects at each observation. - 'mean', The marginal effects at the mean of each regressor. - 'median', The marginal effects at the median of each regressor. - 'zero', The marginal effects at zero for each regressor. - 'all', The marginal effects at each observation. If `at` is 'all' only margeff will be available. Note that if `exog` is specified, then marginal effects for all variables not specified by `exog` are calculated using the `at` option. method : str, optional Options are: - 'dydx' - dy/dx - No transformation is made and marginal effects are returned. This is the default. - 'eyex' - estimate elasticities of variables in `exog` -- d(lny)/d(lnx) - 'dyex' - estimate semi-elasticity -- dy/d(lnx) - 'eydx' - estimate semi-elasticity -- d(lny)/dx Note that tranformations are done after each observation is calculated. Semi-elasticities for binary variables are computed using the midpoint method. 'dyex' and 'eyex' do not make sense for discrete variables. atexog : array_like, optional Optionally, you can provide the exogenous variables over which to get the marginal effects. This should be a dictionary with the key as the zero-indexed column number and the value of the dictionary. Default is None for all independent variables less the constant. dummy : bool, optional If False, treats binary variables (if present) as continuous. This is the default. Else if True, treats binary variables as changing from 0 to 1. Note that any variable that is either 0 or 1 is treated as binary. Each binary variable is treated separately for now. count : bool, optional If False, treats count variables (if present) as continuous. This is the default. Else if True, the marginal effect is the change in probabilities when each observation is increased by one. Returns ------- effects : ndarray the marginal effect corresponding to the input options Notes ----- When using after Poisson, returns the expected number of events per period, assuming that the model is loglinear. """ if self.model.constraint is not None: warnings.warn("marginal effects ignore constraints", ValueWarning) return GEEMargins(self, (at, method, atexog, dummy, count)) def plot_isotropic_dependence(self, ax=None, xpoints=10, min_n=50): """ Create a plot of the pairwise products of within-group residuals against the corresponding time differences. This plot can be used to assess the possible form of an isotropic covariance structure. Parameters ---------- ax : AxesSubplot An axes on which to draw the graph. If None, new figure and axes objects are created xpoints : scalar or array_like If scalar, the number of points equally spaced points on the time difference axis used to define bins for calculating local means. If an array, the specific points that define the bins. min_n : int The minimum sample size in a bin for the mean residual product to be included on the plot. """ from statsmodels.graphics import utils as gutils resid = self.model.cluster_list(self.resid) time = self.model.cluster_list(self.model.time) # All within-group pairwise time distances (xdt) and the # corresponding products of scaled residuals (xre). xre, xdt = [], [] for re, ti in zip(resid, time): ix = np.tril_indices(re.shape[0], 0) re = re[ix[0]] * re[ix[1]] / self.scale ** 2 xre.append(re) dists = np.sqrt(((ti[ix[0], :] - ti[ix[1], :]) ** 2).sum(1)) xdt.append(dists) xre = np.concatenate(xre) xdt = np.concatenate(xdt) if ax is None: fig, ax = gutils.create_mpl_ax(ax) else: fig = ax.get_figure() # Convert to a correlation ii = np.flatnonzero(xdt == 0) v0 = np.mean(xre[ii]) xre /= v0 # Use the simple average to smooth, since fancier smoothers # that trim and downweight outliers give biased results (we # need the actual mean of a skewed distribution). if np.isscalar(xpoints): xpoints = np.linspace(0, max(xdt), xpoints) dg = np.digitize(xdt, xpoints) dgu = np.unique(dg) hist = np.asarray([np.sum(dg == k) for k in dgu]) ii = np.flatnonzero(hist >= min_n) dgu = dgu[ii] dgy = np.asarray([np.mean(xre[dg == k]) for k in dgu]) dgx = np.asarray([np.mean(xdt[dg == k]) for k in dgu]) ax.plot(dgx, dgy, '-', color='orange', lw=5) ax.set_xlabel("Time difference") ax.set_ylabel("Product of scaled residuals") return fig def sensitivity_params(self, dep_params_first, dep_params_last, num_steps): """ Refits the GEE model using a sequence of values for the dependence parameters. Parameters ---------- dep_params_first : array_like The first dep_params in the sequence dep_params_last : array_like The last dep_params in the sequence num_steps : int The number of dep_params in the sequence Returns ------- results : array_like The GEEResults objects resulting from the fits. """ model = self.model import copy cov_struct = copy.deepcopy(self.model.cov_struct) # We are fixing the dependence structure in each run. update_dep = model.update_dep model.update_dep = False dep_params = [] results = [] for x in np.linspace(0, 1, num_steps): dp = x * dep_params_last + (1 - x) * dep_params_first dep_params.append(dp) model.cov_struct = copy.deepcopy(cov_struct) model.cov_struct.dep_params = dp rslt = model.fit(start_params=self.params, ctol=self.ctol, params_niter=self.params_niter, first_dep_update=self.first_dep_update, cov_type=self.cov_type) results.append(rslt) model.update_dep = update_dep return results # FIXME: alias to be removed, temporary backwards compatibility params_sensitivity = sensitivity_params class GEEResultsWrapper(lm.RegressionResultsWrapper): _attrs = { 'centered_resid': 'rows', } _wrap_attrs = wrap.union_dicts(lm.RegressionResultsWrapper._wrap_attrs, _attrs) wrap.populate_wrapper(GEEResultsWrapper, GEEResults) # noqa:E305 class OrdinalGEE(GEE): __doc__ = ( " Ordinal Response Marginal Regression Model using GEE\n" + _gee_init_doc % {'extra_params': base._missing_param_doc, 'family_doc': _gee_ordinal_family_doc, 'example': _gee_ordinal_example}) def __init__(self, endog, exog, groups, time=None, family=None, cov_struct=None, missing='none', offset=None, dep_data=None, constraint=None, **kwargs): if family is None: family = families.Binomial() else: if not isinstance(family, families.Binomial): raise ValueError("ordinal GEE must use a Binomial family") if cov_struct is None: cov_struct = cov_structs.OrdinalIndependence() endog, exog, groups, time, offset = self.setup_ordinal( endog, exog, groups, time, offset) super(OrdinalGEE, self).__init__(endog, exog, groups, time, family, cov_struct, missing, offset, dep_data, constraint) def setup_ordinal(self, endog, exog, groups, time, offset): """ Restructure ordinal data as binary indicators so that they can be analyzed using Generalized Estimating Equations. """ self.endog_orig = endog.copy() self.exog_orig = exog.copy() self.groups_orig = groups.copy() if offset is not None: self.offset_orig = offset.copy() else: self.offset_orig = None offset = np.zeros(len(endog)) if time is not None: self.time_orig = time.copy() else: self.time_orig = None time = np.zeros((len(endog), 1)) exog = np.asarray(exog) endog = np.asarray(endog) groups = np.asarray(groups) time = np.asarray(time) offset = np.asarray(offset) # The unique outcomes, except the greatest one. self.endog_values = np.unique(endog) endog_cuts = self.endog_values[0:-1] ncut = len(endog_cuts) nrows = ncut * len(endog) exog_out = np.zeros((nrows, exog.shape[1]), dtype=np.float64) endog_out = np.zeros(nrows, dtype=np.float64) intercepts = np.zeros((nrows, ncut), dtype=np.float64) groups_out = np.zeros(nrows, dtype=groups.dtype) time_out = np.zeros((nrows, time.shape[1]), dtype=np.float64) offset_out = np.zeros(nrows, dtype=np.float64) jrow = 0 zipper = zip(exog, endog, groups, time, offset) for (exog_row, endog_value, group_value, time_value, offset_value) in zipper: # Loop over thresholds for the indicators for thresh_ix, thresh in enumerate(endog_cuts): exog_out[jrow, :] = exog_row endog_out[jrow] = (int(endog_value > thresh)) intercepts[jrow, thresh_ix] = 1 groups_out[jrow] = group_value time_out[jrow] = time_value offset_out[jrow] = offset_value jrow += 1 exog_out = np.concatenate((intercepts, exog_out), axis=1) # exog column names, including intercepts xnames = ["I(y>%.1f)" % v for v in endog_cuts] if type(self.exog_orig) == pd.DataFrame: xnames.extend(self.exog_orig.columns) else: xnames.extend(["x%d" % k for k in range(1, exog.shape[1] + 1)]) exog_out = pd.DataFrame(exog_out, columns=xnames) # Preserve the endog name if there is one if type(self.endog_orig) == pd.Series: endog_out = pd.Series(endog_out, name=self.endog_orig.name) return endog_out, exog_out, groups_out, time_out, offset_out def _starting_params(self): exposure = getattr(self, "exposure", None) model = GEE(self.endog, self.exog, self.groups, time=self.time, family=families.Binomial(), offset=self.offset, exposure=exposure) result = model.fit() return result.params @Appender(_gee_fit_doc) def fit(self, maxiter=60, ctol=1e-6, start_params=None, params_niter=1, first_dep_update=0, cov_type='robust'): rslt = super(OrdinalGEE, self).fit(maxiter, ctol, start_params, params_niter, first_dep_update, cov_type=cov_type) rslt = rslt._results # use unwrapped instance res_kwds = dict(((k, getattr(rslt, k)) for k in rslt._props)) # Convert the GEEResults to an OrdinalGEEResults ord_rslt = OrdinalGEEResults(self, rslt.params, rslt.cov_params() / rslt.scale, rslt.scale, cov_type=cov_type, attr_kwds=res_kwds) # for k in rslt._props: # setattr(ord_rslt, k, getattr(rslt, k)) # TODO: document or delete return OrdinalGEEResultsWrapper(ord_rslt) class OrdinalGEEResults(GEEResults): __doc__ = ( "This class summarizes the fit of a marginal regression model" "for an ordinal response using GEE.\n" + _gee_results_doc) def plot_distribution(self, ax=None, exog_values=None): """ Plot the fitted probabilities of endog in an ordinal model, for specified values of the predictors. Parameters ---------- ax : AxesSubplot An axes on which to draw the graph. If None, new figure and axes objects are created exog_values : array_like A list of dictionaries, with each dictionary mapping variable names to values at which the variable is held fixed. The values P(endog=y | exog) are plotted for all possible values of y, at the given exog value. Variables not included in a dictionary are held fixed at the mean value. Example: -------- We have a model with covariates 'age' and 'sex', and wish to plot the probabilities P(endog=y | exog) for males (sex=0) and for females (sex=1), as separate paths on the plot. Since 'age' is not included below in the map, it is held fixed at its mean value. >>> ev = [{"sex": 1}, {"sex": 0}] >>> rslt.distribution_plot(exog_values=ev) """ from statsmodels.graphics import utils as gutils if ax is None: fig, ax = gutils.create_mpl_ax(ax) else: fig = ax.get_figure() # If no covariate patterns are specified, create one with all # variables set to their mean values. if exog_values is None: exog_values = [{}, ] exog_means = self.model.exog.mean(0) ix_icept = [i for i, x in enumerate(self.model.exog_names) if x.startswith("I(")] for ev in exog_values: for k in ev.keys(): if k not in self.model.exog_names: raise ValueError("%s is not a variable in the model" % k) # Get the fitted probability for each level, at the given # covariate values. pr = [] for j in ix_icept: xp = np.zeros_like(self.params) xp[j] = 1. for i, vn in enumerate(self.model.exog_names): if i in ix_icept: continue # User-specified value if vn in ev: xp[i] = ev[vn] # Mean value else: xp[i] = exog_means[i] p = 1 / (1 + np.exp(-np.dot(xp, self.params))) pr.append(p) pr.insert(0, 1) pr.append(0) pr = np.asarray(pr) prd = -np.diff(pr) ax.plot(self.model.endog_values, prd, 'o-') ax.set_xlabel("Response value") ax.set_ylabel("Probability") ax.set_ylim(0, 1) return fig def _score_test_submodel(par, sub): """ Return transformation matrices for design matrices. Parameters ---------- par : instance The parent model sub : instance The sub-model Returns ------- qm : array_like Matrix mapping the design matrix of the parent to the design matrix for the sub-model. qc : array_like Matrix mapping the design matrix of the parent to the orthogonal complement of the columnspace of the submodel in the columnspace of the parent. Notes ----- Returns None, None if the provided submodel is not actually a submodel. """ x1 = par.exog x2 = sub.exog u, s, vt = np.linalg.svd(x1, 0) # Get the orthogonal complement of col(x2) in col(x1). a, _, _ = np.linalg.svd(x2, 0) a = u - np.dot(a, np.dot(a.T, u)) x2c, sb, _ = np.linalg.svd(a, 0) x2c = x2c[:, sb > 1e-12] # x1 * qm = x2 qm = np.dot(vt.T, np.dot(u.T, x2) / s[:, None]) e = np.max(np.abs(x2 - np.dot(x1, qm))) if e > 1e-8: return None, None # x1 * qc = x2c qc = np.dot(vt.T, np.dot(u.T, x2c) / s[:, None]) return qm, qc class OrdinalGEEResultsWrapper(GEEResultsWrapper): pass wrap.populate_wrapper(OrdinalGEEResultsWrapper, OrdinalGEEResults) # noqa:E305 class NominalGEE(GEE): __doc__ = ( " Nominal Response Marginal Regression Model using GEE.\n" + _gee_init_doc % {'extra_params': base._missing_param_doc, 'family_doc': _gee_nominal_family_doc, 'example': _gee_nominal_example}) def __init__(self, endog, exog, groups, time=None, family=None, cov_struct=None, missing='none', offset=None, dep_data=None, constraint=None, **kwargs): endog, exog, groups, time, offset = self.setup_nominal( endog, exog, groups, time, offset) if family is None: family = _Multinomial(self.ncut + 1) if cov_struct is None: cov_struct = cov_structs.NominalIndependence() super(NominalGEE, self).__init__( endog, exog, groups, time, family, cov_struct, missing, offset, dep_data, constraint) def _starting_params(self): exposure = getattr(self, "exposure", None) model = GEE(self.endog, self.exog, self.groups, time=self.time, family=families.Binomial(), offset=self.offset, exposure=exposure) result = model.fit() return result.params def setup_nominal(self, endog, exog, groups, time, offset): """ Restructure nominal data as binary indicators so that they can be analyzed using Generalized Estimating Equations. """ self.endog_orig = endog.copy() self.exog_orig = exog.copy() self.groups_orig = groups.copy() if offset is not None: self.offset_orig = offset.copy() else: self.offset_orig = None offset = np.zeros(len(endog)) if time is not None: self.time_orig = time.copy() else: self.time_orig = None time = np.zeros((len(endog), 1)) exog = np.asarray(exog) endog = np.asarray(endog) groups = np.asarray(groups) time = np.asarray(time) offset = np.asarray(offset) # The unique outcomes, except the greatest one. self.endog_values = np.unique(endog) endog_cuts = self.endog_values[0:-1] ncut = len(endog_cuts) self.ncut = ncut nrows = len(endog_cuts) * exog.shape[0] ncols = len(endog_cuts) * exog.shape[1] exog_out = np.zeros((nrows, ncols), dtype=np.float64) endog_out = np.zeros(nrows, dtype=np.float64) groups_out = np.zeros(nrows, dtype=np.float64) time_out = np.zeros((nrows, time.shape[1]), dtype=np.float64) offset_out = np.zeros(nrows, dtype=np.float64) jrow = 0 zipper = zip(exog, endog, groups, time, offset) for (exog_row, endog_value, group_value, time_value, offset_value) in zipper: # Loop over thresholds for the indicators for thresh_ix, thresh in enumerate(endog_cuts): u = np.zeros(len(endog_cuts), dtype=np.float64) u[thresh_ix] = 1 exog_out[jrow, :] = np.kron(u, exog_row) endog_out[jrow] = (int(endog_value == thresh)) groups_out[jrow] = group_value time_out[jrow] = time_value offset_out[jrow] = offset_value jrow += 1 # exog names if isinstance(self.exog_orig, pd.DataFrame): xnames_in = self.exog_orig.columns else: xnames_in = ["x%d" % k for k in range(1, exog.shape[1] + 1)] xnames = [] for tr in endog_cuts: xnames.extend(["%s[%.1f]" % (v, tr) for v in xnames_in]) exog_out = pd.DataFrame(exog_out, columns=xnames) exog_out = pd.DataFrame(exog_out, columns=xnames) # Preserve endog name if there is one if isinstance(self.endog_orig, pd.Series): endog_out = pd.Series(endog_out, name=self.endog_orig.name) return endog_out, exog_out, groups_out, time_out, offset_out def mean_deriv(self, exog, lin_pred): """ Derivative of the expected endog with respect to the parameters. Parameters ---------- exog : array_like The exogeneous data at which the derivative is computed, number of rows must be a multiple of `ncut`. lin_pred : array_like The values of the linear predictor, length must be multiple of `ncut`. Returns ------- The derivative of the expected endog with respect to the parameters. """ expval = np.exp(lin_pred) # Reshape so that each row contains all the indicators # corresponding to one multinomial observation. expval_m = np.reshape(expval, (len(expval) // self.ncut, self.ncut)) # The normalizing constant for the multinomial probabilities. denom = 1 + expval_m.sum(1) denom = np.kron(denom, np.ones(self.ncut, dtype=np.float64)) # The multinomial probabilities mprob = expval / denom # First term of the derivative: denom * expval' / denom^2 = # expval' / denom. dmat = mprob[:, None] * exog # Second term of the derivative: -expval * denom' / denom^2 ddenom = expval[:, None] * exog dmat -= mprob[:, None] * ddenom / denom[:, None] return dmat def mean_deriv_exog(self, exog, params, offset_exposure=None): """ Derivative of the expected endog with respect to exog for the multinomial model, used in analyzing marginal effects. Parameters ---------- exog : array_like The exogeneous data at which the derivative is computed, number of rows must be a multiple of `ncut`. lpr : array_like The linear predictor values, length must be multiple of `ncut`. Returns ------- The value of the derivative of the expected endog with respect to exog. Notes ----- offset_exposure must be set at None for the multinomial family. """ if offset_exposure is not None: warnings.warn("Offset/exposure ignored for the multinomial family", ValueWarning) lpr = np.dot(exog, params) expval = np.exp(lpr) expval_m = np.reshape(expval, (len(expval) // self.ncut, self.ncut)) denom = 1 + expval_m.sum(1) denom = np.kron(denom, np.ones(self.ncut, dtype=np.float64)) bmat0 = np.outer(np.ones(exog.shape[0]), params) # Masking matrix qmat = [] for j in range(self.ncut): ee = np.zeros(self.ncut, dtype=np.float64) ee[j] = 1 qmat.append(np.kron(ee, np.ones(len(params) // self.ncut))) qmat = np.array(qmat) qmat = np.kron(np.ones((exog.shape[0] // self.ncut, 1)), qmat) bmat = bmat0 * qmat dmat = expval[:, None] * bmat / denom[:, None] expval_mb = np.kron(expval_m, np.ones((self.ncut, 1))) expval_mb = np.kron(expval_mb, np.ones((1, self.ncut))) dmat -= expval[:, None] * (bmat * expval_mb) / denom[:, None] ** 2 return dmat @Appender(_gee_fit_doc) def fit(self, maxiter=60, ctol=1e-6, start_params=None, params_niter=1, first_dep_update=0, cov_type='robust'): rslt = super(NominalGEE, self).fit(maxiter, ctol, start_params, params_niter, first_dep_update, cov_type=cov_type) if rslt is None: warnings.warn("GEE updates did not converge", ConvergenceWarning) return None rslt = rslt._results # use unwrapped instance res_kwds = dict(((k, getattr(rslt, k)) for k in rslt._props)) # Convert the GEEResults to a NominalGEEResults nom_rslt = NominalGEEResults(self, rslt.params, rslt.cov_params() / rslt.scale, rslt.scale, cov_type=cov_type, attr_kwds=res_kwds) # TODO: document or delete # for k in rslt._props: # setattr(nom_rslt, k, getattr(rslt, k)) return NominalGEEResultsWrapper(nom_rslt) class NominalGEEResults(GEEResults): __doc__ = ( "This class summarizes the fit of a marginal regression model" "for a nominal response using GEE.\n" + _gee_results_doc) def plot_distribution(self, ax=None, exog_values=None): """ Plot the fitted probabilities of endog in an nominal model, for specified values of the predictors. Parameters ---------- ax : AxesSubplot An axes on which to draw the graph. If None, new figure and axes objects are created exog_values : array_like A list of dictionaries, with each dictionary mapping variable names to values at which the variable is held fixed. The values P(endog=y | exog) are plotted for all possible values of y, at the given exog value. Variables not included in a dictionary are held fixed at the mean value. Example: -------- We have a model with covariates 'age' and 'sex', and wish to plot the probabilities P(endog=y | exog) for males (sex=0) and for females (sex=1), as separate paths on the plot. Since 'age' is not included below in the map, it is held fixed at its mean value. >>> ex = [{"sex": 1}, {"sex": 0}] >>> rslt.distribution_plot(exog_values=ex) """ from statsmodels.graphics import utils as gutils if ax is None: fig, ax = gutils.create_mpl_ax(ax) else: fig = ax.get_figure() # If no covariate patterns are specified, create one with all # variables set to their mean values. if exog_values is None: exog_values = [{}, ] link = self.model.family.link.inverse ncut = self.model.family.ncut k = int(self.model.exog.shape[1] / ncut) exog_means = self.model.exog.mean(0)[0:k] exog_names = self.model.exog_names[0:k] exog_names = [x.split("[")[0] for x in exog_names] params = np.reshape(self.params, (ncut, len(self.params) // ncut)) for ev in exog_values: exog = exog_means.copy() for k in ev.keys(): if k not in exog_names: raise ValueError("%s is not a variable in the model" % k) ii = exog_names.index(k) exog[ii] = ev[k] lpr = np.dot(params, exog) pr = link(lpr) pr = np.r_[pr, 1 - pr.sum()] ax.plot(self.model.endog_values, pr, 'o-') ax.set_xlabel("Response value") ax.set_ylabel("Probability") ax.set_xticks(self.model.endog_values) ax.set_xticklabels(self.model.endog_values) ax.set_ylim(0, 1) return fig class NominalGEEResultsWrapper(GEEResultsWrapper): pass wrap.populate_wrapper(NominalGEEResultsWrapper, NominalGEEResults) # noqa:E305 class _MultinomialLogit(Link): """ The multinomial logit transform, only for use with GEE. Notes ----- The data are assumed coded as binary indicators, where each observed multinomial value y is coded as I(y == S[0]), ..., I(y == S[-1]), where S is the set of possible response labels, excluding the largest one. Thererefore functions in this class should only be called using vector argument whose length is a multiple of |S| = ncut, which is an argument to be provided when initializing the class. call and derivative use a private method _clean to trim p by 1e-10 so that p is in (0, 1) """ def __init__(self, ncut): self.ncut = ncut def inverse(self, lpr): """ Inverse of the multinomial logit transform, which gives the expected values of the data as a function of the linear predictors. Parameters ---------- lpr : array_like (length must be divisible by `ncut`) The linear predictors Returns ------- prob : ndarray Probabilities, or expected values """ expval = np.exp(lpr) denom = 1 + np.reshape(expval, (len(expval) // self.ncut, self.ncut)).sum(1) denom = np.kron(denom, np.ones(self.ncut, dtype=np.float64)) prob = expval / denom return prob class _Multinomial(families.Family): """ Pseudo-link function for fitting nominal multinomial models with GEE. Not for use outside the GEE class. """ links = [_MultinomialLogit, ] variance = varfuncs.binary safe_links = [_MultinomialLogit, ] def __init__(self, nlevels): """ Parameters ---------- nlevels : int The number of distinct categories for the multinomial distribution. """ self.initialize(nlevels) def initialize(self, nlevels): self.ncut = nlevels - 1 self.link = _MultinomialLogit(self.ncut) class GEEMargins(object): """ Estimated marginal effects for a regression model fit with GEE. Parameters ---------- results : GEEResults instance The results instance of a fitted discrete choice model args : tuple Args are passed to `get_margeff`. This is the same as results.get_margeff. See there for more information. kwargs : dict Keyword args are passed to `get_margeff`. This is the same as results.get_margeff. See there for more information. """ def __init__(self, results, args, kwargs={}): self._cache = {} self.results = results self.get_margeff(*args, **kwargs) def _reset(self): self._cache = {} @cache_readonly def tvalues(self): _check_at_is_all(self.margeff_options) return self.margeff / self.margeff_se def summary_frame(self, alpha=.05): """ Returns a DataFrame summarizing the marginal effects. Parameters ---------- alpha : float Number between 0 and 1. The confidence intervals have the probability 1-alpha. Returns ------- frame : DataFrames A DataFrame summarizing the marginal effects. """ _check_at_is_all(self.margeff_options) from pandas import DataFrame names = [_transform_names[self.margeff_options['method']], 'Std. Err.', 'z', 'Pr(>|z|)', 'Conf. Int. Low', 'Cont. Int. Hi.'] ind = self.results.model.exog.var(0) != 0 # True if not a constant exog_names = self.results.model.exog_names var_names = [name for i, name in enumerate(exog_names) if ind[i]] table = np.column_stack((self.margeff, self.margeff_se, self.tvalues, self.pvalues, self.conf_int(alpha))) return DataFrame(table, columns=names, index=var_names) @cache_readonly def pvalues(self): _check_at_is_all(self.margeff_options) return stats.norm.sf(np.abs(self.tvalues)) * 2 def conf_int(self, alpha=.05): """ Returns the confidence intervals of the marginal effects Parameters ---------- alpha : float Number between 0 and 1. The confidence intervals have the probability 1-alpha. Returns ------- conf_int : ndarray An array with lower, upper confidence intervals for the marginal effects. """ _check_at_is_all(self.margeff_options) me_se = self.margeff_se q = stats.norm.ppf(1 - alpha / 2) lower = self.margeff - q * me_se upper = self.margeff + q * me_se return np.asarray(lzip(lower, upper)) def summary(self, alpha=.05): """ Returns a summary table for marginal effects Parameters ---------- alpha : float Number between 0 and 1. The confidence intervals have the probability 1-alpha. Returns ------- Summary : SummaryTable A SummaryTable instance """ _check_at_is_all(self.margeff_options) results = self.results model = results.model title = model.__class__.__name__ + " Marginal Effects" method = self.margeff_options['method'] top_left = [('Dep. Variable:', [model.endog_names]), ('Method:', [method]), ('At:', [self.margeff_options['at']]), ] from statsmodels.iolib.summary import (Summary, summary_params, table_extend) exog_names = model.exog_names[:] # copy smry = Summary() const_idx = model.data.const_idx if const_idx is not None: exog_names.pop(const_idx) J = int(getattr(model, "J", 1)) if J > 1: yname, yname_list = results._get_endog_name(model.endog_names, None, all=True) else: yname = model.endog_names yname_list = [yname] smry.add_table_2cols(self, gleft=top_left, gright=[], yname=yname, xname=exog_names, title=title) # NOTE: add_table_params is not general enough yet for margeff # could use a refactor with getattr instead of hard-coded params # tvalues etc. table = [] conf_int = self.conf_int(alpha) margeff = self.margeff margeff_se = self.margeff_se tvalues = self.tvalues pvalues = self.pvalues if J > 1: for eq in range(J): restup = (results, margeff[:, eq], margeff_se[:, eq], tvalues[:, eq], pvalues[:, eq], conf_int[:, :, eq]) tble = summary_params(restup, yname=yname_list[eq], xname=exog_names, alpha=alpha, use_t=False, skip_header=True) tble.title = yname_list[eq] # overwrite coef with method name header = ['', _transform_names[method], 'std err', 'z', 'P>|z|', '[%3.1f%% Conf. Int.]' % (100 - alpha * 100)] tble.insert_header_row(0, header) # from IPython.core.debugger import Pdb; Pdb().set_trace() table.append(tble) table = table_extend(table, keep_headers=True) else: restup = (results, margeff, margeff_se, tvalues, pvalues, conf_int) table = summary_params(restup, yname=yname, xname=exog_names, alpha=alpha, use_t=False, skip_header=True) header = ['', _transform_names[method], 'std err', 'z', 'P>|z|', '[%3.1f%% Conf. Int.]' % (100 - alpha * 100)] table.insert_header_row(0, header) smry.tables.append(table) return smry def get_margeff(self, at='overall', method='dydx', atexog=None, dummy=False, count=False): self._reset() # always reset the cache when this is called # TODO: if at is not all or overall, we can also put atexog values # in summary table head method = method.lower() at = at.lower() _check_margeff_args(at, method) self.margeff_options = dict(method=method, at=at) results = self.results model = results.model params = results.params exog = model.exog.copy() # copy because values are changed effects_idx = exog.var(0) != 0 const_idx = model.data.const_idx if dummy: _check_discrete_args(at, method) dummy_idx, dummy = _get_dummy_index(exog, const_idx) else: dummy_idx = None if count: _check_discrete_args(at, method) count_idx, count = _get_count_index(exog, const_idx) else: count_idx = None # get the exogenous variables exog = _get_margeff_exog(exog, at, atexog, effects_idx) # get base marginal effects, handled by sub-classes effects = model._derivative_exog(params, exog, method, dummy_idx, count_idx) effects = _effects_at(effects, at) if at == 'all': self.margeff = effects[:, effects_idx] else: # Set standard error of the marginal effects by Delta method. margeff_cov, margeff_se = margeff_cov_with_se( model, params, exog, results.cov_params(), at, model._derivative_exog, dummy_idx, count_idx, method, 1) # do not care about at constant self.margeff_cov = margeff_cov[effects_idx][:, effects_idx] self.margeff_se = margeff_se[effects_idx] self.margeff = effects[effects_idx] statsmodels-0.12.2/statsmodels/genmod/generalized_linear_model.py000066400000000000000000002403651400612667500253470ustar00rootroot00000000000000""" Generalized linear models currently supports estimation using the one-parameter exponential families References ---------- Gill, Jeff. 2000. Generalized Linear Models: A Unified Approach. SAGE QASS Series. Green, PJ. 1984. "Iteratively reweighted least squares for maximum likelihood estimation, and some robust and resistant alternatives." Journal of the Royal Statistical Society, Series B, 46, 149-192. Hardin, J.W. and Hilbe, J.M. 2007. "Generalized Linear Models and Extensions." 2nd ed. Stata Press, College Station, TX. McCullagh, P. and Nelder, J.A. 1989. "Generalized Linear Models." 2nd ed. Chapman & Hall, Boca Rotan. """ import numpy as np from . import families from statsmodels.tools.decorators import (cache_readonly, cached_data, cached_value) from statsmodels.tools.validation import float_like from statsmodels.compat.pandas import Appender import statsmodels.base.model as base import statsmodels.regression.linear_model as lm import statsmodels.base.wrapper as wrap import statsmodels.regression._tools as reg_tools import warnings from statsmodels.graphics._regressionplots_doc import ( _plot_added_variable_doc, _plot_partial_residuals_doc, _plot_ceres_residuals_doc) # need import in module instead of lazily to copy `__doc__` from . import _prediction as pred from statsmodels.genmod._prediction import PredictionResults from statsmodels.tools.sm_exceptions import (PerfectSeparationError, DomainWarning, HessianInversionWarning) from numpy.linalg.linalg import LinAlgError __all__ = ['GLM', 'PredictionResults'] def _check_convergence(criterion, iteration, atol, rtol): return np.allclose(criterion[iteration], criterion[iteration + 1], atol=atol, rtol=rtol) # Remove after 0.13 when bic changes to bic llf class _ModuleVariable: _value = None @property def use_bic_llf(self): return self._value def set_use_bic_llf(self, val): if val not in (True, False, None): raise ValueError("Must be True, False or None") self._value = bool(val) if val is not None else val _use_bic_helper = _ModuleVariable() SET_USE_BIC_LLF = _use_bic_helper.set_use_bic_llf class GLM(base.LikelihoodModel): __doc__ = """ Generalized Linear Models GLM inherits from statsmodels.base.model.LikelihoodModel Parameters ---------- endog : array_like 1d array of endogenous response variable. This array can be 1d or 2d. Binomial family models accept a 2d array with two columns. If supplied, each observation is expected to be [success, failure]. exog : array_like A nobs x k array where `nobs` is the number of observations and `k` is the number of regressors. An intercept is not included by default and should be added by the user (models specified using a formula include an intercept by default). See `statsmodels.tools.add_constant`. family : family class instance The default is Gaussian. To specify the binomial distribution family = sm.family.Binomial() Each family can take a link instance as an argument. See statsmodels.family.family for more information. offset : array_like or None An offset to be included in the model. If provided, must be an array whose length is the number of rows in exog. exposure : array_like or None Log(exposure) will be added to the linear prediction in the model. Exposure is only valid if the log link is used. If provided, it must be an array with the same length as endog. freq_weights : array_like 1d array of frequency weights. The default is None. If None is selected or a blank value, then the algorithm will replace with an array of 1's with length equal to the endog. WARNING: Using weights is not verified yet for all possible options and results, see Notes. var_weights : array_like 1d array of variance (analytic) weights. The default is None. If None is selected or a blank value, then the algorithm will replace with an array of 1's with length equal to the endog. WARNING: Using weights is not verified yet for all possible options and results, see Notes. %(extra_params)s Attributes ---------- df_model : float Model degrees of freedom is equal to p - 1, where p is the number of regressors. Note that the intercept is not reported as a degree of freedom. df_resid : float Residual degrees of freedom is equal to the number of observation n minus the number of regressors p. endog : ndarray See Notes. Note that `endog` is a reference to the data so that if data is already an array and it is changed, then `endog` changes as well. exposure : array_like Include ln(exposure) in model with coefficient constrained to 1. Can only be used if the link is the logarithm function. exog : ndarray See Notes. Note that `exog` is a reference to the data so that if data is already an array and it is changed, then `exog` changes as well. freq_weights : ndarray See Notes. Note that `freq_weights` is a reference to the data so that if data is already an array and it is changed, then `freq_weights` changes as well. var_weights : ndarray See Notes. Note that `var_weights` is a reference to the data so that if data is already an array and it is changed, then `var_weights` changes as well. iteration : int The number of iterations that fit has run. Initialized at 0. family : family class instance The distribution family of the model. Can be any family in statsmodels.families. Default is Gaussian. mu : ndarray The mean response of the transformed variable. `mu` is the value of the inverse of the link function at lin_pred, where lin_pred is the linear predicted value of the WLS fit of the transformed variable. `mu` is only available after fit is called. See statsmodels.families.family.fitted of the distribution family for more information. n_trials : ndarray See Notes. Note that `n_trials` is a reference to the data so that if data is already an array and it is changed, then `n_trials` changes as well. `n_trials` is the number of binomial trials and only available with that distribution. See statsmodels.families.Binomial for more information. normalized_cov_params : ndarray The p x p normalized covariance of the design / exogenous data. This is approximately equal to (X.T X)^(-1) offset : array_like Include offset in model with coefficient constrained to 1. scale : float The estimate of the scale / dispersion of the model fit. Only available after fit is called. See GLM.fit and GLM.estimate_scale for more information. scaletype : str The scaling used for fitting the model. This is only available after fit is called. The default is None. See GLM.fit for more information. weights : ndarray The value of the weights after the last iteration of fit. Only available after fit is called. See statsmodels.families.family for the specific distribution weighting functions. Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.scotland.load(as_pandas=False) >>> data.exog = sm.add_constant(data.exog) Instantiate a gamma family model with the default link function. >>> gamma_model = sm.GLM(data.endog, data.exog, ... family=sm.families.Gamma()) >>> gamma_results = gamma_model.fit() >>> gamma_results.params array([-0.01776527, 0.00004962, 0.00203442, -0.00007181, 0.00011185, -0.00000015, -0.00051868, -0.00000243]) >>> gamma_results.scale 0.0035842831734919055 >>> gamma_results.deviance 0.087388516416999198 >>> gamma_results.pearson_chi2 0.086022796163805704 >>> gamma_results.llf -83.017202161073527 See Also -------- statsmodels.genmod.families.family.Family :ref:`families` :ref:`links` Notes ----- Only the following combinations make sense for family and link: ============= ===== === ===== ====== ======= === ==== ====== ====== ==== Family ident log logit probit cloglog pow opow nbinom loglog logc ============= ===== === ===== ====== ======= === ==== ====== ====== ==== Gaussian x x x x x x x x x inv Gaussian x x x binomial x x x x x x x x x Poisson x x x neg binomial x x x x gamma x x x Tweedie x x x ============= ===== === ===== ====== ======= === ==== ====== ====== ==== Not all of these link functions are currently available. Endog and exog are references so that if the data they refer to are already arrays and these arrays are changed, endog and exog will change. statsmodels supports two separate definitions of weights: frequency weights and variance weights. Frequency weights produce the same results as repeating observations by the frequencies (if those are integers). Frequency weights will keep the number of observations consistent, but the degrees of freedom will change to reflect the new weights. Variance weights (referred to in other packages as analytic weights) are used when ``endog`` represents an an average or mean. This relies on the assumption that that the inverse variance scales proportionally to the weight--an observation that is deemed more credible should have less variance and therefore have more weight. For the ``Poisson`` family--which assumes that occurrences scale proportionally with time--a natural practice would be to use the amount of time as the variance weight and set ``endog`` to be a rate (occurrences per period of time). Similarly, using a compound Poisson family, namely ``Tweedie``, makes a similar assumption about the rate (or frequency) of occurrences having variance proportional to time. Both frequency and variance weights are verified for all basic results with nonrobust or heteroscedasticity robust ``cov_type``. Other robust covariance types have not yet been verified, and at least the small sample correction is currently not based on the correct total frequency count. Currently, all residuals are not weighted by frequency, although they may incorporate ``n_trials`` for ``Binomial`` and ``var_weights`` +---------------+----------------------------------+ | Residual Type | Applicable weights | +===============+==================================+ | Anscombe | ``var_weights`` | +---------------+----------------------------------+ | Deviance | ``var_weights`` | +---------------+----------------------------------+ | Pearson | ``var_weights`` and ``n_trials`` | +---------------+----------------------------------+ | Reponse | ``n_trials`` | +---------------+----------------------------------+ | Working | ``n_trials`` | +---------------+----------------------------------+ WARNING: Loglikelihood and deviance are not valid in models where scale is equal to 1 (i.e., ``Binomial``, ``NegativeBinomial``, and ``Poisson``). If variance weights are specified, then results such as ``loglike`` and ``deviance`` are based on a quasi-likelihood interpretation. The loglikelihood is not correctly specified in this case, and statistics based on it, such AIC or likelihood ratio tests, are not appropriate. """ % {'extra_params': base._missing_param_doc} # Maximum number of endogenous variables when using a formula _formula_max_endog = 2 def __init__(self, endog, exog, family=None, offset=None, exposure=None, freq_weights=None, var_weights=None, missing='none', **kwargs): if (family is not None) and not isinstance(family.link, tuple(family.safe_links)): warnings.warn((f"The {type(family.link).__name__} link function " "does not respect the domain of the " f"{type(family).__name__} family."), DomainWarning) if exposure is not None: exposure = np.log(exposure) if offset is not None: # this should probably be done upstream offset = np.asarray(offset) if freq_weights is not None: freq_weights = np.asarray(freq_weights) if var_weights is not None: var_weights = np.asarray(var_weights) self.freq_weights = freq_weights self.var_weights = var_weights super(GLM, self).__init__(endog, exog, missing=missing, offset=offset, exposure=exposure, freq_weights=freq_weights, var_weights=var_weights, **kwargs) self._check_inputs(family, self.offset, self.exposure, self.endog, self.freq_weights, self.var_weights) if offset is None: delattr(self, 'offset') if exposure is None: delattr(self, 'exposure') self.nobs = self.endog.shape[0] # things to remove_data self._data_attr.extend(['weights', 'mu', 'freq_weights', 'var_weights', 'iweights', '_offset_exposure', 'n_trials']) # register kwds for __init__, offset and exposure are added by super self._init_keys.append('family') self._setup_binomial() # internal usage for recreating a model if 'n_trials' in kwargs: self.n_trials = kwargs['n_trials'] # Construct a combined offset/exposure term. Note that # exposure has already been logged if present. offset_exposure = 0. if hasattr(self, 'offset'): offset_exposure = self.offset if hasattr(self, 'exposure'): offset_exposure = offset_exposure + self.exposure self._offset_exposure = offset_exposure self.scaletype = None def initialize(self): """ Initialize a generalized linear model. """ self.df_model = np.linalg.matrix_rank(self.exog) - 1 if (self.freq_weights is not None) and \ (self.freq_weights.shape[0] == self.endog.shape[0]): self.wnobs = self.freq_weights.sum() self.df_resid = self.wnobs - self.df_model - 1 else: self.wnobs = self.exog.shape[0] self.df_resid = self.exog.shape[0] - self.df_model - 1 def _check_inputs(self, family, offset, exposure, endog, freq_weights, var_weights): # Default family is Gaussian if family is None: family = families.Gaussian() self.family = family if exposure is not None: if not isinstance(self.family.link, families.links.Log): raise ValueError("exposure can only be used with the log " "link function") elif exposure.shape[0] != endog.shape[0]: raise ValueError("exposure is not the same length as endog") if offset is not None: if offset.shape[0] != endog.shape[0]: raise ValueError("offset is not the same length as endog") if freq_weights is not None: if freq_weights.shape[0] != endog.shape[0]: raise ValueError("freq weights not the same length as endog") if len(freq_weights.shape) > 1: raise ValueError("freq weights has too many dimensions") # internal flag to store whether freq_weights were not None self._has_freq_weights = (self.freq_weights is not None) if self.freq_weights is None: self.freq_weights = np.ones((endog.shape[0])) # TODO: check do we want to keep None as sentinel for freq_weights if np.shape(self.freq_weights) == () and self.freq_weights > 1: self.freq_weights = (self.freq_weights * np.ones((endog.shape[0]))) if var_weights is not None: if var_weights.shape[0] != endog.shape[0]: raise ValueError("var weights not the same length as endog") if len(var_weights.shape) > 1: raise ValueError("var weights has too many dimensions") # internal flag to store whether var_weights were not None self._has_var_weights = (var_weights is not None) if var_weights is None: self.var_weights = np.ones((endog.shape[0])) # TODO: check do we want to keep None as sentinel for var_weights self.iweights = np.asarray(self.freq_weights * self.var_weights) def _get_init_kwds(self): # this is a temporary fixup because exposure has been transformed # see #1609, copied from discrete_model.CountModel kwds = super(GLM, self)._get_init_kwds() if 'exposure' in kwds and kwds['exposure'] is not None: kwds['exposure'] = np.exp(kwds['exposure']) return kwds def loglike_mu(self, mu, scale=1.): """ Evaluate the log-likelihood for a generalized linear model. """ scale = float_like(scale, "scale") return self.family.loglike(self.endog, mu, self.var_weights, self.freq_weights, scale) def loglike(self, params, scale=None): """ Evaluate the log-likelihood for a generalized linear model. """ scale = float_like(scale, "scale", optional=True) lin_pred = np.dot(self.exog, params) + self._offset_exposure expval = self.family.link.inverse(lin_pred) if scale is None: scale = self.estimate_scale(expval) llf = self.family.loglike(self.endog, expval, self.var_weights, self.freq_weights, scale) return llf def score_obs(self, params, scale=None): """score first derivative of the loglikelihood for each observation. Parameters ---------- params : ndarray parameter at which score is evaluated scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. Returns ------- score_obs : ndarray, 2d The first derivative of the loglikelihood function evaluated at params for each observation. """ scale = float_like(scale, "scale", optional=True) score_factor = self.score_factor(params, scale=scale) return score_factor[:, None] * self.exog def score(self, params, scale=None): """score, first derivative of the loglikelihood function Parameters ---------- params : ndarray parameter at which score is evaluated scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. Returns ------- score : ndarray_1d The first derivative of the loglikelihood function calculated as the sum of `score_obs` """ scale = float_like(scale, "scale", optional=True) score_factor = self.score_factor(params, scale=scale) return np.dot(score_factor, self.exog) def score_factor(self, params, scale=None): """weights for score for each observation This can be considered as score residuals. Parameters ---------- params : ndarray parameter at which score is evaluated scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. Returns ------- score_factor : ndarray_1d A 1d weight vector used in the calculation of the score_obs. The score_obs are obtained by `score_factor[:, None] * exog` """ scale = float_like(scale, "scale", optional=True) mu = self.predict(params) if scale is None: scale = self.estimate_scale(mu) score_factor = (self.endog - mu) / self.family.link.deriv(mu) score_factor /= self.family.variance(mu) score_factor *= self.iweights * self.n_trials if not scale == 1: score_factor /= scale return score_factor def hessian_factor(self, params, scale=None, observed=True): """Weights for calculating Hessian Parameters ---------- params : ndarray parameter at which Hessian is evaluated scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. observed : bool If True, then the observed Hessian is returned. If false then the expected information matrix is returned. Returns ------- hessian_factor : ndarray, 1d A 1d weight vector used in the calculation of the Hessian. The hessian is obtained by `(exog.T * hessian_factor).dot(exog)` """ # calculating eim_factor mu = self.predict(params) if scale is None: scale = self.estimate_scale(mu) eim_factor = 1 / (self.family.link.deriv(mu)**2 * self.family.variance(mu)) eim_factor *= self.iweights * self.n_trials if not observed: if not scale == 1: eim_factor /= scale return eim_factor # calculating oim_factor, eim_factor is with scale=1 score_factor = self.score_factor(params, scale=1.) if eim_factor.ndim > 1 or score_factor.ndim > 1: raise RuntimeError('something wrong') tmp = self.family.variance(mu) * self.family.link.deriv2(mu) tmp += self.family.variance.deriv(mu) * self.family.link.deriv(mu) tmp = score_factor * tmp # correct for duplicatee iweights in oim_factor and score_factor tmp /= self.iweights * self.n_trials oim_factor = eim_factor * (1 + tmp) if tmp.ndim > 1: raise RuntimeError('something wrong') if not scale == 1: oim_factor /= scale return oim_factor def hessian(self, params, scale=None, observed=None): """Hessian, second derivative of loglikelihood function Parameters ---------- params : ndarray parameter at which Hessian is evaluated scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. observed : bool If True, then the observed Hessian is returned (default). If false then the expected information matrix is returned. Returns ------- hessian : ndarray Hessian, i.e. observed information, or expected information matrix. """ if observed is None: if getattr(self, '_optim_hessian', None) == 'eim': observed = False else: observed = True scale = float_like(scale, "scale", optional=True) tmp = getattr(self, '_tmp_like_exog', np.empty_like(self.exog, dtype=float)) factor = self.hessian_factor(params, scale=scale, observed=observed) np.multiply(self.exog.T, factor, out=tmp.T) return -tmp.T.dot(self.exog) def information(self, params, scale=None): """ Fisher information matrix. """ scale = float_like(scale, "scale", optional=True) return self.hessian(params, scale=scale, observed=False) def _deriv_mean_dparams(self, params): """ Derivative of the expected endog with respect to the parameters. Parameters ---------- params : ndarray parameter at which score is evaluated Returns ------- The value of the derivative of the expected endog with respect to the parameter vector. """ lin_pred = self.predict(params, linear=True) idl = self.family.link.inverse_deriv(lin_pred) dmat = self.exog * idl[:, None] return dmat def _deriv_score_obs_dendog(self, params, scale=None): """derivative of score_obs w.r.t. endog Parameters ---------- params : ndarray parameter at which score is evaluated scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. Returns ------- derivative : ndarray_2d The derivative of the score_obs with respect to endog. This can is given by `score_factor0[:, None] * exog` where `score_factor0` is the score_factor without the residual. """ scale = float_like(scale, "scale", optional=True) mu = self.predict(params) if scale is None: scale = self.estimate_scale(mu) score_factor = 1 / self.family.link.deriv(mu) score_factor /= self.family.variance(mu) score_factor *= self.iweights * self.n_trials if not scale == 1: score_factor /= scale return score_factor[:, None] * self.exog def score_test(self, params_constrained, k_constraints=None, exog_extra=None, observed=True): """score test for restrictions or for omitted variables The covariance matrix for the score is based on the Hessian, i.e. observed information matrix or optionally on the expected information matrix.. Parameters ---------- params_constrained : array_like estimated parameter of the restricted model. This can be the parameter estimate for the current when testing for omitted variables. k_constraints : int or None Number of constraints that were used in the estimation of params restricted relative to the number of exog in the model. This must be provided if no exog_extra are given. If exog_extra is not None, then k_constraints is assumed to be zero if it is None. exog_extra : None or array_like Explanatory variables that are jointly tested for inclusion in the model, i.e. omitted variables. observed : bool If True, then the observed Hessian is used in calculating the covariance matrix of the score. If false then the expected information matrix is used. Returns ------- chi2_stat : float chisquare statistic for the score test p-value : float P-value of the score test based on the chisquare distribution. df : int Degrees of freedom used in the p-value calculation. This is equal to the number of constraints. Notes ----- not yet verified for case with scale not equal to 1. """ if exog_extra is None: if k_constraints is None: raise ValueError('if exog_extra is None, then k_constraints' 'needs to be given') score = self.score(params_constrained) hessian = self.hessian(params_constrained, observed=observed) else: # exog_extra = np.asarray(exog_extra) if k_constraints is None: k_constraints = 0 ex = np.column_stack((self.exog, exog_extra)) k_constraints += ex.shape[1] - self.exog.shape[1] score_factor = self.score_factor(params_constrained) score = (score_factor[:, None] * ex).sum(0) hessian_factor = self.hessian_factor(params_constrained, observed=observed) hessian = -np.dot(ex.T * hessian_factor, ex) from scipy import stats # TODO check sign, why minus? chi2stat = -score.dot(np.linalg.solve(hessian, score[:, None])) pval = stats.chi2.sf(chi2stat, k_constraints) # return a stats results instance instead? Contrast? return chi2stat, pval, k_constraints def _update_history(self, tmp_result, mu, history): """ Helper method to update history during iterative fit. """ history['params'].append(tmp_result.params) history['deviance'].append(self.family.deviance(self.endog, mu, self.var_weights, self.freq_weights, self.scale)) return history def estimate_scale(self, mu): """ Estimate the dispersion/scale. Type of scale can be chose in the fit method. Parameters ---------- mu : ndarray mu is the mean response estimate Returns ------- Estimate of scale Notes ----- The default scale for Binomial, Poisson and Negative Binomial families is 1. The default for the other families is Pearson's Chi-Square estimate. See Also -------- statsmodels.genmod.generalized_linear_model.GLM.fit """ if not self.scaletype: if isinstance(self.family, (families.Binomial, families.Poisson, families.NegativeBinomial)): return 1. else: return self._estimate_x2_scale(mu) if isinstance(self.scaletype, float): return np.array(self.scaletype) if isinstance(self.scaletype, str): if self.scaletype.lower() == 'x2': return self._estimate_x2_scale(mu) elif self.scaletype.lower() == 'dev': return (self.family.deviance(self.endog, mu, self.var_weights, self.freq_weights, 1.) / (self.df_resid)) else: raise ValueError("Scale %s with type %s not understood" % (self.scaletype, type(self.scaletype))) else: raise ValueError("Scale %s with type %s not understood" % (self.scaletype, type(self.scaletype))) def _estimate_x2_scale(self, mu): resid = np.power(self.endog - mu, 2) * self.iweights return np.sum(resid / self.family.variance(mu)) / self.df_resid def estimate_tweedie_power(self, mu, method='brentq', low=1.01, high=5.): """ Tweedie specific function to estimate scale and the variance parameter. The variance parameter is also referred to as p, xi, or shape. Parameters ---------- mu : array_like Fitted mean response variable method : str, defaults to 'brentq' Scipy optimizer used to solve the Pearson equation. Only brentq currently supported. low : float, optional Low end of the bracketing interval [a,b] to be used in the search for the power. Defaults to 1.01. high : float, optional High end of the bracketing interval [a,b] to be used in the search for the power. Defaults to 5. Returns ------- power : float The estimated shape or power. """ if method == 'brentq': from scipy.optimize import brentq def psi_p(power, mu): scale = ((self.iweights * (self.endog - mu) ** 2 / (mu ** power)).sum() / self.df_resid) return (np.sum(self.iweights * ((self.endog - mu) ** 2 / (scale * (mu ** power)) - 1) * np.log(mu)) / self.freq_weights.sum()) power = brentq(psi_p, low, high, args=(mu)) else: raise NotImplementedError('Only brentq can currently be used') return power def predict(self, params, exog=None, exposure=None, offset=None, linear=False): """ Return predicted values for a design matrix Parameters ---------- params : array_like Parameters / coefficients of a GLM. exog : array_like, optional Design / exogenous data. Is exog is None, model exog is used. exposure : array_like, optional Exposure time values, only can be used with the log link function. See notes for details. offset : array_like, optional Offset values. See notes for details. linear : bool If True, returns the linear predicted values. If False, returns the value of the inverse of the model's link function at the linear predicted values. Returns ------- An array of fitted values Notes ----- Any `exposure` and `offset` provided here take precedence over the `exposure` and `offset` used in the model fit. If `exog` is passed as an argument here, then any `exposure` and `offset` values in the fit will be ignored. Exposure values must be strictly positive. """ # Use fit offset if appropriate if offset is None and exog is None and hasattr(self, 'offset'): offset = self.offset elif offset is None: offset = 0. if exposure is not None and not isinstance(self.family.link, families.links.Log): raise ValueError("exposure can only be used with the log link " "function") # Use fit exposure if appropriate if exposure is None and exog is None and hasattr(self, 'exposure'): # Already logged exposure = self.exposure elif exposure is None: exposure = 0. else: exposure = np.log(np.asarray(exposure)) if exog is None: exog = self.exog linpred = np.dot(exog, params) + offset + exposure if linear: return linpred else: return self.family.fitted(linpred) def get_distribution(self, params, scale=1., exog=None, exposure=None, offset=None): """ Return a random number generator for the predictive distribution. Parameters ---------- params : array_like The model parameters. scale : scalar The scale parameter. exog : array_like The predictor variable matrix. Returns ------- gen Frozen random number generator object. Use the ``rvs`` method to generate random values. Notes ----- Due to the behavior of ``scipy.stats.distributions objects``, the returned random number generator must be called with ``gen.rvs(n)`` where ``n`` is the number of observations in the data set used to fit the model. If any other value is used for ``n``, misleading results will be produced. """ scale = float_like(scale, "scale", optional=True) fit = self.predict(params, exog, exposure, offset, linear=False) import scipy.stats.distributions as dist if isinstance(self.family, families.Gaussian): return dist.norm(loc=fit, scale=np.sqrt(scale)) elif isinstance(self.family, families.Binomial): return dist.binom(n=1, p=fit) elif isinstance(self.family, families.Poisson): return dist.poisson(mu=fit) elif isinstance(self.family, families.Gamma): alpha = fit / float(scale) return dist.gamma(alpha, scale=scale) else: raise ValueError("get_distribution not implemented for %s" % self.family.name) def _setup_binomial(self): # this checks what kind of data is given for Binomial. # family will need a reference to endog if this is to be removed from # preprocessing self.n_trials = np.ones((self.endog.shape[0])) # For binomial if isinstance(self.family, families.Binomial): tmp = self.family.initialize(self.endog, self.freq_weights) self.endog = tmp[0] self.n_trials = tmp[1] self._init_keys.append('n_trials') def fit(self, start_params=None, maxiter=100, method='IRLS', tol=1e-8, scale=None, cov_type='nonrobust', cov_kwds=None, use_t=None, full_output=True, disp=False, max_start_irls=3, **kwargs): """ Fits a generalized linear model for a given family. Parameters ---------- start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is family-specific and is given by the ``family.starting_mu(endog)``. If start_params is given then the initial mean will be calculated as ``np.dot(exog, start_params)``. maxiter : int, optional Default is 100. method : str Default is 'IRLS' for iteratively reweighted least squares. Otherwise gradient optimization is used. tol : float Convergence tolerance. Default is 1e-8. scale : str or float, optional `scale` can be 'X2', 'dev', or a float The default value is None, which uses `X2` for Gamma, Gaussian, and Inverse Gaussian. `X2` is Pearson's chi-square divided by `df_resid`. The default is 1 for the Binomial and Poisson families. `dev` is the deviance divided by df_resid cov_type : str The type of parameter estimate covariance matrix to compute. cov_kwds : dict-like Extra arguments for calculating the covariance of the parameter estimates. use_t : bool If True, the Student t-distribution is used for inference. full_output : bool, optional Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. Not used if methhod is IRLS. disp : bool, optional Set to True to print convergence messages. Not used if method is IRLS. max_start_irls : int The number of IRLS iterations used to obtain starting values for gradient optimization. Only relevant if `method` is set to something other than 'IRLS'. atol : float, optional (available with IRLS fits) The absolute tolerance criterion that must be satisfied. Defaults to ``tol``. Convergence is attained when: :math:`rtol * prior + atol > abs(current - prior)` rtol : float, optional (available with IRLS fits) The relative tolerance criterion that must be satisfied. Defaults to 0 which means ``rtol`` is not used. Convergence is attained when: :math:`rtol * prior + atol > abs(current - prior)` tol_criterion : str, optional (available with IRLS fits) Defaults to ``'deviance'``. Can optionally be ``'params'``. wls_method : str, optional (available with IRLS fits) options are 'lstsq', 'pinv' and 'qr' specifies which linear algebra function to use for the irls optimization. Default is `lstsq` which uses the same underlying svd based approach as 'pinv', but is faster during iterations. 'lstsq' and 'pinv' regularize the estimate in singular and near-singular cases by truncating small singular values based on `rcond` of the respective numpy.linalg function. 'qr' is only valid for cases that are not singular nor near-singular. optim_hessian : {'eim', 'oim'}, optional (available with scipy optimizer fits) When 'oim'--the default--the observed Hessian is used in fitting. 'eim' is the expected Hessian. This may provide more stable fits, but adds assumption that the Hessian is correctly specified. Notes ----- If method is 'IRLS', then an additional keyword 'attach_wls' is available. This is currently for internal use only and might change in future versions. If attach_wls' is true, then the final WLS instance of the IRLS iteration is attached to the results instance as `results_wls` attribute. """ if isinstance(scale, str): scale = scale.lower() if scale not in ("x2", "dev"): raise ValueError( "scale must be either X2 or dev when a string." ) elif scale is not None: # GH-6627 try: scale = float(scale) except Exception as exc: raise type(exc)( "scale must be a float if given and no a string." ) self.scaletype = scale if method.lower() == "irls": if cov_type.lower() == 'eim': cov_type = 'nonrobust' return self._fit_irls(start_params=start_params, maxiter=maxiter, tol=tol, scale=scale, cov_type=cov_type, cov_kwds=cov_kwds, use_t=use_t, **kwargs) else: self._optim_hessian = kwargs.get('optim_hessian') self._tmp_like_exog = np.empty_like(self.exog, dtype=float) fit_ = self._fit_gradient(start_params=start_params, method=method, maxiter=maxiter, tol=tol, scale=scale, full_output=full_output, disp=disp, cov_type=cov_type, cov_kwds=cov_kwds, use_t=use_t, max_start_irls=max_start_irls, **kwargs) del self._optim_hessian del self._tmp_like_exog return fit_ def _fit_gradient(self, start_params=None, method="newton", maxiter=100, tol=1e-8, full_output=True, disp=True, scale=None, cov_type='nonrobust', cov_kwds=None, use_t=None, max_start_irls=3, **kwargs): """ Fits a generalized linear model for a given family iteratively using the scipy gradient optimizers. """ # fix scale during optimization, see #4616 scaletype = self.scaletype self.scaletype = 1. if (max_start_irls > 0) and (start_params is None): irls_rslt = self._fit_irls(start_params=start_params, maxiter=max_start_irls, tol=tol, scale=1., cov_type='nonrobust', cov_kwds=None, use_t=None, **kwargs) start_params = irls_rslt.params del irls_rslt rslt = super(GLM, self).fit(start_params=start_params, tol=tol, maxiter=maxiter, full_output=full_output, method=method, disp=disp, **kwargs) # reset scaletype to original self.scaletype = scaletype mu = self.predict(rslt.params) scale = self.estimate_scale(mu) if rslt.normalized_cov_params is None: cov_p = None else: cov_p = rslt.normalized_cov_params / scale if cov_type.lower() == 'eim': oim = False cov_type = 'nonrobust' else: oim = True try: cov_p = np.linalg.inv(-self.hessian(rslt.params, observed=oim)) / scale except LinAlgError: warnings.warn('Inverting hessian failed, no bse or cov_params ' 'available', HessianInversionWarning) cov_p = None results_class = getattr(self, '_results_class', GLMResults) results_class_wrapper = getattr(self, '_results_class_wrapper', GLMResultsWrapper) glm_results = results_class(self, rslt.params, cov_p, scale, cov_type=cov_type, cov_kwds=cov_kwds, use_t=use_t) # TODO: iteration count is not always available history = {'iteration': 0} if full_output: glm_results.mle_retvals = rslt.mle_retvals if 'iterations' in rslt.mle_retvals: history['iteration'] = rslt.mle_retvals['iterations'] glm_results.method = method glm_results.fit_history = history return results_class_wrapper(glm_results) def _fit_irls(self, start_params=None, maxiter=100, tol=1e-8, scale=None, cov_type='nonrobust', cov_kwds=None, use_t=None, **kwargs): """ Fits a generalized linear model for a given family using iteratively reweighted least squares (IRLS). """ attach_wls = kwargs.pop('attach_wls', False) atol = kwargs.get('atol') rtol = kwargs.get('rtol', 0.) tol_criterion = kwargs.get('tol_criterion', 'deviance') wls_method = kwargs.get('wls_method', 'lstsq') atol = tol if atol is None else atol endog = self.endog wlsexog = self.exog if start_params is None: start_params = np.zeros(self.exog.shape[1]) mu = self.family.starting_mu(self.endog) lin_pred = self.family.predict(mu) else: lin_pred = np.dot(wlsexog, start_params) + self._offset_exposure mu = self.family.fitted(lin_pred) self.scale = self.estimate_scale(mu) dev = self.family.deviance(self.endog, mu, self.var_weights, self.freq_weights, self.scale) if np.isnan(dev): raise ValueError("The first guess on the deviance function " "returned a nan. This could be a boundary " " problem and should be reported.") # first guess on the deviance is assumed to be scaled by 1. # params are none to start, so they line up with the deviance history = dict(params=[np.inf, start_params], deviance=[np.inf, dev]) converged = False criterion = history[tol_criterion] # This special case is used to get the likelihood for a specific # params vector. if maxiter == 0: mu = self.family.fitted(lin_pred) self.scale = self.estimate_scale(mu) wls_results = lm.RegressionResults(self, start_params, None) iteration = 0 for iteration in range(maxiter): self.weights = (self.iweights * self.n_trials * self.family.weights(mu)) wlsendog = (lin_pred + self.family.link.deriv(mu) * (self.endog-mu) - self._offset_exposure) wls_mod = reg_tools._MinimalWLS(wlsendog, wlsexog, self.weights, check_endog=True, check_weights=True) wls_results = wls_mod.fit(method=wls_method) lin_pred = np.dot(self.exog, wls_results.params) lin_pred += self._offset_exposure mu = self.family.fitted(lin_pred) history = self._update_history(wls_results, mu, history) self.scale = self.estimate_scale(mu) if endog.squeeze().ndim == 1 and np.allclose(mu - endog, 0): msg = "Perfect separation detected, results not available" raise PerfectSeparationError(msg) converged = _check_convergence(criterion, iteration + 1, atol, rtol) if converged: break self.mu = mu if maxiter > 0: # Only if iterative used wls_method2 = 'pinv' if wls_method == 'lstsq' else wls_method wls_model = lm.WLS(wlsendog, wlsexog, self.weights) wls_results = wls_model.fit(method=wls_method2) glm_results = GLMResults(self, wls_results.params, wls_results.normalized_cov_params, self.scale, cov_type=cov_type, cov_kwds=cov_kwds, use_t=use_t) glm_results.method = "IRLS" glm_results.mle_settings = {} glm_results.mle_settings['wls_method'] = wls_method glm_results.mle_settings['optimizer'] = glm_results.method if (maxiter > 0) and (attach_wls is True): glm_results.results_wls = wls_results history['iteration'] = iteration + 1 glm_results.fit_history = history glm_results.converged = converged return GLMResultsWrapper(glm_results) def fit_regularized(self, method="elastic_net", alpha=0., start_params=None, refit=False, opt_method="bfgs", **kwargs): r""" Return a regularized fit to a linear regression model. Parameters ---------- method : {'elastic_net'} Only the `elastic_net` approach is currently implemented. alpha : scalar or array_like The penalty weight. If a scalar, the same penalty weight applies to all variables in the model. If a vector, it must have the same length as `params`, and contains a penalty weight for each coefficient. start_params : array_like Starting values for `params`. refit : bool If True, the model is refit using only the variables that have non-zero coefficients in the regularized fit. The refitted model is not regularized. opt_method : string The method used for numerical optimization. **kwargs Additional keyword arguments used when fitting the model. Returns ------- GLMResults An array or a GLMResults object, same type returned by `fit`. Notes ----- The penalty is the ``elastic net`` penalty, which is a combination of L1 and L2 penalties. The function that is minimized is: .. math:: -loglike/n + alpha*((1-L1\_wt)*|params|_2^2/2 + L1\_wt*|params|_1) where :math:`|*|_1` and :math:`|*|_2` are the L1 and L2 norms. Post-estimation results are based on the same data used to select variables, hence may be subject to overfitting biases. The elastic_net method uses the following keyword arguments: maxiter : int Maximum number of iterations L1_wt : float Must be in [0, 1]. The L1 penalty has weight L1_wt and the L2 penalty has weight 1 - L1_wt. cnvrg_tol : float Convergence threshold for maximum parameter change after one sweep through all coefficients. zero_tol : float Coefficients below this threshold are treated as zero. """ if kwargs.get("L1_wt", 1) == 0: return self._fit_ridge(alpha, start_params, opt_method) from statsmodels.base.elastic_net import fit_elasticnet if method != "elastic_net": raise ValueError("method for fit_regularied must be elastic_net") defaults = {"maxiter": 50, "L1_wt": 1, "cnvrg_tol": 1e-10, "zero_tol": 1e-10} defaults.update(kwargs) result = fit_elasticnet(self, method=method, alpha=alpha, start_params=start_params, refit=refit, **defaults) self.mu = self.predict(result.params) self.scale = self.estimate_scale(self.mu) if not result.converged: warnings.warn("Elastic net fitting did not converge") return result def _fit_ridge(self, alpha, start_params, method): if start_params is None: start_params = np.zeros(self.exog.shape[1]) def fun(x): return -(self.loglike(x) / self.nobs - np.sum(alpha * x**2) / 2) def grad(x): return -(self.score(x) / self.nobs - alpha * x) from scipy.optimize import minimize from statsmodels.base.elastic_net import (RegularizedResults, RegularizedResultsWrapper) mr = minimize(fun, start_params, jac=grad, method=method) params = mr.x if not mr.success: import warnings ngrad = np.sqrt(np.sum(mr.jac**2)) msg = "GLM ridge optimization may have failed, |grad|=%f" % ngrad warnings.warn(msg) results = RegularizedResults(self, params) results = RegularizedResultsWrapper(results) return results def fit_constrained(self, constraints, start_params=None, **fit_kwds): """fit the model subject to linear equality constraints The constraints are of the form `R params = q` where R is the constraint_matrix and q is the vector of constraint_values. The estimation creates a new model with transformed design matrix, exog, and converts the results back to the original parameterization. Parameters ---------- constraints : formula expression or tuple If it is a tuple, then the constraint needs to be given by two arrays (constraint_matrix, constraint_value), i.e. (R, q). Otherwise, the constraints can be given as strings or list of strings. see t_test for details start_params : None or array_like starting values for the optimization. `start_params` needs to be given in the original parameter space and are internally transformed. **fit_kwds : keyword arguments fit_kwds are used in the optimization of the transformed model. Returns ------- results : Results instance """ from patsy import DesignInfo from statsmodels.base._constraints import (fit_constrained, LinearConstraints) # same pattern as in base.LikelihoodModel.t_test lc = DesignInfo(self.exog_names).linear_constraint(constraints) R, q = lc.coefs, lc.constants # TODO: add start_params option, need access to tranformation # fit_constrained needs to do the transformation params, cov, res_constr = fit_constrained(self, R, q, start_params=start_params, fit_kwds=fit_kwds) # create dummy results Instance, TODO: wire up properly res = self.fit(start_params=params, maxiter=0) # we get a wrapper back res._results.params = params res._results.cov_params_default = cov cov_type = fit_kwds.get('cov_type', 'nonrobust') if cov_type != 'nonrobust': res._results.normalized_cov_params = cov / res_constr.scale else: res._results.normalized_cov_params = None res._results.scale = res_constr.scale k_constr = len(q) res._results.df_resid += k_constr res._results.df_model -= k_constr res._results.constraints = LinearConstraints.from_patsy(lc) res._results.k_constr = k_constr res._results.results_constrained = res_constr return res class GLMResults(base.LikelihoodModelResults): """ Class to contain GLM results. GLMResults inherits from statsmodels.LikelihoodModelResults Attributes ---------- df_model : float See GLM.df_model df_resid : float See GLM.df_resid fit_history : dict Contains information about the iterations. Its keys are `iterations`, `deviance` and `params`. model : class instance Pointer to GLM model instance that called fit. nobs : float The number of observations n. normalized_cov_params : ndarray See GLM docstring params : ndarray The coefficients of the fitted model. Note that interpretation of the coefficients often depends on the distribution family and the data. pvalues : ndarray The two-tailed p-values for the parameters. scale : float The estimate of the scale / dispersion for the model fit. See GLM.fit and GLM.estimate_scale for more information. stand_errors : ndarray The standard errors of the fitted GLM. #TODO still named bse See Also -------- statsmodels.base.model.LikelihoodModelResults """ def __init__(self, model, params, normalized_cov_params, scale, cov_type='nonrobust', cov_kwds=None, use_t=None): super(GLMResults, self).__init__( model, params, normalized_cov_params=normalized_cov_params, scale=scale) self.family = model.family self._endog = model.endog self.nobs = model.endog.shape[0] self._freq_weights = model.freq_weights self._var_weights = model.var_weights self._iweights = model.iweights if isinstance(self.family, families.Binomial): self._n_trials = self.model.n_trials else: self._n_trials = 1 self.df_resid = model.df_resid self.df_model = model.df_model self._cache = {} # are these intermediate results needed or can we just # call the model's attributes? # for remove data and pickle without large arrays self._data_attr.extend(['results_constrained', '_freq_weights', '_var_weights', '_iweights']) self._data_in_cache.extend(['null', 'mu']) self._data_attr_model = getattr(self, '_data_attr_model', []) self._data_attr_model.append('mu') # robust covariance from statsmodels.base.covtype import get_robustcov_results if use_t is None: self.use_t = False # TODO: class default else: self.use_t = use_t # temporary warning ct = (cov_type == 'nonrobust') or (cov_type.upper().startswith('HC')) if self.model._has_freq_weights and not ct: import warnings from statsmodels.tools.sm_exceptions import SpecificationWarning warnings.warn('cov_type not fully supported with freq_weights', SpecificationWarning) if self.model._has_var_weights and not ct: import warnings from statsmodels.tools.sm_exceptions import SpecificationWarning warnings.warn('cov_type not fully supported with var_weights', SpecificationWarning) if cov_type == 'nonrobust': self.cov_type = 'nonrobust' self.cov_kwds = {'description': 'Standard Errors assume that the' + ' covariance matrix of the errors is correctly ' + 'specified.'} else: if cov_kwds is None: cov_kwds = {} get_robustcov_results(self, cov_type=cov_type, use_self=True, use_t=use_t, **cov_kwds) @cached_data def resid_response(self): """ Response residuals. The response residuals are defined as `endog` - `fittedvalues` """ return self._n_trials * (self._endog-self.mu) @cached_data def resid_pearson(self): """ Pearson residuals. The Pearson residuals are defined as (`endog` - `mu`)/sqrt(VAR(`mu`)) where VAR is the distribution specific variance function. See statsmodels.families.family and statsmodels.families.varfuncs for more information. """ return (np.sqrt(self._n_trials) * (self._endog-self.mu) * np.sqrt(self._var_weights) / np.sqrt(self.family.variance(self.mu))) @cached_data def resid_working(self): """ Working residuals. The working residuals are defined as `resid_response`/link'(`mu`). See statsmodels.family.links for the derivatives of the link functions. They are defined analytically. """ # Isn't self.resid_response is already adjusted by _n_trials? val = (self.resid_response * self.family.link.deriv(self.mu)) val *= self._n_trials return val @cached_data def resid_anscombe(self): """ Anscombe residuals. See statsmodels.families.family for distribution- specific Anscombe residuals. Currently, the unscaled residuals are provided. In a future version, the scaled residuals will be provided. """ import warnings warnings.warn('Anscombe residuals currently unscaled. After the 0.12 ' 'release, they will be scaled.', category=FutureWarning) return self.family.resid_anscombe(self._endog, self.fittedvalues, var_weights=self._var_weights, scale=1.) @cached_data def resid_anscombe_scaled(self): """ Scaled Anscombe residuals. See statsmodels.families.family for distribution-specific Anscombe residuals. """ return self.family.resid_anscombe(self._endog, self.fittedvalues, var_weights=self._var_weights, scale=self.scale) @cached_data def resid_anscombe_unscaled(self): """ Unscaled Anscombe residuals. See statsmodels.families.family for distribution-specific Anscombe residuals. """ return self.family.resid_anscombe(self._endog, self.fittedvalues, var_weights=self._var_weights, scale=1.) @cached_data def resid_deviance(self): """ Deviance residuals. See statsmodels.families.family for distribution- specific deviance residuals. """ dev = self.family.resid_dev(self._endog, self.fittedvalues, var_weights=self._var_weights, scale=1.) return dev @cached_value def pearson_chi2(self): """ Pearson's Chi-Squared statistic is defined as the sum of the squares of the Pearson residuals. """ chisq = (self._endog - self.mu)**2 / self.family.variance(self.mu) chisq *= self._iweights * self._n_trials chisqsum = np.sum(chisq) return chisqsum @cached_data def fittedvalues(self): """ The estimated mean response. This is the value of the inverse of the link function at lin_pred, where lin_pred is the linear predicted value obtained by multiplying the design matrix by the coefficient vector. """ return self.mu @cached_data def mu(self): """ See GLM docstring. """ return self.model.predict(self.params) @cache_readonly def null(self): """ Fitted values of the null model """ endog = self._endog model = self.model exog = np.ones((len(endog), 1)) kwargs = model._get_init_kwds() kwargs.pop('family') if hasattr(self.model, '_offset_exposure'): return GLM(endog, exog, family=self.family, **kwargs).fit().fittedvalues else: # correct if fitted is identical across observations wls_model = lm.WLS(endog, exog, weights=self._iweights * self._n_trials) return wls_model.fit().fittedvalues @cache_readonly def deviance(self): """ See statsmodels.families.family for the distribution-specific deviance functions. """ return self.family.deviance(self._endog, self.mu, self._var_weights, self._freq_weights) @cache_readonly def null_deviance(self): """The value of the deviance function for the model fit with a constant as the only regressor.""" return self.family.deviance(self._endog, self.null, self._var_weights, self._freq_weights) @cache_readonly def llnull(self): """ Log-likelihood of the model fit with a constant as the only regressor """ return self.family.loglike(self._endog, self.null, var_weights=self._var_weights, freq_weights=self._freq_weights, scale=self.scale) @cached_value def llf(self): """ Value of the loglikelihood function evalued at params. See statsmodels.families.family for distribution-specific loglikelihoods. """ _modelfamily = self.family if (isinstance(self.family, families.Gaussian) and isinstance(self.family.link, families.links.Power) and (self.family.link.power == 1.)): scale = (np.power(self._endog - self.mu, 2) * self._iweights).sum() scale /= self.model.wnobs else: scale = self.scale val = _modelfamily.loglike(self._endog, self.mu, var_weights=self._var_weights, freq_weights=self._freq_weights, scale=scale) return val @cached_value def aic(self): """ Akaike Information Criterion -2 * `llf` + 2 * (`df_model` + 1) """ return -2 * self.llf + 2 * (self.df_model + 1) @property def bic(self): """ Bayes Information Criterion `deviance` - `df_resid` * log(`nobs`) .. warning:: The current definition is base don the deviance rather than the log-likelihood. This is not consistent with the AIC definition, and after 0.13 both will make use of the log-likelihood definition. Notes ----- The log-likelihood version is defined -2 * `llf` + (`df_model` + 1)*log(n) """ if _use_bic_helper.use_bic_llf not in (True, False): warnings.warn( "The bic value is computed using the deviance formula. After " "0.13 this will change to the log-likelihood based formula. " "This change has no impact on the relative rank of models " "compared using BIC. You can directly access the " "log-likelihood version using the `bic_llf` attribute. You " "can suppress this message by calling " "statsmodels.genmod.generalized_linear_model.SET_USE_BIC_LLF " "with True to get the LLF-based version now or False to retain" "the deviance version.", FutureWarning ) if bool(_use_bic_helper.use_bic_llf): return self.bic_llf return self.bic_deviance @cached_value def bic_deviance(self): """ Bayes Information Criterion Based on the deviance, `deviance` - `df_resid` * log(`nobs`) """ return (self.deviance - (self.model.wnobs - self.df_model - 1) * np.log(self.model.wnobs)) @cached_value def bic_llf(self): """ Bayes Information Criterion Based on the log-likelihood, -2 * `llf` + log(n) * (`df_model` + 1) """ return -2*self.llf + (self.df_model+1)*np.log( self.df_model+self.df_resid+1 ) @Appender(pred.get_prediction_glm.__doc__) def get_prediction(self, exog=None, exposure=None, offset=None, transform=True, linear=False, row_labels=None): import statsmodels.regression._prediction as linpred pred_kwds = {'exposure': exposure, 'offset': offset, 'linear': True} # two calls to a get_prediction duplicates exog generation if patsy res_linpred = linpred.get_prediction(self, exog=exog, transform=transform, row_labels=row_labels, pred_kwds=pred_kwds) pred_kwds['linear'] = False res = pred.get_prediction_glm(self, exog=exog, transform=transform, row_labels=row_labels, linpred=res_linpred, link=self.model.family.link, pred_kwds=pred_kwds) return res def get_hat_matrix_diag(self, observed=True): """ Compute the diagonal of the hat matrix Parameters ---------- observed : bool If true, then observed hessian is used in the hat matrix computation. If false, then the expected hessian is used. In the case of a canonical link function both are the same. Returns ------- hat_matrix_diag : ndarray The diagonal of the hat matrix computed from the observed or expected hessian. """ weights = self.model.hessian_factor(self.params, observed=observed) wexog = np.sqrt(weights)[:, None] * self.model.exog hd = (wexog * np.linalg.pinv(wexog).T).sum(1) return hd def get_influence(self, observed=True): """ Get an instance of GLMInfluence with influence and outlier measures Parameters ---------- observed : bool If true, then observed hessian is used in the hat matrix computation. If false, then the expected hessian is used. In the case of a canonical link function both are the same. Returns ------- infl : GLMInfluence instance The instance has methods to calculate the main influence and outlier measures as attributes. See Also -------- statsmodels.stats.outliers_influence.GLMInfluence """ from statsmodels.stats.outliers_influence import GLMInfluence weights = self.model.hessian_factor(self.params, observed=observed) weights_sqrt = np.sqrt(weights) wexog = weights_sqrt[:, None] * self.model.exog wendog = weights_sqrt * self.model.endog # using get_hat_matrix_diag has duplicated computation hat_matrix_diag = self.get_hat_matrix_diag(observed=observed) infl = GLMInfluence(self, endog=wendog, exog=wexog, resid=self.resid_pearson, hat_matrix_diag=hat_matrix_diag) return infl @Appender(base.LikelihoodModelResults.remove_data.__doc__) def remove_data(self): # GLM has alias/reference in result instance self._data_attr.extend([i for i in self.model._data_attr if '_data.' not in i]) super(self.__class__, self).remove_data() # TODO: what are these in results? self._endog = None self._freq_weights = None self._var_weights = None self._iweights = None self._n_trials = None @Appender(_plot_added_variable_doc % {'extra_params_doc': ''}) def plot_added_variable(self, focus_exog, resid_type=None, use_glm_weights=True, fit_kwargs=None, ax=None): from statsmodels.graphics.regressionplots import plot_added_variable fig = plot_added_variable(self, focus_exog, resid_type=resid_type, use_glm_weights=use_glm_weights, fit_kwargs=fit_kwargs, ax=ax) return fig @Appender(_plot_partial_residuals_doc % {'extra_params_doc': ''}) def plot_partial_residuals(self, focus_exog, ax=None): from statsmodels.graphics.regressionplots import plot_partial_residuals return plot_partial_residuals(self, focus_exog, ax=ax) @Appender(_plot_ceres_residuals_doc % {'extra_params_doc': ''}) def plot_ceres_residuals(self, focus_exog, frac=0.66, cond_means=None, ax=None): from statsmodels.graphics.regressionplots import plot_ceres_residuals return plot_ceres_residuals(self, focus_exog, frac, cond_means=cond_means, ax=ax) def summary(self, yname=None, xname=None, title=None, alpha=.05): """ Summarize the Regression Results Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Names for the exogenous variables, default is `var_#` for ## in the number of regressors. Must match the number of parameters in the model title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : class to hold summary results """ top_left = [('Dep. Variable:', None), ('Model:', None), ('Model Family:', [self.family.__class__.__name__]), ('Link Function:', [self.family.link.__class__.__name__]), ('Method:', [self.method]), ('Date:', None), ('Time:', None), ('No. Iterations:', ["%d" % self.fit_history['iteration']]), ] top_right = [('No. Observations:', None), ('Df Residuals:', None), ('Df Model:', None), ('Scale:', ["%#8.5g" % self.scale]), ('Log-Likelihood:', None), ('Deviance:', ["%#8.5g" % self.deviance]), ('Pearson chi2:', ["%#6.3g" % self.pearson_chi2]) ] if hasattr(self, 'cov_type'): top_left.append(('Covariance Type:', [self.cov_type])) if title is None: title = "Generalized Linear Model Regression Results" # create summary tables from statsmodels.iolib.summary import Summary smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, yname=yname, xname=xname, title=title) smry.add_table_params(self, yname=yname, xname=xname, alpha=alpha, use_t=self.use_t) if hasattr(self, 'constraints'): smry.add_extra_txt(['Model has been estimated subject to linear ' 'equality constraints.']) return smry def summary2(self, yname=None, xname=None, title=None, alpha=.05, float_format="%.4f"): """Experimental summary for regression Results Parameters ---------- yname : str Name of the dependent variable (optional) xname : list[str], optional Names for the exogenous variables, default is `var_#` for ## in the number of regressors. Must match the number of parameters in the model title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals float_format : str print format for floats in parameters summary Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary2.Summary : class to hold summary results """ self.method = 'IRLS' from statsmodels.iolib import summary2 smry = summary2.Summary() with warnings.catch_warnings(): warnings.simplefilter("ignore", FutureWarning) smry.add_base(results=self, alpha=alpha, float_format=float_format, xname=xname, yname=yname, title=title) if hasattr(self, 'constraints'): smry.add_text('Model has been estimated subject to linear ' 'equality constraints.') return smry class GLMResultsWrapper(lm.RegressionResultsWrapper): _attrs = { 'resid_anscombe': 'rows', 'resid_deviance': 'rows', 'resid_pearson': 'rows', 'resid_response': 'rows', 'resid_working': 'rows' } _wrap_attrs = wrap.union_dicts(lm.RegressionResultsWrapper._wrap_attrs, _attrs) wrap.populate_wrapper(GLMResultsWrapper, GLMResults) if __name__ == "__main__": import statsmodels.api as sm data = sm.datasets.longley.load(as_pandas=False) # data.exog = add_constant(data.exog) GLMmod = GLM(data.endog, data.exog).fit() GLMT = GLMmod.summary(returns='tables') # GLMT[0].extend_right(GLMT[1]) # print(GLMT[0]) # print(GLMT[2]) GLMTp = GLMmod.summary(title='Test GLM') """ From Stata . webuse beetle . glm r i.beetle ldose, family(binomial n) link(cloglog) Iteration 0: log likelihood = -79.012269 Iteration 1: log likelihood = -76.94951 Iteration 2: log likelihood = -76.945645 Iteration 3: log likelihood = -76.945645 Generalized linear models No. of obs = 24 Optimization : ML Residual df = 20 Scale parameter = 1 Deviance = 73.76505595 (1/df) Deviance = 3.688253 Pearson = 71.8901173 (1/df) Pearson = 3.594506 Variance function: V(u) = u*(1-u/n) [Binomial] Link function : g(u) = ln(-ln(1-u/n)) [Complementary log-log] AIC = 6.74547 Log likelihood = -76.94564525 BIC = 10.20398 ------------------------------------------------------------------------------ | OIM r | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- beetle | 2 | -.0910396 .1076132 -0.85 0.398 -.3019576 .1198783 3 | -1.836058 .1307125 -14.05 0.000 -2.09225 -1.579867 | ldose | 19.41558 .9954265 19.50 0.000 17.46458 21.36658 _cons | -34.84602 1.79333 -19.43 0.000 -38.36089 -31.33116 ------------------------------------------------------------------------------ """ statsmodels-0.12.2/statsmodels/genmod/qif.py000066400000000000000000000377661400612667500211340ustar00rootroot00000000000000import numpy as np from collections import defaultdict import statsmodels.base.model as base from statsmodels.genmod import families from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod.families import links from statsmodels.genmod.families import varfuncs import statsmodels.regression.linear_model as lm import statsmodels.base.wrapper as wrap from statsmodels.tools.decorators import cache_readonly class QIFCovariance(object): """ A covariance model for quadratic inference function regression. The mat method returns a basis matrix B such that the inverse of the working covariance lies in the linear span of the basis matrices. Subclasses should set the number of basis matrices `num_terms`, so that `mat(d, j)` for j=0, ..., num_terms-1 gives the basis of dimension d.` """ def mat(self, dim, term): """ Returns the term'th basis matrix, which is a dim x dim matrix. """ raise NotImplementedError class QIFIndependence(QIFCovariance): """ Independent working covariance for QIF regression. This covariance model gives identical results to GEE with the independence working covariance. When using QIFIndependence as the working covariance, the QIF value will be zero, and cannot be used for chi^2 testing, or for model selection using AIC, BIC, etc. """ def __init__(self): self.num_terms = 1 def mat(self, dim, term): if term == 0: return np.eye(dim) else: return None class QIFExchangeable(QIFCovariance): """ Exchangeable working covariance for QIF regression. """ def __init__(self): self.num_terms = 2 def mat(self, dim, term): if term == 0: return np.eye(dim) elif term == 1: return np.ones((dim, dim)) else: return None class QIFAutoregressive(QIFCovariance): """ Autoregressive working covariance for QIF regression. """ def __init__(self): self.num_terms = 3 def mat(self, dim, term): if dim < 3: msg = ("Groups must have size at least 3 for " + "autoregressive covariance.") raise ValueError(msg) if term == 0: return np.eye(dim) elif term == 1: mat = np.zeros((dim, dim)) mat.flat[1::(dim+1)] = 1 mat += mat.T return mat elif term == 2: mat = np.zeros((dim, dim)) mat[0, 0] = 1 mat[dim-1, dim-1] = 1 return mat else: return None class QIF(base.Model): """ Fit a regression model using quadratic inference functions (QIF). QIF is an alternative to GEE that can be more efficient, and that offers different approaches for model selection and inference. Parameters ---------- endog : array_like The dependent variables of the regression. exog : array_like The independent variables of the regression. groups : array_like Labels indicating which group each observation belongs to. Observations in different groups should be independent. family : genmod family An instance of a GLM family. cov_struct : QIFCovariance instance An instance of a QIFCovariance. References ---------- A. Qu, B. Lindsay, B. Li (2000). Improving Generalized Estimating Equations using Quadratic Inference Functions, Biometrika 87:4. www.jstor.org/stable/2673612 """ def __init__(self, endog, exog, groups, family=None, cov_struct=None, missing='none', **kwargs): # Handle the family argument if family is None: family = families.Gaussian() else: if not issubclass(family.__class__, families.Family): raise ValueError("QIF: `family` must be a genmod " "family instance") self.family = family self._fit_history = defaultdict(list) # Handle the cov_struct argument if cov_struct is None: cov_struct = QIFIndependence() else: if not isinstance(cov_struct, QIFCovariance): raise ValueError( "QIF: `cov_struct` must be a QIFCovariance instance") self.cov_struct = cov_struct groups = np.asarray(groups) super(QIF, self).__init__(endog, exog, groups=groups, missing=missing, **kwargs) self.group_names = list(set(groups)) self.nobs = len(self.endog) groups_ix = defaultdict(list) for i, g in enumerate(groups): groups_ix[g].append(i) self.groups_ix = [groups_ix[na] for na in self.group_names] self._check_args(groups) def _check_args(self, groups): if len(groups) != len(self.endog): msg = "QIF: groups and endog should have the same length" raise ValueError(msg) if len(self.endog) != self.exog.shape[0]: msg = ("QIF: the length of endog should be equal to the " "number of rows of exog.") raise ValueError(msg) def objective(self, params): """ Calculate the gradient of the QIF objective function. Parameters ---------- params : array_like The model parameters at which the gradient is evaluated. Returns ------- grad : array_like The gradient vector of the QIF objective function. gn_deriv : array_like The gradients of each estimating equation with respect to the parameter. """ endog = self.endog exog = self.exog lpr = np.dot(exog, params) mean = self.family.link.inverse(lpr) va = self.family.variance(mean) # Mean derivative idl = self.family.link.inverse_deriv(lpr) idl2 = self.family.link.inverse_deriv2(lpr) vd = self.family.variance.deriv(mean) m = self.cov_struct.num_terms p = exog.shape[1] d = p * m gn = np.zeros(d) gi = np.zeros(d) gi_deriv = np.zeros((d, p)) gn_deriv = np.zeros((d, p)) cn_deriv = [0] * p cmat = np.zeros((d, d)) fastvar = self.family.variance is varfuncs.constant fastlink = isinstance(self.family.link, links.identity) for ix in self.groups_ix: sd = np.sqrt(va[ix]) resid = endog[ix] - mean[ix] sresid = resid / sd deriv = exog[ix, :] * idl[ix, None] jj = 0 for j in range(m): # The derivative of each term in (5) of Qu et al. # There are four terms involving beta in a product. # Iterated application of the product rule gives # the gradient as a sum of four terms. c = self.cov_struct.mat(len(ix), j) crs1 = np.dot(c, sresid) / sd gi[jj:jj+p] = np.dot(deriv.T, crs1) crs2 = np.dot(c, -deriv / sd[:, None]) / sd[:, None] gi_deriv[jj:jj+p, :] = np.dot(deriv.T, crs2) if not (fastlink and fastvar): for k in range(p): m1 = np.dot(exog[ix, :].T, idl2[ix] * exog[ix, k] * crs1) if not fastvar: vx = -0.5 * vd[ix] * deriv[:, k] / va[ix]**1.5 m2 = np.dot(deriv.T, vx * np.dot(c, sresid)) m3 = np.dot(deriv.T, np.dot(c, vx * resid) / sd) else: m2, m3 = 0, 0 gi_deriv[jj:jj+p, k] += m1 + m2 + m3 jj += p for j in range(p): u = np.outer(gi, gi_deriv[:, j]) cn_deriv[j] += u + u.T gn += gi gn_deriv += gi_deriv cmat += np.outer(gi, gi) ngrp = len(self.groups_ix) gn /= ngrp gn_deriv /= ngrp cmat /= ngrp**2 qif = np.dot(gn, np.linalg.solve(cmat, gn)) gcg = np.zeros(p) for j in range(p): cn_deriv[j] /= len(self.groups_ix)**2 u = np.linalg.solve(cmat, cn_deriv[j]).T u = np.linalg.solve(cmat, u) gcg[j] = np.dot(gn, np.dot(u, gn)) grad = 2 * np.dot(gn_deriv.T, np.linalg.solve(cmat, gn)) - gcg return qif, grad, cmat, gn, gn_deriv def estimate_scale(self, params): """ Estimate the dispersion/scale. The scale parameter for binomial and Poisson families is fixed at 1, otherwise it is estimated from the data. """ if isinstance(self.family, (families.Binomial, families.Poisson)): return 1. if hasattr(self, "ddof_scale"): ddof_scale = self.ddof_scale else: ddof_scale = self.exog[1] lpr = np.dot(self.exog, params) mean = self.family.link.inverse(lpr) resid = self.endog - mean scale = np.sum(resid**2) / (self.nobs - ddof_scale) return scale @classmethod def from_formula(cls, formula, groups, data, subset=None, *args, **kwargs): """ Create a QIF model instance from a formula and dataframe. Parameters ---------- formula : str or generic Formula object The formula specifying the model groups : array_like or string Array of grouping labels. If a string, this is the name of a variable in `data` that contains the grouping labels. data : array_like The data for the model. subset : array_like An array_like object of booleans, integers, or index values that indicate the subset of the data to used when fitting the model. Returns ------- model : QIF model instance """ if isinstance(groups, str): groups = data[groups] model = super(QIF, cls).from_formula( formula, data=data, subset=subset, groups=groups, *args, **kwargs) return model def fit(self, maxiter=100, start_params=None, tol=1e-6, gtol=1e-4, ddof_scale=None): """ Fit a GLM to correlated data using QIF. Parameters ---------- maxiter : int Maximum number of iterations. start_params : array_like, optional Starting values tol : float Convergence threshold for difference of successive estimates. gtol : float Convergence threshold for gradient. ddof_scale : int, optional Degrees of freedom for the scale parameter Returns ------- QIFResults object """ if ddof_scale is None: self.ddof_scale = self.exog.shape[1] else: self.ddof_scale = ddof_scale if start_params is None: model = GLM(self.endog, self.exog, family=self.family) result = model.fit() params = result.params else: params = start_params for _ in range(maxiter): qif, grad, cmat, _, gn_deriv = self.objective(params) gnorm = np.sqrt(np.sum(grad * grad)) self._fit_history["qif"].append(qif) self._fit_history["gradnorm"].append(gnorm) if gnorm < gtol: break cjac = 2 * np.dot(gn_deriv.T, np.linalg.solve(cmat, gn_deriv)) step = np.linalg.solve(cjac, grad) snorm = np.sqrt(np.sum(step * step)) self._fit_history["stepnorm"].append(snorm) if snorm < tol: break params -= step vcov = np.dot(gn_deriv.T, np.linalg.solve(cmat, gn_deriv)) vcov = np.linalg.inv(vcov) scale = self.estimate_scale(params) rslt = QIFResults(self, params, vcov / scale, scale) rslt.fit_history = self._fit_history self._fit_history = defaultdict(list) return QIFResultsWrapper(rslt) class QIFResults(base.LikelihoodModelResults): """Results class for QIF Regression""" def __init__(self, model, params, cov_params, scale, use_t=False, **kwds): super(QIFResults, self).__init__( model, params, normalized_cov_params=cov_params, scale=scale) self.qif, _, _, _, _ = self.model.objective(params) @cache_readonly def aic(self): """ An AIC-like statistic for models fit using QIF. """ if isinstance(self.model.cov_struct, QIFIndependence): msg = "AIC not available with QIFIndependence covariance" raise ValueError(msg) df = self.model.exog.shape[1] return self.qif + 2*df @cache_readonly def bic(self): """ A BIC-like statistic for models fit using QIF. """ if isinstance(self.model.cov_struct, QIFIndependence): msg = "BIC not available with QIFIndependence covariance" raise ValueError(msg) df = self.model.exog.shape[1] return self.qif + np.log(self.model.nobs)*df @cache_readonly def fittedvalues(self): """ Returns the fitted values from the model. """ return self.model.family.link.inverse( np.dot(self.model.exog, self.params)) def summary(self, yname=None, xname=None, title=None, alpha=.05): """ Summarize the QIF regression results Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Names for the exogenous variables, default is `var_#` for ## in the number of regressors. Must match the number of parameters in the model title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : class to hold summary results """ top_left = [('Dep. Variable:', None), ('Method:', ['QIF']), ('Family:', [self.model.family.__class__.__name__]), ('Covariance structure:', [self.model.cov_struct.__class__.__name__]), ('Date:', None), ('Time:', None), ] NY = [len(y) for y in self.model.groups_ix] top_right = [('No. Observations:', [sum(NY)]), ('No. clusters:', [len(NY)]), ('Min. cluster size:', [min(NY)]), ('Max. cluster size:', [max(NY)]), ('Mean cluster size:', ["%.1f" % np.mean(NY)]), ('Scale:', ["%.3f" % self.scale]), ] if title is None: title = self.model.__class__.__name__ + ' ' +\ "Regression Results" # Override the exog variable names if xname is provided as an # argument. if xname is None: xname = self.model.exog_names if yname is None: yname = self.model.endog_names # Create summary table instance from statsmodels.iolib.summary import Summary smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, yname=yname, xname=xname, title=title) smry.add_table_params(self, yname=yname, xname=xname, alpha=alpha, use_t=False) return smry class QIFResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(QIFResultsWrapper, QIFResults) statsmodels-0.12.2/statsmodels/genmod/tests/000077500000000000000000000000001400612667500211225ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/genmod/tests/__init__.py000066400000000000000000000000001400612667500232210ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/genmod/tests/gee_categorical_simulation_check.py000066400000000000000000000205631400612667500302000ustar00rootroot00000000000000""" Assesment of Generalized Estimating Equations using simulation. This script checks ordinal and nominal models for multinomial data. See the generated file "gee_categorical_simulation_check.txt" for results. """ from statsmodels.compat.python import lrange import numpy as np from scipy import stats from statsmodels.genmod.generalized_estimating_equations import GEE,\ gee_setup_ordinal, gee_setup_nominal,\ gee_ordinal_starting_values, Multinomial from statsmodels.genmod.families import Binomial from statsmodels.genmod.cov_struct import GlobalOddsRatio from .gee_gaussian_simulation_check import GEE_simulator class ordinal_simulator(GEE_simulator): # The thresholds where the latent continuous process is cut to # obtain the categorical values. thresholds = None def true_params(self): return np.concatenate((self.thresholds, self.params)) def starting_values(self, nconstraints): beta = gee_ordinal_starting_values(self.endog, len(self.params)) if nconstraints > 0: m = self.exog_ex.shape[1] - nconstraints beta = beta[0:m] return beta def print_dparams(self, dparams_est): OUT.write("Odds ratio estimate: %8.4f\n" % dparams_est[0]) OUT.write("Odds ratio truth: %8.4f\n" % self.dparams[0]) OUT.write("\n") def simulate(self): endog, exog, group, time = [], [], [], [] for i in range(self.ngroups): gsize = np.random.randint(self.group_size_range[0], self.group_size_range[1]) group.append([i,] * gsize) time1 = np.random.normal(size=(gsize,2)) time.append(time1) exog1 = np.random.normal(size=(gsize, len(self.params))) exog.append(exog1) lp = np.dot(exog1, self.params) z = np.random.uniform(size=gsize) z = np.log(z / (1 - z)) + lp endog1 = np.array([np.sum(x > self.thresholds) for x in z]) endog.append(endog1) self.exog = np.concatenate(exog, axis=0) self.endog = np.concatenate(endog) self.time = np.concatenate(time, axis=0) self.group = np.concatenate(group) self.offset = np.zeros(len(self.endog), dtype=np.float64) class nominal_simulator(GEE_simulator): def starting_values(self, nconstraints): return None def true_params(self): return np.concatenate(self.params[:-1]) def print_dparams(self, dparams_est): OUT.write("Odds ratio estimate: %8.4f\n" % dparams_est[0]) OUT.write("Odds ratio truth: %8.4f\n" % self.dparams[0]) OUT.write("\n") def simulate(self): endog, exog, group, time = [], [], [], [] for i in range(self.ngroups): gsize = np.random.randint(self.group_size_range[0], self.group_size_range[1]) group.append([i,] * gsize) time1 = np.random.normal(size=(gsize,2)) time.append(time1) exog1 = np.random.normal(size=(gsize, len(self.params[0]))) exog.append(exog1) # Probabilities for each outcome prob = [np.exp(np.dot(exog1, p)) for p in self.params] prob = np.vstack(prob).T prob /= prob.sum(1)[:, None] m = len(self.params) endog1 = [] for k in range(gsize): pdist = stats.rv_discrete(values=(lrange(m), prob[k,:])) endog1.append(pdist.rvs()) endog.append(np.asarray(endog1)) self.exog = np.concatenate(exog, axis=0) self.endog = np.concatenate(endog).astype(np.int32) self.time = np.concatenate(time, axis=0) self.group = np.concatenate(group) self.offset = np.zeros(len(self.endog), dtype=np.float64) def gendat_ordinal(): os = ordinal_simulator() os.params = np.r_[0., 1] os.ngroups = 200 os.thresholds = [1, 0, -1] os.dparams = [1.,] os.simulate() data = np.concatenate((os.endog[:,None], os.exog, os.group[:,None]), axis=1) os.endog_ex, os.exog_ex, os.intercepts, os.nthresh = \ gee_setup_ordinal(data, 0) os.group_ex = os.exog_ex[:,-1] os.exog_ex = os.exog_ex[:,0:-1] os.exog_ex = np.concatenate((os.intercepts, os.exog_ex), axis=1) va = GlobalOddsRatio(4, "ordinal") lhs = np.array([[0., 0., 0, 1., 0.], [0., 0, 0, 0, 1]]) rhs = np.r_[0., 1] return os, va, Binomial(), (lhs, rhs) def gendat_nominal(): ns = nominal_simulator() # The last component of params must be identically zero ns.params = [np.r_[0., 1], np.r_[-1., 0], np.r_[0., 0]] ns.ngroups = 200 ns.dparams = [1., ] ns.simulate() data = np.concatenate((ns.endog[:,None], ns.exog, ns.group[:,None]), axis=1) ns.endog_ex, ns.exog_ex, ns.exog_ne, ns.nlevel = \ gee_setup_nominal(data, 0, [3,]) ns.group_ex = ns.exog_ne[:,0] va = GlobalOddsRatio(3, "nominal") lhs = np.array([[0., 1., 1, 0],]) rhs = np.r_[0.,] return ns, va, Multinomial(3), (lhs, rhs) if __name__ == '__main__': nrep = 100 OUT = open("gee_categorical_simulation_check.txt", "w") np.set_printoptions(formatter={'all': lambda x: "%8.3f" % x}, suppress=True) # Loop over data generating models gendats = [gendat_nominal, gendat_ordinal] for jg,gendat in enumerate(gendats): dparams = [] params = [] std_errors = [] pvalues = [] for j in range(nrep): da, va, mt, constraint = gendat() beta = da.starting_values(0) md = GEE(da.endog_ex, da.exog_ex, da.group_ex, None, mt, va) mdf = md.fit(start_params = beta) if mdf is None: continue scale_inv = 1 / md.estimate_scale() dparams.append(np.r_[va.dparams, scale_inv]) params.append(np.asarray(mdf.params)) std_errors.append(np.asarray(mdf.standard_errors)) da, va, mt, constraint = gendat() beta = da.starting_values(constraint[0].shape[0]) md = GEE(da.endog_ex, da.exog_ex, da.group_ex, None, mt, va, constraint=constraint) mdf = md.fit(start_params = beta) if mdf is None: continue score = md.score_test_results pvalues.append(score["p-value"]) dparams_mean = np.array(sum(dparams) / len(dparams)) OUT.write("%s data.\n" % ("Nominal", "Ordinal")[jg]) OUT.write("%d runs converged successfully.\n" % len(pvalues)) OUT.write("Checking dependence parameters:\n") da.print_dparams(dparams_mean) params = np.array(params) eparams = params.mean(0) sdparams = params.std(0) std_errors = np.array(std_errors) std_errors = std_errors.mean(0) true_params = da.true_params() OUT.write("Checking parameter values:\n") OUT.write("Observed: ") OUT.write(np.array_str(eparams) + "\n") OUT.write("Expected: ") OUT.write(np.array_str(true_params) + "\n") OUT.write("Absolute difference: ") OUT.write(np.array_str(eparams - true_params) + "\n") OUT.write("Relative difference: ") OUT.write(np.array_str((eparams - true_params) / true_params) + "\n") OUT.write("\n") OUT.write("Checking standard errors:\n") OUT.write("Observed: ") OUT.write(np.array_str(sdparams) + "\n") OUT.write("Expected: ") OUT.write(np.array_str(std_errors) + "\n") OUT.write("Absolute difference: ") OUT.write(np.array_str(sdparams - std_errors) + "\n") OUT.write("Relative difference: ") OUT.write(np.array_str((sdparams - std_errors) / std_errors) + "\n") OUT.write("\n") OUT.write("Checking constrained estimation:\n") OUT.write("Observed Expected\n") pvalues.sort() for q in np.arange(0.1, 0.91, 0.1): OUT.write("%10.3f %10.3f\n" % (pvalues[int(q*len(pvalues))], q)) OUT.write("=" * 80 + "\n\n") OUT.close() statsmodels-0.12.2/statsmodels/genmod/tests/gee_categorical_simulation_check.txt000066400000000000000000000002161400612667500303600ustar00rootroot00000000000000Nominal data. 99 runs converged successfully. Checking dependence parameters: Odds ratio estimate: 1.0028 Odds ratio truth: 1.0000 statsmodels-0.12.2/statsmodels/genmod/tests/gee_gaussian_simulation_check.py000066400000000000000000000232561400612667500275370ustar00rootroot00000000000000""" Assesment of Generalized Estimating Equations using simulation. This script checks Gaussian models. See the generated file "gee_gaussian_simulation_check.txt" for results. """ from statsmodels.compat.python import lrange import scipy import numpy as np from itertools import product from statsmodels.genmod.families import Gaussian from statsmodels.genmod.generalized_estimating_equations import GEE from statsmodels.genmod.cov_struct import Autoregressive, Nested class GEE_simulator(object): # # Parameters that must be defined # # Number of groups ngroups = None # Standard deviation of the pure errors error_sd = None # The regression coefficients params = None # The parameters defining the dependence structure dep_params = None # The true scale parameter scale = None # # Output parameters # # Matrix of exogeneous data (rows are cases, columns are # variables) exog = None # Matrix of endogeneous data (len(endog) = exog.shape[0]) endog = None # Matrix of time information (time.shape[0] = len(endog)) time = None # Group labels (len(groups) = len(endog)) group = None # Group sizes are random within this range group_size_range = [4, 11] # dparams_est is dparams with scale_inv appended def print_dparams(self, dparams_est): raise NotImplementedError class AR_simulator(GEE_simulator): # The distance function for determining AR correlations. distfun = [lambda x, y: np.sqrt(np.sum((x-y)**2)),] def print_dparams(self, dparams_est): OUT.write("AR coefficient estimate: %8.4f\n" % dparams_est[0]) OUT.write("AR coefficient truth: %8.4f\n" % self.dep_params[0]) OUT.write("Error variance estimate: %8.4f\n" % dparams_est[1]) OUT.write("Error variance truth: %8.4f\n" % self.error_sd**2) OUT.write("\n") def simulate(self): endog, exog, group, time = [], [], [], [] for i in range(self.ngroups): gsize = np.random.randint(self.group_size_range[0], self.group_size_range[1]) group.append([i,] * gsize) time1 = np.random.normal(size=(gsize,2)) time.append(time1) exog1 = np.random.normal(size=(gsize, 5)) exog1[:,0] = 1 exog.append(exog1) # Pairwise distances within the cluster distances = scipy.spatial.distance.cdist(time1, time1, self.distfun[0]) # Pairwise correlations within the cluster correlations = self.dep_params[0]**distances correlations_sr = np.linalg.cholesky(correlations) errors = np.dot(correlations_sr, np.random.normal(size=gsize)) endog1 = np.dot(exog1, self.params) + errors * self.error_sd endog.append(endog1) self.exog = np.concatenate(exog, axis=0) self.endog = np.concatenate(endog) self.time = np.concatenate(time, axis=0) self.group = np.concatenate(group) class Nested_simulator(GEE_simulator): # Vector containing list of nest sizes (used instead of # group_size_range). nest_sizes = None # Matrix of nest id's (an output parameter) id_matrix = None def print_dparams(self, dparams_est): for j in range(len(self.nest_sizes)): OUT.write("Nest %d variance estimate: %8.4f\n" % \ (j+1, dparams_est[j])) OUT.write("Nest %d variance truth: %8.4f\n" % \ (j+1, self.dep_params[j])) OUT.write("Error variance estimate: %8.4f\n" % \ (dparams_est[-1] - sum(dparams_est[0:-1]))) OUT.write("Error variance truth: %8.4f\n" % self.error_sd**2) OUT.write("\n") def simulate(self): group_effect_var = self.dep_params[0] vcomp = self.dep_params[1:] vcomp.append(0) endog, exog, group, id_matrix = [], [], [], [] for i in range(self.ngroups): iterators = [lrange(n) for n in self.nest_sizes] # The random effects variances = [np.sqrt(v)*np.random.normal(size=n) for v,n in zip(vcomp, self.nest_sizes)] gpe = np.random.normal() * np.sqrt(group_effect_var) nest_all = [] for j in self.nest_sizes: nest_all.append(set()) for nest in product(*iterators): group.append(i) # The sum of all random effects that apply to this # unit ref = gpe + sum([v[j] for v,j in zip(variances, nest)]) exog1 = np.random.normal(size=5) exog1[0] = 1 exog.append(exog1) error = ref + self.error_sd * np.random.normal() endog1 = np.dot(exog1, self.params) + error endog.append(endog1) for j in range(len(nest)): nest_all[j].add(tuple(nest[0:j+1])) nest1 = [len(x)-1 for x in nest_all] id_matrix.append(nest1[0:-1]) self.exog = np.array(exog) self.endog = np.array(endog) self.group = np.array(group) self.id_matrix = np.array(id_matrix) self.time = np.zeros_like(self.endog) def gen_gendat_ar0(ar): def gendat_ar0(msg = False): ars = AR_simulator() ars.ngroups = 200 ars.params = np.r_[0, -1, 1, 0, 0.5] ars.error_sd = 2 ars.dep_params = [ar,] ars.simulate() return ars, Autoregressive() return gendat_ar0 def gen_gendat_ar1(ar): def gendat_ar1(): ars = AR_simulator() ars.ngroups = 200 ars.params = np.r_[0, -0.8, 1.2, 0, 0.5] ars.error_sd = 2 ars.dep_params = [ar,] ars.simulate() return ars, Autoregressive() return gendat_ar1 def gendat_nested0(): ns = Nested_simulator() ns.error_sd = 1. ns.params = np.r_[0., 1, 1, -1, -1] ns.ngroups = 50 ns.nest_sizes = [10, 5] ns.dep_params = [2., 1.] ns.simulate() return ns, Nested(ns.id_matrix) def gendat_nested1(): ns = Nested_simulator() ns.error_sd = 2. ns.params = np.r_[0, 1, 1.3, -0.8, -1.2] ns.ngroups = 50 ns.nest_sizes = [10, 5] ns.dep_params = [1., 3.] ns.simulate() return ns, Nested(ns.id_matrix) if __name__ == "__main__": try: np.set_printoptions(formatter={'all': lambda x: "%8.3f" % x}, suppress=True) except TypeError: # older numpy versions do not have formatter option pass OUT = open("gee_gaussian_simulation_check.txt", "w") nrep = 100 gendats = [gen_gendat_ar0(ar) for ar in (0, 0.3, 0.6)] gendats.extend([gen_gendat_ar1(ar) for ar in (0, 0.3, 0.6)]) gendats.extend([gendat_nested0, gendat_nested1]) lhs = np.array([[0., 1, 1, 0, 0],]) rhs = np.r_[0.,] # Loop over data generating models for gendat in gendats: pvalues = [] params = [] std_errors = [] dep_params = [] for j in range(nrep): da,va = gendat() ga = Gaussian() md = GEE(da.endog, da.exog, da.group, da.time, ga, va) mdf = md.fit() scale_inv = 1 / md.estimate_scale() dep_params.append(np.r_[va.dep_params, scale_inv]) params.append(np.asarray(mdf.params)) std_errors.append(np.asarray(mdf.standard_errors())) da,va = gendat() ga = Gaussian() md = GEE(da.endog, da.exog, da.group, da.time, ga, va, constraint=(lhs, rhs)) mdf = md.fit() score = md.score_test_results pvalue = score["p-value"] pvalues.append(pvalue) dparams_mean = np.array(sum(dep_params) / len(dep_params)) OUT.write("Checking dependence parameters:\n") da.print_dparams(dparams_mean) params = np.array(params) eparams = params.mean(0) sdparams = params.std(0) std_errors = np.array(std_errors) std_errors = std_errors.mean(0) OUT.write("Checking parameter values:\n") OUT.write("Observed: ") OUT.write(np.array_str(eparams) + "\n") OUT.write("Expected: ") OUT.write(np.array_str(da.params) + "\n") OUT.write("Absolute difference: ") OUT.write(np.array_str(eparams - da.params) + "\n") OUT.write("Relative difference: ") OUT.write(np.array_str((eparams - da.params) / da.params) + "\n") OUT.write("\n") OUT.write("Checking standard errors\n") OUT.write("Observed: ") OUT.write(np.array_str(sdparams) + "\n") OUT.write("Expected: ") OUT.write(np.array_str(std_errors) + "\n") OUT.write("Absolute difference: ") OUT.write(np.array_str(sdparams - std_errors) + "\n") OUT.write("Relative difference: ") OUT.write(np.array_str((sdparams - std_errors) / std_errors) + "\n") OUT.write("\n") pvalues.sort() OUT.write("Checking constrained estimation:\n") OUT.write("Left hand side:\n") OUT.write(np.array_str(lhs) + "\n") OUT.write("Right hand side:\n") OUT.write(np.array_str(rhs) + "\n") OUT.write("Observed p-values Expected Null p-values\n") for q in np.arange(0.1, 0.91, 0.1): OUT.write("%20.3f %20.3f\n" % (pvalues[int(q*len(pvalues))], q)) OUT.write("=" * 80 + "\n\n") OUT.close() statsmodels-0.12.2/statsmodels/genmod/tests/gee_gaussian_simulation_check.txt000066400000000000000000000261571400612667500277310ustar00rootroot00000000000000Checking dependence parameters: AR coefficient estimate: 0.0000 AR coefficient truth: 0.0000 Error variance estimate: 4.0006 Error variance truth: 4.0000 Checking parameter values: Observed: [ -0.005 -1.007 1.008 -0.003 0.494] Expected: [ 0.000 -1.000 1.000 0.000 0.500] Absolute difference: [ -0.005 -0.007 0.008 -0.003 -0.006] Relative difference: [ -inf 0.007 0.008 -inf -0.012] Checking standard errors Observed: [ 0.054 0.056 0.056 0.052 0.053] Expected: [ 0.053 0.053 0.054 0.053 0.053] Absolute difference: [ 0.001 0.003 0.002 -0.001 -0.001] Relative difference: [ 0.023 0.052 0.042 -0.025 -0.012] Checking constrained estimation: Left hand side: [[ 0.000 1.000 1.000 0.000 0.000]] Right hand side: [ 0.000] Observed p-values Expected Null p-values 0.169 0.100 0.284 0.200 0.406 0.300 0.488 0.400 0.600 0.500 0.679 0.600 0.732 0.700 0.810 0.800 0.910 0.900 ================================================================================ Checking dependence parameters: AR coefficient estimate: 0.3766 AR coefficient truth: 0.3000 Error variance estimate: 3.9845 Error variance truth: 4.0000 Checking parameter values: Observed: [ -0.005 -1.002 0.998 -0.003 0.492] Expected: [ 0.000 -1.000 1.000 0.000 0.500] Absolute difference: [ -0.005 -0.002 -0.002 -0.003 -0.008] Relative difference: [ -inf 0.002 -0.002 -inf -0.017] Checking standard errors Observed: [ 0.082 0.055 0.056 0.055 0.054] Expected: [ 0.080 0.054 0.053 0.053 0.053] Absolute difference: [ 0.002 0.002 0.002 0.002 0.001] Relative difference: [ 0.026 0.034 0.044 0.034 0.020] Checking constrained estimation: Left hand side: [[ 0.000 1.000 1.000 0.000 0.000]] Right hand side: [ 0.000] Observed p-values Expected Null p-values 0.152 0.100 0.268 0.200 0.347 0.300 0.437 0.400 0.517 0.500 0.585 0.600 0.705 0.700 0.826 0.800 0.915 0.900 ================================================================================ Checking dependence parameters: AR coefficient estimate: 0.6689 AR coefficient truth: 0.6000 Error variance estimate: 4.0118 Error variance truth: 4.0000 Checking parameter values: Observed: [ -0.009 -0.998 0.996 -0.002 0.493] Expected: [ 0.000 -1.000 1.000 0.000 0.500] Absolute difference: [ -0.009 0.002 -0.004 -0.002 -0.007] Relative difference: [ -inf -0.002 -0.004 -inf -0.014] Checking standard errors Observed: [ 0.102 0.050 0.046 0.050 0.044] Expected: [ 0.106 0.048 0.048 0.048 0.048] Absolute difference: [ -0.004 0.001 -0.002 0.002 -0.004] Relative difference: [ -0.040 0.031 -0.039 0.044 -0.075] Checking constrained estimation: Left hand side: [[ 0.000 1.000 1.000 0.000 0.000]] Right hand side: [ 0.000] Observed p-values Expected Null p-values 0.064 0.100 0.126 0.200 0.191 0.300 0.329 0.400 0.474 0.500 0.609 0.600 0.676 0.700 0.840 0.800 0.934 0.900 ================================================================================ Checking dependence parameters: AR coefficient estimate: 0.0000 AR coefficient truth: 0.0000 Error variance estimate: 3.9885 Error variance truth: 4.0000 Checking parameter values: Observed: [ -0.005 -0.798 1.195 0.005 0.505] Expected: [ 0.000 -0.800 1.200 0.000 0.500] Absolute difference: [ -0.005 0.002 -0.005 0.005 0.005] Relative difference: [ -inf -0.002 -0.004 inf 0.011] Checking standard errors Observed: [ 0.044 0.047 0.054 0.059 0.057] Expected: [ 0.053 0.053 0.053 0.053 0.053] Absolute difference: [ -0.009 -0.005 0.001 0.006 0.004] Relative difference: [ -0.178 -0.098 0.014 0.106 0.071] Checking constrained estimation: Left hand side: [[ 0.000 1.000 1.000 0.000 0.000]] Right hand side: [ 0.000] Observed p-values Expected Null p-values 0.000 0.100 0.000 0.200 0.000 0.300 0.000 0.400 0.000 0.500 0.000 0.600 0.000 0.700 0.000 0.800 0.000 0.900 ================================================================================ Checking dependence parameters: AR coefficient estimate: 0.3810 AR coefficient truth: 0.3000 Error variance estimate: 3.9966 Error variance truth: 4.0000 Checking parameter values: Observed: [ -0.000 -0.797 1.200 -0.002 0.499] Expected: [ 0.000 -0.800 1.200 0.000 0.500] Absolute difference: [ -0.000 0.003 0.000 -0.002 -0.001] Relative difference: [ -inf -0.004 0.000 -inf -0.002] Checking standard errors Observed: [ 0.086 0.062 0.044 0.058 0.053] Expected: [ 0.080 0.053 0.053 0.054 0.054] Absolute difference: [ 0.006 0.008 -0.009 0.004 -0.001] Relative difference: [ 0.074 0.158 -0.165 0.081 -0.010] Checking constrained estimation: Left hand side: [[ 0.000 1.000 1.000 0.000 0.000]] Right hand side: [ 0.000] Observed p-values Expected Null p-values 0.000 0.100 0.000 0.200 0.000 0.300 0.000 0.400 0.000 0.500 0.000 0.600 0.000 0.700 0.000 0.800 0.000 0.900 ================================================================================ Checking dependence parameters: AR coefficient estimate: 0.6660 AR coefficient truth: 0.6000 Error variance estimate: 4.0002 Error variance truth: 4.0000 Checking parameter values: Observed: [ -0.007 -0.793 1.201 -0.006 0.501] Expected: [ 0.000 -0.800 1.200 0.000 0.500] Absolute difference: [ -0.007 0.007 0.001 -0.006 0.001] Relative difference: [ -inf -0.009 0.001 -inf 0.003] Checking standard errors Observed: [ 0.109 0.048 0.046 0.047 0.049] Expected: [ 0.106 0.048 0.048 0.048 0.048] Absolute difference: [ 0.002 -0.000 -0.001 -0.001 0.002] Relative difference: [ 0.023 -0.007 -0.029 -0.018 0.034] Checking constrained estimation: Left hand side: [[ 0.000 1.000 1.000 0.000 0.000]] Right hand side: [ 0.000] Observed p-values Expected Null p-values 0.000 0.100 0.000 0.200 0.000 0.300 0.000 0.400 0.000 0.500 0.000 0.600 0.000 0.700 0.000 0.800 0.000 0.900 ================================================================================ Checking dependence parameters: Nest 1 variance estimate: 1.9752 Nest 1 variance truth: 2.0000 Nest 2 variance estimate: 1.0013 Nest 2 variance truth: 1.0000 Error variance estimate: 1.0089 Error variance truth: 1.0000 Checking parameter values: Observed: [ 0.024 1.002 0.999 -1.000 -1.001] Expected: [ 0.000 1.000 1.000 -1.000 -1.000] Absolute difference: [ 0.024 0.002 -0.001 -0.000 -0.001] Relative difference: [ inf 0.002 -0.001 0.000 0.001] Checking standard errors Observed: [ 0.219 0.024 0.022 0.021 0.020] Expected: [ 0.204 0.021 0.022 0.021 0.022] Absolute difference: [ 0.016 0.002 0.001 -0.001 -0.002] Relative difference: [ 0.077 0.104 0.026 -0.041 -0.089] Checking constrained estimation: Left hand side: [[ 0.000 1.000 1.000 0.000 0.000]] Right hand side: [ 0.000] Observed p-values Expected Null p-values 0.000 0.100 0.000 0.200 0.000 0.300 0.000 0.400 0.000 0.500 0.000 0.600 0.000 0.700 0.000 0.800 0.000 0.900 ================================================================================ Checking dependence parameters: Nest 1 variance estimate: 0.9614 Nest 1 variance truth: 1.0000 Nest 2 variance estimate: 3.0497 Nest 2 variance truth: 3.0000 Error variance estimate: 4.0144 Error variance truth: 4.0000 Checking parameter values: Observed: [ 0.007 0.999 1.297 -0.799 -1.200] Expected: [ 0.000 1.000 1.300 -0.800 -1.200] Absolute difference: [ 0.007 -0.001 -0.003 0.001 0.000] Relative difference: [ inf -0.001 -0.002 -0.001 -0.000] Checking standard errors Observed: [ 0.142 0.047 0.044 0.044 0.040] Expected: [ 0.163 0.044 0.043 0.043 0.042] Absolute difference: [ -0.021 0.003 0.001 0.001 -0.002] Relative difference: [ -0.129 0.077 0.015 0.015 -0.052] Checking constrained estimation: Left hand side: [[ 0.000 1.000 1.000 0.000 0.000]] Right hand side: [ 0.000] Observed p-values Expected Null p-values 0.000 0.100 0.000 0.200 0.000 0.300 0.000 0.400 0.000 0.500 0.000 0.600 0.000 0.700 0.000 0.800 0.000 0.900 ================================================================================ statsmodels-0.12.2/statsmodels/genmod/tests/gee_poisson_simulation_check.py000066400000000000000000000216111400612667500274100ustar00rootroot00000000000000""" Assesment of Generalized Estimating Equations using simulation. This script checks Poisson models. See the generated file "gee_poisson_simulation_check.txt" for results. """ import numpy as np from statsmodels.genmod.families import Poisson from .gee_gaussian_simulation_check import GEE_simulator from statsmodels.genmod.generalized_estimating_equations import GEE from statsmodels.genmod.cov_struct import Exchangeable,Independence class Exchangeable_simulator(GEE_simulator): """ Simulate exchangeable Poisson data. The data within a cluster are simulated as y_i = z_c + z_i. The z_c, and {z_i} are independent Poisson random variables with expected values e_c and {e_i}, respectively. In order for the pairwise correlation to be equal to `f` for all pairs, we need e_c / sqrt((e_c + e_i) * (e_c + e_j)) = f for all i, j. By setting all e_i = e within a cluster, these equations can be satisfied. We thus need e_c * (1 - f) = f * e, which can be solved (non-uniquely) for e and e_c. """ scale_inv = 1. def print_dparams(self, dparams_est): OUT.write("Estimated common pairwise correlation: %8.4f\n" % dparams_est[0]) OUT.write("True common pairwise correlation: %8.4f\n" % self.dparams[0]) OUT.write("Estimated inverse scale parameter: %8.4f\n" % dparams_est[1]) OUT.write("True inverse scale parameter: %8.4f\n" % self.scale_inv) OUT.write("\n") def simulate(self): endog, exog, group, time = [], [], [], [] # Get a basis for the orthogonal complement to params. f = np.sum(self.params**2) u,s,vt = np.linalg.svd(np.eye(len(self.params)) - np.outer(self.params, self.params) / f) params0 = u[:,np.flatnonzero(s > 1e-6)] for i in range(self.ngroups): gsize = np.random.randint(self.group_size_range[0], self.group_size_range[1]) group.append([i,] * gsize) time1 = np.random.normal(size=(gsize, 2)) time.append(time1) e_c = np.random.uniform(low=1, high=10) e = e_c * (1 - self.dparams[0]) / self.dparams[0] common = np.random.poisson(e_c) unique = np.random.poisson(e, gsize) endog1 = common + unique endog.append(endog1) lpr = np.log(e_c + e) * np.ones(gsize) # Create an exog matrix so that E[Y] = log(dot(exog1, params)) exog1 = np.outer(lpr, self.params) / np.sum(self.params**2) emat = np.random.normal(size=(len(lpr), params0.shape[1])) exog1 += np.dot(emat, params0.T) exog.append(exog1) self.exog = np.concatenate(exog, axis=0) self.endog = np.concatenate(endog) self.time = np.concatenate(time, axis=0) self.group = np.concatenate(group) class Overdispersed_simulator(GEE_simulator): """ Use the negative binomial distribution to check GEE estimation using the overdispered Poisson model with independent dependence. Simulating X = np.random.negative_binomial(n, p, size) then EX = (1 - p) * n / p Var(X) = (1 - p) * n / p**2 These equations can be inverted as follows: p = E / V n = E * p / (1 - p) dparams[0] is the common correlation coefficient """ def print_dparams(self, dparams_est): OUT.write("Estimated inverse scale parameter: %8.4f\n" % dparams_est[0]) OUT.write("True inverse scale parameter: %8.4f\n" % self.scale_inv) OUT.write("\n") def simulate(self): endog, exog, group, time = [], [], [], [] # Get a basis for the orthogonal complement to params. f = np.sum(self.params**2) u,s,vt = np.linalg.svd(np.eye(len(self.params)) - np.outer(self.params, self.params) / f) params0 = u[:,np.flatnonzero(s > 1e-6)] for i in range(self.ngroups): gsize = np.random.randint(self.group_size_range[0], self.group_size_range[1]) group.append([i,] * gsize) time1 = np.random.normal(size=(gsize, 2)) time.append(time1) exog1 = np.random.normal(size=(gsize, len(self.params))) exog.append(exog1) E = np.exp(np.dot(exog1, self.params)) V = E * self.scale_inv p = E / V n = E * p / (1 - p) endog1 = np.random.negative_binomial(n, p, gsize) endog.append(endog1) self.exog = np.concatenate(exog, axis=0) self.endog = np.concatenate(endog) self.time = np.concatenate(time, axis=0) self.group = np.concatenate(group) def gendat_exchangeable(): exs = Exchangeable_simulator() exs.params = np.r_[2., 0.2, 0.2, -0.1, -0.2] exs.ngroups = 200 exs.dparams = [0.3,] exs.simulate() return exs, Exchangeable() def gendat_overdispersed(): exs = Overdispersed_simulator() exs.params = np.r_[2., 0.2, 0.2, -0.1, -0.2] exs.ngroups = 200 exs.scale_inv = 2. exs.dparams = [] exs.simulate() return exs, Independence() if __name__ == "__main__": np.set_printoptions(formatter={'all': lambda x: "%8.3f" % x}, suppress=True) OUT = open("gee_poisson_simulation_check.txt", "w") nrep = 100 gendats = [gendat_exchangeable, gendat_overdispersed] lhs = np.array([[0., 1, -1, 0, 0],]) rhs = np.r_[0.0,] # Loop over data generating models for gendat in gendats: pvalues = [] params = [] std_errors = [] dparams = [] for j in range(nrep): da, va = gendat() ga = Poisson() # Poisson seems to be more sensitive to starting values, # so we run the independence model first. md = GEE(da.endog, da.exog, da.group, da.time, ga, Independence()) mdf = md.fit() md = GEE(da.endog, da.exog, da.group, da.time, ga, va) mdf = md.fit(start_params = mdf.params) if mdf is None or (not mdf.converged): print("Failed to converge") continue scale_inv = 1. / md.estimate_scale() dparams.append(np.r_[va.dparams, scale_inv]) params.append(np.asarray(mdf.params)) std_errors.append(np.asarray(mdf.standard_errors)) da,va = gendat() ga = Poisson() md = GEE(da.endog, da.exog, da.group, da.time, ga, va, constraint=(lhs, rhs)) mdf = md.fit() if mdf is None or (not mdf.converged): print("Failed to converge") continue score = md.score_test_results pvalue = score["p-value"] pvalues.append(pvalue) dparams_mean = np.array(sum(dparams) / len(dparams)) OUT.write("Results based on %d successful fits out of %d data sets.\n\n" % (len(dparams), nrep)) OUT.write("Checking dependence parameters:\n") da.print_dparams(dparams_mean) params = np.array(params) eparams = params.mean(0) sdparams = params.std(0) std_errors = np.array(std_errors) std_errors = std_errors.mean(0) OUT.write("Checking parameter values:\n") OUT.write("Observed: ") OUT.write(np.array_str(eparams) + "\n") OUT.write("Expected: ") OUT.write(np.array_str(da.params) + "\n") OUT.write("Absolute difference: ") OUT.write(np.array_str(eparams - da.params) + "\n") OUT.write("Relative difference: ") OUT.write(np.array_str((eparams - da.params) / da.params) + "\n") OUT.write("\n") OUT.write("Checking standard errors\n") OUT.write("Observed: ") OUT.write(np.array_str(sdparams) + "\n") OUT.write("Expected: ") OUT.write(np.array_str(std_errors) + "\n") OUT.write("Absolute difference: ") OUT.write(np.array_str(sdparams - std_errors) + "\n") OUT.write("Relative difference: ") OUT.write(np.array_str((sdparams - std_errors) / std_errors) + "\n") OUT.write("\n") pvalues.sort() OUT.write("Checking constrained estimation:\n") OUT.write("Left hand side:\n") OUT.write(np.array_str(lhs) + "\n") OUT.write("Right hand side:\n") OUT.write(np.array_str(rhs) + "\n") OUT.write("Observed p-values Expected Null p-values\n") for q in np.arange(0.1, 0.91, 0.1): OUT.write("%20.3f %20.3f\n" % (pvalues[int(q*len(pvalues))], q)) OUT.write("=" * 80 + "\n\n") OUT.close() statsmodels-0.12.2/statsmodels/genmod/tests/gee_poisson_simulation_check.txt000066400000000000000000000055661400612667500276120ustar00rootroot00000000000000Results based on 100 successful fits out of 100 data sets.Checking dependence parameters: Estimated common pairwise correlation: 0.2993 True common pairwise correlation: 0.3000 Estimated inverse scale parameter: 1.0104 True inverse scale parameter: 1.0000 Checking parameter values: Observed: [ 1.999 0.198 0.200 -0.100 -0.200] Expected: [ 2.000 0.200 0.200 -0.100 -0.200] Absolute difference: [ -0.001 -0.002 -0.000 0.000 0.000] Relative difference: [ -0.000 -0.009 -0.000 -0.004 -0.002] Checking standard errors Observed: [ 0.007 0.006 0.006 0.006 0.006] Expected: [ 0.007 0.006 0.006 0.006 0.006] Absolute difference: [ 0.000 0.000 0.000 0.000 -0.000] Relative difference: [ 0.046 0.050 0.077 0.042 -0.007] Checking constrained estimation: Left hand side: [[ 0.000 1.000 -1.000 0.000 0.000]] Right hand side: [ 0.000] Observed p-values Expected Null p-values 0.127 0.100 0.206 0.200 0.250 0.300 0.329 0.400 0.403 0.500 0.484 0.600 0.565 0.700 0.645 0.800 0.832 0.900 ================================================================================ Results based on 98 successful fits out of 100 data sets.Checking dependence parameters: Estimated inverse scale parameter: 1.9792 True inverse scale parameter: 2.0000 Checking parameter values: Observed: [ 2.001 0.198 0.199 -0.100 -0.199] Expected: [ 2.000 0.200 0.200 -0.100 -0.200] Absolute difference: [ 0.001 -0.002 -0.001 0.000 0.001] Relative difference: [ 0.000 -0.010 -0.007 -0.004 -0.004] Checking standard errors Observed: [ 0.007 0.014 0.016 0.016 0.014] Expected: [ 0.007 0.014 0.014 0.013 0.013] Absolute difference: [ 0.000 0.001 0.002 0.002 0.001] Relative difference: [ 0.010 0.057 0.150 0.185 0.043] Checking constrained estimation: Left hand side: [[ 0.000 1.000 -1.000 0.000 0.000]] Right hand side: [ 0.000] Observed p-values Expected Null p-values 0.096 0.100 0.147 0.200 0.241 0.300 0.281 0.400 0.459 0.500 0.530 0.600 0.649 0.700 0.849 0.800 0.879 0.900 ================================================================================ statsmodels-0.12.2/statsmodels/genmod/tests/gee_simulation_check.py000066400000000000000000000223311400612667500256360ustar00rootroot00000000000000""" Assesment of Generalized Estimating Equations using simulation. Only Gaussian models are currently checked. See the generated file "gee_simulation_check.txt" for results. """ from statsmodels.compat.python import lrange import scipy import numpy as np from itertools import product from statsmodels.genmod.families import Gaussian from statsmodels.genmod.generalized_estimating_equations import GEE from statsmodels.genmod.cov_struct import Autoregressive, Nested np.set_printoptions(formatter={'all': lambda x: "%8.3f" % x}, suppress=True) OUT = open("gee_simulation_check.txt", "w") class GEE_simulator(object): # # Parameters that must be defined # # Number of groups ngroups = None # Standard deviation of the pure errors error_sd = None # The regression coefficients params = None # The parameters defining the dependence structure dparams = None # # Output parameters # # Matrix of exogeneous data (rows are cases, columns are # variables) exog = None # Matrix of endogeneous data (len(endog) = exog.shape[0]) endog = None # Matrix of time information (time.shape[0] = len(endog)) time = None # Group labels (len(groups) = len(endog)) group = None # Group sizes are random within this range group_size_range = [4, 11] # dparams_est is dparams with scale_inv appended def print_dparams(self, dparams_est): raise NotImplementedError class AR_simulator(GEE_simulator): # The distance function for determining AR correlations. distfun = [lambda x, y: np.sqrt(np.sum((x-y)**2)),] def print_dparams(self, dparams_est): OUT.write("AR coefficient estimate: %8.4f\n" % dparams_est[0]) OUT.write("AR coefficient truth: %8.4f\n" % self.dparams[0]) OUT.write("Error variance estimate: %8.4f\n" % dparams_est[1]) OUT.write("Error variance truth: %8.4f\n" % self.error_sd**2) OUT.write("\n") def simulate(self): endog, exog, group, time = [], [], [], [] for i in range(self.ngroups): gsize = np.random.randint(self.group_size_range[0], self.group_size_range[1]) group.append([i,] * gsize) time1 = np.random.normal(size=(gsize,2)) time.append(time1) exog1 = np.random.normal(size=(gsize, 5)) exog1[:,0] = 1 exog.append(exog1) # Pairwise distances within the cluster distances = scipy.spatial.distance.cdist(time1, time1, self.distfun[0]) # Pairwise correlations within the cluster correlations = self.dparams[0]**distances correlations_sr = np.linalg.cholesky(correlations) errors = np.dot(correlations_sr, np.random.normal(size=gsize)) endog1 = np.dot(exog1, self.params) + errors * self.error_sd endog.append(endog1) self.exog = np.concatenate(exog, axis=0) self.endog = np.concatenate(endog) self.time = np.concatenate(time, axis=0) self.group = np.concatenate(group) class Nested_simulator(GEE_simulator): # Vector containing list of nest sizes (used instead of # group_size_range). nest_sizes = None # Matrix of nest id's (an output parameter) id_matrix = None def print_dparams(self, dparams_est): for j in range(len(self.nest_sizes)): OUT.write("Nest %d variance estimate: %8.4f\n" % \ (j+1, dparams_est[j])) OUT.write("Nest %d variance truth: %8.4f\n" % \ (j+1, self.dparams[j])) OUT.write("Error variance estimate: %8.4f\n" % \ (dparams_est[-1] - sum(dparams_est[0:-1]))) OUT.write("Error variance truth: %8.4f\n" % self.error_sd**2) OUT.write("\n") def simulate(self): group_effect_var = self.dparams[0] vcomp = self.dparams[1:] vcomp.append(0) endog, exog, group, id_matrix = [], [], [], [] for i in range(self.ngroups): iterators = [lrange(n) for n in self.nest_sizes] # The random effects variances = [np.sqrt(v)*np.random.normal(size=n) for v,n in zip(vcomp, self.nest_sizes)] gpe = np.random.normal() * np.sqrt(group_effect_var) nest_all = [] for j in self.nest_sizes: nest_all.append(set()) for nest in product(*iterators): group.append(i) # The sum of all random effects that apply to this # unit ref = gpe + sum([v[j] for v,j in zip(variances, nest)]) exog1 = np.random.normal(size=5) exog1[0] = 1 exog.append(exog1) error = ref + self.error_sd * np.random.normal() endog1 = np.dot(exog1, self.params) + error endog.append(endog1) for j in range(len(nest)): nest_all[j].add(tuple(nest[0:j+1])) nest1 = [len(x)-1 for x in nest_all] id_matrix.append(nest1[0:-1]) self.exog = np.array(exog) self.endog = np.array(endog) self.group = np.array(group) self.id_matrix = np.array(id_matrix) self.time = np.zeros_like(self.endog) def check_constraint(da, va, ga): """ Check the score testing of the parameter constraints. """ def gen_gendat_ar0(ar): def gendat_ar0(msg = False): ars = AR_simulator() ars.ngroups = 200 ars.params = np.r_[0, -1, 1, 0, 0.5] ars.error_sd = 2 ars.dparams = [ar,] ars.simulate() return ars, Autoregressive() return gendat_ar0 def gen_gendat_ar1(ar): def gendat_ar1(): ars = AR_simulator() ars.ngroups = 200 ars.params = np.r_[0, -0.8, 1.2, 0, 0.5] ars.error_sd = 2 ars.dparams = [ar,] ars.simulate() return ars, Autoregressive() return gendat_ar1 def gendat_nested0(): ns = Nested_simulator() ns.error_sd = 1. ns.params = np.r_[0., 1, 1, -1, -1] ns.ngroups = 50 ns.nest_sizes = [10, 5] ns.dparams = [2., 1.] ns.simulate() return ns, Nested(ns.id_matrix) def gendat_nested1(): ns = Nested_simulator() ns.error_sd = 2. ns.params = np.r_[0, 1, 1.3, -0.8, -1.2] ns.ngroups = 50 ns.nest_sizes = [10, 5] ns.dparams = [1., 3.] ns.simulate() return ns, Nested(ns.id_matrix) nrep = 100 gendats = [gen_gendat_ar0(ar) for ar in (0, 0.3, 0.6)] gendats.extend([gen_gendat_ar1(ar) for ar in (0, 0.3, 0.6)]) gendats.extend([gendat_nested0, gendat_nested1]) lhs = np.array([[0., 1, 1, 0, 0],]) rhs = np.r_[0.,] # Loop over data generating models for gendat in gendats: pvalues = [] params = [] std_errors = [] dparams = [] for j in range(nrep): da,va = gendat() ga = Gaussian() md = GEE(da.endog, da.exog, da.group, da.time, ga, va) mdf = md.fit() scale_inv = 1 / md.estimate_scale() dparams.append(np.r_[va.dparams, scale_inv]) params.append(np.asarray(mdf.params)) std_errors.append(np.asarray(mdf.standard_errors)) da,va = gendat() ga = Gaussian() md = GEE(da.endog, da.exog, da.group, da.time, ga, va, constraint=(lhs, rhs)) mdf = md.fit() score = md.score_test_results pvalue = score["p-value"] pvalues.append(pvalue) dparams_mean = np.array(sum(dparams) / len(dparams)) OUT.write("Checking dependence parameters:\n") da.print_dparams(dparams_mean) params = np.array(params) eparams = params.mean(0) sdparams = params.std(0) std_errors = np.array(std_errors) std_errors = std_errors.mean(0) OUT.write("Checking parameter values:\n") OUT.write("Observed: ") OUT.write(np.array_str(eparams) + "\n") OUT.write("Expected: ") OUT.write(np.array_str(da.params) + "\n") OUT.write("Absolute difference: ") OUT.write(np.array_str(eparams - da.params) + "\n") OUT.write("Relative difference: ") OUT.write(np.array_str((eparams - da.params) / da.params) + "\n") OUT.write("\n") OUT.write("Checking standard errors\n") OUT.write("Observed: ") OUT.write(np.array_str(sdparams) + "\n") OUT.write("Expected: ") OUT.write(np.array_str(std_errors) + "\n") OUT.write("Absolute difference: ") OUT.write(np.array_str(sdparams - std_errors) + "\n") OUT.write("Relative difference: ") OUT.write(np.array_str((sdparams - std_errors) / std_errors) + "\n") OUT.write("\n") pvalues.sort() OUT.write("Checking constrained estimation:\n") OUT.write("Left hand side:\n") OUT.write(np.array_str(lhs) + "\n") OUT.write("Right hand side:\n") OUT.write(np.array_str(rhs) + "\n") OUT.write("Observed p-values Expected Null p-values\n") for q in np.arange(0.1, 0.91, 0.1): OUT.write("%20.3f %20.3f\n" % (pvalues[int(q*len(pvalues))], q)) OUT.write("=" * 80 + "\n\n") OUT.close() statsmodels-0.12.2/statsmodels/genmod/tests/results/000077500000000000000000000000001400612667500226235ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/genmod/tests/results/__init__.py000066400000000000000000000000001400612667500247220ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/genmod/tests/results/elastic_net.R000066400000000000000000000015731400612667500252460ustar00rootroot00000000000000library(glmnet) library(R2nparray) rslt = list() for (dtype in c("binomial", "poisson")) { ik = 0 data = read.csv(sprintf("enet_%s.csv", dtype)) endog = data[, 1] exog = data[, 2:dim(data)[2]] exog = as.matrix(exog) for (k in 1:dim(exog)[2]) { exog[,k] = exog[,k] - mean(exog[,k]) exog[,k] = exog[,k] / sd(exog[,k]) } for (alpha in c(0, 0.5, 1)) { fit = glmnet(exog, endog, family=dtype, intercept=FALSE, standardize=FALSE, alpha=alpha) for (q in c(0.3, 0.5, 0.7)) { ii = round(q * length(fit$lambda)) coefs = coef(fit, s=fit$lambda[ii]) coefs = coefs[2:length(coefs)] rname = sprintf("rslt_%s_%d", dtype, ik) ik = ik + 1 rslt[[rname]] = c(alpha, fit$lambda[ii], coefs) } } } R2nparray(rslt, fname="glmnet_r_results.py") statsmodels-0.12.2/statsmodels/genmod/tests/results/elastic_net_generate_tests.py000066400000000000000000000011761400612667500305700ustar00rootroot00000000000000import numpy as np """ Generate data sets for testing elastic net fits of GLMs. """ n = 200 p = 5 # Logistic exog = np.random.normal(size=(n, p)) lin_pred = exog.sum(1) * 0.2 exp_val = 1 / (1 + np.exp(-lin_pred)) endog = 1 * (np.random.uniform(size=n) < exp_val) mat = np.concatenate((endog[:, None], exog), axis=1) np.savetxt("enet_binomial.csv", mat, fmt="%.2f", delimiter=",") # Poisson exog = np.random.normal(size=(n, p)) lin_pred = exog.sum(1) * 0.2 exp_val = np.exp(lin_pred) endog = np.random.poisson(exp_val) mat = 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beta = np.array([1, -2, 1], dtype=np.float64) # Covariate correlations r = 0.4 # Cluster effects of covariates rx = 0.5 # Within-cluster outcome dependence re = 0.3 p = len(beta) OUT = open("gee_logistic_1.csv", "w") for i in range(nclust): n = np.random.randint(3, 6) # Cluster size x = np.random.normal(size=(n, p)) x = rx*np.random.normal() + np.sqrt(1-rx**2)*x x[:, 2] = r*x[:, 1] + np.sqrt(1-r**2)*x[:, 2] pr = 1/(1+np.exp(-np.dot(x, beta))) z = re*np.random.normal() +\ np.sqrt(1-re**2)*np.random.normal(size=n) u = norm.cdf(z) y = 1*(u < pr) for j in range(n): OUT.write("%d, %d," % (i, y[j])) OUT.write(",".join(["%.3f" % b for b in x[j, :]]) + "\n") OUT.close() def generate_linear(): # Number of clusters nclust = 100 # Regression coefficients beta = np.array([1, -2, 1], dtype=np.float64) # Within cluster covariate correlations r = 0.4 # Between cluster covariate effects rx = 0.5 # Within-cluster outcome dependence # re = 0.3 p = len(beta) OUT = open("gee_linear_1.csv", "w") for i in range(nclust): n = np.random.randint(3, 6) # Cluster size x = np.random.normal(size=(n, p)) x = rx*np.random.normal() + np.sqrt(1-rx**2)*x x[:, 2] = r*x[:, 1] + np.sqrt(1-r**2)*x[:, 2] # TODO: should `e` be used somewhere? # e = np.sqrt(1-re**2)*np.random.normal(size=n) + re*np.random.normal() y = np.dot(x, beta) + np.random.normal(size=n) for j in range(n): OUT.write("%d, %d," % (i, y[j])) OUT.write(",".join(["%.3f" % b for b in x[j, :]]) + "\n") OUT.close() def generate_nested_linear(): # Number of clusters (clusters have 10 values, partitioned into 2 # subclusters of size 5). nclust = 200 # Regression coefficients beta = np.array([1, -2, 1], dtype=np.float64) # Top level cluster variance component v1 = 1 # Subcluster variance component v2 = 0.5 # Error variance component v3 = 1.5 p = len(beta) OUT = open("gee_nested_linear_1.csv", "w") for i in range(nclust): x = np.random.normal(size=(10, p)) y = np.dot(x, beta) y += np.sqrt(v1)*np.random.normal() y[0:5] += np.sqrt(v2)*np.random.normal() y[5:10] += np.sqrt(v2)*np.random.normal() y += np.sqrt(v3)*np.random.normal(size=10) for j in range(10): OUT.write("%d, %.3f," % (i, y[j])) OUT.write(",".join(["%.3f" % b for b in x[j, :]]) + "\n") OUT.close() def generate_ordinal(): # Regression coefficients beta = np.zeros(5, dtype=np.float64) beta[2] = 1 beta[4] = -1 rz = 0.5 OUT = open("gee_ordinal_1.csv", "w") for i in range(200): n = np.random.randint(3, 6) # Cluster size x = np.random.normal(size=(n, 5)) for j in range(5): x[:, j] += np.random.normal() pr = np.dot(x, beta) pr = np.array([1, 0, -0.5]) + pr[:, None] pr = 1 / (1 + np.exp(-pr)) z = rz*np.random.normal() +\ np.sqrt(1-rz**2)*np.random.normal(size=n) u = norm.cdf(z) y = (u[:, None] > pr).sum(1) for j in range(n): OUT.write("%d, %d," % (i, y[j])) OUT.write(",".join(["%.3f" % b for b in x[j, :]]) + "\n") OUT.close() def generate_nominal(): # Regression coefficients beta1 = np.r_[0.5, 0.5] beta2 = np.r_[-1, -0.5] p = len(beta1) rz = 0.5 OUT = open("gee_nominal_1.csv", "w") for i in range(200): n = np.random.randint(3, 6) # Cluster size x = np.random.normal(size=(n, p)) x[:, 0] = 1 for j in range(1, x.shape[1]): x[:, j] += np.random.normal() pr1 = np.exp(np.dot(x, beta1))[:, None] pr2 = np.exp(np.dot(x, beta2))[:, None] den = 1 + pr1 + pr2 pr = np.hstack((pr1/den, pr2/den, 1/den)) cpr = np.cumsum(pr, 1) z = rz*np.random.normal() +\ np.sqrt(1-rz**2)*np.random.normal(size=n) u = norm.cdf(z) y = (u[:, None] > cpr).sum(1) for j in range(n): OUT.write("%d, %d," % (i, y[j])) OUT.write(",".join(["%.3f" % b for b in x[j, :]]) + "\n") OUT.close() def generate_poisson(): # Regression coefficients beta = np.zeros(5, dtype=np.float64) beta[2] = 0.5 beta[4] = -0.5 nclust = 100 OUT = open("gee_poisson_1.csv", "w") for i in range(nclust): n = np.random.randint(3, 6) # Cluster size x = np.random.normal(size=(n, 5)) for j in range(5): x[:, j] += np.random.normal() lp = np.dot(x, beta) E = np.exp(lp) y = [np.random.poisson(e) for e in E] y = np.array(y) for j in range(n): OUT.write("%d, %d," % (i, y[j])) OUT.write(",".join(["%.3f" % b for b in x[j, :]]) + "\n") OUT.close() statsmodels-0.12.2/statsmodels/genmod/tests/results/gee_linear_1.csv000066400000000000000000000236171400612667500256630ustar00rootroot000000000000000,-3,0.030,2.837,1.190 0,0,0.214,0.523,-0.125 0,1,1.084,-0.411,-0.038 0,2,-0.826,-0.483,1.285 1,-1,-1.305,1.182,1.151 1,4,0.216,-3.028,-2.207 1,0,-1.650,-0.704,0.738 1,-1,-0.409,-0.934,-1.236 1,3,-0.230,-2.591,-1.539 2,0,-0.155,-0.792,-1.291 2,0,-0.284,-1.262,-1.525 2,-3,-1.263,0.283,-2.494 2,0,-0.645,-0.916,-1.378 3,0,0.350,1.186,2.401 3,0,1.813,2.413,2.090 3,-3,0.394,3.115,1.293 3,0,1.141,1.649,1.440 3,1,1.542,0.308,0.832 4,-2,-0.341,0.759,-0.684 4,-3,-0.751,0.553,0.097 4,-2,-0.563,1.430,0.164 4,2,-0.903,-0.629,0.476 5,0,0.962,1.113,0.563 5,0,-0.073,0.521,0.169 5,0,1.054,1.206,1.446 6,3,1.074,-0.240,0.064 6,0,-1.210,-1.041,-0.241 6,0,-0.143,0.085,1.459 6,2,0.846,0.933,2.384 6,0,-0.228,0.009,0.451 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99,1,-1.869,-0.900,0.706,0.465,1.603 statsmodels-0.12.2/statsmodels/genmod/tests/results/glm_test_resids.py000066400000000000000000011642431400612667500263770ustar00rootroot00000000000000''' This file contains the residuals for testing GLM. All residuals were obtained with Stata. The residuals are column ordered as Pearson, Deviance, Working, Anscombe, and Response Residuals ''' import numpy as np # TODO: wrap super-long lines. maybe put these in csv files? lbw = [-.67369007, -.86512534, -.06703079, -.93506245, -.31217507, -.38301082, -.52323205, -.01427243, -.55879206, -.12793027, -.68788286, -.88025592, -.07003063, -.95205459, -.32119762, -.96932399, -1.1510657, -.12098923, -1.2626094, -.48442686, -1.017216, -1.1919416, -.12709645, -1.3106868, -.50853393, -.56992387, -.75002865, -.04537362, -.80685236, -.24517662, -.38236113, -.52240243, -.01419429, -.5578939, -.12755193, -.70541551, -.89874491, -.07371959, -.97286469, -.33226988, -.53129095, -.70516948, -.03779124, -.75734471, -.22013309, -.59687896, -.78068461, -.05087588, -.84082824, -.26268069, -.72944938, -.92372831, -.07872676, -1.0010676, -.34729955, -.48089188, -.64503581, -.02865125, -.6913447, -.18782188, -1.7509231, -1.6748694, -.13984667, -1.9107428, -.75404181, -1.0993874, -1.2588746, -.13558784, 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1.5465618, .1471632, 1.7447092, .69757645, 1.2580261, 1.3775399, .14540261, 1.5337471, .61279777, 2.2387897, 1.8940894, .11559989, 2.2085158, .83367096, 1.4987735, 1.5346157, .14749226, 1.7295233, .69195908, .87949714, 1.0704799, .10725881, 1.1688167, .43614806, .81628943, 1.0105668, .09596102, 1.0998807, .39987821, 1.0340841, 1.2060057, .12904294, 1.327311, .51675179, 1.7490122, 1.6738861, .13992657, 1.9094491, .75363655, 1.6803635, 1.6378022, .14262258, 1.8622063, .73846784, 1.8051113, 1.7022925, .13748913, 1.9469661, .7651715, 1.5637979, 1.5729326, .14621078, 1.7783904, .70976331, 1.1993095, 1.3351545, .14270545, 1.4820722, .58988546, 1.3197815, 1.4202979, .1471939, 1.5863531, .63527917, .71898726, .91290406, .07655565, .98883657, .34077931, 1.5103554, 1.5415584, .14730892, 1.7383434, .69523097, 3.0022063, 2.1465826, .08091665, 2.5788383, .90013225, .64440768, .83344364, .06083212, .89959036, .29341668, 1.5019795, 1.5365427, .14744358, 1.7319699, .69286925, 1.3305489, 1.4275696, .1474058, 1.5953487, .63903614, .90521582, 1.094089, .11148405, 1.1961638, .45037299, .6236701, .81062745, .05646071, .87413186, .28003914, .71234937, .90599551, .07517106, .9810397, .3366244] # noqa:E501 lbw_resids = np.array(lbw).astype(float).reshape(-1, 5) cpunish = [.29883413, .29637762, 62.478695, .29638095, 1.7736344, .280627, .27622019, 6.5853375, .27623151, .80342558, 4.0930531, 2.9777878, 6.1503069, 3.0157174, 4.6881034, .16338859, .16114971, 1.1563983, .16115474, .31370176, .63595872, .59618385, 1.9109264, .59656954, .91769973, .9059739, .8066189, .99577089, .80822353, .9349684, .0532905, .0529548, .14244545, .05295515, .07395759, -.26830664, -.2766384, -1.0082872, -.27668319, -.41714051, -.62341484, -.68349824, -1.5652763, -.68459104, -.84732188, -1.1015655, -1.2743561, -5.3400286, -1.279951, -1.8643241, -1.2006618, -1.4021282, -6.6206839, -1.40923, -2.1211989, -1.2797534, -1.505173, -7.8054171, -1.5136295, -2.3382067, -.960585, -1.0954134, -3.8587164, -1.0992211, -1.5269969, .10846917, .10649195, .0921891, .10649783, .1027458, .02088367, .02081086, .02023963, .0208109, .02066675, .63647875, .56713011, .24880139, .56824372, .4653791, -.69597083, -.77000601, -1.9377178, -.77151335, -.97909358] # noqa:E501 cpunish_resids = np.array(cpunish).astype(float).reshape(-1, 5) scotvote = [.04317472, .04256856, -8338.93, .04256786, 2.4956853, -.01827077, -.01838325, 2762.4019, -.01838319, -.97334528, .05609817, .05508221, -7252.03, .05508069, 2.8365188, -.02280193, -.02297758, 4525.3102, -.02297747, -1.3300374, -.02505649, -.02526888, 8767.023, -.02526873, -1.7656214, -.1421743, -.14953291, 26174.801, -.14950069, -8.0880132, -.01973673, -.01986809, 5888.0406, -.01986801, -1.318784, .06763015, .06616299, -19473.553, .06616036, 4.4658962, .0202078, .02007327, -3928.3996, .02007319, 1.1706255, -.00841611, -.00843983, 2127.7741, -.00843983, -.53216875, -.04429363, -.04496504, 6971.3512, -.04496419, -2.3914787, .01158536, .01154092, -2667.3324, .01154091, 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5824.1466, -.02654575, -1.5916286, .01183737, .01179098, -4763.0477, .01179097, .87390689, -.03325649, -.03363248, 11219.87, -.03363212, -2.3151557] # noqa:E501 scotvote_resids = np.array(scotvote).astype(float).reshape(-1, 5) star98 = [-1.3375372, -1.3342565, -3674.3805, -1.3343393, -18.732624, .97808463, .99272841, 197.05157, .99291658, 5.7338226, 4.2825696, 4.29447, 7304.117, 4.2983582, 51.167264, .20665475, .20689409, 283.85261, .20689456, 2.2971775, -3.4397844, -3.7418743, -184.10712, -3.7732602, -12.963164, -8.8955127, -8.7070478, -94493.01, -8.7156529, -195.54523, 1.3093612, 1.3040684, 6904.5348, 1.3041169, 22.790356, -2.3354095, -2.3171211, -6891.6853, -2.3175198, -33.497868, -4.9509734, -4.9716533, -7444.4706, -4.9782445, -56.720276, -4.3896461, -4.3936251, -19119.121, -4.3958412, -71.687315, 2.6246727, 2.6002292, 33800.262, 2.6004266, 61.52101, 1.0381778, 1.0655404, 147.40536, 1.0658131, 5.4160865, -5.371452, -5.4255371, -8735.5422, -5.433774, -63.167122, -7.5162302, 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1.1985705, .83253909, -.22061912, .81439502, .85901372, .23502298, .2116479, -.10906943, .21126127, .22925451, -.39761407, -.50587964, .1393689, -.50102296, -.35321552, -.30317936, -.36865385, .27304678, -.36631514, -.36888312, .52891415, .4286696, -.23649281, .42553087, .50957264, .09077196, .08692412, -.04414515, .08689695, .08993709, -.14416059, -.1568803, .14318278, -.15669352, -.18121937, .73647886, .57278216, -.12516194, .56679404, .51397376, -.30020097, -.35901216, .15278503, -.35710415, -.3019801, -.30970783, -.36488812, .0616491, -.36325833, -.22783496, -.13090644, -.14142637, .14714733, -.14128564, -.17148842, 1.7228459, 1.0583109, -.58431917, 1.0175577, 1.5137622, -.22877864, -.25919887, .08362009, -.25852681, -.20609013, -.82510806, -1.6126582, .1515493, -1.4979969, -.59092886, -.64003893, -1.0073362, .1692274, -.97361338, -.51757245, -.13130595, -.14057566, .05050397, -.1404667, -.12031177, -.18244628, -.19973106, .03812658, -.19945858, -.13640887, .02164936, .0214168, -.01169166, .02141638, .02221257, .50690309, .41969105, -.10328319, .41720801, .37581131, 1.0020303, .7351515, -.12375838, .72352927, .62871736] # noqa:E501 invgauss_resids = np.asarray(invgauss).astype(float).reshape(-1, 5) wfs_resids = [-1.168096, -1.274198, -22.17336, -1.276003, -3.11599, 1.11769, 1.074522, 93.39722, 1.074787, 4.886437, .7295976, .715076, 143.1204, .7151231, 4.239254, .6471395, .6355711, 124.1729, .6356048, 3.732567, .5949094, .5789607, 24.55698, .5790298, 2.056012, -.8578523, -.8829973, -123.7017, -.8831246, -4.498492, .9996619, .9733517, 207.696, .9734635, 5.92077, -.3647809, -.3685094, -82.85051, -.3685159, -2.225631, -.5218114, -.5276356, -268.2977, -.5276466, -4.180369, -.9659918, -.9815653, -1084.813, -.981608, -10.04078, .3903325, .3878348, 390.8879, .3878375, 3.905176, -.1136672, -.1140306, -24.22441, -.1140308, -.6789552, 1.404348, 1.344308, 166.2025, 1.344715, 6.894916, .6979978, .6888638, 444.2878, .6888834, 6.004232, -.4536614, -.4585339, -171.4895, -.4585427, -3.280201, -.1426753, -.1432245, -34.60201, -.1432249, -.8897463, 4.041986, 3.678221, 839.28, 3.683146, 23.93493, -.4076838, -.4104721, -420.7155, -.4104753, -4.119822, 1.037925, 1.021274, 1152.838, 1.021318, 10.74897, 1.002495, .9780589, 268.3886, .9781554, 6.461147, -1.810334, -1.851575, -4981.573, -1.851736, -25.3685, -1.028229, -1.038076, -6328.413, -1.038092, -18.84335, -.3727405, -.3743742, -1096.784, -.3743754, -5.341272, .5779432, .5697695, 164.1083, .5697884, 3.798688, 1.083387, 1.055122, 294.6827, 1.055241, 7.019516, .2389214, .2379634, 227.0207, .237964, 2.348868, -.6575496, -.6669395, -330.597, -.6669623, -5.228599, -1.223007, -1.27265, -208.9083, -1.273003, -6.785854, .5404838, .534834, 319.6869, .5348437, 4.536944, -2.227986, -2.295954, -5036.329, -2.296313, -29.24016, .2379562, .2370335, 247.2598, .2370341, 2.410178, 1.05744, 1.030792, 298.8007, 1.030901, 6.939011, .3025656, .3017648, 2051.827, .3017652, 5.726993, -.1662367, -.1664337, -2143.633, -.1664338, -3.898237, .9615754, .9505365, 2399.173, .9505573, 13.04196, .6036977, .5925143, 84.08839, .5925481, 3.12938, -.4469533, -.4512659, -221.0249, -.451273, -3.534449, .9504169, .9381722, 1602.909, .9381981, 11.31303, -1.58407, -1.647805, -602.1467, -1.648254, -11.47494, -.5808498, -.5975259, -27.5484, -.5976085, -2.102526, -.6490194, -.6557381, -799.9641, -.6557499, -6.958708, .6957488, .6903502, 2190.347, .6903571, 10.19701, .1750624, .174529, 150.309, .1745293, 1.663886, .1572418, .1562937, 12.33672, .1562946, .6731502, -.6408126, -.6436554, -9244.279, -.6436575, -15.59954, 1.101677, 1.092417, 10778.35, 1.09243, 23.56244, -.4992968, -.5028596, -835.3172, -.5028639, -5.927292, -.9280973, -1.02178, -6.907707, -1.023576, -1.812064, .6339129, .6277187, 744.4614, .6277287, 6.688065, -.6707486, -.6785607, -647.0199, -.6785761, -6.627439, -1.38237, -1.427934, -602.4287, -1.428195, -10.48056, -1.459774, -1.554047, -125.0777, -1.555148, -6.435521, -1.093153, -1.111322, -1629.418, -1.111374, -12.48719, -.3837357, -.3857544, -717.1755, -.3857562, -4.726757, -.5606073, -.5670648, -326.075, -.5670773, -4.679632, .8169871, .7887753, 38.50973, .7889313, 2.951211, 1.275712, 1.265811, 24735.07, 1.265823, 34.27201, .0862263, .0861666, 766.7436, .0861666, 1.786392, .3344287, .3328024, 485.5152, .3328038, 3.786779, -1.345582, -1.471176, -36.61779, -1.473379, -4.047349, .4774571, .4752944, 2502.141, .475296, 8.29329, .349272, .3477617, 824.9081, .3477628, 4.651336, -.5002936, -.5066125, -158.1673, -.506626, -3.408177, -1.247884, -1.411017, -12.7456, -1.415246, -2.707506, -1.673559, -1.700277, -10051.77, -1.70035, -30.4211, .3986639, .3972206, 2398.038, .3972214, 7.250311, 1.482003, 1.444616, 1148.828, 1.444769, 13.61396, .0587717, .0587566, 3267.75, .0587566, 2.243168, .4706421, .4689196, 4507.782, .4689206, 9.994969, -1.157463, -1.186371, -642.0396, -1.186495, -9.510254] # noqa:E501 wfs_resids = np.asarray(wfs_resids).astype(float).reshape(-1, 5) statsmodels-0.12.2/statsmodels/genmod/tests/results/glmnet_r_results.py000066400000000000000000000036061400612667500265720ustar00rootroot00000000000000import numpy as np rslt_binomial_0 = np.array([ 0, 6.618737, 0.004032037, 0.01433665, 0.01265635, 0.006173346, 0.01067706]) rslt_binomial_1 = np.array([ 0, 1.029661, 0.02180239, 0.07769613, 0.06756466, 0.03156418, 0.05851878]) rslt_binomial_2 = np.array([ 0, 0.1601819, 0.07111087, 0.2544921, 0.2110318, 0.08577924, 0.1984383]) rslt_binomial_3 = np.array([ 0.5, 0.05343991, 0.004990061, 0.2838563, 0.2167881, 0.02370156, 0.2096612]) rslt_binomial_4 = np.array([ 0.5, 0.02313286, 0.0708914, 0.3791042, 0.2938332, 0.07506391, 0.2982251]) rslt_binomial_5 = np.array([ 0.5, 0.009124078, 0.106681, 0.4327268, 0.3362166, 0.1019452, 0.3479955]) rslt_binomial_6 = np.array([ 1, 0.02932512, 0, 0.3085764, 0.2300801, 0.01143652, 0.2291531]) rslt_binomial_7 = np.array([ 1, 0.01269414, 0.07022348, 0.396642, 0.3044255, 0.07151663, 0.31301]) rslt_binomial_8 = np.array([ 1, 0.005494992, 0.1049623, 0.4385186, 0.3391729, 0.09907393, 0.3527401]) rslt_poisson_0 = np.array([ 0, 23.5349, 0.009251658, 0.003730997, 0.01266164, 0.003439135, 0.0141719]) rslt_poisson_1 = np.array([ 0, 3.661269, 0.04842557, 0.02095708, 0.06550316, 0.02029514, 0.07300782]) rslt_poisson_2 = np.array([ 0, 0.5695749, 0.1440462, 0.07208017, 0.182649, 0.07511376, 0.2018242]) rslt_poisson_3 = np.array([ 0.5, 0.1577593, 0.1247603, 0.02857521, 0.185693, 0.03840622, 0.2200925]) rslt_poisson_4 = np.array([ 0.5, 0.05669575, 0.187629, 0.08842012, 0.2348627, 0.09736964, 0.2628845]) rslt_poisson_5 = np.array([ 0.5, 0.0185653, 0.2118078, 0.1121067, 0.2534181, 0.1204543, 0.2784761]) rslt_poisson_6 = np.array([ 1, 0.07887965, 0.1339927, 0.0322772, 0.1969884, 0.0439019, 0.2339252]) rslt_poisson_7 = np.array([ 1, 0.02834788, 0.1927163, 0.09160406, 0.2398164, 0.1010126, 0.2682158]) rslt_poisson_8 = np.array([ 1, 0.0101877, 0.2126847, 0.1123439, 0.2544153, 0.1208601, 0.2796794]) 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"M:\josef_new\stata_work\results_glm_poisson_weights.py" insheet using M:\josef_new\eclipse_ws\statsmodels\statsmodels_py34_pr\statsmodels\datasets\cpunish\cpunish.csv generate LN_VC100k96 = log(vc100k96) generate var10 = 1 in 1 replace var10 = 1 in 2 replace var10 = 1 in 3 replace var10 = 2 in 4 replace var10 = 2 in 5 replace var10 = 2 in 6 replace var10 = 3 in 7 replace var10 = 3 in 8 replace var10 = 3 in 9 replace var10 = 1 in 10 replace var10 = 1 in 11 replace var10 = 1 in 12 replace var10 = 2 in 13 replace var10 = 2 in 14 replace var10 = 2 in 15 replace var10 = 3 in 16 replace var10 = 3 in 17 label variable var10 "fweight" rename var10 fweight label variable LN_VC100k96 "LN_VC100k96" /* for checkin Poisson produces the same, poisson does not allow aweights */ /*poisson executions income perpoverty perblack LN_VC100k96 south degree */ glm executions income perpoverty perblack LN_VC100k96 south degree, family(poisson) /* copied from glm_logit_constrained.do */ /*glm grade gpa tuce psi, family(binomial) constraints(2) */ /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, mu predict predict_linpred_std, stdp predict predict_hat, hat predict score_factor, score predict resid_anscombe, anscombe predict resid_deviance, deviance predict resid_response, response predict resid_pearson, pearson predict resid_working, working local pred predict_mu predict_linpred_std predict_hat local res score_factor resid_response resid_anscombe resid_deviance resid_pearson resid_working mkmat `res', matrix(resids) mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted resids, saving(`filename') format("%16.0g") resname("poisson_none_nonrobust") replace /*------------------*/ drop `pred' `res' glm executions income perpoverty perblack LN_VC100k96 south degree [fweight=fweight], family(poisson) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, mu predict predict_linpred_std, stdp predict predict_hat, hat predict score_factor, score predict resid_anscombe, anscombe predict resid_deviance, deviance predict resid_response, response predict resid_pearson, pearson predict resid_working, working local pred predict_mu predict_linpred_std predict_hat local res score_factor resid_response resid_anscombe resid_deviance resid_pearson resid_working mkmat `res', matrix(resids) mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted resids, saving(`filename') format("%16.0g") resname("poisson_fweight_nonrobust") append /*------------------*/ drop `pred' `res' glm executions income perpoverty perblack LN_VC100k96 south degree [aweight=fweight], family(poisson) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, mu predict predict_linpred_std, stdp predict predict_hat, hat predict score_factor, score predict resid_anscombe, anscombe predict resid_deviance, deviance predict resid_response, response predict resid_pearson, pearson predict resid_working, working local pred predict_mu predict_linpred_std predict_hat local res score_factor resid_response resid_anscombe resid_deviance resid_pearson resid_working mkmat `res', matrix(resids) mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted resids, saving(`filename') format("%16.0g") resname("poisson_aweight_nonrobust") append /*------------------*/ drop `pred' `res' glm executions income perpoverty perblack LN_VC100k96 south degree [pweight=fweight], family(poisson) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, mu predict predict_linpred_std, stdp //predict predict_hat, hat not allowed after robust, pweights implies HC1 predict score_factor, score predict resid_anscombe, anscombe predict resid_deviance, deviance predict resid_response, response predict resid_pearson, pearson predict resid_working, working local pred predict_mu predict_linpred_std //predict_hat local res score_factor resid_response resid_anscombe resid_deviance resid_pearson resid_working mkmat `res', matrix(resids) mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted resids, saving(`filename') format("%16.0g") resname("poisson_pweight_nonrobust") append /*------------------*/ /*******************************************************************/ /*********** next with robust = HC1, do not save resid and similar */ drop `pred' `res' glm executions income perpoverty perblack LN_VC100k96 south degree, family(poisson) vce(robust) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, mu predict predict_linpred_std, stdp //predict predict_hat, hat local pred predict_mu predict_linpred_std //predict_hat mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted, saving(`filename') format("%16.0g") resname("poisson_none_hc1") append /*------------------*/ drop `pred' glm executions income perpoverty perblack LN_VC100k96 south degree [fweight=fweight], family(poisson) vce(robust) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, mu predict predict_linpred_std, stdp //predict predict_hat, hat local pred predict_mu predict_linpred_std //predict_hat mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted, saving(`filename') format("%16.0g") resname("poisson_fweight_hc1") append /*------------------*/ drop `pred' glm executions income perpoverty perblack LN_VC100k96 south degree [aweight=fweight], family(poisson) vce(robust) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, mu predict predict_linpred_std, stdp //predict predict_hat, hat local pred predict_mu predict_linpred_std //predict_hat mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted, saving(`filename') format("%16.0g") resname("poisson_aweight_hc1") append /*------------------*/ drop `pred' glm executions income perpoverty perblack LN_VC100k96 south degree [pweight=fweight], family(poisson) vce(robust) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, mu predict predict_linpred_std, stdp //predict predict_hat, hat local pred predict_mu predict_linpred_std //predict_hat mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted, saving(`filename') format("%16.0g") resname("poisson_pweight_hc1") append /*------------------*/ /*****************************************************************/ /*************************** with cluster robust standard errors */ gen id = (_n - mod(_n, 2)) / 2 drop `pred' glm executions income perpoverty perblack LN_VC100k96 south degree, family(poisson) vce(cluster id) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, mu predict predict_linpred_std, stdp //predict predict_hat, hat local pred predict_mu predict_linpred_std //predict_hat mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted, saving(`filename') format("%16.0g") resname("poisson_none_clu1") append /*------------------*/ drop `pred' glm executions income perpoverty perblack LN_VC100k96 south degree [fweight=fweight], family(poisson) vce(cluster id) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, mu predict predict_linpred_std, stdp //predict predict_hat, hat local pred predict_mu predict_linpred_std //predict_hat mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted, saving(`filename') format("%16.0g") resname("poisson_fweight_clu1") append /*------------------*/ drop `pred' glm executions income perpoverty perblack LN_VC100k96 south degree [aweight=fweight], family(poisson) vce(cluster id) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, mu predict predict_linpred_std, stdp //predict predict_hat, hat local pred predict_mu predict_linpred_std //predict_hat mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted, saving(`filename') format("%16.0g") resname("poisson_aweight_clu1") append /*------------------*/ drop `pred' glm executions income perpoverty perblack LN_VC100k96 south degree [pweight=fweight], family(poisson) vce(cluster id) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, mu predict predict_linpred_std, stdp //predict predict_hat, hat local pred predict_mu predict_linpred_std //predict_hat mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted, saving(`filename') format("%16.0g") resname("poisson_pweight_clu1") append /*------------------*/ /*****************************************************************/ /* gen idn = _n glm executions income perpoverty perblack LN_VC100k96 south degree, family(poisson) vce(cluster idn) */ /* glm grade gpa tuce psi, family(binomial) constraints(2) vce(robust) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) estmat2nparray params_table cov infocrit, saving(`filename') format("%16.0g") resname("constraint2_robust") append /*------------------*/ capture drop fittedvalues fittedvalues_se predict fittedvalues, xb predict fittedvalues_se, stdp outsheet fittedvalues fittedvalues_se using theil_predict.csv, comma replace /*------------------*/ glm executions income perpoverty perblack LN_VC100k96 south degree [aweight=fweight], family(poisson) predict resid_deviance_aw, deviance */ /*------------------*/ drop `pred' regress executions income perpoverty perblack LN_VC100k96 south degree [aweight=fweight], vce(robust) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, xb predict predict_std, stdp //predict predict_stf, stdf //predict predict_str, stdr //predict predict_hat, hat local pred predict_mu predict_std //predict_stf predict_str predict_hat mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted, saving(`filename') format("%16.0g") resname("wls_aweight_robust") append /*------------------*/ drop `pred' regress executions income perpoverty perblack LN_VC100k96 south degree [aweight=fweight], vce(cluster id) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, xb predict predict_std, stdp //predict predict_stf, stdf //predict predict_str, stdr //predict predict_hat, hat local pred predict_mu predict_std //predict_stf predict_str predict_hat mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted, saving(`filename') format("%16.0g") resname("wls_aweight_clu1") append /*------------------*/ drop `pred' regress executions income perpoverty perblack LN_VC100k96 south degree [fweight=fweight], vce(cluster id) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, xb predict predict_std, stdp //predict predict_stf, stdf //predict predict_str, stdr //predict predict_hat, hat local pred predict_mu predict_std //predict_stf predict_str predict_hat mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted, saving(`filename') format("%16.0g") resname("wls_fweight_clu1") append /*------------------*/ drop `pred' regress executions income perpoverty perblack LN_VC100k96 south degree [pweight=fweight], vce(cluster id) /* boiler plate, add matrices if needed */ tempname cov tempname params_table matrix cov = e(V) matrix params_table = r(table)' estat ic matrix infocrit = r(S) predict predict_mu, xb predict predict_std, stdp //predict predict_stf, stdf //predict predict_str, stdr //predict predict_hat, hat local pred predict_mu predict_std //predict_stf predict_str predict_hat mkmat `pred', matrix(predicted) estmat2nparray params_table cov infocrit predicted, saving(`filename') format("%16.0g") resname("wls_pweight_clu1") append /*------------------*/ drop `pred' statsmodels-0.12.2/statsmodels/genmod/tests/results/res_R_var_weight.py000066400000000000000000000203721400612667500264720ustar00rootroot00000000000000# This file auto-generated by test_get_R_tweedie_var_weight.R # Using: R version 3.5.1 (2018-07-02) import numpy as np import pandas as pd import os from statsmodels.tools.tools import Bunch path = os.path.abspath(__file__) dir_path = os.path.dirname(path) res = dict() res['params'] = np.array([ 0.74699331283637337986, -0.031592165334818379796, -0.021959412079720488226 ]) res['bse'] = np.array([ 0.25438368514036091561, 0.011629899831763365614, 0.011034604276375996681 ]) res['deviance'] = 45399.238887 res['ll'] = np.nan res['resids_colnames'] = [ 'resid_response', 'resid_pearson', 'resid_deviance', 'resid_working'] csv_path = os.path.join(dir_path, 'results_tweedie_aweights_nonrobust.csv') resids = np.array(pd.read_csv(csv_path)) res['resids'] = resids results_tweedie_aweights_nonrobust = Bunch(**res) res = dict() res['params'] = np.array([ 4.3171222692811204169, -0.038835175525200764379, 0.54097404989168318412, 1.0560051456310013407]) res['bse'] = np.array([ 0.80693035378427380166, 0.013827354415809251648, 0.18432033392178892584, 0.186384917449112536]) res['deviance'] = 28.440959 res['ll'] = -301.601118 res['resids_colnames'] = [ 'resid_response', 'resid_pearson', 'resid_deviance', 'resid_working'] res['resids'] = np.array([ -6.0158828841102272023, -5.0064618225897614678, -5.5825299715106844189, -6.9511999508118442748, -4.5194555811187591132, -1.557595268795654242, -1.4915816790031248829, -2.8827914717229985442, -0.51945558111875911322, 0.11720852827700145582, -1.9511999508118442748, -3.1808072343012465666, 0.24507818532437042336, 2.1431814907569695094, 0.81919276569875343341, 5.2513574111143244139, 4.6547413066088410005, 5.8191927656987534334, 13.805056937442099496, 13.048800049188155725, -3.5461655328997796488, -4.3171742547402551793, -6.5401065768334341044, -5.6336912448773173168, -9.2050394978136971247, -1.0510357685093119073, 1.4079973153855167567, -3.4735049910420947583, 6.4538344671002203512, 0.52649500895790524169, 4.7868274865566906584, 8.4598934231665658956, 2.2438400124908675082, 14.907031299164781757, -19.462143004837859195, -16.470421414020314899, -3.9684071475551156993, -13.14329303600413823, 1.3380516354871438978, -5.9189306482160155554, -0.46214300483785919482, 4.4406584647078979344, -5.4161390946438174865, 7.5077293157326110418, 12.031592852444884301, 14.598574701805357989, 1.5838609053561825135, 10.391659888606849194, -1.4851751347306552109, -0.83351263530235220056, -0.73623579365799252106, -0.69852881915459330564, -0.5304864305103017541, -0.62668991425384801275, -0.22977168781956672228, -0.36570693035127138648, -0.060972861020603522086, 0.014868911437965813202, -0.4384411678265578427, -0.2844881561451974572, 0.022787537608125515293, 0.41912332605193491908, 0.07326776578220378644, 1.7399635542616316286, 0.44993957566111131285, 0.52046266819145536875, 1.6845824104033622071, 1.3112790531481182121, -0.83064421664412402269, -0.41844541423313824646, -0.48301736324758975938, -0.38498087397118291308, -0.4793033359218865086, -0.19501953776552996556, 0.21037977246201788883, -0.18802631080168147326, 0.67606563544889408668, 0.028500006317870137801, 0.70357919408636093728, 0.62480257265043215309, 0.10810477534578602499, 0.87211481867607798524, -0.76435604815902624676, -1.3913258623193209829, -0.18925649047299358818, -0.40889690490896990482, 0.059043980418843691749, -0.33157319461752626788, -0.040585082486855973694, 0.1884882248536425553, -0.16208153429406677026, 0.30653463749913562042, 0.57379622437595356743, 1.6825261498124608472, 0.047398082132416530232, 0.36323882644517407892, -2.5581754807831980081, -1.3851521395433199491, -1.0922123777693948377, -1.0005518818611833787, -0.67167201555474287389, -0.69718647545513146024, -0.25018637428846979276, -0.42317194149448128515, -0.062258126689424299338, 0.014795849256191397764, -0.47090072427136225874, -0.31707718530745676588, 0.022616711999637318514, 0.38940961248878158685, 0.071551164078391196743, 1.4232712112275127669, 0.39602447412952324068, 0.45043976885155773138, 1.1807262353227552243, 0.97311662116074171269, -0.96387085778973813355, -0.4972022256055589895, -0.59452271009315738048, -0.449713327474644875, -0.58870075509045161066, -0.20099628504835270748, 0.20241883427909049264, -0.20130092403600013951, 0.56500703038717148274, 0.028233670119025004036, 0.64093348203300071209, 0.52804594118935443969, 0.10443781791098502576, 0.70006586509944224161, -1.1671137422196677935, -1.8740944537491481814, -0.20271679195797467909, -0.48346236689503357953, 0.057920368116502723987, -0.35546257706309924984, -0.040833257924115747006, 0.1777983388792870878, -0.17177278732799597383, 0.27984395723434191128, 0.4905212458386473684, 1.3835988461755979184, 0.046669269235505038418, 0.32672761718963955202, -0.85746626383048263342, -0.83351263530235220056, -0.73623579365799252106, -0.69852881915459330564, -0.5304864305103017541, -0.28026424981702369177, -0.22977168781956672228, -0.36570693035127138648, -0.060972861020603522086, 0.014868911437965813202, -0.19607685107891539844, -0.2844881561451974572, 0.022787537608125515293, 0.2419809651197359357, 0.07326776578220378644, 0.77813535714023041034, 0.44993957566111131285, 0.52046266819145536875, 1.6845824104033622071, 1.3112790531481182121, -0.37147538670666468974, -0.41844541423313824646, -0.48301736324758975938, -0.38498087397118291308, -0.4793033359218865086, -0.087215388676862487527, 0.12146281826299824835, -0.18802631080168147326, 0.67606563544889408668, 0.028500006317870137801, 0.31465018110632420045, 0.62480257265043215309, 0.10810477534578602499, 0.87211481867607798524, -0.76435604815902624676, -0.62221984139990293983, -0.18925649047299358818, -0.40889690490896990482, 0.059043980418843691749, -0.19143387316849300173, -0.018150200662609233121, 0.1884882248536425553, -0.16208153429406677026, 0.30653463749913562042, 0.57379622437595356743, 0.75244856898033141146, 0.047398082132416530232, 0.36323882644517407892 ]).reshape((48, 4), order="F") results_gamma_aweights_nonrobust = Bunch(**res) res = dict() res['params'] = np.array([ 0.019083886775238277644, 0.93993818789790006818 ]) res['bse'] = np.array([ 0.021677622811348211396, 0.82525357389082676374 ]) res['deviance'] = 1248.273065 res['ll'] = -52.674985 res['resids_colnames'] = [ 'resid_response', 'resid_pearson', 'resid_deviance', 'resid_working'] res['resids'] = np.array([ 32.059654149533187706, 3.3448403477511448045, 4.0197139294873869275, -0.28159357985674304814, -1.6667828494180003673, 0.13880513444962283565, -0.18150652396610489347, -2.9789626432480238449, -1.2529678442364695634, -3.7054159544565843376, -1.0424256120017099114, -0.88813363987303950431, -3.7241309801112230105, -1.3985915365753158746, -0.9406665144733470374, -0.76290530967944270024, -1.0174777728628758844, 32.059654149533187706, 4.7303185837624086574, 6.9623487577644933566, -0.56318715971348609628, -3.7270397550294447342, 0.27761026889924567129, -0.31437852141451172461, -4.2128893718841595728, -1.2529678442364695634, -5.2402494970261486174, -1.8055341230980426204, -1.7762672797460790086, -8.3274100286416121719, -2.7971830731506317491, -1.6292821960465615483, -1.0789110357551139341, -1.0174777728628758844, 32.059654149533187706, 4.7303185837624086574, 6.9623487577644942448, -0.56318715971348609628, -3.7270397550294447342, 0.27761026889924567129, -0.31437852141451178012, -4.2128893718841595728, -1.2529678442364695634, -5.2402494970261477292, -1.8055341230980428424, -1.7762672797460790086, -8.3274100286416121719, -2.7971830731506317491, -1.6292821960465617703, -1.0789110357551139341, -1.0174777728628758844, 6.4893542112044375614, 0.59146700596171875031, 2.0298652751957457774, -0.065768404825141027481, -0.35715886151117287595, 0.07457850707565569226, -0.083202375043149326417, -0.5983099004142555799, -0.55614102413481192322, -0.78747893710589345062, -0.5103860849943342437, -0.47037647183319014621, -0.78832085642628468847, -0.58308866484712540412, -0.48471311658027066427, -0.43275455890377079182, -0.50433158994313831425 ]).reshape((17, 4), order="F") results_gaussian_aweights_nonrobust = Bunch(**res) statsmodels-0.12.2/statsmodels/genmod/tests/results/results_glm.py000066400000000000000000010263151400612667500255450ustar00rootroot00000000000000""" Results for test_glm.py. Hard-coded from R or Stata. Note that some of the remaining discrepancy vs. Stata may be because Stata uses ML by default unless you specifically ask for IRLS. """ import os import numpy as np import pandas as pd from statsmodels.api import add_constant from statsmodels.genmod.tests.results import glm_test_resids # Test Precisions DECIMAL_4 = 4 DECIMAL_3 = 3 DECIMAL_2 = 2 DECIMAL_1 = 1 DECIMAL_0 = 0 class Longley(object): """ Longley used for TestGlmGaussian Results are from Stata and R. """ def __init__(self): self.resids = np.array([ [267.34002976, 267.34002976, 267.34002976, 267.34002976, 267.34002976], [-94.0139424, -94.0139424, -94.0139424, -94.0139424, -94.0139424], [46.28716776, 46.28716776, 46.28716776, 46.28716776, 46.28716776], [-410.11462193, -410.11462193, -410.11462193, -410.11462193, -410.11462193], [309.71459076, 309.71459076, 309.71459076, 309.71459076, 309.71459076], [-249.31121533, -249.31121533, -249.31121533, -249.31121533, -249.31121533], [-164.0489564, -164.0489564, -164.0489564, -164.0489564, -164.0489564], [-13.18035687, -13.18035687, -13.18035687, -13.18035687, -13.18035687], [14.3047726, 14.3047726, 14.3047726, 14.3047726, 14.3047726], [455.39409455, 455.39409455, 455.39409455, 455.39409455, 455.39409455], [-17.26892711, -17.26892711, -17.26892711, -17.26892711, -17.26892711], [-39.05504252, -39.05504252, -39.05504252, -39.05504252, -39.05504252], [-155.5499736, -155.5499736, -155.5499736, -155.5499736, -155.5499736], [-85.67130804, -85.67130804, -85.67130804, -85.67130804, -85.67130804], [341.93151396, 341.93151396, 341.93151396, 341.93151396, 341.93151396], [-206.75782519, -206.75782519, -206.75782519, -206.75782519, -206.75782519]]) self.null_deviance = 185008826 # taken from R. self.params = np.array([ 1.50618723e+01, -3.58191793e-02, -2.02022980e+00, -1.03322687e+00, -5.11041057e-02, 1.82915146e+03, -3.48225863e+06]) self.bse = np.array([ 8.49149258e+01, 3.34910078e-02, 4.88399682e-01, 2.14274163e-01, 2.26073200e-01, 4.55478499e+02, 8.90420384e+05]) self.aic_R = 235.23486961695903 # R adds 2 for dof to AIC self.aic_Stata = 14.57717943930524 # stata divides by nobs self.deviance = 836424.0555058046 # from R self.scale = 92936.006167311629 self.llf = -109.61743480847952 self.null_deviance = 185008826 # taken from R. Rpy bug self.bic_Stata = 836399.1760177979 # no bic in R? self.df_model = 6 self.df_resid = 9 # TODO: taken from Stata; not available in sm yet self.chi2 = 1981.711859508729 # self.pearson_chi2 = 836424.1293162981 # from Stata (?) self.fittedvalues = np.array([ 60055.659970240202, 61216.013942398131, 60124.71283224225, 61597.114621930756, 62911.285409240052, 63888.31121532945, 65153.048956395127, 63774.180356866214, 66004.695227399934, 67401.605905447621, 68186.268927114084, 66552.055042522494, 68810.549973595422, 69649.67130804155, 68989.068486039061, 70757.757825193927]) class GaussianLog(object): """ Uses generated data. These results are from R and Stata. """ def __init__(self): self.resids = np.array([ [3.20800000e-04, 3.20800000e-04, 8.72100000e-04, 3.20800000e-04, 3.20800000e-04], [8.12100000e-04, 8.12100000e-04, 2.16350000e-03, 8.12100000e-04, 8.12100000e-04], [-2.94800000e-04, -2.94800000e-04, -7.69700000e-04, -2.94800000e-04, -2.94800000e-04], [1.40190000e-03, 1.40190000e-03, 3.58560000e-03, 1.40190000e-03, 1.40190000e-03], [-2.30910000e-03, -2.30910000e-03, -5.78490000e-03, -2.30910000e-03, -2.30910000e-03], [1.10380000e-03, 1.10380000e-03, 2.70820000e-03, 1.10380000e-03, 1.10380000e-03], [-5.14000000e-06, -5.14000000e-06, -1.23000000e-05, -5.14000000e-06, -5.14000000e-06], [-1.65500000e-04, -1.65500000e-04, -3.89200000e-04, -1.65500000e-04, -1.65500000e-04], [-7.55400000e-04, -7.55400000e-04, -1.73870000e-03, -7.55400000e-04, -7.55400000e-04], [-1.39800000e-04, -1.39800000e-04, -3.14800000e-04, -1.39800000e-04, -1.39800000e-04], [-7.17000000e-04, -7.17000000e-04, -1.58000000e-03, -7.17000000e-04, -7.17000000e-04], [-1.12200000e-04, -1.12200000e-04, -2.41900000e-04, -1.12200000e-04, -1.12200000e-04], [3.22100000e-04, 3.22100000e-04, 6.79000000e-04, 3.22100000e-04, 3.22100000e-04], [-3.78000000e-05, -3.78000000e-05, -7.79000000e-05, -3.78000000e-05, -3.78000000e-05], [5.54500000e-04, 5.54500000e-04, 1.11730000e-03, 5.54500000e-04, 5.54500000e-04], [3.38400000e-04, 3.38400000e-04, 6.66300000e-04, 3.38400000e-04, 3.38400000e-04], [9.72000000e-05, 9.72000000e-05, 1.87000000e-04, 9.72000000e-05, 9.72000000e-05], [-7.92900000e-04, -7.92900000e-04, -1.49070000e-03, -7.92900000e-04, -7.92900000e-04], [3.33000000e-04, 3.33000000e-04, 6.11500000e-04, 3.33000000e-04, 3.33000000e-04], [-8.35300000e-04, -8.35300000e-04, -1.49790000e-03, -8.35300000e-04, -8.35300000e-04], [-3.99700000e-04, -3.99700000e-04, -6.99800000e-04, -3.99700000e-04, -3.99700000e-04], [1.41300000e-04, 1.41300000e-04, 2.41500000e-04, 1.41300000e-04, 1.41300000e-04], [-8.50700000e-04, -8.50700000e-04, -1.41920000e-03, -8.50700000e-04, -8.50700000e-04], [1.43000000e-06, 1.43000000e-06, 2.33000000e-06, 1.43000000e-06, 1.43000000e-06], [-9.12000000e-05, -9.12000000e-05, -1.44900000e-04, -9.12000000e-05, -9.12000000e-05], [6.75500000e-04, 6.75500000e-04, 1.04650000e-03, 6.75500000e-04, 6.75500000e-04], [3.97900000e-04, 3.97900000e-04, 6.01100000e-04, 3.97900000e-04, 3.97900000e-04], [1.07000000e-05, 1.07000000e-05, 1.57000000e-05, 1.07000000e-05, 1.07000000e-05], [-8.15200000e-04, -8.15200000e-04, -1.17060000e-03, -8.15200000e-04, -8.15200000e-04], [-8.46400000e-04, -8.46400000e-04, -1.18460000e-03, -8.46400000e-04, -8.46400000e-04], [9.91200000e-04, 9.91200000e-04, 1.35180000e-03, 9.91200000e-04, 9.91200000e-04], [-5.07400000e-04, -5.07400000e-04, -6.74200000e-04, -5.07400000e-04, -5.07400000e-04], [1.08520000e-03, 1.08520000e-03, 1.40450000e-03, 1.08520000e-03, 1.08520000e-03], [9.56100000e-04, 9.56100000e-04, 1.20500000e-03, 9.56100000e-04, 9.56100000e-04], [1.87500000e-03, 1.87500000e-03, 2.30090000e-03, 1.87500000e-03, 1.87500000e-03], [-1.93920000e-03, -1.93920000e-03, -2.31650000e-03, -1.93920000e-03, -1.93920000e-03], [8.16000000e-04, 8.16000000e-04, 9.48700000e-04, 8.16000000e-04, 8.16000000e-04], [1.01520000e-03, 1.01520000e-03, 1.14860000e-03, 1.01520000e-03, 1.01520000e-03], [1.04150000e-03, 1.04150000e-03, 1.14640000e-03, 1.04150000e-03, 1.04150000e-03], [-3.88200000e-04, -3.88200000e-04, -4.15600000e-04, -3.88200000e-04, -3.88200000e-04], [9.95900000e-04, 9.95900000e-04, 1.03690000e-03, 9.95900000e-04, 9.95900000e-04], [-6.82800000e-04, -6.82800000e-04, -6.91200000e-04, -6.82800000e-04, -6.82800000e-04], [-8.11400000e-04, -8.11400000e-04, -7.98500000e-04, -8.11400000e-04, -8.11400000e-04], [-1.79050000e-03, -1.79050000e-03, -1.71250000e-03, -1.79050000e-03, -1.79050000e-03], [6.10000000e-04, 6.10000000e-04, 5.66900000e-04, 6.10000000e-04, 6.10000000e-04], [2.52600000e-04, 2.52600000e-04, 2.28100000e-04, 2.52600000e-04, 2.52600000e-04], [-8.62500000e-04, -8.62500000e-04, -7.56400000e-04, -8.62500000e-04, -8.62500000e-04], [-3.47300000e-04, -3.47300000e-04, -2.95800000e-04, -3.47300000e-04, -3.47300000e-04], [-7.79000000e-05, -7.79000000e-05, -6.44000000e-05, -7.79000000e-05, -7.79000000e-05], [6.72000000e-04, 6.72000000e-04, 5.39400000e-04, 6.72000000e-04, 6.72000000e-04], [-3.72100000e-04, -3.72100000e-04, -2.89900000e-04, -3.72100000e-04, -3.72100000e-04], [-1.22900000e-04, -1.22900000e-04, -9.29000000e-05, -1.22900000e-04, -1.22900000e-04], [-1.63470000e-03, -1.63470000e-03, -1.19900000e-03, -1.63470000e-03, -1.63470000e-03], [2.64400000e-04, 2.64400000e-04, 1.88100000e-04, 2.64400000e-04, 2.64400000e-04], [1.79230000e-03, 1.79230000e-03, 1.23650000e-03, 1.79230000e-03, 1.79230000e-03], [-1.40500000e-04, -1.40500000e-04, -9.40000000e-05, -1.40500000e-04, -1.40500000e-04], [-2.98500000e-04, -2.98500000e-04, -1.93600000e-04, -2.98500000e-04, -2.98500000e-04], [-9.33100000e-04, -9.33100000e-04, -5.86400000e-04, -9.33100000e-04, -9.33100000e-04], [9.11200000e-04, 9.11200000e-04, 5.54900000e-04, 9.11200000e-04, 9.11200000e-04], [-1.31840000e-03, -1.31840000e-03, -7.77900000e-04, -1.31840000e-03, -1.31840000e-03], [-1.30200000e-04, -1.30200000e-04, -7.44000000e-05, -1.30200000e-04, -1.30200000e-04], [9.09300000e-04, 9.09300000e-04, 5.03200000e-04, 9.09300000e-04, 9.09300000e-04], [-2.39500000e-04, -2.39500000e-04, -1.28300000e-04, -2.39500000e-04, -2.39500000e-04], [7.15300000e-04, 7.15300000e-04, 3.71000000e-04, 7.15300000e-04, 7.15300000e-04], [5.45000000e-05, 5.45000000e-05, 2.73000000e-05, 5.45000000e-05, 5.45000000e-05], [2.85310000e-03, 2.85310000e-03, 1.38600000e-03, 2.85310000e-03, 2.85310000e-03], [4.63400000e-04, 4.63400000e-04, 2.17800000e-04, 4.63400000e-04, 4.63400000e-04], [2.80900000e-04, 2.80900000e-04, 1.27700000e-04, 2.80900000e-04, 2.80900000e-04], [5.42000000e-05, 5.42000000e-05, 2.38000000e-05, 5.42000000e-05, 5.42000000e-05], [-3.62300000e-04, -3.62300000e-04, -1.54000000e-04, -3.62300000e-04, -3.62300000e-04], [-1.11900000e-03, -1.11900000e-03, -4.59800000e-04, -1.11900000e-03, -1.11900000e-03], [1.28900000e-03, 1.28900000e-03, 5.11900000e-04, 1.28900000e-03, 1.28900000e-03], [-1.40820000e-03, -1.40820000e-03, -5.40400000e-04, -1.40820000e-03, -1.40820000e-03], [-1.69300000e-04, -1.69300000e-04, -6.28000000e-05, -1.69300000e-04, -1.69300000e-04], [-1.03620000e-03, -1.03620000e-03, -3.71000000e-04, -1.03620000e-03, -1.03620000e-03], [1.49150000e-03, 1.49150000e-03, 5.15800000e-04, 1.49150000e-03, 1.49150000e-03], [-7.22000000e-05, -7.22000000e-05, -2.41000000e-05, -7.22000000e-05, -7.22000000e-05], [5.49000000e-04, 5.49000000e-04, 1.76900000e-04, 5.49000000e-04, 5.49000000e-04], [-2.12320000e-03, -2.12320000e-03, -6.60400000e-04, -2.12320000e-03, -2.12320000e-03], [7.84000000e-06, 7.84000000e-06, 2.35000000e-06, 7.84000000e-06, 7.84000000e-06], [1.15580000e-03, 1.15580000e-03, 3.34700000e-04, 1.15580000e-03, 1.15580000e-03], [4.83400000e-04, 4.83400000e-04, 1.35000000e-04, 4.83400000e-04, 4.83400000e-04], [-5.26100000e-04, -5.26100000e-04, -1.41700000e-04, -5.26100000e-04, -5.26100000e-04], [-1.75100000e-04, -1.75100000e-04, -4.55000000e-05, -1.75100000e-04, -1.75100000e-04], [-1.84600000e-03, -1.84600000e-03, -4.62100000e-04, -1.84600000e-03, -1.84600000e-03], [2.07200000e-04, 2.07200000e-04, 5.00000000e-05, 2.07200000e-04, 2.07200000e-04], [-8.54700000e-04, -8.54700000e-04, -1.98700000e-04, -8.54700000e-04, -8.54700000e-04], [-9.20000000e-05, -9.20000000e-05, -2.06000000e-05, -9.20000000e-05, -9.20000000e-05], [5.35700000e-04, 5.35700000e-04, 1.15600000e-04, 5.35700000e-04, 5.35700000e-04], [-7.67300000e-04, -7.67300000e-04, -1.59400000e-04, -7.67300000e-04, -7.67300000e-04], [-1.79710000e-03, -1.79710000e-03, -3.59500000e-04, -1.79710000e-03, -1.79710000e-03], [1.10910000e-03, 1.10910000e-03, 2.13500000e-04, 1.10910000e-03, 1.10910000e-03], [-5.53800000e-04, -5.53800000e-04, -1.02600000e-04, -5.53800000e-04, -5.53800000e-04], [7.48000000e-04, 7.48000000e-04, 1.33400000e-04, 7.48000000e-04, 7.48000000e-04], [4.23000000e-04, 4.23000000e-04, 7.26000000e-05, 4.23000000e-04, 4.23000000e-04], [-3.16400000e-04, -3.16400000e-04, -5.22000000e-05, -3.16400000e-04, -3.16400000e-04], [-6.63200000e-04, -6.63200000e-04, -1.05200000e-04, -6.63200000e-04, -6.63200000e-04], [1.33540000e-03, 1.33540000e-03, 2.03700000e-04, 1.33540000e-03, 1.33540000e-03], [-7.81200000e-04, -7.81200000e-04, -1.14600000e-04, -7.81200000e-04, -7.81200000e-04], [1.67880000e-03, 1.67880000e-03, 2.36600000e-04, 1.67880000e-03, 1.67880000e-03]]) self.null_deviance = 56.691617808182208 self.params = np.array([ 9.99964386e-01, -1.99896965e-02, -1.00027232e-04]) self.bse = np.array([1.42119293e-04, 1.20276468e-05, 1.87347682e-07]) self.aic_R = -1103.8187213072656 # adds 2 for dof for scale self.aic_Stata = -11.05818072104212 # divides by nobs for e(aic) self.deviance = 8.68876986288542e-05 self.scale = 8.9574946938163984e-07 # from R but e(phi) in Stata self.llf = 555.9093606536328 self.bic_Stata = -446.7014211525822 self.df_model = 2 self.df_resid = 97 self.chi2 = 33207648.86501769 # from Stata not in sm self.fittedvalues = np.array([ 2.7181850213327747, 2.664122305869506, 2.6106125414084405, 2.5576658143523567, 2.5052916730829535, 2.4534991313100165, 2.4022966718815781, 2.3516922510411282, 2.3016933031175575, 2.2523067456332542, 2.2035389848154616, 2.1553959214958001, 2.107882957382607, 2.0610050016905817, 2.0147664781120667, 1.969171332114154, 1.9242230385457144, 1.8799246095383746, 1.8362786026854092, 1.7932871294825108, 1.7509518640143886, 1.7092740518711942, 1.6682545192788105, 1.6278936824271399, 1.5881915569806042, 1.5491477677552221, 1.5107615585467538, 1.4730318020945796, 1.4359570101661721, 1.3995353437472129, 1.3637646233226499, 1.3286423392342188, 1.2941656621002184, 1.2603314532836074, 1.2271362753947765, 1.1945764028156565, 1.162647832232141, 1.1313462931621328, 1.1006672584668622, 1.0706059548334832, 1.0411573732173065, 1.0123162792324054, 0.98407722347970683, 0.95643455180206194, 0.92938241545618494, 0.90291478119174029, 0.87702544122826565, 0.85170802312101246, 0.82695599950720078, 0.80276269772458597, 0.77912130929465073, 0.75602489926313921, 0.73346641539106316, 0.71143869718971686, 0.68993448479364294, 0.66894642766589496, 0.64846709313034534, 0.62848897472617915, 0.60900450038011367, 0.5900060403922629, 0.57148591523195513, 0.55343640314018494, 0.5358497475357491, 0.51871816422248385, 0.50203384839536769, 0.48578898144361343, 0.46997573754920047, 0.45458629007964013, 0.4396128177740814, 0.42504751072218311, 0.41088257613548018, 0.39711024391126759, 0.38372277198930843, 0.37071245150195081, 0.35807161171849949, 0.34579262478494655, 0.33386791026040569, 0.32228993945183393, 0.31105123954884056, 0.30014439756060574, 0.28956206405712448, 0.27929695671718968, 0.26934186368570684, 0.25968964674310463, 0.25033324428976694, 0.24126567414856051, 0.23248003618867552, 0.22396951477412205, 0.21572738104035141, 0.20774699500257574, 0.20002180749946474, 0.19254536197598673, 0.18531129610924435, 0.17831334328122878, 0.17154533390247831, 0.16500119659068577, 0.15867495920834204, 0.15256074976354628, 0.14665279717814039, 0.14094543192735109]) class GaussianInverse(object): """ This test uses generated data. Results are from R and Stata. """ def __init__(self): self.resids = np.array([ [-5.15300000e-04, -5.15300000e-04, 5.14800000e-04, -5.15300000e-04, -5.15300000e-04], [-2.12500000e-04, -2.12500000e-04, 2.03700000e-04, -2.12500000e-04, -2.12500000e-04], [-1.71400000e-04, -1.71400000e-04, 1.57200000e-04, -1.71400000e-04, -1.71400000e-04], [1.94020000e-03, 1.94020000e-03, -1.69710000e-03, 1.94020000e-03, 1.94020000e-03], [-6.81100000e-04, -6.81100000e-04, 5.66900000e-04, -6.81100000e-04, -6.81100000e-04], [1.21370000e-03, 1.21370000e-03, -9.58800000e-04, 1.21370000e-03, 1.21370000e-03], [-1.51090000e-03, -1.51090000e-03, 1.13070000e-03, -1.51090000e-03, -1.51090000e-03], [3.21500000e-04, 3.21500000e-04, -2.27400000e-04, 3.21500000e-04, 3.21500000e-04], [-3.18500000e-04, -3.18500000e-04, 2.12600000e-04, -3.18500000e-04, -3.18500000e-04], [3.75600000e-04, 3.75600000e-04, -2.36300000e-04, 3.75600000e-04, 3.75600000e-04], [4.82300000e-04, 4.82300000e-04, -2.85500000e-04, 4.82300000e-04, 4.82300000e-04], [-1.41870000e-03, -1.41870000e-03, 7.89300000e-04, -1.41870000e-03, -1.41870000e-03], [6.75000000e-05, 6.75000000e-05, -3.52000000e-05, 6.75000000e-05, 6.75000000e-05], [4.06300000e-04, 4.06300000e-04, -1.99100000e-04, 4.06300000e-04, 4.06300000e-04], [-3.61500000e-04, -3.61500000e-04, 1.66000000e-04, -3.61500000e-04, -3.61500000e-04], [-2.97400000e-04, -2.97400000e-04, 1.28000000e-04, -2.97400000e-04, -2.97400000e-04], [-9.32700000e-04, -9.32700000e-04, 3.75800000e-04, -9.32700000e-04, -9.32700000e-04], [1.16270000e-03, 1.16270000e-03, -4.38500000e-04, 1.16270000e-03, 1.16270000e-03], [6.77900000e-04, 6.77900000e-04, -2.39200000e-04, 6.77900000e-04, 6.77900000e-04], [-1.29330000e-03, -1.29330000e-03, 4.27000000e-04, -1.29330000e-03, -1.29330000e-03], [2.24500000e-04, 2.24500000e-04, -6.94000000e-05, 2.24500000e-04, 2.24500000e-04], [1.05510000e-03, 1.05510000e-03, -3.04900000e-04, 1.05510000e-03, 1.05510000e-03], [2.50400000e-04, 2.50400000e-04, -6.77000000e-05, 2.50400000e-04, 2.50400000e-04], [4.08600000e-04, 4.08600000e-04, -1.03400000e-04, 4.08600000e-04, 4.08600000e-04], [-1.67610000e-03, -1.67610000e-03, 3.96800000e-04, -1.67610000e-03, -1.67610000e-03], [7.47600000e-04, 7.47600000e-04, -1.65700000e-04, 7.47600000e-04, 7.47600000e-04], [2.08200000e-04, 2.08200000e-04, -4.32000000e-05, 2.08200000e-04, 2.08200000e-04], [-8.00800000e-04, -8.00800000e-04, 1.55700000e-04, -8.00800000e-04, -8.00800000e-04], [5.81200000e-04, 5.81200000e-04, -1.05900000e-04, 5.81200000e-04, 5.81200000e-04], [1.00980000e-03, 1.00980000e-03, -1.72400000e-04, 1.00980000e-03, 1.00980000e-03], [2.77400000e-04, 2.77400000e-04, -4.44000000e-05, 2.77400000e-04, 2.77400000e-04], [-5.02800000e-04, -5.02800000e-04, 7.55000000e-05, -5.02800000e-04, -5.02800000e-04], [2.69800000e-04, 2.69800000e-04, -3.80000000e-05, 2.69800000e-04, 2.69800000e-04], [2.01300000e-04, 2.01300000e-04, -2.67000000e-05, 2.01300000e-04, 2.01300000e-04], [-1.19690000e-03, -1.19690000e-03, 1.48900000e-04, -1.19690000e-03, -1.19690000e-03], [-6.94200000e-04, -6.94200000e-04, 8.12000000e-05, -6.94200000e-04, -6.94200000e-04], [5.65500000e-04, 5.65500000e-04, -6.22000000e-05, 5.65500000e-04, 5.65500000e-04], [4.93100000e-04, 4.93100000e-04, -5.10000000e-05, 4.93100000e-04, 4.93100000e-04], [3.25000000e-04, 3.25000000e-04, -3.17000000e-05, 3.25000000e-04, 3.25000000e-04], [-7.70200000e-04, -7.70200000e-04, 7.07000000e-05, -7.70200000e-04, -7.70200000e-04], [2.58000000e-05, 2.58000000e-05, -2.23000000e-06, 2.58000000e-05, 2.58000000e-05], [-1.52800000e-04, -1.52800000e-04, 1.25000000e-05, -1.52800000e-04, -1.52800000e-04], [4.52000000e-05, 4.52000000e-05, -3.48000000e-06, 4.52000000e-05, 4.52000000e-05], [-6.83900000e-04, -6.83900000e-04, 4.97000000e-05, -6.83900000e-04, -6.83900000e-04], [-7.77600000e-04, -7.77600000e-04, 5.34000000e-05, -7.77600000e-04, -7.77600000e-04], [1.03170000e-03, 1.03170000e-03, -6.70000000e-05, 1.03170000e-03, 1.03170000e-03], [1.20000000e-03, 1.20000000e-03, -7.37000000e-05, 1.20000000e-03, 1.20000000e-03], [-7.71600000e-04, -7.71600000e-04, 4.48000000e-05, -7.71600000e-04, -7.71600000e-04], [-3.37000000e-04, -3.37000000e-04, 1.85000000e-05, -3.37000000e-04, -3.37000000e-04], [1.19880000e-03, 1.19880000e-03, -6.25000000e-05, 1.19880000e-03, 1.19880000e-03], [-1.54610000e-03, -1.54610000e-03, 7.64000000e-05, -1.54610000e-03, -1.54610000e-03], [9.11600000e-04, 9.11600000e-04, -4.27000000e-05, 9.11600000e-04, 9.11600000e-04], [-4.70800000e-04, -4.70800000e-04, 2.09000000e-05, -4.70800000e-04, -4.70800000e-04], [-1.21550000e-03, -1.21550000e-03, 5.13000000e-05, -1.21550000e-03, -1.21550000e-03], [1.09160000e-03, 1.09160000e-03, -4.37000000e-05, 1.09160000e-03, 1.09160000e-03], [-2.72000000e-04, -2.72000000e-04, 1.04000000e-05, -2.72000000e-04, -2.72000000e-04], [-7.84500000e-04, -7.84500000e-04, 2.84000000e-05, -7.84500000e-04, -7.84500000e-04], [1.53330000e-03, 1.53330000e-03, -5.28000000e-05, 1.53330000e-03, 1.53330000e-03], [-1.84450000e-03, -1.84450000e-03, 6.05000000e-05, -1.84450000e-03, -1.84450000e-03], [1.68550000e-03, 1.68550000e-03, -5.26000000e-05, 1.68550000e-03, 1.68550000e-03], [-3.06100000e-04, -3.06100000e-04, 9.10000000e-06, -3.06100000e-04, -3.06100000e-04], [1.00950000e-03, 1.00950000e-03, -2.86000000e-05, 1.00950000e-03, 1.00950000e-03], [5.22000000e-04, 5.22000000e-04, -1.41000000e-05, 5.22000000e-04, 5.22000000e-04], [-2.18000000e-05, -2.18000000e-05, 5.62000000e-07, -2.18000000e-05, -2.18000000e-05], [-7.80600000e-04, -7.80600000e-04, 1.92000000e-05, -7.80600000e-04, -7.80600000e-04], [6.81400000e-04, 6.81400000e-04, -1.60000000e-05, 6.81400000e-04, 6.81400000e-04], [-1.43800000e-04, -1.43800000e-04, 3.23000000e-06, -1.43800000e-04, -1.43800000e-04], [7.76000000e-04, 7.76000000e-04, -1.66000000e-05, 7.76000000e-04, 7.76000000e-04], [2.54900000e-04, 2.54900000e-04, -5.22000000e-06, 2.54900000e-04, 2.54900000e-04], [5.77500000e-04, 5.77500000e-04, -1.13000000e-05, 5.77500000e-04, 5.77500000e-04], [7.58100000e-04, 7.58100000e-04, -1.42000000e-05, 7.58100000e-04, 7.58100000e-04], [-8.31000000e-04, -8.31000000e-04, 1.49000000e-05, -8.31000000e-04, -8.31000000e-04], [-2.10340000e-03, -2.10340000e-03, 3.62000000e-05, -2.10340000e-03, -2.10340000e-03], [-8.89900000e-04, -8.89900000e-04, 1.47000000e-05, -8.89900000e-04, -8.89900000e-04], [1.08570000e-03, 1.08570000e-03, -1.71000000e-05, 1.08570000e-03, 1.08570000e-03], [-1.88600000e-04, -1.88600000e-04, 2.86000000e-06, -1.88600000e-04, -1.88600000e-04], [9.10000000e-05, 9.10000000e-05, -1.32000000e-06, 9.10000000e-05, 9.10000000e-05], [1.07700000e-03, 1.07700000e-03, -1.50000000e-05, 1.07700000e-03, 1.07700000e-03], [9.04100000e-04, 9.04100000e-04, -1.21000000e-05, 9.04100000e-04, 9.04100000e-04], [-2.20000000e-04, -2.20000000e-04, 2.83000000e-06, -2.20000000e-04, -2.20000000e-04], [-1.64030000e-03, -1.64030000e-03, 2.02000000e-05, -1.64030000e-03, -1.64030000e-03], [2.20600000e-04, 2.20600000e-04, -2.62000000e-06, 2.20600000e-04, 2.20600000e-04], [-2.78300000e-04, -2.78300000e-04, 3.17000000e-06, -2.78300000e-04, -2.78300000e-04], [-4.93000000e-04, -4.93000000e-04, 5.40000000e-06, -4.93000000e-04, -4.93000000e-04], [-1.85000000e-04, -1.85000000e-04, 1.95000000e-06, -1.85000000e-04, -1.85000000e-04], [-7.64000000e-04, -7.64000000e-04, 7.75000000e-06, -7.64000000e-04, -7.64000000e-04], [7.79600000e-04, 7.79600000e-04, -7.61000000e-06, 7.79600000e-04, 7.79600000e-04], [2.88400000e-04, 2.88400000e-04, -2.71000000e-06, 2.88400000e-04, 2.88400000e-04], [1.09370000e-03, 1.09370000e-03, -9.91000000e-06, 1.09370000e-03, 1.09370000e-03], [3.07000000e-04, 3.07000000e-04, -2.68000000e-06, 3.07000000e-04, 3.07000000e-04], [-8.76000000e-04, -8.76000000e-04, 7.37000000e-06, -8.76000000e-04, -8.76000000e-04], [-1.85300000e-04, -1.85300000e-04, 1.50000000e-06, -1.85300000e-04, -1.85300000e-04], [3.24700000e-04, 3.24700000e-04, -2.54000000e-06, 3.24700000e-04, 3.24700000e-04], [4.59600000e-04, 4.59600000e-04, -3.47000000e-06, 4.59600000e-04, 4.59600000e-04], [-2.73300000e-04, -2.73300000e-04, 1.99000000e-06, -2.73300000e-04, -2.73300000e-04], [1.32180000e-03, 1.32180000e-03, -9.29000000e-06, 1.32180000e-03, 1.32180000e-03], [-1.32620000e-03, -1.32620000e-03, 9.00000000e-06, -1.32620000e-03, -1.32620000e-03], [9.62000000e-05, 9.62000000e-05, -6.31000000e-07, 9.62000000e-05, 9.62000000e-05], [-6.04400000e-04, -6.04400000e-04, 3.83000000e-06, -6.04400000e-04, -6.04400000e-04], [-6.66300000e-04, -6.66300000e-04, 4.08000000e-06, -6.66300000e-04, -6.66300000e-04]]) self.null_deviance = 6.8088354977561 # from R, Rpy bug self.params = np.array([1.00045997, 0.01991666, 0.00100126]) self.bse = np.array([4.55214070e-04, 7.00529313e-05, 1.84478509e-06]) self.aic_R = -1123.1528237643774 self.aic_Stata = -11.25152876811373 self.deviance = 7.1612915365488368e-05 self.scale = 7.3827747608449547e-07 self.llf = 565.57641188218872 self.bic_Stata = -446.7014364279675 self.df_model = 2 self.df_resid = 97 self.chi2 = 2704006.698904491 self.fittedvalues = np.array([ 0.99954024, 0.97906956, 0.95758077, 0.93526008, 0.91228657, 0.88882978, 0.8650479, 0.84108646, 0.81707757, 0.79313958, 0.76937709, 0.74588129, 0.72273051, 0.69999099, 0.67771773, 0.65595543, 0.63473944, 0.61409675, 0.59404691, 0.57460297, 0.55577231, 0.53755742, 0.51995663, 0.50296478, 0.48657379, 0.47077316, 0.4555505, 0.44089187, 0.42678213, 0.41320529, 0.40014475, 0.38758348, 0.37550428, 0.36388987, 0.35272306, 0.34198684, 0.33166446, 0.32173953, 0.31219604, 0.30301842, 0.29419156, 0.28570085, 0.27753216, 0.26967189, 0.26210695, 0.25482476, 0.24781324, 0.2410608, 0.23455636, 0.22828931, 0.22224947, 0.21642715, 0.21081306, 0.20539835, 0.20017455, 0.19513359, 0.19026777, 0.18556972, 0.18103243, 0.17664922, 0.1724137, 0.16831977, 0.16436164, 0.16053377, 0.15683086, 0.15324789, 0.14978003, 0.1464227, 0.14317153, 0.14002232, 0.13697109, 0.13401403, 0.1311475, 0.12836802, 0.12567228, 0.1230571, 0.12051944, 0.11805642, 0.11566526, 0.1133433, 0.11108802, 0.10889699, 0.10676788, 0.10469847, 0.10268664, 0.10073034, 0.09882763, 0.09697663, 0.09517555, 0.09342267, 0.09171634, 0.09005498, 0.08843707, 0.08686116, 0.08532585, 0.08382979, 0.0823717, 0.08095035, 0.07956453, 0.07821311]) class Star98(object): """ Star98 class used with TestGlmBinomial """ def __init__(self): self.params = ( -0.0168150366, 0.0099254766, -0.0187242148, -0.0142385609, 0.2544871730, 0.2406936644, 0.0804086739, -1.9521605027, -0.3340864748, -0.1690221685, 0.0049167021, -0.0035799644, -0.0140765648, -0.0040049918, -0.0039063958, 0.0917143006, 0.0489898381, 0.0080407389, 0.0002220095, -0.0022492486, 2.9588779262) self.bse = ( 4.339467e-04, 6.013714e-04, 7.435499e-04, 4.338655e-04, 2.994576e-02, 5.713824e-02, 1.392359e-02, 3.168109e-01, 6.126411e-02, 3.270139e-02, 1.253877e-03, 2.254633e-04, 1.904573e-03, 4.739838e-04, 9.623650e-04, 1.450923e-02, 7.451666e-03, 1.499497e-03, 2.988794e-05, 3.489838e-04, 1.546712e+00) self.null_deviance = 34345.3688931 self.df_null = 302 self.deviance = 4078.76541772 self.df_resid = 282 self.df_model = 20 self.aic_R = 6039.22511799 self.aic_Stata = 19.93143846737438 self.bic_Stata = 2467.493504191302 self.llf = -2998.61255899391 # from R self.llf_Stata = -2998.612927807218 self.scale = 1. self.pearson_chi2 = 4051.921614 self.resids = glm_test_resids.star98_resids self.fittedvalues = np.array([ 0.5833118, 0.75144661, 0.50058272, 0.68534524, 0.32251021, 0.68693601, 0.33299827, 0.65624766, 0.49851481, 0.506736, 0.23954874, 0.86631452, 0.46432936, 0.44171873, 0.66797935, 0.73988491, 0.51966014, 0.42442446, 0.5649369, 0.59251634, 0.34798337, 0.56415024, 0.49974355, 0.3565539, 0.20752309, 0.18269097, 0.44932642, 0.48025128, 0.59965277, 0.58848671, 0.36264203, 0.33333196, 0.74253352, 0.5081886, 0.53421878, 0.56291445, 0.60205239, 0.29174423, 0.2954348, 0.32220414, 0.47977903, 0.23687535, 0.11776464, 0.1557423, 0.27854799, 0.22699533, 0.1819439, 0.32554433, 0.22681989, 0.15785389, 0.15268609, 0.61094772, 0.20743222, 0.51649059, 0.46502006, 0.41031788, 0.59523288, 0.65733285, 0.27835336, 0.2371213, 0.25137045, 0.23953942, 0.27854519, 0.39652413, 0.27023163, 0.61411863, 0.2212025, 0.42005842, 0.55940397, 0.35413774, 0.45724563, 0.57399437, 0.2168918, 0.58308738, 0.17181104, 0.49873249, 0.22832683, 0.14846056, 0.5028073, 0.24513863, 0.48202096, 0.52823155, 0.5086262, 0.46295993, 0.57869402, 0.78363217, 0.21144435, 0.2298366, 0.17954825, 0.32232586, 0.8343015, 0.56217006, 0.47367315, 0.52535649, 0.60350746, 0.43210701, 0.44712008, 0.35858239, 0.2521347, 0.19787004, 0.63256553, 0.51386532, 0.64997027, 0.13402072, 0.81756174, 0.74543642, 0.30825852, 0.23988707, 0.17273125, 0.27880599, 0.17395893, 0.32052828, 0.80467697, 0.18726218, 0.23842081, 0.19020381, 0.85835388, 0.58703615, 0.72415106, 0.64433695, 0.68766653, 0.32923663, 0.16352185, 0.38868816, 0.44980444, 0.74810044, 0.42973792, 0.53762581, 0.72714996, 0.61229484, 0.30267667, 0.24713253, 0.65086008, 0.48957265, 0.54955545, 0.5697156, 0.36406211, 0.48906545, 0.45919413, 0.4930565, 0.39785555, 0.5078719, 0.30159626, 0.28524393, 0.34687707, 0.22522042, 0.52947159, 0.29277287, 0.8585002, 0.60800389, 0.75830521, 0.35648175, 0.69508796, 0.45518355, 0.21567675, 0.39682985, 0.49042948, 0.47615798, 0.60588234, 0.62910299, 0.46005639, 0.71755165, 0.48852156, 0.47940661, 0.60128813, 0.16589699, 0.68512861, 0.46305199, 0.68832227, 0.7006721, 0.56564937, 0.51753941, 0.54261733, 0.56072214, 0.34545715, 0.30226104, 0.3572956, 0.40996287, 0.33517519, 0.36248407, 0.33937041, 0.34140691, 0.2627528, 0.29955161, 0.38581683, 0.24840026, 0.15414272, 0.40415991, 0.53936252, 0.52111887, 0.28060168, 0.45600958, 0.51110589, 0.43757523, 0.46891953, 0.39425249, 0.5834369, 0.55817308, 0.32051259, 0.43567448, 0.34134195, 0.43016545, 0.4885413, 0.28478325, 0.2650776, 0.46784606, 0.46265983, 0.42655938, 0.18972234, 0.60448491, 0.211896, 0.37886032, 0.50727577, 0.39782309, 0.50427121, 0.35882898, 0.39596807, 0.49160806, 0.35618002, 0.6819922, 0.36871093, 0.43079679, 0.67985516, 0.41270595, 0.68952767, 0.52587734, 0.32042126, 0.39120123, 0.56870985, 0.32962349, 0.32168989, 0.54076251, 0.4592907, 0.48480182, 0.4408386, 0.431178, 0.47078232, 0.55911605, 0.30331618, 0.50310393, 0.65036038, 0.45078895, 0.62354291, 0.56435463, 0.50034281, 0.52693538, 0.57217285, 0.49221472, 0.40707122, 0.44226533, 0.3475959, 0.54746396, 0.86385832, 0.48402233, 0.54313657, 0.61586824, 0.27097185, 0.69717808, 0.52156974, 0.50401189, 0.56724181, 0.6577178, 0.42732047, 0.44808396, 0.65435634, 0.54766225, 0.38160648, 0.49890847, 0.50879037, 0.5875452, 0.45101593, 0.5709704, 0.3175516, 0.39813159, 0.28305688, 0.40521062, 0.30120578, 0.26400428, 0.44205496, 0.40545798, 0.39366599, 0.55288196, 0.14104184, 0.17550155, 0.1949095, 0.40255144, 0.21016822, 0.09712017, 0.63151487, 0.25885514, 0.57323748, 0.61836898, 0.43268601, 0.67008878, 0.75801989, 0.50353406, 0.64222315, 0.29925757, 0.32592036, 0.39634977, 0.39582747, 0.41037006, 0.34174944]) class Lbw(object): ''' The LBW data can be found here https://www.stata-press.com/data/r9/rmain.html ''' def __init__(self): # data set up for data not in datasets filename = os.path.join(os.path.dirname(os.path.abspath(__file__)), "stata_lbw_glm.csv") data = pd.read_csv(filename) dummies = pd.get_dummies(data.race, prefix="race", drop_first=False) data = pd.concat([data, dummies], 1) self.endog = data.low design = data[["age", "lwt", "race_black", "race_other", "smoke", "ptl", "ht", "ui"]] self.exog = add_constant(design, prepend=False) # Results for Canonical Logit Link self.params = ( -.02710031, -.01515082, 1.26264728, .86207916, .92334482, .54183656, 1.83251780, .75851348, .46122388) self.bse = ( 0.036449917, 0.006925765, 0.526405169, 0.439146744, 0.400820976, 0.346246857, 0.691623875, 0.459373871, 1.204574885) self.aic_R = 219.447991133 self.aic_Stata = 1.161100482182551 self.deviance = 201.4479911325021 self.scale = 1 self.llf = -100.7239955662511 self.chi2 = 25.65329337867037 # from Stata not used by sm self.null_deviance = 234.671996193219 self.bic_Stata = -742.0664715782335 self.df_resid = 180 self.df_model = 8 self.df_null = 188 self.pearson_chi2 = 182.023342493558 self.resids = glm_test_resids.lbw_resids self.fittedvalues = np.array([ 0.31217507, 0.12793027, 0.32119762, 0.48442686, 0.50853393, 0.24517662, 0.12755193, 0.33226988, 0.22013309, 0.26268069, 0.34729955, 0.18782188, 0.75404181, 0.54723527, 0.35016393, 0.35016393, 0.45824406, 0.25336683, 0.43087357, 0.23284101, 0.20146616, 0.24315597, 0.02725586, 0.22207692, 0.39800383, 0.05584178, 0.28403447, 0.06931188, 0.35371946, 0.3896279, 0.3896279, 0.47812002, 0.60043853, 0.07144772, 0.29995988, 0.17910031, 0.22773411, 0.22691015, 0.06221253, 0.2384528, 0.32633864, 0.05131047, 0.2954536, 0.07364416, 0.57241299, 0.57241299, 0.08272435, 0.23298882, 0.12658158, 0.58967487, 0.46989562, 0.22455631, 0.2348285, 0.29571887, 0.28212464, 0.31499013, 0.68340511, 0.14090647, 0.31448425, 0.28082972, 0.28082972, 0.24918728, 0.27018297, 0.08175784, 0.64808999, 0.38252574, 0.25550797, 0.09113411, 0.40736693, 0.32644055, 0.54367425, 0.29606968, 0.47028421, 0.39972155, 0.25079125, 0.09678472, 0.08807264, 0.27467837, 0.5675742, 0.045619, 0.10719293, 0.04826292, 0.23934092, 0.24179618, 0.23802197, 0.49196179, 0.31379451, 0.10605469, 0.04047396, 0.11620849, 0.09937016, 0.21822964, 0.29770265, 0.83912829, 0.25079125, 0.08548557, 0.06550308, 0.2046457, 0.2046457, 0.08110349, 0.13519643, 0.47862055, 0.38891913, 0.1383964, 0.26176764, 0.31594589, 0.11418612, 0.06324112, 0.28468594, 0.21663702, 0.03827107, 0.27237604, 0.20246694, 0.19042999, 0.15019447, 0.18759474, 0.12308435, 0.19700616, 0.11564002, 0.36595033, 0.07765727, 0.14119063, 0.13584627, 0.11012759, 0.10102472, 0.10002166, 0.07439288, 0.27919958, 0.12491598, 0.06774594, 0.72513764, 0.17714986, 0.67373352, 0.80679436, 0.52908941, 0.15695938, 0.49722003, 0.41970014, 0.62375224, 0.53695622, 0.25474238, 0.79135707, 0.2503871, 0.25352337, 0.33474211, 0.19308929, 0.24658944, 0.25495092, 0.30867144, 0.41240259, 0.59412526, 0.16811226, 0.48282791, 0.36566756, 0.09279325, 0.75337353, 0.57128885, 0.52974123, 0.44548504, 0.77748843, 0.3224082, 0.40054277, 0.29522468, 0.19673553, 0.73781774, 0.57680312, 0.44545573, 0.30242355, 0.38720223, 0.16632904, 0.30804092, 0.56385194, 0.60012179, 0.48324821, 0.24636345, 0.26153216, 0.2348285, 0.29023669, 0.41011454, 0.36472083, 0.65922069, 0.30476903, 0.09986775, 0.70658332, 0.30713075, 0.36096386, 0.54962701, 0.71996086, 0.6633756]) class Scotvote(object): """ Scotvot class is used with TestGlmGamma. """ def __init__(self): self.params = ( 4.961768e-05, 2.034423e-03, -7.181429e-05, 1.118520e-04, -1.467515e-07, -5.186831e-04, -2.42717498e-06, -1.776527e-02) self.bse = ( 1.621577e-05, 5.320802e-04, 2.711664e-05, 4.057691e-05, 1.236569e-07, 2.402534e-04, 7.460253e-07, 1.147922e-02) self.null_deviance = 0.536072 self.df_null = 31 self.deviance = 0.087388516417 self.df_resid = 24 self.df_model = 7 self.aic_R = 182.947045954721 self.aic_Stata = 10.72212 self.bic_Stata = -83.09027 self.llf = -163.5539382 # from Stata, same as ours with scale = 1 # self.llf = -82.47352 # Very close to ours as is self.scale = 0.003584283 self.pearson_chi2 = .0860228056 self.resids = glm_test_resids.scotvote_resids self.fittedvalues = np.array([ 57.80431482, 53.2733447, 50.56347993, 58.33003783, 70.46562169, 56.88801284, 66.81878401, 66.03410393, 57.92937473, 63.23216907, 53.9914785, 61.28993391, 64.81036393, 63.47546816, 60.69696114, 74.83508176, 56.56991106, 72.01804172, 64.35676519, 52.02445881, 64.24933079, 71.15070332, 45.73479688, 54.93318588, 66.98031261, 52.02479973, 56.18413736, 58.12267471, 67.37947398, 60.49162862, 73.82609217, 69.61515621]) class Cancer(object): ''' The Cancer data can be found here https://www.stata-press.com/data/r10/rmain.html ''' def __init__(self): filename = os.path.join(os.path.dirname(os.path.abspath(__file__)), "stata_cancer_glm.csv") data = np.recfromcsv(open(filename, 'rb')) self.endog = data.studytime dummies = pd.get_dummies(pd.Series(data.drug, dtype="category"), drop_first=True) design = np.column_stack((data.age, dummies)).astype(float) self.exog = add_constant(design, prepend=False) class CancerLog(Cancer): """ CancerLog is used TestGlmGammaLog """ def __init__(self): super(CancerLog, self).__init__() self.resids = np.array([ [-8.52598100e-01, -1.45739100e+00, -3.92408100e+01, -1.41526900e+00, -5.78417200e+00], [-8.23683800e-01, -1.35040200e+00, -2.64957500e+01, -1.31777000e+00, -4.67162900e+00], [-7.30450400e-01, -1.07754600e+00, -4.02136400e+01, -1.06208800e+00, -5.41978500e+00], [-7.04471600e-01, -1.01441500e+00, -7.25951500e+01, -1.00172900e+00, -7.15130900e+00], [-5.28668000e-01, -6.68617300e-01, -3.80758100e+01, -6.65304600e-01, -4.48658700e+00], [-2.28658500e-01, -2.48859700e-01, -6.14913600e+00, -2.48707200e-01, -1.18577100e+00], [-1.93939400e-01, -2.08119900e-01, -7.46226500e+00, -2.08031700e-01, -1.20300800e+00], [-3.55635700e-01, -4.09525000e-01, -2.14132500e+01, -4.08815100e-01, -2.75958600e+00], [-5.73360000e-02, -5.84700000e-02, -4.12946200e+00, -5.84681000e-02, -4.86586900e-01], [3.09828000e-02, 3.06685000e-02, 1.86551100e+00, 3.06682000e-02, 2.40413800e-01], [-2.11924300e-01, -2.29071300e-01, -2.18386100e+01, -2.28953000e-01, -2.15130900e+00], [-3.10989000e-01, -3.50739300e-01, -4.19249500e+01, -3.50300400e-01, -3.61084500e+00], [-9.22250000e-03, -9.25100000e-03, -1.13679700e+00, -9.25100000e-03, -1.02392100e-01], [2.39402500e-01, 2.22589700e-01, 1.88577300e+01, 2.22493500e-01, 2.12475600e+00], [3.35166000e-02, 3.31493000e-02, 4.51842400e+00, 3.31489000e-02, 3.89155400e-01], [8.49829400e-01, 6.85180200e-01, 3.57627500e+01, 6.82689900e-01, 5.51291500e+00], [4.12934200e-01, 3.66785200e-01, 4.65392600e+01, 3.66370400e-01, 4.38379500e+00], [4.64148400e-01, 4.07123200e-01, 6.25726500e+01, 4.06561900e-01, 5.38915500e+00], [1.71104600e+00, 1.19474800e+00, 1.12676500e+02, 1.18311900e+00, 1.38850500e+01], [1.26571800e+00, 9.46389000e-01, 1.30431000e+02, 9.40244600e-01, 1.28486900e+01], [-3.48532600e-01, -3.99988300e-01, -2.95638100e+01, -3.99328600e-01, -3.20997700e+00], [-4.04340300e-01, -4.76960100e-01, -4.10254300e+01, -4.75818000e-01, -4.07286500e+00], [-4.92057900e-01, -6.08818300e-01, -9.34509600e+01, -6.06357200e-01, -6.78109700e+00], [-4.02876400e-01, -4.74878400e-01, -9.15226200e+01, -4.73751900e-01, -6.07225700e+00], [-5.15056700e-01, -6.46013300e-01, -2.19014600e+02, -6.43043500e-01, -1.06209700e+01], [-8.70423000e-02, -8.97043000e-02, -1.26361400e+01, -8.96975000e-02, -1.04875100e+00], [1.28362300e-01, 1.23247800e-01, 1.70383300e+01, 1.23231000e-01, 1.47887800e+00], [-2.39271900e-01, -2.61562100e-01, -9.30283300e+01, -2.61384400e-01, -4.71795100e+00], [7.37246500e-01, 6.08186000e-01, 6.25359600e+01, 6.06409700e-01, 6.79002300e+00], [-3.64110000e-02, -3.68626000e-02, -1.41565300e+01, -3.68621000e-02, -7.17951200e-01], [2.68833000e-01, 2.47933100e-01, 6.67934100e+01, 2.47801000e-01, 4.23748400e+00], [5.96389600e-01, 5.07237700e-01, 1.13265500e+02, 5.06180100e-01, 8.21890300e+00], [1.98218000e-02, 1.96923000e-02, 1.00820900e+01, 1.96923000e-02, 4.47040700e-01], [7.74936000e-01, 6.34305300e-01, 2.51883900e+02, 6.32303700e-01, 1.39711800e+01], [-7.63925100e-01, -1.16591700e+00, -4.93461700e+02, -1.14588000e+00, -1.94156600e+01], [-6.23771700e-01, -8.41174800e-01, -4.40679600e+02, -8.34266300e-01, -1.65796100e+01], [-1.63272900e-01, -1.73115100e-01, -6.73975900e+01, -1.73064800e-01, -3.31725800e+00], [-4.28562500e-01, -5.11932900e-01, -4.73787800e+02, -5.10507400e-01, -1.42494800e+01], [8.00693000e-02, 7.80269000e-02, 3.95353400e+01, 7.80226000e-02, 1.77920500e+00], [-2.13674400e-01, -2.31127400e-01, -2.15987000e+02, -2.31005700e-01, -6.79344600e+00], [-1.63544000e-02, -1.64444000e-02, -1.05642100e+01, -1.64444000e-02, -4.15657600e-01], [2.04900500e-01, 1.92372100e-01, 1.10651300e+02, 1.92309400e-01, 4.76156600e+00], [-1.94758900e-01, -2.09067700e-01, -2.35484100e+02, -2.08978200e-01, -6.77219400e+00], [3.16727400e-01, 2.88367800e-01, 1.87065600e+02, 2.88162100e-01, 7.69732400e+00], [6.24234900e-01, 5.27632500e-01, 2.57678500e+02, 5.26448400e-01, 1.26827400e+01], [8.30241100e-01, 6.72002100e-01, 2.86513700e+02, 6.69644800e-01, 1.54232100e+01], [6.55140000e-03, 6.53710000e-03, 7.92130700e+00, 6.53710000e-03, 2.27805800e-01], [3.41595200e-01, 3.08985000e-01, 2.88667600e+02, 3.08733300e-01, 9.93012900e+00]]) self.null_deviance = 27.92207137420696 # From R (bug in rpy) self.params = np.array([ -0.04477778, 0.57437126, 1.05210726, 4.64604002]) self.bse = np.array([0.0147328, 0.19694727, 0.19772507, 0.83534671]) self.aic_R = 331.89022395372069 self.aic_Stata = 7.403608467857651 self.deviance = 16.174635536991005 self.scale = 0.31805268736385695 # self.llf = -160.94511197686035 # From R self.llf = -173.6866032285836 # from Staa self.bic_Stata = -154.1582089453923 # from Stata self.df_model = 3 self.df_resid = 44 self.chi2 = 36.77821448266359 # from Stata not in sm self.fittedvalues = np.array([ 6.78419193, 5.67167253, 7.41979002, 10.15123371, 8.48656317, 5.18582263, 6.20304079, 7.75958258, 8.48656317, 7.75958258, 10.15123371, 11.61071755, 11.10228357, 8.87520908, 11.61071755, 6.48711178, 10.61611394, 11.61071755, 8.11493609, 10.15123371, 9.21009116, 10.07296716, 13.78112366, 15.07225103, 20.62079147, 12.04881666, 11.5211983, 19.71780584, 9.21009116, 19.71780584, 15.76249142, 13.78112366, 22.55271436, 18.02872842, 25.41575239, 26.579678, 20.31745227, 33.24937131, 22.22095589, 31.79337946, 25.41575239, 23.23857437, 34.77204095, 24.30279515, 20.31745227, 18.57700761, 34.77204095, 29.06987768]) class CancerIdentity(Cancer): """ CancerIdentity is used with TestGlmGammaIdentity """ def __init__(self): super(CancerIdentity, self).__init__() self.resids = np.array([ [-8.52598100e-01, -1.45739100e+00, -3.92408100e+01, -1.41526900e+00, -5.78417200e+00], [-8.23683800e-01, -1.35040200e+00, -2.64957500e+01, -1.31777000e+00, -4.67162900e+00], [-7.30450400e-01, -1.07754600e+00, -4.02136400e+01, -1.06208800e+00, -5.41978500e+00], [-7.04471600e-01, -1.01441500e+00, -7.25951500e+01, -1.00172900e+00, -7.15130900e+00], [-5.28668000e-01, -6.68617300e-01, -3.80758100e+01, -6.65304600e-01, -4.48658700e+00], [-2.28658500e-01, -2.48859700e-01, -6.14913600e+00, -2.48707200e-01, -1.18577100e+00], [-1.93939400e-01, -2.08119900e-01, -7.46226500e+00, -2.08031700e-01, -1.20300800e+00], [-3.55635700e-01, -4.09525000e-01, -2.14132500e+01, -4.08815100e-01, -2.75958600e+00], [-5.73360000e-02, -5.84700000e-02, -4.12946200e+00, -5.84681000e-02, -4.86586900e-01], [3.09828000e-02, 3.06685000e-02, 1.86551100e+00, 3.06682000e-02, 2.40413800e-01], [-2.11924300e-01, -2.29071300e-01, -2.18386100e+01, -2.28953000e-01, -2.15130900e+00], [-3.10989000e-01, -3.50739300e-01, -4.19249500e+01, -3.50300400e-01, -3.61084500e+00], [-9.22250000e-03, -9.25100000e-03, -1.13679700e+00, -9.25100000e-03, -1.02392100e-01], [2.39402500e-01, 2.22589700e-01, 1.88577300e+01, 2.22493500e-01, 2.12475600e+00], [3.35166000e-02, 3.31493000e-02, 4.51842400e+00, 3.31489000e-02, 3.89155400e-01], [8.49829400e-01, 6.85180200e-01, 3.57627500e+01, 6.82689900e-01, 5.51291500e+00], [4.12934200e-01, 3.66785200e-01, 4.65392600e+01, 3.66370400e-01, 4.38379500e+00], [4.64148400e-01, 4.07123200e-01, 6.25726500e+01, 4.06561900e-01, 5.38915500e+00], [1.71104600e+00, 1.19474800e+00, 1.12676500e+02, 1.18311900e+00, 1.38850500e+01], [1.26571800e+00, 9.46389000e-01, 1.30431000e+02, 9.40244600e-01, 1.28486900e+01], [-3.48532600e-01, -3.99988300e-01, -2.95638100e+01, -3.99328600e-01, -3.20997700e+00], [-4.04340300e-01, -4.76960100e-01, -4.10254300e+01, -4.75818000e-01, -4.07286500e+00], [-4.92057900e-01, -6.08818300e-01, -9.34509600e+01, -6.06357200e-01, -6.78109700e+00], [-4.02876400e-01, -4.74878400e-01, -9.15226200e+01, -4.73751900e-01, -6.07225700e+00], [-5.15056700e-01, -6.46013300e-01, -2.19014600e+02, -6.43043500e-01, -1.06209700e+01], [-8.70423000e-02, -8.97043000e-02, -1.26361400e+01, -8.96975000e-02, -1.04875100e+00], [1.28362300e-01, 1.23247800e-01, 1.70383300e+01, 1.23231000e-01, 1.47887800e+00], [-2.39271900e-01, -2.61562100e-01, -9.30283300e+01, -2.61384400e-01, -4.71795100e+00], [7.37246500e-01, 6.08186000e-01, 6.25359600e+01, 6.06409700e-01, 6.79002300e+00], [-3.64110000e-02, -3.68626000e-02, -1.41565300e+01, -3.68621000e-02, -7.17951200e-01], [2.68833000e-01, 2.47933100e-01, 6.67934100e+01, 2.47801000e-01, 4.23748400e+00], [5.96389600e-01, 5.07237700e-01, 1.13265500e+02, 5.06180100e-01, 8.21890300e+00], [1.98218000e-02, 1.96923000e-02, 1.00820900e+01, 1.96923000e-02, 4.47040700e-01], [7.74936000e-01, 6.34305300e-01, 2.51883900e+02, 6.32303700e-01, 1.39711800e+01], [-7.63925100e-01, -1.16591700e+00, -4.93461700e+02, -1.14588000e+00, -1.94156600e+01], [-6.23771700e-01, -8.41174800e-01, -4.40679600e+02, -8.34266300e-01, -1.65796100e+01], [-1.63272900e-01, -1.73115100e-01, -6.73975900e+01, -1.73064800e-01, -3.31725800e+00], [-4.28562500e-01, -5.11932900e-01, -4.73787800e+02, -5.10507400e-01, -1.42494800e+01], [8.00693000e-02, 7.80269000e-02, 3.95353400e+01, 7.80226000e-02, 1.77920500e+00], [-2.13674400e-01, -2.31127400e-01, -2.15987000e+02, -2.31005700e-01, -6.79344600e+00], [-1.63544000e-02, -1.64444000e-02, -1.05642100e+01, -1.64444000e-02, -4.15657600e-01], [2.04900500e-01, 1.92372100e-01, 1.10651300e+02, 1.92309400e-01, 4.76156600e+00], [-1.94758900e-01, -2.09067700e-01, -2.35484100e+02, -2.08978200e-01, -6.77219400e+00], [3.16727400e-01, 2.88367800e-01, 1.87065600e+02, 2.88162100e-01, 7.69732400e+00], [6.24234900e-01, 5.27632500e-01, 2.57678500e+02, 5.26448400e-01, 1.26827400e+01], [8.30241100e-01, 6.72002100e-01, 2.86513700e+02, 6.69644800e-01, 1.54232100e+01], [6.55140000e-03, 6.53710000e-03, 7.92130700e+00, 6.53710000e-03, 2.27805800e-01], [3.41595200e-01, 3.08985000e-01, 2.88667600e+02, 3.08733300e-01, 9.93012900e+00]]) self.params = np.array([ -0.5369833, 6.47296332, 16.20336802, 38.96617431]) self.bse = np.array([ 0.13341238, 2.1349966, 3.87411875, 8.19235553]) self.aic_R = 328.39209118952965 # TODO: the below will fail self.aic_Stata = 7.381090276021671 self.deviance = 15.093762327607557 self.scale = 0.29512089119443752 self.null_deviance = 27.92207137420696 # from R bug in RPy # NOTE: our scale is Stata's dispers_p (pearson?) # TODO: if scale is analagous to Stata's dispersion, then this might be # where the discrepancies come from? # self.llf = -159.19604559476483 # From R self.llf = -173.1461666245201 # From Stata self.bic_Stata = -155.2390821535193 self.df_model = 3 self.df_resid = 44 self.chi2 = 51.56632068622578 self.fittedvalues = np.array([ 6.21019277, 4.06225956, 7.28415938, 11.04304251, 8.89510929, 2.98829295, 5.13622616, 7.82114268, 8.89510929, 7.82114268, 11.04304251, 12.65399242, 12.11700911, 9.43209259, 12.65399242, 5.67320947, 11.58002581, 12.65399242, 8.35812599, 11.04304251, 9.46125627, 10.53522287, 14.294106, 15.36807261, 19.12695574, 12.68315609, 12.14617279, 18.58997243, 9.46125627, 18.58997243, 15.90505591, 14.294106, 20.20092234, 17.51600582, 25.63546061, 26.17244391, 22.95054409, 28.85736043, 24.0245107, 28.32037713, 25.63546061, 24.561494, 29.39434374, 25.09847731, 22.95054409, 21.87657748, 29.39434374, 27.24641052]) class Cpunish(object): ''' The following are from the R script in models.datasets.cpunish Slightly different than published results, but should be correct Probably due to rounding in cleaning? ''' def __init__(self): self.params = ( 2.611017e-04, 7.781801e-02, -9.493111e-02, 2.969349e-01, 2.301183e+00, -1.872207e+01, -6.801480e+00) self.bse = ( 5.187132e-05, 7.940193e-02, 2.291926e-02, 4.375164e-01, 4.283826e-01, 4.283961e+00, 4.146850e+00) self.null_deviance = 136.57281747225 self.df_null = 16 self.deviance = 18.591641759528944 self.df_resid = 10 self.df_model = 6 self.aic_R = 77.8546573896503 # same as Stata self.aic_Stata = 4.579685683305706 self.bic_Stata = -9.740492454486446 self.chi2 = 128.8021169250578 # from Stata not in sm self.llf = -31.92732869482515 self.scale = 1 self.pearson_chi2 = 24.75374835 self.resids = glm_test_resids.cpunish_resids self.fittedvalues = np.array([ 35.2263655, 8.1965744, 1.3118966, 3.6862982, 2.0823003, 1.0650316, 1.9260424, 2.4171405, 1.8473219, 2.8643241, 3.1211989, 3.3382067, 2.5269969, 0.8972542, 0.9793332, 0.5346209, 1.9790936]) class Cpunish_offset(Cpunish): ''' Same model as Cpunish but with offset of 100. Many things do not change. ''' def __init__(self): super(Cpunish_offset, self).__init__() self.params = ( -1.140665e+01, 2.611017e-04, 7.781801e-02, -9.493111e-02, 2.969349e-01, 2.301183e+00, -1.872207e+01) self.bse = ( 4.147e+00, 5.187e-05, 7.940e-02, 2.292e-02, 4.375e-01, 4.284e-01, 4.284e+00) class InvGauss(object): ''' Usef Data was generated by Hardin and Hilbe using Stata. Note only the first 5000 observations are used because the models code currently uses np.eye. ''' # FIXME: do something with the commented-out code below # np.random.seed(54321) # x1 = np.abs(stats.norm.ppf((np.random.random(5000)))) # x2 = np.abs(stats.norm.ppf((np.random.random(5000)))) # X = np.column_stack((x1, x2)) # X = add_constant(X) # params = np.array([.5, -.25, 1]) # eta = np.dot(X, params) # mu = 1/np.sqrt(eta) # sigma = .5 # This is not correct. Errors need to be normally distributed # But Y needs to be Inverse Gaussian, so we could build it up # by throwing out data? # Refs: # * Lai (2009) Generating inverse Gaussian random variates by # approximation # * Atkinson (1982) The simulation of generalized inverse gaussian # and hyperbolic random variables seems to be the canonical ref # Y = np.dot(X, params) + np.random.wald(mu, sigma, 1000) # model = GLM(Y, X, family=models.family.InverseGaussian(link=\ # models.family.links.identity())) def __init__(self): # set up data # filename = os.path.join(os.path.dirname(os.path.abspath(__file__)), "inv_gaussian.csv") with open(filename, 'r') as fd: data = np.genfromtxt(fd, delimiter=",", dtype=float)[1:] self.endog = data[:5000, 0] self.exog = data[:5000, 1:] self.exog = add_constant(self.exog, prepend=False) # Results # NOTE: loglikelihood difference in R vs. Stata vs. Models # is the same situation as gamma self.params = (0.4519770, -0.2508288, 1.0359574) self.bse = (0.03148291, 0.02237211, 0.03429943) self.null_deviance = 1520.673165475461 self.df_null = 4999 self.deviance = 1423.943980407997 self.df_resid = 4997 self.df_model = 2 self.aic_R = 5059.41911646446 self.aic_Stata = 1.552280060977946 self.bic_Stata = -41136.47039418921 self.llf = -3877.700354 # Stata is same as ours with scale set to 1 # self.llf = -2525.70955823223 # from R, close to ours self.scale = 0.2867266359127567 self.pearson_chi2 = 1432.771536 self.resids = glm_test_resids.invgauss_resids self.fittedvalues = np.array([ 1.0404339, 0.96831526, 0.81265833, 0.9958362, 1.05433442, 1.09866137, 0.95548191, 1.38082105, 0.98942888, 0.96521958, 1.02684056, 0.91412576, 0.91492102, 0.92639676, 0.96763425, 0.80250852, 0.85281816, 0.90962261, 0.95550299, 0.86386815, 0.94760134, 0.94269533, 0.98960509, 0.84787252, 0.78949111, 0.76873582, 0.98933453, 0.95105574, 0.8489395, 0.88962971, 0.84856357, 0.88567313, 0.84505405, 0.84626147, 0.77250421, 0.90175601, 1.15436378, 0.98375558, 0.83539542, 0.82845381, 0.90703971, 0.85546165, 0.96707286, 0.84127197, 0.82096543, 1.1311227, 0.87617029, 0.91194419, 1.05125511, 0.95330314, 0.75556148, 0.82573228, 0.80424982, 0.83800144, 0.8203644, 0.84423807, 0.98348433, 0.93165089, 0.83968706, 0.79256287, 1.0302839, 0.90982028, 0.99471562, 0.70931825, 0.85471721, 1.02668021, 1.11308301, 0.80497105, 1.02708486, 1.07671424, 0.821108, 0.86373486, 0.99104964, 1.06840593, 0.94947784, 0.80982122, 0.95778065, 1.0254212, 1.03480946, 0.83942363, 1.17194944, 0.91772559, 0.92368795, 1.10410916, 1.12558875, 1.11290791, 0.87816503, 1.04299294, 0.89631173, 1.02093004, 0.86331723, 1.13134858, 1.01807861, 0.98441692, 0.72567667, 1.42760495, 0.78987436, 0.72734482, 0.81750166, 0.86451854, 0.90564264, 0.81022323, 0.98720325, 0.98263709, 0.99364823, 0.7264445, 0.81632452, 0.7627845, 1.10726938, 0.79195664, 0.86836774, 1.01558149, 0.82673675, 0.99529548, 0.97155636, 0.980696, 0.85460503, 1.00460782, 0.77395244, 0.81229831, 0.94078297, 1.05910564, 0.95921954, 0.97841172, 0.93093166, 0.93009865, 0.89888111, 1.18714408, 0.98964763, 1.03388898, 1.67554215, 0.82998876, 1.34100687, 0.86766346, 0.96392316, 0.91371033, 0.76589296, 0.92329051, 0.82560326, 0.96758148, 0.8412995, 1.02550678, 0.74911108, 0.8751611, 1.01389312, 0.87865556, 1.24095868, 0.90678261, 0.85973204, 1.05617845, 0.94163038, 0.88087351, 0.95699844, 0.86083491, 0.89669384, 0.78646825, 1.0014202, 0.82399199, 1.05313139, 1.06458324, 0.88501766, 1.19043294, 0.8458026, 1.00231535, 0.72464305, 0.94790753, 0.7829744, 1.1953009, 0.85574035, 0.95433052, 0.96341484, 0.91362908, 0.94097713, 0.87273804, 0.81126399, 0.72715262, 0.85526116, 0.76015834, 0.8403826, 0.9831501, 1.17104665, 0.78862494, 1.01054909, 0.91511601, 1.0990797, 0.91352124, 1.13671162, 0.98793866, 1.0300545, 1.04490115, 0.85778231, 0.94824343, 1.14510618, 0.81305136, 0.88085051, 0.94743792, 0.94875465, 0.96206997, 0.94493612, 0.93547218, 1.09212018, 0.86934651, 0.90532353, 1.07066001, 1.26197714, 0.93858662, 0.9685039, 0.7946546, 1.03052031, 0.75395899, 0.87527062, 0.82156476, 0.949774, 1.01000235, 0.82613526, 1.0224591, 0.91529149, 0.91608832, 1.09418385, 0.8228272, 1.06337472, 1.05533176, 0.93513063, 1.00055806, 0.95474743, 0.91329368, 0.88711836, 0.95584926, 0.9825458, 0.74954073, 0.96964967, 0.88779583, 0.95321846, 0.95390055, 0.95369029, 0.94326714, 1.31881201, 0.71512263, 0.84526602, 0.92323824, 1.01993108, 0.85155992, 0.81416851, 0.98749128, 1.00034192, 0.98763473, 1.05974138, 1.05912658, 0.89772172, 0.97905626, 1.1534306, 0.92304181, 1.16450278, 0.7142307, 0.99846981, 0.79861247, 0.73939835, 0.93776385, 1.0072242, 0.89159707, 1.05514263, 1.05254569, 0.81005146, 0.95179784, 1.00278795, 1.04910398, 0.88427798, 0.74394266, 0.92941178, 0.83622845, 0.84064958, 0.93426956, 1.03619314, 1.22439347, 0.73510451, 0.82997071, 0.90828036, 0.80866989, 1.34078212, 0.85079169, 0.88346039, 0.76871666, 0.96763454, 0.66936914, 0.94175741, 0.97127617, 1.00844382, 0.83449557, 0.88095564, 1.17711652, 1.0547188, 1.04525593, 0.93817487, 0.77978294, 1.36143199, 1.16127997, 1.03792952, 1.03151637, 0.83837387, 0.94326066, 1.0054787, 0.99656841, 1.05575689, 0.97641643, 0.85108163, 0.82631589, 0.77407305, 0.90566132, 0.91308164, 0.95560906, 1.04523011, 1.03773723, 0.97378685, 0.83999133, 1.06926871, 1.01073982, 0.9804959, 1.06473061, 1.25315673, 0.969175, 0.63443508, 0.84574684, 1.06031239, 0.93834605, 1.01784925, 0.93488249, 0.80240225, 0.88757274, 0.9224097, 0.99158962, 0.87412592, 0.76418199, 0.78044069, 1.03117412, 0.82042521, 1.10272129, 1.09673757, 0.89626935, 1.01678612, 0.84911824, 0.95821431, 0.99169558, 0.86853864, 0.92172772, 0.94046199, 0.89750517, 1.09599258, 0.92387291, 1.07770118, 0.98831383, 0.86352396, 0.83079533, 0.94431185, 1.12424626, 1.02553104, 0.8357513, 0.97019669, 0.76816092, 1.34011343, 0.86489527, 0.82156358, 1.25529129, 0.86820218, 0.96970237, 0.85850546, 0.97429559, 0.84826078, 1.02498396, 0.72478517, 0.993497, 0.76918521, 0.91079198, 0.80988325, 0.75431095, 1.02918073, 0.88884197, 0.82625507, 0.78564563, 0.91505355, 0.88896863, 0.85882361, 0.81538316, 0.67656235, 0.8564822, 0.82473022, 0.92928331, 0.98068415, 0.82605685, 1.0150412, 1.00631678, 0.92405101, 0.88909552, 0.94873568, 0.87657342, 0.8280683, 0.77596382, 0.96598811, 0.78922426, 0.87637606, 0.98698735, 0.92207026, 0.71487846, 1.03845478, 0.70749745, 1.08603388, 0.92697779, 0.86470448, 0.70119494, 1.00596847, 0.91426549, 1.05318838, 0.79621712, 0.96169742, 0.88053405, 0.98963934, 0.94152997, 0.88413591, 0.75035344, 0.86007123, 0.83713514, 0.91234911, 0.79562744, 0.84099675, 1.0334279, 1.00272243, 0.95359383, 0.84292969, 0.94234155, 0.90190899, 0.97302022, 1.1009829, 1.0148975, 0.99082987, 0.75916515, 0.9204784, 0.94477378, 1.01108683, 1.00038149, 0.9259798, 1.19400436, 0.80191877, 0.79565851, 0.81865924, 0.79003506, 0.8995508, 0.73137983, 0.88336018, 0.7855268, 1.04478073, 0.90857981, 1.16076951, 0.76096486, 0.90004113, 0.83819665, 0.95295365, 1.09911441, 0.78498197, 0.95094991, 0.94333419, 0.95131688, 0.82961049, 1.08001761, 1.06426458, 0.94291798, 1.04381938, 0.90380364, 0.74060138, 0.98701862, 0.72250236, 0.86125293, 0.76488061, 0.9858051, 0.98099677, 0.96849209, 0.90053351, 0.88469597, 0.80688516, 1.06396217, 1.02446023, 0.911863, 0.98837746, 0.91102987, 0.92810392, 1.13526335, 1.00419541, 1.00866175, 0.74352261, 0.91051641, 0.81868428, 0.93538014, 0.87822651, 0.93278572, 1.0356074, 1.25158731, 0.98372647, 0.81335741, 1.06441863, 0.80305786, 0.95201148, 0.90283451, 1.17319519, 0.8984894, 0.88911288, 0.91474736, 0.94512294, 0.92956283, 0.86682085, 1.08937227, 0.94825713, 0.9787145, 1.16747163, 0.80863682, 0.98314119, 0.91052823, 0.80913225, 0.78503169, 0.78751737, 1.08932193, 0.86859845, 0.96847458, 0.93468839, 1.10769915, 1.1769249, 0.84916138, 1.00556408, 0.84508585, 0.92617942, 0.93985886, 1.17303268, 0.81172495, 0.93482682, 1.04082486, 1.03209348, 0.97220394, 0.90274672, 0.93686291, 0.91116431, 1.14814563, 0.83279158, 0.95853283, 1.0261179, 0.95779432, 0.86995883, 0.78164915, 0.89946906, 0.9194465, 0.97919367, 0.92719039, 0.89063569, 0.80847805, 0.81192101, 0.75044535, 0.86819023, 1.03420014, 0.8899434, 0.94899544, 0.9860773, 1.10047297, 1.00243849, 0.82153972, 1.14289945, 0.8604684, 0.87187524, 1.00415032, 0.78460709, 0.86319884, 0.92818335, 1.08892111, 1.06841003, 1.00735918, 1.20775251, 0.72613554, 1.25768191, 1.08573511, 0.89671127, 0.91259535, 1.01414208, 0.87422903, 0.82720677, 0.9568079, 1.00450416, 0.91043845, 0.84095709, 1.08010574, 0.69848293, 0.90769214, 0.94713501, 1.14808251, 1.0605676, 1.21734482, 0.78578521, 1.01516235, 0.94330326, 0.98363817, 0.99650084, 0.74280796, 0.96227123, 0.95741454, 1.00980406, 0.93468092, 1.10098591, 1.18175828, 0.8553791, 0.81713219, 0.82912143, 0.87599518, 1.15006511, 1.03151163, 0.8751847, 1.15701331, 0.73394166, 0.91426368, 0.96953458, 1.13901709, 0.83028721, 1.15742641, 0.9395442, 0.98118552, 0.89585426, 0.74147117, 0.8902096, 1.00212097, 0.97665858, 0.92624514, 0.98006601, 0.9507215, 1.00889825, 1.2406772, 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0.85989778, 0.90588737, 1.22832895, 0.65955579, 0.93828405, 0.88946418, 0.92152859, 0.83168025, 0.93346887, 0.96456078, 0.9039245, 1.03598695, 0.78405559, 1.21739525, 0.79019383, 0.84034646, 1.00273203, 0.96356393, 0.948103, 0.90279217, 1.0187839, 0.91630508, 1.15965854, 0.84203423, 0.98803156, 0.91604459, 0.90986512, 0.93384826, 0.76687038, 0.96251902, 0.80648134, 0.77336547, 0.85720164, 0.9351947, 0.88004728, 0.91083961, 1.06225829, 0.90230812, 0.72383932, 0.8343425, 0.8850996, 1.19037918, 0.93595522, 0.85061223, 0.84330949, 0.82397482, 0.92075047, 0.86129584, 0.99296756, 0.84912251, 0.8569699, 0.75252201, 0.80591772, 1.03902954, 1.04379139, 0.87360195, 0.97452318, 0.93240609, 0.85406409, 1.11717394, 0.95758536, 0.82772817, 0.67947416, 0.85957788, 0.93731268, 0.90349227, 0.79464185, 0.99148637, 0.8461071, 0.95399991, 1.04320664, 0.87290871, 0.96780849, 0.99467159, 0.96421545, 0.80174643, 0.86475812, 0.74421362, 0.85230296, 0.89891758, 0.77589592, 0.98331957, 0.87387233, 0.92023388, 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0.94197599, 0.867015, 0.90709762, 0.75604815, 0.91312261, 0.9286002, 0.74623204, 0.87368702, 0.83879278, 0.92224793, 0.81676402, 0.90355168, 0.92762955, 0.91784037, 0.82273304, 0.75947806, 0.92687078, 0.87971276, 1.15037445, 0.86707445, 0.8611453, 0.91921763, 1.07088129, 1.05150864, 1.02162325, 0.90305964, 0.99912687, 0.87693204, 0.6186911, 0.95526533, 1.15975655, 1.00061222, 0.74608861, 0.954568, 0.84965574, 0.79177899, 0.9741051, 1.0119514, 0.79147502, 0.81367071, 0.87757421, 1.01270813, 0.86044808, 0.9689615, 0.9577413, 0.79480242, 0.76073002, 0.83131288, 0.96379259, 0.84679732, 0.82508685, 0.89977283, 0.86766439, 1.12231836, 0.93058445, 1.04584181, 0.88838751, 0.96615893, 0.98731619, 1.05517799, 1.02860493, 0.98881473, 0.85210319, 0.91497438, 0.9275787, 0.97456134, 0.9011687, 0.69417417, 0.89661214, 0.79038577, 1.08118303, 1.0509366, 0.97813138, 0.85714945, 0.97330329, 0.83611871, 0.99772489, 0.83591193, 0.75592677, 0.85392601, 1.02734573, 0.72404609, 0.83534547, 0.91630472, 0.88463459, 1.12044562, 1.10991104, 0.96047701, 1.12342573, 0.72046647, 0.96852239, 0.89605698, 0.98310243, 0.92300659, 0.87794646, 0.83109321, 1.43297752, 0.80609029, 0.8692251, 0.90254649, 0.81647796, 1.07521371, 1.03942973, 0.96156488, 1.25225334, 1.0265727, 0.9518054, 0.87765718, 1.15552582, 0.79577766, 0.66849239, 0.87236017, 1.03437641, 0.98567811, 0.78463682, 1.09573491, 0.89858959, 0.94056747, 1.16075317, 1.06296054, 0.85844006, 0.95475376, 0.67038747, 0.7924646, 0.94009167, 0.88282093, 0.97711174, 0.9209607, 1.03230176, 0.99981312, 1.12345314, 1.11705968, 1.02453864, 0.91724212, 0.98337942, 0.89195196, 0.83800177, 0.95044243, 0.76543521, 0.8613025, 0.83907753, 0.69333275, 0.84411739, 0.68621941, 0.9847701, 1.13328481, 1.1432074, 0.97156328, 0.86464461, 0.74258211, 0.97319505, 1.11453917, 0.87344741, 0.91382664, 1.01635943, 1.38708812, 0.81377942, 1.3828856, 0.74476285, 0.86657537, 1.1216954, 0.91008346, 0.800862, 0.98356936, 0.92409916, 1.13970543, 0.97547004, 0.99385865, 1.16476579, 0.78678084, 1.003947, 0.81491463, 1.19724322, 0.9173622, 0.93274116, 0.80047839, 0.86798029, 0.9433708, 0.82376832, 1.01726905, 0.81914971, 0.73290844]) class Medpar1(object): ''' The medpar1 data can be found here. https://www.stata-press.com/data/hh2/medpar1 ''' def __init__(self): filename = os.path.join(os.path.dirname(os.path.abspath(__file__)), "stata_medpar1_glm.csv") data = pd.read_csv(filename).to_records() self.endog = data.los dummies = pd.get_dummies(data.admitype, prefix="race", drop_first=True) design = np.column_stack((data.codes, dummies)).astype(float) self.exog = add_constant(design, prepend=False) class InvGaussLog(Medpar1): """ InvGaussLog is used with TestGlmInvgaussLog """ def __init__(self): super(InvGaussLog, self).__init__() filename = os.path.join(os.path.dirname(os.path.abspath(__file__)), "medparlogresids.csv") self.resids = pd.read_csv(filename, sep=',', header=None).values self.null_deviance = 335.1539777981053 # from R, Rpy bug self.params = np.array([0.09927544, -0.19161722, 1.05712336]) self.bse = np.array([0.00600728, 0.02632126, 0.04915765]) self.aic_R = 18545.836421595981 self.aic_Stata = 6.619000588187141 self.deviance = 304.27188306012789 self.scale = 0.10240599519220173 # self.llf = -9268.9182107979905 # from R self.llf = -12162.72308108797 # from Stata, big rounding diff with R self.bic_Stata = -29849.51723280784 self.chi2 = 398.5465213008323 # from Stata not in sm self.df_model = 2 self.df_resid = 3673 self.fittedvalues = np.array([ 7.03292237, 7.03292237, 7.03292237, 7.03292237, 5.76642001, 7.03292237, 7.03292237, 6.36826384, 7.03292237, 7.03292237, 7.03292237, 7.03292237, 7.03292237, 5.76642001, 7.03292237, 5.22145448, 7.03292237, 5.22145448, 4.72799187, 4.72799187, 7.03292237, 7.03292237, 6.36826384, 7.03292237, 5.76642001, 7.03292237, 4.28116479, 7.03292237, 7.03292237, 7.03292237, 5.76642001, 7.03292237, 7.03292237, 7.03292237, 7.03292237, 7.03292237, 3.87656588, 7.03292237, 7.03292237, 4.28116479, 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3.90353806, 5.80654132, 3.53462742, 2.89810483, 5.80654132, 3.53462742, 2.89810483, 4.76088805, 5.80654132, 5.80654132, 5.80654132, 4.31095206, 5.80654132, 4.76088805, 3.90353806, 2.89810483, 4.76088805, 5.80654132, 2.6242144, 3.53462742, 4.31095206, 5.25778406, 5.25778406, 3.20058132, 4.31095206, 4.31095206, 3.20058132, 4.31095206, 5.25778406, 4.31095206, 5.25778406, 3.90353806, 4.31095206, 5.80654132, 5.80654132, 5.80654132, 5.80654132, 3.90353806, 5.80654132, 5.80654132, 5.80654132, 4.31095206, 5.80654132, 5.80654132, 5.80654132, 3.90353806, 5.25778406, 3.90353806, 4.31095206, 4.76088805, 3.90353806, 5.80654132, 5.80654132, 5.80654132, 2.89810483, 5.80654132, 5.80654132, 5.80654132, 5.80654132, 5.80654132, 5.80654132, 5.80654132, 3.90353806, 3.20058132, 5.25778406, 4.76088805, 5.25778406]) class InvGaussIdentity(Medpar1): """ Accuracy is different for R vs Stata ML vs Stata IRLS, we are close. """ def __init__(self): super(InvGaussIdentity, self).__init__() self.params = np.array([0.44538838, -1.05872706, 2.83947966]) self.bse = np.array([0.02586783, 0.13830023, 0.20834864]) filename = os.path.join(os.path.dirname(os.path.abspath(__file__)), "igaussident_resids.csv") self.resids = pd.read_csv(filename, sep=',', header=None).values self.null_deviance = 335.1539777981053 # from R, Rpy bug self.df_null = 3675 self.deviance = 305.33661191013988 self.df_resid = 3673 self.df_model = 2 self.aic_R = 18558.677276882016 self.aic_Stata = 6.619290231464371 self.bic_Stata = -29848.45250412075 self.llf_stata = -12163.25544543151 self.chi2 = 567.1229375785638 # in Stata not sm # self.llf = -9275.3386384410078 # from R self.llf = -12163.25545 # from Stata, big diff with R self.scale = 0.10115387793455666 self.pearson_chi2 = 371.5346609292967 # deviance_p in Stata self.fittedvalues = np.array([ 6.84797506, 6.84797506, 6.84797506, 6.84797506, 5.9571983, 6.84797506, 6.84797506, 6.40258668, 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4.89847125, 5.789248, 5.789248, 4.00769449, 5.789248, 3.56230611, 2.67152936, 5.789248, 3.56230611, 2.67152936, 4.89847125, 5.789248, 5.789248, 5.789248, 4.45308287, 5.789248, 4.89847125, 4.00769449, 2.67152936, 4.89847125, 5.789248, 2.22614098, 3.56230611, 4.45308287, 5.34385962, 5.34385962, 3.11691773, 4.45308287, 4.45308287, 3.11691773, 4.45308287, 5.34385962, 4.45308287, 5.34385962, 4.00769449, 4.45308287, 5.789248, 5.789248, 5.789248, 5.789248, 4.00769449, 5.789248, 5.789248, 5.789248, 4.45308287, 5.789248, 5.789248, 5.789248, 4.00769449, 5.34385962, 4.00769449, 4.45308287, 4.89847125, 4.00769449, 5.789248, 5.789248, 5.789248, 2.67152936, 5.789248, 5.789248, 5.789248, 5.789248, 5.789248, 5.789248, 5.789248, 4.00769449, 3.11691773, 5.34385962, 4.89847125, 5.34385962]) class Committee(object): def __init__(self): self.resids = np.array([ [-5.04950800e-01, -6.29721800e-01, -8.35499100e+01, -1.30628500e+00, -6.62028600e+00], [-2.34152200e-01, -2.55423500e-01, -2.16830700e+02, -7.58866000e-01, -7.18370200e+00], [1.02423700e+00, 7.98775800e-01, 4.83736300e+02, 2.50351500e+00, 2.25135300e+01], [-2.85061700e-01, -3.17796600e-01, -7.04115100e+04, -2.37991800e+00, -1.41745600e+02], [2.09902500e-01, 1.96787700e-01, 2.24751400e+03, 9.51945500e-01, 2.17724200e+01], [-4.03483500e-01, -4.75741500e-01, -1.95633600e+04, -2.63502600e+00, -8.89461400e+01], [-1.64413400e-01, -1.74401100e-01, -1.73310300e+04, -1.16235500e+00, -5.34213500e+01], [-4.29607700e-01, -5.13466700e-01, -5.30037000e+03, -2.24496200e+00, -4.78260300e+01], [3.23713000e-01, 2.94184600e-01, 4.11079400e+03, 1.48684400e+00, 3.65598400e+01], [1.50367200e-01, 1.43429400e-01, 7.28532100e+03, 8.85542900e-01, 3.31355000e+01], [4.21288600e-01, 3.73428000e-01, 1.37315700e+03, 1.52133200e+00, 2.41570200e+01], [4.50658700e-01, 3.96586700e-01, 1.70146900e+03, 1.66177900e+00, 2.78032600e+01], [2.43537500e-01, 2.26174000e-01, 3.18402300e+03, 1.13656200e+00, 2.79073400e+01], [1.05182900e+00, 8.16205400e-01, 6.00135200e+03, 3.89079700e+00, 7.97131300e+01], [-5.54450300e-01, -7.12749000e-01, -2.09485200e+03, -2.45496500e+00, -3.42189900e+01], [-6.05750600e-01, -8.06411100e-01, -2.74738200e+02, -1.90774400e+00, -1.30510500e+01], [-3.41215700e-01, -3.90244600e-01, -6.31138000e+02, -1.27022900e+00, -1.47600100e+01], [2.21898500e-01, 2.07328700e-01, 6.91135800e+02, 8.16876400e-01, 1.24392900e+01], [2.45592500e-01, 2.26639200e-01, 1.99250600e-01, 2.57948300e-01, 2.74723700e-01], [-7.58952600e-01, -1.15300800e+00, -2.56739000e+02, -2.40716600e+00, -1.41474200e+01]]) self.null_deviance = 27.81104693643434 # from R, Rpy bug self.params = np.array([ -0.0268147, 1.25103364, 2.91070663, -0.34799563, 0.00659808, -0.31303026, -6.44847076]) self.bse = np.array([ 1.99956263e-02, 4.76820254e-01, 6.48362654e-01, 4.17956107e-01, 1.41512690e-03, 1.07770186e-01, 1.99557656e+00]) self.aic_R = 216.66573352377935 self.aic_Stata = 10.83328660860436 self.deviance = 5.615520158267981 self.scale = 0.38528595746569905 self.llf = -101.33286676188968 # from R self.llf_Stata = -101.3328660860436 # same as R self.bic_Stata = -33.32900074962649 self.chi2 = 5.008550263545408 self.df_model = 6 self.df_resid = 13 self.fittedvalues = np.array([ 12.62019383, 30.18289514, 21.48377849, 496.74068604, 103.23024673, 219.94693494, 324.4301163, 110.82526477, 112.44244488, 219.86056381, 56.84399998, 61.19840382, 114.09290269, 75.29071944, 61.21994387, 21.05130889, 42.75939828, 55.56133536, 0.72532053, 18.14664665]) class Wfs(object): """ Wfs used for TestGlmPoissonOffset Results are from Stata and R. """ def __init__(self): self.resids = glm_test_resids.wfs_resids self.null_deviance = 3731.85161919 # from R self.params = [ .9969348, 1.3693953, 1.6137574, 1.7849111, 1.9764051, .11241858, .15166023, .02297282, -.10127377, -.31014953, -.11709716] self.bse = [ .0527437, .0510688, .0511949, .0512138, .0500341, .0324963, .0283292, .0226563, .0309871, .0552107, .0549118] self.aic_R = 522.14215776 # R adds 2 for dof to AIC self.aic_Stata = 7.459173652869477 # stata divides by nobs # self.deviance = 70.6652992116034 # from Stata self.deviance = 70.665301270867 # from R self.scale = 1.0 self.llf = -250.0710778504317 # from Stata, ours with scale=1 self.bic_Stata = -179.9959200693088 # no bic in R? self.df_model = 10 self.df_resid = 59 # TODO: taken from Stata; not available in sm yet self.chi2 = 2699.138063147485 self.fittedvalues = [ 7.11599, 19.11356, 33.76075, 33.26743, 11.94399, 27.49849, 35.07923, 37.22563, 64.18037, 108.0408, 100.0948, 35.67896, 24.10508, 73.99577, 52.2802, 38.88975, 35.06507, 102.1198, 107.251, 41.53885, 196.3685, 335.8434, 205.3413, 43.20131, 41.98048, 96.65113, 63.2286, 30.78585, 70.46306, 172.2402, 102.5898, 43.06099, 358.273, 549.8983, 183.958, 26.87062, 62.53445, 141.687, 52.47494, 13.10253, 114.9587, 214.803, 90.33611, 18.32685, 592.5995, 457.4376, 140.9273, 3.812064, 111.3119, 97.62744, 57.48056, 19.43552, 130.4872, 151.7268, 69.67963, 13.04879, 721.728, 429.2136, 128.2132, 9.04735, 301.7067, 177.3487, 46.40818, 4.707507, 330.4211, 330.7497, 84.38604, 1456.757, 451.005, 67.51025] class CpunishTweediePower15(object): """ # From R setwd('c:/workspace') data <- read.csv('cpunish.csv', sep=",") library(statmod) library(tweedie) summary(glm(EXECUTIONS ~ INCOME + SOUTH - 1, family=tweedie(var.power=1.5, link.power=1), data=data)) """ def __init__(self): resid_resp = [ 28.90498242, 0.5714367394, 4.3135711827, -3.7417822942, -4.9544111888, 0.4666602184, 0.0747051827, -6.114236142, -1.0048540116, -6.9747602544, -0.7626907093, -0.5688093336, -6.9845579527, -1.1594503855, -0.6365453438, -0.3994222036, -0.732355528] resid_dev = [ 3.83881147757395, 0.113622743768915, 2.01981988071128, -0.938107751845672, -1.29607304923555, 0.316205676540778, 0.045273675744568, -1.69968893354602, -0.699080227540624, -2.1707839733642, -0.568738719015137, -0.451266938413727, -2.17218106358745, -0.774613533242944, -0.493831656345955, -0.336453094366771, -0.551210030548659] resid_pear = [ 6.02294407053171, 0.115516970886608, 2.9148208139849, -0.806210703943481, -1.04601155367613, 0.338668788938945, 0.045708693925888, -1.27176471794657, -0.5964031365026, -1.46974255264233, -0.498557360800493, -0.405777068096011, -1.47045242302365, -0.65086941662954, -0.439928270112046, -0.310433407220704, -0.485001313250992] resid_work = [ 28.9049727916181, 0.571427719513967, 4.31357425907762, -3.74179256698823, -4.9544210736226, 0.466663015515745, 0.0747086948013966, -6.114245735344, -1.00485035431368, -6.97477010217068, -0.76268749374494, -0.568806471745149, -6.98456778258272, -1.15944644619981, -0.636542358439925, -0.399419650775458, -0.732352367853816] self.resid_response = resid_resp self.resid_deviance = resid_dev self.resid_pearson = resid_pear self.resid_working = resid_work # self.null_deviance = 3731.85161919 # N/A self.params = [0.0000471043, 6.4721324886] self.bse = [0.0000246888, 3.5288126173] # self.aic_R = 522.14215776 # R adds 2 for dof to AIC # self.aic_Stata = 7.459173652869477 # stata divides by nobs # self.deviance = 70.6652992116034 # from Stata self.deviance = 36.087307138233 # from R # self.scale = 1.0 # self.llf = -250.0710778504317 # from Stata, ours with scale=1 # self.bic_Stata = -179.9959200693088 # no bic in R? self.df_model = 1 self.df_resid = 15 # TODO: taken from Stata; not available in sm yet # self.chi2 = 2699.138063147485 self.fittedvalues = [ 8.09501758000751, 8.42856326056927, 1.68642881732415, 7.74178229423817, 7.95441118875248, 1.53333978161934, 1.92529481734232, 8.11423614202829, 2.00485401159015, 7.97476025442155, 1.76269070926448, 1.56880933358418, 7.98455795270665, 2.15945038549266, 1.63654534384372, 1.39942220361664, 1.73235552803559] class CpunishTweediePower2(object): """ # From R setwd('c:/workspace') data <- read.csv('cpunish.csv', sep=",") library(statmod) library(tweedie) summary(glm(EXECUTIONS ~ INCOME + SOUTH - 1, family=tweedie(var.power=2, link.power=1), data=data)) """ def __init__(self): resid_resp = [ 28.9397568116168, 0.605199215492085, 4.30845487128123, -3.7059362524505, -4.91921022348665, 0.46200835064931, 0.068864196242604, -6.07952005594693, -1.01093636580438, -6.9396210244365, -0.768038385056284, -0.573568809339664, -6.94944844711606, -1.16600175635393, -0.641510318056987, -0.403667790321936, -0.737611172529194] resid_dev = [ 2.03295746713119, 0.0704291140028282, 1.60058476017728, -0.591230836989137, -0.836067997150736, 0.274690511542166, 0.0352446721149477, -1.13465831620614, -0.625909330466303, -1.5477830210949, -0.520517540529698, -0.421531194473357, -1.54848147513823, -0.684927882583903, -0.45784673829438, -0.320960880764019, -0.505992145923248] resid_pear = [ 3.59043221590711, 0.0720921473930558, 2.54705286789752, -0.480919661289957, -0.621174344999372, 0.300397177607798, 0.0356599448410699, -0.752460543924524, -0.502719222246499, -0.874049404005278, -0.434401419984914, -0.364501892726482, -0.874205109115113, -0.538319857282425, -0.390804925805356, -0.287580717535275, -0.424497254731367] resid_work = [ 28.9397568116168, 0.605199215492085, 4.30845487128123, -3.7059362524505, -4.91921022348665, 0.46200835064931, 0.068864196242604, -6.07952005594693, -1.01093636580438, -6.9396210244365, -0.768038385056284, -0.573568809339664, -6.94944844711606, -1.16600175635393, -0.641510318056987, -0.403667790321936, -0.737611172529194] self.resid_response = resid_resp self.resid_deviance = resid_dev self.resid_pearson = resid_pear self.resid_working = resid_work # self.null_deviance = 3731.85161919 # N/A self.params = [4.72472244209477e-05, 6.43243456540827] self.bse = [1.86839521185429e-05, 3.83231672422612] # self.aic_R = 522.14215776 # R adds 2 for dof to AIC # self.aic_Stata = 7.459173652869477 # stata divides by nobs # self.deviance = 70.6652992116034 # from Stata self.deviance = 15.7840685407599 # from R # self.scale = 1.0 # self.llf = -250.0710778504317 # from Stata, ours with scale=1 # self.bic_Stata = -179.9959200693088 # no bic in R? self.df_model = 1 self.df_resid = 15 # TODO: taken from Stata; not available in sm yet # self.chi2 = 2699.138063147485 self.fittedvalues = [ 8.06024318838318, 8.39480078450791, 1.69154512871877, 7.7059362524505, 7.91921022348665, 1.53799164935069, 1.9311358037574, 8.07952005594693, 2.01093636580438, 7.9396210244365, 1.76803838505628, 1.57356880933966, 7.94944844711606, 2.16600175635393, 1.64151031805699, 1.40366779032194, 1.73761117252919] class CpunishTweedieLog1(object): """ # From R setwd('c:/workspace') data <- read.csv('cpunish.csv', sep=",") library(statmod) library(tweedie) summary(glm(EXECUTIONS ~ INCOME + SOUTH - 1, family=tweedie(var.power=1, link.power=0), data=data)) """ def __init__(self): resid_resp = [ 28.7231009386298, -0.307318358456484, 4.19015460156576, -3.30975297068573, -4.87746969906705, 0.285041779927669, 0.0315071085472043, -6.33304532673002, -1.02436294926752, -6.9340610414309, -0.859055122126197, -0.736490247380883, -6.96145354225969, -1.13750232106315, -0.778363801217565, -0.636042191521576, -0.839322392162821] resid_dev = [ 7.30513948467594, -0.101296157943519, 2.44987904003561, -1.34021826264378, -1.99062116973315, 0.212014827300475, 0.0223969676885324, -2.63775728156667, -0.798884085657077, -3.11862021596631, -0.691356293575324, -0.607658243497501, -3.12628915913493, -0.869326536299756, -0.636663290048755, -0.536212950673418, -0.67812263418512] resid_pear = [ 9.98383729954486, -0.100734032611758, 3.11465040934513, -1.22417704160631, -1.73780566805242, 0.217661565866984, 0.0224564769560215, -2.19386916576256, -0.719962160947025, -2.46172701579962, -0.630049829146329, -0.558895774299477, -2.4671965358931, -0.778034748813176, -0.583676657782738, -0.497265896656757, -0.61887064145702] resid_work = [ 3.47027319357873, -0.0330190014589175, 2.31520029566659, -0.452785885372436, -0.619167053050639, 0.166209168591668, 0.0160057009522403, -0.759991705123147, -0.506017436072008, -0.873961141113221, -0.46209233491888, -0.424125760851072, -0.874394795536774, -0.532164250702372, -0.437685360377137, -0.388768819543728, -0.456321521305397] self.resid_response = resid_resp self.resid_deviance = resid_dev self.resid_working = resid_work self.resid_pearson = resid_pear # self.null_deviance = 3731.85161919 # N/A self.params = [1.65700638623525e-05, 1.54257997850499] self.bse = [1.81044999017907e-05, 0.725739640176733] # self.aic_R = 522.14215776 # R adds 2 for dof to AIC # self.aic_Stata = 7.459173652869477 # stata divides by nobs # self.deviance = 70.6652992116034 # from Stata self.deviance = 95.0325613464258 # from R # self.scale = 1.0 # self.llf = -250.0710778504317 # from Stata, ours with scale=1 # self.bic_Stata = -179.9959200693088 # no bic in R? self.df_model = 1 self.df_resid = 15 # TODO: taken from Stata; not available in sm yet # self.chi2 = 2699.138063147485 self.fittedvalues = [ 8.27689906137016, 9.30731835845648, 1.80984539843424, 7.30975297068573, 7.87746969906705, 1.71495822007233, 1.9684928914528, 8.33304532673002, 2.02436294926752, 7.9340610414309, 1.8590551221262, 1.73649024738088, 7.96145354225969, 2.13750232106315, 1.77836380121756, 1.63604219152158, 1.83932239216282] class FairTweedieLog15(object): """ # From R setwd('c:/workspace') data <- read.csv('fair.csv', sep=",") library(statmod) library(tweedie) model <- glm(affairs ~ rate_marriage + age + yrs_married -1, data=data, family=tweedie(var.power=1.5, link.power = 0)) r <- resid(model, type='response') paste(as.character(r[1:17]), collapse=",") r <- resid(model, type='deviance') paste(as.character(r[1:17]), collapse=",") r <- resid(model, type='pearson') paste(as.character(r[1:17]), collapse=",") r <- resid(model, type='working') paste(as.character(r[1:17]), collapse=",") paste(as.character(model$coefficients[1:17]), collapse=",") s <- summary(model) paste(as.character(sqrt(diag(s$cov.scaled))), collapse=",") s$deviance paste(as.character(model$fitted.values[1:17]), collapse=",") """ def __init__(self): resid_resp = [ -0.997868449815039, 2.69283106662728, 0.677397439981157, 0.220024942629269, 4.30244966465517, 4.12917275616972, 0.669303122309246, 1.64321562230925, 3.73361710426128, 0.271937359562684, 1.70030700747884, 1.55430573164611, -0.263723852468304, 1.51263973164611, 2.75223392654071, 0.310487741565721, 1.28077676333896, -0.722602160018842] resid_dev = [ -1.40274708439925, 2.48476334070913, 0.722690630291423, 0.333179337353702, 4.00781035212304, 3.33344591331998, 1.51543361886727, 2.82502498800952, 2.2795411865605, 0.245239170945663, 0.993721205729013, 1.74920359743562, -0.363141475997386, 1.71412357710318, 2.57445879456298, 0.279858474280908, 1.22953362433333, -1.84397406923697] resid_pear = [ -0.923380371255914, 4.28706294677515, 0.864309147553743, 0.366063826152319, 9.17690493704408, 6.57783985712941, 2.39340023647571, 5.87607098775551, 3.55791152198837, 0.260052421285998, 1.21439278430259, 2.66470328868695, -0.327698246542009, 2.59327105694137, 4.53096038849505, 0.299198418236691, 1.6399313081981, -0.921987034618483] resid_work = [ -0.899807800767353, 5.00583784559752, 0.937441759049674, 0.433762277766879, 11.8128959278604, 7.6822784352496, 3.65998654763585, 8.98568506862295, 3.50120010377224, 0.256207345500911, 1.08551656668241, 3.18923357641756, -0.352302468597673, 3.10374035363038, 5.35005901385941, 0.29552727652976, 1.78077778644209, -1] self.resid_response = resid_resp self.resid_deviance = resid_dev self.resid_working = resid_work self.resid_pearson = resid_pear # self.null_deviance = 3731.85161919 # N/A self.params = [ -0.389168171340452, 0.0670222370664611, -0.0970852004566712] self.bse = [ 0.0323435784513691, 0.0063805300018014, 0.00893580175352525] # self.aic_R = 522.14215776 # R adds 2 for dof to AIC # self.aic_Stata = 7.459173652869477 # stata divides by nobs # self.deviance = 70.6652992116034 # from Stata self.deviance = 20741.82 # from R # self.scale = 1.0 # self.llf = -250.0710778504317 # from Stata, ours with scale=1 # self.bic_Stata = -179.9959200693088 # no bic in R? self.df_model = 2 self.df_resid = 6363 # TODO: taken from Stata; not available in sm yet # self.chi2 = 2699.138063147485 self.fittedvalues = [ 1.10897954981504, 0.537938133372725, 0.722602160018842, 0.507247757370731, 0.364216335344828, 0.537493243830281, 0.182870377690754, 0.182870377690754, 1.06638209573872, 1.06139564043732, 1.56635749252116, 0.487360268353893, 0.748572252468304, 0.487360268353893, 0.514430573459285, 1.05062295843428, 0.71922323666104, 0.722602160018842] statsmodels-0.12.2/statsmodels/genmod/tests/results/results_glm_poisson_weights.py000066400000000000000000002720261400612667500310520ustar00rootroot00000000000000import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch est = dict( deviance=18.59164098607571, dispers=1.859164098607571, deviance_s=18.59164098607571, dispers_s=1.859164098607571, deviance_p=24.75374834715614, dispers_p=2.475374834715614, deviance_ps=24.75374834715614, dispers_ps=2.475374834715614, bic=-9.740492454486454, nbml=0, N=17, ic=3, k=7, k_eq=1, k_dv=1, converged=1, k_autoCns=0, ll=-31.92732830809848, chi2=128.8021169250575, p=2.29729497374e-25, rc=0, aic=4.579685683305704, rank=7, canonical=1, power=0, df_m=6, df=10, vf=1, phi=1, k_eq_model=0, properties="b V", depvar="executions", which="max", technique="nr", singularHmethod="m-marquardt", ml_method="e2", crittype="log likelihood", user="glim_lf", title="Generalized linear models", opt="moptimize", chi2type="Wald", link="glim_l03", varfunc="glim_v3", m="1", a="1", oim="oim", opt1="ML", varfuncf="u", varfunct="Poisson", linkf="ln(u)", linkt="Log", vce="oim", vcetype="OIM", hac_lag="15", marginsok="default", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 predict="glim_p", cmd="glm", cmdline="glm executions income perpoverty perblack LN_VC100k96 south degree, family(poisson)", # noqa:E501 ) params_table = np.array([ .00026110166569, .00005187148786, 5.0336259178483, 4.812884279e-07, .00015943541766, .00036276791372, np.nan, 1.9599639845401, 0, .07781804809828, .07940260798777, .98004398180811, .32706440886796, -.0778082038363, .23344430003287, np.nan, 1.9599639845401, 0, -.09493110013466, .02291930335216, -4.1419714498302, .00003443332141, -.13985210925565, -.05001009101367, np.nan, 1.9599639845401, 0, .29693462055586, .43751760764129, .67868038993144, .49734039404176, -.5605841330232, 1.1544533741349, np.nan, 1.9599639845401, 0, 2.3011832004524, .42838381728481, 5.3717790159251, 7.796361708e-08, 1.4615663470144, 3.1408000538904, np.nan, 1.9599639845401, 0, -18.722067603077, 4.2839791307242, -4.3702518223781, .00001241033322, -27.118512409818, -10.325622796337, np.nan, 1.9599639845401, 0, -6.8014789919532, 4.146873025502, -1.6401464308471, .10097472438129, -14.929200770398, 1.3262427864914, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 2.690651253e-09, 1.942168909e-06, 9.445812833e-08, 4.703695025e-06, -6.082922480e-06, -.00008108248895, -.00013492774575, 1.942168909e-06, .00630477415526, .00017467012687, .00328093520848, -.01768604570302, .11117887243846, -.19441636422025, 9.445812833e-08, .00017467012687, .00052529446615, -.00313545508833, -.00516707569472, -.03253594627601, .01688876616272, 4.703695025e-06, .00328093520848, -.00313545508833, .19142165699616, -.00179497953339, .30391667530759, -1.4489146451821, -6.082922480e-06, -.01768604570302, -.00516707569472, -.00179497953339, .18351269491151, .3016848477378, .36484063612427, -.00008108248895, .11117887243846, -.03253594627601, .30391667530759, .3016848477378, 18.352477192481, -4.0741043266703, -.00013492774575, -.19441636422025, .01688876616272, -1.4489146451821, .36484063612427, -4.0741043266703, 17.196555889636]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 17, np.nan, -31.927328308098, 7, 77.854656616197, 83.68715002459]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 35.226364135742, .16681243479252, .98022246360779, 8.1965742111206, .33106967806816, .89840310811996, 1.3118965625763, .29945519566536, .11764223873615, 3.6862981319427, .35516858100891, .46500706672668, 2.0823004245758, .3434439599514, .24561515450478, 1.0650315284729, .62310123443604, .41350400447845, 1.9260421991348, .40797635912895, .32057955861092, 2.4171404838562, .36215576529503, .31702440977097, 1.8473218679428, .3869916498661, .27665960788727, 2.8643238544464, .43869277834892, .55124300718307, 3.1211984157562, .44224792718887, .61045408248901, 3.338207244873, .42789322137833, .61120104789734, 2.5269968509674, .42458593845367, .45554983615875, .89725440740585, .59187793731689, .31432569026947, .97933322191238, .37813624739647, .14003194868565, .53462094068527, .38791963458061, .08045063912868, 1.9790935516357, .31954729557037, .20208616554737]).reshape(17, 3) predicted_colnames = 'predict_mu predict_linpred_std predict_hat'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] resids = np.array([ 1.773634314537, 1.773634314537, .29638093709946, .29637759923935, .2988341152668, .05034962296486, .80342543125153, .80342543125153, .27623143792152, .27622014284134, .28062695264816, .09801965206861, 4.6881031990051, 4.6881031990051, 3.0157172679901, 2.977787733078, 4.0930528640747, 3.5735311508179, .31370183825493, .31370183825493, .1611547768116, .16114975512028, .16338862478733, .08509942144156, .91769951581955, .91769951581955, .59656941890717, .59618371725082, .63595855236053, .44071426987648, .9349684715271, .9349684715271, .80822360515594, .80661898851395, .90597397089005, .87787866592407, .07395775616169, .07395775616169, .05295527353883, .05295492336154, .05329062789679, .03839882463217, -.41714036464691, -.41714036464691, -.27668312191963, -.27663832902908, -.2683065533638, -.17257598042488, -.84732186794281, -.84732186794281, -.68459099531174, -.68349820375443, -.6234148144722, -.458675801754, -1.8643238544464, -1.8643238544464, -1.2799508571625, -1.274356007576, -1.1015654802322, -.65087747573853, -2.1211984157562, -2.1211984157562, -1.4092296361923, -1.4021278619766, -1.2006615400314, -.67961025238037, -2.338207244873, -2.338207244873, -1.5136297941208, -1.5051733255386, -1.2797535657883, -.70043802261353, -1.5269968509674, -1.5269968509674, -1.0992211103439, -1.0954134464264, -.9605849981308, -.60427337884903, .10274560004473, .10274560004473, .10649761557579, .1064917370677, .10846894979477, .11451110988855, .02066676132381, .02066676132381, .02081091701984, .02081087417901, .02088368684053, .02110289037228, .46537905931473, .46537905931473, .56824368238449, .56713002920151, .63647866249084, .87048417329788, -.97909361124039, -.97909361124039, -.77151334285736, -.77000600099564, -.69597083330154, -.49471819400787]).reshape(17, 6) resids_colnames = ['score_factor', 'resid_response', 'resid_anscombe', 'resid_deviance', 'resid_pearson', 'resid_working'] resids_rownames = ['r'+str(n) for n in range(1, 18)] results_poisson_none_nonrobust = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, resids=resids, resids_colnames=resids_colnames, resids_rownames=resids_rownames, **est ) est = dict( deviance=23.34969514421719, dispers=.8980651978545075, deviance_s=23.34969514421719, dispers_s=.8980651978545075, deviance_p=30.06164170990202, dispers_p=1.156216988842385, deviance_ps=30.06164170990202, dispers_ps=1.156216988842385, bic=-67.5595014539113, nbml=0, N=33, ic=3, k=7, k_eq=1, k_dv=1, converged=1, k_autoCns=0, ll=-52.96941847346162, chi2=183.6836771894393, p=5.59891844113e-37, rc=0, aic=3.634510210512826, rank=7, canonical=1, power=0, df_m=6, df=26, vf=1, phi=1, k_eq_model=0, properties="b V", depvar="executions", which="max", technique="nr", singularHmethod="m-marquardt", ml_method="e2", crittype="log likelihood", user="glim_lf", title="Generalized linear models", opt="moptimize", chi2type="Wald", wtype="fweight", wexp="= fweight", link="glim_l03", varfunc="glim_v3", m="1", a="1", oim="oim", opt1="ML", varfuncf="u", varfunct="Poisson", linkf="ln(u)", linkt="Log", vce="oim", vcetype="OIM", hac_lag="15", marginsok="default", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 predict="glim_p", cmd="glm", cmdline="glm executions income perpoverty perblack LN_VC100k96 south degree [fweight=fweight], family(poisson)", # noqa:E501 ) params_table = np.array([ .00025343868829, .00004015414514, 6.3116444744157, 2.760858933e-10, .00017473800999, .00033213936659, np.nan, 1.9599639845401, 0, .09081422305585, .06472607217881, 1.4030547505642, .16060051303473, -.03604654727537, .21767499338706, np.nan, 1.9599639845401, 0, -.09416451429381, .01795769655821, -5.2436855689475, 1.574003474e-07, -.12936095279319, -.05896807579442, np.nan, 1.9599639845401, 0, .27652273809506, .38626128010796, .7158955669017, .47405583598111, -.48053545953887, 1.033580935729, np.nan, 1.9599639845401, 0, 2.239890838384, .36339399714255, 6.1638080320445, 7.101602988e-10, 1.5276516917866, 2.9521299849815, np.nan, 1.9599639845401, 0, -18.842583191417, 3.736940161486, -5.0422491067996, 4.600917913e-07, -26.16685132031, -11.518315062523, np.nan, 1.9599639845401, 0, -6.5630017977416, 3.2352486362722, -2.0285927097411, .04249979172538, -12.903972605867, -.22203098961573, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 1.612355372e-09, 1.270985149e-06, 8.789752394e-08, -1.636449642e-07, -3.213686689e-06, -.00005643188411, -.00006199883309, 1.270985149e-06, .0041894644197, .00016567874308, -.00066453618021, -.00943379587945, .07218307550995, -.11262571631082, 8.789752394e-08, .00016567874308, .00032247886568, -.00355795369216, -.00391377556228, -.01880905186772, .01900717143416, -1.636449642e-07, -.00066453618021, -.00355795369216, .14919777651064, .02481983169552, .26952997380446, -.95915288407306, -3.213686689e-06, -.00943379587945, -.00391377556228, .02481983169552, .13205519715924, .44364186152042, -.0298149336078, -.00005643188411, .07218307550995, -.01880905186772, .26952997380446, .44364186152042, 13.964721770527, -3.6510403528048, -.00006199883309, -.11262571631082, .01900717143416, -.95915288407306, -.0298149336078, -3.6510403528048, 10.466833738501]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 33, np.nan, -52.969418473462, 7, 119.93883694692, 130.41438987719]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 34.815238952637, .16658315062523, .96612107753754, 7.3026847839355, .32757967710495, .78363972902298, 1.2540435791016, .26076200604439, .08527097851038, 3.9734709262848, .24942673742771, .24720433354378, 2.0739872455597, .24682784080505, .12635557353497, 1.1471545696259, .45427960157394, .23673823475838, 1.7763512134552, .27608770132065, .13540133833885, 2.2698366641998, .25641229748726, .1492355465889, 1.6349502801895, .27634221315384, .12485299259424, 2.7504913806915, .39550569653511, .43024495244026, 2.862185716629, .39729079604149, .45176732540131, 3.5617923736572, .39150056242943, .54592549800873, 2.6135795116425, .29556328058243, .22831618785858, .775799036026, .40655690431595, .12823067605495, .93375068902969, .29390665888786, .08065843582153, .56681954860687, .28863781690598, .04722274839878, 1.8914022445679, .21889741718769, .09062857925892]).reshape(17, 3) predicted_colnames = 'predict_mu predict_linpred_std predict_hat'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] resids = np.array([ 2.1847612857819, 2.1847612857819, .36650228500366, .36649596691132, .3702706694603, .06275302171707, 1.6973150968552, 1.6973150968552, .60597640275955, .60585051774979, .62808901071548, .23242343962193, 4.7459564208984, 4.7459564208984, 3.0897438526154, 3.0483965873718, 4.2380628585815, 3.7845225334167, .02652905881405, .02652905881405, .01329397037625, .01329396758229, .01330873556435, .00667654490098, .92601269483566, .92601269483566, .60273587703705, .60233747959137, .64300429821014, .44648909568787, .8528453707695, .8528453707695, .72065913677216, .71955502033234, .7962681055069, .7434441447258, .22364875674248, .22364875674248, .16446639597416, .16445553302765, .16780391335487, .12590345740318, -.26983660459518, -.26983660459518, -.1828535348177, -.18284019827843, -.1791032999754, -.11887931078672, -.63495022058487, -.63495022058487, -.53598040342331, -.53542107343674, -.49657794833183, -.38836058974266, -1.7504912614822, -1.7504912614822, -1.2204585075378, -1.2154930830002, -1.0554916858673, -.63642859458923, -1.862185716629, -1.862185716629, -1.2788465023041, -1.2732635736465, -1.1007128953934, -.65061664581299, -2.5617923736572, -2.5617923736572, -1.617108464241, -1.6071890592575, -1.3574055433273, -.71924245357513, -1.6135795116425, -1.6135795116425, -1.1469231843948, -1.1426799297333, -.99809640645981, -.61738300323486, .22420094907284, .22420094907284, .24363535642624, .24356025457382, .25454398989677, .28899359703064, .06624934077263, .06624934077263, .06777309626341, .06777160614729, .06855925172567, .07094971090555, .43318045139313, .43318045139313, .51954871416092, .51871728897095, .57536894083023, .76422989368439, -.89140218496323, -.89140218496323, -.7140833735466, -.7128586769104, -.64815932512283, -.47129172086716]).reshape(17, 6) resids_colnames = ['score_factor', 'resid_response', 'resid_anscombe', 'resid_deviance', 'resid_pearson', 'resid_working'] resids_rownames = ['r'+str(n) for n in range(1, 18)] results_poisson_fweight_nonrobust = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, resids=resids, resids_colnames=resids_colnames, resids_rownames=resids_rownames, **est ) est = dict( deviance=12.02863083186947, dispers=1.202863083186947, deviance_s=12.02863083186947, dispers_s=1.202863083186947, deviance_p=15.48630027479802, dispers_p=1.548630027479802, deviance_ps=15.48630027479802, dispers_ps=1.548630027479802, bic=-16.30350260869269, nbml=0, N=17, ic=3, k=7, k_eq=1, k_dv=1, converged=1, k_autoCns=0, ll=-27.28727618329841, chi2=94.62492461274286, p=3.30927661191e-18, rc=0, aic=4.033797198035106, rank=7, canonical=1, power=0, df_m=6, df=10, vf=1, phi=1, k_eq_model=0, properties="b V", depvar="executions", which="max", technique="nr", singularHmethod="m-marquardt", ml_method="e2", crittype="log likelihood", user="glim_lf", title="Generalized linear models", opt="moptimize", chi2type="Wald", wtype="aweight", wexp="= fweight", link="glim_l03", varfunc="glim_v3", m="1", a="1", oim="oim", opt1="ML", varfuncf="u", varfunct="Poisson", linkf="ln(u)", linkt="Log", vce="oim", vcetype="OIM", hac_lag="15", marginsok="default", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 predict="glim_p", cmd="glm", cmdline="glm executions income perpoverty perblack LN_VC100k96 south degree [aweight=fweight], family(poisson)", # noqa:E501 ) params_table = np.array([ .00025343868829, .00005594520811, 4.5301232557793, 5.894928560e-06, .00014378809529, .00036308928129, np.nan, 1.9599639845401, 0, .09081422305585, .09018031800722, 1.0070293059798, .31392069129295, -.08593595235267, .26756439846436, np.nan, 1.9599639845401, 0, -.09416451429381, .02501975991718, -3.7636058301716, .00016748080115, -.14320234263332, -.04512668595429, np.nan, 1.9599639845401, 0, .27652273809507, .53816281293549, .51382728692594, .60737274844619, -.77825699307725, 1.3313024692674, np.nan, 1.9599639845401, 0, 2.239890838384, .50630271729905, 4.424015044464, 9.688326910e-06, 1.2475557472031, 3.2322259295649, np.nan, 1.9599639845401, 0, -18.842583191417, 5.2065333302747, -3.6190267105084, .00029571311817, -29.047201003062, -8.6379653797707, np.nan, 1.9599639845401, 0, -6.5630017977417, 4.5075460479893, -1.4560032727052, .14539171490364, -15.397629710457, 2.2716261149733, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 3.129866310e-09, 2.467206465e-06, 1.706246053e-07, -3.176637541e-07, -6.238332985e-06, -.00010954424563, -.000120350676, 2.467206465e-06, .00813248975588, .00032161167774, -.00128998199687, -.01831266258952, .14012008775466, -.21862639048575, 1.706246053e-07, .00032161167774, .00062598838631, -.00690661599067, -.00759732903266, -.03651168891971, .03689627396044, -3.176637541e-07, -.00128998199687, -.00690661599067, .28961921322663, .04817967329131, .52320524326798, -1.8618850102603, -6.238332985e-06, -.01831266258952, -.00759732903266, .04817967329131, .2563424415444, .86118714295143, -.05787604759173, -.00010954424563, .14012008775466, -.03651168891971, .52320524326798, .86118714295143, 27.107989319261, -7.0873136260377, -.000120350676, -.21862639048575, .03689627396044, -1.8618850102603, -.05787604759173, -7.0873136260377, 20.317971374744]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 17, np.nan, -27.287276183298, 7, 68.574552366597, 74.40704577499]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 34.815238952637, .23209382593632, 1.8754115104675, 7.3026847839355, .45640400052071, 1.521183013916, 1.2540435791016, .36330956220627, .16552601754665, 3.9734709262848, .34751656651497, .47986721992493, 2.0739872455597, .34389564394951, .2452784627676, 1.1471545696259, .63293009996414, .45955070853233, 1.7763512134552, .38466224074364, .2628378868103, 2.2698366641998, .35724925994873, .28969252109528, 1.6349502801895, .38501682877541, .24236169457436, 2.7504913806915, .55104273557663, .83518141508102, 2.862185716629, .55352979898453, .87696009874344, 3.5617923736572, .54546248912811, 1.0597376823425, 2.6135795116425, .41179683804512, .44320201873779, .775799036026, .5664399266243, .24891836941242, .93375068902969, .40948873758316, .15657225251198, .56681954860687, .40214782953262, .09166768193245, 1.8914022445679, .30498126149178, .17592607438564]).reshape(17, 3) predicted_colnames = 'predict_mu predict_linpred_std predict_hat'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] resids = np.array([ 2.1847612857819, 2.1847612857819, .36650228500366, .36649596691132, .3702706694603, .06275302171707, 1.6973150968552, 1.6973150968552, .60597640275955, .60585051774979, .62808901071548, .23242343962193, 4.7459564208984, 4.7459564208984, 3.0897438526154, 3.0483965873718, 4.2380628585815, 3.7845225334167, .02652905881405, .02652905881405, .01329397037625, .01329396758229, .01330873556435, .00667654490098, .92601269483566, .92601269483566, .60273587703705, .60233747959137, .64300429821014, .44648909568787, .8528453707695, .8528453707695, .72065913677216, .71955502033234, .7962681055069, .7434441447258, .22364875674248, .22364875674248, .16446639597416, .16445553302765, .16780391335487, .12590345740318, -.26983660459518, -.26983660459518, -.1828535348177, -.18284019827843, -.1791032999754, -.11887931078672, -.63495022058487, -.63495022058487, -.53598040342331, -.53542107343674, -.49657794833183, -.38836058974266, -1.7504912614822, -1.7504912614822, -1.2204585075378, -1.2154930830002, -1.0554916858673, -.63642859458923, -1.862185716629, -1.862185716629, -1.2788465023041, -1.2732635736465, -1.1007128953934, -.65061664581299, -2.5617923736572, -2.5617923736572, -1.617108464241, -1.6071890592575, -1.3574055433273, -.71924245357513, -1.6135795116425, -1.6135795116425, -1.1469231843948, -1.1426799297333, -.99809640645981, -.61738300323486, .22420094907284, .22420094907284, .24363535642624, .24356025457382, .25454398989677, .28899359703064, .06624934077263, .06624934077263, .06777309626341, .06777160614729, .06855925172567, .07094971090555, .43318045139313, .43318045139313, .51954871416092, .51871728897095, .57536894083023, .76422989368439, -.89140218496323, -.89140218496323, -.7140833735466, -.7128586769104, -.64815932512283, -.47129172086716]).reshape(17, 6) resids_colnames = ['score_factor', 'resid_response', 'resid_anscombe', 'resid_deviance', 'resid_pearson', 'resid_working'] resids_rownames = ['r'+str(n) for n in range(1, 18)] results_poisson_aweight_nonrobust = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, resids=resids, resids_colnames=resids_colnames, resids_rownames=resids_rownames, **est ) est = dict( deviance=23.34969514421719, dispers=2.33496951442172, deviance_s=23.34969514421719, dispers_s=2.33496951442172, deviance_p=30.06164170990202, dispers_p=3.006164170990202, deviance_ps=30.06164170990202, dispers_ps=3.006164170990202, bic=-4.982438296344967, nbml=0, N=17, ic=3, k=7, k_eq=1, k_dv=1, converged=1, k_autoCns=0, ll=-52.96941847346162, chi2=356.6637749656061, p=5.72458312679e-74, rc=0, aic=7.055225702760191, rank=7, canonical=1, power=0, df_m=6, df=10, vf=1, phi=1, k_eq_model=0, properties="b V", depvar="executions", which="max", technique="nr", singularHmethod="m-marquardt", ml_method="e2", crittype="log pseudolikelihood", user="glim_lf", title="Generalized linear models", opt="moptimize", chi2type="Wald", wtype="pweight", wexp="= fweight", link="glim_l03", varfunc="glim_v3", m="1", a="1", oim="oim", opt1="ML", varfuncf="u", varfunct="Poisson", linkf="ln(u)", linkt="Log", vcetype="Robust", hac_lag="15", marginsok="default", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 predict="glim_p", cmd="glm", cmdline="glm executions income perpoverty perblack LN_VC100k96 south degree [pweight=fweight], family(poisson)", # noqa:E501 ) params_table = np.array([ .00025343868829, .0000298866597, 8.4799937786829, 2.252059827e-17, .00019486191167, .00031201546491, np.nan, 1.9599639845401, 0, .09081422305585, .08414617969117, 1.0792435662456, .28047916301946, -.07410925857549, .25573770468718, np.nan, 1.9599639845401, 0, -.09416451429381, .01946961498728, -4.8364856909253, 1.321547815e-06, -.13232425846174, -.05600477012587, np.nan, 1.9599639845401, 0, .27652273809506, .36112179485191, .76573261995571, .44383541350407, -.43126297384714, .98430845003726, np.nan, 1.9599639845401, 0, 2.239890838384, .43098853454849, 5.1971007551989, 2.024206636e-07, 1.3951688329193, 3.0846128438487, np.nan, 1.9599639845401, 0, -18.842583191417, 4.5147658917489, -4.1735460139479, .00002998950578, -27.691361737874, -9.9938046449589, np.nan, 1.9599639845401, 0, -6.5630017977416, 3.3999612612355, -1.930316639948, .0535676165153, -13.226803418595, .10079982311137, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 8.932124278e-10, 1.512127962e-06, 1.877263788e-07, -4.562869239e-06, -2.023379829e-06, -.00001228516761, -.00002423071544, 1.512127962e-06, .00708057955662, .00028427703202, -.0019549511748, -.00596332288528, .20022061835302, -.18678265108673, 1.877263788e-07, .00028427703202, .00037906590775, -.00453407701816, -.00623061980467, -.04659404972535, .02694184589715, -4.562869239e-06, -.0019549511748, -.00453407701816, .13040895071706, .0836259691825, .89260578257395, -.82275604425197, -2.023379829e-06, -.00596332288528, -.00623061980467, .0836259691825, .18575111691225, 1.0698498854979, -.64859219982217, -.00001228516761, .20022061835302, -.04659404972535, .89260578257395, 1.0698498854979, 20.383111057299, -12.482192460755, -.00002423071544, -.18678265108673, .02694184589715, -.82275604425197, -.64859219982217, -12.482192460755, 11.559736577902]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 17, np.nan, -52.969418473462, 7, 119.93883694692, 125.77133035532]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 34.815238952637, .06858423352242, 7.3026847839355, .25687274336815, 1.2540435791016, .41320022940636, 3.9734709262848, .16020278632641, 2.0739872455597, .22170753777027, 1.1471545696259, .51121062040329, 1.7763512134552, .2167394310236, 2.2698366641998, .2456086575985, 1.6349502801895, .25546172261238, 2.7504913806915, .4417819082737, 2.862185716629, .61734634637833, 3.5617923736572, .51518148183823, 2.6135795116425, .34006628394127, .775799036026, .292076587677, .93375068902969, .39795544743538, .56681954860687, .31529840826988, 1.8914022445679, .26116076111794]).reshape(17, 2) predicted_colnames = 'predict_mu predict_linpred_std'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] resids = np.array([ 2.1847612857819, 2.1847612857819, .36650228500366, .36649596691132, .3702706694603, .06275302171707, 1.6973150968552, 1.6973150968552, .60597640275955, .60585051774979, .62808901071548, .23242343962193, 4.7459564208984, 4.7459564208984, 3.0897438526154, 3.0483965873718, 4.2380628585815, 3.7845225334167, .02652905881405, .02652905881405, .01329397037625, .01329396758229, .01330873556435, .00667654490098, .92601269483566, .92601269483566, .60273587703705, .60233747959137, .64300429821014, .44648909568787, .8528453707695, .8528453707695, .72065913677216, .71955502033234, .7962681055069, .7434441447258, .22364875674248, .22364875674248, .16446639597416, .16445553302765, .16780391335487, .12590345740318, -.26983660459518, -.26983660459518, -.1828535348177, -.18284019827843, -.1791032999754, -.11887931078672, -.63495022058487, -.63495022058487, -.53598040342331, -.53542107343674, -.49657794833183, -.38836058974266, -1.7504912614822, -1.7504912614822, -1.2204585075378, -1.2154930830002, -1.0554916858673, -.63642859458923, -1.862185716629, -1.862185716629, -1.2788465023041, -1.2732635736465, -1.1007128953934, -.65061664581299, -2.5617923736572, -2.5617923736572, -1.617108464241, -1.6071890592575, -1.3574055433273, -.71924245357513, -1.6135795116425, -1.6135795116425, -1.1469231843948, -1.1426799297333, -.99809640645981, -.61738300323486, .22420094907284, .22420094907284, .24363535642624, .24356025457382, .25454398989677, .28899359703064, .06624934077263, .06624934077263, .06777309626341, .06777160614729, .06855925172567, .07094971090555, .43318045139313, .43318045139313, .51954871416092, .51871728897095, .57536894083023, .76422989368439, -.89140218496323, -.89140218496323, -.7140833735466, -.7128586769104, -.64815932512283, -.47129172086716]).reshape(17, 6) resids_colnames = ['score_factor', 'resid_response', 'resid_anscombe', 'resid_deviance', 'resid_pearson', 'resid_working'] resids_rownames = ['r'+str(n) for n in range(1, 18)] results_poisson_pweight_nonrobust = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, resids=resids, resids_colnames=resids_colnames, resids_rownames=resids_rownames, **est ) est = dict( k_eq_model=0, phi=1, vf=1, df=10, df_m=6, power=0, canonical=1, rank=7, aic=4.579685683305704, rc=0, p=5.09268495340e-76, chi2=366.2131475852884, ll=-31.92732830809848, k_autoCns=0, converged=1, k_dv=1, k_eq=1, k=7, ic=3, N=17, nbml=0, bic=-9.740492454486454, dispers_ps=2.475374834715614, deviance_ps=24.75374834715614, dispers_p=2.475374834715614, deviance_p=24.75374834715614, dispers_s=1.859164098607571, deviance_s=18.59164098607571, dispers=1.859164098607571, deviance=18.59164098607571, cmdline="glm executions income perpoverty perblack LN_VC100k96 south degree, family(poisson) vce(robust)", # noqa:E501 cmd="glm", predict="glim_p", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 marginsok="default", hac_lag="15", vcetype="Robust", vce="robust", linkt="Log", linkf="ln(u)", varfunct="Poisson", varfuncf="u", opt1="ML", oim="oim", a="1", m="1", varfunc="glim_v3", link="glim_l03", chi2type="Wald", opt="moptimize", title="Generalized linear models", user="glim_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="executions", properties="b V", ) params_table = np.array([ .00026110166569, .00003534474167, 7.3872845963787, 1.498576223e-13, .00019182724497, .0003303760864, np.nan, 1.9599639845401, 0, .07781804809828, .09819599835909, .79247677500784, .42808272865983, -.11464257211148, .27027866830805, np.nan, 1.9599639845401, 0, -.09493110013466, .01944446025221, -4.8821668950083, 1.049263903e-06, -.13304154192782, -.0568206583415, np.nan, 1.9599639845401, 0, .29693462055586, .34917491559373, .85038932436186, .39510866948496, -.38743563831266, .98130487942439, np.nan, 1.9599639845401, 0, 2.3011832004524, .45717041903387, 5.0335347709405, 4.815174289e-07, 1.405145644349, 3.1972207565559, np.nan, 1.9599639845401, 0, -18.722067603077, 4.5006120067298, -4.1598937155841, .00003183957242, -27.543105044656, -9.9010301614985, np.nan, 1.9599639845401, 0, -6.8014789919532, 3.48445447794, -1.9519494471841, .05094420680386, -13.630884274485, .02792629057847, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 1.249250764e-09, 2.158351725e-06, 1.068227835e-07, -5.170410321e-06, -5.047866044e-07, -.00001662944527, -.00004339679838, 2.158351725e-06, .00964245409374, .00008635335196, -.00640596402935, -.00524426268669, .23390140895418, -.22653903184676, 1.068227835e-07, .00008635335196, .0003780870345, -.00382751790532, -.0064534643179, -.05137117620883, .02948709519544, -5.170410321e-06, -.00640596402935, -.00382751790532, .12192312167989, .0907733380116, .89729289134262, -.69004336039169, -5.047866044e-07, -.00524426268669, -.0064534643179, .0907733380116, .20900479203961, .93952111535021, -.75843860743141, -.00001662944527, .23390140895418, -.05137117620883, .89729289134262, .93952111535021, 20.25550843512, -12.691830440798, -.00004339679838, -.22653903184676, .02948709519544, -.69004336039169, -.75843860743141, -12.691830440798, 12.141423008836]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 17, np.nan, -31.927328308098, 7, 77.854656616197, 83.68715002459]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 35.226364135742, .05631958693266, 8.1965742111206, .14089094102383, 1.3118965625763, .51714926958084, 3.6862981319427, .20286601781845, 2.0823004245758, .27275583148003, 1.0650315284729, .58616667985916, 1.9260421991348, .30098018050194, 2.4171404838562, .34251752495766, 1.8473218679428, .29685723781586, 2.8643238544464, .47364214062691, 3.1211984157562, .72507524490356, 3.338207244873, .54493451118469, 2.5269968509674, .34425318241119, .89725440740585, .37162157893181, .97933322191238, .50227928161621, .53462094068527, .40906101465225, 1.9790935516357, .33805811405182]).reshape(17, 2) predicted_colnames = 'predict_mu predict_linpred_std'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] results_poisson_none_hc1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, **est ) est = dict( k_eq_model=0, phi=1, vf=1, df=26, df_m=6, power=0, canonical=1, rank=7, aic=3.634510210512826, rc=0, p=1.5690245831e-115, chi2=549.7874580263729, ll=-52.96941847346162, k_autoCns=0, converged=1, k_dv=1, k_eq=1, k=7, ic=3, N=33, nbml=0, bic=-67.5595014539113, dispers_ps=1.156216988842385, deviance_ps=30.06164170990202, dispers_p=1.156216988842385, deviance_p=30.06164170990202, dispers_s=.8980651978545075, deviance_s=23.34969514421719, dispers=.8980651978545075, deviance=23.34969514421719, cmdline="glm executions income perpoverty perblack LN_VC100k96 south degree [fweight=fweight], family(poisson) vce(robust)", # noqa:E501 cmd="glm", predict="glim_p", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 marginsok="default", hac_lag="15", vcetype="Robust", vce="robust", linkt="Log", linkf="ln(u)", varfunct="Poisson", varfuncf="u", opt1="ML", oim="oim", a="1", m="1", varfunc="glim_v3", link="glim_l03", wexp="= fweight", wtype="fweight", chi2type="Wald", opt="moptimize", title="Generalized linear models", user="glim_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="executions", properties="b V", ) params_table = np.array([ .00025343868829, .0000263369674, 9.6229259983619, 6.398464168e-22, .00020181918073, .00030505819585, np.nan, 1.9599639845401, 0, .09081422305585, .07431850776812, 1.2219597215163, .22172285914198, -.05484737555444, .23647582166613, np.nan, 1.9599639845401, 0, -.09416451429381, .01609416304158, -5.8508487860178, 4.890707145e-09, -.12570849421662, -.06262053437099, np.nan, 1.9599639845401, 0, .27652273809506, .34481886883624, .80193621372381, .42258985672342, -.3993098260138, .95235530220392, np.nan, 1.9599639845401, 0, 2.239890838384, .39682271484988, 5.6445630619491, 1.656012749e-08, 1.4621326090308, 3.0176490677372, np.nan, 1.9599639845401, 0, -18.842583191417, 4.1473740870735, -4.5432562377589, 5.539185130e-06, -26.971287032495, -10.713879350338, np.nan, 1.9599639845401, 0, -6.5630017977416, 3.0810023455152, -2.1301515097173, .03315910688542, -12.601655431235, -.52434816424841, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 6.936358517e-10, 1.301395377e-06, 1.497821854e-07, -4.758016826e-06, -1.852598001e-06, -6.904571080e-06, -.00001327109619, 1.301395377e-06, .00552324059688, .00014714335792, -.00376147485446, -.00118957690573, .15979100738539, -.13853266210904, 1.497821854e-07, .00014714335792, .00025902208401, -.00418693954572, -.00513741847691, -.03987504442994, .02761179707845, -4.758016826e-06, -.00376147485446, -.00418693954572, .1189000523055, .08682729933237, .80541854027627, -.70545315416752, -1.852598001e-06, -.00118957690573, -.00513741847691, .08682729933237, .15746826702083, 1.1366624064282, -.75098089879076, -6.904571080e-06, .15979100738539, -.03987504442994, .80541854027627, 1.1366624064282, 17.200711818129, -11.062121016981, -.00001327109619, -.13853266210904, .02761179707845, -.70545315416752, -.75098089879076, -11.062121016981, 9.49257545307]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 33, np.nan, -52.969418473462, 7, 119.93883694692, 130.41438987719]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 34.815238952637, .06608480215073, 7.3026847839355, .23366995155811, 1.2540435791016, .39606991410255, 3.9734709262848, .12350843846798, 2.0739872455597, .18263976275921, 1.1471545696259, .39735752344131, 1.7763512134552, .17952646315098, 2.2698366641998, .21028706431389, 1.6349502801895, .17675416171551, 2.7504913806915, .42150634527206, 2.862185716629, .58209121227264, 3.5617923736572, .49835306406021, 2.6135795116425, .2456089258194, .775799036026, .23251366615295, .93375068902969, .35320028662682, .56681954860687, .26245352625847, 1.8914022445679, .20374123752117]).reshape(17, 2) predicted_colnames = 'predict_mu predict_linpred_std'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] results_poisson_fweight_hc1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, **est ) est = dict( k_eq_model=0, phi=1, vf=1, df=10, df_m=6, power=0, canonical=1, rank=7, aic=4.033797198035106, rc=0, p=5.72458312675e-74, chi2=356.663774965618, ll=-27.28727618329841, k_autoCns=0, converged=1, k_dv=1, k_eq=1, k=7, ic=3, N=17, nbml=0, bic=-16.30350260869269, dispers_ps=1.548630027479802, deviance_ps=15.48630027479802, dispers_p=1.548630027479802, deviance_p=15.48630027479802, dispers_s=1.202863083186947, deviance_s=12.02863083186947, dispers=1.202863083186947, deviance=12.02863083186947, cmdline="glm executions income perpoverty perblack LN_VC100k96 south degree [aweight=fweight], family(poisson) vce(robust)", # noqa:E501 cmd="glm", predict="glim_p", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 marginsok="default", hac_lag="15", vcetype="Robust", vce="robust", linkt="Log", linkf="ln(u)", varfunct="Poisson", varfuncf="u", opt1="ML", oim="oim", a="1", m="1", varfunc="glim_v3", link="glim_l03", wexp="= fweight", wtype="aweight", chi2type="Wald", opt="moptimize", title="Generalized linear models", user="glim_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="executions", properties="b V", ) params_table = np.array([ .00025343868829, .0000298866597, 8.4799937786833, 2.252059827e-17, .00019486191167, .00031201546491, np.nan, 1.9599639845401, 0, .09081422305585, .08414617969118, 1.0792435662455, .28047916301948, -.0741092585755, .25573770468719, np.nan, 1.9599639845401, 0, -.09416451429381, .01946961498728, -4.8364856909248, 1.321547815e-06, -.13232425846174, -.05600477012587, np.nan, 1.9599639845401, 0, .27652273809507, .36112179485206, .76573261995541, .44383541350425, -.43126297384744, .98430845003758, np.nan, 1.9599639845401, 0, 2.239890838384, .4309885345485, 5.1971007551988, 2.024206636e-07, 1.3951688329193, 3.0846128438488, np.nan, 1.9599639845401, 0, -18.842583191417, 4.5147658917496, -4.1735460139472, .00002998950578, -27.691361737876, -9.9938046449574, np.nan, 1.9599639845401, 0, -6.5630017977417, 3.3999612612367, -1.9303166399474, .05356761651539, -13.226803418597, .10079982311369, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 8.932124278e-10, 1.512127962e-06, 1.877263788e-07, -4.562869239e-06, -2.023379829e-06, -.00001228516761, -.00002423071544, 1.512127962e-06, .00708057955662, .00028427703202, -.00195495117479, -.00596332288528, .2002206183531, -.1867826510868, 1.877263788e-07, .00028427703202, .00037906590775, -.00453407701816, -.00623061980468, -.04659404972537, .02694184589718, -4.562869239e-06, -.00195495117479, -.00453407701816, .13040895071718, .08362596918255, .89260578257483, -.82275604425296, -2.023379829e-06, -.00596332288528, -.00623061980468, .08362596918255, .18575111691226, 1.0698498854982, -.64859219982256, -.00001228516761, .2002206183531, -.04659404972537, .89260578257483, 1.0698498854982, 20.383111057306, -12.482192460764, -.00002423071544, -.1867826510868, .02694184589718, -.82275604425296, -.64859219982256, -12.482192460764, 11.55973657791]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 17, np.nan, -27.287276183298, 7, 68.574552366597, 74.40704577499]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 34.815238952637, .06858423352242, 7.3026847839355, .25687274336815, 1.2540435791016, .41320022940636, 3.9734709262848, .16020278632641, 2.0739872455597, .22170753777027, 1.1471545696259, .51121062040329, 1.7763512134552, .2167394310236, 2.2698366641998, .2456086575985, 1.6349502801895, .25546172261238, 2.7504913806915, .4417819082737, 2.862185716629, .61734634637833, 3.5617923736572, .51518148183823, 2.6135795116425, .34006628394127, .775799036026, .292076587677, .93375068902969, .39795544743538, .56681954860687, .31529840826988, 1.8914022445679, .26116076111794]).reshape(17, 2) predicted_colnames = 'predict_mu predict_linpred_std'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] results_poisson_aweight_hc1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, **est ) est = dict( k_eq_model=0, phi=1, vf=1, df=10, df_m=6, power=0, canonical=1, rank=7, aic=7.055225702760191, rc=0, p=5.72458312679e-74, chi2=356.6637749656061, ll=-52.96941847346162, k_autoCns=0, converged=1, k_dv=1, k_eq=1, k=7, ic=3, N=17, nbml=0, bic=-4.982438296344967, dispers_ps=3.006164170990202, deviance_ps=30.06164170990202, dispers_p=3.006164170990202, deviance_p=30.06164170990202, dispers_s=2.33496951442172, deviance_s=23.34969514421719, dispers=2.33496951442172, deviance=23.34969514421719, cmdline="glm executions income perpoverty perblack LN_VC100k96 south degree [pweight=fweight], family(poisson) vce(robust)", # noqa:E501 cmd="glm", predict="glim_p", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 marginsok="default", hac_lag="15", vcetype="Robust", vce="robust", linkt="Log", linkf="ln(u)", varfunct="Poisson", varfuncf="u", opt1="ML", oim="oim", a="1", m="1", varfunc="glim_v3", link="glim_l03", wexp="= fweight", wtype="pweight", chi2type="Wald", opt="moptimize", title="Generalized linear models", user="glim_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="executions", properties="b V", ) params_table = np.array([ .00025343868829, .0000298866597, 8.4799937786829, 2.252059827e-17, .00019486191167, .00031201546491, np.nan, 1.9599639845401, 0, .09081422305585, .08414617969117, 1.0792435662456, .28047916301946, -.07410925857549, .25573770468718, np.nan, 1.9599639845401, 0, -.09416451429381, .01946961498728, -4.8364856909253, 1.321547815e-06, -.13232425846174, -.05600477012587, np.nan, 1.9599639845401, 0, .27652273809506, .36112179485191, .76573261995571, .44383541350407, -.43126297384714, .98430845003726, np.nan, 1.9599639845401, 0, 2.239890838384, .43098853454849, 5.1971007551989, 2.024206636e-07, 1.3951688329193, 3.0846128438487, np.nan, 1.9599639845401, 0, -18.842583191417, 4.5147658917489, -4.1735460139479, .00002998950578, -27.691361737874, -9.9938046449589, np.nan, 1.9599639845401, 0, -6.5630017977416, 3.3999612612355, -1.930316639948, .0535676165153, -13.226803418595, .10079982311137, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 8.932124278e-10, 1.512127962e-06, 1.877263788e-07, -4.562869239e-06, -2.023379829e-06, -.00001228516761, -.00002423071544, 1.512127962e-06, .00708057955662, .00028427703202, -.0019549511748, -.00596332288528, .20022061835302, -.18678265108673, 1.877263788e-07, .00028427703202, .00037906590775, -.00453407701816, -.00623061980467, -.04659404972535, .02694184589715, -4.562869239e-06, -.0019549511748, -.00453407701816, .13040895071706, .0836259691825, .89260578257395, -.82275604425197, -2.023379829e-06, -.00596332288528, -.00623061980467, .0836259691825, .18575111691225, 1.0698498854979, -.64859219982217, -.00001228516761, .20022061835302, -.04659404972535, .89260578257395, 1.0698498854979, 20.383111057299, -12.482192460755, -.00002423071544, -.18678265108673, .02694184589715, -.82275604425197, -.64859219982217, -12.482192460755, 11.559736577902]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 17, np.nan, -52.969418473462, 7, 119.93883694692, 125.77133035532]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 34.815238952637, .06858423352242, 7.3026847839355, .25687274336815, 1.2540435791016, .41320022940636, 3.9734709262848, .16020278632641, 2.0739872455597, .22170753777027, 1.1471545696259, .51121062040329, 1.7763512134552, .2167394310236, 2.2698366641998, .2456086575985, 1.6349502801895, .25546172261238, 2.7504913806915, .4417819082737, 2.862185716629, .61734634637833, 3.5617923736572, .51518148183823, 2.6135795116425, .34006628394127, .775799036026, .292076587677, .93375068902969, .39795544743538, .56681954860687, .31529840826988, 1.8914022445679, .26116076111794]).reshape(17, 2) predicted_colnames = 'predict_mu predict_linpred_std'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] results_poisson_pweight_hc1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, **est ) est = dict( k_eq_model=0, vf=1, df=10, df_m=6, power=0, canonical=1, rank=7, aic=4.579685683305704, rc=0, p=4.1950730971e-123, chi2=584.908728768987, ll=-31.92732830809848, N_clust=9, k_autoCns=0, converged=1, k_dv=1, k_eq=1, k=7, ic=3, N=17, nbml=0, bic=-9.740492454486454, dispers_ps=2.475374834715614, deviance_ps=24.75374834715614, dispers_p=2.475374834715614, deviance_p=24.75374834715614, dispers_s=1.859164098607571, deviance_s=18.59164098607571, dispers=1.859164098607571, deviance=18.59164098607571, phi=1, cmdline="glm executions income perpoverty perblack LN_VC100k96 south degree, family(poisson) vce(cluster id)", # noqa:E501 cmd="glm", predict="glim_p", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 marginsok="default", hac_lag="15", vcetype="Robust", vce="cluster", linkt="Log", linkf="ln(u)", varfunct="Poisson", varfuncf="u", opt1="ML", clustvar="id", oim="oim", a="1", m="1", varfunc="glim_v3", link="glim_l03", chi2type="Wald", opt="moptimize", title="Generalized linear models", user="glim_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="executions", properties="b V", ) params_table = np.array([ .00026110166569, .00004098448535, 6.3707440379489, 1.881133617e-10, .00018077355048, .0003414297809, np.nan, 1.9599639845401, 0, .07781804809828, .11602998752167, .67067186475175, .50242959011024, -.14959654857083, .3052326447674, np.nan, 1.9599639845401, 0, -.09493110013466, .02432927475974, -3.9019288931601, .00009542919351, -.14261560243373, -.04724659783559, np.nan, 1.9599639845401, 0, .29693462055586, .31774950884716, .93449277587615, .35004976070702, -.32584297288986, .91971221400158, np.nan, 1.9599639845401, 0, 2.3011832004524, .54874508731474, 4.1935376801516, .00002746374324, 1.2256625926223, 3.3767038082826, np.nan, 1.9599639845401, 0, -18.722067603077, 2.8106198749749, -6.6611880780372, 2.716227723e-11, -24.230781332261, -13.213353873894, np.nan, 1.9599639845401, 0, -6.8014789919532, 3.1571598785659, -2.1543029981246, .03121641791743, -12.989398647377, -.61355933652912, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 1.679728039e-09, 4.034336761e-06, 1.735749447e-07, -5.093610363e-06, -4.552211884e-06, .00001563785418, -.00009230028034, 4.034336761e-06, .01346295800428, .00110922683659, -.01950093608551, -.02957572460439, .08545644123676, -.23518641056668, 1.735749447e-07, .00110922683659, .00059191361033, -.00720622811203, -.01195031391163, -.04317371228367, .03351736744645, -5.093610363e-06, -.01950093608551, -.00720622811203, .10096475037261, .13375578883899, .49763538443989, -.27357574414228, -4.552211884e-06, -.02957572460439, -.01195031391163, .13375578883899, .30112117085206, .65342245458316, -.47102547759356, .00001563785418, .08545644123676, -.04317371228367, .49763538443989, .65342245458316, 7.8995840816039, -6.5824964755966, -.00009230028034, -.23518641056668, .03351736744645, -.27357574414228, -.47102547759356, -6.5824964755966, 9.9676584988266]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 17, np.nan, -31.927328308098, 7, 77.854656616197, 83.68715002459]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 35.226364135742, .05941947177052, 8.1965742111206, .09018591046333, 1.3118965625763, .53127920627594, 3.6862981319427, .23996050655842, 2.0823004245758, .33554902672768, 1.0650315284729, .53513532876968, 1.9260421991348, .32360115647316, 2.4171404838562, .33078169822693, 1.8473218679428, .32581362128258, 2.8643238544464, .46489810943604, 3.1211984157562, .71297109127045, 3.338207244873, .58515930175781, 2.5269968509674, .42410242557526, .89725440740585, .40493285655975, .97933322191238, .5560839176178, .53462094068527, .419488966465, 1.9790935516357, .3438538312912]).reshape(17, 2) predicted_colnames = 'predict_mu predict_linpred_std'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] results_poisson_none_clu1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, **est ) est = dict( k_eq_model=0, vf=1, df=26, df_m=6, power=0, canonical=1, rank=7, aic=3.634510210512826, rc=0, p=6.87057569032e-91, chi2=435.380362705941, ll=-52.96941847346162, N_clust=9, k_autoCns=0, converged=1, k_dv=1, k_eq=1, k=7, ic=3, N=33, nbml=0, bic=-67.5595014539113, dispers_ps=1.156216988842385, deviance_ps=30.06164170990202, dispers_p=1.156216988842385, deviance_p=30.06164170990202, dispers_s=.8980651978545075, deviance_s=23.34969514421719, dispers=.8980651978545075, deviance=23.34969514421719, phi=1, cmdline="glm executions income perpoverty perblack LN_VC100k96 south degree [fweight=fweight], family(poisson) vce(cluster id)", # noqa:E501 cmd="glm", predict="glim_p", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 marginsok="default", hac_lag="15", vcetype="Robust", vce="cluster", linkt="Log", linkf="ln(u)", varfunct="Poisson", varfuncf="u", opt1="ML", clustvar="id", oim="oim", a="1", m="1", varfunc="glim_v3", link="glim_l03", wexp="= fweight", wtype="fweight", chi2type="Wald", opt="moptimize", title="Generalized linear models", user="glim_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="executions", properties="b V", ) params_table = np.array([ .00025343868829, .0000293670276, 8.6300422274613, 6.132932700e-18, .00019588037186, .00031099700472, np.nan, 1.9599639845401, 0, .09081422305585, .09800194027664, .92665739881773, .35410444288802, -.10126605030142, .28289449641311, np.nan, 1.9599639845401, 0, -.09416451429381, .02511206083893, -3.7497724658197, .00017699509401, -.14338324911569, -.04494577947193, np.nan, 1.9599639845401, 0, .27652273809506, .36749499886987, .75245306451906, .45177864537662, -.44375422418847, .99679970037859, np.nan, 1.9599639845401, 0, 2.239890838384, .51564197481271, 4.343887712395, .00001399830855, 1.229251138834, 3.250530537934, np.nan, 1.9599639845401, 0, -18.842583191417, 3.2292740757113, -5.8349284543976, 5.381365332e-09, -25.17184407602, -12.513322306813, np.nan, 1.9599639845401, 0, -6.5630017977416, 3.1938260811459, -2.0549026875586, .03988840483712, -12.822785889672, -.30321770581092, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 8.624223101e-10, 2.413510691e-06, 3.123995891e-07, -4.358439015e-06, -8.084672085e-06, -4.785328653e-06, -.00003652286809, 2.413510691e-06, .00960438029799, .00106422375754, -.00911884619892, -.03121758372723, .06803953530989, -.17715756048416, 3.123995891e-07, .00106422375754, .00063061559958, -.00844230553011, -.01177586448603, -.05361546061036, .03844868195577, -4.358439015e-06, -.00911884619892, -.00844230553011, .13505257419436, .14058853110927, .86184257188631, -.74146699290106, -8.084672085e-06, -.03121758372723, -.01177586448603, .14058853110927, .26588664618875, .75712244813913, -.35118919402718, -4.785328653e-06, .06803953530989, -.05361546061036, .86184257188631, .75712244813913, 10.428211056061, -8.3518020608948, -.00003652286809, -.17715756048416, .03844868195577, -.74146699290106, -.35118919402718, -8.3518020608948, 10.200525036608]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 33, np.nan, -52.969418473462, 7, 119.93883694692, 130.41438987719]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 34.815238952637, .07249507308006, 7.3026847839355, .17909966409206, 1.2540435791016, .36725598573685, 3.9734709262848, .1719862818718, 2.0739872455597, .27532628178596, 1.1471545696259, .51580721139908, 1.7763512134552, .23559851944447, 2.2698366641998, .21655206382275, 1.6349502801895, .27835717797279, 2.7504913806915, .44458091259003, 2.862185716629, .54439353942871, 3.5617923736572, .57089400291443, 2.6135795116425, .41426089406013, .775799036026, .35101860761642, .93375068902969, .39217269420624, .56681954860687, .27232182025909, 1.8914022445679, .24083258211613]).reshape(17, 2) predicted_colnames = 'predict_mu predict_linpred_std'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] results_poisson_fweight_clu1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, **est ) est = dict( k_eq_model=0, vf=1, df=10, df_m=6, power=0, canonical=1, rank=7, aic=4.033797198035106, rc=0, p=6.87057569091e-91, chi2=435.3803627057688, ll=-27.28727618329841, N_clust=9, k_autoCns=0, converged=1, k_dv=1, k_eq=1, k=7, ic=3, N=17, nbml=0, bic=-16.30350260869269, dispers_ps=1.548630027479802, deviance_ps=15.48630027479802, dispers_p=1.548630027479802, deviance_p=15.48630027479802, dispers_s=1.202863083186947, deviance_s=12.02863083186947, dispers=1.202863083186947, deviance=12.02863083186947, phi=1, cmdline="glm executions income perpoverty perblack LN_VC100k96 south degree [aweight=fweight], family(poisson) vce(cluster id)", # noqa:E501 cmd="glm", predict="glim_p", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 marginsok="default", hac_lag="15", vcetype="Robust", vce="cluster", linkt="Log", linkf="ln(u)", varfunct="Poisson", varfuncf="u", opt1="ML", clustvar="id", oim="oim", a="1", m="1", varfunc="glim_v3", link="glim_l03", wexp="= fweight", wtype="aweight", chi2type="Wald", opt="moptimize", title="Generalized linear models", user="glim_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="executions", properties="b V", ) params_table = np.array([ .00025343868829, .0000293670276, 8.6300422274633, 6.132932700e-18, .00019588037186, .00031099700472, np.nan, 1.9599639845401, 0, .09081422305585, .09800194027665, .92665739881771, .35410444288803, -.10126605030143, .28289449641312, np.nan, 1.9599639845401, 0, -.09416451429381, .02511206083893, -3.7497724658192, .00017699509401, -.14338324911569, -.04494577947192, np.nan, 1.9599639845401, 0, .27652273809507, .36749499887001, .75245306451881, .45177864537677, -.44375422418873, .99679970037887, np.nan, 1.9599639845401, 0, 2.239890838384, .51564197481271, 4.343887712395, .00001399830855, 1.229251138834, 3.250530537934, np.nan, 1.9599639845401, 0, -18.842583191417, 3.2292740757119, -5.8349284543965, 5.381365332e-09, -25.171844076021, -12.513322306812, np.nan, 1.9599639845401, 0, -6.5630017977417, 3.193826081147, -2.054902687558, .03988840483718, -12.822785889674, -.30321770580895, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 8.624223101e-10, 2.413510691e-06, 3.123995891e-07, -4.358439015e-06, -8.084672085e-06, -4.785328653e-06, -.00003652286809, 2.413510691e-06, .00960438029799, .00106422375754, -.00911884619892, -.03121758372723, .06803953530995, -.1771575604842, 3.123995891e-07, .00106422375754, .00063061559958, -.00844230553012, -.01177586448603, -.05361546061038, .03844868195581, -4.358439015e-06, -.00911884619892, -.00844230553012, .13505257419447, .1405885311093, .86184257188684, -.74146699290197, -8.084672085e-06, -.03121758372723, -.01177586448603, .1405885311093, .26588664618875, .75712244813928, -.35118919402768, -4.785328653e-06, .06803953530995, -.05361546061038, .86184257188684, .75712244813928, 10.428211056065, -8.3518020609031, -.00003652286809, -.1771575604842, .03844868195581, -.74146699290197, -.35118919402768, -8.3518020609031, 10.200525036615]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 17, np.nan, -27.287276183298, 7, 68.574552366597, 74.40704577499]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 34.815238952637, .07249507308006, 7.3026847839355, .17909966409206, 1.2540435791016, .36725598573685, 3.9734709262848, .1719862818718, 2.0739872455597, .27532628178596, 1.1471545696259, .51580721139908, 1.7763512134552, .23559851944447, 2.2698366641998, .21655206382275, 1.6349502801895, .27835714817047, 2.7504913806915, .44458091259003, 2.862185716629, .54439353942871, 3.5617923736572, .57089400291443, 2.6135795116425, .41426089406013, .775799036026, .35101860761642, .93375068902969, .39217269420624, .56681954860687, .27232182025909, 1.8914022445679, .24083258211613]).reshape(17, 2) predicted_colnames = 'predict_mu predict_linpred_std'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] results_poisson_aweight_clu1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, **est ) est = dict( k_eq_model=0, vf=1, df=10, df_m=6, power=0, canonical=1, rank=7, aic=7.055225702760191, rc=0, p=6.87057569032e-91, chi2=435.380362705941, ll=-52.96941847346162, N_clust=9, k_autoCns=0, converged=1, k_dv=1, k_eq=1, k=7, ic=3, N=17, nbml=0, bic=-4.982438296344967, dispers_ps=3.006164170990202, deviance_ps=30.06164170990202, dispers_p=3.006164170990202, deviance_p=30.06164170990202, dispers_s=2.33496951442172, deviance_s=23.34969514421719, dispers=2.33496951442172, deviance=23.34969514421719, phi=1, cmdline="glm executions income perpoverty perblack LN_VC100k96 south degree [pweight=fweight], family(poisson) vce(cluster id)", # noqa:E501 cmd="glm", predict="glim_p", marginsnotok="stdp Anscombe Cooksd Deviance Hat Likelihood Pearson Response Score Working ADJusted STAndardized STUdentized MODified", # noqa:E501 marginsok="default", hac_lag="15", vcetype="Robust", vce="cluster", linkt="Log", linkf="ln(u)", varfunct="Poisson", varfuncf="u", opt1="ML", clustvar="id", oim="oim", a="1", m="1", varfunc="glim_v3", link="glim_l03", wexp="= fweight", wtype="pweight", chi2type="Wald", opt="moptimize", title="Generalized linear models", user="glim_lf", crittype="log pseudolikelihood", ml_method="e2", singularHmethod="m-marquardt", technique="nr", which="max", depvar="executions", properties="b V", ) params_table = np.array([ .00025343868829, .0000293670276, 8.6300422274613, 6.132932700e-18, .00019588037186, .00031099700472, np.nan, 1.9599639845401, 0, .09081422305585, .09800194027664, .92665739881773, .35410444288802, -.10126605030142, .28289449641311, np.nan, 1.9599639845401, 0, -.09416451429381, .02511206083893, -3.7497724658197, .00017699509401, -.14338324911569, -.04494577947193, np.nan, 1.9599639845401, 0, .27652273809506, .36749499886987, .75245306451906, .45177864537662, -.44375422418847, .99679970037859, np.nan, 1.9599639845401, 0, 2.239890838384, .51564197481271, 4.343887712395, .00001399830855, 1.229251138834, 3.250530537934, np.nan, 1.9599639845401, 0, -18.842583191417, 3.2292740757113, -5.8349284543976, 5.381365332e-09, -25.17184407602, -12.513322306813, np.nan, 1.9599639845401, 0, -6.5630017977416, 3.1938260811459, -2.0549026875586, .03988840483712, -12.822785889672, -.30321770581092, np.nan, 1.9599639845401, 0]).reshape(7, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 8.624223101e-10, 2.413510691e-06, 3.123995891e-07, -4.358439015e-06, -8.084672085e-06, -4.785328653e-06, -.00003652286809, 2.413510691e-06, .00960438029799, .00106422375754, -.00911884619892, -.03121758372723, .06803953530989, -.17715756048416, 3.123995891e-07, .00106422375754, .00063061559958, -.00844230553011, -.01177586448603, -.05361546061036, .03844868195577, -4.358439015e-06, -.00911884619892, -.00844230553011, .13505257419436, .14058853110927, .86184257188631, -.74146699290106, -8.084672085e-06, -.03121758372723, -.01177586448603, .14058853110927, .26588664618875, .75712244813913, -.35118919402718, -4.785328653e-06, .06803953530989, -.05361546061036, .86184257188631, .75712244813913, 10.428211056061, -8.3518020608948, -.00003652286809, -.17715756048416, .03844868195577, -.74146699290106, -.35118919402718, -8.3518020608948, 10.200525036608]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 17, np.nan, -52.969418473462, 7, 119.93883694692, 125.77133035532]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 34.815238952637, .07249507308006, 7.3026847839355, .17909966409206, 1.2540435791016, .36725598573685, 3.9734709262848, .1719862818718, 2.0739872455597, .27532628178596, 1.1471545696259, .51580721139908, 1.7763512134552, .23559851944447, 2.2698366641998, .21655206382275, 1.6349502801895, .27835717797279, 2.7504913806915, .44458091259003, 2.862185716629, .54439353942871, 3.5617923736572, .57089400291443, 2.6135795116425, .41426089406013, .775799036026, .35101860761642, .93375068902969, .39217269420624, .56681954860687, .27232182025909, 1.8914022445679, .24083258211613]).reshape(17, 2) predicted_colnames = 'predict_mu predict_linpred_std'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] results_poisson_pweight_clu1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, **est ) est = dict( rank=7, ll_0=-55.23556912834824, ll=-47.54122045581504, r2_a=.3528737432046668, rss=267.3132086911238, mss=393.6105745962962, rmse=5.17023412130557, r2=.5955460895029168, F=.7279778160729128, df_r=10, df_m=6, N=17, cmdline="regress executions income perpoverty perblack LN_VC100k96 south degree [aweight=fweight], vce(robust)", # noqa:E501 title="Linear regression", marginsok="XB default", vce="robust", depvar="executions", cmd="regress", properties="b V", predict="regres_p", model="ols", estat_cmd="regress_estat", wexp="= fweight", wtype="aweight", vcetype="Robust", ) params_table = np.array([ .00177624355887, .00100571734546, 1.7661458926668, .10782432028789, -.00046463433267, .0040171214504, 10, 2.2281388519863, 0, .70240571372092, .54986275700055, 1.2774200557835, .23031379083217, -.5227648584123, 1.9275762858541, 10, 2.2281388519863, 0, -.76566360596606, .46482124106144, -1.6472216377583, .13053265392051, -1.8013498724035, .27002266047141, 10, 2.2281388519863, 0, 5.7915855647065, 5.8518623033717, .98969956305525, .34566324660643, -7.2471761899099, 18.830347319323, 10, 2.2281388519863, 0, 13.018291494864, 7.3741002410906, 1.7654074489417, .10795348742173, -3.412227750751, 29.44881074048, 10, 2.2281388519863, 0, -140.99921608421, 84.973820309491, -1.6593253730463, .12803894207791, -330.33268651749, 48.334254349065, 10, 2.2281388519863, 0, -68.484290889814, 50.764306481463, -1.3490638528633, .20706938025917, -181.5942144553, 44.625632675673, 10, 2.2281388519863, 0]).reshape(7, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 1.011467379e-06, .00038778854684, -.00038909911416, .00356508765632, .0056952104088, -.07926157334067, -.04218673068644, .00038778854684, .30234905153625, -.10112236243026, .59175926747871, 1.4744074711876, -25.6203584288, -14.793319880623, -.00038909911416, -.10112236243026, .21605878614189, -2.3405630815795, -3.2257627901142, 31.66920792546, 20.934058595259, .00356508765632, .59175926747871, -2.3405630815795, 34.244292417623, 34.810403897967, -270.34292245471, -270.19382562804, .0056952104088, 1.4744074711876, -3.2257627901142, 34.810403897967, 54.377354365652, -414.2817137548, -324.24739845086, -.07926157334067, -25.6203584288, 31.66920792546, -270.34292245471, -414.2817137548, 7220.5501379896, 2907.4556071681, -.04218673068644, -14.793319880623, 20.934058595259, -270.19382562804, -324.24739845086, 2907.4556071681, 2577.0148125439]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 17, -55.235569128348, -47.541220455815, 7, 109.08244091163, 114.91493432002]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 23.018356323242, 11.030969619751, 7.6487560272217, 3.2376720905304, 1.3298480510712, 2.4579885005951, 6.7120413780212, 2.8951823711395, .90416890382767, 2.1985862255096, 1.9608836174011, 2.5452246665955, 4.6054129600525, 2.8738057613373, 2.9902882575989, 1.8505314588547, 1.4887162446976, 1.47836124897, 5.9044842720032, 4.8891386985779, 7.0818486213684, 4.6786789894104, 7.5460968017578, 5.5129766464233, 4.1125593185425, 2.3989260196686, -2.7979807853699, 3.8943622112274, -1.4647831916809, 2.8729522228241, -3.5234127044678, 3.7701880931854, 3.9779393672943, 1.9573417901993]).reshape(17, 2) predicted_colnames = 'predict_mu predict_std'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] results_wls_aweight_robust = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, **est ) est = dict( rank=7, ll_0=-55.23556912834824, ll=-47.54122045581504, r2_a=.3528737432046668, rss=267.3132086911238, mss=393.6105745962962, rmse=5.17023412130557, r2=.5955460895029168, F=1.412187242235973, df_r=8, df_m=6, N=17, N_clust=9, cmdline="regress executions income perpoverty perblack LN_VC100k96 south degree [aweight=fweight], vce(cluster id)", # noqa:E501 title="Linear regression", marginsok="XB default", vce="cluster", depvar="executions", cmd="regress", properties="b V", predict="regres_p", model="ols", estat_cmd="regress_estat", wexp="= fweight", wtype="aweight", vcetype="Robust", clustvar="id", ) params_table = np.array([ .00177624355887, .00103574504038, 1.7149428571794, .12469817836724, -.00061218878728, .00416467590501, 8, 2.3060041352042, 0, .70240571372092, .64463869959516, 1.0896114585768, .30761438040884, -.78413379325815, 2.1889452207, 8, 2.3060041352042, 0, -.76566360596606, .50850811868177, -1.5057057652313, .17056206446331, -1.9382854304311, .40695821849901, 8, 2.3060041352042, 0, 5.7915855647065, 6.2948340440059, .92005373362009, .3844480847801, -8.7243277711951, 20.307498900608, 8, 2.3060041352042, 0, 13.018291494864, 7.9526248350517, 1.6369804642972, .14027059672576, -5.3204942604922, 31.357077250221, 8, 2.3060041352042, 0, -140.99921608421, 84.897180497105, -1.6608233071889, .13532738016362, -336.77246537771, 54.774033209288, 8, 2.3060041352042, 0, -68.484290889814, 50.203382265366, -1.3641369923608, .2096627597382, -184.25349799498, 47.284916215355, 8, 2.3060041352042, 0]).reshape(7, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 1.072767789e-06, .00042569049255, -.00044272344175, .00386796354086, .00653558563917, -.08376884119522, -.04513384476642, .00042569049255, .41555905301573, -.07730648264729, -.34087330734824, .82631440946934, -31.768811666606, -10.324414524804, -.00044272344175, -.07730648264729, .25858050676528, -2.8727606144729, -3.9481543148554, 35.836754991381, 24.653552354067, .00386796354086, -.34087330734824, -2.8727606144729, 39.624935641576, 42.351437415382, -335.98208369348, -283.16728769825, .00653558563917, .82631440946934, -3.9481543148554, 42.351437415382, 63.24424176708, -502.21726015398, -366.49477518415, -.08376884119522, -31.768811666606, 35.836754991381, -335.98208369348, -502.21726015398, 7207.531256358, 3532.1379707168, -.04513384476642, -10.324414524804, 24.653552354067, -283.16728769825, -366.49477518415, 3532.1379707168, 2520.3795908825]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 17, -55.235569128348, -47.541220455815, 7, 109.08244091163, 114.91493432002]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 23.018356323242, 11.727355003357, 7.6487560272217, 3.4638004302979, 1.3298480510712, 2.1195623874664, 6.7120413780212, 2.8227334022522, .90416890382767, 2.2036759853363, 1.9608836174011, 2.0707910060883, 4.6054129600525, 2.9022018909454, 2.9902882575989, 1.6939970254898, 1.4887162446976, 1.8477793931961, 5.9044842720032, 4.8752007484436, 7.0818486213684, 4.4365234375, 7.5460968017578, 5.6850047111511, 4.1125593185425, 2.7407164573669, -2.7979807853699, 3.9614858627319, -1.4647831916809, 2.4376966953278, -3.5234127044678, 3.5529434680939, 3.9779393672943, 1.7075037956238]).reshape(17, 2) predicted_colnames = 'predict_mu predict_std'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] results_wls_aweight_clu1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, **est ) est = dict( rank=7, ll_0=-107.2219871314995, ll=-92.28589853187629, r2_a=.5022105716958969, rss=518.9021109886529, mss=764.067585981045, rmse=4.467412394167744, r2=.5955460895029162, F=1.835843414931295, df_r=8, df_m=6, N=33, N_clust=9, cmdline="regress executions income perpoverty perblack LN_VC100k96 south degree [fweight=fweight], vce(cluster id)", # noqa:E501 title="Linear regression", marginsok="XB default", vce="cluster", depvar="executions", cmd="regress", properties="b V", predict="regres_p", model="ols", estat_cmd="regress_estat", wexp="= fweight", wtype="fweight", vcetype="Robust", clustvar="id", ) params_table = np.array([ .00177624355887, .00090840849363, 1.9553357012053, .08627786102497, -.00031855018389, .00387103730162, 8, 2.3060041352042, 0, .70240571372091, .56538554103558, 1.2423482079757, .24928937729829, -.60137568189177, 2.0061871093336, 8, 2.3060041352042, 0, -.76566360596606, .44599112337258, -1.7167687109468, .12435346910262, -1.7941209807276, .26279376879547, 8, 2.3060041352042, 0, 5.7915855647065, 5.5209346785031, 1.0490226568442, .32482245151877, -6.9397126341137, 18.522883763527, 8, 2.3060041352042, 0, 13.018291494864, 6.9749133861223, 1.866444896759, .09894610636006, -3.0658876162246, 29.102470605953, 8, 2.3060041352042, 0, -140.99921608421, 74.459752971542, -1.8936299202886, .09489418422765, -312.70371434287, 30.705282174445, 8, 2.3060041352042, 0, -68.484290889814, 44.031279012175, -1.5553554751584, .15847103736706, -170.02060237022, 33.05202059059, 8, 2.3060041352042, 0]).reshape(7, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 8.252059913e-07, .00032745422504, -.00034055649365, .00297535656989, .0050273735686, -.06443757015017, -.03471834212801, .00032745422504, .31966081001209, -.05946652511329, -.26221023642171, .63562646882257, -24.437547435849, -7.9418573267692, -.00034055649365, -.05946652511329, .19890808212714, -2.2098158572872, -3.037041780658, 27.566734608754, 18.96427104159, .00297535656989, -.26221023642171, -2.2098158572872, 30.480719724298, 32.578028781062, -258.44775668729, -217.82099053713, .0050273735686, .63562646882257, -3.037041780658, 32.578028781062, 48.649416743908, -386.32096934921, -281.91905783396, -.06443757015017, -24.437547435849, 27.566734608754, -258.44775668729, -386.32096934921, 5544.254812583, 2717.0292082435, -.03471834212801, -7.9418573267692, 18.96427104159, -217.82099053713, -281.91905783396, 2717.0292082435, 1938.753531448]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 33, -107.2219871315, -92.285898531876, 7, 198.57179706375, 209.04734999402]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 23.018356323242, 10.285571098328, 7.6487560272217, 3.0379540920258, 1.3298480510712, 1.8589791059494, 6.7120413780212, 2.4757008552551, .90416890382767, 1.9327516555786, 1.9608836174011, 1.8162038326263, 4.6054129600525, 2.5453994274139, 2.9902882575989, 1.485733628273, 1.4887162446976, 1.6206097602844, 5.9044842720032, 4.2758340835571, 7.0818486213684, 3.8910882472992, 7.5460968017578, 4.9860787391663, 4.1125593185425, 2.4037673473358, -2.7979807853699, 3.4744529724121, -1.4647831916809, 2.1380014419556, -3.5234127044678, 3.1161375045776, 3.9779393672943, 1.4975799322128]).reshape(17, 2) predicted_colnames = 'predict_mu predict_std'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] results_wls_fweight_clu1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, **est ) est = dict( rank=7, ll_0=-55.23556912834824, ll=-47.54122045581504, r2_a=.3528737432046668, rss=267.3132086911238, mss=393.6105745962962, rmse=5.17023412130557, r2=.5955460895029168, F=1.412187242235973, df_r=8, df_m=6, N=17, N_clust=9, cmdline="regress executions income perpoverty perblack LN_VC100k96 south degree [pweight=fweight], vce(cluster id)", # noqa:E501 title="Linear regression", marginsok="XB default", vce="cluster", depvar="executions", cmd="regress", properties="b V", predict="regres_p", model="ols", estat_cmd="regress_estat", wexp="= fweight", wtype="pweight", vcetype="Robust", clustvar="id", ) params_table = np.array([ .00177624355887, .00103574504038, 1.7149428571794, .12469817836724, -.00061218878728, .00416467590501, 8, 2.3060041352042, 0, .70240571372092, .64463869959516, 1.0896114585768, .30761438040884, -.78413379325815, 2.1889452207, 8, 2.3060041352042, 0, -.76566360596606, .50850811868177, -1.5057057652313, .17056206446331, -1.9382854304311, .40695821849901, 8, 2.3060041352042, 0, 5.7915855647065, 6.2948340440059, .92005373362009, .3844480847801, -8.7243277711951, 20.307498900608, 8, 2.3060041352042, 0, 13.018291494864, 7.9526248350517, 1.6369804642972, .14027059672576, -5.3204942604922, 31.357077250221, 8, 2.3060041352042, 0, -140.99921608421, 84.897180497105, -1.6608233071889, .13532738016362, -336.77246537771, 54.774033209288, 8, 2.3060041352042, 0, -68.484290889814, 50.203382265366, -1.3641369923608, .2096627597382, -184.25349799498, 47.284916215355, 8, 2.3060041352042, 0]).reshape(7, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov = np.array([ 1.072767789e-06, .00042569049255, -.00044272344175, .00386796354086, .00653558563917, -.08376884119522, -.04513384476642, .00042569049255, .41555905301573, -.07730648264729, -.34087330734824, .82631440946934, -31.768811666606, -10.324414524804, -.00044272344175, -.07730648264729, .25858050676528, -2.8727606144729, -3.9481543148554, 35.836754991381, 24.653552354067, .00386796354086, -.34087330734824, -2.8727606144729, 39.624935641576, 42.351437415382, -335.98208369348, -283.16728769825, .00653558563917, .82631440946934, -3.9481543148554, 42.351437415382, 63.24424176708, -502.21726015398, -366.49477518415, -.08376884119522, -31.768811666606, 35.836754991381, -335.98208369348, -502.21726015398, 7207.531256358, 3532.1379707168, -.04513384476642, -10.324414524804, 24.653552354067, -283.16728769825, -366.49477518415, 3532.1379707168, 2520.3795908825]).reshape(7, 7) cov_colnames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] cov_rownames = ['income', 'perpoverty', 'perblack', 'LN_VC100k96', 'south', 'degree', '_cons'] infocrit = np.array([ 17, -55.235569128348, -47.541220455815, 7, 109.08244091163, 114.91493432002]) infocrit_colnames = 'N ll0 ll df AIC BIC'.split() infocrit_rownames = '.'.split() predicted = np.array([ 23.018356323242, 11.727355003357, 7.6487560272217, 3.4638004302979, 1.3298480510712, 2.1195623874664, 6.7120413780212, 2.8227334022522, .90416890382767, 2.2036759853363, 1.9608836174011, 2.0707910060883, 4.6054129600525, 2.9022018909454, 2.9902882575989, 1.6939970254898, 1.4887162446976, 1.8477793931961, 5.9044842720032, 4.8752007484436, 7.0818486213684, 4.4365234375, 7.5460968017578, 5.6850047111511, 4.1125593185425, 2.7407164573669, -2.7979807853699, 3.9614858627319, -1.4647831916809, 2.4376966953278, -3.5234127044678, 3.5529434680939, 3.9779393672943, 1.7075037956238]).reshape(17, 2) predicted_colnames = 'predict_mu predict_std'.split() predicted_rownames = ['r'+str(n) for n in range(1, 18)] results_wls_pweight_clu1 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, infocrit=infocrit, infocrit_colnames=infocrit_colnames, infocrit_rownames=infocrit_rownames, predicted=predicted, predicted_colnames=predicted_colnames, predicted_rownames=predicted_rownames, **est ) statsmodels-0.12.2/statsmodels/genmod/tests/results/results_tweedie_aweights_nonrobust.csv000066400000000000000000014052171400612667500325650ustar00rootroot00000000000000"V1","V2","V3","V4" -0.519169169314285,-1.28597017046844,-1.83732558009613,-0.823711600363306 2.55470518335245,3.46019223842148,2.14470065506344,3.77879183101721 0.402928158111979,0.403845040295908,0.36861871657613,0.404111622482144 0.270809458146069,0.49730671702117,0.437959618894633,0.593277690983777 3.9285319711191,4.9707908554308,2.78716847707543,5.32224747458835 3.9285319711191,11.1150262546776,6.23229817948523,5.32224747458835 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checking compatibility. # # Usage: # Rscript test_get_R_tweedie_var_weight.R > res_R_var_weight.py cat("# This file auto-generated by test_get_R_tweedie_var_weight.R\n") cat(sprintf("# Using: %s\n", R.Version()$version.string)) cat("import numpy as np\n") cat("import pandas as pd\n") cat("import os\n\n") cat("from statsmodels.tools.tools import Bunch\n\n") cat("path = os.path.abspath(__file__)\n") cat("dir_path = os.path.dirname(path)\n") require(statmod) options(digits=20) x <- (1.5)^(0:19) MISSING <- "MISSING" is.missing <- function(obj) { length(obj) == 1 && obj == MISSING } pyprint <- function(arr, prefix=NULL, suffix=NULL) { if (!is.null(prefix)) { cat(prefix) } if (is.missing(arr)) { cat("None\n") } else { cat("np.array([") cat("\n ") i <- 1 for (val in arr) { cat(val) if (i == length(arr)) { if (i %% 3 != 1) { cat("\n") } } else if (i %% 3 == 0) { cat(",\n ") } else { cat(", ") } i <- 1 + i } cat("])") if (!is.null(dim(arr))) { cat(".reshape((") j <- 1 for (size in dim(arr)) { cat(sprintf("%s", size)) if (j < length(dim(arr))) { cat(", ") } j <- 1 + j } cat("), order=\"F\")") } } if (!is.null(suffix)) { cat(sprintf("%s\n", suffix)) } else { cat("\n") } } cat(" ") out2py <- function(model, name, resid_csv = FALSE){ cat("\nres = dict()\n") pyprint(model$coefficients, prefix = "res['params'] = ") pyprint(diag(vcov(model))^0.5, prefix = "res['bse'] = ") cat(sprintf("res['deviance'] = %f\n", model$deviance)) ll = logLik(model) if (is.na(ll)) { cat("res['ll'] = np.nan\n") } else { cat(sprintf("res['ll'] = %f\n", ll)) } cat("res['resids_colnames'] = [\n 'resid_response', 'resid_pearson', 'resid_deviance', 'resid_working']\n" ) r <- cbind(residuals.glm(model, 'response'), residuals.glm(model, 'pearson'), residuals.glm(model, 'deviance'), residuals.glm(model, 'working')) if (is.character(resid_csv)) { write.csv(r, resid_csv, row.names = FALSE) cat(sprintf("csv_path = os.path.join(dir_path, '%s')\n", resid_csv)) cat(sprintf("resids = np.array(pd.read_csv(csv_path))\n")) cat(sprintf("res['resids'] = resids\n")) } else { pyprint(r, "res['resids'] = ") } cat(sprintf("%s = Bunch(**res)\n", name)) } control <- glm.control(epsilon = 1e-25, maxit = 100) data = read.csv('../../../datasets/fair/fair.csv') data$weights <- rep(1, length(data$rate_marriage)) data$weights[seq(1, length(data$rate_marriage), 5)] <- 5 data$weights[seq(1, length(data$rate_marriage), 13)] <- 3 model <- glm(affairs ~ 1 + age + yrs_married, data = data, family = tweedie(var.power = 1.55, link.power = 0), weights = weights, control = control) out2py(model, "results_tweedie_aweights_nonrobust", "results_tweedie_aweights_nonrobust.csv") data <- read.csv('stata_cancer_glm.csv') data$weights <- rep(1, length(data$studytime)) data$weights[seq(1, length(data$studytime), 5)] <- 5 data$weights[seq(1, length(data$studytime), 13)] <- 3 data$drug <- as.factor(data$drug) model <- glm(studytime ~ 1 + age + drug, data = data, family = Gamma(link = "log"), weights = weights, control = control) out2py(model, "results_gamma_aweights_nonrobust") data <- read.csv('../../../datasets/cpunish/cpunish.csv') data$INCOME <- data$INCOME / 1000 data$weight <- c(1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1) model <- glm(EXECUTIONS ~ INCOME + SOUTH - 1, data = data, family = gaussian(link = "log"), weights = weight, control = control) out2py(model, "results_gaussian_aweights_nonrobust") statsmodels-0.12.2/statsmodels/genmod/tests/test_bayes_mixed_glm.py000066400000000000000000000433661400612667500256770ustar00rootroot00000000000000import numpy as np from statsmodels.genmod.bayes_mixed_glm import (BinomialBayesMixedGLM, PoissonBayesMixedGLM) import pandas as pd from scipy import sparse from numpy.testing import assert_allclose, assert_equal from scipy.optimize import approx_fprime def gen_simple_logit(nc, cs, s): np.random.seed(3799) exog_vc = np.kron(np.eye(nc), np.ones((cs, 1))) exog_fe = np.random.normal(size=(nc * cs, 2)) vc = s * np.random.normal(size=nc) lp = np.dot(exog_fe, np.r_[1, -1]) + np.dot(exog_vc, vc) pr = 1 / (1 + np.exp(-lp)) y = 1 * (np.random.uniform(size=nc * cs) < pr) ident = np.zeros(nc, dtype=int) return y, exog_fe, exog_vc, ident def gen_simple_poisson(nc, cs, s): np.random.seed(3799) exog_vc = np.kron(np.eye(nc), np.ones((cs, 1))) exog_fe = np.random.normal(size=(nc * cs, 2)) vc = s * np.random.normal(size=nc) lp = np.dot(exog_fe, np.r_[0.1, -0.1]) + np.dot(exog_vc, vc) r = np.exp(lp) y = np.random.poisson(r) ident = np.zeros(nc, dtype=int) return y, exog_fe, exog_vc, ident def gen_crossed_logit(nc, cs, s1, s2): np.random.seed(3799) a = np.kron(np.eye(nc), np.ones((cs, 1))) b = np.kron(np.ones((cs, 1)), np.eye(nc)) exog_vc = np.concatenate((a, b), axis=1) exog_fe = np.random.normal(size=(nc * cs, 1)) vc = s1 * np.random.normal(size=2 * nc) vc[nc:] *= s2 / s1 lp = np.dot(exog_fe, np.r_[-0.5]) + np.dot(exog_vc, vc) pr = 1 / (1 + np.exp(-lp)) y = 1 * (np.random.uniform(size=nc * cs) < pr) ident = np.zeros(2 * nc, dtype=int) ident[nc:] = 1 return y, exog_fe, exog_vc, ident def gen_crossed_poisson(nc, cs, s1, s2): np.random.seed(3799) a = np.kron(np.eye(nc), np.ones((cs, 1))) b = np.kron(np.ones((cs, 1)), np.eye(nc)) exog_vc = np.concatenate((a, b), axis=1) exog_fe = np.random.normal(size=(nc * cs, 1)) vc = s1 * np.random.normal(size=2 * nc) vc[nc:] *= s2 / s1 lp = np.dot(exog_fe, np.r_[-0.5]) + np.dot(exog_vc, vc) r = np.exp(lp) y = np.random.poisson(r) ident = np.zeros(2 * nc, dtype=int) ident[nc:] = 1 return y, exog_fe, exog_vc, ident def gen_crossed_logit_pandas(nc, cs, s1, s2): np.random.seed(3799) a = np.kron(np.arange(nc), np.ones(cs)) b = np.kron(np.ones(cs), np.arange(nc)) fe = np.ones(nc * cs) vc = np.zeros(nc * cs) for i in np.unique(a): ii = np.flatnonzero(a == i) vc[ii] += s1 * np.random.normal() for i in np.unique(b): ii = np.flatnonzero(b == i) vc[ii] += s2 * np.random.normal() lp = -0.5 * fe + vc pr = 1 / (1 + np.exp(-lp)) y = 1 * (np.random.uniform(size=nc * cs) < pr) ident = np.zeros(2 * nc, dtype=int) ident[nc:] = 1 df = pd.DataFrame({"fe": fe, "a": a, "b": b, "y": y}) return df def test_simple_logit_map(): y, exog_fe, exog_vc, ident = gen_simple_logit(10, 10, 2) exog_vc = sparse.csr_matrix(exog_vc) glmm = BinomialBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5) rslt = glmm.fit_map() assert_allclose( glmm.logposterior_grad(rslt.params), np.zeros_like(rslt.params), atol=1e-3) # Test the predict method for linear in False, True: for exog in None, exog_fe: pr1 = rslt.predict(linear=linear, exog=exog) pr2 = glmm.predict(rslt.params, linear=linear, exog=exog) assert_allclose(pr1, pr2) if not linear: assert_equal(pr1.min() >= 0, True) assert_equal(pr1.max() <= 1, True) def test_simple_poisson_map(): y, exog_fe, exog_vc, ident = gen_simple_poisson(10, 10, 0.2) exog_vc = sparse.csr_matrix(exog_vc) glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5) rslt1 = glmm1.fit_map() assert_allclose( glmm1.logposterior_grad(rslt1.params), np.zeros_like(rslt1.params), atol=1e-3) # This should give the same answer as above glmm2 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5) rslt2 = glmm2.fit_map() assert_allclose(rslt1.params, rslt2.params, atol=1e-4) # Test the predict method for linear in False, True: for exog in None, exog_fe: pr1 = rslt1.predict(linear=linear, exog=exog) pr2 = rslt2.predict(linear=linear, exog=exog) pr3 = glmm1.predict(rslt1.params, linear=linear, exog=exog) pr4 = glmm2.predict(rslt2.params, linear=linear, exog=exog) assert_allclose(pr1, pr2, rtol=1e-5) assert_allclose(pr2, pr3, rtol=1e-5) assert_allclose(pr3, pr4, rtol=1e-5) if not linear: assert_equal(pr1.min() >= 0, True) assert_equal(pr2.min() >= 0, True) assert_equal(pr3.min() >= 0, True) # Check dimensions and PSD status of cov_params for rslt in rslt1, rslt2: cp = rslt.cov_params() p = len(rslt.params) assert_equal(cp.shape, np.r_[p, p]) np.linalg.cholesky(cp) def test_crossed_logit_map(): y, exog_fe, exog_vc, ident = gen_crossed_logit(10, 10, 1, 2) exog_vc = sparse.csr_matrix(exog_vc) glmm = BinomialBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5) rslt = glmm.fit_map() assert_allclose( glmm.logposterior_grad(rslt.params), np.zeros_like(rslt.params), atol=1e-4) # Check dimensions and PSD status of cov_params cp = rslt.cov_params() p = len(rslt.params) assert_equal(cp.shape, np.r_[p, p]) np.linalg.cholesky(cp) def test_crossed_poisson_map(): y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 1) exog_vc = sparse.csr_matrix(exog_vc) glmm = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5) rslt = glmm.fit_map() assert_allclose( glmm.logposterior_grad(rslt.params), np.zeros_like(rslt.params), atol=1e-4) # Check dimensions and PSD status of cov_params cp = rslt.cov_params() p = len(rslt.params) assert_equal(cp.shape, np.r_[p, p]) np.linalg.cholesky(cp) def test_logit_map_crossed_formula(): data = gen_crossed_logit_pandas(10, 10, 1, 0.5) fml = "y ~ fe" fml_vc = {"a": "0 + C(a)", "b": "0 + C(b)"} glmm = BinomialBayesMixedGLM.from_formula(fml, fml_vc, data, vcp_p=0.5) rslt = glmm.fit_map() assert_allclose( glmm.logposterior_grad(rslt.params), np.zeros_like(rslt.params), atol=1e-4) rslt.summary() r = rslt.random_effects("a") assert_allclose( r.iloc[0, :].values, np.r_[-0.02004904, 0.094014], atol=1e-4) # Check dimensions and PSD status of cov_params cm = rslt.cov_params() p = rslt.params.shape[0] assert_equal(list(cm.shape), [p, p]) np.linalg.cholesky(cm) def test_elbo_grad(): for f in range(2): for j in range(2): if f == 0: if j == 0: y, exog_fe, exog_vc, ident = gen_simple_logit(10, 10, 2) else: y, exog_fe, exog_vc, ident = gen_crossed_logit( 10, 10, 1, 2) elif f == 1: if j == 0: y, exog_fe, exog_vc, ident = gen_simple_poisson( 10, 10, 0.5) else: y, exog_fe, exog_vc, ident = gen_crossed_poisson( 10, 10, 1, 0.5) exog_vc = sparse.csr_matrix(exog_vc) if f == 0: glmm1 = BinomialBayesMixedGLM( y, exog_fe, exog_vc, ident, vcp_p=0.5) else: glmm1 = PoissonBayesMixedGLM( y, exog_fe, exog_vc, ident, vcp_p=0.5) rslt1 = glmm1.fit_map() for k in range(3): if k == 0: vb_mean = rslt1.params vb_sd = np.ones_like(vb_mean) elif k == 1: vb_mean = np.zeros(len(vb_mean)) vb_sd = np.ones_like(vb_mean) else: vb_mean = np.random.normal(size=len(vb_mean)) vb_sd = np.random.uniform(1, 2, size=len(vb_mean)) mean_grad, sd_grad = glmm1.vb_elbo_grad(vb_mean, vb_sd) def elbo(vec): n = len(vec) // 2 return glmm1.vb_elbo(vec[:n], vec[n:]) x = np.concatenate((vb_mean, vb_sd)) g1 = approx_fprime(x, elbo, 1e-5) n = len(x) // 2 mean_grad_n = g1[:n] sd_grad_n = g1[n:] assert_allclose(mean_grad, mean_grad_n, atol=1e-2, rtol=1e-2) assert_allclose(sd_grad, sd_grad_n, atol=1e-2, rtol=1e-2) def test_simple_logit_vb(): y, exog_fe, exog_vc, ident = gen_simple_logit(10, 10, 0) exog_vc = sparse.csr_matrix(exog_vc) glmm1 = BinomialBayesMixedGLM( y, exog_fe, exog_vc, ident, vcp_p=0.5, fe_p=0.5) rslt1 = glmm1.fit_map() glmm2 = BinomialBayesMixedGLM( y, exog_fe, exog_vc, ident, vcp_p=0.5, fe_p=0.5) rslt2 = glmm2.fit_vb(rslt1.params) rslt1.summary() rslt2.summary() assert_allclose( rslt1.params[0:5], np.r_[0.75330405, -0.71643228, -2.49091288, -0.00959806, 0.00450254], rtol=1e-4, atol=1e-4) assert_allclose( rslt2.params[0:5], np.r_[0.79338836, -0.7599833, -0.64149356, -0.24772884, 0.10775366], rtol=1e-4, atol=1e-4) for rslt in rslt1, rslt2: cp = rslt.cov_params() p = len(rslt.params) if rslt is rslt1: assert_equal(cp.shape, np.r_[p, p]) np.linalg.cholesky(cp) else: assert_equal(cp.shape, np.r_[p,]) assert_equal(cp > 0, True*np.ones(p)) def test_simple_poisson_vb(): y, exog_fe, exog_vc, ident = gen_simple_poisson(10, 10, 1) exog_vc = sparse.csr_matrix(exog_vc) glmm1 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5) rslt1 = glmm1.fit_map() glmm2 = PoissonBayesMixedGLM(y, exog_fe, exog_vc, ident, vcp_p=0.5) rslt2 = glmm2.fit_vb(rslt1.params) rslt1.summary() rslt2.summary() assert_allclose( rslt1.params[0:5], np.r_[-0.07233493, -0.06706505, -0.47159649, 1.12575122, -1.02442201], rtol=1e-4, atol=1e-4) assert_allclose( rslt1.cov_params().flat[0:5], np.r_[0.00790914, 0.00080666, -0.00050719, 0.00022648, 0.00046235], rtol=1e-4, atol=1e-4) assert_allclose( rslt2.params[0:5], np.r_[-0.07088814, -0.06373107, -0.22770786, 1.12923746, -1.26161339], rtol=1e-4, atol=1e-4) assert_allclose( rslt2.cov_params()[0:5], np.r_[0.00747782, 0.0092554, 0.04508904, 0.02934488, 0.20312746], rtol=1e-4, atol=1e-4) for rslt in rslt1, rslt2: cp = rslt.cov_params() p = len(rslt.params) if rslt is rslt1: assert_equal(cp.shape, np.r_[p, p]) np.linalg.cholesky(cp) else: assert_equal(cp.shape, np.r_[p,]) assert_equal(cp > 0, True*np.ones(p)) def test_crossed_logit_vb(): y, exog_fe, exog_vc, ident = gen_crossed_logit(10, 10, 1, 2) glmm1 = BinomialBayesMixedGLM( y, exog_fe, exog_vc, ident, vcp_p=0.5, fe_p=0.5) rslt1 = glmm1.fit_map() glmm2 = BinomialBayesMixedGLM( y, exog_fe, exog_vc, ident, vcp_p=0.5, fe_p=0.5) rslt2 = glmm2.fit_vb(mean=rslt1.params) rslt1.summary() rslt2.summary() assert_allclose( rslt1.params[0:5], np.r_[-5.43073978e-01, -2.46197518e+00, -2.36582801e+00, -9.64030461e-03, 2.32701078e-03], rtol=1e-4, atol=1e-4) assert_allclose( rslt1.cov_params().flat[0:5], np.r_[4.12927123e-02, -2.04448923e-04, 4.64829219e-05, 1.20377543e-04, -1.45003234e-04], rtol=1e-4, atol=1e-4) assert_allclose( rslt2.params[0:5], np.r_[-0.70834417, -0.3571011, 0.19126823, -0.36074489, 0.058976], rtol=1e-4, atol=1e-4) assert_allclose( rslt2.cov_params()[0:5], np.r_[0.05212492, 0.04729656, 0.03916944, 0.25921842, 0.25782576], rtol=1e-4, atol=1e-4) for rslt in rslt1, rslt2: cp = rslt.cov_params() p = len(rslt.params) if rslt is rslt1: assert_equal(cp.shape, np.r_[p, p]) np.linalg.cholesky(cp) else: assert_equal(cp.shape, np.r_[p,]) assert_equal(cp > 0, True*np.ones(p)) def test_crossed_logit_vb_formula(): data = gen_crossed_logit_pandas(10, 10, 1, 2) fml = "y ~ fe" fml_vc = {"a": "0 + C(a)", "b": "0 + C(b)"} glmm1 = BinomialBayesMixedGLM.from_formula(fml, fml_vc, data, vcp_p=0.5) rslt1 = glmm1.fit_vb() glmm2 = BinomialBayesMixedGLM( glmm1.endog, glmm1.exog, glmm1.exog_vc, glmm1.ident, vcp_p=0.5) rslt2 = glmm2.fit_vb() assert_allclose(rslt1.params, rslt2.params, atol=1e-4) rslt1.summary() rslt2.summary() for rslt in rslt1, rslt2: cp = rslt.cov_params() p = len(rslt.params) if rslt is rslt1: assert_equal(cp.shape, np.r_[p,]) assert_equal(cp > 0, True*np.ones(p)) else: assert_equal(cp.shape, np.r_[p,]) assert_equal(cp > 0, True*np.ones(p)) def test_crossed_poisson_vb(): y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 0.5) glmm1 = PoissonBayesMixedGLM( y, exog_fe, exog_vc, ident, vcp_p=0.5, fe_p=0.5) rslt1 = glmm1.fit_map() glmm2 = PoissonBayesMixedGLM( y, exog_fe, exog_vc, ident, vcp_p=0.5, fe_p=0.5) rslt2 = glmm2.fit_vb(mean=rslt1.params) rslt1.summary() rslt2.summary() assert_allclose( rslt1.params[0:5], np.r_[-0.54855281, 0.10458834, -0.68777741, -0.01699925, 0.77200546], rtol=1e-4, atol=1e-4) assert_allclose( rslt2.params[0:5], np.r_[-0.54691502, 0.22297158, -0.52673802, -0.06218684, 0.74385237], rtol=1e-4, atol=1e-4) for rslt in rslt1, rslt2: cp = rslt.cov_params() p = len(rslt.params) if rslt is rslt1: assert_equal(cp.shape, np.r_[p, p]) np.linalg.cholesky(cp) else: assert_equal(cp.shape, np.r_[p,]) assert_equal(cp > 0, True*np.ones(p)) def test_poisson_formula(): y, exog_fe, exog_vc, ident = gen_crossed_poisson(10, 10, 1, 0.5) for vb in False, True: glmm1 = PoissonBayesMixedGLM( y, exog_fe, exog_vc, ident) if vb: rslt1 = glmm1.fit_vb() else: rslt1 = glmm1.fit_map() # Build categorical variables that match exog_vc df = pd.DataFrame({"y": y, "x1": exog_fe[:, 0]}) z1 = np.zeros(len(y)) for j,k in enumerate(np.flatnonzero(ident == 0)): z1[exog_vc[:, k] == 1] = j df["z1"] = z1 z2 = np.zeros(len(y)) for j,k in enumerate(np.flatnonzero(ident == 1)): z2[exog_vc[:, k] == 1] = j df["z2"] = z2 fml = "y ~ 0 + x1" vc_fml = {} vc_fml["z1"] = "0 + C(z1)" vc_fml["z2"] = "0 + C(z2)" glmm2 = PoissonBayesMixedGLM.from_formula(fml, vc_fml, df) if vb: rslt2 = glmm2.fit_vb() else: rslt2 = glmm2.fit_map() assert_allclose(rslt1.params, rslt2.params, rtol=1e-5) for rslt in rslt1, rslt2: cp = rslt.cov_params() p = len(rslt.params) if vb: assert_equal(cp.shape, np.r_[p,]) assert_equal(cp > 0, True*np.ones(p)) else: assert_equal(cp.shape, np.r_[p, p]) np.linalg.cholesky(cp) def test_scale_vb(): y, exog_fe, exog_vc, ident = gen_simple_logit(10, 10, 0) exog_fe -= exog_fe.mean(0) exog_fe /= exog_fe.std(0) exog_vc = sparse.csr_matrix(exog_vc) rslts = [] for scale_fe in False, True: glmm = BinomialBayesMixedGLM( y, exog_fe, exog_vc, ident, vcp_p=0.5, fe_p=0.5) rslt = glmm.fit_vb(scale_fe=scale_fe) rslts.append(rslt) assert_allclose(rslts[0].params, rslts[1].params, rtol=1e-4) def test_scale_map(): y, exog_fe, exog_vc, ident = gen_simple_logit(10, 10, 0) exog_fe -= exog_fe.mean(0) exog_fe /= exog_fe.std(0) exog_vc = sparse.csr_matrix(exog_vc) rslts = [] for scale_fe in False, True: glmm = BinomialBayesMixedGLM( y, exog_fe, exog_vc, ident, vcp_p=0.5, fe_p=0.5) rslt = glmm.fit_map(scale_fe=scale_fe) rslts.append(rslt) assert_allclose(rslts[0].params, rslts[1].params, rtol=1e-4) def test_doc_examples(): np.random.seed(8767) n = 200 m = 20 data = pd.DataFrame({"Year": np.random.uniform(0, 1, n), "Village": np.random.randint(0, m, n)}) data['year_cen'] = data['Year'] - data.Year.mean() # Binomial outcome lpr = np.random.normal(size=m)[data.Village] lpr += np.random.normal(size=m)[data.Village] * data.year_cen y = (np.random.uniform(size=n) < 1 / (1 + np.exp(-lpr))) data["y"] = y.astype(int) # These lines should agree with the example in the class docstring. random = {"a": '0 + C(Village)', "b": '0 + C(Village)*year_cen'} model = BinomialBayesMixedGLM.from_formula( 'y ~ year_cen', random, data) result = model.fit_vb() _ = result # Poisson outcome lpr = np.random.normal(size=m)[data.Village] lpr += np.random.normal(size=m)[data.Village] * data.year_cen data["y"] = np.random.poisson(np.exp(lpr)) # These lines should agree with the example in the class docstring. random = {"a": '0 + C(Village)', "b": '0 + C(Village)*year_cen'} model = PoissonBayesMixedGLM.from_formula( 'y ~ year_cen', random, data) result = model.fit_vb() _ = result statsmodels-0.12.2/statsmodels/genmod/tests/test_constrained.py000066400000000000000000000216101400612667500250440ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Unit tests for fit_constrained Tests for Poisson and Binomial are in discrete Created on Sun Jan 7 09:21:39 2018 Author: Josef Perktold """ import warnings import numpy as np from numpy.testing import assert_allclose, assert_equal from statsmodels.tools.tools import add_constant from statsmodels.regression.linear_model import OLS, WLS from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod.families import family from statsmodels.tools.sm_exceptions import ValueWarning class ConstrainedCompareMixin(object): @classmethod def setup_class(cls): nobs, k_exog = 100, 5 np.random.seed(987125) x = np.random.randn(nobs, k_exog - 1) x = add_constant(x) y_true = x.sum(1) / 2 y = y_true + 2 * np.random.randn(nobs) cls.endog = y cls.exog = x cls.idx_uc = [0, 2, 3, 4] cls.idx_p_uc = np.array(cls.idx_uc) cls.idx_c = [1] cls.exogc = xc = x[:, cls.idx_uc] mod_ols_c = OLS(y - 0.5 * x[:, 1], xc) mod_ols_c.exog_names[:] = ['const', 'x2', 'x3', 'x4'] cls.mod2 = mod_ols_c cls.init() def test_params(self): res1 = self.res1 res2 = self.res2 assert_allclose(res1.params[self.idx_p_uc], res2.params, rtol=1e-10) def test_se(self): res1 = self.res1 res2 = self.res2 assert_equal(res1.df_resid, res2.df_resid) assert_allclose(res1.scale, res2.scale, rtol=1e-10) assert_allclose(res1.bse[self.idx_p_uc], res2.bse, rtol=1e-10) assert_allclose(res1.cov_params()[self.idx_p_uc[:, None], self.idx_p_uc], res2.cov_params(), rtol=5e-9, atol=1e-15) def test_resid(self): res1 = self.res1 res2 = self.res2 assert_allclose(res1.resid_response, res2.resid, rtol=1e-10) class TestGLMGaussianOffset(ConstrainedCompareMixin): @classmethod def init(cls): cls.res2 = cls.mod2.fit() mod = GLM(cls.endog, cls.exogc, offset=0.5 * cls.exog[:, cls.idx_c].squeeze()) mod.exog_names[:] = ['const', 'x2', 'x3', 'x4'] cls.res1 = mod.fit() cls.idx_p_uc = np.arange(cls.exogc.shape[1]) class TestGLMGaussianConstrained(ConstrainedCompareMixin): @classmethod def init(cls): cls.res2 = cls.mod2.fit() mod = GLM(cls.endog, cls.exog) mod.exog_names[:] = ['const', 'x1', 'x2', 'x3', 'x4'] cls.res1 = mod.fit_constrained('x1=0.5') class TestGLMGaussianOffsetHC(ConstrainedCompareMixin): @classmethod def init(cls): cov_type = 'HC0' cls.res2 = cls.mod2.fit(cov_type=cov_type) mod = GLM(cls.endog, cls.exogc, offset=0.5 * cls.exog[:, cls.idx_c].squeeze()) mod.exog_names[:] = ['const', 'x2', 'x3', 'x4'] cls.res1 = mod.fit(cov_type=cov_type) cls.idx_p_uc = np.arange(cls.exogc.shape[1]) class TestGLMGaussianConstrainedHC(ConstrainedCompareMixin): @classmethod def init(cls): cov_type = 'HC0' cls.res2 = cls.mod2.fit(cov_type=cov_type) mod = GLM(cls.endog, cls.exog) mod.exog_names[:] = ['const', 'x1', 'x2', 'x3', 'x4'] cls.res1 = mod.fit_constrained('x1=0.5', cov_type=cov_type) class ConstrainedCompareWtdMixin(ConstrainedCompareMixin): @classmethod def setup_class(cls): nobs, k_exog = 100, 5 np.random.seed(987125) x = np.random.randn(nobs, k_exog - 1) x = add_constant(x) cls.aweights = np.random.randint(1, 10, nobs) y_true = x.sum(1) / 2 y = y_true + 2 * np.random.randn(nobs) cls.endog = y cls.exog = x cls.idx_uc = [0, 2, 3, 4] cls.idx_p_uc = np.array(cls.idx_uc) cls.idx_c = [1] cls.exogc = xc = x[:, cls.idx_uc] mod_ols_c = WLS(y - 0.5 * x[:, 1], xc, weights=cls.aweights) mod_ols_c.exog_names[:] = ['const', 'x2', 'x3', 'x4'] cls.mod2 = mod_ols_c cls.init() class TestGLMWtdGaussianOffset(ConstrainedCompareWtdMixin): @classmethod def init(cls): cls.res2 = cls.mod2.fit() mod = GLM(cls.endog, cls.exogc, offset=0.5 * cls.exog[:, cls.idx_c].squeeze(), var_weights=cls.aweights) mod.exog_names[:] = ['const', 'x2', 'x3', 'x4'] cls.res1 = mod.fit() cls.idx_p_uc = np.arange(cls.exogc.shape[1]) class TestGLMWtdGaussianConstrained(ConstrainedCompareWtdMixin): @classmethod def init(cls): cls.res2 = cls.mod2.fit() mod = GLM(cls.endog, cls.exog, var_weights=cls.aweights) mod.exog_names[:] = ['const', 'x1', 'x2', 'x3', 'x4'] cls.res1 = mod.fit_constrained('x1=0.5') class TestGLMWtdGaussianOffsetHC(ConstrainedCompareWtdMixin): @classmethod def init(cls): cov_type = 'HC0' cls.res2 = cls.mod2.fit(cov_type=cov_type) mod = GLM(cls.endog, cls.exogc, offset=0.5 * cls.exog[:, cls.idx_c].squeeze(), var_weights=cls.aweights) mod.exog_names[:] = ['const', 'x2', 'x3', 'x4'] cls.res1 = mod.fit(cov_type=cov_type) cls.idx_p_uc = np.arange(cls.exogc.shape[1]) class TestGLMWtdGaussianConstrainedHC(ConstrainedCompareWtdMixin): @classmethod def init(cls): cov_type = 'HC0' cls.res2 = cls.mod2.fit(cov_type=cov_type) mod = GLM(cls.endog, cls.exog, var_weights=cls.aweights) mod.exog_names[:] = ['const', 'x1', 'x2', 'x3', 'x4'] cls.res1 = mod.fit_constrained('x1=0.5', cov_type=cov_type) class TestGLMBinomialCountConstrained(ConstrainedCompareMixin): @classmethod def setup_class(cls): from statsmodels.datasets.star98 import load #from statsmodels.genmod.tests.results.results_glm import Star98 data = load(as_pandas=False) exog = add_constant(data.exog, prepend=True) offset = np.ones(len(data.endog)) exog_keep = exog[:, :-5] cls.mod2 = GLM(data.endog, exog_keep, family=family.Binomial(), offset=offset) cls.mod1 = GLM(data.endog, exog, family=family.Binomial(), offset=offset) cls.init() @classmethod def init(cls): cls.res2 = cls.mod2.fit() k = cls.mod1.exog.shape[1] cls.idx_p_uc = np.arange(k - 5) constraints = np.eye(k)[-5:] cls.res1 = cls.mod1.fit_constrained(constraints) def test_resid(self): # need to override because res2 does not have resid res1 = self.res1 res2 = self.res2 assert_allclose(res1.resid_response, res2.resid_response, rtol=1e-8) def test_glm_attr(self): for attr in ['llf', 'null_deviance', 'aic', 'df_resid', 'df_model', 'pearson_chi2', 'scale']: assert_allclose(getattr(self.res1, attr), getattr(self.res2, attr), rtol=1e-10) with warnings.catch_warnings(): warnings.simplefilter("ignore", FutureWarning) # FutureWarning to silence BIC warning assert_allclose(self.res1.bic, self.res2.bic, rtol=1e-10) def test_wald(self): res1 = self.res1 res2 = self.res2 k1 = len(res1.params) k2 = len(res2.params) use_f = False with warnings.catch_warnings(): warnings.simplefilter('ignore', ValueWarning) wt2 = res2.wald_test(np.eye(k2)[1:], use_f=use_f) wt1 = res1.wald_test(np.eye(k1)[1:], use_f=use_f) assert_allclose(wt2.pvalue, wt1.pvalue, atol=1e-20) # pvalue = 0 assert_allclose(wt2.statistic, wt1.statistic, rtol=1e-8) assert_equal(wt2.df_denom, wt1.df_denom) use_f = True with warnings.catch_warnings(): warnings.simplefilter('ignore', ValueWarning) wt2 = res2.wald_test(np.eye(k2)[1:], use_f=use_f) wt1 = res1.wald_test(np.eye(k1)[1:], use_f=use_f) assert_allclose(wt2.pvalue, wt1.pvalue, rtol=1) # pvalue = 8e-273 assert_allclose(wt2.statistic, wt1.statistic, rtol=1e-8) assert_equal(wt2.df_denom, wt1.df_denom) assert_equal(wt2.df_num, wt1.df_num) assert_equal(wt2.summary()[-30:], wt1.summary()[-30:]) # smoke with warnings.catch_warnings(): # RuntimeWarnings because of truedivide and scipy distributions # Future to silence BIC warning warnings.simplefilter("ignore", FutureWarning) warnings.simplefilter('ignore', ValueWarning) warnings.simplefilter('ignore', RuntimeWarning) self.res1.summary() self.res1.summary2() class TestGLMBinomialCountConstrainedHC(TestGLMBinomialCountConstrained): @classmethod def init(cls): cls.res2 = cls.mod2.fit(cov_type='HC0') k = cls.mod1.exog.shape[1] cls.idx_p_uc = np.arange(k - 5) constraints = np.eye(k)[-5:] cls.res1 = cls.mod1.fit_constrained(constraints, cov_type='HC0') statsmodels-0.12.2/statsmodels/genmod/tests/test_gee.py000066400000000000000000002162431400612667500233030ustar00rootroot00000000000000""" Test functions for GEE External comparisons are to R and Stata. The statsmodels GEE implementation should generally agree with the R GEE implementation for the independence and exchangeable correlation structures. For other correlation structures, the details of the correlation estimation differ among implementations and the results will not agree exactly. """ from statsmodels.compat import lrange import os import numpy as np import pytest from numpy.testing import (assert_almost_equal, assert_equal, assert_allclose, assert_array_less, assert_raises, assert_warns, assert_) import statsmodels.genmod.generalized_estimating_equations as gee import statsmodels.tools as tools import statsmodels.regression.linear_model as lm from statsmodels.genmod import families from statsmodels.genmod import cov_struct import statsmodels.discrete.discrete_model as discrete import pandas as pd from scipy.stats.distributions import norm import warnings try: import matplotlib.pyplot as plt except ImportError: pass pdf_output = False if pdf_output: from matplotlib.backends.backend_pdf import PdfPages pdf = PdfPages("test_glm.pdf") else: pdf = None def close_or_save(pdf, fig): if pdf_output: pdf.savefig(fig) def load_data(fname, icept=True): """ Load a data set from the results directory. The data set should be a CSV file with the following format: Column 0: Group indicator Column 1: endog variable Columns 2-end: exog variables If `icept` is True, an intercept is prepended to the exog variables. """ cur_dir = os.path.dirname(os.path.abspath(__file__)) Z = np.genfromtxt(os.path.join(cur_dir, 'results', fname), delimiter=",") group = Z[:, 0] endog = Z[:, 1] exog = Z[:, 2:] if icept: exog = np.concatenate((np.ones((exog.shape[0], 1)), exog), axis=1) return endog, exog, group def check_wrapper(results): # check wrapper assert_(isinstance(results.params, pd.Series)) assert_(isinstance(results.fittedvalues, pd.Series)) assert_(isinstance(results.resid, pd.Series)) assert_(isinstance(results.centered_resid, pd.Series)) assert_(isinstance(results._results.params, np.ndarray)) assert_(isinstance(results._results.fittedvalues, np.ndarray)) assert_(isinstance(results._results.resid, np.ndarray)) assert_(isinstance(results._results.centered_resid, np.ndarray)) class TestGEE(object): def test_margins_gaussian(self): # Check marginal effects for a Gaussian GEE fit. Marginal # effects and ordinary effects should be equal. n = 40 np.random.seed(34234) exog = np.random.normal(size=(n, 3)) exog[:, 0] = 1 groups = np.kron(np.arange(n / 4), np.r_[1, 1, 1, 1]) endog = exog[:, 1] + np.random.normal(size=n) model = gee.GEE(endog, exog, groups) result = model.fit( start_params=[-4.88085602e-04, 1.18501903, 4.78820100e-02]) marg = result.get_margeff() assert_allclose(marg.margeff, result.params[1:]) assert_allclose(marg.margeff_se, result.bse[1:]) # smoke test marg.summary() def test_margins_logistic(self): # Check marginal effects for a binomial GEE fit. Comparison # comes from Stata. np.random.seed(34234) endog = np.r_[0, 0, 0, 0, 1, 1, 1, 1] exog = np.ones((8, 2)) exog[:, 1] = np.r_[1, 2, 1, 1, 2, 1, 2, 2] groups = np.arange(8) model = gee.GEE(endog, exog, groups, family=families.Binomial()) result = model.fit( cov_type='naive', start_params=[-3.29583687, 2.19722458]) marg = result.get_margeff() assert_allclose(marg.margeff, np.r_[0.4119796]) assert_allclose(marg.margeff_se, np.r_[0.1379962], rtol=1e-6) def test_margins_multinomial(self): # Check marginal effects for a 2-class multinomial GEE fit, # which should be equivalent to logistic regression. Comparison # comes from Stata. np.random.seed(34234) endog = np.r_[0, 0, 0, 0, 1, 1, 1, 1] exog = np.ones((8, 2)) exog[:, 1] = np.r_[1, 2, 1, 1, 2, 1, 2, 2] groups = np.arange(8) model = gee.NominalGEE(endog, exog, groups) result = model.fit(cov_type='naive', start_params=[ 3.295837, -2.197225]) marg = result.get_margeff() assert_allclose(marg.margeff, np.r_[-0.41197961], rtol=1e-5) assert_allclose(marg.margeff_se, np.r_[0.1379962], rtol=1e-6) @pytest.mark.smoke @pytest.mark.matplotlib def test_nominal_plot(self, close_figures): np.random.seed(34234) endog = np.r_[0, 0, 0, 0, 1, 1, 1, 1] exog = np.ones((8, 2)) exog[:, 1] = np.r_[1, 2, 1, 1, 2, 1, 2, 2] groups = np.arange(8) model = gee.NominalGEE(endog, exog, groups) result = model.fit(cov_type='naive', start_params=[3.295837, -2.197225]) fig = result.plot_distribution() assert_equal(isinstance(fig, plt.Figure), True) def test_margins_poisson(self): # Check marginal effects for a Poisson GEE fit. np.random.seed(34234) endog = np.r_[10, 15, 12, 13, 20, 18, 26, 29] exog = np.ones((8, 2)) exog[:, 1] = np.r_[0, 0, 0, 0, 1, 1, 1, 1] groups = np.arange(8) model = gee.GEE(endog, exog, groups, family=families.Poisson()) result = model.fit(cov_type='naive', start_params=[ 2.52572864, 0.62057649]) marg = result.get_margeff() assert_allclose(marg.margeff, np.r_[11.0928], rtol=1e-6) assert_allclose(marg.margeff_se, np.r_[3.269015], rtol=1e-6) def test_multinomial(self): """ Check the 2-class multinomial (nominal) GEE fit against logistic regression. """ np.random.seed(34234) endog = np.r_[0, 0, 0, 0, 1, 1, 1, 1] exog = np.ones((8, 2)) exog[:, 1] = np.r_[1, 2, 1, 1, 2, 1, 2, 2] groups = np.arange(8) model = gee.NominalGEE(endog, exog, groups) results = model.fit(cov_type='naive', start_params=[ 3.295837, -2.197225]) logit_model = gee.GEE(endog, exog, groups, family=families.Binomial()) logit_results = logit_model.fit(cov_type='naive') assert_allclose(results.params, -logit_results.params, rtol=1e-5) assert_allclose(results.bse, logit_results.bse, rtol=1e-5) def test_weighted(self): # Simple check where the answer can be computed by hand. exog = np.ones(20) weights = np.ones(20) weights[0:10] = 2 endog = np.zeros(20) endog[0:10] += 1 groups = np.kron(np.arange(10), np.r_[1, 1]) model = gee.GEE(endog, exog, groups, weights=weights) result = model.fit() assert_allclose(result.params, np.r_[2 / 3.]) # Comparison against stata using groups with different sizes. weights = np.ones(20) weights[10:] = 2 endog = np.r_[1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8] exog1 = np.r_[1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3] groups = np.r_[1, 1, 2, 2, 2, 2, 4, 4, 5, 5, 6, 6, 6, 6, 8, 8, 9, 9, 10, 10] exog = np.column_stack((np.ones(20), exog1)) # Comparison using independence model model = gee.GEE(endog, exog, groups, weights=weights, cov_struct=cov_struct.Independence()) g = np.mean([2, 4, 2, 2, 4, 2, 2, 2]) fac = 20 / float(20 - g) result = model.fit(ddof_scale=0, scaling_factor=fac) assert_allclose(result.params, np.r_[1.247573, 1.436893], atol=1e-6) assert_allclose(result.scale, 1.808576) # Stata multiples robust SE by sqrt(N / (N - g)), where N is # the total sample size and g is the average group size. assert_allclose(result.bse, np.r_[0.895366, 0.3425498], atol=1e-5) # Comparison using exchangeable model # Smoke test for now model = gee.GEE(endog, exog, groups, weights=weights, cov_struct=cov_struct.Exchangeable()) model.fit(ddof_scale=0) # This is in the release announcement for version 0.6. def test_poisson_epil(self): cur_dir = os.path.dirname(os.path.abspath(__file__)) fname = os.path.join(cur_dir, "results", "epil.csv") data = pd.read_csv(fname) fam = families.Poisson() ind = cov_struct.Independence() mod1 = gee.GEE.from_formula("y ~ age + trt + base", data["subject"], data, cov_struct=ind, family=fam) rslt1 = mod1.fit(cov_type='naive') # Coefficients should agree with GLM from statsmodels.genmod.generalized_linear_model import GLM mod2 = GLM.from_formula("y ~ age + trt + base", data, family=families.Poisson()) rslt2 = mod2.fit() # do not use wrapper, asserts_xxx do not work rslt1 = rslt1._results rslt2 = rslt2._results assert_allclose(rslt1.params, rslt2.params, rtol=1e-6, atol=1e-6) assert_allclose(rslt1.bse, rslt2.bse, rtol=1e-6, atol=1e-6) def test_missing(self): # Test missing data handling for calling from the api. Missing # data handling does not currently work for formulas. np.random.seed(34234) endog = np.random.normal(size=100) exog = np.random.normal(size=(100, 3)) exog[:, 0] = 1 groups = np.kron(lrange(20), np.ones(5)) endog[0] = np.nan endog[5:7] = np.nan exog[10:12, 1] = np.nan mod1 = gee.GEE(endog, exog, groups, missing='drop') rslt1 = mod1.fit() assert_almost_equal(len(mod1.endog), 95) assert_almost_equal(np.asarray(mod1.exog.shape), np.r_[95, 3]) ii = np.isfinite(endog) & np.isfinite(exog).all(1) mod2 = gee.GEE(endog[ii], exog[ii, :], groups[ii], missing='none') rslt2 = mod2.fit() assert_almost_equal(rslt1.params, rslt2.params) assert_almost_equal(rslt1.bse, rslt2.bse) def test_missing_formula(self): # Test missing data handling for formulas. np.random.seed(34234) endog = np.random.normal(size=100) exog1 = np.random.normal(size=100) exog2 = np.random.normal(size=100) exog3 = np.random.normal(size=100) groups = np.kron(lrange(20), np.ones(5)) endog[0] = np.nan endog[5:7] = np.nan exog2[10:12] = np.nan data0 = pd.DataFrame({"endog": endog, "exog1": exog1, "exog2": exog2, "exog3": exog3, "groups": groups}) for k in 0, 1: data = data0.copy() kwargs = {} if k == 1: data["offset"] = 0 data["time"] = 0 kwargs["offset"] = "offset" kwargs["time"] = "time" mod1 = gee.GEE.from_formula("endog ~ exog1 + exog2 + exog3", groups="groups", data=data, missing='drop', **kwargs) rslt1 = mod1.fit() assert_almost_equal(len(mod1.endog), 95) assert_almost_equal(np.asarray(mod1.exog.shape), np.r_[95, 4]) data = data.dropna() kwargs = {} if k == 1: kwargs["offset"] = data["offset"] kwargs["time"] = data["time"] mod2 = gee.GEE.from_formula("endog ~ exog1 + exog2 + exog3", groups=data["groups"], data=data, missing='none', **kwargs) rslt2 = mod2.fit() assert_almost_equal(rslt1.params.values, rslt2.params.values) assert_almost_equal(rslt1.bse.values, rslt2.bse.values) @pytest.mark.parametrize("k1", [False, True]) @pytest.mark.parametrize("k2", [False, True]) def test_invalid_args(self, k1, k2): for j in range(3): p = [20, 20, 20] p[j] = 18 endog = np.zeros(p[0]) exog = np.zeros((p[1], 2)) kwargs = {} kwargs["groups"] = np.zeros(p[2]) if k1: kwargs["exposure"] = np.zeros(18) if k2: kwargs["time"] = np.zeros(18) with assert_raises(ValueError): gee.GEE(endog, exog, **kwargs) def test_default_time(self): # Check that the time defaults work correctly. endog, exog, group = load_data("gee_logistic_1.csv") # Time values for the autoregressive model T = np.zeros(len(endog)) idx = set(group) for ii in idx: jj = np.flatnonzero(group == ii) T[jj] = lrange(len(jj)) family = families.Binomial() va = cov_struct.Autoregressive() md1 = gee.GEE(endog, exog, group, family=family, cov_struct=va) mdf1 = md1.fit() md2 = gee.GEE(endog, exog, group, time=T, family=family, cov_struct=va) mdf2 = md2.fit() assert_almost_equal(mdf1.params, mdf2.params, decimal=6) assert_almost_equal(mdf1.standard_errors(), mdf2.standard_errors(), decimal=6) def test_logistic(self): # R code for comparing results: # library(gee) # Z = read.csv("results/gee_logistic_1.csv", header=FALSE) # Y = Z[,2] # Id = Z[,1] # X1 = Z[,3] # X2 = Z[,4] # X3 = Z[,5] # mi = gee(Y ~ X1 + X2 + X3, id=Id, family=binomial, # corstr="independence") # smi = summary(mi) # u = coefficients(smi) # cfi = paste(u[,1], collapse=",") # sei = paste(u[,4], collapse=",") # me = gee(Y ~ X1 + X2 + X3, id=Id, family=binomial, # corstr="exchangeable") # sme = summary(me) # u = coefficients(sme) # cfe = paste(u[,1], collapse=",") # see = paste(u[,4], collapse=",") # ma = gee(Y ~ X1 + X2 + X3, id=Id, family=binomial, # corstr="AR-M") # sma = summary(ma) # u = coefficients(sma) # cfa = paste(u[,1], collapse=",") # sea = paste(u[,4], collapse=",") # sprintf("cf = [[%s],[%s],[%s]]", cfi, cfe, cfa) # sprintf("se = [[%s],[%s],[%s]]", sei, see, sea) endog, exog, group = load_data("gee_logistic_1.csv") # Time values for the autoregressive model T = np.zeros(len(endog)) idx = set(group) for ii in idx: jj = np.flatnonzero(group == ii) T[jj] = lrange(len(jj)) family = families.Binomial() ve = cov_struct.Exchangeable() vi = cov_struct.Independence() va = cov_struct.Autoregressive() # From R gee cf = [[0.0167272965285882, 1.13038654425893, -1.86896345082962, 1.09397608331333], [0.0178982283915449, 1.13118798191788, -1.86133518416017, 1.08944256230299], [0.0109621937947958, 1.13226505028438, -1.88278757333046, 1.09954623769449]] se = [[0.127291720283049, 0.166725808326067, 0.192430061340865, 0.173141068839597], [0.127045031730155, 0.165470678232842, 0.192052750030501, 0.173174779369249], [0.127240302296444, 0.170554083928117, 0.191045527104503, 0.169776150974586]] for j, v in enumerate((vi, ve, va)): md = gee.GEE(endog, exog, group, T, family, v) mdf = md.fit() if id(v) != id(va): assert_almost_equal(mdf.params, cf[j], decimal=6) assert_almost_equal(mdf.standard_errors(), se[j], decimal=6) # Test with formulas D = np.concatenate((endog[:, None], group[:, None], exog[:, 1:]), axis=1) D = pd.DataFrame(D) D.columns = ["Y", "Id", ] + ["X%d" % (k + 1) for k in range(exog.shape[1] - 1)] for j, v in enumerate((vi, ve)): md = gee.GEE.from_formula("Y ~ X1 + X2 + X3", "Id", D, family=family, cov_struct=v) mdf = md.fit() assert_almost_equal(mdf.params, cf[j], decimal=6) assert_almost_equal(mdf.standard_errors(), se[j], decimal=6) # FIXME: do not leave commented-out # Check for run-time exceptions in summary # print(mdf.summary()) def test_autoregressive(self): dep_params_true = [0, 0.589208623896, 0.559823804948] params_true = [[1.08043787, 1.12709319, 0.90133927], [0.9613677, 1.05826987, 0.90832055], [1.05370439, 0.96084864, 0.93923374]] np.random.seed(342837482) num_group = 100 ar_param = 0.5 k = 3 ga = families.Gaussian() for gsize in 1, 2, 3: ix = np.arange(gsize)[:, None] - np.arange(gsize)[None, :] ix = np.abs(ix) cmat = ar_param ** ix cmat_r = np.linalg.cholesky(cmat) endog = [] exog = [] groups = [] for i in range(num_group): x = np.random.normal(size=(gsize, k)) exog.append(x) expval = x.sum(1) errors = np.dot(cmat_r, np.random.normal(size=gsize)) endog.append(expval + errors) groups.append(i * np.ones(gsize)) endog = np.concatenate(endog) groups = np.concatenate(groups) exog = np.concatenate(exog, axis=0) ar = cov_struct.Autoregressive() md = gee.GEE(endog, exog, groups, family=ga, cov_struct=ar) mdf = md.fit() assert_almost_equal(ar.dep_params, dep_params_true[gsize - 1]) assert_almost_equal(mdf.params, params_true[gsize - 1]) def test_post_estimation(self): family = families.Gaussian() endog, exog, group = load_data("gee_linear_1.csv") ve = cov_struct.Exchangeable() md = gee.GEE(endog, exog, group, None, family, ve) mdf = md.fit() assert_almost_equal(np.dot(exog, mdf.params), mdf.fittedvalues) assert_almost_equal(endog - np.dot(exog, mdf.params), mdf.resid) def test_scoretest(self): # Regression tests np.random.seed(6432) n = 200 # Must be divisible by 4 exog = np.random.normal(size=(n, 4)) endog = exog[:, 0] + exog[:, 1] + exog[:, 2] endog += 3 * np.random.normal(size=n) group = np.kron(np.arange(n / 4), np.ones(4)) # Test under the null. L = np.array([[1., -1, 0, 0]]) R = np.array([0., ]) family = families.Gaussian() va = cov_struct.Independence() mod1 = gee.GEE(endog, exog, group, family=family, cov_struct=va, constraint=(L, R)) res1 = mod1.fit() assert_almost_equal(res1.score_test()["statistic"], 1.08126334) assert_almost_equal(res1.score_test()["p-value"], 0.2984151086) # Test under the alternative. L = np.array([[1., -1, 0, 0]]) R = np.array([1.0, ]) family = families.Gaussian() va = cov_struct.Independence() mod2 = gee.GEE(endog, exog, group, family=family, cov_struct=va, constraint=(L, R)) res2 = mod2.fit() assert_almost_equal(res2.score_test()["statistic"], 3.491110965) assert_almost_equal(res2.score_test()["p-value"], 0.0616991659) # Compare to Wald tests exog = np.random.normal(size=(n, 2)) L = np.array([[1, -1]]) R = np.array([0.]) f = np.r_[1, -1] for i in range(10): endog = exog[:, 0] + (0.5 + i / 10.) * exog[:, 1] +\ np.random.normal(size=n) family = families.Gaussian() va = cov_struct.Independence() mod0 = gee.GEE(endog, exog, group, family=family, cov_struct=va) rslt0 = mod0.fit() family = families.Gaussian() va = cov_struct.Independence() mod1 = gee.GEE(endog, exog, group, family=family, cov_struct=va, constraint=(L, R)) res1 = mod1.fit() se = np.sqrt(np.dot(f, np.dot(rslt0.cov_params(), f))) wald_z = np.dot(f, rslt0.params) / se wald_p = 2 * norm.cdf(-np.abs(wald_z)) score_p = res1.score_test()["p-value"] assert_array_less(np.abs(wald_p - score_p), 0.02) @pytest.mark.parametrize("cov_struct", [cov_struct.Independence, cov_struct.Exchangeable]) def test_compare_score_test(self, cov_struct): np.random.seed(6432) n = 200 # Must be divisible by 4 exog = np.random.normal(size=(n, 4)) group = np.kron(np.arange(n / 4), np.ones(4)) exog_sub = exog[:, [0, 3]] endog = exog_sub.sum(1) + 3 * np.random.normal(size=n) L = np.asarray([[0, 1, 0, 0], [0, 0, 1, 0]]) R = np.zeros(2) mod_lr = gee.GEE(endog, exog, group, constraint=(L, R), cov_struct=cov_struct()) mod_lr.fit() mod_sub = gee.GEE(endog, exog_sub, group, cov_struct=cov_struct()) res_sub = mod_sub.fit() for call_fit in [False, True]: mod = gee.GEE(endog, exog, group, cov_struct=cov_struct()) if call_fit: # Should work with or without fitting the parent model mod.fit() score_results = mod.compare_score_test(res_sub) assert_almost_equal( score_results["statistic"], mod_lr.score_test_results["statistic"]) assert_almost_equal( score_results["p-value"], mod_lr.score_test_results["p-value"]) assert_almost_equal( score_results["df"], mod_lr.score_test_results["df"]) def test_compare_score_test_warnings(self): np.random.seed(6432) n = 200 # Must be divisible by 4 exog = np.random.normal(size=(n, 4)) group = np.kron(np.arange(n / 4), np.ones(4)) exog_sub = exog[:, [0, 3]] endog = exog_sub.sum(1) + 3 * np.random.normal(size=n) # Mismatched cov_struct with assert_warns(UserWarning): mod_sub = gee.GEE(endog, exog_sub, group, cov_struct=cov_struct.Exchangeable()) res_sub = mod_sub.fit() mod = gee.GEE(endog, exog, group, cov_struct=cov_struct.Independence()) mod.compare_score_test(res_sub) # smoketest # Mismatched family with assert_warns(UserWarning): mod_sub = gee.GEE(endog, exog_sub, group, family=families.Gaussian()) res_sub = mod_sub.fit() mod = gee.GEE(endog, exog, group, family=families.Poisson()) mod.compare_score_test(res_sub) # smoketest # Mismatched size with assert_raises(Exception): mod_sub = gee.GEE(endog, exog_sub, group) res_sub = mod_sub.fit() mod = gee.GEE(endog[0:100], exog[:100, :], group[0:100]) mod.compare_score_test(res_sub) # smoketest # Mismatched weights with assert_warns(UserWarning): w = np.random.uniform(size=n) mod_sub = gee.GEE(endog, exog_sub, group, weights=w) res_sub = mod_sub.fit() mod = gee.GEE(endog, exog, group) mod.compare_score_test(res_sub) # smoketest # Parent and submodel are the same dimension with pytest.warns(UserWarning): w = np.random.uniform(size=n) mod_sub = gee.GEE(endog, exog, group) res_sub = mod_sub.fit() mod = gee.GEE(endog, exog, group) mod.compare_score_test(res_sub) # smoketest def test_constraint_covtype(self): # Test constraints with different cov types np.random.seed(6432) n = 200 exog = np.random.normal(size=(n, 4)) endog = exog[:, 0] + exog[:, 1] + exog[:, 2] endog += 3 * np.random.normal(size=n) group = np.kron(np.arange(n / 4), np.ones(4)) L = np.array([[1., -1, 0, 0]]) R = np.array([0., ]) family = families.Gaussian() va = cov_struct.Independence() for cov_type in "robust", "naive", "bias_reduced": model = gee.GEE(endog, exog, group, family=family, cov_struct=va, constraint=(L, R)) result = model.fit(cov_type=cov_type) result.standard_errors(cov_type=cov_type) assert_allclose(result.cov_robust.shape, np.r_[4, 4]) assert_allclose(result.cov_naive.shape, np.r_[4, 4]) if cov_type == "bias_reduced": assert_allclose(result.cov_robust_bc.shape, np.r_[4, 4]) def test_linear(self): # library(gee) # Z = read.csv("results/gee_linear_1.csv", header=FALSE) # Y = Z[,2] # Id = Z[,1] # X1 = Z[,3] # X2 = Z[,4] # X3 = Z[,5] # mi = gee(Y ~ X1 + X2 + X3, id=Id, family=gaussian, # corstr="independence", tol=1e-8, maxit=100) # smi = summary(mi) # u = coefficients(smi) # cfi = paste(u[,1], collapse=",") # sei = paste(u[,4], collapse=",") # me = gee(Y ~ X1 + X2 + X3, id=Id, family=gaussian, # corstr="exchangeable", tol=1e-8, maxit=100) # sme = summary(me) # u = coefficients(sme) # cfe = paste(u[,1], collapse=",") # see = paste(u[,4], collapse=",") # sprintf("cf = [[%s],[%s]]", cfi, cfe) # sprintf("se = [[%s],[%s]]", sei, see) family = families.Gaussian() endog, exog, group = load_data("gee_linear_1.csv") vi = cov_struct.Independence() ve = cov_struct.Exchangeable() # From R gee cf = [[-0.01850226507491, 0.81436304278962, -1.56167635393184, 0.794239361055003], [-0.0182920577154767, 0.814898414022467, -1.56194040106201, 0.793499517527478]] se = [[0.0440733554189401, 0.0479993639119261, 0.0496045952071308, 0.0479467597161284], [0.0440369906460754, 0.0480069787567662, 0.049519758758187, 0.0479760443027526]] for j, v in enumerate((vi, ve)): md = gee.GEE(endog, exog, group, None, family, v) mdf = md.fit() assert_almost_equal(mdf.params, cf[j], decimal=10) assert_almost_equal(mdf.standard_errors(), se[j], decimal=10) # Test with formulas D = np.concatenate((endog[:, None], group[:, None], exog[:, 1:]), axis=1) D = pd.DataFrame(D) D.columns = ["Y", "Id", ] + ["X%d" % (k + 1) for k in range(exog.shape[1] - 1)] for j, v in enumerate((vi, ve)): md = gee.GEE.from_formula("Y ~ X1 + X2 + X3", "Id", D, family=family, cov_struct=v) mdf = md.fit() assert_almost_equal(mdf.params, cf[j], decimal=10) assert_almost_equal(mdf.standard_errors(), se[j], decimal=10) def test_linear_constrained(self): family = families.Gaussian() np.random.seed(34234) exog = np.random.normal(size=(300, 4)) exog[:, 0] = 1 endog = np.dot(exog, np.r_[1, 1, 0, 0.2]) +\ np.random.normal(size=300) group = np.kron(np.arange(100), np.r_[1, 1, 1]) vi = cov_struct.Independence() ve = cov_struct.Exchangeable() L = np.r_[[[0, 0, 0, 1]]] R = np.r_[0, ] for j, v in enumerate((vi, ve)): md = gee.GEE(endog, exog, group, None, family, v, constraint=(L, R)) mdf = md.fit() assert_almost_equal(mdf.params[3], 0, decimal=10) def test_nested_linear(self): family = families.Gaussian() endog, exog, group = load_data("gee_nested_linear_1.csv") group_n = [] for i in range(endog.shape[0] // 10): group_n.extend([0, ] * 5) group_n.extend([1, ] * 5) group_n = np.array(group_n)[:, None] dp = cov_struct.Independence() md = gee.GEE(endog, exog, group, None, family, dp) mdf1 = md.fit() # From statsmodels.GEE (not an independent test) cf = np.r_[-0.1671073, 1.00467426, -2.01723004, 0.97297106] se = np.r_[0.08629606, 0.04058653, 0.04067038, 0.03777989] assert_almost_equal(mdf1.params, cf, decimal=6) assert_almost_equal(mdf1.standard_errors(), se, decimal=6) ne = cov_struct.Nested() md = gee.GEE(endog, exog, group, None, family, ne, dep_data=group_n) mdf2 = md.fit(start_params=mdf1.params) # From statsmodels.GEE (not an independent test) cf = np.r_[-0.16655319, 1.02183688, -2.00858719, 1.00101969] se = np.r_[0.08632616, 0.02913582, 0.03114428, 0.02893991] assert_almost_equal(mdf2.params, cf, decimal=6) assert_almost_equal(mdf2.standard_errors(), se, decimal=6) smry = mdf2.cov_struct.summary() assert_allclose( smry.Variance, np.r_[1.043878, 0.611656, 1.421205], atol=1e-5, rtol=1e-5) def test_nested_pandas(self): np.random.seed(4234) n = 10000 # Outer groups groups = np.kron(np.arange(n // 100), np.ones(100)).astype(int) # Inner groups groups1 = np.kron(np.arange(n // 50), np.ones(50)).astype(int) groups2 = np.kron(np.arange(n // 10), np.ones(10)).astype(int) # Group effects groups_e = np.random.normal(size=n // 100) groups1_e = 2 * np.random.normal(size=n // 50) groups2_e = 3 * np.random.normal(size=n // 10) y = groups_e[groups] + groups1_e[groups1] + groups2_e[groups2] y += 0.5 * np.random.normal(size=n) df = pd.DataFrame({"y": y, "TheGroups": groups, "groups1": groups1, "groups2": groups2}) model = gee.GEE.from_formula("y ~ 1", groups="TheGroups", dep_data="0 + groups1 + groups2", cov_struct=cov_struct.Nested(), data=df) result = model.fit() # The true variances are 1, 4, 9, 0.25 smry = result.cov_struct.summary() assert_allclose( smry.Variance, np.r_[1.437299, 4.421543, 8.905295, 0.258480], atol=1e-5, rtol=1e-5) def test_ordinal(self): family = families.Binomial() endog, exog, groups = load_data("gee_ordinal_1.csv", icept=False) va = cov_struct.GlobalOddsRatio("ordinal") mod = gee.OrdinalGEE(endog, exog, groups, None, family, va) rslt = mod.fit() # Regression test cf = np.r_[1.09250002, 0.0217443, -0.39851092, -0.01812116, 0.03023969, 1.18258516, 0.01803453, -1.10203381] assert_almost_equal(rslt.params, cf, decimal=5) # Regression test se = np.r_[0.10883461, 0.10330197, 0.11177088, 0.05486569, 0.05997153, 0.09168148, 0.05953324, 0.0853862] assert_almost_equal(rslt.bse, se, decimal=5) # Check that we get the correct results type assert_equal(type(rslt), gee.OrdinalGEEResultsWrapper) assert_equal(type(rslt._results), gee.OrdinalGEEResults) @pytest.mark.smoke def test_ordinal_formula(self): np.random.seed(434) n = 40 y = np.random.randint(0, 3, n) groups = np.arange(n) x1 = np.random.normal(size=n) x2 = np.random.normal(size=n) df = pd.DataFrame({"y": y, "groups": groups, "x1": x1, "x2": x2}) model = gee.OrdinalGEE.from_formula("y ~ 0 + x1 + x2", groups, data=df) model.fit() with warnings.catch_warnings(): warnings.simplefilter("ignore") model = gee.NominalGEE.from_formula("y ~ 0 + x1 + x2", groups, data=df) model.fit() @pytest.mark.smoke def test_ordinal_independence(self): np.random.seed(434) n = 40 y = np.random.randint(0, 3, n) groups = np.kron(np.arange(n / 2), np.r_[1, 1]) x = np.random.normal(size=(n, 1)) odi = cov_struct.OrdinalIndependence() model1 = gee.OrdinalGEE(y, x, groups, cov_struct=odi) model1.fit() @pytest.mark.smoke def test_nominal_independence(self): np.random.seed(434) n = 40 y = np.random.randint(0, 3, n) groups = np.kron(np.arange(n / 2), np.r_[1, 1]) x = np.random.normal(size=(n, 1)) with warnings.catch_warnings(): warnings.simplefilter("ignore") nmi = cov_struct.NominalIndependence() model1 = gee.NominalGEE(y, x, groups, cov_struct=nmi) model1.fit() @pytest.mark.smoke @pytest.mark.matplotlib def test_ordinal_plot(self, close_figures): family = families.Binomial() endog, exog, groups = load_data("gee_ordinal_1.csv", icept=False) va = cov_struct.GlobalOddsRatio("ordinal") mod = gee.OrdinalGEE(endog, exog, groups, None, family, va) rslt = mod.fit() fig = rslt.plot_distribution() assert_equal(isinstance(fig, plt.Figure), True) def test_nominal(self): endog, exog, groups = load_data("gee_nominal_1.csv", icept=False) # Test with independence correlation va = cov_struct.Independence() mod1 = gee.NominalGEE(endog, exog, groups, cov_struct=va) rslt1 = mod1.fit() # Regression test cf1 = np.r_[0.450009, 0.451959, -0.918825, -0.468266] se1 = np.r_[0.08915936, 0.07005046, 0.12198139, 0.08281258] assert_allclose(rslt1.params, cf1, rtol=1e-5, atol=1e-5) assert_allclose(rslt1.standard_errors(), se1, rtol=1e-5, atol=1e-5) # Test with global odds ratio dependence va = cov_struct.GlobalOddsRatio("nominal") mod2 = gee.NominalGEE(endog, exog, groups, cov_struct=va) rslt2 = mod2.fit(start_params=rslt1.params) # Regression test cf2 = np.r_[0.455365, 0.415334, -0.916589, -0.502116] se2 = np.r_[0.08803614, 0.06628179, 0.12259726, 0.08411064] assert_allclose(rslt2.params, cf2, rtol=1e-5, atol=1e-5) assert_allclose(rslt2.standard_errors(), se2, rtol=1e-5, atol=1e-5) # Make sure we get the correct results type assert_equal(type(rslt1), gee.NominalGEEResultsWrapper) assert_equal(type(rslt1._results), gee.NominalGEEResults) def test_poisson(self): # library(gee) # Z = read.csv("results/gee_poisson_1.csv", header=FALSE) # Y = Z[,2] # Id = Z[,1] # X1 = Z[,3] # X2 = Z[,4] # X3 = Z[,5] # X4 = Z[,6] # X5 = Z[,7] # mi = gee(Y ~ X1 + X2 + X3 + X4 + X5, id=Id, family=poisson, # corstr="independence", scale.fix=TRUE) # smi = summary(mi) # u = coefficients(smi) # cfi = paste(u[,1], collapse=",") # sei = paste(u[,4], collapse=",") # me = gee(Y ~ X1 + X2 + X3 + X4 + X5, id=Id, family=poisson, # corstr="exchangeable", scale.fix=TRUE) # sme = summary(me) # u = coefficients(sme) # cfe = paste(u[,1], collapse=",") # see = paste(u[,4], collapse=",") # sprintf("cf = [[%s],[%s]]", cfi, cfe) # sprintf("se = [[%s],[%s]]", sei, see) family = families.Poisson() endog, exog, group_n = load_data("gee_poisson_1.csv") vi = cov_struct.Independence() ve = cov_struct.Exchangeable() # From R gee cf = [[-0.0364450410793481, -0.0543209391301178, 0.0156642711741052, 0.57628591338724, -0.00465659951186211, -0.477093153099256], [-0.0315615554826533, -0.0562589480840004, 0.0178419412298561, 0.571512795340481, -0.00363255566297332, -0.475971696727736]] se = [[0.0611309237214186, 0.0390680524493108, 0.0334234174505518, 0.0366860768962715, 0.0304758505008105, 0.0316348058881079], [0.0610840153582275, 0.0376887268649102, 0.0325168379415177, 0.0369786751362213, 0.0296141014225009, 0.0306115470200955]] for j, v in enumerate((vi, ve)): md = gee.GEE(endog, exog, group_n, None, family, v) mdf = md.fit() assert_almost_equal(mdf.params, cf[j], decimal=5) assert_almost_equal(mdf.standard_errors(), se[j], decimal=6) # Test with formulas D = np.concatenate((endog[:, None], group_n[:, None], exog[:, 1:]), axis=1) D = pd.DataFrame(D) D.columns = ["Y", "Id", ] + ["X%d" % (k + 1) for k in range(exog.shape[1] - 1)] for j, v in enumerate((vi, ve)): md = gee.GEE.from_formula("Y ~ X1 + X2 + X3 + X4 + X5", "Id", D, family=family, cov_struct=v) mdf = md.fit() assert_almost_equal(mdf.params, cf[j], decimal=5) assert_almost_equal(mdf.standard_errors(), se[j], decimal=6) # print(mdf.params) def test_groups(self): # Test various group structures (nonconsecutive, different # group sizes, not ordered, string labels) np.random.seed(234) n = 40 x = np.random.normal(size=(n, 2)) y = np.random.normal(size=n) # groups with unequal group sizes groups = np.kron(np.arange(n / 4), np.ones(4)) groups[8:12] = 3 groups[34:36] = 9 model1 = gee.GEE(y, x, groups=groups) result1 = model1.fit() # Unordered groups ix = np.random.permutation(n) y1 = y[ix] x1 = x[ix, :] groups1 = groups[ix] model2 = gee.GEE(y1, x1, groups=groups1) result2 = model2.fit() assert_allclose(result1.params, result2.params) assert_allclose(result1.tvalues, result2.tvalues) # group labels are strings mp = {} import string for j, g in enumerate(set(groups)): mp[g] = string.ascii_letters[j:j + 4] groups2 = [mp[g] for g in groups] model3 = gee.GEE(y, x, groups=groups2) result3 = model3.fit() assert_allclose(result1.params, result3.params) assert_allclose(result1.tvalues, result3.tvalues) def test_compare_OLS(self): # Gaussian GEE with independence correlation should agree # exactly with OLS for parameter estimates and standard errors # derived from the naive covariance estimate. vs = cov_struct.Independence() family = families.Gaussian() np.random.seed(34234) Y = np.random.normal(size=100) X1 = np.random.normal(size=100) X2 = np.random.normal(size=100) X3 = np.random.normal(size=100) groups = np.kron(lrange(20), np.ones(5)) D = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "X3": X3}) md = gee.GEE.from_formula("Y ~ X1 + X2 + X3", groups, D, family=family, cov_struct=vs) mdf = md.fit() ols = lm.OLS.from_formula("Y ~ X1 + X2 + X3", data=D).fit() # do not use wrapper, asserts_xxx do not work ols = ols._results assert_almost_equal(ols.params, mdf.params, decimal=10) se = mdf.standard_errors(cov_type="naive") assert_almost_equal(ols.bse, se, decimal=10) naive_tvalues = mdf.params / np.sqrt(np.diag(mdf.cov_naive)) assert_almost_equal(naive_tvalues, ols.tvalues, decimal=10) def test_formulas(self): # Check formulas, especially passing groups and time as either # variable names or arrays. n = 100 np.random.seed(34234) Y = np.random.normal(size=n) X1 = np.random.normal(size=n) mat = np.concatenate((np.ones((n, 1)), X1[:, None]), axis=1) Time = np.random.uniform(size=n) groups = np.kron(lrange(20), np.ones(5)) data = pd.DataFrame({"Y": Y, "X1": X1, "Time": Time, "groups": groups}) va = cov_struct.Autoregressive() family = families.Gaussian() mod1 = gee.GEE(Y, mat, groups, time=Time, family=family, cov_struct=va) rslt1 = mod1.fit() mod2 = gee.GEE.from_formula("Y ~ X1", groups, data, time=Time, family=family, cov_struct=va) rslt2 = mod2.fit() mod3 = gee.GEE.from_formula("Y ~ X1", groups, data, time="Time", family=family, cov_struct=va) rslt3 = mod3.fit() mod4 = gee.GEE.from_formula("Y ~ X1", "groups", data, time=Time, family=family, cov_struct=va) rslt4 = mod4.fit() mod5 = gee.GEE.from_formula("Y ~ X1", "groups", data, time="Time", family=family, cov_struct=va) rslt5 = mod5.fit() assert_almost_equal(rslt1.params, rslt2.params, decimal=8) assert_almost_equal(rslt1.params, rslt3.params, decimal=8) assert_almost_equal(rslt1.params, rslt4.params, decimal=8) assert_almost_equal(rslt1.params, rslt5.params, decimal=8) check_wrapper(rslt2) def test_compare_logit(self): vs = cov_struct.Independence() family = families.Binomial() np.random.seed(34234) Y = 1 * (np.random.normal(size=100) < 0) X1 = np.random.normal(size=100) X2 = np.random.normal(size=100) X3 = np.random.normal(size=100) groups = np.random.randint(0, 4, size=100) D = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "X3": X3}) mod1 = gee.GEE.from_formula("Y ~ X1 + X2 + X3", groups, D, family=family, cov_struct=vs) rslt1 = mod1.fit() mod2 = discrete.Logit.from_formula("Y ~ X1 + X2 + X3", data=D) rslt2 = mod2.fit(disp=False) assert_almost_equal(rslt1.params.values, rslt2.params.values, decimal=10) def test_compare_poisson(self): vs = cov_struct.Independence() family = families.Poisson() np.random.seed(34234) Y = np.ceil(-np.log(np.random.uniform(size=100))) X1 = np.random.normal(size=100) X2 = np.random.normal(size=100) X3 = np.random.normal(size=100) groups = np.random.randint(0, 4, size=100) D = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "X3": X3}) mod1 = gee.GEE.from_formula("Y ~ X1 + X2 + X3", groups, D, family=family, cov_struct=vs) rslt1 = mod1.fit() mod2 = discrete.Poisson.from_formula("Y ~ X1 + X2 + X3", data=D) rslt2 = mod2.fit(disp=False) assert_almost_equal(rslt1.params.values, rslt2.params.values, decimal=10) def test_predict(self): n = 50 np.random.seed(4324) X1 = np.random.normal(size=n) X2 = np.random.normal(size=n) groups = np.kron(np.arange(n / 2), np.r_[1, 1]) offset = np.random.uniform(1, 2, size=n) Y = np.random.normal(0.1 * (X1 + X2) + offset, size=n) data = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "groups": groups, "offset": offset}) fml = "Y ~ X1 + X2" model = gee.GEE.from_formula(fml, groups, data, family=families.Gaussian(), offset="offset") result = model.fit(start_params=[0, 0.1, 0.1]) assert_equal(result.converged, True) pred1 = result.predict() pred2 = result.predict(offset=data.offset) pred3 = result.predict(exog=data[["X1", "X2"]], offset=data.offset) pred4 = result.predict(exog=data[["X1", "X2"]], offset=0 * data.offset) pred5 = result.predict(offset=0 * data.offset) assert_allclose(pred1, pred2) assert_allclose(pred1, pred3) assert_allclose(pred1, pred4 + data.offset) assert_allclose(pred1, pred5 + data.offset) x1_new = np.random.normal(size=10) x2_new = np.random.normal(size=10) new_exog = pd.DataFrame({"X1": x1_new, "X2": x2_new}) pred6 = result.predict(exog=new_exog) params = result.params pred6_correct = params[0] + params[1] * x1_new + params[2] * x2_new assert_allclose(pred6, pred6_correct) def test_stationary_grid(self): endog = np.r_[4, 2, 3, 1, 4, 5, 6, 7, 8, 3, 2, 4.] exog = np.r_[2, 3, 1, 4, 3, 2, 5, 4, 5, 6, 3, 2] group = np.r_[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3] exog = tools.add_constant(exog) cs = cov_struct.Stationary(max_lag=2, grid=True) model = gee.GEE(endog, exog, group, cov_struct=cs) result = model.fit() se = result.bse * np.sqrt(12 / 9.) # Stata adjustment assert_allclose(cs.covariance_matrix(np.r_[1, 1, 1], 0)[0].sum(), 6.4633538285149452) # Obtained from Stata using: # xtgee y x, i(g) vce(robust) corr(Stationary2) assert_allclose(result.params, np.r_[ 4.463968, -0.0386674], rtol=1e-5, atol=1e-5) assert_allclose(se, np.r_[0.5217202, 0.2800333], rtol=1e-5, atol=1e-5) def test_stationary_nogrid(self): # First test special case where the data follow a grid but we # fit using nogrid endog = np.r_[4, 2, 3, 1, 4, 5, 6, 7, 8, 3, 2, 4.] exog = np.r_[2, 3, 1, 4, 3, 2, 5, 4, 5, 6, 3, 2] time = np.r_[0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2] group = np.r_[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3] exog = tools.add_constant(exog) model = gee.GEE(endog, exog, group, cov_struct=cov_struct.Stationary(max_lag=2, grid=False)) result = model.fit() se = result.bse * np.sqrt(12 / 9.) # Stata adjustment # Obtained from Stata using: # xtgee y x, i(g) vce(robust) corr(Stationary2) assert_allclose(result.params, np.r_[ 4.463968, -0.0386674], rtol=1e-5, atol=1e-5) assert_allclose(se, np.r_[0.5217202, 0.2800333], rtol=1e-5, atol=1e-5) # Smoke test for no grid # TODO: pytest.mark.smoke> time = np.r_[0, 1, 3, 0, 2, 3, 0, 2, 3, 0, 1, 2][:, None] model = gee.GEE(endog, exog, group, time=time, cov_struct=cov_struct.Stationary(max_lag=4, grid=False)) model.fit() def test_predict_exposure(self): n = 50 np.random.seed(34234) X1 = np.random.normal(size=n) X2 = np.random.normal(size=n) groups = np.kron(np.arange(25), np.r_[1, 1]) offset = np.random.uniform(1, 2, size=n) exposure = np.random.uniform(1, 2, size=n) Y = np.random.poisson(0.1 * (X1 + X2) + offset + np.log(exposure), size=n) data = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "groups": groups, "offset": offset, "exposure": exposure}) fml = "Y ~ X1 + X2" model = gee.GEE.from_formula(fml, groups, data, family=families.Poisson(), offset="offset", exposure="exposure") result = model.fit() assert_equal(result.converged, True) pred1 = result.predict() pred2 = result.predict(offset=data["offset"]) pred3 = result.predict(exposure=data["exposure"]) pred4 = result.predict( offset=data["offset"], exposure=data["exposure"]) pred5 = result.predict(exog=data[-10:], offset=data["offset"][-10:], exposure=data["exposure"][-10:]) # without patsy pred6 = result.predict(exog=result.model.exog[-10:], offset=data["offset"][-10:], exposure=data["exposure"][-10:], transform=False) assert_allclose(pred1, pred2) assert_allclose(pred1, pred3) assert_allclose(pred1, pred4) assert_allclose(pred1[-10:], pred5) assert_allclose(pred1[-10:], pred6) def test_offset_formula(self): # Test various ways of passing offset and exposure to `from_formula`. n = 50 np.random.seed(34234) X1 = np.random.normal(size=n) X2 = np.random.normal(size=n) groups = np.kron(np.arange(25), np.r_[1, 1]) offset = np.random.uniform(1, 2, size=n) exposure = np.exp(offset) Y = np.random.poisson(0.1 * (X1 + X2) + 2 * offset, size=n) data = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "groups": groups, "offset": offset, "exposure": exposure}) fml = "Y ~ X1 + X2" model1 = gee.GEE.from_formula(fml, groups, data, family=families.Poisson(), offset="offset") result1 = model1.fit() assert_equal(result1.converged, True) model2 = gee.GEE.from_formula(fml, groups, data, family=families.Poisson(), offset=offset) result2 = model2.fit(start_params=result1.params) assert_allclose(result1.params, result2.params) assert_equal(result2.converged, True) model3 = gee.GEE.from_formula(fml, groups, data, family=families.Poisson(), exposure=exposure) result3 = model3.fit(start_params=result1.params) assert_allclose(result1.params, result3.params) assert_equal(result3.converged, True) model4 = gee.GEE.from_formula(fml, groups, data, family=families.Poisson(), exposure="exposure") result4 = model4.fit(start_params=result1.params) assert_allclose(result1.params, result4.params) assert_equal(result4.converged, True) model5 = gee.GEE.from_formula(fml, groups, data, family=families.Poisson(), exposure="exposure", offset="offset") result5 = model5.fit() assert_equal(result5.converged, True) model6 = gee.GEE.from_formula(fml, groups, data, family=families.Poisson(), offset=2 * offset) result6 = model6.fit(start_params=result5.params) assert_allclose(result5.params, result6.params) assert_equal(result6.converged, True) def test_sensitivity(self): va = cov_struct.Exchangeable() family = families.Gaussian() np.random.seed(34234) n = 100 Y = np.random.normal(size=n) X1 = np.random.normal(size=n) X2 = np.random.normal(size=n) groups = np.kron(np.arange(50), np.r_[1, 1]) D = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2}) mod = gee.GEE.from_formula("Y ~ X1 + X2", groups, D, family=family, cov_struct=va) rslt = mod.fit() ps = rslt.params_sensitivity(0, 0.5, 2) assert_almost_equal(len(ps), 2) assert_almost_equal([x.cov_struct.dep_params for x in ps], [0.0, 0.5]) # Regression test assert_almost_equal([x.params[0] for x in ps], [0.1696214707458818, 0.17836097387799127]) def test_equivalence(self): """ The Equivalence covariance structure can represent an exchangeable covariance structure. Here we check that the results are identical using the two approaches. """ np.random.seed(3424) endog = np.random.normal(size=20) exog = np.random.normal(size=(20, 2)) exog[:, 0] = 1 groups = np.kron(np.arange(5), np.ones(4)) groups[12:] = 3 # Create unequal size groups # Set up an Equivalence covariance structure to mimic an # Exchangeable covariance structure. pairs = {} start = [0, 4, 8, 12] for k in range(4): pairs[k] = {} # Diagonal values (variance parameters) if k < 3: pairs[k][0] = (start[k] + np.r_[0, 1, 2, 3], start[k] + np.r_[0, 1, 2, 3]) else: pairs[k][0] = (start[k] + np.r_[0, 1, 2, 3, 4, 5, 6, 7], start[k] + np.r_[0, 1, 2, 3, 4, 5, 6, 7]) # Off-diagonal pairs (covariance parameters) if k < 3: a, b = np.tril_indices(4, -1) pairs[k][1] = (start[k] + a, start[k] + b) else: a, b = np.tril_indices(8, -1) pairs[k][1] = (start[k] + a, start[k] + b) ex = cov_struct.Exchangeable() model1 = gee.GEE(endog, exog, groups, cov_struct=ex) result1 = model1.fit() for return_cov in False, True: ec = cov_struct.Equivalence(pairs, return_cov=return_cov) model2 = gee.GEE(endog, exog, groups, cov_struct=ec) result2 = model2.fit() # Use large atol/rtol for the correlation case since there # are some small differences in the results due to degree # of freedom differences. if return_cov is True: atol, rtol = 1e-6, 1e-6 else: atol, rtol = 1e-3, 1e-3 assert_allclose(result1.params, result2.params, atol=atol, rtol=rtol) assert_allclose(result1.bse, result2.bse, atol=atol, rtol=rtol) assert_allclose(result1.scale, result2.scale, atol=atol, rtol=rtol) def test_equivalence_from_pairs(self): np.random.seed(3424) endog = np.random.normal(size=50) exog = np.random.normal(size=(50, 2)) exog[:, 0] = 1 groups = np.kron(np.arange(5), np.ones(10)) groups[30:] = 3 # Create unequal size groups # Set up labels. labels = np.kron(np.arange(5), np.ones(10)).astype(np.int32) labels = labels[np.random.permutation(len(labels))] eq = cov_struct.Equivalence(labels=labels, return_cov=True) model1 = gee.GEE(endog, exog, groups, cov_struct=eq) # Call this directly instead of letting init do it to get the # result before reindexing. eq._pairs_from_labels() # Make sure the size is correct to hold every element. for g in model1.group_labels: p = eq.pairs[g] vl = [len(x[0]) for x in p.values()] m = sum(groups == g) assert_allclose(sum(vl), m * (m + 1) / 2) # Check for duplicates. ixs = set([]) for g in model1.group_labels: for v in eq.pairs[g].values(): for a, b in zip(v[0], v[1]): ky = (a, b) assert(ky not in ixs) ixs.add(ky) # Smoke test # TODO: pytest.mark.smoke? eq = cov_struct.Equivalence(labels=labels, return_cov=True) model1 = gee.GEE(endog, exog, groups, cov_struct=eq) with warnings.catch_warnings(): warnings.simplefilter('ignore') model1.fit(maxiter=2) class CheckConsistency(object): start_params = None def test_cov_type(self): mod = self.mod res_robust = mod.fit(start_params=self.start_params) res_naive = mod.fit(start_params=self.start_params, cov_type='naive') res_robust_bc = mod.fit(start_params=self.start_params, cov_type='bias_reduced') # call summary to make sure it does not change cov_type res_naive.summary() res_robust_bc.summary() # check cov_type assert_equal(res_robust.cov_type, 'robust') assert_equal(res_naive.cov_type, 'naive') assert_equal(res_robust_bc.cov_type, 'bias_reduced') # check bse and cov_params # we are comparing different runs of the optimization # bse in ordinal and multinomial have an atol around 5e-10 for two # consecutive calls to fit. rtol = 1e-8 for (res, cov_type, cov) in [ (res_robust, 'robust', res_robust.cov_robust), (res_naive, 'naive', res_robust.cov_naive), (res_robust_bc, 'bias_reduced', res_robust_bc.cov_robust_bc) ]: bse = np.sqrt(np.diag(cov)) assert_allclose(res.bse, bse, rtol=rtol) if cov_type != 'bias_reduced': # cov_type=naive shortcuts calculation of bias reduced # covariance for efficiency bse = res_naive.standard_errors(cov_type=cov_type) assert_allclose(res.bse, bse, rtol=rtol) assert_allclose(res.cov_params(), cov, rtol=rtol, atol=1e-10) assert_allclose(res.cov_params_default, cov, rtol=rtol, atol=1e-10) # assert that we do not have a copy assert_(res_robust.cov_params_default is res_robust.cov_robust) assert_(res_naive.cov_params_default is res_naive.cov_naive) assert_(res_robust_bc.cov_params_default is res_robust_bc.cov_robust_bc) # check exception for misspelled cov_type assert_raises(ValueError, mod.fit, cov_type='robust_bc') class TestGEEPoissonCovType(CheckConsistency): @classmethod def setup_class(cls): endog, exog, group_n = load_data("gee_poisson_1.csv") family = families.Poisson() vi = cov_struct.Independence() cls.mod = gee.GEE(endog, exog, group_n, None, family, vi) cls.start_params = np.array([-0.03644504, -0.05432094, 0.01566427, 0.57628591, -0.0046566, -0.47709315]) def test_wrapper(self): endog, exog, group_n = load_data("gee_poisson_1.csv", icept=False) endog = pd.Series(endog) exog = pd.DataFrame(exog) group_n = pd.Series(group_n) family = families.Poisson() vi = cov_struct.Independence() mod = gee.GEE(endog, exog, group_n, None, family, vi) rslt2 = mod.fit() check_wrapper(rslt2) class TestGEEPoissonFormulaCovType(CheckConsistency): @classmethod def setup_class(cls): endog, exog, group_n = load_data("gee_poisson_1.csv") family = families.Poisson() vi = cov_struct.Independence() # Test with formulas D = np.concatenate((endog[:, None], group_n[:, None], exog[:, 1:]), axis=1) D = pd.DataFrame(D) D.columns = ["Y", "Id", ] + ["X%d" % (k + 1) for k in range(exog.shape[1] - 1)] cls.mod = gee.GEE.from_formula("Y ~ X1 + X2 + X3 + X4 + X5", "Id", D, family=family, cov_struct=vi) cls.start_params = np.array([-0.03644504, -0.05432094, 0.01566427, 0.57628591, -0.0046566, -0.47709315]) class TestGEEOrdinalCovType(CheckConsistency): @classmethod def setup_class(cls): family = families.Binomial() endog, exog, groups = load_data("gee_ordinal_1.csv", icept=False) va = cov_struct.GlobalOddsRatio("ordinal") cls.mod = gee.OrdinalGEE(endog, exog, groups, None, family, va) cls.start_params = np.array([1.09250002, 0.0217443, -0.39851092, -0.01812116, 0.03023969, 1.18258516, 0.01803453, -1.10203381]) def test_wrapper(self): endog, exog, groups = load_data("gee_ordinal_1.csv", icept=False) endog = pd.Series(endog, name='yendog') exog = pd.DataFrame(exog) groups = pd.Series(groups, name='the_group') family = families.Binomial() va = cov_struct.GlobalOddsRatio("ordinal") mod = gee.OrdinalGEE(endog, exog, groups, None, family, va) rslt2 = mod.fit() check_wrapper(rslt2) class TestGEEMultinomialCovType(CheckConsistency): @classmethod def setup_class(cls): endog, exog, groups = load_data("gee_nominal_1.csv", icept=False) # Test with independence correlation va = cov_struct.Independence() cls.mod = gee.NominalGEE(endog, exog, groups, cov_struct=va) cls.start_params = np.array([0.44944752, 0.45569985, -0.92007064, -0.46766728]) def test_wrapper(self): endog, exog, groups = load_data("gee_nominal_1.csv", icept=False) endog = pd.Series(endog, name='yendog') exog = pd.DataFrame(exog) groups = pd.Series(groups, name='the_group') va = cov_struct.Independence() mod = gee.NominalGEE(endog, exog, groups, cov_struct=va) rslt2 = mod.fit() check_wrapper(rslt2) def test_regularized_poisson(): np.random.seed(8735) ng, gs, p = 1000, 5, 5 x = np.random.normal(size=(ng*gs, p)) r = 0.5 x[:, 2] = r*x[:, 1] + np.sqrt(1-r**2)*x[:, 2] lpr = 0.7*(x[:, 1] - x[:, 3]) mean = np.exp(lpr) y = np.random.poisson(mean) groups = np.kron(np.arange(ng), np.ones(gs)) model = gee.GEE(y, x, groups=groups, family=families.Poisson()) result = model.fit_regularized(0.0000001) assert_allclose(result.params, 0.7 * np.r_[0, 1, 0, -1, 0], rtol=0.01, atol=0.12) def test_regularized_gaussian(): # Example 1 from Wang et al. np.random.seed(8735) ng, gs, p = 200, 4, 200 groups = np.kron(np.arange(ng), np.ones(gs)) x = np.zeros((ng*gs, p)) x[:, 0] = 1 * (np.random.uniform(size=ng*gs) < 0.5) x[:, 1] = np.random.normal(size=ng*gs) r = 0.5 for j in range(2, p): eps = np.random.normal(size=ng*gs) x[:, j] = r * x[:, j-1] + np.sqrt(1 - r**2) * eps lpr = np.dot(x[:, 0:4], np.r_[2, 3, 1.5, 2]) s = 0.4 e = np.sqrt(s) * np.kron(np.random.normal(size=ng), np.ones(gs)) e += np.sqrt(1 - s) * np.random.normal(size=ng*gs) y = lpr + e model = gee.GEE(y, x, cov_struct=cov_struct.Exchangeable(), groups=groups) result = model.fit_regularized(0.01, maxiter=100) ex = np.zeros(200) ex[0:4] = np.r_[2, 3, 1.5, 2] assert_allclose(result.params, ex, rtol=0.01, atol=0.2) assert_allclose(model.cov_struct.dep_params, np.r_[s], rtol=0.01, atol=0.05) @pytest.mark.smoke @pytest.mark.matplotlib def test_plots(close_figures): np.random.seed(378) exog = np.random.normal(size=100) endog = np.random.normal(size=(100, 2)) groups = np.kron(np.arange(50), np.r_[1, 1]) model = gee.GEE(exog, endog, groups) result = model.fit() fig = result.plot_added_variable(1) assert_equal(isinstance(fig, plt.Figure), True) fig = result.plot_partial_residuals(1) assert_equal(isinstance(fig, plt.Figure), True) fig = result.plot_ceres_residuals(1) assert_equal(isinstance(fig, plt.Figure), True) fig = result.plot_isotropic_dependence() assert_equal(isinstance(fig, plt.Figure), True) def test_missing(): # gh-1877 data = [['id', 'al', 'status', 'fake', 'grps'], ['4A', 'A', 1, 1, 0], ['5A', 'A', 1, 2.0, 1], ['6A', 'A', 1, 3, 2], ['7A', 'A', 1, 2.0, 3], ['8A', 'A', 1, 1, 4], ['9A', 'A', 1, 2.0, 5], ['11A', 'A', 1, 1, 6], ['12A', 'A', 1, 2.0, 7], ['13A', 'A', 1, 1, 8], ['14A', 'A', 1, 1, 9], ['15A', 'A', 1, 1, 10], ['16A', 'A', 1, 2.0, 11], ['17A', 'A', 1, 3.0, 12], ['18A', 'A', 1, 3.0, 13], ['19A', 'A', 1, 2.0, 14], ['20A', 'A', 1, 2.0, 15], ['2C', 'C', 0, 3.0, 0], ['3C', 'C', 0, 1, 1], ['4C', 'C', 0, 1, 2], ['5C', 'C', 0, 2.0, 3], ['6C', 'C', 0, 1, 4], ['9C', 'C', 0, 1, 5], ['10C', 'C', 0, 3, 6], ['12C', 'C', 0, 3, 7], ['14C', 'C', 0, 2.5, 8], ['15C', 'C', 0, 1, 9], ['17C', 'C', 0, 1, 10], ['22C', 'C', 0, 1, 11], ['23C', 'C', 0, 1, 12], ['24C', 'C', 0, 1, 13], ['32C', 'C', 0, 2.0, 14], ['35C', 'C', 0, 1, 15]] df = pd.DataFrame(data[1:], columns=data[0]) df.loc[df.fake == 1, 'fake'] = np.nan mod = gee.GEE.from_formula('status ~ fake', data=df, groups='grps', cov_struct=cov_struct.Independence(), family=families.Binomial()) df = df.dropna().copy() df['constant'] = 1 mod2 = gee.GEE(df.status, df[['constant', 'fake']], groups=df.grps, cov_struct=cov_struct.Independence(), family=families.Binomial()) assert_equal(mod.endog, mod2.endog) assert_equal(mod.exog, mod2.exog) assert_equal(mod.groups, mod2.groups) res = mod.fit() res2 = mod2.fit() assert_almost_equal(res.params.values, res2.params.values) def simple_qic_data(fam): y = np.r_[0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0] x1 = np.r_[0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0] x2 = np.r_[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] g = np.r_[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4] x1 = x1[:, None] x2 = x2[:, None] return y, x1, x2, g # Test quasi-likelihood by numerical integration in two settings # where there is a closed form expression. @pytest.mark.parametrize("family", [families.Gaussian, families.Poisson]) def test_ql_known(family): fam = family() y, x1, x2, g = simple_qic_data(family) model1 = gee.GEE(y, x1, family=fam, groups=g) result1 = model1.fit(ddof_scale=0) mean1 = result1.fittedvalues model2 = gee.GEE(y, x2, family=fam, groups=g) result2 = model2.fit(ddof_scale=0) mean2 = result2.fittedvalues if family is families.Gaussian: ql1 = -len(y) / 2. ql2 = -len(y) / 2. elif family is families.Poisson: c = np.zeros_like(y) ii = y > 0 c[ii] = y[ii] * np.log(y[ii]) - y[ii] ql1 = np.sum(y * np.log(mean1) - mean1 - c) ql2 = np.sum(y * np.log(mean2) - mean2 - c) else: raise ValueError("Unknown family") qle1 = model1.qic(result1.params, result1.scale, result1.cov_params()) qle2 = model2.qic(result2.params, result2.scale, result2.cov_params()) assert_allclose(ql1, qle1[0], rtol=1e-4) assert_allclose(ql2, qle2[0], rtol=1e-4) with warnings.catch_warnings(): warnings.simplefilter("ignore") qler1 = result1.qic() qler2 = result2.qic() assert_equal(qler1, qle1[1:]) assert_equal(qler2, qle2[1:]) # Compare differences of QL values computed by numerical integration. # Use difference here so that constants that are inconvenient to compute # cancel out. @pytest.mark.parametrize("family", [families.Gaussian, families.Binomial, families.Poisson]) def test_ql_diff(family): fam = family() y, x1, x2, g = simple_qic_data(family) model1 = gee.GEE(y, x1, family=fam, groups=g) result1 = model1.fit(ddof_scale=0) mean1 = result1.fittedvalues model2 = gee.GEE(y, x2, family=fam, groups=g) result2 = model2.fit(ddof_scale=0) mean2 = result2.fittedvalues if family is families.Gaussian: qldiff = 0 elif family is families.Binomial: qldiff = np.sum(y * np.log(mean1 / (1 - mean1)) + np.log(1 - mean1)) qldiff -= np.sum(y * np.log(mean2 / (1 - mean2)) + np.log(1 - mean2)) elif family is families.Poisson: qldiff = (np.sum(y * np.log(mean1) - mean1) - np.sum(y * np.log(mean2) - mean2)) else: raise ValueError("unknown family") qle1, _, _ = model1.qic(result1.params, result1.scale, result1.cov_params()) qle2, _, _ = model2.qic(result2.params, result2.scale, result2.cov_params()) assert_allclose(qle1 - qle2, qldiff, rtol=1e-5, atol=1e-5) def test_qic_warnings(): with pytest.warns(UserWarning): fam = families.Gaussian() y, x1, _, g = simple_qic_data(fam) model = gee.GEE(y, x1, family=fam, groups=g) result = model.fit() result.qic() @pytest.mark.parametrize("reg", [False, True]) def test_quasipoisson(reg): np.random.seed(343) n = 1000 x = np.random.normal(size=(n, 3)) g = np.random.gamma(1, 1, size=n) y = np.random.poisson(g) grp = np.kron(np.arange(100), np.ones(n // 100)) model1 = gee.GEE(y, x, family=families.Poisson(), groups=grp, cov_type="naive") model2 = gee.GEE(y, x, family=families.Poisson(), groups=grp, cov_type="naive") if reg: result1 = model1.fit_regularized(pen_wt=0.1) result2 = model2.fit_regularized(pen_wt=0.1, scale="X2") else: result1 = model1.fit() result2 = model2.fit(scale="X2") # The parameter estimates are the same regardless of how # the scale parameter is handled assert_allclose(result1.params, result2.params) if not reg: # The robust covariance does not depend on the scale parameter, # but the naive covariance does. assert_allclose(result2.cov_naive / result1.cov_naive, result2.scale * np.ones_like(result2.cov_naive)) def test_grid_ar(): np.random.seed(243) r = 0.5 m = 10 ng = 100 ii = np.arange(m) cov = r**np.abs(np.subtract.outer(ii, ii)) covr = np.linalg.cholesky(cov) e = [np.dot(covr, np.random.normal(size=m)) for k in range(ng)] e = 2 * np.concatenate(e) grps = [[k]*m for k in range(ng)] grps = np.concatenate(grps) x = np.random.normal(size=(ng*m, 3)) y = np.dot(x, np.r_[1, -1, 0]) + e model1 = gee.GEE(y, x, groups=grps, cov_struct=cov_struct.Autoregressive()) result1 = model1.fit() model2 = gee.GEE(y, x, groups=grps, cov_struct=cov_struct.Autoregressive(grid=True)) result2 = model2.fit() model3 = gee.GEE(y, x, groups=grps, cov_struct=cov_struct.Stationary(max_lag=1)) result3 = model3.fit() assert_allclose(result1.cov_struct.dep_params, result2.cov_struct.dep_params, rtol=0.05) assert_allclose(result1.cov_struct.dep_params, result3.cov_struct.dep_params[1], rtol=0.05) statsmodels-0.12.2/statsmodels/genmod/tests/test_gee_glm.py000066400000000000000000000105041400612667500241320ustar00rootroot00000000000000 import warnings import numpy as np import pandas as pd from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod import families from statsmodels.genmod.families import links from statsmodels.genmod.generalized_estimating_equations import GEE from statsmodels.genmod.cov_struct import Independence from numpy.testing import assert_allclose class CheckGEEGLM(object): def test_basic(self): res1 = self.result1 res2 = self.result2 assert_allclose(res1.params.values, res2.params.values, rtol=1e-6, atol=1e-10) def test_resid(self): res1 = self.result1 res2 = self.result2 assert_allclose(res1.resid_response, res2.resid_response, rtol=1e-6, atol=1e-10) assert_allclose(res1.resid_pearson, res2.resid_pearson, rtol=1e-6, atol=1e-10) assert_allclose(res1.resid_deviance, res2.resid_deviance, rtol=1e-6, atol=1e-10) with warnings.catch_warnings(): warnings.simplefilter("ignore", category=FutureWarning) assert_allclose(res1.resid_anscombe, res2.resid_anscombe, rtol=1e-6, atol=1e-10) assert_allclose(res1.resid_working, res2.resid_working, rtol=1e-6, atol=1e-10) #def test_compare_logit(self): class TestCompareLogit(CheckGEEGLM): @classmethod def setup_class(cls): vs = Independence() family = families.Binomial() np.random.seed(987126) Y = 1 * (np.random.normal(size=100) < 0) X1 = np.random.normal(size=100) X2 = np.random.normal(size=100) X3 = np.random.normal(size=100) groups = np.random.randint(0, 4, size=100) D = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "X3": X3}) mod1 = GEE.from_formula("Y ~ X1 + X2 + X3", groups, D, family=family, cov_struct=vs) cls.result1 = mod1.fit() mod2 = GLM.from_formula("Y ~ X1 + X2 + X3", data=D, family=family) cls.result2 = mod2.fit(disp=False) class TestComparePoisson(CheckGEEGLM): @classmethod def setup_class(cls): vs = Independence() family = families.Poisson() np.random.seed(987126) Y = np.exp(1 + np.random.normal(size=100)) X1 = np.random.normal(size=100) X2 = np.random.normal(size=100) X3 = np.random.normal(size=100) groups = np.random.randint(0, 4, size=100) D = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "X3": X3}) mod1 = GEE.from_formula("Y ~ X1 + X2 + X3", groups, D, family=family, cov_struct=vs) cls.result1 = mod1.fit() mod2 = GLM.from_formula("Y ~ X1 + X2 + X3", data=D, family=family) cls.result2 = mod2.fit(disp=False) class TestCompareGaussian(CheckGEEGLM): @classmethod def setup_class(cls): vs = Independence() family = families.Gaussian() np.random.seed(987126) Y = np.random.normal(size=100) X1 = np.random.normal(size=100) X2 = np.random.normal(size=100) X3 = np.random.normal(size=100) groups = np.kron(np.arange(20), np.ones(5)) D = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "X3": X3}) md = GEE.from_formula("Y ~ X1 + X2 + X3", groups, D, family=family, cov_struct=vs) cls.result1 = md.fit() cls.result2 = GLM.from_formula("Y ~ X1 + X2 + X3", data=D).fit() class TestCompareGamma(CheckGEEGLM): @classmethod def setup_class(cls): # adjusted for Gamma, not in test_gee.py vs = Independence() family = families.Gamma(link=links.log()) np.random.seed(987126) #Y = np.random.normal(size=100)**2 Y = np.exp(0.1 + np.random.normal(size=100)) # log-normal X1 = np.random.normal(size=100) X2 = np.random.normal(size=100) X3 = np.random.normal(size=100) groups = np.random.randint(0, 4, size=100) D = pd.DataFrame({"Y": Y, "X1": X1, "X2": X2, "X3": X3}) mod1 = GEE.from_formula("Y ~ X1 + X2 + X3", groups, D, family=family, cov_struct=vs) cls.result1 = mod1.fit() mod2 = GLM.from_formula("Y ~ X1 + X2 + X3", data=D, family=family) cls.result2 = mod2.fit(disp=False) statsmodels-0.12.2/statsmodels/genmod/tests/test_glm.py000066400000000000000000002667701400612667500233340ustar00rootroot00000000000000""" Test functions for models.GLM """ import warnings import os import numpy as np from numpy.testing import (assert_almost_equal, assert_equal, assert_raises, assert_allclose, assert_, assert_array_less) import pandas as pd from pandas.testing import assert_series_equal import pytest from scipy import stats import statsmodels.api as sm from statsmodels.genmod.generalized_linear_model import GLM, SET_USE_BIC_LLF from statsmodels.tools.tools import add_constant from statsmodels.tools.sm_exceptions import PerfectSeparationError from statsmodels.discrete import discrete_model as discrete from statsmodels.tools.sm_exceptions import DomainWarning from statsmodels.tools.numdiff import approx_fprime, approx_hess from statsmodels.datasets import cpunish, longley # Test Precisions DECIMAL_4 = 4 DECIMAL_3 = 3 DECIMAL_2 = 2 DECIMAL_1 = 1 DECIMAL_0 = 0 pdf_output = False if pdf_output: from matplotlib.backends.backend_pdf import PdfPages pdf = PdfPages("test_glm.pdf") else: pdf = None def close_or_save(pdf, fig): if pdf_output: pdf.savefig(fig) def teardown_module(): if pdf_output: pdf.close() @pytest.fixture(scope="module") def iris(): cur_dir = os.path.dirname(os.path.abspath(__file__)) return np.genfromtxt(os.path.join(cur_dir, 'results', 'iris.csv'), delimiter=",", skip_header=1) class CheckModelResultsMixin(object): ''' res2 should be either the results from RModelWrap or the results as defined in model_results_data ''' decimal_params = DECIMAL_4 def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, self.decimal_params) decimal_bse = DECIMAL_4 def test_standard_errors(self): assert_allclose(self.res1.bse, self.res2.bse, atol=10**(-self.decimal_bse), rtol=1e-5) decimal_resids = DECIMAL_4 def test_residuals(self): # fix incorrect numbers in resid_working results # residuals for Poisson are also tested in test_glm_weights.py import copy # new numpy would have copy method resid2 = copy.copy(self.res2.resids) resid2[:, 2] *= self.res1.family.link.deriv(self.res1.mu)**2 atol = 10**(-self.decimal_resids) with warnings.catch_warnings(): warnings.simplefilter("ignore", category=FutureWarning) resid_a = self.res1.resid_anscombe resids = np.column_stack((self.res1.resid_pearson, self.res1.resid_deviance, self.res1.resid_working, resid_a, self.res1.resid_response)) assert_allclose(resids, resid2, rtol=1e-6, atol=atol) decimal_aic_R = DECIMAL_4 def test_aic_R(self): # R includes the estimation of the scale as a lost dof # Does not with Gamma though if self.res1.scale != 1: dof = 2 else: dof = 0 if isinstance(self.res1.model.family, (sm.families.NegativeBinomial)): llf = self.res1.model.family.loglike(self.res1.model.endog, self.res1.mu, self.res1.model.var_weights, self.res1.model.freq_weights, scale=1) aic = (-2*llf+2*(self.res1.df_model+1)) else: aic = self.res1.aic assert_almost_equal(aic+dof, self.res2.aic_R, self.decimal_aic_R) decimal_aic_Stata = DECIMAL_4 def test_aic_Stata(self): # Stata uses the below llf for aic definition for these families if isinstance(self.res1.model.family, (sm.families.Gamma, sm.families.InverseGaussian, sm.families.NegativeBinomial)): llf = self.res1.model.family.loglike(self.res1.model.endog, self.res1.mu, self.res1.model.var_weights, self.res1.model.freq_weights, scale=1) aic = (-2*llf+2*(self.res1.df_model+1))/self.res1.nobs else: aic = self.res1.aic/self.res1.nobs assert_almost_equal(aic, self.res2.aic_Stata, self.decimal_aic_Stata) decimal_deviance = DECIMAL_4 def test_deviance(self): assert_almost_equal(self.res1.deviance, self.res2.deviance, self.decimal_deviance) decimal_scale = DECIMAL_4 def test_scale(self): assert_almost_equal(self.res1.scale, self.res2.scale, self.decimal_scale) decimal_loglike = DECIMAL_4 def test_loglike(self): # Stata uses the below llf for these families # We differ with R for them if isinstance(self.res1.model.family, (sm.families.Gamma, sm.families.InverseGaussian, sm.families.NegativeBinomial)): llf = self.res1.model.family.loglike(self.res1.model.endog, self.res1.mu, self.res1.model.var_weights, self.res1.model.freq_weights, scale=1) else: llf = self.res1.llf assert_almost_equal(llf, self.res2.llf, self.decimal_loglike) decimal_null_deviance = DECIMAL_4 def test_null_deviance(self): assert_almost_equal(self.res1.null_deviance, self.res2.null_deviance, self.decimal_null_deviance) decimal_bic = DECIMAL_4 def test_bic(self): with warnings.catch_warnings(): warnings.simplefilter("ignore") assert_almost_equal(self.res1.bic, self.res2.bic_Stata, self.decimal_bic) def test_degrees(self): assert_equal(self.res1.model.df_resid,self.res2.df_resid) decimal_fittedvalues = DECIMAL_4 def test_fittedvalues(self): assert_almost_equal(self.res1.fittedvalues, self.res2.fittedvalues, self.decimal_fittedvalues) def test_tpvalues(self): # test comparing tvalues and pvalues with normal implementation # make sure they use normal distribution (inherited in results class) params = self.res1.params tvalues = params / self.res1.bse pvalues = stats.norm.sf(np.abs(tvalues)) * 2 half_width = stats.norm.isf(0.025) * self.res1.bse conf_int = np.column_stack((params - half_width, params + half_width)) if isinstance(tvalues, pd.Series): assert_series_equal(self.res1.tvalues, tvalues) else: assert_almost_equal(self.res1.tvalues, tvalues) assert_almost_equal(self.res1.pvalues, pvalues) assert_almost_equal(self.res1.conf_int(), conf_int) def test_pearson_chi2(self): if hasattr(self.res2, 'pearson_chi2'): assert_allclose(self.res1.pearson_chi2, self.res2.pearson_chi2, atol=1e-6, rtol=1e-6) @pytest.mark.smoke def test_summary(self): self.res1.summary() @pytest.mark.smoke def test_summary2(self): self.res1.summary2() class CheckComparisonMixin(object): def test_compare_discrete(self): res1 = self.res1 resd = self.resd assert_allclose(res1.llf, resd.llf, rtol=1e-10) score_obs1 = res1.model.score_obs(res1.params * 0.98) score_obsd = resd.model.score_obs(resd.params * 0.98) assert_allclose(score_obs1, score_obsd, rtol=1e-10) # score score1 = res1.model.score(res1.params * 0.98) assert_allclose(score1, score_obs1.sum(0), atol=1e-20) score0 = res1.model.score(res1.params) assert_allclose(score0, np.zeros(score_obs1.shape[1]), atol=5e-7) hessian1 = res1.model.hessian(res1.params * 0.98, observed=False) hessiand = resd.model.hessian(resd.params * 0.98) assert_allclose(hessian1, hessiand, rtol=1e-10) hessian1 = res1.model.hessian(res1.params * 0.98, observed=True) hessiand = resd.model.hessian(resd.params * 0.98) assert_allclose(hessian1, hessiand, rtol=1e-9) def test_score_test(self): res1 = self.res1 # fake example, should be zero, k_constraint should be 0 st, pv, df = res1.model.score_test(res1.params, k_constraints=1) assert_allclose(st, 0, atol=1e-20) assert_allclose(pv, 1, atol=1e-10) assert_equal(df, 1) st, pv, df = res1.model.score_test(res1.params, k_constraints=0) assert_allclose(st, 0, atol=1e-20) assert_(np.isnan(pv), msg=repr(pv)) assert_equal(df, 0) # TODO: no verified numbers largely SMOKE test exog_extra = res1.model.exog[:,1]**2 st, pv, df = res1.model.score_test(res1.params, exog_extra=exog_extra) assert_array_less(0.1, st) assert_array_less(0.1, pv) assert_equal(df, 1) class TestGlmGaussian(CheckModelResultsMixin): @classmethod def setup_class(cls): ''' Test Gaussian family with canonical identity link ''' # Test Precisions cls.decimal_resids = DECIMAL_3 cls.decimal_params = DECIMAL_2 cls.decimal_bic = DECIMAL_0 cls.decimal_bse = DECIMAL_3 from statsmodels.datasets.longley import load cls.data = load(as_pandas=False) cls.data.exog = add_constant(cls.data.exog, prepend=False) cls.res1 = GLM(cls.data.endog, cls.data.exog, family=sm.families.Gaussian()).fit() from .results.results_glm import Longley cls.res2 = Longley() def test_compare_OLS(self): res1 = self.res1 # OLS does not define score_obs from statsmodels.regression.linear_model import OLS resd = OLS(self.data.endog, self.data.exog).fit() self.resd = resd # attach to access from the outside assert_allclose(res1.llf, resd.llf, rtol=1e-10) score_obs1 = res1.model.score_obs(res1.params, scale=None) score_obsd = resd.resid[:, None] / resd.scale * resd.model.exog # low precision because of badly scaled exog assert_allclose(score_obs1, score_obsd, rtol=1e-8) score_obs1 = res1.model.score_obs(res1.params, scale=1) score_obsd = resd.resid[:, None] * resd.model.exog assert_allclose(score_obs1, score_obsd, rtol=1e-8) hess_obs1 = res1.model.hessian(res1.params, scale=None) hess_obsd = -1. / resd.scale * resd.model.exog.T.dot(resd.model.exog) # low precision because of badly scaled exog assert_allclose(hess_obs1, hess_obsd, rtol=1e-8) # FIXME: enable or delete # def setup(self): # if skipR: # raise SkipTest, "Rpy not installed." # Gauss = r.gaussian # self.res2 = RModel(self.data.endog, self.data.exog, r.glm, family=Gauss) # self.res2.resids = np.array(self.res2.resid)[:,None]*np.ones((1,5)) # self.res2.null_deviance = 185008826 # taken from R. Rpy bug? class TestGlmGaussianGradient(TestGlmGaussian): @classmethod def setup_class(cls): ''' Test Gaussian family with canonical identity link ''' # Test Precisions cls.decimal_resids = DECIMAL_3 cls.decimal_params = DECIMAL_2 cls.decimal_bic = DECIMAL_0 cls.decimal_bse = DECIMAL_2 from statsmodels.datasets.longley import load cls.data = load(as_pandas=False) cls.data.exog = add_constant(cls.data.exog, prepend=False) cls.res1 = GLM(cls.data.endog, cls.data.exog, family=sm.families.Gaussian()).fit(method='bfgs') from .results.results_glm import Longley cls.res2 = Longley() class TestGaussianLog(CheckModelResultsMixin): @classmethod def setup_class(cls): # Test Precision cls.decimal_aic_R = DECIMAL_0 cls.decimal_aic_Stata = DECIMAL_2 cls.decimal_loglike = DECIMAL_0 cls.decimal_null_deviance = DECIMAL_1 nobs = 100 x = np.arange(nobs) np.random.seed(54321) # y = 1.0 - .02*x - .001*x**2 + 0.001 * np.random.randn(nobs) cls.X = np.c_[np.ones((nobs,1)),x,x**2] cls.lny = np.exp(-(-1.0 + 0.02*x + 0.0001*x**2)) +\ 0.001 * np.random.randn(nobs) GaussLog_Model = GLM(cls.lny, cls.X, family=sm.families.Gaussian(sm.families.links.log())) cls.res1 = GaussLog_Model.fit() from .results.results_glm import GaussianLog cls.res2 = GaussianLog() # FIXME: enable or delete # def setup(cls): # if skipR: # raise SkipTest, "Rpy not installed" # GaussLogLink = r.gaussian(link = "log") # GaussLog_Res_R = RModel(cls.lny, cls.X, r.glm, family=GaussLogLink) # cls.res2 = GaussLog_Res_R class TestGaussianInverse(CheckModelResultsMixin): @classmethod def setup_class(cls): # Test Precisions cls.decimal_bic = DECIMAL_1 cls.decimal_aic_R = DECIMAL_1 cls.decimal_aic_Stata = DECIMAL_3 cls.decimal_loglike = DECIMAL_1 cls.decimal_resids = DECIMAL_3 nobs = 100 x = np.arange(nobs) np.random.seed(54321) y = 1.0 + 2.0 * x + x**2 + 0.1 * np.random.randn(nobs) cls.X = np.c_[np.ones((nobs,1)),x,x**2] cls.y_inv = (1. + .02*x + .001*x**2)**-1 + .001 * np.random.randn(nobs) InverseLink_Model = GLM(cls.y_inv, cls.X, family=sm.families.Gaussian(sm.families.links.inverse_power())) InverseLink_Res = InverseLink_Model.fit() cls.res1 = InverseLink_Res from .results.results_glm import GaussianInverse cls.res2 = GaussianInverse() # FIXME: enable or delete # def setup(cls): # if skipR: # raise SkipTest, "Rpy not installed." # InverseLink = r.gaussian(link = "inverse") # InverseLink_Res_R = RModel(cls.y_inv, cls.X, r.glm, family=InverseLink) # cls.res2 = InverseLink_Res_R class TestGlmBinomial(CheckModelResultsMixin): @classmethod def setup_class(cls): ''' Test Binomial family with canonical logit link using star98 dataset. ''' cls.decimal_resids = DECIMAL_1 cls.decimal_bic = DECIMAL_2 from statsmodels.datasets.star98 import load from .results.results_glm import Star98 data = load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) cls.res1 = GLM(data.endog, data.exog, family=sm.families.Binomial()).fit() # NOTE: if you want to replicate with RModel # res2 = RModel(data.endog[:,0]/trials, data.exog, r.glm, # family=r.binomial, weights=trials) cls.res2 = Star98() def test_endog_dtype(self): from statsmodels.datasets.star98 import load data = load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) endog = data.endog.astype(int) res2 = GLM(endog, data.exog, family=sm.families.Binomial()).fit() assert_allclose(res2.params, self.res1.params) endog = data.endog.astype(np.double) res3 = GLM(endog, data.exog, family=sm.families.Binomial()).fit() assert_allclose(res3.params, self.res1.params) def test_invalid_endog(self, reset_randomstate): # GH2733 inspired check endog = np.random.randint(0, 100, size=(1000, 3)) exog = np.random.standard_normal((1000, 2)) with pytest.raises(ValueError, match='endog has more than 2 columns'): GLM(endog, exog, family=sm.families.Binomial()) def test_invalid_endog_formula(self, reset_randomstate): # GH2733 n = 200 exog = np.random.normal(size=(n, 2)) endog = np.random.randint(0, 3, size=n).astype(str) # formula interface data = pd.DataFrame({"y": endog, "x1": exog[:, 0], "x2": exog[:, 1]}) with pytest.raises(ValueError, match='array with multiple columns'): sm.GLM.from_formula("y ~ x1 + x2", data, family=sm.families.Binomial()) # FIXME: enable/xfail/skip or delete # TODO: # Non-Canonical Links for the Binomial family require the algorithm to be # slightly changed # class TestGlmBinomialLog(CheckModelResultsMixin): # pass # class TestGlmBinomialLogit(CheckModelResultsMixin): # pass # class TestGlmBinomialProbit(CheckModelResultsMixin): # pass # class TestGlmBinomialCloglog(CheckModelResultsMixin): # pass # class TestGlmBinomialPower(CheckModelResultsMixin): # pass # class TestGlmBinomialLoglog(CheckModelResultsMixin): # pass # class TestGlmBinomialLogc(CheckModelResultsMixin): # TODO: need include logc link # pass class TestGlmBernoulli(CheckModelResultsMixin, CheckComparisonMixin): @classmethod def setup_class(cls): from .results.results_glm import Lbw cls.res2 = Lbw() cls.res1 = GLM(cls.res2.endog, cls.res2.exog, family=sm.families.Binomial()).fit() modd = discrete.Logit(cls.res2.endog, cls.res2.exog) cls.resd = modd.fit(start_params=cls.res1.params * 0.9, disp=False) def test_score_r(self): res1 = self.res1 res2 = self.res2 st, pv, df = res1.model.score_test(res1.params, exog_extra=res1.model.exog[:, 1]**2) st_res = 0.2837680293459376 # (-0.5326988167303712)**2 assert_allclose(st, st_res, rtol=1e-4) st, pv, df = res1.model.score_test(res1.params, exog_extra=res1.model.exog[:, 0]**2) st_res = 0.6713492821514992 # (-0.8193590679009413)**2 assert_allclose(st, st_res, rtol=1e-4) select = list(range(9)) select.pop(7) res1b = GLM(res2.endog, res2.exog.iloc[:, select], family=sm.families.Binomial()).fit() tres = res1b.model.score_test(res1b.params, exog_extra=res1.model.exog[:, -2]) tres = np.asarray(tres[:2]).ravel() tres_r = (2.7864148487452, 0.0950667) assert_allclose(tres, tres_r, rtol=1e-4) cmd_r = """\ data = read.csv("...statsmodels\\statsmodels\\genmod\\tests\\results\\stata_lbw_glm.csv") data["race_black"] = data["race"] == "black" data["race_other"] = data["race"] == "other" mod = glm(low ~ age + lwt + race_black + race_other + smoke + ptl + ht + ui, family=binomial, data=data) options(digits=16) anova(mod, test="Rao") library(statmod) s = glm.scoretest(mod, data["age"]**2) s**2 s = glm.scoretest(mod, data["lwt"]**2) s**2 """ # class TestGlmBernoulliIdentity(CheckModelResultsMixin): # pass # class TestGlmBernoulliLog(CheckModelResultsMixin): # pass # class TestGlmBernoulliProbit(CheckModelResultsMixin): # pass # class TestGlmBernoulliCloglog(CheckModelResultsMixin): # pass # class TestGlmBernoulliPower(CheckModelResultsMixin): # pass # class TestGlmBernoulliLoglog(CheckModelResultsMixin): # pass # class test_glm_bernoulli_logc(CheckModelResultsMixin): # pass class TestGlmGamma(CheckModelResultsMixin): @classmethod def setup_class(cls): ''' Tests Gamma family with canonical inverse link (power -1) ''' # Test Precisions cls.decimal_aic_R = -1 #TODO: off by about 1, we are right with Stata cls.decimal_resids = DECIMAL_2 from statsmodels.datasets.scotland import load from .results.results_glm import Scotvote data = load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) with warnings.catch_warnings(): warnings.simplefilter("ignore") res1 = GLM(data.endog, data.exog, family=sm.families.Gamma()).fit() cls.res1 = res1 # res2 = RModel(data.endog, data.exog, r.glm, family=r.Gamma) res2 = Scotvote() res2.aic_R += 2 # R does not count degree of freedom for scale with gamma cls.res2 = res2 class TestGlmGammaLog(CheckModelResultsMixin): @classmethod def setup_class(cls): # Test Precisions cls.decimal_resids = DECIMAL_3 cls.decimal_aic_R = DECIMAL_0 cls.decimal_fittedvalues = DECIMAL_3 from .results.results_glm import CancerLog res2 = CancerLog() cls.res1 = GLM(res2.endog, res2.exog, family=sm.families.Gamma(link=sm.families.links.log())).fit() cls.res2 = res2 # FIXME: enable or delete # def setup(cls): # if skipR: # raise SkipTest, "Rpy not installed." # cls.res2 = RModel(cls.data.endog, cls.data.exog, r.glm, # family=r.Gamma(link="log")) # cls.res2.null_deviance = 27.92207137420696 # From R (bug in rpy) # cls.res2.bic = -154.1582089453923 # from Stata class TestGlmGammaIdentity(CheckModelResultsMixin): @classmethod def setup_class(cls): # Test Precisions cls.decimal_resids = -100 #TODO Very off from Stata? cls.decimal_params = DECIMAL_2 cls.decimal_aic_R = DECIMAL_0 cls.decimal_loglike = DECIMAL_1 from .results.results_glm import CancerIdentity res2 = CancerIdentity() with warnings.catch_warnings(): warnings.simplefilter("ignore") fam = sm.families.Gamma(link=sm.families.links.identity()) cls.res1 = GLM(res2.endog, res2.exog, family=fam).fit() cls.res2 = res2 # FIXME: enable or delete # def setup(cls): # if skipR: # raise SkipTest, "Rpy not installed." # cls.res2 = RModel(cls.data.endog, cls.data.exog, r.glm, # family=r.Gamma(link="identity")) # cls.res2.null_deviance = 27.92207137420696 # from R, Rpy bug class TestGlmPoisson(CheckModelResultsMixin, CheckComparisonMixin): @classmethod def setup_class(cls): ''' Tests Poisson family with canonical log link. Test results were obtained by R. ''' from .results.results_glm import Cpunish cls.data = cpunish.load(as_pandas=False) cls.data.exog[:, 3] = np.log(cls.data.exog[:, 3]) cls.data.exog = add_constant(cls.data.exog, prepend=False) cls.res1 = GLM(cls.data.endog, cls.data.exog, family=sm.families.Poisson()).fit() cls.res2 = Cpunish() # compare with discrete, start close to save time modd = discrete.Poisson(cls.data.endog, cls.data.exog) cls.resd = modd.fit(start_params=cls.res1.params * 0.9, disp=False) #class TestGlmPoissonIdentity(CheckModelResultsMixin): # pass #class TestGlmPoissonPower(CheckModelResultsMixin): # pass class TestGlmInvgauss(CheckModelResultsMixin): @classmethod def setup_class(cls): ''' Tests the Inverse Gaussian family in GLM. Notes ----- Used the rndivgx.ado file provided by Hardin and Hilbe to generate the data. Results are read from model_results, which were obtained by running R_ig.s ''' # Test Precisions cls.decimal_aic_R = DECIMAL_0 cls.decimal_loglike = DECIMAL_0 from .results.results_glm import InvGauss res2 = InvGauss() res1 = GLM(res2.endog, res2.exog, \ family=sm.families.InverseGaussian()).fit() cls.res1 = res1 cls.res2 = res2 class TestGlmInvgaussLog(CheckModelResultsMixin): @classmethod def setup_class(cls): # Test Precisions cls.decimal_aic_R = -10 # Big difference vs R. cls.decimal_resids = DECIMAL_3 from .results.results_glm import InvGaussLog res2 = InvGaussLog() cls.res1 = GLM(res2.endog, res2.exog, family=sm.families.InverseGaussian( link=sm.families.links.log())).fit() cls.res2 = res2 # FIXME: enable or delete # def setup(cls): # if skipR: # raise SkipTest, "Rpy not installed." # cls.res2 = RModel(cls.data.endog, cls.data.exog, r.glm, # family=r.inverse_gaussian(link="log")) # cls.res2.null_deviance = 335.1539777981053 # from R, Rpy bug # cls.res2.llf = -12162.72308 # from Stata, R's has big rounding diff class TestGlmInvgaussIdentity(CheckModelResultsMixin): @classmethod def setup_class(cls): # Test Precisions cls.decimal_aic_R = -10 #TODO: Big difference vs R cls.decimal_fittedvalues = DECIMAL_3 cls.decimal_params = DECIMAL_3 from .results.results_glm import Medpar1 data = Medpar1() with warnings.catch_warnings(): warnings.simplefilter("ignore") cls.res1 = GLM(data.endog, data.exog, family=sm.families.InverseGaussian( link=sm.families.links.identity())).fit() from .results.results_glm import InvGaussIdentity cls.res2 = InvGaussIdentity() # FIXME: enable or delete # def setup(cls): # if skipR: # raise SkipTest, "Rpy not installed." # cls.res2 = RModel(cls.data.endog, cls.data.exog, r.glm, # family=r.inverse_gaussian(link="identity")) # cls.res2.null_deviance = 335.1539777981053 # from R, Rpy bug # cls.res2.llf = -12163.25545 # from Stata, big diff with R class TestGlmNegbinomial(CheckModelResultsMixin): @classmethod def setup_class(cls): ''' Test Negative Binomial family with log link ''' # Test Precision cls.decimal_resid = DECIMAL_1 cls.decimal_params = DECIMAL_3 cls.decimal_resids = -1 # 1 % mismatch at 0 cls.decimal_fittedvalues = DECIMAL_1 from statsmodels.datasets.committee import load cls.data = load(as_pandas=False) cls.data.exog[:,2] = np.log(cls.data.exog[:,2]) interaction = cls.data.exog[:,2]*cls.data.exog[:,1] cls.data.exog = np.column_stack((cls.data.exog,interaction)) cls.data.exog = add_constant(cls.data.exog, prepend=False) with warnings.catch_warnings(): warnings.simplefilter("ignore", category=DomainWarning) fam = sm.families.NegativeBinomial() cls.res1 = GLM(cls.data.endog, cls.data.exog, family=fam).fit(scale='x2') from .results.results_glm import Committee res2 = Committee() res2.aic_R += 2 # They do not count a degree of freedom for the scale cls.res2 = res2 # FIXME: enable or delete # def setup(self): # if skipR: # raise SkipTest, "Rpy not installed" # r.library('MASS') # this does not work when done in rmodelwrap? # self.res2 = RModel(self.data.endog, self.data.exog, r.glm, # family=r.negative_binomial(1)) # self.res2.null_deviance = 27.8110469364343 # FIXME: enable/xfail/skip or delete #class TestGlmNegbinomial_log(CheckModelResultsMixin): # pass # FIXME: enable/xfail/skip or delete #class TestGlmNegbinomial_power(CheckModelResultsMixin): # pass # FIXME: enable/xfail/skip or delete #class TestGlmNegbinomial_nbinom(CheckModelResultsMixin): # pass class TestGlmPoissonOffset(CheckModelResultsMixin): @classmethod def setup_class(cls): from .results.results_glm import Cpunish_offset cls.decimal_params = DECIMAL_4 cls.decimal_bse = DECIMAL_4 cls.decimal_aic_R = 3 data = cpunish.load(as_pandas=False) data.exog[:, 3] = np.log(data.exog[:, 3]) data.exog = add_constant(data.exog, prepend=True) exposure = [100] * len(data.endog) cls.data = data cls.exposure = exposure cls.res1 = GLM(data.endog, data.exog, family=sm.families.Poisson(), exposure=exposure).fit() cls.res2 = Cpunish_offset() def test_missing(self): # make sure offset is dropped correctly endog = self.data.endog.copy() endog[[2,4,6,8]] = np.nan mod = GLM(endog, self.data.exog, family=sm.families.Poisson(), exposure=self.exposure, missing='drop') assert_equal(mod.exposure.shape[0], 13) def test_offset_exposure(self): # exposure=x and offset=log(x) should have the same effect np.random.seed(382304) endog = np.random.randint(0, 10, 100) exog = np.random.normal(size=(100,3)) exposure = np.random.uniform(1, 2, 100) offset = np.random.uniform(1, 2, 100) mod1 = GLM(endog, exog, family=sm.families.Poisson(), offset=offset, exposure=exposure).fit() offset2 = offset + np.log(exposure) mod2 = GLM(endog, exog, family=sm.families.Poisson(), offset=offset2).fit() assert_almost_equal(mod1.params, mod2.params) assert_allclose(mod1.null, mod2.null, rtol=1e-10) # test recreating model mod1_ = mod1.model kwds = mod1_._get_init_kwds() assert_allclose(kwds['exposure'], exposure, rtol=1e-14) assert_allclose(kwds['offset'], mod1_.offset, rtol=1e-14) mod3 = mod1_.__class__(mod1_.endog, mod1_.exog, **kwds) assert_allclose(mod3.exposure, mod1_.exposure, rtol=1e-14) assert_allclose(mod3.offset, mod1_.offset, rtol=1e-14) # test fit_regularized exposure, see #4605 resr1 = mod1.model.fit_regularized() resr2 = mod2.model.fit_regularized() assert_allclose(resr1.params, resr2.params, rtol=1e-10) def test_predict(self): np.random.seed(382304) endog = np.random.randint(0, 10, 100) exog = np.random.normal(size=(100,3)) exposure = np.random.uniform(1, 2, 100) mod1 = GLM(endog, exog, family=sm.families.Poisson(), exposure=exposure).fit() exog1 = np.random.normal(size=(10,3)) exposure1 = np.random.uniform(1, 2, 10) # Doubling exposure time should double expected response pred1 = mod1.predict(exog=exog1, exposure=exposure1) pred2 = mod1.predict(exog=exog1, exposure=2*exposure1) assert_almost_equal(pred2, 2*pred1) # Check exposure defaults pred3 = mod1.predict() pred4 = mod1.predict(exposure=exposure) pred5 = mod1.predict(exog=exog, exposure=exposure) assert_almost_equal(pred3, pred4) assert_almost_equal(pred4, pred5) # Check offset defaults offset = np.random.uniform(1, 2, 100) mod2 = GLM(endog, exog, offset=offset, family=sm.families.Poisson()).fit() pred1 = mod2.predict() pred2 = mod2.predict(offset=offset) pred3 = mod2.predict(exog=exog, offset=offset) assert_almost_equal(pred1, pred2) assert_almost_equal(pred2, pred3) # Check that offset shifts the linear predictor mod3 = GLM(endog, exog, family=sm.families.Poisson()).fit() offset = np.random.uniform(1, 2, 10) pred1 = mod3.predict(exog=exog1, offset=offset, linear=True) pred2 = mod3.predict(exog=exog1, offset=2*offset, linear=True) assert_almost_equal(pred2, pred1+offset) # Passing exposure as a pandas series should not effect output type assert isinstance( mod1.predict(exog=exog1, exposure=pd.Series(exposure1)), np.ndarray ) def test_perfect_pred(iris): y = iris[:, -1] X = iris[:, :-1] X = X[y != 2] y = y[y != 2] X = add_constant(X, prepend=True) glm = GLM(y, X, family=sm.families.Binomial()) with warnings.catch_warnings(): warnings.simplefilter("ignore", category=RuntimeWarning) assert_raises(PerfectSeparationError, glm.fit) def test_score_test_ols(): # nicer example than Longley from statsmodels.regression.linear_model import OLS np.random.seed(5) nobs = 100 sige = 0.5 x = np.random.uniform(0, 1, size=(nobs, 5)) x[:, 0] = 1 beta = 1. / np.arange(1., x.shape[1] + 1) y = x.dot(beta) + sige * np.random.randn(nobs) res_ols = OLS(y, x).fit() res_olsc = OLS(y, x[:, :-2]).fit() co = res_ols.compare_lm_test(res_olsc, demean=False) res_glm = GLM(y, x[:, :-2], family=sm.families.Gaussian()).fit() co2 = res_glm.model.score_test(res_glm.params, exog_extra=x[:, -2:]) # difference in df_resid versus nobs in scale see #1786 assert_allclose(co[0] * 97 / 100., co2[0], rtol=1e-13) def test_attribute_writable_resettable(): # Regression test for mutables and class constructors. data = sm.datasets.longley.load(as_pandas=False) endog, exog = data.endog, data.exog glm_model = sm.GLM(endog, exog) assert_equal(glm_model.family.link.power, 1.0) glm_model.family.link.power = 2. assert_equal(glm_model.family.link.power, 2.0) glm_model2 = sm.GLM(endog, exog) assert_equal(glm_model2.family.link.power, 1.0) class TestStartParams(CheckModelResultsMixin): @classmethod def setup_class(cls): ''' Test Gaussian family with canonical identity link ''' # Test Precisions cls.decimal_resids = DECIMAL_3 cls.decimal_params = DECIMAL_2 cls.decimal_bic = DECIMAL_0 cls.decimal_bse = DECIMAL_3 from statsmodels.datasets.longley import load cls.data = load(as_pandas=False) cls.data.exog = add_constant(cls.data.exog, prepend=False) params = sm.OLS(cls.data.endog, cls.data.exog).fit().params cls.res1 = GLM(cls.data.endog, cls.data.exog, family=sm.families.Gaussian()).fit(start_params=params) from .results.results_glm import Longley cls.res2 = Longley() def test_glm_start_params(): # see 1604 y2 = np.array('0 1 0 0 0 1'.split(), int) wt = np.array([50,1,50,1,5,10]) y2 = np.repeat(y2, wt) x2 = np.repeat([0,0,0.001,100,-1,-1], wt) mod = sm.GLM(y2, sm.add_constant(x2), family=sm.families.Binomial()) res = mod.fit(start_params=[-4, -5]) np.testing.assert_almost_equal(res.params, [-4.60305022, -5.29634545], 6) def test_loglike_no_opt(): # see 1728 y = np.asarray([0, 1, 0, 0, 1, 1, 0, 1, 1, 1]) x = np.arange(10, dtype=np.float64) def llf(params): lin_pred = params[0] + params[1]*x pr = 1 / (1 + np.exp(-lin_pred)) return np.sum(y*np.log(pr) + (1-y)*np.log(1-pr)) for params in [0,0], [0,1], [0.5,0.5]: mod = sm.GLM(y, sm.add_constant(x), family=sm.families.Binomial()) res = mod.fit(start_params=params, maxiter=0) like = llf(params) assert_almost_equal(like, res.llf) def test_formula_missing_exposure(): # see 2083 import statsmodels.formula.api as smf d = {'Foo': [1, 2, 10, 149], 'Bar': [1, 2, 3, np.nan], 'constant': [1] * 4, 'exposure': np.random.uniform(size=4), 'x': [1, 3, 2, 1.5]} df = pd.DataFrame(d) family = sm.families.Gaussian(link=sm.families.links.log()) mod = smf.glm("Foo ~ Bar", data=df, exposure=df.exposure, family=family) assert_(type(mod.exposure) is np.ndarray, msg='Exposure is not ndarray') exposure = pd.Series(np.random.uniform(size=5)) df.loc[3, 'Bar'] = 4 # nan not relevant for Valueerror for shape mismatch assert_raises(ValueError, smf.glm, "Foo ~ Bar", data=df, exposure=exposure, family=family) assert_raises(ValueError, GLM, df.Foo, df[['constant', 'Bar']], exposure=exposure, family=family) @pytest.mark.matplotlib def test_plots(close_figures): np.random.seed(378) n = 200 exog = np.random.normal(size=(n, 2)) lin_pred = exog[:, 0] + exog[:, 1]**2 prob = 1 / (1 + np.exp(-lin_pred)) endog = 1 * (np.random.uniform(size=n) < prob) model = sm.GLM(endog, exog, family=sm.families.Binomial()) result = model.fit() import pandas as pd from statsmodels.graphics.regressionplots import add_lowess # array interface for j in 0,1: fig = result.plot_added_variable(j) add_lowess(fig.axes[0], frac=0.5) close_or_save(pdf, fig) fig = result.plot_partial_residuals(j) add_lowess(fig.axes[0], frac=0.5) close_or_save(pdf, fig) fig = result.plot_ceres_residuals(j) add_lowess(fig.axes[0], frac=0.5) close_or_save(pdf, fig) # formula interface data = pd.DataFrame({"y": endog, "x1": exog[:, 0], "x2": exog[:, 1]}) model = sm.GLM.from_formula("y ~ x1 + x2", data, family=sm.families.Binomial()) result = model.fit() for j in 0,1: xname = ["x1", "x2"][j] fig = result.plot_added_variable(xname) add_lowess(fig.axes[0], frac=0.5) close_or_save(pdf, fig) fig = result.plot_partial_residuals(xname) add_lowess(fig.axes[0], frac=0.5) close_or_save(pdf, fig) fig = result.plot_ceres_residuals(xname) add_lowess(fig.axes[0], frac=0.5) close_or_save(pdf, fig) def gen_endog(lin_pred, family_class, link, binom_version=0): np.random.seed(872) fam = sm.families mu = link().inverse(lin_pred) if family_class == fam.Binomial: if binom_version == 0: endog = 1*(np.random.uniform(size=len(lin_pred)) < mu) else: endog = np.empty((len(lin_pred), 2)) n = 10 endog[:, 0] = (np.random.uniform(size=(len(lin_pred), n)) < mu[:, None]).sum(1) endog[:, 1] = n - endog[:, 0] elif family_class == fam.Poisson: endog = np.random.poisson(mu) elif family_class == fam.Gamma: endog = np.random.gamma(2, mu) elif family_class == fam.Gaussian: endog = mu + 2 * np.random.normal(size=len(lin_pred)) elif family_class == fam.NegativeBinomial: from scipy.stats.distributions import nbinom endog = nbinom.rvs(mu, 0.5) elif family_class == fam.InverseGaussian: from scipy.stats.distributions import invgauss endog = invgauss.rvs(mu, scale=20) else: raise ValueError return endog @pytest.mark.smoke def test_summary(): np.random.seed(4323) n = 100 exog = np.random.normal(size=(n, 2)) exog[:, 0] = 1 endog = np.random.normal(size=n) for method in ["irls", "cg"]: fa = sm.families.Gaussian() model = sm.GLM(endog, exog, family=fa) rslt = model.fit(method=method) s = rslt.summary() def check_score_hessian(results): # compare models core and hessian with numerical derivatives params = results.params # avoid checking score at MLE, score close to zero sc = results.model.score(params * 0.98, scale=1) # cs currently (0.9) does not work for all families llfunc = lambda x: results.model.loglike(x, scale=1) sc2 = approx_fprime(params * 0.98, llfunc) assert_allclose(sc, sc2, rtol=0.05) hess = results.model.hessian(params, scale=1) hess2 = approx_hess(params, llfunc) assert_allclose(hess, hess2, rtol=0.05) scfunc = lambda x: results.model.score(x, scale=1) hess3 = approx_fprime(params, scfunc) assert_allclose(hess, hess3, rtol=0.05) def test_gradient_irls(): # Compare the results when using gradient optimization and IRLS. # TODO: Find working examples for inverse_squared link np.random.seed(87342) fam = sm.families lnk = sm.families.links families = [(fam.Binomial, [lnk.logit, lnk.probit, lnk.cloglog, lnk.log, lnk.cauchy]), (fam.Poisson, [lnk.log, lnk.identity, lnk.sqrt]), (fam.Gamma, [lnk.log, lnk.identity, lnk.inverse_power]), (fam.Gaussian, [lnk.identity, lnk.log, lnk.inverse_power]), (fam.InverseGaussian, [lnk.log, lnk.identity, lnk.inverse_power, lnk.inverse_squared]), (fam.NegativeBinomial, [lnk.log, lnk.inverse_power, lnk.inverse_squared, lnk.identity])] n = 100 p = 3 exog = np.random.normal(size=(n, p)) exog[:, 0] = 1 skip_one = False for family_class, family_links in families: for link in family_links: for binom_version in 0,1: if family_class != fam.Binomial and binom_version == 1: continue if (family_class, link) == (fam.Poisson, lnk.identity): lin_pred = 20 + exog.sum(1) elif (family_class, link) == (fam.Binomial, lnk.log): lin_pred = -1 + exog.sum(1) / 8 elif (family_class, link) == (fam.Poisson, lnk.sqrt): lin_pred = 2 + exog.sum(1) elif (family_class, link) == (fam.InverseGaussian, lnk.log): #skip_zero = True lin_pred = -1 + exog.sum(1) elif (family_class, link) == (fam.InverseGaussian, lnk.identity): lin_pred = 20 + 5*exog.sum(1) lin_pred = np.clip(lin_pred, 1e-4, np.inf) elif (family_class, link) == (fam.InverseGaussian, lnk.inverse_squared): lin_pred = 0.5 + exog.sum(1) / 5 continue # skip due to non-convergence elif (family_class, link) == (fam.InverseGaussian, lnk.inverse_power): lin_pred = 1 + exog.sum(1) / 5 elif (family_class, link) == (fam.NegativeBinomial, lnk.identity): lin_pred = 20 + 5*exog.sum(1) lin_pred = np.clip(lin_pred, 1e-4, np.inf) elif (family_class, link) == (fam.NegativeBinomial, lnk.inverse_squared): lin_pred = 0.1 + np.random.uniform(size=exog.shape[0]) continue # skip due to non-convergence elif (family_class, link) == (fam.NegativeBinomial, lnk.inverse_power): lin_pred = 1 + exog.sum(1) / 5 elif (family_class, link) == (fam.Gaussian, lnk.inverse_power): # adding skip because of convergence failure skip_one = True # the following fails with identity link, because endog < 0 # elif family_class == fam.Gamma: # lin_pred = 0.5 * exog.sum(1) + np.random.uniform(size=exog.shape[0]) else: lin_pred = np.random.uniform(size=exog.shape[0]) endog = gen_endog(lin_pred, family_class, link, binom_version) with warnings.catch_warnings(): warnings.simplefilter("ignore") mod_irls = sm.GLM(endog, exog, family=family_class(link=link())) rslt_irls = mod_irls.fit(method="IRLS") if not (family_class, link) in [(fam.Poisson, lnk.sqrt), (fam.Gamma, lnk.inverse_power), (fam.InverseGaussian, lnk.identity) ]: check_score_hessian(rslt_irls) # Try with and without starting values. for max_start_irls, start_params in (0, rslt_irls.params), (3, None): # TODO: skip convergence failures for now if max_start_irls > 0 and skip_one: continue with warnings.catch_warnings(): warnings.simplefilter("ignore") mod_gradient = sm.GLM(endog, exog, family=family_class(link=link())) rslt_gradient = mod_gradient.fit(max_start_irls=max_start_irls, start_params=start_params, method="newton", maxiter=300) assert_allclose(rslt_gradient.params, rslt_irls.params, rtol=1e-6, atol=5e-5) assert_allclose(rslt_gradient.llf, rslt_irls.llf, rtol=1e-6, atol=1e-6) assert_allclose(rslt_gradient.scale, rslt_irls.scale, rtol=1e-6, atol=1e-6) # Get the standard errors using expected information. gradient_bse = rslt_gradient.bse ehess = mod_gradient.hessian(rslt_gradient.params, observed=False) gradient_bse = np.sqrt(-np.diag(np.linalg.inv(ehess))) assert_allclose(gradient_bse, rslt_irls.bse, rtol=1e-6, atol=5e-5) # rslt_irls.bse corresponds to observed=True assert_allclose(rslt_gradient.bse, rslt_irls.bse, rtol=0.2, atol=5e-5) rslt_gradient_eim = mod_gradient.fit(max_start_irls=0, cov_type='eim', start_params=rslt_gradient.params, method="newton", maxiter=300) assert_allclose(rslt_gradient_eim.bse, rslt_irls.bse, rtol=5e-5, atol=0) def test_gradient_irls_eim(): # Compare the results when using eime gradient optimization and IRLS. # TODO: Find working examples for inverse_squared link np.random.seed(87342) fam = sm.families lnk = sm.families.links families = [(fam.Binomial, [lnk.logit, lnk.probit, lnk.cloglog, lnk.log, lnk.cauchy]), (fam.Poisson, [lnk.log, lnk.identity, lnk.sqrt]), (fam.Gamma, [lnk.log, lnk.identity, lnk.inverse_power]), (fam.Gaussian, [lnk.identity, lnk.log, lnk.inverse_power]), (fam.InverseGaussian, [lnk.log, lnk.identity, lnk.inverse_power, lnk.inverse_squared]), (fam.NegativeBinomial, [lnk.log, lnk.inverse_power, lnk.inverse_squared, lnk.identity])] n = 100 p = 3 exog = np.random.normal(size=(n, p)) exog[:, 0] = 1 skip_one = False for family_class, family_links in families: for link in family_links: for binom_version in 0, 1: if family_class != fam.Binomial and binom_version == 1: continue if (family_class, link) == (fam.Poisson, lnk.identity): lin_pred = 20 + exog.sum(1) elif (family_class, link) == (fam.Binomial, lnk.log): lin_pred = -1 + exog.sum(1) / 8 elif (family_class, link) == (fam.Poisson, lnk.sqrt): lin_pred = 2 + exog.sum(1) elif (family_class, link) == (fam.InverseGaussian, lnk.log): # skip_zero = True lin_pred = -1 + exog.sum(1) elif (family_class, link) == (fam.InverseGaussian, lnk.identity): lin_pred = 20 + 5*exog.sum(1) lin_pred = np.clip(lin_pred, 1e-4, np.inf) elif (family_class, link) == (fam.InverseGaussian, lnk.inverse_squared): lin_pred = 0.5 + exog.sum(1) / 5 continue # skip due to non-convergence elif (family_class, link) == (fam.InverseGaussian, lnk.inverse_power): lin_pred = 1 + exog.sum(1) / 5 elif (family_class, link) == (fam.NegativeBinomial, lnk.identity): lin_pred = 20 + 5*exog.sum(1) lin_pred = np.clip(lin_pred, 1e-4, np.inf) elif (family_class, link) == (fam.NegativeBinomial, lnk.inverse_squared): lin_pred = 0.1 + np.random.uniform(size=exog.shape[0]) continue # skip due to non-convergence elif (family_class, link) == (fam.NegativeBinomial, lnk.inverse_power): lin_pred = 1 + exog.sum(1) / 5 elif (family_class, link) == (fam.Gaussian, lnk.inverse_power): # adding skip because of convergence failure skip_one = True else: lin_pred = np.random.uniform(size=exog.shape[0]) endog = gen_endog(lin_pred, family_class, link, binom_version) with warnings.catch_warnings(): warnings.simplefilter("ignore") mod_irls = sm.GLM(endog, exog, family=family_class(link=link())) rslt_irls = mod_irls.fit(method="IRLS") # Try with and without starting values. for max_start_irls, start_params in ((0, rslt_irls.params), (3, None)): # TODO: skip convergence failures for now if max_start_irls > 0 and skip_one: continue with warnings.catch_warnings(): warnings.simplefilter("ignore") mod_gradient = sm.GLM(endog, exog, family=family_class(link=link())) rslt_gradient = mod_gradient.fit( max_start_irls=max_start_irls, start_params=start_params, method="newton", optim_hessian='eim' ) assert_allclose(rslt_gradient.params, rslt_irls.params, rtol=1e-6, atol=5e-5) assert_allclose(rslt_gradient.llf, rslt_irls.llf, rtol=1e-6, atol=1e-6) assert_allclose(rslt_gradient.scale, rslt_irls.scale, rtol=1e-6, atol=1e-6) # Get the standard errors using expected information. ehess = mod_gradient.hessian(rslt_gradient.params, observed=False) gradient_bse = np.sqrt(-np.diag(np.linalg.inv(ehess))) assert_allclose(gradient_bse, rslt_irls.bse, rtol=1e-6, atol=5e-5) def test_glm_irls_method(): nobs, k_vars = 50, 4 np.random.seed(987126) x = np.random.randn(nobs, k_vars - 1) exog = add_constant(x, has_constant='add') y = exog.sum(1) + np.random.randn(nobs) mod = GLM(y, exog) res1 = mod.fit() res2 = mod.fit(wls_method='pinv', attach_wls=True) res3 = mod.fit(wls_method='qr', attach_wls=True) # fit_gradient does not attach mle_settings res_g1 = mod.fit(start_params=res1.params, method='bfgs') for r in [res1, res2, res3]: assert_equal(r.mle_settings['optimizer'], 'IRLS') assert_equal(r.method, 'IRLS') assert_equal(res1.mle_settings['wls_method'], 'lstsq') assert_equal(res2.mle_settings['wls_method'], 'pinv') assert_equal(res3.mle_settings['wls_method'], 'qr') assert_(hasattr(res2.results_wls.model, 'pinv_wexog')) assert_(hasattr(res3.results_wls.model, 'exog_Q')) # fit_gradient currently does not attach mle_settings assert_equal(res_g1.method, 'bfgs') class CheckWtdDuplicationMixin(object): decimal_params = DECIMAL_4 @classmethod def setup_class(cls): cls.data = cpunish.load(as_pandas=False) cls.endog = cls.data.endog cls.exog = cls.data.exog np.random.seed(1234) cls.weight = np.random.randint(5, 100, len(cls.endog)) cls.endog_big = np.repeat(cls.endog, cls.weight) cls.exog_big = np.repeat(cls.exog, cls.weight, axis=0) def test_params(self): assert_allclose(self.res1.params, self.res2.params, atol=1e-6, rtol=1e-6) decimal_bse = DECIMAL_4 def test_standard_errors(self): assert_allclose(self.res1.bse, self.res2.bse, rtol=1e-5, atol=1e-6) decimal_resids = DECIMAL_4 # TODO: This does not work... Arrays are of different shape. # Perhaps we use self.res1.model.family.resid_XXX()? """ def test_residuals(self): resids1 = np.column_stack((self.res1.resid_pearson, self.res1.resid_deviance, self.res1.resid_working, self.res1.resid_anscombe, self.res1.resid_response)) resids2 = np.column_stack((self.res1.resid_pearson, self.res2.resid_deviance, self.res2.resid_working, self.res2.resid_anscombe, self.res2.resid_response)) assert_allclose(resids1, resids2, self.decimal_resids) """ def test_aic(self): # R includes the estimation of the scale as a lost dof # Does not with Gamma though assert_allclose(self.res1.aic, self.res2.aic, atol=1e-6, rtol=1e-6) def test_deviance(self): assert_allclose(self.res1.deviance, self.res2.deviance, atol=1e-6, rtol=1e-6) def test_scale(self): assert_allclose(self.res1.scale, self.res2.scale, atol=1e-6, rtol=1e-6) def test_loglike(self): # Stata uses the below llf for these families # We differ with R for them assert_allclose(self.res1.llf, self.res2.llf, 1e-6) decimal_null_deviance = DECIMAL_4 def test_null_deviance(self): assert_allclose(self.res1.null_deviance, self.res2.null_deviance, atol=1e-6, rtol=1e-6) decimal_bic = DECIMAL_4 def test_bic(self): with warnings.catch_warnings(): warnings.simplefilter("ignore") assert_allclose(self.res1.bic, self.res2.bic, atol=1e-6, rtol=1e-6) decimal_fittedvalues = DECIMAL_4 def test_fittedvalues(self): res2_fitted = self.res2.predict(self.res1.model.exog) assert_allclose(self.res1.fittedvalues, res2_fitted, atol=1e-5, rtol=1e-5) decimal_tpvalues = DECIMAL_4 def test_tpvalues(self): # test comparing tvalues and pvalues with normal implementation # make sure they use normal distribution (inherited in results class) assert_allclose(self.res1.tvalues, self.res2.tvalues, atol=1e-6, rtol=2e-4) assert_allclose(self.res1.pvalues, self.res2.pvalues, atol=1e-6, rtol=1e-6) assert_allclose(self.res1.conf_int(), self.res2.conf_int(), atol=1e-6, rtol=1e-6) class TestWtdGlmPoisson(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Poisson family with canonical log link. ''' super(TestWtdGlmPoisson, cls).setup_class() cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=sm.families.Poisson()).fit() cls.res2 = GLM(cls.endog_big, cls.exog_big, family=sm.families.Poisson()).fit() class TestWtdGlmPoissonNewton(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Poisson family with canonical log link. ''' super(TestWtdGlmPoissonNewton, cls).setup_class() start_params = np.array([1.82794424e-04, -4.76785037e-02, -9.48249717e-02, -2.92293226e-04, 2.63728909e+00, -2.05934384e+01]) fit_kwds = dict(method='newton') cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=sm.families.Poisson()).fit(**fit_kwds) fit_kwds = dict(method='newton', start_params=start_params) cls.res2 = GLM(cls.endog_big, cls.exog_big, family=sm.families.Poisson()).fit(**fit_kwds) class TestWtdGlmPoissonHC0(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Poisson family with canonical log link. ''' super(TestWtdGlmPoissonHC0, cls).setup_class() start_params = np.array([1.82794424e-04, -4.76785037e-02, -9.48249717e-02, -2.92293226e-04, 2.63728909e+00, -2.05934384e+01]) fit_kwds = dict(cov_type='HC0') cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=sm.families.Poisson()).fit(**fit_kwds) fit_kwds = dict(cov_type='HC0', start_params=start_params) cls.res2 = GLM(cls.endog_big, cls.exog_big, family=sm.families.Poisson()).fit(**fit_kwds) class TestWtdGlmPoissonClu(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Poisson family with canonical log link. ''' super(TestWtdGlmPoissonClu, cls).setup_class() start_params = np.array([1.82794424e-04, -4.76785037e-02, -9.48249717e-02, -2.92293226e-04, 2.63728909e+00, -2.05934384e+01]) gid = np.arange(1, len(cls.endog) + 1) // 2 fit_kwds = dict(cov_type='cluster', cov_kwds={'groups': gid, 'use_correction':False}) import warnings with warnings.catch_warnings(): warnings.simplefilter("ignore") cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=sm.families.Poisson()).fit(**fit_kwds) gidr = np.repeat(gid, cls.weight) fit_kwds = dict(cov_type='cluster', cov_kwds={'groups': gidr, 'use_correction':False}) cls.res2 = GLM(cls.endog_big, cls.exog_big, family=sm.families.Poisson()).fit(start_params=start_params, **fit_kwds) class TestWtdGlmBinomial(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Binomial family with canonical logit link. ''' super(TestWtdGlmBinomial, cls).setup_class() cls.endog = cls.endog / 100 cls.endog_big = cls.endog_big / 100 cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=sm.families.Binomial()).fit() cls.res2 = GLM(cls.endog_big, cls.exog_big, family=sm.families.Binomial()).fit() class TestWtdGlmNegativeBinomial(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Negative Binomial family with canonical link g(p) = log(p/(p + 1/alpha)) ''' super(TestWtdGlmNegativeBinomial, cls).setup_class() alpha = 1. with warnings.catch_warnings(): warnings.simplefilter("ignore", category=DomainWarning) family_link = sm.families.NegativeBinomial( link=sm.families.links.nbinom(alpha=alpha), alpha=alpha) cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=family_link).fit() cls.res2 = GLM(cls.endog_big, cls.exog_big, family=family_link).fit() class TestWtdGlmGamma(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Gamma family with log link. ''' super(TestWtdGlmGamma, cls).setup_class() family_link = sm.families.Gamma(sm.families.links.log()) cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=family_link).fit() cls.res2 = GLM(cls.endog_big, cls.exog_big, family=family_link).fit() class TestWtdGlmGaussian(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Gaussian family with log link. ''' super(TestWtdGlmGaussian, cls).setup_class() family_link = sm.families.Gaussian(sm.families.links.log()) cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=family_link).fit() cls.res2 = GLM(cls.endog_big, cls.exog_big, family=family_link).fit() class TestWtdGlmInverseGaussian(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests InverseGaussian family with log link. ''' super(TestWtdGlmInverseGaussian, cls).setup_class() family_link = sm.families.InverseGaussian(sm.families.links.log()) cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=family_link).fit() cls.res2 = GLM(cls.endog_big, cls.exog_big, family=family_link).fit() class TestWtdGlmGammaNewton(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Gamma family with log link. ''' super(TestWtdGlmGammaNewton, cls).setup_class() family_link = sm.families.Gamma(sm.families.links.log()) cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=family_link, method='newton').fit() cls.res2 = GLM(cls.endog_big, cls.exog_big, family=family_link, method='newton').fit() class TestWtdGlmGammaScale_X2(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Gamma family with log link. ''' super(TestWtdGlmGammaScale_X2, cls).setup_class() family_link = sm.families.Gamma(sm.families.links.log()) cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=family_link, scale='X2').fit() cls.res2 = GLM(cls.endog_big, cls.exog_big, family=family_link, scale='X2').fit() class TestWtdGlmGammaScale_dev(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Gamma family with log link. ''' super(TestWtdGlmGammaScale_dev, cls).setup_class() family_link = sm.families.Gamma(sm.families.links.log()) cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=family_link, scale='dev').fit() cls.res2 = GLM(cls.endog_big, cls.exog_big, family=family_link, scale='dev').fit() def test_missing(self): endog = self.data.endog.copy() exog = self.data.exog.copy() exog[0, 0] = np.nan endog[[2, 4, 6, 8]] = np.nan freq_weights = self.weight mod_misisng = GLM(endog, exog, family=self.res1.model.family, freq_weights=freq_weights, missing='drop') assert_equal(mod_misisng.freq_weights.shape[0], mod_misisng.endog.shape[0]) assert_equal(mod_misisng.freq_weights.shape[0], mod_misisng.exog.shape[0]) keep_idx = np.array([1, 3, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16]) assert_equal(mod_misisng.freq_weights, self.weight[keep_idx]) class TestWtdTweedieLog(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Tweedie family with log link and var_power=1. ''' super(TestWtdTweedieLog, cls).setup_class() family_link = sm.families.Tweedie(link=sm.families.links.log(), var_power=1) cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=family_link).fit() cls.res2 = GLM(cls.endog_big, cls.exog_big, family=family_link).fit() class TestWtdTweediePower2(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Tweedie family with Power(1) link and var_power=2. ''' cls.data = cpunish.load_pandas() cls.endog = cls.data.endog cls.exog = cls.data.exog[['INCOME', 'SOUTH']] np.random.seed(1234) cls.weight = np.random.randint(5, 100, len(cls.endog)) cls.endog_big = np.repeat(cls.endog.values, cls.weight) cls.exog_big = np.repeat(cls.exog.values, cls.weight, axis=0) link = sm.families.links.Power() family_link = sm.families.Tweedie(link=link, var_power=2) cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=family_link).fit() cls.res2 = GLM(cls.endog_big, cls.exog_big, family=family_link).fit() class TestWtdTweediePower15(CheckWtdDuplicationMixin): @classmethod def setup_class(cls): ''' Tests Tweedie family with Power(0.5) link and var_power=1.5. ''' super(TestWtdTweediePower15, cls).setup_class() family_link = sm.families.Tweedie(link=sm.families.links.Power(0.5), var_power=1.5) cls.res1 = GLM(cls.endog, cls.exog, freq_weights=cls.weight, family=family_link).fit() cls.res2 = GLM(cls.endog_big, cls.exog_big, family=family_link).fit() def test_wtd_patsy_missing(): import pandas as pd data = cpunish.load(as_pandas=False) data.exog[0, 0] = np.nan data.endog[[2, 4, 6, 8]] = np.nan data.pandas = pd.DataFrame(data.exog, columns=data.exog_name) data.pandas['EXECUTIONS'] = data.endog weights = np.arange(1, len(data.endog)+1) formula = """EXECUTIONS ~ INCOME + PERPOVERTY + PERBLACK + VC100k96 + SOUTH + DEGREE""" mod_misisng = GLM.from_formula(formula, data=data.pandas, freq_weights=weights) assert_equal(mod_misisng.freq_weights.shape[0], mod_misisng.endog.shape[0]) assert_equal(mod_misisng.freq_weights.shape[0], mod_misisng.exog.shape[0]) assert_equal(mod_misisng.freq_weights.shape[0], 12) keep_weights = np.array([2, 4, 6, 8, 10, 11, 12, 13, 14, 15, 16, 17]) assert_equal(mod_misisng.freq_weights, keep_weights) class CheckTweedie(object): def test_resid(self): idx1 = len(self.res1.resid_response) - 1 idx2 = len(self.res2.resid_response) - 1 assert_allclose(np.concatenate((self.res1.resid_response[:17], [self.res1.resid_response[idx1]])), np.concatenate((self.res2.resid_response[:17], [self.res2.resid_response[idx2]])), rtol=1e-5, atol=1e-5) assert_allclose(np.concatenate((self.res1.resid_pearson[:17], [self.res1.resid_pearson[idx1]])), np.concatenate((self.res2.resid_pearson[:17], [self.res2.resid_pearson[idx2]])), rtol=1e-5, atol=1e-5) assert_allclose(np.concatenate((self.res1.resid_deviance[:17], [self.res1.resid_deviance[idx1]])), np.concatenate((self.res2.resid_deviance[:17], [self.res2.resid_deviance[idx2]])), rtol=1e-5, atol=1e-5) assert_allclose(np.concatenate((self.res1.resid_working[:17], [self.res1.resid_working[idx1]])), np.concatenate((self.res2.resid_working[:17], [self.res2.resid_working[idx2]])), rtol=1e-5, atol=1e-5) def test_bse(self): assert_allclose(self.res1.bse, self.res2.bse, atol=1e-6, rtol=1e6) def test_params(self): assert_allclose(self.res1.params, self.res2.params, atol=1e-5, rtol=1e-5) def test_deviance(self): assert_allclose(self.res1.deviance, self.res2.deviance, atol=1e-6, rtol=1e-6) def test_df(self): assert_equal(self.res1.df_model, self.res2.df_model) assert_equal(self.res1.df_resid, self.res2.df_resid) def test_fittedvalues(self): idx1 = len(self.res1.fittedvalues) - 1 idx2 = len(self.res2.resid_response) - 1 assert_allclose(np.concatenate((self.res1.fittedvalues[:17], [self.res1.fittedvalues[idx1]])), np.concatenate((self.res2.fittedvalues[:17], [self.res2.fittedvalues[idx2]])), atol=1e-4, rtol=1e-4) def test_summary(self): self.res1.summary() self.res1.summary2() class TestTweediePower15(CheckTweedie): @classmethod def setup_class(cls): from .results.results_glm import CpunishTweediePower15 cls.data = cpunish.load_pandas() cls.exog = cls.data.exog[['INCOME', 'SOUTH']] cls.endog = cls.data.endog family_link = sm.families.Tweedie(link=sm.families.links.Power(1), var_power=1.5) cls.res1 = sm.GLM(endog=cls.data.endog, exog=cls.data.exog[['INCOME', 'SOUTH']], family=family_link).fit() cls.res2 = CpunishTweediePower15() class TestTweediePower2(CheckTweedie): @classmethod def setup_class(cls): from .results.results_glm import CpunishTweediePower2 cls.data = cpunish.load_pandas() cls.exog = cls.data.exog[['INCOME', 'SOUTH']] cls.endog = cls.data.endog family_link = sm.families.Tweedie(link=sm.families.links.Power(1), var_power=2.) cls.res1 = sm.GLM(endog=cls.data.endog, exog=cls.data.exog[['INCOME', 'SOUTH']], family=family_link).fit() cls.res2 = CpunishTweediePower2() class TestTweedieLog1(CheckTweedie): @classmethod def setup_class(cls): from .results.results_glm import CpunishTweedieLog1 cls.data = cpunish.load_pandas() cls.exog = cls.data.exog[['INCOME', 'SOUTH']] cls.endog = cls.data.endog family_link = sm.families.Tweedie(link=sm.families.links.log(), var_power=1.) cls.res1 = sm.GLM(endog=cls.data.endog, exog=cls.data.exog[['INCOME', 'SOUTH']], family=family_link).fit() cls.res2 = CpunishTweedieLog1() class TestTweedieLog15Fair(CheckTweedie): @classmethod def setup_class(cls): from .results.results_glm import FairTweedieLog15 from statsmodels.datasets.fair import load_pandas data = load_pandas() family_link = sm.families.Tweedie(link=sm.families.links.log(), var_power=1.5) cls.res1 = sm.GLM(endog=data.endog, exog=data.exog[['rate_marriage', 'age', 'yrs_married']], family=family_link).fit() cls.res2 = FairTweedieLog15() class CheckTweedieSpecial(object): def test_mu(self): assert_allclose(self.res1.mu, self.res2.mu, rtol=1e-5, atol=1e-5) def test_resid(self): assert_allclose(self.res1.resid_response, self.res2.resid_response, rtol=1e-5, atol=1e-5) assert_allclose(self.res1.resid_pearson, self.res2.resid_pearson, rtol=1e-5, atol=1e-5) assert_allclose(self.res1.resid_deviance, self.res2.resid_deviance, rtol=1e-5, atol=1e-5) assert_allclose(self.res1.resid_working, self.res2.resid_working, rtol=1e-5, atol=1e-5) assert_allclose(self.res1.resid_anscombe_unscaled, self.res2.resid_anscombe_unscaled, rtol=1e-5, atol=1e-5) class TestTweedieSpecialLog0(CheckTweedieSpecial): @classmethod def setup_class(cls): cls.data = cpunish.load_pandas() cls.exog = cls.data.exog[['INCOME', 'SOUTH']] cls.endog = cls.data.endog family1 = sm.families.Gaussian(link=sm.families.links.log()) cls.res1 = sm.GLM(endog=cls.data.endog, exog=cls.data.exog[['INCOME', 'SOUTH']], family=family1).fit() family2 = sm.families.Tweedie(link=sm.families.links.log(), var_power=0) cls.res2 = sm.GLM(endog=cls.data.endog, exog=cls.data.exog[['INCOME', 'SOUTH']], family=family2).fit() class TestTweedieSpecialLog1(CheckTweedieSpecial): @classmethod def setup_class(cls): cls.data = cpunish.load_pandas() cls.exog = cls.data.exog[['INCOME', 'SOUTH']] cls.endog = cls.data.endog family1 = sm.families.Poisson(link=sm.families.links.log()) cls.res1 = sm.GLM(endog=cls.data.endog, exog=cls.data.exog[['INCOME', 'SOUTH']], family=family1).fit() family2 = sm.families.Tweedie(link=sm.families.links.log(), var_power=1) cls.res2 = sm.GLM(endog=cls.data.endog, exog=cls.data.exog[['INCOME', 'SOUTH']], family=family2).fit() class TestTweedieSpecialLog2(CheckTweedieSpecial): @classmethod def setup_class(cls): cls.data = cpunish.load_pandas() cls.exog = cls.data.exog[['INCOME', 'SOUTH']] cls.endog = cls.data.endog family1 = sm.families.Gamma(link=sm.families.links.log()) cls.res1 = sm.GLM(endog=cls.data.endog, exog=cls.data.exog[['INCOME', 'SOUTH']], family=family1).fit() family2 = sm.families.Tweedie(link=sm.families.links.log(), var_power=2) cls.res2 = sm.GLM(endog=cls.data.endog, exog=cls.data.exog[['INCOME', 'SOUTH']], family=family2).fit() class TestTweedieSpecialLog3(CheckTweedieSpecial): @classmethod def setup_class(cls): cls.data = cpunish.load_pandas() cls.exog = cls.data.exog[['INCOME', 'SOUTH']] cls.endog = cls.data.endog family1 = sm.families.InverseGaussian(link=sm.families.links.log()) cls.res1 = sm.GLM(endog=cls.data.endog, exog=cls.data.exog[['INCOME', 'SOUTH']], family=family1).fit() family2 = sm.families.Tweedie(link=sm.families.links.log(), var_power=3) cls.res2 = sm.GLM(endog=cls.data.endog, exog=cls.data.exog[['INCOME', 'SOUTH']], family=family2).fit() @pytest.mark.filterwarnings("ignore:GLM ridge optimization") def test_tweedie_EQL(): # All tests below are regression tests, but the results # are very close to the population values. np.random.seed(3242) n = 500 p = 1.5 # Tweedie variance power x = np.random.normal(size=(n, 4)) lpr = np.dot(x, np.r_[1, -1, 0, 0.5]) mu = np.exp(lpr) lam = 10 * mu**(2 - p) / (2 - p) alp = (2 - p) / (p - 1) bet = 10 * mu**(1 - p) / (p - 1) # Generate Tweedie values using commpound Poisson distribution y = np.empty(n) N = np.random.poisson(lam) for i in range(n): y[i] = np.random.gamma(alp, 1 / bet[i], N[i]).sum() # Un-regularized fit using gradients not IRLS fam = sm.families.Tweedie(var_power=p, eql=True) model1 = sm.GLM(y, x, family=fam) result1 = model1.fit(method="newton") assert_allclose(result1.params, np.array([1.00350497, -0.99656954, 0.00802702, 0.50713209]), rtol=1e-5, atol=1e-5) # Lasso fit using coordinate-wise descent # TODO: The search gets trapped in an infinite oscillation, so use # a slack convergence tolerance. model2 = sm.GLM(y, x, family=fam) result2 = model2.fit_regularized(L1_wt=1, alpha=0.07, maxiter=200, cnvrg_tol=0.01) rtol, atol = 1e-2, 1e-4 assert_allclose(result2.params, np.array([1.00281192, -0.99182638, 0., 0.50448516]), rtol=rtol, atol=atol) # Series of ridge fits using gradients ev = (np.array([1.001778, -0.99388, 0.00797, 0.506183]), np.array([0.985841, -0.969124, 0.007319, 0.497649]), np.array([0.206429, -0.164547, 0.000235, 0.102489])) for j, alpha in enumerate([0.05, 0.5, 0.7]): model3 = sm.GLM(y, x, family=fam) result3 = model3.fit_regularized(L1_wt=0, alpha=alpha) assert_allclose(result3.params, ev[j], rtol=rtol, atol=atol) result4 = model3.fit_regularized(L1_wt=0, alpha=alpha * np.ones(x.shape[1])) assert_allclose(result4.params, result3.params, rtol=rtol, atol=atol) alpha = alpha * np.ones(x.shape[1]) alpha[0] = 0 result5 = model3.fit_regularized(L1_wt=0, alpha=alpha) assert not np.allclose(result5.params, result4.params, rtol=rtol, atol=atol) def test_tweedie_EQL_poisson_limit(): # Test the limiting Poisson case of the Nelder/Pregibon/Tweedie # EQL. np.random.seed(3242) n = 500 x = np.random.normal(size=(n, 3)) x[:, 0] = 1 lpr = 4 + x[:, 1:].sum(1) mn = np.exp(lpr) y = np.random.poisson(mn) for scale in 1.0, 'x2', 'dev': # Un-regularized fit using gradients not IRLS fam = sm.families.Tweedie(var_power=1, eql=True) model1 = sm.GLM(y, x, family=fam) result1 = model1.fit(method="newton", scale=scale) # Poisson GLM model2 = sm.GLM(y, x, family=sm.families.Poisson()) result2 = model2.fit(method="newton", scale=scale) assert_allclose(result1.params, result2.params, atol=1e-6, rtol=1e-6) assert_allclose(result1.bse, result2.bse, 1e-6, 1e-6) def test_tweedie_EQL_upper_limit(): # Test the limiting case of the Nelder/Pregibon/Tweedie # EQL with var = mean^2. These are tests against population # values so accuracy is not high. np.random.seed(3242) n = 500 x = np.random.normal(size=(n, 3)) x[:, 0] = 1 lpr = 4 + x[:, 1:].sum(1) mn = np.exp(lpr) y = np.random.poisson(mn) for scale in 'x2', 'dev', 1.0: # Un-regularized fit using gradients not IRLS fam = sm.families.Tweedie(var_power=2, eql=True) model1 = sm.GLM(y, x, family=fam) result1 = model1.fit(method="newton", scale=scale) assert_allclose(result1.params, np.r_[4, 1, 1], atol=1e-3, rtol=1e-1) def testTweediePowerEstimate(): # Test the Pearson estimate of the Tweedie variance and scale parameters. # # Ideally, this would match the following R code, but I cannot make it work... # # setwd('c:/workspace') # data <- read.csv('cpunish.csv', sep=",") # # library(tweedie) # # y <- c(1.00113835e+05, 6.89668315e+03, 6.15726842e+03, # 1.41718806e+03, 5.11776456e+02, 2.55369154e+02, # 1.07147443e+01, 3.56874698e+00, 4.06797842e-02, # 7.06996731e-05, 2.10165106e-07, 4.34276938e-08, # 1.56354040e-09, 0.00000000e+00, 0.00000000e+00, # 0.00000000e+00, 0.00000000e+00) # # data$NewY <- y # # out <- tweedie.profile( NewY ~ INCOME + SOUTH - 1, # p.vec=c(1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, # 1.9), link.power=0, # data=data,do.plot = TRUE) data = cpunish.load_pandas() y = [1.00113835e+05, 6.89668315e+03, 6.15726842e+03, 1.41718806e+03, 5.11776456e+02, 2.55369154e+02, 1.07147443e+01, 3.56874698e+00, 4.06797842e-02, 7.06996731e-05, 2.10165106e-07, 4.34276938e-08, 1.56354040e-09, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00] model1 = sm.GLM(y, data.exog[['INCOME', 'SOUTH']], family=sm.families.Tweedie(link=sm.families.links.log(), var_power=1.5)) res1 = model1.fit() model2 = sm.GLM((y - res1.mu) ** 2, np.column_stack((np.ones(len(res1.mu)), np.log(res1.mu))), family=sm.families.Gamma(sm.families.links.log())) res2 = model2.fit() # Sample may be too small for this... # assert_allclose(res1.scale, np.exp(res2.params[0]), rtol=0.25) p = model1.estimate_tweedie_power(res1.mu) assert_allclose(p, res2.params[1], rtol=0.25) def test_glm_lasso_6431(): # Based on issue #6431 # Fails with newton-cg as optimizer np.random.seed(123) from statsmodels.regression.linear_model import OLS n = 50 x = np.ones((n, 2)) x[:, 1] = np.arange(0, n) y = 1000 + x[:, 1] + np.random.normal(0, 1, n) params = np.r_[999.82244338, 1.0077889] for method in "bfgs", None: for fun in [OLS, GLM]: # Changing L1_wtValue from 0 to 1e-9 changes # the algorithm from scipy gradient optimization # to statsmodels coordinate descent for L1_wtValue in [0, 1e-9]: model = fun(y, x) if fun == OLS: fit = model.fit_regularized(alpha=0, L1_wt=L1_wtValue) else: fit = model._fit_ridge(alpha=0, start_params=None, method=method) assert_allclose(params, fit.params, atol=1e-6, rtol=1e-6) class TestRegularized(object): def test_regularized(self): import os from .results import glmnet_r_results for dtype in "binomial", "poisson": cur_dir = os.path.dirname(os.path.abspath(__file__)) data = np.loadtxt(os.path.join(cur_dir, "results", "enet_%s.csv" % dtype), delimiter=",") endog = data[:, 0] exog = data[:, 1:] fam = {"binomial" : sm.families.Binomial, "poisson" : sm.families.Poisson}[dtype] for j in range(9): vn = "rslt_%s_%d" % (dtype, j) r_result = getattr(glmnet_r_results, vn) L1_wt = r_result[0] alpha = r_result[1] params = r_result[2:] model = GLM(endog, exog, family=fam()) sm_result = model.fit_regularized(L1_wt=L1_wt, alpha=alpha) # Agreement is OK, see below for further check assert_allclose(params, sm_result.params, atol=1e-2, rtol=0.3) # The penalized log-likelihood that we are maximizing. def plf(params): llf = model.loglike(params) / len(endog) llf = llf - alpha * ((1 - L1_wt)*np.sum(params**2) / 2 + L1_wt*np.sum(np.abs(params))) return llf # Confirm that we are doing better than glmnet. llf_r = plf(params) llf_sm = plf(sm_result.params) assert_equal(np.sign(llf_sm - llf_r), 1) class TestConvergence(object): @classmethod def setup_class(cls): ''' Test Binomial family with canonical logit link using star98 dataset. ''' from statsmodels.datasets.star98 import load data = load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) cls.model = GLM(data.endog, data.exog, family=sm.families.Binomial()) def _when_converged(self, atol=1e-8, rtol=0, tol_criterion='deviance'): for i, dev in enumerate(self.res.fit_history[tol_criterion]): orig = self.res.fit_history[tol_criterion][i] new = self.res.fit_history[tol_criterion][i + 1] if np.allclose(orig, new, atol=atol, rtol=rtol): return i raise ValueError('CONVERGENCE CHECK: It seems this doens\'t converge!') def test_convergence_atol_only(self): atol = 1e-8 rtol = 0 self.res = self.model.fit(atol=atol, rtol=rtol) expected_iterations = self._when_converged(atol=atol, rtol=rtol) actual_iterations = self.res.fit_history['iteration'] # Note the first value is the list is np.inf. The second value # is the initial guess based off of start_params or the # estimate thereof. The third value (index = 2) is the actual "first # iteration" assert_equal(expected_iterations, actual_iterations) assert_equal(len(self.res.fit_history['deviance']) - 2, actual_iterations) def test_convergence_rtol_only(self): atol = 0 rtol = 1e-8 self.res = self.model.fit(atol=atol, rtol=rtol) expected_iterations = self._when_converged(atol=atol, rtol=rtol) actual_iterations = self.res.fit_history['iteration'] # Note the first value is the list is np.inf. The second value # is the initial guess based off of start_params or the # estimate thereof. The third value (index = 2) is the actual "first # iteration" assert_equal(expected_iterations, actual_iterations) assert_equal(len(self.res.fit_history['deviance']) - 2, actual_iterations) def test_convergence_atol_rtol(self): atol = 1e-8 rtol = 1e-8 self.res = self.model.fit(atol=atol, rtol=rtol) expected_iterations = self._when_converged(atol=atol, rtol=rtol) actual_iterations = self.res.fit_history['iteration'] # Note the first value is the list is np.inf. The second value # is the initial guess based off of start_params or the # estimate thereof. The third value (index = 2) is the actual "first # iteration" assert_equal(expected_iterations, actual_iterations) assert_equal(len(self.res.fit_history['deviance']) - 2, actual_iterations) def test_convergence_atol_only_params(self): atol = 1e-8 rtol = 0 self.res = self.model.fit(atol=atol, rtol=rtol, tol_criterion='params') expected_iterations = self._when_converged(atol=atol, rtol=rtol, tol_criterion='params') actual_iterations = self.res.fit_history['iteration'] # Note the first value is the list is np.inf. The second value # is the initial guess based off of start_params or the # estimate thereof. The third value (index = 2) is the actual "first # iteration" assert_equal(expected_iterations, actual_iterations) assert_equal(len(self.res.fit_history['deviance']) - 2, actual_iterations) def test_convergence_rtol_only_params(self): atol = 0 rtol = 1e-8 self.res = self.model.fit(atol=atol, rtol=rtol, tol_criterion='params') expected_iterations = self._when_converged(atol=atol, rtol=rtol, tol_criterion='params') actual_iterations = self.res.fit_history['iteration'] # Note the first value is the list is np.inf. The second value # is the initial guess based off of start_params or the # estimate thereof. The third value (index = 2) is the actual "first # iteration" assert_equal(expected_iterations, actual_iterations) assert_equal(len(self.res.fit_history['deviance']) - 2, actual_iterations) def test_convergence_atol_rtol_params(self): atol = 1e-8 rtol = 1e-8 self.res = self.model.fit(atol=atol, rtol=rtol, tol_criterion='params') expected_iterations = self._when_converged(atol=atol, rtol=rtol, tol_criterion='params') actual_iterations = self.res.fit_history['iteration'] # Note the first value is the list is np.inf. The second value # is the initial guess based off of start_params or the # estimate thereof. The third value (index = 2) is the actual "first # iteration" assert_equal(expected_iterations, actual_iterations) assert_equal(len(self.res.fit_history['deviance']) - 2, actual_iterations) def test_poisson_deviance(): # see #3355 missing term in deviance if resid_response.sum() != 0 np.random.seed(123987) nobs, k_vars = 50, 3-1 x = sm.add_constant(np.random.randn(nobs, k_vars)) mu_true = np.exp(x.sum(1)) y = np.random.poisson(mu_true, size=nobs) mod = sm.GLM(y, x[:, :], family=sm.genmod.families.Poisson()) res = mod.fit() d_i = res.resid_deviance d = res.deviance lr = (mod.family.loglike(y, y+1e-20) - mod.family.loglike(y, res.fittedvalues)) * 2 assert_allclose(d, (d_i**2).sum(), rtol=1e-12) assert_allclose(d, lr, rtol=1e-12) # case without constant, resid_response.sum() != 0 mod_nc = sm.GLM(y, x[:, 1:], family=sm.genmod.families.Poisson()) res_nc = mod_nc.fit() d_i = res_nc.resid_deviance d = res_nc.deviance lr = (mod.family.loglike(y, y+1e-20) - mod.family.loglike(y, res_nc.fittedvalues)) * 2 assert_allclose(d, (d_i**2).sum(), rtol=1e-12) assert_allclose(d, lr, rtol=1e-12) def test_non_invertible_hessian_fails_summary(): # Test when the hessian fails the summary is still available. data = cpunish.load_pandas() data.endog[:] = 1 with warnings.catch_warnings(): # we filter DomainWarning, the convergence problems # and warnings in summary warnings.simplefilter("ignore") mod = sm.GLM(data.endog, data.exog, family=sm.families.Gamma()) res = mod.fit(maxiter=1, method='bfgs', max_start_irls=0) res.summary() def test_int_scale(): # GH-6627, make sure it works with int scale data = longley.load(as_pandas=True) mod = GLM(data.endog, data.exog, family=sm.families.Gaussian()) res = mod.fit(scale=1) assert isinstance(res.params, pd.Series) assert res.scale.dtype == np.float64 @pytest.mark.parametrize("dtype", [np.int8, np.int16, np.int32, np.int64]) def test_int_exog(dtype): # GH-6627, make use of floats internally count1, n1, count2, n2 = 60, 51477.5, 30, 54308.7 y = [count1, count2] x = np.asarray([[1, 1], [1, 0]]).astype(dtype) exposure = np.asarray([n1, n2]) mod = GLM(y, x, exposure=exposure, family=sm.families.Poisson()) res = mod.fit(method='bfgs', max_start_irls=0) assert isinstance(res.params, np.ndarray) def test_glm_bic(iris): X = np.c_[np.ones(100), iris[50:, :4]] y = np.array(iris)[50:, 4].astype(np.int32) y -= 1 SET_USE_BIC_LLF(True) model = GLM(y, X, family=sm.families.Binomial()).fit() # 34.9244 is what glm() of R yields assert_almost_equal(model.bic, 34.9244, decimal=3) assert_almost_equal(model.bic_llf, 34.9244, decimal=3) SET_USE_BIC_LLF(False) assert_almost_equal(model.bic, model.bic_deviance, decimal=3) SET_USE_BIC_LLF(None) def test_glm_bic_warning(iris): X = np.c_[np.ones(100), iris[50:, :4]] y = np.array(iris)[50:, 4].astype(np.int32) y -= 1 model = GLM(y, X, family=sm.families.Binomial()).fit() with pytest.warns(FutureWarning, match="The bic"): assert isinstance(model.bic, float) def test_output_exposure_null(reset_randomstate): # GH 6953 x0 = [np.sin(i / 20) + 2 for i in range(1000)] rs = np.random.RandomState(0) # Variable exposures for each observation exposure = rs.randint(100, 200, size=1000) y = [np.sum(rs.poisson(x, size=e)) for x, e in zip(x0, exposure)] x = add_constant(x0) model = GLM( endog=y, exog=x, exposure=exposure, family=sm.families.Poisson() ).fit() null_model = GLM( endog=y, exog=x[:, 0], exposure=exposure, family=sm.families.Poisson() ).fit() null_model_without_exposure = GLM( endog=y, exog=x[:, 0], family=sm.families.Poisson() ).fit() assert_allclose(model.llnull, null_model.llf) # Check that they are different assert np.abs(null_model_without_exposure.llf - model.llnull) > 1 statsmodels-0.12.2/statsmodels/genmod/tests/test_glm_weights.py000066400000000000000000001164111400612667500250500ustar00rootroot00000000000000""" Test for weights in GLM, Poisson and OLS/WLS, continuous test_glm.py Below is a table outlining the test coverage. ================================= ====================== ====== ===================== === ======= ======== ============== ============= ============== ============= ============== ==== ========= Test Compared To params normalized_cov_params bse loglike deviance resid_response resid_pearson resid_deviance resid_working resid_anscombe chi2 optimizer ================================= ====================== ====== ===================== === ======= ======== ============== ============= ============== ============= ============== ==== ========= TestGlmPoissonPlain stata X X X X X X X X X X bfgs TestGlmPoissonFwNr stata X X X X X X X X X X bfgs TestGlmPoissonAwNr stata X X X X X X X X X X bfgs TestGlmPoissonFwHC stata X X X X X TestGlmPoissonAwHC stata X X X X X TestGlmPoissonFwClu stata X X X X X TestGlmTweedieAwNr R X X X X X X X newton TestGlmGammaAwNr R X X special X X X X X bfgs TestGlmGaussianAwNr R X X special X X X X X bfgs TestRepeatedvsAggregated statsmodels.GLM X X bfgs TestRepeatedvsAverage statsmodels.GLM X X bfgs TestTweedieRepeatedvsAggregated statsmodels.GLM X X bfgs TestTweedieRepeatedvsAverage statsmodels.GLM X X bfgs TestBinomial0RepeatedvsAverage statsmodels.GLM X X TestBinomial0RepeatedvsDuplicated statsmodels.GLM X X bfgs TestBinomialVsVarWeights statsmodels.GLM X X X bfgs TestGlmGaussianWLS statsmodels.WLS X X X bfgs ================================= ====================== ====== ===================== === ======= ======== ============== ============= ============== ============= ============== ==== ========= """ # noqa: E501 import warnings import numpy as np from numpy.testing import (assert_raises, assert_allclose) import pandas as pd import pytest import statsmodels.api as sm from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.tools.tools import add_constant from statsmodels.discrete import discrete_model as discrete from statsmodels.tools.sm_exceptions import SpecificationWarning from .results import results_glm_poisson_weights as res_stata from .results import res_R_var_weight as res_r # load data into module namespace from statsmodels.datasets.cpunish import load cpunish_data = load(as_pandas=False) cpunish_data.exog[:, 3] = np.log(cpunish_data.exog[:, 3]) cpunish_data.exog = add_constant(cpunish_data.exog, prepend=False) class CheckWeight(object): def test_basic(self): res1 = self.res1 res2 = self.res2 assert_allclose(res1.params, res2.params, atol=1e-6, rtol=2e-6) corr_fact = getattr(self, 'corr_fact', 1) if hasattr(res2, 'normalized_cov_params'): assert_allclose(res1.normalized_cov_params, res2.normalized_cov_params, atol=1e-8, rtol=2e-6) if isinstance(self, (TestRepeatedvsAggregated, TestRepeatedvsAverage, TestTweedieRepeatedvsAggregated, TestTweedieRepeatedvsAverage, TestBinomial0RepeatedvsAverage, TestBinomial0RepeatedvsDuplicated)): # Loglikelihood, scale, deviance is different between repeated vs. # exposure/average return None assert_allclose(res1.bse, corr_fact * res2.bse, atol=1e-6, rtol=2e-6) if isinstance(self, TestBinomialVsVarWeights): # Binomial ll and deviance are different for 1d vs. counts... return None if isinstance(self, TestGlmGaussianWLS): # This will not work right now either return None if not isinstance(self, (TestGlmGaussianAwNr, TestGlmGammaAwNr)): # Matching R is hard assert_allclose(res1.llf, res2.ll, atol=1e-6, rtol=1e-7) assert_allclose(res1.deviance, res2.deviance, atol=1e-6, rtol=1e-7) def test_residuals(self): if isinstance(self, (TestRepeatedvsAggregated, TestRepeatedvsAverage, TestTweedieRepeatedvsAggregated, TestTweedieRepeatedvsAverage, TestBinomial0RepeatedvsAverage, TestBinomial0RepeatedvsDuplicated)): # This will not match as different number of records return None res1 = self.res1 res2 = self.res2 if not hasattr(res2, 'resids'): return None # use SkipError instead resid_all = dict(zip(res2.resids_colnames, res2.resids.T)) assert_allclose(res1.resid_response, resid_all['resid_response'], atol= 1e-6, rtol=2e-6) assert_allclose(res1.resid_pearson, resid_all['resid_pearson'], atol= 1e-6, rtol=2e-6) assert_allclose(res1.resid_deviance, resid_all['resid_deviance'], atol= 1e-6, rtol=2e-6) assert_allclose(res1.resid_working, resid_all['resid_working'], atol= 1e-6, rtol=2e-6) if resid_all.get('resid_anscombe') is None: return None # Stata does not use var_weights in anscombe residuals, it seems. # Adjust residuals to match our approach. with warnings.catch_warnings(): warnings.simplefilter("ignore", category=FutureWarning) resid_a = res1.resid_anscombe assert_allclose(resid_a, resid_all['resid_anscombe'] * np.sqrt(res1._var_weights), atol= 1e-6, rtol=2e-6) def test_compare_optimizers(self): res1 = self.res1 if isinstance(res1.model.family, sm.families.Tweedie): method = 'newton' optim_hessian = 'eim' else: method = 'bfgs' optim_hessian = 'oim' if isinstance(self, (TestGlmPoissonFwHC, TestGlmPoissonAwHC, TestGlmPoissonFwClu, TestBinomial0RepeatedvsAverage)): return None start_params = res1.params res2 = self.res1.model.fit(start_params=start_params, method=method, optim_hessian=optim_hessian) assert_allclose(res1.params, res2.params, atol=1e-3, rtol=2e-3) H = res2.model.hessian(res2.params, observed=False) res2_bse = np.sqrt(-np.diag(np.linalg.inv(H))) assert_allclose(res1.bse, res2_bse, atol=1e-3, rtol=1e-3) def test_pearson_chi2(self): if hasattr(self.res2, 'chi2'): assert_allclose(self.res1.pearson_chi2, self.res2.deviance_p, atol=1e-6, rtol=1e-6) class TestGlmPoissonPlain(CheckWeight): @classmethod def setup_class(cls): cls.res1 = GLM(cpunish_data.endog, cpunish_data.exog, family=sm.families.Poisson()).fit() # compare with discrete, start close to save time modd = discrete.Poisson(cpunish_data.endog, cpunish_data.exog) cls.res2 = res_stata.results_poisson_none_nonrobust class TestGlmPoissonFwNr(CheckWeight): @classmethod def setup_class(cls): fweights = [1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 3, 3] fweights = np.array(fweights) cls.res1 = GLM(cpunish_data.endog, cpunish_data.exog, family=sm.families.Poisson(), freq_weights=fweights).fit() # compare with discrete, start close to save time modd = discrete.Poisson(cpunish_data.endog, cpunish_data.exog) cls.res2 = res_stata.results_poisson_fweight_nonrobust class TestGlmPoissonAwNr(CheckWeight): @classmethod def setup_class(cls): fweights = [1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 3, 3] # faking aweights by using normalized freq_weights fweights = np.array(fweights) wsum = fweights.sum() nobs = len(cpunish_data.endog) aweights = fweights / wsum * nobs cls.res1 = GLM(cpunish_data.endog, cpunish_data.exog, family=sm.families.Poisson(), var_weights=aweights).fit() # compare with discrete, start close to save time modd = discrete.Poisson(cpunish_data.endog, cpunish_data.exog) # Need to copy to avoid inplace adjustment from copy import copy cls.res2 = copy(res_stata.results_poisson_aweight_nonrobust) cls.res2.resids = cls.res2.resids.copy() # Need to adjust resids for pearson and deviance to add weights cls.res2.resids[:, 3:5] *= np.sqrt(aweights[:, np.newaxis]) # prob_weights fail with HC, not properly implemented yet class TestGlmPoissonPwNr(CheckWeight): @classmethod def setup_class(cls): fweights = [1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 3, 3] # faking aweights by using normalized freq_weights fweights = np.array(fweights) wsum = fweights.sum() nobs = len(cpunish_data.endog) aweights = fweights / wsum * nobs cls.res1 = GLM(cpunish_data.endog, cpunish_data.exog, family=sm.families.Poisson(), freq_weights=fweights).fit(cov_type='HC1') # compare with discrete, start close to save time #modd = discrete.Poisson(cpunish_data.endog, cpunish_data.exog) cls.res2 = res_stata.results_poisson_pweight_nonrobust # TODO: find more informative reasons why these fail @pytest.mark.xfail(reason='Known to fail', strict=True) def test_basic(self): super(TestGlmPoissonPwNr, self).test_basic() @pytest.mark.xfail(reason='Known to fail', strict=True) def test_compare_optimizers(self): super(TestGlmPoissonPwNr, self).test_compare_optimizers() class TestGlmPoissonFwHC(CheckWeight): @classmethod def setup_class(cls): fweights = [1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 3, 3] # faking aweights by using normalized freq_weights fweights = np.array(fweights) wsum = fweights.sum() nobs = len(cpunish_data.endog) aweights = fweights / wsum * nobs cls.corr_fact = np.sqrt((wsum - 1.) / wsum) mod = GLM(cpunish_data.endog, cpunish_data.exog, family=sm.families.Poisson(), freq_weights=fweights) cls.res1 = mod.fit(cov_type='HC0') #, cov_kwds={'use_correction':False}) # compare with discrete, start close to save time #modd = discrete.Poisson(cpunish_data.endog, cpunish_data.exog) cls.res2 = res_stata.results_poisson_fweight_hc1 # var_weights (aweights fail with HC, not properly implemented yet class TestGlmPoissonAwHC(CheckWeight): @classmethod def setup_class(cls): fweights = [1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 3, 3] # faking aweights by using normalized freq_weights fweights = np.array(fweights) wsum = fweights.sum() nobs = len(cpunish_data.endog) aweights = fweights / wsum * nobs # This is really close when corr_fact = (wsum - 1.) / wsum, but to # avoid having loosen precision of the assert_allclose, I'm doing this # manually. Its *possible* lowering the IRLS convergence criterion # in stata and here will make this less sketchy. cls.corr_fact = np.sqrt((wsum - 1.) / wsum) * 0.98518473599905609 mod = GLM(cpunish_data.endog, cpunish_data.exog, family=sm.families.Poisson(), var_weights=aweights) cls.res1 = mod.fit(cov_type='HC0') #, cov_kwds={'use_correction':False}) # compare with discrete, start close to save time # modd = discrete.Poisson(cpunish_data.endog, cpunish_data.exog) cls.res2 = res_stata.results_poisson_aweight_hc1 class TestGlmPoissonFwClu(CheckWeight): @classmethod def setup_class(cls): fweights = [1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 3, 3] # faking aweights by using normalized freq_weights fweights = np.array(fweights) wsum = fweights.sum() nobs = len(cpunish_data.endog) aweights = fweights / wsum * nobs gid = np.arange(1, 17 + 1) // 2 n_groups = len(np.unique(gid)) # no wnobs yet in sandwich covariance calcualtion cls.corr_fact = 1 / np.sqrt(n_groups / (n_groups - 1)) #np.sqrt((wsum - 1.) / wsum) cov_kwds = {'groups': gid, 'use_correction':False} with pytest.warns(None): mod = GLM(cpunish_data.endog, cpunish_data.exog, family=sm.families.Poisson(), freq_weights=fweights) cls.res1 = mod.fit(cov_type='cluster', cov_kwds=cov_kwds) # compare with discrete, start close to save time #modd = discrete.Poisson(cpunish_data.endog, cpunish_data.exog) cls.res2 = res_stata.results_poisson_fweight_clu1 class TestGlmTweedieAwNr(CheckWeight): @classmethod def setup_class(cls): import statsmodels.formula.api as smf data = sm.datasets.fair.load_pandas() endog = data.endog data = data.exog data['fair'] = endog aweights = np.repeat(1, len(data.index)) aweights[::5] = 5 aweights[::13] = 3 model = smf.glm( 'fair ~ age + yrs_married', data=data, family=sm.families.Tweedie( var_power=1.55, link=sm.families.links.log() ), var_weights=aweights ) cls.res1 = model.fit(rtol=1e-25, atol=0) cls.res2 = res_r.results_tweedie_aweights_nonrobust class TestGlmGammaAwNr(CheckWeight): @classmethod def setup_class(cls): from .results.results_glm import CancerLog res2 = CancerLog() endog = res2.endog exog = res2.exog[:, :-1] exog = sm.add_constant(exog, prepend=True) aweights = np.repeat(1, len(endog)) aweights[::5] = 5 aweights[::13] = 3 model = sm.GLM(endog, exog, family=sm.families.Gamma(link=sm.families.links.log()), var_weights=aweights) cls.res1 = model.fit(rtol=1e-25, atol=0) cls.res2 = res_r.results_gamma_aweights_nonrobust def test_r_llf(self): scale = self.res1.deviance / self.res1._iweights.sum() ll = self.res1.family.loglike(self.res1.model.endog, self.res1.mu, freq_weights=self.res1._var_weights, scale=scale) assert_allclose(ll, self.res2.ll, atol=1e-6, rtol=1e-7) class TestGlmGaussianAwNr(CheckWeight): @classmethod def setup_class(cls): import statsmodels.formula.api as smf data = sm.datasets.cpunish.load_pandas() endog = data.endog data = data.exog data['EXECUTIONS'] = endog data['INCOME'] /= 1000 aweights = np.array([1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) model = smf.glm( 'EXECUTIONS ~ INCOME + SOUTH - 1', data=data, family=sm.families.Gaussian(link=sm.families.links.log()), var_weights=aweights ) cls.res1 = model.fit(rtol=1e-25, atol=0) cls.res2 = res_r.results_gaussian_aweights_nonrobust def test_r_llf(self): res1 = self.res1 res2 = self.res2 model = self.res1.model # Need to make a few adjustments... # First, calculate scale using nobs as denominator scale = res1.scale * model.df_resid / model.wnobs # Calculate llf using adj scale and wts = freq_weights wts = model.freq_weights llf = model.family.loglike(model.endog, res1.mu, freq_weights=wts, scale=scale) # SM uses (essentially) stat's loglike formula... first term is # (endog - mu) ** 2 / scale adj_sm = -1 / 2 * ((model.endog - res1.mu) ** 2).sum() / scale # R has these 2 terms that stata/sm do not adj_r = -model.wnobs / 2 + np.sum(np.log(model.var_weights)) / 2 llf_adj = llf - adj_sm + adj_r assert_allclose(llf_adj, res2.ll, atol=1e-6, rtol=1e-7) def gen_endog(lin_pred, family_class, link, binom_version=0): np.random.seed(872) fam = sm.families mu = link().inverse(lin_pred) if family_class == fam.Binomial: if binom_version == 0: endog = 1*(np.random.uniform(size=len(lin_pred)) < mu) else: endog = np.empty((len(lin_pred), 2)) n = 10 endog[:, 0] = (np.random.uniform(size=(len(lin_pred), n)) < mu[:, None]).sum(1) endog[:, 1] = n - endog[:, 0] elif family_class == fam.Poisson: endog = np.random.poisson(mu) elif family_class == fam.Gamma: endog = np.random.gamma(2, mu) elif family_class == fam.Gaussian: endog = mu + np.random.normal(size=len(lin_pred)) elif family_class == fam.NegativeBinomial: from scipy.stats.distributions import nbinom endog = nbinom.rvs(mu, 0.5) elif family_class == fam.InverseGaussian: from scipy.stats.distributions import invgauss endog = invgauss.rvs(mu) elif family_class == fam.Tweedie: rate = 1 shape = 1.0 scale = mu / (rate * shape) endog = (np.random.poisson(rate, size=scale.shape[0]) * np.random.gamma(shape * scale)) else: raise ValueError return endog def test_wtd_gradient_irls(): # Compare the results when using gradient optimization and IRLS. # TODO: Find working examples for inverse_squared link np.random.seed(87342) fam = sm.families lnk = sm.families.links families = [(fam.Binomial, [lnk.logit, lnk.probit, lnk.cloglog, lnk.log, lnk.cauchy]), (fam.Poisson, [lnk.log, lnk.identity, lnk.sqrt]), (fam.Gamma, [lnk.log, lnk.identity, lnk.inverse_power]), (fam.Gaussian, [lnk.identity, lnk.log, lnk.inverse_power]), (fam.InverseGaussian, [lnk.log, lnk.identity, lnk.inverse_power, lnk.inverse_squared]), (fam.NegativeBinomial, [lnk.log, lnk.inverse_power, lnk.inverse_squared, lnk.identity])] n = 100 p = 3 exog = np.random.normal(size=(n, p)) exog[:, 0] = 1 skip_one = False for family_class, family_links in families: for link in family_links: for binom_version in 0, 1: method = 'bfgs' if family_class != fam.Binomial and binom_version == 1: continue elif family_class == fam.Binomial and link == lnk.cloglog: # Cannot get gradient to converage with var_weights here continue elif family_class == fam.Binomial and link == lnk.log: # Cannot get gradient to converage with var_weights here continue elif (family_class, link) == (fam.Poisson, lnk.identity): lin_pred = 20 + exog.sum(1) elif (family_class, link) == (fam.Binomial, lnk.log): lin_pred = -1 + exog.sum(1) / 8 elif (family_class, link) == (fam.Poisson, lnk.sqrt): lin_pred = -2 + exog.sum(1) elif (family_class, link) == (fam.Gamma, lnk.log): # Cannot get gradient to converge with var_weights here continue elif (family_class, link) == (fam.Gamma, lnk.identity): # Cannot get gradient to converage with var_weights here continue elif (family_class, link) == (fam.Gamma, lnk.inverse_power): # Cannot get gradient to converage with var_weights here continue elif (family_class, link) == (fam.Gaussian, lnk.log): # Cannot get gradient to converage with var_weights here continue elif (family_class, link) == (fam.Gaussian, lnk.inverse_power): # Cannot get gradient to converage with var_weights here continue elif (family_class, link) == (fam.InverseGaussian, lnk.log): # Cannot get gradient to converage with var_weights here lin_pred = -1 + exog.sum(1) continue elif (family_class, link) == (fam.InverseGaussian, lnk.identity): # Cannot get gradient to converage with var_weights here lin_pred = 20 + 5*exog.sum(1) lin_pred = np.clip(lin_pred, 1e-4, np.inf) continue elif (family_class, link) == (fam.InverseGaussian, lnk.inverse_squared): lin_pred = 0.5 + exog.sum(1) / 5 continue # skip due to non-convergence elif (family_class, link) == (fam.InverseGaussian, lnk.inverse_power): lin_pred = 1 + exog.sum(1) / 5 method = 'newton' elif (family_class, link) == (fam.NegativeBinomial, lnk.identity): lin_pred = 20 + 5*exog.sum(1) lin_pred = np.clip(lin_pred, 1e-3, np.inf) method = 'newton' elif (family_class, link) == (fam.NegativeBinomial, lnk.inverse_squared): lin_pred = 0.1 + np.random.uniform(size=exog.shape[0]) continue # skip due to non-convergence elif (family_class, link) == (fam.NegativeBinomial, lnk.inverse_power): # Cannot get gradient to converage with var_weights here lin_pred = 1 + exog.sum(1) / 5 continue elif (family_class, link) == (fam.Gaussian, lnk.inverse_power): # adding skip because of convergence failure skip_one = True else: lin_pred = np.random.uniform(size=exog.shape[0]) endog = gen_endog(lin_pred, family_class, link, binom_version) if binom_version == 0: wts = np.ones_like(endog) tmp = np.random.randint( 2, 5, size=(endog > endog.mean()).sum() ) wts[endog > endog.mean()] = tmp else: wts = np.ones(shape=endog.shape[0]) y = endog[:, 0] / endog.sum(axis=1) tmp = np.random.gamma(2, size=(y > y.mean()).sum()) wts[y > y.mean()] = tmp with warnings.catch_warnings(): warnings.simplefilter("ignore") mod_irls = sm.GLM(endog, exog, var_weights=wts, family=family_class(link=link())) rslt_irls = mod_irls.fit(method="IRLS", atol=1e-10, tol_criterion='params') # Try with and without starting values. for max_start_irls, start_params in ((0, rslt_irls.params), (3, None)): # TODO: skip convergence failures for now if max_start_irls > 0 and skip_one: continue with warnings.catch_warnings(): warnings.simplefilter("ignore") mod_gradient = sm.GLM(endog, exog, var_weights=wts, family=family_class(link=link())) rslt_gradient = mod_gradient.fit( max_start_irls=max_start_irls, start_params=start_params, method=method ) assert_allclose(rslt_gradient.params, rslt_irls.params, rtol=1e-6, atol=5e-5) assert_allclose(rslt_gradient.llf, rslt_irls.llf, rtol=1e-6, atol=1e-6) assert_allclose(rslt_gradient.scale, rslt_irls.scale, rtol=1e-6, atol=1e-6) # Get the standard errors using expected information. gradient_bse = rslt_gradient.bse ehess = mod_gradient.hessian(rslt_gradient.params, observed=False) gradient_bse = np.sqrt(-np.diag(np.linalg.inv(ehess))) assert_allclose(gradient_bse, rslt_irls.bse, rtol=1e-6, atol=5e-5) def get_dummies(x): values = np.sort(np.unique(x)) out = np.zeros(shape=(x.shape[0], len(values) - 1)) for i, v in enumerate(values): if i == 0: continue out[:, i - 1] = np.where(v == x, 1, 0) return out class TestRepeatedvsAggregated(CheckWeight): @classmethod def setup_class(cls): np.random.seed(4321) n = 100 p = 5 exog = np.empty((n, p)) exog[:, 0] = 1 exog[:, 1] = np.random.randint(low=-5, high=5, size=n) x = np.repeat(np.array([1, 2, 3, 4]), n / 4) exog[:, 2:] = get_dummies(x) beta = np.array([-1, 0.1, -0.05, .2, 0.35]) lin_pred = (exog * beta).sum(axis=1) family = sm.families.Poisson link = sm.families.links.log endog = gen_endog(lin_pred, family, link) mod1 = sm.GLM(endog, exog, family=family(link=link())) cls.res1 = mod1.fit() agg = pd.DataFrame(exog) agg['endog'] = endog agg_endog = agg.groupby([0, 1, 2, 3, 4]).sum()[['endog']] agg_wt = agg.groupby([0, 1, 2, 3, 4]).count()[['endog']] agg_exog = np.array(agg_endog.index.tolist()) agg_wt = agg_wt['endog'] agg_endog = agg_endog['endog'] mod2 = sm.GLM(agg_endog, agg_exog, family=family(link=link()), exposure=agg_wt) cls.res2 = mod2.fit() class TestRepeatedvsAverage(CheckWeight): @classmethod def setup_class(cls): np.random.seed(4321) n = 10000 p = 5 exog = np.empty((n, p)) exog[:, 0] = 1 exog[:, 1] = np.random.randint(low=-5, high=5, size=n) x = np.repeat(np.array([1, 2, 3, 4]), n / 4) exog[:, 2:] = get_dummies(x) beta = np.array([-1, 0.1, -0.05, .2, 0.35]) lin_pred = (exog * beta).sum(axis=1) family = sm.families.Poisson link = sm.families.links.log endog = gen_endog(lin_pred, family, link) mod1 = sm.GLM(endog, exog, family=family(link=link())) cls.res1 = mod1.fit() agg = pd.DataFrame(exog) agg['endog'] = endog agg_endog = agg.groupby([0, 1, 2, 3, 4]).sum()[['endog']] agg_wt = agg.groupby([0, 1, 2, 3, 4]).count()[['endog']] agg_exog = np.array(agg_endog.index.tolist()) agg_wt = agg_wt['endog'] avg_endog = agg_endog['endog'] / agg_wt mod2 = sm.GLM(avg_endog, agg_exog, family=family(link=link()), var_weights=agg_wt) cls.res2 = mod2.fit() class TestTweedieRepeatedvsAggregated(CheckWeight): @classmethod def setup_class(cls): np.random.seed(4321) n = 10000 p = 5 exog = np.empty((n, p)) exog[:, 0] = 1 exog[:, 1] = np.random.randint(low=-5, high=5, size=n) x = np.repeat(np.array([1, 2, 3, 4]), n / 4) exog[:, 2:] = get_dummies(x) beta = np.array([7, 0.1, -0.05, .2, 0.35]) lin_pred = (exog * beta).sum(axis=1) family = sm.families.Tweedie link = sm.families.links.log endog = gen_endog(lin_pred, family, link) mod1 = sm.GLM(endog, exog, family=family(link=link(), var_power=1.5)) cls.res1 = mod1.fit(rtol=1e-20, atol=0, tol_criterion='params') agg = pd.DataFrame(exog) agg['endog'] = endog agg_endog = agg.groupby([0, 1, 2, 3, 4]).sum()[['endog']] agg_wt = agg.groupby([0, 1, 2, 3, 4]).count()[['endog']] agg_exog = np.array(agg_endog.index.tolist()) agg_wt = agg_wt['endog'] agg_endog = agg_endog['endog'] mod2 = sm.GLM(agg_endog, agg_exog, family=family(link=link(), var_power=1.5), exposure=agg_wt, var_weights=agg_wt ** 0.5) cls.res2 = mod2.fit(rtol=1e-20, atol=0, tol_criterion='params') class TestTweedieRepeatedvsAverage(CheckWeight): @classmethod def setup_class(cls): np.random.seed(4321) n = 1000 p = 5 exog = np.empty((n, p)) exog[:, 0] = 1 exog[:, 1] = np.random.randint(low=-5, high=5, size=n) x = np.repeat(np.array([1, 2, 3, 4]), n / 4) exog[:, 2:] = get_dummies(x) beta = np.array([7, 0.1, -0.05, .2, 0.35]) lin_pred = (exog * beta).sum(axis=1) family = sm.families.Tweedie link = sm.families.links.log endog = gen_endog(lin_pred, family, link) mod1 = sm.GLM(endog, exog, family=family(link=link(), var_power=1.5)) cls.res1 = mod1.fit(rtol=1e-10, atol=0, tol_criterion='params', scaletype='x2') agg = pd.DataFrame(exog) agg['endog'] = endog agg_endog = agg.groupby([0, 1, 2, 3, 4]).sum()[['endog']] agg_wt = agg.groupby([0, 1, 2, 3, 4]).count()[['endog']] agg_exog = np.array(agg_endog.index.tolist()) agg_wt = agg_wt['endog'] avg_endog = agg_endog['endog'] / agg_wt mod2 = sm.GLM(avg_endog, agg_exog, family=family(link=link(), var_power=1.5), var_weights=agg_wt) cls.res2 = mod2.fit(rtol=1e-10, atol=0, tol_criterion='params') class TestBinomial0RepeatedvsAverage(CheckWeight): @classmethod def setup_class(cls): np.random.seed(4321) n = 20 p = 5 exog = np.empty((n, p)) exog[:, 0] = 1 exog[:, 1] = np.random.randint(low=-5, high=5, size=n) x = np.repeat(np.array([1, 2, 3, 4]), n / 4) exog[:, 2:] = get_dummies(x) beta = np.array([-1, 0.1, -0.05, .2, 0.35]) lin_pred = (exog * beta).sum(axis=1) family = sm.families.Binomial link = sm.families.links.logit endog = gen_endog(lin_pred, family, link, binom_version=0) mod1 = sm.GLM(endog, exog, family=family(link=link())) cls.res1 = mod1.fit(rtol=1e-10, atol=0, tol_criterion='params', scaletype='x2') agg = pd.DataFrame(exog) agg['endog'] = endog agg_endog = agg.groupby([0, 1, 2, 3, 4]).sum()[['endog']] agg_wt = agg.groupby([0, 1, 2, 3, 4]).count()[['endog']] agg_exog = np.array(agg_endog.index.tolist()) agg_wt = agg_wt['endog'] avg_endog = agg_endog['endog'] / agg_wt mod2 = sm.GLM(avg_endog, agg_exog, family=family(link=link()), var_weights=agg_wt) cls.res2 = mod2.fit(rtol=1e-10, atol=0, tol_criterion='params') class TestBinomial0RepeatedvsDuplicated(CheckWeight): @classmethod def setup_class(cls): np.random.seed(4321) n = 10000 p = 5 exog = np.empty((n, p)) exog[:, 0] = 1 exog[:, 1] = np.random.randint(low=-5, high=5, size=n) x = np.repeat(np.array([1, 2, 3, 4]), n / 4) exog[:, 2:] = get_dummies(x) beta = np.array([-1, 0.1, -0.05, .2, 0.35]) lin_pred = (exog * beta).sum(axis=1) family = sm.families.Binomial link = sm.families.links.logit endog = gen_endog(lin_pred, family, link, binom_version=0) wt = np.random.randint(1, 5, n) mod1 = sm.GLM(endog, exog, family=family(link=link()), freq_weights=wt) cls.res1 = mod1.fit() exog_dup = np.repeat(exog, wt, axis=0) endog_dup = np.repeat(endog, wt) mod2 = sm.GLM(endog_dup, exog_dup, family=family(link=link())) cls.res2 = mod2.fit() def test_warnings_raised(): weights = [1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 3, 3] # faking aweights by using normalized freq_weights weights = np.array(weights) gid = np.arange(1, 17 + 1) // 2 cov_kwds = {'groups': gid, 'use_correction': False} with pytest.warns(SpecificationWarning): res1 = GLM(cpunish_data.endog, cpunish_data.exog, family=sm.families.Poisson(), freq_weights=weights ).fit(cov_type='cluster', cov_kwds=cov_kwds) res1.summary() with pytest.warns(SpecificationWarning): res1 = GLM(cpunish_data.endog, cpunish_data.exog, family=sm.families.Poisson(), var_weights=weights ).fit(cov_type='cluster', cov_kwds=cov_kwds) res1.summary() weights = [1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 3, 3] @pytest.mark.parametrize('formatted', [weights, np.asarray(weights), pd.Series(weights)], ids=['list', 'ndarray', 'Series']) def test_weights_different_formats(formatted): check_weights_as_formats(formatted) def check_weights_as_formats(weights): res = GLM(cpunish_data.endog, cpunish_data.exog, family=sm.families.Poisson(), freq_weights=weights ).fit() assert isinstance(res._freq_weights, np.ndarray) assert isinstance(res._var_weights, np.ndarray) assert isinstance(res._iweights, np.ndarray) res = GLM(cpunish_data.endog, cpunish_data.exog, family=sm.families.Poisson(), var_weights=weights ).fit() assert isinstance(res._freq_weights, np.ndarray) assert isinstance(res._var_weights, np.ndarray) assert isinstance(res._iweights, np.ndarray) class TestBinomialVsVarWeights(CheckWeight): @classmethod def setup_class(cls): from statsmodels.datasets.star98 import load data = load(as_pandas=False) data.exog /= data.exog.std(0) data.exog = add_constant(data.exog, prepend=False) cls.res1 = GLM(data.endog, data.exog, family=sm.families.Binomial()).fit() weights = data.endog.sum(axis=1) endog2 = data.endog[:, 0] / weights cls.res2 = GLM(endog2, data.exog, family=sm.families.Binomial(), var_weights=weights).fit() class TestGlmGaussianWLS(CheckWeight): @classmethod def setup_class(cls): import statsmodels.formula.api as smf data = sm.datasets.cpunish.load_pandas() endog = data.endog data = data.exog data['EXECUTIONS'] = endog data['INCOME'] /= 1000 aweights = np.array([1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) model = smf.glm( 'EXECUTIONS ~ INCOME + SOUTH - 1', data=data, family=sm.families.Gaussian(link=sm.families.links.identity()), var_weights=aweights ) wlsmodel = smf.wls( 'EXECUTIONS ~ INCOME + SOUTH - 1', data=data, weights=aweights) cls.res1 = model.fit(rtol=1e-25, atol=1e-25) cls.res2 = wlsmodel.fit() def test_incompatible_input(): weights = [1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 3, 3] exog = cpunish_data.exog endog = cpunish_data.endog family = sm.families.Poisson() # Too short assert_raises(ValueError, GLM, endog, exog, family=family, freq_weights=weights[:-1]) assert_raises(ValueError, GLM, endog, exog, family=family, var_weights=weights[:-1]) # Too long assert_raises(ValueError, GLM, endog, exog, family=family, freq_weights=weights + [3]) assert_raises(ValueError, GLM, endog, exog, family=family, var_weights=weights + [3]) # Too many dimensions assert_raises(ValueError, GLM, endog, exog, family=family, freq_weights=[weights, weights]) assert_raises(ValueError, GLM, endog, exog, family=family, var_weights=[weights, weights]) def test_poisson_residuals(): nobs, k_exog = 100, 5 np.random.seed(987125) x = np.random.randn(nobs, k_exog - 1) x = add_constant(x) y_true = x.sum(1) / 2 y = y_true + 2 * np.random.randn(nobs) exposure = 1 + np.arange(nobs) // 4 yp = np.random.poisson(np.exp(y_true) * exposure) yp[10:15] += 10 fam = sm.families.Poisson() mod_poi_e = GLM(yp, x, family=fam, exposure=exposure) res_poi_e = mod_poi_e.fit() mod_poi_w = GLM(yp / exposure, x, family=fam, var_weights=exposure) res_poi_w = mod_poi_w.fit() assert_allclose(res_poi_e.resid_response / exposure, res_poi_w.resid_response) assert_allclose(res_poi_e.resid_pearson, res_poi_w.resid_pearson) assert_allclose(res_poi_e.resid_deviance, res_poi_w.resid_deviance) with warnings.catch_warnings(): warnings.simplefilter("ignore", category=FutureWarning) assert_allclose(res_poi_e.resid_anscombe, res_poi_w.resid_anscombe) assert_allclose(res_poi_e.resid_anscombe_unscaled, res_poi_w.resid_anscombe) statsmodels-0.12.2/statsmodels/genmod/tests/test_qif.py000066400000000000000000000075101400612667500233150ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_allclose import pandas as pd import pytest from statsmodels.genmod.qif import (QIF, QIFIndependence, QIFExchangeable, QIFAutoregressive) from statsmodels.tools.numdiff import approx_fprime from statsmodels.genmod import families @pytest.mark.parametrize("fam", [families.Gaussian(), families.Poisson(), families.Binomial()]) @pytest.mark.parametrize("cov_struct", [QIFIndependence(), QIFExchangeable(), QIFAutoregressive()]) def test_qif_numdiff(fam, cov_struct): # Test the analytic scores against numeric derivatives np.random.seed(234234) n = 200 q = 4 x = np.random.normal(size=(n, 3)) if isinstance(fam, families.Gaussian): e = np.kron(np.random.normal(size=n//q), np.ones(q)) e = np.sqrt(0.5)*e + np.sqrt(1 - 0.5**2)*np.random.normal(size=n) y = x.sum(1) + e elif isinstance(fam, families.Poisson): y = np.random.poisson(5, size=n) elif isinstance(fam, families.Binomial): y = np.random.randint(0, 2, size=n) g = np.kron(np.arange(n//q), np.ones(q)).astype(int) model = QIF(y, x, groups=g, family=fam, cov_struct=cov_struct) for _ in range(5): pt = np.random.normal(size=3) # Check the Jacobian of the vector of estimating equations. _, grad, _, _, gn_deriv = model.objective(pt) def llf_gn(params): return model.objective(params)[3] gn_numdiff = approx_fprime(pt, llf_gn, 1e-7) assert_allclose(gn_deriv, gn_numdiff, 1e-4) # Check the gradient of the QIF def llf(params): return model.objective(params)[0] grad_numdiff = approx_fprime(pt, llf, 1e-7) assert_allclose(grad, grad_numdiff, 1e-4) @pytest.mark.parametrize("fam", [families.Gaussian(), families.Poisson(), families.Binomial()]) @pytest.mark.parametrize("cov_struct", [QIFIndependence(), QIFExchangeable(), QIFAutoregressive()]) def test_qif_fit(fam, cov_struct): np.random.seed(234234) n = 1000 q = 4 params = np.r_[1, -0.5, 0.2] x = np.random.normal(size=(n, len(params))) if isinstance(fam, families.Gaussian): e = np.kron(np.random.normal(size=n//q), np.ones(q)) e = np.sqrt(0.5)*e + np.sqrt(1 - 0.5**2)*np.random.normal(size=n) y = np.dot(x, params) + e elif isinstance(fam, families.Poisson): lpr = np.dot(x, params) mean = np.exp(lpr) y = np.random.poisson(mean) elif isinstance(fam, families.Binomial): lpr = np.dot(x, params) mean = 1 / (1 + np.exp(-lpr)) y = (np.random.uniform(0, 1, size=n) < mean).astype(int) g = np.kron(np.arange(n // q), np.ones(q)).astype(int) model = QIF(y, x, groups=g, family=fam, cov_struct=cov_struct) rslt = model.fit() # Slack comparison to population values assert_allclose(rslt.params, params, atol=0.05, rtol=0.05) # Smoke test _ = rslt.summary() @pytest.mark.parametrize("cov_struct", [QIFIndependence(), QIFExchangeable(), QIFAutoregressive()]) def test_formula(cov_struct): np.random.seed(3423) y = np.random.normal(size=100) x = np.random.normal(size=(100, 2)) groups = np.kron(np.arange(25), np.ones(4)) model1 = QIF(y, x, groups=groups, cov_struct=cov_struct) result1 = model1.fit() df = pd.DataFrame({"y": y, "x1": x[:, 0], "x2": x[:, 1], "groups": groups}) model2 = QIF.from_formula("y ~ 0 + x1 + x2", groups="groups", cov_struct=cov_struct, data=df) result2 = model2.fit() assert_allclose(result1.params, result2.params) assert_allclose(result1.bse, result2.bse) if not isinstance(cov_struct, QIFIndependence): _ = result2.bic _ = result2.aic statsmodels-0.12.2/statsmodels/genmod/tests/test_score_test.py000066400000000000000000000175431400612667500247170ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Thu May 31 15:39:15 2018 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_allclose from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod import families from statsmodels.discrete.discrete_model import Poisson import statsmodels.stats._diagnostic_other as diao from statsmodels.base._parameter_inference import score_test class TestScoreTest(object): # compares score to wald, and regression test for pvalues rtol_ws = 5e-3 atol_ws = 0 rtol_wooldridge = 0.004 dispersed = False # Poisson correctly specified # regression numbers res_pvalue = [0.31786373532550893, 0.32654081685271297] skip_wooldridge = False res_disptest = np.array([[ 0.13927919, 0.44461477], [ 0.13927919, 0.44461477], [ 0.21295545, 0.41568086], [ 0.14935018, 0.88127732], [ 0.14935018, 0.88127732], [ 0.14841761, 0.8820132 ], [ 0.22836064, 0.81936588]]) res_disptest_g = [0.052247629593715761, 0.81919738867722225] @classmethod def setup_class(cls): nobs, k_vars = 500, 5 np.random.seed(786452) x = np.random.randn(nobs, k_vars) x[:, 0] = 1 x2 = np.random.randn(nobs, 2) xx = np.column_stack((x, x2)) if cls.dispersed: het = np.random.randn(nobs) y = np.random.poisson(np.exp(x.sum(1) * 0.5 + het)) #y_mc = np.random.negative_binomial(np.exp(x.sum(1) * 0.5), 2) else: y = np.random.poisson(np.exp(x.sum(1) * 0.5)) cls.exog_extra = x2 cls.model_full = GLM(y, xx, family=families.Poisson()) cls.model_drop = GLM(y, x, family=families.Poisson()) def test_wald_score(self): mod_full = self.model_full mod_drop = self.model_drop restriction = 'x5=0, x6=0' res_full = mod_full.fit() res_constr = mod_full.fit_constrained('x5=0, x6=0') res_drop = mod_drop.fit() wald = res_full.wald_test(restriction) lm_constr = np.hstack(score_test(res_constr)) lm_extra = np.hstack(score_test(res_drop, exog_extra=self.exog_extra)) res_wald = np.hstack([wald.statistic.squeeze(), wald.pvalue, [wald.df_denom]]) assert_allclose(lm_constr, res_wald, rtol=self.rtol_ws, atol=self.atol_ws) assert_allclose(lm_extra, res_wald, rtol=self.rtol_ws, atol=self.atol_ws) assert_allclose(lm_constr, lm_extra, rtol=1e-12, atol=1e-14) # regression number assert_allclose(lm_constr[1], self.res_pvalue[0], rtol=1e-12, atol=1e-14) cov_type='HC0' res_full_hc = mod_full.fit(cov_type=cov_type, start_params=res_full.params) wald = res_full_hc.wald_test(restriction) lm_constr = np.hstack(score_test(res_constr, cov_type=cov_type)) lm_extra = np.hstack(score_test(res_drop, exog_extra=self.exog_extra, cov_type=cov_type)) res_wald = np.hstack([wald.statistic.squeeze(), wald.pvalue, [wald.df_denom]]) assert_allclose(lm_constr, res_wald, rtol=self.rtol_ws, atol=self.atol_ws) assert_allclose(lm_extra, res_wald, rtol=self.rtol_ws, atol=self.atol_ws) assert_allclose(lm_constr, lm_extra, rtol=1e-13) # regression number assert_allclose(lm_constr[1], self.res_pvalue[1], rtol=1e-12, atol=1e-14) if not self.skip_wooldridge: # compare with Wooldridge auxiliary regression # does not work for Poisson, even with family attribute # diao.lm_test_glm assumes fittedvalues is mean (not linear pred) lm_wooldridge = diao.lm_test_glm(res_drop, self.exog_extra) assert_allclose(lm_wooldridge.pval1, self.res_pvalue[0], rtol=1e-12, atol=1e-14) assert_allclose(lm_wooldridge.pval3, self.res_pvalue[1], rtol=self.rtol_wooldridge) # smoke test lm_wooldridge.summary() def test_dispersion(self): res_drop = self.model_drop.fit() res_test = diao.dispersion_poisson(res_drop) assert_allclose(res_test[0], self.res_disptest, rtol=1e-6, atol=1e-14) # constant only dispersion ex = np.ones((res_drop.model.endog.shape[0], 1)) # ex = np.column_stack((np.ones(res_drop.model.endog.shape[0]), # res_drop.predict())) # or **2 # dispersion_poisson_generic might not be correct # or not clear what the alternative hypothesis is # choosing different `ex` implies different alternative hypotheses res_test = diao.dispersion_poisson_generic(res_drop, ex) assert_allclose(res_test, self.res_disptest_g, rtol=1e-6, atol=1e-14) class TestScoreTestDispersed(TestScoreTest): rtol_ws = 0.11 atol_ws = 0.015 rtol_wooldridge = 0.03 dispersed = True # Poisson is mis-specified res_pvalue = [5.412978775609189e-14, 0.05027602575743518] res_disptest = np.array([[ 1.26473634e+02, 0.00000000e+00], [ 1.26473634e+02, 0.00000000e+00], [ 1.19393621e+02, 0.00000000e+00], [ 4.53940519e+00, 5.64131397e-06], [ 4.53940519e+00, 5.64131397e-06], [ 2.98154154e+00, 2.86801135e-03], [ 4.27569194e+00, 1.90544551e-05]]) res_disptest_g = [17.670784788586968, 2.6262956791721383e-05] class TestScoreTestPoisson(TestScoreTest): # compares score to wald, and regression test for pvalues rtol_ws = 5e-3 atol_ws = 0 rtol_wooldridge = 0.004 dispersed = False # Poisson correctly specified # regression numbers res_pvalue = [0.31786373532550893, 0.32654081685271297] skip_wooldridge = False res_disptest = np.array([[ 0.13927919, 0.44461477], [ 0.13927919, 0.44461477], [ 0.21295545, 0.41568086], [ 0.14935018, 0.88127732], [ 0.14935018, 0.88127732], [ 0.14841761, 0.8820132 ], [ 0.22836064, 0.81936588]]) res_disptest_g = [0.052247629593715761, 0.81919738867722225] @classmethod def setup_class(cls): # copy-paste except for model nobs, k_vars = 500, 5 np.random.seed(786452) x = np.random.randn(nobs, k_vars) x[:, 0] = 1 x2 = np.random.randn(nobs, 2) xx = np.column_stack((x, x2)) if cls.dispersed: het = np.random.randn(nobs) y = np.random.poisson(np.exp(x.sum(1) * 0.5 + het)) #y_mc = np.random.negative_binomial(np.exp(x.sum(1) * 0.5), 2) else: y = np.random.poisson(np.exp(x.sum(1) * 0.5)) cls.exog_extra = x2 cls.model_full = Poisson(y, xx) cls.model_drop = Poisson(y, x) def test_wald_score(self): super(TestScoreTestPoisson, self).test_wald_score() class TestScoreTestPoissonDispersed(TestScoreTestPoisson): rtol_ws = 0.11 atol_ws = 0.015 rtol_wooldridge = 0.03 dispersed = True # Poisson is mis-specified res_pvalue = [5.412978775609189e-14, 0.05027602575743518] res_disptest = np.array([[ 1.26473634e+02, 0.00000000e+00], [ 1.26473634e+02, 0.00000000e+00], [ 1.19393621e+02, 0.00000000e+00], [ 4.53940519e+00, 5.64131397e-06], [ 4.53940519e+00, 5.64131397e-06], [ 2.98154154e+00, 2.86801135e-03], [ 4.27569194e+00, 1.90544551e-05]]) res_disptest_g = [17.670784788586968, 2.6262956791721383e-05] statsmodels-0.12.2/statsmodels/graphics/000077500000000000000000000000001400612667500203075ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/graphics/__init__.py000066400000000000000000000001131400612667500224130ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/graphics/_regressionplots_doc.py000066400000000000000000000170601400612667500251130ustar00rootroot00000000000000_plot_added_variable_doc = """\ Create an added variable plot for a fitted regression model. Parameters ---------- %(extra_params_doc)sfocus_exog : int or string The column index of exog, or a variable name, indicating the variable whose role in the regression is to be assessed. resid_type : str The type of residuals to use for the dependent variable. If None, uses `resid_deviance` for GLM/GEE and `resid` otherwise. use_glm_weights : bool Only used if the model is a GLM or GEE. If True, the residuals for the focus predictor are computed using WLS, with the weights obtained from the IRLS calculations for fitting the GLM. If False, unweighted regression is used. fit_kwargs : dict, optional Keyword arguments to be passed to fit when refitting the model. ax: Axes Matplotlib Axes instance Returns ------- Figure A matplotlib figure instance. """ _plot_partial_residuals_doc = """\ Create a partial residual, or 'component plus residual' plot for a fitted regression model. Parameters ---------- %(extra_params_doc)sfocus_exog : int or string The column index of exog, or variable name, indicating the variable whose role in the regression is to be assessed. ax: Axes Matplotlib Axes instance Returns ------- Figure A matplotlib figure instance. """ _plot_ceres_residuals_doc = """\ Conditional Expectation Partial Residuals (CERES) plot. Produce a CERES plot for a fitted regression model. Parameters ---------- %(extra_params_doc)s focus_exog : {int, str} The column index of results.model.exog, or the variable name, indicating the variable whose role in the regression is to be assessed. frac : float Lowess tuning parameter for the adjusted model used in the CERES analysis. Not used if `cond_means` is provided. cond_means : array_like, optional If provided, the columns of this array span the space of the conditional means E[exog | focus exog], where exog ranges over some or all of the columns of exog (other than the focus exog). ax : matplotlib.Axes instance, optional The axes on which to draw the plot. If not provided, a new axes instance is created. Returns ------- Figure The figure on which the partial residual plot is drawn. Notes ----- `cond_means` is intended to capture the behavior of E[x1 | x2], where x2 is the focus exog and x1 are all the other exog variables. If all the conditional mean relationships are linear, it is sufficient to set cond_means equal to the focus exog. Alternatively, cond_means may consist of one or more columns containing functional transformations of the focus exog (e.g. x2^2) that are thought to capture E[x1 | x2]. If nothing is known or suspected about the form of E[x1 | x2], set `cond_means` to None, and it will be estimated by smoothing each non-focus exog against the focus exog. The values of `frac` control these lowess smooths. If cond_means contains only the focus exog, the results are equivalent to a partial residual plot. If the focus variable is believed to be independent of the other exog variables, `cond_means` can be set to an (empty) nx0 array. References ---------- .. [1] RD Cook and R Croos-Dabrera (1998). Partial residual plots in generalized linear models. Journal of the American Statistical Association, 93:442. .. [2] RD Cook (1993). Partial residual plots. Technometrics 35:4. Examples -------- Using a model built from the the state crime dataset, make a CERES plot with the rate of Poverty as the focus variable. >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> import statsmodels.formula.api as smf >>> from statsmodels.graphics.regressionplots import plot_ceres_residuals >>> crime_data = sm.datasets.statecrime.load_pandas() >>> results = smf.ols('murder ~ hs_grad + urban + poverty + single', ... data=crime_data.data).fit() >>> plot_ceres_residuals(results, 'poverty') >>> plt.show() .. plot:: plots/graphics_regression_ceres_residuals.py """ _plot_influence_doc = """\ Plot of influence in regression. Plots studentized resids vs. leverage. Parameters ---------- {extra_params_doc} external : bool Whether to use externally or internally studentized residuals. It is recommended to leave external as True. alpha : float The alpha value to identify large studentized residuals. Large means abs(resid_studentized) > t.ppf(1-alpha/2, dof=results.df_resid) criterion : str {{'DFFITS', 'Cooks'}} Which criterion to base the size of the points on. Options are DFFITS or Cook's D. size : float The range of `criterion` is mapped to 10**2 - size**2 in points. plot_alpha : float The `alpha` of the plotted points. ax : AxesSubplot An instance of a matplotlib Axes. **kwargs Additional parameters passed through to `plot`. Returns ------- Figure The matplotlib figure that contains the Axes. Notes ----- Row labels for the observations in which the leverage, measured by the diagonal of the hat matrix, is high or the residuals are large, as the combination of large residuals and a high influence value indicates an influence point. The value of large residuals can be controlled using the `alpha` parameter. Large leverage points are identified as hat_i > 2 * (df_model + 1)/nobs. Examples -------- Using a model built from the the state crime dataset, plot the influence in regression. Observations with high leverage, or large residuals will be labeled in the plot to show potential influence points. >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> import statsmodels.formula.api as smf >>> crime_data = sm.datasets.statecrime.load_pandas() >>> results = smf.ols('murder ~ hs_grad + urban + poverty + single', ... data=crime_data.data).fit() >>> sm.graphics.influence_plot(results) >>> plt.show() .. plot:: plots/graphics_regression_influence.py """ _plot_leverage_resid2_doc = """\ Plot leverage statistics vs. normalized residuals squared Parameters ---------- results : results instance A regression results instance alpha : float Specifies the cut-off for large-standardized residuals. Residuals are assumed to be distributed N(0, 1) with alpha=alpha. ax : Axes Matplotlib Axes instance **kwargs Additional parameters passed the plot command. Returns ------- Figure A matplotlib figure instance. Examples -------- Using a model built from the the state crime dataset, plot the leverage statistics vs. normalized residuals squared. Observations with Large-standardized Residuals will be labeled in the plot. >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> import statsmodels.formula.api as smf >>> crime_data = sm.datasets.statecrime.load_pandas() >>> results = smf.ols('murder ~ hs_grad + urban + poverty + single', ... data=crime_data.data).fit() >>> sm.graphics.plot_leverage_resid2(results) >>> plt.show() .. plot:: plots/graphics_regression_leverage_resid2.py """ statsmodels-0.12.2/statsmodels/graphics/agreement.py000066400000000000000000000123351400612667500226340ustar00rootroot00000000000000''' Bland-Altman mean-difference plots Author: Joses Ho License: BSD-3 ''' import numpy as np from . import utils def mean_diff_plot(m1, m2, sd_limit=1.96, ax=None, scatter_kwds=None, mean_line_kwds=None, limit_lines_kwds=None): """ Construct a Tukey/Bland-Altman Mean Difference Plot. Tukey's Mean Difference Plot (also known as a Bland-Altman plot) is a graphical method to analyze the differences between two methods of measurement. The mean of the measures is plotted against their difference. For more information see https://en.wikipedia.org/wiki/Bland-Altman_plot Parameters ---------- m1 : array_like A 1-d array. m2 : array_like A 1-d array. sd_limit : float The limit of agreements expressed in terms of the standard deviation of the differences. If `md` is the mean of the differences, and `sd` is the standard deviation of those differences, then the limits of agreement that will be plotted are md +/- sd_limit * sd. The default of 1.96 will produce 95% confidence intervals for the means of the differences. If sd_limit = 0, no limits will be plotted, and the ylimit of the plot defaults to 3 standard deviations on either side of the mean. ax : AxesSubplot If `ax` is None, then a figure is created. If an axis instance is given, the mean difference plot is drawn on the axis. scatter_kwds : dict Options to to style the scatter plot. Accepts any keywords for the matplotlib Axes.scatter plotting method mean_line_kwds : dict Options to to style the scatter plot. Accepts any keywords for the matplotlib Axes.axhline plotting method limit_lines_kwds : dict Options to to style the scatter plot. Accepts any keywords for the matplotlib Axes.axhline plotting method Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. References ---------- Bland JM, Altman DG (1986). "Statistical methods for assessing agreement between two methods of clinical measurement" Examples -------- Load relevant libraries. >>> import statsmodels.api as sm >>> import numpy as np >>> import matplotlib.pyplot as plt Making a mean difference plot. >>> # Seed the random number generator. >>> # This ensures that the results below are reproducible. >>> np.random.seed(9999) >>> m1 = np.random.random(20) >>> m2 = np.random.random(20) >>> f, ax = plt.subplots(1, figsize = (8,5)) >>> sm.graphics.mean_diff_plot(m1, m2, ax = ax) >>> plt.show() .. plot:: plots/graphics-mean_diff_plot.py """ fig, ax = utils.create_mpl_ax(ax) if len(m1) != len(m2): raise ValueError('m1 does not have the same length as m2.') if sd_limit < 0: raise ValueError('sd_limit ({}) is less than 0.'.format(sd_limit)) means = np.mean([m1, m2], axis=0) diffs = m1 - m2 mean_diff = np.mean(diffs) std_diff = np.std(diffs, axis=0) scatter_kwds = scatter_kwds or {} if 's' not in scatter_kwds: scatter_kwds['s'] = 20 mean_line_kwds = mean_line_kwds or {} limit_lines_kwds = limit_lines_kwds or {} for kwds in [mean_line_kwds, limit_lines_kwds]: if 'color' not in kwds: kwds['color'] = 'gray' if 'linewidth' not in kwds: kwds['linewidth'] = 1 if 'linestyle' not in mean_line_kwds: kwds['linestyle'] = '--' if 'linestyle' not in limit_lines_kwds: kwds['linestyle'] = ':' ax.scatter(means, diffs, **scatter_kwds) # Plot the means against the diffs. ax.axhline(mean_diff, **mean_line_kwds) # draw mean line. # Annotate mean line with mean difference. ax.annotate('mean diff:\n{}'.format(np.round(mean_diff, 2)), xy=(0.99, 0.5), horizontalalignment='right', verticalalignment='center', fontsize=14, xycoords='axes fraction') if sd_limit > 0: half_ylim = (1.5 * sd_limit) * std_diff ax.set_ylim(mean_diff - half_ylim, mean_diff + half_ylim) limit_of_agreement = sd_limit * std_diff lower = mean_diff - limit_of_agreement upper = mean_diff + limit_of_agreement for j, lim in enumerate([lower, upper]): ax.axhline(lim, **limit_lines_kwds) ax.annotate('-SD{}: {}'.format(sd_limit, np.round(lower, 2)), xy=(0.99, 0.07), horizontalalignment='right', verticalalignment='bottom', fontsize=14, xycoords='axes fraction') ax.annotate('+SD{}: {}'.format(sd_limit, np.round(upper, 2)), xy=(0.99, 0.92), horizontalalignment='right', fontsize=14, xycoords='axes fraction') elif sd_limit == 0: half_ylim = 3 * std_diff ax.set_ylim(mean_diff - half_ylim, mean_diff + half_ylim) ax.set_ylabel('Difference', fontsize=15) ax.set_xlabel('Means', fontsize=15) ax.tick_params(labelsize=13) fig.tight_layout() return fig statsmodels-0.12.2/statsmodels/graphics/api.py000066400000000000000000000011351400612667500214320ustar00rootroot00000000000000# flake8: noqa from .functional import hdrboxplot, fboxplot, rainbowplot from .correlation import plot_corr, plot_corr_grid from .gofplots import qqplot from .boxplots import violinplot, beanplot from .regressionplots import (abline_plot, plot_regress_exog, plot_fit, plot_partregress, plot_partregress_grid, plot_ccpr, plot_ccpr_grid, influence_plot, plot_leverage_resid2) from .factorplots import interaction_plot from .plottools import rainbow from . import tsaplots as tsa from .agreement import mean_diff_plot statsmodels-0.12.2/statsmodels/graphics/boxplots.py000066400000000000000000000404561400612667500225440ustar00rootroot00000000000000"""Variations on boxplots.""" # Author: Ralf Gommers # Based on code by Flavio Coelho and Teemu Ikonen. import numpy as np from scipy.stats import gaussian_kde from . import utils __all__ = ['violinplot', 'beanplot'] def violinplot(data, ax=None, labels=None, positions=None, side='both', show_boxplot=True, plot_opts=None): """ Make a violin plot of each dataset in the `data` sequence. A violin plot is a boxplot combined with a kernel density estimate of the probability density function per point. Parameters ---------- data : sequence[array_like] Data arrays, one array per value in `positions`. ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. labels : list[str], optional Tick labels for the horizontal axis. If not given, integers ``1..len(data)`` are used. positions : array_like, optional Position array, used as the horizontal axis of the plot. If not given, spacing of the violins will be equidistant. side : {'both', 'left', 'right'}, optional How to plot the violin. Default is 'both'. The 'left', 'right' options can be used to create asymmetric violin plots. show_boxplot : bool, optional Whether or not to show normal box plots on top of the violins. Default is True. plot_opts : dict, optional A dictionary with plotting options. Any of the following can be provided, if not present in `plot_opts` the defaults will be used:: - 'violin_fc', MPL color. Fill color for violins. Default is 'y'. - 'violin_ec', MPL color. Edge color for violins. Default is 'k'. - 'violin_lw', scalar. Edge linewidth for violins. Default is 1. - 'violin_alpha', float. Transparancy of violins. Default is 0.5. - 'cutoff', bool. If True, limit violin range to data range. Default is False. - 'cutoff_val', scalar. Where to cut off violins if `cutoff` is True. Default is 1.5 standard deviations. - 'cutoff_type', {'std', 'abs'}. Whether cutoff value is absolute, or in standard deviations. Default is 'std'. - 'violin_width' : float. Relative width of violins. Max available space is 1, default is 0.8. - 'label_fontsize', MPL fontsize. Adjusts fontsize only if given. - 'label_rotation', scalar. Adjusts label rotation only if given. Specify in degrees. - 'bw_factor', Adjusts the scipy gaussian_kde kernel. default: None. Options for scalar or callable. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. See Also -------- beanplot : Bean plot, builds on `violinplot`. matplotlib.pyplot.boxplot : Standard boxplot. Notes ----- The appearance of violins can be customized with `plot_opts`. If customization of boxplot elements is required, set `show_boxplot` to False and plot it on top of the violins by calling the Matplotlib `boxplot` function directly. For example:: violinplot(data, ax=ax, show_boxplot=False) ax.boxplot(data, sym='cv', whis=2.5) It can happen that the axis labels or tick labels fall outside the plot area, especially with rotated labels on the horizontal axis. With Matplotlib 1.1 or higher, this can easily be fixed by calling ``ax.tight_layout()``. With older Matplotlib one has to use ``plt.rc`` or ``plt.rcParams`` to fix this, for example:: plt.rc('figure.subplot', bottom=0.25) violinplot(data, ax=ax) References ---------- J.L. Hintze and R.D. Nelson, "Violin Plots: A Box Plot-Density Trace Synergism", The American Statistician, Vol. 52, pp.181-84, 1998. Examples -------- We use the American National Election Survey 1996 dataset, which has Party Identification of respondents as independent variable and (among other data) age as dependent variable. >>> data = sm.datasets.anes96.load_pandas() >>> party_ID = np.arange(7) >>> labels = ["Strong Democrat", "Weak Democrat", "Independent-Democrat", ... "Independent-Indpendent", "Independent-Republican", ... "Weak Republican", "Strong Republican"] Group age by party ID, and create a violin plot with it: >>> plt.rcParams['figure.subplot.bottom'] = 0.23 # keep labels visible >>> age = [data.exog['age'][data.endog == id] for id in party_ID] >>> fig = plt.figure() >>> ax = fig.add_subplot(111) >>> sm.graphics.violinplot(age, ax=ax, labels=labels, ... plot_opts={'cutoff_val':5, 'cutoff_type':'abs', ... 'label_fontsize':'small', ... 'label_rotation':30}) >>> ax.set_xlabel("Party identification of respondent.") >>> ax.set_ylabel("Age") >>> plt.show() .. plot:: plots/graphics_boxplot_violinplot.py """ plot_opts = {} if plot_opts is None else plot_opts if max([np.size(arr) for arr in data]) == 0: msg = "No Data to make Violin: Try again!" raise ValueError(msg) fig, ax = utils.create_mpl_ax(ax) data = list(map(np.asarray, data)) if positions is None: positions = np.arange(len(data)) + 1 # Determine available horizontal space for each individual violin. pos_span = np.max(positions) - np.min(positions) width = np.min([0.15 * np.max([pos_span, 1.]), plot_opts.get('violin_width', 0.8) / 2.]) # Plot violins. for pos_data, pos in zip(data, positions): _single_violin(ax, pos, pos_data, width, side, plot_opts) if show_boxplot: ax.boxplot(data, notch=1, positions=positions, vert=1) # Set ticks and tick labels of horizontal axis. _set_ticks_labels(ax, data, labels, positions, plot_opts) return fig def _single_violin(ax, pos, pos_data, width, side, plot_opts): """""" bw_factor = plot_opts.get('bw_factor', None) def _violin_range(pos_data, plot_opts): """Return array with correct range, with which violins can be plotted.""" cutoff = plot_opts.get('cutoff', False) cutoff_type = plot_opts.get('cutoff_type', 'std') cutoff_val = plot_opts.get('cutoff_val', 1.5) s = 0.0 if not cutoff: if cutoff_type == 'std': s = cutoff_val * np.std(pos_data) else: s = cutoff_val x_lower = kde.dataset.min() - s x_upper = kde.dataset.max() + s return np.linspace(x_lower, x_upper, 100) pos_data = np.asarray(pos_data) # Kernel density estimate for data at this position. kde = gaussian_kde(pos_data, bw_method=bw_factor) # Create violin for pos, scaled to the available space. xvals = _violin_range(pos_data, plot_opts) violin = kde.evaluate(xvals) violin = width * violin / violin.max() if side == 'both': envelope_l, envelope_r = (-violin + pos, violin + pos) elif side == 'right': envelope_l, envelope_r = (pos, violin + pos) elif side == 'left': envelope_l, envelope_r = (-violin + pos, pos) else: msg = "`side` parameter should be one of {'left', 'right', 'both'}." raise ValueError(msg) # Draw the violin. ax.fill_betweenx(xvals, envelope_l, envelope_r, facecolor=plot_opts.get('violin_fc', '#66c2a5'), edgecolor=plot_opts.get('violin_ec', 'k'), lw=plot_opts.get('violin_lw', 1), alpha=plot_opts.get('violin_alpha', 0.5)) return xvals, violin def _set_ticks_labels(ax, data, labels, positions, plot_opts): """Set ticks and labels on horizontal axis.""" # Set xticks and limits. ax.set_xlim([np.min(positions) - 0.5, np.max(positions) + 0.5]) ax.set_xticks(positions) label_fontsize = plot_opts.get('label_fontsize') label_rotation = plot_opts.get('label_rotation') if label_fontsize or label_rotation: from matplotlib.artist import setp if labels is not None: if not len(labels) == len(data): msg = "Length of `labels` should equal length of `data`." raise ValueError(msg) xticknames = ax.set_xticklabels(labels) if label_fontsize: setp(xticknames, fontsize=label_fontsize) if label_rotation: setp(xticknames, rotation=label_rotation) return def beanplot(data, ax=None, labels=None, positions=None, side='both', jitter=False, plot_opts={}): """ Bean plot of each dataset in a sequence. A bean plot is a combination of a `violinplot` (kernel density estimate of the probability density function per point) with a line-scatter plot of all individual data points. Parameters ---------- data : sequence[array_like] Data arrays, one array per value in `positions`. ax : AxesSubplot If given, this subplot is used to plot in instead of a new figure being created. labels : list[str], optional Tick labels for the horizontal axis. If not given, integers ``1..len(data)`` are used. positions : array_like, optional Position array, used as the horizontal axis of the plot. If not given, spacing of the violins will be equidistant. side : {'both', 'left', 'right'}, optional How to plot the violin. Default is 'both'. The 'left', 'right' options can be used to create asymmetric violin plots. jitter : bool, optional If True, jitter markers within violin instead of plotting regular lines around the center. This can be useful if the data is very dense. plot_opts : dict, optional A dictionary with plotting options. All the options for `violinplot` can be specified, they will simply be passed to `violinplot`. Options specific to `beanplot` are: - 'violin_width' : float. Relative width of violins. Max available space is 1, default is 0.8. - 'bean_color', MPL color. Color of bean plot lines. Default is 'k'. Also used for jitter marker edge color if `jitter` is True. - 'bean_size', scalar. Line length as a fraction of maximum length. Default is 0.5. - 'bean_lw', scalar. Linewidth, default is 0.5. - 'bean_show_mean', bool. If True (default), show mean as a line. - 'bean_show_median', bool. If True (default), show median as a marker. - 'bean_mean_color', MPL color. Color of mean line. Default is 'b'. - 'bean_mean_lw', scalar. Linewidth of mean line, default is 2. - 'bean_mean_size', scalar. Line length as a fraction of maximum length. Default is 0.5. - 'bean_median_color', MPL color. Color of median marker. Default is 'r'. - 'bean_median_marker', MPL marker. Marker type, default is '+'. - 'jitter_marker', MPL marker. Marker type for ``jitter=True``. Default is 'o'. - 'jitter_marker_size', int. Marker size. Default is 4. - 'jitter_fc', MPL color. Jitter marker face color. Default is None. - 'bean_legend_text', str. If given, add a legend with given text. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. See Also -------- violinplot : Violin plot, also used internally in `beanplot`. matplotlib.pyplot.boxplot : Standard boxplot. References ---------- P. Kampstra, "Beanplot: A Boxplot Alternative for Visual Comparison of Distributions", J. Stat. Soft., Vol. 28, pp. 1-9, 2008. Examples -------- We use the American National Election Survey 1996 dataset, which has Party Identification of respondents as independent variable and (among other data) age as dependent variable. >>> data = sm.datasets.anes96.load_pandas() >>> party_ID = np.arange(7) >>> labels = ["Strong Democrat", "Weak Democrat", "Independent-Democrat", ... "Independent-Indpendent", "Independent-Republican", ... "Weak Republican", "Strong Republican"] Group age by party ID, and create a violin plot with it: >>> plt.rcParams['figure.subplot.bottom'] = 0.23 # keep labels visible >>> age = [data.exog['age'][data.endog == id] for id in party_ID] >>> fig = plt.figure() >>> ax = fig.add_subplot(111) >>> sm.graphics.beanplot(age, ax=ax, labels=labels, ... plot_opts={'cutoff_val':5, 'cutoff_type':'abs', ... 'label_fontsize':'small', ... 'label_rotation':30}) >>> ax.set_xlabel("Party identification of respondent.") >>> ax.set_ylabel("Age") >>> plt.show() .. plot:: plots/graphics_boxplot_beanplot.py """ fig, ax = utils.create_mpl_ax(ax) data = list(map(np.asarray, data)) if positions is None: positions = np.arange(len(data)) + 1 # Determine available horizontal space for each individual violin. pos_span = np.max(positions) - np.min(positions) violin_width = np.min([0.15 * np.max([pos_span, 1.]), plot_opts.get('violin_width', 0.8) / 2.]) bean_width = np.min([0.15 * np.max([pos_span, 1.]), plot_opts.get('bean_size', 0.5) / 2.]) bean_mean_width = np.min([0.15 * np.max([pos_span, 1.]), plot_opts.get('bean_mean_size', 0.5) / 2.]) legend_txt = plot_opts.get('bean_legend_text', None) for pos_data, pos in zip(data, positions): # Draw violins. xvals, violin = _single_violin(ax, pos, pos_data, violin_width, side, plot_opts) if jitter: # Draw data points at random coordinates within violin envelope. jitter_coord = pos + _jitter_envelope(pos_data, xvals, violin, side) ax.plot(jitter_coord, pos_data, ls='', marker=plot_opts.get('jitter_marker', 'o'), ms=plot_opts.get('jitter_marker_size', 4), mec=plot_opts.get('bean_color', 'k'), mew=1, mfc=plot_opts.get('jitter_fc', 'none'), label=legend_txt) else: # Draw bean lines. ax.hlines(pos_data, pos - bean_width, pos + bean_width, lw=plot_opts.get('bean_lw', 0.5), color=plot_opts.get('bean_color', 'k'), label=legend_txt) # Show legend if required. if legend_txt is not None: _show_legend(ax) legend_txt = None # ensure we get one entry per call to beanplot # Draw mean line. if plot_opts.get('bean_show_mean', True): ax.hlines(np.mean(pos_data), pos - bean_mean_width, pos + bean_mean_width, lw=plot_opts.get('bean_mean_lw', 2.), color=plot_opts.get('bean_mean_color', 'b')) # Draw median marker. if plot_opts.get('bean_show_median', True): ax.plot(pos, np.median(pos_data), marker=plot_opts.get('bean_median_marker', '+'), color=plot_opts.get('bean_median_color', 'r')) # Set ticks and tick labels of horizontal axis. _set_ticks_labels(ax, data, labels, positions, plot_opts) return fig def _jitter_envelope(pos_data, xvals, violin, side): """Determine envelope for jitter markers.""" if side == 'both': low, high = (-1., 1.) elif side == 'right': low, high = (0, 1.) elif side == 'left': low, high = (-1., 0) else: raise ValueError("`side` input incorrect: %s" % side) jitter_envelope = np.interp(pos_data, xvals, violin) jitter_coord = jitter_envelope * np.random.uniform(low=low, high=high, size=pos_data.size) return jitter_coord def _show_legend(ax): """Utility function to show legend.""" leg = ax.legend(loc=1, shadow=True, fancybox=True, labelspacing=0.2, borderpad=0.15) ltext = leg.get_texts() llines = leg.get_lines() frame = leg.get_frame() from matplotlib.artist import setp setp(ltext, fontsize='small') setp(llines, linewidth=1) statsmodels-0.12.2/statsmodels/graphics/correlation.py000066400000000000000000000171131400612667500232050ustar00rootroot00000000000000'''correlation plots Author: Josef Perktold License: BSD-3 example for usage with different options in statsmodels/sandbox/examples/thirdparty/ex_ratereturn.py ''' import numpy as np from . import utils def plot_corr(dcorr, xnames=None, ynames=None, title=None, normcolor=False, ax=None, cmap='RdYlBu_r'): """Plot correlation of many variables in a tight color grid. Parameters ---------- dcorr : ndarray Correlation matrix, square 2-D array. xnames : list[str], optional Labels for the horizontal axis. If not given (None), then the matplotlib defaults (integers) are used. If it is an empty list, [], then no ticks and labels are added. ynames : list[str], optional Labels for the vertical axis. Works the same way as `xnames`. If not given, the same names as for `xnames` are re-used. title : str, optional The figure title. If None, the default ('Correlation Matrix') is used. If ``title=''``, then no title is added. normcolor : bool or tuple of scalars, optional If False (default), then the color coding range corresponds to the range of `dcorr`. If True, then the color range is normalized to (-1, 1). If this is a tuple of two numbers, then they define the range for the color bar. ax : AxesSubplot, optional If `ax` is None, then a figure is created. If an axis instance is given, then only the main plot but not the colorbar is created. cmap : str or Matplotlib Colormap instance, optional The colormap for the plot. Can be any valid Matplotlib Colormap instance or name. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. Examples -------- >>> import numpy as np >>> import matplotlib.pyplot as plt >>> import statsmodels.graphics.api as smg >>> hie_data = sm.datasets.randhie.load_pandas() >>> corr_matrix = np.corrcoef(hie_data.data.T) >>> smg.plot_corr(corr_matrix, xnames=hie_data.names) >>> plt.show() ..plot :: plots/graphics_correlation_plot_corr.py """ if ax is None: create_colorbar = True else: create_colorbar = False fig, ax = utils.create_mpl_ax(ax) nvars = dcorr.shape[0] if ynames is None: ynames = xnames if title is None: title = 'Correlation Matrix' if isinstance(normcolor, tuple): vmin, vmax = normcolor elif normcolor: vmin, vmax = -1.0, 1.0 else: vmin, vmax = None, None axim = ax.imshow(dcorr, cmap=cmap, interpolation='nearest', extent=(0,nvars,0,nvars), vmin=vmin, vmax=vmax) # create list of label positions labelPos = np.arange(0, nvars) + 0.5 if isinstance(ynames, list) and len(ynames) == 0: ax.set_yticks([]) elif ynames is not None: ax.set_yticks(labelPos) ax.set_yticks(labelPos[:-1]+0.5, minor=True) ax.set_yticklabels(ynames[::-1], fontsize='small', horizontalalignment='right') if isinstance(xnames, list) and len(xnames) == 0: ax.set_xticks([]) elif xnames is not None: ax.set_xticks(labelPos) ax.set_xticks(labelPos[:-1]+0.5, minor=True) ax.set_xticklabels(xnames, fontsize='small', rotation=45, horizontalalignment='right') if not title == '': ax.set_title(title) if create_colorbar: fig.colorbar(axim, use_gridspec=True) fig.tight_layout() ax.tick_params(which='minor', length=0) ax.tick_params(direction='out', top=False, right=False) try: ax.grid(True, which='minor', linestyle='-', color='w', lw=1) except AttributeError: # Seems to fail for axes created with AxesGrid. MPL bug? pass return fig def plot_corr_grid(dcorrs, titles=None, ncols=None, normcolor=False, xnames=None, ynames=None, fig=None, cmap='RdYlBu_r'): """ Create a grid of correlation plots. The individual correlation plots are assumed to all have the same variables, axis labels can be specified only once. Parameters ---------- dcorrs : list or iterable of ndarrays List of correlation matrices. titles : list[str], optional List of titles for the subplots. By default no title are shown. ncols : int, optional Number of columns in the subplot grid. If not given, the number of columns is determined automatically. normcolor : bool or tuple, optional If False (default), then the color coding range corresponds to the range of `dcorr`. If True, then the color range is normalized to (-1, 1). If this is a tuple of two numbers, then they define the range for the color bar. xnames : list[str], optional Labels for the horizontal axis. If not given (None), then the matplotlib defaults (integers) are used. If it is an empty list, [], then no ticks and labels are added. ynames : list[str], optional Labels for the vertical axis. Works the same way as `xnames`. If not given, the same names as for `xnames` are re-used. fig : Figure, optional If given, this figure is simply returned. Otherwise a new figure is created. cmap : str or Matplotlib Colormap instance, optional The colormap for the plot. Can be any valid Matplotlib Colormap instance or name. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. Examples -------- >>> import numpy as np >>> import matplotlib.pyplot as plt >>> import statsmodels.api as sm In this example we just reuse the same correlation matrix several times. Of course in reality one would show a different correlation (measuring a another type of correlation, for example Pearson (linear) and Spearman, Kendall (nonlinear) correlations) for the same variables. >>> hie_data = sm.datasets.randhie.load_pandas() >>> corr_matrix = np.corrcoef(hie_data.data.T) >>> sm.graphics.plot_corr_grid([corr_matrix] * 8, xnames=hie_data.names) >>> plt.show() ..plot :: plots/graphics_correlation_plot_corr_grid.py """ if ynames is None: ynames = xnames if not titles: titles = ['']*len(dcorrs) n_plots = len(dcorrs) if ncols is not None: nrows = int(np.ceil(n_plots / float(ncols))) else: # Determine number of rows and columns, square if possible, otherwise # prefer a wide (more columns) over a high layout. if n_plots < 4: nrows, ncols = 1, n_plots else: nrows = int(np.sqrt(n_plots)) ncols = int(np.ceil(n_plots / float(nrows))) # Create a figure with the correct size aspect = min(ncols / float(nrows), 1.8) vsize = np.sqrt(nrows) * 5 fig = utils.create_mpl_fig(fig, figsize=(vsize * aspect + 1, vsize)) for i, c in enumerate(dcorrs): ax = fig.add_subplot(nrows, ncols, i+1) # Ensure to only plot labels on bottom row and left column _xnames = xnames if nrows * ncols - (i+1) < ncols else [] _ynames = ynames if (i+1) % ncols == 1 else [] plot_corr(c, xnames=_xnames, ynames=_ynames, title=titles[i], normcolor=normcolor, ax=ax, cmap=cmap) # Adjust figure margins and add a colorbar fig.subplots_adjust(bottom=0.1, left=0.09, right=0.9, top=0.9) cax = fig.add_axes([0.92, 0.1, 0.025, 0.8]) fig.colorbar(fig.axes[0].images[0], cax=cax) return fig statsmodels-0.12.2/statsmodels/graphics/dotplots.py000066400000000000000000000427561400612667500225470ustar00rootroot00000000000000import numpy as np from . import utils def dot_plot(points, intervals=None, lines=None, sections=None, styles=None, marker_props=None, line_props=None, split_names=None, section_order=None, line_order=None, stacked=False, styles_order=None, striped=False, horizontal=True, show_names="both", fmt_left_name=None, fmt_right_name=None, show_section_titles=None, ax=None): """ Dot plotting (also known as forest and blobbogram). Produce a dotplot similar in style to those in Cleveland's "Visualizing Data" book ([1]_). These are also known as "forest plots". Parameters ---------- points : array_like The quantitative values to be plotted as markers. intervals : array_like The intervals to be plotted around the points. The elements of `intervals` are either scalars or sequences of length 2. A scalar indicates the half width of a symmetric interval. A sequence of length 2 contains the left and right half-widths (respectively) of a nonsymmetric interval. If None, no intervals are drawn. lines : array_like A grouping variable indicating which points/intervals are drawn on a common line. If None, each point/interval appears on its own line. sections : array_like A grouping variable indicating which lines are grouped into sections. If None, everything is drawn in a single section. styles : array_like A grouping label defining the plotting style of the markers and intervals. marker_props : dict A dictionary mapping style codes (the values in `styles`) to dictionaries defining key/value pairs to be passed as keyword arguments to `plot` when plotting markers. Useful keyword arguments are "color", "marker", and "ms" (marker size). line_props : dict A dictionary mapping style codes (the values in `styles`) to dictionaries defining key/value pairs to be passed as keyword arguments to `plot` when plotting interval lines. Useful keyword arguments are "color", "linestyle", "solid_capstyle", and "linewidth". split_names : str If not None, this is used to split the values of `lines` into substrings that are drawn in the left and right margins, respectively. If None, the values of `lines` are drawn in the left margin. section_order : array_like The section labels in the order in which they appear in the dotplot. line_order : array_like The line labels in the order in which they appear in the dotplot. stacked : bool If True, when multiple points or intervals are drawn on the same line, they are offset from each other. styles_order : array_like If stacked=True, this is the order in which the point styles on a given line are drawn from top to bottom (if horizontal is True) or from left to right (if horizontal is False). If None (default), the order is lexical. striped : bool If True, every other line is enclosed in a shaded box. horizontal : bool If True (default), the lines are drawn horizontally, otherwise they are drawn vertically. show_names : str Determines whether labels (names) are shown in the left and/or right margins (top/bottom margins if `horizontal` is True). If `both`, labels are drawn in both margins, if 'left', labels are drawn in the left or top margin. If `right`, labels are drawn in the right or bottom margin. fmt_left_name : callable The left/top margin names are passed through this function before drawing on the plot. fmt_right_name : callable The right/bottom marginnames are passed through this function before drawing on the plot. show_section_titles : bool or None If None, section titles are drawn only if there is more than one section. If False/True, section titles are never/always drawn, respectively. ax : matplotlib.axes The axes on which the dotplot is drawn. If None, a new axes is created. Returns ------- fig : Figure The figure given by `ax.figure` or a new instance. Notes ----- `points`, `intervals`, `lines`, `sections`, `styles` must all have the same length whenever present. References ---------- .. [1] Cleveland, William S. (1993). "Visualizing Data". Hobart Press. .. [2] Jacoby, William G. (2006) "The Dot Plot: A Graphical Display for Labeled Quantitative Values." The Political Methodologist 14(1): 6-14. Examples -------- This is a simple dotplot with one point per line: >>> dot_plot(points=point_values) This dotplot has labels on the lines (if elements in `label_values` are repeated, the corresponding points appear on the same line): >>> dot_plot(points=point_values, lines=label_values) """ import matplotlib.transforms as transforms fig, ax = utils.create_mpl_ax(ax) # Convert to numpy arrays if that is not what we are given. points = np.asarray(points) asarray_or_none = lambda x : None if x is None else np.asarray(x) intervals = asarray_or_none(intervals) lines = asarray_or_none(lines) sections = asarray_or_none(sections) styles = asarray_or_none(styles) # Total number of points npoint = len(points) # Set default line values if needed if lines is None: lines = np.arange(npoint) # Set default section values if needed if sections is None: sections = np.zeros(npoint) # Set default style values if needed if styles is None: styles = np.zeros(npoint) # The vertical space (in inches) for a section title section_title_space = 0.5 # The number of sections nsect = len(set(sections)) if section_order is not None: nsect = len(set(section_order)) # The number of section titles if show_section_titles is False: draw_section_titles = False nsect_title = 0 elif show_section_titles is True: draw_section_titles = True nsect_title = nsect else: draw_section_titles = nsect > 1 nsect_title = nsect if nsect > 1 else 0 # The total vertical space devoted to section titles. section_space_total = section_title_space * nsect_title # Add a bit of room so that points that fall at the axis limits # are not cut in half. ax.set_xmargin(0.02) ax.set_ymargin(0.02) if section_order is None: lines0 = list(set(sections)) lines0.sort() else: lines0 = section_order if line_order is None: lines1 = list(set(lines)) lines1.sort() else: lines1 = line_order # A map from (section,line) codes to index positions. lines_map = {} for i in range(npoint): if section_order is not None and sections[i] not in section_order: continue if line_order is not None and lines[i] not in line_order: continue ky = (sections[i], lines[i]) if ky not in lines_map: lines_map[ky] = [] lines_map[ky].append(i) # Get the size of the axes on the parent figure in inches bbox = ax.get_window_extent().transformed( fig.dpi_scale_trans.inverted()) awidth, aheight = bbox.width, bbox.height # The number of lines in the plot. nrows = len(lines_map) # The positions of the lowest and highest guideline in axes # coordinates (for horizontal dotplots), or the leftmost and # rightmost guidelines (for vertical dotplots). bottom, top = 0, 1 if horizontal: # x coordinate is data, y coordinate is axes trans = transforms.blended_transform_factory(ax.transData, ax.transAxes) else: # x coordinate is axes, y coordinate is data trans = transforms.blended_transform_factory(ax.transAxes, ax.transData) # Space used for a section title, in axes coordinates title_space_axes = section_title_space / aheight # Space between lines if horizontal: dpos = (top - bottom - nsect_title*title_space_axes) /\ float(nrows) else: dpos = (top - bottom) / float(nrows) # Determine the spacing for stacked points if styles_order is not None: style_codes = styles_order else: style_codes = list(set(styles)) style_codes.sort() # Order is top to bottom for horizontal plots, so need to # flip. if horizontal: style_codes = style_codes[::-1] # nval is the maximum number of points on one line. nval = len(style_codes) if nval > 1: stackd = dpos / (2.5*(float(nval)-1)) else: stackd = 0. # Map from style code to its integer position style_codes_map = {x: style_codes.index(x) for x in style_codes} # Setup default marker styles colors = ["r", "g", "b", "y", "k", "purple", "orange"] if marker_props is None: marker_props = {x: {} for x in style_codes} for j in range(nval): sc = style_codes[j] if "color" not in marker_props[sc]: marker_props[sc]["color"] = colors[j % len(colors)] if "marker" not in marker_props[sc]: marker_props[sc]["marker"] = "o" if "ms" not in marker_props[sc]: marker_props[sc]["ms"] = 10 if stackd == 0 else 6 # Setup default line styles if line_props is None: line_props = {x: {} for x in style_codes} for j in range(nval): sc = style_codes[j] if "color" not in line_props[sc]: line_props[sc]["color"] = "grey" if "linewidth" not in line_props[sc]: line_props[sc]["linewidth"] = 2 if stackd > 0 else 8 if horizontal: # The vertical position of the first line. pos = top - dpos/2 if nsect == 1 else top else: # The horizontal position of the first line. pos = bottom + dpos/2 # Points that have already been labeled labeled = set() # Positions of the y axis grid lines ticks = [] # Loop through the sections for k0 in lines0: # Draw a section title if draw_section_titles: if horizontal: y0 = pos + dpos/2 if k0 == lines0[0] else pos ax.fill_between((0, 1), (y0,y0), (pos-0.7*title_space_axes, pos-0.7*title_space_axes), color='darkgrey', transform=ax.transAxes, zorder=1) txt = ax.text(0.5, pos - 0.35*title_space_axes, k0, horizontalalignment='center', verticalalignment='center', transform=ax.transAxes) txt.set_fontweight("bold") pos -= title_space_axes else: m = len([k for k in lines_map if k[0] == k0]) ax.fill_between((pos-dpos/2+0.01, pos+(m-1)*dpos+dpos/2-0.01), (1.01,1.01), (1.06,1.06), color='darkgrey', transform=ax.transAxes, zorder=1, clip_on=False) txt = ax.text(pos + (m-1)*dpos/2, 1.02, k0, horizontalalignment='center', verticalalignment='bottom', transform=ax.transAxes) txt.set_fontweight("bold") jrow = 0 for k1 in lines1: # No data to plot if (k0, k1) not in lines_map: continue # Draw the guideline if horizontal: ax.axhline(pos, color='grey') else: ax.axvline(pos, color='grey') # Set up the labels if split_names is not None: us = k1.split(split_names) if len(us) >= 2: left_label, right_label = us[0], us[1] else: left_label, right_label = k1, None else: left_label, right_label = k1, None if fmt_left_name is not None: left_label = fmt_left_name(left_label) if fmt_right_name is not None: right_label = fmt_right_name(right_label) # Draw the stripe if striped and jrow % 2 == 0: if horizontal: ax.fill_between((0, 1), (pos-dpos/2, pos-dpos/2), (pos+dpos/2, pos+dpos/2), color='lightgrey', transform=ax.transAxes, zorder=0) else: ax.fill_between((pos-dpos/2, pos+dpos/2), (0, 0), (1, 1), color='lightgrey', transform=ax.transAxes, zorder=0) jrow += 1 # Draw the left margin label if show_names.lower() in ("left", "both"): if horizontal: ax.text(-0.1/awidth, pos, left_label, horizontalalignment="right", verticalalignment='center', transform=ax.transAxes, family='monospace') else: ax.text(pos, -0.1/aheight, left_label, horizontalalignment="center", verticalalignment='top', transform=ax.transAxes, family='monospace') # Draw the right margin label if show_names.lower() in ("right", "both"): if right_label is not None: if horizontal: ax.text(1 + 0.1/awidth, pos, right_label, horizontalalignment="left", verticalalignment='center', transform=ax.transAxes, family='monospace') else: ax.text(pos, 1 + 0.1/aheight, right_label, horizontalalignment="center", verticalalignment='bottom', transform=ax.transAxes, family='monospace') # Save the vertical position so that we can place the # tick marks ticks.append(pos) # Loop over the points in one line for ji,jp in enumerate(lines_map[(k0,k1)]): # Calculate the vertical offset yo = 0 if stacked: yo = -dpos/5 + style_codes_map[styles[jp]]*stackd pt = points[jp] # Plot the interval if intervals is not None: # Symmetric interval if np.isscalar(intervals[jp]): lcb, ucb = pt - intervals[jp],\ pt + intervals[jp] # Nonsymmetric interval else: lcb, ucb = pt - intervals[jp][0],\ pt + intervals[jp][1] # Draw the interval if horizontal: ax.plot([lcb, ucb], [pos+yo, pos+yo], '-', transform=trans, **line_props[styles[jp]]) else: ax.plot([pos+yo, pos+yo], [lcb, ucb], '-', transform=trans, **line_props[styles[jp]]) # Plot the point sl = styles[jp] sll = sl if sl not in labeled else None labeled.add(sl) if horizontal: ax.plot([pt,], [pos+yo,], ls='None', transform=trans, label=sll, **marker_props[sl]) else: ax.plot([pos+yo,], [pt,], ls='None', transform=trans, label=sll, **marker_props[sl]) if horizontal: pos -= dpos else: pos += dpos # Set up the axis if horizontal: ax.xaxis.set_ticks_position("bottom") ax.yaxis.set_ticks_position("none") ax.set_yticklabels([]) ax.spines['left'].set_color('none') ax.spines['right'].set_color('none') ax.spines['top'].set_color('none') ax.spines['bottom'].set_position(('axes', -0.1/aheight)) ax.set_ylim(0, 1) ax.yaxis.set_ticks(ticks) ax.autoscale_view(scaley=False, tight=True) else: ax.yaxis.set_ticks_position("left") ax.xaxis.set_ticks_position("none") ax.set_xticklabels([]) ax.spines['bottom'].set_color('none') ax.spines['right'].set_color('none') ax.spines['top'].set_color('none') ax.spines['left'].set_position(('axes', -0.1/awidth)) ax.set_xlim(0, 1) ax.xaxis.set_ticks(ticks) ax.autoscale_view(scalex=False, tight=True) return fig statsmodels-0.12.2/statsmodels/graphics/factorplots.py000066400000000000000000000163551400612667500232330ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Authors: Josef Perktold, Skipper Seabold, Denis A. Engemann """ from statsmodels.compat.python import lrange import numpy as np from statsmodels.graphics.plottools import rainbow import statsmodels.graphics.utils as utils def interaction_plot(x, trace, response, func=np.mean, ax=None, plottype='b', xlabel=None, ylabel=None, colors=None, markers=None, linestyles=None, legendloc='best', legendtitle=None, **kwargs): """ Interaction plot for factor level statistics. Note. If categorial factors are supplied levels will be internally recoded to integers. This ensures matplotlib compatibility. Uses a DataFrame to calculate an `aggregate` statistic for each level of the factor or group given by `trace`. Parameters ---------- x : array_like The `x` factor levels constitute the x-axis. If a `pandas.Series` is given its name will be used in `xlabel` if `xlabel` is None. trace : array_like The `trace` factor levels will be drawn as lines in the plot. If `trace` is a `pandas.Series` its name will be used as the `legendtitle` if `legendtitle` is None. response : array_like The reponse or dependent variable. If a `pandas.Series` is given its name will be used in `ylabel` if `ylabel` is None. func : function Anything accepted by `pandas.DataFrame.aggregate`. This is applied to the response variable grouped by the trace levels. ax : axes, optional Matplotlib axes instance plottype : str {'line', 'scatter', 'both'}, optional The type of plot to return. Can be 'l', 's', or 'b' xlabel : str, optional Label to use for `x`. Default is 'X'. If `x` is a `pandas.Series` it will use the series names. ylabel : str, optional Label to use for `response`. Default is 'func of response'. If `response` is a `pandas.Series` it will use the series names. colors : list, optional If given, must have length == number of levels in trace. markers : list, optional If given, must have length == number of levels in trace linestyles : list, optional If given, must have length == number of levels in trace. legendloc : {None, str, int} Location passed to the legend command. legendtitle : {None, str} Title of the legend. **kwargs These will be passed to the plot command used either plot or scatter. If you want to control the overall plotting options, use kwargs. Returns ------- Figure The figure given by `ax.figure` or a new instance. Examples -------- >>> import numpy as np >>> np.random.seed(12345) >>> weight = np.random.randint(1,4,size=60) >>> duration = np.random.randint(1,3,size=60) >>> days = np.log(np.random.randint(1,30, size=60)) >>> fig = interaction_plot(weight, duration, days, ... colors=['red','blue'], markers=['D','^'], ms=10) >>> import matplotlib.pyplot as plt >>> plt.show() .. plot:: import numpy as np from statsmodels.graphics.factorplots import interaction_plot np.random.seed(12345) weight = np.random.randint(1,4,size=60) duration = np.random.randint(1,3,size=60) days = np.log(np.random.randint(1,30, size=60)) fig = interaction_plot(weight, duration, days, colors=['red','blue'], markers=['D','^'], ms=10) import matplotlib.pyplot as plt #plt.show() """ from pandas import DataFrame fig, ax = utils.create_mpl_ax(ax) response_name = ylabel or getattr(response, 'name', 'response') ylabel = '%s of %s' % (func.__name__, response_name) xlabel = xlabel or getattr(x, 'name', 'X') legendtitle = legendtitle or getattr(trace, 'name', 'Trace') ax.set_ylabel(ylabel) ax.set_xlabel(xlabel) x_values = x_levels = None if isinstance(x[0], str): x_levels = [l for l in np.unique(x)] x_values = lrange(len(x_levels)) x = _recode(x, dict(zip(x_levels, x_values))) data = DataFrame(dict(x=x, trace=trace, response=response)) plot_data = data.groupby(['trace', 'x']).aggregate(func).reset_index() # return data # check plot args n_trace = len(plot_data['trace'].unique()) linestyles = ['-'] * n_trace if linestyles is None else linestyles markers = ['.'] * n_trace if markers is None else markers colors = rainbow(n_trace) if colors is None else colors if len(linestyles) != n_trace: raise ValueError("Must be a linestyle for each trace level") if len(markers) != n_trace: raise ValueError("Must be a marker for each trace level") if len(colors) != n_trace: raise ValueError("Must be a color for each trace level") if plottype == 'both' or plottype == 'b': for i, (values, group) in enumerate(plot_data.groupby(['trace'])): # trace label label = str(group['trace'].values[0]) ax.plot(group['x'], group['response'], color=colors[i], marker=markers[i], label=label, linestyle=linestyles[i], **kwargs) elif plottype == 'line' or plottype == 'l': for i, (values, group) in enumerate(plot_data.groupby(['trace'])): # trace label label = str(group['trace'].values[0]) ax.plot(group['x'], group['response'], color=colors[i], label=label, linestyle=linestyles[i], **kwargs) elif plottype == 'scatter' or plottype == 's': for i, (values, group) in enumerate(plot_data.groupby(['trace'])): # trace label label = str(group['trace'].values[0]) ax.scatter(group['x'], group['response'], color=colors[i], label=label, marker=markers[i], **kwargs) else: raise ValueError("Plot type %s not understood" % plottype) ax.legend(loc=legendloc, title=legendtitle) ax.margins(.1) if all([x_levels, x_values]): ax.set_xticks(x_values) ax.set_xticklabels(x_levels) return fig def _recode(x, levels): """ Recode categorial data to int factor. Parameters ---------- x : array_like array like object supporting with numpy array methods of categorially coded data. levels : dict mapping of labels to integer-codings Returns ------- out : instance numpy.ndarray """ from pandas import Series name = None index = None if isinstance(x, Series): name = x.name index = x.index x = x.values if x.dtype.type not in [np.str_, np.object_]: raise ValueError('This is not a categorial factor.' ' Array of str type required.') elif not isinstance(levels, dict): raise ValueError('This is not a valid value for levels.' ' Dict required.') elif not (np.unique(x) == np.unique(list(levels.keys()))).all(): raise ValueError('The levels do not match the array values.') else: out = np.empty(x.shape[0], dtype=int) for level, coding in levels.items(): out[x == level] = coding if name: out = Series(out, name=name, index=index) return out statsmodels-0.12.2/statsmodels/graphics/functional.py000066400000000000000000000751341400612667500230350ustar00rootroot00000000000000"""Module for functional boxplots.""" from statsmodels.multivariate.pca import PCA from statsmodels.nonparametric.kernel_density import KDEMultivariate from statsmodels.graphics.utils import _import_mpl import numpy as np from scipy.special import comb try: from scipy.optimize import differential_evolution, brute, fmin have_de_optim = True except ImportError: from scipy.optimize import brute, fmin have_de_optim = False from multiprocessing import Pool import itertools from . import utils __all__ = ['hdrboxplot', 'fboxplot', 'rainbowplot', 'banddepth'] class HdrResults(object): """Wrap results and pretty print them.""" def __init__(self, kwds): self.__dict__.update(kwds) def __repr__(self): msg = ("HDR boxplot summary:\n" "-> median:\n{}\n" "-> 50% HDR (max, min):\n{}\n" "-> 90% HDR (max, min):\n{}\n" "-> Extra quantiles (max, min):\n{}\n" "-> Outliers:\n{}\n" "-> Outliers indices:\n{}\n" ).format(self.median, self.hdr_50, self.hdr_90, self.extra_quantiles, self.outliers, self.outliers_idx) return msg def _inverse_transform(pca, data): """ Inverse transform on PCA. Use PCA's `project` method by temporary replacing its factors with `data`. Parameters ---------- pca : statsmodels Principal Component Analysis instance The PCA object to use. data : sequence of ndarrays or 2-D ndarray The vectors of functions to create a functional boxplot from. If a sequence of 1-D arrays, these should all be the same size. The first axis is the function index, the second axis the one along which the function is defined. So ``data[0, :]`` is the first functional curve. Returns ------- projection : ndarray nobs by nvar array of the projection onto ncomp factors """ factors = pca.factors pca.factors = data.reshape(-1, factors.shape[1]) projection = pca.project() pca.factors = factors return projection def _curve_constrained(x, idx, sign, band, pca, ks_gaussian): """Find out if the curve is within the band. The curve value at :attr:`idx` for a given PDF is only returned if within bounds defined by the band. Otherwise, 1E6 is returned. Parameters ---------- x : float Curve in reduced space. idx : int Index value of the components to compute. sign : int Return positive or negative value. band : list of float PDF values `[min_pdf, max_pdf]` to be within. pca : statsmodels Principal Component Analysis instance The PCA object to use. ks_gaussian : KDEMultivariate instance Returns ------- value : float Curve value at `idx`. """ x = x.reshape(1, -1) pdf = ks_gaussian.pdf(x) if band[0] < pdf < band[1]: value = sign * _inverse_transform(pca, x)[0][idx] else: value = 1E6 return value def _min_max_band(args): """ Min and max values at `idx`. Global optimization to find the extrema per component. Parameters ---------- args: list It is a list of an idx and other arguments as a tuple: idx : int Index value of the components to compute The tuple contains: band : list of float PDF values `[min_pdf, max_pdf]` to be within. pca : statsmodels Principal Component Analysis instance The PCA object to use. bounds : sequence ``(min, max)`` pair for each components ks_gaussian : KDEMultivariate instance Returns ------- band : tuple of float ``(max, min)`` curve values at `idx` """ idx, (band, pca, bounds, ks_gaussian, use_brute, seed) = args if have_de_optim and not use_brute: max_ = differential_evolution(_curve_constrained, bounds=bounds, args=(idx, -1, band, pca, ks_gaussian), maxiter=7, seed=seed).x min_ = differential_evolution(_curve_constrained, bounds=bounds, args=(idx, 1, band, pca, ks_gaussian), maxiter=7, seed=seed).x else: max_ = brute(_curve_constrained, ranges=bounds, finish=fmin, args=(idx, -1, band, pca, ks_gaussian)) min_ = brute(_curve_constrained, ranges=bounds, finish=fmin, args=(idx, 1, band, pca, ks_gaussian)) band = (_inverse_transform(pca, max_)[0][idx], _inverse_transform(pca, min_)[0][idx]) return band def hdrboxplot(data, ncomp=2, alpha=None, threshold=0.95, bw=None, xdata=None, labels=None, ax=None, use_brute=False, seed=None): """ High Density Region boxplot Parameters ---------- data : sequence of ndarrays or 2-D ndarray The vectors of functions to create a functional boxplot from. If a sequence of 1-D arrays, these should all be the same size. The first axis is the function index, the second axis the one along which the function is defined. So ``data[0, :]`` is the first functional curve. ncomp : int, optional Number of components to use. If None, returns the as many as the smaller of the number of rows or columns in data. alpha : list of floats between 0 and 1, optional Extra quantile values to compute. Default is None threshold : float between 0 and 1, optional Percentile threshold value for outliers detection. High value means a lower sensitivity to outliers. Default is `0.95`. bw : array_like or str, optional If an array, it is a fixed user-specified bandwidth. If `None`, set to `normal_reference`. If a string, should be one of: - normal_reference: normal reference rule of thumb (default) - cv_ml: cross validation maximum likelihood - cv_ls: cross validation least squares xdata : ndarray, optional The independent variable for the data. If not given, it is assumed to be an array of integers 0..N-1 with N the length of the vectors in `data`. labels : sequence of scalar or str, optional The labels or identifiers of the curves in `data`. If not given, outliers are labeled in the plot with array indices. ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. use_brute : bool Use the brute force optimizer instead of the default differential evolution to find the curves. Default is False. seed : {None, int, np.random.RandomState} Seed value to pass to scipy.optimize.differential_evolution. Can be an integer or RandomState instance. If None, then the default RandomState provided by np.random is used. Returns ------- fig : Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. hdr_res : HdrResults instance An `HdrResults` instance with the following attributes: - 'median', array. Median curve. - 'hdr_50', array. 50% quantile band. [sup, inf] curves - 'hdr_90', list of array. 90% quantile band. [sup, inf] curves. - 'extra_quantiles', list of array. Extra quantile band. [sup, inf] curves. - 'outliers', ndarray. Outlier curves. See Also -------- banddepth, rainbowplot, fboxplot Notes ----- The median curve is the curve with the highest probability on the reduced space of a Principal Component Analysis (PCA). Outliers are defined as curves that fall outside the band corresponding to the quantile given by `threshold`. The non-outlying region is defined as the band made up of all the non-outlying curves. Behind the scene, the dataset is represented as a matrix. Each line corresponding to a 1D curve. This matrix is then decomposed using Principal Components Analysis (PCA). This allows to represent the data using a finite number of modes, or components. This compression process allows to turn the functional representation into a scalar representation of the matrix. In other words, you can visualize each curve from its components. Each curve is thus a point in this reduced space. With 2 components, this is called a bivariate plot (2D plot). In this plot, if some points are adjacent (similar components), it means that back in the original space, the curves are similar. Then, finding the median curve means finding the higher density region (HDR) in the reduced space. Moreover, the more you get away from this HDR, the more the curve is unlikely to be similar to the other curves. Using a kernel smoothing technique, the probability density function (PDF) of the multivariate space can be recovered. From this PDF, it is possible to compute the density probability linked to the cluster of points and plot its contours. Finally, using these contours, the different quantiles can be extracted along with the median curve and the outliers. Steps to produce the HDR boxplot include: 1. Compute a multivariate kernel density estimation 2. Compute contour lines for quantiles 90%, 50% and `alpha` % 3. Plot the bivariate plot 4. Compute median curve along with quantiles and outliers curves. References ---------- [1] R.J. Hyndman and H.L. Shang, "Rainbow Plots, Bagplots, and Boxplots for Functional Data", vol. 19, pp. 29-45, 2010. Examples -------- Load the El Nino dataset. Consists of 60 years worth of Pacific Ocean sea surface temperature data. >>> import matplotlib.pyplot as plt >>> import statsmodels.api as sm >>> data = sm.datasets.elnino.load(as_pandas=False) Create a functional boxplot. We see that the years 1982-83 and 1997-98 are outliers; these are the years where El Nino (a climate pattern characterized by warming up of the sea surface and higher air pressures) occurred with unusual intensity. >>> fig = plt.figure() >>> ax = fig.add_subplot(111) >>> res = sm.graphics.hdrboxplot(data.raw_data[:, 1:], ... labels=data.raw_data[:, 0].astype(int), ... ax=ax) >>> ax.set_xlabel("Month of the year") >>> ax.set_ylabel("Sea surface temperature (C)") >>> ax.set_xticks(np.arange(13, step=3) - 1) >>> ax.set_xticklabels(["", "Mar", "Jun", "Sep", "Dec"]) >>> ax.set_xlim([-0.2, 11.2]) >>> plt.show() .. plot:: plots/graphics_functional_hdrboxplot.py """ fig, ax = utils.create_mpl_ax(ax) if labels is None: # For use with pandas, get the labels if hasattr(data, 'index'): labels = data.index else: labels = np.arange(len(data)) data = np.asarray(data) if xdata is None: xdata = np.arange(data.shape[1]) n_samples, dim = data.shape # PCA and bivariate plot pca = PCA(data, ncomp=ncomp) data_r = pca.factors # Create gaussian kernel ks_gaussian = KDEMultivariate(data_r, bw=bw, var_type='c' * data_r.shape[1]) # Boundaries of the n-variate space bounds = np.array([data_r.min(axis=0), data_r.max(axis=0)]).T # Compute contour line of pvalue linked to a given probability level if alpha is None: alpha = [threshold, 0.9, 0.5] else: alpha.extend([threshold, 0.9, 0.5]) alpha = list(set(alpha)) alpha.sort(reverse=True) n_quantiles = len(alpha) pdf_r = ks_gaussian.pdf(data_r).flatten() pvalues = [np.percentile(pdf_r, (1 - alpha[i]) * 100, interpolation='linear') for i in range(n_quantiles)] # Find mean, outliers curves if have_de_optim and not use_brute: median = differential_evolution(lambda x: - ks_gaussian.pdf(x), bounds=bounds, maxiter=5, seed=seed).x else: median = brute(lambda x: - ks_gaussian.pdf(x), ranges=bounds, finish=fmin) outliers_idx = np.where(pdf_r < pvalues[alpha.index(threshold)])[0] labels_outlier = [labels[i] for i in outliers_idx] outliers = data[outliers_idx] # Find HDR given some quantiles def _band_quantiles(band, use_brute=use_brute, seed=seed): """ Find extreme curves for a quantile band. From the `band` of quantiles, the associated PDF extrema values are computed. If `min_alpha` is not provided (single quantile value), `max_pdf` is set to `1E6` in order not to constrain the problem on high values. An optimization is performed per component in order to find the min and max curves. This is done by comparing the PDF value of a given curve with the band PDF. Parameters ---------- band : array_like alpha values ``(max_alpha, min_alpha)`` ex: ``[0.9, 0.5]`` use_brute : bool Use the brute force optimizer instead of the default differential evolution to find the curves. Default is False. seed : {None, int, np.random.RandomState} Seed value to pass to scipy.optimize.differential_evolution. Can be an integer or RandomState instance. If None, then the default RandomState provided by np.random is used. Returns ------- band_quantiles : list of 1-D array ``(max_quantile, min_quantile)`` (2, n_features) """ min_pdf = pvalues[alpha.index(band[0])] try: max_pdf = pvalues[alpha.index(band[1])] except IndexError: max_pdf = 1E6 band = [min_pdf, max_pdf] pool = Pool() data = zip(range(dim), itertools.repeat((band, pca, bounds, ks_gaussian, seed, use_brute))) band_quantiles = pool.map(_min_max_band, data) pool.terminate() pool.close() band_quantiles = list(zip(*band_quantiles)) return band_quantiles extra_alpha = [i for i in alpha if 0.5 != i and 0.9 != i and threshold != i] if len(extra_alpha) > 0: extra_quantiles = [] for x in extra_alpha: for y in _band_quantiles([x], use_brute=use_brute, seed=seed): extra_quantiles.append(y) else: extra_quantiles = [] # Inverse transform from n-variate plot to dataset dataset's shape median = _inverse_transform(pca, median)[0] hdr_90 = _band_quantiles([0.9, 0.5], use_brute=use_brute, seed=seed) hdr_50 = _band_quantiles([0.5], use_brute=use_brute, seed=seed) hdr_res = HdrResults({ "median": median, "hdr_50": hdr_50, "hdr_90": hdr_90, "extra_quantiles": extra_quantiles, "outliers": outliers, "outliers_idx": outliers_idx }) # Plots ax.plot(np.array([xdata] * n_samples).T, data.T, c='c', alpha=.1, label=None) ax.plot(xdata, median, c='k', label='Median') fill_betweens = [] fill_betweens.append(ax.fill_between(xdata, *hdr_50, color='gray', alpha=.4, label='50% HDR')) fill_betweens.append(ax.fill_between(xdata, *hdr_90, color='gray', alpha=.3, label='90% HDR')) if len(extra_quantiles) != 0: ax.plot(np.array([xdata] * len(extra_quantiles)).T, np.array(extra_quantiles).T, c='y', ls='-.', alpha=.4, label='Extra quantiles') if len(outliers) != 0: for ii, outlier in enumerate(outliers): if labels_outlier is None: label = 'Outliers' else: label = str(labels_outlier[ii]) ax.plot(xdata, outlier, ls='--', alpha=0.7, label=label) handles, labels = ax.get_legend_handles_labels() # Proxy artist for fill_between legend entry # See https://matplotlib.org/1.3.1/users/legend_guide.html plt = _import_mpl() for label, fill_between in zip(['50% HDR', '90% HDR'], fill_betweens): p = plt.Rectangle((0, 0), 1, 1, fc=fill_between.get_facecolor()[0]) handles.append(p) labels.append(label) by_label = dict(zip(labels, handles)) if len(outliers) != 0: by_label.pop('Median') by_label.pop('50% HDR') by_label.pop('90% HDR') ax.legend(by_label.values(), by_label.keys(), loc='best') return fig, hdr_res def fboxplot(data, xdata=None, labels=None, depth=None, method='MBD', wfactor=1.5, ax=None, plot_opts=None): """ Plot functional boxplot. A functional boxplot is the analog of a boxplot for functional data. Functional data is any type of data that varies over a continuum, i.e. curves, probability distributions, seasonal data, etc. The data is first ordered, the order statistic used here is `banddepth`. Plotted are then the median curve, the envelope of the 50% central region, the maximum non-outlying envelope and the outlier curves. Parameters ---------- data : sequence of ndarrays or 2-D ndarray The vectors of functions to create a functional boxplot from. If a sequence of 1-D arrays, these should all be the same size. The first axis is the function index, the second axis the one along which the function is defined. So ``data[0, :]`` is the first functional curve. xdata : ndarray, optional The independent variable for the data. If not given, it is assumed to be an array of integers 0..N-1 with N the length of the vectors in `data`. labels : sequence of scalar or str, optional The labels or identifiers of the curves in `data`. If given, outliers are labeled in the plot. depth : ndarray, optional A 1-D array of band depths for `data`, or equivalent order statistic. If not given, it will be calculated through `banddepth`. method : {'MBD', 'BD2'}, optional The method to use to calculate the band depth. Default is 'MBD'. wfactor : float, optional Factor by which the central 50% region is multiplied to find the outer region (analog of "whiskers" of a classical boxplot). ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. plot_opts : dict, optional A dictionary with plotting options. Any of the following can be provided, if not present in `plot_opts` the defaults will be used:: - 'cmap_outliers', a Matplotlib LinearSegmentedColormap instance. - 'c_inner', valid MPL color. Color of the central 50% region - 'c_outer', valid MPL color. Color of the non-outlying region - 'c_median', valid MPL color. Color of the median. - 'lw_outliers', scalar. Linewidth for drawing outlier curves. - 'lw_median', scalar. Linewidth for drawing the median curve. - 'draw_nonout', bool. If True, also draw non-outlying curves. Returns ------- fig : Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. depth : ndarray A 1-D array containing the calculated band depths of the curves. ix_depth : ndarray A 1-D array of indices needed to order curves (or `depth`) from most to least central curve. ix_outliers : ndarray A 1-D array of indices of outlying curves in `data`. See Also -------- banddepth, rainbowplot Notes ----- The median curve is the curve with the highest band depth. Outliers are defined as curves that fall outside the band created by multiplying the central region by `wfactor`. Note that the range over which they fall outside this band does not matter, a single data point outside the band is enough. If the data is noisy, smoothing may therefore be required. The non-outlying region is defined as the band made up of all the non-outlying curves. References ---------- [1] Y. Sun and M.G. Genton, "Functional Boxplots", Journal of Computational and Graphical Statistics, vol. 20, pp. 1-19, 2011. [2] R.J. Hyndman and H.L. Shang, "Rainbow Plots, Bagplots, and Boxplots for Functional Data", vol. 19, pp. 29-45, 2010. Examples -------- Load the El Nino dataset. Consists of 60 years worth of Pacific Ocean sea surface temperature data. >>> import matplotlib.pyplot as plt >>> import statsmodels.api as sm >>> data = sm.datasets.elnino.load(as_pandas=False) Create a functional boxplot. We see that the years 1982-83 and 1997-98 are outliers; these are the years where El Nino (a climate pattern characterized by warming up of the sea surface and higher air pressures) occurred with unusual intensity. >>> fig = plt.figure() >>> ax = fig.add_subplot(111) >>> res = sm.graphics.fboxplot(data.raw_data[:, 1:], wfactor=2.58, ... labels=data.raw_data[:, 0].astype(int), ... ax=ax) >>> ax.set_xlabel("Month of the year") >>> ax.set_ylabel("Sea surface temperature (C)") >>> ax.set_xticks(np.arange(13, step=3) - 1) >>> ax.set_xticklabels(["", "Mar", "Jun", "Sep", "Dec"]) >>> ax.set_xlim([-0.2, 11.2]) >>> plt.show() .. plot:: plots/graphics_functional_fboxplot.py """ fig, ax = utils.create_mpl_ax(ax) plot_opts = {} if plot_opts is None else plot_opts if plot_opts.get('cmap_outliers') is None: from matplotlib.cm import rainbow_r plot_opts['cmap_outliers'] = rainbow_r data = np.asarray(data) if xdata is None: xdata = np.arange(data.shape[1]) # Calculate band depth if required. if depth is None: if method not in ['MBD', 'BD2']: raise ValueError("Unknown value for parameter `method`.") depth = banddepth(data, method=method) else: if depth.size != data.shape[0]: raise ValueError("Provided `depth` array is not of correct size.") # Inner area is 25%-75% region of band-depth ordered curves. ix_depth = np.argsort(depth)[::-1] median_curve = data[ix_depth[0], :] ix_IQR = data.shape[0] // 2 lower = data[ix_depth[0:ix_IQR], :].min(axis=0) upper = data[ix_depth[0:ix_IQR], :].max(axis=0) # Determine region for outlier detection inner_median = np.median(data[ix_depth[0:ix_IQR], :], axis=0) lower_fence = inner_median - (inner_median - lower) * wfactor upper_fence = inner_median + (upper - inner_median) * wfactor # Find outliers. ix_outliers = [] ix_nonout = [] for ii in range(data.shape[0]): if (np.any(data[ii, :] > upper_fence) or np.any(data[ii, :] < lower_fence)): ix_outliers.append(ii) else: ix_nonout.append(ii) ix_outliers = np.asarray(ix_outliers) # Plot envelope of all non-outlying data lower_nonout = data[ix_nonout, :].min(axis=0) upper_nonout = data[ix_nonout, :].max(axis=0) ax.fill_between(xdata, lower_nonout, upper_nonout, color=plot_opts.get('c_outer', (0.75, 0.75, 0.75))) # Plot central 50% region ax.fill_between(xdata, lower, upper, color=plot_opts.get('c_inner', (0.5, 0.5, 0.5))) # Plot median curve ax.plot(xdata, median_curve, color=plot_opts.get('c_median', 'k'), lw=plot_opts.get('lw_median', 2)) # Plot outliers cmap = plot_opts.get('cmap_outliers') for ii, ix in enumerate(ix_outliers): label = str(labels[ix]) if labels is not None else None ax.plot(xdata, data[ix, :], color=cmap(float(ii) / (len(ix_outliers)-1)), label=label, lw=plot_opts.get('lw_outliers', 1)) if plot_opts.get('draw_nonout', False): for ix in ix_nonout: ax.plot(xdata, data[ix, :], 'k-', lw=0.5) if labels is not None: ax.legend() return fig, depth, ix_depth, ix_outliers def rainbowplot(data, xdata=None, depth=None, method='MBD', ax=None, cmap=None): """ Create a rainbow plot for a set of curves. A rainbow plot contains line plots of all curves in the dataset, colored in order of functional depth. The median curve is shown in black. Parameters ---------- data : sequence of ndarrays or 2-D ndarray The vectors of functions to create a functional boxplot from. If a sequence of 1-D arrays, these should all be the same size. The first axis is the function index, the second axis the one along which the function is defined. So ``data[0, :]`` is the first functional curve. xdata : ndarray, optional The independent variable for the data. If not given, it is assumed to be an array of integers 0..N-1 with N the length of the vectors in `data`. depth : ndarray, optional A 1-D array of band depths for `data`, or equivalent order statistic. If not given, it will be calculated through `banddepth`. method : {'MBD', 'BD2'}, optional The method to use to calculate the band depth. Default is 'MBD'. ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. cmap : Matplotlib LinearSegmentedColormap instance, optional The colormap used to color curves with. Default is a rainbow colormap, with red used for the most central and purple for the least central curves. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. See Also -------- banddepth, fboxplot References ---------- [1] R.J. Hyndman and H.L. Shang, "Rainbow Plots, Bagplots, and Boxplots for Functional Data", vol. 19, pp. 29-25, 2010. Examples -------- Load the El Nino dataset. Consists of 60 years worth of Pacific Ocean sea surface temperature data. >>> import matplotlib.pyplot as plt >>> import statsmodels.api as sm >>> data = sm.datasets.elnino.load(as_pandas=False) Create a rainbow plot: >>> fig = plt.figure() >>> ax = fig.add_subplot(111) >>> res = sm.graphics.rainbowplot(data.raw_data[:, 1:], ax=ax) >>> ax.set_xlabel("Month of the year") >>> ax.set_ylabel("Sea surface temperature (C)") >>> ax.set_xticks(np.arange(13, step=3) - 1) >>> ax.set_xticklabels(["", "Mar", "Jun", "Sep", "Dec"]) >>> ax.set_xlim([-0.2, 11.2]) >>> plt.show() .. plot:: plots/graphics_functional_rainbowplot.py """ fig, ax = utils.create_mpl_ax(ax) if cmap is None: from matplotlib.cm import rainbow_r cmap = rainbow_r data = np.asarray(data) if xdata is None: xdata = np.arange(data.shape[1]) # Calculate band depth if required. if depth is None: if method not in ['MBD', 'BD2']: raise ValueError("Unknown value for parameter `method`.") depth = banddepth(data, method=method) else: if depth.size != data.shape[0]: raise ValueError("Provided `depth` array is not of correct size.") ix_depth = np.argsort(depth)[::-1] # Plot all curves, colored by depth num_curves = data.shape[0] for ii in range(num_curves): ax.plot(xdata, data[ix_depth[ii], :], c=cmap(ii / (num_curves - 1.))) # Plot the median curve median_curve = data[ix_depth[0], :] ax.plot(xdata, median_curve, 'k-', lw=2) return fig def banddepth(data, method='MBD'): """ Calculate the band depth for a set of functional curves. Band depth is an order statistic for functional data (see `fboxplot`), with a higher band depth indicating larger "centrality". In analog to scalar data, the functional curve with highest band depth is called the median curve, and the band made up from the first N/2 of N curves is the 50% central region. Parameters ---------- data : ndarray The vectors of functions to create a functional boxplot from. The first axis is the function index, the second axis the one along which the function is defined. So ``data[0, :]`` is the first functional curve. method : {'MBD', 'BD2'}, optional Whether to use the original band depth (with J=2) of [1]_ or the modified band depth. See Notes for details. Returns ------- ndarray Depth values for functional curves. Notes ----- Functional band depth as an order statistic for functional data was proposed in [1]_ and applied to functional boxplots and bagplots in [2]_. The method 'BD2' checks for each curve whether it lies completely inside bands constructed from two curves. All permutations of two curves in the set of curves are used, and the band depth is normalized to one. Due to the complete curve having to fall within the band, this method yields a lot of ties. The method 'MBD' is similar to 'BD2', but checks the fraction of the curve falling within the bands. It therefore generates very few ties. The algorithm uses the efficient implementation proposed in [3]_. References ---------- .. [1] S. Lopez-Pintado and J. Romo, "On the Concept of Depth for Functional Data", Journal of the American Statistical Association, vol. 104, pp. 718-734, 2009. .. [2] Y. Sun and M.G. Genton, "Functional Boxplots", Journal of Computational and Graphical Statistics, vol. 20, pp. 1-19, 2011. .. [3] Y. Sun, M. G. Gentonb and D. W. Nychkac, "Exact fast computation of band depth for large functional datasets: How quickly can one million curves be ranked?", Journal for the Rapid Dissemination of Statistics Research, vol. 1, pp. 68-74, 2012. """ n, p = data.shape rv = np.argsort(data, axis=0) rmat = np.argsort(rv, axis=0) + 1 # band depth def _fbd2(): down = np.min(rmat, axis=1) - 1 up = n - np.max(rmat, axis=1) return (up * down + n - 1) / comb(n, 2) # modified band depth def _fmbd(): down = rmat - 1 up = n - rmat return ((np.sum(up * down, axis=1) / p) + n - 1) / comb(n, 2) if method == 'BD2': depth = _fbd2() elif method == 'MBD': depth = _fmbd() else: raise ValueError("Unknown input value for parameter `method`.") return depth statsmodels-0.12.2/statsmodels/graphics/gofplots.py000066400000000000000000001032101400612667500225130ustar00rootroot00000000000000from statsmodels.compat.python import lzip import numpy as np from scipy import stats from statsmodels.distributions import ECDF from statsmodels.regression.linear_model import OLS from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.tools import add_constant from . import utils __all__ = ["qqplot", "qqplot_2samples", "qqline", "ProbPlot"] class ProbPlot(object): """ Q-Q and P-P Probability Plots Can take arguments specifying the parameters for dist or fit them automatically. (See fit under kwargs.) Parameters ---------- data : array_like A 1d data array dist : callable Compare x against dist. A scipy.stats or statsmodels distribution. The default is scipy.stats.distributions.norm (a standard normal). Can be a SciPy frozen distribution. fit : bool If fit is false, loc, scale, and distargs are passed to the distribution. If fit is True then the parameters for dist are fit automatically using dist.fit. The quantiles are formed from the standardized data, after subtracting the fitted loc and dividing by the fitted scale. fit cannot be used if dist is a SciPy frozen distribution. distargs : tuple A tuple of arguments passed to dist to specify it fully so dist.ppf may be called. distargs must not contain loc or scale. These values must be passed using the loc or scale inputs. distargs cannot be used if dist is a SciPy frozen distribution. a : float Offset for the plotting position of an expected order statistic, for example. The plotting positions are given by (i - a)/(nobs - 2*a + 1) for i in range(0,nobs+1) loc : float Location parameter for dist. Cannot be used if dist is a SciPy frozen distribution. scale : float Scale parameter for dist. Cannot be used if dist is a SciPy frozen distribution. See Also -------- scipy.stats.probplot Notes ----- 1) Depends on matplotlib. 2) If `fit` is True then the parameters are fit using the distribution's `fit()` method. 3) The call signatures for the `qqplot`, `ppplot`, and `probplot` methods are similar, so examples 1 through 4 apply to all three methods. 4) The three plotting methods are summarized below: ppplot : Probability-Probability plot Compares the sample and theoretical probabilities (percentiles). qqplot : Quantile-Quantile plot Compares the sample and theoretical quantiles probplot : Probability plot Same as a Q-Q plot, however probabilities are shown in the scale of the theoretical distribution (x-axis) and the y-axis contains unscaled quantiles of the sample data. Examples -------- The first example shows a Q-Q plot for regression residuals >>> # example 1 >>> import statsmodels.api as sm >>> from matplotlib import pyplot as plt >>> data = sm.datasets.longley.load(as_pandas=False) >>> data.exog = sm.add_constant(data.exog) >>> model = sm.OLS(data.endog, data.exog) >>> mod_fit = model.fit() >>> res = mod_fit.resid # residuals >>> pplot = sm.ProbPlot(res) >>> fig = pplot.qqplot() >>> h = plt.title("Ex. 1 - qqplot - residuals of OLS fit") >>> plt.show() qqplot of the residuals against quantiles of t-distribution with 4 degrees of freedom: >>> # example 2 >>> import scipy.stats as stats >>> pplot = sm.ProbPlot(res, stats.t, distargs=(4,)) >>> fig = pplot.qqplot() >>> h = plt.title("Ex. 2 - qqplot - residuals against quantiles of t-dist") >>> plt.show() qqplot against same as above, but with mean 3 and std 10: >>> # example 3 >>> pplot = sm.ProbPlot(res, stats.t, distargs=(4,), loc=3, scale=10) >>> fig = pplot.qqplot() >>> h = plt.title("Ex. 3 - qqplot - resids vs quantiles of t-dist") >>> plt.show() Automatically determine parameters for t distribution including the loc and scale: >>> # example 4 >>> pplot = sm.ProbPlot(res, stats.t, fit=True) >>> fig = pplot.qqplot(line="45") >>> h = plt.title("Ex. 4 - qqplot - resids vs. quantiles of fitted t-dist") >>> plt.show() A second `ProbPlot` object can be used to compare two separate sample sets by using the `other` kwarg in the `qqplot` and `ppplot` methods. >>> # example 5 >>> import numpy as np >>> x = np.random.normal(loc=8.25, scale=2.75, size=37) >>> y = np.random.normal(loc=8.75, scale=3.25, size=37) >>> pp_x = sm.ProbPlot(x, fit=True) >>> pp_y = sm.ProbPlot(y, fit=True) >>> fig = pp_x.qqplot(line="45", other=pp_y) >>> h = plt.title("Ex. 5 - qqplot - compare two sample sets") >>> plt.show() In qqplot, sample size of `other` can be equal or larger than the first. In case of larger, size of `other` samples will be reduced to match the size of the first by interpolation >>> # example 6 >>> x = np.random.normal(loc=8.25, scale=2.75, size=37) >>> y = np.random.normal(loc=8.75, scale=3.25, size=57) >>> pp_x = sm.ProbPlot(x, fit=True) >>> pp_y = sm.ProbPlot(y, fit=True) >>> fig = pp_x.qqplot(line="45", other=pp_y) >>> title = "Ex. 6 - qqplot - compare different sample sizes" >>> h = plt.title(title) >>> plt.show() In ppplot, sample size of `other` and the first can be different. `other` will be used to estimate an empirical cumulative distribution function (ECDF). ECDF(x) will be plotted against p(x)=0.5/n, 1.5/n, ..., (n-0.5)/n where x are sorted samples from the first. >>> # example 7 >>> x = np.random.normal(loc=8.25, scale=2.75, size=37) >>> y = np.random.normal(loc=8.75, scale=3.25, size=57) >>> pp_x = sm.ProbPlot(x, fit=True) >>> pp_y = sm.ProbPlot(y, fit=True) >>> pp_y.ppplot(line="45", other=pp_x) >>> plt.title("Ex. 7A- ppplot - compare two sample sets, other=pp_x") >>> pp_x.ppplot(line="45", other=pp_y) >>> plt.title("Ex. 7B- ppplot - compare two sample sets, other=pp_y") >>> plt.show() The following plot displays some options, follow the link to see the code. .. plot:: plots/graphics_gofplots_qqplot.py """ def __init__( self, data, dist=stats.norm, fit=False, distargs=(), a=0, loc=0, scale=1, ): self.data = data self.a = a self.nobs = data.shape[0] self.distargs = distargs self.fit = fit self._is_frozen = isinstance(dist, stats.distributions.rv_frozen) if self._is_frozen and ( fit or loc != 0 or scale != 1 or distargs != () ): raise ValueError( "Frozen distributions cannot be combined with fit, loc, scale" " or distargs." ) # propertes self._cache = {} if self._is_frozen: self.dist = dist dist_gen = dist.dist shapes = dist_gen.shapes if shapes is not None: shape_args = tuple(map(str.strip, shapes.split(","))) else: shape_args = () numargs = len(shape_args) args = dist.args if len(args) >= numargs + 1: self.loc = args[numargs] else: self.loc = dist.kwds.get("loc", loc) if len(args) >= numargs + 2: self.scale = args[numargs + 1] else: self.scale = dist.kwds.get("scale", scale) fit_params = [] for i, arg in enumerate(shape_args): if arg in dist.kwds: value = dist.kwds[arg] else: value = dist.args[i] fit_params.append(value) self.fit_params = np.r_[fit_params, self.loc, self.scale] elif fit: self.fit_params = dist.fit(data) self.loc = self.fit_params[-2] self.scale = self.fit_params[-1] if len(self.fit_params) > 2: self.dist = dist(*self.fit_params[:-2], **dict(loc=0, scale=1)) else: self.dist = dist(loc=0, scale=1) elif distargs or loc != 0 or scale != 1: try: self.dist = dist(*distargs, **dict(loc=loc, scale=scale)) except Exception: distargs = ", ".join([str(da) for da in distargs]) cmd = "dist({distargs}, loc={loc}, scale={scale})" cmd = cmd.format(distargs=distargs, loc=loc, scale=scale) raise TypeError( "Initializing the distribution failed. This " "can occur if distargs contains loc or scale. " "The distribution initialization command " "is:\n{cmd}".format(cmd=cmd) ) self.loc = loc self.scale = scale self.fit_params = np.r_[distargs, loc, scale] else: self.dist = dist self.loc = loc self.scale = scale self.fit_params = np.r_[loc, scale] @cache_readonly def theoretical_percentiles(self): """Theoretical percentiles""" return plotting_pos(self.nobs, self.a) @cache_readonly def theoretical_quantiles(self): """Theoretical quantiles""" try: return self.dist.ppf(self.theoretical_percentiles) except TypeError: msg = "%s requires more parameters to compute ppf".format( self.dist.name, ) raise TypeError(msg) except Exception as exc: msg = "failed to compute the ppf of {0}".format(self.dist.name) raise type(exc)(msg) @cache_readonly def sorted_data(self): """sorted data""" sorted_data = np.array(self.data, copy=True) sorted_data.sort() return sorted_data @cache_readonly def sample_quantiles(self): """sample quantiles""" if self.fit and self.loc != 0 and self.scale != 1: return (self.sorted_data - self.loc) / self.scale else: return self.sorted_data @cache_readonly def sample_percentiles(self): """Sample percentiles""" _check_for(self.dist, "cdf") if self._is_frozen: return self.dist.cdf(self.sorted_data) quantiles = (self.sorted_data - self.fit_params[-2]) / self.fit_params[ -1 ] return self.dist.cdf(quantiles) def ppplot( self, xlabel=None, ylabel=None, line=None, other=None, ax=None, **plotkwargs, ): """ Plot of the percentiles of x versus the percentiles of a distribution. Parameters ---------- xlabel : str or None, optional User-provided labels for the x-axis. If None (default), other values are used depending on the status of the kwarg `other`. ylabel : str or None, optional User-provided labels for the y-axis. If None (default), other values are used depending on the status of the kwarg `other`. line : {None, "45", "s", "r", q"}, optional Options for the reference line to which the data is compared: - "45": 45-degree line - "s": standardized line, the expected order statistics are scaled by the standard deviation of the given sample and have the mean added to them - "r": A regression line is fit - "q": A line is fit through the quartiles. - None: by default no reference line is added to the plot. other : ProbPlot, array_like, or None, optional If provided, ECDF(x) will be plotted against p(x) where x are sorted samples from `self`. ECDF is an empirical cumulative distribution function estimated from `other` and p(x) = 0.5/n, 1.5/n, ..., (n-0.5)/n where n is the number of samples in `self`. If an array-object is provided, it will be turned into a `ProbPlot` instance default parameters. If not provided (default), `self.dist(x)` is be plotted against p(x). ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. **plotkwargs Additional arguments to be passed to the `plot` command. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. """ if other is not None: check_other = isinstance(other, ProbPlot) if not check_other: other = ProbPlot(other) p_x = self.theoretical_percentiles ecdf_x = ECDF(other.sample_quantiles)(self.sample_quantiles) fig, ax = _do_plot( p_x, ecdf_x, self.dist, ax=ax, line=line, **plotkwargs ) if xlabel is None: xlabel = "Probabilities of 2nd Sample" if ylabel is None: ylabel = "Probabilities of 1st Sample" else: fig, ax = _do_plot( self.theoretical_percentiles, self.sample_percentiles, self.dist, ax=ax, line=line, **plotkwargs, ) if xlabel is None: xlabel = "Theoretical Probabilities" if ylabel is None: ylabel = "Sample Probabilities" ax.set_xlabel(xlabel) ax.set_ylabel(ylabel) ax.set_xlim([0.0, 1.0]) ax.set_ylim([0.0, 1.0]) return fig def qqplot( self, xlabel=None, ylabel=None, line=None, other=None, ax=None, **plotkwargs, ): """ Plot of the quantiles of x versus the quantiles/ppf of a distribution. Can also be used to plot against the quantiles of another `ProbPlot` instance. Parameters ---------- xlabel : {None, str} User-provided labels for the x-axis. If None (default), other values are used depending on the status of the kwarg `other`. ylabel : {None, str} User-provided labels for the y-axis. If None (default), other values are used depending on the status of the kwarg `other`. line : {None, "45", "s", "r", q"}, optional Options for the reference line to which the data is compared: - "45" - 45-degree line - "s" - standardized line, the expected order statistics are scaled by the standard deviation of the given sample and have the mean added to them - "r" - A regression line is fit - "q" - A line is fit through the quartiles. - None - by default no reference line is added to the plot. other : {ProbPlot, array_like, None}, optional If provided, the sample quantiles of this `ProbPlot` instance are plotted against the sample quantiles of the `other` `ProbPlot` instance. Sample size of `other` must be equal or larger than this `ProbPlot` instance. If the sample size is larger, sample quantiles of `other` will be interpolated to match the sample size of this `ProbPlot` instance. If an array-like object is provided, it will be turned into a `ProbPlot` instance using default parameters. If not provided (default), the theoretical quantiles are used. ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. **plotkwargs Additional arguments to be passed to the `plot` command. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. """ if other is not None: check_other = isinstance(other, ProbPlot) if not check_other: other = ProbPlot(other) s_self = self.sample_quantiles s_other = other.sample_quantiles if len(s_self) > len(s_other): raise ValueError( "Sample size of `other` must be equal or " + "larger than this `ProbPlot` instance" ) elif len(s_self) < len(s_other): # Use quantiles of the smaller set and interpolate quantiles of # the larger data set p = plotting_pos(self.nobs, self.a) s_other = stats.mstats.mquantiles(s_other, p) fig, ax = _do_plot( s_other, s_self, self.dist, ax=ax, line=line, **plotkwargs ) if xlabel is None: xlabel = "Quantiles of 2nd Sample" if ylabel is None: ylabel = "Quantiles of 1st Sample" else: fig, ax = _do_plot( self.theoretical_quantiles, self.sample_quantiles, self.dist, ax=ax, line=line, **plotkwargs, ) if xlabel is None: xlabel = "Theoretical Quantiles" if ylabel is None: ylabel = "Sample Quantiles" ax.set_xlabel(xlabel) ax.set_ylabel(ylabel) return fig def probplot( self, xlabel=None, ylabel=None, line=None, exceed=False, ax=None, **plotkwargs, ): """ Plot of unscaled quantiles of x against the prob of a distribution. The x-axis is scaled linearly with the quantiles, but the probabilities are used to label the axis. Parameters ---------- xlabel : {None, str}, optional User-provided labels for the x-axis. If None (default), other values are used depending on the status of the kwarg `other`. ylabel : {None, str}, optional User-provided labels for the y-axis. If None (default), other values are used depending on the status of the kwarg `other`. line : {None, "45", "s", "r", q"}, optional Options for the reference line to which the data is compared: - "45" - 45-degree line - "s" - standardized line, the expected order statistics are scaled by the standard deviation of the given sample and have the mean added to them - "r" - A regression line is fit - "q" - A line is fit through the quartiles. - None - by default no reference line is added to the plot. exceed : bool, optional If False (default) the raw sample quantiles are plotted against the theoretical quantiles, show the probability that a sample will not exceed a given value. If True, the theoretical quantiles are flipped such that the figure displays the probability that a sample will exceed a given value. ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. **plotkwargs Additional arguments to be passed to the `plot` command. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. """ if exceed: fig, ax = _do_plot( self.theoretical_quantiles[::-1], self.sorted_data, self.dist, ax=ax, line=line, **plotkwargs, ) if xlabel is None: xlabel = "Probability of Exceedance (%)" else: fig, ax = _do_plot( self.theoretical_quantiles, self.sorted_data, self.dist, ax=ax, line=line, **plotkwargs, ) if xlabel is None: xlabel = "Non-exceedance Probability (%)" if ylabel is None: ylabel = "Sample Quantiles" ax.set_xlabel(xlabel) ax.set_ylabel(ylabel) _fmt_probplot_axis(ax, self.dist, self.nobs) return fig def qqplot( data, dist=stats.norm, distargs=(), a=0, loc=0, scale=1, fit=False, line=None, ax=None, **plotkwargs, ): """ Q-Q plot of the quantiles of x versus the quantiles/ppf of a distribution. Can take arguments specifying the parameters for dist or fit them automatically. (See fit under Parameters.) Parameters ---------- data : array_like A 1d data array. dist : callable Comparison distribution. The default is scipy.stats.distributions.norm (a standard normal). distargs : tuple A tuple of arguments passed to dist to specify it fully so dist.ppf may be called. a : float Offset for the plotting position of an expected order statistic, for example. The plotting positions are given by (i - a)/(nobs - 2*a + 1) for i in range(0,nobs+1) loc : float Location parameter for dist scale : float Scale parameter for dist fit : bool If fit is false, loc, scale, and distargs are passed to the distribution. If fit is True then the parameters for dist are fit automatically using dist.fit. The quantiles are formed from the standardized data, after subtracting the fitted loc and dividing by the fitted scale. line : {None, "45", "s", "r", "q"} Options for the reference line to which the data is compared: - "45" - 45-degree line - "s" - standardized line, the expected order statistics are scaled by the standard deviation of the given sample and have the mean added to them - "r" - A regression line is fit - "q" - A line is fit through the quartiles. - None - by default no reference line is added to the plot. ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. **plotkwargs Additional matplotlib arguments to be passed to the `plot` command. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. See Also -------- scipy.stats.probplot Notes ----- Depends on matplotlib. If `fit` is True then the parameters are fit using the distribution's fit() method. Examples -------- >>> import statsmodels.api as sm >>> from matplotlib import pyplot as plt >>> data = sm.datasets.longley.load(as_pandas=False) >>> exog = sm.add_constant(data.exog) >>> mod_fit = sm.OLS(data.endog, exog).fit() >>> res = mod_fit.resid # residuals >>> fig = sm.qqplot(res) >>> plt.show() qqplot of the residuals against quantiles of t-distribution with 4 degrees of freedom: >>> import scipy.stats as stats >>> fig = sm.qqplot(res, stats.t, distargs=(4,)) >>> plt.show() qqplot against same as above, but with mean 3 and std 10: >>> fig = sm.qqplot(res, stats.t, distargs=(4,), loc=3, scale=10) >>> plt.show() Automatically determine parameters for t distribution including the loc and scale: >>> fig = sm.qqplot(res, stats.t, fit=True, line="45") >>> plt.show() The following plot displays some options, follow the link to see the code. .. plot:: plots/graphics_gofplots_qqplot.py """ probplot = ProbPlot( data, dist=dist, distargs=distargs, fit=fit, a=a, loc=loc, scale=scale ) fig = probplot.qqplot(ax=ax, line=line, **plotkwargs) return fig def qqplot_2samples( data1, data2, xlabel=None, ylabel=None, line=None, ax=None ): """ Q-Q Plot of two samples' quantiles. Can take either two `ProbPlot` instances or two array-like objects. In the case of the latter, both inputs will be converted to `ProbPlot` instances using only the default values - so use `ProbPlot` instances if finer-grained control of the quantile computations is required. Parameters ---------- data1 : {array_like, ProbPlot} Data to plot along x axis. data2 : {array_like, ProbPlot} Data to plot along y axis. Does not need to have the same number of observations as data 1. xlabel : {None, str} User-provided labels for the x-axis. If None (default), other values are used. ylabel : {None, str} User-provided labels for the y-axis. If None (default), other values are used. line : {None, "45", "s", "r", q"} Options for the reference line to which the data is compared: - "45" - 45-degree line - "s" - standardized line, the expected order statistics are scaled by the standard deviation of the given sample and have the mean added to them - "r" - A regression line is fit - "q" - A line is fit through the quartiles. - None - by default no reference line is added to the plot. ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. See Also -------- scipy.stats.probplot Notes ----- 1) Depends on matplotlib. 2) If `data1` and `data2` are not `ProbPlot` instances, instances will be created using the default parameters. Therefore, it is recommended to use `ProbPlot` instance if fine-grained control is needed in the computation of the quantiles. Examples -------- >>> import statsmodels.api as sm >>> import numpy as np >>> import matplotlib.pyplot as plt >>> from statsmodels.graphics.gofplots import qqplot_2samples >>> x = np.random.normal(loc=8.5, scale=2.5, size=37) >>> y = np.random.normal(loc=8.0, scale=3.0, size=37) >>> pp_x = sm.ProbPlot(x) >>> pp_y = sm.ProbPlot(y) >>> qqplot_2samples(pp_x, pp_y) >>> plt.show() .. plot:: plots/graphics_gofplots_qqplot_2samples.py >>> fig = qqplot_2samples(pp_x, pp_y, xlabel=None, ylabel=None, ... line=None, ax=None) """ if not isinstance(data1, ProbPlot): data1 = ProbPlot(data1) if not isinstance(data2, ProbPlot): data2 = ProbPlot(data2) if data2.data.shape[0] >= data1.data.shape[0]: fig = data1.qqplot( xlabel=xlabel, ylabel=ylabel, line=line, other=data2, ax=ax ) else: fig = data2.qqplot( xlabel=ylabel, ylabel=xlabel, line=line, other=data1, ax=ax ) return fig def qqline(ax, line, x=None, y=None, dist=None, fmt="r-", **lineoptions): """ Plot a reference line for a qqplot. Parameters ---------- ax : matplotlib axes instance The axes on which to plot the line line : str {"45","r","s","q"} Options for the reference line to which the data is compared.: - "45" - 45-degree line - "s" - standardized line, the expected order statistics are scaled by the standard deviation of the given sample and have the mean added to them - "r" - A regression line is fit - "q" - A line is fit through the quartiles. - None - By default no reference line is added to the plot. x : ndarray X data for plot. Not needed if line is "45". y : ndarray Y data for plot. Not needed if line is "45". dist : scipy.stats.distribution A scipy.stats distribution, needed if line is "q". fmt : str, optional Line format string passed to `plot`. **lineoptions Additional arguments to be passed to the `plot` command. Notes ----- There is no return value. The line is plotted on the given `ax`. Examples -------- Import the food expenditure dataset. Plot annual food expenditure on x-axis and household income on y-axis. Use qqline to add regression line into the plot. >>> import statsmodels.api as sm >>> import numpy as np >>> import matplotlib.pyplot as plt >>> from statsmodels.graphics.gofplots import qqline >>> foodexp = sm.datasets.engel.load(as_pandas=False) >>> x = foodexp.exog >>> y = foodexp.endog >>> ax = plt.subplot(111) >>> plt.scatter(x, y) >>> ax.set_xlabel(foodexp.exog_name[0]) >>> ax.set_ylabel(foodexp.endog_name) >>> qqline(ax, "r", x, y) >>> plt.show() .. plot:: plots/graphics_gofplots_qqplot_qqline.py """ if line == "45": end_pts = lzip(ax.get_xlim(), ax.get_ylim()) end_pts[0] = min(end_pts[0]) end_pts[1] = max(end_pts[1]) ax.plot(end_pts, end_pts, fmt, **lineoptions) ax.set_xlim(end_pts) ax.set_ylim(end_pts) return # does this have any side effects? if x is None or y is None: raise ValueError("If line is not 45, x and y cannot be None.") x = np.array(x) y = np.array(y) if line == "r": # could use ax.lines[0].get_xdata(), get_ydata(), # but don't know axes are "clean" y = OLS(y, add_constant(x)).fit().fittedvalues ax.plot(x, y, fmt, **lineoptions) elif line == "s": m, b = np.std(y), np.mean(y) ref_line = x * m + b ax.plot(x, ref_line, fmt, **lineoptions) elif line == "q": _check_for(dist, "ppf") q25 = stats.scoreatpercentile(y, 25) q75 = stats.scoreatpercentile(y, 75) theoretical_quartiles = dist.ppf([0.25, 0.75]) m = (q75 - q25) / np.diff(theoretical_quartiles) b = q25 - m * theoretical_quartiles[0] ax.plot(x, m * x + b, fmt, **lineoptions) # about 10x faster than plotting_position in sandbox and mstats def plotting_pos(nobs, a=0.0, b=None): """ Generates sequence of plotting positions Parameters ---------- nobs : int Number of probability points to plot a : float, default 0.0 alpha parameter for the plotting position of an expected order statistic b : float, default None beta parameter for the plotting position of an expected order statistic. If None, then b is set to a. Returns ------- ndarray The plotting positions Notes ----- The plotting positions are given by (i - a)/(nobs + 1 - a - b) for i in range(1, nobs+1) See Also -------- scipy.stats.mstats.plotting_positions Additional information on alpha and beta """ b = a if b is None else b return (np.arange(1.0, nobs + 1) - a) / (nobs + 1 - a - b) def _fmt_probplot_axis(ax, dist, nobs): """ Formats a theoretical quantile axis to display the corresponding probabilities on the quantiles' scale. Parameters ---------- ax : AxesSubplot, optional The axis to be formatted nobs : scalar Number of observations in the sample dist : scipy.stats.distribution A scipy.stats distribution sufficiently specified to implement its ppf() method. Returns ------- There is no return value. This operates on `ax` in place """ _check_for(dist, "ppf") axis_probs = np.linspace(10, 90, 9, dtype=float) small = np.array([1.0, 2, 5]) axis_probs = np.r_[small, axis_probs, 100 - small[::-1]] if nobs >= 50: axis_probs = np.r_[small / 10, axis_probs, 100 - small[::-1] / 10] if nobs >= 500: axis_probs = np.r_[small / 100, axis_probs, 100 - small[::-1] / 100] axis_probs /= 100.0 axis_qntls = dist.ppf(axis_probs) ax.set_xticks(axis_qntls) ax.set_xticklabels( axis_probs * 100, rotation=45, rotation_mode="anchor", horizontalalignment="right", verticalalignment="center", ) ax.set_xlim([axis_qntls.min(), axis_qntls.max()]) def _do_plot( x, y, dist=None, line=None, ax=None, fmt="bo", step=False, **kwargs ): """ Boiler plate plotting function for the `ppplot`, `qqplot`, and `probplot` methods of the `ProbPlot` class Parameters ---------- x : array_like X-axis data to be plotted y : array_like Y-axis data to be plotted dist : scipy.stats.distribution A scipy.stats distribution, needed if `line` is "q". line : {"45", "s", "r", "q", None}, default None Options for the reference line to which the data is compared. ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. fmt : str, optional matplotlib-compatible formatting string for the data markers kwargs : keywords These are passed to matplotlib.plot Returns ------- fig : Figure The figure containing `ax`. ax : AxesSubplot The original axes if provided. Otherwise a new instance. """ plot_style = { "marker": "o", "markerfacecolor": "blue", "linestyle": "none", } plot_style.update(**kwargs) where = plot_style.pop("where", "pre") fig, ax = utils.create_mpl_ax(ax) ax.set_xmargin(0.02) if step: ax.step(x, y, where=where, **plot_style) else: ax.plot(x, y, fmt, **plot_style) if line: if line not in ["r", "q", "45", "s"]: msg = "%s option for line not understood" % line raise ValueError(msg) qqline(ax, line, x=x, y=y, dist=dist) return fig, ax def _check_for(dist, attr="ppf"): if not hasattr(dist, attr): raise AttributeError(f"distribution must have a {attr} method") statsmodels-0.12.2/statsmodels/graphics/mosaicplot.py000066400000000000000000000645011400612667500230410ustar00rootroot00000000000000"""Create a mosaic plot from a contingency table. It allows to visualize multivariate categorical data in a rigorous and informative way. see the docstring of the mosaic function for more informations. """ # Author: Enrico Giampieri - 21 Jan 2013 from statsmodels.compat.python import lrange, lzip import numpy as np from itertools import product from numpy import iterable, r_, cumsum, array from statsmodels.graphics import utils from pandas import DataFrame __all__ = ["mosaic"] def _normalize_split(proportion): """ return a list of proportions of the available space given the division if only a number is given, it will assume a split in two pieces """ if not iterable(proportion): if proportion == 0: proportion = array([0.0, 1.0]) elif proportion >= 1: proportion = array([1.0, 0.0]) elif proportion < 0: raise ValueError("proportions should be positive," "given value: {}".format(proportion)) else: proportion = array([proportion, 1.0 - proportion]) proportion = np.asarray(proportion, dtype=float) if np.any(proportion < 0): raise ValueError("proportions should be positive," "given value: {}".format(proportion)) if np.allclose(proportion, 0): raise ValueError("at least one proportion should be " "greater than zero".format(proportion)) # ok, data are meaningful, so go on if len(proportion) < 2: return array([0.0, 1.0]) left = r_[0, cumsum(proportion)] left /= left[-1] * 1.0 return left def _split_rect(x, y, width, height, proportion, horizontal=True, gap=0.05): """ Split the given rectangle in n segments whose proportion is specified along the given axis if a gap is inserted, they will be separated by a certain amount of space, retaining the relative proportion between them a gap of 1 correspond to a plot that is half void and the remaining half space is proportionally divided among the pieces. """ x, y, w, h = float(x), float(y), float(width), float(height) if (w < 0) or (h < 0): raise ValueError("dimension of the square less than" "zero w={} h=()".format(w, h)) proportions = _normalize_split(proportion) # extract the starting point and the dimension of each subdivision # in respect to the unit square starting = proportions[:-1] amplitude = proportions[1:] - starting # how much each extrema is going to be displaced due to gaps starting += gap * np.arange(len(proportions) - 1) # how much the squares plus the gaps are extended extension = starting[-1] + amplitude[-1] - starting[0] # normalize everything for fit again in the original dimension starting /= extension amplitude /= extension # bring everything to the original square starting = (x if horizontal else y) + starting * (w if horizontal else h) amplitude = amplitude * (w if horizontal else h) # create each 4-tuple for each new block results = [(s, y, a, h) if horizontal else (x, s, w, a) for s, a in zip(starting, amplitude)] return results def _reduce_dict(count_dict, partial_key): """ Make partial sum on a counter dict. Given a match for the beginning of the category, it will sum each value. """ L = len(partial_key) count = sum(v for k, v in count_dict.items() if k[:L] == partial_key) return count def _key_splitting(rect_dict, keys, values, key_subset, horizontal, gap): """ Given a dictionary where each entry is a rectangle, a list of key and value (count of elements in each category) it split each rect accordingly, as long as the key start with the tuple key_subset. The other keys are returned without modification. """ result = {} L = len(key_subset) for name, (x, y, w, h) in rect_dict.items(): if key_subset == name[:L]: # split base on the values given divisions = _split_rect(x, y, w, h, values, horizontal, gap) for key, rect in zip(keys, divisions): result[name + (key,)] = rect else: result[name] = (x, y, w, h) return result def _tuplify(obj): """convert an object in a tuple of strings (even if it is not iterable, like a single integer number, but keep the string healthy) """ if np.iterable(obj) and not isinstance(obj, str): res = tuple(str(o) for o in obj) else: res = (str(obj),) return res def _categories_level(keys): """use the Ordered dict to implement a simple ordered set return each level of each category [[key_1_level_1,key_2_level_1],[key_1_level_2,key_2_level_2]] """ res = [] for i in zip(*(keys)): tuplefied = _tuplify(i) res.append(list(dict([(j, None) for j in tuplefied]))) return res def _hierarchical_split(count_dict, horizontal=True, gap=0.05): """ Split a square in a hierarchical way given a contingency table. Hierarchically split the unit square in alternate directions in proportion to the subdivision contained in the contingency table count_dict. This is the function that actually perform the tiling for the creation of the mosaic plot. If the gap array has been specified it will insert a corresponding amount of space (proportional to the unit length), while retaining the proportionality of the tiles. Parameters ---------- count_dict : dict Dictionary containing the contingency table. Each category should contain a non-negative number with a tuple as index. It expects that all the combination of keys to be represents; if that is not true, will automatically consider the missing values as 0 horizontal : bool The starting direction of the split (by default along the horizontal axis) gap : float or array of floats The list of gaps to be applied on each subdivision. If the length of the given array is less of the number of subcategories (or if it's a single number) it will extend it with exponentially decreasing gaps Returns --------- base_rect : dict A dictionary containing the result of the split. To each key is associated a 4-tuple of coordinates that are required to create the corresponding rectangle: 0 - x position of the lower left corner 1 - y position of the lower left corner 2 - width of the rectangle 3 - height of the rectangle """ # this is the unit square that we are going to divide base_rect = dict([(tuple(), (0, 0, 1, 1))]) # get the list of each possible value for each level categories_levels = _categories_level(list(count_dict.keys())) L = len(categories_levels) # recreate the gaps vector starting from an int if not np.iterable(gap): gap = [gap / 1.5 ** idx for idx in range(L)] # extend if it's too short if len(gap) < L: last = gap[-1] gap = list(*gap) + [last / 1.5 ** idx for idx in range(L)] # trim if it's too long gap = gap[:L] # put the count dictionay in order for the keys # this will allow some code simplification count_ordered = dict([(k, count_dict[k]) for k in list(product(*categories_levels))]) for cat_idx, cat_enum in enumerate(categories_levels): # get the partial key up to the actual level base_keys = list(product(*categories_levels[:cat_idx])) for key in base_keys: # for each partial and each value calculate how many # observation we have in the counting dictionary part_count = [_reduce_dict(count_ordered, key + (partial,)) for partial in cat_enum] # reduce the gap for subsequents levels new_gap = gap[cat_idx] # split the given subkeys in the rectangle dictionary base_rect = _key_splitting(base_rect, cat_enum, part_count, key, horizontal, new_gap) horizontal = not horizontal return base_rect def _single_hsv_to_rgb(hsv): """Transform a color from the hsv space to the rgb.""" from matplotlib.colors import hsv_to_rgb return hsv_to_rgb(array(hsv).reshape(1, 1, 3)).reshape(3) def _create_default_properties(data): """"Create the default properties of the mosaic given the data first it will varies the color hue (first category) then the color saturation (second category) and then the color value (third category). If a fourth category is found, it will put decoration on the rectangle. Does not manage more than four level of categories """ categories_levels = _categories_level(list(data.keys())) Nlevels = len(categories_levels) # first level, the hue L = len(categories_levels[0]) # hue = np.linspace(1.0, 0.0, L+1)[:-1] hue = np.linspace(0.0, 1.0, L + 2)[:-2] # second level, the saturation L = len(categories_levels[1]) if Nlevels > 1 else 1 saturation = np.linspace(0.5, 1.0, L + 1)[:-1] # third level, the value L = len(categories_levels[2]) if Nlevels > 2 else 1 value = np.linspace(0.5, 1.0, L + 1)[:-1] # fourth level, the hatch L = len(categories_levels[3]) if Nlevels > 3 else 1 hatch = ['', '/', '-', '|', '+'][:L + 1] # convert in list and merge with the levels hue = lzip(list(hue), categories_levels[0]) saturation = lzip(list(saturation), categories_levels[1] if Nlevels > 1 else ['']) value = lzip(list(value), categories_levels[2] if Nlevels > 2 else ['']) hatch = lzip(list(hatch), categories_levels[3] if Nlevels > 3 else ['']) # create the properties dictionary properties = {} for h, s, v, t in product(hue, saturation, value, hatch): hv, hn = h sv, sn = s vv, vn = v tv, tn = t level = (hn,) + ((sn,) if sn else tuple()) level = level + ((vn,) if vn else tuple()) level = level + ((tn,) if tn else tuple()) hsv = array([hv, sv, vv]) prop = {'color': _single_hsv_to_rgb(hsv), 'hatch': tv, 'lw': 0} properties[level] = prop return properties def _normalize_data(data, index): """normalize the data to a dict with tuples of strings as keys right now it works with: 0 - dictionary (or equivalent mappable) 1 - pandas.Series with simple or hierarchical indexes 2 - numpy.ndarrays 3 - everything that can be converted to a numpy array 4 - pandas.DataFrame (via the _normalize_dataframe function) """ # if data is a dataframe we need to take a completely new road # before coming back here. Use the hasattr to avoid importing # pandas explicitly if hasattr(data, 'pivot') and hasattr(data, 'groupby'): data = _normalize_dataframe(data, index) index = None # can it be used as a dictionary? try: items = list(data.items()) except AttributeError: # ok, I cannot use the data as a dictionary # Try to convert it to a numpy array, or die trying data = np.asarray(data) temp = {} for idx in np.ndindex(data.shape): name = tuple(i for i in idx) temp[name] = data[idx] data = temp items = list(data.items()) # make all the keys a tuple, even if simple numbers data = dict([_tuplify(k), v] for k, v in items) categories_levels = _categories_level(list(data.keys())) # fill the void in the counting dictionary indexes = product(*categories_levels) contingency = dict([(k, data.get(k, 0)) for k in indexes]) data = contingency # reorder the keys order according to the one specified by the user # or if the index is None convert it into a simple list # right now it does not do any check, but can be modified in the future index = lrange(len(categories_levels)) if index is None else index contingency = {} for key, value in data.items(): new_key = tuple(key[i] for i in index) contingency[new_key] = value data = contingency return data def _normalize_dataframe(dataframe, index): """Take a pandas DataFrame and count the element present in the given columns, return a hierarchical index on those columns """ #groupby the given keys, extract the same columns and count the element # then collapse them with a mean data = dataframe[index].dropna() grouped = data.groupby(index, sort=False) counted = grouped[index].count() averaged = counted.mean(axis=1) # Fill empty missing with 0, see GH5639 averaged = averaged.fillna(0.0) return averaged def _statistical_coloring(data): """evaluate colors from the indipendence properties of the matrix It will encounter problem if one category has all zeros """ data = _normalize_data(data, None) categories_levels = _categories_level(list(data.keys())) Nlevels = len(categories_levels) total = 1.0 * sum(v for v in data.values()) # count the proportion of observation # for each level that has the given name # at each level levels_count = [] for level_idx in range(Nlevels): proportion = {} for level in categories_levels[level_idx]: proportion[level] = 0.0 for key, value in data.items(): if level == key[level_idx]: proportion[level] += value proportion[level] /= total levels_count.append(proportion) # for each key I obtain the expected value # and it's standard deviation from a binomial distribution # under the hipothesys of independence expected = {} for key, value in data.items(): base = 1.0 for i, k in enumerate(key): base *= levels_count[i][k] expected[key] = base * total, np.sqrt(total * base * (1.0 - base)) # now we have the standard deviation of distance from the # expected value for each tile. We create the colors from this sigmas = dict((k, (data[k] - m) / s) for k, (m, s) in expected.items()) props = {} for key, dev in sigmas.items(): red = 0.0 if dev < 0 else (dev / (1 + dev)) blue = 0.0 if dev > 0 else (dev / (-1 + dev)) green = (1.0 - red - blue) / 2.0 hatch = 'x' if dev > 2 else 'o' if dev < -2 else '' props[key] = {'color': [red, green, blue], 'hatch': hatch} return props def _get_position(x, w, h, W): if W == 0: return x return (x + w / 2.0) * w * h / W def _create_labels(rects, horizontal, ax, rotation): """find the position of the label for each value of each category right now it supports only up to the four categories ax: the axis on which the label should be applied rotation: the rotation list for each side """ categories = _categories_level(list(rects.keys())) if len(categories) > 4: msg = ("maximum of 4 level supported for axes labeling... and 4" "is already a lot of levels, are you sure you need them all?") raise ValueError(msg) labels = {} #keep it fixed as will be used a lot of times items = list(rects.items()) vertical = not horizontal #get the axis ticks and labels locator to put the correct values! ax2 = ax.twinx() ax3 = ax.twiny() #this is the order of execution for horizontal disposition ticks_pos = [ax.set_xticks, ax.set_yticks, ax3.set_xticks, ax2.set_yticks] ticks_lab = [ax.set_xticklabels, ax.set_yticklabels, ax3.set_xticklabels, ax2.set_yticklabels] #for the vertical one, rotate it by one if vertical: ticks_pos = ticks_pos[1:] + ticks_pos[:1] ticks_lab = ticks_lab[1:] + ticks_lab[:1] #clean them for pos, lab in zip(ticks_pos, ticks_lab): pos([]) lab([]) #for each level, for each value in the level, take the mean of all #the sublevel that correspond to that partial key for level_idx, level in enumerate(categories): #this dictionary keep the labels only for this level level_ticks = dict() for value in level: #to which level it should refer to get the preceding #values of labels? it's rather a tricky question... #this is dependent on the side. It's a very crude management #but I couldn't think a more general way... if horizontal: if level_idx == 3: index_select = [-1, -1, -1] else: index_select = [+0, -1, -1] else: if level_idx == 3: index_select = [+0, -1, +0] else: index_select = [-1, -1, -1] #now I create the base key name and append the current value #It will search on all the rects to find the corresponding one #and use them to evaluate the mean position basekey = tuple(categories[i][index_select[i]] for i in range(level_idx)) basekey = basekey + (value,) subset = dict((k, v) for k, v in items if basekey == k[:level_idx + 1]) #now I extract the center of all the tiles and make a weighted #mean of all these center on the area of the tile #this should give me the (more or less) correct position #of the center of the category vals = list(subset.values()) W = sum(w * h for (x, y, w, h) in vals) x_lab = sum(_get_position(x, w, h, W) for (x, y, w, h) in vals) y_lab = sum(_get_position(y, h, w, W) for (x, y, w, h) in vals) #now base on the ordering, select which position to keep #needs to be written in a more general form of 4 level are enough? #should give also the horizontal and vertical alignment side = (level_idx + vertical) % 4 level_ticks[value] = y_lab if side % 2 else x_lab #now we add the labels of this level to the correct axis ticks_pos[level_idx](list(level_ticks.values())) ticks_lab[level_idx](list(level_ticks.keys()), rotation=rotation[level_idx]) return labels def mosaic(data, index=None, ax=None, horizontal=True, gap=0.005, properties=lambda key: None, labelizer=None, title='', statistic=False, axes_label=True, label_rotation=0.0): """Create a mosaic plot from a contingency table. It allows to visualize multivariate categorical data in a rigorous and informative way. Parameters ---------- data : {dict, Series, ndarray, DataFrame} The contingency table that contains the data. Each category should contain a non-negative number with a tuple as index. It expects that all the combination of keys to be represents; if that is not true, will automatically consider the missing values as 0. The order of the keys will be the same as the one of insertion. If a dict of a Series (or any other dict like object) is used, it will take the keys as labels. If a np.ndarray is provided, it will generate a simple numerical labels. index : list, optional Gives the preferred order for the category ordering. If not specified will default to the given order. It does not support named indexes for hierarchical Series. If a DataFrame is provided, it expects a list with the name of the columns. ax : Axes, optional The graph where display the mosaic. If not given, will create a new figure horizontal : bool, optional The starting direction of the split (by default along the horizontal axis) gap : {float, sequence[float]} The list of gaps to be applied on each subdivision. If the length of the given array is less of the number of subcategories (or if it's a single number) it will extend it with exponentially decreasing gaps properties : dict[str, callable], optional A function that for each tile in the mosaic take the key of the tile and returns the dictionary of properties of the generated Rectangle, like color, hatch or similar. A default properties set will be provided fot the keys whose color has not been defined, and will use color variation to help visually separates the various categories. It should return None to indicate that it should use the default property for the tile. A dictionary of the properties for each key can be passed, and it will be internally converted to the correct function labelizer : dict[str, callable], optional A function that generate the text to display at the center of each tile base on the key of that tile title : str, optional The title of the axis statistic : bool, optional If true will use a crude statistical model to give colors to the plot. If the tile has a constraint that is more than 2 standard deviation from the expected value under independence hypothesis, it will go from green to red (for positive deviations, blue otherwise) and will acquire an hatching when crosses the 3 sigma. axes_label : bool, optional Show the name of each value of each category on the axis (default) or hide them. label_rotation : {float, list[float]} The rotation of the axis label (if present). If a list is given each axis can have a different rotation Returns --------- fig : Figure The figure containing the plot. rects : dict A dictionary that has the same keys of the original dataset, that holds a reference to the coordinates of the tile and the Rectangle that represent it. References ---------- A Brief History of the Mosaic Display Michael Friendly, York University, Psychology Department Journal of Computational and Graphical Statistics, 2001 Mosaic Displays for Loglinear Models. Michael Friendly, York University, Psychology Department Proceedings of the Statistical Graphics Section, 1992, 61-68. Mosaic displays for multi-way contingency tables. Michael Friendly, York University, Psychology Department Journal of the american statistical association March 1994, Vol. 89, No. 425, Theory and Methods Examples ---------- >>> import numpy as np >>> import pandas as pd >>> import matplotlib.pyplot as plt >>> from statsmodels.graphics.mosaicplot import mosaic The most simple use case is to take a dictionary and plot the result >>> data = {'a': 10, 'b': 15, 'c': 16} >>> mosaic(data, title='basic dictionary') >>> plt.show() A more useful example is given by a dictionary with multiple indices. In this case we use a wider gap to a better visual separation of the resulting plot >>> data = {('a', 'b'): 1, ('a', 'c'): 2, ('d', 'b'): 3, ('d', 'c'): 4} >>> mosaic(data, gap=0.05, title='complete dictionary') >>> plt.show() The same data can be given as a simple or hierarchical indexed Series >>> rand = np.random.random >>> from itertools import product >>> tuples = list(product(['bar', 'baz', 'foo', 'qux'], ['one', 'two'])) >>> index = pd.MultiIndex.from_tuples(tuples, names=['first', 'second']) >>> data = pd.Series(rand(8), index=index) >>> mosaic(data, title='hierarchical index series') >>> plt.show() The third accepted data structure is the np array, for which a very simple index will be created. >>> rand = np.random.random >>> data = 1+rand((2,2)) >>> mosaic(data, title='random non-labeled array') >>> plt.show() If you need to modify the labeling and the coloring you can give a function tocreate the labels and one with the graphical properties starting from the key tuple >>> data = {'a': 10, 'b': 15, 'c': 16} >>> props = lambda key: {'color': 'r' if 'a' in key else 'gray'} >>> labelizer = lambda k: {('a',): 'first', ('b',): 'second', ... ('c',): 'third'}[k] >>> mosaic(data, title='colored dictionary', properties=props, ... labelizer=labelizer) >>> plt.show() Using a DataFrame as source, specifying the name of the columns of interest >>> gender = ['male', 'male', 'male', 'female', 'female', 'female'] >>> pet = ['cat', 'dog', 'dog', 'cat', 'dog', 'cat'] >>> data = pd.DataFrame({'gender': gender, 'pet': pet}) >>> mosaic(data, ['pet', 'gender'], title='DataFrame as Source') >>> plt.show() .. plot :: plots/graphics_mosaicplot_mosaic.py """ if isinstance(data, DataFrame) and index is None: raise ValueError("You must pass an index if data is a DataFrame." " See examples.") from matplotlib.patches import Rectangle #from pylab import Rectangle fig, ax = utils.create_mpl_ax(ax) # normalize the data to a dict with tuple of strings as keys data = _normalize_data(data, index) # split the graph into different areas rects = _hierarchical_split(data, horizontal=horizontal, gap=gap) # if there is no specified way to create the labels # create a default one if labelizer is None: labelizer = lambda k: "\n".join(k) if statistic: default_props = _statistical_coloring(data) else: default_props = _create_default_properties(data) if isinstance(properties, dict): color_dict = properties properties = lambda key: color_dict.get(key, None) for k, v in rects.items(): # create each rectangle and put a label on it x, y, w, h = v conf = properties(k) props = conf if conf else default_props[k] text = labelizer(k) Rect = Rectangle((x, y), w, h, label=text, **props) ax.add_patch(Rect) ax.text(x + w / 2, y + h / 2, text, ha='center', va='center', size='smaller') #creating the labels on the axis #o clearing it if axes_label: if np.iterable(label_rotation): rotation = label_rotation else: rotation = [label_rotation] * 4 labels = _create_labels(rects, horizontal, ax, rotation) else: ax.set_xticks([]) ax.set_xticklabels([]) ax.set_yticks([]) ax.set_yticklabels([]) ax.set_title(title) return fig, rects statsmodels-0.12.2/statsmodels/graphics/plot_grids.py000066400000000000000000000136521400612667500230360ustar00rootroot00000000000000'''create scatterplot with confidence ellipsis Author: Josef Perktold License: BSD-3 TODO: update script to use sharex, sharey, and visible=False see https://www.scipy.org/Cookbook/Matplotlib/Multiple_Subplots_with_One_Axis_Label for sharex I need to have the ax of the last_row when editing the earlier rows. Or you axes_grid1, imagegrid http://matplotlib.sourceforge.net/mpl_toolkits/axes_grid/users/overview.html ''' import numpy as np from scipy import stats from . import utils __all__ = ['scatter_ellipse'] def _make_ellipse(mean, cov, ax, level=0.95, color=None): """Support function for scatter_ellipse.""" from matplotlib.patches import Ellipse v, w = np.linalg.eigh(cov) u = w[0] / np.linalg.norm(w[0]) angle = np.arctan(u[1]/u[0]) angle = 180 * angle / np.pi # convert to degrees v = 2 * np.sqrt(v * stats.chi2.ppf(level, 2)) #get size corresponding to level ell = Ellipse(mean[:2], v[0], v[1], 180 + angle, facecolor='none', edgecolor=color, #ls='dashed', #for debugging lw=1.5) ell.set_clip_box(ax.bbox) ell.set_alpha(0.5) ax.add_artist(ell) def scatter_ellipse(data, level=0.9, varnames=None, ell_kwds=None, plot_kwds=None, add_titles=False, keep_ticks=False, fig=None): """Create a grid of scatter plots with confidence ellipses. ell_kwds, plot_kdes not used yet looks ok with 5 or 6 variables, too crowded with 8, too empty with 1 Parameters ---------- data : array_like Input data. level : scalar, optional Default is 0.9. varnames : list[str], optional Variable names. Used for y-axis labels, and if `add_titles` is True also for titles. If not given, integers 1..data.shape[1] are used. ell_kwds : dict, optional UNUSED plot_kwds : dict, optional UNUSED add_titles : bool, optional Whether or not to add titles to each subplot. Default is False. Titles are constructed from `varnames`. keep_ticks : bool, optional If False (default), remove all axis ticks. fig : Figure, optional If given, this figure is simply returned. Otherwise a new figure is created. Returns ------- Figure If `fig` is None, the created figure. Otherwise `fig` itself. Examples -------- >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> import numpy as np >>> from statsmodels.graphics.plot_grids import scatter_ellipse >>> data = sm.datasets.statecrime.load_pandas().data >>> fig = plt.figure(figsize=(8,8)) >>> scatter_ellipse(data, varnames=data.columns, fig=fig) >>> plt.show() ..plot :: plots/graphics_correlation_plot_corr_grid.py """ fig = utils.create_mpl_fig(fig) import matplotlib.ticker as mticker data = np.asanyarray(data) #needs mean and cov nvars = data.shape[1] if varnames is None: #assuming single digit, nvars<=10 else use 'var%2d' varnames = ['var%d' % i for i in range(nvars)] plot_kwds_ = dict(ls='none', marker='.', color='k', alpha=0.5) if plot_kwds: plot_kwds_.update(plot_kwds) ell_kwds_= dict(color='k') if ell_kwds: ell_kwds_.update(ell_kwds) dmean = data.mean(0) dcov = np.cov(data, rowvar=0) for i in range(1, nvars): #print '---' ax_last=None for j in range(i): #print i,j, i*(nvars-1)+j+1 ax = fig.add_subplot(nvars-1, nvars-1, (i-1)*(nvars-1)+j+1) ## #sharey=ax_last) #sharey does not allow empty ticks? ## if j == 0: ## print 'new ax_last', j ## ax_last = ax ## ax.set_ylabel(varnames[i]) #TODO: make sure we have same xlim and ylim formatter = mticker.FormatStrFormatter('% 3.1f') ax.yaxis.set_major_formatter(formatter) ax.xaxis.set_major_formatter(formatter) idx = np.array([j,i]) ax.plot(*data[:,idx].T, **plot_kwds_) if np.isscalar(level): level = [level] for alpha in level: _make_ellipse(dmean[idx], dcov[idx[:,None], idx], ax, level=alpha, **ell_kwds_) if add_titles: ax.set_title('%s-%s' % (varnames[i], varnames[j])) if not ax.is_first_col(): if not keep_ticks: ax.set_yticks([]) else: ax.yaxis.set_major_locator(mticker.MaxNLocator(3)) else: ax.set_ylabel(varnames[i]) if ax.is_last_row(): ax.set_xlabel(varnames[j]) else: if not keep_ticks: ax.set_xticks([]) else: ax.xaxis.set_major_locator(mticker.MaxNLocator(3)) dcorr = np.corrcoef(data, rowvar=0) dc = dcorr[idx[:,None], idx] xlim = ax.get_xlim() ylim = ax.get_ylim() ## xt = xlim[0] + 0.1 * (xlim[1] - xlim[0]) ## yt = ylim[0] + 0.1 * (ylim[1] - ylim[0]) ## if dc[1,0] < 0 : ## yt = ylim[0] + 0.1 * (ylim[1] - ylim[0]) ## else: ## yt = ylim[1] - 0.2 * (ylim[1] - ylim[0]) yrangeq = ylim[0] + 0.4 * (ylim[1] - ylim[0]) if dc[1,0] < -0.25 or (dc[1,0] < 0.25 and dmean[idx][1] > yrangeq): yt = ylim[0] + 0.1 * (ylim[1] - ylim[0]) else: yt = ylim[1] - 0.2 * (ylim[1] - ylim[0]) xt = xlim[0] + 0.1 * (xlim[1] - xlim[0]) ax.text(xt, yt, '$\\rho=%0.2f$'% dc[1,0]) for ax in fig.axes: if ax.is_last_row(): # or ax.is_first_col(): ax.xaxis.set_major_locator(mticker.MaxNLocator(3)) if ax.is_first_col(): ax.yaxis.set_major_locator(mticker.MaxNLocator(3)) return fig statsmodels-0.12.2/statsmodels/graphics/plottools.py000066400000000000000000000011721400612667500227210ustar00rootroot00000000000000import numpy as np def rainbow(n): """ Returns a list of colors sampled at equal intervals over the spectrum. Parameters ---------- n : int The number of colors to return Returns ------- R : (n,3) array An of rows of RGB color values Notes ----- Converts from HSV coordinates (0, 1, 1) to (1, 1, 1) to RGB. Based on the Sage function of the same name. """ from matplotlib import colors R = np.ones((1,n,3)) R[0,:,0] = np.linspace(0, 1, n, endpoint=False) #Note: could iterate and use colorsys.hsv_to_rgb return colors.hsv_to_rgb(R).squeeze() statsmodels-0.12.2/statsmodels/graphics/regressionplots.py000066400000000000000000001255501400612667500241330ustar00rootroot00000000000000'''Partial Regression plot and residual plots to find misspecification Author: Josef Perktold License: BSD-3 Created: 2011-01-23 update 2011-06-05 : start to convert example to usable functions 2011-10-27 : docstrings ''' from statsmodels.compat.python import lrange, lzip from statsmodels.compat.pandas import Appender import numpy as np import pandas as pd from patsy import dmatrix from statsmodels.regression.linear_model import OLS, GLS, WLS from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod.generalized_estimating_equations import GEE from statsmodels.sandbox.regression.predstd import wls_prediction_std from statsmodels.graphics import utils from statsmodels.nonparametric.smoothers_lowess import lowess from statsmodels.tools.tools import maybe_unwrap_results from ._regressionplots_doc import ( _plot_added_variable_doc, _plot_partial_residuals_doc, _plot_ceres_residuals_doc, _plot_influence_doc, _plot_leverage_resid2_doc) __all__ = ['plot_fit', 'plot_regress_exog', 'plot_partregress', 'plot_ccpr', 'plot_regress_exog', 'plot_partregress_grid', 'plot_ccpr_grid', 'add_lowess', 'abline_plot', 'influence_plot', 'plot_leverage_resid2', 'added_variable_resids', 'partial_resids', 'ceres_resids', 'plot_added_variable', 'plot_partial_residuals', 'plot_ceres_residuals'] #TODO: consider moving to influence module def _high_leverage(results): #TODO: replace 1 with k_constant return 2. * (results.df_model + 1)/results.nobs def add_lowess(ax, lines_idx=0, frac=.2, **lowess_kwargs): """ Add Lowess line to a plot. Parameters ---------- ax : AxesSubplot The Axes to which to add the plot lines_idx : int This is the line on the existing plot to which you want to add a smoothed lowess line. frac : float The fraction of the points to use when doing the lowess fit. lowess_kwargs Additional keyword arguments are passes to lowess. Returns ------- Figure The figure that holds the instance. """ y0 = ax.get_lines()[lines_idx]._y x0 = ax.get_lines()[lines_idx]._x lres = lowess(y0, x0, frac=frac, **lowess_kwargs) ax.plot(lres[:, 0], lres[:, 1], 'r', lw=1.5) return ax.figure def plot_fit(results, exog_idx, y_true=None, ax=None, vlines=True, **kwargs): """ Plot fit against one regressor. This creates one graph with the scatterplot of observed values compared to fitted values. Parameters ---------- results : Results A result instance with resid, model.endog and model.exog as attributes. exog_idx : {int, str} Name or index of regressor in exog matrix. y_true : array_like. optional If this is not None, then the array is added to the plot. ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. vlines : bool, optional If this not True, then the uncertainty of the fit is not plotted. **kwargs The keyword arguments are passed to the plot command for the fitted values points. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. Examples -------- Load the Statewide Crime data set and perform linear regression with `poverty` and `hs_grad` as variables and `murder` as the response >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> data = sm.datasets.statecrime.load_pandas().data >>> murder = data['murder'] >>> X = data[['poverty', 'hs_grad']] >>> X["constant"] = 1 >>> y = murder >>> model = sm.OLS(y, X) >>> results = model.fit() Create a plot just for the variable 'Poverty': >>> fig, ax = plt.subplots() >>> fig = sm.graphics.plot_fit(results, 0, ax=ax) >>> ax.set_ylabel("Murder Rate") >>> ax.set_xlabel("Poverty Level") >>> ax.set_title("Linear Regression") >>> plt.show() .. plot:: plots/graphics_plot_fit_ex.py """ fig, ax = utils.create_mpl_ax(ax) exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model) results = maybe_unwrap_results(results) #maybe add option for wendog, wexog y = results.model.endog x1 = results.model.exog[:, exog_idx] x1_argsort = np.argsort(x1) y = y[x1_argsort] x1 = x1[x1_argsort] ax.plot(x1, y, 'bo', label=results.model.endog_names) if y_true is not None: ax.plot(x1, y_true[x1_argsort], 'b-', label='True values') title = 'Fitted values versus %s' % exog_name ax.plot(x1, results.fittedvalues[x1_argsort], 'D', color='r', label='fitted', **kwargs) if vlines is True: _, iv_l, iv_u = wls_prediction_std(results) ax.vlines(x1, iv_l[x1_argsort], iv_u[x1_argsort], linewidth=1, color='k', alpha=.7) #ax.fill_between(x1, iv_l[x1_argsort], iv_u[x1_argsort], alpha=0.1, # color='k') ax.set_title(title) ax.set_xlabel(exog_name) ax.set_ylabel(results.model.endog_names) ax.legend(loc='best', numpoints=1) return fig def plot_regress_exog(results, exog_idx, fig=None): """Plot regression results against one regressor. This plots four graphs in a 2 by 2 figure: 'endog versus exog', 'residuals versus exog', 'fitted versus exog' and 'fitted plus residual versus exog' Parameters ---------- results : result instance A result instance with resid, model.endog and model.exog as attributes. exog_idx : int or str Name or index of regressor in exog matrix. fig : Figure, optional If given, this figure is simply returned. Otherwise a new figure is created. Returns ------- Figure The value of `fig` if provided. Otherwise a new instance. Examples -------- Load the Statewide Crime data set and build a model with regressors including the rate of high school graduation (hs_grad), population in urban areas (urban), households below poverty line (poverty), and single person households (single). Outcome variable is the murder rate (murder). Build a 2 by 2 figure based on poverty showing fitted versus actual murder rate, residuals versus the poverty rate, partial regression plot of poverty, and CCPR plot for poverty rate. >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plot >>> import statsmodels.formula.api as smf >>> fig = plt.figure(figsize=(8, 6)) >>> crime_data = sm.datasets.statecrime.load_pandas() >>> results = smf.ols('murder ~ hs_grad + urban + poverty + single', ... data=crime_data.data).fit() >>> sm.graphics.plot_regress_exog(results, 'poverty', fig=fig) >>> plt.show() .. plot:: plots/graphics_regression_regress_exog.py """ fig = utils.create_mpl_fig(fig) exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model) results = maybe_unwrap_results(results) #maybe add option for wendog, wexog y_name = results.model.endog_names x1 = results.model.exog[:, exog_idx] prstd, iv_l, iv_u = wls_prediction_std(results) ax = fig.add_subplot(2, 2, 1) ax.plot(x1, results.model.endog, 'o', color='b', alpha=0.9, label=y_name) ax.plot(x1, results.fittedvalues, 'D', color='r', label='fitted', alpha=.5) ax.vlines(x1, iv_l, iv_u, linewidth=1, color='k', alpha=.7) ax.set_title('Y and Fitted vs. X', fontsize='large') ax.set_xlabel(exog_name) ax.set_ylabel(y_name) ax.legend(loc='best') ax = fig.add_subplot(2, 2, 2) ax.plot(x1, results.resid, 'o') ax.axhline(y=0, color='black') ax.set_title('Residuals versus %s' % exog_name, fontsize='large') ax.set_xlabel(exog_name) ax.set_ylabel("resid") ax = fig.add_subplot(2, 2, 3) exog_noti = np.ones(results.model.exog.shape[1], bool) exog_noti[exog_idx] = False exog_others = results.model.exog[:, exog_noti] from pandas import Series fig = plot_partregress(results.model.data.orig_endog, Series(x1, name=exog_name, index=results.model.data.row_labels), exog_others, obs_labels=False, ax=ax) ax.set_title('Partial regression plot', fontsize='large') #ax.set_ylabel("Fitted values") #ax.set_xlabel(exog_name) ax = fig.add_subplot(2, 2, 4) fig = plot_ccpr(results, exog_idx, ax=ax) ax.set_title('CCPR Plot', fontsize='large') #ax.set_xlabel(exog_name) #ax.set_ylabel("Fitted values + resids") fig.suptitle('Regression Plots for %s' % exog_name, fontsize="large") fig.tight_layout() fig.subplots_adjust(top=.90) return fig def _partial_regression(endog, exog_i, exog_others): """Partial regression. regress endog on exog_i conditional on exog_others uses OLS Parameters ---------- endog : array_like exog : array_like exog_others : array_like Returns ------- res1c : OLS results instance (res1a, res1b) : tuple of OLS results instances results from regression of endog on exog_others and of exog_i on exog_others """ #FIXME: This function does not appear to be used. res1a = OLS(endog, exog_others).fit() res1b = OLS(exog_i, exog_others).fit() res1c = OLS(res1a.resid, res1b.resid).fit() return res1c, (res1a, res1b) def plot_partregress(endog, exog_i, exog_others, data=None, title_kwargs={}, obs_labels=True, label_kwargs={}, ax=None, ret_coords=False, **kwargs): """Plot partial regression for a single regressor. Parameters ---------- endog : {ndarray, str} The endogenous or response variable. If string is given, you can use a arbitrary translations as with a formula. exog_i : {ndarray, str} The exogenous, explanatory variable. If string is given, you can use a arbitrary translations as with a formula. exog_others : {ndarray, list[str]} Any other exogenous, explanatory variables. If a list of strings is given, each item is a term in formula. You can use a arbitrary translations as with a formula. The effect of these variables will be removed by OLS regression. data : {DataFrame, dict} Some kind of data structure with names if the other variables are given as strings. title_kwargs : dict Keyword arguments to pass on for the title. The key to control the fonts is fontdict. obs_labels : {bool, array_like} Whether or not to annotate the plot points with their observation labels. If obs_labels is a boolean, the point labels will try to do the right thing. First it will try to use the index of data, then fall back to the index of exog_i. Alternatively, you may give an array-like object corresponding to the observation numbers. label_kwargs : dict Keyword arguments that control annotate for the observation labels. ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. ret_coords : bool If True will return the coordinates of the points in the plot. You can use this to add your own annotations. **kwargs The keyword arguments passed to plot for the points. Returns ------- fig : Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. coords : list, optional If ret_coords is True, return a tuple of arrays (x_coords, y_coords). See Also -------- plot_partregress_grid : Plot partial regression for a set of regressors. Notes ----- The slope of the fitted line is the that of `exog_i` in the full multiple regression. The individual points can be used to assess the influence of points on the estimated coefficient. Examples -------- Load the Statewide Crime data set and plot partial regression of the rate of high school graduation (hs_grad) on the murder rate(murder). The effects of the percent of the population living in urban areas (urban), below the poverty line (poverty) , and in a single person household (single) are removed by OLS regression. >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> crime_data = sm.datasets.statecrime.load_pandas() >>> sm.graphics.plot_partregress(endog='murder', exog_i='hs_grad', ... exog_others=['urban', 'poverty', 'single'], ... data=crime_data.data, obs_labels=False) >>> plt.show() .. plot:: plots/graphics_regression_partregress.py More detailed examples can be found in the Regression Plots notebook on the examples page. """ #NOTE: there is no interaction between possible missing data and #obs_labels yet, so this will need to be tweaked a bit for this case fig, ax = utils.create_mpl_ax(ax) # strings, use patsy to transform to data if isinstance(endog, str): endog = dmatrix(endog + "-1", data) if isinstance(exog_others, str): RHS = dmatrix(exog_others, data) elif isinstance(exog_others, list): RHS = "+".join(exog_others) RHS = dmatrix(RHS, data) else: RHS = exog_others RHS_isemtpy = False if isinstance(RHS, np.ndarray) and RHS.size==0: RHS_isemtpy = True elif isinstance(RHS, pd.DataFrame) and RHS.empty: RHS_isemtpy = True if isinstance(exog_i, str): exog_i = dmatrix(exog_i + "-1", data) # all arrays or pandas-like if RHS_isemtpy: endog = np.asarray(endog) exog_i = np.asarray(exog_i) ax.plot(endog, exog_i, 'o', **kwargs) fitted_line = OLS(endog, exog_i).fit() x_axis_endog_name = 'x' if isinstance(exog_i, np.ndarray) else exog_i.name y_axis_endog_name = 'y' if isinstance(endog, np.ndarray) else endog.design_info.column_names[0] else: res_yaxis = OLS(endog, RHS).fit() res_xaxis = OLS(exog_i, RHS).fit() xaxis_resid = res_xaxis.resid yaxis_resid = res_yaxis.resid x_axis_endog_name = res_xaxis.model.endog_names y_axis_endog_name = res_yaxis.model.endog_names ax.plot(xaxis_resid, yaxis_resid, 'o', **kwargs) fitted_line = OLS(yaxis_resid, xaxis_resid).fit() fig = abline_plot(0, fitted_line.params[0], color='k', ax=ax) if x_axis_endog_name == 'y': # for no names regression will just get a y x_axis_endog_name = 'x' # this is misleading, so use x ax.set_xlabel("e(%s | X)" % x_axis_endog_name) ax.set_ylabel("e(%s | X)" % y_axis_endog_name) ax.set_title('Partial Regression Plot', **title_kwargs) # NOTE: if we want to get super fancy, we could annotate if a point is # clicked using this widget # http://stackoverflow.com/questions/4652439/ # is-there-a-matplotlib-equivalent-of-matlabs-datacursormode/ # 4674445#4674445 if obs_labels is True: if data is not None: obs_labels = data.index elif hasattr(exog_i, "index"): obs_labels = exog_i.index else: obs_labels = res_xaxis.model.data.row_labels #NOTE: row_labels can be None. #Maybe we should fix this to never be the case. if obs_labels is None: obs_labels = lrange(len(exog_i)) if obs_labels is not False: # could be array_like if len(obs_labels) != len(exog_i): raise ValueError("obs_labels does not match length of exog_i") label_kwargs.update(dict(ha="center", va="bottom")) ax = utils.annotate_axes(lrange(len(obs_labels)), obs_labels, lzip(res_xaxis.resid, res_yaxis.resid), [(0, 5)] * len(obs_labels), "x-large", ax=ax, **label_kwargs) if ret_coords: return fig, (res_xaxis.resid, res_yaxis.resid) else: return fig def plot_partregress_grid(results, exog_idx=None, grid=None, fig=None): """ Plot partial regression for a set of regressors. Parameters ---------- results : Results instance A regression model results instance. exog_idx : {None, list[int], list[str]} The indices or column names of the exog used in the plot, default is all. grid : {None, tuple[int]} If grid is given, then it is used for the arrangement of the subplots. The format of grid is (nrows, ncols). If grid is None, then ncol is one, if there are only 2 subplots, and the number of columns is two otherwise. fig : Figure, optional If given, this figure is simply returned. Otherwise a new figure is created. Returns ------- Figure If `fig` is None, the created figure. Otherwise `fig` itself. See Also -------- plot_partregress : Plot partial regression for a single regressor. plot_ccpr : Plot CCPR against one regressor Notes ----- A subplot is created for each explanatory variable given by exog_idx. The partial regression plot shows the relationship between the response and the given explanatory variable after removing the effect of all other explanatory variables in exog. References ---------- See http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partregr.htm Examples -------- Using the state crime dataset separately plot the effect of the each variable on the on the outcome, murder rate while accounting for the effect of all other variables in the model visualized with a grid of partial regression plots. >>> from statsmodels.graphics.regressionplots import plot_partregress_grid >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> import statsmodels.formula.api as smf >>> fig = plt.figure(figsize=(8, 6)) >>> crime_data = sm.datasets.statecrime.load_pandas() >>> results = smf.ols('murder ~ hs_grad + urban + poverty + single', ... data=crime_data.data).fit() >>> plot_partregress_grid(results, fig=fig) >>> plt.show() .. plot:: plots/graphics_regression_partregress_grid.py """ import pandas fig = utils.create_mpl_fig(fig) exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model) # TODO: maybe add option for using wendog, wexog instead y = pandas.Series(results.model.endog, name=results.model.endog_names) exog = results.model.exog k_vars = exog.shape[1] # this function does not make sense if k_vars=1 nrows = (len(exog_idx) + 1) // 2 ncols = 1 if nrows == len(exog_idx) else 2 if grid is not None: nrows, ncols = grid if ncols > 1: title_kwargs = {"fontdict": {"fontsize": 'small'}} # for indexing purposes other_names = np.array(results.model.exog_names) for i, idx in enumerate(exog_idx): others = lrange(k_vars) others.pop(idx) exog_others = pandas.DataFrame(exog[:, others], columns=other_names[others]) ax = fig.add_subplot(nrows, ncols, i + 1) plot_partregress(y, pandas.Series(exog[:, idx], name=other_names[idx]), exog_others, ax=ax, title_kwargs=title_kwargs, obs_labels=False) ax.set_title("") fig.suptitle("Partial Regression Plot", fontsize="large") fig.tight_layout() fig.subplots_adjust(top=.95) return fig def plot_ccpr(results, exog_idx, ax=None): """ Plot CCPR against one regressor. Generates a component and component-plus-residual (CCPR) plot. Parameters ---------- results : result instance A regression results instance. exog_idx : {int, str} Exogenous, explanatory variable. If string is given, it should be the variable name that you want to use, and you can use arbitrary translations as with a formula. ax : AxesSubplot, optional If given, it is used to plot in instead of a new figure being created. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. See Also -------- plot_ccpr_grid : Creates CCPR plot for multiple regressors in a plot grid. Notes ----- The CCPR plot provides a way to judge the effect of one regressor on the response variable by taking into account the effects of the other independent variables. The partial residuals plot is defined as Residuals + B_i*X_i versus X_i. The component adds the B_i*X_i versus X_i to show where the fitted line would lie. Care should be taken if X_i is highly correlated with any of the other independent variables. If this is the case, the variance evident in the plot will be an underestimate of the true variance. References ---------- http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm Examples -------- Using the state crime dataset plot the effect of the rate of single households ('single') on the murder rate while accounting for high school graduation rate ('hs_grad'), percentage of people in an urban area, and rate of poverty ('poverty'). >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plot >>> import statsmodels.formula.api as smf >>> crime_data = sm.datasets.statecrime.load_pandas() >>> results = smf.ols('murder ~ hs_grad + urban + poverty + single', ... data=crime_data.data).fit() >>> sm.graphics.plot_ccpr(results, 'single') >>> plt.show() .. plot:: plots/graphics_regression_ccpr.py """ fig, ax = utils.create_mpl_ax(ax) exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model) results = maybe_unwrap_results(results) x1 = results.model.exog[:, exog_idx] #namestr = ' for %s' % self.name if self.name else '' x1beta = x1*results.params[exog_idx] ax.plot(x1, x1beta + results.resid, 'o') from statsmodels.tools.tools import add_constant mod = OLS(x1beta, add_constant(x1)).fit() params = mod.params fig = abline_plot(*params, **dict(ax=ax)) #ax.plot(x1, x1beta, '-') ax.set_title('Component and component plus residual plot') ax.set_ylabel("Residual + %s*beta_%d" % (exog_name, exog_idx)) ax.set_xlabel("%s" % exog_name) return fig def plot_ccpr_grid(results, exog_idx=None, grid=None, fig=None): """ Generate CCPR plots against a set of regressors, plot in a grid. Generates a grid of component and component-plus-residual (CCPR) plots. Parameters ---------- results : result instance A results instance with exog and params. exog_idx : None or list of int The indices or column names of the exog used in the plot. grid : None or tuple of int (nrows, ncols) If grid is given, then it is used for the arrangement of the subplots. If grid is None, then ncol is one, if there are only 2 subplots, and the number of columns is two otherwise. fig : Figure, optional If given, this figure is simply returned. Otherwise a new figure is created. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. See Also -------- plot_ccpr : Creates CCPR plot for a single regressor. Notes ----- Partial residual plots are formed as:: Res + Betahat(i)*Xi versus Xi and CCPR adds:: Betahat(i)*Xi versus Xi References ---------- See http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ccpr.htm Examples -------- Using the state crime dataset separately plot the effect of the each variable on the on the outcome, murder rate while accounting for the effect of all other variables in the model. >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> import statsmodels.formula.api as smf >>> fig = plt.figure(figsize=(8, 8)) >>> crime_data = sm.datasets.statecrime.load_pandas() >>> results = smf.ols('murder ~ hs_grad + urban + poverty + single', ... data=crime_data.data).fit() >>> sm.graphics.plot_ccpr_grid(results, fig=fig) >>> plt.show() .. plot:: plots/graphics_regression_ccpr_grid.py """ fig = utils.create_mpl_fig(fig) exog_name, exog_idx = utils.maybe_name_or_idx(exog_idx, results.model) if grid is not None: nrows, ncols = grid else: if len(exog_idx) > 2: nrows = int(np.ceil(len(exog_idx)/2.)) ncols = 2 else: nrows = len(exog_idx) ncols = 1 seen_constant = 0 for i, idx in enumerate(exog_idx): if results.model.exog[:, idx].var() == 0: seen_constant = 1 continue ax = fig.add_subplot(nrows, ncols, i+1-seen_constant) fig = plot_ccpr(results, exog_idx=idx, ax=ax) ax.set_title("") fig.suptitle("Component-Component Plus Residual Plot", fontsize="large") fig.tight_layout() fig.subplots_adjust(top=.95) return fig def abline_plot(intercept=None, slope=None, horiz=None, vert=None, model_results=None, ax=None, **kwargs): """ Plot a line given an intercept and slope. Parameters ---------- intercept : float The intercept of the line. slope : float The slope of the line. horiz : float or array_like Data for horizontal lines on the y-axis. vert : array_like Data for verterical lines on the x-axis. model_results : statsmodels results instance Any object that has a two-value `params` attribute. Assumed that it is (intercept, slope). ax : axes, optional Matplotlib axes instance. **kwargs Options passed to matplotlib.pyplot.plt. Returns ------- Figure The figure given by `ax.figure` or a new instance. Examples -------- >>> import numpy as np >>> import statsmodels.api as sm >>> np.random.seed(12345) >>> X = sm.add_constant(np.random.normal(0, 20, size=30)) >>> y = np.dot(X, [25, 3.5]) + np.random.normal(0, 30, size=30) >>> mod = sm.OLS(y,X).fit() >>> fig = sm.graphics.abline_plot(model_results=mod) >>> ax = fig.axes[0] >>> ax.scatter(X[:,1], y) >>> ax.margins(.1) >>> import matplotlib.pyplot as plt >>> plt.show() .. plot:: plots/graphics_regression_abline.py """ if ax is not None: # get axis limits first thing, do not change these x = ax.get_xlim() else: x = None fig, ax = utils.create_mpl_ax(ax) if model_results: intercept, slope = model_results.params if x is None: x = [model_results.model.exog[:, 1].min(), model_results.model.exog[:, 1].max()] else: if not (intercept is not None and slope is not None): raise ValueError("specify slope and intercepty or model_results") if x is None: x = ax.get_xlim() data_y = [x[0]*slope+intercept, x[1]*slope+intercept] ax.set_xlim(x) #ax.set_ylim(y) from matplotlib.lines import Line2D class ABLine2D(Line2D): def __init__(self, *args, **kwargs): super(ABLine2D, self).__init__(*args, **kwargs) self.id_xlim_callback = None self.id_ylim_callback = None def remove(self): ax = self.axes if self.id_xlim_callback: ax.callbacks.disconnect(self.id_xlim_callback) if self.id_ylim_callback: ax.callbacks.disconnect(self.id_ylim_callback) super(ABLine2D, self).remove() def update_datalim(self, ax): ax.set_autoscale_on(False) children = ax.get_children() ablines = [child for child in children if child is self] abline = ablines[0] x = ax.get_xlim() y = [x[0] * slope + intercept, x[1] * slope + intercept] abline.set_data(x, y) ax.figure.canvas.draw() # TODO: how to intercept something like a margins call and adjust? line = ABLine2D(x, data_y, **kwargs) ax.add_line(line) line.id_xlim_callback = ax.callbacks.connect('xlim_changed', line.update_datalim) line.id_ylim_callback = ax.callbacks.connect('ylim_changed', line.update_datalim) if horiz: ax.hline(horiz) if vert: ax.vline(vert) return fig @Appender(_plot_influence_doc.format(**{ 'extra_params_doc': "results: object\n" " Results for a fitted regression model.\n" " influence: instance\n" " The instance of Influence for model."})) def _influence_plot(results, influence, external=True, alpha=.05, criterion="cooks", size=48, plot_alpha=.75, ax=None, **kwargs): infl = influence fig, ax = utils.create_mpl_ax(ax) if criterion.lower().startswith('coo'): psize = infl.cooks_distance[0] elif criterion.lower().startswith('dff'): psize = np.abs(infl.dffits[0]) else: raise ValueError("Criterion %s not understood" % criterion) # scale the variables #TODO: what is the correct scaling and the assumption here? #we want plots to be comparable across different plots #so we would need to use the expected distribution of criterion probably old_range = np.ptp(psize) new_range = size**2 - 8**2 psize = (psize - psize.min()) * new_range/old_range + 8**2 leverage = infl.hat_matrix_diag if external: resids = infl.resid_studentized_external else: resids = infl.resid_studentized from scipy import stats cutoff = stats.t.ppf(1.-alpha/2, results.df_resid) large_resid = np.abs(resids) > cutoff large_leverage = leverage > _high_leverage(results) large_points = np.logical_or(large_resid, large_leverage) ax.scatter(leverage, resids, s=psize, alpha=plot_alpha) # add point labels labels = results.model.data.row_labels if labels is None: labels = lrange(len(resids)) ax = utils.annotate_axes(np.where(large_points)[0], labels, lzip(leverage, resids), lzip(-(psize/2)**.5, (psize/2)**.5), "x-large", ax) # TODO: make configurable or let people do it ex-post? font = {"fontsize": 16, "color": "black"} ax.set_ylabel("Studentized Residuals", **font) ax.set_xlabel("H Leverage", **font) ax.set_title("Influence Plot", **font) return fig @Appender(_plot_influence_doc.format(**{ 'extra_params_doc': "results : Results\n" " Results for a fitted regression model."})) def influence_plot(results, external=True, alpha=.05, criterion="cooks", size=48, plot_alpha=.75, ax=None, **kwargs): infl = results.get_influence() res = _influence_plot(results, infl, external=external, alpha=alpha, criterion=criterion, size=size, plot_alpha=plot_alpha, ax=ax, **kwargs) return res @Appender(_plot_leverage_resid2_doc.format({ 'extra_params_doc': "results: object\n" " Results for a fitted regression model\n" "influence: instance\n" " instance of Influence for model"})) def _plot_leverage_resid2(results, influence, alpha=.05, ax=None, **kwargs): from scipy.stats import zscore, norm fig, ax = utils.create_mpl_ax(ax) infl = influence leverage = infl.hat_matrix_diag resid = zscore(infl.resid) ax.plot(resid**2, leverage, 'o', **kwargs) ax.set_xlabel("Normalized residuals**2") ax.set_ylabel("Leverage") ax.set_title("Leverage vs. Normalized residuals squared") large_leverage = leverage > _high_leverage(results) #norm or t here if standardized? cutoff = norm.ppf(1.-alpha/2) large_resid = np.abs(resid) > cutoff labels = results.model.data.row_labels if labels is None: labels = lrange(int(results.nobs)) index = np.where(np.logical_or(large_leverage, large_resid))[0] ax = utils.annotate_axes(index, labels, lzip(resid**2, leverage), [(0, 5)]*int(results.nobs), "large", ax=ax, ha="center", va="bottom") ax.margins(.075, .075) return fig @Appender(_plot_leverage_resid2_doc.format({ 'extra_params_doc': "results : object\n" " Results for a fitted regression model"})) def plot_leverage_resid2(results, alpha=.05, ax=None, **kwargs): infl = results.get_influence() return _plot_leverage_resid2(results, infl, alpha=alpha, ax=ax, **kwargs) @Appender(_plot_added_variable_doc % { 'extra_params_doc': "results : object\n" " Results for a fitted regression model"}) def plot_added_variable(results, focus_exog, resid_type=None, use_glm_weights=True, fit_kwargs=None, ax=None): model = results.model fig, ax = utils.create_mpl_ax(ax) endog_resid, focus_exog_resid =\ added_variable_resids(results, focus_exog, resid_type=resid_type, use_glm_weights=use_glm_weights, fit_kwargs=fit_kwargs) ax.plot(focus_exog_resid, endog_resid, 'o', alpha=0.6) ax.set_title('Added variable plot', fontsize='large') if isinstance(focus_exog, str): xname = focus_exog else: xname = model.exog_names[focus_exog] ax.set_xlabel(xname, size=15) ax.set_ylabel(model.endog_names + " residuals", size=15) return fig @Appender(_plot_partial_residuals_doc % { 'extra_params_doc': "results : object\n" " Results for a fitted regression model"}) def plot_partial_residuals(results, focus_exog, ax=None): # Docstring attached below model = results.model focus_exog, focus_col = utils.maybe_name_or_idx(focus_exog, model) pr = partial_resids(results, focus_exog) focus_exog_vals = results.model.exog[:, focus_col] fig, ax = utils.create_mpl_ax(ax) ax.plot(focus_exog_vals, pr, 'o', alpha=0.6) ax.set_title('Partial residuals plot', fontsize='large') if isinstance(focus_exog, str): xname = focus_exog else: xname = model.exog_names[focus_exog] ax.set_xlabel(xname, size=15) ax.set_ylabel("Component plus residual", size=15) return fig @Appender(_plot_ceres_residuals_doc % { 'extra_params_doc': "results : Results\n" " Results instance of a fitted regression " "model."}) def plot_ceres_residuals(results, focus_exog, frac=0.66, cond_means=None, ax=None): model = results.model focus_exog, focus_col = utils.maybe_name_or_idx(focus_exog, model) presid = ceres_resids(results, focus_exog, frac=frac, cond_means=cond_means) focus_exog_vals = model.exog[:, focus_col] fig, ax = utils.create_mpl_ax(ax) ax.plot(focus_exog_vals, presid, 'o', alpha=0.6) ax.set_title('CERES residuals plot', fontsize='large') ax.set_xlabel(focus_exog, size=15) ax.set_ylabel("Component plus residual", size=15) return fig def ceres_resids(results, focus_exog, frac=0.66, cond_means=None): """ Calculate the CERES residuals (Conditional Expectation Partial Residuals) for a fitted model. Parameters ---------- results : model results instance The fitted model for which the CERES residuals are calculated. focus_exog : int The column of results.model.exog used as the 'focus variable'. frac : float, optional Lowess smoothing parameter for estimating the conditional means. Not used if `cond_means` is provided. cond_means : array_like, optional If provided, the columns of this array are the conditional means E[exog | focus exog], where exog ranges over some or all of the columns of exog other than focus exog. If this is an empty nx0 array, the conditional means are treated as being zero. If None, the conditional means are estimated. Returns ------- An array containing the CERES residuals. Notes ----- If `cond_means` is not provided, it is obtained by smoothing each column of exog (except the focus column) against the focus column. Currently only supports GLM, GEE, and OLS models. """ model = results.model if not isinstance(model, (GLM, GEE, OLS)): raise ValueError("ceres residuals not available for %s" % model.__class__.__name__) focus_exog, focus_col = utils.maybe_name_or_idx(focus_exog, model) # Indices of non-focus columns ix_nf = range(len(results.params)) ix_nf = list(ix_nf) ix_nf.pop(focus_col) nnf = len(ix_nf) # Estimate the conditional means if not provided. if cond_means is None: # Below we calculate E[x | focus] where x is each column other # than the focus column. We do not want the intercept when we do # this so we remove it here. pexog = model.exog[:, ix_nf] pexog -= pexog.mean(0) u, s, vt = np.linalg.svd(pexog, 0) ii = np.flatnonzero(s > 1e-6) pexog = u[:, ii] fcol = model.exog[:, focus_col] cond_means = np.empty((len(fcol), pexog.shape[1])) for j in range(pexog.shape[1]): # Get the fitted values for column i given the other # columns (skip the intercept). y0 = pexog[:, j] cf = lowess(y0, fcol, frac=frac, return_sorted=False) cond_means[:, j] = cf new_exog = np.concatenate((model.exog[:, ix_nf], cond_means), axis=1) # Refit the model using the adjusted exog values klass = model.__class__ init_kwargs = model._get_init_kwds() new_model = klass(model.endog, new_exog, **init_kwargs) new_result = new_model.fit() # The partial residual, with respect to l(x2) (notation of Cook 1998) presid = model.endog - new_result.fittedvalues if isinstance(model, (GLM, GEE)): presid *= model.family.link.deriv(new_result.fittedvalues) if new_exog.shape[1] > nnf: presid += np.dot(new_exog[:, nnf:], new_result.params[nnf:]) return presid def partial_resids(results, focus_exog): """ Returns partial residuals for a fitted model with respect to a 'focus predictor'. Parameters ---------- results : results instance A fitted regression model. focus col : int The column index of model.exog with respect to which the partial residuals are calculated. Returns ------- An array of partial residuals. References ---------- RD Cook and R Croos-Dabrera (1998). Partial residual plots in generalized linear models. Journal of the American Statistical Association, 93:442. """ # TODO: could be a method of results # TODO: see Cook et al (1998) for a more general definition # The calculation follows equation (8) from Cook's paper. model = results.model resid = model.endog - results.predict() if isinstance(model, (GLM, GEE)): resid *= model.family.link.deriv(results.fittedvalues) elif isinstance(model, (OLS, GLS, WLS)): pass # No need to do anything else: raise ValueError("Partial residuals for '%s' not implemented." % type(model)) if type(focus_exog) is str: focus_col = model.exog_names.index(focus_exog) else: focus_col = focus_exog focus_val = results.params[focus_col] * model.exog[:, focus_col] return focus_val + resid def added_variable_resids(results, focus_exog, resid_type=None, use_glm_weights=True, fit_kwargs=None): """ Residualize the endog variable and a 'focus' exog variable in a regression model with respect to the other exog variables. Parameters ---------- results : regression results instance A fitted model including the focus exog and all other predictors of interest. focus_exog : {int, str} The column of results.model.exog or a variable name that is to be residualized against the other predictors. resid_type : str The type of residuals to use for the dependent variable. If None, uses `resid_deviance` for GLM/GEE and `resid` otherwise. use_glm_weights : bool Only used if the model is a GLM or GEE. If True, the residuals for the focus predictor are computed using WLS, with the weights obtained from the IRLS calculations for fitting the GLM. If False, unweighted regression is used. fit_kwargs : dict, optional Keyword arguments to be passed to fit when refitting the model. Returns ------- endog_resid : array_like The residuals for the original exog focus_exog_resid : array_like The residuals for the focus predictor Notes ----- The 'focus variable' residuals are always obtained using linear regression. Currently only GLM, GEE, and OLS models are supported. """ model = results.model if not isinstance(model, (GEE, GLM, OLS)): raise ValueError("model type %s not supported for added variable residuals" % model.__class__.__name__) exog = model.exog endog = model.endog focus_exog, focus_col = utils.maybe_name_or_idx(focus_exog, model) focus_exog_vals = exog[:, focus_col] # Default residuals if resid_type is None: if isinstance(model, (GEE, GLM)): resid_type = "resid_deviance" else: resid_type = "resid" ii = range(exog.shape[1]) ii = list(ii) ii.pop(focus_col) reduced_exog = exog[:, ii] start_params = results.params[ii] klass = model.__class__ kwargs = model._get_init_kwds() new_model = klass(endog, reduced_exog, **kwargs) args = {"start_params": start_params} if fit_kwargs is not None: args.update(fit_kwargs) new_result = new_model.fit(**args) if not new_result.converged: raise ValueError("fit did not converge when calculating added variable residuals") try: endog_resid = getattr(new_result, resid_type) except AttributeError: raise ValueError("'%s' residual type not available" % resid_type) import statsmodels.regression.linear_model as lm if isinstance(model, (GLM, GEE)) and use_glm_weights: weights = model.family.weights(results.fittedvalues) if hasattr(model, "data_weights"): weights = weights * model.data_weights lm_results = lm.WLS(focus_exog_vals, reduced_exog, weights).fit() else: lm_results = lm.OLS(focus_exog_vals, reduced_exog).fit() focus_exog_resid = lm_results.resid return endog_resid, focus_exog_resid statsmodels-0.12.2/statsmodels/graphics/tests/000077500000000000000000000000001400612667500214515ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/graphics/tests/__init__.py000066400000000000000000000000001400612667500235500ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/graphics/tests/test_agreement.py000066400000000000000000000022541400612667500250340ustar00rootroot00000000000000import numpy as np import pandas as pd import pytest from statsmodels.graphics.agreement import mean_diff_plot try: import matplotlib.pyplot as plt except ImportError: pass @pytest.mark.matplotlib def test_mean_diff_plot(close_figures): # Seed the random number generator. # This ensures that the results below are reproducible. np.random.seed(11111) m1 = np.random.random(20) m2 = np.random.random(20) fig = plt.figure() ax = fig.add_subplot(111) # basic test. mean_diff_plot(m1, m2, ax=ax) # Test with pandas Series. p1 = pd.Series(m1) p2 = pd.Series(m2) mean_diff_plot(p1, p2) # Test plotting on assigned axis. fig, ax = plt.subplots(2) mean_diff_plot(m1, m2, ax=ax[0]) # Test the setting of confidence intervals. mean_diff_plot(m1, m2, sd_limit=0) # Test asethetic controls. mean_diff_plot(m1, m2, scatter_kwds={'color': 'green', 's': 10}) mean_diff_plot(m1, m2, mean_line_kwds={'color': 'green', 'lw': 5}) mean_diff_plot(m1, m2, limit_lines_kwds={'color': 'green', 'lw': 5, 'ls': 'dotted'}) statsmodels-0.12.2/statsmodels/graphics/tests/test_boxplots.py000066400000000000000000000065751400612667500247510ustar00rootroot00000000000000import numpy as np import pytest from statsmodels.graphics.boxplots import violinplot, beanplot from statsmodels.datasets import anes96 try: import matplotlib.pyplot as plt except ImportError: pass @pytest.fixture(scope="module") def age_and_labels(): # Test violinplot and beanplot with the same dataset. data = anes96.load_pandas() party_ID = np.arange(7) labels = ["Strong Democrat", "Weak Democrat", "Independent-Democrat", "Independent-Independent", "Independent-Republican", "Weak Republican", "Strong Republican"] age = [data.exog['age'][data.endog == id] for id in party_ID] age = np.array(age, dtype="object") return age, labels # TODO: Remove once SciPy 1.5.0 is the minimum IGNORE_VISIBLE_DEPR = """\ ignore:Creating an ndarray from ragged nested sequences:\ numpy.VisibleDeprecationWarning:""" @pytest.mark.filterwarnings(IGNORE_VISIBLE_DEPR) @pytest.mark.matplotlib def test_violinplot(age_and_labels, close_figures): age, labels = age_and_labels fig, ax = plt.subplots(1, 1) violinplot(age, ax=ax, labels=labels, plot_opts={'cutoff_val': 5, 'cutoff_type': 'abs', 'label_fontsize': 'small', 'label_rotation': 30}) @pytest.mark.filterwarnings(IGNORE_VISIBLE_DEPR) @pytest.mark.matplotlib def test_violinplot_bw_factor(age_and_labels, close_figures): age, labels = age_and_labels fig, ax = plt.subplots(1, 1) violinplot(age, ax=ax, labels=labels, plot_opts={'cutoff_val': 5, 'cutoff_type': 'abs', 'label_fontsize': 'small', 'label_rotation': 30, 'bw_factor': .2}) @pytest.mark.matplotlib def test_beanplot(age_and_labels, close_figures): age, labels = age_and_labels fig, ax = plt.subplots(1, 1) beanplot(age, ax=ax, labels=labels, plot_opts={'cutoff_val': 5, 'cutoff_type': 'abs', 'label_fontsize': 'small', 'label_rotation': 30}) @pytest.mark.matplotlib def test_beanplot_jitter(age_and_labels, close_figures): age, labels = age_and_labels fig, ax = plt.subplots(1, 1) beanplot(age, ax=ax, labels=labels, jitter=True, plot_opts={'cutoff_val': 5, 'cutoff_type': 'abs', 'label_fontsize': 'small', 'label_rotation': 30}) @pytest.mark.matplotlib def test_beanplot_side_right(age_and_labels, close_figures): age, labels = age_and_labels fig, ax = plt.subplots(1, 1) beanplot(age, ax=ax, labels=labels, jitter=True, side='right', plot_opts={'cutoff_val': 5, 'cutoff_type': 'abs', 'label_fontsize': 'small', 'label_rotation': 30}) @pytest.mark.matplotlib def test_beanplot_side_left(age_and_labels, close_figures): age, labels = age_and_labels fig, ax = plt.subplots(1, 1) beanplot(age, ax=ax, labels=labels, jitter=True, side='left', plot_opts={'cutoff_val': 5, 'cutoff_type': 'abs', 'label_fontsize': 'small', 'label_rotation': 30}) @pytest.mark.matplotlib def test_beanplot_legend_text(age_and_labels, close_figures): age, labels = age_and_labels fig, ax = plt.subplots(1, 1) beanplot(age, ax=ax, labels=labels, plot_opts={'bean_legend_text': 'text'}) statsmodels-0.12.2/statsmodels/graphics/tests/test_correlation.py000066400000000000000000000015171400612667500254070ustar00rootroot00000000000000import numpy as np import pytest from statsmodels.graphics.correlation import plot_corr, plot_corr_grid from statsmodels.datasets import randhie @pytest.mark.matplotlib def test_plot_corr(close_figures): hie_data = randhie.load_pandas() corr_matrix = np.corrcoef(hie_data.data.values.T) plot_corr(corr_matrix, xnames=hie_data.names) plot_corr(corr_matrix, xnames=[], ynames=hie_data.names) plot_corr(corr_matrix, normcolor=True, title='', cmap='jet') @pytest.mark.matplotlib def test_plot_corr_grid(close_figures): hie_data = randhie.load_pandas() corr_matrix = np.corrcoef(hie_data.data.values.T) plot_corr_grid([corr_matrix] * 2, xnames=hie_data.names) plot_corr_grid([corr_matrix] * 5, xnames=[], ynames=hie_data.names) plot_corr_grid([corr_matrix] * 3, normcolor=True, titles='', cmap='jet') statsmodels-0.12.2/statsmodels/graphics/tests/test_dotplot.py000066400000000000000000000353151400612667500245560ustar00rootroot00000000000000import numpy as np import pytest from statsmodels.graphics.dotplots import dot_plot import pandas as pd # If true, the output is written to a multi-page pdf file. pdf_output = False try: import matplotlib.pyplot as plt except ImportError: pass def close_or_save(pdf, fig): if pdf_output: pdf.savefig(fig) @pytest.mark.matplotlib def test_all(close_figures, reset_randomstate): if pdf_output: from matplotlib.backends.backend_pdf import PdfPages pdf = PdfPages("test_dotplot.pdf") else: pdf = None # Basic dotplot with points only plt.clf() points = range(20) ax = plt.axes() fig = dot_plot(points, ax=ax) ax.set_title("Basic horizontal dotplot") close_or_save(pdf, fig) # Basic vertical dotplot plt.clf() points = range(20) ax = plt.axes() fig = dot_plot(points, ax=ax, horizontal=False) ax.set_title("Basic vertical dotplot") close_or_save(pdf, fig) # Tall and skinny plt.figure(figsize=(4,12)) ax = plt.axes() vals = np.arange(40) fig = dot_plot(points, ax=ax) ax.set_title("Tall and skinny dotplot") ax.set_xlabel("x axis label") close_or_save(pdf, fig) # Short and wide plt.figure(figsize=(12,4)) ax = plt.axes() vals = np.arange(40) fig = dot_plot(points, ax=ax, horizontal=False) ax.set_title("Short and wide dotplot") ax.set_ylabel("y axis label") close_or_save(pdf, fig) # Tall and skinny striped dotplot plt.figure(figsize=(4,12)) ax = plt.axes() points = np.arange(40) fig = dot_plot(points, ax=ax, striped=True) ax.set_title("Tall and skinny striped dotplot") ax.set_xlim(-10, 50) close_or_save(pdf, fig) # Short and wide striped plt.figure(figsize=(12,4)) ax = plt.axes() points = np.arange(40) fig = dot_plot(points, ax=ax, striped=True, horizontal=False) ax.set_title("Short and wide striped dotplot") ax.set_ylim(-10, 50) close_or_save(pdf, fig) # Basic dotplot with few points plt.figure() ax = plt.axes() points = np.arange(4) fig = dot_plot(points, ax=ax) ax.set_title("Basic horizontal dotplot with few lines") close_or_save(pdf, fig) # Basic dotplot with few points plt.figure() ax = plt.axes() points = np.arange(4) fig = dot_plot(points, ax=ax, horizontal=False) ax.set_title("Basic vertical dotplot with few lines") close_or_save(pdf, fig) # Manually set the x axis limits plt.figure() ax = plt.axes() points = np.arange(20) fig = dot_plot(points, ax=ax) ax.set_xlim(-10, 30) ax.set_title("Dotplot with adjusted horizontal range") close_or_save(pdf, fig) # Left row labels plt.clf() ax = plt.axes() lines = ["ABCDEFGH"[np.random.randint(0, 8)] for k in range(20)] points = np.random.normal(size=20) fig = dot_plot(points, lines=lines, ax=ax) ax.set_title("Dotplot with user-supplied labels in the left margin") close_or_save(pdf, fig) # Left and right row labels plt.clf() ax = plt.axes() points = np.random.normal(size=20) lines = ["ABCDEFGH"[np.random.randint(0, 8)] + "::" + str(k+1) for k in range(20)] fig = dot_plot(points, lines=lines, ax=ax, split_names="::") ax.set_title("Dotplot with user-supplied labels in both margins") close_or_save(pdf, fig) # Both sides row labels plt.clf() ax = plt.axes([0.1, 0.1, 0.88, 0.8]) points = np.random.normal(size=20) lines = ["ABCDEFGH"[np.random.randint(0, 8)] + "::" + str(k+1) for k in range(20)] fig = dot_plot(points, lines=lines, ax=ax, split_names="::", horizontal=False) txt = ax.set_title("Vertical dotplot with user-supplied labels in both margins") txt.set_position((0.5, 1.06)) close_or_save(pdf, fig) # Custom colors and symbols plt.clf() ax = plt.axes([0.1, 0.07, 0.78, 0.85]) points = np.random.normal(size=20) lines = np.kron(range(5), np.ones(4)).astype(np.int32) styles = np.kron(np.ones(5), range(4)).astype(np.int32) marker_props = {k: {"color": "rgbc"[k], "marker": "osvp"[k], "ms": 7, "alpha": 0.6} for k in range(4)} fig = dot_plot(points, lines=lines, styles=styles, ax=ax, marker_props=marker_props) ax.set_title("Dotplot with custom colors and symbols") close_or_save(pdf, fig) # Basic dotplot with symmetric intervals plt.clf() ax = plt.axes() points = range(20) fig = dot_plot(points, intervals=np.ones(20), ax=ax) ax.set_title("Dotplot with symmetric intervals") close_or_save(pdf, fig) # Basic dotplot with symmetric intervals, pandas inputs. plt.clf() ax = plt.axes() points = pd.Series(range(20)) intervals = pd.Series(np.ones(20)) fig = dot_plot(points, intervals=intervals, ax=ax) ax.set_title("Dotplot with symmetric intervals (Pandas inputs)") close_or_save(pdf, fig) # Basic dotplot with nonsymmetric intervals plt.clf() ax = plt.axes() points = np.arange(20) intervals = [(1, 3) for i in range(20)] fig = dot_plot(points, intervals=intervals, ax=ax) ax.set_title("Dotplot with nonsymmetric intervals") close_or_save(pdf, fig) # Vertical dotplot with nonsymmetric intervals plt.clf() ax = plt.axes() points = np.arange(20) intervals = [(1, 3) for i in range(20)] fig = dot_plot(points, intervals=intervals, ax=ax, horizontal=False) ax.set_title("Vertical dotplot with nonsymmetric intervals") close_or_save(pdf, fig) # Dotplot with nonsymmetric intervals, adjust line properties plt.clf() ax = plt.axes() points = np.arange(20) intervals = [(1, 3) for x in range(20)] line_props = {0: {"color": "lightgrey", "solid_capstyle": "round"}} fig = dot_plot(points, intervals=intervals, line_props=line_props, ax=ax) ax.set_title("Dotplot with custom line properties") close_or_save(pdf, fig) # Dotplot with two points per line and a legend plt.clf() ax = plt.axes([0.1, 0.1, 0.75, 0.8]) points = 5*np.random.normal(size=40) lines = np.kron(range(20), (1,1)) intervals = [(1,3) for k in range(40)] styles = np.kron(np.ones(20), (0,1)).astype(np.int32) styles = [["Cat", "Dog"][i] for i in styles] fig = dot_plot(points, intervals=intervals, lines=lines, styles=styles, ax=ax, stacked=True) handles, labels = ax.get_legend_handles_labels() leg = plt.figlegend(handles, labels, "center right", numpoints=1, handletextpad=0.0001) leg.draw_frame(False) ax.set_title("Dotplot with two points per line") close_or_save(pdf, fig) # Dotplot with two points per line and a legend plt.clf() ax = plt.axes([0.1, 0.1, 0.75, 0.8]) fig = dot_plot(points, intervals=intervals, lines=lines, styles=styles, ax=ax, stacked=True, styles_order=["Dog", "Cat"]) handles, labels = ax.get_legend_handles_labels() leg = plt.figlegend(handles, labels, "center right", numpoints=1, handletextpad=0.0001) leg.draw_frame(False) ax.set_title("Dotplot with two points per line (reverse order)") close_or_save(pdf, fig) # Vertical dotplot with two points per line and a legend plt.clf() ax = plt.axes([0.1, 0.1, 0.75, 0.8]) points = 5*np.random.normal(size=40) lines = np.kron(range(20), (1,1)) intervals = [(1,3) for k in range(40)] styles = np.kron(np.ones(20), (0,1)).astype(np.int32) styles = [["Cat", "Dog"][i] for i in styles] fig = dot_plot(points, intervals=intervals, lines=lines, styles=styles, ax=ax, stacked=True, horizontal=False) handles, labels = ax.get_legend_handles_labels() leg = plt.figlegend(handles, labels, "center right", numpoints=1, handletextpad=0.0001) leg.draw_frame(False) ax.set_title("Vertical dotplot with two points per line") close_or_save(pdf, fig) # Vertical dotplot with two points per line and a legend plt.clf() ax = plt.axes([0.1, 0.1, 0.75, 0.8]) styles_order = ["Dog", "Cat"] fig = dot_plot(points, intervals=intervals, lines=lines, styles=styles, ax=ax, stacked=True, horizontal=False, styles_order=styles_order) handles, labels = ax.get_legend_handles_labels() lh = dict(zip(labels, handles)) handles = [lh[l] for l in styles_order] leg = plt.figlegend(handles, styles_order, "center right", numpoints=1, handletextpad=0.0001) leg.draw_frame(False) ax.set_title("Vertical dotplot with two points per line (reverse order)") close_or_save(pdf, fig) # Vertical dotplot with two points per line and a legend plt.clf() ax = plt.axes([0.1, 0.1, 0.75, 0.8]) points = 5*np.random.normal(size=40) lines = np.kron(range(20), (1,1)) intervals = [(1,3) for k in range(40)] styles = np.kron(np.ones(20), (0,1)).astype(np.int32) styles = [["Cat", "Dog"][i] for i in styles] fig = dot_plot(points, intervals=intervals, lines=lines, styles=styles, ax=ax, stacked=True, striped=True, horizontal=False) handles, labels = ax.get_legend_handles_labels() leg = plt.figlegend(handles, labels, "center right", numpoints=1, handletextpad=0.0001) leg.draw_frame(False) plt.ylim(-20, 20) ax.set_title("Vertical dotplot with two points per line") close_or_save(pdf, fig) # Dotplot with color-matched points and intervals plt.clf() ax = plt.axes([0.1, 0.1, 0.75, 0.8]) points = 5*np.random.normal(size=40) lines = np.kron(range(20), (1,1)) intervals = [(1,3) for k in range(40)] styles = np.kron(np.ones(20), (0,1)).astype(np.int32) styles = [["Cat", "Dog"][i] for i in styles] marker_props = {"Cat": {"color": "orange"}, "Dog": {"color": "purple"}} line_props = {"Cat": {"color": "orange"}, "Dog": {"color": "purple"}} fig = dot_plot(points, intervals=intervals, lines=lines, styles=styles, ax=ax, stacked=True, marker_props=marker_props, line_props=line_props) handles, labels = ax.get_legend_handles_labels() leg = plt.figlegend(handles, labels, "center right", numpoints=1, handletextpad=0.0001) leg.draw_frame(False) ax.set_title("Dotplot with color-matched points and intervals") close_or_save(pdf, fig) # Dotplot with color-matched points and intervals plt.clf() ax = plt.axes([0.1, 0.1, 0.75, 0.8]) points = 5*np.random.normal(size=40) lines = np.kron(range(20), (1,1)) intervals = [(1,3) for k in range(40)] styles = np.kron(np.ones(20), (0,1)).astype(np.int32) styles = [["Cat", "Dog"][i] for i in styles] marker_props = {"Cat": {"color": "orange"}, "Dog": {"color": "purple"}} line_props = {"Cat": {"color": "orange"}, "Dog": {"color": "purple"}} fig = dot_plot(points, intervals=intervals, lines=lines, styles=styles, ax=ax, stacked=True, marker_props=marker_props, line_props=line_props, horizontal=False) handles, labels = ax.get_legend_handles_labels() leg = plt.figlegend(handles, labels, "center right", numpoints=1, handletextpad=0.0001) leg.draw_frame(False) ax.set_title("Dotplot with color-matched points and intervals") close_or_save(pdf, fig) # Dotplot with sections plt.clf() ax = plt.axes() points = range(30) lines = np.kron(range(15), (1,1)).astype(np.int32) styles = np.kron(np.ones(15), (0,1)).astype(np.int32) sections = np.kron((0,1,2), np.ones(10)).astype(np.int32) sections = [["Axx", "Byy", "Czz"][k] for k in sections] fig = dot_plot(points, lines=lines, styles=styles, sections=sections, ax=ax) ax.set_title("Dotplot with sections") close_or_save(pdf, fig) # Vertical dotplot with sections plt.clf() ax = plt.axes([0.1,0.1,0.9,0.75]) points = range(30) lines = np.kron(range(15), (1,1)).astype(np.int32) styles = np.kron(np.ones(15), (0,1)).astype(np.int32) sections = np.kron((0,1,2), np.ones(10)).astype(np.int32) sections = [["Axx", "Byy", "Czz"][k] for k in sections] fig = dot_plot(points, lines=lines, styles=styles, sections=sections, ax=ax, horizontal=False) txt = ax.set_title("Vertical dotplot with sections") txt.set_position((0.5, 1.08)) close_or_save(pdf, fig) # Reorder sections plt.clf() ax = plt.axes() points = range(30) lines = np.kron(range(15), (1,1)).astype(np.int32) styles = np.kron(np.ones(15), (0,1)).astype(np.int32) sections = np.kron((0,1,2), np.ones(10)).astype(np.int32) sections = [["Axx", "Byy", "Czz"][k] for k in sections] fig = dot_plot(points, lines=lines, styles=styles, sections=sections, ax=ax, section_order=["Byy", "Axx", "Czz"]) ax.set_title("Dotplot with sections in specified order") close_or_save(pdf, fig) # Reorder the lines. plt.figure() ax = plt.axes() points = np.arange(4) lines = ["A", "B", "C", "D"] line_order = ["B", "C", "A", "D"] fig = dot_plot(points, lines=lines, line_order=line_order, ax=ax) ax.set_title("Dotplot with reordered lines") close_or_save(pdf, fig) # Format labels plt.clf() points = range(20) lines = ["%d::%d" % (i, 100+i) for i in range(20)] fmt_left = lambda x : "lft_" + x fmt_right = lambda x : "rgt_" + x ax = plt.axes() fig = dot_plot(points, lines=lines, ax=ax, split_names="::", fmt_left_name=fmt_left, fmt_right_name=fmt_right) ax.set_title("Horizontal dotplot with name formatting") close_or_save(pdf, fig) # Right names only plt.clf() points = range(20) lines = ["%d::%d" % (i, 100+i) for i in range(20)] ax = plt.axes() fig = dot_plot(points, lines=lines, ax=ax, split_names="::", show_names="right") ax.set_title("Show right names only") close_or_save(pdf, fig) # Dotplot with different numbers of points per line plt.clf() ax = plt.axes([0.1, 0.1, 0.75, 0.8]) points = 5*np.random.normal(size=40) lines = [] ii = 0 while len(lines) < 40: for k in range(np.random.randint(1, 4)): lines.append(ii) ii += 1 styles = np.kron(np.ones(20), (0,1)).astype(np.int32) styles = [["Cat", "Dog"][i] for i in styles] fig = dot_plot(points, lines=lines, styles=styles, ax=ax, stacked=True) handles, labels = ax.get_legend_handles_labels() leg = plt.figlegend(handles, labels, "center right", numpoints=1, handletextpad=0.0001) leg.draw_frame(False) ax.set_title("Dotplot with different numbers of points per line") close_or_save(pdf, fig) if pdf_output: pdf.close() statsmodels-0.12.2/statsmodels/graphics/tests/test_factorplots.py000066400000000000000000000057321400612667500254310ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_raises, assert_equal from pandas import Series import pytest from statsmodels.graphics.factorplots import interaction_plot, _recode try: import matplotlib.pyplot as plt except ImportError: pass class TestInteractionPlot(object): @classmethod def setup_class(cls): np.random.seed(12345) cls.weight = np.random.randint(1,4,size=60) cls.duration = np.random.randint(1,3,size=60) cls.days = np.log(np.random.randint(1,30, size=60)) @pytest.mark.matplotlib def test_plot_both(self, close_figures): fig = interaction_plot(self.weight, self.duration, self.days, colors=['red','blue'], markers=['D','^'], ms=10) @pytest.mark.matplotlib def test_plot_rainbow(self, close_figures): fig = interaction_plot(self.weight, self.duration, self.days, markers=['D','^'], ms=10) @pytest.mark.matplotlib @pytest.mark.parametrize('astype', ['str', 'int']) def test_plot_pandas(self, astype, close_figures): weight = Series(self.weight, name='Weight').astype(astype) duration = Series(self.duration, name='Duration') days = Series(self.days, name='Days') fig = interaction_plot(weight, duration, days, markers=['D', '^'], ms=10) ax = fig.axes[0] trace = ax.get_legend().get_title().get_text() assert_equal(trace, 'Duration') assert_equal(ax.get_ylabel(), 'mean of Days') assert_equal(ax.get_xlabel(), 'Weight') @pytest.mark.matplotlib def test_formatting(self, close_figures): fig = interaction_plot(self.weight, self.duration, self.days, colors=['r','g'], linestyles=['--','-.']) assert_equal(isinstance(fig, plt.Figure), True) @pytest.mark.matplotlib def test_formatting_errors(self, close_figures): assert_raises(ValueError, interaction_plot, self.weight, self.duration, self.days, markers=['D']) assert_raises(ValueError, interaction_plot, self.weight, self.duration, self.days, colors=['b','r','g']) assert_raises(ValueError, interaction_plot, self.weight, self.duration, self.days, linestyles=['--','-.',':']) @pytest.mark.matplotlib def test_plottype(self, close_figures): fig = interaction_plot(self.weight, self.duration, self.days, plottype='line') assert_equal(isinstance(fig, plt.Figure), True) fig = interaction_plot(self.weight, self.duration, self.days, plottype='scatter') assert_equal(isinstance(fig, plt.Figure), True) assert_raises(ValueError, interaction_plot, self.weight, self.duration, self.days, plottype='unknown') def test_recode_series(self): series = Series(['a', 'b'] * 10, index=np.arange(0, 40, 2), name='index_test') series_ = _recode(series, {'a': 0, 'b': 1}) assert_equal(series_.index.values, series.index.values, err_msg='_recode changed the index') statsmodels-0.12.2/statsmodels/graphics/tests/test_functional.py000066400000000000000000000210171400612667500252250ustar00rootroot00000000000000 import numpy as np from numpy.testing import assert_equal, assert_almost_equal import pytest from statsmodels.datasets import elnino from statsmodels.graphics.functional import \ hdrboxplot, banddepth, fboxplot, rainbowplot try: import matplotlib.pyplot as plt except ImportError: pass data = elnino.load(as_pandas=False) labels = data.raw_data[:, 0].astype(int) data = data.raw_data[:, 1:] @pytest.mark.matplotlib def test_hdr_basic(close_figures): try: _, hdr = hdrboxplot(data, labels=labels, seed=12345) except WindowsError: pytest.xfail('Multiprocess randomly crashes in Windows testing') assert len(hdr.extra_quantiles) == 0 median_t = [24.247, 25.625, 25.964, 24.999, 23.648, 22.302, 21.231, 20.366, 20.168, 20.434, 21.111, 22.299] assert_almost_equal(hdr.median, median_t, decimal=2) quant = np.vstack([hdr.outliers, hdr.hdr_90, hdr.hdr_50]) quant_t = np.vstack([[24.36, 25.42, 25.40, 24.96, 24.21, 23.35, 22.50, 21.89, 22.04, 22.88, 24.57, 25.89], [27.25, 28.23, 28.85, 28.82, 28.37, 27.43, 25.73, 23.88, 22.26, 22.22, 22.21, 23.19], [23.70, 26.08, 27.17, 26.74, 26.77, 26.15, 25.59, 24.95, 24.69, 24.64, 25.85, 27.08], [28.12, 28.82, 29.24, 28.45, 27.36, 25.19, 23.61, 22.27, 21.31, 21.37, 21.60, 22.81], [25.48, 26.99, 27.51, 27.04, 26.23, 24.94, 23.69, 22.72, 22.26, 22.64, 23.33, 24.44], [23.11, 24.50, 24.66, 23.44, 21.74, 20.58, 19.68, 18.84, 18.76, 18.99, 19.66, 20.86], [24.84, 26.23, 26.67, 25.93, 24.87, 23.57, 22.46, 21.45, 21.26, 21.57, 22.14, 23.41], [23.62, 25.10, 25.34, 24.22, 22.74, 21.52, 20.40, 19.56, 19.63, 19.67, 20.37, 21.76]]) assert_almost_equal(quant, quant_t, decimal=0) labels_pos = np.all(np.in1d(data, hdr.outliers).reshape(data.shape), axis=1) outliers = labels[labels_pos] assert_equal([1982, 1983, 1997, 1998], outliers) assert_equal(labels[hdr.outliers_idx], outliers) @pytest.mark.slow @pytest.mark.matplotlib def test_hdr_basic_brute(close_figures, reset_randomstate): try: _, hdr = hdrboxplot(data, ncomp=2, labels=labels, use_brute=True) except WindowsError: pytest.xfail('Multiprocess randomly crashes in Windows testing') assert len(hdr.extra_quantiles) == 0 median_t = [24.247, 25.625, 25.964, 24.999, 23.648, 22.302, 21.231, 20.366, 20.168, 20.434, 21.111, 22.299] assert_almost_equal(hdr.median, median_t, decimal=2) @pytest.mark.slow @pytest.mark.matplotlib def test_hdr_plot(close_figures): fig = plt.figure() ax = fig.add_subplot(111) try: hdrboxplot(data, labels=labels.tolist(), ax=ax, threshold=1, seed=12345) except WindowsError: pytest.xfail('Multiprocess randomly crashes in Windows testing') ax.set_xlabel("Month of the year") ax.set_ylabel("Sea surface temperature (C)") ax.set_xticks(np.arange(13, step=3) - 1) ax.set_xticklabels(["", "Mar", "Jun", "Sep", "Dec"]) ax.set_xlim([-0.2, 11.2]) @pytest.mark.slow @pytest.mark.matplotlib def test_hdr_alpha(close_figures): try: _, hdr = hdrboxplot(data, alpha=[0.7], seed=12345) except WindowsError: pytest.xfail('Multiprocess randomly crashes in Windows testing') extra_quant_t = np.vstack([[25.1, 26.5, 27.0, 26.4, 25.4, 24.1, 23.0, 22.0, 21.7, 22.1, 22.7, 23.8], [23.4, 24.8, 25.0, 23.9, 22.4, 21.1, 20.0, 19.3, 19.2, 19.4, 20.1, 21.3]]) assert_almost_equal(hdr.extra_quantiles, extra_quant_t, decimal=0) @pytest.mark.slow @pytest.mark.matplotlib def test_hdr_multiple_alpha(close_figures): try: _, hdr = hdrboxplot(data, alpha=[0.4, 0.92], seed=12345) except WindowsError: pytest.xfail('Multiprocess randomly crashes in Windows testing') extra_quant_t = [[25.712, 27.052, 27.711, 27.200, 26.162, 24.833, 23.639, 22.378, 22.250, 22.640, 23.472, 24.649], [22.973, 24.526, 24.608, 23.343, 21.908, 20.655, 19.750, 19.046, 18.812, 18.989, 19.520, 20.685], [24.667, 26.033, 26.416, 25.584, 24.308, 22.849, 21.684, 20.948, 20.483, 21.019, 21.751, 22.890], [23.873, 25.371, 25.667, 24.644, 23.177, 21.923, 20.791, 20.015, 19.697, 19.951, 20.622, 21.858]] assert_almost_equal(hdr.extra_quantiles, np.vstack(extra_quant_t), decimal=0) @pytest.mark.slow @pytest.mark.matplotlib def test_hdr_threshold(close_figures): try: _, hdr = hdrboxplot(data, alpha=[0.8], threshold=0.93, seed=12345) except WindowsError: pytest.xfail('Multiprocess randomly crashes in Windows testing') labels_pos = np.all(np.in1d(data, hdr.outliers).reshape(data.shape), axis=1) outliers = labels[labels_pos] assert_equal([1968, 1982, 1983, 1997, 1998], outliers) @pytest.mark.matplotlib def test_hdr_bw(close_figures): try: _, hdr = hdrboxplot(data, bw='cv_ml', seed=12345) except WindowsError: pytest.xfail('Multiprocess randomly crashes in Windows testing') median_t = [24.25, 25.64, 25.99, 25.04, 23.71, 22.38, 21.31, 20.44, 20.24, 20.51, 21.19, 22.38] assert_almost_equal(hdr.median, median_t, decimal=2) @pytest.mark.slow @pytest.mark.matplotlib def test_hdr_ncomp(close_figures): try: _, hdr = hdrboxplot(data, ncomp=3, seed=12345) except WindowsError: pytest.xfail('Multiprocess randomly crashes in Windows testing') median_t = [24.33, 25.71, 26.04, 25.08, 23.74, 22.40, 21.32, 20.45, 20.25, 20.53, 21.20, 22.39] assert_almost_equal(hdr.median, median_t, decimal=2) def test_banddepth_BD2(): xx = np.arange(500) / 150. y1 = 1 + 0.5 * np.sin(xx) y2 = 0.3 + np.sin(xx + np.pi/6) y3 = -0.5 + np.sin(xx + np.pi/6) y4 = -1 + 0.3 * np.cos(xx + np.pi/6) data = np.asarray([y1, y2, y3, y4]) depth = banddepth(data, method='BD2') expected_depth = [0.5, 5./6, 5./6, 0.5] assert_almost_equal(depth, expected_depth) # Plot to visualize why we expect this output # fig = plt.figure() # ax = fig.add_subplot(111) # for ii, yy in enumerate([y1, y2, y3, y4]): # ax.plot(xx, yy, label="y%s" % ii) # ax.legend() # plt.close(fig) def test_banddepth_MBD(): xx = np.arange(5001) / 5000. y1 = np.zeros(xx.shape) y2 = 2 * xx - 1 y3 = np.ones(xx.shape) * 0.5 y4 = np.ones(xx.shape) * -0.25 data = np.asarray([y1, y2, y3, y4]) depth = banddepth(data, method='MBD') expected_depth = [5./6, (2*(0.75-3./8)+3)/6, 3.5/6, (2*3./8+3)/6] assert_almost_equal(depth, expected_depth, decimal=4) @pytest.mark.matplotlib def test_fboxplot_rainbowplot(close_figures): # Test fboxplot and rainbowplot together, is much faster. def harmfunc(t): """Test function, combination of a few harmonic terms.""" # Constant, 0 with p=0.9, 1 with p=1 - for creating outliers ci = int(np.random.random() > 0.9) a1i = np.random.random() * 0.05 a2i = np.random.random() * 0.05 b1i = (0.15 - 0.1) * np.random.random() + 0.1 b2i = (0.15 - 0.1) * np.random.random() + 0.1 func = (1 - ci) * (a1i * np.sin(t) + a2i * np.cos(t)) + \ ci * (b1i * np.sin(t) + b2i * np.cos(t)) return func np.random.seed(1234567) # Some basic test data, Model 6 from Sun and Genton. t = np.linspace(0, 2 * np.pi, 250) data = [harmfunc(t) for _ in range(20)] # fboxplot test fig = plt.figure() ax = fig.add_subplot(111) _, depth, ix_depth, ix_outliers = fboxplot(data, wfactor=2, ax=ax) ix_expected = np.array([13, 4, 15, 19, 8, 6, 3, 16, 9, 7, 1, 5, 2, 12, 17, 11, 14, 10, 0, 18]) assert_equal(ix_depth, ix_expected) ix_expected2 = np.array([2, 11, 17, 18]) assert_equal(ix_outliers, ix_expected2) # rainbowplot test (re-uses depth variable) xdata = np.arange(data[0].size) fig = rainbowplot(data, xdata=xdata, depth=depth, cmap=plt.cm.rainbow) statsmodels-0.12.2/statsmodels/graphics/tests/test_gofplots.py000066400000000000000000000463561400612667500247350ustar00rootroot00000000000000import numpy as np import numpy.testing as nptest from numpy.testing import assert_equal import pytest from scipy import stats import statsmodels.api as sm from statsmodels.graphics import gofplots from statsmodels.graphics.gofplots import ( ProbPlot, qqline, qqplot, qqplot_2samples, ) from statsmodels.graphics.utils import _import_mpl class BaseProbplotMixin: def setup(self): try: import matplotlib.pyplot as plt self.fig, self.ax = plt.subplots() except ImportError: pass self.other_array = np.random.normal(size=self.prbplt.data.shape) self.other_prbplot = ProbPlot(self.other_array) self.plot_options = dict( marker="d", markerfacecolor="cornflowerblue", markeredgecolor="white", alpha=0.5, ) @pytest.mark.matplotlib def test_qqplot(self, close_figures): self.prbplt.qqplot(ax=self.ax, line=self.line, **self.plot_options) @pytest.mark.matplotlib def test_ppplot(self, close_figures): self.prbplt.ppplot(ax=self.ax, line=self.line) @pytest.mark.matplotlib def test_probplot(self, close_figures): self.prbplt.probplot(ax=self.ax, line=self.line, **self.plot_options) @pytest.mark.matplotlib def test_probplot_exceed(self, close_figures): self.prbplt.probplot( ax=self.ax, exceed=True, line=self.line, **self.plot_options ) @pytest.mark.matplotlib def test_qqplot_other_array(self, close_figures): self.prbplt.qqplot( ax=self.ax, line=self.line, other=self.other_array, **self.plot_options, ) @pytest.mark.matplotlib def test_ppplot_other_array(self, close_figures): self.prbplt.ppplot( ax=self.ax, line=self.line, other=self.other_array, **self.plot_options, ) @pytest.mark.xfail(strict=True) @pytest.mark.matplotlib def test_probplot_other_array(self, close_figures): self.prbplt.probplot( ax=self.ax, line=self.line, other=self.other_array, **self.plot_options, ) @pytest.mark.matplotlib def test_qqplot_other_prbplt(self, close_figures): self.prbplt.qqplot( ax=self.ax, line=self.line, other=self.other_prbplot, **self.plot_options, ) @pytest.mark.matplotlib def test_ppplot_other_prbplt(self, close_figures): self.prbplt.ppplot( ax=self.ax, line=self.line, other=self.other_prbplot, **self.plot_options, ) @pytest.mark.xfail(strict=True) @pytest.mark.matplotlib def test_probplot_other_prbplt(self, close_figures): self.prbplt.probplot( ax=self.ax, line=self.line, other=self.other_prbplot, **self.plot_options, ) @pytest.mark.matplotlib def test_qqplot_custom_labels(self, close_figures): self.prbplt.qqplot( ax=self.ax, line=self.line, xlabel="Custom X-Label", ylabel="Custom Y-Label", **self.plot_options, ) @pytest.mark.matplotlib def test_ppplot_custom_labels(self, close_figures): self.prbplt.ppplot( ax=self.ax, line=self.line, xlabel="Custom X-Label", ylabel="Custom Y-Label", **self.plot_options, ) @pytest.mark.matplotlib def test_probplot_custom_labels(self, close_figures): self.prbplt.probplot( ax=self.ax, line=self.line, xlabel="Custom X-Label", ylabel="Custom Y-Label", **self.plot_options, ) @pytest.mark.matplotlib def test_qqplot_pltkwargs(self, close_figures): self.prbplt.qqplot( ax=self.ax, line=self.line, marker="d", markerfacecolor="cornflowerblue", markeredgecolor="white", alpha=0.5, ) @pytest.mark.matplotlib def test_ppplot_pltkwargs(self, close_figures): self.prbplt.ppplot( ax=self.ax, line=self.line, marker="d", markerfacecolor="cornflowerblue", markeredgecolor="white", alpha=0.5, ) @pytest.mark.matplotlib def test_probplot_pltkwargs(self, close_figures): self.prbplt.probplot( ax=self.ax, line=self.line, marker="d", markerfacecolor="cornflowerblue", markeredgecolor="white", alpha=0.5, ) def test_fit_params(self): assert self.prbplt.fit_params[-2] == self.prbplt.loc assert self.prbplt.fit_params[-1] == self.prbplt.scale class TestProbPlotLongelyNoFit(BaseProbplotMixin): def setup(self): np.random.seed(5) self.data = sm.datasets.longley.load() self.data.exog = sm.add_constant(self.data.exog, prepend=False) self.mod_fit = sm.OLS(self.data.endog, self.data.exog).fit() self.prbplt = ProbPlot( self.mod_fit.resid, dist=stats.t, distargs=(4,), fit=False ) self.line = "r" super().setup() class TestProbPlotLongelyWithFit(BaseProbplotMixin): def setup(self): np.random.seed(5) self.data = sm.datasets.longley.load(as_pandas=False) self.data.exog = sm.add_constant(self.data.exog, prepend=False) self.mod_fit = sm.OLS(self.data.endog, self.data.exog).fit() self.prbplt = ProbPlot( self.mod_fit.resid, dist=stats.t, distargs=(4,), fit=True ) self.line = "r" super().setup() class TestProbPlotRandomNormalMinimal(BaseProbplotMixin): def setup(self): np.random.seed(5) self.data = np.random.normal(loc=8.25, scale=3.25, size=37) self.prbplt = ProbPlot(self.data) self.line = None super(TestProbPlotRandomNormalMinimal, self).setup() class TestProbPlotRandomNormalWithFit(BaseProbplotMixin): def setup(self): np.random.seed(5) self.data = np.random.normal(loc=8.25, scale=3.25, size=37) self.prbplt = ProbPlot(self.data, fit=True) self.line = "q" super(TestProbPlotRandomNormalWithFit, self).setup() class TestProbPlotRandomNormalFullDist(BaseProbplotMixin): def setup(self): np.random.seed(5) self.data = np.random.normal(loc=8.25, scale=3.25, size=37) self.prbplt = ProbPlot(self.data, dist=stats.norm(loc=8.5, scale=3.0)) self.line = "45" super().setup() def test_loc_set(self): assert self.prbplt.loc == 8.5 def test_scale_set(self): assert self.prbplt.scale == 3.0 def test_exceptions(self): with pytest.raises(ValueError): ProbPlot(self.data, dist=stats.norm(loc=8.5, scale=3.0), fit=True) with pytest.raises(ValueError): ProbPlot( self.data, dist=stats.norm(loc=8.5, scale=3.0), distargs=(8.5, 3.0), ) with pytest.raises(ValueError): ProbPlot(self.data, dist=stats.norm(loc=8.5, scale=3.0), loc=8.5) with pytest.raises(ValueError): ProbPlot(self.data, dist=stats.norm(loc=8.5, scale=3.0), scale=3.0) class TestCompareSamplesDifferentSize: def setup(self): np.random.seed(5) self.data1 = ProbPlot(np.random.normal(loc=8.25, scale=3.25, size=37)) self.data2 = ProbPlot(np.random.normal(loc=8.25, scale=3.25, size=55)) @pytest.mark.matplotlib def test_qqplot(self, close_figures): self.data1.qqplot(other=self.data2) with pytest.raises(ValueError): self.data2.qqplot(other=self.data1) @pytest.mark.matplotlib def test_ppplot(self, close_figures): self.data1.ppplot(other=self.data2) self.data2.ppplot(other=self.data1) class TestProbPlotRandomNormalLocScaleDist(BaseProbplotMixin): def setup(self): np.random.seed(5) self.data = np.random.normal(loc=8.25, scale=3.25, size=37) self.prbplt = ProbPlot(self.data, loc=8, scale=3) self.line = "45" super(TestProbPlotRandomNormalLocScaleDist, self).setup() def test_loc_set(self): assert self.prbplt.loc == 8 def test_scale_set(self): assert self.prbplt.scale == 3 def test_loc_set_in_dist(self): assert self.prbplt.dist.mean() == 8.0 def test_scale_set_in_dist(self): assert self.prbplt.dist.var() == 9.0 class TestTopLevel: def setup(self): self.data = sm.datasets.longley.load(as_pandas=False) self.data.exog = sm.add_constant(self.data.exog, prepend=False) self.mod_fit = sm.OLS(self.data.endog, self.data.exog).fit() self.res = self.mod_fit.resid self.prbplt = ProbPlot(self.mod_fit.resid, dist=stats.t, distargs=(4,)) self.other_array = np.random.normal(size=self.prbplt.data.shape) self.other_prbplot = ProbPlot(self.other_array) @pytest.mark.matplotlib def test_qqplot(self, close_figures): qqplot(self.res, line="r") @pytest.mark.matplotlib def test_qqplot_pltkwargs(self, close_figures): qqplot( self.res, line="r", marker="d", markerfacecolor="cornflowerblue", markeredgecolor="white", alpha=0.5, ) @pytest.mark.matplotlib def test_qqplot_2samples_prob_plot_objects(self, close_figures): # also tests all valuesg for line for line in ["r", "q", "45", "s"]: # test with `ProbPlot` instances qqplot_2samples(self.prbplt, self.other_prbplot, line=line) @pytest.mark.matplotlib def test_qqplot_2samples_arrays(self, close_figures): # also tests all values for line for line in ["r", "q", "45", "s"]: # test with arrays qqplot_2samples(self.res, self.other_array, line=line) def test_invalid_dist_config(close_figures): # GH 4226 np.random.seed(5) data = sm.datasets.longley.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) mod_fit = sm.OLS(data.endog, data.exog).fit() with pytest.raises(TypeError, match=r"dist\(0, 1, 4, loc=0, scale=1\)"): ProbPlot(mod_fit.resid, stats.t, distargs=(0, 1, 4)) @pytest.mark.matplotlib def test_qqplot_unequal(): rs = np.random.RandomState(0) data1 = rs.standard_normal(100) data2 = rs.standard_normal(200) fig1 = qqplot_2samples(data1, data2) fig2 = qqplot_2samples(data2, data1) x1, y1 = fig1.get_axes()[0].get_children()[0].get_data() x2, y2 = fig2.get_axes()[0].get_children()[0].get_data() np.testing.assert_allclose(x1, x2) np.testing.assert_allclose(y1, y2) numobj1 = len(fig1.get_axes()[0].get_children()) numobj2 = len(fig2.get_axes()[0].get_children()) assert numobj1 == numobj2 @pytest.mark.matplotlib def test_qqplot(self, close_figures): qqplot(self.res, line="r") @pytest.mark.matplotlib def test_qqplot_2samples_prob_plot_obj(self, close_figures): # also tests all values for line for line in ["r", "q", "45", "s"]: # test with `ProbPlot` instances qqplot_2samples(self.prbplt, self.other_prbplot, line=line) @pytest.mark.matplotlib def test_qqplot_2samples_arrays(self, close_figures): # also tests all values for line for line in ["r", "q", "45", "s"]: # test with arrays qqplot_2samples(self.res, self.other_array, line=line) class TestCheckDist: def test_good(self): gofplots._check_for(stats.norm, "ppf") gofplots._check_for(stats.norm, "cdf") def test_bad(self): with pytest.raises(AttributeError): gofplots._check_for("junk", "ppf") with pytest.raises(AttributeError): gofplots._check_for("junk", "cdf") class TestDoPlot: def setup(self): try: import matplotlib.pyplot as plt self.fig, self.ax = plt.subplots() except ImportError: pass self.x = [0.2, 0.6, 2.0, 4.5, 10.0, 50.0, 83.0, 99.1, 99.7] self.y = [1.2, 1.4, 1.7, 2.1, 3.2, 3.7, 4.5, 5.1, 6.3] self.full_options = { "marker": "s", "markerfacecolor": "cornflowerblue", "markeredgecolor": "firebrick", "markeredgewidth": 1.25, "linestyle": "--", } self.step_options = {"linestyle": "-", "where": "mid"} @pytest.mark.matplotlib def test_baseline(self, close_figures): plt = _import_mpl() fig, ax = gofplots._do_plot(self.x, self.y) assert isinstance(fig, plt.Figure) assert isinstance(ax, plt.Axes) assert self.fig is not fig assert self.ax is not ax @pytest.mark.matplotlib def test_with_ax(self, close_figures): plt = _import_mpl() fig, ax = gofplots._do_plot(self.x, self.y, ax=self.ax) assert isinstance(fig, plt.Figure) assert isinstance(ax, plt.Axes) assert self.fig is fig assert self.ax is ax @pytest.mark.matplotlib def test_plot_full_options(self, close_figures): gofplots._do_plot( self.x, self.y, ax=self.ax, step=False, **self.full_options, ) @pytest.mark.matplotlib def test_step_baseline(self, close_figures): gofplots._do_plot( self.x, self.y, ax=self.ax, step=True, **self.step_options, ) @pytest.mark.matplotlib def test_step_full_options(self, close_figures): gofplots._do_plot( self.x, self.y, ax=self.ax, step=True, **self.full_options, ) @pytest.mark.matplotlib def test_plot_qq_line(self, close_figures): gofplots._do_plot(self.x, self.y, ax=self.ax, line="r") @pytest.mark.matplotlib def test_step_qq_line(self, close_figures): gofplots._do_plot(self.x, self.y, ax=self.ax, step=True, line="r") class TestQQLine: def setup(self): np.random.seed(0) self.x = np.sort(np.random.normal(loc=2.9, scale=1.2, size=37)) self.y = np.sort(np.random.normal(loc=3.0, scale=1.1, size=37)) try: import matplotlib.pyplot as plt self.fig, self.ax = plt.subplots() self.ax.plot(self.x, self.y, "ko") except ImportError: pass self.lineoptions = { "linewidth": 2, "dashes": (10, 1, 3, 4), "color": "green", } self.fmt = "bo-" @pytest.mark.matplotlib def test_badline(self): with pytest.raises(ValueError): qqline(self.ax, "junk") @pytest.mark.matplotlib def test_non45_no_x(self, close_figures): with pytest.raises(ValueError): qqline(self.ax, "s", y=self.y) @pytest.mark.matplotlib def test_non45_no_y(self, close_figures): with pytest.raises(ValueError): qqline(self.ax, "s", x=self.x) @pytest.mark.matplotlib def test_non45_no_x_no_y(self, close_figures): with pytest.raises(ValueError): qqline(self.ax, "s") @pytest.mark.matplotlib def test_45(self, close_figures): nchildren = len(self.ax.get_children()) qqline(self.ax, "45") assert len(self.ax.get_children()) > nchildren @pytest.mark.matplotlib def test_45_fmt(self, close_figures): qqline(self.ax, "45", fmt=self.fmt) @pytest.mark.matplotlib def test_45_fmt_lineoptions(self, close_figures): qqline(self.ax, "45", fmt=self.fmt, **self.lineoptions) @pytest.mark.matplotlib def test_r(self, close_figures): nchildren = len(self.ax.get_children()) qqline(self.ax, "r", x=self.x, y=self.y) assert len(self.ax.get_children()) > nchildren @pytest.mark.matplotlib def test_r_fmt(self, close_figures): qqline(self.ax, "r", x=self.x, y=self.y, fmt=self.fmt) @pytest.mark.matplotlib def test_r_fmt_lineoptions(self, close_figures): qqline( self.ax, "r", x=self.x, y=self.y, fmt=self.fmt, **self.lineoptions ) @pytest.mark.matplotlib def test_s(self, close_figures): nchildren = len(self.ax.get_children()) qqline(self.ax, "s", x=self.x, y=self.y) assert len(self.ax.get_children()) > nchildren @pytest.mark.matplotlib def test_s_fmt(self, close_figures): qqline(self.ax, "s", x=self.x, y=self.y, fmt=self.fmt) @pytest.mark.matplotlib def test_s_fmt_lineoptions(self, close_figures): qqline( self.ax, "s", x=self.x, y=self.y, fmt=self.fmt, **self.lineoptions ) @pytest.mark.matplotlib def test_q(self, close_figures): nchildren = len(self.ax.get_children()) qqline(self.ax, "q", dist=stats.norm, x=self.x, y=self.y) assert len(self.ax.get_children()) > nchildren @pytest.mark.matplotlib def test_q_fmt(self, close_figures): qqline(self.ax, "q", dist=stats.norm, x=self.x, y=self.y, fmt=self.fmt) @pytest.mark.matplotlib def test_q_fmt_lineoptions(self, close_figures): qqline( self.ax, "q", dist=stats.norm, x=self.x, y=self.y, fmt=self.fmt, **self.lineoptions, ) class TestPlottingPosition: def setup(self): self.N = 13 self.data = np.arange(self.N) def do_test(self, alpha, beta): smpp = gofplots.plotting_pos(self.N, a=alpha, b=beta) sppp = stats.mstats.plotting_positions( self.data, alpha=alpha, beta=beta ) nptest.assert_array_almost_equal(smpp, sppp, decimal=5) @pytest.mark.matplotlib def test_weibull(self, close_figures): self.do_test(0, 0) @pytest.mark.matplotlib def test_lininterp(self, close_figures): self.do_test(0, 1) @pytest.mark.matplotlib def test_piecewise(self, close_figures): self.do_test(0.5, 0.5) @pytest.mark.matplotlib def test_approx_med_unbiased(self, close_figures): self.do_test(1.0 / 3.0, 1.0 / 3.0) @pytest.mark.matplotlib def test_cunnane(self, close_figures): self.do_test(0.4, 0.4) def test_param_unpacking(): expected = np.array([2.0, 3, 0, 1]) pp = ProbPlot(np.empty(100), dist=stats.beta(2, 3)) assert_equal(pp.fit_params, expected) pp = ProbPlot(np.empty(100), stats.beta(2, b=3)) assert_equal(pp.fit_params, expected) pp = ProbPlot(np.empty(100), stats.beta(a=2, b=3)) assert_equal(pp.fit_params, expected) expected = np.array([2.0, 3, 4, 1]) pp = ProbPlot(np.empty(100), stats.beta(2, 3, 4)) assert_equal(pp.fit_params, expected) pp = ProbPlot(np.empty(100), stats.beta(a=2, b=3, loc=4)) assert_equal(pp.fit_params, expected) expected = np.array([2.0, 3, 4, 5]) pp = ProbPlot(np.empty(100), stats.beta(2, 3, 4, 5)) assert_equal(pp.fit_params, expected) pp = ProbPlot(np.empty(100), stats.beta(2, 3, 4, scale=5)) assert_equal(pp.fit_params, expected) pp = ProbPlot(np.empty(100), stats.beta(2, 3, loc=4, scale=5)) assert_equal(pp.fit_params, expected) pp = ProbPlot(np.empty(100), stats.beta(2, b=3, loc=4, scale=5)) assert_equal(pp.fit_params, expected) pp = ProbPlot(np.empty(100), stats.beta(a=2, b=3, loc=4, scale=5)) assert_equal(pp.fit_params, expected) statsmodels-0.12.2/statsmodels/graphics/tests/test_mosaicplot.py000066400000000000000000000451511400612667500252420ustar00rootroot00000000000000from statsmodels.compat.python import lrange from io import BytesIO from itertools import product import numpy as np import pandas as pd import pytest from numpy.testing import assert_, assert_raises from statsmodels.api import datasets # utilities for the tests try: import matplotlib.pyplot as plt # noqa:F401 except ImportError: pass # the main drawing function from statsmodels.graphics.mosaicplot import mosaic # other functions to be tested for accuracy from statsmodels.graphics.mosaicplot import _hierarchical_split from statsmodels.graphics.mosaicplot import _reduce_dict from statsmodels.graphics.mosaicplot import _key_splitting from statsmodels.graphics.mosaicplot import _normalize_split from statsmodels.graphics.mosaicplot import _split_rect @pytest.mark.matplotlib def test_data_conversion(close_figures): # It will not reorder the elements # so the dictionary will look odd # as it key order has the c and b # keys swapped import pandas _, ax = plt.subplots(4, 4) data = {'ax': 1, 'bx': 2, 'cx': 3} mosaic(data, ax=ax[0, 0], title='basic dict', axes_label=False) data = pandas.Series(data) mosaic(data, ax=ax[0, 1], title='basic series', axes_label=False) data = [1, 2, 3] mosaic(data, ax=ax[0, 2], title='basic list', axes_label=False) data = np.asarray(data) mosaic(data, ax=ax[0, 3], title='basic array', axes_label=False) data = {('ax', 'cx'): 1, ('bx', 'cx'): 2, ('ax', 'dx'): 3, ('bx', 'dx'): 4} mosaic(data, ax=ax[1, 0], title='compound dict', axes_label=False) mosaic(data, ax=ax[2, 0], title='inverted keys dict', index=[1, 0], axes_label=False) data = pandas.Series(data) mosaic(data, ax=ax[1, 1], title='compound series', axes_label=False) mosaic(data, ax=ax[2, 1], title='inverted keys series', index=[1, 0]) data = [[1, 2], [3, 4]] mosaic(data, ax=ax[1, 2], title='compound list', axes_label=False) mosaic(data, ax=ax[2, 2], title='inverted keys list', index=[1, 0]) data = np.array([[1, 2], [3, 4]]) mosaic(data, ax=ax[1, 3], title='compound array', axes_label=False) mosaic(data, ax=ax[2, 3], title='inverted keys array', index=[1, 0], axes_label=False) gender = ['male', 'male', 'male', 'female', 'female', 'female'] pet = ['cat', 'dog', 'dog', 'cat', 'dog', 'cat'] data = pandas.DataFrame({'gender': gender, 'pet': pet}) mosaic(data, ['gender'], ax=ax[3, 0], title='dataframe by key 1', axes_label=False) mosaic(data, ['pet'], ax=ax[3, 1], title='dataframe by key 2', axes_label=False) mosaic(data, ['gender', 'pet'], ax=ax[3, 2], title='both keys', axes_label=False) mosaic(data, ['pet', 'gender'], ax=ax[3, 3], title='keys inverted', axes_label=False) plt.suptitle('testing data conversion (plot 1 of 4)') @pytest.mark.matplotlib def test_mosaic_simple(close_figures): # display a simple plot of 4 categories of data, splitted in four # levels with increasing size for each group # creation of the levels key_set = (['male', 'female'], ['old', 'adult', 'young'], ['worker', 'unemployed'], ['healty', 'ill']) # the cartesian product of all the categories is # the complete set of categories keys = list(product(*key_set)) data = dict(zip(keys, range(1, 1 + len(keys)))) # which colours should I use for the various categories? # put it into a dict props = {} #males and females in blue and red props[('male',)] = {'color': 'b'} props[('female',)] = {'color': 'r'} # all the groups corresponding to ill groups have a different color for key in keys: if 'ill' in key: if 'male' in key: props[key] = {'color': 'BlueViolet' , 'hatch': '+'} else: props[key] = {'color': 'Crimson' , 'hatch': '+'} # mosaic of the data, with given gaps and colors mosaic(data, gap=0.05, properties=props, axes_label=False) plt.suptitle('syntetic data, 4 categories (plot 2 of 4)') @pytest.mark.matplotlib def test_mosaic(close_figures): # make the same analysis on a known dataset # load the data and clean it a bit affairs = datasets.fair.load_pandas() datas = affairs.exog # any time greater than 0 is cheating datas['cheated'] = affairs.endog > 0 # sort by the marriage quality and give meaningful name # [rate_marriage, age, yrs_married, children, # religious, educ, occupation, occupation_husb] datas = datas.sort_values(['rate_marriage', 'religious']) num_to_desc = {1: 'awful', 2: 'bad', 3: 'intermediate', 4: 'good', 5: 'wonderful'} datas['rate_marriage'] = datas['rate_marriage'].map(num_to_desc) num_to_faith = {1: 'non religious', 2: 'poorly religious', 3: 'religious', 4: 'very religious'} datas['religious'] = datas['religious'].map(num_to_faith) num_to_cheat = {False: 'faithful', True: 'cheated'} datas['cheated'] = datas['cheated'].map(num_to_cheat) # finished cleaning _, ax = plt.subplots(2, 2) mosaic(datas, ['rate_marriage', 'cheated'], ax=ax[0, 0], title='by marriage happiness') mosaic(datas, ['religious', 'cheated'], ax=ax[0, 1], title='by religiosity') mosaic(datas, ['rate_marriage', 'religious', 'cheated'], ax=ax[1, 0], title='by both', labelizer=lambda k:'') ax[1, 0].set_xlabel('marriage rating') ax[1, 0].set_ylabel('religion status') mosaic(datas, ['religious', 'rate_marriage'], ax=ax[1, 1], title='inter-dependence', axes_label=False) plt.suptitle("extramarital affairs (plot 3 of 4)") @pytest.mark.matplotlib def test_mosaic_very_complex(close_figures): # make a scattermatrix of mosaic plots to show the correlations between # each pair of variable in a dataset. Could be easily converted into a # new function that does this automatically based on the type of data key_name = ['gender', 'age', 'health', 'work'] key_base = (['male', 'female'], ['old', 'young'], ['healty', 'ill'], ['work', 'unemployed']) keys = list(product(*key_base)) data = dict(zip(keys, range(1, 1 + len(keys)))) props = {} props[('male', 'old')] = {'color': 'r'} props[('female',)] = {'color': 'pink'} L = len(key_base) _, axes = plt.subplots(L, L) for i in range(L): for j in range(L): m = set(range(L)).difference(set((i, j))) if i == j: axes[i, i].text(0.5, 0.5, key_name[i], ha='center', va='center') axes[i, i].set_xticks([]) axes[i, i].set_xticklabels([]) axes[i, i].set_yticks([]) axes[i, i].set_yticklabels([]) else: ji = max(i, j) ij = min(i, j) temp_data = dict([((k[ij], k[ji]) + tuple(k[r] for r in m), v) for k, v in data.items()]) keys = list(temp_data.keys()) for k in keys: value = _reduce_dict(temp_data, k[:2]) temp_data[k[:2]] = value del temp_data[k] mosaic(temp_data, ax=axes[i, j], axes_label=False, properties=props, gap=0.05, horizontal=i > j) plt.suptitle('old males should look bright red, (plot 4 of 4)') @pytest.mark.matplotlib def test_axes_labeling(close_figures): from numpy.random import rand key_set = (['male', 'female'], ['old', 'adult', 'young'], ['worker', 'unemployed'], ['yes', 'no']) # the cartesian product of all the categories is # the complete set of categories keys = list(product(*key_set)) data = dict(zip(keys, rand(len(keys)))) lab = lambda k: ''.join(s[0] for s in k) fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(16, 8)) mosaic(data, ax=ax1, labelizer=lab, horizontal=True, label_rotation=45) mosaic(data, ax=ax2, labelizer=lab, horizontal=False, label_rotation=[0, 45, 90, 0]) #fig.tight_layout() fig.suptitle("correct alignment of the axes labels") @pytest.mark.smoke @pytest.mark.matplotlib def test_mosaic_empty_cells(close_figures): # GH#2286 import pandas as pd mydata = pd.DataFrame({'id2': {64: 'Angelica', 65: 'DXW_UID', 66: 'casuid01', 67: 'casuid01', 68: 'EC93_uid', 69: 'EC93_uid', 70: 'EC93_uid', 60: 'DXW_UID', 61: 'AtmosFox', 62: 'DXW_UID', 63: 'DXW_UID'}, 'id1': {64: 'TGP', 65: 'Retention01', 66: 'default', 67: 'default', 68: 'Musa_EC_9_3', 69: 'Musa_EC_9_3', 70: 'Musa_EC_9_3', 60: 'default', 61: 'default', 62: 'default', 63: 'default'}}) ct = pd.crosstab(mydata.id1, mydata.id2) _, vals = mosaic(ct.T.unstack()) _, vals = mosaic(mydata, ['id1','id2']) eq = lambda x, y: assert_(np.allclose(x, y)) def test_recursive_split(): keys = list(product('mf')) data = dict(zip(keys, [1] * len(keys))) res = _hierarchical_split(data, gap=0) assert_(list(res.keys()) == keys) res[('m',)] = (0.0, 0.0, 0.5, 1.0) res[('f',)] = (0.5, 0.0, 0.5, 1.0) keys = list(product('mf', 'yao')) data = dict(zip(keys, [1] * len(keys))) res = _hierarchical_split(data, gap=0) assert_(list(res.keys()) == keys) res[('m', 'y')] = (0.0, 0.0, 0.5, 1 / 3) res[('m', 'a')] = (0.0, 1 / 3, 0.5, 1 / 3) res[('m', 'o')] = (0.0, 2 / 3, 0.5, 1 / 3) res[('f', 'y')] = (0.5, 0.0, 0.5, 1 / 3) res[('f', 'a')] = (0.5, 1 / 3, 0.5, 1 / 3) res[('f', 'o')] = (0.5, 2 / 3, 0.5, 1 / 3) def test__reduce_dict(): data = dict(zip(list(product('mf', 'oy', 'wn')), [1] * 8)) eq(_reduce_dict(data, ('m',)), 4) eq(_reduce_dict(data, ('m', 'o')), 2) eq(_reduce_dict(data, ('m', 'o', 'w')), 1) data = dict(zip(list(product('mf', 'oy', 'wn')), lrange(8))) eq(_reduce_dict(data, ('m',)), 6) eq(_reduce_dict(data, ('m', 'o')), 1) eq(_reduce_dict(data, ('m', 'o', 'w')), 0) def test__key_splitting(): # subdivide starting with an empty tuple base_rect = {tuple(): (0, 0, 1, 1)} res = _key_splitting(base_rect, ['a', 'b'], [1, 1], tuple(), True, 0) assert_(list(res.keys()) == [('a',), ('b',)]) eq(res[('a',)], (0, 0, 0.5, 1)) eq(res[('b',)], (0.5, 0, 0.5, 1)) # subdivide a in two sublevel res_bis = _key_splitting(res, ['c', 'd'], [1, 1], ('a',), False, 0) assert_(list(res_bis.keys()) == [('a', 'c'), ('a', 'd'), ('b',)]) eq(res_bis[('a', 'c')], (0.0, 0.0, 0.5, 0.5)) eq(res_bis[('a', 'd')], (0.0, 0.5, 0.5, 0.5)) eq(res_bis[('b',)], (0.5, 0, 0.5, 1)) # starting with a non empty tuple and uneven distribution base_rect = {('total',): (0, 0, 1, 1)} res = _key_splitting(base_rect, ['a', 'b'], [1, 2], ('total',), True, 0) assert_(list(res.keys()) == [('total',) + (e,) for e in ['a', 'b']]) eq(res[('total', 'a')], (0, 0, 1 / 3, 1)) eq(res[('total', 'b')], (1 / 3, 0, 2 / 3, 1)) def test_proportion_normalization(): # extremes should give the whole set, as well # as if 0 is inserted eq(_normalize_split(0.), [0.0, 0.0, 1.0]) eq(_normalize_split(1.), [0.0, 1.0, 1.0]) eq(_normalize_split(2.), [0.0, 1.0, 1.0]) # negative values should raise ValueError assert_raises(ValueError, _normalize_split, -1) assert_raises(ValueError, _normalize_split, [1., -1]) assert_raises(ValueError, _normalize_split, [1., -1, 0.]) # if everything is zero it will complain assert_raises(ValueError, _normalize_split, [0.]) assert_raises(ValueError, _normalize_split, [0., 0.]) # one-element array should return the whole interval eq(_normalize_split([0.5]), [0.0, 1.0]) eq(_normalize_split([1.]), [0.0, 1.0]) eq(_normalize_split([2.]), [0.0, 1.0]) # simple division should give two pieces for x in [0.3, 0.5, 0.9]: eq(_normalize_split(x), [0., x, 1.0]) # multiple division should split as the sum of the components for x, y in [(0.25, 0.5), (0.1, 0.8), (10., 30.)]: eq(_normalize_split([x, y]), [0., x / (x + y), 1.0]) for x, y, z in [(1., 1., 1.), (0.1, 0.5, 0.7), (10., 30., 40)]: eq(_normalize_split( [x, y, z]), [0., x / (x + y + z), (x + y) / (x + y + z), 1.0]) def test_false_split(): # if you ask it to be divided in only one piece, just return the original # one pure_square = [0., 0., 1., 1.] conf_h = dict(proportion=[1], gap=0.0, horizontal=True) conf_v = dict(proportion=[1], gap=0.0, horizontal=False) eq(_split_rect(*pure_square, **conf_h), pure_square) eq(_split_rect(*pure_square, **conf_v), pure_square) conf_h = dict(proportion=[1], gap=0.5, horizontal=True) conf_v = dict(proportion=[1], gap=0.5, horizontal=False) eq(_split_rect(*pure_square, **conf_h), pure_square) eq(_split_rect(*pure_square, **conf_v), pure_square) # identity on a void rectangle should not give anything strange null_square = [0., 0., 0., 0.] conf = dict(proportion=[1], gap=0.0, horizontal=True) eq(_split_rect(*null_square, **conf), null_square) conf = dict(proportion=[1], gap=1.0, horizontal=True) eq(_split_rect(*null_square, **conf), null_square) # splitting a negative rectangle should raise error neg_square = [0., 0., -1., 0.] conf = dict(proportion=[1], gap=0.0, horizontal=True) assert_raises(ValueError, _split_rect, *neg_square, **conf) conf = dict(proportion=[1, 1], gap=0.0, horizontal=True) assert_raises(ValueError, _split_rect, *neg_square, **conf) conf = dict(proportion=[1], gap=0.5, horizontal=True) assert_raises(ValueError, _split_rect, *neg_square, **conf) conf = dict(proportion=[1, 1], gap=0.5, horizontal=True) assert_raises(ValueError, _split_rect, *neg_square, **conf) def test_rect_pure_split(): pure_square = [0., 0., 1., 1.] # division in two equal pieces from the perfect square h_2split = [(0.0, 0.0, 0.5, 1.0), (0.5, 0.0, 0.5, 1.0)] conf_h = dict(proportion=[1, 1], gap=0.0, horizontal=True) eq(_split_rect(*pure_square, **conf_h), h_2split) v_2split = [(0.0, 0.0, 1.0, 0.5), (0.0, 0.5, 1.0, 0.5)] conf_v = dict(proportion=[1, 1], gap=0.0, horizontal=False) eq(_split_rect(*pure_square, **conf_v), v_2split) # division in two non-equal pieces from the perfect square h_2split = [(0.0, 0.0, 1 / 3, 1.0), (1 / 3, 0.0, 2 / 3, 1.0)] conf_h = dict(proportion=[1, 2], gap=0.0, horizontal=True) eq(_split_rect(*pure_square, **conf_h), h_2split) v_2split = [(0.0, 0.0, 1.0, 1 / 3), (0.0, 1 / 3, 1.0, 2 / 3)] conf_v = dict(proportion=[1, 2], gap=0.0, horizontal=False) eq(_split_rect(*pure_square, **conf_v), v_2split) # division in three equal pieces from the perfect square h_2split = [(0.0, 0.0, 1 / 3, 1.0), (1 / 3, 0.0, 1 / 3, 1.0), (2 / 3, 0.0, 1 / 3, 1.0)] conf_h = dict(proportion=[1, 1, 1], gap=0.0, horizontal=True) eq(_split_rect(*pure_square, **conf_h), h_2split) v_2split = [(0.0, 0.0, 1.0, 1 / 3), (0.0, 1 / 3, 1.0, 1 / 3), (0.0, 2 / 3, 1.0, 1 / 3)] conf_v = dict(proportion=[1, 1, 1], gap=0.0, horizontal=False) eq(_split_rect(*pure_square, **conf_v), v_2split) # division in three non-equal pieces from the perfect square h_2split = [(0.0, 0.0, 1 / 4, 1.0), (1 / 4, 0.0, 1 / 2, 1.0), (3 / 4, 0.0, 1 / 4, 1.0)] conf_h = dict(proportion=[1, 2, 1], gap=0.0, horizontal=True) eq(_split_rect(*pure_square, **conf_h), h_2split) v_2split = [(0.0, 0.0, 1.0, 1 / 4), (0.0, 1 / 4, 1.0, 1 / 2), (0.0, 3 / 4, 1.0, 1 / 4)] conf_v = dict(proportion=[1, 2, 1], gap=0.0, horizontal=False) eq(_split_rect(*pure_square, **conf_v), v_2split) # splitting on a void rectangle should give multiple void null_square = [0., 0., 0., 0.] conf = dict(proportion=[1, 1], gap=0.0, horizontal=True) eq(_split_rect(*null_square, **conf), [null_square, null_square]) conf = dict(proportion=[1, 2], gap=1.0, horizontal=True) eq(_split_rect(*null_square, **conf), [null_square, null_square]) def test_rect_deformed_split(): non_pure_square = [1., -1., 1., 0.5] # division in two equal pieces from the perfect square h_2split = [(1.0, -1.0, 0.5, 0.5), (1.5, -1.0, 0.5, 0.5)] conf_h = dict(proportion=[1, 1], gap=0.0, horizontal=True) eq(_split_rect(*non_pure_square, **conf_h), h_2split) v_2split = [(1.0, -1.0, 1.0, 0.25), (1.0, -0.75, 1.0, 0.25)] conf_v = dict(proportion=[1, 1], gap=0.0, horizontal=False) eq(_split_rect(*non_pure_square, **conf_v), v_2split) # division in two non-equal pieces from the perfect square h_2split = [(1.0, -1.0, 1 / 3, 0.5), (1 + 1 / 3, -1.0, 2 / 3, 0.5)] conf_h = dict(proportion=[1, 2], gap=0.0, horizontal=True) eq(_split_rect(*non_pure_square, **conf_h), h_2split) v_2split = [(1.0, -1.0, 1.0, 1 / 6), (1.0, 1 / 6 - 1, 1.0, 2 / 6)] conf_v = dict(proportion=[1, 2], gap=0.0, horizontal=False) eq(_split_rect(*non_pure_square, **conf_v), v_2split) def test_gap_split(): pure_square = [0., 0., 1., 1.] # null split conf_h = dict(proportion=[1], gap=1.0, horizontal=True) eq(_split_rect(*pure_square, **conf_h), pure_square) # equal split h_2split = [(0.0, 0.0, 0.25, 1.0), (0.75, 0.0, 0.25, 1.0)] conf_h = dict(proportion=[1, 1], gap=1.0, horizontal=True) eq(_split_rect(*pure_square, **conf_h), h_2split) # disequal split h_2split = [(0.0, 0.0, 1 / 6, 1.0), (0.5 + 1 / 6, 0.0, 1 / 3, 1.0)] conf_h = dict(proportion=[1, 2], gap=1.0, horizontal=True) eq(_split_rect(*pure_square, **conf_h), h_2split) @pytest.mark.matplotlib def test_default_arg_index(close_figures): # 2116 df = pd.DataFrame({'size' : ['small', 'large', 'large', 'small', 'large', 'small'], 'length' : ['long', 'short', 'short', 'long', 'long', 'short']}) assert_raises(ValueError, mosaic, data=df, title='foobar') @pytest.mark.matplotlib def test_missing_category(close_figures): # GH5639 animal = ['dog', 'dog', 'dog', 'cat', 'dog', 'cat', 'cat', 'dog', 'dog', 'cat'] size = ['medium', 'large', 'medium', 'medium', 'medium', 'medium', 'large', 'large', 'large', 'small'] testdata = pd.DataFrame({'animal': animal, 'size': size}) testdata['size'] = pd.Categorical(testdata['size'], categories=['small', 'medium', 'large']) testdata = testdata.sort_values('size') fig, _ = mosaic(testdata, ['animal', 'size']) bio = BytesIO() fig.savefig(bio, format='png') statsmodels-0.12.2/statsmodels/graphics/tests/test_regressionplots.py000066400000000000000000000265771400612667500263450ustar00rootroot00000000000000import numpy as np import pytest import statsmodels.api as sm from numpy.testing import assert_equal, assert_raises, assert_array_less from statsmodels.graphics.regressionplots import (plot_fit, plot_ccpr, plot_regress_exog, abline_plot, plot_partregress_grid, plot_ccpr_grid, add_lowess, plot_added_variable, plot_partial_residuals, plot_ceres_residuals, influence_plot, plot_leverage_resid2) from pandas import Series, DataFrame try: import matplotlib.pyplot as plt except ImportError: pass pdf_output = False if pdf_output: from matplotlib.backends.backend_pdf import PdfPages pdf = PdfPages("test_regressionplots.pdf") else: pdf = None def close_or_save(pdf, fig): if pdf_output: pdf.savefig(fig) class TestPlot(object): @classmethod def setup_class(cls): nsample = 100 sig = 0.5 x1 = np.linspace(0, 20, nsample) x2 = 5 + 3 * np.random.randn(nsample) x = np.c_[x1, x2, np.sin(0.5 * x1), (x2 - 5) ** 2, np.ones(nsample)] beta = [0.5, 0.5, 1, -0.04, 5.] y_true = np.dot(x, beta) y = y_true + sig * np.random.normal(size=nsample) exog0 = sm.add_constant(np.c_[x1, x2], prepend=False) cls.res = sm.OLS(y, exog0).fit() cls.res_true = sm.OLS(y, x).fit() @pytest.mark.matplotlib def test_plot_fit(self, close_figures): res = self.res fig = plot_fit(res, 0, y_true=None) x0 = res.model.exog[:, 0] yf = res.fittedvalues y = res.model.endog px1, px2 = fig.axes[0].get_lines()[0].get_data() np.testing.assert_equal(x0, px1) np.testing.assert_equal(y, px2) px1, px2 = fig.axes[0].get_lines()[1].get_data() np.testing.assert_equal(x0, px1) np.testing.assert_equal(yf, px2) close_or_save(pdf, fig) @pytest.mark.matplotlib def test_plot_oth(self, close_figures): # just test that they run res = self.res plot_fit(res, 0, y_true=None) plot_partregress_grid(res, exog_idx=[0, 1]) # GH 5873 plot_partregress_grid(self.res_true, grid=(2, 3)) plot_regress_exog(res, exog_idx=0) plot_ccpr(res, exog_idx=0) plot_ccpr_grid(res, exog_idx=[0]) fig = plot_ccpr_grid(res, exog_idx=[0,1]) for ax in fig.axes: add_lowess(ax) close_or_save(pdf, fig) @pytest.mark.matplotlib def test_plot_influence(self, close_figures): infl = self.res.get_influence() fig = influence_plot(self.res) assert_equal(isinstance(fig, plt.Figure), True) # test that we have the correct criterion for sizes #3103 try: sizes = fig.axes[0].get_children()[0]._sizes ex = sm.add_constant(infl.cooks_distance[0]) ssr = sm.OLS(sizes, ex).fit().ssr assert_array_less(ssr, 1e-12) except AttributeError: import warnings warnings.warn('test not compatible with matplotlib version') fig = influence_plot(self.res, criterion='DFFITS') assert_equal(isinstance(fig, plt.Figure), True) try: sizes = fig.axes[0].get_children()[0]._sizes ex = sm.add_constant(np.abs(infl.dffits[0])) ssr = sm.OLS(sizes, ex).fit().ssr assert_array_less(ssr, 1e-12) except AttributeError: pass assert_raises(ValueError, influence_plot, self.res, criterion='unknown') @pytest.mark.matplotlib def test_plot_leverage_resid2(self, close_figures): fig = plot_leverage_resid2(self.res) assert_equal(isinstance(fig, plt.Figure), True) class TestPlotPandas(TestPlot): def setup(self): nsample = 100 sig = 0.5 x1 = np.linspace(0, 20, nsample) x2 = 5 + 3* np.random.randn(nsample) X = np.c_[x1, x2, np.sin(0.5*x1), (x2-5)**2, np.ones(nsample)] beta = [0.5, 0.5, 1, -0.04, 5.] y_true = np.dot(X, beta) y = y_true + sig * np.random.normal(size=nsample) exog0 = sm.add_constant(np.c_[x1, x2], prepend=False) exog0 = DataFrame(exog0, columns=["const", "var1", "var2"]) y = Series(y, name="outcome") res = sm.OLS(y, exog0).fit() self.res = res data = DataFrame(exog0, columns=["const", "var1", "var2"]) data['y'] = y self.data = data class TestPlotFormula(TestPlotPandas): @pytest.mark.matplotlib def test_one_column_exog(self, close_figures): from statsmodels.formula.api import ols res = ols("y~var1-1", data=self.data).fit() plot_regress_exog(res, "var1") res = ols("y~var1", data=self.data).fit() plot_regress_exog(res, "var1") class TestABLine(object): @classmethod def setup_class(cls): np.random.seed(12345) X = sm.add_constant(np.random.normal(0, 20, size=30)) y = np.dot(X, [25, 3.5]) + np.random.normal(0, 30, size=30) mod = sm.OLS(y,X).fit() cls.X = X cls.y = y cls.mod = mod @pytest.mark.matplotlib def test_abline_model(self, close_figures): fig = abline_plot(model_results=self.mod) ax = fig.axes[0] ax.scatter(self.X[:,1], self.y) close_or_save(pdf, fig) @pytest.mark.matplotlib def test_abline_model_ax(self, close_figures): fig = plt.figure() ax = fig.add_subplot(111) ax.scatter(self.X[:,1], self.y) fig = abline_plot(model_results=self.mod, ax=ax) close_or_save(pdf, fig) @pytest.mark.matplotlib def test_abline_ab(self, close_figures): mod = self.mod intercept, slope = mod.params fig = abline_plot(intercept=intercept, slope=slope) close_or_save(pdf, fig) @pytest.mark.matplotlib def test_abline_ab_ax(self, close_figures): mod = self.mod intercept, slope = mod.params fig = plt.figure() ax = fig.add_subplot(111) ax.scatter(self.X[:,1], self.y) fig = abline_plot(intercept=intercept, slope=slope, ax=ax) close_or_save(pdf, fig) @pytest.mark.matplotlib def test_abline_remove(self, close_figures): mod = self.mod intercept, slope = mod.params fig = plt.figure() ax = fig.add_subplot(111) ax.scatter(self.X[:,1], self.y) abline_plot(intercept=intercept, slope=slope, ax=ax) abline_plot(intercept=intercept, slope=2*slope, ax=ax) lines = ax.get_lines() lines.pop(0).remove() close_or_save(pdf, fig) class TestABLinePandas(TestABLine): @classmethod def setup_class(cls): np.random.seed(12345) X = sm.add_constant(np.random.normal(0, 20, size=30)) y = np.dot(X, [25, 3.5]) + np.random.normal(0, 30, size=30) cls.X = X cls.y = y X = DataFrame(X, columns=["const", "someX"]) y = Series(y, name="outcome") mod = sm.OLS(y,X).fit() cls.mod = mod class TestAddedVariablePlot(object): @pytest.mark.matplotlib def test_added_variable_poisson(self, close_figures): np.random.seed(3446) n = 100 p = 3 exog = np.random.normal(size=(n, p)) lin_pred = 4 + exog[:, 0] + 0.2 * exog[:, 1]**2 expval = np.exp(lin_pred) endog = np.random.poisson(expval) model = sm.GLM(endog, exog, family=sm.families.Poisson()) results = model.fit() for focus_col in 0, 1, 2: for use_glm_weights in False, True: for resid_type in "resid_deviance", "resid_response": weight_str = ["Unweighted", "Weighted"][use_glm_weights] # Run directly and called as a results method. for j in 0, 1: if j == 0: fig = plot_added_variable(results, focus_col, use_glm_weights=use_glm_weights, resid_type=resid_type) ti = "Added variable plot" else: fig = results.plot_added_variable(focus_col, use_glm_weights=use_glm_weights, resid_type=resid_type) ti = "Added variable plot (called as method)" ax = fig.get_axes()[0] add_lowess(ax) ax.set_position([0.1, 0.1, 0.8, 0.7]) effect_str = ["Linear effect, slope=1", "Quadratic effect", "No effect"][focus_col] ti += "\nPoisson regression\n" ti += effect_str + "\n" ti += weight_str + "\n" ti += "Using '%s' residuals" % resid_type ax.set_title(ti) close_or_save(pdf, fig) close_figures() class TestPartialResidualPlot(object): @pytest.mark.matplotlib def test_partial_residual_poisson(self, close_figures): np.random.seed(3446) n = 100 p = 3 exog = np.random.normal(size=(n, p)) exog[:, 0] = 1 lin_pred = 4 + exog[:, 1] + 0.2*exog[:, 2]**2 expval = np.exp(lin_pred) endog = np.random.poisson(expval) model = sm.GLM(endog, exog, family=sm.families.Poisson()) results = model.fit() for focus_col in 1, 2: for j in 0,1: if j == 0: fig = plot_partial_residuals(results, focus_col) else: fig = results.plot_partial_residuals(focus_col) ax = fig.get_axes()[0] add_lowess(ax) ax.set_position([0.1, 0.1, 0.8, 0.77]) effect_str = ["Intercept", "Linear effect, slope=1", "Quadratic effect"][focus_col] ti = "Partial residual plot" if j == 1: ti += " (called as method)" ax.set_title(ti + "\nPoisson regression\n" + effect_str) close_or_save(pdf, fig) class TestCERESPlot(object): @pytest.mark.matplotlib def test_ceres_poisson(self, close_figures): np.random.seed(3446) n = 100 p = 3 exog = np.random.normal(size=(n, p)) exog[:, 0] = 1 lin_pred = 4 + exog[:, 1] + 0.2*exog[:, 2]**2 expval = np.exp(lin_pred) endog = np.random.poisson(expval) model = sm.GLM(endog, exog, family=sm.families.Poisson()) results = model.fit() for focus_col in 1, 2: for j in 0, 1: if j == 0: fig = plot_ceres_residuals(results, focus_col) else: fig = results.plot_ceres_residuals(focus_col) ax = fig.get_axes()[0] add_lowess(ax) ax.set_position([0.1, 0.1, 0.8, 0.77]) effect_str = ["Intercept", "Linear effect, slope=1", "Quadratic effect"][focus_col] ti = "CERES plot" if j == 1: ti += " (called as method)" ax.set_title(ti + "\nPoisson regression\n" + effect_str) close_or_save(pdf, fig) statsmodels-0.12.2/statsmodels/graphics/tests/test_tsaplots.py000066400000000000000000000201721400612667500247350ustar00rootroot00000000000000from statsmodels.compat.python import lmap from io import BytesIO import numpy as np import pandas as pd from numpy.testing import assert_equal, assert_ import pytest import statsmodels.api as sm from statsmodels.graphics.tsaplots import ( plot_acf, plot_pacf, month_plot, quarter_plot, seasonal_plot, plot_predict, ) import statsmodels.tsa.arima_process as tsp from statsmodels.tsa.ar_model import AutoReg from statsmodels.tsa.arima.model import ARIMA try: import matplotlib.pyplot as plt except ImportError: pass @pytest.mark.matplotlib def test_plot_acf(close_figures): # Just test that it runs. fig = plt.figure() ax = fig.add_subplot(111) ar = np.r_[1.0, -0.9] ma = np.r_[1.0, 0.9] armaprocess = tsp.ArmaProcess(ar, ma) rs = np.random.RandomState(1234) acf = armaprocess.generate_sample(100, distrvs=rs.standard_normal) plot_acf(acf, ax=ax, lags=10) plot_acf(acf, ax=ax) plot_acf(acf, ax=ax, alpha=None) @pytest.mark.matplotlib def test_plot_acf_irregular(close_figures): # Just test that it runs. fig = plt.figure() ax = fig.add_subplot(111) ar = np.r_[1.0, -0.9] ma = np.r_[1.0, 0.9] armaprocess = tsp.ArmaProcess(ar, ma) rs = np.random.RandomState(1234) acf = armaprocess.generate_sample(100, distrvs=rs.standard_normal) plot_acf(acf, ax=ax, lags=np.arange(1, 11)) plot_acf(acf, ax=ax, lags=10, zero=False) plot_acf(acf, ax=ax, alpha=None, zero=False) @pytest.mark.matplotlib def test_plot_pacf(close_figures): # Just test that it runs. fig = plt.figure() ax = fig.add_subplot(111) ar = np.r_[1.0, -0.9] ma = np.r_[1.0, 0.9] armaprocess = tsp.ArmaProcess(ar, ma) rs = np.random.RandomState(1234) pacf = armaprocess.generate_sample(100, distrvs=rs.standard_normal) plot_pacf(pacf, ax=ax) plot_pacf(pacf, ax=ax, alpha=None) @pytest.mark.matplotlib def test_plot_pacf_kwargs(close_figures): # Just test that it runs. fig = plt.figure() ax = fig.add_subplot(111) ar = np.r_[1.0, -0.9] ma = np.r_[1.0, 0.9] armaprocess = tsp.ArmaProcess(ar, ma) rs = np.random.RandomState(1234) pacf = armaprocess.generate_sample(100, distrvs=rs.standard_normal) buff = BytesIO() plot_pacf(pacf, ax=ax) fig.savefig(buff, format="rgba") buff_linestyle = BytesIO() fig_linestyle = plt.figure() ax = fig_linestyle.add_subplot(111) plot_pacf(pacf, ax=ax, ls="-") fig_linestyle.savefig(buff_linestyle, format="rgba") buff_with_vlines = BytesIO() fig_with_vlines = plt.figure() ax = fig_with_vlines.add_subplot(111) vlines_kwargs = {"linestyles": "dashdot"} plot_pacf(pacf, ax=ax, vlines_kwargs=vlines_kwargs) fig_with_vlines.savefig(buff_with_vlines, format="rgba") buff.seek(0) buff_linestyle.seek(0) buff_with_vlines.seek(0) plain = buff.read() linestyle = buff_linestyle.read() with_vlines = buff_with_vlines.read() assert_(plain != linestyle) assert_(with_vlines != plain) assert_(linestyle != with_vlines) @pytest.mark.matplotlib def test_plot_acf_kwargs(close_figures): # Just test that it runs. fig = plt.figure() ax = fig.add_subplot(111) ar = np.r_[1.0, -0.9] ma = np.r_[1.0, 0.9] armaprocess = tsp.ArmaProcess(ar, ma) rs = np.random.RandomState(1234) acf = armaprocess.generate_sample(100, distrvs=rs.standard_normal) buff = BytesIO() plot_acf(acf, ax=ax) fig.savefig(buff, format="rgba") buff_with_vlines = BytesIO() fig_with_vlines = plt.figure() ax = fig_with_vlines.add_subplot(111) vlines_kwargs = {"linestyles": "dashdot"} plot_acf(acf, ax=ax, vlines_kwargs=vlines_kwargs) fig_with_vlines.savefig(buff_with_vlines, format="rgba") buff.seek(0) buff_with_vlines.seek(0) plain = buff.read() with_vlines = buff_with_vlines.read() assert_(with_vlines != plain) @pytest.mark.matplotlib def test_plot_acf_missing(close_figures): # Just test that it runs. fig = plt.figure() ax = fig.add_subplot(111) ar = np.r_[1.0, -0.9] ma = np.r_[1.0, 0.9] armaprocess = tsp.ArmaProcess(ar, ma) rs = np.random.RandomState(1234) acf = armaprocess.generate_sample(100, distrvs=rs.standard_normal) acf[::13] = np.nan buff = BytesIO() plot_acf(acf, ax=ax, missing="drop") fig.savefig(buff, format="rgba") buff.seek(0) fig = plt.figure() ax = fig.add_subplot(111) buff_conservative = BytesIO() plot_acf(acf, ax=ax, missing="conservative") fig.savefig(buff_conservative, format="rgba") buff_conservative.seek(0) assert_(buff.read() != buff_conservative.read()) @pytest.mark.matplotlib def test_plot_pacf_irregular(close_figures): # Just test that it runs. fig = plt.figure() ax = fig.add_subplot(111) ar = np.r_[1.0, -0.9] ma = np.r_[1.0, 0.9] armaprocess = tsp.ArmaProcess(ar, ma) rs = np.random.RandomState(1234) pacf = armaprocess.generate_sample(100, distrvs=rs.standard_normal) plot_pacf(pacf, ax=ax, lags=np.arange(1, 11)) plot_pacf(pacf, ax=ax, lags=10, zero=False) plot_pacf(pacf, ax=ax, alpha=None, zero=False) @pytest.mark.matplotlib def test_plot_month(close_figures): dta = sm.datasets.elnino.load_pandas().data dta["YEAR"] = dta.YEAR.astype(int).apply(str) dta = dta.set_index("YEAR").T.unstack() dates = pd.to_datetime(["-".join([x[1], x[0]]) for x in dta.index.values]) # test dates argument fig = month_plot(dta.values, dates=dates, ylabel="el nino") # test with a TimeSeries DatetimeIndex with no freq dta.index = pd.DatetimeIndex(dates) fig = month_plot(dta) # w freq dta.index = pd.DatetimeIndex(dates, freq="MS") fig = month_plot(dta) # test with a TimeSeries PeriodIndex dta.index = pd.PeriodIndex(dates, freq="M") fig = month_plot(dta) @pytest.mark.matplotlib def test_plot_quarter(close_figures): dta = sm.datasets.macrodata.load_pandas().data dates = lmap( "Q".join, zip( dta.year.astype(int).apply(str), dta.quarter.astype(int).apply(str) ), ) # test dates argument quarter_plot(dta.unemp.values, dates) # test with a DatetimeIndex with no freq dta.set_index(pd.to_datetime(dates), inplace=True) quarter_plot(dta.unemp) # w freq # see pandas #6631 dta.index = pd.DatetimeIndex(pd.to_datetime(dates), freq="QS-Oct") quarter_plot(dta.unemp) # w PeriodIndex dta.index = pd.PeriodIndex(pd.to_datetime(dates), freq="Q") quarter_plot(dta.unemp) @pytest.mark.matplotlib def test_seasonal_plot(close_figures): rs = np.random.RandomState(1234) data = rs.randn(20, 12) data += 6 * np.sin(np.arange(12.0) / 11 * np.pi)[None, :] data = data.ravel() months = np.tile(np.arange(1, 13), (20, 1)) months = months.ravel() df = pd.DataFrame([data, months], index=["data", "months"]).T grouped = df.groupby("months")["data"] labels = [ "Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec", ] fig = seasonal_plot(grouped, labels) ax = fig.get_axes()[0] output = [tl.get_text() for tl in ax.get_xticklabels()] assert_equal(labels, output) @pytest.mark.matplotlib @pytest.mark.parametrize( "model_and_args", [(AutoReg, dict(lags=2, old_names=False)), (ARIMA, dict(order=(2, 0, 0)))], ) @pytest.mark.parametrize("use_pandas", [True, False]) @pytest.mark.parametrize("alpha", [None, 0.10]) def test_predict_plot(use_pandas, model_and_args, alpha): model, kwargs = model_and_args rs = np.random.RandomState(0) y = rs.standard_normal(1000) for i in range(2, 1000): y[i] += 1.8 * y[i - 1] - 0.9 * y[i - 2] y = y[100:] if use_pandas: index = pd.date_range("1960-1-1", freq="M", periods=y.shape[0] + 24) start = index[index.shape[0] // 2] end = index[-1] y = pd.Series(y, index=index[:-24]) else: start = y.shape[0] // 2 end = y.shape[0] + 24 res = model(y, **kwargs).fit() fig = plot_predict(res, start, end, alpha=alpha) assert isinstance(fig, plt.Figure) statsmodels-0.12.2/statsmodels/graphics/tsaplots.py000066400000000000000000000411201400612667500225300ustar00rootroot00000000000000"""Correlation plot functions.""" from statsmodels.compat.pandas import deprecate_kwarg import numpy as np import pandas as pd from statsmodels.graphics import utils from statsmodels.tsa.stattools import acf, pacf def _prepare_data_corr_plot(x, lags, zero): zero = bool(zero) irregular = False if zero else True if lags is None: # GH 4663 - use a sensible default value nobs = x.shape[0] lim = min(int(np.ceil(10 * np.log10(nobs))), nobs - 1) lags = np.arange(not zero, lim + 1) elif np.isscalar(lags): lags = np.arange(not zero, int(lags) + 1) # +1 for zero lag else: irregular = True lags = np.asanyarray(lags).astype(int) nlags = lags.max(0) return lags, nlags, irregular def _plot_corr( ax, title, acf_x, confint, lags, irregular, use_vlines, vlines_kwargs, **kwargs, ): if irregular: acf_x = acf_x[lags] if confint is not None: confint = confint[lags] if use_vlines: ax.vlines(lags, [0], acf_x, **vlines_kwargs) ax.axhline(**kwargs) kwargs.setdefault("marker", "o") kwargs.setdefault("markersize", 5) if "ls" not in kwargs: # gh-2369 kwargs.setdefault("linestyle", "None") ax.margins(0.05) ax.plot(lags, acf_x, **kwargs) ax.set_title(title) if confint is not None: if lags[0] == 0: lags = lags[1:] confint = confint[1:] acf_x = acf_x[1:] lags = lags.astype(float) lags[0] -= 0.5 lags[-1] += 0.5 ax.fill_between( lags, confint[:, 0] - acf_x, confint[:, 1] - acf_x, alpha=0.25 ) @deprecate_kwarg("unbiased", "adjusted") def plot_acf( x, ax=None, lags=None, *, alpha=0.05, use_vlines=True, adjusted=False, fft=False, missing="none", title="Autocorrelation", zero=True, vlines_kwargs=None, **kwargs, ): """ Plot the autocorrelation function Plots lags on the horizontal and the correlations on vertical axis. Parameters ---------- x : array_like Array of time-series values ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. lags : {int, array_like}, optional An int or array of lag values, used on horizontal axis. Uses np.arange(lags) when lags is an int. If not provided, ``lags=np.arange(len(corr))`` is used. alpha : scalar, optional If a number is given, the confidence intervals for the given level are returned. For instance if alpha=.05, 95 % confidence intervals are returned where the standard deviation is computed according to Bartlett's formula. If None, no confidence intervals are plotted. use_vlines : bool, optional If True, vertical lines and markers are plotted. If False, only markers are plotted. The default marker is 'o'; it can be overridden with a ``marker`` kwarg. adjusted : bool If True, then denominators for autocovariance are n-k, otherwise n fft : bool, optional If True, computes the ACF via FFT. missing : str, optional A string in ['none', 'raise', 'conservative', 'drop'] specifying how the NaNs are to be treated. title : str, optional Title to place on plot. Default is 'Autocorrelation' zero : bool, optional Flag indicating whether to include the 0-lag autocorrelation. Default is True. vlines_kwargs : dict, optional Optional dictionary of keyword arguments that are passed to vlines. **kwargs : kwargs, optional Optional keyword arguments that are directly passed on to the Matplotlib ``plot`` and ``axhline`` functions. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. See Also -------- matplotlib.pyplot.xcorr matplotlib.pyplot.acorr Notes ----- Adapted from matplotlib's `xcorr`. Data are plotted as ``plot(lags, corr, **kwargs)`` kwargs is used to pass matplotlib optional arguments to both the line tracing the autocorrelations and for the horizontal line at 0. These options must be valid for a Line2D object. vlines_kwargs is used to pass additional optional arguments to the vertical lines connecting each autocorrelation to the axis. These options must be valid for a LineCollection object. Examples -------- >>> import pandas as pd >>> import matplotlib.pyplot as plt >>> import statsmodels.api as sm >>> dta = sm.datasets.sunspots.load_pandas().data >>> dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008')) >>> del dta["YEAR"] >>> sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40) >>> plt.show() .. plot:: plots/graphics_tsa_plot_acf.py """ fig, ax = utils.create_mpl_ax(ax) lags, nlags, irregular = _prepare_data_corr_plot(x, lags, zero) vlines_kwargs = {} if vlines_kwargs is None else vlines_kwargs confint = None # acf has different return type based on alpha acf_x = acf( x, nlags=nlags, alpha=alpha, fft=fft, adjusted=adjusted, missing=missing, ) if alpha is not None: acf_x, confint = acf_x _plot_corr( ax, title, acf_x, confint, lags, irregular, use_vlines, vlines_kwargs, **kwargs, ) return fig def plot_pacf( x, ax=None, lags=None, alpha=0.05, method="ywadjusted", use_vlines=True, title="Partial Autocorrelation", zero=True, vlines_kwargs=None, **kwargs, ): """ Plot the partial autocorrelation function Parameters ---------- x : array_like Array of time-series values ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. lags : {int, array_like}, optional An int or array of lag values, used on horizontal axis. Uses np.arange(lags) when lags is an int. If not provided, ``lags=np.arange(len(corr))`` is used. alpha : float, optional If a number is given, the confidence intervals for the given level are returned. For instance if alpha=.05, 95 % confidence intervals are returned where the standard deviation is computed according to 1/sqrt(len(x)) method : {'ywunbiased', 'ywmle', 'ols'} Specifies which method for the calculations to use: - yw or ywunbiased : yule walker with bias correction in denominator for acovf. Default. - ywm or ywmle : yule walker without bias correction - ols - regression of time series on lags of it and on constant - ld or ldunbiased : Levinson-Durbin recursion with bias correction - ldb or ldbiased : Levinson-Durbin recursion without bias correction use_vlines : bool, optional If True, vertical lines and markers are plotted. If False, only markers are plotted. The default marker is 'o'; it can be overridden with a ``marker`` kwarg. title : str, optional Title to place on plot. Default is 'Partial Autocorrelation' zero : bool, optional Flag indicating whether to include the 0-lag autocorrelation. Default is True. vlines_kwargs : dict, optional Optional dictionary of keyword arguments that are passed to vlines. **kwargs : kwargs, optional Optional keyword arguments that are directly passed on to the Matplotlib ``plot`` and ``axhline`` functions. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. See Also -------- matplotlib.pyplot.xcorr matplotlib.pyplot.acorr Notes ----- Plots lags on the horizontal and the correlations on vertical axis. Adapted from matplotlib's `xcorr`. Data are plotted as ``plot(lags, corr, **kwargs)`` kwargs is used to pass matplotlib optional arguments to both the line tracing the autocorrelations and for the horizontal line at 0. These options must be valid for a Line2D object. vlines_kwargs is used to pass additional optional arguments to the vertical lines connecting each autocorrelation to the axis. These options must be valid for a LineCollection object. Examples -------- >>> import pandas as pd >>> import matplotlib.pyplot as plt >>> import statsmodels.api as sm >>> dta = sm.datasets.sunspots.load_pandas().data >>> dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008')) >>> del dta["YEAR"] >>> sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40) >>> plt.show() .. plot:: plots/graphics_tsa_plot_pacf.py """ fig, ax = utils.create_mpl_ax(ax) vlines_kwargs = {} if vlines_kwargs is None else vlines_kwargs lags, nlags, irregular = _prepare_data_corr_plot(x, lags, zero) confint = None if alpha is None: acf_x = pacf(x, nlags=nlags, alpha=alpha, method=method) else: acf_x, confint = pacf(x, nlags=nlags, alpha=alpha, method=method) _plot_corr( ax, title, acf_x, confint, lags, irregular, use_vlines, vlines_kwargs, **kwargs, ) return fig def seasonal_plot(grouped_x, xticklabels, ylabel=None, ax=None): """ Consider using one of month_plot or quarter_plot unless you need irregular plotting. Parameters ---------- grouped_x : iterable of DataFrames Should be a GroupBy object (or similar pair of group_names and groups as DataFrames) with a DatetimeIndex or PeriodIndex xticklabels : list of str List of season labels, one for each group. ylabel : str Lable for y axis ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. """ fig, ax = utils.create_mpl_ax(ax) start = 0 ticks = [] for season, df in grouped_x: df = df.copy() # or sort balks for series. may be better way df.sort_index() nobs = len(df) x_plot = np.arange(start, start + nobs) ticks.append(x_plot.mean()) ax.plot(x_plot, df.values, "k") ax.hlines( df.values.mean(), x_plot[0], x_plot[-1], colors="r", linewidth=3 ) start += nobs ax.set_xticks(ticks) ax.set_xticklabels(xticklabels) ax.set_ylabel(ylabel) ax.margins(0.1, 0.05) return fig def month_plot(x, dates=None, ylabel=None, ax=None): """ Seasonal plot of monthly data. Parameters ---------- x : array_like Seasonal data to plot. If dates is None, x must be a pandas object with a PeriodIndex or DatetimeIndex with a monthly frequency. dates : array_like, optional If `x` is not a pandas object, then dates must be supplied. ylabel : str, optional The label for the y-axis. Will attempt to use the `name` attribute of the Series. ax : Axes, optional Existing axes instance. Returns ------- Figure If `ax` is provided, the Figure instance attached to `ax`. Otherwise a new Figure instance. Examples -------- >>> import statsmodels.api as sm >>> import pandas as pd >>> dta = sm.datasets.elnino.load_pandas().data >>> dta['YEAR'] = dta.YEAR.astype(int).astype(str) >>> dta = dta.set_index('YEAR').T.unstack() >>> dates = pd.to_datetime(list(map(lambda x: '-'.join(x) + '-1', ... dta.index.values))) >>> dta.index = pd.DatetimeIndex(dates, freq='MS') >>> fig = sm.graphics.tsa.month_plot(dta) .. plot:: plots/graphics_tsa_month_plot.py """ if dates is None: from statsmodels.tools.data import _check_period_index _check_period_index(x, freq="M") else: x = pd.Series(x, index=pd.PeriodIndex(dates, freq="M")) xticklabels = ["j", "f", "m", "a", "m", "j", "j", "a", "s", "o", "n", "d"] return seasonal_plot( x.groupby(lambda y: y.month), xticklabels, ylabel=ylabel, ax=ax ) def quarter_plot(x, dates=None, ylabel=None, ax=None): """ Seasonal plot of quarterly data Parameters ---------- x : array_like Seasonal data to plot. If dates is None, x must be a pandas object with a PeriodIndex or DatetimeIndex with a monthly frequency. dates : array_like, optional If `x` is not a pandas object, then dates must be supplied. ylabel : str, optional The label for the y-axis. Will attempt to use the `name` attribute of the Series. ax : matplotlib.axes, optional Existing axes instance. Returns ------- Figure If `ax` is provided, the Figure instance attached to `ax`. Otherwise a new Figure instance. Examples -------- >>> import statsmodels.api as sm >>> import pandas as pd >>> dta = sm.datasets.elnino.load_pandas().data >>> dta['YEAR'] = dta.YEAR.astype(int).astype(str) >>> dta = dta.set_index('YEAR').T.unstack() >>> dates = pd.to_datetime(list(map(lambda x: '-'.join(x) + '-1', ... dta.index.values))) >>> dta.index = dates.to_period('Q') >>> fig = sm.graphics.tsa.quarter_plot(dta) .. plot:: plots/graphics_tsa_quarter_plot.py """ if dates is None: from statsmodels.tools.data import _check_period_index _check_period_index(x, freq="Q") else: x = pd.Series(x, index=pd.PeriodIndex(dates, freq="Q")) xticklabels = ["q1", "q2", "q3", "q4"] return seasonal_plot( x.groupby(lambda y: y.quarter), xticklabels, ylabel=ylabel, ax=ax ) def plot_predict( result, start=None, end=None, dynamic=False, alpha=0.05, ax=None, **predict_kwargs, ): """ Parameters ---------- result : Result Any model result supporting ``get_prediction``. start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, i.e., the last forecast is end. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. dynamic : bool, int, str, or datetime, optional Integer offset relative to `start` at which to begin dynamic prediction. Can also be an absolute date string to parse or a datetime type (these are not interpreted as offsets). Prior to this observation, true endogenous values will be used for prediction; starting with this observation and continuing through the end of prediction, forecasted endogenous values will be used instead. alpha : {float, None} The tail probability not covered by the confidence interval. Must be in (0, 1). Confidence interval is constructed assuming normally distributed shocks. If None, figure will not show the confidence interval. ax : AxesSubplot matplotlib Axes instance to use **predict_kwargs Any additional keyword arguments to pass to ``result.get_prediction``. Returns ------- Figure matplotlib Figure containing the prediction plot """ from statsmodels.graphics.utils import _import_mpl, create_mpl_ax _ = _import_mpl() fig, ax = create_mpl_ax(ax) from statsmodels.tsa.base.prediction import PredictionResults # use predict so you set dates pred: PredictionResults = result.get_prediction( start=start, end=end, dynamic=dynamic, **predict_kwargs ) mean = pred.predicted_mean if isinstance(mean, (pd.Series, pd.DataFrame)): x = mean.index mean.plot(ax=ax, label="forecast") else: x = np.arange(mean.shape[0]) ax.plot(x, mean) if alpha is not None: label = f"{1-alpha:.0%} confidence interval" ci = pred.conf_int(alpha) conf_int = np.asarray(ci) ax.fill_between( x, conf_int[:, 0], conf_int[:, 1], color="gray", alpha=0.5, label=label, ) ax.legend(loc="best") return fig statsmodels-0.12.2/statsmodels/graphics/tukeyplot.py000066400000000000000000000045301400612667500227230ustar00rootroot00000000000000import numpy as np import matplotlib.pyplot as plt import matplotlib.lines as lines def tukeyplot(results, dim=None, yticklabels=None): npairs = len(results) fig = plt.figure() fsp = fig.add_subplot(111) fsp.axis([-50,50,0.5,10.5]) fsp.set_title('95 % family-wise confidence level') fsp.title.set_y(1.025) fsp.set_yticks(np.arange(1,11)) fsp.set_yticklabels(['V-T','V-S','T-S','V-P','T-P','S-P','V-M', 'T-M','S-M','P-M']) #fsp.yaxis.set_major_locator(mticker.MaxNLocator(npairs)) fsp.yaxis.grid(True, linestyle='-', color='gray') fsp.set_xlabel('Differences in mean levels of Var', labelpad=8) fsp.xaxis.tick_bottom() fsp.yaxis.tick_left() xticklines = fsp.get_xticklines() for xtickline in xticklines: xtickline.set_marker(lines.TICKDOWN) xtickline.set_markersize(10) xlabels = fsp.get_xticklabels() for xlabel in xlabels: xlabel.set_y(-.04) yticklines = fsp.get_yticklines() for ytickline in yticklines: ytickline.set_marker(lines.TICKLEFT) ytickline.set_markersize(10) ylabels = fsp.get_yticklabels() for ylabel in ylabels: ylabel.set_x(-.04) for pair in range(npairs): data = .5+results[pair]/100. #fsp.axhline(y=npairs-pair, xmin=data[0], xmax=data[1], linewidth=1.25, fsp.axhline(y=npairs-pair, xmin=data.mean(), xmax=data[1], linewidth=1.25, color='blue', marker="|", markevery=1) fsp.axhline(y=npairs-pair, xmin=data[0], xmax=data.mean(), linewidth=1.25, color='blue', marker="|", markevery=1) #for pair in range(npairs): # data = .5+results[pair]/100. # data = results[pair] # data = np.r_[data[0],data.mean(),data[1]] # l = plt.plot(data, [npairs-pair]*len(data), color='black', # linewidth=.5, marker="|", markevery=1) fsp.axvline(x=0, linestyle="--", color='black') fig.subplots_adjust(bottom=.125) results = np.array([[-10.04391794, 26.34391794], [-21.45225794, 14.93557794], [ 5.61441206, 42.00224794], [-13.40225794, 22.98557794], [-29.60225794, 6.78557794], [ -2.53558794, 33.85224794], [-21.55225794, 14.83557794], [ 8.87275206, 45.26058794], [-10.14391794, 26.24391794], [-37.21058794, -0.82275206]]) #plt.show() statsmodels-0.12.2/statsmodels/graphics/utils.py000066400000000000000000000077001400612667500220250ustar00rootroot00000000000000"""Helper functions for graphics with Matplotlib.""" from statsmodels.compat.python import lrange __all__ = ['create_mpl_ax', 'create_mpl_fig'] def _import_mpl(): """This function is not needed outside this utils module.""" try: import matplotlib.pyplot as plt except: raise ImportError("Matplotlib is not found.") return plt def create_mpl_ax(ax=None): """Helper function for when a single plot axis is needed. Parameters ---------- ax : AxesSubplot, optional If given, this subplot is used to plot in instead of a new figure being created. Returns ------- fig : Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. ax : AxesSubplot The created axis if `ax` is None, otherwise the axis that was passed in. Notes ----- This function imports `matplotlib.pyplot`, which should only be done to create (a) figure(s) with ``plt.figure``. All other functionality exposed by the pyplot module can and should be imported directly from its Matplotlib module. See Also -------- create_mpl_fig Examples -------- A plotting function has a keyword ``ax=None``. Then calls: >>> from statsmodels.graphics import utils >>> fig, ax = utils.create_mpl_ax(ax) """ if ax is None: plt = _import_mpl() fig = plt.figure() ax = fig.add_subplot(111) else: fig = ax.figure return fig, ax def create_mpl_fig(fig=None, figsize=None): """Helper function for when multiple plot axes are needed. Those axes should be created in the functions they are used in, with ``fig.add_subplot()``. Parameters ---------- fig : Figure, optional If given, this figure is simply returned. Otherwise a new figure is created. Returns ------- Figure If `fig` is None, the created figure. Otherwise the input `fig` is returned. See Also -------- create_mpl_ax """ if fig is None: plt = _import_mpl() fig = plt.figure(figsize=figsize) return fig def maybe_name_or_idx(idx, model): """ Give a name or an integer and return the name and integer location of the column in a design matrix. """ if idx is None: idx = lrange(model.exog.shape[1]) if isinstance(idx, int): exog_name = model.exog_names[idx] exog_idx = idx # anticipate index as list and recurse elif isinstance(idx, (tuple, list)): exog_name = [] exog_idx = [] for item in idx: exog_name_item, exog_idx_item = maybe_name_or_idx(item, model) exog_name.append(exog_name_item) exog_idx.append(exog_idx_item) else: # assume we've got a string variable exog_name = idx exog_idx = model.exog_names.index(idx) return exog_name, exog_idx def get_data_names(series_or_dataframe): """ Input can be an array or pandas-like. Will handle 1d array-like but not 2d. Returns a str for 1d data or a list of strings for 2d data. """ names = getattr(series_or_dataframe, 'name', None) if not names: names = getattr(series_or_dataframe, 'columns', None) if not names: shape = getattr(series_or_dataframe, 'shape', [1]) nvars = 1 if len(shape) == 1 else series_or_dataframe.shape[1] names = ["X%d" for _ in range(nvars)] if nvars == 1: names = names[0] else: names = names.tolist() return names def annotate_axes(index, labels, points, offset_points, size, ax, **kwargs): """ Annotate Axes with labels, points, offset_points according to the given index. """ for i in index: label = labels[i] point = points[i] offset = offset_points[i] ax.annotate(label, point, xytext=offset, textcoords="offset points", size=size, **kwargs) return ax statsmodels-0.12.2/statsmodels/imputation/000077500000000000000000000000001400612667500207005ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/imputation/__init__.py000066400000000000000000000001131400612667500230040ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/imputation/bayes_mi.py000066400000000000000000000322771400612667500230550ustar00rootroot00000000000000import numpy as np import pandas as pd from statsmodels.base.model import LikelihoodModelResults class BayesGaussMI(object): """ Bayesian Imputation using a Gaussian model. The approach is Bayesian. The goal is to sample from the joint distribution of the mean vector, covariance matrix, and missing data values given the observed data values. Conjugate priors for the population mean and covariance matrix are used. Gibbs sampling is used to update the mean vector, covariance matrix, and missing data values in turn. After burn-in, the imputed complete data sets from the Gibbs chain can be used in multiple imputation analyses (MI). Parameters ---------- data : ndarray The array of data to be imputed. Values in the array equal to NaN are imputed. mean_prior : ndarray, optional The covariance matrix of the Gaussian prior distribution for the mean vector. If not provided, the identity matrix is used. cov_prior : ndarray, optional The center matrix for the inverse Wishart prior distribution for the covariance matrix. If not provided, the identity matrix is used. cov_prior_df : positive float The degrees of freedom of the inverse Wishart prior distribution for the covariance matrix. Defaults to 1. Examples -------- A basic example with OLS. Data is generated assuming 10% is missing at random. >>> import numpy as np >>> x = np.random.standard_normal((1000, 2)) >>> x.flat[np.random.sample(2000) < 0.1] = np.nan The imputer is used with ``MI``. >>> import statsmodels.api as sm >>> def model_args_fn(x): ... # Return endog, exog from x ... return x[:, 0], x[:, 1:] >>> imp = sm.BayesGaussMI(x) >>> mi = sm.MI(imp, sm.OLS, model_args_fn) """ def __init__(self, data, mean_prior=None, cov_prior=None, cov_prior_df=1): self.exog_names = None if type(data) is pd.DataFrame: self.exog_names = data.columns data = np.asarray(data) self.data = data self._data = data self.mask = np.isnan(data) self.nobs = self.mask.shape[0] self.nvar = self.mask.shape[1] # Identify all distinct missing data patterns z = 1 + np.log(1 + np.arange(self.mask.shape[1])) c = np.dot(self.mask, z) rowmap = {} for i, v in enumerate(c): if v == 0: # No missing values continue if v not in rowmap: rowmap[v] = [] rowmap[v].append(i) self.patterns = [np.asarray(v) for v in rowmap.values()] # Simple starting values for mean and covariance p = self._data.shape[1] self.cov = np.eye(p) mean = [] for i in range(p): v = self._data[:, i] v = v[np.isfinite(v)] if len(v) == 0: msg = "Column %d has no observed values" % i raise ValueError(msg) mean.append(v.mean()) self.mean = np.asarray(mean) # Default covariance matrix of the (Gaussian) mean prior if mean_prior is None: mean_prior = np.eye(p) self.mean_prior = mean_prior # Default center matrix of the (inverse Wishart) covariance prior if cov_prior is None: cov_prior = np.eye(p) self.cov_prior = cov_prior # Degrees of freedom for the (inverse Wishart) covariance prior self.cov_prior_df = cov_prior_df def update(self): """ Cycle through all Gibbs updates. """ self.update_data() # Need to update data first self.update_mean() self.update_cov() def update_data(self): """ Gibbs update of the missing data values. """ for ix in self.patterns: i = ix[0] ix_miss = np.flatnonzero(self.mask[i, :]) ix_obs = np.flatnonzero(~self.mask[i, :]) mm = self.mean[ix_miss] mo = self.mean[ix_obs] voo = self.cov[ix_obs, :][:, ix_obs] vmm = self.cov[ix_miss, :][:, ix_miss] vmo = self.cov[ix_miss, :][:, ix_obs] r = self._data[ix, :][:, ix_obs] - mo cm = mm + np.dot(vmo, np.linalg.solve(voo, r.T)).T cv = vmm - np.dot(vmo, np.linalg.solve(voo, vmo.T)) cs = np.linalg.cholesky(cv) u = np.random.normal(size=(len(ix), len(ix_miss))) self._data[np.ix_(ix, ix_miss)] = cm + np.dot(u, cs.T) # Set the user-visible data set. if self.exog_names is not None: self.data = pd.DataFrame( self._data, columns=self.exog_names, copy=False) else: self.data = self._data def update_mean(self): """ Gibbs update of the mean vector. Do not call until update_data has been called once. """ # https://stats.stackexchange.com/questions/28744/multivariate-normal-posterior # Posterior covariance matrix of the mean cm = np.linalg.solve(self.cov/self.nobs + self.mean_prior, self.mean_prior / self.nobs) cm = np.dot(self.cov, cm) # Posterior mean of the mean vm = np.linalg.solve(self.cov, self._data.sum(0)) vm = np.dot(cm, vm) # Sample r = np.linalg.cholesky(cm) self.mean = vm + np.dot(r, np.random.normal(0, 1, self.nvar)) def update_cov(self): """ Gibbs update of the covariance matrix. Do not call until update_data has been called once. """ # https://stats.stackexchange.com/questions/50844/estimating-the-covariance-posterior-distribution-of-a-multivariate-gaussian r = self._data - self.mean gr = np.dot(r.T, r) a = gr + self.cov_prior df = int(np.ceil(self.nobs + self.cov_prior_df)) r = np.linalg.cholesky(np.linalg.inv(a)) x = np.dot(np.random.normal(size=(df, self.nvar)), r.T) ma = np.dot(x.T, x) self.cov = np.linalg.inv(ma) class MI(object): """ MI performs multiple imputation using a provided imputer object. Parameters ---------- imp : object An imputer class, such as BayesGaussMI. model : model class Any statsmodels model class. model_args_fn : function A function taking an imputed dataset as input and returning endog, exog. If the model is fit using a formula, returns a DataFrame used to build the model. Optional when a formula is used. model_kwds_fn : function, optional A function taking an imputed dataset as input and returning a dictionary of model keyword arguments. formula : str, optional If provided, the model is constructed using the `from_formula` class method, otherwise the `__init__` method is used. fit_args : list-like, optional List of arguments to be passed to the fit method fit_kwds : dict-like, optional Keyword arguments to be passed to the fit method xfunc : function mapping ndarray to ndarray A function that is applied to the complete data matrix prior to fitting the model burn : int Number of burn-in iterations nrep : int Number of imputed data sets to use in the analysis skip : int Number of Gibbs iterations to skip between successive multiple imputation fits. Notes ----- The imputer object must have an 'update' method, and a 'data' attribute that contains the current imputed dataset. xfunc can be used to introduce domain constraints, e.g. when imputing binary data the imputed continuous values can be rounded to 0/1. """ def __init__(self, imp, model, model_args_fn=None, model_kwds_fn=None, formula=None, fit_args=None, fit_kwds=None, xfunc=None, burn=100, nrep=20, skip=10): # The imputer self.imp = imp # The number of imputed data sets to skip between each imputed # data set tha that is used in the analysis. self.skip = skip # The model class self.model = model self.formula = formula if model_args_fn is None: def f(x): return [] model_args_fn = f self.model_args_fn = model_args_fn if model_kwds_fn is None: def f(x): return {} model_kwds_fn = f self.model_kwds_fn = model_kwds_fn if fit_args is None: def f(x): return [] fit_args = f self.fit_args = fit_args if fit_kwds is None: def f(x): return {} fit_kwds = f self.fit_kwds = fit_kwds self.xfunc = xfunc self.nrep = nrep self.skip = skip # Burn-in for k in range(burn): imp.update() def fit(self, results_cb=None): """ Impute datasets, fit models, and pool results. Parameters ---------- results_cb : function, optional If provided, each results instance r is passed through `results_cb`, then appended to the `results` attribute of the MIResults object. To save complete results, use `results_cb=lambda x: x`. The default behavior is to save no results. Returns ------- A MIResults object. """ par, cov = [], [] all_results = [] for k in range(self.nrep): for k in range(self.skip+1): self.imp.update() da = self.imp.data if self.xfunc is not None: da = self.xfunc(da) if self.formula is None: model = self.model(*self.model_args_fn(da), **self.model_kwds_fn(da)) else: model = self.model.from_formula( self.formula, *self.model_args_fn(da), **self.model_kwds_fn(da)) result = model.fit(*self.fit_args(da), **self.fit_kwds(da)) if results_cb is not None: all_results.append(results_cb(result)) par.append(np.asarray(result.params.copy())) cov.append(np.asarray(result.cov_params().copy())) params, cov_params, fmi = self._combine(par, cov) r = MIResults(self, model, params, cov_params) r.fmi = fmi r.results = all_results return r def _combine(self, par, cov): # Helper function to apply "Rubin's combining rule" par = np.asarray(par) # Number of imputations m = par.shape[0] # Point estimate params = par.mean(0) # Within-imputation covariance wcov = sum(cov) / len(cov) # Between-imputation covariance bcov = np.cov(par.T) bcov = np.atleast_2d(bcov) # Overall covariance covp = wcov + (1 + 1/float(m))*bcov # Fraction of missing information fmi = (1 + 1/float(m)) * np.diag(bcov) / np.diag(covp) return params, covp, fmi class MIResults(LikelihoodModelResults): """ A results class for multiple imputation (MI). Parameters ---------- mi : MI instance The MI object that produced the results model : instance of statsmodels model class This can be any instance from the multiple imputation runs. It is used to get class information, the specific parameter and data values are not used. params : array_like The overall multiple imputation parameter estimates. normalized_cov_params : array_like (2d) The overall variance covariance matrix of the estimates. """ def __init__(self, mi, model, params, normalized_cov_params): super(MIResults, self).__init__(model, params, normalized_cov_params) self.mi = mi self._model = model def summary(self, title=None, alpha=.05): """ Summarize the results of running multiple imputation. Parameters ---------- title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float Significance level for the confidence intervals Returns ------- smry : Summary instance This holds the summary tables and text, which can be printed or converted to various output formats. """ from statsmodels.iolib import summary2 smry = summary2.Summary() float_format = "%8.3f" info = {} info["Method:"] = "MI" info["Model:"] = self.mi.model.__name__ info["Dependent variable:"] = self._model.endog_names info["Sample size:"] = "%d" % self.mi.imp.data.shape[0] info["Num. imputations"] = "%d" % self.mi.nrep smry.add_dict(info, align='l', float_format=float_format) param = summary2.summary_params(self, alpha=alpha) param["FMI"] = self.fmi smry.add_df(param, float_format=float_format) smry.add_title(title=title, results=self) return smry statsmodels-0.12.2/statsmodels/imputation/mice.py000066400000000000000000001305621400612667500221760ustar00rootroot00000000000000""" Overview -------- This module implements the Multiple Imputation through Chained Equations (MICE) approach to handling missing data in statistical data analyses. The approach has the following steps: 0. Impute each missing value with the mean of the observed values of the same variable. 1. For each variable in the data set with missing values (termed the 'focus variable'), do the following: 1a. Fit an 'imputation model', which is a regression model for the focus variable, regressed on the observed and (current) imputed values of some or all of the other variables. 1b. Impute the missing values for the focus variable. Currently this imputation must use the 'predictive mean matching' (pmm) procedure. 2. Once all variables have been imputed, fit the 'analysis model' to the data set. 3. Repeat steps 1-2 multiple times and combine the results using a 'combining rule' to produce point estimates of all parameters in the analysis model and standard errors for them. The imputations for each variable are based on an imputation model that is specified via a model class and a formula for the regression relationship. The default model is OLS, with a formula specifying main effects for all other variables. The MICE procedure can be used in one of two ways: * If the goal is only to produce imputed data sets, the MICEData class can be used to wrap a data frame, providing facilities for doing the imputation. Summary plots are available for assessing the performance of the imputation. * If the imputed data sets are to be used to fit an additional 'analysis model', a MICE instance can be used. After specifying the MICE instance and running it, the results are combined using the `combine` method. Results and various summary plots are then available. Terminology ----------- The primary goal of the analysis is usually to fit and perform inference using an 'analysis model'. If an analysis model is not specified, then imputed datasets are produced for later use. The MICE procedure involves a family of imputation models. There is one imputation model for each variable with missing values. An imputation model may be conditioned on all or a subset of the remaining variables, using main effects, transformations, interactions, etc. as desired. A 'perturbation method' is a method for setting the parameter estimate in an imputation model. The 'gaussian' perturbation method first fits the model (usually using maximum likelihood, but it could use any statsmodels fit procedure), then sets the parameter vector equal to a draw from the Gaussian approximation to the sampling distribution for the fit. The 'bootstrap' perturbation method sets the parameter vector equal to a fitted parameter vector obtained when fitting the conditional model to a bootstrapped version of the data set. Class structure --------------- There are two main classes in the module: * 'MICEData' wraps a Pandas dataframe, incorporating information about the imputation model for each variable with missing values. It can be used to produce multiply imputed data sets that are to be further processed or distributed to other researchers. A number of plotting procedures are provided to visualize the imputation results and missing data patterns. The `history_func` hook allows any features of interest of the imputed data sets to be saved for further analysis. * 'MICE' takes both a 'MICEData' object and an analysis model specification. It runs the multiple imputation, fits the analysis models, and combines the results to produce a `MICEResults` object. The summary method of this results object can be used to see the key estimands and inferential quantities. Notes ----- By default, to conserve memory 'MICEData' saves very little information from one iteration to the next. The data set passed by the user is copied on entry, but then is over-written each time new imputations are produced. If using 'MICE', the fitted analysis models and results are saved. MICEData includes a `history_callback` hook that allows arbitrary information from the intermediate datasets to be saved for future use. References ---------- JL Schafer: 'Multiple Imputation: A Primer', Stat Methods Med Res, 1999. TE Raghunathan et al.: 'A Multivariate Technique for Multiply Imputing Missing Values Using a Sequence of Regression Models', Survey Methodology, 2001. SAS Institute: 'Predictive Mean Matching Method for Monotone Missing Data', SAS 9.2 User's Guide, 2014. A Gelman et al.: 'Multiple Imputation with Diagnostics (mi) in R: Opening Windows into the Black Box', Journal of Statistical Software, 2009. """ import pandas as pd import numpy as np import patsy from statsmodels.base.model import LikelihoodModelResults from statsmodels.regression.linear_model import OLS from collections import defaultdict _mice_data_example_1 = """ >>> imp = mice.MICEData(data) >>> imp.set_imputer('x1', formula='x2 + np.square(x2) + x3') >>> for j in range(20): ... imp.update_all() ... imp.data.to_csv('data%02d.csv' % j)""" _mice_data_example_2 = """ >>> imp = mice.MICEData(data) >>> j = 0 >>> for data in imp: ... imp.data.to_csv('data%02d.csv' % j) ... j += 1""" class PatsyFormula(object): """ A simple wrapper for a string to be interpreted as a Patsy formula. """ def __init__(self, formula): self.formula = "0 + " + formula class MICEData(object): __doc__ = """\ Wrap a data set to allow missing data handling with MICE. Parameters ---------- data : Pandas data frame The data set, which is copied internally. perturbation_method : str The default perturbation method k_pmm : int The number of nearest neighbors to use during predictive mean matching. Can also be specified in `fit`. history_callback : function A function that is called after each complete imputation cycle. The return value is appended to `history`. The MICEData object is passed as the sole argument to `history_callback`. Notes ----- Allowed perturbation methods are 'gaussian' (the model parameters are set to a draw from the Gaussian approximation to the posterior distribution), and 'boot' (the model parameters are set to the estimated values obtained when fitting a bootstrapped version of the data set). `history_callback` can be implemented to have side effects such as saving the current imputed data set to disk. Examples -------- Draw 20 imputations from a data set called `data` and save them in separate files with filename pattern `dataXX.csv`. The variables other than `x1` are imputed using linear models fit with OLS, with mean structures containing main effects of all other variables in `data`. The variable named `x1` has a conditional mean structure that includes an additional term for x2^2. %(_mice_data_example_1)s Impute using default models, using the MICEData object as an iterator. %(_mice_data_example_2)s """ % {'_mice_data_example_1': _mice_data_example_1, '_mice_data_example_2': _mice_data_example_2} def __init__(self, data, perturbation_method='gaussian', k_pmm=20, history_callback=None): if data.columns.dtype != np.dtype('O'): msg = "MICEData data column names should be string type" raise ValueError(msg) self.regularized = dict() # Drop observations where all variables are missing. This # also has the effect of copying the data frame. self.data = data.dropna(how='all').reset_index(drop=True) self.history_callback = history_callback self.history = [] self.predict_kwds = {} # Assign the same perturbation method for all variables. # Can be overridden when calling 'set_imputer'. self.perturbation_method = defaultdict(lambda: perturbation_method) # Map from variable name to indices of observed/missing # values. self.ix_obs = {} self.ix_miss = {} for col in self.data.columns: ix_obs, ix_miss = self._split_indices(self.data[col]) self.ix_obs[col] = ix_obs self.ix_miss[col] = ix_miss # Most recent model instance and results instance for each variable. self.models = {} self.results = {} # Map from variable names to the conditional formula. self.conditional_formula = {} # Map from variable names to init/fit args of the conditional # models. self.init_kwds = defaultdict(lambda: dict()) self.fit_kwds = defaultdict(lambda: dict()) # Map from variable names to the model class. self.model_class = {} # Map from variable names to most recent params update. self.params = {} # Set default imputers. for vname in data.columns: self.set_imputer(vname) # The order in which variables are imputed in each cycle. # Impute variables with the fewest missing values first. vnames = list(data.columns) nmiss = [len(self.ix_miss[v]) for v in vnames] nmiss = np.asarray(nmiss) ii = np.argsort(nmiss) ii = ii[sum(nmiss == 0):] self._cycle_order = [vnames[i] for i in ii] self._initial_imputation() self.k_pmm = k_pmm def next_sample(self): """ Returns the next imputed dataset in the imputation process. Returns ------- data : array_like An imputed dataset from the MICE chain. Notes ----- `MICEData` does not have a `skip` parameter. Consecutive values returned by `next_sample` are immediately consecutive in the imputation chain. The returned value is a reference to the data attribute of the class and should be copied before making any changes. """ self.update_all(1) return self.data def _initial_imputation(self): """ Use a PMM-like procedure for initial imputed values. For each variable, missing values are imputed as the observed value that is closest to the mean over all observed values. """ for col in self.data.columns: di = self.data[col] - self.data[col].mean() di = np.abs(di) ix = di.idxmin() imp = self.data[col].loc[ix] self.data[col].fillna(imp, inplace=True) def _split_indices(self, vec): null = pd.isnull(vec) ix_obs = np.flatnonzero(~null) ix_miss = np.flatnonzero(null) if len(ix_obs) == 0: raise ValueError("variable to be imputed has no observed values") return ix_obs, ix_miss def set_imputer(self, endog_name, formula=None, model_class=None, init_kwds=None, fit_kwds=None, predict_kwds=None, k_pmm=20, perturbation_method=None, regularized=False): """ Specify the imputation process for a single variable. Parameters ---------- endog_name : str Name of the variable to be imputed. formula : str Conditional formula for imputation. Defaults to a formula with main effects for all other variables in dataset. The formula should only include an expression for the mean structure, e.g. use 'x1 + x2' not 'x4 ~ x1 + x2'. model_class : statsmodels model Conditional model for imputation. Defaults to OLS. See below for more information. init_kwds : dit-like Keyword arguments passed to the model init method. fit_kwds : dict-like Keyword arguments passed to the model fit method. predict_kwds : dict-like Keyword arguments passed to the model predict method. k_pmm : int Determines number of neighboring observations from which to randomly sample when using predictive mean matching. perturbation_method : str Either 'gaussian' or 'bootstrap'. Determines the method for perturbing parameters in the imputation model. If None, uses the default specified at class initialization. regularized : dict If regularized[name]=True, `fit_regularized` rather than `fit` is called when fitting imputation models for this variable. When regularized[name]=True for any variable, perturbation_method must be set to boot. Notes ----- The model class must meet the following conditions: * A model must have a 'fit' method that returns an object. * The object returned from `fit` must have a `params` attribute that is an array-like object. * The object returned from `fit` must have a cov_params method that returns a square array-like object. * The model must have a `predict` method. """ if formula is None: main_effects = [x for x in self.data.columns if x != endog_name] fml = endog_name + " ~ " + " + ".join(main_effects) self.conditional_formula[endog_name] = fml else: fml = endog_name + " ~ " + formula self.conditional_formula[endog_name] = fml if model_class is None: self.model_class[endog_name] = OLS else: self.model_class[endog_name] = model_class if init_kwds is not None: self.init_kwds[endog_name] = init_kwds if fit_kwds is not None: self.fit_kwds[endog_name] = fit_kwds if predict_kwds is not None: self.predict_kwds[endog_name] = predict_kwds if perturbation_method is not None: self.perturbation_method[endog_name] = perturbation_method self.k_pmm = k_pmm self.regularized[endog_name] = regularized def _store_changes(self, col, vals): """ Fill in dataset with imputed values. Parameters ---------- col : str Name of variable to be filled in. vals : ndarray Array of imputed values to use for filling-in missing values. """ ix = self.ix_miss[col] if len(ix) > 0: self.data.iloc[ix, self.data.columns.get_loc(col)] = np.atleast_1d(vals) def update_all(self, n_iter=1): """ Perform a specified number of MICE iterations. Parameters ---------- n_iter : int The number of updates to perform. Only the result of the final update will be available. Notes ----- The imputed values are stored in the class attribute `self.data`. """ for k in range(n_iter): for vname in self._cycle_order: self.update(vname) if self.history_callback is not None: hv = self.history_callback(self) self.history.append(hv) def get_split_data(self, vname): """ Return endog and exog for imputation of a given variable. Parameters ---------- vname : str The variable for which the split data is returned. Returns ------- endog_obs : DataFrame Observed values of the variable to be imputed. exog_obs : DataFrame Current values of the predictors where the variable to be imputed is observed. exog_miss : DataFrame Current values of the predictors where the variable to be Imputed is missing. init_kwds : dict-like The init keyword arguments for `vname`, processed through Patsy as required. fit_kwds : dict-like The fit keyword arguments for `vname`, processed through Patsy as required. """ formula = self.conditional_formula[vname] endog, exog = patsy.dmatrices(formula, self.data, return_type="dataframe") # Rows with observed endog ixo = self.ix_obs[vname] endog_obs = np.asarray(endog.iloc[ixo]) exog_obs = np.asarray(exog.iloc[ixo, :]) # Rows with missing endog ixm = self.ix_miss[vname] exog_miss = np.asarray(exog.iloc[ixm, :]) predict_obs_kwds = {} if vname in self.predict_kwds: kwds = self.predict_kwds[vname] predict_obs_kwds = self._process_kwds(kwds, ixo) predict_miss_kwds = {} if vname in self.predict_kwds: kwds = self.predict_kwds[vname] predict_miss_kwds = self._process_kwds(kwds, ixo) return (endog_obs, exog_obs, exog_miss, predict_obs_kwds, predict_miss_kwds) def _process_kwds(self, kwds, ix): kwds = kwds.copy() for k in kwds: v = kwds[k] if isinstance(v, PatsyFormula): mat = patsy.dmatrix(v.formula, self.data, return_type="dataframe") mat = np.asarray(mat)[ix, :] if mat.shape[1] == 1: mat = mat[:, 0] kwds[k] = mat return kwds def get_fitting_data(self, vname): """ Return the data needed to fit a model for imputation. The data is used to impute variable `vname`, and therefore only includes cases for which `vname` is observed. Values of type `PatsyFormula` in `init_kwds` or `fit_kwds` are processed through Patsy and subset to align with the model's endog and exog. Parameters ---------- vname : str The variable for which the fitting data is returned. Returns ------- endog : DataFrame Observed values of `vname`. exog : DataFrame Regression design matrix for imputing `vname`. init_kwds : dict-like The init keyword arguments for `vname`, processed through Patsy as required. fit_kwds : dict-like The fit keyword arguments for `vname`, processed through Patsy as required. """ # Rows with observed endog ix = self.ix_obs[vname] formula = self.conditional_formula[vname] endog, exog = patsy.dmatrices(formula, self.data, return_type="dataframe") endog = np.asarray(endog.iloc[ix, 0]) exog = np.asarray(exog.iloc[ix, :]) init_kwds = self._process_kwds(self.init_kwds[vname], ix) fit_kwds = self._process_kwds(self.fit_kwds[vname], ix) return endog, exog, init_kwds, fit_kwds def plot_missing_pattern(self, ax=None, row_order="pattern", column_order="pattern", hide_complete_rows=False, hide_complete_columns=False, color_row_patterns=True): """ Generate an image showing the missing data pattern. Parameters ---------- ax : AxesSubplot Axes on which to draw the plot. row_order : str The method for ordering the rows. Must be one of 'pattern', 'proportion', or 'raw'. column_order : str The method for ordering the columns. Must be one of 'pattern', 'proportion', or 'raw'. hide_complete_rows : bool If True, rows with no missing values are not drawn. hide_complete_columns : bool If True, columns with no missing values are not drawn. color_row_patterns : bool If True, color the unique row patterns, otherwise use grey and white as colors. Returns ------- A figure containing a plot of the missing data pattern. """ # Create an indicator matrix for missing values. miss = np.zeros(self.data.shape) cols = self.data.columns for j, col in enumerate(cols): ix = self.ix_miss[col] miss[ix, j] = 1 # Order the columns as requested if column_order == "proportion": ix = np.argsort(miss.mean(0)) elif column_order == "pattern": cv = np.cov(miss.T) u, s, vt = np.linalg.svd(cv, 0) ix = np.argsort(cv[:, 0]) elif column_order == "raw": ix = np.arange(len(cols)) else: raise ValueError( column_order + " is not an allowed value for `column_order`.") miss = miss[:, ix] cols = [cols[i] for i in ix] # Order the rows as requested if row_order == "proportion": ix = np.argsort(miss.mean(1)) elif row_order == "pattern": x = 2**np.arange(miss.shape[1]) rky = np.dot(miss, x) ix = np.argsort(rky) elif row_order == "raw": ix = np.arange(miss.shape[0]) else: raise ValueError( row_order + " is not an allowed value for `row_order`.") miss = miss[ix, :] if hide_complete_rows: ix = np.flatnonzero((miss == 1).any(1)) miss = miss[ix, :] if hide_complete_columns: ix = np.flatnonzero((miss == 1).any(0)) miss = miss[:, ix] cols = [cols[i] for i in ix] from statsmodels.graphics import utils as gutils from matplotlib.colors import LinearSegmentedColormap if ax is None: fig, ax = gutils.create_mpl_ax(ax) else: fig = ax.get_figure() if color_row_patterns: x = 2**np.arange(miss.shape[1]) rky = np.dot(miss, x) _, rcol = np.unique(rky, return_inverse=True) miss *= 1 + rcol[:, None] ax.imshow(miss, aspect="auto", interpolation="nearest", cmap='gist_ncar_r') else: cmap = LinearSegmentedColormap.from_list("_", ["white", "darkgrey"]) ax.imshow(miss, aspect="auto", interpolation="nearest", cmap=cmap) ax.set_ylabel("Cases") ax.set_xticks(range(len(cols))) ax.set_xticklabels(cols, rotation=90) return fig def plot_bivariate(self, col1_name, col2_name, lowess_args=None, lowess_min_n=40, jitter=None, plot_points=True, ax=None): """ Plot observed and imputed values for two variables. Displays a scatterplot of one variable against another. The points are colored according to whether the values are observed or imputed. Parameters ---------- col1_name : str The variable to be plotted on the horizontal axis. col2_name : str The variable to be plotted on the vertical axis. lowess_args : dictionary A dictionary of dictionaries, keys are 'ii', 'io', 'oi' and 'oo', where 'o' denotes 'observed' and 'i' denotes imputed. See Notes for details. lowess_min_n : int Minimum sample size to plot a lowess fit jitter : float or tuple Standard deviation for jittering points in the plot. Either a single scalar applied to both axes, or a tuple containing x-axis jitter and y-axis jitter, respectively. plot_points : bool If True, the data points are plotted. ax : AxesSubplot Axes on which to plot, created if not provided. Returns ------- The matplotlib figure on which the plot id drawn. """ from statsmodels.graphics import utils as gutils from statsmodels.nonparametric.smoothers_lowess import lowess if lowess_args is None: lowess_args = {} if ax is None: fig, ax = gutils.create_mpl_ax(ax) else: fig = ax.get_figure() ax.set_position([0.1, 0.1, 0.7, 0.8]) ix1i = self.ix_miss[col1_name] ix1o = self.ix_obs[col1_name] ix2i = self.ix_miss[col2_name] ix2o = self.ix_obs[col2_name] ix_ii = np.intersect1d(ix1i, ix2i) ix_io = np.intersect1d(ix1i, ix2o) ix_oi = np.intersect1d(ix1o, ix2i) ix_oo = np.intersect1d(ix1o, ix2o) vec1 = np.asarray(self.data[col1_name]) vec2 = np.asarray(self.data[col2_name]) if jitter is not None: if np.isscalar(jitter): jitter = (jitter, jitter) vec1 += jitter[0] * np.random.normal(size=len(vec1)) vec2 += jitter[1] * np.random.normal(size=len(vec2)) # Plot the points keys = ['oo', 'io', 'oi', 'ii'] lak = {'i': 'imp', 'o': 'obs'} ixs = {'ii': ix_ii, 'io': ix_io, 'oi': ix_oi, 'oo': ix_oo} color = {'oo': 'grey', 'ii': 'red', 'io': 'orange', 'oi': 'lime'} if plot_points: for ky in keys: ix = ixs[ky] lab = lak[ky[0]] + "/" + lak[ky[1]] ax.plot(vec1[ix], vec2[ix], 'o', color=color[ky], label=lab, alpha=0.6) # Plot the lowess fits for ky in keys: ix = ixs[ky] if len(ix) < lowess_min_n: continue if ky in lowess_args: la = lowess_args[ky] else: la = {} ix = ixs[ky] lfit = lowess(vec2[ix], vec1[ix], **la) if plot_points: ax.plot(lfit[:, 0], lfit[:, 1], '-', color=color[ky], alpha=0.6, lw=4) else: lab = lak[ky[0]] + "/" + lak[ky[1]] ax.plot(lfit[:, 0], lfit[:, 1], '-', color=color[ky], alpha=0.6, lw=4, label=lab) ha, la = ax.get_legend_handles_labels() pad = 0.0001 if plot_points else 0.5 leg = fig.legend(ha, la, 'center right', numpoints=1, handletextpad=pad) leg.draw_frame(False) ax.set_xlabel(col1_name) ax.set_ylabel(col2_name) return fig def plot_fit_obs(self, col_name, lowess_args=None, lowess_min_n=40, jitter=None, plot_points=True, ax=None): """ Plot fitted versus imputed or observed values as a scatterplot. Parameters ---------- col_name : str The variable to be plotted on the horizontal axis. lowess_args : dict-like Keyword arguments passed to lowess fit. A dictionary of dictionaries, keys are 'o' and 'i' denoting 'observed' and 'imputed', respectively. lowess_min_n : int Minimum sample size to plot a lowess fit jitter : float or tuple Standard deviation for jittering points in the plot. Either a single scalar applied to both axes, or a tuple containing x-axis jitter and y-axis jitter, respectively. plot_points : bool If True, the data points are plotted. ax : AxesSubplot Axes on which to plot, created if not provided. Returns ------- The matplotlib figure on which the plot is drawn. """ from statsmodels.graphics import utils as gutils from statsmodels.nonparametric.smoothers_lowess import lowess if lowess_args is None: lowess_args = {} if ax is None: fig, ax = gutils.create_mpl_ax(ax) else: fig = ax.get_figure() ax.set_position([0.1, 0.1, 0.7, 0.8]) ixi = self.ix_miss[col_name] ixo = self.ix_obs[col_name] vec1 = np.asarray(self.data[col_name]) # Fitted values formula = self.conditional_formula[col_name] endog, exog = patsy.dmatrices(formula, self.data, return_type="dataframe") results = self.results[col_name] vec2 = results.predict(exog=exog) vec2 = self._get_predicted(vec2) if jitter is not None: if np.isscalar(jitter): jitter = (jitter, jitter) vec1 += jitter[0] * np.random.normal(size=len(vec1)) vec2 += jitter[1] * np.random.normal(size=len(vec2)) # Plot the points keys = ['o', 'i'] ixs = {'o': ixo, 'i': ixi} lak = {'o': 'obs', 'i': 'imp'} color = {'o': 'orange', 'i': 'lime'} if plot_points: for ky in keys: ix = ixs[ky] ax.plot(vec1[ix], vec2[ix], 'o', color=color[ky], label=lak[ky], alpha=0.6) # Plot the lowess fits for ky in keys: ix = ixs[ky] if len(ix) < lowess_min_n: continue if ky in lowess_args: la = lowess_args[ky] else: la = {} ix = ixs[ky] lfit = lowess(vec2[ix], vec1[ix], **la) ax.plot(lfit[:, 0], lfit[:, 1], '-', color=color[ky], alpha=0.6, lw=4, label=lak[ky]) ha, la = ax.get_legend_handles_labels() leg = fig.legend(ha, la, 'center right', numpoints=1) leg.draw_frame(False) ax.set_xlabel(col_name + " observed or imputed") ax.set_ylabel(col_name + " fitted") return fig def plot_imputed_hist(self, col_name, ax=None, imp_hist_args=None, obs_hist_args=None, all_hist_args=None): """ Display imputed values for one variable as a histogram. Parameters ---------- col_name : str The name of the variable to be plotted. ax : AxesSubplot An axes on which to draw the histograms. If not provided, one is created. imp_hist_args : dict Keyword arguments to be passed to pyplot.hist when creating the histogram for imputed values. obs_hist_args : dict Keyword arguments to be passed to pyplot.hist when creating the histogram for observed values. all_hist_args : dict Keyword arguments to be passed to pyplot.hist when creating the histogram for all values. Returns ------- The matplotlib figure on which the histograms were drawn """ from statsmodels.graphics import utils as gutils if imp_hist_args is None: imp_hist_args = {} if obs_hist_args is None: obs_hist_args = {} if all_hist_args is None: all_hist_args = {} if ax is None: fig, ax = gutils.create_mpl_ax(ax) else: fig = ax.get_figure() ax.set_position([0.1, 0.1, 0.7, 0.8]) ixm = self.ix_miss[col_name] ixo = self.ix_obs[col_name] imp = self.data[col_name].iloc[ixm] obs = self.data[col_name].iloc[ixo] for di in imp_hist_args, obs_hist_args, all_hist_args: if 'histtype' not in di: di['histtype'] = 'step' ha, la = [], [] if len(imp) > 0: h = ax.hist(np.asarray(imp), **imp_hist_args) ha.append(h[-1][0]) la.append("Imp") h1 = ax.hist(np.asarray(obs), **obs_hist_args) h2 = ax.hist(np.asarray(self.data[col_name]), **all_hist_args) ha.extend([h1[-1][0], h2[-1][0]]) la.extend(["Obs", "All"]) leg = fig.legend(ha, la, 'center right', numpoints=1) leg.draw_frame(False) ax.set_xlabel(col_name) ax.set_ylabel("Frequency") return fig # Try to identify any auxiliary arrays (e.g. status vector in # PHReg) that need to be bootstrapped along with exog and endog. def _boot_kwds(self, kwds, rix): for k in kwds: v = kwds[k] # This is only relevant for ndarrays if not isinstance(v, np.ndarray): continue # Handle 1d vectors if (v.ndim == 1) and (v.shape[0] == len(rix)): kwds[k] = v[rix] # Handle 2d arrays if (v.ndim == 2) and (v.shape[0] == len(rix)): kwds[k] = v[rix, :] return kwds def _perturb_bootstrap(self, vname): """ Perturbs the model's parameters using a bootstrap. """ endog, exog, init_kwds, fit_kwds = self.get_fitting_data(vname) m = len(endog) rix = np.random.randint(0, m, m) endog = endog[rix] exog = exog[rix, :] init_kwds = self._boot_kwds(init_kwds, rix) fit_kwds = self._boot_kwds(fit_kwds, rix) klass = self.model_class[vname] self.models[vname] = klass(endog, exog, **init_kwds) if vname in self.regularized and self.regularized[vname]: self.results[vname] = ( self.models[vname].fit_regularized(**fit_kwds)) else: self.results[vname] = self.models[vname].fit(**fit_kwds) self.params[vname] = self.results[vname].params def _perturb_gaussian(self, vname): """ Gaussian perturbation of model parameters. The normal approximation to the sampling distribution of the parameter estimates is used to define the mean and covariance structure of the perturbation distribution. """ endog, exog, init_kwds, fit_kwds = self.get_fitting_data(vname) klass = self.model_class[vname] self.models[vname] = klass(endog, exog, **init_kwds) self.results[vname] = self.models[vname].fit(**fit_kwds) cov = self.results[vname].cov_params() mu = self.results[vname].params self.params[vname] = np.random.multivariate_normal(mean=mu, cov=cov) def perturb_params(self, vname): if self.perturbation_method[vname] == "gaussian": self._perturb_gaussian(vname) elif self.perturbation_method[vname] == "boot": self._perturb_bootstrap(vname) else: raise ValueError("unknown perturbation method") def impute(self, vname): # Wrap this in case we later add additional imputation # methods. self.impute_pmm(vname) def update(self, vname): """ Impute missing values for a single variable. This is a two-step process in which first the parameters are perturbed, then the missing values are re-imputed. Parameters ---------- vname : str The name of the variable to be updated. """ self.perturb_params(vname) self.impute(vname) # work-around for inconsistent predict return values def _get_predicted(self, obj): if isinstance(obj, np.ndarray): return obj elif isinstance(obj, pd.Series): return obj.values elif hasattr(obj, 'predicted_values'): return obj.predicted_values else: raise ValueError( "cannot obtain predicted values from %s" % obj.__class__) def impute_pmm(self, vname): """ Use predictive mean matching to impute missing values. Notes ----- The `perturb_params` method must be called first to define the model. """ k_pmm = self.k_pmm endog_obs, exog_obs, exog_miss, predict_obs_kwds, predict_miss_kwds = ( self.get_split_data(vname)) # Predict imputed variable for both missing and non-missing # observations model = self.models[vname] pendog_obs = model.predict(self.params[vname], exog_obs, **predict_obs_kwds) pendog_miss = model.predict(self.params[vname], exog_miss, **predict_miss_kwds) pendog_obs = self._get_predicted(pendog_obs) pendog_miss = self._get_predicted(pendog_miss) # Jointly sort the observed and predicted endog values for the # cases with observed values. ii = np.argsort(pendog_obs) endog_obs = endog_obs[ii] pendog_obs = pendog_obs[ii] # Find the closest match to the predicted endog values for # cases with missing endog values. ix = np.searchsorted(pendog_obs, pendog_miss) # Get the indices for the closest k_pmm values on # either side of the closest index. ixm = ix[:, None] + np.arange(-k_pmm, k_pmm)[None, :] # Account for boundary effects msk = np.nonzero((ixm < 0) | (ixm > len(endog_obs) - 1)) ixm = np.clip(ixm, 0, len(endog_obs) - 1) # Get the distances dx = pendog_miss[:, None] - pendog_obs[ixm] dx = np.abs(dx) dx[msk] = np.inf # Closest positions in ix, row-wise. dxi = np.argsort(dx, 1)[:, 0:k_pmm] # Choose a column for each row. ir = np.random.randint(0, k_pmm, len(pendog_miss)) # Unwind the indices jj = np.arange(dxi.shape[0]) ix = dxi[(jj, ir)] iz = ixm[(jj, ix)] imputed_miss = np.array(endog_obs[iz]).squeeze() self._store_changes(vname, imputed_miss) _mice_example_1 = """ >>> imp = mice.MICEData(data) >>> fml = 'y ~ x1 + x2 + x3 + x4' >>> mice = mice.MICE(fml, sm.OLS, imp) >>> results = mice.fit(10, 10) >>> print(results.summary()) .. literalinclude:: ../plots/mice_example_1.txt """ _mice_example_2 = """ >>> imp = mice.MICEData(data) >>> fml = 'y ~ x1 + x2 + x3 + x4' >>> mice = mice.MICE(fml, sm.OLS, imp) >>> results = [] >>> for k in range(10): >>> x = mice.next_sample() >>> results.append(x) """ class MICE(object): __doc__ = """\ Multiple Imputation with Chained Equations. This class can be used to fit most statsmodels models to data sets with missing values using the 'multiple imputation with chained equations' (MICE) approach.. Parameters ---------- model_formula : str The model formula to be fit to the imputed data sets. This formula is for the 'analysis model'. model_class : statsmodels model The model to be fit to the imputed data sets. This model class if for the 'analysis model'. data : MICEData instance MICEData object containing the data set for which missing values will be imputed n_skip : int The number of imputed datasets to skip between consecutive imputed datasets that are used for analysis. init_kwds : dict-like Dictionary of keyword arguments passed to the init method of the analysis model. fit_kwds : dict-like Dictionary of keyword arguments passed to the fit method of the analysis model. Examples -------- Run all MICE steps and obtain results: %(mice_example_1)s Obtain a sequence of fitted analysis models without combining to obtain summary:: %(mice_example_2)s """ % {'mice_example_1': _mice_example_1, 'mice_example_2': _mice_example_2} def __init__(self, model_formula, model_class, data, n_skip=3, init_kwds=None, fit_kwds=None): self.model_formula = model_formula self.model_class = model_class self.n_skip = n_skip self.data = data self.results_list = [] self.init_kwds = init_kwds if init_kwds is not None else {} self.fit_kwds = fit_kwds if fit_kwds is not None else {} def next_sample(self): """ Perform one complete MICE iteration. A single MICE iteration updates all missing values using their respective imputation models, then fits the analysis model to the imputed data. Returns ------- params : array_like The model parameters for the analysis model. Notes ----- This function fits the analysis model and returns its parameter estimate. The parameter vector is not stored by the class and is not used in any subsequent calls to `combine`. Use `fit` to run all MICE steps together and obtain summary results. The complete cycle of missing value imputation followed by fitting the analysis model is repeated `n_skip + 1` times and the analysis model parameters from the final fit are returned. """ # Impute missing values self.data.update_all(self.n_skip + 1) start_params = None if len(self.results_list) > 0: start_params = self.results_list[-1].params # Fit the analysis model. model = self.model_class.from_formula(self.model_formula, self.data.data, **self.init_kwds) self.fit_kwds.update({"start_params": start_params}) result = model.fit(**self.fit_kwds) return result def fit(self, n_burnin=10, n_imputations=10): """ Fit a model using MICE. Parameters ---------- n_burnin : int The number of burn-in cycles to skip. n_imputations : int The number of data sets to impute """ # Run without fitting the analysis model self.data.update_all(n_burnin) for j in range(n_imputations): result = self.next_sample() self.results_list.append(result) self.endog_names = result.model.endog_names self.exog_names = result.model.exog_names return self.combine() def combine(self): """ Pools MICE imputation results. This method can only be used after the `run` method has been called. Returns estimates and standard errors of the analysis model parameters. Returns a MICEResults instance. """ # Extract a few things from the models that were fit to # imputed data sets. params_list = [] cov_within = 0. scale_list = [] for results in self.results_list: results_uw = results._results params_list.append(results_uw.params) cov_within += results_uw.cov_params() scale_list.append(results.scale) params_list = np.asarray(params_list) scale_list = np.asarray(scale_list) # The estimated parameters for the MICE analysis params = params_list.mean(0) # The average of the within-imputation covariances cov_within /= len(self.results_list) # The between-imputation covariance cov_between = np.cov(params_list.T) # The estimated covariance matrix for the MICE analysis f = 1 + 1 / float(len(self.results_list)) cov_params = cov_within + f * cov_between # Fraction of missing information fmi = f * np.diag(cov_between) / np.diag(cov_params) # Set up a results instance scale = np.mean(scale_list) results = MICEResults(self, params, cov_params / scale) results.scale = scale results.frac_miss_info = fmi results.exog_names = self.exog_names results.endog_names = self.endog_names results.model_class = self.model_class return results class MICEResults(LikelihoodModelResults): def __init__(self, model, params, normalized_cov_params): super(MICEResults, self).__init__(model, params, normalized_cov_params) def summary(self, title=None, alpha=.05): """ Summarize the results of running MICE. Parameters ---------- title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float Significance level for the confidence intervals Returns ------- smry : Summary instance This holds the summary tables and text, which can be printed or converted to various output formats. """ from statsmodels.iolib import summary2 smry = summary2.Summary() float_format = "%8.3f" info = {} info["Method:"] = "MICE" info["Model:"] = self.model_class.__name__ info["Dependent variable:"] = self.endog_names info["Sample size:"] = "%d" % self.model.data.data.shape[0] info["Scale"] = "%.2f" % self.scale info["Num. imputations"] = "%d" % len(self.model.results_list) smry.add_dict(info, align='l', float_format=float_format) param = summary2.summary_params(self, alpha=alpha) param["FMI"] = self.frac_miss_info smry.add_df(param, float_format=float_format) smry.add_title(title=title, results=self) return smry statsmodels-0.12.2/statsmodels/imputation/ros.py000066400000000000000000000450251400612667500220630ustar00rootroot00000000000000""" Implementation of Regression on Order Statistics for imputing left- censored (non-detect data) Method described in *Nondetects and Data Analysis* by Dennis R. Helsel (John Wiley, 2005) to estimate the left-censored (non-detect) values of a dataset. Author: Paul M. Hobson Company: Geosyntec Consultants (Portland, OR) Date: 2016-06-14 """ import warnings import numpy from scipy import stats import pandas def _ros_sort(df, observations, censorship, warn=False): """ This function prepares a dataframe for ROS. It sorts ascending with left-censored observations first. Censored observations larger than the maximum uncensored observations are removed from the dataframe. Parameters ---------- df : pandas.DataFrame observations : str Name of the column in the dataframe that contains observed values. Censored values should be set to the detection (upper) limit. censorship : str Name of the column in the dataframe that indicates that a observation is left-censored. (i.e., True -> censored, False -> uncensored) Returns ------ sorted_df : pandas.DataFrame The sorted dataframe with all columns dropped except the observation and censorship columns. """ # separate uncensored data from censored data censored = df[df[censorship]].sort_values(observations, axis=0) uncensored = df[~df[censorship]].sort_values(observations, axis=0) if censored[observations].max() > uncensored[observations].max(): censored = censored[censored[observations] <= uncensored[observations].max()] if warn: msg = ("Dropping censored observations greater than " "the max uncensored observation.") warnings.warn(msg) return censored.append(uncensored)[[observations, censorship]].reset_index(drop=True) def cohn_numbers(df, observations, censorship): r""" Computes the Cohn numbers for the detection limits in the dataset. The Cohn Numbers are: - :math:`A_j =` the number of uncensored obs above the jth threshold. - :math:`B_j =` the number of observations (cen & uncen) below the jth threshold. - :math:`C_j =` the number of censored observations at the jth threshold. - :math:`\mathrm{PE}_j =` the probability of exceeding the jth threshold - :math:`\mathrm{DL}_j =` the unique, sorted detection limits - :math:`\mathrm{DL}_{j+1} = \mathrm{DL}_j` shifted down a single index (row) Parameters ---------- dataframe : pandas.DataFrame observations : str Name of the column in the dataframe that contains observed values. Censored values should be set to the detection (upper) limit. censorship : str Name of the column in the dataframe that indicates that a observation is left-censored. (i.e., True -> censored, False -> uncensored) Returns ------- cohn : pandas.DataFrame """ def nuncen_above(row): """ A, the number of uncensored obs above the given threshold. """ # index of observations above the lower_dl DL above = df[observations] >= row['lower_dl'] # index of observations below the upper_dl DL below = df[observations] < row['upper_dl'] # index of non-detect observations detect = ~df[censorship] # return the number of observations where all conditions are True return df[above & below & detect].shape[0] def nobs_below(row): """ B, the number of observations (cen & uncen) below the given threshold """ # index of data less than the lower_dl DL less_than = df[observations] < row['lower_dl'] # index of data less than or equal to the lower_dl DL less_thanequal = df[observations] <= row['lower_dl'] # index of detects, non-detects uncensored = ~df[censorship] censored = df[censorship] # number observations less than or equal to lower_dl DL and non-detect LTE_censored = df[less_thanequal & censored].shape[0] # number of observations less than lower_dl DL and detected LT_uncensored = df[less_than & uncensored].shape[0] # return the sum return LTE_censored + LT_uncensored def ncen_equal(row): """ C, the number of censored observations at the given threshold. """ censored_index = df[censorship] censored_data = df[observations][censored_index] censored_below = censored_data == row['lower_dl'] return censored_below.sum() def set_upper_limit(cohn): """ Sets the upper_dl DL for each row of the Cohn dataframe. """ if cohn.shape[0] > 1: return cohn['lower_dl'].shift(-1).fillna(value=numpy.inf) else: return [numpy.inf] def compute_PE(A, B): """ Computes the probability of excedance for each row of the Cohn dataframe. """ N = len(A) PE = numpy.empty(N, dtype='float64') PE[-1] = 0.0 for j in range(N-2, -1, -1): PE[j] = PE[j+1] + (1 - PE[j+1]) * A[j] / (A[j] + B[j]) return PE # unique, sorted detection limts censored_data = df[censorship] DLs = pandas.unique(df.loc[censored_data, observations]) DLs.sort() # if there is a observations smaller than the minimum detection limit, # add that value to the array if DLs.shape[0] > 0: if df[observations].min() < DLs.min(): DLs = numpy.hstack([df[observations].min(), DLs]) # create a dataframe # (editted for pandas 0.14 compatibility; see commit 63f162e # when `pipe` and `assign` are available) cohn = pandas.DataFrame(DLs, columns=['lower_dl']) cohn.loc[:, 'upper_dl'] = set_upper_limit(cohn) cohn.loc[:, 'nuncen_above'] = cohn.apply(nuncen_above, axis=1) cohn.loc[:, 'nobs_below'] = cohn.apply(nobs_below, axis=1) cohn.loc[:, 'ncen_equal'] = cohn.apply(ncen_equal, axis=1) cohn = cohn.reindex(range(DLs.shape[0] + 1)) cohn.loc[:, 'prob_exceedance'] = compute_PE(cohn['nuncen_above'], cohn['nobs_below']) else: dl_cols = ['lower_dl', 'upper_dl', 'nuncen_above', 'nobs_below', 'ncen_equal', 'prob_exceedance'] cohn = pandas.DataFrame(numpy.empty((0, len(dl_cols))), columns=dl_cols) return cohn def _detection_limit_index(obs, cohn): """ Locates the corresponding detection limit for each observation. Basically, creates an array of indices for the detection limits (Cohn numbers) corresponding to each data point. Parameters ---------- obs : float A single observation from the larger dataset. cohn : pandas.DataFrame DataFrame of Cohn numbers. Returns ------- det_limit_index : int The index of the corresponding detection limit in `cohn` See Also -------- cohn_numbers """ if cohn.shape[0] > 0: index, = numpy.where(cohn['lower_dl'] <= obs) det_limit_index = index[-1] else: det_limit_index = 0 return det_limit_index def _ros_group_rank(df, dl_idx, censorship): """ Ranks each observation within the data groups. In this case, the groups are defined by the record's detection limit index and censorship status. Parameters ---------- df : pandas.DataFrame dl_idx : str Name of the column in the dataframe the index of the observations' corresponding detection limit in the `cohn` dataframe. censorship : str Name of the column in the dataframe that indicates that a observation is left-censored. (i.e., True -> censored, False -> uncensored) Returns ------- ranks : numpy.array Array of ranks for the dataset. """ # (editted for pandas 0.14 compatibility; see commit 63f162e # when `pipe` and `assign` are available) ranks = df.copy() ranks.loc[:, 'rank'] = 1 ranks = ( ranks.groupby(by=[dl_idx, censorship])['rank'] .transform(lambda g: g.cumsum()) ) return ranks def _ros_plot_pos(row, censorship, cohn): """ ROS-specific plotting positions. Computes the plotting position for an observation based on its rank, censorship status, and detection limit index. Parameters ---------- row : pandas.Series or dict-like Full observation (row) from a censored dataset. Requires a 'rank', 'detection_limit', and `censorship` column. censorship : str Name of the column in the dataframe that indicates that a observation is left-censored. (i.e., True -> censored, False -> uncensored) cohn : pandas.DataFrame DataFrame of Cohn numbers. Returns ------- plotting_position : float See Also -------- cohn_numbers """ DL_index = row['det_limit_index'] rank = row['rank'] censored = row[censorship] dl_1 = cohn.iloc[DL_index] dl_2 = cohn.iloc[DL_index + 1] if censored: return (1 - dl_1['prob_exceedance']) * rank / (dl_1['ncen_equal']+1) else: return (1 - dl_1['prob_exceedance']) + (dl_1['prob_exceedance'] - dl_2['prob_exceedance']) * \ rank / (dl_1['nuncen_above']+1) def _norm_plot_pos(observations): """ Computes standard normal (Gaussian) plotting positions using scipy. Parameters ---------- observations : array_like Sequence of observed quantities. Returns ------- plotting_position : array of floats """ ppos, sorted_res = stats.probplot(observations, fit=False) return stats.norm.cdf(ppos) def plotting_positions(df, censorship, cohn): """ Compute the plotting positions for the observations. The ROS-specific plotting postions are based on the observations' rank, censorship status, and corresponding detection limit. Parameters ---------- df : pandas.DataFrame censorship : str Name of the column in the dataframe that indicates that a observation is left-censored. (i.e., True -> censored, False -> uncensored) cohn : pandas.DataFrame DataFrame of Cohn numbers. Returns ------- plotting_position : array of float See Also -------- cohn_numbers """ plot_pos = df.apply(lambda r: _ros_plot_pos(r, censorship, cohn), axis=1) # correctly sort the plotting positions of the ND data: ND_plotpos = plot_pos[df[censorship]] ND_plotpos.values.sort() plot_pos[df[censorship]] = ND_plotpos return plot_pos def _impute(df, observations, censorship, transform_in, transform_out): """ Executes the basic regression on order stat (ROS) proceedure. Uses ROS to impute censored from the best-fit line of a probability plot of the uncensored values. Parameters ---------- df : pandas.DataFrame observations : str Name of the column in the dataframe that contains observed values. Censored values should be set to the detection (upper) limit. censorship : str Name of the column in the dataframe that indicates that a observation is left-censored. (i.e., True -> censored, False -> uncensored) transform_in, transform_out : callable Transformations to be applied to the data prior to fitting the line and after estimated values from that line. Typically, `numpy.log` and `numpy.exp` are used, respectively. Returns ------- estimated : pandas.DataFrame A new dataframe with two new columns: "estimated" and "final". The "estimated" column contains of the values inferred from the best-fit line. The "final" column contains the estimated values only where the original observations were censored, and the original observations everwhere else. """ # detect/non-detect selectors uncensored_mask = ~df[censorship] censored_mask = df[censorship] # fit a line to the logs of the detected data fit_params = stats.linregress( df['Zprelim'][uncensored_mask], transform_in(df[observations][uncensored_mask]) ) # pull out the slope and intercept for use later slope, intercept = fit_params[:2] # model the data based on the best-fit curve # (editted for pandas 0.14 compatibility; see commit 63f162e # when `pipe` and `assign` are available) df.loc[:, 'estimated'] = transform_out(slope * df['Zprelim'][censored_mask] + intercept) df.loc[:, 'final'] = numpy.where(df[censorship], df['estimated'], df[observations]) return df def _do_ros(df, observations, censorship, transform_in, transform_out): """ DataFrame-centric function to impute censored valies with ROS. Prepares a dataframe for, and then esimates the values of a censored dataset using Regression on Order Statistics Parameters ---------- df : pandas.DataFrame observations : str Name of the column in the dataframe that contains observed values. Censored values should be set to the detection (upper) limit. censorship : str Name of the column in the dataframe that indicates that a observation is left-censored. (i.e., True -> censored, False -> uncensored) transform_in, transform_out : callable Transformations to be applied to the data prior to fitting the line and after estimated values from that line. Typically, `numpy.log` and `numpy.exp` are used, respectively. Returns ------- estimated : pandas.DataFrame A new dataframe with two new columns: "estimated" and "final". The "estimated" column contains of the values inferred from the best-fit line. The "final" column contains the estimated values only where the original observations were censored, and the original observations everwhere else. """ # compute the Cohn numbers cohn = cohn_numbers(df, observations=observations, censorship=censorship) # (editted for pandas 0.14 compatibility; see commit 63f162e # when `pipe` and `assign` are available) modeled = _ros_sort(df, observations=observations, censorship=censorship) modeled.loc[:, 'det_limit_index'] = modeled[observations].apply(_detection_limit_index, args=(cohn,)) modeled.loc[:, 'rank'] = _ros_group_rank(modeled, 'det_limit_index', censorship) modeled.loc[:, 'plot_pos'] = plotting_positions(modeled, censorship, cohn) modeled.loc[:, 'Zprelim'] = stats.norm.ppf(modeled['plot_pos']) return _impute(modeled, observations, censorship, transform_in, transform_out) def impute_ros(observations, censorship, df=None, min_uncensored=2, max_fraction_censored=0.8, substitution_fraction=0.5, transform_in=numpy.log, transform_out=numpy.exp, as_array=True): """ Impute censored dataset using Regression on Order Statistics (ROS). Method described in *Nondetects and Data Analysis* by Dennis R. Helsel (John Wiley, 2005) to estimate the left-censored (non-detect) values of a dataset. When there is insufficient non-censorded data, simple substitution is used. Parameters ---------- observations : str or array-like Label of the column or the float array of censored observations censorship : str Label of the column or the bool array of the censorship status of the observations. * True if censored, * False if uncensored df : pandas.DataFrame, optional If `observations` and `censorship` are labels, this is the DataFrame that contains those columns. min_uncensored : int (default is 2) The minimum number of uncensored values required before ROS can be used to impute the censored observations. When this criterion is not met, simple substituion is used instead. max_fraction_censored : float (default is 0.8) The maximum fraction of censored data below which ROS can be used to impute the censored observations. When this fraction is exceeded, simple substituion is used instead. substitution_fraction : float (default is 0.5) The fraction of the detection limit to be used during simple substitution of the censored values. transform_in : callable (default is numpy.log) Transformation to be applied to the values prior to fitting a line to the plotting positions vs. uncensored values. transform_out : callable (default is numpy.exp) Transformation to be applied to the imputed censored values estimated from the previously computed best-fit line. as_array : bool (default is True) When True, a numpy array of the imputed observations is returned. Otherwise, a modified copy of the original dataframe with all of the intermediate calculations is returned. Returns ------- imputed : numpy.array (default) or pandas.DataFrame The final observations where the censored values have either been imputed through ROS or substituted as a fraction of the detection limit. Notes ----- This function requires pandas 0.14 or more recent. """ # process arrays into a dataframe, if necessary if df is None: df = pandas.DataFrame({'obs': observations, 'cen': censorship}) observations = 'obs' censorship = 'cen' # basic counts/metrics of the dataset N_observations = df.shape[0] N_censored = df[censorship].astype(int).sum() N_uncensored = N_observations - N_censored fraction_censored = N_censored / N_observations # add plotting positions if there are no censored values # (editted for pandas 0.14 compatibility; see commit 63f162e # when `pipe` and `assign` are available) if N_censored == 0: output = df[[observations, censorship]].copy() output.loc[:, 'final'] = df[observations] # substitute w/ fraction of the DLs if there's insufficient # uncensored data # (editted for pandas 0.14 compatibility; see commit 63f162e # when `pipe` and `assign` are available) elif (N_uncensored < min_uncensored) or (fraction_censored > max_fraction_censored): output = df[[observations, censorship]].copy() output.loc[:, 'final'] = df[observations] output.loc[df[censorship], 'final'] *= substitution_fraction # normal ROS stuff else: output = _do_ros(df, observations, censorship, transform_in, transform_out) # convert to an array if necessary if as_array: output = output['final'].values return output statsmodels-0.12.2/statsmodels/imputation/tests/000077500000000000000000000000001400612667500220425ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/imputation/tests/__init__.py000066400000000000000000000000001400612667500241410ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/imputation/tests/test_bayes_mi.py000066400000000000000000000117541400612667500252530ustar00rootroot00000000000000import numpy as np import pandas as pd import statsmodels.api as sm from statsmodels.imputation.bayes_mi import BayesGaussMI, MI from numpy.testing import assert_allclose, assert_equal def test_pat(): x = np.asarray([[1, np.nan, 3], [np.nan, 2, np.nan], [3, np.nan, 0], [np.nan, 1, np.nan], [3, 2, 1]]) bm = BayesGaussMI(x) assert_allclose(bm.patterns[0], np.r_[0, 2]) assert_allclose(bm.patterns[1], np.r_[1, 3]) def test_2x2(): # Generate correlated data with mean and variance np.random.seed(3434) x = np.random.normal(size=(1000, 2)) r = 0.5 x[:, 1] = r*x[:, 0] + np.sqrt(1-r**2)*x[:, 1] x[:, 0] *= 2 x[:, 1] *= 3 x[:, 0] += 1 x[:, 1] -= 2 # Introduce some missing values u = np.random.normal(size=x.shape[0]) x[u > 1, 0] = np.nan u = np.random.normal(size=x.shape[0]) x[u > 1, 1] = np.nan bm = BayesGaussMI(x) # Burn-in for k in range(500): bm.update() # Estimate the posterior mean mean = 0 cov = 0 dmean = 0 dcov = 0 for k in range(500): bm.update() mean += bm.mean cov += bm.cov dmean += bm.data.mean(0) dcov += np.cov(bm.data.T) mean /= 500 cov /= 500 dmean /= 500 dcov /= 500 assert_allclose(mean, np.r_[1, -2], 0.1) assert_allclose(dmean, np.r_[1, -2], 0.1) assert_allclose(cov, np.asarray([[4, 6*r], [6*r, 9]]), 0.1) assert_allclose(dcov, np.asarray([[4, 6*r], [6*r, 9]]), 0.1) def test_MI(): np.random.seed(414) x = np.random.normal(size=(200, 4)) x[[1, 3, 9], 0] = np.nan x[[1, 4, 3], 1] = np.nan x[[2, 11, 21], 2] = np.nan x[[11, 22, 99], 3] = np.nan def model_args_fn(x): # Return endog, exog # Regress x0 on x1 and x2 if type(x) is np.ndarray: return (x[:, 0], x[:, 1:]) else: return (x.iloc[:, 0].values, x.iloc[:, 1:].values) for j in (0, 1): np.random.seed(2342) imp = BayesGaussMI(x.copy()) mi = MI(imp, sm.OLS, model_args_fn, burn=0) r = mi.fit() r.summary() # smoke test # TODO: why does the test tolerance need to be so slack? # There is unexpected variation across versions on travis. assert_allclose(r.params, np.r_[ -0.05347919, -0.02479701, 0.10075517], 0.25, 0) c = np.asarray([[0.00418232, 0.00029746, -0.00035057], [0.00029746, 0.00407264, 0.00019496], [-0.00035057, 0.00019496, 0.00509413]]) assert_allclose(r.cov_params(), c, 0.3, 0) # Test with ndarray and pandas input x = pd.DataFrame(x) def test_MI_stat(): # Test for MI where we know statistically what should happen. The # analysis model is x0 ~ x1 with standard error 1/sqrt(n) for the # slope parameter. The nominal n is 1000, but half of the cases # have missing x1. Then we introduce x2 that is either # independent of x1, or almost perfectly correlated with x1. In # the first case the SE is 1/sqrt(500), in the second case the SE # is 1/sqrt(1000). np.random.seed(414) z = np.random.normal(size=(1000, 3)) z[:, 0] += 0.5*z[:, 1] # Control the degree to which x2 proxies for x1 exp = [1/np.sqrt(500), 1/np.sqrt(1000)] fmi = [0.5, 0] for j, r in enumerate((0, 0.9999)): x = z.copy() x[:, 2] = r*x[:, 1] + np.sqrt(1 - r**2)*x[:, 2] x[0:500, 1] = np.nan def model_args(x): # Return endog, exog # Regress x1 on x2 return (x[:, 0], x[:, 1]) np.random.seed(2342) imp = BayesGaussMI(x.copy()) mi = MI(imp, sm.OLS, model_args, nrep=100, skip=10) r = mi.fit() # Check the SE d = np.abs(r.bse[0] - exp[j]) / exp[j] assert(d < 0.03) # Check the FMI d = np.abs(r.fmi[0] - fmi[j]) assert(d < 0.05) def test_mi_formula(): np.random.seed(414) x = np.random.normal(size=(200, 4)) x[[1, 3, 9], 0] = np.nan x[[1, 4, 3], 1] = np.nan x[[2, 11, 21], 2] = np.nan x[[11, 22, 99], 3] = np.nan df = pd.DataFrame({"y": x[:, 0], "x1": x[:, 1], "x2": x[:, 2], "x3": x[:, 3]}) fml = "y ~ 0 + x1 + x2 + x3" def model_kwds_fn(x): return {"data": x} np.random.seed(2342) imp = BayesGaussMI(df.copy()) mi = MI(imp, sm.OLS, formula=fml, burn=0, model_kwds_fn=model_kwds_fn) results_cb = lambda x: x r = mi.fit(results_cb=results_cb) r.summary() # smoke test # TODO: why does the test tolerance need to be so slack? # There is unexpected variation across versions on travis. assert_allclose(r.params, np.r_[ -0.05347919, -0.02479701, 0.10075517], 0.25, 0) c = np.asarray([[0.00418232, 0.00029746, -0.00035057], [0.00029746, 0.00407264, 0.00019496], [-0.00035057, 0.00019496, 0.00509413]]) assert_allclose(r.cov_params(), c, 0.3, 0) assert_equal(len(r.results), 20) statsmodels-0.12.2/statsmodels/imputation/tests/test_mice.py000066400000000000000000000302101400612667500243640ustar00rootroot00000000000000import numpy as np import pandas as pd import pytest from statsmodels.imputation import mice import statsmodels.api as sm from numpy.testing import assert_equal, assert_allclose import warnings try: import matplotlib.pyplot as plt except ImportError: pass pdf_output = False if pdf_output: from matplotlib.backends.backend_pdf import PdfPages pdf = PdfPages("test_mice.pdf") else: pdf = None def close_or_save(pdf, fig): if pdf_output: pdf.savefig(fig) def teardown_module(): if pdf_output: pdf.close() def gendat(): """ Create a data set with missing values. """ np.random.seed(34243) n = 200 p = 5 exog = np.random.normal(size=(n, p)) exog[:, 0] = exog[:, 1] - exog[:, 2] + 2*exog[:, 4] exog[:, 0] += np.random.normal(size=n) exog[:, 2] = 1*(exog[:, 2] > 0) endog = exog.sum(1) + np.random.normal(size=n) df = pd.DataFrame(exog) df.columns = ["x%d" % k for k in range(1, p+1)] df["y"] = endog df.x1[0:60] = np.nan df.x2[0:40] = np.nan df.x3[10:30:2] = np.nan df.x4[20:50:3] = np.nan df.x5[40:45] = np.nan df.y[30:100:2] = np.nan return df class TestMICEData(object): def test_default(self): # Test with all defaults. df = gendat() orig = df.copy() mx = pd.notnull(df) imp_data = mice.MICEData(df) nrow, ncol = df.shape assert_allclose(imp_data.ix_miss['x1'], np.arange(60)) assert_allclose(imp_data.ix_obs['x1'], np.arange(60, 200)) assert_allclose(imp_data.ix_miss['x2'], np.arange(40)) assert_allclose(imp_data.ix_miss['x3'], np.arange(10, 30, 2)) assert_allclose(imp_data.ix_obs['x3'], np.concatenate((np.arange(10), np.arange(11, 30, 2), np.arange(30, 200)))) assert_equal([set(imp_data.data[col]) for col in imp_data.data], [set(df[col].dropna()) for col in df]) for k in range(3): imp_data.update_all() assert_equal(imp_data.data.shape[0], nrow) assert_equal(imp_data.data.shape[1], ncol) assert_allclose(orig[mx], imp_data.data[mx]) assert_equal([set(imp_data.data[col]) for col in imp_data.data], [set(df[col].dropna()) for col in df]) fml = 'x1 ~ x2 + x3 + x4 + x5 + y' assert_equal(imp_data.conditional_formula['x1'], fml) assert_equal(imp_data._cycle_order, ['x5', 'x3', 'x4', 'y', 'x2', 'x1']) # Should make a copy assert(not (df is imp_data.data)) (endog_obs, exog_obs, exog_miss, predict_obs_kwds, predict_miss_kwds) = imp_data.get_split_data('x3') assert_equal(len(endog_obs), 190) assert_equal(exog_obs.shape, [190, 6]) assert_equal(exog_miss.shape, [10, 6]) def test_settingwithcopywarning(self): "Test that MICEData does not throw a SettingWithCopyWarning when imputing (https://github.com/statsmodels/statsmodels/issues/5430)" df = gendat() # There need to be some ints in here for the error to be thrown df['intcol'] = np.arange(len(df)) df['intcol'] = df.intcol.astype('int32') miceData = mice.MICEData(df) with pd.option_context('mode.chained_assignment', 'warn'): with warnings.catch_warnings(record=True) as ws: warnings.simplefilter('always') miceData.update_all() assert len(ws) == 0 def test_next_sample(self): df = gendat() imp_data = mice.MICEData(df) all_x = [] for j in range(2): x = imp_data.next_sample() assert(isinstance(x, pd.DataFrame)) assert_equal(df.shape, x.shape) all_x.append(x) # The returned dataframes are all the same object assert(all_x[0] is all_x[1]) def test_pertmeth(self): # Test with specified perturbation method. df = gendat() orig = df.copy() mx = pd.notnull(df) nrow, ncol = df.shape for pert_meth in "gaussian", "boot": imp_data = mice.MICEData(df, perturbation_method=pert_meth) for k in range(2): imp_data.update_all() assert_equal(imp_data.data.shape[0], nrow) assert_equal(imp_data.data.shape[1], ncol) assert_allclose(orig[mx], imp_data.data[mx]) assert_equal(imp_data._cycle_order, ['x5', 'x3', 'x4', 'y', 'x2', 'x1']) def test_phreg(self): np.random.seed(8742) n = 300 x1 = np.random.normal(size=n) x2 = np.random.normal(size=n) event_time = np.random.exponential(size=n) * np.exp(x1) obs_time = np.random.exponential(size=n) time = np.where(event_time < obs_time, event_time, obs_time) status = np.where(time == event_time, 1, 0) df = pd.DataFrame({"time": time, "status": status, "x1": x1, "x2": x2}) df.loc[10:40, 'time'] = np.nan df.loc[10:40, 'status'] = np.nan df.loc[30:50, 'x1'] = np.nan df.loc[40:60, 'x2'] = np.nan from statsmodels.duration.hazard_regression import PHReg # Save the dataset size at each iteration. hist = [] def cb(imp): hist.append(imp.data.shape) for pm in "gaussian", "boot": idata = mice.MICEData(df, perturbation_method=pm, history_callback=cb) idata.set_imputer("time", "0 + x1 + x2", model_class=PHReg, init_kwds={"status": mice.PatsyFormula("status")}, predict_kwds={"pred_type": "hr"}, perturbation_method=pm) x = idata.next_sample() assert(isinstance(x, pd.DataFrame)) assert(all([val == (299, 4) for val in hist])) def test_set_imputer(self): # Test with specified perturbation method. from statsmodels.regression.linear_model import RegressionResultsWrapper from statsmodels.genmod.generalized_linear_model import GLMResultsWrapper df = gendat() orig = df.copy() mx = pd.notnull(df) nrow, ncol = df.shape imp_data = mice.MICEData(df) imp_data.set_imputer('x1', 'x3 + x4 + x3*x4') imp_data.set_imputer('x2', 'x4 + I(x5**2)') imp_data.set_imputer('x3', model_class=sm.GLM, init_kwds={"family": sm.families.Binomial()}) imp_data.update_all() assert_equal(imp_data.data.shape[0], nrow) assert_equal(imp_data.data.shape[1], ncol) assert_allclose(orig[mx], imp_data.data[mx]) for j in range(1, 6): if j == 3: assert_equal(isinstance(imp_data.models['x3'], sm.GLM), True) assert_equal(isinstance(imp_data.models['x3'].family, sm.families.Binomial), True) assert_equal(isinstance(imp_data.results['x3'], GLMResultsWrapper), True) else: assert_equal(isinstance(imp_data.models['x%d' % j], sm.OLS), True) assert_equal(isinstance(imp_data.results['x%d' % j], RegressionResultsWrapper), True) fml = 'x1 ~ x3 + x4 + x3*x4' assert_equal(imp_data.conditional_formula['x1'], fml) fml = 'x4 ~ x1 + x2 + x3 + x5 + y' assert_equal(imp_data.conditional_formula['x4'], fml) assert_equal(imp_data._cycle_order, ['x5', 'x3', 'x4', 'y', 'x2', 'x1']) @pytest.mark.matplotlib def test_plot_missing_pattern(self, close_figures): df = gendat() imp_data = mice.MICEData(df) for row_order in "pattern", "raw": for hide_complete_rows in False, True: for color_row_patterns in False, True: plt.clf() fig = imp_data.plot_missing_pattern(row_order=row_order, hide_complete_rows=hide_complete_rows, color_row_patterns=color_row_patterns) close_or_save(pdf, fig) close_figures() @pytest.mark.matplotlib def test_plot_bivariate(self, close_figures): df = gendat() imp_data = mice.MICEData(df) imp_data.update_all() plt.clf() for plot_points in False, True: fig = imp_data.plot_bivariate('x2', 'x4', plot_points=plot_points) fig.get_axes()[0].set_title('plot_bivariate') close_or_save(pdf, fig) close_figures() @pytest.mark.matplotlib def test_fit_obs(self, close_figures): df = gendat() imp_data = mice.MICEData(df) imp_data.update_all() plt.clf() for plot_points in False, True: fig = imp_data.plot_fit_obs('x4', plot_points=plot_points) fig.get_axes()[0].set_title('plot_fit_scatterplot') close_or_save(pdf, fig) close_figures() @pytest.mark.matplotlib def test_plot_imputed_hist(self, close_figures): df = gendat() imp_data = mice.MICEData(df) imp_data.update_all() plt.clf() for plot_points in False, True: fig = imp_data.plot_imputed_hist('x4') fig.get_axes()[0].set_title('plot_imputed_hist') close_or_save(pdf, fig) close_figures() class TestMICE(object): def test_MICE(self): df = gendat() imp_data = mice.MICEData(df) mi = mice.MICE("y ~ x1 + x2 + x1:x2", sm.OLS, imp_data) result = mi.fit(1, 3) assert(issubclass(result.__class__, mice.MICEResults)) # Smoke test for results smr = result.summary() def test_MICE1(self): df = gendat() imp_data = mice.MICEData(df) mi = mice.MICE("y ~ x1 + x2 + x1:x2", sm.OLS, imp_data) from statsmodels.regression.linear_model import RegressionResultsWrapper for j in range(3): x = mi.next_sample() assert(issubclass(x.__class__, RegressionResultsWrapper)) def test_MICE1_regularized(self): df = gendat() imp = mice.MICEData(df, perturbation_method='boot') imp.set_imputer('x1', 'x2 + y', fit_kwds={'alpha': 1, 'L1_wt': 0}) imp.update_all() def test_MICE2(self): from statsmodels.genmod.generalized_linear_model import GLMResultsWrapper df = gendat() imp_data = mice.MICEData(df) mi = mice.MICE("x3 ~ x1 + x2", sm.GLM, imp_data, init_kwds={"family": sm.families.Binomial()}) for j in range(3): x = mi.next_sample() assert(isinstance(x, GLMResultsWrapper)) assert(isinstance(x.family, sm.families.Binomial)) @pytest.mark.slow def test_combine(self): np.random.seed(3897) x1 = np.random.normal(size=300) x2 = np.random.normal(size=300) y = x1 + x2 + np.random.normal(size=300) x1[0:100] = np.nan x2[250:] = np.nan df = pd.DataFrame({"x1": x1, "x2": x2, "y": y}) idata = mice.MICEData(df) mi = mice.MICE("y ~ x1 + x2", sm.OLS, idata, n_skip=20) result = mi.fit(10, 20) fmi = np.asarray([0.1778143, 0.11057262, 0.29626521]) assert_allclose(result.frac_miss_info, fmi, atol=1e-5) params = np.asarray([-0.03486102, 0.96236808, 0.9970371]) assert_allclose(result.params, params, atol=1e-5) tvalues = np.asarray([-0.54674776, 15.28091069, 13.61359403]) assert_allclose(result.tvalues, tvalues, atol=1e-5) def test_micedata_miss1(): # test for #4375 np.random.seed(0) data = pd.DataFrame(np.random.rand(50, 4)) data.columns = ['var1', 'var2', 'var3', 'var4'] # one column with a single missing value data.iloc[1, 1] = np.nan data.iloc[[1, 3], 2] = np.nan data_imp = mice.MICEData(data) data_imp.update_all() assert_equal(data_imp.data.isnull().values.sum(), 0) ix_miss = {'var1': np.array([], dtype=np.int64), 'var2': np.array([1], dtype=np.int64), 'var3': np.array([1, 3], dtype=np.int64), 'var4': np.array([], dtype=np.int64)} for k in ix_miss: assert_equal(data_imp.ix_miss[k], ix_miss[k]) statsmodels-0.12.2/statsmodels/imputation/tests/test_ros.py000066400000000000000000000664101400612667500242650ustar00rootroot00000000000000from statsmodels.compat.pandas import assert_series_equal, assert_frame_equal from io import StringIO from textwrap import dedent import numpy as np import numpy.testing as npt import numpy from numpy.testing import assert_equal import pandas import pytest from statsmodels.imputation import ros def load_basic_data(): raw_csv = StringIO( "res,qual\n2.00,=\n4.20,=\n4.62,=\n5.00,ND\n5.00,ND\n5.50,ND\n" "5.57,=\n5.66,=\n5.75,ND\n5.86,=\n6.65,=\n6.78,=\n6.79,=\n7.50,=\n" "7.50,=\n7.50,=\n8.63,=\n8.71,=\n8.99,=\n9.50,ND\n9.50,ND\n9.85,=\n" "10.82,=\n11.00,ND\n11.25,=\n11.25,=\n12.20,=\n14.92,=\n16.77,=\n" "17.81,=\n19.16,=\n19.19,=\n19.64,=\n20.18,=\n22.97,=\n" ) df = pandas.read_csv(raw_csv) df.loc[:, 'conc'] = df['res'] df.loc[:, 'censored'] = df['qual'] == 'ND' return df def load_intermediate_data(): df = pandas.DataFrame([ {'censored': True, 'conc': 5.0, 'det_limit_index': 1, 'rank': 1}, {'censored': True, 'conc': 5.0, 'det_limit_index': 1, 'rank': 2}, {'censored': True, 'conc': 5.5, 'det_limit_index': 2, 'rank': 1}, {'censored': True, 'conc': 5.75, 'det_limit_index': 3, 'rank': 1}, {'censored': True, 'conc': 9.5, 'det_limit_index': 4, 'rank': 1}, {'censored': True, 'conc': 9.5, 'det_limit_index': 4, 'rank': 2}, {'censored': True, 'conc': 11.0, 'det_limit_index': 5, 'rank': 1}, {'censored': False, 'conc': 2.0, 'det_limit_index': 0, 'rank': 1}, {'censored': False, 'conc': 4.2, 'det_limit_index': 0, 'rank': 2}, {'censored': False, 'conc': 4.62, 'det_limit_index': 0, 'rank': 3}, {'censored': False, 'conc': 5.57, 'det_limit_index': 2, 'rank': 1}, {'censored': False, 'conc': 5.66, 'det_limit_index': 2, 'rank': 2}, {'censored': False, 'conc': 5.86, 'det_limit_index': 3, 'rank': 1}, {'censored': False, 'conc': 6.65, 'det_limit_index': 3, 'rank': 2}, {'censored': False, 'conc': 6.78, 'det_limit_index': 3, 'rank': 3}, {'censored': False, 'conc': 6.79, 'det_limit_index': 3, 'rank': 4}, {'censored': False, 'conc': 7.5, 'det_limit_index': 3, 'rank': 5}, {'censored': False, 'conc': 7.5, 'det_limit_index': 3, 'rank': 6}, {'censored': False, 'conc': 7.5, 'det_limit_index': 3, 'rank': 7}, {'censored': False, 'conc': 8.63, 'det_limit_index': 3, 'rank': 8}, {'censored': False, 'conc': 8.71, 'det_limit_index': 3, 'rank': 9}, {'censored': False, 'conc': 8.99, 'det_limit_index': 3, 'rank': 10}, {'censored': False, 'conc': 9.85, 'det_limit_index': 4, 'rank': 1}, {'censored': False, 'conc': 10.82, 'det_limit_index': 4, 'rank': 2}, {'censored': False, 'conc': 11.25, 'det_limit_index': 5, 'rank': 1}, {'censored': False, 'conc': 11.25, 'det_limit_index': 5, 'rank': 2}, {'censored': False, 'conc': 12.2, 'det_limit_index': 5, 'rank': 3}, {'censored': False, 'conc': 14.92, 'det_limit_index': 5, 'rank': 4}, {'censored': False, 'conc': 16.77, 'det_limit_index': 5, 'rank': 5}, {'censored': False, 'conc': 17.81, 'det_limit_index': 5, 'rank': 6}, {'censored': False, 'conc': 19.16, 'det_limit_index': 5, 'rank': 7}, {'censored': False, 'conc': 19.19, 'det_limit_index': 5, 'rank': 8}, {'censored': False, 'conc': 19.64, 'det_limit_index': 5, 'rank': 9}, {'censored': False, 'conc': 20.18, 'det_limit_index': 5, 'rank': 10}, {'censored': False, 'conc': 22.97, 'det_limit_index': 5, 'rank': 11} ]) return df def load_advanced_data(): df = pandas.DataFrame([ {'Zprelim': -1.4456202174142005, 'censored': True, 'conc': 5.0, 'det_limit_index': 1, 'plot_pos': 0.07414187643020594, 'rank': 1}, {'Zprelim': -1.2201035333697587, 'censored': True, 'conc': 5.0, 'det_limit_index': 1, 'plot_pos': 0.11121281464530891, 'rank': 2}, {'Zprelim': -1.043822530159519, 'censored': True, 'conc': 5.5, 'det_limit_index': 2, 'plot_pos': 0.14828375286041187, 'rank': 1}, {'Zprelim': -1.0438225301595188, 'censored': True, 'conc': 5.75, 'det_limit_index': 3, 'plot_pos': 0.1482837528604119, 'rank': 1}, {'Zprelim': -0.8109553641377003, 'censored': True, 'conc': 9.5, 'det_limit_index': 4, 'plot_pos': 0.20869565217391303, 'rank': 1}, {'Zprelim': -0.4046779045300476, 'censored': True, 'conc': 9.5, 'det_limit_index': 4, 'plot_pos': 0.34285714285714286, 'rank': 2}, {'Zprelim': -0.20857169501420522, 'censored': True, 'conc': 11.0, 'det_limit_index': 5, 'plot_pos': 0.41739130434782606, 'rank': 1}, {'Zprelim': -1.5927654676048002, 'censored': False, 'conc': 2.0, 'det_limit_index': 0, 'plot_pos': 0.055606407322654455, 'rank': 1}, {'Zprelim': -1.2201035333697587, 'censored': False, 'conc': 4.2, 'det_limit_index': 0, 'plot_pos': 0.11121281464530891, 'rank': 2}, {'Zprelim': -0.9668111610681008, 'censored': False, 'conc': 4.62, 'det_limit_index': 0, 'plot_pos': 0.16681922196796337, 'rank': 3}, {'Zprelim': -0.6835186393930371, 'censored': False, 'conc': 5.57, 'det_limit_index': 2, 'plot_pos': 0.24713958810068648, 'rank': 1}, {'Zprelim': -0.6072167256926887, 'censored': False, 'conc': 5.66, 'det_limit_index': 2, 'plot_pos': 0.27185354691075514, 'rank': 2}, {'Zprelim': -0.44953240276543616, 'censored': False, 'conc': 5.86, 'det_limit_index': 3, 'plot_pos': 0.3265238194299979, 'rank': 1}, {'Zprelim': -0.36788328223414807, 'censored': False, 'conc': 6.65, 'det_limit_index': 3, 'plot_pos': 0.35648013313917204, 'rank': 2}, {'Zprelim': -0.28861907892223937, 'censored': False, 'conc': 6.78, 'det_limit_index': 3, 'plot_pos': 0.38643644684834616, 'rank': 3}, {'Zprelim': -0.21113039741112186, 'censored': False, 'conc': 6.79, 'det_limit_index': 3, 'plot_pos': 0.4163927605575203, 'rank': 4}, {'Zprelim': -0.1348908823006299, 'censored': False, 'conc': 7.5, 'det_limit_index': 3, 'plot_pos': 0.4463490742666944, 'rank': 5}, {'Zprelim': -0.05942854708257491, 'censored': False, 'conc': 7.5, 'det_limit_index': 3, 'plot_pos': 0.4763053879758685, 'rank': 6}, {'Zprelim': 0.015696403006170083, 'censored': False, 'conc': 7.5, 'det_limit_index': 3, 'plot_pos': 0.5062617016850427, 'rank': 7}, {'Zprelim': 0.09091016994359362, 'censored': False, 'conc': 8.63, 'det_limit_index': 3, 'plot_pos': 0.5362180153942168, 'rank': 8}, {'Zprelim': 0.16664251178856201, 'censored': False, 'conc': 8.71, 'det_limit_index': 3, 'plot_pos': 0.5661743291033909, 'rank': 9}, {'Zprelim': 0.24334426739770573, 'censored': False, 'conc': 8.99, 'det_limit_index': 3, 'plot_pos': 0.596130642812565, 'rank': 10}, {'Zprelim': 0.3744432988606558, 'censored': False, 'conc': 9.85, 'det_limit_index': 4, 'plot_pos': 0.6459627329192545, 'rank': 1}, {'Zprelim': 0.4284507519609981, 'censored': False, 'conc': 10.82, 'det_limit_index': 4, 'plot_pos': 0.6658385093167701, 'rank': 2}, {'Zprelim': 0.5589578655042562, 'censored': False, 'conc': 11.25, 'det_limit_index': 5, 'plot_pos': 0.7119047619047619, 'rank': 1}, {'Zprelim': 0.6374841609623771, 'censored': False, 'conc': 11.25, 'det_limit_index': 5, 'plot_pos': 0.7380952380952381, 'rank': 2}, {'Zprelim': 0.7201566171385521, 'censored': False, 'conc': 12.2, 'det_limit_index': 5, 'plot_pos': 0.7642857142857142, 'rank': 3}, {'Zprelim': 0.8080746339118065, 'censored': False, 'conc': 14.92, 'det_limit_index': 5, 'plot_pos': 0.7904761904761904, 'rank': 4}, {'Zprelim': 0.9027347916438648, 'censored': False, 'conc': 16.77, 'det_limit_index': 5, 'plot_pos': 0.8166666666666667, 'rank': 5}, {'Zprelim': 1.0062699858608395, 'censored': False, 'conc': 17.81, 'det_limit_index': 5, 'plot_pos': 0.8428571428571429, 'rank': 6}, {'Zprelim': 1.1219004674623523, 'censored': False, 'conc': 19.16, 'det_limit_index': 5, 'plot_pos': 0.8690476190476191, 'rank': 7}, {'Zprelim': 1.2548759122271174, 'censored': False, 'conc': 19.19, 'det_limit_index': 5, 'plot_pos': 0.8952380952380953, 'rank': 8}, {'Zprelim': 1.414746425534976, 'censored': False, 'conc': 19.64, 'det_limit_index': 5, 'plot_pos': 0.9214285714285714, 'rank': 9}, {'Zprelim': 1.622193585315426, 'censored': False, 'conc': 20.18, 'det_limit_index': 5, 'plot_pos': 0.9476190476190476, 'rank': 10}, {'Zprelim': 1.9399896117517081, 'censored': False, 'conc': 22.97, 'det_limit_index': 5, 'plot_pos': 0.9738095238095239, 'rank': 11} ]) return df def load_basic_cohn(): cohn = pandas.DataFrame([ {'lower_dl': 2.0, 'ncen_equal': 0.0, 'nobs_below': 0.0, 'nuncen_above': 3.0, 'prob_exceedance': 1.0, 'upper_dl': 5.0}, {'lower_dl': 5.0, 'ncen_equal': 2.0, 'nobs_below': 5.0, 'nuncen_above': 0.0, 'prob_exceedance': 0.77757437070938218, 'upper_dl': 5.5}, {'lower_dl': 5.5, 'ncen_equal': 1.0, 'nobs_below': 6.0, 'nuncen_above': 2.0, 'prob_exceedance': 0.77757437070938218, 'upper_dl': 5.75}, {'lower_dl': 5.75, 'ncen_equal': 1.0, 'nobs_below': 9.0, 'nuncen_above': 10.0, 'prob_exceedance': 0.7034324942791762, 'upper_dl': 9.5}, {'lower_dl': 9.5, 'ncen_equal': 2.0, 'nobs_below': 21.0, 'nuncen_above': 2.0, 'prob_exceedance': 0.37391304347826088, 'upper_dl': 11.0}, {'lower_dl': 11.0, 'ncen_equal': 1.0, 'nobs_below': 24.0, 'nuncen_above': 11.0, 'prob_exceedance': 0.31428571428571428, 'upper_dl': numpy.inf}, {'lower_dl': numpy.nan, 'ncen_equal': numpy.nan, 'nobs_below': numpy.nan, 'nuncen_above': numpy.nan, 'prob_exceedance': 0.0, 'upper_dl': numpy.nan} ]) return cohn class Test__ros_sort(object): def setup(self): self.df = load_basic_data() self.expected_baseline = pandas.DataFrame([ {'censored': True, 'conc': 5.0}, {'censored': True, 'conc': 5.0}, {'censored': True, 'conc': 5.5}, {'censored': True, 'conc': 5.75}, {'censored': True, 'conc': 9.5}, {'censored': True, 'conc': 9.5}, {'censored': True, 'conc': 11.0}, {'censored': False, 'conc': 2.0}, {'censored': False, 'conc': 4.2}, {'censored': False, 'conc': 4.62}, {'censored': False, 'conc': 5.57}, {'censored': False, 'conc': 5.66}, {'censored': False, 'conc': 5.86}, {'censored': False, 'conc': 6.65}, {'censored': False, 'conc': 6.78}, {'censored': False, 'conc': 6.79}, {'censored': False, 'conc': 7.5}, {'censored': False, 'conc': 7.5}, {'censored': False, 'conc': 7.5}, {'censored': False, 'conc': 8.63}, {'censored': False, 'conc': 8.71}, {'censored': False, 'conc': 8.99}, {'censored': False, 'conc': 9.85}, {'censored': False, 'conc': 10.82}, {'censored': False, 'conc': 11.25}, {'censored': False, 'conc': 11.25}, {'censored': False, 'conc': 12.2}, {'censored': False, 'conc': 14.92}, {'censored': False, 'conc': 16.77}, {'censored': False, 'conc': 17.81}, {'censored': False, 'conc': 19.16}, {'censored': False, 'conc': 19.19}, {'censored': False, 'conc': 19.64}, {'censored': False, 'conc': 20.18}, {'censored': False, 'conc': 22.97}, ])[['conc', 'censored']] self.expected_with_warning = self.expected_baseline.iloc[:-1] def test_baseline(self): result = ros._ros_sort(self.df, 'conc', 'censored') assert_frame_equal(result, self.expected_baseline) def test_censored_greater_than_max(self): df = self.df.copy() max_row = df['conc'].idxmax() df.loc[max_row, 'censored'] = True result = ros._ros_sort(df, 'conc', 'censored') assert_frame_equal(result, self.expected_with_warning) class Test_cohn_numbers(object): def setup(self): self.df = load_basic_data() self.final_cols = ['lower_dl', 'upper_dl', 'nuncen_above', 'nobs_below', 'ncen_equal', 'prob_exceedance'] self.expected_baseline = pandas.DataFrame([ {'lower_dl': 2.0, 'ncen_equal': 0.0, 'nobs_below': 0.0, 'nuncen_above': 3.0, 'prob_exceedance': 1.0, 'upper_dl': 5.0}, {'lower_dl': 5.0, 'ncen_equal': 2.0, 'nobs_below': 5.0, 'nuncen_above': 0.0, 'prob_exceedance': 0.77757437070938218, 'upper_dl': 5.5}, {'lower_dl': 5.5, 'ncen_equal': 1.0, 'nobs_below': 6.0, 'nuncen_above': 2.0, 'prob_exceedance': 0.77757437070938218, 'upper_dl': 5.75}, {'lower_dl': 5.75, 'ncen_equal': 1.0, 'nobs_below': 9.0, 'nuncen_above': 10.0, 'prob_exceedance': 0.7034324942791762, 'upper_dl': 9.5}, {'lower_dl': 9.5, 'ncen_equal': 2.0, 'nobs_below': 21.0, 'nuncen_above': 2.0, 'prob_exceedance': 0.37391304347826088, 'upper_dl': 11.0}, {'lower_dl': 11.0, 'ncen_equal': 1.0, 'nobs_below': 24.0, 'nuncen_above': 11.0, 'prob_exceedance': 0.31428571428571428, 'upper_dl': numpy.inf}, {'lower_dl': numpy.nan, 'ncen_equal': numpy.nan, 'nobs_below': numpy.nan, 'nuncen_above': numpy.nan, 'prob_exceedance': 0.0, 'upper_dl': numpy.nan} ])[self.final_cols] def test_baseline(self): result = ros.cohn_numbers(self.df, observations='conc', censorship='censored') assert_frame_equal(result, self.expected_baseline) def test_no_NDs(self): _df = self.df.copy() _df['qual'] = False result = ros.cohn_numbers(_df, observations='conc', censorship='qual') assert result.shape == (0, 6) class Test__detection_limit_index(object): def setup(self): self.cohn = load_basic_cohn() self.empty_cohn = pandas.DataFrame(numpy.empty((0, 7))) def test_empty(self): assert_equal(ros._detection_limit_index(None, self.empty_cohn), 0) def test_populated(self): assert_equal(ros._detection_limit_index(3.5, self.cohn), 0) assert_equal(ros._detection_limit_index(6.0, self.cohn), 3) assert_equal(ros._detection_limit_index(12.0, self.cohn), 5) def test_out_of_bounds(self): with pytest.raises(IndexError): ros._detection_limit_index(0, self.cohn) def test__ros_group_rank(): df = pandas.DataFrame({ 'dl_idx': [1] * 12, 'params': list('AABCCCDE') + list('DCBA'), 'values': list(range(12)) }) result = ros._ros_group_rank(df, 'dl_idx', 'params') expected = pandas.Series([1, 2, 1, 1, 2, 3, 1, 1, 2, 4, 2, 3], name='rank') assert_series_equal(result.astype(int), expected.astype(int)) class Test__ros_plot_pos(object): def setup(self): self.cohn = load_basic_cohn() def test_uncensored_1(self): row = {'censored': False, 'det_limit_index': 2, 'rank': 1} result = ros._ros_plot_pos(row, 'censored', self.cohn) assert_equal(result, 0.24713958810068648) def test_uncensored_2(self): row = {'censored': False, 'det_limit_index': 2, 'rank': 12} result = ros._ros_plot_pos(row, 'censored', self.cohn) assert_equal(result, 0.51899313501144173) def test_censored_1(self): row = {'censored': True, 'det_limit_index': 5, 'rank': 4} result = ros._ros_plot_pos(row, 'censored', self.cohn) assert_equal(result, 1.3714285714285714) def test_censored_2(self): row = {'censored': True, 'det_limit_index': 4, 'rank': 2} result = ros._ros_plot_pos(row, 'censored', self.cohn) assert_equal(result, 0.41739130434782606) def test__norm_plot_pos(): result = ros._norm_plot_pos([1, 2, 3, 4]) expected = numpy.array([ 0.159104, 0.385452, 0.614548, 0.840896]) npt.assert_array_almost_equal(result, expected) def test_plotting_positions(): df = load_intermediate_data() cohn = load_basic_cohn() results = ros.plotting_positions(df, 'censored', cohn) expected = numpy.array([ 0.07414188, 0.11121281, 0.14828375, 0.14828375, 0.20869565, 0.34285714, 0.4173913 , 0.05560641, 0.11121281, 0.16681922, 0.24713959, 0.27185355, 0.32652382, 0.35648013, 0.38643645, 0.41639276, 0.44634907, 0.47630539, 0.5062617 , 0.53621802, 0.56617433, 0.59613064, 0.64596273, 0.66583851, 0.71190476, 0.73809524, 0.76428571, 0.79047619, 0.81666667, 0.84285714, 0.86904762, 0.8952381 , 0.92142857, 0.94761905, 0.97380952 ]) npt.assert_array_almost_equal(results, expected) def test__impute(): expected = numpy.array([ 3.11279729, 3.60634338, 4.04602788, 4.04602788, 4.71008116, 6.14010906, 6.97841457, 2. , 4.2 , 4.62 , 5.57 , 5.66 , 5.86 , 6.65 , 6.78 , 6.79 , 7.5 , 7.5 , 7.5 , 8.63 , 8.71 , 8.99 , 9.85 , 10.82 , 11.25 , 11.25 , 12.2 , 14.92 , 16.77 , 17.81 , 19.16 , 19.19 , 19.64 , 20.18 , 22.97 ]) df = load_advanced_data() df = ros._impute(df, 'conc', 'censored', numpy.log, numpy.exp) result = df['final'].values npt.assert_array_almost_equal(result, expected) def test__do_ros(): expected = numpy.array([ 3.11279729, 3.60634338, 4.04602788, 4.04602788, 4.71008116, 6.14010906, 6.97841457, 2. , 4.2 , 4.62 , 5.57 , 5.66 , 5.86 , 6.65 , 6.78 , 6.79 , 7.5 , 7.5 , 7.5 , 8.63 , 8.71 , 8.99 , 9.85 , 10.82 , 11.25 , 11.25 , 12.2 , 14.92 , 16.77 , 17.81 , 19.16 , 19.19 , 19.64 , 20.18 , 22.97 ]) df = load_basic_data() df = ros._do_ros(df, 'conc', 'censored', numpy.log, numpy.exp) result = df['final'].values npt.assert_array_almost_equal(result, expected) class CheckROSMixin(object): def test_ros_df(self): result = ros.impute_ros(self.rescol, self.cencol, df=self.df) npt.assert_array_almost_equal( sorted(result), sorted(self.expected_final), decimal=self.decimal ) def test_ros_arrays(self): result = ros.impute_ros(self.df[self.rescol], self.df[self.cencol], df=None) npt.assert_array_almost_equal( sorted(result), sorted(self.expected_final), decimal=self.decimal ) def test_cohn(self): cols = [ 'nuncen_above', 'nobs_below', 'ncen_equal', 'prob_exceedance' ] cohn = ros.cohn_numbers(self.df, self.rescol, self.cencol) # Use round in place of the deprecated check_less_precise arg assert_frame_equal( np.round(cohn[cols], 3), np.round(self.expected_cohn[cols], 3), ) class Test_ROS_HelselAppendixB(CheckROSMixin): """ Appendix B dataset from "Estimation of Descriptive Statists for Multiply Censored Water Quality Data", Water Resources Research, Vol 24, No 12, pp 1997 - 2004. December 1988. """ decimal = 2 res = numpy.array([ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 10., 10., 10., 3.0, 7.0, 9.0, 12., 15., 20., 27., 33., 50. ]) cen = numpy.array([ True, True, True, True, True, True, True, True, True, False, False, False, False, False, False, False, False, False ]) rescol = 'obs' cencol = 'cen' df = pandas.DataFrame({rescol: res, cencol: cen}) expected_final = numpy.array([ 0.47, 0.85, 1.11, 1.27, 1.76, 2.34, 2.50, 3.00, 3.03, 4.80, 7.00, 9.00, 12.0, 15.0, 20.0, 27.0, 33.0, 50.0 ]) expected_cohn = pandas.DataFrame({ 'nuncen_above': numpy.array([3.0, 6.0, numpy.nan]), 'nobs_below': numpy.array([6.0, 12.0, numpy.nan]), 'ncen_equal': numpy.array([6.0, 3.0, numpy.nan]), 'prob_exceedance': numpy.array([0.55556, 0.33333, 0.0]), }) class Test_ROS_HelselArsenic(CheckROSMixin): """ Oahu arsenic data from Nondetects and Data Analysis by Dennis R. Helsel (John Wiley, 2005) Plotting positions are fudged since relative to source data since modeled data is what matters and (source data plot positions are not uniformly spaced, which seems weird) """ decimal = 2 res = numpy.array([ 3.2, 2.8, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 1.7, 1.5, 1.0, 1.0, 1.0, 1.0, 0.9, 0.9, 0.7, 0.7, 0.6, 0.5, 0.5, 0.5 ]) cen = numpy.array([ False, False, True, True, True, True, True, True, True, True, False, False, True, True, True, True, False, True, False, False, False, False, False, False ]) rescol = 'obs' cencol = 'cen' df = pandas.DataFrame({rescol: res, cencol: cen}) expected_final = numpy.array([ 3.20, 2.80, 1.42, 1.14, 0.95, 0.81, 0.68, 0.57, 0.46, 0.35, 1.70, 1.50, 0.98, 0.76, 0.58, 0.41, 0.90, 0.61, 0.70, 0.70, 0.60, 0.50, 0.50, 0.50 ]) expected_cohn = pandas.DataFrame({ 'nuncen_above': numpy.array([6.0, 1.0, 2.0, 2.0, numpy.nan]), 'nobs_below': numpy.array([0.0, 7.0, 12.0, 22.0, numpy.nan]), 'ncen_equal': numpy.array([0.0, 1.0, 4.0, 8.0, numpy.nan]), 'prob_exceedance': numpy.array([1.0, 0.3125, 0.21429, 0.0833, 0.0]), }) class Test_ROS_RNADAdata(CheckROSMixin): decimal = 3 datastring = StringIO(dedent("""\ res cen 0.090 True 0.090 True 0.090 True 0.101 False 0.136 False 0.340 False 0.457 False 0.514 False 0.629 False 0.638 False 0.774 False 0.788 False 0.900 True 0.900 True 0.900 True 1.000 True 1.000 True 1.000 True 1.000 True 1.000 True 1.000 False 1.000 True 1.000 True 1.000 True 1.000 True 1.000 True 1.000 True 1.000 True 1.000 True 1.000 True 1.000 True 1.000 True 1.000 True 1.100 False 2.000 False 2.000 False 2.404 False 2.860 False 3.000 False 3.000 False 3.705 False 4.000 False 5.000 False 5.960 False 6.000 False 7.214 False 16.000 False 17.716 False 25.000 False 51.000 False""")) rescol = 'res' cencol = 'cen' df = pandas.read_csv(datastring, sep=r'\s+') expected_final = numpy.array([ 0.01907990, 0.03826254, 0.06080717, 0.10100000, 0.13600000, 0.34000000, 0.45700000, 0.51400000, 0.62900000, 0.63800000, 0.77400000, 0.78800000, 0.08745914, 0.25257575, 0.58544205, 0.01711153, 0.03373885, 0.05287083, 0.07506079, 0.10081573, 1.00000000, 0.13070334, 0.16539309, 0.20569039, 0.25257575, 0.30725491, 0.37122555, 0.44636843, 0.53507405, 0.64042242, 0.76644378, 0.91850581, 1.10390531, 1.10000000, 2.00000000, 2.00000000, 2.40400000, 2.86000000, 3.00000000, 3.00000000, 3.70500000, 4.00000000, 5.00000000, 5.96000000, 6.00000000, 7.21400000, 16.00000000, 17.71600000, 25.00000000, 51.00000000 ]) expected_cohn = pandas.DataFrame({ 'nuncen_above': numpy.array([9., 0.0, 18., numpy.nan]), 'nobs_below': numpy.array([3., 15., 32., numpy.nan]), 'ncen_equal': numpy.array([3., 3., 17., numpy.nan]), 'prob_exceedance': numpy.array([0.84, 0.36, 0.36, 0]), }) class Test_NoOp_ZeroND(CheckROSMixin): decimal = 2 numpy.random.seed(0) N = 20 res = numpy.random.lognormal(size=N) cen = [False] * N rescol = 'obs' cencol = 'cen' df = pandas.DataFrame({rescol: res, cencol: cen}) expected_final = numpy.array([ 0.38, 0.43, 0.81, 0.86, 0.90, 1.13, 1.15, 1.37, 1.40, 1.49, 1.51, 1.56, 2.14, 2.59, 2.66, 4.28, 4.46, 5.84, 6.47, 9.4 ]) expected_cohn = pandas.DataFrame({ 'nuncen_above': numpy.array([]), 'nobs_below': numpy.array([]), 'ncen_equal': numpy.array([]), 'prob_exceedance': numpy.array([]), }) class Test_ROS_OneND(CheckROSMixin): decimal = 3 res = numpy.array([ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 10., 10., 10., 3.0, 7.0, 9.0, 12., 15., 20., 27., 33., 50. ]) cen = numpy.array([ True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False ]) rescol = 'conc' cencol = 'cen' df = pandas.DataFrame({rescol: res, cencol: cen}) expected_final = numpy.array([ 0.24, 1.0, 1.0, 1.0, 1.0, 1.0, 10., 10., 10., 3.0 , 7.0, 9.0, 12., 15., 20., 27., 33., 50. ]) expected_cohn = pandas.DataFrame({ 'nuncen_above': numpy.array([17.0, numpy.nan]), 'nobs_below': numpy.array([1.0, numpy.nan]), 'ncen_equal': numpy.array([1.0, numpy.nan]), 'prob_exceedance': numpy.array([0.94444, 0.0]), }) class Test_HalfDLs_80pctNDs(CheckROSMixin): decimal = 3 res = numpy.array([ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 10., 10., 10., 3.0, 7.0, 9.0, 12., 15., 20., 27., 33., 50. ]) cen = numpy.array([ True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, False, False, False ]) rescol = 'value' cencol = 'qual' df = pandas.DataFrame({rescol: res, cencol: cen}) expected_final = numpy.array([ 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 5.0, 5.0, 5.0, 1.5, 3.5, 4.5, 6.0, 7.5, 10., 27., 33., 50. ]) expected_cohn = pandas.DataFrame({ 'nuncen_above': numpy.array([0., 0., 0., 0., 0., 0., 0., 3., numpy.nan]), 'nobs_below': numpy.array([6., 7., 8., 9., 12., 13., 14., 15., numpy.nan]), 'ncen_equal': numpy.array([6., 1., 1., 1., 3., 1., 1., 1., numpy.nan]), 'prob_exceedance': numpy.array([0.16667] * 8 + [0.]), }) class Test_HaflDLs_OneUncensored(CheckROSMixin): decimal = 3 res = numpy.array([1.0, 1.0, 12., 15., ]) cen = numpy.array([True, True, True, False ]) rescol = 'value' cencol = 'qual' df = pandas.DataFrame({rescol: res, cencol: cen}) expected_final = numpy.array([0.5, 0.5, 6. , 15.]) expected_cohn = pandas.DataFrame({ 'nuncen_above': numpy.array([0., 1., numpy.nan]), 'nobs_below': numpy.array([2., 3., numpy.nan]), 'ncen_equal': numpy.array([2., 1., numpy.nan]), 'prob_exceedance': numpy.array([0.25, 0.25, 0.]), }) class Test_ROS_MaxCen_GT_MaxUncen(Test_ROS_HelselAppendixB): res = numpy.array([ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 10., 10., 10., 3.0, 7.0, 9.0, 12., 15., 20., 27., 33., 50., 60, 70 ]) cen = numpy.array([ True, True, True, True, True, True, True, True, True, False, False, False, False, False, False, False, False, False, True, True ]) class Test_ROS_OnlyDL_GT_MaxUncen(Test_NoOp_ZeroND): numpy.random.seed(0) N = 20 res = [ 0.38, 0.43, 0.81, 0.86, 0.90, 1.13, 1.15, 1.37, 1.40, 1.49, 1.51, 1.56, 2.14, 2.59, 2.66, 4.28, 4.46, 5.84, 6.47, 9.40, 10.0, 10.0 ] cen = ([False] * N) + [True, True] statsmodels-0.12.2/statsmodels/interface/000077500000000000000000000000001400612667500204475ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/interface/__init__.py000066400000000000000000000000001400612667500225460ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/iolib/000077500000000000000000000000001400612667500176055ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/iolib/__init__.py000066400000000000000000000005261400612667500217210ustar00rootroot00000000000000from .foreign import StataReader, genfromdta, savetxt from .table import SimpleTable, csv2st from .smpickle import save_pickle, load_pickle from statsmodels.tools._testing import PytestTester __all__ = ['test', 'csv2st', 'SimpleTable', 'StataReader', 'savetxt', 'save_pickle', 'load_pickle', 'genfromdta'] test = PytestTester() statsmodels-0.12.2/statsmodels/iolib/api.py000066400000000000000000000004401400612667500207260ustar00rootroot00000000000000__all__ = [ "StataReader", "StataWriter", "SimpleTable", "genfromdta", "savetxt", "csv2st", "save_pickle", "load_pickle" ] from .foreign import StataReader, genfromdta, savetxt, StataWriter from .table import SimpleTable, csv2st from .smpickle import save_pickle, load_pickle statsmodels-0.12.2/statsmodels/iolib/foreign.py000066400000000000000000001232371400612667500216200ustar00rootroot00000000000000""" Input/Output tools for working with binary data. The Stata input tools were originally written by Joe Presbrey as part of PyDTA. You can find more information here http://presbrey.mit.edu/PyDTA See Also -------- numpy.lib.io """ import warnings from statsmodels.compat.python import (lzip, lmap, lrange, lfilter, asbytes, asstr) from struct import unpack, calcsize, pack from struct import error as struct_error import datetime import sys import numpy as np import statsmodels.tools.data as data_util from pandas import isnull from pandas.io.stata import StataMissingValue from statsmodels.iolib.openfile import get_file_obj _date_formats = ["%tc", "%tC", "%td", "%tw", "%tm", "%tq", "%th", "%ty"] def _datetime_to_stata_elapsed(date, fmt): """ Convert from datetime to SIF. http://www.stata.com/help.cgi?datetime Parameters ---------- date : datetime.datetime The date to convert to the Stata Internal Format given by fmt fmt : str The format to convert to. Can be, tc, td, tw, tm, tq, th, ty """ if not isinstance(date, datetime.datetime): raise ValueError("date should be datetime.datetime format") stata_epoch = datetime.datetime(1960, 1, 1) if fmt in ["%tc", "tc"]: delta = date - stata_epoch return (delta.days * 86400000 + delta.seconds*1000 + delta.microseconds/1000) elif fmt in ["%tC", "tC"]: from warnings import warn warn("Stata Internal Format tC not supported.", UserWarning) return date elif fmt in ["%td", "td"]: return (date- stata_epoch).days elif fmt in ["%tw", "tw"]: return (52*(date.year-stata_epoch.year) + (date - datetime.datetime(date.year, 1, 1)).days / 7) elif fmt in ["%tm", "tm"]: return (12 * (date.year - stata_epoch.year) + date.month - 1) elif fmt in ["%tq", "tq"]: return 4*(date.year-stata_epoch.year) + int((date.month - 1)/3) elif fmt in ["%th", "th"]: return 2 * (date.year - stata_epoch.year) + int(date.month > 6) elif fmt in ["%ty", "ty"]: return date.year else: raise ValueError("fmt %s not understood" % fmt) def _stata_elapsed_date_to_datetime(date, fmt): """ Convert from SIF to datetime. http://www.stata.com/help.cgi?datetime Parameters ---------- date : int The Stata Internal Format date to convert to datetime according to fmt fmt : str The format to convert to. Can be, tc, td, tw, tm, tq, th, ty Examples -------- >>> _stata_elapsed_date_to_datetime(52, "%tw") datetime.datetime(1961, 1, 1, 0, 0) Notes ----- datetime/c - tc milliseconds since 01jan1960 00:00:00.000, assuming 86,400 s/day datetime/C - tC - NOT IMPLEMENTED milliseconds since 01jan1960 00:00:00.000, adjusted for leap seconds date - td days since 01jan1960 (01jan1960 = 0) weekly date - tw weeks since 1960w1 This assumes 52 weeks in a year, then adds 7 * remainder of the weeks. The datetime value is the start of the week in terms of days in the year, not ISO calendar weeks. monthly date - tm months since 1960m1 quarterly date - tq quarters since 1960q1 half-yearly date - th half-years since 1960h1 yearly date - ty years since 0000 If you do not have pandas with datetime support, then you cannot do milliseconds accurately. """ #NOTE: we could run into overflow / loss of precision situations here # casting to int, but I'm not sure what to do. datetime will not deal with # numpy types and numpy datetime is not mature enough / we cannot rely on # pandas version > 0.7.1 #TODO: IIRC relative delta does not play well with np.datetime? date = int(date) stata_epoch = datetime.datetime(1960, 1, 1) if fmt in ["%tc", "tc"]: from dateutil.relativedelta import relativedelta return stata_epoch + relativedelta(microseconds=date*1000) elif fmt in ["%tC", "tC"]: from warnings import warn warn("Encountered %tC format. Leaving in Stata Internal Format.", UserWarning) return date elif fmt in ["%td", "td"]: return stata_epoch + datetime.timedelta(int(date)) elif fmt in ["%tw", "tw"]: # does not count leap days - 7 days is a week year = datetime.datetime(stata_epoch.year + date // 52, 1, 1) day_delta = (date % 52 ) * 7 return year + datetime.timedelta(int(day_delta)) elif fmt in ["%tm", "tm"]: year = stata_epoch.year + date // 12 month_delta = (date % 12 ) + 1 return datetime.datetime(year, month_delta, 1) elif fmt in ["%tq", "tq"]: year = stata_epoch.year + date // 4 month_delta = (date % 4) * 3 + 1 return datetime.datetime(year, month_delta, 1) elif fmt in ["%th", "th"]: year = stata_epoch.year + date // 2 month_delta = (date % 2) * 6 + 1 return datetime.datetime(year, month_delta, 1) elif fmt in ["%ty", "ty"]: if date > 0: return datetime.datetime(date, 1, 1) else: # do not do negative years bc cannot mix dtypes in column raise ValueError("Year 0 and before not implemented") else: raise ValueError("Date fmt %s not understood" % fmt) ### Helper classes for StataReader ### class _StataVariable(object): """ A dataset variable. Not intended for public use. Parameters ---------- variable_data Attributes ---------- format : str Stata variable format. See notes for more information. index : int Zero-index column index of variable. label : str Data Label name : str Variable name type : str Stata data type. See notes for more information. value_format : str Value format. Notes ----- More information: http://www.stata.com/help.cgi?format """ def __init__(self, variable_data): self._data = variable_data def __int__(self): """the variable's index within an observation""" return self.index def __str__(self): """the name of the variable""" return self.name @property def index(self): """the variable's index within an observation""" return self._data[0] @property def type(self): """ The data type of variable Possible types are: {1..244:string, b:byte, h:int, l:long, f:float, d:double) """ return self._data[1] @property def name(self): """the name of the variable""" return self._data[2] @property def format(self): """the variable's Stata format""" return self._data[4] @property def value_format(self): """the variable's value format""" return self._data[5] @property def label(self): """The variable's label""" return self._data[6] class StataReader(object): """ Stata .dta file reader. .. deprecated:: 0.11 Use pandas.read_stata or pandas.io.stata.StataReader Provides methods to return the metadata of a Stata .dta file and a generator for the data itself. Parameters ---------- file : file-like A file-like object representing a Stata .dta file. missing_values : bool If missing_values is True, parse missing_values and return a Missing Values object instead of None. encoding : str, optional Used for Python 3 only. Encoding to use when reading the .dta file. Defaults to `locale.getpreferredencoding` See Also -------- statsmodels.iolib.foreign.genfromdta pandas.read_stata pandas.io.stata.StataReader Notes ----- This is known only to work on file formats 113 (Stata 8/9), 114 (Stata 10/11), and 115 (Stata 12). Needs to be tested on older versions. Known not to work on format 104, 108. If you have the documentation for older formats, please contact the developers. For more information about the .dta format see http://www.stata.com/help.cgi?dta http://www.stata.com/help.cgi?dta_113 """ _header = {} _data_location = 0 _col_sizes = () _has_string_data = False _missing_values = False #type code #-------------------- #str1 1 = 0x01 #str2 2 = 0x02 #... #str244 244 = 0xf4 #byte 251 = 0xfb (sic) #int 252 = 0xfc #long 253 = 0xfd #float 254 = 0xfe #double 255 = 0xff #-------------------- #NOTE: the byte type seems to be reserved for categorical variables # with a label, but the underlying variable is -127 to 100 # we're going to drop the label and cast to int DTYPE_MAP = dict(lzip(lrange(1,245), ['a' + str(i) for i in range(1,245)]) + \ [(251, np.int16),(252, np.int32),(253, int), (254, np.float32), (255, np.float64)]) TYPE_MAP = lrange(251)+list('bhlfd') #NOTE: technically, some of these are wrong. there are more numbers # that can be represented. it's the 27 ABOVE and BELOW the max listed # numeric data type in [U] 12.2.2 of the 11.2 manual MISSING_VALUES = { 'b': (-127,100), 'h': (-32767, 32740), 'l': (-2147483647, 2147483620), 'f': (-1.701e+38, +1.701e+38), 'd': (-1.798e+308, +8.988e+307) } def __init__(self, fname, missing_values=False, encoding=None): warnings.warn( "StataReader is deprecated as of 0.10.0 and will be removed after" " the 0.12 release. Use pandas.read_stata or " "pandas.io.stata.StataReader instead.", FutureWarning) if encoding is None: import locale self._encoding = locale.getpreferredencoding() else: self._encoding = encoding self._missing_values = missing_values self._parse_header(fname) def file_headers(self): """ Returns all .dta file headers. out: dict Has keys typlist, data_label, lbllist, varlist, nvar, filetype, ds_format, nobs, fmtlist, vlblist, time_stamp, srtlist, byteorder """ return self._header def file_format(self): """ Returns the file format. Returns ------- out : int Notes ----- Format 113: Stata 8/9 Format 114: Stata 10/11 Format 115: Stata 12 """ return self._header['ds_format'] def file_label(self): """ Returns the dataset's label. Returns ------- out: str """ return self._header['data_label'] def file_timestamp(self): """ Returns the date and time Stata recorded on last file save. Returns ------- out : str """ return self._header['time_stamp'] def variables(self): """ Returns a list of the dataset's StataVariables objects. """ return lmap(_StataVariable, zip(lrange(self._header['nvar']), self._header['typlist'], self._header['varlist'], self._header['srtlist'], self._header['fmtlist'], self._header['lbllist'], self._header['vlblist'])) def dataset(self, as_dict=False): """ Returns a Python generator object for iterating over the dataset. Parameters ---------- as_dict : bool, optional If as_dict is True, yield each row of observations as a dict. If False, yields each row of observations as a list. Returns ------- Generator object for iterating over the dataset. Yields each row of observations as a list by default. Notes ----- If missing_values is True during instantiation of StataReader then observations with StataMissingValue(s) are not filtered and should be handled by your application. """ try: self._file.seek(self._data_location) except Exception: pass if as_dict: vars = lmap(str, self.variables()) for i in range(len(self)): yield dict(zip(vars, self._next())) else: for i in range(self._header['nobs']): yield self._next() ### Python special methods def __len__(self): """ Return the number of observations in the dataset. This value is taken directly from the header and includes observations with missing values. """ return self._header['nobs'] def __getitem__(self, k): """ Seek to an observation indexed k in the file and return it, ordered by Stata's output to the .dta file. k is zero-indexed. Prefer using R.data() for performance. """ if not (isinstance(k, int)) or k < 0 or k > len(self)-1: raise IndexError(k) loc = self._data_location + sum(self._col_size()) * k if self._file.tell() != loc: self._file.seek(loc) return self._next() # Private methods def _null_terminate(self, s, encoding): null_byte = asbytes('\x00') try: s = s.lstrip(null_byte)[:s.index(null_byte)] except Exception: pass return s.decode(encoding) def _parse_header(self, file_object): self._file = file_object encoding = self._encoding # parse headers self._header['ds_format'] = unpack('b', self._file.read(1))[0] if self._header['ds_format'] not in [113, 114, 115]: raise ValueError("Only file formats >= 113 (Stata >= 9)" " are supported. Got format %s. Please report " "if you think this error is incorrect." % self._header['ds_format']) byteorder = self._header['byteorder'] = unpack('b', self._file.read(1))[0]==0x1 and '>' or '<' self._header['filetype'] = unpack('b', self._file.read(1))[0] self._file.read(1) nvar = self._header['nvar'] = unpack(byteorder+'h', self._file.read(2))[0] self._header['nobs'] = unpack(byteorder+'i', self._file.read(4))[0] self._header['data_label'] = self._null_terminate(self._file.read(81), encoding) self._header['time_stamp'] = self._null_terminate(self._file.read(18), encoding) # parse descriptors typlist =[ord(self._file.read(1)) for i in range(nvar)] self._header['typlist'] = [self.TYPE_MAP[typ] for typ in typlist] self._header['dtyplist'] = [self.DTYPE_MAP[typ] for typ in typlist] self._header['varlist'] = [self._null_terminate(self._file.read(33), encoding) for i in range(nvar)] self._header['srtlist'] = unpack(byteorder+('h'*(nvar+1)), self._file.read(2*(nvar+1)))[:-1] if self._header['ds_format'] <= 113: self._header['fmtlist'] = \ [self._null_terminate(self._file.read(12), encoding) \ for i in range(nvar)] else: self._header['fmtlist'] = \ [self._null_terminate(self._file.read(49), encoding) \ for i in range(nvar)] self._header['lbllist'] = [self._null_terminate(self._file.read(33), encoding) for i in range(nvar)] self._header['vlblist'] = [self._null_terminate(self._file.read(81), encoding) for i in range(nvar)] # ignore expansion fields # When reading, read five bytes; the last four bytes now tell you the # size of the next read, which you discard. You then continue like # this until you read 5 bytes of zeros. while True: data_type = unpack(byteorder+'b', self._file.read(1))[0] data_len = unpack(byteorder+'i', self._file.read(4))[0] if data_type == 0: break self._file.read(data_len) # other state vars self._data_location = self._file.tell() self._has_string_data = len(lfilter(lambda x: isinstance(x, int), self._header['typlist'])) > 0 self._col_size() def _calcsize(self, fmt): return isinstance(fmt, int) and fmt or \ calcsize(self._header['byteorder']+fmt) def _col_size(self, k = None): """Calculate size of a data record.""" if len(self._col_sizes) == 0: self._col_sizes = lmap(lambda x: self._calcsize(x), self._header['typlist']) if k is None: return self._col_sizes else: return self._col_sizes[k] def _unpack(self, fmt, byt): d = unpack(self._header['byteorder']+fmt, byt)[0] if fmt[-1] in self.MISSING_VALUES: nmin, nmax = self.MISSING_VALUES[fmt[-1]] if d < nmin or d > nmax: if self._missing_values: return StataMissingValue(nmax, d) else: return None return d def _next(self): typlist = self._header['typlist'] if self._has_string_data: data = [None]*self._header['nvar'] for i in range(len(data)): if isinstance(typlist[i], int): data[i] = self._null_terminate(self._file.read(typlist[i]), self._encoding) else: data[i] = self._unpack(typlist[i], self._file.read(self._col_size(i))) return data else: return lmap(lambda i: self._unpack(typlist[i], self._file.read(self._col_size(i))), lrange(self._header['nvar'])) def _set_endianness(endianness): if endianness.lower() in ["<", "little"]: return "<" elif endianness.lower() in [">", "big"]: return ">" else: # pragma : no cover raise ValueError("Endianness %s not understood" % endianness) def _dtype_to_stata_type(dtype): """ Converts dtype types to stata types. Returns the byte of the given ordinal. See TYPE_MAP and comments for an explanation. This is also explained in the dta spec. 1 - 244 are strings of this length 251 - chr(251) - for int8 and int16, byte 252 - chr(252) - for int32, int 253 - chr(253) - for int64, long 254 - chr(254) - for float32, float 255 - chr(255) - double, double If there are dates to convert, then dtype will already have the correct type inserted. """ #TODO: expand to handle datetime to integer conversion if dtype.type == np.string_: return chr(dtype.itemsize) elif dtype.type == np.object_: # try to coerce it to the biggest string # not memory efficient, what else could we do? return chr(244) elif dtype == np.float64: return chr(255) elif dtype == np.float32: return chr(254) elif dtype == np.int64: return chr(253) elif dtype == np.int32: return chr(252) elif dtype == np.int8 or dtype == np.int16: # ok to assume bytes? return chr(251) else: # pragma : no cover raise ValueError("Data type %s not currently understood. " "Please report an error to the developers." % dtype) def _dtype_to_default_stata_fmt(dtype): """ Maps numpy dtype to stata's default format for this type. Not terribly important since users can change this in Stata. Semantics are string -> "%DDs" where DD is the length of the string float64 -> "%10.0g" float32 -> "%9.0g" int64 -> "%9.0g" int32 -> "%9.0g" int16 -> "%9.0g" int8 -> "%8.0g" """ #TODO: expand this to handle a default datetime format? if dtype.type == np.string_: return "%" + str(dtype.itemsize) + "s" elif dtype.type == np.object_: return "%244s" elif dtype == np.float64: return "%10.0g" elif dtype == np.float32: return "%9.0g" elif dtype == np.int64: return "%9.0g" elif dtype == np.int32: return "%8.0g" elif dtype == np.int8 or dtype == np.int16: # ok to assume bytes? return "%8.0g" else: # pragma : no cover raise ValueError("Data type %s not currently understood. " "Please report an error to the developers." % dtype) def _pad_bytes(name, length): """ Takes a char string and pads it wih null bytes until it's length chars """ return name + "\x00" * (length - len(name)) def _default_names(nvar): """ Returns default Stata names v1, v2, ... vnvar """ return ["v%d" % i for i in range(1,nvar+1)] def _convert_datetime_to_stata_type(fmt): """ Converts from one of the stata date formats to a type in TYPE_MAP """ if fmt in ["tc", "%tc", "td", "%td", "tw", "%tw", "tm", "%tm", "tq", "%tq", "th", "%th", "ty", "%ty"]: return np.float64 # Stata expects doubles for SIFs else: raise ValueError("fmt %s not understood" % fmt) def _maybe_convert_to_int_keys(convert_dates, varlist): new_dict = {} for key in convert_dates: if not convert_dates[key].startswith("%"): # make sure proper fmts convert_dates[key] = "%" + convert_dates[key] if key in varlist: new_dict.update({varlist.index(key) : convert_dates[key]}) else: if not isinstance(key, int): raise ValueError("convery_dates key is not in varlist " "and is not an int") new_dict.update({key : convert_dates[key]}) return new_dict _type_converters = {253 : int, 252 : int} class StataWriter(object): """ A class for writing Stata binary dta files from array-like objects .. deprecated:: 0.11 Use pandas.read_stata or pandas.io.stata.StataReader Parameters ---------- fname : file path or buffer Where to save the dta file. data : array_like Array-like input to save. Pandas objects are also accepted. convert_dates : dict Dictionary mapping column of datetime types to the stata internal format that you want to use for the dates. Options are 'tc', 'td', 'tm', 'tw', 'th', 'tq', 'ty'. Column can be either a number or a name. encoding : str Default is latin-1. Note that Stata does not support unicode. byteorder : str Can be ">", "<", "little", or "big". The default is None which uses `sys.byteorder` Returns ------- writer : StataWriter instance The StataWriter instance has a write_file method, which will write the file to the given `fname`. Examples -------- >>> writer = StataWriter('./data_file.dta', data) >>> writer.write_file() Or with dates >>> writer = StataWriter('./date_data_file.dta', date, {2 : 'tw'}) >>> writer.write_file() """ #type code #-------------------- #str1 1 = 0x01 #str2 2 = 0x02 #... #str244 244 = 0xf4 #byte 251 = 0xfb (sic) #int 252 = 0xfc #long 253 = 0xfd #float 254 = 0xfe #double 255 = 0xff #-------------------- #NOTE: the byte type seems to be reserved for categorical variables # with a label, but the underlying variable is -127 to 100 # we're going to drop the label and cast to int DTYPE_MAP = dict(lzip(lrange(1,245), ['a' + str(i) for i in range(1,245)]) + \ [(251, np.int16),(252, np.int32),(253, int), (254, np.float32), (255, np.float64)]) TYPE_MAP = lrange(251)+list('bhlfd') MISSING_VALUES = { 'b': 101, 'h': 32741, 'l' : 2147483621, 'f': 1.7014118346046923e+38, 'd': 8.98846567431158e+307} def __init__(self, fname, data, convert_dates=None, encoding="latin-1", byteorder=None): warnings.warn( "StataWriter is deprecated as of 0.10.0 and will be removed after" " the 0.12 release. Use pandas.DataFrame.to_stata or " "pandas.io.stata.StatWriter instead.", FutureWarning) self._convert_dates = convert_dates # attach nobs, nvars, data, varlist, typlist if data_util._is_using_pandas(data, None): self._prepare_pandas(data) elif data_util._is_array_like(data, None): data = np.asarray(data) if data_util._is_structured_ndarray(data): self._prepare_structured_array(data) else: if convert_dates is not None: raise ValueError("Not able to convert dates in a plain" " ndarray.") self._prepare_ndarray(data) else: # pragma : no cover raise ValueError("Type %s for data not understood" % type(data)) if byteorder is None: byteorder = sys.byteorder self._byteorder = _set_endianness(byteorder) self._encoding = encoding self._file = get_file_obj(fname, 'wb', encoding) def _write(self, to_write): """ Helper to call asbytes before writing to file for Python 3 compat. """ self._file.write(asbytes(to_write)) def _prepare_structured_array(self, data): self.nobs = len(data) self.nvar = len(data.dtype) self.data = data self.datarows = iter(data) dtype = data.dtype descr = dtype.descr if dtype.names is None: varlist = _default_names(self.nvar) else: varlist = dtype.names # check for datetime and change the type convert_dates = self._convert_dates if convert_dates is not None: convert_dates = _maybe_convert_to_int_keys(convert_dates, varlist) self._convert_dates = convert_dates for key in convert_dates: descr[key] = ( descr[key][0], _convert_datetime_to_stata_type(convert_dates[key]) ) dtype = np.dtype(descr) self.varlist = varlist self.typlist = [_dtype_to_stata_type(dtype[i]) for i in range(self.nvar)] self.fmtlist = [_dtype_to_default_stata_fmt(dtype[i]) for i in range(self.nvar)] # set the given format for the datetime cols if convert_dates is not None: for key in convert_dates: self.fmtlist[key] = convert_dates[key] def _prepare_ndarray(self, data): if data.ndim == 1: data = data[:,None] self.nobs, self.nvar = data.shape self.data = data self.datarows = iter(data) #TODO: this should be user settable dtype = data.dtype self.varlist = _default_names(self.nvar) self.typlist = [_dtype_to_stata_type(dtype) for i in range(self.nvar)] self.fmtlist = [_dtype_to_default_stata_fmt(dtype) for i in range(self.nvar)] def _prepare_pandas(self, data): #NOTE: we might need a different API / class for pandas objects so # we can set different semantics - handle this with a PR to pandas.io class DataFrameRowIter(object): def __init__(self, data): self.data = data def __iter__(self): for i, row in data.iterrows(): yield row data = data.reset_index() self.datarows = DataFrameRowIter(data) self.nobs, self.nvar = data.shape self.data = data self.varlist = data.columns.tolist() dtypes = data.dtypes convert_dates = self._convert_dates if convert_dates is not None: convert_dates = _maybe_convert_to_int_keys(convert_dates, self.varlist) self._convert_dates = convert_dates for key in convert_dates: new_type = _convert_datetime_to_stata_type(convert_dates[key]) dtypes[key] = np.dtype(new_type) self.typlist = [_dtype_to_stata_type(dt) for dt in dtypes] self.fmtlist = [_dtype_to_default_stata_fmt(dt) for dt in dtypes] # set the given format for the datetime cols if convert_dates is not None: for key in convert_dates: self.fmtlist[key] = convert_dates[key] def write_file(self): self._write_header() self._write_descriptors() self._write_variable_labels() # write 5 zeros for expansion fields self._write(_pad_bytes("", 5)) if self._convert_dates is None: self._write_data_nodates() else: self._write_data_dates() #self._write_value_labels() def _write_header(self, data_label=None, time_stamp=None): byteorder = self._byteorder # ds_format - just use 114 self._write(pack("b", 114)) # byteorder self._write(byteorder == ">" and "\x01" or "\x02") # filetype self._write("\x01") # unused self._write("\x00") # number of vars, 2 bytes self._write(pack(byteorder+"h", self.nvar)[:2]) # number of obs, 4 bytes self._write(pack(byteorder+"i", self.nobs)[:4]) # data label 81 bytes, char, null terminated if data_label is None: self._write(self._null_terminate(_pad_bytes("", 80), self._encoding)) else: self._write(self._null_terminate(_pad_bytes(data_label[:80], 80), self._encoding)) # time stamp, 18 bytes, char, null terminated # format dd Mon yyyy hh:mm if time_stamp is None: time_stamp = datetime.datetime.now() elif not isinstance(time_stamp, datetime): raise ValueError("time_stamp should be datetime type") self._write(self._null_terminate( time_stamp.strftime("%d %b %Y %H:%M"), self._encoding)) def _write_descriptors(self, typlist=None, varlist=None, srtlist=None, fmtlist=None, lbllist=None): nvar = self.nvar # typlist, length nvar, format byte array for typ in self.typlist: self._write(typ) # varlist, length 33*nvar, char array, null terminated for name in self.varlist: name = self._null_terminate(name, self._encoding) name = _pad_bytes(asstr(name[:32]), 33) self._write(name) # srtlist, 2*(nvar+1), int array, encoded by byteorder srtlist = _pad_bytes("", (2*(nvar+1))) self._write(srtlist) # fmtlist, 49*nvar, char array for fmt in self.fmtlist: self._write(_pad_bytes(fmt, 49)) # lbllist, 33*nvar, char array #NOTE: this is where you could get fancy with pandas categorical type for i in range(nvar): self._write(_pad_bytes("", 33)) def _write_variable_labels(self, labels=None): nvar = self.nvar if labels is None: for i in range(nvar): self._write(_pad_bytes("", 81)) def _write_data_nodates(self): data = self.datarows byteorder = self._byteorder TYPE_MAP = self.TYPE_MAP typlist = self.typlist for row in data: #row = row.squeeze().tolist() # needed for structured arrays for i,var in enumerate(row): typ = ord(typlist[i]) if typ <= 244: # we've got a string if len(var) < typ: var = _pad_bytes(asstr(var), len(var) + 1) self._write(var) else: try: if typ in _type_converters: var = _type_converters[typ](var) self._write(pack(byteorder+TYPE_MAP[typ], var)) except struct_error: # have to be strict about type pack will not do any # kind of casting self._write(pack(byteorder+TYPE_MAP[typ], _type_converters[typ](var))) def _write_data_dates(self): convert_dates = self._convert_dates data = self.datarows byteorder = self._byteorder TYPE_MAP = self.TYPE_MAP MISSING_VALUES = self.MISSING_VALUES typlist = self.typlist for row in data: #row = row.squeeze().tolist() # needed for structured arrays for i,var in enumerate(row): typ = ord(typlist[i]) #NOTE: If anyone finds this terribly slow, there is # a vectorized way to convert dates, see genfromdta for going # from int to datetime and reverse it. will copy data though if i in convert_dates: var = _datetime_to_stata_elapsed(var, self.fmtlist[i]) if typ <= 244: # we've got a string if isnull(var): var = "" # missing string if len(var) < typ: var = _pad_bytes(var, len(var) + 1) self._write(var) else: if isnull(var): # this only matters for floats var = MISSING_VALUES[typ] self._write(pack(byteorder+TYPE_MAP[typ], var)) def _null_terminate(self, s, encoding): null_byte = '\x00' s += null_byte return s.encode(encoding) def genfromdta(fname, missing_flt=-999., encoding=None, pandas=False, convert_dates=True): """ Returns an ndarray or DataFrame from a Stata .dta file. .. deprecated:: 0.11 Use pandas.read_stata or pandas.io.stata.StataReader Parameters ---------- fname : str or filehandle Stata .dta file. missing_flt : numeric The numeric value to replace missing values with. Will be used for any numeric value. encoding : str, optional Used for Python 3 only. Encoding to use when reading the .dta file. Defaults to `locale.getpreferredencoding` pandas : bool Optionally return a DataFrame instead of an ndarray convert_dates : bool If convert_dates is True, then Stata formatted dates will be converted to datetime types according to the variable's format. """ warnings.warn( "genfromdta is deprecated as of 0.10.0 and will be removed after the " "0.12 release future version. Use pandas.read_stata instead.", FutureWarning) if isinstance(fname, str): fhd = StataReader(open(fname, 'rb'), missing_values=False, encoding=encoding) elif not hasattr(fname, 'read'): raise TypeError("The input should be a string or a filehandle. "\ "(got %s instead)" % type(fname)) else: fhd = StataReader(fname, missing_values=False, encoding=encoding) # validate_names = np.lib._iotools.NameValidator(excludelist=excludelist, # deletechars=deletechars, # case_sensitive=case_sensitive) #TODO: This needs to handle the byteorder? header = fhd.file_headers() types = header['dtyplist'] nobs = header['nobs'] numvars = header['nvar'] varnames = header['varlist'] fmtlist = header['fmtlist'] dataname = header['data_label'] labels = header['vlblist'] # labels are thrown away unless DataArray # type is used data = np.zeros((nobs,numvars)) stata_dta = fhd.dataset() dt = np.dtype(lzip(varnames, types)) data = np.zeros((nobs), dtype=dt) # init final array for rownum,line in enumerate(stata_dta): # does not handle missing value objects, just casts # None will only work without missing value object. if None in line: for i,val in enumerate(line): #NOTE: This will only be scalar types because missing strings # are empty not None in Stata if val is None: line[i] = missing_flt data[rownum] = tuple(line) if pandas: from pandas import DataFrame data = DataFrame.from_records(data) if convert_dates: cols = np.where(lmap(lambda x : x in _date_formats, fmtlist))[0] for col in cols: i = col col = data.columns[col] data[col] = data[col].apply(_stata_elapsed_date_to_datetime, args=(fmtlist[i],)) elif convert_dates: # date_cols = np.where(map(lambda x : x in _date_formats, # fmtlist))[0] # make the dtype for the datetime types cols = np.where(lmap(lambda x: x in _date_formats, fmtlist))[0] dtype = data.dtype.descr dtype = [(sub_dtype[0], object) if i in cols else sub_dtype for i, sub_dtype in enumerate(dtype)] data = data.astype(dtype) # have to copy for col in cols: def convert(x): return _stata_elapsed_date_to_datetime(x, fmtlist[col]) data[data.dtype.names[col]] = lmap(convert, data[data.dtype.names[col]]) return data def savetxt(fname, X, names=None, fmt='%.18e', delimiter=' '): """ Save an array to a text file. This is just a copy of numpy.savetxt patched to support structured arrays or a header of names. Does not include py3 support now in savetxt. Parameters ---------- fname : filename or file handle If the filename ends in ``.gz``, the file is automatically saved in compressed gzip format. `loadtxt` understands gzipped files transparently. X : array_like Data to be saved to a text file. names : list, optional If given names will be the column header in the text file. If None and X is a structured or recarray then the names are taken from X.dtype.names. fmt : str or sequence of strs A single format (%10.5f), a sequence of formats, or a multi-format string, e.g. 'Iteration %d -- %10.5f', in which case `delimiter` is ignored. delimiter : str Character separating columns. See Also -------- save : Save an array to a binary file in NumPy ``.npy`` format savez : Save several arrays into a ``.npz`` compressed archive Notes ----- Further explanation of the `fmt` parameter (``%[flag]width[.precision]specifier``): flags: ``-`` : left justify ``+`` : Forces to preceed result with + or -. ``0`` : Left pad the number with zeros instead of space (see width). width: Minimum number of characters to be printed. The value is not truncated if it has more characters. precision: - For integer specifiers (eg. ``d,i,o,x``), the minimum number of digits. - For ``e, E`` and ``f`` specifiers, the number of digits to print after the decimal point. - For ``g`` and ``G``, the maximum number of significant digits. - For ``s``, the maximum number of characters. specifiers: ``c`` : character ``d`` or ``i`` : signed decimal integer ``e`` or ``E`` : scientific notation with ``e`` or ``E``. ``f`` : decimal floating point ``g,G`` : use the shorter of ``e,E`` or ``f`` ``o`` : signed octal ``s`` : str of characters ``u`` : unsigned decimal integer ``x,X`` : unsigned hexadecimal integer This explanation of ``fmt`` is not complete, for an exhaustive specification see [1]_. References ---------- .. [1] `Format Specification Mini-Language `_, Python Documentation. Examples -------- >>> savetxt('test.out', x, delimiter=',') # x is an array >>> savetxt('test.out', (x,y,z)) # x,y,z equal sized 1D arrays >>> savetxt('test.out', x, fmt='%1.4e') # use exponential notation """ with get_file_obj(fname, 'w') as fh: X = np.asarray(X) # Handle 1-dimensional arrays if X.ndim == 1: # Common case -- 1d array of numbers if X.dtype.names is None: X = np.atleast_2d(X).T ncol = 1 # Complex dtype -- each field indicates a separate column else: ncol = len(X.dtype.descr) else: ncol = X.shape[1] # `fmt` can be a string with multiple insertion points or a list of formats. # E.g. '%10.5f\t%10d' or ('%10.5f', '$10d') if isinstance(fmt, (list, tuple)): if len(fmt) != ncol: raise AttributeError('fmt has wrong shape. %s' % str(fmt)) format = delimiter.join(fmt) elif isinstance(fmt, str): if fmt.count('%') == 1: fmt = [fmt, ]*ncol format = delimiter.join(fmt) elif fmt.count('%') != ncol: raise AttributeError('fmt has wrong number of %% formats. %s' % fmt) else: format = fmt # handle names if names is None and X.dtype.names: names = X.dtype.names if names is not None: fh.write(delimiter.join(names) + '\n') for row in X: fh.write(format % tuple(row) + '\n') statsmodels-0.12.2/statsmodels/iolib/openfile.py000066400000000000000000000036671400612667500217740ustar00rootroot00000000000000""" Handle file opening for read/write """ from numpy.lib._iotools import _is_string_like class EmptyContextManager(object): """ This class is needed to allow file-like object to be used as context manager, but without getting closed. """ def __init__(self, obj): self._obj = obj def __enter__(self): '''When entering, return the embedded object''' return self._obj def __exit__(self, *args): '''Do not hide anything''' return False def __getattr__(self, name): return getattr(self._obj, name) def _open(fname, mode, encoding): if fname.endswith('.gz'): import gzip return gzip.open(fname, mode, encoding=encoding) else: return open(fname, mode, encoding=encoding) def get_file_obj(fname, mode='r', encoding=None): """ Light wrapper to handle strings, path objects and let files (anything else) pass through. It also handle '.gz' files. Parameters ---------- fname : str, path object or file-like object File to open / forward mode : str Argument passed to the 'open' or 'gzip.open' function encoding : str For Python 3 only, specify the encoding of the file Returns ------- A file-like object that is always a context-manager. If the `fname` was already a file-like object, the returned context manager *will not close the file*. """ if _is_string_like(fname): return _open(fname, mode, encoding) try: return open(fname, mode, encoding=encoding) # handle pathlib-like objs except TypeError: try: # Make sure the object has the write methods if "r" in mode: fname.read if "w" in mode or "a" in mode: fname.write except AttributeError: raise ValueError("fname must be a string or a file-like object") return EmptyContextManager(fname) statsmodels-0.12.2/statsmodels/iolib/smpickle.py000066400000000000000000000015721400612667500217730ustar00rootroot00000000000000"""Helper files for pickling""" from statsmodels.iolib.openfile import get_file_obj def save_pickle(obj, fname): """ Save the object to file via pickling. Parameters ---------- fname : str Filename to pickle to """ import pickle with get_file_obj(fname, 'wb') as fout: pickle.dump(obj, fout, protocol=-1) def load_pickle(fname): """ Load a previously saved object .. warning:: Loading pickled models is not secure against erroneous or maliciously constructed data. Never unpickle data received from an untrusted or unauthenticated source. Parameters ---------- fname : str Filename to unpickle Notes ----- This method can be used to load *both* models and results. """ import pickle with get_file_obj(fname, 'rb') as fin: return pickle.load(fin) statsmodels-0.12.2/statsmodels/iolib/stata_summary_examples.py000066400000000000000000000110071400612667500247450ustar00rootroot00000000000000 """. regress totemp gnpdefl gnp unemp armed pop year Source | SS df MS Number of obs = 16 -------------+------------------------------ F( 6, 9) = 330.29 Model | 184172402 6 30695400.3 Prob > F = 0.0000 Residual | 836424.129 9 92936.0144 R-squared = 0.9955 -------------+------------------------------ Adj R-squared = 0.9925 Total | 185008826 15 12333921.7 Root MSE = 304.85 ------------------------------------------------------------------------------ totemp | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gnpdefl | 15.06167 84.91486 0.18 0.863 -177.0291 207.1524 gnp | -.0358191 .033491 -1.07 0.313 -.111581 .0399428 unemp | -2.020229 .4883995 -4.14 0.003 -3.125065 -.9153928 armed | -1.033227 .2142741 -4.82 0.001 -1.517948 -.5485049 pop | -.0511045 .2260731 -0.23 0.826 -.5625173 .4603083 year | 1829.151 455.4785 4.02 0.003 798.7873 2859.515 _cons | -3482258 890420.3 -3.91 0.004 -5496529 -1467987 ------------------------------------------------------------------------------ """ #From Stata using Longley dataset as in the test and example for GLM """ . glm totemp gnpdefl gnp unemp armed pop year Iteration 0: log likelihood = -109.61744 Generalized linear models No. of obs = 16 Optimization : ML Residual df = 9 Scale parameter = 92936.01 Deviance = 836424.1293 (1/df) Deviance = 92936.01 Pearson = 836424.1293 (1/df) Pearson = 92936.01 Variance function: V(u) = 1 [Gaussian] Link function : g(u) = u [Identity] AIC = 14.57718 Log likelihood = -109.6174355 BIC = 836399.2 ------------------------------------------------------------------------------ | OIM totemp | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- gnpdefl | 15.06167 84.91486 0.18 0.859 -151.3684 181.4917 gnp | -.0358191 .033491 -1.07 0.285 -.1014603 .029822 unemp | -2.020229 .4883995 -4.14 0.000 -2.977475 -1.062984 armed | -1.033227 .2142741 -4.82 0.000 -1.453196 -.6132571 pop | -.0511045 .2260731 -0.23 0.821 -.4941996 .3919906 year | 1829.151 455.4785 4.02 0.000 936.4298 2721.873 _cons | -3482258 890420.3 -3.91 0.000 -5227450 -1737066 ------------------------------------------------------------------------------ """ #RLM Example """ . rreg stackloss airflow watertemp acidconc Huber iteration 1: maximum difference in weights = .48402478 Huber iteration 2: maximum difference in weights = .07083248 Huber iteration 3: maximum difference in weights = .03630349 Biweight iteration 4: maximum difference in weights = .2114744 Biweight iteration 5: maximum difference in weights = .04709559 Biweight iteration 6: maximum difference in weights = .01648123 Biweight iteration 7: maximum difference in weights = .01050023 Biweight iteration 8: maximum difference in weights = .0027233 Robust regression Number of obs = 21 F( 3, 17) = 74.15 Prob > F = 0.0000 ------------------------------------------------------------------------------ stackloss | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- airflow | .8526511 .1223835 6.97 0.000 .5944446 1.110858 watertemp | .8733594 .3339811 2.61 0.018 .1687209 1.577998 acidconc | -.1224349 .1418364 -0.86 0.400 -.4216836 .1768139 _cons | -41.6703 10.79559 -3.86 0.001 -64.447 -18.89361 ------------------------------------------------------------------------------ """ statsmodels-0.12.2/statsmodels/iolib/summary.py000066400000000000000000000740701400612667500216640ustar00rootroot00000000000000import copy from itertools import zip_longest import time from statsmodels.compat.python import lrange, lmap, lzip import numpy as np from statsmodels.iolib.table import SimpleTable from statsmodels.iolib.tableformatting import (gen_fmt, fmt_2, fmt_params, fmt_2cols) from .summary2 import _model_types def forg(x, prec=3): if prec == 3: # for 3 decimals if (abs(x) >= 1e4) or (abs(x) < 1e-4): return '%9.3g' % x else: return '%9.3f' % x elif prec == 4: if (abs(x) >= 1e4) or (abs(x) < 1e-4): return '%10.4g' % x else: return '%10.4f' % x else: raise ValueError("`prec` argument must be either 3 or 4, not {prec}" .format(prec=prec)) def d_or_f(x, width=6): """convert number to string with either integer of float formatting This is used internally for nobs and degrees of freedom which are usually integers but can be float in some cases. Parameters ---------- x : int or float width : int only used if x is nan Returns ------- str : str number as formatted string """ if np.isnan(x): return (width - 3) * ' ' + 'NaN' if x // 1 == x: return "%#6d" % x else: return "%#8.2f" % x def summary(self, yname=None, xname=None, title=0, alpha=.05, returns='text', model_info=None): """ Parameters ---------- yname : str optional, Default is `Y` xname : list[str] optional, Default is `X.#` for # in p the number of regressors Confidance interval : (0,1) not implimented title : str optional, Defualt is 'Generalized linear model' returns : str 'text', 'table', 'csv', 'latex', 'html' Returns ------- Default : returns='print' Prints the summarirized results Option : returns='text' Prints the summarirized results Option : returns='table' SimpleTable instance : summarizing the fit of a linear model. Option : returns='csv' returns a string of csv of the results, to import into a spreadsheet Option : returns='latex' Not implimented yet Option : returns='HTML' Not implimented yet Examples (needs updating) -------- >>> import statsmodels as sm >>> data = sm.datasets.longley.load(as_pandas=False) >>> data.exog = sm.add_constant(data.exog) >>> ols_results = sm.OLS(data.endog, data.exog).results >>> print ols_results.summary() ... Notes ----- conf_int calculated from normal dist. """ if title == 0: title = _model_types[self.model.__class__.__name__] if xname is not None and len(xname) != len(self.params): # GH 2298 raise ValueError('User supplied xnames must have the same number of ' 'entries as the number of model parameters ' '({0})'.format(len(self.params))) yname, xname = _getnames(self, yname, xname) time_now = time.localtime() time_of_day = [time.strftime("%H:%M:%S", time_now)] date = time.strftime("%a, %d %b %Y", time_now) modeltype = self.model.__class__.__name__ nobs = self.nobs df_model = self.df_model df_resid = self.df_resid #General part of the summary table, Applicable to all? models #------------------------------------------------------------ # TODO: define this generically, overwrite in model classes #replace definition of stubs data by single list #e.g. gen_left = [('Model type:', [modeltype]), ('Date:', [date]), ('Dependent Variable:', yname), # TODO: What happens with multiple names? ('df model', [df_model]) ] gen_stubs_left, gen_data_left = zip_longest(*gen_left) #transpose row col gen_title = title gen_header = None gen_table_left = SimpleTable(gen_data_left, gen_header, gen_stubs_left, title=gen_title, txt_fmt=gen_fmt ) gen_stubs_right = ('Method:', 'Time:', 'Number of Obs:', 'df resid') gen_data_right = ([modeltype], #was dist family need to look at more time_of_day, [nobs], [df_resid] ) gen_table_right = SimpleTable(gen_data_right, gen_header, gen_stubs_right, title=gen_title, txt_fmt=gen_fmt ) gen_table_left.extend_right(gen_table_right) general_table = gen_table_left # Parameters part of the summary table # ------------------------------------ # Note: this is not necessary since we standardized names, # only t versus normal tstats = {'OLS': self.t(), 'GLS': self.t(), 'GLSAR': self.t(), 'WLS': self.t(), 'RLM': self.t(), 'GLM': self.t()} prob_stats = {'OLS': self.pvalues, 'GLS': self.pvalues, 'GLSAR': self.pvalues, 'WLS': self.pvalues, 'RLM': self.pvalues, 'GLM': self.pvalues } # Dictionary to store the header names for the parameter part of the # summary table. look up by modeltype alp = str((1-alpha)*100)+'%' param_header = { 'OLS' : ['coef', 'std err', 't', 'P>|t|', alp + ' Conf. Interval'], 'GLS' : ['coef', 'std err', 't', 'P>|t|', alp + ' Conf. Interval'], 'GLSAR' : ['coef', 'std err', 't', 'P>|t|', alp + ' Conf. Interval'], 'WLS' : ['coef', 'std err', 't', 'P>|t|', alp + ' Conf. Interval'], 'GLM' : ['coef', 'std err', 't', 'P>|t|', alp + ' Conf. Interval'], #glm uses t-distribution 'RLM' : ['coef', 'std err', 'z', 'P>|z|', alp + ' Conf. Interval'] #checke z } params_stubs = xname params = self.params conf_int = self.conf_int(alpha) std_err = self.bse exog_len = lrange(len(xname)) tstat = tstats[modeltype] prob_stat = prob_stats[modeltype] # Simpletable should be able to handle the formating params_data = lzip(["%#6.4g" % (params[i]) for i in exog_len], ["%#6.4f" % (std_err[i]) for i in exog_len], ["%#6.4f" % (tstat[i]) for i in exog_len], ["%#6.4f" % (prob_stat[i]) for i in exog_len], ["(%#5g, %#5g)" % tuple(conf_int[i]) for i in exog_len]) parameter_table = SimpleTable(params_data, param_header[modeltype], params_stubs, title=None, txt_fmt=fmt_2 ) #special table #------------- #TODO: exists in linear_model, what about other models #residual diagnostics #output options #-------------- #TODO: JP the rest needs to be fixed, similar to summary in linear_model def ols_printer(): """ print summary table for ols models """ table = str(general_table)+'\n'+str(parameter_table) return table def glm_printer(): table = str(general_table)+'\n'+str(parameter_table) return table printers = {'OLS': ols_printer, 'GLM': glm_printer} if returns == 'print': try: return printers[modeltype]() except KeyError: return printers['OLS']() def _getnames(self, yname=None, xname=None): '''extract names from model or construct names ''' if yname is None: if getattr(self.model, 'endog_names', None) is not None: yname = self.model.endog_names else: yname = 'y' if xname is None: if getattr(self.model, 'exog_names', None) is not None: xname = self.model.exog_names else: xname = ['var_%d' % i for i in range(len(self.params))] return yname, xname def summary_top(results, title=None, gleft=None, gright=None, yname=None, xname=None): '''generate top table(s) TODO: this still uses predefined model_methods ? allow gleft, gright to be 1 element tuples instead of filling with None? ''' #change of names ? gen_left, gen_right = gleft, gright # time and names are always included time_now = time.localtime() time_of_day = [time.strftime("%H:%M:%S", time_now)] date = time.strftime("%a, %d %b %Y", time_now) yname, xname = _getnames(results, yname=yname, xname=xname) # create dictionary with default # use lambdas because some values raise exception if they are not available default_items = dict([ ('Dependent Variable:', lambda: [yname]), ('Dep. Variable:', lambda: [yname]), ('Model:', lambda: [results.model.__class__.__name__]), ('Date:', lambda: [date]), ('Time:', lambda: time_of_day), ('Number of Obs:', lambda: [results.nobs]), ('No. Observations:', lambda: [d_or_f(results.nobs)]), ('Df Model:', lambda: [d_or_f(results.df_model)]), ('Df Residuals:', lambda: [d_or_f(results.df_resid)]), ('Log-Likelihood:', lambda: ["%#8.5g" % results.llf]) # does not exist for RLM - exception ]) if title is None: title = results.model.__class__.__name__ + 'Regression Results' if gen_left is None: # default: General part of the summary table, Applicable to all? models gen_left = [('Dep. Variable:', None), ('Model type:', None), ('Date:', None), ('No. Observations:', None), ('Df model:', None), ('Df resid:', None)] try: llf = results.llf # noqa: F841 gen_left.append(('Log-Likelihood', None)) except: # AttributeError, NotImplementedError pass gen_right = [] gen_title = title gen_header = None # replace missing (None) values with default values gen_left_ = [] for item, value in gen_left: if value is None: value = default_items[item]() # let KeyErrors raise exception gen_left_.append((item, value)) gen_left = gen_left_ if gen_right: gen_right_ = [] for item, value in gen_right: if value is None: value = default_items[item]() # let KeyErrors raise exception gen_right_.append((item, value)) gen_right = gen_right_ # check nothing was missed missing_values = [k for k,v in gen_left + gen_right if v is None] assert missing_values == [], missing_values # pad both tables to equal number of rows if gen_right: if len(gen_right) < len(gen_left): # fill up with blank lines to same length gen_right += [(' ', ' ')] * (len(gen_left) - len(gen_right)) elif len(gen_right) > len(gen_left): # fill up with blank lines to same length, just to keep it symmetric gen_left += [(' ', ' ')] * (len(gen_right) - len(gen_left)) # padding in SimpleTable does not work like I want #force extra spacing and exact string length in right table gen_right = [('%-21s' % (' '+k), v) for k,v in gen_right] gen_stubs_right, gen_data_right = zip_longest(*gen_right) #transpose row col gen_table_right = SimpleTable(gen_data_right, gen_header, gen_stubs_right, title=gen_title, txt_fmt=fmt_2cols ) else: gen_table_right = [] #because .extend_right seems works with [] #moved below so that we can pad if needed to match length of gen_right #transpose rows and columns, `unzip` gen_stubs_left, gen_data_left = zip_longest(*gen_left) #transpose row col gen_table_left = SimpleTable(gen_data_left, gen_header, gen_stubs_left, title=gen_title, txt_fmt=fmt_2cols ) gen_table_left.extend_right(gen_table_right) general_table = gen_table_left return general_table def summary_params(results, yname=None, xname=None, alpha=.05, use_t=True, skip_header=False, title=None): '''create a summary table for the parameters Parameters ---------- res : results instance some required information is directly taken from the result instance yname : {str, None} optional name for the endogenous variable, default is "y" xname : {list[str], None} optional names for the exogenous variables, default is "var_xx" alpha : float significance level for the confidence intervals use_t : bool indicator whether the p-values are based on the Student-t distribution (if True) or on the normal distribution (if False) skip_headers : bool If false (default), then the header row is added. If true, then no header row is added. Returns ------- params_table : SimpleTable instance ''' # Parameters part of the summary table # ------------------------------------ # Note: this is not necessary since we standardized names, # only t versus normal if isinstance(results, tuple): # for multivariate endog # TODO: check whether I do not want to refactor this #we need to give parameter alpha to conf_int results, params, std_err, tvalues, pvalues, conf_int = results else: params = results.params std_err = results.bse tvalues = results.tvalues # is this sometimes called zvalues pvalues = results.pvalues conf_int = results.conf_int(alpha) if params.size == 0: return SimpleTable([['No Model Parameters']]) # Dictionary to store the header names for the parameter part of the # summary table. look up by modeltype if use_t: param_header = ['coef', 'std err', 't', 'P>|t|', '[' + str(alpha/2), str(1-alpha/2) + ']'] else: param_header = ['coef', 'std err', 'z', 'P>|z|', '[' + str(alpha/2), str(1-alpha/2) + ']'] if skip_header: param_header = None _, xname = _getnames(results, yname=yname, xname=xname) if len(xname) != len(params): raise ValueError('xnames and params do not have the same length') params_stubs = xname exog_idx = lrange(len(xname)) params_data = lzip([forg(params[i], prec=4) for i in exog_idx], [forg(std_err[i]) for i in exog_idx], [forg(tvalues[i]) for i in exog_idx], ["%#6.3f" % (pvalues[i]) for i in exog_idx], [forg(conf_int[i,0]) for i in exog_idx], [forg(conf_int[i,1]) for i in exog_idx]) parameter_table = SimpleTable(params_data, param_header, params_stubs, title=title, txt_fmt=fmt_params ) return parameter_table def summary_params_frame(results, yname=None, xname=None, alpha=.05, use_t=True): '''create a summary table for the parameters Parameters ---------- res : results instance some required information is directly taken from the result instance yname : {str, None} optional name for the endogenous variable, default is "y" xname : {list[str], None} optional names for the exogenous variables, default is "var_xx" alpha : float significance level for the confidence intervals use_t : bool indicator whether the p-values are based on the Student-t distribution (if True) or on the normal distribution (if False) skip_headers : bool If false (default), then the header row is added. If true, then no header row is added. Returns ------- params_table : SimpleTable instance ''' # Parameters part of the summary table # ------------------------------------ # Note: this is not necessary since we standardized names, # only t versus normal if isinstance(results, tuple): # for multivariate endog # TODO: check whether I do not want to refactor this #we need to give parameter alpha to conf_int results, params, std_err, tvalues, pvalues, conf_int = results else: params = results.params std_err = results.bse tvalues = results.tvalues #is this sometimes called zvalues pvalues = results.pvalues conf_int = results.conf_int(alpha) # Dictionary to store the header names for the parameter part of the # summary table. look up by modeltype if use_t: param_header = ['coef', 'std err', 't', 'P>|t|', 'Conf. Int. Low', 'Conf. Int. Upp.'] else: param_header = ['coef', 'std err', 'z', 'P>|z|', 'Conf. Int. Low', 'Conf. Int. Upp.'] _, xname = _getnames(results, yname=yname, xname=xname) from pandas import DataFrame table = np.column_stack((params, std_err, tvalues, pvalues, conf_int)) return DataFrame(table, columns=param_header, index=xname) def summary_params_2d(result, extras=None, endog_names=None, exog_names=None, title=None): '''create summary table of regression parameters with several equations This allows interleaving of parameters with bse and/or tvalues Parameters ---------- result : result instance the result instance with params and attributes in extras extras : list[str] additional attributes to add below a parameter row, e.g. bse or tvalues endog_names : {list[str], None} names for rows of the parameter array (multivariate endog) exog_names : {list[str], None} names for columns of the parameter array (exog) alpha : float level for confidence intervals, default 0.95 title : None or string Returns ------- tables : list of SimpleTable this contains a list of all seperate Subtables table_all : SimpleTable the merged table with results concatenated for each row of the parameter array ''' if endog_names is None: # TODO: note the [1:] is specific to current MNLogit endog_names = ['endog_%d' % i for i in np.unique(result.model.endog)[1:]] if exog_names is None: exog_names = ['var%d' % i for i in range(len(result.params))] # TODO: check formatting options with different values res_params = [[forg(item, prec=4) for item in row] for row in result.params] if extras: extras_list = [[['%10s' % ('(' + forg(v, prec=3).strip() + ')') for v in col] for col in getattr(result, what)] for what in extras ] data = lzip(res_params, *extras_list) data = [i for j in data for i in j] #flatten stubs = lzip(endog_names, *[['']*len(endog_names)]*len(extras)) stubs = [i for j in stubs for i in j] #flatten else: data = res_params stubs = endog_names txt_fmt = copy.deepcopy(fmt_params) txt_fmt["data_fmts"] = ["%s"]*result.params.shape[1] return SimpleTable(data, headers=exog_names, stubs=stubs, title=title, txt_fmt=txt_fmt) def summary_params_2dflat(result, endog_names=None, exog_names=None, alpha=0.05, use_t=True, keep_headers=True, endog_cols=False): '''summary table for parameters that are 2d, e.g. multi-equation models Parameters ---------- result : result instance the result instance with params, bse, tvalues and conf_int endog_names : {list[str], None} names for rows of the parameter array (multivariate endog) exog_names : {list[str], None} names for columns of the parameter array (exog) alpha : float level for confidence intervals, default 0.95 use_t : bool indicator whether the p-values are based on the Student-t distribution (if True) or on the normal distribution (if False) keep_headers : bool If true (default), then sub-tables keep their headers. If false, then only the first headers are kept, the other headerse are blanked out endog_cols : bool If false (default) then params and other result statistics have equations by rows. If true, then equations are assumed to be in columns. Not implemented yet. Returns ------- tables : list of SimpleTable this contains a list of all seperate Subtables table_all : SimpleTable the merged table with results concatenated for each row of the parameter array ''' res = result params = res.params if params.ndim == 2: # we've got multiple equations n_equ = params.shape[1] if len(endog_names) != params.shape[1]: raise ValueError('endog_names has wrong length') else: if len(endog_names) != len(params): raise ValueError('endog_names has wrong length') n_equ = 1 #VAR does not have conf_int #params = res.params.T # this is a convention for multi-eq models # check that we have the right length of names if not isinstance(endog_names, list): # TODO: this might be specific to multinomial logit type, move? if endog_names is None: endog_basename = 'endog' else: endog_basename = endog_names # TODO: note, the [1:] is specific to current MNLogit endog_names = res.model.endog_names[1:] tables = [] for eq in range(n_equ): restup = (res, res.params[:,eq], res.bse[:,eq], res.tvalues[:,eq], res.pvalues[:,eq], res.conf_int(alpha)[eq]) skiph = False tble = summary_params(restup, yname=endog_names[eq], xname=exog_names, alpha=alpha, use_t=use_t, skip_header=skiph) tables.append(tble) # add titles, they will be moved to header lines in table_extend for i in range(len(endog_names)): tables[i].title = endog_names[i] table_all = table_extend(tables, keep_headers=keep_headers) return tables, table_all def table_extend(tables, keep_headers=True): '''extend a list of SimpleTables, adding titles to header of subtables This function returns the merged table as a deepcopy, in contrast to the SimpleTable extend method. Parameters ---------- tables : list of SimpleTable instances keep_headers : bool If true, then all headers are kept. If falls, then the headers of subtables are blanked out. Returns ------- table_all : SimpleTable merged tables as a single SimpleTable instance ''' from copy import deepcopy for ii, t in enumerate(tables[:]): #[1:]: t = deepcopy(t) #move title to first cell of header # TODO: check if we have multiline headers if t[0].datatype == 'header': t[0][0].data = t.title t[0][0]._datatype = None t[0][0].row = t[0][1].row if not keep_headers and (ii > 0): for c in t[0][1:]: c.data = '' # add separating line and extend tables if ii == 0: table_all = t else: r1 = table_all[-1] r1.add_format('txt', row_dec_below='-') table_all.extend(t) table_all.title = None return table_all def summary_return(tables, return_fmt='text'): # join table parts then print if return_fmt == 'text': strdrop = lambda x: str(x).rsplit('\n',1)[0] # convert to string drop last line return '\n'.join(lmap(strdrop, tables[:-1]) + [str(tables[-1])]) elif return_fmt == 'tables': return tables elif return_fmt == 'csv': return '\n'.join(x.as_csv() for x in tables) elif return_fmt == 'latex': # TODO: insert \hline after updating SimpleTable table = copy.deepcopy(tables[0]) del table[-1] for part in tables[1:]: table.extend(part) return table.as_latex_tabular() elif return_fmt == 'html': return "\n".join(table.as_html() for table in tables) else: raise ValueError('available output formats are text, csv, latex, html') class Summary(object): """ Result summary Construction does not take any parameters. Tables and text can be added with the `add_` methods. Attributes ---------- tables : list of tables Contains the list of SimpleTable instances, horizontally concatenated tables are not saved separately. extra_txt : str extra lines that are added to the text output, used for warnings and explanations. """ def __init__(self): self.tables = [] self.extra_txt = None def __str__(self): return self.as_text() def __repr__(self): return str(type(self)) + '\n"""\n' + self.__str__() + '\n"""' def _repr_html_(self): '''Display as HTML in IPython notebook.''' return self.as_html() def add_table_2cols(self, res, title=None, gleft=None, gright=None, yname=None, xname=None): """ Add a double table, 2 tables with one column merged horizontally Parameters ---------- res : results instance some required information is directly taken from the result instance title : str, optional if None, then a default title is used. gleft : list[tuple], optional elements for the left table, tuples are (name, value) pairs If gleft is None, then a default table is created gright : list[tuple], optional elements for the right table, tuples are (name, value) pairs yname : str, optional optional name for the endogenous variable, default is "y" xname : list[str], optional optional names for the exogenous variables, default is "var_xx". Must match the number of parameters in the model. """ table = summary_top(res, title=title, gleft=gleft, gright=gright, yname=yname, xname=xname) self.tables.append(table) def add_table_params(self, res, yname=None, xname=None, alpha=.05, use_t=True): '''create and add a table for the parameter estimates Parameters ---------- res : results instance some required information is directly taken from the result instance yname : {str, None} optional name for the endogenous variable, default is "y" xname : {list[str], None} optional names for the exogenous variables, default is "var_xx" alpha : float significance level for the confidence intervals use_t : bool indicator whether the p-values are based on the Student-t distribution (if True) or on the normal distribution (if False) Returns ------- None : table is attached ''' if res.params.ndim == 1: table = summary_params(res, yname=yname, xname=xname, alpha=alpha, use_t=use_t) elif res.params.ndim == 2: _, table = summary_params_2dflat(res, endog_names=yname, exog_names=xname, alpha=alpha, use_t=use_t) else: raise ValueError('params has to be 1d or 2d') self.tables.append(table) def add_extra_txt(self, etext): '''add additional text that will be added at the end in text format Parameters ---------- etext : list[str] string with lines that are added to the text output. ''' self.extra_txt = '\n'.join(etext) def as_text(self): '''return tables as string Returns ------- txt : str summary tables and extra text as one string ''' txt = summary_return(self.tables, return_fmt='text') if self.extra_txt is not None: txt = txt + '\n\n' + self.extra_txt return txt def as_latex(self): '''return tables as string Returns ------- latex : str summary tables and extra text as string of Latex Notes ----- This currently merges tables with different number of columns. It is recommended to use `as_latex_tabular` directly on the individual tables. ''' latex = summary_return(self.tables, return_fmt='latex') if self.extra_txt is not None: latex = latex + '\n\n' + self.extra_txt.replace('\n', ' \\newline\n ') return latex def as_csv(self): '''return tables as string Returns ------- csv : str concatenated summary tables in comma delimited format ''' csv = summary_return(self.tables, return_fmt='csv') if self.extra_txt is not None: csv = csv + '\n\n' + self.extra_txt return csv def as_html(self): '''return tables as string Returns ------- html : str concatenated summary tables in HTML format ''' html = summary_return(self.tables, return_fmt='html') if self.extra_txt is not None: html = html + '

' + self.extra_txt.replace('\n', '
') return html statsmodels-0.12.2/statsmodels/iolib/summary2.py000066400000000000000000000516331400612667500217460ustar00rootroot00000000000000from statsmodels.compat.python import lzip import datetime from functools import reduce import re import textwrap import numpy as np import pandas as pd from .table import SimpleTable from .tableformatting import fmt_latex, fmt_txt class Summary(object): def __init__(self): self.tables = [] self.settings = [] self.extra_txt = [] self.title = None self._merge_latex = False def __str__(self): return self.as_text() def __repr__(self): return str(type(self)) + '\n"""\n' + self.__str__() + '\n"""' def _repr_html_(self): """Display as HTML in IPython notebook.""" return self.as_html() def add_df(self, df, index=True, header=True, float_format='%.4f', align='r'): """ Add the contents of a DataFrame to summary table Parameters ---------- df : DataFrame header : bool Reproduce the DataFrame column labels in summary table index : bool Reproduce the DataFrame row labels in summary table float_format : str Formatting to float data columns align : str Data alignment (l/c/r) """ settings = {'index': index, 'header': header, 'float_format': float_format, 'align': align} self.tables.append(df) self.settings.append(settings) def add_array(self, array, align='r', float_format="%.4f"): """Add the contents of a Numpy array to summary table Parameters ---------- array : numpy array (2D) float_format : str Formatting to array if type is float align : str Data alignment (l/c/r) """ table = pd.DataFrame(array) self.add_df(table, index=False, header=False, float_format=float_format, align=align) def add_dict(self, d, ncols=2, align='l', float_format="%.4f"): """Add the contents of a Dict to summary table Parameters ---------- d : dict Keys and values are automatically coerced to strings with str(). Users are encouraged to format them before using add_dict. ncols : int Number of columns of the output table align : str Data alignment (l/c/r) float_format : str Formatting to float data columns """ keys = [_formatter(x, float_format) for x in d.keys()] vals = [_formatter(x, float_format) for x in d.values()] data = np.array(lzip(keys, vals)) if data.shape[0] % ncols != 0: pad = ncols - (data.shape[0] % ncols) data = np.vstack([data, np.array(pad * [['', '']])]) data = np.split(data, ncols) data = reduce(lambda x, y: np.hstack([x, y]), data) self.add_array(data, align=align) def add_text(self, string): """Append a note to the bottom of the summary table. In ASCII tables, the note will be wrapped to table width. Notes are not indendented. """ self.extra_txt.append(string) def add_title(self, title=None, results=None): """Insert a title on top of the summary table. If a string is provided in the title argument, that string is printed. If no title string is provided but a results instance is provided, statsmodels attempts to construct a useful title automatically. """ if isinstance(title, str): self.title = title else: if results is not None: model = results.model.__class__.__name__ if model in _model_types: model = _model_types[model] self.title = 'Results: ' + model else: self.title = '' def add_base(self, results, alpha=0.05, float_format="%.4f", title=None, xname=None, yname=None): """Try to construct a basic summary instance. Parameters ---------- results : Model results instance alpha : float significance level for the confidence intervals (optional) float_format: str Float formatting for summary of parameters (optional) title : str Title of the summary table (optional) xname : list[str] of length equal to the number of parameters Names of the independent variables (optional) yname : str Name of the dependent variable (optional) """ param = summary_params(results, alpha=alpha, use_t=results.use_t) info = summary_model(results) if xname is not None: param.index = xname if yname is not None: info['Dependent Variable:'] = yname self.add_dict(info, align='l') self.add_df(param, float_format=float_format) self.add_title(title=title, results=results) def as_text(self): """Generate ASCII Summary Table """ tables = self.tables settings = self.settings title = self.title extra_txt = self.extra_txt pad_col, pad_index, widest = _measure_tables(tables, settings) rule_equal = widest * '=' simple_tables = _simple_tables(tables, settings, pad_col, pad_index) tab = [x.as_text() for x in simple_tables] tab = '\n'.join(tab) tab = tab.split('\n') tab[0] = rule_equal tab.append(rule_equal) tab = '\n'.join(tab) if title is not None: title = title if len(title) < widest: title = ' ' * int(widest / 2 - len(title) / 2) + title else: title = '' txt = [textwrap.wrap(x, widest) for x in extra_txt] txt = ['\n'.join(x) for x in txt] txt = '\n'.join(txt) out = '\n'.join([title, tab, txt]) return out def as_html(self): """Generate HTML Summary Table """ tables = self.tables settings = self.settings simple_tables = _simple_tables(tables, settings) tab = [x.as_html() for x in simple_tables] tab = '\n'.join(tab) return tab def as_latex(self, label=''): """Generate LaTeX Summary Table Parameters ---------- label : str Label of the summary table that can be referenced in a latex document (optional) """ tables = self.tables settings = self.settings title = self.title if title is not None: title = '\\caption{' + title + '}' else: title = '\\caption{}' label = '\\label{' + label + '}' simple_tables = _simple_tables(tables, settings) tab = [x.as_latex_tabular() for x in simple_tables] tab = '\n\n'.join(tab) to_replace = ('\\\\hline\\n\\\\hline\\n\\\\' 'end{tabular}\\n\\\\begin{tabular}{.*}\\n') if self._merge_latex: # create single tabular object for summary_col tab = re.sub(to_replace, r'\\midrule\n', tab) out = '\\begin{table}', title, label, tab, '\\end{table}' out = '\n'.join(out) return out def _measure_tables(tables, settings): """Compare width of ascii tables in a list and calculate padding values. We add space to each col_sep to get us as close as possible to the width of the largest table. Then, we add a few spaces to the first column to pad the rest. """ simple_tables = _simple_tables(tables, settings) tab = [x.as_text() for x in simple_tables] length = [len(x.splitlines()[0]) for x in tab] len_max = max(length) pad_sep = [] pad_index = [] for i in range(len(tab)): nsep = max(tables[i].shape[1] - 1, 1) pad = int((len_max - length[i]) / nsep) pad_sep.append(pad) len_new = length[i] + nsep * pad pad_index.append(len_max - len_new) return pad_sep, pad_index, max(length) # Useful stuff # TODO: be more specific _model_types = {'OLS': 'Ordinary least squares', 'GLS': 'Generalized least squares', 'GLSAR': 'Generalized least squares with AR(p)', 'WLS': 'Weighted least squares', 'RLM': 'Robust linear model', 'NBin': 'Negative binomial model', 'GLM': 'Generalized linear model' } def summary_model(results): """ Create a dict with information about the model """ def time_now(*args, **kwds): now = datetime.datetime.now() return now.strftime('%Y-%m-%d %H:%M') info = {} info['Model:'] = lambda x: x.model.__class__.__name__ info['Model Family:'] = lambda x: x.family.__class.__name__ info['Link Function:'] = lambda x: x.family.link.__class__.__name__ info['Dependent Variable:'] = lambda x: x.model.endog_names info['Date:'] = time_now info['No. Observations:'] = lambda x: "%#6d" % x.nobs info['Df Model:'] = lambda x: "%#6d" % x.df_model info['Df Residuals:'] = lambda x: "%#6d" % x.df_resid info['Converged:'] = lambda x: x.mle_retvals['converged'] info['No. Iterations:'] = lambda x: x.mle_retvals['iterations'] info['Method:'] = lambda x: x.method info['Norm:'] = lambda x: x.fit_options['norm'] info['Scale Est.:'] = lambda x: x.fit_options['scale_est'] info['Cov. Type:'] = lambda x: x.fit_options['cov'] rsquared_type = '' if results.k_constant else ' (uncentered)' info['R-squared' + rsquared_type + ':'] = lambda x: "%#8.3f" % x.rsquared info['Adj. R-squared' + rsquared_type + ':'] = lambda x: "%#8.3f" % x.rsquared_adj # noqa:E501 info['Pseudo R-squared:'] = lambda x: "%#8.3f" % x.prsquared info['AIC:'] = lambda x: "%8.4f" % x.aic info['BIC:'] = lambda x: "%8.4f" % x.bic info['Log-Likelihood:'] = lambda x: "%#8.5g" % x.llf info['LL-Null:'] = lambda x: "%#8.5g" % x.llnull info['LLR p-value:'] = lambda x: "%#8.5g" % x.llr_pvalue info['Deviance:'] = lambda x: "%#8.5g" % x.deviance info['Pearson chi2:'] = lambda x: "%#6.3g" % x.pearson_chi2 info['F-statistic:'] = lambda x: "%#8.4g" % x.fvalue info['Prob (F-statistic):'] = lambda x: "%#6.3g" % x.f_pvalue info['Scale:'] = lambda x: "%#8.5g" % x.scale out = {} for key, func in info.items(): try: out[key] = func(results) except (AttributeError, KeyError, NotImplementedError): # NOTE: some models do not have loglike defined (RLM), # so raise NotImplementedError pass return out def summary_params(results, yname=None, xname=None, alpha=.05, use_t=True, skip_header=False, float_format="%.4f"): """create a summary table of parameters from results instance Parameters ---------- res : results instance some required information is directly taken from the result instance yname : {str, None} optional name for the endogenous variable, default is "y" xname : {list[str], None} optional names for the exogenous variables, default is "var_xx" alpha : float significance level for the confidence intervals use_t : bool indicator whether the p-values are based on the Student-t distribution (if True) or on the normal distribution (if False) skip_header : bool If false (default), then the header row is added. If true, then no header row is added. float_format : str float formatting options (e.g. ".3g") Returns ------- params_table : SimpleTable instance """ if isinstance(results, tuple): results, params, bse, tvalues, pvalues, conf_int = results else: params = results.params bse = results.bse tvalues = results.tvalues pvalues = results.pvalues conf_int = results.conf_int(alpha) data = np.array([params, bse, tvalues, pvalues]).T data = np.hstack([data, conf_int]) data = pd.DataFrame(data) if use_t: data.columns = ['Coef.', 'Std.Err.', 't', 'P>|t|', '[' + str(alpha / 2), str(1 - alpha / 2) + ']'] else: data.columns = ['Coef.', 'Std.Err.', 'z', 'P>|z|', '[' + str(alpha / 2), str(1 - alpha / 2) + ']'] if not xname: try: data.index = results.model.data.param_names except AttributeError: data.index = results.model.exog_names else: data.index = xname return data # Vertical summary instance for multiple models def _col_params(result, float_format='%.4f', stars=True): """Stack coefficients and standard errors in single column """ # Extract parameters res = summary_params(result) # Format float for col in res.columns[:2]: res[col] = res[col].apply(lambda x: float_format % x) # Std.Errors in parentheses res.iloc[:, 1] = '(' + res.iloc[:, 1] + ')' # Significance stars if stars: idx = res.iloc[:, 3] < .1 res.loc[idx, res.columns[0]] = res.loc[idx, res.columns[0]] + '*' idx = res.iloc[:, 3] < .05 res.loc[idx, res.columns[0]] = res.loc[idx, res.columns[0]] + '*' idx = res.iloc[:, 3] < .01 res.loc[idx, res.columns[0]] = res.loc[idx, res.columns[0]] + '*' # Stack Coefs and Std.Errors res = res.iloc[:, :2] res = res.stack() rsquared = getattr(result, 'rsquared', np.nan) rsquared_adj = getattr(result, 'rsquared_adj', np.nan) r2 = pd.Series({('R-squared', ""): rsquared, ('R-squared Adj.', ""): rsquared_adj}) if r2.notnull().any(): r2 = r2.apply(lambda x: float_format % x) res = pd.concat([res, r2], axis=0) res = pd.DataFrame(res) res.columns = [str(result.model.endog_names)] return res def _col_info(result, info_dict=None): """Stack model info in a column """ if info_dict is None: info_dict = {} out = [] index = [] for i in info_dict: if isinstance(info_dict[i], dict): # this is a specific model info_dict, but not for this result... continue try: out.append(info_dict[i](result)) except AttributeError: out.append('') index.append(i) out = pd.DataFrame({str(result.model.endog_names): out}, index=index) return out def _make_unique(list_of_names): if len(set(list_of_names)) == len(list_of_names): return list_of_names # pandas does not like it if multiple columns have the same names from collections import defaultdict name_counter = defaultdict(str) header = [] for _name in list_of_names: name_counter[_name] += "I" header.append(_name + " " + name_counter[_name]) return header def summary_col(results, float_format='%.4f', model_names=(), stars=False, info_dict=None, regressor_order=(), drop_omitted=False): """ Summarize multiple results instances side-by-side (coefs and SEs) Parameters ---------- results : statsmodels results instance or list of result instances float_format : str, optional float format for coefficients and standard errors Default : '%.4f' model_names : list[str], optional Must have same length as the number of results. If the names are not unique, a roman number will be appended to all model names stars : bool print significance stars info_dict : dict, default None dict of functions to be applied to results instances to retrieve model info. To use specific information for different models, add a (nested) info_dict with model name as the key. Example: `info_dict = {"N":lambda x:(x.nobs), "R2": ..., "OLS":{ "R2":...}}` would only show `R2` for OLS regression models, but additionally `N` for all other results. Default : None (use the info_dict specified in result.default_model_infos, if this property exists) regressor_order : list[str], optional list of names of the regressors in the desired order. All regressors not specified will be appended to the end of the list. drop_omitted : bool, optional Includes regressors that are not specified in regressor_order. If False, regressors not specified will be appended to end of the list. If True, only regressors in regressor_order will be included. """ if not isinstance(results, list): results = [results] cols = [_col_params(x, stars=stars, float_format=float_format) for x in results] # Unique column names (pandas has problems merging otherwise) if model_names: colnames = _make_unique(model_names) else: colnames = _make_unique([x.columns[0] for x in cols]) for i in range(len(cols)): cols[i].columns = [colnames[i]] def merg(x, y): return x.merge(y, how='outer', right_index=True, left_index=True) summ = reduce(merg, cols) if regressor_order: varnames = summ.index.get_level_values(0).tolist() vc = pd.Series(varnames).value_counts() varnames = vc.loc[vc == 2].index.tolist() ordered = [x for x in regressor_order if x in varnames] unordered = [x for x in varnames if x not in regressor_order] new_order = ordered + unordered other = [x for x in summ.index.get_level_values(0) if x not in new_order] new_order += other if drop_omitted: for uo in unordered: new_order.remove(uo) summ = summ.loc[new_order] idx = [] index = summ.index.get_level_values(0) for i in range(0, index.shape[0], 2): idx.append(index[i]) if (i + 1) < index.shape[0] and (index[i] == index[i + 1]): idx.append("") else: idx.append(index[i + 1]) summ.index = idx # add infos about the models. if info_dict: cols = [_col_info(x, info_dict.get(x.model.__class__.__name__, info_dict)) for x in results] else: cols = [_col_info(x, getattr(x, "default_model_infos", None)) for x in results] # use unique column names, otherwise the merge will not succeed for df, name in zip(cols, _make_unique([df.columns[0] for df in cols])): df.columns = [name] def merg(x, y): return x.merge(y, how='outer', right_index=True, left_index=True) info = reduce(merg, cols) dat = pd.DataFrame(np.vstack([summ, info])) # pd.concat better, but error dat.columns = summ.columns dat.index = pd.Index(summ.index.tolist() + info.index.tolist()) summ = dat summ = summ.fillna('') smry = Summary() smry._merge_latex = True smry.add_df(summ, header=True, align='l') smry.add_text('Standard errors in parentheses.') if stars: smry.add_text('* p<.1, ** p<.05, ***p<.01') return smry def _formatter(element, float_format='%.4f'): try: out = float_format % element except (ValueError, TypeError): out = str(element) return out.strip() def _df_to_simpletable(df, align='r', float_format="%.4f", header=True, index=True, table_dec_above='-', table_dec_below=None, header_dec_below='-', pad_col=0, pad_index=0): dat = df.copy() dat = dat.applymap(lambda x: _formatter(x, float_format)) if header: headers = [str(x) for x in dat.columns.tolist()] else: headers = None if index: stubs = [str(x) + int(pad_index) * ' ' for x in dat.index.tolist()] else: dat.iloc[:, 0] = [str(x) + int(pad_index) * ' ' for x in dat.iloc[:, 0]] stubs = None st = SimpleTable(np.array(dat), headers=headers, stubs=stubs, ltx_fmt=fmt_latex, txt_fmt=fmt_txt) st.output_formats['latex']['data_aligns'] = align st.output_formats['latex']['header_align'] = align st.output_formats['txt']['data_aligns'] = align st.output_formats['txt']['table_dec_above'] = table_dec_above st.output_formats['txt']['table_dec_below'] = table_dec_below st.output_formats['txt']['header_dec_below'] = header_dec_below st.output_formats['txt']['colsep'] = ' ' * int(pad_col + 1) return st def _simple_tables(tables, settings, pad_col=None, pad_index=None): simple_tables = [] float_format = settings[0]['float_format'] if settings else '%.4f' if pad_col is None: pad_col = [0] * len(tables) if pad_index is None: pad_index = [0] * len(tables) for i, v in enumerate(tables): index = settings[i]['index'] header = settings[i]['header'] align = settings[i]['align'] simple_tables.append(_df_to_simpletable(v, align=align, float_format=float_format, header=header, index=index, pad_col=pad_col[i], pad_index=pad_index[i])) return simple_tables statsmodels-0.12.2/statsmodels/iolib/table.py000066400000000000000000001007011400612667500212450ustar00rootroot00000000000000""" Provides a simple table class. A SimpleTable is essentially a list of lists plus some formatting functionality. Dependencies: the Python 2.5+ standard library. Installation: just copy this module into your working directory (or anywhere in your pythonpath). Basic use:: mydata = [[11,12],[21,22]] # data MUST be 2-dimensional myheaders = [ "Column 1", "Column 2" ] mystubs = [ "Row 1", "Row 2" ] tbl = SimpleTable(mydata, myheaders, mystubs, title="Title") print( tbl ) print( tbl.as_csv() ) A SimpleTable is inherently (but not rigidly) rectangular. You should create it from a *rectangular* (2d!) iterable of data. Each item in your rectangular iterable will become the data of a single Cell. In principle, items can be any object, not just numbers and strings. However, default conversion during table production is by simple string interpolation. (So you cannot have a tuple as a data item *and* rely on the default conversion.) A SimpleTable allows only one column (the first) of stubs at initilization, concatenation of tables allows you to produce tables with interior stubs. (You can also assign the datatype 'stub' to the cells in any column, or use ``insert_stubs``.) A SimpleTable can be concatenated with another SimpleTable or extended by another SimpleTable. :: table1.extend_right(table2) table1.extend(table2) A SimpleTable can be initialized with `datatypes`: a list of ints that provide indexes into `data_fmts` and `data_aligns`. Each data cell is assigned a datatype, which will control formatting. If you do not specify the `datatypes` list, it will be set to ``range(ncols)`` where `ncols` is the number of columns in the data. (I.e., cells in a column have their own datatype.) This means that you can just specify `data_fmts` without bothering to provide a `datatypes` list. If ``len(datatypes)'] if self.title: title = '%s' % self.title formatted_rows.append(title) formatted_rows.extend(row.as_string('html', **fmt) for row in self) formatted_rows.append('') return '\n'.join(formatted_rows) def as_latex_tabular(self, center=True, **fmt_dict): '''Return string, the table as a LaTeX tabular environment. Note: will require the booktabs package.''' # fetch the text format, override with fmt_dict fmt = self._get_fmt('latex', **fmt_dict) formatted_rows = [] if center: formatted_rows.append(r'\begin{center}') table_dec_above = fmt['table_dec_above'] or '' table_dec_below = fmt['table_dec_below'] or '' prev_aligns = None last = None for row in self + [last]: if row == last: aligns = None else: aligns = row.get_aligns('latex', **fmt) if aligns != prev_aligns: # When the number/type of columns changes... if prev_aligns: # ... if there is a tabular to close, close it... formatted_rows.append(table_dec_below) formatted_rows.append(r'\end{tabular}') if aligns: # ... and if there are more lines, open a new one: formatted_rows.append(r'\begin{tabular}{%s}' % aligns) if not prev_aligns: # (with a nice line if it's the top of the whole table) formatted_rows.append(table_dec_above) if row != last: formatted_rows.append( row.as_string(output_format='latex', **fmt)) prev_aligns = aligns # tabular does not support caption, but make it available for # figure environment if self.title: title = r'%%\caption{%s}' % self.title formatted_rows.append(title) if center: formatted_rows.append(r'\end{center}') # Replace $$ due to bug in GH 5444 return '\n'.join(formatted_rows).replace('$$', ' ') def extend_right(self, table): """Return None. Extend each row of `self` with corresponding row of `table`. Does **not** import formatting from ``table``. This generally makes sense only if the two tables have the same number of rows, but that is not enforced. :note: To extend append a table below, just use `extend`, which is the ordinary list method. This generally makes sense only if the two tables have the same number of columns, but that is not enforced. """ for row1, row2 in zip(self, table): row1.extend(row2) def label_cells(self, func): """Return None. Labels cells based on `func`. If ``func(cell) is None`` then its datatype is not changed; otherwise it is set to ``func(cell)``. """ for row in self: for cell in row: label = func(cell) if label is not None: cell.datatype = label @property def data(self): return [row.data for row in self] def pad(s, width, align): """Return string padded with spaces, based on alignment parameter.""" if align == 'l': s = s.ljust(width) elif align == 'r': s = s.rjust(width) else: s = s.center(width) return s class Row(list): """Provides a table row as a list of cells. A row can belong to a SimpleTable, but does not have to. """ def __init__(self, seq, datatype='data', table=None, celltype=None, dec_below='row_dec_below', **fmt_dict): """ Parameters ---------- seq : sequence of data or cells table : SimpleTable datatype : str ('data' or 'header') dec_below : str (e.g., 'header_dec_below' or 'row_dec_below') decoration tag, identifies the decoration to go below the row. (Decoration is repeated as needed for text formats.) """ self.datatype = datatype self.table = table if celltype is None: if table is None: celltype = Cell else: celltype = table._Cell self._Cell = celltype self._fmt = fmt_dict self.special_fmts = dict() # special formatting for any output format self.dec_below = dec_below list.__init__(self, (celltype(cell, row=self) for cell in seq)) def add_format(self, output_format, **fmt_dict): """ Return None. Adds row-instance specific formatting for the specified output format. Example: myrow.add_format('txt', row_dec_below='+-') """ output_format = get_output_format(output_format) if output_format not in self.special_fmts: self.special_fmts[output_format] = dict() self.special_fmts[output_format].update(fmt_dict) def insert_stub(self, loc, stub): """Return None. Inserts a stub cell in the row at `loc`. """ _Cell = self._Cell if not isinstance(stub, _Cell): stub = stub stub = _Cell(stub, datatype='stub', row=self) self.insert(loc, stub) def _get_fmt(self, output_format, **fmt_dict): """Return dict, the formatting options. """ output_format = get_output_format(output_format) # first get the default formatting try: fmt = default_fmts[output_format].copy() except KeyError: raise ValueError('Unknown format: %s' % output_format) # second get table specific formatting (if possible) try: fmt.update(self.table.output_formats[output_format]) except AttributeError: pass # finally, add formatting for this row and this call fmt.update(self._fmt) fmt.update(fmt_dict) special_fmt = self.special_fmts.get(output_format, None) if special_fmt is not None: fmt.update(special_fmt) return fmt def get_aligns(self, output_format, **fmt_dict): """Return string, sequence of column alignments. Ensure comformable data_aligns in `fmt_dict`.""" fmt = self._get_fmt(output_format, **fmt_dict) return ''.join(cell.alignment(output_format, **fmt) for cell in self) def as_string(self, output_format='txt', **fmt_dict): """Return string: the formatted row. This is the default formatter for rows. Override this to get different formatting. A row formatter must accept as arguments a row (self) and an output format, one of ('html', 'txt', 'csv', 'latex'). """ fmt = self._get_fmt(output_format, **fmt_dict) # get column widths try: colwidths = self.table.get_colwidths(output_format, **fmt) except AttributeError: colwidths = fmt.get('colwidths') if colwidths is None: colwidths = (0,) * len(self) colsep = fmt['colsep'] row_pre = fmt.get('row_pre', '') row_post = fmt.get('row_post', '') formatted_cells = [] for cell, width in zip(self, colwidths): content = cell.format(width, output_format=output_format, **fmt) formatted_cells.append(content) formatted_row = row_pre + colsep.join(formatted_cells) + row_post formatted_row = self._decorate_below(formatted_row, output_format, **fmt) return formatted_row def _decorate_below(self, row_as_string, output_format, **fmt_dict): """This really only makes sense for the text and latex output formats. """ dec_below = fmt_dict.get(self.dec_below, None) if dec_below is None: result = row_as_string else: output_format = get_output_format(output_format) if output_format == 'txt': row0len = len(row_as_string) dec_len = len(dec_below) repeat, addon = divmod(row0len, dec_len) result = row_as_string + "\n" + (dec_below * repeat + dec_below[:addon]) elif output_format == 'latex': result = row_as_string + "\n" + dec_below else: raise ValueError("I cannot decorate a %s header." % output_format) return result @property def data(self): return [cell.data for cell in self] class Cell(object): """Provides a table cell. A cell can belong to a Row, but does not have to. """ def __init__(self, data='', datatype=None, row=None, **fmt_dict): if isinstance(data, Cell): # might have passed a Cell instance self.data = data.data self._datatype = data.datatype self._fmt = data._fmt else: self.data = data self._datatype = datatype self._fmt = dict() self._fmt.update(fmt_dict) self.row = row def __str__(self): return '%s' % self.data def _get_fmt(self, output_format, **fmt_dict): """Return dict, the formatting options. """ output_format = get_output_format(output_format) # first get the default formatting try: fmt = default_fmts[output_format].copy() except KeyError: raise ValueError('Unknown format: %s' % output_format) # then get any table specific formtting try: fmt.update(self.row.table.output_formats[output_format]) except AttributeError: pass # then get any row specific formtting try: fmt.update(self.row._fmt) except AttributeError: pass # finally add formatting for this instance and call fmt.update(self._fmt) fmt.update(fmt_dict) return fmt def alignment(self, output_format, **fmt_dict): fmt = self._get_fmt(output_format, **fmt_dict) datatype = self.datatype data_aligns = fmt.get('data_aligns', 'c') if isinstance(datatype, int): align = data_aligns[datatype % len(data_aligns)] elif datatype == 'stub': # still support deprecated `stubs_align` align = fmt.get('stubs_align') or fmt.get('stub_align', 'l') elif datatype in fmt: label_align = '%s_align' % datatype align = fmt.get(label_align, 'c') else: raise ValueError('Unknown cell datatype: %s' % datatype) return align @staticmethod def _latex_escape(data, fmt, output_format): if output_format != 'latex': return data if "replacements" in fmt: if isinstance(data, str): for repl in sorted(fmt["replacements"]): data = data.replace(repl, fmt["replacements"][repl]) return data def format(self, width, output_format='txt', **fmt_dict): """Return string. This is the default formatter for cells. Override this to get different formating. A cell formatter must accept as arguments a cell (self) and an output format, one of ('html', 'txt', 'csv', 'latex'). It will generally respond to the datatype, one of (int, 'header', 'stub'). """ fmt = self._get_fmt(output_format, **fmt_dict) data = self.data datatype = self.datatype data_fmts = fmt.get('data_fmts') if data_fmts is None: # chk allow for deprecated use of data_fmt data_fmt = fmt.get('data_fmt') if data_fmt is None: data_fmt = '%s' data_fmts = [data_fmt] if isinstance(datatype, int): datatype = datatype % len(data_fmts) # constrain to indexes data_fmt = data_fmts[datatype] if isinstance(data_fmt, str): content = data_fmt % (data,) elif callable(data_fmt): content = data_fmt(data) else: raise TypeError("Must be a string or a callable") if datatype == 0: content = self._latex_escape(content, fmt, output_format) elif datatype in fmt: data = self._latex_escape(data, fmt, output_format) dfmt = fmt.get(datatype) try: content = dfmt % (data,) except TypeError: # dfmt is not a substitution string content = dfmt else: raise ValueError('Unknown cell datatype: %s' % datatype) align = self.alignment(output_format, **fmt) return pad(content, width, align) def get_datatype(self): if self._datatype is None: dtype = self.row.datatype else: dtype = self._datatype return dtype def set_datatype(self, val): # TODO: add checking self._datatype = val datatype = property(get_datatype, set_datatype) # begin: default formats for SimpleTable """ Some formatting suggestions: - if you want rows to have no extra spacing, set colwidths=0 and colsep=''. (Naturally the columns will not align.) - if you want rows to have minimal extra spacing, set colwidths=1. The columns will align. - to get consistent formatting, you should leave all field width handling to SimpleTable: use 0 as the field width in data_fmts. E.g., :: data_fmts = ["%#0.6g","%#0.6g","%#0.4g","%#0.4g"], colwidths = 14, data_aligns = "r", """ default_txt_fmt = dict( fmt='txt', # basic table formatting table_dec_above='=', table_dec_below='-', title_align='c', # basic row formatting row_pre='', row_post='', header_dec_below='-', row_dec_below=None, colwidths=None, colsep=' ', data_aligns="r", # GH 1477 # data formats # data_fmt="%s", #deprecated; use data_fmts data_fmts=["%s"], # labeled alignments # stubs_align='l', #deprecated; use data_fmts stub_align='l', header_align='c', # labeled formats header_fmt='%s', # deprecated; just use 'header' stub_fmt='%s', # deprecated; just use 'stub' header='%s', stub='%s', empty_cell='', # deprecated; just use 'empty' empty='', missing='--', ) default_csv_fmt = dict( fmt='csv', table_dec_above=None, # '', table_dec_below=None, # '', # basic row formatting row_pre='', row_post='', header_dec_below=None, # '', row_dec_below=None, title_align='', data_aligns="l", colwidths=None, colsep=',', # data formats data_fmt='%s', # deprecated; use data_fmts data_fmts=['%s'], # labeled alignments # stubs_align='l', # deprecated; use data_fmts stub_align="l", header_align='c', # labeled formats header_fmt='"%s"', # deprecated; just use 'header' stub_fmt='"%s"', # deprecated; just use 'stub' empty_cell='', # deprecated; just use 'empty' header='%s', stub='%s', empty='', missing='--', ) default_html_fmt = dict( # basic table formatting table_dec_above=None, table_dec_below=None, header_dec_below=None, row_dec_below=None, title_align='c', # basic row formatting colwidths=None, colsep=' ', row_pre='\n ', row_post='\n', data_aligns="c", # data formats data_fmts=['%s'], data_fmt="%s", # deprecated; use data_fmts # labeled alignments # stubs_align='l', #deprecated; use data_fmts stub_align='l', header_align='c', # labeled formats header_fmt='%s', # deprecated; just use `header` stub_fmt='%s', # deprecated; just use `stub` empty_cell='', # deprecated; just use `empty` header='%s', stub='%s', empty='', missing='--', ) default_latex_fmt = dict( fmt='ltx', # basic table formatting table_dec_above=r'\toprule', table_dec_below=r'\bottomrule', header_dec_below=r'\midrule', row_dec_below=None, strip_backslash=True, # NotImplemented # row formatting row_post=r' \\', data_aligns='c', colwidths=None, colsep=' & ', # data formats data_fmts=['%s'], data_fmt='%s', # deprecated; use data_fmts # labeled alignments # stubs_align='l', # deprecated; use data_fmts stub_align='l', header_align='c', empty_align='l', # labeled formats header_fmt=r'\textbf{%s}', # deprecated; just use 'header' stub_fmt=r'\textbf{%s}', # deprecated; just use 'stub' empty_cell='', # deprecated; just use 'empty' header=r'\textbf{%s}', stub=r'\textbf{%s}', empty='', missing='--', # replacements will be processed in lexicographical order replacements={"#": r"\#", "$": r"\$", "%": r"\%", "&": r"\&", ">": r"$>$", "_": r"\_", "|": r"$|$"} ) default_fmts = dict( html=default_html_fmt, txt=default_txt_fmt, latex=default_latex_fmt, csv=default_csv_fmt ) output_format_translations = dict( htm='html', text='txt', ltx='latex' ) def get_output_format(output_format): if output_format not in ('html', 'txt', 'latex', 'csv'): try: output_format = output_format_translations[output_format] except KeyError: raise ValueError('unknown output format %s' % output_format) return output_format statsmodels-0.12.2/statsmodels/iolib/tableformatting.py000066400000000000000000000066061400612667500233510ustar00rootroot00000000000000""" Summary Table formating This is here to help keep the formating consistent across the different models """ import copy gen_fmt = { "data_fmts": ["%s", "%s", "%s", "%s", "%s"], "empty_cell": '', "colwidths": 7, "colsep": ' ', "row_pre": ' ', "row_post": ' ', "table_dec_above": '": ', "table_dec_below": None, "header_dec_below": None, "header_fmt": '%s', "stub_fmt": '%s', "title_align": 'c', "header_align": 'r', "data_aligns": "r", "stubs_align": "l", "fmt": 'txt' } # Note table_1l_fmt over rides the below formating unless it is not # appended to table_1l fmt_1_right = { "data_fmts": ["%s", "%s", "%s", "%s", "%s"], "empty_cell": '', "colwidths": 16, "colsep": ' ', "row_pre": '', "row_post": '', "table_dec_above": '": ', "table_dec_below": None, "header_dec_below": None, "header_fmt": '%s', "stub_fmt": '%s', "title_align": 'c', "header_align": 'r', "data_aligns": "r", "stubs_align": "l", "fmt": 'txt' } fmt_2 = { "data_fmts": ["%s", "%s", "%s", "%s"], "empty_cell": '', "colwidths": 10, "colsep": ' ', "row_pre": ' ', "row_post": ' ', "table_dec_above": '": ', "table_dec_below": '": ', "header_dec_below": '-', "header_fmt": '%s', "stub_fmt": '%s', "title_align": 'c', "header_align": 'r', "data_aligns": 'r', "stubs_align": 'l', "fmt": 'txt' } # new version # TODO: as of when? compared to what? is old version needed? fmt_base = { "data_fmts": ["%s", "%s", "%s", "%s", "%s"], "empty_cell": '', "colwidths": 10, "colsep": ' ', "row_pre": '', "row_post": '', "table_dec_above": '=', "table_dec_below": '=', # TODO need '=' at the last subtable "header_dec_below": '-', "header_fmt": '%s', "stub_fmt": '%s', "title_align": 'c', "header_align": 'r', "data_aligns": 'r', "stubs_align": 'l', "fmt": 'txt' } fmt_2cols = copy.deepcopy(fmt_base) fmt2 = { "data_fmts": ["%18s", "-%19s", "%18s", "%19s"], # TODO: TODO: what? "colsep": ' ', "colwidths": 18, "stub_fmt": '-%21s', } fmt_2cols.update(fmt2) fmt_params = copy.deepcopy(fmt_base) fmt3 = { "data_fmts": ["%s", "%s", "%8s", "%s", "%11s", "%11s"], } fmt_params.update(fmt3) """ Summary Table formating This is here to help keep the formating consistent across the different models """ fmt_latex = { 'colsep': ' & ', 'colwidths': None, 'data_aligns': 'r', 'data_fmt': '%s', 'data_fmts': ['%s'], 'empty': '', 'empty_cell': '', 'fmt': 'ltx', 'header': '%s', 'header_align': 'c', 'header_dec_below': '\\hline', 'header_fmt': '%s', 'missing': '--', 'row_dec_below': None, 'row_post': ' \\\\', 'strip_backslash': True, 'stub': '%s', 'stub_align': 'l', 'stub_fmt': '%s', 'table_dec_above': '\\hline', 'table_dec_below': '\\hline'} fmt_txt = { 'colsep': ' ', 'colwidths': None, 'data_aligns': 'r', 'data_fmts': ['%s'], 'empty': '', 'empty_cell': '', 'fmt': 'txt', 'header': '%s', 'header_align': 'c', 'header_dec_below': '-', 'header_fmt': '%s', 'missing': '--', 'row_dec_below': None, 'row_post': '', 'row_pre': '', 'stub': '%s', 'stub_align': 'l', 'stub_fmt': '%s', 'table_dec_above': '-', 'table_dec_below': None, 'title_align': 'c'} statsmodels-0.12.2/statsmodels/iolib/tests/000077500000000000000000000000001400612667500207475ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/iolib/tests/__init__.py000066400000000000000000000000001400612667500230460ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/iolib/tests/gen_dates.do000066400000000000000000000004421400612667500232240ustar00rootroot00000000000000insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/iolib/tests/stata_dates.csv" format datetime_c %tc format datetime_big_c %tC format date %td format weekly_date %tw format monthly_date %tm format quarterly_date %tq format half_yearly_date %th format yearly_date %ty statsmodels-0.12.2/statsmodels/iolib/tests/results/000077500000000000000000000000001400612667500224505ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/iolib/tests/results/__init__.py000066400000000000000000000000001400612667500245470ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/iolib/tests/results/data_missing.dta000066400000000000000000000021521400612667500256040ustar00rootroot00000000000000r€Ú ß€Ú ßÑ É@çH @ æÈ@4 U@iy@ 9 Oct 2012 11:02þÿûüýfloat_missdouble_missbyte_misssint_misslong_miss%9.0g%10.0g%8.0g%8.0g%12.0g~Cß ÍC ÍC ÍCàeååÿÿC~Cß ÍC ÍC ÍCàeååÿÿC~Cß ÍC ÍC ÍCàeååÿÿC~Cß ÍC ÍC ÍCàeååÿÿC~Cß ÍC ÍC ÍCàeååÿÿCàeååÿÿstatsmodels-0.12.2/statsmodels/iolib/tests/results/macrodata.py000066400000000000000000000560211400612667500247610ustar00rootroot00000000000000from numpy import array macrodata_result = array([ (1959.0, 1.0, 2710.349, 1707.4, 286.898, 470.045, 1886.9, 28.98, 139.7, 2.82, 5.8, 177.146, 0.0, 0.0), (1959.0, 2.0, 2778.801, 1733.7, 310.859, 481.301, 1919.7, 29.15, 141.7, 3.08, 5.1, 177.83, 2.34, 0.74), (1959.0, 3.0, 2775.488, 1751.8, 289.226, 491.26, 1916.4, 29.35, 140.5, 3.82, 5.3, 178.657, 2.74, 1.09), (1959.0, 4.0, 2785.204, 1753.7, 299.356, 484.052, 1931.3, 29.37, 140.0, 4.33, 5.6, 179.386, 0.27, 4.06), (1960.0, 1.0, 2847.699, 1770.5, 331.722, 462.199, 1955.5, 29.54, 139.6, 3.5, 5.2, 180.007, 2.31, 1.19), (1960.0, 2.0, 2834.39, 1792.9, 298.152, 460.4, 1966.1, 29.55, 140.2, 2.68, 5.2, 180.671, 0.14, 2.55), (1960.0, 3.0, 2839.022, 1785.8, 296.375, 474.676, 1967.8, 29.75, 140.9, 2.36, 5.6, 181.528, 2.7, -0.34), (1960.0, 4.0, 2802.616, 1788.2, 259.764, 476.434, 1966.6, 29.84, 141.1, 2.29, 6.3, 182.287, 1.21, 1.08), (1961.0, 1.0, 2819.264, 1787.7, 266.405, 475.854, 1984.5, 29.81, 142.1, 2.37, 6.8, 182.992, -0.4, 2.77), (1961.0, 2.0, 2872.005, 1814.3, 286.246, 480.328, 2014.4, 29.92, 142.9, 2.29, 7.0, 183.691, 1.47, 0.81), (1961.0, 3.0, 2918.419, 1823.1, 310.227, 493.828, 2041.9, 29.98, 144.1, 2.32, 6.8, 184.524, 0.8, 1.52), (1961.0, 4.0, 2977.83, 1859.6, 315.463, 502.521, 2082.0, 30.04, 145.2, 2.6, 6.2, 185.242, 0.8, 1.8), (1962.0, 1.0, 3031.241, 1879.4, 334.271, 520.96, 2101.7, 30.21, 146.4, 2.73, 5.6, 185.874, 2.26, 0.47), (1962.0, 2.0, 3064.709, 1902.5, 331.039, 523.066, 2125.2, 30.22, 146.5, 2.78, 5.5, 186.538, 0.13, 2.65), (1962.0, 3.0, 3093.047, 1917.9, 336.962, 538.838, 2137.0, 30.38, 146.7, 2.78, 5.6, 187.323, 2.11, 0.67), (1962.0, 4.0, 3100.563, 1945.1, 325.65, 535.912, 2154.6, 30.44, 148.3, 2.87, 5.5, 188.013, 0.79, 2.08), (1963.0, 1.0, 3141.087, 1958.2, 343.721, 522.917, 2172.5, 30.48, 149.7, 2.9, 5.8, 188.58, 0.53, 2.38), (1963.0, 2.0, 3180.447, 1976.9, 348.73, 518.108, 2193.1, 30.69, 151.3, 3.03, 5.7, 189.242, 2.75, 0.29), (1963.0, 3.0, 3240.332, 2003.8, 360.102, 546.893, 2217.9, 30.75, 152.6, 3.38, 5.5, 190.028, 0.78, 2.6), (1963.0, 4.0, 3264.967, 2020.6, 364.534, 532.383, 2254.6, 30.94, 153.7, 3.52, 5.6, 190.668, 2.46, 1.06), (1964.0, 1.0, 3338.246, 2060.5, 379.523, 529.686, 2299.6, 30.95, 154.8, 3.51, 5.5, 191.245, 0.13, 3.38), (1964.0, 2.0, 3376.587, 2096.7, 377.778, 526.175, 2362.1, 31.02, 156.8, 3.47, 5.2, 191.889, 0.9, 2.57), (1964.0, 3.0, 3422.469, 2135.2, 386.754, 522.008, 2392.7, 31.12, 159.2, 3.53, 5.0, 192.631, 1.29, 2.25), (1964.0, 4.0, 3431.957, 2141.2, 389.91, 514.603, 2420.4, 31.28, 160.7, 3.76, 5.0, 193.223, 2.05, 1.71), (1965.0, 1.0, 3516.251, 2188.8, 429.145, 508.006, 2447.4, 31.38, 162.0, 3.93, 4.9, 193.709, 1.28, 2.65), (1965.0, 2.0, 3563.96, 2213.0, 429.119, 508.931, 2474.5, 31.58, 163.1, 3.84, 4.7, 194.303, 2.54, 1.3), (1965.0, 3.0, 3636.285, 2251.0, 444.444, 529.446, 2542.6, 31.65, 166.0, 3.93, 4.4, 194.997, 0.89, 3.04), (1965.0, 4.0, 3724.014, 2314.3, 446.493, 544.121, 2594.1, 31.88, 169.1, 4.35, 4.1, 195.539, 2.9, 1.46), (1966.0, 1.0, 3815.423, 2348.5, 484.244, 556.593, 2618.4, 32.28, 171.8, 4.62, 3.9, 195.999, 4.99, -0.37), (1966.0, 2.0, 3828.124, 2354.5, 475.408, 571.371, 2624.7, 32.45, 170.3, 4.65, 3.8, 196.56, 2.1, 2.55), (1966.0, 3.0, 3853.301, 2381.5, 470.697, 594.514, 2657.8, 32.85, 171.2, 5.23, 3.8, 197.207, 4.9, 0.33), (1966.0, 4.0, 3884.52, 2391.4, 472.957, 599.528, 2688.2, 32.9, 171.9, 5.0, 3.7, 197.736, 0.61, 4.39), (1967.0, 1.0, 3918.74, 2405.3, 460.007, 640.682, 2728.4, 33.1, 174.2, 4.22, 3.8, 198.206, 2.42, 1.8), (1967.0, 2.0, 3919.556, 2438.1, 440.393, 631.43, 2750.8, 33.4, 178.1, 3.78, 3.8, 198.712, 3.61, 0.17), (1967.0, 3.0, 3950.826, 2450.6, 453.033, 641.504, 2777.1, 33.7, 181.6, 4.42, 3.8, 199.311, 3.58, 0.84), (1967.0, 4.0, 3980.97, 2465.7, 462.834, 640.234, 2797.4, 34.1, 184.3, 4.9, 3.9, 199.808, 4.72, 0.18), (1968.0, 1.0, 4063.013, 2524.6, 472.907, 651.378, 2846.2, 34.4, 186.6, 5.18, 3.7, 200.208, 3.5, 1.67), (1968.0, 2.0, 4131.998, 2563.3, 492.026, 646.145, 2893.5, 34.9, 190.5, 5.5, 3.5, 200.706, 5.77, -0.28), (1968.0, 3.0, 4160.267, 2611.5, 476.053, 640.615, 2899.3, 35.3, 194.0, 5.21, 3.5, 201.29, 4.56, 0.65), (1968.0, 4.0, 4178.293, 2623.5, 480.998, 636.729, 2918.4, 35.7, 198.7, 5.85, 3.4, 201.76, 4.51, 1.34), (1969.0, 1.0, 4244.1, 2652.9, 512.686, 633.224, 2923.4, 36.3, 200.7, 6.08, 3.4, 202.161, 6.67, -0.58), (1969.0, 2.0, 4256.46, 2669.8, 508.601, 623.16, 2952.9, 36.8, 201.7, 6.49, 3.4, 202.677, 5.47, 1.02), (1969.0, 3.0, 4283.378, 2682.7, 520.36, 623.613, 3012.9, 37.3, 202.9, 7.02, 3.6, 203.302, 5.4, 1.63), (1969.0, 4.0, 4263.261, 2704.1, 492.334, 606.9, 3034.9, 37.9, 206.2, 7.64, 3.6, 203.849, 6.38, 1.26), (1970.0, 1.0, 4256.573, 2720.7, 476.925, 594.888, 3050.1, 38.5, 206.7, 6.76, 4.2, 204.401, 6.28, 0.47), (1970.0, 2.0, 4264.289, 2733.2, 478.419, 576.257, 3103.5, 38.9, 208.0, 6.66, 4.8, 205.052, 4.13, 2.52), (1970.0, 3.0, 4302.259, 2757.1, 486.594, 567.743, 3145.4, 39.4, 212.9, 6.15, 5.2, 205.788, 5.11, 1.04), (1970.0, 4.0, 4256.637, 2749.6, 458.406, 564.666, 3135.1, 39.9, 215.5, 4.86, 5.8, 206.466, 5.04, -0.18), (1971.0, 1.0, 4374.016, 2802.2, 517.935, 542.709, 3197.3, 40.1, 220.0, 3.65, 5.9, 207.065, 2.0, 1.65), (1971.0, 2.0, 4398.829, 2827.9, 533.986, 534.905, 3245.3, 40.6, 224.9, 4.76, 5.9, 207.661, 4.96, -0.19), (1971.0, 3.0, 4433.943, 2850.4, 541.01, 532.646, 3259.7, 40.9, 227.2, 4.7, 6.0, 208.345, 2.94, 1.75), (1971.0, 4.0, 4446.264, 2897.8, 524.085, 516.14, 3294.2, 41.2, 230.1, 3.87, 6.0, 208.917, 2.92, 0.95), (1972.0, 1.0, 4525.769, 2936.5, 561.147, 518.192, 3314.9, 41.5, 235.6, 3.55, 5.8, 209.386, 2.9, 0.64), (1972.0, 2.0, 4633.101, 2992.6, 595.495, 526.473, 3346.1, 41.8, 238.8, 3.86, 5.7, 209.896, 2.88, 0.98), (1972.0, 3.0, 4677.503, 3038.8, 603.97, 498.116, 3414.6, 42.2, 245.0, 4.47, 5.6, 210.479, 3.81, 0.66), (1972.0, 4.0, 4754.546, 3110.1, 607.104, 496.54, 3550.5, 42.7, 251.5, 5.09, 5.3, 210.985, 4.71, 0.38), (1973.0, 1.0, 4876.166, 3167.0, 645.654, 504.838, 3590.7, 43.7, 252.7, 5.98, 5.0, 211.42, 9.26, -3.28), (1973.0, 2.0, 4932.571, 3165.4, 675.837, 497.033, 3626.2, 44.2, 257.5, 7.19, 4.9, 211.909, 4.55, 2.64), (1973.0, 3.0, 4906.252, 3176.7, 649.412, 475.897, 3644.4, 45.6, 259.0, 8.06, 4.8, 212.475, 12.47, -4.41), (1973.0, 4.0, 4953.05, 3167.4, 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12303.533, 8555.8, 2082.231, 876.385, 9175.9, 190.8, 1361.0, 1.63, 5.4, 294.066, 3.58, -1.95), (2004.0, 4.0, 12410.282, 8654.2, 2125.152, 865.596, 9303.4, 191.8, 1366.6, 2.2, 5.4, 294.741, 2.09, 0.11), (2005.0, 1.0, 12534.113, 8719.0, 2170.299, 869.204, 9189.6, 193.8, 1357.8, 2.69, 5.3, 295.308, 4.15, -1.46), (2005.0, 2.0, 12587.535, 8802.9, 2131.468, 870.044, 9253.0, 194.7, 1366.6, 3.01, 5.1, 295.994, 1.85, 1.16), (2005.0, 3.0, 12683.153, 8865.6, 2154.949, 890.394, 9308.0, 199.2, 1375.0, 3.52, 5.0, 296.77, 9.14, -5.62), (2005.0, 4.0, 12748.699, 8888.5, 2232.193, 875.557, 9358.7, 199.4, 1380.6, 4.0, 4.9, 297.435, 0.4, 3.6), (2006.0, 1.0, 12915.938, 8986.6, 2264.721, 900.511, 9533.8, 200.7, 1380.5, 4.51, 4.7, 298.061, 2.6, 1.91), (2006.0, 2.0, 12962.462, 9035.0, 2261.247, 892.839, 9617.3, 202.7, 1369.2, 4.82, 4.7, 298.766, 3.97, 0.85), (2006.0, 3.0, 12965.916, 9090.7, 2229.636, 892.002, 9662.5, 201.9, 1369.4, 4.9, 4.7, 299.593, -1.58, 6.48), (2006.0, 4.0, 13060.679, 9181.6, 2165.966, 894.404, 9788.8, 203.574, 1373.6, 4.92, 4.4, 300.32, 3.3, 1.62), (2007.0, 1.0, 13099.901, 9265.1, 2132.609, 882.766, 9830.2, 205.92, 1379.7, 4.95, 4.5, 300.977, 4.58, 0.36), (2007.0, 2.0, 13203.977, 9291.5, 2162.214, 898.713, 9842.7, 207.338, 1370.0, 4.72, 4.5, 301.714, 2.75, 1.97), (2007.0, 3.0, 13321.109, 9335.6, 2166.491, 918.983, 9883.9, 209.133, 1379.2, 4.0, 4.7, 302.509, 3.45, 0.55), (2007.0, 4.0, 13391.249, 9363.6, 2123.426, 925.11, 9886.2, 212.495, 1377.4, 3.01, 4.8, 303.204, 6.38, -3.37), (2008.0, 1.0, 13366.865, 9349.6, 2082.886, 943.372, 9826.8, 213.997, 1384.0, 1.56, 4.9, 303.803, 2.82, -1.26), (2008.0, 2.0, 13415.266, 9351.0, 2026.518, 961.28, 10059.0, 218.61, 1409.3, 1.74, 5.4, 304.483, 8.53, -6.79), (2008.0, 3.0, 13324.6, 9267.7, 1990.693, 991.551, 9838.3, 216.889, 1474.7, 1.17, 6.0, 305.27, -3.16, 4.33), (2008.0, 4.0, 13141.92, 9195.3, 1857.661, 1007.273, 9920.4, 212.174, 1576.5, 0.12, 6.9, 305.952, -8.79, 8.91), (2009.0, 1.0, 12925.41, 9209.2, 1558.494, 996.287, 9926.4, 212.671, 1592.8, 0.22, 8.1, 306.547, 0.94, -0.71), (2009.0, 2.0, 12901.504, 9189.0, 1456.678, 1023.528, 10077.5, 214.469, 1653.6, 0.18, 9.2, 307.226, 3.37, -3.19), (2009.0, 3.0, 12990.341, 9256.0, 1486.398, 1044.088, 10040.6, 216.385, 1673.9, 0.12, 9.6, 308.013, 3.56, -3.44)], dtype=[('year', 'i4'), ('quarter', 'i2'), ('realgdp', 'f4'), ('realcons', 'f4'), ('realinv', 'f4'), ('realgovt', 'f4'), ('realdpi', 'f4'), ('cpi', 'f4'), ('m1', 'f4'), ('tbilrate', 'f4'), ('unemp', 'f4'), ('pop', 'f4'), ('infl', 'f4'), ('realint', 'f4')]) statsmodels-0.12.2/statsmodels/iolib/tests/results/time_series_examples.dta000066400000000000000000000033401400612667500273500ustar00rootroot00000000000000r2âå C³5@`É@çH @ æÈ@4 U@iy@ 8 Oct 2012 18:34ÿÿüüüûûüdatetime_cdatetime_big_cdateweekly_datemonthly_datequarterly_datehalf_yearly_dateyearly_date%tc0g%tC0g%tdg%twg%tmg%tqg%thg%tyg>°è>°€ gB€ gBome/skipper/s>°è>°€ gB€ gBome/skipper/s>°è>°€ gB€ gBome/skipper/s>°è>°€ gB€ gBome/skipper/s>°è>°€ gB€ gBome/skipper/s>°è>°€ gB€ gBome/skipper/s>°è>°€ gB€ gBome/skipper/s>°è>°€ gB€ gBome/skipper/s(Ùí‡uB€¡êì‡uBjG) X:dÚ˜kÁ¦“6Á÷§ýÄÿîöstatsmodels-0.12.2/statsmodels/iolib/tests/stata_dates.csv000066400000000000000000000003071400612667500237600ustar00rootroot00000000000000datetime_c,datetime_big_c,date,weekly_date,monthly_date,quarterly_date,half_yearly_date,yearly_date 1479597200000,1479596223000,18282,2601,600,58,100,2010 -14200000,-1479590,-2282,-601,-60,-18,-10,2 statsmodels-0.12.2/statsmodels/iolib/tests/test_data.csv000066400000000000000000000003121400612667500234300ustar00rootroot00000000000000"year","quarter","realgdp","realcons","realinv","realgovt","realdpi","cpi","m1","tbilrate","unemp","pop","infl","realint" 1959,1,2710.349,1707.4,286.898,470.045,1886.9,28.980,139.7,2.82,5.8,177.146,0,0 statsmodels-0.12.2/statsmodels/iolib/tests/test_foreign.py000066400000000000000000000173431400612667500240210ustar00rootroot00000000000000""" Tests for iolib/foreign.py """ from statsmodels.compat.pandas import assert_frame_equal import os import warnings from datetime import datetime from io import BytesIO from numpy.testing import assert_array_equal, assert_, assert_equal import numpy as np from pandas import DataFrame, isnull, Timestamp import pytest from statsmodels.compat.python import asbytes from statsmodels.iolib.foreign import (StataWriter, genfromdta, _datetime_to_stata_elapsed, _stata_elapsed_date_to_datetime) from statsmodels.datasets import macrodata # Test precisions DECIMAL_4 = 4 DECIMAL_3 = 3 curdir = os.path.dirname(os.path.abspath(__file__)) def test_genfromdta(): # Test genfromdta vs. results/macrodta.npy created with genfromtxt. # NOTE: Stata handles data very oddly. Round tripping from csv to dta # to ndarray 2710.349 (csv) -> 2510.2491 (stata) -> 2710.34912109375 # (dta/ndarray) from .results.macrodata import macrodata_result as res2 with pytest.warns(FutureWarning): res1 = genfromdta(curdir+'/../../datasets/macrodata/macrodata.dta') assert_array_equal(res1 == res2, True) def test_genfromdta_pandas(): dta = macrodata.load_pandas().data curdir = os.path.dirname(os.path.abspath(__file__)) with pytest.warns(FutureWarning): res1 = genfromdta(curdir+'/../../datasets/macrodata/macrodata.dta', pandas=True) res1 = res1.astype(float) assert_frame_equal(res1, dta.astype(float)) def test_stata_writer_structured(): buf = BytesIO() dta = macrodata.load(as_pandas=False).data dtype = dta.dtype dt = [('year', int), ('quarter', int)] + dtype.descr[2:] dta = dta.astype(np.dtype(dt)) with pytest.warns(FutureWarning): writer = StataWriter(buf, dta) writer.write_file() buf.seek(0) with pytest.warns(FutureWarning): dta2 = genfromdta(buf) assert_array_equal(dta, dta2) def test_stata_writer_array(): buf = BytesIO() dta = macrodata.load(as_pandas=False).data dta = DataFrame.from_records(dta) dta.columns = ["v%d" % i for i in range(1,15)] with pytest.warns(FutureWarning): writer = StataWriter(buf, dta.values) writer.write_file() buf.seek(0) with pytest.warns(FutureWarning): dta2 = genfromdta(buf) dta = dta.to_records(index=False) assert_array_equal(dta, dta2) def test_missing_roundtrip(): buf = BytesIO() dta = np.array([(np.nan, np.inf, "")], dtype=[("double_miss", float), ("float_miss", np.float32), ("string_miss", "a1")]) with pytest.warns(FutureWarning): writer = StataWriter(buf, dta) writer.write_file() buf.seek(0) with pytest.warns(FutureWarning): dta = genfromdta(buf, missing_flt=np.nan) assert_(isnull(dta[0][0])) assert_(isnull(dta[0][1])) assert_(dta[0][2] == asbytes("")) with pytest.warns(FutureWarning): dta = genfromdta(os.path.join(curdir, "results/data_missing.dta"), missing_flt=-999) assert_(np.all([dta[0][i] == -999 for i in range(5)])) def test_stata_writer_pandas(): buf = BytesIO() dta = macrodata.load_pandas().data dta4 = dta.copy() for col in ('year','quarter'): dta[col] = dta[col].astype(np.int64) dta4[col] = dta4[col].astype(np.int32) # dta is int64 'i8' given to Stata writer with pytest.warns(FutureWarning): writer = StataWriter(buf, dta) with warnings.catch_warnings(record=True) as w: writer.write_file() assert len(w) == 0 buf.seek(0) with pytest.warns(FutureWarning): dta2 = genfromdta(buf) dta5 = DataFrame.from_records(dta2) # dta2 is int32 'i4' returned from Stata reader if dta5.dtypes[1] is np.dtype('int64'): assert_frame_equal(dta.reset_index(), dta5) else: # do not check index because it has different size, int32 versus int64 assert_frame_equal(dta4, dta5[dta5.columns[1:]]) def test_stata_writer_unicode(): # make sure to test with characters outside the latin-1 encoding pass def test_genfromdta_datetime(): results = [(datetime(2006, 11, 19, 23, 13, 20), 1479596223000, datetime(2010, 1, 20), datetime(2010, 1, 8), datetime(2010, 1, 1), datetime(1974, 7, 1), datetime(2010, 1, 1), datetime(2010, 1, 1)), (datetime(1959, 12, 31, 20, 3, 20), -1479590, datetime(1953, 10, 2), datetime(1948, 6, 10), datetime(1955, 1, 1), datetime(1955, 7, 1), datetime(1955, 1, 1), datetime(2, 1, 1))] with pytest.warns(FutureWarning): dta = genfromdta(os.path.join(curdir, "results/time_series_examples.dta")) assert_array_equal(dta[0].tolist(), results[0]) assert_array_equal(dta[1].tolist(), results[1]) with warnings.catch_warnings(record=True): with pytest.warns(FutureWarning): dta = genfromdta(os.path.join(curdir, "results/time_series_examples.dta"), pandas=True) for i, row in enumerate(results): new = [] for val in row: if isinstance(val, datetime) and val.year > 2: new.append(Timestamp(val)) else: new.append(val) results[i] = new assert dta.iloc[0].tolist() == results[0] assert dta.iloc[1].tolist() == results[1] def test_date_converters(): ms = [-1479597200000, -1e6, -1e5, -100, 1e5, 1e6, 1479597200000] days = [-1e5, -1200, -800, -365, -50, 0, 50, 365, 800, 1200, 1e5] weeks = [-1e4, -1e2, -53, -52, -51, 0, 51, 52, 53, 1e2, 1e4] months = [-1e4, -1e3, -100, -13, -12, -11, 0, 11, 12, 13, 100, 1e3, 1e4] quarter = [-100, -50, -5, -4, -3, 0, 3, 4, 5, 50, 100] half = [-50, 40, 30, 10, 3, 2, 1, 0, 1, 2, 3, 10, 30, 40, 50] year = [1, 50, 500, 1000, 1500, 1975, 2075] for i in ms: assert_equal(_datetime_to_stata_elapsed( _stata_elapsed_date_to_datetime(i, "tc"), "tc"), i) for i in days: assert_equal(_datetime_to_stata_elapsed( _stata_elapsed_date_to_datetime(i, "td"), "td"), i) for i in weeks: assert_equal(_datetime_to_stata_elapsed( _stata_elapsed_date_to_datetime(i, "tw"), "tw"), i) for i in months: assert_equal(_datetime_to_stata_elapsed( _stata_elapsed_date_to_datetime(i, "tm"), "tm"), i) for i in quarter: assert_equal(_datetime_to_stata_elapsed( _stata_elapsed_date_to_datetime(i, "tq"), "tq"), i) for i in half: assert_equal(_datetime_to_stata_elapsed( _stata_elapsed_date_to_datetime(i, "th"), "th"), i) for i in year: assert_equal(_datetime_to_stata_elapsed( _stata_elapsed_date_to_datetime(i, "ty"), "ty"), i) def test_datetime_roundtrip(): dta = np.array([(1, datetime(2010, 1, 1), 2), (2, datetime(2010, 2, 1), 3), (4, datetime(2010, 3, 1), 5)], dtype=[('var1', float), ('var2', object), ('var3', float)]) buf = BytesIO() with pytest.warns(FutureWarning): writer = StataWriter(buf, dta, {"var2" : "tm"}) writer.write_file() buf.seek(0) with pytest.warns(FutureWarning): dta2 = genfromdta(buf) assert_equal(dta, dta2) dta = DataFrame.from_records(dta) buf = BytesIO() with pytest.warns(FutureWarning): writer = StataWriter(buf, dta, {"var2" : "tm"}) writer.write_file() buf.seek(0) with pytest.warns(FutureWarning): dta2 = genfromdta(buf, pandas=True) assert_frame_equal(dta, dta2.drop('index', axis=1)) statsmodels-0.12.2/statsmodels/iolib/tests/test_pickle.py000066400000000000000000000017211400612667500236300ustar00rootroot00000000000000from io import BytesIO import pathlib import tempfile from numpy.testing import assert_equal from statsmodels.compat.python import lrange from statsmodels.iolib.smpickle import save_pickle, load_pickle def test_pickle(): tmpdir = tempfile.mkdtemp(prefix="pickle") a = lrange(10) # test with str path_str = tmpdir + "/res.pkl" save_pickle(a, path_str) b = load_pickle(path_str) assert_equal(a, b) # test with pathlib path_pathlib = pathlib.Path(tmpdir) / "res2.pkl" save_pickle(a, path_pathlib) c = load_pickle(path_pathlib) assert_equal(a, c) # cleanup, tested on Windows try: import os os.remove(path_str) os.remove(path_pathlib) os.rmdir(tmpdir) except (OSError, IOError): pass assert not os.path.exists(tmpdir) # test with file handle fh = BytesIO() save_pickle(a, fh) fh.seek(0, 0) d = load_pickle(fh) fh.close() assert_equal(a, d) statsmodels-0.12.2/statsmodels/iolib/tests/test_summary.py000066400000000000000000000043441400612667500240620ustar00rootroot00000000000000'''examples to check summary, not converted to tests yet ''' import numpy as np # noqa: F401 import pytest from statsmodels.datasets import macrodata from statsmodels.regression.linear_model import OLS def test_escaped_variable_name(): # Rename 'cpi' column to 'CPI_' data = macrodata.load(True).data data.rename(columns={'cpi': 'CPI_'}, inplace=True) mod = OLS.from_formula('CPI_ ~ 1 + np.log(realgdp)', data=data) res = mod.fit() assert 'CPI\\_' in res.summary().as_latex() assert 'CPI_' in res.summary().as_text() def test_wrong_len_xname(reset_randomstate): y = np.random.randn(100) x = np.random.randn(100, 2) res = OLS(y, x).fit() with pytest.raises(ValueError): res.summary(xname=['x1']) with pytest.raises(ValueError): res.summary(xname=['x1', 'x2', 'x3']) if __name__ == '__main__': from statsmodels.regression.tests.test_regression import TestOLS #def mytest(): aregression = TestOLS() TestOLS.setup_class() results = aregression.res1 r_summary = str(results.summary_old()) print(r_summary) olsres = results print('\n\n') r_summary = str(results.summary()) print(r_summary) print('\n\n') from statsmodels.discrete.tests.test_discrete import TestProbitNewton aregression = TestProbitNewton() TestProbitNewton.setup_class() results = aregression.res1 r_summary = str(results.summary()) print(r_summary) print('\n\n') probres = results from statsmodels.robust.tests.test_rlm import TestHampel aregression = TestHampel() #TestHampel.setup_class() results = aregression.res1 r_summary = str(results.summary()) print(r_summary) rlmres = results print('\n\n') from statsmodels.genmod.tests.test_glm import TestGlmBinomial aregression = TestGlmBinomial() #TestGlmBinomial.setup_class() results = aregression.res1 r_summary = str(results.summary()) print(r_summary) #print(results.summary2(return_fmt='latex')) #print(results.summary2(return_fmt='csv')) smry = olsres.summary() print(smry.as_csv()) # import matplotlib.pyplot as plt # plt.plot(rlmres.model.endog,'o') # plt.plot(rlmres.fittedvalues,'-') # # plt.show() statsmodels-0.12.2/statsmodels/iolib/tests/test_summary2.py000066400000000000000000000122371400612667500241440ustar00rootroot00000000000000import warnings import numpy as np import pandas as pd import pytest from numpy.testing import assert_equal from statsmodels.iolib.summary2 import summary_col from statsmodels.tools.tools import add_constant from statsmodels.regression.linear_model import OLS class TestSummaryLatex(object): def test_summarycol(self): # Test for latex output of summary_col object desired = r''' \begin{table} \caption{} \label{} \begin{center} \begin{tabular}{lll} \hline & y I & y II \\ \hline const & 7.7500 & 12.4231 \\ & (1.1058) & (3.1872) \\ x1 & -0.7500 & -1.5769 \\ & (0.2368) & (0.6826) \\ R-squared & 0.7697 & 0.6401 \\ R-squared Adj. & 0.6930 & 0.5202 \\ \hline \end{tabular} \end{center} \end{table} ''' x = [1, 5, 7, 3, 5] x = add_constant(x) y1 = [6, 4, 2, 7, 4] y2 = [8, 5, 0, 12, 4] reg1 = OLS(y1, x).fit() reg2 = OLS(y2, x).fit() actual = summary_col([reg1, reg2]).as_latex() actual = '\n%s\n' % actual assert_equal(desired, actual) def test_summarycol_float_format(self): # Test for latex output of summary_col object desired = r""" ========================== y I y II -------------------------- const 7.7 12.4 (1.1) (3.2) x1 -0.7 -1.6 (0.2) (0.7) R-squared 0.8 0.6 R-squared Adj. 0.7 0.5 ========================== Standard errors in parentheses. """ # noqa:W291 x = [1, 5, 7, 3, 5] x = add_constant(x) y1 = [6, 4, 2, 7, 4] y2 = [8, 5, 0, 12, 4] reg1 = OLS(y1, x).fit() reg2 = OLS(y2, x).fit() actual = summary_col([reg1, reg2], float_format='%0.1f').as_text() actual = '%s\n' % actual assert_equal(actual, desired) starred = summary_col([reg1, reg2], stars=True, float_format='%0.1f') assert "7.7***" in str(starred) assert "12.4**" in str(starred) assert "12.4***" not in str(starred) def test_summarycol_drop_omitted(self): # gh-3702 x = [1, 5, 7, 3, 5] x = add_constant(x) x2 = np.concatenate([x, np.array([[3], [9], [-1], [4], [0]])], 1) y1 = [6, 4, 2, 7, 4] y2 = [8, 5, 0, 12, 4] reg1 = OLS(y1, x).fit() reg2 = OLS(y2, x2).fit() actual = summary_col([reg1, reg2], regressor_order=['const', 'x1'], drop_omitted=True) assert 'x2' not in str(actual) actual = summary_col([reg1, reg2], regressor_order=['x1'], drop_omitted=False) assert 'const' in str(actual) assert 'x2' in str(actual) def test_summary_col_ordering_preserved(self): # gh-3767 x = [1, 5, 7, 3, 5] x = add_constant(x) x2 = np.concatenate([x, np.array([[3], [9], [-1], [4], [0]])], 1) x2 = pd.DataFrame(x2, columns=['const', 'b', 'a']) y1 = [6, 4, 2, 7, 4] y2 = [8, 5, 0, 12, 4] reg1 = OLS(y1, x2).fit() reg2 = OLS(y2, x2).fit() info_dict = {'R2': lambda x: '{:.3f}'.format(int(x.rsquared)), 'N': lambda x: '{0:d}'.format(int(x.nobs))} original = actual = summary_col([reg1, reg2], float_format='%0.4f') actual = summary_col([reg1, reg2], regressor_order=['a', 'b'], float_format='%0.4f', info_dict=info_dict) variables = ('const', 'b', 'a') for line in str(original).split('\n'): for variable in variables: if line.startswith(variable): assert line in str(actual) def test_OLSsummary(self): # Test that latex output of regular OLS output still contains # multiple tables x = [1, 5, 7, 3, 5] x = add_constant(x) y1 = [6, 4, 2, 7, 4] reg1 = OLS(y1, x).fit() with warnings.catch_warnings(): warnings.simplefilter("ignore") actual = reg1.summary().as_latex() string_to_find = r'''\end{tabular} \begin{tabular}''' result = string_to_find in actual assert (result is True) def test_ols_summary_rsquared_label(): # Check that the "uncentered" label is correctly added after rsquared x = [1, 5, 7, 3, 5, 2, 5, 3] y = [6, 4, 2, 7, 4, 9, 10, 2] reg_with_constant = OLS(y, add_constant(x)).fit() r2_str = 'R-squared:' with pytest.warns(UserWarning): assert r2_str in str(reg_with_constant.summary2()) with pytest.warns(UserWarning): assert r2_str in str(reg_with_constant.summary()) reg_without_constant = OLS(y, x, hasconst=False).fit() r2_str = 'R-squared (uncentered):' with pytest.warns(UserWarning): assert r2_str in str(reg_without_constant.summary2()) with pytest.warns(UserWarning): assert r2_str in str(reg_without_constant.summary()) def test_summary_col_r2(): # GH 6578 y = [1, 1, 4, 2] * 4 x = add_constant([1, 2, 3, 4] * 4) mod = OLS(endog=y, exog=x).fit() table = summary_col(results=mod) assert "R-squared " in str(table) assert "R-squared Adj." in str(table) statsmodels-0.12.2/statsmodels/iolib/tests/test_summary_old.py000066400000000000000000000066651400612667500247300ustar00rootroot00000000000000import warnings import pytest @pytest.mark.xfail(strict=True) def test_regression_summary(): #little luck getting this test to pass (It should?), can be used for #visual testing of the regression.summary table #fixed, might fail at minute changes from statsmodels.regression.tests.test_regression import TestOLS #from test_regression import TestOLS import time from string import Template t = time.localtime() desired = Template( ''' Summary of Regression Results ======================================= | Dependent Variable: y| | Model: OLS| | Method: Least Squares| | Date: $XXcurrentXdateXX| | Time: $XXtimeXXX| | # obs: 16.0| | Df residuals: 9.0| | Df model: 6.0| ============================================================================== | coefficient std. error t-statistic prob. | ------------------------------------------------------------------------------ | x1 15.06 84.91 0.1774 0.8631 | | x2 -0.03582 0.03349 -1.0695 0.3127 | | x3 -2.020 0.4884 -4.1364 0.0025 | | x4 -1.033 0.2143 -4.8220 0.0009 | | x5 -0.05110 0.2261 -0.2261 0.8262 | | x6 1829. 455.5 4.0159 0.0030 | | const -3.482e+06 8.904e+05 -3.9108 0.0036 | ============================================================================== | Models stats Residual stats | ------------------------------------------------------------------------------ | R-squared: 0.9955 Durbin-Watson: 2.559 | | Adjusted R-squared: 0.9925 Omnibus: 0.7486 | | F-statistic: 330.3 Prob(Omnibus): 0.6878 | | Prob (F-statistic): 4.984e-10 JB: 0.6841 | | Log likelihood: -109.6 Prob(JB): 0.7103 | | AIC criterion: 233.2 Skew: 0.4200 | | BIC criterion: 238.6 Kurtosis: 2.434 | ------------------------------------------------------------------------------''' ).substitute(XXcurrentXdateXX = str(time.strftime("%a, %d %b %Y",t)), XXtimeXXX = str(time.strftime("%H:%M:%S",t))) desired = str(desired) aregression = TestOLS() TestOLS.setup_class() results = aregression.res1 # be quiet! original_filters = warnings.filters[:] # copy original warnings.simplefilter("ignore") try: r_summary = str(results.summary_old()) finally: warnings.filters = original_filters # restore filters ## print('###') ## print(r_summary) ## print('###') ## print(desired) ## print('###') actual = r_summary import numpy as np actual = '\n'.join((line.rstrip() for line in actual.split('\n'))) # print len(actual), len(desired) # print repr(actual) # print repr(desired) # counter = 0 # for c1,c2 in zip(actual, desired): # if not c1==c2 and counter<20: # print c1,c2 # counter += 1 np.testing.assert_(actual == desired) statsmodels-0.12.2/statsmodels/iolib/tests/test_table.py000066400000000000000000000212031400612667500234450ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_equal from statsmodels.iolib.table import SimpleTable, default_txt_fmt from statsmodels.iolib.table import default_latex_fmt from statsmodels.iolib.table import default_html_fmt import pandas from statsmodels.regression.linear_model import OLS ltx_fmt1 = default_latex_fmt.copy() html_fmt1 = default_html_fmt.copy() class TestSimpleTable(object): def test_simple_table_1(self): # Basic test, test_simple_table_1 desired = ''' ===================== header1 header2 --------------------- stub1 1.30312 2.73999 stub2 1.95038 2.65765 --------------------- ''' test1data = [[1.30312, 2.73999],[1.95038, 2.65765]] test1stubs = ('stub1', 'stub2') test1header = ('header1', 'header2') actual = SimpleTable(test1data, test1header, test1stubs, txt_fmt=default_txt_fmt) actual = '\n%s\n' % actual.as_text() assert_equal(desired, str(actual)) def test_simple_table_2(self): # Test SimpleTable.extend_right() desired = ''' ============================================================= header s1 header d1 header s2 header d2 ------------------------------------------------------------- stub R1 C1 10.30312 10.73999 stub R1 C2 50.95038 50.65765 stub R2 C1 90.30312 90.73999 stub R2 C2 40.95038 40.65765 ------------------------------------------------------------- ''' data1 = [[10.30312, 10.73999], [90.30312, 90.73999]] data2 = [[50.95038, 50.65765], [40.95038, 40.65765]] stubs1 = ['stub R1 C1', 'stub R2 C1'] stubs2 = ['stub R1 C2', 'stub R2 C2'] header1 = ['header s1', 'header d1'] header2 = ['header s2', 'header d2'] actual1 = SimpleTable(data1, header1, stubs1, txt_fmt=default_txt_fmt) actual2 = SimpleTable(data2, header2, stubs2, txt_fmt=default_txt_fmt) actual1.extend_right(actual2) actual = '\n%s\n' % actual1.as_text() assert_equal(desired, str(actual)) def test_simple_table_3(self): # Test SimpleTable.extend() as in extend down desired = ''' ============================== header s1 header d1 ------------------------------ stub R1 C1 10.30312 10.73999 stub R2 C1 90.30312 90.73999 header s2 header d2 ------------------------------ stub R1 C2 50.95038 50.65765 stub R2 C2 40.95038 40.65765 ------------------------------ ''' data1 = [[10.30312, 10.73999], [90.30312, 90.73999]] data2 = [[50.95038, 50.65765], [40.95038, 40.65765]] stubs1 = ['stub R1 C1', 'stub R2 C1'] stubs2 = ['stub R1 C2', 'stub R2 C2'] header1 = ['header s1', 'header d1'] header2 = ['header s2', 'header d2'] actual1 = SimpleTable(data1, header1, stubs1, txt_fmt=default_txt_fmt) actual2 = SimpleTable(data2, header2, stubs2, txt_fmt=default_txt_fmt) actual1.extend(actual2) actual = '\n%s\n' % actual1.as_text() assert_equal(desired, str(actual)) def test_simple_table_4(self): # Basic test, test_simple_table_4 test uses custom txt_fmt txt_fmt1 = dict(data_fmts = ['%3.2f', '%d'], empty_cell = ' ', colwidths = 1, colsep=' * ', row_pre = '* ', row_post = ' *', table_dec_above='*', table_dec_below='*', header_dec_below='*', header_fmt = '%s', stub_fmt = '%s', title_align='r', header_align = 'r', data_aligns = "r", stubs_align = "l", fmt = 'txt' ) ltx_fmt1 = default_latex_fmt.copy() html_fmt1 = default_html_fmt.copy() cell0data = 0.0000 cell1data = 1 row0data = [cell0data, cell1data] row1data = [2, 3.333] table1data = [ row0data, row1data ] test1stubs = ('stub1', 'stub2') test1header = ('header1', 'header2') tbl = SimpleTable(table1data, test1header, test1stubs,txt_fmt=txt_fmt1, ltx_fmt=ltx_fmt1, html_fmt=html_fmt1) def test_txt_fmt1(self): # Limited test of custom txt_fmt desired = """ ***************************** * * header1 * header2 * ***************************** * stub1 * 0.00 * 1 * * stub2 * 2.00 * 3 * ***************************** """ actual = '\n%s\n' % tbl.as_text() #print(actual) #print(desired) assert_equal(actual, desired) def test_ltx_fmt1(self): # Limited test of custom ltx_fmt desired = r""" \begin{tabular}{lcc} \toprule & \textbf{header1} & \textbf{header2} \\ \midrule \textbf{stub1} & 0.0 & 1 \\ \textbf{stub2} & 2 & 3.333 \\ \bottomrule \end{tabular} """ actual = '\n%s\n' % tbl.as_latex_tabular(center=False) #print(actual) #print(desired) assert_equal(actual, desired) # Test "center=True" (the default): desired_centered = r""" \begin{center} %s \end{center} """ % desired[1:-1] actual_centered = '\n%s\n' % tbl.as_latex_tabular() assert_equal(actual_centered, desired_centered) def test_html_fmt1(self): # Limited test of custom html_fmt desired = """
header1 header2
stub1 0.0 1
stub2 2 3.333
""" # noqa:W291 actual = '\n%s\n' % tbl.as_html() assert_equal(actual, desired) test_txt_fmt1(self) test_ltx_fmt1(self) test_html_fmt1(self) def test_simple_table_special_chars(self): # Simple table with characters: (%, >, |, _, $, &, #) cell0c_data = 22 cell1c_data = 1053 row0c_data = [cell0c_data, cell1c_data] row1c_data = [23, 6250.4] table1c_data = [ row0c_data, row1c_data ] test1c_stubs = ('>stub1%', 'stub_2') test1c_header = ('#header1$', 'header&|') tbl_c = SimpleTable(table1c_data, test1c_header, test1c_stubs, ltx_fmt=ltx_fmt1) def test_ltx_special_chars(self): # Test for special characters (latex) in headers and stubs desired = r""" \begin{tabular}{lcc} \toprule & \textbf{\#header1\$} & \textbf{header\&$|$} \\ \midrule \textbf{$>$stub1\%} & 22 & 1053 \\ \textbf{stub\_2} & 23 & 6250.4 \\ \bottomrule \end{tabular} """ actual = '\n%s\n' % tbl_c.as_latex_tabular(center=False) assert_equal(actual, desired) test_ltx_special_chars(self) def test_regression_with_tuples(self): i = pandas.Series([1, 2, 3, 4] * 10, name="i") y = pandas.Series([1, 2, 3, 4, 5] * 8, name="y") x = pandas.Series([1, 2, 3, 4, 5, 6, 7, 8] * 5, name="x") df = pandas.DataFrame(index=i.index) df = df.join(i) endo = df.join(y) exo = df.join(x) endo_groups = endo.groupby("i") exo_groups = exo.groupby("i") exo_df = exo_groups.agg([np.sum, np.max]) endo_df = endo_groups.agg([np.sum, np.max]) reg = OLS(exo_df[[("x", "sum")]], endo_df).fit() interesting_lines = [] import warnings with warnings.catch_warnings(): # Catch ominormal warning, not interesting here warnings.simplefilter("ignore") for line in str(reg.summary()).splitlines(): if "_" in line: interesting_lines.append(line[:38]) desired = ["Dep. Variable: x_sum ", "y_sum 1.4595 0.209 ", "y_amax 0.2432 0.035 "] assert_equal(sorted(desired), sorted(interesting_lines)) def test_default_alignment(self): desired = ''' ===================== header1 header2 --------------------- stub1 1.30312 2.73 stub2 1.95038 2.6 --------------------- ''' test1data = [[1.30312, 2.73], [1.95038, 2.6]] test1stubs = ('stub1', 'stub2') test1header = ('header1', 'header2') actual = SimpleTable(test1data, test1header, test1stubs, txt_fmt=default_txt_fmt) actual = '\n%s\n' % actual.as_text() assert_equal(desired, str(actual)) statsmodels-0.12.2/statsmodels/iolib/tests/test_table_econpy.py000066400000000000000000000101661400612667500250300ustar00rootroot00000000000000''' Unit tests table.py. :see: http://docs.python.org/lib/minimal-example.html for an intro to unittest :see: http://agiletesting.blogspot.com/2005/01/python-unit-testing-part-1-unittest.html :see: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/305292 ''' import numpy as np from numpy.testing import assert_equal __docformat__ = "restructuredtext en" from statsmodels.iolib.table import Cell, SimpleTable from statsmodels.iolib.table import default_latex_fmt from statsmodels.iolib.table import default_html_fmt ltx_fmt1 = default_latex_fmt.copy() html_fmt1 = default_html_fmt.copy() txt_fmt1 = dict( data_fmts = ['%0.2f', '%d'], empty_cell = ' ', colwidths = 1, colsep=' * ', row_pre = '* ', row_post = ' *', table_dec_above='*', table_dec_below='*', header_dec_below='*', header_fmt = '%s', stub_fmt = '%s', title_align='r', header_align = 'r', data_aligns = "r", stubs_align = "l", fmt = 'txt' ) cell0data = 0.0000 cell1data = 1 row0data = [cell0data, cell1data] row1data = [2, 3.333] table1data = [ row0data, row1data ] test1stubs = ('stub1', 'stub2') test1header = ('header1', 'header2') #test1header = ('header1\nheader1a', 'header2\nheader2a') tbl = SimpleTable(table1data, test1header, test1stubs, txt_fmt=txt_fmt1, ltx_fmt=ltx_fmt1, html_fmt=html_fmt1) def custom_labeller(cell): if cell.data is np.nan: return 'missing' class TestCell(object): def test_celldata(self): celldata = cell0data, cell1data, row1data[0], row1data[1] cells = [Cell(datum, datatype=i % 2) for i, datum in enumerate(celldata)] for cell, datum in zip(cells, celldata): assert_equal(cell.data, datum) class TestSimpleTable(object): def test_txt_fmt1(self): # Limited test of custom txt_fmt desired = """ ***************************** * * header1 * header2 * ***************************** * stub1 * 0.00 * 1 * * stub2 * 2.00 * 3 * ***************************** """ actual = '\n%s\n' % tbl.as_text() #print('actual') #print(actual) #print('desired') #print(desired) assert_equal(actual, desired) def test_ltx_fmt1(self): # Limited test of custom ltx_fmt desired = r""" \begin{center} \begin{tabular}{lcc} \toprule & \textbf{header1} & \textbf{header2} \\ \midrule \textbf{stub1} & 0.0 & 1 \\ \textbf{stub2} & 2 & 3.333 \\ \bottomrule \end{tabular} \end{center} """ actual = '\n%s\n' % tbl.as_latex_tabular() #print(actual) #print(desired) assert_equal(actual, desired) def test_html_fmt1(self): # Limited test of custom html_fmt desired = """
header1 header2
stub1 0.0 1
stub2 2 3.333
""" #the previous has significant trailing whitespace that got removed #desired = '''\n\n\n \n\n\n \n\n\n \n\n
header1 header2
stub1 0.0 1
stub2 2 3.333
\n''' actual = '\n%s\n' % tbl.as_html() actual = '\n'.join((line.rstrip() for line in actual.split('\n'))) #print(actual) #print(desired) #print len(actual), len(desired) assert_equal(actual, desired) def test_customlabel(self): # Limited test of custom custom labeling tbl = SimpleTable(table1data, test1header, test1stubs, txt_fmt=txt_fmt1) tbl[1][1].data = np.nan tbl.label_cells(custom_labeller) #print([[c.datatype for c in row] for row in tbl]) desired = """ ***************************** * * header1 * header2 * ***************************** * stub1 * -- * 1 * * stub2 * 2.00 * 3 * ***************************** """ actual = '\n%s\n' % tbl.as_text(missing='--') assert_equal(actual, desired) statsmodels-0.12.2/statsmodels/miscmodels/000077500000000000000000000000001400612667500206465ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/miscmodels/__init__.py000066400000000000000000000001131400612667500227520ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/miscmodels/api.py000066400000000000000000000003611400612667500217710ustar00rootroot00000000000000__all__ = ["TLinearModel", "PoissonGMLE", "PoissonOffsetGMLE", "PoissonZiGMLE"] from .tmodel import TLinearModel from .count import (PoissonGMLE, PoissonOffsetGMLE, PoissonZiGMLE, #NonlinearDeltaCov ) statsmodels-0.12.2/statsmodels/miscmodels/count.py000066400000000000000000000177411400612667500223620ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Mon Jul 26 08:34:59 2010 Author: josef-pktd changes: added offset and zero-inflated version of Poisson - kind of ok, need better test cases, - a nan in ZIP bse, need to check hessian calculations - found error in ZIP loglike - all tests pass with Issues ------ * If true model is not zero-inflated then numerical Hessian for ZIP has zeros for the inflation probability and is not invertible. -> hessian inverts and bse look ok if row and column are dropped, pinv also works * GenericMLE: still get somewhere (where?) "CacheWriteWarning: The attribute 'bse' cannot be overwritten" * bfgs is too fragile, does not come back * `nm` is slow but seems to work * need good start_params and their use in genericmle needs to be checked for consistency, set as attribute or method (called as attribute) * numerical hessian needs better scaling * check taking parts out of the loop, e.g. factorial(endog) could be precalculated """ import numpy as np from scipy import stats from scipy.special import factorial from statsmodels.base.model import GenericLikelihoodModel def maxabs(arr1, arr2): return np.max(np.abs(arr1 - arr2)) def maxabsrel(arr1, arr2): return np.max(np.abs(arr2 / arr1 - 1)) class NonlinearDeltaCov(object): '''Asymptotic covariance by Deltamethod the function is designed for 2d array, with rows equal to the number of equations and columns equal to the number of parameters. 1d params work by chance ? fun: R^{m*k) -> R^{m} where m is number of equations and k is the number of parameters. equations follow Greene ''' def __init__(self, fun, params, cov_params): self.fun = fun self.params = params self.cov_params = cov_params def grad(self, params=None, **kwds): if params is None: params = self.params kwds.setdefault('epsilon', 1e-4) from statsmodels.tools.numdiff import approx_fprime return approx_fprime(params, self.fun, **kwds) def cov(self): g = self.grad() covar = np.dot(np.dot(g, self.cov_params), g.T) return covar def expected(self): # rename: misnomer, this is the MLE of the fun return self.fun(self.params) def wald(self, value): m = self.expected() v = self.cov() df = np.size(m) diff = m - value lmstat = np.dot(np.dot(diff.T, np.linalg.inv(v)), diff) return lmstat, stats.chi2.sf(lmstat, df) class PoissonGMLE(GenericLikelihoodModel): '''Maximum Likelihood Estimation of Poisson Model This is an example for generic MLE which has the same statistical model as discretemod.Poisson. Except for defining the negative log-likelihood method, all methods and results are generic. Gradients and Hessian and all resulting statistics are based on numerical differentiation. ''' # copied from discretemod.Poisson def nloglikeobs(self, params): """ Loglikelihood of Poisson model Parameters ---------- params : array_like The parameters of the model. Returns ------- The log likelihood of the model evaluated at `params` Notes -------- .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right] """ XB = np.dot(self.exog, params) endog = self.endog return np.exp(XB) - endog*XB + np.log(factorial(endog)) def predict_distribution(self, exog): '''return frozen scipy.stats distribution with mu at estimated prediction ''' if not hasattr(self, "result"): # TODO: why would this be ValueError instead of AttributeError? # TODO: Why even make this a Model attribute in the first place? # It belongs on the Results class raise ValueError else: result = self.result params = result.params mu = np.exp(np.dot(exog, params)) return stats.poisson(mu, loc=0) class PoissonOffsetGMLE(GenericLikelihoodModel): '''Maximum Likelihood Estimation of Poisson Model This is an example for generic MLE which has the same statistical model as discretemod.Poisson but adds offset Except for defining the negative log-likelihood method, all methods and results are generic. Gradients and Hessian and all resulting statistics are based on numerical differentiation. ''' def __init__(self, endog, exog=None, offset=None, missing='none', **kwds): # let them be none in case user wants to use inheritance if offset is not None: if offset.ndim == 1: offset = offset[:,None] #need column self.offset = offset.ravel() else: self.offset = 0. super(PoissonOffsetGMLE, self).__init__(endog, exog, missing=missing, **kwds) #this was added temporarily for bug-hunting, but should not be needed # def loglike(self, params): # return -self.nloglikeobs(params).sum(0) # original copied from discretemod.Poisson def nloglikeobs(self, params): """ Loglikelihood of Poisson model Parameters ---------- params : array_like The parameters of the model. Returns ------- The log likelihood of the model evaluated at `params` Notes -------- .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right] """ XB = self.offset + np.dot(self.exog, params) endog = self.endog nloglik = np.exp(XB) - endog*XB + np.log(factorial(endog)) return nloglik class PoissonZiGMLE(GenericLikelihoodModel): '''Maximum Likelihood Estimation of Poisson Model This is an example for generic MLE which has the same statistical model as discretemod.Poisson but adds offset and zero-inflation. Except for defining the negative log-likelihood method, all methods and results are generic. Gradients and Hessian and all resulting statistics are based on numerical differentiation. There are numerical problems if there is no zero-inflation. ''' def __init__(self, endog, exog=None, offset=None, missing='none', **kwds): # let them be none in case user wants to use inheritance super(PoissonZiGMLE, self).__init__(endog, exog, missing=missing, **kwds) if offset is not None: if offset.ndim == 1: offset = offset[:,None] #need column self.offset = offset.ravel() #which way? else: self.offset = 0. #TODO: it's not standard pattern to use default exog if exog is None: self.exog = np.ones((self.nobs,1)) self.nparams = self.exog.shape[1] #what's the shape in regression for exog if only constant self.start_params = np.hstack((np.ones(self.nparams), 0)) self.cloneattr = ['start_params'] #needed for t_test and summary self.exog_names.append('zi') # original copied from discretemod.Poisson def nloglikeobs(self, params): """ Loglikelihood of Poisson model Parameters ---------- params : array_like The parameters of the model. Returns ------- The log likelihood of the model evaluated at `params` Notes -------- .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right] """ beta = params[:-1] gamm = 1 / (1 + np.exp(params[-1])) #check this # replace with np.dot(self.exogZ, gamma) #print(np.shape(self.offset), self.exog.shape, beta.shape XB = self.offset + np.dot(self.exog, beta) endog = self.endog nloglik = -np.log(1-gamm) + np.exp(XB) - endog*XB + np.log(factorial(endog)) nloglik[endog==0] = - np.log(gamm + np.exp(-nloglik[endog==0])) return nloglik statsmodels-0.12.2/statsmodels/miscmodels/nonlinls.py000066400000000000000000000221641400612667500230610ustar00rootroot00000000000000'''Non-linear least squares Author: Josef Perktold based on scipy.optimize.curve_fit ''' import numpy as np from scipy import optimize from statsmodels.base.model import Model class Results(object): '''just a dummy placeholder for now most results from RegressionResults can be used here ''' pass ##def getjaccov(retval, n): ## '''calculate something and raw covariance matrix from return of optimize.leastsq ## ## I cannot figure out how to recover the Jacobian, or whether it is even ## possible ## ## this is a partial copy of scipy.optimize.leastsq ## ''' ## info = retval[-1] ## #n = len(x0) #nparams, where do I get this ## cov_x = None ## if info in [1,2,3,4]: ## from numpy.dual import inv ## from numpy.linalg import LinAlgError ## perm = np.take(np.eye(n), retval[1]['ipvt']-1,0) ## r = np.triu(np.transpose(retval[1]['fjac'])[:n,:]) ## R = np.dot(r, perm) ## try: ## cov_x = inv(np.dot(np.transpose(R),R)) ## except LinAlgError: ## print 'cov_x not available' ## pass ## return r, R, cov_x ## ##def _general_function(params, xdata, ydata, function): ## return function(xdata, *params) - ydata ## ##def _weighted_general_function(params, xdata, ydata, function, weights): ## return weights * (function(xdata, *params) - ydata) ## class NonlinearLS(Model): #or subclass a model r'''Base class for estimation of a non-linear model with least squares This class is supposed to be subclassed, and the subclass has to provide a method `_predict` that defines the non-linear function `f(params) that is predicting the endogenous variable. The model is assumed to be :math: y = f(params) + error and the estimator minimizes the sum of squares of the estimated error. :math: min_parmas \sum (y - f(params))**2 f has to return the prediction for each observation. Exogenous or explanatory variables should be accessed as attributes of the class instance, and can be given as arguments when the instance is created. Warning: Weights are not correctly handled yet in the results statistics, but included when estimating the parameters. similar to scipy.optimize.curve_fit API difference: params are array_like not split up, need n_params information includes now weights similar to curve_fit no general sigma yet (OLS and WLS, but no GLS) This is currently holding on to intermediate results that are not necessary but useful for testing. Fit returns and instance of RegressionResult, in contrast to the linear model, results in this case are based on a local approximation, essentially y = f(X, params) is replaced by y = grad * params where grad is the Gradient or Jacobian with the shape (nobs, nparams). See for example Greene Examples -------- class Myfunc(NonlinearLS): def _predict(self, params): x = self.exog a, b, c = params return a*np.exp(-b*x) + c Ff we have data (y, x), we can create an instance and fit it with mymod = Myfunc(y, x) myres = mymod.fit(nparams=3) and use the non-linear regression results, for example myres.params myres.bse myres.tvalues ''' #NOTE: This needs to call super for data checking def __init__(self, endog=None, exog=None, weights=None, sigma=None, missing='none'): self.endog = endog self.exog = exog if sigma is not None: sigma = np.asarray(sigma) if sigma.ndim < 2: self.sigma = sigma self.weights = 1./sigma else: raise ValueError('correlated errors are not handled yet') else: self.weights = None def predict(self, exog, params=None): #copied from GLS, Model has different signature return self._predict(params) def _predict(self, params): pass def start_value(self): return None def geterrors(self, params, weights=None): if weights is None: if self.weights is None: return self.endog - self._predict(params) else: weights = self.weights return weights * (self.endog - self._predict(params)) def errorsumsquares(self, params): return (self.geterrors(params)**2).sum() def fit(self, start_value=None, nparams=None, **kw): #if hasattr(self, 'start_value'): #I added start_value even if it's empty, not sure about it #but it makes a visible placeholder if start_value is not None: p0 = start_value else: #nesting so that start_value is only calculated if it is needed p0 = self.start_value() if p0 is not None: pass elif nparams is not None: p0 = 0.1 * np.ones(nparams) else: raise ValueError('need information about start values for' + 'optimization') func = self.geterrors res = optimize.leastsq(func, p0, full_output=1, **kw) (popt, pcov, infodict, errmsg, ier) = res if ier not in [1,2,3,4]: msg = "Optimal parameters not found: " + errmsg raise RuntimeError(msg) err = infodict['fvec'] ydata = self.endog if (len(ydata) > len(p0)) and pcov is not None: #this can use the returned errors instead of recalculating s_sq = (err**2).sum()/(len(ydata)-len(p0)) pcov = pcov * s_sq else: pcov = None self.df_resid = len(ydata)-len(p0) self.df_model = len(p0) fitres = Results() fitres.params = popt fitres.pcov = pcov fitres.rawres = res self.wendog = self.endog #add weights self.wexog = self.jac_predict(popt) pinv_wexog = np.linalg.pinv(self.wexog) self.normalized_cov_params = np.dot(pinv_wexog, np.transpose(pinv_wexog)) #TODO: check effect of `weights` on result statistics #I think they are correctly included in cov_params #maybe not anymore, I'm not using pcov of leastsq #direct calculation with jac_predict misses the weights ## if not weights is None ## fitres.wexogw = self.weights * self.jacpredict(popt) from statsmodels.regression import RegressionResults results = RegressionResults beta = popt lfit = RegressionResults(self, beta, normalized_cov_params=self.normalized_cov_params) lfit.fitres = fitres #mainly for testing self._results = lfit return lfit def fit_minimal(self, start_value, **kwargs): '''minimal fitting with no extra calculations''' func = self.geterrors res = optimize.leastsq(func, start_value, full_output=0, **kwargs) return res def fit_random(self, ntries=10, rvs_generator=None, nparams=None): '''fit with random starting values this could be replaced with a global fitter ''' if nparams is None: nparams = self.nparams if rvs_generator is None: rvs = np.random.uniform(low=-10, high=10, size=(ntries, nparams)) else: rvs = rvs_generator(size=(ntries, nparams)) results = np.array([np.r_[self.fit_minimal(rv), rv] for rv in rvs]) #selct best results and check how many solutions are within 1e-6 of best #not sure what leastsq returns return results def jac_predict(self, params): '''jacobian of prediction function using complex step derivative This assumes that the predict function does not use complex variable but is designed to do so. ''' from statsmodels.tools.numdiff import approx_fprime_cs jaccs_err = approx_fprime_cs(params, self._predict) return jaccs_err class Myfunc(NonlinearLS): #predict model.Model has a different signature ## def predict(self, params, exog=None): ## if not exog is None: ## x = exog ## else: ## x = self.exog ## a, b, c = params ## return a*np.exp(-b*x) + c def _predict(self, params): x = self.exog a, b, c = params return a*np.exp(-b*x) + c if __name__ == '__main__': def func0(x, a, b, c): return a*np.exp(-b*x) + c def func(params, x): a, b, c = params return a*np.exp(-b*x) + c def error(params, x, y): return y - func(params, x) def error2(params, x, y): return (y - func(params, x))**2 x = np.linspace(0,4,50) params = np.array([2.5, 1.3, 0.5]) y0 = func(params, x) y = y0 + 0.2*np.random.normal(size=len(x)) res = optimize.leastsq(error, params, args=(x, y), full_output=True) ## r, R, c = getjaccov(res[1:], 3) mod = Myfunc(y, x) resmy = mod.fit(nparams=3) cf_params, cf_pcov = optimize.curve_fit(func0, x, y) cf_bse = np.sqrt(np.diag(cf_pcov)) print(res[0]) print(cf_params) print(resmy.params) print(cf_bse) print(resmy.bse) statsmodels-0.12.2/statsmodels/miscmodels/tests/000077500000000000000000000000001400612667500220105ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/miscmodels/tests/__init__.py000066400000000000000000000000001400612667500241070ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/miscmodels/tests/results_tmodel.py000066400000000000000000000273511400612667500254370ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Jun 30 23:14:36 2013 Author: Josef Perktold """ import numpy as np from statsmodels.tools.testing import Holder res_t_dfest = Holder() # > tfit3 <- tlm(m.marietta~CRSP, data=mm, start=list(dof = 3), estDof=TRUE) # > cat_items(tfit3, "res_t_dfest.") res_t_dfest.random = np.array([ 0.6242843, 1.349205, 1.224172, 1.272655, 1.323455, 1.091313, 1.227218, 0.0316284, 0.7202973, 1.038392, 1.091907, 0.7966355, 0.784222, 0.5042926, 0.1964543, 1.172123, 1.017338, 0.8799186, 0.7849335, 0.790158, 0.8121724, 1.286998, 0.7286052, 1.330104, 1.054037, 1.299656, 1.285306, 1.271166, 1.106877, 1.303909, 0.4250416, 1.277096, 1.160106, 0.1871806, 1.074168, 1.197795, 1.046638, 1.104423, 1.301670, 1.333217, 0.8156778, 1.309934, 1.142454, 1.347481, 0.6605017, 1.035725, 1.172666, 1.281746, 0.8796436, 0.9597098, 0.6221453, 1.149490, 1.291864, 1.207619, 1.239625, 1.351065, 1.248711, 0.3532520, 0.6067273, 0.8180234 ]) res_t_dfest.dof = 2.837183 res_t_dfest.dofse = 1.175296 res_t_dfest.iter = 7 res_t_dfest.logLik = 71.81292 res_t_dfest.endTime = 0.01 loc_fit = Holder() #> cat_items(tfit3$loc.fit, "loc_fit.") loc_fit.coefficients = np.array([-0.007248461, 1.263751]) loc_fit.residuals = np.array([ -0.09133902, 0.004151492, -0.02737765, 0.02117769, 0.01251936, -0.0413709, -0.02701702, 0.5465314, -0.07922967, -0.04651135, -0.04131256, 0.07064283, -0.07199043, -0.1096804, 0.2051536, 0.0331728, 0.04853971, 0.06197657, 0.07191273, -0.07134392, 0.06897908, -0.01907315, -0.0782573, -0.01096341, 0.04500034, -0.01704652, -0.01933079, 0.02138696, 0.03983612, -0.01631880, 0.1249257, -0.02054422, -0.03443716, 0.2110156, -0.04304691, 0.03038995, 0.04571555, 0.04007908, -0.01670529, 0.01015959, 0.06860706, -0.01523742, 0.03625959, 0.005138716, -0.08656302, -0.04676856, -0.03311507, -0.01986418, -0.06200429, 0.05410242, 0.09163019, 0.03553772, 0.01831594, -0.02928904, 0.02551524, 0.002713425, 0.02437713, -0.1422379, 0.09376145, -0.06835877 ]) loc_fit.fitted_values = np.array([ -0.04516098, -0.0810515, -0.03012235, 0.03142231, -0.05741936, -0.0445291, -0.04718298, 0.1413686, 0.002229668, 0.1315113, 0.04431256, 0.004757169, 0.03079043, 0.02068043, 0.02674643, 0.0755272, -0.01103971, 0.03382343, -0.05451273, -0.001056083, 0.00602092, -0.03972685, 0.0162573, -0.02683659, -0.02810034, -0.06285348, 0.004630794, -0.01078696, -0.08193612, 0.01271880, -0.03732572, 0.1230442, -0.01546284, -0.01571559, -0.02835309, 0.01651005, 0.08538445, 0.00602092, -0.01609471, -0.01975959, 0.05859294, 0.00753742, -0.01975959, -0.02013872, -0.06133698, 0.04026856, 0.07211507, 0.04216418, -0.006995711, 0.07969758, 0.05416981, -0.02923772, 0.05088406, 0.005389044, -0.08231524, 0.07868658, -0.1132771, 0.05353794, 0.009938546, -0.04794123 ]) loc_fit.effects = np.array([ -0.4809681, 6.645774, -0.6803134, 0.8423367, 0.5333795, -0.9748358, -0.6818408, 0.6716256, -1.239349, -0.9454051, -0.919986, 1.546571, -1.206974, -1.185012, 1.167586, 1.162168, 1.367571, 1.521386, 1.514811, -1.224234, 1.541103, -0.4658513, -1.229607, -0.2132594, 1.309335, -0.4211133, -0.4462804, 0.8224875, 1.194665, -0.3537337, 1.443046, -0.4086050, -0.8295162, 1.122057, -0.9918254, 1.065403, 1.388378, 1.252209, -0.3826760, 0.4819511, 1.571469, -0.3244968, 1.166818, 0.3190928, -1.280510, -1.004244, -0.7489287, -0.4386115, -1.182836, 1.485040, 1.594513, 1.146952, 0.773323, -0.7043392, 0.888233, 0.2990213, 0.8402323, -1.040679, 1.564756, -1.241512 ]) loc_fit.weights = np.array([ 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666, 260.7666 ]) loc_fit.qr = '''structure(list(qr = structure(c(-125.083961390618, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, 0.129099444873581, -1.09802870774065, 5.25877087979451, 0.068920957251135, -0.0806236351850806, 0.135248743629416, 0.103927288950783, 0.110375823737560, -0.34777721920871, -0.00968975253053064, -0.323825518572109, -0.111945089863713, -0.0158312142322233, -0.0790882697596574, -0.0545224229528869, -0.0692619310369492, -0.187792141879617, 0.0225529214033557, -0.0864580238016886, 0.128186062672469, -0.00170585231833022, -0.0189019450830696, 0.092258511717567, -0.0437748649749248, 0.0609370570389346, 0.064007787889781, 0.148452886288055, -0.0155241411471386, 0.0219387752331864, 0.194820922135834, -0.0351768185925551, 0.0864241231009591, -0.303251621871439, 0.0333004793813178, 0.0339146255514870, 0.0646219340599502, -0.044389011145094, -0.211743842516218, -0.0189019450830696, 0.0348358448067410, 0.0437409642741953, -0.146644348478276, -0.0225868221040852, 0.0437409642741953, 0.0446621835294492, 0.144768009267039, -0.102118751141005, -0.179501168582332, -0.106724847417274, 0.0127265826806475, -0.19792555368741, -0.135896790500314, 0.0667714456555426, -0.127912890288114, -0.0173665796576464, 0.195742141391088, -0.195468969006733, 0.270975047236823, -0.134361425074891, -0.0284212107206932, 0.112218262248068), assign = 0:1, .Dim = c(60L, 2L), .Dimnames = list(c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60"), c("(Intercept)", "CRSP"))), qraux = c(1.12909944487358, 1.19267141054024), pivot = 1:2, tol = 1e-07, rank = 2L), .Names = c("qr", "qraux", "pivot", "tol", "rank"), class = "qr")''' loc_fit.method = 'maximum likelihood' loc_fit.formula = '''m.marietta ~ CRSP''' loc_fit.terms = '''m.marietta ~ CRSP''' loc_fit.iter = 7 loc_fit.call = '''tlm(lform = m.marietta ~ CRSP, data = mm, start = list(dof = 3), estDof = TRUE)''' #> s = summary(tfit3) #> cat_items(s$loc.summary, prefix="loc_fit.") # renamed coefficient -> table loc_fit.table = np.array([ -0.007248461, 1.263751, 0.008167043, 0.1901585, -0.8875258, 6.645774, 0.3784616, 1.150536e-08 ]).reshape(2,4, order='F') loc_fit.table_rownames = ['(Intercept)', 'CRSP', ] loc_fit.table_colnames = ['Estimate', 'Std. Error', 't value', 'Pr(>|t|)', ] loc_fit.dispersion = 1 loc_fit.cov_unscaled = np.array([ 6.670059e-05, -0.0003174268, -0.0003174268, 0.03616026 ]).reshape(2,2, order='F') loc_fit.cov_unscaled_rownames = ['(Intercept)', 'CRSP', ] loc_fit.cov_unscaled_colnames = ['(Intercept)', 'CRSP', ] loc_fit.cov_scaled = np.array([ 6.670059e-05, -0.0003174268, -0.0003174268, 0.03616026 ]).reshape(2,2, order='F') loc_fit.cov_scaled_rownames = ['(Intercept)', 'CRSP', ] loc_fit.cov_scaled_colnames = ['(Intercept)', 'CRSP', ] scale_fit = Holder() #> cat_items(tfit3$scale.fit, "scale_fit.") scale_fit.coefficients = -5.983115 scale_fit.residuals = np.array([ 2.193327, -2.038408, -1.308573, -1.591579, -1.888103, -0.5330418, -1.326357, 5.653531, 1.632833, -0.2240806, -0.5364947, 1.187192, 1.259662, 2.893897, 4.691185, -1.004751, -0.1011940, 0.7009929, 1.255535, 1.224993, 1.096490, -1.675302, 1.584339, -1.926915, -0.3154245, -1.749184, -1.665424, -1.582882, -0.6238652, -1.774011, 3.356624, -1.617496, -0.9346065, 4.74536, -0.4329547, -1.154602, -0.2722567, -0.6095562, -1.76094, -1.945082, 1.076003, -1.809181, -0.8315554, -2.028347, 1.98188, -0.2085298, -1.007913, -1.644641, 0.702596, 0.2351866, 2.205829, -0.8726262, -1.703705, -1.211949, -1.398769, -2.049267, -1.451807, 3.775749, 2.295868, 1.062300 ]) scale_fit.fitted_values = np.array([ 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962, 0.002520962 ]) scale_fit.effects = np.array([ 32.31074, -1.595974, -1.087148, -1.284454, -1.491184, -0.5464648, -1.099547, 3.766681, 0.9635367, -0.3310637, -0.5488721, 0.6528456, 0.70337, 1.842724, 3.095754, -0.8753306, -0.2453897, 0.3138777, 0.7004929, 0.6791996, 0.5896097, -1.342824, 0.9297278, -1.518243, -0.3947467, -1.394333, -1.335937, -1.278391, -0.6097849, -1.411642, 2.165327, -1.302523, -0.826427, 3.133524, -0.4766862, -0.979803, -0.364651, -0.599809, -1.402529, -1.530909, 0.5753267, -1.436162, -0.754582, -1.588959, 1.206885, -0.3202220, -0.8775351, -1.321448, 0.3149953, -0.01087243, 1.363017, -0.7832157, -1.362626, -1.019784, -1.150031, -1.603544, -1.187008, 2.457531, 1.425790, 0.5657731 ]) scale_fit.weights = np.array([ 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579, 0.4860579 ]) scale_fit.formula = '''m.marietta ~ 1''' scale_fit.terms = '''m.marietta ~ 1''' scale_fit.iter = 7 scale_fit.call = '''tlm(lform = m.marietta ~ CRSP, data = mm, start = list(dof = 3), estDof = TRUE)''' res_t_dfest.loc_fit = loc_fit res_t_dfest.scale_fit = scale_fit statsmodels-0.12.2/statsmodels/miscmodels/tests/test_generic_mle.py000066400000000000000000000157001400612667500256750ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Jun 28 14:19:26 2013 Author: Josef Perktold """ import numpy as np from scipy import stats from statsmodels.base.model import GenericLikelihoodModel from numpy.testing import (assert_array_less, assert_almost_equal, assert_allclose, assert_) class MyPareto(GenericLikelihoodModel): '''Maximum Likelihood Estimation pareto distribution first version: iid case, with constant parameters ''' def initialize(self): #TODO needed or not super(MyPareto, self).initialize() #start_params needs to be attribute self.start_params = np.array([1.5, self.endog.min() - 1.5, 1.]) #copied from stats.distribution def pdf(self, x, b): return b * x**(-b-1) def loglike(self, params): return -self.nloglikeobs(params).sum(0) # TODO: design start_params needs to be an attribute, # so it can be overwritten # @property # def start_params(self): # return np.array([1.5, self.endog.min() - 1.5, 1.]) def nloglikeobs(self, params): #print params.shape if self.fixed_params is not None: #print 'using fixed' params = self.expandparams(params) b = params[0] loc = params[1] scale = params[2] #loc = np.dot(self.exog, beta) endog = self.endog x = (endog - loc)/scale logpdf = np.log(b) - (b+1.)*np.log(x) #use np_log(1 + x) for Pareto II logpdf -= np.log(scale) #lb = loc + scale #logpdf[endog|z|' assert check_str in str(summ) def test_use_t_summary(self): orig_val = self.res1.use_t self.res1.use_t = True summ = self.res1.summary() assert 'P>|t|' in str(summ) self.res1.use_t = orig_val def test_ttest(self): self.res1.t_test(np.eye(len(self.res1.params))) def test_params(self): params = self.res1.params params_true = np.array([2,0,2]) if self.res1.model.fixed_paramsmask is not None: params_true = params_true[self.res1.model.fixed_paramsmask] assert_allclose(params, params_true, atol=1.5) assert_allclose(params, np.zeros(len(params)), atol=4) assert_allclose(self.res1.bse, np.zeros(len(params)), atol=0.5) if not self.skip_bsejac: assert_allclose(self.res1.bse, self.res1.bsejac, rtol=0.05, atol=0.15) # bsejhj is very different from the other two # use huge atol as sanity check for availability assert_allclose(self.res1.bsejhj, self.res1.bsejac, rtol=0.05, atol=1.5) class TestMyPareto1(CheckGenericMixin): @classmethod def setup_class(cls): params = [2, 0, 2] nobs = 100 np.random.seed(1234) rvs = stats.pareto.rvs(*params, **dict(size=nobs)) mod_par = MyPareto(rvs) mod_par.fixed_params = None mod_par.fixed_paramsmask = None mod_par.df_model = 3 mod_par.df_resid = mod_par.endog.shape[0] - mod_par.df_model mod_par.data.xnames = ['shape', 'loc', 'scale'] cls.mod = mod_par cls.res1 = mod_par.fit(disp=None) # Note: possible problem with parameters close to min data boundary # see issue #968 cls.skip_bsejac = True def test_minsupport(self): # rough sanity checks for convergence params = self.res1.params x_min = self.res1.endog.min() p_min = params[1] + params[2] assert_array_less(p_min, x_min) assert_almost_equal(p_min, x_min, decimal=2) class TestMyParetoRestriction(CheckGenericMixin): @classmethod def setup_class(cls): params = [2, 0, 2] nobs = 50 np.random.seed(1234) rvs = stats.pareto.rvs(*params, **dict(size=nobs)) mod_par = MyPareto(rvs) fixdf = np.nan * np.ones(3) fixdf[1] = -0.1 mod_par.fixed_params = fixdf mod_par.fixed_paramsmask = np.isnan(fixdf) mod_par.start_params = mod_par.start_params[mod_par.fixed_paramsmask] mod_par.df_model = 2 mod_par.df_resid = mod_par.endog.shape[0] - mod_par.df_model mod_par.data.xnames = ['shape', 'scale'] cls.mod = mod_par cls.res1 = mod_par.fit(disp=None) # Note: loc is fixed, no problems with parameters close to min data cls.skip_bsejac = False class TwoPeakLLHNoExog(GenericLikelihoodModel): """Fit height of signal peak over background.""" start_params = [10, 1000] cloneattr = ['start_params', 'signal', 'background'] exog_names = ['n_signal', 'n_background'] endog_names = ['alpha'] def __init__(self, endog, exog=None, signal=None, background=None, *args, **kwargs): # assume we know the shape + location of the two components, # so we re-use their PDFs here self.signal = signal self.background = background super(TwoPeakLLHNoExog, self).__init__(endog=endog, exog=exog, *args, **kwargs) def loglike(self, params): # pylint: disable=E0202 return -self.nloglike(params) def nloglike(self, params): endog = self.endog return self.nlnlike(params, endog) def nlnlike(self, params, endog): n_sig = params[0] n_bkg = params[1] if (n_sig < 0) or n_bkg < 0: return np.inf n_tot = n_bkg + n_sig alpha = endog sig = self.signal.pdf(alpha) bkg = self.background.pdf(alpha) sumlogl = np.sum(np.log((n_sig * sig) + (n_bkg * bkg))) sumlogl -= n_tot return -sumlogl class TestTwoPeakLLHNoExog(object): @classmethod def setup_class(cls): np.random.seed(42) pdf_a = stats.halfcauchy(loc=0, scale=1) pdf_b = stats.uniform(loc=0, scale=100) n_a = 50 n_b = 200 params = [n_a, n_b] X = np.concatenate([pdf_a.rvs(size=n_a), pdf_b.rvs(size=n_b), ])[:, np.newaxis] cls.X = X cls.params = params cls.pdf_a = pdf_a cls.pdf_b = pdf_b def test_fit(self): np.random.seed(42) llh_noexog = TwoPeakLLHNoExog(self.X, signal=self.pdf_a, background=self.pdf_b) res = llh_noexog.fit() assert_allclose(res.params, self.params, rtol=1e-1) # TODO: nan if exog is None, assert_(np.isnan(res.df_resid)) res_bs = res.bootstrap(nrep=50) assert_allclose(res_bs[2].mean(0), self.params, rtol=1e-1) # SMOKE test, res.summary() statsmodels-0.12.2/statsmodels/miscmodels/tests/test_poisson.py000066400000000000000000000166061400612667500251240ustar00rootroot00000000000000'''Testing GenericLikelihoodModel variations on Poisson ''' import pytest import numpy as np from numpy.testing import assert_almost_equal from scipy import stats import statsmodels.api as sm from statsmodels.miscmodels.count import PoissonGMLE, PoissonOffsetGMLE, \ PoissonZiGMLE from statsmodels.discrete.discrete_model import Poisson from statsmodels.tools.sm_exceptions import ValueWarning DEC = 4 DEC4 = 4 DEC5 = 5 class CompareMixin(object): def test_params(self): assert_almost_equal(self.res.params, self.res_glm.params, DEC5) assert_almost_equal(self.res.params, self.res_discrete.params, DEC5) def test_cov_params(self): assert_almost_equal(self.res.bse, self.res_glm.bse, DEC5) assert_almost_equal(self.res.bse, self.res_discrete.bse, DEC5) #TODO check problem with the following, precision is low, #dof error? last t-value is 22, 23, error is around 1% for PoissonMLE #this was with constant=1, #now changed constant=0.1 to make it less significant and test passes #overall precision for tstat looks like 1% #assert_almost_equal(self.res.tval, self.res_glm.t(), DEC) assert_almost_equal(self.res.tvalues, self.res_discrete.tvalues, DEC4) #assert_almost_equal(self.res.params, self.res_discrete.params) assert_almost_equal(self.res.pvalues, self.res_discrete.pvalues, DEC) def test_ttest(self): tt = self.res.t_test(np.eye(len(self.res.params))) from scipy import stats pvalue = stats.norm.sf(np.abs(tt.tvalue)) * 2 assert_almost_equal(tt.tvalue, self.res.tvalues, DEC) assert_almost_equal(pvalue, self.res.pvalues, DEC) @pytest.mark.smoke def test_summary(self): self.res.summary() class TestPoissonMLE(CompareMixin): @classmethod def setup_class(cls): # generate artificial data np.random.seed(98765678) nobs = 200 rvs = np.random.randn(nobs,6) data_exog = rvs data_exog = sm.add_constant(data_exog, prepend=False) xbeta = 0.1 + 0.1*rvs.sum(1) data_endog = np.random.poisson(np.exp(xbeta)) #estimate discretemod.Poisson as benchmark cls.res_discrete = Poisson(data_endog, data_exog).fit(disp=0) mod_glm = sm.GLM(data_endog, data_exog, family=sm.families.Poisson()) cls.res_glm = mod_glm.fit() #estimate generic MLE cls.mod = PoissonGMLE(data_endog, data_exog) cls.res = cls.mod.fit(start_params=0.9 * cls.res_discrete.params, method='bfgs', disp=0) def test_predict_distribution(self): res = self.res model = self.mod with pytest.raises(ValueError): # No "result" attribute model.predict_distribution(model.exog) try: model.result = res dist = model.predict_distribution(model.exog) assert isinstance(dist, stats._distn_infrastructure.rv_frozen) assert_almost_equal(dist.mean(), np.exp(model.exog.dot(res.params)), 15) finally: # leave the model object how we found it model.__delattr__("result") class TestPoissonOffset(CompareMixin): #this uses the first exog to construct an offset variable @classmethod def setup_class(cls): # generate artificial data np.random.seed(98765678) nobs = 200 rvs = np.random.randn(nobs,6) data_exog = rvs data_exog = sm.add_constant(data_exog, prepend=False) xbeta = 1 + 0.1*rvs.sum(1) data_endog = np.random.poisson(np.exp(xbeta)) mod_glm = sm.GLM(data_endog, data_exog, family=sm.families.Poisson()) cls.res_glm = mod_glm.fit() #estimate generic MLE #cls.mod = PoissonGMLE(data_endog, data_exog) #res = cls.mod.fit() #create offset variable based on first exog cls.res_discrete = Poisson(data_endog, data_exog).fit(disp=0) offset = cls.res_discrete.params[0] * data_exog[:,0] #1d ??? #estimate discretemod.Poisson as benchmark, now has offset cls.res_discrete = Poisson(data_endog, data_exog[:,1:], offset=offset).fit(disp=0) mod_glm = sm.GLM(data_endog, data_exog, family=sm.families.Poisson()) cls.res_glm = mod_glm.fit() #cls.res = PoissonOffsetGMLE(data_endog, data_exog[:,1:], offset=offset).fit(start_params = np.ones(6)/2., method='nm') modo = PoissonOffsetGMLE(data_endog, data_exog[:,1:], offset=offset) cls.res = modo.fit(start_params = 0.9*cls.res_discrete.params, method='bfgs', disp=0) def test_params(self): assert_almost_equal(self.res.params, self.res_glm.params[1:], DEC) assert_almost_equal(self.res.params, self.res_discrete.params, DEC) def test_cov_params(self): assert_almost_equal(self.res.bse, self.res_glm.bse[1:], DEC-1) assert_almost_equal(self.res.bse, self.res_discrete.bse, DEC5) #precision of next is very low ??? #assert_almost_equal(self.res.tval, self.res_glm.t()[1:], DEC) #assert_almost_equal(self.res.params, self.res_discrete.params) #DEC = DEC - 1 class TestPoissonZi(CompareMixin): #this uses the first exog to construct an offset variable @classmethod def setup_class(cls): # generate artificial data np.random.seed(98765678) nobs = 200 rvs = np.random.randn(nobs,6) data_exog = rvs data_exog = sm.add_constant(data_exog, prepend=False) xbeta = 1 + 0.1*rvs.sum(1) data_endog = np.random.poisson(np.exp(xbeta)) mod_glm = sm.GLM(data_endog, data_exog, family=sm.families.Poisson()) cls.res_glm = mod_glm.fit() #estimate generic MLE #cls.mod = PoissonGMLE(data_endog, data_exog) #res = cls.mod.fit() #create offset variable based on first exog cls.res_discrete = Poisson(data_endog, data_exog).fit(disp=0) offset = cls.res_discrete.params[0] * data_exog[:,0] #1d ??? #estimate discretemod.Poisson as benchmark, now has offset cls.res_discrete = Poisson(data_endog, data_exog[:,1:], offset=offset).fit(disp=0) # Note : ZI has one extra parameter cls.res = PoissonZiGMLE(data_endog, data_exog[:,1:], offset=offset).fit( start_params=np.r_[0.9*cls.res_discrete.params,10], method='bfgs', disp=0) cls.decimal = 4 def test_params(self): assert_almost_equal(self.res.params[:-1], self.res_glm.params[1:], self.decimal) assert_almost_equal(self.res.params[:-1], self.res_discrete.params, self.decimal) def test_cov_params(self): #skip until I have test with zero-inflated data #use bsejac for now since it seems to work assert_almost_equal(self.res.bsejac[:-1], self.res_glm.bse[1:], self.decimal-2) assert_almost_equal(self.res.bsejac[:-1], self.res_discrete.bse, self.decimal-2) #assert_almost_equal(self.res.tval[:-1], self.res_glm.t()[1:], self.decimal) def test_exog_names_warning(self): mod = self.res.model mod1 = PoissonOffsetGMLE(mod.endog, mod.exog, offset=mod.offset) from numpy.testing import assert_warns mod1.data.xnames = mod1.data.xnames * 2 assert_warns(ValueWarning, mod1.fit, disp=0) statsmodels-0.12.2/statsmodels/miscmodels/tests/test_tarma.py000066400000000000000000000103241400612667500245250ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Thu Jul 04 23:44:33 2013 Author: Josef Perktold """ from functools import partial import numpy as np import pytest from numpy.testing import assert_allclose from statsmodels.miscmodels.tmodel import TArma from statsmodels.tsa.arima_process import arma_generate_sample from statsmodels.tsa.arma_mle import Arma class CheckTArmaMixin(object): def test_params(self): attrs = ['params', 'bse', 'tvalues', 'pvalues', 'bsejhj', 'bsejac'] for row, attr in enumerate(attrs): assert_allclose(getattr(self.res, attr), self.res1_table[row], atol=1e-4, rtol=1e-3) assert_allclose(self.res.conf_int(), self.res1_conf_int, atol=1e-4, rtol=1e-3) @pytest.mark.smoke def test_smoke(self): # TODO: break into well-scoped tests self.res.summary() rmat = np.eye(len(self.res.params)) self.res.t_test(rmat) self.res.f_test(rmat) def test_fit_ls(self): assert_allclose(self.res_ls[0], self.ls_params, atol=1e-4, rtol=1e-3) self.res_ls[1] # this is bse unscaled I think bse = np.sqrt(np.diag(self.res_ls[1])) assert_allclose(bse, self.ls_bse, atol=1e-4, rtol=1e-3) class TestTArma(CheckTArmaMixin): # regression test for TArma @classmethod def setup_class(cls): nobs = 500 ar = [1, -0.5, 0.1] ma = [1, 0.7] dist = partial(np.random.standard_t, 3) np.random.seed(8659567) x = arma_generate_sample(ar, ma, nobs, scale=1, distrvs=dist, burnin=500) mod = TArma(x) order = (2, 1) cls.res_ls = mod.fit(order=order) cls.res = mod.fit_mle(order=order, start_params=np.r_[cls.res_ls[0], 5, 1], method='nm', disp=False) cls.res1_table = np.array( [[0.46157133, -0.07694534, 0.70051876, 2.88693312, 0.97283396], [0.04957594, 0.04345499, 0.03492473, 0.40854823, 0.05568439], [9.31038915, -1.77069050, 20.05795605, 7.06632146, 17.47049812], [0.00000000, 0.07661218, 0.00000000, 0.00000000, 0.00000000], [0.05487968, 0.04213054, 0.03102404, 0.37860956, 0.05228474], [0.04649728, 0.04569133, 0.03990779, 0.44315449, 0.05996759]]) cls.res1_conf_int = np.array([[0.36440426, 0.55873839], [-0.16211556, 0.00822488], [0.63206754, 0.76896998], [2.08619331, 3.68767294], [0.86369457, 1.08197335]]) cls.ls_params = np.array([0.43393123, -0.08402678, 0.73293058]) cls.ls_bse = np.array([0.03777410, 0.03567847, 0.02744488]) class TestArma(CheckTArmaMixin): # regression test for TArma @classmethod def setup_class(cls): nobs = 500 ar = [1, -0.5, 0.1] ma = [1, 0.7] dist = partial(np.random.standard_t, 3) np.random.seed(8659567) x = arma_generate_sample(ar, ma, nobs, scale=1, distrvs=dist, burnin=500) mod = Arma(x) order = (2, 1) cls.res_ls = mod.fit(order=order) cls.res = mod.fit_mle(order=order, start_params=np.r_[cls.res_ls[0], 1], method='nm', disp=False) cls.res1_table = np.array( [[0.43390720, -0.08402653, 0.73292344, 1.61661128], [0.05854268, 0.055629410, 0.04034178, 0.05112070], [7.41181020, -1.51046975, 18.16785075, 31.62341666], [0.00000000, 0.130923600, 0.00000000, 0.00000000], [0.06713617, 0.054691380, 0.03785006, 0.10710930], [0.05504093, 0.057484900, 0.04350945, 0.02510928]]) cls.res1_conf_int = np.array([[0.31916567, 0.54864874], [-0.19305817, 0.02500510], [0.65385501, 0.81199188], [1.51641655, 1.71680602]]) cls.ls_params = np.array([0.43393123, -0.08402678, 0.73293058]) cls.ls_bse = np.array([0.0377741, 0.03567847, 0.02744488]) statsmodels-0.12.2/statsmodels/miscmodels/tests/test_tmodel.py000066400000000000000000000161761400612667500247200ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Jun 30 20:25:22 2013 Author: Josef Perktold """ import pytest import numpy as np from numpy.testing import assert_allclose from statsmodels.tools.tools import add_constant from statsmodels.tools.testing import Holder from statsmodels.miscmodels.tmodel import TLinearModel mm = Holder() mm.date_label = ["Apr.1982", "Apr.1983", "Apr.1984", "Apr.1985", "Apr.1986", "Aug.1982", "Aug.1983", "Aug.1984", "Aug.1985", "Aug.1986", "Dec.1982", "Dec.1983", "Dec.1984", "Dec.1985", "Dec.1986", "Feb.1284", "Feb.1982", "Feb.1983", "Feb.1985", "Feb.1986", "Jan.1982", "Jan.1983", "Jan.1984", "Jan.1985", "Jan.1986", "Jul.1982", "July1983", "July1984", "July1985", "July1986", "June1982", "June1983", "June1984", "June1985", "June1986", "Mar.1982", "Mar.1983", "Mar.1984", "Mar.1985", "Mar.1986", "May1982", "May1983", "May1984", "May1985", "May1986", "Nov.1982", "Nov.1983", "Nov.1984", "Nov.1985", "Nov.1986", "Oct.1982", "Oct.1983", "Oct.1984", "Oct.1985", "Oct.1986", "Sept.1982", "Sept.1983", "Sept.1984", "Sept.1985", "Sept.1986"] mm.m_marietta = np.array([ -0.1365, -0.0769, -0.0575, 0.0526, -0.0449, -0.0859, -0.0742, 0.6879, -0.077, 0.085, 0.003, 0.0754, -0.0412, -0.089, 0.2319, 0.1087, 0.0375, 0.0958, 0.0174, -0.0724, 0.075, -0.0588, -0.062, -0.0378, 0.0169, -0.0799, -0.0147, 0.0106, -0.0421, -0.0036, 0.0876, 0.1025, -0.0499, 0.1953, -0.0714, 0.0469, 0.1311, 0.0461, -0.0328, -0.0096, 0.1272, -0.0077, 0.0165, -0.015, -0.1479, -0.0065, 0.039, 0.0223, -0.069, 0.1338, 0.1458, 0.0063, 0.0692, -0.0239, -0.0568, 0.0814, -0.0889, -0.0887, 0.1037, -0.1163 ]) mm.CRSP = np.array([ -0.03, -0.0584, -0.0181, 0.0306, -0.0397, -0.0295, -0.0316, 0.1176, 0.0075, 0.1098, 0.0408, 0.0095, 0.0301, 0.0221, 0.0269, 0.0655, -0.003, 0.0325, -0.0374, 0.0049, 0.0105, -0.0257, 0.0186, -0.0155, -0.0165, -0.044, 0.0094, -0.0028, -0.0591, 0.0158, -0.0238, 0.1031, -0.0065, -0.0067, -0.0167, 0.0188, 0.0733, 0.0105, -0.007, -0.0099, 0.0521, 0.0117, -0.0099, -0.0102, -0.0428, 0.0376, 0.0628, 0.0391, 2e-04, 0.0688, 0.0486, -0.0174, 0.046, 0.01, -0.0594, 0.068, -0.0839, 0.0481, 0.0136, -0.0322 ]) mm.am_can = np.array([ -0.0596, -0.17, 0.0276, 0.0058, -0.0106, 0.045, -0.0243, 0.1135, -0.0331, 0.0468, -0.0223, -0.0026, 0.0166, 0.0343, 0.0443, 0.1477, 0.1728, -0.0372, -0.0451, -0.0257, 0.0509, 0.0035, 0.1334, -0.0458, 0.1199, -0.0766, -0.0511, -0.0194, -0.0687, 0.0928, -0.0704, 0.0905, 0.0232, -0.0054, 0.0082, 0.0242, 0.0153, 0.0016, 0.028, 0.0088, 0.0734, 0.0315, -0.0276, 0.0162, -0.0975, 0.0563, 0.1368, -0.069, 0.1044, 0.1636, -0.019, -0.0746, 0.0433, 0.0306, 0.0636, 0.0917, -0.0796, 0.0778, -0.0353, -0.0137 ]) mm.date = np.array([ 21, 17, 36, 1, 41, 31, 26, 6, 56, 51, 46, 11, 22, 18, 37, 2, 42, 32, 27, 7, 57, 52, 47, 12, 23, 16, 38, 3, 43, 33, 28, 8, 58, 53, 48, 13, 24, 19, 39, 4, 44, 34, 29, 9, 59, 54, 49, 14, 25, 20, 40, 5, 45, 35, 30, 10, 60, 55, 50, 15 ]) class CheckTLinearModelMixin(object): def test_basic(self): res1 = self.res1 res2 = self.res2 # location assert_allclose(res1.params[:-2], res2.loc_fit.coefficients, atol=3e-5) assert_allclose(res1.bse[:-2], res2.loc_fit.table[:, 1], rtol=0.003, atol=1e-5) assert_allclose(res1.tvalues[:-2], res2.loc_fit.table[:, 2], rtol=0.003, atol=1e-5) assert_allclose(res1.pvalues[:-2], res2.loc_fit.table[:, 3], rtol=0.009, atol=1e-5) # df assert_allclose(res1.params[-2], res2.dof, rtol=5e-5) assert_allclose(res1.bse[-2], res2.dofse, rtol=0.16, atol=1e-5) # scale scale_est = np.sqrt(res2.scale_fit.fitted_values.mean()) assert_allclose(res1.params[-1], scale_est, atol=1e-5) assert_allclose(res1.llf, res2.logLik, atol=1e-5) def test_bse(self): # check that they are roughly the same res1 = self.res1 assert_allclose(res1.bsejac, res1.bse, rtol=0.15, atol=0.002) assert_allclose(res1.bsejac, res1.bse, rtol=0.1, atol=0.004) def test_fitted(self): res1 = self.res1 res2 = self.res2 fittedvalues = res1.predict() resid = res1.model.endog - fittedvalues assert_allclose(fittedvalues, res2.loc_fit.fitted_values, rtol=0.00025) assert_allclose(resid, res2.loc_fit.residuals, atol=2e-6) #rtol=0.00036) #TODO: no resid available as attribute #assert_allclose(res1.resid, res2.loc_fit.residuals) #assert_allclose(res1.fittedvalues, res2.loc_fit.fitted_values) def test_formula(self): res1 = self.res1 resf = self.resf # converges slightly differently why? assert_allclose(res1.params, resf.params, atol=1e-4) #rtol=2e-5, assert_allclose(res1.bse, resf.bse, rtol=5e-5) assert_allclose(res1.model.endog, resf.model.endog, rtol=1e-10) assert_allclose(res1.model.exog, resf.model.exog, rtol=1e-10) @pytest.mark.smoke def test_smoke(self): # TODO: break into well-scoped tests res1 = self.res1 resf = self.resf contr = np.eye(len(res1.params)) # smoke test for summary and t_test, f_test res1.summary() res1.t_test(contr) res1.f_test(contr) resf.summary() resf.t_test(contr) resf.f_test(contr) class TestTModel(CheckTLinearModelMixin): @classmethod def setup_class(cls): endog = mm.m_marietta exog = add_constant(mm.CRSP) mod = TLinearModel(endog, exog) res = mod.fit(method='bfgs', disp=False) modf = TLinearModel.from_formula("price ~ CRSP", data={"price":mm.m_marietta, "CRSP":mm.CRSP}) resf = modf.fit(method='bfgs', disp=False) from .results_tmodel import res_t_dfest as res2 cls.res2 = res2 cls.res1 = res # take from module scope temporarily cls.resf = resf class TestTModelFixed(object): @classmethod def setup_class(cls): endog = mm.m_marietta exog = add_constant(mm.CRSP) mod = TLinearModel(endog, exog, fix_df=3) res = mod.fit(method='bfgs', disp=False) modf = TLinearModel.from_formula("price ~ CRSP", data={"price":mm.m_marietta, "CRSP":mm.CRSP}, fix_df=3) resf = modf.fit(method='bfgs', disp=False) #TODO: no reference results yet #from results_tmodel import res_t_dfest as res2 #cls.res2 = res2 cls.res1 = res # take from module scope temporarily cls.resf = resf @pytest.mark.smoke def test_smoke(self): # TODO: break into well-scoped tests res1 = self.res1 resf = self.resf contr = np.eye(len(res1.params)) # smoke test for summary and t_test, f_test res1.summary() res1.t_test(contr) res1.f_test(contr) resf.summary() resf.t_test(contr) resf.f_test(contr) statsmodels-0.12.2/statsmodels/miscmodels/tmodel.py000066400000000000000000000156751400612667500225220ustar00rootroot00000000000000"""Linear Model with Student-t distributed errors Because the t distribution has fatter tails than the normal distribution, it can be used to model observations with heavier tails and observations that have some outliers. For the latter case, the t-distribution provides more robust estimators for mean or mean parameters (what about var?). References ---------- Kenneth L. Lange, Roderick J. A. Little, Jeremy M. G. Taylor (1989) Robust Statistical Modeling Using the t Distribution Journal of the American Statistical Association Vol. 84, No. 408 (Dec., 1989), pp. 881-896 Published by: American Statistical Association Stable URL: http://www.jstor.org/stable/2290063 not read yet Created on 2010-09-24 Author: josef-pktd License: BSD TODO ---- * add starting values based on OLS * bugs: store_params does not seem to be defined, I think this was a module global for debugging - commented out * parameter restriction: check whether version with some fixed parameters works """ #mostly copied from the examples directory written for trying out generic mle. import numpy as np from scipy import special, stats from statsmodels.base.model import GenericLikelihoodModel from statsmodels.tsa.arma_mle import Arma #redefine some shortcuts np_log = np.log np_pi = np.pi sps_gamln = special.gammaln class TLinearModel(GenericLikelihoodModel): '''Maximum Likelihood Estimation of Linear Model with t-distributed errors This is an example for generic MLE. Except for defining the negative log-likelihood method, all methods and results are generic. Gradients and Hessian and all resulting statistics are based on numerical differentiation. ''' def initialize(self): # TODO: here or in __init__ self.k_vars = self.exog.shape[1] if not hasattr(self, 'fix_df'): self.fix_df = False if self.fix_df is False: # df will be estimated, no parameter restrictions self.fixed_params = None self.fixed_paramsmask = None self.k_params = self.exog.shape[1] + 2 extra_params_names = ['df', 'scale'] else: # df fixed self.k_params = self.exog.shape[1] + 1 fixdf = np.nan * np.zeros(self.exog.shape[1] + 2) fixdf[-2] = self.fix_df self.fixed_params = fixdf self.fixed_paramsmask = np.isnan(fixdf) extra_params_names = ['scale'] self._set_extra_params_names(extra_params_names) self._set_start_params() super(TLinearModel, self).initialize() def _set_start_params(self, start_params=None, use_kurtosis=False): if start_params is not None: self.start_params = start_params else: from statsmodels.regression.linear_model import OLS res_ols = OLS(self.endog, self.exog).fit() start_params = 0.1*np.ones(self.k_params) start_params[:self.k_vars] = res_ols.params if self.fix_df is False: if use_kurtosis: kurt = stats.kurtosis(res_ols.resid) df = 6./kurt + 4 else: df = 5 start_params[-2] = df #TODO adjust scale for df start_params[-1] = np.sqrt(res_ols.scale) self.start_params = start_params def loglike(self, params): return -self.nloglikeobs(params).sum(0) def nloglikeobs(self, params): """ Loglikelihood of linear model with t distributed errors. Parameters ---------- params : ndarray The parameters of the model. The last 2 parameters are degrees of freedom and scale. Returns ------- loglike : ndarray The log likelihood of the model evaluated at `params` for each observation defined by self.endog and self.exog. Notes ----- .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right] The t distribution is the standard t distribution and not a standardized t distribution, which means that the scale parameter is not equal to the standard deviation. self.fixed_params and self.expandparams can be used to fix some parameters. (I doubt this has been tested in this model.) """ #print len(params), #store_params.append(params) if self.fixed_params is not None: #print 'using fixed' params = self.expandparams(params) beta = params[:-2] df = params[-2] scale = np.abs(params[-1]) #TODO check behavior around zero loc = np.dot(self.exog, beta) endog = self.endog x = (endog - loc)/scale #next part is stats.t._logpdf lPx = sps_gamln((df+1)/2) - sps_gamln(df/2.) lPx -= 0.5*np_log(df*np_pi) + (df+1)/2.*np_log(1+(x**2)/df) lPx -= np_log(scale) # correction for scale return -lPx def predict(self, params, exog=None): if exog is None: exog = self.exog return np.dot(exog, params[:self.exog.shape[1]]) class TArma(Arma): '''Univariate Arma Model with t-distributed errors This inherit all methods except loglike from tsa.arma_mle.Arma This uses the standard t-distribution, the implied variance of the error is not equal to scale, but :: error_variance = df/(df-2)*scale**2 Notes ----- This might be replaced by a standardized t-distribution with scale**2 equal to variance ''' def loglike(self, params): return -self.nloglikeobs(params).sum(0) #add for Jacobian calculation bsejac in GenericMLE, copied from loglike def nloglikeobs(self, params): """ Loglikelihood for arma model for each observation, t-distribute Notes ----- The ancillary parameter is assumed to be the last element of the params vector """ errorsest = self.geterrors(params[:-2]) #sigma2 = np.maximum(params[-1]**2, 1e-6) #do I need this #axis = 0 #nobs = len(errorsest) df = params[-2] scale = np.abs(params[-1]) llike = - stats.t._logpdf(errorsest/scale, df) + np_log(scale) return llike #TODO rename fit_mle -> fit, fit -> fit_ls def fit_mle(self, order, start_params=None, method='nm', maxiter=5000, tol=1e-08, **kwds): nar, nma = order if start_params is not None: if len(start_params) != nar + nma + 2: raise ValueError('start_param need sum(order) + 2 elements') else: start_params = np.concatenate((0.05*np.ones(nar + nma), [5, 1])) res = super(TArma, self).fit_mle(order=order, start_params=start_params, method=method, maxiter=maxiter, tol=tol, **kwds) return res statsmodels-0.12.2/statsmodels/miscmodels/try_mlecov.py000066400000000000000000000154771400612667500234210ustar00rootroot00000000000000'''Multivariate Normal Model with full covariance matrix toeplitz structure is not exploited, need cholesky or inv for toeplitz Author: josef-pktd ''' import numpy as np from scipy import linalg from scipy.linalg import toeplitz import statsmodels.api as sm from statsmodels.base.model import GenericLikelihoodModel from statsmodels.tsa.arima_process import ( arma_acovf, arma_generate_sample, ArmaProcess ) def mvn_loglike_sum(x, sigma): '''loglike multivariate normal copied from GLS and adjusted names not sure why this differes from mvn_loglike ''' nobs = len(x) nobs2 = nobs / 2.0 SSR = (x**2).sum() llf = -np.log(SSR) * nobs2 # concentrated likelihood llf -= (1+np.log(np.pi/nobs2))*nobs2 # with likelihood constant if np.any(sigma) and sigma.ndim == 2: #FIXME: robust-enough check? unneeded if _det_sigma gets defined llf -= .5*np.log(np.linalg.det(sigma)) return llf def mvn_loglike(x, sigma): '''loglike multivariate normal assumes x is 1d, (nobs,) and sigma is 2d (nobs, nobs) brute force from formula no checking of correct inputs use of inv and log-det should be replace with something more efficient ''' #see numpy thread #Sturla: sqmahal = (cx*cho_solve(cho_factor(S),cx.T).T).sum(axis=1) sigmainv = linalg.inv(sigma) logdetsigma = np.log(np.linalg.det(sigma)) nobs = len(x) llf = - np.dot(x, np.dot(sigmainv, x)) llf -= nobs * np.log(2 * np.pi) llf -= logdetsigma llf *= 0.5 return llf def mvn_loglike_chol(x, sigma): '''loglike multivariate normal assumes x is 1d, (nobs,) and sigma is 2d (nobs, nobs) brute force from formula no checking of correct inputs use of inv and log-det should be replace with something more efficient ''' #see numpy thread #Sturla: sqmahal = (cx*cho_solve(cho_factor(S),cx.T).T).sum(axis=1) sigmainv = np.linalg.inv(sigma) cholsigmainv = np.linalg.cholesky(sigmainv).T x_whitened = np.dot(cholsigmainv, x) logdetsigma = np.log(np.linalg.det(sigma)) nobs = len(x) from scipy import stats print('scipy.stats') print(np.log(stats.norm.pdf(x_whitened)).sum()) llf = - np.dot(x_whitened.T, x_whitened) llf -= nobs * np.log(2 * np.pi) llf -= logdetsigma llf *= 0.5 return llf, logdetsigma, 2 * np.sum(np.log(np.diagonal(cholsigmainv))) #0.5 * np.dot(x_whitened.T, x_whitened) + nobs * np.log(2 * np.pi) + logdetsigma) def mvn_nloglike_obs(x, sigma): '''loglike multivariate normal assumes x is 1d, (nobs,) and sigma is 2d (nobs, nobs) brute force from formula no checking of correct inputs use of inv and log-det should be replace with something more efficient ''' #see numpy thread #Sturla: sqmahal = (cx*cho_solve(cho_factor(S),cx.T).T).sum(axis=1) #Still wasteful to calculate pinv first sigmainv = np.linalg.inv(sigma) cholsigmainv = np.linalg.cholesky(sigmainv).T #2 * np.sum(np.log(np.diagonal(np.linalg.cholesky(A)))) #Dag mailinglist # logdet not needed ??? #logdetsigma = 2 * np.sum(np.log(np.diagonal(cholsigmainv))) x_whitened = np.dot(cholsigmainv, x) #sigmainv = linalg.cholesky(sigma) logdetsigma = np.log(np.linalg.det(sigma)) sigma2 = 1. # error variance is included in sigma llike = 0.5 * (np.log(sigma2) - 2.* np.log(np.diagonal(cholsigmainv)) + (x_whitened**2)/sigma2 + np.log(2*np.pi)) return llike def invertibleroots(ma): proc = ArmaProcess(ma=ma) return proc.invertroots(retnew=False) def getpoly(self, params): ar = np.r_[[1], -params[:self.nar]] ma = np.r_[[1], params[-self.nma:]] import numpy.polynomial as poly return poly.Polynomial(ar), poly.Polynomial(ma) class MLEGLS(GenericLikelihoodModel): '''ARMA model with exact loglikelhood for short time series Inverts (nobs, nobs) matrix, use only for nobs <= 200 or so. This class is a pattern for small sample GLS-like models. Intended use for loglikelihood of initial observations for ARMA. TODO: This might be missing the error variance. Does it assume error is distributed N(0,1) Maybe extend to mean handling, or assume it is already removed. ''' def _params2cov(self, params, nobs): '''get autocovariance matrix from ARMA regression parameter ar parameters are assumed to have rhs parameterization ''' ar = np.r_[[1], -params[:self.nar]] ma = np.r_[[1], params[-self.nma:]] #print('ar', ar #print('ma', ma #print('nobs', nobs autocov = arma_acovf(ar, ma, nobs=nobs) #print('arma_acovf(%r, %r, nobs=%d)' % (ar, ma, nobs) #print(autocov.shape #something is strange fixed in aram_acovf autocov = autocov[:nobs] sigma = toeplitz(autocov) return sigma def loglike(self, params): sig = self._params2cov(params[:-1], self.nobs) sig = sig * params[-1]**2 loglik = mvn_loglike(self.endog, sig) return loglik def fit_invertible(self, *args, **kwds): res = self.fit(*args, **kwds) ma = np.r_[[1], res.params[self.nar: self.nar+self.nma]] mainv, wasinvertible = invertibleroots(ma) if not wasinvertible: start_params = res.params.copy() start_params[self.nar: self.nar+self.nma] = mainv[1:] #need to add args kwds res = self.fit(start_params=start_params) return res if __name__ == '__main__': nobs = 50 ar = [1.0, -0.8, 0.1] ma = [1.0, 0.1, 0.2] #ma = [1] np.random.seed(9875789) y = arma_generate_sample(ar,ma,nobs,2) y -= y.mean() #I have not checked treatment of mean yet, so remove mod = MLEGLS(y) mod.nar, mod.nma = 2, 2 #needs to be added, no init method mod.nobs = len(y) res = mod.fit(start_params=[0.1, -0.8, 0.2, 0.1, 1.]) print('DGP', ar, ma) print(res.params) from statsmodels.regression import yule_walker print(yule_walker(y, 2)) #resi = mod.fit_invertible(start_params=[0.1,0,0.2,0, 0.5]) #print(resi.params arpoly, mapoly = getpoly(mod, res.params[:-1]) data = sm.datasets.sunspots.load(as_pandas=False) #ys = data.endog[-100:] ## ys = data.endog[12:]-data.endog[:-12] ## ys -= ys.mean() ## mods = MLEGLS(ys) ## mods.nar, mods.nma = 13, 1 #needs to be added, no init method ## mods.nobs = len(ys) ## ress = mods.fit(start_params=np.r_[0.4, np.zeros(12), [0.2, 5.]],maxiter=200) ## print(ress.params ## import matplotlib.pyplot as plt ## plt.plot(data.endog[1]) ## #plt.show() sigma = mod._params2cov(res.params[:-1], nobs) * res.params[-1]**2 print(mvn_loglike(y, sigma)) llo = mvn_nloglike_obs(y, sigma) print(llo.sum(), llo.shape) print(mvn_loglike_chol(y, sigma)) print(mvn_loglike_sum(y, sigma)) statsmodels-0.12.2/statsmodels/multivariate/000077500000000000000000000000001400612667500212155ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/multivariate/__init__.py000066400000000000000000000001131400612667500233210ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/multivariate/api.py000066400000000000000000000003651400612667500223440ustar00rootroot00000000000000__all__ = [ "PCA", "MANOVA", "Factor", "FactorResults", "CanCorr", "factor_rotation" ] from .pca import PCA from .manova import MANOVA from .factor import Factor, FactorResults from .cancorr import CanCorr from . import factor_rotation statsmodels-0.12.2/statsmodels/multivariate/cancorr.py000066400000000000000000000134571400612667500232300ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Canonical correlation analysis author: Yichuan Liu """ import numpy as np from numpy.linalg import svd import scipy import pandas as pd from statsmodels.base.model import Model from statsmodels.iolib import summary2 from .multivariate_ols import multivariate_stats class CanCorr(Model): """ Canonical correlation analysis using singular value decomposition For matrices exog=x and endog=y, find projections x_cancoef and y_cancoef such that: x1 = x * x_cancoef, x1' * x1 is identity matrix y1 = y * y_cancoef, y1' * y1 is identity matrix and the correlation between x1 and y1 is maximized. Attributes ---------- endog : ndarray See Parameters. exog : ndarray See Parameters. cancorr : ndarray The canonical correlation values y_cancoeff : ndarray The canonical coefficients for endog x_cancoeff : ndarray The canonical coefficients for exog References ---------- .. [*] http://numerical.recipes/whp/notes/CanonCorrBySVD.pdf .. [*] http://www.csun.edu/~ata20315/psy524/docs/Psy524%20Lecture%208%20CC.pdf .. [*] http://www.mathematica-journal.com/2014/06/canonical-correlation-analysis/ """ # noqa:E501 def __init__(self, endog, exog, tolerance=1e-8, missing='none', hasconst=None, **kwargs): super(CanCorr, self).__init__(endog, exog, missing=missing, hasconst=hasconst, **kwargs) self._fit(tolerance) def _fit(self, tolerance=1e-8): """Fit the model A ValueError is raised if there are singular values smaller than the tolerance. The treatment of singular arrays might change in future. Parameters ---------- tolerance : float eigenvalue tolerance, values smaller than which is considered 0 """ nobs, k_yvar = self.endog.shape nobs, k_xvar = self.exog.shape k = np.min([k_yvar, k_xvar]) x = np.array(self.exog) x = x - x.mean(0) y = np.array(self.endog) y = y - y.mean(0) ux, sx, vx = svd(x, 0) # vx_ds = vx.T divided by sx vx_ds = vx.T mask = sx > tolerance if mask.sum() < len(mask): raise ValueError('exog is collinear.') vx_ds[:, mask] /= sx[mask] uy, sy, vy = svd(y, 0) # vy_ds = vy.T divided by sy vy_ds = vy.T mask = sy > tolerance if mask.sum() < len(mask): raise ValueError('endog is collinear.') vy_ds[:, mask] /= sy[mask] u, s, v = svd(ux.T.dot(uy), 0) # Correct any roundoff self.cancorr = np.array([max(0, min(s[i], 1)) for i in range(len(s))]) self.x_cancoef = vx_ds.dot(u[:, :k]) self.y_cancoef = vy_ds.dot(v.T[:, :k]) def corr_test(self): """Approximate F test Perform multivariate statistical tests of the hypothesis that there is no canonical correlation between endog and exog. For each canonical correlation, testing its significance based on Wilks' lambda. Returns ------- CanCorrTestResults instance """ nobs, k_yvar = self.endog.shape nobs, k_xvar = self.exog.shape eigenvals = np.power(self.cancorr, 2) stats = pd.DataFrame(columns=['Canonical Correlation', "Wilks' lambda", 'Num DF','Den DF', 'F Value','Pr > F'], index=list(range(len(eigenvals) - 1, -1, -1))) prod = 1 for i in range(len(eigenvals) - 1, -1, -1): prod *= 1 - eigenvals[i] p = k_yvar - i q = k_xvar - i r = (nobs - k_yvar - 1) - (p - q + 1) / 2 u = (p * q - 2) / 4 df1 = p * q if p ** 2 + q ** 2 - 5 > 0: t = np.sqrt(((p * q) ** 2 - 4) / (p ** 2 + q ** 2 - 5)) else: t = 1 df2 = r * t - 2 * u lmd = np.power(prod, 1 / t) F = (1 - lmd) / lmd * df2 / df1 stats.loc[i, 'Canonical Correlation'] = self.cancorr[i] stats.loc[i, "Wilks' lambda"] = prod stats.loc[i, 'Num DF'] = df1 stats.loc[i, 'Den DF'] = df2 stats.loc[i, 'F Value'] = F pval = scipy.stats.f.sf(F, df1, df2) stats.loc[i, 'Pr > F'] = pval ''' # Wilk's Chi square test of each canonical correlation df = (p - i + 1) * (q - i + 1) chi2 = a * np.log(prod) pval = stats.chi2.sf(chi2, df) stats.loc[i, 'Canonical correlation'] = self.cancorr[i] stats.loc[i, 'Chi-square'] = chi2 stats.loc[i, 'DF'] = df stats.loc[i, 'Pr > ChiSq'] = pval ''' ind = stats.index.values[::-1] stats = stats.loc[ind, :] # Multivariate tests (remember x has mean removed) stats_mv = multivariate_stats(eigenvals, k_yvar, k_xvar, nobs - k_xvar - 1) return CanCorrTestResults(stats, stats_mv) class CanCorrTestResults(object): """ Canonical correlation results class Attributes ---------- stats : DataFrame Contain statistical tests results for each canonical correlation stats_mv : DataFrame Contain the multivariate statistical tests results """ def __init__(self, stats, stats_mv): self.stats = stats self.stats_mv = stats_mv def __str__(self): return self.summary().__str__() def summary(self): summ = summary2.Summary() summ.add_title('Cancorr results') summ.add_df(self.stats) summ.add_dict({'': ''}) summ.add_dict({'Multivariate Statistics and F Approximations': ''}) summ.add_df(self.stats_mv) return summ statsmodels-0.12.2/statsmodels/multivariate/factor.py000066400000000000000000001051671400612667500230570ustar00rootroot00000000000000# -*- coding: utf-8 -*- import warnings import numpy as np from numpy.linalg import eigh, inv, norm, matrix_rank import pandas as pd from scipy.optimize import minimize from statsmodels.tools.decorators import cache_readonly from statsmodels.base.model import Model from statsmodels.iolib import summary2 from statsmodels.graphics.utils import _import_mpl from .factor_rotation import rotate_factors, promax _opt_defaults = {'gtol': 1e-7} def _check_args_1(endog, n_factor, corr, nobs): msg = "Either endog or corr must be provided." if endog is not None and corr is not None: raise ValueError(msg) if endog is None and corr is None: warnings.warn('Both endog and corr are provided, ' + 'corr will be used for factor analysis.') if n_factor <= 0: raise ValueError('n_factor must be larger than 0! %d < 0' % (n_factor)) if nobs is not None and endog is not None: warnings.warn("nobs is ignored when endog is provided") def _check_args_2(endog, n_factor, corr, nobs, k_endog): if n_factor > k_endog: raise ValueError('n_factor cannot be greater than the number' ' of variables! %d > %d' % (n_factor, k_endog)) if np.max(np.abs(np.diag(corr) - 1)) > 1e-10: raise ValueError("corr must be a correlation matrix") if corr.shape[0] != corr.shape[1]: raise ValueError('Correlation matrix corr must be a square ' '(rows %d != cols %d)' % corr.shape) class Factor(Model): """ Factor analysis Parameters ---------- endog : array_like Variables in columns, observations in rows. May be `None` if `corr` is not `None`. n_factor : int The number of factors to extract corr : array_like Directly specify the correlation matrix instead of estimating it from `endog`. If provided, `endog` is not used for the factor analysis, it may be used in post-estimation. method : str The method to extract factors, currently must be either 'pa' for principal axis factor analysis or 'ml' for maximum likelihood estimation. smc : True or False Whether or not to apply squared multiple correlations (method='pa') endog_names : str Names of endogenous variables. If specified, it will be used instead of the column names in endog nobs : int The number of observations, not used if endog is present. Needs to be provided for inference if endog is None. missing : 'none', 'drop', or 'raise' Missing value handling for endog, default is row-wise deletion 'drop' If 'none', no nan checking is done. If 'drop', any observations with nans are dropped. If 'raise', an error is raised. Notes ----- **Experimental** Supported rotations: 'varimax', 'quartimax', 'biquartimax', 'equamax', 'oblimin', 'parsimax', 'parsimony', 'biquartimin', 'promax' If method='ml', the factors are rotated to satisfy condition IC3 of Bai and Li (2012). This means that the scores have covariance I, so the model for the covariance matrix is L * L' + diag(U), where L are the loadings and U are the uniquenesses. In addition, L' * diag(U)^{-1} L must be diagonal. References ---------- .. [*] Hofacker, C. (2004). Exploratory Factor Analysis, Mathematical Marketing. http://www.openaccesstexts.org/pdf/Quant_Chapter_11_efa.pdf .. [*] J Bai, K Li (2012). Statistical analysis of factor models of high dimension. Annals of Statistics. https://arxiv.org/pdf/1205.6617.pdf """ def __init__(self, endog=None, n_factor=1, corr=None, method='pa', smc=True, endog_names=None, nobs=None, missing='drop'): _check_args_1(endog, n_factor, corr, nobs) if endog is not None: super(Factor, self).__init__(endog, exog=None, missing=missing) endog = self.endog # after preprocessing like missing, asarray k_endog = endog.shape[1] nobs = endog.shape[0] corr = self.corr = np.corrcoef(endog, rowvar=0) elif corr is not None: corr = self.corr = np.asarray(corr) k_endog = self.corr.shape[0] self.endog = None else: msg = "Either endog or corr must be provided." raise ValueError(msg) _check_args_2(endog, n_factor, corr, nobs, k_endog) self.n_factor = n_factor self.loadings = None self.communality = None self.method = method self.smc = smc self.nobs = nobs self.method = method self.corr = corr self.k_endog = k_endog if endog_names is None: if hasattr(corr, 'index'): endog_names = corr.index if hasattr(corr, 'columns'): endog_names = corr.columns self.endog_names = endog_names @property def endog_names(self): """Names of endogenous variables""" if self._endog_names is not None: return self._endog_names else: if self.endog is not None: return self.data.ynames else: d = 0 n = self.corr.shape[0] - 1 while n > 0: d += 1 n //= 10 return [('var%0' + str(d) + 'd') % i for i in range(self.corr.shape[0])] @endog_names.setter def endog_names(self, value): # Check validity of endog_names: if value is not None: if len(value) != self.corr.shape[0]: raise ValueError('The length of `endog_names` must ' 'equal the number of variables.') self._endog_names = np.asarray(value) else: self._endog_names = None def fit(self, maxiter=50, tol=1e-8, start=None, opt_method='BFGS', opt=None, em_iter=3): """ Estimate factor model parameters. Parameters ---------- maxiter : int Maximum number of iterations for iterative estimation algorithms tol : float Stopping criteria (error tolerance) for iterative estimation algorithms start : array_like Starting values, currently only used for ML estimation opt_method : str Optimization method for ML estimation opt : dict-like Keyword arguments passed to optimizer, only used for ML estimation em_iter : int The number of EM iterations before starting gradient optimization, only used for ML estimation. Returns ------- FactorResults Results class instance. """ method = self.method.lower() if method == 'pa': return self._fit_pa(maxiter=maxiter, tol=tol) elif method == 'ml': return self._fit_ml(start, em_iter, opt_method, opt) else: msg = "Unknown factor extraction approach '%s'" % self.method raise ValueError(msg) def _fit_pa(self, maxiter=50, tol=1e-8): """ Extract factors using the iterative principal axis method Parameters ---------- maxiter : int Maximum number of iterations for communality estimation tol : float If `norm(communality - last_communality) < tolerance`, estimation stops Returns ------- results : FactorResults instance """ R = self.corr.copy() # inplace modification below # Parameter validation self.n_comp = matrix_rank(R) if self.n_factor > self.n_comp: raise ValueError('n_factor must be smaller or equal to the rank' ' of endog! %d > %d' % (self.n_factor, self.n_comp)) if maxiter <= 0: raise ValueError('n_max_iter must be larger than 0! %d < 0' % (maxiter)) if tol <= 0 or tol > 0.01: raise ValueError('tolerance must be larger than 0 and smaller than' ' 0.01! Got %f instead' % (tol)) # Initial communality estimation if self.smc: c = 1 - 1 / np.diag(inv(R)) else: c = np.ones(len(R)) # Iterative communality estimation eigenvals = None for i in range(maxiter): # Get eigenvalues/eigenvectors of R with diag replaced by # communality for j in range(len(R)): R[j, j] = c[j] L, V = eigh(R, UPLO='U') c_last = np.array(c) ind = np.argsort(L) ind = ind[::-1] L = L[ind] n_pos = (L > 0).sum() V = V[:, ind] eigenvals = np.array(L) # Select eigenvectors with positive eigenvalues n = np.min([n_pos, self.n_factor]) sL = np.diag(np.sqrt(L[:n])) V = V[:, :n] # Calculate new loadings and communality A = V.dot(sL) c = np.power(A, 2).sum(axis=1) if norm(c_last - c) < tol: break self.eigenvals = eigenvals self.communality = c self.uniqueness = 1 - c self.loadings = A return FactorResults(self) # Unpacks the model parameters from a flat vector, used for ML # estimation. The first k_endog elements of par are the square # roots of the uniquenesses. The remaining elements are the # factor loadings, packed one factor at a time. def _unpack(self, par): return (par[0:self.k_endog]**2, np.reshape(par[self.k_endog:], (-1, self.k_endog)).T) # Packs the model parameters into a flat parameter, used for ML # estimation. def _pack(self, load, uniq): return np.concatenate((np.sqrt(uniq), load.T.flat)) def loglike(self, par): """ Evaluate the log-likelihood function. Parameters ---------- par : ndarray or tuple of 2 ndarray's The model parameters, either a packed representation of the model parameters or a 2-tuple containing a `k_endog x n_factor` matrix of factor loadings and a `k_endog` vector of uniquenesses. Returns ------- float The value of the log-likelihood evaluated at par. """ if type(par) is np.ndarray: uniq, load = self._unpack(par) else: load, uniq = par[0], par[1] loadu = load / uniq[:, None] lul = np.dot(load.T, loadu) # log|GG' + S| # Using matrix determinant lemma: # |GG' + S| = |I + G'S^{-1}G|*|S| lul.flat[::lul.shape[0]+1] += 1 _, ld = np.linalg.slogdet(lul) v = np.sum(np.log(uniq)) + ld # tr((GG' + S)^{-1}C) # Using Sherman-Morrison-Woodbury w = np.sum(1 / uniq) b = np.dot(load.T, self.corr / uniq[:, None]) b = np.linalg.solve(lul, b) b = np.dot(loadu, b) w -= np.trace(b) # Scaled log-likelihood return -(v + w) / (2*self.k_endog) def score(self, par): """ Evaluate the score function (first derivative of loglike). Parameters ---------- par : ndarray or tuple of 2 ndarray's The model parameters, either a packed representation of the model parameters or a 2-tuple containing a `k_endog x n_factor` matrix of factor loadings and a `k_endog` vector of uniquenesses. Returns ------- ndarray The score function evaluated at par. """ if type(par) is np.ndarray: uniq, load = self._unpack(par) else: load, uniq = par[0], par[1] # Center term of SMW loadu = load / uniq[:, None] c = np.dot(load.T, loadu) c.flat[::c.shape[0]+1] += 1 d = np.linalg.solve(c, load.T) # Precompute these terms lud = np.dot(loadu, d) cu = (self.corr / uniq) / uniq[:, None] r = np.dot(cu, load) lul = np.dot(lud.T, load) luz = np.dot(cu, lul) # First term du = 2*np.sqrt(uniq) * (1/uniq - (d * load.T).sum(0) / uniq**2) dl = 2*(loadu - np.dot(lud, loadu)) # Second term h = np.dot(lud, cu) f = np.dot(h, lud.T) du -= 2*np.sqrt(uniq) * (np.diag(cu) - 2*np.diag(h) + np.diag(f)) dl -= 2*r dl += 2*np.dot(lud, r) dl += 2*luz dl -= 2*np.dot(lud, luz) # Cannot use _pack because we are working with the square root # uniquenesses directly. return -np.concatenate((du, dl.T.flat)) / (2*self.k_endog) # Maximum likelihood factor analysis. def _fit_ml(self, start, em_iter, opt_method, opt): """estimate Factor model using Maximum Likelihood """ # Starting values if start is None: load, uniq = self._fit_ml_em(em_iter) start = self._pack(load, uniq) elif len(start) == 2: if len(start[1]) != start[0].shape[0]: msg = "Starting values have incompatible dimensions" raise ValueError(msg) start = self._pack(start[0], start[1]) else: raise ValueError("Invalid starting values") def nloglike(par): return -self.loglike(par) def nscore(par): return -self.score(par) # Do the optimization if opt is None: opt = _opt_defaults r = minimize(nloglike, start, jac=nscore, method=opt_method, options=opt) if not r.success: warnings.warn("Fitting did not converge") par = r.x uniq, load = self._unpack(par) if uniq.min() < 1e-10: warnings.warn("Some uniquenesses are nearly zero") # Rotate solution to satisfy IC3 of Bai and Li load = self._rotate(load, uniq) self.uniqueness = uniq self.communality = 1 - uniq self.loadings = load self.mle_retvals = r return FactorResults(self) def _fit_ml_em(self, iter): """estimate Factor model using EM algorithm """ # Starting values np.random.seed(3427) load = 0.1*np.random.normal(size=(self.k_endog, self.n_factor)) uniq = 0.5 * np.ones(self.k_endog) for k in range(iter): loadu = load / uniq[:, None] f = np.dot(load.T, loadu) f.flat[::f.shape[0]+1] += 1 r = np.linalg.solve(f, loadu.T) q = np.dot(loadu.T, load) h = np.dot(r, load) c = load - np.dot(load, h) c /= uniq[:, None] g = np.dot(q, r) e = np.dot(g, self.corr) d = np.dot(loadu.T, self.corr) - e a = np.dot(d, c) a -= np.dot(load.T, c) a.flat[::a.shape[0]+1] += 1 b = np.dot(self.corr, c) load = np.linalg.solve(a, b.T).T uniq = np.diag(self.corr) - (load * d.T).sum(1) return load, uniq def _rotate(self, load, uniq): """rotate loadings for MLE """ # Rotations used in ML estimation. load, s, _ = np.linalg.svd(load, 0) load *= s if self.nobs is None: nobs = 1 else: nobs = self.nobs cm = np.dot(load.T, load / uniq[:, None]) / nobs _, f = np.linalg.eig(cm) load = np.dot(load, f) return load class FactorResults(object): """ Factor results class For result summary, scree/loading plots and factor rotations Parameters ---------- factor : Factor Fitted Factor class Attributes ---------- uniqueness : ndarray The uniqueness (variance of uncorrelated errors unique to each variable) communality : ndarray 1 - uniqueness loadings : ndarray Each column is the loading vector for one factor loadings_no_rot : ndarray Unrotated loadings, not available under maximum likelihood analysis. eigenvals : ndarray The eigenvalues for a factor analysis obtained using principal components; not available under ML estimation. n_comp : int Number of components (factors) nbs : int Number of observations fa_method : str The method used to obtain the decomposition, either 'pa' for 'principal axes' or 'ml' for maximum likelihood. df : int Degrees of freedom of the factor model. Notes ----- Under ML estimation, the default rotation (used for `loadings`) is condition IC3 of Bai and Li (2012). Under this rotation, the factor scores are iid and standardized. If `G` is the canonical loadings and `U` is the vector of uniquenesses, then the covariance matrix implied by the factor analysis is `GG' + diag(U)`. Status: experimental, Some refactoring will be necessary when new features are added. """ def __init__(self, factor): self.model = factor self.endog_names = factor.endog_names self.loadings_no_rot = factor.loadings if hasattr(factor, "eigenvals"): self.eigenvals = factor.eigenvals self.communality = factor.communality self.uniqueness = factor.uniqueness self.rotation_method = None self.fa_method = factor.method self.n_comp = factor.loadings.shape[1] self.nobs = factor.nobs self._factor = factor if hasattr(factor, "mle_retvals"): self.mle_retvals = factor.mle_retvals p, k = self.loadings_no_rot.shape self.df = ((p - k)**2 - (p + k)) // 2 # no rotation, overwritten in `rotate` self.loadings = factor.loadings self.rotation_matrix = np.eye(self.n_comp) def __str__(self): return self.summary().__str__() def rotate(self, method): """ Apply rotation, inplace modification of this Results instance Parameters ---------- method : str Rotation to be applied. Allowed methods are varimax, quartimax, biquartimax, equamax, oblimin, parsimax, parsimony, biquartimin, promax. Returns ------- None : nothing returned, modifications are inplace Notes ----- Warning: 'varimax', 'quartimax' and 'oblimin' are verified against R or Stata. Some rotation methods such as promax do not produce the same results as the R or Stata default functions. See Also -------- factor_rotation : subpackage that implements rotation methods """ self.rotation_method = method if method not in ['varimax', 'quartimax', 'biquartimax', 'equamax', 'oblimin', 'parsimax', 'parsimony', 'biquartimin', 'promax']: raise ValueError('Unknown rotation method %s' % (method)) if method in ['varimax', 'quartimax', 'biquartimax', 'equamax', 'parsimax', 'parsimony', 'biquartimin']: self.loadings, T = rotate_factors(self.loadings_no_rot, method) elif method == 'oblimin': self.loadings, T = rotate_factors(self.loadings_no_rot, 'quartimin') elif method == 'promax': self.loadings, T = promax(self.loadings_no_rot) else: raise ValueError('rotation method not recognized') self.rotation_matrix = T def _corr_factors(self): """correlation of factors implied by rotation If the rotation is oblique, then the factors are correlated. currently not cached Returns ------- corr_f : ndarray correlation matrix of rotated factors, assuming initial factors are orthogonal """ T = self.rotation_matrix corr_f = T.T.dot(T) return corr_f def factor_score_params(self, method='bartlett'): """ Compute factor scoring coefficient matrix The coefficient matrix is not cached. Parameters ---------- method : 'bartlett' or 'regression' Method to use for factor scoring. 'regression' can be abbreviated to `reg` Returns ------- coeff_matrix : ndarray matrix s to compute factors f from a standardized endog ys. ``f = ys dot s`` Notes ----- The `regression` method follows the Stata definition. Method bartlett and regression are verified against Stats. Two unofficial methods, 'ols' and 'gls', produce similar factor scores but are not verified. See Also -------- statsmodels.multivariate.factor.FactorResults.factor_scoring """ L = self.loadings T = self.rotation_matrix.T #TODO: check row versus column convention for T uni = 1 - self.communality #self.uniqueness if method == 'bartlett': s_mat = np.linalg.inv(L.T.dot(L/(uni[:,None]))).dot((L.T / uni)).T elif method.startswith('reg'): corr = self.model.corr corr_f = self._corr_factors() # if orthogonal then corr_f is just eye s_mat = corr_f.dot(L.T.dot(np.linalg.inv(corr))).T elif method == 'ols': # not verified corr = self.model.corr corr_f = self._corr_factors() s_mat = corr_f.dot(np.linalg.pinv(L)).T elif method == 'gls': # not verified #s_mat = np.linalg.inv(1*np.eye(L.shape[1]) + L.T.dot(L/(uni[:,None]))) corr = self.model.corr corr_f = self._corr_factors() s_mat = np.linalg.inv(np.linalg.inv(corr_f) + L.T.dot(L/(uni[:,None]))) s_mat = s_mat.dot(L.T / uni).T else: raise ValueError('method not available, use "bartlett ' + 'or "regression"') return s_mat def factor_scoring(self, endog=None, method='bartlett', transform=True): """ factor scoring: compute factors for endog If endog was not provided when creating the factor class, then a standarized endog needs to be provided here. Parameters ---------- method : 'bartlett' or 'regression' Method to use for factor scoring. 'regression' can be abbreviated to `reg` transform : bool If transform is true and endog is provided, then it will be standardized using mean and scale of original data, which has to be available in this case. If transform is False, then a provided endog will be used unchanged. The original endog in the Factor class will always be standardized if endog is None, independently of `transform`. Returns ------- factor_score : ndarray estimated factors using scoring matrix s and standarized endog ys ``f = ys dot s`` Notes ----- Status: transform option is experimental and might change. See Also -------- statsmodels.multivariate.factor.FactorResults.factor_score_params """ if transform is False and endog is not None: # no transformation in this case endog = np.asarray(endog) else: # we need to standardize with the original mean and scale if self.model.endog is not None: m = self.model.endog.mean(0) s = self.model.endog.std(ddof=1, axis=0) if endog is None: endog = self.model.endog else: endog = np.asarray(endog) else: raise ValueError('If transform is True, then `endog` needs ' + 'to be available in the Factor instance.') endog = (endog - m) / s s_mat = self.factor_score_params(method=method) factors = endog.dot(s_mat) return factors def summary(self): """Summary""" summ = summary2.Summary() summ.add_title('Factor analysis results') loadings_no_rot = pd.DataFrame( self.loadings_no_rot, columns=["factor %d" % (i) for i in range(self.loadings_no_rot.shape[1])], index=self.endog_names ) if hasattr(self, "eigenvals"): # eigenvals not available for ML method eigenvals = pd.DataFrame( [self.eigenvals], columns=self.endog_names, index=['']) summ.add_dict({'': 'Eigenvalues'}) summ.add_df(eigenvals) communality = pd.DataFrame([self.communality], columns=self.endog_names, index=['']) summ.add_dict({'': ''}) summ.add_dict({'': 'Communality'}) summ.add_df(communality) summ.add_dict({'': ''}) summ.add_dict({'': 'Pre-rotated loadings'}) summ.add_df(loadings_no_rot) summ.add_dict({'': ''}) if self.rotation_method is not None: loadings = pd.DataFrame( self.loadings, columns=["factor %d" % (i) for i in range(self.loadings.shape[1])], index=self.endog_names ) summ.add_dict({'': '%s rotated loadings' % (self.rotation_method)}) summ.add_df(loadings) return summ def get_loadings_frame(self, style='display', sort_=True, threshold=0.3, highlight_max=True, color_max='yellow', decimals=None): """get loadings matrix as DataFrame or pandas Styler Parameters ---------- style : 'display' (default), 'raw' or 'strings' Style to use for display * 'raw' returns just a DataFrame of the loadings matrix, no options are applied * 'display' add sorting and styling as defined by other keywords * 'strings' returns a DataFrame with string elements with optional sorting and suppressing small loading coefficients. sort_ : bool If True, then the rows of the DataFrame is sorted by contribution of each factor. applies if style is either 'display' or 'strings' threshold : float If the threshold is larger than zero, then loading coefficients are either colored white (if style is 'display') or replace by empty string (if style is 'strings'). highlight_max : bool This add a background color to the largest coefficient in each row. color_max : html color default is 'yellow'. color for background of row maximum decimals : None or int If None, then pandas default precision applies. Otherwise values are rounded to the specified decimals. If style is 'display', then the underlying dataframe is not changed. If style is 'strings', then values are rounded before conversion to strings. Returns ------- loadings : DataFrame or pandas Styler instance The return is a pandas Styler instance, if style is 'display' and at least one of highlight_max, threshold or decimals is applied. Otherwise, the returned loadings is a DataFrame. Examples -------- >>> mod = Factor(df, 3, smc=True) >>> res = mod.fit() >>> res.get_loadings_frame(style='display', decimals=3, threshold=0.2) To get a sorted DataFrame, all styling options need to be turned off: >>> df_sorted = res.get_loadings_frame(style='display', ... highlight_max=False, decimals=None, threshold=0) Options except for highlighting are available for plain test or Latex usage: >>> lds = res_u.get_loadings_frame(style='strings', decimals=3, ... threshold=0.3) >>> print(lds.to_latex()) """ loadings_df = pd.DataFrame( self.loadings, columns=["factor %d" % (i) for i in range(self.loadings.shape[1])], index=self.endog_names ) if style not in ['raw', 'display', 'strings']: msg = "style has to be one of 'raw', 'display', 'strings'" raise ValueError(msg) if style == 'raw': return loadings_df # add sorting and some formatting if sort_ is True: loadings_df2 = loadings_df.copy() n_f = len(loadings_df2) high = np.abs(loadings_df2.values).argmax(1) loadings_df2['high'] = high loadings_df2['largest'] = np.abs(loadings_df.values[np.arange(n_f), high]) loadings_df2.sort_values(by=['high', 'largest'], ascending=[True, False], inplace=True) loadings_df = loadings_df2.drop(['high', 'largest'], axis=1) if style == 'display': sty = None if threshold > 0: def color_white_small(val): """ Takes a scalar and returns a string with the css property `'color: white'` for small values, black otherwise. takes threshold from outer scope """ color = 'white' if np.abs(val) < threshold else 'black' return 'color: %s' % color sty = loadings_df.style.applymap(color_white_small) if highlight_max is True: def highlight_max(s): ''' highlight the maximum in a Series yellow. ''' s = np.abs(s) is_max = s == s.max() return ['background-color: '+ color_max if v else '' for v in is_max] if sty is None: sty = loadings_df.style sty = sty.apply(highlight_max, axis=1) if decimals is not None: if sty is None: sty = loadings_df.style sty.format("{:.%sf}" % decimals) if sty is None: return loadings_df else: return sty if style == 'strings': ld = loadings_df if decimals is not None: ld = ld.round(decimals) ld = ld.astype(str) if threshold > 0: ld[loadings_df.abs() < threshold] = '' return ld def plot_scree(self, ncomp=None): """ Plot of the ordered eigenvalues and variance explained for the loadings Parameters ---------- ncomp : int, optional Number of loadings to include in the plot. If None, will included the same as the number of maximum possible loadings Returns ------- Figure Handle to the figure. """ _import_mpl() from .plots import plot_scree return plot_scree(self.eigenvals, self.n_comp, ncomp) def plot_loadings(self, loading_pairs=None, plot_prerotated=False): """ Plot factor loadings in 2-d plots Parameters ---------- loading_pairs : None or a list of tuples Specify plots. Each tuple (i, j) represent one figure, i and j is the loading number for x-axis and y-axis, respectively. If `None`, all combinations of the loadings will be plotted. plot_prerotated : True or False If True, the loadings before rotation applied will be plotted. If False, rotated loadings will be plotted. Returns ------- figs : a list of figure handles """ _import_mpl() from .plots import plot_loadings if self.rotation_method is None: plot_prerotated = True loadings = self.loadings_no_rot if plot_prerotated else self.loadings if plot_prerotated: title = 'Prerotated Factor Pattern' else: title = '%s Rotated Factor Pattern' % (self.rotation_method) var_explained = self.eigenvals / self.n_comp * 100 return plot_loadings(loadings, loading_pairs=loading_pairs, title=title, row_names=self.endog_names, percent_variance=var_explained) @cache_readonly def fitted_cov(self): """ Returns the fitted covariance matrix. """ c = np.dot(self.loadings, self.loadings.T) c.flat[::c.shape[0]+1] += self.uniqueness return c @cache_readonly def uniq_stderr(self, kurt=0): """ The standard errors of the uniquenesses. Parameters ---------- kurt : float Excess kurtosis Notes ----- If excess kurtosis is known, provide as `kurt`. Standard errors are only available if the model was fit using maximum likelihood. If `endog` is not provided, `nobs` must be provided to obtain standard errors. These are asymptotic standard errors. See Bai and Li (2012) for conditions under which the standard errors are valid. The standard errors are only applicable to the original, unrotated maximum likelihood solution. """ if self.fa_method.lower() != "ml": msg = "Standard errors only available under ML estimation" raise ValueError(msg) if self.nobs is None: msg = "nobs is required to obtain standard errors." raise ValueError(msg) v = self.uniqueness**2 * (2 + kurt) return np.sqrt(v / self.nobs) @cache_readonly def load_stderr(self): """ The standard errors of the loadings. Standard errors are only available if the model was fit using maximum likelihood. If `endog` is not provided, `nobs` must be provided to obtain standard errors. These are asymptotic standard errors. See Bai and Li (2012) for conditions under which the standard errors are valid. The standard errors are only applicable to the original, unrotated maximum likelihood solution. """ if self.fa_method.lower() != "ml": msg = "Standard errors only available under ML estimation" raise ValueError(msg) if self.nobs is None: msg = "nobs is required to obtain standard errors." raise ValueError(msg) v = np.outer(self.uniqueness, np.ones(self.loadings.shape[1])) return np.sqrt(v / self.nobs) statsmodels-0.12.2/statsmodels/multivariate/factor_rotation/000077500000000000000000000000001400612667500244125ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/multivariate/factor_rotation/COPYRIGHTS.txt000066400000000000000000000005101400612667500266420ustar00rootroot00000000000000The license of this package can be found in LICENSE.txt This file contains a Python version of the gradient projection rotation algorithms (GPA) developed by Bernaards, C.A. and Jennrich, R.I. The code is based on code developed Bernaards, C.A. and Jennrich, R.I. and is ported and made available with permission of the authors.statsmodels-0.12.2/statsmodels/multivariate/factor_rotation/LICENSE.txt000066400000000000000000000027431400612667500262430ustar00rootroot00000000000000Copyright (c) 2015, Martin van der Schans All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.statsmodels-0.12.2/statsmodels/multivariate/factor_rotation/__init__.py000066400000000000000000000023501400612667500265230ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Package with factor rotation algorithms. This file contains a Python version of the gradient projection rotation algorithms (GPA) developed by Bernaards, C.A. and Jennrich, R.I. The code is based on the Matlab version of the code developed Bernaards, C.A. and Jennrich, R.I. and is ported and made available with permission of the authors. Additionally, several analytic rotation methods are implemented. References ---------- [1] Bernaards, C.A. and Jennrich, R.I. (2005) Gradient Projection Algorithms and Software for Arbitrary Rotation Criteria in Factor Analysis. Educational and Psychological Measurement, 65 (5), 676-696. [2] Jennrich, R.I. (2001). A simple general procedure for orthogonal rotation. Psychometrika, 66, 289-306. [3] Jennrich, R.I. (2002). A simple general method for oblique rotation. Psychometrika, 67, 7-19. [4] http://www.stat.ucla.edu/research/gpa/matlab.net [5] http://www.stat.ucla.edu/research/gpa/GPderfree.txt """ from ._wrappers import rotate_factors from ._analytic_rotation import target_rotation, procrustes, promax from statsmodels.tools._testing import PytestTester __all__ = ['rotate_factors', 'target_rotation', 'procrustes', 'promax', 'test'] test = PytestTester() statsmodels-0.12.2/statsmodels/multivariate/factor_rotation/_analytic_rotation.py000066400000000000000000000076501400612667500306560ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ This file contains analytic implementations of rotation methods. """ import numpy as np import scipy as sp def target_rotation(A, H, full_rank=False): r""" Analytically performs orthogonal rotations towards a target matrix, i.e., we minimize: .. math:: \phi(L) =\frac{1}{2}\|AT-H\|^2. where :math:`T` is an orthogonal matrix. This problem is also known as an orthogonal Procrustes problem. Under the assumption that :math:`A^*H` has full rank, the analytical solution :math:`T` is given by: .. math:: T = (A^*HH^*A)^{-\frac{1}{2}}A^*H, see Green (1952). In other cases the solution is given by :math:`T = UV`, where :math:`U` and :math:`V` result from the singular value decomposition of :math:`A^*H`: .. math:: A^*H = U\Sigma V, see Schonemann (1966). Parameters ---------- A : numpy matrix (default None) non rotated factors H : numpy matrix target matrix full_rank : bool (default FAlse) if set to true full rank is assumed Returns ------- The matrix :math:`T`. References ---------- [1] Green (1952, Psychometrika) - The orthogonal approximation of an oblique structure in factor analysis [2] Schonemann (1966) - A generalized solution of the orthogonal procrustes problem [3] Gower, Dijksterhuis (2004) - Procrustes problems """ ATH = A.T.dot(H) if full_rank or np.linalg.matrix_rank(ATH) == A.shape[1]: T = sp.linalg.fractional_matrix_power(ATH.dot(ATH.T), -1/2).dot(ATH) else: U, D, V = np.linalg.svd(ATH, full_matrices=False) T = U.dot(V) return T def procrustes(A, H): r""" Analytically solves the following Procrustes problem: .. math:: \phi(L) =\frac{1}{2}\|AT-H\|^2. (With no further conditions on :math:`H`) Under the assumption that :math:`A^*H` has full rank, the analytical solution :math:`T` is given by: .. math:: T = (A^*HH^*A)^{-\frac{1}{2}}A^*H, see Navarra, Simoncini (2010). Parameters ---------- A : numpy matrix non rotated factors H : numpy matrix target matrix full_rank : bool (default False) if set to true full rank is assumed Returns ------- The matrix :math:`T`. References ---------- [1] Navarra, Simoncini (2010) - A guide to empirical orthogonal functions for climate data analysis """ return np.linalg.inv(A.T.dot(A)).dot(A.T).dot(H) def promax(A, k=2): r""" Performs promax rotation of the matrix :math:`A`. This method was not very clear to me from the literature, this implementation is as I understand it should work. Promax rotation is performed in the following steps: * Determine varimax rotated patterns :math:`V`. * Construct a rotation target matrix :math:`|V_{ij}|^k/V_{ij}` * Perform procrustes rotation towards the target to obtain T * Determine the patterns First, varimax rotation a target matrix :math:`H` is determined with orthogonal varimax rotation. Then, oblique target rotation is performed towards the target. Parameters ---------- A : numpy matrix non rotated factors k : float parameter, should be positive References ---------- [1] Browne (2001) - An overview of analytic rotation in exploratory factor analysis [2] Navarra, Simoncini (2010) - A guide to empirical orthogonal functions for climate data analysis """ assert k > 0 # define rotation target using varimax rotation: from ._wrappers import rotate_factors V, T = rotate_factors(A, 'varimax') H = np.abs(V)**k/V # solve procrustes problem S = procrustes(A, H) # np.linalg.inv(A.T.dot(A)).dot(A.T).dot(H); # normalize d = np.sqrt(np.diag(np.linalg.inv(S.T.dot(S)))) D = np.diag(d) T = np.linalg.inv(S.dot(D)).T return A.dot(T), T statsmodels-0.12.2/statsmodels/multivariate/factor_rotation/_gpa_rotation.py000066400000000000000000000443401400612667500276160ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ This file contains a Python version of the gradient projection rotation algorithms (GPA) developed by Bernaards, C.A. and Jennrich, R.I. The code is based on code developed Bernaards, C.A. and Jennrich, R.I. and is ported and made available with permission of the authors. References ---------- [1] Bernaards, C.A. and Jennrich, R.I. (2005) Gradient Projection Algorithms and Software for Arbitrary Rotation Criteria in Factor Analysis. Educational and Psychological Measurement, 65 (5), 676-696. [2] Jennrich, R.I. (2001). A simple general procedure for orthogonal rotation. Psychometrika, 66, 289-306. [3] Jennrich, R.I. (2002). A simple general method for oblique rotation. Psychometrika, 67, 7-19. [4] http://www.stat.ucla.edu/research/gpa/matlab.net [5] http://www.stat.ucla.edu/research/gpa/GPderfree.txt """ import numpy as np def GPA(A, ff=None, vgQ=None, T=None, max_tries=501, rotation_method='orthogonal', tol=1e-5): r""" The gradient projection algorithm (GPA) minimizes a target function :math:`\phi(L)`, where :math:`L` is a matrix with rotated factors. For orthogonal rotation methods :math:`L=AT`, where :math:`T` is an orthogonal matrix. For oblique rotation matrices :math:`L=A(T^*)^{-1}`, where :math:`T` is a normal matrix, i.e., :math:`TT^*=T^*T`. Oblique rotations relax the orthogonality constraint in order to gain simplicity in the interpretation. Parameters ---------- A : numpy matrix non rotated factors T : numpy matrix (default identity matrix) initial guess of rotation matrix ff : function (defualt None) criterion :math:`\phi` to optimize. Should have A, T, L as keyword arguments and mapping to a float. Only used (and required) if vgQ is not provided. vgQ : function (defualt None) criterion :math:`\phi` to optimize and its derivative. Should have A, T, L as keyword arguments and mapping to a tuple containing a float and vector. Can be omitted if ff is provided. max_tries : int (default 501) maximum number of iterations rotation_method : str should be one of {orthogonal, oblique} tol : float stop criterion, algorithm stops if Frobenius norm of gradient is smaller then tol """ # pre processing if rotation_method not in ['orthogonal', 'oblique']: raise ValueError('rotation_method should be one of ' '{orthogonal, oblique}') if vgQ is None: if ff is None: raise ValueError('ff should be provided if vgQ is not') derivative_free = True Gff = lambda x: Gf(x, lambda y: ff(T=y, A=A, L=None)) else: derivative_free = False if T is None: T = np.eye(A.shape[1]) # pre processing for iteration al = 1 table = [] # pre processing for iteration: initialize f and G if derivative_free: f = ff(T=T, A=A, L=None) G = Gff(T) elif rotation_method == 'orthogonal': # and not derivative_free L = A.dot(T) f, Gq = vgQ(L=L) G = (A.T).dot(Gq) else: # i.e. rotation_method == 'oblique' and not derivative_free Ti = np.linalg.inv(T) L = A.dot(Ti.T) f, Gq = vgQ(L=L) G = -((L.T).dot(Gq).dot(Ti)).T # iteration for i_try in range(0, max_tries): # determine Gp if rotation_method == 'orthogonal': M = (T.T).dot(G) S = (M + M.T)/2 Gp = G - T.dot(S) else: # i.e. if rotation_method == 'oblique': Gp = G-T.dot(np.diag(np.sum(T*G, axis=0))) s = np.linalg.norm(Gp, 'fro') table.append([i_try, f, np.log10(s), al]) # if we are close stop if s < tol: break # update T al = 2*al for i in range(11): # determine Tt X = T - al*Gp if rotation_method == 'orthogonal': U, D, V = np.linalg.svd(X, full_matrices=False) Tt = U.dot(V) else: # i.e. if rotation_method == 'oblique': v = 1/np.sqrt(np.sum(X**2, axis=0)) Tt = X.dot(np.diag(v)) # calculate objective using Tt if derivative_free: ft = ff(T=Tt, A=A, L=None) elif rotation_method == 'orthogonal': # and not derivative_free L = A.dot(Tt) ft, Gq = vgQ(L=L) else: # i.e. rotation_method == 'oblique' and not derivative_free Ti = np.linalg.inv(Tt) L = A.dot(Ti.T) ft, Gq = vgQ(L=L) # if sufficient improvement in objective -> use this T if ft < f-.5*s**2*al: break al = al/2 # post processing for next iteration T = Tt f = ft if derivative_free: G = Gff(T) elif rotation_method == 'orthogonal': # and not derivative_free G = (A.T).dot(Gq) else: # i.e. rotation_method == 'oblique' and not derivative_free G = -((L.T).dot(Gq).dot(Ti)).T # post processing Th = T Lh = rotateA(A, T, rotation_method=rotation_method) Phi = (T.T).dot(T) return Lh, Phi, Th, table def Gf(T, ff): """ Subroutine for the gradient of f using numerical derivatives. """ k = T.shape[0] ep = 1e-4 G = np.zeros((k, k)) for r in range(k): for s in range(k): dT = np.zeros((k, k)) dT[r, s] = ep G[r, s] = (ff(T+dT)-ff(T-dT))/(2*ep) return G def rotateA(A, T, rotation_method='orthogonal'): r""" For orthogonal rotation methods :math:`L=AT`, where :math:`T` is an orthogonal matrix. For oblique rotation matrices :math:`L=A(T^*)^{-1}`, where :math:`T` is a normal matrix, i.e., :math:`TT^*=T^*T`. Oblique rotations relax the orthogonality constraint in order to gain simplicity in the interpretation. """ if rotation_method == 'orthogonal': L = A.dot(T) elif rotation_method == 'oblique': L = A.dot(np.linalg.inv(T.T)) else: # i.e. if rotation_method == 'oblique': raise ValueError('rotation_method should be one of ' '{orthogonal, oblique}') return L def oblimin_objective(L=None, A=None, T=None, gamma=0, rotation_method='orthogonal', return_gradient=True): r""" Objective function for the oblimin family for orthogonal or oblique rotation wich minimizes: .. math:: \phi(L) = \frac{1}{4}(L\circ L,(I-\gamma C)(L\circ L)N), where :math:`L` is a :math:`p\times k` matrix, :math:`N` is :math:`k\times k` matrix with zeros on the diagonal and ones elsewhere, :math:`C` is a :math:`p\times p` matrix with elements equal to :math:`1/p`, :math:`(X,Y)=\operatorname{Tr}(X^*Y)` is the Frobenius norm and :math:`\circ` is the element-wise product or Hadamard product. The gradient is given by .. math:: L\circ\left[(I-\gamma C) (L \circ L)N\right]. Either :math:`L` should be provided or :math:`A` and :math:`T` should be provided. For orthogonal rotations :math:`L` satisfies .. math:: L = AT, where :math:`T` is an orthogonal matrix. For oblique rotations :math:`L` satisfies .. math:: L = A(T^*)^{-1}, where :math:`T` is a normal matrix. The oblimin family is parametrized by the parameter :math:`\gamma`. For orthogonal rotations: * :math:`\gamma=0` corresponds to quartimax, * :math:`\gamma=\frac{1}{2}` corresponds to biquartimax, * :math:`\gamma=1` corresponds to varimax, * :math:`\gamma=\frac{1}{p}` corresponds to equamax. For oblique rotations rotations: * :math:`\gamma=0` corresponds to quartimin, * :math:`\gamma=\frac{1}{2}` corresponds to biquartimin. Parameters ---------- L : numpy matrix (default None) rotated factors, i.e., :math:`L=A(T^*)^{-1}=AT` A : numpy matrix (default None) non rotated factors T : numpy matrix (default None) rotation matrix gamma : float (default 0) a parameter rotation_method : str should be one of {orthogonal, oblique} return_gradient : bool (default True) toggles return of gradient """ if L is None: assert(A is not None and T is not None) L = rotateA(A, T, rotation_method=rotation_method) p, k = L.shape L2 = L**2 N = np.ones((k, k))-np.eye(k) if np.isclose(gamma, 0): X = L2.dot(N) else: C = np.ones((p, p))/p X = (np.eye(p) - gamma*C).dot(L2).dot(N) phi = np.sum(L2*X)/4 if return_gradient: Gphi = L*X return phi, Gphi else: return phi def orthomax_objective(L=None, A=None, T=None, gamma=0, return_gradient=True): r""" Objective function for the orthomax family for orthogonal rotation wich minimizes the following objective: .. math:: \phi(L) = -\frac{1}{4}(L\circ L,(I-\gamma C)(L\circ L)), where :math:`0\leq\gamma\leq1`, :math:`L` is a :math:`p\times k` matrix, :math:`C` is a :math:`p\times p` matrix with elements equal to :math:`1/p`, :math:`(X,Y)=\operatorname{Tr}(X^*Y)` is the Frobenius norm and :math:`\circ` is the element-wise product or Hadamard product. Either :math:`L` should be provided or :math:`A` and :math:`T` should be provided. For orthogonal rotations :math:`L` satisfies .. math:: L = AT, where :math:`T` is an orthogonal matrix. The orthomax family is parametrized by the parameter :math:`\gamma`: * :math:`\gamma=0` corresponds to quartimax, * :math:`\gamma=\frac{1}{2}` corresponds to biquartimax, * :math:`\gamma=1` corresponds to varimax, * :math:`\gamma=\frac{1}{p}` corresponds to equamax. Parameters ---------- L : numpy matrix (default None) rotated factors, i.e., :math:`L=A(T^*)^{-1}=AT` A : numpy matrix (default None) non rotated factors T : numpy matrix (default None) rotation matrix gamma : float (default 0) a parameter return_gradient : bool (default True) toggles return of gradient """ assert 0 <= gamma <= 1, "Gamma should be between 0 and 1" if L is None: assert(A is not None and T is not None) L = rotateA(A, T, rotation_method='orthogonal') p, k = L.shape L2 = L**2 if np.isclose(gamma, 0): X = L2 else: C = np.ones((p, p))/p X = (np.eye(p)-gamma*C).dot(L2) phi = -np.sum(L2*X)/4 if return_gradient: Gphi = -L*X return phi, Gphi else: return phi def CF_objective(L=None, A=None, T=None, kappa=0, rotation_method='orthogonal', return_gradient=True): r""" Objective function for the Crawford-Ferguson family for orthogonal and oblique rotation wich minimizes the following objective: .. math:: \phi(L) =\frac{1-\kappa}{4} (L\circ L,(L\circ L)N) -\frac{1}{4}(L\circ L,M(L\circ L)), where :math:`0\leq\kappa\leq1`, :math:`L` is a :math:`p\times k` matrix, :math:`N` is :math:`k\times k` matrix with zeros on the diagonal and ones elsewhere, :math:`M` is :math:`p\times p` matrix with zeros on the diagonal and ones elsewhere :math:`(X,Y)=\operatorname{Tr}(X^*Y)` is the Frobenius norm and :math:`\circ` is the element-wise product or Hadamard product. The gradient is given by .. math:: d\phi(L) = (1-\kappa) L\circ\left[(L\circ L)N\right] -\kappa L\circ \left[M(L\circ L)\right]. Either :math:`L` should be provided or :math:`A` and :math:`T` should be provided. For orthogonal rotations :math:`L` satisfies .. math:: L = AT, where :math:`T` is an orthogonal matrix. For oblique rotations :math:`L` satisfies .. math:: L = A(T^*)^{-1}, where :math:`T` is a normal matrix. For orthogonal rotations the oblimin (and orthomax) family of rotations is equivalent to the Crawford-Ferguson family. To be more precise: * :math:`\kappa=0` corresponds to quartimax, * :math:`\kappa=\frac{1}{p}` corresponds to variamx, * :math:`\kappa=\frac{k-1}{p+k-2}` corresponds to parsimax, * :math:`\kappa=1` corresponds to factor parsimony. Parameters ---------- L : numpy matrix (default None) rotated factors, i.e., :math:`L=A(T^*)^{-1}=AT` A : numpy matrix (default None) non rotated factors T : numpy matrix (default None) rotation matrix gamma : float (default 0) a parameter rotation_method : str should be one of {orthogonal, oblique} return_gradient : bool (default True) toggles return of gradient """ assert 0 <= kappa <= 1, "Kappa should be between 0 and 1" if L is None: assert(A is not None and T is not None) L = rotateA(A, T, rotation_method=rotation_method) p, k = L.shape L2 = L**2 X = None if not np.isclose(kappa, 1): N = np.ones((k, k)) - np.eye(k) X = (1 - kappa)*L2.dot(N) if not np.isclose(kappa, 0): M = np.ones((p, p)) - np.eye(p) if X is None: X = kappa*M.dot(L2) else: X += kappa*M.dot(L2) phi = np.sum(L2 * X) / 4 if return_gradient: Gphi = L*X return phi, Gphi else: return phi def vgQ_target(H, L=None, A=None, T=None, rotation_method='orthogonal'): r""" Subroutine for the value of vgQ using orthogonal or oblique rotation towards a target matrix, i.e., we minimize: .. math:: \phi(L) =\frac{1}{2}\|L-H\|^2 and the gradient is given by .. math:: d\phi(L)=L-H. Either :math:`L` should be provided or :math:`A` and :math:`T` should be provided. For orthogonal rotations :math:`L` satisfies .. math:: L = AT, where :math:`T` is an orthogonal matrix. For oblique rotations :math:`L` satisfies .. math:: L = A(T^*)^{-1}, where :math:`T` is a normal matrix. Parameters ---------- H : numpy matrix target matrix L : numpy matrix (default None) rotated factors, i.e., :math:`L=A(T^*)^{-1}=AT` A : numpy matrix (default None) non rotated factors T : numpy matrix (default None) rotation matrix rotation_method : str should be one of {orthogonal, oblique} """ if L is None: assert(A is not None and T is not None) L = rotateA(A, T, rotation_method=rotation_method) q = np.linalg.norm(L-H, 'fro')**2 Gq = 2*(L-H) return q, Gq def ff_target(H, L=None, A=None, T=None, rotation_method='orthogonal'): r""" Subroutine for the value of f using (orthogonal or oblique) rotation towards a target matrix, i.e., we minimize: .. math:: \phi(L) =\frac{1}{2}\|L-H\|^2. Either :math:`L` should be provided or :math:`A` and :math:`T` should be provided. For orthogonal rotations :math:`L` satisfies .. math:: L = AT, where :math:`T` is an orthogonal matrix. For oblique rotations :math:`L` satisfies .. math:: L = A(T^*)^{-1}, where :math:`T` is a normal matrix. Parameters ---------- H : numpy matrix target matrix L : numpy matrix (default None) rotated factors, i.e., :math:`L=A(T^*)^{-1}=AT` A : numpy matrix (default None) non rotated factors T : numpy matrix (default None) rotation matrix rotation_method : str should be one of {orthogonal, oblique} """ if L is None: assert(A is not None and T is not None) L = rotateA(A, T, rotation_method=rotation_method) return np.linalg.norm(L-H, 'fro')**2 def vgQ_partial_target(H, W=None, L=None, A=None, T=None): r""" Subroutine for the value of vgQ using orthogonal rotation towards a partial target matrix, i.e., we minimize: .. math:: \phi(L) =\frac{1}{2}\|W\circ(L-H)\|^2, where :math:`\circ` is the element-wise product or Hadamard product and :math:`W` is a matrix whose entries can only be one or zero. The gradient is given by .. math:: d\phi(L)=W\circ(L-H). Either :math:`L` should be provided or :math:`A` and :math:`T` should be provided. For orthogonal rotations :math:`L` satisfies .. math:: L = AT, where :math:`T` is an orthogonal matrix. Parameters ---------- H : numpy matrix target matrix W : numpy matrix (default matrix with equal weight one for all entries) matrix with weights, entries can either be one or zero L : numpy matrix (default None) rotated factors, i.e., :math:`L=A(T^*)^{-1}=AT` A : numpy matrix (default None) non rotated factors T : numpy matrix (default None) rotation matrix """ if W is None: return vgQ_target(H, L=L, A=A, T=T) if L is None: assert(A is not None and T is not None) L = rotateA(A, T, rotation_method='orthogonal') q = np.linalg.norm(W*(L-H), 'fro')**2 Gq = 2*W*(L-H) return q, Gq def ff_partial_target(H, W=None, L=None, A=None, T=None): r""" Subroutine for the value of vgQ using orthogonal rotation towards a partial target matrix, i.e., we minimize: .. math:: \phi(L) =\frac{1}{2}\|W\circ(L-H)\|^2, where :math:`\circ` is the element-wise product or Hadamard product and :math:`W` is a matrix whose entries can only be one or zero. Either :math:`L` should be provided or :math:`A` and :math:`T` should be provided. For orthogonal rotations :math:`L` satisfies .. math:: L = AT, where :math:`T` is an orthogonal matrix. Parameters ---------- H : numpy matrix target matrix W : numpy matrix (default matrix with equal weight one for all entries) matrix with weights, entries can either be one or zero L : numpy matrix (default None) rotated factors, i.e., :math:`L=A(T^*)^{-1}=AT` A : numpy matrix (default None) non rotated factors T : numpy matrix (default None) rotation matrix """ if W is None: return ff_target(H, L=L, A=A, T=T) if L is None: assert(A is not None and T is not None) L = rotateA(A, T, rotation_method='orthogonal') q = np.linalg.norm(W*(L-H), 'fro')**2 return q statsmodels-0.12.2/statsmodels/multivariate/factor_rotation/_wrappers.py000066400000000000000000000325051400612667500267730ustar00rootroot00000000000000# -*- coding: utf-8 -*- from ._analytic_rotation import target_rotation from ._gpa_rotation import oblimin_objective, orthomax_objective, CF_objective from ._gpa_rotation import ff_partial_target, ff_target from ._gpa_rotation import vgQ_partial_target, vgQ_target from ._gpa_rotation import rotateA, GPA __all__ = [] def rotate_factors(A, method, *method_args, **algorithm_kwargs): r""" Subroutine for orthogonal and oblique rotation of the matrix :math:`A`. For orthogonal rotations :math:`A` is rotated to :math:`L` according to .. math:: L = AT, where :math:`T` is an orthogonal matrix. And, for oblique rotations :math:`A` is rotated to :math:`L` according to .. math:: L = A(T^*)^{-1}, where :math:`T` is a normal matrix. Parameters ---------- A : numpy matrix (default None) non rotated factors method : str should be one of the methods listed below method_args : list additional arguments that should be provided with each method algorithm_kwargs : dictionary algorithm : str (default gpa) should be one of: * 'gpa': a numerical method * 'gpa_der_free': a derivative free numerical method * 'analytic' : an analytic method Depending on the algorithm, there are algorithm specific keyword arguments. For the gpa and gpa_der_free, the following keyword arguments are available: max_tries : int (default 501) maximum number of iterations tol : float stop criterion, algorithm stops if Frobenius norm of gradient is smaller then tol For analytic, the supported arguments depend on the method, see above. See the lower level functions for more details. Returns ------- The tuple :math:`(L,T)` Notes ----- What follows is a list of available methods. Depending on the method additional argument are required and different algorithms are available. The algorithm_kwargs are additional keyword arguments passed to the selected algorithm (see the parameters section). Unless stated otherwise, only the gpa and gpa_der_free algorithm are available. Below, * :math:`L` is a :math:`p\times k` matrix; * :math:`N` is :math:`k\times k` matrix with zeros on the diagonal and ones elsewhere; * :math:`M` is :math:`p\times p` matrix with zeros on the diagonal and ones elsewhere; * :math:`C` is a :math:`p\times p` matrix with elements equal to :math:`1/p`; * :math:`(X,Y)=\operatorname{Tr}(X^*Y)` is the Frobenius norm; * :math:`\circ` is the element-wise product or Hadamard product. oblimin : orthogonal or oblique rotation that minimizes .. math:: \phi(L) = \frac{1}{4}(L\circ L,(I-\gamma C)(L\circ L)N). For orthogonal rotations: * :math:`\gamma=0` corresponds to quartimax, * :math:`\gamma=\frac{1}{2}` corresponds to biquartimax, * :math:`\gamma=1` corresponds to varimax, * :math:`\gamma=\frac{1}{p}` corresponds to equamax. For oblique rotations rotations: * :math:`\gamma=0` corresponds to quartimin, * :math:`\gamma=\frac{1}{2}` corresponds to biquartimin. method_args: gamma : float oblimin family parameter rotation_method : str should be one of {orthogonal, oblique} orthomax : orthogonal rotation that minimizes .. math:: \phi(L) = -\frac{1}{4}(L\circ L,(I-\gamma C)(L\circ L)), where :math:`0\leq\gamma\leq1`. The orthomax family is equivalent to the oblimin family (when restricted to orthogonal rotations). Furthermore, * :math:`\gamma=0` corresponds to quartimax, * :math:`\gamma=\frac{1}{2}` corresponds to biquartimax, * :math:`\gamma=1` corresponds to varimax, * :math:`\gamma=\frac{1}{p}` corresponds to equamax. method_args: gamma : float (between 0 and 1) orthomax family parameter CF : Crawford-Ferguson family for orthogonal and oblique rotation which minimizes: .. math:: \phi(L) =\frac{1-\kappa}{4} (L\circ L,(L\circ L)N) -\frac{1}{4}(L\circ L,M(L\circ L)), where :math:`0\leq\kappa\leq1`. For orthogonal rotations the oblimin (and orthomax) family of rotations is equivalent to the Crawford-Ferguson family. To be more precise: * :math:`\kappa=0` corresponds to quartimax, * :math:`\kappa=\frac{1}{p}` corresponds to varimax, * :math:`\kappa=\frac{k-1}{p+k-2}` corresponds to parsimax, * :math:`\kappa=1` corresponds to factor parsimony. method_args: kappa : float (between 0 and 1) Crawford-Ferguson family parameter rotation_method : str should be one of {orthogonal, oblique} quartimax : orthogonal rotation method minimizes the orthomax objective with :math:`\gamma=0` biquartimax : orthogonal rotation method minimizes the orthomax objective with :math:`\gamma=\frac{1}{2}` varimax : orthogonal rotation method minimizes the orthomax objective with :math:`\gamma=1` equamax : orthogonal rotation method minimizes the orthomax objective with :math:`\gamma=\frac{1}{p}` parsimax : orthogonal rotation method minimizes the Crawford-Ferguson family objective with :math:`\kappa=\frac{k-1}{p+k-2}` parsimony : orthogonal rotation method minimizes the Crawford-Ferguson family objective with :math:`\kappa=1` quartimin : oblique rotation method that minimizes minimizes the oblimin objective with :math:`\gamma=0` quartimin : oblique rotation method that minimizes minimizes the oblimin objective with :math:`\gamma=\frac{1}{2}` target : orthogonal or oblique rotation that rotates towards a target matrix : math:`H` by minimizing the objective .. math:: \phi(L) =\frac{1}{2}\|L-H\|^2. method_args: H : numpy matrix target matrix rotation_method : str should be one of {orthogonal, oblique} For orthogonal rotations the algorithm can be set to analytic in which case the following keyword arguments are available: full_rank : bool (default False) if set to true full rank is assumed partial_target : orthogonal (default) or oblique rotation that partially rotates towards a target matrix :math:`H` by minimizing the objective: .. math:: \phi(L) =\frac{1}{2}\|W\circ(L-H)\|^2. method_args: H : numpy matrix target matrix W : numpy matrix (default matrix with equal weight one for all entries) matrix with weights, entries can either be one or zero Examples -------- >>> A = np.random.randn(8,2) >>> L, T = rotate_factors(A,'varimax') >>> np.allclose(L,A.dot(T)) >>> L, T = rotate_factors(A,'orthomax',0.5) >>> np.allclose(L,A.dot(T)) >>> L, T = rotate_factors(A,'quartimin',0.5) >>> np.allclose(L,A.dot(np.linalg.inv(T.T))) """ if 'algorithm' in algorithm_kwargs: algorithm = algorithm_kwargs['algorithm'] algorithm_kwargs.pop('algorithm') else: algorithm = 'gpa' assert not ('rotation_method' in algorithm_kwargs), ( 'rotation_method cannot be provided as keyword argument') L = None T = None ff = None vgQ = None p, k = A.shape # set ff or vgQ to appropriate objective function, compute solution using # recursion or analytically compute solution if method == 'orthomax': assert len(method_args) == 1, ('Only %s family parameter should be ' 'provided' % method) rotation_method = 'orthogonal' gamma = method_args[0] if algorithm == 'gpa': vgQ = lambda L=None, A=None, T=None: orthomax_objective( L=L, A=A, T=T, gamma=gamma, return_gradient=True) elif algorithm == 'gpa_der_free': ff = lambda L=None, A=None, T=None: orthomax_objective( L=L, A=A, T=T, gamma=gamma, return_gradient=False) else: raise ValueError('Algorithm %s is not possible for %s ' 'rotation' % (algorithm, method)) elif method == 'oblimin': assert len(method_args) == 2, ('Both %s family parameter and ' 'rotation_method should be ' 'provided' % method) rotation_method = method_args[1] assert rotation_method in ['orthogonal', 'oblique'], ( 'rotation_method should be one of {orthogonal, oblique}') gamma = method_args[0] if algorithm == 'gpa': vgQ = lambda L=None, A=None, T=None: oblimin_objective( L=L, A=A, T=T, gamma=gamma, return_gradient=True) elif algorithm == 'gpa_der_free': ff = lambda L=None, A=None, T=None: oblimin_objective( L=L, A=A, T=T, gamma=gamma, rotation_method=rotation_method, return_gradient=False) else: raise ValueError('Algorithm %s is not possible for %s ' 'rotation' % (algorithm, method)) elif method == 'CF': assert len(method_args) == 2, ('Both %s family parameter and ' 'rotation_method should be provided' % method) rotation_method = method_args[1] assert rotation_method in ['orthogonal', 'oblique'], ( 'rotation_method should be one of {orthogonal, oblique}') kappa = method_args[0] if algorithm == 'gpa': vgQ = lambda L=None, A=None, T=None: CF_objective( L=L, A=A, T=T, kappa=kappa, rotation_method=rotation_method, return_gradient=True) elif algorithm == 'gpa_der_free': ff = lambda L=None, A=None, T=None: CF_objective( L=L, A=A, T=T, kappa=kappa, rotation_method=rotation_method, return_gradient=False) else: raise ValueError('Algorithm %s is not possible for %s ' 'rotation' % (algorithm, method)) elif method == 'quartimax': return rotate_factors(A, 'orthomax', 0, **algorithm_kwargs) elif method == 'biquartimax': return rotate_factors(A, 'orthomax', 0.5, **algorithm_kwargs) elif method == 'varimax': return rotate_factors(A, 'orthomax', 1, **algorithm_kwargs) elif method == 'equamax': return rotate_factors(A, 'orthomax', 1/p, **algorithm_kwargs) elif method == 'parsimax': return rotate_factors(A, 'CF', (k-1)/(p+k-2), 'orthogonal', **algorithm_kwargs) elif method == 'parsimony': return rotate_factors(A, 'CF', 1, 'orthogonal', **algorithm_kwargs) elif method == 'quartimin': return rotate_factors(A, 'oblimin', 0, 'oblique', **algorithm_kwargs) elif method == 'biquartimin': return rotate_factors(A, 'oblimin', 0.5, 'oblique', **algorithm_kwargs) elif method == 'target': assert len(method_args) == 2, ( 'only the rotation target and orthogonal/oblique should be provide' ' for %s rotation' % method) H = method_args[0] rotation_method = method_args[1] assert rotation_method in ['orthogonal', 'oblique'], ( 'rotation_method should be one of {orthogonal, oblique}') if algorithm == 'gpa': vgQ = lambda L=None, A=None, T=None: vgQ_target( H, L=L, A=A, T=T, rotation_method=rotation_method) elif algorithm == 'gpa_der_free': ff = lambda L=None, A=None, T=None: ff_target( H, L=L, A=A, T=T, rotation_method=rotation_method) elif algorithm == 'analytic': assert rotation_method == 'orthogonal', ( 'For analytic %s rotation only orthogonal rotation is ' 'supported') T = target_rotation(A, H, **algorithm_kwargs) else: raise ValueError('Algorithm %s is not possible for %s rotation' % (algorithm, method)) elif method == 'partial_target': assert len(method_args) == 2, ('2 additional arguments are expected ' 'for %s rotation' % method) H = method_args[0] W = method_args[1] rotation_method = 'orthogonal' if algorithm == 'gpa': vgQ = lambda L=None, A=None, T=None: vgQ_partial_target( H, W=W, L=L, A=A, T=T) elif algorithm == 'gpa_der_free': ff = lambda L=None, A=None, T=None: ff_partial_target( H, W=W, L=L, A=A, T=T) else: raise ValueError('Algorithm %s is not possible for %s ' 'rotation' % (algorithm, method)) else: raise ValueError('Invalid method') # compute L and T if not already done if T is None: L, phi, T, table = GPA(A, vgQ=vgQ, ff=ff, rotation_method=rotation_method, **algorithm_kwargs) if L is None: assert T is not None, 'Cannot compute L without T' L = rotateA(A, T, rotation_method=rotation_method) return L, T statsmodels-0.12.2/statsmodels/multivariate/factor_rotation/tests/000077500000000000000000000000001400612667500255545ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/multivariate/factor_rotation/tests/__init__.py000066400000000000000000000000001400612667500276530ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/multivariate/factor_rotation/tests/test_rotation.py000066400000000000000000000524551400612667500310370ustar00rootroot00000000000000import unittest import numpy as np from statsmodels.multivariate.factor_rotation._wrappers import rotate_factors from statsmodels.multivariate.factor_rotation._gpa_rotation import ( ff_partial_target, vgQ_partial_target, ff_target, vgQ_target, CF_objective, orthomax_objective, oblimin_objective, GPA) from statsmodels.multivariate.factor_rotation._analytic_rotation import ( target_rotation) class TestAnalyticRotation(unittest.TestCase): @staticmethod def str2matrix(A): A = A.lstrip().rstrip().split('\n') A = np.array([row.split() for row in A]).astype(float) return A def test_target_rotation(self): """ Rotation towards target matrix example http://www.stat.ucla.edu/research/gpa """ A = self.str2matrix(""" .830 -.396 .818 -.469 .777 -.470 .798 -.401 .786 .500 .672 .458 .594 .444 .647 .333 """) H = self.str2matrix(""" .8 -.3 .8 -.4 .7 -.4 .9 -.4 .8 .5 .6 .4 .5 .4 .6 .3 """) T = target_rotation(A, H) L = A.dot(T) L_required = self.str2matrix(""" 0.84168 -0.37053 0.83191 -0.44386 0.79096 -0.44611 0.80985 -0.37650 0.77040 0.52371 0.65774 0.47826 0.58020 0.46189 0.63656 0.35255 """) self.assertTrue(np.allclose(L, L_required, atol=1e-05)) T = target_rotation(A, H, full_rank=True) L = A.dot(T) self.assertTrue(np.allclose(L, L_required, atol=1e-05)) def test_orthogonal_target(self): """ Rotation towards target matrix example http://www.stat.ucla.edu/research/gpa """ A = self.str2matrix(""" .830 -.396 .818 -.469 .777 -.470 .798 -.401 .786 .500 .672 .458 .594 .444 .647 .333 """) H = self.str2matrix(""" .8 -.3 .8 -.4 .7 -.4 .9 -.4 .8 .5 .6 .4 .5 .4 .6 .3 """) vgQ = lambda L=None, A=None, T=None: vgQ_target(H, L=L, A=A, T=T) L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal') T_analytic = target_rotation(A, H) self.assertTrue(np.allclose(T, T_analytic, atol=1e-05)) class TestGPARotation(unittest.TestCase): @staticmethod def str2matrix(A): A = A.lstrip().rstrip().split('\n') A = np.array([row.split() for row in A]).astype(float) return A @classmethod def get_A(cls): return cls.str2matrix(""" .830 -.396 .818 -.469 .777 -.470 .798 -.401 .786 .500 .672 .458 .594 .444 .647 .333 """) @classmethod def get_quartimin_example(cls): A = cls.get_A() table_required = cls.str2matrix(""" 0.00000 0.42806 -0.46393 1.00000 1.00000 0.41311 -0.57313 0.25000 2.00000 0.38238 -0.36652 0.50000 3.00000 0.31850 -0.21011 0.50000 4.00000 0.20937 -0.13838 0.50000 5.00000 0.12379 -0.35583 0.25000 6.00000 0.04289 -0.53244 0.50000 7.00000 0.01098 -0.86649 0.50000 8.00000 0.00566 -1.65798 0.50000 9.00000 0.00558 -2.13212 0.25000 10.00000 0.00557 -2.49020 0.25000 11.00000 0.00557 -2.84585 0.25000 12.00000 0.00557 -3.20320 0.25000 13.00000 0.00557 -3.56143 0.25000 14.00000 0.00557 -3.92005 0.25000 15.00000 0.00557 -4.27885 0.25000 16.00000 0.00557 -4.63772 0.25000 17.00000 0.00557 -4.99663 0.25000 18.00000 0.00557 -5.35555 0.25000 """) L_required = cls.str2matrix(""" 0.891822 0.056015 0.953680 -0.023246 0.929150 -0.046503 0.876683 0.033658 0.013701 0.925000 -0.017265 0.821253 -0.052445 0.764953 0.085890 0.683115 """) return A, table_required, L_required @classmethod def get_biquartimin_example(cls): A = cls.get_A() table_required = cls.str2matrix(""" 0.00000 0.21632 -0.54955 1.00000 1.00000 0.19519 -0.46174 0.50000 2.00000 0.09479 -0.16365 1.00000 3.00000 -0.06302 -0.32096 0.50000 4.00000 -0.21304 -0.46562 1.00000 5.00000 -0.33199 -0.33287 1.00000 6.00000 -0.35108 -0.63990 0.12500 7.00000 -0.35543 -1.20916 0.12500 8.00000 -0.35568 -2.61213 0.12500 9.00000 -0.35568 -2.97910 0.06250 10.00000 -0.35568 -3.32645 0.06250 11.00000 -0.35568 -3.66021 0.06250 12.00000 -0.35568 -3.98564 0.06250 13.00000 -0.35568 -4.30635 0.06250 14.00000 -0.35568 -4.62451 0.06250 15.00000 -0.35568 -4.94133 0.06250 16.00000 -0.35568 -5.25745 0.06250 """) L_required = cls.str2matrix(""" 1.01753 -0.13657 1.11338 -0.24643 1.09200 -0.26890 1.00676 -0.16010 -0.26534 1.11371 -0.26972 0.99553 -0.29341 0.93561 -0.10806 0.80513 """) return A, table_required, L_required @classmethod def get_biquartimin_example_derivative_free(cls): A = cls.get_A() table_required = cls.str2matrix(""" 0.00000 0.21632 -0.54955 1.00000 1.00000 0.19519 -0.46174 0.50000 2.00000 0.09479 -0.16365 1.00000 3.00000 -0.06302 -0.32096 0.50000 4.00000 -0.21304 -0.46562 1.00000 5.00000 -0.33199 -0.33287 1.00000 6.00000 -0.35108 -0.63990 0.12500 7.00000 -0.35543 -1.20916 0.12500 8.00000 -0.35568 -2.61213 0.12500 9.00000 -0.35568 -2.97910 0.06250 10.00000 -0.35568 -3.32645 0.06250 11.00000 -0.35568 -3.66021 0.06250 12.00000 -0.35568 -3.98564 0.06250 13.00000 -0.35568 -4.30634 0.06250 14.00000 -0.35568 -4.62451 0.06250 15.00000 -0.35568 -4.94133 0.06250 16.00000 -0.35568 -6.32435 0.12500 """) L_required = cls.str2matrix(""" 1.01753 -0.13657 1.11338 -0.24643 1.09200 -0.26890 1.00676 -0.16010 -0.26534 1.11371 -0.26972 0.99553 -0.29342 0.93561 -0.10806 0.80513 """) return A, table_required, L_required @classmethod def get_quartimax_example_derivative_free(cls): A = cls.get_A() table_required = cls.str2matrix(""" 0.00000 -0.72073 -0.65498 1.00000 1.00000 -0.88561 -0.34614 2.00000 2.00000 -1.01992 -1.07152 1.00000 3.00000 -1.02237 -1.51373 0.50000 4.00000 -1.02269 -1.96205 0.50000 5.00000 -1.02273 -2.41116 0.50000 6.00000 -1.02273 -2.86037 0.50000 7.00000 -1.02273 -3.30959 0.50000 8.00000 -1.02273 -3.75881 0.50000 9.00000 -1.02273 -4.20804 0.50000 10.00000 -1.02273 -4.65726 0.50000 11.00000 -1.02273 -5.10648 0.50000 """) L_required = cls.str2matrix(""" 0.89876 0.19482 0.93394 0.12974 0.90213 0.10386 0.87651 0.17128 0.31558 0.87647 0.25113 0.77349 0.19801 0.71468 0.30786 0.65933 """) return A, table_required, L_required def test_orthomax(self): """ Quartimax example http://www.stat.ucla.edu/research/gpa """ A = self.get_A() vgQ = lambda L=None, A=None, T=None: orthomax_objective( L=L, A=A, T=T, gamma=0, return_gradient=True) L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal') table_required = self.str2matrix(""" 0.00000 -0.72073 -0.65498 1.00000 1.00000 -0.88561 -0.34614 2.00000 2.00000 -1.01992 -1.07152 1.00000 3.00000 -1.02237 -1.51373 0.50000 4.00000 -1.02269 -1.96205 0.50000 5.00000 -1.02273 -2.41116 0.50000 6.00000 -1.02273 -2.86037 0.50000 7.00000 -1.02273 -3.30959 0.50000 8.00000 -1.02273 -3.75881 0.50000 9.00000 -1.02273 -4.20804 0.50000 10.00000 -1.02273 -4.65726 0.50000 11.00000 -1.02273 -5.10648 0.50000 """) L_required = self.str2matrix(""" 0.89876 0.19482 0.93394 0.12974 0.90213 0.10386 0.87651 0.17128 0.31558 0.87647 0.25113 0.77349 0.19801 0.71468 0.30786 0.65933 """) self.assertTrue(np.allclose(table, table_required, atol=1e-05)) self.assertTrue(np.allclose(L, L_required, atol=1e-05)) # oblimin criterion gives same result vgQ = lambda L=None, A=None, T=None: oblimin_objective( L=L, A=A, T=T, gamma=0, rotation_method='orthogonal', return_gradient=True) L_oblimin, phi2, T2, table2 = GPA(A, vgQ=vgQ, rotation_method='orthogonal') self.assertTrue(np.allclose(L, L_oblimin, atol=1e-05)) # derivative free quartimax out = self.get_quartimax_example_derivative_free() A, table_required, L_required = out ff = lambda L=None, A=None, T=None: orthomax_objective( L=L, A=A, T=T, gamma=0, return_gradient=False) L, phi, T, table = GPA(A, ff=ff, rotation_method='orthogonal') self.assertTrue(np.allclose(table, table_required, atol=1e-05)) self.assertTrue(np.allclose(L, L_required, atol=1e-05)) def test_equivalence_orthomax_oblimin(self): """ These criteria should be equivalent when restricted to orthogonal rotation. See Hartman 1976 page 299. """ A = self.get_A() gamma = 0 # quartimax vgQ = lambda L=None, A=None, T=None: orthomax_objective( L=L, A=A, T=T, gamma=gamma, return_gradient=True) L_orthomax, phi, T, table = GPA( A, vgQ=vgQ, rotation_method='orthogonal') vgQ = lambda L=None, A=None, T=None: oblimin_objective( L=L, A=A, T=T, gamma=gamma, rotation_method='orthogonal', return_gradient=True) L_oblimin, phi2, T2, table2 = GPA(A, vgQ=vgQ, rotation_method='orthogonal') self.assertTrue(np.allclose(L_orthomax, L_oblimin, atol=1e-05)) gamma = 1 # varimax vgQ = lambda L=None, A=None, T=None: orthomax_objective( L=L, A=A, T=T, gamma=gamma, return_gradient=True) L_orthomax, phi, T, table = GPA( A, vgQ=vgQ, rotation_method='orthogonal') vgQ = lambda L=None, A=None, T=None: oblimin_objective( L=L, A=A, T=T, gamma=gamma, rotation_method='orthogonal', return_gradient=True) L_oblimin, phi2, T2, table2 = GPA( A, vgQ=vgQ, rotation_method='orthogonal') self.assertTrue(np.allclose(L_orthomax, L_oblimin, atol=1e-05)) def test_orthogonal_target(self): """ Rotation towards target matrix example http://www.stat.ucla.edu/research/gpa """ A = self.get_A() H = self.str2matrix(""" .8 -.3 .8 -.4 .7 -.4 .9 -.4 .8 .5 .6 .4 .5 .4 .6 .3 """) vgQ = lambda L=None, A=None, T=None: vgQ_target(H, L=L, A=A, T=T) L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal') table_required = self.str2matrix(""" 0.00000 0.05925 -0.61244 1.00000 1.00000 0.05444 -1.14701 0.12500 2.00000 0.05403 -1.68194 0.12500 3.00000 0.05399 -2.21689 0.12500 4.00000 0.05399 -2.75185 0.12500 5.00000 0.05399 -3.28681 0.12500 6.00000 0.05399 -3.82176 0.12500 7.00000 0.05399 -4.35672 0.12500 8.00000 0.05399 -4.89168 0.12500 9.00000 0.05399 -5.42664 0.12500 """) L_required = self.str2matrix(""" 0.84168 -0.37053 0.83191 -0.44386 0.79096 -0.44611 0.80985 -0.37650 0.77040 0.52371 0.65774 0.47826 0.58020 0.46189 0.63656 0.35255 """) self.assertTrue(np.allclose(table, table_required, atol=1e-05)) self.assertTrue(np.allclose(L, L_required, atol=1e-05)) ff = lambda L=None, A=None, T=None: ff_target(H, L=L, A=A, T=T) L2, phi, T2, table = GPA(A, ff=ff, rotation_method='orthogonal') self.assertTrue(np.allclose(L, L2, atol=1e-05)) self.assertTrue(np.allclose(T, T2, atol=1e-05)) vgQ = lambda L=None, A=None, T=None: vgQ_target( H, L=L, A=A, T=T, rotation_method='oblique') L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='oblique') ff = lambda L=None, A=None, T=None: ff_target( H, L=L, A=A, T=T, rotation_method='oblique') L2, phi, T2, table = GPA(A, ff=ff, rotation_method='oblique') self.assertTrue(np.allclose(L, L2, atol=1e-05)) self.assertTrue(np.allclose(T, T2, atol=1e-05)) def test_orthogonal_partial_target(self): """ Rotation towards target matrix example http://www.stat.ucla.edu/research/gpa """ A = self.get_A() H = self.str2matrix(""" .8 -.3 .8 -.4 .7 -.4 .9 -.4 .8 .5 .6 .4 .5 .4 .6 .3 """) W = self.str2matrix(""" 1 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 """) vgQ = lambda L=None, A=None, T=None: vgQ_partial_target( H, W, L=L, A=A, T=T) L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal') table_required = self.str2matrix(""" 0.00000 0.02559 -0.84194 1.00000 1.00000 0.02203 -1.27116 0.25000 2.00000 0.02154 -1.71198 0.25000 3.00000 0.02148 -2.15713 0.25000 4.00000 0.02147 -2.60385 0.25000 5.00000 0.02147 -3.05114 0.25000 6.00000 0.02147 -3.49863 0.25000 7.00000 0.02147 -3.94619 0.25000 8.00000 0.02147 -4.39377 0.25000 9.00000 0.02147 -4.84137 0.25000 10.00000 0.02147 -5.28897 0.25000 """) L_required = self.str2matrix(""" 0.84526 -0.36228 0.83621 -0.43571 0.79528 -0.43836 0.81349 -0.36857 0.76525 0.53122 0.65303 0.48467 0.57565 0.46754 0.63308 0.35876 """) self.assertTrue(np.allclose(table, table_required, atol=1e-05)) self.assertTrue(np.allclose(L, L_required, atol=1e-05)) ff = lambda L=None, A=None, T=None: ff_partial_target( H, W, L=L, A=A, T=T) L2, phi, T2, table = GPA(A, ff=ff, rotation_method='orthogonal') self.assertTrue(np.allclose(L, L2, atol=1e-05)) self.assertTrue(np.allclose(T, T2, atol=1e-05)) def test_oblimin(self): # quartimin A, table_required, L_required = self.get_quartimin_example() vgQ = lambda L=None, A=None, T=None: oblimin_objective( L=L, A=A, T=T, gamma=0, rotation_method='oblique') L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='oblique') self.assertTrue(np.allclose(table, table_required, atol=1e-05)) self.assertTrue(np.allclose(L, L_required, atol=1e-05)) # quartimin derivative free ff = lambda L=None, A=None, T=None: oblimin_objective( L=L, A=A, T=T, gamma=0, rotation_method='oblique', return_gradient=False) L, phi, T, table = GPA(A, ff=ff, rotation_method='oblique') self.assertTrue(np.allclose(L, L_required, atol=1e-05)) self.assertTrue(np.allclose(table, table_required, atol=1e-05)) # biquartimin A, table_required, L_required = self.get_biquartimin_example() vgQ = lambda L=None, A=None, T=None: oblimin_objective( L=L, A=A, T=T, gamma=1/2, rotation_method='oblique') L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='oblique') self.assertTrue(np.allclose(table, table_required, atol=1e-05)) self.assertTrue(np.allclose(L, L_required, atol=1e-05)) # quartimin derivative free out = self.get_biquartimin_example_derivative_free() A, table_required, L_required = out ff = lambda L=None, A=None, T=None: oblimin_objective( L=L, A=A, T=T, gamma=1/2, rotation_method='oblique', return_gradient=False) L, phi, T, table = GPA(A, ff=ff, rotation_method='oblique') self.assertTrue(np.allclose(L, L_required, atol=1e-05)) self.assertTrue(np.allclose(table, table_required, atol=1e-05)) def test_CF(self): # quartimax out = self.get_quartimax_example_derivative_free() A, table_required, L_required = out vgQ = lambda L=None, A=None, T=None: CF_objective( L=L, A=A, T=T, kappa=0, rotation_method='orthogonal', return_gradient=True) L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal') self.assertTrue(np.allclose(L, L_required, atol=1e-05)) # quartimax derivative free ff = lambda L=None, A=None, T=None: CF_objective( L=L, A=A, T=T, kappa=0, rotation_method='orthogonal', return_gradient=False) L, phi, T, table = GPA(A, ff=ff, rotation_method='orthogonal') self.assertTrue(np.allclose(L, L_required, atol=1e-05)) # varimax p, k = A.shape vgQ = lambda L=None, A=None, T=None: orthomax_objective( L=L, A=A, T=T, gamma=1, return_gradient=True) L_vm, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal') vgQ = lambda L=None, A=None, T=None: CF_objective( L=L, A=A, T=T, kappa=1/p, rotation_method='orthogonal', return_gradient=True) L_CF, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal') ff = lambda L=None, A=None, T=None: CF_objective( L=L, A=A, T=T, kappa=1/p, rotation_method='orthogonal', return_gradient=False) L_CF_df, phi, T, table = GPA(A, ff=ff, rotation_method='orthogonal') self.assertTrue(np.allclose(L_vm, L_CF, atol=1e-05)) self.assertTrue(np.allclose(L_CF, L_CF_df, atol=1e-05)) class TestWrappers(unittest.TestCase): @staticmethod def str2matrix(A): A = A.lstrip().rstrip().split('\n') A = np.array([row.split() for row in A]).astype(float) return A def get_A(self): return self.str2matrix(""" .830 -.396 .818 -.469 .777 -.470 .798 -.401 .786 .500 .672 .458 .594 .444 .647 .333 """) def get_H(self): return self.str2matrix(""" .8 -.3 .8 -.4 .7 -.4 .9 -.4 .8 .5 .6 .4 .5 .4 .6 .3 """) def get_W(self): return self.str2matrix(""" 1 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 """) def _test_template(self, method, *method_args, **algorithms): A = self.get_A() algorithm1 = 'gpa' if 'algorithm1' not in algorithms else algorithms[ 'algorithm1'] if 'algorithm`' not in algorithms: algorithm2 = 'gpa_der_free' else: algorithms['algorithm1'] L1, T1 = rotate_factors(A, method, *method_args, algorithm=algorithm1) L2, T2 = rotate_factors(A, method, *method_args, algorithm=algorithm2) self.assertTrue(np.allclose(L1, L2, atol=1e-5)) self.assertTrue(np.allclose(T1, T2, atol=1e-5)) def test_methods(self): """ Quartimax derivative free example http://www.stat.ucla.edu/research/gpa """ # orthomax, oblimin and CF are tested indirectly methods = ['quartimin', 'biquartimin', 'quartimax', 'biquartimax', 'varimax', 'equamax', 'parsimax', 'parsimony', 'target', 'partial_target'] for method in methods: method_args = [] if method == 'target': method_args = [self.get_H(), 'orthogonal'] self._test_template(method, *method_args) method_args = [self.get_H(), 'oblique'] self._test_template(method, *method_args) method_args = [self.get_H(), 'orthogonal'] self._test_template(method, *method_args, algorithm2='analytic') elif method == 'partial_target': method_args = [self.get_H(), self.get_W()] self._test_template(method, *method_args) statsmodels-0.12.2/statsmodels/multivariate/manova.py000066400000000000000000000103411400612667500230470ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Multivariate analysis of variance author: Yichuan Liu """ import numpy as np from statsmodels.compat.pandas import Substitution from statsmodels.base.model import Model from .multivariate_ols import MultivariateTestResults from .multivariate_ols import _multivariate_ols_fit from .multivariate_ols import _multivariate_ols_test, _hypotheses_doc __docformat__ = 'restructuredtext en' class MANOVA(Model): """ Multivariate Analysis of Variance The implementation of MANOVA is based on multivariate regression and does not assume that the explanatory variables are categorical. Any type of variables as in regression is allowed. Parameters ---------- endog : array_like Dependent variables. A nobs x k_endog array where nobs is the number of observations and k_endog is the number of dependent variables. exog : array_like Independent variables. A nobs x k_exog array where nobs is the number of observations and k_exog is the number of independent variables. An intercept is not included by default and should be added by the user. Models specified using a formula include an intercept by default. Attributes ---------- endog : ndarray See Parameters. exog : ndarray See Parameters. Notes ----- MANOVA is used though the `mv_test` function, and `fit` is not used. The ``from_formula`` interface is the recommended method to specify a model and simplifies testing without needing to manually configure the contrast matrices. References ---------- .. [*] ftp://public.dhe.ibm.com/software/analytics/spss/documentation/ statistics/20.0/en/client/Manuals/IBM_SPSS_Statistics_Algorithms.pdf """ _formula_max_endog = None def __init__(self, endog, exog, missing='none', hasconst=None, **kwargs): if len(endog.shape) == 1 or endog.shape[1] == 1: raise ValueError('There must be more than one dependent variable' ' to fit MANOVA!') super(MANOVA, self).__init__(endog, exog, missing=missing, hasconst=hasconst, **kwargs) self._fittedmod = _multivariate_ols_fit(self.endog, self.exog) def fit(self): raise NotImplementedError('fit is not needed to use MANOVA. Call' 'mv_test directly on a MANOVA instance.') @Substitution(hypotheses_doc=_hypotheses_doc) def mv_test(self, hypotheses=None): """ Linear hypotheses testing Parameters ---------- %(hypotheses_doc)s Returns ------- results: MultivariateTestResults Notes ----- Testing the linear hypotheses L * params * M = 0 where `params` is the regression coefficient matrix for the linear model y = x * params If the model is not specified using the formula interfact, then the hypotheses test each included exogenous variable, one at a time. In most applications with categorical variables, the ``from_formula`` interface should be preferred when specifying a model since it provides knowledge about the model when specifying the hypotheses. """ if hypotheses is None: if (hasattr(self, 'data') and self.data is not None and hasattr(self.data, 'design_info')): terms = self.data.design_info.term_name_slices hypotheses = [] for key in terms: L_contrast = np.eye(self.exog.shape[1])[terms[key], :] hypotheses.append([key, L_contrast, None]) else: hypotheses = [] for i in range(self.exog.shape[1]): name = 'x%d' % (i) L = np.zeros([1, self.exog.shape[1]]) L[0, i] = 1 hypotheses.append([name, L, None]) results = _multivariate_ols_test(hypotheses, self._fittedmod, self.exog_names, self.endog_names) return MultivariateTestResults(results, self.endog_names, self.exog_names) statsmodels-0.12.2/statsmodels/multivariate/multivariate_ols.py000066400000000000000000000453701400612667500251630ustar00rootroot00000000000000# -*- coding: utf-8 -*- """General linear model author: Yichuan Liu """ import numpy as np from numpy.linalg import eigvals, inv, solve, matrix_rank, pinv, svd from scipy import stats import pandas as pd from patsy import DesignInfo from statsmodels.compat.pandas import Substitution from statsmodels.base.model import Model from statsmodels.iolib import summary2 __docformat__ = 'restructuredtext en' _hypotheses_doc = \ """hypotheses : list[tuple] Hypothesis `L*B*M = C` to be tested where B is the parameters in regression Y = X*B. Each element is a tuple of length 2, 3, or 4: * (name, contrast_L) * (name, contrast_L, transform_M) * (name, contrast_L, transform_M, constant_C) containing a string `name`, the contrast matrix L, the transform matrix M (for transforming dependent variables), and right-hand side constant matrix constant_C, respectively. contrast_L : 2D array or an array of strings Left-hand side contrast matrix for hypotheses testing. If 2D array, each row is an hypotheses and each column is an independent variable. At least 1 row (1 by k_exog, the number of independent variables) is required. If an array of strings, it will be passed to patsy.DesignInfo().linear_constraint. transform_M : 2D array or an array of strings or None, optional Left hand side transform matrix. If `None` or left out, it is set to a k_endog by k_endog identity matrix (i.e. do not transform y matrix). If an array of strings, it will be passed to patsy.DesignInfo().linear_constraint. constant_C : 2D array or None, optional Right-hand side constant matrix. if `None` or left out it is set to a matrix of zeros Must has the same number of rows as contrast_L and the same number of columns as transform_M If `hypotheses` is None: 1) the effect of each independent variable on the dependent variables will be tested. Or 2) if model is created using a formula, `hypotheses` will be created according to `design_info`. 1) and 2) is equivalent if no additional variables are created by the formula (e.g. dummy variables for categorical variables and interaction terms) """ def _multivariate_ols_fit(endog, exog, method='svd', tolerance=1e-8): """ Solve multivariate linear model y = x * params where y is dependent variables, x is independent variables Parameters ---------- endog : array_like each column is a dependent variable exog : array_like each column is a independent variable method : str 'svd' - Singular value decomposition 'pinv' - Moore-Penrose pseudoinverse tolerance : float, a small positive number Tolerance for eigenvalue. Values smaller than tolerance is considered zero. Returns ------- a tuple of matrices or values necessary for hypotheses testing .. [*] https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_introreg_sect012.htm Notes ----- Status: experimental and incomplete """ y = endog x = exog nobs, k_endog = y.shape nobs1, k_exog= x.shape if nobs != nobs1: raise ValueError('x(n=%d) and y(n=%d) should have the same number of ' 'rows!' % (nobs1, nobs)) # Calculate the matrices necessary for hypotheses testing df_resid = nobs - k_exog if method == 'pinv': # Regression coefficients matrix pinv_x = pinv(x) params = pinv_x.dot(y) # inverse of x'x inv_cov = pinv_x.dot(pinv_x.T) if matrix_rank(inv_cov,tol=tolerance) < k_exog: raise ValueError('Covariance of x singular!') # Sums of squares and cross-products of residuals # Y'Y - (X * params)'B * params t = x.dot(params) sscpr = np.subtract(y.T.dot(y), t.T.dot(t)) return (params, df_resid, inv_cov, sscpr) elif method == 'svd': u, s, v = svd(x, 0) if (s > tolerance).sum() < len(s): raise ValueError('Covariance of x singular!') invs = 1. / s params = v.T.dot(np.diag(invs)).dot(u.T).dot(y) inv_cov = v.T.dot(np.diag(np.power(invs, 2))).dot(v) t = np.diag(s).dot(v).dot(params) sscpr = np.subtract(y.T.dot(y), t.T.dot(t)) return (params, df_resid, inv_cov, sscpr) else: raise ValueError('%s is not a supported method!' % method) def multivariate_stats(eigenvals, r_err_sscp, r_contrast, df_resid, tolerance=1e-8): """ For multivariate linear model Y = X * B Testing hypotheses L*B*M = 0 where L is contrast matrix, B is the parameters of the multivariate linear model and M is dependent variable transform matrix. T = L*inv(X'X)*L' H = M'B'L'*inv(T)*LBM E = M'(Y'Y - B'X'XB)M Parameters ---------- eigenvals : ndarray The eigenvalues of inv(E + H)*H r_err_sscp : int Rank of E + H r_contrast : int Rank of T matrix df_resid : int Residual degree of freedom (n_samples minus n_variables of X) tolerance : float smaller than which eigenvalue is considered 0 Returns ------- A DataFrame References ---------- .. [*] https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_introreg_sect012.htm """ v = df_resid p = r_err_sscp q = r_contrast s = np.min([p, q]) ind = eigenvals > tolerance n_e = ind.sum() eigv2 = eigenvals[ind] eigv1 = np.array([i / (1 - i) for i in eigv2]) m = (np.abs(p - q) - 1) / 2 n = (v - p - 1) / 2 cols = ['Value', 'Num DF', 'Den DF', 'F Value', 'Pr > F'] index = ["Wilks' lambda", "Pillai's trace", "Hotelling-Lawley trace", "Roy's greatest root"] results = pd.DataFrame(columns=cols, index=index) def fn(x): return np.real([x])[0] results.loc["Wilks' lambda", 'Value'] = fn(np.prod(1 - eigv2)) results.loc["Pillai's trace", 'Value'] = fn(eigv2.sum()) results.loc["Hotelling-Lawley trace", 'Value'] = fn(eigv1.sum()) results.loc["Roy's greatest root", 'Value'] = fn(eigv1.max()) r = v - (p - q + 1)/2 u = (p*q - 2) / 4 df1 = p * q if p*p + q*q - 5 > 0: t = np.sqrt((p*p*q*q - 4) / (p*p + q*q - 5)) else: t = 1 df2 = r*t - 2*u lmd = results.loc["Wilks' lambda", 'Value'] lmd = np.power(lmd, 1 / t) F = (1 - lmd) / lmd * df2 / df1 results.loc["Wilks' lambda", 'Num DF'] = df1 results.loc["Wilks' lambda", 'Den DF'] = df2 results.loc["Wilks' lambda", 'F Value'] = F pval = stats.f.sf(F, df1, df2) results.loc["Wilks' lambda", 'Pr > F'] = pval V = results.loc["Pillai's trace", 'Value'] df1 = s * (2*m + s + 1) df2 = s * (2*n + s + 1) F = df2 / df1 * V / (s - V) results.loc["Pillai's trace", 'Num DF'] = df1 results.loc["Pillai's trace", 'Den DF'] = df2 results.loc["Pillai's trace", 'F Value'] = F pval = stats.f.sf(F, df1, df2) results.loc["Pillai's trace", 'Pr > F'] = pval U = results.loc["Hotelling-Lawley trace", 'Value'] if n > 0: b = (p + 2*n) * (q + 2*n) / 2 / (2*n + 1) / (n - 1) df1 = p * q df2 = 4 + (p*q + 2) / (b - 1) c = (df2 - 2) / 2 / n F = df2 / df1 * U / c else: df1 = s * (2*m + s + 1) df2 = s * (s*n + 1) F = df2 / df1 / s * U results.loc["Hotelling-Lawley trace", 'Num DF'] = df1 results.loc["Hotelling-Lawley trace", 'Den DF'] = df2 results.loc["Hotelling-Lawley trace", 'F Value'] = F pval = stats.f.sf(F, df1, df2) results.loc["Hotelling-Lawley trace", 'Pr > F'] = pval sigma = results.loc["Roy's greatest root", 'Value'] r = np.max([p, q]) df1 = r df2 = v - r + q F = df2 / df1 * sigma results.loc["Roy's greatest root", 'Num DF'] = df1 results.loc["Roy's greatest root", 'Den DF'] = df2 results.loc["Roy's greatest root", 'F Value'] = F pval = stats.f.sf(F, df1, df2) results.loc["Roy's greatest root", 'Pr > F'] = pval return results def _multivariate_ols_test(hypotheses, fit_results, exog_names, endog_names): def fn(L, M, C): # .. [1] https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_introreg_sect012.htm params, df_resid, inv_cov, sscpr = fit_results # t1 = (L * params)M t1 = L.dot(params).dot(M) - C # H = t1'L(X'X)^L't1 t2 = L.dot(inv_cov).dot(L.T) q = matrix_rank(t2) H = t1.T.dot(inv(t2)).dot(t1) # E = M'(Y'Y - B'(X'X)B)M E = M.T.dot(sscpr).dot(M) return E, H, q, df_resid return _multivariate_test(hypotheses, exog_names, endog_names, fn) @Substitution(hypotheses_doc=_hypotheses_doc) def _multivariate_test(hypotheses, exog_names, endog_names, fn): """ Multivariate linear model hypotheses testing For y = x * params, where y are the dependent variables and x are the independent variables, testing L * params * M = 0 where L is the contrast matrix for hypotheses testing and M is the transformation matrix for transforming the dependent variables in y. Algorithm: T = L*inv(X'X)*L' H = M'B'L'*inv(T)*LBM E = M'(Y'Y - B'X'XB)M And then finding the eigenvalues of inv(H + E)*H .. [*] https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_introreg_sect012.htm Parameters ---------- %(hypotheses_doc)s k_xvar : int The number of independent variables k_yvar : int The number of dependent variables fn : function a function fn(contrast_L, transform_M) that returns E, H, q, df_resid where q is the rank of T matrix Returns ------- results : MANOVAResults """ k_xvar = len(exog_names) k_yvar = len(endog_names) results = {} for hypo in hypotheses: if len(hypo) ==2: name, L = hypo M = None C = None elif len(hypo) == 3: name, L, M = hypo C = None elif len(hypo) == 4: name, L, M, C = hypo else: raise ValueError('hypotheses must be a tuple of length 2, 3 or 4.' ' len(hypotheses)=%d' % len(hypo)) if any(isinstance(j, str) for j in L): L = DesignInfo(exog_names).linear_constraint(L).coefs else: if not isinstance(L, np.ndarray) or len(L.shape) != 2: raise ValueError('Contrast matrix L must be a 2-d array!') if L.shape[1] != k_xvar: raise ValueError('Contrast matrix L should have the same ' 'number of columns as exog! %d != %d' % (L.shape[1], k_xvar)) if M is None: M = np.eye(k_yvar) elif any(isinstance(j, str) for j in M): M = DesignInfo(endog_names).linear_constraint(M).coefs.T else: if M is not None: if not isinstance(M, np.ndarray) or len(M.shape) != 2: raise ValueError('Transform matrix M must be a 2-d array!') if M.shape[0] != k_yvar: raise ValueError('Transform matrix M should have the same ' 'number of rows as the number of columns ' 'of endog! %d != %d' % (M.shape[0], k_yvar)) if C is None: C = np.zeros([L.shape[0], M.shape[1]]) elif not isinstance(C, np.ndarray): raise ValueError('Constant matrix C must be a 2-d array!') if C.shape[0] != L.shape[0]: raise ValueError('contrast L and constant C must have the same ' 'number of rows! %d!=%d' % (L.shape[0], C.shape[0])) if C.shape[1] != M.shape[1]: raise ValueError('transform M and constant C must have the same ' 'number of columns! %d!=%d' % (M.shape[1], C.shape[1])) E, H, q, df_resid = fn(L, M, C) EH = np.add(E, H) p = matrix_rank(EH) # eigenvalues of inv(E + H)H eigv2 = np.sort(eigvals(solve(EH, H))) stat_table = multivariate_stats(eigv2, p, q, df_resid) results[name] = {'stat':stat_table, 'contrast_L':L, 'transform_M':M, 'constant_C':C} return results class _MultivariateOLS(Model): """ Multivariate linear model via least squares Parameters ---------- endog : array_like Dependent variables. A nobs x k_endog array where nobs is the number of observations and k_endog is the number of dependent variables exog : array_like Independent variables. A nobs x k_exog array where nobs is the number of observations and k_exog is the number of independent variables. An intercept is not included by default and should be added by the user (models specified using a formula include an intercept by default) Attributes ---------- endog : ndarray See Parameters. exog : ndarray See Parameters. """ _formula_max_endog = None def __init__(self, endog, exog, missing='none', hasconst=None, **kwargs): if len(endog.shape) == 1 or endog.shape[1] == 1: raise ValueError('There must be more than one dependent variable' ' to fit multivariate OLS!') super(_MultivariateOLS, self).__init__(endog, exog, missing=missing, hasconst=hasconst, **kwargs) def fit(self, method='svd'): self._fittedmod = _multivariate_ols_fit( self.endog, self.exog, method=method) return _MultivariateOLSResults(self) class _MultivariateOLSResults(object): """ _MultivariateOLS results class """ def __init__(self, fitted_mv_ols): if (hasattr(fitted_mv_ols, 'data') and hasattr(fitted_mv_ols.data, 'design_info')): self.design_info = fitted_mv_ols.data.design_info else: self.design_info = None self.exog_names = fitted_mv_ols.exog_names self.endog_names = fitted_mv_ols.endog_names self._fittedmod = fitted_mv_ols._fittedmod def __str__(self): return self.summary().__str__() @Substitution(hypotheses_doc=_hypotheses_doc) def mv_test(self, hypotheses=None): """ Linear hypotheses testing Parameters ---------- %(hypotheses_doc)s Returns ------- results: _MultivariateOLSResults Notes ----- Tests hypotheses of the form L * params * M = C where `params` is the regression coefficient matrix for the linear model y = x * params, `L` is the contrast matrix, `M` is the dependent variable transform matrix and C is the constant matrix. """ k_xvar = len(self.exog_names) if hypotheses is None: if self.design_info is not None: terms = self.design_info.term_name_slices hypotheses = [] for key in terms: L_contrast = np.eye(k_xvar)[terms[key], :] hypotheses.append([key, L_contrast, None]) else: hypotheses = [] for i in range(k_xvar): name = 'x%d' % (i) L = np.zeros([1, k_xvar]) L[i] = 1 hypotheses.append([name, L, None]) results = _multivariate_ols_test(hypotheses, self._fittedmod, self.exog_names, self.endog_names) return MultivariateTestResults(results, self.endog_names, self.exog_names) def summary(self): raise NotImplementedError class MultivariateTestResults(object): """ Multivariate test results class Returned by `mv_test` method of `_MultivariateOLSResults` class Attributes ---------- results : dict For hypothesis name `key`: results[key]['stat'] contains the multivariate test results results[key]['contrast_L'] contains the contrast_L matrix results[key]['transform_M'] contains the transform_M matrix results[key]['constant_C'] contains the constant_C matrix endog_names : str exog_names : str summary_frame : multiindex dataframe Returns results as a multiindex dataframe """ def __init__(self, mv_test_df, endog_names, exog_names): self.results = mv_test_df self.endog_names = endog_names self.exog_names = exog_names def __str__(self): return self.summary().__str__() def __getitem__(self, item): return self.results[item] @property def summary_frame(self): """ Return results as a multiindex dataframe """ df = [] for key in self.results: tmp = self.results[key]['stat'].copy() tmp.loc[:, 'Effect'] = key df.append(tmp.reset_index()) df = pd.concat(df, axis=0) df = df.set_index(['Effect', 'index']) df.index.set_names(['Effect', 'Statistic'], inplace=True) return df def summary(self, show_contrast_L=False, show_transform_M=False, show_constant_C=False): """ Parameters ---------- contrast_L : True or False Whether to show contrast_L matrix transform_M : True or False Whether to show transform_M matrix """ summ = summary2.Summary() summ.add_title('Multivariate linear model') for key in self.results: summ.add_dict({'':''}) df = self.results[key]['stat'].copy() df = df.reset_index() c = df.columns.values c[0] = key df.columns = c df.index = ['', '', '', ''] summ.add_df(df) if show_contrast_L: summ.add_dict({key:' contrast L='}) df = pd.DataFrame(self.results[key]['contrast_L'], columns=self.exog_names) summ.add_df(df) if show_transform_M: summ.add_dict({key:' transform M='}) df = pd.DataFrame(self.results[key]['transform_M'], index=self.endog_names) summ.add_df(df) if show_constant_C: summ.add_dict({key:' constant C='}) df = pd.DataFrame(self.results[key]['constant_C']) summ.add_df(df) return summ statsmodels-0.12.2/statsmodels/multivariate/pca.py000066400000000000000000000776221400612667500223500ustar00rootroot00000000000000"""Principal Component Analysis Author: josef-pktd Modified by Kevin Sheppard """ import numpy as np import pandas as pd from statsmodels.tools.sm_exceptions import (ValueWarning, EstimationWarning) from statsmodels.tools.validation import (string_like, array_like, bool_like, float_like, int_like, ) def _norm(x): return np.sqrt(np.sum(x * x)) class PCA(object): """ Principal Component Analysis Parameters ---------- data : array_like Variables in columns, observations in rows. ncomp : int, optional Number of components to return. If None, returns the as many as the smaller of the number of rows or columns in data. standardize : bool, optional Flag indicating to use standardized data with mean 0 and unit variance. standardized being True implies demean. Using standardized data is equivalent to computing principal components from the correlation matrix of data. demean : bool, optional Flag indicating whether to demean data before computing principal components. demean is ignored if standardize is True. Demeaning data but not standardizing is equivalent to computing principal components from the covariance matrix of data. normalize : bool , optional Indicates whether to normalize the factors to have unit inner product. If False, the loadings will have unit inner product. gls : bool, optional Flag indicating to implement a two-step GLS estimator where in the first step principal components are used to estimate residuals, and then the inverse residual variance is used as a set of weights to estimate the final principal components. Setting gls to True requires ncomp to be less then the min of the number of rows or columns. weights : ndarray, optional Series weights to use after transforming data according to standardize or demean when computing the principal components. method : str, optional Sets the linear algebra routine used to compute eigenvectors: * 'svd' uses a singular value decomposition (default). * 'eig' uses an eigenvalue decomposition of a quadratic form * 'nipals' uses the NIPALS algorithm and can be faster than SVD when ncomp is small and nvars is large. See notes about additional changes when using NIPALS. missing : {str, None} Method for missing data. Choices are: * 'drop-row' - drop rows with missing values. * 'drop-col' - drop columns with missing values. * 'drop-min' - drop either rows or columns, choosing by data retention. * 'fill-em' - use EM algorithm to fill missing value. ncomp should be set to the number of factors required. * `None` raises if data contains NaN values. tol : float, optional Tolerance to use when checking for convergence when using NIPALS. max_iter : int, optional Maximum iterations when using NIPALS. tol_em : float Tolerance to use when checking for convergence of the EM algorithm. max_em_iter : int Maximum iterations for the EM algorithm. Attributes ---------- factors : array or DataFrame nobs by ncomp array of of principal components (scores) scores : array or DataFrame nobs by ncomp array of of principal components - identical to factors loadings : array or DataFrame ncomp by nvar array of principal component loadings for constructing the factors coeff : array or DataFrame nvar by ncomp array of principal component loadings for constructing the projections projection : array or DataFrame nobs by var array containing the projection of the data onto the ncomp estimated factors rsquare : array or Series ncomp array where the element in the ith position is the R-square of including the fist i principal components. Note: values are calculated on the transformed data, not the original data ic : array or DataFrame ncomp by 3 array containing the Bai and Ng (2003) Information criteria. Each column is a different criteria, and each row represents the number of included factors. eigenvals : array or Series nvar array of eigenvalues eigenvecs : array or DataFrame nvar by nvar array of eigenvectors weights : ndarray nvar array of weights used to compute the principal components, normalized to unit length transformed_data : ndarray Standardized, demeaned and weighted data used to compute principal components and related quantities cols : ndarray Array of indices indicating columns used in the PCA rows : ndarray Array of indices indicating rows used in the PCA Notes ----- The default options perform principal component analysis on the demeaned, unit variance version of data. Setting standardize to False will instead only demean, and setting both standardized and demean to False will not alter the data. Once the data have been transformed, the following relationships hold when the number of components (ncomp) is the same as tne minimum of the number of observation or the number of variables. .. math: X' X = V \\Lambda V' .. math: F = X V .. math: X = F V' where X is the `data`, F is the array of principal components (`factors` or `scores`), and V is the array of eigenvectors (`loadings`) and V' is the array of factor coefficients (`coeff`). When weights are provided, the principal components are computed from the modified data .. math: \\Omega^{-\\frac{1}{2}} X where :math:`\\Omega` is a diagonal matrix composed of the weights. For example, when using the GLS version of PCA, the elements of :math:`\\Omega` will be the inverse of the variances of the residuals from .. math: X - F V' where the number of factors is less than the rank of X References ---------- .. [*] J. Bai and S. Ng, "Determining the number of factors in approximate factor models," Econometrica, vol. 70, number 1, pp. 191-221, 2002 Examples -------- Basic PCA using the correlation matrix of the data >>> import numpy as np >>> from statsmodels.multivariate.pca import PCA >>> x = np.random.randn(100)[:, None] >>> x = x + np.random.randn(100, 100) >>> pc = PCA(x) Note that the principal components are computed using a SVD and so the correlation matrix is never constructed, unless method='eig'. PCA using the covariance matrix of the data >>> pc = PCA(x, standardize=False) Limiting the number of factors returned to 1 computed using NIPALS >>> pc = PCA(x, ncomp=1, method='nipals') >>> pc.factors.shape (100, 1) """ def __init__(self, data, ncomp=None, standardize=True, demean=True, normalize=True, gls=False, weights=None, method='svd', missing=None, tol=5e-8, max_iter=1000, tol_em=5e-8, max_em_iter=100): self._index = None self._columns = [] if isinstance(data, pd.DataFrame): self._index = data.index self._columns = data.columns self.data = array_like(data, "data", ndim=2) # Store inputs self._gls = bool_like(gls, "gls") self._normalize = bool_like(normalize, "normalize") self._tol = float_like(tol, "tol") if not 0 < self._tol < 1: raise ValueError('tol must be strictly between 0 and 1') self._max_iter = int_like(max_iter, "int_like") self._max_em_iter = int_like(max_em_iter, "max_em_iter") self._tol_em = float_like(tol_em, "tol_em") # Prepare data self._standardize = bool_like(standardize, "standardize") self._demean = bool_like(demean, "demean") self._nobs, self._nvar = self.data.shape weights = array_like(weights, "weights", maxdim=1, optional=True) if weights is None: weights = np.ones(self._nvar) else: weights = np.array(weights).flatten() if weights.shape[0] != self._nvar: raise ValueError('weights should have nvar elements') weights = weights / np.sqrt((weights ** 2.0).mean()) self.weights = weights # Check ncomp against maximum min_dim = min(self._nobs, self._nvar) self._ncomp = min_dim if ncomp is None else ncomp if self._ncomp > min_dim: import warnings warn = 'The requested number of components is more than can be ' \ 'computed from data. The maximum number of components is ' \ 'the minimum of the number of observations or variables' warnings.warn(warn, ValueWarning) self._ncomp = min_dim self._method = method # Workaround to avoid instance methods in __dict__ if self._method not in ('eig', 'svd', 'nipals'): raise ValueError('method {0} is not known.'.format(method)) self.rows = np.arange(self._nobs) self.cols = np.arange(self._nvar) # Handle missing self._missing = string_like(missing, "missing", optional=True) self._adjusted_data = self.data self._adjust_missing() # Update size self._nobs, self._nvar = self._adjusted_data.shape if self._ncomp == np.min(self.data.shape): self._ncomp = np.min(self._adjusted_data.shape) elif self._ncomp > np.min(self._adjusted_data.shape): raise ValueError('When adjusting for missing values, user ' 'provided ncomp must be no larger than the ' 'smallest dimension of the ' 'missing-value-adjusted data size.') # Attributes and internal values self._tss = 0.0 self._ess = None self.transformed_data = None self._mu = None self._sigma = None self._ess_indiv = None self._tss_indiv = None self.scores = self.factors = None self.loadings = None self.coeff = None self.eigenvals = None self.eigenvecs = None self.projection = None self.rsquare = None self.ic = None # Prepare data self.transformed_data = self._prepare_data() # Perform the PCA self._pca() if gls: self._compute_gls_weights() self.transformed_data = self._prepare_data() self._pca() # Final calculations self._compute_rsquare_and_ic() if self._index is not None: self._to_pandas() def _adjust_missing(self): """ Implements alternatives for handling missing values """ def keep_col(x): index = np.logical_not(np.any(np.isnan(x), 0)) return x[:, index], index def keep_row(x): index = np.logical_not(np.any(np.isnan(x), 1)) return x[index, :], index if self._missing == 'drop-col': self._adjusted_data, index = keep_col(self.data) self.cols = np.where(index)[0] self.weights = self.weights[index] elif self._missing == 'drop-row': self._adjusted_data, index = keep_row(self.data) self.rows = np.where(index)[0] elif self._missing == 'drop-min': drop_col, drop_col_index = keep_col(self.data) drop_col_size = drop_col.size drop_row, drop_row_index = keep_row(self.data) drop_row_size = drop_row.size if drop_row_size > drop_col_size: self._adjusted_data = drop_row self.rows = np.where(drop_row_index)[0] else: self._adjusted_data = drop_col self.weights = self.weights[drop_col_index] self.cols = np.where(drop_col_index)[0] elif self._missing == 'fill-em': self._adjusted_data = self._fill_missing_em() elif self._missing is None: if not np.isfinite(self._adjusted_data).all(): raise ValueError("""\ data contains non-finite values (inf, NaN). You should drop these values or use one of the methods for adjusting data for missing-values.""") else: raise ValueError('missing method is not known.') if self._index is not None: self._columns = self._columns[self.cols] self._index = self._index[self.rows] # Check adjusted data size if self._adjusted_data.size == 0: raise ValueError('Removal of missing values has eliminated ' 'all data.') def _compute_gls_weights(self): """ Computes GLS weights based on percentage of data fit """ projection = np.asarray(self.project(transform=False)) errors = self.transformed_data - projection if self._ncomp == self._nvar: raise ValueError('gls can only be used when ncomp < nvar ' 'so that residuals have non-zero variance') var = (errors ** 2.0).mean(0) weights = 1.0 / var weights = weights / np.sqrt((weights ** 2.0).mean()) nvar = self._nvar eff_series_perc = (1.0 / sum((weights / weights.sum()) ** 2.0)) / nvar if eff_series_perc < 0.1: eff_series = int(np.round(eff_series_perc * nvar)) import warnings warn = f"""\ Many series are being down weighted by GLS. Of the {nvar} series, the GLS estimates are based on only {eff_series} (effective) series.""" warnings.warn(warn, EstimationWarning) self.weights = weights def _pca(self): """ Main PCA routine """ self._compute_eig() self._compute_pca_from_eig() self.projection = self.project() def __repr__(self): string = self.__str__() string = string[:-1] string += ', id: ' + hex(id(self)) + ')' return string def __str__(self): string = 'Principal Component Analysis(' string += 'nobs: ' + str(self._nobs) + ', ' string += 'nvar: ' + str(self._nvar) + ', ' if self._standardize: kind = 'Standardize (Correlation)' elif self._demean: kind = 'Demean (Covariance)' else: kind = 'None' string += 'transformation: ' + kind + ', ' if self._gls: string += 'GLS, ' string += 'normalization: ' + str(self._normalize) + ', ' string += 'number of components: ' + str(self._ncomp) + ', ' string += 'method: ' + 'Eigenvalue' if self._method == 'eig' else 'SVD' string += ')' return string def _prepare_data(self): """ Standardize or demean data. """ adj_data = self._adjusted_data if np.all(np.isnan(adj_data)): return np.empty(adj_data.shape[1]).fill(np.nan) self._mu = np.nanmean(adj_data, axis=0) self._sigma = np.sqrt(np.nanmean((adj_data - self._mu) ** 2.0, axis=0)) if self._standardize: data = (adj_data - self._mu) / self._sigma elif self._demean: data = (adj_data - self._mu) else: data = adj_data return data / np.sqrt(self.weights) def _compute_eig(self): """ Wrapper for actual eigenvalue method This is a workaround to avoid instance methods in __dict__ """ if self._method == 'eig': return self._compute_using_eig() elif self._method == 'svd': return self._compute_using_svd() else: # self._method == 'nipals' return self._compute_using_nipals() def _compute_using_svd(self): """SVD method to compute eigenvalues and eigenvecs""" x = self.transformed_data u, s, v = np.linalg.svd(x) self.eigenvals = s ** 2.0 self.eigenvecs = v.T def _compute_using_eig(self): """ Eigenvalue decomposition method to compute eigenvalues and eigenvectors """ x = self.transformed_data self.eigenvals, self.eigenvecs = np.linalg.eigh(x.T.dot(x)) def _compute_using_nipals(self): """ NIPALS implementation to compute small number of eigenvalues and eigenvectors """ x = self.transformed_data if self._ncomp > 1: x = x + 0.0 # Copy tol, max_iter, ncomp = self._tol, self._max_iter, self._ncomp vals = np.zeros(self._ncomp) vecs = np.zeros((self._nvar, self._ncomp)) for i in range(ncomp): max_var_ind = np.argmax(x.var(0)) factor = x[:, [max_var_ind]] _iter = 0 diff = 1.0 while diff > tol and _iter < max_iter: vec = x.T.dot(factor) / (factor.T.dot(factor)) vec = vec / np.sqrt(vec.T.dot(vec)) factor_last = factor factor = x.dot(vec) / (vec.T.dot(vec)) diff = _norm(factor - factor_last) / _norm(factor) _iter += 1 vals[i] = (factor ** 2).sum() vecs[:, [i]] = vec if ncomp > 1: x -= factor.dot(vec.T) self.eigenvals = vals self.eigenvecs = vecs def _fill_missing_em(self): """ EM algorithm to fill missing values """ non_missing = np.logical_not(np.isnan(self.data)) # If nothing missing, return without altering the data if np.all(non_missing): return self.data # 1. Standardized data as needed data = self.transformed_data = np.asarray(self._prepare_data()) ncomp = self._ncomp # 2. Check for all nans col_non_missing = np.sum(non_missing, 1) row_non_missing = np.sum(non_missing, 0) if np.any(col_non_missing < ncomp) or np.any(row_non_missing < ncomp): raise ValueError('Implementation requires that all columns and ' 'all rows have at least ncomp non-missing values') # 3. Get mask mask = np.isnan(data) # 4. Compute mean mu = np.nanmean(data, 0) # 5. Replace missing with mean projection = np.ones((self._nobs, 1)) * mu projection_masked = projection[mask] data[mask] = projection_masked # 6. Compute eigenvalues and fit diff = 1.0 _iter = 0 while diff > self._tol_em and _iter < self._max_em_iter: last_projection_masked = projection_masked # Set transformed data to compute eigenvalues self.transformed_data = data # Call correct eig function here self._compute_eig() # Call function to compute factors and projection self._compute_pca_from_eig() projection = np.asarray(self.project(transform=False, unweight=False)) projection_masked = projection[mask] data[mask] = projection_masked delta = last_projection_masked - projection_masked diff = _norm(delta) / _norm(projection_masked) _iter += 1 # Must copy to avoid overwriting original data since replacing values data = self._adjusted_data + 0.0 projection = np.asarray(self.project()) data[mask] = projection[mask] return data def _compute_pca_from_eig(self): """ Compute relevant statistics after eigenvalues have been computed """ # Ensure sorted largest to smallest vals, vecs = self.eigenvals, self.eigenvecs indices = np.argsort(vals) indices = indices[::-1] vals = vals[indices] vecs = vecs[:, indices] if (vals <= 0).any(): # Discard and warn num_good = vals.shape[0] - (vals <= 0).sum() if num_good < self._ncomp: import warnings warnings.warn('Only {num:d} eigenvalues are positive. ' 'This is the maximum number of components ' 'that can be extracted.'.format(num=num_good), EstimationWarning) self._ncomp = num_good vals[num_good:] = np.finfo(np.float64).tiny # Use ncomp for the remaining calculations vals = vals[:self._ncomp] vecs = vecs[:, :self._ncomp] self.eigenvals, self.eigenvecs = vals, vecs # Select correct number of components to return self.scores = self.factors = self.transformed_data.dot(vecs) self.loadings = vecs self.coeff = vecs.T if self._normalize: self.coeff = (self.coeff.T * np.sqrt(vals)).T self.factors /= np.sqrt(vals) self.scores = self.factors def _compute_rsquare_and_ic(self): """ Final statistics to compute """ # TSS and related calculations # TODO: This needs careful testing, with and without weights, # gls, standardized and demean weights = self.weights ss_data = self.transformed_data * np.sqrt(weights) self._tss_indiv = np.sum(ss_data ** 2, 0) self._tss = np.sum(self._tss_indiv) self._ess = np.zeros(self._ncomp + 1) self._ess_indiv = np.zeros((self._ncomp + 1, self._nvar)) for i in range(self._ncomp + 1): # Projection in the same space as transformed_data projection = self.project(ncomp=i, transform=False, unweight=False) indiv_rss = (projection ** 2).sum(axis=0) rss = indiv_rss.sum() self._ess[i] = self._tss - rss self._ess_indiv[i, :] = self._tss_indiv - indiv_rss self.rsquare = 1.0 - self._ess / self._tss # Information Criteria ess = self._ess invalid = ess <= 0 # Prevent log issues of 0 if invalid.any(): last_obs = (np.where(invalid)[0]).min() ess = ess[:last_obs] log_ess = np.log(ess) r = np.arange(ess.shape[0]) nobs, nvar = self._nobs, self._nvar sum_to_prod = (nobs + nvar) / (nobs * nvar) min_dim = min(nobs, nvar) penalties = np.array([sum_to_prod * np.log(1.0 / sum_to_prod), sum_to_prod * np.log(min_dim), np.log(min_dim) / min_dim]) penalties = penalties[:, None] ic = log_ess + r * penalties self.ic = ic.T def project(self, ncomp=None, transform=True, unweight=True): """ Project series onto a specific number of factors. Parameters ---------- ncomp : int, optional Number of components to use. If omitted, all components initially computed are used. transform : bool, optional Flag indicating whether to return the projection in the original space of the data (True, default) or in the space of the standardized/demeaned data. unweight : bool, optional Flag indicating whether to undo the effects of the estimation weights. Returns ------- array_like The nobs by nvar array of the projection onto ncomp factors. Notes ----- """ # Projection needs to be scaled/shifted based on inputs ncomp = self._ncomp if ncomp is None else ncomp if ncomp > self._ncomp: raise ValueError('ncomp must be smaller than the number of ' 'components computed.') factors = np.asarray(self.factors) coeff = np.asarray(self.coeff) projection = factors[:, :ncomp].dot(coeff[:ncomp, :]) if transform or unweight: projection *= np.sqrt(self.weights) if transform: # Remove the weights, which do not depend on transformation if self._standardize: projection *= self._sigma if self._standardize or self._demean: projection += self._mu if self._index is not None: projection = pd.DataFrame(projection, columns=self._columns, index=self._index) return projection def _to_pandas(self): """ Returns pandas DataFrames for all values """ index = self._index # Principal Components num_zeros = np.ceil(np.log10(self._ncomp)) comp_str = 'comp_{0:0' + str(int(num_zeros)) + 'd}' cols = [comp_str.format(i) for i in range(self._ncomp)] df = pd.DataFrame(self.factors, columns=cols, index=index) self.scores = self.factors = df # Projections df = pd.DataFrame(self.projection, columns=self._columns, index=index) self.projection = df # Weights df = pd.DataFrame(self.coeff, index=cols, columns=self._columns) self.coeff = df # Loadings df = pd.DataFrame(self.loadings, index=self._columns, columns=cols) self.loadings = df # eigenvals self.eigenvals = pd.Series(self.eigenvals) self.eigenvals.name = 'eigenvals' # eigenvecs vec_str = comp_str.replace('comp', 'eigenvec') cols = [vec_str.format(i) for i in range(self.eigenvecs.shape[1])] self.eigenvecs = pd.DataFrame(self.eigenvecs, columns=cols) # R2 self.rsquare = pd.Series(self.rsquare) self.rsquare.index.name = 'ncomp' self.rsquare.name = 'rsquare' # IC self.ic = pd.DataFrame(self.ic, columns=['IC_p1', 'IC_p2', 'IC_p3']) self.ic.index.name = 'ncomp' def plot_scree(self, ncomp=None, log_scale=True, cumulative=False, ax=None): """ Plot of the ordered eigenvalues Parameters ---------- ncomp : int, optional Number of components ot include in the plot. If None, will included the same as the number of components computed log_scale : boot, optional Flag indicating whether ot use a log scale for the y-axis cumulative : bool, optional Flag indicating whether to plot the eigenvalues or cumulative eigenvalues ax : AxesSubplot, optional An axes on which to draw the graph. If omitted, new a figure is created Returns ------- matplotlib.figure.Figure The handle to the figure. """ import statsmodels.graphics.utils as gutils fig, ax = gutils.create_mpl_ax(ax) ncomp = self._ncomp if ncomp is None else ncomp vals = np.asarray(self.eigenvals) vals = vals[:self._ncomp] if cumulative: vals = np.cumsum(vals) if log_scale: ax.set_yscale('log') ax.plot(np.arange(ncomp), vals[: ncomp], 'bo') ax.autoscale(tight=True) xlim = np.array(ax.get_xlim()) sp = xlim[1] - xlim[0] xlim += 0.02 * np.array([-sp, sp]) ax.set_xlim(xlim) ylim = np.array(ax.get_ylim()) scale = 0.02 if log_scale: sp = np.log(ylim[1] / ylim[0]) ylim = np.exp(np.array([np.log(ylim[0]) - scale * sp, np.log(ylim[1]) + scale * sp])) else: sp = ylim[1] - ylim[0] ylim += scale * np.array([-sp, sp]) ax.set_ylim(ylim) ax.set_title('Scree Plot') ax.set_ylabel('Eigenvalue') ax.set_xlabel('Component Number') fig.tight_layout() return fig def plot_rsquare(self, ncomp=None, ax=None): """ Box plots of the individual series R-square against the number of PCs. Parameters ---------- ncomp : int, optional Number of components ot include in the plot. If None, will plot the minimum of 10 or the number of computed components. ax : AxesSubplot, optional An axes on which to draw the graph. If omitted, new a figure is created. Returns ------- matplotlib.figure.Figure The handle to the figure. """ import statsmodels.graphics.utils as gutils fig, ax = gutils.create_mpl_ax(ax) ncomp = 10 if ncomp is None else ncomp ncomp = min(ncomp, self._ncomp) # R2s in rows, series in columns r2s = 1.0 - self._ess_indiv / self._tss_indiv r2s = r2s[1:] r2s = r2s[:ncomp] ax.boxplot(r2s.T) ax.set_title('Individual Input $R^2$') ax.set_ylabel('$R^2$') ax.set_xlabel('Number of Included Principal Components') return fig def pca(data, ncomp=None, standardize=True, demean=True, normalize=True, gls=False, weights=None, method='svd'): """ Perform Principal Component Analysis (PCA). Parameters ---------- data : ndarray Variables in columns, observations in rows. ncomp : int, optional Number of components to return. If None, returns the as many as the smaller to the number of rows or columns of data. standardize : bool, optional Flag indicating to use standardized data with mean 0 and unit variance. standardized being True implies demean. demean : bool, optional Flag indicating whether to demean data before computing principal components. demean is ignored if standardize is True. normalize : bool , optional Indicates whether th normalize the factors to have unit inner product. If False, the loadings will have unit inner product. gls : bool, optional Flag indicating to implement a two-step GLS estimator where in the first step principal components are used to estimate residuals, and then the inverse residual variance is used as a set of weights to estimate the final principal components weights : ndarray, optional Series weights to use after transforming data according to standardize or demean when computing the principal components. method : str, optional Determines the linear algebra routine uses. 'eig', the default, uses an eigenvalue decomposition. 'svd' uses a singular value decomposition. Returns ------- factors : {ndarray, DataFrame} Array (nobs, ncomp)of of principal components (also known as scores). loadings : {ndarray, DataFrame} Array (ncomp, nvar) of principal component loadings for constructing the factors. projection : {ndarray, DataFrame} Array (nobs, nvar) containing the projection of the data onto the ncomp estimated factors. rsquare : {ndarray, Series} Array (ncomp,) where the element in the ith position is the R-square of including the fist i principal components. The values are calculated on the transformed data, not the original data. ic : {ndarray, DataFrame} Array (ncomp, 3) containing the Bai and Ng (2003) Information criteria. Each column is a different criteria, and each row represents the number of included factors. eigenvals : {ndarray, Series} Array of eigenvalues (nvar,). eigenvecs : {ndarray, DataFrame} Array of eigenvectors. (nvar, nvar). Notes ----- This is a simple function wrapper around the PCA class. See PCA for more information and additional methods. """ pc = PCA(data, ncomp=ncomp, standardize=standardize, demean=demean, normalize=normalize, gls=gls, weights=weights, method=method) return (pc.factors, pc.loadings, pc.projection, pc.rsquare, pc.ic, pc.eigenvals, pc.eigenvecs) statsmodels-0.12.2/statsmodels/multivariate/plots.py000066400000000000000000000104201400612667500227250ustar00rootroot00000000000000import matplotlib.pyplot as plt import numpy as np def plot_scree(eigenvals, total_var, ncomp=None, x_label='factor'): """ Plot of the ordered eigenvalues and variance explained for the loadings Parameters ---------- eigenvals : array_like The eigenvalues total_var : float the total variance (for plotting percent variance explained) ncomp : int, optional Number of factors to include in the plot. If None, will included the same as the number of maximum possible loadings x_label : str label of x-axis Returns ------- Figure Handle to the figure. """ fig = plt.figure() ncomp = len(eigenvals) if ncomp is None else ncomp vals = eigenvals vals = vals[:ncomp] # vals = np.cumsum(vals) ax = fig.add_subplot(121) ax.plot(np.arange(ncomp), vals[: ncomp], 'b-o') ax.autoscale(tight=True) xlim = np.array(ax.get_xlim()) sp = xlim[1] - xlim[0] xlim += 0.02 * np.array([-sp, sp]) ax.set_xticks(np.arange(ncomp)) ax.set_xlim(xlim) ylim = np.array(ax.get_ylim()) scale = 0.02 sp = ylim[1] - ylim[0] ylim += scale * np.array([-sp, sp]) ax.set_ylim(ylim) ax.set_title('Scree Plot') ax.set_ylabel('Eigenvalue') ax.set_xlabel(x_label) per_variance = vals / total_var cumper_variance = np.cumsum(per_variance) ax = fig.add_subplot(122) ax.plot(np.arange(ncomp), per_variance[: ncomp], 'b-o') ax.plot(np.arange(ncomp), cumper_variance[: ncomp], 'g--o') ax.autoscale(tight=True) xlim = np.array(ax.get_xlim()) sp = xlim[1] - xlim[0] xlim += 0.02 * np.array([-sp, sp]) ax.set_xticks(np.arange(ncomp)) ax.set_xlim(xlim) ylim = np.array(ax.get_ylim()) scale = 0.02 sp = ylim[1] - ylim[0] ylim += scale * np.array([-sp, sp]) ax.set_ylim(ylim) ax.set_title('Variance Explained') ax.set_ylabel('Proportion') ax.set_xlabel(x_label) ax.legend(['Proportion', 'Cumulative'], loc=5) fig.tight_layout() return fig def plot_loadings(loadings, col_names=None, row_names=None, loading_pairs=None, percent_variance=None, title='Factor patterns'): """ Plot factor loadings in 2-d plots Parameters ---------- loadings : array like Each column is a component (or factor) col_names : a list of strings column names of `loadings` row_names : a list of strings row names of `loadings` loading_pairs : None or a list of tuples Specify plots. Each tuple (i, j) represent one figure, i and j is the loading number for x-axis and y-axis, respectively. If `None`, all combinations of the loadings will be plotted. percent_variance : array_like The percent variance explained by each factor. Returns ------- figs : a list of figure handles """ k_var, n_factor = loadings.shape if loading_pairs is None: loading_pairs = [] for i in range(n_factor): for j in range(i + 1,n_factor): loading_pairs.append([i, j]) if col_names is None: col_names = ["factor %d" % i for i in range(n_factor)] if row_names is None: row_names = ["var %d" % i for i in range(k_var)] figs = [] for item in loading_pairs: i = item[0] j = item[1] fig = plt.figure(figsize=(7, 7)) figs.append(fig) ax = fig.add_subplot(111) for k in range(loadings.shape[0]): plt.text(loadings[k, i], loadings[k, j], row_names[k], fontsize=12) ax.plot(loadings[:, i], loadings[:, j], 'bo') ax.set_title(title) if percent_variance is not None: x_str = '%s (%.1f%%)' % (col_names[i], percent_variance[i]) y_str = '%s (%.1f%%)' % (col_names[j], percent_variance[j]) ax.set_xlabel(x_str) ax.set_ylabel(y_str) else: ax.set_xlabel(col_names[i]) ax.set_ylabel(col_names[j]) v = 1.05 xlim = np.array([-v, v]) ylim = np.array([-v, v]) ax.plot(xlim, [0, 0], 'k--') ax.plot([0, 0], ylim, 'k--') ax.set_aspect('equal', 'datalim') ax.set_xlim(xlim) ax.set_ylim(ylim) fig.tight_layout() return figs statsmodels-0.12.2/statsmodels/multivariate/tests/000077500000000000000000000000001400612667500223575ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/multivariate/tests/__init__.py000066400000000000000000000000001400612667500244560ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/multivariate/tests/results/000077500000000000000000000000001400612667500240605ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/multivariate/tests/results/__init__.py000066400000000000000000000000001400612667500261570ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/multivariate/tests/results/datamlw.py000066400000000000000000000363231400612667500260720ustar00rootroot00000000000000from numpy import array from statsmodels.tools.testing import Holder data = Holder() data.comment = 'generated data, divide by 1000' data.name = 'data' data.xo = array([ [-419, -731, -1306, -1294], [6, 529, -200, -437], [-27, -833, -6, -564], [-304, -273, -502, -739], [1377, -912, 927, 280], [-375, -517, -514, 49], [247, -504, 123, -259], [712, 534, -773, 286], [195, -1080, 3256, -178], [-854, 75, -706, -1084], [-1219, -612, -15, -203], [550, -628, -483, -2686], [-365, 1376, -1266, 317], [-489, 544, -195, 431], [-656, 854, 840, -723], [16, -1385, -880, -460], [258, -2252, 96, 54], [2049, -750, -1115, 381], [-65, 280, -777, 416], [755, 82, -806, 1027], [-39, -170, -2134, 743], [-859, 780, 746, -133], [762, 252, -450, -459], [-941, -202, 49, -202], [-54, 115, 455, 388], [-1348, 1246, 1430, -480], [229, -535, -1831, 1524], [-651, -167, 2116, 483], [-1249, -1373, 888, -1092], [-75, -2162, 486, -496], [2436, -1627, -1069, 162], [-63, 560, -601, 587], [-60, 1051, -277, 1323], [1329, -1294, 68, 5], [1532, -633, -923, 696], [669, 895, -1762, -375], [1129, -548, 2064, 609], [1320, 573, 2119, 270], [-213, -412, -2517, 1685], [73, -979, 1312, -1220], [-1360, -2107, -237, 1522], [-645, 205, -543, -169], [-212, 1072, 543, -128], [-352, -129, -605, -904], [511, 85, 167, -1914], [1515, 1862, 942, 1622], [-465, 623, -495, -89], [-1396, -979, 1758, 128], [-255, -47, 980, 501], [-1282, -58, -49, -610], [-889, -1177, -492, 494], [1415, 1146, 696, -722], [1237, -224, -1609, -64], [-528, -1625, 231, 883], [-327, 1636, -476, -361], [-781, 793, 1882, 234], [-506, -561, 1988, -810], [-1233, 1467, -261, 2164], [53, 1069, 824, 2123], [-1200, -441, -321, 339], [1606, 298, -995, 1292], [-1740, -672, -1628, -129], [-1450, -354, 224, -657], [-2556, 1006, -706, -1453], [-717, -463, 345, -1821], [1056, -38, -420, -455], [-523, 565, 425, 1138], [-1030, -187, 683, 78], [-214, -312, -1171, -528], [819, 736, -265, 423], [1339, 351, 1142, 579], [-387, -126, -1573, 2346], [969, 2, 327, -134], [163, 227, 90, 2021], [1022, -1076, 174, 304], [1042, 1317, 311, 880], [2018, -840, 295, 2651], [-277, 566, 1147, -189], [20, 467, 1262, 263], [-663, 1061, -1552, -1159], [1830, 391, 2534, -199], [-487, 752, -1061, 351], [-2138, -556, -367, -457], [-868, -411, -559, 726], [1770, 819, -892, -363], [553, -736, -169, -490], [388, -503, 809, -821], [-516, -1452, -192, 483], [493, 2904, 1318, 2591], [175, 584, -1001, 1675], [1316, -1596, -460, 1500], [1212, 214, -644, -696], [-501, 338, 1197, -841], [-587, -469, -1101, 24], [-1205, 1910, 659, 1232], [-150, 398, 594, 394], [34, -663, 235, -334], [-1580, 647, 239, -351], [-2177, -345, 1215, -1494], [1923, 329, -152, 1128]]) princomp1 = Holder() princomp1.comment = 'mlab.princomp(x, nout=3)' princomp1.factors = array([ [-.83487832815382, -1.75681522344645, -.50882660928949, -.59661466511045], [-.18695786699253, -.10732909330422, .23971799542554, -.75468286946853], [-.57403949255604, -.39667006607544, -.7927838094217, .02652621881328], [-.60828125251513, -.75979035898754, -.20148864200404, -.40278856050237], [.55997928601548, .88869370546643, -1.55474410845786, .23033958281961], [-.18023239851961, -.72398923145328, -.07056264751117, .29292391015376], [-.189029743271, -.05888596186903, -.63882208368513, -.05682951829677], [.94694345324739, -.33448036234864, .16665867708366, -.67190948646953], [-1.355171899399, 2.58899695901774, -1.53157119606928, .93743278678908], [-1.06797676403358, -1.01894055566289, .29181722134698, -.65261957826524], [-1.08919199915725, -.5395876105009, .18846579824378, .61935728909742], [-1.36598849770841, -1.00986627679465, -1.6090477073157, -1.82708847399443], # noqa:E501 [.561511276285, -.74919011595195, 1.49872898209738, -.80588545345232], [.04805787176428, -.05522267212748, .82943784435024, .01537039050312], [-1.12006939155398, .73462770352006, .58868274831601, -.67786987413505], [-.26087838474316, -1.33362289066951, -1.02932517860259, .24865839951801], [-.24666198784909, -.58247196399204, -1.78971960966265, 1.18908143657302], [1.80675592845666, -.73341258204636, -1.45012544705912, -.44875329121288], [.4794281391435, -.57169295903913, 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[1.35642227654922, .53204130038923, .69844068787197, 1.04544871561741], [.57797880484094, .08044525072063, -1.32634695941334, .35179408060132], [1.29437232500619, 1.07461562326311, .54545226737269, -.6836610122092], [2.74736726573105, .90881277479338, -.98342785084735, 1.38171127911719], [-.67749479829901, 1.10093727650063, .28416704607992, -.24984509303044], [-.24513961858774, 1.32098977907584, .16904762754153, .00886790270539], [-.5392290825383, -1.43851802284774, 1.0064737206577, -1.52649870396689], [.19486366400459, 2.77236000318994, -1.32201258472682, -.75922390642504], [.33271229220962, -.78464273816827, 1.09930224781861, -.32184679755027], [-1.72814706427698, -1.09275114767838, .7451569579997, .72871211772761], [-.035506207751, -.72161367235521, .52828318684787, .87177739169758], [1.31224955134141, -.22742530984642, -.44682270809773, -1.72769462581607], [-.07125058353119, -.36850925227739, -1.01188688859296, -.24962251325969], [-.69840680770104, .4925285516285, -1.0255829922787, -.36214090052941], [-.2530614593082, -.68595709316063, -.56882710610856, 1.25787365685572], [1.93782484285419, 2.67095706598253, 2.4023579082791, -.09112046819432], [1.57782156817208, -.39819017512275, 1.01938038947667, .39718992194809], [1.6839282738726, -.37808442385434, -1.36566197748227, 1.22029200163339], [.54652714502605, -.38206797548206, -.70554510441189, -1.31224358889695], [-1.30026063006148, .90642495630747, .02711437433058, -.44482098905042], [-.1239033493518, -1.29112252171673, .18092802221218, .22673242779457], [.01152882540055, 1.13242883415094, 2.34980443084773, .17712319903618], [-.0505195424414, .6807219067402, .37771832345982, .0842510459176], [-.44230076745505, -.07002728477811, -.6716520563439, .09637247949641], [-1.31245480585229, -.01674966464909, 1.21063252882651, -.03927111631335], [-2.94268586886381, .20925236551048, .30321714445262, .22027672852006], [2.04121905977187, .58496246543101, -.5192457175416, -.37212298770116]]) princomp1.values = array([ [1.29489288337888], [1.12722515391348], [.94682423958163], [.65890241090379]]) princomp1.name = 'princomp1' princomp1.coef = array([ [.65989917631713, .22621848650964, -.5882833472413, -.40899997165748], [.15824945056105, .3189419948895, .71689623797385, -.5994104597619], [-.3488766362785, .90294049788532, -.17151017930575, .1832151967827], [.64635538301471, .17832458477678, .33251578268108, .66321815082225]]) princomp2 = Holder() princomp2.comment = 'mlab.princomp(x[:20,], nout=3)' princomp2.factors = array([ [.74592631465403, -.92093638563647, 1.10020213969681, -.20234362115983], [.40379773814409, -.23694214086306, -.53526599590626, .48048423978257], [-.43826559396565, -.26267383420164, .35939862515391, -.15176605914773], [.29427656853499, -.56363285386285, .19525662206552, -.0384830001072], [-1.4327917748351, 1.18414191887856, .05435949672922, .46861687286613], [.23033214569426, -.00452237842477, .00346120473054, -.61483888402985], [-.40976419499281, .10137131352284, 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array([ [1.16965204468073], [.77687367815155], [.72297937656591], [.32548581375971]]) princomp2.name = 'princomp2' princomp2.coef = array([ [-.13957162231397, .6561182967648, .32256106777669, .66781951188167], [.49534264552989, -.08241251099014, -.6919444767593, .51870674049413], [-.85614372781797, -.11427402995055, -.47665923729502, .16357058078438], [.04661912785591, .74138950947638, -.43584764555793, -.50813884128056]]) princomp3 = Holder() princomp3.comment = 'mlab.princomp(x[:20,]-x[:20,].mean(0), nout=3)' princomp3.factors = array([ [.74592631465403, -.92093638563647, 1.10020213969681, -.20234362115983], [.40379773814409, -.23694214086306, -.53526599590626, .48048423978257], [-.43826559396565, -.26267383420164, .35939862515391, -.15176605914773], [.29427656853499, -.56363285386285, .19525662206552, -.0384830001072], [-1.4327917748351, 1.18414191887856, .05435949672922, .46861687286613], [.23033214569426, -.00452237842477, .00346120473054, -.61483888402985], [-.40976419499281, 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princomp3.values = array([ [1.16965204468073], [.77687367815155], [.72297937656591], [.32548581375971]]) princomp3.name = 'princomp3' princomp3.coef = array([ [-.13957162231397, .6561182967648, .32256106777669, .66781951188167], [.49534264552989, -.08241251099014, -.6919444767593, .51870674049413], [-.85614372781797, -.11427402995055, -.47665923729502, .16357058078438], [.04661912785591, .74138950947638, -.43584764555793, -.50813884128056]]) statsmodels-0.12.2/statsmodels/multivariate/tests/results/factor_data.csv000066400000000000000000000072071400612667500270520ustar00rootroot00000000000000var1,var2,var3,var4,var5 2.3358,0.0044,0.3163,0.8698,1.4817 3.1387,-0.1494,1.1793,2.1482,-0.2141 0.0501,0.6111,-0.892,1.0971,-2.6557 -0.029,-1.7519,-0.5098,-0.5294,0.2512 -0.0012,-0.8835,3.1745,3.6743,2.9339 1.3228,0.1419,0.6433,2.5167,0.9105 0.9066,-0.7031,-0.9839,-0.0551,0.049 -1.5817,-1.332,1.0518,-1.1584,-0.9183 2.9412,-1.9048,-1.328,0.3225,-0.2039 -1.5636,-1.506,1.6153,1.8511,0.9356 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2, 110, 43]]) def test_cancorr(): # Compare results to SAS example: # https://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/ # viewer.htm#statug_cancorr_sect020.htm X1 = data_fit.iloc[:, :3] Y1 = data_fit.iloc[:, 3:] mod = CanCorr(Y1, X1) r = mod.corr_test() assert_almost_equal(r.stats_mv.loc["Wilks' lambda", 'Value'], 0.35039053, decimal=8) assert_almost_equal(r.stats_mv.loc["Pillai's trace", 'Value'], 0.67848151, decimal=8) assert_almost_equal(r.stats_mv.loc["Hotelling-Lawley trace", 'Value'], 1.77194146, decimal=8) assert_almost_equal(r.stats_mv.loc["Roy's greatest root", 'Value'], 1.72473874, decimal=8) assert_almost_equal(r.stats_mv.loc["Wilks' lambda", 'F Value'], 2.05, decimal=2) assert_almost_equal(r.stats_mv.loc["Pillai's trace", 'F Value'], 1.56, decimal=2) assert_almost_equal(r.stats_mv.loc["Hotelling-Lawley trace", 'F Value'], 2.64, decimal=2) assert_almost_equal(r.stats_mv.loc["Roy's greatest root", 'F Value'], 9.20, decimal=2) assert_almost_equal(r.stats_mv.loc["Wilks' lambda", 'Num DF'], 9, decimal=3) assert_almost_equal(r.stats_mv.loc["Pillai's trace", 'Num DF'], 9, decimal=3) assert_almost_equal(r.stats_mv.loc["Hotelling-Lawley trace", 'Num DF'], 9, decimal=3) assert_almost_equal(r.stats_mv.loc["Roy's greatest root", 'Num DF'], 3, decimal=3) assert_almost_equal(r.stats_mv.loc["Wilks' lambda", 'Den DF'], 34.223, decimal=3) assert_almost_equal(r.stats_mv.loc["Pillai's trace", 'Den DF'], 48, decimal=3) assert_almost_equal(r.stats_mv.loc["Hotelling-Lawley trace", 'Den DF'], 19.053, decimal=3) assert_almost_equal(r.stats_mv.loc["Roy's greatest root", 'Den DF'], 16, decimal=3) assert_almost_equal(r.stats_mv.loc["Wilks' lambda", 'Pr > F'], 0.0635, decimal=4) assert_almost_equal(r.stats_mv.loc["Pillai's trace", 'Pr > F'], 0.1551, decimal=4) assert_almost_equal(r.stats_mv.loc["Hotelling-Lawley trace", 'Pr > F'], 0.0357, decimal=4) assert_almost_equal(r.stats_mv.loc["Roy's greatest root", 'Pr > F'], 0.0009, decimal=4) assert_almost_equal(r.stats.loc[0, "Wilks' lambda"], 0.35039053, decimal=8) assert_almost_equal(r.stats.loc[1, "Wilks' lambda"], 0.95472266, decimal=8) assert_almost_equal(r.stats.loc[2, "Wilks' lambda"], 0.99473355, decimal=8) assert_almost_equal(r.stats.loc[0, 'F Value'], 2.05, decimal=2) assert_almost_equal(r.stats.loc[1, 'F Value'], 0.18, decimal=2) assert_almost_equal(r.stats.loc[2, 'F Value'], 0.08, decimal=2) assert_almost_equal(r.stats.loc[0, 'Num DF'], 9, decimal=2) assert_almost_equal(r.stats.loc[1, 'Num DF'], 4, decimal=2) assert_almost_equal(r.stats.loc[2, 'Num DF'], 1, decimal=2) assert_almost_equal(r.stats.loc[0, 'Den DF'], 34.223, decimal=3) assert_almost_equal(r.stats.loc[1, 'Den DF'], 30, decimal=2) assert_almost_equal(r.stats.loc[2, 'Den DF'], 16, decimal=2) assert_almost_equal(r.stats.loc[0, 'Pr > F'], 0.0635, decimal=4) assert_almost_equal(r.stats.loc[1, 'Pr > F'], 0.9491, decimal=4) assert_almost_equal(r.stats.loc[2, 'Pr > F'], 0.7748, decimal=4) statsmodels-0.12.2/statsmodels/multivariate/tests/test_factor.py000066400000000000000000000257301400612667500252550ustar00rootroot00000000000000# -*- coding: utf-8 -*- import os import numpy as np import pandas as pd from statsmodels.multivariate.factor import Factor from numpy.testing import (assert_equal, assert_array_almost_equal, assert_, assert_raises, assert_array_equal, assert_array_less, assert_allclose) import pytest try: import matplotlib.pyplot as plt missing_matplotlib = False plt.switch_backend('Agg') except ImportError: missing_matplotlib = True # Example data # https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/ # viewer.htm#statug_introreg_sect012.htm X = pd.DataFrame([['Minas Graes', 2.068, 2.070, 1.580, 1, 0], ['Minas Graes', 2.068, 2.074, 1.602, 2, 1], ['Minas Graes', 2.090, 2.090, 1.613, 3, 0], ['Minas Graes', 2.097, 2.093, 1.613, 4, 1], ['Minas Graes', 2.117, 2.125, 1.663, 5, 0], ['Minas Graes', 2.140, 2.146, 1.681, 6, 1], ['Matto Grosso', 2.045, 2.054, 1.580, 7, 0], ['Matto Grosso', 2.076, 2.088, 1.602, 8, 1], ['Matto Grosso', 2.090, 2.093, 1.643, 9, 0], ['Matto Grosso', 2.111, 2.114, 1.643, 10, 1], ['Santa Cruz', 2.093, 2.098, 1.653, 11, 0], ['Santa Cruz', 2.100, 2.106, 1.623, 12, 1], ['Santa Cruz', 2.104, 2.101, 1.653, 13, 0]], columns=['Loc', 'Basal', 'Occ', 'Max', 'id', 'alt']) def test_auto_col_name(): # Test auto generated variable names when endog_names is None mod = Factor(None, 2, corr=np.eye(11), endog_names=None, smc=False) assert_array_equal(mod.endog_names, ['var00', 'var01', 'var02', 'var03', 'var04', 'var05', 'var06', 'var07', 'var08', 'var09', 'var10']) def test_direct_corr_matrix(): # Test specifying the correlation matrix directly mod = Factor(None, 2, corr=np.corrcoef(X.iloc[:, 1:-1], rowvar=0), smc=False) results = mod.fit(tol=1e-10) a = np.array([[0.965392158864, 0.225880658666255], [0.967587154301, 0.212758741910989], [0.929891035996, -0.000603217967568], [0.486822656362, -0.869649573289374]]) assert_array_almost_equal(results.loadings, a, decimal=8) # Test set and get endog_names mod.endog_names = X.iloc[:, 1:-1].columns assert_array_equal(mod.endog_names, ['Basal', 'Occ', 'Max', 'id']) # Test set endog_names with the wrong number of elements assert_raises(ValueError, setattr, mod, 'endog_names', X.iloc[:, :1].columns) def test_unknown_fa_method_error(): # Test raise error if an unkonwn FA method is specified in fa.method mod = Factor(X.iloc[:, 1:-1], 2, method='ab') assert_raises(ValueError, mod.fit) def test_example_compare_to_R_output(): # Testing basic functions and compare to R output # R code for producing the results: # library(psych) # library(GPArotation) # Basal = c(2.068, 2.068, 2.09, 2.097, 2.117, 2.14, 2.045, 2.076, 2.09, 2.111, 2.093, 2.1, 2.104) # Occ = c(2.07, 2.074, 2.09, 2.093, 2.125, 2.146, 2.054, 2.088, 2.093, 2.114, 2.098, 2.106, 2.101) # Max = c(1.58, 1.602, 1.613, 1.613, 1.663, 1.681, 1.58, 1.602, 1.643, 1.643, 1.653, 1.623, 1.653) # id = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13) # Y <- cbind(Basal, Occ, Max, id) # a <- fa(Y, nfactors=2, fm="pa", rotate="none", SMC=FALSE, min.err=1e-10) # b <- cbind(a$loadings[,1], -a$loadings[,2]) # b # a <- fa(Y, nfactors=2, fm="pa", rotate="Promax", SMC=TRUE, min.err=1e-10) # b <- cbind(a$loadings[,1], a$loadings[,2]) # b # a <- fa(Y, nfactors=2, fm="pa", rotate="Varimax", SMC=TRUE, min.err=1e-10) # b <- cbind(a$loadings[,1], a$loadings[,2]) # b # a <- fa(Y, nfactors=2, fm="pa", rotate="quartimax", SMC=TRUE, min.err=1e-10) # b <- cbind(a$loadings[,1], -a$loadings[,2]) # b # a <- fa(Y, nfactors=2, fm="pa", rotate="oblimin", SMC=TRUE, min.err=1e-10) # b <- cbind(a$loadings[,1], a$loadings[,2]) # b # No rotation without squared multiple correlations prior # produce same results as in R `fa` mod = Factor(X.iloc[:, 1:-1], 2, smc=False) results = mod.fit(tol=1e-10) a = np.array([[0.965392158864, 0.225880658666255], [0.967587154301, 0.212758741910989], [0.929891035996, -0.000603217967568], [0.486822656362, -0.869649573289374]]) assert_array_almost_equal(results.loadings, a, decimal=8) # No rotation WITH squared multiple correlations prior # produce same results as in R `fa` mod = Factor(X.iloc[:, 1:-1], 2, smc=True) results = mod.fit() a = np.array([[0.97541115, 0.20280987], [0.97113975, 0.17207499], [0.9618705, -0.2004196], [0.37570708, -0.45821379]]) assert_array_almost_equal(results.loadings, a, decimal=8) # Same as R GRArotation results.rotate('varimax') a = np.array([[0.98828898, -0.12587155], [0.97424206, -0.15354033], [0.84418097, -0.502714], [0.20601929, -0.55558235]]) assert_array_almost_equal(results.loadings, a, decimal=8) results.rotate('quartimax') # Same as R fa a = np.array([[0.98935598, 0.98242714, 0.94078972, 0.33442284], [0.117190049, 0.086943252, -0.283332952, -0.489159543]]) assert_array_almost_equal(results.loadings, a.T, decimal=8) results.rotate('equamax') # Not the same as R fa results.rotate('promax') # Not the same as R fa results.rotate('biquartimin') # Not the same as R fa results.rotate('oblimin') # Same as R fa a = np.array([[1.02834170170, 1.00178840104, 0.71824931384, -0.00013510048], [0.06563421, 0.03096076, -0.39658839, -0.59261944]]) assert_array_almost_equal(results.loadings, a.T, decimal=8) # Testing result summary string results.rotate('varimax') desired = ( """ Factor analysis results ============================= Eigenvalues ----------------------------- Basal Occ Max id ----------------------------- 2.9609 0.3209 0.0000 -0.0000 ----------------------------- ----------------------------- Communality ----------------------------- Basal Occ Max id ----------------------------- 0.9926 0.9727 0.9654 0.3511 ----------------------------- ----------------------------- Pre-rotated loadings ----------------------------------- factor 0 factor 1 ----------------------------------- Basal 0.9754 0.2028 Occ 0.9711 0.1721 Max 0.9619 -0.2004 id 0.3757 -0.4582 ----------------------------- ----------------------------- varimax rotated loadings ----------------------------------- factor 0 factor 1 ----------------------------------- Basal 0.9883 -0.1259 Occ 0.9742 -0.1535 Max 0.8442 -0.5027 id 0.2060 -0.5556 ============================= """) actual = results.summary().as_text() actual = "\n".join(line.rstrip() for line in actual.splitlines()) + "\n" assert_equal(actual, desired) @pytest.mark.skipif(missing_matplotlib, reason='matplotlib not available') def test_plots(close_figures): mod = Factor(X.iloc[:, 1:], 3) results = mod.fit() results.rotate('oblimin') fig = results.plot_scree() fig_loadings = results.plot_loadings() assert_equal(3, len(fig_loadings)) @pytest.mark.smoke def test_getframe_smoke(): # mostly smoke tests for now mod = Factor(X.iloc[:, 1:-1], 2, smc=True) res = mod.fit() df = res.get_loadings_frame(style='raw') assert_(isinstance(df, pd.DataFrame)) lds = res.get_loadings_frame(style='strings', decimals=3, threshold=0.3) lds.to_latex() # The Styler option require jinja2, skip if not available try: from jinja2 import Template # noqa:F401 except ImportError: return # TODO: separate this and do pytest.skip? try: from pandas.io import formats as pd_formats except ImportError: from pandas import formats as pd_formats ldf = res.get_loadings_frame(style='display') assert_(isinstance(ldf, pd_formats.style.Styler)) assert_(isinstance(ldf.data, pd.DataFrame)) res.get_loadings_frame(style='display', decimals=3, threshold=0.2) res.get_loadings_frame(style='display', decimals=3, color_max='GAINSBORO') res.get_loadings_frame(style='display', decimals=3, threshold=0.45, highlight_max=False, sort_=False) def test_factor_missing(): xm = X.iloc[:, 1:-1].copy() nobs, k_endog = xm.shape xm.iloc[2,2] = np.nan mod = Factor(xm, 2) assert_equal(mod.nobs, nobs - 1) assert_equal(mod.k_endog, k_endog) assert_equal(mod.endog.shape, (nobs - 1, k_endog)) def _zscore(x): # helper function return (x - x.mean(0)) / x.std(0) @pytest.mark.smoke def test_factor_scoring(): path = os.path.abspath(__file__) dir_path = os.path.dirname(path) csv_path = os.path.join(dir_path, 'results', 'factor_data.csv') y = pd.read_csv(csv_path) csv_path = os.path.join(dir_path, 'results', 'factors_stata.csv') f_s = pd.read_csv(csv_path) # mostly smoke tests for now mod = Factor(y, 2) res = mod.fit(maxiter=1) res.rotate('varimax') f_reg = res.factor_scoring(method='reg') assert_allclose(f_reg * [1, -1], f_s[["f1", 'f2']].values, atol=1e-4, rtol=1e-3) f_bart = res.factor_scoring() assert_allclose(f_bart * [1, -1], f_s[["f1b", 'f2b']].values, atol=1e-4, rtol=1e-3) # check we have high correlation to ols and gls f_ols = res.factor_scoring(method='ols') f_gls = res.factor_scoring(method='gls') f_reg_z = _zscore(f_reg) f_ols_z = _zscore(f_ols) f_gls_z = _zscore(f_gls) assert_array_less(0.98, (f_ols_z * f_reg_z).mean(0)) assert_array_less(0.999, (f_gls_z * f_reg_z).mean(0)) # with oblique rotation res.rotate('oblimin') # Note: Stata has second factor with flipped sign compared to statsmodels assert_allclose(res._corr_factors()[0, 1], (-1) * 0.25651037, rtol=1e-3) f_reg = res.factor_scoring(method='reg') assert_allclose(f_reg * [1, -1], f_s[["f1o", 'f2o']].values, atol=1e-4, rtol=1e-3) f_bart = res.factor_scoring() assert_allclose(f_bart * [1, -1], f_s[["f1ob", 'f2ob']].values, atol=1e-4, rtol=1e-3) # check we have high correlation to ols and gls f_ols = res.factor_scoring(method='ols') f_gls = res.factor_scoring(method='gls') f_reg_z = _zscore(f_reg) f_ols_z = _zscore(f_ols) f_gls_z = _zscore(f_gls) assert_array_less(0.97, (f_ols_z * f_reg_z).mean(0)) assert_array_less(0.999, (f_gls_z * f_reg_z).mean(0)) # check provided endog f_ols2 = res.factor_scoring(method='ols', endog=res.model.endog) assert_allclose(f_ols2, f_ols, rtol=1e-13) statsmodels-0.12.2/statsmodels/multivariate/tests/test_manova.py000066400000000000000000000203061400612667500252520ustar00rootroot00000000000000# -*- coding: utf-8 -*- import numpy as np import pandas as pd import pytest from numpy.testing import assert_almost_equal, assert_raises from statsmodels.multivariate.manova import MANOVA from statsmodels.multivariate.multivariate_ols import MultivariateTestResults from statsmodels.tools import add_constant # Example data # https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/ # viewer.htm#statug_introreg_sect012.htm X = pd.DataFrame([['Minas Graes', 2.068, 2.070, 1.580], ['Minas Graes', 2.068, 2.074, 1.602], ['Minas Graes', 2.090, 2.090, 1.613], ['Minas Graes', 2.097, 2.093, 1.613], ['Minas Graes', 2.117, 2.125, 1.663], ['Minas Graes', 2.140, 2.146, 1.681], ['Matto Grosso', 2.045, 2.054, 1.580], ['Matto Grosso', 2.076, 2.088, 1.602], ['Matto Grosso', 2.090, 2.093, 1.643], ['Matto Grosso', 2.111, 2.114, 1.643], ['Santa Cruz', 2.093, 2.098, 1.653], ['Santa Cruz', 2.100, 2.106, 1.623], ['Santa Cruz', 2.104, 2.101, 1.653]], columns=['Loc', 'Basal', 'Occ', 'Max']) def test_manova_sas_example(): # Results should be the same as figure 4.5 of # https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/ # viewer.htm#statug_introreg_sect012.htm mod = MANOVA.from_formula('Basal + Occ + Max ~ Loc', data=X) r = mod.mv_test() assert_almost_equal(r['Loc']['stat'].loc["Wilks' lambda", 'Value'], 0.60143661, decimal=8) assert_almost_equal(r['Loc']['stat'].loc["Pillai's trace", 'Value'], 0.44702843, decimal=8) assert_almost_equal(r['Loc']['stat'].loc["Hotelling-Lawley trace", 'Value'], 0.58210348, decimal=8) assert_almost_equal(r['Loc']['stat'].loc["Roy's greatest root", 'Value'], 0.35530890, decimal=8) assert_almost_equal(r['Loc']['stat'].loc["Wilks' lambda", 'F Value'], 0.77, decimal=2) assert_almost_equal(r['Loc']['stat'].loc["Pillai's trace", 'F Value'], 0.86, decimal=2) assert_almost_equal(r['Loc']['stat'].loc["Hotelling-Lawley trace", 'F Value'], 0.75, decimal=2) assert_almost_equal(r['Loc']['stat'].loc["Roy's greatest root", 'F Value'], 1.07, decimal=2) assert_almost_equal(r['Loc']['stat'].loc["Wilks' lambda", 'Num DF'], 6, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Pillai's trace", 'Num DF'], 6, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Hotelling-Lawley trace", 'Num DF'], 6, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Roy's greatest root", 'Num DF'], 3, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Wilks' lambda", 'Den DF'], 16, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Pillai's trace", 'Den DF'], 18, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Hotelling-Lawley trace", 'Den DF'], 9.0909, decimal=4) assert_almost_equal(r['Loc']['stat'].loc["Roy's greatest root", 'Den DF'], 9, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Wilks' lambda", 'Pr > F'], 0.6032, decimal=4) assert_almost_equal(r['Loc']['stat'].loc["Pillai's trace", 'Pr > F'], 0.5397, decimal=4) assert_almost_equal(r['Loc']['stat'].loc["Hotelling-Lawley trace", 'Pr > F'], 0.6272, decimal=4) assert_almost_equal(r['Loc']['stat'].loc["Roy's greatest root", 'Pr > F'], 0.4109, decimal=4) def test_manova_no_formula(): # Same as previous test only skipping formula interface exog = add_constant(pd.get_dummies(X[['Loc']], drop_first=True)) endog = X[['Basal', 'Occ', 'Max']] mod = MANOVA(endog, exog) intercept = np.zeros((1, 3)) intercept[0, 0] = 1 loc = np.zeros((2, 3)) loc[0, 1] = loc[1, 2] = 1 hypotheses = [('Intercept', intercept), ('Loc', loc)] r = mod.mv_test(hypotheses) assert_almost_equal(r['Loc']['stat'].loc["Wilks' lambda", 'Value'], 0.60143661, decimal=8) assert_almost_equal(r['Loc']['stat'].loc["Pillai's trace", 'Value'], 0.44702843, decimal=8) assert_almost_equal(r['Loc']['stat'].loc["Hotelling-Lawley trace", 'Value'], 0.58210348, decimal=8) assert_almost_equal(r['Loc']['stat'].loc["Roy's greatest root", 'Value'], 0.35530890, decimal=8) assert_almost_equal(r['Loc']['stat'].loc["Wilks' lambda", 'F Value'], 0.77, decimal=2) assert_almost_equal(r['Loc']['stat'].loc["Pillai's trace", 'F Value'], 0.86, decimal=2) assert_almost_equal(r['Loc']['stat'].loc["Hotelling-Lawley trace", 'F Value'], 0.75, decimal=2) assert_almost_equal(r['Loc']['stat'].loc["Roy's greatest root", 'F Value'], 1.07, decimal=2) assert_almost_equal(r['Loc']['stat'].loc["Wilks' lambda", 'Num DF'], 6, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Pillai's trace", 'Num DF'], 6, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Hotelling-Lawley trace", 'Num DF'], 6, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Roy's greatest root", 'Num DF'], 3, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Wilks' lambda", 'Den DF'], 16, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Pillai's trace", 'Den DF'], 18, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Hotelling-Lawley trace", 'Den DF'], 9.0909, decimal=4) assert_almost_equal(r['Loc']['stat'].loc["Roy's greatest root", 'Den DF'], 9, decimal=3) assert_almost_equal(r['Loc']['stat'].loc["Wilks' lambda", 'Pr > F'], 0.6032, decimal=4) assert_almost_equal(r['Loc']['stat'].loc["Pillai's trace", 'Pr > F'], 0.5397, decimal=4) assert_almost_equal(r['Loc']['stat'].loc["Hotelling-Lawley trace", 'Pr > F'], 0.6272, decimal=4) assert_almost_equal(r['Loc']['stat'].loc["Roy's greatest root", 'Pr > F'], 0.4109, decimal=4) @pytest.mark.smoke def test_manova_no_formula_no_hypothesis(): # Same as previous test only skipping formula interface exog = add_constant(pd.get_dummies(X[['Loc']], drop_first=True)) endog = X[['Basal', 'Occ', 'Max']] mod = MANOVA(endog, exog) r = mod.mv_test() assert isinstance(r, MultivariateTestResults) def test_manova_test_input_validation(): mod = MANOVA.from_formula('Basal + Occ + Max ~ Loc', data=X) hypothesis = [('test', np.array([[1, 1, 1]]), None)] mod.mv_test(hypothesis) hypothesis = [('test', np.array([[1, 1]]), None)] assert_raises(ValueError, mod.mv_test, hypothesis) """ assert_raises_regex(ValueError, ('Contrast matrix L should have the same number of ' 'columns as exog! 2 != 3'), mod.mv_test, hypothesis) """ hypothesis = [('test', np.array([[1, 1, 1]]), np.array([[1], [1], [1]]))] mod.mv_test(hypothesis) hypothesis = [('test', np.array([[1, 1, 1]]), np.array([[1], [1]]))] assert_raises(ValueError, mod.mv_test, hypothesis) """ assert_raises_regex(ValueError, ('Transform matrix M should have the same number of ' 'rows as the number of columns of endog! 2 != 3'), mod.mv_test, hypothesis) """ def test_endog_1D_array(): assert_raises(ValueError, MANOVA.from_formula, 'Basal ~ Loc', X) statsmodels-0.12.2/statsmodels/multivariate/tests/test_ml_factor.py000066400000000000000000000126351400612667500257450ustar00rootroot00000000000000import numpy as np from statsmodels.multivariate.factor import Factor from numpy.testing import assert_allclose, assert_equal from scipy.optimize import approx_fprime # A small model for basic testing def _toy(): uniq = np.r_[4, 9, 16] load = np.asarray([[3, 1, 2], [2, 5, 8]]).T par = np.r_[2, 3, 4, 3, 1, 2, 2, 5, 8] corr = np.asarray([[1, .5, .25], [.5, 1, .5], [.25, .5, 1]]) return uniq, load, corr, par def test_loglike(): uniq, load, corr, par = _toy() fa = Factor(n_factor=2, corr=corr) # Two ways of passing the parameters to loglike ll1 = fa.loglike((load, uniq)) ll2 = fa.loglike(par) assert_allclose(ll1, ll2) def test_score(): uniq, load, corr, par = _toy() fa = Factor(n_factor=2, corr=corr) def f(par): return fa.loglike(par) par2 = np.r_[0.1, 0.2, 0.3, 0.4, 0.3, 0.1, 0.2, -0.2, 0, 0.8, 0.5, 0] for pt in (par, par2): g1 = approx_fprime(pt, f, 1e-8) g2 = fa.score(pt) assert_allclose(g1, g2, atol=1e-3) def test_exact(): # Test if we can recover exact factor-structured matrices with # default starting values. np.random.seed(23324) # Works for larger k_var but slow for routine testing. for k_var in 5, 10, 25: for n_factor in 1, 2, 3: load = np.random.normal(size=(k_var, n_factor)) uniq = np.linspace(1, 2, k_var) c = np.dot(load, load.T) c.flat[::c.shape[0]+1] += uniq s = np.sqrt(np.diag(c)) c /= np.outer(s, s) fa = Factor(corr=c, n_factor=n_factor, method='ml') rslt = fa.fit() assert_allclose(rslt.fitted_cov, c, rtol=1e-4, atol=1e-4) rslt.summary() # smoke test def test_exact_em(): # Test if we can recover exact factor-structured matrices with # default starting values using the EM algorithm. np.random.seed(23324) # Works for larger k_var but slow for routine testing. for k_var in 5, 10, 25: for n_factor in 1, 2, 3: load = np.random.normal(size=(k_var, n_factor)) uniq = np.linspace(1, 2, k_var) c = np.dot(load, load.T) c.flat[::c.shape[0]+1] += uniq s = np.sqrt(np.diag(c)) c /= np.outer(s, s) fa = Factor(corr=c, n_factor=n_factor, method='ml') load_e, uniq_e = fa._fit_ml_em(200) c_e = np.dot(load_e, load_e.T) c_e.flat[::c_e.shape[0]+1] += uniq_e assert_allclose(c_e, c, rtol=1e-4, atol=1e-4) def test_em(): n_factor = 1 cor = np.asarray([[1, 0.5, 0.3], [0.5, 1, 0], [0.3, 0, 1]]) fa = Factor(corr=cor, n_factor=n_factor, method='ml') rslt = fa.fit(opt={'gtol': 1e-3}) load_opt = rslt.loadings uniq_opt = rslt.uniqueness load_em, uniq_em = fa._fit_ml_em(1000) cc = np.dot(load_em, load_em.T) cc.flat[::cc.shape[0]+1] += uniq_em assert_allclose(cc, rslt.fitted_cov, rtol=1e-2, atol=1e-2) def test_1factor(): """ # R code: r = 0.4 p = 4 ii = seq(0, p-1) ii = outer(ii, ii, "-") ii = abs(ii) cm = r^ii fa = factanal(covmat=cm, factors=1) print(fa, digits=10) """ r = 0.4 p = 4 ii = np.arange(p) cm = r ** np.abs(np.subtract.outer(ii, ii)) fa = Factor(corr=cm, n_factor=1, method='ml') rslt = fa.fit() if rslt.loadings[0, 0] < 0: rslt.loadings[:, 0] *= -1 # R solution, but our likelihood is higher # uniq = np.r_[0.8392472054, 0.5820958187, 0.5820958187, 0.8392472054] # load = np.asarray([[0.4009399224, 0.6464550935, 0.6464550935, # 0.4009399224]]).T # l1 = fa.loglike(fa._pack(load, uniq)) # l2 = fa.loglike(fa._pack(rslt.loadings, rslt.uniqueness)) # So use a smoke test uniq = np.r_[0.85290232, 0.60916033, 0.55382266, 0.82610666] load = np.asarray([[0.38353316], [0.62517171], [0.66796508], [0.4170052]]) assert_allclose(load, rslt.loadings, rtol=1e-3, atol=1e-3) assert_allclose(uniq, rslt.uniqueness, rtol=1e-3, atol=1e-3) assert_equal(rslt.df, 2) def test_2factor(): """ # R code: r = 0.4 p = 6 ii = seq(0, p-1) ii = outer(ii, ii, "-") ii = abs(ii) cm = r^ii factanal(covmat=cm, factors=2) """ r = 0.4 p = 6 ii = np.arange(p) cm = r ** np.abs(np.subtract.outer(ii, ii)) fa = Factor(corr=cm, n_factor=2, nobs=100, method='ml') rslt = fa.fit() for j in 0, 1: if rslt.loadings[0, j] < 0: rslt.loadings[:, j] *= -1 uniq = np.r_[0.782, 0.367, 0.696, 0.696, 0.367, 0.782] assert_allclose(uniq, rslt.uniqueness, rtol=1e-3, atol=1e-3) loads = [np.r_[0.323, 0.586, 0.519, 0.519, 0.586, 0.323], np.r_[0.337, 0.538, 0.187, -0.187, -0.538, -0.337]] for k in 0, 1: if np.dot(loads[k], rslt.loadings[:, k]) < 0: loads[k] *= -1 assert_allclose(loads[k], rslt.loadings[:, k], rtol=1e-3, atol=1e-3) assert_equal(rslt.df, 4) # Smoke test for standard errors e = np.asarray([0.11056836, 0.05191071, 0.09836349, 0.09836349, 0.05191071, 0.11056836]) assert_allclose(rslt.uniq_stderr, e, atol=1e-4) e = np.asarray([[0.08842151, 0.08842151], [0.06058582, 0.06058582], [0.08339874, 0.08339874], [0.08339874, 0.08339874], [0.06058582, 0.06058582], [0.08842151, 0.08842151]]) assert_allclose(rslt.load_stderr, e, atol=1e-4) statsmodels-0.12.2/statsmodels/multivariate/tests/test_multivariate_ols.py000066400000000000000000000214571400612667500273640ustar00rootroot00000000000000# -*- coding: utf-8 -*- import numpy as np import pandas as pd from statsmodels.multivariate.multivariate_ols import _MultivariateOLS from numpy.testing import assert_array_almost_equal, assert_raises import patsy data = pd.DataFrame([['Morphine', 'N', .04, .20, .10, .08], ['Morphine', 'N', .02, .06, .02, .02], ['Morphine', 'N', .07, 1.40, .48, .24], ['Morphine', 'N', .17, .57, .35, .24], ['Morphine', 'Y', .10, .09, .13, .14], ['placebo', 'Y', .07, .07, .06, .07], ['placebo', 'Y', .05, .07, .06, .07], ['placebo', 'N', .03, .62, .31, .22], ['placebo', 'N', .03, 1.05, .73, .60], ['placebo', 'N', .07, .83, 1.07, .80], ['Trimethaphan', 'N', .09, 3.13, 2.06, 1.23], ['Trimethaphan', 'Y', .10, .09, .09, .08], ['Trimethaphan', 'Y', .08, .09, .09, .10], ['Trimethaphan', 'Y', .13, .10, .12, .12], ['Trimethaphan', 'Y', .06, .05, .05, .05]], columns=['Drug', 'Depleted', 'Histamine0', 'Histamine1', 'Histamine3', 'Histamine5']) for i in range(2, 6): data.iloc[:, i] = np.log(data.iloc[:, i]) def compare_r_output_dogs_data(method): ''' Testing within-subject effect interact with 2 between-subject effect Compares with R car library Anova(, type=3) output Note: The test statistis Phillai, Wilks, Hotelling-Lawley and Roy are the same as R output but the approximate F and degree of freedoms can be different. This is due to the fact that this implementation is based on SAS formula [1] .. [*] https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_introreg_sect012.htm ''' # Repeated measures with orthogonal polynomial contrasts coding mod = _MultivariateOLS.from_formula( 'Histamine0 + Histamine1 + Histamine3 + Histamine5 ~ Drug * Depleted', data) r = mod.fit(method=method) r = r.mv_test() a = [[2.68607660e-02, 4, 6, 5.43435304e+01, 7.59585610e-05], [9.73139234e-01, 4, 6, 5.43435304e+01, 7.59585610e-05], [3.62290202e+01, 4, 6, 5.43435304e+01, 7.59585610e-05], [3.62290202e+01, 4, 6, 5.43435304e+01, 7.59585610e-05]] assert_array_almost_equal(r['Intercept']['stat'].values, a, decimal=6) a = [[8.39646619e-02, 8, 1.20000000e+01, 3.67658068e+00, 2.12614444e-02], [1.18605382e+00, 8, 1.40000000e+01, 2.55003861e+00, 6.01270701e-02], [7.69391362e+00, 8, 6.63157895e+00, 5.50814270e+00, 2.07392260e-02], [7.25036952e+00, 4, 7.00000000e+00, 1.26881467e+01, 2.52669877e-03]] assert_array_almost_equal(r['Drug']['stat'].values, a, decimal=6) a = [[0.32048892, 4., 6., 3.18034906, 0.10002373], [0.67951108, 4., 6., 3.18034906, 0.10002373], [2.12023271, 4., 6., 3.18034906, 0.10002373], [2.12023271, 4., 6., 3.18034906, 0.10002373]] assert_array_almost_equal(r['Depleted']['stat'].values, a, decimal=6) a = [[0.15234366, 8., 12., 2.34307678, 0.08894239], [1.13013353, 8., 14., 2.27360606, 0.08553213], [3.70989596, 8., 6.63157895, 2.65594824, 0.11370285], [3.1145597, 4., 7., 5.45047947, 0.02582767]] assert_array_almost_equal(r['Drug:Depleted']['stat'].values, a, decimal=6) def test_glm_dogs_example(): compare_r_output_dogs_data(method='svd') compare_r_output_dogs_data(method='pinv') def test_specify_L_M_by_string(): mod = _MultivariateOLS.from_formula( 'Histamine0 + Histamine1 + Histamine3 + Histamine5 ~ Drug * Depleted', data) r = mod.fit() r1 = r.mv_test(hypotheses=[['Intercept', ['Intercept'], None]]) a = [[2.68607660e-02, 4, 6, 5.43435304e+01, 7.59585610e-05], [9.73139234e-01, 4, 6, 5.43435304e+01, 7.59585610e-05], [3.62290202e+01, 4, 6, 5.43435304e+01, 7.59585610e-05], [3.62290202e+01, 4, 6, 5.43435304e+01, 7.59585610e-05]] assert_array_almost_equal(r1['Intercept']['stat'].values, a, decimal=6) L = ['Intercept', 'Drug[T.Trimethaphan]', 'Drug[T.placebo]'] M = ['Histamine1', 'Histamine3', 'Histamine5'] r1 = r.mv_test(hypotheses=[['a', L, M]]) a = [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]] assert_array_almost_equal(r1['a']['contrast_L'], a, decimal=10) a = [[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]] assert_array_almost_equal(r1['a']['transform_M'].T, a, decimal=10) def test_independent_variable_singular(): data1 = data.copy() data1['dup'] = data1['Drug'] mod = _MultivariateOLS.from_formula( 'Histamine0 + Histamine1 + Histamine3 + Histamine5 ~ Drug * dup', data1) assert_raises(ValueError, mod.fit) mod = _MultivariateOLS.from_formula( 'Histamine0 + Histamine1 + Histamine3 + Histamine5 ~ Drug * dup', data1) assert_raises(ValueError, mod.fit) def test_from_formula_vs_no_formula(): mod = _MultivariateOLS.from_formula( 'Histamine0 + Histamine1 + Histamine3 + Histamine5 ~ Drug * Depleted', data) r = mod.fit(method='svd') r0 = r.mv_test() endog, exog = patsy.dmatrices( 'Histamine0 + Histamine1 + Histamine3 + Histamine5 ~ Drug * Depleted', data, return_type="dataframe") L = np.array([[1, 0, 0, 0, 0, 0]]) # DataFrame input r = _MultivariateOLS(endog, exog).fit(method='svd') r1 = r.mv_test(hypotheses=[['Intercept', L, None]]) assert_array_almost_equal(r1['Intercept']['stat'].values, r0['Intercept']['stat'].values, decimal=6) # Numpy array input r = _MultivariateOLS(endog.values, exog.values).fit(method='svd') r1 = r.mv_test(hypotheses=[['Intercept', L, None]]) assert_array_almost_equal(r1['Intercept']['stat'].values, r0['Intercept']['stat'].values, decimal=6) L = np.array([[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], ]) r1 = r.mv_test(hypotheses=[['Drug', L, None]]) # DataFrame input r = _MultivariateOLS(endog, exog).fit(method='svd') r1 = r.mv_test(hypotheses=[['Drug', L, None]]) assert_array_almost_equal(r1['Drug']['stat'].values, r0['Drug']['stat'].values, decimal=6) # Numpy array input r = _MultivariateOLS(endog.values, exog.values).fit(method='svd') r1 = r.mv_test(hypotheses=[['Drug', L, None]]) assert_array_almost_equal(r1['Drug']['stat'].values, r0['Drug']['stat'].values, decimal=6) def test_L_M_matrices_1D_array(): mod = _MultivariateOLS.from_formula( 'Histamine0 + Histamine1 + Histamine3 + Histamine5 ~ Drug * Depleted', data) r = mod.fit(method='svd') L = np.array([1, 0, 0, 0, 0, 0]) assert_raises(ValueError, r.mv_test, hypotheses=[['Drug', L, None]]) L = np.array([[1, 0, 0, 0, 0, 0]]) M = np.array([1, 0, 0, 0, 0, 0]) assert_raises(ValueError, r.mv_test, hypotheses=[['Drug', L, M]]) def test_exog_1D_array(): mod = _MultivariateOLS.from_formula( 'Histamine0 + Histamine1 + Histamine3 + Histamine5 ~ 0 + Depleted', data) r = mod.fit(method='svd') r0 = r.mv_test() a = [[0.0019, 8.0000, 20.0000, 55.0013, 0.0000], [1.8112, 8.0000, 22.0000, 26.3796, 0.0000], [97.8858, 8.0000, 12.1818, 117.1133, 0.0000], [93.2742, 4.0000, 11.0000, 256.5041, 0.0000]] assert_array_almost_equal(r0['Depleted']['stat'].values, a, decimal=4) def test_endog_1D_array(): assert_raises(ValueError, _MultivariateOLS.from_formula, 'Histamine0 ~ 0 + Depleted', data) def test_affine_hypothesis(): # Testing affine hypothesis, compared with R car linearHypothesis # Note: The test statistis Phillai, Wilks, Hotelling-Lawley # and Roy are the same as R output but the approximate F and degree # of freedoms can be different. This is due to the fact that this # implementation is based on SAS formula [1] mod = _MultivariateOLS.from_formula( 'Histamine0 + Histamine1 + Histamine3 + Histamine5 ~ Drug * Depleted', data) r = mod.fit(method='svd') L = np.array([[0, 1.2, 1.1, 1.3, 1.5, 1.4], [0, 3.2, 2.1, 3.3, 5.5, 4.4]]) M = None C = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) r0 = r.mv_test(hypotheses=[('test1', L, M, C)]) a = [[0.0269, 8.0000, 12.0000, 7.6441, 0.0010], [1.4277, 8.0000, 14.0000, 4.3657, 0.0080], [19.2678, 8.0000, 6.6316, 13.7940, 0.0016], [18.3470, 4.0000, 7.0000, 32.1072, 0.0001]] assert_array_almost_equal(r0['test1']['stat'].values, a, decimal=4) r0.summary(show_contrast_L=True, show_transform_M=True, show_constant_C=True) statsmodels-0.12.2/statsmodels/multivariate/tests/test_pca.py000066400000000000000000000376351400612667500245510ustar00rootroot00000000000000from statsmodels.compat.platform import PLATFORM_WIN32 import warnings import numpy as np import pandas as pd import pytest from numpy.testing import assert_allclose, assert_equal, assert_raises from statsmodels.multivariate.pca import PCA, pca from statsmodels.multivariate.tests.results.datamlw import (data, princomp1, princomp2) from statsmodels.tools.sm_exceptions import EstimationWarning DECIMAL_5 = .00001 class TestPCA(object): @classmethod def setup_class(cls): rs = np.random.RandomState() rs.seed(1234) k = 3 n = 100 t = 200 lam = 2 norm_rng = rs.standard_normal e = norm_rng((t, n)) f = norm_rng((t, k)) b = rs.standard_gamma(lam, size=(k, n)) / lam cls.x = f.dot(b) + e cls.x_copy = cls.x + 0.0 cls.rs = rs k = 3 n = 300 t = 200 lam = 2 norm_rng = rs.standard_normal e = norm_rng((t, n)) f = norm_rng((t, k)) b = rs.standard_gamma(lam, size=(k, n)) / lam cls.x_wide = f.dot(b) + e @pytest.mark.smoke @pytest.mark.matplotlib def test_smoke_plot_and_repr(self, close_figures): pc = PCA(self.x) fig = pc.plot_scree() fig = pc.plot_scree(ncomp=10) fig = pc.plot_scree(log_scale=False) fig = pc.plot_scree(cumulative=True) fig = pc.plot_rsquare() fig = pc.plot_rsquare(ncomp=5) # Additional smoke test pc.__repr__() pc = PCA(self.x, standardize=False) pc.__repr__() pc = PCA(self.x, standardize=False, demean=False) pc.__repr__() pc = PCA(self.x, ncomp=2, gls=True) assert "GLS" in pc.__repr__() # Check data for no changes assert_equal(self.x, pc.data) def test_eig_svd_equiv(self): # Test leading components since the tail end can differ pc_eig = PCA(self.x) pc_svd = PCA(self.x, method='svd') assert_allclose(pc_eig.projection, pc_svd.projection) assert_allclose(np.abs(pc_eig.factors[:, :2]), np.abs(pc_svd.factors[:, :2])) assert_allclose(np.abs(pc_eig.coeff[:2, :]), np.abs(pc_svd.coeff[:2, :])) assert_allclose(pc_eig.eigenvals, pc_svd.eigenvals) assert_allclose(np.abs(pc_eig.eigenvecs[:, :2]), np.abs(pc_svd.eigenvecs[:, :2])) pc_svd = PCA(self.x, method='svd', ncomp=2) pc_nipals = PCA(self.x, method='nipals', ncomp=2) assert_allclose(np.abs(pc_nipals.factors), np.abs(pc_svd.factors), atol=DECIMAL_5) assert_allclose(np.abs(pc_nipals.coeff), np.abs(pc_svd.coeff), atol=DECIMAL_5) assert_allclose(pc_nipals.eigenvals, pc_svd.eigenvals, atol=DECIMAL_5) assert_allclose(np.abs(pc_nipals.eigenvecs), np.abs(pc_svd.eigenvecs), atol=DECIMAL_5) # Check data for no changes assert_equal(self.x, pc_svd.data) # Check data for no changes assert_equal(self.x, pc_eig.data) # Check data for no changes assert_equal(self.x, pc_nipals.data) def test_options(self): pc = PCA(self.x) pc_no_norm = PCA(self.x, normalize=False) assert_allclose(pc.factors.dot(pc.coeff), pc_no_norm.factors.dot(pc_no_norm.coeff)) princomp = pc.factors assert_allclose(princomp.T.dot(princomp), np.eye(100), atol=1e-5) weights = pc_no_norm.coeff assert_allclose(weights.T.dot(weights), np.eye(100), atol=1e-5) pc_10 = PCA(self.x, ncomp=10) assert_allclose(pc.factors[:, :10], pc_10.factors) assert_allclose(pc.coeff[:10, :], pc_10.coeff) assert_allclose(pc.rsquare[:(10 + 1)], pc_10.rsquare) assert_allclose(pc.eigenvals[:10], pc_10.eigenvals) assert_allclose(pc.eigenvecs[:, :10], pc_10.eigenvecs) pc = PCA(self.x, standardize=False, normalize=False) mu = self.x.mean(0) xdm = self.x - mu xpx = xdm.T.dot(xdm) val, vec = np.linalg.eigh(xpx) ind = np.argsort(val) ind = ind[::-1] val = val[ind] vec = vec[:, ind] assert_allclose(xdm, pc.transformed_data) assert_allclose(val, pc.eigenvals) assert_allclose(np.abs(vec), np.abs(pc.eigenvecs)) assert_allclose(np.abs(pc.factors), np.abs(xdm.dot(vec))) assert_allclose(pc.projection, xdm + mu) pc = PCA(self.x, standardize=False, demean=False, normalize=False) x = self.x xpx = x.T.dot(x) val, vec = np.linalg.eigh(xpx) ind = np.argsort(val) ind = ind[::-1] val = val[ind] vec = vec[:, ind] assert_allclose(x, pc.transformed_data) assert_allclose(val, pc.eigenvals) assert_allclose(np.abs(vec), np.abs(pc.eigenvecs)) assert_allclose(np.abs(pc.factors), np.abs(x.dot(vec))) def test_against_reference(self): # Test against MATLAB, which by default demeans but does not standardize x = data.xo / 1000.0 pc = PCA(x, normalize=False, standardize=False) ref = princomp1 assert_allclose(np.abs(pc.factors), np.abs(ref.factors)) assert_allclose(pc.factors.dot(pc.coeff) + x.mean(0), x) assert_allclose(np.abs(pc.coeff), np.abs(ref.coef.T)) assert_allclose(pc.factors.dot(pc.coeff), ref.factors.dot(ref.coef.T)) pc = PCA(x[:20], normalize=False, standardize=False) mu = x[:20].mean(0) ref = princomp2 assert_allclose(np.abs(pc.factors), np.abs(ref.factors)) assert_allclose(pc.factors.dot(pc.coeff) + mu, x[:20]) assert_allclose(np.abs(pc.coeff), np.abs(ref.coef.T)) assert_allclose(pc.factors.dot(pc.coeff), ref.factors.dot(ref.coef.T)) def test_warnings_and_errors(self): with warnings.catch_warnings(record=True) as w: pc = PCA(self.x, ncomp=300) assert_equal(len(w), 1) with warnings.catch_warnings(record=True) as w: rs = self.rs x = rs.standard_normal((200, 1)) * np.ones(200) pc = PCA(x, method='eig') assert_equal(len(w), 1) assert_raises(ValueError, PCA, self.x, method='unknown') assert_raises(ValueError, PCA, self.x, missing='unknown') assert_raises(ValueError, PCA, self.x, tol=2.0) assert_raises(ValueError, PCA, np.nan * np.ones((200, 100)), tol=2.0) @pytest.mark.matplotlib def test_pandas(self, close_figures): pc = PCA(pd.DataFrame(self.x)) pc1 = PCA(self.x) assert_allclose(pc.factors.values, pc1.factors) fig = pc.plot_scree() fig = pc.plot_scree(ncomp=10) fig = pc.plot_scree(log_scale=False) fig = pc.plot_rsquare() fig = pc.plot_rsquare(ncomp=5) proj = pc.project(2) PCA(pd.DataFrame(self.x), ncomp=4, gls=True) PCA(pd.DataFrame(self.x), ncomp=4, standardize=False) def test_gls_and_weights(self): assert_raises(ValueError, PCA, self.x, gls=True) assert_raises(ValueError, PCA, self.x, weights=np.array([1.0, 1.0])) # Pre-standardize to make comparison simple x = (self.x - self.x.mean(0)) x = x / (x ** 2.0).mean(0) pc_gls = PCA(x, ncomp=1, standardize=False, demean=False, gls=True) pc = PCA(x, ncomp=1, standardize=False, demean=False) errors = x - pc.projection var = (errors ** 2.0).mean(0) weights = 1.0 / var weights = weights / np.sqrt((weights ** 2.0).mean()) assert_allclose(weights, pc_gls.weights) assert_equal(x, pc_gls.data) assert_equal(x, pc.data) pc_weights = PCA(x, ncomp=1, standardize=False, demean=False, weights=weights) assert_allclose(weights, pc_weights.weights) assert_allclose(np.abs(pc_weights.factors), np.abs(pc_gls.factors)) @pytest.mark.slow def test_wide(self): pc = PCA(self.x_wide) assert_equal(pc.factors.shape[1], self.x_wide.shape[0]) assert_equal(pc.eigenvecs.shape[1], min(np.array(self.x_wide.shape))) pc = PCA(pd.DataFrame(self.x_wide)) assert_equal(pc.factors.shape[1], self.x_wide.shape[0]) assert_equal(pc.eigenvecs.shape[1], min(np.array(self.x_wide.shape))) def test_projection(self): pc = PCA(self.x, ncomp=5) mu = self.x.mean(0) demean_x = self.x - mu coef = np.linalg.pinv(pc.factors).dot(demean_x) direct = pc.factors.dot(coef) assert_allclose(pc.projection, direct + mu) pc = PCA(self.x, standardize=False, ncomp=5) coef = np.linalg.pinv(pc.factors).dot(demean_x) direct = pc.factors.dot(coef) assert_allclose(pc.projection, direct + mu) pc = PCA(self.x, standardize=False, demean=False, ncomp=5) coef = np.linalg.pinv(pc.factors).dot(self.x) direct = pc.factors.dot(coef) assert_allclose(pc.projection, direct) pc = PCA(self.x, ncomp=5, gls=True) mu = self.x.mean(0) demean_x = self.x - mu coef = np.linalg.pinv(pc.factors).dot(demean_x) direct = pc.factors.dot(coef) assert_allclose(pc.projection, direct + mu) pc = PCA(self.x, standardize=False, ncomp=5) coef = np.linalg.pinv(pc.factors).dot(demean_x) direct = pc.factors.dot(coef) assert_allclose(pc.projection, direct + mu) pc = PCA(self.x, standardize=False, demean=False, ncomp=5, gls=True) coef = np.linalg.pinv(pc.factors).dot(self.x) direct = pc.factors.dot(coef) assert_allclose(pc.projection, direct) # Test error for too many factors project = pc.project assert_raises(ValueError, project, 6) @pytest.mark.skipif(PLATFORM_WIN32, reason='Windows 32-bit') def test_replace_missing(self): x = self.x.copy() x[::5, ::7] = np.nan pc = PCA(x, missing='drop-row') x_dropped_row = x[np.logical_not(np.any(np.isnan(x), 1))] pc_dropped = PCA(x_dropped_row) assert_allclose(pc.projection, pc_dropped.projection) assert_equal(x, pc.data) pc = PCA(x, missing='drop-col') x_dropped_col = x[:, np.logical_not(np.any(np.isnan(x), 0))] pc_dropped = PCA(x_dropped_col) assert_allclose(pc.projection, pc_dropped.projection) assert_equal(x, pc.data) pc = PCA(x, missing='drop-min') if x_dropped_row.size > x_dropped_col.size: x_dropped_min = x_dropped_row else: x_dropped_min = x_dropped_col pc_dropped = PCA(x_dropped_min) assert_allclose(pc.projection, pc_dropped.projection) assert_equal(x, pc.data) pc = PCA(x, ncomp=3, missing='fill-em') missing = np.isnan(x) mu = np.nanmean(x, axis=0) errors = x - mu sigma = np.sqrt(np.nanmean(errors ** 2, axis=0)) x_std = errors / sigma x_std[missing] = 0.0 last = x_std[missing] delta = 1.0 count = 0 while delta > 5e-8: pc_temp = PCA(x_std, ncomp=3, standardize=False, demean=False) x_std[missing] = pc_temp.projection[missing] current = x_std[missing] diff = current - last delta = np.sqrt(np.sum(diff ** 2)) / np.sqrt(np.sum(current ** 2)) last = current count += 1 x = self.x + 0.0 projection = pc_temp.projection * sigma + mu x[missing] = projection[missing] assert_allclose(pc._adjusted_data, x) # Check data for no changes assert_equal(self.x, self.x_copy) x = self.x pc = PCA(x) pc_dropped = PCA(x, missing='drop-row') assert_allclose(pc.projection, pc_dropped.projection, atol=DECIMAL_5) pc_dropped = PCA(x, missing='drop-col') assert_allclose(pc.projection, pc_dropped.projection, atol=DECIMAL_5) pc_dropped = PCA(x, missing='drop-min') assert_allclose(pc.projection, pc_dropped.projection, atol=DECIMAL_5) pc = PCA(x, ncomp=3) pc_dropped = PCA(x, ncomp=3, missing='fill-em') assert_allclose(pc.projection, pc_dropped.projection, atol=DECIMAL_5) # Test too many missing for missing='fill-em' x = self.x.copy() x[:, :] = np.nan assert_raises(ValueError, PCA, x, missing='drop-row') assert_raises(ValueError, PCA, x, missing='drop-col') assert_raises(ValueError, PCA, x, missing='drop-min') assert_raises(ValueError, PCA, x, missing='fill-em') def test_rsquare(self): x = self.x + 0.0 mu = x.mean(0) x_demean = x - mu std = np.std(x, 0) x_std = x_demean / std pc = PCA(self.x) nvar = x.shape[1] rsquare = np.zeros(nvar + 1) tss = np.sum(x_std ** 2) for i in range(nvar + 1): errors = x_std - pc.project(i, transform=False, unweight=False) rsquare[i] = 1.0 - np.sum(errors ** 2) / tss assert_allclose(rsquare, pc.rsquare) pc = PCA(self.x, standardize=False) tss = np.sum(x_demean ** 2) for i in range(nvar + 1): errors = x_demean - pc.project(i, transform=False, unweight=False) rsquare[i] = 1.0 - np.sum(errors ** 2) / tss assert_allclose(rsquare, pc.rsquare) pc = PCA(self.x, standardize=False, demean=False) tss = np.sum(x ** 2) for i in range(nvar + 1): errors = x - pc.project(i, transform=False, unweight=False) rsquare[i] = 1.0 - np.sum(errors ** 2) / tss assert_allclose(rsquare, pc.rsquare) @pytest.mark.slow def test_missing_dataframe(self): x = self.x.copy() x[::5, ::7] = np.nan pc = PCA(x, ncomp=3, missing='fill-em') x = pd.DataFrame(x) pc_df = PCA(x, ncomp=3, missing='fill-em') assert_allclose(pc.coeff, pc_df.coeff) assert_allclose(pc.factors, pc_df.factors) pc_df_nomissing = PCA(pd.DataFrame(self.x.copy()), ncomp=3) assert isinstance(pc_df.coeff, type(pc_df_nomissing.coeff)) assert isinstance(pc_df.data, type(pc_df_nomissing.data)) assert isinstance(pc_df.eigenvals, type(pc_df_nomissing.eigenvals)) assert isinstance(pc_df.eigenvecs, type(pc_df_nomissing.eigenvecs)) x = self.x.copy() x[::5, ::7] = np.nan x_df = pd.DataFrame(x) pc = PCA(x, missing='drop-row') pc_df = PCA(x_df, missing='drop-row') assert_allclose(pc.coeff, pc_df.coeff) assert_allclose(pc.factors, pc_df.factors) pc = PCA(x, missing='drop-col') pc_df = PCA(x_df, missing='drop-col') assert_allclose(pc.coeff, pc_df.coeff) assert_allclose(pc.factors, pc_df.factors) pc = PCA(x, missing='drop-min') pc_df = PCA(x_df, missing='drop-min') assert_allclose(pc.coeff, pc_df.coeff) assert_allclose(pc.factors, pc_df.factors) def test_equivalence(self): x = self.x.copy() assert_allclose(PCA(x).factors, pca(x)[0]) def test_missing(): data = np.empty((200, 50)) data[0, 0] = np.nan with pytest.raises(ValueError, match="data contains non-finite values"): PCA(data) def test_too_many_missing(reset_randomstate): data = np.random.standard_normal((200, 50)) data[0, :-3] = np.nan with pytest.raises(ValueError): PCA(data, ncomp=5, missing="drop-col") p = PCA(data, missing="drop-min") assert max(p.factors.shape) == max(data.shape) - 1 def test_gls_warning(reset_randomstate): data = np.random.standard_normal((400, 200)) data[:, 1:] = data[:, :1] + .01 * data[:, 1:] with pytest.warns(EstimationWarning, match="Many series are being down weighted"): factors = PCA(data, ncomp=2, gls=True).factors assert factors.shape == (data.shape[0], 2) statsmodels-0.12.2/statsmodels/nonparametric/000077500000000000000000000000001400612667500213515ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/nonparametric/__init__.py000066400000000000000000000003451400612667500234640ustar00rootroot00000000000000""" Tools for nonparametric statistics, mainly density estimation and regression. For an overview of this module, see docs/source/nonparametric.rst """ from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/nonparametric/_kernel_base.py000066400000000000000000000436211400612667500243420ustar00rootroot00000000000000""" Module containing the base object for multivariate kernel density and regression, plus some utilities. """ import copy import numpy as np from scipy import optimize from scipy.stats.mstats import mquantiles try: import joblib has_joblib = True except ImportError: has_joblib = False from . import kernels kernel_func = dict(wangryzin=kernels.wang_ryzin, aitchisonaitken=kernels.aitchison_aitken, gaussian=kernels.gaussian, aitchison_aitken_reg = kernels.aitchison_aitken_reg, wangryzin_reg = kernels.wang_ryzin_reg, gauss_convolution=kernels.gaussian_convolution, wangryzin_convolution=kernels.wang_ryzin_convolution, aitchisonaitken_convolution=kernels.aitchison_aitken_convolution, gaussian_cdf=kernels.gaussian_cdf, aitchisonaitken_cdf=kernels.aitchison_aitken_cdf, wangryzin_cdf=kernels.wang_ryzin_cdf, d_gaussian=kernels.d_gaussian, tricube=kernels.tricube) def _compute_min_std_IQR(data): """Compute minimum of std and IQR for each variable.""" s1 = np.std(data, axis=0) q75 = mquantiles(data, 0.75, axis=0).data[0] q25 = mquantiles(data, 0.25, axis=0).data[0] s2 = (q75 - q25) / 1.349 # IQR dispersion = np.minimum(s1, s2) return dispersion def _compute_subset(class_type, data, bw, co, do, n_cvars, ix_ord, ix_unord, n_sub, class_vars, randomize, bound): """"Compute bw on subset of data. Called from ``GenericKDE._compute_efficient_*``. Notes ----- Needs to be outside the class in order for joblib to be able to pickle it. """ if randomize: np.random.shuffle(data) sub_data = data[:n_sub, :] else: sub_data = data[bound[0]:bound[1], :] if class_type == 'KDEMultivariate': from .kernel_density import KDEMultivariate var_type = class_vars[0] sub_model = KDEMultivariate(sub_data, var_type, bw=bw, defaults=EstimatorSettings(efficient=False)) elif class_type == 'KDEMultivariateConditional': from .kernel_density import KDEMultivariateConditional k_dep, dep_type, indep_type = class_vars endog = sub_data[:, :k_dep] exog = sub_data[:, k_dep:] sub_model = KDEMultivariateConditional(endog, exog, dep_type, indep_type, bw=bw, defaults=EstimatorSettings(efficient=False)) elif class_type == 'KernelReg': from .kernel_regression import KernelReg var_type, k_vars, reg_type = class_vars endog = _adjust_shape(sub_data[:, 0], 1) exog = _adjust_shape(sub_data[:, 1:], k_vars) sub_model = KernelReg(endog=endog, exog=exog, reg_type=reg_type, var_type=var_type, bw=bw, defaults=EstimatorSettings(efficient=False)) else: raise ValueError("class_type not recognized, should be one of " \ "{KDEMultivariate, KDEMultivariateConditional, KernelReg}") # Compute dispersion in next 4 lines if class_type == 'KernelReg': sub_data = sub_data[:, 1:] dispersion = _compute_min_std_IQR(sub_data) fct = dispersion * n_sub**(-1. / (n_cvars + co)) fct[ix_unord] = n_sub**(-2. / (n_cvars + do)) fct[ix_ord] = n_sub**(-2. / (n_cvars + do)) sample_scale_sub = sub_model.bw / fct #TODO: check if correct bw_sub = sub_model.bw return sample_scale_sub, bw_sub class GenericKDE (object): """ Base class for density estimation and regression KDE classes. """ def _compute_bw(self, bw): """ Computes the bandwidth of the data. Parameters ---------- bw : {array_like, str} If array_like: user-specified bandwidth. If a string, should be one of: - cv_ml: cross validation maximum likelihood - normal_reference: normal reference rule of thumb - cv_ls: cross validation least squares Notes ----- The default values for bw is 'normal_reference'. """ if bw is None: bw = 'normal_reference' if not isinstance(bw, str): self._bw_method = "user-specified" res = np.asarray(bw) else: # The user specified a bandwidth selection method self._bw_method = bw # Workaround to avoid instance methods in __dict__ if bw == 'normal_reference': bwfunc = self._normal_reference elif bw == 'cv_ml': bwfunc = self._cv_ml else: # bw == 'cv_ls' bwfunc = self._cv_ls res = bwfunc() return res def _compute_dispersion(self, data): """ Computes the measure of dispersion. The minimum of the standard deviation and interquartile range / 1.349 Notes ----- Reimplemented in `KernelReg`, because the first column of `data` has to be removed. References ---------- See the user guide for the np package in R. In the notes on bwscaling option in npreg, npudens, npcdens there is a discussion on the measure of dispersion """ return _compute_min_std_IQR(data) def _get_class_vars_type(self): """Helper method to be able to pass needed vars to _compute_subset. Needs to be implemented by subclasses.""" pass def _compute_efficient(self, bw): """ Computes the bandwidth by estimating the scaling factor (c) in n_res resamples of size ``n_sub`` (in `randomize` case), or by dividing ``nobs`` into as many ``n_sub`` blocks as needed (if `randomize` is False). References ---------- See p.9 in socserv.mcmaster.ca/racine/np_faq.pdf """ if bw is None: self._bw_method = 'normal_reference' if isinstance(bw, str): self._bw_method = bw else: self._bw_method = "user-specified" return bw nobs = self.nobs n_sub = self.n_sub data = copy.deepcopy(self.data) n_cvars = self.data_type.count('c') co = 4 # 2*order of continuous kernel do = 4 # 2*order of discrete kernel _, ix_ord, ix_unord = _get_type_pos(self.data_type) # Define bounds for slicing the data if self.randomize: # randomize chooses blocks of size n_sub, independent of nobs bounds = [None] * self.n_res else: bounds = [(i * n_sub, (i+1) * n_sub) for i in range(nobs // n_sub)] if nobs % n_sub > 0: bounds.append((nobs - nobs % n_sub, nobs)) n_blocks = self.n_res if self.randomize else len(bounds) sample_scale = np.empty((n_blocks, self.k_vars)) only_bw = np.empty((n_blocks, self.k_vars)) class_type, class_vars = self._get_class_vars_type() if has_joblib: # `res` is a list of tuples (sample_scale_sub, bw_sub) res = joblib.Parallel(n_jobs=self.n_jobs)( joblib.delayed(_compute_subset)( class_type, data, bw, co, do, n_cvars, ix_ord, ix_unord, \ n_sub, class_vars, self.randomize, bounds[i]) \ for i in range(n_blocks)) else: res = [] for i in range(n_blocks): res.append(_compute_subset(class_type, data, bw, co, do, n_cvars, ix_ord, ix_unord, n_sub, class_vars, self.randomize, bounds[i])) for i in range(n_blocks): sample_scale[i, :] = res[i][0] only_bw[i, :] = res[i][1] s = self._compute_dispersion(data) order_func = np.median if self.return_median else np.mean m_scale = order_func(sample_scale, axis=0) # TODO: Check if 1/5 is correct in line below! bw = m_scale * s * nobs**(-1. / (n_cvars + co)) bw[ix_ord] = m_scale[ix_ord] * nobs**(-2./ (n_cvars + do)) bw[ix_unord] = m_scale[ix_unord] * nobs**(-2./ (n_cvars + do)) if self.return_only_bw: bw = np.median(only_bw, axis=0) return bw def _set_defaults(self, defaults): """Sets the default values for the efficient estimation""" self.n_res = defaults.n_res self.n_sub = defaults.n_sub self.randomize = defaults.randomize self.return_median = defaults.return_median self.efficient = defaults.efficient self.return_only_bw = defaults.return_only_bw self.n_jobs = defaults.n_jobs def _normal_reference(self): """ Returns Scott's normal reference rule of thumb bandwidth parameter. Notes ----- See p.13 in [2] for an example and discussion. The formula for the bandwidth is .. math:: h = 1.06n^{-1/(4+q)} where ``n`` is the number of observations and ``q`` is the number of variables. """ X = np.std(self.data, axis=0) return 1.06 * X * self.nobs ** (- 1. / (4 + self.data.shape[1])) def _set_bw_bounds(self, bw): """ Sets bandwidth lower bound to effectively zero )1e-10), and for discrete values upper bound to 1. """ bw[bw < 0] = 1e-10 _, ix_ord, ix_unord = _get_type_pos(self.data_type) bw[ix_ord] = np.minimum(bw[ix_ord], 1.) bw[ix_unord] = np.minimum(bw[ix_unord], 1.) return bw def _cv_ml(self): r""" Returns the cross validation maximum likelihood bandwidth parameter. Notes ----- For more details see p.16, 18, 27 in Ref. [1] (see module docstring). Returns the bandwidth estimate that maximizes the leave-out-out likelihood. The leave-one-out log likelihood function is: .. math:: \ln L=\sum_{i=1}^{n}\ln f_{-i}(X_{i}) The leave-one-out kernel estimator of :math:`f_{-i}` is: .. math:: f_{-i}(X_{i})=\frac{1}{(n-1)h} \sum_{j=1,j\neq i}K_{h}(X_{i},X_{j}) where :math:`K_{h}` represents the Generalized product kernel estimator: .. math:: K_{h}(X_{i},X_{j})=\prod_{s=1}^ {q}h_{s}^{-1}k\left(\frac{X_{is}-X_{js}}{h_{s}}\right) """ # the initial value for the optimization is the normal_reference h0 = self._normal_reference() bw = optimize.fmin(self.loo_likelihood, x0=h0, args=(np.log, ), maxiter=1e3, maxfun=1e3, disp=0, xtol=1e-3) bw = self._set_bw_bounds(bw) # bound bw if necessary return bw def _cv_ls(self): r""" Returns the cross-validation least squares bandwidth parameter(s). Notes ----- For more details see pp. 16, 27 in Ref. [1] (see module docstring). Returns the value of the bandwidth that maximizes the integrated mean square error between the estimated and actual distribution. The integrated mean square error (IMSE) is given by: .. math:: \int\left[\hat{f}(x)-f(x)\right]^{2}dx This is the general formula for the IMSE. The IMSE differs for conditional (``KDEMultivariateConditional``) and unconditional (``KDEMultivariate``) kernel density estimation. """ h0 = self._normal_reference() bw = optimize.fmin(self.imse, x0=h0, maxiter=1e3, maxfun=1e3, disp=0, xtol=1e-3) bw = self._set_bw_bounds(bw) # bound bw if necessary return bw def loo_likelihood(self): raise NotImplementedError class EstimatorSettings(object): """ Object to specify settings for density estimation or regression. `EstimatorSettings` has several properties related to how bandwidth estimation for the `KDEMultivariate`, `KDEMultivariateConditional`, `KernelReg` and `CensoredKernelReg` classes behaves. Parameters ---------- efficient : bool, optional If True, the bandwidth estimation is to be performed efficiently -- by taking smaller sub-samples and estimating the scaling factor of each subsample. This is useful for large samples (nobs >> 300) and/or multiple variables (k_vars > 3). If False (default), all data is used at the same time. randomize : bool, optional If True, the bandwidth estimation is to be performed by taking `n_res` random resamples (with replacement) of size `n_sub` from the full sample. If set to False (default), the estimation is performed by slicing the full sample in sub-samples of size `n_sub` so that all samples are used once. n_sub : int, optional Size of the sub-samples. Default is 50. n_res : int, optional The number of random re-samples used to estimate the bandwidth. Only has an effect if ``randomize == True``. Default value is 25. return_median : bool, optional If True (default), the estimator uses the median of all scaling factors for each sub-sample to estimate the bandwidth of the full sample. If False, the estimator uses the mean. return_only_bw : bool, optional If True, the estimator is to use the bandwidth and not the scaling factor. This is *not* theoretically justified. Should be used only for experimenting. n_jobs : int, optional The number of jobs to use for parallel estimation with ``joblib.Parallel``. Default is -1, meaning ``n_cores - 1``, with ``n_cores`` the number of available CPU cores. See the `joblib documentation `_ for more details. Examples -------- >>> settings = EstimatorSettings(randomize=True, n_jobs=3) >>> k_dens = KDEMultivariate(data, var_type, defaults=settings) """ def __init__(self, efficient=False, randomize=False, n_res=25, n_sub=50, return_median=True, return_only_bw=False, n_jobs=-1): self.efficient = efficient self.randomize = randomize self.n_res = n_res self.n_sub = n_sub self.return_median = return_median self.return_only_bw = return_only_bw # TODO: remove this? self.n_jobs = n_jobs class LeaveOneOut(object): """ Generator to give leave-one-out views on X. Parameters ---------- X : array_like 2-D array. Examples -------- >>> X = np.random.normal(0, 1, [10,2]) >>> loo = LeaveOneOut(X) >>> for x in loo: ... print x Notes ----- A little lighter weight than sklearn LOO. We do not need test index. Also passes views on X, not the index. """ def __init__(self, X): self.X = np.asarray(X) def __iter__(self): X = self.X nobs, k_vars = np.shape(X) for i in range(nobs): index = np.ones(nobs, dtype=bool) index[i] = False yield X[index, :] def _get_type_pos(var_type): ix_cont = np.array([c == 'c' for c in var_type]) ix_ord = np.array([c == 'o' for c in var_type]) ix_unord = np.array([c == 'u' for c in var_type]) return ix_cont, ix_ord, ix_unord def _adjust_shape(dat, k_vars): """ Returns an array of shape (nobs, k_vars) for use with `gpke`.""" dat = np.asarray(dat) if dat.ndim > 2: dat = np.squeeze(dat) if dat.ndim == 1 and k_vars > 1: # one obs many vars nobs = 1 elif dat.ndim == 1 and k_vars == 1: # one obs one var nobs = len(dat) else: if np.shape(dat)[0] == k_vars and np.shape(dat)[1] != k_vars: dat = dat.T nobs = np.shape(dat)[0] # ndim >1 so many obs many vars dat = np.reshape(dat, (nobs, k_vars)) return dat def gpke(bw, data, data_predict, var_type, ckertype='gaussian', okertype='wangryzin', ukertype='aitchisonaitken', tosum=True): r""" Returns the non-normalized Generalized Product Kernel Estimator Parameters ---------- bw : 1-D ndarray The user-specified bandwidth parameters. data : 1D or 2-D ndarray The training data. data_predict : 1-D ndarray The evaluation points at which the kernel estimation is performed. var_type : str, optional The variable type (continuous, ordered, unordered). ckertype : str, optional The kernel used for the continuous variables. okertype : str, optional The kernel used for the ordered discrete variables. ukertype : str, optional The kernel used for the unordered discrete variables. tosum : bool, optional Whether or not to sum the calculated array of densities. Default is True. Returns ------- dens : array_like The generalized product kernel density estimator. Notes ----- The formula for the multivariate kernel estimator for the pdf is: .. math:: f(x)=\frac{1}{nh_{1}...h_{q}}\sum_{i=1}^ {n}K\left(\frac{X_{i}-x}{h}\right) where .. math:: K\left(\frac{X_{i}-x}{h}\right) = k\left( \frac{X_{i1}-x_{1}}{h_{1}}\right)\times k\left( \frac{X_{i2}-x_{2}}{h_{2}}\right)\times...\times k\left(\frac{X_{iq}-x_{q}}{h_{q}}\right) """ kertypes = dict(c=ckertype, o=okertype, u=ukertype) #Kval = [] #for ii, vtype in enumerate(var_type): # func = kernel_func[kertypes[vtype]] # Kval.append(func(bw[ii], data[:, ii], data_predict[ii])) #Kval = np.column_stack(Kval) Kval = np.empty(data.shape) for ii, vtype in enumerate(var_type): func = kernel_func[kertypes[vtype]] Kval[:, ii] = func(bw[ii], data[:, ii], data_predict[ii]) iscontinuous = np.array([c == 'c' for c in var_type]) dens = Kval.prod(axis=1) / np.prod(bw[iscontinuous]) if tosum: return dens.sum(axis=0) else: return dens statsmodels-0.12.2/statsmodels/nonparametric/_smoothers_lowess.pyx000066400000000000000000000516741400612667500257060ustar00rootroot00000000000000#cython: boundscheck=False, wraparound=False, cdivision=True, language_level=3 """ Univariate lowess function, like in R. References ---------- Hastie, Tibshirani, Friedman. (2009) The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition: Chapter 6. Cleveland, W.S. (1979) "Robust Locally Weighted Regression and Smoothing Scatterplots". Journal of the American Statistical Association 74 (368): 829-836. """ cimport numpy as np import numpy as np from cpython cimport bool cimport cython # there's no fmax in math.h with windows SDK apparently cdef inline double fmax(double x, double y): return x if x >= y else y DTYPE = np.double ctypedef np.double_t DTYPE_t cdef double NAN = float("NaN") def lowess(np.ndarray[DTYPE_t, ndim = 1] endog, np.ndarray[DTYPE_t, ndim = 1] exog, np.ndarray[DTYPE_t, ndim = 1] xvals, np.ndarray[DTYPE_t, ndim = 1] resid_weights, double frac = 2.0 / 3.0, Py_ssize_t it = 3, double delta = 0.0, bint given_xvals = False): """lowess(endog, exog, frac=2.0/3.0, it=3, delta=0.0) LOWESS (Locally Weighted Scatterplot Smoothing) A lowess function that outs smoothed estimates of endog at the given exog values from points (exog, endog) Parameters ---------- endog : 1-D numpy array The y-values of the observed points exog : 1-D numpy array The x-values of the observed points. exog has to be increasing. resid_weights : 1-D numpy array The weightings of the observed points frac : float Between 0 and 1. The fraction of the data used when estimating each y-value. it : int The number of residual-based reweightings to perform. delta : float Distance within which to use linear-interpolation instead of weighted regression. given_xvals : bool Whether xvals was provided as a an argument or whether we are just using xvals = exog Returns ------- out : numpy array A numpy array with two columns. The first column is the sorted x values and the second column the associated estimated y-values. resid_weights: numpy array A numpy array with the residual weights on the data points computed from the iterations performed Notes ----- This lowess function implements the algorithm given in the reference below using local linear estimates. Suppose the input data has N points. The algorithm works by estimating the `smooth` y_i by taking the frac*N closest points to (x_i,y_i) based on their x values and estimating y_i using a weighted linear regression. The weight for (x_j,y_j) is tricube function applied to |x_i-x_j|. If it > 1, then further weighted local linear regressions are performed, where the weights are the same as above times the _lowess_bisquare function of the residuals. Each iteration takes approximately the same amount of time as the original fit, so these iterations are expensive. They are most useful when the noise has extremely heavy tails, such as Cauchy noise. Noise with less heavy-tails, such as t-distributions with df>2, are less problematic. The weights downgrade the influence of points with large residuals. In the extreme case, points whose residuals are larger than 6 times the median absolute residual are given weight 0. delta can be used to save computations. For each x_i, regressions are skipped for points closer than delta. The next regression is fit for the farthest point within delta of x_i and all points in between are estimated by linearly interpolating between the two regression fits. Judicious choice of delta can cut computation time considerably for large data (N > 5000). A good choice is delta = 0.01 * range(exog). Some experimentation is likely required to find a good choice of frac and iter for a particular dataset. References ---------- Cleveland, W.S. (1979) "Robust Locally Weighted Regression and Smoothing Scatterplots". Journal of the American Statistical Association 74 (368): 829-836. Examples -------- The below allows a comparison between how different the fits from lowess for different values of frac can be. >>> import numpy as np >>> import statsmodels.api as sm >>> lowess = sm.nonparametric.lowess >>> x = np.random.uniform(low = -2*np.pi, high = 2*np.pi, size=500) >>> y = np.sin(x) + np.random.normal(size=len(x)) >>> z = lowess(y, x) >>> w = lowess(y, x, frac=1./3) This gives a similar comparison for when it is 0 vs not. >>> import numpy as np >>> import scipy.stats as stats >>> import statsmodels.api as sm >>> lowess = sm.nonparametric.lowess >>> x = np.random.uniform(low = -2*np.pi, high = 2*np.pi, size=500) >>> y = np.sin(x) + stats.cauchy.rvs(size=len(x)) >>> z = lowess(y, x, frac= 1./3, it=0) >>> w = lowess(y, x, frac=1./3) """ cdef: Py_ssize_t n int k Py_ssize_t robiter, i, left_end, right_end int last_fit_i, np.ndarray[DTYPE_t, ndim = 1] x, y np.ndarray[DTYPE_t, ndim = 1] y_fit np.ndarray[DTYPE_t, ndim = 1] weights DTYPE_t xval y = endog # now just alias x = exog if not 0 <= frac <= 1: raise ValueError("Lowess `frac` must be in the range [0,1]!") n = x.shape[0] out_n = xvals.shape[0] # The number of neighbors in each regression. # round up if close to integer k = int(frac * n + 1e-10) # frac should be set, so that 2 <= k <= n. # Conform them instead of throwing error. if k < 2: k = 2 if k > n: k = n y_fit = np.zeros(out_n, dtype = DTYPE) it += 1 # Add one to it for initial run. for robiter in range(it): i = 0 last_fit_i = -1 left_end = 0 right_end = k y_fit = np.zeros(out_n, dtype = DTYPE) # 'do' Fit y[i]'s 'until' the end of the regression while True: # The x value at which we will fit this time xval = xvals[i] # Re-initialize the weights for each point xval. weights = np.zeros(n, dtype = DTYPE) # Describe the neighborhood around the current xval. left_end, right_end, radius = update_neighborhood(x, xval, n, left_end, right_end) # Calculate the weights for the regression in this neighborhood. # Determine if at least some weights are positive, so a regression # is ok. reg_ok = calculate_weights(x, weights, resid_weights, xval, left_end, right_end, radius) # If ok, run the regression calculate_y_fit(x, y, i, xval, y_fit, weights, left_end, right_end, reg_ok, fill_with_nans=given_xvals) # If we skipped some points (because of how delta was set), go back # and fit them by linear interpolation. if last_fit_i < (i - 1): interpolate_skipped_fits(xvals, y_fit, i, last_fit_i) # Update the last fit counter to indicate we've now fit this point. # Find the next i for which we'll run a regression. i, last_fit_i = update_indices(xvals, y_fit, delta, i, out_n, last_fit_i) if last_fit_i >= out_n-1: break # Calculate residual weights if not given_xvals: resid_weights = calculate_residual_weights(y, y_fit) return (np.array([xvals, y_fit]).T, resid_weights) def update_neighborhood(np.ndarray[DTYPE_t, ndim = 1] x, DTYPE_t xval, Py_ssize_t n, Py_ssize_t left_end, Py_ssize_t right_end): """ Find the indices bounding the k-nearest-neighbors of the current point. Parameters ---------- x : 1-D numpy array The input x-values xval : float The x-value of the point currently being fit. n : indexing integer The length of the input vectors, x and y. left_end : indexing integer The index of the left-most point in the neighborhood of the previously-fit x-value. right_end: indexing integer The index of the right-most point in the neighborhood of the previous x-value. Non-inclusive, s.t. the neighborhood is x[left_end] <= x < x[right_end]. Returns ------- left_end : indexing integer The index of the left-most point in the neighborhood of xval (the current point). right_end: indexing integer The index of the right-most point in the neighborhood of xval. Non-inclusive, s.t. the neighborhood is x[left_end] <= x < x[right_end]. radius : float The radius of the current neighborhood. The larger of distances between xval and its left-most or right-most neighbor. """ cdef double radius # A subtle loop. Start from the current neighborhood range: # [left_end, right_end). Shift both ends rightwards by one # (so that the neighborhood still contains k points), until # the current point is in the center (or just to the left of # the center) of the neighborhood. This neighborhood will # contain the k-nearest neighbors of xval. # # Once the right end hits the end of the data, hold the # neighborhood the same for the remaining xvals. while True: if right_end < n: if (xval > (x[left_end] + x[right_end]) / 2.0): left_end += 1 right_end += 1 else: break else: break radius = fmax(xval - x[left_end], x[right_end-1] - xval) return left_end, right_end, radius cdef bool calculate_weights(np.ndarray[DTYPE_t, ndim = 1] x, np.ndarray[DTYPE_t, ndim = 1] weights, np.ndarray[DTYPE_t, ndim = 1] resid_weights, DTYPE_t xval, Py_ssize_t left_end, Py_ssize_t right_end, double radius): """ Calculate weights Parameters ---------- x : 1-D vector The input x-values. weights : 1-D numpy array The vector of regression weights. resid_weights : 1-D numpy array The vector of residual weights from the last iteration. xval: float The x-value of the point currently being fit. left_end: indexing integer The index of the left-most point in the neighborhood of x[i]. right_end : indexing integer The index of the right-most point in the neighborhood of x[i]. Non-inclusive, s.t. the neighborhood is x[left_end] <= x < x[right_end]. radius : float The radius of the current neighborhood. The larger of distances between x[i] and its left-most or right-most neighbor. Returns ------- reg_ok : bool If True, at least some points have positive weight, and the regression will be run. If False, the regression is skipped and y_fit[i] is set to equal y[i]. Also, changes elements of weights in-place. """ cdef: np.ndarray[DTYPE_t, ndim = 1] x_j = x[left_end:right_end] np.ndarray[DTYPE_t, ndim = 1] dist_i_j = np.abs(x_j - xval) / radius bint reg_ok = True double sum_weights # Assign the distance measure to the weights, then apply the tricube # function to change in-place. weights[left_end:right_end] = dist_i_j tricube(weights[left_end:right_end]) weights[left_end:right_end] = (weights[left_end:right_end] * resid_weights[left_end:right_end]) sum_weights = np.sum(weights[left_end:right_end]) if sum_weights <= 0.0 or (np.sum(weights[left_end:right_end] != 0) == 1): # 2nd condition checks if only 1 local weight is non-zero, which # will give a divisor of zero in calculate_y_fit # see 1960 reg_ok = False else: weights[left_end:right_end] = weights[left_end:right_end] / sum_weights return reg_ok cdef void calculate_y_fit(np.ndarray[DTYPE_t, ndim = 1] x, np.ndarray[DTYPE_t, ndim = 1] y, Py_ssize_t i, DTYPE_t xval, np.ndarray[DTYPE_t, ndim = 1] y_fit, np.ndarray[DTYPE_t, ndim = 1] weights, Py_ssize_t left_end, Py_ssize_t right_end, bint reg_ok, bint fill_with_nans = False): """ Calculate smoothed/fitted y-value by weighted regression. Parameters ---------- x : 1-D numpy array The vector of input x-values. y : 1-D numpy array The vector of input y-values. i : indexing integer The index of the point currently being fit. xval: float The x-value of the point currently being fit. y_fit: 1-D numpy array The vector of fitted y-values. weights : 1-D numpy array The vector of regression weights. left_end : indexing integer The index of the left-most point in the neighborhood of xval. right_end: indexing integers The index of the right-most point in the neighborhood of xval. Non-inclusive, s.t. the neighborhood is x[left_end] <= x < x[right_end]. reg_ok : bool If True, at least some points have positive weight, and the regression will be run. If False, the regression is skipped and y_fit[i] is set to equal y[i]. fill_with_nans: bool If True, values with no valid regression will be filled with NaN Otherwise, we use the original value in `y` of that point. If x and xval are not the same, this must be False. Returns ------- Nothing. Changes y_fit[i] in-place. Notes ----- No regression function (e.g. lstsq) is called. Instead "projection vector" p_i_j is calculated, and y_fit[i] = sum(p_i_j * y[j]) = y_fit[i] for j s.t. x[j] is in the neighborhood of xval. p_i_j is a function of the weights, xval, and its neighbors. """ cdef: double sum_weighted_x = 0, weighted_sqdev_x = 0, p_i_j if not reg_ok: if fill_with_nans: # Fill a bad regression (weights all zeros) with nans y_fit[i] = NAN else: # Fill a bad regression with the original value # only possible when not using xvals distinct from x y_fit[i] = y[i] else: for j in range(left_end, right_end): sum_weighted_x += weights[j] * x[j] for j in range(left_end, right_end): weighted_sqdev_x += weights[j] * (x[j] - sum_weighted_x) ** 2 for j in range(left_end, right_end): p_i_j = weights[j] * (1.0 + (xval - sum_weighted_x) * (x[j] - sum_weighted_x) / weighted_sqdev_x) y_fit[i] += p_i_j * y[j] cdef void interpolate_skipped_fits(np.ndarray[DTYPE_t, ndim = 1] xvals, np.ndarray[DTYPE_t, ndim = 1] y_fit, Py_ssize_t i, Py_ssize_t last_fit_i): """ Calculate smoothed/fitted y by linear interpolation between the current and previous y fitted by weighted regression. Called only if delta > 0. Parameters ---------- xvals : 1-D numpy array The vector of x-values where regression is performed. y_fit : 1-D numpy array The vector of fitted y-values i : indexing integer The index of the point currently being fit by weighted regression. last_fit_i : indexing integer The index of the last point fit by weighted regression. Returns ------- None Values changed in-place. """ cdef np.ndarray[DTYPE_t, ndim = 1] a a = xvals[(last_fit_i + 1): i] - xvals[last_fit_i] a = a / (xvals[i] - xvals[last_fit_i]) y_fit[(last_fit_i + 1): i] = a * y_fit[i] + (1.0 - a) * y_fit[last_fit_i] def update_indices(np.ndarray[DTYPE_t, ndim = 1] xvals, np.ndarray[DTYPE_t, ndim = 1] y_fit, double delta, Py_ssize_t i, Py_ssize_t out_n, Py_ssize_t last_fit_i): """ Update the counters of the local regression. Parameters ---------- xvals : 1-D numpy array The vector of x-values where regression is performed. y_fit : 1-D numpy array The vector of fitted y-values delta : float Indicates the range of x values within which linear interpolation should be used to estimate y_fit instead of weighted regression. i : indexing integer The index of the current point being fit. out_n : indexing integer The length of the input vector xvals. last_fit_i : indexing integer The last point at which y_fit was calculated. Returns ------- i : indexing integer The next point at which to run a weighted regression. last_fit_i : indexing integer The updated last point at which y_fit was calculated Notes ----- The relationship between the outputs is s.t. xvals[i+1] > xvals[last_fit_i] + delta. """ cdef: Py_ssize_t k double cutpoint last_fit_i = i k = last_fit_i # For most points within delta of the current point, we skip the # weighted linear regression (which save much computation of # weights and fitted points). Instead, we'll jump to the last # point within delta, fit the weighted regression at that point, # and linearly interpolate in between. # This loop increments until we fall just outside of delta distance, # copying the results for any repeated x's along the way. cutpoint = xvals[last_fit_i] + delta for k in range(last_fit_i + 1, out_n): if xvals[k] > cutpoint: break if xvals[k] == xvals[last_fit_i]: # if tied with previous x-value, just use the already # fitted y, and update the last-fit counter. y_fit[k] = y_fit[last_fit_i] last_fit_i = k # i, which indicates the next point to fit the regression at, is # either one prior to k (since k should be the first point outside # of delta) or is just incremented + 1 if k = i+1. This insures we # always step forward. i = max(k-1, last_fit_i + 1) return i, last_fit_i def calculate_residual_weights(np.ndarray[DTYPE_t, ndim = 1] y, np.ndarray[DTYPE_t, ndim = 1] y_fit): """ Calculate residual weights for the next `robustifying` iteration. Parameters ---------- y: 1-D numpy array The vector of actual input y-values. y_fit: 1-D numpy array The vector of fitted y-values from the current iteration. Returns ------- resid_weights: 1-D numpy array The vector of residual weights, to be used in the next iteration of regressions. """ std_resid = np.abs(y - y_fit) median = np.median(std_resid) if median == 0: std_resid[std_resid > 0] = 1 else: std_resid /= 6.0 * median # Some trimming of outlier residuals. std_resid[std_resid >= 1.0] = 1.0 #std_resid[std_resid >= 0.999] = 1.0 #std_resid[std_resid <= 0.001] = 0.0 resid_weights = bisquare(std_resid) return resid_weights cdef void tricube(np.ndarray[DTYPE_t, ndim = 1] x): """ The tri-cubic function (1 - x**3)**3. Used to weight neighboring points along the x-axis based on their distance to the current point. Parameters ---------- x: 1-D numpy array A vector of neighbors` distances from the current point, in units of the neighborhood radius. Returns ------- Nothing. Changes array elements in-place """ # fast_array_cube is an elementwise, in-place cubed-power # operator. fast_array_cube(x) x[:] = np.negative(x) x += 1 fast_array_cube(x) cdef void fast_array_cube(np.ndarray[DTYPE_t, ndim = 1] x): """ A fast, elementwise, in-place cube operator. Called by the tricube function. Parameters ---------- x: 1-D numpy array Returns ------- Nothing. Changes array elements in-place. """ x2 = x*x x *= x2 def bisquare(np.ndarray[DTYPE_t, ndim = 1] x): """ The bi-square function (1 - x**2)**2. Used to weight the residuals in the `robustifying` iterations. Called by the calculate_residual_weights function. Parameters ---------- x: 1-D numpy array A vector of absolute regression residuals, in units of 6 times the median absolute residual. Returns ------- A 1-D numpy array of residual weights. """ return (1.0 - x**2)**2 statsmodels-0.12.2/statsmodels/nonparametric/api.py000066400000000000000000000006511400612667500224760ustar00rootroot00000000000000__all__ = [ "KDEUnivariate", "KDEMultivariate", "KDEMultivariateConditional", "EstimatorSettings", "KernelReg", "KernelCensoredReg", "lowess", "bandwidths" ] from .kde import KDEUnivariate from .smoothers_lowess import lowess from . import bandwidths from .kernel_density import \ KDEMultivariate, KDEMultivariateConditional, EstimatorSettings from .kernel_regression import KernelReg, KernelCensoredReg statsmodels-0.12.2/statsmodels/nonparametric/bandwidths.py000066400000000000000000000107421400612667500240560ustar00rootroot00000000000000import numpy as np from scipy.stats import scoreatpercentile from statsmodels.compat.pandas import Substitution from statsmodels.sandbox.nonparametric import kernels def _select_sigma(x, percentile=25): """ Returns the smaller of std(X, ddof=1) or normalized IQR(X) over axis 0. References ---------- Silverman (1986) p.47 """ # normalize = norm.ppf(.75) - norm.ppf(.25) normalize = 1.349 IQR = (scoreatpercentile(x, 75) - scoreatpercentile(x, 25)) / normalize std_dev = np.std(x, axis=0, ddof=1) if IQR > 0: return np.minimum(std_dev, IQR) else: return std_dev ## Univariate Rule of Thumb Bandwidths ## def bw_scott(x, kernel=None): """ Scott's Rule of Thumb Parameters ---------- x : array_like Array for which to get the bandwidth kernel : CustomKernel object Unused Returns ------- bw : float The estimate of the bandwidth Notes ----- Returns 1.059 * A * n ** (-1/5.) where :: A = min(std(x, ddof=1), IQR/1.349) IQR = np.subtract.reduce(np.percentile(x, [75,25])) References ---------- Scott, D.W. (1992) Multivariate Density Estimation: Theory, Practice, and Visualization. """ A = _select_sigma(x) n = len(x) return 1.059 * A * n ** (-0.2) def bw_silverman(x, kernel=None): """ Silverman's Rule of Thumb Parameters ---------- x : array_like Array for which to get the bandwidth kernel : CustomKernel object Unused Returns ------- bw : float The estimate of the bandwidth Notes ----- Returns .9 * A * n ** (-1/5.) where :: A = min(std(x, ddof=1), IQR/1.349) IQR = np.subtract.reduce(np.percentile(x, [75,25])) References ---------- Silverman, B.W. (1986) `Density Estimation.` """ A = _select_sigma(x) n = len(x) return .9 * A * n ** (-0.2) def bw_normal_reference(x, kernel=None): """ Plug-in bandwidth with kernel specific constant based on normal reference. This bandwidth minimizes the mean integrated square error if the true distribution is the normal. This choice is an appropriate bandwidth for single peaked distributions that are similar to the normal distribution. Parameters ---------- x : array_like Array for which to get the bandwidth kernel : CustomKernel object Used to calculate the constant for the plug-in bandwidth. The default is a Gaussian kernel. Returns ------- bw : float The estimate of the bandwidth Notes ----- Returns C * A * n ** (-1/5.) where :: A = min(std(x, ddof=1), IQR/1.349) IQR = np.subtract.reduce(np.percentile(x, [75,25])) C = constant from Hansen (2009) When using a Gaussian kernel this is equivalent to the 'scott' bandwidth up to two decimal places. This is the accuracy to which the 'scott' constant is specified. References ---------- Silverman, B.W. (1986) `Density Estimation.` Hansen, B.E. (2009) `Lecture Notes on Nonparametrics.` """ if kernel is None: kernel = kernels.Gaussian() C = kernel.normal_reference_constant A = _select_sigma(x) n = len(x) return C * A * n ** (-0.2) ## Plug-In Methods ## ## Least Squares Cross-Validation ## ## Helper Functions ## bandwidth_funcs = { "scott": bw_scott, "silverman": bw_silverman, "normal_reference": bw_normal_reference, } @Substitution(", ".join(sorted(bandwidth_funcs.keys()))) def select_bandwidth(x, bw, kernel): """ Selects bandwidth for a selection rule bw this is a wrapper around existing bandwidth selection rules Parameters ---------- x : array_like Array for which to get the bandwidth bw : str name of bandwidth selection rule, currently supported are: %s kernel : not used yet Returns ------- bw : float The estimate of the bandwidth """ bw = bw.lower() if bw not in bandwidth_funcs: raise ValueError("Bandwidth %s not understood" % bw) bandwidth = bandwidth_funcs[bw](x, kernel) if np.any(bandwidth == 0): # eventually this can fall back on another selection criterion. err = "Selected KDE bandwidth is 0. Cannot estimate density. " \ "Either provide the bandwidth during initialization or use " \ "an alternative method." raise RuntimeError(err) else: return bandwidth statsmodels-0.12.2/statsmodels/nonparametric/kde.py000066400000000000000000000452251400612667500224760ustar00rootroot00000000000000""" Univariate Kernel Density Estimators References ---------- Racine, Jeff. (2008) "Nonparametric Econometrics: A Primer," Foundation and Trends in Econometrics: Vol 3: No 1, pp1-88. http://dx.doi.org/10.1561/0800000009 https://en.wikipedia.org/wiki/Kernel_%28statistics%29 Silverman, B.W. Density Estimation for Statistics and Data Analysis. """ import numpy as np from scipy import integrate, stats from statsmodels.sandbox.nonparametric import kernels from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.validation import array_like, float_like from . import bandwidths from .kdetools import forrt, revrt, silverman_transform from .linbin import fast_linbin # Kernels Switch for estimators kernel_switch = dict( gau=kernels.Gaussian, epa=kernels.Epanechnikov, uni=kernels.Uniform, tri=kernels.Triangular, biw=kernels.Biweight, triw=kernels.Triweight, cos=kernels.Cosine, cos2=kernels.Cosine2, ) def _checkisfit(self): try: self.density except Exception: raise ValueError("Call fit to fit the density first") # Kernel Density Estimator Class class KDEUnivariate(object): """ Univariate Kernel Density Estimator. Parameters ---------- endog : array_like The variable for which the density estimate is desired. Notes ----- If cdf, sf, cumhazard, or entropy are computed, they are computed based on the definition of the kernel rather than the FFT approximation, even if the density is fit with FFT = True. `KDEUnivariate` is much faster than `KDEMultivariate`, due to its FFT-based implementation. It should be preferred for univariate, continuous data. `KDEMultivariate` also supports mixed data. See Also -------- KDEMultivariate kdensity, kdensityfft Examples -------- >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> nobs = 300 >>> np.random.seed(1234) # Seed random generator >>> dens = sm.nonparametric.KDEUnivariate(np.random.normal(size=nobs)) >>> dens.fit() >>> plt.plot(dens.cdf) >>> plt.show() """ def __init__(self, endog): self.endog = array_like(endog, "endog", ndim=1, contiguous=True) def fit( self, kernel="gau", bw="normal_reference", fft=True, weights=None, gridsize=None, adjust=1, cut=3, clip=(-np.inf, np.inf), ): """ Attach the density estimate to the KDEUnivariate class. Parameters ---------- kernel : str The Kernel to be used. Choices are: - "biw" for biweight - "cos" for cosine - "epa" for Epanechnikov - "gau" for Gaussian. - "tri" for triangular - "triw" for triweight - "uni" for uniform bw : str, float, callable The bandwidth to use. Choices are: - "scott" - 1.059 * A * nobs ** (-1/5.), where A is `min(std(x),IQR/1.34)` - "silverman" - .9 * A * nobs ** (-1/5.), where A is `min(std(x),IQR/1.34)` - "normal_reference" - C * A * nobs ** (-1/5.), where C is calculated from the kernel. Equivalent (up to 2 dp) to the "scott" bandwidth for gaussian kernels. See bandwidths.py - If a float is given, its value is used as the bandwidth. - If a callable is given, it's return value is used. The callable should take exactly two parameters, i.e., fn(x, kern), and return a float, where: * x - the clipped input data * kern - the kernel instance used fft : bool Whether or not to use FFT. FFT implementation is more computationally efficient. However, only the Gaussian kernel is implemented. If FFT is False, then a 'nobs' x 'gridsize' intermediate array is created. gridsize : int If gridsize is None, max(len(x), 50) is used. cut : float Defines the length of the grid past the lowest and highest values of x so that the kernel goes to zero. The end points are -/+ cut*bw*{min(x) or max(x)} adjust : float An adjustment factor for the bw. Bandwidth becomes bw * adjust. Returns ------- KDEUnivariate The instance fit, """ if isinstance(bw, str): self.bw_method = bw else: self.bw_method = "user-given" if not callable(bw): bw = float_like(bw, "bw") endog = self.endog if fft: if kernel != "gau": msg = "Only gaussian kernel is available for fft" raise NotImplementedError(msg) if weights is not None: msg = "Weights are not implemented for fft" raise NotImplementedError(msg) density, grid, bw = kdensityfft( endog, kernel=kernel, bw=bw, adjust=adjust, weights=weights, gridsize=gridsize, clip=clip, cut=cut, ) else: density, grid, bw = kdensity( endog, kernel=kernel, bw=bw, adjust=adjust, weights=weights, gridsize=gridsize, clip=clip, cut=cut, ) self.density = density self.support = grid self.bw = bw self.kernel = kernel_switch[kernel](h=bw) # we instantiate twice, # should this passed to funcs? # put here to ensure empty cache after re-fit with new options self.kernel.weights = weights if weights is not None: self.kernel.weights /= weights.sum() self._cache = {} return self @cache_readonly def cdf(self): """ Returns the cumulative distribution function evaluated at the support. Notes ----- Will not work if fit has not been called. """ _checkisfit(self) kern = self.kernel if kern.domain is None: # TODO: test for grid point at domain bound a, b = -np.inf, np.inf else: a, b = kern.domain def func(x, s): return kern.density(s, x) support = self.support support = np.r_[a, support] gridsize = len(support) endog = self.endog probs = [ integrate.quad(func, support[i - 1], support[i], args=endog)[0] for i in range(1, gridsize) ] return np.cumsum(probs) @cache_readonly def cumhazard(self): """ Returns the hazard function evaluated at the support. Notes ----- Will not work if fit has not been called. """ _checkisfit(self) return -np.log(self.sf) @cache_readonly def sf(self): """ Returns the survival function evaluated at the support. Notes ----- Will not work if fit has not been called. """ _checkisfit(self) return 1 - self.cdf @cache_readonly def entropy(self): """ Returns the differential entropy evaluated at the support Notes ----- Will not work if fit has not been called. 1e-12 is added to each probability to ensure that log(0) is not called. """ _checkisfit(self) def entr(x, s): pdf = kern.density(s, x) return pdf * np.log(pdf + 1e-12) kern = self.kernel if kern.domain is not None: a, b = self.domain else: a, b = -np.inf, np.inf endog = self.endog # TODO: below could run into integr problems, cf. stats.dist._entropy return -integrate.quad(entr, a, b, args=(endog,))[0] @cache_readonly def icdf(self): """ Inverse Cumulative Distribution (Quantile) Function Notes ----- Will not work if fit has not been called. Uses `scipy.stats.mstats.mquantiles`. """ _checkisfit(self) gridsize = len(self.density) return stats.mstats.mquantiles(self.endog, np.linspace(0, 1, gridsize)) def evaluate(self, point): """ Evaluate density at a point or points. Parameters ---------- point : {float, ndarray} Point(s) at which to evaluate the density. """ _checkisfit(self) return self.kernel.density(self.endog, point) # Kernel Density Estimator Functions def kdensity( x, kernel="gau", bw="normal_reference", weights=None, gridsize=None, adjust=1, clip=(-np.inf, np.inf), cut=3, retgrid=True, ): """ Rosenblatt-Parzen univariate kernel density estimator. Parameters ---------- x : array_like The variable for which the density estimate is desired. kernel : str The Kernel to be used. Choices are - "biw" for biweight - "cos" for cosine - "epa" for Epanechnikov - "gau" for Gaussian. - "tri" for triangular - "triw" for triweight - "uni" for uniform bw : str, float, callable The bandwidth to use. Choices are: - "scott" - 1.059 * A * nobs ** (-1/5.), where A is `min(std(x),IQR/1.34)` - "silverman" - .9 * A * nobs ** (-1/5.), where A is `min(std(x),IQR/1.34)` - "normal_reference" - C * A * nobs ** (-1/5.), where C is calculated from the kernel. Equivalent (up to 2 dp) to the "scott" bandwidth for gaussian kernels. See bandwidths.py - If a float is given, its value is used as the bandwidth. - If a callable is given, it's return value is used. The callable should take exactly two parameters, i.e., fn(x, kern), and return a float, where: * x - the clipped input data * kern - the kernel instance used weights : array or None Optional weights. If the x value is clipped, then this weight is also dropped. gridsize : int If gridsize is None, max(len(x), 50) is used. adjust : float An adjustment factor for the bw. Bandwidth becomes bw * adjust. clip : tuple Observations in x that are outside of the range given by clip are dropped. The number of observations in x is then shortened. cut : float Defines the length of the grid past the lowest and highest values of x so that the kernel goes to zero. The end points are -/+ cut*bw*{min(x) or max(x)} retgrid : bool Whether or not to return the grid over which the density is estimated. Returns ------- density : ndarray The densities estimated at the grid points. grid : ndarray, optional The grid points at which the density is estimated. Notes ----- Creates an intermediate (`gridsize` x `nobs`) array. Use FFT for a more computationally efficient version. """ x = np.asarray(x) if x.ndim == 1: x = x[:, None] clip_x = np.logical_and(x > clip[0], x < clip[1]) x = x[clip_x] nobs = len(x) # after trim if gridsize is None: gridsize = max(nobs, 50) # do not need to resize if no FFT # handle weights if weights is None: weights = np.ones(nobs) q = nobs else: # ensure weights is a numpy array weights = np.asarray(weights) if len(weights) != len(clip_x): msg = "The length of the weights must be the same as the given x." raise ValueError(msg) weights = weights[clip_x.squeeze()] q = weights.sum() # Get kernel object corresponding to selection kern = kernel_switch[kernel]() if callable(bw): bw = float(bw(x, kern)) # user passed a callable custom bandwidth function elif isinstance(bw, str): bw = bandwidths.select_bandwidth(x, bw, kern) # will cross-val fit this pattern? else: bw = float_like(bw, "bw") bw *= adjust a = np.min(x, axis=0) - cut * bw b = np.max(x, axis=0) + cut * bw grid = np.linspace(a, b, gridsize) k = ( x.T - grid[:, None] ) / bw # uses broadcasting to make a gridsize x nobs # set kernel bandwidth kern.seth(bw) # truncate to domain if ( kern.domain is not None ): # will not work for piecewise kernels like parzen z_lo, z_high = kern.domain domain_mask = (k < z_lo) | (k > z_high) k = kern(k) # estimate density k[domain_mask] = 0 else: k = kern(k) # estimate density k[k < 0] = 0 # get rid of any negative values, do we need this? dens = np.dot(k, weights) / (q * bw) if retgrid: return dens, grid, bw else: return dens, bw def kdensityfft( x, kernel="gau", bw="normal_reference", weights=None, gridsize=None, adjust=1, clip=(-np.inf, np.inf), cut=3, retgrid=True, ): """ Rosenblatt-Parzen univariate kernel density estimator Parameters ---------- x : array_like The variable for which the density estimate is desired. kernel : str ONLY GAUSSIAN IS CURRENTLY IMPLEMENTED. "bi" for biweight "cos" for cosine "epa" for Epanechnikov, default "epa2" for alternative Epanechnikov "gau" for Gaussian. "par" for Parzen "rect" for rectangular "tri" for triangular bw : str, float, callable The bandwidth to use. Choices are: - "scott" - 1.059 * A * nobs ** (-1/5.), where A is `min(std(x),IQR/1.34)` - "silverman" - .9 * A * nobs ** (-1/5.), where A is `min(std(x),IQR/1.34)` - "normal_reference" - C * A * nobs ** (-1/5.), where C is calculated from the kernel. Equivalent (up to 2 dp) to the "scott" bandwidth for gaussian kernels. See bandwidths.py - If a float is given, its value is used as the bandwidth. - If a callable is given, it's return value is used. The callable should take exactly two parameters, i.e., fn(x, kern), and return a float, where: * x - the clipped input data * kern - the kernel instance used weights : array or None WEIGHTS ARE NOT CURRENTLY IMPLEMENTED. Optional weights. If the x value is clipped, then this weight is also dropped. gridsize : int If gridsize is None, min(len(x), 512) is used. Note that the provided number is rounded up to the next highest power of 2. adjust : float An adjustment factor for the bw. Bandwidth becomes bw * adjust. clip : tuple Observations in x that are outside of the range given by clip are dropped. The number of observations in x is then shortened. cut : float Defines the length of the grid past the lowest and highest values of x so that the kernel goes to zero. The end points are -/+ cut*bw*{x.min() or x.max()} retgrid : bool Whether or not to return the grid over which the density is estimated. Returns ------- density : ndarray The densities estimated at the grid points. grid : ndarray, optional The grid points at which the density is estimated. Notes ----- Only the default kernel is implemented. Weights are not implemented yet. This follows Silverman (1982) with changes suggested by Jones and Lotwick (1984). However, the discretization step is replaced by linear binning of Fan and Marron (1994). This should be extended to accept the parts that are dependent only on the data to speed things up for cross-validation. References ---------- Fan, J. and J.S. Marron. (1994) `Fast implementations of nonparametric curve estimators`. Journal of Computational and Graphical Statistics. 3.1, 35-56. Jones, M.C. and H.W. Lotwick. (1984) `Remark AS R50: A Remark on Algorithm AS 176. Kernal Density Estimation Using the Fast Fourier Transform`. Journal of the Royal Statistical Society. Series C. 33.1, 120-2. Silverman, B.W. (1982) `Algorithm AS 176. Kernel density estimation using the Fast Fourier Transform. Journal of the Royal Statistical Society. Series C. 31.2, 93-9. """ x = np.asarray(x) # will not work for two columns. x = x[np.logical_and(x > clip[0], x < clip[1])] # Get kernel object corresponding to selection kern = kernel_switch[kernel]() if callable(bw): bw = float(bw(x, kern)) # user passed a callable custom bandwidth function elif isinstance(bw, str): # if bw is None, select optimal bandwidth for kernel bw = bandwidths.select_bandwidth(x, bw, kern) # will cross-val fit this pattern? else: bw = float_like(bw, "bw") bw *= adjust nobs = len(x) # after trim # 1 Make grid and discretize the data if gridsize is None: gridsize = np.max((nobs, 512.0)) gridsize = 2 ** np.ceil(np.log2(gridsize)) # round to next power of 2 a = np.min(x) - cut * bw b = np.max(x) + cut * bw grid, delta = np.linspace(a, b, int(gridsize), retstep=True) RANGE = b - a # TODO: Fix this? # This is the Silverman binning function, but I believe it's buggy (SS) # weighting according to Silverman # count = counts(x,grid) # binned = np.zeros_like(grid) #xi_{k} in Silverman # j = 0 # for k in range(int(gridsize-1)): # if count[k]>0: # there are points of x in the grid here # Xingrid = x[j:j+count[k]] # get all these points # # get weights at grid[k],grid[k+1] # binned[k] += np.sum(grid[k+1]-Xingrid) # binned[k+1] += np.sum(Xingrid-grid[k]) # j += count[k] # binned /= (nobs)*delta**2 # normalize binned to sum to 1/delta # NOTE: THE ABOVE IS WRONG, JUST TRY WITH LINEAR BINNING binned = fast_linbin(x, a, b, gridsize) / (delta * nobs) # step 2 compute FFT of the weights, using Munro (1976) FFT convention y = forrt(binned) # step 3 and 4 for optimal bw compute zstar and the density estimate f # do not have to redo the above if just changing bw, ie., for cross val # NOTE: silverman_transform is the closed form solution of the FFT of the # gaussian kernel. Not yet sure how to generalize it. zstar = silverman_transform(bw, gridsize, RANGE) * y # 3.49 in Silverman # 3.50 w Gaussian kernel f = revrt(zstar) if retgrid: return f, grid, bw else: return f, bw statsmodels-0.12.2/statsmodels/nonparametric/kdetools.py000066400000000000000000000025061400612667500235520ustar00rootroot00000000000000#### Convenience Functions to be moved to kerneltools #### import numpy as np def forrt(X, m=None): """ RFFT with order like Munro (1976) FORTT routine. """ if m is None: m = len(X) y = np.fft.rfft(X, m) / m return np.r_[y.real, y[1:-1].imag] def revrt(X, m=None): """ Inverse of forrt. Equivalent to Munro (1976) REVRT routine. """ if m is None: m = len(X) i = int(m // 2 + 1) y = X[:i] + np.r_[0, X[i:], 0] * 1j return np.fft.irfft(y)*m def silverman_transform(bw, M, RANGE): """ FFT of Gaussian kernel following to Silverman AS 176. Notes ----- Underflow is intentional as a dampener. """ J = np.arange(M/2+1) FAC1 = 2*(np.pi*bw/RANGE)**2 JFAC = J**2*FAC1 BC = 1 - 1. / 3 * (J * 1./M*np.pi)**2 FAC = np.exp(-JFAC)/BC kern_est = np.r_[FAC, FAC[1:-1]] return kern_est def counts(x, v): """ Counts the number of elements of x that fall within the grid points v Notes ----- Using np.digitize and np.bincount """ idx = np.digitize(x, v) try: # numpy 1.6 return np.bincount(idx, minlength=len(v)) except: bc = np.bincount(idx) return np.r_[bc, np.zeros(len(v) - len(bc))] def kdesum(x, axis=0): return np.asarray([np.sum(x[i] - x, axis) for i in range(len(x))]) statsmodels-0.12.2/statsmodels/nonparametric/kernel_density.py000066400000000000000000000624361400612667500247550ustar00rootroot00000000000000""" Multivariate Conditional and Unconditional Kernel Density Estimation with Mixed Data Types. References ---------- [1] Racine, J., Li, Q. Nonparametric econometrics: theory and practice. Princeton University Press. (2007) [2] Racine, Jeff. "Nonparametric Econometrics: A Primer," Foundation and Trends in Econometrics: Vol 3: No 1, pp1-88. (2008) http://dx.doi.org/10.1561/0800000009 [3] Racine, J., Li, Q. "Nonparametric Estimation of Distributions with Categorical and Continuous Data." Working Paper. (2000) [4] Racine, J. Li, Q. "Kernel Estimation of Multivariate Conditional Distributions Annals of Economics and Finance 5, 211-235 (2004) [5] Liu, R., Yang, L. "Kernel estimation of multivariate cumulative distribution function." Journal of Nonparametric Statistics (2008) [6] Li, R., Ju, G. "Nonparametric Estimation of Multivariate CDF with Categorical and Continuous Data." Working Paper [7] Li, Q., Racine, J. "Cross-validated local linear nonparametric regression" Statistica Sinica 14(2004), pp. 485-512 [8] Racine, J.: "Consistent Significance Testing for Nonparametric Regression" Journal of Business & Economics Statistics [9] Racine, J., Hart, J., Li, Q., "Testing the Significance of Categorical Predictor Variables in Nonparametric Regression Models", 2006, Econometric Reviews 25, 523-544 """ # TODO: make default behavior efficient=True above a certain n_obs import numpy as np from . import kernels from ._kernel_base import GenericKDE, EstimatorSettings, gpke, \ LeaveOneOut, _adjust_shape __all__ = ['KDEMultivariate', 'KDEMultivariateConditional', 'EstimatorSettings'] class KDEMultivariate(GenericKDE): """ Multivariate kernel density estimator. This density estimator can handle univariate as well as multivariate data, including mixed continuous / ordered discrete / unordered discrete data. It also provides cross-validated bandwidth selection methods (least squares, maximum likelihood). Parameters ---------- data : list of ndarrays or 2-D ndarray The training data for the Kernel Density Estimation, used to determine the bandwidth(s). If a 2-D array, should be of shape (num_observations, num_variables). If a list, each list element is a separate observation. var_type : str The type of the variables: - c : continuous - u : unordered (discrete) - o : ordered (discrete) The string should contain a type specifier for each variable, so for example ``var_type='ccuo'``. bw : array_like or str, optional If an array, it is a fixed user-specified bandwidth. If a string, should be one of: - normal_reference: normal reference rule of thumb (default) - cv_ml: cross validation maximum likelihood - cv_ls: cross validation least squares defaults : EstimatorSettings instance, optional The default values for (efficient) bandwidth estimation. Attributes ---------- bw : array_like The bandwidth parameters. See Also -------- KDEMultivariateConditional Examples -------- >>> import statsmodels.api as sm >>> nobs = 300 >>> np.random.seed(1234) # Seed random generator >>> c1 = np.random.normal(size=(nobs,1)) >>> c2 = np.random.normal(2, 1, size=(nobs,1)) Estimate a bivariate distribution and display the bandwidth found: >>> dens_u = sm.nonparametric.KDEMultivariate(data=[c1,c2], ... var_type='cc', bw='normal_reference') >>> dens_u.bw array([ 0.39967419, 0.38423292]) """ def __init__(self, data, var_type, bw=None, defaults=None): self.var_type = var_type self.k_vars = len(self.var_type) self.data = _adjust_shape(data, self.k_vars) self.data_type = var_type self.nobs, self.k_vars = np.shape(self.data) if self.nobs <= self.k_vars: raise ValueError("The number of observations must be larger " \ "than the number of variables.") defaults = EstimatorSettings() if defaults is None else defaults self._set_defaults(defaults) if not self.efficient: self.bw = self._compute_bw(bw) else: self.bw = self._compute_efficient(bw) def __repr__(self): """Provide something sane to print.""" rpr = "KDE instance\n" rpr += "Number of variables: k_vars = " + str(self.k_vars) + "\n" rpr += "Number of samples: nobs = " + str(self.nobs) + "\n" rpr += "Variable types: " + self.var_type + "\n" rpr += "BW selection method: " + self._bw_method + "\n" return rpr def loo_likelihood(self, bw, func=lambda x: x): r""" Returns the leave-one-out likelihood function. The leave-one-out likelihood function for the unconditional KDE. Parameters ---------- bw : array_like The value for the bandwidth parameter(s). func : callable, optional Function to transform the likelihood values (before summing); for the log likelihood, use ``func=np.log``. Default is ``f(x) = x``. Notes ----- The leave-one-out kernel estimator of :math:`f_{-i}` is: .. math:: f_{-i}(X_{i})=\frac{1}{(n-1)h} \sum_{j=1,j\neq i}K_{h}(X_{i},X_{j}) where :math:`K_{h}` represents the generalized product kernel estimator: .. math:: K_{h}(X_{i},X_{j}) = \prod_{s=1}^{q}h_{s}^{-1}k\left(\frac{X_{is}-X_{js}}{h_{s}}\right) """ LOO = LeaveOneOut(self.data) L = 0 for i, X_not_i in enumerate(LOO): f_i = gpke(bw, data=-X_not_i, data_predict=-self.data[i, :], var_type=self.var_type) L += func(f_i) return -L def pdf(self, data_predict=None): r""" Evaluate the probability density function. Parameters ---------- data_predict : array_like, optional Points to evaluate at. If unspecified, the training data is used. Returns ------- pdf_est : array_like Probability density function evaluated at `data_predict`. Notes ----- The probability density is given by the generalized product kernel estimator: .. math:: K_{h}(X_{i},X_{j}) = \prod_{s=1}^{q}h_{s}^{-1}k\left(\frac{X_{is}-X_{js}}{h_{s}}\right) """ if data_predict is None: data_predict = self.data else: data_predict = _adjust_shape(data_predict, self.k_vars) pdf_est = [] for i in range(np.shape(data_predict)[0]): pdf_est.append(gpke(self.bw, data=self.data, data_predict=data_predict[i, :], var_type=self.var_type) / self.nobs) pdf_est = np.squeeze(pdf_est) return pdf_est def cdf(self, data_predict=None): r""" Evaluate the cumulative distribution function. Parameters ---------- data_predict : array_like, optional Points to evaluate at. If unspecified, the training data is used. Returns ------- cdf_est : array_like The estimate of the cdf. Notes ----- See https://en.wikipedia.org/wiki/Cumulative_distribution_function For more details on the estimation see Ref. [5] in module docstring. The multivariate CDF for mixed data (continuous and ordered/unordered discrete) is estimated by: .. math:: F(x^{c},x^{d})=n^{-1}\sum_{i=1}^{n}\left[G(\frac{x^{c}-X_{i}}{h})\sum_{u\leq x^{d}}L(X_{i}^{d},x_{i}^{d}, \lambda)\right] where G() is the product kernel CDF estimator for the continuous and L() for the discrete variables. Used bandwidth is ``self.bw``. """ if data_predict is None: data_predict = self.data else: data_predict = _adjust_shape(data_predict, self.k_vars) cdf_est = [] for i in range(np.shape(data_predict)[0]): cdf_est.append(gpke(self.bw, data=self.data, data_predict=data_predict[i, :], var_type=self.var_type, ckertype="gaussian_cdf", ukertype="aitchisonaitken_cdf", okertype='wangryzin_cdf') / self.nobs) cdf_est = np.squeeze(cdf_est) return cdf_est def imse(self, bw): r""" Returns the Integrated Mean Square Error for the unconditional KDE. Parameters ---------- bw : array_like The bandwidth parameter(s). Returns ------- CV : float The cross-validation objective function. Notes ----- See p. 27 in [1]_ for details on how to handle the multivariate estimation with mixed data types see p.6 in [2]_. The formula for the cross-validation objective function is: .. math:: CV=\frac{1}{n^{2}}\sum_{i=1}^{n}\sum_{j=1}^{N} \bar{K}_{h}(X_{i},X_{j})-\frac{2}{n(n-1)}\sum_{i=1}^{n} \sum_{j=1,j\neq i}^{N}K_{h}(X_{i},X_{j}) Where :math:`\bar{K}_{h}` is the multivariate product convolution kernel (consult [2]_ for mixed data types). References ---------- .. [1] Racine, J., Li, Q. Nonparametric econometrics: theory and practice. Princeton University Press. (2007) .. [2] Racine, J., Li, Q. "Nonparametric Estimation of Distributions with Categorical and Continuous Data." Working Paper. (2000) """ #F = 0 #for i in range(self.nobs): # k_bar_sum = gpke(bw, data=-self.data, # data_predict=-self.data[i, :], # var_type=self.var_type, # ckertype='gauss_convolution', # okertype='wangryzin_convolution', # ukertype='aitchisonaitken_convolution') # F += k_bar_sum ## there is a + because loo_likelihood returns the negative #return (F / self.nobs**2 + self.loo_likelihood(bw) * \ # 2 / ((self.nobs) * (self.nobs - 1))) # The code below is equivalent to the commented-out code above. It's # about 20% faster due to some code being moved outside the for-loops # and shared by gpke() and loo_likelihood(). F = 0 kertypes = dict(c=kernels.gaussian_convolution, o=kernels.wang_ryzin_convolution, u=kernels.aitchison_aitken_convolution) nobs = self.nobs data = -self.data var_type = self.var_type ix_cont = np.array([c == 'c' for c in var_type]) _bw_cont_product = bw[ix_cont].prod() Kval = np.empty(data.shape) for i in range(nobs): for ii, vtype in enumerate(var_type): Kval[:, ii] = kertypes[vtype](bw[ii], data[:, ii], data[i, ii]) dens = Kval.prod(axis=1) / _bw_cont_product k_bar_sum = dens.sum(axis=0) F += k_bar_sum # sum of prod kernel over nobs kertypes = dict(c=kernels.gaussian, o=kernels.wang_ryzin, u=kernels.aitchison_aitken) LOO = LeaveOneOut(self.data) L = 0 # leave-one-out likelihood Kval = np.empty((data.shape[0]-1, data.shape[1])) for i, X_not_i in enumerate(LOO): for ii, vtype in enumerate(var_type): Kval[:, ii] = kertypes[vtype](bw[ii], -X_not_i[:, ii], data[i, ii]) dens = Kval.prod(axis=1) / _bw_cont_product L += dens.sum(axis=0) # CV objective function, eq. (2.4) of Ref. [3] return (F / nobs**2 - 2 * L / (nobs * (nobs - 1))) def _get_class_vars_type(self): """Helper method to be able to pass needed vars to _compute_subset.""" class_type = 'KDEMultivariate' class_vars = (self.var_type, ) return class_type, class_vars class KDEMultivariateConditional(GenericKDE): """ Conditional multivariate kernel density estimator. Calculates ``P(Y_1,Y_2,...Y_n | X_1,X_2...X_m) = P(X_1, X_2,...X_n, Y_1, Y_2,..., Y_m)/P(X_1, X_2,..., X_m)``. The conditional density is by definition the ratio of the two densities, see [1]_. Parameters ---------- endog : list of ndarrays or 2-D ndarray The training data for the dependent variables, used to determine the bandwidth(s). If a 2-D array, should be of shape (num_observations, num_variables). If a list, each list element is a separate observation. exog : list of ndarrays or 2-D ndarray The training data for the independent variable; same shape as `endog`. dep_type : str The type of the dependent variables: c : Continuous u : Unordered (Discrete) o : Ordered (Discrete) The string should contain a type specifier for each variable, so for example ``dep_type='ccuo'``. indep_type : str The type of the independent variables; specified like `dep_type`. bw : array_like or str, optional If an array, it is a fixed user-specified bandwidth. If a string, should be one of: - normal_reference: normal reference rule of thumb (default) - cv_ml: cross validation maximum likelihood - cv_ls: cross validation least squares defaults : Instance of class EstimatorSettings The default values for the efficient bandwidth estimation Attributes ---------- bw : array_like The bandwidth parameters See Also -------- KDEMultivariate References ---------- .. [1] https://en.wikipedia.org/wiki/Conditional_probability_distribution Examples -------- >>> import statsmodels.api as sm >>> nobs = 300 >>> c1 = np.random.normal(size=(nobs,1)) >>> c2 = np.random.normal(2,1,size=(nobs,1)) >>> dens_c = sm.nonparametric.KDEMultivariateConditional(endog=[c1], ... exog=[c2], dep_type='c', indep_type='c', bw='normal_reference') >>> dens_c.bw # show computed bandwidth array([ 0.41223484, 0.40976931]) """ def __init__(self, endog, exog, dep_type, indep_type, bw, defaults=None): self.dep_type = dep_type self.indep_type = indep_type self.data_type = dep_type + indep_type self.k_dep = len(self.dep_type) self.k_indep = len(self.indep_type) self.endog = _adjust_shape(endog, self.k_dep) self.exog = _adjust_shape(exog, self.k_indep) self.nobs, self.k_dep = np.shape(self.endog) self.data = np.column_stack((self.endog, self.exog)) self.k_vars = np.shape(self.data)[1] defaults = EstimatorSettings() if defaults is None else defaults self._set_defaults(defaults) if not self.efficient: self.bw = self._compute_bw(bw) else: self.bw = self._compute_efficient(bw) def __repr__(self): """Provide something sane to print.""" rpr = "KDEMultivariateConditional instance\n" rpr += "Number of independent variables: k_indep = " + \ str(self.k_indep) + "\n" rpr += "Number of dependent variables: k_dep = " + \ str(self.k_dep) + "\n" rpr += "Number of observations: nobs = " + str(self.nobs) + "\n" rpr += "Independent variable types: " + self.indep_type + "\n" rpr += "Dependent variable types: " + self.dep_type + "\n" rpr += "BW selection method: " + self._bw_method + "\n" return rpr def loo_likelihood(self, bw, func=lambda x: x): """ Returns the leave-one-out conditional likelihood of the data. If `func` is not equal to the default, what's calculated is a function of the leave-one-out conditional likelihood. Parameters ---------- bw : array_like The bandwidth parameter(s). func : callable, optional Function to transform the likelihood values (before summing); for the log likelihood, use ``func=np.log``. Default is ``f(x) = x``. Returns ------- L : float The value of the leave-one-out function for the data. Notes ----- Similar to ``KDE.loo_likelihood`, but substitute ``f(y|x)=f(x,y)/f(x)`` for ``f(x)``. """ yLOO = LeaveOneOut(self.data) xLOO = LeaveOneOut(self.exog).__iter__() L = 0 for i, Y_j in enumerate(yLOO): X_not_i = next(xLOO) f_yx = gpke(bw, data=-Y_j, data_predict=-self.data[i, :], var_type=(self.dep_type + self.indep_type)) f_x = gpke(bw[self.k_dep:], data=-X_not_i, data_predict=-self.exog[i, :], var_type=self.indep_type) f_i = f_yx / f_x L += func(f_i) return -L def pdf(self, endog_predict=None, exog_predict=None): r""" Evaluate the probability density function. Parameters ---------- endog_predict : array_like, optional Evaluation data for the dependent variables. If unspecified, the training data is used. exog_predict : array_like, optional Evaluation data for the independent variables. Returns ------- pdf : array_like The value of the probability density at `endog_predict` and `exog_predict`. Notes ----- The formula for the conditional probability density is: .. math:: f(y|x)=\frac{f(x,y)}{f(x)} with .. math:: f(x)=\prod_{s=1}^{q}h_{s}^{-1}k \left(\frac{x_{is}-x_{js}}{h_{s}}\right) where :math:`k` is the appropriate kernel for each variable. """ if endog_predict is None: endog_predict = self.endog else: endog_predict = _adjust_shape(endog_predict, self.k_dep) if exog_predict is None: exog_predict = self.exog else: exog_predict = _adjust_shape(exog_predict, self.k_indep) pdf_est = [] data_predict = np.column_stack((endog_predict, exog_predict)) for i in range(np.shape(data_predict)[0]): f_yx = gpke(self.bw, data=self.data, data_predict=data_predict[i, :], var_type=(self.dep_type + self.indep_type)) f_x = gpke(self.bw[self.k_dep:], data=self.exog, data_predict=exog_predict[i, :], var_type=self.indep_type) pdf_est.append(f_yx / f_x) return np.squeeze(pdf_est) def cdf(self, endog_predict=None, exog_predict=None): r""" Cumulative distribution function for the conditional density. Parameters ---------- endog_predict : array_like, optional The evaluation dependent variables at which the cdf is estimated. If not specified the training dependent variables are used. exog_predict : array_like, optional The evaluation independent variables at which the cdf is estimated. If not specified the training independent variables are used. Returns ------- cdf_est : array_like The estimate of the cdf. Notes ----- For more details on the estimation see [2]_, and p.181 in [1]_. The multivariate conditional CDF for mixed data (continuous and ordered/unordered discrete) is estimated by: .. math:: F(y|x)=\frac{n^{-1}\sum_{i=1}^{n}G(\frac{y-Y_{i}}{h_{0}}) W_{h}(X_{i},x)}{\widehat{\mu}(x)} where G() is the product kernel CDF estimator for the dependent (y) variable(s) and W() is the product kernel CDF estimator for the independent variable(s). References ---------- .. [1] Racine, J., Li, Q. Nonparametric econometrics: theory and practice. Princeton University Press. (2007) .. [2] Liu, R., Yang, L. "Kernel estimation of multivariate cumulative distribution function." Journal of Nonparametric Statistics (2008) """ if endog_predict is None: endog_predict = self.endog else: endog_predict = _adjust_shape(endog_predict, self.k_dep) if exog_predict is None: exog_predict = self.exog else: exog_predict = _adjust_shape(exog_predict, self.k_indep) N_data_predict = np.shape(exog_predict)[0] cdf_est = np.empty(N_data_predict) for i in range(N_data_predict): mu_x = gpke(self.bw[self.k_dep:], data=self.exog, data_predict=exog_predict[i, :], var_type=self.indep_type) / self.nobs mu_x = np.squeeze(mu_x) cdf_endog = gpke(self.bw[0:self.k_dep], data=self.endog, data_predict=endog_predict[i, :], var_type=self.dep_type, ckertype="gaussian_cdf", ukertype="aitchisonaitken_cdf", okertype='wangryzin_cdf', tosum=False) cdf_exog = gpke(self.bw[self.k_dep:], data=self.exog, data_predict=exog_predict[i, :], var_type=self.indep_type, tosum=False) S = (cdf_endog * cdf_exog).sum(axis=0) cdf_est[i] = S / (self.nobs * mu_x) return cdf_est def imse(self, bw): r""" The integrated mean square error for the conditional KDE. Parameters ---------- bw : array_like The bandwidth parameter(s). Returns ------- CV : float The cross-validation objective function. Notes ----- For more details see pp. 156-166 in [1]_. For details on how to handle the mixed variable types see [2]_. The formula for the cross-validation objective function for mixed variable types is: .. math:: CV(h,\lambda)=\frac{1}{n}\sum_{l=1}^{n} \frac{G_{-l}(X_{l})}{\left[\mu_{-l}(X_{l})\right]^{2}}- \frac{2}{n}\sum_{l=1}^{n}\frac{f_{-l}(X_{l},Y_{l})}{\mu_{-l}(X_{l})} where .. math:: G_{-l}(X_{l}) = n^{-2}\sum_{i\neq l}\sum_{j\neq l} K_{X_{i},X_{l}} K_{X_{j},X_{l}}K_{Y_{i},Y_{j}}^{(2)} where :math:`K_{X_{i},X_{l}}` is the multivariate product kernel and :math:`\mu_{-l}(X_{l})` is the leave-one-out estimator of the pdf. :math:`K_{Y_{i},Y_{j}}^{(2)}` is the convolution kernel. The value of the function is minimized by the ``_cv_ls`` method of the `GenericKDE` class to return the bw estimates that minimize the distance between the estimated and "true" probability density. References ---------- .. [1] Racine, J., Li, Q. Nonparametric econometrics: theory and practice. Princeton University Press. (2007) .. [2] Racine, J., Li, Q. "Nonparametric Estimation of Distributions with Categorical and Continuous Data." Working Paper. (2000) """ zLOO = LeaveOneOut(self.data) CV = 0 nobs = float(self.nobs) expander = np.ones((self.nobs - 1, 1)) for ii, Z in enumerate(zLOO): X = Z[:, self.k_dep:] Y = Z[:, :self.k_dep] Ye_L = np.kron(Y, expander) Ye_R = np.kron(expander, Y) Xe_L = np.kron(X, expander) Xe_R = np.kron(expander, X) K_Xi_Xl = gpke(bw[self.k_dep:], data=Xe_L, data_predict=self.exog[ii, :], var_type=self.indep_type, tosum=False) K_Xj_Xl = gpke(bw[self.k_dep:], data=Xe_R, data_predict=self.exog[ii, :], var_type=self.indep_type, tosum=False) K2_Yi_Yj = gpke(bw[0:self.k_dep], data=Ye_L, data_predict=Ye_R, var_type=self.dep_type, ckertype='gauss_convolution', okertype='wangryzin_convolution', ukertype='aitchisonaitken_convolution', tosum=False) G = (K_Xi_Xl * K_Xj_Xl * K2_Yi_Yj).sum() / nobs**2 f_X_Y = gpke(bw, data=-Z, data_predict=-self.data[ii, :], var_type=(self.dep_type + self.indep_type)) / nobs m_x = gpke(bw[self.k_dep:], data=-X, data_predict=-self.exog[ii, :], var_type=self.indep_type) / nobs CV += (G / m_x ** 2) - 2 * (f_X_Y / m_x) return CV / nobs def _get_class_vars_type(self): """Helper method to be able to pass needed vars to _compute_subset.""" class_type = 'KDEMultivariateConditional' class_vars = (self.k_dep, self.dep_type, self.indep_type) return class_type, class_vars statsmodels-0.12.2/statsmodels/nonparametric/kernel_regression.py000066400000000000000000001040241400612667500254440ustar00rootroot00000000000000""" Multivariate Conditional and Unconditional Kernel Density Estimation with Mixed Data Types References ---------- [1] Racine, J., Li, Q. Nonparametric econometrics: theory and practice. Princeton University Press. (2007) [2] Racine, Jeff. "Nonparametric Econometrics: A Primer," Foundation and Trends in Econometrics: Vol 3: No 1, pp1-88. (2008) http://dx.doi.org/10.1561/0800000009 [3] Racine, J., Li, Q. "Nonparametric Estimation of Distributions with Categorical and Continuous Data." Working Paper. (2000) [4] Racine, J. Li, Q. "Kernel Estimation of Multivariate Conditional Distributions Annals of Economics and Finance 5, 211-235 (2004) [5] Liu, R., Yang, L. "Kernel estimation of multivariate cumulative distribution function." Journal of Nonparametric Statistics (2008) [6] Li, R., Ju, G. "Nonparametric Estimation of Multivariate CDF with Categorical and Continuous Data." Working Paper [7] Li, Q., Racine, J. "Cross-validated local linear nonparametric regression" Statistica Sinica 14(2004), pp. 485-512 [8] Racine, J.: "Consistent Significance Testing for Nonparametric Regression" Journal of Business & Economics Statistics [9] Racine, J., Hart, J., Li, Q., "Testing the Significance of Categorical Predictor Variables in Nonparametric Regression Models", 2006, Econometric Reviews 25, 523-544 """ # TODO: make default behavior efficient=True above a certain n_obs import copy import numpy as np from scipy import optimize from scipy.stats.mstats import mquantiles from ._kernel_base import GenericKDE, EstimatorSettings, gpke, \ LeaveOneOut, _get_type_pos, _adjust_shape, _compute_min_std_IQR, kernel_func __all__ = ['KernelReg', 'KernelCensoredReg'] class KernelReg(GenericKDE): """ Nonparametric kernel regression class. Calculates the conditional mean ``E[y|X]`` where ``y = g(X) + e``. Note that the "local constant" type of regression provided here is also known as Nadaraya-Watson kernel regression; "local linear" is an extension of that which suffers less from bias issues at the edge of the support. Note that specifying a custom kernel works only with "local linear" kernel regression. For example, a custom ``tricube`` kernel yields LOESS regression. Parameters ---------- endog : array_like This is the dependent variable. exog : array_like The training data for the independent variable(s) Each element in the list is a separate variable var_type : str The type of the variables, one character per variable: - c: continuous - u: unordered (discrete) - o: ordered (discrete) reg_type : {'lc', 'll'}, optional Type of regression estimator. 'lc' means local constant and 'll' local Linear estimator. Default is 'll' bw : str or array_like, optional Either a user-specified bandwidth or the method for bandwidth selection. If a string, valid values are 'cv_ls' (least-squares cross-validation) and 'aic' (AIC Hurvich bandwidth estimation). Default is 'cv_ls'. User specified bandwidth must have as many entries as the number of variables. ckertype : str, optional The kernel used for the continuous variables. okertype : str, optional The kernel used for the ordered discrete variables. ukertype : str, optional The kernel used for the unordered discrete variables. defaults : EstimatorSettings instance, optional The default values for the efficient bandwidth estimation. Attributes ---------- bw : array_like The bandwidth parameters. """ def __init__(self, endog, exog, var_type, reg_type='ll', bw='cv_ls', ckertype='gaussian', okertype='wangryzin', ukertype='aitchisonaitken', defaults=None): self.var_type = var_type self.data_type = var_type self.reg_type = reg_type self.ckertype = ckertype self.okertype = okertype self.ukertype = ukertype if not (self.ckertype in kernel_func and self.ukertype in kernel_func and self.okertype in kernel_func): raise ValueError('user specified kernel must be a supported ' 'kernel from statsmodels.nonparametric.kernels.') self.k_vars = len(self.var_type) self.endog = _adjust_shape(endog, 1) self.exog = _adjust_shape(exog, self.k_vars) self.data = np.column_stack((self.endog, self.exog)) self.nobs = np.shape(self.exog)[0] self.est = dict(lc=self._est_loc_constant, ll=self._est_loc_linear) defaults = EstimatorSettings() if defaults is None else defaults self._set_defaults(defaults) if not isinstance(bw, str): bw = np.asarray(bw) if len(bw) != self.k_vars: raise ValueError('bw must have the same dimension as the ' 'number of variables.') if not self.efficient: self.bw = self._compute_reg_bw(bw) else: self.bw = self._compute_efficient(bw) def _compute_reg_bw(self, bw): if not isinstance(bw, str): self._bw_method = "user-specified" return np.asarray(bw) else: # The user specified a bandwidth selection method e.g. 'cv_ls' self._bw_method = bw # Workaround to avoid instance methods in __dict__ if bw == 'cv_ls': res = self.cv_loo else: # bw == 'aic' res = self.aic_hurvich X = np.std(self.exog, axis=0) h0 = 1.06 * X * \ self.nobs ** (- 1. / (4 + np.size(self.exog, axis=1))) func = self.est[self.reg_type] bw_estimated = optimize.fmin(res, x0=h0, args=(func, ), maxiter=1e3, maxfun=1e3, disp=0) return bw_estimated def _est_loc_linear(self, bw, endog, exog, data_predict): """ Local linear estimator of g(x) in the regression ``y = g(x) + e``. Parameters ---------- bw : array_like Vector of bandwidth value(s). endog : 1D array_like The dependent variable. exog : 1D or 2D array_like The independent variable(s). data_predict : 1D array_like of length K, where K is the number of variables. The point at which the density is estimated. Returns ------- D_x : array_like The value of the conditional mean at `data_predict`. Notes ----- See p. 81 in [1] and p.38 in [2] for the formulas. Unlike other methods, this one requires that `data_predict` be 1D. """ nobs, k_vars = exog.shape ker = gpke(bw, data=exog, data_predict=data_predict, var_type=self.var_type, ckertype=self.ckertype, ukertype=self.ukertype, okertype=self.okertype, tosum=False) / float(nobs) # Create the matrix on p.492 in [7], after the multiplication w/ K_h,ij # See also p. 38 in [2] #ix_cont = np.arange(self.k_vars) # Use all vars instead of continuous only # Note: because ix_cont was defined here such that it selected all # columns, I removed the indexing with it from exog/data_predict. # Convert ker to a 2-D array to make matrix operations below work ker = ker[:, np.newaxis] M12 = exog - data_predict M22 = np.dot(M12.T, M12 * ker) M12 = (M12 * ker).sum(axis=0) M = np.empty((k_vars + 1, k_vars + 1)) M[0, 0] = ker.sum() M[0, 1:] = M12 M[1:, 0] = M12 M[1:, 1:] = M22 ker_endog = ker * endog V = np.empty((k_vars + 1, 1)) V[0, 0] = ker_endog.sum() V[1:, 0] = ((exog - data_predict) * ker_endog).sum(axis=0) mean_mfx = np.dot(np.linalg.pinv(M), V) mean = mean_mfx[0] mfx = mean_mfx[1:, :] return mean, mfx def _est_loc_constant(self, bw, endog, exog, data_predict): """ Local constant estimator of g(x) in the regression y = g(x) + e Parameters ---------- bw : array_like Array of bandwidth value(s). endog : 1D array_like The dependent variable. exog : 1D or 2D array_like The independent variable(s). data_predict : 1D or 2D array_like The point(s) at which the density is estimated. Returns ------- G : ndarray The value of the conditional mean at `data_predict`. B_x : ndarray The marginal effects. """ ker_x = gpke(bw, data=exog, data_predict=data_predict, var_type=self.var_type, ckertype=self.ckertype, ukertype=self.ukertype, okertype=self.okertype, tosum=False) ker_x = np.reshape(ker_x, np.shape(endog)) G_numer = (ker_x * endog).sum(axis=0) G_denom = ker_x.sum(axis=0) G = G_numer / G_denom nobs = exog.shape[0] f_x = G_denom / float(nobs) ker_xc = gpke(bw, data=exog, data_predict=data_predict, var_type=self.var_type, ckertype='d_gaussian', #okertype='wangryzin_reg', tosum=False) ker_xc = ker_xc[:, np.newaxis] d_mx = -(endog * ker_xc).sum(axis=0) / float(nobs) #* np.prod(bw[:, ix_cont])) d_fx = -ker_xc.sum(axis=0) / float(nobs) #* np.prod(bw[:, ix_cont])) B_x = d_mx / f_x - G * d_fx / f_x B_x = (G_numer * d_fx - G_denom * d_mx) / (G_denom**2) #B_x = (f_x * d_mx - m_x * d_fx) / (f_x ** 2) return G, B_x def aic_hurvich(self, bw, func=None): """ Computes the AIC Hurvich criteria for the estimation of the bandwidth. Parameters ---------- bw : str or array_like See the ``bw`` parameter of `KernelReg` for details. Returns ------- aic : ndarray The AIC Hurvich criteria, one element for each variable. func : None Unused here, needed in signature because it's used in `cv_loo`. References ---------- See ch.2 in [1] and p.35 in [2]. """ H = np.empty((self.nobs, self.nobs)) for j in range(self.nobs): H[:, j] = gpke(bw, data=self.exog, data_predict=self.exog[j,:], ckertype=self.ckertype, ukertype=self.ukertype, okertype=self.okertype, var_type=self.var_type, tosum=False) denom = H.sum(axis=1) H = H / denom gx = KernelReg(endog=self.endog, exog=self.exog, var_type=self.var_type, reg_type=self.reg_type, bw=bw, defaults=EstimatorSettings(efficient=False)).fit()[0] gx = np.reshape(gx, (self.nobs, 1)) sigma = ((self.endog - gx)**2).sum(axis=0) / float(self.nobs) frac = (1 + np.trace(H) / float(self.nobs)) / \ (1 - (np.trace(H) + 2) / float(self.nobs)) #siga = np.dot(self.endog.T, (I - H).T) #sigb = np.dot((I - H), self.endog) #sigma = np.dot(siga, sigb) / float(self.nobs) aic = np.log(sigma) + frac return aic def cv_loo(self, bw, func): r""" The cross-validation function with leave-one-out estimator. Parameters ---------- bw : array_like Vector of bandwidth values. func : callable function Returns the estimator of g(x). Can be either ``_est_loc_constant`` (local constant) or ``_est_loc_linear`` (local_linear). Returns ------- L : float The value of the CV function. Notes ----- Calculates the cross-validation least-squares function. This function is minimized by compute_bw to calculate the optimal value of `bw`. For details see p.35 in [2] .. math:: CV(h)=n^{-1}\sum_{i=1}^{n}(Y_{i}-g_{-i}(X_{i}))^{2} where :math:`g_{-i}(X_{i})` is the leave-one-out estimator of g(X) and :math:`h` is the vector of bandwidths """ LOO_X = LeaveOneOut(self.exog) LOO_Y = LeaveOneOut(self.endog).__iter__() L = 0 for ii, X_not_i in enumerate(LOO_X): Y = next(LOO_Y) G = func(bw, endog=Y, exog=-X_not_i, data_predict=-self.exog[ii, :])[0] L += (self.endog[ii] - G) ** 2 # Note: There might be a way to vectorize this. See p.72 in [1] return L / self.nobs def r_squared(self): r""" Returns the R-Squared for the nonparametric regression. Notes ----- For more details see p.45 in [2] The R-Squared is calculated by: .. math:: R^{2}=\frac{\left[\sum_{i=1}^{n} (Y_{i}-\bar{y})(\hat{Y_{i}}-\bar{y}\right]^{2}}{\sum_{i=1}^{n} (Y_{i}-\bar{y})^{2}\sum_{i=1}^{n}(\hat{Y_{i}}-\bar{y})^{2}}, where :math:`\hat{Y_{i}}` is the mean calculated in `fit` at the exog points. """ Y = np.squeeze(self.endog) Yhat = self.fit()[0] Y_bar = np.mean(Yhat) R2_numer = (((Y - Y_bar) * (Yhat - Y_bar)).sum())**2 R2_denom = ((Y - Y_bar)**2).sum(axis=0) * \ ((Yhat - Y_bar)**2).sum(axis=0) return R2_numer / R2_denom def fit(self, data_predict=None): """ Returns the mean and marginal effects at the `data_predict` points. Parameters ---------- data_predict : array_like, optional Points at which to return the mean and marginal effects. If not given, ``data_predict == exog``. Returns ------- mean : ndarray The regression result for the mean (i.e. the actual curve). mfx : ndarray The marginal effects, i.e. the partial derivatives of the mean. """ func = self.est[self.reg_type] if data_predict is None: data_predict = self.exog else: data_predict = _adjust_shape(data_predict, self.k_vars) N_data_predict = np.shape(data_predict)[0] mean = np.empty((N_data_predict,)) mfx = np.empty((N_data_predict, self.k_vars)) for i in range(N_data_predict): mean_mfx = func(self.bw, self.endog, self.exog, data_predict=data_predict[i, :]) mean[i] = mean_mfx[0] mfx_c = np.squeeze(mean_mfx[1]) mfx[i, :] = mfx_c return mean, mfx def sig_test(self, var_pos, nboot=50, nested_res=25, pivot=False): """ Significance test for the variables in the regression. Parameters ---------- var_pos : sequence The position of the variable in exog to be tested. Returns ------- sig : str The level of significance: - `*` : at 90% confidence level - `**` : at 95% confidence level - `***` : at 99* confidence level - "Not Significant" : if not significant """ var_pos = np.asarray(var_pos) ix_cont, ix_ord, ix_unord = _get_type_pos(self.var_type) if np.any(ix_cont[var_pos]): if np.any(ix_ord[var_pos]) or np.any(ix_unord[var_pos]): raise ValueError("Discrete variable in hypothesis. Must be continuous") Sig = TestRegCoefC(self, var_pos, nboot, nested_res, pivot) else: Sig = TestRegCoefD(self, var_pos, nboot) return Sig.sig def __repr__(self): """Provide something sane to print.""" rpr = "KernelReg instance\n" rpr += "Number of variables: k_vars = " + str(self.k_vars) + "\n" rpr += "Number of samples: N = " + str(self.nobs) + "\n" rpr += "Variable types: " + self.var_type + "\n" rpr += "BW selection method: " + self._bw_method + "\n" rpr += "Estimator type: " + self.reg_type + "\n" return rpr def _get_class_vars_type(self): """Helper method to be able to pass needed vars to _compute_subset.""" class_type = 'KernelReg' class_vars = (self.var_type, self.k_vars, self.reg_type) return class_type, class_vars def _compute_dispersion(self, data): """ Computes the measure of dispersion. The minimum of the standard deviation and interquartile range / 1.349 References ---------- See the user guide for the np package in R. In the notes on bwscaling option in npreg, npudens, npcdens there is a discussion on the measure of dispersion """ data = data[:, 1:] return _compute_min_std_IQR(data) class KernelCensoredReg(KernelReg): """ Nonparametric censored regression. Calculates the conditional mean ``E[y|X]`` where ``y = g(X) + e``, where y is left-censored. Left censored variable Y is defined as ``Y = min {Y', L}`` where ``L`` is the value at which ``Y`` is censored and ``Y'`` is the true value of the variable. Parameters ---------- endog : list with one element which is array_like This is the dependent variable. exog : list The training data for the independent variable(s) Each element in the list is a separate variable dep_type : str The type of the dependent variable(s) c: Continuous u: Unordered (Discrete) o: Ordered (Discrete) reg_type : str Type of regression estimator lc: Local Constant Estimator ll: Local Linear Estimator bw : array_like Either a user-specified bandwidth or the method for bandwidth selection. cv_ls: cross-validation least squares aic: AIC Hurvich Estimator ckertype : str, optional The kernel used for the continuous variables. okertype : str, optional The kernel used for the ordered discrete variables. ukertype : str, optional The kernel used for the unordered discrete variables. censor_val : float Value at which the dependent variable is censored defaults : EstimatorSettings instance, optional The default values for the efficient bandwidth estimation Attributes ---------- bw : array_like The bandwidth parameters """ def __init__(self, endog, exog, var_type, reg_type, bw='cv_ls', ckertype='gaussian', ukertype='aitchison_aitken_reg', okertype='wangryzin_reg', censor_val=0, defaults=None): self.var_type = var_type self.data_type = var_type self.reg_type = reg_type self.ckertype = ckertype self.okertype = okertype self.ukertype = ukertype if not (self.ckertype in kernel_func and self.ukertype in kernel_func and self.okertype in kernel_func): raise ValueError('user specified kernel must be a supported ' 'kernel from statsmodels.nonparametric.kernels.') self.k_vars = len(self.var_type) self.endog = _adjust_shape(endog, 1) self.exog = _adjust_shape(exog, self.k_vars) self.data = np.column_stack((self.endog, self.exog)) self.nobs = np.shape(self.exog)[0] self.est = dict(lc=self._est_loc_constant, ll=self._est_loc_linear) defaults = EstimatorSettings() if defaults is None else defaults self._set_defaults(defaults) self.censor_val = censor_val if self.censor_val is not None: self.censored(censor_val) else: self.W_in = np.ones((self.nobs, 1)) if not self.efficient: self.bw = self._compute_reg_bw(bw) else: self.bw = self._compute_efficient(bw) def censored(self, censor_val): # see pp. 341-344 in [1] self.d = (self.endog != censor_val) * 1. ix = np.argsort(np.squeeze(self.endog)) self.sortix = ix self.sortix_rev = np.zeros(ix.shape, int) self.sortix_rev[ix] = np.arange(len(ix)) self.endog = np.squeeze(self.endog[ix]) self.endog = _adjust_shape(self.endog, 1) self.exog = np.squeeze(self.exog[ix]) self.d = np.squeeze(self.d[ix]) self.W_in = np.empty((self.nobs, 1)) for i in range(1, self.nobs + 1): P=1 for j in range(1, i): P *= ((self.nobs - j)/(float(self.nobs)-j+1))**self.d[j-1] self.W_in[i-1,0] = P * self.d[i-1] / (float(self.nobs) - i + 1 ) def __repr__(self): """Provide something sane to print.""" rpr = "KernelCensoredReg instance\n" rpr += "Number of variables: k_vars = " + str(self.k_vars) + "\n" rpr += "Number of samples: nobs = " + str(self.nobs) + "\n" rpr += "Variable types: " + self.var_type + "\n" rpr += "BW selection method: " + self._bw_method + "\n" rpr += "Estimator type: " + self.reg_type + "\n" return rpr def _est_loc_linear(self, bw, endog, exog, data_predict, W): """ Local linear estimator of g(x) in the regression ``y = g(x) + e``. Parameters ---------- bw : array_like Vector of bandwidth value(s) endog : 1D array_like The dependent variable exog : 1D or 2D array_like The independent variable(s) data_predict : 1D array_like of length K, where K is the number of variables. The point at which the density is estimated Returns ------- D_x : array_like The value of the conditional mean at data_predict Notes ----- See p. 81 in [1] and p.38 in [2] for the formulas Unlike other methods, this one requires that data_predict be 1D """ nobs, k_vars = exog.shape ker = gpke(bw, data=exog, data_predict=data_predict, var_type=self.var_type, ckertype=self.ckertype, ukertype=self.ukertype, okertype=self.okertype, tosum=False) # Create the matrix on p.492 in [7], after the multiplication w/ K_h,ij # See also p. 38 in [2] # Convert ker to a 2-D array to make matrix operations below work ker = W * ker[:, np.newaxis] M12 = exog - data_predict M22 = np.dot(M12.T, M12 * ker) M12 = (M12 * ker).sum(axis=0) M = np.empty((k_vars + 1, k_vars + 1)) M[0, 0] = ker.sum() M[0, 1:] = M12 M[1:, 0] = M12 M[1:, 1:] = M22 ker_endog = ker * endog V = np.empty((k_vars + 1, 1)) V[0, 0] = ker_endog.sum() V[1:, 0] = ((exog - data_predict) * ker_endog).sum(axis=0) mean_mfx = np.dot(np.linalg.pinv(M), V) mean = mean_mfx[0] mfx = mean_mfx[1:, :] return mean, mfx def cv_loo(self, bw, func): r""" The cross-validation function with leave-one-out estimator Parameters ---------- bw : array_like Vector of bandwidth values func : callable function Returns the estimator of g(x). Can be either ``_est_loc_constant`` (local constant) or ``_est_loc_linear`` (local_linear). Returns ------- L : float The value of the CV function Notes ----- Calculates the cross-validation least-squares function. This function is minimized by compute_bw to calculate the optimal value of bw For details see p.35 in [2] .. math:: CV(h)=n^{-1}\sum_{i=1}^{n}(Y_{i}-g_{-i}(X_{i}))^{2} where :math:`g_{-i}(X_{i})` is the leave-one-out estimator of g(X) and :math:`h` is the vector of bandwidths """ LOO_X = LeaveOneOut(self.exog) LOO_Y = LeaveOneOut(self.endog).__iter__() LOO_W = LeaveOneOut(self.W_in).__iter__() L = 0 for ii, X_not_i in enumerate(LOO_X): Y = next(LOO_Y) w = next(LOO_W) G = func(bw, endog=Y, exog=-X_not_i, data_predict=-self.exog[ii, :], W=w)[0] L += (self.endog[ii] - G) ** 2 # Note: There might be a way to vectorize this. See p.72 in [1] return L / self.nobs def fit(self, data_predict=None): """ Returns the marginal effects at the data_predict points. """ func = self.est[self.reg_type] if data_predict is None: data_predict = self.exog else: data_predict = _adjust_shape(data_predict, self.k_vars) N_data_predict = np.shape(data_predict)[0] mean = np.empty((N_data_predict,)) mfx = np.empty((N_data_predict, self.k_vars)) for i in range(N_data_predict): mean_mfx = func(self.bw, self.endog, self.exog, data_predict=data_predict[i, :], W=self.W_in) mean[i] = mean_mfx[0] mfx_c = np.squeeze(mean_mfx[1]) mfx[i, :] = mfx_c return mean, mfx class TestRegCoefC(object): """ Significance test for continuous variables in a nonparametric regression. The null hypothesis is ``dE(Y|X)/dX_not_i = 0``, the alternative hypothesis is ``dE(Y|X)/dX_not_i != 0``. Parameters ---------- model : KernelReg instance This is the nonparametric regression model whose elements are tested for significance. test_vars : tuple, list of integers, array_like index of position of the continuous variables to be tested for significance. E.g. (1,3,5) jointly tests variables at position 1,3 and 5 for significance. nboot : int Number of bootstrap samples used to determine the distribution of the test statistic in a finite sample. Default is 400 nested_res : int Number of nested resamples used to calculate lambda. Must enable the pivot option pivot : bool Pivot the test statistic by dividing by its standard error Significantly increases computational time. But pivot statistics have more desirable properties (See references) Attributes ---------- sig : str The significance level of the variable(s) tested "Not Significant": Not significant at the 90% confidence level Fails to reject the null "*": Significant at the 90% confidence level "**": Significant at the 95% confidence level "***": Significant at the 99% confidence level Notes ----- This class allows testing of joint hypothesis as long as all variables are continuous. References ---------- Racine, J.: "Consistent Significance Testing for Nonparametric Regression" Journal of Business & Economics Statistics. Chapter 12 in [1]. """ # Significance of continuous vars in nonparametric regression # Racine: Consistent Significance Testing for Nonparametric Regression # Journal of Business & Economics Statistics def __init__(self, model, test_vars, nboot=400, nested_res=400, pivot=False): self.nboot = nboot self.nres = nested_res self.test_vars = test_vars self.model = model self.bw = model.bw self.var_type = model.var_type self.k_vars = len(self.var_type) self.endog = model.endog self.exog = model.exog self.gx = model.est[model.reg_type] self.test_vars = test_vars self.pivot = pivot self.run() def run(self): self.test_stat = self._compute_test_stat(self.endog, self.exog) self.sig = self._compute_sig() def _compute_test_stat(self, Y, X): """ Computes the test statistic. See p.371 in [8]. """ lam = self._compute_lambda(Y, X) t = lam if self.pivot: se_lam = self._compute_se_lambda(Y, X) t = lam / float(se_lam) return t def _compute_lambda(self, Y, X): """Computes only lambda -- the main part of the test statistic""" n = np.shape(X)[0] Y = _adjust_shape(Y, 1) X = _adjust_shape(X, self.k_vars) b = KernelReg(Y, X, self.var_type, self.model.reg_type, self.bw, defaults = EstimatorSettings(efficient=False)).fit()[1] b = b[:, self.test_vars] b = np.reshape(b, (n, len(self.test_vars))) #fct = np.std(b) # Pivot the statistic by dividing by SE fct = 1. # Do not Pivot -- Bootstrapping works better if Pivot lam = ((b / fct) ** 2).sum() / float(n) return lam def _compute_se_lambda(self, Y, X): """ Calculates the SE of lambda by nested resampling Used to pivot the statistic. Bootstrapping works better with estimating pivotal statistics but slows down computation significantly. """ n = np.shape(Y)[0] lam = np.empty(shape=(self.nres,)) for i in range(self.nres): ind = np.random.randint(0, n, size=(n, 1)) Y1 = Y[ind, 0] X1 = X[ind, :] lam[i] = self._compute_lambda(Y1, X1) se_lambda = np.std(lam) return se_lambda def _compute_sig(self): """ Computes the significance value for the variable(s) tested. The empirical distribution of the test statistic is obtained through bootstrapping the sample. The null hypothesis is rejected if the test statistic is larger than the 90, 95, 99 percentiles. """ t_dist = np.empty(shape=(self.nboot, )) Y = self.endog X = copy.deepcopy(self.exog) n = np.shape(Y)[0] X[:, self.test_vars] = np.mean(X[:, self.test_vars], axis=0) # Calculate the restricted mean. See p. 372 in [8] M = KernelReg(Y, X, self.var_type, self.model.reg_type, self.bw, defaults=EstimatorSettings(efficient=False)).fit()[0] M = np.reshape(M, (n, 1)) e = Y - M e = e - np.mean(e) # recenter residuals for i in range(self.nboot): ind = np.random.randint(0, n, size=(n, 1)) e_boot = e[ind, 0] Y_boot = M + e_boot t_dist[i] = self._compute_test_stat(Y_boot, self.exog) self.t_dist = t_dist sig = "Not Significant" if self.test_stat > mquantiles(t_dist, 0.9): sig = "*" if self.test_stat > mquantiles(t_dist, 0.95): sig = "**" if self.test_stat > mquantiles(t_dist, 0.99): sig = "***" return sig class TestRegCoefD(TestRegCoefC): """ Significance test for the categorical variables in a nonparametric regression. Parameters ---------- model : Instance of KernelReg class This is the nonparametric regression model whose elements are tested for significance. test_vars : tuple, list of one element index of position of the discrete variable to be tested for significance. E.g. (3) tests variable at position 3 for significance. nboot : int Number of bootstrap samples used to determine the distribution of the test statistic in a finite sample. Default is 400 Attributes ---------- sig : str The significance level of the variable(s) tested "Not Significant": Not significant at the 90% confidence level Fails to reject the null "*": Significant at the 90% confidence level "**": Significant at the 95% confidence level "***": Significant at the 99% confidence level Notes ----- This class currently does not allow joint hypothesis. Only one variable can be tested at a time References ---------- See [9] and chapter 12 in [1]. """ def _compute_test_stat(self, Y, X): """Computes the test statistic""" dom_x = np.sort(np.unique(self.exog[:, self.test_vars])) n = np.shape(X)[0] model = KernelReg(Y, X, self.var_type, self.model.reg_type, self.bw, defaults = EstimatorSettings(efficient=False)) X1 = copy.deepcopy(X) X1[:, self.test_vars] = 0 m0 = model.fit(data_predict=X1)[0] m0 = np.reshape(m0, (n, 1)) zvec = np.zeros((n, 1)) # noqa:E741 for i in dom_x[1:] : X1[:, self.test_vars] = i m1 = model.fit(data_predict=X1)[0] m1 = np.reshape(m1, (n, 1)) zvec += (m1 - m0) ** 2 # noqa:E741 avg = zvec.sum(axis=0) / float(n) return avg def _compute_sig(self): """Calculates the significance level of the variable tested""" m = self._est_cond_mean() Y = self.endog X = self.exog n = np.shape(X)[0] u = Y - m u = u - np.mean(u) # center fct1 = (1 - 5**0.5) / 2. fct2 = (1 + 5**0.5) / 2. u1 = fct1 * u u2 = fct2 * u r = fct2 / (5 ** 0.5) I_dist = np.empty((self.nboot,1)) for j in range(self.nboot): u_boot = copy.deepcopy(u2) prob = np.random.uniform(0,1, size = (n,1)) ind = prob < r u_boot[ind] = u1[ind] Y_boot = m + u_boot I_dist[j] = self._compute_test_stat(Y_boot, X) sig = "Not Significant" if self.test_stat > mquantiles(I_dist, 0.9): sig = "*" if self.test_stat > mquantiles(I_dist, 0.95): sig = "**" if self.test_stat > mquantiles(I_dist, 0.99): sig = "***" return sig def _est_cond_mean(self): """ Calculates the expected conditional mean m(X, Z=l) for all possible l """ self.dom_x = np.sort(np.unique(self.exog[:, self.test_vars])) X = copy.deepcopy(self.exog) m=0 for i in self.dom_x: X[:, self.test_vars] = i m += self.model.fit(data_predict = X)[0] m = m / float(len(self.dom_x)) m = np.reshape(m, (np.shape(self.exog)[0], 1)) return m statsmodels-0.12.2/statsmodels/nonparametric/kernels.py000066400000000000000000000155251400612667500233760ustar00rootroot00000000000000""" Module of kernels that are able to handle continuous as well as categorical variables (both ordered and unordered). This is a slight deviation from the current approach in statsmodels.nonparametric.kernels where each kernel is a class object. Having kernel functions rather than classes makes extension to a multivariate kernel density estimation much easier. NOTE: As it is, this module does not interact with the existing API """ import numpy as np from scipy.special import erf #TODO: # - make sure we only receive int input for wang-ryzin and aitchison-aitken # - Check for the scalar Xi case everywhere def aitchison_aitken(h, Xi, x, num_levels=None): r""" The Aitchison-Aitken kernel, used for unordered discrete random variables. Parameters ---------- h : 1-D ndarray, shape (K,) The bandwidths used to estimate the value of the kernel function. Xi : 2-D ndarray of ints, shape (nobs, K) The value of the training set. x : 1-D ndarray, shape (K,) The value at which the kernel density is being estimated. num_levels : bool, optional Gives the user the option to specify the number of levels for the random variable. If False, the number of levels is calculated from the data. Returns ------- kernel_value : ndarray, shape (nobs, K) The value of the kernel function at each training point for each var. Notes ----- See p.18 of [2]_ for details. The value of the kernel L if :math:`X_{i}=x` is :math:`1-\lambda`, otherwise it is :math:`\frac{\lambda}{c-1}`. Here :math:`c` is the number of levels plus one of the RV. References ---------- .. [*] J. Aitchison and C.G.G. Aitken, "Multivariate binary discrimination by the kernel method", Biometrika, vol. 63, pp. 413-420, 1976. .. [*] Racine, Jeff. "Nonparametric Econometrics: A Primer," Foundation and Trends in Econometrics: Vol 3: No 1, pp1-88., 2008. """ Xi = Xi.reshape(Xi.size) # seems needed in case Xi is scalar if num_levels is None: num_levels = np.asarray(np.unique(Xi).size) kernel_value = np.ones(Xi.size) * h / (num_levels - 1) idx = Xi == x kernel_value[idx] = (idx * (1 - h))[idx] return kernel_value def wang_ryzin(h, Xi, x): r""" The Wang-Ryzin kernel, used for ordered discrete random variables. Parameters ---------- h : scalar or 1-D ndarray, shape (K,) The bandwidths used to estimate the value of the kernel function. Xi : ndarray of ints, shape (nobs, K) The value of the training set. x : scalar or 1-D ndarray of shape (K,) The value at which the kernel density is being estimated. Returns ------- kernel_value : ndarray, shape (nobs, K) The value of the kernel function at each training point for each var. Notes ----- See p. 19 in [1]_ for details. The value of the kernel L if :math:`X_{i}=x` is :math:`1-\lambda`, otherwise it is :math:`\frac{1-\lambda}{2}\lambda^{|X_{i}-x|}`, where :math:`\lambda` is the bandwidth. References ---------- .. [*] Racine, Jeff. "Nonparametric Econometrics: A Primer," Foundation and Trends in Econometrics: Vol 3: No 1, pp1-88., 2008. http://dx.doi.org/10.1561/0800000009 .. [*] M.-C. Wang and J. van Ryzin, "A class of smooth estimators for discrete distributions", Biometrika, vol. 68, pp. 301-309, 1981. """ Xi = Xi.reshape(Xi.size) # seems needed in case Xi is scalar kernel_value = 0.5 * (1 - h) * (h ** abs(Xi - x)) idx = Xi == x kernel_value[idx] = (idx * (1 - h))[idx] return kernel_value def gaussian(h, Xi, x): """ Gaussian Kernel for continuous variables Parameters ---------- h : 1-D ndarray, shape (K,) The bandwidths used to estimate the value of the kernel function. Xi : 1-D ndarray, shape (K,) The value of the training set. x : 1-D ndarray, shape (K,) The value at which the kernel density is being estimated. Returns ------- kernel_value : ndarray, shape (nobs, K) The value of the kernel function at each training point for each var. """ return (1. / np.sqrt(2 * np.pi)) * np.exp(-(Xi - x)**2 / (h**2 * 2.)) def tricube(h, Xi, x): """ Tricube Kernel for continuous variables Parameters ---------- h : 1-D ndarray, shape (K,) The bandwidths used to estimate the value of the kernel function. Xi : 1-D ndarray, shape (K,) The value of the training set. x : 1-D ndarray, shape (K,) The value at which the kernel density is being estimated. Returns ------- kernel_value : ndarray, shape (nobs, K) The value of the kernel function at each training point for each var. """ u = (Xi - x) / h u[np.abs(u) > 1] = 0 return (70. / 81) * (1 - np.abs(u)**3)**3 def gaussian_convolution(h, Xi, x): """ Calculates the Gaussian Convolution Kernel """ return (1. / np.sqrt(4 * np.pi)) * np.exp(- (Xi - x)**2 / (h**2 * 4.)) def wang_ryzin_convolution(h, Xi, Xj): # This is the equivalent of the convolution case with the Gaussian Kernel # However it is not exactly convolution. Think of a better name # References ordered = np.zeros(Xi.size) for x in np.unique(Xi): ordered += wang_ryzin(h, Xi, x) * wang_ryzin(h, Xj, x) return ordered def aitchison_aitken_convolution(h, Xi, Xj): Xi_vals = np.unique(Xi) ordered = np.zeros(Xi.size) num_levels = Xi_vals.size for x in Xi_vals: ordered += aitchison_aitken(h, Xi, x, num_levels=num_levels) * \ aitchison_aitken(h, Xj, x, num_levels=num_levels) return ordered def gaussian_cdf(h, Xi, x): return 0.5 * h * (1 + erf((x - Xi) / (h * np.sqrt(2)))) def aitchison_aitken_cdf(h, Xi, x_u): x_u = int(x_u) Xi_vals = np.unique(Xi) ordered = np.zeros(Xi.size) num_levels = Xi_vals.size for x in Xi_vals: if x <= x_u: #FIXME: why a comparison for unordered variables? ordered += aitchison_aitken(h, Xi, x, num_levels=num_levels) return ordered def wang_ryzin_cdf(h, Xi, x_u): ordered = np.zeros(Xi.size) for x in np.unique(Xi): if x <= x_u: ordered += wang_ryzin(h, Xi, x) return ordered def d_gaussian(h, Xi, x): # The derivative of the Gaussian Kernel return 2 * (Xi - x) * gaussian(h, Xi, x) / h**2 def aitchison_aitken_reg(h, Xi, x): """ A version for the Aitchison-Aitken kernel for nonparametric regression. Suggested by Li and Racine. """ kernel_value = np.ones(Xi.size) ix = Xi != x inDom = ix * h kernel_value[ix] = inDom[ix] return kernel_value def wang_ryzin_reg(h, Xi, x): """ A version for the Wang-Ryzin kernel for nonparametric regression. Suggested by Li and Racine in [1] ch.4 """ return h ** abs(Xi - x) statsmodels-0.12.2/statsmodels/nonparametric/linbin.pyx000066400000000000000000000021341400612667500233660ustar00rootroot00000000000000#!python #cython: boundscheck=False, wraparound=False, cdivision=True """ cython -a fast_linbin.pyx gcc -shared -pthread -fPIC -fwrapv -O2 -Wall -fno-strict-aliasing -I/usr/include/python2.7 -I/usr/local/lib/python2.7/dist-packages/numpy/core/include/ -o fast_linbin.so fast_linbin.c """ cimport cython cimport numpy as np import numpy as np ctypedef np.float64_t DOUBLE ctypedef np.int_t INT def fast_linbin(np.ndarray[DOUBLE] X, double a, double b, int M, int trunc=1): """ Linear Binning as described in Fan and Marron (1994) """ cdef: Py_ssize_t i, li_i int nobs = X.shape[0] double delta = (b - a)/(M - 1) np.ndarray[DOUBLE] gcnts = np.zeros(M, float) np.ndarray[DOUBLE] lxi = (X - a)/delta np.ndarray[INT] li = lxi.astype(int) np.ndarray[DOUBLE] rem = lxi - li for i in range(nobs): li_i = li[i] if li_i > 1 and li_i < M: gcnts[li_i] = gcnts[li_i] + 1 - rem[i] gcnts[li_i+1] = gcnts[li_i+1] + rem[i] if li_i > M and trunc == 0: gcnts[M] = gcnts[M] + 1 return gcnts statsmodels-0.12.2/statsmodels/nonparametric/smoothers_lowess.py000066400000000000000000000224621400612667500253500ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Lowess - wrapper for cythonized extension Author : Chris Jordan-Squire Author : Carl Vogel Author : Josef Perktold """ import numpy as np from ._smoothers_lowess import lowess as _lowess def lowess(endog, exog, frac=2.0/3.0, it=3, delta=0.0, xvals=None, is_sorted=False, missing='drop', return_sorted=True): '''LOWESS (Locally Weighted Scatterplot Smoothing) A lowess function that outs smoothed estimates of endog at the given exog values from points (exog, endog) Parameters ---------- endog : 1-D numpy array The y-values of the observed points exog : 1-D numpy array The x-values of the observed points frac : float Between 0 and 1. The fraction of the data used when estimating each y-value. it : int The number of residual-based reweightings to perform. delta : float Distance within which to use linear-interpolation instead of weighted regression. xvals: 1-D numpy array Values of the exogenous variable at which to evaluate the regression. If supplied, cannot use delta. is_sorted : bool If False (default), then the data will be sorted by exog before calculating lowess. If True, then it is assumed that the data is already sorted by exog. If xvals is specified, then it too must be sorted if is_sorted is True. missing : str Available options are 'none', 'drop', and 'raise'. If 'none', no nan checking is done. If 'drop', any observations with nans are dropped. If 'raise', an error is raised. Default is 'drop'. return_sorted : bool If True (default), then the returned array is sorted by exog and has missing (nan or infinite) observations removed. If False, then the returned array is in the same length and the same sequence of observations as the input array. Returns ------- out : {ndarray, float} The returned array is two-dimensional if return_sorted is True, and one dimensional if return_sorted is False. If return_sorted is True, then a numpy array with two columns. The first column contains the sorted x (exog) values and the second column the associated estimated y (endog) values. If return_sorted is False, then only the fitted values are returned, and the observations will be in the same order as the input arrays. If xvals is provided, then return_sorted is ignored and the returned array is always one dimensional, containing the y values fitted at the x values provided by xvals. Notes ----- This lowess function implements the algorithm given in the reference below using local linear estimates. Suppose the input data has N points. The algorithm works by estimating the `smooth` y_i by taking the frac*N closest points to (x_i,y_i) based on their x values and estimating y_i using a weighted linear regression. The weight for (x_j,y_j) is tricube function applied to abs(x_i-x_j). If it > 1, then further weighted local linear regressions are performed, where the weights are the same as above times the _lowess_bisquare function of the residuals. Each iteration takes approximately the same amount of time as the original fit, so these iterations are expensive. They are most useful when the noise has extremely heavy tails, such as Cauchy noise. Noise with less heavy-tails, such as t-distributions with df>2, are less problematic. The weights downgrade the influence of points with large residuals. In the extreme case, points whose residuals are larger than 6 times the median absolute residual are given weight 0. `delta` can be used to save computations. For each `x_i`, regressions are skipped for points closer than `delta`. The next regression is fit for the farthest point within delta of `x_i` and all points in between are estimated by linearly interpolating between the two regression fits. Judicious choice of delta can cut computation time considerably for large data (N > 5000). A good choice is ``delta = 0.01 * range(exog)``. If `xvals` is provided, the regression is then computed at those points and the fit values are returned. Otherwise, the regression is run at points of `exog`. Some experimentation is likely required to find a good choice of `frac` and `iter` for a particular dataset. References ---------- Cleveland, W.S. (1979) "Robust Locally Weighted Regression and Smoothing Scatterplots". Journal of the American Statistical Association 74 (368): 829-836. Examples -------- The below allows a comparison between how different the fits from lowess for different values of frac can be. >>> import numpy as np >>> import statsmodels.api as sm >>> lowess = sm.nonparametric.lowess >>> x = np.random.uniform(low = -2*np.pi, high = 2*np.pi, size=500) >>> y = np.sin(x) + np.random.normal(size=len(x)) >>> z = lowess(y, x) >>> w = lowess(y, x, frac=1./3) This gives a similar comparison for when it is 0 vs not. >>> import numpy as np >>> import scipy.stats as stats >>> import statsmodels.api as sm >>> lowess = sm.nonparametric.lowess >>> x = np.random.uniform(low = -2*np.pi, high = 2*np.pi, size=500) >>> y = np.sin(x) + stats.cauchy.rvs(size=len(x)) >>> z = lowess(y, x, frac= 1./3, it=0) >>> w = lowess(y, x, frac=1./3) ''' endog = np.asarray(endog, float) exog = np.asarray(exog, float) # Whether xvals argument was provided given_xvals = (xvals is not None) # Inputs should be vectors (1-D arrays) of the # same length. if exog.ndim != 1: raise ValueError('exog must be a vector') if endog.ndim != 1: raise ValueError('endog must be a vector') if endog.shape[0] != exog.shape[0] : raise ValueError('exog and endog must have same length') if missing in ['drop', 'raise']: mask_valid = (np.isfinite(exog) & np.isfinite(endog)) all_valid = np.all(mask_valid) if all_valid: y = endog x = exog else: if missing == 'drop': x = exog[mask_valid] y = endog[mask_valid] else: raise ValueError('nan or inf found in data') elif missing == 'none': y = endog x = exog all_valid = True # we assume it's true if missing='none' else: raise ValueError("missing can only be 'none', 'drop' or 'raise'") if not is_sorted: # Sort both inputs according to the ascending order of x values sort_index = np.argsort(x) x = np.array(x[sort_index]) y = np.array(y[sort_index]) if not given_xvals: # If given no explicit x values, we use the x-values in the exog array xvals = exog xvalues = x xvals_all_valid = all_valid if missing == 'drop': xvals_mask_valid = mask_valid else: if delta != 0.0: raise ValueError("Cannot have non-zero 'delta' and 'xvals' values") # TODO: allow this again # With explicit xvals, we ignore 'return_sorted' and always # use the order provided return_sorted = False if missing in ['drop', 'raise']: xvals_mask_valid = np.isfinite(xvals) xvals_all_valid = np.all(xvals_mask_valid) if xvals_all_valid: xvalues = xvals else: if missing == 'drop': xvalues = xvals[xvals_mask_valid] else: raise ValueError("nan or inf found in xvals") if not is_sorted: sort_index = np.argsort(xvalues) xvalues = np.array(xvalues[sort_index]) else: xvals_all_valid = True if not given_xvals: # Run LOWESS on the data points res, _ = _lowess(y, x, x, np.ones_like(x), frac=frac, it=it, delta=delta, given_xvals=False) else: # First run LOWESS on the data points to get the weights of the data points # using it-1 iterations, last iter done next if it > 0: _, weights = _lowess(y, x, x, np.ones_like(x), frac=frac, it=it-1, delta=delta, given_xvals=False) else: weights = np.ones_like(x) # Then run once more using those supplied weights at the points provided by xvals # No extra iterations are performed here since weights are fixed res, _ = _lowess(y, x, xvalues, weights, frac=frac, it=0, delta=delta, given_xvals=True) _, yfitted = res.T if return_sorted: return res else: # rebuild yfitted with original indices # a bit messy: y might have been selected twice if not is_sorted: yfitted_ = np.empty_like(xvalues) yfitted_.fill(np.nan) yfitted_[sort_index] = yfitted yfitted = yfitted_ else: yfitted = yfitted if not xvals_all_valid: yfitted_ = np.empty_like(xvals) yfitted_.fill(np.nan) yfitted_[xvals_mask_valid] = yfitted yfitted = yfitted_ # we do not need to return exog anymore return yfitted statsmodels-0.12.2/statsmodels/nonparametric/smoothers_lowess_old.py000066400000000000000000000242221400612667500262020ustar00rootroot00000000000000""" Univariate lowess function, like in R. References ---------- Hastie, Tibshirani, Friedman. (2009) The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition: Chapter 6. Cleveland, W.S. (1979) "Robust Locally Weighted Regression and Smoothing Scatterplots". Journal of the American Statistical Association 74 (368): 829-836. """ import numpy as np from numpy.linalg import lstsq def lowess(endog, exog, frac=2./3, it=3): """ LOWESS (Locally Weighted Scatterplot Smoothing) A lowess function that outs smoothed estimates of endog at the given exog values from points (exog, endog) Parameters ---------- endog : 1-D numpy array The y-values of the observed points exog : 1-D numpy array The x-values of the observed points frac : float Between 0 and 1. The fraction of the data used when estimating each y-value. it : int The number of residual-based reweightings to perform. Returns ------- out: numpy array A numpy array with two columns. The first column is the sorted x values and the second column the associated estimated y-values. Notes ----- This lowess function implements the algorithm given in the reference below using local linear estimates. Suppose the input data has N points. The algorithm works by estimating the true ``y_i`` by taking the frac*N closest points to ``(x_i,y_i)`` based on their x values and estimating ``y_i`` using a weighted linear regression. The weight for ``(x_j,y_j)`` is `_lowess_tricube` function applied to ``|x_i-x_j|``. If ``iter > 0``, then further weighted local linear regressions are performed, where the weights are the same as above times the `_lowess_bisquare` function of the residuals. Each iteration takes approximately the same amount of time as the original fit, so these iterations are expensive. They are most useful when the noise has extremely heavy tails, such as Cauchy noise. Noise with less heavy-tails, such as t-distributions with ``df > 2``, are less problematic. The weights downgrade the influence of points with large residuals. In the extreme case, points whose residuals are larger than 6 times the median absolute residual are given weight 0. Some experimentation is likely required to find a good choice of frac and iter for a particular dataset. References ---------- Cleveland, W.S. (1979) "Robust Locally Weighted Regression and Smoothing Scatterplots". Journal of the American Statistical Association 74 (368): 829-836. Examples -------- The below allows a comparison between how different the fits from `lowess` for different values of frac can be. >>> import numpy as np >>> import statsmodels.api as sm >>> lowess = sm.nonparametric.lowess >>> x = np.random.uniform(low=-2*np.pi, high=2*np.pi, size=500) >>> y = np.sin(x) + np.random.normal(size=len(x)) >>> z = lowess(y, x) >>> w = lowess(y, x, frac=1./3) This gives a similar comparison for when it is 0 vs not. >>> import scipy.stats as stats >>> x = np.random.uniform(low=-2*np.pi, high=2*np.pi, size=500) >>> y = np.sin(x) + stats.cauchy.rvs(size=len(x)) >>> z = lowess(y, x, frac= 1./3, it=0) >>> w = lowess(y, x, frac=1./3) """ x = exog if exog.ndim != 1: raise ValueError('exog must be a vector') if endog.ndim != 1: raise ValueError('endog must be a vector') if endog.shape[0] != x.shape[0] : raise ValueError('exog and endog must have same length') n = exog.shape[0] fitted = np.zeros(n) k = int(frac * n) index_array = np.argsort(exog) x_copy = np.array(exog[index_array]) #, dtype ='float32') y_copy = endog[index_array] fitted, weights = _lowess_initial_fit(x_copy, y_copy, k, n) for i in range(it): _lowess_robustify_fit(x_copy, y_copy, fitted, weights, k, n) out = np.array([x_copy, fitted]).T out.shape = (n,2) return out def _lowess_initial_fit(x_copy, y_copy, k, n): """ The initial weighted local linear regression for lowess. Parameters ---------- x_copy : 1-d ndarray The x-values/exogenous part of the data being smoothed y_copy : 1-d ndarray The y-values/ endogenous part of the data being smoothed k : int The number of data points which affect the linear fit for each estimated point n : int The total number of points Returns ------- fitted : 1-d ndarray The fitted y-values weights : 2-d ndarray An n by k array. The contribution to the weights in the local linear fit coming from the distances between the x-values """ weights = np.zeros((n,k), dtype = x_copy.dtype) nn_indices = [0,k] X = np.ones((k,2)) fitted = np.zeros(n) for i in range(n): #note: all _lowess functions are inplace, no return left_width = x_copy[i] - x_copy[nn_indices[0]] right_width = x_copy[nn_indices[1]-1] - x_copy[i] width = max(left_width, right_width) _lowess_wt_standardize(weights[i,:], x_copy[nn_indices[0]:nn_indices[1]], x_copy[i], width) _lowess_tricube(weights[i,:]) weights[i,:] = np.sqrt(weights[i,:]) X[:,1] = x_copy[nn_indices[0]:nn_indices[1]] y_i = weights[i,:] * y_copy[nn_indices[0]:nn_indices[1]] beta = lstsq(weights[i,:].reshape(k,1) * X, y_i, rcond=-1)[0] fitted[i] = beta[0] + beta[1]*x_copy[i] _lowess_update_nn(x_copy, nn_indices, i+1) return fitted, weights def _lowess_wt_standardize(weights, new_entries, x_copy_i, width): """ The initial phase of creating the weights. Subtract the current x_i and divide by the width. Parameters ---------- weights : ndarray The memory where (new_entries - x_copy_i)/width will be placed new_entries : ndarray The x-values of the k closest points to x[i] x_copy_i : float x[i], the i'th point in the (sorted) x values width : float The maximum distance between x[i] and any point in new_entries Returns ------- Nothing. The modifications are made to weight in place. """ weights[:] = new_entries weights -= x_copy_i weights /= width def _lowess_robustify_fit(x_copy, y_copy, fitted, weights, k, n): """ Additional weighted local linear regressions, performed if iter>0. They take into account the sizes of the residuals, to eliminate the effect of extreme outliers. Parameters ---------- x_copy : 1-d ndarray The x-values/exogenous part of the data being smoothed y_copy : 1-d ndarray The y-values/ endogenous part of the data being smoothed fitted : 1-d ndarray The fitted y-values from the previous iteration weights : 2-d ndarray An n by k array. The contribution to the weights in the local linear fit coming from the distances between the x-values k : int The number of data points which affect the linear fit for each estimated point n : int The total number of points Returns ------- Nothing. The fitted values are modified in place. """ nn_indices = [0,k] X = np.ones((k,2)) residual_weights = np.copy(y_copy) residual_weights.shape = (n,) residual_weights -= fitted residual_weights = np.absolute(residual_weights)#, out=residual_weights) s = np.median(residual_weights) residual_weights /= (6*s) too_big = residual_weights>=1 _lowess_bisquare(residual_weights) residual_weights[too_big] = 0 for i in range(n): total_weights = weights[i,:] * np.sqrt(residual_weights[nn_indices[0]: nn_indices[1]]) X[:,1] = x_copy[nn_indices[0]:nn_indices[1]] y_i = total_weights * y_copy[nn_indices[0]:nn_indices[1]] total_weights.shape = (k,1) beta = lstsq(total_weights * X, y_i, rcond=-1)[0] fitted[i] = beta[0] + beta[1] * x_copy[i] _lowess_update_nn(x_copy, nn_indices, i+1) def _lowess_update_nn(x, cur_nn,i): """ Update the endpoints of the nearest neighbors to the ith point. Parameters ---------- x : iterable The sorted points of x-values cur_nn : list of length 2 The two current indices between which are the k closest points to x[i]. (The actual value of k is irrelevant for the algorithm. i : int The index of the current value in x for which the k closest points are desired. Returns ------- Nothing. It modifies cur_nn in place. """ while True: if cur_nn[1] 0 def test_fit_self(reset_randomstate): x = np.random.standard_normal(100) kde = KDE(x) assert isinstance(kde, KDE) assert isinstance(kde.fit(), KDE) class TestKDECustomBandwidth(object): decimal_density = 7 @classmethod def setup_class(cls): cls.kde = KDE(Xi) cls.weights_200 = np.linspace(1, 100, 200) cls.weights_100 = np.linspace(1, 100, 100) def test_check_is_fit_ok_with_custom_bandwidth(self): def custom_bw(X, kern): return np.std(X) * len(X) kde = self.kde.fit(bw=custom_bw) assert isinstance(kde, KDE) def test_check_is_fit_ok_with_standard_custom_bandwidth(self): # Note, we are passing the function, not the string - this is intended kde = self.kde.fit(bw=bandwidths.bw_silverman) s1 = kde.support.copy() d1 = kde.density.copy() kde = self.kde.fit(bw='silverman') npt.assert_almost_equal(s1, kde.support, self.decimal_density) npt.assert_almost_equal(d1, kde.density, self.decimal_density) @pytest.mark.parametrize("fft", [True, False]) def test_check_is_fit_ok_with_float_bandwidth(self, fft): # Note, we are passing the function, not the string - this is intended kde = self.kde.fit(bw=bandwidths.bw_silverman, fft=fft) s1 = kde.support.copy() d1 = kde.density.copy() kde = self.kde.fit(bw=kde.bw, fft=fft) npt.assert_almost_equal(s1, kde.support, self.decimal_density) npt.assert_almost_equal(d1, kde.density, self.decimal_density) statsmodels-0.12.2/statsmodels/nonparametric/tests/test_kernel_density.py000066400000000000000000000446431400612667500271560ustar00rootroot00000000000000import numpy as np import numpy.testing as npt import pytest from numpy.testing import assert_allclose, assert_equal import statsmodels.api as sm nparam = sm.nonparametric class KDETestBase(object): def setup(self): nobs = 60 np.random.seed(123456) self.o = np.random.binomial(2, 0.7, size=(nobs, 1)) self.o2 = np.random.binomial(3, 0.7, size=(nobs, 1)) self.c1 = np.random.normal(size=(nobs, 1)) self.c2 = np.random.normal(10, 1, size=(nobs, 1)) self.c3 = np.random.normal(10, 2, size=(nobs, 1)) self.noise = np.random.normal(size=(nobs, 1)) b0 = 0.3 b1 = 1.2 b2 = 3.7 # regression coefficients self.y = b0 + b1 * self.c1 + b2 * self.c2 + self.noise self.y2 = b0 + b1 * self.c1 + b2 * self.c2 + self.o + self.noise # Italy data from R's np package (the first 50 obs) R>> data (Italy) self.Italy_gdp = \ [8.556, 12.262, 9.587, 8.119, 5.537, 6.796, 8.638, 6.483, 6.212, 5.111, 6.001, 7.027, 4.616, 3.922, 4.688, 3.957, 3.159, 3.763, 3.829, 5.242, 6.275, 8.518, 11.542, 9.348, 8.02, 5.527, 6.865, 8.666, 6.672, 6.289, 5.286, 6.271, 7.94, 4.72, 4.357, 4.672, 3.883, 3.065, 3.489, 3.635, 5.443, 6.302, 9.054, 12.485, 9.896, 8.33, 6.161, 7.055, 8.717, 6.95] self.Italy_year = \ [1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1953, 1953, 1953, 1953, 1953, 1953, 1953, 1953] # OECD panel data from NP R>> data(oecdpanel) self.growth = \ [-0.0017584, 0.00740688, 0.03424461, 0.03848719, 0.02932506, 0.03769199, 0.0466038, 0.00199456, 0.03679607, 0.01917304, -0.00221, 0.00787269, 0.03441118, -0.0109228, 0.02043064, -0.0307962, 0.02008947, 0.00580313, 0.00344502, 0.04706358, 0.03585851, 0.01464953, 0.04525762, 0.04109222, -0.0087903, 0.04087915, 0.04551403, 0.036916, 0.00369293, 0.0718669, 0.02577732, -0.0130759, -0.01656641, 0.00676429, 0.08833017, 0.05092105, 0.02005877, 0.00183858, 0.03903173, 0.05832116, 0.0494571, 0.02078484, 0.09213897, 0.0070534, 0.08677202, 0.06830603, -0.00041, 0.0002856, 0.03421225, -0.0036825] self.oecd = \ [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0] self.weights = np.random.random(nobs) class TestKDEUnivariate(KDETestBase): def test_pdf_non_fft(self): kde = nparam.KDEUnivariate(self.noise) kde.fit(fft=False, bw='scott') grid = kde.support testx = [grid[10*i] for i in range(6)] # Test against values from R 'ks' package kde_expected = [0.00016808277984236013, 0.030759614592368954, 0.14123404934759243, 0.28807147408162409, 0.25594519303876273, 0.056593973915651047] kde_vals0 = kde.density[10 * np.arange(6)] kde_vals = kde.evaluate(testx) npt.assert_allclose(kde_vals, kde_expected, atol=1e-6) npt.assert_allclose(kde_vals0, kde_expected, atol=1e-6) def test_weighted_pdf_non_fft(self): kde = nparam.KDEUnivariate(self.noise) kde.fit(weights=self.weights, fft=False, bw='scott') grid = kde.support testx = [grid[10*i] for i in range(6)] # Test against values from R 'ks' package kde_expected = [9.1998858033950757e-05, 0.018761981151370496, 0.14425925509365087, 0.30307631742267443, 0.2405445849994125, 0.06433170684797665] kde_vals0 = kde.density[10 * np.arange(6)] kde_vals = kde.evaluate(testx) npt.assert_allclose(kde_vals, kde_expected, atol=1e-6) npt.assert_allclose(kde_vals0, kde_expected, atol=1e-6) def test_all_samples_same_location_bw(self): x = np.ones(100) kde = nparam.KDEUnivariate(x) with pytest.raises(RuntimeError, match="Selected KDE bandwidth is 0"): kde.fit() def test_int(self, reset_randomstate): x = np.random.randint(0, 100, size=1000) kde = nparam.KDEUnivariate(x) kde.fit() kde_double = nparam.KDEUnivariate(x.astype("double")) kde_double.fit() assert_allclose(kde.bw, kde_double.bw) class TestKDEMultivariate(KDETestBase): @pytest.mark.slow def test_pdf_mixeddata_CV_LS(self): dens_u = nparam.KDEMultivariate(data=[self.c1, self.o, self.o2], var_type='coo', bw='cv_ls') npt.assert_allclose(dens_u.bw, [0.70949447, 0.08736727, 0.09220476], atol=1e-6) # Matches R to 3 decimals; results seem more stable than with R. # Can be checked with following code: # import rpy2.robjects as robjects # from rpy2.robjects.packages import importr # NP = importr('np') # r = robjects.r # D = {"S1": robjects.FloatVector(c1), "S2":robjects.FloatVector(c2), # "S3":robjects.FloatVector(c3), "S4":robjects.FactorVector(o), # "S5":robjects.FactorVector(o2)} # df = robjects.DataFrame(D) # formula = r('~S1+ordered(S4)+ordered(S5)') # r_bw = NP.npudensbw(formula, data=df, bwmethod='cv.ls') @pytest.mark.slow def test_pdf_mixeddata_LS_vs_ML(self): dens_ls = nparam.KDEMultivariate(data=[self.c1, self.o, self.o2], var_type='coo', bw='cv_ls') dens_ml = nparam.KDEMultivariate(data=[self.c1, self.o, self.o2], var_type='coo', bw='cv_ml') npt.assert_allclose(dens_ls.bw, dens_ml.bw, atol=0, rtol=0.5) def test_pdf_mixeddata_CV_ML(self): # Test ML cross-validation dens_ml = nparam.KDEMultivariate(data=[self.c1, self.o, self.c2], var_type='coc', bw='cv_ml') R_bw = [1.021563, 2.806409e-14, 0.5142077] npt.assert_allclose(dens_ml.bw, R_bw, atol=0.1, rtol=0.1) @pytest.mark.slow def test_pdf_continuous(self): # Test for only continuous data dens = nparam.KDEMultivariate(data=[self.growth, self.Italy_gdp], var_type='cc', bw='cv_ls') # take the first data points from the training set sm_result = np.squeeze(dens.pdf()[0:5]) R_result = [1.6202284, 0.7914245, 1.6084174, 2.4987204, 1.3705258] ## CODE TO REPRODUCE THE RESULTS IN R ## library(np) ## data(oecdpanel) ## data (Italy) ## bw <-npudensbw(formula = ~oecdpanel$growth[1:50] + Italy$gdp[1:50], ## bwmethod ='cv.ls') ## fhat <- fitted(npudens(bws=bw)) ## fhat[1:5] npt.assert_allclose(sm_result, R_result, atol=1e-3) def test_pdf_ordered(self): # Test for only ordered data dens = nparam.KDEMultivariate(data=[self.oecd], var_type='o', bw='cv_ls') sm_result = np.squeeze(dens.pdf()[0:5]) R_result = [0.7236395, 0.7236395, 0.2763605, 0.2763605, 0.7236395] # lower tol here. only 2nd decimal npt.assert_allclose(sm_result, R_result, atol=1e-1) @pytest.mark.slow def test_unordered_CV_LS(self): dens = nparam.KDEMultivariate(data=[self.growth, self.oecd], var_type='cu', bw='cv_ls') R_result = [0.0052051, 0.05835941] npt.assert_allclose(dens.bw, R_result, atol=1e-2) def test_continuous_cdf(self, data_predict=None): dens = nparam.KDEMultivariate(data=[self.Italy_gdp, self.growth], var_type='cc', bw='cv_ml') sm_result = dens.cdf()[0:5] R_result = [0.192180770, 0.299505196, 0.557303666, 0.513387712, 0.210985350] npt.assert_allclose(sm_result, R_result, atol=1e-3) def test_mixeddata_cdf(self, data_predict=None): dens = nparam.KDEMultivariate(data=[self.Italy_gdp, self.oecd], var_type='cu', bw='cv_ml') sm_result = dens.cdf()[0:5] R_result = [0.54700010, 0.65907039, 0.89676865, 0.74132941, 0.25291361] npt.assert_allclose(sm_result, R_result, atol=1e-3) @pytest.mark.slow def test_continuous_cvls_efficient(self): nobs = 400 np.random.seed(12345) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) Y = 0.3 +1.2 * C1 - 0.9 * C2 dens_efficient = nparam.KDEMultivariate(data=[Y, C1], var_type='cc', bw='cv_ls', defaults=nparam.EstimatorSettings(efficient=True, n_sub=100)) #dens = nparam.KDEMultivariate(data=[Y, C1], var_type='cc', bw='cv_ls', # defaults=nparam.EstimatorSettings(efficient=False)) #bw = dens.bw bw = np.array([0.3404, 0.1666]) npt.assert_allclose(bw, dens_efficient.bw, atol=0.1, rtol=0.2) @pytest.mark.slow def test_continuous_cvml_efficient(self): nobs = 400 np.random.seed(12345) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) Y = 0.3 +1.2 * C1 - 0.9 * C2 dens_efficient = nparam.KDEMultivariate(data=[Y, C1], var_type='cc', bw='cv_ml', defaults=nparam.EstimatorSettings(efficient=True, n_sub=100)) #dens = nparam.KDEMultivariate(data=[Y, C1], var_type='cc', bw='cv_ml', # defaults=nparam.EstimatorSettings(efficient=False)) #bw = dens.bw bw = np.array([0.4471, 0.2861]) npt.assert_allclose(bw, dens_efficient.bw, atol=0.1, rtol = 0.2) @pytest.mark.slow def test_efficient_notrandom(self): nobs = 400 np.random.seed(12345) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) Y = 0.3 +1.2 * C1 - 0.9 * C2 dens_efficient = nparam.KDEMultivariate(data=[Y, C1], var_type='cc', bw='cv_ml', defaults=nparam.EstimatorSettings(efficient=True, randomize=False, n_sub=100)) dens = nparam.KDEMultivariate(data=[Y, C1], var_type='cc', bw='cv_ml') npt.assert_allclose(dens.bw, dens_efficient.bw, atol=0.1, rtol = 0.2) def test_efficient_user_specified_bw(self): nobs = 400 np.random.seed(12345) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) bw_user=[0.23, 434697.22] dens = nparam.KDEMultivariate(data=[C1, C2], var_type='cc', bw=bw_user, defaults=nparam.EstimatorSettings(efficient=True, randomize=False, n_sub=100)) npt.assert_equal(dens.bw, bw_user) class TestKDEMultivariateConditional(KDETestBase): @pytest.mark.slow def test_mixeddata_CV_LS(self): dens_ls = nparam.KDEMultivariateConditional(endog=[self.Italy_gdp], exog=[self.Italy_year], dep_type='c', indep_type='o', bw='cv_ls') # R result: [1.6448, 0.2317373] npt.assert_allclose(dens_ls.bw, [1.01203728, 0.31905144], atol=1e-5) def test_continuous_CV_ML(self): dens_ml = nparam.KDEMultivariateConditional(endog=[self.Italy_gdp], exog=[self.growth], dep_type='c', indep_type='c', bw='cv_ml') # Results from R npt.assert_allclose(dens_ml.bw, [0.5341164, 0.04510836], atol=1e-3) @pytest.mark.slow def test_unordered_CV_LS(self): dens_ls = nparam.KDEMultivariateConditional(endog=[self.oecd], exog=[self.growth], dep_type='u', indep_type='c', bw='cv_ls') # TODO: assert missing def test_pdf_continuous(self): # Hardcode here the bw that will be calculated is we had used # ``bw='cv_ml'``. That calculation is slow, and tested in other tests. bw_cv_ml = np.array([0.010043, 12095254.7]) # TODO: odd numbers (?!) dens = nparam.KDEMultivariateConditional(endog=[self.growth], exog=[self.Italy_gdp], dep_type='c', indep_type='c', bw=bw_cv_ml) sm_result = np.squeeze(dens.pdf()[0:5]) R_result = [11.97964, 12.73290, 13.23037, 13.46438, 12.22779] npt.assert_allclose(sm_result, R_result, atol=1e-3) @pytest.mark.slow def test_pdf_mixeddata(self): dens = nparam.KDEMultivariateConditional(endog=[self.Italy_gdp], exog=[self.Italy_year], dep_type='c', indep_type='o', bw='cv_ls') sm_result = np.squeeze(dens.pdf()[0:5]) #R_result = [0.08469226, 0.01737731, 0.05679909, 0.09744726, 0.15086674] expected = [0.08592089, 0.0193275, 0.05310327, 0.09642667, 0.171954] ## CODE TO REPRODUCE IN R ## library(np) ## data (Italy) ## bw <- npcdensbw(formula = ## Italy$gdp[1:50]~ordered(Italy$year[1:50]),bwmethod='cv.ls') ## fhat <- fitted(npcdens(bws=bw)) ## fhat[1:5] npt.assert_allclose(sm_result, expected, atol=0, rtol=1e-5) def test_continuous_normal_ref(self): # test for normal reference rule of thumb with continuous data dens_nm = nparam.KDEMultivariateConditional(endog=[self.Italy_gdp], exog=[self.growth], dep_type='c', indep_type='c', bw='normal_reference') sm_result = dens_nm.bw R_result = [1.283532, 0.01535401] # TODO: here we need a smaller tolerance.check! npt.assert_allclose(sm_result, R_result, atol=1e-1) # test default bandwidth method, should be normal_reference dens_nm2 = nparam.KDEMultivariateConditional(endog=[self.Italy_gdp], exog=[self.growth], dep_type='c', indep_type='c', bw=None) assert_allclose(dens_nm2.bw, dens_nm.bw, rtol=1e-10) assert_equal(dens_nm2._bw_method, 'normal_reference') # check repr works #3125 repr(dens_nm2) def test_continuous_cdf(self): dens_nm = nparam.KDEMultivariateConditional(endog=[self.Italy_gdp], exog=[self.growth], dep_type='c', indep_type='c', bw='normal_reference') sm_result = dens_nm.cdf()[0:5] R_result = [0.81304920, 0.95046942, 0.86878727, 0.71961748, 0.38685423] npt.assert_allclose(sm_result, R_result, atol=1e-3) @pytest.mark.slow def test_mixeddata_cdf(self): dens = nparam.KDEMultivariateConditional(endog=[self.Italy_gdp], exog=[self.Italy_year], dep_type='c', indep_type='o', bw='cv_ls') sm_result = dens.cdf()[0:5] #R_result = [0.8118257, 0.9724863, 0.8843773, 0.7720359, 0.4361867] expected = [0.83378885, 0.97684477, 0.90655143, 0.79393161, 0.43629083] npt.assert_allclose(sm_result, expected, atol=0, rtol=1e-5) @pytest.mark.slow def test_continuous_cvml_efficient(self): nobs = 500 np.random.seed(12345) ovals = np.random.binomial(2, 0.5, size=(nobs, )) C1 = np.random.normal(size=(nobs, )) noise = np.random.normal(size=(nobs, )) b0 = 3 b1 = 1.2 b2 = 3.7 # regression coefficients Y = b0+ b1 * C1 + b2*ovals + noise dens_efficient = nparam.KDEMultivariateConditional(endog=[Y], exog=[C1], dep_type='c', indep_type='c', bw='cv_ml', defaults=nparam.EstimatorSettings(efficient=True, n_sub=50)) #dens = nparam.KDEMultivariateConditional(endog=[Y], exog=[C1], # dep_type='c', indep_type='c', bw='cv_ml') #bw = dens.bw bw_expected = np.array([0.73387, 0.43715]) npt.assert_allclose(dens_efficient.bw, bw_expected, atol=0, rtol=1e-3) def test_efficient_user_specified_bw(self): nobs = 400 np.random.seed(12345) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) bw_user=[0.23, 434697.22] dens = nparam.KDEMultivariate(data=[C1, C2], var_type='cc', bw=bw_user, defaults=nparam.EstimatorSettings(efficient=True, randomize=False, n_sub=100)) npt.assert_equal(dens.bw, bw_user) @pytest.mark.parametrize("kernel", ["biw", "cos", "epa", "gau", "tri", "triw", "uni"]) def test_all_kernels(kernel, reset_randomstate): data = np.random.normal(size=200) x_grid = np.linspace(min(data), max(data), 200) density = sm.nonparametric.KDEUnivariate(data) density.fit(kernel="gau", fft=False) assert isinstance(density.evaluate(x_grid), np.ndarray) statsmodels-0.12.2/statsmodels/nonparametric/tests/test_kernel_regression.py000066400000000000000000000370701400612667500276530ustar00rootroot00000000000000 import pytest import numpy as np import numpy.testing as npt import statsmodels.api as sm nparam = sm.nonparametric class KernelRegressionTestBase(object): @classmethod def setup_class(cls): nobs = 60 np.random.seed(123456) cls.o = np.random.binomial(2, 0.7, size=(nobs, 1)) cls.o2 = np.random.binomial(3, 0.7, size=(nobs, 1)) cls.c1 = np.random.normal(size=(nobs, 1)) cls.c2 = np.random.normal(10, 1, size=(nobs, 1)) cls.c3 = np.random.normal(10, 2, size=(nobs, 1)) cls.noise = np.random.normal(size=(nobs, 1)) b0 = 0.3 b1 = 1.2 b2 = 3.7 # regression coefficients cls.y = b0 + b1 * cls.c1 + b2 * cls.c2 + cls.noise cls.y2 = b0 + b1 * cls.c1 + b2 * cls.c2 + cls.o + cls.noise # Italy data from R's np package (the first 50 obs) R>> data (Italy) cls.Italy_gdp = \ [8.556, 12.262, 9.587, 8.119, 5.537, 6.796, 8.638, 6.483, 6.212, 5.111, 6.001, 7.027, 4.616, 3.922, 4.688, 3.957, 3.159, 3.763, 3.829, 5.242, 6.275, 8.518, 11.542, 9.348, 8.02, 5.527, 6.865, 8.666, 6.672, 6.289, 5.286, 6.271, 7.94, 4.72, 4.357, 4.672, 3.883, 3.065, 3.489, 3.635, 5.443, 6.302, 9.054, 12.485, 9.896, 8.33, 6.161, 7.055, 8.717, 6.95] cls.Italy_year = \ [1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1953, 1953, 1953, 1953, 1953, 1953, 1953, 1953] # OECD panel data from NP R>> data(oecdpanel) cls.growth = \ [-0.0017584, 0.00740688, 0.03424461, 0.03848719, 0.02932506, 0.03769199, 0.0466038, 0.00199456, 0.03679607, 0.01917304, -0.00221, 0.00787269, 0.03441118, -0.0109228, 0.02043064, -0.0307962, 0.02008947, 0.00580313, 0.00344502, 0.04706358, 0.03585851, 0.01464953, 0.04525762, 0.04109222, -0.0087903, 0.04087915, 0.04551403, 0.036916, 0.00369293, 0.0718669, 0.02577732, -0.0130759, -0.01656641, 0.00676429, 0.08833017, 0.05092105, 0.02005877, 0.00183858, 0.03903173, 0.05832116, 0.0494571, 0.02078484, 0.09213897, 0.0070534, 0.08677202, 0.06830603, -0.00041, 0.0002856, 0.03421225, -0.0036825] cls.oecd = \ [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0] def write2file(self, file_name, data): # pragma: no cover """Write some data to a csv file. Only use for debugging!""" import csv data_file = csv.writer(open(file_name, "w")) data = np.column_stack(data) nobs = max(np.shape(data)) K = min(np.shape(data)) data = np.reshape(data, (nobs,K)) for i in range(nobs): data_file.writerow(list(data[i, :])) class TestKernelReg(KernelRegressionTestBase): def test_ordered_lc_cvls(self): model = nparam.KernelReg(endog=[self.Italy_gdp], exog=[self.Italy_year], reg_type='lc', var_type='o', bw='cv_ls') sm_bw = model.bw R_bw = 0.1390096 sm_mean, sm_mfx = model.fit() sm_mean = sm_mean[0:5] sm_mfx = sm_mfx[0:5] R_mean = 6.190486 sm_R2 = model.r_squared() R_R2 = 0.1435323 ## CODE TO REPRODUCE IN R ## library(np) ## data(Italy) ## attach(Italy) ## bw <- npregbw(formula=gdp[1:50]~ordered(year[1:50])) npt.assert_allclose(sm_bw, R_bw, atol=1e-2) npt.assert_allclose(sm_mean, R_mean, atol=1e-2) npt.assert_allclose(sm_R2, R_R2, atol=1e-2) def test_continuousdata_lc_cvls(self): model = nparam.KernelReg(endog=[self.y], exog=[self.c1, self.c2], reg_type='lc', var_type='cc', bw='cv_ls') # Bandwidth sm_bw = model.bw R_bw = [0.6163835, 0.1649656] # Conditional Mean sm_mean, sm_mfx = model.fit() sm_mean = sm_mean[0:5] sm_mfx = sm_mfx[0:5] R_mean = [31.49157, 37.29536, 43.72332, 40.58997, 36.80711] # R-Squared sm_R2 = model.r_squared() R_R2 = 0.956381720885 npt.assert_allclose(sm_bw, R_bw, atol=1e-2) npt.assert_allclose(sm_mean, R_mean, atol=1e-2) npt.assert_allclose(sm_R2, R_R2, atol=1e-2) def test_continuousdata_ll_cvls(self): model = nparam.KernelReg(endog=[self.y], exog=[self.c1, self.c2], reg_type='ll', var_type='cc', bw='cv_ls') sm_bw = model.bw R_bw = [1.717891, 2.449415] sm_mean, sm_mfx = model.fit() sm_mean = sm_mean[0:5] sm_mfx = sm_mfx[0:5] R_mean = [31.16003, 37.30323, 44.49870, 40.73704, 36.19083] sm_R2 = model.r_squared() R_R2 = 0.9336019 npt.assert_allclose(sm_bw, R_bw, atol=1e-2) npt.assert_allclose(sm_mean, R_mean, atol=1e-2) npt.assert_allclose(sm_R2, R_R2, atol=1e-2) def test_continuous_mfx_ll_cvls(self, file_name='RegData.csv'): nobs = 200 np.random.seed(1234) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) C3 = np.random.beta(0.5,0.2, size=(nobs,)) noise = np.random.normal(size=(nobs, )) b0 = 3 b1 = 1.2 b2 = 3.7 # regression coefficients b3 = 2.3 Y = b0+ b1 * C1 + b2*C2+ b3 * C3 + noise bw_cv_ls = np.array([0.96075, 0.5682, 0.29835]) model = nparam.KernelReg(endog=[Y], exog=[C1, C2, C3], reg_type='ll', var_type='ccc', bw=bw_cv_ls) sm_mean, sm_mfx = model.fit() sm_mean = sm_mean[0:5] npt.assert_allclose(sm_mfx[0,:], [b1,b2,b3], rtol=2e-1) def test_mixed_mfx_ll_cvls(self, file_name='RegData.csv'): nobs = 200 np.random.seed(1234) ovals = np.random.binomial(2, 0.5, size=(nobs, )) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) noise = np.random.normal(size=(nobs, )) b0 = 3 b1 = 1.2 b2 = 3.7 # regression coefficients b3 = 2.3 Y = b0+ b1 * C1 + b2*C2+ b3 * ovals + noise bw_cv_ls = np.array([1.04726, 1.67485, 0.39852]) model = nparam.KernelReg(endog=[Y], exog=[C1, C2, ovals], reg_type='ll', var_type='cco', bw=bw_cv_ls) sm_mean, sm_mfx = model.fit() # TODO: add expected result sm_R2 = model.r_squared() # noqa: F841 npt.assert_allclose(sm_mfx[0, :], [b1, b2, b3], rtol=2e-1) @pytest.mark.slow @pytest.mark.xfail(reason="Test does not make much sense - always passes " "with very small bw.") def test_mfx_nonlinear_ll_cvls(self, file_name='RegData.csv'): nobs = 200 np.random.seed(1234) C1 = np.random.normal(size=(nobs,)) C2 = np.random.normal(2, 1, size=(nobs,)) C3 = np.random.beta(0.5,0.2, size=(nobs,)) noise = np.random.normal(size=(nobs,)) b0 = 3 b1 = 1.2 b3 = 2.3 Y = b0+ b1 * C1 * C2 + b3 * C3 + noise model = nparam.KernelReg(endog=[Y], exog=[C1, C2, C3], reg_type='ll', var_type='ccc', bw='cv_ls') sm_bw = model.bw sm_mean, sm_mfx = model.fit() sm_R2 = model.r_squared() # Theoretical marginal effects mfx1 = b1 * C2 mfx2 = b1 * C1 npt.assert_allclose(sm_mean, Y, rtol = 2e-1) npt.assert_allclose(sm_mfx[:, 0], mfx1, rtol=2e-1) npt.assert_allclose(sm_mfx[0:10, 1], mfx2[0:10], rtol=2e-1) @pytest.mark.slow def test_continuous_cvls_efficient(self): nobs = 500 np.random.seed(12345) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) b0 = 3 b1 = 1.2 b2 = 3.7 # regression coefficients Y = b0+ b1 * C1 + b2*C2 model_efficient = nparam.KernelReg(endog=[Y], exog=[C1], reg_type='lc', var_type='c', bw='cv_ls', defaults=nparam.EstimatorSettings(efficient=True, n_sub=100)) model = nparam.KernelReg(endog=[Y], exog=[C1], reg_type='ll', var_type='c', bw='cv_ls') npt.assert_allclose(model.bw, model_efficient.bw, atol=5e-2, rtol=1e-1) @pytest.mark.slow def test_censored_ll_cvls(self): nobs = 200 np.random.seed(1234) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) noise = np.random.normal(size=(nobs, )) Y = 0.3 +1.2 * C1 - 0.9 * C2 + noise Y[Y>0] = 0 # censor the data model = nparam.KernelCensoredReg(endog=[Y], exog=[C1, C2], reg_type='ll', var_type='cc', bw='cv_ls', censor_val=0) sm_mean, sm_mfx = model.fit() npt.assert_allclose(sm_mfx[0,:], [1.2, -0.9], rtol = 2e-1) @pytest.mark.slow def test_continuous_lc_aic(self): nobs = 200 np.random.seed(1234) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) noise = np.random.normal(size=(nobs, )) Y = 0.3 +1.2 * C1 - 0.9 * C2 + noise #self.write2file('RegData.csv', (Y, C1, C2)) #CODE TO PRODUCE BANDWIDTH ESTIMATION IN R #library(np) #data <- read.csv('RegData.csv', header=FALSE) #bw <- npregbw(formula=data$V1 ~ data$V2 + data$V3, # bwmethod='cv.aic', regtype='lc') model = nparam.KernelReg(endog=[Y], exog=[C1, C2], reg_type='lc', var_type='cc', bw='aic') #R_bw = [0.4017893, 0.4943397] # Bandwidth obtained in R bw_expected = [0.3987821, 0.50933458] npt.assert_allclose(model.bw, bw_expected, rtol=1e-3) @pytest.mark.slow def test_significance_continuous(self): nobs = 250 np.random.seed(12345) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) C3 = np.random.beta(0.5,0.2, size=(nobs,)) noise = np.random.normal(size=(nobs, )) b1 = 1.2 b2 = 3.7 # regression coefficients Y = b1 * C1 + b2 * C2 + noise # This is the cv_ls bandwidth estimated earlier bw=[11108137.1087194, 1333821.85150218] model = nparam.KernelReg(endog=[Y], exog=[C1, C3], reg_type='ll', var_type='cc', bw=bw) nboot = 45 # Number of bootstrap samples sig_var12 = model.sig_test([0,1], nboot=nboot) # H0: b1 = 0 and b2 = 0 npt.assert_equal(sig_var12 == 'Not Significant', False) sig_var1 = model.sig_test([0], nboot=nboot) # H0: b1 = 0 npt.assert_equal(sig_var1 == 'Not Significant', False) sig_var2 = model.sig_test([1], nboot=nboot) # H0: b2 = 0 npt.assert_equal(sig_var2 == 'Not Significant', True) @pytest.mark.slow def test_significance_discrete(self): nobs = 200 np.random.seed(12345) ovals = np.random.binomial(2, 0.5, size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) C3 = np.random.beta(0.5,0.2, size=(nobs,)) noise = np.random.normal(size=(nobs, )) b1 = 1.2 b2 = 3.7 # regression coefficients Y = b1 * ovals + b2 * C2 + noise bw= [3.63473198e+00, 1.21404803e+06] # This is the cv_ls bandwidth estimated earlier # The cv_ls bandwidth was estimated earlier to save time model = nparam.KernelReg(endog=[Y], exog=[ovals, C3], reg_type='ll', var_type='oc', bw=bw) # This was also tested with local constant estimator nboot = 45 # Number of bootstrap samples sig_var1 = model.sig_test([0], nboot=nboot) # H0: b1 = 0 npt.assert_equal(sig_var1 == 'Not Significant', False) sig_var2 = model.sig_test([1], nboot=nboot) # H0: b2 = 0 npt.assert_equal(sig_var2 == 'Not Significant', True) def test_user_specified_kernel(self): model = nparam.KernelReg(endog=[self.y], exog=[self.c1, self.c2], reg_type='ll', var_type='cc', bw='cv_ls', ckertype='tricube') # Bandwidth sm_bw = model.bw R_bw = [0.581663, 0.5652] # Conditional Mean sm_mean, sm_mfx = model.fit() sm_mean = sm_mean[0:5] sm_mfx = sm_mfx[0:5] R_mean = [30.926714, 36.994604, 44.438358, 40.680598, 35.961593] # R-Squared sm_R2 = model.r_squared() R_R2 = 0.934825 npt.assert_allclose(sm_bw, R_bw, atol=1e-2) npt.assert_allclose(sm_mean, R_mean, atol=1e-2) npt.assert_allclose(sm_R2, R_R2, atol=1e-2) def test_censored_user_specified_kernel(self): model = nparam.KernelCensoredReg(endog=[self.y], exog=[self.c1, self.c2], reg_type='ll', var_type='cc', bw='cv_ls', censor_val=0, ckertype='tricube') # Bandwidth sm_bw = model.bw R_bw = [0.581663, 0.5652] # Conditional Mean sm_mean, sm_mfx = model.fit() sm_mean = sm_mean[0:5] sm_mfx = sm_mfx[0:5] R_mean = [29.205526, 29.538008, 31.667581, 31.978866, 30.926714] # R-Squared sm_R2 = model.r_squared() R_R2 = 0.934825 npt.assert_allclose(sm_bw, R_bw, atol=1e-2) npt.assert_allclose(sm_mean, R_mean, atol=1e-2) npt.assert_allclose(sm_R2, R_R2, atol=1e-2) def test_efficient_user_specificed_bw(self): bw_user=[0.23, 434697.22] model = nparam.KernelReg(endog=[self.y], exog=[self.c1, self.c2], reg_type='lc', var_type='cc', bw=bw_user, defaults=nparam.EstimatorSettings(efficient=True)) # Bandwidth npt.assert_equal(model.bw, bw_user) def test_censored_efficient_user_specificed_bw(self): nobs = 200 np.random.seed(1234) C1 = np.random.normal(size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) noise = np.random.normal(size=(nobs, )) Y = 0.3 +1.2 * C1 - 0.9 * C2 + noise Y[Y>0] = 0 # censor the data bw_user=[0.23, 434697.22] model = nparam.KernelCensoredReg(endog=[Y], exog=[C1, C2], reg_type='ll', var_type='cc', bw=bw_user, censor_val=0, defaults=nparam.EstimatorSettings(efficient=True)) # Bandwidth npt.assert_equal(model.bw, bw_user) def test_invalid_bw(): # GH4873 x = np.arange(400) y = x ** 2 with pytest.raises(ValueError): nparam.KernelReg(x, y, 'c', bw=[12.5, 1.]) def test_invalid_kernel(): x = np.arange(400) y = x ** 2 # silverman kernel is not currently in statsmodels kernel library with pytest.raises(ValueError): nparam.KernelReg(x, y, reg_type='ll', var_type='cc', bw='cv_ls', ckertype='silverman') with pytest.raises(ValueError): nparam.KernelCensoredReg(x, y, reg_type='ll', var_type='cc', bw='cv_ls', censor_val=0, ckertype='silverman') statsmodels-0.12.2/statsmodels/nonparametric/tests/test_kernels.py000066400000000000000000000104731400612667500255740ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sat Dec 14 17:23:25 2013 Author: Josef Perktold """ import os import numpy as np from numpy.testing import assert_allclose, assert_array_less import pytest from statsmodels.sandbox.nonparametric import kernels DEBUG = 0 curdir = os.path.dirname(os.path.abspath(__file__)) fname = 'results/results_kernel_regression.csv' results = np.recfromcsv(os.path.join(curdir, fname)) y = results['accident'] x = results['service'] positive = x >= 0 x = np.log(x[positive]) y = y[positive] xg = np.linspace(x.min(), x.max(), 40) # grid points default in Stata # FIXME: do not leave this commented-out; use or move/remove #kern_name = 'gau' #kern = kernels.Gaussian() #kern_name = 'epan2' #kern = kernels.Epanechnikov() #kern_name = 'rec' #kern = kernels.Uniform() # ours looks awful #kern_name = 'tri' #kern = kernels.Triangular() #kern_name = 'cos' #kern = kernels.Cosine() #does not match up, nan in Stata results ? #kern_name = 'bi' #kern = kernels.Biweight() class CheckKernelMixin(object): se_rtol = 0.7 upp_rtol = 0.1 low_rtol = 0.2 low_atol = 0.3 def test_smoothconf(self): kern_name = self.kern_name kern = self.kern #fittedg = np.array([kernels.Epanechnikov().smoothconf(x, y, xi) for xi in xg]) fittedg = np.array([kern.smoothconf(x, y, xi) for xi in xg]) # attach for inspection from outside of test run self.fittedg = fittedg res_fitted = results['s_' + kern_name] res_se = results['se_' + kern_name] crit = 1.9599639845400545 # norm.isf(0.05 / 2) # implied standard deviation from conf_int se = (fittedg[:, 2] - fittedg[:, 1]) / crit fitted = fittedg[:, 1] # check both rtol & atol assert_allclose(fitted, res_fitted, rtol=5e-7, atol=1e-20) assert_allclose(fitted, res_fitted, rtol=0, atol=1e-6) # TODO: check we are using a different algorithm for se # The following are very rough checks self.se = se self.res_se = res_se se_valid = np.isfinite(res_se) # if np.any(~se_valid): # print('nan in stata result', self.__class__.__name__) assert_allclose(se[se_valid], res_se[se_valid], rtol=self.se_rtol, atol=0.2) # check that most values are closer mask = np.abs(se - res_se) > (0.2 + 0.2 * res_se) if not hasattr(self, 'se_n_diff'): se_n_diff = 40 * 0.125 else: se_n_diff = self.se_n_diff assert_array_less(mask.sum(), se_n_diff + 1) # at most 5 large diffs # Stata only displays ci, does not save it res_upp = res_fitted + crit * res_se res_low = res_fitted - crit * res_se self.res_fittedg = np.column_stack((res_low, res_fitted, res_upp)) assert_allclose(fittedg[se_valid, 2], res_upp[se_valid], rtol=self.upp_rtol, atol=0.2) assert_allclose(fittedg[se_valid, 0], res_low[se_valid], rtol=self.low_rtol, atol=self.low_atol) #assert_allclose(fitted, res_fitted, rtol=0, atol=1e-6) @pytest.mark.slow @pytest.mark.smoke # TOOD: make this an actual test? def test_smoothconf_data(self): kern = self.kern crit = 1.9599639845400545 # norm.isf(0.05 / 2) # no reference results saved to csv yet fitted_x = np.array([kern.smoothconf(x, y, xi) for xi in x]) class TestEpan(CheckKernelMixin): kern_name = 'epan2' kern = kernels.Epanechnikov() class TestGau(CheckKernelMixin): kern_name = 'gau' kern = kernels.Gaussian() class TestUniform(CheckKernelMixin): kern_name = 'rec' kern = kernels.Uniform() se_rtol = 0.8 se_n_diff = 8 upp_rtol = 0.4 low_rtol = 0.2 low_atol = 0.8 class TestTriangular(CheckKernelMixin): kern_name = 'tri' kern = kernels.Triangular() se_n_diff = 10 upp_rtol = 0.15 low_rtol = 0.3 class TestCosine(CheckKernelMixin): # Stata results for Cosine look strange, has nans kern_name = 'cos' kern = kernels.Cosine2() @pytest.mark.xfail(reason="NaN mismatch", raises=AssertionError, strict=True) def test_smoothconf(self): super(TestCosine, self).test_smoothconf() class TestBiweight(CheckKernelMixin): kern_name = 'bi' kern = kernels.Biweight() se_n_diff = 9 low_rtol = 0.3 statsmodels-0.12.2/statsmodels/nonparametric/tests/test_lowess.py000066400000000000000000000154521400612667500254470ustar00rootroot00000000000000''' Lowess testing suite. Expected outcomes are generated by R's lowess function given the same arguments. The R script test_lowess_r_outputs.R can be used to generate the expected outcomes. The delta tests utilize Silverman's motorcycle collision data, available in R's MASS package. ''' import os import numpy as np from numpy.testing import (assert_almost_equal, assert_, assert_raises, assert_equal) from statsmodels.nonparametric.smoothers_lowess import lowess # Number of decimals to test equality with. # The default is 7. curdir = os.path.dirname(os.path.abspath(__file__)) rpath = os.path.join(curdir, 'results') class TestLowess(object): def test_import(self): #this does not work #from statsmodels.api.nonparametric import lowess as lowess1 import statsmodels.api as sm lowess1 = sm.nonparametric.lowess assert_(lowess is lowess1) def test_flat(self): test_data = { 'x': np.arange(20), 'y': np.zeros(20), 'out': np.zeros(20)} expected_lowess = np.array([test_data['x'], test_data['out']]).T actual_lowess = lowess(test_data['y'], test_data['x']) assert_almost_equal(expected_lowess, actual_lowess, 7) def test_range(self): test_data = { 'x': np.arange(20), 'y': np.arange(20), 'out': np.arange(20)} expected_lowess = np.array([test_data['x'], test_data['out']]).T actual_lowess = lowess(test_data['y'], test_data['x']) assert_almost_equal(expected_lowess, actual_lowess, 7) @staticmethod def generate(name, fname, x='x', y='y', out='out', kwargs=None, decimal=7): kwargs = {} if kwargs is None else kwargs data = np.genfromtxt(os.path.join(rpath, fname), delimiter=',', names=True) assert_almost_equal.description = name if callable(kwargs): kwargs = kwargs(data) result = lowess(data[y], data[x], **kwargs) expect = np.array([data[x], data[out]]).T assert_almost_equal(result, expect, decimal) # TODO: Refactor as parametrized test once nose is permanently dropped def test_simple(self): self.generate('test_simple', 'test_lowess_simple.csv') def test_iter_0(self): self.generate('test_iter_0', 'test_lowess_iter.csv', out='out_0', kwargs={'it': 0}) def test_iter_0_3(self): self.generate('test_iter_0', 'test_lowess_iter.csv', out='out_3', kwargs={'it': 3}) def test_frac_2_3(self): self.generate('test_frac_2_3', 'test_lowess_frac.csv', out='out_2_3', kwargs={'frac': 2. / 3}) def test_frac_1_5(self): self.generate('test_frac_1_5', 'test_lowess_frac.csv', out='out_1_5', kwargs={'frac': 1. / 5}) def test_delta_0(self): self.generate('test_delta_0', 'test_lowess_delta.csv', out='out_0', kwargs={'frac': 0.1}) def test_delta_rdef(self): self.generate('test_delta_Rdef', 'test_lowess_delta.csv', out='out_Rdef', kwargs=lambda data: {'frac': .1, 'delta': .01 * np.ptp(data['x'])}) def test_delta_1(self): self.generate('test_delta_1', 'test_lowess_delta.csv', out='out_1', kwargs={'frac': 0.1, 'delta': 1 + 1e-10}, decimal=10) def test_options(self): rfile = os.path.join(rpath, 'test_lowess_simple.csv') test_data = np.genfromtxt(open(rfile, 'rb'), delimiter = ',', names = True) y, x = test_data['y'], test_data['x'] res1_fitted = test_data['out'] expected_lowess = np.array([test_data['x'], test_data['out']]).T # check skip sorting actual_lowess1 = lowess(y, x, is_sorted=True) assert_almost_equal(actual_lowess1, expected_lowess, decimal=13) # check skip missing actual_lowess = lowess(y, x, is_sorted=True, missing='none') assert_almost_equal(actual_lowess, actual_lowess1, decimal=13) # check order/index, returns yfitted only actual_lowess = lowess(y[::-1], x[::-1], return_sorted=False) assert_almost_equal(actual_lowess, actual_lowess1[::-1, 1], decimal=13) # check returns yfitted only actual_lowess = lowess(y, x, return_sorted=False, missing='none', is_sorted=True) assert_almost_equal(actual_lowess, actual_lowess1[:, 1], decimal=13) # check integer input actual_lowess = lowess(np.round(y).astype(int), x, is_sorted=True) actual_lowess1 = lowess(np.round(y), x, is_sorted=True) assert_almost_equal(actual_lowess, actual_lowess1, decimal=13) assert_(actual_lowess.dtype is np.dtype(float)) # this will also have duplicate x actual_lowess = lowess(y, np.round(x).astype(int), is_sorted=True) actual_lowess1 = lowess(y, np.round(x), is_sorted=True) assert_almost_equal(actual_lowess, actual_lowess1, decimal=13) assert_(actual_lowess.dtype is np.dtype(float)) # Test specifying xvals explicitly perm_idx = np.arange(len(x)//2) np.random.shuffle(perm_idx) actual_lowess2 = lowess(y, x, xvals = x[perm_idx], return_sorted=False) assert_almost_equal(actual_lowess[perm_idx,1], actual_lowess2, decimal=13) # check with nans, this changes the arrays y[[5, 6]] = np.nan x[3] = np.nan mask_valid = np.isfinite(x) & np.isfinite(y) #actual_lowess1[[3, 5, 6], 1] = np.nan actual_lowess = lowess(y, x, is_sorted=True) actual_lowess1 = lowess(y[mask_valid], x[mask_valid], is_sorted=True) assert_almost_equal(actual_lowess, actual_lowess1, decimal=13) assert_raises(ValueError, lowess, y, x, missing='raise') perm_idx = np.arange(len(x)) np.random.shuffle(perm_idx) yperm = y[perm_idx] xperm = x[perm_idx] actual_lowess2 = lowess(yperm, xperm, is_sorted=False) assert_almost_equal(actual_lowess, actual_lowess2, decimal=13) actual_lowess3 = lowess(yperm, xperm, is_sorted=False, return_sorted=False) mask_valid = np.isfinite(xperm) & np.isfinite(yperm) assert_equal(np.isnan(actual_lowess3), ~mask_valid) # get valid sorted smoothed y from actual_lowess3 sort_idx = np.argsort(xperm) yhat = actual_lowess3[sort_idx] yhat = yhat[np.isfinite(yhat)] assert_almost_equal(yhat, actual_lowess2[:,1], decimal=13) # Test specifying xvals explicitly, now with nans perm_idx = np.arange(actual_lowess.shape[0]) actual_lowess4 = lowess(y, x, xvals = actual_lowess[perm_idx,0], return_sorted=False) assert_almost_equal(actual_lowess[perm_idx,1], actual_lowess4, decimal=13) def test_returns_inputs(): # see 1960 y = [0] * 10 + [1] * 10 x = np.arange(20) result = lowess(y, x, frac=.4) assert_almost_equal(result, np.column_stack((x, y))) statsmodels-0.12.2/statsmodels/regression/000077500000000000000000000000001400612667500206675ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/regression/__init__.py000066400000000000000000000002251400612667500227770ustar00rootroot00000000000000from .linear_model import yule_walker from statsmodels.tools._testing import PytestTester __all__ = ['yule_walker', 'test'] test = PytestTester() statsmodels-0.12.2/statsmodels/regression/_prediction.py000066400000000000000000000151211400612667500235400ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Dec 19 11:29:18 2014 Author: Josef Perktold License: BSD-3 """ import numpy as np from scipy import stats import pandas as pd # this is similar to ContrastResults after t_test, copied and adjusted class PredictionResults(object): """ Results class for predictions. Parameters ---------- predicted_mean : ndarray The array containing the prediction means. var_pred_mean : ndarray The array of the variance of the prediction means. var_resid : ndarray The array of residual variances. df : int The degree of freedom used if dist is 't'. dist : {'norm', 't', object} Either a string for the normal or t distribution or another object that exposes a `ppf` method. row_labels : list[str] Row labels used in summary frame. """ def __init__(self, predicted_mean, var_pred_mean, var_resid, df=None, dist=None, row_labels=None): self.predicted_mean = predicted_mean self.var_pred_mean = var_pred_mean self.df = df self.var_resid = var_resid self.row_labels = row_labels if dist is None or dist == 'norm': self.dist = stats.norm self.dist_args = () elif dist == 't': self.dist = stats.t self.dist_args = (self.df,) else: self.dist = dist self.dist_args = () @property def se_obs(self): return np.sqrt(self.var_pred_mean + self.var_resid) @property def se_mean(self): return np.sqrt(self.var_pred_mean) def conf_int(self, obs=False, alpha=0.05): """ Returns the confidence interval of the value, `effect` of the constraint. This is currently only available for t and z tests. Parameters ---------- alpha : float, optional The significance level for the confidence interval. ie., The default `alpha` = .05 returns a 95% confidence interval. Returns ------- ci : ndarray, (k_constraints, 2) The array has the lower and the upper limit of the confidence interval in the columns. """ se = self.se_obs if obs else self.se_mean q = self.dist.ppf(1 - alpha / 2., *self.dist_args) lower = self.predicted_mean - q * se upper = self.predicted_mean + q * se return np.column_stack((lower, upper)) def summary_frame(self, alpha=0.05): # TODO: finish and cleanup ci_obs = self.conf_int(alpha=alpha, obs=True) # need to split ci_mean = self.conf_int(alpha=alpha, obs=False) to_include = {} to_include['mean'] = self.predicted_mean to_include['mean_se'] = self.se_mean to_include['mean_ci_lower'] = ci_mean[:, 0] to_include['mean_ci_upper'] = ci_mean[:, 1] to_include['obs_ci_lower'] = ci_obs[:, 0] to_include['obs_ci_upper'] = ci_obs[:, 1] self.table = to_include # pandas dict does not handle 2d_array # data = np.column_stack(list(to_include.values())) # names = .... res = pd.DataFrame(to_include, index=self.row_labels, columns=to_include.keys()) return res def get_prediction(self, exog=None, transform=True, weights=None, row_labels=None, pred_kwds=None): """ Compute prediction results. Parameters ---------- exog : array_like, optional The values for which you want to predict. transform : bool, optional If the model was fit via a formula, do you want to pass exog through the formula. Default is True. E.g., if you fit a model y ~ log(x1) + log(x2), and transform is True, then you can pass a data structure that contains x1 and x2 in their original form. Otherwise, you'd need to log the data first. weights : array_like, optional Weights interpreted as in WLS, used for the variance of the predicted residual. row_labels : list A list of row labels to use. If not provided, read `exog` is available. **kwargs Some models can take additional keyword arguments, see the predict method of the model for the details. Returns ------- linear_model.PredictionResults The prediction results instance contains prediction and prediction variance and can on demand calculate confidence intervals and summary tables for the prediction of the mean and of new observations. """ # prepare exog and row_labels, based on base Results.predict if transform and hasattr(self.model, 'formula') and exog is not None: from patsy import dmatrix if isinstance(exog, pd.Series): # GH-6509 exog = pd.DataFrame(exog) exog = dmatrix(self.model.data.design_info, exog) if exog is not None: if row_labels is None: row_labels = getattr(exog, 'index', None) if callable(row_labels): row_labels = None exog = np.asarray(exog) if exog.ndim == 1: # Params informs whether a row or column vector if self.params.shape[0] > 1: exog = exog[None, :] else: exog = exog[:, None] exog = np.atleast_2d(exog) # needed in count model shape[1] else: exog = self.model.exog if weights is None: weights = getattr(self.model, 'weights', None) if row_labels is None: row_labels = getattr(self.model.data, 'row_labels', None) # need to handle other arrays, TODO: is delegating to model possible ? if weights is not None: weights = np.asarray(weights) if (weights.size > 1 and (weights.ndim != 1 or weights.shape[0] == exog.shape[1])): raise ValueError('weights has wrong shape') if pred_kwds is None: pred_kwds = {} predicted_mean = self.model.predict(self.params, exog, **pred_kwds) covb = self.cov_params() var_pred_mean = (exog * np.dot(covb, exog.T).T).sum(1) var_resid = self.scale # self.mse_resid / weights # TODO: check that we have correct scale, Refactor scale #??? # special case for now: if self.cov_type == 'fixed scale': var_resid = self.cov_kwds['scale'] if weights is not None: var_resid /= weights dist = ['norm', 't'][self.use_t] return PredictionResults(predicted_mean, var_pred_mean, var_resid, df=self.df_resid, dist=dist, row_labels=row_labels) statsmodels-0.12.2/statsmodels/regression/_tools.py000066400000000000000000000103661400612667500225460ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch class _MinimalWLS(object): """ Minimal implementation of WLS optimized for performance. Parameters ---------- endog : array_like 1-d endogenous response variable. The dependent variable. exog : array_like A nobs x k array where `nobs` is the number of observations and `k` is the number of regressors. An intercept is not included by default and should be added by the user. See :func:`statsmodels.tools.add_constant`. weights : array_like, optional 1d array of weights. If you supply 1/W then the variables are pre- multiplied by 1/sqrt(W). If no weights are supplied the default value is 1 and WLS reults are the same as OLS. check_endog : bool, optional Flag indicating whether to check for inf/nan in endog. If True and any are found, ValueError is raised. check_weights : bool, optional Flag indicating whether to check for inf/nan in weights. If True and any are found, ValueError is raised. Notes ----- Provides only resid, scale, fittedvalues, model.weights which are used by methods that iteratively apply WLS. Does not perform any checks on the input data for type or shape compatibility """ msg = 'NaN, inf or invalid value detected in {0}, estimation infeasible.' def __init__(self, endog, exog, weights=1.0, check_endog=False, check_weights=False): self.endog = endog self.exog = exog self.weights = weights w_half = np.sqrt(weights) if check_weights: if not np.all(np.isfinite(w_half)): raise ValueError(self.msg.format('weights')) if check_endog: if not np.all(np.isfinite(endog)): raise ValueError(self.msg.format('endog')) self.wendog = w_half * endog if np.isscalar(weights): self.wexog = w_half * exog else: self.wexog = np.asarray(w_half)[:, None] * exog def fit(self, method='pinv'): """ Minimal implementation of WLS optimized for performance. Parameters ---------- method : str, optional Method to use to estimate parameters. "pinv", "qr" or "lstsq" * "pinv" uses the Moore-Penrose pseudoinverse to solve the least squares problem. * "qr" uses the QR factorization. * "lstsq" uses the least squares implementation in numpy.linalg Returns ------- results : namedtuple Named tuple containing the fewest terms needed to implement iterative estimation in models. Currently * params : Estimated parameters * fittedvalues : Fit values using original data * resid : Residuals using original data * model : namedtuple with one field, weights * scale : scale computed using weighted residuals Notes ----- Does not perform and checks on the input data See Also -------- statsmodels.regression.linear_model.WLS """ if method == 'pinv': pinv_wexog = np.linalg.pinv(self.wexog) params = pinv_wexog.dot(self.wendog) elif method == 'qr': Q, R = np.linalg.qr(self.wexog) params = np.linalg.solve(R, np.dot(Q.T, self.wendog)) else: params, _, _, _ = np.linalg.lstsq(self.wexog, self.wendog, rcond=-1) return self.results(params) def results(self, params): """ Construct results params : ndarray Model parameters Notes ----- Allows results to be constructed from either existing parameters or when estimated using using ``fit`` """ fitted_values = self.exog.dot(params) resid = self.endog - fitted_values wresid = self.wendog - self.wexog.dot(params) df_resid = self.wexog.shape[0] - self.wexog.shape[1] scale = np.dot(wresid, wresid) / df_resid return Bunch(params=params, fittedvalues=fitted_values, resid=resid, model=self, scale=scale) statsmodels-0.12.2/statsmodels/regression/dimred.py000066400000000000000000000475671400612667500225300ustar00rootroot00000000000000import warnings import numpy as np import pandas as pd from statsmodels.base import model import statsmodels.base.wrapper as wrap from statsmodels.tools.sm_exceptions import ConvergenceWarning class _DimReductionRegression(model.Model): """ A base class for dimension reduction regression methods. """ def __init__(self, endog, exog, **kwargs): super(_DimReductionRegression, self).__init__(endog, exog, **kwargs) def _prep(self, n_slice): # Sort the data by endog ii = np.argsort(self.endog) x = self.exog[ii, :] # Whiten the data x -= x.mean(0) covx = np.dot(x.T, x) / x.shape[0] covxr = np.linalg.cholesky(covx) x = np.linalg.solve(covxr, x.T).T self.wexog = x self._covxr = covxr # Split the data into slices self._split_wexog = np.array_split(x, n_slice) class SlicedInverseReg(_DimReductionRegression): """ Sliced Inverse Regression (SIR) Parameters ---------- endog : array_like (1d) The dependent variable exog : array_like (2d) The covariates References ---------- KC Li (1991). Sliced inverse regression for dimension reduction. JASA 86, 316-342. """ def fit(self, slice_n=20, **kwargs): """ Estimate the EDR space using Sliced Inverse Regression. Parameters ---------- slice_n : int, optional Target number of observations per slice """ # Sample size per slice if len(kwargs) > 0: msg = "SIR.fit does not take any extra keyword arguments" warnings.warn(msg) # Number of slices n_slice = self.exog.shape[0] // slice_n self._prep(n_slice) mn = [z.mean(0) for z in self._split_wexog] n = [z.shape[0] for z in self._split_wexog] mn = np.asarray(mn) n = np.asarray(n) # Estimate Cov E[X | Y=y] mnc = np.dot(mn.T, n[:, None] * mn) / n.sum() a, b = np.linalg.eigh(mnc) jj = np.argsort(-a) a = a[jj] b = b[:, jj] params = np.linalg.solve(self._covxr.T, b) results = DimReductionResults(self, params, eigs=a) return DimReductionResultsWrapper(results) def _regularized_objective(self, A): # The objective function for regularized SIR p = self.k_vars covx = self._covx mn = self._slice_means ph = self._slice_props v = 0 A = np.reshape(A, (p, self.ndim)) # The penalty for k in range(self.ndim): u = np.dot(self.pen_mat, A[:, k]) v += np.sum(u * u) # The SIR objective function covxa = np.dot(covx, A) q, _ = np.linalg.qr(covxa) qd = np.dot(q, np.dot(q.T, mn.T)) qu = mn.T - qd v += np.dot(ph, (qu * qu).sum(0)) return v def _regularized_grad(self, A): # The gradient of the objective function for regularized SIR p = self.k_vars ndim = self.ndim covx = self._covx n_slice = self.n_slice mn = self._slice_means ph = self._slice_props A = A.reshape((p, ndim)) # Penalty gradient gr = 2 * np.dot(self.pen_mat.T, np.dot(self.pen_mat, A)) A = A.reshape((p, ndim)) covxa = np.dot(covx, A) covx2a = np.dot(covx, covxa) Q = np.dot(covxa.T, covxa) Qi = np.linalg.inv(Q) jm = np.zeros((p, ndim)) qcv = np.linalg.solve(Q, covxa.T) ft = [None] * (p * ndim) for q in range(p): for r in range(ndim): jm *= 0 jm[q, r] = 1 umat = np.dot(covx2a.T, jm) umat += umat.T umat = -np.dot(Qi, np.dot(umat, Qi)) fmat = np.dot(np.dot(covx, jm), qcv) fmat += np.dot(covxa, np.dot(umat, covxa.T)) fmat += np.dot(covxa, np.linalg.solve(Q, np.dot(jm.T, covx))) ft[q*ndim + r] = fmat ch = np.linalg.solve(Q, np.dot(covxa.T, mn.T)) cu = mn - np.dot(covxa, ch).T for i in range(n_slice): u = cu[i, :] v = mn[i, :] for q in range(p): for r in range(ndim): f = np.dot(u, np.dot(ft[q*ndim + r], v)) gr[q, r] -= 2 * ph[i] * f return gr.ravel() def fit_regularized(self, ndim=1, pen_mat=None, slice_n=20, maxiter=100, gtol=1e-3, **kwargs): """ Estimate the EDR space using regularized SIR. Parameters ---------- ndim : int The number of EDR directions to estimate pen_mat : array_like A 2d array such that the squared Frobenius norm of `dot(pen_mat, dirs)`` is added to the objective function, where `dirs` is an orthogonal array whose columns span the estimated EDR space. slice_n : int, optional Target number of observations per slice maxiter :int The maximum number of iterations for estimating the EDR space. gtol : float If the norm of the gradient of the objective function falls below this value, the algorithm has converged. Returns ------- A results class instance. Notes ----- If each row of `exog` can be viewed as containing the values of a function evaluated at equally-spaced locations, then setting the rows of `pen_mat` to [[1, -2, 1, ...], [0, 1, -2, 1, ..], ...] will give smooth EDR coefficients. This is a form of "functional SIR" using the squared second derivative as a penalty. References ---------- L. Ferre, A.F. Yao (2003). Functional sliced inverse regression analysis. Statistics: a journal of theoretical and applied statistics 37(6) 475-488. """ if len(kwargs) > 0: msg = "SIR.fit_regularized does not take keyword arguments" warnings.warn(msg) if pen_mat is None: raise ValueError("pen_mat is a required argument") start_params = kwargs.get("start_params", None) # Sample size per slice slice_n = kwargs.get("slice_n", 20) # Number of slices n_slice = self.exog.shape[0] // slice_n # Sort the data by endog ii = np.argsort(self.endog) x = self.exog[ii, :] x -= x.mean(0) covx = np.cov(x.T) # Split the data into slices split_exog = np.array_split(x, n_slice) mn = [z.mean(0) for z in split_exog] n = [z.shape[0] for z in split_exog] mn = np.asarray(mn) n = np.asarray(n) self._slice_props = n / n.sum() self.ndim = ndim self.k_vars = covx.shape[0] self.pen_mat = pen_mat self._covx = covx self.n_slice = n_slice self._slice_means = mn if start_params is None: params = np.zeros((self.k_vars, ndim)) params[0:ndim, 0:ndim] = np.eye(ndim) params = params else: if start_params.shape[1] != ndim: msg = "Shape of start_params is not compatible with ndim" raise ValueError(msg) params = start_params params, _, cnvrg = _grass_opt(params, self._regularized_objective, self._regularized_grad, maxiter, gtol) if not cnvrg: g = self._regularized_grad(params.ravel()) gn = np.sqrt(np.dot(g, g)) msg = "SIR.fit_regularized did not converge, |g|=%f" % gn warnings.warn(msg) results = DimReductionResults(self, params, eigs=None) return DimReductionResultsWrapper(results) class PrincipalHessianDirections(_DimReductionRegression): """ Principal Hessian Directions (PHD) Parameters ---------- endog : array_like (1d) The dependent variable exog : array_like (2d) The covariates Returns ------- A model instance. Call `fit` to obtain a results instance, from which the estimated parameters can be obtained. References ---------- KC Li (1992). On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another application of Stein's lemma. JASA 87:420. """ def fit(self, **kwargs): """ Estimate the EDR space using PHD. Parameters ---------- resid : bool, optional If True, use least squares regression to remove the linear relationship between each covariate and the response, before conducting PHD. Returns ------- A results instance which can be used to access the estimated parameters. """ resid = kwargs.get("resid", False) y = self.endog - self.endog.mean() x = self.exog - self.exog.mean(0) if resid: from statsmodels.regression.linear_model import OLS r = OLS(y, x).fit() y = r.resid cm = np.einsum('i,ij,ik->jk', y, x, x) cm /= len(y) cx = np.cov(x.T) cb = np.linalg.solve(cx, cm) a, b = np.linalg.eig(cb) jj = np.argsort(-np.abs(a)) a = a[jj] params = b[:, jj] results = DimReductionResults(self, params, eigs=a) return DimReductionResultsWrapper(results) class SlicedAverageVarianceEstimation(_DimReductionRegression): """ Sliced Average Variance Estimation (SAVE) Parameters ---------- endog : array_like (1d) The dependent variable exog : array_like (2d) The covariates bc : bool, optional If True, use the bias-corrected CSAVE method of Li and Zhu. References ---------- RD Cook. SAVE: A method for dimension reduction and graphics in regression. http://www.stat.umn.edu/RegGraph/RecentDev/save.pdf Y Li, L-X Zhu (2007). Asymptotics for sliced average variance estimation. The Annals of Statistics. https://arxiv.org/pdf/0708.0462.pdf """ def __init__(self, endog, exog, **kwargs): super(SAVE, self).__init__(endog, exog, **kwargs) self.bc = False if "bc" in kwargs and kwargs["bc"] is True: self.bc = True def fit(self, **kwargs): """ Estimate the EDR space. Parameters ---------- slice_n : int Number of observations per slice """ # Sample size per slice slice_n = kwargs.get("slice_n", 50) # Number of slices n_slice = self.exog.shape[0] // slice_n self._prep(n_slice) cv = [np.cov(z.T) for z in self._split_wexog] ns = [z.shape[0] for z in self._split_wexog] p = self.wexog.shape[1] if not self.bc: # Cook's original approach vm = 0 for w, cvx in zip(ns, cv): icv = np.eye(p) - cvx vm += w * np.dot(icv, icv) vm /= len(cv) else: # The bias-corrected approach of Li and Zhu # \Lambda_n in Li, Zhu av = 0 for c in cv: av += np.dot(c, c) av /= len(cv) # V_n in Li, Zhu vn = 0 for x in self._split_wexog: r = x - x.mean(0) for i in range(r.shape[0]): u = r[i, :] m = np.outer(u, u) vn += np.dot(m, m) vn /= self.exog.shape[0] c = np.mean(ns) k1 = c * (c - 1) / ((c - 1)**2 + 1) k2 = (c - 1) / ((c - 1)**2 + 1) av2 = k1 * av - k2 * vn vm = np.eye(p) - 2 * sum(cv) / len(cv) + av2 a, b = np.linalg.eigh(vm) jj = np.argsort(-a) a = a[jj] b = b[:, jj] params = np.linalg.solve(self._covxr.T, b) results = DimReductionResults(self, params, eigs=a) return DimReductionResultsWrapper(results) class DimReductionResults(model.Results): """ Results class for a dimension reduction regression. Notes ----- The `params` attribute is a matrix whose columns span the effective dimension reduction (EDR) space. Some methods produce a corresponding set of eigenvalues (`eigs`) that indicate how much information is contained in each basis direction. """ def __init__(self, model, params, eigs): super(DimReductionResults, self).__init__( model, params) self.eigs = eigs class DimReductionResultsWrapper(wrap.ResultsWrapper): _attrs = { 'params': 'columns', } _wrap_attrs = _attrs wrap.populate_wrapper(DimReductionResultsWrapper, # noqa:E305 DimReductionResults) def _grass_opt(params, fun, grad, maxiter, gtol): """ Minimize a function on a Grassmann manifold. Parameters ---------- params : array_like Starting value for the optimization. fun : function The function to be minimized. grad : function The gradient of fun. maxiter : int The maximum number of iterations. gtol : float Convergence occurs when the gradient norm falls below this value. Returns ------- params : array_like The minimizing value for the objective function. fval : float The smallest achieved value of the objective function. cnvrg : bool True if the algorithm converged to a limit point. Notes ----- `params` is 2-d, but `fun` and `grad` should take 1-d arrays `params.ravel()` as arguments. Reference --------- A Edelman, TA Arias, ST Smith (1998). The geometry of algorithms with orthogonality constraints. SIAM J Matrix Anal Appl. http://math.mit.edu/~edelman/publications/geometry_of_algorithms.pdf """ p, d = params.shape params = params.ravel() f0 = fun(params) cnvrg = False for _ in range(maxiter): # Project the gradient to the tangent space g = grad(params) g -= np.dot(g, params) * params / np.dot(params, params) if np.sqrt(np.sum(g * g)) < gtol: cnvrg = True break gm = g.reshape((p, d)) u, s, vt = np.linalg.svd(gm, 0) paramsm = params.reshape((p, d)) pa0 = np.dot(paramsm, vt.T) def geo(t): # Parameterize the geodesic path in the direction # of the gradient as a function of a real value t. pa = pa0 * np.cos(s * t) + u * np.sin(s * t) return np.dot(pa, vt).ravel() # Try to find a downhill step along the geodesic path. step = 2. while step > 1e-10: pa = geo(-step) f1 = fun(pa) if f1 < f0: params = pa f0 = f1 break step /= 2 params = params.reshape((p, d)) return params, f0, cnvrg class CovarianceReduction(_DimReductionRegression): """ Dimension reduction for covariance matrices (CORE). Parameters ---------- endog : array_like The dependent variable, treated as group labels exog : array_like The independent variables. dim : int The dimension of the subspace onto which the covariance matrices are projected. Returns ------- A model instance. Call `fit` on the model instance to obtain a results instance, which contains the fitted model parameters. Notes ----- This is a likelihood-based dimension reduction procedure based on Wishart models for sample covariance matrices. The goal is to find a projection matrix P so that C_i | P'C_iP and C_j | P'C_jP are equal in distribution for all i, j, where the C_i are the within-group covariance matrices. The model and methodology are as described in Cook and Forzani. The optimization method follows Edelman et. al. References ---------- DR Cook, L Forzani (2008). Covariance reducing models: an alternative to spectral modeling of covariance matrices. Biometrika 95:4. A Edelman, TA Arias, ST Smith (1998). The geometry of algorithms with orthogonality constraints. SIAM J Matrix Anal Appl. http://math.mit.edu/~edelman/publications/geometry_of_algorithms.pdf """ def __init__(self, endog, exog, dim): super(CovarianceReduction, self).__init__(endog, exog) covs, ns = [], [] df = pd.DataFrame(self.exog, index=self.endog) for _, v in df.groupby(df.index): covs.append(v.cov().values) ns.append(v.shape[0]) self.nobs = len(endog) # The marginal covariance covm = 0 for i, _ in enumerate(covs): covm += covs[i] * ns[i] covm /= self.nobs self.covm = covm self.covs = covs self.ns = ns self.dim = dim def loglike(self, params): """ Evaluate the log-likelihood Parameters ---------- params : array_like The projection matrix used to reduce the covariances, flattened to 1d. Returns the log-likelihood. """ p = self.covm.shape[0] proj = params.reshape((p, self.dim)) c = np.dot(proj.T, np.dot(self.covm, proj)) _, ldet = np.linalg.slogdet(c) f = self.nobs * ldet / 2 for j, c in enumerate(self.covs): c = np.dot(proj.T, np.dot(c, proj)) _, ldet = np.linalg.slogdet(c) f -= self.ns[j] * ldet / 2 return f def score(self, params): """ Evaluate the score function. Parameters ---------- params : array_like The projection matrix used to reduce the covariances, flattened to 1d. Returns the score function evaluated at 'params'. """ p = self.covm.shape[0] proj = params.reshape((p, self.dim)) c0 = np.dot(proj.T, np.dot(self.covm, proj)) cP = np.dot(self.covm, proj) g = self.nobs * np.linalg.solve(c0, cP.T).T for j, c in enumerate(self.covs): c0 = np.dot(proj.T, np.dot(c, proj)) cP = np.dot(c, proj) g -= self.ns[j] * np.linalg.solve(c0, cP.T).T return g.ravel() def fit(self, start_params=None, maxiter=200, gtol=1e-4): """ Fit the covariance reduction model. Parameters ---------- start_params : array_like Starting value for the projection matrix. May be rectangular, or flattened. maxiter : int The maximum number of gradient steps to take. gtol : float Convergence criterion for the gradient norm. Returns ------- A results instance that can be used to access the fitted parameters. """ p = self.covm.shape[0] d = self.dim # Starting value for params if start_params is None: params = np.zeros((p, d)) params[0:d, 0:d] = np.eye(d) params = params else: params = start_params # _grass_opt is designed for minimization, we are doing maximization # here so everything needs to be flipped. params, llf, cnvrg = _grass_opt(params, lambda x: -self.loglike(x), lambda x: -self.score(x), maxiter, gtol) llf *= -1 if not cnvrg: g = self.score(params.ravel()) gn = np.sqrt(np.sum(g * g)) msg = "CovReduce optimization did not converge, |g|=%f" % gn warnings.warn(msg, ConvergenceWarning) results = DimReductionResults(self, params, eigs=None) results.llf = llf return DimReductionResultsWrapper(results) # aliases for expert users SIR = SlicedInverseReg PHD = PrincipalHessianDirections SAVE = SlicedAverageVarianceEstimation CORE = CovarianceReduction statsmodels-0.12.2/statsmodels/regression/feasible_gls.py000066400000000000000000000155751400612667500236750ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Tue Dec 20 20:24:20 2011 Author: Josef Perktold License: BSD-3 """ import numpy as np from statsmodels.regression.linear_model import OLS, GLS, WLS def atleast_2dcols(x): x = np.asarray(x) if x.ndim == 1: x = x[:,None] return x class GLSHet2(GLS): '''WLS with heteroscedasticity that depends on explanatory variables note: mixing GLS sigma and weights for heteroscedasticity might not make sense I think rewriting following the pattern of GLSAR is better stopping criteria: improve in GLSAR also, e.g. change in rho ''' def __init__(self, endog, exog, exog_var, sigma=None): self.exog_var = atleast_2dcols(exog_var) super(self.__class__, self).__init__(endog, exog, sigma=sigma) def fit(self, lambd=1.): #maybe iterate #preliminary estimate res_gls = GLS(self.endog, self.exog, sigma=self.sigma).fit() res_resid = OLS(res_gls.resid**2, self.exog_var).fit() #or log-link #res_resid = OLS(np.log(res_gls.resid**2), self.exog_var).fit() #here I could use whiten and current instance instead of delegating #but this is easier #see pattern of GLSAR, calls self.initialize and self.fit res_wls = WLS(self.endog, self.exog, weights=1./res_resid.fittedvalues).fit() res_wls._results.results_residual_regression = res_resid return res_wls class GLSHet(WLS): """ A regression model with an estimated heteroscedasticity. A subclass of WLS, that additionally estimates the weight matrix as a function of additional explanatory variables. Parameters ---------- endog : array_like exog : array_like exog_var : array_like, 1d or 2d regressors, explanatory variables for the variance weights : array_like or None If weights are given, then they are used in the first step estimation. link : link function or None If None, then the variance is assumed to be a linear combination of the exog_var. If given, then ... not tested yet *extra attributes* history : dict contains the parameter estimates in both regression for each iteration result instance has results_residual_regression : OLS result instance result of heteroscedasticity estimation except for fit_iterative all methods are inherited from WLS. Notes ----- GLSHet is considered to be experimental. `fit` is just standard WLS fit for fixed weights `fit_iterative` updates the estimate for weights, see its docstring The two alternative for handling heteroscedasticity in the data are to use heteroscedasticity robust standard errors or estimating the heteroscedasticity Estimating heteroscedasticity and using weighted least squares produces smaller confidence intervals for the estimated parameters then the heteroscedasticity robust standard errors if the heteroscedasticity is correctly specified. If the heteroscedasticity is incorrectly specified then the estimated covariance is inconsistent. Stock and Watson for example argue in favor of using OLS with heteroscedasticity robust standard errors instead of GLSHet sind we are seldom sure enough about the correct specification (in economics). GLSHet has asymptotically the same distribution as WLS if the true weights are know. In both cases the asymptotic distribution of the parameter estimates is the normal distribution. The assumption of the model: y = X*beta + u, with E(u) = 0, E(X*u)=0, var(u_i) = z_i*gamma or for vector of all observations Sigma = diag(Z*gamma) where y : endog (nobs) X : exog (nobs, k_vars) Z : exog_var (nobs, k_vars2) beta, gamma estimated parameters If a link is specified, then the heteroscedasticity is var(u_i) = link.inverse(z_i*gamma), or link(var(u_i)) = z_i*gamma for example for log-linkg var(u_i) = exp(z_i*gamma) Usage : see example .... TODO: test link option """ def __init__(self, endog, exog, exog_var=None, weights=None, link=None): self.exog_var = atleast_2dcols(exog_var) if weights is None: weights = np.ones(endog.shape) if link is not None: self.link = link self.linkinv = link.inverse #as defined in families.links else: self.link = lambda x: x #no transformation self.linkinv = lambda x: x super(self.__class__, self).__init__(endog, exog, weights=weights) def iterative_fit(self, maxiter=3): """ Perform an iterative two-step procedure to estimate a WLS model. The model is assumed to have heteroskedastic errors. The variance is estimated by OLS regression of the link transformed squared residuals on Z, i.e.:: link(sigma_i) = x_i*gamma. Parameters ---------- maxiter : int, optional the number of iterations Notes ----- maxiter=1: returns the estimated based on given weights maxiter=2: performs a second estimation with the updated weights, this is 2-step estimation maxiter>2: iteratively estimate and update the weights TODO: possible extension stop iteration if change in parameter estimates is smaller than x_tol Repeated calls to fit_iterative, will do one redundant pinv_wexog calculation. Calling fit_iterative(maxiter) ones does not do any redundant recalculations (whitening or calculating pinv_wexog). """ import collections self.history = collections.defaultdict(list) #not really necessary res_resid = None #if maxiter < 2 no updating for i in range(maxiter): #pinv_wexog is cached if hasattr(self, 'pinv_wexog'): del self.pinv_wexog #self.initialize() #print 'wls self', results = self.fit() self.history['self_params'].append(results.params) if not i == maxiter-1: #skip for last iteration, could break instead #print 'ols', self.results_old = results #for debugging #estimate heteroscedasticity res_resid = OLS(self.link(results.resid**2), self.exog_var).fit() self.history['ols_params'].append(res_resid.params) #update weights self.weights = 1./self.linkinv(res_resid.fittedvalues) self.weights /= self.weights.max() #not required self.weights[self.weights < 1e-14] = 1e-14 #clip #print 'in iter', i, self.weights.var() #debug, do weights change self.initialize() #note results is the wrapper, results._results is the results instance results._results.results_residual_regression = res_resid return results statsmodels-0.12.2/statsmodels/regression/linear_model.py000066400000000000000000003354441400612667500237100ustar00rootroot00000000000000# TODO: Determine which tests are valid for GLSAR, and under what conditions # TODO: Fix issue with constant and GLS # TODO: GLS: add options Iterative GLS, for iterative fgls if sigma is None # TODO: GLS: default if sigma is none should be two-step GLS # TODO: Check nesting when performing model based tests, lr, wald, lm """ This module implements standard regression models: Generalized Least Squares (GLS) Ordinary Least Squares (OLS) Weighted Least Squares (WLS) Generalized Least Squares with autoregressive error terms GLSAR(p) Models are specified with an endogenous response variable and an exogenous design matrix and are fit using their `fit` method. Subclasses that have more complicated covariance matrices should write over the 'whiten' method as the fit method prewhitens the response by calling 'whiten'. General reference for regression models: D. C. Montgomery and E.A. Peck. "Introduction to Linear Regression Analysis." 2nd. Ed., Wiley, 1992. Econometrics references for regression models: R. Davidson and J.G. MacKinnon. "Econometric Theory and Methods," Oxford, 2004. W. Green. "Econometric Analysis," 5th ed., Pearson, 2003. """ from statsmodels.compat.python import lrange, lzip from statsmodels.compat.pandas import Appender import numpy as np from scipy.linalg import toeplitz from scipy import stats from scipy import optimize from statsmodels.tools.tools import pinv_extended from statsmodels.tools.decorators import (cache_readonly, cache_writable) import statsmodels.base.model as base import statsmodels.base.wrapper as wrap from statsmodels.emplike.elregress import _ELRegOpts import warnings from statsmodels.tools.sm_exceptions import InvalidTestWarning from statsmodels.tools.validation import string_like # need import in module instead of lazily to copy `__doc__` from statsmodels.regression._prediction import PredictionResults from . import _prediction as pred __docformat__ = 'restructuredtext en' __all__ = ['GLS', 'WLS', 'OLS', 'GLSAR', 'PredictionResults', 'RegressionResultsWrapper'] _fit_regularized_doc =\ r""" Return a regularized fit to a linear regression model. Parameters ---------- method : str Either 'elastic_net' or 'sqrt_lasso'. alpha : scalar or array_like The penalty weight. If a scalar, the same penalty weight applies to all variables in the model. If a vector, it must have the same length as `params`, and contains a penalty weight for each coefficient. L1_wt : scalar The fraction of the penalty given to the L1 penalty term. Must be between 0 and 1 (inclusive). If 0, the fit is a ridge fit, if 1 it is a lasso fit. start_params : array_like Starting values for ``params``. profile_scale : bool If True the penalized fit is computed using the profile (concentrated) log-likelihood for the Gaussian model. Otherwise the fit uses the residual sum of squares. refit : bool If True, the model is refit using only the variables that have non-zero coefficients in the regularized fit. The refitted model is not regularized. **kwargs Additional keyword arguments that contain information used when constructing a model using the formula interface. Returns ------- statsmodels.base.elastic_net.RegularizedResults The regularized results. Notes ----- The elastic net uses a combination of L1 and L2 penalties. The implementation closely follows the glmnet package in R. The function that is minimized is: .. math:: 0.5*RSS/n + alpha*((1-L1\_wt)*|params|_2^2/2 + L1\_wt*|params|_1) where RSS is the usual regression sum of squares, n is the sample size, and :math:`|*|_1` and :math:`|*|_2` are the L1 and L2 norms. For WLS and GLS, the RSS is calculated using the whitened endog and exog data. Post-estimation results are based on the same data used to select variables, hence may be subject to overfitting biases. The elastic_net method uses the following keyword arguments: maxiter : int Maximum number of iterations cnvrg_tol : float Convergence threshold for line searches zero_tol : float Coefficients below this threshold are treated as zero. The square root lasso approach is a variation of the Lasso that is largely self-tuning (the optimal tuning parameter does not depend on the standard deviation of the regression errors). If the errors are Gaussian, the tuning parameter can be taken to be alpha = 1.1 * np.sqrt(n) * norm.ppf(1 - 0.05 / (2 * p)) where n is the sample size and p is the number of predictors. The square root lasso uses the following keyword arguments: zero_tol : float Coefficients below this threshold are treated as zero. The cvxopt module is required to estimate model using the square root lasso. References ---------- .. [*] Friedman, Hastie, Tibshirani (2008). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software 33(1), 1-22 Feb 2010. .. [*] A Belloni, V Chernozhukov, L Wang (2011). Square-root Lasso: pivotal recovery of sparse signals via conic programming. Biometrika 98(4), 791-806. https://arxiv.org/pdf/1009.5689.pdf """ def _get_sigma(sigma, nobs): """ Returns sigma (matrix, nobs by nobs) for GLS and the inverse of its Cholesky decomposition. Handles dimensions and checks integrity. If sigma is None, returns None, None. Otherwise returns sigma, cholsigmainv. """ if sigma is None: return None, None sigma = np.asarray(sigma).squeeze() if sigma.ndim == 0: sigma = np.repeat(sigma, nobs) if sigma.ndim == 1: if sigma.shape != (nobs,): raise ValueError("Sigma must be a scalar, 1d of length %s or a 2d " "array of shape %s x %s" % (nobs, nobs, nobs)) cholsigmainv = 1/np.sqrt(sigma) else: if sigma.shape != (nobs, nobs): raise ValueError("Sigma must be a scalar, 1d of length %s or a 2d " "array of shape %s x %s" % (nobs, nobs, nobs)) cholsigmainv = np.linalg.cholesky(np.linalg.inv(sigma)).T return sigma, cholsigmainv class RegressionModel(base.LikelihoodModel): """ Base class for linear regression models. Should not be directly called. Intended for subclassing. """ def __init__(self, endog, exog, **kwargs): super(RegressionModel, self).__init__(endog, exog, **kwargs) self._data_attr.extend(['pinv_wexog', 'weights']) def initialize(self): """Initialize model components.""" self.wexog = self.whiten(self.exog) self.wendog = self.whiten(self.endog) # overwrite nobs from class Model: self.nobs = float(self.wexog.shape[0]) self._df_model = None self._df_resid = None self.rank = None @property def df_model(self): """ The model degree of freedom. The dof is defined as the rank of the regressor matrix minus 1 if a constant is included. """ if self._df_model is None: if self.rank is None: self.rank = np.linalg.matrix_rank(self.exog) self._df_model = float(self.rank - self.k_constant) return self._df_model @df_model.setter def df_model(self, value): self._df_model = value @property def df_resid(self): """ The residual degree of freedom. The dof is defined as the number of observations minus the rank of the regressor matrix. """ if self._df_resid is None: if self.rank is None: self.rank = np.linalg.matrix_rank(self.exog) self._df_resid = self.nobs - self.rank return self._df_resid @df_resid.setter def df_resid(self, value): self._df_resid = value def whiten(self, x): """ Whiten method that must be overwritten by individual models. Parameters ---------- x : array_like Data to be whitened. """ raise NotImplementedError("Subclasses must implement.") def fit(self, method="pinv", cov_type='nonrobust', cov_kwds=None, use_t=None, **kwargs): """ Full fit of the model. The results include an estimate of covariance matrix, (whitened) residuals and an estimate of scale. Parameters ---------- method : str, optional Can be "pinv", "qr". "pinv" uses the Moore-Penrose pseudoinverse to solve the least squares problem. "qr" uses the QR factorization. cov_type : str, optional See `regression.linear_model.RegressionResults` for a description of the available covariance estimators. cov_kwds : list or None, optional See `linear_model.RegressionResults.get_robustcov_results` for a description required keywords for alternative covariance estimators. use_t : bool, optional Flag indicating to use the Student's t distribution when computing p-values. Default behavior depends on cov_type. See `linear_model.RegressionResults.get_robustcov_results` for implementation details. **kwargs Additional keyword arguments that contain information used when constructing a model using the formula interface. Returns ------- RegressionResults The model estimation results. See Also -------- RegressionResults The results container. RegressionResults.get_robustcov_results A method to change the covariance estimator used when fitting the model. Notes ----- The fit method uses the pseudoinverse of the design/exogenous variables to solve the least squares minimization. """ if method == "pinv": if not (hasattr(self, 'pinv_wexog') and hasattr(self, 'normalized_cov_params') and hasattr(self, 'rank')): self.pinv_wexog, singular_values = pinv_extended(self.wexog) self.normalized_cov_params = np.dot( self.pinv_wexog, np.transpose(self.pinv_wexog)) # Cache these singular values for use later. self.wexog_singular_values = singular_values self.rank = np.linalg.matrix_rank(np.diag(singular_values)) beta = np.dot(self.pinv_wexog, self.wendog) elif method == "qr": if not (hasattr(self, 'exog_Q') and hasattr(self, 'exog_R') and hasattr(self, 'normalized_cov_params') and hasattr(self, 'rank')): Q, R = np.linalg.qr(self.wexog) self.exog_Q, self.exog_R = Q, R self.normalized_cov_params = np.linalg.inv(np.dot(R.T, R)) # Cache singular values from R. self.wexog_singular_values = np.linalg.svd(R, 0, 0) self.rank = np.linalg.matrix_rank(R) else: Q, R = self.exog_Q, self.exog_R # used in ANOVA self.effects = effects = np.dot(Q.T, self.wendog) beta = np.linalg.solve(R, effects) else: raise ValueError('method has to be "pinv" or "qr"') if self._df_model is None: self._df_model = float(self.rank - self.k_constant) if self._df_resid is None: self.df_resid = self.nobs - self.rank if isinstance(self, OLS): lfit = OLSResults( self, beta, normalized_cov_params=self.normalized_cov_params, cov_type=cov_type, cov_kwds=cov_kwds, use_t=use_t) else: lfit = RegressionResults( self, beta, normalized_cov_params=self.normalized_cov_params, cov_type=cov_type, cov_kwds=cov_kwds, use_t=use_t, **kwargs) return RegressionResultsWrapper(lfit) def predict(self, params, exog=None): """ Return linear predicted values from a design matrix. Parameters ---------- params : array_like Parameters of a linear model. exog : array_like, optional Design / exogenous data. Model exog is used if None. Returns ------- array_like An array of fitted values. Notes ----- If the model has not yet been fit, params is not optional. """ # JP: this does not look correct for GLMAR # SS: it needs its own predict method if exog is None: exog = self.exog return np.dot(exog, params) def get_distribution(self, params, scale, exog=None, dist_class=None): """ Construct a random number generator for the predictive distribution. Parameters ---------- params : array_like The model parameters (regression coefficients). scale : scalar The variance parameter. exog : array_like The predictor variable matrix. dist_class : class A random number generator class. Must take 'loc' and 'scale' as arguments and return a random number generator implementing an ``rvs`` method for simulating random values. Defaults to normal. Returns ------- gen Frozen random number generator object with mean and variance determined by the fitted linear model. Use the ``rvs`` method to generate random values. Notes ----- Due to the behavior of ``scipy.stats.distributions objects``, the returned random number generator must be called with ``gen.rvs(n)`` where ``n`` is the number of observations in the data set used to fit the model. If any other value is used for ``n``, misleading results will be produced. """ fit = self.predict(params, exog) if dist_class is None: from scipy.stats.distributions import norm dist_class = norm gen = dist_class(loc=fit, scale=np.sqrt(scale)) return gen class GLS(RegressionModel): __doc__ = r""" Generalized Least Squares %(params)s sigma : scalar or array The array or scalar `sigma` is the weighting matrix of the covariance. The default is None for no scaling. If `sigma` is a scalar, it is assumed that `sigma` is an n x n diagonal matrix with the given scalar, `sigma` as the value of each diagonal element. If `sigma` is an n-length vector, then `sigma` is assumed to be a diagonal matrix with the given `sigma` on the diagonal. This should be the same as WLS. %(extra_params)s Attributes ---------- pinv_wexog : ndarray `pinv_wexog` is the p x n Moore-Penrose pseudoinverse of `wexog`. cholsimgainv : ndarray The transpose of the Cholesky decomposition of the pseudoinverse. df_model : float p - 1, where p is the number of regressors including the intercept. of freedom. df_resid : float Number of observations n less the number of parameters p. llf : float The value of the likelihood function of the fitted model. nobs : float The number of observations n. normalized_cov_params : ndarray p x p array :math:`(X^{T}\Sigma^{-1}X)^{-1}` results : RegressionResults instance A property that returns the RegressionResults class if fit. sigma : ndarray `sigma` is the n x n covariance structure of the error terms. wexog : ndarray Design matrix whitened by `cholsigmainv` wendog : ndarray Response variable whitened by `cholsigmainv` See Also -------- WLS : Fit a linear model using Weighted Least Squares. OLS : Fit a linear model using Ordinary Least Squares. Notes ----- If sigma is a function of the data making one of the regressors a constant, then the current postestimation statistics will not be correct. Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.longley.load(as_pandas=False) >>> data.exog = sm.add_constant(data.exog) >>> ols_resid = sm.OLS(data.endog, data.exog).fit().resid >>> res_fit = sm.OLS(ols_resid[1:], ols_resid[:-1]).fit() >>> rho = res_fit.params `rho` is a consistent estimator of the correlation of the residuals from an OLS fit of the longley data. It is assumed that this is the true rho of the AR process data. >>> from scipy.linalg import toeplitz >>> order = toeplitz(np.arange(16)) >>> sigma = rho**order `sigma` is an n x n matrix of the autocorrelation structure of the data. >>> gls_model = sm.GLS(data.endog, data.exog, sigma=sigma) >>> gls_results = gls_model.fit() >>> print(gls_results.summary()) """ % {'params': base._model_params_doc, 'extra_params': base._missing_param_doc + base._extra_param_doc} def __init__(self, endog, exog, sigma=None, missing='none', hasconst=None, **kwargs): # TODO: add options igls, for iterative fgls if sigma is None # TODO: default if sigma is none should be two-step GLS sigma, cholsigmainv = _get_sigma(sigma, len(endog)) super(GLS, self).__init__(endog, exog, missing=missing, hasconst=hasconst, sigma=sigma, cholsigmainv=cholsigmainv, **kwargs) # store attribute names for data arrays self._data_attr.extend(['sigma', 'cholsigmainv']) def whiten(self, x): """ GLS whiten method. Parameters ---------- x : array_like Data to be whitened. Returns ------- ndarray The value np.dot(cholsigmainv,X). See Also -------- GLS : Fit a linear model using Generalized Least Squares. """ x = np.asarray(x) if self.sigma is None or self.sigma.shape == (): return x elif self.sigma.ndim == 1: if x.ndim == 1: return x * self.cholsigmainv else: return x * self.cholsigmainv[:, None] else: return np.dot(self.cholsigmainv, x) def loglike(self, params): r""" Compute the value of the Gaussian log-likelihood function at params. Given the whitened design matrix, the log-likelihood is evaluated at the parameter vector `params` for the dependent variable `endog`. Parameters ---------- params : array_like The model parameters. Returns ------- float The value of the log-likelihood function for a GLS Model. Notes ----- The log-likelihood function for the normal distribution is .. math:: -\frac{n}{2}\log\left(\left(Y-\hat{Y}\right)^{\prime} \left(Y-\hat{Y}\right)\right) -\frac{n}{2}\left(1+\log\left(\frac{2\pi}{n}\right)\right) -\frac{1}{2}\log\left(\left|\Sigma\right|\right) Y and Y-hat are whitened. """ # TODO: combine this with OLS/WLS loglike and add _det_sigma argument nobs2 = self.nobs / 2.0 SSR = np.sum((self.wendog - np.dot(self.wexog, params))**2, axis=0) llf = -np.log(SSR) * nobs2 # concentrated likelihood llf -= (1+np.log(np.pi/nobs2))*nobs2 # with likelihood constant if np.any(self.sigma): # FIXME: robust-enough check? unneeded if _det_sigma gets defined if self.sigma.ndim == 2: det = np.linalg.slogdet(self.sigma) llf -= .5*det[1] else: llf -= 0.5*np.sum(np.log(self.sigma)) # with error covariance matrix return llf def hessian_factor(self, params, scale=None, observed=True): """ Compute weights for calculating Hessian. Parameters ---------- params : ndarray The parameter at which Hessian is evaluated. scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. observed : bool If True, then the observed Hessian is returned. If false then the expected information matrix is returned. Returns ------- ndarray A 1d weight vector used in the calculation of the Hessian. The hessian is obtained by `(exog.T * hessian_factor).dot(exog)`. """ if self.sigma is None or self.sigma.shape == (): return np.ones(self.exog.shape[0]) elif self.sigma.ndim == 1: return self.cholsigmainv else: return np.diag(self.cholsigmainv) @Appender(_fit_regularized_doc) def fit_regularized(self, method="elastic_net", alpha=0., L1_wt=1., start_params=None, profile_scale=False, refit=False, **kwargs): if not np.isscalar(alpha): alpha = np.asarray(alpha) # Need to adjust since RSS/n term in elastic net uses nominal # n in denominator if self.sigma is not None: alpha = alpha * np.sum(1 / np.diag(self.sigma)) / len(self.endog) rslt = OLS(self.wendog, self.wexog).fit_regularized( method=method, alpha=alpha, L1_wt=L1_wt, start_params=start_params, profile_scale=profile_scale, refit=refit, **kwargs) from statsmodels.base.elastic_net import ( RegularizedResults, RegularizedResultsWrapper) rrslt = RegularizedResults(self, rslt.params) return RegularizedResultsWrapper(rrslt) class WLS(RegressionModel): __doc__ = """ Weighted Least Squares The weights are presumed to be (proportional to) the inverse of the variance of the observations. That is, if the variables are to be transformed by 1/sqrt(W) you must supply weights = 1/W. %(params)s weights : array_like, optional A 1d array of weights. If you supply 1/W then the variables are pre- multiplied by 1/sqrt(W). If no weights are supplied the default value is 1 and WLS results are the same as OLS. %(extra_params)s Attributes ---------- weights : ndarray The stored weights supplied as an argument. See Also -------- GLS : Fit a linear model using Generalized Least Squares. OLS : Fit a linear model using Ordinary Least Squares. Notes ----- If the weights are a function of the data, then the post estimation statistics such as fvalue and mse_model might not be correct, as the package does not yet support no-constant regression. Examples -------- >>> import statsmodels.api as sm >>> Y = [1,3,4,5,2,3,4] >>> X = range(1,8) >>> X = sm.add_constant(X) >>> wls_model = sm.WLS(Y,X, weights=list(range(1,8))) >>> results = wls_model.fit() >>> results.params array([ 2.91666667, 0.0952381 ]) >>> results.tvalues array([ 2.0652652 , 0.35684428]) >>> print(results.t_test([1, 0])) >>> print(results.f_test([0, 1])) """ % {'params': base._model_params_doc, 'extra_params': base._missing_param_doc + base._extra_param_doc} def __init__(self, endog, exog, weights=1., missing='none', hasconst=None, **kwargs): weights = np.array(weights) if weights.shape == (): if (missing == 'drop' and 'missing_idx' in kwargs and kwargs['missing_idx'] is not None): # patsy may have truncated endog weights = np.repeat(weights, len(kwargs['missing_idx'])) else: weights = np.repeat(weights, len(endog)) # handle case that endog might be of len == 1 if len(weights) == 1: weights = np.array([weights.squeeze()]) else: weights = weights.squeeze() super(WLS, self).__init__(endog, exog, missing=missing, weights=weights, hasconst=hasconst, **kwargs) nobs = self.exog.shape[0] weights = self.weights # Experimental normalization of weights weights = weights / np.sum(weights) * nobs if weights.size != nobs and weights.shape[0] != nobs: raise ValueError('Weights must be scalar or same length as design') def whiten(self, x): """ Whitener for WLS model, multiplies each column by sqrt(self.weights). Parameters ---------- x : array_like Data to be whitened. Returns ------- array_like The whitened values sqrt(weights)*X. """ x = np.asarray(x) if x.ndim == 1: return x * np.sqrt(self.weights) elif x.ndim == 2: return np.sqrt(self.weights)[:, None] * x def loglike(self, params): r""" Compute the value of the gaussian log-likelihood function at params. Given the whitened design matrix, the log-likelihood is evaluated at the parameter vector `params` for the dependent variable `Y`. Parameters ---------- params : array_like The parameter estimates. Returns ------- float The value of the log-likelihood function for a WLS Model. Notes -------- .. math:: -\frac{n}{2}\log SSR -\frac{n}{2}\left(1+\log\left(\frac{2\pi}{n}\right)\right) -\frac{1}{2}\log\left(\left|W\right|\right) where :math:`W` is a diagonal weight matrix matrix and :math:`SSR=\left(Y-\hat{Y}\right)^\prime W \left(Y-\hat{Y}\right)` is the sum of the squared weighted residuals. """ nobs2 = self.nobs / 2.0 SSR = np.sum((self.wendog - np.dot(self.wexog, params))**2, axis=0) llf = -np.log(SSR) * nobs2 # concentrated likelihood llf -= (1+np.log(np.pi/nobs2))*nobs2 # with constant llf += 0.5 * np.sum(np.log(self.weights)) return llf def hessian_factor(self, params, scale=None, observed=True): """ Compute the weights for calculating the Hessian. Parameters ---------- params : ndarray The parameter at which Hessian is evaluated. scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. observed : bool If True, then the observed Hessian is returned. If false then the expected information matrix is returned. Returns ------- ndarray A 1d weight vector used in the calculation of the Hessian. The hessian is obtained by `(exog.T * hessian_factor).dot(exog)`. """ return self.weights @Appender(_fit_regularized_doc) def fit_regularized(self, method="elastic_net", alpha=0., L1_wt=1., start_params=None, profile_scale=False, refit=False, **kwargs): # Docstring attached below if not np.isscalar(alpha): alpha = np.asarray(alpha) # Need to adjust since RSS/n in elastic net uses nominal n in # denominator alpha = alpha * np.sum(self.weights) / len(self.weights) rslt = OLS(self.wendog, self.wexog).fit_regularized( method=method, alpha=alpha, L1_wt=L1_wt, start_params=start_params, profile_scale=profile_scale, refit=refit, **kwargs) from statsmodels.base.elastic_net import ( RegularizedResults, RegularizedResultsWrapper) rrslt = RegularizedResults(self, rslt.params) return RegularizedResultsWrapper(rrslt) class OLS(WLS): __doc__ = """ Ordinary Least Squares %(params)s %(extra_params)s Attributes ---------- weights : scalar Has an attribute weights = array(1.0) due to inheritance from WLS. See Also -------- WLS : Fit a linear model using Weighted Least Squares. GLS : Fit a linear model using Generalized Least Squares. Notes ----- No constant is added by the model unless you are using formulas. Examples -------- >>> import statsmodels.api as sm >>> import numpy as np >>> duncan_prestige = sm.datasets.get_rdataset("Duncan", "carData") >>> Y = duncan_prestige.data['income'] >>> X = duncan_prestige.data['education'] >>> X = sm.add_constant(X) >>> model = sm.OLS(Y,X) >>> results = model.fit() >>> results.params const 10.603498 education 0.594859 dtype: float64 >>> results.tvalues const 2.039813 education 6.892802 dtype: float64 >>> print(results.t_test([1, 0])) Test for Constraints ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ c0 10.6035 5.198 2.040 0.048 0.120 21.087 ============================================================================== >>> print(results.f_test(np.identity(2))) """ % {'params': base._model_params_doc, 'extra_params': base._missing_param_doc + base._extra_param_doc} def __init__(self, endog, exog=None, missing='none', hasconst=None, **kwargs): super(OLS, self).__init__(endog, exog, missing=missing, hasconst=hasconst, **kwargs) if "weights" in self._init_keys: self._init_keys.remove("weights") def loglike(self, params, scale=None): """ The likelihood function for the OLS model. Parameters ---------- params : array_like The coefficients with which to estimate the log-likelihood. scale : float or None If None, return the profile (concentrated) log likelihood (profiled over the scale parameter), else return the log-likelihood using the given scale value. Returns ------- float The likelihood function evaluated at params. """ nobs2 = self.nobs / 2.0 nobs = float(self.nobs) resid = self.endog - np.dot(self.exog, params) if hasattr(self, 'offset'): resid -= self.offset ssr = np.sum(resid**2) if scale is None: # profile log likelihood llf = -nobs2*np.log(2*np.pi) - nobs2*np.log(ssr / nobs) - nobs2 else: # log-likelihood llf = -nobs2 * np.log(2 * np.pi * scale) - ssr / (2*scale) return llf def whiten(self, x): """ OLS model whitener does nothing. Parameters ---------- x : array_like Data to be whitened. Returns ------- array_like The input array unmodified. See Also -------- OLS : Fit a linear model using Ordinary Least Squares. """ return x def score(self, params, scale=None): """ Evaluate the score function at a given point. The score corresponds to the profile (concentrated) log-likelihood in which the scale parameter has been profiled out. Parameters ---------- params : array_like The parameter vector at which the score function is computed. scale : float or None If None, return the profile (concentrated) log likelihood (profiled over the scale parameter), else return the log-likelihood using the given scale value. Returns ------- ndarray The score vector. """ if not hasattr(self, "_wexog_xprod"): self._setup_score_hess() xtxb = np.dot(self._wexog_xprod, params) sdr = -self._wexog_x_wendog + xtxb if scale is None: ssr = self._wendog_xprod - 2 * np.dot(self._wexog_x_wendog.T, params) ssr += np.dot(params, xtxb) return -self.nobs * sdr / ssr else: return -sdr / scale def _setup_score_hess(self): y = self.wendog if hasattr(self, 'offset'): y = y - self.offset self._wendog_xprod = np.sum(y * y) self._wexog_xprod = np.dot(self.wexog.T, self.wexog) self._wexog_x_wendog = np.dot(self.wexog.T, y) def hessian(self, params, scale=None): """ Evaluate the Hessian function at a given point. Parameters ---------- params : array_like The parameter vector at which the Hessian is computed. scale : float or None If None, return the profile (concentrated) log likelihood (profiled over the scale parameter), else return the log-likelihood using the given scale value. Returns ------- ndarray The Hessian matrix. """ if not hasattr(self, "_wexog_xprod"): self._setup_score_hess() xtxb = np.dot(self._wexog_xprod, params) if scale is None: ssr = self._wendog_xprod - 2 * np.dot(self._wexog_x_wendog.T, params) ssr += np.dot(params, xtxb) ssrp = -2*self._wexog_x_wendog + 2*xtxb hm = self._wexog_xprod / ssr - np.outer(ssrp, ssrp) / ssr**2 return -self.nobs * hm / 2 else: return -self._wexog_xprod / scale def hessian_factor(self, params, scale=None, observed=True): """ Calculate the weights for the Hessian. Parameters ---------- params : ndarray The parameter at which Hessian is evaluated. scale : None or float If scale is None, then the default scale will be calculated. Default scale is defined by `self.scaletype` and set in fit. If scale is not None, then it is used as a fixed scale. observed : bool If True, then the observed Hessian is returned. If false then the expected information matrix is returned. Returns ------- ndarray A 1d weight vector used in the calculation of the Hessian. The hessian is obtained by `(exog.T * hessian_factor).dot(exog)`. """ return np.ones(self.exog.shape[0]) @Appender(_fit_regularized_doc) def fit_regularized(self, method="elastic_net", alpha=0., L1_wt=1., start_params=None, profile_scale=False, refit=False, **kwargs): # In the future we could add support for other penalties, e.g. SCAD. if method not in ("elastic_net", "sqrt_lasso"): msg = "Unknown method '%s' for fit_regularized" % method raise ValueError(msg) # Set default parameters. defaults = {"maxiter": 50, "cnvrg_tol": 1e-10, "zero_tol": 1e-8} defaults.update(kwargs) if method == "sqrt_lasso": from statsmodels.base.elastic_net import ( RegularizedResults, RegularizedResultsWrapper ) params = self._sqrt_lasso(alpha, refit, defaults["zero_tol"]) results = RegularizedResults(self, params) return RegularizedResultsWrapper(results) from statsmodels.base.elastic_net import fit_elasticnet if L1_wt == 0: return self._fit_ridge(alpha) # If a scale parameter is passed in, the non-profile # likelihood (residual sum of squares divided by -2) is used, # otherwise the profile likelihood is used. if profile_scale: loglike_kwds = {} score_kwds = {} hess_kwds = {} else: loglike_kwds = {"scale": 1} score_kwds = {"scale": 1} hess_kwds = {"scale": 1} return fit_elasticnet(self, method=method, alpha=alpha, L1_wt=L1_wt, start_params=start_params, loglike_kwds=loglike_kwds, score_kwds=score_kwds, hess_kwds=hess_kwds, refit=refit, check_step=False, **defaults) def _sqrt_lasso(self, alpha, refit, zero_tol): try: import cvxopt except ImportError: msg = 'sqrt_lasso fitting requires the cvxopt module' raise ValueError(msg) n = len(self.endog) p = self.exog.shape[1] h0 = cvxopt.matrix(0., (2*p+1, 1)) h1 = cvxopt.matrix(0., (n+1, 1)) h1[1:, 0] = cvxopt.matrix(self.endog, (n, 1)) G0 = cvxopt.spmatrix([], [], [], (2*p+1, 2*p+1)) for i in range(1, 2*p+1): G0[i, i] = -1 G1 = cvxopt.matrix(0., (n+1, 2*p+1)) G1[0, 0] = -1 G1[1:, 1:p+1] = self.exog G1[1:, p+1:] = -self.exog c = cvxopt.matrix(alpha / n, (2*p + 1, 1)) c[0] = 1 / np.sqrt(n) from cvxopt import solvers solvers.options["show_progress"] = False rslt = solvers.socp(c, Gl=G0, hl=h0, Gq=[G1], hq=[h1]) x = np.asarray(rslt['x']).flat bp = x[1:p+1] bn = x[p+1:] params = bp - bn if not refit: return params ii = np.flatnonzero(np.abs(params) > zero_tol) rfr = OLS(self.endog, self.exog[:, ii]).fit() params *= 0 params[ii] = rfr.params return params def _fit_ridge(self, alpha): """ Fit a linear model using ridge regression. Parameters ---------- alpha : scalar or array_like The penalty weight. If a scalar, the same penalty weight applies to all variables in the model. If a vector, it must have the same length as `params`, and contains a penalty weight for each coefficient. Notes ----- Equivalent to fit_regularized with L1_wt = 0 (but implemented more efficiently). """ u, s, vt = np.linalg.svd(self.exog, 0) v = vt.T q = np.dot(u.T, self.endog) * s s2 = s * s if np.isscalar(alpha): sd = s2 + alpha * self.nobs params = q / sd params = np.dot(v, params) else: alpha = np.asarray(alpha) vtav = self.nobs * np.dot(vt, alpha[:, None] * v) d = np.diag(vtav) + s2 np.fill_diagonal(vtav, d) r = np.linalg.solve(vtav, q) params = np.dot(v, r) from statsmodels.base.elastic_net import RegularizedResults return RegularizedResults(self, params) class GLSAR(GLS): __doc__ = """ Generalized Least Squares with AR covariance structure %(params)s rho : int The order of the autoregressive covariance. %(extra_params)s Notes ----- GLSAR is considered to be experimental. The linear autoregressive process of order p--AR(p)--is defined as: TODO Examples -------- >>> import statsmodels.api as sm >>> X = range(1,8) >>> X = sm.add_constant(X) >>> Y = [1,3,4,5,8,10,9] >>> model = sm.GLSAR(Y, X, rho=2) >>> for i in range(6): ... results = model.fit() ... print("AR coefficients: {0}".format(model.rho)) ... rho, sigma = sm.regression.yule_walker(results.resid, ... order=model.order) ... model = sm.GLSAR(Y, X, rho) ... AR coefficients: [ 0. 0.] AR coefficients: [-0.52571491 -0.84496178] AR coefficients: [-0.6104153 -0.86656458] AR coefficients: [-0.60439494 -0.857867 ] AR coefficients: [-0.6048218 -0.85846157] AR coefficients: [-0.60479146 -0.85841922] >>> results.params array([-0.66661205, 1.60850853]) >>> results.tvalues array([ -2.10304127, 21.8047269 ]) >>> print(results.t_test([1, 0])) >>> print(results.f_test(np.identity(2))) Or, equivalently >>> model2 = sm.GLSAR(Y, X, rho=2) >>> res = model2.iterative_fit(maxiter=6) >>> model2.rho array([-0.60479146, -0.85841922]) """ % {'params': base._model_params_doc, 'extra_params': base._missing_param_doc + base._extra_param_doc} # TODO: Complete docstring def __init__(self, endog, exog=None, rho=1, missing='none', hasconst=None, **kwargs): # this looks strange, interpreting rho as order if it is int if isinstance(rho, (int, np.integer)): self.order = int(rho) self.rho = np.zeros(self.order, np.float64) else: self.rho = np.squeeze(np.asarray(rho)) if len(self.rho.shape) not in [0, 1]: raise ValueError("AR parameters must be a scalar or a vector") if self.rho.shape == (): self.rho.shape = (1,) self.order = self.rho.shape[0] if exog is None: # JP this looks wrong, should be a regression on constant # results for rho estimate now identical to yule-walker on y # super(AR, self).__init__(endog, add_constant(endog)) super(GLSAR, self).__init__(endog, np.ones((endog.shape[0], 1)), missing=missing, hasconst=None, **kwargs) else: super(GLSAR, self).__init__(endog, exog, missing=missing, **kwargs) def iterative_fit(self, maxiter=3, rtol=1e-4, **kwargs): """ Perform an iterative two-stage procedure to estimate a GLS model. The model is assumed to have AR(p) errors, AR(p) parameters and regression coefficients are estimated iteratively. Parameters ---------- maxiter : int, optional The number of iterations. rtol : float, optional Relative tolerance between estimated coefficients to stop the estimation. Stops if max(abs(last - current) / abs(last)) < rtol. **kwargs Additional keyword arguments passed to `fit`. Returns ------- RegressionResults The results computed using an iterative fit. """ # TODO: update this after going through example. converged = False i = -1 # need to initialize for maxiter < 1 (skip loop) history = {'params': [], 'rho': [self.rho]} for i in range(maxiter - 1): if hasattr(self, 'pinv_wexog'): del self.pinv_wexog self.initialize() results = self.fit() history['params'].append(results.params) if i == 0: last = results.params else: diff = np.max(np.abs(last - results.params) / np.abs(last)) if diff < rtol: converged = True break last = results.params self.rho, _ = yule_walker(results.resid, order=self.order, df=None) history['rho'].append(self.rho) # why not another call to self.initialize # Use kwarg to insert history if not converged and maxiter > 0: # maxiter <= 0 just does OLS if hasattr(self, 'pinv_wexog'): del self.pinv_wexog self.initialize() # if converged then this is a duplicate fit, because we did not # update rho results = self.fit(history=history, **kwargs) results.iter = i + 1 # add last fit to history, not if duplicate fit if not converged: results.history['params'].append(results.params) results.iter += 1 results.converged = converged return results def whiten(self, x): """ Whiten a series of columns according to an AR(p) covariance structure. Whitening using this method drops the initial p observations. Parameters ---------- x : array_like The data to be whitened. Returns ------- ndarray The whitened data. """ # TODO: notation for AR process x = np.asarray(x, np.float64) _x = x.copy() # the following loops over the first axis, works for 1d and nd for i in range(self.order): _x[(i + 1):] = _x[(i + 1):] - self.rho[i] * x[0:-(i + 1)] return _x[self.order:] def yule_walker(x, order=1, method="adjusted", df=None, inv=False, demean=True): """ Estimate AR(p) parameters from a sequence using the Yule-Walker equations. Adjusted or maximum-likelihood estimator (mle) Parameters ---------- x : array_like A 1d array. order : int, optional The order of the autoregressive process. Default is 1. method : str, optional Method can be 'adjusted' or 'mle' and this determines denominator in estimate of autocorrelation function (ACF) at lag k. If 'mle', the denominator is n=X.shape[0], if 'adjusted' the denominator is n-k. The default is adjusted. df : int, optional Specifies the degrees of freedom. If `df` is supplied, then it is assumed the X has `df` degrees of freedom rather than `n`. Default is None. inv : bool If inv is True the inverse of R is also returned. Default is False. demean : bool True, the mean is subtracted from `X` before estimation. Returns ------- rho : ndarray AR(p) coefficients computed using the Yule-Walker method. sigma : float The estimate of the residual standard deviation. See Also -------- burg : Burg's AR estimator. Notes ----- See https://en.wikipedia.org/wiki/Autoregressive_moving_average_model for further details. Examples -------- >>> import statsmodels.api as sm >>> from statsmodels.datasets.sunspots import load >>> data = load(as_pandas=False) >>> rho, sigma = sm.regression.yule_walker(data.endog, order=4, ... method="mle") >>> rho array([ 1.28310031, -0.45240924, -0.20770299, 0.04794365]) >>> sigma 16.808022730464351 """ # TODO: define R better, look back at notes and technical notes on YW. # First link here is useful # http://www-stat.wharton.upenn.edu/~steele/Courses/956/ResourceDetails/YuleWalkerAndMore.htm method = string_like( method, "method", options=("adjusted", "unbiased", "mle") ) if method == "unbiased": warnings.warn( "unbiased is deprecated in factor of adjusted to reflect that the " "term is adjusting the sample size used in the autocovariance " "calculation rather than estimating an unbiased autocovariance. " "After release 0.13, using 'unbiased' will raise.", FutureWarning, ) method = "adjusted" if method not in ("adjusted", "mle"): raise ValueError("ACF estimation method must be 'adjusted' or 'MLE'") x = np.array(x, dtype=np.float64) if demean: x -= x.mean() n = df or x.shape[0] # this handles df_resid ie., n - p adj_needed = method == "adjusted" if x.ndim > 1 and x.shape[1] != 1: raise ValueError("expecting a vector to estimate AR parameters") r = np.zeros(order+1, np.float64) r[0] = (x ** 2).sum() / n for k in range(1, order+1): r[k] = (x[0:-k] * x[k:]).sum() / (n - k * adj_needed) R = toeplitz(r[:-1]) rho = np.linalg.solve(R, r[1:]) sigmasq = r[0] - (r[1:]*rho).sum() if inv: return rho, np.sqrt(sigmasq), np.linalg.inv(R) else: return rho, np.sqrt(sigmasq) def burg(endog, order=1, demean=True): """ Compute Burg's AP(p) parameter estimator. Parameters ---------- endog : array_like The endogenous variable. order : int, optional Order of the AR. Default is 1. demean : bool, optional Flag indicating to subtract the mean from endog before estimation. Returns ------- rho : ndarray The AR(p) coefficients computed using Burg's algorithm. sigma2 : float The estimate of the residual variance. See Also -------- yule_walker : Estimate AR parameters using the Yule-Walker method. Notes ----- AR model estimated includes a constant that is estimated using the sample mean (see [1]_). This value is not reported. References ---------- .. [1] Brockwell, P.J. and Davis, R.A., 2016. Introduction to time series and forecasting. Springer. Examples -------- >>> import statsmodels.api as sm >>> from statsmodels.datasets.sunspots import load >>> data = load(as_pandas=True) >>> rho, sigma2 = sm.regression.linear_model.burg(data.endog, order=4) >>> rho array([ 1.30934186, -0.48086633, -0.20185982, 0.05501941]) >>> sigma2 271.2467306963966 """ # Avoid circular imports from statsmodels.tsa.stattools import levinson_durbin_pacf, pacf_burg endog = np.squeeze(np.asarray(endog)) if endog.ndim != 1: raise ValueError('endog must be 1-d or squeezable to 1-d.') order = int(order) if order < 1: raise ValueError('order must be an integer larger than 1') if demean: endog = endog - endog.mean() pacf, sigma = pacf_burg(endog, order, demean=demean) ar, _ = levinson_durbin_pacf(pacf) return ar, sigma[-1] class RegressionResults(base.LikelihoodModelResults): r""" This class summarizes the fit of a linear regression model. It handles the output of contrasts, estimates of covariance, etc. Parameters ---------- model : RegressionModel The regression model instance. params : ndarray The estimated parameters. normalized_cov_params : ndarray The normalized covariance parameters. scale : float The estimated scale of the residuals. cov_type : str The covariance estimator used in the results. cov_kwds : dict Additional keywords used in the covariance specification. use_t : bool Flag indicating to use the Student's t in inference. **kwargs Additional keyword arguments used to initialize the results. Attributes ---------- pinv_wexog See model class docstring for implementation details. cov_type Parameter covariance estimator used for standard errors and t-stats. df_model Model degrees of freedom. The number of regressors `p`. Does not include the constant if one is present. df_resid Residual degrees of freedom. `n - p - 1`, if a constant is present. `n - p` if a constant is not included. het_scale adjusted squared residuals for heteroscedasticity robust standard errors. Is only available after `HC#_se` or `cov_HC#` is called. See HC#_se for more information. history Estimation history for iterative estimators. model A pointer to the model instance that called fit() or results. params The linear coefficients that minimize the least squares criterion. This is usually called Beta for the classical linear model. """ _cache = {} # needs to be a class attribute for scale setter? def __init__(self, model, params, normalized_cov_params=None, scale=1., cov_type='nonrobust', cov_kwds=None, use_t=None, **kwargs): super(RegressionResults, self).__init__( model, params, normalized_cov_params, scale) # Keep wresid since needed by predict self._data_in_cache.remove("wresid") self._cache = {} if hasattr(model, 'wexog_singular_values'): self._wexog_singular_values = model.wexog_singular_values else: self._wexog_singular_values = None self.df_model = model.df_model self.df_resid = model.df_resid if cov_type == 'nonrobust': self.cov_type = 'nonrobust' self.cov_kwds = { 'description': 'Standard Errors assume that the ' + 'covariance matrix of the errors is correctly ' + 'specified.'} if use_t is None: use_t = True # TODO: class default self.use_t = use_t else: if cov_kwds is None: cov_kwds = {} if 'use_t' in cov_kwds: # TODO: we want to get rid of 'use_t' in cov_kwds use_t_2 = cov_kwds.pop('use_t') if use_t is None: use_t = use_t_2 # TODO: warn or not? self.get_robustcov_results(cov_type=cov_type, use_self=True, use_t=use_t, **cov_kwds) for key in kwargs: setattr(self, key, kwargs[key]) def conf_int(self, alpha=.05, cols=None): """ Compute the confidence interval of the fitted parameters. Parameters ---------- alpha : float, optional The `alpha` level for the confidence interval. The default `alpha` = .05 returns a 95% confidence interval. cols : array_like, optional Columns to included in returned confidence intervals. Returns ------- array_like The confidence intervals. Notes ----- The confidence interval is based on Student's t-distribution. """ # keep method for docstring for now ci = super(RegressionResults, self).conf_int(alpha=alpha, cols=cols) return ci @cache_readonly def nobs(self): """Number of observations n.""" return float(self.model.wexog.shape[0]) @cache_readonly def fittedvalues(self): """The predicted values for the original (unwhitened) design.""" return self.model.predict(self.params, self.model.exog) @cache_readonly def wresid(self): """ The residuals of the transformed/whitened regressand and regressor(s). """ return self.model.wendog - self.model.predict( self.params, self.model.wexog) @cache_readonly def resid(self): """The residuals of the model.""" return self.model.endog - self.model.predict( self.params, self.model.exog) # TODO: fix writable example @cache_writable() def scale(self): """ A scale factor for the covariance matrix. The Default value is ssr/(n-p). Note that the square root of `scale` is often called the standard error of the regression. """ wresid = self.wresid return np.dot(wresid, wresid) / self.df_resid @cache_readonly def ssr(self): """Sum of squared (whitened) residuals.""" wresid = self.wresid return np.dot(wresid, wresid) @cache_readonly def centered_tss(self): """The total (weighted) sum of squares centered about the mean.""" model = self.model weights = getattr(model, 'weights', None) sigma = getattr(model, 'sigma', None) if weights is not None: mean = np.average(model.endog, weights=weights) return np.sum(weights * (model.endog - mean)**2) elif sigma is not None: # Exactly matches WLS when sigma is diagonal iota = np.ones_like(model.endog) iota = model.whiten(iota) mean = model.wendog.dot(iota) / iota.dot(iota) err = model.endog - mean err = model.whiten(err) return np.sum(err**2) else: centered_endog = model.wendog - model.wendog.mean() return np.dot(centered_endog, centered_endog) @cache_readonly def uncentered_tss(self): """ Uncentered sum of squares. The sum of the squared values of the (whitened) endogenous response variable. """ wendog = self.model.wendog return np.dot(wendog, wendog) @cache_readonly def ess(self): """ The explained sum of squares. If a constant is present, the centered total sum of squares minus the sum of squared residuals. If there is no constant, the uncentered total sum of squares is used. """ if self.k_constant: return self.centered_tss - self.ssr else: return self.uncentered_tss - self.ssr @cache_readonly def rsquared(self): """ R-squared of the model. This is defined here as 1 - `ssr`/`centered_tss` if the constant is included in the model and 1 - `ssr`/`uncentered_tss` if the constant is omitted. """ if self.k_constant: return 1 - self.ssr/self.centered_tss else: return 1 - self.ssr/self.uncentered_tss @cache_readonly def rsquared_adj(self): """ Adjusted R-squared. This is defined here as 1 - (`nobs`-1)/`df_resid` * (1-`rsquared`) if a constant is included and 1 - `nobs`/`df_resid` * (1-`rsquared`) if no constant is included. """ return 1 - (np.divide(self.nobs - self.k_constant, self.df_resid) * (1 - self.rsquared)) @cache_readonly def mse_model(self): """ Mean squared error the model. The explained sum of squares divided by the model degrees of freedom. """ if np.all(self.df_model == 0.0): return np.full_like(self.ess, np.nan) return self.ess/self.df_model @cache_readonly def mse_resid(self): """ Mean squared error of the residuals. The sum of squared residuals divided by the residual degrees of freedom. """ if np.all(self.df_resid == 0.0): return np.full_like(self.ssr, np.nan) return self.ssr/self.df_resid @cache_readonly def mse_total(self): """ Total mean squared error. The uncentered total sum of squares divided by the number of observations. """ if np.all(self.df_resid + self.df_model == 0.0): return np.full_like(self.centered_tss, np.nan) if self.k_constant: return self.centered_tss / (self.df_resid + self.df_model) else: return self.uncentered_tss / (self.df_resid + self.df_model) @cache_readonly def fvalue(self): """ F-statistic of the fully specified model. Calculated as the mean squared error of the model divided by the mean squared error of the residuals if the nonrobust covariance is used. Otherwise computed using a Wald-like quadratic form that tests whether all coefficients (excluding the constant) are zero. """ if hasattr(self, 'cov_type') and self.cov_type != 'nonrobust': # with heteroscedasticity or correlation robustness k_params = self.normalized_cov_params.shape[0] mat = np.eye(k_params) const_idx = self.model.data.const_idx # TODO: What if model includes implicit constant, e.g. all # dummies but no constant regressor? # TODO: Restats as LM test by projecting orthogonalizing # to constant? if self.model.data.k_constant == 1: # if constant is implicit, return nan see #2444 if const_idx is None: return np.nan idx = lrange(k_params) idx.pop(const_idx) mat = mat[idx] # remove constant if mat.size == 0: # see #3642 return np.nan ft = self.f_test(mat) # using backdoor to set another attribute that we already have self._cache['f_pvalue'] = float(ft.pvalue) return float(ft.fvalue) else: # for standard homoscedastic case return self.mse_model/self.mse_resid @cache_readonly def f_pvalue(self): """The p-value of the F-statistic.""" # Special case for df_model 0 if self.df_model == 0: return np.full_like(self.fvalue, np.nan) return stats.f.sf(self.fvalue, self.df_model, self.df_resid) @cache_readonly def bse(self): """The standard errors of the parameter estimates.""" return np.sqrt(np.diag(self.cov_params())) @cache_readonly def aic(self): r""" Akaike's information criteria. For a model with a constant :math:`-2llf + 2(df\_model + 1)`. For a model without a constant :math:`-2llf + 2(df\_model)`. """ return -2 * self.llf + 2 * (self.df_model + self.k_constant) @cache_readonly def bic(self): r""" Bayes' information criteria. For a model with a constant :math:`-2llf + \log(n)(df\_model+1)`. For a model without a constant :math:`-2llf + \log(n)(df\_model)`. """ return (-2 * self.llf + np.log(self.nobs) * (self.df_model + self.k_constant)) @cache_readonly def eigenvals(self): """ Return eigenvalues sorted in decreasing order. """ if self._wexog_singular_values is not None: eigvals = self._wexog_singular_values ** 2 else: eigvals = np.linalg.linalg.eigvalsh(np.dot(self.model.wexog.T, self.model.wexog)) return np.sort(eigvals)[::-1] @cache_readonly def condition_number(self): """ Return condition number of exogenous matrix. Calculated as ratio of largest to smallest eigenvalue. """ eigvals = self.eigenvals return np.sqrt(eigvals[0]/eigvals[-1]) # TODO: make these properties reset bse def _HCCM(self, scale): H = np.dot(self.model.pinv_wexog, scale[:, None] * self.model.pinv_wexog.T) return H def _abat_diagonal(self, a, b): # equivalent to np.diag(a @ b @ a.T) return np.einsum('ij,ik,kj->i', a, a, b) @cache_readonly def cov_HC0(self): """ Heteroscedasticity robust covariance matrix. See HC0_se. """ self.het_scale = self.wresid**2 cov_HC0 = self._HCCM(self.het_scale) return cov_HC0 @cache_readonly def cov_HC1(self): """ Heteroscedasticity robust covariance matrix. See HC1_se. """ self.het_scale = self.nobs/(self.df_resid)*(self.wresid**2) cov_HC1 = self._HCCM(self.het_scale) return cov_HC1 @cache_readonly def cov_HC2(self): """ Heteroscedasticity robust covariance matrix. See HC2_se. """ wexog = self.model.wexog h = self._abat_diagonal(wexog, self.normalized_cov_params) self.het_scale = self.wresid**2/(1-h) cov_HC2 = self._HCCM(self.het_scale) return cov_HC2 @cache_readonly def cov_HC3(self): """ Heteroscedasticity robust covariance matrix. See HC3_se. """ wexog = self.model.wexog h = self._abat_diagonal(wexog, self.normalized_cov_params) self.het_scale = (self.wresid / (1 - h))**2 cov_HC3 = self._HCCM(self.het_scale) return cov_HC3 @cache_readonly def HC0_se(self): """ White's (1980) heteroskedasticity robust standard errors. Notes ----- Defined as sqrt(diag(X.T X)^(-1)X.T diag(e_i^(2)) X(X.T X)^(-1) where e_i = resid[i]. When HC0_se or cov_HC0 is called the RegressionResults instance will then have another attribute `het_scale`, which is in this case is just resid**2. """ return np.sqrt(np.diag(self.cov_HC0)) @cache_readonly def HC1_se(self): """ MacKinnon and White's (1985) heteroskedasticity robust standard errors. Notes ----- Defined as sqrt(diag(n/(n-p)*HC_0). When HC1_se or cov_HC1 is called the RegressionResults instance will then have another attribute `het_scale`, which is in this case is n/(n-p)*resid**2. """ return np.sqrt(np.diag(self.cov_HC1)) @cache_readonly def HC2_se(self): """ MacKinnon and White's (1985) heteroskedasticity robust standard errors. Notes ----- Defined as (X.T X)^(-1)X.T diag(e_i^(2)/(1-h_ii)) X(X.T X)^(-1) where h_ii = x_i(X.T X)^(-1)x_i.T When HC2_se or cov_HC2 is called the RegressionResults instance will then have another attribute `het_scale`, which is in this case is resid^(2)/(1-h_ii). """ return np.sqrt(np.diag(self.cov_HC2)) @cache_readonly def HC3_se(self): """ MacKinnon and White's (1985) heteroskedasticity robust standard errors. Notes ----- Defined as (X.T X)^(-1)X.T diag(e_i^(2)/(1-h_ii)^(2)) X(X.T X)^(-1) where h_ii = x_i(X.T X)^(-1)x_i.T. When HC3_se or cov_HC3 is called the RegressionResults instance will then have another attribute `het_scale`, which is in this case is resid^(2)/(1-h_ii)^(2). """ return np.sqrt(np.diag(self.cov_HC3)) @cache_readonly def resid_pearson(self): """ Residuals, normalized to have unit variance. Returns ------- array_like The array `wresid` normalized by the sqrt of the scale to have unit variance. """ if not hasattr(self, 'resid'): raise ValueError('Method requires residuals.') eps = np.finfo(self.wresid.dtype).eps if np.sqrt(self.scale) < 10 * eps * self.model.endog.mean(): # do not divide if scale is zero close to numerical precision warnings.warn( "All residuals are 0, cannot compute normed residuals.", RuntimeWarning ) return self.wresid else: return self.wresid / np.sqrt(self.scale) def _is_nested(self, restricted): """ Parameters ---------- restricted : Result instance The restricted model is assumed to be nested in the current model. The result instance of the restricted model is required to have two attributes, residual sum of squares, `ssr`, residual degrees of freedom, `df_resid`. Returns ------- nested : bool True if nested, otherwise false Notes ----- A most nests another model if the regressors in the smaller model are spanned by the regressors in the larger model and the regressand is identical. """ if self.model.nobs != restricted.model.nobs: return False full_rank = self.model.rank restricted_rank = restricted.model.rank if full_rank <= restricted_rank: return False restricted_exog = restricted.model.wexog full_wresid = self.wresid scores = restricted_exog * full_wresid[:, None] score_l2 = np.sqrt(np.mean(scores.mean(0) ** 2)) # TODO: Could be improved, and may fail depending on scale of # regressors return np.allclose(score_l2, 0) def compare_lm_test(self, restricted, demean=True, use_lr=False): """ Use Lagrange Multiplier test to test a set of linear restrictions. Parameters ---------- restricted : Result instance The restricted model is assumed to be nested in the current model. The result instance of the restricted model is required to have two attributes, residual sum of squares, `ssr`, residual degrees of freedom, `df_resid`. demean : bool Flag indicating whether the demean the scores based on the residuals from the restricted model. If True, the covariance of the scores are used and the LM test is identical to the large sample version of the LR test. use_lr : bool A flag indicating whether to estimate the covariance of the model scores using the unrestricted model. Setting the to True improves the power of the test. Returns ------- lm_value : float The test statistic which has a chi2 distributed. p_value : float The p-value of the test statistic. df_diff : int The degrees of freedom of the restriction, i.e. difference in df between models. Notes ----- The LM test examines whether the scores from the restricted model are 0. If the null is true, and the restrictions are valid, then the parameters of the restricted model should be close to the minimum of the sum of squared errors, and so the scores should be close to zero, on average. """ import statsmodels.stats.sandwich_covariance as sw from numpy.linalg import inv if not self._is_nested(restricted): raise ValueError("Restricted model is not nested by full model.") wresid = restricted.wresid wexog = self.model.wexog scores = wexog * wresid[:, None] n = self.nobs df_full = self.df_resid df_restr = restricted.df_resid df_diff = (df_restr - df_full) s = scores.mean(axis=0) if use_lr: scores = wexog * self.wresid[:, None] demean = False if demean: scores = scores - scores.mean(0)[None, :] # Form matters here. If homoskedastics can be sigma^2 (X'X)^-1 # If Heteroskedastic then the form below is fine # If HAC then need to use HAC # If Cluster, should use cluster cov_type = getattr(self, 'cov_type', 'nonrobust') if cov_type == 'nonrobust': sigma2 = np.mean(wresid**2) xpx = np.dot(wexog.T, wexog) / n s_inv = inv(sigma2 * xpx) elif cov_type in ('HC0', 'HC1', 'HC2', 'HC3'): s_inv = inv(np.dot(scores.T, scores) / n) elif cov_type == 'HAC': maxlags = self.cov_kwds['maxlags'] s_inv = inv(sw.S_hac_simple(scores, maxlags) / n) elif cov_type == 'cluster': # cluster robust standard errors groups = self.cov_kwds['groups'] # TODO: Might need demean option in S_crosssection by group? s_inv = inv(sw.S_crosssection(scores, groups)) else: raise ValueError('Only nonrobust, HC, HAC and cluster are ' + 'currently connected') lm_value = n * (s @ s_inv @ s.T) p_value = stats.chi2.sf(lm_value, df_diff) return lm_value, p_value, df_diff def compare_f_test(self, restricted): """ Use F test to test whether restricted model is correct. Parameters ---------- restricted : Result instance The restricted model is assumed to be nested in the current model. The result instance of the restricted model is required to have two attributes, residual sum of squares, `ssr`, residual degrees of freedom, `df_resid`. Returns ------- f_value : float The test statistic which has an F distribution. p_value : float The p-value of the test statistic. df_diff : int The degrees of freedom of the restriction, i.e. difference in df between models. Notes ----- See mailing list discussion October 17, This test compares the residual sum of squares of the two models. This is not a valid test, if there is unspecified heteroscedasticity or correlation. This method will issue a warning if this is detected but still return the results under the assumption of homoscedasticity and no autocorrelation (sphericity). """ has_robust1 = getattr(self, 'cov_type', 'nonrobust') != 'nonrobust' has_robust2 = (getattr(restricted, 'cov_type', 'nonrobust') != 'nonrobust') if has_robust1 or has_robust2: warnings.warn('F test for comparison is likely invalid with ' + 'robust covariance, proceeding anyway', InvalidTestWarning) ssr_full = self.ssr ssr_restr = restricted.ssr df_full = self.df_resid df_restr = restricted.df_resid df_diff = (df_restr - df_full) f_value = (ssr_restr - ssr_full) / df_diff / ssr_full * df_full p_value = stats.f.sf(f_value, df_diff, df_full) return f_value, p_value, df_diff def compare_lr_test(self, restricted, large_sample=False): """ Likelihood ratio test to test whether restricted model is correct. Parameters ---------- restricted : Result instance The restricted model is assumed to be nested in the current model. The result instance of the restricted model is required to have two attributes, residual sum of squares, `ssr`, residual degrees of freedom, `df_resid`. large_sample : bool Flag indicating whether to use a heteroskedasticity robust version of the LR test, which is a modified LM test. Returns ------- lr_stat : float The likelihood ratio which is chisquare distributed with df_diff degrees of freedom. p_value : float The p-value of the test statistic. df_diff : int The degrees of freedom of the restriction, i.e. difference in df between models. Notes ----- The exact likelihood ratio is valid for homoskedastic data, and is defined as .. math:: D=-2\\log\\left(\\frac{\\mathcal{L}_{null}} {\\mathcal{L}_{alternative}}\\right) where :math:`\\mathcal{L}` is the likelihood of the model. With :math:`D` distributed as chisquare with df equal to difference in number of parameters or equivalently difference in residual degrees of freedom. The large sample version of the likelihood ratio is defined as .. math:: D=n s^{\\prime}S^{-1}s where :math:`s=n^{-1}\\sum_{i=1}^{n} s_{i}` .. math:: s_{i} = x_{i,alternative} \\epsilon_{i,null} is the average score of the model evaluated using the residuals from null model and the regressors from the alternative model and :math:`S` is the covariance of the scores, :math:`s_{i}`. The covariance of the scores is estimated using the same estimator as in the alternative model. This test compares the loglikelihood of the two models. This may not be a valid test, if there is unspecified heteroscedasticity or correlation. This method will issue a warning if this is detected but still return the results without taking unspecified heteroscedasticity or correlation into account. This test compares the loglikelihood of the two models. This may not be a valid test, if there is unspecified heteroscedasticity or correlation. This method will issue a warning if this is detected but still return the results without taking unspecified heteroscedasticity or correlation into account. is the average score of the model evaluated using the residuals from null model and the regressors from the alternative model and :math:`S` is the covariance of the scores, :math:`s_{i}`. The covariance of the scores is estimated using the same estimator as in the alternative model. """ # TODO: put into separate function, needs tests # See mailing list discussion October 17, if large_sample: return self.compare_lm_test(restricted, use_lr=True) has_robust1 = (getattr(self, 'cov_type', 'nonrobust') != 'nonrobust') has_robust2 = ( getattr(restricted, 'cov_type', 'nonrobust') != 'nonrobust') if has_robust1 or has_robust2: warnings.warn('Likelihood Ratio test is likely invalid with ' + 'robust covariance, proceeding anyway', InvalidTestWarning) llf_full = self.llf llf_restr = restricted.llf df_full = self.df_resid df_restr = restricted.df_resid lrdf = (df_restr - df_full) lrstat = -2*(llf_restr - llf_full) lr_pvalue = stats.chi2.sf(lrstat, lrdf) return lrstat, lr_pvalue, lrdf def get_robustcov_results(self, cov_type='HC1', use_t=None, **kwargs): """ Create new results instance with robust covariance as default. Parameters ---------- cov_type : str The type of robust sandwich estimator to use. See Notes below. use_t : bool If true, then the t distribution is used for inference. If false, then the normal distribution is used. If `use_t` is None, then an appropriate default is used, which is `True` if the cov_type is nonrobust, and `False` in all other cases. **kwargs Required or optional arguments for robust covariance calculation. See Notes below. Returns ------- RegressionResults This method creates a new results instance with the requested robust covariance as the default covariance of the parameters. Inferential statistics like p-values and hypothesis tests will be based on this covariance matrix. Notes ----- The following covariance types and required or optional arguments are currently available: - 'fixed scale' and optional keyword argument 'scale' which uses a predefined scale estimate with default equal to one. - 'HC0', 'HC1', 'HC2', 'HC3' and no keyword arguments: heteroscedasticity robust covariance - 'HAC' and keywords - `maxlag` integer (required) : number of lags to use - `kernel` callable or str (optional) : kernel currently available kernels are ['bartlett', 'uniform'], default is Bartlett - `use_correction` bool (optional) : If true, use small sample correction - 'cluster' and required keyword `groups`, integer group indicator - `groups` array_like, integer (required) : index of clusters or groups - `use_correction` bool (optional) : If True the sandwich covariance is calculated with a small sample correction. If False the sandwich covariance is calculated without small sample correction. - `df_correction` bool (optional) If True (default), then the degrees of freedom for the inferential statistics and hypothesis tests, such as pvalues, f_pvalue, conf_int, and t_test and f_test, are based on the number of groups minus one instead of the total number of observations minus the number of explanatory variables. `df_resid` of the results instance is also adjusted. When `use_t` is also True, then pvalues are computed using the Student's t distribution using the corrected values. These may differ substantially from p-values based on the normal is the number of groups is sma... If False, then `df_resid` of the results instance is not adjusted. - 'hac-groupsum' Driscoll and Kraay, heteroscedasticity and autocorrelation robust standard errors in panel data keywords - `time` array_like (required) : index of time periods - `maxlag` integer (required) : number of lags to use - `kernel` callable or str (optional). The available kernels are ['bartlett', 'uniform']. The default is Bartlett. - `use_correction` False or string in ['hac', 'cluster'] (optional). If False the the sandwich covariance is calculated without small sample correction. If `use_correction = 'cluster'` (default), then the same small sample correction as in the case of `covtype='cluster'` is used. - `df_correction` bool (optional) The adjustment to df_resid, see cov_type 'cluster' above # TODO: we need more options here - 'hac-panel' heteroscedasticity and autocorrelation robust standard errors in panel data. The data needs to be sorted in this case, the time series for each panel unit or cluster need to be stacked. The membership to a timeseries of an individual or group can be either specified by group indicators or by increasing time periods. keywords - either `groups` or `time` : array_like (required) `groups` : indicator for groups `time` : index of time periods - `maxlag` integer (required) : number of lags to use - `kernel` callable or str (optional) currently available kernels are ['bartlett', 'uniform'], default is Bartlett - `use_correction` False or string in ['hac', 'cluster'] (optional) If False the sandwich covariance is calculated without small sample correction. - `df_correction` bool (optional) adjustment to df_resid, see cov_type 'cluster' above # TODO: we need more options here Reminder: `use_correction` in "hac-groupsum" and "hac-panel" is not bool, needs to be in [False, 'hac', 'cluster'] TODO: Currently there is no check for extra or misspelled keywords, except in the case of cov_type `HCx` """ import statsmodels.stats.sandwich_covariance as sw from statsmodels.base.covtype import normalize_cov_type, descriptions cov_type = normalize_cov_type(cov_type) if 'kernel' in kwargs: kwargs['weights_func'] = kwargs.pop('kernel') if 'weights_func' in kwargs and not callable(kwargs['weights_func']): kwargs['weights_func'] = sw.kernel_dict[kwargs['weights_func']] # TODO: make separate function that returns a robust cov plus info use_self = kwargs.pop('use_self', False) if use_self: res = self else: res = self.__class__( self.model, self.params, normalized_cov_params=self.normalized_cov_params, scale=self.scale) res.cov_type = cov_type # use_t might already be defined by the class, and already set if use_t is None: use_t = self.use_t res.cov_kwds = {'use_t': use_t} # store for information res.use_t = use_t adjust_df = False if cov_type in ['cluster', 'hac-panel', 'hac-groupsum']: df_correction = kwargs.get('df_correction', None) # TODO: check also use_correction, do I need all combinations? if df_correction is not False: # i.e. in [None, True]: # user did not explicitely set it to False adjust_df = True res.cov_kwds['adjust_df'] = adjust_df # verify and set kwargs, and calculate cov # TODO: this should be outsourced in a function so we can reuse it in # other models # TODO: make it DRYer repeated code for checking kwargs if cov_type in ['fixed scale', 'fixed_scale']: res.cov_kwds['description'] = descriptions['fixed_scale'] res.cov_kwds['scale'] = scale = kwargs.get('scale', 1.) res.cov_params_default = scale * res.normalized_cov_params elif cov_type.upper() in ('HC0', 'HC1', 'HC2', 'HC3'): if kwargs: raise ValueError('heteroscedasticity robust covariance ' 'does not use keywords') res.cov_kwds['description'] = descriptions[cov_type.upper()] res.cov_params_default = getattr(self, 'cov_' + cov_type.upper()) elif cov_type.lower() == 'hac': # TODO: check if required, default in cov_hac_simple maxlags = kwargs['maxlags'] res.cov_kwds['maxlags'] = maxlags weights_func = kwargs.get('weights_func', sw.weights_bartlett) res.cov_kwds['weights_func'] = weights_func use_correction = kwargs.get('use_correction', False) res.cov_kwds['use_correction'] = use_correction res.cov_kwds['description'] = descriptions['HAC'].format( maxlags=maxlags, correction=['without', 'with'][use_correction]) res.cov_params_default = sw.cov_hac_simple( self, nlags=maxlags, weights_func=weights_func, use_correction=use_correction) elif cov_type.lower() == 'cluster': # cluster robust standard errors, one- or two-way groups = kwargs['groups'] if not hasattr(groups, 'shape'): groups = np.asarray(groups).T if groups.ndim >= 2: groups = groups.squeeze() res.cov_kwds['groups'] = groups use_correction = kwargs.get('use_correction', True) res.cov_kwds['use_correction'] = use_correction if groups.ndim == 1: if adjust_df: # need to find number of groups # duplicate work self.n_groups = n_groups = len(np.unique(groups)) res.cov_params_default = sw.cov_cluster( self, groups, use_correction=use_correction) elif groups.ndim == 2: if hasattr(groups, 'values'): groups = groups.values if adjust_df: # need to find number of groups # duplicate work n_groups0 = len(np.unique(groups[:, 0])) n_groups1 = len(np.unique(groups[:, 1])) self.n_groups = (n_groups0, n_groups1) n_groups = min(n_groups0, n_groups1) # use for adjust_df # Note: sw.cov_cluster_2groups has 3 returns res.cov_params_default = sw.cov_cluster_2groups( self, groups, use_correction=use_correction)[0] else: raise ValueError('only two groups are supported') res.cov_kwds['description'] = descriptions['cluster'] elif cov_type.lower() == 'hac-panel': # cluster robust standard errors res.cov_kwds['time'] = time = kwargs.get('time', None) res.cov_kwds['groups'] = groups = kwargs.get('groups', None) # TODO: nlags is currently required # nlags = kwargs.get('nlags', True) # res.cov_kwds['nlags'] = nlags # TODO: `nlags` or `maxlags` res.cov_kwds['maxlags'] = maxlags = kwargs['maxlags'] use_correction = kwargs.get('use_correction', 'hac') res.cov_kwds['use_correction'] = use_correction weights_func = kwargs.get('weights_func', sw.weights_bartlett) res.cov_kwds['weights_func'] = weights_func if groups is not None: groups = np.asarray(groups) tt = (np.nonzero(groups[:-1] != groups[1:])[0] + 1).tolist() nobs_ = len(groups) elif time is not None: time = np.asarray(time) # TODO: clumsy time index in cov_nw_panel tt = (np.nonzero(time[1:] < time[:-1])[0] + 1).tolist() nobs_ = len(time) else: raise ValueError('either time or groups needs to be given') groupidx = lzip([0] + tt, tt + [nobs_]) self.n_groups = n_groups = len(groupidx) res.cov_params_default = sw.cov_nw_panel(self, maxlags, groupidx, weights_func=weights_func, use_correction=use_correction) res.cov_kwds['description'] = descriptions['HAC-Panel'] elif cov_type.lower() == 'hac-groupsum': # Driscoll-Kraay standard errors res.cov_kwds['time'] = time = kwargs['time'] # TODO: nlags is currently required # nlags = kwargs.get('nlags', True) # res.cov_kwds['nlags'] = nlags # TODO: `nlags` or `maxlags` res.cov_kwds['maxlags'] = maxlags = kwargs['maxlags'] use_correction = kwargs.get('use_correction', 'cluster') res.cov_kwds['use_correction'] = use_correction weights_func = kwargs.get('weights_func', sw.weights_bartlett) res.cov_kwds['weights_func'] = weights_func if adjust_df: # need to find number of groups tt = (np.nonzero(time[1:] < time[:-1])[0] + 1) self.n_groups = n_groups = len(tt) + 1 res.cov_params_default = sw.cov_nw_groupsum( self, maxlags, time, weights_func=weights_func, use_correction=use_correction) res.cov_kwds['description'] = descriptions['HAC-Groupsum'] else: raise ValueError('cov_type not recognized. See docstring for ' + 'available options and spelling') if adjust_df: # Note: df_resid is used for scale and others, add new attribute res.df_resid_inference = n_groups - 1 return res @Appender(pred.get_prediction.__doc__) def get_prediction(self, exog=None, transform=True, weights=None, row_labels=None, **kwargs): return pred.get_prediction( self, exog=exog, transform=transform, weights=weights, row_labels=row_labels, **kwargs) def summary(self, yname=None, xname=None, title=None, alpha=.05): """ Summarize the Regression Results. Parameters ---------- yname : str, optional Name of endogenous (response) variable. The Default is `y`. xname : list[str], optional Names for the exogenous variables. Default is `var_##` for ## in the number of regressors. Must match the number of parameters in the model. title : str, optional Title for the top table. If not None, then this replaces the default title. alpha : float The significance level for the confidence intervals. Returns ------- Summary Instance holding the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : A class that holds summary results. """ from statsmodels.stats.stattools import ( jarque_bera, omni_normtest, durbin_watson) jb, jbpv, skew, kurtosis = jarque_bera(self.wresid) omni, omnipv = omni_normtest(self.wresid) eigvals = self.eigenvals condno = self.condition_number # TODO: Avoid adding attributes in non-__init__ self.diagn = dict(jb=jb, jbpv=jbpv, skew=skew, kurtosis=kurtosis, omni=omni, omnipv=omnipv, condno=condno, mineigval=eigvals[-1]) # TODO not used yet # diagn_left_header = ['Models stats'] # diagn_right_header = ['Residual stats'] # TODO: requiring list/iterable is a bit annoying # need more control over formatting # TODO: default do not work if it's not identically spelled top_left = [('Dep. Variable:', None), ('Model:', None), ('Method:', ['Least Squares']), ('Date:', None), ('Time:', None), ('No. Observations:', None), ('Df Residuals:', None), ('Df Model:', None), ] if hasattr(self, 'cov_type'): top_left.append(('Covariance Type:', [self.cov_type])) rsquared_type = '' if self.k_constant else ' (uncentered)' top_right = [('R-squared' + rsquared_type + ':', ["%#8.3f" % self.rsquared]), ('Adj. R-squared' + rsquared_type + ':', ["%#8.3f" % self.rsquared_adj]), ('F-statistic:', ["%#8.4g" % self.fvalue]), ('Prob (F-statistic):', ["%#6.3g" % self.f_pvalue]), ('Log-Likelihood:', None), ('AIC:', ["%#8.4g" % self.aic]), ('BIC:', ["%#8.4g" % self.bic]) ] diagn_left = [('Omnibus:', ["%#6.3f" % omni]), ('Prob(Omnibus):', ["%#6.3f" % omnipv]), ('Skew:', ["%#6.3f" % skew]), ('Kurtosis:', ["%#6.3f" % kurtosis]) ] diagn_right = [('Durbin-Watson:', ["%#8.3f" % durbin_watson(self.wresid)] ), ('Jarque-Bera (JB):', ["%#8.3f" % jb]), ('Prob(JB):', ["%#8.3g" % jbpv]), ('Cond. No.', ["%#8.3g" % condno]) ] if title is None: title = self.model.__class__.__name__ + ' ' + "Regression Results" # create summary table instance from statsmodels.iolib.summary import Summary smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, yname=yname, xname=xname, title=title) smry.add_table_params(self, yname=yname, xname=xname, alpha=alpha, use_t=self.use_t) smry.add_table_2cols(self, gleft=diagn_left, gright=diagn_right, yname=yname, xname=xname, title="") # add warnings/notes, added to text format only etext = [] if not self.k_constant: etext.append( "R² is computed without centering (uncentered) since the " "model does not contain a constant." ) if hasattr(self, 'cov_type'): etext.append(self.cov_kwds['description']) if self.model.exog.shape[0] < self.model.exog.shape[1]: wstr = "The input rank is higher than the number of observations." etext.append(wstr) if eigvals[-1] < 1e-10: wstr = "The smallest eigenvalue is %6.3g. This might indicate " wstr += "that there are\n" wstr += "strong multicollinearity problems or that the design " wstr += "matrix is singular." wstr = wstr % eigvals[-1] etext.append(wstr) elif condno > 1000: # TODO: what is recommended? wstr = "The condition number is large, %6.3g. This might " wstr += "indicate that there are\n" wstr += "strong multicollinearity or other numerical " wstr += "problems." wstr = wstr % condno etext.append(wstr) if etext: etext = ["[{0}] {1}".format(i + 1, text) for i, text in enumerate(etext)] etext.insert(0, "Notes:") smry.add_extra_txt(etext) return smry def summary2(self, yname=None, xname=None, title=None, alpha=.05, float_format="%.4f"): """ Experimental summary function to summarize the regression results. Parameters ---------- yname : str The name of the dependent variable (optional). xname : list[str], optional Names for the exogenous variables. Default is `var_##` for ## in the number of regressors. Must match the number of parameters in the model. title : str, optional Title for the top table. If not None, then this replaces the default title. alpha : float The significance level for the confidence intervals. float_format : str The format for floats in parameters summary. Returns ------- Summary Instance holding the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary2.Summary A class that holds summary results. """ # Diagnostics from statsmodels.stats.stattools import (jarque_bera, omni_normtest, durbin_watson) jb, jbpv, skew, kurtosis = jarque_bera(self.wresid) omni, omnipv = omni_normtest(self.wresid) dw = durbin_watson(self.wresid) eigvals = self.eigenvals condno = self.condition_number eigvals = np.sort(eigvals) # in increasing order diagnostic = dict([ ('Omnibus:', "%.3f" % omni), ('Prob(Omnibus):', "%.3f" % omnipv), ('Skew:', "%.3f" % skew), ('Kurtosis:', "%.3f" % kurtosis), ('Durbin-Watson:', "%.3f" % dw), ('Jarque-Bera (JB):', "%.3f" % jb), ('Prob(JB):', "%.3f" % jbpv), ('Condition No.:', "%.0f" % condno) ]) # Summary from statsmodels.iolib import summary2 smry = summary2.Summary() smry.add_base(results=self, alpha=alpha, float_format=float_format, xname=xname, yname=yname, title=title) smry.add_dict(diagnostic) # Warnings if eigvals[-1] < 1e-10: warn = "The smallest eigenvalue is %6.3g. This might indicate that\ there are strong multicollinearity problems or that the design\ matrix is singular." % eigvals[-1] smry.add_text(warn) if condno > 1000: warn = "* The condition number is large (%.g). This might indicate \ strong multicollinearity or other numerical problems." % condno smry.add_text(warn) return smry class OLSResults(RegressionResults): """ Results class for for an OLS model. Parameters ---------- model : RegressionModel The regression model instance. params : ndarray The estimated parameters. normalized_cov_params : ndarray The normalized covariance parameters. scale : float The estimated scale of the residuals. cov_type : str The covariance estimator used in the results. cov_kwds : dict Additional keywords used in the covariance specification. use_t : bool Flag indicating to use the Student's t in inference. **kwargs Additional keyword arguments used to initialize the results. See Also -------- RegressionResults Results store for WLS and GLW models. Notes ----- Most of the methods and attributes are inherited from RegressionResults. The special methods that are only available for OLS are: - get_influence - outlier_test - el_test - conf_int_el """ def get_influence(self): """ Calculate influence and outlier measures. Returns ------- OLSInfluence The instance containing methods to calculate the main influence and outlier measures for the OLS regression. See Also -------- statsmodels.stats.outliers_influence.OLSInfluence A class that exposes methods to examine observation influence. """ from statsmodels.stats.outliers_influence import OLSInfluence return OLSInfluence(self) def outlier_test(self, method='bonf', alpha=.05, labels=None, order=False, cutoff=None): """ Test observations for outliers according to method. Parameters ---------- method : str The method to use in the outlier test. Must be one of: - `bonferroni` : one-step correction - `sidak` : one-step correction - `holm-sidak` : - `holm` : - `simes-hochberg` : - `hommel` : - `fdr_bh` : Benjamini/Hochberg - `fdr_by` : Benjamini/Yekutieli See `statsmodels.stats.multitest.multipletests` for details. alpha : float The familywise error rate (FWER). labels : None or array_like If `labels` is not None, then it will be used as index to the returned pandas DataFrame. See also Returns below. order : bool Whether or not to order the results by the absolute value of the studentized residuals. If labels are provided they will also be sorted. cutoff : None or float in [0, 1] If cutoff is not None, then the return only includes observations with multiple testing corrected p-values strictly below the cutoff. The returned array or dataframe can be empty if t. Returns ------- array_like Returns either an ndarray or a DataFrame if labels is not None. Will attempt to get labels from model_results if available. The columns are the Studentized residuals, the unadjusted p-value, and the corrected p-value according to method. Notes ----- The unadjusted p-value is stats.t.sf(abs(resid), df) where df = df_resid - 1. """ from statsmodels.stats.outliers_influence import outlier_test return outlier_test(self, method, alpha, labels=labels, order=order, cutoff=cutoff) def el_test(self, b0_vals, param_nums, return_weights=0, ret_params=0, method='nm', stochastic_exog=1): """ Test single or joint hypotheses using Empirical Likelihood. Parameters ---------- b0_vals : 1darray The hypothesized value of the parameter to be tested. param_nums : 1darray The parameter number to be tested. return_weights : bool If true, returns the weights that optimize the likelihood ratio at b0_vals. The default is False. ret_params : bool If true, returns the parameter vector that maximizes the likelihood ratio at b0_vals. Also returns the weights. The default is False. method : str Can either be 'nm' for Nelder-Mead or 'powell' for Powell. The optimization method that optimizes over nuisance parameters. The default is 'nm'. stochastic_exog : bool When True, the exogenous variables are assumed to be stochastic. When the regressors are nonstochastic, moment conditions are placed on the exogenous variables. Confidence intervals for stochastic regressors are at least as large as non-stochastic regressors. The default is True. Returns ------- tuple The p-value and -2 times the log-likelihood ratio for the hypothesized values. Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.stackloss.load(as_pandas=False) >>> endog = data.endog >>> exog = sm.add_constant(data.exog) >>> model = sm.OLS(endog, exog) >>> fitted = model.fit() >>> fitted.params >>> array([-39.91967442, 0.7156402 , 1.29528612, -0.15212252]) >>> fitted.rsquared >>> 0.91357690446068196 >>> # Test that the slope on the first variable is 0 >>> fitted.el_test([0], [1]) >>> (27.248146353888796, 1.7894660442330235e-07) """ params = np.copy(self.params) opt_fun_inst = _ELRegOpts() # to store weights if len(param_nums) == len(params): llr = opt_fun_inst._opt_nuis_regress( [], param_nums=param_nums, endog=self.model.endog, exog=self.model.exog, nobs=self.model.nobs, nvar=self.model.exog.shape[1], params=params, b0_vals=b0_vals, stochastic_exog=stochastic_exog) pval = 1 - stats.chi2.cdf(llr, len(param_nums)) if return_weights: return llr, pval, opt_fun_inst.new_weights else: return llr, pval x0 = np.delete(params, param_nums) args = (param_nums, self.model.endog, self.model.exog, self.model.nobs, self.model.exog.shape[1], params, b0_vals, stochastic_exog) if method == 'nm': llr = optimize.fmin(opt_fun_inst._opt_nuis_regress, x0, maxfun=10000, maxiter=10000, full_output=1, disp=0, args=args)[1] if method == 'powell': llr = optimize.fmin_powell(opt_fun_inst._opt_nuis_regress, x0, full_output=1, disp=0, args=args)[1] pval = 1 - stats.chi2.cdf(llr, len(param_nums)) if ret_params: return llr, pval, opt_fun_inst.new_weights, opt_fun_inst.new_params elif return_weights: return llr, pval, opt_fun_inst.new_weights else: return llr, pval def conf_int_el(self, param_num, sig=.05, upper_bound=None, lower_bound=None, method='nm', stochastic_exog=True): """ Compute the confidence interval using Empirical Likelihood. Parameters ---------- param_num : float The parameter for which the confidence interval is desired. sig : float The significance level. Default is 0.05. upper_bound : float The maximum value the upper limit can be. Default is the 99.9% confidence value under OLS assumptions. lower_bound : float The minimum value the lower limit can be. Default is the 99.9% confidence value under OLS assumptions. method : str Can either be 'nm' for Nelder-Mead or 'powell' for Powell. The optimization method that optimizes over nuisance parameters. The default is 'nm'. stochastic_exog : bool When True, the exogenous variables are assumed to be stochastic. When the regressors are nonstochastic, moment conditions are placed on the exogenous variables. Confidence intervals for stochastic regressors are at least as large as non-stochastic regressors. The default is True. Returns ------- lowerl : float The lower bound of the confidence interval. upperl : float The upper bound of the confidence interval. See Also -------- el_test : Test parameters using Empirical Likelihood. Notes ----- This function uses brentq to find the value of beta where test_beta([beta], param_num)[1] is equal to the critical value. The function returns the results of each iteration of brentq at each value of beta. The current function value of the last printed optimization should be the critical value at the desired significance level. For alpha=.05, the value is 3.841459. To ensure optimization terminated successfully, it is suggested to do el_test([lower_limit], [param_num]). If the optimization does not terminate successfully, consider switching optimization algorithms. If optimization is still not successful, try changing the values of start_int_params. If the current function value repeatedly jumps from a number between 0 and the critical value and a very large number (>50), the starting parameters of the interior minimization need to be changed. """ r0 = stats.chi2.ppf(1 - sig, 1) if upper_bound is None: upper_bound = self.conf_int(.01)[param_num][1] if lower_bound is None: lower_bound = self.conf_int(.01)[param_num][0] def f(b0): return self.el_test(np.array([b0]), np.array([param_num]), method=method, stochastic_exog=stochastic_exog)[0] - r0 lowerl = optimize.brenth(f, lower_bound, self.params[param_num]) upperl = optimize.brenth(f, self.params[param_num], upper_bound) # ^ Seems to be faster than brentq in most cases return (lowerl, upperl) class RegressionResultsWrapper(wrap.ResultsWrapper): _attrs = { 'chisq': 'columns', 'sresid': 'rows', 'weights': 'rows', 'wresid': 'rows', 'bcov_unscaled': 'cov', 'bcov_scaled': 'cov', 'HC0_se': 'columns', 'HC1_se': 'columns', 'HC2_se': 'columns', 'HC3_se': 'columns', 'norm_resid': 'rows', } _wrap_attrs = wrap.union_dicts(base.LikelihoodResultsWrapper._attrs, _attrs) _methods = {} _wrap_methods = wrap.union_dicts( base.LikelihoodResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(RegressionResultsWrapper, RegressionResults) statsmodels-0.12.2/statsmodels/regression/mixed_linear_model.py000066400000000000000000003145171400612667500250740ustar00rootroot00000000000000""" Linear mixed effects models are regression models for dependent data. They can be used to estimate regression relationships involving both means and variances. These models are also known as multilevel linear models, and hierarchical linear models. The MixedLM class fits linear mixed effects models to data, and provides support for some common post-estimation tasks. This is a group-based implementation that is most efficient for models in which the data can be partitioned into independent groups. Some models with crossed effects can be handled by specifying a model with a single group. The data are partitioned into disjoint groups. The probability model for group i is: Y = X*beta + Z*gamma + epsilon where * n_i is the number of observations in group i * Y is a n_i dimensional response vector (called endog in MixedLM) * X is a n_i x k_fe dimensional design matrix for the fixed effects (called exog in MixedLM) * beta is a k_fe-dimensional vector of fixed effects parameters (called fe_params in MixedLM) * Z is a design matrix for the random effects with n_i rows (called exog_re in MixedLM). The number of columns in Z can vary by group as discussed below. * gamma is a random vector with mean 0. The covariance matrix for the first `k_re` elements of `gamma` (called cov_re in MixedLM) is common to all groups. The remaining elements of `gamma` are variance components as discussed in more detail below. Each group receives its own independent realization of gamma. * epsilon is a n_i dimensional vector of iid normal errors with mean 0 and variance sigma^2; the epsilon values are independent both within and between groups Y, X and Z must be entirely observed. beta, Psi, and sigma^2 are estimated using ML or REML estimation, and gamma and epsilon are random so define the probability model. The marginal mean structure is E[Y | X, Z] = X*beta. If only the mean structure is of interest, GEE is an alternative to using linear mixed models. Two types of random effects are supported. Standard random effects are correlated with each other in arbitrary ways. Every group has the same number (`k_re`) of standard random effects, with the same joint distribution (but with independent realizations across the groups). Variance components are uncorrelated with each other, and with the standard random effects. Each variance component has mean zero, and all realizations of a given variance component have the same variance parameter. The number of realized variance components per variance parameter can differ across the groups. The primary reference for the implementation details is: MJ Lindstrom, DM Bates (1988). "Newton Raphson and EM algorithms for linear mixed effects models for repeated measures data". Journal of the American Statistical Association. Volume 83, Issue 404, pages 1014-1022. See also this more recent document: http://econ.ucsb.edu/~doug/245a/Papers/Mixed%20Effects%20Implement.pdf All the likelihood, gradient, and Hessian calculations closely follow Lindstrom and Bates 1988, adapted to support variance components. The following two documents are written more from the perspective of users: http://lme4.r-forge.r-project.org/lMMwR/lrgprt.pdf http://lme4.r-forge.r-project.org/slides/2009-07-07-Rennes/3Longitudinal-4.pdf Notation: * `cov_re` is the random effects covariance matrix (referred to above as Psi) and `scale` is the (scalar) error variance. For a single group, the marginal covariance matrix of endog given exog is scale*I + Z * cov_re * Z', where Z is the design matrix for the random effects in one group. * `vcomp` is a vector of variance parameters. The length of `vcomp` is determined by the number of keys in either the `exog_vc` argument to ``MixedLM``, or the `vc_formula` argument when using formulas to fit a model. Notes: 1. Three different parameterizations are used in different places. The regression slopes (usually called `fe_params`) are identical in all three parameterizations, but the variance parameters differ. The parameterizations are: * The "user parameterization" in which cov(endog) = scale*I + Z * cov_re * Z', as described above. This is the main parameterization visible to the user. * The "profile parameterization" in which cov(endog) = I + Z * cov_re1 * Z'. This is the parameterization of the profile likelihood that is maximized to produce parameter estimates. (see Lindstrom and Bates for details). The "user" cov_re is equal to the "profile" cov_re1 times the scale. * The "square root parameterization" in which we work with the Cholesky factor of cov_re1 instead of cov_re directly. This is hidden from the user. All three parameterizations can be packed into a vector by (optionally) concatenating `fe_params` together with the lower triangle or Cholesky square root of the dependence structure, followed by the variance parameters for the variance components. The are stored as square roots if (and only if) the random effects covariance matrix is stored as its Cholesky factor. Note that when unpacking, it is important to either square or reflect the dependence structure depending on which parameterization is being used. Two score methods are implemented. One takes the score with respect to the elements of the random effects covariance matrix (used for inference once the MLE is reached), and the other takes the score with respect to the parameters of the Cholesky square root of the random effects covariance matrix (used for optimization). The numerical optimization uses GLS to avoid explicitly optimizing over the fixed effects parameters. The likelihood that is optimized is profiled over both the scale parameter (a scalar) and the fixed effects parameters (if any). As a result of this profiling, it is difficult and unnecessary to calculate the Hessian of the profiled log likelihood function, so that calculation is not implemented here. Therefore, optimization methods requiring the Hessian matrix such as the Newton-Raphson algorithm cannot be used for model fitting. """ import warnings import numpy as np from scipy.stats.distributions import norm from scipy import sparse import pandas as pd import patsy from statsmodels.base._penalties import Penalty import statsmodels.base.model as base from statsmodels.tools.decorators import cache_readonly from statsmodels.tools import data as data_tools from statsmodels.tools.sm_exceptions import ConvergenceWarning _warn_cov_sing = "The random effects covariance matrix is singular." def _dot(x, y): """ Returns the dot product of the arrays, works for sparse and dense. """ if isinstance(x, np.ndarray) and isinstance(y, np.ndarray): return np.dot(x, y) elif sparse.issparse(x): return x.dot(y) elif sparse.issparse(y): return y.T.dot(x.T).T # From numpy, adapted to work with sparse and dense arrays. def _multi_dot_three(A, B, C): """ Find best ordering for three arrays and do the multiplication. Doing in manually instead of using dynamic programing is approximately 15 times faster. """ # cost1 = cost((AB)C) cost1 = (A.shape[0] * A.shape[1] * B.shape[1] + # (AB) A.shape[0] * B.shape[1] * C.shape[1]) # (--)C # cost2 = cost((AB)C) cost2 = (B.shape[0] * B.shape[1] * C.shape[1] + # (BC) A.shape[0] * A.shape[1] * C.shape[1]) # A(--) if cost1 < cost2: return _dot(_dot(A, B), C) else: return _dot(A, _dot(B, C)) def _dotsum(x, y): """ Returns sum(x * y), where '*' is the pointwise product, computed efficiently for dense and sparse matrices. """ if sparse.issparse(x): return x.multiply(y).sum() else: # This way usually avoids allocating a temporary. return np.dot(x.ravel(), y.ravel()) class VCSpec(object): """ Define the variance component structure of a multilevel model. An instance of the class contains three attributes: - names : names[k] is the name of variance component k. - mats : mats[k][i] is the design matrix for group index i in variance component k. - colnames : colnames[k][i] is the list of column names for mats[k][i]. The groups in colnames and mats must be in sorted order. """ def __init__(self, names, colnames, mats): self.names = names self.colnames = colnames self.mats = mats def _get_exog_re_names(self, exog_re): """ Passes through if given a list of names. Otherwise, gets pandas names or creates some generic variable names as needed. """ if self.k_re == 0: return [] if isinstance(exog_re, pd.DataFrame): return exog_re.columns.tolist() elif isinstance(exog_re, pd.Series) and exog_re.name is not None: return [exog_re.name] elif isinstance(exog_re, list): return exog_re # Default names defnames = ["x_re{0:1d}".format(k + 1) for k in range(exog_re.shape[1])] return defnames class MixedLMParams(object): """ This class represents a parameter state for a mixed linear model. Parameters ---------- k_fe : int The number of covariates with fixed effects. k_re : int The number of covariates with random coefficients (excluding variance components). k_vc : int The number of variance components parameters. Notes ----- This object represents the parameter state for the model in which the scale parameter has been profiled out. """ def __init__(self, k_fe, k_re, k_vc): self.k_fe = k_fe self.k_re = k_re self.k_re2 = k_re * (k_re + 1) // 2 self.k_vc = k_vc self.k_tot = self.k_fe + self.k_re2 + self.k_vc self._ix = np.tril_indices(self.k_re) def from_packed(params, k_fe, k_re, use_sqrt, has_fe): """ Create a MixedLMParams object from packed parameter vector. Parameters ---------- params : array_like The mode parameters packed into a single vector. k_fe : int The number of covariates with fixed effects k_re : int The number of covariates with random effects (excluding variance components). use_sqrt : bool If True, the random effects covariance matrix is provided as its Cholesky factor, otherwise the lower triangle of the covariance matrix is stored. has_fe : bool If True, `params` contains fixed effects parameters. Otherwise, the fixed effects parameters are set to zero. Returns ------- A MixedLMParams object. """ k_re2 = int(k_re * (k_re + 1) / 2) # The number of covariance parameters. if has_fe: k_vc = len(params) - k_fe - k_re2 else: k_vc = len(params) - k_re2 pa = MixedLMParams(k_fe, k_re, k_vc) cov_re = np.zeros((k_re, k_re)) ix = pa._ix if has_fe: pa.fe_params = params[0:k_fe] cov_re[ix] = params[k_fe:k_fe+k_re2] else: pa.fe_params = np.zeros(k_fe) cov_re[ix] = params[0:k_re2] if use_sqrt: cov_re = np.dot(cov_re, cov_re.T) else: cov_re = (cov_re + cov_re.T) - np.diag(np.diag(cov_re)) pa.cov_re = cov_re if k_vc > 0: if use_sqrt: pa.vcomp = params[-k_vc:]**2 else: pa.vcomp = params[-k_vc:] else: pa.vcomp = np.array([]) return pa from_packed = staticmethod(from_packed) def from_components(fe_params=None, cov_re=None, cov_re_sqrt=None, vcomp=None): """ Create a MixedLMParams object from each parameter component. Parameters ---------- fe_params : array_like The fixed effects parameter (a 1-dimensional array). If None, there are no fixed effects. cov_re : array_like The random effects covariance matrix (a square, symmetric 2-dimensional array). cov_re_sqrt : array_like The Cholesky (lower triangular) square root of the random effects covariance matrix. vcomp : array_like The variance component parameters. If None, there are no variance components. Returns ------- A MixedLMParams object. """ if vcomp is None: vcomp = np.empty(0) if fe_params is None: fe_params = np.empty(0) if cov_re is None and cov_re_sqrt is None: cov_re = np.empty((0, 0)) k_fe = len(fe_params) k_vc = len(vcomp) k_re = cov_re.shape[0] if cov_re is not None else cov_re_sqrt.shape[0] pa = MixedLMParams(k_fe, k_re, k_vc) pa.fe_params = fe_params if cov_re_sqrt is not None: pa.cov_re = np.dot(cov_re_sqrt, cov_re_sqrt.T) elif cov_re is not None: pa.cov_re = cov_re pa.vcomp = vcomp return pa from_components = staticmethod(from_components) def copy(self): """ Returns a copy of the object. """ obj = MixedLMParams(self.k_fe, self.k_re, self.k_vc) obj.fe_params = self.fe_params.copy() obj.cov_re = self.cov_re.copy() obj.vcomp = self.vcomp.copy() return obj def get_packed(self, use_sqrt, has_fe=False): """ Return the model parameters packed into a single vector. Parameters ---------- use_sqrt : bool If True, the Cholesky square root of `cov_re` is included in the packed result. Otherwise the lower triangle of `cov_re` is included. has_fe : bool If True, the fixed effects parameters are included in the packed result, otherwise they are omitted. """ if self.k_re > 0: if use_sqrt: try: L = np.linalg.cholesky(self.cov_re) except np.linalg.LinAlgError: L = np.diag(np.sqrt(np.diag(self.cov_re))) cpa = L[self._ix] else: cpa = self.cov_re[self._ix] else: cpa = np.zeros(0) if use_sqrt: vcomp = np.sqrt(self.vcomp) else: vcomp = self.vcomp if has_fe: pa = np.concatenate((self.fe_params, cpa, vcomp)) else: pa = np.concatenate((cpa, vcomp)) return pa def _smw_solver(s, A, AtA, Qi, di): r""" Returns a solver for the linear system: .. math:: (sI + ABA^\prime) y = x The returned function f satisfies f(x) = y as defined above. B and its inverse matrix are block diagonal. The upper left block of :math:`B^{-1}` is Qi and its lower right block is diag(di). Parameters ---------- s : scalar See above for usage A : ndarray p x q matrix, in general q << p, may be sparse. AtA : square ndarray :math:`A^\prime A`, a q x q matrix. Qi : square symmetric ndarray The matrix `B` is q x q, where q = r + d. `B` consists of a r x r diagonal block whose inverse is `Qi`, and a d x d diagonal block, whose inverse is diag(di). di : 1d array_like See documentation for Qi. Returns ------- A function for solving a linear system, as documented above. Notes ----- Uses Sherman-Morrison-Woodbury identity: https://en.wikipedia.org/wiki/Woodbury_matrix_identity """ # Use SMW identity qmat = AtA / s m = Qi.shape[0] qmat[0:m, 0:m] += Qi if sparse.issparse(A): qmat[m:, m:] += sparse.diags(di) def solver(rhs): ql = A.T.dot(rhs) # Based on profiling, the next line can be the # majority of the entire run time of fitting the model. ql = sparse.linalg.spsolve(qmat, ql) if ql.ndim < rhs.ndim: # spsolve squeezes nx1 rhs ql = ql[:, None] ql = A.dot(ql) return rhs / s - ql / s**2 else: d = qmat.shape[0] qmat.flat[m*(d+1)::d+1] += di qmati = np.linalg.solve(qmat, A.T) def solver(rhs): # A is tall and qmati is wide, so we want # A * (qmati * rhs) not (A * qmati) * rhs ql = np.dot(qmati, rhs) ql = np.dot(A, ql) return rhs / s - ql / s**2 return solver def _smw_logdet(s, A, AtA, Qi, di, B_logdet): r""" Returns the log determinant of .. math:: sI + ABA^\prime Uses the matrix determinant lemma to accelerate the calculation. B is assumed to be positive definite, and s > 0, therefore the determinant is positive. Parameters ---------- s : positive scalar See above for usage A : ndarray p x q matrix, in general q << p. AtA : square ndarray :math:`A^\prime A`, a q x q matrix. Qi : square symmetric ndarray The matrix `B` is q x q, where q = r + d. `B` consists of a r x r diagonal block whose inverse is `Qi`, and a d x d diagonal block, whose inverse is diag(di). di : 1d array_like See documentation for Qi. B_logdet : real The log determinant of B Returns ------- The log determinant of s*I + A*B*A'. Notes ----- Uses the matrix determinant lemma: https://en.wikipedia.org/wiki/Matrix_determinant_lemma """ p = A.shape[0] ld = p * np.log(s) qmat = AtA / s m = Qi.shape[0] qmat[0:m, 0:m] += Qi if sparse.issparse(qmat): qmat[m:, m:] += sparse.diags(di) # There are faster but much more difficult ways to do this # https://stackoverflow.com/questions/19107617 lu = sparse.linalg.splu(qmat) dl = lu.L.diagonal().astype(np.complex128) du = lu.U.diagonal().astype(np.complex128) ld1 = np.log(dl).sum() + np.log(du).sum() ld1 = ld1.real else: d = qmat.shape[0] qmat.flat[m*(d+1)::d+1] += di _, ld1 = np.linalg.slogdet(qmat) return B_logdet + ld + ld1 def _convert_vc(exog_vc): vc_names = [] vc_colnames = [] vc_mats = [] # Get the groups in sorted order groups = set([]) for k, v in exog_vc.items(): groups |= set(v.keys()) groups = list(groups) groups.sort() for k, v in exog_vc.items(): vc_names.append(k) colnames, mats = [], [] for g in groups: try: colnames.append(v[g].columns) except AttributeError: colnames.append([str(j) for j in range(v[g].shape[1])]) mats.append(v[g]) vc_colnames.append(colnames) vc_mats.append(mats) ii = np.argsort(vc_names) vc_names = [vc_names[i] for i in ii] vc_colnames = [vc_colnames[i] for i in ii] vc_mats = [vc_mats[i] for i in ii] return VCSpec(vc_names, vc_colnames, vc_mats) class MixedLM(base.LikelihoodModel): """ Linear Mixed Effects Model Parameters ---------- endog : 1d array_like The dependent variable exog : 2d array_like A matrix of covariates used to determine the mean structure (the "fixed effects" covariates). groups : 1d array_like A vector of labels determining the groups -- data from different groups are independent exog_re : 2d array_like A matrix of covariates used to determine the variance and covariance structure (the "random effects" covariates). If None, defaults to a random intercept for each group. exog_vc : VCSpec instance or dict-like (deprecated) A VCSPec instance defines the structure of the variance components in the model. Alternatively, see notes below for a dictionary-based format. The dictionary format is deprecated and may be removed at some point in the future. use_sqrt : bool If True, optimization is carried out using the lower triangle of the square root of the random effects covariance matrix, otherwise it is carried out using the lower triangle of the random effects covariance matrix. missing : str The approach to missing data handling Notes ----- If `exog_vc` is not a `VCSpec` instance, then it must be a dictionary of dictionaries. Specifically, `exog_vc[a][g]` is a matrix whose columns are linearly combined using independent random coefficients. This random term then contributes to the variance structure of the data for group `g`. The random coefficients all have mean zero, and have the same variance. The matrix must be `m x k`, where `m` is the number of observations in group `g`. The number of columns may differ among the top-level groups. The covariates in `exog`, `exog_re` and `exog_vc` may (but need not) partially or wholly overlap. `use_sqrt` should almost always be set to True. The main use case for use_sqrt=False is when complicated patterns of fixed values in the covariance structure are set (using the `free` argument to `fit`) that cannot be expressed in terms of the Cholesky factor L. Examples -------- A basic mixed model with fixed effects for the columns of ``exog`` and a random intercept for each distinct value of ``group``: >>> model = sm.MixedLM(endog, exog, groups) >>> result = model.fit() A mixed model with fixed effects for the columns of ``exog`` and correlated random coefficients for the columns of ``exog_re``: >>> model = sm.MixedLM(endog, exog, groups, exog_re=exog_re) >>> result = model.fit() A mixed model with fixed effects for the columns of ``exog`` and independent random coefficients for the columns of ``exog_re``: >>> free = MixedLMParams.from_components( fe_params=np.ones(exog.shape[1]), cov_re=np.eye(exog_re.shape[1])) >>> model = sm.MixedLM(endog, exog, groups, exog_re=exog_re) >>> result = model.fit(free=free) A different way to specify independent random coefficients for the columns of ``exog_re``. In this example ``groups`` must be a Pandas Series with compatible indexing with ``exog_re``, and ``exog_re`` has two columns. >>> g = pd.groupby(groups, by=groups).groups >>> vc = {} >>> vc['1'] = {k : exog_re.loc[g[k], 0] for k in g} >>> vc['2'] = {k : exog_re.loc[g[k], 1] for k in g} >>> model = sm.MixedLM(endog, exog, groups, vcomp=vc) >>> result = model.fit() """ def __init__(self, endog, exog, groups, exog_re=None, exog_vc=None, use_sqrt=True, missing='none', **kwargs): _allowed_kwargs = ["missing_idx", "design_info", "formula"] for x in kwargs.keys(): if x not in _allowed_kwargs: raise ValueError( "argument %s not permitted for MixedLM initialization" % x) self.use_sqrt = use_sqrt # Some defaults self.reml = True self.fe_pen = None self.re_pen = None if isinstance(exog_vc, dict): warnings.warn("Using deprecated variance components format") # Convert from old to new representation exog_vc = _convert_vc(exog_vc) if exog_vc is not None: self.k_vc = len(exog_vc.names) self.exog_vc = exog_vc else: self.k_vc = 0 self.exog_vc = VCSpec([], [], []) # If there is one covariate, it may be passed in as a column # vector, convert these to 2d arrays. # TODO: Can this be moved up in the class hierarchy? # yes, it should be done up the hierarchy if (exog is not None and data_tools._is_using_ndarray_type(exog, None) and exog.ndim == 1): exog = exog[:, None] if (exog_re is not None and data_tools._is_using_ndarray_type(exog_re, None) and exog_re.ndim == 1): exog_re = exog_re[:, None] # Calling super creates self.endog, etc. as ndarrays and the # original exog, endog, etc. are self.data.endog, etc. super(MixedLM, self).__init__(endog, exog, groups=groups, exog_re=exog_re, missing=missing, **kwargs) self._init_keys.extend(["use_sqrt", "exog_vc"]) # Number of fixed effects parameters self.k_fe = exog.shape[1] if exog_re is None and len(self.exog_vc.names) == 0: # Default random effects structure (random intercepts). self.k_re = 1 self.k_re2 = 1 self.exog_re = np.ones((len(endog), 1), dtype=np.float64) self.data.exog_re = self.exog_re names = ['Group Var'] self.data.param_names = self.exog_names + names self.data.exog_re_names = names self.data.exog_re_names_full = names elif exog_re is not None: # Process exog_re the same way that exog is handled # upstream # TODO: this is wrong and should be handled upstream wholly self.data.exog_re = exog_re self.exog_re = np.asarray(exog_re) if self.exog_re.ndim == 1: self.exog_re = self.exog_re[:, None] # Model dimensions # Number of random effect covariates self.k_re = self.exog_re.shape[1] # Number of covariance parameters self.k_re2 = self.k_re * (self.k_re + 1) // 2 else: # All random effects are variance components self.k_re = 0 self.k_re2 = 0 if not self.data._param_names: # HACK: could have been set in from_formula already # needs refactor (param_names, exog_re_names, exog_re_names_full) = self._make_param_names(exog_re) self.data.param_names = param_names self.data.exog_re_names = exog_re_names self.data.exog_re_names_full = exog_re_names_full self.k_params = self.k_fe + self.k_re2 # Convert the data to the internal representation, which is a # list of arrays, corresponding to the groups. group_labels = list(set(groups)) group_labels.sort() row_indices = dict((s, []) for s in group_labels) for i, g in enumerate(groups): row_indices[g].append(i) self.row_indices = row_indices self.group_labels = group_labels self.n_groups = len(self.group_labels) # Split the data by groups self.endog_li = self.group_list(self.endog) self.exog_li = self.group_list(self.exog) self.exog_re_li = self.group_list(self.exog_re) # Precompute this. if self.exog_re is None: self.exog_re2_li = None else: self.exog_re2_li = [np.dot(x.T, x) for x in self.exog_re_li] # The total number of observations, summed over all groups self.nobs = len(self.endog) self.n_totobs = self.nobs # Set the fixed effects parameter names if self.exog_names is None: self.exog_names = ["FE%d" % (k + 1) for k in range(self.exog.shape[1])] # Precompute this self._aex_r = [] self._aex_r2 = [] for i in range(self.n_groups): a = self._augment_exog(i) self._aex_r.append(a) ma = _dot(a.T, a) self._aex_r2.append(ma) # Precompute this self._lin, self._quad = self._reparam() def _make_param_names(self, exog_re): """ Returns the full parameter names list, just the exogenous random effects variables, and the exogenous random effects variables with the interaction terms. """ exog_names = list(self.exog_names) exog_re_names = _get_exog_re_names(self, exog_re) param_names = [] jj = self.k_fe for i in range(len(exog_re_names)): for j in range(i + 1): if i == j: param_names.append(exog_re_names[i] + " Var") else: param_names.append(exog_re_names[j] + " x " + exog_re_names[i] + " Cov") jj += 1 vc_names = [x + " Var" for x in self.exog_vc.names] return exog_names + param_names + vc_names, exog_re_names, param_names @classmethod def from_formula(cls, formula, data, re_formula=None, vc_formula=None, subset=None, use_sparse=False, missing='none', *args, **kwargs): """ Create a Model from a formula and dataframe. Parameters ---------- formula : str or generic Formula object The formula specifying the model data : array_like The data for the model. See Notes. re_formula : str A one-sided formula defining the variance structure of the model. The default gives a random intercept for each group. vc_formula : dict-like Formulas describing variance components. `vc_formula[vc]` is the formula for the component with variance parameter named `vc`. The formula is processed into a matrix, and the columns of this matrix are linearly combined with independent random coefficients having mean zero and a common variance. subset : array_like An array-like object of booleans, integers, or index values that indicate the subset of df to use in the model. Assumes df is a `pandas.DataFrame` missing : str Either 'none' or 'drop' args : extra arguments These are passed to the model kwargs : extra keyword arguments These are passed to the model with one exception. The ``eval_env`` keyword is passed to patsy. It can be either a :class:`patsy:patsy.EvalEnvironment` object or an integer indicating the depth of the namespace to use. For example, the default ``eval_env=0`` uses the calling namespace. If you wish to use a "clean" environment set ``eval_env=-1``. Returns ------- model : Model instance Notes ----- `data` must define __getitem__ with the keys in the formula terms args and kwargs are passed on to the model instantiation. E.g., a numpy structured or rec array, a dictionary, or a pandas DataFrame. If the variance component is intended to produce random intercepts for disjoint subsets of a group, specified by string labels or a categorical data value, always use '0 +' in the formula so that no overall intercept is included. If the variance components specify random slopes and you do not also want a random group-level intercept in the model, then use '0 +' in the formula to exclude the intercept. The variance components formulas are processed separately for each group. If a variable is categorical the results will not be affected by whether the group labels are distinct or re-used over the top-level groups. Examples -------- Suppose we have data from an educational study with students nested in classrooms nested in schools. The students take a test, and we want to relate the test scores to the students' ages, while accounting for the effects of classrooms and schools. The school will be the top-level group, and the classroom is a nested group that is specified as a variance component. Note that the schools may have different number of classrooms, and the classroom labels may (but need not be) different across the schools. >>> vc = {'classroom': '0 + C(classroom)'} >>> MixedLM.from_formula('test_score ~ age', vc_formula=vc, \ re_formula='1', groups='school', data=data) Now suppose we also have a previous test score called 'pretest'. If we want the relationship between pretest scores and the current test to vary by classroom, we can specify a random slope for the pretest score >>> vc = {'classroom': '0 + C(classroom)', 'pretest': '0 + pretest'} >>> MixedLM.from_formula('test_score ~ age + pretest', vc_formula=vc, \ re_formula='1', groups='school', data=data) The following model is almost equivalent to the previous one, but here the classroom random intercept and pretest slope may be correlated. >>> vc = {'classroom': '0 + C(classroom)'} >>> MixedLM.from_formula('test_score ~ age + pretest', vc_formula=vc, \ re_formula='1 + pretest', groups='school', \ data=data) """ if "groups" not in kwargs.keys(): raise AttributeError("'groups' is a required keyword argument " + "in MixedLM.from_formula") groups = kwargs["groups"] # If `groups` is a variable name, retrieve the data for the # groups variable. group_name = "Group" if isinstance(groups, str): group_name = groups groups = np.asarray(data[groups]) else: groups = np.asarray(groups) del kwargs["groups"] # Bypass all upstream missing data handling to properly handle # variance components if missing == 'drop': data, groups = _handle_missing(data, groups, formula, re_formula, vc_formula) missing = 'none' if re_formula is not None: if re_formula.strip() == "1": # Work around Patsy bug, fixed by 0.3. exog_re = np.ones((data.shape[0], 1)) exog_re_names = [group_name] else: eval_env = kwargs.get('eval_env', None) if eval_env is None: eval_env = 1 elif eval_env == -1: from patsy import EvalEnvironment eval_env = EvalEnvironment({}) exog_re = patsy.dmatrix(re_formula, data, eval_env=eval_env) exog_re_names = exog_re.design_info.column_names exog_re_names = [x.replace("Intercept", group_name) for x in exog_re_names] exog_re = np.asarray(exog_re) if exog_re.ndim == 1: exog_re = exog_re[:, None] else: exog_re = None if vc_formula is None: exog_re_names = [group_name] else: exog_re_names = [] if vc_formula is not None: eval_env = kwargs.get('eval_env', None) if eval_env is None: eval_env = 1 elif eval_env == -1: from patsy import EvalEnvironment eval_env = EvalEnvironment({}) vc_mats = [] vc_colnames = [] vc_names = [] gb = data.groupby(groups) kylist = sorted(gb.groups.keys()) vcf = sorted(vc_formula.keys()) for vc_name in vcf: md = patsy.ModelDesc.from_formula(vc_formula[vc_name]) vc_names.append(vc_name) evc_mats, evc_colnames = [], [] for group_ix, group in enumerate(kylist): ii = gb.groups[group] mat = patsy.dmatrix( md, data.loc[ii, :], eval_env=eval_env, return_type='dataframe') evc_colnames.append(mat.columns.tolist()) if use_sparse: evc_mats.append(sparse.csr_matrix(mat)) else: evc_mats.append(np.asarray(mat)) vc_mats.append(evc_mats) vc_colnames.append(evc_colnames) exog_vc = VCSpec(vc_names, vc_colnames, vc_mats) else: exog_vc = VCSpec([], [], []) kwargs["subset"] = None kwargs["exog_re"] = exog_re kwargs["exog_vc"] = exog_vc kwargs["groups"] = groups mod = super(MixedLM, cls).from_formula( formula, data, *args, **kwargs) # expand re names to account for pairs of RE (param_names, exog_re_names, exog_re_names_full) = mod._make_param_names(exog_re_names) mod.data.param_names = param_names mod.data.exog_re_names = exog_re_names mod.data.exog_re_names_full = exog_re_names_full if vc_formula is not None: mod.data.vcomp_names = mod.exog_vc.names return mod def predict(self, params, exog=None): """ Return predicted values from a design matrix. Parameters ---------- params : array_like Parameters of a mixed linear model. Can be either a MixedLMParams instance, or a vector containing the packed model parameters in which the fixed effects parameters are at the beginning of the vector, or a vector containing only the fixed effects parameters. exog : array_like, optional Design / exogenous data for the fixed effects. Model exog is used if None. Returns ------- An array of fitted values. Note that these predicted values only reflect the fixed effects mean structure of the model. """ if exog is None: exog = self.exog if isinstance(params, MixedLMParams): params = params.fe_params else: params = params[0:self.k_fe] return np.dot(exog, params) def group_list(self, array): """ Returns `array` split into subarrays corresponding to the grouping structure. """ if array is None: return None if array.ndim == 1: return [np.array(array[self.row_indices[k]]) for k in self.group_labels] else: return [np.array(array[self.row_indices[k], :]) for k in self.group_labels] def fit_regularized(self, start_params=None, method='l1', alpha=0, ceps=1e-4, ptol=1e-6, maxit=200, **fit_kwargs): """ Fit a model in which the fixed effects parameters are penalized. The dependence parameters are held fixed at their estimated values in the unpenalized model. Parameters ---------- method : str of Penalty object Method for regularization. If a string, must be 'l1'. alpha : array_like Scalar or vector of penalty weights. If a scalar, the same weight is applied to all coefficients; if a vector, it contains a weight for each coefficient. If method is a Penalty object, the weights are scaled by alpha. For L1 regularization, the weights are used directly. ceps : positive real scalar Fixed effects parameters smaller than this value in magnitude are treated as being zero. ptol : positive real scalar Convergence occurs when the sup norm difference between successive values of `fe_params` is less than `ptol`. maxit : int The maximum number of iterations. **fit_kwargs Additional keyword arguments passed to fit. Returns ------- A MixedLMResults instance containing the results. Notes ----- The covariance structure is not updated as the fixed effects parameters are varied. The algorithm used here for L1 regularization is a"shooting" or cyclic coordinate descent algorithm. If method is 'l1', then `fe_pen` and `cov_pen` are used to obtain the covariance structure, but are ignored during the L1-penalized fitting. References ---------- Friedman, J. H., Hastie, T. and Tibshirani, R. Regularized Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, 33(1) (2008) http://www.jstatsoft.org/v33/i01/paper http://statweb.stanford.edu/~tibs/stat315a/Supplements/fuse.pdf """ if isinstance(method, str) and (method.lower() != 'l1'): raise ValueError("Invalid regularization method") # If method is a smooth penalty just optimize directly. if isinstance(method, Penalty): # Scale the penalty weights by alpha method.alpha = alpha fit_kwargs.update({"fe_pen": method}) return self.fit(**fit_kwargs) if np.isscalar(alpha): alpha = alpha * np.ones(self.k_fe, dtype=np.float64) # Fit the unpenalized model to get the dependence structure. mdf = self.fit(**fit_kwargs) fe_params = mdf.fe_params cov_re = mdf.cov_re vcomp = mdf.vcomp scale = mdf.scale try: cov_re_inv = np.linalg.inv(cov_re) except np.linalg.LinAlgError: cov_re_inv = None for itr in range(maxit): fe_params_s = fe_params.copy() for j in range(self.k_fe): if abs(fe_params[j]) < ceps: continue # The residuals fe_params[j] = 0. expval = np.dot(self.exog, fe_params) resid_all = self.endog - expval # The loss function has the form # a*x^2 + b*x + pwt*|x| a, b = 0., 0. for group_ix, group in enumerate(self.group_labels): vc_var = self._expand_vcomp(vcomp, group_ix) exog = self.exog_li[group_ix] ex_r, ex2_r = self._aex_r[group_ix], self._aex_r2[group_ix] resid = resid_all[self.row_indices[group]] solver = _smw_solver(scale, ex_r, ex2_r, cov_re_inv, 1 / vc_var) x = exog[:, j] u = solver(x) a += np.dot(u, x) b -= 2 * np.dot(u, resid) pwt1 = alpha[j] if b > pwt1: fe_params[j] = -(b - pwt1) / (2 * a) elif b < -pwt1: fe_params[j] = -(b + pwt1) / (2 * a) if np.abs(fe_params_s - fe_params).max() < ptol: break # Replace the fixed effects estimates with their penalized # values, leave the dependence parameters in their unpenalized # state. params_prof = mdf.params.copy() params_prof[0:self.k_fe] = fe_params scale = self.get_scale(fe_params, mdf.cov_re_unscaled, mdf.vcomp) # Get the Hessian including only the nonzero fixed effects, # then blow back up to the full size after inverting. hess, sing = self.hessian(params_prof) if sing: warnings.warn(_warn_cov_sing) pcov = np.nan * np.ones_like(hess) ii = np.abs(params_prof) > ceps ii[self.k_fe:] = True ii = np.flatnonzero(ii) hess1 = hess[ii, :][:, ii] pcov[np.ix_(ii, ii)] = np.linalg.inv(-hess1) params_object = MixedLMParams.from_components(fe_params, cov_re=cov_re) results = MixedLMResults(self, params_prof, pcov / scale) results.params_object = params_object results.fe_params = fe_params results.cov_re = cov_re results.scale = scale results.cov_re_unscaled = mdf.cov_re_unscaled results.method = mdf.method results.converged = True results.cov_pen = self.cov_pen results.k_fe = self.k_fe results.k_re = self.k_re results.k_re2 = self.k_re2 results.k_vc = self.k_vc return MixedLMResultsWrapper(results) def get_fe_params(self, cov_re, vcomp, tol=1e-10): """ Use GLS to update the fixed effects parameter estimates. Parameters ---------- cov_re : array_like (2d) The covariance matrix of the random effects. vcomp : array_like (1d) The variance components. tol : float A tolerance parameter to determine when covariances are singular. Returns ------- params : ndarray The GLS estimates of the fixed effects parameters. singular : bool True if the covariance is singular """ if self.k_fe == 0: return np.array([]), False sing = False if self.k_re == 0: cov_re_inv = np.empty((0, 0)) else: w, v = np.linalg.eigh(cov_re) if w.min() < tol: # Singular, use pseudo-inverse sing = True ii = np.flatnonzero(w >= tol) if len(ii) == 0: cov_re_inv = np.zeros_like(cov_re) else: vi = v[:, ii] wi = w[ii] cov_re_inv = np.dot(vi / wi, vi.T) else: cov_re_inv = np.linalg.inv(cov_re) # Cache these quantities that do not change. if not hasattr(self, "_endex_li"): self._endex_li = [] for group_ix, _ in enumerate(self.group_labels): mat = np.concatenate( (self.exog_li[group_ix], self.endog_li[group_ix][:, None]), axis=1) self._endex_li.append(mat) xtxy = 0. for group_ix, group in enumerate(self.group_labels): vc_var = self._expand_vcomp(vcomp, group_ix) if vc_var.size > 0: if vc_var.min() < tol: # Pseudo-inverse sing = True ii = np.flatnonzero(vc_var >= tol) vc_vari = np.zeros_like(vc_var) vc_vari[ii] = 1 / vc_var[ii] else: vc_vari = 1 / vc_var else: vc_vari = np.empty(0) exog = self.exog_li[group_ix] ex_r, ex2_r = self._aex_r[group_ix], self._aex_r2[group_ix] solver = _smw_solver(1., ex_r, ex2_r, cov_re_inv, vc_vari) u = solver(self._endex_li[group_ix]) xtxy += np.dot(exog.T, u) if sing: fe_params = np.dot(np.linalg.pinv(xtxy[:, 0:-1]), xtxy[:, -1]) else: fe_params = np.linalg.solve(xtxy[:, 0:-1], xtxy[:, -1]) return fe_params, sing def _reparam(self): """ Returns parameters of the map converting parameters from the form used in optimization to the form returned to the user. Returns ------- lin : list-like Linear terms of the map quad : list-like Quadratic terms of the map Notes ----- If P are the standard form parameters and R are the transformed parameters (i.e. with the Cholesky square root covariance and square root transformed variance components), then P[i] = lin[i] * R + R' * quad[i] * R """ k_fe, k_re, k_re2, k_vc = self.k_fe, self.k_re, self.k_re2, self.k_vc k_tot = k_fe + k_re2 + k_vc ix = np.tril_indices(self.k_re) lin = [] for k in range(k_fe): e = np.zeros(k_tot) e[k] = 1 lin.append(e) for k in range(k_re2): lin.append(np.zeros(k_tot)) for k in range(k_vc): lin.append(np.zeros(k_tot)) quad = [] # Quadratic terms for fixed effects. for k in range(k_tot): quad.append(np.zeros((k_tot, k_tot))) # Quadratic terms for random effects covariance. ii = np.tril_indices(k_re) ix = [(a, b) for a, b in zip(ii[0], ii[1])] for i1 in range(k_re2): for i2 in range(k_re2): ix1 = ix[i1] ix2 = ix[i2] if (ix1[1] == ix2[1]) and (ix1[0] <= ix2[0]): ii = (ix2[0], ix1[0]) k = ix.index(ii) quad[k_fe+k][k_fe+i2, k_fe+i1] += 1 for k in range(k_tot): quad[k] = 0.5*(quad[k] + quad[k].T) # Quadratic terms for variance components. km = k_fe + k_re2 for k in range(km, km+k_vc): quad[k][k, k] = 1 return lin, quad def _expand_vcomp(self, vcomp, group_ix): """ Replicate variance parameters to match a group's design. Parameters ---------- vcomp : array_like The variance parameters for the variance components. group_ix : int The group index Returns an expanded version of vcomp, in which each variance parameter is copied as many times as there are independent realizations of the variance component in the given group. """ if len(vcomp) == 0: return np.empty(0) vc_var = [] for j in range(len(self.exog_vc.names)): d = self.exog_vc.mats[j][group_ix].shape[1] vc_var.append(vcomp[j] * np.ones(d)) if len(vc_var) > 0: return np.concatenate(vc_var) else: # Cannot reach here? return np.empty(0) def _augment_exog(self, group_ix): """ Concatenate the columns for variance components to the columns for other random effects to obtain a single random effects exog matrix for a given group. """ ex_r = self.exog_re_li[group_ix] if self.k_re > 0 else None if self.k_vc == 0: return ex_r ex = [ex_r] if self.k_re > 0 else [] any_sparse = False for j, _ in enumerate(self.exog_vc.names): ex.append(self.exog_vc.mats[j][group_ix]) any_sparse |= sparse.issparse(ex[-1]) if any_sparse: for j, x in enumerate(ex): if not sparse.issparse(x): ex[j] = sparse.csr_matrix(x) ex = sparse.hstack(ex) ex = sparse.csr_matrix(ex) else: ex = np.concatenate(ex, axis=1) return ex def loglike(self, params, profile_fe=True): """ Evaluate the (profile) log-likelihood of the linear mixed effects model. Parameters ---------- params : MixedLMParams, or array_like. The parameter value. If array-like, must be a packed parameter vector containing only the covariance parameters. profile_fe : bool If True, replace the provided value of `fe_params` with the GLS estimates. Returns ------- The log-likelihood value at `params`. Notes ----- The scale parameter `scale` is always profiled out of the log-likelihood. In addition, if `profile_fe` is true the fixed effects parameters are also profiled out. """ if type(params) is not MixedLMParams: params = MixedLMParams.from_packed(params, self.k_fe, self.k_re, self.use_sqrt, has_fe=False) cov_re = params.cov_re vcomp = params.vcomp # Move to the profile set if profile_fe: fe_params, sing = self.get_fe_params(cov_re, vcomp) if sing: self._cov_sing += 1 else: fe_params = params.fe_params if self.k_re > 0: try: cov_re_inv = np.linalg.inv(cov_re) except np.linalg.LinAlgError: cov_re_inv = np.linalg.pinv(cov_re) self._cov_sing += 1 _, cov_re_logdet = np.linalg.slogdet(cov_re) else: cov_re_inv = np.zeros((0, 0)) cov_re_logdet = 0 # The residuals expval = np.dot(self.exog, fe_params) resid_all = self.endog - expval likeval = 0. # Handle the covariance penalty if (self.cov_pen is not None) and (self.k_re > 0): likeval -= self.cov_pen.func(cov_re, cov_re_inv) # Handle the fixed effects penalty if (self.fe_pen is not None): likeval -= self.fe_pen.func(fe_params) xvx, qf = 0., 0. for group_ix, group in enumerate(self.group_labels): vc_var = self._expand_vcomp(vcomp, group_ix) cov_aug_logdet = cov_re_logdet + np.sum(np.log(vc_var)) exog = self.exog_li[group_ix] ex_r, ex2_r = self._aex_r[group_ix], self._aex_r2[group_ix] solver = _smw_solver(1., ex_r, ex2_r, cov_re_inv, 1 / vc_var) resid = resid_all[self.row_indices[group]] # Part 1 of the log likelihood (for both ML and REML) ld = _smw_logdet(1., ex_r, ex2_r, cov_re_inv, 1 / vc_var, cov_aug_logdet) likeval -= ld / 2. # Part 2 of the log likelihood (for both ML and REML) u = solver(resid) qf += np.dot(resid, u) # Adjustment for REML if self.reml: mat = solver(exog) xvx += np.dot(exog.T, mat) if self.reml: likeval -= (self.n_totobs - self.k_fe) * np.log(qf) / 2. _, ld = np.linalg.slogdet(xvx) likeval -= ld / 2. likeval -= (self.n_totobs - self.k_fe) * np.log(2 * np.pi) / 2. likeval += ((self.n_totobs - self.k_fe) * np.log(self.n_totobs - self.k_fe) / 2.) likeval -= (self.n_totobs - self.k_fe) / 2. else: likeval -= self.n_totobs * np.log(qf) / 2. likeval -= self.n_totobs * np.log(2 * np.pi) / 2. likeval += self.n_totobs * np.log(self.n_totobs) / 2. likeval -= self.n_totobs / 2. return likeval def _gen_dV_dPar(self, ex_r, solver, group_ix, max_ix=None): """ A generator that yields the element-wise derivative of the marginal covariance matrix with respect to the random effects variance and covariance parameters. ex_r : array_like The random effects design matrix solver : function A function that given x returns V^{-1}x, where V is the group's marginal covariance matrix. group_ix : int The group index max_ix : {int, None} If not None, the generator ends when this index is reached. """ axr = solver(ex_r) # Regular random effects jj = 0 for j1 in range(self.k_re): for j2 in range(j1 + 1): if max_ix is not None and jj > max_ix: return # Need 2d mat_l, mat_r = ex_r[:, j1:j1+1], ex_r[:, j2:j2+1] vsl, vsr = axr[:, j1:j1+1], axr[:, j2:j2+1] yield jj, mat_l, mat_r, vsl, vsr, j1 == j2 jj += 1 # Variance components for j, _ in enumerate(self.exog_vc.names): if max_ix is not None and jj > max_ix: return mat = self.exog_vc.mats[j][group_ix] axmat = solver(mat) yield jj, mat, mat, axmat, axmat, True jj += 1 def score(self, params, profile_fe=True): """ Returns the score vector of the profile log-likelihood. Notes ----- The score vector that is returned is computed with respect to the parameterization defined by this model instance's `use_sqrt` attribute. """ if type(params) is not MixedLMParams: params = MixedLMParams.from_packed( params, self.k_fe, self.k_re, self.use_sqrt, has_fe=False) if profile_fe: params.fe_params, sing = \ self.get_fe_params(params.cov_re, params.vcomp) if sing: msg = "Random effects covariance is singular" warnings.warn(msg) if self.use_sqrt: score_fe, score_re, score_vc = self.score_sqrt( params, calc_fe=not profile_fe) else: score_fe, score_re, score_vc = self.score_full( params, calc_fe=not profile_fe) if self._freepat is not None: score_fe *= self._freepat.fe_params score_re *= self._freepat.cov_re[self._freepat._ix] score_vc *= self._freepat.vcomp if profile_fe: return np.concatenate((score_re, score_vc)) else: return np.concatenate((score_fe, score_re, score_vc)) def score_full(self, params, calc_fe): """ Returns the score with respect to untransformed parameters. Calculates the score vector for the profiled log-likelihood of the mixed effects model with respect to the parameterization in which the random effects covariance matrix is represented in its full form (not using the Cholesky factor). Parameters ---------- params : MixedLMParams or array_like The parameter at which the score function is evaluated. If array-like, must contain the packed random effects parameters (cov_re and vcomp) without fe_params. calc_fe : bool If True, calculate the score vector for the fixed effects parameters. If False, this vector is not calculated, and a vector of zeros is returned in its place. Returns ------- score_fe : array_like The score vector with respect to the fixed effects parameters. score_re : array_like The score vector with respect to the random effects parameters (excluding variance components parameters). score_vc : array_like The score vector with respect to variance components parameters. Notes ----- `score_re` is taken with respect to the parameterization in which `cov_re` is represented through its lower triangle (without taking the Cholesky square root). """ fe_params = params.fe_params cov_re = params.cov_re vcomp = params.vcomp try: cov_re_inv = np.linalg.inv(cov_re) except np.linalg.LinAlgError: cov_re_inv = np.linalg.pinv(cov_re) self._cov_sing += 1 score_fe = np.zeros(self.k_fe) score_re = np.zeros(self.k_re2) score_vc = np.zeros(self.k_vc) # Handle the covariance penalty. if self.cov_pen is not None: score_re -= self.cov_pen.deriv(cov_re, cov_re_inv) # Handle the fixed effects penalty. if calc_fe and (self.fe_pen is not None): score_fe -= self.fe_pen.deriv(fe_params) # resid' V^{-1} resid, summed over the groups (a scalar) rvir = 0. # exog' V^{-1} resid, summed over the groups (a k_fe # dimensional vector) xtvir = 0. # exog' V^{_1} exog, summed over the groups (a k_fe x k_fe # matrix) xtvix = 0. # V^{-1} exog' dV/dQ_jj exog V^{-1}, where Q_jj is the jj^th # covariance parameter. xtax = [0., ] * (self.k_re2 + self.k_vc) # Temporary related to the gradient of log |V| dlv = np.zeros(self.k_re2 + self.k_vc) # resid' V^{-1} dV/dQ_jj V^{-1} resid (a scalar) rvavr = np.zeros(self.k_re2 + self.k_vc) for group_ix, group in enumerate(self.group_labels): vc_var = self._expand_vcomp(vcomp, group_ix) exog = self.exog_li[group_ix] ex_r, ex2_r = self._aex_r[group_ix], self._aex_r2[group_ix] solver = _smw_solver(1., ex_r, ex2_r, cov_re_inv, 1 / vc_var) # The residuals resid = self.endog_li[group_ix] if self.k_fe > 0: expval = np.dot(exog, fe_params) resid = resid - expval if self.reml: viexog = solver(exog) xtvix += np.dot(exog.T, viexog) # Contributions to the covariance parameter gradient vir = solver(resid) for (jj, matl, matr, vsl, vsr, sym) in\ self._gen_dV_dPar(ex_r, solver, group_ix): dlv[jj] = _dotsum(matr, vsl) if not sym: dlv[jj] += _dotsum(matl, vsr) ul = _dot(vir, matl) ur = ul.T if sym else _dot(matr.T, vir) ulr = np.dot(ul, ur) rvavr[jj] += ulr if not sym: rvavr[jj] += ulr.T if self.reml: ul = _dot(viexog.T, matl) ur = ul.T if sym else _dot(matr.T, viexog) ulr = np.dot(ul, ur) xtax[jj] += ulr if not sym: xtax[jj] += ulr.T # Contribution of log|V| to the covariance parameter # gradient. if self.k_re > 0: score_re -= 0.5 * dlv[0:self.k_re2] if self.k_vc > 0: score_vc -= 0.5 * dlv[self.k_re2:] rvir += np.dot(resid, vir) if calc_fe: xtvir += np.dot(exog.T, vir) fac = self.n_totobs if self.reml: fac -= self.k_fe if calc_fe and self.k_fe > 0: score_fe += fac * xtvir / rvir if self.k_re > 0: score_re += 0.5 * fac * rvavr[0:self.k_re2] / rvir if self.k_vc > 0: score_vc += 0.5 * fac * rvavr[self.k_re2:] / rvir if self.reml: xtvixi = np.linalg.inv(xtvix) for j in range(self.k_re2): score_re[j] += 0.5 * _dotsum(xtvixi.T, xtax[j]) for j in range(self.k_vc): score_vc[j] += 0.5 * _dotsum(xtvixi.T, xtax[self.k_re2 + j]) return score_fe, score_re, score_vc def score_sqrt(self, params, calc_fe=True): """ Returns the score with respect to transformed parameters. Calculates the score vector with respect to the parameterization in which the random effects covariance matrix is represented through its Cholesky square root. Parameters ---------- params : MixedLMParams or array_like The model parameters. If array-like must contain packed parameters that are compatible with this model instance. calc_fe : bool If True, calculate the score vector for the fixed effects parameters. If False, this vector is not calculated, and a vector of zeros is returned in its place. Returns ------- score_fe : array_like The score vector with respect to the fixed effects parameters. score_re : array_like The score vector with respect to the random effects parameters (excluding variance components parameters). score_vc : array_like The score vector with respect to variance components parameters. """ score_fe, score_re, score_vc = self.score_full(params, calc_fe=calc_fe) params_vec = params.get_packed(use_sqrt=True, has_fe=True) score_full = np.concatenate((score_fe, score_re, score_vc)) scr = 0. for i in range(len(params_vec)): v = self._lin[i] + 2 * np.dot(self._quad[i], params_vec) scr += score_full[i] * v score_fe = scr[0:self.k_fe] score_re = scr[self.k_fe:self.k_fe + self.k_re2] score_vc = scr[self.k_fe + self.k_re2:] return score_fe, score_re, score_vc def hessian(self, params): """ Returns the model's Hessian matrix. Calculates the Hessian matrix for the linear mixed effects model with respect to the parameterization in which the covariance matrix is represented directly (without square-root transformation). Parameters ---------- params : MixedLMParams or array_like The model parameters at which the Hessian is calculated. If array-like, must contain the packed parameters in a form that is compatible with this model instance. Returns ------- hess : 2d ndarray The Hessian matrix, evaluated at `params`. sing : boolean If True, the covariance matrix is singular and a pseudo-inverse is returned. """ if type(params) is not MixedLMParams: params = MixedLMParams.from_packed(params, self.k_fe, self.k_re, use_sqrt=self.use_sqrt, has_fe=True) fe_params = params.fe_params vcomp = params.vcomp cov_re = params.cov_re sing = False if self.k_re > 0: try: cov_re_inv = np.linalg.inv(cov_re) except np.linalg.LinAlgError: cov_re_inv = np.linalg.pinv(cov_re) sing = True else: cov_re_inv = np.empty((0, 0)) # Blocks for the fixed and random effects parameters. hess_fe = 0. hess_re = np.zeros((self.k_re2 + self.k_vc, self.k_re2 + self.k_vc)) hess_fere = np.zeros((self.k_re2 + self.k_vc, self.k_fe)) fac = self.n_totobs if self.reml: fac -= self.exog.shape[1] rvir = 0. xtvix = 0. xtax = [0., ] * (self.k_re2 + self.k_vc) m = self.k_re2 + self.k_vc B = np.zeros(m) D = np.zeros((m, m)) F = [[0.] * m for k in range(m)] for group_ix, group in enumerate(self.group_labels): vc_var = self._expand_vcomp(vcomp, group_ix) vc_vari = np.zeros_like(vc_var) ii = np.flatnonzero(vc_var >= 1e-10) if len(ii) > 0: vc_vari[ii] = 1 / vc_var[ii] if len(ii) < len(vc_var): sing = True exog = self.exog_li[group_ix] ex_r, ex2_r = self._aex_r[group_ix], self._aex_r2[group_ix] solver = _smw_solver(1., ex_r, ex2_r, cov_re_inv, vc_vari) # The residuals resid = self.endog_li[group_ix] if self.k_fe > 0: expval = np.dot(exog, fe_params) resid = resid - expval viexog = solver(exog) xtvix += np.dot(exog.T, viexog) vir = solver(resid) rvir += np.dot(resid, vir) for (jj1, matl1, matr1, vsl1, vsr1, sym1) in\ self._gen_dV_dPar(ex_r, solver, group_ix): ul = _dot(viexog.T, matl1) ur = _dot(matr1.T, vir) hess_fere[jj1, :] += np.dot(ul, ur) if not sym1: ul = _dot(viexog.T, matr1) ur = _dot(matl1.T, vir) hess_fere[jj1, :] += np.dot(ul, ur) if self.reml: ul = _dot(viexog.T, matl1) ur = ul if sym1 else np.dot(viexog.T, matr1) ulr = _dot(ul, ur.T) xtax[jj1] += ulr if not sym1: xtax[jj1] += ulr.T ul = _dot(vir, matl1) ur = ul if sym1 else _dot(vir, matr1) B[jj1] += np.dot(ul, ur) * (1 if sym1 else 2) # V^{-1} * dV/d_theta E = [(vsl1, matr1)] if not sym1: E.append((vsr1, matl1)) for (jj2, matl2, matr2, vsl2, vsr2, sym2) in\ self._gen_dV_dPar(ex_r, solver, group_ix, jj1): re = sum([_multi_dot_three(matr2.T, x[0], x[1].T) for x in E]) vt = 2 * _dot(_multi_dot_three(vir[None, :], matl2, re), vir[:, None]) if not sym2: le = sum([_multi_dot_three(matl2.T, x[0], x[1].T) for x in E]) vt += 2 * _dot(_multi_dot_three( vir[None, :], matr2, le), vir[:, None]) D[jj1, jj2] += vt if jj1 != jj2: D[jj2, jj1] += vt rt = _dotsum(vsl2, re.T) / 2 if not sym2: rt += _dotsum(vsr2, le.T) / 2 hess_re[jj1, jj2] += rt if jj1 != jj2: hess_re[jj2, jj1] += rt if self.reml: ev = sum([_dot(x[0], _dot(x[1].T, viexog)) for x in E]) u1 = _dot(viexog.T, matl2) u2 = _dot(matr2.T, ev) um = np.dot(u1, u2) F[jj1][jj2] += um + um.T if not sym2: u1 = np.dot(viexog.T, matr2) u2 = np.dot(matl2.T, ev) um = np.dot(u1, u2) F[jj1][jj2] += um + um.T hess_fe -= fac * xtvix / rvir hess_re = hess_re - 0.5 * fac * (D/rvir - np.outer(B, B) / rvir**2) hess_fere = -fac * hess_fere / rvir if self.reml: QL = [np.linalg.solve(xtvix, x) for x in xtax] for j1 in range(self.k_re2 + self.k_vc): for j2 in range(j1 + 1): a = _dotsum(QL[j1].T, QL[j2]) a -= np.trace(np.linalg.solve(xtvix, F[j1][j2])) a *= 0.5 hess_re[j1, j2] += a if j1 > j2: hess_re[j2, j1] += a # Put the blocks together to get the Hessian. m = self.k_fe + self.k_re2 + self.k_vc hess = np.zeros((m, m)) hess[0:self.k_fe, 0:self.k_fe] = hess_fe hess[0:self.k_fe, self.k_fe:] = hess_fere.T hess[self.k_fe:, 0:self.k_fe] = hess_fere hess[self.k_fe:, self.k_fe:] = hess_re return hess, sing def get_scale(self, fe_params, cov_re, vcomp): """ Returns the estimated error variance based on given estimates of the slopes and random effects covariance matrix. Parameters ---------- fe_params : array_like The regression slope estimates cov_re : 2d array_like Estimate of the random effects covariance matrix vcomp : array_like Estimate of the variance components Returns ------- scale : float The estimated error variance. """ try: cov_re_inv = np.linalg.inv(cov_re) except np.linalg.LinAlgError: cov_re_inv = np.linalg.pinv(cov_re) warnings.warn(_warn_cov_sing) qf = 0. for group_ix, group in enumerate(self.group_labels): vc_var = self._expand_vcomp(vcomp, group_ix) exog = self.exog_li[group_ix] ex_r, ex2_r = self._aex_r[group_ix], self._aex_r2[group_ix] solver = _smw_solver(1., ex_r, ex2_r, cov_re_inv, 1 / vc_var) # The residuals resid = self.endog_li[group_ix] if self.k_fe > 0: expval = np.dot(exog, fe_params) resid = resid - expval mat = solver(resid) qf += np.dot(resid, mat) if self.reml: qf /= (self.n_totobs - self.k_fe) else: qf /= self.n_totobs return qf def fit(self, start_params=None, reml=True, niter_sa=0, do_cg=True, fe_pen=None, cov_pen=None, free=None, full_output=False, method=None, **fit_kwargs): """ Fit a linear mixed model to the data. Parameters ---------- start_params : array_like or MixedLMParams Starting values for the profile log-likelihood. If not a `MixedLMParams` instance, this should be an array containing the packed parameters for the profile log-likelihood, including the fixed effects parameters. reml : bool If true, fit according to the REML likelihood, else fit the standard likelihood using ML. niter_sa : int Currently this argument is ignored and has no effect on the results. cov_pen : CovariancePenalty object A penalty for the random effects covariance matrix do_cg : bool, defaults to True If False, the optimization is skipped and a results object at the given (or default) starting values is returned. fe_pen : Penalty object A penalty on the fixed effects free : MixedLMParams object If not `None`, this is a mask that allows parameters to be held fixed at specified values. A 1 indicates that the corresponding parameter is estimated, a 0 indicates that it is fixed at its starting value. Setting the `cov_re` component to the identity matrix fits a model with independent random effects. Note that some optimization methods do not respect this constraint (bfgs and lbfgs both work). full_output : bool If true, attach iteration history to results method : str Optimization method. Can be a scipy.optimize method name, or a list of such names to be tried in sequence. **fit_kwargs Additional keyword arguments passed to fit. Returns ------- A MixedLMResults instance. """ _allowed_kwargs = ['gtol', 'maxiter', 'eps', 'maxcor', 'ftol', 'tol', 'disp', 'maxls'] for x in fit_kwargs.keys(): if x not in _allowed_kwargs: warnings.warn("Argument %s not used by MixedLM.fit" % x) if method is None: method = ['bfgs', 'lbfgs', 'cg'] elif isinstance(method, str): method = [method] for meth in method: if meth.lower() in ["newton", "ncg"]: raise ValueError( "method %s not available for MixedLM" % meth) self.reml = reml self.cov_pen = cov_pen self.fe_pen = fe_pen self._cov_sing = 0 self._freepat = free if full_output: hist = [] else: hist = None if start_params is None: params = MixedLMParams(self.k_fe, self.k_re, self.k_vc) params.fe_params = np.zeros(self.k_fe) params.cov_re = np.eye(self.k_re) params.vcomp = np.ones(self.k_vc) else: if isinstance(start_params, MixedLMParams): params = start_params else: # It's a packed array if len(start_params) == self.k_fe + self.k_re2 + self.k_vc: params = MixedLMParams.from_packed( start_params, self.k_fe, self.k_re, self.use_sqrt, has_fe=True) elif len(start_params) == self.k_re2 + self.k_vc: params = MixedLMParams.from_packed( start_params, self.k_fe, self.k_re, self.use_sqrt, has_fe=False) else: raise ValueError("invalid start_params") if do_cg: fit_kwargs["retall"] = hist is not None if "disp" not in fit_kwargs: fit_kwargs["disp"] = False packed = params.get_packed(use_sqrt=self.use_sqrt, has_fe=False) if niter_sa > 0: warnings.warn("niter_sa is currently ignored") # Try optimizing one or more times for j in range(len(method)): rslt = super(MixedLM, self).fit(start_params=packed, skip_hessian=True, method=method[j], **fit_kwargs) if rslt.mle_retvals['converged']: break packed = rslt.params if j + 1 < len(method): next_method = method[j + 1] warnings.warn( "Retrying MixedLM optimization with %s" % next_method, ConvergenceWarning) else: msg = ("MixedLM optimization failed, " + "trying a different optimizer may help.") warnings.warn(msg, ConvergenceWarning) # The optimization succeeded params = np.atleast_1d(rslt.params) if hist is not None: hist.append(rslt.mle_retvals) converged = rslt.mle_retvals['converged'] if not converged: gn = self.score(rslt.params) gn = np.sqrt(np.sum(gn**2)) msg = "Gradient optimization failed, |grad| = %f" % gn warnings.warn(msg, ConvergenceWarning) # Convert to the final parameterization (i.e. undo the square # root transform of the covariance matrix, and the profiling # over the error variance). params = MixedLMParams.from_packed( params, self.k_fe, self.k_re, use_sqrt=self.use_sqrt, has_fe=False) cov_re_unscaled = params.cov_re vcomp_unscaled = params.vcomp fe_params, sing = self.get_fe_params(cov_re_unscaled, vcomp_unscaled) params.fe_params = fe_params scale = self.get_scale(fe_params, cov_re_unscaled, vcomp_unscaled) cov_re = scale * cov_re_unscaled vcomp = scale * vcomp_unscaled f1 = (self.k_re > 0) and (np.min(np.abs(np.diag(cov_re))) < 0.01) f2 = (self.k_vc > 0) and (np.min(np.abs(vcomp)) < 0.01) if f1 or f2: msg = "The MLE may be on the boundary of the parameter space." warnings.warn(msg, ConvergenceWarning) # Compute the Hessian at the MLE. Note that this is the # Hessian with respect to the random effects covariance matrix # (not its square root). It is used for obtaining standard # errors, not for optimization. hess, sing = self.hessian(params) if sing: warnings.warn(_warn_cov_sing) hess_diag = np.diag(hess) if free is not None: pcov = np.zeros_like(hess) pat = self._freepat.get_packed(use_sqrt=False, has_fe=True) ii = np.flatnonzero(pat) hess_diag = hess_diag[ii] if len(ii) > 0: hess1 = hess[np.ix_(ii, ii)] pcov[np.ix_(ii, ii)] = np.linalg.inv(-hess1) else: pcov = np.linalg.inv(-hess) if np.any(hess_diag >= 0): msg = ("The Hessian matrix at the estimated parameter values " + "is not positive definite.") warnings.warn(msg, ConvergenceWarning) # Prepare a results class instance params_packed = params.get_packed(use_sqrt=False, has_fe=True) results = MixedLMResults(self, params_packed, pcov / scale) results.params_object = params results.fe_params = fe_params results.cov_re = cov_re results.vcomp = vcomp results.scale = scale results.cov_re_unscaled = cov_re_unscaled results.method = "REML" if self.reml else "ML" results.converged = converged results.hist = hist results.reml = self.reml results.cov_pen = self.cov_pen results.k_fe = self.k_fe results.k_re = self.k_re results.k_re2 = self.k_re2 results.k_vc = self.k_vc results.use_sqrt = self.use_sqrt results.freepat = self._freepat return MixedLMResultsWrapper(results) def get_distribution(self, params, scale, exog): return _mixedlm_distribution(self, params, scale, exog) class _mixedlm_distribution(object): """ A private class for simulating data from a given mixed linear model. Parameters ---------- model : MixedLM instance A mixed linear model params : array_like A parameter vector defining a mixed linear model. See notes for more information. scale : scalar The unexplained variance exog : array_like An array of fixed effect covariates. If None, model.exog is used. Notes ----- The params array is a vector containing fixed effects parameters, random effects parameters, and variance component parameters, in that order. The lower triangle of the random effects covariance matrix is stored. The random effects and variance components parameters are divided by the scale parameter. This class is used in Mediation, and possibly elsewhere. """ def __init__(self, model, params, scale, exog): self.model = model self.exog = exog if exog is not None else model.exog po = MixedLMParams.from_packed( params, model.k_fe, model.k_re, False, True) self.fe_params = po.fe_params self.cov_re = scale * po.cov_re self.vcomp = scale * po.vcomp self.scale = scale group_idx = np.zeros(model.nobs, dtype=int) for k, g in enumerate(model.group_labels): group_idx[model.row_indices[g]] = k self.group_idx = group_idx def rvs(self, n): """ Return a vector of simulated values from a mixed linear model. The parameter n is ignored, but required by the interface """ model = self.model # Fixed effects y = np.dot(self.exog, self.fe_params) # Random effects u = np.random.normal(size=(model.n_groups, model.k_re)) u = np.dot(u, np.linalg.cholesky(self.cov_re).T) y += (u[self.group_idx, :] * model.exog_re).sum(1) # Variance components for j, _ in enumerate(model.exog_vc.names): ex = model.exog_vc.mats[j] v = self.vcomp[j] for i, g in enumerate(model.group_labels): exg = ex[i] ii = model.row_indices[g] u = np.random.normal(size=exg.shape[1]) y[ii] += np.sqrt(v) * np.dot(exg, u) # Residual variance y += np.sqrt(self.scale) * np.random.normal(size=len(y)) return y class MixedLMResults(base.LikelihoodModelResults, base.ResultMixin): ''' Class to contain results of fitting a linear mixed effects model. MixedLMResults inherits from statsmodels.LikelihoodModelResults Parameters ---------- See statsmodels.LikelihoodModelResults Attributes ---------- model : class instance Pointer to MixedLM model instance that called fit. normalized_cov_params : ndarray The sampling covariance matrix of the estimates params : ndarray A packed parameter vector for the profile parameterization. The first `k_fe` elements are the estimated fixed effects coefficients. The remaining elements are the estimated variance parameters. The variance parameters are all divided by `scale` and are not the variance parameters shown in the summary. fe_params : ndarray The fitted fixed-effects coefficients cov_re : ndarray The fitted random-effects covariance matrix bse_fe : ndarray The standard errors of the fitted fixed effects coefficients bse_re : ndarray The standard errors of the fitted random effects covariance matrix and variance components. The first `k_re * (k_re + 1)` parameters are the standard errors for the lower triangle of `cov_re`, the remaining elements are the standard errors for the variance components. See Also -------- statsmodels.LikelihoodModelResults ''' def __init__(self, model, params, cov_params): super(MixedLMResults, self).__init__(model, params, normalized_cov_params=cov_params) self.nobs = self.model.nobs self.df_resid = self.nobs - np.linalg.matrix_rank(self.model.exog) @cache_readonly def fittedvalues(self): """ Returns the fitted values for the model. The fitted values reflect the mean structure specified by the fixed effects and the predicted random effects. """ fit = np.dot(self.model.exog, self.fe_params) re = self.random_effects for group_ix, group in enumerate(self.model.group_labels): ix = self.model.row_indices[group] mat = [] if self.model.exog_re_li is not None: mat.append(self.model.exog_re_li[group_ix]) for j in range(self.k_vc): mat.append(self.model.exog_vc.mats[j][group_ix]) mat = np.concatenate(mat, axis=1) fit[ix] += np.dot(mat, re[group]) return fit @cache_readonly def resid(self): """ Returns the residuals for the model. The residuals reflect the mean structure specified by the fixed effects and the predicted random effects. """ return self.model.endog - self.fittedvalues @cache_readonly def bse_fe(self): """ Returns the standard errors of the fixed effect regression coefficients. """ p = self.model.exog.shape[1] return np.sqrt(np.diag(self.cov_params())[0:p]) @cache_readonly def bse_re(self): """ Returns the standard errors of the variance parameters. The first `k_re x (k_re + 1)` elements of the returned array are the standard errors of the lower triangle of `cov_re`. The remaining elements are the standard errors of the variance components. Note that the sampling distribution of variance parameters is strongly skewed unless the sample size is large, so these standard errors may not give meaningful confidence intervals or p-values if used in the usual way. """ p = self.model.exog.shape[1] return np.sqrt(self.scale * np.diag(self.cov_params())[p:]) def _expand_re_names(self, group_ix): names = list(self.model.data.exog_re_names) for j, v in enumerate(self.model.exog_vc.names): vg = self.model.exog_vc.colnames[j][group_ix] na = ["%s[%s]" % (v, s) for s in vg] names.extend(na) return names @cache_readonly def random_effects(self): """ The conditional means of random effects given the data. Returns ------- random_effects : dict A dictionary mapping the distinct `group` values to the conditional means of the random effects for the group given the data. """ try: cov_re_inv = np.linalg.inv(self.cov_re) except np.linalg.LinAlgError: raise ValueError("Cannot predict random effects from " + "singular covariance structure.") vcomp = self.vcomp k_re = self.k_re ranef_dict = {} for group_ix, group in enumerate(self.model.group_labels): endog = self.model.endog_li[group_ix] exog = self.model.exog_li[group_ix] ex_r = self.model._aex_r[group_ix] ex2_r = self.model._aex_r2[group_ix] vc_var = self.model._expand_vcomp(vcomp, group_ix) # Get the residuals relative to fixed effects resid = endog if self.k_fe > 0: expval = np.dot(exog, self.fe_params) resid = resid - expval solver = _smw_solver(self.scale, ex_r, ex2_r, cov_re_inv, 1 / vc_var) vir = solver(resid) xtvir = _dot(ex_r.T, vir) xtvir[0:k_re] = np.dot(self.cov_re, xtvir[0:k_re]) xtvir[k_re:] *= vc_var ranef_dict[group] = pd.Series( xtvir, index=self._expand_re_names(group_ix)) return ranef_dict @cache_readonly def random_effects_cov(self): """ Returns the conditional covariance matrix of the random effects for each group given the data. Returns ------- random_effects_cov : dict A dictionary mapping the distinct values of the `group` variable to the conditional covariance matrix of the random effects given the data. """ try: cov_re_inv = np.linalg.inv(self.cov_re) except np.linalg.LinAlgError: cov_re_inv = None vcomp = self.vcomp ranef_dict = {} for group_ix in range(self.model.n_groups): ex_r = self.model._aex_r[group_ix] ex2_r = self.model._aex_r2[group_ix] label = self.model.group_labels[group_ix] vc_var = self.model._expand_vcomp(vcomp, group_ix) solver = _smw_solver(self.scale, ex_r, ex2_r, cov_re_inv, 1 / vc_var) n = ex_r.shape[0] m = self.cov_re.shape[0] mat1 = np.empty((n, m + len(vc_var))) mat1[:, 0:m] = np.dot(ex_r[:, 0:m], self.cov_re) mat1[:, m:] = np.dot(ex_r[:, m:], np.diag(vc_var)) mat2 = solver(mat1) mat2 = np.dot(mat1.T, mat2) v = -mat2 v[0:m, 0:m] += self.cov_re ix = np.arange(m, v.shape[0]) v[ix, ix] += vc_var na = self._expand_re_names(group_ix) v = pd.DataFrame(v, index=na, columns=na) ranef_dict[label] = v return ranef_dict # Need to override since t-tests are only used for fixed effects # parameters. def t_test(self, r_matrix, scale=None, use_t=None): """ Compute a t-test for a each linear hypothesis of the form Rb = q Parameters ---------- r_matrix : array_like If an array is given, a p x k 2d array or length k 1d array specifying the linear restrictions. It is assumed that the linear combination is equal to zero. scale : float, optional An optional `scale` to use. Default is the scale specified by the model fit. use_t : bool, optional If use_t is None, then the default of the model is used. If use_t is True, then the p-values are based on the t distribution. If use_t is False, then the p-values are based on the normal distribution. Returns ------- res : ContrastResults instance The results for the test are attributes of this results instance. The available results have the same elements as the parameter table in `summary()`. """ if scale is not None: import warnings warnings.warn('scale is has no effect and is deprecated. It will' 'be removed in the next version.', DeprecationWarning) if r_matrix.shape[1] != self.k_fe: raise ValueError("r_matrix for t-test should have %d columns" % self.k_fe) d = self.k_re2 + self.k_vc z0 = np.zeros((r_matrix.shape[0], d)) r_matrix = np.concatenate((r_matrix, z0), axis=1) tst_rslt = super(MixedLMResults, self).t_test(r_matrix, use_t=use_t) return tst_rslt def summary(self, yname=None, xname_fe=None, xname_re=None, title=None, alpha=.05): """ Summarize the mixed model regression results. Parameters ---------- yname : str, optional Default is `y` xname_fe : list[str], optional Fixed effects covariate names xname_re : list[str], optional Random effects covariate names title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary2.Summary : class to hold summary results """ from statsmodels.iolib import summary2 smry = summary2.Summary() info = {} info["Model:"] = "MixedLM" if yname is None: yname = self.model.endog_names param_names = self.model.data.param_names[:] k_fe_params = len(self.fe_params) k_re_params = len(param_names) - len(self.fe_params) if xname_fe is not None: if len(xname_fe) != k_fe_params: msg = "xname_fe should be a list of length %d" % k_fe_params raise ValueError(msg) param_names[:k_fe_params] = xname_fe if xname_re is not None: if len(xname_re) != k_re_params: msg = "xname_re should be a list of length %d" % k_re_params raise ValueError(msg) param_names[k_fe_params:] = xname_re info["No. Observations:"] = str(self.model.n_totobs) info["No. Groups:"] = str(self.model.n_groups) gs = np.array([len(x) for x in self.model.endog_li]) info["Min. group size:"] = "%.0f" % min(gs) info["Max. group size:"] = "%.0f" % max(gs) info["Mean group size:"] = "%.1f" % np.mean(gs) info["Dependent Variable:"] = yname info["Method:"] = self.method info["Scale:"] = self.scale info["Log-Likelihood:"] = self.llf info["Converged:"] = "Yes" if self.converged else "No" smry.add_dict(info) smry.add_title("Mixed Linear Model Regression Results") float_fmt = "%.3f" sdf = np.nan * np.ones((self.k_fe + self.k_re2 + self.k_vc, 6)) # Coefficient estimates sdf[0:self.k_fe, 0] = self.fe_params # Standard errors sdf[0:self.k_fe, 1] = np.sqrt(np.diag(self.cov_params()[0:self.k_fe])) # Z-scores sdf[0:self.k_fe, 2] = sdf[0:self.k_fe, 0] / sdf[0:self.k_fe, 1] # p-values sdf[0:self.k_fe, 3] = 2 * norm.cdf(-np.abs(sdf[0:self.k_fe, 2])) # Confidence intervals qm = -norm.ppf(alpha / 2) sdf[0:self.k_fe, 4] = sdf[0:self.k_fe, 0] - qm * sdf[0:self.k_fe, 1] sdf[0:self.k_fe, 5] = sdf[0:self.k_fe, 0] + qm * sdf[0:self.k_fe, 1] # All random effects variances and covariances jj = self.k_fe for i in range(self.k_re): for j in range(i + 1): sdf[jj, 0] = self.cov_re[i, j] sdf[jj, 1] = np.sqrt(self.scale) * self.bse[jj] jj += 1 # Variance components for i in range(self.k_vc): sdf[jj, 0] = self.vcomp[i] sdf[jj, 1] = np.sqrt(self.scale) * self.bse[jj] jj += 1 sdf = pd.DataFrame(index=param_names, data=sdf) sdf.columns = ['Coef.', 'Std.Err.', 'z', 'P>|z|', '[' + str(alpha/2), str(1-alpha/2) + ']'] for col in sdf.columns: sdf[col] = [float_fmt % x if np.isfinite(x) else "" for x in sdf[col]] smry.add_df(sdf, align='r') return smry @cache_readonly def llf(self): return self.model.loglike(self.params_object, profile_fe=False) @cache_readonly def aic(self): """Akaike information criterion""" if self.reml: return np.nan if self.freepat is not None: df = self.freepat.get_packed(use_sqrt=False, has_fe=True).sum() + 1 else: df = self.params.size + 1 return -2 * (self.llf - df) @cache_readonly def bic(self): """Bayesian information criterion""" if self.reml: return np.nan if self.freepat is not None: df = self.freepat.get_packed(use_sqrt=False, has_fe=True).sum() + 1 else: df = self.params.size + 1 return -2 * self.llf + np.log(self.nobs) * df def profile_re(self, re_ix, vtype, num_low=5, dist_low=1., num_high=5, dist_high=1., **fit_kwargs): """ Profile-likelihood inference for variance parameters. Parameters ---------- re_ix : int If vtype is `re`, this value is the index of the variance parameter for which to construct a profile likelihood. If `vtype` is 'vc' then `re_ix` is the name of the variance parameter to be profiled. vtype : str Either 're' or 'vc', depending on whether the profile analysis is for a random effect or a variance component. num_low : int The number of points at which to calculate the likelihood below the MLE of the parameter of interest. dist_low : float The distance below the MLE of the parameter of interest to begin calculating points on the profile likelihood. num_high : int The number of points at which to calculate the likelihood above the MLE of the parameter of interest. dist_high : float The distance above the MLE of the parameter of interest to begin calculating points on the profile likelihood. **fit_kwargs Additional keyword arguments passed to fit. Returns ------- An array with two columns. The first column contains the values to which the parameter of interest is constrained. The second column contains the corresponding likelihood values. Notes ----- Only variance parameters can be profiled. """ pmodel = self.model k_fe = pmodel.k_fe k_re = pmodel.k_re k_vc = pmodel.k_vc endog, exog = pmodel.endog, pmodel.exog # Need to permute the columns of the random effects design # matrix so that the profiled variable is in the first column. if vtype == 're': ix = np.arange(k_re) ix[0] = re_ix ix[re_ix] = 0 exog_re = pmodel.exog_re.copy()[:, ix] # Permute the covariance structure to match the permuted # design matrix. params = self.params_object.copy() cov_re_unscaled = params.cov_re cov_re_unscaled = cov_re_unscaled[np.ix_(ix, ix)] params.cov_re = cov_re_unscaled ru0 = cov_re_unscaled[0, 0] # Convert dist_low and dist_high to the profile # parameterization cov_re = self.scale * cov_re_unscaled low = (cov_re[0, 0] - dist_low) / self.scale high = (cov_re[0, 0] + dist_high) / self.scale elif vtype == 'vc': re_ix = self.model.exog_vc.names.index(re_ix) params = self.params_object.copy() vcomp = self.vcomp low = (vcomp[re_ix] - dist_low) / self.scale high = (vcomp[re_ix] + dist_high) / self.scale ru0 = vcomp[re_ix] / self.scale # Define the sequence of values to which the parameter of # interest will be constrained. if low <= 0: raise ValueError("dist_low is too large and would result in a " "negative variance. Try a smaller value.") left = np.linspace(low, ru0, num_low + 1) right = np.linspace(ru0, high, num_high+1)[1:] rvalues = np.concatenate((left, right)) # Indicators of which parameters are free and fixed. free = MixedLMParams(k_fe, k_re, k_vc) if self.freepat is None: free.fe_params = np.ones(k_fe) vcomp = np.ones(k_vc) mat = np.ones((k_re, k_re)) else: # If a freepat already has been specified, we add the # constraint to it. free.fe_params = self.freepat.fe_params vcomp = self.freepat.vcomp mat = self.freepat.cov_re if vtype == 're': mat = mat[np.ix_(ix, ix)] if vtype == 're': mat[0, 0] = 0 else: vcomp[re_ix] = 0 free.cov_re = mat free.vcomp = vcomp klass = self.model.__class__ init_kwargs = pmodel._get_init_kwds() if vtype == 're': init_kwargs['exog_re'] = exog_re likev = [] for x in rvalues: model = klass(endog, exog, **init_kwargs) if vtype == 're': cov_re = params.cov_re.copy() cov_re[0, 0] = x params.cov_re = cov_re else: params.vcomp[re_ix] = x # TODO should use fit_kwargs rslt = model.fit(start_params=params, free=free, reml=self.reml, cov_pen=self.cov_pen, **fit_kwargs)._results likev.append([x * rslt.scale, rslt.llf]) likev = np.asarray(likev) return likev class MixedLMResultsWrapper(base.LikelihoodResultsWrapper): _attrs = {'bse_re': ('generic_columns', 'exog_re_names_full'), 'fe_params': ('generic_columns', 'xnames'), 'bse_fe': ('generic_columns', 'xnames'), 'cov_re': ('generic_columns_2d', 'exog_re_names'), 'cov_re_unscaled': ('generic_columns_2d', 'exog_re_names'), } _upstream_attrs = base.LikelihoodResultsWrapper._wrap_attrs _wrap_attrs = base.wrap.union_dicts(_attrs, _upstream_attrs) _methods = {} _upstream_methods = base.LikelihoodResultsWrapper._wrap_methods _wrap_methods = base.wrap.union_dicts(_methods, _upstream_methods) def _handle_missing(data, groups, formula, re_formula, vc_formula): tokens = set([]) forms = [formula] if re_formula is not None: forms.append(re_formula) if vc_formula is not None: forms.extend(vc_formula.values()) import tokenize from io import StringIO from statsmodels.compat.python import asunicode skiptoks = {"(", ")", "*", ":", "+", "-", "**", "/"} for fml in forms: # Unicode conversion is for Py2 compatability rl = StringIO(fml) def rlu(): line = rl.readline() return asunicode(line, 'ascii') g = tokenize.generate_tokens(rlu) for tok in g: if tok not in skiptoks: tokens.add(tok.string) tokens = sorted(tokens & set(data.columns)) data = data[tokens] ii = pd.notnull(data).all(1) if type(groups) != "str": ii &= pd.notnull(groups) return data.loc[ii, :], groups[np.asarray(ii)] statsmodels-0.12.2/statsmodels/regression/process_regression.py000066400000000000000000000657231400612667500251740ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ This module implements maximum likelihood-based estimation (MLE) of Gaussian models for finite-dimensional observations made on infinite-dimensional processes. The ProcessMLE class supports regression analyses on grouped data, where the observations within a group are dependent (they are made on the same underlying process). The main application is repeated measures regression for temporal (longitudinal) data, in which the repeated measures occur at arbitrary real-valued time points. The mean structure is specified as a linear model. The covariance parameters depend on covariates via a link function. """ import numpy as np import pandas as pd import patsy import statsmodels.base.model as base import statsmodels.api as sm import collections from scipy.optimize import minimize from statsmodels.iolib import summary2 from statsmodels.tools.numdiff import approx_fprime import warnings class ProcessCovariance(object): r""" A covariance model for a process indexed by a real parameter. An implementation of this class is based on a positive definite correlation function h that maps real numbers to the interval [0, 1], such as the Gaussian (squared exponential) correlation function :math:`\exp(-x^2)`. It also depends on a positive scaling function `s` and a positive smoothness function `u`. """ def get_cov(self, time, sc, sm): """ Returns the covariance matrix for given time values. Parameters ---------- time : array_like The time points for the observations. If len(time) = p, a pxp covariance matrix is returned. sc : array_like The scaling parameters for the observations. sm : array_like The smoothness parameters for the observation. See class docstring for details. """ raise NotImplementedError def jac(self, time, sc, sm): """ The Jacobian of the covariance with respect to the parameters. See get_cov for parameters. Returns ------- jsc : list-like jsc[i] is the derivative of the covariance matrix with respect to the i^th scaling parameter. jsm : list-like jsm[i] is the derivative of the covariance matrix with respect to the i^th smoothness parameter. """ raise NotImplementedError class GaussianCovariance(ProcessCovariance): r""" An implementation of ProcessCovariance using the Gaussian kernel. This class represents a parametric covariance model for a Gaussian process as described in the work of Paciorek et al. cited below. Following Paciorek et al [1]_, the covariance between observations with index `i` and `j` is given by: .. math:: s[i] \cdot s[j] \cdot h(|time[i] - time[j]| / \sqrt{(u[i] + u[j]) / 2}) \cdot \frac{u[i]^{1/4}u[j]^{1/4}}{\sqrt{(u[i] + u[j])/2}} The ProcessMLE class allows linear models with this covariance structure to be fit using maximum likelihood (ML), which is equivalent to generalized least squares (GLS) in this setting. The mean and covariance parameters of the model are fit jointly. The mean, scaling, and smoothing parameters can be linked to covariates. The mean parameters are linked linearly, and the scaling and smoothing parameters use an exponential link to preserve positivity. The reference of Paciorek et al. below provides more details. Note that here we only implement the 1-dimensional version of their approach. References ---------- .. [1] Paciorek, C. J. and Schervish, M. J. (2006). Spatial modeling using a new class of nonstationary covariance functions. Environmetrics, 17:483–506. https://papers.nips.cc/paper/2350-nonstationary-covariance-functions-for-gaussian-process-regression.pdf """ def get_cov(self, time, sc, sm): da = np.subtract.outer(time, time) ds = np.add.outer(sm, sm) / 2 qmat = da * da / ds cm = np.exp(-qmat / 2) / np.sqrt(ds) cm *= np.outer(sm, sm)**0.25 cm *= np.outer(sc, sc) return cm def jac(self, time, sc, sm): da = np.subtract.outer(time, time) ds = np.add.outer(sm, sm) / 2 sds = np.sqrt(ds) daa = da * da qmat = daa / ds p = len(time) eqm = np.exp(-qmat / 2) sm4 = np.outer(sm, sm)**0.25 cmx = eqm * sm4 / sds dq0 = -daa / ds**2 di = np.zeros((p, p)) fi = np.zeros((p, p)) scc = np.outer(sc, sc) # Derivatives with respect to the smoothing parameters. jsm = [] for i, _ in enumerate(sm): di *= 0 di[i, :] += 0.5 di[:, i] += 0.5 dbottom = 0.5 * di / sds dtop = -0.5 * eqm * dq0 * di b = dtop / sds - eqm * dbottom / ds c = eqm / sds v = 0.25 * sm**0.25 / sm[i]**0.75 fi *= 0 fi[i, :] = v fi[:, i] = v fi[i, i] = 0.5 / sm[i]**0.5 b = c * fi + b * sm4 b *= scc jsm.append(b) # Derivatives with respect to the scaling parameters. jsc = [] for i in range(0, len(sc)): b = np.zeros((p, p)) b[i, :] = cmx[i, :] * sc b[:, i] += cmx[:, i] * sc jsc.append(b) return jsc, jsm def _check_args(endog, exog, exog_scale, exog_smooth, exog_noise, time, groups): v = [ len(endog), exog.shape[0], exog_scale.shape[0], exog_smooth.shape[0], exog_noise.shape[0], len(time), len(groups) ] if min(v) != max(v): msg = ("The leading dimensions of all array arguments " + "must be equal.") raise ValueError(msg) class ProcessMLE(base.LikelihoodModel): """ Fit a Gaussian mean/variance regression model. This class fits a one-dimensional Gaussian process model with parametrized mean and covariance structures to grouped data. For each group, there is an independent realization of a latent Gaussian process indexed by an observed real-valued time variable.. The data consist of the Gaussian process observed at a finite number of `time` values. The process mean and variance can be lined to covariates. The mean structure is linear in the covariates. The covariance structure is non-stationary, and is defined parametrically through 'scaling', and 'smoothing' parameters. The covariance of the process between two observations in the same group is a function of the distance between the time values of the two observations. The scaling and smoothing parameters can be linked to covariates. The observed data are modeled as the sum of the Gaussian process realization and independent white noise. The standard deviation of the white noise can be linked to covariates. The data should be provided in 'long form', with a group label to indicate which observations belong to the same group. Observations in different groups are always independent. Parameters ---------- endog : array_like The dependent variable. exog : array_like The design matrix for the mean structure exog_scale : array_like The design matrix for the scaling structure exog_smooth : array_like The design matrix for the smoothness structure exog_noise : array_like The design matrix for the white noise structure. The linear predictor is the log of the white noise standard deviation. time : array_like (1-dimensional) The univariate index values, used to calculate distances between observations in the same group, which determines their correlations. groups : array_like (1-dimensional) The group values. cov : a ProcessCovariance instance Defaults to GaussianCovariance. """ def __init__(self, endog, exog, exog_scale, exog_smooth, exog_noise, time, groups, cov=None, **kwargs): super(ProcessMLE, self).__init__( endog, exog, exog_scale=exog_scale, exog_smooth=exog_smooth, exog_noise=exog_noise, time=time, groups=groups, **kwargs) # Create parameter names xnames = [] if hasattr(exog, "columns"): xnames = list(exog.columns) else: xnames = ["Mean%d" % j for j in range(exog.shape[1])] if hasattr(exog_scale, "columns"): xnames += list(exog_scale.columns) else: xnames += ["Scale%d" % j for j in range(exog_scale.shape[1])] if hasattr(exog_smooth, "columns"): xnames += list(exog_smooth.columns) else: xnames += ["Smooth%d" % j for j in range(exog_smooth.shape[1])] if hasattr(exog_noise, "columns"): xnames += list(exog_noise.columns) else: xnames += ["Noise%d" % j for j in range(exog_noise.shape[1])] self.data.param_names = xnames if cov is None: cov = GaussianCovariance() self.cov = cov _check_args(endog, exog, exog_scale, exog_smooth, exog_noise, time, groups) groups_ix = collections.defaultdict(lambda: []) for i, g in enumerate(groups): groups_ix[g].append(i) self._groups_ix = groups_ix # Default, can be set in call to fit. self.verbose = False self.k_exog = self.exog.shape[1] self.k_scale = self.exog_scale.shape[1] self.k_smooth = self.exog_smooth.shape[1] self.k_noise = self.exog_noise.shape[1] def _split_param_names(self): xnames = self.data.param_names q = 0 mean_names = xnames[q:q+self.k_exog] q += self.k_exog scale_names = xnames[q:q+self.k_scale] q += self.k_scale smooth_names = xnames[q:q+self.k_smooth] q += self.k_noise noise_names = xnames[q:q+self.k_noise] return mean_names, scale_names, smooth_names, noise_names @classmethod def from_formula(cls, formula, data, subset=None, drop_cols=None, *args, **kwargs): if "scale_formula" in kwargs: scale_formula = kwargs["scale_formula"] else: raise ValueError("scale_formula is a required argument") if "smooth_formula" in kwargs: smooth_formula = kwargs["smooth_formula"] else: raise ValueError("smooth_formula is a required argument") if "noise_formula" in kwargs: noise_formula = kwargs["noise_formula"] else: raise ValueError("noise_formula is a required argument") if "time" in kwargs: time = kwargs["time"] else: raise ValueError("time is a required argument") if "groups" in kwargs: groups = kwargs["groups"] else: raise ValueError("groups is a required argument") if subset is not None: warnings.warn("'subset' is ignored") if drop_cols is not None: warnings.warn("'drop_cols' is ignored") if isinstance(time, str): time = np.asarray(data[time]) if isinstance(groups, str): groups = np.asarray(data[groups]) exog_scale = patsy.dmatrix(scale_formula, data) scale_design_info = exog_scale.design_info scale_names = scale_design_info.column_names exog_scale = np.asarray(exog_scale) exog_smooth = patsy.dmatrix(smooth_formula, data) smooth_design_info = exog_smooth.design_info smooth_names = smooth_design_info.column_names exog_smooth = np.asarray(exog_smooth) exog_noise = patsy.dmatrix(noise_formula, data) noise_design_info = exog_noise.design_info noise_names = noise_design_info.column_names exog_noise = np.asarray(exog_noise) mod = super(ProcessMLE, cls).from_formula( formula, data=data, subset=None, exog_scale=exog_scale, exog_smooth=exog_smooth, exog_noise=exog_noise, time=time, groups=groups) mod.data.scale_design_info = scale_design_info mod.data.smooth_design_info = smooth_design_info mod.data.noise_design_info = noise_design_info mod.data.param_names = (mod.exog_names + scale_names + smooth_names + noise_names) return mod def unpack(self, z): """ Split the packed parameter vector into blocks. """ # Mean parameters pm = self.exog.shape[1] mnpar = z[0:pm] # Standard deviation parameters pv = self.exog_scale.shape[1] scpar = z[pm:pm + pv] # Smoothness parameters ps = self.exog_smooth.shape[1] smpar = z[pm + pv:pm + pv + ps] # Observation white noise standard deviation nopar = z[pm + pv + ps:] return mnpar, scpar, smpar, nopar def _get_start(self): # Use OLS to get starting values for mean structure parameters model = sm.OLS(self.endog, self.exog) result = model.fit() m = self.exog_scale.shape[1] + self.exog_smooth.shape[1] m += self.exog_noise.shape[1] return np.concatenate((result.params, np.zeros(m))) def loglike(self, params): """ Calculate the log-likelihood function for the model. Parameters ---------- params : array_like The packed parameters for the model. Returns ------- The log-likelihood value at the given parameter point. Notes ----- The mean, scaling, and smoothing parameters are packed into a vector. Use `unpack` to access the component vectors. """ mnpar, scpar, smpar, nopar = self.unpack(params) # Residuals resid = self.endog - np.dot(self.exog, mnpar) # Scaling parameters sc = np.exp(np.dot(self.exog_scale, scpar)) # Smoothness parameters sm = np.exp(np.dot(self.exog_smooth, smpar)) # White noise standard deviation no = np.exp(np.dot(self.exog_noise, nopar)) # Get the log-likelihood ll = 0. for _, ix in self._groups_ix.items(): # Get the covariance matrix for this person. cm = self.cov.get_cov(self.time[ix], sc[ix], sm[ix]) cm.flat[::cm.shape[0] + 1] += no[ix]**2 re = resid[ix] ll -= 0.5 * np.linalg.slogdet(cm)[1] ll -= 0.5 * np.dot(re, np.linalg.solve(cm, re)) if self.verbose: print("L=", ll) return ll def score(self, params): """ Calculate the score function for the model. Parameters ---------- params : array_like The packed parameters for the model. Returns ------- The score vector at the given parameter point. Notes ----- The mean, scaling, and smoothing parameters are packed into a vector. Use `unpack` to access the component vectors. """ mnpar, scpar, smpar, nopar = self.unpack(params) pm, pv, ps = len(mnpar), len(scpar), len(smpar) # Residuals resid = self.endog - np.dot(self.exog, mnpar) # Scaling sc = np.exp(np.dot(self.exog_scale, scpar)) # Smoothness sm = np.exp(np.dot(self.exog_smooth, smpar)) # White noise standard deviation no = np.exp(np.dot(self.exog_noise, nopar)) # Get the log-likelihood score = np.zeros(len(mnpar) + len(scpar) + len(smpar) + len(nopar)) for _, ix in self._groups_ix.items(): sc_i = sc[ix] sm_i = sm[ix] no_i = no[ix] resid_i = resid[ix] time_i = self.time[ix] exog_i = self.exog[ix, :] exog_scale_i = self.exog_scale[ix, :] exog_smooth_i = self.exog_smooth[ix, :] exog_noise_i = self.exog_noise[ix, :] # Get the covariance matrix for this person. cm = self.cov.get_cov(time_i, sc_i, sm_i) cm.flat[::cm.shape[0] + 1] += no[ix]**2 cmi = np.linalg.inv(cm) jacv, jacs = self.cov.jac(time_i, sc_i, sm_i) # The derivatives for the mean parameters. dcr = np.linalg.solve(cm, resid_i) score[0:pm] += np.dot(exog_i.T, dcr) # The derivatives for the scaling parameters. rx = np.outer(resid_i, resid_i) qm = np.linalg.solve(cm, rx) qm = 0.5 * np.linalg.solve(cm, qm.T) scx = sc_i[:, None] * exog_scale_i for i, _ in enumerate(ix): jq = np.sum(jacv[i] * qm) score[pm:pm + pv] += jq * scx[i, :] score[pm:pm + pv] -= 0.5 * np.sum(jacv[i] * cmi) * scx[i, :] # The derivatives for the smoothness parameters. smx = sm_i[:, None] * exog_smooth_i for i, _ in enumerate(ix): jq = np.sum(jacs[i] * qm) score[pm + pv:pm + pv + ps] += jq * smx[i, :] score[pm + pv:pm + pv + ps] -= ( 0.5 * np.sum(jacs[i] * cmi) * smx[i, :]) # The derivatives with respect to the standard deviation parameters sno = no_i[:, None]**2 * exog_noise_i score[pm + pv + ps:] -= np.dot(cmi.flat[::cm.shape[0] + 1], sno) bm = np.dot(cmi, np.dot(rx, cmi)) score[pm + pv + ps:] += np.dot(bm.flat[::bm.shape[0] + 1], sno) if self.verbose: print("|G|=", np.sqrt(np.sum(score * score))) return score def hessian(self, params): hess = approx_fprime(params, self.score) return hess def fit(self, start_params=None, method=None, maxiter=None, **kwargs): """ Fit a grouped Gaussian process regression using MLE. Parameters ---------- start_params : array_like Optional starting values. method : str or array of str Method or sequence of methods for scipy optimize. maxiter : int The maximum number of iterations in the optimization. Returns ------- An instance of ProcessMLEResults. """ if "verbose" in kwargs: self.verbose = kwargs["verbose"] minim_opts = {} if "minim_opts" in kwargs: minim_opts = kwargs["minim_opts"] if start_params is None: start_params = self._get_start() if isinstance(method, str): method = [method] elif method is None: method = ["powell", "bfgs"] for j, meth in enumerate(method): if meth not in ("powell",): def jac(x): return -self.score(x) else: jac = None if maxiter is not None: if np.isscalar(maxiter): minim_opts["maxiter"] = maxiter else: minim_opts["maxiter"] = maxiter[j % len(maxiter)] f = minimize( lambda x: -self.loglike(x), method=meth, x0=start_params, jac=jac, options=minim_opts) if not f.success: msg = "Fitting did not converge" if jac is not None: msg += ", |gradient|=%.6f" % np.sqrt(np.sum(f.jac**2)) if j < len(method) - 1: msg += ", trying %s next..." % method[j+1] warnings.warn(msg) if np.isfinite(f.x).all(): start_params = f.x hess = self.hessian(f.x) try: cov_params = -np.linalg.inv(hess) except Exception: cov_params = None class rslt: pass r = rslt() r.params = f.x r.normalized_cov_params = cov_params r.optim_retvals = f r.scale = 1 rslt = ProcessMLEResults(self, r) return rslt def covariance(self, time, scale_params, smooth_params, scale_data, smooth_data): """ Returns a Gaussian process covariance matrix. Parameters ---------- time : array_like The time points at which the fitted covariance matrix is calculated. scale_params : array_like The regression parameters for the scaling part of the covariance structure. smooth_params : array_like The regression parameters for the smoothing part of the covariance structure. scale_data : DataFrame The data used to determine the scale parameter, must have len(time) rows. smooth_data : DataFrame The data used to determine the smoothness parameter, must have len(time) rows. Returns ------- A covariance matrix. Notes ----- If the model was fit using formulas, `scale` and `smooth` should be Dataframes, containing all variables that were present in the respective scaling and smoothing formulas used to fit the model. Otherwise, `scale` and `smooth` should contain data arrays whose columns align with the fitted scaling and smoothing parameters. The covariance is only for the Gaussian process and does not include the white noise variance. """ if not hasattr(self.data, "scale_design_info"): sca = np.dot(scale_data, scale_params) smo = np.dot(smooth_data, smooth_params) else: sc = patsy.dmatrix(self.data.scale_design_info, scale_data) sm = patsy.dmatrix(self.data.smooth_design_info, smooth_data) sca = np.exp(np.dot(sc, scale_params)) smo = np.exp(np.dot(sm, smooth_params)) return self.cov.get_cov(time, sca, smo) def predict(self, params, exog=None, *args, **kwargs): """ Obtain predictions of the mean structure. Parameters ---------- params : array_like The model parameters, may be truncated to include only mean parameters. exog : array_like The design matrix for the mean structure. If not provided, the model's design matrix is used. """ if exog is None: exog = self.exog elif hasattr(self.data, "design_info"): # Run the provided data through the formula if present exog = patsy.dmatrix(self.data.design_info, exog) if len(params) > exog.shape[1]: params = params[0:exog.shape[1]] return np.dot(exog, params) class ProcessMLEResults(base.GenericLikelihoodModelResults): """ Results class for Gaussian process regression models. """ def __init__(self, model, mlefit): super(ProcessMLEResults, self).__init__( model, mlefit) pa = model.unpack(mlefit.params) self.mean_params = pa[0] self.scale_params = pa[1] self.smooth_params = pa[2] self.no_params = pa[3] self.df_resid = model.endog.shape[0] - len(mlefit.params) self.k_exog = self.model.exog.shape[1] self.k_scale = self.model.exog_scale.shape[1] self.k_smooth = self.model.exog_smooth.shape[1] self.k_noise = self.model.exog_noise.shape[1] def predict(self, exog=None, transform=True, *args, **kwargs): if not transform: warnings.warn("'transform=False' is ignored in predict") if len(args) > 0 or len(kwargs) > 0: warnings.warn("extra arguments ignored in 'predict'") return self.model.predict(self.params, exog) def covariance(self, time, scale, smooth): """ Returns a fitted covariance matrix. Parameters ---------- time : array_like The time points at which the fitted covariance matrix is calculated. scale : array_like The data used to determine the scale parameter, must have len(time) rows. smooth : array_like The data used to determine the smoothness parameter, must have len(time) rows. Returns ------- A covariance matrix. Notes ----- If the model was fit using formulas, `scale` and `smooth` should be Dataframes, containing all variables that were present in the respective scaling and smoothing formulas used to fit the model. Otherwise, `scale` and `smooth` should be data arrays whose columns align with the fitted scaling and smoothing parameters. """ return self.model.covariance(time, self.scale_params, self.smooth_params, scale, smooth) def covariance_group(self, group): # Check if the group exists, since _groups_ix is a # DefaultDict use len instead of catching a KeyError. ix = self.model._groups_ix[group] if len(ix) == 0: msg = "Group '%s' does not exist" % str(group) raise ValueError(msg) scale_data = self.model.exog_scale[ix, :] smooth_data = self.model.exog_smooth[ix, :] _, scale_names, smooth_names, _ = self.model._split_param_names() scale_data = pd.DataFrame(scale_data, columns=scale_names) smooth_data = pd.DataFrame(smooth_data, columns=smooth_names) time = self.model.time[ix] return self.model.covariance(time, self.scale_params, self.smooth_params, scale_data, smooth_data) def summary(self, yname=None, xname=None, title=None, alpha=0.05): df = pd.DataFrame() df["Type"] = (["Mean"] * self.k_exog + ["Scale"] * self.k_scale + ["Smooth"] * self.k_smooth + ["SD"] * self.k_noise) df["coef"] = self.params try: df["std err"] = np.sqrt(np.diag(self.cov_params())) except Exception: df["std err"] = np.nan from scipy.stats.distributions import norm df["tvalues"] = df.coef / df["std err"] df["P>|t|"] = 2 * norm.sf(np.abs(df.tvalues)) f = norm.ppf(1 - alpha / 2) df["[%.3f" % (alpha / 2)] = df.coef - f * df["std err"] df["%.3f]" % (1 - alpha / 2)] = df.coef + f * df["std err"] df.index = self.model.data.param_names summ = summary2.Summary() if title is None: title = "Gaussian process regression results" summ.add_title(title) summ.add_df(df) return summ statsmodels-0.12.2/statsmodels/regression/quantile_regression.py000066400000000000000000000333741400612667500253350ustar00rootroot00000000000000#!/usr/bin/env python ''' Quantile regression model Model parameters are estimated using iterated reweighted least squares. The asymptotic covariance matrix estimated using kernel density estimation. Author: Vincent Arel-Bundock License: BSD-3 Created: 2013-03-19 The original IRLS function was written for Matlab by Shapour Mohammadi, University of Tehran, 2008 (shmohammadi@gmail.com), with some lines based on code written by James P. Lesage in Applied Econometrics Using MATLAB(1999).PP. 73-4. Translated to python with permission from original author by Christian Prinoth (christian at prinoth dot name). ''' import numpy as np import warnings import scipy.stats as stats from numpy.linalg import pinv from scipy.stats import norm from statsmodels.tools.decorators import cache_readonly from statsmodels.regression.linear_model import (RegressionModel, RegressionResults, RegressionResultsWrapper) from statsmodels.tools.sm_exceptions import (ConvergenceWarning, IterationLimitWarning) class QuantReg(RegressionModel): '''Quantile Regression Estimate a quantile regression model using iterative reweighted least squares. Parameters ---------- endog : array or dataframe endogenous/response variable exog : array or dataframe exogenous/explanatory variable(s) Notes ----- The Least Absolute Deviation (LAD) estimator is a special case where quantile is set to 0.5 (q argument of the fit method). The asymptotic covariance matrix is estimated following the procedure in Greene (2008, p.407-408), using either the logistic or gaussian kernels (kernel argument of the fit method). References ---------- General: * Birkes, D. and Y. Dodge(1993). Alternative Methods of Regression, John Wiley and Sons. * Green,W. H. (2008). Econometric Analysis. Sixth Edition. International Student Edition. * Koenker, R. (2005). Quantile Regression. New York: Cambridge University Press. * LeSage, J. P.(1999). Applied Econometrics Using MATLAB, Kernels (used by the fit method): * Green (2008) Table 14.2 Bandwidth selection (used by the fit method): * Bofinger, E. (1975). Estimation of a density function using order statistics. Australian Journal of Statistics 17: 1-17. * Chamberlain, G. (1994). Quantile regression, censoring, and the structure of wages. In Advances in Econometrics, Vol. 1: Sixth World Congress, ed. C. A. Sims, 171-209. Cambridge: Cambridge University Press. * Hall, P., and S. Sheather. (1988). On the distribution of the Studentized quantile. Journal of the Royal Statistical Society, Series B 50: 381-391. Keywords: Least Absolute Deviation(LAD) Regression, Quantile Regression, Regression, Robust Estimation. ''' def __init__(self, endog, exog, **kwargs): super(QuantReg, self).__init__(endog, exog, **kwargs) def whiten(self, data): """ QuantReg model whitener does nothing: returns data. """ return data def fit(self, q=.5, vcov='robust', kernel='epa', bandwidth='hsheather', max_iter=1000, p_tol=1e-6, **kwargs): """ Solve by Iterative Weighted Least Squares Parameters ---------- q : float Quantile must be strictly between 0 and 1 vcov : str, method used to calculate the variance-covariance matrix of the parameters. Default is ``robust``: - robust : heteroskedasticity robust standard errors (as suggested in Greene 6th edition) - iid : iid errors (as in Stata 12) kernel : str, kernel to use in the kernel density estimation for the asymptotic covariance matrix: - epa: Epanechnikov - cos: Cosine - gau: Gaussian - par: Parzene bandwidth : str, Bandwidth selection method in kernel density estimation for asymptotic covariance estimate (full references in QuantReg docstring): - hsheather: Hall-Sheather (1988) - bofinger: Bofinger (1975) - chamberlain: Chamberlain (1994) """ if q <= 0 or q >= 1: raise Exception('q must be strictly between 0 and 1') kern_names = ['biw', 'cos', 'epa', 'gau', 'par'] if kernel not in kern_names: raise Exception("kernel must be one of " + ', '.join(kern_names)) else: kernel = kernels[kernel] if bandwidth == 'hsheather': bandwidth = hall_sheather elif bandwidth == 'bofinger': bandwidth = bofinger elif bandwidth == 'chamberlain': bandwidth = chamberlain else: raise Exception("bandwidth must be in 'hsheather', 'bofinger', 'chamberlain'") endog = self.endog exog = self.exog nobs = self.nobs exog_rank = np.linalg.matrix_rank(self.exog) self.rank = exog_rank self.df_model = float(self.rank - self.k_constant) self.df_resid = self.nobs - self.rank n_iter = 0 xstar = exog beta = np.ones(exog_rank) # TODO: better start, initial beta is used only for convergence check # Note the following does not work yet, # the iteration loop always starts with OLS as initial beta # if start_params is not None: # if len(start_params) != rank: # raise ValueError('start_params has wrong length') # beta = start_params # else: # # start with OLS # beta = np.dot(np.linalg.pinv(exog), endog) diff = 10 cycle = False history = dict(params = [], mse=[]) while n_iter < max_iter and diff > p_tol and not cycle: n_iter += 1 beta0 = beta xtx = np.dot(xstar.T, exog) xty = np.dot(xstar.T, endog) beta = np.dot(pinv(xtx), xty) resid = endog - np.dot(exog, beta) mask = np.abs(resid) < .000001 resid[mask] = ((resid[mask] >= 0) * 2 - 1) * .000001 resid = np.where(resid < 0, q * resid, (1-q) * resid) resid = np.abs(resid) xstar = exog / resid[:, np.newaxis] diff = np.max(np.abs(beta - beta0)) history['params'].append(beta) history['mse'].append(np.mean(resid*resid)) if (n_iter >= 300) and (n_iter % 100 == 0): # check for convergence circle, should not happen for ii in range(2, 10): if np.all(beta == history['params'][-ii]): cycle = True warnings.warn("Convergence cycle detected", ConvergenceWarning) break if n_iter == max_iter: warnings.warn("Maximum number of iterations (" + str(max_iter) + ") reached.", IterationLimitWarning) e = endog - np.dot(exog, beta) # Greene (2008, p.407) writes that Stata 6 uses this bandwidth: # h = 0.9 * np.std(e) / (nobs**0.2) # Instead, we calculate bandwidth as in Stata 12 iqre = stats.scoreatpercentile(e, 75) - stats.scoreatpercentile(e, 25) h = bandwidth(nobs, q) h = min(np.std(endog), iqre / 1.34) * (norm.ppf(q + h) - norm.ppf(q - h)) fhat0 = 1. / (nobs * h) * np.sum(kernel(e / h)) if vcov == 'robust': d = np.where(e > 0, (q/fhat0)**2, ((1-q)/fhat0)**2) xtxi = pinv(np.dot(exog.T, exog)) xtdx = np.dot(exog.T * d[np.newaxis, :], exog) vcov = xtxi @ xtdx @ xtxi elif vcov == 'iid': vcov = (1. / fhat0)**2 * q * (1 - q) * pinv(np.dot(exog.T, exog)) else: raise Exception("vcov must be 'robust' or 'iid'") lfit = QuantRegResults(self, beta, normalized_cov_params=vcov) lfit.q = q lfit.iterations = n_iter lfit.sparsity = 1. / fhat0 lfit.bandwidth = h lfit.history = history return RegressionResultsWrapper(lfit) def _parzen(u): z = np.where(np.abs(u) <= .5, 4./3 - 8. * u**2 + 8. * np.abs(u)**3, 8. * (1 - np.abs(u))**3 / 3.) z[np.abs(u) > 1] = 0 return z kernels = {} kernels['biw'] = lambda u: 15. / 16 * (1 - u**2)**2 * np.where(np.abs(u) <= 1, 1, 0) kernels['cos'] = lambda u: np.where(np.abs(u) <= .5, 1 + np.cos(2 * np.pi * u), 0) kernels['epa'] = lambda u: 3. / 4 * (1-u**2) * np.where(np.abs(u) <= 1, 1, 0) kernels['gau'] = lambda u: norm.pdf(u) kernels['par'] = _parzen #kernels['bet'] = lambda u: np.where(np.abs(u) <= 1, .75 * (1 - u) * (1 + u), 0) #kernels['log'] = lambda u: logistic.pdf(u) * (1 - logistic.pdf(u)) #kernels['tri'] = lambda u: np.where(np.abs(u) <= 1, 1 - np.abs(u), 0) #kernels['trw'] = lambda u: 35. / 32 * (1 - u**2)**3 * np.where(np.abs(u) <= 1, 1, 0) #kernels['uni'] = lambda u: 1. / 2 * np.where(np.abs(u) <= 1, 1, 0) def hall_sheather(n, q, alpha=.05): z = norm.ppf(q) num = 1.5 * norm.pdf(z)**2. den = 2. * z**2. + 1. h = n**(-1. / 3) * norm.ppf(1. - alpha / 2.)**(2./3) * (num / den)**(1./3) return h def bofinger(n, q): num = 9. / 2 * norm.pdf(2 * norm.ppf(q))**4 den = (2 * norm.ppf(q)**2 + 1)**2 h = n**(-1. / 5) * (num / den)**(1. / 5) return h def chamberlain(n, q, alpha=.05): return norm.ppf(1 - alpha / 2) * np.sqrt(q*(1 - q) / n) class QuantRegResults(RegressionResults): '''Results instance for the QuantReg model''' @cache_readonly def prsquared(self): q = self.q endog = self.model.endog e = self.resid e = np.where(e < 0, (1 - q) * e, q * e) e = np.abs(e) ered = endog - stats.scoreatpercentile(endog, q * 100) ered = np.where(ered < 0, (1 - q) * ered, q * ered) ered = np.abs(ered) return 1 - np.sum(e) / np.sum(ered) #@cache_readonly def scale(self): return 1. @cache_readonly def bic(self): return np.nan @cache_readonly def aic(self): return np.nan @cache_readonly def llf(self): return np.nan @cache_readonly def rsquared(self): return np.nan @cache_readonly def rsquared_adj(self): return np.nan @cache_readonly def mse(self): return np.nan @cache_readonly def mse_model(self): return np.nan @cache_readonly def mse_total(self): return np.nan @cache_readonly def centered_tss(self): return np.nan @cache_readonly def uncentered_tss(self): return np.nan @cache_readonly def HC0_se(self): raise NotImplementedError @cache_readonly def HC1_se(self): raise NotImplementedError @cache_readonly def HC2_se(self): raise NotImplementedError @cache_readonly def HC3_se(self): raise NotImplementedError def summary(self, yname=None, xname=None, title=None, alpha=.05): """Summarize the Regression Results Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Names for the exogenous variables. Default is `var_##` for ## in the number of regressors. Must match the number of parameters in the model title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : class to hold summary results """ eigvals = self.eigenvals condno = self.condition_number top_left = [('Dep. Variable:', None), ('Model:', None), ('Method:', ['Least Squares']), ('Date:', None), ('Time:', None) ] top_right = [('Pseudo R-squared:', ["%#8.4g" % self.prsquared]), ('Bandwidth:', ["%#8.4g" % self.bandwidth]), ('Sparsity:', ["%#8.4g" % self.sparsity]), ('No. Observations:', None), ('Df Residuals:', None), ('Df Model:', None) ] if title is None: title = self.model.__class__.__name__ + ' ' + "Regression Results" # create summary table instance from statsmodels.iolib.summary import Summary smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, yname=yname, xname=xname, title=title) smry.add_table_params(self, yname=yname, xname=xname, alpha=alpha, use_t=self.use_t) # add warnings/notes, added to text format only etext = [] if eigvals[-1] < 1e-10: wstr = "The smallest eigenvalue is %6.3g. This might indicate " wstr += "that there are\n" wstr += "strong multicollinearity problems or that the design " wstr += "matrix is singular." wstr = wstr % eigvals[-1] etext.append(wstr) elif condno > 1000: # TODO: what is recommended wstr = "The condition number is large, %6.3g. This might " wstr += "indicate that there are\n" wstr += "strong multicollinearity or other numerical " wstr += "problems." wstr = wstr % condno etext.append(wstr) if etext: smry.add_extra_txt(etext) return smry statsmodels-0.12.2/statsmodels/regression/recursive_ls.py000066400000000000000000000763221400612667500237600ustar00rootroot00000000000000""" Recursive least squares model Author: Chad Fulton License: Simplified-BSD """ import numpy as np import pandas as pd from statsmodels.compat.pandas import Appender from statsmodels.tools.data import _is_using_pandas from statsmodels.tsa.statespace.mlemodel import ( MLEModel, MLEResults, MLEResultsWrapper, PredictionResults, PredictionResultsWrapper) from statsmodels.tsa.statespace.tools import concat from statsmodels.tools.tools import Bunch from statsmodels.tools.decorators import cache_readonly import statsmodels.base.wrapper as wrap # Columns are alpha = 0.1, 0.05, 0.025, 0.01, 0.005 _cusum_squares_scalars = np.array([ [1.0729830, 1.2238734, 1.3581015, 1.5174271, 1.6276236], [-0.6698868, -0.6700069, -0.6701218, -0.6702672, -0.6703724], [-0.5816458, -0.7351697, -0.8858694, -1.0847745, -1.2365861] ]) class RecursiveLS(MLEModel): r""" Recursive least squares Parameters ---------- endog : array_like The observed time-series process :math:`y` exog : array_like Array of exogenous regressors, shaped nobs x k. constraints : array_like, str, or tuple - array : An r x k array where r is the number of restrictions to test and k is the number of regressors. It is assumed that the linear combination is equal to zero. - str : The full hypotheses to test can be given as a string. See the examples. - tuple : A tuple of arrays in the form (R, q), ``q`` can be either a scalar or a length p row vector. Notes ----- Recursive least squares (RLS) corresponds to expanding window ordinary least squares (OLS). This model applies the Kalman filter to compute recursive estimates of the coefficients and recursive residuals. References ---------- .. [*] Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods: Second Edition. Oxford University Press. """ def __init__(self, endog, exog, constraints=None, **kwargs): # Standardize data endog_using_pandas = _is_using_pandas(endog, None) if not endog_using_pandas: endog = np.asanyarray(endog) exog_is_using_pandas = _is_using_pandas(exog, None) if not exog_is_using_pandas: exog = np.asarray(exog) # Make sure we have 2-dimensional array if exog.ndim == 1: if not exog_is_using_pandas: exog = exog[:, None] else: exog = pd.DataFrame(exog) self.k_exog = exog.shape[1] # Handle constraints self.k_constraints = 0 self._r_matrix = self._q_matrix = None if constraints is not None: from patsy import DesignInfo from statsmodels.base.data import handle_data data = handle_data(endog, exog, **kwargs) names = data.param_names LC = DesignInfo(names).linear_constraint(constraints) self._r_matrix, self._q_matrix = LC.coefs, LC.constants self.k_constraints = self._r_matrix.shape[0] constraint_endog = np.zeros((len(endog), len(self._r_matrix))) if endog_using_pandas: constraint_endog = pd.DataFrame(constraint_endog, index=endog.index) endog = concat([endog, constraint_endog], axis=1) endog.values[:, 1:] = self._q_matrix[:, 0] else: endog[:, 1:] = self._q_matrix[:, 0] # Handle coefficient initialization kwargs.setdefault('initialization', 'diffuse') # Initialize the state space representation super(RecursiveLS, self).__init__( endog, k_states=self.k_exog, exog=exog, **kwargs) # Use univariate filtering by default self.ssm.filter_univariate = True # Concentrate the scale out of the likelihood function self.ssm.filter_concentrated = True # Setup the state space representation self['design'] = np.zeros((self.k_endog, self.k_states, self.nobs)) self['design', 0] = self.exog[:, :, None].T if self._r_matrix is not None: self['design', 1:, :] = self._r_matrix[:, :, None] self['transition'] = np.eye(self.k_states) # Notice that the filter output does not depend on the measurement # variance, so we set it here to 1 self['obs_cov', 0, 0] = 1. self['transition'] = np.eye(self.k_states) # Linear constraints are technically imposed by adding "fake" endog # variables that are used during filtering, but for all model- and # results-based purposes we want k_endog = 1. if self._r_matrix is not None: self.k_endog = 1 @classmethod def from_formula(cls, formula, data, subset=None, constraints=None): return super(MLEModel, cls).from_formula(formula, data, subset, constraints=constraints) def _validate_can_fix_params(self, param_names): raise ValueError('Linear constraints on coefficients should be given' ' using the `constraints` argument in constructing.' ' the model. Other parameter constraints are not' ' available in the resursive least squares model.') def fit(self): """ Fits the model by application of the Kalman filter Returns ------- RecursiveLSResults """ smoother_results = self.smooth(return_ssm=True) with self.ssm.fixed_scale(smoother_results.scale): res = self.smooth() return res def filter(self, return_ssm=False, **kwargs): # Get the state space output result = super(RecursiveLS, self).filter([], transformed=True, cov_type='none', return_ssm=True, **kwargs) # Wrap in a results object if not return_ssm: params = result.filtered_state[:, -1] cov_kwds = { 'custom_cov_type': 'nonrobust', 'custom_cov_params': result.filtered_state_cov[:, :, -1], 'custom_description': ('Parameters and covariance matrix' ' estimates are RLS estimates' ' conditional on the entire sample.') } result = RecursiveLSResultsWrapper( RecursiveLSResults(self, params, result, cov_type='custom', cov_kwds=cov_kwds) ) return result def smooth(self, return_ssm=False, **kwargs): # Get the state space output result = super(RecursiveLS, self).smooth([], transformed=True, cov_type='none', return_ssm=True, **kwargs) # Wrap in a results object if not return_ssm: params = result.filtered_state[:, -1] cov_kwds = { 'custom_cov_type': 'nonrobust', 'custom_cov_params': result.filtered_state_cov[:, :, -1], 'custom_description': ('Parameters and covariance matrix' ' estimates are RLS estimates' ' conditional on the entire sample.') } result = RecursiveLSResultsWrapper( RecursiveLSResults(self, params, result, cov_type='custom', cov_kwds=cov_kwds) ) return result @property def endog_names(self): endog_names = super(RecursiveLS, self).endog_names return endog_names[0] if isinstance(endog_names, list) else endog_names @property def param_names(self): return self.exog_names @property def start_params(self): # Only parameter is the measurement disturbance standard deviation return np.zeros(0) def update(self, params, **kwargs): """ Update the parameters of the model Updates the representation matrices to fill in the new parameter values. Parameters ---------- params : array_like Array of new parameters. transformed : bool, optional Whether or not `params` is already transformed. If set to False, `transform_params` is called. Default is True.. Returns ------- params : array_like Array of parameters. """ pass class RecursiveLSResults(MLEResults): """ Class to hold results from fitting a recursive least squares model. Parameters ---------- model : RecursiveLS instance The fitted model instance Attributes ---------- specification : dictionary Dictionary including all attributes from the recursive least squares model instance. See Also -------- statsmodels.tsa.statespace.kalman_filter.FilterResults statsmodels.tsa.statespace.mlemodel.MLEResults """ def __init__(self, model, params, filter_results, cov_type='opg', **kwargs): super(RecursiveLSResults, self).__init__( model, params, filter_results, cov_type, **kwargs) # Since we are overriding params with things that are not MLE params, # need to adjust df's q = max(self.loglikelihood_burn, self.k_diffuse_states) self.df_model = q - self.model.k_constraints self.df_resid = self.nobs_effective - self.df_model # Save _init_kwds self._init_kwds = self.model._get_init_kwds() # Save the model specification self.specification = Bunch(**{ 'k_exog': self.model.k_exog, 'k_constraints': self.model.k_constraints}) # Adjust results to remove "faux" endog from the constraints if self.model._r_matrix is not None: for name in ['forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov']: setattr(self, name, getattr(self, name)[0:1]) @property def recursive_coefficients(self): """ Estimates of regression coefficients, recursively estimated Returns ------- out: Bunch Has the following attributes: - `filtered`: a time series array with the filtered estimate of the component - `filtered_cov`: a time series array with the filtered estimate of the variance/covariance of the component - `smoothed`: a time series array with the smoothed estimate of the component - `smoothed_cov`: a time series array with the smoothed estimate of the variance/covariance of the component - `offset`: an integer giving the offset in the state vector where this component begins """ out = None spec = self.specification start = offset = 0 end = offset + spec.k_exog out = Bunch( filtered=self.filtered_state[start:end], filtered_cov=self.filtered_state_cov[start:end, start:end], smoothed=None, smoothed_cov=None, offset=offset ) if self.smoothed_state is not None: out.smoothed = self.smoothed_state[start:end] if self.smoothed_state_cov is not None: out.smoothed_cov = ( self.smoothed_state_cov[start:end, start:end]) return out @cache_readonly def resid_recursive(self): r""" Recursive residuals Returns ------- resid_recursive : array_like An array of length `nobs` holding the recursive residuals. Notes ----- These quantities are defined in, for example, Harvey (1989) section 5.4. In fact, there he defines the standardized innovations in equation 5.4.1, but in his version they have non-unit variance, whereas the standardized forecast errors computed by the Kalman filter here assume unit variance. To convert to Harvey's definition, we need to multiply by the standard deviation. Harvey notes that in smaller samples, "although the second moment of the :math:`\tilde \sigma_*^{-1} \tilde v_t`'s is unity, the variance is not necessarily equal to unity as the mean need not be equal to zero", and he defines an alternative version (which are not provided here). """ return (self.filter_results.standardized_forecasts_error[0] * self.scale**0.5) @cache_readonly def cusum(self): r""" Cumulative sum of standardized recursive residuals statistics Returns ------- cusum : array_like An array of length `nobs - k_exog` holding the CUSUM statistics. Notes ----- The CUSUM statistic takes the form: .. math:: W_t = \frac{1}{\hat \sigma} \sum_{j=k+1}^t w_j where :math:`w_j` is the recursive residual at time :math:`j` and :math:`\hat \sigma` is the estimate of the standard deviation from the full sample. Excludes the first `k_exog` datapoints. Due to differences in the way :math:`\hat \sigma` is calculated, the output of this function differs slightly from the output in the R package strucchange and the Stata contributed .ado file cusum6. The calculation in this package is consistent with the description of Brown et al. (1975) References ---------- .. [*] Brown, R. L., J. Durbin, and J. M. Evans. 1975. "Techniques for Testing the Constancy of Regression Relationships over Time." Journal of the Royal Statistical Society. Series B (Methodological) 37 (2): 149-92. """ d = max(self.nobs_diffuse, self.loglikelihood_burn) return (np.cumsum(self.resid_recursive[d:]) / np.std(self.resid_recursive[d:], ddof=1)) @cache_readonly def cusum_squares(self): r""" Cumulative sum of squares of standardized recursive residuals statistics Returns ------- cusum_squares : array_like An array of length `nobs - k_exog` holding the CUSUM of squares statistics. Notes ----- The CUSUM of squares statistic takes the form: .. math:: s_t = \left ( \sum_{j=k+1}^t w_j^2 \right ) \Bigg / \left ( \sum_{j=k+1}^T w_j^2 \right ) where :math:`w_j` is the recursive residual at time :math:`j`. Excludes the first `k_exog` datapoints. References ---------- .. [*] Brown, R. L., J. Durbin, and J. M. Evans. 1975. "Techniques for Testing the Constancy of Regression Relationships over Time." Journal of the Royal Statistical Society. Series B (Methodological) 37 (2): 149-92. """ d = max(self.nobs_diffuse, self.loglikelihood_burn) numer = np.cumsum(self.resid_recursive[d:]**2) denom = numer[-1] return numer / denom @cache_readonly def llf_recursive_obs(self): """ (float) Loglikelihood at observation, computed from recursive residuals """ from scipy.stats import norm return np.log(norm.pdf(self.resid_recursive, loc=0, scale=self.scale**0.5)) @cache_readonly def llf_recursive(self): """ (float) Loglikelihood defined by recursive residuals, equivalent to OLS """ return np.sum(self.llf_recursive_obs) @cache_readonly def ssr(self): """ssr""" d = max(self.nobs_diffuse, self.loglikelihood_burn) return (self.nobs - d) * self.filter_results.obs_cov[0, 0, 0] @cache_readonly def centered_tss(self): """Centered tss""" return np.sum((self.filter_results.endog[0] - np.mean(self.filter_results.endog))**2) @cache_readonly def uncentered_tss(self): """uncentered tss""" return np.sum((self.filter_results.endog[0])**2) @cache_readonly def ess(self): """ess""" if self.k_constant: return self.centered_tss - self.ssr else: return self.uncentered_tss - self.ssr @cache_readonly def rsquared(self): """rsquared""" if self.k_constant: return 1 - self.ssr / self.centered_tss else: return 1 - self.ssr / self.uncentered_tss @cache_readonly def mse_model(self): """mse_model""" return self.ess / self.df_model @cache_readonly def mse_resid(self): """mse_resid""" return self.ssr / self.df_resid @cache_readonly def mse_total(self): """mse_total""" if self.k_constant: return self.centered_tss / (self.df_resid + self.df_model) else: return self.uncentered_tss / (self.df_resid + self.df_model) @Appender(MLEResults.get_prediction.__doc__) def get_prediction(self, start=None, end=None, dynamic=False, index=None, **kwargs): # Note: need to override this, because we currently do not support # dynamic prediction or forecasts when there are constraints. if start is None: start = self.model._index[0] # Handle start, end, dynamic start, end, out_of_sample, prediction_index = ( self.model._get_prediction_index(start, end, index)) # Handle `dynamic` if isinstance(dynamic, (bytes, str)): dynamic, _, _ = self.model._get_index_loc(dynamic) if self.model._r_matrix is not None and (out_of_sample or dynamic): raise NotImplementedError('Cannot yet perform out-of-sample or' ' dynamic prediction in models with' ' constraints.') # Perform the prediction # This is a (k_endog x npredictions) array; do not want to squeeze in # case of npredictions = 1 prediction_results = self.filter_results.predict( start, end + out_of_sample + 1, dynamic, **kwargs) # Return a new mlemodel.PredictionResults object res_obj = PredictionResults(self, prediction_results, row_labels=prediction_index) return PredictionResultsWrapper(res_obj) def plot_recursive_coefficient(self, variables=0, alpha=0.05, legend_loc='upper left', fig=None, figsize=None): r""" Plot the recursively estimated coefficients on a given variable Parameters ---------- variables : {int, str, list[int], list[str]}, optional Integer index or string name of the variable whose coefficient will be plotted. Can also be an iterable of integers or strings. Default is the first variable. alpha : float, optional The confidence intervals for the coefficient are (1 - alpha) % legend_loc : str, optional The location of the legend in the plot. Default is upper left. fig : Figure, optional If given, subplots are created in this figure instead of in a new figure. Note that the grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Notes ----- All plots contain (1 - `alpha`) % confidence intervals. """ # Get variables if isinstance(variables, (int, str)): variables = [variables] k_variables = len(variables) # If a string was given for `variable`, try to get it from exog names exog_names = self.model.exog_names for i in range(k_variables): variable = variables[i] if isinstance(variable, str): variables[i] = exog_names.index(variable) # Create the plot from scipy.stats import norm from statsmodels.graphics.utils import _import_mpl, create_mpl_fig plt = _import_mpl() fig = create_mpl_fig(fig, figsize) for i in range(k_variables): variable = variables[i] ax = fig.add_subplot(k_variables, 1, i + 1) # Get dates, if applicable if hasattr(self.data, 'dates') and self.data.dates is not None: dates = self.data.dates._mpl_repr() else: dates = np.arange(self.nobs) d = max(self.nobs_diffuse, self.loglikelihood_burn) # Plot the coefficient coef = self.recursive_coefficients ax.plot(dates[d:], coef.filtered[variable, d:], label='Recursive estimates: %s' % exog_names[variable]) # Legend handles, labels = ax.get_legend_handles_labels() # Get the critical value for confidence intervals if alpha is not None: critical_value = norm.ppf(1 - alpha / 2.) # Plot confidence intervals std_errors = np.sqrt(coef.filtered_cov[variable, variable, :]) ci_lower = ( coef.filtered[variable] - critical_value * std_errors) ci_upper = ( coef.filtered[variable] + critical_value * std_errors) ci_poly = ax.fill_between( dates[d:], ci_lower[d:], ci_upper[d:], alpha=0.2 ) ci_label = ('$%.3g \\%%$ confidence interval' % ((1 - alpha)*100)) # Only add CI to legend for the first plot if i == 0: # Proxy artist for fill_between legend entry # See https://matplotlib.org/1.3.1/users/legend_guide.html p = plt.Rectangle((0, 0), 1, 1, fc=ci_poly.get_facecolor()[0]) handles.append(p) labels.append(ci_label) ax.legend(handles, labels, loc=legend_loc) # Remove xticks for all but the last plot if i < k_variables - 1: ax.xaxis.set_ticklabels([]) fig.tight_layout() return fig def _cusum_significance_bounds(self, alpha, ddof=0, points=None): """ Parameters ---------- alpha : float, optional The significance bound is alpha %. ddof : int, optional The number of periods additional to `k_exog` to exclude in constructing the bounds. Default is zero. This is usually used only for testing purposes. points : iterable, optional The points at which to evaluate the significance bounds. Default is two points, beginning and end of the sample. Notes ----- Comparing against the cusum6 package for Stata, this does not produce exactly the same confidence bands (which are produced in cusum6 by lw, uw) because they burn the first k_exog + 1 periods instead of the first k_exog. If this change is performed (so that `tmp = (self.nobs - d - 1)**0.5`), then the output here matches cusum6. The cusum6 behavior does not seem to be consistent with Brown et al. (1975); it is likely they did that because they needed three initial observations to get the initial OLS estimates, whereas we do not need to do that. """ # Get the constant associated with the significance level if alpha == 0.01: scalar = 1.143 elif alpha == 0.05: scalar = 0.948 elif alpha == 0.10: scalar = 0.950 else: raise ValueError('Invalid significance level.') # Get the points for the significance bound lines d = max(self.nobs_diffuse, self.loglikelihood_burn) tmp = (self.nobs - d - ddof)**0.5 def upper_line(x): return scalar * tmp + 2 * scalar * (x - d) / tmp if points is None: points = np.array([d, self.nobs]) return -upper_line(points), upper_line(points) def plot_cusum(self, alpha=0.05, legend_loc='upper left', fig=None, figsize=None): r""" Plot the CUSUM statistic and significance bounds. Parameters ---------- alpha : float, optional The plotted significance bounds are alpha %. legend_loc : str, optional The location of the legend in the plot. Default is upper left. fig : Figure, optional If given, subplots are created in this figure instead of in a new figure. Note that the grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Notes ----- Evidence of parameter instability may be found if the CUSUM statistic moves out of the significance bounds. References ---------- .. [*] Brown, R. L., J. Durbin, and J. M. Evans. 1975. "Techniques for Testing the Constancy of Regression Relationships over Time." Journal of the Royal Statistical Society. Series B (Methodological) 37 (2): 149-92. """ # Create the plot from statsmodels.graphics.utils import _import_mpl, create_mpl_fig _import_mpl() fig = create_mpl_fig(fig, figsize) ax = fig.add_subplot(1, 1, 1) # Get dates, if applicable if hasattr(self.data, 'dates') and self.data.dates is not None: dates = self.data.dates._mpl_repr() else: dates = np.arange(self.nobs) d = max(self.nobs_diffuse, self.loglikelihood_burn) # Plot cusum series and reference line ax.plot(dates[d:], self.cusum, label='CUSUM') ax.hlines(0, dates[d], dates[-1], color='k', alpha=0.3) # Plot significance bounds lower_line, upper_line = self._cusum_significance_bounds(alpha) ax.plot([dates[d], dates[-1]], upper_line, 'k--', label='%d%% significance' % (alpha * 100)) ax.plot([dates[d], dates[-1]], lower_line, 'k--') ax.legend(loc=legend_loc) return fig def _cusum_squares_significance_bounds(self, alpha, points=None): """ Notes ----- Comparing against the cusum6 package for Stata, this does not produce exactly the same confidence bands (which are produced in cusum6 by lww, uww) because they use a different method for computing the critical value; in particular, they use tabled values from Table C, pp. 364-365 of "The Econometric Analysis of Time Series" Harvey, (1990), and use the value given to 99 observations for any larger number of observations. In contrast, we use the approximating critical values suggested in Edgerton and Wells (1994) which allows computing relatively good approximations for any number of observations. """ # Get the approximate critical value associated with the significance # level d = max(self.nobs_diffuse, self.loglikelihood_burn) n = 0.5 * (self.nobs - d) - 1 try: ix = [0.1, 0.05, 0.025, 0.01, 0.005].index(alpha / 2) except ValueError: raise ValueError('Invalid significance level.') scalars = _cusum_squares_scalars[:, ix] crit = scalars[0] / n**0.5 + scalars[1] / n + scalars[2] / n**1.5 # Get the points for the significance bound lines if points is None: points = np.array([d, self.nobs]) line = (points - d) / (self.nobs - d) return line - crit, line + crit def plot_cusum_squares(self, alpha=0.05, legend_loc='upper left', fig=None, figsize=None): r""" Plot the CUSUM of squares statistic and significance bounds. Parameters ---------- alpha : float, optional The plotted significance bounds are alpha %. legend_loc : str, optional The location of the legend in the plot. Default is upper left. fig : Figure, optional If given, subplots are created in this figure instead of in a new figure. Note that the grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Notes ----- Evidence of parameter instability may be found if the CUSUM of squares statistic moves out of the significance bounds. Critical values used in creating the significance bounds are computed using the approximate formula of [1]_. References ---------- .. [*] Brown, R. L., J. Durbin, and J. M. Evans. 1975. "Techniques for Testing the Constancy of Regression Relationships over Time." Journal of the Royal Statistical Society. Series B (Methodological) 37 (2): 149-92. .. [1] Edgerton, David, and Curt Wells. 1994. "Critical Values for the Cusumsq Statistic in Medium and Large Sized Samples." Oxford Bulletin of Economics and Statistics 56 (3): 355-65. """ # Create the plot from statsmodels.graphics.utils import _import_mpl, create_mpl_fig _import_mpl() fig = create_mpl_fig(fig, figsize) ax = fig.add_subplot(1, 1, 1) # Get dates, if applicable if hasattr(self.data, 'dates') and self.data.dates is not None: dates = self.data.dates._mpl_repr() else: dates = np.arange(self.nobs) d = max(self.nobs_diffuse, self.loglikelihood_burn) # Plot cusum series and reference line ax.plot(dates[d:], self.cusum_squares, label='CUSUM of squares') ref_line = (np.arange(d, self.nobs) - d) / (self.nobs - d) ax.plot(dates[d:], ref_line, 'k', alpha=0.3) # Plot significance bounds lower_line, upper_line = self._cusum_squares_significance_bounds(alpha) ax.plot([dates[d], dates[-1]], upper_line, 'k--', label='%d%% significance' % (alpha * 100)) ax.plot([dates[d], dates[-1]], lower_line, 'k--') ax.legend(loc=legend_loc) return fig class RecursiveLSResultsWrapper(MLEResultsWrapper): _attrs = {} _wrap_attrs = wrap.union_dicts(MLEResultsWrapper._wrap_attrs, _attrs) _methods = {} _wrap_methods = wrap.union_dicts(MLEResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(RecursiveLSResultsWrapper, # noqa:E305 RecursiveLSResults) statsmodels-0.12.2/statsmodels/regression/rolling.py000066400000000000000000000665121400612667500227210ustar00rootroot00000000000000""" Rolling OLS and WLS Implements an efficient rolling estimator that avoids repeated matrix multiplication. Copyright (c) 2019 Kevin Sheppard License: 3-clause BSD """ from statsmodels.compat.numpy import lstsq from statsmodels.compat.pandas import Appender, Substitution, cache_readonly from collections import namedtuple import numpy as np from pandas import DataFrame, MultiIndex, Series from scipy import stats from statsmodels.base import model from statsmodels.base.model import LikelihoodModelResults, Model from statsmodels.regression.linear_model import ( RegressionModel, RegressionResults, ) from statsmodels.tools.validation import array_like, int_like, string_like def strip4(line): if line.startswith(" "): return line[4:] return line RollingStore = namedtuple( "RollingStore", [ "params", "ssr", "llf", "nobs", "s2", "xpxi", "xeex", "centered_tss", "uncentered_tss", ], ) common_params = "\n".join(map(strip4, model._model_params_doc.split("\n"))) window_parameters = """\ window : int Length of the rolling window. Must be strictly larger than the number of variables in the model. """ weight_parameters = """ weights : array_like, optional A 1d array of weights. If you supply 1/W then the variables are pre- multiplied by 1/sqrt(W). If no weights are supplied the default value is 1 and WLS results are the same as OLS. """ _missing_param_doc = """\ min_nobs : {int, None} Minimum number of observations required to estimate a model when data are missing. If None, the minimum depends on the number of regressors in the model. Must be smaller than window. missing : str, default "drop" Available options are "drop", "skip" and "raise". If "drop", any observations with nans are dropped and the estimates are computed using only the non-missing values in each window. If 'skip' blocks containing missing values are skipped and the corresponding results contains NaN. If 'raise', an error is raised. Default is 'drop'. expanding : bool, default False If True, then the initial observations after min_nobs are filled using an expanding scheme until ``window`` observations are available, after which rolling is used. """ extra_base = _missing_param_doc extra_parameters = window_parameters + weight_parameters + extra_base _doc = """ Rolling %(model_type)s Least Squares %(parameters)s %(extra_parameters)s See Also -------- statsmodels.regression.linear_model.%(model)s %(model)s estimation and parameter testing. Notes ----- Tested against %(model)s for accuracy. Results may differ from %(model)s applied to windows of data if this model contains an implicit constant (i.e., includes dummies for all categories) rather than an explicit constant (e.g., a column of 1s). Examples -------- >>> from statsmodels.regression.rolling import Rolling%(model)s >>> from statsmodels.datasets import longley >>> data = longley.load(as_pandas=False) >>> exog = add_constant(data.exog, prepend=False) >>> mod = Rolling%(model)s(data.endog, exog) >>> rolling_res = mod.fit(reset=50) Use params_only to skip all calculations except parameter estimation >>> rolling_params = mod.fit(params_only=True) Use expanding and min_nobs to fill the initial results using an expanding scheme until window observation, and the roll. >>> mod = Rolling%(model)s(data.endog, exog, window=60, min_nobs=12, ... expanding=True) >>> rolling_res = mod.fit() """ @Substitution( model_type="Weighted", model="WLS", parameters=common_params, extra_parameters=extra_parameters, ) @Appender(_doc) class RollingWLS(object): def __init__( self, endog, exog, window=None, *, weights=None, min_nobs=None, missing="drop", expanding=False ): # Call Model.__init__ twice to use const detection in first pass # But to not drop in the second pass missing = string_like( missing, "missing", options=("drop", "raise", "skip") ) temp_msng = "drop" if missing != "raise" else "raise" Model.__init__(self, endog, exog, missing=temp_msng, hasconst=None) k_const = self.k_constant const_idx = self.data.const_idx Model.__init__(self, endog, exog, missing="none", hasconst=False) self.k_constant = k_const self.data.const_idx = const_idx self._y = array_like(endog, "endog") nobs = self._y.shape[0] self._x = array_like(exog, "endog", ndim=2, shape=(nobs, None)) window = int_like(window, "window", optional=True) weights = array_like(weights, "weights", optional=True, shape=(nobs,)) self._window = window if window is not None else self._y.shape[0] self._weighted = weights is not None self._weights = np.ones(nobs) if weights is None else weights w12 = np.sqrt(self._weights) self._wy = w12 * self._y self._wx = w12[:, None] * self._x min_nobs = int_like(min_nobs, "min_nobs", optional=True) self._min_nobs = min_nobs if min_nobs is not None else self._x.shape[1] if self._min_nobs < self._x.shape[1] or self._min_nobs > self._window: raise ValueError( "min_nobs must be larger than the number of " "regressors in the model and less than window" ) self._expanding = expanding self._is_nan = np.zeros_like(self._y, dtype=bool) self._has_nan = self._find_nans() self.const_idx = self.data.const_idx self._skip_missing = missing == "skip" def _handle_data(self, endog, exog, missing, hasconst, **kwargs): return Model._handle_data( self, endog, exog, missing, hasconst, **kwargs ) def _find_nans(self): nans = np.isnan(self._y) nans |= np.any(np.isnan(self._x), axis=1) nans |= np.isnan(self._weights) self._is_nan[:] = nans has_nan = np.cumsum(nans) w = self._window has_nan[w - 1 :] = has_nan[w - 1 :] - has_nan[: -(w - 1)] if self._expanding: has_nan[: self._min_nobs] = False else: has_nan[: w - 1] = False return has_nan.astype(bool) def _get_data(self, idx): window = self._window if idx >= window: loc = slice(idx - window, idx) else: loc = slice(idx) y = self._y[loc] wy = self._wy[loc] wx = self._wx[loc] weights = self._weights[loc] missing = self._is_nan[loc] not_missing = ~missing if np.any(missing): y = y[not_missing] wy = wy[not_missing] wx = wx[not_missing] weights = weights[not_missing] return y, wy, wx, weights, not_missing def _fit_single(self, idx, wxpwx, wxpwy, nobs, store, params_only, method): if nobs < self._min_nobs: return try: wxpwxi = np.linalg.inv(wxpwx) if method == "inv": params = wxpwxi @ wxpwy else: _, wy, wx, _, _ = self._get_data(idx) if method == "lstsq": params = lstsq(wx, wy)[0] else: # 'pinv' wxpwxiwxp = np.linalg.pinv(wx) params = wxpwxiwxp @ wy except np.linalg.LinAlgError: return store.params[idx - 1] = params if params_only: return y, wy, wx, weights, _ = self._get_data(idx) wresid, ssr, llf = self._loglike(params, wy, wx, weights, nobs) wxwresid = wx * wresid[:, None] wxepwxe = wxwresid.T @ wxwresid tot_params = wx.shape[1] s2 = ssr / (nobs - tot_params) centered_tss, uncentered_tss = self._sum_of_squares(y, wy, weights) store.ssr[idx - 1] = ssr store.llf[idx - 1] = llf store.nobs[idx - 1] = nobs store.s2[idx - 1] = s2 store.xpxi[idx - 1] = wxpwxi store.xeex[idx - 1] = wxepwxe store.centered_tss[idx - 1] = centered_tss store.uncentered_tss[idx - 1] = uncentered_tss def _loglike(self, params, wy, wx, weights, nobs): nobs2 = nobs / 2.0 wresid = wy - wx @ params ssr = np.sum(wresid ** 2, axis=0) llf = -np.log(ssr) * nobs2 # concentrated likelihood llf -= (1 + np.log(np.pi / nobs2)) * nobs2 # with constant llf += 0.5 * np.sum(np.log(weights)) return wresid, ssr, llf def _sum_of_squares(self, y, wy, weights): mean = np.average(y, weights=weights) centered_tss = np.sum(weights * (y - mean) ** 2) uncentered_tss = np.dot(wy, wy) return centered_tss, uncentered_tss def _reset(self, idx): """Compute xpx and xpy using a single dot product""" _, wy, wx, _, not_missing = self._get_data(idx) nobs = not_missing.sum() xpx = wx.T @ wx xpy = wx.T @ wy return xpx, xpy, nobs def fit( self, method="inv", cov_type="nonrobust", cov_kwds=None, reset=None, use_t=False, params_only=False, ): """ Estimate model parameters. Parameters ---------- method : {'inv', 'lstsq', 'pinv'} Method to use when computing the the model parameters. * 'inv' - use moving windows inner-products and matrix inversion. This method is the fastest, but may be less accurate than the other methods. * 'lstsq' - Use numpy.linalg.lstsq * 'pinv' - Use numpy.linalg.pinv. This method matches the default estimator in non-moving regression estimators. cov_type : {'nonrobust', 'HCCM', 'HC0'} Covariance estimator: * nonrobust - The classic OLS covariance estimator * HCCM, HC0 - White heteroskedasticity robust covariance cov_kwds : dict Unused reset : int, optional Interval to recompute the moving window inner products used to estimate the model parameters. Smaller values improve accuracy, although in practice this setting is not required to be set. use_t : bool, optional Flag indicating to use the Student's t distribution when computing p-values. params_only : bool, optional Flag indicating that only parameters should be computed. Avoids calculating all other statistics or performing inference. Returns ------- RollingRegressionResults Estimation results where all pre-sample values are nan-filled. """ method = string_like( method, "method", options=("inv", "lstsq", "pinv") ) reset = int_like(reset, "reset", optional=True) reset = self._y.shape[0] if reset is None else reset if reset < 1: raise ValueError("reset must be a positive integer") nobs, k = self._x.shape store = RollingStore( params=np.full((nobs, k), np.nan), ssr=np.full(nobs, np.nan), llf=np.full(nobs, np.nan), nobs=np.zeros(nobs, dtype=int), s2=np.full(nobs, np.nan), xpxi=np.full((nobs, k, k), np.nan), xeex=np.full((nobs, k, k), np.nan), centered_tss=np.full(nobs, np.nan), uncentered_tss=np.full(nobs, np.nan), ) w = self._window first = self._min_nobs if self._expanding else w xpx, xpy, nobs = self._reset(first) if not (self._has_nan[first - 1] and self._skip_missing): self._fit_single(first, xpx, xpy, nobs, store, params_only, method) wx, wy = self._wx, self._wy for i in range(first + 1, self._x.shape[0] + 1): if self._has_nan[i - 1] and self._skip_missing: continue if i % reset == 0: xpx, xpy, nobs = self._reset(i) else: if not self._is_nan[i - w - 1] and i > w: remove_x = wx[i - w - 1 : i - w] xpx -= remove_x.T @ remove_x xpy -= remove_x.T @ wy[i - w - 1 : i - w] nobs -= 1 if not self._is_nan[i - 1]: add_x = wx[i - 1 : i] xpx += add_x.T @ add_x xpy += add_x.T @ wy[i - 1 : i] nobs += 1 self._fit_single(i, xpx, xpy, nobs, store, params_only, method) return RollingRegressionResults( self, store, self.k_constant, use_t, cov_type ) @classmethod @Appender(Model.from_formula.__doc__) def from_formula( cls, formula, data, window, weights=None, subset=None, *args, **kwargs ): if subset is not None: data = data.loc[subset] eval_env = kwargs.pop("eval_env", None) if eval_env is None: eval_env = 2 elif eval_env == -1: from patsy import EvalEnvironment eval_env = EvalEnvironment({}) else: eval_env += 1 # we're going down the stack again missing = kwargs.get("missing", "skip") from patsy import dmatrices, NAAction na_action = NAAction(on_NA="raise", NA_types=[]) result = dmatrices( formula, data, eval_env, return_type="dataframe", NA_action=na_action, ) endog, exog = result if (endog.ndim > 1 and endog.shape[1] > 1) or endog.ndim > 2: raise ValueError( "endog has evaluated to an array with multiple " "columns that has shape {0}. This occurs when " "the variable converted to endog is non-numeric" " (e.g., bool or str).".format(endog.shape) ) kwargs.update({"missing": missing, "window": window}) if weights is not None: kwargs["weights"] = weights mod = cls(endog, exog, *args, **kwargs) mod.formula = formula # since we got a dataframe, attach the original mod.data.frame = data return mod extra_parameters = window_parameters + extra_base @Substitution( model_type="Ordinary", model="OLS", parameters=common_params, extra_parameters=extra_parameters, ) @Appender(_doc) class RollingOLS(RollingWLS): def __init__( self, endog, exog, window=None, *, min_nobs=None, missing="drop", expanding=False ): super().__init__( endog, exog, window, weights=None, min_nobs=min_nobs, missing=missing, expanding=expanding, ) class RollingRegressionResults(object): """ Results from rolling regressions Parameters ---------- model : RollingWLS Model instance store : RollingStore Container for raw moving window results k_constant : bool Flag indicating that the model contains a constant use_t : bool Flag indicating to use the Student's t distribution when computing p-values. cov_type : str Name of covariance estimator """ _data_in_cache = tuple() def __init__( self, model, store: RollingStore, k_constant, use_t, cov_type ): self.model = model self._params = store.params self._ssr = store.ssr self._llf = store.llf self._nobs = store.nobs self._s2 = store.s2 self._xpxi = store.xpxi self._xepxe = store.xeex self._centered_tss = store.centered_tss self._uncentered_tss = store.uncentered_tss self._k_constant = k_constant self._nvar = self._xpxi.shape[-1] if use_t is None: use_t = cov_type == "nonrobust" self._use_t = use_t self._cov_type = cov_type self._use_pandas = self.model.data.row_labels is not None self._data_attr = [] def _wrap(self, val): """Wrap output as pandas Series or DataFrames as needed""" if not self._use_pandas: return val col_names = self.model.data.param_names row_names = self.model.data.row_labels if val.ndim == 1: return Series(val, index=row_names) if val.ndim == 2: return DataFrame(val, columns=col_names, index=row_names) else: # ndim == 3 mi = MultiIndex.from_product((row_names, col_names)) val = np.reshape(val, (-1, val.shape[-1])) return DataFrame(val, columns=col_names, index=mi) @cache_readonly @Appender(RegressionResults.aic.func.__doc__) def aic(self): return self._wrap(RegressionResults.aic.func(self)) @cache_readonly @Appender(RegressionResults.bic.func.__doc__) def bic(self): with np.errstate(divide="ignore"): return self._wrap(RegressionResults.bic.func(self)) @cache_readonly def params(self): """Estimated model parameters""" return self._wrap(self._params) @cache_readonly @Appender(RegressionResults.ssr.func.__doc__) def ssr(self): return self._wrap(self._ssr) @cache_readonly @Appender(RegressionResults.llf.func.__doc__) def llf(self): return self._wrap(self._llf) @cache_readonly @Appender(RegressionModel.df_model.__doc__) def df_model(self): return self._nvar - self._k_constant @cache_readonly def k_constant(self): """Flag indicating whether the model contains a constant""" return self._k_constant @cache_readonly @Appender(RegressionResults.centered_tss.func.__doc__) def centered_tss(self): return self._centered_tss @cache_readonly @Appender(RegressionResults.uncentered_tss.func.__doc__) def uncentered_tss(self): return self._uncentered_tss @cache_readonly @Appender(RegressionResults.rsquared.func.__doc__) def rsquared(self): return self._wrap(RegressionResults.rsquared.func(self)) @cache_readonly @Appender(RegressionResults.rsquared_adj.func.__doc__) def rsquared_adj(self): return self._wrap(RegressionResults.rsquared_adj.func(self)) @cache_readonly @Appender(RegressionResults.nobs.func.__doc__) def nobs(self): return self._wrap(self._nobs) @cache_readonly @Appender(RegressionModel.df_resid.__doc__) def df_resid(self): return self._wrap(self._nobs - self.df_model - self._k_constant) @cache_readonly @Appender(RegressionResults.use_t.__doc__) def use_t(self): return self._use_t @cache_readonly @Appender(RegressionResults.ess.func.__doc__) def ess(self): return self._wrap(RegressionResults.ess.func(self)) @cache_readonly @Appender(RegressionResults.mse_model.func.__doc__) def mse_model(self): return self._wrap(RegressionResults.mse_model.func(self)) @cache_readonly @Appender(RegressionResults.mse_resid.func.__doc__) def mse_resid(self): return self._wrap(RegressionResults.mse_resid.func(self)) @cache_readonly @Appender(RegressionResults.mse_total.func.__doc__) def mse_total(self): return self._wrap(RegressionResults.mse_total.func(self)) @cache_readonly def _cov_params(self): if self._cov_type == "nonrobust": return self._s2[:, None, None] * self._xpxi else: return self._xpxi @ self._xepxe @ self._xpxi def cov_params(self): """ Estimated parameter covariance Returns ------- array_like The estimated model covariances. If the original input is a numpy array, the returned covariance is a 3-d array with shape (nobs, nvar, nvar). If the original inputs are pandas types, then the returned covariance is a DataFrame with a MultiIndex with key (observation, variable), so that the covariance for observation with index i is cov.loc[i]. """ return self._wrap(self._cov_params) @cache_readonly @Appender(RegressionResults.f_pvalue.func.__doc__) def f_pvalue(self): with np.errstate(invalid="ignore"): return self._wrap(RegressionResults.f_pvalue.func(self)) @cache_readonly @Appender(RegressionResults.fvalue.func.__doc__) def fvalue(self): if self._cov_type == "nonrobust": return self.mse_model / self.mse_resid else: nobs = self._params.shape[0] stat = np.full(nobs, np.nan) k = self._params.shape[1] r = np.eye(k) locs = list(range(k)) if self.k_constant: locs.pop(self.model.const_idx) if not locs: return stat r = r[locs] vcv = self._cov_params rvcvr = r @ vcv @ r.T p = self._params for i in range(nobs): rp = p[i : i + 1] @ r.T denom = rp.shape[1] inv_cov = np.linalg.inv(rvcvr[i]) stat[i] = (rp @ inv_cov @ rp.T) / denom return stat @cache_readonly @Appender(RegressionResults.bse.func.__doc__) def bse(self): with np.errstate(invalid="ignore"): return self._wrap(np.sqrt(np.diagonal(self._cov_params, 0, 2))) @cache_readonly @Appender(LikelihoodModelResults.tvalues.func.__doc__) def tvalues(self): with np.errstate(invalid="ignore"): return self._wrap(LikelihoodModelResults.tvalues.func(self)) @cache_readonly @Appender(LikelihoodModelResults.pvalues.func.__doc__) def pvalues(self): if self.use_t: df_resid = getattr(self, "df_resid_inference", self.df_resid) df_resid = np.asarray(df_resid)[:, None] with np.errstate(invalid="ignore"): return stats.t.sf(np.abs(self.tvalues), df_resid) * 2 else: with np.errstate(invalid="ignore"): return stats.norm.sf(np.abs(self.tvalues)) * 2 def _conf_int(self, alpha, cols): bse = np.asarray(self.bse) if self.use_t: dist = stats.t df_resid = getattr(self, "df_resid_inference", self.df_resid) df_resid = np.asarray(df_resid)[:, None] q = dist.ppf(1 - alpha / 2, df_resid) else: dist = stats.norm q = dist.ppf(1 - alpha / 2) params = np.asarray(self.params) lower = params - q * bse upper = params + q * bse if cols is not None: cols = np.asarray(cols) lower = lower[:, cols] upper = upper[:, cols] return np.asarray(list(zip(lower, upper))) @Appender(LikelihoodModelResults.conf_int.__doc__) def conf_int(self, alpha=0.05, cols=None): ci = self._conf_int(alpha, cols) if not self._use_pandas: return ci ci_names = ("lower", "upper") row_names = self.model.data.row_labels col_names = self.model.data.param_names if cols is not None: col_names = [col_names[i] for i in cols] mi = MultiIndex.from_product((col_names, ci_names)) ci = np.reshape(np.swapaxes(ci, 1, 2), (ci.shape[0], -1)) return DataFrame(ci, columns=mi, index=row_names) @property def cov_type(self): """Name of covariance estimator""" return self._cov_type @classmethod @Appender(LikelihoodModelResults.load.__doc__) def load(cls, fname): return LikelihoodModelResults.load(fname) remove_data = LikelihoodModelResults.remove_data @Appender(LikelihoodModelResults.save.__doc__) def save(self, fname, remove_data=False): return LikelihoodModelResults.save(self, fname, remove_data) def plot_recursive_coefficient( self, variables=None, alpha=0.05, legend_loc="upper left", fig=None, figsize=None, ): r""" Plot the recursively estimated coefficients on a given variable Parameters ---------- variables : {int, str, Iterable[int], Iterable[str], None}, optional Integer index or string name of the variables whose coefficients to plot. Can also be an iterable of integers or strings. Default plots all coefficients. alpha : float, optional The confidence intervals for the coefficient are (1 - alpha)%. Set to None to exclude confidence intervals. legend_loc : str, optional The location of the legend in the plot. Default is upper left. fig : Figure, optional If given, subplots are created in this figure instead of in a new figure. Note that the grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Returns ------- Figure The matplotlib Figure object. """ from statsmodels.graphics.utils import _import_mpl, create_mpl_fig if alpha is not None: ci = self._conf_int(alpha, None) row_labels = self.model.data.row_labels if row_labels is None: row_labels = np.arange(self._params.shape[0]) k_variables = self._params.shape[1] param_names = self.model.data.param_names if variables is None: variable_idx = list(range(k_variables)) else: if isinstance(variables, (int, str)): variables = [variables] variable_idx = [] for i in range(len(variables)): variable = variables[i] if variable in param_names: variable_idx.append(param_names.index(variable)) elif isinstance(variable, int): variable_idx.append(variable) else: msg = ( "variable {0} is not an integer and was not found " "in the list of variable " "names: {1}".format( variables[i], ", ".join(param_names) ) ) raise ValueError(msg) _import_mpl() fig = create_mpl_fig(fig, figsize) loc = 0 import pandas as pd if isinstance(row_labels, pd.PeriodIndex): row_labels = row_labels.to_timestamp() row_labels = np.asarray(row_labels) for i in variable_idx: ax = fig.add_subplot(len(variable_idx), 1, loc + 1) params = self._params[:, i] valid = ~np.isnan(self._params[:, i]) row_lbl = row_labels[valid] ax.plot(row_lbl, params[valid]) if alpha is not None: this_ci = np.reshape(ci[:, :, i], (-1, 2)) if not np.all(np.isnan(this_ci)): ax.plot( row_lbl, this_ci[:, 0][valid], "k:", label="Lower CI" ) ax.plot( row_lbl, this_ci[:, 1][valid], "k:", label="Upper CI" ) if loc == 0: ax.legend(loc=legend_loc) ax.set_xlim(row_lbl[0], row_lbl[-1]) ax.set_title(param_names[i]) loc += 1 fig.tight_layout() return fig statsmodels-0.12.2/statsmodels/regression/tests/000077500000000000000000000000001400612667500220315ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/regression/tests/__init__.py000066400000000000000000000000001400612667500241300ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/regression/tests/lme_examples.R000066400000000000000000000001731400612667500246300ustar00rootroot00000000000000library(lme4) library(MASS) md = lmer(size ~ Time + (1 | tree), Sitka) md = lmer(size ~ Time + (1 + Time | tree), Sitka) 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"756",50.09998,23.099998,3,6430,2,3,5 "757",57.59998,35,4,6430,2,3,5 "758",62.29999,54.299995,5,6430,2,3,5 "759",66,73.399996,6,6430,2,3,5 "760",76.09998,81.899996,7,6430,2,3,5 "761",81.5,96.099998,8,6430,2,3,5 "762",84.29999,114.299995,9,6430,2,3,5 "763",97.89996,133.799995,10,6430,2,3,5 "764",108.59998,163.799995,11,6430,2,3,5 "765",109,198.299995,12,6430,2,3,5 "766",26.79999,NA,1,8050,1,3,20 "767",33.59998,10.900002,2,8050,1,3,20 "768",42.09998,25.100002,3,8050,1,3,20 "769",47.89999,38,4,8050,1,3,20 "770",56.19998,54.400002,5,8050,1,3,20 "771",63.39999,74.200001,6,8050,1,3,20 "772",71.79999,89.900002,7,8050,1,3,20 "773",80,111,8,8050,1,3,20 "774",87.59998,135.800003,9,8050,1,3,20 "775",94.89996,159.600006,10,8050,1,3,20 "776",101,188.200001,11,8050,1,3,20 "777",112,224,12,8050,1,3,20 "778",21.89999,NA,1,8053,3,3,20 "779",26.79999,9.6,2,8053,3,3,20 "780",34.69998,21.800003,3,8053,3,3,20 "781",41.29999,36.700001,4,8053,3,3,20 "782",48.69998,51.800003,5,8053,3,3,20 "783",57.89999,71.400002,6,8053,3,3,20 "784",65.39996,91.600006,7,8053,3,3,20 "785",71.29999,115.800003,8,8053,3,3,20 "786",80.59998,138,9,8053,3,3,20 "787",88.39996,163,10,8053,3,3,20 "788",96.29999,188,11,8053,3,3,20 "789",103.5,217.800001,12,8053,3,3,20 "790",24,NA,1,8139,1,3,23 "791",26.79999,6,2,8139,1,3,23 "792",33,20,3,8139,1,3,23 "793",39.09998,30.300003,4,8139,1,3,23 "794",46.39999,45.100002,5,8139,1,3,23 "795",54,61.400002,6,8139,1,3,23 "796",61.59998,74.400002,7,8139,1,3,23 "797",68.79999,91.800003,8,8139,1,3,23 "798",72.19995,109.5,9,8139,1,3,23 "799",77.19995,128,10,8139,1,3,23 "800",83.79999,144.400002,11,8139,1,3,23 "801",90.79999,160.300003,12,8139,1,3,23 "802",35.39999,NA,1,8192,1,3,21 "803",42.29999,15.100002,2,8192,1,3,21 "804",49.5,29.800003,3,8192,1,3,21 "805",58.69998,48.5,4,8192,1,3,21 "806",66.59998,70,5,8192,1,3,21 "807",71.39996,87.300001,6,8192,1,3,21 "808",78.79999,104.200001,7,8192,1,3,21 "809",85.5,125.5,8,8192,1,3,21 "810",91.29999,144.900002,9,8192,1,3,21 "811",97.79999,165,10,8192,1,3,21 "812",108,197,11,8192,1,3,21 "813",113,220,12,8192,1,3,21 "814",22.09999,NA,1,8269,3,3,22 "815",26.29999,6,2,8269,3,3,22 "816",33.29999,16.800001,3,8269,3,3,22 "817",38,27.400002,4,8269,3,3,22 "818",39.59998,36.200001,5,8269,3,3,22 "819",41.39999,43.300003,6,8269,3,3,22 "820",46.29999,54,7,8269,3,3,22 "821",52.39999,70,8,8269,3,3,22 "822",59.39999,90,9,8269,3,3,22 "823",66.69995,112.5,10,8269,3,3,22 "824",73.89996,128,11,8269,3,3,22 "825",76.79999,141.5,12,8269,3,3,22 "826",23.7,NA,1,8270,1,3,22 "827",28.79999,7.6,2,8270,1,3,22 "828",35.09998,18.5,3,8270,1,3,22 "829",43,33.200001,4,8270,1,3,22 "830",49.09998,44.900002,5,8270,1,3,22 "831",58.79999,60,6,8270,1,3,22 "832",65.39996,75.800003,7,8270,1,3,22 "833",68.5,91,8,8270,1,3,22 "834",79,108.5,9,8270,1,3,22 "835",90.69995,133.200001,10,8270,1,3,22 "836",98,151.200005,11,8270,1,3,22 "837",104,167.800001,12,8270,1,3,22 "838",27.29999,NA,1,8439,3,3,24 "839",31.2,8.8,2,8439,3,3,24 "840",37,20,3,8439,3,3,24 "841",43.89999,33.200001,4,8439,3,3,24 "842",49.79999,44.800003,5,8439,3,3,24 "843",57.19998,58,6,8439,3,3,24 "844",65.19995,74.600002,7,8439,3,3,24 "845",73.19995,94.900002,8,8439,3,3,24 "846",78.79999,108.8,9,8439,3,3,24 "847",87.39996,128,10,8439,3,3,24 "848",95,149,11,8439,3,3,24 "849",100.5,158.600006,12,8439,3,3,24 "850",25.7,NA,1,8442,1,3,24 "851",28.7,6.6,2,8442,1,3,24 "852",33.39999,15.800003,3,8442,1,3,24 "853",40,27,4,8442,1,3,24 "854",46.69998,40,5,8442,1,3,24 "855",56.59998,52,6,8442,1,3,24 "856",65.19995,66,7,8442,1,3,24 "857",73.19995,83.800003,8,8442,1,3,24 "858",81.69995,99.800003,9,8442,1,3,24 "859",90.29999,115.200001,10,8442,1,3,24 "860",96,133.200001,11,8442,1,3,24 "861",103.5,151.400002,12,8442,1,3,24 statsmodels-0.12.2/statsmodels/regression/tests/results/generate_lasso.py000066400000000000000000000011701400612667500270760ustar00rootroot00000000000000import numpy as np """ Generate data sets for testing OLS.fit_regularized After running this script, rerun lasso_r_results.R in R to rebuild the results file "glmnet_r_results.py". Currently only tests OLS. Our implementation covers GLS, but it's not clear if glmnet does. """ n = 300 p = 5 np.random.seed(83423) exog = np.random.normal(size=(n, p)) params = (-1.)**np.arange(p) params[::3] = 0 expval = np.dot(exog, params) endog = expval + np.random.normal(size=n) data = np.concatenate((endog[:, None], exog), axis=1) data = np.around(100*data) fname = "lasso_data.csv" np.savetxt(fname, data, fmt="%.0f", delimiter=",") statsmodels-0.12.2/statsmodels/regression/tests/results/generate_lme.py000066400000000000000000000037561400612667500265460ustar00rootroot00000000000000""" Generate test data sets for lme. After running this script, run lme_results.R with R to update the output. """ import numpy as np import os np.random.seed(348491) # Number of groups ngroup = 100 # Sample size range per group n_min = 1 n_max = 5 dsix = 0 # Number of random effects for pr in [1, 2]: re_sd = np.linspace(-0.5, 1.5, pr) # Number of fixed effects for pf in [1, 2, 3]: # Error standard deviation for sig in [0.5, 2]: params = np.linspace(-1, 1, pf) endog = [] exog_fe = [] exog_re = [] groups = [] for i in range(ngroup): n = np.random.randint(n_min, n_max, 1) x_fe = np.random.normal(size=(n, pf)) x_re = np.zeros((n, pr)) u = np.linspace(-1, 1, n) for j in range(pr): x_re[:, j] = u**j re = np.random.normal(size=pr) * re_sd expval = np.dot(x_fe, params) + np.dot(x_re, re) endog.append(expval + sig*np.random.normal(size=n)) exog_fe.append(x_fe) exog_re.append(x_re) groups.append(i*np.ones(n)) endog = np.concatenate(endog) exog_fe = np.concatenate(exog_fe, axis=0) exog_re = np.concatenate(exog_re, axis=0) groups = np.concatenate(groups, axis=0) data = np.concatenate((groups[:, None], endog[:, None], exog_fe, exog_re), axis=1) header = (["groups,endog"] + ["exog_fe_%d" % k for k in range(pf)] + ["exog_re_%d" % k for k in range(pr)]) header = ",".join(header) cur_dir = os.path.dirname(os.path.abspath(__file__)) fname = os.path.join(cur_dir, "lme%02d.csv" % dsix) np.savetxt(fname, data, fmt="%.3f", header=header, delimiter=",", comments="") dsix += 1 statsmodels-0.12.2/statsmodels/regression/tests/results/glmnet_r_results.py000066400000000000000000000153071400612667500275020ustar00rootroot00000000000000import numpy as np rslt_0 = np.array([ 100, 2, 0, 38.51677, -0.0002828592, -0.01440669]) rslt_1 = np.array([ 100, 2, 0, 5.991962, -0.00144282, -0.08156386]) rslt_2 = np.array([ 100, 2, 0, 0.9321552, -0.003400212, -0.2968083]) rslt_3 = np.array([ 100, 2, 0.5, 0.2352493, 0, -0.4099712]) rslt_4 = np.array([ 100, 2, 0.5, 0.07703354, 0, -0.5185569]) rslt_5 = np.array([ 100, 2, 0.5, 0.02522501, 0, -0.5578565]) rslt_6 = np.array([ 100, 2, 1, 0.1416793, 0, -0.4346288]) rslt_7 = np.array([ 100, 2, 1, 0.04639359, 0, -0.530877]) rslt_8 = np.array([ 100, 2, 1, 0.01829859, 0, -0.5592558]) rslt_9 = np.array([ 100, 3, 0, 38.51677, -0.0002931891, -0.01441805, 0.01019003]) rslt_10 = np.array([ 100, 3, 0, 5.991962, -0.00177573, -0.08193033, 0.05812813]) rslt_11 = np.array([ 100, 3, 0, 0.9321552, -0.007886374, -0.3017527, 0.2167204]) rslt_12 = np.array([ 100, 3, 0.5, 0.2143504, 0, -0.4350311, 0.2878706]) rslt_13 = np.array([ 100, 3, 0.5, 0.07019009, 0, -0.540186, 0.3830582]) rslt_14 = np.array([ 100, 3, 0.5, 0.02298409, -0.007207869, -0.5779581, 0.417658]) rslt_15 = np.array([ 100, 3, 1, 0.1176247, 0, -0.4728138, 0.3103276]) rslt_16 = np.array([ 100, 3, 1, 0.03851677, 0, -0.5564642, 0.393978]) rslt_17 = np.array([ 100, 3, 1, 0.01384221, -0.004948496, -0.5824816, 0.4202673]) rslt_18 = np.array([ 100, 5, 0, 38.51677, -0.0002957436, -0.01439344, 0.01022347, -0.001361073, 0.01156754]) rslt_19 = np.array([ 100, 5, 0, 5.991962, -0.001844459, -0.08115691, 0.05920275, -0.006436703, 0.06552873]) rslt_20 = np.array([ 100, 5, 0, 0.9321552, -0.008226096, -0.2921193, 0.2311589, -0.008479325, 0.2404427]) rslt_21 = np.array([ 100, 5, 0.5, 0.2143504, 0, -0.4132961, 0.3222149, 0, 0.3262246]) rslt_22 = np.array([ 100, 5, 0.5, 0.0639546, 0, -0.5145012, 0.4359585, 0, 0.4294001]) rslt_23 = np.array([ 100, 5, 0.5, 0.02094225, -0.00787628, -0.5466386, 0.4728884, 0.0106367, 0.4627422]) rslt_24 = np.array([ 100, 5, 1, 0.1176247, 0, -0.4469856, 0.3513112, 0, 0.3519996]) rslt_25 = np.array([ 100, 5, 1, 0.03851677, 0, -0.5243974, 0.4448608, 0, 0.4370223]) rslt_26 = np.array([ 100, 5, 1, 0.01261251, -0.00600524, -0.5501652, 0.4761259, 0.009292623, 0.4655236]) rslt_27 = np.array([ 200, 2, 0, 37.37243, -0.0006197982, -0.01442844]) rslt_28 = np.array([ 200, 2, 0, 5.813939, -0.002965157, -0.0813082]) rslt_29 = np.array([ 200, 2, 0, 0.9044607, -0.0046755, -0.2916905]) rslt_30 = np.array([ 200, 2, 0.5, 0.207982, 0, -0.4102587]) rslt_31 = np.array([ 200, 2, 0.5, 0.06810473, 0, -0.5061677]) rslt_32 = np.array([ 200, 2, 0.5, 0.02230123, 0, -0.5404787]) rslt_33 = np.array([ 200, 2, 1, 0.11413, 0, -0.443054]) rslt_34 = np.array([ 200, 2, 1, 0.03737243, 0, -0.5201972]) rslt_35 = np.array([ 200, 2, 1, 0.01343095, 0, -0.544259]) rslt_36 = np.array([ 200, 3, 0, 37.37243, -0.0006182692, -0.01444479, 0.01107838]) rslt_37 = np.array([ 200, 3, 0, 5.813939, -0.002912734, -0.08183274, 0.06300276]) rslt_38 = np.array([ 200, 3, 0, 0.9044607, -0.003838731, -0.298655, 0.2325274]) rslt_39 = np.array([ 200, 3, 0.5, 0.207982, 0, -0.426489, 0.3142956]) rslt_40 = np.array([ 200, 3, 0.5, 0.06810473, 0, -0.5287444, 0.4093069]) rslt_41 = np.array([ 200, 3, 0.5, 0.02230123, 0, -0.5654985, 0.4434813]) rslt_42 = np.array([ 200, 3, 1, 0.1252575, 0, -0.450539, 0.3272248]) rslt_43 = np.array([ 200, 3, 1, 0.04101619, 0, -0.540326, 0.4170119]) rslt_44 = np.array([ 200, 3, 1, 0.01343095, 0, -0.5697273, 0.4464131]) rslt_45 = np.array([ 200, 5, 0, 37.37243, -0.0006213086, -0.01441334, 0.01110832, -0.00159415, 0.01237059]) rslt_46 = np.array([ 200, 5, 0, 5.813939, -0.003007826, -0.08084357, 0.06395108, -0.008286656, 0.06957285]) rslt_47 = np.array([ 200, 5, 0, 0.9044607, -0.004970054, -0.2862855, 0.2446989, -0.02121838, 0.2488685]) rslt_48 = np.array([ 200, 5, 0.5, 0.207982, 0, -0.398901, 0.3436805, 0, 0.3354236]) rslt_49 = np.array([ 200, 5, 0.5, 0.06810473, 0, -0.4912754, 0.4492343, 0, 0.4280285]) rslt_50 = np.array([ 200, 5, 0.5, 0.02230123, 0, -0.5240797, 0.4869532, -0.007872715, 0.4611676]) rslt_51 = np.array([ 200, 5, 1, 0.11413, 0, -0.4298238, 0.3738058, 0, 0.3604706]) rslt_52 = np.array([ 200, 5, 1, 0.03737243, 0, -0.5044899, 0.4632316, 0, 0.4395307]) rslt_53 = np.array([ 200, 5, 1, 0.01343095, 0, -0.5276608, 0.4907892, -0.005343287, 0.4641237]) rslt_54 = np.array([ 300, 2, 0, 34.28346, -0.0003952878, -0.01440603]) rslt_55 = np.array([ 300, 2, 0, 5.333396, -0.001501322, -0.08029644]) rslt_56 = np.array([ 300, 2, 0, 0.8297037, 0.002123792, -0.2786158]) rslt_57 = np.array([ 300, 2, 0.5, 0.1907915, 0, -0.3787717]) rslt_58 = np.array([ 300, 2, 0.5, 0.06247562, 0, -0.4648646]) rslt_59 = np.array([ 300, 2, 0.5, 0.02045795, 0.008282189, -0.4960003]) rslt_60 = np.array([ 300, 2, 1, 0.1046967, 0, -0.4057543]) rslt_61 = np.array([ 300, 2, 1, 0.03428346, 0, -0.476403]) rslt_62 = np.array([ 300, 2, 1, 0.01232084, 0.006463487, -0.4988773]) rslt_63 = np.array([ 300, 3, 0, 34.28346, -0.000389794, -0.01441521, 0.01276503]) rslt_64 = np.array([ 300, 3, 0, 5.333396, -0.001327446, -0.08058424, 0.07142295]) rslt_65 = np.array([ 300, 3, 0, 0.8297037, 0.004333533, -0.2821765, 0.2505531]) rslt_66 = np.array([ 300, 3, 0.5, 0.2093935, 0, -0.3745606, 0.3227598]) rslt_67 = np.array([ 300, 3, 0.5, 0.06856692, 0, -0.4707627, 0.4155033]) rslt_68 = np.array([ 300, 3, 0.5, 0.02045795, 0.01586083, -0.5078635, 0.4505092]) rslt_69 = np.array([ 300, 3, 1, 0.1149045, 0, -0.4043541, 0.347238]) rslt_70 = np.array([ 300, 3, 1, 0.03762605, 0, -0.483917, 0.4268009]) rslt_71 = np.array([ 300, 3, 1, 0.01232084, 0.01417268, -0.5109371, 0.4530943]) rslt_72 = np.array([ 300, 5, 0, 34.28346, -0.0003887545, -0.01441065, 0.01279253, -0.001336729, 0.01332977]) rslt_73 = np.array([ 300, 5, 0, 5.333396, -0.001294265, -0.08044256, 0.07228947, -0.006888477, 0.07488032]) rslt_74 = np.array([ 300, 5, 0, 0.8297037, 0.00476926, -0.2804704, 0.2614478, -0.01761104, 0.2661808]) rslt_75 = np.array([ 300, 5, 0.5, 0.2093935, 0, -0.3705814, 0.347887, 0, 0.351998]) rslt_76 = np.array([ 300, 5, 0.5, 0.06856692, 0, -0.465371, 0.449883, 0, 0.4508697]) rslt_77 = np.array([ 300, 5, 0.5, 0.02045795, 0.01744528, -0.5021737, 0.4881574, -0.007930221, 0.4878982]) rslt_78 = np.array([ 300, 5, 1, 0.1149045, 0, -0.3996701, 0.3772643, 0, 0.3807041]) rslt_79 = np.array([ 300, 5, 1, 0.03762605, 0, -0.4782089, 0.4633918, 0, 0.4639368]) rslt_80 = np.array([ 300, 5, 1, 0.01232084, 0.01578941, -0.5051176, 0.4915133, -0.005703398, 0.4910846]) 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159,-63,-45,118,139,-8 21,-100,-128,-158,-61,-12 48,41,-54,248,62,-185 statsmodels-0.12.2/statsmodels/regression/tests/results/lasso_r_results.R000066400000000000000000000020311400612667500270740ustar00rootroot00000000000000library(glmnet) library(R2nparray) # Run the glmnet lasso (elastic net) on all the test data sets data = read.csv("lasso_data.csv", header=FALSE) ik = 0 rslt = list() for (n in c(100, 200, 300)) { for (p in c(2, 3, 5)) { endog = data[1:n, 1] exog = data[1:n, 2:(p+1)] exog = as.matrix(exog) endog = (endog - mean(endog)) / sd(endog) for (k in 1:p) { exog[,k] = exog[,k] - mean(exog[,k]) exog[,k] = exog[,k] / sd(exog[,k]) } for (alpha in c(0, 0.5, 1)) { fit = glmnet(exog, endog, intercept=FALSE, standardize=FALSE, alpha=alpha) for (q in c(0.3, 0.5, 0.7)) { ii = round(q * length(fit$lambda)) coefs = coef(fit, s=fit$lambda[ii]) coefs = coefs[2:length(coefs)] rname = sprintf("rslt_%d", ik) ik = ik + 1 rslt[[rname]] = c(n, p, alpha, fit$lambda[ii], coefs) } } } } R2nparray(rslt, fname="glmnet_r_results.py") statsmodels-0.12.2/statsmodels/regression/tests/results/leverage_influence_ols_nostars.txt000066400000000000000000000343171400612667500325530ustar00rootroot00000000000000 residual leverage influence DFFITS u 0<=h<=1 u h/(1-h) 1959:2 -2.0742 0.026 -0.054583 -0.032 1959:3 -16.829 0.010 -0.17499 -0.162 1959:4 17.807 0.006 0.11026 0.132 1960:1 14.214 0.023 0.33301 0.206 1960:2 -24.269 0.015 -0.36715 -0.284 1960:3 5.7992 0.008 0.049617 0.050 1960:4 -20.886 0.034 -0.73335 -0.375 1961:1 9.8798 0.005 0.05179 0.067 1961:2 7.4863 0.014 0.10314 0.083 1961:3 14.11 0.010 0.13739 0.131 1961:4 -18.151 0.015 -0.27316 -0.211 1962:1 2.6465 0.011 0.030731 0.027 1962:2 -13.329 0.006 -0.083492 -0.099 1962:3 2.0981 0.006 0.013157 0.016 1962:4 -8.0123 0.007 -0.056953 -0.063 1963:1 9.6415 0.007 0.06812 0.076 1963:2 -5.0585 0.007 -0.035805 -0.040 1963:3 -10.143 0.014 -0.13973 -0.112 1963:4 2.7192 0.006 0.016533 0.020 1964:1 -12.585 0.019 -0.23723 -0.163 1964:2 -10.268 0.009 -0.088872 -0.090 1964:3 -3.1627 0.008 -0.025489 -0.027 1964:4 9.2701 0.007 0.067079 0.074 1965:1 6.4275 0.022 0.14784 0.092 1965:2 -12.496 0.008 -0.10223 -0.106 1965:3 -10.836 0.015 -0.16227 -0.125 1965:4 -28.524 0.023 -0.67634 -0.422 1966:1 0.41525 0.022 0.0095312 0.006 1966:2 -3.9265 0.008 -0.032508 -0.033 1966:3 -4.4059 0.006 -0.026898 -0.032 1966:4 -2.5184 0.006 -0.014469 -0.018 1967:1 -14.274 0.011 -0.16548 -0.145 1967:2 -7.2071 0.009 -0.064055 -0.064 1967:3 7.0015 0.006 0.041966 0.051 1967:4 5.2597 0.005 0.027186 0.035 1968:1 -17.488 0.016 -0.29267 -0.214 1968:2 -3.098 0.010 -0.032174 -0.030 1968:3 -15.821 0.007 -0.10969 -0.124 1968:4 6.4495 0.006 0.039111 0.047 1969:1 8.4822 0.009 0.076508 0.076 1969:2 0.83748 0.009 0.007586 0.007 1969:3 8.2205 0.005 0.042642 0.055 1969:4 -3.4261 0.015 -0.05238 -0.040 1970:1 0.28305 0.011 0.0030162 0.003 1970:2 7.8525 0.008 0.060957 0.065 1970:3 2.2956 0.006 0.013765 0.017 1970:4 4.9034 0.027 0.13486 0.077 1971:1 10.614 0.031 0.34456 0.182 1971:2 12.805 0.005 0.068279 0.088 1971:3 0.68069 0.007 0.0045619 0.005 1971:4 -7.0127 0.007 -0.047212 -0.054 1972:1 6.3863 0.012 0.074474 0.065 1972:2 -7.3721 0.021 -0.16064 -0.103 1972:3 -0.95255 0.005 -0.0050441 -0.006 1972:4 -16.627 0.010 -0.17016 -0.159 1973:1 -9.8533 0.026 -0.25905 -0.151 1973:2 5.6197 0.021 0.12265 0.078 1973:3 4.5097 0.017 0.080032 0.057 1973:4 5.179 0.029 0.15387 0.084 1974:1 -3.1457 0.033 -0.10821 -0.055 1974:2 1.08 0.021 0.022905 0.015 1974:3 2.4398 0.032 0.080559 0.042 1974:4 16.85 0.045 0.79075 0.350 1975:1 -48.281 0.043 -2.1902 -1.037 1975:2 -17.841 0.006 -0.10532 -0.129 1975:3 11.599 0.018 0.2142 0.149 1975:4 -2.5892 0.009 -0.023227 -0.023 1976:1 8.8047 0.024 0.2192 0.131 1976:2 14.779 0.006 0.094697 0.111 1976:3 1.0038 0.010 0.0097456 0.009 1976:4 -1.156 0.010 -0.01127 -0.011 1977:1 7.9332 0.010 0.077599 0.074 1977:2 2.2751 0.037 0.086679 0.042 1977:3 -0.45568 0.013 -0.0061948 -0.005 1977:4 -1.2479 0.009 -0.011785 -0.011 1978:1 10.833 0.010 0.10458 0.100 1978:2 -32.23 0.072 -2.5075 -0.892 1978:3 2.6192 0.020 0.053266 0.035 1978:4 -5.7424 0.015 -0.088262 -0.067 1979:1 6.9597 0.008 0.052818 0.057 1979:2 5.2803 0.019 0.10193 0.069 1979:3 -13.413 0.026 -0.35491 -0.207 1979:4 -3.6896 0.012 -0.043521 -0.038 1980:1 -0.70094 0.018 -0.012507 -0.009 1980:2 7.3702 0.060 0.46678 0.178 1980:3 -19.233 0.013 -0.25082 -0.208 1980:4 16.33 0.013 0.217 0.178 1981:1 13.303 0.017 0.23446 0.167 1981:2 7.2551 0.033 0.24794 0.127 1981:3 15.318 0.014 0.21378 0.171 1981:4 19.5 0.051 1.0428 0.435 1982:1 -1.2325 0.068 -0.090284 -0.032 1982:2 6.0687 0.064 0.4129 0.153 1982:3 12.515 0.014 0.17407 0.139 1982:4 -25.737 0.022 -0.56739 -0.365 1983:1 7.234 0.045 0.33773 0.149 1983:2 10.245 0.025 0.26194 0.155 1983:3 4.2063 0.021 0.090006 0.058 1983:4 16.804 0.024 0.41352 0.250 1984:1 17.996 0.017 0.31173 0.224 1984:2 -4.2825 0.018 -0.079641 -0.055 1984:3 5.9567 0.026 0.16111 0.093 1984:4 -7.4108 0.023 -0.172 -0.107 1985:1 -16.758 0.019 -0.33137 -0.223 1985:2 3.6384 0.008 0.028555 0.030 1985:3 -19.283 0.016 -0.30668 -0.230 1985:4 14.153 0.011 0.15085 0.138 1986:1 -6.8394 0.005 -0.037411 -0.047 1986:2 0.21312 0.071 0.016406 0.006 1986:3 -18.126 0.007 -0.13387 -0.147 1986:4 3.3595 0.007 0.023536 0.026 1987:1 12.522 0.005 0.066831 0.086 1987:2 -7.8712 0.006 -0.044228 -0.055 1987:3 -4.1257 0.005 -0.021252 -0.028 1987:4 11.053 0.011 0.11837 0.107 1988:1 -21.337 0.006 -0.12956 -0.157 1988:2 -2.2261 0.007 -0.014779 -0.017 1988:3 4.3039 0.006 0.024997 0.031 1988:4 -6.9168 0.008 -0.054036 -0.057 1989:1 10.457 0.009 0.094882 0.093 1989:2 -6.7649 0.006 -0.039373 -0.048 1989:3 -6.8402 0.009 -0.059272 -0.060 1989:4 4.5364 0.016 0.0739 0.054 1990:1 -4.1645 0.005 -0.023026 -0.029 1990:2 4.7673 0.009 0.043593 0.043 1990:3 1.6749 0.010 0.017602 0.016 1990:4 -2.1491 0.027 -0.060722 -0.034 1991:1 3.0644 0.017 0.052763 0.038 1991:2 -1.4489 0.013 -0.01868 -0.015 1991:3 13.369 0.006 0.086494 0.101 1991:4 19.045 0.007 0.12493 0.145 1992:1 -18.029 0.006 -0.10394 -0.129 1992:2 16.942 0.006 0.09862 0.122 1992:3 -4.1448 0.006 -0.02545 -0.030 1992:4 3.3586 0.008 0.02638 0.028 1993:1 15.572 0.008 0.13114 0.134 1993:2 1.5315 0.006 0.0094249 0.011 1993:3 0.67663 0.005 0.0036734 0.005 1993:4 7.0721 0.008 0.059242 0.061 1994:1 10.12 0.005 0.053258 0.069 1994:2 8.9972 0.007 0.065707 0.072 1994:3 -8.4192 0.005 -0.043756 -0.057 1994:4 9.6114 0.006 0.057062 0.069 1995:1 10.836 0.008 0.086906 0.091 1995:2 -3.7803 0.008 -0.029172 -0.031 1995:3 -6.9312 0.008 -0.055583 -0.058 1995:4 10.256 0.007 0.0707 0.080 1996:1 4.0309 0.005 0.021694 0.028 1996:2 0.4955 0.011 0.0053216 0.005 1996:3 15.719 0.006 0.1017 0.119 1996:4 -9.3751 0.006 -0.054944 -0.067 1997:1 6.5172 0.005 0.034166 0.044 1997:2 10.854 0.012 0.13379 0.113 1997:3 -2.9846 0.010 -0.030983 -0.028 1997:4 3.8535 0.006 0.021563 0.027 1998:1 14.065 0.010 0.13561 0.130 1998:2 -8.2154 0.012 -0.10053 -0.085 1998:3 -0.60661 0.008 -0.0046736 -0.005 1998:4 -6.1779 0.012 -0.074119 -0.063 1999:1 7.8563 0.006 0.045995 0.056 1999:2 -4.6266 0.005 -0.023074 -0.031 1999:3 -1.1028 0.008 -0.0083415 -0.009 1999:4 -6.8508 0.011 -0.079265 -0.069 2000:1 0.73293 0.007 0.0054868 0.006 2000:2 3.6035 0.014 0.049842 0.040 2000:3 2.708 0.008 0.022145 0.023 2000:4 1.3636 0.008 0.010847 0.011 2001:1 -5.3679 0.013 -0.070967 -0.058 2001:2 -1.6618 0.006 -0.010209 -0.012 2001:3 6.5455 0.012 0.07979 0.068 2001:4 -19.04 0.007 -0.1294 -0.148 2002:1 8.6579 0.005 0.043551 0.057 2002:2 3.8596 0.012 0.048695 0.041 2002:3 1.6741 0.006 0.010859 0.013 2002:4 8.1865 0.012 0.10312 0.086 2003:1 1.2353 0.013 0.016361 0.013 2003:2 -2.2006 0.007 -0.01465 -0.017 2003:3 -5.4225 0.012 -0.064693 -0.056 2003:4 7.3162 0.012 0.085825 0.074 2004:1 -2.0091 0.013 -0.027416 -0.022 2004:2 13.225 0.010 0.13921 0.128 2004:3 0.34955 0.015 0.0053195 0.004 2004:4 1.3304 0.013 0.017246 0.014 2005:1 0.58582 0.006 0.0037749 0.004 2005:2 -6.0779 0.011 -0.068898 -0.061 2005:3 1.3355 0.005 0.0066849 0.009 2005:4 11.099 0.040 0.45714 0.215 2006:1 -5.3245 0.010 -0.054333 -0.050 2006:2 3.7492 0.006 0.023831 0.028 2006:3 3.9062 0.009 0.034228 0.034 2006:4 -10.87 0.024 -0.26209 -0.160 2007:1 -0.97833 0.006 -0.0063771 -0.007 2007:2 1.3714 0.006 0.0078089 0.010 2007:3 -3.9713 0.005 -0.021069 -0.027 2007:4 -7.4003 0.006 -0.043073 -0.053 2008:1 2.8908 0.026 0.077049 0.045 2008:2 -8.5902 0.011 -0.093244 -0.084 2008:3 10.043 0.064 0.6827 0.253 2008:4 8.6286 0.042 0.37961 0.173 2009:1 -26.221 0.086 -2.4808 -0.800 2009:2 -14.74 0.014 -0.20334 -0.163 2009:3 3.5952 0.020 0.071804 0.048 ('*' indicates a leverage point) Cross-validation criterion = 23908.4 statsmodels-0.12.2/statsmodels/regression/tests/results/lme00.csv000066400000000000000000000141641400612667500251720ustar00rootroot00000000000000groups,endog,exog_fe_0,exog_re_0 0.000,-0.300,0.408,1.000 1.000,-1.805,1.528,1.000 1.000,1.753,-0.970,1.000 1.000,2.657,-1.657,1.000 2.000,1.533,-1.171,1.000 3.000,0.647,-0.951,1.000 3.000,-0.555,-0.150,1.000 4.000,2.158,-2.215,1.000 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statsmodels-0.12.2/statsmodels/regression/tests/results/lme_r_results.py000066400000000000000000000364631400612667500267770ustar00rootroot00000000000000import numpy as np coef_ml_drf_0 = np.array([-0.9887517]) vcov_ml_drf_0 = np.array([0.001317148]).reshape(1, 1, order='F') cov_re_ml_drf_0 = np.array([0.2522485]).reshape(1, 1, order='F') scale_ml_drf_0 = np.array([0.2718486]) loglike_ml_drf_0 = np.array([-240.1254]) ranef_mean_ml_drf_0 = np.array([0.04977167]) ranef_condvar_ml_drf_0 = np.array([0.130841]) coef_reml_drf_0 = np.array([-0.9887533]) vcov_reml_drf_0 = np.array([0.001323559]).reshape(1, 1, order='F') cov_re_reml_drf_0 = np.array([0.2524129]).reshape(1, 1, order='F') scale_reml_drf_0 = np.array([0.2733467]) loglike_reml_drf_0 = np.array([-242.5214]) ranef_mean_reml_drf_0 = np.array([0.04964696]) ranef_condvar_reml_drf_0 = np.array([0.1312315]) coef_ml_drf_1 = np.array([-0.9115929]) vcov_ml_drf_1 = np.array([0.01340632]).reshape(1, 1, order='F') cov_re_ml_drf_1 = np.array([0]).reshape(1, 1, order='F') scale_ml_drf_1 = np.array([4.050921]) loglike_ml_drf_1 = np.array([-538.0763]) ranef_mean_ml_drf_1 = np.array([0]) ranef_condvar_ml_drf_1 = np.array([0]) coef_reml_drf_1 = np.array([-0.9115929]) vcov_reml_drf_1 = np.array([0.01345931]).reshape(1, 1, order='F') cov_re_reml_drf_1 = np.array([2.839777e-14]).reshape(1, 1, order='F') scale_reml_drf_1 = np.array([4.066932]) loglike_reml_drf_1 = np.array([-539.3124]) ranef_mean_reml_drf_1 = np.array([2.424384e-14]) ranef_condvar_reml_drf_1 = np.array([2.839777e-14]) coef_ml_drf_2 = np.array([-1.012044, 0.9789052]) vcov_ml_drf_2 = np.array([ 0.00117849, 1.458744e-05, 1.458744e-05, 0.001054926]).reshape(2, 2, order='F') cov_re_ml_drf_2 = np.array([0.1596058]).reshape(1, 1, order='F') scale_ml_drf_2 = np.array([0.2129146]) loglike_ml_drf_2 = np.array([-200.319]) ranef_mean_ml_drf_2 = np.array([0.3197174]) ranef_condvar_ml_drf_2 = np.array([0.09122291]) coef_reml_drf_2 = np.array([-1.012137, 0.9790792]) vcov_reml_drf_2 = np.array([ 0.001190455, 1.482666e-05, 1.482666e-05, 0.001066002]).reshape(2, 2, order='F') cov_re_reml_drf_2 = np.array([0.1595015]).reshape(1, 1, order='F') scale_reml_drf_2 = np.array([0.2154276]) loglike_reml_drf_2 = np.array([-205.275]) ranef_mean_reml_drf_2 = np.array([0.3172978]) ranef_condvar_reml_drf_2 = np.array([0.09164674]) coef_ml_drf_3 = np.array([-1.028053, 0.8602685]) vcov_ml_drf_3 = np.array([ 0.01398831, 0.001592619, 0.001592619, 0.01602274]).reshape(2, 2, order='F') cov_re_ml_drf_3 = np.array([0.8130996]).reshape(1, 1, order='F') scale_ml_drf_3 = np.array([3.100447]) loglike_ml_drf_3 = np.array([-477.1707]) ranef_mean_ml_drf_3 = np.array([-0.2641747]) ranef_condvar_ml_drf_3 = np.array([0.6441656]) coef_reml_drf_3 = np.array([-1.027583, 0.8605714]) vcov_reml_drf_3 = np.array([ 0.01411922, 0.001607343, 0.001607343, 0.01617574]).reshape(2, 2, order='F') cov_re_reml_drf_3 = np.array([0.8117898]).reshape(1, 1, order='F') scale_reml_drf_3 = np.array([3.13369]) loglike_reml_drf_3 = np.array([-479.5354]) ranef_mean_reml_drf_3 = np.array([-0.2614875]) ranef_condvar_reml_drf_3 = np.array([0.6447625]) coef_ml_drf_4 = np.array([-1.005151, -0.003657404, 1.054786]) vcov_ml_drf_4 = np.array([ 0.001190639, -5.327162e-05, 5.992985e-05, -5.327162e-05, 0.001460303, -2.662532e-05, 5.992985e-05, -2.662532e-05, 0.00148609]).reshape(3, 3, order='F') cov_re_ml_drf_4 = np.array([0.1703249]).reshape(1, 1, order='F') scale_ml_drf_4 = np.array([0.251763]) loglike_ml_drf_4 = np.array([-231.6389]) ranef_mean_ml_drf_4 = np.array([-0.2063164]) ranef_condvar_ml_drf_4 = np.array([0.0459578]) coef_reml_drf_4 = np.array([-1.005067, -0.003496032, 1.054666]) vcov_reml_drf_4 = np.array([ 0.001206925, -5.4182e-05, 6.073475e-05, -5.4182e-05, 0.001479871, -2.723494e-05, 6.073475e-05, -2.723494e-05, 0.001506198]).reshape(3, 3, order='F') cov_re_reml_drf_4 = np.array([0.1705659]).reshape(1, 1, order='F') scale_reml_drf_4 = np.array([0.2556394]) loglike_reml_drf_4 = np.array([-238.761]) ranef_mean_reml_drf_4 = np.array([-0.2055303]) ranef_condvar_reml_drf_4 = np.array([0.04649027]) coef_ml_drf_5 = np.array([-0.8949725, 0.08141558, 1.052529]) vcov_ml_drf_5 = np.array([ 0.01677563, 0.0008077524, -0.001255011, 0.0008077524, 0.01719346, 0.0009266736, -0.001255011, 0.0009266736, 0.01608435]).reshape(3, 3, order='F') cov_re_ml_drf_5 = np.array([0.3444677]).reshape(1, 1, order='F') scale_ml_drf_5 = np.array([4.103944]) loglike_ml_drf_5 = np.array([-579.4568]) ranef_mean_ml_drf_5 = np.array([0.08254713]) ranef_condvar_ml_drf_5 = np.array([0.3177935]) coef_reml_drf_5 = np.array([-0.8946164, 0.08134261, 1.052486]) vcov_reml_drf_5 = np.array([ 0.0169698, 0.0008162714, -0.001268635, 0.0008162714, 0.01739219, 0.0009345538, -0.001268635, 0.0009345538, 0.01627074]).reshape(3, 3, order='F') cov_re_reml_drf_5 = np.array([0.3420993]).reshape(1, 1, order='F') scale_reml_drf_5 = np.array([4.155737]) loglike_reml_drf_5 = np.array([-582.8377]) ranef_mean_reml_drf_5 = np.array([0.08111449]) ranef_condvar_reml_drf_5 = np.array([0.3160797]) coef_ml_drf_6 = np.array([-0.8885425]) vcov_ml_drf_6 = np.array([0.002443738]).reshape(1, 1, order='F') cov_re_ml_drf_6 = np.array([ 0.2595201, 0.04591071, 0.04591071, 2.204612]).reshape(2, 2, order='F') scale_ml_drf_6 = np.array([0.243133]) loglike_ml_drf_6 = np.array([-382.551]) ranef_mean_ml_drf_6 = np.array([-0.0597406, 0.6037288]) ranef_condvar_ml_drf_6 = np.array([ 0.2420741, 0.2222169, 0.2222169, 0.4228908]).reshape(2, 2, order='F') coef_reml_drf_6 = np.array([-0.8883881]) vcov_reml_drf_6 = np.array([0.002461581]).reshape(1, 1, order='F') cov_re_reml_drf_6 = np.array([ 0.2595767, 0.04590012, 0.04590012, 2.204822]).reshape(2, 2, order='F') scale_reml_drf_6 = np.array([0.2453537]) loglike_reml_drf_6 = np.array([-384.6373]) ranef_mean_reml_drf_6 = np.array([-0.05969892, 0.6031793]) ranef_condvar_reml_drf_6 = np.array([ 0.2421365, 0.2221108, 0.2221108, 0.4244443]).reshape(2, 2, order='F') coef_ml_irf_6 = np.array([-0.8874992]) vcov_ml_irf_6 = np.array([0.002445505]).reshape(1, 1, order='F') cov_re_ml_irf_6 = np.array([ 0.2587624, 0, 0, 2.188653]).reshape(2, 2, order='F') scale_ml_irf_6 = np.array([0.2432694]) loglike_ml_irf_6 = np.array([-382.6581]) coef_reml_irf_6 = np.array([-0.8873394]) vcov_reml_irf_6 = np.array([0.002463375]).reshape(1, 1, order='F') cov_re_reml_irf_6 = np.array([ 0.2588157, 0, 0, 2.188876]).reshape(2, 2, order='F') scale_reml_irf_6 = np.array([0.2454935]) loglike_reml_irf_6 = np.array([-384.7441]) coef_ml_drf_7 = np.array([-0.9645281]) vcov_ml_drf_7 = np.array([0.01994]).reshape(1, 1, order='F') cov_re_ml_drf_7 = np.array([ 0.2051329, 0.0734377, 0.0734377, 3.285381]).reshape(2, 2, order='F') scale_ml_drf_7 = np.array([3.423247]) loglike_ml_drf_7 = np.array([-587.7101]) ranef_mean_ml_drf_7 = np.array([0.07007965, -0.2920284]) ranef_condvar_ml_drf_7 = np.array([ 0.1823183, 0.02247519, 0.02247519, 1.125011]).reshape(2, 2, order='F') coef_reml_drf_7 = np.array([-0.9647862]) vcov_reml_drf_7 = np.array([0.02002546]).reshape(1, 1, order='F') cov_re_reml_drf_7 = np.array([ 0.2056226, 0.0726139, 0.0726139, 3.2876]).reshape(2, 2, order='F') scale_reml_drf_7 = np.array([3.440244]) loglike_reml_drf_7 = np.array([-588.7476]) ranef_mean_reml_drf_7 = np.array([0.07000628, -0.2916737]) ranef_condvar_reml_drf_7 = np.array([ 0.1828266, 0.02229138, 0.02229138, 1.128947]).reshape(2, 2, order='F') coef_ml_irf_7 = np.array([-0.9665524]) vcov_ml_irf_7 = np.array([0.01998144]).reshape(1, 1, order='F') cov_re_ml_irf_7 = np.array([ 0.2021561, 0, 0, 3.270735]).reshape(2, 2, order='F') scale_ml_irf_7 = np.array([3.423186]) loglike_ml_irf_7 = np.array([-587.7456]) coef_reml_irf_7 = np.array([-0.9667854]) vcov_reml_irf_7 = np.array([0.02006657]).reshape(1, 1, order='F') cov_re_reml_irf_7 = np.array([ 0.2026938, 0, 0, 3.273129]).reshape(2, 2, order='F') scale_reml_irf_7 = np.array([3.440197]) loglike_reml_irf_7 = np.array([-588.782]) coef_ml_drf_8 = np.array([-1.083882, 0.8955623]) vcov_ml_drf_8 = np.array([ 0.002491643, 0.0001693531, 0.0001693531, 0.00253309]).reshape(2, 2, order='F') cov_re_ml_drf_8 = np.array([ 0.1506188, 0.126091, 0.126091, 2.485462]).reshape(2, 2, order='F') scale_ml_drf_8 = np.array([0.2586519]) loglike_ml_drf_8 = np.array([-363.6234]) ranef_mean_ml_drf_8 = np.array([0.2852326, -0.5047804]) ranef_condvar_ml_drf_8 = np.array([ 0.05400391, 0.002330104, 0.002330104, 0.122761]).reshape(2, 2, order='F') coef_reml_drf_8 = np.array([-1.083938, 0.8956893]) vcov_reml_drf_8 = np.array([ 0.002528969, 0.0001712206, 0.0001712206, 0.002573335]).reshape(2, 2, order='F') cov_re_reml_drf_8 = np.array([ 0.1505098, 0.1256311, 0.1256311, 2.484219]).reshape(2, 2, order='F') scale_reml_drf_8 = np.array([0.2635901]) loglike_reml_drf_8 = np.array([-367.7667]) ranef_mean_reml_drf_8 = np.array([0.2829798, -0.5042857]) ranef_condvar_reml_drf_8 = np.array([ 0.05463632, 0.002393538, 0.002393538, 0.1249828]).reshape(2, 2, order='F') coef_ml_irf_8 = np.array([-1.079481, 0.898216]) vcov_ml_irf_8 = np.array([ 0.002511536, 0.0001812511, 0.0001812511, 0.002573405]).reshape(2, 2, order='F') cov_re_ml_irf_8 = np.array([ 0.1498568, 0, 0, 2.403849]).reshape(2, 2, order='F') scale_ml_irf_8 = np.array([0.2605245]) loglike_ml_irf_8 = np.array([-364.4824]) coef_reml_irf_8 = np.array([-1.07952, 0.8983678]) vcov_reml_irf_8 = np.array([ 0.002549354, 0.0001833386, 0.0001833386, 0.002614672]).reshape(2, 2, order='F') cov_re_reml_irf_8 = np.array([ 0.1497193, 0, 0, 2.403076]).reshape(2, 2, order='F') scale_reml_irf_8 = np.array([0.2655558]) loglike_reml_irf_8 = np.array([-368.6141]) coef_ml_drf_9 = np.array([-1.272698, 0.8617471]) vcov_ml_drf_9 = np.array([ 0.02208544, 0.001527479, 0.001527479, 0.02597528]).reshape(2, 2, order='F') cov_re_ml_drf_9 = np.array([ 0.510175, 0.08826114, 0.08826114, 3.342888]).reshape(2, 2, order='F') scale_ml_drf_9 = np.array([3.722112]) loglike_ml_drf_9 = np.array([-589.8274]) ranef_mean_ml_drf_9 = np.array([0.03253644, 0.224043]) ranef_condvar_ml_drf_9 = np.array([ 0.3994872, 0.02478884, 0.02478884, 1.195077]).reshape(2, 2, order='F') coef_reml_drf_9 = np.array([-1.272483, 0.861814]) vcov_reml_drf_9 = np.array([ 0.02228589, 0.001535598, 0.001535598, 0.0262125]).reshape(2, 2, order='F') cov_re_reml_drf_9 = np.array([ 0.5123204, 0.08897376, 0.08897376, 3.341722]).reshape(2, 2, order='F') scale_reml_drf_9 = np.array([3.764058]) loglike_reml_drf_9 = np.array([-591.7188]) ranef_mean_reml_drf_9 = np.array([0.03239688, 0.2230525]) ranef_condvar_reml_drf_9 = np.array([ 0.401762, 0.02521271, 0.02521271, 1.203536]).reshape(2, 2, order='F') coef_ml_irf_9 = np.array([-1.277018, 0.86395]) vcov_ml_irf_9 = np.array([ 0.02205706, 0.001509887, 0.001509887, 0.02599941]).reshape(2, 2, order='F') cov_re_ml_irf_9 = np.array([ 0.5086816, 0, 0, 3.312757]).reshape(2, 2, order='F') scale_ml_irf_9 = np.array([3.72105]) loglike_ml_irf_9 = np.array([-589.8628]) coef_reml_irf_9 = np.array([-1.276822, 0.8640243]) vcov_reml_irf_9 = np.array([ 0.02225705, 0.001517774, 0.001517774, 0.02623682]).reshape(2, 2, order='F') cov_re_reml_irf_9 = np.array([ 0.5107725, 0, 0, 3.31152]).reshape(2, 2, order='F') scale_reml_irf_9 = np.array([3.762967]) loglike_reml_irf_9 = np.array([-591.7543]) coef_ml_drf_10 = np.array([-0.9419566, -0.02359824, 1.085796]) vcov_ml_drf_10 = np.array([ 0.001963536, -0.0003221793, 0.0001950186, -0.0003221793, 0.002534251, 0.0004107718, 0.0001950186, 0.0004107718, 0.002580736]).reshape(3, 3, order='F') cov_re_ml_drf_10 = np.array([ 0.2040541, 0.09038325, 0.09038325, 2.218903]).reshape(2, 2, order='F') scale_ml_drf_10 = np.array([0.2558286]) loglike_ml_drf_10 = np.array([-379.6591]) ranef_mean_ml_drf_10 = np.array([0.03876325, -0.725853]) ranef_condvar_ml_drf_10 = np.array([ 0.1988816, 0.1872403, 0.1872403, 0.4052274]).reshape(2, 2, order='F') coef_reml_drf_10 = np.array([-0.9426367, -0.02336203, 1.085733]) vcov_reml_drf_10 = np.array([ 0.002011348, -0.0003300612, 0.0002002948, -0.0003300612, 0.002589149, 0.000418987, 0.0002002948, 0.000418987, 0.002637433]).reshape(3, 3, order='F') cov_re_reml_drf_10 = np.array([ 0.2034827, 0.09063836, 0.09063836, 2.219191]).reshape(2, 2, order='F') scale_reml_drf_10 = np.array([0.2630213]) loglike_reml_drf_10 = np.array([-386.0008]) ranef_mean_reml_drf_10 = np.array([0.03838686, -0.7240812]) ranef_condvar_reml_drf_10 = np.array([ 0.1983981, 0.1865469, 0.1865469, 0.4100937]).reshape(2, 2, order='F') coef_ml_irf_10 = np.array([-0.9441033, -0.01755913, 1.088568]) vcov_ml_irf_10 = np.array([ 0.001960114, -0.0003215658, 0.0001944005, -0.0003215658, 0.00253441, 0.0004061179, 0.0001944005, 0.0004061179, 0.002589158]).reshape(3, 3, order='F') cov_re_ml_irf_10 = np.array([ 0.2032228, 0, 0, 2.192893]).reshape(2, 2, order='F') scale_ml_irf_10 = np.array([0.2553399]) loglike_ml_irf_10 = np.array([-380.162]) coef_reml_irf_10 = np.array([-0.9448257, -0.01722993, 1.088557]) vcov_reml_irf_10 = np.array([ 0.00200783, -0.0003294349, 0.0001996613, -0.0003294349, 0.00258937, 0.0004141667, 0.0001996613, 0.0004141667, 0.002646242]).reshape(3, 3, order='F') cov_re_reml_irf_10 = np.array([ 0.2026653, 0, 0, 2.193124]).reshape(2, 2, order='F') scale_reml_irf_10 = np.array([0.2625147]) loglike_reml_irf_10 = np.array([-386.5024]) coef_ml_drf_11 = np.array([-1.36971, 0.1596278, 0.8588724]) vcov_ml_drf_11 = np.array([ 0.0232326, 0.00172214, 0.002275343, 0.00172214, 0.02318941, 0.0004755663, 0.002275343, 0.0004755663, 0.02123474]).reshape(3, 3, order='F') cov_re_ml_drf_11 = np.array([ 0.3719096, 0.332198, 0.332198, 1.120588]).reshape(2, 2, order='F') scale_ml_drf_11 = np.array([4.849781]) loglike_ml_drf_11 = np.array([-601.6432]) ranef_mean_ml_drf_11 = np.array([-0.4256917, -0.3907759]) ranef_condvar_ml_drf_11 = np.array([ 0.2987928, 0.1992074, 0.1992074, 0.7477486]).reshape(2, 2, order='F') coef_reml_drf_11 = np.array([-1.370236, 0.1597671, 0.8585994]) vcov_reml_drf_11 = np.array([ 0.02351795, 0.001749756, 0.002301599, 0.001749756, 0.02346869, 0.0004785668, 0.002301599, 0.0004785668, 0.02149093]).reshape(3, 3, order='F') cov_re_reml_drf_11 = np.array([ 0.3680346, 0.3324419, 0.3324419, 1.118623]).reshape(2, 2, order='F') scale_reml_drf_11 = np.array([4.922222]) loglike_reml_drf_11 = np.array([-604.5746]) ranef_mean_reml_drf_11 = np.array([-0.4168539, -0.3879533]) ranef_condvar_reml_drf_11 = np.array([ 0.2965372, 0.2010191, 0.2010191, 0.7503986]).reshape(2, 2, order='F') coef_ml_irf_11 = np.array([-1.370117, 0.1414964, 0.8466083]) vcov_ml_irf_11 = np.array([ 0.02319951, 0.001705996, 0.002265252, 0.001705996, 0.02345623, 0.000514879, 0.002265252, 0.000514879, 0.02153162]).reshape(3, 3, order='F') cov_re_ml_irf_11 = np.array([ 0.4004789, 0, 0, 1.108087]).reshape(2, 2, order='F') scale_ml_irf_11 = np.array([4.78776]) loglike_ml_irf_11 = np.array([-602.308]) coef_reml_irf_11 = np.array([-1.370663, 0.1417561, 0.8464232]) vcov_reml_irf_11 = np.array([ 0.02348548, 0.001734072, 0.002291519, 0.001734072, 0.02373715, 0.0005177618, 0.002291519, 0.0005177618, 0.02178966]).reshape(3, 3, order='F') cov_re_reml_irf_11 = np.array([ 0.3966454, 0, 0, 1.106551]).reshape(2, 2, order='F') scale_reml_irf_11 = np.array([4.860342]) loglike_reml_irf_11 = np.array([-605.2274]) statsmodels-0.12.2/statsmodels/regression/tests/results/lme_results.R000066400000000000000000000060161400612667500262160ustar00rootroot00000000000000library(lme4) library(R2nparray) files = list.files(path="results", pattern="lme...csv") rslt = list() # Check the code with a sequence of data files with different # dimensions and random effects structures. for (file in files) { # Fit a model with independent random effects (irf=TRUE) or # dependent random effects (irf=FALSE). for (irf in c(FALSE, TRUE)) { if (irf) { rf = "irf" } else { rf = "drf" } # Use REML or ML estimation for (reml in c(FALSE, TRUE)) { if (reml) { meth = "reml" } else { meth = "ml" } data = read.csv(paste("results", file, sep="/")) exog_fe_ix = grep("exog_fe", names(data)) exog_re_ix = grep("exog_re", names(data)) # No need to check independent random effects when there is # only one of them. if (irf & (length(exog_re_ix) == 1)) { next } pr = length(exog_re_ix) fml_fe = paste(names(data)[exog_fe_ix], collapse="+") if (irf) { st = NULL for (ik in exog_re_ix) { st[length(st) + 1] = sprintf("(0 + %s | groups)", names(data)[ik]) } fml_re = paste(st, collapse="+") fml = sprintf("endog ~ 0 + %s + %s", fml_fe, fml_re) } else { fml_re = paste(names(data)[exog_re_ix], collapse="+") fml = sprintf("endog ~ 0 + %s + (0 + %s | groups)", fml_fe, fml_re) } md = lmer(as.formula(fml), data=data, REML=reml) ds_ix = as.integer(substr(file, 4, 6)) rslt[[sprintf("coef_%s_%s_%d", meth, rf, ds_ix)]] = as.vector(fixef(md)) rslt[[sprintf("vcov_%s_%s_%d", meth, rf, ds_ix)]] = as.matrix(vcov(md)) if (irf) { rev = NULL for (k in 1:length(exog_re_ix)) { rev[k] = as.numeric(VarCorr(md)[[k]]) } rev = diag(rev) rslt[[sprintf("cov_re_%s_%s_%d", meth, rf, ds_ix)]] = rev } else { rslt[[sprintf("cov_re_%s_%s_%d", meth, rf, ds_ix)]] = array(as.numeric(VarCorr(md)$groups), c(pr, pr)) } rslt[[sprintf("scale_%s_%s_%d", meth, rf, ds_ix)]] = attr(VarCorr(md), "sc")^2 rslt[[sprintf("loglike_%s_%s_%d", meth, rf, ds_ix)]] = as.numeric(logLik(md)) # Apparently lmer does not support these things when the random effects # are independent. if (!irf) { reo = ranef(md, condVar=TRUE) re = as.matrix(reo$groups) condvar = attr(reo$groups, "postVar") rslt[[sprintf("ranef_mean_%s_%s_%d", meth, rf, ds_ix)]] = re[1,] rslt[[sprintf("ranef_condvar_%s_%s_%d", meth, rf, ds_ix)]] = condvar[,,1] } } } } R2nparray(rslt, fname="lme_r_results.py") statsmodels-0.12.2/statsmodels/regression/tests/results/macro_gr_corc_stata.py000066400000000000000000000255341400612667500301100ustar00rootroot00000000000000import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch est = dict( N=201, df_m=2, df_r=198, F=221.0377347263228, r2=.6906614775140222, rmse=10.66735221013527, mss=50304.8300537672, rss=22530.89582866539, r2_a=.6875368459737599, ll=-759.5001027340874, N_gaps=0, tol=1.00000000000e-06, max_ic=100, ic=4, dw=1.993977855026291, dw_0=2.213805016982909, rho=-.1080744185979703, rank=3, cmd="prais", title="Prais-Winsten AR(1) regression", cmdline="prais g_realinv g_realgdp L.realint, corc rhotype(tscorr)", tranmeth="corc", method="iterated", depvar="g_realinv", predict="prais_p", rhotype="tscorr", vce="ols", properties="b V", ) params_table = np.array([ 4.3704012379033, .20815070994319, 20.996331163589, 2.939551581e-52, 3.9599243998713, 4.7808780759353, 198, 1.9720174778363, 0, -.5792713864578, .26801792119756, -2.1613158697355, .03187117882819, -1.1078074114328, -.05073536148285, 198, 1.9720174778363, 0, -9.509886614971, .99049648344574, -9.6011311235432, 3.656321106e-18, -11.463162992061, -7.5566102378806, 198, 1.9720174778363, 0]).reshape(3, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = 'g_realgdp L.realint _cons'.split() cov = np.array([ .04609356125016, -.00228616599156, -.13992917065996, -.00228616599156, .08103590074551, -.10312637237487, -.13992917065996, -.10312637237487, 1.1416832888557]).reshape(3, 3) cov_colnames = 'g_realgdp L.realint _cons'.split() cov_rownames = 'g_realgdp L.realint _cons'.split() fittedvalues = np.array([ 34.092961143383, -12.024019193439, -4.0322884907855, 26.930266763436, -18.388570551209, -8.1324920108371, -31.875322937642, .21814034941388, 21.286872048596, 18.046781817358, 24.839977757054, 20.524927286892, 9.4135589847345, 5.0452309081846, -5.6551802066401, 11.985460837387, 10.881000973745, 22.932381778173, 2.2243337561549, 28.678018086877, 8.4960232938048, 12.595931232461, -5.9735838194583, 31.918171668207, 12.51486507374, 24.858076725235, 30.404510147102, 32.036251557873, -3.4858432808681, .47271857077911, 4.4052813399748, 3.2797897853075, -10.188593201973, 4.2830255779438, 3.2910087767189, 26.047109629787, 18.955198396277, 2.5715957164729, -2.3281798982217, 17.032381944743, -4.0901785042795, .91987313367478, -18.683722252157, -12.984352504073, -6.6160771495293, 4.5273942020195, -28.749156193466, 38.148138299645, -.57670949517535, 4.4996010868259, -5.6725761358388, 20.923003763987, 31.094336738501, 6.5964070665898, 18.667129468109, 34.425102067117, 12.495888351027, -20.391896794875, 9.6404042884163, -23.337183583421, -3.2089713311258, -25.745423471535, -13.275374642526, -29.102203184727, 3.6718187868943, 20.796143264795, 13.375486730466, 30.503754833333, 1.9832701043709, -.33573283324142, 3.8454619057923, 11.198841650909, 27.300615912881, 21.617271919636, -10.213387774549, -3.041115945304, 58.662013692103, 9.3875351174185, 14.62429232726, -7.0289661733807, -6.3287417283568, 5.3688078321969, -3.9071766792954, -2.3350903711443, -45.218293861742, -12.518622374718, 22.354531985202, 24.642689788549, -26.596828143888, 8.8860015710942, -35.108835611339, -42.53255546273, -6.0981548538498, -17.177799997821, -11.40329039155, 7.0180843697455, 26.705585327159, 21.928461900264, 23.355257443029, 21.894505946705, 17.657379506229, 3.4294676089343, .97440677130275, 3.509217298751, 3.2828913970637, 14.944972085155, 1.2923006012963, 6.0435554866624, -8.8442213362579, 5.4509233390479, -2.6794059247137, -.48161809935521, 8.4201161664985, 4.549532431433, 18.996304264647, -1.8170413137623, 11.849281819014, -1.7066851102854, 12.218564198008, 4.6715818362824, 2.108627710813, 2.1972303599907, -8.5249858114578, 8.0728543937531, -4.5685185423019, -11.135138151837, -24.047910391406, -19.615146607087, -.44428684605231, -3.4877810606396, -3.9736701841582, 9.0239662841874, 8.5557600343168, 8.2271736548708, 9.0458357352972, -6.3116081663522, 1.5636968490473, -.95723547143789, 13.44821815082, 6.7721586886424, 13.649238514998, 1.1579094135284, 8.6396143031575, -6.7325794361447, -7.0767574403351, 3.1400395218988, .91586368309611, 1.2368141501238, 19.694940608963, 4.0145204498294, 8.3107956501685, 2.7428657521209, 13.988676494758, 10.116898229369, 2.524027931198, 4.6794023157157, 3.5155627033849, 11.945878601415, 18.880925278224, 4.5865622289454, 3.2393307465763, 11.062953867859, 20.793966231154, -6.3076444941097, 23.178864105791, -8.9873099715132, -1.107322743866, -16.332040882272, .42734142108626, -15.050781890016, -4.6612306163595, 4.565652288529, .80725599873503, -.87706444767528, -8.5407936802022, -1.3521383036839, 4.4765977604986, 19.623863498831, 7.1113956960438, 3.9798487855641, 3.6934842863203, 4.6801104799091, 6.7218162617593, 7.7832579175778, -1.2290990957424, 3.0474310004174, 2.7567736850761, 11.188206993423, -4.3306276498455, -9.5365114805844, -.53338170341178, -5.206342794124, 4.1154674910376, 4.7884361973806, -.64799653797949, -10.743852791188, -2.461403042047, -17.431541988995, -36.151189705211, -43.711601400093, -12.334881925913, 4.3341943478598]) fittedvalues_colnames = 'fittedvalues'.split() fittedvalues_rownames = ['r'+str(n) for n in range(1, 203)] fittedvalues_se = np.array([ 1.6473872957314, 1.0113850707964, .7652190209006, 1.534040692487, 1.2322657893516, .91158310011358, 1.8788908534927, .69811681139453, 1.1767226952576, .98858641944986, 1.2396486964702, 1.0822616701665, .7753481322096, .76860948102754, .82419167032501, .82704859414698, .82559058693092, 1.1856589638289, .75525402187835, 1.3922568629515, .91202394595876, .88520111465725, .83302439819375, 1.5372725435314, .89177714550085, 1.2372408530959, 1.5528101417195, 1.5366212693726, .89043286423929, .75705684478985, .73518329909511, 1.0572392569996, .93211401184553, .75196863280241, .69360947719119, 1.3106012580927, 1.0209999290642, .81133440956099, .75559203443239, .94831739014224, .93322729630976, .69417535741881, 1.2398628905688, 1.0261547060202, .86379439641561, .75032871325094, 1.6696098440084, 1.8282957404356, .70460484132802, .79812152719782, .8016314317639, 1.0872600753814, 1.4987341895633, .70529145955969, 1.0149968053074, 1.6467690495895, 1.4677194036031, 1.3384921199391, 1.7046600039586, 1.8412203199988, 1.4367363864341, 1.8103264820977, 2.1242535073081, 2.1101077640804, .745443770473, 1.3651585515035, .94103291060948, 1.5981517654886, .77654854940188, .96643611834989, .97013991129283, .97997241479455, 1.9501042753844, 1.1758285978818, .9603215961611, .96398854110297, 2.7840981863809, 1.413576103565, 1.2364541532613, .85434724833597, 1.3715636637071, 1.6066244823944, 1.0686828612843, 1.3176342918943, 2.5021204574497, 1.1330278834213, 1.1636905462155, 1.3340487203567, 1.8517041947194, 1.1639745295786, 2.304428659791, 2.6786336953086, 2.5354570978302, 1.1805089049206, 1.4742162139537, 2.1143611509083, 1.5986085606212, 1.4576906503482, 1.5624993432094, 1.3158885079997, 1.3538646144937, 1.619414838601, 1.5015020934095, 1.3855500128549, .86402762365746, 1.2492579410465, 1.0127848313981, .7158840034754, 2.6885176805365, .83774886448436, .81595294371756, .70504062914926, .73023061883128, .69228489060199, 1.0360869522995, .75590017576772, .80137295502042, .73813943198212, .87064014103306, .93205385237951, .73787688995958, .90978243354856, 1.2648707813937, .72349602267222, .93927915871284, 1.0172563832871, 1.6776109713009, 1.3175046180712, 1.1171209329088, .78301185980687, .78918856044216, .74112029520399, .74451851348435, .76567972163601, .87244845911018, .90049784898067, .76120214907789, .71166085065751, .90870901548966, .70296598825213, .84621726620383, .69493630035748, .75059818136305, .87986442867509, .86277076414594, .87380573440987, .80727321528666, .70768449827207, 1.040570485976, .78088040381913, .74507562843308, .69792915007094, 1.0988781063157, 1.0027100639643, .72261812289435, .96179349200945, 1.0868653716913, .86400879397201, 1.094197020208, .74093235691985, .67984744050458, .8543509596351, 1.0818096940792, .84834713756928, 1.1852779873098, .89126223599075, .87108400982232, 1.1499249237911, .75958251908371, 1.1014705573844, .80471862911078, .68374044074715, 1.1058743822208, .78261190454279, 1.1081858646506, 1.1333032178191, .79529240253276, 1.0984357956297, 1.0696598625923, 1.1524457583105, 1.0091448954756, 1.2183914737714, 1.1249902630054, .78498039737187, 1.04667102358, .68135274836726, 1.9934991355412, .995276050357, .77642057869112, .92353879856007, 1.5308870921603, .78757917918954, .73146117757714, .70335029981046, .73869949489316, 1.6122142696964, 1.023758116961, 2.5353634753616, 2.1057022389201, 3.0080233992196, 1.1648858140616, 1.3964393384387]) fittedvalues_se_colnames = 'fittedvalues_se'.split() fittedvalues_se_rownames = ['r'+str(n) for n in range(1, 203)] results = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, fittedvalues=fittedvalues, fittedvalues_colnames=fittedvalues_colnames, fittedvalues_rownames=fittedvalues_rownames, fittedvalues_se=fittedvalues_se, fittedvalues_se_colnames=fittedvalues_se_colnames, fittedvalues_se_rownames=fittedvalues_se_rownames, **est ) statsmodels-0.12.2/statsmodels/regression/tests/results/pastes.csv000066400000000000000000000026611400612667500255530ustar00rootroot00000000000000"","strength","batch","cask","sample" "1",62.8,"A","a","A:a" "2",62.6,"A","a","A:a" "3",60.1,"A","b","A:b" "4",62.3,"A","b","A:b" "5",62.7,"A","c","A:c" "6",63.1,"A","c","A:c" "7",60,"B","a","B:a" "8",61.4,"B","a","B:a" "9",57.5,"B","b","B:b" "10",56.9,"B","b","B:b" "11",61.1,"B","c","B:c" "12",58.9,"B","c","B:c" "13",58.7,"C","a","C:a" "14",57.5,"C","a","C:a" "15",63.9,"C","b","C:b" "16",63.1,"C","b","C:b" "17",65.4,"C","c","C:c" "18",63.7,"C","c","C:c" "19",57.1,"D","a","D:a" "20",56.4,"D","a","D:a" "21",56.9,"D","b","D:b" "22",58.6,"D","b","D:b" "23",64.7,"D","c","D:c" "24",64.5,"D","c","D:c" "25",55.1,"E","a","E:a" "26",55.1,"E","a","E:a" "27",54.7,"E","b","E:b" "28",54.2,"E","b","E:b" "29",58.8,"E","c","E:c" "30",57.5,"E","c","E:c" "31",63.4,"F","a","F:a" "32",64.9,"F","a","F:a" "33",59.3,"F","b","F:b" "34",58.1,"F","b","F:b" "35",60.5,"F","c","F:c" "36",60,"F","c","F:c" "37",62.5,"G","a","G:a" "38",62.6,"G","a","G:a" "39",61,"G","b","G:b" "40",58.7,"G","b","G:b" "41",56.9,"G","c","G:c" "42",57.7,"G","c","G:c" "43",59.2,"H","a","H:a" "44",59.4,"H","a","H:a" "45",65.2,"H","b","H:b" "46",66,"H","b","H:b" "47",64.8,"H","c","H:c" "48",64.1,"H","c","H:c" "49",54.8,"I","a","I:a" "50",54.8,"I","a","I:a" "51",64,"I","b","I:b" "52",64,"I","b","I:b" "53",57.7,"I","c","I:c" "54",56.8,"I","c","I:c" "55",58.3,"J","a","J:a" "56",59.3,"J","a","J:a" "57",59.2,"J","b","J:b" "58",59.2,"J","b","J:b" "59",58.9,"J","c","J:c" "60",56.6,"J","c","J:c" statsmodels-0.12.2/statsmodels/regression/tests/results/results_grunfeld_ols_robust_cluster.py000066400000000000000000000560001400612667500335100ustar00rootroot00000000000000import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch est = dict( N_clust=10, N=200, df_m=2, df_r=9, F=51.59060716590177, r2=.8124080178314147, rmse=94.40840193979599, mss=7604093.484267689, rss=1755850.432294737, r2_a=.8105035307027997, ll=-1191.80235741801, ll_0=-1359.150955647688, rank=3, cmdline="regress invest mvalue kstock, vce(cluster company)", title="Linear regression", marginsok="XB default", vce="cluster", depvar="invest", cmd="regress", properties="b V", predict="regres_p", model="ols", estat_cmd="regress_estat", vcetype="Robust", clustvar="company", ) params_table = np.array([ .11556215606596, .01589433647768, 7.2706499090564, .00004710548549, .07960666895505, .15151764317688, 9, 2.2621571627982, 0, .23067848754982, .08496711097464, 2.7149150406994, .02380515903536, .03846952885627, .42288744624337, 9, 2.2621571627982, 0, -42.714369016733, 20.425202580078, -2.0912580352272, .06604843284516, -88.919387334862, 3.4906493013959, 9, 2.2621571627982, 0]).reshape(3, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = 'mvalue kstock _cons'.split() cov = np.array([ .00025262993207, -.00065043385106, .20961897960949, -.00065043385106, .00721940994738, -1.2171040967615, .20961897960949, -1.2171040967615, 417.18890043724]).reshape(3, 3) cov_colnames = 'mvalue kstock _cons'.split() cov_rownames = 'mvalue kstock _cons'.split() results_cluster = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( N=200, inexog_ct=2, exexog_ct=0, endog_ct=0, partial_ct=0, N_clust=10, df_m=2, sdofminus=0, dofminus=0, r2=.8124080178314146, rmse=93.69766358599176, rss=1755850.432294737, mss=7604093.484267682, r2_a=.8105035307027995, F=51.59060716590192, Fp=.0000117341240941, Fdf1=2, Fdf2=9, yy=13620706.07273678, yyc=9359943.916562419, partialcons=0, cons=1, jdf=0, j=0, ll=-1191.802357418011, rankV=3, rankS=3, rankxx=3, rankzz=3, r2c=.8124080178314146, r2u=.8710896173136538, clustvar="company", hacsubtitleV="Statistics robust to heteroskedasticity and clustering on company", # noqa:E501 hacsubtitleB="Estimates efficient for homoskedasticity only", title="OLS estimation", predict="ivreg2_p", version="03.1.07", cmdline="ivreg2 invest mvalue kstock, cluster(company)", cmd="ivreg2", model="ols", depvar="invest", vcetype="Robust", vce="robust cluster", partialsmall="small", inexog="mvalue kstock", insts="mvalue kstock", properties="b V", ) params_table = np.array([ .11556215606596, .01500272788516, 7.7027429245215, 1.331761148e-14, .08615734974119, .14496696239074, np.nan, 1.9599639845401, 0, .23067848754982, .08020079648691, 2.8762618035529, .00402415789383, .07348781490405, .38786916019559, np.nan, 1.9599639845401, 0, -42.714369016733, 19.27943055305, -2.2155410088072, .02672295281194, -80.501358543152, -4.9273794903145, np.nan, 1.9599639845401, 0]).reshape(3, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'mvalue kstock _cons'.split() cov = np.array([ .000225081844, -.00057950714469, .1867610305767, -.00057950714469, .00643216775713, -1.0843847053056, .1867610305767, -1.0843847053056, 371.69644244987]).reshape(3, 3) cov_colnames = 'mvalue kstock _cons'.split() cov_rownames = 'mvalue kstock _cons'.split() results_cluster_large = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( N=200, N_g=10, df_m=2, df_r=9, F=97.97910905239282, r2=.8124080178314147, rmse=94.40840193979599, lag=4, cmd="xtscc", predict="xtscc_p", method="Pooled OLS", depvar="invest", vcetype="Drisc/Kraay", title="Regression with Driscoll-Kraay standard errors", groupvar="company", properties="b V", ) params_table = np.array([ .11556215606596, .0134360177573, 8.6009231420662, .00001235433261, .08516777225681, .14595653987512, 9, 2.2621571627982, 0, .23067848754982, .04930800664089, 4.678317037431, .00115494570515, .11913602714384, .3422209479558, 9, 2.2621571627982, 0, -42.714369016733, 12.190347184209, -3.5039501641153, .0066818746948, -70.290850216489, -15.137887816977, 9, 2.2621571627982, 0]).reshape(3, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = 'mvalue kstock _cons'.split() cov = np.array([ .00018052657317, -.00035661054613, -.06728261073866, -.00035661054613, .0024312795189, -.32394785247278, -.06728261073866, -.32394785247278, 148.60456447156]).reshape(3, 3) cov_colnames = 'mvalue kstock _cons'.split() cov_rownames = 'mvalue kstock _cons'.split() results_nw_groupsum4 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( df_m=2, df_r=197, F=73.07593045506036, N=200, lag=4, rank=3, title="Regression with Newey-West standard errors", cmd="newey", cmdline="newey invest mvalue kstock, lag(4) force", estat_cmd="newey_estat", predict="newey_p", vcetype="Newey-West", depvar="invest", properties="b V", ) params_table = np.array([ .11556215606596, .01142785251475, 10.112324771147, 1.251631065e-19, .0930255277205, .13809878441142, 197, 1.9720790337785, 0, .23067848754982, .06842168281423, 3.3714237660029, .00089998163666, .09574552141602, .36561145368361, 197, 1.9720790337785, 0, -42.714369016733, 16.179042041128, -2.6401049523298, .00895205094219, -74.620718612662, -10.808019420804, 197, 1.9720790337785, 0]).reshape(3, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = 'mvalue kstock _cons'.split() cov = np.array([ .0001305958131, -.00022910455176, .00889686530849, -.00022910455176, .00468152667913, -.88403667445531, .00889686530849, -.88403667445531, 261.76140136858]).reshape(3, 3) cov_colnames = 'mvalue kstock _cons'.split() cov_rownames = 'mvalue kstock _cons'.split() results_nw_panel4 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( N=200, inexog_ct=2, exexog_ct=0, endog_ct=0, partial_ct=0, df_r=9, N_clust=10, N_clust1=10, N_clust2=20, df_m=2, sdofminus=0, dofminus=0, r2=.8124080178314146, rmse=94.40840193979601, rss=1755850.432294737, mss=7604093.484267682, r2_a=.8105035307027995, F=57.99124535923564, Fp=7.21555935862e-06, Fdf1=2, partialcons=0, cons=1, jdf=0, j=0, ll=-1191.802357418011, rankV=3, rankS=3, rankxx=3, rankzz=3, r2c=.8124080178314146, r2u=.8710896173136538, yyc=9359943.916562419, yy=13620706.07273678, Fdf2=9, clustvar="company time", hacsubtitleV="Statistics robust to heteroskedasticity and clustering on company and time", # noqa:E501 hacsubtitleB="Estimates efficient for homoskedasticity only", title="OLS estimation", predict="ivreg2_p", version="03.1.07", cmdline="ivreg2 invest mvalue kstock, cluster(company time) small", cmd="ivreg2", model="ols", depvar="invest", vcetype="Robust", clustvar2="time", clustvar1="company", vce="robust two-way cluster", partialsmall="small", small="small", inexog="mvalue kstock", insts="mvalue kstock", properties="b V", ) params_table = np.array([ .11556215606596, .01635175387097, 7.0672636695645, .00005873628221, .07857191892244, .15255239320949, 9, 2.2621571627982, 0, .23067848754982, .07847391274682, 2.9395563375824, .01649863150032, .05315816373679, .40819881136285, 9, 2.2621571627982, 0, -42.714369016733, 19.505607409785, -2.189850750062, .05626393734425, -86.839118533508, 1.4103805000422, 9, 2.2621571627982, 0]).reshape(3, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = 'mvalue kstock _cons'.split() cov = np.array([ .00026737985466, -.00070163493529, .19641438763743, -.00070163493529, .0061581549818, -.99627581152391, .19641438763743, -.99627581152391, 380.46872042467]).reshape(3, 3) cov_colnames = 'mvalue kstock _cons'.split() cov_rownames = 'mvalue kstock _cons'.split() results_cluster_2groups_small = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( N=200, inexog_ct=2, exexog_ct=0, endog_ct=0, partial_ct=0, N_clust=10, N_clust1=10, N_clust2=20, df_m=2, sdofminus=0, dofminus=0, r2=.8124080178314146, rmse=93.69766358599176, rss=1755850.432294737, mss=7604093.484267682, r2_a=.8105035307027995, F=57.99124535923565, Fp=7.21555935862e-06, Fdf1=2, Fdf2=9, partialcons=0, cons=1, jdf=0, j=0, ll=-1191.802357418011, rankV=3, rankS=3, rankxx=3, rankzz=3, r2c=.8124080178314146, r2u=.8710896173136538, yyc=9359943.916562419, yy=13620706.07273678, clustvar="company time", hacsubtitleV="Statistics robust to heteroskedasticity and clustering on company and time", # noqa:E501 hacsubtitleB="Estimates efficient for homoskedasticity only", title="OLS estimation", predict="ivreg2_p", version="03.1.07", cmdline="ivreg2 invest mvalue kstock, cluster(company time)", cmd="ivreg2", model="ols", depvar="invest", vcetype="Robust", clustvar2="time", clustvar1="company", vce="robust two-way cluster", partialsmall="small", inexog="mvalue kstock", insts="mvalue kstock", properties="b V", ) params_table = np.array([ .11556215606596, .01543448599542, 7.487269488613, 7.032121917e-14, .08531111939505, .14581319273688, np.nan, 1.9599639845401, 0, .23067848754982, .07407184066336, 3.1142534799181, .00184410987255, .08550034758104, .3758566275186, np.nan, 1.9599639845401, 0, -42.714369016733, 18.411420987265, -2.319993065515, .02034125246974, -78.800091055978, -6.6286469774879, np.nan, 1.9599639845401, 0]).reshape(3, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'mvalue kstock _cons'.split() cov = np.array([ .00023822335794, -.00062512499511, .17499633632219, -.00062512499511, .00548663757926, -.88763669036779, .17499633632219, -.88763669036779, 338.98042277032]).reshape(3, 3) cov_colnames = 'mvalue kstock _cons'.split() cov_rownames = 'mvalue kstock _cons'.split() results_cluster_2groups_large = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( N=200, inexog_ct=2, exexog_ct=0, endog_ct=0, partial_ct=0, bw=5, N_clust=20, df_m=2, sdofminus=0, dofminus=0, r2=.8124080178314146, rmse=93.69766358599176, rss=1755850.432294737, mss=7604093.484267682, r2_a=.8105035307027995, F=92.14467466912147, Fp=1.66368179227e-10, Fdf1=2, Fdf2=19, yy=13620706.07273678, partialcons=0, cons=1, jdf=0, j=0, ll=-1191.802357418011, rankV=3, rankS=3, rankxx=3, rankzz=3, r2c=.8124080178314146, r2u=.8710896173136538, yyc=9359943.916562419, clustvar="year", hacsubtitleV2="and kernel-robust to common correlated disturbances (Driscoll-Kraay)", # noqa:E501 hacsubtitleV="Statistics robust to heteroskedasticity and clustering on year", # noqa:E501 hacsubtitleB="Estimates efficient for homoskedasticity only", title="OLS estimation", predict="ivreg2_p", version="03.1.07", cmdline="ivreg2 invest mvalue kstock, dkraay(5)", cmd="ivreg2", model="ols", depvar="invest", vcetype="Robust", vce="cluster ac bartlett bw=5", partialsmall="small", ivar="company", tvar="year", kernel="Bartlett", inexog="mvalue kstock", insts="mvalue kstock", properties="b V", ) params_table = np.array([ .11556215606596, .0134360177573, 8.6009231420662, 7.907743030e-18, .08922804516602, .14189626696591, np.nan, 1.9599639845401, 0, .23067848754982, .04930800664089, 4.678317037431, 2.892390940e-06, .13403657038422, .32732040471542, np.nan, 1.9599639845401, 0, -42.714369016733, 12.190347184209, -3.5039501641153, .00045841113727, -66.607010456823, -18.821727576643, np.nan, 1.9599639845401, 0]).reshape(3, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'mvalue kstock _cons'.split() cov = np.array([ .00018052657317, -.00035661054613, -.06728261073866, -.00035661054613, .0024312795189, -.32394785247278, -.06728261073866, -.32394785247278, 148.60456447156]).reshape(3, 3) cov_colnames = 'mvalue kstock _cons'.split() cov_rownames = 'mvalue kstock _cons'.split() results_nw_groupsum4_ivreg_large = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( N=200, inexog_ct=2, exexog_ct=0, endog_ct=0, partial_ct=0, bw=5, df_r=19, N_clust=20, df_m=2, sdofminus=0, dofminus=0, r2=.8124080178314146, rmse=94.40840193979601, rss=1755850.432294737, mss=7604093.484267682, r2_a=.8105035307027995, F=92.14467466912149, Fp=1.66368179227e-10, Fdf1=2, Fdf2=19, partialcons=0, cons=1, jdf=0, j=0, ll=-1191.802357418011, rankV=3, rankS=3, rankxx=3, rankzz=3, r2c=.8124080178314146, r2u=.8710896173136538, yyc=9359943.916562419, yy=13620706.07273678, clustvar="year", hacsubtitleV2="and kernel-robust to common correlated disturbances (Driscoll-Kraay)", # noqa:E501 hacsubtitleV="Statistics robust to heteroskedasticity and clustering on year", # noqa:E501 hacsubtitleB="Estimates efficient for homoskedasticity only", title="OLS estimation", predict="ivreg2_p", version="03.1.07", cmdline="ivreg2 invest mvalue kstock, dkraay(5) small", cmd="ivreg2", model="ols", depvar="invest", vcetype="Robust", vce="cluster ac bartlett bw=5", partialsmall="small", small="small", ivar="company", tvar="year", kernel="Bartlett", inexog="mvalue kstock", insts="mvalue kstock", properties="b V", ) params_table = np.array([ .11556215606596, .0138548615926, 8.3409101775303, 8.967911239e-08, .08656359748216, .14456071464977, 19, 2.0930240544083, 0, .23067848754982, .0508450956047, 4.5368876743442, .00022550505646, .12425847940049, .33709849569915, 19, 2.0930240544083, 0, -42.714369016733, 12.570359466158, -3.3980228752988, .00301793225123, -69.02443375196, -16.404304281506, 19, 2.0930240544083, 0]).reshape(3, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = 'mvalue kstock _cons'.split() cov = np.array([ .00019195718975, -.00037919048186, -.07154282413568, -.00037919048186, .00258522374705, -.34445964542925, -.07154282413568, -.34445964542925, 158.01393710842]).reshape(3, 3) cov_colnames = 'mvalue kstock _cons'.split() cov_rownames = 'mvalue kstock _cons'.split() results_nw_groupsum4_ivreg_small = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) # ---------------------------------------------------------------- # WLS est = dict( N=200, df_m=2, df_r=197, F=158.2726503915062, r2=.7728224625923459, rmse=35.1783035325949, mss=829335.6968772264, rss=243790.0687679817, r2_a=.7705160916541971, ll=-994.3622459900876, ll_0=-1142.564592396746, rank=3, cmdline="regress invest mvalue kstock [aw=1/mvalue], robust", title="Linear regression", marginsok="XB default", vce="robust", depvar="invest", cmd="regress", properties="b V", predict="regres_p", model="ols", estat_cmd="regress_estat", wexp="= 1/mvalue", wtype="aweight", vcetype="Robust", ) params_table = np.array([ .11694307068216, .00768545583365, 15.2161528494, 4.371656843e-35, .10178674436759, .13209939699674, 197, 1.9720790337785, 0, .10410756769914, .00986959606725, 10.548310892334, 6.565731752e-21, .08464394422305, .12357119117523, 197, 1.9720790337785, 0, -9.2723336171089, 2.3458404391932, -3.9526702081656, .00010767530575, -13.898516363832, -4.6461508703863, 197, 1.9720790337785, 0]).reshape(3, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = 'mvalue kstock _cons'.split() cov = np.array([ .00005906623137, 6.805470065e-06, -.01210153268743, 6.805470065e-06, .00009740892653, -.01511046663892, -.01210153268743, -.01511046663892, 5.502967366154]).reshape(3, 3) cov_colnames = 'mvalue kstock _cons'.split() cov_rownames = 'mvalue kstock _cons'.split() results_hc1_wls_small = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( N_clust=10, N=200, df_m=2, df_r=9, F=22.90591346432732, r2=.7728224625923459, rmse=35.1783035325949, mss=829335.6968772264, rss=243790.0687679817, r2_a=.7705160916541971, ll=-994.3622459900876, ll_0=-1142.564592396746, rank=3, cmdline="regress invest mvalue kstock[aw=1/mvalue], vce(cluster company)", title="Linear regression", marginsok="XB default", vce="cluster", depvar="invest", cmd="regress", properties="b V", predict="regres_p", model="ols", estat_cmd="regress_estat", wexp="= 1/mvalue", wtype="aweight", vcetype="Robust", clustvar="company", ) params_table = np.array([ .11694307068216, .02609630113434, 4.4812124936848, .00152974827456, .05790913614858, .17597700521575, 9, 2.2621571627982, 0, .10410756769914, .02285882773869, 4.5543703679489, .00137730504553, .05239730679689, .15581782860139, 9, 2.2621571627982, 0, -9.2723336171089, 5.7204731422962, -1.6209032690934, .13948922172294, -22.212942910549, 3.6682756763312, 9, 2.2621571627982, 0]).reshape(3, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = 'mvalue kstock _cons'.split() cov = np.array([ .00068101693289, -.00006496077364, -.08926939086077, -.00006496077364, .00052252600559, -.0697116307149, -.08926939086077, -.0697116307149, 32.723812971732]).reshape(3, 3) cov_colnames = 'mvalue kstock _cons'.split() cov_rownames = 'mvalue kstock _cons'.split() results_cluster_wls_small = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( N=200, inexog_ct=2, exexog_ct=0, endog_ct=0, partial_ct=0, N_clust=10, df_m=2, sdofminus=0, dofminus=0, r2=.772822462592346, rmse=34.91346937558495, rss=243790.0687679817, mss=829335.6968772268, r2_a=.7705160916541972, F=22.9059134643273, Fp=.000294548654088, Fdf1=2, Fdf2=9, yy=1401938.856802022, yyc=1073125.765645209, partialcons=0, cons=1, jdf=0, j=0, ll=-994.3622459900874, rankV=3, rankS=3, rankxx=3, rankzz=3, r2c=.772822462592346, r2u=.8261050632949187, clustvar="company", hacsubtitleV="Statistics robust to heteroskedasticity and clustering on company", # noqa:E501 hacsubtitleB="Estimates efficient for homoskedasticity only", title="OLS estimation", predict="ivreg2_p", version="03.1.07", cmdline="ivreg2 invest mvalue kstock [aw=1/mvalue], cluster(company)", cmd="ivreg2", wtype="aweight", wexp="=1/mvalue", model="ols", depvar="invest", vcetype="Robust", vce="robust cluster", partialsmall="small", inexog="mvalue kstock", insts="mvalue kstock", properties="b V", ) params_table = np.array([ .11694307068216, .02463240320082, 4.7475298990826, 2.059159576e-06, .06866444755588, .16522169380844, np.nan, 1.9599639845401, 0, .10410756769914, .02157653909108, 4.8250355286218, 1.399783125e-06, .06181832816961, .14639680722867, np.nan, 1.9599639845401, 0, -9.2723336171089, 5.3995775192484, -1.7172331694572, .08593657730569, -19.855311086568, 1.31064385235, np.nan, 1.9599639845401, 0]).reshape(3, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'mvalue kstock _cons'.split() cov = np.array([ .00060675528745, -.00005787711139, -.07953498994782, -.00005787711139, .00046554703915, -.06210991017966, -.07953498994782, -.06210991017966, 29.155437386372]).reshape(3, 3) cov_colnames = 'mvalue kstock _cons'.split() cov_rownames = 'mvalue kstock _cons'.split() results_cluster_wls_large = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) statsmodels-0.12.2/statsmodels/regression/tests/results/results_macro_ols_robust.py000066400000000000000000000312401400612667500312410ustar00rootroot00000000000000'''autogenerated and edited by hand ''' import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch est = dict( N=202, df_m=2, df_r=199, F=92.94502024547633, r2=.6769775594319385, rmse=10.7037959322668, mss=47782.65712176046, rss=22799.67822456265, r2_a=.6737311027428123, ll=-763.9752181602238, ll_0=-878.1085999159409, rank=3, cmdline="regress g_realinv g_realgdp L.realint, vce(robust)", title="Linear regression", marginsok="XB default", vce="robust", depvar="g_realinv", cmd="regress", properties="b V", predict="regres_p", model="ols", estat_cmd="regress_estat", vcetype="Robust", ) params_table = np.array([ 4.3742216647032, .32355452428856, 13.519272136038, 5.703151404e-30, 3.7361862031101, 5.0122571262963, 199, 1.9719565442518, 0, -.61399696947899, .32772840315987, -1.8734933059173, .06246625509181, -1.2602631388273, .0322691998693, 199, 1.9719565442518, 0, -9.4816727746549, 1.3690593206013, -6.9256843965613, 5.860240898e-11, -12.181398261383, -6.7819472879264, 199, 1.9719565442518, 0]).reshape(3, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = 'g_realgdp L.realint _cons'.split() cov = np.array([ .1046875301876, -.00084230205782, -.34205013876828, -.00084230205782, .10740590623772, -.14114426417778, -.34205013876828, -.14114426417778, 1.8743234233252]).reshape(3, 3) cov_colnames = 'g_realgdp L.realint _cons'.split() cov_rownames = 'g_realgdp L.realint _cons'.split() results_hc0 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) # -------------------------------------------------------------- est = dict( df_m=2, df_r=199, F=89.45120275471848, N=202, lag=4, rank=3, title="Regression with Newey-West standard errors", cmd="newey", cmdline="newey g_realinv g_realgdp L.realint, lag(4)", estat_cmd="newey_estat", predict="newey_p", vcetype="Newey-West", depvar="g_realinv", properties="b V", ) params_table = np.array([ 4.3742216647032, .33125644884286, 13.204940401864, 5.282334606e-29, 3.7209983425819, 5.0274449868245, 199, 1.9719565442518, 0, -.61399696947899, .29582347593197, -2.0755518727668, .03922090940364, -1.1973480087863, -.03064593017165, 199, 1.9719565442518, 0, -9.4816727746549, 1.1859338087713, -7.9951112823729, 1.036821797e-13, -11.820282709911, -7.1430628393989, 199, 1.9719565442518, 0]).reshape(3, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = 'g_realgdp L.realint _cons'.split() cov = np.array([ .10973083489998, .0003953117603, -.31803287070833, .0003953117603, .08751152891247, -.06062111121649, -.31803287070833, -.06062111121649, 1.4064389987868]).reshape(3, 3) cov_colnames = 'g_realgdp L.realint _cons'.split() cov_rownames = 'g_realgdp L.realint _cons'.split() results_newey4 = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( N=202, inexog_ct=2, exexog_ct=0, endog_ct=0, partial_ct=0, bw=5, df_r=199, df_m=2, sdofminus=0, dofminus=0, r2=.6769775594319388, rmse=10.7037959322668, rss=22799.67822456265, mss=47782.65712176055, r2_a=.6737311027428126, F=89.45120275471867, Fp=1.93466284646e-28, Fdf1=2, Fdf2=199, yy=72725.68049533673, partialcons=0, cons=1, jdf=0, j=0, ll=-763.9752181602239, rankV=3, rankS=3, rankxx=3, rankzz=3, r2c=.6769775594319388, r2u=.6864975608440735, yyc=70582.33534632321, hacsubtitleV="Statistics robust to heteroskedasticity and autocorrelation", hacsubtitleB="Estimates efficient for homoskedasticity only", title="OLS estimation", predict="ivreg2_p", version="02.2.08", cmdline="ivreg2 g_realinv g_realgdp L.realint, robust bw(5) small", cmd="ivreg2", model="ols", depvar="g_realinv", vcetype="Robust", partialsmall="small", small="small", tvar="qu", kernel="Bartlett", inexog="g_realgdp L.realint", insts="g_realgdp L.realint", properties="b V", ) params_table = np.array([ 4.3742216647032, .33125644884286, 13.204940401864, 5.282334606e-29, 3.7209983425819, 5.0274449868245, 199, 1.9719565442518, 0, -.61399696947899, .29582347593197, -2.0755518727668, .03922090940364, -1.1973480087863, -.03064593017165, 199, 1.9719565442518, 0, -9.4816727746549, 1.1859338087713, -7.9951112823729, 1.036821797e-13, -11.820282709911, -7.1430628393989, 199, 1.9719565442518, 0]).reshape(3, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = 'g_realgdp L.realint _cons'.split() cov = np.array([ .10973083489998, .0003953117603, -.31803287070833, .0003953117603, .08751152891247, -.06062111121649, -.31803287070833, -.06062111121649, 1.4064389987868]).reshape(3, 3) cov_colnames = 'g_realgdp L.realint _cons'.split() cov_rownames = 'g_realgdp L.realint _cons'.split() results_ivhac4_small = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( N=202, inexog_ct=2, exexog_ct=0, endog_ct=0, partial_ct=0, bw=5, df_m=2, sdofminus=0, dofminus=0, r2=.6769775594319388, rmse=10.6240149746225, rss=22799.67822456265, mss=47782.65712176055, r2_a=.6737311027428126, F=89.45120275471867, Fp=1.93466284646e-28, Fdf1=2, Fdf2=199, yy=72725.68049533673, yyc=70582.33534632321, partialcons=0, cons=1, jdf=0, j=0, ll=-763.9752181602239, rankV=3, rankS=3, rankxx=3, rankzz=3, r2c=.6769775594319388, r2u=.6864975608440735, hacsubtitleV="Statistics robust to heteroskedasticity and autocorrelation", hacsubtitleB="Estimates efficient for homoskedasticity only", title="OLS estimation", predict="ivreg2_p", version="02.2.08", cmdline="ivreg2 g_realinv g_realgdp L.realint, robust bw(5)", cmd="ivreg2", model="ols", depvar="g_realinv", vcetype="Robust", partialsmall="small", tvar="qu", kernel="Bartlett", inexog="g_realgdp L.realint", insts="g_realgdp L.realint", properties="b V", ) params_table = np.array([ 4.3742216647032, .32878742225811, 13.304102798888, 2.191074740e-40, 3.7298101585076, 5.0186331708989, np.nan, 1.9599639845401, 0, -.61399696947899, .29361854972141, -2.0911382133777, .03651567605333, -1.1894787521258, -.03851518683214, np.nan, 1.9599639845401, 0, -9.4816727746549, 1.1770944273439, -8.055150508231, 7.938107001e-16, -11.788735458652, -7.1746100906581, np.nan, 1.9599639845401, 0]).reshape(3, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'g_realgdp L.realint _cons'.split() cov = np.array([ .10810116903513, .00038944079356, -.31330961025227, .00038944079356, .0862118527405, -.05972079768357, -.31330961025227, -.05972079768357, 1.385551290884]).reshape(3, 3) cov_colnames = 'g_realgdp L.realint _cons'.split() cov_rownames = 'g_realgdp L.realint _cons'.split() results_ivhac4_large = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) # -------------------------------------------------------------- est = dict( N=202, inexog_ct=2, exexog_ct=0, endog_ct=0, partial_ct=0, df_r=199, df_m=2, sdofminus=0, dofminus=0, r2=.6769775594319388, rmse=10.7037959322668, rss=22799.67822456265, mss=47782.65712176055, r2_a=.6737311027428126, F=92.94502024547634, Fp=3.12523087723e-29, Fdf1=2, Fdf2=199, yy=72725.68049533673, yyc=70582.33534632321, partialcons=0, cons=1, jdf=0, j=0, ll=-763.9752181602239, rankV=3, rankS=3, rankxx=3, rankzz=3, r2c=.6769775594319388, r2u=.6864975608440735, hacsubtitleV="Statistics robust to heteroskedasticity", hacsubtitleB="Estimates efficient for homoskedasticity only", title="OLS estimation", predict="ivreg2_p", version="02.2.08", cmdline="ivreg2 g_realinv g_realgdp L.realint, robust small", cmd="ivreg2", model="ols", depvar="g_realinv", vcetype="Robust", partialsmall="small", small="small", inexog="g_realgdp L.realint", insts="g_realgdp L.realint", properties="b V", ) params_table = np.array([ 4.3742216647032, .32355452428856, 13.519272136038, 5.703151404e-30, 3.7361862031101, 5.0122571262963, 199, 1.9719565442518, 0, -.61399696947899, .32772840315987, -1.8734933059173, .06246625509181, -1.2602631388273, .0322691998693, 199, 1.9719565442518, 0, -9.4816727746549, 1.3690593206013, -6.9256843965613, 5.860240898e-11, -12.181398261383, -6.7819472879264, 199, 1.9719565442518, 0]).reshape(3, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = 'g_realgdp L.realint _cons'.split() cov = np.array([ .1046875301876, -.00084230205782, -.34205013876828, -.00084230205782, .10740590623772, -.14114426417778, -.34205013876828, -.14114426417778, 1.8743234233252]).reshape(3, 3) cov_colnames = 'g_realgdp L.realint _cons'.split() cov_rownames = 'g_realgdp L.realint _cons'.split() results_ivhc0_small = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) # -------------------------------------------------------------- est = dict( N=202, inexog_ct=2, exexog_ct=0, endog_ct=0, partial_ct=0, df_m=2, sdofminus=0, dofminus=0, r2=.6769775594319388, rmse=10.6240149746225, rss=22799.67822456265, mss=47782.65712176055, r2_a=.6737311027428126, F=92.94502024547633, Fp=3.12523087723e-29, Fdf1=2, Fdf2=199, yy=72725.68049533673, yyc=70582.33534632321, r2u=.6864975608440735, partialcons=0, cons=1, jdf=0, j=0, ll=-763.9752181602239, rankV=3, rankS=3, rankxx=3, rankzz=3, r2c=.6769775594319388, hacsubtitleV="Statistics robust to heteroskedasticity", hacsubtitleB="Estimates efficient for homoskedasticity only", title="OLS estimation", predict="ivreg2_p", version="02.2.08", cmdline="ivreg2 g_realinv g_realgdp L.realint, robust", cmd="ivreg2", model="ols", depvar="g_realinv", vcetype="Robust", partialsmall="small", inexog="g_realgdp L.realint", insts="g_realgdp L.realint", properties="b V", ) params_table = np.array([ 4.3742216647032, .32114290415293, 13.620795004769, 3.012701837e-42, 3.7447931386729, 5.0036501907336, np.nan, 1.9599639845401, 0, -.61399696947899, .32528567293437, -1.8875622892954, .05908473670106, -1.2515451731172, .02355123415926, np.nan, 1.9599639845401, 0, -9.4816727746549, 1.3588550094989, -6.9776927695558, 3.000669464e-12, -12.144979653484, -6.8183658958253, np.nan, 1.9599639845401, 0]).reshape(3, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = 'g_realgdp L.realint _cons'.split() cov = np.array([ .10313276488778, -.00082979262132, -.33697018621231, -.00082979262132, .10581076901637, -.13904806223455, -.33697018621231, -.13904806223455, 1.8464869368401]).reshape(3, 3) cov_colnames = 'g_realgdp L.realint _cons'.split() cov_rownames = 'g_realgdp L.realint _cons'.split() results_ivhc0_large = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) statsmodels-0.12.2/statsmodels/regression/tests/results/results_quantile_regression.py000066400000000000000000000657761400612667500317740ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch epanechnikov_hsheather_q75 = Bunch() epanechnikov_hsheather_q75.table = np.array([ [.6440143, .0122001, 52.79, 0.000, .6199777, .6680508], [62.39648, 13.5509, 4.60, 0.000, 35.69854, 89.09443] ]) epanechnikov_hsheather_q75.psrsquared = 0.6966 epanechnikov_hsheather_q75.rank = 2 epanechnikov_hsheather_q75.sparsity = 223.784434936344 epanechnikov_hsheather_q75.bwidth = .1090401129546568 # epanechnikov_hsheather_q75.kbwidth = 59.62067927472172 # Stata 12 results epanechnikov_hsheather_q75.kbwidth = 59.30 # TODO: why do we need lower tol? epanechnikov_hsheather_q75.df_m = 1 epanechnikov_hsheather_q75.df_r = 233 epanechnikov_hsheather_q75.f_r = .0044685860313942 epanechnikov_hsheather_q75.N = 235 epanechnikov_hsheather_q75.q_v = 745.2352905273438 epanechnikov_hsheather_q75.q = .75 epanechnikov_hsheather_q75.sum_rdev = 43036.06956481934 epanechnikov_hsheather_q75.sum_adev = 13058.50008841318 epanechnikov_hsheather_q75.convcode = 0 biweight_bofinger = Bunch() biweight_bofinger.table = np.array([ [.5601805, .0136491, 41.04, 0.000, .533289, .5870719], [81.48233, 15.1604, 5.37, 0.000, 51.61335, 111.3513] ]) biweight_bofinger.psrsquared = 0.6206 biweight_bofinger.rank = 2 biweight_bofinger.sparsity = 216.8218989750115 biweight_bofinger.bwidth = .2173486679767846 biweight_bofinger.kbwidth = 91.50878448104551 biweight_bofinger.df_m = 1 biweight_bofinger.df_r = 233 biweight_bofinger.f_r = .0046120802590851 biweight_bofinger.N = 235 biweight_bofinger.q_v = 582.541259765625 biweight_bofinger.q = .5 biweight_bofinger.sum_rdev = 46278.05667114258 biweight_bofinger.sum_adev = 17559.93220318131 biweight_bofinger.convcode = 0 biweight_hsheather = Bunch() biweight_hsheather.table = np.array([ [.5601805, .0128449, 43.61, 0.000, .5348735, .5854875], [81.48233, 14.26713, 5.71, 0.000, 53.37326, 109.5914] ]) biweight_hsheather.psrsquared = 0.6206 biweight_hsheather.rank = 2 biweight_hsheather.sparsity = 204.0465407204423 biweight_hsheather.bwidth = .1574393314202373 biweight_hsheather.kbwidth = 64.53302151153288 biweight_hsheather.df_m = 1 biweight_hsheather.df_r = 233 biweight_hsheather.f_r = .0049008427022052 biweight_hsheather.N = 235 biweight_hsheather.q_v = 582.541259765625 biweight_hsheather.q = .5 biweight_hsheather.sum_rdev = 46278.05667114258 biweight_hsheather.sum_adev = 17559.93220318131 biweight_hsheather.convcode = 0 biweight_chamberlain = Bunch() biweight_chamberlain.table = np.array([ [.5601805, .0114969, 48.72, 0.000, .5375294, .5828315], [81.48233, 12.76983, 6.38, 0.000, 56.32325, 106.6414] ]) biweight_chamberlain.psrsquared = 0.6206 biweight_chamberlain.rank = 2 biweight_chamberlain.sparsity = 182.6322495257494 biweight_chamberlain.bwidth = .063926976464458 biweight_chamberlain.kbwidth = 25.61257055690209 biweight_chamberlain.df_m = 1 biweight_chamberlain.df_r = 233 biweight_chamberlain.f_r = .005475484218131 biweight_chamberlain.N = 235 biweight_chamberlain.q_v = 582.541259765625 biweight_chamberlain.q = .5 biweight_chamberlain.sum_rdev = 46278.05667114258 biweight_chamberlain.sum_adev = 17559.93220318131 biweight_chamberlain.convcode = 0 epanechnikov_bofinger = Bunch() epanechnikov_bofinger.table = np.array([ [.5601805, .0209663, 26.72, 0.000, .5188727, .6014882], [81.48233, 23.28774, 3.50, 0.001, 35.60088, 127.3638] ]) epanechnikov_bofinger.psrsquared = 0.6206 epanechnikov_bofinger.rank = 2 epanechnikov_bofinger.sparsity = 333.0579553401614 epanechnikov_bofinger.bwidth = .2173486679767846 epanechnikov_bofinger.kbwidth = 91.50878448104551 epanechnikov_bofinger.df_m = 1 epanechnikov_bofinger.df_r = 233 epanechnikov_bofinger.f_r = .0030024804511235 epanechnikov_bofinger.N = 235 epanechnikov_bofinger.q_v = 582.541259765625 epanechnikov_bofinger.q = .5 epanechnikov_bofinger.sum_rdev = 46278.05667114258 epanechnikov_bofinger.sum_adev = 17559.93220318131 epanechnikov_bofinger.convcode = 0 epanechnikov_hsheather = Bunch() epanechnikov_hsheather.table = np.array([ [.5601805, .0170484, 32.86, 0.000, .5265918, .5937692], [81.48233, 18.93605, 4.30, 0.000, 44.17457, 118.7901] ]) epanechnikov_hsheather.psrsquared = 0.6206 epanechnikov_hsheather.rank = 2 epanechnikov_hsheather.sparsity = 270.8207209067576 epanechnikov_hsheather.bwidth = .1574393314202373 epanechnikov_hsheather.kbwidth = 64.53302151153288 epanechnikov_hsheather.df_m = 1 epanechnikov_hsheather.df_r = 233 epanechnikov_hsheather.f_r = .0036924796472434 epanechnikov_hsheather.N = 235 epanechnikov_hsheather.q_v = 582.541259765625 epanechnikov_hsheather.q = .5 epanechnikov_hsheather.sum_rdev = 46278.05667114258 epanechnikov_hsheather.sum_adev = 17559.93220318131 epanechnikov_hsheather.convcode = 0 epanechnikov_chamberlain = Bunch() epanechnikov_chamberlain.table = np.array([ [.5601805, .0130407, 42.96, 0.000, .5344876, .5858733], [81.48233, 14.48467, 5.63, 0.000, 52.94468, 110.02] ]) epanechnikov_chamberlain.psrsquared = 0.6206 epanechnikov_chamberlain.rank = 2 epanechnikov_chamberlain.sparsity = 207.1576340635951 epanechnikov_chamberlain.bwidth = .063926976464458 epanechnikov_chamberlain.kbwidth = 25.61257055690209 epanechnikov_chamberlain.df_m = 1 epanechnikov_chamberlain.df_r = 233 epanechnikov_chamberlain.f_r = .0048272418466269 epanechnikov_chamberlain.N = 235 epanechnikov_chamberlain.q_v = 582.541259765625 epanechnikov_chamberlain.q = .5 epanechnikov_chamberlain.sum_rdev = 46278.05667114258 epanechnikov_chamberlain.sum_adev = 17559.93220318131 epanechnikov_chamberlain.convcode = 0 epan2_bofinger = Bunch() epan2_bofinger.table = np.array([ [.5601805, .0143484, 39.04, 0.000, .5319113, .5884496], [81.48233, 15.93709, 5.11, 0.000, 50.08313, 112.8815] ]) epan2_bofinger.psrsquared = 0.6206 epan2_bofinger.rank = 2 epan2_bofinger.sparsity = 227.9299402797656 epan2_bofinger.bwidth = .2173486679767846 epan2_bofinger.kbwidth = 91.50878448104551 epan2_bofinger.df_m = 1 epan2_bofinger.df_r = 233 epan2_bofinger.f_r = .0043873130435281 epan2_bofinger.N = 235 epan2_bofinger.q_v = 582.541259765625 epan2_bofinger.q = .5 epan2_bofinger.sum_rdev = 46278.05667114258 epan2_bofinger.sum_adev = 17559.93220318131 epan2_bofinger.convcode = 0 epan2_hsheather = Bunch() epan2_hsheather.table = np.array([ [.5601805, .0131763, 42.51, 0.000, .5342206, .5861403], [81.48233, 14.63518, 5.57, 0.000, 52.64815, 110.3165] ]) epan2_hsheather.psrsquared = 0.6206 epan2_hsheather.rank = 2 epan2_hsheather.sparsity = 209.3102085912557 epan2_hsheather.bwidth = .1574393314202373 epan2_hsheather.kbwidth = 64.53302151153288 epan2_hsheather.df_m = 1 epan2_hsheather.df_r = 233 epan2_hsheather.f_r = .0047775978378236 epan2_hsheather.N = 235 epan2_hsheather.q_v = 582.541259765625 epan2_hsheather.q = .5 epan2_hsheather.sum_rdev = 46278.05667114258 epan2_hsheather.sum_adev = 17559.93220318131 epan2_hsheather.convcode = 0 epan2_chamberlain = Bunch() epan2_chamberlain.table = np.array([ [.5601805, .0117925, 47.50, 0.000, .5369469, .583414], [81.48233, 13.0982, 6.22, 0.000, 55.67629, 107.2884] ]) epan2_chamberlain.psrsquared = 0.6206 epan2_chamberlain.rank = 2 epan2_chamberlain.sparsity = 187.3286437436797 epan2_chamberlain.bwidth = .063926976464458 epan2_chamberlain.kbwidth = 25.61257055690209 epan2_chamberlain.df_m = 1 epan2_chamberlain.df_r = 233 epan2_chamberlain.f_r = .0053382119253919 epan2_chamberlain.N = 235 epan2_chamberlain.q_v = 582.541259765625 epan2_chamberlain.q = .5 epan2_chamberlain.sum_rdev = 46278.05667114258 epan2_chamberlain.sum_adev = 17559.93220318131 epan2_chamberlain.convcode = 0 rectangle_bofinger = Bunch() rectangle_bofinger.table = np.array([ [.5601805, .0158331, 35.38, 0.000, .5289861, .5913748], [81.48233, 17.5862, 4.63, 0.000, 46.83404, 116.1306] ]) rectangle_bofinger.psrsquared = 0.6206 rectangle_bofinger.rank = 2 rectangle_bofinger.sparsity = 251.515372550242 rectangle_bofinger.bwidth = .2173486679767846 rectangle_bofinger.kbwidth = 91.50878448104551 rectangle_bofinger.df_m = 1 rectangle_bofinger.df_r = 233 rectangle_bofinger.f_r = .0039759001203803 rectangle_bofinger.N = 235 rectangle_bofinger.q_v = 582.541259765625 rectangle_bofinger.q = .5 rectangle_bofinger.sum_rdev = 46278.05667114258 rectangle_bofinger.sum_adev = 17559.93220318131 rectangle_bofinger.convcode = 0 rectangle_hsheather = Bunch() rectangle_hsheather.table = np.array([ [.5601805, .0137362, 40.78, 0.000, .5331174, .5872435], [81.48233, 15.25712, 5.34, 0.000, 51.42279, 111.5419] ]) rectangle_hsheather.psrsquared = 0.6206 rectangle_hsheather.rank = 2 rectangle_hsheather.sparsity = 218.2051806505069 rectangle_hsheather.bwidth = .1574393314202373 rectangle_hsheather.kbwidth = 64.53302151153288 rectangle_hsheather.df_m = 1 rectangle_hsheather.df_r = 233 rectangle_hsheather.f_r = .004582842611797 rectangle_hsheather.N = 235 rectangle_hsheather.q_v = 582.541259765625 rectangle_hsheather.q = .5 rectangle_hsheather.sum_rdev = 46278.05667114258 rectangle_hsheather.sum_adev = 17559.93220318131 rectangle_hsheather.convcode = 0 rectangle_chamberlain = Bunch() rectangle_chamberlain.table = np.array([ [.5601805, .0118406, 47.31, 0.000, .5368522, .5835087], [81.48233, 13.1516, 6.20, 0.000, 55.57108, 107.3936] ]) rectangle_chamberlain.psrsquared = 0.6206 rectangle_chamberlain.rank = 2 rectangle_chamberlain.sparsity = 188.0923150272497 rectangle_chamberlain.bwidth = .063926976464458 rectangle_chamberlain.kbwidth = 25.61257055690209 rectangle_chamberlain.df_m = 1 rectangle_chamberlain.df_r = 233 rectangle_chamberlain.f_r = .0053165383171297 rectangle_chamberlain.N = 235 rectangle_chamberlain.q_v = 582.541259765625 rectangle_chamberlain.q = .5 rectangle_chamberlain.sum_rdev = 46278.05667114258 rectangle_chamberlain.sum_adev = 17559.93220318131 rectangle_chamberlain.convcode = 0 triangle_bofinger = Bunch() triangle_bofinger.table = np.array([ [.5601805, .0138712, 40.38, 0.000, .5328515, .5875094], [81.48233, 15.40706, 5.29, 0.000, 51.12738, 111.8373] ]) triangle_bofinger.psrsquared = 0.6206 triangle_bofinger.rank = 2 triangle_bofinger.sparsity = 220.3495620604223 triangle_bofinger.bwidth = .2173486679767846 triangle_bofinger.kbwidth = 91.50878448104551 triangle_bofinger.df_m = 1 triangle_bofinger.df_r = 233 triangle_bofinger.f_r = .0045382436463649 triangle_bofinger.N = 235 triangle_bofinger.q_v = 582.541259765625 triangle_bofinger.q = .5 triangle_bofinger.sum_rdev = 46278.05667114258 triangle_bofinger.sum_adev = 17559.93220318131 triangle_bofinger.convcode = 0 triangle_hsheather = Bunch() triangle_hsheather.table = np.array([ [.5601805, .0128874, 43.47, 0.000, .5347898, .5855711], [81.48233, 14.31431, 5.69, 0.000, 53.2803, 109.6844] ]) triangle_hsheather.psrsquared = 0.6206 triangle_hsheather.rank = 2 triangle_hsheather.sparsity = 204.7212998199564 triangle_hsheather.bwidth = .1574393314202373 triangle_hsheather.kbwidth = 64.53302151153288 triangle_hsheather.df_m = 1 triangle_hsheather.df_r = 233 triangle_hsheather.f_r = .004884689579831 triangle_hsheather.N = 235 triangle_hsheather.q_v = 582.541259765625 triangle_hsheather.q = .5 triangle_hsheather.sum_rdev = 46278.05667114258 triangle_hsheather.sum_adev = 17559.93220318131 triangle_hsheather.convcode = 0 triangle_chamberlain = Bunch() triangle_chamberlain.table = np.array([ [.5601805, .0115725, 48.41, 0.000, .5373803, .5829806], [81.48233, 12.85389, 6.34, 0.000, 56.15764, 106.807] ]) triangle_chamberlain.psrsquared = 0.6206 triangle_chamberlain.rank = 2 triangle_chamberlain.sparsity = 183.8344452913298 triangle_chamberlain.bwidth = .063926976464458 triangle_chamberlain.kbwidth = 25.61257055690209 triangle_chamberlain.df_m = 1 triangle_chamberlain.df_r = 233 triangle_chamberlain.f_r = .0054396769790083 triangle_chamberlain.N = 235 triangle_chamberlain.q_v = 582.541259765625 triangle_chamberlain.q = .5 triangle_chamberlain.sum_rdev = 46278.05667114258 triangle_chamberlain.sum_adev = 17559.93220318131 triangle_chamberlain.convcode = 0 gaussian_bofinger = Bunch() gaussian_bofinger.table = np.array([ [.5601805, .0197311, 28.39, 0.000, .5213062, .5990547], [81.48233, 21.91582, 3.72, 0.000, 38.30383, 124.6608] ]) gaussian_bofinger.psrsquared = 0.6206 gaussian_bofinger.rank = 2 gaussian_bofinger.sparsity = 313.4370075776719 gaussian_bofinger.bwidth = .2173486679767846 gaussian_bofinger.kbwidth = 91.50878448104551 gaussian_bofinger.df_m = 1 gaussian_bofinger.df_r = 233 gaussian_bofinger.f_r = .0031904337261521 gaussian_bofinger.N = 235 gaussian_bofinger.q_v = 582.541259765625 gaussian_bofinger.q = .5 gaussian_bofinger.sum_rdev = 46278.05667114258 gaussian_bofinger.sum_adev = 17559.93220318131 gaussian_bofinger.convcode = 0 gaussian_hsheather = Bunch() gaussian_hsheather.table = np.array([ [.5601805, .016532, 33.88, 0.000, .5276092, .5927518], [81.48233, 18.36248, 4.44, 0.000, 45.30462, 117.66] ]) gaussian_hsheather.psrsquared = 0.6206 gaussian_hsheather.rank = 2 gaussian_hsheather.sparsity = 262.6175743002715 gaussian_hsheather.bwidth = .1574393314202373 gaussian_hsheather.kbwidth = 64.53302151153288 gaussian_hsheather.df_m = 1 gaussian_hsheather.df_r = 233 gaussian_hsheather.f_r = .0038078182797341 gaussian_hsheather.N = 235 gaussian_hsheather.q_v = 582.541259765625 gaussian_hsheather.q = .5 gaussian_hsheather.sum_rdev = 46278.05667114258 gaussian_hsheather.sum_adev = 17559.93220318131 gaussian_hsheather.convcode = 0 gaussian_chamberlain = Bunch() gaussian_chamberlain.table = np.array([ [.5601805, .0128123, 43.72, 0.000, .5349378, .5854232], [81.48233, 14.23088, 5.73, 0.000, 53.44468, 109.52] ]) gaussian_chamberlain.psrsquared = 0.6206 gaussian_chamberlain.rank = 2 gaussian_chamberlain.sparsity = 203.5280962791137 gaussian_chamberlain.bwidth = .063926976464458 gaussian_chamberlain.kbwidth = 25.61257055690209 gaussian_chamberlain.df_m = 1 gaussian_chamberlain.df_r = 233 gaussian_chamberlain.f_r = .004913326554328 gaussian_chamberlain.N = 235 gaussian_chamberlain.q_v = 582.541259765625 gaussian_chamberlain.q = .5 gaussian_chamberlain.sum_rdev = 46278.05667114258 gaussian_chamberlain.sum_adev = 17559.93220318131 gaussian_chamberlain.convcode = 0 cosine_bofinger = Bunch() cosine_bofinger.table = np.array([ [.5601805, .0121011, 46.29, 0.000, .536339, .5840219], [81.48233, 13.44092, 6.06, 0.000, 55.00106, 107.9636] ]) cosine_bofinger.psrsquared = 0.6206 cosine_bofinger.rank = 2 cosine_bofinger.sparsity = 192.2302014415605 cosine_bofinger.bwidth = .2173486679767846 cosine_bofinger.kbwidth = 91.50878448104551 cosine_bofinger.df_m = 1 cosine_bofinger.df_r = 233 cosine_bofinger.f_r = .0052020961976883 cosine_bofinger.N = 235 cosine_bofinger.q_v = 582.541259765625 cosine_bofinger.q = .5 cosine_bofinger.sum_rdev = 46278.05667114258 cosine_bofinger.sum_adev = 17559.93220318131 cosine_bofinger.convcode = 0 cosine_hsheather = Bunch() cosine_hsheather.table = np.array([ [.5601805, .0116679, 48.01, 0.000, .5371924, .5831685], [81.48233, 12.9598, 6.29, 0.000, 55.94897, 107.0157] ]) cosine_hsheather.psrsquared = 0.6206 cosine_hsheather.rank = 2 cosine_hsheather.sparsity = 185.349198428224 cosine_hsheather.bwidth = .1574393314202373 cosine_hsheather.kbwidth = 64.53302151153288 cosine_hsheather.df_m = 1 cosine_hsheather.df_r = 233 cosine_hsheather.f_r = .0053952216059205 cosine_hsheather.N = 235 cosine_hsheather.q_v = 582.541259765625 cosine_hsheather.q = .5 cosine_hsheather.sum_rdev = 46278.05667114258 cosine_hsheather.sum_adev = 17559.93220318131 cosine_hsheather.convcode = 0 cosine_chamberlain = Bunch() cosine_chamberlain.table = np.array([ [.5601805, .0106479, 52.61, 0.000, .539202, .5811589], [81.48233, 11.82688, 6.89, 0.000, 58.18104, 104.7836] ]) cosine_chamberlain.psrsquared = 0.6206 cosine_chamberlain.rank = 2 cosine_chamberlain.sparsity = 169.1463943762948 cosine_chamberlain.bwidth = .063926976464458 cosine_chamberlain.kbwidth = 25.61257055690209 cosine_chamberlain.df_m = 1 cosine_chamberlain.df_r = 233 cosine_chamberlain.f_r = .0059120385254878 cosine_chamberlain.N = 235 cosine_chamberlain.q_v = 582.541259765625 cosine_chamberlain.q = .5 cosine_chamberlain.sum_rdev = 46278.05667114258 cosine_chamberlain.sum_adev = 17559.93220318131 cosine_chamberlain.convcode = 0 parzen_bofinger = Bunch() parzen_bofinger.table = np.array([ [.5601805, .012909, 43.39, 0.000, .5347471, .5856138], [81.48233, 14.33838, 5.68, 0.000, 53.23289, 109.7318] ]) parzen_bofinger.psrsquared = 0.6206 parzen_bofinger.rank = 2 parzen_bofinger.sparsity = 205.0654663067616 parzen_bofinger.bwidth = .2173486679767846 parzen_bofinger.kbwidth = 91.50878448104551 parzen_bofinger.df_m = 1 parzen_bofinger.df_r = 233 parzen_bofinger.f_r = .0048764914834762 parzen_bofinger.N = 235 parzen_bofinger.q_v = 582.541259765625 parzen_bofinger.q = .5 parzen_bofinger.sum_rdev = 46278.05667114258 parzen_bofinger.sum_adev = 17559.93220318131 parzen_bofinger.convcode = 0 parzen_hsheather = Bunch() parzen_hsheather.table = np.array([ [.5601805, .0122688, 45.66, 0.000, .5360085, .5843524], [81.48233, 13.62723, 5.98, 0.000, 54.63401, 108.3307] ]) parzen_hsheather.psrsquared = 0.6206 parzen_hsheather.rank = 2 parzen_hsheather.sparsity = 194.8946558099188 parzen_hsheather.bwidth = .1574393314202373 parzen_hsheather.kbwidth = 64.53302151153288 parzen_hsheather.df_m = 1 parzen_hsheather.df_r = 233 parzen_hsheather.f_r = .0051309770185556 parzen_hsheather.N = 235 parzen_hsheather.q_v = 582.541259765625 parzen_hsheather.q = .5 parzen_hsheather.sum_rdev = 46278.05667114258 parzen_hsheather.sum_adev = 17559.93220318131 parzen_hsheather.convcode = 0 parzen_chamberlain = Bunch() parzen_chamberlain.table = np.array([ [.5601805, .0110507, 50.69, 0.000, .5384084, .5819526], [81.48233, 12.2743, 6.64, 0.000, 57.29954, 105.6651] ]) parzen_chamberlain.psrsquared = 0.6206 parzen_chamberlain.rank = 2 parzen_chamberlain.sparsity = 175.5452813763412 parzen_chamberlain.bwidth = .063926976464458 parzen_chamberlain.kbwidth = 25.61257055690209 parzen_chamberlain.df_m = 1 parzen_chamberlain.df_r = 233 parzen_chamberlain.f_r = .0056965359146063 parzen_chamberlain.N = 235 parzen_chamberlain.q_v = 582.541259765625 parzen_chamberlain.q = .5 parzen_chamberlain.sum_rdev = 46278.05667114258 parzen_chamberlain.sum_adev = 17559.93220318131 parzen_chamberlain.convcode = 0 Rquantreg = Bunch() Rquantreg.fittedvalues = np.array([ 278.946531823426, 327.662259651587, 472.195784028597, 366.902127539958, 411.817682123087, 490.131199885949, 443.36524597881, 503.536477958636, 636.406081281679, 709.736288922034, 312.165058899648, 357.917286612496, 427.907157504212, 333.474578745265, 396.777813086185, 447.125068738706, 325.117049130677, 349.771067249961, 481.598886608367, 306.106158691415, 388.420502955027, 511.05437589194, 313.836609745169, 372.960145596262, 485.358358918327, 284.379882747628, 346.21761302202, 470.314386890694, 292.735362869831, 345.174109237497, 431.875199165716, 312.003504742171, 396.809344806674, 474.141604734191, 463.93526593027, 430.280150030025, 453.602705891221, 579.151509166254, 320.586493222875, 379.637682965454, 261.63071606774, 452.262394881918, 560.558633285135, 361.453261675451, 433.779038355879, 334.560374744198, 465.46340752116, 615.361560833631, 934.235038902725, 699.263962186247, 403.470311834164, 431.875199165716, 610.619729234566, 592.662336978523, 365.021855935831, 494.3226340628, 571.610146001548, 820.79435094965, 1244.13870203673, 480.7121636877, 1031.46758784013, 362.238578597709, 467.705425607653, 577.073721157792, 591.087071047729, 323.397708458532, 569.0193777981, 547.264281981988, 304.861831677351, 727.261856258699, 382.899300447742, 380.080019200391, 387.548077543462, 455.939284414524, 461.007422390708, 469.504909066202, 571.628605113602, 482.528691661418, 447.239662606701, 443.405235218729, 617.975233440748, 888.754433927184, 390.908239427091, 479.934781986261, 872.520684097057, 468.389025193617, 467.583874563025, 600.891141536243, 328.94286096288, 524.54251098332, 697.904660068404, 443.782036008026, 501.879849409525, 647.703493205875, 458.730704476452, 401.721440320659, 507.49016247142, 722.834547664808, 380.206920088912, 481.131145133749, 299.904199685339, 347.488751302111, 488.171723133137, 368.620444647759, 1135.31179977255, 831.440717300088, 578.509405496803, 437.83023460596, 618.056493326843, 550.238043601025, 289.910800377653, 583.813030650723, 502.185524461957, 519.079736225537, 280.441976767315, 334.638935071642, 489.10661171308, 651.842445716676, 1050.52148262534, 346.050058523346, 729.252186278533, 558.451123252156, 529.859949563712, 668.51276154189, 1113.66644452647, 747.093352541566, 858.247029841287, 917.230577685989, 390.29683477012, 339.650965997876, 350.536705877117, 295.394850812194, 502.711215489629, 465.29644549865, 398.753783734842, 328.660789278315, 747.883662637697, 2102.02108846944, 499.727307212846, 278.882398125705, 335.933513242034, 387.198765462081, 672.019128653175, 439.917678218736, 461.755563134383, 669.580269655421, 614.886877182468, 657.691667171562, 913.373865558921, 596.066409235456, 562.142375003233, 844.328711460744, 517.593907165227, 463.853902738299, 1087.39298812569, 583.363256443676, 601.337926899021, 720.657238588974, 386.421327566452, 493.072243052398, 493.072243052398, 493.072243052398, 487.416418391789, 625.768736956952, 717.442211022949, 649.545102325439, 315.764483006998, 387.279123698926, 725.770230770932, 534.438688677752, 265.753297513836, 265.753297513836, 275.266770483504, 444.714192650306, 357.226955834115, 466.694950404995, 521.878226495306, 514.492832530541, 401.82351113515, 308.781536524607, 410.920025494164, 506.942199600954, 426.771590593594, 444.329655290455, 567.951437149727, 314.044484679614, 341.637888287124, 390.011222091572, 371.617953454683, 491.650387255751, 309.86707973756, 339.215312155678, 401.313514123063, 274.198577993648, 366.737853359169, 602.621623875386, 397.5527766612, 431.743315417498, 502.103203876367, 758.493699184236, 354.616793574895, 495.299694296035, 445.994704272822, 461.179388784645, 492.398877810457, 300.177654706392, 351.604018662754, 397.001476569931, 443.325261537312, 495.754449130328, 597.467889923833, 495.384438403965, 563.913157758648, 890.789267794131, 326.949960612346, 296.399786939819, 336.191062827908, 406.145865402583, 678.81933687482, 997.557647439337, 365.6649642219, 415.242904378452, 543.581822640472, 310.924419326878, 519.951702825405, 751.022676264054, 422.151172626615, 604.684498888169, 836.51478813311, 277.051441764913, 287.126391607546, 327.57744312456, 343.712072517474, 408.684566875422, 535.079861284096 ]) Rquantreg.residuals = np.array([ -23.1071072288498, -16.7035925924416, 13.4842301424879, 36.0952280042049, 83.7430928106889, 143.666615246444, 187.391321726407, 196.904426307396, 194.552540223671, 105.623928368427, 25.8363284299391, 54.4440518161423, 92.0934604769094, 118.926894162067, 115.9422447507, 211.714461564889, 67.4824476183351, 93.7875665496341, 158.517491105043, 27.7332282843317, 78.537815573821, 32.3425283712905, 3.88323401131549, 51.360750756311, 33.6032971350797, 53.6215045819588, 73.423561609355, 6.00566204286901, 93.6248004402887, 78.1042405680565, 71.4819720245138, 42.635363803128, 100.508824022316, 114.377859224531, 190.661878666847, 120.44727756794, 74.7742708230821, 61.3298388891191, 80.7338623237625, 56.3613389354645, 14.9298935780977, 136.086423177107, 103.639168918795, 83.406904735325, 29.1204765079443, 43.2188638018142, 87.68702809519, 195.534593927816, 133.719017238015, 350.614829501073, 119.230897841979, 140.205463451968, 296.7772153462, 218.915256717207, 62.7756642652107, 155.675830060721, 288.990008558354, 322.6267348787, 788.540488171593, 109.906163322267, 538.923550476946, 121.241446063999, 132.774973479468, 119.128384587689, 183.709108010048, 67.2007219409504, 43.5425230980599, 161.49786961119, -7.94264590491014, 344.200840210711, 113.698279589573, 123.317422174319, -29.9069666643728, -25.6016916976065, 163.691619008174, 113.036341875648, 8.59293713333579, 61.3520511228119, 141.397517015987, 184.594660239251, 94.1259408216085, 79.6405061341515, 91.6733481942127, 113.234603595283, 161.045070172193, 225.290448255665, 226.095598886257, 160.387924286533, 32.4551953759993, 103.909707216036, 73.543904350086, 313.336630439861, 319.717144678425, 374.616677214425, 220.710022883649, 137.027675366142, 172.507934775539, 254.168723294869, 180.994568087336, 247.26860148984, 72.4144228992704, 14.0322012670994, 29.7478676180694, 91.1972063421171, -271.391948301552, -1.13686837721616e-13, -43.7483617057195, -45.7799925843755, 316.918702117259, 263.070052700293, -26.2008042070246, 185.270818370404, 128.400761958987, 126.90766445377, 39.11640958216, 13.8128950328002, 125.400191450337, 10.1671163220818, 453.849292287238, 60.1679571929374, -37.0832869573327, 29.6859273527971, -18.5990635840888, 32.0472277998125, 187.478653019356, 131.972664872163, 54.6380484088667, 592.550594160211, 93.7637141660844, 60.0193510971532, 93.5633996863289, -46.5847395899585, 25.0901440883857, 35.3349035566588, 38.0569510057356, 46.1382548463761, -21.4915275364559, -274.821124029843, 23.7637774954742, 56.1174237129451, 137.267370647069, 194.004180243594, 257.734838779675, 151.279738459292, 175.792712085095, 5.37066578891586, 161.87201799729, 301.825301306357, 337.590468355399, 141.753670144823, 248.534867350933, 138.672153434971, 191.302922030722, 169.266111420092, 337.411668163301, 247.595365061674, 324.241547334534, 441.345158140916, -2.96336484193375, 128.045086149367, 128.045086149367, 128.045086149367, 61.183812841238, 119.466557499153, 120.358284525061, 145.795139311381, 102.833084929086, 121.51832618868, 157.507780852421, 208.08888035649, -23.4330955930956, -23.4330955930956, -9.26578861762408, 170.044609958764, 28.0914420512634, 48.9250186205624, 186.600476930648, 219.742798279756, 31.1774726408891, 18.6372355131512, 18.1199081442213, 112.698628091063, -25.9726125403696, 176.470984835994, 252.045003846191, 46.8335329758523, 54.1229163256514, 51.9888300300891, 32.4204776768067, 179.14892185478, -12.2969284011601, 14.2728509760057, -17.3759292437432, 10.6022252751131, 64.362111397076, 198.730134737533, 50.898482335236, 146.167755331756, 68.4178084237137, 106.826836694182, 89.9409707510827, 185.120132493866, 130.283190180665, 170.618786347098, 116.24297250849, 0.822265604206791, 26.3943953963694, 0, 145.19420242141, 186.007125906439, 209.892380176326, 201.416658681816, 247.283084092749, 414.930873548859, 115.050091509315, 57.2015105045924, 131.809734683313, 120.611481397197, 211.419693391706, 321.245634797383, -34.6644264712713, 1.15862100546684, 53.2587319600932, 97.5747986822971, 255.069199707627, 387.139369759176, 63.3685935821613, 168.076643464964, 157.44822913826, 28.387531965303, 19.3926869633912, -28.3781151570223, 124.288724993746, 113.917339005042, 215.240302135105 ]) statsmodels-0.12.2/statsmodels/regression/tests/results/results_regression.py000066400000000000000000000231301400612667500300440ustar00rootroot00000000000000""" Hard-coded results for test_regression """ # REGRESSION MODEL RESULTS : OLS, GLS, WLS, AR import numpy as np class Longley(object): ''' The results for the Longley dataset were obtained from NIST http://www.itl.nist.gov/div898/strd/general/dataarchive.html Other results were obtained from Stata ''' def __init__(self): self.params = ( 15.0618722713733, -0.358191792925910E-01, -2.02022980381683, -1.03322686717359, -0.511041056535807E-01, 1829.15146461355, -3482258.63459582) self.bse = ( 84.9149257747669, 0.334910077722432E-01, 0.488399681651699, 0.214274163161675, 0.226073200069370, 455.478499142212, 890420.383607373) self.scale = 92936.0061673238 self.rsquared = 0.995479004577296 self.rsquared_adj = 0.99246501 self.df_model = 6 self.df_resid = 9 self.ess = 184172401.944494 self.ssr = 836424.055505915 self.mse_model = 30695400.3240823 self.mse_resid = 92936.0061673238 self.mse_total = (self.ess + self.ssr)/(self.df_model + self.df_resid) self.fvalue = 330.285339234588 self.llf = -109.6174 self.aic = 233.2349 self.bic = 238.643 self.pvalues = np.array([ 0.86314083, 0.31268106, 0.00253509, 0.00094437, 0.8262118, 0.0030368, 0.0035604]) # pvalues from rmodelwrap self.resid = np.array(( 267.34003, -94.01394, 46.28717, -410.11462, 309.71459, -249.31122, -164.04896, -13.18036, 14.30477, 455.39409, -17.26893, -39.05504, -155.54997, -85.67131, 341.93151, -206.75783)) # Obtained from R using # m$residuals / sqrt(sum(m$residuals * m$residuals) / m$df.residual) self.resid_pearson = np.array(( 0.87694426, -0.30838998, 0.15183385, -1.34528175, 1.01594375, -0.81780510, -0.53812289, -0.04323497, 0.04692334, 1.49381010, -0.05664654, -0.12811061, -0.51024404, -0.28102399, 1.12162357, -0.67821900)) def conf_int(self): # a method to be consistent with sm return [ (-177.0291, 207.1524), (-.111581, .0399428), (-3.125065, -.9153928), (-1.517948, -.5485049), (-.5625173, .4603083), (798.7873, 2859.515), (-5496529, -1467987)] HC0_se = (51.22035, 0.02458, 0.38324, 0.14625, 0.15821, 428.38438, 832212) HC1_se = (68.29380, 0.03277, 0.51099, 0.19499, 0.21094, 571.17917, 1109615) HC2_se = (67.49208, 0.03653, 0.55334, 0.20522, 0.22324, 617.59295, 1202370) HC3_se = (91.11939, 0.05562, 0.82213, 0.29879, 0.32491, 922.80784, 1799477) class LongleyGls(object): ''' The following results were obtained from running the test script with R. ''' def __init__(self): self.params = (6.73894832e-02, -4.74273904e-01, 9.48988771e+04) self.bse = (1.07033903e-02, 1.53385472e-01, 1.39447723e+04) self.llf = -121.4294962954981 self.fittedvalues = [ 59651.8255, 60860.1385, 60226.5336, 61467.1268, 63914.0846, 64561.9553, 64935.9028, 64249.1684, 66010.0426, 66834.7630, 67612.9309, 67018.8998, 68918.7758, 69310.1280, 69181.4207, 70598.8734] self.resid = [ 671.174465, 261.861502, -55.533603, -280.126803, -693.084618, -922.955349, 53.097212, -488.168351, 8.957367, 1022.236970, 556.069099, -505.899787, -263.775842, 253.871965, 149.579309, -47.873374] self.scale = 542.443043098**2 self.tvalues = [6.296088, -3.092039, 6.805337] self.pvalues = [2.761673e-05, 8.577197e-03, 1.252284e-05] self.bic = 253.118790021 self.aic = 250.858992591 class CCardWLS(object): def __init__(self): self.params = [ -2.6941851611, 158.426977524, -7.24928987289, 60.4487736936, -114.10886935] self.bse = [ 3.807306306, 76.39115431, 9.724337321, 58.55088753, 139.6874965] # NOTE: we compute the scale differently than they do for analytic # weights self.scale = 189.0025755829012 ** 2 self.rsquared = .2549143871187359 self.rsquared_adj = .2104316639616448 self.df_model = 4 self.df_resid = 67 self.ess = 818838.8079468152 self.ssr = 2393372.229657007 self.mse_model = 818838.8079468152 / 4 self.mse_resid = 2393372.229657007 / 67 self.mse_total = (self.ess + self.ssr) / 71. self.fvalue = 5.730638077585917 self.llf = -476.9792946562806 self.aic = 963.95858931256 self.bic = 975.34191990764 # pvalues from R self.pvalues = [ 0.4816259843354, 0.0419360764848, 0.4585895209814, 0.3055904431658, 0.4168883565685] self.resid = [ -286.964904785, -128.071563721, -405.860900879, -20.1363945007, -169.824432373, -82.6842575073, -283.314300537, -52.1719360352, 433.822174072, -190.607543945, -118.839683533, -133.97076416, -85.5728149414, 66.8180847168, -107.571769714, -149.883285522, -140.972610474, 75.9255981445, -135.979736328, -415.701263428, 130.080032349, 25.2313785553, 1042.14013672, -75.6622238159, 177.336639404, 315.870544434, -8.72801017761, 240.823760986, 54.6106033325, 65.6312484741, -40.9218444824, 24.6115856171, -131.971786499, 36.1587944031, 92.5052108765, -136.837036133, 242.73274231, -65.0315093994, 20.1536407471, -15.8874826431, 27.3513431549, -173.861785889, -113.121154785, -37.1303443909, 1510.31530762, 582.916931152, -17.8628063202, -132.77381897, -108.896934509, 12.4665794373, -122.014572144, -158.986968994, -175.798873901, 405.886505127, 99.3692703247, 85.3450698853, -179.15007019, -34.1245117188, -33.4909172058, -20.7287139893, -116.217689514, 53.8837738037, -52.1533050537, -100.632293701, 34.9342498779, -96.6685943604, -367.32925415, -40.1300048828, -72.8692245483, -60.8728256226, -35.9937324524, -222.944747925] self.resid_pearson = [ -0.90569581, -0.75496938, -1.28663890, -0.11309411, -0.24746253, -0.47181831, -1.02062293, -0.31403683, 1.62862142, -0.84973225, -0.42919669, -0.78007426, -0.63913772, 0.29787637, -0.38364568, -0.21381846, -0.85577361, 0.54156452, -0.48496031, -1.15374603, 0.41145856, 0.23996158, 2.70305838, -0.53171027, 0.79057028, 1.82433320, -0.04150362, 0.97048328, 0.13667658, 0.26750667, -0.12690810, 0.11703354, -0.72689772, 0.34160874, 0.71332338, -0.75079661, 1.73137185, -0.39477348, 0.04107215, -0.11332274, 0.22952063, -0.88580496, -0.67239515, -0.17656300, 4.48867723, 2.61499898, -0.16988320, -0.63136893, -0.68135396, 0.06351572, -0.64467367, -0.37800911, -0.64304809, 1.88607184, 0.57624742, 0.60875207, -0.78636761, -0.17897383, -0.21716827, -0.07885570, -0.57566752, 0.25202879, -0.29176531, -0.54378274, 0.30203654, -0.57460072, -0.72378394, -0.23853382, -0.17325464, -0.24121979, -0.10269489, -0.57826451] def conf_int(self): # a method to be consistent with sm return [ (-10.2936, 4.90523), (5.949595, 310.9044), (-26.65915, 12.16057), (-56.41929, 177.3168), (-392.9263, 164.7085)] class LongleyRTO(object): def __init__(self): # Regression Through the Origin model # from Stata, make sure you force double to replicate self.params = [ -52.993523, .07107319, -.42346599, -.57256869, -.41420348, 48.417859] self.bse = [ 129.5447812, .0301663805, .4177363573, .2789908665, .3212848136, 17.68947719] self.scale = 475.1655079819532**2 self.rsquared = .9999670130705958 self.rsquared_adj = .9999472209129532 self.df_model = 6 self.df_resid = 10 self.ess = 68443718827.40025 self.ssr = 2257822.599757476 self.mse_model = 68443718827.40025 / 6 self.mse_resid = 2257822.599757476 / 10 self.mse_total = (self.ess + self.ssr) / 16. self.fvalue = 50523.39573737409 self.llf = -117.5615983965251 self.aic = 247.123196793 self.bic = 251.758729126 self.pvalues = [ 0.6911082828354, 0.0402241925699, 0.3346175334102, 0.0672506018552, 0.2263470345100, 0.0209367642585] self.resid = [ 279.902740479, -130.324661255, 90.7322845459, -401.312530518, -440.467681885, -543.54510498, 201.321121216, 215.908889771, 73.0936813354, 913.216918945, 424.824859619, -8.56475830078, -361.329742432, 27.3456058502, 151.28956604, -492.499359131] # Obtained from R using # m$residuals / sqrt(sum(m$residuals * m$residuals) / m$df.residual) self.resid_pearson = [ 0.58906369, -0.27427213, 0.19094881, -0.84457419, -0.92697740, -1.14390695, 0.42368630, 0.45438671, 0.15382784, 1.92189233, 0.89405658, -0.01802479, -0.76042924, 0.05754964, 0.31839340, -1.03647964] def conf_int(self): return [ (-341.6373, 235.6502), (.0038583, .1382881), (-1.354241, .5073086), (-1.194199, .0490617), (-1.130071, .3016637), (9.003248, 87.83247)] statsmodels-0.12.2/statsmodels/regression/tests/results/results_rls_R.csv000066400000000000000000000337161400612667500271230ustar00rootroot00000000000000"beta1","beta2","rec_resid","cusum" 20.0003289473666,0.0651315789473821,0.244954345907551,0.00193563605335298 27.2660687432794,0.01385606874334,0.203040661455013,0.00354006900657476 38.67905442175,-0.0670068027209533,0.270280443387117,0.00567583258651052 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statsmodels-0.12.2/statsmodels/regression/tests/results/results_theil_textile.py000066400000000000000000000042311400612667500305300ustar00rootroot00000000000000import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch est = dict( rmse=.0136097497582343, r2=.9741055881598619, N=17, df_r=14, compat=.860625753607033, vrank=2, pvalue=.6503055973535645, frac_sample=.7935370014985163, frac_prior=.2064629985014838, cmd="tgmixed", predict="regres_p", depvar="lconsump", marginsok="XB default", cmdline="tgmixed lconsump lincome lprice, prior(lprice -0.7 0.15 lincome 1 0.15) cov(lprice lincome -0.01)", # noqa:E501 prior="lprice -0.7 0.15 lincome 1 0.15", properties="b V", ) params_table = np.array([ 1.0893571039001, .10338923727975, 10.53646523141, 4.871483239e-08, .86760924410848, 1.3111049636916, 14, 2.1447866879178, 0, -.82054628653043, .03496499383295, -23.467651401591, 1.218701708e-12, -.89553873984647, -.74555383321439, 14, 2.1447866879178, 0, 1.4666439879147, .20347802665937, 7.2078740490733, 4.509300573e-06, 1.0302270250519, 1.9030609507775, 14, 2.1447866879178, 0]).reshape(3, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = 'lincome lprice _cons'.split() cov = np.array([ .01068933438529, -.00081953185523, -.0199747086722, -.00081953185523, .00122255079374, -.00064024357954, -.0199747086722, -.00064024357954, .04140330733319]).reshape(3, 3) cov_colnames = 'lincome lprice _cons'.split() cov_rownames = 'lincome lprice _cons'.split() cov_prior = np.array([ .0225, -.01, 0, -.01, .0225, 0, 0, 0, 0]).reshape(3, 3) cov_prior_colnames = 'lincome lprice _cons'.split() cov_prior_rownames = 'lincome lprice _cons'.split() results_theil_textile = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, cov_prior=cov_prior, cov_prior_colnames=cov_prior_colnames, cov_prior_rownames=cov_prior_rownames, **est ) statsmodels-0.12.2/statsmodels/regression/tests/results/test_rls.R000066400000000000000000000012461400612667500255170ustar00rootroot00000000000000library(quantreg) library(strucchange) macrodata <- read.csv('/Users/fulton/projects/statsmodels/statsmodels/datasets/macrodata/macrodata.csv') y <- macrodata$cpi X <- cbind(rep(1, nrow(macrodata)), macrodata$m1) rec_beta <- lm.fit.recursive(X, y, int=FALSE) rec_resid <- recresid(cpi ~ 1 + m1, data=macrodata) cusum <- efp(cpi ~ 1 + m1, data=macrodata, type=c("Rec-CUSUM")) output <- data.frame(cbind(t(rec_beta[,3:203]), rec_resid, cusum$process[2:202])) names(output) <- c('beta1', 'beta2', 'rec_resid', 'cusum') write.csv(output, '/Users/fulton/projects/statsmodels/statsmodels/regression/tests/results/results_rls_R.csv', row.names=FALSE) print(cusum$sigma) # 9.163565 statsmodels-0.12.2/statsmodels/regression/tests/results/test_rls.do000066400000000000000000000011541400612667500257160ustar00rootroot00000000000000insheet using /Users/fulton/projects/statsmodels/statsmodels/datasets/macrodata/macrodata.csv, clear gen tq = yq(year, quarter) format tq %tq tsset tq cusum6 cpi m1, rr(rr) cs(cusum) lw(lw) uw(uw) cs2(cusum2) lww(lww) uww(uww) noplot outsheet rr-lww using results_rls_stata.csv, comma replace // Section for restricted least squares constraint 1 m1 + unemp = 1 cnsreg infl m1 unemp, c(1) disp %18.13f e(ll) // -534.4292052931121 matrix list e(b), format(%15.13f) // -0.0018477514060 1.0018477514060 -0.7001083844336 mata: se=sqrt(diagonal(st_matrix("e(V)"))) mata: se // .0005369357, .0005369357, .4699552366 statsmodels-0.12.2/statsmodels/regression/tests/results/theil_textile_predict.csv000066400000000000000000000005551400612667500306310ustar00rootroot00000000000000fittedvalues,fittedvalues_se 1.984849,.0067426 1.9948384,.00629217 2.0042656,.00589781 2.0620794,.00437274 2.0785806,.00396735 2.0859353,.00479328 2.0879624,.00511938 2.1264076,.00510187 2.1729304,.00450289 2.180025,.00410166 2.1866386,.00438359 2.1494782,.00502813 2.1481932,.00468026 2.2217135,.00622614 2.1993129,.00468301 2.1967881,.0046891 2.1963122,.00451292 statsmodels-0.12.2/statsmodels/regression/tests/test_cov.py000066400000000000000000000022411400612667500242300ustar00rootroot00000000000000"""Example: minimal OLS """ import numpy as np from numpy.testing import assert_almost_equal, assert_allclose import statsmodels.api as sm def test_HC_use(): np.random.seed(0) nsample = 100 x = np.linspace(0,10, 100) X = sm.add_constant(np.column_stack((x, x**2)), prepend=False) beta = np.array([1, 0.1, 10]) y = np.dot(X, beta) + np.random.normal(size=nsample) results = sm.OLS(y, X).fit() # test cov_params idx = np.array([1, 2]) cov12 = results.cov_params(column=[1, 2], cov_p=results.cov_HC0) assert_almost_equal(cov12, results.cov_HC0[idx[:, None], idx], decimal=15) #test t_test tvals = results.params/results.HC0_se ttest = results.t_test(np.eye(3), cov_p=results.cov_HC0) assert_almost_equal(ttest.tvalue, tvals, decimal=14) assert_almost_equal(ttest.sd, results.HC0_se, decimal=14) #test f_test ftest = results.f_test(np.eye(3)[:-1], cov_p=results.cov_HC0) slopes = results.params[:-1] idx = np.array([0,1]) cov_slopes = results.cov_HC0[idx[:,None], idx] fval = np.dot(slopes, np.dot(np.linalg.inv(cov_slopes), slopes))/len(idx) assert_allclose(ftest.fvalue, fval, rtol=12) statsmodels-0.12.2/statsmodels/regression/tests/test_dimred.py000066400000000000000000000150321400612667500247070ustar00rootroot00000000000000import numpy as np import pandas as pd import pytest from statsmodels.regression.dimred import ( SlicedInverseReg, SAVE, PHD, CORE) from numpy.testing import (assert_equal, assert_allclose) from statsmodels.tools.numdiff import approx_fprime def test_poisson(): np.random.seed(43242) # Generate a non-orthogonal design matrix xmat = np.random.normal(size=(500, 5)) xmat[:, 1] = 0.5*xmat[:, 0] + np.sqrt(1 - 0.5**2) * xmat[:, 1] xmat[:, 3] = 0.5*xmat[:, 2] + np.sqrt(1 - 0.5**2) * xmat[:, 3] b = np.r_[0, 1, -1, 0, 0.5] lpr = np.dot(xmat, b) ev = np.exp(lpr) y = np.random.poisson(ev) for method in range(6): if method == 0: model = SlicedInverseReg(y, xmat) rslt = model.fit() elif method == 1: model = SAVE(y, xmat) rslt = model.fit(slice_n=100) elif method == 2: model = SAVE(y, xmat, bc=True) rslt = model.fit(slice_n=100) elif method == 3: df = pd.DataFrame({"y": y, "x0": xmat[:, 0], "x1": xmat[:, 1], "x2": xmat[:, 2], "x3": xmat[:, 3], "x4": xmat[:, 4]}) model = SlicedInverseReg.from_formula( "y ~ 0 + x0 + x1 + x2 + x3 + x4", data=df) rslt = model.fit() elif method == 4: model = PHD(y, xmat) rslt = model.fit() elif method == 5: model = PHD(y, xmat) rslt = model.fit(resid=True) # Check for concentration in one direction (this is # a single index model) assert_equal(np.abs(rslt.eigs[0] / rslt.eigs[1]) > 5, True) # Check that the estimated direction aligns with the true # direction params = np.asarray(rslt.params) q = np.dot(params[:, 0], b) q /= np.sqrt(np.sum(params[:, 0]**2)) q /= np.sqrt(np.sum(b**2)) assert_equal(np.abs(q) > 0.95, True) def test_sir_regularized_numdiff(): # Use numeric gradients to check the analytic gradient # for the regularized SIRobjective function. np.random.seed(93482) n = 1000 p = 10 xmat = np.random.normal(size=(n, p)) y1 = np.dot(xmat, np.linspace(-1, 1, p)) y2 = xmat.sum(1) y = y2 / (1 + y1**2) + np.random.normal(size=n) model = SlicedInverseReg(y, xmat) _ = model.fit() # Second difference penalty matrix. fmat = np.zeros((p-2, p)) for i in range(p-2): fmat[i, i:i+3] = [1, -2, 1] with pytest.warns(UserWarning, match="SIR.fit_regularized did not"): _ = model.fit_regularized(2, 3*fmat) # Compare the gradients to the numerical derivatives for _ in range(5): pa = np.random.normal(size=(p, 2)) pa, _, _ = np.linalg.svd(pa, 0) gn = approx_fprime(pa.ravel(), model._regularized_objective, 1e-7) gr = model._regularized_grad(pa.ravel()) assert_allclose(gn, gr, atol=1e-5, rtol=1e-4) def test_sir_regularized_1d(): # Compare regularized SIR to traditional SIR, in a setting where the # regularization is compatible with the true parameters (i.e. there # is no regularization bias). np.random.seed(93482) n = 1000 p = 10 xmat = np.random.normal(size=(n, p)) y = np.dot(xmat[:, 0:4], np.r_[1, 1, -1, -1]) + np.random.normal(size=n) model = SlicedInverseReg(y, xmat) rslt = model.fit() # The penalty drives p[0] ~ p[1] and p[2] ~ p[3]] fmat = np.zeros((2, p)) fmat[0, 0:2] = [1, -1] fmat[1, 2:4] = [1, -1] rslt2 = model.fit_regularized(1, 3*fmat) pa0 = np.zeros(p) pa0[0:4] = [1, 1, -1, -1] pa1 = rslt.params[:, 0] pa2 = rslt2.params[:, 0:2] # Compare two 1d subspaces def sim(x, y): x = x / np.sqrt(np.sum(x * x)) y = y / np.sqrt(np.sum(y * y)) return 1 - np.abs(np.dot(x, y)) # Regularized SIRshould be closer to the truth than traditional SIR assert_equal(sim(pa0, pa1) > sim(pa0, pa2), True) # Regularized SIR should be close to the truth assert_equal(sim(pa0, pa2) < 1e-3, True) # Regularized SIR should have a smaller penalty value than traditional SIR assert_equal(np.sum(np.dot(fmat, pa1)**2) > np.sum(np.dot(fmat, pa2)**2), True) def test_sir_regularized_2d(): # Compare regularized SIR to traditional SIR when there is no penalty. # The two procedures should agree exactly. np.random.seed(93482) n = 1000 p = 10 xmat = np.random.normal(size=(n, p)) y1 = np.dot(xmat[:, 0:4], np.r_[1, 1, -1, -1]) y2 = np.dot(xmat[:, 4:8], np.r_[1, 1, -1, -1]) y = y1 + np.arctan(y2) + np.random.normal(size=n) model = SlicedInverseReg(y, xmat) rslt1 = model.fit() fmat = np.zeros((1, p)) for d in 1, 2, 3, 4: if d < 3: rslt2 = model.fit_regularized(d, fmat) else: with pytest.warns(UserWarning, match="SIR.fit_regularized did"): rslt2 = model.fit_regularized(d, fmat) pa1 = rslt1.params[:, 0:d] pa1, _, _ = np.linalg.svd(pa1, 0) pa2 = rslt2.params _, s, _ = np.linalg.svd(np.dot(pa1.T, pa2)) assert_allclose(np.sum(s), d, atol=1e-1, rtol=1e-1) def test_covreduce(): np.random.seed(34324) p = 4 endog = [] exog = [] for k in range(3): c = np.eye(p) x = np.random.normal(size=(2, 2)) # The differences between the covariance matrices # are all in the first 2 rows/columns. c[0:2, 0:2] = np.dot(x.T, x) cr = np.linalg.cholesky(c) m = 1000*k + 50*k x = np.random.normal(size=(m, p)) x = np.dot(x, cr.T) exog.append(x) endog.append(k * np.ones(m)) endog = np.concatenate(endog) exog = np.concatenate(exog, axis=0) for dim in 1, 2, 3: cr = CORE(endog, exog, dim) pt = np.random.normal(size=(p, dim)) pt, _, _ = np.linalg.svd(pt, 0) gn = approx_fprime(pt.ravel(), cr.loglike, 1e-7) g = cr.score(pt.ravel()) assert_allclose(g, gn, 1e-5, 1e-5) rslt = cr.fit() proj = rslt.params assert_equal(proj.shape[0], p) assert_equal(proj.shape[1], dim) assert_allclose(np.dot(proj.T, proj), np.eye(dim), 1e-8, 1e-8) if dim == 2: # Here we know the approximate truth projt = np.zeros((p, 2)) projt[0:2, 0:2] = np.eye(2) assert_allclose(np.trace(np.dot(proj.T, projt)), 2, rtol=1e-3, atol=1e-3) statsmodels-0.12.2/statsmodels/regression/tests/test_glsar_gretl.py000066400000000000000000000625441400612667500257620ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Tests of GLSAR and diagnostics against Gretl Created on Thu Feb 02 21:15:47 2012 Author: Josef Perktold License: BSD-3 """ import os import numpy as np from numpy.testing import (assert_almost_equal, assert_equal, assert_allclose, assert_array_less) from statsmodels.regression.linear_model import OLS, GLSAR from statsmodels.tools.tools import add_constant from statsmodels.datasets import macrodata import statsmodels.stats.sandwich_covariance as sw import statsmodels.stats.diagnostic as smsdia import statsmodels.stats.outliers_influence as oi def compare_ftest(contrast_res, other, decimal=(5,4)): assert_almost_equal(contrast_res.fvalue, other[0], decimal=decimal[0]) assert_almost_equal(contrast_res.pvalue, other[1], decimal=decimal[1]) assert_equal(contrast_res.df_num, other[2]) assert_equal(contrast_res.df_denom, other[3]) assert_equal("f", other[4]) class TestGLSARGretl(object): def test_all(self): d = macrodata.load_pandas().data #import datasetswsm.greene as g #d = g.load('5-1') #growth rates gs_l_realinv = 400 * np.diff(np.log(d['realinv'].values)) gs_l_realgdp = 400 * np.diff(np.log(d['realgdp'].values)) #simple diff, not growthrate, I want heteroscedasticity later for testing endogd = np.diff(d['realinv']) exogd = add_constant(np.c_[np.diff(d['realgdp'].values), d['realint'][:-1].values]) endogg = gs_l_realinv exogg = add_constant(np.c_[gs_l_realgdp, d['realint'][:-1].values]) res_ols = OLS(endogg, exogg).fit() #print res_ols.params mod_g1 = GLSAR(endogg, exogg, rho=-0.108136) res_g1 = mod_g1.fit() #print res_g1.params mod_g2 = GLSAR(endogg, exogg, rho=-0.108136) #-0.1335859) from R res_g2 = mod_g2.iterative_fit(maxiter=5) #print res_g2.params rho = -0.108136 # coefficient std. error t-ratio p-value 95% CONFIDENCE INTERVAL partable = np.array([ [-9.50990, 0.990456, -9.602, 3.65e-018, -11.4631, -7.55670], # *** [ 4.37040, 0.208146, 21.00, 2.93e-052, 3.95993, 4.78086], # *** [-0.579253, 0.268009, -2.161, 0.0319, -1.10777, -0.0507346]]) # ** #Statistics based on the rho-differenced data: result_gretl_g1 = dict( endog_mean = ("Mean dependent var", 3.113973), endog_std = ("S.D. dependent var", 18.67447), ssr = ("Sum squared resid", 22530.90), mse_resid_sqrt = ("S.E. of regression", 10.66735), rsquared = ("R-squared", 0.676973), rsquared_adj = ("Adjusted R-squared", 0.673710), fvalue = ("F(2, 198)", 221.0475), f_pvalue = ("P-value(F)", 3.56e-51), resid_acf1 = ("rho", -0.003481), dw = ("Durbin-Watson", 1.993858)) #fstatistic, p-value, df1, df2 reset_2_3 = [5.219019, 0.00619, 2, 197, "f"] reset_2 = [7.268492, 0.00762, 1, 198, "f"] reset_3 = [5.248951, 0.023, 1, 198, "f"] #LM-statistic, p-value, df arch_4 = [7.30776, 0.120491, 4, "chi2"] #multicollinearity vif = [1.002, 1.002] cond_1norm = 6862.0664 determinant = 1.0296049e+009 reciprocal_condition_number = 0.013819244 #Chi-square(2): test-statistic, pvalue, df normality = [20.2792, 3.94837e-005, 2] #tests res = res_g1 #with rho from Gretl #basic assert_almost_equal(res.params, partable[:,0], 4) assert_almost_equal(res.bse, partable[:,1], 6) assert_almost_equal(res.tvalues, partable[:,2], 2) assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2) #assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl #assert_almost_equal(res.rsquared, result_gretl_g1['rsquared'][1], decimal=7) #FAIL #assert_almost_equal(res.rsquared_adj, result_gretl_g1['rsquared_adj'][1], decimal=7) #FAIL assert_almost_equal(np.sqrt(res.mse_resid), result_gretl_g1['mse_resid_sqrt'][1], decimal=5) assert_almost_equal(res.fvalue, result_gretl_g1['fvalue'][1], decimal=4) assert_allclose(res.f_pvalue, result_gretl_g1['f_pvalue'][1], rtol=1e-2) #assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO #arch #sm_arch = smsdia.acorr_lm(res.wresid**2, maxlag=4, autolag=None) sm_arch = smsdia.het_arch(res.wresid, nlags=4) assert_almost_equal(sm_arch[0], arch_4[0], decimal=4) assert_almost_equal(sm_arch[1], arch_4[1], decimal=6) #tests res = res_g2 #with estimated rho #estimated lag coefficient assert_almost_equal(res.model.rho, rho, decimal=3) #basic assert_almost_equal(res.params, partable[:,0], 4) assert_almost_equal(res.bse, partable[:,1], 3) assert_almost_equal(res.tvalues, partable[:,2], 2) assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2) #assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl #assert_almost_equal(res.rsquared, result_gretl_g1['rsquared'][1], decimal=7) #FAIL #assert_almost_equal(res.rsquared_adj, result_gretl_g1['rsquared_adj'][1], decimal=7) #FAIL assert_almost_equal(np.sqrt(res.mse_resid), result_gretl_g1['mse_resid_sqrt'][1], decimal=5) assert_almost_equal(res.fvalue, result_gretl_g1['fvalue'][1], decimal=0) assert_almost_equal(res.f_pvalue, result_gretl_g1['f_pvalue'][1], decimal=6) #assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO c = oi.reset_ramsey(res, degree=2) compare_ftest(c, reset_2, decimal=(2,4)) c = oi.reset_ramsey(res, degree=3) compare_ftest(c, reset_2_3, decimal=(2,4)) #arch #sm_arch = smsdia.acorr_lm(res.wresid**2, maxlag=4, autolag=None) sm_arch = smsdia.het_arch(res.wresid, nlags=4) assert_almost_equal(sm_arch[0], arch_4[0], decimal=1) assert_almost_equal(sm_arch[1], arch_4[1], decimal=2) ''' Performing iterative calculation of rho... ITER RHO ESS 1 -0.10734 22530.9 2 -0.10814 22530.9 Model 4: Cochrane-Orcutt, using observations 1959:3-2009:3 (T = 201) Dependent variable: ds_l_realinv rho = -0.108136 coefficient std. error t-ratio p-value ------------------------------------------------------------- const -9.50990 0.990456 -9.602 3.65e-018 *** ds_l_realgdp 4.37040 0.208146 21.00 2.93e-052 *** realint_1 -0.579253 0.268009 -2.161 0.0319 ** Statistics based on the rho-differenced data: Mean dependent var 3.113973 S.D. dependent var 18.67447 Sum squared resid 22530.90 S.E. of regression 10.66735 R-squared 0.676973 Adjusted R-squared 0.673710 F(2, 198) 221.0475 P-value(F) 3.56e-51 rho -0.003481 Durbin-Watson 1.993858 ''' ''' RESET test for specification (squares and cubes) Test statistic: F = 5.219019, with p-value = P(F(2,197) > 5.21902) = 0.00619 RESET test for specification (squares only) Test statistic: F = 7.268492, with p-value = P(F(1,198) > 7.26849) = 0.00762 RESET test for specification (cubes only) Test statistic: F = 5.248951, with p-value = P(F(1,198) > 5.24895) = 0.023: ''' ''' Test for ARCH of order 4 coefficient std. error t-ratio p-value -------------------------------------------------------- alpha(0) 97.0386 20.3234 4.775 3.56e-06 *** alpha(1) 0.176114 0.0714698 2.464 0.0146 ** alpha(2) -0.0488339 0.0724981 -0.6736 0.5014 alpha(3) -0.0705413 0.0737058 -0.9571 0.3397 alpha(4) 0.0384531 0.0725763 0.5298 0.5968 Null hypothesis: no ARCH effect is present Test statistic: LM = 7.30776 with p-value = P(Chi-square(4) > 7.30776) = 0.120491: ''' ''' Variance Inflation Factors Minimum possible value = 1.0 Values > 10.0 may indicate a collinearity problem ds_l_realgdp 1.002 realint_1 1.002 VIF(j) = 1/(1 - R(j)^2), where R(j) is the multiple correlation coefficient between variable j and the other independent variables Properties of matrix X'X: 1-norm = 6862.0664 Determinant = 1.0296049e+009 Reciprocal condition number = 0.013819244 ''' ''' Test for ARCH of order 4 - Null hypothesis: no ARCH effect is present Test statistic: LM = 7.30776 with p-value = P(Chi-square(4) > 7.30776) = 0.120491 Test of common factor restriction - Null hypothesis: restriction is acceptable Test statistic: F(2, 195) = 0.426391 with p-value = P(F(2, 195) > 0.426391) = 0.653468 Test for normality of residual - Null hypothesis: error is normally distributed Test statistic: Chi-square(2) = 20.2792 with p-value = 3.94837e-005: ''' #no idea what this is ''' Augmented regression for common factor test OLS, using observations 1959:3-2009:3 (T = 201) Dependent variable: ds_l_realinv coefficient std. error t-ratio p-value --------------------------------------------------------------- const -10.9481 1.35807 -8.062 7.44e-014 *** ds_l_realgdp 4.28893 0.229459 18.69 2.40e-045 *** realint_1 -0.662644 0.334872 -1.979 0.0492 ** ds_l_realinv_1 -0.108892 0.0715042 -1.523 0.1294 ds_l_realgdp_1 0.660443 0.390372 1.692 0.0923 * realint_2 0.0769695 0.341527 0.2254 0.8219 Sum of squared residuals = 22432.8 Test of common factor restriction Test statistic: F(2, 195) = 0.426391, with p-value = 0.653468 ''' ################ with OLS, HAC errors #Model 5: OLS, using observations 1959:2-2009:3 (T = 202) #Dependent variable: ds_l_realinv #HAC standard errors, bandwidth 4 (Bartlett kernel) #coefficient std. error t-ratio p-value 95% CONFIDENCE INTERVAL #for confidence interval t(199, 0.025) = 1.972 partable = np.array([ [-9.48167, 1.17709, -8.055, 7.17e-014, -11.8029, -7.16049], # *** [4.37422, 0.328787, 13.30, 2.62e-029, 3.72587, 5.02258], #*** [-0.613997, 0.293619, -2.091, 0.0378, -1.19300, -0.0349939]]) # ** result_gretl_g1 = dict( endog_mean = ("Mean dependent var", 3.257395), endog_std = ("S.D. dependent var", 18.73915), ssr = ("Sum squared resid", 22799.68), mse_resid_sqrt = ("S.E. of regression", 10.70380), rsquared = ("R-squared", 0.676978), rsquared_adj = ("Adjusted R-squared", 0.673731), fvalue = ("F(2, 199)", 90.79971), f_pvalue = ("P-value(F)", 9.53e-29), llf = ("Log-likelihood", -763.9752), aic = ("Akaike criterion", 1533.950), bic = ("Schwarz criterion", 1543.875), hqic = ("Hannan-Quinn", 1537.966), resid_acf1 = ("rho", -0.107341), dw = ("Durbin-Watson", 2.213805)) linear_logs = [1.68351, 0.430953, 2, "chi2"] #for logs: dropping 70 nan or incomplete observations, T=133 #(res_ols.model.exog <=0).any(1).sum() = 69 ?not 70 linear_squares = [7.52477, 0.0232283, 2, "chi2"] #Autocorrelation, Breusch-Godfrey test for autocorrelation up to order 4 lm_acorr4 = [1.17928, 0.321197, 4, 195, "F"] lm2_acorr4 = [4.771043, 0.312, 4, "chi2"] acorr_ljungbox4 = [5.23587, 0.264, 4, "chi2"] #break cusum_Harvey_Collier = [0.494432, 0.621549, 198, "t"] #stats.t.sf(0.494432, 198)*2 #see cusum results in files break_qlr = [3.01985, 0.1, 3, 196, "maxF"] #TODO check this, max at 2001:4 break_chow = [13.1897, 0.00424384, 3, "chi2"] # break at 1984:1 arch_4 = [3.43473, 0.487871, 4, "chi2"] normality = [23.962, 0.00001, 2, "chi2"] het_white = [33.503723, 0.000003, 5, "chi2"] het_breusch_pagan = [1.302014, 0.521520, 2, "chi2"] #TODO: not available het_breusch_pagan_konker = [0.709924, 0.701200, 2, "chi2"] reset_2_3 = [5.219019, 0.00619, 2, 197, "f"] reset_2 = [7.268492, 0.00762, 1, 198, "f"] reset_3 = [5.248951, 0.023, 1, 198, "f"] #not available cond_1norm = 5984.0525 determinant = 7.1087467e+008 reciprocal_condition_number = 0.013826504 vif = [1.001, 1.001] names = 'date residual leverage influence DFFITS'.split() cur_dir = os.path.abspath(os.path.dirname(__file__)) fpath = os.path.join(cur_dir, 'results/leverage_influence_ols_nostars.txt') lev = np.genfromtxt(fpath, skip_header=3, skip_footer=1, converters={0:lambda s: s}) #either numpy 1.6 or python 3.2 changed behavior if np.isnan(lev[-1]['f1']): lev = np.genfromtxt(fpath, skip_header=3, skip_footer=2, converters={0:lambda s: s}) lev.dtype.names = names res = res_ols #for easier copying cov_hac = sw.cov_hac_simple(res, nlags=4, use_correction=False) bse_hac = sw.se_cov(cov_hac) assert_almost_equal(res.params, partable[:,0], 5) assert_almost_equal(bse_hac, partable[:,1], 5) #TODO assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2) assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=4) #not in gretl assert_almost_equal(res.rsquared, result_gretl_g1['rsquared'][1], decimal=6) #FAIL assert_almost_equal(res.rsquared_adj, result_gretl_g1['rsquared_adj'][1], decimal=6) #FAIL assert_almost_equal(np.sqrt(res.mse_resid), result_gretl_g1['mse_resid_sqrt'][1], decimal=5) #f-value is based on cov_hac I guess #res2 = res.get_robustcov_results(cov_type='HC1') # TODO: fvalue differs from Gretl, trying any of the HCx #assert_almost_equal(res2.fvalue, result_gretl_g1['fvalue'][1], decimal=0) #FAIL #assert_approx_equal(res.f_pvalue, result_gretl_g1['f_pvalue'][1], significant=1) #FAIL #assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO c = oi.reset_ramsey(res, degree=2) compare_ftest(c, reset_2, decimal=(6,5)) c = oi.reset_ramsey(res, degree=3) compare_ftest(c, reset_2_3, decimal=(6,5)) linear_sq = smsdia.linear_lm(res.resid, res.model.exog) assert_almost_equal(linear_sq[0], linear_squares[0], decimal=6) assert_almost_equal(linear_sq[1], linear_squares[1], decimal=7) hbpk = smsdia.het_breuschpagan(res.resid, res.model.exog) assert_almost_equal(hbpk[0], het_breusch_pagan_konker[0], decimal=6) assert_almost_equal(hbpk[1], het_breusch_pagan_konker[1], decimal=6) hw = smsdia.het_white(res.resid, res.model.exog) assert_almost_equal(hw[:2], het_white[:2], 6) #arch #sm_arch = smsdia.acorr_lm(res.resid**2, maxlag=4, autolag=None) sm_arch = smsdia.het_arch(res.resid, nlags=4) assert_almost_equal(sm_arch[0], arch_4[0], decimal=5) assert_almost_equal(sm_arch[1], arch_4[1], decimal=6) vif2 = [oi.variance_inflation_factor(res.model.exog, k) for k in [1,2]] infl = oi.OLSInfluence(res_ols) #print np.max(np.abs(lev['DFFITS'] - infl.dffits[0])) #print np.max(np.abs(lev['leverage'] - infl.hat_matrix_diag)) #print np.max(np.abs(lev['influence'] - infl.influence)) #just added this based on Gretl #just rough test, low decimal in Gretl output, assert_almost_equal(lev['residual'], res.resid, decimal=3) assert_almost_equal(lev['DFFITS'], infl.dffits[0], decimal=3) assert_almost_equal(lev['leverage'], infl.hat_matrix_diag, decimal=3) assert_almost_equal(lev['influence'], infl.influence, decimal=4) def test_GLSARlag(): #test that results for lag>1 is close to lag=1, and smaller ssr from statsmodels.datasets import macrodata d2 = macrodata.load_pandas().data g_gdp = 400*np.diff(np.log(d2['realgdp'].values)) g_inv = 400*np.diff(np.log(d2['realinv'].values)) exogg = add_constant(np.c_[g_gdp, d2['realint'][:-1].values], prepend=False) mod1 = GLSAR(g_inv, exogg, 1) res1 = mod1.iterative_fit(5) mod4 = GLSAR(g_inv, exogg, 4) res4 = mod4.iterative_fit(10) assert_array_less(np.abs(res1.params / res4.params - 1), 0.03) assert_array_less(res4.ssr, res1.ssr) assert_array_less(np.abs(res4.bse / res1.bse) - 1, 0.015) assert_array_less(np.abs((res4.fittedvalues / res1.fittedvalues - 1).mean()), 0.015) assert_equal(len(mod4.rho), 4) if __name__ == '__main__': t = TestGLSARGretl() t.test_all() ''' Model 5: OLS, using observations 1959:2-2009:3 (T = 202) Dependent variable: ds_l_realinv HAC standard errors, bandwidth 4 (Bartlett kernel) coefficient std. error t-ratio p-value ------------------------------------------------------------- const -9.48167 1.17709 -8.055 7.17e-014 *** ds_l_realgdp 4.37422 0.328787 13.30 2.62e-029 *** realint_1 -0.613997 0.293619 -2.091 0.0378 ** Mean dependent var 3.257395 S.D. dependent var 18.73915 Sum squared resid 22799.68 S.E. of regression 10.70380 R-squared 0.676978 Adjusted R-squared 0.673731 F(2, 199) 90.79971 P-value(F) 9.53e-29 Log-likelihood -763.9752 Akaike criterion 1533.950 Schwarz criterion 1543.875 Hannan-Quinn 1537.966 rho -0.107341 Durbin-Watson 2.213805 QLR test for structural break - Null hypothesis: no structural break Test statistic: max F(3, 196) = 3.01985 at observation 2001:4 (10 percent critical value = 4.09) Non-linearity test (logs) - Null hypothesis: relationship is linear Test statistic: LM = 1.68351 with p-value = P(Chi-square(2) > 1.68351) = 0.430953 Non-linearity test (squares) - Null hypothesis: relationship is linear Test statistic: LM = 7.52477 with p-value = P(Chi-square(2) > 7.52477) = 0.0232283 LM test for autocorrelation up to order 4 - Null hypothesis: no autocorrelation Test statistic: LMF = 1.17928 with p-value = P(F(4,195) > 1.17928) = 0.321197 CUSUM test for parameter stability - Null hypothesis: no change in parameters Test statistic: Harvey-Collier t(198) = 0.494432 with p-value = P(t(198) > 0.494432) = 0.621549 Chow test for structural break at observation 1984:1 - Null hypothesis: no structural break Asymptotic test statistic: Chi-square(3) = 13.1897 with p-value = 0.00424384 Test for ARCH of order 4 - Null hypothesis: no ARCH effect is present Test statistic: LM = 3.43473 with p-value = P(Chi-square(4) > 3.43473) = 0.487871: #ANOVA Analysis of Variance: Sum of squares df Mean square Regression 47782.7 2 23891.3 Residual 22799.7 199 114.571 Total 70582.3 201 351.156 R^2 = 47782.7 / 70582.3 = 0.676978 F(2, 199) = 23891.3 / 114.571 = 208.528 [p-value 1.47e-049] #LM-test autocorrelation Breusch-Godfrey test for autocorrelation up to order 4 OLS, using observations 1959:2-2009:3 (T = 202) Dependent variable: uhat coefficient std. error t-ratio p-value ------------------------------------------------------------ const 0.0640964 1.06719 0.06006 0.9522 ds_l_realgdp -0.0456010 0.217377 -0.2098 0.8341 realint_1 0.0511769 0.293136 0.1746 0.8616 uhat_1 -0.104707 0.0719948 -1.454 0.1475 uhat_2 -0.00898483 0.0742817 -0.1210 0.9039 uhat_3 0.0837332 0.0735015 1.139 0.2560 uhat_4 -0.0636242 0.0737363 -0.8629 0.3893 Unadjusted R-squared = 0.023619 Test statistic: LMF = 1.179281, with p-value = P(F(4,195) > 1.17928) = 0.321 Alternative statistic: TR^2 = 4.771043, with p-value = P(Chi-square(4) > 4.77104) = 0.312 Ljung-Box Q' = 5.23587, with p-value = P(Chi-square(4) > 5.23587) = 0.264: RESET test for specification (squares and cubes) Test statistic: F = 5.219019, with p-value = P(F(2,197) > 5.21902) = 0.00619 RESET test for specification (squares only) Test statistic: F = 7.268492, with p-value = P(F(1,198) > 7.26849) = 0.00762 RESET test for specification (cubes only) Test statistic: F = 5.248951, with p-value = P(F(1,198) > 5.24895) = 0.023 #heteroscedasticity White White's test for heteroskedasticity OLS, using observations 1959:2-2009:3 (T = 202) Dependent variable: uhat^2 coefficient std. error t-ratio p-value ------------------------------------------------------------- const 104.920 21.5848 4.861 2.39e-06 *** ds_l_realgdp -29.7040 6.24983 -4.753 3.88e-06 *** realint_1 -6.93102 6.95607 -0.9964 0.3203 sq_ds_l_realg 4.12054 0.684920 6.016 8.62e-09 *** X2_X3 2.89685 1.38571 2.091 0.0379 ** sq_realint_1 0.662135 1.10919 0.5970 0.5512 Unadjusted R-squared = 0.165860 Test statistic: TR^2 = 33.503723, with p-value = P(Chi-square(5) > 33.503723) = 0.000003: #heteroscedasticity Breusch-Pagan (original) Breusch-Pagan test for heteroskedasticity OLS, using observations 1959:2-2009:3 (T = 202) Dependent variable: scaled uhat^2 coefficient std. error t-ratio p-value ------------------------------------------------------------- const 1.09468 0.192281 5.693 4.43e-08 *** ds_l_realgdp -0.0323119 0.0386353 -0.8363 0.4040 realint_1 0.00410778 0.0512274 0.08019 0.9362 Explained sum of squares = 2.60403 Test statistic: LM = 1.302014, with p-value = P(Chi-square(2) > 1.302014) = 0.521520 #heteroscedasticity Breusch-Pagan Koenker Breusch-Pagan test for heteroskedasticity OLS, using observations 1959:2-2009:3 (T = 202) Dependent variable: scaled uhat^2 (Koenker robust variant) coefficient std. error t-ratio p-value ------------------------------------------------------------ const 10.6870 21.7027 0.4924 0.6230 ds_l_realgdp -3.64704 4.36075 -0.8363 0.4040 realint_1 0.463643 5.78202 0.08019 0.9362 Explained sum of squares = 33174.2 Test statistic: LM = 0.709924, with p-value = P(Chi-square(2) > 0.709924) = 0.701200 ########## forecast #forecast mean y For 95% confidence intervals, t(199, 0.025) = 1.972 Obs ds_l_realinv prediction std. error 95% interval 2008:3 -7.134492 -17.177905 2.946312 -22.987904 - -11.367905 2008:4 -27.665860 -36.294434 3.036851 -42.282972 - -30.305896 2009:1 -70.239280 -44.018178 4.007017 -51.919841 - -36.116516 2009:2 -27.024588 -12.284842 1.427414 -15.099640 - -9.470044 2009:3 8.078897 4.483669 1.315876 1.888819 - 7.078520 Forecast evaluation statistics Mean Error -3.7387 Mean Squared Error 218.61 Root Mean Squared Error 14.785 Mean Absolute Error 12.646 Mean Percentage Error -7.1173 Mean Absolute Percentage Error -43.867 Theil's U 0.4365 Bias proportion, UM 0.06394 Regression proportion, UR 0.13557 Disturbance proportion, UD 0.80049 #forecast actual y For 95% confidence intervals, t(199, 0.025) = 1.972 Obs ds_l_realinv prediction std. error 95% interval 2008:3 -7.134492 -17.177905 11.101892 -39.070353 - 4.714544 2008:4 -27.665860 -36.294434 11.126262 -58.234939 - -14.353928 2009:1 -70.239280 -44.018178 11.429236 -66.556135 - -21.480222 2009:2 -27.024588 -12.284842 10.798554 -33.579120 - 9.009436 2009:3 8.078897 4.483669 10.784377 -16.782652 - 25.749991 Forecast evaluation statistics Mean Error -3.7387 Mean Squared Error 218.61 Root Mean Squared Error 14.785 Mean Absolute Error 12.646 Mean Percentage Error -7.1173 Mean Absolute Percentage Error -43.867 Theil's U 0.4365 Bias proportion, UM 0.06394 Regression proportion, UR 0.13557 Disturbance proportion, UD 0.80049 ''' statsmodels-0.12.2/statsmodels/regression/tests/test_glsar_stata.py000066400000000000000000000065741400612667500257620ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Testing GLSAR against STATA Created on Wed May 30 09:25:24 2012 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_almost_equal, assert_allclose, assert_equal from statsmodels.regression.linear_model import GLSAR from statsmodels.tools.tools import add_constant from statsmodels.datasets import macrodata class CheckStataResultsMixin(object): def test_params_table(self): res, results = self.res, self.results assert_almost_equal(res.params, results.params, 3) assert_almost_equal(res.bse, results.bse, 3) # assert_almost_equal(res.tvalues, results.tvalues, 3) 0.0003 assert_allclose(res.tvalues, results.tvalues, atol=0, rtol=0.004) assert_allclose(res.pvalues, results.pvalues, atol=1e-7, rtol=0.004) class CheckStataResultsPMixin(CheckStataResultsMixin): def test_predicted(self): res, results = self.res, self.results assert_allclose(res.fittedvalues, results.fittedvalues, rtol=0.002) predicted = res.predict(res.model.exog) #should be equal assert_allclose(predicted, results.fittedvalues, rtol=0.0016) # not yet # assert_almost_equal(res.fittedvalues_se, results.fittedvalues_se, 4) class TestGLSARCorc(CheckStataResultsPMixin): @classmethod def setup_class(cls): d2 = macrodata.load_pandas().data g_gdp = 400*np.diff(np.log(d2['realgdp'].values)) g_inv = 400*np.diff(np.log(d2['realinv'].values)) exogg = add_constant(np.c_[g_gdp, d2['realint'][:-1].values], prepend=False) mod1 = GLSAR(g_inv, exogg, 1) cls.res = mod1.iterative_fit(5) from .results.macro_gr_corc_stata import results cls.results = results def test_rho(self): assert_almost_equal(self.res.model.rho, self.results.rho, 3) # pylint: disable-msg=E1101 assert_almost_equal(self.res.llf, self.results.ll, 4) def test_glsar_arima(self): from statsmodels.tsa.arima.model import ARIMA endog = self.res.model.endog exog = self.res.model.exog mod1 = GLSAR(endog, exog, 3) res = mod1.iterative_fit(10) mod_arma = ARIMA(endog, order=(3,0,0), exog=exog[:, :-1]) res_arma = mod_arma.fit() assert_allclose(res.params, res_arma.params[[1,2,0]], atol=0.01, rtol=1e-2) assert_allclose(res.model.rho, res_arma.params[3:6], atol=0.05, rtol=1e-3) assert_allclose(res.bse, res_arma.bse[[1,2,0]], atol=0.1, rtol=1e-3) assert_equal(len(res.history['params']), 5) # this should be identical, history has last fit assert_equal(res.history['params'][-1], res.params) res2 = mod1.iterative_fit(4, rtol=0) assert_equal(len(res2.history['params']), 4) assert_equal(len(res2.history['rho']), 4) def test_glsar_iter0(self): endog = self.res.model.endog exog = self.res.model.exog rho = np.array([ 0.207, 0.275, 1.033]) mod1 = GLSAR(endog, exog, rho) res1 = mod1.fit() res0 = mod1.iterative_fit(0) res0b = mod1.iterative_fit(1) # check iterative_fit(0) or iterative_fit(1) does not update rho assert_allclose(res0.params, res1.params, rtol=1e-11) assert_allclose(res0b.params, res1.params, rtol=1e-11) assert_allclose(res0.model.rho, rho, rtol=1e-11) assert_allclose(res0b.model.rho, rho, rtol=1e-11) statsmodels-0.12.2/statsmodels/regression/tests/test_lme.py000066400000000000000000001277521400612667500242350ustar00rootroot00000000000000from statsmodels.compat.platform import PLATFORM_OSX import os import csv import warnings import numpy as np import pandas as pd from scipy import sparse import pytest from statsmodels.regression.mixed_linear_model import ( MixedLM, MixedLMParams, _smw_solver, _smw_logdet) from numpy.testing import (assert_almost_equal, assert_equal, assert_allclose, assert_) from statsmodels.base import _penalties as penalties import statsmodels.tools.numdiff as nd from .results import lme_r_results # TODO: add tests with unequal group sizes class R_Results(object): """ A class for holding various results obtained from fitting one data set using lmer in R. Parameters ---------- meth : str Either "ml" or "reml". irfs : str Either "irf", for independent random effects, or "drf" for dependent random effects. ds_ix : int The number of the data set """ def __init__(self, meth, irfs, ds_ix): bname = "_%s_%s_%d" % (meth, irfs, ds_ix) self.coef = getattr(lme_r_results, "coef" + bname) self.vcov_r = getattr(lme_r_results, "vcov" + bname) self.cov_re_r = getattr(lme_r_results, "cov_re" + bname) self.scale_r = getattr(lme_r_results, "scale" + bname) self.loglike = getattr(lme_r_results, "loglike" + bname) if hasattr(lme_r_results, "ranef_mean" + bname): self.ranef_postmean = getattr(lme_r_results, "ranef_mean" + bname) self.ranef_condvar = getattr(lme_r_results, "ranef_condvar" + bname) self.ranef_condvar = np.atleast_2d(self.ranef_condvar) # Load the data file cur_dir = os.path.dirname(os.path.abspath(__file__)) rdir = os.path.join(cur_dir, 'results') fname = os.path.join(rdir, "lme%02d.csv" % ds_ix) with open(fname) as fid: rdr = csv.reader(fid) header = next(rdr) data = [[float(x) for x in line] for line in rdr] data = np.asarray(data) # Split into exog, endog, etc. self.endog = data[:, header.index("endog")] self.groups = data[:, header.index("groups")] ii = [i for i, x in enumerate(header) if x.startswith("exog_fe")] self.exog_fe = data[:, ii] ii = [i for i, x in enumerate(header) if x.startswith("exog_re")] self.exog_re = data[:, ii] def loglike_function(model, profile_fe, has_fe): # Returns a function that evaluates the negative log-likelihood for # the given model. def f(x): params = MixedLMParams.from_packed( x, model.k_fe, model.k_re, model.use_sqrt, has_fe=has_fe) return -model.loglike(params, profile_fe=profile_fe) return f class TestMixedLM(object): # Test analytic scores and Hessian using numeric differentiation @pytest.mark.slow @pytest.mark.parametrize("use_sqrt", [False, True]) @pytest.mark.parametrize("reml", [False, True]) @pytest.mark.parametrize("profile_fe", [False, True]) def test_compare_numdiff(self, use_sqrt, reml, profile_fe): n_grp = 200 grpsize = 5 k_fe = 3 k_re = 2 np.random.seed(3558) exog_fe = np.random.normal(size=(n_grp * grpsize, k_fe)) exog_re = np.random.normal(size=(n_grp * grpsize, k_re)) exog_re[:, 0] = 1 exog_vc = np.random.normal(size=(n_grp * grpsize, 3)) slopes = np.random.normal(size=(n_grp, k_re)) slopes[:, -1] *= 2 slopes = np.kron(slopes, np.ones((grpsize, 1))) slopes_vc = np.random.normal(size=(n_grp, 3)) slopes_vc = np.kron(slopes_vc, np.ones((grpsize, 1))) slopes_vc[:, -1] *= 2 re_values = (slopes * exog_re).sum(1) vc_values = (slopes_vc * exog_vc).sum(1) err = np.random.normal(size=n_grp * grpsize) endog = exog_fe.sum(1) + re_values + vc_values + err groups = np.kron(range(n_grp), np.ones(grpsize)) vc = {"a": {}, "b": {}} for i in range(n_grp): ix = np.flatnonzero(groups == i) vc["a"][i] = exog_vc[ix, 0:2] vc["b"][i] = exog_vc[ix, 2:3] with pytest.warns(UserWarning, match="Using deprecated variance"): model = MixedLM( endog, exog_fe, groups, exog_re, exog_vc=vc, use_sqrt=use_sqrt) rslt = model.fit(reml=reml) loglike = loglike_function( model, profile_fe=profile_fe, has_fe=not profile_fe) try: # Test the score at several points. for kr in range(5): fe_params = np.random.normal(size=k_fe) cov_re = np.random.normal(size=(k_re, k_re)) cov_re = np.dot(cov_re.T, cov_re) vcomp = np.random.normal(size=2)**2 params = MixedLMParams.from_components( fe_params, cov_re=cov_re, vcomp=vcomp) params_vec = params.get_packed( has_fe=not profile_fe, use_sqrt=use_sqrt) # Check scores gr = -model.score(params, profile_fe=profile_fe) ngr = nd.approx_fprime(params_vec, loglike) assert_allclose(gr, ngr, rtol=1e-3) # Check Hessian matrices at the MLE (we do not have # the profile Hessian matrix and we do not care # about the Hessian for the square root # transformed parameter). if (profile_fe is False) and (use_sqrt is False): hess, sing = model.hessian(rslt.params_object) if sing: pytest.fail("hessian should not be singular") hess *= -1 params_vec = rslt.params_object.get_packed( use_sqrt=False, has_fe=True) loglike_h = loglike_function( model, profile_fe=False, has_fe=True) nhess = nd.approx_hess(params_vec, loglike_h) assert_allclose(hess, nhess, rtol=1e-3) except AssertionError: # See GH#5628; because this test fails unpredictably but only on # OSX, we only xfail it there. if PLATFORM_OSX: pytest.xfail("fails on OSX due to unresolved " "numerical differences") else: raise def test_default_re(self): np.random.seed(3235) exog = np.random.normal(size=(300, 4)) groups = np.kron(np.arange(100), [1, 1, 1]) g_errors = np.kron(np.random.normal(size=100), [1, 1, 1]) endog = exog.sum(1) + g_errors + np.random.normal(size=300) mdf1 = MixedLM(endog, exog, groups).fit() mdf2 = MixedLM(endog, exog, groups, np.ones(300)).fit() assert_almost_equal(mdf1.params, mdf2.params, decimal=8) def test_history(self): np.random.seed(3235) exog = np.random.normal(size=(300, 4)) groups = np.kron(np.arange(100), [1, 1, 1]) g_errors = np.kron(np.random.normal(size=100), [1, 1, 1]) endog = exog.sum(1) + g_errors + np.random.normal(size=300) mod = MixedLM(endog, exog, groups) rslt = mod.fit(full_output=True) assert_equal(hasattr(rslt, "hist"), True) @pytest.mark.slow @pytest.mark.smoke def test_profile_inference(self): np.random.seed(9814) k_fe = 2 gsize = 3 n_grp = 100 exog = np.random.normal(size=(n_grp * gsize, k_fe)) exog_re = np.ones((n_grp * gsize, 1)) groups = np.kron(np.arange(n_grp), np.ones(gsize)) vca = np.random.normal(size=n_grp * gsize) vcb = np.random.normal(size=n_grp * gsize) errors = 0 g_errors = np.kron(np.random.normal(size=100), np.ones(gsize)) errors += g_errors + exog_re[:, 0] rc = np.random.normal(size=n_grp) errors += np.kron(rc, np.ones(gsize)) * vca rc = np.random.normal(size=n_grp) errors += np.kron(rc, np.ones(gsize)) * vcb errors += np.random.normal(size=n_grp * gsize) endog = exog.sum(1) + errors vc = {"a": {}, "b": {}} for k in range(n_grp): ii = np.flatnonzero(groups == k) vc["a"][k] = vca[ii][:, None] vc["b"][k] = vcb[ii][:, None] with pytest.warns(UserWarning, match="Using deprecated variance"): rslt = MixedLM(endog, exog, groups=groups, exog_re=exog_re, exog_vc=vc).fit() rslt.profile_re(0, vtype='re', dist_low=1, num_low=3, dist_high=1, num_high=3) rslt.profile_re('b', vtype='vc', dist_low=0.5, num_low=3, dist_high=0.5, num_high=3) def test_vcomp_1(self): # Fit the same model using constrained random effects and # variance components. np.random.seed(4279) exog = np.random.normal(size=(400, 1)) exog_re = np.random.normal(size=(400, 2)) groups = np.kron(np.arange(100), np.ones(4)) slopes = np.random.normal(size=(100, 2)) slopes[:, 1] *= 2 slopes = np.kron(slopes, np.ones((4, 1))) * exog_re errors = slopes.sum(1) + np.random.normal(size=400) endog = exog.sum(1) + errors free = MixedLMParams(1, 2, 0) free.fe_params = np.ones(1) free.cov_re = np.eye(2) free.vcomp = np.zeros(0) model1 = MixedLM(endog, exog, groups, exog_re=exog_re) result1 = model1.fit(free=free) exog_vc = {"a": {}, "b": {}} for k, group in enumerate(model1.group_labels): ix = model1.row_indices[group] exog_vc["a"][group] = exog_re[ix, 0:1] exog_vc["b"][group] = exog_re[ix, 1:2] with pytest.warns(UserWarning, match="Using deprecated variance"): model2 = MixedLM(endog, exog, groups, exog_vc=exog_vc) result2 = model2.fit() result2.summary() assert_allclose(result1.fe_params, result2.fe_params, atol=1e-4) assert_allclose( np.diag(result1.cov_re), result2.vcomp, atol=1e-2, rtol=1e-4) assert_allclose( result1.bse[[0, 1, 3]], result2.bse, atol=1e-2, rtol=1e-2) def test_vcomp_2(self): # Simulated data comparison to R np.random.seed(6241) n = 1600 exog = np.random.normal(size=(n, 2)) groups = np.kron(np.arange(n / 16), np.ones(16)) # Build up the random error vector errors = 0 # The random effects exog_re = np.random.normal(size=(n, 2)) slopes = np.random.normal(size=(n // 16, 2)) slopes = np.kron(slopes, np.ones((16, 1))) * exog_re errors += slopes.sum(1) # First variance component subgroups1 = np.kron(np.arange(n / 4), np.ones(4)) errors += np.kron(2 * np.random.normal(size=n // 4), np.ones(4)) # Second variance component subgroups2 = np.kron(np.arange(n / 2), np.ones(2)) errors += np.kron(2 * np.random.normal(size=n // 2), np.ones(2)) # iid errors errors += np.random.normal(size=n) endog = exog.sum(1) + errors df = pd.DataFrame(index=range(n)) df["y"] = endog df["groups"] = groups df["x1"] = exog[:, 0] df["x2"] = exog[:, 1] df["z1"] = exog_re[:, 0] df["z2"] = exog_re[:, 1] df["v1"] = subgroups1 df["v2"] = subgroups2 # Equivalent model in R: # df.to_csv("tst.csv") # model = lmer(y ~ x1 + x2 + (0 + z1 + z2 | groups) + (1 | v1) + (1 | # v2), df) vcf = {"a": "0 + C(v1)", "b": "0 + C(v2)"} model1 = MixedLM.from_formula( "y ~ x1 + x2", groups=groups, re_formula="0+z1+z2", vc_formula=vcf, data=df) result1 = model1.fit() # Compare to R assert_allclose( result1.fe_params, [0.16527, 0.99911, 0.96217], rtol=1e-4) assert_allclose( result1.cov_re, [[1.244, 0.146], [0.146, 1.371]], rtol=1e-3) assert_allclose(result1.vcomp, [4.024, 3.997], rtol=1e-3) assert_allclose( result1.bse.iloc[0:3], [0.12610, 0.03938, 0.03848], rtol=1e-3) def test_vcomp_3(self): # Test a model with vcomp but no other random effects, using formulas. np.random.seed(4279) x1 = np.random.normal(size=400) groups = np.kron(np.arange(100), np.ones(4)) slopes = np.random.normal(size=100) slopes = np.kron(slopes, np.ones(4)) * x1 y = slopes + np.random.normal(size=400) vc_fml = {"a": "0 + x1"} df = pd.DataFrame({"y": y, "x1": x1, "groups": groups}) model = MixedLM.from_formula( "y ~ 1", groups="groups", vc_formula=vc_fml, data=df) result = model.fit() result.summary() assert_allclose( result.resid.iloc[0:4], np.r_[-1.180753, 0.279966, 0.578576, -0.667916], rtol=1e-3) assert_allclose( result.fittedvalues.iloc[0:4], np.r_[-0.101549, 0.028613, -0.224621, -0.126295], rtol=1e-3) def test_sparse(self): cur_dir = os.path.dirname(os.path.abspath(__file__)) rdir = os.path.join(cur_dir, 'results') fname = os.path.join(rdir, 'pastes.csv') # Dense data = pd.read_csv(fname) vcf = {"cask": "0 + cask"} model = MixedLM.from_formula( "strength ~ 1", groups="batch", re_formula="1", vc_formula=vcf, data=data) result = model.fit() # Sparse model2 = MixedLM.from_formula( "strength ~ 1", groups="batch", re_formula="1", vc_formula=vcf, use_sparse=True, data=data) result2 = model2.fit() assert_allclose(result.params, result2.params) assert_allclose(result.bse, result2.bse) def test_dietox(self): # dietox data from geepack using random intercepts # # Fit in R using # # library(geepack) # rm = lmer(Weight ~ Time + (1 | Pig), data=dietox) # rm = lmer(Weight ~ Time + (1 | Pig), REML=FALSE, data=dietox) # # Comments below are R code used to extract the numbers used # for comparison. cur_dir = os.path.dirname(os.path.abspath(__file__)) rdir = os.path.join(cur_dir, 'results') fname = os.path.join(rdir, 'dietox.csv') # REML data = pd.read_csv(fname) model = MixedLM.from_formula("Weight ~ Time", groups="Pig", data=data) result = model.fit() # fixef(rm) assert_allclose( result.fe_params, np.r_[15.723523, 6.942505], rtol=1e-5) # sqrt(diag(vcov(rm))) assert_allclose( result.bse[0:2], np.r_[0.78805374, 0.03338727], rtol=1e-5) # attr(VarCorr(rm), "sc")^2 assert_allclose(result.scale, 11.36692, rtol=1e-5) # VarCorr(rm)[[1]][[1]] assert_allclose(result.cov_re, 40.39395, rtol=1e-5) # logLik(rm) assert_allclose( model.loglike(result.params_object), -2404.775, rtol=1e-5) # ML data = pd.read_csv(fname) model = MixedLM.from_formula("Weight ~ Time", groups="Pig", data=data) result = model.fit(reml=False) # fixef(rm) assert_allclose( result.fe_params, np.r_[15.723517, 6.942506], rtol=1e-5) # sqrt(diag(vcov(rm))) assert_allclose( result.bse[0:2], np.r_[0.7829397, 0.0333661], rtol=1e-5) # attr(VarCorr(rm), "sc")^2 assert_allclose(result.scale, 11.35251, rtol=1e-5) # VarCorr(rm)[[1]][[1]] assert_allclose(result.cov_re, 39.82097, rtol=1e-5) # logLik(rm) assert_allclose( model.loglike(result.params_object), -2402.932, rtol=1e-5) def test_dietox_slopes(self): # dietox data from geepack using random intercepts # # Fit in R using # # library(geepack) # r = lmer(Weight ~ Time + (1 + Time | Pig), data=dietox) # r = lmer(Weight ~ Time + (1 + Time | Pig), REML=FALSE, data=dietox) # # Comments below are the R code used to extract the constants # for comparison. cur_dir = os.path.dirname(os.path.abspath(__file__)) rdir = os.path.join(cur_dir, 'results') fname = os.path.join(rdir, 'dietox.csv') # REML data = pd.read_csv(fname) model = MixedLM.from_formula( "Weight ~ Time", groups="Pig", re_formula="1 + Time", data=data) result = model.fit(method="cg") # fixef(r) assert_allclose( result.fe_params, np.r_[15.738650, 6.939014], rtol=1e-5) # sqrt(diag(vcov(r))) assert_allclose( result.bse[0:2], np.r_[0.5501253, 0.0798254], rtol=1e-3) # attr(VarCorr(r), "sc")^2 assert_allclose(result.scale, 6.03745, rtol=1e-3) # as.numeric(VarCorr(r)[[1]]) assert_allclose( result.cov_re.values.ravel(), np.r_[19.4934552, 0.2938323, 0.2938323, 0.4160620], rtol=1e-1) # logLik(r) assert_allclose( model.loglike(result.params_object), -2217.047, rtol=1e-5) # ML data = pd.read_csv(fname) model = MixedLM.from_formula( "Weight ~ Time", groups="Pig", re_formula="1 + Time", data=data) result = model.fit(method='cg', reml=False) # fixef(r) assert_allclose(result.fe_params, np.r_[15.73863, 6.93902], rtol=1e-5) # sqrt(diag(vcov(r))) assert_allclose( result.bse[0:2], np.r_[0.54629282, 0.07926954], rtol=1e-3) # attr(VarCorr(r), "sc")^2 assert_allclose(result.scale, 6.037441, rtol=1e-3) # as.numeric(VarCorr(r)[[1]]) assert_allclose( result.cov_re.values.ravel(), np.r_[19.190922, 0.293568, 0.293568, 0.409695], rtol=1e-2) # logLik(r) assert_allclose( model.loglike(result.params_object), -2215.753, rtol=1e-5) def test_pastes_vcomp(self): # pastes data from lme4 # # Fit in R using: # # r = lmer(strength ~ (1|batch) + (1|batch:cask), data=data) # r = lmer(strength ~ (1|batch) + (1|batch:cask), data=data, # reml=FALSE) cur_dir = os.path.dirname(os.path.abspath(__file__)) rdir = os.path.join(cur_dir, 'results') fname = os.path.join(rdir, 'pastes.csv') data = pd.read_csv(fname) vcf = {"cask": "0 + cask"} # REML model = MixedLM.from_formula( "strength ~ 1", groups="batch", re_formula="1", vc_formula=vcf, data=data) result = model.fit() # fixef(r) assert_allclose(result.fe_params.iloc[0], 60.0533, rtol=1e-3) # sqrt(diag(vcov(r))) assert_allclose(result.bse.iloc[0], 0.6769, rtol=1e-3) # VarCorr(r)$batch[[1]] assert_allclose(result.cov_re.iloc[0, 0], 1.657, rtol=1e-3) # attr(VarCorr(r), "sc")^2 assert_allclose(result.scale, 0.678, rtol=1e-3) # logLik(r) assert_allclose(result.llf, -123.49, rtol=1e-1) # do not provide aic/bic with REML assert_equal(result.aic, np.nan) assert_equal(result.bic, np.nan) # resid(r)[1:5] resid = np.r_[0.17133538, -0.02866462, -1.08662875, 1.11337125, -0.12093607] assert_allclose(result.resid[0:5], resid, rtol=1e-3) # predict(r)[1:5] fit = np.r_[62.62866, 62.62866, 61.18663, 61.18663, 62.82094] assert_allclose(result.fittedvalues[0:5], fit, rtol=1e-4) # ML model = MixedLM.from_formula( "strength ~ 1", groups="batch", re_formula="1", vc_formula=vcf, data=data) result = model.fit(reml=False) # fixef(r) assert_allclose(result.fe_params.iloc[0], 60.0533, rtol=1e-3) # sqrt(diag(vcov(r))) assert_allclose(result.bse.iloc[0], 0.642, rtol=1e-3) # VarCorr(r)$batch[[1]] assert_allclose(result.cov_re.iloc[0, 0], 1.199, rtol=1e-3) # attr(VarCorr(r), "sc")^2 assert_allclose(result.scale, 0.67799, rtol=1e-3) # logLik(r) assert_allclose(result.llf, -123.997, rtol=1e-1) # AIC(r) assert_allclose(result.aic, 255.9944, rtol=1e-3) # BIC(r) assert_allclose(result.bic, 264.3718, rtol=1e-3) @pytest.mark.slow def test_vcomp_formula(self): np.random.seed(6241) n = 800 exog = np.random.normal(size=(n, 2)) exog[:, 0] = 1 ex_vc = [] groups = np.kron(np.arange(n / 4), np.ones(4)) errors = 0 exog_re = np.random.normal(size=(n, 2)) slopes = np.random.normal(size=(n // 4, 2)) slopes = np.kron(slopes, np.ones((4, 1))) * exog_re errors += slopes.sum(1) ex_vc = np.random.normal(size=(n, 4)) slopes = np.random.normal(size=(n // 4, 4)) slopes[:, 2:] *= 2 slopes = np.kron(slopes, np.ones((4, 1))) * ex_vc errors += slopes.sum(1) errors += np.random.normal(size=n) endog = exog.sum(1) + errors exog_vc = {"a": {}, "b": {}} for k, group in enumerate(range(int(n / 4))): ix = np.flatnonzero(groups == group) exog_vc["a"][group] = ex_vc[ix, 0:2] exog_vc["b"][group] = ex_vc[ix, 2:] with pytest.warns(UserWarning, match="Using deprecated variance"): model1 = MixedLM(endog, exog, groups, exog_re=exog_re, exog_vc=exog_vc) result1 = model1.fit() df = pd.DataFrame(exog[:, 1:], columns=["x1"]) df["y"] = endog df["re1"] = exog_re[:, 0] df["re2"] = exog_re[:, 1] df["vc1"] = ex_vc[:, 0] df["vc2"] = ex_vc[:, 1] df["vc3"] = ex_vc[:, 2] df["vc4"] = ex_vc[:, 3] vc_formula = {"a": "0 + vc1 + vc2", "b": "0 + vc3 + vc4"} model2 = MixedLM.from_formula( "y ~ x1", groups=groups, re_formula="0 + re1 + re2", vc_formula=vc_formula, data=df) result2 = model2.fit() assert_allclose(result1.fe_params, result2.fe_params, rtol=1e-8) assert_allclose(result1.cov_re, result2.cov_re, rtol=1e-8) assert_allclose(result1.vcomp, result2.vcomp, rtol=1e-8) assert_allclose(result1.params, result2.params, rtol=1e-8) assert_allclose(result1.bse, result2.bse, rtol=1e-8) def test_formulas(self): np.random.seed(2410) exog = np.random.normal(size=(300, 4)) exog_re = np.random.normal(size=300) groups = np.kron(np.arange(100), [1, 1, 1]) g_errors = exog_re * np.kron(np.random.normal(size=100), [1, 1, 1]) endog = exog.sum(1) + g_errors + np.random.normal(size=300) mod1 = MixedLM(endog, exog, groups, exog_re) # test the names assert_(mod1.data.xnames == ["x1", "x2", "x3", "x4"]) assert_(mod1.data.exog_re_names == ["x_re1"]) assert_(mod1.data.exog_re_names_full == ["x_re1 Var"]) rslt1 = mod1.fit() # Fit with a formula, passing groups as the actual values. df = pd.DataFrame({"endog": endog}) for k in range(exog.shape[1]): df["exog%d" % k] = exog[:, k] df["exog_re"] = exog_re fml = "endog ~ 0 + exog0 + exog1 + exog2 + exog3" re_fml = "0 + exog_re" mod2 = MixedLM.from_formula(fml, df, re_formula=re_fml, groups=groups) assert_(mod2.data.xnames == ["exog0", "exog1", "exog2", "exog3"]) assert_(mod2.data.exog_re_names == ["exog_re"]) assert_(mod2.data.exog_re_names_full == ["exog_re Var"]) rslt2 = mod2.fit() assert_almost_equal(rslt1.params, rslt2.params) # Fit with a formula, passing groups as the variable name. df["groups"] = groups mod3 = MixedLM.from_formula( fml, df, re_formula=re_fml, groups="groups") assert_(mod3.data.xnames == ["exog0", "exog1", "exog2", "exog3"]) assert_(mod3.data.exog_re_names == ["exog_re"]) assert_(mod3.data.exog_re_names_full == ["exog_re Var"]) rslt3 = mod3.fit(start_params=rslt2.params) assert_allclose(rslt1.params, rslt3.params, rtol=1e-4) # Check default variance structure with non-formula model # creation, also use different exog_re that produces a zero # estimated variance parameter. exog_re = np.ones(len(endog), dtype=np.float64) mod4 = MixedLM(endog, exog, groups, exog_re) with warnings.catch_warnings(): warnings.simplefilter("ignore") rslt4 = mod4.fit() from statsmodels.formula.api import mixedlm mod5 = mixedlm(fml, df, groups="groups") assert_(mod5.data.exog_re_names == ["groups"]) assert_(mod5.data.exog_re_names_full == ["groups Var"]) with warnings.catch_warnings(): warnings.simplefilter("ignore") rslt5 = mod5.fit() assert_almost_equal(rslt4.params, rslt5.params) @pytest.mark.slow def test_regularized(self): np.random.seed(3453) exog = np.random.normal(size=(400, 5)) groups = np.kron(np.arange(100), np.ones(4)) expected_endog = exog[:, 0] - exog[:, 2] endog = expected_endog +\ np.kron(np.random.normal(size=100), np.ones(4)) +\ np.random.normal(size=400) # L1 regularization md = MixedLM(endog, exog, groups) mdf1 = md.fit_regularized(alpha=1.) mdf1.summary() # L1 regularization md = MixedLM(endog, exog, groups) mdf2 = md.fit_regularized(alpha=10 * np.ones(5)) mdf2.summary() # L2 regularization pen = penalties.L2() mdf3 = md.fit_regularized(method=pen, alpha=0.) mdf3.summary() # L2 regularization pen = penalties.L2() with warnings.catch_warnings(): warnings.simplefilter("ignore") mdf4 = md.fit_regularized(method=pen, alpha=10.) mdf4.summary() # Pseudo-Huber regularization pen = penalties.PseudoHuber(0.3) mdf5 = md.fit_regularized(method=pen, alpha=1.) mdf5.summary() # ------------------------------------------------------------------ class TestMixedLMSummary(object): # Test various aspects of the MixedLM summary @classmethod def setup_class(cls): # Setup the model and estimate it. pid = np.repeat([0, 1], 5) x0 = np.repeat([1], 10) x1 = [1, 5, 7, 3, 5, 1, 2, 6, 9, 8] x2 = [6, 2, 1, 0, 1, 4, 3, 8, 2, 1] y = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] df = pd.DataFrame({"y": y, "pid": pid, "x0": x0, "x1": x1, "x2": x2}) endog = df["y"].values exog = df[["x0", "x1", "x2"]].values groups = df["pid"].values cls.res = MixedLM(endog, exog, groups=groups).fit() def test_summary(self): # Test that the summary correctly includes all variables. summ = self.res.summary() desired = ["const", "x1", "x2", "Group Var"] # Second table is summary of params actual = summ.tables[1].index.values assert_equal(actual, desired) def test_summary_xname_fe(self): # Test that the `xname_fe` argument is reflected in the summary table. summ = self.res.summary(xname_fe=["Constant", "Age", "Weight"]) desired = ["Constant", "Age", "Weight", "Group Var"] actual = summ.tables[ 1].index.values # Second table is summary of params assert_equal(actual, desired) def test_summary_xname_re(self): # Test that the `xname_re` argument is reflected in the summary table. summ = self.res.summary(xname_re=["Random Effects"]) desired = ["const", "x1", "x2", "Random Effects"] actual = summ.tables[ 1].index.values # Second table is summary of params assert_equal(actual, desired) # ------------------------------------------------------------------ # TODO: better name def do1(reml, irf, ds_ix): # No need to check independent random effects when there is # only one of them. if irf and ds_ix < 6: return irfs = "irf" if irf else "drf" meth = "reml" if reml else "ml" rslt = R_Results(meth, irfs, ds_ix) # Fit the model md = MixedLM(rslt.endog, rslt.exog_fe, rslt.groups, rslt.exog_re) if not irf: # Free random effects covariance if np.any(np.diag(rslt.cov_re_r) < 1e-5): with warnings.catch_warnings(): warnings.simplefilter("ignore") mdf = md.fit(gtol=1e-7, reml=reml) else: mdf = md.fit(gtol=1e-7, reml=reml) else: # Independent random effects k_fe = rslt.exog_fe.shape[1] k_re = rslt.exog_re.shape[1] free = MixedLMParams(k_fe, k_re, 0) free.fe_params = np.ones(k_fe) free.cov_re = np.eye(k_re) free.vcomp = np.array([]) if np.any(np.diag(rslt.cov_re_r) < 1e-5): with warnings.catch_warnings(): warnings.simplefilter("ignore") mdf = md.fit(reml=reml, gtol=1e-7, free=free) else: mdf = md.fit(reml=reml, gtol=1e-7, free=free) assert_almost_equal(mdf.fe_params, rslt.coef, decimal=4) assert_almost_equal(mdf.cov_re, rslt.cov_re_r, decimal=4) assert_almost_equal(mdf.scale, rslt.scale_r, decimal=4) k_fe = md.k_fe assert_almost_equal( rslt.vcov_r, mdf.cov_params()[0:k_fe, 0:k_fe], decimal=3) assert_almost_equal(mdf.llf, rslt.loglike[0], decimal=2) # Not supported in R except for independent random effects if not irf: assert_almost_equal( mdf.random_effects[0], rslt.ranef_postmean, decimal=3) assert_almost_equal( mdf.random_effects_cov[0], rslt.ranef_condvar, decimal=3) # ------------------------------------------------------------------ # Run all the tests against R cur_dir = os.path.dirname(os.path.abspath(__file__)) rdir = os.path.join(cur_dir, 'results') fnames = os.listdir(rdir) fnames = [x for x in fnames if x.startswith("lme") and x.endswith(".csv")] # Copied from #3847 @pytest.mark.parametrize('fname', fnames) @pytest.mark.parametrize('reml', [False, True]) @pytest.mark.parametrize('irf', [False, True]) def test_r(fname, reml, irf): ds_ix = int(fname[3:5]) do1(reml, irf, ds_ix) # ------------------------------------------------------------------ def test_mixed_lm_wrapper(): # a bit more complicated model to test np.random.seed(2410) exog = np.random.normal(size=(300, 4)) exog_re = np.random.normal(size=300) groups = np.kron(np.arange(100), [1, 1, 1]) g_errors = exog_re * np.kron(np.random.normal(size=100), [1, 1, 1]) endog = exog.sum(1) + g_errors + np.random.normal(size=300) # Fit with a formula, passing groups as the actual values. df = pd.DataFrame({"endog": endog}) for k in range(exog.shape[1]): df["exog%d" % k] = exog[:, k] df["exog_re"] = exog_re fml = "endog ~ 0 + exog0 + exog1 + exog2 + exog3" re_fml = "~ exog_re" mod2 = MixedLM.from_formula(fml, df, re_formula=re_fml, groups=groups) result = mod2.fit() result.summary() xnames = ["exog0", "exog1", "exog2", "exog3"] re_names = ["Group", "exog_re"] re_names_full = ["Group Var", "Group x exog_re Cov", "exog_re Var"] assert_(mod2.data.xnames == xnames) assert_(mod2.data.exog_re_names == re_names) assert_(mod2.data.exog_re_names_full == re_names_full) params = result.params assert_(params.index.tolist() == xnames + re_names_full) bse = result.bse assert_(bse.index.tolist() == xnames + re_names_full) tvalues = result.tvalues assert_(tvalues.index.tolist() == xnames + re_names_full) cov_params = result.cov_params() assert_(cov_params.index.tolist() == xnames + re_names_full) assert_(cov_params.columns.tolist() == xnames + re_names_full) fe = result.fe_params assert_(fe.index.tolist() == xnames) bse_fe = result.bse_fe assert_(bse_fe.index.tolist() == xnames) cov_re = result.cov_re assert_(cov_re.index.tolist() == re_names) assert_(cov_re.columns.tolist() == re_names) cov_re_u = result.cov_re_unscaled assert_(cov_re_u.index.tolist() == re_names) assert_(cov_re_u.columns.tolist() == re_names) bse_re = result.bse_re assert_(bse_re.index.tolist() == re_names_full) def test_random_effects(): np.random.seed(23429) # Default model (random effects only) ngrp = 100 gsize = 10 rsd = 2 gsd = 3 mn = gsd * np.random.normal(size=ngrp) gmn = np.kron(mn, np.ones(gsize)) y = gmn + rsd * np.random.normal(size=ngrp * gsize) gr = np.kron(np.arange(ngrp), np.ones(gsize)) x = np.ones(ngrp * gsize) model = MixedLM(y, x, groups=gr) result = model.fit() re = result.random_effects assert_(isinstance(re, dict)) assert_(len(re) == ngrp) assert_(isinstance(re[0], pd.Series)) assert_(len(re[0]) == 1) # Random intercept only, set explicitly model = MixedLM(y, x, exog_re=x, groups=gr) result = model.fit() re = result.random_effects assert_(isinstance(re, dict)) assert_(len(re) == ngrp) assert_(isinstance(re[0], pd.Series)) assert_(len(re[0]) == 1) # Random intercept and slope xr = np.random.normal(size=(ngrp * gsize, 2)) xr[:, 0] = 1 qp = np.linspace(-1, 1, gsize) xr[:, 1] = np.kron(np.ones(ngrp), qp) model = MixedLM(y, x, exog_re=xr, groups=gr) result = model.fit() re = result.random_effects assert_(isinstance(re, dict)) assert_(len(re) == ngrp) assert_(isinstance(re[0], pd.Series)) assert_(len(re[0]) == 2) @pytest.mark.slow def test_handle_missing(): np.random.seed(23423) df = np.random.normal(size=(100, 6)) df = pd.DataFrame(df) df.columns = ["y", "g", "x1", "z1", "c1", "c2"] df["g"] = np.kron(np.arange(50), np.ones(2)) re = np.random.normal(size=(50, 4)) re = np.kron(re, np.ones((2, 1))) df["y"] = re[:, 0] + re[:, 1] * df.z1 + re[:, 2] * df.c1 df["y"] += re[:, 3] * df.c2 + np.random.normal(size=100) df.loc[1, "y"] = np.NaN df.loc[2, "g"] = np.NaN df.loc[3, "x1"] = np.NaN df.loc[4, "z1"] = np.NaN df.loc[5, "c1"] = np.NaN df.loc[6, "c2"] = np.NaN fml = "y ~ x1" re_formula = "1 + z1" vc_formula = {"a": "0 + c1", "b": "0 + c2"} for include_re in False, True: for include_vc in False, True: kwargs = {} dx = df.copy() va = ["y", "g", "x1"] if include_re: kwargs["re_formula"] = re_formula va.append("z1") if include_vc: kwargs["vc_formula"] = vc_formula va.extend(["c1", "c2"]) dx = dx[va].dropna() # Some of these models are severely misspecified with # small n, so produce convergence warnings. Not relevant # to what we are checking here. with warnings.catch_warnings(): warnings.simplefilter("ignore") # Drop missing externally model1 = MixedLM.from_formula( fml, groups="g", data=dx, **kwargs) result1 = model1.fit() # MixeLM handles missing model2 = MixedLM.from_formula( fml, groups="g", data=df, missing='drop', **kwargs) result2 = model2.fit() assert_allclose(result1.params, result2.params) assert_allclose(result1.bse, result2.bse) assert_equal(len(result1.fittedvalues), result1.nobs) def test_summary_col(): from statsmodels.iolib.summary2 import summary_col ids = [1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3] x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15] # hard coded simulated y # ids = np.asarray(ids) # np.random.seed(123987) # y = x + np.array([-1, 0, 1])[ids - 1] + 2 * np.random.randn(len(y)) y = np.array([ 1.727, -1.037, 2.904, 3.569, 4.629, 5.736, 6.747, 7.020, 5.624, 10.155, 10.400, 17.164, 17.276, 14.988, 14.453 ]) d = {'Y': y, 'X': x, 'IDS': ids} d = pd.DataFrame(d) # provide start_params to speed up convergence sp1 = np.array([-1.26722599, 1.1617587, 0.19547518]) mod1 = MixedLM.from_formula('Y ~ X', d, groups=d['IDS']) results1 = mod1.fit(start_params=sp1) sp2 = np.array([3.48416861, 0.55287862, 1.38537901]) mod2 = MixedLM.from_formula('X ~ Y', d, groups=d['IDS']) results2 = mod2.fit(start_params=sp2) out = summary_col([results1, results2], stars=True) s = ('\n=============================\n Y X \n' '-----------------------------\nGroup Var 0.1955 1.3854 \n' ' (0.6032) (2.7377) \nIntercept -1.2672 3.4842* \n' ' (1.6546) (1.8882) \nX 1.1618*** \n' ' (0.1959) \nY 0.5529***\n' ' (0.2080) \n=============================\n' 'Standard errors in\nparentheses.\n* p<.1, ** p<.05, ***p<.01') assert_equal(str(out), s) @pytest.mark.slow def test_random_effects_getters(): # Simulation-based test to make sure that the BLUPs and actual # random effects line up. np.random.seed(34234) ng = 500 # number of groups m = 10 # group size y, x, z, v0, v1, g, b, c0, c1 = [], [], [], [], [], [], [], [], [] for i in range(ng): # Fixed effects xx = np.random.normal(size=(m, 2)) yy = xx[:, 0] + 0.5 * np.random.normal(size=m) # Random effects (re_formula) zz = np.random.normal(size=(m, 2)) bb = np.random.normal(size=2) bb[0] *= 3 bb[1] *= 1 yy += np.dot(zz, bb).flat b.append(bb) # First variance component vv0 = np.kron(np.r_[0, 1], np.ones(m // 2)).astype(int) cc0 = np.random.normal(size=2) yy += cc0[vv0] v0.append(vv0) c0.append(cc0) # Second variance component vv1 = np.kron(np.ones(m // 2), np.r_[0, 1]).astype(int) cc1 = np.random.normal(size=2) yy += cc1[vv1] v1.append(vv1) c1.append(cc1) y.append(yy) x.append(xx) z.append(zz) g.append(["g%d" % i] * m) y = np.concatenate(y) x = np.concatenate(x) z = np.concatenate(z) v0 = np.concatenate(v0) v1 = np.concatenate(v1) g = np.concatenate(g) df = pd.DataFrame({ "y": y, "x0": x[:, 0], "x1": x[:, 1], "z0": z[:, 0], "z1": z[:, 1], "v0": v0, "v1": v1, "g": g }) b = np.asarray(b) c0 = np.asarray(c0) c1 = np.asarray(c1) cc = np.concatenate((c0, c1), axis=1) model = MixedLM.from_formula( "y ~ x0 + x1", re_formula="~0 + z0 + z1", vc_formula={ "v0": "~0+C(v0)", "v1": "0+C(v1)" }, groups="g", data=df) result = model.fit() ref = result.random_effects b0 = [ref["g%d" % k][0:2] for k in range(ng)] b0 = np.asarray(b0) assert (np.corrcoef(b0[:, 0], b[:, 0])[0, 1] > 0.8) assert (np.corrcoef(b0[:, 1], b[:, 1])[0, 1] > 0.8) cf0 = [ref["g%d" % k][2:6] for k in range(ng)] cf0 = np.asarray(cf0) for k in range(4): assert (np.corrcoef(cf0[:, k], cc[:, k])[0, 1] > 0.8) # Smoke test for predictive covariances refc = result.random_effects_cov for g in refc.keys(): p = ref[g].size assert (refc[g].shape == (p, p)) def check_smw_solver(p, q, r, s): # Helper to check that _smw_solver results do in fact solve the desired # SMW equation d = q - r A = np.random.normal(size=(p, q)) AtA = np.dot(A.T, A) B = np.zeros((q, q)) B[0:r, 0:r] = np.random.normal(size=(r, r)) di = np.random.uniform(size=d) B[r:q, r:q] = np.diag(1 / di) Qi = np.linalg.inv(B[0:r, 0:r]) s = 0.5 x = np.random.normal(size=p) y2 = np.linalg.solve(s * np.eye(p, p) + np.dot(A, np.dot(B, A.T)), x) f = _smw_solver(s, A, AtA, Qi, di) y1 = f(x) assert_allclose(y1, y2) f = _smw_solver(s, sparse.csr_matrix(A), sparse.csr_matrix(AtA), Qi, di) y1 = f(x) assert_allclose(y1, y2) class TestSMWSolver(object): @classmethod def setup_class(cls): np.random.seed(23) @pytest.mark.parametrize("p", [5, 10]) @pytest.mark.parametrize("q", [4, 8]) @pytest.mark.parametrize("r", [2, 3]) @pytest.mark.parametrize("s", [0, 0.5]) def test_smw_solver(self, p, q, r, s): check_smw_solver(p, q, r, s) def check_smw_logdet(p, q, r, s): # Helper to check that _smw_logdet results match non-optimized equivalent d = q - r A = np.random.normal(size=(p, q)) AtA = np.dot(A.T, A) B = np.zeros((q, q)) c = np.random.normal(size=(r, r)) B[0:r, 0:r] = np.dot(c.T, c) di = np.random.uniform(size=d) B[r:q, r:q] = np.diag(1 / di) Qi = np.linalg.inv(B[0:r, 0:r]) s = 0.5 _, d2 = np.linalg.slogdet(s * np.eye(p, p) + np.dot(A, np.dot(B, A.T))) _, bd = np.linalg.slogdet(B) d1 = _smw_logdet(s, A, AtA, Qi, di, bd) # GH 5642, OSX OpenBlas tolerance increase rtol = 1e-6 if PLATFORM_OSX else 1e-7 assert_allclose(d1, d2, rtol=rtol) class TestSMWLogdet(object): @classmethod def setup_class(cls): np.random.seed(23) @pytest.mark.parametrize("p", [5, 10]) @pytest.mark.parametrize("q", [4, 8]) @pytest.mark.parametrize("r", [2, 3]) @pytest.mark.parametrize("s", [0, 0.5]) def test_smw_logdet(self, p, q, r, s): check_smw_logdet(p, q, r, s) def test_singular(): # Issue #7051 np.random.seed(3423) n = 100 data = np.random.randn(n, 2) df = pd.DataFrame(data, columns=['Y', 'X']) df['class'] = pd.Series([i % 3 for i in df.index], index=df.index) with pytest.warns(Warning) as wrn: md = MixedLM.from_formula("Y ~ X", df, groups=df['class']) mdf = md.fit() mdf.summary() if not wrn: pytest.fail("warning expected") def test_get_distribution(): np.random.seed(234) n = 100 n_groups = 10 fe_params = np.r_[1, -2] cov_re = np.asarray([[1, 0.5], [0.5, 2]]) vcomp = np.r_[0.5**2, 1.5**2] scale = 1.5 exog_fe = np.random.normal(size=(n, 2)) exog_re = np.random.normal(size=(n, 2)) exog_vca = np.random.normal(size=(n, 2)) exog_vcb = np.random.normal(size=(n, 2)) groups = np.repeat(np.arange(n_groups, dtype=int), n / n_groups) ey = np.dot(exog_fe, fe_params) u = np.random.normal(size=(n_groups, 2)) u = np.dot(u, np.linalg.cholesky(cov_re).T) u1 = np.sqrt(vcomp[0]) * np.random.normal(size=(n_groups, 2)) u2 = np.sqrt(vcomp[1]) * np.random.normal(size=(n_groups, 2)) y = ey + (u[groups, :] * exog_re).sum(1) y += (u1[groups, :] * exog_vca).sum(1) y += (u2[groups, :] * exog_vcb).sum(1) y += np.sqrt(scale) * np.random.normal(size=n) df = pd.DataFrame({"y": y, "x1": exog_fe[:, 0], "x2": exog_fe[:, 1], "z0": exog_re[:, 0], "z1": exog_re[:, 1], "grp": groups}) df["z2"] = exog_vca[:, 0] df["z3"] = exog_vca[:, 1] df["z4"] = exog_vcb[:, 0] df["z5"] = exog_vcb[:, 1] vcf = {"a": "0 + z2 + z3", "b": "0 + z4 + z5"} m = MixedLM.from_formula("y ~ 0 + x1 + x2", groups="grp", re_formula="0 + z0 + z1", vc_formula=vcf, data=df) # Build a params vector that is comparable to # MixedLMResults.params import statsmodels mp = statsmodels.regression.mixed_linear_model.MixedLMParams po = mp.from_components(fe_params=fe_params, cov_re=cov_re, vcomp=vcomp) pa = po.get_packed(has_fe=True, use_sqrt=False) pa[len(fe_params):] /= scale # Get a realization dist = m.get_distribution(pa, scale, None) yr = dist.rvs(0) # Check the overall variance v = (np.dot(exog_re, cov_re) * exog_re).sum(1).mean() v += vcomp[0] * (exog_vca**2).sum(1).mean() v += vcomp[1] * (exog_vcb**2).sum(1).mean() v += scale assert_allclose(np.var(yr - ey), v, rtol=1e-2, atol=1e-4) statsmodels-0.12.2/statsmodels/regression/tests/test_predict.py000066400000000000000000000233601400612667500251000ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Apr 20 17:12:53 2014 author: Josef Perktold """ import numpy as np from numpy.testing import assert_allclose, assert_equal import pandas as pd from statsmodels.regression.linear_model import OLS, WLS from statsmodels.sandbox.regression.predstd import wls_prediction_std from statsmodels.regression._prediction import get_prediction def test_predict_se(): # this test does not use reference values # checks conistency across options, and compares to direct calculation # generate dataset nsample = 50 x1 = np.linspace(0, 20, nsample) x = np.c_[x1, (x1 - 5)**2, np.ones(nsample)] np.random.seed(0)#9876789) #9876543) beta = [0.5, -0.01, 5.] y_true2 = np.dot(x, beta) w = np.ones(nsample) w[int(nsample * 6. / 10):] = 3 sig = 0.5 y2 = y_true2 + sig * w * np.random.normal(size=nsample) x2 = x[:,[0,2]] # estimate OLS res2 = OLS(y2, x2).fit() #direct calculation covb = res2.cov_params() predvar = res2.mse_resid + (x2 * np.dot(covb, x2.T).T).sum(1) predstd = np.sqrt(predvar) prstd, iv_l, iv_u = wls_prediction_std(res2) np.testing.assert_almost_equal(prstd, predstd, 15) #stats.t.isf(0.05/2., 50 - 2) q = 2.0106347546964458 ci_half = q * predstd np.testing.assert_allclose(iv_u, res2.fittedvalues + ci_half, rtol=1e-12) np.testing.assert_allclose(iv_l, res2.fittedvalues - ci_half, rtol=1e-12) prstd, iv_l, iv_u = wls_prediction_std(res2, x2[:3,:]) np.testing.assert_equal(prstd, prstd[:3]) np.testing.assert_allclose(iv_u, res2.fittedvalues[:3] + ci_half[:3], rtol=1e-12) np.testing.assert_allclose(iv_l, res2.fittedvalues[:3] - ci_half[:3], rtol=1e-12) # check WLS res3 = WLS(y2, x2, 1. / w).fit() #direct calculation covb = res3.cov_params() predvar = res3.mse_resid * w + (x2 * np.dot(covb, x2.T).T).sum(1) predstd = np.sqrt(predvar) prstd, iv_l, iv_u = wls_prediction_std(res3) np.testing.assert_almost_equal(prstd, predstd, 15) #stats.t.isf(0.05/2., 50 - 2) q = 2.0106347546964458 ci_half = q * predstd np.testing.assert_allclose(iv_u, res3.fittedvalues + ci_half, rtol=1e-12) np.testing.assert_allclose(iv_l, res3.fittedvalues - ci_half, rtol=1e-12) # testing shapes of exog prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-1:,:], weights=3.) np.testing.assert_equal(prstd, prstd[-1]) prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-1,:], weights=3.) np.testing.assert_equal(prstd, prstd[-1]) prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-2:,:], weights=3.) np.testing.assert_equal(prstd, prstd[-2:]) prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-2:,:], weights=[3, 3]) np.testing.assert_equal(prstd, prstd[-2:]) prstd, iv_l, iv_u = wls_prediction_std(res3, x2[:3,:]) np.testing.assert_equal(prstd, prstd[:3]) np.testing.assert_allclose(iv_u, res3.fittedvalues[:3] + ci_half[:3], rtol=1e-12) np.testing.assert_allclose(iv_l, res3.fittedvalues[:3] - ci_half[:3], rtol=1e-12) #use wrong size for exog #prstd, iv_l, iv_u = wls_prediction_std(res3, x2[-1,0], weights=3.) np.testing.assert_raises(ValueError, wls_prediction_std, res3, x2[-1,0], weights=3.) # check some weight values sew1 = wls_prediction_std(res3, x2[-3:,:])[0]**2 for wv in np.linspace(0.5, 3, 5): sew = wls_prediction_std(res3, x2[-3:,:], weights=1. / wv)[0]**2 np.testing.assert_allclose(sew, sew1 + res3.scale * (wv - 1)) class TestWLSPrediction(object): @classmethod def setup_class(cls): # from example wls.py nsample = 50 x = np.linspace(0, 20, nsample) X = np.column_stack((x, (x - 5)**2)) from statsmodels.tools.tools import add_constant X = add_constant(X) beta = [5., 0.5, -0.01] sig = 0.5 w = np.ones(nsample) w[int(nsample * 6. / 10):] = 3 y_true = np.dot(X, beta) e = np.random.normal(size=nsample) y = y_true + sig * w * e X = X[:,[0,1]] # ### WLS knowing the true variance ratio of heteroscedasticity mod_wls = WLS(y, X, weights=1./w) cls.res_wls = mod_wls.fit() def test_ci(self): res_wls = self.res_wls prstd, iv_l, iv_u = wls_prediction_std(res_wls) pred_res = get_prediction(res_wls) ci = pred_res.conf_int(obs=True) assert_allclose(pred_res.se_obs, prstd, rtol=1e-13) assert_allclose(ci, np.column_stack((iv_l, iv_u)), rtol=1e-13) sf = pred_res.summary_frame() col_names = ['mean', 'mean_se', 'mean_ci_lower', 'mean_ci_upper', 'obs_ci_lower', 'obs_ci_upper'] assert_equal(sf.columns.tolist(), col_names) pred_res2 = res_wls.get_prediction() ci2 = pred_res2.conf_int(obs=True) assert_allclose(pred_res2.se_obs, prstd, rtol=1e-13) assert_allclose(ci2, np.column_stack((iv_l, iv_u)), rtol=1e-13) sf2 = pred_res2.summary_frame() assert_equal(sf2.columns.tolist(), col_names) # check that list works, issue 4437 x = res_wls.model.exog.mean(0) pred_res3 = res_wls.get_prediction([x]) ci3 = pred_res3.conf_int(obs=True) pred_res3b = res_wls.get_prediction(x.tolist()) ci3b = pred_res3b.conf_int(obs=True) assert_allclose(pred_res3b.se_obs, pred_res3.se_obs, rtol=1e-13) assert_allclose(ci3b, ci3, rtol=1e-13) res_df = pred_res3b.summary_frame() assert_equal(res_df.index.values, [0]) x = res_wls.model.exog[-2:] pred_res3 = res_wls.get_prediction(x) ci3 = pred_res3.conf_int(obs=True) pred_res3b = res_wls.get_prediction(x.tolist()) ci3b = pred_res3b.conf_int(obs=True) assert_allclose(pred_res3b.se_obs, pred_res3.se_obs, rtol=1e-13) assert_allclose(ci3b, ci3, rtol=1e-13) res_df = pred_res3b.summary_frame() assert_equal(res_df.index.values, [0, 1]) def test_glm(self): # prelimnimary, getting started with basic test for GLM.get_prediction from statsmodels.genmod.generalized_linear_model import GLM res_wls = self.res_wls mod_wls = res_wls.model y, X, wi = mod_wls.endog, mod_wls.exog, mod_wls.weights w_sqrt = np.sqrt(wi) # notation wi is weights, `w` is var mod_glm = GLM(y * w_sqrt, X * w_sqrt[:,None]) # compare using t distribution res_glm = mod_glm.fit(use_t=True) pred_glm = res_glm.get_prediction() sf_glm = pred_glm.summary_frame() pred_res_wls = res_wls.get_prediction() sf_wls = pred_res_wls.summary_frame() n_compare = 30 # in glm with predict wendog assert_allclose(sf_glm.values[:n_compare], sf_wls.values[:n_compare, :4]) # compare using normal distribution res_glm = mod_glm.fit() # default use_t=False pred_glm = res_glm.get_prediction() sf_glm = pred_glm.summary_frame() res_wls = mod_wls.fit(use_t=False) pred_res_wls = res_wls.get_prediction() sf_wls = pred_res_wls.summary_frame() assert_allclose(sf_glm.values[:n_compare], sf_wls.values[:n_compare, :4]) # function for parameter transformation # should be separate test method from statsmodels.genmod._prediction import params_transform_univariate rates = params_transform_univariate(res_glm.params, res_glm.cov_params()) rates2 = np.column_stack((np.exp(res_glm.params), res_glm.bse * np.exp(res_glm.params), np.exp(res_glm.conf_int()))) assert_allclose(rates.summary_frame().values, rates2, rtol=1e-13) from statsmodels.genmod.families import links # with identity transform pt = params_transform_univariate(res_glm.params, res_glm.cov_params(), link=links.identity()) assert_allclose(pt.tvalues, res_glm.tvalues, rtol=1e-13) assert_allclose(pt.se_mean, res_glm.bse, rtol=1e-13) ptt = pt.t_test() assert_allclose(ptt[0], res_glm.tvalues, rtol=1e-13) assert_allclose(ptt[1], res_glm.pvalues, rtol=1e-13) # prediction with exog and no weights does not error res_glm = mod_glm.fit() pred_glm = res_glm.get_prediction(X) # check that list works, issue 4437 x = res_glm.model.exog.mean(0) pred_res3 = res_glm.get_prediction(x) ci3 = pred_res3.conf_int() pred_res3b = res_glm.get_prediction(x.tolist()) ci3b = pred_res3b.conf_int() assert_allclose(pred_res3b.se_mean, pred_res3.se_mean, rtol=1e-13) assert_allclose(ci3b, ci3, rtol=1e-13) res_df = pred_res3b.summary_frame() assert_equal(res_df.index.values, [0]) x = res_glm.model.exog[-2:] pred_res3 = res_glm.get_prediction(x) ci3 = pred_res3.conf_int() pred_res3b = res_glm.get_prediction(x.tolist()) ci3b = pred_res3b.conf_int() assert_allclose(pred_res3b.se_mean, pred_res3.se_mean, rtol=1e-13) assert_allclose(ci3b, ci3, rtol=1e-13) res_df = pred_res3b.summary_frame() assert_equal(res_df.index.values, [0, 1]) def test_predict_remove_data(): # GH6887 endog = [i + np.random.normal(scale=0.1) for i in range(100)] exog = [i for i in range(100)] model = OLS(endog, exog, weights=[1 for _ in range(100)]).fit() model.remove_data() scalar = model.get_prediction(1).predicted_mean one_d = model.get_prediction([1]).predicted_mean assert_allclose(scalar, one_d) series = model.get_prediction(pd.Series([1])).predicted_mean assert_allclose(scalar, series) statsmodels-0.12.2/statsmodels/regression/tests/test_processreg.py000066400000000000000000000124141400612667500256200ustar00rootroot00000000000000# -*- coding: utf-8 -*- from statsmodels.compat.platform import PLATFORM_OSX from statsmodels.regression.process_regression import ( ProcessMLE, GaussianCovariance) import numpy as np import pandas as pd import pytest import collections import statsmodels.tools.numdiff as nd from numpy.testing import assert_allclose, assert_equal def model1(): mn_par = np.r_[1, 0, -1, 0] sc_par = np.r_[1, 1] sm_par = np.r_[0.5, 0.1] no_par = np.r_[0.25, 0.25] return mn_par, sc_par, sm_par, no_par def setup1(n, get_model): mn_par, sc_par, sm_par, no_par = get_model() groups = np.kron(np.arange(n // 5), np.ones(5)) time = np.kron(np.ones(n // 5), np.arange(5)) time_z = (time - time.mean()) / time.std() x_mean = np.random.normal(size=(n, len(mn_par))) x_sc = np.random.normal(size=(n, len(sc_par))) x_sc[:, 0] = 1 x_sc[:, 1] = time_z x_sm = np.random.normal(size=(n, len(sm_par))) x_sm[:, 0] = 1 x_sm[:, 1] = time_z x_no = np.random.normal(size=(n, len(no_par))) x_no[:, 0] = 1 x_no[:, 1] = time_z mn = np.dot(x_mean, mn_par) sc = np.exp(np.dot(x_sc, sc_par)) sm = np.exp(np.dot(x_sm, sm_par)) no = np.exp(np.dot(x_no, no_par)) y = mn.copy() gc = GaussianCovariance() ix = collections.defaultdict(lambda: []) for i, g in enumerate(groups): ix[g].append(i) for g, ii in ix.items(): c = gc.get_cov(time[ii], sc[ii], sm[ii]) r = np.linalg.cholesky(c) y[ii] += np.dot(r, np.random.normal(size=len(ii))) # Additive white noise y += no * np.random.normal(size=y.shape) return y, x_mean, x_sc, x_sm, x_no, time, groups def run_arrays(n, get_model): y, x_mean, x_sc, x_sm, x_no, time, groups = setup1(n, get_model) preg = ProcessMLE(y, x_mean, x_sc, x_sm, x_no, time, groups) return preg.fit() @pytest.mark.slow def test_arrays(): np.random.seed(8234) f = run_arrays(1000, model1) mod = f.model f.summary() # Smoke test # Compare the parameter estimates to population values. epar = np.concatenate(model1()) assert_allclose(f.params, epar, atol=0.3, rtol=0.3) # Test the fitted covariance matrix cv = f.covariance(mod.time[0:5], mod.exog_scale[0:5, :], mod.exog_smooth[0:5, :]) assert_allclose(cv, cv.T) # Check symmetry a, _ = np.linalg.eig(cv) assert_equal(a > 0, True) # Check PSD # Test predict yhat = f.predict() assert_equal(np.corrcoef(yhat, mod.endog)[0, 1] > 0.2, True) yhatm = f.predict(exog=mod.exog) assert_equal(yhat, yhatm) yhat0 = mod.predict(params=f.params, exog=mod.exog) assert_equal(yhat, yhat0) # Smoke test t-test f.t_test(np.eye(len(f.params))) def run_formula(n, get_model): y, x_mean, x_sc, x_sm, x_no, time, groups = setup1(n, get_model) df = pd.DataFrame({ "y": y, "x1": x_mean[:, 0], "x2": x_mean[:, 1], "x3": x_mean[:, 2], "x4": x_mean[:, 3], "xsc1": x_sc[:, 0], "xsc2": x_sc[:, 1], "xsm1": x_sm[:, 0], "xsm2": x_sm[:, 1], "xno1": x_no[:, 0], "xno2": x_no[:, 1], "time": time, "groups": groups }) mean_formula = "y ~ 0 + x1 + x2 + x3 + x4" scale_formula = "0 + xsc1 + xsc2" smooth_formula = "0 + xsm1 + xsm2" noise_formula = "0 + xno1 + xno2" preg = ProcessMLE.from_formula( mean_formula, data=df, scale_formula=scale_formula, smooth_formula=smooth_formula, noise_formula=noise_formula, time="time", groups="groups") f = preg.fit() return f, df @pytest.mark.slow def test_formulas(): np.random.seed(8789) f, df = run_formula(1000, model1) mod = f.model f.summary() # Smoke test # Compare the parameter estimates to population values. epar = np.concatenate(model1()) assert_allclose(f.params, epar, atol=0.1, rtol=1) # Test the fitted covariance matrix exog_scale = pd.DataFrame(mod.exog_scale[0:5, :], columns=["xsc1", "xsc2"]) exog_smooth = pd.DataFrame(mod.exog_smooth[0:5, :], columns=["xsm1", "xsm2"]) cv = f.covariance(mod.time[0:5], exog_scale, exog_smooth) assert_allclose(cv, cv.T) a, _ = np.linalg.eig(cv) assert_equal(a > 0, True) # Test predict yhat = f.predict() assert_equal(np.corrcoef(yhat, mod.endog)[0, 1] > 0.2, True) yhatm = f.predict(exog=df) assert_equal(yhat, yhatm) yhat0 = mod.predict(params=f.params, exog=df) assert_equal(yhat, yhat0) # Smoke test t-test f.t_test(np.eye(len(f.params))) # Test the score functions using numerical derivatives. def test_score_numdiff(): y, x_mean, x_sc, x_sm, x_no, time, groups = setup1(1000, model1) preg = ProcessMLE(y, x_mean, x_sc, x_sm, x_no, time, groups) def loglike(x): return preg.loglike(x) q = x_mean.shape[1] + x_sc.shape[1] + x_sm.shape[1] + x_no.shape[1] np.random.seed(342) atol = 2e-3 if PLATFORM_OSX else 1e-2 for _ in range(5): par0 = preg._get_start() par = par0 + 0.1 * np.random.normal(size=q) score = preg.score(par) score_nd = nd.approx_fprime(par, loglike, epsilon=1e-7) assert_allclose(score, score_nd, atol=atol, rtol=1e-4) statsmodels-0.12.2/statsmodels/regression/tests/test_quantile_regression.py000066400000000000000000000233451400612667500275330ustar00rootroot00000000000000import scipy.stats import numpy as np import statsmodels.api as sm from numpy.testing import assert_allclose, assert_equal, assert_almost_equal from patsy import dmatrices # pylint: disable=E0611 from statsmodels.regression.quantile_regression import QuantReg from .results.results_quantile_regression import ( biweight_chamberlain, biweight_hsheather, biweight_bofinger, cosine_chamberlain, cosine_hsheather, cosine_bofinger, gaussian_chamberlain, gaussian_hsheather, gaussian_bofinger, epan2_chamberlain, epan2_hsheather, epan2_bofinger, parzen_chamberlain, parzen_hsheather, parzen_bofinger, # rectangle_chamberlain, rectangle_hsheather, rectangle_bofinger, # triangle_chamberlain, triangle_hsheather, triangle_bofinger, # epanechnikov_chamberlain, epanechnikov_hsheather, epanechnikov_bofinger, epanechnikov_hsheather_q75, Rquantreg) idx = ['income', 'Intercept'] class CheckModelResultsMixin(object): def test_params(self): assert_allclose(np.ravel(self.res1.params.loc[idx]), self.res2.table[:, 0], rtol=1e-3) def test_bse(self): assert_equal(self.res1.scale, 1) assert_allclose(np.ravel(self.res1.bse.loc[idx]), self.res2.table[:, 1], rtol=1e-3) def test_tvalues(self): assert_allclose(np.ravel(self.res1.tvalues.loc[idx]), self.res2.table[:, 2], rtol=1e-2) def test_pvalues(self): pvals_stata = scipy.stats.t.sf(self.res2.table[:, 2], self.res2.df_r) assert_allclose(np.ravel(self.res1.pvalues.loc[idx]), pvals_stata, rtol=1.1) # test that we use the t distribution for the p-values pvals_t = scipy.stats.t.sf(self.res1.tvalues, self.res2.df_r) * 2 assert_allclose(np.ravel(self.res1.pvalues), pvals_t, rtol=1e-9, atol=1e-10) def test_conf_int(self): assert_allclose(self.res1.conf_int().loc[idx], self.res2.table[:, -2:], rtol=1e-3) def test_nobs(self): assert_allclose(self.res1.nobs, self.res2.N, rtol=1e-3) def test_df_model(self): assert_allclose(self.res1.df_model, self.res2.df_m, rtol=1e-3) def test_df_resid(self): assert_allclose(self.res1.df_resid, self.res2.df_r, rtol=1e-3) def test_prsquared(self): assert_allclose(self.res1.prsquared, self.res2.psrsquared, rtol=1e-3) def test_sparsity(self): assert_allclose(np.array(self.res1.sparsity), self.res2.sparsity, rtol=1e-3) def test_bandwidth(self): assert_allclose(np.array(self.res1.bandwidth), self.res2.kbwidth, rtol=1e-3) d = {('biw', 'bofinger'): biweight_bofinger, ('biw', 'chamberlain'): biweight_chamberlain, ('biw', 'hsheather'): biweight_hsheather, ('cos', 'bofinger'): cosine_bofinger, ('cos', 'chamberlain'): cosine_chamberlain, ('cos', 'hsheather'): cosine_hsheather, ('gau', 'bofinger'): gaussian_bofinger, ('gau', 'chamberlain'): gaussian_chamberlain, ('gau', 'hsheather'): gaussian_hsheather, ('par', 'bofinger'): parzen_bofinger, ('par', 'chamberlain'): parzen_chamberlain, ('par', 'hsheather'): parzen_hsheather, # ('rec','bofinger'): rectangle_bofinger, # ('rec','chamberlain'): rectangle_chamberlain, # ('rec','hsheather'): rectangle_hsheather, # ('tri','bofinger'): triangle_bofinger, # ('tri','chamberlain'): triangle_chamberlain, # ('tri','hsheather'): triangle_hsheather, ('epa', 'bofinger'): epan2_bofinger, ('epa', 'chamberlain'): epan2_chamberlain, ('epa', 'hsheather'): epan2_hsheather # ('epa2', 'bofinger'): epan2_bofinger, # ('epa2', 'chamberlain'): epan2_chamberlain, # ('epa2', 'hsheather'): epan2_hsheather } def setup_fun(kernel='gau', bandwidth='bofinger'): data = sm.datasets.engel.load_pandas().data y, X = dmatrices('foodexp ~ income', data, return_type='dataframe') statsm = QuantReg(y, X).fit(vcov='iid', kernel=kernel, bandwidth=bandwidth) stata = d[(kernel, bandwidth)] return statsm, stata def test_fitted_residuals(): data = sm.datasets.engel.load_pandas().data y, X = dmatrices('foodexp ~ income', data, return_type='dataframe') res = QuantReg(y, X).fit(q=.1) # Note: maxabs relative error with fitted is 1.789e-09 assert_almost_equal(np.array(res.fittedvalues), Rquantreg.fittedvalues, 5) assert_almost_equal(np.array(res.predict()), Rquantreg.fittedvalues, 5) assert_almost_equal(np.array(res.resid), Rquantreg.residuals, 5) class TestEpanechnikovHsheatherQ75(CheckModelResultsMixin): # Vincent Arel-Bundock also spot-checked q=.1 @classmethod def setup_class(cls): data = sm.datasets.engel.load_pandas().data y, X = dmatrices('foodexp ~ income', data, return_type='dataframe') cls.res1 = QuantReg(y, X).fit(q=.75, vcov='iid', kernel='epa', bandwidth='hsheather') cls.res2 = epanechnikov_hsheather_q75 class TestEpanechnikovBofinger(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('epa', 'bofinger') class TestEpanechnikovChamberlain(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('epa', 'chamberlain') class TestEpanechnikovHsheather(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('epa', 'hsheather') class TestGaussianBofinger(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('gau', 'bofinger') class TestGaussianChamberlain(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('gau', 'chamberlain') class TestGaussianHsheather(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('gau', 'hsheather') class TestBiweightBofinger(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('biw', 'bofinger') class TestBiweightChamberlain(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('biw', 'chamberlain') class TestBiweightHsheather(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('biw', 'hsheather') class TestCosineBofinger(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('cos', 'bofinger') class TestCosineChamberlain(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('cos', 'chamberlain') class TestCosineHsheather(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('cos', 'hsheather') class TestParzeneBofinger(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('par', 'bofinger') class TestParzeneChamberlain(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('par', 'chamberlain') class TestParzeneHsheather(CheckModelResultsMixin): @classmethod def setup_class(cls): cls.res1, cls.res2 = setup_fun('par', 'hsheather') # class TestTriangleBofinger(CheckModelResultsMixin): # @classmethod # def setup_class(cls): # cls.res1, cls.res2 = setup_fun('tri', 'bofinger') # class TestTriangleChamberlain(CheckModelResultsMixin): # @classmethod # def setup_class(cls): # cls.res1, cls.res2 = setup_fun('tri', 'chamberlain') # class TestTriangleHsheather(CheckModelResultsMixin): # @classmethod # def setup_class(cls): # cls.res1, cls.res2 = setup_fun('tri', 'hsheather') def test_zero_resid(): # smoke and regression tests X = np.array([[1, 0], [0, 1], [0, 2.1], [0, 3.1]], dtype=np.float64) y = np.array([0, 1, 2, 3], dtype=np.float64) res = QuantReg(y, X).fit(0.5, bandwidth='chamberlain') # 'bofinger') res.summary() assert_allclose(res.params, np.array([0.0, 0.96774163]), rtol=1e-4, atol=1e-20) assert_allclose(res.bse, np.array([0.0447576, 0.01154867]), rtol=1e-4, atol=1e-20) assert_allclose(res.resid, np.array([0.0, 3.22583680e-02, -3.22574272e-02, 9.40732912e-07]), rtol=1e-4, atol=1e-20) X = np.array([[1, 0], [0.1, 1], [0, 2.1], [0, 3.1]], dtype=np.float64) y = np.array([0, 1, 2, 3], dtype=np.float64) res = QuantReg(y, X).fit(0.5, bandwidth='chamberlain') res.summary() assert_allclose(res.params, np.array([9.99982796e-08, 9.67741630e-01]), rtol=1e-4, atol=1e-20) assert_allclose(res.bse, np.array([0.04455029, 0.01155251]), rtol=1e-4, atol=1e-20) assert_allclose(res.resid, np.array([-9.99982796e-08, 3.22583598e-02, -3.22574234e-02, 9.46361860e-07]), rtol=1e-4, atol=1e-20) def test_use_t_summary(): X = np.array([[1, 0], [0, 1], [0, 2.1], [0, 3.1]], dtype=np.float64) y = np.array([0, 1, 2, 3], dtype=np.float64) res = QuantReg(y, X).fit(0.5, bandwidth='chamberlain', use_t=True) summ = res.summary() assert 'P>|t|' in str(summ) assert 'P>|z|' not in str(summ) def test_alpha_summary(): X = np.array([[1, 0], [0, 1], [0, 2.1], [0, 3.1]], dtype=np.float64) y = np.array([0, 1, 2, 3], dtype=np.float64) res = QuantReg(y, X).fit(0.5, bandwidth='chamberlain', use_t=True) summ_20 = res.summary(alpha=.2) assert '[0.025 0.975]' not in str(summ_20) assert '[0.1 0.9]' in str(summ_20) statsmodels-0.12.2/statsmodels/regression/tests/test_recursive_ls.py000066400000000000000000000442301400612667500261520ustar00rootroot00000000000000""" Tests for recursive least squares models Author: Chad Fulton License: Simplified-BSD """ import numpy as np import pandas as pd import pytest from scipy.stats import norm import os from statsmodels.datasets import macrodata from statsmodels.regression.linear_model import OLS from statsmodels.genmod.api import GLM from statsmodels.tools.eval_measures import aic, bic from statsmodels.regression.recursive_ls import RecursiveLS from statsmodels.stats.diagnostic import recursive_olsresiduals from statsmodels.tools import add_constant from statsmodels.tools.sm_exceptions import ValueWarning from numpy.testing import assert_equal, assert_raises, assert_allclose current_path = os.path.dirname(os.path.abspath(__file__)) results_R_path = 'results' + os.sep + 'results_rls_R.csv' results_R = pd.read_csv(current_path + os.sep + results_R_path) results_stata_path = 'results' + os.sep + 'results_rls_stata.csv' results_stata = pd.read_csv(current_path + os.sep + results_stata_path) dta = macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-07-01', freq='QS') endog = dta['cpi'] exog = add_constant(dta['m1']) def test_endog(): # Tests for numpy input mod = RecursiveLS(endog.values, exog.values) res = mod.fit() # Test the RLS estimates against OLS estimates mod_ols = OLS(endog, exog) res_ols = mod_ols.fit() assert_allclose(res.params, res_ols.params) # Tests for 1-dim exog mod = RecursiveLS(endog, dta['m1'].values) res = mod.fit() # Test the RLS estimates against OLS estimates mod_ols = OLS(endog, dta['m1']) res_ols = mod_ols.fit() assert_allclose(res.params, res_ols.params) def test_ols(): # More comprehensive tests against OLS estimates mod = RecursiveLS(endog, dta['m1']) res = mod.fit() mod_ols = OLS(endog, dta['m1']) res_ols = mod_ols.fit() # Regression coefficients, standard errors, and estimated scale assert_allclose(res.params, res_ols.params) assert_allclose(res.bse, res_ols.bse) # Note: scale here is computed according to Harvey, 1989, 4.2.5, and is # the called the ML estimator and sometimes (e.g. later in section 5) # denoted \tilde \sigma_*^2 assert_allclose(res.filter_results.obs_cov[0, 0], res_ols.scale) # OLS residuals are equivalent to smoothed forecast errors # (the latter are defined as e_t|T by Harvey, 1989, 5.4.5) # (this follows since the smoothed state simply contains the # full-information estimates of the regression coefficients) actual = (mod.endog[:, 0] - np.sum(mod['design', 0, :, :] * res.smoothed_state, axis=0)) assert_allclose(actual, res_ols.resid) # Given the estimate of scale as `sum(v_t^2 / f_t) / (T - d)` (see # Harvey, 1989, 4.2.5 on p. 183), then llf_recursive is equivalent to the # full OLS loglikelihood (i.e. without the scale concentrated out). desired = mod_ols.loglike(res_ols.params, scale=res_ols.scale) assert_allclose(res.llf_recursive, desired) # Alternatively, we can constrcut the concentrated OLS loglikelihood # by computing the scale term with `nobs` in the denominator rather than # `nobs - d`. scale_alternative = np.sum(( res.standardized_forecasts_error[0, 1:] * res.filter_results.obs_cov[0, 0]**0.5)**2) / mod.nobs llf_alternative = np.log(norm.pdf(res.resid_recursive, loc=0, scale=scale_alternative**0.5)).sum() assert_allclose(llf_alternative, res_ols.llf) # Prediction actual = res.forecast(10, design=np.ones((1, 1, 10))) assert_allclose(actual, res_ols.predict(np.ones((10, 1)))) # Sums of squares, R^2 assert_allclose(res.ess, res_ols.ess) assert_allclose(res.ssr, res_ols.ssr) assert_allclose(res.centered_tss, res_ols.centered_tss) assert_allclose(res.uncentered_tss, res_ols.uncentered_tss) assert_allclose(res.rsquared, res_ols.rsquared) # Mean squares assert_allclose(res.mse_model, res_ols.mse_model) assert_allclose(res.mse_resid, res_ols.mse_resid) assert_allclose(res.mse_total, res_ols.mse_total) # Hypothesis tests actual = res.t_test('m1 = 0') desired = res_ols.t_test('m1 = 0') assert_allclose(actual.statistic, desired.statistic) assert_allclose(actual.pvalue, desired.pvalue, atol=1e-15) actual = res.f_test('m1 = 0') desired = res_ols.f_test('m1 = 0') assert_allclose(actual.statistic, desired.statistic) assert_allclose(actual.pvalue, desired.pvalue, atol=1e-15) # Information criteria # Note: the llf and llf_obs given in the results are based on the Kalman # filter and so the ic given in results will not be identical to the # OLS versions. Additionally, llf_recursive is comparable to the # non-concentrated llf, and not the concentrated llf that is by default # used in OLS. Compute new ic based on llf_alternative to compare. actual_aic = aic(llf_alternative, res.nobs_effective, res.df_model) assert_allclose(actual_aic, res_ols.aic) actual_bic = bic(llf_alternative, res.nobs_effective, res.df_model) assert_allclose(actual_bic, res_ols.bic) def test_glm(constraints=None): # More comprehensive tests against GLM estimates (this is sort of redundant # given `test_ols`, but this is mostly to complement the tests in # `test_glm_constrained`) endog = dta.infl exog = add_constant(dta[['unemp', 'm1']]) mod = RecursiveLS(endog, exog, constraints=constraints) res = mod.fit() mod_glm = GLM(endog, exog) if constraints is None: res_glm = mod_glm.fit() else: res_glm = mod_glm.fit_constrained(constraints=constraints) # Regression coefficients, standard errors, and estimated scale assert_allclose(res.params, res_glm.params) assert_allclose(res.bse, res_glm.bse, atol=1e-6) # Note: scale here is computed according to Harvey, 1989, 4.2.5, and is # the called the ML estimator and sometimes (e.g. later in section 5) # denoted \tilde \sigma_*^2 assert_allclose(res.filter_results.obs_cov[0, 0], res_glm.scale) # DoF # Note: GLM does not include intercept in DoF, so modify by -1 assert_equal(res.df_model - 1, res_glm.df_model) # OLS residuals are equivalent to smoothed forecast errors # (the latter are defined as e_t|T by Harvey, 1989, 5.4.5) # (this follows since the smoothed state simply contains the # full-information estimates of the regression coefficients) actual = (mod.endog[:, 0] - np.sum(mod['design', 0, :, :] * res.smoothed_state, axis=0)) assert_allclose(actual, res_glm.resid_response, atol=1e-7) # Given the estimate of scale as `sum(v_t^2 / f_t) / (T - d)` (see # Harvey, 1989, 4.2.5 on p. 183), then llf_recursive is equivalent to the # full OLS loglikelihood (i.e. without the scale concentrated out). desired = mod_glm.loglike(res_glm.params, scale=res_glm.scale) assert_allclose(res.llf_recursive, desired) # Alternatively, we can construct the concentrated OLS loglikelihood # by computing the scale term with `nobs` in the denominator rather than # `nobs - d`. scale_alternative = np.sum(( res.standardized_forecasts_error[0, 1:] * res.filter_results.obs_cov[0, 0]**0.5)**2) / mod.nobs llf_alternative = np.log(norm.pdf(res.resid_recursive, loc=0, scale=scale_alternative**0.5)).sum() assert_allclose(llf_alternative, res_glm.llf) # Prediction # TODO: prediction in this case is not working. if constraints is None: design = np.ones((1, 3, 10)) actual = res.forecast(10, design=design) assert_allclose(actual, res_glm.predict(np.ones((10, 3)))) else: design = np.ones((2, 3, 10)) assert_raises(NotImplementedError, res.forecast, 10, design=design) # Hypothesis tests actual = res.t_test('m1 = 0') desired = res_glm.t_test('m1 = 0') assert_allclose(actual.statistic, desired.statistic) assert_allclose(actual.pvalue, desired.pvalue, atol=1e-15) actual = res.f_test('m1 = 0') desired = res_glm.f_test('m1 = 0') assert_allclose(actual.statistic, desired.statistic) assert_allclose(actual.pvalue, desired.pvalue) # Information criteria # Note: the llf and llf_obs given in the results are based on the Kalman # filter and so the ic given in results will not be identical to the # OLS versions. Additionally, llf_recursive is comparable to the # non-concentrated llf, and not the concentrated llf that is by default # used in OLS. Compute new ic based on llf_alternative to compare. actual_aic = aic(llf_alternative, res.nobs_effective, res.df_model) assert_allclose(actual_aic, res_glm.aic) # See gh#1733 for details on why the BIC does not match while AIC does # actual_bic = bic(llf_alternative, res.nobs_effective, res.df_model) # assert_allclose(actual_bic, res_glm.bic) def test_glm_constrained(): test_glm(constraints='m1 + unemp = 1') def test_filter(): # Basic test for filtering mod = RecursiveLS(endog, exog) res = mod.filter() # Test the RLS estimates against OLS estimates mod_ols = OLS(endog, exog) res_ols = mod_ols.fit() assert_allclose(res.params, res_ols.params) def test_estimates(): mod = RecursiveLS(endog, exog) res = mod.fit() # Test for start_params assert_equal(mod.start_params, 0) # Test the RLS coefficient estimates against those from R (quantreg) # Due to initialization issues, we get more agreement as we get # farther from the initial values. assert_allclose(res.recursive_coefficients.filtered[:, 2:10].T, results_R.iloc[:8][['beta1', 'beta2']], rtol=1e-5) assert_allclose(res.recursive_coefficients.filtered[:, 9:20].T, results_R.iloc[7:18][['beta1', 'beta2']]) assert_allclose(res.recursive_coefficients.filtered[:, 19:].T, results_R.iloc[17:][['beta1', 'beta2']]) # Test the RLS estimates against OLS estimates mod_ols = OLS(endog, exog) res_ols = mod_ols.fit() assert_allclose(res.params, res_ols.params) @pytest.mark.matplotlib def test_plots(close_figures): exog = add_constant(dta[['m1', 'pop']]) mod = RecursiveLS(endog, exog) res = mod.fit() # Basic plot try: from pandas.plotting import register_matplotlib_converters register_matplotlib_converters() except ImportError: pass fig = res.plot_recursive_coefficient() # Specific variable fig = res.plot_recursive_coefficient(variables=['m1']) # All variables fig = res.plot_recursive_coefficient(variables=[0, 'm1', 'pop']) # Basic plot fig = res.plot_cusum() # Other alphas for alpha in [0.01, 0.10]: fig = res.plot_cusum(alpha=alpha) # Invalid alpha assert_raises(ValueError, res.plot_cusum, alpha=0.123) # Basic plot fig = res.plot_cusum_squares() # Numpy input (no dates) mod = RecursiveLS(endog.values, exog.values) res = mod.fit() # Basic plot fig = res.plot_recursive_coefficient() # Basic plot fig = res.plot_cusum() # Basic plot fig = res.plot_cusum_squares() def test_from_formula(): with pytest.warns(ValueWarning, match="No frequency information"): mod = RecursiveLS.from_formula('cpi ~ m1', data=dta) res = mod.fit() # Test the RLS estimates against OLS estimates mod_ols = OLS.from_formula('cpi ~ m1', data=dta) res_ols = mod_ols.fit() assert_allclose(res.params, res_ols.params) def test_resid_recursive(): mod = RecursiveLS(endog, exog) res = mod.fit() # Test the recursive residuals against those from R (strucchange) assert_allclose(res.resid_recursive[2:10].T, results_R.iloc[:8]['rec_resid']) assert_allclose(res.resid_recursive[9:20].T, results_R.iloc[7:18]['rec_resid']) assert_allclose(res.resid_recursive[19:].T, results_R.iloc[17:]['rec_resid']) # Test the RLS estimates against those from Stata (cusum6) assert_allclose(res.resid_recursive[3:], results_stata.iloc[3:]['rr'], atol=1e-5, rtol=1e-5) # Test the RLS estimates against statsmodels estimates mod_ols = OLS(endog, exog) res_ols = mod_ols.fit() desired_resid_recursive = recursive_olsresiduals(res_ols)[4][2:] assert_allclose(res.resid_recursive[2:], desired_resid_recursive) def test_cusum(): mod = RecursiveLS(endog, exog) res = mod.fit() # Test the cusum statistics against those from R (strucchange) # These values are not even close to ours, to Statas, or to the alternate # statsmodels values # assert_allclose(res.cusum, results_R['cusum']) # Test the cusum statistics against Stata (cusum6) # Note: cusum6 excludes the first 3 elements due to OLS initialization # whereas we exclude only the first 2. Also there are initialization # differences (as seen above in the recursive residuals). # Here we explicitly reverse engineer our cusum to match their to show the # equivalence d = res.nobs_diffuse cusum = res.cusum * np.std(res.resid_recursive[d:], ddof=1) cusum -= res.resid_recursive[d] cusum /= np.std(res.resid_recursive[d+1:], ddof=1) cusum = cusum[1:] assert_allclose(cusum, results_stata.iloc[3:]['cusum'], atol=1e-6, rtol=1e-5) # Test the cusum statistics against statsmodels estimates mod_ols = OLS(endog, exog) res_ols = mod_ols.fit() desired_cusum = recursive_olsresiduals(res_ols)[-2][1:] assert_allclose(res.cusum, desired_cusum, rtol=1e-6) # Test the cusum bounds against Stata (cusum6) # Again note that cusum6 excludes the first 3 elements, so we need to # change the ddof and points. actual_bounds = res._cusum_significance_bounds( alpha=0.05, ddof=1, points=np.arange(d+1, res.nobs)) desired_bounds = results_stata.iloc[3:][['lw', 'uw']].T assert_allclose(actual_bounds, desired_bounds, rtol=1e-6) # Test the cusum bounds against statsmodels actual_bounds = res._cusum_significance_bounds( alpha=0.05, ddof=0, points=np.arange(d, res.nobs)) desired_bounds = recursive_olsresiduals(res_ols)[-1] assert_allclose(actual_bounds, desired_bounds) # Test for invalid calls assert_raises(ValueError, res._cusum_squares_significance_bounds, alpha=0.123) def test_stata(): # Test the cusum and cusumsq statistics against Stata (cusum6) mod = RecursiveLS(endog, exog, loglikelihood_burn=3) with pytest.warns(UserWarning): res = mod.fit() d = max(res.nobs_diffuse, res.loglikelihood_burn) assert_allclose(res.resid_recursive[3:], results_stata.iloc[3:]['rr'], atol=1e-5, rtol=1e-5) assert_allclose(res.cusum, results_stata.iloc[3:]['cusum'], atol=1e-5) assert_allclose(res.cusum_squares, results_stata.iloc[3:]['cusum2'], atol=1e-5) actual_bounds = res._cusum_significance_bounds( alpha=0.05, ddof=0, points=np.arange(d+1, res.nobs+1)) desired_bounds = results_stata.iloc[3:][['lw', 'uw']].T assert_allclose(actual_bounds, desired_bounds, atol=1e-5) # Note: Stata uses a set of tabulated critical values whereas we use an # approximation formula, so this test is quite imprecise actual_bounds = res._cusum_squares_significance_bounds( alpha=0.05, points=np.arange(d+1, res.nobs+1)) desired_bounds = results_stata.iloc[3:][['lww', 'uww']].T assert_allclose(actual_bounds, desired_bounds, atol=1e-2) def test_constraints_stata(): endog = dta['infl'] exog = add_constant(dta[['m1', 'unemp']]) mod = RecursiveLS(endog, exog, constraints='m1 + unemp = 1') res = mod.fit() # See tests/results/test_rls.do desired = [-0.7001083844336, -0.0018477514060, 1.0018477514060] assert_allclose(res.params, desired) # See tests/results/test_rls.do desired = [.4699552366, .0005369357, .0005369357] assert_allclose(res.bse[0], desired[0], atol=1e-1) assert_allclose(res.bse[1:], desired[1:], atol=1e-4) # See tests/results/test_rls.do desired = -534.4292052931121 # Note that to compute what Stata reports as the llf, we need to use a # different denominator for estimating the scale, and then compute the # llf from the alternative recursive residuals scale_alternative = np.sum(( res.standardized_forecasts_error[0, 1:] * res.filter_results.obs_cov[0, 0]**0.5)**2) / mod.nobs llf_alternative = np.log(norm.pdf(res.resid_recursive, loc=0, scale=scale_alternative**0.5)).sum() assert_allclose(llf_alternative, desired) def test_multiple_constraints(): endog = dta['infl'] exog = add_constant(dta[['m1', 'unemp', 'cpi']]) constraints = [ 'm1 + unemp = 1', 'cpi = 0', ] mod = RecursiveLS(endog, exog, constraints=constraints) res = mod.fit() # See tests/results/test_rls.do desired = [-0.7001083844336, -0.0018477514060, 1.0018477514060, 0] assert_allclose(res.params, desired, atol=1e-10) # See tests/results/test_rls.do desired = [.4699552366, .0005369357, .0005369357, 0] assert_allclose(res.bse[0], desired[0], atol=1e-1) assert_allclose(res.bse[1:-1], desired[1:-1], atol=1e-4) # See tests/results/test_rls.do desired = -534.4292052931121 # Note that to compute what Stata reports as the llf, we need to use a # different denominator for estimating the scale, and then compute the # llf from the alternative recursive residuals scale_alternative = np.sum(( res.standardized_forecasts_error[0, 1:] * res.filter_results.obs_cov[0, 0]**0.5)**2) / mod.nobs llf_alternative = np.log(norm.pdf(res.resid_recursive, loc=0, scale=scale_alternative**0.5)).sum() assert_allclose(llf_alternative, desired) def test_fix_params(): mod = RecursiveLS([0, 1, 0, 1], [1, 1, 1, 1]) with pytest.raises(ValueError, match=('Linear constraints on coefficients' ' should be given')): with mod.fix_params({'const': 0.1}): mod.fit() with pytest.raises(ValueError, match=('Linear constraints on coefficients' ' should be given')): mod.fit_constrained({'const': 0.1}) statsmodels-0.12.2/statsmodels/regression/tests/test_regression.py000066400000000000000000001402511400612667500256250ustar00rootroot00000000000000""" Test functions for models.regression """ # TODO: Test for LM from statsmodels.compat.python import lrange import warnings import pandas as pd import numpy as np from numpy.testing import (assert_almost_equal, assert_, assert_raises, assert_equal, assert_allclose) import pytest from scipy.linalg import toeplitz from statsmodels.tools.tools import add_constant from statsmodels.regression.linear_model import (OLS, WLS, GLS, yule_walker, burg) from statsmodels.datasets import longley from scipy.stats import t as student_t DECIMAL_4 = 4 DECIMAL_3 = 3 DECIMAL_2 = 2 DECIMAL_1 = 1 DECIMAL_7 = 7 DECIMAL_0 = 0 try: import cvxopt # noqa:F401 has_cvxopt = True except ImportError: has_cvxopt = False class CheckRegressionResults(object): """ res2 contains results from Rmodelwrap or were obtained from a statistical packages such as R, Stata, or SAS and were written to model_results """ decimal_params = DECIMAL_4 def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, self.decimal_params) decimal_standarderrors = DECIMAL_4 def test_standarderrors(self): assert_almost_equal(self.res1.bse, self.res2.bse, self.decimal_standarderrors) decimal_confidenceintervals = DECIMAL_4 def test_confidenceintervals(self): # NOTE: stata rounds residuals (at least) to sig digits so approx_equal conf1 = self.res1.conf_int() conf2 = self.res2.conf_int() for i in range(len(conf1)): assert_allclose(conf1[i][0], conf2[i][0], rtol=10**-self.decimal_confidenceintervals) assert_allclose(conf1[i][1], conf2[i][1], rtol=10**-self.decimal_confidenceintervals) decimal_conf_int_subset = DECIMAL_4 def test_conf_int_subset(self): if len(self.res1.params) > 1: ci1 = self.res1.conf_int(cols=(1, 2)) ci2 = self.res1.conf_int()[1:3] assert_almost_equal(ci1, ci2, self.decimal_conf_int_subset) else: pass decimal_scale = DECIMAL_4 def test_scale(self): assert_almost_equal(self.res1.scale, self.res2.scale, self.decimal_scale) decimal_rsquared = DECIMAL_4 def test_rsquared(self): assert_almost_equal(self.res1.rsquared, self.res2.rsquared, self.decimal_rsquared) decimal_rsquared_adj = DECIMAL_4 def test_rsquared_adj(self): assert_almost_equal(self.res1.rsquared_adj, self.res2.rsquared_adj, self.decimal_rsquared_adj) def test_degrees(self): assert_equal(self.res1.model.df_model, self.res2.df_model) assert_equal(self.res1.model.df_resid, self.res2.df_resid) decimal_ess = DECIMAL_4 def test_ess(self): # Explained Sum of Squares assert_almost_equal(self.res1.ess, self.res2.ess, self.decimal_ess) decimal_ssr = DECIMAL_4 def test_sumof_squaredresids(self): assert_almost_equal(self.res1.ssr, self.res2.ssr, self.decimal_ssr) decimal_mse_resid = DECIMAL_4 def test_mse_resid(self): # Mean squared error of residuals assert_almost_equal(self.res1.mse_model, self.res2.mse_model, self.decimal_mse_resid) decimal_mse_model = DECIMAL_4 def test_mse_model(self): assert_almost_equal(self.res1.mse_resid, self.res2.mse_resid, self.decimal_mse_model) decimal_mse_total = DECIMAL_4 def test_mse_total(self): assert_almost_equal(self.res1.mse_total, self.res2.mse_total, self.decimal_mse_total, err_msg="Test class %s" % self) decimal_fvalue = DECIMAL_4 def test_fvalue(self): # did not change this, not sure it should complain -inf not equal -inf # if not (np.isinf(self.res1.fvalue) and np.isinf(self.res2.fvalue)): assert_almost_equal(self.res1.fvalue, self.res2.fvalue, self.decimal_fvalue) decimal_loglike = DECIMAL_4 def test_loglike(self): assert_almost_equal(self.res1.llf, self.res2.llf, self.decimal_loglike) decimal_aic = DECIMAL_4 def test_aic(self): assert_almost_equal(self.res1.aic, self.res2.aic, self.decimal_aic) decimal_bic = DECIMAL_4 def test_bic(self): assert_almost_equal(self.res1.bic, self.res2.bic, self.decimal_bic) decimal_pvalues = DECIMAL_4 def test_pvalues(self): assert_almost_equal(self.res1.pvalues, self.res2.pvalues, self.decimal_pvalues) decimal_wresid = DECIMAL_4 def test_wresid(self): assert_almost_equal(self.res1.wresid, self.res2.wresid, self.decimal_wresid) decimal_resids = DECIMAL_4 def test_resids(self): assert_almost_equal(self.res1.resid, self.res2.resid, self.decimal_resids) decimal_norm_resids = DECIMAL_4 def test_norm_resids(self): assert_almost_equal(self.res1.resid_pearson, self.res2.resid_pearson, self.decimal_norm_resids) # TODO: test fittedvalues and what else? class TestOLS(CheckRegressionResults): @classmethod def setup_class(cls): from .results.results_regression import Longley data = longley.load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) res1 = OLS(data.endog, data.exog).fit() res2 = Longley() res2.wresid = res1.wresid # workaround hack cls.res1 = res1 cls.res2 = res2 res_qr = OLS(data.endog, data.exog).fit(method="qr") model_qr = OLS(data.endog, data.exog) Q, R = np.linalg.qr(data.exog) model_qr.exog_Q, model_qr.exog_R = Q, R model_qr.normalized_cov_params = np.linalg.inv(np.dot(R.T, R)) model_qr.rank = np.linalg.matrix_rank(R) res_qr2 = model_qr.fit(method="qr") cls.res_qr = res_qr cls.res_qr_manual = res_qr2 def test_eigenvalues(self): eigenval_perc_diff = (self.res_qr.eigenvals - self.res_qr_manual.eigenvals) eigenval_perc_diff /= self.res_qr.eigenvals zeros = np.zeros_like(eigenval_perc_diff) assert_almost_equal(eigenval_perc_diff, zeros, DECIMAL_7) # Robust error tests. Compare values computed with SAS def test_HC0_errors(self): # They are split up because the copied results do not have any # DECIMAL_4 places for the last place. assert_almost_equal(self.res1.HC0_se[:-1], self.res2.HC0_se[:-1], DECIMAL_4) assert_allclose(np.round(self.res1.HC0_se[-1]), self.res2.HC0_se[-1]) def test_HC1_errors(self): assert_almost_equal(self.res1.HC1_se[:-1], self.res2.HC1_se[:-1], DECIMAL_4) # Note: tolerance is tight; rtol=3e-7 fails while 4e-7 passes assert_allclose(self.res1.HC1_se[-1], self.res2.HC1_se[-1], rtol=4e-7) def test_HC2_errors(self): assert_almost_equal(self.res1.HC2_se[:-1], self.res2.HC2_se[:-1], DECIMAL_4) # Note: tolerance is tight; rtol=4e-7 fails while 5e-7 passes assert_allclose(self.res1.HC2_se[-1], self.res2.HC2_se[-1], rtol=5e-7) def test_HC3_errors(self): assert_almost_equal(self.res1.HC3_se[:-1], self.res2.HC3_se[:-1], DECIMAL_4) # Note: tolerance is tight; rtol=1e-7 fails while 1.5e-7 passes assert_allclose(self.res1.HC3_se[-1], self.res2.HC3_se[-1], rtol=1.5e-7) def test_qr_params(self): assert_almost_equal(self.res1.params, self.res_qr.params, 6) def test_qr_normalized_cov_params(self): # todo: need assert_close assert_almost_equal(np.ones_like(self.res1.normalized_cov_params), self.res1.normalized_cov_params / self.res_qr.normalized_cov_params, 5) def test_missing(self): data = longley.load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) data.endog[[3, 7, 14]] = np.nan mod = OLS(data.endog, data.exog, missing='drop') assert_equal(mod.endog.shape[0], 13) assert_equal(mod.exog.shape[0], 13) def test_rsquared_adj_overfit(self): # Test that if df_resid = 0, rsquared_adj = 0. # This is a regression test for user issue: # https://github.com/statsmodels/statsmodels/issues/868 with warnings.catch_warnings(record=True): x = np.random.randn(5) y = np.random.randn(5, 6) results = OLS(x, y).fit() rsquared_adj = results.rsquared_adj assert_equal(rsquared_adj, np.nan) def test_qr_alternatives(self): assert_allclose(self.res_qr.params, self.res_qr_manual.params, rtol=5e-12) def test_norm_resid(self): resid = self.res1.wresid norm_resid = resid / np.sqrt(np.sum(resid**2.0) / self.res1.df_resid) model_norm_resid = self.res1.resid_pearson assert_almost_equal(model_norm_resid, norm_resid, DECIMAL_7) def test_norm_resid_zero_variance(self): with warnings.catch_warnings(record=True): y = self.res1.model.endog res = OLS(y, y).fit() assert_allclose(res.scale, 0, atol=1e-20) assert_allclose(res.wresid, res.resid_pearson, atol=5e-11) class TestRTO(CheckRegressionResults): @classmethod def setup_class(cls): from .results.results_regression import LongleyRTO data = longley.load(as_pandas=False) res1 = OLS(data.endog, data.exog).fit() res2 = LongleyRTO() res2.wresid = res1.wresid # workaround hack cls.res1 = res1 cls.res2 = res2 res_qr = OLS(data.endog, data.exog).fit(method="qr") cls.res_qr = res_qr class TestFtest(object): """ Tests f_test vs. RegressionResults """ @classmethod def setup_class(cls): data = longley.load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) cls.res1 = OLS(data.endog, data.exog).fit() R = np.identity(7)[:-1, :] cls.Ftest = cls.res1.f_test(R) def test_F(self): assert_almost_equal(self.Ftest.fvalue, self.res1.fvalue, DECIMAL_4) def test_p(self): assert_almost_equal(self.Ftest.pvalue, self.res1.f_pvalue, DECIMAL_4) def test_Df_denom(self): assert_equal(self.Ftest.df_denom, self.res1.model.df_resid) def test_Df_num(self): assert_equal(self.Ftest.df_num, 6) class TestFTest2(object): """ A joint test that the coefficient on GNP = the coefficient on UNEMP and that the coefficient on POP = the coefficient on YEAR for the Longley dataset. Ftest1 is from statsmodels. Results are from Rpy using R's car library. """ @classmethod def setup_class(cls): data = longley.load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) res1 = OLS(data.endog, data.exog).fit() R2 = [[0, 1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 1, -1, 0]] cls.Ftest1 = res1.f_test(R2) hyp = 'x2 = x3, x5 = x6' cls.NewFtest1 = res1.f_test(hyp) def test_new_ftest(self): assert_equal(self.NewFtest1.fvalue, self.Ftest1.fvalue) def test_fvalue(self): assert_almost_equal(self.Ftest1.fvalue, 9.7404618732968196, DECIMAL_4) def test_pvalue(self): assert_almost_equal(self.Ftest1.pvalue, 0.0056052885317493459, DECIMAL_4) def test_df_denom(self): assert_equal(self.Ftest1.df_denom, 9) def test_df_num(self): assert_equal(self.Ftest1.df_num, 2) class TestFtestQ(object): """ A joint hypothesis test that Rb = q. Coefficient tests are essentially made up. Test values taken from Stata. """ @classmethod def setup_class(cls): data = longley.load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) res1 = OLS(data.endog, data.exog).fit() R = np.array([[0, 1, 1, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0]]) q = np.array([0, 0, 0, 1, 0]) cls.Ftest1 = res1.f_test((R, q)) def test_fvalue(self): assert_almost_equal(self.Ftest1.fvalue, 70.115557, 5) def test_pvalue(self): assert_almost_equal(self.Ftest1.pvalue, 6.229e-07, 10) def test_df_denom(self): assert_equal(self.Ftest1.df_denom, 9) def test_df_num(self): assert_equal(self.Ftest1.df_num, 5) class TestTtest(object): """ Test individual t-tests. Ie., are the coefficients significantly different than zero. """ @classmethod def setup_class(cls): data = longley.load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) cls.res1 = OLS(data.endog, data.exog).fit() R = np.identity(7) cls.Ttest = cls.res1.t_test(R) hyp = 'x1 = 0, x2 = 0, x3 = 0, x4 = 0, x5 = 0, x6 = 0, const = 0' cls.NewTTest = cls.res1.t_test(hyp) def test_new_tvalue(self): assert_equal(self.NewTTest.tvalue, self.Ttest.tvalue) def test_tvalue(self): assert_almost_equal(self.Ttest.tvalue, self.res1.tvalues, DECIMAL_4) def test_sd(self): assert_almost_equal(self.Ttest.sd, self.res1.bse, DECIMAL_4) def test_pvalue(self): assert_almost_equal(self.Ttest.pvalue, student_t.sf( np.abs(self.res1.tvalues), self.res1.model.df_resid)*2, DECIMAL_4) def test_df_denom(self): assert_equal(self.Ttest.df_denom, self.res1.model.df_resid) def test_effect(self): assert_almost_equal(self.Ttest.effect, self.res1.params) class TestTtest2(object): """ Tests the hypothesis that the coefficients on POP and YEAR are equal. Results from RPy using 'car' package. """ @classmethod def setup_class(cls): R = np.zeros(7) R[4:6] = [1, -1] data = longley.load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) res1 = OLS(data.endog, data.exog).fit() cls.Ttest1 = res1.t_test(R) def test_tvalue(self): assert_almost_equal(self.Ttest1.tvalue, -4.0167754636397284, DECIMAL_4) def test_sd(self): assert_almost_equal(self.Ttest1.sd, 455.39079425195314, DECIMAL_4) def test_pvalue(self): assert_almost_equal(self.Ttest1.pvalue, 2*0.0015163772380932246, DECIMAL_4) def test_df_denom(self): assert_equal(self.Ttest1.df_denom, 9) def test_effect(self): assert_almost_equal(self.Ttest1.effect, -1829.2025687186533, DECIMAL_4) class TestGLS(object): """ These test results were obtained by replication with R. """ @classmethod def setup_class(cls): from .results.results_regression import LongleyGls data = longley.load(as_pandas=False) exog = add_constant(np.column_stack( (data.exog[:, 1], data.exog[:, 4])), prepend=False) tmp_results = OLS(data.endog, exog).fit() rho = np.corrcoef(tmp_results.resid[1:], tmp_results.resid[:-1])[0][1] # by assumption order = toeplitz(np.arange(16)) sigma = rho**order GLS_results = GLS(data.endog, exog, sigma=sigma).fit() cls.res1 = GLS_results cls.res2 = LongleyGls() # attach for test_missing cls.sigma = sigma cls.exog = exog cls.endog = data.endog def test_aic(self): # Note: tolerance is tight; rtol=3e-3 fails while 4e-3 passes assert_allclose(self.res1.aic+2, self.res2.aic, rtol=4e-3) def test_bic(self): # Note: tolerance is tight; rtol=1e-2 fails while 1.5e-2 passes assert_allclose(self.res1.bic, self.res2.bic, rtol=1.5e-2) def test_loglike(self): assert_almost_equal(self.res1.llf, self.res2.llf, DECIMAL_0) def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, DECIMAL_1) def test_resid(self): assert_almost_equal(self.res1.resid, self.res2.resid, DECIMAL_4) def test_scale(self): assert_almost_equal(self.res1.scale, self.res2.scale, DECIMAL_4) def test_tvalues(self): assert_almost_equal(self.res1.tvalues, self.res2.tvalues, DECIMAL_4) def test_standarderrors(self): assert_almost_equal(self.res1.bse, self.res2.bse, DECIMAL_4) def test_fittedvalues(self): assert_almost_equal(self.res1.fittedvalues, self.res2.fittedvalues, DECIMAL_4) def test_pvalues(self): assert_almost_equal(self.res1.pvalues, self.res2.pvalues, DECIMAL_4) def test_missing(self): endog = self.endog.copy() # copy or changes endog for other methods endog[[4, 7, 14]] = np.nan mod = GLS(endog, self.exog, sigma=self.sigma, missing='drop') assert_equal(mod.endog.shape[0], 13) assert_equal(mod.exog.shape[0], 13) assert_equal(mod.sigma.shape, (13, 13)) class TestGLS_alt_sigma(CheckRegressionResults): """ Test that GLS with no argument is equivalent to OLS. """ @classmethod def setup_class(cls): data = longley.load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) ols_res = OLS(data.endog, data.exog).fit() gls_res = GLS(data.endog, data.exog).fit() gls_res_scalar = GLS(data.endog, data.exog, sigma=1) cls.endog = data.endog cls.exog = data.exog cls.res1 = gls_res cls.res2 = ols_res cls.res3 = gls_res_scalar # self.res2.conf_int = self.res2.conf_int() def test_wrong_size_sigma_1d(self): n = len(self.endog) assert_raises(ValueError, GLS, self.endog, self.exog, sigma=np.ones(n-1)) def test_wrong_size_sigma_2d(self): n = len(self.endog) assert_raises(ValueError, GLS, self.endog, self.exog, sigma=np.ones((n-1, n-1))) # FIXME: do not leave commented-out, use or move/remove # def check_confidenceintervals(self, conf1, conf2): # assert_almost_equal(conf1, conf2, DECIMAL_4) class TestLM(object): @classmethod def setup_class(cls): # TODO: Test HAC method rs = np.random.RandomState(1234) x = rs.randn(100, 3) b = np.ones((3, 1)) e = rs.randn(100, 1) y = np.dot(x, b) + e # Cases? # Homoskedastic # HC0 cls.res1_full = OLS(y, x).fit() cls.res1_restricted = OLS(y, x[:, 0]).fit() cls.res2_full = cls.res1_full.get_robustcov_results('HC0') cls.res2_restricted = cls.res1_restricted.get_robustcov_results('HC0') cls.x = x cls.Y = y def test_LM_homoskedastic(self): resid = self.res1_restricted.wresid n = resid.shape[0] x = self.x S = np.dot(resid, resid) / n * np.dot(x.T, x) / n Sinv = np.linalg.inv(S) s = np.mean(x * resid[:, None], 0) LMstat = n * np.dot(np.dot(s, Sinv), s.T) LMstat_OLS = self.res1_full.compare_lm_test(self.res1_restricted) LMstat2 = LMstat_OLS[0] assert_almost_equal(LMstat, LMstat2, DECIMAL_7) def test_LM_heteroskedastic_nodemean(self): resid = self.res1_restricted.wresid n = resid.shape[0] x = self.x scores = x * resid[:, None] S = np.dot(scores.T, scores) / n Sinv = np.linalg.inv(S) s = np.mean(scores, 0) LMstat = n * np.dot(np.dot(s, Sinv), s.T) LMstat_OLS = self.res2_full.compare_lm_test(self.res2_restricted, demean=False) LMstat2 = LMstat_OLS[0] assert_almost_equal(LMstat, LMstat2, DECIMAL_7) def test_LM_heteroskedastic_demean(self): resid = self.res1_restricted.wresid n = resid.shape[0] x = self.x scores = x * resid[:, None] scores_demean = scores - scores.mean(0) S = np.dot(scores_demean.T, scores_demean) / n Sinv = np.linalg.inv(S) s = np.mean(scores, 0) LMstat = n * np.dot(np.dot(s, Sinv), s.T) LMstat_OLS = self.res2_full.compare_lm_test(self.res2_restricted) LMstat2 = LMstat_OLS[0] assert_almost_equal(LMstat, LMstat2, DECIMAL_7) def test_LM_heteroskedastic_LRversion(self): resid = self.res1_restricted.wresid resid_full = self.res1_full.wresid n = resid.shape[0] x = self.x scores = x * resid[:, None] s = np.mean(scores, 0) scores = x * resid_full[:, None] S = np.dot(scores.T, scores) / n Sinv = np.linalg.inv(S) LMstat = n * np.dot(np.dot(s, Sinv), s.T) LMstat_OLS = self.res2_full.compare_lm_test(self.res2_restricted, use_lr=True) LMstat2 = LMstat_OLS[0] assert_almost_equal(LMstat, LMstat2, DECIMAL_7) def test_LM_nonnested(self): assert_raises(ValueError, self.res2_restricted.compare_lm_test, self.res2_full) class TestOLS_GLS_WLS_equivalence(object): @classmethod def setup_class(cls): data = longley.load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) y = data.endog x = data.exog n = y.shape[0] w = np.ones(n) cls.results = [] cls.results.append(OLS(y, x).fit()) cls.results.append(WLS(y, x, w).fit()) cls.results.append(GLS(y, x, 100*w).fit()) cls.results.append(GLS(y, x, np.diag(0.1*w)).fit()) def test_ll(self): llf = np.array([r.llf for r in self.results]) llf_1 = np.ones_like(llf) * self.results[0].llf assert_almost_equal(llf, llf_1, DECIMAL_7) ic = np.array([r.aic for r in self.results]) ic_1 = np.ones_like(ic) * self.results[0].aic assert_almost_equal(ic, ic_1, DECIMAL_7) ic = np.array([r.bic for r in self.results]) ic_1 = np.ones_like(ic) * self.results[0].bic assert_almost_equal(ic, ic_1, DECIMAL_7) def test_params(self): params = np.array([r.params for r in self.results]) params_1 = np.array([self.results[0].params] * len(self.results)) assert_allclose(params, params_1) def test_ss(self): bse = np.array([r.bse for r in self.results]) bse_1 = np.array([self.results[0].bse] * len(self.results)) assert_allclose(bse, bse_1) def test_rsquared(self): rsquared = np.array([r.rsquared for r in self.results]) rsquared_1 = np.array([self.results[0].rsquared] * len(self.results)) assert_almost_equal(rsquared, rsquared_1, DECIMAL_7) class TestGLS_WLS_equivalence(TestOLS_GLS_WLS_equivalence): # reuse test methods @classmethod def setup_class(cls): data = longley.load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) y = data.endog x = data.exog n = y.shape[0] np.random.seed(5) w = np.random.uniform(0.5, 1, n) w_inv = 1. / w cls.results = [] cls.results.append(WLS(y, x, w).fit()) cls.results.append(WLS(y, x, 0.01 * w).fit()) cls.results.append(GLS(y, x, 100 * w_inv).fit()) cls.results.append(GLS(y, x, np.diag(0.1 * w_inv)).fit()) class TestNonFit(object): @classmethod def setup_class(cls): data = longley.load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) cls.endog = data.endog cls.exog = data.exog cls.ols_model = OLS(data.endog, data.exog) def test_df_resid(self): df_resid = self.endog.shape[0] - self.exog.shape[1] assert_equal(self.ols_model.df_resid, 9) class TestWLS_CornerCases(object): @classmethod def setup_class(cls): cls.exog = np.ones((1,)) cls.endog = np.ones((1,)) weights = 1 cls.wls_res = WLS(cls.endog, cls.exog, weights=weights).fit() def test_wrong_size_weights(self): weights = np.ones((10, 10)) assert_raises(ValueError, WLS, self.endog, self.exog, weights=weights) class TestWLSExogWeights(CheckRegressionResults): # Test WLS with Greene's credit card data # reg avgexp age income incomesq ownrent [aw=1/incomesq] @classmethod def setup_class(cls): from .results.results_regression import CCardWLS from statsmodels.datasets.ccard import load dta = load(as_pandas=False) dta.exog = add_constant(dta.exog, prepend=False) nobs = 72. weights = 1 / dta.exog[:, 2] # for comparison with stata analytic weights scaled_weights = ((weights * nobs) / weights.sum()) cls.res1 = WLS(dta.endog, dta.exog, weights=scaled_weights).fit() cls.res2 = CCardWLS() cls.res2.wresid = scaled_weights ** .5 * cls.res2.resid # correction because we use different definition for loglike/llf corr_ic = 2 * (cls.res1.llf - cls.res2.llf) cls.res2.aic -= corr_ic cls.res2.bic -= corr_ic cls.res2.llf += 0.5 * np.sum(np.log(cls.res1.model.weights)) def test_wls_example(): # example from the docstring, there was a note about a bug, should # be fixed now Y = [1, 3, 4, 5, 2, 3, 4] x = lrange(1, 8) x = add_constant(x, prepend=False) wls_model = WLS(Y, x, weights=lrange(1, 8)).fit() # taken from R lm.summary assert_almost_equal(wls_model.fvalue, 0.127337843215, 6) assert_almost_equal(wls_model.scale, 2.44608530786**2, 6) def test_wls_tss(): y = np.array([22, 22, 22, 23, 23, 23]) x = [[1, 0], [1, 0], [1, 1], [0, 1], [0, 1], [0, 1]] ols_mod = OLS(y, add_constant(x, prepend=False)).fit() yw = np.array([22, 22, 23.]) Xw = [[1, 0], [1, 1], [0, 1]] w = np.array([2, 1, 3.]) wls_mod = WLS(yw, add_constant(Xw, prepend=False), weights=w).fit() assert_equal(ols_mod.centered_tss, wls_mod.centered_tss) class TestWLSScalarVsArray(CheckRegressionResults): @classmethod def setup_class(cls): from statsmodels.datasets.longley import load dta = load(as_pandas=False) dta.exog = add_constant(dta.exog, prepend=True) wls_scalar = WLS(dta.endog, dta.exog, weights=1./3).fit() weights = [1/3.] * len(dta.endog) wls_array = WLS(dta.endog, dta.exog, weights=weights).fit() cls.res1 = wls_scalar cls.res2 = wls_array class TestWLS_GLS(CheckRegressionResults): @classmethod def setup_class(cls): from statsmodels.datasets.ccard import load data = load(as_pandas=False) cls.res1 = WLS(data.endog, data.exog, weights=1/data.exog[:, 2]).fit() cls.res2 = GLS(data.endog, data.exog, sigma=data.exog[:,2 ]).fit() def check_confidenceintervals(self, conf1, conf2): # FIXME: never called assert_almost_equal(conf1, conf2(), DECIMAL_4) def test_wls_missing(): from statsmodels.datasets.ccard import load data = load(as_pandas=False) endog = data.endog endog[[10, 25]] = np.nan mod = WLS(data.endog, data.exog, weights=1 / data.exog[:, 2], missing='drop') assert_equal(mod.endog.shape[0], 70) assert_equal(mod.exog.shape[0], 70) assert_equal(mod.weights.shape[0], 70) class TestWLS_OLS(CheckRegressionResults): @classmethod def setup_class(cls): data = longley.load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) cls.res1 = OLS(data.endog, data.exog).fit() cls.res2 = WLS(data.endog, data.exog).fit() def check_confidenceintervals(self, conf1, conf2): # FIXME: never called assert_almost_equal(conf1, conf2(), DECIMAL_4) class TestGLS_OLS(CheckRegressionResults): @classmethod def setup_class(cls): data = longley.load(as_pandas=False) data.exog = add_constant(data.exog, prepend=False) cls.res1 = GLS(data.endog, data.exog).fit() cls.res2 = OLS(data.endog, data.exog).fit() def check_confidenceintervals(self, conf1, conf2): # FIXME: never called assert_almost_equal(conf1, conf2(), DECIMAL_4) # FIXME: do not leave this commented-out sitting here # TODO: test AR # why the two-stage in AR? # class TestAR(object): # from statsmodels.datasets.sunspots import load # data = load(as_pandas=False) # model = AR(data.endog, rho=4).fit() # R_res = RModel(data.endog, aic="FALSE", order_max=4)# # def test_params(self): # assert_almost_equal(self.model.rho, # pass # def test_order(self): # In R this can be defined or chosen by minimizing the AIC if aic=True # pass class TestYuleWalker(object): @classmethod def setup_class(cls): from statsmodels.datasets.sunspots import load data = load(as_pandas=False) cls.rho, cls.sigma = yule_walker(data.endog, order=4, method="mle") cls.R_params = [1.2831003105694765, -0.45240924374091945, -0.20770298557575195, 0.047943648089542337] def test_params(self): assert_almost_equal(self.rho, self.R_params, DECIMAL_4) class TestDataDimensions(CheckRegressionResults): @classmethod def setup_class(cls): np.random.seed(54321) cls.endog_n_ = np.random.uniform(0, 20, size=30) cls.endog_n_one = cls.endog_n_[:, None] cls.exog_n_ = np.random.uniform(0, 20, size=30) cls.exog_n_one = cls.exog_n_[:, None] cls.degen_exog = cls.exog_n_one[:-1] cls.mod1 = OLS(cls.endog_n_one, cls.exog_n_one) cls.mod1.df_model += 1 cls.res1 = cls.mod1.fit() # Note that these are created for every subclass.. # A little extra overhead probably cls.mod2 = OLS(cls.endog_n_one, cls.exog_n_one) cls.mod2.df_model += 1 cls.res2 = cls.mod2.fit() def check_confidenceintervals(self, conf1, conf2): # FIXME: never called assert_almost_equal(conf1, conf2(), DECIMAL_4) class TestGLS_large_data(TestDataDimensions): @classmethod def setup_class(cls): super(TestGLS_large_data, cls).setup_class() nobs = 1000 y = np.random.randn(nobs, 1) x = np.random.randn(nobs, 20) sigma = np.ones_like(y) cls.gls_res = GLS(y, x, sigma=sigma).fit() cls.gls_res_scalar = GLS(y, x, sigma=1).fit() cls.gls_res_none = GLS(y, x).fit() cls.ols_res = OLS(y, x).fit() def test_large_equal_params(self): assert_almost_equal(self.ols_res.params, self.gls_res.params, DECIMAL_7) def test_large_equal_loglike(self): assert_almost_equal(self.ols_res.llf, self.gls_res.llf, DECIMAL_7) def test_large_equal_params_none(self): assert_almost_equal(self.gls_res.params, self.gls_res_none.params, DECIMAL_7) class TestNxNx(TestDataDimensions): @classmethod def setup_class(cls): super(TestNxNx, cls).setup_class() cls.mod2 = OLS(cls.endog_n_, cls.exog_n_) cls.mod2.df_model += 1 cls.res2 = cls.mod2.fit() class TestNxOneNx(TestDataDimensions): @classmethod def setup_class(cls): super(TestNxOneNx, cls).setup_class() cls.mod2 = OLS(cls.endog_n_one, cls.exog_n_) cls.mod2.df_model += 1 cls.res2 = cls.mod2.fit() class TestNxNxOne(TestDataDimensions): @classmethod def setup_class(cls): super(TestNxNxOne, cls).setup_class() cls.mod2 = OLS(cls.endog_n_, cls.exog_n_one) cls.mod2.df_model += 1 cls.res2 = cls.mod2.fit() def test_bad_size(): np.random.seed(54321) data = np.random.uniform(0, 20, 31) assert_raises(ValueError, OLS, data, data[1:]) def test_const_indicator(): rs = np.random.RandomState(12345) x = rs.randint(0, 3, size=30) x = pd.get_dummies(pd.Series(x, dtype="category"), drop_first=False) y = np.dot(x, [1., 2., 3.]) + rs.normal(size=30) resc = OLS(y, add_constant(x.iloc[:, 1:], prepend=True)).fit() res = OLS(y, x, hasconst=True).fit() assert_almost_equal(resc.rsquared, res.rsquared, 12) assert res.model.data.k_constant == 1 assert resc.model.data.k_constant == 1 def test_fvalue_const_only(): rs = np.random.RandomState(12345) x = rs.randint(0, 3, size=30) x = pd.get_dummies(pd.Series(x, dtype="category"), drop_first=False) x.iloc[:, 0] = 1 y = np.dot(x, [1., 2., 3.]) + rs.normal(size=30) res = OLS(y, x, hasconst=True).fit(cov_type='HC1') assert not np.isnan(res.fvalue) assert isinstance(res.fvalue, float) assert isinstance(res.f_pvalue, float) def test_conf_int_single_regressor(): # GH#706 single-regressor model (i.e. no intercept) with 1D exog # should get passed to DataFrame for conf_int y = pd.Series(np.random.randn(10)) x = pd.Series(np.ones(10)) res = OLS(y, x).fit() conf_int = res.conf_int() np.testing.assert_equal(conf_int.shape, (1, 2)) np.testing.assert_(isinstance(conf_int, pd.DataFrame)) def test_summary_as_latex(): # GH#734 import re dta = longley.load_pandas() x = dta.exog x["constant"] = 1 y = dta.endog res = OLS(y, x).fit() with pytest.warns(UserWarning): table = res.summary().as_latex() # replace the date and time table = re.sub("(?<=\n\\\\textbf\\{Date:\\} &).+?&", " Sun, 07 Apr 2013 &", table) table = re.sub("(?<=\n\\\\textbf\\{Time:\\} &).+?&", " 13:46:07 &", table) expected = """\\begin{center} \\begin{tabular}{lclc} \\toprule \\textbf{Dep. Variable:} & TOTEMP & \\textbf{ R-squared: } & 0.995 \\\\ \\textbf{Model:} & OLS & \\textbf{ Adj. R-squared: } & 0.992 \\\\ \\textbf{Method:} & Least Squares & \\textbf{ F-statistic: } & 330.3 \\\\ \\textbf{Date:} & Sun, 07 Apr 2013 & \\textbf{ Prob (F-statistic):} & 4.98e-10 \\\\ \\textbf{Time:} & 13:46:07 & \\textbf{ Log-Likelihood: } & -109.62 \\\\ \\textbf{No. Observations:} & 16 & \\textbf{ AIC: } & 233.2 \\\\ \\textbf{Df Residuals:} & 9 & \\textbf{ BIC: } & 238.6 \\\\ \\textbf{Df Model:} & 6 & \\textbf{ } & \\\\ \\bottomrule \\end{tabular} \\begin{tabular}{lcccccc} & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]} \\\\ \\midrule \\textbf{GNPDEFL} & 15.0619 & 84.915 & 0.177 & 0.863 & -177.029 & 207.153 \\\\ \\textbf{GNP} & -0.0358 & 0.033 & -1.070 & 0.313 & -0.112 & 0.040 \\\\ \\textbf{UNEMP} & -2.0202 & 0.488 & -4.136 & 0.003 & -3.125 & -0.915 \\\\ \\textbf{ARMED} & -1.0332 & 0.214 & -4.822 & 0.001 & -1.518 & -0.549 \\\\ \\textbf{POP} & -0.0511 & 0.226 & -0.226 & 0.826 & -0.563 & 0.460 \\\\ \\textbf{YEAR} & 1829.1515 & 455.478 & 4.016 & 0.003 & 798.788 & 2859.515 \\\\ \\textbf{constant} & -3.482e+06 & 8.9e+05 & -3.911 & 0.004 & -5.5e+06 & -1.47e+06 \\\\ \\bottomrule \\end{tabular} \\begin{tabular}{lclc} \\textbf{Omnibus:} & 0.749 & \\textbf{ Durbin-Watson: } & 2.559 \\\\ \\textbf{Prob(Omnibus):} & 0.688 & \\textbf{ Jarque-Bera (JB): } & 0.684 \\\\ \\textbf{Skew:} & 0.420 & \\textbf{ Prob(JB): } & 0.710 \\\\ \\textbf{Kurtosis:} & 2.434 & \\textbf{ Cond. No. } & 4.86e+09 \\\\ \\bottomrule \\end{tabular} %\\caption{OLS Regression Results} \\end{center} Notes: \\newline [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. \\newline [2] The condition number is large, 4.86e+09. This might indicate that there are \\newline strong multicollinearity or other numerical problems.""" assert_equal(table, expected) class TestRegularizedFit(object): # Make sure there are no problems when no variables are selected. def test_empty_model(self): np.random.seed(742) n = 100 endog = np.random.normal(size=n) exog = np.random.normal(size=(n, 3)) for cls in OLS, WLS, GLS: model = cls(endog, exog) result = model.fit_regularized(alpha=1000) assert_equal(result.params, 0.) def test_regularized(self): import os from .results import glmnet_r_results cur_dir = os.path.dirname(os.path.abspath(__file__)) data = np.loadtxt(os.path.join(cur_dir, "results", "lasso_data.csv"), delimiter=",") tests = [x for x in dir(glmnet_r_results) if x.startswith("rslt_")] for test in tests: vec = getattr(glmnet_r_results, test) n = vec[0] p = vec[1] L1_wt = float(vec[2]) lam = float(vec[3]) params = vec[4:].astype(np.float64) endog = data[0:int(n), 0] exog = data[0:int(n), 1:(int(p)+1)] endog = endog - endog.mean() endog /= endog.std(ddof=1) exog = exog - exog.mean(0) exog /= exog.std(0, ddof=1) for cls in OLS, WLS, GLS: mod = cls(endog, exog) rslt = mod.fit_regularized(L1_wt=L1_wt, alpha=lam) assert_almost_equal(rslt.params, params, decimal=3) # Smoke test for profile likelihood mod.fit_regularized(L1_wt=L1_wt, alpha=lam, profile_scale=True) def test_regularized_weights(self): np.random.seed(1432) exog1 = np.random.normal(size=(100, 3)) endog1 = exog1[:, 0] + exog1[:, 1] + np.random.normal(size=100) exog2 = np.random.normal(size=(100, 3)) endog2 = exog2[:, 0] + exog2[:, 1] + np.random.normal(size=100) exog_a = np.vstack((exog1, exog1, exog2)) endog_a = np.concatenate((endog1, endog1, endog2)) # Should be equivalent to exog_a, endog_a. exog_b = np.vstack((exog1, exog2)) endog_b = np.concatenate((endog1, endog2)) wgts = np.ones(200) wgts[0:100] = 2 sigma = np.diag(1/wgts) for L1_wt in 0, 0.5, 1: for alpha in 0, 1: mod1 = OLS(endog_a, exog_a) rslt1 = mod1.fit_regularized(L1_wt=L1_wt, alpha=alpha) mod2 = WLS(endog_b, exog_b, weights=wgts) rslt2 = mod2.fit_regularized(L1_wt=L1_wt, alpha=alpha) mod3 = GLS(endog_b, exog_b, sigma=sigma) rslt3 = mod3.fit_regularized(L1_wt=L1_wt, alpha=alpha) assert_almost_equal(rslt1.params, rslt2.params, decimal=3) assert_almost_equal(rslt1.params, rslt3.params, decimal=3) def test_regularized_weights_list(self): np.random.seed(132) exog1 = np.random.normal(size=(100, 3)) endog1 = exog1[:, 0] + exog1[:, 1] + np.random.normal(size=100) exog2 = np.random.normal(size=(100, 3)) endog2 = exog2[:, 0] + exog2[:, 1] + np.random.normal(size=100) exog_a = np.vstack((exog1, exog1, exog2)) endog_a = np.concatenate((endog1, endog1, endog2)) # Should be equivalent to exog_a, endog_a. exog_b = np.vstack((exog1, exog2)) endog_b = np.concatenate((endog1, endog2)) wgts = np.ones(200) wgts[0:100] = 2 sigma = np.diag(1/wgts) for L1_wt in 0, 0.5, 1: for alpha_element in 0, 1: alpha = [alpha_element,] * 3 mod1 = OLS(endog_a, exog_a) rslt1 = mod1.fit_regularized(L1_wt=L1_wt, alpha=alpha) mod2 = WLS(endog_b, exog_b, weights=wgts) rslt2 = mod2.fit_regularized(L1_wt=L1_wt, alpha=alpha) mod3 = GLS(endog_b, exog_b, sigma=sigma) rslt3 = mod3.fit_regularized(L1_wt=L1_wt, alpha=alpha) assert_almost_equal(rslt1.params, rslt2.params, decimal=3) assert_almost_equal(rslt1.params, rslt3.params, decimal=3) def test_formula_missing_cat(): # gh-805 import statsmodels.api as sm from statsmodels.formula.api import ols from patsy import PatsyError dta = sm.datasets.grunfeld.load_pandas().data dta.loc[dta.index[0], 'firm'] = np.nan mod = ols(formula='value ~ invest + capital + firm + year', data=dta.dropna()) res = mod.fit() mod2 = ols(formula='value ~ invest + capital + firm + year', data=dta) res2 = mod2.fit() assert_almost_equal(res.params.values, res2.params.values) assert_raises(PatsyError, ols, 'value ~ invest + capital + firm + year', data=dta, missing='raise') def test_missing_formula_predict(): # see 2171 nsample = 30 data = np.linspace(0, 10, nsample) null = np.array([np.nan]) data = pd.DataFrame({'x': np.concatenate((data, null))}) beta = np.array([1, 0.1]) e = np.random.normal(size=nsample+1) data['y'] = beta[0] + beta[1] * data['x'] + e model = OLS.from_formula('y ~ x', data=data) fit = model.fit() fit.predict(exog=data[:-1]) def test_fvalue_implicit_constant(): # if constant is implicit, return nan see #2444 nobs = 100 np.random.seed(2) x = np.random.randn(nobs, 1) x = ((x > 0) == [True, False]).astype(int) y = x.sum(1) + np.random.randn(nobs) from statsmodels.regression.linear_model import OLS, WLS res = OLS(y, x).fit(cov_type='HC1') assert_(np.isnan(res.fvalue)) assert_(np.isnan(res.f_pvalue)) res.summary() res = WLS(y, x).fit(cov_type='HC1') assert_(np.isnan(res.fvalue)) assert_(np.isnan(res.f_pvalue)) res.summary() def test_fvalue_only_constant(): # if only constant in model, return nan see #3642 nobs = 20 np.random.seed(2) x = np.ones(nobs) y = np.random.randn(nobs) from statsmodels.regression.linear_model import OLS, WLS res = OLS(y, x).fit(cov_type='hac', cov_kwds={'maxlags': 3}) assert_(np.isnan(res.fvalue)) assert_(np.isnan(res.f_pvalue)) res.summary() res = WLS(y, x).fit(cov_type='HC1') assert_(np.isnan(res.fvalue)) assert_(np.isnan(res.f_pvalue)) res.summary() def test_ridge(): n = 100 p = 5 np.random.seed(3132) xmat = np.random.normal(size=(n, p)) yvec = xmat.sum(1) + np.random.normal(size=n) v = np.ones(p) v[0] = 0 for a in (0, 1, 10): for alpha in (a, a*np.ones(p), a*v): model1 = OLS(yvec, xmat) result1 = model1._fit_ridge(alpha=alpha) model2 = OLS(yvec, xmat) result2 = model2.fit_regularized(alpha=alpha, L1_wt=0) assert_allclose(result1.params, result2.params) model3 = OLS(yvec, xmat) result3 = model3.fit_regularized(alpha=alpha, L1_wt=1e-10) assert_allclose(result1.params, result3.params) fv1 = result1.fittedvalues fv2 = np.dot(xmat, result1.params) assert_allclose(fv1, fv2) def test_regularized_refit(): n = 100 p = 5 np.random.seed(3132) xmat = np.random.normal(size=(n, p)) # covariates 0 and 2 matter yvec = xmat[:, 0] + xmat[:, 2] + np.random.normal(size=n) model1 = OLS(yvec, xmat) result1 = model1.fit_regularized(alpha=2., L1_wt=0.5, refit=True) model2 = OLS(yvec, xmat[:, [0, 2]]) result2 = model2.fit() ii = [0, 2] assert_allclose(result1.params[ii], result2.params) assert_allclose(result1.bse[ii], result2.bse) def test_regularized_predict(): n = 100 p = 5 np.random.seed(3132) xmat = np.random.normal(size=(n, p)) yvec = xmat.sum(1) + np.random.normal(size=n) wgt = np.random.uniform(1, 2, n) for klass in WLS, GLS: model1 = klass(yvec, xmat, weights=wgt) result1 = model1.fit_regularized(alpha=2., L1_wt=0.5, refit=True) params = result1.params fittedvalues = np.dot(xmat, params) pr = model1.predict(result1.params) assert_allclose(fittedvalues, pr) assert_allclose(result1.fittedvalues, pr) pr = result1.predict() assert_allclose(fittedvalues, pr) def test_regularized_options(): n = 100 p = 5 np.random.seed(3132) xmat = np.random.normal(size=(n, p)) yvec = xmat.sum(1) + np.random.normal(size=n) model1 = OLS(yvec - 1, xmat) result1 = model1.fit_regularized(alpha=1., L1_wt=0.5) model2 = OLS(yvec, xmat, offset=1) result2 = model2.fit_regularized(alpha=1., L1_wt=0.5, start_params=np.zeros(5)) assert_allclose(result1.params, result2.params) def test_burg(): rnd = np.random.RandomState(12345) e = rnd.randn(10001) y = e[1:] + 0.5 * e[:-1] # R, ar.burg expected = [ [0.3909931], [0.4602607, -0.1771582], [0.47473245, -0.21475602, 0.08168813], [0.4787017, -0.2251910, 0.1047554, -0.0485900], [0.47975462, - 0.22746106, 0.10963527, -0.05896347, 0.02167001] ] for i in range(1, 6): ar, _ = burg(y, i) assert_allclose(ar, expected[i - 1], atol=1e-6) as_nodemean, _ = burg(1 + y, i, False) assert np.all(ar != as_nodemean) def test_burg_errors(): with pytest.raises(ValueError): burg(np.ones((100, 2))) with pytest.raises(ValueError): burg(np.random.randn(100), 0) with pytest.raises(ValueError): burg(np.random.randn(100), 'apple') @pytest.mark.skipif(not has_cvxopt, reason="sqrt_lasso requires cvxopt") def test_sqrt_lasso(): np.random.seed(234923) # Based on the example in the Belloni paper n = 100 p = 500 ii = np.arange(p) cx = 0.5 ** np.abs(np.subtract.outer(ii, ii)) cxr = np.linalg.cholesky(cx) x = np.dot(np.random.normal(size=(n, p)), cxr.T) b = np.zeros(p) b[0:5] = [1, 1, 1, 1, 1] from scipy.stats.distributions import norm alpha = 1.1 * np.sqrt(n) * norm.ppf(1 - 0.05 / (2 * p)) # Use very low noise level for a unit test y = np.dot(x, b) + 0.25 * np.random.normal(size=n) # At low noise levels, the sqrt lasso should be around a # factor of 3 from the oracle without refit, and should # almost equal the oracle with refit. expected_oracle = {False: 3, True: 1} # Used for regression testing expected_params = {False: np.r_[0.87397122, 0.96051874, 0.9905915 , 0.93868953, 0.90771773], True: np.r_[0.95114241, 1.0302987 , 1.01723074, 0.97587343, 0.99846403]} for refit in False, True: rslt = OLS(y, x).fit_regularized(method="sqrt_lasso", alpha=alpha, refit=refit) err = rslt.params - b numer = np.sqrt(np.dot(err, np.dot(cx, err))) oracle = OLS(y, x[:, 0:5]).fit() oracle_err = np.zeros(p) oracle_err[0:5] = oracle.params - b[0:5] denom = np.sqrt(np.dot(oracle_err, np.dot(cx, oracle_err))) # Check performance relative to oracle, should be around assert_allclose(numer / denom, expected_oracle[refit], rtol=0.5, atol=0.1) # Regression test the parameters assert_allclose(rslt.params[0:5], expected_params[refit], rtol=1e-5, atol=1e-5) def test_bool_regressor(reset_randomstate): exog = np.random.randint(0, 2, size=(100, 2)).astype(bool) endog = np.random.standard_normal(100) bool_res = OLS(endog, exog).fit() res = OLS(endog, exog.astype(np.double)).fit() assert_allclose(bool_res.params, res.params) def test_ols_constant(reset_randomstate): y = np.random.standard_normal((200)) x = np.ones((200, 1)) res = OLS(y, x).fit() with pytest.warns(None) as recording: assert np.isnan(res.fvalue) assert np.isnan(res.f_pvalue) assert len(recording) == 0 def test_summary_no_constant(): rs = np.random.RandomState(0) x = rs.standard_normal((100,2)) y = rs.standard_normal(100) summary = OLS(y, x).fit().summary() assert "R² is computed " in summary.as_text() statsmodels-0.12.2/statsmodels/regression/tests/test_robustcov.py000066400000000000000000001011271400612667500254720ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Testing OLS robust covariance matrices against STATA Created on Mon Oct 28 15:25:14 2013 Author: Josef Perktold """ import pytest import numpy as np from scipy import stats from numpy.testing import (assert_allclose, assert_equal, assert_warns, assert_raises) from statsmodels.regression.linear_model import OLS, WLS import statsmodels.stats.sandwich_covariance as sw from statsmodels.tools.tools import add_constant from statsmodels.datasets import macrodata from statsmodels.tools.sm_exceptions import InvalidTestWarning from .results import results_macro_ols_robust as res from .results import results_grunfeld_ols_robust_cluster as res2 # TODO: implement test_hac_simple class CheckOLSRobust(object): def test_basic(self): res1 = self.res1 res2 = self.res2 rtol = getattr(self, 'rtol', 1e-10) assert_allclose(res1.params, res2.params, rtol=rtol) assert_allclose(self.bse_robust, res2.bse, rtol=rtol) assert_allclose(self.cov_robust, res2.cov, rtol=rtol) @pytest.mark.smoke def test_t_test_summary(self): res1 = self.res1 mat = np.eye(len(res1.params)) # TODO: if the t_test call is expensive, possibly make it a fixture? tt = res1.t_test(mat, cov_p=self.cov_robust) tt.summary() @pytest.mark.smoke def test_t_test_summary_frame(self): res1 = self.res1 mat = np.eye(len(res1.params)) tt = res1.t_test(mat, cov_p=self.cov_robust) tt.summary_frame() @pytest.mark.smoke def test_f_test_summary(self): res1 = self.res1 mat = np.eye(len(res1.params)) ft = res1.f_test(mat[:-1], cov_p=self.cov_robust) ft.summary() def test_tests(self): # TODO: break into well-scoped tests # Note: differences between small (t-distribution, ddof) and large (normal) # F statistic has no ddof correction in large, but uses F distribution (?) res1 = self.res1 res2 = self.res2 rtol = getattr(self, 'rtol', 1e-10) rtolh = getattr(self, 'rtolh', 1e-12) mat = np.eye(len(res1.params)) tt = res1.t_test(mat, cov_p=self.cov_robust) # has 'effect', 'pvalue', 'sd', 'tvalue' # TODO confint missing assert_allclose(tt.effect, res2.params, rtol=rtol) assert_allclose(tt.sd, res2.bse, rtol=rtol) assert_allclose(tt.tvalue, res2.tvalues, rtol=rtol) if self.small: assert_allclose(tt.pvalue, res2.pvalues, rtol=5 * rtol) else: pval = stats.norm.sf(np.abs(tt.tvalue)) * 2 assert_allclose(pval, res2.pvalues, rtol=5 * rtol, atol=1e-25) ft = res1.f_test(mat[:-1], cov_p=self.cov_robust) if self.small: #'df_denom', 'df_num', 'fvalue', 'pvalue' assert_allclose(ft.fvalue, res2.F, rtol=rtol) # f-pvalue is not directly available in Stata results, but is in ivreg2 if hasattr(res2, 'Fp'): assert_allclose(ft.pvalue, res2.Fp, rtol=rtol) else: if not getattr(self, 'skip_f', False): dof_corr = res1.df_resid * 1. / res1.nobs assert_allclose(ft.fvalue * dof_corr, res2.F, rtol=rtol) if hasattr(res2, 'df_r'): assert_equal(ft.df_num, res2.df_m) assert_equal(ft.df_denom, res2.df_r) else: # ivreg2 assert_equal(ft.df_num, res2.Fdf1) assert_equal(ft.df_denom, res2.Fdf2) class TestOLSRobust1(CheckOLSRobust): # compare with regress robust def setup(self): res_ols = self.res1 self.bse_robust = res_ols.HC1_se self.cov_robust = res_ols.cov_HC1 self.small = True self.res2 = res.results_hc0 @classmethod def setup_class(cls): d2 = macrodata.load_pandas().data g_gdp = 400*np.diff(np.log(d2['realgdp'].values)) g_inv = 400*np.diff(np.log(d2['realinv'].values)) exogg = add_constant(np.c_[g_gdp, d2['realint'][:-1].values], prepend=False) cls.res1 = res_ols = OLS(g_inv, exogg).fit() class TestOLSRobust2(TestOLSRobust1): # compare with ivreg robust small def setup(self): res_ols = self.res1 self.bse_robust = res_ols.HC1_se self.cov_robust = res_ols.cov_HC1 self.small = True self.res2 = res.results_ivhc0_small class TestOLSRobust3(TestOLSRobust1): # compare with ivreg robust (not small) def setup(self): res_ols = self.res1 self.bse_robust = res_ols.HC0_se self.cov_robust = res_ols.cov_HC0 self.small = False self.res2 = res.results_ivhc0_large class TestOLSRobustHacSmall(TestOLSRobust1): # compare with ivreg robust small def setup(self): res_ols = self.res1 cov1 = sw.cov_hac_simple(res_ols, nlags=4, use_correction=True) se1 = sw.se_cov(cov1) self.bse_robust = se1 self.cov_robust = cov1 self.small = True self.res2 = res.results_ivhac4_small class TestOLSRobustHacLarge(TestOLSRobust1): # compare with ivreg robust (not small) def setup(self): res_ols = self.res1 cov1 = sw.cov_hac_simple(res_ols, nlags=4, use_correction=False) se1 = sw.se_cov(cov1) self.bse_robust = se1 self.cov_robust = cov1 self.small = False self.res2 = res.results_ivhac4_large class CheckOLSRobustNewMixin(object): # This uses the robust covariance as default covariance def test_compare(self): rtol = getattr(self, 'rtol', 1e-10) assert_allclose(self.cov_robust, self.cov_robust2, rtol=rtol) assert_allclose(self.bse_robust, self.bse_robust2, rtol=rtol) def test_fvalue(self): if not getattr(self, 'skip_f', False): rtol = getattr(self, 'rtol', 1e-10) assert_allclose(self.res1.fvalue, self.res2.F, rtol=rtol) if hasattr(self.res2, 'Fp'): # only available with ivreg2 assert_allclose(self.res1.f_pvalue, self.res2.Fp, rtol=rtol) else: raise pytest.skip("TODO: document why this test is skipped") def test_confint(self): rtol = getattr(self, 'rtol', 1e-10) ci1 = self.res1.conf_int() ci2 = self.res2.params_table[:,4:6] assert_allclose(ci1, ci2, rtol=rtol) # check critical value crit1 = np.diff(ci1, 1).ravel() / 2 / self.res1.bse crit2 = np.diff(ci1, 1).ravel() / 2 / self.res1.bse assert_allclose(crit1, crit2, rtol=12) def test_ttest(self): res1 = self.res1 res2 = self.res2 rtol = getattr(self, 'rtol', 1e-10) rtolh = getattr(self, 'rtol', 1e-12) mat = np.eye(len(res1.params)) tt = res1.t_test(mat, cov_p=self.cov_robust) # has 'effect', 'pvalue', 'sd', 'tvalue' # TODO confint missing assert_allclose(tt.effect, res2.params, rtol=rtolh) assert_allclose(tt.sd, res2.bse, rtol=rtol) assert_allclose(tt.tvalue, res2.tvalues, rtol=rtolh) assert_allclose(tt.pvalue, res2.pvalues, rtol=5 * rtol) ci1 = tt.conf_int() ci2 = self.res2.params_table[:,4:6] assert_allclose(ci1, ci2, rtol=rtol) def test_scale(self): res1 = self.res1 res2 = self.res2 rtol = 1e-5 # Note we always use df_resid for scale # Stata uses nobs or df_resid for rmse, not always available in Stata #assert_allclose(res1.scale, res2.rmse**2 * res2.N / (res2.N - res2.df_m - 1), rtol=rtol) skip = False if hasattr(res2, 'rss'): scale = res2.rss / (res2.N - res2.df_m - 1) elif hasattr(res2, 'rmse'): scale = res2.rmse**2 else: skip = True if isinstance(res1.model, WLS): skip = True # Stata uses different scaling and using unweighted resid for rmse if not skip: assert_allclose(res1.scale, scale, rtol=rtol) if not res2.vcetype == 'Newey-West': # no rsquared in Stata r2 = res2.r2 if hasattr(res2, 'r2') else res2.r2c assert_allclose(res1.rsquared, r2, rtol=rtol, err_msg=str(skip)) # consistency checks, not against Stata df_resid = res1.nobs - res1.df_model - 1 assert_equal(res1.df_resid, df_resid) # variance of resid_pearson is 1, with ddof, and loc=0 psum = (res1.resid_pearson**2).sum() assert_allclose(psum, df_resid, rtol=1e-13) @pytest.mark.smoke def test_summary(self): self.res1.summary() class TestOLSRobust2SmallNew(TestOLSRobust1, CheckOLSRobustNewMixin): # compare with ivreg robust small def setup(self): res_ols = self.res1.get_robustcov_results('HC1', use_t=True) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() self.bse_robust2 = res_ols.HC1_se self.cov_robust2 = res_ols.cov_HC1 self.small = True self.res2 = res.results_ivhc0_small def test_compare(self): #check that we get a warning using the nested compare methods res1 = self.res1 endog = res1.model.endog exog = res1.model.exog[:, [0, 2]] # drop one variable res_ols2 = OLS(endog, exog).fit() # results from Stata r_pval = .0307306938402991 r_chi2 = 4.667944083588736 r_df = 1 assert_warns(InvalidTestWarning, res1.compare_lr_test, res_ols2) import warnings with warnings.catch_warnings(): warnings.simplefilter("ignore") chi2, pval, df = res1.compare_lr_test(res_ols2) assert_allclose(chi2, r_chi2, rtol=1e-11) assert_allclose(pval, r_pval, rtol=1e-11) assert_equal(df, r_df) assert_warns(InvalidTestWarning, res1.compare_f_test, res_ols2) #fva, pval, df = res1.compare_f_test(res_ols2) class TestOLSRobustHACSmallNew(TestOLSRobust1, CheckOLSRobustNewMixin): # compare with ivreg robust small def setup(self): res_ols = self.res1.get_robustcov_results('HAC', maxlags=4, use_correction=True, use_t=True) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_hac_simple(res_ols, nlags=4, use_correction=True) se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = True self.res2 = res.results_ivhac4_small class TestOLSRobust2LargeNew(TestOLSRobust1, CheckOLSRobustNewMixin): # compare with ivreg robust small def setup(self): res_ols = self.res1.get_robustcov_results('HC0') res_ols.use_t = False self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() self.bse_robust2 = res_ols.HC0_se self.cov_robust2 = res_ols.cov_HC0 self.small = False self.res2 = res.results_ivhc0_large @pytest.mark.skip(reason="not refactored yet for `large`") def test_fvalue(self): super(TestOLSRobust2LargeNew, self).test_fvalue() @pytest.mark.skip(reason="not refactored yet for `large`") def test_confint(self): super(TestOLSRobust2LargeNew, self).test_confint() ####################################################### # cluster robust standard errors ####################################################### class CheckOLSRobustCluster(CheckOLSRobust): # compare with regress robust @classmethod def setup_class(cls): #import pandas as pa from statsmodels.datasets import grunfeld dtapa = grunfeld.data.load_pandas() #Stata example/data seems to miss last firm dtapa_endog = dtapa.endog[:200] dtapa_exog = dtapa.exog[:200] exog = add_constant(dtapa_exog[['value', 'capital']], prepend=False) #asserts do not work for pandas cls.res1 = OLS(dtapa_endog, exog).fit() firm_names, firm_id = np.unique(np.asarray(dtapa_exog[['firm']], 'S20'), return_inverse=True) cls.groups = firm_id #time indicator in range(max Ti) time = np.asarray(dtapa_exog[['year']]) time -= time.min() cls.time = np.squeeze(time).astype(int) # nw_panel function requires interval bounds cls.tidx = [(i*20, 20*(i+1)) for i in range(10)] class TestOLSRobustCluster2(CheckOLSRobustCluster, CheckOLSRobustNewMixin): # compare with `reg cluster` def setup(self): res_ols = self.res1.get_robustcov_results('cluster', groups=self.groups, use_correction=True, use_t=True) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_cluster(self.res1, self.groups, use_correction=True) se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = True self.res2 = res2.results_cluster self.rtol = 1e-6 self.rtolh = 1e-10 class TestOLSRobustCluster2Input(CheckOLSRobustCluster, CheckOLSRobustNewMixin): # compare with `reg cluster` def setup(self): import pandas as pd fat_array = self.groups.reshape(-1, 1) fat_groups = pd.DataFrame(fat_array) res_ols = self.res1.get_robustcov_results('cluster', groups=fat_groups, use_correction=True, use_t=True) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_cluster(self.res1, self.groups, use_correction=True) se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = True self.res2 = res2.results_cluster self.rtol = 1e-6 self.rtolh = 1e-10 def test_too_many_groups(self): long_groups = self.groups.reshape(-1, 1) groups3 = np.hstack((long_groups, long_groups, long_groups)) assert_raises(ValueError, self.res1.get_robustcov_results,'cluster', groups=groups3, use_correction=True, use_t=True) def test_2way_dataframe(self): import pandas as pd long_groups = self.groups.reshape(-1, 1) groups2 = pd.DataFrame(np.hstack((long_groups, long_groups))) res = self.res1.get_robustcov_results( 'cluster', groups=groups2, use_correction=True, use_t=True) class TestOLSRobustCluster2Fit(CheckOLSRobustCluster, CheckOLSRobustNewMixin): # copy, past uses fit method # compare with `reg cluster` def setup(self): res_ols = self.res1.model.fit(cov_type='cluster', cov_kwds=dict(groups=self.groups, use_correction=True, use_t=True)) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_cluster(self.res1, self.groups, use_correction=True) se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = True self.res2 = res2.results_cluster self.rtol = 1e-6 self.rtolh = 1e-10 def test_basic_inference(self): res1 = self.res1 res2 = self.res2 rtol = 1e-7 assert_allclose(res1.params, res2.params, rtol=1e-8) assert_allclose(res1.bse, res2.bse, rtol=rtol) assert_allclose(res1.pvalues, res2.pvalues, rtol=rtol, atol=1e-20) ci = res2.params_table[:, 4:6] assert_allclose(res1.conf_int(), ci, rtol=5e-7, atol=1e-20) class TestOLSRobustCluster2Large(CheckOLSRobustCluster, CheckOLSRobustNewMixin): # compare with `reg cluster` def setup(self): res_ols = self.res1.get_robustcov_results('cluster', groups=self.groups, use_correction=False, use_t=False, df_correction=True) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_cluster(self.res1, self.groups, use_correction=False) se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = False self.res2 = res2.results_cluster_large self.skip_f = True self.rtol = 1e-6 self.rtolh = 1e-10 @pytest.mark.skip(reason="GH#1189 issuecomment-29141741") def test_f_value(self): super(TestOLSRobustCluster2Large, self).test_fvalue() class TestOLSRobustCluster2LargeFit(CheckOLSRobustCluster, CheckOLSRobustNewMixin): # compare with `reg cluster` def setup(self): model = OLS(self.res1.model.endog, self.res1.model.exog) #res_ols = self.res1.model.fit(cov_type='cluster', res_ols = model.fit(cov_type='cluster', cov_kwds=dict(groups=self.groups, use_correction=False, use_t=False, df_correction=True)) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_cluster(self.res1, self.groups, use_correction=False) se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = False self.res2 = res2.results_cluster_large self.skip_f = True self.rtol = 1e-6 self.rtolh = 1e-10 @pytest.mark.skip(reason="GH#1189 issuecomment-29141741") def test_fvalue(self): super(TestOLSRobustCluster2LargeFit, self).test_fvalue() class TestOLSRobustClusterGS(CheckOLSRobustCluster, CheckOLSRobustNewMixin): # compare with `reg cluster` def setup(self): res_ols = self.res1.get_robustcov_results('nw-groupsum', time=self.time, maxlags=4, use_correction=False, use_t=True) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_nw_groupsum(self.res1, 4, self.time, use_correction=False) se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = True self.res2 = res2.results_nw_groupsum4 self.skip_f = True self.rtol = 1e-6 self.rtolh = 1e-10 class TestOLSRobustClusterGSFit(CheckOLSRobustCluster, CheckOLSRobustNewMixin): # compare with `reg cluster` def setup(self): res_ols = self.res1.model.fit(cov_type='nw-groupsum', cov_kwds=dict(time=self.time, maxlags=4, use_correction=False, use_t=True)) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_nw_groupsum(self.res1, 4, self.time, use_correction=False) se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = True self.res2 = res2.results_nw_groupsum4 self.skip_f = True self.rtol = 1e-6 self.rtolh = 1e-10 class TestOLSRobustClusterNWP(CheckOLSRobustCluster, CheckOLSRobustNewMixin): # compare with `reg cluster` def setup(self): res_ols = self.res1.get_robustcov_results('nw-panel', time=self.time, maxlags=4, use_correction='hac', use_t=True, df_correction=False) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_nw_panel(self.res1, 4, self.tidx) se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = True self.res2 = res2.results_nw_panel4 self.skip_f = True self.rtol = 1e-6 self.rtolh = 1e-10 def test_keyword(self): # check corrected keyword res_ols = self.res1.get_robustcov_results('hac-panel', time=self.time, maxlags=4, use_correction='hac', use_t=True, df_correction=False) assert_allclose(res_ols.bse, self.res1.bse, rtol=1e-12) class TestOLSRobustClusterNWPGroupsFit(CheckOLSRobustCluster, CheckOLSRobustNewMixin): # compare with `reg cluster` def setup(self): res_ols = self.res1.model.fit(cov_type='nw-panel', cov_kwds = dict(groups=self.groups, maxlags=4, use_correction='hac', use_t=True, df_correction=False)) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_nw_panel(self.res1, 4, self.tidx) se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = True self.res2 = res2.results_nw_panel4 self.skip_f = True self.rtol = 1e-6 self.rtolh = 1e-10 # TODO: low precision/agreement class TestOLSRobustCluster2G(CheckOLSRobustCluster, CheckOLSRobustNewMixin): # compare with `reg cluster` def setup(self): res_ols = self.res1.get_robustcov_results('cluster', groups=(self.groups, self.time), use_correction=True, use_t=True) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_cluster_2groups(self.res1, self.groups, group2=self.time, use_correction=True)[0] se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = True self.res2 = res2.results_cluster_2groups_small self.rtol = 0.35 # only f_pvalue and confint for constant differ >rtol=0.05 self.rtolh = 1e-10 class TestOLSRobustCluster2GLarge(CheckOLSRobustCluster, CheckOLSRobustNewMixin): # compare with `reg cluster` def setup(self): res_ols = self.res1.get_robustcov_results('cluster', groups=(self.groups, self.time), use_correction=False, #True, use_t=False) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_cluster_2groups(self.res1, self.groups, group2=self.time, use_correction=False)[0] se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = False self.res2 = res2.results_cluster_2groups_large self.skip_f = True self.rtol = 1e-7 self.rtolh = 1e-10 ###################################### # WLS ###################################### class CheckWLSRobustCluster(CheckOLSRobust): # compare with regress robust @classmethod def setup_class(cls): #import pandas as pa from statsmodels.datasets import grunfeld dtapa = grunfeld.data.load_pandas() #Stata example/data seems to miss last firm dtapa_endog = dtapa.endog[:200] dtapa_exog = dtapa.exog[:200] exog = add_constant(dtapa_exog[['value', 'capital']], prepend=False) #asserts do not work for pandas cls.res1 = WLS(dtapa_endog, exog, weights=1/dtapa_exog['value']).fit() firm_names, firm_id = np.unique(np.asarray(dtapa_exog[['firm']], 'S20'), return_inverse=True) cls.groups = firm_id #time indicator in range(max Ti) time = np.asarray(dtapa_exog[['year']]) time -= time.min() cls.time = np.squeeze(time).astype(int) # nw_panel function requires interval bounds cls.tidx = [(i*20, 20*(i+1)) for i in range(10)] # not available yet for WLS class TestWLSRobustCluster2(CheckWLSRobustCluster, CheckOLSRobustNewMixin): # compare with `reg cluster` def setup(self): res_ols = self.res1.get_robustcov_results('cluster', groups=self.groups, use_correction=True, use_t=True) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_cluster(self.res1, self.groups, use_correction=True) se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = True self.res2 = res2.results_cluster_wls_small self.rtol = 1e-6 self.rtolh = 1e-10 # not available yet for WLS class TestWLSRobustCluster2Large(CheckWLSRobustCluster, CheckOLSRobustNewMixin): # compare with `reg cluster` def setup(self): res_ols = self.res1.get_robustcov_results('cluster', groups=self.groups, use_correction=False, use_t=False, df_correction=True) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() cov1 = sw.cov_cluster(self.res1, self.groups, use_correction=False) se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = False self.res2 = res2.results_cluster_wls_large self.skip_f = True self.rtol = 1e-6 self.rtolh = 1e-10 class TestWLSRobustSmall(CheckWLSRobustCluster, CheckOLSRobustNewMixin): # compare with `reg cluster` def setup(self): res_ols = self.res1.get_robustcov_results('HC1', use_t=True) self.res3 = self.res1 self.res1 = res_ols self.bse_robust = res_ols.bse self.cov_robust = res_ols.cov_params() #TODO: check standalone function #cov1 = sw.cov_cluster(self.res1, self.groups, use_correction=False) cov1 = res_ols.cov_HC1 se1 = sw.se_cov(cov1) self.bse_robust2 = se1 self.cov_robust2 = cov1 self.small = True self.res2 = res2.results_hc1_wls_small self.skip_f = True self.rtol = 1e-6 self.rtolh = 1e-10 class TestWLSOLSRobustSmall(object): @classmethod def setup_class(cls): # import pandas as pa from statsmodels.datasets import grunfeld dtapa = grunfeld.data.load_pandas() # Stata example/data seems to miss last firm dtapa_endog = dtapa.endog[:200] dtapa_exog = dtapa.exog[:200] exog = add_constant(dtapa_exog[['value', 'capital']], prepend=False) # asserts do not work for pandas cls.res_wls = WLS(dtapa_endog, exog, weights=1/dtapa_exog['value']).fit() w_sqrt = 1 / np.sqrt(np.asarray(dtapa_exog['value'])) cls.res_ols = OLS(dtapa_endog * w_sqrt, np.asarray(exog) * w_sqrt[:, None]).fit() ids = np.asarray(dtapa_exog[['firm']], 'S20') firm_names, firm_id = np.unique(ids, return_inverse=True) cls.groups = firm_id # time indicator in range(max Ti) time = np.asarray(dtapa_exog[['year']]) time -= time.min() cls.time = np.squeeze(time).astype(int) # nw_panel function requires interval bounds cls.tidx = [(i*20, 20*(i+1)) for i in range(10)] def test_all(self): all_cov = [('HC0', dict(use_t=True)), ('HC1', dict(use_t=True)), ('HC2', dict(use_t=True)), ('HC3', dict(use_t=True))] for cov_type, kwds in all_cov: res1 = self.res_ols.get_robustcov_results(cov_type, **kwds) res2 = self.res_wls.get_robustcov_results(cov_type, **kwds) assert_allclose(res1.params, res2.params, rtol=1e-13) assert_allclose(res1.cov_params(), res2.cov_params(), rtol=1e-13) assert_allclose(res1.bse, res2.bse, rtol=1e-13) assert_allclose(res1.pvalues, res2.pvalues, rtol=1e-13) mat = np.eye(len(res1.params)) ft1 = res1.f_test(mat) ft2 = res2.f_test(mat) assert_allclose(ft1.fvalue, ft2.fvalue, rtol=1e-12) assert_allclose(ft1.pvalue, ft2.pvalue, rtol=5e-11) def test_fixed_scale(self): cov_type = 'fixed_scale' kwds = {} res1 = self.res_ols.get_robustcov_results(cov_type, **kwds) res2 = self.res_wls.get_robustcov_results(cov_type, **kwds) assert_allclose(res1.params, res2.params, rtol=1e-13) assert_allclose(res1.cov_params(), res2.cov_params(), rtol=1e-13) assert_allclose(res1.bse, res2.bse, rtol=1e-13) assert_allclose(res1.pvalues, res2.pvalues, rtol=1e-12) tt = res2.t_test(np.eye(len(res2.params)), cov_p=res2.normalized_cov_params) assert_allclose(res2.cov_params(), res2.normalized_cov_params, rtol=1e-13) assert_allclose(res2.bse, tt.sd, rtol=1e-13) assert_allclose(res2.pvalues, tt.pvalue, rtol=1e-13) assert_allclose(res2.tvalues, tt.tvalue, rtol=1e-13) # using cov_type in fit mod = self.res_wls.model mod3 = WLS(mod.endog, mod.exog, weights=mod.weights) res3 = mod3.fit(cov_type=cov_type, cov_kwds=kwds) tt = res3.t_test(np.eye(len(res3.params)), cov_p=res3.normalized_cov_params) assert_allclose(res3.cov_params(), res3.normalized_cov_params, rtol=1e-13) assert_allclose(res3.bse, tt.sd, rtol=1e-13) assert_allclose(res3.pvalues, tt.pvalue, rtol=1e-13) assert_allclose(res3.tvalues, tt.tvalue, rtol=1e-13) def test_cov_type_fixed_scale(): # this is a unit test from scipy curvefit for `absolute_sigma` keyword xdata = np.array([0, 1, 2, 3, 4, 5]) ydata = np.array([1, 1, 5, 7, 8, 12]) sigma = np.array([1, 2, 1, 2, 1, 2]) xdata = np.column_stack((xdata, np.ones(len(xdata)))) weights = 1. / sigma**2 res = WLS(ydata, xdata, weights=weights).fit() assert_allclose(res.bse, [0.20659803, 0.57204404], rtol=1e-3) res = WLS(ydata, xdata, weights=weights).fit() assert_allclose(res.bse, [0.20659803, 0.57204404], rtol=1e-3) res = WLS(ydata, xdata, weights=weights).fit(cov_type='fixed scale') assert_allclose(res.bse, [0.30714756, 0.85045308], rtol=1e-3) res = WLS(ydata, xdata, weights=weights / 9.).fit(cov_type='fixed scale') assert_allclose(res.bse, [3*0.30714756, 3*0.85045308], rtol=1e-3) res = WLS(ydata, xdata, weights=weights).fit(cov_type='fixed scale', cov_kwds={'scale':9}) assert_allclose(res.bse, [3*0.30714756, 3*0.85045308], rtol=1e-3) statsmodels-0.12.2/statsmodels/regression/tests/test_rolling.py000066400000000000000000000241641400612667500251170ustar00rootroot00000000000000from io import BytesIO from itertools import product import numpy as np import pandas as pd import pytest from numpy.testing import assert_allclose, assert_array_equal from statsmodels import tools from statsmodels.regression.linear_model import WLS from statsmodels.regression.rolling import RollingWLS, RollingOLS def gen_data(nobs, nvar, const, pandas=False, missing=0.0, weights=False): rs = np.random.RandomState(987499302) x = rs.standard_normal((nobs, nvar)) cols = ["x{0}".format(i) for i in range(nvar)] if const: x = tools.add_constant(x) cols = ["const"] + cols if missing > 0.0: mask = rs.random_sample(x.shape) < missing x[mask] = np.nan if x.shape[1] > 1: y = x[:, :-1].sum(1) + rs.standard_normal(nobs) else: y = x.sum(1) + rs.standard_normal(nobs) w = rs.chisquare(5, y.shape[0]) / 5 if pandas: idx = pd.date_range("12-31-1999", periods=nobs) x = pd.DataFrame(x, index=idx, columns=cols) y = pd.Series(y, index=idx, name="y") w = pd.Series(w, index=idx, name="weights") if not weights: w = None return y, x, w nobs = (250,) nvar = (3, 0) tf = (True, False) missing = (0, 0.1) params = list(product(nobs, nvar, tf, tf, missing)) params = [param for param in params if param[1] + param[2] > 0] ids = ["-".join(map(str, param)) for param in params] basic_params = [param for param in params if params[2] and params[4]] weighted_params = [param + (tf,) for param in params for tf in (True, False)] weighted_ids = ["-".join(map(str, param)) for param in weighted_params] @pytest.fixture(scope="module", params=params, ids=ids) def data(request): return gen_data(*request.param) @pytest.fixture(scope="module", params=basic_params, ids=ids) def basic_data(request): return gen_data(*request.param) @pytest.fixture(scope="module", params=weighted_params, ids=weighted_ids) def weighted_data(request): return gen_data(*request.param) def get_single(x, idx): if isinstance(x, (pd.Series, pd.DataFrame)): return x.iloc[idx] return x[idx] def get_sub(x, idx, window): if isinstance(x, (pd.Series, pd.DataFrame)): out = x.iloc[idx - window : idx] return np.asarray(out) return x[idx - window : idx] def test_has_nan(data): y, x, w = data mod = RollingWLS(y, x, window=100, weights=w) has_nan = np.zeros(y.shape[0], dtype=bool) for i in range(100, y.shape[0] + 1): _y = get_sub(y, i, 100) _x = get_sub(x, i, 100) has_nan[i - 1] = np.squeeze( (np.any(np.isnan(_y)) or np.any(np.isnan(_x))) ) assert_array_equal(mod._has_nan, has_nan) def test_weighted_against_wls(weighted_data): y, x, w = weighted_data mod = RollingWLS(y, x, weights=w, window=100) res = mod.fit(use_t=True) for i in range(100, y.shape[0]): _y = get_sub(y, i, 100) _x = get_sub(x, i, 100) if w is not None: _w = get_sub(w, i, 100) else: _w = np.ones_like(_y) wls = WLS(_y, _x, weights=_w, missing="drop").fit() rolling_params = get_single(res.params, i - 1) rolling_nobs = get_single(res.nobs, i - 1) assert_allclose(rolling_params, wls.params) assert_allclose(rolling_nobs, wls.nobs) assert_allclose(get_single(res.ssr, i - 1), wls.ssr) assert_allclose(get_single(res.llf, i - 1), wls.llf) assert_allclose(get_single(res.aic, i - 1), wls.aic) assert_allclose(get_single(res.bic, i - 1), wls.bic) assert_allclose(get_single(res.centered_tss, i - 1), wls.centered_tss) assert_allclose(res.df_model, wls.df_model) assert_allclose(get_single(res.df_resid, i - 1), wls.df_resid) assert_allclose(get_single(res.ess, i - 1), wls.ess, atol=1e-8) assert_allclose(res.k_constant, wls.k_constant) assert_allclose(get_single(res.mse_model, i - 1), wls.mse_model) assert_allclose(get_single(res.mse_resid, i - 1), wls.mse_resid) assert_allclose(get_single(res.mse_total, i - 1), wls.mse_total) assert_allclose( get_single(res.rsquared, i - 1), wls.rsquared, atol=1e-8 ) assert_allclose( get_single(res.rsquared_adj, i - 1), wls.rsquared_adj, atol=1e-8 ) assert_allclose( get_single(res.uncentered_tss, i - 1), wls.uncentered_tss ) @pytest.mark.parametrize("cov_type", ["nonrobust", "HC0"]) @pytest.mark.parametrize("use_t", [None, True, False]) def test_against_wls_inference(data, use_t, cov_type): y, x, w = data mod = RollingWLS(y, x, window=100, weights=w) res = mod.fit(use_t=use_t, cov_type=cov_type) ci_cols = ci = res.conf_int() test_cols = x.shape[1] > 3 # This is a smoke test of cov_params to make sure it works res.cov_params() if test_cols: ci_cols = res.conf_int(cols=[0, 2]) # Skip to improve performance for i in range(100, y.shape[0]): _y = get_sub(y, i, 100) _x = get_sub(x, i, 100) wls = WLS(_y, _x, missing="drop").fit(use_t=use_t, cov_type=cov_type) assert_allclose(get_single(res.tvalues, i - 1), wls.tvalues) assert_allclose(get_single(res.bse, i - 1), wls.bse) assert_allclose(get_single(res.pvalues, i - 1), wls.pvalues, atol=1e-8) assert_allclose(get_single(res.fvalue, i - 1), wls.fvalue) with np.errstate(invalid="ignore"): assert_allclose( get_single(res.f_pvalue, i - 1), wls.f_pvalue, atol=1e-8 ) assert res.cov_type == wls.cov_type assert res.use_t == wls.use_t wls_ci = wls.conf_int() if isinstance(ci, pd.DataFrame): ci_val = ci.iloc[i - 1] ci_val = np.asarray(ci_val).reshape((-1, 2)) else: ci_val = ci[i - 1].T assert_allclose(ci_val, wls_ci) if test_cols: wls_ci = wls.conf_int(cols=[0, 2]) if isinstance(ci_cols, pd.DataFrame): ci_val = ci_cols.iloc[i - 1] ci_val = np.asarray(ci_val).reshape((-1, 2)) else: ci_val = ci_cols[i - 1].T assert_allclose(ci_val, wls_ci) def test_raise(data): y, x, w = data mod = RollingWLS(y, x, window=100, missing="drop", weights=w) res = mod.fit() params = np.asarray(res.params) assert np.all(np.isfinite(params[99:])) if not np.any(np.isnan(y)): return mod = RollingWLS(y, x, window=100, missing="skip") res = mod.fit() params = np.asarray(res.params) assert np.any(np.isnan(params[100:])) def test_error(): y, x, _ = gen_data(250, 2, True) with pytest.raises(ValueError, match="reset must be a positive integer"): RollingWLS(y, x,).fit(reset=-1) with pytest.raises(ValueError): RollingWLS(y, x).fit(method="unknown") with pytest.raises(ValueError, match="min_nobs must be larger"): RollingWLS(y, x, min_nobs=1) with pytest.raises(ValueError, match="min_nobs must be larger"): RollingWLS(y, x, window=60, min_nobs=100) def test_save_load(data): y, x, w = data res = RollingOLS(y, x, window=60).fit() fh = BytesIO() # test wrapped results load save pickle res.save(fh) fh.seek(0, 0) res_unpickled = res.__class__.load(fh) assert type(res_unpickled) is type(res) # noqa: E721 fh = BytesIO() # test wrapped results load save pickle res.save(fh, remove_data=True) fh.seek(0, 0) res_unpickled = res.__class__.load(fh) assert type(res_unpickled) is type(res) # noqa: E721 def test_formula(): y, x, w = gen_data(250, 3, True, pandas=True) fmla = "y ~ 1 + x0 + x1 + x2" data = pd.concat([y, x], axis=1) mod = RollingWLS.from_formula(fmla, window=100, data=data, weights=w) res = mod.fit() alt = RollingWLS(y, x, window=100) alt_res = alt.fit() assert_allclose(res.params, alt_res.params) ols_mod = RollingOLS.from_formula(fmla, window=100, data=data) ols_mod.fit() @pytest.mark.matplotlib def test_plot(): import matplotlib.pyplot as plt y, x, w = gen_data(250, 3, True, pandas=True) fmla = "y ~ 1 + x0 + x1 + x2" data = pd.concat([y, x], axis=1) mod = RollingWLS.from_formula(fmla, window=100, data=data, weights=w) res = mod.fit() fig = res.plot_recursive_coefficient() assert isinstance(fig, plt.Figure) res.plot_recursive_coefficient(variables=2, alpha=None, figsize=(30, 7)) res.plot_recursive_coefficient(variables="x0", alpha=None, figsize=(30, 7)) res.plot_recursive_coefficient( variables=[0, 2], alpha=None, figsize=(30, 7) ) res.plot_recursive_coefficient( variables=["x0"], alpha=None, figsize=(30, 7) ) res.plot_recursive_coefficient( variables=["x0", "x1", "x2"], alpha=None, figsize=(30, 7) ) with pytest.raises(ValueError, match="variable x4 is not an integer"): res.plot_recursive_coefficient(variables="x4") fig = plt.Figure() with pytest.warns(Warning): # Just silence the warning out = res.plot_recursive_coefficient(fig=fig) assert out is fig res.plot_recursive_coefficient(alpha=None, figsize=(30, 7)) def test_methods(basic_data): y, x, _ = basic_data mod = RollingOLS(y, x, 150) res_inv = mod.fit(method="inv") res_lstsq = mod.fit(method="lstsq") res_pinv = mod.fit(method="pinv") assert_allclose(res_inv.params, res_lstsq.params) assert_allclose(res_inv.params, res_pinv.params) def test_min_nobs(basic_data): y, x, w = basic_data if not np.any(np.isnan(np.asarray(x))): return mod = RollingOLS(y, x, 150) res = mod.fit() # Ensures that the constraint binds min_nobs = res.nobs[res.nobs != 0].min() + 1 mod = RollingOLS(y, x, 150, min_nobs=min_nobs) res = mod.fit() assert np.all(res.nobs[res.nobs != 0] >= min_nobs) def test_expanding(basic_data): y, x, w = basic_data xa = np.asarray(x) mod = RollingOLS(y, x, 150, min_nobs=50, expanding=True) res = mod.fit() params = np.asarray(res.params) assert np.all(np.isnan(params[:49])) first = np.where(np.cumsum(np.all(np.isfinite(xa), axis=1)) >= 50)[0][0] assert np.all(np.isfinite(params[first:])) statsmodels-0.12.2/statsmodels/regression/tests/test_theil.py000066400000000000000000000322731400612667500245560ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Mon May 05 17:29:56 2014 Author: Josef Perktold """ import os import numpy as np import pandas as pd import pytest from numpy.testing import assert_allclose from statsmodels.regression.linear_model import OLS, GLS from statsmodels.sandbox.regression.penalized import TheilGLS class TestTheilTextile(object): @classmethod def setup_class(cls): cur_dir = os.path.dirname(os.path.abspath(__file__)) filepath = os.path.join(cur_dir, "results", "theil_textile_predict.csv") cls.res_predict = pd.read_csv(filepath, sep=",") names = "year lconsump lincome lprice".split() data = np.array('''\ 1923 1.99651 1.98543 2.00432 1924 1.99564 1.99167 2.00043 1925 2 2 2 1926 2.04766 2.02078 1.95713 1927 2.08707 2.02078 1.93702 1928 2.07041 2.03941 1.95279 1929 2.08314 2.04454 1.95713 1930 2.13354 2.05038 1.91803 1931 2.18808 2.03862 1.84572 1932 2.18639 2.02243 1.81558 1933 2.20003 2.00732 1.78746 1934 2.14799 1.97955 1.79588 1935 2.13418 1.98408 1.80346 1936 2.22531 1.98945 1.72099 1937 2.18837 2.0103 1.77597 1938 2.17319 2.00689 1.77452 1939 2.2188 2.0162 1.78746'''.split(), float).reshape(-1, 4) endog = data[:, 1] # constant at the end to match Stata exog = np.column_stack((data[:, 2:], np.ones(endog.shape[0]))) #prior(lprice -0.7 0.15 lincome 1 0.15) cov(lprice lincome -0.01) r_matrix = np.array([[1, 0, 0], [0, 1, 0]]) r_mean = [1, -0.7] cov_r = np.array([[0.15**2, -0.01], [-0.01, 0.15**2]]) mod = TheilGLS(endog, exog, r_matrix, q_matrix=r_mean, sigma_prior=cov_r) cls.res1 = mod.fit(cov_type='data-prior', use_t=True) #cls.res1._cache['scale'] = 0.0001852252884817586 # from tg_mixed cls.res1._cache['scale'] = 0.00018334123641580062 # from OLS from .results import results_theil_textile as resmodule cls.res2 = resmodule.results_theil_textile def test_basic(self): pt = self.res2.params_table[:,:6].T params2, bse2, tvalues2, pvalues2, ci_low, ci_upp = pt assert_allclose(self.res1.params, params2, rtol=2e-6) #TODO tgmixed seems to use scale from initial OLS, not from final res # np.sqrt(res.scale / res_ols.scale) # see below mse_resid which is equal to scale corr_fact = 0.9836026210570028 corr_fact = 0.97376865041463734 corr_fact = 1 assert_allclose(self.res1.bse / corr_fact, bse2, rtol=2e-6) assert_allclose(self.res1.tvalues * corr_fact, tvalues2, rtol=2e-6) # pvalues are very small #assert_allclose(self.res1.pvalues, pvalues2, atol=2e-6) #assert_allclose(self.res1.pvalues, pvalues2, rtol=0.7) ci = self.res1.conf_int() # not scale corrected assert_allclose(ci[:,0], ci_low, rtol=0.01) assert_allclose(ci[:,1], ci_upp, rtol=0.01) assert_allclose(self.res1.rsquared, self.res2.r2, rtol=2e-6) # Note: tgmixed is using k_exog for df_resid corr_fact = self.res1.df_resid / self.res2.df_r assert_allclose(np.sqrt(self.res1.mse_resid * corr_fact), self.res2.rmse, rtol=2e-6) assert_allclose(self.res1.fittedvalues, self.res_predict['fittedvalues'], atol=5e7) def test_other(self): tc = self.res1.test_compatibility() assert_allclose(np.squeeze(tc[0]), self.res2.compat, rtol=2e-6) assert_allclose(np.squeeze(tc[1]), self.res2.pvalue, rtol=2e-6) frac = self.res1.share_data() # TODO check again, I guess tgmixed uses final scale in hatmatrix # but I'm not sure, it passed in previous version, but now we override # scale with OLS scale # assert_allclose(frac, self.res2.frac_sample, rtol=2e-6) # regression tests: assert_allclose(frac, 0.6946116246864239, rtol=2e-6) def test_no_penalization(self): res_ols = OLS(self.res1.model.endog, self.res1.model.exog).fit() res_theil = self.res1.model.fit(pen_weight=0, cov_type='data-prior') assert_allclose(res_theil.params, res_ols.params, rtol=1e-10) assert_allclose(res_theil.bse, res_ols.bse, rtol=1e-10) @pytest.mark.smoke def test_summary(self): with pytest.warns(UserWarning): self.res1.summary() class CheckEquivalenceMixin(object): tol = {'default': (1e-4, 1e-20)} @classmethod def get_sample(cls): np.random.seed(987456) nobs, k_vars = 200, 5 beta = 0.5 * np.array([0.1, 1, 1, 0, 0]) x = np.random.randn(nobs, k_vars) x[:, 0] = 1 y = np.dot(x, beta) + 2 * np.random.randn(nobs) return y, x def test_attributes(self): attributes_fit = ['params', 'rsquared', 'df_resid', 'df_model', 'llf', 'aic', 'bic' #'fittedvalues', 'resid' ] attributes_inference = ['bse', 'tvalues', 'pvalues'] import copy attributes = copy.copy(attributes_fit) if not getattr(self, 'skip_inference', False): attributes.extend(attributes_inference) for att in attributes: r1 = getattr(self.res1, att) r2 = getattr(self.res2, att) if not np.size(r1) == 1: r1 = r1[:len(r2)] # check if we have overwritten tolerance rtol, atol = self.tol.get(att, self.tol['default']) message = 'attribute: ' + att #+ '\n%r\n\%r' % (r1, r2) assert_allclose(r1, r2, rtol=rtol, atol=atol, err_msg=message) # models are not close enough for some attributes at high precision assert_allclose(self.res1.fittedvalues, self.res1.fittedvalues, rtol=1e-3, atol=1e-4) assert_allclose(self.res1.resid, self.res1.resid, rtol=1e-3, atol=1e-4) class TestTheil1(CheckEquivalenceMixin): # penalize last two parameters to zero @classmethod def setup_class(cls): y, x = cls.get_sample() mod1 = TheilGLS(y, x, sigma_prior=[0, 0, 1., 1.]) cls.res1 = mod1.fit(200000) cls.res2 = OLS(y, x[:, :3]).fit() class TestTheil2(CheckEquivalenceMixin): # no penalization = same as OLS @classmethod def setup_class(cls): y, x = cls.get_sample() mod1 = TheilGLS(y, x, sigma_prior=[0, 0, 1., 1.]) cls.res1 = mod1.fit(0) cls.res2 = OLS(y, x).fit() class TestTheil3(CheckEquivalenceMixin): # perfect multicollinearity = same as OLS in terms of fit # inference: bse, ... is different @classmethod def setup_class(cls): cls.skip_inference = True y, x = cls.get_sample() xd = np.column_stack((x, x)) #sp = np.zeros(5), np.ones(5) r_matrix = np.eye(5, 10, 5) mod1 = TheilGLS(y, xd, r_matrix=r_matrix) #sigma_prior=[0, 0, 1., 1.]) cls.res1 = mod1.fit(0.001, cov_type='data-prior') cls.res2 = OLS(y, x).fit() class TestTheilGLS(CheckEquivalenceMixin): # penalize last two parameters to zero @classmethod def setup_class(cls): y, x = cls.get_sample() nobs = len(y) weights = (np.arange(nobs) < (nobs // 2)) + 0.5 mod1 = TheilGLS(y, x, sigma=weights, sigma_prior=[0, 0, 1., 1.]) cls.res1 = mod1.fit(200000) cls.res2 = GLS(y, x[:, :3], sigma=weights).fit() class TestTheilLinRestriction(CheckEquivalenceMixin): # impose linear restriction with small uncertainty - close to OLS @classmethod def setup_class(cls): y, x = cls.get_sample() #merge var1 and var2 x2 = x[:, :2].copy() x2[:, 1] += x[:, 2] #mod1 = TheilGLS(y, x, r_matrix =[[0, 1, -1, 0, 0]]) mod1 = TheilGLS(y, x[:, :3], r_matrix =[[0, 1, -1]]) cls.res1 = mod1.fit(200000) cls.res2 = OLS(y, x2).fit() # adjust precision, careful: cls.tol is mutable tol = {'pvalues': (1e-4, 2e-7), 'tvalues': (5e-4, 0)} tol.update(cls.tol) cls.tol = tol class TestTheilLinRestrictionApprox(CheckEquivalenceMixin): # impose linear restriction with some uncertainty @classmethod def setup_class(cls): y, x = cls.get_sample() #merge var1 and var2 x2 = x[:, :2].copy() x2[:, 1] += x[:, 2] #mod1 = TheilGLS(y, x, r_matrix =[[0, 1, -1, 0, 0]]) mod1 = TheilGLS(y, x[:, :3], r_matrix =[[0, 1, -1]]) cls.res1 = mod1.fit(100) cls.res2 = OLS(y, x2).fit() # adjust precision, careful: cls.tol is mutable import copy tol = copy.copy(cls.tol) tol2 = {'default': (0.15, 0), 'params': (0.05, 0), 'pvalues': (0.02, 0.001), } tol.update(tol2) cls.tol = tol class TestTheilPanel(object): @classmethod def setup_class(cls): #example 3 nobs = 300 nobs_i = 5 n_groups = nobs // nobs_i k_vars = 3 from statsmodels.sandbox.panel.random_panel import PanelSample dgp = PanelSample(nobs, k_vars, n_groups, seed=303305) # add random intercept, using same RandomState dgp.group_means = 2 + dgp.random_state.randn(n_groups) print('seed', dgp.seed) y = dgp.generate_panel() x = np.column_stack((dgp.exog[:,1:], dgp.groups[:,None] == np.arange(n_groups))) cls.dgp = dgp cls.endog = y cls.exog = x cls.res_ols = OLS(y, x).fit() def test_regression(self): y = self.endog x = self.exog n_groups, k_vars = self.dgp.n_groups, self.dgp.k_vars Rg = (np.eye(n_groups-1) - 1. / n_groups * np.ones((n_groups - 1, n_groups-1))) R = np.c_[np.zeros((n_groups - 1, k_vars)), Rg] r = np.zeros(n_groups - 1) R[:, k_vars-1] = -1 lambd = 1 #1e-4 mod = TheilGLS(y, x, r_matrix=R, q_matrix=r, sigma_prior=lambd) res = mod.fit() # regression test params1 = np.array([ 0.9751655 , 1.05215277, 0.37135028, 2.0492626 , 2.82062503, 2.82139775, 1.92940468, 2.96942081, 2.86349583, 3.20695368, 4.04516422, 3.04918839, 4.54748808, 3.49026961, 3.15529618, 4.25552932, 2.65471759, 3.62328747, 3.07283053, 3.49485898, 3.42301424, 2.94677593, 2.81549427, 2.24895113, 2.29222784, 2.89194946, 3.17052308, 2.37754241, 3.54358533, 3.79838425, 1.91189071, 1.15976407, 4.05629691, 1.58556827, 4.49941666, 4.08608599, 3.1889269 , 2.86203652, 3.06785013, 1.9376162 , 2.90657681, 3.71910592, 3.15607617, 3.58464547, 2.15466323, 4.87026717, 2.92909833, 2.64998337, 2.891171 , 4.04422964, 3.54616122, 4.12135273, 3.70232028, 3.8314497 , 2.2591451 , 2.39321422, 3.13064532, 2.1569678 , 2.04667506, 3.92064689, 3.66243644, 3.11742725]) assert_allclose(res.params, params1) pen_weight_aicc = mod.select_pen_weight(method='aicc') pen_weight_gcv = mod.select_pen_weight(method='gcv') pen_weight_cv = mod.select_pen_weight(method='cv') pen_weight_bic = mod.select_pen_weight(method='bic') assert_allclose(pen_weight_gcv, pen_weight_aicc, rtol=0.1) # regression tests: assert_allclose(pen_weight_aicc, 4.77333984, rtol=1e-4) assert_allclose(pen_weight_gcv, 4.45546875, rtol=1e-4) assert_allclose(pen_weight_bic, 9.35957031, rtol=1e-4) assert_allclose(pen_weight_cv, 1.99277344, rtol=1e-4) def test_combine_subset_regression(self): # split sample into two, use first sample as prior for second endog = self.endog exog = self.exog nobs = len(endog) n05 = nobs // 2 np.random.seed(987125) # shuffle to get random subsamples shuffle_idx = np.random.permutation(np.arange(nobs)) ys = endog[shuffle_idx] xs = exog[shuffle_idx] k = 10 res_ols0 = OLS(ys[:n05], xs[:n05, :k]).fit() res_ols1 = OLS(ys[n05:], xs[n05:, :k]).fit() w = res_ols1.scale / res_ols0.scale #1.01 mod_1 = TheilGLS(ys[n05:], xs[n05:, :k], r_matrix=np.eye(k), q_matrix=res_ols0.params, sigma_prior=w * res_ols0.cov_params()) res_1p = mod_1.fit(cov_type='data-prior') res_1s = mod_1.fit(cov_type='sandwich') res_olsf = OLS(ys, xs[:, :k]).fit() assert_allclose(res_1p.params, res_olsf.params, rtol=1e-9) corr_fact = np.sqrt(res_1p.scale / res_olsf.scale) # corrct for differences in scale computation assert_allclose(res_1p.bse, res_olsf.bse * corr_fact, rtol=1e-3) # regression test, does not verify numbers # especially why are these smaller than OLS on full sample # in larger sample, nobs=600, those were close to full OLS bse1 = np.array([ 0.26589869, 0.15224812, 0.38407399, 0.75679949, 0.66084200, 0.54174080, 0.53697607, 0.66006377, 0.38228551, 0.53920485]) assert_allclose(res_1s.bse, bse1, rtol=1e-7) statsmodels-0.12.2/statsmodels/regression/tests/test_tools.py000066400000000000000000000051641400612667500246100ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_allclose import pytest from statsmodels.regression.linear_model import WLS from statsmodels.regression._tools import _MinimalWLS class TestMinimalWLS(object): @classmethod def setup_class(cls): rs = np.random.RandomState(1234) cls.exog1 = rs.randn(200, 5) cls.endog1 = cls.exog1.sum(1) + rs.randn(200) cls.weights1 = 1.0 + np.sin(np.arange(200.0) / 100.0 * np.pi) cls.exog2 = rs.randn(50, 1) cls.endog2 = 0.3 * cls.exog2.ravel() + rs.randn(50) cls.weights2 = 1.0 + np.log(np.arange(1.0, 51.0)) @pytest.mark.parametrize('check', [True, False]) def test_equivalence_with_wls(self, check): res = WLS(self.endog1, self.exog1).fit() minres = _MinimalWLS(self.endog1, self.exog1, check_endog=check, check_weights=check).fit() assert_allclose(res.params, minres.params) assert_allclose(res.resid, minres.resid) res = WLS(self.endog2, self.exog2).fit() minres = _MinimalWLS(self.endog2, self.exog2, check_endog=check, check_weights=check).fit() assert_allclose(res.params, minres.params) assert_allclose(res.resid, minres.resid) res = WLS(self.endog1, self.exog1, weights=self.weights1).fit() minres = _MinimalWLS(self.endog1, self.exog1, weights=self.weights1, check_endog=check, check_weights=check).fit() assert_allclose(res.params, minres.params) assert_allclose(res.resid, minres.resid) res = WLS(self.endog2, self.exog2, weights=self.weights2).fit() minres = _MinimalWLS(self.endog2, self.exog2, weights=self.weights2, check_endog=check, check_weights=check).fit() assert_allclose(res.params, minres.params) assert_allclose(res.resid, minres.resid) @pytest.mark.parametrize('bad_value', [np.nan, np.inf]) def test_inf_nan(self, bad_value): with pytest.raises( ValueError, match=r'detected in endog, estimation infeasible'): endog = self.endog1.copy() endog[0] = bad_value _MinimalWLS(endog, self.exog1, self.weights1, check_endog=True, check_weights=True).fit() with pytest.raises( ValueError, match=r'detected in weights, estimation infeasible'): weights = self.weights1.copy() weights[-1] = bad_value _MinimalWLS(self.endog1, self.exog1, weights, check_endog=True, check_weights=True).fit() statsmodels-0.12.2/statsmodels/robust/000077500000000000000000000000001400612667500200255ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/robust/__init__.py000066400000000000000000000004041400612667500221340ustar00rootroot00000000000000""" Robust statistical models """ __all__ = ["norms", "mad", "Huber", "HuberScale", "hubers_scale", "test"] from . import norms from .scale import mad, Huber, HuberScale, hubers_scale from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/robust/_qn.pyx000066400000000000000000000106631400612667500213520ustar00rootroot00000000000000#!python #cython: wraparound=False, boundscheck=False, cdivision=True import numpy as np def _high_weighted_median(double[::1] a, int[::1] weights): """ Computes a weighted high median of a. This is defined as the smallest a[j] such that the sum over all a[i]<=a[j] is strictly greater than half the total sum of the weights """ cdef: double[::1] a_cp = np.copy(a) int[::1] weights_cp = np.copy(weights) int n = a_cp.shape[0] double[::1] sorted_a = np.zeros((n,), dtype=np.double) double[::1] a_cand = np.zeros((n,), dtype=np.double) int[::1] weights_cand = np.zeros((n,), dtype=np.intc) int kcand = 0 int wleft, wright, wmid, wtot, wrest = 0 double trial = 0 wtot = np.sum(weights_cp) while True: wleft = 0 wmid = 0 wright = 0 for i in range(n): sorted_a[i] = a_cp[i] sorted_a = np.partition(sorted_a, kth=n//2) trial = sorted_a[n//2] for i in range(n): if a_cp[i] < trial: wleft = wleft + weights_cp[i] elif a_cp[i] > trial: wright = wright + weights_cp[i] else: wmid = wmid + weights_cp[i] kcand = 0 if 2 * (wrest + wleft) > wtot: for i in range(n): if a_cp[i] < trial: a_cand[kcand] = a_cp[i] weights_cand[kcand] = weights_cp[i] kcand = kcand + 1 elif 2 * (wrest + wleft + wmid) <= wtot: for i in range(n): if a_cp[i] > trial: a_cand[kcand] = a_cp[i] weights_cand[kcand] = weights_cp[i] kcand = kcand + 1 wrest = wrest + wleft + wmid else: break n = kcand for i in range(n): a_cp[i] = a_cand[i] weights_cp[i] = weights_cand[i] return trial def _qn(double[:] a, double c): """ Computes the Qn robust estimator of scale, a more efficient alternative to the MAD. The implementation follows the algorithm described in Croux and Rousseeuw (1992). Parameters ---------- a : array_like Input array. c : float, optional The normalization constant, used to get consistent estimates of the standard deviation at the normal distribution. Defined as 1/(np.sqrt(2) * scipy.stats.norm.ppf(5/8)), which is 2.219144. Returns ------- The Qn robust estimator of scale """ cdef: int n = a.shape[0] int h = n/2 + 1 int k = h * (h - 1) / 2 int n_left = n * (n + 1) / 2 int n_right = n * n int k_new = k + n_left Py_ssize_t i, j, jh, l = 0 int sump, sumq = 0 double trial, output = 0 double[::1] a_sorted = np.sort(a) int[::1] left = np.array([n - i + 1 for i in range(0, n)], dtype=np.intc) int[::1] right = np.array([n if i <= h else n - (i - h) for i in range(0, n)], dtype=np.intc) int[::1] weights = np.zeros((n,), dtype=np.intc) double[::1] work = np.zeros((n,), dtype=np.double) int[::1] p = np.zeros((n,), dtype=np.intc) int[::1] q = np.zeros((n,), dtype=np.intc) while n_right - n_left > n: j = 0 for i in range(1, n): if left[i] <= right[i]: weights[j] = right[i] - left[i] + 1 jh = left[i] + weights[j] // 2 work[j] = a_sorted[i] - a_sorted[n - jh] j = j + 1 trial = _high_weighted_median(work[:j], weights[:j]) j = 0 for i in range(n - 1, -1, -1): while j < n and (a_sorted[i] - a_sorted[n - j - 1]) < trial: j = j + 1 p[i] = j j = n + 1 for i in range(n): while (a_sorted[i] - a_sorted[n - j + 1]) > trial: j = j - 1 q[i] = j sump = np.sum(p) sumq = np.sum(q) - n if k_new <= sump: right = np.copy(p) n_right = sump elif k_new > sumq: left = np.copy(q) n_left = sumq else: output = c * trial return output j = 0 for i in range(1, n): for l in range(left[i], right[i] + 1): work[j] = a_sorted[i] - a_sorted[n - l] j = j + 1 k_new = k_new - (n_left + 1) output = c * np.sort(work[:j])[k_new] return output statsmodels-0.12.2/statsmodels/robust/norms.py000066400000000000000000000472651400612667500215530ustar00rootroot00000000000000import numpy as np # TODO: add plots to weighting functions for online docs. class RobustNorm(object): """ The parent class for the norms used for robust regression. Lays out the methods expected of the robust norms to be used by statsmodels.RLM. See Also -------- statsmodels.rlm Notes ----- Currently only M-estimators are available. References ---------- PJ Huber. 'Robust Statistics' John Wiley and Sons, Inc., New York, 1981. DC Montgomery, EA Peck. 'Introduction to Linear Regression Analysis', John Wiley and Sons, Inc., New York, 2001. R Venables, B Ripley. 'Modern Applied Statistics in S' Springer, New York, 2002. """ def rho(self, z): """ The robust criterion estimator function. Abstract method: -2 loglike used in M-estimator """ raise NotImplementedError def psi(self, z): """ Derivative of rho. Sometimes referred to as the influence function. Abstract method: psi = rho' """ raise NotImplementedError def weights(self, z): """ Returns the value of psi(z) / z Abstract method: psi(z) / z """ raise NotImplementedError def psi_deriv(self, z): """ Derivative of psi. Used to obtain robust covariance matrix. See statsmodels.rlm for more information. Abstract method: psi_derive = psi' """ raise NotImplementedError def __call__(self, z): """ Returns the value of estimator rho applied to an input """ return self.rho(z) class LeastSquares(RobustNorm): """ Least squares rho for M-estimation and its derived functions. See Also -------- statsmodels.robust.norms.RobustNorm """ def rho(self, z): """ The least squares estimator rho function Parameters ---------- z : ndarray 1d array Returns ------- rho : ndarray rho(z) = (1/2.)*z**2 """ return z**2 * 0.5 def psi(self, z): """ The psi function for the least squares estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z """ return np.asarray(z) def weights(self, z): """ The least squares estimator weighting function for the IRLS algorithm. The psi function scaled by the input z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = np.ones(z.shape) """ z = np.asarray(z) return np.ones(z.shape, np.float64) def psi_deriv(self, z): """ The derivative of the least squares psi function. Returns ------- psi_deriv : ndarray ones(z.shape) Notes ----- Used to estimate the robust covariance matrix. """ return np.ones(z.shape, np.float64) class HuberT(RobustNorm): """ Huber's T for M estimation. Parameters ---------- t : float, optional The tuning constant for Huber's t function. The default value is 1.345. See Also -------- statsmodels.robust.norms.RobustNorm """ def __init__(self, t=1.345): self.t = t def _subset(self, z): """ Huber's T is defined piecewise over the range for z """ z = np.asarray(z) return np.less_equal(np.abs(z), self.t) def rho(self, z): r""" The robust criterion function for Huber's t. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = .5*z**2 for \|z\| <= t rho(z) = \|z\|*t - .5*t**2 for \|z\| > t """ z = np.asarray(z) test = self._subset(z) return (test * 0.5 * z**2 + (1 - test) * (np.abs(z) * self.t - 0.5 * self.t**2)) def psi(self, z): r""" The psi function for Huber's t estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z for \|z\| <= t psi(z) = sign(z)*t for \|z\| > t """ z = np.asarray(z) test = self._subset(z) return test * z + (1 - test) * self.t * np.sign(z) def weights(self, z): r""" Huber's t weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = 1 for \|z\| <= t weights(z) = t/\|z\| for \|z\| > t """ z = np.asarray(z) test = self._subset(z) absz = np.abs(z) absz[test] = 1.0 return test + (1 - test) * self.t / absz def psi_deriv(self, z): """ The derivative of Huber's t psi function Notes ----- Used to estimate the robust covariance matrix. """ return np.less_equal(np.abs(z), self.t) # TODO: untested, but looks right. RamsayE not available in R or SAS? class RamsayE(RobustNorm): """ Ramsay's Ea for M estimation. Parameters ---------- a : float, optional The tuning constant for Ramsay's Ea function. The default value is 0.3. See Also -------- statsmodels.robust.norms.RobustNorm """ def __init__(self, a=.3): self.a = a def rho(self, z): r""" The robust criterion function for Ramsay's Ea. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = a**-2 * (1 - exp(-a*\|z\|)*(1 + a*\|z\|)) """ z = np.asarray(z) return (1 - np.exp(-self.a * np.abs(z)) * (1 + self.a * np.abs(z))) / self.a**2 def psi(self, z): r""" The psi function for Ramsay's Ea estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z*exp(-a*\|z\|) """ z = np.asarray(z) return z * np.exp(-self.a * np.abs(z)) def weights(self, z): r""" Ramsay's Ea weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = exp(-a*\|z\|) """ z = np.asarray(z) return np.exp(-self.a * np.abs(z)) def psi_deriv(self, z): """ The derivative of Ramsay's Ea psi function. Notes ----- Used to estimate the robust covariance matrix. """ a = self.a x = np.exp(-a * np.abs(z)) dx = -a * x * np.sign(z) y = z dy = 1 return x * dy + y * dx class AndrewWave(RobustNorm): """ Andrew's wave for M estimation. Parameters ---------- a : float, optional The tuning constant for Andrew's Wave function. The default value is 1.339. See Also -------- statsmodels.robust.norms.RobustNorm """ def __init__(self, a=1.339): self.a = a def _subset(self, z): """ Andrew's wave is defined piecewise over the range of z. """ z = np.asarray(z) return np.less_equal(np.abs(z), self.a * np.pi) def rho(self, z): r""" The robust criterion function for Andrew's wave. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = a*(1-cos(z/a)) for \|z\| <= a*pi rho(z) = 2*a for \|z\| > a*pi """ a = self.a z = np.asarray(z) test = self._subset(z) return (test * a * (1 - np.cos(z / a)) + (1 - test) * 2 * a) def psi(self, z): r""" The psi function for Andrew's wave The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = sin(z/a) for \|z\| <= a*pi psi(z) = 0 for \|z\| > a*pi """ a = self.a z = np.asarray(z) test = self._subset(z) return test * np.sin(z / a) def weights(self, z): r""" Andrew's wave weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = sin(z/a)/(z/a) for \|z\| <= a*pi weights(z) = 0 for \|z\| > a*pi """ a = self.a z = np.asarray(z) test = self._subset(z) ratio = z / a small = np.abs(ratio) < np.finfo(np.double).eps if np.any(small): weights = np.ones_like(ratio) large = ~small ratio = ratio[large] weights[large] = test[large] * np.sin(ratio) / ratio else: weights = test * np.sin(ratio) / ratio return weights def psi_deriv(self, z): """ The derivative of Andrew's wave psi function Notes ----- Used to estimate the robust covariance matrix. """ test = self._subset(z) return test*np.cos(z / self.a)/self.a # TODO: this is untested class TrimmedMean(RobustNorm): """ Trimmed mean function for M-estimation. Parameters ---------- c : float, optional The tuning constant for Ramsay's Ea function. The default value is 2.0. See Also -------- statsmodels.robust.norms.RobustNorm """ def __init__(self, c=2.): self.c = c def _subset(self, z): """ Least trimmed mean is defined piecewise over the range of z. """ z = np.asarray(z) return np.less_equal(np.abs(z), self.c) def rho(self, z): r""" The robust criterion function for least trimmed mean. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = (1/2.)*z**2 for \|z\| <= c rho(z) = 0 for \|z\| > c """ z = np.asarray(z) test = self._subset(z) return test * z**2 * 0.5 def psi(self, z): r""" The psi function for least trimmed mean The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z for \|z\| <= c psi(z) = 0 for \|z\| > c """ z = np.asarray(z) test = self._subset(z) return test * z def weights(self, z): r""" Least trimmed mean weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = 1 for \|z\| <= c weights(z) = 0 for \|z\| > c """ z = np.asarray(z) test = self._subset(z) return test def psi_deriv(self, z): """ The derivative of least trimmed mean psi function Notes ----- Used to estimate the robust covariance matrix. """ test = self._subset(z) return test class Hampel(RobustNorm): """ Hampel function for M-estimation. Parameters ---------- a : float, optional b : float, optional c : float, optional The tuning constants for Hampel's function. The default values are a,b,c = 2, 4, 8. See Also -------- statsmodels.robust.norms.RobustNorm """ def __init__(self, a=2., b=4., c=8.): self.a = a self.b = b self.c = c def _subset(self, z): """ Hampel's function is defined piecewise over the range of z """ z = np.abs(np.asarray(z)) t1 = np.less_equal(z, self.a) t2 = np.less_equal(z, self.b) * np.greater(z, self.a) t3 = np.less_equal(z, self.c) * np.greater(z, self.b) return t1, t2, t3 def rho(self, z): r""" The robust criterion function for Hampel's estimator Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = (1/2.)*z**2 for \|z\| <= a rho(z) = a*\|z\| - 1/2.*a**2 for a < \|z\| <= b rho(z) = a*(c*\|z\|-(1/2.)*z**2)/(c-b) for b < \|z\| <= c rho(z) = a*(b + c - a) for \|z\| > c """ z = np.abs(z) a = self.a b = self.b c = self.c t1, t2, t3 = self._subset(z) v = (t1 * z**2 * 0.5 + t2 * (a * z - a**2 * 0.5) + t3 * (a * (c * z - z**2 * 0.5) / (c - b) - 7 * a**2 / 6.) + (1 - t1 + t2 + t3) * a * (b + c - a)) return v def psi(self, z): r""" The psi function for Hampel's estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z for \|z\| <= a psi(z) = a*sign(z) for a < \|z\| <= b psi(z) = a*sign(z)*(c - \|z\|)/(c-b) for b < \|z\| <= c psi(z) = 0 for \|z\| > c """ z = np.asarray(z) a = self.a b = self.b c = self.c t1, t2, t3 = self._subset(z) s = np.sign(z) z = np.abs(z) v = s * (t1 * z + t2 * a*s + t3 * a*s * (c - z) / (c - b)) return v def weights(self, z): r""" Hampel weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = 1 for \|z\| <= a weights(z) = a/\|z\| for a < \|z\| <= b weights(z) = a*(c - \|z\|)/(\|z\|*(c-b)) for b < \|z\| <= c weights(z) = 0 for \|z\| > c """ z = np.asarray(z) a = self.a b = self.b c = self.c t1, t2, t3 = self._subset(z) v = np.zeros_like(z) v[t1] = 1.0 abs_z = np.abs(z) v[t2] = a / abs_z[t2] abs_zt3 = abs_z[t3] v[t3] = a * (c - abs_zt3) / (abs_zt3 * (c - b)) v[np.where(np.isnan(v))] = 1. # TODO: for some reason 0 returns a nan? return v def psi_deriv(self, z): t1, t2, t3 = self._subset(z) a, b, c = self.a, self.b, self.c # default is t1 d = np.zeros_like(z) d[t1] = 1.0 zt3 = z[t3] d[t3] = (a * np.sign(zt3) * zt3) / (np.abs(zt3) * (c - b)) return d class TukeyBiweight(RobustNorm): """ Tukey's biweight function for M-estimation. Parameters ---------- c : float, optional The tuning constant for Tukey's Biweight. The default value is c = 4.685. Notes ----- Tukey's biweight is sometime's called bisquare. """ def __init__(self, c=4.685): self.c = c def _subset(self, z): """ Tukey's biweight is defined piecewise over the range of z """ z = np.abs(np.asarray(z)) return np.less_equal(z, self.c) def rho(self, z): r""" The robust criterion function for Tukey's biweight estimator Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = -(1 - (z/c)**2)**3 * c**2/6. for \|z\| <= R rho(z) = 0 for \|z\| > R """ subset = self._subset(z) return -(1 - (z / self.c)**2)**3 * subset * self.c**2 / 6. def psi(self, z): r""" The psi function for Tukey's biweight estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z*(1 - (z/c)**2)**2 for \|z\| <= R psi(z) = 0 for \|z\| > R """ z = np.asarray(z) subset = self._subset(z) return z * (1 - (z / self.c)**2)**2 * subset def weights(self, z): r""" Tukey's biweight weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray psi(z) = (1 - (z/c)**2)**2 for \|z\| <= R psi(z) = 0 for \|z\| > R """ subset = self._subset(z) return (1 - (z / self.c)**2)**2 * subset def psi_deriv(self, z): """ The derivative of Tukey's biweight psi function Notes ----- Used to estimate the robust covariance matrix. """ subset = self._subset(z) return subset * ((1 - (z/self.c)**2)**2 - (4*z**2/self.c**2) * (1-(z/self.c)**2)) def estimate_location(a, scale, norm=None, axis=0, initial=None, maxiter=30, tol=1.0e-06): """ M-estimator of location using self.norm and a current estimator of scale. This iteratively finds a solution to norm.psi((a-mu)/scale).sum() == 0 Parameters ---------- a : ndarray Array over which the location parameter is to be estimated scale : ndarray Scale parameter to be used in M-estimator norm : RobustNorm, optional Robust norm used in the M-estimator. The default is HuberT(). axis : int, optional Axis along which to estimate the location parameter. The default is 0. initial : ndarray, optional Initial condition for the location parameter. Default is None, which uses the median of a. niter : int, optional Maximum number of iterations. The default is 30. tol : float, optional Toleration for convergence. The default is 1e-06. Returns ------- mu : ndarray Estimate of location """ if norm is None: norm = HuberT() if initial is None: mu = np.median(a, axis) else: mu = initial for iter in range(maxiter): W = norm.weights((a-mu)/scale) nmu = np.sum(W*a, axis) / np.sum(W, axis) if np.alltrue(np.less(np.abs(mu - nmu), scale * tol)): return nmu else: mu = nmu raise ValueError("location estimator failed to converge in %d iterations" % maxiter) statsmodels-0.12.2/statsmodels/robust/robust_linear_model.py000066400000000000000000000535571400612667500244460ustar00rootroot00000000000000""" Robust linear models with support for the M-estimators listed under :ref:`norms `. References ---------- PJ Huber. 'Robust Statistics' John Wiley and Sons, Inc., New York. 1981. PJ Huber. 1973, 'The 1972 Wald Memorial Lectures: Robust Regression: Asymptotics, Conjectures, and Monte Carlo.' The Annals of Statistics, 1.5, 799-821. R Venables, B Ripley. 'Modern Applied Statistics in S' Springer, New York, 2002. """ import numpy as np import scipy.stats as stats from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.sm_exceptions import ConvergenceWarning import statsmodels.regression.linear_model as lm import statsmodels.regression._tools as reg_tools import statsmodels.robust.norms as norms import statsmodels.robust.scale as scale import statsmodels.base.model as base import statsmodels.base.wrapper as wrap __all__ = ['RLM'] def _check_convergence(criterion, iteration, tol, maxiter): cond = np.abs(criterion[iteration] - criterion[iteration - 1]) return not (np.any(cond > tol) and iteration < maxiter) class RLM(base.LikelihoodModel): __doc__ = """ Robust Linear Model Estimate a robust linear model via iteratively reweighted least squares given a robust criterion estimator. %(params)s M : statsmodels.robust.norms.RobustNorm, optional The robust criterion function for downweighting outliers. The current options are LeastSquares, HuberT, RamsayE, AndrewWave, TrimmedMean, Hampel, and TukeyBiweight. The default is HuberT(). See statsmodels.robust.norms for more information. %(extra_params)s Attributes ---------- df_model : float The degrees of freedom of the model. The number of regressors p less one for the intercept. Note that the reported model degrees of freedom does not count the intercept as a regressor, though the model is assumed to have an intercept. df_resid : float The residual degrees of freedom. The number of observations n less the number of regressors p. Note that here p does include the intercept as using a degree of freedom. endog : ndarray See above. Note that endog is a reference to the data so that if data is already an array and it is changed, then `endog` changes as well. exog : ndarray See above. Note that endog is a reference to the data so that if data is already an array and it is changed, then `endog` changes as well. M : statsmodels.robust.norms.RobustNorm See above. Robust estimator instance instantiated. nobs : float The number of observations n pinv_wexog : ndarray The pseudoinverse of the design / exogenous data array. Note that RLM has no whiten method, so this is just the pseudo inverse of the design. normalized_cov_params : ndarray The p x p normalized covariance of the design / exogenous data. This is approximately equal to (X.T X)^(-1) Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.stackloss.load(as_pandas=False) >>> data.exog = sm.add_constant(data.exog) >>> rlm_model = sm.RLM(data.endog, data.exog, \ M=sm.robust.norms.HuberT()) >>> rlm_results = rlm_model.fit() >>> rlm_results.params array([ 0.82938433, 0.92606597, -0.12784672, -41.02649835]) >>> rlm_results.bse array([ 0.11100521, 0.30293016, 0.12864961, 9.79189854]) >>> rlm_results_HC2 = rlm_model.fit(cov="H2") >>> rlm_results_HC2.params array([ 0.82938433, 0.92606597, -0.12784672, -41.02649835]) >>> rlm_results_HC2.bse array([ 0.11945975, 0.32235497, 0.11796313, 9.08950419]) >>> mod = sm.RLM(data.endog, data.exog, M=sm.robust.norms.Hampel()) >>> rlm_hamp_hub = mod.fit(scale_est=sm.robust.scale.HuberScale()) >>> rlm_hamp_hub.params array([ 0.73175452, 1.25082038, -0.14794399, -40.27122257]) """ % {'params': base._model_params_doc, 'extra_params': base._missing_param_doc} def __init__(self, endog, exog, M=None, missing='none', **kwargs): self.M = M if M is not None else norms.HuberT() super(base.LikelihoodModel, self).__init__(endog, exog, missing=missing, **kwargs) self._initialize() # things to remove_data self._data_attr.extend(['weights', 'pinv_wexog']) def _initialize(self): """ Initializes the model for the IRLS fit. Resets the history and number of iterations. """ self.pinv_wexog = np.linalg.pinv(self.exog) self.normalized_cov_params = np.dot(self.pinv_wexog, np.transpose(self.pinv_wexog)) self.df_resid = (float(self.exog.shape[0] - np.linalg.matrix_rank(self.exog))) self.df_model = float(np.linalg.matrix_rank(self.exog) - 1) self.nobs = float(self.endog.shape[0]) def score(self, params): raise NotImplementedError def information(self, params): raise NotImplementedError def predict(self, params, exog=None): """ Return linear predicted values from a design matrix. Parameters ---------- params : array_like Parameters of a linear model exog : array_like, optional. Design / exogenous data. Model exog is used if None. Returns ------- An array of fitted values """ # copied from linear_model # TODO: then is it needed? if exog is None: exog = self.exog return np.dot(exog, params) def loglike(self, params): raise NotImplementedError def deviance(self, tmp_results): """ Returns the (unnormalized) log-likelihood from the M estimator. """ tmp_resid = self.endog - tmp_results.fittedvalues return self.M(tmp_resid / tmp_results.scale).sum() def _update_history(self, tmp_results, history, conv): history['params'].append(tmp_results.params) history['scale'].append(tmp_results.scale) if conv == 'dev': history['deviance'].append(self.deviance(tmp_results)) elif conv == 'sresid': history['sresid'].append(tmp_results.resid / tmp_results.scale) elif conv == 'weights': history['weights'].append(tmp_results.model.weights) return history def _estimate_scale(self, resid): """ Estimates the scale based on the option provided to the fit method. """ if isinstance(self.scale_est, str): if self.scale_est.lower() == 'mad': return scale.mad(resid, center=0) else: raise ValueError("Option %s for scale_est not understood" % self.scale_est) elif isinstance(self.scale_est, scale.HuberScale): return self.scale_est(self.df_resid, self.nobs, resid) else: return scale.scale_est(self, resid) ** 2 def fit(self, maxiter=50, tol=1e-8, scale_est='mad', init=None, cov='H1', update_scale=True, conv='dev', start_params=None): """ Fits the model using iteratively reweighted least squares. The IRLS routine runs until the specified objective converges to `tol` or `maxiter` has been reached. Parameters ---------- conv : str Indicates the convergence criteria. Available options are "coefs" (the coefficients), "weights" (the weights in the iteration), "sresid" (the standardized residuals), and "dev" (the un-normalized log-likelihood for the M estimator). The default is "dev". cov : str, optional 'H1', 'H2', or 'H3' Indicates how the covariance matrix is estimated. Default is 'H1'. See rlm.RLMResults for more information. init : str Specifies method for the initial estimates of the parameters. Default is None, which means that the least squares estimate is used. Currently it is the only available choice. maxiter : int The maximum number of iterations to try. Default is 50. scale_est : str or HuberScale() 'mad' or HuberScale() Indicates the estimate to use for scaling the weights in the IRLS. The default is 'mad' (median absolute deviation. Other options are 'HuberScale' for Huber's proposal 2. Huber's proposal 2 has optional keyword arguments d, tol, and maxiter for specifying the tuning constant, the convergence tolerance, and the maximum number of iterations. See statsmodels.robust.scale for more information. tol : float The convergence tolerance of the estimate. Default is 1e-8. update_scale : Bool If `update_scale` is False then the scale estimate for the weights is held constant over the iteration. Otherwise, it is updated for each fit in the iteration. Default is True. start_params : array_like, optional Initial guess of the solution of the optimizer. If not provided, the initial parameters are computed using OLS. Returns ------- results : statsmodels.rlm.RLMresults Results instance """ if cov.upper() not in ["H1", "H2", "H3"]: raise ValueError("Covariance matrix %s not understood" % cov) else: self.cov = cov.upper() conv = conv.lower() if conv not in ["weights", "coefs", "dev", "sresid"]: raise ValueError("Convergence argument %s not understood" % conv) self.scale_est = scale_est if start_params is None: wls_results = lm.WLS(self.endog, self.exog).fit() else: start_params = np.asarray(start_params, dtype=np.double).squeeze() if (start_params.shape[0] != self.exog.shape[1] or start_params.ndim != 1): raise ValueError('start_params must by a 1-d array with {0} ' 'values'.format(self.exog.shape[1])) fake_wls = reg_tools._MinimalWLS(self.endog, self.exog, weights=np.ones_like(self.endog), check_weights=False) wls_results = fake_wls.results(start_params) if not init: self.scale = self._estimate_scale(wls_results.resid) history = dict(params=[np.inf], scale=[]) if conv == 'coefs': criterion = history['params'] elif conv == 'dev': history.update(dict(deviance=[np.inf])) criterion = history['deviance'] elif conv == 'sresid': history.update(dict(sresid=[np.inf])) criterion = history['sresid'] elif conv == 'weights': history.update(dict(weights=[np.inf])) criterion = history['weights'] # done one iteration so update history = self._update_history(wls_results, history, conv) iteration = 1 converged = 0 while not converged: if self.scale == 0.0: import warnings warnings.warn('Estimated scale is 0.0 indicating that the most' ' last iteration produced a perfect fit of the ' 'weighted data.', ConvergenceWarning) break self.weights = self.M.weights(wls_results.resid / self.scale) wls_results = reg_tools._MinimalWLS(self.endog, self.exog, weights=self.weights, check_weights=True).fit() if update_scale is True: self.scale = self._estimate_scale(wls_results.resid) history = self._update_history(wls_results, history, conv) iteration += 1 converged = _check_convergence(criterion, iteration, tol, maxiter) results = RLMResults(self, wls_results.params, self.normalized_cov_params, self.scale) history['iteration'] = iteration results.fit_history = history results.fit_options = dict(cov=cov.upper(), scale_est=scale_est, norm=self.M.__class__.__name__, conv=conv) # norm is not changed in fit, no old state # doing the next causes exception # self.cov = self.scale_est = None #reset for additional fits # iteration and history could contain wrong state with repeated fit return RLMResultsWrapper(results) class RLMResults(base.LikelihoodModelResults): """ Class to contain RLM results Attributes ---------- bcov_scaled : ndarray p x p scaled covariance matrix specified in the model fit method. The default is H1. H1 is defined as ``k**2 * (1/df_resid*sum(M.psi(sresid)**2)*scale**2)/ ((1/nobs*sum(M.psi_deriv(sresid)))**2) * (X.T X)^(-1)`` where ``k = 1 + (df_model +1)/nobs * var_psiprime/m**2`` where ``m = mean(M.psi_deriv(sresid))`` and ``var_psiprime = var(M.psi_deriv(sresid))`` H2 is defined as ``k * (1/df_resid) * sum(M.psi(sresid)**2) *scale**2/ ((1/nobs)*sum(M.psi_deriv(sresid)))*W_inv`` H3 is defined as ``1/k * (1/df_resid * sum(M.psi(sresid)**2)*scale**2 * (W_inv X.T X W_inv))`` where `k` is defined as above and ``W_inv = (M.psi_deriv(sresid) exog.T exog)^(-1)`` See the technical documentation for cleaner formulae. bcov_unscaled : ndarray The usual p x p covariance matrix with scale set equal to 1. It is then just equivalent to normalized_cov_params. bse : ndarray An array of the standard errors of the parameters. The standard errors are taken from the robust covariance matrix specified in the argument to fit. chisq : ndarray An array of the chi-squared values of the parameter estimates. df_model See RLM.df_model df_resid See RLM.df_resid fit_history : dict Contains information about the iterations. Its keys are `deviance`, `params`, `iteration` and the convergence criteria specified in `RLM.fit`, if different from `deviance` or `params`. fit_options : dict Contains the options given to fit. fittedvalues : ndarray The linear predicted values. dot(exog, params) model : statsmodels.rlm.RLM A reference to the model instance nobs : float The number of observations n normalized_cov_params : ndarray See RLM.normalized_cov_params params : ndarray The coefficients of the fitted model pinv_wexog : ndarray See RLM.pinv_wexog pvalues : ndarray The p values associated with `tvalues`. Note that `tvalues` are assumed to be distributed standard normal rather than Student's t. resid : ndarray The residuals of the fitted model. endog - fittedvalues scale : float The type of scale is determined in the arguments to the fit method in RLM. The reported scale is taken from the residuals of the weighted least squares in the last IRLS iteration if update_scale is True. If update_scale is False, then it is the scale given by the first OLS fit before the IRLS iterations. sresid : ndarray The scaled residuals. tvalues : ndarray The "t-statistics" of params. These are defined as params/bse where bse are taken from the robust covariance matrix specified in the argument to fit. weights : ndarray The reported weights are determined by passing the scaled residuals from the last weighted least squares fit in the IRLS algorithm. See Also -------- statsmodels.base.model.LikelihoodModelResults """ def __init__(self, model, params, normalized_cov_params, scale): super(RLMResults, self).__init__(model, params, normalized_cov_params, scale) self.model = model self.df_model = model.df_model self.df_resid = model.df_resid self.nobs = model.nobs self._cache = {} # for remove_data self._data_in_cache.extend(['sresid']) self.cov_params_default = self.bcov_scaled # TODO: "pvals" should come from chisq on bse? @cache_readonly def fittedvalues(self): return np.dot(self.model.exog, self.params) @cache_readonly def resid(self): return self.model.endog - self.fittedvalues # before bcov @cache_readonly def sresid(self): if self.scale == 0.0: sresid = self.resid.copy() sresid[:] = 0.0 return sresid return self.resid / self.scale @cache_readonly def bcov_unscaled(self): return self.normalized_cov_params @cache_readonly def weights(self): return self.model.weights @cache_readonly def bcov_scaled(self): model = self.model m = np.mean(model.M.psi_deriv(self.sresid)) var_psiprime = np.var(model.M.psi_deriv(self.sresid)) k = 1 + (self.df_model + 1) / self.nobs * var_psiprime / m ** 2 if model.cov == "H1": ss_psi = np.sum(model.M.psi(self.sresid) ** 2) s_psi_deriv = np.sum(model.M.psi_deriv(self.sresid)) return k ** 2 * (1 / self.df_resid * ss_psi * self.scale ** 2) /\ ((1 / self.nobs * s_psi_deriv) ** 2) *\ model.normalized_cov_params else: W = np.dot(model.M.psi_deriv(self.sresid) * model.exog.T, model.exog) W_inv = np.linalg.inv(W) # [W_jk]^-1 = [SUM(psi_deriv(Sr_i)*x_ij*x_jk)]^-1 # where Sr are the standardized residuals if model.cov == "H2": # These are correct, based on Huber (1973) 8.13 return k * (1 / self.df_resid) * np.sum( model.M.psi(self.sresid) ** 2) * self.scale ** 2 \ / ((1 / self.nobs) * np.sum(model.M.psi_deriv(self.sresid))) * W_inv elif model.cov == "H3": return k ** -1 * 1 / self.df_resid * np.sum( model.M.psi(self.sresid) ** 2) * self.scale ** 2 \ * np.dot( np.dot(W_inv, np.dot(model.exog.T, model.exog)), W_inv) @cache_readonly def pvalues(self): return stats.norm.sf(np.abs(self.tvalues)) * 2 @cache_readonly def bse(self): return np.sqrt(np.diag(self.bcov_scaled)) @cache_readonly def chisq(self): return (self.params / self.bse) ** 2 def summary(self, yname=None, xname=None, title=0, alpha=.05, return_fmt='text'): """ This is for testing the new summary setup """ top_left = [('Dep. Variable:', None), ('Model:', None), ('Method:', ['IRLS']), ('Norm:', [self.fit_options['norm']]), ('Scale Est.:', [self.fit_options['scale_est']]), ('Cov Type:', [self.fit_options['cov']]), ('Date:', None), ('Time:', None), ('No. Iterations:', ["%d" % self.fit_history['iteration']]) ] top_right = [('No. Observations:', None), ('Df Residuals:', None), ('Df Model:', None) ] if title is not None: title = "Robust linear Model Regression Results" # boiler plate from statsmodels.iolib.summary import Summary smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, yname=yname, xname=xname, title=title) smry.add_table_params(self, yname=yname, xname=xname, alpha=alpha, use_t=self.use_t) # add warnings/notes, added to text format only etext = [] wstr = ("If the model instance has been used for another fit with " "different fit parameters, then the fit options might not be " "the correct ones anymore .") etext.append(wstr) if etext: smry.add_extra_txt(etext) return smry def summary2(self, xname=None, yname=None, title=None, alpha=.05, float_format="%.4f"): """Experimental summary function for regression results Parameters ---------- yname : str Name of the dependent variable (optional) xname : list[str], optional Names for the exogenous variables. Default is `var_##` for ## in the number of regressors. Must match the number of parameters in the model title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals float_format : str print format for floats in parameters summary Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary2.Summary : class to hold summary results """ from statsmodels.iolib import summary2 smry = summary2.Summary() smry.add_base(results=self, alpha=alpha, float_format=float_format, xname=xname, yname=yname, title=title) return smry class RLMResultsWrapper(lm.RegressionResultsWrapper): pass wrap.populate_wrapper(RLMResultsWrapper, RLMResults) # noqa:E305 statsmodels-0.12.2/statsmodels/robust/scale.py000066400000000000000000000304751400612667500214770ustar00rootroot00000000000000""" Support and standalone functions for Robust Linear Models References ---------- PJ Huber. 'Robust Statistics' John Wiley and Sons, Inc., New York, 1981. R Venables, B Ripley. 'Modern Applied Statistics in S' Springer, New York, 2002. C Croux, PJ Rousseeuw, 'Time-efficient algorithms for two highly robust estimators of scale' Computational statistics. Physica, Heidelberg, 1992. """ from statsmodels.compat.pandas import Appender import numpy as np from scipy.stats import norm as Gaussian from statsmodels.tools import tools from statsmodels.tools.validation import array_like, float_like from . import norms from ._qn import _qn def mad(a, c=Gaussian.ppf(3 / 4.0), axis=0, center=np.median): """ The Median Absolute Deviation along given axis of an array Parameters ---------- a : array_like Input array. c : float, optional The normalization constant. Defined as scipy.stats.norm.ppf(3/4.), which is approximately 0.6745. axis : int, optional The default is 0. Can also be None. center : callable or float If a callable is provided, such as the default `np.median` then it is expected to be called center(a). The axis argument will be applied via np.apply_over_axes. Otherwise, provide a float. Returns ------- mad : float `mad` = median(abs(`a` - center))/`c` """ a = array_like(a, "a", ndim=None) c = float_like(c, "c") if not a.size: center_val = 0.0 elif callable(center): if axis is not None: center_val = np.apply_over_axes(center, a, axis) else: center_val = center(a.ravel()) else: center_val = float_like(center, "center") return np.median((np.abs(a - center_val)) / c, axis=axis) def iqr(a, c=Gaussian.ppf(3 / 4) - Gaussian.ppf(1 / 4), axis=0): """ The normalized interquartile range along given axis of an array Parameters ---------- a : array_like Input array. c : float, optional The normalization constant, used to get consistent estimates of the standard deviation at the normal distribution. Defined as scipy.stats.norm.ppf(3/4.) - scipy.stats.norm.ppf(1/4.), which is approximately 1.349. axis : int, optional The default is 0. Can also be None. Returns ------- The normalized interquartile range """ a = array_like(a, "a", ndim=None) c = float_like(c, "c") if a.ndim == 0: raise ValueError("a should have at least one dimension") elif a.size == 0: return np.nan else: quantiles = np.quantile(a, [0.25, 0.75], axis=axis) return np.squeeze(np.diff(quantiles, axis=0) / c) def qn_scale(a, c=1 / (np.sqrt(2) * Gaussian.ppf(5 / 8)), axis=0): """ Computes the Qn robust estimator of scale The Qn scale estimator is a more efficient alternative to the MAD. The Qn scale estimator of an array a of length n is defined as c * {abs(a[i] - a[j]): i>> import numpy as np >>> import statsmodels.api as sm >>> chem_data = np.array([2.20, 2.20, 2.4, 2.4, 2.5, 2.7, 2.8, 2.9, 3.03, ... 3.03, 3.10, 3.37, 3.4, 3.4, 3.4, 3.5, 3.6, 3.7, 3.7, 3.7, 3.7, ... 3.77, 5.28, 28.95]) >>> sm.robust.scale.huber(chem_data) (array(3.2054980819923693), array(0.67365260010478967)) """ def __init__(self, c=1.5, tol=1.0e-08, maxiter=30, norm=None): self.c = c self.maxiter = maxiter self.tol = tol self.norm = norm tmp = 2 * Gaussian.cdf(c) - 1 self.gamma = tmp + c ** 2 * (1 - tmp) - 2 * c * Gaussian.pdf(c) def __call__(self, a, mu=None, initscale=None, axis=0): """ Compute Huber's proposal 2 estimate of scale, using an optional initial value of scale and an optional estimate of mu. If mu is supplied, it is not reestimated. Parameters ---------- a : ndarray 1d array mu : float or None, optional If the location mu is supplied then it is not reestimated. Default is None, which means that it is estimated. initscale : float or None, optional A first guess on scale. If initscale is None then the standardized median absolute deviation of a is used. Notes ----- `Huber` minimizes the function sum(psi((a[i]-mu)/scale)**2) as a function of (mu, scale), where psi(x) = np.clip(x, -self.c, self.c) """ a = np.asarray(a) if mu is None: n = a.shape[0] - 1 mu = np.median(a, axis=axis) est_mu = True else: n = a.shape[0] mu = mu est_mu = False if initscale is None: scale = mad(a, axis=axis) else: scale = initscale scale = tools.unsqueeze(scale, axis, a.shape) mu = tools.unsqueeze(mu, axis, a.shape) return self._estimate_both(a, scale, mu, axis, est_mu, n) def _estimate_both(self, a, scale, mu, axis, est_mu, n): """ Estimate scale and location simultaneously with the following pseudo_loop: while not_converged: mu, scale = estimate_location(a, scale, mu), estimate_scale(a, scale, mu) where estimate_location is an M-estimator and estimate_scale implements the check used in Section 5.5 of Venables & Ripley """ # noqa:E501 for _ in range(self.maxiter): # Estimate the mean along a given axis if est_mu: if self.norm is None: # This is a one-step fixed-point estimator # if self.norm == norms.HuberT # It should be faster than using norms.HuberT nmu = ( np.clip( a, mu - self.c * scale, mu + self.c * scale ).sum(axis) / a.shape[axis] ) else: nmu = norms.estimate_location( a, scale, self.norm, axis, mu, self.maxiter, self.tol ) else: # Effectively, do nothing nmu = mu.squeeze() nmu = tools.unsqueeze(nmu, axis, a.shape) subset = np.less_equal(np.abs((a - mu) / scale), self.c) card = subset.sum(axis) scale_num = np.sum(subset * (a - nmu) ** 2, axis) scale_denom = n * self.gamma - (a.shape[axis] - card) * self.c ** 2 nscale = np.sqrt(scale_num / scale_denom) nscale = tools.unsqueeze(nscale, axis, a.shape) test1 = np.alltrue( np.less_equal(np.abs(scale - nscale), nscale * self.tol) ) test2 = np.alltrue( np.less_equal(np.abs(mu - nmu), nscale * self.tol) ) if not (test1 and test2): mu = nmu scale = nscale else: return nmu.squeeze(), nscale.squeeze() raise ValueError( "joint estimation of location and scale failed " "to converge in %d iterations" % self.maxiter ) huber = Huber() class HuberScale(object): r""" Huber's scaling for fitting robust linear models. Huber's scale is intended to be used as the scale estimate in the IRLS algorithm and is slightly different than the `Huber` class. Parameters ---------- d : float, optional d is the tuning constant for Huber's scale. Default is 2.5 tol : float, optional The convergence tolerance maxiter : int, optiona The maximum number of iterations. The default is 30. Methods ------- call Return's Huber's scale computed as below Notes -------- Huber's scale is the iterative solution to scale_(i+1)**2 = 1/(n*h)*sum(chi(r/sigma_i)*sigma_i**2 where the Huber function is chi(x) = (x**2)/2 for \|x\| < d chi(x) = (d**2)/2 for \|x\| >= d and the Huber constant h = (n-p)/n*(d**2 + (1-d**2)*\ scipy.stats.norm.cdf(d) - .5 - d*sqrt(2*pi)*exp(-0.5*d**2) """ def __init__(self, d=2.5, tol=1e-08, maxiter=30): self.d = d self.tol = tol self.maxiter = maxiter def __call__(self, df_resid, nobs, resid): h = ( df_resid / nobs * ( self.d ** 2 + (1 - self.d ** 2) * Gaussian.cdf(self.d) - 0.5 - self.d / (np.sqrt(2 * np.pi)) * np.exp(-0.5 * self.d ** 2) ) ) s = mad(resid) def subset(x): return np.less(np.abs(resid / x), self.d) def chi(s): return subset(s) * (resid / s) ** 2 / 2 + (1 - subset(s)) * ( self.d ** 2 / 2 ) scalehist = [np.inf, s] niter = 1 while ( np.abs(scalehist[niter - 1] - scalehist[niter]) > self.tol and niter < self.maxiter ): nscale = np.sqrt( 1 / (nobs * h) * np.sum(chi(scalehist[-1])) * scalehist[-1] ** 2 ) scalehist.append(nscale) niter += 1 # TODO: raise on convergence failure? return scalehist[-1] hubers_scale = HuberScale() statsmodels-0.12.2/statsmodels/robust/tests/000077500000000000000000000000001400612667500211675ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/robust/tests/__init__.py000066400000000000000000000000001400612667500232660ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/robust/tests/results/000077500000000000000000000000001400612667500226705ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/robust/tests/results/__init__.py000066400000000000000000000000001400612667500247670ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/robust/tests/results/results_rlm.py000066400000000000000000000455241400612667500256270ustar00rootroot00000000000000# RLM MODEL RESULTS import numpy as np def _shift_intercept(arr): """ A convenience function to make the SAS covariance matrix compatible with statsmodels.rlm covariance """ arr = np.asarray(arr) side = int(np.sqrt(len(arr))) return np.roll(np.roll(arr.reshape(side, side), -1, axis=1), -1, axis=0) class Huber(object): """ """ def __init__(self): self.params = np.array([0.82937387, 0.92610818, -0.12784916, -41.02653105]) self.bse = np.array([0.11118035, 0.3034081, 0.12885259, 9.8073472]) self.scale = 2.4407137948148447 self.weights = np.array([ 1., 1., 0.7858871, 0.50494094, 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0.36814106]) self.resid = np.array([ 3.05027584, -2.07757332, 4.17721071, 6.50163171, -1.64615192, -2.57226011, -1.73127333, -0.73127333, -2.25476463, 0.48083217, 1.63147461, 1.42973363, -2.26346951, -0.78323693, 2.26646556, 0.88291808, -0.83307835, 0.06186577, 0.26360675, 1.54306186, -8.91752986]) self.df_model = 3 self.df_resid = 17 self.bcov_unscaled = np.array([ [1.72887367e-03, -3.47079127e-03, -6.79080082e-04, 2.73387119e-02], [-3.47079127e-03, 1.28754242e-02, 9.95952051e-07, -6.19611175e-02], [-6.79080082e-04, 9.95952051e-07, 2.32216722e-03, -1.59355028e-01], [2.73387119e-02, -6.19611175e-02, -1.59355028e-01, 1.34527267e+01]]) # From R self.fittedvalues = np.array([ 38.94972416, 39.07757332, 32.82278929, 21.49836829, 19.64615192, 20.57226011, 20.73127333, 20.73127333, 17.25476463, 13.51916783, 12.36852539, 11.57026637, 13.26346951, 12.78323693, 5.73353444, 6.11708192, 8.83307835, 7.93813423, 8.73639325, 13.45693814, 23.91752986]) self.tvalues = np.array([7.45971657, 3.0523516, -0.99221261, -4.18324448]) # from R this is equivalent to # self.res1.params/np.sqrt(np.diag(self.res1.bcov_scaled)) # The below are taken from SAS huber_h1 = [ 95.8813, 0.19485, -0.44161, -1.13577, 0.1949, 0.01232, -0.02474, -0.00484, -0.4416, -0.02474, 0.09177, 0.00001, -1.1358, -0.00484, 0.00001, 0.01655] h1 = _shift_intercept(huber_h1) huber_h2 = [ 82.6191, 0.07942, -0.23915, -0.95604, 0.0794, 0.01427, -0.03013, -0.00344, -0.2392, -0.03013, 0.10391, -0.00166, -0.9560, -0.00344, -0.00166, 0.01392] h2 = _shift_intercept(huber_h2) huber_h3 = [ 70.1633, -0.04533, -0.00790, -0.78618, -0.0453, 0.01656, -0.03608, -0.00203, -0.0079, -0.03608, 0.11610, -0.00333, -0.7862, -0.00203, -0.00333, 0.01138] h3 = _shift_intercept(huber_h3) class Hampel(object): """ """ def __init__(self): self.params = np.array([0.74108304, 1.22507934, -0.14552506, -40.47473236]) self.bse = np.array([0.13482596, 0.36793632, 0.1562567, 11.89315426]) self.scale = 3.0882646556217064 self.weights = np.array([ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0.80629719]) self.resid = np.array([ 3.06267708, -2.08284798, 4.36377602, 5.78635972, -1.7634816, -2.98856094, -2.34048993, -1.34048993, -3.02422878, 1.08249252, 2.39221804, 2.47177232, -1.62645737, -0.25076107, 2.32088237, 0.88430719, -1.37812296, -0.35944755, -0.43900184, 1.40555003, -7.65988702]) self.df_model = 3 self.df_resid = 17 self.bcov_unscaled = np.array([ [1.72887367e-03, -3.47079127e-03, -6.79080082e-04, 2.73387119e-02], [-3.47079127e-03, 1.28754242e-02, 9.95952051e-07, -6.19611175e-02], [-6.79080082e-04, 9.95952051e-07, 2.32216722e-03, -1.59355028e-01], [2.73387119e-02, -6.19611175e-02, -1.59355028e-01, 1.34527267e+01]]) self.fittedvalues = np.array([ 38.93732292, 39.08284798, 32.63622398, 22.21364028, 19.7634816, 20.98856094, 21.34048993, 21.34048993, 18.02422878, 12.91750748, 11.60778196, 10.52822768, 12.62645737, 12.25076107, 5.67911763, 6.11569281, 9.37812296, 8.35944755, 9.43900184, 13.59444997, 22.65988702]) self.tvalues = np.array([5.49659011, 3.32959607, -0.93132046, -3.40319578]) hampel_h1 = [ 141.309, 0.28717, -0.65085, -1.67388, 0.287, 0.01816, -0.03646, -0.00713, -0.651, -0.03646, 0.13524, 0.00001, -1.674, -0.00713, 0.00001, 0.02439] h1 = _shift_intercept(hampel_h1) hampel_h2 = [ 135.248, 0.18207, -0.36884, -1.60217, 0.182, 0.02120, -0.04563, -0.00567, -0.369, -0.04563, 0.15860, -0.00290, -1.602, -0.00567, -0.00290, 0.02329] h2 = _shift_intercept(hampel_h2) hampel_h3 = [ 128.921, 0.05409, -0.02445, -1.52732, 0.054, 0.02514, -0.05732, -0.00392, -0.024, -0.05732, 0.18871, -0.00652, -1.527, -0.00392, -0.00652, 0.02212] h3 = _shift_intercept(hampel_h3) class BiSquare(object): def __init__(self): self.params = np.array([0.9275471, 0.65073222, -0.11233103, -42.28525369]) self.bse = np.array([0.10805398, 0.29487634, 0.12522928, 9.5315672]) self.scale = 2.2818858795649497 self.weights = np.array([ 0.89283149, 0.88496132, 0.79040651, 0.3358111, 0.94617358, 0.90040725, 0.96630596, 0.99729171, 0.94968061, 0.99900087, 0.98959903, 0.99831448, 0.84731833, 0.96455873, 0.91767906, 0.98724523, 0.99762848, 0.99694419, 0.98650731, 0.95897484, 0.00222999]) self.resid = np.array([ 2.50917802, -2.60315301, 3.56070896, 6.93256033, -1.76597524, -2.41670746, -1.39345348, -.39345348, -1.70651907, -0.23917521, 0.77180408, 0.31020526, -3.01451315, -1.42960401, 2.19218084, 0.85518774, -0.36817892, 0.4181383, 0.87973712, 1.53911661, -10.43556344]) self.df_model = 3 self.df_resid = 17 self.bcov_unscaled = np.array([ [1.72887367e-03, -3.47079127e-03, -6.79080082e-04, 2.73387119e-02], [-3.47079127e-03, 1.28754242e-02, 9.95952051e-07, -6.19611175e-02], [-6.79080082e-04, 9.95952051e-07, 2.32216722e-03, -1.59355028e-01], [2.73387119e-02, -6.19611175e-02, -1.59355028e-01, 1.34527267e+01]]) self.fittedvalues = np.array([ 39.49082198, 39.60315301, 33.43929104, 21.06743967, 19.76597524, 20.41670746, 20.39345348, 20.39345348, 16.70651907, 14.23917521, 13.22819592, 12.68979474, 14.01451315, 13.42960401, 5.80781916, 6.14481226, 8.36817892, 7.5818617, 8.12026288, 13.46088339, 25.43556344]) self.tvalues = np.array([8.58410823, 2.20679698, -0.8970029, -4.43633799]) bisquare_h1 = [ 90.3354, 0.18358, -0.41607, -1.07007, 0.1836, 0.01161, -0.02331, -0.00456, -0.4161, -0.02331, 0.08646, 0.00001, -1.0701, -0.00456, 0.00001, 0.01559] h1 = _shift_intercept(bisquare_h1) bisquare_h2 = [ 67.82521, 0.091288, -0.29038, -0.78124, 0.091288, 0.013849, -0.02914, -0.00352, -0.29038, -0.02914, 0.101088, -0.001, -0.78124, -0.00352, -0.001, 0.011766] h2 = _shift_intercept(bisquare_h2) bisquare_h3 = [ 48.8983, 0.000442, -0.15919, -0.53523, 0.000442, 0.016113, -0.03461, -0.00259, -0.15919, -0.03461, 0.112728, -0.00164, -0.53523, -0.00259, -0.00164, 0.008414] h3 = _shift_intercept(bisquare_h3) class Andrews(object): def __init__(self): self.params = [0.9282, 0.6492, -.1123, -42.2930] self.bse = [.1061, .2894, .1229, 9.3561] self.scale = 2.2801 self.df_model = 3. self.df_resid = 17. # bcov_unscaled not defined because it is not given as part of SAS self.resid = [ 2.503338458, -2.608934536, 3.5548678338, 6.9333705014, -1.768179527, -2.417404513, -1.392991531, -0.392991531, -1.704759385, -0.244545418, 0.7659115325, 0.3028635237, -3.019999429, -1.434221475, 2.1912017882, 0.8543828047, -0.366664104, 0.4192468573, 0.8822948661, 1.5378731634, -10.44592783] self.sresids = [ 1.0979293816, -1.144242351, 1.5591155202, 3.040879735, -0.775498914, -1.06023995, -0.610946684, -0.172360612, -0.747683723, -0.107254214, 0.3359181307, 0.1328317233, -1.324529688, -0.629029563, 0.9610305856, 0.3747203984, -0.160813769, 0.1838758324, 0.3869622398, 0.6744897502, -4.581438458] self.weights = [ 0.8916509101, 0.8826581922, 0.7888664106, 0.3367252734, 0.9450252405, 0.8987321912, 0.9656622, 0.9972406688, 0.948837669, 0.9989310017, 0.9895434667, 0.998360628, 0.8447116551, 0.9636222149, 0.916330067, 0.9869982597, 0.9975977354, 0.9968600162, 0.9861384742, 0.9582432444, 0] def conf_int(self): # method to be consistent with sm return [(0.7203, 1.1360), (.0819, 1.2165), (-.3532, .1287), (-60.6305, -23.9555)] andrews_h1 = [ 87.5357, 0.177891, -0.40318, -1.03691, 0.177891, 0.01125, -0.02258, -0.00442, -0.40318, -0.02258, 0.083779, 6.481E-6, -1.03691, -0.00442, 6.481E-6, 0.01511] h1 = _shift_intercept(andrews_h1) andrews_h2 = [ 66.50472, 0.10489, -0.3246, -0.76664, 0.10489, 0.012786, -0.02651, -0.0036, -0.3246, -0.02651, 0.09406, -0.00065, -0.76664, -0.0036, -0.00065, 0.011567] h2 = _shift_intercept(andrews_h2) andrews_h3 = [ 48.62157, 0.034949, -0.24633, -0.53394, 0.034949, 0.014088, -0.02956, -0.00287, -0.24633, -0.02956, 0.100628, -0.00104, -0.53394, -0.00287, -0.00104, 0.008441] h3 = _shift_intercept(andrews_h3) # RLM Results with Huber's Proposal 2 # Obtained from SAS class HuberHuber(object): def __init__(self): self.h1 = [ 114.4936, 0.232675, -0.52734, -1.35624, 0.232675, 0.014714, -0.02954, -0.00578, -0.52734, -0.02954, 0.10958, 8.476E-6, -1.35624, -0.00578, 8.476E-6, 0.019764] self.h1 = _shift_intercept(self.h1) self.h2 = [ 103.2876, 0.152602, -0.33476, -1.22084, 0.152602, 0.016904, -0.03766, -0.00434, -0.33476, -0.03766, 0.132043, -0.00214, -1.22084, -0.00434, -0.00214, 0.017739] self.h2 = _shift_intercept(self.h2) self.h3 = [ 91.7544, 0.064027, -0.11379, -1.08249, 0.064027, 0.019509, -0.04702, -0.00278, -0.11379, -0.04702, 0.157872, -0.00462, -1.08249, -0.00278, -0.00462, 0.015677] self.h3 = _shift_intercept(self.h3) self.resid = [ 2.909155172, -2.225912162, 4.134132661, 6.163172632, -1.741815737, -2.789321552, -2.02642336, -1.02642336, -2.593402734, 0.698655, 1.914261011, 1.826699492, -2.031210331, -0.592975466, 2.306098648, 0.900896645, -1.037551854, -0.092080512, -0.004518993, 1.471737448, -8.498372406] self.sresids = [ 0.883018497, -0.675633129, 1.25483702, 1.870713355, -0.528694904, -0.84664529, -0.615082113, -0.311551209, -0.787177874, 0.212063383, 0.581037374, 0.554459746, -0.616535106, -0.179986379, 0.699972205, 0.273449972, -0.314929051, -0.027949281, -0.001371654, 0.446717797, -2.579518651] self.weights = [ 1, 1, 1, 0.718977066, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.52141511] self.params = (.7990, 1.0475, -0.1351, -41.0892) self.bse = (.1213, .3310, .1406, 10.7002) self.scale = 3.2946 self.df_model = 3 self.df_resid = 17 def conf_int(self): # method for consistency with sm return [(0.5612, 1.0367), (.3987, 1.6963), (-.4106, .1405), (-62.0611, -20.1172)] class HampelHuber(object): def __init__(self): self.h1 = [ 147.4727, 0.299695, -0.67924, -1.7469, 0.299695, 0.018952, -0.03805, -0.00744, -0.67924, -0.03805, 0.141144, 0.000011, -1.7469, -0.00744, 0.000011, 0.025456] self.h1 = _shift_intercept(self.h1) self.h2 = [ 141.148, 0.190007, -0.38493, -1.67206, 0.190007, 0.02213, -0.04762, -0.00592, -0.38493, -0.04762, 0.165518, -0.00303, -1.67206, -0.00592, -0.00303, 0.024301] self.h2 = _shift_intercept(self.h2) self.h3 = [ 134.5444, 0.05645, -0.02552, -1.59394, 0.05645, 0.026232, -0.05982, -0.00409, -0.02552, -0.05982, 0.196946, -0.0068, -1.59394, -0.00409, -0.0068, 0.023083] self.h3 = _shift_intercept(self.h3) self.resid = [ 3.125725599, -2.022218392, 4.434082972, 5.753880172, -1.744479058, -2.995299443, -2.358455878, -1.358455878, -3.068281354, 1.150212629, 2.481708553, 2.584584946, -1.553899388, -0.177335865, 2.335744732, 0.891912757, -1.43012351, -0.394515569, -0.497391962, 1.407968887, -7.505098501] self.sresids = [ 0.952186413, -0.616026205, 1.350749906, 1.752798302, -0.531418771, -0.912454834, -0.718453867, -0.413824947, -0.934687235, 0.350388031, 0.756000196, 0.787339321, -0.473362692, -0.054021633, 0.711535395, 0.27170242, -0.43565698, -0.120180852, -0.151519976, 0.428908041, -2.28627005] self.weights = [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.874787298] self.params = (.7318, 1.2508, -0.1479, -40.2712) self.bse = (.1377, .3757, .1596, 12.1438) self.scale = 3.2827 self.df_model = 3 self.df_resid = 17 def conf_int(self): return [(0.4619, 1.0016), (.5145, 1.9872), (-.4607, .1648), (-64.0727, -16.4697)] class BisquareHuber(object): def __init__(self): self.h1 = [ 129.9556, 0.264097, -0.59855, -1.5394, 0.264097, 0.016701, -0.03353, -0.00656, -0.59855, -0.03353, 0.124379, 9.621E-6, -1.5394, -0.00656, 9.621E-6, 0.022433] self.h1 = _shift_intercept(self.h1) self.h2 = [ 109.7685, 0.103038, -0.25926, -1.28355, 0.103038, 0.0214, -0.04688, -0.00453, -0.25926, -0.04688, 0.158535, -0.00327, -1.28355, -0.00453, -0.00327, 0.018892] self.h2 = _shift_intercept(self.h2) self.h3 = [ 91.80527, -0.09171, 0.171716, -1.05244, -0.09171, 0.027999, -0.06493, -0.00223, 0.171716, -0.06493, 0.203254, -0.0071, -1.05244, -0.00223, -0.0071, 0.015584] self.h3 = _shift_intercept(self.h3) self.resid = [ 3.034895447, -2.09863887, 4.229870063, 6.18871385, -1.715906134, -2.763596142, -2.010080245, -1.010080245, -2.590747917, 0.712961901, 1.914770759, 1.82892645, -2.019969464, -0.598781979, 2.260467209, 0.859864256, -1.057306197, -0.122565974, -0.036721665, 1.471074632, -8.432085298] self.sresids = [ 0.918227061, -0.634956635, 1.279774287, 1.872435025, -0.519158394, -0.836143718, -0.608162656, -0.305606249, -.78384738, 0.215711191, 0.579326161, 0.553353415, -0.611154703, -0.181165324, 0.683918836, 0.26015744, -0.319894764, -0.037083121, -0.011110375, 0.445083055, -2.551181429] self.weights = [ 0.924649089, 0.963600796, 0.856330585, 0.706048833, 0.975591792, 0.937309703, 0.966582366, 0.991507994, 0.944798311, 0.995764589, 0.969652425, 0.972293856, 0.966255569, 0.997011618, 0.957833493, 0.993842376, 0.990697247, 0.9998747, 0.999988752, 0.982030803, 0.494874977] self.params = (.7932, 1.0477, -0.1335, -40.8949) self.bse = (.1292, .3527, .1498, 11.3998) self.scale = 3.3052 self.df_model = 3 self.df_resid = 17 def conf_int(self): return [(0.5399, 1.0465), (.3565, 1.7389), (-.4271, .1600), (-63.2381, -18.5517)] class AndrewsHuber(object): def __init__(self): self.h1 = [ 129.9124, 0.264009, -0.59836, -1.53888, 0.264009, 0.016696, -0.03352, -0.00656, -0.59836, -0.03352, 0.124337, 9.618E-6, -1.53888, -0.00656, 9.618E-6, 0.022425] self.h1 = _shift_intercept(self.h1) self.h2 = [ 109.7595, 0.105022, -0.26535, -1.28332, .105022, 0.021321, -0.04664, -0.00456, -0.26535, -0.04664, 0.157885, -0.00321, -1.28332, -0.00456, -0.00321, 0.018895] self.h2 = _shift_intercept(self.h2) self.h3 = [ 91.82518, -0.08649, 0.155965, -1.05238, -0.08649, 0.027785, -0.06427, -0.0023, 0.155965, -0.06427, 0.201544, -0.00693, -1.05238, -0.0023, -0.00693, 0.015596] self.h3 = _shift_intercept(self.h3) self.resid = [ 3.040515104, -2.093093543, 4.235081748, 6.188729166, -1.714119676, -2.762695255, -2.009618953, -1.009618953, -2.591649784, 0.715967584, 1.918445405, 1.833412337, -2.016815123, -0.595695587, 2.260536347, 0.859710406, -1.059386228, -0.1241257, -0.039092633, 1.471556455, -8.424624872] self.sresids = [ 0.919639919, -0.633081011, 1.280950793, 1.871854667, -0.518455862, -0.835610004, -0.607833129, -0.305371248, -0.783875269, 0.216552902, 0.580256606, 0.554537345, -0.610009696, -0.180175208, 0.683726076, 0.260029627, -0.320423952, -0.037543293, -0.011824031, 0.445089734, -2.548127888] self.weights = [ 0.923215335, 0.963157359, 0.854300342, 0.704674258, 0.975199805, 0.936344742, 0.9660077, 0.991354016, 0.943851708, 0.995646409, 0.968993767, 0.971658421, 0.965766352, 0.99698502, 0.957106815, 0.993726436, 0.990483134, 0.999868981, 0.999987004, 0.981686004, 0.496752113] self.params = (.7928, 1.0486, -0.1336, -40.8818) self.bse = (.1292, .3526, .1498, 11.3979) self.scale = 3.3062 self.df_model = 3 self.df_resid = 17 def conf_int(self): return [(0.5395, 1.0460), (.3575, 1.7397), (-.4271, .1599), (-63.2213, -18.5423)] statsmodels-0.12.2/statsmodels/robust/tests/test_rlm.py000066400000000000000000000301461400612667500233760ustar00rootroot00000000000000""" Test functions for sm.rlm """ import numpy as np from numpy.testing import assert_almost_equal, assert_allclose import pytest from scipy import stats import statsmodels.api as sm from statsmodels.robust.robust_linear_model import RLM from statsmodels.robust import norms from statsmodels.robust.scale import HuberScale DECIMAL_4 = 4 DECIMAL_3 = 3 DECIMAL_2 = 2 DECIMAL_1 = 1 class CheckRlmResultsMixin(object): ''' res2 contains results from Rmodelwrap or were obtained from a statistical packages such as R, Stata, or SAS and written to results.results_rlm Covariance matrices were obtained from SAS and are imported from results.results_rlm ''' def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, DECIMAL_4) decimal_standarderrors = DECIMAL_4 def test_standarderrors(self): assert_almost_equal(self.res1.bse, self.res2.bse, self.decimal_standarderrors) # TODO: get other results from SAS, though if it works for one... def test_confidenceintervals(self): if not hasattr(self.res2, 'conf_int'): pytest.skip("Results from R") assert_almost_equal(self.res1.conf_int(), self.res2.conf_int(), DECIMAL_4) decimal_scale = DECIMAL_4 def test_scale(self): assert_almost_equal(self.res1.scale, self.res2.scale, self.decimal_scale) def test_weights(self): assert_almost_equal(self.res1.weights, self.res2.weights, DECIMAL_4) def test_residuals(self): assert_almost_equal(self.res1.resid, self.res2.resid, DECIMAL_4) def test_degrees(self): assert_almost_equal(self.res1.model.df_model, self.res2.df_model, DECIMAL_4) assert_almost_equal(self.res1.model.df_resid, self.res2.df_resid, DECIMAL_4) def test_bcov_unscaled(self): if not hasattr(self.res2, 'bcov_unscaled'): pytest.skip("No unscaled cov matrix from SAS") assert_almost_equal(self.res1.bcov_unscaled, self.res2.bcov_unscaled, DECIMAL_4) decimal_bcov_scaled = DECIMAL_4 def test_bcov_scaled(self): assert_almost_equal(self.res1.bcov_scaled, self.res2.h1, self.decimal_bcov_scaled) assert_almost_equal(self.res1.h2, self.res2.h2, self.decimal_bcov_scaled) assert_almost_equal(self.res1.h3, self.res2.h3, self.decimal_bcov_scaled) def test_tvalues(self): if not hasattr(self.res2, 'tvalues'): pytest.skip("No tvalues in benchmark") assert_allclose(self.res1.tvalues, self.res2.tvalues, rtol=0.003) def test_tpvalues(self): # test comparing tvalues and pvalues with normal implementation # make sure they use normal distribution (inherited in results class) params = self.res1.params tvalues = params / self.res1.bse pvalues = stats.norm.sf(np.abs(tvalues)) * 2 half_width = stats.norm.isf(0.025) * self.res1.bse conf_int = np.column_stack((params - half_width, params + half_width)) assert_almost_equal(self.res1.tvalues, tvalues) assert_almost_equal(self.res1.pvalues, pvalues) assert_almost_equal(self.res1.conf_int(), conf_int) class TestRlm(CheckRlmResultsMixin): @classmethod def setup_class(cls): from statsmodels.datasets.stackloss import load cls.data = load(as_pandas=False) # class attributes for subclasses cls.data.exog = sm.add_constant(cls.data.exog, prepend=False) # Test precisions cls.decimal_standarderrors = DECIMAL_1 cls.decimal_scale = DECIMAL_3 model = RLM(cls.data.endog, cls.data.exog, M=norms.HuberT()) cls.model = model results = model.fit() h2 = model.fit(cov="H2").bcov_scaled h3 = model.fit(cov="H3").bcov_scaled cls.res1 = results cls.res1.h2 = h2 cls.res1.h3 = h3 def setup(self): from .results.results_rlm import Huber self.res2 = Huber() @pytest.mark.smoke def test_summary(self): self.res1.summary() @pytest.mark.smoke def test_summary2(self): self.res1.summary2() @pytest.mark.smoke def test_chisq(self): assert isinstance(self.res1.chisq, np.ndarray) @pytest.mark.smoke def test_predict(self): assert isinstance(self.model.predict(self.res1.params), np.ndarray) class TestHampel(TestRlm): @classmethod def setup_class(cls): super(TestHampel, cls).setup_class() # Test precisions cls.decimal_standarderrors = DECIMAL_2 cls.decimal_scale = DECIMAL_3 cls.decimal_bcov_scaled = DECIMAL_3 model = RLM(cls.data.endog, cls.data.exog, M=norms.Hampel()) results = model.fit() h2 = model.fit(cov="H2").bcov_scaled h3 = model.fit(cov="H3").bcov_scaled cls.res1 = results cls.res1.h2 = h2 cls.res1.h3 = h3 def setup(self): from .results.results_rlm import Hampel self.res2 = Hampel() class TestRlmBisquare(TestRlm): @classmethod def setup_class(cls): super(TestRlmBisquare, cls).setup_class() # Test precisions cls.decimal_standarderrors = DECIMAL_1 model = RLM(cls.data.endog, cls.data.exog, M=norms.TukeyBiweight()) results = model.fit() h2 = model.fit(cov="H2").bcov_scaled h3 = model.fit(cov="H3").bcov_scaled cls.res1 = results cls.res1.h2 = h2 cls.res1.h3 = h3 def setup(self): from .results.results_rlm import BiSquare self.res2 = BiSquare() class TestRlmAndrews(TestRlm): @classmethod def setup_class(cls): super(TestRlmAndrews, cls).setup_class() model = RLM(cls.data.endog, cls.data.exog, M=norms.AndrewWave()) results = model.fit() h2 = model.fit(cov="H2").bcov_scaled h3 = model.fit(cov="H3").bcov_scaled cls.res1 = results cls.res1.h2 = h2 cls.res1.h3 = h3 def setup(self): from .results.results_rlm import Andrews self.res2 = Andrews() # -------------------------------------------------------------------- # tests with Huber scaling class TestRlmHuber(CheckRlmResultsMixin): @classmethod def setup_class(cls): from statsmodels.datasets.stackloss import load cls.data = load(as_pandas=False) cls.data.exog = sm.add_constant(cls.data.exog, prepend=False) model = RLM(cls.data.endog, cls.data.exog, M=norms.HuberT()) results = model.fit(scale_est=HuberScale()) h2 = model.fit(cov="H2", scale_est=HuberScale()).bcov_scaled h3 = model.fit(cov="H3", scale_est=HuberScale()).bcov_scaled cls.res1 = results cls.res1.h2 = h2 cls.res1.h3 = h3 def setup(self): from .results.results_rlm import HuberHuber self.res2 = HuberHuber() class TestHampelHuber(TestRlm): @classmethod def setup_class(cls): super(TestHampelHuber, cls).setup_class() model = RLM(cls.data.endog, cls.data.exog, M=norms.Hampel()) results = model.fit(scale_est=HuberScale()) h2 = model.fit(cov="H2", scale_est=HuberScale()).bcov_scaled h3 = model.fit(cov="H3", scale_est=HuberScale()).bcov_scaled cls.res1 = results cls.res1.h2 = h2 cls.res1.h3 = h3 def setup(self): from .results.results_rlm import HampelHuber self.res2 = HampelHuber() class TestRlmBisquareHuber(TestRlm): @classmethod def setup_class(cls): super(TestRlmBisquareHuber, cls).setup_class() model = RLM(cls.data.endog, cls.data.exog, M=norms.TukeyBiweight()) results = model.fit(scale_est=HuberScale()) h2 = model.fit(cov="H2", scale_est=HuberScale()).bcov_scaled h3 = model.fit(cov="H3", scale_est=HuberScale()).bcov_scaled cls.res1 = results cls.res1.h2 = h2 cls.res1.h3 = h3 def setup(self): from .results.results_rlm import BisquareHuber self.res2 = BisquareHuber() class TestRlmAndrewsHuber(TestRlm): @classmethod def setup_class(cls): super(TestRlmAndrewsHuber, cls).setup_class() model = RLM(cls.data.endog, cls.data.exog, M=norms.AndrewWave()) results = model.fit(scale_est=HuberScale()) h2 = model.fit(cov="H2", scale_est=HuberScale()).bcov_scaled h3 = model.fit(cov="H3", scale_est=HuberScale()).bcov_scaled cls.res1 = results cls.res1.h2 = h2 cls.res1.h3 = h3 def setup(self): from .results.results_rlm import AndrewsHuber self.res2 = AndrewsHuber() class TestRlmSresid(CheckRlmResultsMixin): # Check GH#187 @classmethod def setup_class(cls): from statsmodels.datasets.stackloss import load cls.data = load(as_pandas=False) # class attributes for subclasses cls.data.exog = sm.add_constant(cls.data.exog, prepend=False) # Test precisions cls.decimal_standarderrors = DECIMAL_1 cls.decimal_scale = DECIMAL_3 model = RLM(cls.data.endog, cls.data.exog, M=norms.HuberT()) results = model.fit(conv='sresid') h2 = model.fit(cov="H2").bcov_scaled h3 = model.fit(cov="H3").bcov_scaled cls.res1 = results cls.res1.h2 = h2 cls.res1.h3 = h3 def setup(self): from .results.results_rlm import Huber self.res2 = Huber() @pytest.mark.smoke def test_missing(): # see GH#2083 import statsmodels.formula.api as smf d = {'Foo': [1, 2, 10, 149], 'Bar': [1, 2, 3, np.nan]} smf.rlm('Foo ~ Bar', data=d) def test_rlm_start_values(): data = sm.datasets.stackloss.load_pandas() exog = sm.add_constant(data.exog, prepend=False) model = RLM(data.endog, exog, M=norms.HuberT()) results = model.fit() start_params = [0.7156402, 1.29528612, -0.15212252, -39.91967442] result_sv = model.fit(start_params=start_params) assert_allclose(results.params, result_sv.params) def test_rlm_start_values_errors(): data = sm.datasets.stackloss.load_pandas() exog = sm.add_constant(data.exog, prepend=False) model = RLM(data.endog, exog, M=norms.HuberT()) start_params = [0.7156402, 1.29528612, -0.15212252] with pytest.raises(ValueError): model.fit(start_params=start_params) start_params = np.array([start_params, start_params]).T with pytest.raises(ValueError): model.fit(start_params=start_params) @pytest.fixture(scope='module', params=[norms.AndrewWave, norms.LeastSquares, norms.HuberT, norms.TrimmedMean, norms.TukeyBiweight, norms.Hampel, norms.RamsayE]) def norm(request): return request.param() @pytest.fixture(scope='module') def perfect_fit_data(request): from statsmodels.tools.tools import Bunch rs = np.random.RandomState(1249328932) exog = rs.standard_normal((1000, 1)) endog = exog + exog ** 2 exog = sm.add_constant(np.c_[exog, exog ** 2]) return Bunch(endog=endog, exog=exog, const=(3.2 * np.ones_like(endog))) def test_perfect_fit(perfect_fit_data, norm): res = RLM(perfect_fit_data.endog, perfect_fit_data.exog, M=norm).fit() assert_allclose(res.params, np.array([0, 1, 1]), atol=1e-8) def test_perfect_const(perfect_fit_data, norm): res = RLM(perfect_fit_data.const, perfect_fit_data.exog, M=norm).fit() assert_allclose(res.params, np.array([3.2, 0, 0]), atol=1e-8) @pytest.mark.parametrize('conv', ('weights', 'coefs', 'sresid')) def test_alt_criterion(conv): data = sm.datasets.stackloss.load(as_pandas=True) data.exog = sm.add_constant(data.exog, prepend=False) base = RLM(data.endog, data.exog, M=norms.HuberT()).fit() alt = RLM(data.endog, data.exog, M=norms.HuberT()).fit(conv=conv) assert_allclose(base.params, alt.params) def test_bad_criterion(): data = sm.datasets.stackloss.load(as_pandas=True) data.exog = sm.add_constant(data.exog, prepend=False) mod = RLM(data.endog, data.exog, M=norms.HuberT()) with pytest.raises(ValueError, match='Convergence argument unknown'): mod.fit(conv='unknown') statsmodels-0.12.2/statsmodels/robust/tests/test_scale.py000066400000000000000000000207141400612667500236730ustar00rootroot00000000000000""" Test functions for models.robust.scale """ import numpy as np from numpy.random import standard_normal from numpy.testing import assert_almost_equal, assert_equal import pytest from scipy.stats import norm as Gaussian import statsmodels.api as sm import statsmodels.robust.scale as scale from statsmodels.robust.scale import mad # Example from Section 5.5, Venables & Ripley (2002) DECIMAL = 4 # TODO: Can replicate these tests using stackloss data and R if this # data is a problem class TestChem(object): @classmethod def setup_class(cls): cls.chem = np.array( [ 2.20, 2.20, 2.4, 2.4, 2.5, 2.7, 2.8, 2.9, 3.03, 3.03, 3.10, 3.37, 3.4, 3.4, 3.4, 3.5, 3.6, 3.7, 3.7, 3.7, 3.7, 3.77, 5.28, 28.95, ] ) def test_mean(self): assert_almost_equal(np.mean(self.chem), 4.2804, DECIMAL) def test_median(self): assert_almost_equal(np.median(self.chem), 3.385, DECIMAL) def test_mad(self): assert_almost_equal(scale.mad(self.chem), 0.52632, DECIMAL) def test_iqr(self): assert_almost_equal(scale.iqr(self.chem), 0.68570, DECIMAL) def test_qn(self): assert_almost_equal(scale.qn_scale(self.chem), 0.73231, DECIMAL) def test_huber_scale(self): assert_almost_equal(scale.huber(self.chem)[0], 3.20549, DECIMAL) def test_huber_location(self): assert_almost_equal(scale.huber(self.chem)[1], 0.67365, DECIMAL) def test_huber_huberT(self): n = scale.norms.HuberT() n.t = 1.5 h = scale.Huber(norm=n) assert_almost_equal( scale.huber(self.chem)[0], h(self.chem)[0], DECIMAL ) assert_almost_equal( scale.huber(self.chem)[1], h(self.chem)[1], DECIMAL ) def test_huber_Hampel(self): hh = scale.Huber(norm=scale.norms.Hampel()) assert_almost_equal(hh(self.chem)[0], 3.17434, DECIMAL) assert_almost_equal(hh(self.chem)[1], 0.66782, DECIMAL) class TestMad(object): @classmethod def setup_class(cls): np.random.seed(54321) cls.X = standard_normal((40, 10)) def test_mad(self): m = scale.mad(self.X) assert_equal(m.shape, (10,)) def test_mad_empty(self): empty = np.empty(0) assert np.isnan(scale.mad(empty)) empty = np.empty((10, 100, 0)) assert_equal(scale.mad(empty, axis=1), np.empty((10, 0))) empty = np.empty((100, 100, 0, 0)) assert_equal(scale.mad(empty, axis=-1), np.empty((100, 100, 0))) def test_mad_center(self): n = scale.mad(self.X, center=0) assert_equal(n.shape, (10,)) with pytest.raises(TypeError): scale.mad(self.X, center=None) assert_almost_equal( scale.mad(self.X, center=1), np.median(np.abs(self.X - 1), axis=0) / Gaussian.ppf(3 / 4.0), DECIMAL, ) class TestMadAxes(object): @classmethod def setup_class(cls): np.random.seed(54321) cls.X = standard_normal((40, 10, 30)) def test_axis0(self): m = scale.mad(self.X, axis=0) assert_equal(m.shape, (10, 30)) def test_axis1(self): m = scale.mad(self.X, axis=1) assert_equal(m.shape, (40, 30)) def test_axis2(self): m = scale.mad(self.X, axis=2) assert_equal(m.shape, (40, 10)) def test_axisneg1(self): m = scale.mad(self.X, axis=-1) assert_equal(m.shape, (40, 10)) class TestIqr(object): @classmethod def setup_class(cls): np.random.seed(54321) cls.X = standard_normal((40, 10)) def test_iqr(self): m = scale.iqr(self.X) assert_equal(m.shape, (10,)) def test_iqr_empty(self): empty = np.empty(0) assert np.isnan(scale.iqr(empty)) empty = np.empty((10, 100, 0)) assert_equal(scale.iqr(empty, axis=1), np.empty((10, 0))) empty = np.empty((100, 100, 0, 0)) assert_equal(scale.iqr(empty, axis=-1), np.empty((100, 100, 0))) empty = np.empty(shape=()) with pytest.raises(ValueError): scale.iqr(empty) class TestIqrAxes(object): @classmethod def setup_class(cls): np.random.seed(54321) cls.X = standard_normal((40, 10, 30)) def test_axis0(self): m = scale.iqr(self.X, axis=0) assert_equal(m.shape, (10, 30)) def test_axis1(self): m = scale.iqr(self.X, axis=1) assert_equal(m.shape, (40, 30)) def test_axis2(self): m = scale.iqr(self.X, axis=2) assert_equal(m.shape, (40, 10)) def test_axisneg1(self): m = scale.iqr(self.X, axis=-1) assert_equal(m.shape, (40, 10)) class TestQn(object): @classmethod def setup_class(cls): np.random.seed(54321) cls.normal = standard_normal(size=40) cls.range = np.arange(0, 40) cls.exponential = np.random.exponential(size=40) cls.stackloss = sm.datasets.stackloss.load_pandas().data cls.sunspot = sm.datasets.sunspots.load_pandas().data.SUNACTIVITY def test_qn_naive(self): assert_almost_equal( scale.qn_scale(self.normal), scale._qn_naive(self.normal), DECIMAL ) assert_almost_equal( scale.qn_scale(self.range), scale._qn_naive(self.range), DECIMAL ) assert_almost_equal( scale.qn_scale(self.exponential), scale._qn_naive(self.exponential), DECIMAL, ) def test_qn_robustbase(self): # from R's robustbase with finite.corr = FALSE assert_almost_equal(scale.qn_scale(self.range), 13.3148, DECIMAL) assert_almost_equal( scale.qn_scale(self.stackloss), np.array([8.87656, 8.87656, 2.21914, 4.43828]), DECIMAL, ) # sunspot.year from datasets in R only goes up to 289 assert_almost_equal( scale.qn_scale(self.sunspot[0:289]), 33.50901, DECIMAL ) def test_qn_empty(self): empty = np.empty(0) assert np.isnan(scale.qn_scale(empty)) empty = np.empty((10, 100, 0)) assert_equal(scale.qn_scale(empty, axis=1), np.empty((10, 0))) empty = np.empty((100, 100, 0, 0)) assert_equal(scale.qn_scale(empty, axis=-1), np.empty((100, 100, 0))) empty = np.empty(shape=()) with pytest.raises(ValueError): scale.iqr(empty) class TestQnAxes(object): @classmethod def setup_class(cls): np.random.seed(54321) cls.X = standard_normal((40, 10, 30)) def test_axis0(self): m = scale.qn_scale(self.X, axis=0) assert_equal(m.shape, (10, 30)) def test_axis1(self): m = scale.qn_scale(self.X, axis=1) assert_equal(m.shape, (40, 30)) def test_axis2(self): m = scale.qn_scale(self.X, axis=2) assert_equal(m.shape, (40, 10)) def test_axisneg1(self): m = scale.qn_scale(self.X, axis=-1) assert_equal(m.shape, (40, 10)) class TestHuber(object): @classmethod def setup_class(cls): np.random.seed(54321) cls.X = standard_normal((40, 10)) def test_huber_result_shape(self): h = scale.Huber(maxiter=100) m, s = h(self.X) assert_equal(m.shape, (10,)) class TestHuberAxes(object): @classmethod def setup_class(cls): np.random.seed(54321) cls.X = standard_normal((40, 10, 30)) cls.h = scale.Huber(maxiter=1000, tol=1.0e-05) def test_default(self): m, s = self.h(self.X, axis=0) assert_equal(m.shape, (10, 30)) def test_axis1(self): m, s = self.h(self.X, axis=1) assert_equal(m.shape, (40, 30)) def test_axis2(self): m, s = self.h(self.X, axis=2) assert_equal(m.shape, (40, 10)) def test_axisneg1(self): m, s = self.h(self.X, axis=-1) assert_equal(m.shape, (40, 10)) def test_mad_axis_none(): # GH 7027 a = np.array([[0, 1, 2], [2, 3, 2]]) def m(x): return np.median(x) direct = mad(a=a, axis=None) custom = mad(a=a, axis=None, center=m) axis0 = mad(a=a.ravel(), axis=0) np.testing.assert_allclose(direct, custom) np.testing.assert_allclose(direct, axis0) statsmodels-0.12.2/statsmodels/sandbox/000077500000000000000000000000001400612667500201455ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/__init__.py000066400000000000000000000001501400612667500222520ustar00rootroot00000000000000'''This is sandbox code ''' from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/sandbox/archive/000077500000000000000000000000001400612667500215665ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/archive/__init__.py000066400000000000000000000000001400612667500236650ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/archive/linalg_covmat.py000066400000000000000000000204701400612667500247620ustar00rootroot00000000000000import math import numpy as np from scipy import linalg, stats, special from .linalg_decomp_1 import SvdArray #univariate standard normal distribution #following from scipy.stats.distributions with adjustments sqrt2pi = math.sqrt(2 * np.pi) logsqrt2pi = math.log(sqrt2pi) class StandardNormal(object): '''Distribution of vector x, with independent distribution N(0,1) this is the same as univariate normal for pdf and logpdf other methods not checked/adjusted yet ''' def rvs(self, size): return np.random.standard_normal(size) def pdf(self, x): return np.exp(-x**2 * 0.5) / sqrt2pi def logpdf(self, x): return -x**2 * 0.5 - logsqrt2pi def _cdf(self, x): return special.ndtr(x) def _logcdf(self, x): return np.log(special.ndtr(x)) def _ppf(self, q): return special.ndtri(q) class AffineTransform(object): '''affine full rank transformation of a multivariate distribution no dimension checking, assumes everything broadcasts correctly first version without bound support provides distribution of y given distribution of x y = const + tmat * x ''' def __init__(self, const, tmat, dist): self.const = const self.tmat = tmat self.dist = dist self.nrv = len(const) if not np.equal(self.nrv, tmat.shape).all(): raise ValueError('dimension of const and tmat do not agree') #replace the following with a linalgarray class self.tmatinv = linalg.inv(tmat) self.absdet = np.abs(np.linalg.det(self.tmat)) self.logabsdet = np.log(np.abs(np.linalg.det(self.tmat))) self.dist def rvs(self, size): #size can only be integer not yet tuple print((size,)+(self.nrv,)) return self.transform(self.dist.rvs(size=(size,)+(self.nrv,))) def transform(self, x): #return np.dot(self.tmat, x) + self.const return np.dot(x, self.tmat) + self.const def invtransform(self, y): return np.dot(self.tmatinv, y - self.const) def pdf(self, x): return 1. / self.absdet * self.dist.pdf(self.invtransform(x)) def logpdf(self, x): return - self.logabsdet + self.dist.logpdf(self.invtransform(x)) class MultivariateNormalChol(object): '''multivariate normal distribution with cholesky decomposition of sigma ignoring mean at the beginning, maybe needs testing for broadcasting to contemporaneously but not intertemporaly correlated random variable, which axis?, maybe swapaxis or rollaxis if x.ndim != mean.ndim == (sigma.ndim - 1) initially 1d is ok, 2d should work with iid in axis 0 and mvn in axis 1 ''' def __init__(self, mean, sigma): self.mean = mean self.sigma = sigma self.sigmainv = sigmainv self.cholsigma = linalg.cholesky(sigma) #the following makes it lower triangular with increasing time self.cholsigmainv = linalg.cholesky(sigmainv)[::-1,::-1] #todo: this might be a trick todo backward instead of forward filtering def whiten(self, x): return np.dot(cholsigmainv, x) def logpdf_obs(self, x): x = x - self.mean x_whitened = self.whiten(x) #sigmainv = linalg.cholesky(sigma) logdetsigma = np.log(np.linalg.det(sigma)) sigma2 = 1. # error variance is included in sigma llike = 0.5 * (np.log(sigma2) - 2.* np.log(np.diagonal(self.cholsigmainv)) + (x_whitened**2)/sigma2 + np.log(2*np.pi)) return llike def logpdf(self, x): return self.logpdf_obs(x).sum(-1) def pdf(self, x): return np.exp(self.logpdf(x)) class MultivariateNormal(object): def __init__(self, mean, sigma): self.mean = mean self.sigma = SvdArray(sigma) def loglike_ar1(x, rho): '''loglikelihood of AR(1) process, as a test case sigma_u partially hard coded Greene chapter 12 eq. (12-31) ''' x = np.asarray(x) u = np.r_[x[0], x[1:] - rho * x[:-1]] sigma_u2 = 2*(1-rho**2) loglik = 0.5*(-(u**2).sum(0) / sigma_u2 + np.log(1-rho**2) - x.shape[0] * (np.log(2*np.pi) + np.log(sigma_u2))) return loglik def ar2transform(x, arcoefs): ''' (Greene eq 12-30) ''' a1, a2 = arcoefs y = np.zeros_like(x) y[0] = np.sqrt((1+a2) * ((1-a2)**2 - a1**2) / (1-a2)) * x[0] y[1] = np.sqrt(1-a2**2) * x[2] - a1 * np.sqrt(1-a1**2)/(1-a2) * x[1] #TODO:wrong index in x y[2:] = x[2:] - a1 * x[1:-1] - a2 * x[:-2] return y def mvn_loglike(x, sigma): '''loglike multivariate normal assumes x is 1d, (nobs,) and sigma is 2d (nobs, nobs) brute force from formula no checking of correct inputs use of inv and log-det should be replace with something more efficient ''' #see numpy thread #Sturla: sqmahal = (cx*cho_solve(cho_factor(S),cx.T).T).sum(axis=1) sigmainv = linalg.inv(sigma) logdetsigma = np.log(np.linalg.det(sigma)) nobs = len(x) llf = - np.dot(x, np.dot(sigmainv, x)) llf -= nobs * np.log(2 * np.pi) llf -= logdetsigma llf *= 0.5 return llf def mvn_nloglike_obs(x, sigma): '''loglike multivariate normal assumes x is 1d, (nobs,) and sigma is 2d (nobs, nobs) brute force from formula no checking of correct inputs use of inv and log-det should be replace with something more efficient ''' #see numpy thread #Sturla: sqmahal = (cx*cho_solve(cho_factor(S),cx.T).T).sum(axis=1) #Still wasteful to calculate pinv first sigmainv = linalg.inv(sigma) cholsigmainv = linalg.cholesky(sigmainv) #2 * np.sum(np.log(np.diagonal(np.linalg.cholesky(A)))) #Dag mailinglist # logdet not needed ??? #logdetsigma = 2 * np.sum(np.log(np.diagonal(cholsigmainv))) x_whitened = np.dot(cholsigmainv, x) #sigmainv = linalg.cholesky(sigma) logdetsigma = np.log(np.linalg.det(sigma)) sigma2 = 1. # error variance is included in sigma llike = 0.5 * (np.log(sigma2) - 2.* np.log(np.diagonal(cholsigmainv)) + (x_whitened**2)/sigma2 + np.log(2*np.pi)) return llike, (x_whitened**2) nobs = 10 x = np.arange(nobs) autocov = 2*0.8**np.arange(nobs)# +0.01 * np.random.randn(nobs) sigma = linalg.toeplitz(autocov) #sigma = np.diag(1+np.random.randn(10)**2) cholsigma = linalg.cholesky(sigma).T#, lower=True) sigmainv = linalg.inv(sigma) cholsigmainv = linalg.cholesky(sigmainv) #2 * np.sum(np.log(np.diagonal(np.linalg.cholesky(A)))) #Dag mailinglist # logdet not needed ??? #logdetsigma = 2 * np.sum(np.log(np.diagonal(cholsigmainv))) x_whitened = np.dot(cholsigmainv, x) #sigmainv = linalg.cholesky(sigma) logdetsigma = np.log(np.linalg.det(sigma)) sigma2 = 1. # error variance is included in sigma llike = 0.5 * (np.log(sigma2) - 2.* np.log(np.diagonal(cholsigmainv)) + (x_whitened**2)/sigma2 + np.log(2*np.pi)) ll, ls = mvn_nloglike_obs(x, sigma) #the following are all the same for diagonal sigma print(ll.sum(), 'll.sum()') print(llike.sum(), 'llike.sum()') print(np.log(stats.norm._pdf(x_whitened)).sum() - 0.5 * logdetsigma,) print('stats whitened') print(np.log(stats.norm.pdf(x,scale=np.sqrt(np.diag(sigma)))).sum(),) print('stats scaled') print(0.5*(np.dot(linalg.cho_solve((linalg.cho_factor(sigma, lower=False)[0].T, False),x.T), x) + nobs*np.log(2*np.pi) - 2.* np.log(np.diagonal(cholsigmainv)).sum())) print(0.5*(np.dot(linalg.cho_solve((linalg.cho_factor(sigma)[0].T, False),x.T), x) + nobs*np.log(2*np.pi)- 2.* np.log(np.diagonal(cholsigmainv)).sum())) print(0.5*(np.dot(linalg.cho_solve(linalg.cho_factor(sigma),x.T), x) + nobs*np.log(2*np.pi)- 2.* np.log(np.diagonal(cholsigmainv)).sum())) print(mvn_loglike(x, sigma)) normtransf = AffineTransform(np.zeros(nobs), cholsigma, StandardNormal()) print(normtransf.logpdf(x_whitened).sum()) #print(normtransf.rvs(5) print(loglike_ar1(x, 0.8)) mch = MultivariateNormalChol(np.zeros(nobs), sigma) print(mch.logpdf(x)) #from .linalg_decomp_1 import tiny2zero #print(tiny2zero(mch.cholsigmainv / mch.cholsigmainv[-1,-1]) xw = mch.whiten(x) print('xSigmax', np.dot(xw,xw)) print('xSigmax', np.dot(x,linalg.cho_solve(linalg.cho_factor(mch.sigma),x))) print('xSigmax', np.dot(x,linalg.cho_solve((mch.cholsigma, False),x))) statsmodels-0.12.2/statsmodels/sandbox/archive/linalg_decomp_1.py000066400000000000000000000170071400612667500251620ustar00rootroot00000000000000'''Recipes for more efficient work with linalg using classes intended for use for multivariate normal and linear regression calculations x is the data (nobs, nvars) m is the moment matrix (x'x) or a covariance matrix Sigma examples: x'sigma^{-1}x z = Px where P=Sigma^{-1/2} or P=Sigma^{1/2} Initially assume positive definite, then add spectral cutoff and regularization of moment matrix, and extend to PCA maybe extend to sparse if some examples work out (transformation matrix P for random effect and for toeplitz) Author: josef-pktd Created on 2010-10-20 ''' import numpy as np from scipy import linalg from statsmodels.tools.decorators import cache_readonly class PlainMatrixArray(object): '''Class that defines linalg operation on an array simplest version as benchmark linear algebra recipes for multivariate normal and linear regression calculations ''' def __init__(self, data=None, sym=None): if data is not None: if sym is None: self.x = np.asarray(data) self.m = np.dot(self.x.T, self.x) else: raise ValueError('data and sym cannot be both given') elif sym is not None: self.m = np.asarray(sym) self.x = np.eye(*self.m.shape) #default else: raise ValueError('either data or sym need to be given') @cache_readonly def minv(self): return np.linalg.inv(self.m) def m_y(self, y): return np.dot(self.m, y) def minv_y(self, y): return np.dot(self.minv, y) @cache_readonly def mpinv(self): return linalg.pinv(self.m) @cache_readonly def xpinv(self): return linalg.pinv(self.x) def yt_m_y(self, y): return np.dot(y.T, np.dot(self.m, y)) def yt_minv_y(self, y): return np.dot(y.T, np.dot(self.minv, y)) #next two are redundant def y_m_yt(self, y): return np.dot(y, np.dot(self.m, y.T)) def y_minv_yt(self, y): return np.dot(y, np.dot(self.minv, y.T)) @cache_readonly def mdet(self): return linalg.det(self.m) @cache_readonly def mlogdet(self): return np.log(linalg.det(self.m)) @cache_readonly def meigh(self): evals, evecs = linalg.eigh(self.m) sortind = np.argsort(evals)[::-1] return evals[sortind], evecs[:,sortind] @cache_readonly def mhalf(self): evals, evecs = self.meigh return np.dot(np.diag(evals**0.5), evecs.T) #return np.dot(evecs, np.dot(np.diag(evals**0.5), evecs.T)) #return np.dot(evecs, 1./np.sqrt(evals) * evecs.T)) @cache_readonly def minvhalf(self): evals, evecs = self.meigh return np.dot(evecs, 1./np.sqrt(evals) * evecs.T) class SvdArray(PlainMatrixArray): '''Class that defines linalg operation on an array svd version, where svd is taken on original data array, if or when it matters no spectral cutoff in first version ''' def __init__(self, data=None, sym=None): super(SvdArray, self).__init__(data=data, sym=sym) u, s, v = np.linalg.svd(self.x, full_matrices=1) self.u, self.s, self.v = u, s, v self.sdiag = linalg.diagsvd(s, *x.shape) self.sinvdiag = linalg.diagsvd(1./s, *x.shape) def _sdiagpow(self, p): return linalg.diagsvd(np.power(self.s, p), *x.shape) @cache_readonly def minv(self): sinvv = np.dot(self.sinvdiag, self.v) return np.dot(sinvv.T, sinvv) @cache_readonly def meigh(self): evecs = self.v.T evals = self.s**2 return evals, evecs @cache_readonly def mdet(self): return self.meigh[0].prod() @cache_readonly def mlogdet(self): return np.log(self.meigh[0]).sum() @cache_readonly def mhalf(self): return np.dot(np.diag(self.s), self.v) @cache_readonly def xxthalf(self): return np.dot(self.u, self.sdiag) @cache_readonly def xxtinvhalf(self): return np.dot(self.u, self.sinvdiag) class CholArray(PlainMatrixArray): '''Class that defines linalg operation on an array cholesky version, where svd is taken on original data array, if or when it matters plan: use cholesky factor and cholesky solve nothing implemented yet ''' def __init__(self, data=None, sym=None): super(SvdArray, self).__init__(data=data, sym=sym) def yt_minv_y(self, y): '''xSigmainvx does not use stored cholesky yet ''' return np.dot(x,linalg.cho_solve(linalg.cho_factor(self.m),x)) #same as #lower = False #if cholesky(sigma) is used, default is upper #np.dot(x,linalg.cho_solve((self.cholsigma, lower),x)) def testcompare(m1, m2): from numpy.testing import assert_almost_equal, assert_approx_equal decimal = 12 #inv assert_almost_equal(m1.minv, m2.minv, decimal=decimal) #matrix half and invhalf #fix sign in test, should this be standardized s1 = np.sign(m1.mhalf.sum(1))[:,None] s2 = np.sign(m2.mhalf.sum(1))[:,None] scorr = s1/s2 assert_almost_equal(m1.mhalf, m2.mhalf * scorr, decimal=decimal) assert_almost_equal(m1.minvhalf, m2.minvhalf, decimal=decimal) #eigenvalues, eigenvectors evals1, evecs1 = m1.meigh evals2, evecs2 = m2.meigh assert_almost_equal(evals1, evals2, decimal=decimal) #normalization can be different: evecs in columns s1 = np.sign(evecs1.sum(0)) s2 = np.sign(evecs2.sum(0)) scorr = s1/s2 assert_almost_equal(evecs1, evecs2 * scorr, decimal=decimal) #determinant assert_approx_equal(m1.mdet, m2.mdet, significant=13) assert_approx_equal(m1.mlogdet, m2.mlogdet, significant=13) ####### helper function for interactive work def tiny2zero(x, eps = 1e-15): '''replace abs values smaller than eps by zero, makes copy ''' mask = np.abs(x.copy()) < eps x[mask] = 0 return x def maxabs(x): return np.max(np.abs(x)) if __name__ == '__main__': n = 5 y = np.arange(n) x = np.random.randn(100,n) autocov = 2*0.8**np.arange(n) +0.01 * np.random.randn(n) sigma = linalg.toeplitz(autocov) mat = PlainMatrixArray(sym=sigma) print(tiny2zero(mat.mhalf)) mih = mat.minvhalf print(tiny2zero(mih)) #for nicer printing mat2 = PlainMatrixArray(data=x) print(maxabs(mat2.yt_minv_y(np.dot(x.T, x)) - mat2.m)) print(tiny2zero(mat2.minv_y(mat2.m))) mat3 = SvdArray(data=x) print(mat3.meigh[0]) print(mat2.meigh[0]) testcompare(mat2, mat3) ''' m = np.dot(x.T, x) u,s,v = np.linalg.svd(x, full_matrices=1) Sig = linalg.diagsvd(s,*x.shape) >>> np.max(np.abs(np.dot(u, np.dot(Sig, v)) - x)) 3.1086244689504383e-015 >>> np.max(np.abs(np.dot(u.T, u) - np.eye(100))) 3.3306690738754696e-016 >>> np.max(np.abs(np.dot(v.T, v) - np.eye(5))) 6.6613381477509392e-016 >>> np.max(np.abs(np.dot(Sig.T, Sig) - np.diag(s**2))) 5.6843418860808015e-014 >>> evals,evecs = linalg.eigh(np.dot(x.T, x)) >>> evals[::-1] array([ 123.36404464, 112.17036442, 102.04198468, 76.60832278, 74.70484487]) >>> s**2 array([ 123.36404464, 112.17036442, 102.04198468, 76.60832278, 74.70484487]) >>> np.max(np.abs(np.dot(v.T, np.dot(np.diag(s**2), v)) - m)) 1.1368683772161603e-013 >>> us = np.dot(u, Sig) >>> np.max(np.abs(np.dot(us, us.T) - np.dot(x, x.T))) 1.0658141036401503e-014 >>> sv = np.dot(Sig, v) >>> np.max(np.abs(np.dot(sv.T, sv) - np.dot(x.T, x))) 1.1368683772161603e-013 ''' statsmodels-0.12.2/statsmodels/sandbox/archive/tsa.py000066400000000000000000000027371400612667500227400ustar00rootroot00000000000000'''Collection of alternative implementations for time series analysis >>> signal.fftconvolve(x,x[::-1])[len(x)-1:len(x)+10]/x.shape[0] array([ 2.12286549e+00, 1.27450889e+00, 7.86898619e-02, -5.80017553e-01, -5.74814915e-01, -2.28006995e-01, 9.39554926e-02, 2.00610244e-01, 1.32239575e-01, 1.24504352e-03, -8.81846018e-02]) >>> sm.tsa.stattools.acovf(X, fft=True)[:order+1] array([ 2.12286549e+00, 1.27450889e+00, 7.86898619e-02, -5.80017553e-01, -5.74814915e-01, -2.28006995e-01, 9.39554926e-02, 2.00610244e-01, 1.32239575e-01, 1.24504352e-03, -8.81846018e-02]) >>> import nitime.utils as ut >>> ut.autocov(s)[:order+1] array([ 2.12286549e+00, 1.27450889e+00, 7.86898619e-02, -5.80017553e-01, -5.74814915e-01, -2.28006995e-01, 9.39554926e-02, 2.00610244e-01, 1.32239575e-01, 1.24504352e-03, -8.81846018e-02]) ''' import numpy as np def acovf_fft(x, demean=True): '''autocovariance function with call to fftconvolve, biased Parameters ---------- x : array_like timeseries, signal demean : bool If true, then demean time series Returns ------- acovf : ndarray autocovariance for data, same length as x might work for nd in parallel with time along axis 0 ''' from scipy import signal x = np.asarray(x) if demean: x = x - x.mean() signal.fftconvolve(x,x[::-1])[len(x)-1:len(x)+10]/x.shape[0] statsmodels-0.12.2/statsmodels/sandbox/bspline.py000066400000000000000000000477461400612667500221750ustar00rootroot00000000000000''' Bspines and smoothing splines. General references: Craven, P. and Wahba, G. (1978) "Smoothing noisy data with spline functions. Estimating the correct degree of smoothing by the method of generalized cross-validation." Numerische Mathematik, 31(4), 377-403. Hastie, Tibshirani and Friedman (2001). "The Elements of Statistical Learning." Springer-Verlag. 536 pages. Hutchison, M. and Hoog, F. "Smoothing noisy data with spline functions." Numerische Mathematik, 47(1), 99-106. ''' import numpy as np import numpy.linalg as L from scipy.linalg import solveh_banded from scipy.optimize import golden from models import _hbspline #removed because this was segfaulting # Issue warning regarding heavy development status of this module import warnings _msg = """ The bspline code is technology preview and requires significant work on the public API and documentation. The API will likely change in the future """ warnings.warn(_msg, FutureWarning) def _band2array(a, lower=0, symmetric=False, hermitian=False): """ Take an upper or lower triangular banded matrix and return a numpy array. INPUTS: a -- a matrix in upper or lower triangular banded matrix lower -- is the matrix upper or lower triangular? symmetric -- if True, return the original result plus its transpose hermitian -- if True (and symmetric False), return the original result plus its conjugate transposed """ n = a.shape[1] r = a.shape[0] _a = 0 if not lower: for j in range(r): _b = np.diag(a[r-1-j],k=j)[j:(n+j),j:(n+j)] _a += _b if symmetric and j > 0: _a += _b.T elif hermitian and j > 0: _a += _b.conjugate().T else: for j in range(r): _b = np.diag(a[j],k=j)[0:n,0:n] _a += _b if symmetric and j > 0: _a += _b.T elif hermitian and j > 0: _a += _b.conjugate().T _a = _a.T return _a def _upper2lower(ub): """ Convert upper triangular banded matrix to lower banded form. INPUTS: ub -- an upper triangular banded matrix OUTPUTS: lb lb -- a lower triangular banded matrix with same entries as ub """ lb = np.zeros(ub.shape, ub.dtype) nrow, ncol = ub.shape for i in range(ub.shape[0]): lb[i,0:(ncol-i)] = ub[nrow-1-i,i:ncol] lb[i,(ncol-i):] = ub[nrow-1-i,0:i] return lb def _lower2upper(lb): """ Convert lower triangular banded matrix to upper banded form. INPUTS: lb -- a lower triangular banded matrix OUTPUTS: ub ub -- an upper triangular banded matrix with same entries as lb """ ub = np.zeros(lb.shape, lb.dtype) nrow, ncol = lb.shape for i in range(lb.shape[0]): ub[nrow-1-i,i:ncol] = lb[i,0:(ncol-i)] ub[nrow-1-i,0:i] = lb[i,(ncol-i):] return ub def _triangle2unit(tb, lower=0): """ Take a banded triangular matrix and return its diagonal and the unit matrix: the banded triangular matrix with 1's on the diagonal, i.e. each row is divided by the corresponding entry on the diagonal. INPUTS: tb -- a lower triangular banded matrix lower -- if True, then tb is assumed to be lower triangular banded, in which case return value is also lower triangular banded. OUTPUTS: d, b d -- diagonal entries of tb b -- unit matrix: if lower is False, b is upper triangular banded and its rows of have been divided by d, else lower is True, b is lower triangular banded and its columns have been divieed by d. """ if lower: d = tb[0].copy() else: d = tb[-1].copy() if lower: return d, (tb / d) else: lnum = _upper2lower(tb) return d, _lower2upper(lnum / d) def _trace_symbanded(a, b, lower=0): """ Compute the trace(ab) for two upper or banded real symmetric matrices stored either in either upper or lower form. INPUTS: a, b -- two banded real symmetric matrices (either lower or upper) lower -- if True, a and b are assumed to be the lower half OUTPUTS: trace trace -- trace(ab) """ if lower: t = _zero_triband(a * b, lower=1) return t[0].sum() + 2 * t[1:].sum() else: t = _zero_triband(a * b, lower=0) return t[-1].sum() + 2 * t[:-1].sum() def _zero_triband(a, lower=0): """ Explicitly zero out unused elements of a real symmetric banded matrix. INPUTS: a -- a real symmetric banded matrix (either upper or lower hald) lower -- if True, a is assumed to be the lower half """ nrow, ncol = a.shape if lower: for i in range(nrow): a[i, (ncol-i):] = 0. else: for i in range(nrow): a[i, 0:i] = 0. return a class BSpline(object): ''' Bsplines of a given order and specified knots. Implementation is based on description in Chapter 5 of Hastie, Tibshirani and Friedman (2001). "The Elements of Statistical Learning." Springer-Verlag. 536 pages. INPUTS: knots -- a sorted array of knots with knots[0] the lower boundary, knots[1] the upper boundary and knots[1:-1] the internal knots. order -- order of the Bspline, default is 4 which yields cubic splines M -- number of additional boundary knots, if None it defaults to order coef -- an optional array of real-valued coefficients for the Bspline of shape (knots.shape + 2 * (M - 1) - order,). x -- an optional set of x values at which to evaluate the Bspline to avoid extra evaluation in the __call__ method ''' # FIXME: update parameter names, replace single character names # FIXME: `order` should be actual spline order (implemented as order+1) ## FIXME: update the use of spline order in extension code (evaluate is recursively called) # FIXME: eliminate duplicate M and m attributes (m is order, M is related to tau size) def __init__(self, knots, order=4, M=None, coef=None, x=None): knots = np.squeeze(np.unique(np.asarray(knots))) if knots.ndim != 1: raise ValueError('expecting 1d array for knots') self.m = order if M is None: M = self.m self.M = M self.tau = np.hstack([[knots[0]]*(self.M-1), knots, [knots[-1]]*(self.M-1)]) self.K = knots.shape[0] - 2 if coef is None: self.coef = np.zeros((self.K + 2 * self.M - self.m), np.float64) else: self.coef = np.squeeze(coef) if self.coef.shape != (self.K + 2 * self.M - self.m): raise ValueError('coefficients of Bspline have incorrect shape') if x is not None: self.x = x def _setx(self, x): self._x = x self._basisx = self.basis(self._x) def _getx(self): return self._x x = property(_getx, _setx) def __call__(self, *args): """ Evaluate the BSpline at a given point, yielding a matrix B and return B * self.coef INPUTS: args -- optional arguments. If None, it returns self._basisx, the BSpline evaluated at the x values passed in __init__. Otherwise, return the BSpline evaluated at the first argument args[0]. OUTPUTS: y y -- value of Bspline at specified x values BUGS: If self has no attribute x, an exception will be raised because self has no attribute _basisx. """ if not args: b = self._basisx.T else: x = args[0] b = np.asarray(self.basis(x)).T return np.squeeze(np.dot(b, self.coef)) def basis_element(self, x, i, d=0): """ Evaluate a particular basis element of the BSpline, or its derivative. INPUTS: x -- x values at which to evaluate the basis element i -- which element of the BSpline to return d -- the order of derivative OUTPUTS: y y -- value of d-th derivative of the i-th basis element of the BSpline at specified x values """ x = np.asarray(x, np.float64) _shape = x.shape if _shape == (): x.shape = (1,) x.shape = (np.product(_shape,axis=0),) if i < self.tau.shape[0] - 1: # TODO: OWNDATA flags... v = _hbspline.evaluate(x, self.tau, self.m, d, i, i+1) else: return np.zeros(x.shape, np.float64) if (i == self.tau.shape[0] - self.m): v = np.where(np.equal(x, self.tau[-1]), 1, v) v.shape = _shape return v def basis(self, x, d=0, lower=None, upper=None): """ Evaluate the basis of the BSpline or its derivative. If lower or upper is specified, then only the [lower:upper] elements of the basis are returned. INPUTS: x -- x values at which to evaluate the basis element i -- which element of the BSpline to return d -- the order of derivative lower -- optional lower limit of the set of basis elements upper -- optional upper limit of the set of basis elements OUTPUTS: y y -- value of d-th derivative of the basis elements of the BSpline at specified x values """ x = np.asarray(x) _shape = x.shape if _shape == (): x.shape = (1,) x.shape = (np.product(_shape,axis=0),) if upper is None: upper = self.tau.shape[0] - self.m if lower is None: lower = 0 upper = min(upper, self.tau.shape[0] - self.m) lower = max(0, lower) d = np.asarray(d) if d.shape == (): v = _hbspline.evaluate(x, self.tau, self.m, int(d), lower, upper) else: if d.shape[0] != 2: raise ValueError("if d is not an integer, expecting a jx2 \ array with first row indicating order \ of derivative, second row coefficient in front.") v = 0 for i in range(d.shape[1]): v += d[1,i] * _hbspline.evaluate(x, self.tau, self.m, d[0,i], lower, upper) v.shape = (upper-lower,) + _shape if upper == self.tau.shape[0] - self.m: v[-1] = np.where(np.equal(x, self.tau[-1]), 1, v[-1]) return v def gram(self, d=0): """ Compute Gram inner product matrix, storing it in lower triangular banded form. The (i,j) entry is G_ij = integral b_i^(d) b_j^(d) where b_i are the basis elements of the BSpline and (d) is the d-th derivative. If d is a matrix then, it is assumed to specify a differential operator as follows: the first row represents the order of derivative with the second row the coefficient corresponding to that order. For instance: [[2, 3], [3, 1]] represents 3 * f^(2) + 1 * f^(3). INPUTS: d -- which derivative to apply to each basis element, if d is a matrix, it is assumed to specify a differential operator as above OUTPUTS: gram gram -- the matrix of inner products of (derivatives) of the BSpline elements """ d = np.squeeze(d) if np.asarray(d).shape == (): self.g = _hbspline.gram(self.tau, self.m, int(d), int(d)) else: d = np.asarray(d) if d.shape[0] != 2: raise ValueError("if d is not an integer, expecting a jx2 \ array with first row indicating order \ of derivative, second row coefficient in front.") if d.shape == (2,): d.shape = (2,1) self.g = 0 for i in range(d.shape[1]): for j in range(d.shape[1]): self.g += d[1,i]* d[1,j] * _hbspline.gram(self.tau, self.m, int(d[0,i]), int(d[0,j])) self.g = self.g.T self.d = d return np.nan_to_num(self.g) class SmoothingSpline(BSpline): penmax = 30. method = "target_df" target_df = 5 default_pen = 1.0e-03 optimize = True ''' A smoothing spline, which can be used to smooth scatterplots, i.e. a list of (x,y) tuples. See fit method for more information. ''' def fit(self, y, x=None, weights=None, pen=0.): """ Fit the smoothing spline to a set of (x,y) pairs. INPUTS: y -- response variable x -- if None, uses self.x weights -- optional array of weights pen -- constant in front of Gram matrix OUTPUTS: None The smoothing spline is determined by self.coef, subsequent calls of __call__ will be the smoothing spline. ALGORITHM: Formally, this solves a minimization: fhat = ARGMIN_f SUM_i=1^n (y_i-f(x_i))^2 + pen * int f^(2)^2 int is integral. pen is lambda (from Hastie) See Chapter 5 of Hastie, Tibshirani and Friedman (2001). "The Elements of Statistical Learning." Springer-Verlag. 536 pages. for more details. TODO: Should add arbitrary derivative penalty instead of just second derivative. """ banded = True if x is None: x = self._x bt = self._basisx.copy() else: bt = self.basis(x) if pen == 0.: # cannot use cholesky for singular matrices banded = False if x.shape != y.shape: raise ValueError('x and y shape do not agree, by default x are \ the Bspline\'s internal knots') if pen >= self.penmax: pen = self.penmax if weights is not None: self.weights = weights else: self.weights = 1. _w = np.sqrt(self.weights) bt *= _w # throw out rows with zeros (this happens at boundary points!) mask = np.flatnonzero(1 - np.alltrue(np.equal(bt, 0), axis=0)) bt = bt[:,mask] y = y[mask] self.df_total = y.shape[0] bty = np.squeeze(np.dot(bt, _w * y)) self.N = y.shape[0] if not banded: self.btb = np.dot(bt, bt.T) _g = _band2array(self.g, lower=1, symmetric=True) self.coef, _, self.rank = L.lstsq(self.btb + pen*_g, bty)[0:3] self.rank = min(self.rank, self.btb.shape[0]) del(_g) else: self.btb = np.zeros(self.g.shape, np.float64) nband, nbasis = self.g.shape for i in range(nbasis): for k in range(min(nband, nbasis-i)): self.btb[k,i] = (bt[i] * bt[i+k]).sum() bty.shape = (1,bty.shape[0]) self.pen = pen self.chol, self.coef = solveh_banded(self.btb + pen*self.g, bty, lower=1) self.coef = np.squeeze(self.coef) self.resid = y * self.weights - np.dot(self.coef, bt) self.pen = pen del(bty) del(mask) del(bt) def smooth(self, y, x=None, weights=None): if self.method == "target_df": if hasattr(self, 'pen'): self.fit(y, x=x, weights=weights, pen=self.pen) else: self.fit_target_df(y, x=x, weights=weights, df=self.target_df) elif self.method == "optimize_gcv": self.fit_optimize_gcv(y, x=x, weights=weights) def gcv(self): """ Generalized cross-validation score of current fit. Craven, P. and Wahba, G. "Smoothing noisy data with spline functions. Estimating the correct degree of smoothing by the method of generalized cross-validation." Numerische Mathematik, 31(4), 377-403. """ norm_resid = (self.resid**2).sum() return norm_resid / (self.df_total - self.trace()) def df_resid(self): """ Residual degrees of freedom in the fit. self.N - self.trace() where self.N is the number of observations of last fit. """ return self.N - self.trace() def df_fit(self): """ How many degrees of freedom used in the fit? self.trace() """ return self.trace() def trace(self): """ Trace of the smoothing matrix S(pen) TODO: addin a reference to Wahba, and whoever else I used. """ if self.pen > 0: _invband = _hbspline.invband(self.chol.copy()) tr = _trace_symbanded(_invband, self.btb, lower=1) return tr else: return self.rank def fit_target_df(self, y, x=None, df=None, weights=None, tol=1.0e-03, apen=0, bpen=1.0e-03): """ Fit smoothing spline with approximately df degrees of freedom used in the fit, i.e. so that self.trace() is approximately df. Uses binary search strategy. In general, df must be greater than the dimension of the null space of the Gram inner product. For cubic smoothing splines, this means that df > 2. INPUTS: y -- response variable x -- if None, uses self.x df -- target degrees of freedom weights -- optional array of weights tol -- (relative) tolerance for convergence apen -- lower bound of penalty for binary search bpen -- upper bound of penalty for binary search OUTPUTS: None The smoothing spline is determined by self.coef, subsequent calls of __call__ will be the smoothing spline. """ df = df or self.target_df olddf = y.shape[0] - self.m if hasattr(self, "pen"): self.fit(y, x=x, weights=weights, pen=self.pen) curdf = self.trace() if np.fabs(curdf - df) / df < tol: return if curdf > df: apen, bpen = self.pen, 2 * self.pen else: apen, bpen = 0., self.pen while True: curpen = 0.5 * (apen + bpen) self.fit(y, x=x, weights=weights, pen=curpen) curdf = self.trace() if curdf > df: apen, bpen = curpen, 2 * curpen else: apen, bpen = apen, curpen if apen >= self.penmax: raise ValueError("penalty too large, try setting penmax \ higher or decreasing df") if np.fabs(curdf - df) / df < tol: break def fit_optimize_gcv(self, y, x=None, weights=None, tol=1.0e-03, brack=(-100,20)): """ Fit smoothing spline trying to optimize GCV. Try to find a bracketing interval for scipy.optimize.golden based on bracket. It is probably best to use target_df instead, as it is sometimes difficult to find a bracketing interval. INPUTS: y -- response variable x -- if None, uses self.x df -- target degrees of freedom weights -- optional array of weights tol -- (relative) tolerance for convergence brack -- an initial guess at the bracketing interval OUTPUTS: None The smoothing spline is determined by self.coef, subsequent calls of __call__ will be the smoothing spline. """ def _gcv(pen, y, x): self.fit(y, x=x, pen=np.exp(pen)) a = self.gcv() return a a = golden(_gcv, args=(y,x), brack=brack, tol=tol) statsmodels-0.12.2/statsmodels/sandbox/datarich/000077500000000000000000000000001400612667500217245ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/datarich/__init__.py000066400000000000000000000143241400612667500240410ustar00rootroot00000000000000''' Econometrics for a Datarich Environment ======================================= Introduction ------------ In many cases we are performing statistical analysis when many observed variables are available, when we are in a data rich environment. Machine learning has a wide variety of tools for dimension reduction and penalization when there are many varibles compared to the number of observation. Chemometrics has a long tradition of using Partial Least Squares, NIPALS and similar in these cases. In econometrics the same problem shows up when there are either many possible regressors, many (weak) instruments or when there are a large number of moment conditions in GMM. This section is intended to collect some models and tools in this area that are relevant for the statical analysis and econometrics. Covariance Matrices =================== Several methods are available to reduce the small sample noise in estimated covariance matrices with many variable. Some applications: weighting matrix with many moments, covariance matrix for portfolio choice Dimension Reduction =================== Principal Component and Partial Least Squares try to extract the important low dimensional factors from the data with many variables. Regression with many regressors =============================== Factor models, selection of regressors and shrinkage and penalization are used to improve the statistical properties, when the presence of too many regressors leads to over-fitting and too noisy small sample estimators and statistics. Regression with many moments or many instruments ================================================ The same tools apply and can be used in these two cases. e.g. Tychonov regularization of weighting matrix in GMM, similar to Ridge regression, the weighting matrix can be shrunk towards the identity matrix. Simplest case will be part of GMM. I do not know how much will be standalone functions. Intended Content ================ PLS --- what should be available in class? Factormodel and supporting helper functions ------------------------------------------- PCA based ~~~~~~~~~ First version based PCA on Stock/Watson and Bai/Ng, and recent papers on the selection of the number of factors. Not sure about Forni et al. in approach. Basic support of this needs additional results for PCA, error covariance matrix of data on reduced factors, required for criteria in Bai/Ng. Selection criteria based on eigenvalue cutoffs. Paper on PCA and structural breaks. Could add additional results during find_nfact to test for parameter stability. I have not read the paper yet. Idea: for forecasting, use up to h-step ahead endogenous variables to directly get the forecasts. Asymptotic results and distribution: not too much idea yet. Standard OLS results are conditional on factors, paper by Haerdle (abstract seems to suggest that this is ok, Park 2009). Simulation: add function to simulate DGP of Bai/Ng and recent extension. Sensitivity of selection criteria to heteroscedasticity and autocorrelation. Bai, J. & Ng, S., 2002. Determining the Number of Factors in Approximate Factor Models. Econometrica, 70(1), pp.191-221. Kapetanios, G., 2010. A Testing Procedure for Determining the Number of Factors in Approximate Factor Models With Large Datasets. Journal of Business and Economic Statistics, 28(3), pp.397-409. Onatski, A., 2010. Determining the Number of Factors from Empirical Distribution of Eigenvalues. Review of Economics and Statistics, 92(4), pp.1004-1016. Alessi, L., Barigozzi, M. & Capasso, M., 2010. Improved penalization for determining the number of factors in approximate factor models. Statistics & Probability Letters, 80(23-24), pp.1806-1813. Breitung, J. & Eickmeier, S., Testing for structural breaks in dynamic factor models. Journal of Econometrics, In Press, Accepted Manuscript. Available at: http://www.sciencedirect.com/science/article/B6VC0-51G3W92-1/2/f45ce2332443374fd770e42e5a68ddb4 [Accessed November 15, 2010]. Croux, C., Renault, E. & Werker, B., 2004. Dynamic factor models. Journal of Econometrics, 119(2), pp.223-230. Forni, M. et al., 2009. Opening the Black Box: Structural Factor Models with Large Cross Sections. Econometric Theory, 25(05), pp.1319-1347. Forni, M. et al., 2000. The Generalized Dynamic-Factor Model: Identification and Estimation. Review of Economics and Statistics, 82(4), pp.540-554. Forni, M. & Lippi, M., The general dynamic factor model: One-sided representation results. Journal of Econometrics, In Press, Accepted Manuscript. Available at: http://www.sciencedirect.com/science/article/B6VC0-51FNPJN-1/2/4fcdd0cfb66e3050ff5d19bf2752ed19 [Accessed November 15, 2010]. Kapetanios, G., 2010. A Testing Procedure for Determining the Number of Factors in Approximate Factor Models With Large Datasets. Journal of Business and Economic Statistics, 28(3), pp.397-409. Onatski, A., 2010. Determining the Number of Factors from Empirical Distribution of Eigenvalues. Review of Economics and Statistics, 92(4), pp.1004-1016. Park, B.U. et al., 2009. Time Series Modelling With Semiparametric Factor Dynamics. Journal of the American Statistical Association, 104(485), pp.284-298. other factor algorithm ~~~~~~~~~~~~~~~~~~~~~~ PLS should fit in reasonably well. Bai/Ng have a recent paper, where they compare LASSO, PCA, and similar, individual and in combination. Check how much we can use scikits.learn for this. miscellaneous ~~~~~~~~~~~~~ Time series modeling of factors for prediction, ARMA, VARMA. SUR and correlation structure What about sandwich estimation, robust covariance matrices? Similarity to Factor-Garch and Go-Garch Updating: incremental PCA, ...? TODO next ========= MVOLS : OLS with multivariate endogenous and identical exogenous variables. rewrite and expand current varma_process.VAR PCA : write a class after all, and/or adjust the current donated class and keep adding required statistics, e.g. residual variance, projection of X on k-factors, ... updating ? FactorModelUnivariate : started, does basic principal component regression, based on standard information criteria, not Bai/Ng adjusted FactorModelMultivariate : follow pattern for univariate version and use MVOLS ''' statsmodels-0.12.2/statsmodels/sandbox/datarich/factormodels.py000066400000000000000000000153161400612667500247660ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Nov 14 08:21:41 2010 Author: josef-pktd License: BSD (3-clause) """ import numpy as np import statsmodels.api as sm from statsmodels.sandbox.tools import pca from statsmodels.sandbox.tools.cross_val import LeaveOneOut #converting example Principal Component Regression to a class #from sandbox/example_pca_regression.py class FactorModelUnivariate(object): ''' Todo: check treatment of const, make it optional ? add hasconst (0 or 1), needed when selecting nfact+hasconst options are arguments in calc_factors, should be more public instead cross-validation is slow for large number of observations ''' def __init__(self, endog, exog): #do this in a superclass? self.endog = np.asarray(endog) self.exog = np.asarray(exog) def calc_factors(self, x=None, keepdim=0, addconst=True): '''get factor decomposition of exogenous variables This uses principal component analysis to obtain the factors. The number of factors kept is the maximum that will be considered in the regression. ''' if x is None: x = self.exog else: x = np.asarray(x) xred, fact, evals, evecs = pca(x, keepdim=keepdim, normalize=1) self.exog_reduced = xred #self.factors = fact if addconst: self.factors = sm.add_constant(fact, prepend=True) self.hasconst = 1 #needs to be int else: self.factors = fact self.hasconst = 0 #needs to be int self.evals = evals self.evecs = evecs def fit_fixed_nfact(self, nfact): if not hasattr(self, 'factors_wconst'): self.calc_factors() return sm.OLS(self.endog, self.factors[:,:nfact+1]).fit() def fit_find_nfact(self, maxfact=None, skip_crossval=True, cv_iter=None): '''estimate the model and selection criteria for up to maxfact factors The selection criteria that are calculated are AIC, BIC, and R2_adj. and additionally cross-validation prediction error sum of squares if `skip_crossval` is false. Cross-validation is not used by default because it can be time consuming to calculate. By default the cross-validation method is Leave-one-out on the full dataset. A different cross-validation sample can be specified as an argument to cv_iter. Results are attached in `results_find_nfact` ''' #print 'OLS on Factors' if not hasattr(self, 'factors'): self.calc_factors() hasconst = self.hasconst if maxfact is None: maxfact = self.factors.shape[1] - hasconst if (maxfact+hasconst) < 1: raise ValueError('nothing to do, number of factors (incl. constant) should ' + 'be at least 1') #temporary safety maxfact = min(maxfact, 10) y0 = self.endog results = [] #xred, fact, eva, eve = pca(x0, keepdim=0, normalize=1) for k in range(1, maxfact+hasconst): #k includes now the constnat #xred, fact, eva, eve = pca(x0, keepdim=k, normalize=1) # this is faster and same result fact = self.factors[:,:k] res = sm.OLS(y0, fact).fit() ## print 'k =', k ## print res.params ## print 'aic: ', res.aic ## print 'bic: ', res.bic ## print 'llf: ', res.llf ## print 'R2 ', res.rsquared ## print 'R2 adj', res.rsquared_adj if not skip_crossval: if cv_iter is None: cv_iter = LeaveOneOut(len(y0)) prederr2 = 0. for inidx, outidx in cv_iter: res_l1o = sm.OLS(y0[inidx], fact[inidx,:]).fit() #print data.endog[outidx], res.model.predict(data.exog[outidx,:]), prederr2 += (y0[outidx] - res_l1o.model.predict(res_l1o.params, fact[outidx,:]))**2. else: prederr2 = np.nan results.append([k, res.aic, res.bic, res.rsquared_adj, prederr2]) self.results_find_nfact = results = np.array(results) self.best_nfact = np.r_[(np.argmin(results[:,1:3],0), np.argmax(results[:,3],0), np.argmin(results[:,-1],0))] def summary_find_nfact(self): '''provides a summary for the selection of the number of factors Returns ------- sumstr : str summary of the results for selecting the number of factors ''' if not hasattr(self, 'results_find_nfact'): self.fit_find_nfact() results = self.results_find_nfact sumstr = '' sumstr += '\n' + 'Best result for k, by AIC, BIC, R2_adj, L1O' # best = np.r_[(np.argmin(results[:,1:3],0), np.argmax(results[:,3],0), # np.argmin(results[:,-1],0))] sumstr += '\n' + ' '*19 + '%5d %4d %6d %5d' % tuple(self.best_nfact) from statsmodels.iolib.table import SimpleTable headers = 'k, AIC, BIC, R2_adj, L1O'.split(', ') numformat = ['%6d'] + ['%10.3f']*4 #'%10.4f' txt_fmt1 = dict(data_fmts = numformat) tabl = SimpleTable(results, headers, None, txt_fmt=txt_fmt1) sumstr += '\n' + "PCA regression on simulated data," sumstr += '\n' + "DGP: 2 factors and 4 explanatory variables" sumstr += '\n' + tabl.__str__() sumstr += '\n' + "Notes: k is number of components of PCA," sumstr += '\n' + " constant is added additionally" sumstr += '\n' + " k=0 means regression on constant only" sumstr += '\n' + " L1O: sum of squared prediction errors for leave-one-out" return sumstr if __name__ == '__main__': examples = [1] if 1 in examples: nobs = 500 f0 = np.c_[np.random.normal(size=(nobs,2)), np.ones((nobs,1))] f2xcoef = np.c_[np.repeat(np.eye(2),2,0),np.arange(4)[::-1]].T f2xcoef = np.array([[ 1., 1., 0., 0.], [ 0., 0., 1., 1.], [ 3., 2., 1., 0.]]) f2xcoef = np.array([[ 0.1, 3., 1., 0.], [ 0., 0., 1.5, 0.1], [ 3., 2., 1., 0.]]) x0 = np.dot(f0, f2xcoef) x0 += 0.1*np.random.normal(size=x0.shape) ytrue = np.dot(f0,[1., 1., 1.]) y0 = ytrue + 0.1*np.random.normal(size=ytrue.shape) mod = FactorModelUnivariate(y0, x0) print(mod.summary_find_nfact()) print("with cross validation - slower") mod.fit_find_nfact(maxfact=None, skip_crossval=False, cv_iter=None) print(mod.summary_find_nfact()) statsmodels-0.12.2/statsmodels/sandbox/descstats.py000066400000000000000000000150701400612667500225170ustar00rootroot00000000000000''' Glue for returning descriptive statistics. ''' import numpy as np from scipy import stats import os from statsmodels.stats.descriptivestats import sign_test ############################################# # #============================================ # Univariate Descriptive Statistics #============================================ # def descstats(data, cols=None, axis=0): ''' Prints descriptive statistics for one or multiple variables. Parameters ---------- data: numpy array `x` is the data v: list, optional A list of the column number or field names (for a recarray) of variables. Default is all columns. axis: 1 or 0 axis order of data. Default is 0 for column-ordered data. Examples -------- >>> descstats(data.exog,v=['x_1','x_2','x_3']) ''' x = np.array(data) # or rather, the data we're interested in if isinstance(x, np.recarray): # deprecated: remove recarray support after 0.12 import warnings from statsmodels.tools.sm_exceptions import recarray_warning warnings.warn(recarray_warning, FutureWarning) if cols is None: # if isinstance(x, np.recarray): # cols = np.array(len(x.dtype.names)) if not isinstance(x, np.recarray) and x.ndim == 1: x = x[:,None] if x.shape[1] == 1: desc = ''' --------------------------------------------- Univariate Descriptive Statistics --------------------------------------------- Var. Name %(name)12s ---------- Obs. %(nobs)22i Range %(range)22s Sum of Wts. %(sum)22s Coeff. of Variation %(coeffvar)22.4g Mode %(mode)22.4g Skewness %(skewness)22.4g Repeats %(nmode)22i Kurtosis %(kurtosis)22.4g Mean %(mean)22.4g Uncorrected SS %(uss)22.4g Median %(median)22.4g Corrected SS %(ss)22.4g Variance %(variance)22.4g Sum Observations %(sobs)22.4g Std. Dev. %(stddev)22.4g ''' % {'name': cols, 'sum': 'N/A', 'nobs': len(x), 'mode': \ stats.mode(x)[0][0], 'nmode': stats.mode(x)[1][0], \ 'mean': x.mean(), 'median': np.median(x), 'range': \ '('+str(x.min())+', '+str(x.max())+')', 'variance': \ x.var(), 'stddev': x.std(), 'coeffvar': \ stats.variation(x), 'skewness': stats.skew(x), \ 'kurtosis': stats.kurtosis(x), 'uss': np.sum(x**2, axis=0),\ 'ss': np.sum((x-x.mean())**2, axis=0), 'sobs': np.sum(x)} desc+= ''' Percentiles ------------- 1 %% %12.4g 5 %% %12.4g 10 %% %12.4g 25 %% %12.4g 50 %% %12.4g 75 %% %12.4g 90 %% %12.4g 95 %% %12.4g 99 %% %12.4g ''' % tuple([stats.scoreatpercentile(x,per) for per in (1,5,10,25, 50,75,90,95,99)]) t,p_t=stats.ttest_1samp(x,0) M,p_M=sign_test(x) S,p_S=stats.wilcoxon(np.squeeze(x)) desc+= ''' Tests of Location (H0: Mu0=0) ----------------------------- Test Statistic Two-tailed probability -----------------+----------------------------------------- Student's t | t %7.5f Pr > |t| <%.4f Sign | M %8.2f Pr >= |M| <%.4f Signed Rank | S %8.2f Pr >= |S| <%.4f ''' % (t,p_t,M,p_M,S,p_S) # Should this be part of a 'descstats' # in any event these should be split up, so that they can be called # individually and only returned together if someone calls summary # or something of the sort elif x.shape[1] > 1: desc =''' Var. Name | Obs. Mean Std. Dev. Range ------------+--------------------------------------------------------'''+\ os.linesep # for recarrays with columns passed as names # if isinstance(cols[0],str): # for var in cols: # desc += "%(name)15s %(obs)9i %(mean)12.4g %(stddev)12.4g \ #%(range)20s" % {'name': var, 'obs': len(x[var]), 'mean': x[var].mean(), # 'stddev': x[var].std(), 'range': '('+str(x[var].min())+', '\ # +str(x[var].max())+')'+os.linesep} # else: for var in range(x.shape[1]): xv = x[:, var] kwargs = { 'name': var, 'obs': len(xv), 'mean': xv.mean(), 'stddev': xv.std(), 'range': '('+str(xv.min())+', '+str(xv.max())+')'+os.linesep } desc += ("%(name)15s %(obs)9i %(mean)12.4g %(stddev)12.4g " "%(range)20s" % kwargs) else: raise ValueError("data not understood") return desc #if __name__=='__main__': # test descstats # import os # loc='http://eagle1.american.edu/~js2796a/data/handguns_data.csv' # relpath=(load_dataset(loc)) # dta=np.recfromcsv(relpath) # descstats(dta,['stpop']) # raw_input('Hit enter for multivariate test') # descstats(dta,['stpop','avginc','vio']) # with plain arrays # import string2dummy as s2d # dts=s2d.string2dummy(dta) # ndts=np.vstack(dts[col] for col in dts.dtype.names) # observations in columns and data in rows # is easier for the call to stats # what to make of # ndts=np.column_stack(dts[col] for col in dts.dtype.names) # ntda=ntds.swapaxis(1,0) # ntda is ntds returns false? # or now we just have detailed information about the different strings # would this approach ever be inappropriate for a string typed variable # other than dates? # descstats(ndts, [1]) # raw_input("Enter to try second part") # descstats(ndts, [1,20,3]) if __name__ == '__main__': import statsmodels.api as sm data = sm.datasets.longley.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) sum1 = descstats(data.exog) sum1a = descstats(data.exog[:,:1]) # loc='http://eagle1.american.edu/~js2796a/data/handguns_data.csv' # dta=np.recfromcsv(loc) # summary2 = descstats(dta,['stpop']) # summary3 = descstats(dta,['stpop','avginc','vio']) #TODO: needs a by argument # summary4 = descstats(dta) this fails # this is a bug # p = dta[['stpop']] # p.view(dtype = np.float, type = np.ndarray) # this works # p.view(dtype = np.int, type = np.ndarray) ### This is *really* slow ### if os.path.isfile('./Econ724_PS_I_Data.csv'): data2 = np.recfromcsv('./Econ724_PS_I_Data.csv') sum2 = descstats(data2.ahe) sum3 = descstats(np.column_stack((data2.ahe,data2.yrseduc))) sum4 = descstats(np.column_stack(([data2[_] for \ _ in data2.dtype.names]))) statsmodels-0.12.2/statsmodels/sandbox/distributions/000077500000000000000000000000001400612667500230475ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/distributions/__init__.py000066400000000000000000000012301400612667500251540ustar00rootroot00000000000000'''temporary location for enhancements to scipy.stats includes ^^^^^^^^ * Per Brodtkorb's estimation enhancements to scipy.stats.distributions - distributions_per.py is copy of scipy.stats.distributions.py with changes - distributions_profile.py partially extracted classes and functions to separate code into more managable pieces * josef's extra distribution and helper functions - moment helpers - goodness of fit test - fitting distributions with some fixed parameters - find best distribution that fits data: working script * example and test folders to keep all together status ^^^^^^ mixed status : from not-working to well-tested ''' statsmodels-0.12.2/statsmodels/sandbox/distributions/copula.py000066400000000000000000000277211400612667500247150ustar00rootroot00000000000000''' Which Archimedean is Best? Extreme Value copulas formulas are based on Genest 2009 References ---------- Genest, C., 2009. Rank-based inference for bivariate extreme-value copulas. The Annals of Statistics, 37(5), pp.2990-3022. ''' import numpy as np from scipy.special import expm1 def copula_bv_indep(u,v): '''independent bivariate copula ''' return u*v def copula_bv_min(u,v): '''comonotonic bivariate copula ''' return np.minimum(u, v) def copula_bv_max(u, v): '''countermonotonic bivariate copula ''' return np.maximum(u + v - 1, 0) def copula_bv_clayton(u, v, theta): '''Clayton or Cook, Johnson bivariate copula ''' if not theta > 0: raise ValueError('theta needs to be strictly positive') return np.power(np.power(u, -theta) + np.power(v, -theta) - 1, -theta) def copula_bv_frank(u, v, theta): '''Cook, Johnson bivariate copula ''' if not theta > 0: raise ValueError('theta needs to be strictly positive') cdfv = -np.log(1 + expm1(-theta*u) * expm1(-theta*v) / expm1(-theta))/theta cdfv = np.minimum(cdfv, 1) #necessary for example if theta=100 return cdfv def copula_bv_gauss(u, v, rho): raise NotImplementedError def copula_bv_t(u, v, rho, df): raise NotImplementedError #Archimedean Copulas through generator functions #=============================================== #not used yet class Transforms(object): def __init__(self): pass class TransfFrank(object): def evaluate(self, t, theta): return - (np.log(-expm1(-theta*t)) - np.log(-expm1(-theta))) #return - np.log(expm1(-theta*t) / expm1(-theta)) def inverse(self, phi, theta): return -np.log1p(np.exp(-phi) * expm1(-theta)) / theta def deriv(self, t, theta): tmp = np.exp(-t*theta) return theta * tmp/(1 + tmp) def deriv2(self, t, theta): tmp1 = - t * theta tmp2 = (1. + np.exp(tmp1)) d2 = theta**2 * (-np.exp(tmp1) / tmp2 + np.exp(2*tmp1) / tmp2**2) return d2 def is_completly_monotonic(self, theta): #range of theta for which it is copula for d>2 (more than 2 rvs) return theta > 0 & theta < 1 class TransfClayton(object): def _checkargs(self, theta): return theta > 0 def evaluate(self, t, theta): return np.power(t, -theta) - 1. def inverse(self, phi, theta): return np.power(1 + phi, -theta) def deriv(self, t, theta): return -theta * np.power(t, -theta-1) def deriv2(self, t, theta): return theta * (theta + 1) * np.power(t, -theta-2) def is_completly_monotonic(self, theta): return theta > 0 class TransfGumbel(object): ''' requires theta >=1 ''' def _checkargs(self, theta): return theta >= 1 def evaluate(self, t, theta): return np.power(-np.log(t), theta) def inverse(self, phi, theta): return np.exp(-np.power(phi, 1. / theta)) def deriv(self, t, theta): return - theta * (-np.log(t))**(theta - 1) / t def deriv2(self, t, theta): tmp1 = np.log(t) d2 = (theta*(-1)**(1 + theta) * tmp1**(theta-1) * (1 - theta) + theta*(-1)**(1 + theta)*tmp1**theta)/(t**2*tmp1) #d2 = (theta * tmp1**(-1 + theta) * (1 - theta) + theta * tmp1**theta # ) / (t**2 * tmp1) return d2 def is_completly_monotonic(self, theta): return theta > 1 class TransfIndep(object): def evaluate(self, t): return -np.log(t) def inverse(self, phi): return np.exp(-phi) def deriv(self, t): return - 1./t def deriv2(self, t): return - 1./t**2 def copula_bv_archimedean(u, v, transform, args=()): ''' ''' phi = transform.evaluate phi_inv = transform.inverse cdfv = phi_inv(phi(u, *args) + phi(v, *args), *args) return cdfv def copula_mv_archimedean(u, transform, args=(), axis=-1): '''generic multivariate Archimedean copula ''' phi = transform.evaluate phi_inv = transform.inverse cdfv = phi_inv(phi(u, *args).sum(axis), *args) return cdfv def copula_power_mv_archimedean(u, transform, alpha, beta, args=(), axis=-1): '''generic multivariate Archimedean copula with additional power transforms Nelson p.144, equ. 4.5.2 ''' def phi(u, alpha, beta, args=()): return np.power(transform.evaluate(np.power(u, alpha), *args), beta) def phi_inv(t, alpha, beta, args=()): return np.power(transform.evaluate(np.power(t, 1./beta), *args), 1./alpha) cdfv = phi_inv(phi(u, *args).sum(axis), *args) return cdfv class CopulaArchimedean(object): def __init__(self, transform): self.transform = transform def cdf(self, u, args=(), axis=-1): '''evaluate cdf of multivariate Archimedean copula ''' phi = self.transform.evaluate phi_inv = self.transform.inverse cdfv = phi_inv(phi(u, *args).sum(axis), *args) return cdfv def pdf(self, u, args=(), axis=-1): '''evaluate cdf of multivariate Archimedean copula ''' phi = self.transform.evaluate phi_inv = self.transform.inverse phi_d1 = self.transform.deriv phi_d2 = self.transform.deriv2 cdfv = self.cdf(u, args=args, axis=axis) pdfv = - np.product(phi_d1(u, *args), axis) pdfv *= phi_d2(cdfv, *args) pdfv /= phi_d1(cdfv, *args)**3 return pdfv #Extreme Value Copulas #===================== def copula_bv_ev(u, v, transform, args=()): '''generic bivariate extreme value copula ''' return np.exp(np.log(u * v) * (transform(np.log(v)/np.log(u*v), *args))) def transform_tawn(t, a1, a2, theta): '''asymmetric logistic model of Tawn 1988 special case: a1=a2=1 : Gumbel restrictions: - theta in (0,1] - a1, a2 in [0,1] ''' def _check_args(a1, a2, theta): condth = (theta > 0) and (theta <= 1) conda1 = (a1 >= 0) and (a1 <= 1) conda2 = (a2 >= 0) and (a2 <= 1) return condth and conda1 and conda2 if not np.all(_check_args(a1, a2, theta)): raise ValueError('invalid args') transf = (1 - a1) * (1-t) transf += (1 - a2) * t transf += ((a1 * t)**(1./theta) + (a2 * (1-t))**(1./theta))**theta return transf def transform_joe(t, a1, a2, theta): '''asymmetric negative logistic model of Joe 1990 special case: a1=a2=1 : symmetric negative logistic of Galambos 1978 restrictions: - theta in (0,inf) - a1, a2 in (0,1] ''' def _check_args(a1, a2, theta): condth = (theta > 0) conda1 = (a1 > 0) and (a1 <= 1) conda2 = (a2 > 0) and (a2 <= 1) return condth and conda1 and conda2 if not np.all(_check_args(a1, a2, theta)): raise ValueError('invalid args') transf = 1 - ((a1 * (1-t))**(-1./theta) + (a2 * t)**(-1./theta))**(-theta) return transf def transform_tawn2(t, theta, k): '''asymmetric mixed model of Tawn 1988 special case: k=0, theta in [0,1] : symmetric mixed model of Tiago de Oliveira 1980 restrictions: - theta > 0 - theta + 3*k > 0 - theta + k <= 1 - theta + 2*k <= 1 ''' def _check_args(theta, k): condth = (theta >= 0) cond1 = (theta + 3*k > 0) and (theta + k <= 1) and (theta + 2*k <= 1) return condth and cond1 if not np.all(_check_args(theta, k)): raise ValueError('invalid args') transf = 1 - (theta + k) * t + theta * t*t + k * t**3 return transf def transform_bilogistic(t, beta, delta): '''bilogistic model of Coles and Tawn 1994, Joe, Smith and Weissman 1992 restrictions: - (beta, delta) in (0,1)^2 or - (beta, delta) in (-inf,0)^2 not vectorized because of numerical integration ''' def _check_args(beta, delta): cond1 = (beta > 0) and (beta <= 1) and (delta > 0) and (delta <= 1) cond2 = (beta < 0) and (delta < 0) return cond1 | cond2 if not np.all(_check_args(beta, delta)): raise ValueError('invalid args') def _integrant(w): term1 = (1 - beta) * np.power(w, -beta) * (1-t) term2 = (1 - delta) * np.power(1-w, -delta) * t np.maximum(term1, term2) from scipy.integrate import quad transf = quad(_integrant, 0, 1) return transf def transform_hr(t, lamda): '''model of Huesler Reiss 1989 special case: a1=a2=1 : symmetric negative logistic of Galambos 1978 restrictions: - lambda in (0,inf) ''' def _check_args(lamda): cond = (lamda > 0) return cond if not np.all(_check_args(lamda)): raise ValueError('invalid args') term = np.log((1. - t) / t) * 0.5 / lamda from scipy.stats import norm #use special if I want to avoid stats import transf = (1 - t) * norm._cdf(lamda + term) + t * norm._cdf(lamda - term) return transf def transform_tev(t, rho, x): '''t-EV model of Demarta and McNeil 2005 restrictions: - rho in (-1,1) - x > 0 ''' def _check_args(rho, x): cond1 = (x > 0) cond2 = (rho > 0) and (rho < 1) return cond1 and cond2 if not np.all(_check_args(rho, x)): raise ValueError('invalid args') from scipy.stats import t as stats_t #use special if I want to avoid stats import z = np.sqrt(1. + x) * (np.power(t/(1.-t), 1./x) - rho) z /= np.sqrt(1 - rho*rho) transf = (1 - t) * stats_t._cdf(z, x+1) + t * stats_t._cdf(z, x+1) return transf #========================================================================== #define dictionary of copulas by names and aliases copulanamesbv = {'indep' : copula_bv_indep, 'i' : copula_bv_indep, 'min' : copula_bv_min, 'max' : copula_bv_max, 'clayton' : copula_bv_clayton, 'cookjohnson' : copula_bv_clayton, 'cj' : copula_bv_clayton, 'frank' : copula_bv_frank, 'gauss' : copula_bv_gauss, 'normal' : copula_bv_gauss, 't' : copula_bv_t} class CopulaDistributionBivariate(object): '''bivariate copula class Instantiation needs the arguments, cop_args, that are required for copula ''' def __init__(self, marginalcdfs, copula, copargs=()): if copula in copulanamesbv: self.copula = copulanamesbv[copula] else: #see if we can call it as a copula function try: tmp = copula(0.5, 0.5, *copargs) except: #blanket since we throw again raise ValueError('copula needs to be a copula name or callable') self.copula = copula #no checking done on marginals self.marginalcdfs = marginalcdfs self.copargs = copargs def cdf(self, xy, args=None): '''xx needs to be iterable, instead of x,y for extension to multivariate ''' x, y = xy if args is None: args = self.copargs return self.copula(self.marginalcdfs[0](x), self.marginalcdfs[1](y), *args) class CopulaDistribution(object): '''bivariate copula class Instantiation needs the arguments, cop_args, that are required for copula ''' def __init__(self, marginalcdfs, copula, copargs=()): if copula in copulanamesbv: self.copula = copulanamesbv[copula] else: #see if we can call it as a copula function try: tmp = copula(0.5, 0.5, *copargs) except: #blanket since we throw again raise ValueError('copula needs to be a copula name or callable') self.copula = copula #no checking done on marginals self.marginalcdfs = marginalcdfs self.copargs = copargs def cdf(self, xy, args=None): '''xx needs to be iterable, instead of x,y for extension to multivariate ''' x, y = xy if args is None: args = self.copargs return self.copula(self.marginalcdfs[0](x), self.marginalcdfs[1](y), *args) statsmodels-0.12.2/statsmodels/sandbox/distributions/estimators.py000066400000000000000000000555711400612667500256300ustar00rootroot00000000000000'''estimate distribution parameters by various methods method of moments or matching quantiles, and Maximum Likelihood estimation based on binned data and Maximum Product-of-Spacings Warning: I'm still finding cut-and-paste and refactoring errors, e.g. hardcoded variables from outer scope in functions some results do not seem to make sense for Pareto case, looks better now after correcting some name errors initially loosely based on a paper and blog for quantile matching by John D. Cook formula for gamma quantile (ppf) matching by him (from paper) http://www.codeproject.com/KB/recipes/ParameterPercentile.aspx http://www.johndcook.com/blog/2010/01/31/parameters-from-percentiles/ this is what I actually used (in parts): http://www.bepress.com/mdandersonbiostat/paper55/ quantile based estimator ^^^^^^^^^^^^^^^^^^^^^^^^ only special cases for number or parameters so far Is there a literature for GMM estimation of distribution parameters? check found one: Wu/Perloff 2007 binned estimator ^^^^^^^^^^^^^^^^ * I added this also * use it for chisquare tests with estimation distribution parameters * move this to distribution_extras (next to gof tests powerdiscrepancy and continuous) or add to distribution_patch example: t-distribution * works with quantiles if they contain tail quantiles * results with momentcondquant do not look as good as mle estimate TODOs * rearange and make sure I do not use module globals (as I did initially) DONE make two version exactly identified method of moments with fsolve and GMM (?) version with fmin and maybe the special cases of JD Cook update: maybe exact (MM) version is not so interesting compared to GMM * add semifrozen version of moment and quantile based estimators, e.g. for beta (both loc and scale fixed), or gamma (loc fixed) * add beta example to the semifrozen MLE, fitfr, code -> added method of moment estimator to _fitstart for beta * start a list of how well different estimators, especially current mle work for the different distributions * need general GMM code (with optimal weights ?), looks like a good example for it * get example for binned data estimation, mailing list a while ago * any idea when these are better than mle ? * check language: I use quantile to mean the value of the random variable, not quantile between 0 and 1. * for GMM: move moment conditions to separate function, so that they can be used for further analysis, e.g. covariance matrix of parameter estimates * question: Are GMM properties different for matching quantiles with cdf or ppf? Estimate should be the same, but derivatives of moment conditions differ. * add maximum spacings estimator, Wikipedia, Per Brodtkorb -> basic version Done * add parameter estimation based on empirical characteristic function (Carrasco/Florens), especially for stable distribution * provide a model class based on estimating all distributions, and collect all distribution specific information References ---------- Ximing Wu, Jeffrey M. Perloff, GMM estimation of a maximum entropy distribution with interval data, Journal of Econometrics, Volume 138, Issue 2, 'Information and Entropy Econometrics' - A Volume in Honor of Arnold Zellner, June 2007, Pages 532-546, ISSN 0304-4076, DOI: 10.1016/j.jeconom.2006.05.008. http://www.sciencedirect.com/science/article/B6VC0-4K606TK-4/2/78bc07c6245546374490f777a6bdbbcc http://escholarship.org/uc/item/7jf5w1ht (working paper) Johnson, Kotz, Balakrishnan: Volume 2 Author : josef-pktd License : BSD created : 2010-04-20 changes: added Maximum Product-of-Spacings 2010-05-12 ''' import numpy as np from scipy import stats, optimize, special cache = {} #module global storage for temp results, not used # the next two use distfn from module scope - not anymore def gammamomentcond(distfn, params, mom2, quantile=None): '''estimate distribution parameters based method of moments (mean, variance) for distributions with 1 shape parameter and fixed loc=0. Returns ------- cond : function Notes ----- first test version, quantile argument not used ''' def cond(params): alpha, scale = params mom2s = distfn.stats(alpha, 0.,scale) #quantil return np.array(mom2)-mom2s return cond def gammamomentcond2(distfn, params, mom2, quantile=None): '''estimate distribution parameters based method of moments (mean, variance) for distributions with 1 shape parameter and fixed loc=0. Returns ------- difference : ndarray difference between theoretical and empirical moments Notes ----- first test version, quantile argument not used The only difference to previous function is return type. ''' alpha, scale = params mom2s = distfn.stats(alpha, 0.,scale) return np.array(mom2)-mom2s ######### fsolve does not move in small samples, fmin not very accurate def momentcondunbound(distfn, params, mom2, quantile=None): '''moment conditions for estimating distribution parameters using method of moments, uses mean, variance and one quantile for distributions with 1 shape parameter. Returns ------- difference : ndarray difference between theoretical and empirical moments and quantiles ''' shape, loc, scale = params mom2diff = np.array(distfn.stats(shape, loc,scale)) - mom2 if quantile is not None: pq, xq = quantile #ppfdiff = distfn.ppf(pq, alpha) cdfdiff = distfn.cdf(xq, shape, loc, scale) - pq return np.concatenate([mom2diff, cdfdiff[:1]]) return mom2diff ###### loc scale only def momentcondunboundls(distfn, params, mom2, quantile=None, shape=None): '''moment conditions for estimating loc and scale of a distribution with method of moments using either 2 quantiles or 2 moments (not both). Returns ------- difference : ndarray difference between theoretical and empirical moments or quantiles ''' loc, scale = params mom2diff = np.array(distfn.stats(shape, loc, scale)) - mom2 if quantile is not None: pq, xq = quantile #ppfdiff = distfn.ppf(pq, alpha) cdfdiff = distfn.cdf(xq, shape, loc, scale) - pq #return np.concatenate([mom2diff, cdfdiff[:1]]) return cdfdiff return mom2diff ######### try quantile GMM with identity weight matrix #(just a guess that's what it is def momentcondquant(distfn, params, mom2, quantile=None, shape=None): '''moment conditions for estimating distribution parameters by matching quantiles, defines as many moment conditions as quantiles. Returns ------- difference : ndarray difference between theoretical and empirical quantiles Notes ----- This can be used for method of moments or for generalized method of moments. ''' #this check looks redundant/unused know if len(params) == 2: loc, scale = params elif len(params) == 3: shape, loc, scale = params else: #raise NotImplementedError pass #see whether this might work, seems to work for beta with 2 shape args #mom2diff = np.array(distfn.stats(*params)) - mom2 #if not quantile is None: pq, xq = quantile #ppfdiff = distfn.ppf(pq, alpha) cdfdiff = distfn.cdf(xq, *params) - pq #return np.concatenate([mom2diff, cdfdiff[:1]]) return cdfdiff #return mom2diff def fitquantilesgmm(distfn, x, start=None, pquant=None, frozen=None): if pquant is None: pquant = np.array([0.01, 0.05,0.1,0.4,0.6,0.9,0.95,0.99]) if start is None: if hasattr(distfn, '_fitstart'): start = distfn._fitstart(x) else: start = [1]*distfn.numargs + [0.,1.] #TODO: vectorize this: xqs = [stats.scoreatpercentile(x, p) for p in pquant*100] mom2s = None parest = optimize.fmin(lambda params:np.sum( momentcondquant(distfn, params, mom2s,(pquant,xqs), shape=None)**2), start) return parest def fitbinned(distfn, freq, binedges, start, fixed=None): '''estimate parameters of distribution function for binned data using MLE Parameters ---------- distfn : distribution instance needs to have cdf method, as in scipy.stats freq : ndarray, 1d frequency count, e.g. obtained by histogram binedges : ndarray, 1d binedges including lower and upper bound start : tuple or array_like ? starting values, needs to have correct length Returns ------- paramest : ndarray estimated parameters Notes ----- todo: add fixed parameter option added factorial ''' if fixed is not None: raise NotImplementedError nobs = np.sum(freq) lnnobsfact = special.gammaln(nobs+1) def nloglike(params): '''negative loglikelihood function of binned data corresponds to multinomial ''' prob = np.diff(distfn.cdf(binedges, *params)) return -(lnnobsfact + np.sum(freq*np.log(prob)- special.gammaln(freq+1))) return optimize.fmin(nloglike, start) def fitbinnedgmm(distfn, freq, binedges, start, fixed=None, weightsoptimal=True): '''estimate parameters of distribution function for binned data using GMM Parameters ---------- distfn : distribution instance needs to have cdf method, as in scipy.stats freq : ndarray, 1d frequency count, e.g. obtained by histogram binedges : ndarray, 1d binedges including lower and upper bound start : tuple or array_like ? starting values, needs to have correct length fixed : None not used yet weightsoptimal : bool If true, then the optimal weighting matrix for GMM is used. If false, then the identity matrix is used Returns ------- paramest : ndarray estimated parameters Notes ----- todo: add fixed parameter option added factorial ''' if fixed is not None: raise NotImplementedError nobs = np.sum(freq) if weightsoptimal: weights = freq/float(nobs) else: weights = np.ones(len(freq)) freqnormed = freq/float(nobs) # skip turning weights into matrix diag(freq/float(nobs)) def gmmobjective(params): '''negative loglikelihood function of binned data corresponds to multinomial ''' prob = np.diff(distfn.cdf(binedges, *params)) momcond = freqnormed - prob return np.dot(momcond*weights, momcond) return optimize.fmin(gmmobjective, start) #Addition from try_maxproductspacings: """Estimating Parameters of Log-Normal Distribution with Maximum Likelihood and Maximum Product-of-Spacings MPS definiton from JKB page 233 Created on Tue May 11 13:52:50 2010 Author: josef-pktd License: BSD """ def hess_ndt(fun, pars, args, options): import numdifftools as ndt if not ('stepMax' in options or 'stepFix' in options): options['stepMax'] = 1e-5 f = lambda params: fun(params, *args) h = ndt.Hessian(f, **options) return h(pars), h def logmps(params, xsorted, dist): '''calculate negative log of Product-of-Spacings Parameters ---------- params : array_like, tuple ? parameters of the distribution funciton xsorted : array_like data that is already sorted dist : instance of a distribution class only cdf method is used Returns ------- mps : float negative log of Product-of-Spacings Notes ----- MPS definiton from JKB page 233 ''' xcdf = np.r_[0., dist.cdf(xsorted, *params), 1.] D = np.diff(xcdf) return -np.log(D).mean() def getstartparams(dist, data): '''get starting values for estimation of distribution parameters Parameters ---------- dist : distribution instance the distribution instance needs to have either a method fitstart or an attribute numargs data : ndarray data for which preliminary estimator or starting value for parameter estimation is desired Returns ------- x0 : ndarray preliminary estimate or starting value for the parameters of the distribution given the data, including loc and scale ''' if hasattr(dist, 'fitstart'): #x0 = getattr(dist, 'fitstart')(data) x0 = dist.fitstart(data) else: if np.isfinite(dist.a): x0 = np.r_[[1.]*dist.numargs, (data.min()-1), 1.] else: x0 = np.r_[[1.]*dist.numargs, (data.mean()-1), 1.] return x0 def fit_mps(dist, data, x0=None): '''Estimate distribution parameters with Maximum Product-of-Spacings Parameters ---------- params : array_like, tuple ? parameters of the distribution funciton xsorted : array_like data that is already sorted dist : instance of a distribution class only cdf method is used Returns ------- x : ndarray estimates for the parameters of the distribution given the data, including loc and scale ''' xsorted = np.sort(data) if x0 is None: x0 = getstartparams(dist, xsorted) args = (xsorted, dist) print(x0) #print(args) return optimize.fmin(logmps, x0, args=args) if __name__ == '__main__': #Example: gamma - distribution #----------------------------- print('\n\nExample: gamma Distribution') print( '---------------------------') alpha = 2 xq = [0.5, 4] pq = [0.1, 0.9] print(stats.gamma.ppf(pq, alpha)) xq = stats.gamma.ppf(pq, alpha) print(np.diff((stats.gamma.ppf(pq, np.linspace(0.01,4,10)[:,None])*xq[::-1]))) #optimize.bisect(lambda alpha: np.diff((stats.gamma.ppf(pq, alpha)*xq[::-1]))) print(optimize.fsolve(lambda alpha: np.diff((stats.gamma.ppf(pq, alpha)*xq[::-1])), 3.)) distfn = stats.gamma mcond = gammamomentcond(distfn, [5.,10], mom2=stats.gamma.stats(alpha, 0.,1.), quantile=None) print(optimize.fsolve(mcond, [1.,2.])) mom2 = stats.gamma.stats(alpha, 0.,1.) print(optimize.fsolve(lambda params:gammamomentcond2(distfn, params, mom2), [1.,2.])) grvs = stats.gamma.rvs(alpha, 0.,2., size=1000) mom2 = np.array([grvs.mean(), grvs.var()]) alphaestq = optimize.fsolve(lambda params:gammamomentcond2(distfn, params, mom2), [1.,3.]) print(alphaestq) print('scale = ', xq/stats.gamma.ppf(pq, alphaestq)) #Example beta - distribution #--------------------------- #Warning: this example had cut-and-paste errors print('\n\nExample: beta Distribution') print( '--------------------------') #monkey patching : ## if hasattr(stats.beta, '_fitstart'): ## del stats.beta._fitstart #bug in _fitstart #raises AttributeError: _fitstart #stats.distributions.beta_gen._fitstart = lambda self, data : np.array([1,1,0,1]) #_fitstart seems to require a tuple stats.distributions.beta_gen._fitstart = lambda self, data : (5,5,0,1) pq = np.array([0.01, 0.05,0.1,0.4,0.6,0.9,0.95,0.99]) #rvsb = stats.beta.rvs(0.5,0.15,size=200) rvsb = stats.beta.rvs(10,15,size=2000) print('true params', 10, 15, 0, 1) print(stats.beta.fit(rvsb)) xqsb = [stats.scoreatpercentile(rvsb, p) for p in pq*100] mom2s = np.array([rvsb.mean(), rvsb.var()]) betaparest_gmmquantile = optimize.fmin(lambda params:np.sum(momentcondquant(stats.beta, params, mom2s,(pq,xqsb), shape=None)**2), [10,10, 0., 1.], maxiter=2000) print('betaparest_gmmquantile', betaparest_gmmquantile) #result sensitive to initial condition #Example t - distribution #------------------------ print('\n\nExample: t Distribution') print( '-----------------------') nobs = 1000 distfn = stats.t pq = np.array([0.1,0.9]) paramsdgp = (5, 0, 1) trvs = distfn.rvs(5, 0, 1, size=nobs) xqs = [stats.scoreatpercentile(trvs, p) for p in pq*100] mom2th = distfn.stats(*paramsdgp) mom2s = np.array([trvs.mean(), trvs.var()]) tparest_gmm3quantilefsolve = optimize.fsolve(lambda params:momentcondunbound(distfn,params, mom2s,(pq,xqs)), [10,1.,2.]) print('tparest_gmm3quantilefsolve', tparest_gmm3quantilefsolve) tparest_gmm3quantile = optimize.fmin(lambda params:np.sum(momentcondunbound(distfn,params, mom2s,(pq,xqs))**2), [10,1.,2.]) print('tparest_gmm3quantile', tparest_gmm3quantile) print(distfn.fit(trvs)) ## ##distfn = stats.t ##pq = np.array([0.1,0.9]) ##paramsdgp = (5, 0, 1) ##trvs = distfn.rvs(5, 0, 1, size=nobs) ##xqs = [stats.scoreatpercentile(trvs, p) for p in pq*100] ##mom2th = distfn.stats(*paramsdgp) ##mom2s = np.array([trvs.mean(), trvs.var()]) print(optimize.fsolve(lambda params:momentcondunboundls(distfn, params, mom2s,shape=5), [1.,2.])) print(optimize.fmin(lambda params:np.sum(momentcondunboundls(distfn, params, mom2s,shape=5)**2), [1.,2.])) print(distfn.fit(trvs)) #loc, scale, based on quantiles print(optimize.fsolve(lambda params:momentcondunboundls(distfn, params, mom2s,(pq,xqs),shape=5), [1.,2.])) ## pq = np.array([0.01, 0.05,0.1,0.4,0.6,0.9,0.95,0.99]) #paramsdgp = (5, 0, 1) xqs = [stats.scoreatpercentile(trvs, p) for p in pq*100] tparest_gmmquantile = optimize.fmin(lambda params:np.sum(momentcondquant(distfn, params, mom2s,(pq,xqs), shape=None)**2), [10, 1.,2.]) print('tparest_gmmquantile', tparest_gmmquantile) tparest_gmmquantile2 = fitquantilesgmm(distfn, trvs, start=[10, 1.,2.], pquant=None, frozen=None) print('tparest_gmmquantile2', tparest_gmmquantile2) ## #use trvs from before bt = stats.t.ppf(np.linspace(0,1,21),5) ft,bt = np.histogram(trvs,bins=bt) print('fitbinned t-distribution') tparest_mlebinew = fitbinned(stats.t, ft, bt, [10, 0, 1]) tparest_gmmbinewidentity = fitbinnedgmm(stats.t, ft, bt, [10, 0, 1]) tparest_gmmbinewoptimal = fitbinnedgmm(stats.t, ft, bt, [10, 0, 1], weightsoptimal=False) print(paramsdgp) #Note: this can be used for chisquare test and then has correct asymptotic # distribution for a distribution with estimated parameters, find ref again #TODO combine into test with binning included, check rule for number of bins #bt2 = stats.t.ppf(np.linspace(trvs.,1,21),5) ft2,bt2 = np.histogram(trvs,bins=50) 'fitbinned t-distribution' tparest_mlebinel = fitbinned(stats.t, ft2, bt2, [10, 0, 1]) tparest_gmmbinelidentity = fitbinnedgmm(stats.t, ft2, bt2, [10, 0, 1]) tparest_gmmbineloptimal = fitbinnedgmm(stats.t, ft2, bt2, [10, 0, 1], weightsoptimal=False) tparest_mle = stats.t.fit(trvs) np.set_printoptions(precision=6) print('sample size', nobs) print('true (df, loc, scale) ', paramsdgp) print('parest_mle ', tparest_mle) print print('tparest_mlebinel ', tparest_mlebinel) print('tparest_gmmbinelidentity ', tparest_gmmbinelidentity) print('tparest_gmmbineloptimal ', tparest_gmmbineloptimal) print print('tparest_mlebinew ', tparest_mlebinew) print('tparest_gmmbinewidentity ', tparest_gmmbinewidentity) print('tparest_gmmbinewoptimal ', tparest_gmmbinewoptimal) print print('tparest_gmmquantileidentity', tparest_gmmquantile) print('tparest_gmm3quantilefsolve ', tparest_gmm3quantilefsolve) print('tparest_gmm3quantile ', tparest_gmm3quantile) ''' example results: standard error for df estimate looks large note: iI do not impose that df is an integer, (b/c not necessary) need Monte Carlo to check variance of estimators sample size 1000 true (df, loc, scale) (5, 0, 1) parest_mle [ 4.571405 -0.021493 1.028584] tparest_mlebinel [ 4.534069 -0.022605 1.02962 ] tparest_gmmbinelidentity [ 2.653056 0.012807 0.896958] tparest_gmmbineloptimal [ 2.437261 -0.020491 0.923308] tparest_mlebinew [ 2.999124 -0.0199 0.948811] tparest_gmmbinewidentity [ 2.900939 -0.020159 0.93481 ] tparest_gmmbinewoptimal [ 2.977764 -0.024925 0.946487] tparest_gmmquantileidentity [ 3.940797 -0.046469 1.002001] tparest_gmm3quantilefsolve [ 10. 1. 2.] tparest_gmm3quantile [ 6.376101 -0.029322 1.112403] ''' #Example with Maximum Product of Spacings Estimation #=================================================== #Example: Lognormal Distribution #------------------------------- #tough problem for MLE according to JKB #but not sure for which parameters print('\n\nExample: Lognormal Distribution') print( '-------------------------------') sh = np.exp(10) sh = 0.01 print(sh) x = stats.lognorm.rvs(sh,loc=100, scale=10,size=200) print(x.min()) print(stats.lognorm.fit(x, 1.,loc=x.min()-1,scale=1)) xsorted = np.sort(x) x0 = [1., x.min()-1, 1] args = (xsorted, stats.lognorm) print(optimize.fmin(logmps,x0,args=args)) #Example: Lomax, Pareto, Generalized Pareto Distributions #-------------------------------------------------------- #partially a follow-up to the discussion about numpy.random.pareto #Reference: JKB #example Maximum Product of Spacings Estimation # current results: # does not look very good yet sensitivity to starting values # Pareto and Generalized Pareto look like a tough estimation problemprint('\n\nExample: Lognormal Distribution' print('\n\nExample: Lomax, Pareto, Generalized Pareto Distributions') print( '--------------------------------------------------------') p2rvs = stats.genpareto.rvs(2, size=500) #Note: is Lomax without +1; and classical Pareto with +1 p2rvssorted = np.sort(p2rvs) argsp = (p2rvssorted, stats.pareto) x0p = [1., p2rvs.min()-5, 1] print(optimize.fmin(logmps,x0p,args=argsp)) print(stats.pareto.fit(p2rvs, 0.5, loc=-20, scale=0.5)) print('gpdparest_ mle', stats.genpareto.fit(p2rvs)) parsgpd = fit_mps(stats.genpareto, p2rvs) print('gpdparest_ mps', parsgpd) argsgpd = (p2rvssorted, stats.genpareto) options = dict(stepFix=1e-7) #hess_ndt(fun, pars, argsgdp, options) #the results for the following look strange, maybe refactoring error he, h = hess_ndt(logmps, parsgpd, argsgpd, options) print(np.linalg.eigh(he)[0]) f = lambda params: logmps(params, *argsgpd) print(f(parsgpd)) #add binned fp2, bp2 = np.histogram(p2rvs, bins=50) 'fitbinned t-distribution' gpdparest_mlebinel = fitbinned(stats.genpareto, fp2, bp2, x0p) gpdparest_gmmbinelidentity = fitbinnedgmm(stats.genpareto, fp2, bp2, x0p) print('gpdparest_mlebinel', gpdparest_mlebinel) print('gpdparest_gmmbinelidentity', gpdparest_gmmbinelidentity) gpdparest_gmmquantile2 = fitquantilesgmm( stats.genpareto, p2rvs, start=x0p, pquant=None, frozen=None) print('gpdparest_gmmquantile2', gpdparest_gmmquantile2) print(fitquantilesgmm(stats.genpareto, p2rvs, start=x0p, pquant=np.linspace(0.01,0.99,10), frozen=None)) fp2, bp2 = np.histogram( p2rvs, bins=stats.genpareto(2).ppf(np.linspace(0,0.99,10))) print('fitbinnedgmm equal weight bins') print(fitbinnedgmm(stats.genpareto, fp2, bp2, x0p)) statsmodels-0.12.2/statsmodels/sandbox/distributions/examples/000077500000000000000000000000001400612667500246655ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/distributions/examples/__init__.py000066400000000000000000000000021400612667500267660ustar00rootroot00000000000000# statsmodels-0.12.2/statsmodels/sandbox/distributions/examples/ex_extras.py000066400000000000000000000077171400612667500272550ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Feb 19 12:39:49 2014 Author: Josef Perktold """ import numpy as np from scipy import stats from statsmodels.sandbox.distributions.extras import (SkewNorm_gen, skewnorm, ACSkewT_gen, NormExpan_gen, pdf_moments, ExpTransf_gen, LogTransf_gen) from statsmodels.stats.moment_helpers import mc2mvsk, mnc2mc, mvsk2mnc def example_n(): print(skewnorm.pdf(1,0), stats.norm.pdf(1), skewnorm.pdf(1,0) - stats.norm.pdf(1)) print(skewnorm.pdf(1,1000), stats.chi.pdf(1,1), skewnorm.pdf(1,1000) - stats.chi.pdf(1,1)) print(skewnorm.pdf(-1,-1000), stats.chi.pdf(1,1), skewnorm.pdf(-1,-1000) - stats.chi.pdf(1,1)) rvs = skewnorm.rvs(0,size=500) print('sample mean var: ', rvs.mean(), rvs.var()) print('theoretical mean var', skewnorm.stats(0)) rvs = skewnorm.rvs(5,size=500) print('sample mean var: ', rvs.mean(), rvs.var()) print('theoretical mean var', skewnorm.stats(5)) print(skewnorm.cdf(1,0), stats.norm.cdf(1), skewnorm.cdf(1,0) - stats.norm.cdf(1)) print(skewnorm.cdf(1,1000), stats.chi.cdf(1,1), skewnorm.cdf(1,1000) - stats.chi.cdf(1,1)) print(skewnorm.sf(0.05,1000), stats.chi.sf(0.05,1), skewnorm.sf(0.05,1000) - stats.chi.sf(0.05,1)) def example_T(): skewt = ACSkewT_gen() rvs = skewt.rvs(10,0,size=500) print('sample mean var: ', rvs.mean(), rvs.var()) print('theoretical mean var', skewt.stats(10,0)) print('t mean var', stats.t.stats(10)) print(skewt.stats(10,1000)) # -> folded t distribution, as alpha -> inf rvs = np.abs(stats.t.rvs(10,size=1000)) print(rvs.mean(), rvs.var()) def examples_normexpand(): skewnorm = SkewNorm_gen() rvs = skewnorm.rvs(5,size=100) normexpan = NormExpan_gen(rvs, mode='sample') smvsk = stats.describe(rvs)[2:] print('sample: mu,sig,sk,kur') print(smvsk) dmvsk = normexpan.stats(moments='mvsk') print('normexpan: mu,sig,sk,kur') print(dmvsk) print('mvsk diff distribution - sample') print(np.array(dmvsk) - np.array(smvsk)) print('normexpan attributes mvsk') print(mc2mvsk(normexpan.cnt)) print(normexpan.mvsk) mnc = mvsk2mnc(dmvsk) mc = mnc2mc(mnc) print('central moments') print(mc) print('non-central moments') print(mnc) pdffn = pdf_moments(mc) print('\npdf approximation from moments') print('pdf at', mc[0]-1,mc[0]+1) print(pdffn([mc[0]-1,mc[0]+1])) print(normexpan.pdf([mc[0]-1,mc[0]+1])) def examples_transf(): ##lognormal = ExpTransf(a=0.0, xa=-10.0, name = 'Log transformed normal') ##print(lognormal.cdf(1)) ##print(stats.lognorm.cdf(1,1)) ##print(lognormal.stats()) ##print(stats.lognorm.stats(1)) ##print(lognormal.rvs(size=10)) print('Results for lognormal') lognormalg = ExpTransf_gen(stats.norm, a=0, name = 'Log transformed normal general') print(lognormalg.cdf(1)) print(stats.lognorm.cdf(1,1)) print(lognormalg.stats()) print(stats.lognorm.stats(1)) print(lognormalg.rvs(size=5)) ##print('Results for loggamma') ##loggammag = ExpTransf_gen(stats.gamma) ##print(loggammag._cdf(1,10)) ##print(stats.loggamma.cdf(1,10)) print('Results for expgamma') loggammaexpg = LogTransf_gen(stats.gamma) print(loggammaexpg._cdf(1,10)) print(stats.loggamma.cdf(1,10)) print(loggammaexpg._cdf(2,15)) print(stats.loggamma.cdf(2,15)) # this requires change in scipy.stats.distribution #print(loggammaexpg.cdf(1,10)) print('Results for loglaplace') loglaplaceg = LogTransf_gen(stats.laplace) print(loglaplaceg._cdf(2)) print(stats.loglaplace.cdf(2,1)) loglaplaceexpg = ExpTransf_gen(stats.laplace) print(loglaplaceexpg._cdf(2)) stats.loglaplace.cdf(3,3) #0.98148148148148151 loglaplaceexpg._cdf(3,0,1./3) #0.98148148148148151 if __name__ == '__main__': example_n() example_T() examples_normexpand() examples_transf() statsmodels-0.12.2/statsmodels/sandbox/distributions/examples/ex_fitfr.py000066400000000000000000000016371400612667500270540ustar00rootroot00000000000000'''Example for estimating distribution parameters when some are fixed. This uses currently a patched version of the distributions, two methods are added to the continuous distributions. This has no side effects. It also adds bounds to vonmises, which changes the behavior of it for some methods. ''' import numpy as np from scipy import stats # Note the following import attaches methods to scipy.stats.distributions # and adds bounds to stats.vonmises # from statsmodels.sandbox.distributions import sppatch np.random.seed(12345) x = stats.gamma.rvs(2.5, loc=0, scale=1.2, size=200) #estimate all parameters print(stats.gamma.fit(x)) print(stats.gamma.fit_fr(x, frozen=[np.nan, np.nan, np.nan])) #estimate shape parameter only print(stats.gamma.fit_fr(x, frozen=[np.nan, 0., 1.2])) np.random.seed(12345) x = stats.lognorm.rvs(2, loc=0, scale=2, size=200) print(stats.lognorm.fit_fr(x, frozen=[np.nan, 0., np.nan])) statsmodels-0.12.2/statsmodels/sandbox/distributions/examples/ex_gof.py000066400000000000000000000006101400612667500265030ustar00rootroot00000000000000from scipy import stats from statsmodels.stats import gof poissrvs = stats.poisson.rvs(0.6, size = 200) freq, expfreq, histsupp = gof.gof_binning_discrete(poissrvs, stats.poisson, (0.6,), nsupp=20) (chi2val, pval) = stats.chisquare(freq, expfreq) print(chi2val, pval) print(gof.gof_chisquare_discrete(stats.poisson, (0.6,), poissrvs, 0.05, 'Poisson')) statsmodels-0.12.2/statsmodels/sandbox/distributions/examples/ex_mvelliptical.py000066400000000000000000000120141400612667500304160ustar00rootroot00000000000000# -*- coding: utf-8 -*- """examples for multivariate normal and t distributions Created on Fri Jun 03 16:00:26 2011 @author: josef for comparison I used R mvtnorm version 0.9-96 """ import numpy as np from numpy.testing import assert_array_almost_equal import matplotlib.pyplot as plt import statsmodels.api as sm import statsmodels.distributions.mixture_rvs as mix import statsmodels.sandbox.distributions.mv_normal as mvd cov3 = np.array([[ 1. , 0.5 , 0.75], [ 0.5 , 1.5 , 0.6 ], [ 0.75, 0.6 , 2. ]]) mu = np.array([-1, 0.0, 2.0]) #************** multivariate normal distribution *************** mvn3 = mvd.MVNormal(mu, cov3) #compare with random sample x = mvn3.rvs(size=1000000) xli = [[2., 1., 1.5], [0., 2., 1.5], [1.5, 1., 2.5], [0., 1., 1.5]] xliarr = np.asarray(xli).T[None,:, :] #from R session #pmvnorm(lower=-Inf,upper=(x[0,.]-mu)/sqrt(diag(cov3)),mean=rep(0,3),corr3) r_cdf = [0.3222292, 0.3414643, 0.5450594, 0.3116296] r_cdf_errors = [1.715116e-05, 1.590284e-05, 5.356471e-05, 3.567548e-05] n_cdf = [mvn3.cdf(a) for a in xli] assert_array_almost_equal(r_cdf, n_cdf, decimal=4) print(n_cdf) print('') print((x>> np.random.seed(464239857) >>> rvstsq = squaretg.rvs(10,size=100000) >>> squaretg.moment(4,10) 2734.3750000000009 >>> (rvstsq**4).mean() 2739.672765170933 >>> squaretg.moment(3,10) 78.124999999997044 >>> (rvstsq**3).mean() 84.13950048850549 >>> squaretg.stats(10, moments='mvsk') (array(1.2500000000000022), array(4.6874999999630909), array(5.7735026919777912), array(106.00000000170148)) >>> stats.describe(rvstsq) (100000, (3.2953470738423724e-009, 92.649615690914473), 1.2534924690963247, 4.7741427958594098, 6.1562177957041895, 100.99331166052181) ''' # checking the distribution # fraction of observations in each decile dec = squaretg.ppf(np.linspace(0.,1,11),10) freq,edges = np.histogram(rvstsq, bins=dec) print(freq/float(len(rvstsq))) import matplotlib.pyplot as plt freq,edges,_ = plt.hist(rvstsq, bins=50, range=(0,4),normed=True) edges += (edges[1]-edges[0])/2.0 plt.plot(edges[:-1], squaretg.pdf(edges[:-1], 10), 'r') #plt.show() #plt.close() ''' >>> plt.plot(edges[:-1], squaretg.pdf(edges[:-1], 10), 'r') [] >>> plt.fill(edges[4:8], squaretg.pdf(edges[4:8], 10), 'r') [] >>> plt.show() >>> plt.fill_between(edges[4:8], squaretg.pdf(edges[4:8], 10), y2=0, 'r') SyntaxError: non-keyword arg after keyword arg (, line 1) >>> plt.fill_between(edges[4:8], squaretg.pdf(edges[4:8], 10), 0, 'r') Traceback (most recent call last): AttributeError: 'module' object has no attribute 'fill_between' >>> fig = figure() Traceback (most recent call last): NameError: name 'figure' is not defined >>> ax1 = fig.add_subplot(311) Traceback (most recent call last): NameError: name 'fig' is not defined >>> fig = plt.figure() >>> ax1 = fig.add_subplot(111) >>> ax1.fill_between(edges[4:8], squaretg.pdf(edges[4:8], 10), 0, 'r') Traceback (most recent call last): AttributeError: 'AxesSubplot' object has no attribute 'fill_between' >>> ax1.fill(edges[4:8], squaretg.pdf(edges[4:8], 10), 0, 'r') Traceback (most recent call last): ''' import pytest pytest.main([__file__, '-vvs', '-x', '--pdb']) statsmodels-0.12.2/statsmodels/sandbox/distributions/examples/matchdist.py000066400000000000000000000230311400612667500272160ustar00rootroot00000000000000'''given a 1D sample of observation, find a matching distribution * estimate maximum likelihood parameter for each distribution * rank estimated distribution by Kolmogorov-Smirnov and Anderson-Darling test statistics Author: Josef Pktd License: Simplified BSD original December 2008 TODO: * refactor to result class * split estimation by support, add option and choose automatically * ''' from scipy import stats import numpy as np import matplotlib.pyplot as plt #stats.distributions.beta_gen._fitstart = lambda self, data : (5,5,0,1) def plothist(x,distfn, args, loc, scale, right=1): plt.figure() # the histogram of the data n, bins, patches = plt.hist(x, 25, normed=1, facecolor='green', alpha=0.75) maxheight = max([p.get_height() for p in patches]) print(maxheight) axlim = list(plt.axis()) #print(axlim) axlim[-1] = maxheight*1.05 #plt.axis(tuple(axlim)) ## print(bins) ## print('args in plothist', args) # add a 'best fit' line #yt = stats.norm.pdf( bins, loc=loc, scale=scale) yt = distfn.pdf( bins, loc=loc, scale=scale, *args) yt[yt>maxheight]=maxheight lt = plt.plot(bins, yt, 'r--', linewidth=1) ys = stats.t.pdf( bins, 10,scale=10,)*right ls = plt.plot(bins, ys, 'b-', linewidth=1) plt.xlabel('Smarts') plt.ylabel('Probability') plt.title(r'$\mathrm{Testing: %s :}\ \mu=%f,\ \sigma=%f$' % (distfn.name,loc,scale)) #plt.axis([bins[0], bins[-1], 0, 0.134+0.05]) plt.grid(True) plt.draw() #plt.show() #plt.close() #targetdist = ['norm','t','truncnorm','johnsonsu','johnsonsb', targetdist = ['norm','alpha', 'anglit', 'arcsine', 'beta', 'betaprime', 'bradford', 'burr', 'fisk', 'cauchy', 'chi', 'chi2', 'cosine', 'dgamma', 'dweibull', 'erlang', 'expon', 'exponweib', 'exponpow', 'fatiguelife', 'foldcauchy', 'f', 'foldnorm', 'frechet_r', 'weibull_min', 'frechet_l', 'weibull_max', 'genlogistic', 'genpareto', 'genexpon', 'genextreme', 'gamma', 'gengamma', 'genhalflogistic', 'gompertz', 'gumbel_r', 'gumbel_l', 'halfcauchy', 'halflogistic', 'halfnorm', 'hypsecant', 'gausshyper', 'invgamma', 'invnorm', 'invweibull', 'johnsonsb', 'johnsonsu', 'laplace', 'levy', 'levy_l', 'logistic', 'loggamma', 'loglaplace', 'lognorm', 'gilbrat', 'maxwell', 'mielke', 'nakagami', 'ncx2', 'ncf', 't', 'nct', 'pareto', 'lomax', 'powerlaw', 'powerlognorm', 'powernorm', 'rdist', 'rayleigh', 'reciprocal', 'rice', 'recipinvgauss', 'semicircular', 'triang', 'truncexpon', 'truncnorm', 'tukeylambda', 'uniform', 'vonmises', 'wald', 'wrapcauchy', 'binom', 'bernoulli', 'nbinom', 'geom', 'hypergeom', 'logser', 'poisson', 'planck', 'boltzmann', 'randint', 'zipf', 'dlaplace'] left = [] right = [] finite = [] unbound = [] other = [] contdist = [] discrete = [] categ = {('open','open'):'unbound', ('0','open'):'right',('open','0',):'left', ('finite','finite'):'finite',('oth','oth'):'other'} categ = {('open','open'):unbound, ('0','open'):right,('open','0',):left, ('finite','finite'):finite,('oth','oth'):other} categ2 = { ('open', '0') : ['frechet_l', 'weibull_max', 'levy_l'], ('finite', 'finite') : ['anglit', 'cosine', 'rdist', 'semicircular'], ('0', 'open') : ['alpha', 'burr', 'fisk', 'chi', 'chi2', 'erlang', 'expon', 'exponweib', 'exponpow', 'fatiguelife', 'foldcauchy', 'f', 'foldnorm', 'frechet_r', 'weibull_min', 'genpareto', 'genexpon', 'gamma', 'gengamma', 'genhalflogistic', 'gompertz', 'halfcauchy', 'halflogistic', 'halfnorm', 'invgamma', 'invnorm', 'invweibull', 'levy', 'loglaplace', 'lognorm', 'gilbrat', 'maxwell', 'mielke', 'nakagami', 'ncx2', 'ncf', 'lomax', 'powerlognorm', 'rayleigh', 'rice', 'recipinvgauss', 'truncexpon', 'wald'], ('open', 'open') : ['cauchy', 'dgamma', 'dweibull', 'genlogistic', 'genextreme', 'gumbel_r', 'gumbel_l', 'hypsecant', 'johnsonsu', 'laplace', 'logistic', 'loggamma', 't', 'nct', 'powernorm', 'reciprocal', 'truncnorm', 'tukeylambda', 'vonmises'], ('0', 'finite') : ['arcsine', 'beta', 'betaprime', 'bradford', 'gausshyper', 'johnsonsb', 'powerlaw', 'triang', 'uniform', 'wrapcauchy'], ('finite', 'open') : ['pareto'] } #Note: weibull_max == frechet_l right_incorrect = ['genextreme'] right_all = categ2[('0', 'open')] + categ2[('0', 'finite')] + categ2[('finite', 'open')]\ + right_incorrect for distname in targetdist: distfn = getattr(stats,distname) if hasattr(distfn,'_pdf'): if np.isinf(distfn.a): low = 'open' elif distfn.a == 0: low = '0' else: low = 'finite' if np.isinf(distfn.b): high = 'open' elif distfn.b == 0: high = '0' else: high = 'finite' contdist.append(distname) categ.setdefault((low,high),[]).append(distname) not_good = ['genextreme', 'reciprocal', 'vonmises'] # 'genextreme' is right (or left?), 'reciprocal' requires 00] rightfactor = 1 rvs_right = rvs_pos print('='*50) print('samplesize = ', n) for distname in targetdist: distfn = getattr(stats,distname) if distname in right_all: rvs = rvs_right rind = rightfactor else: rvs = rvs_orig rind = 1 print('-'*30) print('target = %s' % distname) sm = rvs.mean() sstd = np.sqrt(rvs.var()) ssupp = (rvs.min(), rvs.max()) if distname in ['truncnorm','betaprime','reciprocal']: par0 = (sm-2*sstd,sm+2*sstd) par_est = tuple(distfn.fit(rvs,loc=sm,scale=sstd,*par0)) elif distname == 'norm': par_est = tuple(distfn.fit(rvs,loc=sm,scale=sstd)) elif distname == 'genextreme': par_est = tuple(distfn.fit(rvs,-5,loc=sm,scale=sstd)) elif distname == 'wrapcauchy': par_est = tuple(distfn.fit(rvs,0.5,loc=0,scale=sstd)) elif distname == 'f': par_est = tuple(distfn.fit(rvs,10,15,loc=0,scale=1)) elif distname in right: sm = rvs.mean() sstd = np.sqrt(rvs.var()) par_est = tuple(distfn.fit(rvs,loc=0,scale=1)) else: sm = rvs.mean() sstd = np.sqrt(rvs.var()) par_est = tuple(distfn.fit(rvs,loc=sm,scale=sstd)) print('fit', par_est) arg_est = par_est[:-2] loc_est = par_est[-2] scale_est = par_est[-1] rvs_normed = (rvs-loc_est)/scale_est ks_stat, ks_pval = stats.kstest(rvs_normed,distname, arg_est) print('kstest', ks_stat, ks_pval) quant = 0.1 crit = distfn.ppf(1-quant*float(rind), loc=loc_est, scale=scale_est,*par_est) tail_prob = stats.t.sf(crit,dgp_arg,scale=dgp_scale) print('crit, prob', quant, crit, tail_prob) #if distname == 'norm': #plothist(rvs,loc_est,scale_est) #args = tuple() results.append([distname,ks_stat, ks_pval,arg_est,loc_est,scale_est,crit,tail_prob ]) #plothist(rvs,distfn,arg_est,loc_est,scale_est) #plothist(rvs,distfn,arg_est,loc_est,scale_est) #plt.show() #plt.close() #TODO: collect results and compare tail quantiles from operator import itemgetter res_sort = sorted(results, key = itemgetter(2)) res_sort.reverse() #kstest statistic: smaller is better, pval larger is better print('number of distributions', len(res_sort)) imagedir = 'matchresults' import os if not os.path.exists(imagedir): os.makedirs(imagedir) for ii,di in enumerate(res_sort): distname,ks_stat, ks_pval,arg_est,loc_est,scale_est,crit,tail_prob = di[:] distfn = getattr(stats,distname) if distname in right_all: rvs = rvs_right rind = rightfactor ri = 'r' else: rvs = rvs_orig ri = '' rind = 1 print('%s ks-stat = %f, ks-pval = %f tail_prob = %f)' % \ (distname, ks_stat, ks_pval, tail_prob)) ## print('arg_est = %s, loc_est = %f scale_est = %f)' % \ ## (repr(arg_est),loc_est,scale_est)) plothist(rvs,distfn,arg_est,loc_est,scale_est,right = rind) plt.savefig(os.path.join(imagedir,'%s%s%02d_%s.png'% (prefix, ri,ii, distname))) ##plt.show() ##plt.close() statsmodels-0.12.2/statsmodels/sandbox/distributions/extras.py000066400000000000000000001142701400612667500247340ustar00rootroot00000000000000'''Various extensions to distributions * skew normal and skew t distribution by Azzalini, A. & Capitanio, A. * Gram-Charlier expansion distribution (using 4 moments), * distributions based on non-linear transformation - Transf_gen - ExpTransf_gen, LogTransf_gen - TransfTwo_gen (defines as examples: square, negative square and abs transformations) - this versions are without __new__ * mnvormcdf, mvstdnormcdf : cdf, rectangular integral for multivariate normal distribution TODO: * Where is Transf_gen for general monotonic transformation ? found and added it * write some docstrings, some parts I do not remember * add Box-Cox transformation, parametrized ? this is only partially cleaned, still includes test examples as functions main changes * add transf_gen (2010-05-09) * added separate example and tests (2010-05-09) * collect transformation function into classes Example ------- >>> logtg = Transf_gen(stats.t, np.exp, np.log, numargs = 1, a=0, name = 'lnnorm', longname = 'Exp transformed normal', extradoc = '\ndistribution of y = exp(x), with x standard normal' 'precision for moment andstats is not very high, 2-3 decimals') >>> logtg.cdf(5, 6) 0.92067704211191848 >>> stats.t.cdf(np.log(5), 6) 0.92067704211191848 >>> logtg.pdf(5, 6) 0.021798547904239293 >>> stats.t.pdf(np.log(5), 6) 0.10899273954837908 >>> stats.t.pdf(np.log(5), 6)/5. #derivative 0.021798547909675815 Author: josef-pktd License: BSD ''' import numpy as np from numpy import poly1d,sqrt, exp import scipy from scipy import stats, special from scipy.stats import distributions from statsmodels.stats.moment_helpers import mvsk2mc, mc2mvsk #note copied from distr_skewnorm_0.py class SkewNorm_gen(distributions.rv_continuous): '''univariate Skew-Normal distribution of Azzalini class follows scipy.stats.distributions pattern but with __init__ ''' def __init__(self): #super(SkewNorm_gen,self).__init__( distributions.rv_continuous.__init__(self, name = 'Skew Normal distribution', shapes = 'alpha', extradoc = ''' ''' ) def _argcheck(self, alpha): return 1 #(alpha >= 0) def _rvs(self, alpha): # see http://azzalini.stat.unipd.it/SN/faq.html delta = alpha/np.sqrt(1+alpha**2) u0 = stats.norm.rvs(size=self._size) u1 = delta*u0 + np.sqrt(1-delta**2)*stats.norm.rvs(size=self._size) return np.where(u0>0, u1, -u1) def _munp(self, n, alpha): # use pdf integration with _mom0_sc if only _pdf is defined. # default stats calculation uses ppf, which is much slower return self._mom0_sc(n, alpha) def _pdf(self,x,alpha): # 2*normpdf(x)*normcdf(alpha*x) return 2.0/np.sqrt(2*np.pi)*np.exp(-x**2/2.0) * special.ndtr(alpha*x) def _stats_skip(self,x,alpha,moments='mvsk'): #skip for now to force moment integration as check pass skewnorm = SkewNorm_gen() # generated the same way as distributions in stats.distributions class SkewNorm2_gen(distributions.rv_continuous): '''univariate Skew-Normal distribution of Azzalini class follows scipy.stats.distributions pattern ''' def _argcheck(self, alpha): return 1 #where(alpha>=0, 1, 0) def _pdf(self,x,alpha): # 2*normpdf(x)*normcdf(alpha*x return 2.0/np.sqrt(2*np.pi)*np.exp(-x**2/2.0) * special.ndtr(alpha*x) skewnorm2 = SkewNorm2_gen(name = 'Skew Normal distribution', shapes = 'alpha', extradoc = ''' -inf < alpha < inf''') class ACSkewT_gen(distributions.rv_continuous): '''univariate Skew-T distribution of Azzalini class follows scipy.stats.distributions pattern but with __init__ ''' def __init__(self): #super(SkewT_gen,self).__init__( distributions.rv_continuous.__init__(self, name = 'Skew T distribution', shapes = 'df, alpha', extradoc = ''' Skewed T distribution by Azzalini, A. & Capitanio, A. (2003)_ the pdf is given by: pdf(x) = 2.0 * t.pdf(x, df) * t.cdf(df+1, alpha*x*np.sqrt((1+df)/(x**2+df))) with alpha >=0 Note: different from skewed t distribution by Hansen 1999 .._ Azzalini, A. & Capitanio, A. (2003), Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-t distribution, appears in J.Roy.Statist.Soc, series B, vol.65, pp.367-389 ''' ) def _argcheck(self, df, alpha): return (alpha == alpha)*(df>0) ## def _arg_check(self, alpha): ## return np.where(alpha>=0, 0, 1) ## def _argcheck(self, alpha): ## return np.where(alpha>=0, 1, 0) def _rvs(self, df, alpha): # see http://azzalini.stat.unipd.it/SN/faq.html #delta = alpha/np.sqrt(1+alpha**2) V = stats.chi2.rvs(df, size=self._size) z = skewnorm.rvs(alpha, size=self._size) return z/np.sqrt(V/df) def _munp(self, n, df, alpha): # use pdf integration with _mom0_sc if only _pdf is defined. # default stats calculation uses ppf return self._mom0_sc(n, df, alpha) def _pdf(self, x, df, alpha): # 2*normpdf(x)*normcdf(alpha*x) return 2.0*distributions.t._pdf(x, df) * special.stdtr(df+1, alpha*x*np.sqrt((1+df)/(x**2+df))) ## ##def mvsk2cm(*args): ## mu,sig,sk,kur = args ## # Get central moments ## cnt = [None]*4 ## cnt[0] = mu ## cnt[1] = sig #*sig ## cnt[2] = sk * sig**1.5 ## cnt[3] = (kur+3.0) * sig**2.0 ## return cnt ## ## ##def mvsk2m(args): ## mc, mc2, skew, kurt = args#= self._stats(*args,**mdict) ## mnc = mc ## mnc2 = mc2 + mc*mc ## mc3 = skew*(mc2**1.5) # 3rd central moment ## mnc3 = mc3+3*mc*mc2+mc**3 # 3rd non-central moment ## mc4 = (kurt+3.0)*(mc2**2.0) # 4th central moment ## mnc4 = mc4+4*mc*mc3+6*mc*mc*mc2+mc**4 ## return (mc, mc2, mc3, mc4), (mnc, mnc2, mnc3, mnc4) ## ##def mc2mvsk(args): ## mc, mc2, mc3, mc4 = args ## skew = mc3 / mc2**1.5 ## kurt = mc4 / mc2**2.0 - 3.0 ## return (mc, mc2, skew, kurt) ## ##def m2mc(args): ## mnc, mnc2, mnc3, mnc4 = args ## mc = mnc ## mc2 = mnc2 - mnc*mnc ## #mc3 = skew*(mc2**1.5) # 3rd central moment ## mc3 = mnc3 - (3*mc*mc2+mc**3) # 3rd central moment ## #mc4 = (kurt+3.0)*(mc2**2.0) # 4th central moment ## mc4 = mnc4 - (4*mc*mc3+6*mc*mc*mc2+mc**4) ## return (mc, mc2, mc3, mc4) def _hermnorm(N): # return the negatively normalized hermite polynomials up to order N-1 # (inclusive) # using the recursive relationship # p_n+1 = p_n(x)' - x*p_n(x) # and p_0(x) = 1 plist = [None]*N plist[0] = poly1d(1) for n in range(1,N): plist[n] = plist[n-1].deriv() - poly1d([1,0])*plist[n-1] return plist def pdf_moments_st(cnt): """Return the Gaussian expanded pdf function given the list of central moments (first one is mean). version of scipy.stats, any changes ? the scipy.stats version has a bug and returns normal distribution """ N = len(cnt) if N < 2: raise ValueError("At least two moments must be given to " "approximate the pdf.") totp = poly1d(1) sig = sqrt(cnt[1]) mu = cnt[0] if N > 2: Dvals = _hermnorm(N+1) for k in range(3,N+1): # Find Ck Ck = 0.0 for n in range((k-3)/2): m = k-2*n if m % 2: # m is odd momdiff = cnt[m-1] else: momdiff = cnt[m-1] - sig*sig*scipy.factorial2(m-1) Ck += Dvals[k][m] / sig**m * momdiff # Add to totp raise SystemError print(Dvals) print(Ck) totp = totp + Ck*Dvals[k] def thisfunc(x): xn = (x-mu)/sig return totp(xn)*exp(-xn*xn/2.0)/sqrt(2*np.pi)/sig return thisfunc, totp def pdf_mvsk(mvsk): """Return the Gaussian expanded pdf function given the list of 1st, 2nd moment and skew and Fisher (excess) kurtosis. Parameters ---------- mvsk : list of mu, mc2, skew, kurt distribution is matched to these four moments Returns ------- pdffunc : function function that evaluates the pdf(x), where x is the non-standardized random variable. Notes ----- Changed so it works only if four arguments are given. Uses explicit formula, not loop. This implements a Gram-Charlier expansion of the normal distribution where the first 2 moments coincide with those of the normal distribution but skew and kurtosis can deviate from it. In the Gram-Charlier distribution it is possible that the density becomes negative. This is the case when the deviation from the normal distribution is too large. References ---------- https://en.wikipedia.org/wiki/Edgeworth_series Johnson N.L., S. Kotz, N. Balakrishnan: Continuous Univariate Distributions, Volume 1, 2nd ed., p.30 """ N = len(mvsk) if N < 4: raise ValueError("Four moments must be given to " "approximate the pdf.") mu, mc2, skew, kurt = mvsk totp = poly1d(1) sig = sqrt(mc2) if N > 2: Dvals = _hermnorm(N+1) C3 = skew/6.0 C4 = kurt/24.0 # Note: Hermite polynomial for order 3 in _hermnorm is negative # instead of positive totp = totp - C3*Dvals[3] + C4*Dvals[4] def pdffunc(x): xn = (x-mu)/sig return totp(xn)*np.exp(-xn*xn/2.0)/np.sqrt(2*np.pi)/sig return pdffunc def pdf_moments(cnt): """Return the Gaussian expanded pdf function given the list of central moments (first one is mean). Changed so it works only if four arguments are given. Uses explicit formula, not loop. Notes ----- This implements a Gram-Charlier expansion of the normal distribution where the first 2 moments coincide with those of the normal distribution but skew and kurtosis can deviate from it. In the Gram-Charlier distribution it is possible that the density becomes negative. This is the case when the deviation from the normal distribution is too large. References ---------- https://en.wikipedia.org/wiki/Edgeworth_series Johnson N.L., S. Kotz, N. Balakrishnan: Continuous Univariate Distributions, Volume 1, 2nd ed., p.30 """ N = len(cnt) if N < 2: raise ValueError("At least two moments must be given to " "approximate the pdf.") mc, mc2, mc3, mc4 = cnt skew = mc3 / mc2**1.5 kurt = mc4 / mc2**2.0 - 3.0 # Fisher kurtosis, excess kurtosis totp = poly1d(1) sig = sqrt(cnt[1]) mu = cnt[0] if N > 2: Dvals = _hermnorm(N+1) ## for k in range(3,N+1): ## # Find Ck ## Ck = 0.0 ## for n in range((k-3)/2): ## m = k-2*n ## if m % 2: # m is odd ## momdiff = cnt[m-1] ## else: ## momdiff = cnt[m-1] - sig*sig*scipy.factorial2(m-1) ## Ck += Dvals[k][m] / sig**m * momdiff ## # Add to totp ## raise ## print Dvals ## print Ck ## totp = totp + Ck*Dvals[k] C3 = skew/6.0 C4 = kurt/24.0 totp = totp - C3*Dvals[3] + C4*Dvals[4] def thisfunc(x): xn = (x-mu)/sig return totp(xn)*np.exp(-xn*xn/2.0)/np.sqrt(2*np.pi)/sig return thisfunc class NormExpan_gen(distributions.rv_continuous): '''Gram-Charlier Expansion of Normal distribution class follows scipy.stats.distributions pattern but with __init__ ''' def __init__(self,args, **kwds): #todo: replace with super call distributions.rv_continuous.__init__(self, name = 'Normal Expansion distribution', shapes = ' ', extradoc = ''' The distribution is defined as the Gram-Charlier expansion of the normal distribution using the first four moments. The pdf is given by pdf(x) = (1+ skew/6.0 * H(xc,3) + kurt/24.0 * H(xc,4))*normpdf(xc) where xc = (x-mu)/sig is the standardized value of the random variable and H(xc,3) and H(xc,4) are Hermite polynomials Note: This distribution has to be parametrized during initialization and instantiation, and does not have a shape parameter after instantiation (similar to frozen distribution except for location and scale.) Location and scale can be used as with other distributions, however note, that they are relative to the initialized distribution. ''' ) #print args, kwds mode = kwds.get('mode', 'sample') if mode == 'sample': mu,sig,sk,kur = stats.describe(args)[2:] self.mvsk = (mu,sig,sk,kur) cnt = mvsk2mc((mu,sig,sk,kur)) elif mode == 'mvsk': cnt = mvsk2mc(args) self.mvsk = args elif mode == 'centmom': cnt = args self.mvsk = mc2mvsk(cnt) else: raise ValueError("mode must be 'mvsk' or centmom") self.cnt = cnt #self.mvsk = (mu,sig,sk,kur) #self._pdf = pdf_moments(cnt) self._pdf = pdf_mvsk(self.mvsk) def _munp(self,n): # use pdf integration with _mom0_sc if only _pdf is defined. # default stats calculation uses ppf return self._mom0_sc(n) def _stats_skip(self): # skip for now to force numerical integration of pdf for testing return self.mvsk ## copied from nonlinear_transform_gen.py ''' A class for the distribution of a non-linear monotonic transformation of a continuous random variable simplest usage: example: create log-gamma distribution, i.e. y = log(x), where x is gamma distributed (also available in scipy.stats) loggammaexpg = Transf_gen(stats.gamma, np.log, np.exp) example: what is the distribution of the discount factor y=1/(1+x) where interest rate x is normally distributed with N(mux,stdx**2)')? (just to come up with a story that implies a nice transformation) invnormalg = Transf_gen(stats.norm, inversew, inversew_inv, decr=True, a=-np.inf) This class does not work well for distributions with difficult shapes, e.g. 1/x where x is standard normal, because of the singularity and jump at zero. Note: I'm working from my version of scipy.stats.distribution. But this script runs under scipy 0.6.0 (checked with numpy: 1.2.0rc2 and python 2.4) This is not yet thoroughly tested, polished or optimized TODO: * numargs handling is not yet working properly, numargs needs to be specified (default = 0 or 1) * feeding args and kwargs to underlying distribution is untested and incomplete * distinguish args and kwargs for the transformed and the underlying distribution - currently all args and no kwargs are transmitted to underlying distribution - loc and scale only work for transformed, but not for underlying distribution - possible to separate args for transformation and underlying distribution parameters * add _rvs as method, will be faster in many cases Created on Tuesday, October 28, 2008, 12:40:37 PM Author: josef-pktd License: BSD ''' def get_u_argskwargs(**kwargs): #Todo: What's this? wrong spacing, used in Transf_gen TransfTwo_gen u_kwargs = dict((k.replace('u_','',1),v) for k,v in kwargs.items() if k.startswith('u_')) u_args = u_kwargs.pop('u_args',None) return u_args, u_kwargs class Transf_gen(distributions.rv_continuous): '''a class for non-linear monotonic transformation of a continuous random variable ''' def __init__(self, kls, func, funcinv, *args, **kwargs): #print args #print kwargs self.func = func self.funcinv = funcinv #explicit for self.__dict__.update(kwargs) #need to set numargs because inspection does not work self.numargs = kwargs.pop('numargs', 0) #print self.numargs name = kwargs.pop('name','transfdist') longname = kwargs.pop('longname','Non-linear transformed distribution') extradoc = kwargs.pop('extradoc',None) a = kwargs.pop('a', -np.inf) b = kwargs.pop('b', np.inf) self.decr = kwargs.pop('decr', False) #defines whether it is a decreasing (True) # or increasing (False) monotonic transformation self.u_args, self.u_kwargs = get_u_argskwargs(**kwargs) self.kls = kls #(self.u_args, self.u_kwargs) # possible to freeze the underlying distribution super(Transf_gen,self).__init__(a=a, b=b, name = name, longname = longname, extradoc = extradoc) def _rvs(self, *args, **kwargs): self.kls._size = self._size return self.funcinv(self.kls._rvs(*args)) def _cdf(self,x,*args, **kwargs): #print args if not self.decr: return self.kls._cdf(self.funcinv(x),*args, **kwargs) #note scipy _cdf only take *args not *kwargs else: return 1.0 - self.kls._cdf(self.funcinv(x),*args, **kwargs) def _ppf(self, q, *args, **kwargs): if not self.decr: return self.func(self.kls._ppf(q,*args, **kwargs)) else: return self.func(self.kls._ppf(1-q,*args, **kwargs)) def inverse(x): return np.divide(1.0,x) mux, stdx = 0.05, 0.1 mux, stdx = 9.0, 1.0 def inversew(x): return 1.0/(1+mux+x*stdx) def inversew_inv(x): return (1.0/x - 1.0 - mux)/stdx #.np.divide(1.0,x)-10 def identit(x): return x invdnormalg = Transf_gen(stats.norm, inversew, inversew_inv, decr=True, #a=-np.inf, numargs = 0, name = 'discf', longname = 'normal-based discount factor', extradoc = '\ndistribution of discount factor y=1/(1+x)) with x N(0.05,0.1**2)') lognormalg = Transf_gen(stats.norm, np.exp, np.log, numargs = 2, a=0, name = 'lnnorm', longname = 'Exp transformed normal', extradoc = '\ndistribution of y = exp(x), with x standard normal' 'precision for moment andstats is not very high, 2-3 decimals') loggammaexpg = Transf_gen(stats.gamma, np.log, np.exp, numargs=1) ## copied form nonlinear_transform_short.py '''univariate distribution of a non-linear monotonic transformation of a random variable ''' class ExpTransf_gen(distributions.rv_continuous): '''Distribution based on log/exp transformation the constructor can be called with a distribution class and generates the distribution of the transformed random variable ''' def __init__(self, kls, *args, **kwargs): #print args #print kwargs #explicit for self.__dict__.update(kwargs) if 'numargs' in kwargs: self.numargs = kwargs['numargs'] else: self.numargs = 1 if 'name' in kwargs: name = kwargs['name'] else: name = 'Log transformed distribution' if 'a' in kwargs: a = kwargs['a'] else: a = 0 super(ExpTransf_gen,self).__init__(a=0, name = name) self.kls = kls def _cdf(self,x,*args): pass #print args return self.kls.cdf(np.log(x),*args) def _ppf(self, q, *args): return np.exp(self.kls.ppf(q,*args)) class LogTransf_gen(distributions.rv_continuous): '''Distribution based on log/exp transformation the constructor can be called with a distribution class and generates the distribution of the transformed random variable ''' def __init__(self, kls, *args, **kwargs): #explicit for self.__dict__.update(kwargs) if 'numargs' in kwargs: self.numargs = kwargs['numargs'] else: self.numargs = 1 if 'name' in kwargs: name = kwargs['name'] else: name = 'Log transformed distribution' if 'a' in kwargs: a = kwargs['a'] else: a = 0 super(LogTransf_gen,self).__init__(a=a, name = name) self.kls = kls def _cdf(self,x, *args): #print args return self.kls._cdf(np.exp(x),*args) def _ppf(self, q, *args): return np.log(self.kls._ppf(q,*args)) ## copied from transformtwo.py ''' Created on Apr 28, 2009 @author: Josef Perktold ''' ''' A class for the distribution of a non-linear u-shaped or hump shaped transformation of a continuous random variable This is a companion to the distributions of non-linear monotonic transformation to the case when the inverse mapping is a 2-valued correspondence, for example for absolute value or square simplest usage: example: create squared distribution, i.e. y = x**2, where x is normal or t distributed This class does not work well for distributions with difficult shapes, e.g. 1/x where x is standard normal, because of the singularity and jump at zero. This verifies for normal - chi2, normal - halfnorm, foldnorm, and t - F TODO: * numargs handling is not yet working properly, numargs needs to be specified (default = 0 or 1) * feeding args and kwargs to underlying distribution works in t distribution example * distinguish args and kwargs for the transformed and the underlying distribution - currently all args and no kwargs are transmitted to underlying distribution - loc and scale only work for transformed, but not for underlying distribution - possible to separate args for transformation and underlying distribution parameters * add _rvs as method, will be faster in many cases ''' class TransfTwo_gen(distributions.rv_continuous): '''Distribution based on a non-monotonic (u- or hump-shaped transformation) the constructor can be called with a distribution class, and functions that define the non-linear transformation. and generates the distribution of the transformed random variable Note: the transformation, it's inverse and derivatives need to be fully specified: func, funcinvplus, funcinvminus, derivplus, derivminus. Currently no numerical derivatives or inverse are calculated This can be used to generate distribution instances similar to the distributions in scipy.stats. ''' #a class for non-linear non-monotonic transformation of a continuous random variable def __init__(self, kls, func, funcinvplus, funcinvminus, derivplus, derivminus, *args, **kwargs): #print args #print kwargs self.func = func self.funcinvplus = funcinvplus self.funcinvminus = funcinvminus self.derivplus = derivplus self.derivminus = derivminus #explicit for self.__dict__.update(kwargs) #need to set numargs because inspection does not work self.numargs = kwargs.pop('numargs', 0) #print self.numargs name = kwargs.pop('name','transfdist') longname = kwargs.pop('longname','Non-linear transformed distribution') extradoc = kwargs.pop('extradoc',None) a = kwargs.pop('a', -np.inf) # attached to self in super b = kwargs.pop('b', np.inf) # self.a, self.b would be overwritten self.shape = kwargs.pop('shape', False) #defines whether it is a `u` shaped or `hump' shaped # transformation self.u_args, self.u_kwargs = get_u_argskwargs(**kwargs) self.kls = kls #(self.u_args, self.u_kwargs) # possible to freeze the underlying distribution super(TransfTwo_gen,self).__init__(a=a, b=b, name = name, shapes = kls.shapes, longname = longname, extradoc = extradoc) # add enough info for self.freeze() to be able to reconstruct the instance try: self._ctor_param.update(dict(kls=kls, func=func, funcinvplus=funcinvplus, funcinvminus=funcinvminus, derivplus=derivplus, derivminus=derivminus, shape=self.shape)) except AttributeError: # scipy < 0.14 does not have this, ignore and do nothing pass def _rvs(self, *args): self.kls._size = self._size #size attached to self, not function argument return self.func(self.kls._rvs(*args)) def _pdf(self,x,*args, **kwargs): #print args if self.shape == 'u': signpdf = 1 elif self.shape == 'hump': signpdf = -1 else: raise ValueError('shape can only be `u` or `hump`') return signpdf * (self.derivplus(x)*self.kls._pdf(self.funcinvplus(x),*args, **kwargs) - self.derivminus(x)*self.kls._pdf(self.funcinvminus(x),*args, **kwargs)) #note scipy _cdf only take *args not *kwargs def _cdf(self,x,*args, **kwargs): #print args if self.shape == 'u': return self.kls._cdf(self.funcinvplus(x),*args, **kwargs) - \ self.kls._cdf(self.funcinvminus(x),*args, **kwargs) #note scipy _cdf only take *args not *kwargs else: return 1.0 - self._sf(x,*args, **kwargs) def _sf(self,x,*args, **kwargs): #print args if self.shape == 'hump': return self.kls._cdf(self.funcinvplus(x),*args, **kwargs) - \ self.kls._cdf(self.funcinvminus(x),*args, **kwargs) #note scipy _cdf only take *args not *kwargs else: return 1.0 - self._cdf(x, *args, **kwargs) def _munp(self, n,*args, **kwargs): return self._mom0_sc(n,*args) # ppf might not be possible in general case? # should be possible in symmetric case # def _ppf(self, q, *args, **kwargs): # if self.shape == 'u': # return self.func(self.kls._ppf(q,*args, **kwargs)) # elif self.shape == 'hump': # return self.func(self.kls._ppf(1-q,*args, **kwargs)) #TODO: rename these functions to have unique names class SquareFunc(object): '''class to hold quadratic function with inverse function and derivative using instance methods instead of class methods, if we want extension to parametrized function ''' def inverseplus(self, x): return np.sqrt(x) def inverseminus(self, x): return 0.0 - np.sqrt(x) def derivplus(self, x): return 0.5/np.sqrt(x) def derivminus(self, x): return 0.0 - 0.5/np.sqrt(x) def squarefunc(self, x): return np.power(x,2) sqfunc = SquareFunc() squarenormalg = TransfTwo_gen(stats.norm, sqfunc.squarefunc, sqfunc.inverseplus, sqfunc.inverseminus, sqfunc.derivplus, sqfunc.derivminus, shape='u', a=0.0, b=np.inf, numargs = 0, name = 'squarenorm', longname = 'squared normal distribution', extradoc = '\ndistribution of the square of a normal random variable' +\ ' y=x**2 with x N(0.0,1)') #u_loc=l, u_scale=s) squaretg = TransfTwo_gen(stats.t, sqfunc.squarefunc, sqfunc.inverseplus, sqfunc.inverseminus, sqfunc.derivplus, sqfunc.derivminus, shape='u', a=0.0, b=np.inf, numargs = 1, name = 'squarenorm', longname = 'squared t distribution', extradoc = '\ndistribution of the square of a t random variable' +\ ' y=x**2 with x t(dof,0.0,1)') def inverseplus(x): return np.sqrt(-x) def inverseminus(x): return 0.0 - np.sqrt(-x) def derivplus(x): return 0.0 - 0.5/np.sqrt(-x) def derivminus(x): return 0.5/np.sqrt(-x) def negsquarefunc(x): return -np.power(x,2) negsquarenormalg = TransfTwo_gen(stats.norm, negsquarefunc, inverseplus, inverseminus, derivplus, derivminus, shape='hump', a=-np.inf, b=0.0, numargs = 0, name = 'negsquarenorm', longname = 'negative squared normal distribution', extradoc = '\ndistribution of the negative square of a normal random variable' +\ ' y=-x**2 with x N(0.0,1)') #u_loc=l, u_scale=s) def inverseplus(x): return x def inverseminus(x): return 0.0 - x def derivplus(x): return 1.0 def derivminus(x): return 0.0 - 1.0 def absfunc(x): return np.abs(x) absnormalg = TransfTwo_gen(stats.norm, np.abs, inverseplus, inverseminus, derivplus, derivminus, shape='u', a=0.0, b=np.inf, numargs = 0, name = 'absnorm', longname = 'absolute of normal distribution', extradoc = '\ndistribution of the absolute value of a normal random variable' +\ ' y=abs(x) with x N(0,1)') #copied from mvncdf.py '''multivariate normal probabilities and cumulative distribution function a wrapper for scipy.stats.kde.mvndst SUBROUTINE MVNDST( N, LOWER, UPPER, INFIN, CORREL, MAXPTS, & ABSEPS, RELEPS, ERROR, VALUE, INFORM ) * * A subroutine for computing multivariate normal probabilities. * This subroutine uses an algorithm given in the paper * "Numerical Computation of Multivariate Normal Probabilities", in * J. of Computational and Graphical Stat., 1(1992), pp. 141-149, by * Alan Genz * Department of Mathematics * Washington State University * Pullman, WA 99164-3113 * Email : AlanGenz@wsu.edu * * Parameters * * N INTEGER, the number of variables. * LOWER REAL, array of lower integration limits. * UPPER REAL, array of upper integration limits. * INFIN INTEGER, array of integration limits flags: * if INFIN(I) < 0, Ith limits are (-infinity, infinity); * if INFIN(I) = 0, Ith limits are (-infinity, UPPER(I)]; * if INFIN(I) = 1, Ith limits are [LOWER(I), infinity); * if INFIN(I) = 2, Ith limits are [LOWER(I), UPPER(I)]. * CORREL REAL, array of correlation coefficients; the correlation * coefficient in row I column J of the correlation matrix * should be stored in CORREL( J + ((I-2)*(I-1))/2 ), for J < I. * The correlation matrix must be positive semidefinite. * MAXPTS INTEGER, maximum number of function values allowed. This * parameter can be used to limit the time. A sensible * strategy is to start with MAXPTS = 1000*N, and then * increase MAXPTS if ERROR is too large. * ABSEPS REAL absolute error tolerance. * RELEPS REAL relative error tolerance. * ERROR REAL estimated absolute error, with 99% confidence level. * VALUE REAL estimated value for the integral * INFORM INTEGER, termination status parameter: * if INFORM = 0, normal completion with ERROR < EPS; * if INFORM = 1, completion with ERROR > EPS and MAXPTS * function vaules used; increase MAXPTS to * decrease ERROR; * if INFORM = 2, N > 500 or N < 1. * >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[10.0,10.0],[0,0],[0.5]) (2e-016, 1.0, 0) >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[100.0,100.0],[0,0],[0.0]) (2e-016, 1.0, 0) >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[1.0,1.0],[0,0],[0.0]) (2e-016, 0.70786098173714096, 0) >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[0.001,1.0],[0,0],[0.0]) (2e-016, 0.42100802096993045, 0) >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[0.001,10.0],[0,0],[0.0]) (2e-016, 0.50039894221391101, 0) >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[0.001,100.0],[0,0],[0.0]) (2e-016, 0.50039894221391101, 0) >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[0.01,100.0],[0,0],[0.0]) (2e-016, 0.5039893563146316, 0) >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[0.1,100.0],[0,0],[0.0]) (2e-016, 0.53982783727702899, 0) >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[0.1,100.0],[2,2],[0.0]) (2e-016, 0.019913918638514494, 0) >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[0.0,0.0],[0,0],[0.0]) (2e-016, 0.25, 0) >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[0.0,0.0],[-1,0],[0.0]) (2e-016, 0.5, 0) >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[0.0,0.0],[-1,0],[0.5]) (2e-016, 0.5, 0) >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[0.0,0.0],[0,0],[0.5]) (2e-016, 0.33333333333333337, 0) >>> scipy.stats.kde.mvn.mvndst([0.0,0.0],[0.0,0.0],[0,0],[0.99]) (2e-016, 0.47747329317779391, 0) ''' #from scipy.stats import kde informcode = {0: 'normal completion with ERROR < EPS', 1: '''completion with ERROR > EPS and MAXPTS function values used; increase MAXPTS to decrease ERROR;''', 2: 'N > 500 or N < 1'} def mvstdnormcdf(lower, upper, corrcoef, **kwds): '''standardized multivariate normal cumulative distribution function This is a wrapper for scipy.stats.kde.mvn.mvndst which calculates a rectangular integral over a standardized multivariate normal distribution. This function assumes standardized scale, that is the variance in each dimension is one, but correlation can be arbitrary, covariance = correlation matrix Parameters ---------- lower, upper : array_like, 1d lower and upper integration limits with length equal to the number of dimensions of the multivariate normal distribution. It can contain -np.inf or np.inf for open integration intervals corrcoef : float or array_like specifies correlation matrix in one of three ways, see notes optional keyword parameters to influence integration * maxpts : int, maximum number of function values allowed. This parameter can be used to limit the time. A sensible strategy is to start with `maxpts` = 1000*N, and then increase `maxpts` if ERROR is too large. * abseps : float absolute error tolerance. * releps : float relative error tolerance. Returns ------- cdfvalue : float value of the integral Notes ----- The correlation matrix corrcoef can be given in 3 different ways If the multivariate normal is two-dimensional than only the correlation coefficient needs to be provided. For general dimension the correlation matrix can be provided either as a one-dimensional array of the upper triangular correlation coefficients stacked by rows, or as full square correlation matrix See Also -------- mvnormcdf : cdf of multivariate normal distribution without standardization Examples -------- >>> print(mvstdnormcdf([-np.inf,-np.inf], [0.0,np.inf], 0.5)) 0.5 >>> corr = [[1.0, 0, 0.5],[0,1,0],[0.5,0,1]] >>> print(mvstdnormcdf([-np.inf,-np.inf,-100.0], [0.0,0.0,0.0], corr, abseps=1e-6)) 0.166666399198 >>> print(mvstdnormcdf([-np.inf,-np.inf,-100.0],[0.0,0.0,0.0],corr, abseps=1e-8)) something wrong completion with ERROR > EPS and MAXPTS function values used; increase MAXPTS to decrease ERROR; 1.048330348e-006 0.166666546218 >>> print(mvstdnormcdf([-np.inf,-np.inf,-100.0],[0.0,0.0,0.0], corr, \ maxpts=100000, abseps=1e-8)) 0.166666588293 ''' n = len(lower) #do not know if converting to array is necessary, #but it makes ndim check possible lower = np.array(lower) upper = np.array(upper) corrcoef = np.array(corrcoef) correl = np.zeros(int(n*(n-1)/2.0)) #dtype necessary? if (lower.ndim != 1) or (upper.ndim != 1): raise ValueError('can handle only 1D bounds') if len(upper) != n: raise ValueError('bounds have different lengths') if n==2 and corrcoef.size==1: correl = corrcoef #print 'case scalar rho', n elif corrcoef.ndim == 1 and len(corrcoef) == n*(n-1)/2.0: #print 'case flat corr', corrcoeff.shape correl = corrcoef elif corrcoef.shape == (n,n): #print 'case square corr', correl.shape correl = corrcoef[np.tril_indices(n, -1)] # for ii in range(n): # for jj in range(ii): # correl[ jj + ((ii-2)*(ii-1))/2] = corrcoef[ii,jj] else: raise ValueError('corrcoef has incorrect dimension') if 'maxpts' not in kwds: if n >2: kwds['maxpts'] = 10000*n lowinf = np.isneginf(lower) uppinf = np.isposinf(upper) infin = 2.0*np.ones(n) np.putmask(infin,lowinf,0)# infin.putmask(0,lowinf) np.putmask(infin,uppinf,1) #infin.putmask(1,uppinf) #this has to be last np.putmask(infin,lowinf*uppinf,-1) ## #remove infs ## np.putmask(lower,lowinf,-100)# infin.putmask(0,lowinf) ## np.putmask(upper,uppinf,100) #infin.putmask(1,uppinf) #print lower,',',upper,',',infin,',',correl #print correl.shape #print kwds.items() error, cdfvalue, inform = scipy.stats.kde.mvn.mvndst(lower,upper,infin,correl,**kwds) if inform: print('something wrong', informcode[inform], error) return cdfvalue def mvnormcdf(upper, mu, cov, lower=None, **kwds): '''multivariate normal cumulative distribution function This is a wrapper for scipy.stats.kde.mvn.mvndst which calculates a rectangular integral over a multivariate normal distribution. Parameters ---------- lower, upper : array_like, 1d lower and upper integration limits with length equal to the number of dimensions of the multivariate normal distribution. It can contain -np.inf or np.inf for open integration intervals mu : array_lik, 1d list or array of means cov : array_like, 2d specifies covariance matrix optional keyword parameters to influence integration * maxpts : int, maximum number of function values allowed. This parameter can be used to limit the time. A sensible strategy is to start with `maxpts` = 1000*N, and then increase `maxpts` if ERROR is too large. * abseps : float absolute error tolerance. * releps : float relative error tolerance. Returns ------- cdfvalue : float value of the integral Notes ----- This function normalizes the location and scale of the multivariate normal distribution and then uses `mvstdnormcdf` to call the integration. See Also -------- mvstdnormcdf : location and scale standardized multivariate normal cdf ''' upper = np.array(upper) if lower is None: lower = -np.ones(upper.shape) * np.inf else: lower = np.array(lower) cov = np.array(cov) stdev = np.sqrt(np.diag(cov)) # standard deviation vector #do I need to make sure stdev is float and not int? #is this correct to normalize to corr? lower = (lower - mu)/stdev upper = (upper - mu)/stdev divrow = np.atleast_2d(stdev) corr = cov/divrow/divrow.T #v/np.sqrt(np.atleast_2d(np.diag(covv)))/np.sqrt(np.atleast_2d(np.diag(covv))).T return mvstdnormcdf(lower, upper, corr, **kwds) statsmodels-0.12.2/statsmodels/sandbox/distributions/genpareto.py000066400000000000000000000235121400612667500254100ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Thu Aug 12 14:59:03 2010 Warning: not tried out or tested yet, Done Author: josef-pktd """ import numpy as np from scipy import stats from scipy.special import comb from scipy.stats.distributions import rv_continuous import matplotlib.pyplot as plt from numpy import where, inf from numpy import abs as np_abs ## Generalized Pareto with reversed sign of c as in literature class genpareto2_gen(rv_continuous): def _argcheck(self, c): c = np.asarray(c) self.b = where(c > 0, 1.0/np_abs(c), inf) return where(c==0, 0, 1) def _pdf(self, x, c): Px = np.power(1-c*x,-1.0+1.0/c) return Px def _logpdf(self, x, c): return (-1.0+1.0/c) * np.log1p(-c*x) def _cdf(self, x, c): return 1.0 - np.power(1-c*x,1.0/c) def _ppf(self, q, c): vals = -1.0/c * (np.power(1-q, c)-1) return vals def _munp(self, n, c): k = np.arange(0,n+1) val = (1.0/c)**n * np.sum(comb(n,k)*(-1)**k / (1.0+c*k),axis=0) return where(c*n > -1, val, inf) def _entropy(self, c): if (c < 0): return 1-c else: self.b = 1.0 / c return rv_continuous._entropy(self, c) genpareto2 = genpareto2_gen(a=0.0,name='genpareto', longname="A generalized Pareto", shapes='c',extradoc=""" Generalized Pareto distribution genpareto2.pdf(x,c) = (1+c*x)**(-1-1/c) for c != 0, and for x >= 0 for all c, and x < 1/abs(c) for c < 0. """) shape, loc, scale = 0.5, 0, 1 rv = np.arange(5) quant = [0.01, 0.1, 0.5, 0.9, 0.99] for method, x in [('pdf', rv), ('cdf', rv), ('sf', rv), ('ppf', quant), ('isf', quant)]: print(getattr(genpareto2, method)(x, shape, loc, scale)) print(getattr(stats.genpareto, method)(x, -shape, loc, scale)) print(genpareto2.stats(shape, loc, scale, moments='mvsk')) print(stats.genpareto.stats(-shape, loc, scale, moments='mvsk')) print(genpareto2.entropy(shape, loc, scale)) print(stats.genpareto.entropy(-shape, loc, scale)) def paramstopot(thresh, shape, scale): '''transform shape scale for peak over threshold y = x-u|x>u ~ GPD(k, sigma-k*u) if x ~ GPD(k, sigma) notation of de Zea Bermudez, Kotz k, sigma is shape, scale ''' return shape, scale - shape*thresh def paramsfrompot(thresh, shape, scalepot): return shape, scalepot + shape*thresh def warnif(cond, msg): if not cond: print(msg, 'does not hold') def meanexcess(thresh, shape, scale): '''mean excess function of genpareto assert are inequality conditions in de Zea Bermudez, Kotz ''' warnif(shape > -1, 'shape > -1') warnif(thresh >= 0, 'thresh >= 0') #make it weak inequality warnif((scale - shape*thresh) > 0, '(scale - shape*thresh) > 0') return (scale - shape*thresh) / (1 + shape) def meanexcess_plot(data, params=None, lidx=100, uidx=10, method='emp', plot=0): if method == 'est': #does not make much sense yet, #estimate the parameters and use theoretical meanexcess if params is None: raise NotImplementedError else: pass #estimate parames elif method == 'emp': #calculate meanexcess from data datasorted = np.sort(data) meanexcess = (datasorted[::-1].cumsum())/np.arange(1,len(data)+1) - datasorted[::-1] meanexcess = meanexcess[::-1] if plot: plt.plot(datasorted[:-uidx], meanexcess[:-uidx]) if params is not None: shape, scale = params plt.plot(datasorted[:-uidx], (scale - datasorted[:-uidx] * shape) / (1. + shape)) return datasorted, meanexcess print(meanexcess(5, -0.5, 10)) print(meanexcess(5, -2, 10)) data = genpareto2.rvs(-0.75, scale=5, size=1000) #data = np.random.uniform(50, size=1000) #data = stats.norm.rvs(0, np.sqrt(50), size=1000) #data = stats.pareto.rvs(1.5, np.sqrt(50), size=1000) tmp = meanexcess_plot(data, params=(-0.75, 5), plot=1) print(tmp[1][-20:]) print(tmp[0][-20:]) #plt.show() def meanexcess_emp(data): datasorted = np.sort(data).astype(float) meanexcess = (datasorted[::-1].cumsum())/np.arange(1,len(data)+1) - datasorted[::-1] meancont = (datasorted[::-1].cumsum())/np.arange(1,len(data)+1) meanexcess = meanexcess[::-1] return datasorted, meanexcess, meancont[::-1] def meanexcess_dist(self, lb, *args, **kwds): #default function in expect is identity # need args in call if np.ndim(lb) == 0: return self.expect(lb=lb, conditional=True) else: return np.array([self.expect(lb=lbb, conditional=True) for lbb in lb]) ds, me, mc = meanexcess_emp(1.*np.arange(1,10)) print(ds) print(me) print(mc) print(meanexcess_dist(stats.norm, lb=0.5)) print(meanexcess_dist(stats.norm, lb=[-np.inf, -0.5, 0, 0.5])) rvs = stats.norm.rvs(size=100000) rvs = rvs - rvs.mean() print(rvs.mean(), rvs[rvs>-0.5].mean(), rvs[rvs>0].mean(), rvs[rvs>0.5].mean()) ''' [ 1. 0.5 0. 0. 0. ] [ 1. 0.5 0. 0. 0. ] [ 0. 0.75 1. 1. 1. ] [ 0. 0.75 1. 1. 1. ] [ 1. 0.25 0. 0. 0. ] [ 1. 0.25 0. 0. 0. ] [ 0.01002513 0.1026334 0.58578644 1.36754447 1.8 ] [ 0.01002513 0.1026334 0.58578644 1.36754447 1.8 ] [ 1.8 1.36754447 0.58578644 0.1026334 0.01002513] [ 1.8 1.36754447 0.58578644 0.1026334 0.01002513] (array(0.66666666666666674), array(0.22222222222222243), array(0.56568542494923058), array(-0.60000000000032916)) (array(0.66666666666666674), array(0.22222222222222243), array(0.56568542494923058), array(-0.60000000000032916)) 0.5 0.5 25.0 shape > -1 does not hold -20 [ 41.4980671 42.83145298 44.24197578 45.81622844 47.57145212 49.52692287 51.70553275 54.0830766 56.61358997 59.53409167 62.8970042 66.73494156 71.04227973 76.24015612 82.71835988 89.79611663 99.4252195 106.2372462 94.83432424 0. ] [ 15.79736355 16.16373531 17.44204268 17.47968055 17.73264951 18.23939099 19.02638455 20.79746264 23.7169161 24.48807136 25.90496638 28.35556795 32.27623618 34.65714495 37.37093362 47.32957609 51.27970515 78.98913941 129.04309012 189.66864848] >>> np.arange(10) array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> meanexcess_emp(np.arange(10)) (array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]), array([4, 4, 5, 5, 5, 6, 6, 5, 4, 0]), array([9, 8, 8, 7, 7, 6, 6, 5, 5, 4])) >>> meanexcess_emp(1*np.arange(10)) (array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]), array([4, 4, 5, 5, 5, 6, 6, 5, 4, 0]), array([9, 8, 8, 7, 7, 6, 6, 5, 5, 4])) >>> meanexcess_emp(1.*np.arange(10)) (array([ 0., 1., 2., 3., 4., 5., 6., 7., 8., 9.]), array([ 4.5 , 4.88888889, 5.25 , 5.57142857, 5.83333333, 6. , 6. , 5.66666667, 4.5 , 0. ]), array([ 9. , 8.5, 8. , 7.5, 7. , 6.5, 6. , 5.5, 5. , 4.5])) >>> meanexcess_emp(0.5**np.arange(10)) (array([ 0.00195313, 0.00390625, 0.0078125 , 0.015625 , 0.03125 , 0.0625 , 0.125 , 0.25 , 0.5 , 1. ]), array([ 0.19960938, 0.22135417, 0.24804688, 0.28125 , 0.32291667, 0.375 , 0.4375 , 0.5 , 0.5 , 0. ]), array([ 1. , 0.75 , 0.58333333, 0.46875 , 0.3875 , 0.328125 , 0.28348214, 0.24902344, 0.22178819, 0.19980469])) >>> meanexcess_emp(np.arange(10)**0.5) (array([ 0. , 1. , 1.41421356, 1.73205081, 2. , 2.23606798, 2.44948974, 2.64575131, 2.82842712, 3. ]), array([ 1.93060005, 2.03400006, 2.11147337, 2.16567659, 2.19328936, 2.18473364, 2.11854461, 1.94280904, 1.5 , 0. ]), array([ 3. , 2.91421356, 2.82472615, 2.73091704, 2.63194723, 2.52662269, 2.41311242, 2.28825007, 2.14511117, 1.93060005])) >>> meanexcess_emp(np.arange(10)**-2) (array([-2147483648, 0, 0, 0, 0, 0, 0, 0, 0, 1]), array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]), array([ 1, 0, 0, 0, 0, 0, 0, 0, 0, -214748365])) >>> meanexcess_emp(np.arange(10)**(-0.5)) (array([ 0.33333333, 0.35355339, 0.37796447, 0.40824829, 0.4472136 , 0.5 , 0.57735027, 0.70710678, 1. , Inf]), array([ Inf, Inf, Inf, Inf, Inf, Inf, Inf, Inf, Inf, NaN]), array([ Inf, Inf, Inf, Inf, Inf, Inf, Inf, Inf, Inf, Inf])) >>> np.arange(10)**(-0.5) array([ Inf, 1. , 0.70710678, 0.57735027, 0.5 , 0.4472136 , 0.40824829, 0.37796447, 0.35355339, 0.33333333]) >>> meanexcess_emp(np.arange(1,10)**(-0.5)) (array([ 0.33333333, 0.35355339, 0.37796447, 0.40824829, 0.4472136 , 0.5 , 0.57735027, 0.70710678, 1. ]), array([ 0.4857152 , 0.50223543, 0.51998842, 0.53861177, 0.55689141, 0.57111426, 0.56903559, 0.5 , 0. ]), array([ 1. , 0.85355339, 0.76148568, 0.69611426, 0.64633413, 0.60665316, 0.57398334, 0.5464296 , 0.52275224])) >>> meanexcess_emp(np.arange(1,10)) (array([1, 2, 3, 4, 5, 6, 7, 8, 9]), array([4, 5, 5, 5, 6, 6, 5, 4, 0]), array([9, 8, 8, 7, 7, 6, 6, 5, 5])) >>> meanexcess_emp(1.*np.arange(1,10)) (array([ 1., 2., 3., 4., 5., 6., 7., 8., 9.]), array([ 4.88888889, 5.25 , 5.57142857, 5.83333333, 6. , 6. , 5.66666667, 4.5 , 0. ]), array([ 9. , 8.5, 8. , 7.5, 7. , 6.5, 6. , 5.5, 5. ])) >>> datasorted = np.sort(1.*np.arange(1,10)) >>> (datasorted[::-1].cumsum()-datasorted[::-1]) array([ 0., 9., 17., 24., 30., 35., 39., 42., 44.]) >>> datasorted[::-1].cumsum() array([ 9., 17., 24., 30., 35., 39., 42., 44., 45.]) >>> datasorted[::-1] array([ 9., 8., 7., 6., 5., 4., 3., 2., 1.]) >>> ''' statsmodels-0.12.2/statsmodels/sandbox/distributions/gof_new.py000066400000000000000000000516111400612667500250510ustar00rootroot00000000000000'''More Goodness of fit tests contains GOF : 1 sample gof tests based on Stephens 1970, plus AD A^2 bootstrap : vectorized bootstrap p-values for gof test with fitted parameters Created : 2011-05-21 Author : Josef Perktold parts based on ks_2samp and kstest from scipy.stats (license: Scipy BSD, but were completely rewritten by Josef Perktold) References ---------- ''' from statsmodels.compat.python import lmap import numpy as np from scipy.stats import distributions from statsmodels.tools.decorators import cache_readonly from scipy.special import kolmogorov as ksprob #from scipy.stats unchanged def ks_2samp(data1, data2): """ Computes the Kolmogorov-Smirnof statistic on 2 samples. This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution. Parameters ---------- a, b : sequence of 1-D ndarrays two arrays of sample observations assumed to be drawn from a continuous distribution, sample sizes can be different Returns ------- D : float KS statistic p-value : float two-tailed p-value Notes ----- This tests whether 2 samples are drawn from the same distribution. Note that, like in the case of the one-sample K-S test, the distribution is assumed to be continuous. This is the two-sided test, one-sided tests are not implemented. The test uses the two-sided asymptotic Kolmogorov-Smirnov distribution. If the K-S statistic is small or the p-value is high, then we cannot reject the hypothesis that the distributions of the two samples are the same. Examples -------- >>> from scipy import stats >>> import numpy as np >>> from scipy.stats import ks_2samp >>> #fix random seed to get the same result >>> np.random.seed(12345678) >>> n1 = 200 # size of first sample >>> n2 = 300 # size of second sample different distribution we can reject the null hypothesis since the pvalue is below 1% >>> rvs1 = stats.norm.rvs(size=n1,loc=0.,scale=1) >>> rvs2 = stats.norm.rvs(size=n2,loc=0.5,scale=1.5) >>> ks_2samp(rvs1,rvs2) (0.20833333333333337, 4.6674975515806989e-005) slightly different distribution we cannot reject the null hypothesis at a 10% or lower alpha since the pvalue at 0.144 is higher than 10% >>> rvs3 = stats.norm.rvs(size=n2,loc=0.01,scale=1.0) >>> ks_2samp(rvs1,rvs3) (0.10333333333333333, 0.14498781825751686) identical distribution we cannot reject the null hypothesis since the pvalue is high, 41% >>> rvs4 = stats.norm.rvs(size=n2,loc=0.0,scale=1.0) >>> ks_2samp(rvs1,rvs4) (0.07999999999999996, 0.41126949729859719) """ data1, data2 = lmap(np.asarray, (data1, data2)) n1 = data1.shape[0] n2 = data2.shape[0] n1 = len(data1) n2 = len(data2) data1 = np.sort(data1) data2 = np.sort(data2) data_all = np.concatenate([data1,data2]) #reminder: searchsorted inserts 2nd into 1st array cdf1 = np.searchsorted(data1,data_all,side='right')/(1.0*n1) cdf2 = (np.searchsorted(data2,data_all,side='right'))/(1.0*n2) d = np.max(np.absolute(cdf1-cdf2)) #Note: d absolute not signed distance en = np.sqrt(n1*n2/float(n1+n2)) try: prob = ksprob((en+0.12+0.11/en)*d) except: prob = 1.0 return d, prob #from scipy.stats unchanged def kstest(rvs, cdf, args=(), N=20, alternative = 'two_sided', mode='approx',**kwds): """ Perform the Kolmogorov-Smirnov test for goodness of fit This performs a test of the distribution G(x) of an observed random variable against a given distribution F(x). Under the null hypothesis the two distributions are identical, G(x)=F(x). The alternative hypothesis can be either 'two_sided' (default), 'less' or 'greater'. The KS test is only valid for continuous distributions. Parameters ---------- rvs : str or array or callable string: name of a distribution in scipy.stats array: 1-D observations of random variables callable: function to generate random variables, requires keyword argument `size` cdf : str or callable string: name of a distribution in scipy.stats, if rvs is a string then cdf can evaluate to `False` or be the same as rvs callable: function to evaluate cdf args : tuple, sequence distribution parameters, used if rvs or cdf are strings N : int sample size if rvs is string or callable alternative : 'two_sided' (default), 'less' or 'greater' defines the alternative hypothesis (see explanation) mode : 'approx' (default) or 'asymp' defines the distribution used for calculating p-value 'approx' : use approximation to exact distribution of test statistic 'asymp' : use asymptotic distribution of test statistic Returns ------- D : float KS test statistic, either D, D+ or D- p-value : float one-tailed or two-tailed p-value Notes ----- In the one-sided test, the alternative is that the empirical cumulative distribution function of the random variable is "less" or "greater" than the cumulative distribution function F(x) of the hypothesis, G(x)<=F(x), resp. G(x)>=F(x). Examples -------- >>> from scipy import stats >>> import numpy as np >>> from scipy.stats import kstest >>> x = np.linspace(-15,15,9) >>> kstest(x,'norm') (0.44435602715924361, 0.038850142705171065) >>> np.random.seed(987654321) # set random seed to get the same result >>> kstest('norm','',N=100) (0.058352892479417884, 0.88531190944151261) is equivalent to this >>> np.random.seed(987654321) >>> kstest(stats.norm.rvs(size=100),'norm') (0.058352892479417884, 0.88531190944151261) Test against one-sided alternative hypothesis: >>> np.random.seed(987654321) Shift distribution to larger values, so that cdf_dgp(x)< norm.cdf(x): >>> x = stats.norm.rvs(loc=0.2, size=100) >>> kstest(x,'norm', alternative = 'less') (0.12464329735846891, 0.040989164077641749) Reject equal distribution against alternative hypothesis: less >>> kstest(x,'norm', alternative = 'greater') (0.0072115233216311081, 0.98531158590396395) Do not reject equal distribution against alternative hypothesis: greater >>> kstest(x,'norm', mode='asymp') (0.12464329735846891, 0.08944488871182088) Testing t distributed random variables against normal distribution: With 100 degrees of freedom the t distribution looks close to the normal distribution, and the kstest does not reject the hypothesis that the sample came from the normal distribution >>> np.random.seed(987654321) >>> stats.kstest(stats.t.rvs(100,size=100),'norm') (0.072018929165471257, 0.67630062862479168) With 3 degrees of freedom the t distribution looks sufficiently different from the normal distribution, that we can reject the hypothesis that the sample came from the normal distribution at a alpha=10% level >>> np.random.seed(987654321) >>> stats.kstest(stats.t.rvs(3,size=100),'norm') (0.131016895759829, 0.058826222555312224) """ if isinstance(rvs, str): #cdf = getattr(stats, rvs).cdf if (not cdf) or (cdf == rvs): cdf = getattr(distributions, rvs).cdf rvs = getattr(distributions, rvs).rvs else: raise AttributeError('if rvs is string, cdf has to be the same distribution') if isinstance(cdf, str): cdf = getattr(distributions, cdf).cdf if callable(rvs): kwds = {'size':N} vals = np.sort(rvs(*args,**kwds)) else: vals = np.sort(rvs) N = len(vals) cdfvals = cdf(vals, *args) if alternative in ['two_sided', 'greater']: Dplus = (np.arange(1.0, N+1)/N - cdfvals).max() if alternative == 'greater': return Dplus, distributions.ksone.sf(Dplus,N) if alternative in ['two_sided', 'less']: Dmin = (cdfvals - np.arange(0.0, N)/N).max() if alternative == 'less': return Dmin, distributions.ksone.sf(Dmin,N) if alternative == 'two_sided': D = np.max([Dplus,Dmin]) if mode == 'asymp': return D, distributions.kstwobign.sf(D*np.sqrt(N)) if mode == 'approx': pval_two = distributions.kstwobign.sf(D*np.sqrt(N)) if N > 2666 or pval_two > 0.80 - N*0.3/1000.0 : return D, distributions.kstwobign.sf(D*np.sqrt(N)) else: return D, distributions.ksone.sf(D,N)*2 #TODO: split into modification and pvalue functions separately ? # for separate testing and combining different pieces def dplus_st70_upp(stat, nobs): mod_factor = np.sqrt(nobs) + 0.12 + 0.11 / np.sqrt(nobs) stat_modified = stat * mod_factor pval = np.exp(-2 * stat_modified**2) digits = np.sum(stat > np.array([0.82, 0.82, 1.00])) #repeat low to get {0,2,3} return stat_modified, pval, digits dminus_st70_upp = dplus_st70_upp def d_st70_upp(stat, nobs): mod_factor = np.sqrt(nobs) + 0.12 + 0.11 / np.sqrt(nobs) stat_modified = stat * mod_factor pval = 2 * np.exp(-2 * stat_modified**2) digits = np.sum(stat > np.array([0.91, 0.91, 1.08])) #repeat low to get {0,2,3} return stat_modified, pval, digits def v_st70_upp(stat, nobs): mod_factor = np.sqrt(nobs) + 0.155 + 0.24 / np.sqrt(nobs) #repeat low to get {0,2,3} stat_modified = stat * mod_factor zsqu = stat_modified**2 pval = (8 * zsqu - 2) * np.exp(-2 * zsqu) digits = np.sum(stat > np.array([1.06, 1.06, 1.26])) return stat_modified, pval, digits def wsqu_st70_upp(stat, nobs): nobsinv = 1. / nobs stat_modified = (stat - 0.4 * nobsinv + 0.6 * nobsinv**2) * (1 + nobsinv) pval = 0.05 * np.exp(2.79 - 6 * stat_modified) digits = np.nan # some explanation in txt #repeat low to get {0,2,3} return stat_modified, pval, digits def usqu_st70_upp(stat, nobs): nobsinv = 1. / nobs stat_modified = (stat - 0.1 * nobsinv + 0.1 * nobsinv**2) stat_modified *= (1 + 0.8 * nobsinv) pval = 2 * np.exp(- 2 * stat_modified * np.pi**2) digits = np.sum(stat > np.array([0.29, 0.29, 0.34])) #repeat low to get {0,2,3} return stat_modified, pval, digits def a_st70_upp(stat, nobs): nobsinv = 1. / nobs stat_modified = (stat - 0.7 * nobsinv + 0.9 * nobsinv**2) stat_modified *= (1 + 1.23 * nobsinv) pval = 1.273 * np.exp(- 2 * stat_modified / 2. * np.pi**2) digits = np.sum(stat > np.array([0.11, 0.11, 0.452])) #repeat low to get {0,2,3} return stat_modified, pval, digits gof_pvals = {} gof_pvals['stephens70upp'] = { 'd_plus' : dplus_st70_upp, 'd_minus' : dplus_st70_upp, 'd' : d_st70_upp, 'v' : v_st70_upp, 'wsqu' : wsqu_st70_upp, 'usqu' : usqu_st70_upp, 'a' : a_st70_upp } def pval_kstest_approx(D, N): pval_two = distributions.kstwobign.sf(D*np.sqrt(N)) if N > 2666 or pval_two > 0.80 - N*0.3/1000.0 : return D, distributions.kstwobign.sf(D*np.sqrt(N)), np.nan else: return D, distributions.ksone.sf(D,N)*2, np.nan gof_pvals['scipy'] = { 'd_plus' : lambda Dplus, N: (Dplus, distributions.ksone.sf(Dplus, N), np.nan), 'd_minus' : lambda Dmin, N: (Dmin, distributions.ksone.sf(Dmin,N), np.nan), 'd' : lambda D, N: (D, distributions.kstwobign.sf(D*np.sqrt(N)), np.nan) } gof_pvals['scipy_approx'] = { 'd' : pval_kstest_approx } class GOF(object): '''One Sample Goodness of Fit tests includes Kolmogorov-Smirnov D, D+, D-, Kuiper V, Cramer-von Mises W^2, U^2 and Anderson-Darling A, A^2. The p-values for all tests except for A^2 are based on the approximatiom given in Stephens 1970. A^2 has currently no p-values. For the Kolmogorov-Smirnov test the tests as given in scipy.stats are also available as options. design: I might want to retest with different distributions, to calculate data summary statistics only once, or add separate class that holds summary statistics and data (sounds good). ''' def __init__(self, rvs, cdf, args=(), N=20): if isinstance(rvs, str): #cdf = getattr(stats, rvs).cdf if (not cdf) or (cdf == rvs): cdf = getattr(distributions, rvs).cdf rvs = getattr(distributions, rvs).rvs else: raise AttributeError('if rvs is string, cdf has to be the same distribution') if isinstance(cdf, str): cdf = getattr(distributions, cdf).cdf if callable(rvs): kwds = {'size':N} vals = np.sort(rvs(*args,**kwds)) else: vals = np.sort(rvs) N = len(vals) cdfvals = cdf(vals, *args) self.nobs = N self.vals_sorted = vals self.cdfvals = cdfvals @cache_readonly def d_plus(self): nobs = self.nobs cdfvals = self.cdfvals return (np.arange(1.0, nobs+1)/nobs - cdfvals).max() @cache_readonly def d_minus(self): nobs = self.nobs cdfvals = self.cdfvals return (cdfvals - np.arange(0.0, nobs)/nobs).max() @cache_readonly def d(self): return np.max([self.d_plus, self.d_minus]) @cache_readonly def v(self): '''Kuiper''' return self.d_plus + self.d_minus @cache_readonly def wsqu(self): '''Cramer von Mises''' nobs = self.nobs cdfvals = self.cdfvals #use literal formula, TODO: simplify with arange(,,2) wsqu = ((cdfvals - (2. * np.arange(1., nobs+1) - 1)/nobs/2.)**2).sum() \ + 1./nobs/12. return wsqu @cache_readonly def usqu(self): nobs = self.nobs cdfvals = self.cdfvals #use literal formula, TODO: simplify with arange(,,2) usqu = self.wsqu - nobs * (cdfvals.mean() - 0.5)**2 return usqu @cache_readonly def a(self): nobs = self.nobs cdfvals = self.cdfvals #one loop instead of large array msum = 0 for j in range(1,nobs): mj = cdfvals[j] - cdfvals[:j] mask = (mj > 0.5) mj[mask] = 1 - mj[mask] msum += mj.sum() a = nobs / 4. - 2. / nobs * msum return a @cache_readonly def asqu(self): '''Stephens 1974, does not have p-value formula for A^2''' nobs = self.nobs cdfvals = self.cdfvals asqu = -((2. * np.arange(1., nobs+1) - 1) * (np.log(cdfvals) + np.log(1-cdfvals[::-1]) )).sum()/nobs - nobs return asqu def get_test(self, testid='d', pvals='stephens70upp'): ''' ''' #print gof_pvals[pvals][testid] stat = getattr(self, testid) if pvals == 'stephens70upp': return gof_pvals[pvals][testid](stat, self.nobs), stat else: return gof_pvals[pvals][testid](stat, self.nobs) def gof_mc(randfn, distr, nobs=100): #print '\nIs it correctly sized?' from collections import defaultdict results = defaultdict(list) for i in range(1000): rvs = randfn(nobs) goft = GOF(rvs, distr) for ti in all_gofs: results[ti].append(goft.get_test(ti, 'stephens70upp')[0][1]) resarr = np.array([results[ti] for ti in all_gofs]) print(' ', ' '.join(all_gofs)) print('at 0.01:', (resarr < 0.01).mean(1)) print('at 0.05:', (resarr < 0.05).mean(1)) print('at 0.10:', (resarr < 0.1).mean(1)) def asquare(cdfvals, axis=0): '''vectorized Anderson Darling A^2, Stephens 1974''' ndim = len(cdfvals.shape) nobs = cdfvals.shape[axis] slice_reverse = [slice(None)] * ndim #might make copy if not specific axis??? islice = [None] * ndim islice[axis] = slice(None) slice_reverse[axis] = slice(None, None, -1) asqu = -((2. * np.arange(1., nobs+1)[tuple(islice)] - 1) * (np.log(cdfvals) + np.log(1-cdfvals[tuple(slice_reverse)]))/nobs).sum(axis) \ - nobs return asqu #class OneSGOFFittedVec(object): # '''for vectorized fitting''' # currently I use the bootstrap as function instead of full class #note: kwds loc and scale are a pain # I would need to overwrite rvs, fit and cdf depending on fixed parameters #def bootstrap(self, distr, args=(), kwds={}, nobs=200, nrep=1000, def bootstrap(distr, args=(), nobs=200, nrep=100, value=None, batch_size=None): '''Monte Carlo (or parametric bootstrap) p-values for gof currently hardcoded for A^2 only assumes vectorized fit_vec method, builds and analyses (nobs, nrep) sample in one step rename function to less generic this works also with nrep=1 ''' #signature similar to kstest ? #delegate to fn ? #rvs_kwds = {'size':(nobs, nrep)} #rvs_kwds.update(kwds) #it will be better to build a separate batch function that calls bootstrap #keep batch if value is true, but batch iterate from outside if stat is returned if batch_size is not None: if value is None: raise ValueError('using batching requires a value') n_batch = int(np.ceil(nrep/float(batch_size))) count = 0 for irep in range(n_batch): rvs = distr.rvs(args, **{'size':(batch_size, nobs)}) params = distr.fit_vec(rvs, axis=1) params = lmap(lambda x: np.expand_dims(x, 1), params) cdfvals = np.sort(distr.cdf(rvs, params), axis=1) stat = asquare(cdfvals, axis=1) count += (stat >= value).sum() return count / float(n_batch * batch_size) else: #rvs = distr.rvs(args, **kwds) #extension to distribution kwds ? rvs = distr.rvs(args, **{'size':(nrep, nobs)}) params = distr.fit_vec(rvs, axis=1) params = lmap(lambda x: np.expand_dims(x, 1), params) cdfvals = np.sort(distr.cdf(rvs, params), axis=1) stat = asquare(cdfvals, axis=1) if value is None: #return all bootstrap results stat_sorted = np.sort(stat) return stat_sorted else: #calculate and return specific p-value return (stat >= value).mean() def bootstrap2(value, distr, args=(), nobs=200, nrep=100): '''Monte Carlo (or parametric bootstrap) p-values for gof currently hardcoded for A^2 only non vectorized, loops over all parametric bootstrap replications and calculates and returns specific p-value, rename function to less generic ''' #signature similar to kstest ? #delegate to fn ? #rvs_kwds = {'size':(nobs, nrep)} #rvs_kwds.update(kwds) count = 0 for irep in range(nrep): #rvs = distr.rvs(args, **kwds) #extension to distribution kwds ? rvs = distr.rvs(args, **{'size':nobs}) params = distr.fit_vec(rvs) cdfvals = np.sort(distr.cdf(rvs, params)) stat = asquare(cdfvals, axis=0) count += (stat >= value) return count * 1. / nrep class NewNorm(object): '''just a holder for modified distributions ''' def fit_vec(self, x, axis=0): return x.mean(axis), x.std(axis) def cdf(self, x, args): return distributions.norm.cdf(x, loc=args[0], scale=args[1]) def rvs(self, args, size): loc=args[0] scale=args[1] return loc + scale * distributions.norm.rvs(size=size) if __name__ == '__main__': from scipy import stats #rvs = np.random.randn(1000) rvs = stats.t.rvs(3, size=200) print('scipy kstest') print(kstest(rvs, 'norm')) goft = GOF(rvs, 'norm') print(goft.get_test()) all_gofs = ['d', 'd_plus', 'd_minus', 'v', 'wsqu', 'usqu', 'a'] for ti in all_gofs: print(ti, goft.get_test(ti, 'stephens70upp')) print('\nIs it correctly sized?') from collections import defaultdict results = defaultdict(list) nobs = 200 for i in range(100): rvs = np.random.randn(nobs) goft = GOF(rvs, 'norm') for ti in all_gofs: results[ti].append(goft.get_test(ti, 'stephens70upp')[0][1]) resarr = np.array([results[ti] for ti in all_gofs]) print(' ', ' '.join(all_gofs)) print('at 0.01:', (resarr < 0.01).mean(1)) print('at 0.05:', (resarr < 0.05).mean(1)) print('at 0.10:', (resarr < 0.1).mean(1)) gof_mc(lambda nobs: stats.t.rvs(3, size=nobs), 'norm', nobs=200) nobs = 200 nrep = 100 bt = bootstrap(NewNorm(), args=(0,1), nobs=nobs, nrep=nrep, value=None) quantindex = np.floor(nrep * np.array([0.99, 0.95, 0.9])).astype(int) print(bt[quantindex]) #the bootstrap results match Stephens pretty well for nobs=100, but not so well for #large (1000) or small (20) nobs ''' >>> np.array([15.0, 10.0, 5.0, 2.5, 1.0])/100. #Stephens array([ 0.15 , 0.1 , 0.05 , 0.025, 0.01 ]) >>> nobs = 100 >>> [bootstrap(NewNorm(), args=(0,1), nobs=nobs, nrep=10000, value=c/ (1 + 4./nobs - 25./nobs**2)) for c in [0.576, 0.656, 0.787, 0.918, 1.092]] [0.1545, 0.10009999999999999, 0.049000000000000002, 0.023, 0.0104] >>> ''' statsmodels-0.12.2/statsmodels/sandbox/distributions/multivariate.py000066400000000000000000000113471400612667500261350ustar00rootroot00000000000000'''Multivariate Distribution Probability of a multivariate t distribution Now also mvstnormcdf has tests against R mvtnorm Still need non-central t, extra options, and convenience function for location, scale version. Author: Josef Perktold License: BSD (3-clause) Reference: Genz and Bretz for formula ''' import numpy as np from scipy import integrate, stats, special from scipy.stats import chi from .extras import mvstdnormcdf from numpy import exp as np_exp from numpy import log as np_log from scipy.special import gamma as sps_gamma from scipy.special import gammaln as sps_gammaln def chi2_pdf(self, x, df): '''pdf of chi-square distribution''' #from scipy.stats.distributions Px = x**(df/2.0-1)*np.exp(-x/2.0) Px /= special.gamma(df/2.0)* 2**(df/2.0) return Px def chi_pdf(x, df): tmp = (df-1.)*np_log(x) + (-x*x*0.5) - (df*0.5-1)*np_log(2.0) \ - sps_gammaln(df*0.5) return np_exp(tmp) #return x**(df-1.)*np_exp(-x*x*0.5)/(2.0)**(df*0.5-1)/sps_gamma(df*0.5) def chi_logpdf(x, df): tmp = (df-1.)*np_log(x) + (-x*x*0.5) - (df*0.5-1)*np_log(2.0) \ - sps_gammaln(df*0.5) return tmp def funbgh(s, a, b, R, df): sqrt_df = np.sqrt(df+0.5) ret = chi_logpdf(s,df) ret += np_log(mvstdnormcdf(s*a/sqrt_df, s*b/sqrt_df, R, maxpts=1000000, abseps=1e-6)) ret = np_exp(ret) return ret def funbgh2(s, a, b, R, df): n = len(a) sqrt_df = np.sqrt(df) #np.power(s, df-1) * np_exp(-s*s*0.5) return np_exp((df-1)*np_log(s)-s*s*0.5) \ * mvstdnormcdf(s*a/sqrt_df, s*b/sqrt_df, R[np.tril_indices(n, -1)], maxpts=1000000, abseps=1e-4) def bghfactor(df): return np.power(2.0, 1-df*0.5) / sps_gamma(df*0.5) def mvstdtprob(a, b, R, df, ieps=1e-5, quadkwds=None, mvstkwds=None): """ Probability of rectangular area of standard t distribution assumes mean is zero and R is correlation matrix Notes ----- This function does not calculate the estimate of the combined error between the underlying multivariate normal probability calculations and the integration. """ kwds = dict(args=(a, b, R, df), epsabs=1e-4, epsrel=1e-2, limit=150) if quadkwds is not None: kwds.update(quadkwds) lower, upper = chi.ppf([ieps, 1 - ieps], df) res, err = integrate.quad(funbgh2, lower, upper, **kwds) prob = res * bghfactor(df) return prob #written by Enzo Michelangeli, style changes by josef-pktd # Student's T random variable def multivariate_t_rvs(m, S, df=np.inf, n=1): '''generate random variables of multivariate t distribution Parameters ---------- m : array_like mean of random variable, length determines dimension of random variable S : array_like square array of covariance matrix df : int or float degrees of freedom n : int number of observations, return random array will be (n, len(m)) Returns ------- rvs : ndarray, (n, len(m)) each row is an independent draw of a multivariate t distributed random variable ''' m = np.asarray(m) d = len(m) if df == np.inf: x = 1. else: x = np.random.chisquare(df, n)/df z = np.random.multivariate_normal(np.zeros(d),S,(n,)) return m + z/np.sqrt(x)[:,None] # same output format as random.multivariate_normal if __name__ == '__main__': corr = np.asarray([[1.0, 0, 0.5],[0,1,0],[0.5,0,1]]) corr_indep = np.asarray([[1.0, 0, 0],[0,1,0],[0,0,1]]) corr_equal = np.asarray([[1.0, 0.5, 0.5],[0.5,1,0.5],[0.5,0.5,1]]) R = corr_equal a = np.array([-np.inf,-np.inf,-100.0]) a = np.array([-0.96,-0.96,-0.96]) b = np.array([0.0,0.0,0.0]) b = np.array([0.96,0.96, 0.96]) a[:] = -1 b[:] = 3 df = 10. sqrt_df = np.sqrt(df) print(mvstdnormcdf(a, b, corr, abseps=1e-6)) #print integrate.quad(funbgh, 0, np.inf, args=(a,b,R,df)) print((stats.t.cdf(b[0], df) - stats.t.cdf(a[0], df))**3) s = 1 print(mvstdnormcdf(s*a/sqrt_df, s*b/sqrt_df, R)) df=4 print(mvstdtprob(a, b, R, df)) S = np.array([[1.,.5],[.5,1.]]) print(multivariate_t_rvs([10.,20.], S, 2, 5)) nobs = 10000 rvst = multivariate_t_rvs([10.,20.], S, 2, nobs) print(np.sum((rvst<[10.,20.]).all(1),0) * 1. / nobs) print(mvstdtprob(-np.inf*np.ones(2), np.zeros(2), R[:2,:2], 2)) ''' > lower <- -1 > upper <- 3 > df <- 4 > corr <- diag(3) > delta <- rep(0, 3) > pmvt(lower=lower, upper=upper, delta=delta, df=df, corr=corr) [1] 0.5300413 attr(,"error") [1] 4.321136e-05 attr(,"msg") [1] "Normal Completion" > (pt(upper, df) - pt(lower, df))**3 [1] 0.4988254 ''' statsmodels-0.12.2/statsmodels/sandbox/distributions/mv_measures.py000066400000000000000000000141601400612667500257510ustar00rootroot00000000000000'''using multivariate dependence and divergence measures The standard correlation coefficient measures only linear dependence between random variables. kendall's tau measures any monotonic relationship also non-linear. mutual information measures any kind of dependence, but does not distinguish between positive and negative relationship mutualinfo_kde and mutualinfo_binning follow Khan et al. 2007 Shiraj Khan, Sharba Bandyopadhyay, Auroop R. Ganguly, Sunil Saigal, David J. Erickson, III, Vladimir Protopopescu, and George Ostrouchov, Relative performance of mutual information estimation methods for quantifying the dependence among short and noisy data, Phys. Rev. E 76, 026209 (2007) http://pre.aps.org/abstract/PRE/v76/i2/e026209 ''' import numpy as np from scipy import stats from scipy.stats import gaussian_kde import statsmodels.sandbox.infotheo as infotheo def mutualinfo_kde(y, x, normed=True): '''mutual information of two random variables estimated with kde ''' nobs = len(x) if not len(y) == nobs: raise ValueError('both data arrays need to have the same size') x = np.asarray(x, float) y = np.asarray(y, float) yx = np.vstack((y,x)) kde_x = gaussian_kde(x)(x) kde_y = gaussian_kde(y)(y) kde_yx = gaussian_kde(yx)(yx) mi_obs = np.log(kde_yx) - np.log(kde_x) - np.log(kde_y) mi = mi_obs.sum() / nobs if normed: mi_normed = np.sqrt(1. - np.exp(-2 * mi)) return mi_normed else: return mi def mutualinfo_kde_2sample(y, x, normed=True): '''mutual information of two random variables estimated with kde ''' nobs = len(x) x = np.asarray(x, float) y = np.asarray(y, float) #yx = np.vstack((y,x)) kde_x = gaussian_kde(x.T)(x.T) kde_y = gaussian_kde(y.T)(x.T) #kde_yx = gaussian_kde(yx)(yx) mi_obs = np.log(kde_x) - np.log(kde_y) if len(mi_obs) != nobs: raise ValueError("Wrong number of observations") mi = mi_obs.mean() if normed: mi_normed = np.sqrt(1. - np.exp(-2 * mi)) return mi_normed else: return mi def mutualinfo_binned(y, x, bins, normed=True): '''mutual information of two random variables estimated with kde Notes ----- bins='auto' selects the number of bins so that approximately 5 observations are expected to be in each bin under the assumption of independence. This follows roughly the description in Kahn et al. 2007 ''' nobs = len(x) if not len(y) == nobs: raise ValueError('both data arrays need to have the same size') x = np.asarray(x, float) y = np.asarray(y, float) #yx = np.vstack((y,x)) ## fyx, binsy, binsx = np.histogram2d(y, x, bins=bins) ## fx, binsx_ = np.histogram(x, bins=binsx) ## fy, binsy_ = np.histogram(y, bins=binsy) if bins == 'auto': ys = np.sort(y) xs = np.sort(x) #quantiles = np.array([0,0.25, 0.4, 0.6, 0.75, 1]) qbin_sqr = np.sqrt(5./nobs) quantiles = np.linspace(0, 1, 1./qbin_sqr) quantile_index = ((nobs-1)*quantiles).astype(int) #move edges so that they do not coincide with an observation shift = 1e-6 + np.ones(quantiles.shape) shift[0] -= 2*1e-6 binsy = ys[quantile_index] + shift binsx = xs[quantile_index] + shift elif np.size(bins) == 1: binsy = bins binsx = bins elif (len(bins) == 2): binsy, binsx = bins ## if np.size(bins[0]) == 1: ## binsx = bins[0] ## if np.size(bins[1]) == 1: ## binsx = bins[1] fx, binsx = np.histogram(x, bins=binsx) fy, binsy = np.histogram(y, bins=binsy) fyx, binsy, binsx = np.histogram2d(y, x, bins=(binsy, binsx)) pyx = fyx * 1. / nobs px = fx * 1. / nobs py = fy * 1. / nobs mi_obs = pyx * (np.log(pyx+1e-10) - np.log(py)[:,None] - np.log(px)) mi = mi_obs.sum() if normed: mi_normed = np.sqrt(1. - np.exp(-2 * mi)) return mi_normed, (pyx, py, px, binsy, binsx), mi_obs else: return mi if __name__ == '__main__': import statsmodels.api as sm funtype = ['linear', 'quadratic'][1] nobs = 200 sig = 2#5. #x = np.linspace(-3, 3, nobs) + np.random.randn(nobs) x = np.sort(3*np.random.randn(nobs)) exog = sm.add_constant(x, prepend=True) #y = 0 + np.log(1+x**2) + sig * np.random.randn(nobs) if funtype == 'quadratic': y = 0 + x**2 + sig * np.random.randn(nobs) if funtype == 'linear': y = 0 + x + sig * np.random.randn(nobs) print('correlation') print(np.corrcoef(y,x)[0, 1]) print('pearsonr', stats.pearsonr(y,x)) print('spearmanr', stats.spearmanr(y,x)) print('kendalltau', stats.kendalltau(y,x)) pxy, binsx, binsy = np.histogram2d(x,y, bins=5) px, binsx_ = np.histogram(x, bins=binsx) py, binsy_ = np.histogram(y, bins=binsy) print('mutualinfo', infotheo.mutualinfo(px*1./nobs, py*1./nobs, 1e-15+pxy*1./nobs, logbase=np.e)) print('mutualinfo_kde normed', mutualinfo_kde(y,x)) print('mutualinfo_kde ', mutualinfo_kde(y,x, normed=False)) mi_normed, (pyx2, py2, px2, binsy2, binsx2), mi_obs = \ mutualinfo_binned(y, x, 5, normed=True) print('mutualinfo_binned normed', mi_normed) print('mutualinfo_binned ', mi_obs.sum()) mi_normed, (pyx2, py2, px2, binsy2, binsx2), mi_obs = \ mutualinfo_binned(y, x, 'auto', normed=True) print('auto') print('mutualinfo_binned normed', mi_normed) print('mutualinfo_binned ', mi_obs.sum()) ys = np.sort(y) xs = np.sort(x) by = ys[((nobs-1)*np.array([0, 0.25, 0.4, 0.6, 0.75, 1])).astype(int)] bx = xs[((nobs-1)*np.array([0, 0.25, 0.4, 0.6, 0.75, 1])).astype(int)] mi_normed, (pyx2, py2, px2, binsy2, binsx2), mi_obs = \ mutualinfo_binned(y, x, (by,bx), normed=True) print('quantiles') print('mutualinfo_binned normed', mi_normed) print('mutualinfo_binned ', mi_obs.sum()) doplot = 1#False if doplot: import matplotlib.pyplot as plt plt.plot(x, y, 'o') olsres = sm.OLS(y, exog).fit() plt.plot(x, olsres.fittedvalues) statsmodels-0.12.2/statsmodels/sandbox/distributions/mv_normal.py000066400000000000000000001134221400612667500254160ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Multivariate Normal and t distributions Created on Sat May 28 15:38:23 2011 @author: Josef Perktold TODO: * renaming, - after adding t distribution, cov does not make sense for Sigma DONE - should mean also be renamed to mu, if there will be distributions with mean != mu * not sure about corner cases - behavior with (almost) singular sigma or transforms - df <= 2, is everything correct if variance is not finite or defined ? * check to return possibly univariate distribution for marginals or conditional distributions, does univariate special case work? seems ok for conditional * are all the extra transformation methods useful outside of testing ? - looks like I have some mixup in definitions of standardize, normalize * new methods marginal, conditional, ... just added, typos ? - largely tested for MVNormal, not yet for MVT DONE * conditional: reusing, vectorizing, should we reuse a projection matrix or allow for a vectorized, conditional_mean similar to OLS.predict * add additional things similar to LikelihoodModelResults? quadratic forms, F distribution, and others ??? * add Delta method for nonlinear functions here, current function is hidden somewhere in miscmodels * raise ValueErrors for wrong input shapes, currently only partially checked * quantile method (ppf for equal bounds for multiple testing) is missing http://svitsrv25.epfl.ch/R-doc/library/mvtnorm/html/qmvt.html seems to use just a root finder for inversion of cdf * normalize has ambiguous definition, and mixing it up in different versions std from sigma or std from cov ? I would like to get what I need for mvt-cdf, or not univariate standard t distribution has scale=1 but std>1 FIXED: add std_sigma, and normalize uses std_sigma * more work: bivariate distributions, inherit from multivariate but overwrite some methods for better efficiency, e.g. cdf and expect I kept the original MVNormal0 class as reference, can be deleted See Also -------- sandbox/examples/ex_mvelliptical.py Examples -------- Note, several parts of these examples are random and the numbers will not be (exactly) the same. >>> import numpy as np >>> import statsmodels.sandbox.distributions.mv_normal as mvd >>> >>> from numpy.testing import assert_array_almost_equal >>> >>> cov3 = np.array([[ 1. , 0.5 , 0.75], ... [ 0.5 , 1.5 , 0.6 ], ... [ 0.75, 0.6 , 2. ]]) >>> mu = np.array([-1, 0.0, 2.0]) multivariate normal distribution -------------------------------- >>> mvn3 = mvd.MVNormal(mu, cov3) >>> mvn3.rvs(size=3) array([[-0.08559948, -1.0319881 , 1.76073533], [ 0.30079522, 0.55859618, 4.16538667], [-1.36540091, -1.50152847, 3.87571161]]) >>> mvn3.std array([ 1. , 1.22474487, 1.41421356]) >>> a = [0.0, 1.0, 1.5] >>> mvn3.pdf(a) 0.013867410439318712 >>> mvn3.cdf(a) 0.31163181123730122 Monte Carlo integration >>> mvn3.expect_mc(lambda x: (x>> mvn3.expect_mc(lambda x: (x>> mvt3 = mvd.MVT(mu, cov3, 4) >>> mvt3.rvs(size=4) array([[-0.94185437, 0.3933273 , 2.40005487], [ 0.07563648, 0.06655433, 7.90752238], [ 1.06596474, 0.32701158, 2.03482886], [ 3.80529746, 7.0192967 , 8.41899229]]) >>> mvt3.pdf(a) 0.010402959362646937 >>> mvt3.cdf(a) 0.30269483623249821 >>> mvt3.expect_mc(lambda x: (x>> mvt3.cov array([[ 2. , 1. , 1.5], [ 1. , 3. , 1.2], [ 1.5, 1.2, 4. ]]) >>> mvt3.corr array([[ 1. , 0.40824829, 0.53033009], [ 0.40824829, 1. , 0.34641016], [ 0.53033009, 0.34641016, 1. ]]) get normalized distribution >>> mvt3n = mvt3.normalized() >>> mvt3n.sigma array([[ 1. , 0.40824829, 0.53033009], [ 0.40824829, 1. , 0.34641016], [ 0.53033009, 0.34641016, 1. ]]) >>> mvt3n.cov array([[ 2. , 0.81649658, 1.06066017], [ 0.81649658, 2. , 0.69282032], [ 1.06066017, 0.69282032, 2. ]]) What's currently there? >>> [i for i in dir(mvn3) if not i[0]=='_'] ['affine_transformed', 'cdf', 'cholsigmainv', 'conditional', 'corr', 'cov', 'expect_mc', 'extra_args', 'logdetsigma', 'logpdf', 'marginal', 'mean', 'normalize', 'normalized', 'normalized2', 'nvars', 'pdf', 'rvs', 'sigma', 'sigmainv', 'standardize', 'standardized', 'std', 'std_sigma', 'whiten'] >>> [i for i in dir(mvt3) if not i[0]=='_'] ['affine_transformed', 'cdf', 'cholsigmainv', 'corr', 'cov', 'df', 'expect_mc', 'extra_args', 'logdetsigma', 'logpdf', 'marginal', 'mean', 'normalize', 'normalized', 'normalized2', 'nvars', 'pdf', 'rvs', 'sigma', 'sigmainv', 'standardize', 'standardized', 'std', 'std_sigma', 'whiten'] """ import numpy as np from scipy import special from statsmodels.sandbox.distributions.multivariate import mvstdtprob from .extras import mvnormcdf def expect_mc(dist, func=lambda x: 1, size=50000): '''calculate expected value of function by Monte Carlo integration Parameters ---------- dist : distribution instance needs to have rvs defined as a method for drawing random numbers func : callable function for which expectation is calculated, this function needs to be vectorized, integration is over axis=0 size : int number of random samples to use in the Monte Carlo integration, Notes ----- this does not batch Returns ------- expected value : ndarray return of function func integrated over axis=0 by MonteCarlo, this will have the same shape as the return of func without axis=0 Examples -------- integrate probability that both observations are negative >>> mvn = mve.MVNormal([0,0],2.) >>> mve.expect_mc(mvn, lambda x: (x>> c = stats.norm.isf(0.05, scale=np.sqrt(2.)) >>> expect_mc(mvn, lambda x: (np.abs(x)>np.array([c, c])), size=100000) array([ 0.09969, 0.0986 ]) or calling the method >>> mvn.expect_mc(lambda x: (np.abs(x)>np.array([c, c])), size=100000) array([ 0.09937, 0.10075]) ''' def fun(x): return func(x) # * dist.pdf(x) rvs = dist.rvs(size=size) return fun(rvs).mean(0) def expect_mc_bounds(dist, func=lambda x: 1, size=50000, lower=None, upper=None, conditional=False, overfact=1.2): '''calculate expected value of function by Monte Carlo integration Parameters ---------- dist : distribution instance needs to have rvs defined as a method for drawing random numbers func : callable function for which expectation is calculated, this function needs to be vectorized, integration is over axis=0 size : int minimum number of random samples to use in the Monte Carlo integration, the actual number used can be larger because of oversampling. lower : None or array_like lower integration bounds, if None, then it is set to -inf upper : None or array_like upper integration bounds, if None, then it is set to +inf conditional : bool If true, then the expectation is conditional on being in within [lower, upper] bounds, otherwise it is unconditional overfact : float oversampling factor, the actual number of random variables drawn in each attempt are overfact * remaining draws. Extra draws are also used in the integration. Notes ----- this does not batch Returns ------- expected value : ndarray return of function func integrated over axis=0 by MonteCarlo, this will have the same shape as the return of func without axis=0 Examples -------- >>> mvn = mve.MVNormal([0,0],2.) >>> mve.expect_mc_bounds(mvn, lambda x: np.ones(x.shape[0]), lower=[-10,-10],upper=[0,0]) 0.24990416666666668 get 3 marginal moments with one integration >>> mvn = mve.MVNormal([0,0],1.) >>> mve.expect_mc_bounds(mvn, lambda x: np.dstack([x, x**2, x**3, x**4]), lower=[-np.inf,-np.inf], upper=[np.inf,np.inf]) array([[ 2.88629497e-03, 9.96706297e-01, -2.51005344e-03, 2.95240921e+00], [ -5.48020088e-03, 9.96004409e-01, -2.23803072e-02, 2.96289203e+00]]) >>> from scipy import stats >>> [stats.norm.moment(i) for i in [1,2,3,4]] [0.0, 1.0, 0.0, 3.0] ''' #call rvs once to find length of random vector rvsdim = dist.rvs(size=1).shape[-1] if lower is None: lower = -np.inf * np.ones(rvsdim) else: lower = np.asarray(lower) if upper is None: upper = np.inf * np.ones(rvsdim) else: upper = np.asarray(upper) def fun(x): return func(x) # * dist.pdf(x) rvsli = [] used = 0 #remain = size #inplace changes size total = 0 while True: remain = size - used #just a temp variable rvs = dist.rvs(size=int(remain * overfact)) total += int(size * overfact) rvsok = rvs[((rvs >= lower) & (rvs <= upper)).all(-1)] #if rvsok.ndim == 1: #possible shape problems if only 1 random vector rvsok = np.atleast_2d(rvsok) used += rvsok.shape[0] rvsli.append(rvsok) #[:remain]) use extras instead print(used) if used >= size: break rvs = np.vstack(rvsli) print(rvs.shape) assert used == rvs.shape[0] #saftey check mean_conditional = fun(rvs).mean(0) if conditional: return mean_conditional else: return mean_conditional * (used * 1. / total) def bivariate_normal(x, mu, cov): """ Bivariate Gaussian distribution for equal shape *X*, *Y*. See `bivariate normal `_ at mathworld. """ X, Y = np.transpose(x) mux, muy = mu sigmax, sigmaxy, tmp, sigmay = np.ravel(cov) sigmax, sigmay = np.sqrt(sigmax), np.sqrt(sigmay) Xmu = X-mux Ymu = Y-muy rho = sigmaxy/(sigmax*sigmay) z = Xmu**2/sigmax**2 + Ymu**2/sigmay**2 - 2*rho*Xmu*Ymu/(sigmax*sigmay) denom = 2*np.pi*sigmax*sigmay*np.sqrt(1-rho**2) return np.exp( -z/(2*(1-rho**2))) / denom class BivariateNormal(object): #TODO: make integration limits more flexible # or normalize before integration def __init__(self, mean, cov): self.mean = mu self.cov = cov self.sigmax, self.sigmaxy, tmp, self.sigmay = np.ravel(cov) self.nvars = 2 def rvs(self, size=1): return np.random.multivariate_normal(self.mean, self.cov, size=size) def pdf(self, x): return bivariate_normal(x, self.mean, self.cov) def logpdf(self, x): #TODO: replace this return np.log(self.pdf(x)) def cdf(self, x): return self.expect(upper=x) def expect(self, func=lambda x: 1, lower=(-10,-10), upper=(10,10)): def fun(x, y): x = np.column_stack((x,y)) return func(x) * self.pdf(x) from scipy.integrate import dblquad return dblquad(fun, lower[0], upper[0], lambda y: lower[1], lambda y: upper[1]) def kl(self, other): '''Kullback-Leibler divergence between this and another distribution int f(x) (log f(x) - log g(x)) dx where f is the pdf of self, and g is the pdf of other uses double integration with scipy.integrate.dblquad limits currently hardcoded ''' fun = lambda x : self.logpdf(x) - other.logpdf(x) return self.expect(fun) def kl_mc(self, other, size=500000): fun = lambda x : self.logpdf(x) - other.logpdf(x) rvs = self.rvs(size=size) return fun(rvs).mean() class MVElliptical(object): '''Base Class for multivariate elliptical distributions, normal and t contains common initialization, and some common methods subclass needs to implement at least rvs and logpdf methods ''' #getting common things between normal and t distribution def __init__(self, mean, sigma, *args, **kwds): '''initialize instance Parameters ---------- mean : array_like parameter mu (might be renamed), for symmetric distributions this is the mean sigma : array_like, 2d dispersion matrix, covariance matrix in normal distribution, but only proportional to covariance matrix in t distribution args : list distribution specific arguments, e.g. df for t distribution kwds : dict currently not used ''' self.extra_args = [] self.mean = np.asarray(mean) self.sigma = sigma = np.asarray(sigma) sigma = np.squeeze(sigma) self.nvars = nvars = len(mean) #self.covchol = np.linalg.cholesky(sigma) #in the following sigma is original, self.sigma is full matrix if sigma.shape == (): #iid self.sigma = np.eye(nvars) * sigma self.sigmainv = np.eye(nvars) / sigma self.cholsigmainv = np.eye(nvars) / np.sqrt(sigma) elif (sigma.ndim == 1) and (len(sigma) == nvars): #independent heteroskedastic self.sigma = np.diag(sigma) self.sigmainv = np.diag(1. / sigma) self.cholsigmainv = np.diag( 1. / np.sqrt(sigma)) elif sigma.shape == (nvars, nvars): #python tuple comparison #general self.sigmainv = np.linalg.pinv(sigma) self.cholsigmainv = np.linalg.cholesky(self.sigmainv).T else: raise ValueError('sigma has invalid shape') #store logdetsigma for logpdf self.logdetsigma = np.log(np.linalg.det(self.sigma)) def rvs(self, size=1): '''random variable Parameters ---------- size : int or tuple the number and shape of random variables to draw. Returns ------- rvs : ndarray the returned random variables with shape given by size and the dimension of the multivariate random vector as additional last dimension ''' raise NotImplementedError def logpdf(self, x): '''logarithm of probability density function Parameters ---------- x : array_like can be 1d or 2d, if 2d, then each row is taken as independent multivariate random vector Returns ------- logpdf : float or array probability density value of each random vector this should be made to work with 2d x, with multivariate normal vector in each row and iid across rows does not work now because of dot in whiten ''' raise NotImplementedError def cdf(self, x, **kwds): '''cumulative distribution function Parameters ---------- x : array_like can be 1d or 2d, if 2d, then each row is taken as independent multivariate random vector kwds : dict contains options for the numerical calculation of the cdf Returns ------- cdf : float or array probability density value of each random vector ''' raise NotImplementedError def affine_transformed(self, shift, scale_matrix): '''affine transformation define in subclass because of distribution specific restrictions''' #implemented in subclass at least for now raise NotImplementedError def whiten(self, x): """ whiten the data by linear transformation Parameters ---------- x : array_like, 1d or 2d Data to be whitened, if 2d then each row contains an independent sample of the multivariate random vector Returns ------- np.dot(x, self.cholsigmainv.T) Notes ----- This only does rescaling, it does not subtract the mean, use standardize for this instead See Also -------- standardize : subtract mean and rescale to standardized random variable. """ x = np.asarray(x) return np.dot(x, self.cholsigmainv.T) def pdf(self, x): '''probability density function Parameters ---------- x : array_like can be 1d or 2d, if 2d, then each row is taken as independent multivariate random vector Returns ------- pdf : float or array probability density value of each random vector ''' return np.exp(self.logpdf(x)) def standardize(self, x): '''standardize the random variable, i.e. subtract mean and whiten Parameters ---------- x : array_like, 1d or 2d Data to be whitened, if 2d then each row contains an independent sample of the multivariate random vector Returns ------- np.dot(x - self.mean, self.cholsigmainv.T) Notes ----- See Also -------- whiten : rescale random variable, standardize without subtracting mean. ''' return self.whiten(x - self.mean) def standardized(self): '''return new standardized MVNormal instance ''' return self.affine_transformed(-self.mean, self.cholsigmainv) def normalize(self, x): '''normalize the random variable, i.e. subtract mean and rescale The distribution will have zero mean and sigma equal to correlation Parameters ---------- x : array_like, 1d or 2d Data to be whitened, if 2d then each row contains an independent sample of the multivariate random vector Returns ------- (x - self.mean)/std_sigma Notes ----- See Also -------- whiten : rescale random variable, standardize without subtracting mean. ''' std_ = np.atleast_2d(self.std_sigma) return (x - self.mean)/std_ #/std_.T def normalized(self, demeaned=True): '''return a normalized distribution where sigma=corr if demeaned is True, then mean will be set to zero ''' if demeaned: mean_new = np.zeros_like(self.mean) else: mean_new = self.mean / self.std_sigma sigma_new = self.corr args = [getattr(self, ea) for ea in self.extra_args] return self.__class__(mean_new, sigma_new, *args) def normalized2(self, demeaned=True): '''return a normalized distribution where sigma=corr second implementation for testing affine transformation ''' if demeaned: shift = -self.mean else: shift = self.mean * (1. / self.std_sigma - 1.) return self.affine_transformed(shift, np.diag(1. / self.std_sigma)) #the following "standardizes" cov instead #return self.affine_transformed(shift, self.cholsigmainv) @property def std(self): '''standard deviation, square root of diagonal elements of cov ''' return np.sqrt(np.diag(self.cov)) @property def std_sigma(self): '''standard deviation, square root of diagonal elements of sigma ''' return np.sqrt(np.diag(self.sigma)) @property def corr(self): '''correlation matrix''' return self.cov / np.outer(self.std, self.std) expect_mc = expect_mc def marginal(self, indices): '''return marginal distribution for variables given by indices this should be correct for normal and t distribution Parameters ---------- indices : array_like, int list of indices of variables in the marginal distribution Returns ------- mvdist : instance new instance of the same multivariate distribution class that contains the marginal distribution of the variables given in indices ''' indices = np.asarray(indices) mean_new = self.mean[indices] sigma_new = self.sigma[indices[:,None], indices] args = [getattr(self, ea) for ea in self.extra_args] return self.__class__(mean_new, sigma_new, *args) #parts taken from linear_model, but heavy adjustments class MVNormal0(object): '''Class for Multivariate Normal Distribution original full version, kept for testing, new version inherits from MVElliptical uses Cholesky decomposition of covariance matrix for the transformation of the data ''' def __init__(self, mean, cov): self.mean = mean self.cov = cov = np.asarray(cov) cov = np.squeeze(cov) self.nvars = nvars = len(mean) #in the following cov is original, self.cov is full matrix if cov.shape == (): #iid self.cov = np.eye(nvars) * cov self.covinv = np.eye(nvars) / cov self.cholcovinv = np.eye(nvars) / np.sqrt(cov) elif (cov.ndim == 1) and (len(cov) == nvars): #independent heteroskedastic self.cov = np.diag(cov) self.covinv = np.diag(1. / cov) self.cholcovinv = np.diag( 1. / np.sqrt(cov)) elif cov.shape == (nvars, nvars): #python tuple comparison #general self.covinv = np.linalg.pinv(cov) self.cholcovinv = np.linalg.cholesky(self.covinv).T else: raise ValueError('cov has invalid shape') #store logdetcov for logpdf self.logdetcov = np.log(np.linalg.det(self.cov)) def whiten(self, x): """ whiten the data by linear transformation Parameters ---------- X : array_like, 1d or 2d Data to be whitened, if 2d then each row contains an independent sample of the multivariate random vector Returns ------- np.dot(x, self.cholcovinv.T) Notes ----- This only does rescaling, it does not subtract the mean, use standardize for this instead See Also -------- standardize : subtract mean and rescale to standardized random variable. """ x = np.asarray(x) if np.any(self.cov): #return np.dot(self.cholcovinv, x) return np.dot(x, self.cholcovinv.T) else: return x def rvs(self, size=1): '''random variable Parameters ---------- size : int or tuple the number and shape of random variables to draw. Returns ------- rvs : ndarray the returned random variables with shape given by size and the dimension of the multivariate random vector as additional last dimension Notes ----- uses numpy.random.multivariate_normal directly ''' return np.random.multivariate_normal(self.mean, self.cov, size=size) def pdf(self, x): '''probability density function Parameters ---------- x : array_like can be 1d or 2d, if 2d, then each row is taken as independent multivariate random vector Returns ------- pdf : float or array probability density value of each random vector ''' return np.exp(self.logpdf(x)) def logpdf(self, x): '''logarithm of probability density function Parameters ---------- x : array_like can be 1d or 2d, if 2d, then each row is taken as independent multivariate random vector Returns ------- logpdf : float or array probability density value of each random vector this should be made to work with 2d x, with multivariate normal vector in each row and iid across rows does not work now because of dot in whiten ''' x = np.asarray(x) x_whitened = self.whiten(x - self.mean) SSR = np.sum(x_whitened**2, -1) llf = -SSR llf -= self.nvars * np.log(2. * np.pi) llf -= self.logdetcov llf *= 0.5 return llf expect_mc = expect_mc class MVNormal(MVElliptical): '''Class for Multivariate Normal Distribution uses Cholesky decomposition of covariance matrix for the transformation of the data ''' __name__ == 'Multivariate Normal Distribution' def rvs(self, size=1): '''random variable Parameters ---------- size : int or tuple the number and shape of random variables to draw. Returns ------- rvs : ndarray the returned random variables with shape given by size and the dimension of the multivariate random vector as additional last dimension Notes ----- uses numpy.random.multivariate_normal directly ''' return np.random.multivariate_normal(self.mean, self.sigma, size=size) def logpdf(self, x): '''logarithm of probability density function Parameters ---------- x : array_like can be 1d or 2d, if 2d, then each row is taken as independent multivariate random vector Returns ------- logpdf : float or array probability density value of each random vector this should be made to work with 2d x, with multivariate normal vector in each row and iid across rows does not work now because of dot in whiten ''' x = np.asarray(x) x_whitened = self.whiten(x - self.mean) SSR = np.sum(x_whitened**2, -1) llf = -SSR llf -= self.nvars * np.log(2. * np.pi) llf -= self.logdetsigma llf *= 0.5 return llf def cdf(self, x, **kwds): '''cumulative distribution function Parameters ---------- x : array_like can be 1d or 2d, if 2d, then each row is taken as independent multivariate random vector kwds : dict contains options for the numerical calculation of the cdf Returns ------- cdf : float or array probability density value of each random vector ''' #lower = -np.inf * np.ones_like(x) #return mvstdnormcdf(lower, self.standardize(x), self.corr, **kwds) return mvnormcdf(x, self.mean, self.cov, **kwds) @property def cov(self): '''covariance matrix''' return self.sigma def affine_transformed(self, shift, scale_matrix): '''return distribution of an affine transform for full rank scale_matrix only Parameters ---------- shift : array_like shift of mean scale_matrix : array_like linear transformation matrix Returns ------- mvt : instance of MVNormal instance of multivariate normal distribution given by affine transformation Notes ----- the affine transformation is defined by y = a + B x where a is shift, B is a scale matrix for the linear transformation Notes ----- This should also work to select marginal distributions, but not tested for this case yet. currently only tested because it's called by standardized ''' B = scale_matrix #tmp variable mean_new = np.dot(B, self.mean) + shift sigma_new = np.dot(np.dot(B, self.sigma), B.T) return MVNormal(mean_new, sigma_new) def conditional(self, indices, values): r'''return conditional distribution indices are the variables to keep, the complement is the conditioning set values are the values of the conditioning variables \bar{\mu} = \mu_1 + \Sigma_{12} \Sigma_{22}^{-1} \left( a - \mu_2 \right) and covariance matrix \overline{\Sigma} = \Sigma_{11} - \Sigma_{12} \Sigma_{22}^{-1} \Sigma_{21}.T Parameters ---------- indices : array_like, int list of indices of variables in the marginal distribution given : array_like values of the conditioning variables Returns ------- mvn : instance of MVNormal new instance of the MVNormal class that contains the conditional distribution of the variables given in indices for given values of the excluded variables. ''' #indices need to be nd arrays for broadcasting keep = np.asarray(indices) given = np.asarray([i for i in range(self.nvars) if i not in keep]) sigmakk = self.sigma[keep[:, None], keep] sigmagg = self.sigma[given[:, None], given] sigmakg = self.sigma[keep[:, None], given] sigmagk = self.sigma[given[:, None], keep] sigma_new = sigmakk - np.dot(sigmakg, np.linalg.solve(sigmagg, sigmagk)) mean_new = self.mean[keep] + \ np.dot(sigmakg, np.linalg.solve(sigmagg, values-self.mean[given])) # #or # sig = np.linalg.solve(sigmagg, sigmagk).T # mean_new = self.mean[keep] + np.dot(sigmakg, values-self.mean[given]) # sigma_new = sigmakk - np.dot(sigmakg, sig) return MVNormal(mean_new, sigma_new) #redefine some shortcuts np_log = np.log np_pi = np.pi sps_gamln = special.gammaln class MVT(MVElliptical): __name__ == 'Multivariate Student T Distribution' def __init__(self, mean, sigma, df): '''initialize instance Parameters ---------- mean : array_like parameter mu (might be renamed), for symmetric distributions this is the mean sigma : array_like, 2d dispersion matrix, covariance matrix in normal distribution, but only proportional to covariance matrix in t distribution args : list distribution specific arguments, e.g. df for t distribution kwds : dict currently not used ''' super(MVT, self).__init__(mean, sigma) self.extra_args = ['df'] #overwrites extra_args of super self.df = df def rvs(self, size=1): '''random variables with Student T distribution Parameters ---------- size : int or tuple the number and shape of random variables to draw. Returns ------- rvs : ndarray the returned random variables with shape given by size and the dimension of the multivariate random vector as additional last dimension - TODO: Not sure if this works for size tuples with len>1. Notes ----- generated as a chi-square mixture of multivariate normal random variables. does this require df>2 ? ''' from .multivariate import multivariate_t_rvs return multivariate_t_rvs(self.mean, self.sigma, df=self.df, n=size) def logpdf(self, x): '''logarithm of probability density function Parameters ---------- x : array_like can be 1d or 2d, if 2d, then each row is taken as independent multivariate random vector Returns ------- logpdf : float or array probability density value of each random vector ''' x = np.asarray(x) df = self.df nvars = self.nvars x_whitened = self.whiten(x - self.mean) #should be float llf = - nvars * np_log(df * np_pi) llf -= self.logdetsigma llf -= (df + nvars) * np_log(1 + np.sum(x_whitened**2,-1) / df) llf *= 0.5 llf += sps_gamln((df + nvars) / 2.) - sps_gamln(df / 2.) return llf def cdf(self, x, **kwds): '''cumulative distribution function Parameters ---------- x : array_like can be 1d or 2d, if 2d, then each row is taken as independent multivariate random vector kwds : dict contains options for the numerical calculation of the cdf Returns ------- cdf : float or array probability density value of each random vector ''' lower = -np.inf * np.ones_like(x) #std_sigma = np.sqrt(np.diag(self.sigma)) upper = (x - self.mean)/self.std_sigma return mvstdtprob(lower, upper, self.corr, self.df, **kwds) #mvstdtcdf does not exist yet #return mvstdtcdf(lower, x, self.corr, df, **kwds) @property def cov(self): '''covariance matrix The covariance matrix for the t distribution does not exist for df<=2, and is equal to sigma * df/(df-2) for df>2 ''' if self.df <= 2: return np.nan * np.ones_like(self.sigma) else: return self.df / (self.df - 2.) * self.sigma def affine_transformed(self, shift, scale_matrix): '''return distribution of a full rank affine transform for full rank scale_matrix only Parameters ---------- shift : array_like shift of mean scale_matrix : array_like linear transformation matrix Returns ------- mvt : instance of MVT instance of multivariate t distribution given by affine transformation Notes ----- This checks for eigvals<=0, so there are possible problems for cases with positive eigenvalues close to zero. see: http://www.statlect.com/mcdstu1.htm I'm not sure about general case, non-full rank transformation are not multivariate t distributed. y = a + B x where a is shift, B is full rank scale matrix with same dimension as sigma ''' #full rank method could also be in elliptical and called with super #after the rank check B = scale_matrix #tmp variable as shorthand if not B.shape == (self.nvars, self.nvars): if (np.linalg.eigvals(B) <= 0).any(): raise ValueError('affine transform has to be full rank') mean_new = np.dot(B, self.mean) + shift sigma_new = np.dot(np.dot(B, self.sigma), B.T) return MVT(mean_new, sigma_new, self.df) def quad2d(func=lambda x: 1, lower=(-10,-10), upper=(10,10)): def fun(x, y): x = np.column_stack((x,y)) return func(x) from scipy.integrate import dblquad return dblquad(fun, lower[0], upper[0], lambda y: lower[1], lambda y: upper[1]) if __name__ == '__main__': from numpy.testing import assert_almost_equal, assert_array_almost_equal examples = ['mvn'] mu = (0,0) covx = np.array([[1.0, 0.5], [0.5, 1.0]]) mu3 = [-1, 0., 2.] cov3 = np.array([[ 1. , 0.5 , 0.75], [ 0.5 , 1.5 , 0.6 ], [ 0.75, 0.6 , 2. ]]) if 'mvn' in examples: bvn = BivariateNormal(mu, covx) rvs = bvn.rvs(size=1000) print(rvs.mean(0)) print(np.cov(rvs, rowvar=0)) print(bvn.expect()) print(bvn.cdf([0,0])) bvn1 = BivariateNormal(mu, np.eye(2)) bvn2 = BivariateNormal(mu, 4*np.eye(2)) fun = lambda x : np.log(bvn1.pdf(x)) - np.log(bvn.pdf(x)) print(bvn1.expect(fun)) print(bvn1.kl(bvn2), bvn1.kl_mc(bvn2)) print(bvn2.kl(bvn1), bvn2.kl_mc(bvn1)) print(bvn1.kl(bvn), bvn1.kl_mc(bvn)) mvn = MVNormal(mu, covx) mvn.pdf([0,0]) mvn.pdf(np.zeros((2,2))) #np.dot(mvn.cholcovinv.T, mvn.cholcovinv) - mvn.covinv cov3 = np.array([[ 1. , 0.5 , 0.75], [ 0.5 , 1.5 , 0.6 ], [ 0.75, 0.6 , 2. ]]) mu3 = [-1, 0., 2.] mvn3 = MVNormal(mu3, cov3) mvn3.pdf((0., 2., 3.)) mvn3.logpdf((0., 2., 3.)) #comparisons with R mvtnorm::dmvnorm #decimal=14 # mvn3.logpdf(cov3) - [-7.667977543898155, -6.917977543898155, -5.167977543898155] # #decimal 18 # mvn3.pdf(cov3) - [0.000467562492721686, 0.000989829804859273, 0.005696077243833402] # #cheating new mean, same cov # mvn3.mean = np.array([0,0,0]) # #decimal= 16 # mvn3.pdf(cov3) - [0.02914269740502042, 0.02269635555984291, 0.01767593948287269] #as asserts r_val = [-7.667977543898155, -6.917977543898155, -5.167977543898155] assert_array_almost_equal( mvn3.logpdf(cov3), r_val, decimal = 14) #decimal 18 r_val = [0.000467562492721686, 0.000989829804859273, 0.005696077243833402] assert_array_almost_equal( mvn3.pdf(cov3), r_val, decimal = 17) #cheating new mean, same cov, too dangerous, got wrong instance in tests #mvn3.mean = np.array([0,0,0]) mvn3c = MVNormal(np.array([0,0,0]), cov3) r_val = [0.02914269740502042, 0.02269635555984291, 0.01767593948287269] assert_array_almost_equal( mvn3c.pdf(cov3), r_val, decimal = 16) mvn3b = MVNormal((0,0,0), 1) fun = lambda x : np.log(mvn3.pdf(x)) - np.log(mvn3b.pdf(x)) print(mvn3.expect_mc(fun)) print(mvn3.expect_mc(fun, size=200000)) mvt = MVT((0,0), 1, 5) assert_almost_equal(mvt.logpdf(np.array([0.,0.])), -1.837877066409345, decimal=15) assert_almost_equal(mvt.pdf(np.array([0.,0.])), 0.1591549430918953, decimal=15) mvt.logpdf(np.array([1.,1.]))-(-3.01552989458359) mvt1 = MVT((0,0), 1, 1) mvt1.logpdf(np.array([1.,1.]))-(-3.48579549941151) #decimal=16 rvs = mvt.rvs(100000) assert_almost_equal(np.cov(rvs, rowvar=0), mvt.cov, decimal=1) mvt31 = MVT(mu3, cov3, 1) assert_almost_equal(mvt31.pdf(cov3), [0.0007276818698165781, 0.0009980625182293658, 0.0027661422056214652], decimal=18) mvt = MVT(mu3, cov3, 3) assert_almost_equal(mvt.pdf(cov3), [0.000863777424247410, 0.001277510788307594, 0.004156314279452241], decimal=17) statsmodels-0.12.2/statsmodels/sandbox/distributions/otherdist.py000066400000000000000000000235651400612667500254410ustar00rootroot00000000000000'''Parametric Mixture Distributions Created on Sat Jun 04 2011 Author: Josef Perktold Notes: Compound Poisson has mass point at zero https://en.wikipedia.org/wiki/Compound_Poisson_distribution and would need special treatment need a distribution that has discrete mass points and contiuous range, e.g. compound Poisson, Tweedie (for some parameter range), pdf of Tobit model (?) - truncation with clipping Question: Metaclasses and class factories for generating new distributions from existing distributions by transformation, mixing, compounding ''' import numpy as np from scipy import stats class ParametricMixtureD(object): '''mixtures with a discrete distribution The mixing distribution is a discrete distribution like scipy.stats.poisson. All distribution in the mixture of the same type and parametrized by the outcome of the mixing distribution and have to be a continuous distribution (or have a pdf method). As an example, a mixture of normal distributed random variables with Poisson as the mixing distribution. assumes vectorized shape, loc and scale as in scipy.stats.distributions assume mixing_dist is frozen initialization looks fragile for all possible cases of lower and upper bounds of the distributions. ''' def __init__(self, mixing_dist, base_dist, bd_args_func, bd_kwds_func, cutoff=1e-3): '''create a mixture distribution Parameters ---------- mixing_dist : discrete frozen distribution mixing distribution base_dist : continuous distribution parametrized distributions in the mixture bd_args_func : callable function that builds the tuple of args for the base_dist. The function obtains as argument the values in the support of the mixing distribution and should return an empty tuple or a tuple of arrays. bd_kwds_func : callable function that builds the dictionary of kwds for the base_dist. The function obtains as argument the values in the support of the mixing distribution and should return an empty dictionary or a dictionary with arrays as values. cutoff : float If the mixing distribution has infinite support, then the distribution is truncated with approximately (subject to integer conversion) the cutoff probability in the missing tail. Random draws that are outside the truncated range are clipped, that is assigned to the highest or lowest value in the truncated support. ''' self.mixing_dist = mixing_dist self.base_dist = base_dist #self.bd_args = bd_args if not np.isneginf(mixing_dist.dist.a): lower = mixing_dist.dist.a else: lower = mixing_dist.ppf(1e-4) if not np.isposinf(mixing_dist.dist.b): upper = mixing_dist.dist.b else: upper = mixing_dist.isf(1e-4) self.ma = lower self.mb = upper mixing_support = np.arange(lower, upper+1) self.mixing_probs = mixing_dist.pmf(mixing_support) self.bd_args = bd_args_func(mixing_support) self.bd_kwds = bd_kwds_func(mixing_support) def rvs(self, size=1): mrvs = self.mixing_dist.rvs(size) #TODO: check strange cases ? this assumes continous integers mrvs_idx = (np.clip(mrvs, self.ma, self.mb) - self.ma).astype(int) bd_args = tuple(md[mrvs_idx] for md in self.bd_args) bd_kwds = dict((k, self.bd_kwds[k][mrvs_idx]) for k in self.bd_kwds) kwds = {'size':size} kwds.update(bd_kwds) rvs = self.base_dist.rvs(*self.bd_args, **kwds) return rvs, mrvs_idx def pdf(self, x): x = np.asarray(x) if np.size(x) > 1: x = x[...,None] #[None, ...] bd_probs = self.base_dist.pdf(x, *self.bd_args, **self.bd_kwds) prob = (bd_probs * self.mixing_probs).sum(-1) return prob, bd_probs def cdf(self, x): x = np.asarray(x) if np.size(x) > 1: x = x[...,None] #[None, ...] bd_probs = self.base_dist.cdf(x, *self.bd_args, **self.bd_kwds) prob = (bd_probs * self.mixing_probs).sum(-1) return prob, bd_probs #try: class ClippedContinuous(object): '''clipped continuous distribution with a masspoint at clip_lower Notes ----- first version, to try out possible designs insufficient checks for valid arguments and not clear whether it works for distributions that have compact support clip_lower is fixed and independent of the distribution parameters. The clip_lower point in the pdf has to be interpreted as a mass point, i.e. different treatment in integration and expect function, which means none of the generic methods for this can be used. maybe this will be better designed as a mixture between a degenerate or discrete and a continuous distribution Warning: uses equality to check for clip_lower values in function arguments, since these are floating points, the comparison might fail if clip_lower values are not exactly equal. We could add a check whether the values are in a small neighborhood, but it would be expensive (need to search and check all values). ''' def __init__(self, base_dist, clip_lower): self.base_dist = base_dist self.clip_lower = clip_lower def _get_clip_lower(self, kwds): '''helper method to get clip_lower from kwds or attribute ''' if 'clip_lower' not in kwds: clip_lower = self.clip_lower else: clip_lower = kwds.pop('clip_lower') return clip_lower, kwds def rvs(self, *args, **kwds): clip_lower, kwds = self._get_clip_lower(kwds) rvs_ = self.base_dist.rvs(*args, **kwds) #same as numpy.clip ? rvs_[rvs_ < clip_lower] = clip_lower return rvs_ def pdf(self, x, *args, **kwds): x = np.atleast_1d(x) if 'clip_lower' not in kwds: clip_lower = self.clip_lower else: #allow clip_lower to be a possible parameter clip_lower = kwds.pop('clip_lower') pdf_raw = np.atleast_1d(self.base_dist.pdf(x, *args, **kwds)) clip_mask = (x == self.clip_lower) if np.any(clip_mask): clip_prob = self.base_dist.cdf(clip_lower, *args, **kwds) pdf_raw[clip_mask] = clip_prob #the following will be handled by sub-classing rv_continuous pdf_raw[x < clip_lower] = 0 return pdf_raw def cdf(self, x, *args, **kwds): if 'clip_lower' not in kwds: clip_lower = self.clip_lower else: #allow clip_lower to be a possible parameter clip_lower = kwds.pop('clip_lower') cdf_raw = self.base_dist.cdf(x, *args, **kwds) #not needed if equality test is used ## clip_mask = (x == self.clip_lower) ## if np.any(clip_mask): ## clip_prob = self.base_dist.cdf(clip_lower, *args, **kwds) ## pdf_raw[clip_mask] = clip_prob #the following will be handled by sub-classing rv_continuous #if self.a is defined cdf_raw[x < clip_lower] = 0 return cdf_raw def sf(self, x, *args, **kwds): if 'clip_lower' not in kwds: clip_lower = self.clip_lower else: #allow clip_lower to be a possible parameter clip_lower = kwds.pop('clip_lower') sf_raw = self.base_dist.sf(x, *args, **kwds) sf_raw[x <= clip_lower] = 1 return sf_raw def ppf(self, x, *args, **kwds): raise NotImplementedError def plot(self, x, *args, **kwds): clip_lower, kwds = self._get_clip_lower(kwds) mass = self.pdf(clip_lower, *args, **kwds) xr = np.concatenate(([clip_lower+1e-6], x[x>clip_lower])) import matplotlib.pyplot as plt #x = np.linspace(-4, 4, 21) #plt.figure() plt.xlim(clip_lower-0.1, x.max()) #remove duplicate calculation xpdf = self.pdf(x, *args, **kwds) plt.ylim(0, max(mass, xpdf.max())*1.1) plt.plot(xr, self.pdf(xr, *args, **kwds)) #plt.vline(clip_lower, self.pdf(clip_lower, *args, **kwds)) plt.stem([clip_lower], [mass], linefmt='b-', markerfmt='bo', basefmt='r-') return if __name__ == '__main__': doplots = 1 #*********** Poisson-Normal Mixture mdist = stats.poisson(2.) bdist = stats.norm bd_args_fn = lambda x: () #bd_kwds_fn = lambda x: {'loc': np.atleast_2d(10./(1+x))} bd_kwds_fn = lambda x: {'loc': x, 'scale': 0.1*np.ones_like(x)} #10./(1+x)} pd = ParametricMixtureD(mdist, bdist, bd_args_fn, bd_kwds_fn) print(pd.pdf(1)) p, bp = pd.pdf(np.linspace(0,20,21)) pc, bpc = pd.cdf(np.linspace(0,20,21)) print(pd.rvs()) rvs, m = pd.rvs(size=1000) if doplots: import matplotlib.pyplot as plt plt.hist(rvs, bins = 100) plt.title('poisson mixture of normal distributions') #********** clipped normal distribution (Tobit) bdist = stats.norm clip_lower_ = 0. #-0.5 cnorm = ClippedContinuous(bdist, clip_lower_) x = np.linspace(1e-8, 4, 11) print(cnorm.pdf(x)) print(cnorm.cdf(x)) if doplots: #plt.figure() #cnorm.plot(x) plt.figure() cnorm.plot(x = np.linspace(-1, 4, 51), loc=0.5, scale=np.sqrt(2)) plt.title('clipped normal distribution') fig = plt.figure() for i, loc in enumerate([0., 0.5, 1.,2.]): fig.add_subplot(2,2,i+1) cnorm.plot(x = np.linspace(-1, 4, 51), loc=loc, scale=np.sqrt(2)) plt.title('clipped normal, loc = %3.2f' % loc) loc = 1.5 rvs = cnorm.rvs(loc=loc, size=2000) plt.figure() plt.hist(rvs, bins=50) plt.title('clipped normal rvs, loc = %3.2f' % loc) #plt.show() statsmodels-0.12.2/statsmodels/sandbox/distributions/quantize.py000066400000000000000000000102011400612667500252530ustar00rootroot00000000000000'''Quantizing a continuous distribution in 2d Author: josef-pktd ''' from statsmodels.compat.python import lmap import numpy as np def prob_bv_rectangle(lower, upper, cdf): '''helper function for probability of a rectangle in a bivariate distribution Parameters ---------- lower : array_like tuple of lower integration bounds upper : array_like tuple of upper integration bounds cdf : callable cdf(x,y), cumulative distribution function of bivariate distribution how does this generalize to more than 2 variates ? ''' probuu = cdf(*upper) probul = cdf(upper[0], lower[1]) problu = cdf(lower[0], upper[1]) probll = cdf(*lower) return probuu - probul - problu + probll def prob_mv_grid(bins, cdf, axis=-1): '''helper function for probability of a rectangle grid in a multivariate distribution how does this generalize to more than 2 variates ? bins : tuple tuple of bin edges, currently it is assumed that they broadcast correctly ''' if not isinstance(bins, np.ndarray): bins = lmap(np.asarray, bins) n_dim = len(bins) bins_ = [] #broadcast if binedges are 1d if all(lmap(np.ndim, bins) == np.ones(n_dim)): for d in range(n_dim): sl = [None]*n_dim sl[d] = slice(None) bins_.append(bins[d][sl]) else: #assume it is already correctly broadcasted n_dim = bins.shape[0] bins_ = bins print(len(bins)) cdf_values = cdf(bins_) probs = cdf_values.copy() for d in range(n_dim): probs = np.diff(probs, axis=d) return probs def prob_quantize_cdf(binsx, binsy, cdf): '''quantize a continuous distribution given by a cdf Parameters ---------- binsx : array_like, 1d binedges ''' binsx = np.asarray(binsx) binsy = np.asarray(binsy) nx = len(binsx) - 1 ny = len(binsy) - 1 probs = np.nan * np.ones((nx, ny)) #np.empty(nx,ny) cdf_values = cdf(binsx[:,None], binsy) cdf_func = lambda x, y: cdf_values[x,y] for xind in range(1, nx+1): for yind in range(1, ny+1): upper = (xind, yind) lower = (xind-1, yind-1) #print upper,lower, probs[xind-1,yind-1] = prob_bv_rectangle(lower, upper, cdf_func) assert not np.isnan(probs).any() return probs def prob_quantize_cdf_old(binsx, binsy, cdf): '''quantize a continuous distribution given by a cdf old version without precomputing cdf values Parameters ---------- binsx : array_like, 1d binedges ''' binsx = np.asarray(binsx) binsy = np.asarray(binsy) nx = len(binsx) - 1 ny = len(binsy) - 1 probs = np.nan * np.ones((nx, ny)) #np.empty(nx,ny) for xind in range(1, nx+1): for yind in range(1, ny+1): upper = (binsx[xind], binsy[yind]) lower = (binsx[xind-1], binsy[yind-1]) #print upper,lower, probs[xind-1,yind-1] = prob_bv_rectangle(lower, upper, cdf) assert not np.isnan(probs).any() return probs if __name__ == '__main__': from numpy.testing import assert_almost_equal unif_2d = lambda x,y: x*y assert_almost_equal(prob_bv_rectangle([0,0], [1,0.5], unif_2d), 0.5, 14) assert_almost_equal(prob_bv_rectangle([0,0], [0.5,0.5], unif_2d), 0.25, 14) arr1b = np.array([[ 0.05, 0.05, 0.05, 0.05], [ 0.05, 0.05, 0.05, 0.05], [ 0.05, 0.05, 0.05, 0.05], [ 0.05, 0.05, 0.05, 0.05], [ 0.05, 0.05, 0.05, 0.05]]) arr1a = prob_quantize_cdf(np.linspace(0,1,6), np.linspace(0,1,5), unif_2d) assert_almost_equal(arr1a, arr1b, 14) arr2b = np.array([[ 0.25], [ 0.25], [ 0.25], [ 0.25]]) arr2a = prob_quantize_cdf(np.linspace(0,1,5), np.linspace(0,1,2), unif_2d) assert_almost_equal(arr2a, arr2b, 14) arr3b = np.array([[ 0.25, 0.25, 0.25, 0.25]]) arr3a = prob_quantize_cdf(np.linspace(0,1,2), np.linspace(0,1,5), unif_2d) assert_almost_equal(arr3a, arr3b, 14) statsmodels-0.12.2/statsmodels/sandbox/distributions/sppatch.py000066400000000000000000000567241400612667500251010ustar00rootroot00000000000000'''patching scipy to fit distributions and expect method This adds new methods to estimate continuous distribution parameters with some fixed/frozen parameters. It also contains functions that calculate the expected value of a function for any continuous or discrete distribution It temporarily also contains Bootstrap and Monte Carlo function for testing the distribution fit, but these are neither general nor verified. Author: josef-pktd License: Simplified BSD ''' from statsmodels.compat.python import lmap import numpy as np from scipy import stats, optimize, integrate ########## patching scipy #vonmises does not define finite bounds, because it is intended for circular #support which does not define a proper pdf on the real line stats.distributions.vonmises.a = -np.pi stats.distributions.vonmises.b = np.pi #the next 3 functions are for fit with some fixed parameters #As they are written, they do not work as functions, only as methods def _fitstart(self, x): '''example method, method of moment estimator as starting values Parameters ---------- x : ndarray data for which the parameters are estimated Returns ------- est : tuple preliminary estimates used as starting value for fitting, not necessarily a consistent estimator Notes ----- This needs to be written and attached to each individual distribution This example was written for the gamma distribution, but not verified with literature ''' loc = np.min([x.min(),0]) a = 4/stats.skew(x)**2 scale = np.std(x) / np.sqrt(a) return (a, loc, scale) def _fitstart_beta(self, x, fixed=None): '''method of moment estimator as starting values for beta distribution Parameters ---------- x : ndarray data for which the parameters are estimated fixed : None or array_like sequence of numbers and np.nan to indicate fixed parameters and parameters to estimate Returns ------- est : tuple preliminary estimates used as starting value for fitting, not necessarily a consistent estimator Notes ----- This needs to be written and attached to each individual distribution References ---------- for method of moment estimator for known loc and scale https://en.wikipedia.org/wiki/Beta_distribution#Parameter_estimation http://www.itl.nist.gov/div898/handbook/eda/section3/eda366h.htm NIST reference also includes reference to MLE in Johnson, Kotz, and Balakrishan, Volume II, pages 221-235 ''' #todo: separate out this part to be used for other compact support distributions # e.g. rdist, vonmises, and truncnorm # but this might not work because it might still be distribution specific a, b = x.min(), x.max() eps = (a-b)*0.01 if fixed is None: #this part not checked with books loc = a - eps scale = (a - b) * (1 + 2*eps) else: if np.isnan(fixed[-2]): #estimate loc loc = a - eps else: loc = fixed[-2] if np.isnan(fixed[-1]): #estimate scale scale = (b + eps) - loc else: scale = fixed[-1] #method of moment for known loc scale: scale = float(scale) xtrans = (x - loc)/scale xm = xtrans.mean() xv = xtrans.var() tmp = (xm*(1-xm)/xv - 1) p = xm * tmp q = (1 - xm) * tmp return (p, q, loc, scale) #check return type and should fixed be returned ? def _fitstart_poisson(self, x, fixed=None): '''maximum likelihood estimator as starting values for Poisson distribution Parameters ---------- x : ndarray data for which the parameters are estimated fixed : None or array_like sequence of numbers and np.nan to indicate fixed parameters and parameters to estimate Returns ------- est : tuple preliminary estimates used as starting value for fitting, not necessarily a consistent estimator Notes ----- This needs to be written and attached to each individual distribution References ---------- MLE : https://en.wikipedia.org/wiki/Poisson_distribution#Maximum_likelihood ''' #todo: separate out this part to be used for other compact support distributions # e.g. rdist, vonmises, and truncnorm # but this might not work because it might still be distribution specific a = x.min() eps = 0 # is this robust ? if fixed is None: #this part not checked with books loc = a - eps else: if np.isnan(fixed[-1]): #estimate loc loc = a - eps else: loc = fixed[-1] #MLE for standard (unshifted, if loc=0) Poisson distribution xtrans = (x - loc) lambd = xtrans.mean() #second derivative d loglike/ dlambd Not used #dlldlambd = 1/lambd # check return (lambd, loc) #check return type and should fixed be returned ? def nnlf_fr(self, thetash, x, frmask): # new frozen version # - sum (log pdf(x, theta),axis=0) # where theta are the parameters (including loc and scale) # try: if frmask is not None: theta = frmask.copy() theta[np.isnan(frmask)] = thetash else: theta = thetash loc = theta[-2] scale = theta[-1] args = tuple(theta[:-2]) except IndexError: raise ValueError("Not enough input arguments.") if not self._argcheck(*args) or scale <= 0: return np.inf x = np.array((x-loc) / scale) cond0 = (x <= self.a) | (x >= self.b) if (np.any(cond0)): return np.inf else: N = len(x) #raise ValueError return self._nnlf(x, *args) + N*np.log(scale) def fit_fr(self, data, *args, **kwds): '''estimate distribution parameters by MLE taking some parameters as fixed Parameters ---------- data : ndarray, 1d data for which the distribution parameters are estimated, args : list ? check starting values for optimization kwds : - 'frozen' : array_like values for frozen distribution parameters and, for elements with np.nan, the corresponding parameter will be estimated Returns ------- argest : ndarray estimated parameters Examples -------- generate random sample >>> np.random.seed(12345) >>> x = stats.gamma.rvs(2.5, loc=0, scale=1.2, size=200) estimate all parameters >>> stats.gamma.fit(x) array([ 2.0243194 , 0.20395655, 1.44411371]) >>> stats.gamma.fit_fr(x, frozen=[np.nan, np.nan, np.nan]) array([ 2.0243194 , 0.20395655, 1.44411371]) keep loc fixed, estimate shape and scale parameters >>> stats.gamma.fit_fr(x, frozen=[np.nan, 0.0, np.nan]) array([ 2.45603985, 1.27333105]) keep loc and scale fixed, estimate shape parameter >>> stats.gamma.fit_fr(x, frozen=[np.nan, 0.0, 1.0]) array([ 3.00048828]) >>> stats.gamma.fit_fr(x, frozen=[np.nan, 0.0, 1.2]) array([ 2.57792969]) estimate only scale parameter for fixed shape and loc >>> stats.gamma.fit_fr(x, frozen=[2.5, 0.0, np.nan]) array([ 1.25087891]) Notes ----- self is an instance of a distribution class. This can be attached to scipy.stats.distributions.rv_continuous *Todo* * check if docstring is correct * more input checking, args is list ? might also apply to current fit method ''' loc0, scale0 = lmap(kwds.get, ['loc', 'scale'],[0.0, 1.0]) Narg = len(args) if Narg == 0 and hasattr(self, '_fitstart'): x0 = self._fitstart(data) elif Narg > self.numargs: raise ValueError("Too many input arguments.") else: args += (1.0,)*(self.numargs-Narg) # location and scale are at the end x0 = args + (loc0, scale0) if 'frozen' in kwds: frmask = np.array(kwds['frozen']) if len(frmask) != self.numargs+2: raise ValueError("Incorrect number of frozen arguments.") else: # keep starting values for not frozen parameters for n in range(len(frmask)): # Troubleshooting ex_generic_mle_tdist if isinstance(frmask[n], np.ndarray) and frmask[n].size == 1: frmask[n] = frmask[n].item() # If there were array elements, then frmask will be object-dtype, # in which case np.isnan will raise TypeError frmask = frmask.astype(np.float64) x0 = np.array(x0)[np.isnan(frmask)] else: frmask = None #print(x0 #print(frmask return optimize.fmin(self.nnlf_fr, x0, args=(np.ravel(data), frmask), disp=0) #The next two functions/methods calculate expected value of an arbitrary #function, however for the continuous functions intquad is use, which might #require continuouity or smoothness in the function. #TODO: add option for Monte Carlo integration def expect(self, fn=None, args=(), loc=0, scale=1, lb=None, ub=None, conditional=False): '''calculate expected value of a function with respect to the distribution location and scale only tested on a few examples Parameters ---------- all parameters are keyword parameters fn : function (default: identity mapping) Function for which integral is calculated. Takes only one argument. args : tuple argument (parameters) of the distribution lb, ub : numbers lower and upper bound for integration, default is set to the support of the distribution conditional : bool (False) If true then the integral is corrected by the conditional probability of the integration interval. The return value is the expectation of the function, conditional on being in the given interval. Returns ------- expected value : float Notes ----- This function has not been checked for it's behavior when the integral is not finite. The integration behavior is inherited from scipy.integrate.quad. ''' if fn is None: def fun(x, *args): return x*self.pdf(x, loc=loc, scale=scale, *args) else: def fun(x, *args): return fn(x)*self.pdf(x, loc=loc, scale=scale, *args) if lb is None: lb = loc + self.a * scale #(self.a - loc)/(1.0*scale) if ub is None: ub = loc + self.b * scale #(self.b - loc)/(1.0*scale) if conditional: invfac = (self.sf(lb, loc=loc, scale=scale, *args) - self.sf(ub, loc=loc, scale=scale, *args)) else: invfac = 1.0 return integrate.quad(fun, lb, ub, args=args)[0]/invfac def expect_v2(self, fn=None, args=(), loc=0, scale=1, lb=None, ub=None, conditional=False): '''calculate expected value of a function with respect to the distribution location and scale only tested on a few examples Parameters ---------- all parameters are keyword parameters fn : function (default: identity mapping) Function for which integral is calculated. Takes only one argument. args : tuple argument (parameters) of the distribution lb, ub : numbers lower and upper bound for integration, default is set using quantiles of the distribution, see Notes conditional : bool (False) If true then the integral is corrected by the conditional probability of the integration interval. The return value is the expectation of the function, conditional on being in the given interval. Returns ------- expected value : float Notes ----- This function has not been checked for it's behavior when the integral is not finite. The integration behavior is inherited from scipy.integrate.quad. The default limits are lb = self.ppf(1e-9, *args), ub = self.ppf(1-1e-9, *args) For some heavy tailed distributions, 'alpha', 'cauchy', 'halfcauchy', 'levy', 'levy_l', and for 'ncf', the default limits are not set correctly even when the expectation of the function is finite. In this case, the integration limits, lb and ub, should be chosen by the user. For example, for the ncf distribution, ub=1000 works in the examples. There are also problems with numerical integration in some other cases, for example if the distribution is very concentrated and the default limits are too large. ''' #changes: 20100809 #correction and refactoring how loc and scale are handled #uses now _pdf #needs more testing for distribution with bound support, e.g. genpareto if fn is None: def fun(x, *args): return (loc + x*scale)*self._pdf(x, *args) else: def fun(x, *args): return fn(loc + x*scale)*self._pdf(x, *args) if lb is None: #lb = self.a try: lb = self.ppf(1e-9, *args) #1e-14 quad fails for pareto except ValueError: lb = self.a else: lb = max(self.a, (lb - loc)/(1.0*scale)) #transform to standardized if ub is None: #ub = self.b try: ub = self.ppf(1-1e-9, *args) except ValueError: ub = self.b else: ub = min(self.b, (ub - loc)/(1.0*scale)) if conditional: invfac = self._sf(lb,*args) - self._sf(ub,*args) else: invfac = 1.0 return integrate.quad(fun, lb, ub, args=args, limit=500)[0]/invfac ### for discrete distributions #TODO: check that for a distribution with finite support the calculations are # done with one array summation (np.dot) #based on _drv2_moment(self, n, *args), but streamlined def expect_discrete(self, fn=None, args=(), loc=0, lb=None, ub=None, conditional=False): '''calculate expected value of a function with respect to the distribution for discrete distribution Parameters ---------- (self : distribution instance as defined in scipy stats) fn : function (default: identity mapping) Function for which integral is calculated. Takes only one argument. args : tuple argument (parameters) of the distribution optional keyword parameters lb, ub : numbers lower and upper bound for integration, default is set to the support of the distribution, lb and ub are inclusive (ul<=k<=ub) conditional : bool (False) If true then the expectation is corrected by the conditional probability of the integration interval. The return value is the expectation of the function, conditional on being in the given interval (k such that ul<=k<=ub). Returns ------- expected value : float Notes ----- * function is not vectorized * accuracy: uses self.moment_tol as stopping criterium for heavy tailed distribution e.g. zipf(4), accuracy for mean, variance in example is only 1e-5, increasing precision (moment_tol) makes zipf very slow * suppnmin=100 internal parameter for minimum number of points to evaluate could be added as keyword parameter, to evaluate functions with non-monotonic shapes, points include integers in (-suppnmin, suppnmin) * uses maxcount=1000 limits the number of points that are evaluated to break loop for infinite sums (a maximum of suppnmin+1000 positive plus suppnmin+1000 negative integers are evaluated) ''' #moment_tol = 1e-12 # increase compared to self.moment_tol, # too slow for only small gain in precision for zipf #avoid endless loop with unbound integral, eg. var of zipf(2) maxcount = 1000 suppnmin = 100 #minimum number of points to evaluate (+ and -) if fn is None: def fun(x): #loc and args from outer scope return (x+loc)*self._pmf(x, *args) else: def fun(x): #loc and args from outer scope return fn(x+loc)*self._pmf(x, *args) # used pmf because _pmf does not check support in randint # and there might be problems(?) with correct self.a, self.b at this stage # maybe not anymore, seems to work now with _pmf self._argcheck(*args) # (re)generate scalar self.a and self.b if lb is None: lb = (self.a) else: lb = lb - loc if ub is None: ub = (self.b) else: ub = ub - loc if conditional: invfac = self.sf(lb,*args) - self.sf(ub+1,*args) else: invfac = 1.0 tot = 0.0 low, upp = self._ppf(0.001, *args), self._ppf(0.999, *args) low = max(min(-suppnmin, low), lb) upp = min(max(suppnmin, upp), ub) supp = np.arange(low, upp+1, self.inc) #check limits #print('low, upp', low, upp tot = np.sum(fun(supp)) diff = 1e100 pos = upp + self.inc count = 0 #handle cases with infinite support while (pos <= ub) and (diff > self.moment_tol) and count <= maxcount: diff = fun(pos) tot += diff pos += self.inc count += 1 if self.a < 0: #handle case when self.a = -inf diff = 1e100 pos = low - self.inc while (pos >= lb) and (diff > self.moment_tol) and count <= maxcount: diff = fun(pos) tot += diff pos -= self.inc count += 1 if count > maxcount: # replace with proper warning print('sum did not converge') return tot/invfac stats.distributions.rv_continuous.fit_fr = fit_fr stats.distributions.rv_continuous.nnlf_fr = nnlf_fr stats.distributions.rv_continuous.expect = expect stats.distributions.rv_discrete.expect = expect_discrete stats.distributions.beta_gen._fitstart = _fitstart_beta #not tried out yet stats.distributions.poisson_gen._fitstart = _fitstart_poisson #not tried out yet ########## end patching scipy def distfitbootstrap(sample, distr, nrepl=100): '''run bootstrap for estimation of distribution parameters hard coded: only one shape parameter is allowed and estimated, loc=0 and scale=1 are fixed in the estimation Parameters ---------- sample : ndarray original sample data for bootstrap distr : distribution instance with fit_fr method nrepl : int number of bootstrap replications Returns ------- res : array (nrepl,) parameter estimates for all bootstrap replications ''' nobs = len(sample) res = np.zeros(nrepl) for ii in range(nrepl): rvsind = np.random.randint(nobs, size=nobs) x = sample[rvsind] res[ii] = distr.fit_fr(x, frozen=[np.nan, 0.0, 1.0]) return res def distfitmc(sample, distr, nrepl=100, distkwds={}): '''run Monte Carlo for estimation of distribution parameters hard coded: only one shape parameter is allowed and estimated, loc=0 and scale=1 are fixed in the estimation Parameters ---------- sample : ndarray original sample data, in Monte Carlo only used to get nobs, distr : distribution instance with fit_fr method nrepl : int number of Monte Carlo replications Returns ------- res : array (nrepl,) parameter estimates for all Monte Carlo replications ''' arg = distkwds.pop('arg') nobs = len(sample) res = np.zeros(nrepl) for ii in range(nrepl): x = distr.rvs(arg, size=nobs, **distkwds) res[ii] = distr.fit_fr(x, frozen=[np.nan, 0.0, 1.0]) return res def printresults(sample, arg, bres, kind='bootstrap'): '''calculate and print(Bootstrap or Monte Carlo result Parameters ---------- sample : ndarray original sample data arg : float (for general case will be array) bres : ndarray parameter estimates from Bootstrap or Monte Carlo run kind : {'bootstrap', 'montecarlo'} output is printed for Mootstrap (default) or Monte Carlo Returns ------- None, currently only printing Notes ----- still a bit a mess because it is used for both Bootstrap and Monte Carlo made correction: reference point for bootstrap is estimated parameter not clear: I'm not doing any ddof adjustment in estimation of variance, do we need ddof>0 ? todo: return results and string instead of printing ''' print('true parameter value') print(arg) print('MLE estimate of parameters using sample (nobs=%d)'% (nobs)) argest = distr.fit_fr(sample, frozen=[np.nan, 0.0, 1.0]) print(argest) if kind == 'bootstrap': #bootstrap compares to estimate from sample argorig = arg arg = argest print('%s distribution of parameter estimate (nrepl=%d)'% (kind, nrepl)) print('mean = %f, bias=%f' % (bres.mean(0), bres.mean(0)-arg)) print('median', np.median(bres, axis=0)) print('var and std', bres.var(0), np.sqrt(bres.var(0))) bmse = ((bres - arg)**2).mean(0) print('mse, rmse', bmse, np.sqrt(bmse)) bressorted = np.sort(bres) print('%s confidence interval (90%% coverage)' % kind) print(bressorted[np.floor(nrepl*0.05)], bressorted[np.floor(nrepl*0.95)]) print('%s confidence interval (90%% coverage) normal approximation' % kind) print(stats.norm.ppf(0.05, loc=bres.mean(), scale=bres.std()),) print(stats.norm.isf(0.05, loc=bres.mean(), scale=bres.std())) print('Kolmogorov-Smirnov test for normality of %s distribution' % kind) print(' - estimated parameters, p-values not really correct') print(stats.kstest(bres, 'norm', (bres.mean(), bres.std()))) if __name__ == '__main__': examplecases = ['largenumber', 'bootstrap', 'montecarlo'][:] if 'largenumber' in examplecases: print('\nDistribution: vonmises') for nobs in [200]:#[20000, 1000, 100]: x = stats.vonmises.rvs(1.23, loc=0, scale=1, size=nobs) print('\nnobs:', nobs) print('true parameter') print('1.23, loc=0, scale=1') print('unconstrained') print(stats.vonmises.fit(x)) print(stats.vonmises.fit_fr(x, frozen=[np.nan, np.nan, np.nan])) print('with fixed loc and scale') print(stats.vonmises.fit_fr(x, frozen=[np.nan, 0.0, 1.0])) print('\nDistribution: gamma') distr = stats.gamma arg, loc, scale = 2.5, 0., 20. for nobs in [200]:#[20000, 1000, 100]: x = distr.rvs(arg, loc=loc, scale=scale, size=nobs) print('\nnobs:', nobs) print('true parameter') print('%f, loc=%f, scale=%f' % (arg, loc, scale)) print('unconstrained') print(distr.fit(x)) print(distr.fit_fr(x, frozen=[np.nan, np.nan, np.nan])) print('with fixed loc and scale') print(distr.fit_fr(x, frozen=[np.nan, 0.0, 1.0])) print('with fixed loc') print(distr.fit_fr(x, frozen=[np.nan, 0.0, np.nan])) ex = ['gamma', 'vonmises'][0] if ex == 'gamma': distr = stats.gamma arg, loc, scale = 2.5, 0., 1 elif ex == 'vonmises': distr = stats.vonmises arg, loc, scale = 1.5, 0., 1 else: raise ValueError('wrong example') nobs = 100 nrepl = 1000 sample = distr.rvs(arg, loc=loc, scale=scale, size=nobs) print('\nDistribution:', distr) if 'bootstrap' in examplecases: print('\nBootstrap') bres = distfitbootstrap(sample, distr, nrepl=nrepl ) printresults(sample, arg, bres) if 'montecarlo' in examplecases: print('\nMonteCarlo') mcres = distfitmc(sample, distr, nrepl=nrepl, distkwds=dict(arg=arg, loc=loc, scale=scale)) printresults(sample, arg, mcres, kind='montecarlo') statsmodels-0.12.2/statsmodels/sandbox/distributions/tests/000077500000000000000000000000001400612667500242115ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/distributions/tests/__init__.py000066400000000000000000000000001400612667500263100ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/distributions/tests/_est_fit.py000066400000000000000000000050001400612667500263520ustar00rootroot00000000000000# NOTE: contains only one test, _est_cont_fit, that is renamed so that # the test runner does not run it # I put this here for the record and for the case when someone wants to # verify the quality of fit # with current parameters: relatively small sample size, default starting values # Ran 84 tests in 401.797s # FAILED (failures=15) import numpy as np from scipy import stats from .distparams import distcont # this is not a proper statistical test for convergence, but only # verifies that the estimate and true values do not differ by too much n_repl1 = 1000 # sample size for first run n_repl2 = 5000 # sample size for second run, if first run fails thresh_percent = 0.25 # percent of true parameters for fail cut-off thresh_min = 0.75 # minimum difference estimate - true to fail test #distcont = [['genextreme', (3.3184017469423535,)]] def _est_cont_fit(): # this tests the closeness of the estimated parameters to the true # parameters with fit method of continuous distributions # Note: is slow, some distributions do not converge with sample size <= 10000 for distname, arg in distcont: yield check_cont_fit, distname,arg def check_cont_fit(distname,arg): distfn = getattr(stats, distname) rvs = distfn.rvs(size=n_repl1,*arg) est = distfn.fit(rvs) #,*arg) # start with default values truearg = np.hstack([arg,[0.0,1.0]]) diff = est-truearg txt = '' diffthreshold = np.max(np.vstack([truearg*thresh_percent, np.ones(distfn.numargs+2)*thresh_min]),0) # threshold for location diffthreshold[-2] = np.max([np.abs(rvs.mean())*thresh_percent,thresh_min]) if np.any(np.isnan(est)): raise AssertionError('nan returned in fit') else: if np.any((np.abs(diff) - diffthreshold) > 0.0): ## txt = 'WARNING - diff too large with small sample' ## print 'parameter diff =', diff - diffthreshold, txt rvs = np.concatenate([rvs,distfn.rvs(size=n_repl2-n_repl1,*arg)]) est = distfn.fit(rvs) #,*arg) truearg = np.hstack([arg,[0.0,1.0]]) diff = est-truearg if np.any((np.abs(diff) - diffthreshold) > 0.0): txt = 'parameter: %s\n' % str(truearg) txt += 'estimated: %s\n' % str(est) txt += 'diff : %s\n' % str(diff) raise AssertionError('fit not very good in %s\n' % distfn.name + txt) if __name__ == "__main__": import pytest pytest.main([__file__, '-vvs', '-x', '--pdb']) statsmodels-0.12.2/statsmodels/sandbox/distributions/tests/check_moments.py000066400000000000000000000124151400612667500274050ustar00rootroot00000000000000'''script to test expect and moments in distributions.stats method not written as a test, prints results, renamed to prevent test runner from running it ''' import numpy as np from scipy import stats #from statsmodels.stats.moment_helpers import mnc2mvsk from statsmodels.sandbox.distributions.sppatch import expect_v2 from .distparams import distcont specialcases = {'ncf':{'ub':1000} # diverges if it's too large, checked for mean } #next functions are copies from sm.stats.moment_helpers def mc2mvsk(args): '''convert central moments to mean, variance, skew, kurtosis ''' mc, mc2, mc3, mc4 = args skew = np.divide(mc3, mc2**1.5) kurt = np.divide(mc4, mc2**2.0) - 3.0 return (mc, mc2, skew, kurt) def mnc2mvsk(args): '''convert central moments to mean, variance, skew, kurtosis ''' #convert four non-central moments to central moments mnc, mnc2, mnc3, mnc4 = args mc = mnc mc2 = mnc2 - mnc*mnc mc3 = mnc3 - (3*mc*mc2+mc**3) # 3rd central moment mc4 = mnc4 - (4*mc*mc3+6*mc*mc*mc2+mc**4) return mc2mvsk((mc, mc2, mc3, mc4)) def mom_nc0(x): return 1. def mom_nc1(x): return x def mom_nc2(x): return x*x def mom_nc3(x): return x*x*x def mom_nc4(x): return np.power(x,4) res = {} distex = [] distlow = [] distok = [] distnonfinite = [] def check_cont_basic(): #results saved in module global variable for distname, distargs in distcont[:]: #if distname not in distex_0: continue distfn = getattr(stats, distname) ## np.random.seed(765456) ## sn = 1000 ## rvs = distfn.rvs(size=sn,*arg) ## sm = rvs.mean() ## sv = rvs.var() ## skurt = stats.kurtosis(rvs) ## sskew = stats.skew(rvs) m,v,s,k = distfn.stats(*distargs, **dict(moments='mvsk')) st = np.array([m,v,s,k]) mask = np.isfinite(st) if mask.sum() < 4: distnonfinite.append(distname) print(distname) #print 'stats ', m,v,s,k expect = distfn.expect expect = lambda *args, **kwds : expect_v2(distfn, *args, **kwds) special_kwds = specialcases.get(distname, {}) mnc0 = expect(mom_nc0, args=distargs, **special_kwds) mnc1 = expect(args=distargs, **special_kwds) mnc2 = expect(mom_nc2, args=distargs, **special_kwds) mnc3 = expect(mom_nc3, args=distargs, **special_kwds) mnc4 = expect(mom_nc4, args=distargs, **special_kwds) mnc1_lc = expect(args=distargs, loc=1, scale=2, **special_kwds) #print mnc1, mnc2, mnc3, mnc4 try: me, ve, se, ke = mnc2mvsk((mnc1, mnc2, mnc3, mnc4)) except: print('exception', mnc1, mnc2, mnc3, mnc4, st) me, ve, se, ke = [np.nan]*4 if mask.size > 0: distex.append(distname) #print 'expect', me, ve, se, ke, #print mnc1, mnc2, mnc3, mnc4 em = np.array([me, ve, se, ke]) diff = st[mask] - em[mask] print(diff, mnc1_lc - (1 + 2*mnc1)) if np.size(diff)>0 and np.max(np.abs(diff)) > 1e-3: distlow.append(distname) else: distok.append(distname) res[distname] = [mnc0, st, em, diff, mnc1_lc] def nct_kurt_bug(): '''test for incorrect kurtosis of nct D. Hogben, R. S. Pinkham, M. B. Wilk: The Moments of the Non-Central t-DistributionAuthor(s): Biometrika, Vol. 48, No. 3/4 (Dec., 1961), pp. 465-468 ''' from numpy.testing import assert_almost_equal mvsk_10_1 = (1.08372, 1.325546, 0.39993, 1.2499424941142943) assert_almost_equal(stats.nct.stats(10, 1, moments='mvsk'), mvsk_10_1, decimal=6) c1=np.array([1.08372]) c2=np.array([.0755460, 1.25000]) c3 = np.array([.0297802, .580566]) c4 = np.array([0.0425458, 1.17491, 6.25]) #calculation for df=10, for arbitrary nc nc = 1 mc1 = c1.item() mc2 = (c2*nc**np.array([2,0])).sum() mc3 = (c3*nc**np.array([3,1])).sum() mc4 = c4=np.array([0.0425458, 1.17491, 6.25]) mvsk_nc = mc2mvsk((mc1,mc2,mc3,mc4)) if __name__ == '__main__': check_cont_basic() #print [(k, v[0]) for k,v in res.items() if np.abs(v[0]-1)>1e-3] #print [(k, v[2][0], 1+2*v[2][0]) for k,v in res.items() if np.abs(v[-1]-(1+2*v[2][0]))>1e-3] mean_ = [(k, v[1][0], v[2][0]) for k,v in res.items() if np.abs(v[1][0] - v[2][0])>1e-6 and np.isfinite(v[1][0])] var_ = [(k, v[1][1], v[2][1]) for k,v in res.items() if np.abs(v[1][1] - v[2][1])>1e-2 and np.isfinite(v[1][1])] skew = [(k, v[1][2], v[2][2]) for k,v in res.items() if np.abs(v[1][2] - v[2][2])>1e-2 and np.isfinite(v[1][1])] kurt = [(k, v[1][3], v[2][3]) for k,v in res.items() if np.abs(v[1][3] - v[2][3])>1e-2 and np.isfinite(v[1][1])] from statsmodels.iolib import SimpleTable if len(mean_) > 0: print('\nMean difference at least 1e-6') print(SimpleTable(mean_, headers=['distname', 'diststats', 'expect'])) print('\nVariance difference at least 1e-2') print(SimpleTable(var_, headers=['distname', 'diststats', 'expect'])) print('\nSkew difference at least 1e-2') print(SimpleTable(skew, headers=['distname', 'diststats', 'expect'])) print('\nKurtosis difference at least 1e-2') print(SimpleTable(kurt, headers=['distname', 'diststats', 'expect'])) statsmodels-0.12.2/statsmodels/sandbox/distributions/tests/distparams.py000066400000000000000000000120121400612667500267260ustar00rootroot00000000000000 distcont = [ ['alpha', (3.5704770516650459,)], ['anglit', ()], ['arcsine', ()], ['beta', (2.3098496451481823, 0.62687954300963677)], ['betaprime', (5, 6)], # avoid unbound error in entropy with (100, 86)], ['bradford', (0.29891359763170633,)], ['burr', (10.5, 4.3)], #incorrect mean and var for(0.94839838075366045, 4.3820284068855795)], ['cauchy', ()], ['chi', (78,)], ['chi2', (55,)], ['cosine', ()], ['dgamma', (1.1023326088288166,)], ['dweibull', (2.0685080649914673,)], ['erlang', (20,)], #correction numargs = 1 ['expon', ()], ['exponpow', (2.697119160358469,)], ['exponweib', (2.8923945291034436, 1.9505288745913174)], ['f', (29, 18)], #['fatiguelife', (29,)], #correction numargs = 1, variance very large ['fatiguelife', (2,)], ['fisk', (3.0857548622253179,)], ['foldcauchy', (4.7164673455831894,)], ['foldnorm', (1.9521253373555869,)], ['frechet_l', (3.6279911255583239,)], ['frechet_r', (1.8928171603534227,)], ['gamma', (1.9932305483800778,)], ['gausshyper', (13.763771604130699, 3.1189636648681431, 2.5145980350183019, 5.1811649903971615)], #veryslow ['genexpon', (9.1325976465418908, 16.231956600590632, 3.2819552690843983)], ['genextreme', (-0.1,)], # sample mean test fails for (3.3184017469423535,)], ['gengamma', (4.4162385429431925, 3.1193091679242761)], ['genhalflogistic', (0.77274727809929322,)], ['genlogistic', (0.41192440799679475,)], ['genpareto', (0.1,)], # use case with finite moments ['gilbrat', ()], ['gompertz', (0.94743713075105251,)], ['gumbel_l', ()], ['gumbel_r', ()], ['halfcauchy', ()], ['halflogistic', ()], ['halfnorm', ()], ['hypsecant', ()], #['invgamma', (2.0668996136993067,)], #convergence problem with expect #['invgamma', (3.0,)], ['invgamma', (5.0,)], #kurtosis requires alpha > 4 ['invnorm', (0.14546264555347513,)], ['invweibull', (10.58,)], # sample mean test fails at(0.58847112119264788,)] ['johnsonsb', (4.3172675099141058, 3.1837781130785063)], ['johnsonsu', (2.554395574161155, 2.2482281679651965)], ['ksone', (1000,)], #replace 22 by 100 to avoid failing range, ticket 956 ['kstwobign', ()], ['laplace', ()], ['levy', ()], ['levy_l', ()], # ['levy_stable', (0.35667405469844993, # -0.67450531578494011)], #NotImplementedError # rvs not tested ['loggamma', (0.41411931826052117,)], ['logistic', ()], ['loglaplace', (3.2505926592051435,)], ['lognorm', (0.95368226960575331,)], ['lomax', (1.8771398388773268,)], #this has infinite variance ['lomax', (10,)], #first 4 moments are finite ['maxwell', ()], ['mielke', (10.4, 3.6)], # sample mean test fails for (4.6420495492121487, 0.59707419545516938)], # mielke: good results if 2nd parameter >2, weird mean or var below ['nakagami', (4.9673794866666237,)], ['ncf', (27, 27, 0.41578441799226107)], ['nct', (14, 0.24045031331198066)], ['ncx2', (21, 1.0560465975116415)], ['norm', ()], ['pareto', (2.621716532144454,)], ['powerlaw', (1.6591133289905851,)], ['powerlognorm', (2.1413923530064087, 0.44639540782048337)], ['powernorm', (4.4453652254590779,)], ['rayleigh', ()], ['rdist', (0.9,)], # feels also slow # ['rdist', (3.8266985793976525,)], #veryslow, especially rvs #['rdist', (541.0,)], # from ticket #758 #veryslow ['recipinvgauss', (0.63004267809369119,)], ['reciprocal', (0.0062309367010521255, 1.0062309367010522)], ['rice', (0.7749725210111873,)], ['semicircular', ()], ['t', (2.7433514990818093,)], ['triang', (0.15785029824528218,)], ['truncexpon', (4.6907725456810478,)], ['truncnorm', (-1.0978730080013919, 2.7306754109031979)], ['tukeylambda', (3.1321477856738267,)], ['uniform', ()], ['vonmises', (3.9939042581071398,)], ['wald', ()], ['weibull_max', (2.8687961709100187,)], ['weibull_min', (1.7866166930421596,)], ['wrapcauchy', (0.031071279018614728,)]] distdiscrete = [ ['bernoulli',(0.3,)], ['binom', (5, 0.4)], ['boltzmann',(1.4, 19)], ['dlaplace', (0.8,)], #0.5 ['geom', (0.5,)], ['hypergeom',(30, 12, 6)], ['hypergeom',(21,3,12)], #numpy.random (3,18,12) numpy ticket:921 ['hypergeom',(21,18,11)], #numpy.random (18,3,11) numpy ticket:921 ['logser', (0.6,)], # reenabled, numpy ticket:921 ['nbinom', (5, 0.5)], ['nbinom', (0.4, 0.4)], #from tickets: 583 ['planck', (0.51,)], #4.1 ['poisson', (0.6,)], ['randint', (7, 31)], ['skellam', (15, 8)], ['zipf', (4,)] ] # arg=4 is ok, # Zipf broken for arg = 2, e.g. weird .stats # looking closer, mean, var should be inf for arg=2 distslow = ['rdist', 'gausshyper', 'recipinvgauss', 'ksone', 'genexpon', 'vonmises', 'rice', 'mielke', 'semicircular', 'cosine', 'invweibull', 'powerlognorm', 'johnsonsu', 'kstwobign'] statsmodels-0.12.2/statsmodels/sandbox/distributions/tests/test_extras.py000066400000000000000000000112361400612667500271330ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Apr 17 22:13:36 2011 @author: josef """ import numpy as np from numpy.testing import assert_, assert_almost_equal from statsmodels.sandbox.distributions.extras import (skewnorm, skewnorm2, ACSkewT_gen) def test_skewnorm(): #library("sn") #dsn(c(-2,-1,0,1,2), shape=10) #psn(c(-2,-1,0,1,2), shape=10) #noquote(sprintf("%.15e,", snp)) pdf_r = np.array([2.973416551551523e-90, 3.687562713971017e-24, 3.989422804014327e-01, 4.839414490382867e-01, 1.079819330263761e-01]) pdf_sn = skewnorm.pdf([-2,-1,0,1,2], 10) #res = (snp-snp_r)/snp assert_(np.allclose(pdf_sn, pdf_r,rtol=1e-13, atol=0)) pdf_sn2 = skewnorm2.pdf([-2,-1,0,1,2], 10) assert_(np.allclose(pdf_sn2, pdf_r, rtol=1e-13, atol=0)) cdf_r = np.array([0.000000000000000e+00, 0.000000000000000e+00, 3.172551743055357e-02, 6.826894921370859e-01, 9.544997361036416e-01]) cdf_sn = skewnorm.cdf([-2,-1,0,1,2], 10) maxabs = np.max(np.abs(cdf_sn - cdf_r)) maxrel = np.max(np.abs(cdf_sn - cdf_r)/(cdf_r+1e-50)) msg = "maxabs=%15.13g, maxrel=%15.13g\n%r\n%r" % (maxabs, maxrel, cdf_sn, cdf_r) #assert_(np.allclose(cdf_sn, cdf_r, rtol=1e-13, atol=1e-25), msg=msg) assert_almost_equal(cdf_sn, cdf_r, decimal=10) cdf_sn2 = skewnorm2.cdf([-2,-1,0,1,2], 10) maxabs = np.max(np.abs(cdf_sn2 - cdf_r)) maxrel = np.max(np.abs(cdf_sn2 - cdf_r)/(cdf_r+1e-50)) msg = "maxabs=%15.13g, maxrel=%15.13g" % (maxabs, maxrel) #assert_(np.allclose(cdf_sn2, cdf_r, rtol=1e-13, atol=1e-25), msg=msg) assert_almost_equal(cdf_sn2, cdf_r, decimal=10, err_msg=msg) def test_skewt(): skewt = ACSkewT_gen() x = [-2, -1, -0.5, 0, 1, 2] #noquote(sprintf("%.15e,", dst(c(-2,-1, -0.5,0,1,2), shape=10))) #default in R:sn is df=inf pdf_r = np.array([2.973416551551523e-90, 3.687562713971017e-24, 2.018401586422970e-07, 3.989422804014327e-01, 4.839414490382867e-01, 1.079819330263761e-01]) pdf_st = skewt.pdf(x, 1000000, 10) pass np.allclose(pdf_st, pdf_r, rtol=0, atol=1e-6) np.allclose(pdf_st, pdf_r, rtol=1e-1, atol=0) #noquote(sprintf("%.15e,", pst(c(-2,-1, -0.5,0,1,2), shape=10))) cdf_r = np.array([0.000000000000000e+00, 0.000000000000000e+00, 3.729478836866917e-09, 3.172551743055357e-02, 6.826894921370859e-01, 9.544997361036416e-01]) cdf_st = skewt.cdf(x, 1000000, 10) np.allclose(cdf_st, cdf_r, rtol=0, atol=1e-6) np.allclose(cdf_st, cdf_r, rtol=1e-1, atol=0) #assert_(np.allclose(cdf_st, cdf_r, rtol=1e-13, atol=1e-15)) #noquote(sprintf("%.15e,", dst(c(-2,-1, -0.5,0,1,2), shape=10, df=5))) pdf_r = np.array([2.185448836190663e-07, 1.272381597868587e-05, 5.746937644959992e-04, 3.796066898224945e-01, 4.393468708859825e-01, 1.301804021075493e-01]) pdf_st = skewt.pdf(x, 5, 10) #args = (df, alpha) assert_(np.allclose(pdf_st, pdf_r, rtol=1e-13, atol=1e-25)) #noquote(sprintf("%.15e,", pst(c(-2,-1, -0.5,0,1,2), shape=10, df=5))) cdf_r = np.array([8.822783669199699e-08, 2.638467463775795e-06, 6.573106017198583e-05, 3.172551743055352e-02, 6.367851708183412e-01, 8.980606093979784e-01]) cdf_st = skewt.cdf(x, 5, 10) #args = (df, alpha) assert_(np.allclose(cdf_st, cdf_r, rtol=1e-10, atol=0)) #noquote(sprintf("%.15e,", dst(c(-2,-1, -0.5,0,1,2), shape=10, df=1))) pdf_r = np.array([3.941955996757291e-04, 1.568067236862745e-03, 6.136996029432048e-03, 3.183098861837907e-01, 3.167418189469279e-01, 1.269297588738406e-01]) pdf_st = skewt.pdf(x, 1, 10) #args = (df, alpha) = (1, 10)) assert_(np.allclose(pdf_st, pdf_r, rtol=1e-13, atol=1e-25)) #noquote(sprintf("%.15e,", pst(c(-2,-1, -0.5,0,1,2), shape=10, df=1))) cdf_r = np.array([7.893671370544414e-04, 1.575817262600422e-03, 3.128720749105560e-03, 3.172551743055351e-02, 5.015758172626005e-01, 7.056221318361879e-01]) cdf_st = skewt.cdf(x, 1, 10) #args = (df, alpha) = (1, 10) assert_(np.allclose(cdf_st, cdf_r, rtol=1e-13, atol=1e-25)) if __name__ == '__main__': import pytest pytest.main([__file__, '-vvs', '-x', '--pdb']) print('Done') ''' >>> skewt.pdf([-2,-1,0,1,2], 10000000, 10) array([ 2.98557345e-90, 3.68850289e-24, 3.98942271e-01, 4.83941426e-01, 1.07981952e-01]) >>> skewt.pdf([-2,-1,0,1,2], np.inf, 10) array([ nan, nan, nan, nan, nan]) ''' statsmodels-0.12.2/statsmodels/sandbox/distributions/tests/test_gof_new.py000066400000000000000000000017021400612667500272460ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_array_almost_equal from statsmodels.sandbox.distributions.gof_new import bootstrap, NewNorm def test_loop_vectorized_batch_equivalence(): # test equality of loop, vectorized, batch-vectorized nobs = 200 np.random.seed(8765679) resu1 = bootstrap(NewNorm(), args=(0, 1), nobs=nobs, nrep=100, value=0.576/(1 + 4./nobs - 25./nobs**2)) np.random.seed(8765679) tmp = [bootstrap(NewNorm(), args=(0, 1), nobs=nobs, nrep=1) for _ in range(100)] resu2 = (np.array(tmp) > 0.576/(1 + 4./nobs - 25./nobs**2)).mean() np.random.seed(8765679) tmp = [bootstrap(NewNorm(), args=(0, 1), nobs=nobs, nrep=1, value=0.576/(1 + 4./nobs - 25./nobs**2), batch_size=10) for _ in range(10)] resu3 = np.array(tmp).mean() assert_array_almost_equal(resu1, resu2, 15) assert_array_almost_equal(resu2, resu3, 15) statsmodels-0.12.2/statsmodels/sandbox/distributions/tests/test_multivariate.py000066400000000000000000000143461400612667500303400ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sat Apr 16 15:02:13 2011 @author: Josef Perktold """ import numpy as np from numpy.testing import (assert_almost_equal, assert_array_almost_equal, assert_allclose) from statsmodels.sandbox.distributions.multivariate import ( mvstdtprob, mvstdnormcdf) from statsmodels.sandbox.distributions.mv_normal import MVT, MVNormal class Test_MVN_MVT_prob(object): #test for block integratal, cdf, of multivariate t and normal #comparison results from R @classmethod def setup_class(cls): cls.corr_equal = np.asarray([[1.0, 0.5, 0.5],[0.5,1,0.5],[0.5,0.5,1]]) cls.a = -1 * np.ones(3) cls.b = 3 * np.ones(3) cls.df = 4 corr2 = cls.corr_equal.copy() corr2[2,1] = -0.5 cls.corr2 = corr2 def test_mvn_mvt_1(self): a, b = self.a, self.b df = self.df corr_equal = self.corr_equal #result from R, mvtnorm with option #algorithm = GenzBretz(maxpts = 100000, abseps = 0.000001, releps = 0) # or higher probmvt_R = 0.60414 #report, ed error approx. 7.5e-06 probmvn_R = 0.673970 #reported error approx. 6.4e-07 assert_almost_equal(probmvt_R, mvstdtprob(a, b, corr_equal, df), 4) assert_almost_equal(probmvn_R, mvstdnormcdf(a, b, corr_equal, abseps=1e-5), 4) mvn_high = mvstdnormcdf(a, b, corr_equal, abseps=1e-8, maxpts=10000000) assert_almost_equal(probmvn_R, mvn_high, 5) #this still barely fails sometimes at 6 why?? error is -7.2627419411830374e-007 #>>> 0.67396999999999996 - 0.67397072627419408 #-7.2627419411830374e-007 #>>> assert_almost_equal(0.67396999999999996, 0.67397072627419408, 6) #Fail def test_mvn_mvt_2(self): a, b = self.a, self.b df = self.df corr2 = self.corr2 probmvn_R = 0.6472497 #reported error approx. 7.7e-08 probmvt_R = 0.5881863 #highest reported error up to approx. 1.99e-06 assert_almost_equal(probmvt_R, mvstdtprob(a, b, corr2, df), 4) assert_almost_equal(probmvn_R, mvstdnormcdf(a, b, corr2, abseps=1e-5), 4) def test_mvn_mvt_3(self): a, b = self.a, self.b df = self.df corr2 = self.corr2 a2 = a.copy() a2[:] = -np.inf # using higher precision in R, error approx. 6.866163e-07 probmvn_R = 0.9961141 # using higher precision in R, error approx. 1.6e-07 probmvt_R = 0.9522146 quadkwds = {'epsabs': 1e-08} probmvt = mvstdtprob(a2, b, corr2, df, quadkwds=quadkwds) assert_allclose(probmvt_R, probmvt, atol=5e-4) probmvn = mvstdnormcdf(a2, b, corr2, maxpts=100000, abseps=1e-5) assert_allclose(probmvn_R, probmvn, atol=1e-4) def test_mvn_mvt_4(self): a, bl = self.a, self.b df = self.df corr2 = self.corr2 #from 0 to inf #print '0 inf' a2 = a.copy() a2[:] = -np.inf probmvn_R = 0.1666667 #error approx. 6.1e-08 probmvt_R = 0.1666667 #error approx. 8.2e-08 assert_almost_equal(probmvt_R, mvstdtprob(np.zeros(3), -a2, corr2, df), 4) assert_almost_equal(probmvn_R, mvstdnormcdf(np.zeros(3), -a2, corr2, maxpts=100000, abseps=1e-5), 4) def test_mvn_mvt_5(self): a, bl = self.a, self.b df = self.df corr2 = self.corr2 #unequal integration bounds #print "ue" a3 = np.array([0.5, -0.5, 0.5]) probmvn_R = 0.06910487 #using higher precision in R, error approx. 3.5e-08 probmvt_R = 0.05797867 #using higher precision in R, error approx. 5.8e-08 assert_almost_equal(mvstdtprob(a3, a3+1, corr2, df), probmvt_R, 4) assert_almost_equal(probmvn_R, mvstdnormcdf(a3, a3+1, corr2, maxpts=100000, abseps=1e-5), 4) class TestMVDistributions(object): #this is not well organized @classmethod def setup_class(cls): covx = np.array([[1.0, 0.5], [0.5, 1.0]]) mu3 = [-1, 0., 2.] cov3 = np.array([[ 1. , 0.5 , 0.75], [ 0.5 , 1.5 , 0.6 ], [ 0.75, 0.6 , 2. ]]) cls.mu3 = mu3 cls.cov3 = cov3 mvn3 = MVNormal(mu3, cov3) mvn3c = MVNormal(np.array([0,0,0]), cov3) cls.mvn3 = mvn3 cls.mvn3c = mvn3c def test_mvn_pdf(self): cov3 = self.cov3 mvn3 = self.mvn3 r_val = [-7.667977543898155, -6.917977543898155, -5.167977543898155] assert_array_almost_equal(mvn3.logpdf(cov3), r_val, decimal=14) # decimal 18 r_val = [0.000467562492721686, 0.000989829804859273, 0.005696077243833402] assert_array_almost_equal(mvn3.pdf(cov3), r_val, decimal=17) mvn3b = MVNormal(np.array([0, 0, 0]), cov3) r_val = [0.02914269740502042, 0.02269635555984291, 0.01767593948287269] assert_array_almost_equal(mvn3b.pdf(cov3), r_val, decimal=16) def test_mvt_pdf(self, reset_randomstate): cov3 = self.cov3 mu3 = self.mu3 mvt = MVT((0, 0), 1, 5) assert_almost_equal(mvt.logpdf(np.array([0., 0.])), -1.837877066409345, decimal=15) assert_almost_equal(mvt.pdf(np.array([0., 0.])), 0.1591549430918953, decimal=15) mvt.logpdf(np.array([1., 1.])) - (-3.01552989458359) mvt1 = MVT((0, 0), 1, 1) mvt1.logpdf(np.array([1., 1.])) - (-3.48579549941151) # decimal=16 rvs = mvt.rvs(100000) assert_almost_equal(np.cov(rvs, rowvar=False), mvt.cov, decimal=1) mvt31 = MVT(mu3, cov3, 1) assert_almost_equal(mvt31.pdf(cov3), [0.0007276818698165781, 0.0009980625182293658, 0.0027661422056214652], decimal=17) mvt = MVT(mu3, cov3, 3) assert_almost_equal(mvt.pdf(cov3), [0.000863777424247410, 0.001277510788307594, 0.004156314279452241], decimal=17) if __name__ == '__main__': import pytest pytest.main([__file__, '-vvs', '-x', '--pdb']) statsmodels-0.12.2/statsmodels/sandbox/distributions/tests/test_norm_expan.py000066400000000000000000000053671400612667500300030ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Unit tests for Gram-Charlier exansion No reference results, test based on consistency and normal case. Created on Wed Feb 19 12:39:49 2014 Author: Josef Perktold """ import pytest import numpy as np from scipy import stats from numpy.testing import assert_allclose, assert_array_less from statsmodels.sandbox.distributions.extras import NormExpan_gen class CheckDistribution(object): @pytest.mark.smoke def test_dist1(self): self.dist1.rvs(size=10) self.dist1.pdf(np.linspace(-4, 4, 11)) def test_cdf_ppf_roundtrip(self): # round trip probs = np.linspace(0.001, 0.999, 6) ppf = self.dist2.ppf(probs) cdf = self.dist2.cdf(ppf) assert_allclose(cdf, probs, rtol=1e-6) sf = self.dist2.sf(ppf) assert_allclose(sf, 1 - probs, rtol=1e-6) class CheckExpandNorm(CheckDistribution): def test_pdf(self): scale = getattr(self, 'scale', 1) x = np.linspace(-4, 4, 11) * scale pdf2 = self.dist2.pdf(x) pdf1 = self.dist1.pdf(x) atol_pdf = getattr(self, 'atol_pdf', 0) assert_allclose(((pdf2 - pdf1)**2).mean(), 0, rtol=1e-6, atol=atol_pdf) assert_allclose(pdf2, pdf1, rtol=1e-6, atol=atol_pdf) def test_mvsk(self): #compare defining mvsk with numerical integration, generic stats mvsk2 = self.dist2.mvsk mvsk1 = self.dist2.stats(moments='mvsk') assert_allclose(mvsk2, mvsk1, rtol=1e-6, atol=1e-13) # check mvsk that was used to generate distribution assert_allclose(self.dist2.mvsk, self.mvsk, rtol=1e-12) class TestExpandNormMom(CheckExpandNorm): # compare with normal, skew=0, excess_kurtosis=0 @classmethod def setup_class(kls): kls.scale = 2 kls.dist1 = stats.norm(1, 2) kls.mvsk = [1., 2**2, 0, 0] kls.dist2 = NormExpan_gen(kls.mvsk, mode='mvsk') class TestExpandNormSample(object): # do not subclass CheckExpandNorm, # precision not high enough because of mvsk from data @classmethod def setup_class(kls): kls.dist1 = dist1 = stats.norm(1, 2) np.random.seed(5999) kls.rvs = dist1.rvs(size=200) #rvs = np.concatenate([rvs, -rvs]) # fix mean and std of sample #rvs = (rvs - rvs.mean())/rvs.std(ddof=1) * np.sqrt(2) + 1 kls.dist2 = NormExpan_gen(kls.rvs, mode='sample') kls.scale = 2 kls.atol_pdf = 1e-3 def test_ks(self): # cdf is slow # Kolmogorov-Smirnov test against generating sample stat, pvalue = stats.kstest(self.rvs, self.dist2.cdf) assert_array_less(0.25, pvalue) def test_mvsk(self): mvsk = stats.describe(self.rvs)[-4:] assert_allclose(self.dist2.mvsk, mvsk, rtol=1e-12) statsmodels-0.12.2/statsmodels/sandbox/distributions/tests/test_transf.py000066400000000000000000000146021400612667500271220ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun May 09 22:35:21 2010 Author: josef-pktd License: BSD todo: change moment calculation, (currently uses default _ppf method - I think) >>> lognormalg.moment(4) Warning: The algorithm does not converge. Roundoff error is detected in the extrapolation table. It is assumed that the requested tolerance cannot be achieved, and that the returned result (if full_output = 1) is the best which can be obtained. array(2981.0032380193438) """ import warnings # for silencing, see above... import numpy as np from numpy.testing import assert_almost_equal from scipy import stats, special from statsmodels.sandbox.distributions.extras import ( squarenormalg, absnormalg, negsquarenormalg, squaretg) # some patches to scipy.stats.distributions so tests work and pass # this should be necessary only for older scipy #patch frozen distributions with a name stats.distributions.rv_frozen.name = property(lambda self: self.dist.name) #patch f distribution, correct skew and maybe kurtosis def f_stats(self, dfn, dfd): arr, where, inf, sqrt, nan = np.array, np.where, np.inf, np.sqrt, np.nan v2 = arr(dfd*1.0) v1 = arr(dfn*1.0) mu = where(v2 > 2, v2 / arr(v2 - 2), inf) mu2 = 2*v2*v2*(v2+v1-2)/(v1*(v2-2)**2 * (v2-4)) mu2 = where(v2 > 4, mu2, inf) #g1 = 2*(v2+2*v1-2)/(v2-6)*sqrt((2*v2-4)/(v1*(v2+v1-2))) g1 = 2*(v2+2*v1-2.)/(v2-6.)*np.sqrt(2*(v2-4.)/(v1*(v2+v1-2.))) g1 = where(v2 > 6, g1, nan) #g2 = 3/(2*v2-16)*(8+g1*g1*(v2-6)) g2 = 3/(2.*v2-16)*(8+g1*g1*(v2-6.)) g2 = where(v2 > 8, g2, nan) return mu, mu2, g1, g2 #stats.distributions.f_gen._stats = f_stats stats.f.__class__._stats = f_stats #correct kurtosis by subtracting 3 (Fisher) #after this it matches halfnorm for arg close to zero def foldnorm_stats(self, c): arr, where, inf, sqrt, nan = np.array, np.where, np.inf, np.sqrt, np.nan exp = np.exp pi = np.pi fac = special.erf(c/sqrt(2)) mu = sqrt(2.0/pi)*exp(-0.5*c*c)+c*fac mu2 = c*c + 1 - mu*mu c2 = c*c g1 = sqrt(2/pi)*exp(-1.5*c2)*(4-pi*exp(c2)*(2*c2+1.0)) g1 += 2*c*fac*(6*exp(-c2) + 3*sqrt(2*pi)*c*exp(-c2/2.0)*fac + \ pi*c*(fac*fac-1)) g1 /= pi*mu2**1.5 g2 = c2*c2+6*c2+3+6*(c2+1)*mu*mu - 3*mu**4 g2 -= 4*exp(-c2/2.0)*mu*(sqrt(2.0/pi)*(c2+2)+c*(c2+3)*exp(c2/2.0)*fac) g2 /= mu2**2.0 g2 -= 3. return mu, mu2, g1, g2 #stats.distributions.foldnorm_gen._stats = foldnorm_stats stats.foldnorm.__class__._stats = foldnorm_stats #----------------------------- DECIMAL = 5 class Test_Transf2(object): @classmethod def setup_class(cls): cls.dist_equivalents = [ #transf, stats.lognorm(1)) #The below fails on the SPARC box with scipy 10.1 #(lognormalg, stats.lognorm(1)), #transf2 (squarenormalg, stats.chi2(1)), (absnormalg, stats.halfnorm), (absnormalg, stats.foldnorm(1e-5)), #try frozen #(negsquarenormalg, 1-stats.chi2), # will not work as distribution (squaretg(10), stats.f(1, 10)) ] #try both frozen l,s = 0.0, 1.0 cls.ppfq = [0.1,0.5,0.9] cls.xx = [0.95,1.0,1.1] cls.nxx = [-0.95,-1.0,-1.1] def test_equivalent(self): xx, ppfq = self.xx, self.ppfq for d1,d2 in self.dist_equivalents: ## print d1.name assert_almost_equal(d1.cdf(xx), d2.cdf(xx), err_msg='cdf'+d1.name) assert_almost_equal(d1.pdf(xx), d2.pdf(xx), err_msg='pdf '+d1.name+d2.name) assert_almost_equal(d1.sf(xx), d2.sf(xx), err_msg='sf '+d1.name+d2.name) assert_almost_equal(d1.ppf(ppfq), d2.ppf(ppfq), err_msg='ppq '+d1.name+d2.name) assert_almost_equal(d1.isf(ppfq), d2.isf(ppfq), err_msg='isf '+d1.name+d2.name) self.d1 = d1 self.d2 = d2 ## print d1, d2 ## print d1.moment(3) ## print d2.moment(3) #work around bug#1293 if hasattr(d2, 'dist'): d2mom = d2.dist.moment(3, *d2.args) else: d2mom = d2.moment(3) assert_almost_equal(d1.moment(3), d2mom, DECIMAL, err_msg='moment '+d1.name+d2.name) # silence warnings in scipy, works for versions # after print changed to warning in scipy orig_filter = warnings.filters[:] warnings.simplefilter('ignore') try: s1 = d1.stats(moments='mvsk') s2 = d2.stats(moments='mvsk') finally: warnings.filters = orig_filter #stats(moments='k') prints warning for lognormalg assert_almost_equal(s1[:2], s2[:2], err_msg='stats '+d1.name+d2.name) assert_almost_equal(s1[2:], s2[2:], decimal=2, #lognorm for kurtosis err_msg='stats '+d1.name+d2.name) def test_equivalent_negsq(self): #special case negsquarenormalg #negsquarenormalg.cdf(x) == stats.chi2(1).cdf(-x), for x<=0 xx, nxx, ppfq = self.xx, self.nxx, self.ppfq d1,d2 = (negsquarenormalg, stats.chi2(1)) #print d1.name assert_almost_equal(d1.cdf(nxx), 1-d2.cdf(xx), err_msg='cdf'+d1.name) assert_almost_equal(d1.pdf(nxx), d2.pdf(xx)) assert_almost_equal(d1.sf(nxx), 1-d2.sf(xx)) assert_almost_equal(d1.ppf(ppfq), -d2.ppf(ppfq)[::-1]) assert_almost_equal(d1.isf(ppfq), -d2.isf(ppfq)[::-1]) assert_almost_equal(d1.moment(3), -d2.moment(3)) ch2oddneg = [v*(-1)**(i+1) for i,v in enumerate(d2.stats(moments='mvsk'))] assert_almost_equal(d1.stats(moments='mvsk'), ch2oddneg, err_msg='stats '+d1.name+d2.name) if __name__ == '__main__': tt = Test_Transf2() tt.test_equivalent() tt.test_equivalent_negsq() debug = 0 if debug: print(negsquarenormalg.ppf([0.1,0.5,0.9])) print(stats.chi2.ppf([0.1,0.5,0.9],1)) print(negsquarenormalg.a) print(negsquarenormalg.b) print(absnormalg.stats( moments='mvsk')) print(stats.foldnorm(1e-10).stats( moments='mvsk')) print(stats.halfnorm.stats( moments='mvsk')) statsmodels-0.12.2/statsmodels/sandbox/distributions/transform_functions.py000066400000000000000000000071071400612667500275310ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Nonlinear Transformation classes Created on Sat Apr 16 16:06:11 2011 Author: Josef Perktold License : BSD """ import numpy as np class TransformFunction(object): def __call__(self, x): self.func(x) ## Hump and U-shaped functions class SquareFunc(TransformFunction): '''class to hold quadratic function with inverse function and derivative using instance methods instead of class methods, if we want extension to parametrized function ''' def func(self, x): return np.power(x, 2.) def inverseplus(self, x): return np.sqrt(x) def inverseminus(self, x): return 0.0 - np.sqrt(x) def derivplus(self, x): return 0.5/np.sqrt(x) def derivminus(self, x): return 0.0 - 0.5/np.sqrt(x) class NegSquareFunc(TransformFunction): '''negative quadratic function ''' def func(self, x): return -np.power(x,2) def inverseplus(self, x): return np.sqrt(-x) def inverseminus(self, x): return 0.0 - np.sqrt(-x) def derivplus(self, x): return 0.0 - 0.5/np.sqrt(-x) def derivminus(self, x): return 0.5/np.sqrt(-x) class AbsFunc(TransformFunction): '''class for absolute value transformation ''' def func(self, x): return np.abs(x) def inverseplus(self, x): return x def inverseminus(self, x): return 0.0 - x def derivplus(self, x): return 1.0 def derivminus(self, x): return 0.0 - 1.0 ## monotonic functions # more monotone functions in families.links, some for restricted domains class LogFunc(TransformFunction): def func(self, x): return np.log(x) def inverse(self, y): return np.exp(y) def deriv(self, x): return 1./x class ExpFunc(TransformFunction): def func(self, x): return np.exp(x) def inverse(self, y): return np.log(y) def deriv(self, x): return np.exp(x) class BoxCoxNonzeroFunc(TransformFunction): def __init__(self, lamda): self.lamda = lamda def func(self, x): return (np.power(x, self.lamda) - 1)/self.lamda def inverse(self, y): return (self.lamda * y + 1)/self.lamda def deriv(self, x): return np.power(x, self.lamda - 1) class AffineFunc(TransformFunction): def __init__(self, constant, slope): self.constant = constant self.slope = slope def func(self, x): return self.constant + self.slope * x def inverse(self, y): return (y - self.constant) / self.slope def deriv(self, x): return self.slope class ChainFunc(TransformFunction): def __init__(self, finn, fout): self.finn = finn self.fout = fout def func(self, x): return self.fout.func(self.finn.func(x)) def inverse(self, y): return self.f1.inverse(self.fout.inverse(y)) def deriv(self, x): z = self.finn.func(x) return self.fout.deriv(z) * self.finn.deriv(x) #def inverse(x): # return np.divide(1.0,x) # #mux, stdx = 0.05, 0.1 #mux, stdx = 9.0, 1.0 #def inversew(x): # return 1.0/(1+mux+x*stdx) #def inversew_inv(x): # return (1.0/x - 1.0 - mux)/stdx #.np.divide(1.0,x)-10 # #def identit(x): # return x if __name__ == '__main__': absf = AbsFunc() absf.func(5) == 5 absf.func(-5) == 5 absf.inverseplus(5) == 5 absf.inverseminus(5) == -5 chainf = ChainFunc(AffineFunc(1,2), BoxCoxNonzeroFunc(2)) print(chainf.func(3.)) chainf2 = ChainFunc(BoxCoxNonzeroFunc(2), AffineFunc(1,2)) print(chainf.func(3.)) statsmodels-0.12.2/statsmodels/sandbox/distributions/transformed.py000066400000000000000000000375771400612667500257700ustar00rootroot00000000000000 ## copied from nonlinear_transform_gen.py ''' A class for the distribution of a non-linear monotonic transformation of a continuous random variable simplest usage: example: create log-gamma distribution, i.e. y = log(x), where x is gamma distributed (also available in scipy.stats) loggammaexpg = Transf_gen(stats.gamma, np.log, np.exp) example: what is the distribution of the discount factor y=1/(1+x) where interest rate x is normally distributed with N(mux,stdx**2)')? (just to come up with a story that implies a nice transformation) invnormalg = Transf_gen(stats.norm, inversew, inversew_inv, decr=True, a=-np.inf) This class does not work well for distributions with difficult shapes, e.g. 1/x where x is standard normal, because of the singularity and jump at zero. Note: I'm working from my version of scipy.stats.distribution. But this script runs under scipy 0.6.0 (checked with numpy: 1.2.0rc2 and python 2.4) This is not yet thoroughly tested, polished or optimized TODO: * numargs handling is not yet working properly, numargs needs to be specified (default = 0 or 1) * feeding args and kwargs to underlying distribution is untested and incomplete * distinguish args and kwargs for the transformed and the underlying distribution - currently all args and no kwargs are transmitted to underlying distribution - loc and scale only work for transformed, but not for underlying distribution - possible to separate args for transformation and underlying distribution parameters * add _rvs as method, will be faster in many cases Created on Tuesday, October 28, 2008, 12:40:37 PM Author: josef-pktd License: BSD ''' from scipy import stats from scipy.stats import distributions import numpy as np def get_u_argskwargs(**kwargs): #Todo: What's this? wrong spacing, used in Transf_gen TransfTwo_gen u_kwargs = dict((k.replace('u_','',1),v) for k,v in kwargs.items() if k.startswith('u_')) u_args = u_kwargs.pop('u_args',None) return u_args, u_kwargs class Transf_gen(distributions.rv_continuous): '''a class for non-linear monotonic transformation of a continuous random variable ''' def __init__(self, kls, func, funcinv, *args, **kwargs): #print(args #print(kwargs self.func = func self.funcinv = funcinv #explicit for self.__dict__.update(kwargs) #need to set numargs because inspection does not work self.numargs = kwargs.pop('numargs', 0) #print(self.numargs name = kwargs.pop('name','transfdist') longname = kwargs.pop('longname','Non-linear transformed distribution') extradoc = kwargs.pop('extradoc',None) a = kwargs.pop('a', -np.inf) b = kwargs.pop('b', np.inf) self.decr = kwargs.pop('decr', False) #defines whether it is a decreasing (True) # or increasing (False) monotonic transformation self.u_args, self.u_kwargs = get_u_argskwargs(**kwargs) self.kls = kls #(self.u_args, self.u_kwargs) # possible to freeze the underlying distribution super(Transf_gen,self).__init__(a=a, b=b, name = name, shapes=kls.shapes, longname = longname, extradoc = extradoc) def _cdf(self,x,*args, **kwargs): #print(args if not self.decr: return self.kls._cdf(self.funcinv(x),*args, **kwargs) #note scipy _cdf only take *args not *kwargs else: return 1.0 - self.kls._cdf(self.funcinv(x),*args, **kwargs) def _ppf(self, q, *args, **kwargs): if not self.decr: return self.func(self.kls._ppf(q,*args, **kwargs)) else: return self.func(self.kls._ppf(1-q,*args, **kwargs)) def inverse(x): return np.divide(1.0,x) mux, stdx = 0.05, 0.1 mux, stdx = 9.0, 1.0 def inversew(x): return 1.0/(1+mux+x*stdx) def inversew_inv(x): return (1.0/x - 1.0 - mux)/stdx #.np.divide(1.0,x)-10 def identit(x): return x invdnormalg = Transf_gen(stats.norm, inversew, inversew_inv, decr=True, #a=-np.inf, numargs = 0, name = 'discf', longname = 'normal-based discount factor', extradoc = '\ndistribution of discount factor y=1/(1+x)) with x N(0.05,0.1**2)') lognormalg = Transf_gen(stats.norm, np.exp, np.log, numargs = 2, a=0, name = 'lnnorm', longname = 'Exp transformed normal', extradoc = '\ndistribution of y = exp(x), with x standard normal' 'precision for moment andstats is not very high, 2-3 decimals') loggammaexpg = Transf_gen(stats.gamma, np.log, np.exp, numargs=1) ## copied form nonlinear_transform_short.py '''univariate distribution of a non-linear monotonic transformation of a random variable ''' class ExpTransf_gen(distributions.rv_continuous): '''Distribution based on log/exp transformation the constructor can be called with a distribution class and generates the distribution of the transformed random variable ''' def __init__(self, kls, *args, **kwargs): #print(args #print(kwargs #explicit for self.__dict__.update(kwargs) if 'numargs' in kwargs: self.numargs = kwargs['numargs'] else: self.numargs = 1 if 'name' in kwargs: name = kwargs['name'] else: name = 'Log transformed distribution' if 'a' in kwargs: a = kwargs['a'] else: a = 0 super(ExpTransf_gen,self).__init__(a=a, name=name) self.kls = kls def _cdf(self,x,*args): #print(args return self.kls._cdf(np.log(x),*args) def _ppf(self, q, *args): return np.exp(self.kls._ppf(q,*args)) class LogTransf_gen(distributions.rv_continuous): '''Distribution based on log/exp transformation the constructor can be called with a distribution class and generates the distribution of the transformed random variable ''' def __init__(self, kls, *args, **kwargs): #explicit for self.__dict__.update(kwargs) if 'numargs' in kwargs: self.numargs = kwargs['numargs'] else: self.numargs = 1 if 'name' in kwargs: name = kwargs['name'] else: name = 'Log transformed distribution' if 'a' in kwargs: a = kwargs['a'] else: a = 0 super(LogTransf_gen,self).__init__(a=a, name = name) self.kls = kls def _cdf(self,x, *args): #print(args return self.kls._cdf(np.exp(x),*args) def _ppf(self, q, *args): return np.log(self.kls._ppf(q,*args)) def examples_transf(): ##lognormal = ExpTransf(a=0.0, xa=-10.0, name = 'Log transformed normal') ##print(lognormal.cdf(1) ##print(stats.lognorm.cdf(1,1) ##print(lognormal.stats() ##print(stats.lognorm.stats(1) ##print(lognormal.rvs(size=10) print('Results for lognormal') lognormalg = ExpTransf_gen(stats.norm, a=0, name = 'Log transformed normal general') print(lognormalg.cdf(1)) print(stats.lognorm.cdf(1,1)) print(lognormalg.stats()) print(stats.lognorm.stats(1)) print(lognormalg.rvs(size=5)) ##print('Results for loggamma' ##loggammag = ExpTransf_gen(stats.gamma) ##print(loggammag._cdf(1,10) ##print(stats.loggamma.cdf(1,10) print('Results for expgamma') loggammaexpg = LogTransf_gen(stats.gamma) print(loggammaexpg._cdf(1,10)) print(stats.loggamma.cdf(1,10)) print(loggammaexpg._cdf(2,15)) print(stats.loggamma.cdf(2,15)) # this requires change in scipy.stats.distribution #print(loggammaexpg.cdf(1,10) print('Results for loglaplace') loglaplaceg = LogTransf_gen(stats.laplace) print(loglaplaceg._cdf(2,10)) print(stats.loglaplace.cdf(2,10)) loglaplaceexpg = ExpTransf_gen(stats.laplace) print(loglaplaceexpg._cdf(2,10)) ## copied from transformtwo.py ''' Created on Apr 28, 2009 @author: Josef Perktold ''' ''' A class for the distribution of a non-linear u-shaped or hump shaped transformation of a continuous random variable This is a companion to the distributions of non-linear monotonic transformation to the case when the inverse mapping is a 2-valued correspondence, for example for absolute value or square simplest usage: example: create squared distribution, i.e. y = x**2, where x is normal or t distributed This class does not work well for distributions with difficult shapes, e.g. 1/x where x is standard normal, because of the singularity and jump at zero. This verifies for normal - chi2, normal - halfnorm, foldnorm, and t - F TODO: * numargs handling is not yet working properly, numargs needs to be specified (default = 0 or 1) * feeding args and kwargs to underlying distribution works in t distribution example * distinguish args and kwargs for the transformed and the underlying distribution - currently all args and no kwargs are transmitted to underlying distribution - loc and scale only work for transformed, but not for underlying distribution - possible to separate args for transformation and underlying distribution parameters * add _rvs as method, will be faster in many cases ''' class TransfTwo_gen(distributions.rv_continuous): '''Distribution based on a non-monotonic (u- or hump-shaped transformation) the constructor can be called with a distribution class, and functions that define the non-linear transformation. and generates the distribution of the transformed random variable Note: the transformation, it's inverse and derivatives need to be fully specified: func, funcinvplus, funcinvminus, derivplus, derivminus. Currently no numerical derivatives or inverse are calculated This can be used to generate distribution instances similar to the distributions in scipy.stats. ''' #a class for non-linear non-monotonic transformation of a continuous random variable def __init__(self, kls, func, funcinvplus, funcinvminus, derivplus, derivminus, *args, **kwargs): #print(args #print(kwargs self.func = func self.funcinvplus = funcinvplus self.funcinvminus = funcinvminus self.derivplus = derivplus self.derivminus = derivminus #explicit for self.__dict__.update(kwargs) #need to set numargs because inspection does not work self.numargs = kwargs.pop('numargs', 0) #print(self.numargs name = kwargs.pop('name','transfdist') longname = kwargs.pop('longname','Non-linear transformed distribution') extradoc = kwargs.pop('extradoc',None) a = kwargs.pop('a', -np.inf) # attached to self in super b = kwargs.pop('b', np.inf) # self.a, self.b would be overwritten self.shape = kwargs.pop('shape', False) #defines whether it is a `u` shaped or `hump' shaped # transformation self.u_args, self.u_kwargs = get_u_argskwargs(**kwargs) self.kls = kls #(self.u_args, self.u_kwargs) # possible to freeze the underlying distribution super(TransfTwo_gen,self).__init__(a=a, b=b, name = name, shapes=kls.shapes, longname = longname, extradoc = extradoc) def _rvs(self, *args): self.kls._size = self._size #size attached to self, not function argument return self.func(self.kls._rvs(*args)) def _pdf(self,x,*args, **kwargs): #print(args if self.shape == 'u': signpdf = 1 elif self.shape == 'hump': signpdf = -1 else: raise ValueError('shape can only be `u` or `hump`') return signpdf * (self.derivplus(x)*self.kls._pdf(self.funcinvplus(x),*args, **kwargs) - self.derivminus(x)*self.kls._pdf(self.funcinvminus(x),*args, **kwargs)) #note scipy _cdf only take *args not *kwargs def _cdf(self,x,*args, **kwargs): #print(args if self.shape == 'u': return self.kls._cdf(self.funcinvplus(x),*args, **kwargs) - \ self.kls._cdf(self.funcinvminus(x),*args, **kwargs) #note scipy _cdf only take *args not *kwargs else: return 1.0 - self._sf(x,*args, **kwargs) def _sf(self,x,*args, **kwargs): #print(args if self.shape == 'hump': return self.kls._cdf(self.funcinvplus(x),*args, **kwargs) - \ self.kls._cdf(self.funcinvminus(x),*args, **kwargs) #note scipy _cdf only take *args not *kwargs else: return 1.0 - self._cdf(x, *args, **kwargs) def _munp(self, n,*args, **kwargs): return self._mom0_sc(n,*args) # ppf might not be possible in general case? # should be possible in symmetric case # def _ppf(self, q, *args, **kwargs): # if self.shape == 'u': # return self.func(self.kls._ppf(q,*args, **kwargs)) # elif self.shape == 'hump': # return self.func(self.kls._ppf(1-q,*args, **kwargs)) #TODO: rename these functions to have unique names class SquareFunc(object): '''class to hold quadratic function with inverse function and derivative using instance methods instead of class methods, if we want extension to parametrized function ''' def inverseplus(self, x): return np.sqrt(x) def inverseminus(self, x): return 0.0 - np.sqrt(x) def derivplus(self, x): return 0.5/np.sqrt(x) def derivminus(self, x): return 0.0 - 0.5/np.sqrt(x) def squarefunc(self, x): return np.power(x,2) sqfunc = SquareFunc() squarenormalg = TransfTwo_gen(stats.norm, sqfunc.squarefunc, sqfunc.inverseplus, sqfunc.inverseminus, sqfunc.derivplus, sqfunc.derivminus, shape='u', a=0.0, b=np.inf, numargs = 0, name = 'squarenorm', longname = 'squared normal distribution', extradoc = '\ndistribution of the square of a normal random variable' +\ ' y=x**2 with x N(0.0,1)') #u_loc=l, u_scale=s) squaretg = TransfTwo_gen(stats.t, sqfunc.squarefunc, sqfunc.inverseplus, sqfunc.inverseminus, sqfunc.derivplus, sqfunc.derivminus, shape='u', a=0.0, b=np.inf, numargs = 1, name = 'squarenorm', longname = 'squared t distribution', extradoc = '\ndistribution of the square of a t random variable' +\ ' y=x**2 with x t(dof,0.0,1)') def inverseplus(x): return np.sqrt(-x) def inverseminus(x): return 0.0 - np.sqrt(-x) def derivplus(x): return 0.0 - 0.5/np.sqrt(-x) def derivminus(x): return 0.5/np.sqrt(-x) def negsquarefunc(x): return -np.power(x,2) negsquarenormalg = TransfTwo_gen(stats.norm, negsquarefunc, inverseplus, inverseminus, derivplus, derivminus, shape='hump', a=-np.inf, b=0.0, numargs = 0, name = 'negsquarenorm', longname = 'negative squared normal distribution', extradoc = '\ndistribution of the negative square of a normal random variable' +\ ' y=-x**2 with x N(0.0,1)') #u_loc=l, u_scale=s) def inverseplus(x): return x def inverseminus(x): return 0.0 - x def derivplus(x): return 1.0 def derivminus(x): return 0.0 - 1.0 def absfunc(x): return np.abs(x) absnormalg = TransfTwo_gen(stats.norm, np.abs, inverseplus, inverseminus, derivplus, derivminus, shape='u', a=0.0, b=np.inf, numargs = 0, name = 'absnorm', longname = 'absolute of normal distribution', extradoc = '\ndistribution of the absolute value of a normal random variable' +\ ' y=abs(x) with x N(0,1)') statsmodels-0.12.2/statsmodels/sandbox/distributions/try_max.py000066400000000000000000000045111400612667500251050ustar00rootroot00000000000000''' adjusted from Denis on pystatsmodels mailing list there might still be problems with loc and scale, ''' from scipy import stats __date__ = "2010-12-29 dec" class MaxDist(stats.rv_continuous): """ max of n of scipy.stats normal expon ... Example: maxnormal10 = RVmax( scipy.stats.norm, 10 ) sample = maxnormal10( size=1000 ) sample.cdf = cdf ^ n, ppf ^ (1/n) """ def __init__( self, dist, n ): self.dist = dist self.n = n extradoc = 'maximumdistribution is the distribution of the '\ + 'maximum of n i.i.d. random variable' super(MaxDist, self).__init__(name='maxdist', a=dist.a, b=dist.b, longname = 'A maximumdistribution', extradoc = extradoc) def _pdf(self, x, *args, **kw): return self.n * self.dist.pdf(x, *args, **kw) \ * self.dist.cdf(x, *args, **kw )**(self.n-1) def _cdf(self, x, *args, **kw): return self.dist.cdf(x, *args, **kw)**self.n def _ppf(self, q, *args, **kw): # y = F(x) ^ n <=> x = F-1( y ^ 1/n) return self.dist.ppf(q**(1./self.n), *args, **kw) ## def rvs( self, *args, **kw ): ## size = kw.pop( "size", 1 ) ## u = np.random.uniform( size=size, **kw ) ** (1 / self.n) ## return self.dist.ppf( u, **kw ) maxdistr = MaxDist(stats.norm, 10) print(maxdistr.rvs(size=10)) print(maxdistr.stats(moments = 'mvsk')) ''' >>> print maxdistr.stats(moments = 'mvsk') (array(1.5387527308351818), array(0.34434382328492852), array(0.40990510188513779), array(0.33139861783918922)) >>> rvs = np.random.randn(1000,10) >>> stats.describe(rvs.max(1)) (1000, (-0.028558517753519492, 3.6134958002753685), 1.5560520428553426, 0.34965234046170773, 0.48504309950278557, 0.17691859056779258) >>> rvs2 = maxdistr.rvs(size=1000) >>> stats.describe(rvs2) (1000, (-0.015290995091401905, 3.3227019151170931), 1.5248146840651813, 0.32827518543128631, 0.23998620901199566, -0.080555658370268013) >>> rvs2 = maxdistr.rvs(size=10000) >>> stats.describe(rvs2) (10000, (-0.15855091764294812, 4.1898138060896937), 1.532862047388899, 0.34361316060467512, 0.43128838106936973, 0.41115043864619061) >>> maxdistr.pdf(1.5) 0.69513824417156755 #integrating the pdf >>> maxdistr.expect() 1.5387527308351729 >>> maxdistr.expect(lambda x:1) 0.99999999999999956 ''' statsmodels-0.12.2/statsmodels/sandbox/distributions/try_pot.py000066400000000000000000000036271400612667500251310ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed May 04 06:09:18 2011 @author: josef """ import numpy as np def mean_residual_life(x, frac=None, alpha=0.05): '''empirical mean residual life or expected shortfall Parameters ---------- x : 1-dimensional array_like frac : list[float], optional All entries must be between 0 and 1 alpha : float, default 0.05 FIXME: not actually used. TODO: check formula for std of mean does not include case for all observations last observations std is zero vectorize loop using cumsum frac does not work yet ''' axis = 0 # searchsorted is 1d only x = np.asarray(x) nobs = x.shape[axis] xsorted = np.sort(x, axis=axis) if frac is None: xthreshold = xsorted else: xthreshold = xsorted[np.floor(nobs * frac).astype(int)] # use searchsorted instead of simple index in case of ties xlargerindex = np.searchsorted(xsorted, xthreshold, side='right') # TODO:replace loop with cumsum ? result = [] for i in range(len(xthreshold)-1): k_ind = xlargerindex[i] rmean = x[k_ind:].mean() # this does not work for last observations, nans rstd = x[k_ind:].std() rmstd = rstd/np.sqrt(nobs-k_ind) # std error of mean, check formula result.append((k_ind, xthreshold[i], rmean, rmstd)) res = np.array(result) crit = 1.96 # TODO: without loading stats, crit = -stats.t.ppf(0.05) confint = res[:, 1:2] + crit * res[:, -1:] * np.array([[-1, 1]]) return np.column_stack((res, confint)) expected_shortfall = mean_residual_life # alias if __name__ == "__main__": rvs = np.random.standard_t(5, size=10) res = mean_residual_life(rvs) print(res) rmean = [rvs[i:].mean() for i in range(len(rvs))] print(res[:, 2] - rmean[1:]) res_frac = mean_residual_life(rvs, frac=[0.5]) print(res_frac) statsmodels-0.12.2/statsmodels/sandbox/examples/000077500000000000000000000000001400612667500217635ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/examples/bayesprior.py000066400000000000000000000154631400612667500245250ustar00rootroot00000000000000# # This script examines the predictive prior densities of two local level # models given the same priors for parameters that appear to be the same. # Reference: Del Negro and Schorfheide. try: import pymc pymc_installed = 1 except: print("pymc not imported") pymc_installed = 0 import numpy as np from matplotlib import pyplot as plt from scipy import stats, integrate from scipy.stats import rv_continuous from scipy.special import gammaln, gammaincinv, gammainc from numpy import log,exp #np.random.seed(12345) class igamma_gen(rv_continuous): def _pdf(self, x, a, b): return exp(self._logpdf(x,a,b)) def _logpdf(self, x, a, b): return a*log(b) - gammaln(a) -(a+1)*log(x) - b/x def _cdf(self, x, a, b): return 1.0-gammainc(a,b/x) # why is this different than the wiki? def _ppf(self, q, a, b): return b/gammaincinv(a,1-q) #NOTE: should be correct, work through invgamma example and 2 param inv gamma #CDF def _munp(self, n, a, b): args = (a,b) super(igamma_gen, self)._munp(self, n, *args) #TODO: is this robust for differential entropy in this case? closed form or #shortcuts in special? def _entropy(self, *args): def integ(x): val = self._pdf(x, *args) return val*log(val) entr = -integrate.quad(integ, self.a, self.b)[0] if not np.isnan(entr): return entr else: raise ValueError("Problem with integration. Returned nan.") igamma = igamma_gen(a=0.0, name='invgamma', longname="An inverted gamma", shapes = 'a,b', extradoc=""" Inverted gamma distribution invgamma.pdf(x,a,b) = b**a*x**(-a-1)/gamma(a) * exp(-b/x) for x > 0, a > 0, b>0. """) #NOTE: the above is unnecessary. B takes the same role as the scale parameter # in inverted gamma palpha = np.random.gamma(400.,.005, size=10000) print("First moment: %s\nSecond moment: %s" % (palpha.mean(),palpha.std())) palpha = palpha[0] prho = np.random.beta(49.5,49.5, size=1e5) print("Beta Distribution") print("First moment: %s\nSecond moment: %s" % (prho.mean(),prho.std())) prho = prho[0] psigma = igamma.rvs(1.,4.**2/2, size=1e5) print("Inverse Gamma Distribution") print("First moment: %s\nSecond moment: %s" % (psigma.mean(),psigma.std())) # First do the univariate case # y_t = theta_t + epsilon_t # epsilon ~ N(0,1) # Where theta ~ N(mu,lambda**2) # or the model # y_t = theta2_t + theta1_t * y_t-1 + epsilon_t # Prior 1: # theta1 ~ uniform(0,1) # theta2|theta1 ~ N(mu,lambda**2) # Prior 2: # theta1 ~ U(0,1) # theta2|theta1 ~ N(mu(1-theta1),lambda**2(1-theta1)**2) draws = 400 # prior beliefs, from JME paper mu_, lambda_ = 1.,2. # Model 1 y1y2 = np.zeros((draws,2)) for draw in range(draws): theta = np.random.normal(mu_,lambda_**2) y1 = theta + np.random.normal() y2 = theta + np.random.normal() y1y2[draw] = y1,y2 # log marginal distribution lnp1p2_mod1 = stats.norm.pdf(y1,loc=mu_, scale=lambda_**2+1)*\ stats.norm.pdf(y2,mu_,scale=lambda_**2+1) # Model 2 pmu_pairsp1 = np.zeros((draws,2)) y1y2pairsp1 = np.zeros((draws,2)) # prior 1 for draw in range(draws): theta1 = np.random.uniform(0,1) theta2 = np.random.normal(mu_, lambda_**2) # mu = theta2/(1-theta1) #do not do this to maintain independence theta2 is the _location_ # y1 = np.random.normal(mu_, lambda_**2) y1 = theta2 # pmu_pairsp1[draw] = mu, theta1 pmu_pairsp1[draw] = theta2, theta1 # mean, autocorr y2 = theta2 + theta1 * y1 + np.random.normal() y1y2pairsp1[draw] = y1,y2 # for a = 0, b = 1 - epsilon = .99999 # mean of u is .5*.99999 # variance is 1./12 * .99999**2 # Model 2 pmu_pairsp2 = np.zeros((draws,2)) y1y2pairsp2 = np.zeros((draws,2)) # prior 2 theta12_2 = [] for draw in range(draws): # y1 = np.random.uniform(-4,6) theta1 = np.random.uniform(0,1) theta2 = np.random.normal(mu_*(1-theta1), lambda_**2*(1-theta1)**2) theta12_2.append([theta1,theta2]) mu = theta2/(1-theta1) y1 = np.random.normal(mu_,lambda_**2) y2 = theta2 + theta1 * y1 + np.random.normal() pmu_pairsp2[draw] = mu, theta1 y1y2pairsp2[draw] = y1,y2 fig = plt.figure() fsp = fig.add_subplot(221) fsp.scatter(pmu_pairsp1[:,0], pmu_pairsp1[:,1], color='b', facecolor='none') fsp.set_ylabel('Autocorrelation (Y)') fsp.set_xlabel('Mean (Y)') fsp.set_title('Model 2 (P1)') fsp.axis([-20,20,0,1]) fsp = fig.add_subplot(222) fsp.scatter(pmu_pairsp2[:,0],pmu_pairsp2[:,1], color='b', facecolor='none') fsp.set_title('Model 2 (P2)') fsp.set_ylabel('Autocorrelation (Y)') fsp.set_xlabel('Mean (Y)') fsp.set_title('Model 2 (P2)') fsp.axis([-20,20,0,1]) fsp = fig.add_subplot(223) fsp.scatter(y1y2pairsp1[:,0], y1y2pairsp1[:,1], color='b', marker='o', facecolor='none') fsp.scatter(y1y2[:,0], y1y2[:,1], color ='g', marker='+') fsp.set_title('Model 1 vs. Model 2 (P1)') fsp.set_ylabel('Y(2)') fsp.set_xlabel('Y(1)') fsp.axis([-20,20,-20,20]) fsp = fig.add_subplot(224) fsp.scatter(y1y2pairsp2[:,0], y1y2pairsp2[:,1], color='b', marker='o') fsp.scatter(y1y2[:,0], y1y2[:,1], color='g', marker='+') fsp.set_title('Model 1 vs. Model 2 (P2)') fsp.set_ylabel('Y(2)') fsp.set_xlabel('Y(1)') fsp.axis([-20,20,-20,20]) #plt.show() #TODO: this does not look the same as the working paper? #NOTE: but it matches the language? I think mine is right! # Contour plots. # on the basis of observed data. ie., the mgrid #np.mgrid[6:-4:10j,-4:6:10j] # Example 2: # 2 NK Phillips Curves # Structural form # M1: y_t = 1/alpha *E_t[y_t+1] + mu_t # mu_t = p1 * mu_t-1 + epsilon_t # epsilon_t ~ N(0,sigma2) # Reduced form Law of Motion # M1: y_t = p1*y_t-1 + 1/(1-p1/alpha)*epsilon_t # specify prior for M1 # for i = 1,2 # theta_i = [alpha # p_i # sigma] # truncate effective priors by the determinancy region # for determinancy we need alpha > 1 # p in [0,1) # palpha ~ Gamma(2.00,.10) # mean = 2.00 # std = .1 which implies k = 400, theta = .005 palpha = np.random.gamma(400,.005) # pi ~ Beta(.5,.05) pi = np.random.beta(49.5, 49.5) # psigma ~ InvGamma(1.00,4.00) #def invgamma(a,b): # return np.sqrt(b*a**2/np.sum(np.random.random(b,1)**2, axis=1)) #NOTE: Use inverse gamma distribution igamma psigma = igamma.rvs(1.,4.0, size=1e6) #TODO: parameterization is not correct vs. # Del Negro and Schorfheide if pymc_installed: psigma2 = pymc.rinverse_gamma(1.,4.0, size=1e6) else: psigma2 = stats.invgamma.rvs(1., scale=4.0, size=1e6) nsims = 500 y = np.zeros((nsims)) #for i in range(1,nsims): # y[i] = .9*y[i-1] + 1/(1-p1/alpha) + np.random.normal() #Are these supposed to be sampled jointly? # InvGamma(sigma|v,s) propto sigma**(-v-1)*e**(-vs**2/2*sigma**2) #igamma = # M2: y_t = 1/alpha * E_t[y_t+1] + p2*y_t-1 + mu_t # mu_t ~ epsilon_t # epsilon_t ~ n(0,sigma2) # Reduced form Law of Motion # y_t = 1/2 (alpha-sqrt(alpha**2-4*p2*alpha)) * y_t-1 + 2*alpha/(alpha + \ # sqrt(alpha**2 - 4*p2*alpha)) * epsilon_t statsmodels-0.12.2/statsmodels/sandbox/examples/dji_table.csv000066400000000000000000043342411400612667500244300ustar00rootroot00000000000000Date,Open,High,Low,Close,Volume,Adj Close 2010-02-12,10137.23,10140.18,9962.13,10099.14,4160680000,10099.14 2010-02-11,10037.85,10184.85,9963.19,10144.19,4400870000,10144.19 2010-02-10,10055.46,10120.15,9946.26,10038.38,4251450000,10038.38 2010-02-09,9910.28,10154.24,9910.28,10058.64,5114260000,10058.64 2010-02-08,10005.43,10059.24,9882.85,9908.39,4089820000,9908.39 2010-02-05,10003.69,10078.89,9822.84,10012.23,6438900000,10012.23 2010-02-04,10273.12,10273.12,9984.35,10002.18,5859690000,10002.18 2010-02-03,10291.73,10356.86,10192.03,10270.55,4285450000,10270.55 2010-02-02,10186.13,10333.35,10138.75,10296.85,4749540000,10296.85 2010-02-01,10068.99,10227.24,10068.99,10185.53,4077610000,10185.53 2010-01-29,10122.04,10272.29,10014.35,10067.33,5412850000,10067.33 2010-01-28,10236.92,10310.68,10023.80,10120.46,5452400000,10120.46 2010-01-27,10194.29,10294.13,10060.98,10236.16,5319120000,10236.16 2010-01-26,10195.35,10323.00,10102.17,10194.29,4731910000,10194.29 2010-01-25,10175.10,10316.65,10135.95,10196.86,4481390000,10196.86 2010-01-22,10389.58,10450.04,10133.15,10172.98,6208650000,10172.98 2010-01-21,10603.91,10651.14,10334.18,10389.88,6874289600,10389.88 2010-01-20,10719.69,10719.69,10492.36,10603.15,4810560000,10603.15 2010-01-19,10608.37,10763.45,10555.47,10725.43,4724830000,10725.43 2010-01-15,10706.99,10736.54,10529.09,10609.65,4758730000,10609.65 2010-01-14,10680.16,10767.15,10619.02,10710.55,3915200000,10710.55 2010-01-13,10628.09,10747.12,10569.07,10680.77,4170360000,10680.77 2010-01-12,10662.86,10701.48,10523.35,10627.26,4716160000,10627.26 2010-01-11,10620.31,10739.87,10538.91,10663.99,4255780000,10663.99 2010-01-08,10606.40,10653.11,10509.74,10618.19,4389590000,10618.19 2010-01-07,10571.11,10655.60,10471.73,10606.86,5270680000,10606.86 2010-01-06,10564.72,10655.22,10488.28,10573.68,4972660000,10573.68 2010-01-05,10584.56,10647.14,10468.86,10572.02,2491020000,10572.02 2010-01-04,10430.69,10641.62,10430.69,10583.96,3991400000,10583.96 2009-12-31,10548.51,10578.74,10420.56,10428.05,2076990000,10428.05 2009-12-30,10544.36,10583.28,10470.75,10548.51,2277300000,10548.51 2009-12-29,10547.83,10605.65,10518.59,10545.41,2491020000,10545.41 2009-12-28,10517.91,10550.78,10517.91,10547.07,2716400000,10547.07 2009-12-24,10467.12,10541.26,10450.95,10520.10,1267710000,10520.10 2009-12-23,10464.32,10520.93,10409.00,10466.44,3166870000,10466.44 2009-12-22,10414.67,10511.56,10399.33,10464.93,3641130000,10464.93 2009-12-21,10330.10,10489.41,10330.10,10414.14,3977340000,10414.14 2009-12-18,10309.39,10412.55,10237.75,10328.89,6325890000,10328.89 2009-12-17,10439.99,10439.99,10279.39,10308.26,7615070400,10308.26 2009-12-16,10449.81,10552.75,10401.90,10441.12,4829820000,10441.12 2009-12-15,10499.31,10542.09,10380.96,10452.00,5045100000,10452.00 2009-12-14,10471.28,10566.88,10431.60,10501.05,4548490000,10501.05 2009-12-11,10403.41,10516.47,10385.42,10471.50,3791090000,10471.50 2009-12-10,10336.00,10479.06,10332.14,10405.83,3996490000,10405.83 2009-12-09,10282.85,10377.11,10207.29,10337.05,4115410000,10337.05 2009-12-08,10385.42,10385.42,10216.44,10285.97,4748030000,10285.97 2009-12-07,10386.86,10478.23,10321.11,10390.11,4103360000,10390.11 2009-12-04,10368.57,10549.04,10285.44,10388.90,5781140000,10388.90 2009-12-03,10455.63,10533.55,10338.49,10366.15,4810030000,10366.15 2009-12-02,10470.44,10537.63,10386.03,10452.68,3941340000,10452.68 2009-12-01,10343.82,10537.03,10343.82,10471.58,4249310000,10471.58 2009-11-30,10309.77,10394.34,10238.05,10344.84,3895520000,10344.84 2009-11-27,10452.23,10452.23,10179.33,10309.92,2362910000,10309.92 2009-11-25,10432.96,10513.60,10385.65,10464.40,3036350000,10464.40 2009-11-24,10451.25,10488.66,10335.62,10433.71,3700820000,10433.71 2009-11-23,10320.13,10524.40,10320.13,10450.95,3827920000,10450.95 2009-11-20,10327.91,10377.41,10237.60,10318.16,3751230000,10318.16 2009-11-19,10425.33,10425.33,10226.41,10332.44,4178030000,10332.44 2009-11-18,10426.27,10471.28,10330.33,10426.31,4293340000,10426.31 2009-11-17,10404.77,10465.76,10318.69,10437.42,3824070000,10437.42 2009-11-16,10267.53,10465.83,10267.53,10406.96,4565850000,10406.96 2009-11-13,10197.85,10332.29,10162.93,10270.47,3792610000,10270.47 2009-11-12,10289.82,10341.21,10157.64,10197.47,4160250000,10197.47 2009-11-11,10247.42,10357.38,10217.19,10291.26,4286700000,10291.26 2009-11-10,10223.01,10300.33,10148.12,10246.97,4394770000,10246.97 2009-11-09,10020.62,10248.93,10020.62,10226.94,4460030000,10226.94 2009-11-06,10001.35,10077.08,9898.49,10023.42,4277130000,10023.42 2009-11-05,9807.80,10043.75,9807.80,10005.96,4848350000,10005.96 2009-11-04,9767.30,9962.35,9745.76,9802.14,5635510000,9802.14 2009-11-03,9787.47,9844.84,9649.78,9771.91,5487500000,9771.91 2009-11-02,9712.13,9883.68,9647.06,9789.44,6202640000,9789.44 2009-10-30,9961.52,9980.19,9664.89,9712.73,6512420000,9712.73 2009-10-29,9762.91,9996.67,9762.91,9962.58,5595040000,9962.58 2009-10-28,9881.11,9940.89,9723.31,9762.69,6600350000,9762.69 2009-10-27,9868.34,9994.55,9802.36,9882.17,5337380000,9882.17 2009-10-26,9972.33,10107.99,9817.55,9867.96,6363380000,9867.96 2009-10-23,10099.90,10138.59,9908.70,9972.18,4767460000,9972.18 2009-10-22,9946.18,10133.08,9879.07,10081.31,5192410000,10081.31 2009-10-21,10038.84,10157.94,9909.83,9949.36,5616290000,9949.36 2009-10-20,10092.42,10157.26,9952.98,10041.48,5396930000,10041.48 2009-10-19,9996.67,10146.61,9967.49,10092.19,4619240000,10092.19 2009-10-16,10061.36,10072.62,9884.51,9995.91,4894740000,9995.91 2009-10-15,10014.88,10087.43,9916.93,10062.94,5369780000,10062.94 2009-10-14,9873.55,10064.98,9873.55,10015.86,5406420000,10015.86 2009-10-13,9883.98,9935.53,9780.90,9871.06,4320480000,9871.06 2009-10-12,9865.24,9978.07,9814.45,9885.80,3710430000,9885.80 2009-10-09,9786.04,9890.41,9731.32,9864.94,3763780000,9864.94 2009-10-08,9728.22,9872.50,9709.78,9786.87,4988400000,9786.87 2009-10-07,9725.69,9782.56,9634.96,9725.58,4238220000,9725.58 2009-10-06,9601.26,9793.37,9601.26,9731.25,5029840000,9731.25 2009-10-05,9488.73,9640.33,9449.81,9599.75,4313310000,9599.75 2009-10-02,9507.62,9571.71,9378.77,9487.67,5583240000,9487.67 2009-10-01,9711.60,9714.70,9482.98,9509.28,5791450000,9509.28 2009-09-30,9741.83,9817.17,9583.04,9712.28,5998860000,9712.28 2009-09-29,9789.74,9861.99,9705.10,9742.20,4949900000,9742.20 2009-09-28,9663.23,9861.39,9658.09,9789.36,3726950000,9789.36 2009-09-25,9706.68,9781.73,9605.19,9665.19,4507090000,9665.19 2009-09-24,9749.99,9836.82,9637.53,9707.44,5505610000,9707.44 2009-09-23,9830.63,9937.72,9724.90,9748.55,5531930000,9748.55 2009-09-22,9779.61,9890.71,9742.96,9829.87,5246600000,9829.87 2009-09-21,9818.61,9846.12,9688.40,9778.86,4615280000,9778.86 2009-09-18,9784.75,9898.57,9751.27,9820.20,5607970000,9820.20 2009-09-17,9789.82,9896.38,9706.23,9783.92,6668110000,9783.92 2009-09-16,9683.71,9837.05,9648.95,9791.71,6793529600,9791.71 2009-09-15,9626.42,9745.91,9553.80,9683.41,6185620000,9683.41 2009-09-14,9598.08,9662.10,9492.96,9626.80,4979610000,9626.80 2009-09-11,9625.44,9698.67,9532.11,9605.41,4922600000,9605.41 2009-09-10,9546.54,9666.55,9479.20,9627.48,5191380000,9627.48 2009-09-09,9496.59,9604.43,9435.45,9547.22,5202550000,9547.22 2009-09-08,9440.13,9564.45,9402.80,9497.34,5235160000,9497.34 2009-09-04,9345.36,9465.37,9302.28,9441.27,4097370000,9441.27 2009-09-03,9282.03,9350.27,9252.93,9344.61,4624280000,9344.61 2009-09-02,9306.21,9378.77,9223.08,9280.67,5842730000,9280.67 2009-09-01,9492.32,9573.67,9275.15,9310.60,6862360000,9310.60 2009-08-31,9542.91,9552.97,9389.27,9496.28,5004560000,9496.28 2009-08-28,9582.74,9666.71,9476.63,9544.20,5785780000,9544.20 2009-08-27,9541.63,9629.98,9440.43,9580.63,5785880000,9580.63 2009-08-26,9538.61,9613.65,9446.71,9543.52,5080060000,9543.52 2009-08-25,9509.21,9646.53,9485.70,9539.29,5768740000,9539.29 2009-08-24,9506.18,9625.89,9442.17,9509.28,6302450000,9509.28 2009-08-21,9347.86,9549.19,9347.86,9505.96,5885550000,9505.96 2009-08-20,9278.55,9385.72,9237.52,9350.05,4893160000,9350.05 2009-08-19,9208.68,9333.34,9099.14,9279.16,4257000000,9279.16 2009-08-18,9134.36,9262.08,9124.08,9217.94,4198970000,9217.94 2009-08-17,9313.85,9313.85,9078.28,9135.34,4854970000,9135.34 2009-08-14,9398.04,9425.17,9214.47,9321.40,4940750000,9321.40 2009-08-13,9362.29,9448.97,9269.26,9398.19,5250660000,9398.19 2009-08-12,9236.06,9442.47,9199.80,9361.61,5498170000,9361.61 2009-08-11,9334.33,9351.86,9180.23,9241.45,5773160000,9241.45 2009-08-10,9368.41,9420.56,9249.99,9337.95,5406080000,9337.95 2009-08-07,9258.45,9466.89,9258.45,9370.07,6827089600,9370.07 2009-08-06,9277.19,9378.01,9168.44,9256.26,6753380000,9256.26 2009-08-05,9315.36,9374.38,9173.20,9280.97,7242120000,9280.97 2009-08-04,9285.05,9370.30,9207.21,9320.19,5713700000,9320.19 2009-08-03,9173.65,9342.11,9162.09,9286.56,5603440000,9286.56 2009-07-31,9154.61,9264.65,9081.30,9171.61,5139070000,9171.61 2009-07-30,9072.84,9298.13,9072.84,9154.46,6035180000,9154.46 2009-07-29,9092.34,9141.23,8967.26,9070.72,5178770000,9070.72 2009-07-28,9106.92,9154.76,8980.03,9096.72,5490350000,9096.72 2009-07-27,9093.09,9154.23,8996.58,9108.51,4631290000,9108.51 2009-07-24,9066.11,9144.48,8955.77,9093.24,4458300000,9093.24 2009-07-23,8882.31,9143.05,8837.95,9069.29,5761650000,9069.29 2009-07-22,8912.39,8993.48,8802.13,8881.26,4634100000,8881.26 2009-07-21,8848.15,8991.07,8780.82,8915.94,5309300000,8915.94 2009-07-20,8746.05,8884.43,8717.26,8848.15,4853150000,8848.15 2009-07-17,8711.89,8797.97,8638.81,8743.94,5141380000,8743.94 2009-07-16,8612.66,8750.28,8543.97,8711.82,4898640000,8711.82 2009-07-15,8363.95,8643.04,8363.95,8616.21,5238830000,8616.21 2009-07-14,8331.37,8407.48,8255.27,8359.49,4149030000,8359.49 2009-07-13,8146.82,8348.08,8106.16,8331.68,4499440000,8331.68 2009-07-10,8182.49,8216.65,8057.57,8146.52,3912080000,8146.52 2009-07-09,8179.01,8273.48,8117.27,8183.17,4347170000,8183.17 2009-07-08,8157.02,8259.05,8057.94,8178.41,5721780000,8178.41 2009-07-07,8324.95,8355.48,8138.51,8163.60,4673300000,8163.60 2009-07-06,8279.30,8364.02,8156.49,8324.87,4712580000,8324.87 2009-07-02,8503.00,8503.00,8260.41,8280.74,3931000000,8280.74 2009-07-01,8447.53,8610.32,8447.00,8504.06,3919400000,8504.06 2009-06-30,8528.93,8584.17,8369.99,8447.00,4627570000,8447.00 2009-06-29,8440.13,8569.59,8406.57,8529.38,4211760000,8529.38 2009-06-26,8468.54,8509.73,8364.17,8438.39,6076660000,8438.39 2009-06-25,8299.25,8512.60,8236.07,8472.40,4911240000,8472.40 2009-06-24,8323.51,8456.83,8246.20,8299.86,4636720000,8299.86 2009-06-23,8340.44,8413.22,8239.17,8322.91,5071020000,8322.91 2009-06-22,8538.52,8538.52,8306.66,8339.01,4903940000,8339.01 2009-06-19,8556.96,8665.26,8476.02,8539.73,5713390000,8539.73 2009-06-18,8496.73,8634.28,8438.61,8555.60,4684010000,8555.60 2009-06-17,8504.36,8602.99,8421.46,8497.18,5523650000,8497.18 2009-06-16,8612.44,8688.69,8483.58,8504.67,4951200000,8504.67 2009-06-15,8798.50,8798.50,8540.87,8612.13,4697880000,8612.13 2009-06-12,8770.01,8850.95,8671.61,8799.26,4528120000,8799.26 2009-06-11,8736.23,8911.11,8697.99,8770.92,5500840000,8770.92 2009-06-10,8763.66,8871.36,8625.21,8739.02,5379420000,8739.02 2009-06-09,8764.83,8854.80,8688.99,8763.06,4439950000,8763.06 2009-06-08,8759.35,8832.13,8593.84,8764.49,4483430000,8764.49 2009-06-05,8751.75,8900.48,8673.41,8763.13,5277910000,8763.13 2009-06-04,8665.72,8802.59,8609.17,8750.24,5352890000,8750.24 2009-06-03,8740.07,8750.83,8556.90,8675.24,5323770000,8675.24 2009-06-02,8721.60,8832.16,8635.25,8740.87,5987340000,8740.87 2009-06-01,8501.53,8797.58,8501.53,8721.44,6370440000,8721.44 2009-05-29,8404.04,8541.27,8323.91,8500.33,6050420000,8500.33 2009-05-28,8300.50,8463.70,8221.65,8403.80,5738980000,8403.80 2009-05-27,8473.65,8534.66,8280.82,8300.02,5698800000,8300.02 2009-05-26,8275.33,8523.59,8194.33,8473.49,5667050000,8473.49 2009-05-22,8292.21,8415.75,8218.86,8277.32,5155320000,8277.32 2009-05-21,8416.07,8416.07,8185.25,8292.13,6019840000,8292.13 2009-05-20,8471.82,8645.85,8376.40,8422.04,8205060000,8422.04 2009-05-19,8502.48,8594.16,8402.61,8474.85,6616270000,8474.85 2009-05-18,8270.15,8534.66,8270.15,8504.08,5702150000,8504.08 2009-05-15,8326.22,8422.28,8206.67,8268.64,5439720000,8268.64 2009-05-14,8285.92,8427.93,8218.94,8331.32,6134870000,8331.32 2009-05-13,8461.80,8461.80,8208.74,8284.89,7091820000,8284.89 2009-05-12,8419.17,8574.88,8306.47,8469.11,6871750400,8469.11 2009-05-11,8569.23,8569.23,8347.41,8418.77,6150600000,8418.77 2009-05-08,8410.73,8657.96,8388.11,8574.65,8163280000,8574.65 2009-05-07,8513.56,8651.51,8296.04,8409.85,9120100000,8409.85 2009-05-06,8403.48,8608.26,8350.12,8512.28,8555040000,8512.28 2009-05-05,8425.55,8520.80,8321.37,8410.65,6882860000,8410.65 2009-05-04,8213.60,8488.87,8213.60,8426.74,7038840000,8426.74 2009-05-01,8167.41,8278.28,8047.54,8212.41,5312170000,8212.41 2009-04-30,8188.51,8383.81,8083.62,8168.12,6862540000,8168.12 2009-04-29,8018.31,8278.12,8018.31,8185.73,6101620000,8185.73 2009-04-28,8023.56,8136.74,7898.75,8016.95,6328000000,8016.95 2009-04-27,8073.82,8152.27,7920.42,8025.00,5613460000,8025.00 2009-04-24,7957.45,8182.30,7905.60,8076.29,7114440000,8076.29 2009-04-23,7886.81,8015.36,7762.80,7957.06,6563100000,7957.06 2009-04-22,7964.78,8111.02,7802.46,7886.57,7327860000,7886.57 2009-04-21,7841.73,8027.54,7699.79,7969.56,7436489600,7969.56 2009-04-20,8128.94,8128.94,7801.58,7841.73,6973960000,7841.73 2009-04-17,8125.43,8251.20,8024.92,8131.33,7352009600,8131.33 2009-04-16,8029.14,8201.81,7933.08,8125.43,6598670000,8125.43 2009-04-15,7914.92,8069.92,7808.19,8029.62,6241100000,8029.62 2009-04-14,8057.41,8076.05,7840.53,7920.18,7569840000,7920.18 2009-04-13,8082.02,8146.86,7888.96,8057.81,6434890000,8057.81 2009-04-09,7839.89,8150.44,7839.89,8083.38,7600710400,8083.38 2009-04-08,7788.68,7925.36,7715.09,7837.11,5938460000,7837.11 2009-04-07,7968.92,7968.92,7733.56,7789.56,5155580000,7789.56 2009-04-06,8016.16,8037.42,7830.66,7975.85,6210000000,7975.85 2009-04-03,7980.63,8090.71,7850.33,8017.59,5855640000,8017.59 2009-04-02,7763.99,8129.33,7763.99,7978.08,7542809600,7978.08 2009-04-01,7606.13,7804.77,7450.74,7761.60,6034140000,7761.60 2009-03-31,7523.77,7744.24,7502.98,7608.92,6089100000,7608.92 2009-03-30,7773.31,7773.31,7406.85,7522.02,5912660000,7522.02 2009-03-27,7922.57,7922.57,7695.97,7776.18,5600210000,7776.18 2009-03-26,7752.36,7969.00,7709.19,7924.56,6992960000,7924.56 2009-03-25,7659.81,7897.48,7539.54,7749.81,7687180000,7749.81 2009-03-24,7773.47,7837.11,7585.98,7660.21,6767980000,7660.21 2009-03-23,7279.25,7789.24,7279.25,7775.86,7715769600,7775.86 2009-03-20,7402.31,7524.81,7215.77,7278.38,7643720000,7278.38 2009-03-19,7489.68,7624.45,7325.13,7400.80,9033870400,7400.80 2009-03-18,7395.70,7592.03,7218.24,7486.58,9098449600,7486.58 2009-03-17,7218.00,7407.41,7129.60,7395.70,6156800000,7395.70 2009-03-16,7225.33,7428.75,7171.41,7216.97,7883540000,7216.97 2009-03-13,7219.20,7241.98,7106.34,7223.98,6787089600,7223.98 2009-03-12,6932.39,7198.25,6840.79,7170.06,7326630400,7170.06 2009-03-11,6923.13,7078.22,6804.55,6930.40,7287809600,6930.40 2009-03-10,6547.01,6951.50,6547.01,6926.49,8618329600,6926.49 2009-03-09,6625.74,6758.44,6440.08,6547.05,7277320000,6547.05 2009-03-06,6595.16,6776.44,6443.27,6626.94,7331830400,6626.94 2009-03-05,6874.01,6874.01,6531.28,6594.44,7507249600,6594.44 2009-03-04,6726.50,7012.19,6715.11,6875.84,7673620000,6875.84 2009-03-03,6764.81,6922.59,6661.74,6726.02,7583230400,6726.02 2009-03-02,7056.48,7056.48,6736.69,6763.29,7868289600,6763.29 2009-02-27,7180.97,7244.61,6952.06,7062.93,8926480000,7062.93 2009-02-26,7269.06,7451.13,7135.25,7182.08,7599969600,7182.08 2009-02-25,7349.58,7442.13,7123.94,7270.89,7483640000,7270.89 2009-02-24,7115.34,7396.34,7077.35,7350.94,7234489600,7350.94 2009-02-23,7365.99,7477.10,7092.64,7114.78,6509300000,7114.78 2009-02-20,7461.49,7500.44,7226.29,7365.67,8210590400,7365.67 2009-02-19,7555.23,7679.01,7420.63,7465.95,5746940000,7465.95 2009-02-18,7546.35,7661.56,7451.37,7555.63,5740710000,7555.63 2009-02-17,7845.63,7845.63,7502.59,7552.60,5907820000,7552.60 2009-02-13,7933.00,8005.96,7811.38,7850.41,5296650000,7850.41 2009-02-12,7931.97,7956.02,7662.04,7932.76,6476460000,7932.76 2009-02-11,7887.05,8042.36,7820.14,7939.53,5926460000,7939.53 2009-02-10,8269.36,8293.17,7835.83,7888.88,6770169600,7888.88 2009-02-09,8281.38,8376.56,8137.70,8270.87,5574370000,8270.87 2009-02-06,8056.38,8360.07,8044.03,8280.59,6484100000,8280.59 2009-02-05,7954.83,8138.65,7811.70,8063.07,6624030000,8063.07 2009-02-04,8070.32,8197.04,7899.79,7956.66,6420450000,7956.66 2009-02-03,7936.99,8157.13,7855.19,8078.36,5886310000,8078.36 2009-02-02,8000.62,8053.43,7796.17,7936.83,5673270000,7936.83 2009-01-30,8149.01,8243.95,7924.88,8000.86,5350580000,8000.86 2009-01-29,8373.06,8373.06,8092.14,8149.01,5067060000,8149.01 2009-01-28,8175.93,8446.33,8175.93,8375.45,6199180000,8375.45 2009-01-27,8117.39,8264.10,8042.60,8174.73,5353260000,8174.73 2009-01-26,8078.04,8278.12,7971.15,8116.03,6039940000,8116.03 2009-01-23,8108.79,8187.88,7856.86,8077.56,5832160000,8077.56 2009-01-22,8224.43,8239.33,7925.75,8122.80,5843830000,8122.80 2009-01-21,7949.17,8286.40,7890.63,8228.10,6467830000,8228.10 2009-01-20,8279.63,8309.02,7920.66,7949.09,6375230000,7949.09 2009-01-16,8215.67,8424.59,8086.01,8281.22,6786040000,8281.22 2009-01-15,8196.24,8326.06,7949.65,8212.49,7807350400,8212.49 2009-01-14,8446.01,8446.01,8097.95,8200.14,5407880000,8200.14 2009-01-13,8474.61,8584.68,8325.59,8448.56,5567460000,8448.56 2009-01-12,8599.26,8653.97,8391.85,8473.97,4725050000,8473.97 2009-01-09,8738.80,8800.45,8541.75,8599.18,4716500000,8599.18 2009-01-08,8769.94,8807.14,8593.52,8742.46,4991550000,8742.46 2009-01-07,8996.94,8996.94,8690.45,8769.70,4704940000,8769.70 2009-01-06,8954.57,9175.19,8868.07,9015.10,5392620000,9015.10 2009-01-05,9027.13,9093.47,8841.70,8952.89,5413910000,8952.89 2009-01-02,8772.25,9080.57,8725.10,9034.69,4048270000,9034.69 2008-12-31,8666.48,8862.65,8634.06,8776.39,4172940000,8776.39 2008-12-30,8487.51,8700.89,8463.70,8668.39,3627800000,8668.39 2008-12-29,8515.87,8575.60,8349.24,8483.93,3323430000,8483.93 2008-12-26,8468.71,8581.58,8434.94,8515.55,1880050000,8515.55 2008-12-24,8428.17,8498.26,8417.02,8468.48,1546550000,8468.48 2008-12-23,8518.65,8647.60,8376.80,8419.49,4051970000,8419.49 2008-12-22,8573.37,8672.06,8351.79,8519.69,4869850000,8519.69 2008-12-19,8606.50,8823.78,8499.06,8579.11,6705310000,8579.11 2008-12-18,8823.94,8946.36,8516.02,8604.99,5675000000,8604.99 2008-12-17,8921.91,9001.96,8701.13,8824.34,5907380000,8824.34 2008-12-16,8565.65,8985.63,8534.03,8924.14,6009780000,8924.14 2008-12-15,8628.81,8738.40,8431.04,8564.53,4982390000,8564.53 2008-12-12,8563.10,8705.43,8272.22,8629.68,5959590000,8629.68 2008-12-11,8750.13,8861.86,8480.18,8565.09,5513840000,8565.09 2008-12-10,8693.00,8942.46,8589.86,8761.42,5942130000,8761.42 2008-12-09,8934.10,8978.14,8591.69,8691.33,5693110000,8691.33 2008-12-08,8637.65,9151.61,8637.65,8934.18,6553600000,8934.18 2008-12-05,8376.08,8722.47,8084.25,8635.42,6165370000,8635.42 2008-12-04,8587.07,8705.98,8222.84,8376.24,5860390000,8376.24 2008-12-03,8409.14,8654.77,8170.19,8591.69,6221880000,8591.69 2008-12-02,8153.75,8490.62,8072.47,8419.09,6170100000,8419.09 2008-12-01,8826.89,8826.89,8123.04,8149.09,6052010000,8149.09 2008-11-28,8690.24,8840.33,8687.05,8829.04,2740860000,8829.04 2008-11-26,8464.49,8760.46,8250.80,8726.61,5793260000,8726.61 2008-11-25,8445.14,8682.09,8244.43,8479.47,6952700000,8479.47 2008-11-24,8048.09,8624.27,8023.32,8443.39,7879440000,8443.39 2008-11-21,7552.37,8121.45,7392.27,8046.42,9495900000,8046.42 2008-11-20,7995.53,8224.35,7464.51,7552.29,9093740000,7552.29 2008-11-19,8420.69,8534.34,7967.33,7997.28,6548600000,7997.28 2008-11-18,8273.34,8540.08,8075.81,8424.75,6679470000,8424.75 2008-11-17,8494.84,8596.31,8197.12,8273.58,4927490000,8273.58 2008-11-14,8822.19,8980.93,8421.08,8497.31,5881030000,8497.31 2008-11-13,8281.14,8898.41,7947.74,8835.25,7849120000,8835.25 2008-11-12,8684.52,8684.52,8235.66,8282.66,5764180000,8282.66 2008-11-11,8864.32,8892.20,8499.62,8693.96,4998340000,8693.96 2008-11-10,8946.60,9212.94,8735.61,8870.54,4572000000,8870.54 2008-11-07,8696.03,9032.54,8661.22,8943.81,4931640000,8943.81 2008-11-06,9134.01,9216.37,8607.14,8695.79,6102230000,8695.79 2008-11-05,9616.60,9628.15,9086.06,9139.27,5426640000,9139.27 2008-11-04,9323.89,9711.46,9323.89,9625.28,5531290000,9625.28 2008-11-03,9326.04,9488.92,9175.03,9319.83,4492280000,9319.83 2008-10-31,9179.09,9498.48,9014.78,9325.01,6394350000,9325.01 2008-10-30,9004.66,9380.36,8916.81,9180.69,6175830000,9180.69 2008-10-29,9062.33,9405.05,8800.61,8990.96,7077800000,8990.96 2008-10-28,8178.72,9112.51,8153.79,9065.12,7096950400,9065.12 2008-10-27,8375.92,8639.64,8085.37,8175.77,5558050000,8175.77 2008-10-24,8683.21,8683.21,8088.63,8378.95,6550050000,8378.95 2008-10-23,8519.77,8864.48,8200.06,8691.25,7189900000,8691.25 2008-10-22,9027.84,9027.84,8324.07,8519.21,6147980000,8519.21 2008-10-21,9179.11,9293.07,9017.30,9045.21,5121830000,9045.21 2008-10-20,8852.30,9305.89,8799.49,9265.43,5175640000,9265.43 2008-10-17,8975.35,9304.38,8640.83,8852.22,6581780000,8852.22 2008-10-16,8577.04,9073.64,8176.17,8979.26,7984500000,8979.26 2008-10-15,9301.91,9301.91,8516.50,8577.91,6542330000,8577.91 2008-10-14,9388.97,9924.28,9050.06,9310.99,8161990400,9310.99 2008-10-13,8462.42,9501.91,8462.42,9387.61,7263369600,9387.61 2008-10-10,8568.67,8989.13,7773.71,8451.19,11456230400,8451.19 2008-10-09,9261.69,9522.77,8523.27,8579.19,8285670400,8579.19 2008-10-08,9437.23,9778.04,9042.97,9258.10,8716329600,9258.10 2008-10-07,9955.42,10205.04,9391.67,9447.11,7069209600,9447.11 2008-10-06,10322.52,10322.52,9503.10,9955.50,7956020000,9955.50 2008-10-03,10483.96,10844.69,10261.75,10325.38,6716120000,10325.38 2008-10-02,10825.54,10843.10,10368.08,10482.85,6285640000,10482.85 2008-10-01,10847.40,11022.06,10495.99,10831.07,5782130000,10831.07 2008-09-30,10371.58,10922.03,10371.58,10850.66,6065000000,10850.66 2008-09-29,11139.62,11139.62,10266.76,10365.45,7305060000,10365.45 2008-09-26,11019.04,11218.48,10781.37,11143.13,5383610000,11143.13 2008-09-25,10827.17,11206.05,10799.77,11022.06,5877640000,11022.06 2008-09-24,10850.02,11041.02,10696.38,10825.17,4820360000,10825.17 2008-09-23,11015.69,11214.65,10763.77,10854.17,5185730000,10854.17 2008-09-22,11394.42,11450.81,10956.43,11015.69,5368130000,11015.69 2008-09-19,11027.51,11415.48,11027.51,11388.44,9387169600,11388.44 2008-09-18,10609.01,11149.07,10403.75,11019.69,10082689600,11019.69 2008-09-17,11056.58,11068.87,10521.81,10609.66,9431870400,10609.66 2008-09-16,10905.62,11193.12,10604.70,11059.02,9459830400,11059.02 2008-09-15,11416.37,11416.37,10849.85,10917.51,8279510400,10917.51 2008-09-12,11429.32,11532.72,11191.08,11421.99,6273260000,11421.99 2008-09-11,11264.44,11461.15,11018.72,11433.71,6869249600,11433.71 2008-09-10,11233.91,11453.50,11135.64,11268.92,6543440000,11268.92 2008-09-09,11514.73,11623.50,11209.81,11230.73,7380630400,11230.73 2008-09-08,11224.87,11656.64,11224.87,11510.74,7351340000,11510.74 2008-09-05,11185.63,11301.73,10998.77,11220.96,5017080000,11220.96 2008-09-04,11532.48,11532.48,11130.26,11188.23,5212500000,11188.23 2008-09-03,11506.01,11629.69,11328.84,11532.88,5056980000,11532.88 2008-09-02,11545.63,11831.29,11444.79,11516.92,4783560000,11516.92 2008-08-29,11713.23,11730.49,11508.78,11543.55,3288120000,11543.55 2008-08-28,11499.87,11756.46,11493.72,11715.18,3854280000,11715.18 2008-08-27,11412.46,11575.14,11349.69,11502.51,3499610000,11502.51 2008-08-26,11383.56,11483.62,11284.47,11412.87,3587570000,11412.87 2008-08-25,11626.19,11626.19,11336.82,11386.25,3420600000,11386.25 2008-08-22,11426.79,11684.00,11426.79,11628.06,3741070000,11628.06 2008-08-21,11415.23,11501.29,11263.63,11430.21,4032590000,11430.21 2008-08-20,11345.94,11511.06,11240.18,11417.43,4555030000,11417.43 2008-08-19,11478.09,11501.45,11260.53,11348.55,4159760000,11348.55 2008-08-18,11659.65,11744.49,11410.18,11479.39,3829290000,11479.39 2008-08-15,11611.21,11776.41,11540.05,11659.90,4041820000,11659.90 2008-08-14,11532.07,11744.33,11399.84,11615.93,4064000000,11615.93 2008-08-13,11632.81,11689.05,11377.37,11532.96,4787600000,11532.96 2008-08-12,11781.70,11830.39,11541.43,11642.47,4711290000,11642.47 2008-08-11,11729.67,11933.55,11580.19,11782.35,5067310000,11782.35 2008-08-08,11432.09,11808.49,11344.23,11734.32,4966810000,11734.32 2008-08-07,11655.42,11680.50,11355.63,11431.43,5319380000,11431.43 2008-08-06,11603.64,11745.71,11454.64,11656.07,4873420000,11656.07 2008-08-05,11286.02,11652.24,11286.02,11615.77,1219310000,11615.77 2008-08-04,11326.32,11449.67,11144.59,11284.15,4562280000,11284.15 2008-08-01,11379.89,11512.61,11205.41,11326.32,4684870000,11326.32 2008-07-31,11577.99,11631.16,11317.69,11378.02,5346050000,11378.02 2008-07-30,11397.56,11681.47,11328.68,11583.69,5631330000,11583.69 2008-07-29,11133.44,11444.05,11086.13,11397.56,5414240000,11397.56 2008-07-28,11369.47,11439.25,11094.76,11131.08,4282960000,11131.08 2008-07-25,11341.14,11540.78,11252.47,11370.69,4672560000,11370.69 2008-07-24,11630.34,11714.21,11288.79,11349.28,6127980000,11349.28 2008-07-23,11603.39,11820.21,11410.02,11632.38,6705830000,11632.38 2008-07-22,11457.90,11692.79,11273.32,11602.50,6180230000,11602.50 2008-07-21,11495.02,11663.40,11339.02,11467.34,4630640000,11467.34 2008-07-18,11436.56,11599.57,11290.50,11496.57,5653280000,11496.57 2008-07-17,11238.39,11538.50,11118.46,11446.66,7365209600,11446.66 2008-07-16,10961.89,11308.41,10831.61,11239.28,6738630400,11239.28 2008-07-15,11050.80,11201.67,10731.96,10962.54,7363640000,10962.54 2008-07-14,11103.64,11299.70,10972.63,11055.19,5434860000,11055.19 2008-07-11,11226.17,11292.04,10908.64,11100.54,6742200000,11100.54 2008-07-10,11148.01,11351.24,11006.01,11229.02,5840430000,11229.02 2008-07-09,11381.93,11505.12,11115.61,11147.44,5181000000,11147.44 2008-07-08,11225.03,11459.52,11101.19,11384.21,6034110000,11384.21 2008-07-07,11289.19,11477.52,11094.44,11231.96,5265420000,11231.96 2008-07-03,11297.33,11336.49,11158.02,11288.53,3247590000,11288.53 2008-07-02,11382.34,11510.41,11180.58,11215.51,5276090000,11215.51 2008-07-01,11344.64,11465.79,11106.65,11382.26,5846290000,11382.26 2008-06-30,11345.70,11504.55,11226.34,11350.01,5032330000,11350.01 2008-06-27,11452.85,11556.33,11248.48,11346.51,6208260000,11346.51 2008-06-26,11808.57,11808.57,11431.92,11453.42,5231280000,11453.42 2008-06-25,11805.31,12008.70,11683.75,11811.83,4825640000,11811.83 2008-06-24,11842.36,11962.37,11668.53,11807.43,4705050000,11807.43 2008-06-23,11843.83,11986.96,11731.06,11842.36,4186370000,11842.36 2008-06-20,12062.19,12078.23,11785.04,11842.69,5324900000,11842.69 2008-06-19,12022.54,12188.31,11881.03,12063.09,4811670000,12063.09 2008-06-18,12158.68,12212.33,11947.07,12029.06,4573570000,12029.06 2008-06-17,12269.65,12378.67,12114.14,12160.30,3801960000,12160.30 2008-06-16,12306.86,12381.44,12139.79,12269.08,3706940000,12269.08 2008-06-13,12144.59,12376.72,12096.23,12307.35,4080420000,12307.35 2008-06-12,12089.63,12337.72,12041.43,12141.58,4734240000,12141.58 2008-06-11,12286.34,12317.20,12029.46,12083.77,4779980000,12083.77 2008-06-10,12277.71,12425.98,12116.58,12289.76,4635070000,12289.76 2008-06-09,12210.13,12406.36,12102.50,12280.32,4404570000,12280.32 2008-06-06,12602.74,12602.74,12180.50,12209.81,4771660000,12209.81 2008-06-05,12388.81,12652.81,12358.07,12604.45,4350790000,12604.45 2008-06-04,12391.86,12540.37,12283.74,12390.48,4338640000,12390.48 2008-06-03,12503.20,12620.98,12317.61,12402.85,4396380000,12402.85 2008-06-02,12637.67,12645.40,12385.76,12503.82,3714320000,12503.82 2008-05-30,12647.36,12750.84,12555.60,12638.32,3845630000,12638.32 2008-05-29,12593.87,12760.21,12493.47,12646.22,3894440000,12646.22 2008-05-28,12542.90,12693.77,12437.38,12594.03,3927240000,12594.03 2008-05-27,12479.63,12626.84,12397.56,12548.35,3588860000,12548.35 2008-05-23,12620.90,12637.43,12420.20,12479.63,3516380000,12479.63 2008-05-22,12597.69,12743.68,12515.78,12625.62,3955960000,12625.62 2008-05-21,12824.94,12926.71,12550.39,12601.19,4517990000,12601.19 2008-05-20,13026.04,13026.04,12742.29,12828.68,3854320000,12828.68 2008-05-19,12985.41,13170.97,12899.19,13028.16,3683970000,13028.16 2008-05-16,12992.74,13069.52,12860.60,12986.80,3842590000,12986.80 2008-05-15,12891.29,13028.16,12798.39,12992.66,3836480000,12992.66 2008-05-14,12825.12,13037.44,12806.21,12898.38,3979370000,12898.38 2008-05-13,12872.08,12957.65,12716.16,12832.18,4018590000,12832.18 2008-05-12,12768.38,12903.33,12746.36,12876.05,3370630000,12876.05 2008-05-09,12860.68,12871.75,12648.09,12745.88,3518620000,12745.88 2008-05-08,12814.84,12965.95,12727.56,12866.78,3827550000,12866.78 2008-05-07,13010.82,13097.77,12756.14,12814.35,4075860000,12814.35 2008-05-06,12968.89,13071.07,12817.53,13020.83,3924100000,13020.83 2008-05-05,13056.57,13105.75,12896.50,12969.54,3410090000,12969.54 2008-05-02,13012.53,13191.49,12931.35,13058.20,3953030000,13058.20 2008-05-01,12818.34,13079.94,12721.94,13010.00,4448780000,13010.00 2008-04-30,12831.45,13052.91,12746.45,12820.13,4508890000,12820.13 2008-04-29,12870.37,12970.27,12737.82,12831.94,3815320000,12831.94 2008-04-28,12890.76,13015.62,12791.55,12871.75,3607000000,12871.75 2008-04-25,12848.38,12987.29,12703.70,12891.86,3891150000,12891.86 2008-04-24,12764.68,12979.88,12651.51,12848.95,4461660000,12848.95 2008-04-23,12721.45,12883.80,12627.00,12763.22,4103610000,12763.22 2008-04-22,12825.02,12870.86,12604.53,12720.23,3821900000,12720.23 2008-04-21,12850.91,12902.69,12666.08,12825.02,3420570000,12825.02 2008-04-18,12626.76,12965.47,12626.76,12849.36,4222380000,12849.36 2008-04-17,12617.40,12725.93,12472.71,12620.49,3713880000,12620.49 2008-04-16,12371.51,12670.56,12371.51,12619.27,4260370000,12619.27 2008-04-15,12303.60,12459.36,12223.97,12362.47,3581230000,12362.47 2008-04-14,12324.77,12430.86,12208.42,12302.06,3565020000,12302.06 2008-04-11,12579.78,12579.78,12280.89,12325.42,3723790000,12325.42 2008-04-10,12526.78,12705.90,12447.96,12581.98,3686150000,12581.98 2008-04-09,12574.65,12686.93,12416.53,12527.26,3556670000,12527.26 2008-04-08,12602.66,12664.38,12440.55,12576.44,3602500000,12576.44 2008-04-07,12612.59,12786.83,12550.22,12612.43,3747780000,12612.43 2008-04-04,12626.35,12738.30,12489.40,12609.42,3703100000,12609.42 2008-04-03,12604.69,12734.97,12455.04,12626.03,3920100000,12626.03 2008-04-02,12651.67,12790.28,12488.22,12608.92,4320440000,12608.92 2008-04-01,12266.64,12693.93,12266.64,12654.36,4745120000,12654.36 2008-03-31,12215.92,12384.84,12095.18,12262.89,4188990000,12262.89 2008-03-28,12303.92,12441.67,12164.22,12216.40,3686980000,12216.40 2008-03-27,12421.88,12528.13,12264.76,12302.46,4037930000,12302.46 2008-03-26,12531.79,12531.79,12309.62,12422.86,4055670000,12422.86 2008-03-25,12547.34,12639.82,12397.62,12532.60,4145120000,12532.60 2008-03-24,12361.97,12687.61,12346.17,12548.64,4499000000,12548.64 2008-03-20,12102.43,12434.34,12024.68,12361.32,6145220000,12361.32 2008-03-19,12391.52,12525.19,12077.27,12099.66,5358550000,12099.66 2008-03-18,11975.92,12411.63,11975.92,12392.66,5335630000,12392.66 2008-03-17,11946.45,12119.69,11650.44,11972.25,5683010000,11972.25 2008-03-14,12146.39,12249.86,11781.43,11951.09,5153780000,11951.09 2008-03-13,12096.49,12242.29,11832.88,12145.74,5073360000,12145.74 2008-03-12,12148.61,12360.58,12037.79,12110.24,4414280000,12110.24 2008-03-11,11741.33,12205.98,11741.33,12156.81,5109080000,12156.81 2008-03-10,11893.04,11993.75,11691.47,11740.15,4261240000,11740.15 2008-03-07,12039.09,12131.33,11778.66,11893.69,4565410000,11893.69 2008-03-06,12254.59,12267.86,12010.03,12040.39,4323460000,12040.39 2008-03-05,12204.93,12392.74,12105.36,12254.99,4277710000,12254.99 2008-03-04,12259.14,12291.22,11991.06,12213.80,4757180000,12213.80 2008-03-03,12264.36,12344.71,12101.29,12258.90,4117570000,12258.90 2008-02-29,12579.58,12579.58,12210.30,12266.39,4426730000,12266.39 2008-02-28,12689.28,12713.99,12463.32,12582.18,3938580000,12582.18 2008-02-27,12683.54,12815.59,12527.64,12694.28,3904700000,12694.28 2008-02-26,12569.48,12771.14,12449.08,12684.92,4096060000,12684.92 2008-02-25,12380.77,12612.47,12292.03,12570.22,3866350000,12570.22 2008-02-22,12281.09,12429.05,12116.92,12381.02,3572660000,12381.02 2008-02-21,12426.85,12545.79,12225.36,12284.30,3696660000,12284.30 2008-02-20,12333.31,12489.29,12159.42,12427.26,3870520000,12427.26 2008-02-19,12349.59,12571.11,12276.81,12337.22,3613550000,12337.22 2008-02-15,12376.66,12441.20,12216.68,12348.21,3583300000,12348.21 2008-02-14,12551.51,12611.26,12332.03,12376.98,3644760000,12376.98 2008-02-13,12368.12,12627.76,12354.22,12552.24,3856420000,12552.24 2008-02-12,12241.56,12524.12,12207.90,12373.41,4044640000,12373.41 2008-02-11,12181.89,12332.76,12006.79,12240.01,3593140000,12240.01 2008-02-08,12248.47,12330.97,12058.01,12182.13,3768490000,12182.13 2008-02-07,12196.20,12366.99,12045.00,12247.00,4589160000,12247.00 2008-02-06,12257.25,12436.33,12142.14,12200.10,4008120000,12200.10 2008-02-05,12631.85,12631.85,12234.97,12265.13,4315740000,12265.13 2008-02-04,12743.11,12810.34,12557.61,12635.16,3495780000,12635.16 2008-02-01,12638.17,12841.88,12510.05,12743.19,4650770000,12743.19 2008-01-31,12438.28,12734.74,12197.09,12650.36,4970290000,12650.36 2008-01-30,12480.14,12715.96,12311.55,12442.83,4742760000,12442.83 2008-01-29,12385.19,12604.92,12262.29,12480.30,4232960000,12480.30 2008-01-28,12205.71,12423.81,12061.42,12383.89,4100930000,12383.89 2008-01-25,12391.70,12590.69,12103.61,12207.17,4882250000,12207.17 2008-01-24,12272.69,12522.82,12114.83,12378.61,5735300000,12378.61 2008-01-23,11969.08,12339.10,11530.12,12270.17,3241680000,12270.17 2008-01-22,12092.72,12167.42,11508.74,11971.19,6544690000,11971.19 2008-01-18,12159.94,12441.85,11953.71,12099.30,6004840000,12099.30 2008-01-17,12467.05,12597.85,12089.38,12159.21,5303130000,12159.21 2008-01-16,12476.81,12699.05,12294.48,12466.16,5440620000,12466.16 2008-01-15,12777.50,12777.50,12425.92,12501.11,4601640000,12501.11 2008-01-14,12613.78,12866.10,12596.95,12778.15,3682090000,12778.15 2008-01-11,12850.74,12863.34,12495.91,12606.30,4495840000,12606.30 2008-01-10,12733.11,12931.29,12632.15,12853.09,5170490000,12853.09 2008-01-09,12590.21,12814.97,12431.53,12735.31,5351030000,12735.31 2008-01-08,12820.90,12998.11,12511.03,12589.07,4705390000,12589.07 2008-01-07,12801.15,12984.95,12640.44,12827.49,4221260000,12827.49 2008-01-04,13046.56,13049.65,12740.51,12800.18,4166000000,12800.18 2008-01-03,13044.12,13197.43,12968.44,13056.72,3429500000,13056.72 2008-01-02,13261.82,13338.23,12969.42,13043.96,3452650000,13043.96 2007-12-31,13364.16,13423.91,13197.35,13264.82,2440880000,13264.82 2007-12-28,13361.23,13494.30,13272.14,13365.87,2420510000,13365.87 2007-12-27,13549.17,13551.53,13325.71,13359.61,2365770000,13359.61 2007-12-26,13547.95,13614.53,13440.16,13551.69,2010500000,13551.69 2007-12-24,13487.12,13562.72,13451.35,13550.04,2200000,13550.04 2007-12-21,13241.66,13518.20,13241.66,13450.65,4508590000,13450.65 2007-12-20,13206.46,13354.00,13112.98,13245.64,3526890000,13245.64 2007-12-19,13231.98,13368.79,13097.77,13207.27,3401300000,13207.27 2007-12-18,13168.66,13346.84,13059.32,13232.47,3723690000,13232.47 2007-12-17,13339.20,13378.38,13111.92,13167.20,3569030000,13167.20 2007-12-14,13515.11,13557.54,13284.66,13339.85,3401050000,13339.85 2007-12-13,13473.98,13586.73,13281.00,13517.96,3635170000,13517.96 2007-12-12,13434.80,13778.98,13299.61,13473.90,4482120000,13473.90 2007-12-11,13726.87,13850.92,13374.89,13432.77,4080180000,13432.77 2007-12-10,13623.55,13807.02,13582.50,13727.03,2911760000,13727.03 2007-12-07,13618.27,13744.02,13514.22,13625.58,3177710000,13625.58 2007-12-06,13445.85,13652.49,13362.37,13619.89,3568570000,13619.89 2007-12-05,13244.01,13513.00,13244.01,13444.96,3663660000,13444.96 2007-12-04,13311.24,13395.21,13139.56,13248.73,3343620000,13248.73 2007-12-03,13368.22,13490.24,13207.60,13314.57,3323250000,13314.57 2007-11-30,13314.25,13570.31,13225.32,13371.72,4422200000,13371.72 2007-11-29,13287.91,13399.03,13150.21,13311.73,3524730000,13311.73 2007-11-28,12958.04,13353.51,12958.04,13289.45,4508020000,13289.45 2007-11-27,12744.78,13040.38,12711.98,12958.44,4320720000,12958.44 2007-11-26,12979.99,13104.44,12707.26,12743.44,3706470000,12743.44 2007-11-23,12889.45,12981.56,12796.29,12980.88,1612720000,12980.88 2007-11-21,13006.65,13055.59,12725.39,12799.04,4076230000,12799.04 2007-11-20,12955.92,13179.23,12800.74,13010.14,4875150000,13010.14 2007-11-19,13176.30,13195.48,12871.14,12958.44,4119650000,12958.44 2007-11-16,13109.48,13293.44,12987.22,13176.79,4168870000,13176.79 2007-11-15,13230.68,13333.59,13007.95,13110.05,3941010000,13110.05 2007-11-14,13305.47,13465.20,13159.88,13231.01,4031470000,13231.01 2007-11-13,12975.11,13357.57,12975.11,13307.09,4141310000,13307.09 2007-11-12,13039.16,13238.73,12910.40,12987.55,4192520000,12987.55 2007-11-09,13261.17,13321.81,12920.65,13042.74,4587050000,13042.74 2007-11-08,13299.70,13463.66,13001.93,13266.29,5439720000,13266.29 2007-11-07,13646.72,13646.72,13269.46,13300.02,4353160000,13300.02 2007-11-06,13542.34,13716.55,13460.73,13660.94,3879160000,13660.94 2007-11-05,13592.58,13666.15,13393.67,13543.40,3819330000,13543.40 2007-11-02,13569.90,13708.58,13381.64,13595.10,4285990000,13595.10 2007-11-01,13924.16,13924.16,13522.75,13567.87,4241470000,13567.87 2007-10-31,13792.06,13990.65,13711.59,13930.01,3953070000,13930.01 2007-10-30,13869.04,13930.91,13719.80,13792.47,3212520000,13792.47 2007-10-29,13807.35,13966.18,13748.33,13870.26,3124480000,13870.26 2007-10-26,13675.66,13885.95,13622.01,13806.70,3612120000,13806.70 2007-10-25,13677.85,13819.78,13471.87,13671.92,4183960000,13671.92 2007-10-24,13675.58,13751.50,13423.74,13675.25,4003300000,13675.25 2007-10-23,13568.93,13754.91,13494.95,13676.23,3309120000,13676.23 2007-10-22,13521.62,13636.80,13337.90,13566.97,3471830000,13566.97 2007-10-19,13888.47,13888.47,13478.94,13522.02,4160970000,13522.02 2007-10-18,13887.90,13984.39,13746.22,13888.96,3203210000,13888.96 2007-10-17,13920.66,14075.84,13738.66,13892.54,3638070000,13892.54 2007-10-16,13986.34,14061.37,13810.68,13912.94,3234560000,13912.94 2007-10-15,14092.43,14157.38,13877.82,13984.80,3139290000,13984.80 2007-10-12,14016.34,14168.51,13949.85,14093.08,2788690000,14093.08 2007-10-11,14079.10,14279.96,13917.82,14015.12,3911260000,14015.12 2007-10-10,14165.02,14225.66,13963.26,14078.69,3044760000,14078.69 2007-10-09,14043.73,14198.83,13980.90,14164.53,2932040000,14164.53 2007-10-08,14065.36,14134.05,13747.41,14043.73,2040650000,14043.73 2007-10-05,13969.07,14169.49,13965.05,14066.01,2919030000,14066.01 2007-10-04,13967.89,14074.54,13894.98,13974.31,2690430000,13974.31 2007-10-03,14038.86,14090.48,13883.43,13968.05,3065320000,13968.05 2007-10-02,14087.14,14166.16,13951.72,14047.31,3101910000,14047.31 2007-10-01,13895.71,14147.30,13869.86,14087.55,3281990000,14087.55 2007-09-28,13912.94,13994.64,13802.96,13895.63,2925350000,13895.63 2007-09-27,13879.53,13991.63,13811.17,13912.94,2872180000,13912.94 2007-09-26,13779.30,13962.61,13741.26,13878.15,3237390000,13878.15 2007-09-25,13757.84,13847.10,13629.16,13778.65,3187770000,13778.65 2007-09-24,13821.57,13930.74,13702.89,13759.06,3131310000,13759.06 2007-09-21,13768.33,13948.95,13740.61,13820.19,3679460000,13820.19 2007-09-20,13813.52,13893.02,13680.21,13766.70,2957700000,13766.70 2007-09-19,13740.61,13936.68,13689.80,13815.56,3846750000,13815.56 2007-09-18,13403.18,13772.15,13379.68,13739.39,3708940000,13739.39 2007-09-17,13441.95,13514.71,13306.69,13403.42,2598390000,13403.42 2007-09-14,13421.39,13507.55,13273.68,13442.52,2641740000,13442.52 2007-09-13,13292.38,13519.91,13292.38,13424.88,2877080000,13424.88 2007-09-12,13298.31,13408.62,13195.40,13291.65,2885720000,13291.65 2007-09-11,13129.40,13369.77,13124.68,13308.39,3015330000,13308.39 2007-09-10,13116.39,13280.67,12992.02,13127.85,2835720000,13127.85 2007-09-07,13360.74,13360.74,13059.16,13113.38,3191080000,13113.38 2007-09-06,13306.44,13464.79,13217.11,13363.35,2459590000,13363.35 2007-09-05,13442.85,13442.85,13203.86,13305.47,2991600000,13305.47 2007-09-04,13358.39,13521.86,13248.57,13448.86,2766600000,13448.86 2007-08-31,13240.84,13472.35,13240.84,13357.74,2731610000,13357.74 2007-08-30,13287.91,13355.46,13126.39,13238.73,2582960000,13238.73 2007-08-29,13043.07,13336.93,13020.63,13289.29,2824070000,13289.29 2007-08-28,13318.43,13319.61,13024.29,13041.85,3078090000,13041.85 2007-08-27,13377.16,13438.46,13248.32,13322.13,2406180000,13322.13 2007-08-24,13231.78,13402.20,13174.27,13378.87,2541400000,13378.87 2007-08-23,13237.27,13358.22,13127.69,13235.88,3084390000,13235.88 2007-08-22,13088.26,13304.33,13075.34,13236.13,3309120000,13236.13 2007-08-21,13120.05,13228.57,12975.68,13090.86,3012150000,13090.86 2007-08-20,13078.51,13245.80,12938.77,13121.35,3321340000,13121.35 2007-08-17,12848.05,13289.70,12847.24,13079.08,3570040000,13079.08 2007-08-16,12859.52,12996.73,12455.92,12845.78,6509300000,12845.78 2007-08-15,13021.93,13184.51,12800.83,12861.47,4290930000,12861.47 2007-08-14,13235.72,13309.04,12974.30,13028.92,3814630000,13028.92 2007-08-13,13238.24,13440.08,13163.54,13236.53,3696280000,13236.53 2007-08-10,13270.59,13386.43,12958.04,13239.54,5345780000,13239.54 2007-08-09,13652.33,13675.66,13196.05,13270.68,5889600000,13270.68 2007-08-08,13497.23,13769.63,13386.92,13657.86,5499560000,13657.86 2007-08-07,13467.72,13635.09,13282.38,13504.30,4909390000,13504.30 2007-08-06,13183.13,13501.86,13077.05,13468.78,5067200000,13468.78 2007-08-03,13462.25,13539.50,13156.79,13181.91,4272110000,13181.91 2007-08-02,13357.82,13547.47,13272.79,13463.33,4368850000,13463.33 2007-08-01,13211.09,13431.06,13041.77,13362.37,5256780000,13362.37 2007-07-31,13360.66,13579.41,13182.15,13211.99,4524520000,13211.99 2007-07-30,13266.21,13445.12,13143.87,13358.31,4128780000,13358.31 2007-07-27,13472.68,13589.17,13228.57,13265.47,4784650000,13265.47 2007-07-26,13783.12,13793.61,13307.74,13473.57,4472550000,13473.57 2007-07-25,13718.25,13919.77,13607.70,13785.07,4283200000,13785.07 2007-07-24,13940.90,13967.65,13661.51,13716.95,4115830000,13716.95 2007-07-23,13851.73,14039.59,13819.54,13943.42,3102700000,13943.42 2007-07-20,14000.73,14039.67,13745.65,13851.08,3745780000,13851.08 2007-07-19,13918.79,14121.04,13860.18,14000.41,3251450000,14000.41 2007-07-18,13955.05,14020.89,13768.73,13918.22,3609220000,13918.22 2007-07-17,13951.96,14095.60,13880.67,13971.55,3007140000,13971.55 2007-07-16,13907.09,14053.57,13834.33,13950.98,2704110000,13950.98 2007-07-13,13859.86,13982.93,13784.83,13907.25,2801120000,13907.25 2007-07-12,13579.33,13889.45,13579.33,13861.73,3489600000,13861.73 2007-07-11,13500.40,13638.75,13435.45,13577.87,3082920000,13577.87 2007-07-10,13648.59,13685.90,13463.57,13501.70,3244280000,13501.70 2007-07-09,13612.66,13739.06,13563.89,13649.97,2715330000,13649.97 2007-07-06,13559.01,13670.46,13501.54,13611.68,2441520000,13611.68 2007-07-05,13576.24,13637.78,13459.84,13565.84,2622950000,13565.84 2007-07-03,13556.87,13592.07,13531.83,13577.30,1560790000,13577.30 2007-07-02,13409.60,13586.97,13406.59,13535.43,2648990000,13535.43 2007-06-29,13422.61,13556.16,13291.32,13408.62,3165410000,13408.62 2007-06-28,13427.48,13537.47,13342.05,13422.28,3006710000,13422.28 2007-06-27,13336.93,13455.36,13205.08,13427.73,3398150000,13427.73 2007-06-26,13352.37,13491.70,13272.79,13337.66,3398530000,13337.66 2007-06-25,13360.09,13519.34,13273.68,13352.05,3287250000,13352.05 2007-06-22,13545.03,13564.13,13323.51,13360.26,4284320000,13360.26 2007-06-21,13486.66,13596.56,13368.79,13545.84,3161110000,13545.84 2007-06-20,13636.56,13735.08,13469.43,13489.42,3286900000,13489.42 2007-06-19,13611.68,13705.41,13527.14,13635.42,2873590000,13635.42 2007-06-18,13639.00,13720.29,13560.15,13612.98,2480240000,13612.98 2007-06-15,13556.65,13741.18,13556.65,13639.48,3406030000,13639.48 2007-06-14,13482.43,13622.66,13444.07,13553.73,2813630000,13553.73 2007-06-13,13287.62,13502.76,13287.62,13482.35,3077930000,13482.35 2007-06-12,13424.39,13474.12,13264.05,13295.01,3056200000,13295.01 2007-06-11,13423.74,13519.88,13335.16,13424.96,2525280000,13424.96 2007-06-08,13267.14,13445.19,13207.73,13424.39,2993460000,13424.39 2007-06-07,13463.48,13517.85,13236.34,13266.73,3538470000,13266.73 2007-06-06,13590.66,13606.75,13403.10,13465.67,2964190000,13465.67 2007-06-05,13673.19,13689.40,13523.70,13595.46,2939450000,13595.46 2007-06-04,13667.21,13723.37,13575.14,13676.32,2738930000,13676.32 2007-06-01,13628.69,13756.69,13562.54,13668.11,2927020000,13668.11 2007-05-31,13633.00,13718.82,13564.49,13627.64,3335530000,13627.64 2007-05-30,13517.89,13650.64,13403.26,13633.08,2980210000,13633.08 2007-05-29,13507.28,13603.26,13428.86,13521.34,2571790000,13521.34 2007-05-25,13441.94,13571.48,13410.00,13507.28,2316250000,13507.28 2007-05-24,13522.60,13645.52,13391.56,13441.13,3365530000,13441.13 2007-05-23,13540.84,13648.69,13476.72,13525.65,3084260000,13525.65 2007-05-22,13544.99,13632.03,13466.57,13539.95,2860500000,13539.95 2007-05-21,13556.53,13636.98,13473.31,13542.88,3465360000,13542.88 2007-05-18,13476.40,13611.95,13454.46,13556.53,2959050000,13556.53 2007-05-17,13486.96,13558.24,13384.89,13476.72,2868640000,13476.72 2007-05-16,13374.13,13526.54,13325.49,13487.53,2915350000,13487.53 2007-05-15,13346.05,13518.33,13302.65,13383.84,3071020000,13383.84 2007-05-14,13325.81,13432.84,13265.02,13346.78,2776130000,13346.78 2007-05-11,13212.20,13373.35,13192.62,13326.22,2720780000,13326.22 2007-05-10,13359.05,13376.20,13161.08,13215.13,3031240000,13215.13 2007-05-09,13300.62,13410.17,13229.92,13362.87,2935550000,13362.87 2007-05-08,13309.40,13359.05,13192.45,13309.07,2795720000,13309.07 2007-05-07,13264.13,13385.06,13218.87,13312.97,2545090000,13312.97 2007-05-04,13243.08,13340.60,13176.61,13264.62,2761930000,13264.62 2007-05-03,13206.65,13306.55,13131.42,13241.38,3007970000,13241.38 2007-05-02,13133.94,13291.60,13105.34,13211.88,3189800000,13211.88 2007-05-01,13062.75,13188.96,12993.02,13136.14,3400350000,13136.14 2007-04-30,13120.21,13226.99,13003.91,13062.91,3093420000,13062.91 2007-04-27,13104.04,13195.05,13002.37,13120.94,2732810000,13120.94 2007-04-26,13088.84,13197.49,13016.43,13105.50,3211800000,13105.50 2007-04-25,12951.42,13142.31,12929.80,13089.89,3252590000,13089.89 2007-04-24,12919.64,13033.66,12845.12,12953.94,3119750000,12953.94 2007-04-23,12961.49,13029.59,12867.96,12919.40,2575020000,12919.40 2007-04-20,12811.15,13035.77,12811.15,12961.98,3329940000,12961.98 2007-04-19,12799.77,12889.17,12677.47,12808.63,2913610000,12808.63 2007-04-18,12771.08,12871.21,12691.20,12803.84,2971330000,12803.84 2007-04-17,12719.56,12837.40,12669.50,12773.04,2920570000,12773.04 2007-04-16,12611.64,12770.60,12596.36,12720.46,2870140000,12720.46 2007-04-13,12551.91,12654.47,12504.04,12612.13,2690020000,12612.13 2007-04-12,12483.64,12580.92,12407.50,12552.96,2770570000,12552.96 2007-04-11,12573.12,12618.63,12432.53,12484.62,2950190000,12484.62 2007-04-10,12568.49,12641.87,12496.48,12573.85,2510110000,12573.85 2007-04-09,12562.64,12641.22,12505.83,12569.14,2349410000,12569.14 2007-04-05,12505.73,12573.02,12501.25,12560.83,2357230000,12560.83 2007-04-04,12511.36,12591.81,12444.55,12530.05,2616320000,12530.05 2007-04-03,12431.28,12534.49,12378.94,12510.93,2921760000,12510.93 2007-04-02,12354.52,12450.81,12284.54,12382.30,2875880000,12382.30 2007-03-30,12348.91,12442.40,12237.87,12354.35,2903960000,12354.35 2007-03-29,12301.48,12424.77,12251.89,12348.75,2854710000,12348.75 2007-03-28,12396.49,12415.56,12234.50,12300.36,3000440000,12300.36 2007-03-27,12468.59,12484.54,12336.89,12397.29,2673040000,12397.29 2007-03-26,12480.37,12526.27,12339.53,12469.07,2754660000,12469.07 2007-03-23,12460.50,12550.07,12396.89,12481.01,2619020000,12481.01 2007-03-22,12446.72,12524.03,12364.21,12461.14,3129970000,12461.14 2007-03-21,12288.98,12489.02,12220.49,12447.52,3184770000,12447.52 2007-03-20,12226.81,12324.31,12172.66,12288.10,2795940000,12288.10 2007-03-19,12110.41,12273.52,12110.41,12226.17,2777180000,12226.17 2007-03-16,12160.16,12226.01,12053.05,12110.41,3393640000,12110.41 2007-03-15,12133.16,12228.42,12060.10,12159.68,2821900000,12159.68 2007-03-14,12074.52,12187.88,11926.79,12133.40,3758350000,12133.40 2007-03-13,12307.49,12319.66,12049.85,12075.96,3485570000,12075.96 2007-03-12,12275.68,12385.44,12205.58,12318.62,2664000000,12318.62 2007-03-09,12262.06,12379.51,12200.62,12276.32,2623050000,12276.32 2007-03-08,12193.33,12355.47,12183.79,12260.70,3014850000,12260.70 2007-03-07,12204.46,12315.18,12122.11,12192.45,3141350000,12192.45 2007-03-06,12051.17,12252.61,12051.17,12207.59,3358160000,12207.59 2007-03-05,12111.61,12220.16,11973.58,12050.41,3480520000,12050.41 2007-03-02,12233.78,12293.15,12064.91,12114.10,3312260000,12114.10 2007-03-01,12265.59,12338.89,11996.17,12234.34,3874910000,12234.34 2007-02-28,12214.92,12396.81,12122.03,12268.63,3925250000,12268.63 2007-02-27,12628.90,12628.90,12078.85,12216.24,4065230000,12216.24 2007-02-26,12647.88,12746.34,12562.72,12632.26,2822170000,12632.26 2007-02-23,12679.89,12726.79,12578.51,12647.48,2579950000,12647.48 2007-02-22,12735.77,12792.97,12621.93,12686.02,1950770000,12686.02 2007-02-21,12782.87,12813.88,12662.79,12738.41,2606980000,12738.41 2007-02-20,12766.85,12845.76,12675.04,12786.64,2337860000,12786.64 2007-02-16,12764.13,12829.42,12685.86,12767.57,2399450000,12767.57 2007-02-15,12741.70,12828.38,12681.85,12765.01,2490920000,12765.01 2007-02-14,12651.29,12793.29,12623.21,12741.86,2699290000,12741.86 2007-02-13,12549.19,12702.36,12549.19,12654.85,2652150000,12654.85 2007-02-12,12595.90,12605.11,12536.77,12552.55,2395680000,12552.55 2007-02-09,12638.03,12725.59,12518.58,12580.83,2951810000,12580.83 2007-02-08,12639.16,12666.88,12576.59,12637.63,2816180000,12637.63 2007-02-07,12656.86,12748.99,12589.56,12666.87,2618820000,12666.87 2007-02-06,12661.66,12738.41,12586.44,12666.31,2608710000,12666.31 2007-02-05,12641.08,12681.06,12630.50,12661.74,2439430000,12661.74 2007-02-02,12673.84,12740.65,12582.99,12653.49,2569450000,12653.49 2007-02-01,12617.20,12741.30,12563.85,12673.68,2914890000,12673.68 2007-01-31,12520.03,12685.54,12461.30,12621.69,2976690000,12621.69 2007-01-30,12484.70,12538.06,12463.07,12523.31,2706250000,12523.31 2007-01-29,12487.10,12599.74,12422.93,12490.78,2730480000,12490.78 2007-01-26,12503.28,12582.67,12391.44,12487.02,2626620000,12487.02 2007-01-25,12621.77,12670.48,12461.54,12502.56,2994330000,12502.56 2007-01-24,12534.37,12659.42,12489.98,12621.77,2783180000,12621.77 2007-01-23,12467.96,12553.44,12467.96,12533.80,2975070000,12533.80 2007-01-22,12566.33,12619.04,12389.68,12477.16,2540120000,12477.16 2007-01-19,12567.93,12649.89,12462.50,12565.53,2777480000,12565.53 2007-01-18,12575.06,12674.16,12487.90,12567.93,2822430000,12567.93 2007-01-17,12563.53,12613.28,12550.95,12577.15,2690270000,12577.15 2007-01-16,12555.84,12638.27,12489.90,12582.59,2599530000,12582.59 2007-01-12,12514.66,12616.08,12432.30,12556.08,2686480000,12556.08 2007-01-11,12442.96,12586.12,12413.72,12514.98,2857870000,12514.98 2007-01-10,12417.00,12487.18,12313.01,12442.16,2764660000,12442.16 2007-01-09,12424.77,12516.66,12337.85,12416.60,3038380000,12416.60 2007-01-08,12393.93,12445.37,12337.53,12423.49,2763340000,12423.49 2007-01-05,12480.05,12504.40,12326.79,12398.01,2919400000,12398.01 2007-01-04,12467.32,12510.26,12405.47,12480.69,3004460000,12480.69 2007-01-03,12459.54,12630.34,12373.82,12474.52,3429160000,12474.52 2006-12-29,12500.48,12560.16,12423.81,12463.15,1678200000,12463.15 2006-12-28,12510.57,12566.17,12440.23,12501.52,1508570000,12501.52 2006-12-27,12463.46,12518.34,12407.62,12510.57,1667370000,12510.57 2006-12-26,12341.94,12439.19,12301.40,12407.63,1310310000,12407.63 2006-12-22,12407.87,12417.96,12341.77,12343.21,1647590000,12343.21 2006-12-21,12461.62,12526.59,12369.97,12421.25,2322410000,12421.25 2006-12-20,12471.32,12549.35,12393.45,12463.87,2387630000,12463.87 2006-12-19,12439.51,12517.78,12348.50,12471.32,2717060000,12471.32 2006-12-18,12446.24,12545.74,12372.30,12441.27,2568140000,12441.27 2006-12-15,12417.96,12536.37,12377.35,12445.52,3229580000,12445.52 2006-12-14,12317.50,12472.76,12271.44,12416.76,2729700000,12416.76 2006-12-13,12312.71,12411.55,12263.19,12317.50,2552260000,12317.50 2006-12-12,12328.24,12396.01,12222.65,12315.58,2738170000,12315.58 2006-12-11,12306.21,12399.54,12245.32,12328.48,2289900000,12328.48 2006-12-08,12256.21,12332.16,12243.31,12307.48,2440460000,12307.48 2006-12-07,12310.13,12396.33,12233.06,12278.41,2743150000,12278.41 2006-12-06,12328.72,12390.88,12239.95,12309.25,2725280000,12309.25 2006-12-05,12283.69,12398.57,12218.24,12331.60,2755700000,12331.60 2006-12-04,12195.57,12349.87,12149.27,12283.85,2766320000,12283.85 2006-12-01,12220.97,12289.30,12070.52,12194.13,2800980000,12194.13 2006-11-30,12226.73,12317.10,12118.42,12221.93,4006230000,12221.93 2006-11-29,12134.40,12283.05,12119.70,12226.73,2790970000,12226.73 2006-11-28,12095.27,12148.78,12073.40,12136.44,2639750000,12136.44 2006-11-27,12279.13,12303.32,12079.01,12121.71,2711210000,12121.71 2006-11-24,12321.71,12340.89,12219.28,12280.17,832550000,12280.17 2006-11-22,12321.91,12403.54,12238.43,12326.95,2237710000,12326.95 2006-11-21,12312.13,12409.31,12233.94,12321.59,2597940000,12321.59 2006-11-20,12340.71,12400.10,12257.34,12316.54,2546710000,12316.54 2006-11-17,12293.49,12342.55,12278.20,12342.55,2726100000,12342.55 2006-11-16,12250.05,12375.37,12204.00,12305.82,2835730000,12305.82 2006-11-15,12214.37,12326.07,12156.37,12251.71,2831130000,12251.71 2006-11-14,12132.44,12261.15,12051.68,12218.01,3027480000,12218.01 2006-11-13,12084.89,12164.22,12084.89,12131.88,2386340000,12131.88 2006-11-10,12102.74,12173.08,12074.01,12108.43,2290200000,12108.43 2006-11-09,12174.70,12236.10,12039.59,12103.30,3012050000,12103.30 2006-11-08,12147.38,12233.54,12051.60,12176.54,2814820000,12176.54 2006-11-07,12104.75,12239.94,12065.20,12156.77,2636390000,12156.77 2006-11-06,11985.16,12146.45,11973.23,12105.55,2533550000,12105.55 2006-11-03,12018.30,12095.30,11928.97,11986.04,2419730000,11986.04 2006-11-02,12023.98,12070.25,11938.89,12018.54,2646180000,12018.54 2006-11-01,12080.25,12160.70,11972.99,12031.02,2821160000,12031.02 2006-10-31,12086.18,12160.46,11986.84,12080.73,2803030000,12080.73 2006-10-30,12074.01,12117.07,12050.23,12086.49,2770440000,12086.49 2006-10-27,12164.78,12202.72,12024.78,12090.26,2458450000,12090.26 2006-10-26,12134.84,12236.10,12037.99,12163.66,2793350000,12163.66 2006-10-25,12127.24,12212.16,12017.66,12134.68,2953540000,12134.68 2006-10-24,12116.51,12204.80,12028.14,12127.88,2876890000,12127.88 2006-10-23,12001.33,12177.35,11940.41,12116.91,2480430000,12116.91 2006-10-20,12013.01,12087.38,11881.34,12002.37,2526410000,12002.37 2006-10-19,11988.92,12082.33,11911.44,12011.73,2619830000,12011.73 2006-10-18,11947.62,12108.91,11900.79,11992.68,2658840000,11992.68 2006-10-17,11977.40,12024.54,11849.16,11950.02,2519620000,11950.02 2006-10-16,11957.70,11996.92,11945.70,11980.59,2305920000,11980.59 2006-10-13,11947.22,12009.97,11862.29,11960.51,2482920000,11960.51 2006-10-12,11896.63,11959.14,11852.12,11947.70,2514350000,11947.70 2006-10-11,11865.49,11907.60,11762.72,11852.13,2521000000,11852.13 2006-10-10,11857.73,11930.33,11778.09,11867.17,2376140000,11867.17 2006-10-09,11849.56,11923.53,11759.36,11857.81,1935170000,11857.81 2006-10-06,11865.49,11921.04,11743.35,11850.21,2523000000,11850.21 2006-10-05,11832.51,11869.33,11821.55,11866.69,2817240000,11866.69 2006-10-04,11722.94,11879.18,11654.02,11850.61,3019880000,11850.61 2006-10-03,11670.11,11794.41,11608.23,11727.34,2682690000,11727.34 2006-10-02,11678.99,11773.60,11608.79,11670.35,2154480000,11670.35 2006-09-29,11718.05,11782.49,11642.17,11679.07,2273430000,11679.07 2006-09-28,11689.40,11775.36,11625.92,11718.45,2397820000,11718.45 2006-09-27,11670.19,11775.60,11595.75,11689.24,2749190000,11689.24 2006-09-26,11575.73,11723.74,11517.54,11669.39,2673350000,11669.39 2006-09-25,11536.67,11616.23,11486.00,11575.81,2710240000,11575.81 2006-09-22,11532.91,11588.62,11423.57,11508.10,2162880000,11508.10 2006-09-21,11611.67,11677.39,11471.76,11533.23,2627440000,11533.23 2006-09-20,11542.28,11680.19,11514.50,11613.19,2543070000,11613.19 2006-09-19,11554.60,11605.67,11450.30,11540.91,2390850000,11540.91 2006-09-18,11538.35,11588.22,11528.43,11555.00,2325080000,11555.00 2006-09-15,11528.75,11661.38,11504.57,11560.77,3198030000,11560.77 2006-09-14,11508.82,11548.84,11495.77,11527.39,2351220000,11527.39 2006-09-13,11487.69,11605.59,11423.73,11543.32,2597220000,11543.32 2006-09-12,11412.52,11512.74,11396.83,11498.09,2791580000,11498.09 2006-09-11,11389.87,11468.88,11295.90,11396.84,2506430000,11396.84 2006-09-08,11332.24,11448.30,11295.18,11392.11,2132890000,11392.11 2006-09-07,11405.16,11443.66,11273.89,11331.44,2325850000,11331.44 2006-09-06,11421.33,11469.27,11395.15,11406.20,2329870000,11406.20 2006-09-05,11461.83,11533.87,11385.95,11469.28,2114480000,11469.28 2006-09-01,11427.41,11476.40,11381.14,11464.15,1800520000,11464.15 2006-08-31,11383.47,11451.03,11326.80,11381.15,1974540000,11381.15 2006-08-30,11365.98,11452.95,11309.99,11382.91,2060690000,11382.91 2006-08-29,11352.65,11432.38,11255.88,11369.94,2093720000,11369.94 2006-08-28,11285.33,11411.24,11240.91,11352.01,1834920000,11352.01 2006-08-25,11301.22,11350.09,11218.66,11284.05,1667580000,11284.05 2006-08-24,11297.82,11386.59,11232.83,11304.46,1930320000,11304.46 2006-08-23,11337.12,11394.75,11238.67,11297.90,1893670000,11297.90 2006-08-22,11344.41,11426.13,11279.25,11339.84,1908740000,11339.84 2006-08-21,11353.29,11381.46,11322.31,11345.04,1759240000,11345.04 2006-08-18,11333.76,11437.66,11273.49,11381.47,2033910000,11381.47 2006-08-17,11321.19,11372.34,11298.54,11334.96,2458340000,11334.96 2006-08-16,11224.91,11373.78,11207.85,11327.12,2554570000,11327.12 2006-08-15,11098.03,11271.25,11098.03,11230.26,2334100000,11230.26 2006-08-14,11089.07,11242.83,11049.68,11097.87,2118020000,11097.87 2006-08-11,11103.55,11121.40,11042.88,11088.02,2004540000,11088.02 2006-08-10,11073.14,11176.47,10998.06,11124.37,2402190000,11124.37 2006-08-09,11168.47,11296.22,11044.64,11076.18,2555180000,11076.18 2006-08-08,11218.18,11319.51,11117.80,11173.59,2457840000,11173.59 2006-08-07,11239.47,11294.14,11143.02,11219.38,2045660000,11219.38 2006-08-04,11244.59,11367.94,11165.11,11240.35,2530970000,11240.35 2006-08-03,11195.28,11304.78,11101.55,11242.59,2728440000,11242.59 2006-08-02,11167.91,11228.98,11124.52,11199.92,2610750000,11199.92 2006-08-01,11184.80,11210.65,11035.92,11125.73,2527690000,11125.73 2006-07-31,11218.90,11265.80,11115.24,11185.68,2461300000,11185.68 2006-07-28,11102.11,11282.05,11102.11,11219.70,2480420000,11219.70 2006-07-27,11104.19,11245.47,11040.80,11100.43,2776710000,11100.43 2006-07-26,11102.91,11208.09,10987.41,11102.51,2667710000,11102.51 2006-07-25,11037.59,11133.73,11000.05,11103.71,2563930000,11103.71 2006-07-24,10868.70,11096.35,10868.70,11051.05,2312720000,11051.05 2006-07-21,10937.94,10995.73,10778.58,10868.38,2704090000,10868.38 2006-07-20,11007.26,11098.75,10884.47,10928.10,2345580000,10928.10 2006-07-19,10854.22,11038.16,10796.74,11011.42,2701980000,11011.42 2006-07-18,10745.84,10867.02,10658.35,10799.23,2481750000,10799.23 2006-07-17,10739.35,10858.22,10668.35,10747.36,2146410000,10747.36 2006-07-14,10846.53,10892.64,10664.43,10739.35,2467120000,10739.35 2006-07-13,11012.62,11015.19,10790.82,10846.29,2545760000,10846.29 2006-07-12,11133.97,11181.12,10973.37,11013.18,2250450000,11013.18 2006-07-11,11102.59,11186.32,10987.33,11134.77,2310850000,11134.77 2006-07-10,11130.53,11174.47,11090.10,11103.55,1854590000,11103.55 2006-07-07,11224.18,11227.62,11040.32,11090.67,1988150000,11090.67 2006-07-06,11147.12,11301.58,11117.16,11225.30,2009160000,11225.30 2006-07-05,11225.06,11239.47,11083.94,11151.82,2165070000,11151.82 2006-07-03,11149.34,11277.09,11146.06,11228.02,1114470000,11228.02 2006-06-30,11190.80,11288.86,11100.11,11150.22,3049560000,11150.22 2006-06-29,10974.36,11225.06,10974.36,11190.80,2621250000,11190.80 2006-06-28,10925.30,11026.07,10869.02,10973.56,2085490000,10973.56 2006-06-27,11048.24,11064.09,10920.73,10924.74,2203130000,10924.74 2006-06-26,10990.29,11089.07,10937.06,11045.28,1878580000,11045.28 2006-06-23,11019.19,11098.67,10932.82,10989.09,2017270000,10989.09 2006-06-22,11077.78,11127.73,10954.83,11019.11,2148180000,11019.11 2006-06-21,10975.24,11165.91,10952.43,11079.46,2361230000,11079.46 2006-06-20,10942.03,11066.73,10895.28,10974.84,2232950000,10974.84 2006-06-19,11014.87,11098.99,10886.63,10942.11,2517200000,10942.11 2006-06-16,11009.10,11045.04,10984.29,11014.54,2783390000,11014.54 2006-06-15,10817.48,11049.85,10788.34,11015.19,2775480000,11015.19 2006-06-14,10713.10,10816.99,10699.25,10816.91,2667990000,10816.91 2006-06-13,10783.14,10893.04,10653.23,10706.14,3215770000,10706.14 2006-06-12,10892.00,10969.32,10767.61,10792.58,2247010000,10792.58 2006-06-09,10939.14,11015.67,10842.89,10891.92,2214000000,10891.92 2006-06-08,10929.70,11032.15,10726.15,10938.82,3543790000,10938.82 2006-06-07,11002.06,11107.48,10897.76,10930.90,2644170000,10930.90 2006-06-06,11048.24,11140.45,10890.24,11002.14,2697650000,11002.14 2006-06-05,11247.55,11259.96,11025.75,11048.72,2313470000,11048.72 2006-06-02,11260.52,11329.28,11158.06,11247.87,2295540000,11247.87 2006-06-01,11169.03,11290.86,11115.40,11260.28,2360160000,11260.28 2006-05-31,11091.15,11225.78,11050.40,11168.31,2692160000,11168.31 2006-05-30,11277.25,11277.25,11071.70,11094.43,2176190000,11094.43 2006-05-26,11211.69,11329.36,11177.43,11278.61,1814020000,11278.61 2006-05-25,11114.96,11258.12,11089.55,11211.05,2372730000,11211.05 2006-05-24,11100.11,11241.15,10980.29,11117.32,2999030000,11117.32 2006-05-23,11126.29,11254.68,11068.49,11098.35,2605250000,11098.35 2006-05-22,11092.90,11175.03,11040.16,11125.32,2773010000,11125.32 2006-05-19,11124.37,11254.60,11009.98,11144.06,2982300000,11144.06 2006-05-18,11206.17,11301.26,11096.35,11128.29,2537490000,11128.29 2006-05-17,11410.13,11412.28,11139.17,11205.61,2830200000,11205.61 2006-05-16,11428.21,11520.42,11334.64,11419.89,2386210000,11419.89 2006-05-15,11380.43,11485.61,11273.65,11428.77,2505660000,11428.77 2006-05-12,11500.01,11551.40,11336.96,11380.99,2567970000,11380.99 2006-05-11,11639.29,11660.58,11449.74,11500.73,2531520000,11500.73 2006-05-10,11630.48,11709.09,11545.64,11642.65,2268550000,11642.65 2006-05-09,11584.62,11684.28,11535.71,11639.77,2157290000,11639.77 2006-05-08,11576.37,11665.14,11504.09,11584.54,2151300000,11584.54 2006-05-05,11440.62,11616.16,11440.62,11577.74,2294760000,11577.74 2006-05-04,11401.80,11512.18,11366.82,11438.86,2431450000,11438.86 2006-05-03,11414.69,11472.96,11308.55,11400.28,2395230000,11400.28 2006-05-02,11372.74,11427.43,11343.28,11416.44,2403470000,11416.44 2006-05-01,11367.78,11476.96,11304.30,11343.29,2437040000,11343.29 2006-04-28,11358.33,11462.95,11278.13,11367.14,2419920000,11367.14 2006-04-27,11349.53,11465.75,11220.74,11382.51,2772010000,11382.51 2006-04-26,11283.25,11428.77,11256.12,11354.49,2502690000,11354.49 2006-04-25,11336.56,11401.32,11213.05,11283.25,2366380000,11283.25 2006-04-24,11346.81,11420.05,11246.35,11336.32,2117330000,11336.32 2006-04-21,11343.45,11468.16,11272.61,11347.45,2392630000,11347.45 2006-04-20,11278.53,11429.25,11221.30,11342.89,2512920000,11342.89 2006-04-19,11265.40,11379.79,11181.84,11278.77,2447310000,11278.77 2006-04-18,11074.58,11302.30,11064.01,11268.77,2595440000,11268.77 2006-04-17,11137.33,11203.13,11017.43,11073.78,1794650000,11073.78 2006-04-13,11130.13,11210.73,11053.29,11137.65,1891940000,11137.65 2006-04-12,11089.47,11194.00,11052.17,11129.97,1938100000,11129.97 2006-04-11,11141.33,11220.98,11017.99,11089.63,2232880000,11089.63 2006-04-10,11119.88,11211.37,11083.06,11141.33,1898320000,11141.33 2006-04-07,11228.10,11268.92,11108.75,11120.04,2082470000,11120.04 2006-04-06,11233.01,11294.30,11137.57,11216.50,2281680000,11216.50 2006-04-05,11203.21,11290.30,11141.82,11239.55,2420020000,11239.55 2006-04-04,11142.54,11269.17,11094.03,11203.85,2147660000,11203.85 2006-04-03,11113.00,11287.02,11101.07,11144.94,2494080000,11144.94 2006-03-31,11151.34,11229.47,11069.78,11109.32,2236710000,11109.32 2006-03-30,11195.36,11259.08,11118.12,11150.70,2294560000,11150.70 2006-03-29,11154.94,11283.97,11117.48,11215.70,2143540000,11215.70 2006-03-28,11250.11,11312.31,11132.05,11154.54,2148580000,11154.54 2006-03-27,11280.13,11314.96,11194.07,11250.11,2029700000,11250.11 2006-03-24,11270.61,11353.21,11197.21,11279.97,2326070000,11279.97 2006-03-23,11317.35,11363.46,11207.85,11270.29,1980940000,11270.29 2006-03-22,11234.51,11358.01,11200.22,11317.43,2039810000,11317.43 2006-03-21,11275.89,11364.34,11188.56,11235.47,2147370000,11235.47 2006-03-20,11278.93,11350.73,11208.33,11274.53,1976830000,11274.53 2006-03-17,11294.94,11294.94,11253.23,11279.65,2549620000,11279.65 2006-03-16,11210.97,11324.80,11176.07,11253.24,2292180000,11253.24 2006-03-15,11149.76,11258.28,11097.23,11209.77,2293000000,11209.77 2006-03-14,11076.02,11190.96,11030.23,11151.34,2165270000,11151.34 2006-03-13,11067.61,11157.82,11019.75,11076.02,2070330000,11076.02 2006-03-10,10972.92,11125.41,10948.43,11076.34,2123450000,11076.34 2006-03-09,11005.66,11093.39,10923.86,10972.28,2140110000,10972.28 2006-03-08,10977.08,11065.61,10885.99,11005.74,2442870000,11005.74 2006-03-07,10957.31,11032.31,10885.35,10980.69,2268050000,10980.69 2006-03-06,11022.47,11084.66,10899.76,10958.59,2280190000,10958.59 2006-03-03,11024.23,11125.01,10942.99,11021.59,2152950000,11021.59 2006-03-02,11052.57,11090.91,10951.71,11025.51,2494590000,11025.51 2006-03-01,10993.25,11115.80,10960.60,11053.53,2308320000,11053.53 2006-02-28,11096.75,11115.24,10947.07,10993.41,2370860000,10993.41 2006-02-27,11062.81,11180.48,11038.72,11097.55,1975320000,11097.55 2006-02-24,11068.33,11085.38,11010.46,11061.85,1933010000,11061.85 2006-02-23,11133.52,11167.83,11017.27,11069.22,2144210000,11069.22 2006-02-22,11086.98,11159.02,11064.25,11137.17,2222380000,11137.17 2006-02-21,11115.48,11182.68,11011.18,11069.06,2104320000,11069.06 2006-02-17,11119.56,11178.80,11035.44,11115.32,2128260000,11115.32 2006-02-16,11059.05,11154.14,10997.66,11120.68,2251490000,11120.68 2006-02-15,11025.67,11115.56,10940.18,11058.97,2317590000,11058.97 2006-02-14,10890.72,11071.54,10873.62,11028.39,2437940000,11028.39 2006-02-13,10915.21,10982.93,10824.60,10892.32,1850080000,10892.32 2006-02-10,10883.51,10972.76,10787.62,10919.05,2290050000,10919.05 2006-02-09,10859.42,11003.50,10800.91,10883.35,2441920000,10883.35 2006-02-08,10742.16,10897.44,10712.30,10858.62,2456860000,10858.62 2006-02-07,10796.42,10874.79,10691.97,10749.76,2366370000,10749.76 2006-02-06,10793.30,10868.62,10725.91,10798.27,2132360000,10798.27 2006-02-03,10849.57,10905.28,10725.35,10793.62,2282210000,10793.62 2006-02-02,10950.11,10987.73,10800.35,10851.98,2565300000,10851.98 2006-02-01,10862.14,11001.82,10815.39,10953.95,2589410000,10953.95 2006-01-31,10900.40,10970.28,10807.55,10864.86,2708310000,10864.86 2006-01-30,10913.13,10930.34,10887.67,10899.92,2282730000,10899.92 2006-01-27,10815.32,10988.29,10766.01,10907.21,2623620000,10907.21 2006-01-26,10768.17,10827.96,10709.73,10809.47,2856780000,10809.47 2006-01-25,10713.26,10832.93,10615.20,10709.74,2617060000,10709.74 2006-01-24,10690.21,10804.75,10624.49,10712.22,2608720000,10712.22 2006-01-23,10668.75,10783.70,10607.36,10688.77,2256070000,10688.77 2006-01-20,10880.71,10890.08,10637.21,10667.39,2845810000,10667.39 2006-01-19,10855.18,10965.00,10796.66,10880.71,2444020000,10880.71 2006-01-18,10890.08,10934.90,10778.33,10854.86,2233200000,10854.86 2006-01-17,10957.55,10977.01,10841.17,10896.32,2179970000,10896.32 2006-01-13,10961.48,11033.04,10888.88,10959.87,2206510000,10959.87 2006-01-12,11043.12,11070.10,10918.09,10962.36,2318350000,10962.36 2006-01-11,11011.66,11099.15,10939.86,11043.44,2406130000,11043.44 2006-01-10,11010.46,11054.49,10902.96,11011.58,2373080000,11011.58 2006-01-09,10959.47,11053.93,10906.33,11011.90,2301490000,11011.90 2006-01-06,10875.45,11005.98,10846.21,10959.31,2446560000,10959.31 2006-01-05,10880.39,10951.39,10797.55,10882.15,2433340000,10882.15 2006-01-04,10843.97,10946.27,10772.89,10880.15,2515330000,10880.15 2006-01-03,10718.30,10888.40,10650.18,10847.41,2554570000,10847.41 2005-12-30,10783.86,10801.87,10675.64,10717.50,1443500000,10717.50 2005-12-29,10795.70,10870.71,10747.76,10784.82,1382540000,10784.82 2005-12-28,10778.25,10858.07,10750.40,10796.26,1422360000,10796.26 2005-12-27,10883.75,10956.99,10754.16,10777.77,1540470000,10777.77 2005-12-23,10901.68,10904.40,10869.98,10883.27,1285810000,10883.27 2005-12-22,10831.56,10928.34,10785.93,10889.44,1888500000,10889.44 2005-12-21,10805.63,10933.70,10776.01,10833.73,2065170000,10833.73 2005-12-20,10836.93,10905.28,10754.56,10805.55,1996690000,10805.55 2005-12-19,10875.51,10970.04,10781.70,10836.53,2208810000,10836.53 2005-12-16,10881.67,10978.21,10830.84,10875.59,2584190000,10875.59 2005-12-15,10883.43,10985.01,10803.55,10881.67,2180590000,10881.67 2005-12-14,10821.32,10953.07,10786.34,10883.51,2145520000,10883.51 2005-12-13,10765.69,10902.64,10694.29,10823.72,2390020000,10823.72 2005-12-12,10778.66,10857.02,10707.18,10767.77,1876550000,10767.77 2005-12-09,10751.76,10845.33,10694.05,10778.58,1896290000,10778.58 2005-12-08,10808.43,10871.11,10705.17,10755.12,2178300000,10755.12 2005-12-07,10856.86,10916.89,10737.27,10810.91,2093830000,10810.91 2005-12-06,10835.41,10956.13,10809.15,10856.86,2110740000,10856.86 2005-12-05,10876.95,10923.37,10766.57,10835.01,2325840000,10835.01 2005-12-02,10912.01,10952.83,10818.36,10877.51,2125580000,10877.51 2005-12-01,10806.03,10969.97,10806.03,10912.57,2614830000,10912.57 2005-11-30,10883.91,10959.80,10789.38,10805.87,2374690000,10805.87 2005-11-29,10888.48,10994.85,10850.29,10888.16,2268340000,10888.16 2005-11-28,10932.74,10992.39,10839.37,10890.72,2016900000,10890.72 2005-11-25,10915.13,10997.50,10883.55,10931.62,724940000,10931.62 2005-11-23,10865.90,10950.59,10855.42,10916.09,1985400000,10916.09 2005-11-22,10815.96,10907.77,10729.99,10871.43,2291420000,10871.43 2005-11-21,10766.33,10871.11,10708.86,10820.28,2117350000,10820.28 2005-11-18,10719.34,10865.58,10663.79,10766.33,2453290000,10766.33 2005-11-17,10677.00,10778.50,10619.61,10720.22,2298040000,10720.22 2005-11-16,10697.81,10710.78,10653.14,10674.76,2121580000,10674.76 2005-11-15,10697.01,10783.62,10610.08,10686.44,2359370000,10686.44 2005-11-14,10686.60,10756.88,10618.89,10697.17,1899780000,10697.17 2005-11-11,10641.30,10725.99,10595.89,10686.04,1773140000,10686.04 2005-11-10,10550.61,10655.22,10519.71,10640.10,2378460000,10640.10 2005-11-09,10539.24,10637.78,10466.24,10546.21,2214460000,10546.21 2005-11-08,10574.18,10606.80,10478.49,10539.72,1965050000,10539.72 2005-11-07,10531.24,10632.34,10488.74,10586.23,1987580000,10586.23 2005-11-04,10523.23,10593.51,10441.59,10530.76,2050510000,10530.76 2005-11-03,10470.49,10613.84,10421.98,10522.59,2716630000,10522.59 2005-11-02,10406.29,10527.32,10347.70,10472.73,2648090000,10472.73 2005-11-01,10437.51,10510.03,10352.42,10406.77,2457850000,10406.77 2005-10-31,10403.17,10539.16,10372.67,10440.07,2567470000,10440.07 2005-10-28,10231.15,10433.51,10213.14,10402.77,2379400000,10402.77 2005-10-27,10334.81,10348.66,10229.95,10229.95,2395370000,10229.95 2005-10-26,10377.39,10474.18,10283.10,10344.98,2467750000,10344.98 2005-10-25,10383.88,10457.52,10282.78,10377.87,2312470000,10377.87 2005-10-24,10219.15,10411.57,10219.15,10385.00,2197790000,10385.00 2005-10-21,10282.22,10354.02,10161.60,10215.22,2470920000,10215.22 2005-10-20,10411.73,10483.21,10230.27,10281.10,2617250000,10281.10 2005-10-19,10277.18,10444.15,10173.52,10414.13,2703590000,10414.13 2005-10-18,10349.14,10412.85,10233.47,10285.26,2197010000,10285.26 2005-10-17,10287.42,10419.58,10213.06,10348.10,2054570000,10348.10 2005-10-14,10216.59,10327.21,10165.12,10287.34,2188940000,10287.34 2005-10-13,10216.91,10309.20,10098.18,10216.59,2351150000,10216.59 2005-10-12,10247.40,10308.23,10186.17,10216.90,2491280000,10216.90 2005-10-11,10239.16,10361.15,10195.13,10253.17,2299040000,10253.17 2005-10-10,10292.95,10378.19,10184.09,10238.76,2195990000,10238.76 2005-10-07,10287.42,10387.48,10221.47,10292.31,2126080000,10292.31 2005-10-06,10317.36,10425.98,10200.81,10287.10,2792030000,10287.10 2005-10-05,10434.81,10477.21,10299.27,10317.36,2546780000,10317.36 2005-10-04,10534.36,10618.41,10409.89,10441.11,2341420000,10441.11 2005-10-03,10569.50,10637.00,10486.17,10535.48,2097490000,10535.48 2005-09-30,10540.51,10569.81,10526.34,10568.70,2097520000,10568.70 2005-09-29,10472.61,10583.43,10389.01,10552.78,2176120000,10552.78 2005-09-28,10456.61,10560.02,10390.05,10473.08,2106980000,10473.08 2005-09-27,10444.58,10534.31,10376.83,10456.21,1976270000,10456.21 2005-09-26,10420.22,10544.98,10381.53,10443.63,2022220000,10443.63 2005-09-23,10421.81,10494.42,10328.59,10419.59,1973020000,10419.59 2005-09-22,10376.20,10489.64,10303.51,10422.05,2424720000,10422.05 2005-09-21,10484.23,10512.02,10335.28,10378.03,2548150000,10378.03 2005-09-20,10558.19,10642.26,10453.98,10481.52,2319250000,10481.52 2005-09-19,10641.87,10656.75,10497.29,10557.63,2076540000,10557.63 2005-09-16,10560.50,10696.24,10539.64,10641.94,3152470000,10641.94 2005-09-15,10545.85,10627.85,10488.05,10558.75,2079340000,10558.75 2005-09-14,10545.85,10627.85,10488.05,10558.75,1986750000,10558.75 2005-09-13,10673.71,10701.57,10561.61,10597.44,2082360000,10597.44 2005-09-12,10678.41,10743.77,10618.13,10682.94,1938050000,10682.94 2005-09-09,10594.10,10727.53,10573.47,10678.56,1992560000,10678.56 2005-09-08,10633.11,10670.60,10530.01,10595.93,1955380000,10595.93 2005-09-07,10588.68,10667.10,10534.23,10633.50,2067700000,10633.50 2005-09-06,10447.69,10621.96,10447.69,10589.24,1932090000,10589.24 2005-09-02,10460.67,10536.14,10400.88,10447.37,1640160000,10447.37 2005-09-01,10481.44,10557.47,10382.09,10459.63,2229860000,10459.63 2005-08-31,10415.84,10484.55,10357.65,10481.60,2365510000,10481.60 2005-08-30,10461.54,10476.83,10329.15,10412.82,1916470000,10412.82 2005-08-29,10396.90,10508.35,10321.42,10463.05,1599450000,10463.05 2005-08-26,10450.95,10480.01,10355.02,10397.29,1541090000,10397.29 2005-08-25,10434.39,10506.60,10391.71,10450.63,1571110000,10450.63 2005-08-24,10519.34,10584.30,10407.56,10434.87,1930800000,10434.87 2005-08-23,10571.01,10604.29,10475.63,10519.58,1678620000,10519.58 2005-08-22,10559.78,10669.81,10509.07,10569.89,1621330000,10569.89 2005-08-19,10552.70,10656.59,10503.90,10559.23,1558790000,10559.23 2005-08-18,10531.12,10592.34,10517.67,10554.92,1808170000,10554.92 2005-08-17,10505.60,10625.86,10472.45,10550.71,1859150000,10550.71 2005-08-16,10631.59,10650.14,10489.24,10513.45,1820410000,10513.45 2005-08-15,10599.19,10687.72,10532.48,10634.38,1562880000,10634.38 2005-08-12,10682.70,10688.68,10549.19,10600.30,1709300000,10600.30 2005-08-11,10591.83,10721.56,10549.43,10685.89,1941560000,10685.89 2005-08-10,10606.52,10746.87,10553.81,10594.41,2172320000,10594.41 2005-08-09,10537.65,10662.80,10537.01,10615.67,1897520000,10615.67 2005-08-08,10557.24,10635.65,10497.45,10536.93,1804140000,10536.93 2005-08-05,10610.34,10643.46,10512.49,10558.03,1930280000,10558.03 2005-08-04,10696.80,10709.77,10568.70,10610.10,1981220000,10610.10 2005-08-03,10681.51,10735.17,10600.02,10697.59,1999980000,10697.59 2005-08-02,10623.79,10729.60,10600.62,10683.74,2043120000,10683.74 2005-08-01,10641.78,10713.51,10578.97,10623.15,1716870000,10623.15 2005-07-29,10705.16,10754.60,10608.27,10640.91,1789600000,10640.91 2005-07-28,10633.50,10745.68,10603.49,10705.55,2001680000,10705.55 2005-07-27,10579.45,10689.31,10530.50,10637.09,1945800000,10637.09 2005-07-26,10597.60,10667.90,10535.58,10579.77,1934180000,10579.77 2005-07-25,10651.66,10709.69,10565.12,10596.48,1717580000,10596.48 2005-07-22,10624.19,10702.21,10552.54,10651.18,1766990000,10651.18 2005-07-21,10690.03,10735.33,10567.98,10627.77,2129840000,10627.77 2005-07-20,10629.52,10726.81,10535.10,10689.15,2063340000,10689.15 2005-07-19,10576.90,10718.69,10573.00,10646.56,2041280000,10646.56 2005-07-18,10640.19,10681.99,10533.59,10574.99,1582100000,10574.99 2005-07-15,10629.44,10698.07,10559.46,10640.83,1716400000,10640.83 2005-07-14,10559.86,10696.96,10559.86,10628.88,2048710000,10628.88 2005-07-13,10513.36,10596.98,10481.36,10557.39,1812500000,10557.39 2005-07-12,10519.49,10583.02,10444.46,10513.89,1932010000,10513.89 2005-07-11,10449.60,10570.67,10425.97,10519.72,1846300000,10519.72 2005-07-08,10302.90,10486.50,10279.65,10449.14,1900810000,10449.14 2005-07-07,10269.76,10337.84,10142.24,10302.29,1952440000,10302.29 2005-07-06,10366.52,10413.23,10242.21,10270.68,1883470000,10270.68 2005-07-05,10292.62,10388.91,10282.64,10371.80,1805820000,10371.80 2005-07-01,10273.59,10380.78,10239.91,10303.44,1593820000,10303.44 2005-06-30,10374.18,10458.19,10253.49,10274.97,2109490000,10274.97 2005-06-29,10405.94,10472.46,10332.52,10374.48,1769280000,10374.48 2005-06-28,10291.01,10434.18,10285.86,10405.63,1772410000,10405.63 2005-06-27,10298.07,10377.55,10229.40,10290.78,1738620000,10290.78 2005-06-24,10422.28,10452.82,10266.30,10297.83,2418800000,10297.83 2005-06-23,10587.09,10617.39,10401.49,10421.44,2029920000,10421.44 2005-06-22,10599.36,10676.24,10543.28,10587.93,1823250000,10587.93 2005-06-21,10608.88,10670.56,10545.89,10599.67,1720700000,10599.67 2005-06-20,10621.54,10656.66,10539.21,10609.10,1714530000,10609.10 2005-06-17,10580.41,10710.38,10561.00,10623.07,2407370000,10623.07 2005-06-16,10566.76,10632.20,10501.92,10578.65,1776040000,10578.65 2005-06-15,10548.65,10628.67,10471.69,10566.37,1840440000,10566.37 2005-06-14,10521.95,10617.01,10473.92,10547.57,1698150000,10547.57 2005-06-13,10503.57,10611.10,10437.32,10522.56,1661350000,10522.56 2005-06-10,10503.02,10581.13,10410.50,10512.63,1664180000,10512.63 2005-06-09,10477.75,10556.90,10410.80,10503.02,1824120000,10503.02 2005-06-08,10484.84,10575.81,10439.77,10476.86,1715490000,10476.86 2005-06-07,10466.00,10603.15,10454.18,10483.07,1851370000,10483.07 2005-06-06,10461.64,10519.79,10410.28,10467.03,1547120000,10467.03 2005-06-03,10552.82,10572.18,10427.35,10460.97,1627520000,10460.97 2005-06-02,10548.83,10590.07,10478.26,10553.49,1813790000,10553.49 2005-06-01,10462.86,10616.15,10433.48,10549.87,1810100000,10549.87 2005-05-31,10541.89,10574.92,10437.77,10467.48,1840680000,10467.48 2005-05-27,10537.08,10579.94,10489.35,10542.55,1381430000,10542.55 2005-05-26,10458.68,10581.87,10450.55,10537.60,1654110000,10537.60 2005-05-25,10503.17,10516.17,10396.46,10457.80,1742180000,10457.80 2005-05-24,10522.68,10550.24,10433.78,10503.68,1681000000,10503.68 2005-05-23,10472.80,10589.92,10438.36,10523.56,1681170000,10523.56 2005-05-20,10492.75,10535.24,10400.60,10471.91,1631750000,10471.91 2005-05-19,10464.45,10538.71,10394.39,10493.19,1775860000,10493.19 2005-05-18,10323.19,10518.17,10323.19,10464.45,2266320000,10464.45 2005-05-17,10247.49,10357.30,10175.81,10331.88,1887260000,10331.88 2005-05-16,10139.61,10274.39,10118.32,10252.29,1856860000,10252.29 2005-05-13,10188.23,10268.85,10062.76,10140.12,2188590000,10140.12 2005-05-12,10299.74,10357.37,10155.86,10189.48,1995290000,10189.48 2005-05-11,10272.91,10355.31,10172.86,10300.25,1834970000,10300.25 2005-05-10,10382.94,10389.96,10230.35,10281.11,1889660000,10281.11 2005-05-09,10345.40,10416.56,10288.95,10384.34,1857020000,10384.34 2005-05-06,10339.71,10454.40,10300.70,10345.40,1707200000,10345.40 2005-05-05,10384.49,10447.08,10276.75,10340.38,1997100000,10340.38 2005-05-04,10255.25,10412.20,10239.95,10384.64,2306480000,10384.64 2005-05-03,10251.04,10327.37,10169.39,10256.95,2167020000,10256.95 2005-05-02,10192.00,10309.86,10149.06,10251.70,1980040000,10251.70 2005-04-29,10073.47,10231.31,10021.23,10192.51,2362360000,10192.51 2005-04-28,10194.58,10229.09,10036.74,10070.37,2182270000,10070.37 2005-04-27,10150.32,10250.23,10048.27,10198.80,2151520000,10198.80 2005-04-26,10240.99,10298.85,10108.79,10151.13,1959740000,10151.13 2005-04-25,10158.52,10305.87,10148.25,10242.47,1795030000,10242.47 2005-04-22,10216.68,10266.48,10055.29,10157.71,2045880000,10157.71 2005-04-21,10010.51,10250.30,10010.51,10218.60,2308560000,10218.60 2005-04-20,10131.18,10232.34,9978.74,10012.36,2217050000,10012.36 2005-04-19,10071.55,10220.21,10021.08,10127.41,2142700000,10127.41 2005-04-18,10088.54,10183.50,9961.52,10071.25,2180670000,10071.25 2005-04-15,10276.61,10311.26,10059.36,10087.51,2689960000,10087.51 2005-04-14,10403.71,10457.06,10248.23,10278.75,2355040000,10278.75 2005-04-13,10507.45,10567.38,10355.16,10403.93,2049740000,10403.93 2005-04-12,10448.63,10552.60,10331.21,10507.97,1979830000,10507.97 2005-04-11,10462.08,10530.58,10393.36,10448.56,1525310000,10448.56 2005-04-08,10546.32,10584.60,10445.31,10461.34,1661330000,10461.34 2005-04-07,10485.88,10589.99,10434.30,10546.32,1900620000,10546.32 2005-04-06,10453.45,10557.18,10434.22,10486.02,1797400000,10486.02 2005-04-05,10421.14,10530.14,10372.59,10458.46,1870800000,10458.46 2005-04-04,10401.71,10496.44,10307.64,10421.14,2079770000,10421.14 2005-04-01,10504.57,10600.56,10349.02,10404.30,2168690000,10404.30 2005-03-31,10541.59,10586.15,10448.19,10503.76,2214230000,10503.76 2005-03-30,10405.77,10564.80,10395.21,10540.93,2097110000,10540.93 2005-03-29,10486.10,10565.46,10351.76,10405.70,2223250000,10405.70 2005-03-28,10444.13,10568.05,10412.79,10485.65,1746220000,10485.65 2005-03-24,10457.06,10554.60,10415.16,10442.87,1721720000,10442.87 2005-03-23,10470.58,10558.51,10384.34,10456.02,2246870000,10456.02 2005-03-22,10565.39,10651.41,10446.78,10470.51,2114470000,10470.51 2005-03-21,10629.90,10662.93,10503.46,10565.39,1819440000,10565.39 2005-03-18,10627.83,10709.85,10520.60,10629.67,2344370000,10629.67 2005-03-17,10633.30,10707.86,10561.10,10626.35,1581930000,10626.35 2005-03-16,10741.63,10764.16,10569.30,10633.07,1653190000,10633.07 2005-03-15,10804.29,10884.76,10716.87,10745.10,1513530000,10745.10 2005-03-14,10773.92,10859.12,10709.26,10804.51,1437430000,10804.51 2005-03-11,10845.30,10897.68,10728.62,10774.36,1449820000,10774.36 2005-03-10,10806.28,10907.45,10757.36,10851.51,1604020000,10851.51 2005-03-09,10912.32,10949.20,10768.66,10805.62,1704970000,10805.62 2005-03-08,10935.60,10996.56,10863.40,10912.62,1523090000,10912.62 2005-03-07,10940.55,11027.15,10886.09,10936.86,1488830000,10936.86 2005-03-04,10834.51,10996.93,10834.51,10940.55,1636820000,10940.55 2005-03-03,10812.27,10904.34,10744.14,10833.03,1616240000,10833.03 2005-03-02,10825.68,10896.66,10736.16,10811.97,1568540000,10811.97 2005-03-01,10794.98,10849.14,10769.04,10830.00,1708060000,10830.00 2005-02-28,10842.05,10877.07,10709.41,10766.23,1795480000,10766.23 2005-02-25,10748.42,10871.53,10698.32,10841.60,1523680000,10841.60 2005-02-24,10672.24,10779.39,10612.24,10748.79,1518750000,10748.79 2005-02-23,10609.28,10735.42,10583.64,10673.79,1501090000,10673.79 2005-02-22,10783.38,10806.36,10596.79,10611.20,1744940000,10611.20 2005-02-18,10755.15,10854.98,10682.29,10785.22,1551200000,10785.22 2005-02-17,10835.03,10873.60,10729.95,10754.26,1580120000,10754.26 2005-02-16,10832.03,10889.78,10746.21,10834.88,1490100000,10834.88 2005-02-15,10791.06,10886.31,10745.10,10837.32,1527080000,10837.32 2005-02-14,10795.72,10853.80,10722.63,10791.13,1290180000,10791.13 2005-02-11,10742.92,10865.69,10680.15,10796.01,1562300000,10796.01 2005-02-10,10665.00,10803.92,10633.67,10749.61,1491670000,10749.61 2005-02-09,10717.76,10781.38,10621.84,10664.11,1511040000,10664.11 2005-02-08,10712.51,10783.97,10647.85,10724.63,1416170000,10724.63 2005-02-07,10715.76,10774.80,10650.59,10715.76,1347270000,10715.76 2005-02-04,10593.17,10750.94,10553.93,10716.13,1648160000,10716.13 2005-02-03,10592.21,10640.69,10511.96,10593.10,1554460000,10593.10 2005-02-02,10551.05,10638.25,10501.02,10596.79,1561740000,10596.79 2005-02-01,10489.72,10609.73,10464.38,10551.94,1681980000,10551.94 2005-01-31,10428.76,10559.77,10414.49,10489.94,1679800000,10489.94 2005-01-28,10470.58,10520.61,10331.58,10427.20,1641800000,10427.20 2005-01-27,10498.14,10535.16,10379.47,10467.40,1600600000,10467.40 2005-01-26,10463.19,10571.66,10433.56,10498.59,1635900000,10498.59 2005-01-25,10369.42,10534.72,10369.42,10461.56,1610400000,10461.56 2005-01-24,10393.58,10491.71,10317.10,10368.61,1494600000,10368.61 2005-01-21,10471.98,10541.30,10370.97,10392.99,1643500000,10392.99 2005-01-20,10538.90,10582.09,10414.72,10471.47,1692000000,10471.47 2005-01-19,10626.05,10668.40,10519.20,10539.97,1498700000,10539.97 2005-01-18,10554.23,10665.44,10456.61,10628.79,1596800000,10628.79 2005-01-14,10506.71,10606.47,10475.01,10558.00,1335400000,10558.00 2005-01-13,10617.41,10650.96,10463.26,10505.83,1510300000,10505.83 2005-01-12,10561.32,10648.52,10481.37,10617.78,1562100000,10617.78 2005-01-11,10619.77,10632.63,10504.72,10556.22,1488800000,10556.22 2005-01-10,10603.44,10696.85,10544.99,10621.03,1490400000,10621.03 2005-01-07,10624.80,10697.81,10545.80,10603.96,1477900000,10603.96 2005-01-06,10593.19,10708.37,10555.48,10622.88,1569100000,10622.88 2005-01-05,10629.53,10736.16,10561.03,10597.83,1738900000,10597.83 2005-01-04,10727.81,10803.62,10587.48,10630.78,1720200000,10630.78 2005-01-03,10783.75,10892.67,10694.18,10729.43,1505900000,10729.43 2004-12-31,10800.30,10849.81,10759.94,10783.01,786900000,10783.01 2004-12-30,10829.12,10880.03,10781.67,10800.30,829800000,10800.30 2004-12-29,10853.72,10872.71,10771.26,10829.19,924900000,10829.19 2004-12-28,10776.06,10890.82,10774.51,10854.54,984200000,10854.54 2004-12-27,10828.01,10892.52,10755.67,10776.13,922000000,10776.13 2004-12-23,10815.00,10895.10,10780.12,10827.12,956100000,10827.12 2004-12-22,10752.34,10861.33,10709.78,10815.89,1390800000,10815.89 2004-12-21,10661.89,10789.66,10646.60,10759.43,1483700000,10759.43 2004-12-20,10652.14,10769.13,10622.20,10661.60,1422800000,10661.60 2004-12-17,10704.83,10766.01,10562.76,10649.92,2335000000,10649.92 2004-12-16,10691.71,10776.43,10612.31,10705.64,1793900000,10705.64 2004-12-15,10675.71,10749.53,10601.74,10691.45,1695800000,10691.45 2004-12-14,10640.53,10715.76,10571.67,10676.45,1544400000,10676.45 2004-12-13,10543.44,10678.52,10520.61,10638.32,1436100000,10638.32 2004-12-10,10552.16,10616.23,10469.62,10543.22,1443700000,10543.22 2004-12-09,10492.45,10579.94,10389.81,10552.82,1624700000,10552.82 2004-12-08,10438.77,10550.16,10395.05,10494.23,1525200000,10494.23 2004-12-07,10546.80,10612.90,10423.21,10440.58,1533900000,10440.58 2004-12-06,10591.32,10614.82,10490.31,10547.06,1354400000,10547.06 2004-12-03,10597.90,10670.47,10515.73,10592.21,1566700000,10592.21 2004-12-02,10590.44,10670.02,10485.21,10585.12,1774900000,10585.12 2004-12-01,10425.80,10618.59,10421.66,10590.22,1772800000,10590.22 2004-11-30,10475.27,10530.80,10380.58,10428.02,1553500000,10428.02 2004-11-29,10520.64,10590.73,10390.92,10475.90,1378500000,10475.90 2004-11-26,10518.69,10574.70,10479.52,10522.23,504580000,10522.23 2004-11-24,10493.86,10565.76,10451.66,10520.31,1149600000,10520.31 2004-11-23,10486.69,10547.28,10407.18,10492.60,1428300000,10492.60 2004-11-22,10455.73,10535.46,10380.95,10489.42,1392700000,10489.42 2004-11-19,10571.63,10588.29,10419.89,10456.91,1526600000,10456.91 2004-11-18,10549.20,10639.43,10499.62,10572.55,1456700000,10572.55 2004-11-17,10481.83,10655.09,10470.21,10549.57,1684200000,10549.57 2004-11-16,10549.79,10570.56,10445.31,10487.65,1364400000,10487.65 2004-11-15,10541.89,10612.31,10463.34,10550.24,1453300000,10550.24 2004-11-12,10469.21,10565.48,10419.77,10539.01,1531600000,10539.01 2004-11-11,10386.95,10513.42,10364.10,10469.84,1393000000,10469.84 2004-11-10,10378.59,10470.21,10330.54,10385.48,1504300000,10385.48 2004-11-09,10387.62,10466.81,10327.00,10386.37,1450800000,10386.37 2004-11-08,10385.15,10452.58,10313.51,10391.31,1358700000,10391.31 2004-11-05,10317.05,10458.10,10279.96,10387.54,1724400000,10387.54 2004-11-04,10132.48,10352.81,10076.36,10314.76,1782700000,10314.76 2004-11-03,10137.05,10253.27,10062.80,10137.05,1767500000,10137.05 2004-11-02,10053.87,10180.85,9976.29,10035.73,1659000000,10035.73 2004-11-01,10028.73,10124.44,9953.29,10054.39,1395900000,10054.39 2004-10-29,10004.69,10083.44,9936.77,10027.47,1500800000,10027.47 2004-10-28,9998.94,10074.89,9900.42,10004.54,1628200000,10004.54 2004-10-27,9888.25,10051.96,9807.80,10002.03,1741900000,10002.03 2004-10-26,9750.59,9914.65,9718.94,9888.48,1685400000,9888.48 2004-10-25,9757.22,9827.20,9660.18,9749.99,1380500000,9749.99 2004-10-22,9863.85,9920.99,9732.81,9757.81,1469600000,9757.81 2004-10-21,9884.65,9969.07,9769.16,9865.76,1673000000,9865.76 2004-10-20,9895.19,9957.05,9766.95,9886.93,1685700000,9886.93 2004-10-19,9958.38,10064.20,9854.19,9897.62,1737500000,9897.62 2004-10-18,9932.98,10002.18,9816.73,9956.32,1373300000,9956.32 2004-10-15,9895.63,10022.31,9845.56,9933.38,1645100000,9933.38 2004-10-14,10002.54,10048.48,9837.22,9894.45,1489500000,9894.45 2004-10-13,10085.21,10157.11,9935.08,10002.33,1546200000,10002.33 2004-10-12,10080.42,10121.49,9985.44,10077.18,1320100000,10077.18 2004-10-11,10056.09,10142.74,10017.67,10081.97,943800000,10081.97 2004-10-08,10124.11,10177.53,10013.91,10055.20,1291600000,10055.20 2004-10-07,10239.84,10267.57,10086.83,10125.40,1447500000,10125.40 2004-10-06,10170.70,10267.14,10112.20,10239.92,1416700000,10239.92 2004-10-05,10216.76,10253.93,10123.19,10177.68,1418400000,10177.68 2004-10-04,10191.40,10313.81,10153.79,10216.54,1534000000,10216.54 2004-10-01,10082.04,10237.05,10081.38,10192.65,1582200000,10192.65 2004-09-30,10136.38,10155.49,9987.36,10080.27,1748000000,10080.27 2004-09-29,10078.06,10160.50,10002.57,10136.24,1402900000,10136.24 2004-09-28,9989.73,10132.04,9950.71,10077.40,1396600000,10077.40 2004-09-27,10046.65,10077.32,9952.78,9988.54,1263500000,9988.54 2004-09-24,10039.42,10111.39,9993.92,10047.24,1255400000,10047.24 2004-09-23,10108.29,10134.84,9999.67,10038.90,1286300000,10038.90 2004-09-22,10244.05,10244.05,10075.33,10109.18,1379900000,10109.18 2004-09-21,10204.52,10291.39,10159.54,10244.93,1325000000,10244.93 2004-09-20,10283.87,10293.23,10152.90,10204.89,1197600000,10204.89 2004-09-17,10245.82,10352.37,10219.71,10284.46,1422600000,10284.46 2004-09-16,10231.59,10315.72,10194.35,10244.49,1113900000,10244.49 2004-09-15,10316.90,10324.87,10195.60,10231.36,1256000000,10231.36 2004-09-14,10315.13,10374.79,10260.93,10318.16,1204500000,10318.16 2004-09-13,10306.65,10380.47,10250.61,10314.76,1299800000,10314.76 2004-09-10,10289.47,10348.68,10196.19,10313.07,1261200000,10313.07 2004-09-09,10313.36,10337.33,10269.49,10289.10,1371300000,10289.10 2004-09-08,10342.42,10390.64,10267.94,10313.36,1246300000,10313.36 2004-09-07,10261.52,10388.95,10255.62,10341.16,1214400000,10341.16 2004-09-03,10277.82,10346.99,10229.52,10260.20,924170000,10260.20 2004-09-02,10168.39,10312.99,10129.01,10290.28,1118400000,10290.28 2004-09-01,10170.12,10230.48,10092.37,10168.46,1142100000,10168.46 2004-08-31,10121.97,10198.03,10056.09,10173.92,1138200000,10173.92 2004-08-30,10193.83,10226.87,10110.43,10122.52,843100000,10122.52 2004-08-27,10174.07,10235.49,10143.91,10195.01,845400000,10195.01 2004-08-26,10181.07,10225.61,10124.88,10173.41,1023600000,10173.41 2004-08-25,10098.49,10224.29,10041.93,10181.74,1192200000,10181.74 2004-08-24,10074.89,10165.07,10044.66,10098.63,1092500000,10098.63 2004-08-23,10111.10,10159.54,10046.72,10073.05,1021900000,10073.05 2004-08-20,10040.81,10143.76,9989.65,10110.14,1199900000,10110.14 2004-08-19,10082.78,10111.91,9972.39,10040.82,1249400000,10040.82 2004-08-18,9964.22,10097.01,9910.82,10083.15,1282500000,10083.15 2004-08-17,9955.50,10053.21,9916.05,9972.83,1267800000,9972.83 2004-08-16,9825.35,9987.58,9807.44,9954.55,1206200000,9954.55 2004-08-13,9814.11,9897.34,9746.60,9825.35,1175100000,9825.35 2004-08-12,9936.48,9940.02,9780.52,9814.59,1405100000,9814.59 2004-08-11,9931.24,9981.61,9804.63,9938.32,1410400000,9938.32 2004-08-10,9815.55,9961.70,9798.44,9944.67,1245600000,9944.67 2004-08-09,9816.14,9902.49,9773.74,9814.66,1086000000,9814.66 2004-08-06,9960.67,9963.47,9767.54,9815.33,1521000000,9815.33 2004-08-05,10127.10,10158.44,9945.84,9963.03,1397400000,9963.03 2004-08-04,10117.96,10186.16,10029.02,10126.51,1369200000,10126.51 2004-08-03,10178.27,10228.49,10064.57,10120.24,1338300000,10120.24 2004-08-02,10138.45,10224.29,10063.75,10179.16,1276000000,10179.16 2004-07-30,10129.12,10194.13,10045.76,10139.71,1298200000,10139.71 2004-07-29,10115.52,10213.08,10049.74,10129.24,1530100000,10129.24 2004-07-28,10084.03,10170.31,9966.34,10117.07,1554300000,10117.07 2004-07-27,9963.54,10133.95,9942.75,10085.14,1610800000,10085.14 2004-07-26,9964.71,10054.32,9874.38,9961.92,1413400000,9961.92 2004-07-23,10045.46,10069.51,9893.93,9962.22,1337500000,9962.22 2004-07-22,10047.60,10114.41,9906.62,10050.33,1680800000,10050.33 2004-07-21,10156.30,10279.96,10027.92,10046.13,1679500000,10046.13 2004-07-20,10094.43,10186.90,10031.24,10149.07,1445800000,10149.07 2004-07-19,10140.95,10211.60,10027.33,10094.06,1319900000,10094.06 2004-07-16,10162.34,10289.40,10095.32,10139.78,1450300000,10139.78 2004-07-15,10208.20,10275.27,10115.81,10163.16,1408700000,10163.16 2004-07-14,10232.84,10313.95,10129.31,10208.80,1462000000,10208.80 2004-07-13,10238.37,10297.58,10188.45,10247.59,1199700000,10247.59 2004-07-12,10211.75,10284.39,10130.42,10238.22,1114600000,10238.22 2004-07-09,10173.12,10277.16,10150.32,10213.22,1186300000,10213.22 2004-07-08,10238.52,10297.73,10134.99,10171.56,1401100000,10171.56 2004-07-07,10211.92,10300.53,10156.45,10240.29,1328600000,10240.29 2004-07-06,10280.26,10308.43,10163.60,10219.34,1283300000,10219.34 2004-07-02,10334.00,10371.40,10228.71,10282.83,1085000000,10282.83 2004-07-01,10434.00,10473.23,10255.55,10334.16,1495700000,10334.16 2004-06-30,10413.43,10489.16,10348.98,10435.48,1473800000,10435.48 2004-06-29,10356.35,10460.25,10315.65,10413.43,1375000000,10413.43 2004-06-28,10377.52,10505.16,10317.64,10357.09,1354600000,10357.09 2004-06-25,10444.24,10514.67,10329.88,10371.84,1812900000,10371.84 2004-06-24,10477.43,10530.01,10398.16,10443.81,1394900000,10443.81 2004-06-23,10395.14,10498.67,10323.32,10479.57,1444200000,10479.57 2004-06-22,10370.21,10431.05,10284.24,10395.07,1382300000,10395.07 2004-06-21,10417.82,10471.76,10336.44,10371.47,1123900000,10371.47 2004-06-18,10375.82,10471.84,10328.20,10416.41,1500600000,10416.41 2004-06-17,10378.59,10417.69,10308.25,10377.52,1296700000,10377.52 2004-06-16,10380.23,10433.52,10320.60,10379.58,1168400000,10379.58 2004-06-15,10336.51,10464.04,10319.89,10380.43,1345900000,10380.43 2004-06-14,10401.23,10403.50,10283.48,10334.73,1179400000,10334.73 2004-06-10,10367.80,10448.00,10333.94,10410.10,1160600000,10410.10 2004-06-09,10431.10,10466.59,10325.07,10368.44,1276800000,10368.44 2004-06-08,10389.41,10462.97,10323.94,10432.52,1190300000,10432.52 2004-06-07,10243.31,10410.81,10243.31,10391.08,1211800000,10391.08 2004-06-04,10196.83,10327.84,10196.83,10242.82,1115300000,10242.82 2004-06-03,10261.85,10309.46,10163.40,10195.91,1232400000,10195.91 2004-06-02,10199.78,10310.10,10170.57,10262.97,1251700000,10262.97 2004-06-01,10187.18,10254.17,10104.07,10202.65,1238000000,10202.65 2004-05-28,10205.83,10250.27,10137.14,10188.45,1172600000,10188.45 2004-05-27,10109.89,10267.66,10106.13,10205.20,1447500000,10205.20 2004-05-26,10116.84,10175.75,10034.16,10109.89,1369400000,10109.89 2004-05-25,9958.08,10139.27,9895.41,10117.62,1545700000,10117.62 2004-05-24,9968.02,10084.91,9891.22,9958.43,1227500000,9958.43 2004-05-21,9939.34,10058.50,9910.81,9966.74,1258600000,9966.74 2004-05-20,9939.12,10014.50,9867.73,9937.64,1211000000,9937.64 2004-05-19,9962.55,10124.79,9919.90,9937.71,1548600000,9937.71 2004-05-18,9906.71,10028.27,9895.77,9968.51,1353000000,9968.51 2004-05-17,10009.92,10009.92,9827.21,9906.91,1430100000,9906.91 2004-05-14,10008.43,10096.69,9912.45,10012.87,1335900000,10012.87 2004-05-13,10044.31,10100.24,9924.94,10010.74,1411100000,10010.74 2004-05-12,10011.52,10089.87,9822.10,10045.16,1697600000,10045.16 2004-05-11,9989.24,10092.78,9928.91,10019.47,1533800000,10019.47 2004-05-10,10116.28,10116.28,9881.86,9990.02,1918400000,9990.02 2004-05-07,10240.62,10302.93,10086.94,10117.34,1653600000,10117.34 2004-05-06,10308.20,10332.10,10147.21,10241.26,1509300000,10241.26 2004-05-05,10316.98,10382.98,10249.63,10310.95,1469000000,10310.95 2004-05-04,10314.32,10403.14,10232.31,10317.20,1662100000,10317.20 2004-05-03,10227.27,10365.74,10199.67,10314.00,1571600000,10314.00 2004-04-30,10273.06,10374.61,10198.39,10225.57,1634700000,10225.57 2004-04-29,10339.41,10443.81,10199.31,10272.27,1859000000,10272.27 2004-04-28,10476.67,10479.58,10301.65,10342.60,1855600000,10342.60 2004-04-27,10445.38,10570.92,10410.52,10478.16,1518000000,10478.16 2004-04-26,10472.91,10540.26,10396.75,10444.73,1290600000,10444.73 2004-04-23,10463.11,10543.95,10362.97,10472.84,1396100000,10472.84 2004-04-22,10314.99,10529.12,10255.88,10461.20,1826700000,10461.20 2004-04-21,10311.87,10398.53,10200.38,10317.27,1738100000,10317.27 2004-04-20,10437.85,10530.61,10297.39,10314.50,1508500000,10314.50 2004-04-19,10451.62,10501.79,10351.97,10437.85,1194900000,10437.85 2004-04-16,10398.32,10500.57,10343.74,10451.97,1487800000,10451.97 2004-04-15,10377.95,10481.21,10279.37,10397.46,1568700000,10397.46 2004-04-14,10378.10,10453.39,10259.35,10377.95,1547700000,10377.95 2004-04-13,10516.05,10572.13,10343.17,10381.28,1423200000,10381.28 2004-04-12,10444.38,10559.28,10439.27,10515.56,1102400000,10515.56 2004-04-08,10482.77,10590.15,10383.84,10442.03,1199800000,10442.03 2004-04-07,10569.26,10580.51,10422.74,10480.15,1458800000,10480.15 2004-04-06,10553.76,10596.37,10467.26,10570.81,1397700000,10570.81 2004-04-05,10470.59,10582.22,10423.33,10558.37,1413700000,10558.37 2004-04-02,10375.33,10548.74,10375.33,10470.59,1629200000,10470.59 2004-04-01,10357.52,10449.33,10299.48,10373.33,1560700000,10373.33 2004-03-31,10380.89,10428.59,10287.11,10357.70,1560700000,10357.70 2004-03-30,10327.63,10411.41,10264.15,10381.70,1332400000,10381.70 2004-03-29,10212.91,10389.93,10212.91,10329.63,1405500000,10329.63 2004-03-26,10218.37,10306.22,10145.63,10212.97,1319100000,10212.97 2004-03-25,10049.56,10246.15,10049.56,10218.82,1471700000,10218.82 2004-03-24,10065.41,10140.23,9975.86,10048.23,1527800000,10048.23 2004-03-23,10066.67,10177.04,10020.75,10063.64,1458200000,10063.64 2004-03-22,10185.93,10185.93,9985.19,10064.75,1452300000,10064.75 2004-03-19,10295.85,10355.41,10163.71,10186.60,1457400000,10186.60 2004-03-18,10298.96,10355.04,10187.78,10295.78,1369200000,10295.78 2004-03-17,10184.30,10356.59,10184.30,10300.30,1490100000,10300.30 2004-03-16,10103.41,10253.26,10085.34,10184.67,1500700000,10184.67 2004-03-15,10238.45,10252.68,10066.08,10102.89,1600600000,10102.89 2004-03-12,10130.67,10281.63,10097.04,10240.08,1388500000,10240.08 2004-03-11,10288.85,10356.22,10102.75,10128.38,1889900000,10128.38 2004-03-10,10457.59,10523.11,10259.34,10296.89,1648400000,10296.89 2004-03-09,10529.52,10567.03,10391.48,10456.96,1499400000,10456.96 2004-03-08,10595.37,10677.85,10505.85,10529.48,1254400000,10529.48 2004-03-05,10582.59,10681.40,10497.11,10595.55,1398200000,10595.55 2004-03-04,10593.48,10645.33,10522.59,10588.00,1265800000,10588.00 2004-03-03,10588.59,10651.03,10506.66,10593.11,1334500000,10593.11 2004-03-02,10678.36,10713.92,10539.40,10591.48,1476000000,10591.48 2004-03-01,10582.25,10720.14,10568.74,10678.14,1497100000,10678.14 2004-02-27,10581.55,10689.55,10519.03,10583.92,1540400000,10583.92 2004-02-26,10598.14,10652.96,10493.70,10580.14,1383900000,10580.14 2004-02-25,10566.59,10660.73,10509.40,10601.62,1360700000,10601.62 2004-02-24,10609.55,10681.40,10479.33,10566.37,1543600000,10566.37 2004-02-23,10619.55,10711.84,10508.89,10609.62,1380400000,10609.62 2004-02-20,10666.29,10722.77,10559.11,10619.03,1479600000,10619.03 2004-02-19,10674.59,10794.95,10626.44,10664.73,1562800000,10664.73 2004-02-18,10706.68,10764.36,10623.62,10671.99,1382400000,10671.99 2004-02-17,10628.88,10762.07,10628.88,10714.88,1396500000,10714.88 2004-02-13,10696.22,10755.47,10578.66,10627.85,1329200000,10627.85 2004-02-12,10735.18,10775.03,10636.44,10694.07,1464300000,10694.07 2004-02-11,10605.48,10779.40,10561.55,10737.70,1699300000,10737.70 2004-02-10,10578.74,10667.03,10511.18,10613.85,1403900000,10613.85 2004-02-09,10592.00,10634.81,10433.70,10579.03,1303500000,10579.03 2004-02-06,10494.89,10634.81,10433.70,10593.03,1477600000,10593.03 2004-02-05,10469.33,10566.37,10399.92,10495.55,1566600000,10495.55 2004-02-04,10503.11,10567.85,10394.81,10470.74,1634800000,10470.74 2004-02-03,10499.48,10571.48,10414.15,10505.18,1476900000,10505.18 2004-02-02,10487.78,10614.44,10395.55,10499.18,1599200000,10499.18 2004-01-30,10510.22,10551.03,10385.56,10488.07,1635000000,10488.07 2004-01-29,10467.41,10611.56,10369.92,10510.29,1921900000,10510.29 2004-01-28,10610.07,10703.25,10412.44,10468.37,1842000000,10468.37 2004-01-27,10701.10,10748.81,10579.33,10609.92,1673100000,10609.92 2004-01-26,10568.00,10725.18,10510.44,10702.51,1480600000,10702.51 2004-01-23,10625.25,10691.77,10490.14,10568.29,1561200000,10568.29 2004-01-22,10624.22,10717.40,10545.03,10623.18,1693700000,10623.18 2004-01-21,10522.77,10665.70,10453.11,10623.62,1757600000,10623.62 2004-01-20,10601.40,10676.96,10447.92,10528.66,1698200000,10528.66 2004-01-16,10556.37,10666.88,10503.70,10600.51,1721100000,10600.51 2004-01-15,10534.52,10639.03,10454.52,10553.85,1695000000,10553.85 2004-01-14,10428.67,10573.85,10426.89,10538.37,1514600000,10538.37 2004-01-13,10485.18,10539.25,10341.19,10427.18,1595900000,10427.18 2004-01-12,10461.55,10543.03,10389.85,10485.18,1510200000,10485.18 2004-01-09,10589.25,10603.48,10420.52,10458.89,1720700000,10458.89 2004-01-08,10530.07,10651.99,10480.59,10592.44,1868400000,10592.44 2004-01-07,10535.46,10587.55,10432.00,10529.03,1704900000,10529.03 2004-01-06,10543.85,10584.07,10454.37,10538.66,1494500000,10538.66 2004-01-05,10411.85,10575.92,10411.85,10544.07,1578200000,10544.07 2004-01-02,10452.74,10554.96,10367.41,10409.85,1153200000,10409.85 2003-12-31,10426.30,10494.44,10382.89,10453.92,1027500000,10453.92 2003-12-30,10449.70,10493.11,10374.52,10425.04,1012600000,10425.04 2003-12-29,10321.35,10457.78,10319.70,10450.00,1058800000,10450.00 2003-12-26,10305.85,10368.89,10282.22,10324.67,356070000,10324.67 2003-12-24,10341.41,10365.63,10263.04,10305.19,518060000,10305.19 2003-12-23,10337.56,10421.48,10265.71,10341.26,1145300000,10341.26 2003-12-22,10276.48,10371.11,10216.08,10338.00,1251700000,10338.00 2003-12-19,10249.48,10345.44,10189.63,10278.22,1657300000,10278.22 2003-12-18,10141.41,10278.82,10117.78,10248.08,1579900000,10248.08 2003-12-17,10128.75,10186.67,10040.08,10145.26,1441700000,10145.26 2003-12-16,10023.34,10173.19,9986.23,10129.56,1547900000,10129.56 2003-12-15,10046.53,10180.97,9994.38,10022.82,1520800000,10022.82 2003-12-12,10008.75,10091.71,9946.60,10042.16,1223100000,10042.16 2003-12-11,9922.45,10056.97,9896.16,10008.16,1441100000,10008.16 2003-12-10,9922.38,10000.53,9848.97,9921.86,1444000000,9921.86 2003-12-09,9966.45,10048.75,9887.57,9923.42,1465500000,9923.42 2003-12-08,9862.01,9997.34,9824.83,9965.27,1218900000,9965.27 2003-12-05,9923.27,9954.16,9819.05,9862.68,1265900000,9862.68 2003-12-04,9874.83,9978.08,9814.97,9930.82,1463100000,9930.82 2003-12-03,9851.94,9974.45,9824.31,9873.42,1441700000,9873.42 2003-12-02,9899.64,9936.97,9798.83,9853.64,1383200000,9853.64 2003-12-01,9785.35,9943.34,9777.64,9899.05,1375000000,9899.05 2003-11-28,9779.72,9832.16,9733.20,9782.46,487220000,9782.46 2003-11-26,9763.49,9838.01,9689.05,9779.57,1097700000,9779.57 2003-11-25,9748.68,9821.94,9679.13,9763.94,1333700000,9763.94 2003-11-24,9629.87,9788.60,9629.87,9747.79,1302800000,9747.79 2003-11-21,9622.02,9692.53,9556.68,9628.53,1273800000,9628.53 2003-11-20,9688.46,9756.09,9576.91,9619.42,1326700000,9619.42 2003-11-19,9620.68,9731.94,9584.31,9690.46,1326200000,9690.46 2003-11-18,9711.44,9792.16,9601.35,9624.16,1354300000,9624.16 2003-11-17,9765.64,9775.35,9603.57,9710.83,1374300000,9710.83 2003-11-14,9836.46,9919.19,9709.13,9768.68,1356100000,9768.68 2003-11-13,9846.97,9895.71,9740.53,9837.94,1383000000,9837.94 2003-11-12,9729.50,9882.60,9700.02,9848.83,1349300000,9848.83 2003-11-11,9756.53,9801.21,9673.64,9737.79,1162500000,9737.79 2003-11-10,9807.49,9861.05,9702.46,9756.53,1243600000,9756.53 2003-11-07,9857.12,9945.71,9770.31,9809.79,1440500000,9809.79 2003-11-06,9820.68,9888.90,9738.53,9856.97,1453900000,9856.97 2003-11-05,9837.64,9883.86,9746.98,9820.83,1401800000,9820.83 2003-11-04,9857.49,9905.94,9770.46,9838.83,1417600000,9838.83 2003-11-03,9802.46,9936.31,9792.60,9858.46,1378200000,9858.46 2003-10-31,9786.75,9880.08,9745.94,9801.12,1498900000,9801.12 2003-10-30,9772.01,9882.97,9719.20,9786.61,1629700000,9786.61 2003-10-29,9747.05,9830.23,9663.27,9774.53,1562600000,9774.53 2003-10-28,9609.72,9769.57,9592.54,9748.31,1629200000,9748.31 2003-10-27,9584.54,9696.98,9553.80,9608.16,1371800000,9608.16 2003-10-24,9600.98,9631.50,9463.28,9582.46,1420300000,9582.46 2003-10-23,9597.20,9661.05,9517.50,9613.13,1604300000,9613.13 2003-10-22,9741.98,9741.98,9551.65,9598.24,1647200000,9598.24 2003-10-21,9778.31,9824.90,9697.94,9747.64,1498000000,9747.64 2003-10-20,9721.50,9816.97,9665.35,9777.94,1172600000,9777.94 2003-10-17,9791.86,9833.12,9679.72,9721.79,1352000000,9721.79 2003-10-16,9798.68,9838.53,9679.13,9791.72,1417700000,9791.72 2003-10-15,9824.09,9901.64,9731.57,9803.05,1521100000,9803.05 2003-10-14,9763.27,9833.42,9696.90,9812.98,1271900000,9812.98 2003-10-13,9675.72,9814.97,9675.72,9764.38,1040500000,9764.38 2003-10-10,9682.90,9743.12,9622.31,9674.68,1108100000,9674.68 2003-10-09,9633.35,9798.08,9617.35,9680.01,1578700000,9680.01 2003-10-08,9653.33,9699.35,9571.35,9630.90,1262500000,9630.90 2003-10-07,9593.28,9672.68,9512.76,9654.61,1279500000,9654.61 2003-10-06,9572.39,9656.09,9524.39,9594.98,1025800000,9594.98 2003-10-03,9492.54,9701.87,9492.54,9572.31,1570500000,9572.31 2003-10-02,9464.76,9539.20,9397.87,9487.80,1269300000,9487.80 2003-10-01,9275.06,9472.69,9275.06,9469.20,1566300000,9469.20 2003-09-30,9378.10,9393.35,9199.43,9275.06,1590500000,9275.06 2003-09-29,9314.42,9431.54,9259.68,9380.24,1366500000,9380.24 2003-09-26,9342.43,9407.89,9257.99,9313.08,1472500000,9313.08 2003-09-25,9425.58,9493.44,9311.47,9343.96,1530000000,9343.96 2003-09-24,9575.97,9612.53,9400.67,9425.51,1556000000,9425.51 2003-09-23,9535.76,9623.34,9479.41,9576.04,1301700000,9576.04 2003-09-22,9641.80,9641.87,9467.83,9535.41,1278800000,9535.41 2003-09-19,9661.80,9719.49,9582.64,9644.82,1518600000,9644.82 2003-09-18,9544.04,9691.55,9513.37,9659.13,1498800000,9659.13 2003-09-17,9566.08,9641.45,9510.28,9545.65,1338210000,9545.65 2003-09-16,9449.16,9587.90,9426.84,9567.34,1403200000,9567.34 2003-09-15,9471.19,9541.02,9396.03,9448.81,1151300000,9448.81 2003-09-12,9456.88,9517.37,9348.59,9471.55,1236700000,9471.55 2003-09-11,9415.05,9540.60,9374.49,9459.76,1335900000,9459.76 2003-09-10,9504.88,9545.51,9373.08,9420.46,1582100000,9420.46 2003-09-09,9584.92,9617.02,9459.85,9507.20,1414800000,9507.20 2003-09-08,9503.41,9638.57,9492.25,9586.29,1299300000,9586.29 2003-09-05,9589.52,9602.22,9441.93,9503.34,1465200000,9503.34 2003-09-04,9569.09,9661.80,9492.74,9587.90,1453900000,9587.90 2003-09-03,9521.86,9632.75,9465.72,9568.46,1675600000,9568.46 2003-09-02,9416.67,9563.83,9357.44,9523.27,1470500000,9523.27 2003-08-29,9373.33,9444.25,9320.52,9415.82,945100000,9415.82 2003-08-28,9334.35,9415.68,9246.48,9374.21,1165200000,9374.21 2003-08-27,9339.82,9387.82,9280.03,9333.79,1051400000,9333.79 2003-08-26,9316.03,9372.45,9203.54,9340.45,1178700000,9340.45 2003-08-25,9349.44,9381.51,9242.56,9317.64,971700000,9317.64 2003-08-22,9436.04,9535.97,9323.26,9348.87,1308900000,9348.87 2003-08-21,9399.96,9517.37,9345.71,9423.68,1407100000,9423.68 2003-08-20,9420.13,9454.49,9324.03,9397.51,1210800000,9397.51 2003-08-19,9412.17,9490.60,9315.25,9428.90,1300600000,9428.90 2003-08-18,9320.66,9466.79,9309.16,9412.45,1127600000,9412.45 2003-08-15,9308.52,9360.27,9253.20,9321.69,636370000,9321.69 2003-08-14,9272.25,9356.63,9193.33,9310.56,1186800000,9310.56 2003-08-13,9303.69,9350.19,9213.43,9271.76,1208800000,9271.76 2003-08-12,9218.12,9329.04,9163.29,9310.06,1132300000,9310.06 2003-08-11,9189.62,9275.61,9124.00,9217.35,1022200000,9217.35 2003-08-08,9127.36,9230.37,9097.74,9191.09,1086600000,9191.09 2003-08-07,9060.48,9171.13,9003.63,9126.45,1389300000,9126.45 2003-08-06,9032.96,9151.38,8964.13,9061.74,1491000000,9061.74 2003-08-05,9185.27,9210.21,9024.77,9036.32,1351700000,9036.32 2003-08-04,9154.18,9231.84,9033.66,9186.04,1318700000,9186.04 2003-08-01,9232.68,9266.37,9100.12,9153.97,1390600000,9153.97 2003-07-31,9199.35,9398.02,9183.80,9233.80,1608000000,9233.80 2003-07-30,9204.39,9272.88,9131.70,9200.05,1391900000,9200.05 2003-07-29,9268.19,9327.36,9135.62,9204.46,1508900000,9204.46 2003-07-28,9284.92,9356.77,9182.96,9266.51,1328600000,9266.51 2003-07-25,9113.85,9296.62,9062.38,9284.57,1397500000,9284.57 2003-07-24,9196.56,9313.99,9092.98,9112.51,1559000000,9112.51 2003-07-23,9159.08,9249.91,9064.69,9194.24,1362700000,9194.24 2003-07-22,9098.65,9221.83,9008.60,9158.45,1439700000,9158.45 2003-07-21,9187.80,9219.87,9025.12,9096.69,1254200000,9096.69 2003-07-18,9052.29,9212.31,9034.36,9188.15,1365200000,9188.15 2003-07-17,9089.34,9160.27,8968.82,9050.82,1661400000,9050.82 2003-07-16,9133.70,9185.63,9005.23,9094.59,1662000000,9094.59 2003-07-15,9179.18,9260.42,9054.60,9128.97,1518600000,9128.97 2003-07-14,9126.45,9316.44,9126.45,9177.15,1448900000,9177.15 2003-07-11,9036.39,9176.59,9009.01,9119.59,1212700000,9119.59 2003-07-10,9154.53,9154.53,8978.13,9036.04,1465700000,9036.04 2003-07-09,9221.90,9270.22,9077.91,9156.21,1618000000,9156.21 2003-07-08,9213.48,9281.77,9122.24,9223.09,1565700000,9223.09 2003-07-07,9073.92,9289.90,9073.92,9216.79,1429100000,9216.79 2003-07-03,9141.16,9164.48,9014.06,9070.21,775900000,9070.21 2003-07-02,9043.54,9168.82,9025.12,9142.84,1519300000,9142.84 2003-07-01,8983.66,9068.05,8843.61,9040.95,1460200000,9040.95 2003-06-30,8990.74,9100.12,8934.71,8985.44,1587200000,8985.44 2003-06-27,9079.74,9135.91,8938.26,8989.05,1267800000,8989.05 2003-06-26,9011.06,9118.82,8953.83,9079.04,1387400000,9079.04 2003-06-25,9109.57,9195.20,8984.29,9011.53,1459200000,9011.53 2003-06-24,9071.48,9179.25,9020.08,9109.85,1388300000,9109.85 2003-06-23,9199.49,9215.32,9003.83,9072.95,1398100000,9072.95 2003-06-20,9180.93,9306.36,9149.21,9200.75,1698000000,9200.75 2003-06-19,9293.80,9346.34,9134.50,9179.53,1530100000,9179.53 2003-06-18,9322.67,9363.15,9185.17,9293.80,1488900000,9293.80 2003-06-17,9319.66,9406.50,9234.78,9323.02,1479700000,9323.02 2003-06-16,9117.56,9335.49,9117.56,9318.96,1345900000,9318.96 2003-06-13,9197.88,9234.23,9042.63,9117.12,1271600000,9117.12 2003-06-12,9184.29,9270.64,9089.38,9196.55,1553100000,9196.55 2003-06-11,9048.85,9202.08,9010.13,9183.22,1520000000,9183.22 2003-06-10,8980.79,9111.11,8946.06,9054.89,1275400000,9054.89 2003-06-09,9061.18,9109.43,8909.78,8980.00,1307000000,8980.00 2003-06-06,9045.57,9248.71,9008.87,9062.79,1837200000,9062.79 2003-06-05,9036.67,9106.70,8905.37,9041.30,1693100000,9041.30 2003-06-04,8919.94,9076.94,8882.75,9038.98,1618700000,9038.98 2003-06-03,8898.23,8973.02,8823.51,8922.95,1450200000,8922.95 2003-06-02,8851.45,9040.46,8833.66,8897.81,1662500000,8897.81 2003-05-30,8711.46,8897.04,8711.46,8850.26,1688800000,8850.26 2003-05-29,8787.23,8895.99,8657.96,8711.18,1685800000,8711.18 2003-05-28,8781.84,8885.34,8721.90,8793.12,1559000000,8793.12 2003-05-27,8600.54,8812.30,8523.64,8781.35,1532000000,8781.35 2003-05-23,8594.02,8668.47,8513.98,8601.38,1201000000,8601.38 2003-05-22,8516.99,8650.33,8495.35,8594.02,1448500000,8594.02 2003-05-21,8485.62,8577.64,8389.68,8516.43,1457800000,8516.43 2003-05-20,8494.09,8593.61,8394.51,8491.36,1505300000,8491.36 2003-05-19,8676.52,8676.52,8455.72,8493.39,1375700000,8493.39 2003-05-16,8710.36,8766.36,8614.33,8678.97,1505500000,8678.97 2003-05-15,8649.22,8766.58,8613.84,8713.14,1508700000,8713.14 2003-05-14,8673.29,8744.94,8575.96,8647.82,1401800000,8647.82 2003-05-13,8722.88,8757.40,8611.18,8679.25,1418100000,8679.25 2003-05-12,8603.90,8764.12,8544.24,8726.73,1378800000,8726.73 2003-05-09,8492.69,8637.58,8482.89,8604.60,1326100000,8604.60 2003-05-08,8558.67,8591.01,8435.61,8491.22,1379600000,8491.22 2003-05-07,8585.42,8650.82,8494.87,8560.63,1531900000,8560.63 2003-05-06,8531.28,8658.18,8486.88,8588.36,1649600000,8588.36 2003-05-05,8583.17,8643.11,8472.67,8531.57,1446300000,8531.57 2003-05-02,8453.48,8612.86,8389.40,8582.68,1554300000,8582.68 2003-05-01,8478.48,8519.09,8328.55,8454.25,1397500000,8454.25 2003-04-30,8501.38,8557.62,8402.36,8480.09,1788510000,8480.09 2003-04-29,8472.88,8578.55,8414.61,8502.99,1525600000,8502.99 2003-04-28,8306.84,8515.80,8290.46,8471.61,1273000000,8471.61 2003-04-25,8438.98,8453.06,8258.80,8306.35,1335800000,8306.35 2003-04-24,8512.44,8527.99,8363.28,8440.04,1648100000,8440.04 2003-04-23,8484.92,8587.72,8398.65,8515.66,1667200000,8515.66 2003-04-22,8326.38,8509.43,8238.14,8484.99,1631200000,8484.99 2003-04-21,8336.67,8423.09,8270.56,8328.90,1118700000,8328.90 2003-04-17,8255.79,8388.28,8172.52,8337.65,1430600000,8337.65 2003-04-16,8405.72,8459.15,8217.27,8257.61,1587600000,8257.61 2003-04-15,8347.66,8443.11,8251.38,8402.36,1460200000,8402.36 2003-04-14,8203.97,8375.19,8175.60,8351.10,1131000000,8351.10 2003-04-11,8223.22,8360.76,8156.77,8203.41,1141600000,8203.41 2003-04-10,8198.99,8274.56,8109.85,8221.33,1275300000,8221.33 2003-04-09,8299.28,8404.25,8174.90,8197.94,1293700000,8197.94 2003-04-08,8299.12,8382.43,8222.24,8298.92,1235400000,8298.92 2003-04-07,8284.15,8550.40,8272.24,8300.41,1494000000,8300.41 2003-04-04,8240.59,8348.29,8176.66,8277.15,1241200000,8277.15 2003-04-03,8285.76,8378.76,8199.49,8240.38,1351500000,8240.38 2003-04-02,8070.98,8342.27,8070.98,8285.06,1589800000,8285.06 2003-04-01,7992.83,8133.03,7947.38,8069.86,1461600000,8069.86 2003-03-31,8142.83,8142.83,7903.97,7992.13,1495500000,7992.13 2003-03-28,8198.85,8224.83,8070.77,8145.77,1227000000,8145.77 2003-03-27,8226.39,8272.03,8085.40,8201.45,1232900000,8201.45 2003-03-26,8279.88,8323.01,8165.52,8229.88,1319700000,8229.88 2003-03-25,8216.85,8355.93,8155.65,8280.23,1333400000,8280.23 2003-03-24,8514.82,8514.82,8166.78,8214.68,1293000000,8214.68 2003-03-21,8290.38,8552.08,8290.38,8521.97,1883710000,8521.97 2003-03-20,8264.68,8335.20,8122.59,8286.60,1439100000,8286.60 2003-03-19,8193.04,8304.04,8116.01,8265.45,1473400000,8265.45 2003-03-18,8142.69,8253.48,8057.54,8194.23,1555100000,8194.23 2003-03-17,7857.96,8163.56,7763.56,8141.92,1700420000,8141.92 2003-03-14,7822.17,7961.60,7761.25,7859.71,1541900000,7859.71 2003-03-13,7555.29,7847.03,7555.29,7821.75,1816300000,7821.75 2003-03-12,7517.76,7582.96,7397.31,7552.07,1620000000,7552.07 2003-03-11,7568.53,7673.98,7488.00,7524.06,1427700000,7524.06 2003-03-10,7739.40,7739.40,7545.77,7568.18,1255000000,7568.18 2003-03-07,7671.75,7780.57,7536.18,7740.03,1368500000,7740.03 2003-03-06,7774.76,7795.07,7624.97,7673.99,1299200000,7673.99 2003-03-05,7702.35,7801.79,7639.82,7775.60,1332700000,7775.60 2003-03-04,7838.14,7859.08,7688.98,7704.87,1256600000,7704.87 2003-03-03,7890.24,7997.66,7809.05,7837.86,1208900000,7837.86 2003-02-28,7886.11,7987.80,7826.72,7891.08,1373300000,7891.08 2003-02-27,7807.96,7950.46,7774.34,7884.99,1287800000,7884.99 2003-02-26,7907.39,7944.93,7767.62,7806.98,1374400000,7806.98 2003-02-25,7856.42,7931.14,7700.53,7909.50,1483700000,7909.50 2003-02-24,8017.34,8017.34,7828.06,7858.24,1229200000,7858.24 2003-02-21,7915.52,8055.79,7843.81,8018.11,1398200000,8018.11 2003-02-20,8002.70,8051.37,7858.24,7914.96,1194100000,7914.96 2003-02-19,8033.80,8079.11,7913.70,8000.60,1075600000,8000.60 2003-02-18,7909.30,8114.82,7909.30,8041.15,1250800000,8041.15 2003-02-14,7750.90,7936.56,7704.96,7908.80,1404600000,7908.80 2003-02-13,7756.55,7817.88,7602.81,7749.87,1489300000,7749.87 2003-02-12,7836.36,7892.96,7720.39,7758.17,1260500000,7758.17 2003-02-11,7920.93,8010.89,7798.69,7843.11,1307000000,7843.11 2003-02-10,7865.74,7963.03,7777.98,7920.11,1238200000,7920.11 2003-02-07,7932.45,8019.46,7811.10,7864.23,1276800000,7864.23 2003-02-06,7981.95,8031.66,7855.87,7929.30,1430900000,7929.30 2003-02-05,8014.45,8162.96,7950.42,7985.18,1450800000,7985.18 2003-02-04,8104.61,8104.61,7915.93,8013.29,1451600000,8013.29 2003-02-03,8053.74,8189.35,8032.90,8109.82,1258500000,8109.82 2003-01-31,7939.72,8121.37,7884.66,8053.81,1578530000,8053.81 2003-01-30,8109.14,8169.81,7918.19,7945.13,1510300000,7945.13 2003-01-29,8087.95,8173.31,7916.89,8110.71,1595400000,8110.71 2003-01-28,7991.07,8153.36,7954.95,8088.84,1459100000,8088.84 2003-01-27,8128.54,8167.41,7929.16,7989.56,1435900000,7989.56 2003-01-24,8367.89,8367.89,8092.00,8131.01,1574800000,8131.01 2003-01-23,8320.72,8437.69,8215.61,8369.47,1744550000,8369.47 2003-01-22,8439.54,8493.50,8270.94,8318.73,1560800000,8318.73 2003-01-21,8586.26,8650.43,8421.03,8442.90,1335200000,8442.90 2003-01-17,8695.82,8695.82,8523.60,8586.74,1358200000,8586.74 2003-01-16,8721.12,8837.47,8634.46,8697.87,1534600000,8697.87 2003-01-15,8843.64,8865.65,8674.43,8723.18,1432100000,8723.18 2003-01-14,8787.22,8865.41,8717.56,8842.62,1379400000,8842.62 2003-01-13,8787.83,8896.09,8721.12,8785.98,1396300000,8785.98 2003-01-10,8776.04,8846.25,8654.21,8784.89,1485400000,8784.89 2003-01-09,8596.68,8814.09,8596.68,8776.18,1560300000,8776.18 2003-01-08,8735.93,8749.44,8549.72,8595.31,1467600000,8595.31 2003-01-07,8775.84,8843.37,8661.20,8740.59,1545200000,8740.59 2003-01-06,8602.78,8826.71,8578.86,8773.57,1435900000,8773.57 2003-01-03,8607.38,8669.91,8503.71,8601.69,1130800000,8601.69 2003-01-02,8342.38,8633.02,8342.38,8607.52,1229200000,8607.52 2002-12-31,8332.24,8400.46,8216.44,8341.63,1088500000,8341.63 2002-12-30,8304.06,8405.67,8214.93,8332.85,1057800000,8332.85 2002-12-27,8429.28,8470.05,8272.31,8303.78,758400000,8303.78 2002-12-26,8448.86,8587.98,8392.23,8432.61,721100000,8432.61 2002-12-24,8491.99,8522.98,8407.45,8448.11,458310000,8448.11 2002-12-23,8511.39,8573.92,8418.90,8493.29,1112100000,8493.29 2002-12-20,8367.41,8557.47,8367.41,8511.32,1782730000,8511.32 2002-12-19,8441.94,8530.25,8302.41,8364.80,1385900000,8364.80 2002-12-18,8531.31,8553.76,8367.89,8447.35,1446200000,8447.35 2002-12-17,8626.99,8672.38,8495.21,8535.39,1251800000,8535.39 2002-12-16,8436.59,8649.06,8421.58,8627.40,1271600000,8627.40 2002-12-13,8536.07,8563.16,8374.68,8433.71,1330800000,8433.71 2002-12-12,8590.99,8662.71,8466.21,8538.40,1255300000,8538.40 2002-12-11,8571.52,8669.91,8452.84,8589.14,1285100000,8589.14 2002-12-10,8473.61,8624.93,8419.86,8574.26,1286600000,8574.26 2002-12-09,8643.99,8643.99,8438.24,8473.41,1320800000,8473.41 2002-12-06,8620.88,8707.21,8469.16,8645.77,1241100000,8645.77 2002-12-05,8740.66,8796.68,8572.00,8623.28,1250200000,8623.28 2002-12-04,8734.22,8834.04,8600.93,8737.85,1588900000,8737.85 2002-12-03,8861.13,8882.04,8649.89,8742.93,1488400000,8742.93 2002-12-02,8902.95,9076.35,8757.60,8862.57,1612000000,8862.57 2002-11-29,8933.67,8995.78,8847.42,8896.09,643460000,8896.09 2002-11-27,8678.96,8975.08,8678.96,8931.68,1350300000,8931.68 2002-11-26,8844.12,8845.01,8634.53,8676.42,1543600000,8676.42 2002-11-25,8804.97,8918.03,8717.63,8849.40,1574000000,8849.40 2002-11-22,8842.41,8944.16,8732.23,8804.84,1626800000,8804.84 2002-11-21,8625.48,8910.83,8619.58,8845.15,2415100000,8845.15 2002-11-20,8469.57,8675.12,8402.72,8623.01,1517300000,8623.01 2002-11-19,8484.93,8566.45,8355.62,8474.78,1337400000,8474.78 2002-11-18,8579.74,8671.41,8444.26,8486.57,1282600000,8486.57 2002-11-15,8535.64,8622.30,8421.10,8579.09,1400100000,8579.09 2002-11-14,8403.69,8596.50,8396.27,8542.13,1488100000,8542.13 2002-11-13,8380.32,8523.47,8237.65,8398.49,1463400000,8398.49 2002-11-12,8356.73,8557.25,8286.13,8386.00,1377100000,8386.00 2002-11-11,8535.81,8541.09,8315.40,8358.95,1113000000,8358.95 2002-11-08,8585.75,8688.96,8455.01,8537.13,1446500000,8537.13 2002-11-07,8766.08,8766.08,8517.78,8586.24,1466900000,8586.24 2002-11-06,8677.17,8841.61,8561.48,8771.01,1623700000,8771.01 2002-11-05,8568.76,8730.92,8497.60,8678.27,1354100000,8678.27 2002-11-04,8521.60,8787.30,8510.08,8571.60,1645900000,8571.60 2002-11-01,8395.64,8569.24,8271.77,8517.64,1450400000,8517.64 2002-10-31,8427.34,8538.17,8293.17,8397.03,1641300000,8397.03 2002-10-30,8363.95,8502.32,8273.99,8427.41,1422300000,8427.41 2002-10-29,8367.28,8456.19,8161.01,8368.94,1529700000,8368.94 2002-10-28,8448.98,8601.01,8281.34,8368.04,1382600000,8368.04 2002-10-25,8317.48,8474.92,8210.74,8443.99,1340400000,8443.99 2002-10-24,8495.38,8607.04,8253.60,8317.34,1700570000,8317.34 2002-10-23,8448.56,8546.57,8256.79,8494.27,1593900000,8494.27 2002-10-22,8534.08,8543.65,8303.33,8450.16,1549200000,8450.16 2002-10-21,8320.74,8580.13,8191.87,8538.24,1447000000,8538.24 2002-10-18,8287.72,8383.16,8115.72,8322.40,1423100000,8322.40 2002-10-17,8038.31,8395.99,8038.31,8275.04,1780390000,8275.04 2002-10-16,8232.10,8232.10,7958.34,8036.03,1585000000,8036.03 2002-10-15,7883.23,8304.58,7883.23,8255.68,1956000000,8255.68 2002-10-14,7848.21,7948.91,7725.23,7877.40,1200300000,7877.40 2002-10-11,7540.74,7919.57,7540.74,7850.29,1854130000,7850.29 2002-10-10,7286.34,7588.25,7181.47,7533.95,2090230000,7533.95 2002-10-09,7499.96,7500.03,7215.39,7286.27,1885030000,7286.27 2002-10-08,7425.82,7680.57,7294.53,7501.49,1938430000,7501.49 2002-10-07,7528.68,7685.42,7368.46,7422.84,1576500000,7422.84 2002-10-04,7719.34,7817.06,7428.32,7528.40,1835930000,7528.40 2002-10-03,7753.46,7943.64,7638.47,7717.19,1674500000,7717.19 2002-10-02,7936.57,7996.77,7696.66,7755.61,1668900000,7755.61 2002-10-01,7593.04,7964.24,7558.36,7938.79,1780900000,7938.79 2002-09-30,7698.81,7729.53,7422.28,7591.93,1721870000,7591.93 2002-09-27,7996.01,7997.12,7664.89,7701.45,1507300000,7701.45 2002-09-26,7844.62,8086.86,7800.97,7997.12,1650000000,7997.12 2002-09-25,7687.16,7939.90,7641.87,7841.82,1651500000,7841.82 2002-09-24,7871.23,7893.36,7606.77,7683.13,1670240000,7683.13 2002-09-23,7984.77,7984.77,7738.06,7872.15,1381100000,7872.15 2002-09-20,7945.93,8081.04,7868.60,7986.02,1792800000,7986.02 2002-09-19,8170.65,8170.65,7904.87,7942.39,1524000000,7942.39 2002-09-18,8203.07,8283.49,8013.42,8172.45,1501000000,8172.45 2002-09-17,8386.35,8508.61,8169.88,8207.55,1448600000,8207.55 2002-09-16,8311.79,8435.04,8214.27,8380.18,1001400000,8380.18 2002-09-13,8377.68,8414.79,8175.85,8312.69,1271000000,8312.69 2002-09-12,8574.94,8574.94,8334.82,8379.41,1191600000,8379.41 2002-09-11,8604.27,8767.82,8545.11,8581.17,846600000,8581.17 2002-09-10,8520.14,8660.94,8447.73,8602.61,1186400000,8602.61 2002-09-09,8425.88,8584.30,8288.28,8519.38,1130600000,8519.38 2002-09-06,8296.46,8526.80,8296.46,8427.20,1184500000,8427.20 2002-09-05,8420.20,8420.20,8173.56,8283.70,1401300000,8283.70 2002-09-04,8308.53,8495.03,8216.98,8425.12,1372100000,8425.12 2002-09-03,8659.27,8659.27,8282.87,8308.05,1323400000,8308.05 2002-08-30,8669.26,8811.72,8572.85,8663.50,929900000,8663.50 2002-08-29,8690.69,8769.34,8514.10,8670.99,1271100000,8670.99 2002-08-28,8823.93,8832.18,8610.79,8694.09,1146600000,8694.09 2002-08-27,8917.49,9040.04,8747.77,8824.41,1307700000,8824.41 2002-08-26,8873.93,8981.23,8723.43,8919.01,1016900000,8919.01 2002-08-23,9051.49,9051.49,8806.38,8872.96,1071500000,8872.96 2002-08-22,8961.18,9129.10,8860.34,9053.64,1373000000,9053.64 2002-08-21,8866.14,9033.52,8768.51,8957.23,1353100000,8957.23 2002-08-20,8986.50,8989.69,8789.13,8872.07,1308500000,8872.07 2002-08-19,8777.09,9037.38,8720.81,8990.79,1299800000,8990.79 2002-08-16,8813.07,8899.42,8644.59,8778.06,1265300000,8778.06 2002-08-15,8745.04,8914.37,8620.98,8818.14,1505100000,8818.14 2002-08-14,8479.14,8778.89,8295.34,8743.31,1533800000,8743.31 2002-08-13,8683.15,8801.87,8445.91,8482.39,1297700000,8482.39 2002-08-12,8741.92,8753.14,8528.15,8688.89,1036500000,8688.89 2002-08-09,8707.24,8824.92,8538.46,8745.45,1294900000,8745.45 2002-08-08,8456.29,8755.70,8364.29,8712.02,1646700000,8712.02 2002-08-07,8282.25,8520.95,8171.70,8456.15,1490400000,8456.15 2002-08-06,8049.93,8472.28,8049.93,8274.09,1514100000,8274.09 2002-08-05,8312.92,8371.00,7991.43,8043.63,1425500000,8043.63 2002-08-02,8504.96,8566.36,8179.80,8313.13,1538100000,8313.13 2002-08-01,8732.58,8758.40,8430.68,8506.62,1672200000,8506.62 2002-07-31,8678.65,8793.36,8463.21,8736.59,2049360000,8736.59 2002-07-30,8707.03,8806.86,8484.05,8680.03,1826090000,8680.03 2002-07-29,8267.99,8749.12,8267.99,8711.88,1778650000,8711.88 2002-07-26,8192.61,8350.10,8039.89,8264.39,1796100000,8264.39 2002-07-25,8185.89,8390.39,7893.34,8186.31,2424700000,8186.31 2002-07-24,7698.46,8243.07,7489.53,8191.29,2775560000,8191.29 2002-07-23,7785.55,8007.91,7590.75,7702.34,2441020000,7702.34 2002-07-22,8015.04,8173.08,7668.35,7784.58,2248060000,7784.58 2002-07-19,8356.74,8356.74,7940.83,8019.26,2654100000,8019.26 2002-07-18,8540.47,8683.84,8350.72,8409.49,1736300000,8409.49 2002-07-17,8476.21,8765.39,8401.12,8542.48,2566500000,8542.48 2002-07-16,8635.31,8697.69,8346.29,8473.11,1843700000,8473.11 2002-07-15,8681.28,8720.18,8220.78,8639.19,2574800000,8639.19 2002-07-12,8805.33,8903.00,8555.15,8684.53,1607400000,8684.53 2002-07-11,8812.12,8937.87,8557.84,8801.53,2080480000,8801.53 2002-07-10,9098.16,9188.71,8772.94,8813.50,1816900000,8813.50 2002-07-09,9273.38,9357.35,9065.88,9096.09,1348900000,9096.09 2002-07-08,9375.70,9433.08,9184.90,9274.90,1184400000,9274.90 2002-07-05,9061.54,9399.65,9054.97,9379.50,699400000,9379.50 2002-07-03,9006.37,9140.32,8832.89,9054.97,1527800000,9054.97 2002-07-02,9104.95,9185.88,8918.11,9007.75,1823000000,9007.75 2002-07-01,9239.25,9381.37,9059.88,9109.79,1425500000,9109.79 2002-06-28,9270.33,9435.44,9131.49,9243.26,2117000000,9243.26 2002-06-27,9122.12,9342.33,8992.32,9269.92,1908600000,9269.92 2002-06-26,9108.22,9207.07,8831.92,9120.11,336570000,9120.11 2002-06-25,9285.56,9457.38,9089.17,9126.82,1513700000,9126.82 2002-06-24,9252.47,9417.23,9046.04,9281.82,1552600000,9281.82 2002-06-21,9430.66,9456.76,9186.71,9253.79,1497200000,9253.79 2002-06-20,9561.64,9628.11,9390.10,9431.77,1389700000,9431.77 2002-06-19,9702.00,9760.20,9514.29,9561.57,1336100000,9561.57 2002-06-18,9684.52,9775.83,9588.29,9706.12,1193100000,9706.12 2002-06-17,9476.50,9736.58,9462.30,9687.42,1236600000,9687.42 2002-06-14,9498.92,9538.93,9229.63,9474.21,1549000000,9474.21 2002-06-13,9612.87,9671.64,9454.41,9502.80,1405500000,9502.80 2002-06-12,9515.12,9682.37,9380.82,9617.71,1795720000,9617.71 2002-06-11,9647.62,9794.17,9487.91,9517.26,1212400000,9517.26 2002-06-10,9587.38,9744.33,9509.91,9645.40,1226200000,9645.40 2002-06-07,9592.38,9668.18,9416.33,9589.67,1341300000,9589.67 2002-06-06,9795.70,9820.41,9552.85,9624.64,1601500000,9624.64 2002-06-05,9688.53,9860.91,9636.82,9796.80,1300100000,9796.80 2002-06-04,9710.34,9798.74,9541.36,9687.84,1466600000,9687.84 2002-06-03,9923.94,10016.04,9685.49,9709.79,1324300000,9709.79 2002-05-31,9915.15,10074.16,9865.89,9925.25,1277300000,9925.25 2002-05-30,9915.01,9995.76,9769.64,9911.69,1286600000,9911.69 2002-05-29,9976.94,10056.31,9860.42,9923.04,1081800000,9923.04 2002-05-28,10106.54,10144.53,9917.64,9981.58,996500000,9981.58 2002-05-24,10211.92,10255.93,10054.58,10104.26,885400000,10104.26 2002-05-23,10158.30,10268.87,10044.20,10216.08,1192900000,10216.08 2002-05-22,10098.58,10200.78,10004.41,10157.88,1136300000,10157.88 2002-05-21,10229.08,10322.15,10060.46,10105.71,1169200000,10105.71 2002-05-20,10348.93,10357.44,10164.39,10229.50,989800000,10229.50 2002-05-17,10291.05,10400.62,10209.49,10353.08,1274400000,10353.08 2002-05-16,10242.11,10374.05,10168.64,10289.21,1256600000,10289.21 2002-05-15,10288.56,10382.97,10152.97,10243.68,1420200000,10243.68 2002-05-14,10119.34,10346.59,10119.34,10298.14,1414500000,10298.14 2002-05-13,9938.82,10148.71,9892.73,10109.66,1088600000,10109.66 2002-05-10,10040.25,10115.23,9891.04,9939.92,1171900000,9939.92 2002-05-09,10137.96,10185.08,9966.63,10037.42,1153000000,10037.42 2002-05-08,9847.96,10203.76,9847.96,10141.83,1502000000,10141.83 2002-05-07,9810.53,9985.32,9749.73,9836.55,1354700000,9836.55 2002-05-06,10005.80,10081.98,9780.29,9808.04,1122600000,9808.04 2002-05-03,10091.73,10130.97,9891.49,10006.63,1284500000,10006.63 2002-05-02,10057.62,10182.94,9970.92,10091.87,1364000000,10091.87 2002-05-01,9944.90,10121.21,9778.42,10059.63,1451400000,10059.63 2002-04-30,9818.90,10063.64,9775.10,9946.22,1628600000,9946.22 2002-04-29,9910.52,10012.16,9767.15,9819.87,1314700000,9819.87 2002-04-26,10037.42,10127.85,9875.44,9910.72,1374200000,9910.72 2002-04-25,10028.70,10103.64,9864.08,10035.06,1517400000,10035.06 2002-04-24,10090.07,10209.64,9984.00,10030.43,1373200000,10030.43 2002-04-23,10137.20,10243.06,10003.84,10089.24,1388500000,10089.24 2002-04-22,10256.00,10299.39,10056.45,10136.43,1181800000,10136.43 2002-04-19,10212.69,10338.83,10151.52,10257.11,1185000000,10257.11 2002-04-18,10219.47,10334.67,10010.22,10205.28,1359300000,10205.28 2002-04-17,10299.66,10379.51,10137.47,10220.78,1376900000,10220.78 2002-04-16,10100.38,10365.12,10100.38,10301.32,1341300000,10301.32 2002-04-15,10189.57,10261.05,10037.90,10093.67,1120400000,10093.67 2002-04-12,10178.57,10312.26,10083.92,10190.82,1282100000,10190.82 2002-04-11,10378.89,10425.87,10116.37,10176.08,1505600000,10176.08 2002-04-10,10210.40,10437.43,10175.18,10381.73,1447900000,10381.73 2002-04-09,10249.84,10362.98,10156.57,10208.67,1235400000,10208.67 2002-04-08,10258.91,10300.78,10049.94,10249.08,1095300000,10249.08 2002-04-05,10235.80,10403.66,10169.79,10271.64,1110200000,10271.64 2002-04-04,10199.54,10301.53,10118.10,10235.17,1283800000,10235.17 2002-04-03,10311.81,10377.09,10116.02,10198.29,1219700000,10198.29 2002-04-02,10352.46,10394.94,10204.66,10313.71,1176700000,10313.71 2002-04-01,10402.07,10434.52,10226.59,10362.70,1050900000,10362.70 2002-03-28,10429.68,10537.48,10341.59,10403.94,1147600000,10403.94 2002-03-27,10351.28,10490.15,10300.29,10426.91,1180100000,10426.91 2002-03-26,10280.51,10475.00,10233.65,10353.36,1223600000,10353.36 2002-03-25,10428.43,10497.76,10255.59,10281.67,1057900000,10281.67 2002-03-22,10477.70,10537.62,10324.23,10427.67,1243300000,10427.67 2002-03-21,10501.99,10577.82,10326.99,10479.84,1339200000,10479.84 2002-03-20,10626.85,10634.84,10455.56,10501.57,1304900000,10501.57 2002-03-19,10578.38,10722.78,10530.63,10635.25,1255000000,10635.25 2002-03-18,10608.54,10707.01,10488.84,10577.75,1169500000,10577.75 2002-03-15,10516.45,10663.69,10452.10,10607.23,1493900000,10607.23 2002-03-14,10501.29,10615.74,10421.17,10517.14,1208800000,10517.14 2002-03-13,10620.17,10648.68,10427.67,10501.85,1354000000,10501.85 2002-03-12,10604.32,10682.72,10462.34,10632.35,1304400000,10632.35 2002-03-11,10570.07,10679.68,10470.85,10611.24,1210200000,10611.24 2002-03-08,10531.67,10728.87,10480.33,10572.49,1412000000,10572.49 2002-03-07,10578.10,10663.82,10405.95,10525.37,1517400000,10525.37 2002-03-06,10431.96,10637.19,10393.84,10574.29,1541300000,10574.29 2002-03-05,10591.38,10639.96,10349.90,10433.41,1549300000,10433.41 2002-03-04,10368.10,10656.50,10313.01,10586.82,1594300000,10586.82 2002-03-01,10111.04,10397.09,10086.51,10368.86,1456500000,10368.86 2002-02-28,10130.28,10283.89,10055.34,10106.13,1392200000,10106.13 2002-02-27,10117.65,10315.72,10025.86,10127.58,1393800000,10127.58 2002-02-26,10145.86,10241.89,9986.84,10115.26,1309200000,10115.26 2002-02-25,9969.75,10204.04,9934.94,10145.71,1367400000,10145.71 2002-02-22,9834.89,10032.45,9726.67,9968.15,1411000000,9968.15 2002-02-21,9933.56,10072.98,9788.11,9834.68,1381600000,9834.68 2002-02-20,9742.37,9990.78,9674.91,9941.17,1438900000,9941.17 2002-02-19,9899.24,9923.39,9704.03,9745.14,1189900000,9745.14 2002-02-15,10000.83,10065.37,9843.54,9903.04,1359200000,9903.04 2002-02-14,9989.67,10092.29,9905.95,10001.99,1272500000,10001.99 2002-02-13,9856.99,10056.24,9839.18,9989.67,1215900000,9989.67 2002-02-12,9880.35,9943.24,9766.18,9863.74,1094200000,9863.74 2002-02-11,9739.81,9933.07,9668.34,9884.78,1159400000,9884.78 2002-02-08,9627.65,9795.38,9503.52,9744.24,1371900000,9744.24 2002-02-07,9650.97,9799.67,9562.12,9625.44,1441600000,9625.44 2002-02-06,9682.04,9801.33,9558.18,9653.39,1665800000,9653.39 2002-02-05,9684.74,9842.77,9553.96,9685.43,1778300000,9685.43 2002-02-04,9905.46,9940.96,9648.55,9687.09,1437600000,9687.09 2002-02-01,9923.04,10022.82,9795.45,9907.26,1367200000,9907.26 2002-01-31,9763.20,9963.79,9701.76,9920.00,1557000000,9920.00 2002-01-30,9619.14,9821.81,9443.32,9762.86,2019600000,9762.86 2002-01-29,9865.54,9952.59,9576.65,9618.24,1812000000,9618.24 2002-01-28,9843.05,9959.44,9746.66,9865.75,1186800000,9865.75 2002-01-25,9793.23,9949.54,9697.47,9840.08,1345100000,9840.08 2002-01-24,9734.21,9926.71,9670.99,9796.07,1552800000,9796.07 2002-01-23,9710.96,9853.64,9588.49,9730.96,1479200000,9730.96 2002-01-22,9772.34,9905.26,9652.01,9713.80,1311600000,9713.80 2002-01-18,9830.94,9873.98,9673.11,9771.85,1333300000,9771.85 2002-01-17,9712.21,9910.11,9684.39,9850.04,1380100000,9850.04 2002-01-16,9916.54,9923.32,9661.00,9712.27,1482500000,9712.27 2002-01-15,9892.73,10038.94,9805.33,9924.15,1386900000,9924.15 2002-01-14,9985.38,10038.87,9831.98,9891.42,1286400000,9891.42 2002-01-11,10069.52,10163.77,9938.12,9987.53,1211900000,9987.53 2002-01-10,10092.50,10174.91,9956.67,10067.86,1299000000,10067.86 2002-01-09,10153.18,10311.98,10049.25,10094.09,1452000000,10094.09 2002-01-08,10195.76,10270.53,10063.43,10150.55,1258800000,10150.55 2002-01-07,10261.33,10345.40,10137.61,10197.05,1308300000,10197.05 2002-01-04,10176.84,10341.87,10132.14,10259.74,1513000000,10259.74 2002-01-03,10073.88,10227.36,10002.54,10172.14,1398900000,10172.14 2002-01-02,10021.71,10125.85,9889.69,10073.40,1171000000,10073.40 2001-12-31,10136.36,10178.71,10002.96,10021.57,943600000,10021.57 2001-12-28,10133.94,10220.78,10067.17,10136.99,917400000,10136.99 2001-12-27,10088.71,10187.71,10036.10,10131.31,876300000,10131.31 2001-12-26,10035.55,10203.28,10014.10,10088.14,791100000,10088.14 2001-12-24,10036.59,10114.91,9987.39,10035.34,439670000,10035.34 2001-12-21,9986.84,10148.13,9935.70,10035.34,1694000000,10035.34 2001-12-20,10064.13,10141.21,9912.76,9985.18,1490500000,9985.18 2001-12-19,9994.59,10142.95,9876.96,10070.49,1484900000,10070.49 2001-12-18,9893.22,10066.27,9876.19,9998.39,1354000000,9998.39 2001-12-17,9809.42,9996.25,9747.77,9891.97,1260400000,9891.97 2001-12-14,9764.72,9888.44,9661.14,9811.15,1306800000,9811.15 2001-12-13,9889.13,9927.95,9691.30,9766.45,1511500000,9766.45 2001-12-12,9887.27,9985.59,9745.42,9894.81,1449700000,9894.81 2001-12-11,9925.60,10063.98,9794.48,9888.37,1367200000,9888.37 2001-12-10,10047.04,10123.78,9868.03,9921.45,1218700000,9921.45 2001-12-07,10099.14,10160.24,9938.54,10049.46,1248200000,10049.46 2001-12-06,10113.53,10220.23,9997.98,10099.14,1487900000,10099.14 2001-12-05,9891.35,10195.04,9875.92,10114.29,1765300000,10114.29 2001-12-04,9765.55,9937.29,9700.24,9893.84,1318500000,9893.84 2001-12-03,9848.93,9861.94,9651.87,9763.96,1202900000,9763.96 2001-11-30,9828.80,9945.80,9752.26,9851.56,1343600000,9851.56 2001-11-29,9710.34,9873.29,9629.72,9829.42,1375700000,9829.42 2001-11-28,9867.06,9889.13,9662.80,9711.86,1423700000,9711.86 2001-11-27,9980.33,10021.48,9776.07,9872.60,1288000000,9872.60 2001-11-26,9961.58,10054.58,9862.22,9982.75,1129800000,9982.75 2001-11-23,9833.09,9983.24,9804.37,9959.71,410300000,9959.71 2001-11-21,9894.19,9932.31,9746.45,9834.68,1029300000,9834.68 2001-11-20,9968.64,10023.37,9825.06,9901.38,1330200000,9901.38 2001-11-19,9870.45,10040.46,9826.96,9976.46,1316800000,9976.46 2001-11-16,9871.51,9967.94,9754.07,9866.99,1337400000,9866.99 2001-11-15,9824.65,9967.46,9745.43,9872.39,1454500000,9872.39 2001-11-14,9751.13,9943.18,9683.97,9823.61,1443400000,9823.61 2001-11-13,9551.43,9811.29,9551.43,9750.95,1370100000,9750.95 2001-11-12,9606.13,9642.25,9347.76,9554.37,991600000,9554.37 2001-11-09,9586.96,9692.35,9478.75,9608.00,1093800000,9608.00 2001-11-08,9558.39,9765.00,9506.91,9587.52,1517500000,9587.52 2001-11-07,9584.68,9695.67,9457.99,9554.37,1411300000,9554.37 2001-11-06,9437.09,9627.44,9315.79,9591.12,1356000000,9591.12 2001-11-05,9326.59,9534.58,9326.59,9441.03,1267700000,9441.03 2001-11-02,9264.52,9406.93,9152.91,9323.54,1121900000,9323.54 2001-11-01,9087.45,9320.77,8987.61,9263.90,1317400000,9263.90 2001-10-31,9123.64,9281.68,9018.26,9075.14,1352500000,9075.14 2001-10-30,9264.52,9265.34,9011.96,9121.98,1297400000,9121.98 2001-10-29,9543.37,9543.37,9232.83,9269.50,1106100000,9269.50 2001-10-26,9462.28,9626.54,9369.35,9545.17,1244500000,9545.17 2001-10-25,9342.29,9491.48,9143.09,9462.90,1364400000,9462.90 2001-10-24,9341.40,9456.40,9218.29,9345.62,1336200000,9345.62 2001-10-23,9379.17,9499.78,9249.02,9340.08,1317300000,9340.08 2001-10-22,9203.91,9438.75,9101.08,9377.03,1105700000,9377.03 2001-10-19,9162.81,9278.36,9027.74,9204.11,1294900000,9204.11 2001-10-18,9230.75,9310.33,9061.02,9163.22,1262900000,9163.22 2001-10-17,9389.76,9539.22,9199.89,9232.97,1452200000,9232.97 2001-10-16,9346.31,9479.37,9239.68,9384.23,1210500000,9384.23 2001-10-15,9340.84,9417.51,9181.07,9347.62,1024700000,9347.62 2001-10-12,9409.07,9426.30,9146.34,9344.16,1331400000,9344.16 2001-10-11,9242.63,9522.61,9204.04,9410.45,1704580000,9410.45 2001-10-10,9052.30,9305.97,8975.15,9240.86,1312400000,9240.86 2001-10-09,9066.56,9168.42,8927.34,9052.44,1227800000,9052.44 2001-10-08,9115.75,9187.85,8937.86,9067.94,979000000,9067.94 2001-10-05,9058.83,9208.41,8894.47,9119.77,1301700000,9119.77 2001-10-04,9127.24,9259.61,8982.28,9060.88,1609100000,9060.88 2001-10-03,8946.02,9193.32,8800.99,9123.78,1650600000,9123.78 2001-10-02,8836.69,9001.03,8737.61,8950.59,1289800000,8950.59 2001-10-01,8845.97,8931.70,8659.90,8836.83,1175600000,8836.83 2001-09-28,8679.07,8945.68,8633.75,8847.56,1727400000,8847.56 2001-09-27,8567.46,8757.47,8398.14,8681.42,1467000000,8681.42 2001-09-26,8660.06,8766.81,8457.37,8567.39,1519100000,8567.39 2001-09-25,8605.59,8778.23,8435.56,8659.97,1613800000,8659.97 2001-09-24,8242.32,8733.39,8242.32,8603.86,1746600000,8603.86 2001-09-21,8356.56,8484.22,7926.93,8235.81,2317300000,8235.81 2001-09-20,8375.72,8711.38,8304.45,8376.21,2004800000,8376.21 2001-09-19,8903.54,8990.37,8453.01,8759.13,2120550000,8759.13 2001-09-18,8922.70,9126.89,8743.91,8903.40,1650410000,8903.40 2001-09-17,9294.55,9294.55,8755.46,8920.70,2330830000,8920.70 2001-09-10,9603.36,9740.44,9431.07,9605.51,1276600000,9605.51 2001-09-07,9841.25,9842.08,9507.04,9605.85,1424300000,9605.85 2001-09-06,10028.35,10053.73,9762.03,9840.84,1359700000,9840.84 2001-09-05,9998.12,10140.79,9820.98,10033.27,1384500000,10033.27 2001-09-04,9946.98,10238.50,9858.34,9997.49,1178300000,9997.49 2001-08-31,9918.96,10072.22,9846.72,9949.75,920100000,9949.75 2001-08-30,10077.07,10149.10,9829.35,9919.58,1157000000,9919.58 2001-08-29,10224.45,10292.60,10030.43,10090.90,963700000,10090.90 2001-08-28,10382.56,10405.88,10175.60,10222.03,987100000,10222.03 2001-08-27,10422.76,10498.03,10334.88,10382.35,842600000,10382.35 2001-08-24,10232.48,10487.52,10190.34,10423.17,1043600000,10423.17 2001-08-23,10276.41,10357.09,10142.66,10229.15,986200000,10229.15 2001-08-22,10170.30,10340.76,10099.07,10276.90,1110800000,10276.90 2001-08-21,10320.07,10436.39,10132.92,10174.14,1041600000,10174.14 2001-08-20,10239.33,10388.23,10146.05,10320.07,897100000,10320.07 2001-08-17,10385.46,10418.68,10143.49,10240.78,974300000,10240.78 2001-08-16,10342.10,10460.82,10198.15,10392.52,1055400000,10392.52 2001-08-15,10407.05,10530.36,10289.01,10345.95,1065600000,10345.95 2001-08-14,10416.95,10513.68,10333.29,10412.17,964600000,10412.17 2001-08-13,10411.90,10504.82,10314.95,10415.91,837600000,10415.91 2001-08-10,10296.89,10473.34,10164.67,10416.25,960900000,10416.25 2001-08-09,10291.15,10361.52,10160.51,10298.56,1104200000,10298.56 2001-08-08,10456.18,10509.80,10245.68,10293.50,1124600000,10293.50 2001-08-07,10399.03,10520.11,10324.50,10458.74,1012000000,10458.74 2001-08-06,10504.13,10549.59,10337.23,10401.31,811700000,10401.31 2001-08-03,10550.01,10592.98,10381.10,10512.78,939900000,10512.78 2001-08-02,10513.47,10663.07,10454.53,10551.18,1218300000,10551.18 2001-08-01,10527.38,10659.33,10423.31,10510.01,1340300000,10510.01 2001-07-31,10403.18,10639.40,10364.84,10522.81,1129200000,10522.81 2001-07-30,10418.68,10513.26,10301.05,10401.72,909100000,10401.72 2001-07-27,10451.89,10516.38,10316.27,10416.67,1015300000,10416.67 2001-07-26,10403.46,10498.73,10237.46,10455.63,1213900000,10455.63 2001-07-25,10241.75,10466.28,10159.34,10405.67,1280700000,10405.67 2001-07-24,10423.80,10469.40,10170.82,10241.12,1198700000,10241.12 2001-07-23,10576.92,10644.73,10374.81,10424.42,986900000,10424.42 2001-07-20,10606.19,10668.33,10456.25,10576.65,1170900000,10576.65 2001-07-19,10574.33,10758.14,10480.54,10610.00,1343500000,10610.00 2001-07-18,10594.54,10676.83,10374.55,10569.83,1316300000,10569.83 2001-07-17,10468.62,10683.76,10363.51,10606.39,1238100000,10606.39 2001-07-16,10537.98,10649.02,10374.55,10472.12,1039800000,10472.12 2001-07-13,10478.39,10615.42,10374.01,10539.06,1121700000,10539.06 2001-07-12,10269.31,10542.02,10249.58,10478.99,1394000000,10478.99 2001-07-11,10174.70,10355.83,10049.38,10241.02,1384100000,10241.02 2001-07-10,10300.82,10406.87,10104.06,10175.64,1263800000,10175.64 2001-07-09,10253.62,10389.91,10166.55,10299.40,1045700000,10299.40 2001-07-06,10476.73,10483.82,10176.26,10252.68,1056700000,10252.68 2001-07-05,10566.23,10617.47,10403.57,10479.86,934900000,10479.86 2001-07-03,10588.89,10648.00,10479.99,10571.11,622110000,10571.11 2001-07-02,10504.95,10707.24,10397.20,10593.72,1128300000,10593.72 2001-06-29,10565.27,10729.18,10374.32,10502.40,1832360000,10502.40 2001-06-28,10438.73,10736.43,10429.74,10566.21,1327300000,10566.21 2001-06-27,10470.35,10608.48,10351.10,10434.84,1162100000,10434.84 2001-06-26,10497.30,10600.90,10313.40,10472.48,1198900000,10472.48 2001-06-25,10607.88,10711.19,10417.93,10504.22,1050100000,10504.22 2001-06-22,10716.50,10753.27,10513.61,10604.59,1189200000,10604.59 2001-06-21,10646.39,10848.47,10512.67,10715.43,1546820000,10715.43 2001-06-20,10593.79,10770.88,10480.20,10647.33,1350100000,10647.33 2001-06-19,10654.30,10793.46,10514.74,10596.67,1184900000,10596.67 2001-06-18,10622.50,10781.45,10531.78,10645.38,1111600000,10645.38 2001-06-15,10690.13,10792.25,10495.69,10623.64,1635550000,10623.64 2001-06-14,10868.27,10874.91,10604.45,10690.13,1242900000,10690.13 2001-06-13,10942.00,11065.92,10817.21,10871.62,1063600000,10871.62 2001-06-12,10914.67,11009.93,10744.99,10948.38,1136500000,10948.38 2001-06-11,10974.79,11038.56,10819.29,10922.09,870100000,10922.09 2001-06-08,11095.62,11096.46,10882.92,10977.00,726200000,10977.00 2001-06-07,11069.58,11169.34,10940.11,11090.74,1089600000,11090.74 2001-06-06,11177.73,11236.68,10998.48,11070.24,1061900000,11070.24 2001-06-05,11061.39,11234.98,10973.10,11175.84,1116800000,11175.84 2001-06-04,10991.77,11125.99,10898.80,11061.52,836500000,11061.52 2001-06-01,10913.57,11063.61,10793.46,10990.41,1015000000,10990.41 2001-05-31,10873.23,11023.25,10798.53,10911.94,1226600000,10911.94 2001-05-30,11032.96,11089.89,10819.74,10872.64,1158600000,10872.64 2001-05-29,11004.66,11162.96,10913.44,11039.14,1026000000,11039.14 2001-05-25,11122.03,11166.92,10949.01,11005.37,828100000,11005.37 2001-05-24,11107.07,11248.19,10977.20,11122.42,1100700000,11122.42 2001-05-23,11257.76,11308.44,11033.16,11105.51,1134800000,11105.51 2001-05-22,11339.80,11411.63,11162.83,11257.24,1260400000,11257.24 2001-05-21,11299.14,11436.42,11149.82,11337.92,1174900000,11337.92 2001-05-18,11245.78,11374.87,11123.01,11301.74,1130800000,11301.74 2001-05-17,11218.65,11413.46,11104.34,11248.58,1355600000,11248.58 2001-05-16,10864.74,11258.21,10779.66,11215.92,1405300000,11215.92 2001-05-15,10877.46,10979.35,10752.73,10872.97,1071800000,10872.97 2001-05-14,10819.55,10930.09,10730.74,10877.33,858200000,10877.33 2001-05-11,10908.30,10969.39,10716.16,10821.31,906200000,10821.31 2001-05-10,10868.87,11049.39,10826.90,10910.44,1056700000,10910.44 2001-05-09,10875.96,10964.84,10739.78,10866.98,1132400000,10866.98 2001-05-08,10936.66,11001.66,10755.07,10883.51,1006300000,10883.51 2001-05-07,10952.35,11059.51,10822.74,10935.17,949000000,10935.17 2001-05-04,10793.20,10989.95,10638.48,10951.24,1082100000,10951.24 2001-05-03,10872.32,10911.06,10657.99,10796.65,1137900000,10796.65 2001-05-02,10902.77,11024.31,10726.77,10876.68,1342200000,10876.68 2001-05-01,10734.05,10966.07,10669.32,10898.34,1181300000,10898.34 2001-04-30,10814.41,10973.15,10666.13,10734.97,1226000000,10734.97 2001-04-27,10694.95,10894.60,10632.36,10810.05,1091300000,10810.05 2001-04-26,10633.01,10820.72,10533.98,10692.35,1345200000,10692.35 2001-04-25,10453.43,10675.95,10373.14,10625.20,1203600000,10625.20 2001-04-24,10529.75,10694.61,10401.45,10454.34,1216500000,10454.34 2001-04-23,10571.00,10669.71,10393.05,10532.23,1012600000,10532.23 2001-04-20,10690.33,10755.46,10445.43,10579.85,1338700000,10579.85 2001-04-19,10616.09,10768.28,10468.79,10693.71,1486800000,10693.71 2001-04-18,10226.88,10806.41,10215.69,10615.83,1918900000,10615.83 2001-04-17,10151.73,10286.61,9980.22,10216.73,1109600000,10216.73 2001-04-16,10118.16,10282.38,9991.14,10158.56,913900000,10158.56 2001-04-12,10013.08,10178.22,9862.71,10126.94,1102000000,10126.94 2001-04-11,10109.05,10246.59,9898.77,10013.47,1290300000,10013.47 2001-04-10,9850.35,10226.85,9850.35,10102.74,1349600000,10102.74 2001-04-09,9793.58,9999.35,9699.92,9845.15,1062800000,9845.15 2001-04-06,9913.94,9951.73,9600.91,9791.09,1266800000,9791.09 2001-04-05,9527.21,9969.92,9527.21,9918.05,1368000000,9918.05 2001-04-04,9480.95,9693.05,9303.48,9515.42,1425590000,9515.42 2001-04-03,9774.78,9779.74,9385.43,9485.71,1386100000,9485.71 2001-04-02,9877.16,10043.02,9638.35,9777.93,1204200000,9777.93 2001-03-30,9799.47,9998.49,9685.07,9878.78,1280800000,9878.78 2001-03-29,9784.94,9950.22,9583.67,9799.06,1234500000,9799.06 2001-03-28,9939.68,9939.68,9607.06,9785.35,1333400000,9785.35 2001-03-27,9687.93,10012.98,9584.29,9947.54,1314200000,9947.54 2001-03-26,9509.25,9820.50,9489.75,9687.53,1114000000,9687.53 2001-03-23,9395.58,9631.80,9249.63,9504.78,1364900000,9504.78 2001-03-22,9490.66,9565.40,9047.56,9389.48,1723950000,9389.48 2001-03-21,9717.46,9807.08,9391.42,9487.00,1346300000,9487.00 2001-03-20,9961.14,10130.45,9675.51,9720.76,1235900000,9720.76 2001-03-19,9820.05,10059.08,9720.94,9959.11,1126200000,9959.11 2001-03-16,10023.55,10119.44,9720.17,9823.41,1543560000,9823.41 2001-03-15,9982.92,10190.80,9887.68,10031.28,1259500000,10031.28 2001-03-14,10279.42,10279.42,9817.74,9973.46,1397400000,9973.46 2001-03-13,10206.89,10397.83,10021.60,10290.80,1360900000,10290.80 2001-03-12,10638.52,10638.63,10138.90,10208.25,1229000000,10208.25 2001-03-09,10850.11,10874.15,10520.42,10644.62,1085900000,10644.62 2001-03-08,10727.16,10940.45,10625.95,10858.25,1114100000,10858.25 2001-03-07,10591.86,10822.23,10524.76,10729.60,1132200000,10729.60 2001-03-06,10570.17,10759.40,10508.43,10591.22,1091800000,10591.22 2001-03-05,10468.93,10659.52,10393.59,10562.30,929200000,10562.30 2001-03-02,10438.04,10645.57,10239.81,10466.31,1294000000,10466.31 2001-03-01,10493.25,10605.23,10236.92,10450.14,1294900000,10450.14 2001-02-28,10639.32,10750.23,10374.62,10495.28,1225300000,10495.28 2001-02-27,10638.44,10787.29,10463.92,10636.88,1114100000,10636.88 2001-02-26,10447.59,10701.92,10347.59,10642.53,1130800000,10642.53 2001-02-23,10529.25,10595.01,10225.14,10441.90,1231300000,10441.90 2001-02-22,10527.80,10694.50,10278.93,10526.81,1365900000,10526.81 2001-02-21,10721.29,10828.48,10468.32,10526.58,1208500000,10526.58 2001-02-20,10800.23,10988.29,10612.25,10730.88,1112200000,10730.88 2001-02-16,10884.11,10946.11,10652.33,10799.82,1257200000,10799.82 2001-02-15,10800.65,11023.44,10694.43,10891.02,1153700000,10891.02 2001-02-14,10899.42,10989.61,10683.39,10795.41,1150300000,10795.41 2001-02-13,10950.18,11114.44,10774.98,10903.32,1075200000,10903.32 2001-02-12,10779.42,11024.92,10727.02,10946.77,1039100000,10946.77 2001-02-09,10878.51,10979.12,10682.77,10781.45,1075500000,10781.45 2001-02-08,10940.62,11080.42,10776.04,10880.55,1107200000,10880.55 2001-02-07,10948.95,11140.09,10794.29,10946.72,1158300000,10946.72 2001-02-06,10965.03,11117.80,10820.28,10957.42,1059600000,10957.42 2001-02-05,10860.44,11061.42,10759.98,10965.85,1013000000,10965.85 2001-02-02,10982.71,11093.01,10786.69,10864.10,1048400000,10864.10 2001-02-01,10884.82,11063.95,10759.85,10983.63,1118800000,10983.63 2001-01-31,10882.25,11072.28,10705.23,10887.36,1295300000,10887.36 2001-01-30,10702.19,10950.38,10609.77,10881.20,1149800000,10881.20 2001-01-29,10657.13,10832.56,10515.99,10702.19,1053100000,10702.19 2001-01-26,10727.08,10874.28,10506.26,10659.98,1098000000,10659.98 2001-01-25,10644.53,10882.42,10520.90,10729.52,1258000000,10729.52 2001-01-24,10651.85,10795.80,10483.49,10646.97,1309000000,10646.97 2001-01-23,10575.80,10773.94,10459.91,10649.81,1232600000,10649.81 2001-01-22,10581.90,10749.44,10371.66,10578.24,1164000000,10578.24 2001-01-19,10686.00,10792.14,10448.93,10587.59,1407800000,10587.59 2001-01-18,10584.57,10834.43,10466.01,10678.28,1445000000,10678.28 2001-01-17,10660.95,10817.35,10442.83,10584.34,1349100000,10584.34 2001-01-16,10525.78,10751.48,10362.72,10652.66,1205700000,10652.66 2001-01-12,10608.74,10743.75,10339.94,10525.38,1276000000,10525.38 2001-01-11,10600.20,10808.00,10400.94,10609.55,1411200000,10609.55 2001-01-10,10568.48,10728.30,10325.71,10604.27,1296500000,10604.27 2001-01-09,10625.21,10801.09,10387.12,10572.55,1191300000,10572.55 2001-01-08,10658.73,10818.98,10407.85,10621.35,1115500000,10621.35 2001-01-05,10912.81,10990.59,10492.84,10662.01,1430800000,10662.01 2001-01-04,10944.94,11224.41,10672.58,10912.41,216940000,10912.41 2001-01-03,10637.42,11212.62,10367.19,10945.75,188070000,10945.75 2001-01-02,10790.92,10916.98,10450.55,10646.15,1129400000,10646.15 2000-12-29,10868.76,11031.05,10675.75,10787.99,1035500000,10787.99 2000-12-28,10795.20,11009.44,10645.42,10868.76,1015300000,10868.76 2000-12-27,10690.10,10944.60,10551.00,10803.16,1092700000,10803.16 2000-12-26,10638.21,10813.78,10479.71,10692.44,806500000,10692.44 2000-12-22,10495.26,10772.07,10364.06,10635.56,1087100000,10635.56 2000-12-21,10314.38,10651.96,10158.16,10487.29,1449900000,10487.29 2000-12-20,10580.97,10604.08,10197.59,10318.93,1421600000,10318.93 2000-12-19,10643.14,10865.35,10441.41,10584.37,1324900000,10584.37 2000-12-18,10433.34,10783.82,10417.43,10645.42,1189900000,10645.42 2000-12-15,10647.98,10706.84,10324.24,10434.96,156110000,10434.96 2000-12-14,10794.82,10864.49,10508.53,10674.99,1061300000,10674.99 2000-12-13,10777.95,11002.23,10653.76,10794.44,1195100000,10794.44 2000-12-12,10722.77,10968.77,10582.09,10768.27,1083400000,10768.27 2000-12-11,10719.36,10931.33,10521.04,10725.80,1202400000,10725.80 2000-12-08,10632.14,10896.82,10534.69,10712.91,1358300000,10712.91 2000-12-07,10644.66,10791.40,10448.99,10617.36,1128000000,10617.36 2000-12-06,10896.14,10995.41,10513.84,10664.38,1399300000,10664.38 2000-12-05,10576.78,11044.70,10504.36,10898.72,900300000,10898.72 2000-12-04,10377.33,10701.35,10227.17,10560.95,1103000000,10560.95 2000-12-01,10416.76,10645.42,10238.54,10373.54,1195200000,10373.54 2000-11-30,10610.53,10690.16,10204.80,10414.49,1186530000,10414.49 2000-11-29,10502.74,10746.66,10383.02,10629.11,402100000,10629.11 2000-11-28,10537.86,10730.35,10356.47,10507.58,1028200000,10507.58 2000-11-27,10479.33,10758.04,10411.08,10546.07,946100000,10546.07 2000-11-24,10403.87,10596.50,10354.20,10470.23,404870000,10470.23 2000-11-22,10484.26,10589.67,10251.06,10399.32,963200000,10399.32 2000-11-21,10465.57,10676.13,10303.39,10494.50,1137100000,10494.50 2000-11-20,10624.18,10707.22,10331.45,10462.65,955800000,10462.65 2000-11-17,10657.13,10824.77,10462.55,10629.87,1070400000,10629.87 2000-11-16,10705.33,10857.38,10536.30,10656.03,956300000,10656.03 2000-11-15,10681.21,10863.83,10544.17,10707.60,1066800000,10707.60 2000-11-14,10528.25,10809.61,10484.64,10681.06,1118800000,10681.06 2000-11-13,10595.35,10701.54,10273.24,10517.25,1129300000,10517.25 2000-11-10,10813.78,10886.20,10497.53,10602.95,962500000,10602.95 2000-11-09,10902.11,10989.34,10576.40,10834.25,1111000000,10834.25 2000-11-08,10954.34,11152.02,10779.27,10907.06,909300000,10907.06 2000-11-07,10978.72,11105.75,10825.15,10952.18,880900000,10952.18 2000-11-06,10820.60,11092.10,10741.73,10977.21,930900000,10977.21 2000-11-03,10883.17,10996.17,10650.72,10817.95,997700000,10817.95 2000-11-02,10903.17,11071.06,10731.49,10880.51,1167700000,10880.51 2000-11-01,10966.21,11103.10,10736.42,10899.47,1206800000,10899.47 2000-10-31,10835.39,11108.79,10681.06,10971.14,1366400000,10971.14 2000-10-30,10588.06,10944.98,10506.25,10835.77,1186500000,10835.77 2000-10-27,10381.60,10696.43,10296.70,10590.62,1086300000,10590.62 2000-10-26,10330.18,10563.25,10128.18,10380.12,1303800000,10380.12 2000-10-25,10395.66,10563.99,10170.08,10326.48,1315600000,10326.48 2000-10-24,10273.57,10583.96,10136.69,10393.07,1158600000,10393.07 2000-10-23,10230.29,10496.28,10078.24,10271.72,1046800000,10271.72 2000-10-20,10141.13,10406.76,9925.82,10226.59,1177400000,10226.59 2000-10-19,10014.61,10317.23,9901.77,10142.98,1297900000,10142.98 2000-10-18,10085.99,10171.47,9571.40,9975.02,1441700000,9975.02 2000-10-17,10242.87,10402.32,9924.34,10089.71,1161500000,10089.71 2000-10-16,10184.78,10428.95,10033.84,10238.80,1005400000,10238.80 2000-10-13,10031.62,10325.37,9883.27,10192.18,1223900000,10192.18 2000-10-12,10424.14,10462.25,9873.66,10034.58,1388600000,10034.58 2000-10-11,10521.07,10647.23,10228.44,10413.79,1387500000,10413.79 2000-10-10,10569.17,10744.52,10377.16,10524.40,1044000000,10524.40 2000-10-09,10596.91,10762.10,10438.94,10568.43,716600000,10568.43 2000-10-06,10726.76,10871.42,10440.05,10596.54,1150100000,10596.54 2000-10-05,10783.72,10940.23,10570.28,10724.92,1176100000,10724.92 2000-10-04,10723.33,10972.41,10596.54,10784.48,1167400000,10784.48 2000-10-03,10709.84,10976.11,10561.03,10719.74,1098100000,10719.74 2000-10-02,10659.06,10876.23,10479.27,10700.13,1051200000,10700.13 2000-09-29,10821.40,10923.21,10552.15,10650.92,1197100000,10650.92 2000-09-28,10629.84,10948.00,10539.48,10824.06,1206200000,10824.06 2000-09-27,10634.45,10821.10,10439.31,10628.36,1174700000,10628.36 2000-09-26,10806.30,10915.44,10499.61,10631.32,1106600000,10631.32 2000-09-25,10847.37,11039.47,10664.24,10808.15,982400000,10808.15 2000-09-22,10678.30,10936.53,10505.16,10847.37,1185500000,10847.37 2000-09-21,10680.52,10902.12,10548.08,10765.52,1105400000,10765.52 2000-09-20,10794.47,10906.93,10500.35,10687.92,1104000000,10687.92 2000-09-19,10812.22,10960.95,10645.38,10789.29,1024900000,10789.29 2000-09-18,10926.42,11053.80,10693.84,10808.52,962500000,10808.52 2000-09-15,11087.84,11203.26,10857.73,10927.00,1268400000,10927.00 2000-09-14,11189.58,11285.39,10986.47,11087.47,1014000000,11087.47 2000-09-13,11225.03,11350.87,11020.14,11182.18,1068300000,11182.18 2000-09-12,11197.71,11351.98,11015.70,11233.23,991200000,11233.23 2000-09-11,11219.54,11367.15,11043.07,11195.49,899300000,11195.49 2000-09-08,11261.72,11381.95,11059.72,11220.65,961000000,11220.65 2000-09-07,11316.01,11444.84,11124.83,11259.87,985500000,11259.87 2000-09-06,11253.58,11518.83,11186.25,11310.64,995100000,11310.64 2000-09-05,11221.76,11382.69,11094.50,11260.61,838500000,11260.61 2000-09-01,11219.54,11406.74,11130.01,11238.78,767700000,11238.78 2000-08-31,11105.23,11415.99,11040.85,11215.10,1056600000,11215.10 2000-08-30,11209.01,11282.06,11034.57,11103.01,818400000,11103.01 2000-08-29,11249.27,11356.42,11100.79,11215.10,795600000,11215.10 2000-08-28,11194.48,11410.44,11123.35,11252.84,733600000,11252.84 2000-08-25,11180.54,11301.41,11073.59,11192.63,685600000,11192.63 2000-08-24,11143.91,11302.51,11009.12,11182.74,837100000,11182.74 2000-08-23,11130.55,11253.06,10990.44,11144.65,871000000,11144.65 2000-08-22,11082.20,11274.67,11000.33,11139.15,818800000,11139.15 2000-08-21,11058.85,11193.73,10945.39,11079.81,731600000,11079.81 2000-08-18,11051.20,11180.54,10933.30,11046.48,821400000,11046.48 2000-08-17,11010.95,11180.91,10899.24,11055.64,922400000,11055.64 2000-08-16,11068.83,11171.02,10888.62,11008.39,929800000,11008.39 2000-08-15,11175.05,11227.06,10965.54,11067.00,895900000,11067.00 2000-08-14,11027.07,11232.92,10928.91,11176.14,783800000,11176.14 2000-08-11,10905.98,11131.83,10841.37,11027.80,835500000,11027.80 2000-08-10,10901.06,11069.93,10779.47,10908.76,940800000,10908.76 2000-08-09,10970.94,11097.03,10780.02,10905.83,1054000000,10905.83 2000-08-08,10865.15,11083.11,10741.38,10976.89,992200000,10976.89 2000-08-07,10773.98,10973.23,10657.50,10867.01,854800000,10867.01 2000-08-04,10713.36,10873.97,10555.68,10767.75,956000000,10767.75 2000-08-03,10679.37,10844.30,10518.68,10706.58,1095600000,10706.58 2000-08-02,10609.15,10818.66,10514.29,10687.53,986300000,10687.53 2000-08-01,10523.81,10728.92,10428.58,10606.95,938700000,10606.95 2000-07-31,10514.29,10727.09,10374.00,10521.98,952600000,10521.98 2000-07-28,10594.97,10732.14,10367.28,10511.17,980000000,10511.17 2000-07-27,10516.83,10745.93,10450.01,10586.13,1156400000,10586.13 2000-07-26,10689.36,10790.13,10447.18,10516.48,1235800000,10516.48 2000-07-25,10689.28,10867.20,10557.49,10699.97,969400000,10699.97 2000-07-24,10731.44,10895.84,10545.47,10685.12,880300000,10685.12 2000-07-21,10843.51,10949.58,10614.06,10733.56,968300000,10733.56 2000-07-20,10700.68,10980.34,10671.33,10843.87,1064600000,10843.87 2000-07-19,10724.15,10907.15,10587.89,10696.08,909400000,10696.08 2000-07-18,10799.16,10895.57,10613.00,10739.92,908300000,10739.92 2000-07-17,10812.40,10969.38,10653.30,10804.27,906000000,10804.27 2000-07-14,10793.31,10935.44,10661.43,10812.75,960600000,10812.75 2000-07-13,10774.92,10963.02,10643.40,10788.71,1026800000,10788.71 2000-07-12,10722.24,10930.84,10639.51,10783.76,1001200000,10783.76 2000-07-11,10649.06,10877.46,10544.76,10727.19,980500000,10727.19 2000-07-10,10627.14,10792.25,10520.01,10646.58,838700000,10646.58 2000-07-07,10483.33,10742.04,10419.25,10635.98,931700000,10635.98 2000-07-06,10481.45,10644.11,10303.28,10481.47,947300000,10481.47 2000-07-05,10538.23,10674.16,10362.33,10483.60,1019300000,10483.60 2000-07-03,10450.36,10610.17,10353.66,10560.67,451900000,10560.67 2000-06-30,10393.09,10626.79,10161.51,10447.89,1459700000,10447.89 2000-06-29,10523.90,10582.94,10279.24,10398.04,1110900000,10398.04 2000-06-28,10506.39,10712.70,10399.10,10527.79,1095100000,10527.79 2000-06-27,10541.58,10741.69,10384.60,10504.46,1042500000,10504.46 2000-06-26,10403.69,10680.26,10365.15,10542.99,889000000,10542.99 2000-06-23,10376.47,10555.37,10283.13,10404.75,847600000,10404.75 2000-06-22,10495.97,10596.73,10256.97,10376.12,1022700000,10376.12 2000-06-21,10446.83,10607.69,10312.48,10497.74,1009600000,10497.74 2000-06-20,10558.90,10632.09,10318.84,10435.16,1031500000,10435.16 2000-06-19,10448.40,10733.56,10322.02,10557.84,921700000,10557.84 2000-06-16,10717.76,10784.47,10393.44,10449.30,1250800000,10449.30 2000-06-15,10689.63,10889.48,10552.89,10714.82,1011400000,10714.82 2000-06-14,10632.46,10860.84,10542.99,10687.95,929700000,10687.95 2000-06-13,10562.31,10751.86,10395.56,10621.84,935900000,10621.84 2000-06-12,10615.12,10757.60,10476.88,10564.21,774100000,10564.21 2000-06-09,10678.47,10848.38,10515.52,10614.06,786000000,10614.06 2000-06-08,10818.78,10887.72,10524.92,10668.72,854300000,10668.72 2000-06-07,10733.48,10974.07,10588.64,10812.86,854600000,10812.86 2000-06-06,10822.61,10916.97,10592.82,10735.57,950100000,10735.57 2000-06-05,10793.11,10951.79,10629.03,10815.30,838600000,10815.30 2000-06-02,10660.09,11013.05,10600.46,10794.76,1162400000,10794.76 2000-06-01,10532.27,10780.37,10422.95,10652.20,960100000,10652.20 2000-05-31,10528.28,10692.73,10377.37,10522.33,960500000,10522.33 2000-05-30,10302.31,10596.00,10287.94,10527.13,844200000,10527.13 2000-05-26,10322.89,10487.72,10163.20,10299.24,722600000,10299.24 2000-05-25,10529.87,10644.32,10207.75,10323.92,984500000,10323.92 2000-05-24,10420.90,10679.53,10240.99,10535.35,1152300000,10535.35 2000-05-23,10539.12,10671.74,10325.63,10422.27,869900000,10422.27 2000-05-22,10624.79,10718.00,10308.15,10542.55,869000000,10542.55 2000-05-19,10764.22,10821.83,10468.18,10626.85,853700000,10626.85 2000-05-18,10771.80,10938.34,10669.00,10777.28,807900000,10777.28 2000-05-17,10930.64,10947.25,10648.78,10769.74,820500000,10769.74 2000-05-16,10816.01,11086.72,10723.48,10934.57,955500000,10934.57 2000-05-15,10606.97,10902.36,10509.31,10807.78,854600000,10807.78 2000-05-12,10549.06,10780.37,10444.54,10609.37,858200000,10609.37 2000-05-11,10369.27,10676.88,10315.69,10545.97,953600000,10545.97 2000-05-10,10533.09,10649.95,10169.77,10367.78,1006400000,10367.78 2000-05-09,10607.54,10765.75,10435.96,10536.75,896600000,10536.75 2000-05-08,10571.31,10744.22,10400.40,10603.63,787600000,10603.63 2000-05-05,10409.70,10688.61,10312.91,10577.86,805500000,10577.86 2000-05-04,10478.89,10631.53,10293.05,10412.49,925800000,10412.49 2000-05-03,10732.21,10754.39,10345.17,10480.13,991600000,10480.13 2000-05-02,10805.58,10932.47,10580.65,10731.12,1011500000,10731.12 2000-05-01,10749.42,11001.34,10622.22,10811.78,966300000,10811.78 2000-04-28,10892.76,11005.07,10632.46,10733.91,984600000,10733.91 2000-04-27,10941.91,11024.61,10650.14,10888.10,1111000000,10888.10 2000-04-26,11127.92,11246.75,10816.44,10945.50,999600000,10945.50 2000-04-25,10916.65,11265.67,10764.62,11124.82,1071100000,11124.82 2000-04-24,10822.33,11060.29,10579.10,10906.10,868700000,10906.10 2000-04-20,10668.19,10941.47,10582.51,10844.05,896200000,10844.05 2000-04-19,10748.97,10909.20,10503.40,10674.96,1001400000,10674.96 2000-04-18,10584.02,10941.78,10424.90,10767.42,1109400000,10767.42 2000-04-17,10303.29,10721.50,10128.62,10582.51,1204700000,10582.51 2000-04-14,10922.85,10922.85,10173.92,10305.77,1279700000,10305.77 2000-04-13,11132.58,11290.80,10806.51,10923.55,1032000000,10923.55 2000-04-12,11283.05,11600.43,11026.47,11125.13,1175900000,11125.13 2000-04-11,11180.98,11459.58,11024.22,11287.08,971400000,11287.08 2000-04-10,11114.89,11404.35,10955.43,11186.56,853700000,11186.56 2000-04-07,11122.03,11317.79,10932.78,11111.48,891600000,11111.48 2000-04-06,11029.56,11303.83,10921.07,11114.27,1008000000,11114.27 2000-04-05,11163.29,11326.79,10894.00,11033.92,1110300000,11033.92 2000-04-04,11225.34,11531.24,10682.72,11164.84,1515460000,11164.84 2000-04-03,10863.28,11344.17,10821.71,11221.93,1021700000,11221.93 2000-03-31,10993.28,11244.58,10801.23,10921.92,1227400000,10921.92 2000-03-30,11008.17,11258.23,10796.58,10980.25,1193400000,10980.25 2000-03-29,10939.05,11214.48,10792.24,11018.72,1061900000,11018.72 2000-03-28,11023.68,11192.76,10804.65,10936.11,959100000,10936.11 2000-03-27,11093.25,11274.98,10881.90,11025.85,901000000,11025.85 2000-03-24,11107.45,11311.28,10901.44,11112.72,1052200000,11112.72 2000-03-23,10884.38,11224.72,10737.63,11119.86,1078300000,11119.86 2000-03-22,10916.96,11054.71,10671.86,10866.70,1075000000,10866.70 2000-03-21,10680.24,11012.20,10515.50,10907.34,1065900000,10907.34 2000-03-20,10594.75,10866.08,10456.86,10680.24,920800000,10680.24 2000-03-17,10629.98,10849.32,10399.15,10595.23,1295100000,10595.23 2000-03-16,10139.58,10716.23,10139.58,10630.60,1482300000,10630.60 2000-03-15,9808.15,10294.60,9676.90,10131.41,1302800000,10131.41 2000-03-14,9957.67,10149.41,9747.33,9811.24,1094000000,9811.24 2000-03-13,9911.22,10111.25,9670.07,9947.13,1016100000,9947.13 2000-03-10,10008.55,10211.77,9792.93,9928.82,1138800000,9928.82 2000-03-09,9855.29,10097.28,9667.28,10010.73,1123000000,10010.73 2000-03-08,9800.69,10037.41,9611.75,9856.53,1203000000,9856.53 2000-03-07,10197.61,10208.66,9651.77,9796.03,1314100000,9796.03 2000-03-06,10358.96,10518.91,10038.65,10170.50,1029000000,10170.50 2000-03-03,10171.12,10581.89,10148.16,10367.20,1150300000,10367.20 2000-03-02,10135.44,10361.61,9986.53,10164.92,1198600000,10164.92 2000-03-01,10128.11,10355.72,9935.96,10137.93,1274100000,10137.93 2000-02-29,10039.58,10332.14,9926.65,10128.31,1204300000,10128.31 2000-02-28,9854.66,10228.52,9760.36,10038.65,1026500000,10038.65 2000-02-25,10090.77,10196.02,9767.80,9862.12,1065200000,9862.12 2000-02-24,10242.48,10321.90,9877.94,10092.63,1215000000,10092.63 2000-02-23,10294.82,10443.21,10077.74,10225.73,993700000,10225.73 2000-02-22,10219.83,10446.62,10011.66,10304.84,980000000,10304.84 2000-02-18,10514.57,10562.34,10129.24,10219.52,1042300000,10219.52 2000-02-17,10565.76,10768.66,10348.66,10514.57,1034800000,10514.57 2000-02-16,10711.82,10831.64,10468.65,10561.41,1018800000,10561.41 2000-02-15,10520.15,10821.09,10377.44,10718.09,1092100000,10718.09 2000-02-14,10431.65,10674.96,10327.56,10519.84,927300000,10519.84 2000-02-11,10638.64,10763.38,10301.12,10425.21,1025700000,10425.21 2000-02-10,10697.92,10853.67,10491.30,10643.63,1058800000,10643.63 2000-02-09,10948.82,11016.54,10647.97,10699.16,1050500000,10699.16 2000-02-08,10904.26,11139.40,10826.67,10957.60,1047700000,10957.60 2000-02-07,10965.97,11097.52,10732.67,10905.79,918100000,10905.79 2000-02-04,11014.37,11200.83,10847.54,10963.80,1045100000,10963.80 2000-02-03,11010.48,11207.97,10799.68,11013.44,1146500000,11013.44 2000-02-02,11037.64,11228.44,10876.00,11003.20,1038600000,11003.20 2000-02-01,10937.74,11187.18,10798.44,11041.05,981000000,11041.05 2000-01-31,10735.77,11059.67,10610.43,10940.53,993800000,10940.53 2000-01-28,11024.92,11115.20,10649.21,10738.87,1095800000,10738.87 2000-01-27,11035.55,11274.36,10818.30,11028.02,1129500000,11028.02 2000-01-26,11025.85,11280.87,10870.73,11032.99,1117300000,11032.99 2000-01-25,11010.96,11228.75,10779.83,11029.89,1073700000,11029.89 2000-01-24,11251.94,11501.15,10849.01,11008.17,1115800000,11008.17 2000-01-21,11356.26,11513.87,11113.65,11251.71,1209800000,11251.71 2000-01-20,11490.29,11654.72,11194.32,11351.30,1100700000,11351.30 2000-01-19,11535.24,11710.57,11320.28,11489.36,1087800000,11489.36 2000-01-18,11719.19,11834.67,11397.22,11560.72,1056700000,11560.72 2000-01-14,11619.35,11908.50,11506.42,11722.98,1085900000,11722.98 2000-01-13,11558.24,11761.14,11421.42,11582.43,1030400000,11582.43 2000-01-12,11506.73,11751.83,11385.74,11551.10,974600000,11551.10 2000-01-11,11568.47,11748.11,11398.30,11511.08,1014000000,11511.08 2000-01-10,11532.48,11765.17,11427.00,11572.20,1064800000,11572.20 2000-01-07,11247.06,11655.65,11168.26,11522.56,1225200000,11522.56 2000-01-06,11113.37,11447.79,10963.18,11253.26,1092300000,11253.26 2000-01-05,10989.37,11337.65,10862.66,11122.65,1085500000,11122.65 2000-01-04,11349.75,11358.44,10907.03,10997.93,1009000000,10997.93 2000-01-03,11501.85,11641.07,11180.98,11357.51,931800000,11357.51 1999-12-31,11453.48,11598.26,11368.05,11497.12,374050000,11497.12 1999-12-30,11484.36,11640.33,11388.94,11452.86,554680000,11452.86 1999-12-29,11472.88,11658.68,11367.53,11484.66,567860000,11484.66 1999-12-28,11389.24,11613.72,11302.08,11476.71,655400000,11476.71 1999-12-27,11410.65,11603.02,11253.15,11391.08,722600000,11391.08 1999-12-23,11202.07,11506.38,11202.07,11405.76,728600000,11405.76 1999-12-22,11199.45,11375.17,11075.76,11203.60,850000000,11203.60 1999-12-21,11142.43,11336.03,10973.61,11200.54,963500000,11200.54 1999-12-20,11254.50,11417.38,11026.22,11144.27,904600000,11144.27 1999-12-17,11259.26,11497.20,11103.59,11257.43,1349800000,11257.43 1999-12-16,11224.40,11396.89,11016.13,11244.89,1070300000,11244.89 1999-12-15,11158.78,11400.48,11014.60,11225.32,1033900000,11225.32 1999-12-14,11195.34,11336.33,11027.13,11160.17,1027800000,11160.17 1999-12-13,11217.46,11379.46,11024.38,11192.59,977600000,11192.59 1999-12-10,11137.85,11358.66,11042.12,11224.70,987200000,11224.70 1999-12-09,11073.62,11327.46,10962.60,11134.79,1122100000,11134.79 1999-12-08,11107.26,11273.33,10957.41,11068.12,957000000,11068.12 1999-12-07,11221.65,11351.32,10993.49,11106.65,1085800000,11106.65 1999-12-06,11286.79,11412.79,11100.53,11225.01,916800000,11225.01 1999-12-03,11046.10,11423.50,11046.10,11286.18,1006400000,11286.18 1999-12-02,10995.02,11183.72,10896.24,11039.06,900700000,11039.06 1999-12-01,10876.47,11111.24,10798.07,10998.39,884000000,10998.39 1999-11-30,10945.49,11142.13,10785.22,10877.81,951500000,10877.81 1999-11-29,10985.73,11059.25,10813.97,10947.92,866100000,10947.92 1999-11-26,11007.26,11115.83,10938.44,10988.91,312120000,10988.91 1999-11-24,11000.22,11131.12,10859.23,11008.17,734800000,11008.17 1999-11-23,11090.29,11178.83,10899.60,10995.63,926100000,10995.63 1999-11-22,11008.78,11195.34,10887.67,11089.52,873500000,11089.52 1999-11-19,11033.25,11146.41,10871.77,11003.89,893800000,11003.89 1999-11-18,10887.67,11147.02,10859.92,11035.70,1022800000,11035.70 1999-11-17,10929.00,11040.90,10774.21,10883.09,960000000,10883.09 1999-11-16,10762.89,10992.88,10691.94,10932.33,942200000,10932.33 1999-11-15,10764.73,10899.22,10626.80,10760.75,795700000,10760.75 1999-11-12,10593.51,10845.16,10513.03,10769.32,900200000,10769.32 1999-11-11,10603.25,10716.71,10485.20,10595.30,891300000,10595.30 1999-11-10,10611.94,10713.04,10449.42,10597.74,984700000,10597.74 1999-11-09,10715.10,10806.02,10506.61,10617.32,854300000,10617.32 1999-11-08,10668.42,10838.74,10548.20,10718.85,806800000,10718.85 1999-11-05,10639.95,10885.53,10636.59,10704.48,1007300000,10704.48 1999-11-04,10612.42,10817.95,10523.43,10639.64,981700000,10639.64 1999-11-03,10582.54,10759.22,10485.50,10609.06,914400000,10609.06 1999-11-02,10653.71,10816.11,10508.14,10581.84,904500000,10581.84 1999-11-01,10730.78,10828.96,10568.08,10648.51,861000000,10648.51 1999-10-29,10629.18,10883.10,10580.11,10729.86,1120500000,10729.86 1999-10-28,10397.67,10726.70,10397.67,10622.53,1135100000,10622.53 1999-10-27,10302.76,10515.21,10172.32,10394.89,950100000,10394.89 1999-10-26,10350.88,10486.39,10208.73,10302.13,878300000,10302.13 1999-10-25,10468.98,10518.37,10225.82,10349.93,777000000,10349.93 1999-10-22,10581.69,10581.69,10301.18,10470.25,959200000,10470.25 1999-10-21,10390.71,10414.52,10047.57,10297.69,1012500000,10297.69 1999-10-20,10203.31,10485.13,10144.46,10392.36,928800000,10392.36 1999-10-19,10117.54,10418.01,10093.80,10204.93,905700000,10204.93 1999-10-18,10018.45,10221.08,9884.20,10116.28,818700000,10116.28 1999-10-15,10286.61,10286.61,9911.43,10019.71,912600000,10019.71 1999-10-14,10230.89,10416.74,10071.64,10286.61,892300000,10286.61 1999-10-13,10412.31,10495.89,10173.58,10232.16,821500000,10232.16 1999-10-12,10648.81,10659.58,10366.08,10417.06,778300000,10417.06 1999-10-11,10649.76,10781.16,10545.60,10648.18,655900000,10648.18 1999-10-08,10534.52,10743.48,10423.71,10649.76,897300000,10649.76 1999-10-07,10588.34,10687.12,10430.99,10537.05,827800000,10537.05 1999-10-06,10399.77,10655.46,10340.75,10588.34,895200000,10588.34 1999-10-05,10401.23,10578.21,10250.20,10400.59,965700000,10400.59 1999-10-04,10274.58,10538.32,10220.44,10401.23,803300000,10401.23 1999-10-01,10335.69,10425.92,10108.05,10273.00,896200000,10273.00 1999-09-30,10214.11,10456.32,10156.85,10336.95,1017600000,10336.95 1999-09-29,10274.27,10408.51,10119.76,10213.48,856000000,10213.48 1999-09-28,10300.51,10386.03,10055.17,10275.53,885400000,10275.53 1999-09-27,10279.33,10498.74,10201.76,10303.39,780600000,10303.39 1999-09-24,10311.94,10428.14,10128.63,10279.33,872800000,10279.33 1999-09-23,10524.07,10643.75,10260.33,10318.59,890800000,10318.59 1999-09-22,10599.42,10688.39,10407.56,10524.07,822200000,10524.07 1999-09-21,10822.95,10822.95,10517.10,10598.47,817300000,10598.47 1999-09-20,10801.87,10918.88,10715.93,10823.90,568000000,10823.90 1999-09-17,10745.38,10946.74,10690.61,10803.63,861900000,10803.63 1999-09-16,10795.77,10876.46,10592.46,10737.46,739000000,10737.46 1999-09-15,10910.40,11049.96,10757.41,10801.42,787300000,10801.42 1999-09-14,11028.74,11061.04,10815.67,10910.33,734500000,10910.33 1999-09-13,11027.40,11146.52,10886.90,11030.33,657900000,11030.33 1999-09-10,11087.00,11218.39,10965.74,11028.43,808500000,11028.43 1999-09-09,11031.28,11172.17,10900.83,11079.40,773900000,11079.40 1999-09-08,11034.13,11164.89,10898.62,11036.34,791200000,11036.34 1999-09-07,11079.08,11191.80,10910.65,11034.13,715300000,11034.13 1999-09-03,10922.36,11155.70,10922.36,11078.45,663200000,11078.45 1999-09-02,10923.95,10923.95,10669.71,10843.21,687100000,10843.21 1999-09-01,10828.44,11013.55,10784.32,10937.88,708200000,10937.88 1999-08-31,10909.70,11079.08,10725.43,10829.28,861700000,10829.28 1999-08-30,11087.69,11176.60,10869.81,10914.13,597900000,10914.13 1999-08-27,11198.45,11295.33,11021.14,11090.17,570050000,11090.17 1999-08-26,11326.04,11393.48,11133.86,11198.45,719000000,11198.45 1999-08-25,11282.38,11428.94,11106.31,11326.04,864600000,11326.04 1999-08-24,11297.54,11404.87,11135.76,11283.30,732700000,11283.30 1999-08-23,11099.66,11344.09,11087.95,11299.76,682600000,11299.76 1999-08-20,10963.84,11155.07,10916.35,11100.61,661200000,11100.61 1999-08-19,10988.85,11037.29,10809.65,10963.84,684200000,10963.84 1999-08-18,11109.66,11153.49,10913.50,10991.38,682800000,10991.38 1999-08-17,11049.64,11180.08,10963.52,11117.08,691500000,11117.08 1999-08-16,10980.11,11105.05,10853.98,11046.79,583550000,11046.79 1999-08-13,10822.00,11049.64,10822.00,10973.65,691700000,10973.65 1999-08-12,10785.65,10967.64,10688.07,10789.39,745600000,10789.39 1999-08-11,10650.59,10878.99,10596.26,10787.80,792300000,10787.80 1999-08-10,10704.22,10812.82,10487.34,10655.15,836200000,10655.15 1999-08-09,10714.03,10854.61,10571.56,10707.70,684300000,10707.70 1999-08-06,10792.58,10896.08,10584.54,10714.03,698900000,10714.03 1999-08-05,10675.41,10876.77,10509.19,10793.82,859300000,10793.82 1999-08-04,10675.66,10901.78,10585.17,10674.77,789300000,10674.77 1999-08-03,10645.96,10812.82,10538.00,10677.31,739600000,10677.31 1999-08-02,10654.83,10849.23,10551.30,10645.96,649550000,10645.96 1999-07-30,10791.29,10897.98,10594.99,10655.15,736800000,10655.15 1999-07-29,10920.15,10920.15,10672.24,10791.29,770100000,10791.29 1999-07-28,10979.04,11090.48,10851.13,10972.07,690900000,10972.07 1999-07-27,10863.16,11079.40,10834.35,10979.04,723800000,10979.04 1999-07-26,10910.96,11014.50,10748.86,10863.16,613450000,10863.16 1999-07-23,10979.67,11069.59,10813.77,10910.96,630580000,10910.96 1999-07-22,11002.78,11140.51,10796.67,10969.22,771700000,10969.22 1999-07-21,10998.94,11142.72,10865.69,11002.78,785500000,11002.78 1999-07-20,11130.06,11245.62,10914.13,10996.13,754800000,10996.13 1999-07-19,11209.84,11321.61,11069.90,11187.68,642330000,11187.68 1999-07-16,11188.63,11300.08,11069.27,11209.84,714100000,11209.84 1999-07-15,11200.03,11313.37,11072.75,11186.41,818800000,11186.41 1999-07-14,11202.24,11289.95,11051.86,11148.10,756100000,11148.10 1999-07-13,11106.31,11277.60,11013.55,11175.02,736000000,11175.02 1999-07-12,11234.22,11314.64,11087.95,11200.98,685300000,11200.98 1999-07-09,11142.72,11284.25,11050.59,11193.70,701000000,11193.70 1999-07-08,11118.66,11290.58,10985.68,11126.89,830600000,11126.89 1999-07-07,11129.74,11268.42,11008.16,11187.36,791200000,11187.36 1999-07-06,11119.93,11291.21,11021.78,11135.12,722900000,11135.12 1999-07-02,11089.53,11205.41,10995.50,11139.24,613570000,11139.24 1999-07-01,10972.39,11156.65,10841.63,11066.42,843400000,11066.42 1999-06-30,10805.22,11120.24,10657.36,10970.80,1117000000,10970.80 1999-06-29,10673.83,10855.56,10589.61,10815.35,820100000,10815.35 1999-06-28,10633.93,10792.24,10535.15,10655.15,652910000,10655.15 1999-06-25,10586.44,10719.42,10477.21,10552.56,623460000,10552.56 1999-06-24,10620.32,10736.83,10404.07,10534.83,690400000,10534.83 1999-06-23,10702.32,10791.29,10542.75,10666.86,731800000,10666.86 1999-06-22,10768.49,10879.94,10639.63,10721.63,716500000,10721.63 1999-06-21,10865.06,10960.36,10684.91,10815.98,686600000,10815.98 1999-06-18,10885.00,10978.09,10751.39,10855.56,914500000,10855.56 1999-06-17,10732.71,10936.61,10642.80,10841.63,700300000,10841.63 1999-06-16,10709.92,10883.74,10608.92,10784.95,806800000,10784.95 1999-06-15,10612.09,10740.00,10500.01,10594.99,696600000,10594.99 1999-06-14,10490.83,10691.24,10414.52,10563.33,669400000,10563.33 1999-06-11,10619.69,10744.11,10386.98,10490.51,698200000,10490.51 1999-06-10,10621.58,10736.20,10452.52,10621.27,716500000,10621.27 1999-06-09,10780.84,10871.39,10602.59,10690.29,662000000,10690.29 1999-06-08,10878.35,10954.66,10671.93,10765.64,685900000,10765.64 1999-06-07,10805.20,11016.40,10718.47,10909.38,664300000,10909.38 1999-06-04,10702.64,10892.60,10558.26,10799.84,694500000,10799.84 1999-06-03,10629.18,10767.86,10515.52,10663.69,719600000,10663.69 1999-06-02,10591.82,10694.09,10388.24,10577.89,728000000,10577.89 1999-06-01,10549.08,10717.20,10334.42,10596.26,683800000,10596.26 1999-05-28,10489.56,10690.07,10389.94,10559.74,649960000,10559.74 1999-05-27,10643.04,10734.21,10372.96,10466.93,811400000,10466.93 1999-05-26,10580.94,10818.08,10416.06,10702.16,870800000,10702.16 1999-05-25,10651.73,10818.96,10494.52,10531.09,826700000,10531.09 1999-05-24,10829.87,10924.26,10568.85,10654.67,754700000,10654.67 1999-05-21,10879.13,10974.69,10728.12,10829.28,686600000,10829.28 1999-05-20,10892.40,11020.70,10773.83,10866.74,752200000,10866.74 1999-05-19,10836.67,10988.85,10722.81,10887.39,801100000,10887.39 1999-05-18,10895.94,11017.75,10678.86,10836.95,753400000,10836.95 1999-05-17,10864.35,10976.32,10677.64,10853.47,665500000,10853.47 1999-05-14,10950.26,11076.55,10787.03,10913.32,727800000,10913.32 1999-05-13,11087.71,11244.36,10931.36,11107.19,796900000,11107.19 1999-05-12,11002.38,11146.71,10759.54,11000.37,825500000,11000.37 1999-05-11,11059.65,11185.08,10882.11,11026.15,836100000,11026.15 1999-05-10,11029.25,11173.05,10876.38,11007.25,773300000,11007.25 1999-05-07,10967.16,11135.54,10838.29,11031.59,814900000,11031.59 1999-05-06,10909.02,11093.44,10730.33,10946.82,875400000,10946.82 1999-05-05,10902.72,11055.36,10711.15,10955.41,913500000,10955.41 1999-05-04,11012.11,11140.12,10787.32,10886.11,933100000,10886.11 1999-05-03,10788.75,11083.13,10701.12,11014.69,811400000,11014.69 1999-04-30,10933.94,11072.25,10603.76,10789.04,936500000,10789.04 1999-04-29,10864.64,11052.49,10710.00,10878.38,1003600000,10878.38 1999-04-28,10806.22,11050.77,10665.90,10845.45,951700000,10845.45 1999-04-27,10781.88,10977.46,10647.29,10831.71,891700000,10831.71 1999-04-26,10721.17,10854.33,10540.47,10718.59,712000000,10718.59 1999-04-23,10646.71,10858.34,10530.45,10689.67,744900000,10689.67 1999-04-22,10735.77,10896.42,10517.85,10727.18,927900000,10727.18 1999-04-21,10462.58,10702.56,10309.09,10581.42,920000000,10581.42 1999-04-20,10440.53,10610.06,10212.87,10448.55,985400000,10448.55 1999-04-19,10566.07,10879.76,10284.39,10440.53,1214400000,10440.53 1999-04-16,10497.26,10632.90,10299.55,10493.89,1002300000,10493.89 1999-04-15,10411.66,10673.90,10201.31,10462.72,1089800000,10462.72 1999-04-14,10436.91,10692.49,10196.87,10411.66,952000000,10411.66 1999-04-13,10340.62,10512.11,10239.33,10395.01,810900000,10395.01 1999-04-12,10094.19,10384.46,10042.02,10339.51,810800000,10339.51 1999-04-09,10166.62,10298.71,10035.09,10173.84,716100000,10173.84 1999-04-08,10083.93,10282.62,9980.69,10197.70,850500000,10197.70 1999-04-07,10023.43,10166.62,9859.98,10085.31,816400000,10085.31 1999-04-06,9985.69,10097.25,9862.48,9963.49,787500000,9963.49 1999-04-05,9893.84,10080.87,9826.40,10007.33,695800000,10007.33 1999-04-01,9825.29,9927.69,9707.91,9832.51,703000000,9832.51 1999-03-31,9968.21,10025.10,9744.82,9786.16,924300000,9786.16 1999-03-30,10003.84,10035.36,9812.53,9913.26,729000000,9913.26 1999-03-29,9879.41,10089.48,9837.78,10006.78,747900000,10006.78 1999-03-26,9795.88,9923.53,9700.69,9822.24,707200000,9822.24 1999-03-25,9735.66,9916.59,9666.28,9836.39,784200000,9836.39 1999-03-24,9702.08,9803.09,9547.23,9666.84,761900000,9666.84 1999-03-23,9846.66,9897.72,9593.85,9671.83,811300000,9671.83 1999-03-22,9901.88,10005.95,9796.99,9890.51,658200000,9890.51 1999-03-19,10107.79,10158.57,9856.37,9903.55,914700000,9903.55 1999-03-18,9958.59,10060.62,9776.17,9997.62,831000000,9997.62 1999-03-17,9939.90,10024.54,9792.55,9879.41,752300000,9879.41 1999-03-16,9969.32,10062.84,9857.48,9930.47,751900000,9930.47 1999-03-15,9880.24,10027.59,9807.53,9958.77,727200000,9958.77 1999-03-12,9927.14,10042.58,9779.78,9876.35,825800000,9876.35 1999-03-11,9815.86,9992.35,9742.32,9897.44,904800000,9897.44 1999-03-10,9735.10,9849.71,9624.94,9772.84,841900000,9772.84 1999-03-09,9703.47,9856.65,9586.08,9693.76,803700000,9693.76 1999-03-08,9728.72,9825.02,9616.33,9727.61,714600000,9727.61 1999-03-05,9636.65,9799.92,9558.41,9736.08,834900000,9736.08 1999-03-04,9339.18,9549.99,9272.08,9467.40,770900000,9467.40 1999-03-03,9311.74,9397.86,9163.41,9275.88,751700000,9275.88 1999-03-02,9382.10,9494.57,9216.66,9297.61,753600000,9297.61 1999-03-01,9315.27,9419.32,9167.76,9324.78,699500000,9324.78 1999-02-26,9382.64,9459.52,9177.54,9306.58,784600000,9306.58 1999-02-25,9395.66,9446.32,9200.27,9366.34,740500000,9366.34 1999-02-24,9547.88,9662.77,9357.81,9399.67,782000000,9399.67 1999-02-23,9549.21,9659.58,9425.26,9544.42,781100000,9544.42 1999-02-22,9346.62,9596.13,9289.04,9552.68,718500000,9552.68 1999-02-19,9284.51,9430.59,9218.13,9339.95,700000000,9339.95 1999-02-18,9239.72,9368.48,9145.09,9298.63,742400000,9298.63 1999-02-17,9240.79,9409.53,9124.03,9195.47,735100000,9195.47 1999-02-16,9333.34,9458.46,9187.10,9297.03,653760000,9297.03 1999-02-12,9346.47,9437.35,9161.35,9274.89,691500000,9274.89 1999-02-11,9176.28,9423.19,9088.49,9363.46,815800000,9363.46 1999-02-10,9135.86,9267.68,9025.41,9177.31,721400000,9177.31 1999-02-09,9268.46,9361.92,9076.13,9133.03,736000000,9133.03 1999-02-08,9318.66,9427.83,9148.99,9291.11,705400000,9291.11 1999-02-05,9317.12,9457.43,9141.27,9304.24,872000000,9304.24 1999-02-04,9389.72,9511.50,9178.60,9304.50,854400000,9304.50 1999-02-03,9275.41,9454.09,9176.80,9366.81,876500000,9366.81 1999-02-02,9318.40,9394.10,9146.16,9274.12,845500000,9274.12 1999-02-01,9405.43,9513.05,9266.91,9345.70,799400000,9345.70 1999-01-29,9317.37,9457.18,9172.16,9358.83,917000000,9358.83 1999-01-28,9220.57,9384.83,9134.57,9281.33,848800000,9281.33 1999-01-27,9378.65,9461.04,9135.86,9200.23,893800000,9200.23 1999-01-26,9210.78,9408.77,9118.35,9324.58,896400000,9324.58 1999-01-25,9117.58,9273.09,8994.26,9203.32,723900000,9203.32 1999-01-22,9149.51,9289.31,8998.89,9120.67,785900000,9120.67 1999-01-21,9371.96,9479.83,9150.28,9264.08,871800000,9264.08 1999-01-20,9395.64,9555.01,9230.35,9335.91,905700000,9335.91 1999-01-19,9408.52,9499.14,9165.73,9355.22,785500000,9355.22 1999-01-15,9200.74,9381.74,9124.02,9340.55,798100000,9340.55 1999-01-14,9315.06,9380.20,9052.44,9120.93,797200000,9120.93 1999-01-13,9213.62,9485.24,9134.06,9349.56,931500000,9349.56 1999-01-12,9599.55,9680.40,9394.87,9474.68,800200000,9474.68 1999-01-11,9613.97,9751.46,9446.36,9619.89,818000000,9619.89 1999-01-08,9612.17,9759.44,9447.91,9643.32,937800000,9643.32 1999-01-07,9445.33,9616.29,9369.12,9537.76,863000000,9537.76 1999-01-06,9399.25,9608.05,9331.02,9544.97,986900000,9544.97 1999-01-05,9201.00,9389.46,9137.66,9311.19,775000000,9311.19 1999-01-04,9212.84,9393.84,9089.00,9184.27,877000000,9184.27 1998-12-31,9271.55,9343.64,9106.77,9181.43,719200000,9181.43 1998-12-30,9310.17,9390.75,9211.30,9274.64,594220000,9274.64 1998-12-29,9222.63,9375.30,9152.34,9320.98,586490000,9320.98 1998-12-28,9251.21,9330.50,9133.54,9226.75,531560000,9226.75 1998-12-24,9202.29,9289.57,9146.42,9217.99,246980000,9217.99 1998-12-23,9085.91,9255.84,9022.58,9202.03,697500000,9202.03 1998-12-22,9000.95,9122.99,8909.29,9044.46,680500000,9044.46 1998-12-21,8903.89,9150.54,8874.28,8988.85,744800000,8988.85 1998-12-18,8902.86,9012.28,8789.31,8903.63,839600000,8903.63 1998-12-17,8787.55,8959.76,8725.21,8875.82,739400000,8875.82 1998-12-16,8843.38,8922.94,8675.52,8790.60,725500000,8790.60 1998-12-15,8725.72,8878.40,8614.75,8823.30,777900000,8823.30 1998-12-14,8767.95,8868.10,8610.63,8695.60,741800000,8695.60 1998-12-11,8814.29,8916.24,8680.41,8821.76,688900000,8821.76 1998-12-10,9008.42,9034.42,8795.24,8841.58,748600000,8841.58 1998-12-09,9025.41,9138.18,8881.23,9009.19,694200000,9009.19 1998-12-08,9038.03,9153.63,8903.37,9027.98,727700000,9027.98 1998-12-07,9031.59,9146.93,8946.11,9070.47,671200000,9070.47 1998-12-04,8964.91,9078.70,8873.76,9016.14,709700000,9016.14 1998-12-03,9031.33,9112.69,8839.78,8879.68,799100000,8879.68 1998-12-02,9039.57,9154.40,8922.94,9064.54,727400000,9064.54 1998-12-01,9039.57,9214.65,8934.52,9133.54,789200000,9133.54 1998-11-30,9292.40,9348.53,9074.07,9116.55,687900000,9116.55 1998-11-27,9333.85,9403.62,9263.82,9333.08,256950000,9333.08 1998-11-25,9292.91,9387.66,9199.20,9314.28,583580000,9314.28 1998-11-24,9327.93,9457.95,9219.28,9301.15,766200000,9301.15 1998-11-23,9225.72,9425.77,9137.92,9374.27,774100000,9374.27 1998-11-20,9129.94,9215.93,9048.32,9159.55,721200000,9159.55 1998-11-19,9081.02,9147.96,8967.22,9056.05,671000000,9056.05 1998-11-18,8988.85,9095.70,8897.96,9041.11,652510000,9041.11 1998-11-17,8991.17,9158.26,8870.42,8986.28,705200000,8986.28 1998-11-16,8921.14,9093.12,8885.09,9011.25,615580000,9011.25 1998-11-13,8863.21,8982.16,8782.62,8919.59,602270000,8919.59 1998-11-12,8823.04,8951.26,8733.70,8829.74,662300000,8829.74 1998-11-11,8922.42,8980.35,8759.19,8823.82,715700000,8823.82 1998-11-10,8895.17,9020.00,8760.99,8863.98,671300000,8863.98 1998-11-09,8980.87,9024.89,8813.00,8897.96,592990000,8897.96 1998-11-06,8902.86,9042.40,8831.02,8975.46,683100000,8975.46 1998-11-05,8782.11,8943.79,8676.55,8915.47,770200000,8915.47 1998-11-04,8801.93,8933.49,8660.33,8783.14,861100000,8783.14 1998-11-03,8708.99,8819.18,8601.88,8706.15,704300000,8706.15 1998-11-02,8645.65,8804.51,8573.56,8706.15,753800000,8706.15 1998-10-30,8591.58,8718.25,8481.39,8592.10,785000000,8592.10 1998-10-29,8371.22,8539.83,8305.54,8495.03,699400000,8495.03 1998-10-28,8372.74,8504.04,8271.55,8371.97,677500000,8371.97 1998-10-27,8503.79,8586.69,8309.92,8366.04,764500000,8366.04 1998-10-26,8483.96,8564.03,8349.57,8432.21,609910000,8432.21 1998-10-23,8531.34,8589.01,8366.04,8452.29,637640000,8452.29 1998-10-22,8519.03,8629.17,8334.12,8533.14,754900000,8533.14 1998-10-21,8504.67,8641.02,8380.72,8519.23,745100000,8519.23 1998-10-20,8540.09,8713.62,8419.08,8505.85,958200000,8505.85 1998-10-19,8415.48,8591.07,8321.50,8466.45,738600000,8466.45 1998-10-16,8384.84,8521.29,8244.26,8416.76,1042200000,8416.76 1998-10-15,7953.07,8375.57,7885.62,8299.36,937600000,8299.36 1998-10-14,7925.01,8107.29,7812.75,7968.78,791200000,7968.78 1998-10-13,7982.68,8093.90,7805.29,7938.14,733300000,7938.14 1998-10-12,8038.03,8162.65,7931.19,8001.47,691100000,8001.47 1998-10-09,7806.57,7976.76,7628.15,7899.52,878100000,7899.52 1998-10-08,7734.48,7822.02,7399.78,7731.91,1114600000,7731.91 1998-10-07,7754.82,7913.94,7558.89,7741.69,977000000,7741.69 1998-10-06,7733.97,7951.53,7646.43,7742.98,845700000,7742.98 1998-10-05,7760.75,7866.82,7507.14,7726.24,817500000,7726.24 1998-10-02,7631.50,7866.31,7496.84,7784.69,902900000,7784.69 1998-10-01,7749.42,7856.26,7540.87,7632.53,899700000,7632.53 1998-09-30,8025.42,8097.51,7775.42,7842.62,800100000,7842.62 1998-09-29,8141.28,8253.79,7946.63,8080.52,760100000,8080.52 1998-09-28,8114.76,8239.37,7986.80,8108.84,690500000,8108.84 1998-09-25,7911.10,8127.89,7849.06,8028.77,736800000,8028.77 1998-09-24,8117.33,8227.53,7906.73,8001.99,805900000,8001.99 1998-09-23,7988.60,8198.43,7891.79,8154.41,899700000,8154.41 1998-09-22,7987.83,8038.29,7816.87,7897.20,694900000,7897.20 1998-09-21,7739.12,8008.43,7653.64,7933.25,609880000,7933.25 1998-09-18,7942.77,8012.03,7759.97,7895.66,794700000,7895.66 1998-09-17,7905.96,8001.99,7795.50,7873.77,694500000,7873.77 1998-09-16,8061.46,8159.30,7923.46,8089.78,797500000,8089.78 1998-09-15,7918.83,8087.21,7840.30,8024.39,724600000,8024.39 1998-09-14,7936.08,8081.29,7848.03,7945.35,714400000,7945.35 1998-09-11,7583.61,7866.31,7497.10,7795.50,819100000,7795.50 1998-09-10,7680.42,7761.00,7469.04,7615.54,880300000,7615.54 1998-09-09,7995.04,8094.16,7796.79,7865.02,704300000,7865.02 1998-09-08,7964.91,8103.69,7779.03,8020.78,814800000,8020.78 1998-09-04,7737.32,7831.29,7450.24,7640.25,780300000,7640.25 1998-09-03,7679.13,7841.59,7499.68,7682.22,880500000,7682.22 1998-09-02,7901.06,8036.23,7710.54,7782.37,894600000,7782.37 1998-09-01,7583.09,7937.37,7379.70,7827.43,1216600000,7827.43 1998-08-31,8078.97,8149.00,7517.70,7539.07,917500000,7539.07 1998-08-28,8193.54,8301.68,7951.27,8051.68,840300000,8051.68 1998-08-27,8377.89,8448.69,8062.24,8165.99,938600000,8165.99 1998-08-26,8492.97,8639.47,8396.68,8523.35,674100000,8523.35 1998-08-25,8632.00,8740.91,8510.22,8602.65,664900000,8602.65 1998-08-24,8584.63,8680.66,8452.29,8566.61,558100000,8566.61 1998-08-21,8600.34,8600.34,8307.60,8533.65,725700000,8533.65 1998-08-20,8639.47,8726.75,8538.29,8611.41,621630000,8611.41 1998-08-19,8745.80,8797.81,8635.61,8693.28,633630000,8693.28 1998-08-18,8593.90,8767.69,8551.93,8714.65,690600000,8714.65 1998-08-17,8404.66,8613.98,8350.34,8574.85,584380000,8574.85 1998-08-14,8531.85,8635.87,8342.10,8425.00,644030000,8425.00 1998-08-13,8535.46,8656.46,8399.51,8459.50,660700000,8459.50 1998-08-12,8528.76,8621.71,8437.10,8552.96,711700000,8552.96 1998-08-11,8431.44,8538.29,8263.32,8462.85,774400000,8462.85 1998-08-10,8585.40,8689.16,8491.17,8574.85,579180000,8574.85 1998-08-07,8610.63,8745.03,8490.40,8598.02,759100000,8598.02 1998-08-06,8513.83,8671.14,8415.22,8577.68,768400000,8577.68 1998-08-05,8493.75,8641.79,8316.10,8546.78,851600000,8546.78 1998-08-04,8859.86,8896.68,8463.37,8487.31,852600000,8487.31 1998-08-03,8868.10,8948.17,8729.58,8786.74,620400000,8786.74 1998-07-31,9024.64,9109.34,8810.94,8883.29,645910000,8883.29 1998-07-30,8962.85,9113.20,8884.83,9026.95,687400000,9026.95 1998-07-29,8976.49,9039.57,8831.28,8914.96,644350000,8914.96 1998-07-28,8982.16,9065.57,8786.48,8934.78,703600000,8934.78 1998-07-27,8905.17,9084.63,8806.05,9028.24,619990000,9028.24 1998-07-24,9002.24,9077.67,8814.29,8937.36,698600000,8937.36 1998-07-23,9130.46,9196.11,8892.56,8932.98,741600000,8932.98 1998-07-22,9185.71,9264.85,8996.83,9128.91,739800000,9128.91 1998-07-21,9296.26,9369.12,9145.65,9190.19,659700000,9190.19 1998-07-20,9340.55,9408.26,9206.15,9295.75,560580000,9295.75 1998-07-17,9328.19,9412.64,9259.96,9337.97,618030000,9337.97 1998-07-16,9233.23,9368.35,9173.19,9328.19,677800000,9328.19 1998-07-15,9246.57,9388.69,9165.99,9234.47,723900000,9234.47 1998-07-14,9100.07,9314.54,9087.20,9245.54,700300000,9245.54 1998-07-13,9107.03,9186.58,9020.52,9096.21,574880000,9096.21 1998-07-10,9098.53,9194.82,8976.23,9105.74,576080000,9105.74 1998-07-09,9135.36,9217.07,9014.30,9089.78,663600000,9089.78 1998-07-08,9107.96,9231.27,9041.70,9174.97,607230000,9174.97 1998-07-07,9094.76,9209.85,9001.84,9085.04,624890000,9085.04 1998-07-06,9017.53,9137.11,8965.97,9091.77,514750000,9091.77 1998-07-02,9037.71,9094.01,8956.25,9025.26,510210000,9025.26 1998-07-01,9011.56,9103.23,8918.64,9048.67,701600000,9048.67 1998-06-30,9010.81,9085.79,8868.57,8952.02,757200000,8952.02 1998-06-29,9002.34,9099.24,8930.84,8997.36,564350000,8997.36 1998-06-26,8948.28,9047.93,8879.78,8944.54,520050000,8944.54 1998-06-25,8950.52,9079.56,8863.58,8935.58,669900000,8935.58 1998-06-24,8828.46,8970.20,8740.52,8923.87,714900000,8923.87 1998-06-23,8789.35,8877.78,8724.83,8828.46,657100000,8828.46 1998-06-22,8705.65,8805.04,8639.38,8711.13,531550000,8711.13 1998-06-19,8844.90,8885.01,8664.79,8712.87,715500000,8712.87 1998-06-18,8825.72,8900.20,8740.77,8813.01,590440000,8813.01 1998-06-17,8745.51,8932.34,8695.43,8829.46,744400000,8829.46 1998-06-16,8666.04,8751.24,8524.55,8665.29,664600000,8665.29 1998-06-15,8723.34,8818.99,8588.32,8627.93,595820000,8627.93 1998-06-12,8812.77,8891.24,8660.56,8834.94,633300000,8834.94 1998-06-11,8975.43,9015.54,8774.40,8811.77,627470000,8811.77 1998-06-10,9031.98,9145.08,8891.98,8971.70,609410000,8971.70 1998-06-09,9074.58,9130.13,8966.72,9049.92,563610000,9049.92 1998-06-08,9052.66,9155.04,8994.12,9069.60,543390000,9069.60 1998-06-05,8920.88,9057.39,8866.57,9037.71,558440000,9037.71 1998-06-04,8798.07,8916.64,8719.85,8870.56,577470000,8870.56 1998-06-03,8909.42,8970.20,8769.67,8803.80,584480000,8803.80 1998-06-02,8961.48,9014.05,8838.92,8891.24,590930000,8891.24 1998-06-01,8907.93,9023.01,8805.04,8922.37,537660000,8922.37 1998-05-29,9004.83,9060.13,8859.60,8899.95,556780000,8899.95 1998-05-28,8947.53,9040.70,8861.59,8970.20,588900000,8970.20 1998-05-27,8902.45,9015.04,8760.95,8936.57,682040000,8936.57 1998-05-26,9167.00,9201.63,8949.78,8963.73,541410000,8963.73 1998-05-22,9153.05,9209.35,9040.70,9114.44,444070000,9114.44 1998-05-21,9173.48,9248.96,9058.64,9132.37,551970000,9132.37 1998-05-20,9101.98,9219.06,9010.56,9171.48,587240000,9171.48 1998-05-19,9097.00,9164.51,8997.36,9054.65,566020000,9054.65 1998-05-18,9088.53,9171.23,8972.20,9050.91,519100000,9050.91 1998-05-15,9161.52,9240.74,9051.91,9096.00,621990000,9096.00 1998-05-14,9136.86,9266.89,9077.07,9172.23,578380000,9172.23 1998-05-13,9178.06,9283.09,9119.67,9211.84,600010000,9211.84 1998-05-12,9098.00,9214.08,9023.51,9161.77,604420000,9161.77 1998-05-11,9125.65,9231.52,9045.43,9091.52,560840000,9091.52 1998-05-08,8981.91,9143.09,8951.27,9055.15,567890000,9055.15 1998-05-07,9044.44,9102.98,8914.90,8976.68,582240000,8976.68 1998-05-06,9174.72,9223.80,9017.28,9054.65,606540000,9054.65 1998-05-05,9189.92,9251.95,9062.37,9147.57,583630000,9147.57 1998-05-04,9201.38,9311.98,9134.86,9192.66,551700000,9192.66 1998-05-01,9106.47,9211.84,9015.54,9147.07,581970000,9147.07 1998-04-30,9018.28,9169.99,8970.95,9063.37,695600000,9063.37 1998-04-29,8899.21,9036.47,8857.85,8951.52,638790000,8951.52 1998-04-28,8920.88,9051.16,8828.71,8898.96,678600000,8898.96 1998-04-27,8937.07,9026.25,8796.08,8917.64,685960000,8917.64 1998-04-24,9143.83,9206.36,8983.65,9064.62,633890000,9064.62 1998-04-23,9176.96,9269.88,9061.88,9143.33,653190000,9143.33 1998-04-22,9184.93,9287.32,9083.80,9176.72,696740000,9176.72 1998-04-21,9137.85,9250.20,9051.41,9184.94,675640000,9184.94 1998-04-20,9166.75,9245.22,9027.25,9141.84,595190000,9141.84 1998-04-17,9077.57,9213.58,9010.06,9167.50,672290000,9167.50 1998-04-16,9162.27,9204.12,8978.92,9076.57,699570000,9076.57 1998-04-15,9110.45,9249.95,9017.53,9162.27,685020000,9162.27 1998-04-14,9014.30,9177.96,8971.45,9110.20,613730000,9110.20 1998-04-13,8997.11,9107.21,8870.31,9012.30,564480000,9012.30 1998-04-09,8891.48,9062.12,8891.48,8994.86,548940000,8994.86 1998-04-08,8951.52,9023.51,8821.73,8891.48,616330000,8891.48 1998-04-07,8995.36,9072.34,8862.34,8956.50,670760000,8956.50 1998-04-06,9051.16,9170.74,8958.49,9033.23,625810000,9033.23 1998-04-03,8986.64,9085.79,8896.22,8983.41,653880000,8983.41 1998-04-02,8900.20,9025.26,8829.21,8986.64,674340000,8986.64 1998-04-01,8818.50,8935.33,8715.61,8868.32,677310000,8868.32 1998-03-31,8852.12,8937.57,8726.32,8799.81,674930000,8799.81 1998-03-30,8802.30,8877.04,8701.66,8782.12,497400000,8782.12 1998-03-27,8835.68,8941.31,8741.77,8796.08,582190000,8796.08 1998-03-26,8847.89,8931.09,8769.92,8846.89,606770000,8846.89 1998-03-25,8943.05,8997.11,8780.88,8872.80,676550000,8872.80 1998-03-24,8887.00,8962.48,8815.01,8904.44,605720000,8904.44 1998-03-23,8839.42,8939.31,8758.71,8816.25,631350000,8816.25 1998-03-20,8814.01,8957.25,8766.43,8906.43,717310000,8906.43 1998-03-19,8776.89,8855.11,8708.64,8803.05,598240000,8803.05 1998-03-18,8749.24,8825.72,8655.83,8775.40,632690000,8775.40 1998-03-17,8706.64,8812.52,8633.41,8749.99,680960000,8749.99 1998-03-16,8647.36,8760.45,8573.37,8718.85,548980000,8718.85 1998-03-13,8669.28,8733.30,8563.90,8602.52,597800000,8602.52 1998-03-12,8622.20,8725.58,8576.86,8659.56,594940000,8659.56 1998-03-11,8682.73,8740.52,8599.28,8675.75,655260000,8675.75 1998-03-10,8623.19,8688.71,8550.45,8643.12,631920000,8643.12 1998-03-09,8601.02,8661.56,8482.45,8567.14,624700000,8567.14 1998-03-06,8505.86,8610.49,8432.62,8569.39,665500000,8569.39 1998-03-05,8480.20,8536.80,8377.32,8444.33,648270000,8444.33 1998-03-04,8524.55,8609.99,8454.79,8539.24,644280000,8539.24 1998-03-03,8532.77,8632.16,8464.26,8584.83,612360000,8584.83 1998-03-02,8528.78,8649.35,8427.89,8550.45,591470000,8550.45 1998-02-27,8532.77,8616.72,8426.15,8545.72,574480000,8545.72 1998-02-26,8471.48,8541.98,8377.82,8490.67,646280000,8490.67 1998-02-25,8455.29,8510.60,8362.37,8457.78,611350000,8457.78 1998-02-24,8370.10,8457.78,8303.83,8370.10,589880000,8370.10 1998-02-23,8381.31,8490.92,8331.98,8410.20,550730000,8410.20 1998-02-20,8350.67,8449.06,8291.88,8413.94,594300000,8413.94 1998-02-19,8379.56,8463.26,8327.25,8375.58,581820000,8375.58 1998-02-18,8419.17,8503.12,8326.75,8451.06,606000000,8451.06 1998-02-17,8439.35,8483.94,8335.97,8398.50,605890000,8398.50 1998-02-13,8346.68,8416.43,8269.21,8370.10,531940000,8370.10 1998-02-12,8260.49,8412.20,8206.93,8369.60,611480000,8369.60 1998-02-11,8298.60,8367.61,8223.87,8314.55,599300000,8314.55 1998-02-10,8241.81,8368.10,8149.88,8295.61,642800000,8295.61 1998-02-09,8185.26,8256.75,8104.55,8180.52,524810000,8180.52 1998-02-06,8178.28,8255.26,8102.30,8189.49,569650000,8189.49 1998-02-05,8129.71,8215.65,8037.54,8117.25,703980000,8117.25 1998-02-04,8160.35,8188.00,8050.99,8129.71,695420000,8129.71 1998-02-03,8107.78,8193.23,8010.63,8160.35,692120000,8160.35 1998-02-02,7987.46,8157.86,7987.46,8107.78,724320000,8107.78 1998-01-30,7973.02,8023.83,7850.95,7906.50,613380000,7906.50 1998-01-29,7915.47,8015.12,7883.09,7973.02,750760000,7973.02 1998-01-28,7815.08,7985.97,7761.52,7915.47,708470000,7915.47 1998-01-27,7712.94,7890.56,7677.07,7815.08,679140000,7815.08 1998-01-26,7700.74,7813.59,7629.99,7712.94,555080000,7712.94 1998-01-23,7730.88,7814.08,7609.31,7700.74,635770000,7700.74 1998-01-22,7794.40,7833.26,7637.71,7730.88,646570000,7730.88 1998-01-21,7873.12,7874.87,7707.96,7794.40,626160000,7794.40 1998-01-20,7753.55,7908.00,7696.01,7873.12,644790000,7873.12 1998-01-16,7691.77,7846.47,7687.04,7753.55,670080000,7753.55 1998-01-15,7784.69,7803.87,7651.66,7691.77,569050000,7691.77 1998-01-14,7732.13,7836.25,7669.10,7784.69,603280000,7784.69 1998-01-13,7647.18,7791.17,7610.31,7732.13,646740000,7732.13 1998-01-12,7580.42,7706.22,7391.59,7647.18,705450000,7647.18 1998-01-09,7802.62,7815.08,7513.41,7580.42,746420000,7580.42 1998-01-08,7902.27,7935.40,7733.12,7802.62,652140000,7802.62 1998-01-07,7906.25,7943.87,7751.56,7902.27,667390000,7902.27 1998-01-06,7978.99,7999.17,7832.52,7906.25,618360000,7906.25 1998-01-05,7965.04,8072.91,7865.40,7978.99,628070000,7978.99 1998-01-02,7908.25,8001.41,7845.47,7965.04,366730000,7965.04 1997-12-31,7915.97,7995.93,7833.76,7908.25,467280000,7908.25 1997-12-30,7792.41,7958.32,7787.68,7915.97,499500000,7915.97 1997-12-29,7712.94,7835.01,7712.94,7792.41,443160000,7792.41 1997-12-26,7660.13,7743.34,7634.72,7679.31,154900000,7679.31 1997-12-24,7691.77,7767.75,7624.26,7660.13,265980000,7660.13 1997-12-23,7819.31,7874.12,7667.11,7691.77,515070000,7691.77 1997-12-22,7756.29,7892.05,7710.45,7819.31,530670000,7819.31 1997-12-19,7846.50,7878.60,7563.23,7756.29,793200000,7756.29 1997-12-18,7957.41,7991.48,7781.35,7846.50,618870000,7846.50 1997-12-17,7976.31,8068.81,7879.08,7957.41,618900000,7957.41 1997-12-16,7922.59,8069.06,7889.52,7976.31,623320000,7976.31 1997-12-15,7838.30,7992.72,7807.96,7922.59,597150000,7922.59 1997-12-12,7848.99,7947.21,7756.73,7838.30,579280000,7838.30 1997-12-11,7961.64,7961.64,7778.37,7848.99,631770000,7848.99 1997-12-10,8049.66,8077.27,7881.07,7978.79,602290000,7978.79 1997-12-09,8110.84,8142.67,7990.98,8049.66,539130000,8049.66 1997-12-08,8149.13,8195.88,8057.37,8110.84,490320000,8110.84 1997-12-05,8050.16,8209.56,7980.04,8149.13,563590000,8149.13 1997-12-04,8032.01,8159.58,7978.30,8050.16,633470000,8050.16 1997-12-03,8018.83,8118.30,7915.63,8032.01,624610000,8032.01 1997-12-02,8013.11,8096.66,7935.03,8018.83,576120000,8018.83 1997-12-01,7823.62,8048.92,7823.62,8013.11,590300000,8013.11 1997-11-28,7794.78,7872.86,7786.08,7823.13,189070000,7823.13 1997-11-26,7808.95,7893.50,7749.77,7794.78,487750000,7794.78 1997-11-25,7767.92,7880.32,7706.00,7808.95,587890000,7808.95 1997-11-24,7881.07,7887.28,7723.41,7767.92,514920000,7767.92 1997-11-21,7826.61,7934.53,7758.47,7881.07,611000000,7881.07 1997-11-20,7724.74,7889.77,7718.19,7826.61,602610000,7826.61 1997-11-19,7650.82,7779.75,7599.50,7724.74,542720000,7724.74 1997-11-18,7698.22,7772.62,7607.11,7650.82,521380000,7650.82 1997-11-17,7613.49,7781.71,7613.49,7698.22,576540000,7698.22 1997-11-14,7487.76,7634.61,7431.03,7572.48,635760000,7572.48 1997-11-13,7401.32,7546.45,7334.77,7487.76,653960000,7487.76 1997-11-12,7558.73,7573.22,7359.32,7401.32,585340000,7401.32 1997-11-11,7552.59,7599.74,7518.21,7558.73,435660000,7558.73 1997-11-10,7581.32,7687.90,7511.83,7552.59,464140000,7552.59 1997-11-07,7646.89,7646.89,7460.99,7581.32,569980000,7581.32 1997-11-06,7692.57,7758.63,7597.78,7683.24,522890000,7683.24 1997-11-05,7689.13,7791.78,7628.96,7692.57,565680000,7692.57 1997-11-04,7674.39,7757.15,7583.29,7689.13,541590000,7689.13 1997-11-03,7443.07,7674.39,7443.07,7674.39,564740000,7674.39 1997-10-31,7381.67,7544.24,7329.61,7442.08,638070000,7442.08 1997-10-30,7506.67,7569.78,7340.42,7381.67,712230000,7381.67 1997-10-29,7498.32,7664.08,7409.67,7506.67,777660000,7506.67 1997-10-28,7161.15,7553.57,6936.45,7498.32,1202550000,7498.32 1997-10-27,7715.41,7717.37,7150.10,7161.15,693730000,7161.15 1997-10-24,7847.77,7975.47,7645.91,7715.41,677630000,7715.41 1997-10-23,7957.05,7957.05,7767.22,7847.77,673270000,7847.77 1997-10-22,8060.44,8124.78,7941.33,8034.65,613490000,8034.65 1997-10-21,7921.44,8090.40,7909.41,8060.44,582310000,8060.44 1997-10-20,7847.03,7966.63,7774.83,7921.44,483880000,7921.44 1997-10-17,7938.88,7953.61,7731.12,7847.03,624980000,7847.03 1997-10-16,8057.98,8146.14,7880.18,7938.88,597010000,7938.88 1997-10-15,8096.29,8127.48,7997.57,8057.98,505310000,8057.98 1997-10-14,8072.22,8168.24,7990.20,8096.29,510330000,8096.29 1997-10-13,8045.21,8150.31,8026.30,8072.22,354800000,8072.22 1997-10-10,8061.42,8091.38,7961.96,8045.21,500680000,8045.21 1997-10-09,8095.06,8127.72,7980.87,8061.42,551840000,8061.42 1997-10-08,8178.31,8208.52,8019.92,8095.06,573110000,8095.06 1997-10-07,8100.22,8218.34,8058.96,8178.31,551970000,8178.31 1997-10-06,8038.58,8160.63,8017.71,8100.22,495620000,8100.22 1997-10-03,8027.53,8183.22,7937.89,8038.58,623370000,8038.58 1997-10-02,8015.50,8087.45,7943.79,8027.53,474760000,8027.53 1997-10-01,7945.26,8081.06,7909.41,8015.50,598660000,8015.50 1997-09-30,7991.43,8045.70,7900.08,7945.26,587500000,7945.26 1997-09-29,7922.18,8030.48,7862.99,7991.43,477100000,7991.43 1997-09-26,7853.66,7970.80,7853.66,7922.18,505340000,7922.18 1997-09-25,7906.71,7962.45,7802.34,7848.01,524880000,7848.01 1997-09-24,7970.06,8065.84,7866.43,7906.71,639460000,7906.71 1997-09-23,7996.83,8048.16,7885.34,7970.06,522930000,7970.06 1997-09-22,7917.27,8078.36,7889.27,7996.83,490900000,7996.83 1997-09-19,7922.72,7972.29,7821.69,7917.27,631040000,7917.27 1997-09-18,7886.44,8049.36,7858.93,7922.72,566830000,7922.72 1997-09-17,7895.92,7981.54,7816.47,7886.44,590550000,7886.44 1997-09-16,7721.14,7951.18,7709.75,7895.92,636380000,7895.92 1997-09-15,7742.97,7832.86,7680.95,7721.14,468030000,7721.14 1997-09-12,7660.98,7779.67,7584.56,7742.97,544150000,7742.97 1997-09-11,7719.28,7745.29,7556.23,7660.98,575020000,7660.98 1997-09-10,7851.91,7868.16,7686.30,7719.28,517620000,7719.28 1997-09-09,7835.18,7922.05,7768.52,7851.91,502200000,7851.91 1997-09-08,7822.41,7921.35,7795.00,7835.18,466430000,7835.18 1997-09-05,7867.24,7952.01,7765.27,7822.41,536400000,7822.41 1997-09-04,7894.64,7936.45,7788.50,7867.24,559310000,7867.24 1997-09-03,7879.78,7972.22,7828.45,7894.64,549060000,7894.64 1997-09-02,7650.99,7903.47,7650.99,7879.78,491870000,7879.78 1997-08-29,7694.43,7729.73,7580.85,7622.42,413910000,7622.42 1997-08-28,7787.33,7831.70,7634.50,7694.43,486300000,7694.43 1997-08-27,7782.22,7850.51,7666.55,7787.33,492150000,7787.33 1997-08-26,7859.57,7891.62,7734.61,7782.22,449110000,7782.22 1997-08-25,7887.91,7974.08,7791.75,7859.57,388990000,7859.57 1997-08-22,7893.95,7904.86,7695.36,7887.91,460160000,7887.91 1997-08-21,8021.23,8043.06,7834.02,7893.95,499000000,7893.95 1997-08-20,7918.10,8037.95,7870.95,8021.23,521270000,8021.23 1997-08-19,7803.36,7947.37,7776.65,7918.10,545630000,7918.10 1997-08-18,7694.66,7847.49,7588.28,7803.36,514330000,7803.36 1997-08-15,7919.26,7919.26,7685.14,7694.66,537820000,7694.66 1997-08-14,7928.32,8027.73,7843.54,7942.03,530460000,7942.03 1997-08-13,7960.84,8075.58,7848.19,7928.32,587210000,7928.32 1997-08-12,8062.11,8132.49,7926.46,7960.84,499310000,7960.84 1997-08-11,8031.22,8122.27,7922.52,8062.11,480340000,8062.11 1997-08-08,8170.58,8170.58,7961.07,8031.22,563420000,8031.22 1997-08-07,8259.31,8340.14,8158.73,8188.00,576030000,8188.00 1997-08-06,8187.54,8302.05,8130.63,8259.31,565200000,8259.31 1997-08-05,8198.45,8251.88,8129.93,8187.54,525710000,8187.54 1997-08-04,8194.04,8261.40,8097.65,8198.45,456000000,8198.45 1997-08-01,8222.61,8287.65,8062.11,8194.04,513750000,8194.04 1997-07-31,8254.89,8328.99,8160.36,8222.61,547830000,8222.61 1997-07-30,8174.53,8313.19,8156.88,8254.89,568470000,8254.89 1997-07-29,8121.11,8232.36,8049.34,8174.53,544540000,8174.53 1997-07-28,8113.44,8221.68,8051.89,8121.11,466920000,8121.11 1997-07-25,8116.93,8200.31,8037.95,8113.44,521510000,8113.44 1997-07-24,8088.36,8174.53,7968.51,8116.93,571020000,8116.93 1997-07-23,8061.65,8199.15,8024.95,8088.36,616930000,8088.36 1997-07-22,7906.72,8093.93,7870.72,8061.65,579590000,8061.65 1997-07-21,7890.46,7981.51,7783.85,7906.72,459500000,7906.72 1997-07-18,8020.77,8057.23,7829.61,7890.46,589710000,7890.46 1997-07-17,8038.88,8136.67,7910.67,8020.77,629250000,8020.77 1997-07-16,7975.71,8108.10,7919.73,8038.88,647390000,8038.88 1997-07-15,7922.98,8037.03,7843.78,7975.71,598370000,7975.71 1997-07-14,7921.82,8001.26,7831.00,7922.98,485960000,7922.98 1997-07-11,7886.76,7984.02,7837.68,7921.82,500050000,7921.82 1997-07-10,7842.43,7953.94,7777.06,7886.76,551340000,7886.76 1997-07-09,7962.31,8027.68,7775.48,7842.43,589110000,7842.43 1997-07-08,7858.49,8000.08,7824.33,7962.31,526010000,7962.31 1997-07-07,7895.81,7983.79,7805.34,7858.49,518780000,7858.49 1997-07-03,7805.79,7952.35,7805.79,7895.81,374680000,7895.81 1997-07-02,7722.33,7814.38,7648.14,7795.38,526970000,7795.38 1997-07-01,7672.79,7801.04,7613.53,7722.33,544190000,7722.33 1997-06-30,7687.72,7768.01,7571.46,7672.79,561540000,7672.79 1997-06-27,7654.25,7793.12,7627.33,7687.72,472540000,7687.72 1997-06-26,7689.98,7754.22,7581.64,7654.25,499780000,7654.25 1997-06-25,7758.06,7832.48,7615.57,7689.98,603040000,7689.98 1997-06-24,7787.01,7787.01,7602.90,7758.06,542650000,7758.06 1997-06-23,7796.51,7816.87,7592.04,7604.26,492940000,7604.26 1997-06-20,7777.06,7868.44,7733.64,7796.51,653110000,7796.51 1997-06-19,7718.71,7834.51,7697.45,7777.06,536940000,7777.06 1997-06-18,7760.78,7789.28,7651.30,7718.71,491740000,7718.71 1997-06-17,7772.09,7834.97,7680.71,7760.78,543010000,7760.78 1997-06-16,7782.04,7829.99,7712.37,7772.09,414280000,7772.09 1997-06-13,7711.47,7829.08,7683.42,7782.04,575810000,7782.04 1997-06-12,7575.83,7741.42,7569.66,7711.47,592730000,7711.47 1997-06-11,7539.27,7633.96,7476.29,7575.83,513740000,7575.83 1997-06-10,7478.50,7599.61,7459.12,7539.27,526980000,7539.27 1997-06-09,7435.78,7548.52,7412.44,7478.50,465810000,7478.50 1997-06-06,7305.29,7473.98,7290.26,7435.78,488940000,7435.78 1997-06-05,7269.66,7376.97,7241.33,7305.29,452610000,7305.29 1997-06-04,7312.15,7350.36,7214.29,7269.66,466690000,7269.66 1997-06-03,7289.40,7379.98,7225.02,7312.15,527120000,7312.15 1997-06-02,7331.04,7383.84,7244.76,7289.40,435950000,7289.40 1997-05-30,7330.18,7385.99,7203.99,7331.04,537200000,7331.04 1997-05-29,7357.23,7404.44,7272.24,7330.18,462600000,7330.18 1997-05-28,7383.41,7430.20,7287.26,7357.23,487340000,7357.23 1997-05-27,7345.91,7421.32,7276.68,7383.41,436150000,7383.41 1997-05-23,7260.61,7382.58,7260.61,7345.91,417030000,7345.91 1997-05-22,7290.69,7348.79,7210.33,7258.13,426940000,7258.13 1997-05-21,7303.46,7385.47,7218.99,7290.69,540730000,7290.69 1997-05-20,7228.88,7336.02,7123.38,7303.46,450850000,7303.46 1997-05-19,7194.67,7274.21,7140.69,7228.88,345140000,7228.88 1997-05-16,7332.31,7332.31,7192.61,7194.67,486780000,7194.67 1997-05-15,7286.16,7363.63,7225.99,7333.55,458180000,7333.55 1997-05-14,7274.21,7381.76,7238.35,7286.16,504960000,7286.16 1997-05-13,7292.75,7350.85,7211.16,7274.21,489760000,7274.21 1997-05-12,7169.53,7317.47,7156.35,7292.75,459370000,7292.75 1997-05-09,7136.62,7235.76,7079.63,7169.53,455690000,7169.53 1997-05-08,7085.65,7236.96,7040.30,7136.62,534120000,7136.62 1997-05-07,7225.32,7246.60,7064.78,7085.65,500580000,7085.65 1997-05-06,7213.68,7299.98,7139.43,7225.32,603680000,7225.32 1997-05-05,7071.20,7220.91,7029.46,7213.68,549410000,7213.68 1997-05-02,6976.48,7104.51,6935.54,7071.20,499770000,7071.20 1997-05-01,7008.99,7041.90,6891.39,6976.48,460380000,6976.48 1997-04-30,6962.03,7081.23,6912.26,7008.99,562830000,7008.99 1997-04-29,6820.75,6998.15,6820.75,6962.03,547690000,6962.03 1997-04-28,6738.87,6826.37,6691.51,6783.02,404470000,6783.02 1997-04-25,6792.25,6826.77,6681.08,6738.87,414350000,6738.87 1997-04-24,6812.72,6923.90,6742.89,6792.25,493640000,6792.25 1997-04-23,6833.59,6902.23,6746.50,6812.72,489350000,6812.72 1997-04-22,6660.21,6858.08,6628.50,6833.59,507500000,6833.59 1997-04-21,6703.55,6768.17,6594.38,6660.21,397300000,6660.21 1997-04-18,6658.60,6749.71,6616.46,6703.55,468940000,6703.55 1997-04-17,6679.87,6750.91,6600.80,6658.60,503760000,6658.60 1997-04-16,6587.16,6708.77,6506.08,6679.87,498820000,6679.87 1997-04-15,6457.92,6626.09,6457.92,6587.16,507370000,6587.16 1997-04-14,6391.69,6487.22,6315.84,6451.90,406800000,6451.90 1997-04-11,6529.48,6529.48,6358.42,6391.69,444380000,6391.69 1997-04-10,6563.84,6626.91,6495.48,6540.05,421790000,6540.05 1997-04-09,6609.16,6662.41,6521.16,6563.84,451500000,6563.84 1997-04-08,6555.91,6638.62,6491.71,6609.16,450790000,6609.16 1997-04-07,6526.07,6639.00,6508.70,6555.91,453790000,6555.91 1997-04-04,6477.35,6561.57,6376.90,6526.07,544580000,6526.07 1997-04-03,6517.01,6540.43,6379.16,6477.35,498010000,6477.35 1997-04-02,6611.05,6636.73,6476.60,6517.01,478210000,6517.01 1997-04-01,6583.48,6667.70,6482.64,6611.05,515770000,6611.05 1997-03-31,6740.59,6743.23,6532.49,6583.48,555880000,6583.48 1997-03-27,6880.70,6918.47,6654.86,6740.59,476790000,6740.59 1997-03-26,6876.17,6954.72,6811.21,6880.70,506670000,6880.70 1997-03-25,6905.25,6984.94,6832.74,6876.17,487520000,6876.17 1997-03-24,6804.79,6933.58,6746.63,6905.25,451970000,6905.25 1997-03-21,6820.28,6890.52,6742.85,6804.79,544830000,6804.79 1997-03-20,6877.68,6901.47,6765.14,6820.28,497480000,6820.28 1997-03-19,6896.56,6944.15,6794.22,6877.68,539200000,6877.68 1997-03-18,6955.48,6997.40,6841.05,6896.56,467490000,6896.56 1997-03-17,6935.46,7004.20,6820.28,6955.48,495260000,6955.48 1997-03-14,6878.89,6996.27,6851.19,6935.46,491540000,6935.46 1997-03-13,7023.59,7023.59,6852.72,6878.89,507560000,6878.89 1997-03-12,7085.16,7111.72,6988.96,7039.37,490200000,7039.37 1997-03-11,7079.39,7158.28,7026.28,7085.16,493250000,7085.16 1997-03-10,7000.89,7103.25,6970.10,7079.39,468780000,7079.39 1997-03-07,6944.70,7047.07,6927.00,7000.89,508270000,7000.89 1997-03-06,6945.85,7017.05,6896.60,6944.70,540310000,6944.70 1997-03-05,6852.72,6966.64,6836.95,6945.85,532500000,6945.85 1997-03-04,6918.92,6983.95,6814.63,6852.72,537890000,6852.72 1997-03-03,6877.74,6957.01,6798.46,6918.92,437220000,6918.92 1997-02-28,6925.07,6978.18,6820.78,6877.74,508280000,6877.74 1997-02-27,6983.18,7028.59,6885.44,6925.07,467190000,6925.07 1997-02-26,7037.83,7076.31,6878.12,6983.18,573920000,6983.18 1997-02-25,7008.20,7099.79,6935.08,7037.83,527450000,7037.83 1997-02-24,6931.62,7049.76,6868.50,7008.20,462450000,7008.20 1997-02-21,6927.38,6984.72,6869.27,6931.62,478450000,6931.62 1997-02-20,7020.13,7035.91,6890.82,6927.38,492220000,6927.38 1997-02-19,7067.46,7112.87,6980.87,7020.13,519350000,7020.13 1997-02-18,6988.96,7084.39,6946.62,7067.46,474110000,7067.46 1997-02-14,7022.44,7074.77,6935.85,6988.96,491540000,6988.96 1997-02-13,6961.63,7074.39,6924.30,7022.44,593710000,7022.44 1997-02-12,6858.11,6976.64,6844.26,6961.63,563890000,6961.63 1997-02-11,6806.54,6887.36,6756.90,6858.11,483090000,6858.11 1997-02-10,6855.80,6908.14,6771.14,6806.54,471590000,6806.54 1997-02-07,6773.06,6906.22,6747.28,6855.80,540910000,6855.80 1997-02-06,6746.90,6821.17,6683.40,6773.06,519660000,6773.06 1997-02-05,6833.48,6913.14,6704.56,6746.90,580520000,6746.90 1997-02-04,6806.16,6859.65,6738.43,6833.48,506530000,6833.48 1997-02-03,6813.09,6858.11,6733.04,6806.16,463600000,6806.16 1997-01-31,6823.86,6912.37,6769.99,6813.09,578550000,6813.09 1997-01-30,6740.74,6845.03,6719.96,6823.86,524160000,6823.86 1997-01-29,6656.08,6766.91,6627.98,6740.74,498390000,6740.74 1997-01-28,6660.69,6823.48,6612.20,6656.08,541580000,6656.08 1997-01-27,6696.48,6748.82,6598.73,6660.69,445760000,6660.69 1997-01-24,6755.75,6798.08,6629.91,6696.48,542920000,6696.48 1997-01-23,6850.03,6953.55,6724.19,6755.75,685070000,6755.75 1997-01-22,6883.90,6913.14,6801.16,6850.03,587300000,6850.03 1997-01-21,6843.87,6934.69,6771.14,6883.90,571280000,6883.90 1997-01-20,6833.10,6893.13,6777.30,6843.87,440470000,6843.87 1997-01-17,6765.37,6863.88,6732.66,6833.10,534640000,6833.10 1997-01-16,6726.88,6818.47,6688.40,6765.37,537290000,6765.37 1997-01-15,6762.29,6800.77,6669.93,6726.88,524990000,6726.88 1997-01-14,6709.18,6816.17,6689.94,6762.29,531600000,6762.29 1997-01-13,6703.79,6773.45,6647.99,6709.18,445400000,6709.18 1997-01-10,6625.67,6725.35,6530.62,6703.79,545860000,6703.79 1997-01-09,6549.48,6677.24,6520.23,6625.67,555370000,6625.67 1997-01-08,6600.66,6650.30,6509.84,6549.48,557510000,6549.48 1997-01-07,6567.18,6621.82,6481.75,6600.66,538220000,6600.66 1997-01-06,6544.09,6647.22,6508.30,6567.18,531350000,6567.18 1997-01-03,6442.49,6586.42,6437.10,6544.09,452970000,6544.09 1997-01-02,6448.27,6511.38,6318.96,6442.49,463230000,6442.49 1996-12-31,6549.37,6580.90,6421.74,6448.27,399760000,6448.27 1996-12-30,6560.91,6623.96,6518.23,6549.37,339060000,6549.37 1996-12-27,6546.68,6607.81,6510.93,6560.91,253810000,6560.91 1996-12-26,6522.85,6594.74,6495.94,6546.68,254630000,6546.68 1996-12-24,6489.02,6546.68,6467.10,6522.85,165140000,6522.85 1996-12-23,6484.40,6539.76,6428.27,6489.02,343280000,6489.02 1996-12-20,6473.64,6597.43,6445.19,6484.40,654340000,6484.40 1996-12-19,6352.15,6499.40,6352.15,6473.64,526410000,6473.64 1996-12-18,6308.33,6399.06,6272.96,6346.77,500490000,6346.77 1996-12-17,6268.35,6354.46,6206.83,6308.33,519840000,6308.33 1996-12-16,6304.87,6388.68,6227.98,6268.35,447560000,6268.35 1996-12-13,6303.71,6377.14,6227.59,6304.87,458540000,6304.87 1996-12-12,6402.52,6465.57,6283.72,6303.71,492920000,6303.71 1996-12-11,6457.88,6457.88,6317.94,6402.52,494210000,6402.52 1996-12-10,6463.94,6545.56,6427.04,6473.25,446120000,6473.25 1996-12-09,6381.94,6496.73,6375.98,6463.94,381570000,6463.94 1996-12-06,6437.10,6441.20,6274.24,6381.94,500860000,6381.94 1996-12-05,6422.94,6491.14,6363.31,6437.10,483710000,6437.10 1996-12-04,6442.69,6482.20,6339.46,6422.94,498240000,6422.94 1996-12-03,6521.70,6577.23,6422.94,6442.69,516160000,6442.69 1996-12-02,6521.70,6553.01,6439.34,6521.70,412520000,6521.70 1996-11-29,6499.34,6551.15,6490.40,6521.70,151550000,6521.70 1996-11-27,6528.41,6566.43,6457.97,6499.34,377780000,6499.34 1996-11-26,6547.79,6606.30,6475.49,6528.41,527380000,6528.41 1996-11-25,6471.76,6565.68,6443.44,6547.79,475260000,6547.79 1996-11-22,6418.47,6498.22,6402.44,6471.76,525210000,6471.76 1996-11-21,6430.02,6463.56,6370.02,6418.47,464430000,6418.47 1996-11-20,6397.60,6482.20,6370.02,6430.02,497900000,6430.02 1996-11-19,6346.91,6428.16,6323.06,6397.60,461980000,6397.60 1996-11-18,6348.03,6407.66,6297.34,6346.91,388520000,6346.91 1996-11-15,6313.00,6414.37,6277.22,6348.03,529100000,6348.03 1996-11-14,6274.24,6350.64,6232.50,6313.00,480350000,6313.00 1996-11-13,6266.04,6317.10,6206.78,6274.24,429840000,6274.24 1996-11-12,6255.60,6314.49,6199.70,6266.04,472940000,6266.04 1996-11-11,6219.82,6292.87,6198.58,6255.60,353960000,6255.60 1996-11-08,6206.04,6247.40,6151.62,6219.82,402320000,6219.82 1996-11-07,6177.71,6238.83,6130.38,6206.04,502530000,6206.04 1996-11-06,6081.18,6200.44,6060.69,6177.71,509600000,6177.71 1996-11-05,6041.68,6125.53,6029.01,6081.18,492860000,6081.18 1996-11-04,6021.93,6083.05,5981.30,6041.68,398790000,6041.68 1996-11-01,6029.38,6082.67,5975.34,6021.93,465510000,6021.93 1996-10-31,5993.23,6063.67,5955.59,6029.38,488500000,6029.38 1996-10-30,6007.02,6055.84,5956.71,5993.23,437770000,5993.23 1996-10-29,5972.73,6054.72,5938.82,6007.02,443890000,6007.02 1996-10-28,6007.02,6063.67,5952.61,5972.73,383630000,5972.73 1996-10-25,5992.48,6047.64,5954.47,6007.02,367640000,6007.02 1996-10-24,6036.46,6080.07,5953.72,5992.48,418970000,5992.48 1996-10-23,6061.80,6081.93,5965.65,6036.46,442170000,6036.46 1996-10-22,6090.87,6114.73,6015.59,6061.80,410790000,6061.80 1996-10-21,6094.23,6162.80,6027.89,6090.87,414630000,6090.87 1996-10-18,6059.20,6119.57,6011.49,6094.23,473020000,6094.23 1996-10-17,6020.81,6101.31,5994.72,6059.20,478550000,6059.20 1996-10-16,6004.78,6056.21,5943.66,6020.81,441410000,6020.81 1996-10-15,6010.00,6077.83,5951.12,6004.78,458980000,6004.78 1996-10-14,5969.38,6043.91,5952.61,6010.00,322000000,6010.00 1996-10-11,5921.67,5999.56,5912.36,5969.38,396050000,5969.38 1996-10-10,5930.62,5956.71,5876.58,5921.67,394950000,5921.67 1996-10-09,5966.77,5985.03,5892.23,5930.62,408450000,5930.62 1996-10-08,5979.81,6032.36,5930.24,5966.77,435070000,5966.77 1996-10-07,5992.86,6025.28,5945.15,5979.81,380750000,5979.81 1996-10-04,5932.85,6023.79,5917.20,5992.86,463940000,5992.86 1996-10-03,5933.97,5972.36,5887.76,5932.85,386500000,5932.85 1996-10-02,5904.90,5966.02,5888.88,5933.97,440130000,5933.97 1996-10-01,5882.17,5942.17,5833.72,5904.90,421550000,5904.90 1996-09-30,5845.18,5934.32,5845.18,5882.17,394260000,5882.17 1996-09-27,5868.85,5903.99,5819.65,5872.92,414760000,5872.92 1996-09-26,5877.36,5928.04,5828.90,5868.85,500870000,5868.85 1996-09-25,5874.03,5928.77,5827.42,5877.36,451710000,5877.36 1996-09-24,5894.74,5952.08,5831.86,5874.03,460150000,5874.03 1996-09-23,5888.46,5913.24,5820.39,5894.74,297760000,5894.74 1996-09-20,5867.74,5925.82,5840.74,5888.46,519420000,5888.46 1996-09-19,5877.36,5908.80,5818.17,5867.74,398580000,5867.74 1996-09-18,5888.83,5919.90,5838.15,5877.36,396600000,5877.36 1996-09-17,5889.20,5929.51,5830.38,5888.83,449850000,5888.83 1996-09-16,5838.52,5920.64,5823.72,5889.20,430080000,5889.20 1996-09-13,5786.73,5871.44,5786.73,5838.52,488360000,5838.52 1996-09-12,5754.92,5815.59,5739.76,5771.94,398820000,5771.94 1996-09-11,5727.18,5777.49,5696.85,5754.92,376880000,5754.92 1996-09-10,5733.84,5767.87,5681.68,5727.18,372960000,5727.18 1996-09-09,5662.08,5756.40,5662.08,5733.84,311530000,5733.84 1996-09-06,5606.96,5696.48,5585.51,5659.86,348710000,5659.86 1996-09-05,5656.90,5669.47,5592.53,5606.96,361430000,5606.96 1996-09-04,5648.39,5682.05,5608.81,5656.90,351290000,5656.90 1996-09-03,5616.21,5667.99,5550.37,5648.39,345740000,5648.39 1996-08-30,5647.65,5659.86,5571.45,5616.21,258380000,5616.21 1996-08-29,5712.38,5716.82,5615.47,5647.65,321120000,5647.65 1996-08-28,5711.27,5747.89,5678.72,5712.38,296440000,5712.38 1996-08-27,5693.89,5735.32,5670.58,5711.27,310520000,5711.27 1996-08-26,5722.74,5742.71,5665.41,5693.89,281430000,5693.89 1996-08-23,5733.47,5761.58,5679.09,5722.74,308010000,5722.74 1996-08-22,5689.82,5761.95,5662.45,5733.47,354950000,5733.47 1996-08-21,5721.26,5734.95,5648.76,5689.82,348820000,5689.82 1996-08-20,5699.44,5747.52,5670.21,5721.26,334960000,5721.26 1996-08-19,5689.45,5728.66,5664.30,5699.44,294080000,5699.44 1996-08-16,5665.78,5722.74,5646.54,5689.45,337650000,5689.45 1996-08-15,5666.88,5701.66,5633.22,5665.78,323950000,5665.78 1996-08-14,5647.28,5695.00,5614.36,5666.88,343470000,5666.88 1996-08-13,5618.06,5713.86,5618.06,5647.28,362470000,5647.28 1996-08-12,5681.31,5746.04,5625.83,5704.98,312170000,5704.98 1996-08-09,5713.49,5747.15,5654.31,5681.31,327280000,5681.31 1996-08-08,5718.67,5746.41,5661.34,5713.49,334570000,5713.49 1996-08-07,5696.11,5754.55,5659.12,5718.67,394340000,5718.67 1996-08-06,5674.28,5716.45,5630.26,5696.11,347290000,5696.11 1996-08-05,5679.83,5719.04,5639.14,5674.28,307240000,5674.28 1996-08-02,5601.41,5703.51,5601.41,5679.83,442080000,5679.83 1996-08-01,5528.91,5628.79,5507.83,5594.75,439110000,5594.75 1996-07-31,5481.93,5558.13,5460.48,5528.91,403560000,5528.91 1996-07-30,5434.59,5503.73,5403.52,5481.93,341090000,5481.93 1996-07-29,5473.06,5497.47,5414.61,5434.59,281560000,5434.59 1996-07-26,5422.01,5503.02,5397.97,5473.06,349900000,5473.06 1996-07-25,5355.80,5469.36,5355.80,5422.01,405390000,5422.01 1996-07-24,5346.55,5402.04,5244.83,5354.69,463030000,5354.69 1996-07-23,5390.94,5447.90,5313.63,5346.55,421900000,5346.55 1996-07-22,5426.82,5446.05,5346.92,5390.94,327300000,5390.94 1996-07-19,5464.18,5490.44,5393.53,5426.82,408070000,5426.82 1996-07-18,5376.88,5500.43,5352.10,5464.18,474460000,5464.18 1996-07-17,5358.76,5465.29,5325.10,5376.88,513830000,5376.88 1996-07-16,5349.51,5438.66,5170.11,5358.76,68290000,5358.76 1996-07-15,5510.56,5527.93,5326.98,5349.51,419020000,5349.51 1996-07-12,5520.54,5562.65,5455.16,5510.56,397790000,5510.56 1996-07-11,5600.33,5600.33,5447.77,5520.54,520470000,5520.54 1996-07-10,5581.86,5628.03,5515.00,5603.65,421350000,5603.65 1996-07-09,5550.83,5622.49,5540.12,5581.86,379200000,5581.86 1996-07-08,5588.14,5622.12,5519.80,5550.83,367560000,5550.83 1996-07-05,5657.58,5657.58,5570.77,5588.14,181470000,5588.14 1996-07-03,5720.38,5749.93,5656.47,5703.02,336260000,5703.02 1996-07-02,5729.98,5769.88,5668.29,5720.38,388000000,5720.38 1996-07-01,5654.63,5749.19,5637.26,5729.98,345750000,5729.98 1996-06-28,5677.53,5724.44,5625.81,5654.63,470460000,5654.63 1996-06-27,5682.70,5715.21,5616.21,5677.53,405580000,5677.53 1996-06-26,5719.27,5739.22,5652.04,5682.70,386520000,5682.70 1996-06-25,5717.79,5760.27,5668.66,5719.27,391900000,5719.27 1996-06-24,5705.23,5770.61,5688.61,5717.79,333840000,5717.79 1996-06-21,5659.43,5722.22,5639.11,5705.23,520340000,5705.23 1996-06-20,5648.35,5709.30,5606.97,5659.43,441060000,5659.43 1996-06-19,5628.03,5693.78,5600.70,5648.35,383610000,5648.35 1996-06-18,5652.78,5683.44,5607.71,5628.03,373290000,5628.03 1996-06-17,5649.45,5689.72,5614.36,5652.78,298410000,5652.78 1996-06-14,5657.95,5687.13,5609.93,5649.45,390630000,5649.45 1996-06-13,5668.29,5714.84,5622.86,5657.95,397620000,5657.95 1996-06-12,5668.66,5725.55,5637.63,5668.29,397190000,5668.29 1996-06-11,5687.87,5747.71,5637.63,5668.66,405390000,5668.66 1996-06-10,5697.11,5727.03,5643.54,5687.87,337480000,5687.87 1996-06-07,5667.19,5708.93,5559.69,5697.11,445710000,5697.11 1996-06-06,5697.48,5750.67,5639.48,5667.19,464800000,5667.19 1996-06-05,5665.71,5718.53,5631.35,5697.48,380360000,5697.48 1996-06-04,5624.71,5697.84,5616.58,5665.71,386040000,5665.71 1996-06-03,5643.18,5662.75,5587.40,5624.71,318470000,5624.71 1996-05-31,5693.41,5712.62,5614.36,5643.18,351750000,5643.18 1996-05-30,5673.83,5734.41,5625.07,5693.41,381960000,5693.41 1996-05-29,5709.67,5743.65,5632.46,5673.83,346730000,5673.83 1996-05-28,5762.86,5798.69,5680.48,5709.67,341480000,5709.67 1996-05-24,5762.12,5815.68,5722.59,5762.86,329150000,5762.86 1996-05-23,5778.00,5833.04,5704.12,5762.12,431850000,5762.12 1996-05-22,5736.26,5803.49,5687.87,5778.00,423670000,5778.00 1996-05-21,5748.82,5794.63,5698.21,5736.26,409610000,5736.26 1996-05-20,5687.50,5778.74,5657.58,5748.82,385000000,5748.82 1996-05-17,5635.05,5729.61,5631.35,5687.50,429140000,5687.50 1996-05-16,5625.44,5677.53,5577.42,5635.05,392070000,5635.05 1996-05-15,5624.71,5691.57,5590.72,5625.44,447790000,5625.44 1996-05-14,5582.60,5663.12,5566.71,5624.71,460440000,5624.71 1996-05-13,5518.14,5601.80,5495.42,5582.60,394180000,5582.60 1996-05-10,5478.03,5559.68,5478.03,5518.14,428370000,5518.14 1996-05-09,5474.06,5534.76,5419.87,5475.14,404310000,5475.14 1996-05-08,5420.95,5486.34,5327.74,5474.06,495460000,5474.06 1996-05-07,5464.31,5486.34,5392.05,5420.95,410770000,5420.95 1996-05-06,5478.03,5528.97,5397.83,5464.31,375820000,5464.31 1996-05-03,5498.27,5555.71,5439.74,5478.03,434010000,5478.03 1996-05-02,5575.22,5578.11,5455.27,5498.27,442960000,5498.27 1996-05-01,5569.08,5619.29,5523.56,5575.22,404620000,5575.22 1996-04-30,5573.41,5606.29,5522.83,5569.08,393390000,5569.08 1996-04-29,5567.99,5611.71,5515.25,5573.41,344030000,5573.41 1996-04-26,5566.91,5618.57,5517.78,5567.99,402530000,5567.99 1996-04-25,5553.90,5601.23,5490.68,5566.91,461120000,5566.91 1996-04-24,5588.59,5619.29,5512.36,5553.90,494220000,5553.90 1996-04-23,5564.74,5621.82,5534.76,5588.59,452690000,5588.59 1996-04-22,5535.48,5610.62,5516.33,5564.74,397460000,5564.74 1996-04-19,5551.74,5593.64,5504.41,5535.48,435690000,5535.48 1996-04-18,5549.93,5600.51,5493.93,5551.74,415150000,5551.74 1996-04-17,5620.02,5653.25,5500.07,5549.93,465200000,5549.93 1996-04-16,5592.92,5656.14,5554.99,5620.02,453310000,5620.02 1996-04-15,5532.59,5614.60,5517.41,5592.92,346370000,5592.92 1996-04-12,5487.07,5577.39,5445.16,5532.59,413270000,5532.59 1996-04-11,5485.98,5540.17,5382.66,5487.07,519710000,5487.07 1996-04-10,5560.41,5601.23,5452.02,5485.98,475150000,5485.98 1996-04-09,5594.37,5644.58,5530.06,5560.41,426790000,5560.41 1996-04-08,5624.71,5624.71,5518.14,5594.37,411810000,5594.37 1996-04-04,5689.74,5737.07,5633.02,5682.88,383400000,5682.88 1996-04-03,5671.68,5712.50,5619.29,5689.74,386620000,5689.74 1996-04-02,5637.72,5706.72,5597.26,5671.68,406640000,5671.68 1996-04-01,5587.14,5670.23,5562.57,5637.72,392120000,5637.72 1996-03-29,5630.85,5682.88,5550.29,5587.14,413510000,5587.14 1996-03-28,5626.88,5664.45,5564.74,5630.85,370750000,5630.85 1996-03-27,5670.60,5703.47,5596.53,5626.88,406280000,5626.88 1996-03-26,5643.86,5701.30,5595.81,5670.60,400090000,5670.60 1996-03-25,5636.64,5712.14,5592.92,5643.86,336700000,5643.86 1996-03-22,5626.88,5681.07,5589.67,5636.64,329390000,5636.64 1996-03-21,5655.42,5696.25,5590.03,5626.88,367180000,5626.88 1996-03-20,5669.51,5724.06,5590.39,5655.42,409780000,5655.42 1996-03-19,5683.60,5755.86,5619.66,5669.51,438300000,5669.51 1996-03-18,5584.97,5706.00,5573.41,5683.60,437100000,5683.60 1996-03-15,5586.06,5628.69,5523.56,5584.97,529970000,5584.97 1996-03-14,5568.72,5662.29,5536.56,5586.06,492630000,5586.06 1996-03-13,5583.89,5626.52,5513.80,5568.72,413030000,5568.72 1996-03-12,5581.00,5622.55,5464.67,5583.89,454980000,5583.89 1996-03-11,5470.45,5605.20,5425.29,5581.00,449500000,5581.00 1996-03-08,5612.79,5612.79,5395.30,5470.45,546550000,5470.45 1996-03-07,5629.77,5667.34,5572.33,5641.69,425790000,5641.69 1996-03-06,5642.42,5700.22,5585.70,5629.77,428220000,5629.77 1996-03-05,5600.15,5655.78,5558.24,5642.42,445700000,5642.42 1996-03-04,5536.56,5646.39,5511.99,5600.15,417270000,5600.15 1996-03-01,5485.62,5573.41,5424.20,5536.56,471480000,5536.56 1996-02-29,5506.21,5562.21,5440.46,5485.62,453170000,5485.62 1996-02-28,5549.21,5625.07,5487.07,5506.21,447790000,5506.21 1996-02-27,5565.10,5597.26,5478.76,5549.21,431340000,5549.21 1996-02-26,5630.49,5647.83,5530.42,5565.10,399330000,5565.10 1996-02-23,5608.46,5693.36,5546.32,5630.49,443130000,5630.49 1996-02-22,5515.97,5638.44,5511.63,5608.46,494750000,5608.46 1996-02-21,5458.53,5548.12,5440.82,5515.97,431220000,5515.97 1996-02-20,5503.32,5515.97,5393.50,5458.53,395910000,5458.53 1996-02-16,5551.37,5563.30,5470.45,5503.32,445570000,5503.32 1996-02-15,5579.55,5623.27,5514.88,5551.37,415320000,5551.37 1996-02-14,5601.23,5633.02,5534.39,5579.55,421790000,5579.55 1996-02-13,5600.15,5644.94,5530.06,5601.23,441540000,5601.23 1996-02-12,5541.62,5643.50,5531.14,5600.15,401490000,5600.15 1996-02-09,5539.45,5603.76,5474.06,5541.62,477640000,5541.62 1996-02-08,5492.12,5559.68,5441.55,5539.45,474970000,5539.45 1996-02-07,5459.61,5520.30,5423.84,5492.12,462730000,5492.12 1996-02-06,5407.59,5483.82,5371.82,5459.61,465940000,5459.61 1996-02-05,5373.99,5433.96,5319.43,5407.59,377760000,5407.59 1996-02-02,5405.06,5442.99,5338.94,5373.99,420020000,5373.99 1996-02-01,5395.30,5438.29,5335.69,5405.06,461610000,5405.06 1996-01-31,5381.21,5433.24,5314.38,5395.30,472210000,5395.30 1996-01-30,5304.98,5409.75,5288.73,5381.21,464350000,5381.21 1996-01-29,5271.75,5338.22,5246.82,5304.98,363330000,5304.98 1996-01-26,5216.83,5293.78,5187.21,5271.75,385700000,5271.75 1996-01-25,5242.84,5289.45,5173.84,5216.83,453270000,5216.83 1996-01-24,5192.27,5297.04,5176.73,5242.84,476380000,5242.84 1996-01-23,5219.36,5241.76,5141.33,5192.27,416910000,5192.27 1996-01-22,5184.68,5254.77,5133.02,5219.36,398040000,5219.36 1996-01-19,5124.35,5214.66,5087.49,5184.68,497720000,5184.68 1996-01-18,5066.90,5166.98,5032.58,5124.35,450410000,5124.35 1996-01-17,5088.22,5133.38,5028.61,5066.90,458720000,5066.90 1996-01-16,5043.78,5116.04,5000.79,5088.22,425220000,5088.22 1996-01-15,5061.12,5099.42,5012.71,5043.78,306180000,5043.78 1996-01-12,5065.10,5114.23,5000.07,5061.12,383400000,5061.12 1996-01-11,5032.94,5099.78,5002.96,5065.10,408800000,5065.10 1996-01-10,5130.13,5151.69,5000.07,5032.94,496830000,5032.94 1996-01-09,5197.70,5239.23,5100.86,5130.13,417400000,5130.13 1996-01-08,5181.43,5207.08,5179.98,5197.70,130360000,5197.70 1996-01-05,5173.84,5217.55,5107.00,5181.43,437110000,5181.43 1996-01-04,5194.07,5259.46,5114.23,5173.84,512580000,5173.84 1996-01-03,5177.45,5252.60,5143.13,5194.07,468950000,5194.07 1996-01-02,5117.12,5208.16,5087.13,5177.45,364180000,5177.45 1995-12-29,5095.80,5144.58,5063.65,5117.12,319680000,5117.12 1995-12-28,5105.92,5132.65,5062.21,5095.80,288470000,5095.80 1995-12-27,5110.26,5146.74,5077.74,5105.92,252270000,5105.92 1995-12-26,5097.97,5149.27,5072.32,5110.26,217030000,5110.26 1995-12-22,5096.53,5146.74,5064.01,5097.97,289600000,5097.97 1995-12-21,5059.32,5135.91,5031.50,5096.53,415780000,5096.53 1995-12-20,5109.89,5173.48,5047.39,5059.32,437650000,5059.32 1995-12-19,5075.21,5146.02,5016.68,5109.89,18440000,5109.89 1995-12-18,5159.39,5159.39,5042.70,5075.21,426230000,5075.21 1995-12-15,5182.15,5217.55,5135.54,5176.73,636780000,5176.73 1995-12-14,5216.47,5266.69,5148.55,5182.15,461960000,5182.15 1995-12-13,5174.92,5246.10,5144.22,5216.47,414680000,5216.47 1995-12-12,5184.32,5226.23,5132.29,5174.92,349410000,5174.92 1995-12-11,5156.86,5225.50,5122.18,5184.32,342050000,5184.32 1995-12-08,5159.39,5200.21,5115.31,5156.86,327500000,5156.86 1995-12-07,5199.13,5211.05,5124.35,5159.39,379260000,5159.39 1995-12-06,5177.45,5234.53,5147.47,5199.13,417750000,5199.13 1995-12-05,5139.52,5216.83,5108.45,5177.45,434000000,5177.45 1995-12-04,5087.13,5157.58,5057.87,5139.52,405080000,5139.52 1995-12-01,5074.49,5133.02,5038.36,5087.13,392650000,5087.13 1995-11-30,5105.56,5143.13,5033.17,5074.49,439470000,5074.49 1995-11-29,5078.10,5126.51,5047.03,5105.56,398230000,5105.56 1995-11-28,5070.88,5105.56,5006.21,5078.10,408860000,5078.10 1995-11-27,5048.84,5114.23,5034.03,5070.88,356180000,5070.88 1995-11-24,5041.61,5072.68,5028.61,5048.84,125870000,5048.84 1995-11-22,5023.55,5096.17,4982.72,5041.61,404900000,5041.61 1995-11-21,4983.09,5050.28,4948.04,5023.55,405860000,5023.55 1995-11-20,4989.95,5030.77,4946.60,4983.09,333110000,4983.09 1995-11-17,4969.36,5022.10,4934.31,4989.95,429990000,4989.95 1995-11-16,4922.75,5003.68,4902.16,4969.36,418430000,4969.36 1995-11-15,4871.81,4939.73,4835.69,4922.75,373090000,4922.75 1995-11-14,4872.90,4923.11,4826.29,4871.81,353650000,4871.81 1995-11-13,4870.37,4909.75,4821.23,4872.90,292390000,4872.90 1995-11-10,4864.23,4896.02,4820.51,4870.37,297950000,4870.37 1995-11-09,4852.67,4902.52,4811.84,4864.23,379500000,4864.23 1995-11-08,4797.03,4877.59,4775.71,4852.67,359770000,4852.67 1995-11-07,4814.01,4839.30,4770.66,4797.03,365720000,4797.03 1995-11-06,4825.57,4862.78,4779.33,4814.01,309090000,4814.01 1995-11-03,4808.59,4858.81,4774.63,4825.57,344360000,4825.57 1995-11-02,4766.68,4833.16,4745.00,4808.59,396150000,4808.59 1995-11-01,4755.48,4801.73,4719.72,4766.68,377930000,4766.68 1995-10-31,4756.57,4821.96,4735.97,4755.48,377350000,4755.48 1995-10-30,4741.75,4798.84,4716.46,4756.57,318840000,4756.57 1995-10-27,4703.82,4766.68,4653.24,4741.75,378820000,4741.75 1995-10-26,4753.68,4777.88,4655.05,4703.82,464190000,4703.82 1995-10-25,4783.66,4824.49,4708.88,4753.68,433570000,4753.68 1995-10-24,4755.48,4819.07,4730.92,4783.66,415400000,4783.66 1995-10-23,4794.86,4805.70,4724.41,4755.48,329720000,4755.48 1995-10-20,4802.45,4836.41,4758.37,4794.86,388140000,4794.86 1995-10-19,4777.52,4830.27,4744.28,4802.45,406620000,4802.45 1995-10-18,4795.95,4837.49,4747.53,4777.52,411270000,4777.52 1995-10-17,4784.38,4831.35,4747.90,4795.95,352940000,4795.95 1995-10-16,4793.78,4823.04,4751.51,4784.38,299520000,4784.38 1995-10-13,4764.88,4845.08,4749.70,4793.78,373970000,4793.78 1995-10-12,4735.25,4790.16,4709.24,4764.88,343930000,4764.88 1995-10-11,4720.80,4773.91,4686.43,4735.25,343060000,4735.25 1995-10-10,4726.22,4745.73,4638.43,4720.80,412670000,4720.80 1995-10-09,4769.21,4781.13,4691.54,4726.22,275280000,4726.22 1995-10-06,4762.71,4805.70,4731.64,4769.21,314170000,4769.21 1995-10-05,4740.67,4794.86,4705.63,4762.71,367410000,4762.71 1995-10-04,4749.70,4787.27,4689.01,4740.67,339350000,4740.67 1995-10-03,4761.26,4791.61,4702.74,4749.70,385890000,4749.70 1995-10-02,4789.08,4817.98,4732.72,4761.26,304990000,4761.26 1995-09-29,4787.64,4834.96,4757.65,4789.08,337670000,4789.08 1995-09-28,4762.35,4810.03,4731.64,4787.64,367610000,4787.64 1995-09-27,4765.60,4790.16,4692.98,4762.35,410970000,4762.35 1995-09-26,4769.93,4816.54,4738.86,4765.60,362550000,4765.60 1995-09-25,4764.15,4804.62,4728.02,4769.93,273110000,4769.93 1995-09-22,4767.40,4789.44,4706.35,4764.15,370750000,4764.15 1995-09-21,4792.69,4820.15,4728.75,4767.40,367060000,4767.40 1995-09-20,4767.04,4828.46,4746.45,4792.69,402530000,4792.69 1995-09-19,4780.41,4798.11,4734.53,4767.04,371080000,4767.04 1995-09-18,4797.57,4814.01,4729.47,4780.41,328630000,4780.41 1995-09-15,4801.80,4839.48,4762.35,4797.57,459370000,4797.57 1995-09-14,4765.52,4830.32,4731.36,4801.80,382860000,4801.80 1995-09-13,4747.21,4801.09,4697.55,4765.52,381450000,4765.52 1995-09-12,4704.94,4762.35,4689.45,4747.21,342580000,4747.21 1995-09-11,4700.72,4744.04,4672.54,4704.94,296820000,4704.94 1995-09-08,4669.72,4722.91,4648.59,4700.72,317260000,4700.72 1995-09-07,4683.81,4710.58,4640.14,4669.72,321710000,4669.72 1995-09-06,4670.08,4716.21,4648.95,4683.81,369510000,4683.81 1995-09-05,4647.54,4697.90,4625.70,4670.08,332660000,4670.08 1995-09-01,4610.56,4672.19,4594.71,4647.54,255710000,4647.54 1995-08-31,4604.57,4634.51,4582.38,4610.56,300890000,4610.56 1995-08-30,4608.44,4639.79,4582.38,4604.57,329780000,4604.57 1995-08-29,4594.00,4625.35,4554.21,4608.44,311290000,4608.44 1995-08-28,4601.40,4632.39,4566.53,4594.00,267860000,4594.00 1995-08-25,4580.62,4629.93,4569.70,4601.40,255990000,4601.40 1995-08-24,4584.85,4618.30,4552.80,4580.62,299200000,4580.62 1995-08-23,4620.42,4636.27,4571.81,4584.85,291380000,4584.85 1995-08-22,4614.78,4646.13,4580.62,4620.42,290350000,4620.42 1995-08-21,4617.60,4676.42,4593.65,4614.78,303200000,4614.78 1995-08-18,4630.63,4665.15,4597.88,4617.60,312030000,4617.60 1995-08-17,4639.08,4659.16,4587.66,4630.63,354460000,4630.63 1995-08-16,4640.84,4673.60,4593.30,4639.08,390070000,4639.08 1995-08-15,4659.86,4672.89,4602.10,4640.84,330040000,4640.84 1995-08-14,4618.30,4677.12,4601.75,4659.86,263750000,4659.86 1995-08-11,4643.66,4659.51,4584.85,4618.30,267850000,4618.30 1995-08-10,4671.49,4698.96,4621.47,4643.66,306660000,4643.66 1995-08-09,4693.32,4712.34,4649.30,4671.49,303390000,4671.49 1995-08-08,4693.32,4722.55,4654.23,4693.32,305150000,4693.32 1995-08-07,4683.46,4727.84,4667.26,4693.32,276040000,4693.32 1995-08-04,4701.42,4728.54,4660.57,4683.46,314730000,4683.46 1995-08-03,4690.15,4720.44,4632.04,4701.42,353110000,4701.42 1995-08-02,4700.37,4772.56,4667.96,4690.15,374310000,4690.15 1995-08-01,4708.47,4742.98,4648.59,4700.37,334770000,4700.37 1995-07-31,4715.51,4753.55,4671.13,4708.47,291950000,4708.47 1995-07-28,4732.77,4762.70,4686.28,4715.51,311580000,4715.51 1995-07-27,4707.06,4767.99,4691.56,4732.77,356570000,4732.77 1995-07-26,4714.45,4750.73,4665.15,4707.06,393460000,4707.06 1995-07-25,4668.67,4743.69,4651.76,4714.45,373210000,4714.45 1995-07-24,4641.55,4701.42,4620.42,4668.67,315170000,4668.67 1995-07-21,4641.55,4676.06,4596.82,4641.55,427770000,4641.55 1995-07-20,4628.87,4684.52,4578.51,4641.55,383380000,4641.55 1995-07-19,4686.28,4698.60,4530.26,4628.87,489850000,4628.87 1995-07-18,4734.53,4734.53,4648.24,4686.28,372230000,4686.28 1995-07-17,4708.82,4767.63,4681.35,4736.29,322540000,4736.29 1995-07-14,4727.48,4736.99,4664.79,4708.82,312930000,4708.82 1995-07-13,4727.29,4766.58,4676.06,4727.48,387470000,4727.48 1995-07-12,4680.60,4747.00,4654.66,4727.29,416000000,4727.29 1995-07-11,4702.39,4724.52,4647.74,4680.60,376770000,4680.60 1995-07-10,4702.73,4747.69,4670.91,4702.39,409700000,4702.39 1995-07-07,4664.00,4740.77,4628.38,4702.73,466540000,4702.73 1995-07-06,4615.23,4681.98,4587.91,4664.00,420470000,4664.00 1995-07-05,4585.15,4652.24,4561.63,4615.23,357810000,4615.23 1995-07-03,4556.10,4594.83,4536.04,4585.15,117870000,4585.15 1995-06-30,4550.56,4606.24,4513.90,4556.10,311320000,4556.10 1995-06-29,4556.79,4592.76,4510.45,4550.56,313060000,4550.56 1995-06-28,4542.61,4587.22,4512.87,4556.79,368060000,4556.79 1995-06-27,4551.25,4592.41,4511.48,4542.61,346950000,4542.61 1995-06-26,4585.84,4600.02,4536.38,4551.25,296720000,4551.25 1995-06-23,4589.64,4609.70,4549.18,4585.84,321530000,4585.84 1995-06-22,4547.10,4614.20,4535.35,4589.64,420950000,4589.64 1995-06-21,4550.56,4583.07,4517.02,4547.10,398210000,4547.10 1995-06-20,4553.68,4587.22,4497.99,4550.56,382290000,4550.56 1995-06-19,4510.79,4577.19,4498.69,4553.68,322620000,4553.68 1995-06-16,4496.27,4533.96,4482.43,4510.79,442740000,4510.79 1995-06-15,4491.08,4527.74,4466.87,4496.27,334640000,4496.27 1995-06-14,4484.51,4510.79,4449.23,4491.08,330750000,4491.08 1995-06-13,4446.46,4504.91,4440.24,4484.51,339620000,4484.51 1995-06-12,4423.99,4482.09,4415.69,4446.46,287830000,4446.46 1995-06-09,4458.57,4466.87,4394.59,4423.99,328960000,4423.99 1995-06-08,4462.03,4492.12,4431.59,4458.57,289880000,4458.57 1995-06-07,4485.20,4497.65,4432.29,4462.03,327790000,4462.03 1995-06-06,4476.55,4520.47,4446.46,4485.20,340470000,4485.20 1995-06-05,4444.39,4510.45,4417.76,4476.55,337520000,4476.55 1995-06-02,4472.75,4496.27,4406.35,4444.39,366000000,4444.39 1995-06-01,4465.14,4499.72,4421.56,4472.75,345890000,4472.75 1995-05-31,4378.68,4467.91,4360.70,4465.14,358160000,4465.14 1995-05-30,4369.00,4412.92,4334.41,4378.68,283020000,4378.68 1995-05-26,4412.23,4423.64,4338.91,4369.00,290730000,4369.00 1995-05-25,4427.44,4451.31,4375.91,4412.23,341820000,4412.23 1995-05-24,4436.44,4480.70,4390.78,4438.16,391750000,4438.16 1995-05-23,4395.63,4451.65,4372.46,4436.44,362690000,4436.44 1995-05-22,4341.33,4416.03,4337.87,4395.63,285600000,4395.63 1995-05-19,4340.64,4368.65,4287.38,4341.33,354010000,4341.33 1995-05-18,4422.60,4426.41,4330.95,4340.64,351850000,4340.64 1995-05-17,4435.05,4452.69,4386.63,4422.60,347930000,4422.60 1995-05-16,4437.47,4464.10,4408.08,4435.05,366180000,4435.05 1995-05-15,4430.56,4468.94,4398.74,4437.47,316240000,4437.47 1995-05-12,4411.19,4463.07,4371.07,4430.56,361000000,4430.56 1995-05-11,4404.62,4446.12,4365.19,4411.19,339900000,4411.19 1995-05-10,4390.78,4440.24,4347.55,4404.62,381990000,4404.62 1995-05-09,4383.87,4421.22,4360.00,4390.78,361430000,4390.78 1995-05-08,4343.40,4407.04,4316.43,4383.87,291810000,4383.87 1995-05-05,4359.66,4389.75,4310.55,4343.40,342380000,4343.40 1995-05-04,4373.15,4426.41,4329.92,4359.66,434920000,4359.66 1995-05-03,4328.88,4392.51,4312.28,4373.15,392290000,4373.15 1995-05-02,4316.08,4348.25,4288.42,4328.88,300660000,4328.88 1995-05-01,4321.27,4352.74,4278.73,4316.08,296830000,4316.08 1995-04-28,4314.70,4348.94,4270.78,4321.27,320270000,4321.27 1995-04-27,4299.83,4335.10,4269.05,4314.70,350850000,4314.70 1995-04-26,4300.17,4324.73,4267.32,4299.83,350790000,4299.83 1995-04-25,4303.98,4337.18,4267.32,4300.17,351790000,4300.17 1995-04-24,4270.09,4328.88,4239.65,4303.98,325760000,4303.98 1995-04-21,4230.66,4296.37,4214.41,4270.09,403210000,4270.09 1995-04-20,4207.49,4263.86,4186.39,4230.66,368440000,4230.66 1995-04-19,4179.13,4232.39,4143.51,4207.49,377520000,4207.49 1995-04-18,4195.38,4221.67,4152.15,4179.13,344680000,4179.13 1995-04-17,4208.18,4260.06,4174.63,4195.38,333930000,4195.38 1995-04-13,4197.81,4243.46,4173.94,4208.18,301510000,4208.18 1995-04-12,4187.08,4221.67,4163.57,4197.81,327880000,4197.81 1995-04-11,4198.15,4229.97,4168.06,4187.08,309710000,4187.08 1995-04-10,4192.62,4219.94,4163.91,4198.15,260980000,4198.15 1995-04-07,4205.41,4226.86,4154.23,4192.62,314750000,4192.62 1995-04-06,4200.57,4239.31,4179.13,4205.41,320460000,4205.41 1995-04-05,4201.61,4229.62,4166.33,4200.57,315170000,4200.57 1995-04-04,4168.41,4220.98,4154.23,4201.61,330550000,4201.61 1995-04-03,4157.69,4202.30,4129.68,4168.41,287380000,4168.41 1995-03-31,4172.56,4194.00,4100.28,4157.69,352940000,4157.69 1995-03-30,4160.80,4213.37,4128.29,4172.56,362020000,4172.56 1995-03-29,4151.81,4213.71,4121.72,4160.80,385910000,4160.80 1995-03-28,4157.34,4176.02,4120.68,4151.81,320360000,4151.81 1995-03-27,4138.67,4177.40,4113.08,4157.34,296160000,4157.34 1995-03-24,4087.83,4155.27,4087.14,4138.67,358370000,4138.67 1995-03-23,4082.99,4107.89,4046.33,4087.83,318490000,4087.83 1995-03-22,4072.61,4107.54,4039.07,4082.99,313120000,4082.99 1995-03-21,4083.68,4122.41,4046.67,4072.61,367110000,4072.61 1995-03-20,4073.65,4115.15,4051.17,4083.68,301720000,4083.68 1995-03-17,4069.15,4101.66,4044.94,4073.65,415810000,4073.65 1995-03-16,4038.37,4095.78,4021.77,4069.15,336330000,4069.15 1995-03-15,4048.75,4070.19,4008.63,4038.37,309540000,4038.37 1995-03-14,4025.23,4087.14,4014.86,4048.75,346140000,4048.75 1995-03-13,4035.61,4060.85,3999.29,4025.23,275280000,4025.23 1995-03-10,3983.39,4054.97,3978.20,4035.61,383000000,4035.61 1995-03-09,3979.23,4011.40,3953.99,3983.39,319100000,3983.39 1995-03-08,3962.63,4002.41,3944.65,3979.23,349700000,3979.23 1995-03-07,3997.56,4009.67,3935.31,3962.63,355550000,3962.63 1995-03-06,3989.61,4015.89,3944.31,3997.56,298850000,3997.56 1995-03-03,3979.93,4004.83,3946.03,3989.61,330840000,3989.61 1995-03-02,3994.80,4009.67,3947.07,3979.93,329430000,3979.93 1995-03-01,4011.05,4033.19,3960.56,3994.80,362590000,3994.80 1995-02-28,3988.57,4021.43,3967.48,4011.05,317120000,4011.05 1995-02-27,4011.74,4033.19,3966.78,3988.57,285790000,3988.57 1995-02-24,4003.33,4033.61,3974.06,4011.74,302850000,4011.74 1995-02-23,3979.45,4034.62,3979.45,4003.33,394100000,4003.33 1995-02-22,3963.97,4002.32,3944.46,3973.05,339140000,3973.05 1995-02-21,3953.54,3989.88,3930.66,3963.97,308060000,3963.97 1995-02-17,3987.52,4001.99,3937.05,3953.54,350560000,3953.54 1995-02-16,3986.17,4011.07,3948.16,3987.52,360990000,3987.52 1995-02-15,3958.25,4019.15,3937.73,3986.17,377940000,3986.17 1995-02-14,3954.21,3984.83,3930.66,3958.25,300720000,3958.25 1995-02-13,3939.07,3974.74,3920.57,3954.21,256210000,3954.21 1995-02-10,3932.68,3962.96,3908.46,3939.07,295550000,3939.07 1995-02-09,3935.37,3967.33,3904.76,3932.68,325570000,3932.68 1995-02-08,3937.39,3967.67,3909.13,3935.37,317910000,3935.37 1995-02-07,3937.73,3960.27,3907.45,3937.39,317110000,3937.39 1995-02-06,3928.64,3964.31,3900.04,3937.73,325660000,3937.73 1995-02-03,3876.16,3959.60,3876.16,3928.64,440950000,3928.64 1995-02-02,3847.56,3884.23,3828.38,3870.77,322030000,3870.77 1995-02-01,3843.86,3886.25,3809.21,3847.56,395300000,3847.56 1995-01-31,3832.08,3872.12,3809.54,3843.86,411570000,3843.86 1995-01-30,3857.99,3881.20,3794.40,3832.08,318530000,3832.08 1995-01-27,3870.44,3914.18,3827.37,3857.99,339490000,3857.99 1995-01-26,3871.45,3903.41,3839.15,3870.44,304650000,3870.44 1995-01-25,3862.70,3908.79,3832.08,3871.45,342240000,3871.45 1995-01-24,3867.41,3898.36,3840.16,3862.70,315410000,3862.70 1995-01-23,3869.43,3885.58,3815.26,3867.41,325810000,3867.41 1995-01-20,3882.21,3898.70,3826.70,3869.43,376870000,3869.43 1995-01-19,3928.98,3929.99,3866.74,3882.21,297220000,3882.21 1995-01-18,3930.66,3950.85,3889.95,3928.98,343100000,3928.98 1995-01-17,3932.34,3953.88,3895.33,3930.66,330890000,3930.66 1995-01-16,3908.46,3955.56,3889.95,3932.34,315800000,3932.34 1995-01-13,3859.00,3924.27,3852.61,3908.46,336740000,3908.46 1995-01-12,3862.03,3886.59,3831.41,3859.00,313040000,3859.00 1995-01-11,3866.74,3899.71,3824.68,3862.03,346310000,3862.03 1995-01-10,3861.35,3912.49,3844.87,3866.74,352440000,3866.74 1995-01-09,3867.41,3889.28,3834.44,3861.35,278710000,3861.35 1995-01-06,3850.92,3902.40,3823.67,3867.41,308070000,3867.41 1995-01-05,3857.65,3876.83,3825.35,3850.92,309140000,3850.92 1995-01-04,3838.48,3876.83,3815.26,3857.65,319510000,3857.65 1995-01-03,3834.44,3864.72,3805.50,3838.48,262450000,3838.48 1994-12-30,3833.43,3874.48,3812.91,3834.44,256260000,3834.44 1994-12-29,3839.49,3867.41,3812.91,3833.43,250650000,3833.43 1994-12-28,3861.69,3871.45,3816.94,3839.49,246260000,3839.49 1994-12-27,3833.43,3882.21,3832.08,3861.69,211180000,3861.69 1994-12-23,3814.92,3860.01,3808.53,3833.43,196540000,3833.43 1994-12-22,3801.80,3850.59,3780.61,3814.92,339670000,3814.92 1994-12-21,3767.15,3836.46,3761.77,3801.80,378790000,3801.80 1994-12-20,3790.70,3807.19,3752.35,3767.15,325510000,3767.15 1994-12-19,3807.19,3815.26,3764.46,3790.70,271850000,3790.70 1994-12-16,3765.47,3817.95,3758.07,3807.19,481860000,3807.19 1994-12-15,3746.29,3794.07,3729.13,3765.47,332790000,3765.47 1994-12-14,3715.34,3772.20,3700.53,3746.29,355000000,3746.29 1994-12-13,3718.37,3749.32,3690.78,3715.34,307110000,3715.34 1994-12-12,3691.11,3734.52,3667.90,3718.37,285730000,3718.37 1994-12-09,3685.73,3713.32,3638.97,3691.11,336440000,3691.11 1994-12-08,3735.52,3757.39,3670.25,3685.73,362280000,3685.73 1994-12-07,3745.95,3758.07,3700.87,3735.52,283490000,3735.52 1994-12-06,3741.92,3762.10,3703.56,3745.95,298890000,3745.95 1994-12-05,3745.62,3779.93,3715.67,3741.92,258480000,3741.92 1994-12-02,3700.87,3755.04,3680.68,3745.62,284740000,3745.62 1994-12-01,3739.23,3755.37,3680.68,3700.87,285920000,3700.87 1994-11-30,3738.55,3783.30,3718.37,3739.23,300800000,3739.23 1994-11-29,3739.56,3755.04,3703.90,3738.55,286580000,3738.55 1994-11-28,3708.27,3759.41,3693.13,3739.56,265020000,3739.56 1994-11-25,3675.97,3722.40,3675.97,3708.27,118290000,3708.27 1994-11-23,3677.99,3704.91,3612.05,3674.63,430730000,3674.63 1994-11-22,3769.51,3787.34,3669.58,3677.99,387270000,3677.99 1994-11-21,3815.26,3845.20,3758.74,3769.51,293030000,3769.51 1994-11-18,3828.05,3844.87,3773.21,3815.26,356730000,3815.26 1994-11-17,3845.20,3868.08,3797.77,3828.05,323190000,3828.05 1994-11-16,3826.36,3864.38,3803.82,3845.20,296980000,3845.20 1994-11-15,3829.73,3871.45,3794.40,3826.36,336330000,3826.36 1994-11-14,3801.47,3849.91,3795.07,3829.73,260380000,3829.73 1994-11-11,3821.99,3830.06,3779.93,3801.47,220800000,3801.47 1994-11-10,3831.75,3873.47,3821.99,3821.99,280910000,3821.99 1994-11-09,3830.74,3882.89,3798.44,3831.75,341500000,3831.75 1994-11-08,3808.87,3857.65,3798.75,3830.74,290860000,3830.74 1994-11-07,3807.52,3830.40,3781.62,3808.87,255030000,3808.87 1994-11-04,3845.88,3879.52,3802.81,3807.52,280560000,3807.52 1994-11-03,3837.13,3872.46,3814.25,3845.88,284480000,3845.88 1994-11-02,3863.37,3888.94,3820.31,3837.13,331360000,3837.13 1994-11-01,3908.12,3919.90,3836.79,3863.37,314940000,3863.37 1994-10-31,3930.66,3956.90,3889.28,3908.12,302810000,3908.12 1994-10-28,3875.15,3953.54,3863.37,3930.66,381450000,3930.66 1994-10-27,3848.23,3893.99,3834.44,3875.15,327790000,3875.15 1994-10-26,3850.59,3891.97,3816.61,3848.23,322560000,3848.23 1994-10-25,3855.30,3883.56,3803.49,3850.59,326100000,3850.59 1994-10-24,3891.30,3925.61,3840.16,3855.30,282800000,3855.30 1994-10-21,3911.15,3921.58,3861.35,3891.30,309410000,3891.30 1994-10-20,3936.04,3954.89,3873.13,3911.15,326100000,3911.15 1994-10-19,3917.54,3958.25,3887.93,3936.04,317030000,3936.04 1994-10-18,3923.93,3945.46,3892.64,3917.54,259730000,3917.54 1994-10-17,3910.47,3949.84,3883.22,3923.93,238490000,3923.93 1994-10-14,3889.95,3927.97,3862.03,3910.47,251770000,3910.47 1994-10-13,3878.18,3944.12,3878.18,3889.95,337900000,3889.95 1994-10-12,3876.83,3903.07,3844.87,3875.15,269550000,3875.15 1994-10-11,3828.96,3898.36,3828.96,3876.83,355540000,3876.83 1994-10-10,3797.43,3843.19,3789.36,3821.32,213110000,3821.32 1994-10-07,3775.56,3826.03,3754.37,3797.43,284230000,3797.43 1994-10-06,3787.34,3810.89,3752.01,3775.56,272620000,3775.56 1994-10-05,3801.13,3811.56,3736.20,3787.34,359670000,3787.34 1994-10-04,3846.89,3873.47,3788.35,3801.13,325620000,3801.13 1994-10-03,3843.19,3872.79,3809.21,3846.89,269130000,3846.89 1994-09-30,3854.63,3891.30,3825.69,3843.19,292060000,3843.19 1994-09-29,3878.18,3892.64,3834.78,3854.63,302280000,3854.63 1994-09-28,3863.04,3904.76,3854.29,3878.18,330020000,3878.18 1994-09-27,3849.24,3891.63,3828.72,3863.04,290330000,3863.04 1994-09-26,3831.75,3869.43,3804.50,3849.24,272530000,3849.24 1994-09-23,3837.13,3872.46,3806.51,3831.75,300060000,3831.75 1994-09-22,3851.60,3882.55,3818.29,3837.13,305210000,3837.13 1994-09-21,3869.09,3886.92,3806.85,3851.60,355330000,3851.60 1994-09-20,3932.01,3932.01,3859.67,3869.09,326050000,3869.09 1994-09-19,3933.35,3972.72,3909.80,3936.72,272920000,3936.72 1994-09-16,3953.88,3955.22,3894.66,3933.35,410750000,3933.35 1994-09-15,3895.33,3959.93,3883.90,3953.88,281890000,3953.88 1994-09-14,3879.86,3918.55,3856.64,3895.33,297480000,3895.33 1994-09-13,3860.34,3905.76,3854.29,3879.86,293370000,3879.86 1994-09-12,3874.81,3897.02,3843.86,3860.34,244680000,3860.34 1994-09-09,3902.06,3902.06,3844.20,3874.81,293330000,3874.81 1994-09-08,3886.25,3926.96,3872.46,3908.46,295010000,3908.46 1994-09-07,3898.70,3920.90,3860.68,3886.25,292110000,3886.25 1994-09-06,3885.58,3918.55,3860.01,3898.70,199670000,3898.70 1994-09-02,3901.44,3928.64,3871.98,3885.58,216150000,3885.58 1994-09-01,3913.42,3927.99,3871.66,3901.44,285670000,3901.44 1994-08-31,3917.30,3954.54,3878.78,3913.42,354650000,3913.42 1994-08-30,3898.85,3934.14,3875.87,3917.30,294520000,3917.30 1994-08-29,3881.05,3927.34,3869.39,3898.85,266080000,3898.85 1994-08-26,3836.69,3903.38,3836.69,3881.05,305120000,3881.05 1994-08-25,3846.73,3872.63,3810.47,3829.89,284200000,3829.89 1994-08-24,3775.83,3852.56,3767.41,3846.73,309780000,3846.73 1994-08-23,3751.22,3804.64,3745.07,3775.83,307240000,3775.83 1994-08-22,3755.11,3771.94,3722.41,3751.22,235870000,3751.22 1994-08-19,3755.43,3785.22,3727.59,3755.11,276630000,3755.11 1994-08-18,3776.48,3793.63,3736.98,3755.43,287330000,3755.43 1994-08-17,3784.57,3812.09,3754.46,3776.48,309250000,3776.48 1994-08-16,3760.29,3804.64,3732.45,3784.57,306640000,3784.57 1994-08-15,3768.71,3798.17,3742.16,3760.29,223210000,3760.29 1994-08-12,3750.90,3792.66,3738.27,3768.71,249270000,3768.71 1994-08-11,3766.76,3785.86,3728.56,3750.90,275690000,3750.90 1994-08-10,3755.76,3793.97,3738.27,3766.76,279470000,3766.76 1994-08-09,3753.81,3773.89,3728.56,3755.76,259130000,3755.76 1994-08-08,3747.02,3780.68,3732.77,3753.81,217670000,3753.81 1994-08-05,3765.79,3769.68,3725.00,3747.02,230270000,3747.02 1994-08-04,3792.66,3807.23,3752.52,3765.79,289150000,3765.79 1994-08-03,3796.22,3815.00,3762.88,3792.66,283840000,3792.66 1994-08-02,3798.17,3829.25,3776.48,3796.22,294740000,3796.22 1994-08-01,3764.50,3809.50,3749.28,3798.17,258180000,3798.17 1994-07-29,3730.83,3782.63,3726.30,3764.50,269560000,3764.50 1994-07-28,3720.47,3757.05,3701.69,3730.83,247560000,3730.83 1994-07-27,3735.68,3753.17,3693.27,3720.47,251680000,3720.47 1994-07-26,3741.84,3764.50,3706.22,3735.68,232670000,3735.68 1994-07-25,3735.04,3762.56,3713.67,3741.84,213470000,3741.84 1994-07-22,3732.45,3765.15,3707.19,3735.04,261090000,3735.04 1994-07-21,3727.27,3763.20,3684.86,3732.45,292080000,3732.45 1994-07-20,3748.31,3763.85,3706.22,3727.27,267740000,3727.27 1994-07-19,3755.43,3777.45,3726.30,3748.31,251530000,3748.31 1994-07-18,3753.81,3779.39,3725.00,3755.43,227480000,3755.43 1994-07-15,3739.25,3769.35,3712.37,3753.81,275860000,3753.81 1994-07-14,3704.28,3763.53,3697.48,3739.25,319950000,3739.25 1994-07-13,3702.66,3738.27,3683.89,3704.28,265840000,3704.28 1994-07-12,3702.99,3725.32,3660.90,3702.66,252250000,3702.66 1994-07-11,3709.14,3735.36,3671.26,3702.99,222580000,3702.99 1994-07-08,3688.42,3728.56,3660.90,3709.14,236520000,3709.14 1994-07-07,3674.50,3714.32,3656.04,3688.42,258500000,3688.42 1994-07-06,3652.48,3698.13,3631.11,3674.50,233640000,3674.50 1994-07-05,3646.65,3680.65,3621.73,3652.48,193030000,3652.48 1994-07-01,3624.96,3675.79,3611.04,3646.65,199030000,3646.65 1994-06-30,3667.05,3683.56,3610.72,3624.96,294110000,3624.96 1994-06-29,3669.64,3711.73,3645.68,3667.05,263890000,3667.05 1994-06-28,3685.50,3705.58,3630.47,3669.64,265880000,3669.64 1994-06-27,3636.94,3694.89,3603.92,3685.50,250110000,3685.50 1994-06-24,3699.09,3704.80,3616.65,3636.94,261260000,3636.94 1994-06-23,3724.77,3752.04,3685.14,3699.09,256480000,3699.09 1994-06-22,3707.97,3748.87,3694.65,3724.77,251110000,3724.77 1994-06-21,3741.90,3756.80,3674.68,3707.97,298730000,3707.97 1994-06-20,3771.07,3771.07,3716.21,3741.90,229520000,3741.90 1994-06-17,3811.34,3821.48,3764.09,3776.78,373400000,3776.78 1994-06-16,3790.41,3830.68,3771.39,3811.34,254880000,3811.34 1994-06-15,3814.83,3838.29,3772.02,3790.41,269740000,3790.41 1994-06-14,3783.12,3839.88,3769.17,3814.83,288550000,3814.83 1994-06-13,3773.45,3808.17,3741.26,3783.12,242810000,3783.12 1994-06-10,3753.14,3798.68,3739.60,3773.45,222480000,3773.45 1994-06-09,3749.45,3776.83,3721.45,3753.14,252870000,3753.14 1994-06-08,3755.91,3780.83,3721.45,3749.45,256000000,3749.45 1994-06-07,3768.52,3788.52,3733.14,3755.91,234680000,3755.91 1994-06-06,3772.22,3812.83,3749.75,3768.52,259080000,3768.52 1994-06-03,3758.99,3792.22,3732.52,3772.22,271490000,3772.22 1994-06-02,3760.83,3791.60,3732.83,3758.99,271150000,3758.99 1994-06-01,3758.37,3785.14,3717.76,3760.83,279910000,3760.83 1994-05-31,3757.14,3783.29,3725.45,3758.37,216700000,3758.37 1994-05-27,3753.46,3772.18,3723.68,3757.14,186430000,3757.14 1994-05-26,3755.30,3785.07,3722.76,3753.46,255740000,3753.46 1994-05-25,3745.17,3768.19,3710.79,3755.30,254410000,3755.30 1994-05-24,3742.41,3786.30,3707.11,3745.17,280040000,3745.17 1994-05-23,3766.35,3770.65,3711.40,3742.41,249390000,3742.41 1994-05-20,3758.98,3788.76,3721.84,3766.35,295180000,3766.35 1994-05-19,3732.89,3782.92,3707.72,3758.98,303680000,3758.98 1994-05-18,3720.61,3761.74,3683.16,3732.89,339280000,3732.89 1994-05-17,3671.50,3735.04,3653.70,3720.61,311280000,3720.61 1994-05-16,3659.68,3694.21,3628.52,3671.50,234680000,3671.50 1994-05-13,3652.84,3690.32,3626.37,3659.68,252070000,3659.68 1994-05-12,3629.04,3682.58,3624.58,3652.84,272770000,3652.84 1994-05-11,3656.41,3678.42,3609.71,3629.04,277400000,3629.04 1994-05-10,3629.04,3684.67,3627.56,3656.41,297660000,3656.41 1994-05-09,3669.50,3676.93,3612.39,3629.04,250870000,3629.04 1994-05-06,3695.97,3702.51,3625.77,3669.50,291910000,3669.50 1994-05-05,3697.75,3731.07,3675.45,3695.97,255690000,3695.97 1994-05-04,3714.41,3730.17,3670.09,3697.75,267940000,3697.75 1994-05-03,3701.02,3736.12,3669.79,3714.41,288270000,3714.41 1994-05-02,3681.69,3734.04,3648.97,3701.02,296130000,3701.02 1994-04-29,3668.31,3707.87,3642.13,3681.69,293970000,3681.69 1994-04-28,3699.54,3723.93,3640.35,3668.31,325200000,3668.31 1994-04-26,3705.78,3733.15,3669.79,3699.54,288110000,3699.54 1994-04-25,3648.68,3721.25,3635.29,3705.78,262220000,3705.78 1994-04-22,3652.54,3690.32,3621.01,3648.68,295710000,3648.68 1994-04-21,3598.71,3673.96,3582.94,3652.54,378760000,3652.54 1994-04-20,3619.82,3662.66,3546.65,3598.71,366540000,3598.71 1994-04-19,3620.42,3670.39,3567.18,3619.82,323280000,3619.82 1994-04-18,3661.47,3679.61,3593.35,3620.42,271450000,3620.42 1994-04-15,3663.25,3699.24,3631.13,3661.47,309550000,3661.47 1994-04-14,3661.47,3693.59,3625.77,3663.25,275130000,3663.25 1994-04-13,3681.69,3704.30,3616.85,3661.47,278030000,3661.47 1994-04-12,3688.83,3722.14,3661.17,3681.69,256250000,3681.69 1994-04-11,3674.26,3720.66,3651.35,3688.83,243180000,3688.83 1994-04-08,3693.26,3717.15,3644.03,3674.26,264090000,3674.26 1994-04-07,3679.73,3712.83,3642.59,3693.26,289280000,3693.26 1994-04-06,3675.41,3722.34,3643.16,3679.73,302000000,3679.73 1994-04-05,3625.02,3698.15,3625.02,3675.41,366890000,3675.41 1994-04-04,3633.08,3633.08,3520.80,3593.35,344390000,3593.35 1994-03-31,3626.75,3673.10,3544.12,3635.96,403580000,3635.96 1994-03-30,3699.02,3718.88,3612.36,3626.75,390520000,3626.75 1994-03-29,3762.35,3771.86,3689.23,3699.02,301630000,3699.02 1994-03-28,3774.73,3793.45,3719.74,3762.35,287360000,3762.35 1994-03-25,3821.09,3845.85,3764.66,3774.73,249670000,3774.73 1994-03-24,3865.42,3865.42,3792.58,3821.09,303800000,3821.09 1994-03-23,3862.55,3901.41,3839.80,3869.46,284600000,3869.46 1994-03-22,3864.85,3896.23,3840.66,3862.55,283090000,3862.55 1994-03-21,3895.65,3898.25,3838.65,3864.85,247390000,3864.85 1994-03-18,3865.14,3911.78,3838.65,3895.65,462240000,3895.65 1994-03-17,3848.15,3891.34,3821.66,3865.14,303950000,3865.14 1994-03-16,3849.59,3879.53,3819.94,3848.15,306820000,3848.15 1994-03-15,3862.98,3888.46,3826.85,3849.59,329260000,3849.59 1994-03-14,3862.70,3894.21,3835.96,3862.98,260160000,3862.98 1994-03-11,3830.62,3872.83,3806.69,3862.70,303250000,3862.70 1994-03-10,3853.41,3865.51,3801.63,3830.62,369370000,3830.62 1994-03-09,3851.72,3874.52,3817.95,3853.41,309810000,3853.41 1994-03-08,3856.22,3881.55,3822.45,3851.72,298110000,3851.72 1994-03-07,3832.30,3882.40,3824.71,3856.22,285580000,3856.22 1994-03-04,3824.42,3868.04,3800.50,3832.30,311850000,3832.30 1994-03-03,3831.74,3862.13,3784.74,3824.42,291960000,3824.42 1994-03-02,3809.23,3845.25,3741.69,3831.74,361130000,3831.74 1994-03-01,3832.02,3848.34,3772.93,3809.23,304450000,3809.23 1994-02-28,3838.78,3874.52,3817.95,3832.02,267610000,3832.02 1994-02-25,3839.90,3868.89,3811.76,3838.78,273680000,3838.78 1994-02-24,3891.68,3895.62,3823.86,3839.90,342940000,3839.90 1994-02-23,3911.66,3931.36,3872.83,3891.68,309910000,3891.68 1994-02-22,3887.46,3928.83,3873.39,3911.66,270900000,3911.66 1994-02-18,3922.64,3931.92,3869.73,3887.46,293210000,3887.46 1994-02-17,3937.27,3975.82,3894.21,3922.64,340030000,3922.64 1994-02-16,3928.27,3964.85,3906.32,3937.27,295450000,3937.27 1994-02-15,3904.06,3950.50,3891.40,3928.27,306790000,3928.27 1994-02-14,3894.78,3935.86,3873.67,3904.06,263190000,3904.06 1994-02-11,3895.34,3920.95,3855.94,3894.78,213740000,3894.78 1994-02-10,3931.92,3953.59,3882.96,3895.34,327250000,3895.34 1994-02-09,3906.03,3956.97,3887.74,3931.92,332670000,3931.92 1994-02-08,3906.32,3951.34,3873.67,3906.03,318180000,3906.03 1994-02-07,3871.42,3923.48,3840.75,3906.32,348270000,3906.32 1994-02-04,3967.66,3979.76,3857.63,3871.42,378380000,3871.42 1994-02-03,3975.54,3995.52,3932.77,3967.66,318350000,3967.66 1994-02-02,3964.01,3997.78,3937.27,3975.54,328960000,3975.54 1994-02-01,3978.36,3998.06,3938.12,3964.01,322510000,3964.01 1994-01-31,3945.43,4002.84,3937.27,3978.36,322870000,3978.36 1994-01-28,3926.30,3971.89,3919.54,3945.43,313140000,3945.43 1994-01-27,3908.00,3951.34,3876.77,3926.30,346500000,3926.30 1994-01-26,3895.34,3934.74,3863.82,3908.00,304660000,3908.00 1994-01-25,3912.79,3937.55,3863.82,3895.34,326120000,3895.34 1994-01-24,3914.48,3947.68,3882.11,3912.79,296900000,3912.79 1994-01-21,3891.96,3933.33,3875.36,3914.48,346220000,3914.48 1994-01-20,3884.37,3915.60,3857.91,3891.96,310450000,3891.96 1994-01-19,3870.29,3909.97,3839.34,3884.37,311370000,3884.37 1994-01-18,3870.29,3905.19,3840.75,3870.29,309730000,3870.29 1994-01-17,3867.20,3896.75,3833.71,3870.29,233980000,3870.29 1994-01-14,3842.43,3891.96,3830.62,3867.20,304910000,3867.20 1994-01-13,3848.63,3864.67,3808.38,3842.43,277970000,3842.43 1994-01-12,3850.31,3876.49,3809.79,3848.63,310690000,3848.63 1994-01-11,3865.51,3885.21,3823.02,3850.31,305490000,3850.31 1994-01-10,3820.77,3874.52,3804.72,3865.51,319490000,3865.51 1994-01-07,3803.88,3842.15,3778.83,3820.77,324920000,3820.77 1994-01-06,3798.82,3843.84,3771.52,3803.88,367880000,3803.88 1994-01-05,3783.90,3821.33,3750.41,3798.82,400030000,3798.82 1994-01-04,3756.60,3798.25,3718.89,3783.90,326600000,3783.90 1994-01-03,3754.09,3790.70,3715.24,3756.60,270140000,3756.60 1993-12-31,3775.88,3804.11,3745.15,3754.09,168590000,3754.09 1993-12-30,3794.33,3806.34,3759.96,3775.88,195860000,3775.88 1993-12-29,3793.77,3818.92,3764.43,3794.33,269570000,3794.33 1993-12-28,3792.93,3813.33,3766.10,3793.77,200960000,3793.77 1993-12-27,3757.72,3804.95,3750.46,3792.93,171200000,3792.93 1993-12-23,3762.19,3791.81,3739.56,3757.72,227240000,3757.72 1993-12-22,3745.15,3780.64,3725.86,3762.19,272440000,3762.19 1993-12-21,3755.21,3774.77,3719.72,3745.15,273370000,3745.15 1993-12-20,3751.57,3777.84,3728.66,3755.21,255900000,3755.21 1993-12-17,3726.14,3768.90,3706.30,3751.57,363750000,3751.57 1993-12-16,3716.92,3756.60,3694.29,3726.14,284620000,3726.14 1993-12-15,3742.63,3776.44,3689.82,3716.92,331770000,3716.92 1993-12-14,3764.43,3785.94,3726.70,3742.63,275050000,3742.63 1993-12-13,3740.67,3780.64,3711.33,3764.43,256580000,3764.43 1993-12-10,3729.78,3758.84,3704.91,3740.67,245620000,3740.67 1993-12-09,3734.53,3764.43,3709.94,3729.78,287570000,3729.78 1993-12-08,3718.88,3756.60,3693.73,3734.53,314460000,3734.53 1993-12-07,3710.21,3746.82,3689.26,3718.88,285690000,3718.88 1993-12-06,3704.07,3738.44,3687.30,3710.21,292370000,3710.21 1993-12-03,3702.11,3726.98,3677.80,3704.07,268780000,3704.07 1993-12-02,3697.08,3725.30,3674.17,3702.11,256370000,3702.11 1993-12-01,3683.95,3731.73,3673.33,3697.08,293870000,3697.08 1993-11-30,3677.80,3713.57,3654.88,3683.95,290250000,3683.95 1993-11-29,3683.95,3721.67,3654.33,3677.80,272710000,3677.80 1993-11-26,3687.58,3703.23,3660.75,3683.95,90220000,3683.95 1993-11-24,3674.17,3709.94,3654.33,3687.58,230630000,3687.58 1993-11-23,3670.25,3702.67,3649.57,3674.17,261590000,3674.17 1993-11-22,3694.01,3697.92,3627.78,3670.25,280130000,3670.25 1993-11-19,3685.34,3711.05,3640.07,3694.01,302970000,3694.01 1993-11-18,3704.35,3721.95,3649.57,3685.34,313480000,3685.34 1993-11-17,3710.77,3749.90,3660.19,3704.35,319560000,3704.35 1993-11-16,3677.52,3723.91,3653.77,3710.77,303980000,3710.77 1993-11-15,3684.51,3705.74,3653.49,3677.52,251030000,3677.52 1993-11-12,3662.43,3707.42,3648.74,3684.51,326240000,3684.51 1993-11-11,3663.55,3700.43,3638.40,3662.43,287110000,3662.43 1993-11-10,3640.07,3683.39,3616.60,3663.55,283450000,3663.55 1993-11-09,3647.90,3689.82,3623.03,3640.07,278290000,3640.07 1993-11-08,3643.43,3674.17,3621.91,3647.90,232340000,3647.90 1993-11-05,3624.98,3663.83,3585.86,3643.43,336900000,3643.43 1993-11-04,3661.87,3681.99,3609.61,3624.98,323430000,3624.98 1993-11-03,3697.64,3714.69,3638.40,3661.87,342110000,3661.87 1993-11-02,3692.61,3724.75,3656.00,3697.64,304780000,3697.64 1993-11-01,3680.59,3708.26,3656.84,3692.61,256030000,3692.61 1993-10-29,3687.86,3712.45,3656.84,3680.59,270570000,3680.59 1993-10-28,3664.66,3713.57,3657.96,3687.86,301220000,3687.86 1993-10-27,3672.49,3692.33,3634.76,3664.66,279830000,3664.66 1993-10-26,3673.61,3701.55,3636.16,3672.49,284530000,3672.49 1993-10-25,3649.30,3694.01,3618.28,3673.61,260310000,3673.61 1993-10-22,3636.16,3697.92,3612.13,3649.30,301440000,3649.30 1993-10-21,3645.10,3678.36,3610.45,3636.16,288820000,3636.16 1993-10-20,3635.32,3667.74,3611.85,3645.10,305670000,3645.10 1993-10-19,3642.31,3669.97,3601.79,3635.32,304400000,3635.32 1993-10-18,3629.73,3675.84,3595.92,3642.31,329570000,3642.31 1993-10-15,3621.63,3664.66,3596.20,3629.73,366110000,3629.73 1993-10-14,3603.19,3652.09,3574.40,3621.63,353820000,3621.63 1993-10-13,3593.13,3628.34,3574.12,3603.19,290930000,3603.19 1993-10-12,3593.41,3619.39,3575.24,3593.13,263970000,3593.13 1993-10-11,3584.74,3611.01,3565.46,3593.41,183190000,3593.41 1993-10-08,3583.63,3610.45,3550.37,3584.74,243590000,3584.74 1993-10-07,3598.99,3616.32,3564.90,3583.63,255210000,3583.63 1993-10-06,3587.26,3620.79,3570.21,3598.99,277070000,3598.99 1993-10-05,3577.76,3616.88,3553.72,3587.26,294570000,3587.26 1993-10-04,3581.11,3603.19,3550.65,3577.76,229380000,3577.76 1993-10-01,3555.12,3605.14,3541.71,3581.11,256870000,3581.11 1993-09-30,3566.30,3583.63,3528.57,3555.12,282740000,3555.12 1993-09-29,3566.02,3596.48,3538.91,3566.30,277690000,3566.30 1993-09-28,3567.70,3589.49,3542.27,3566.02,243320000,3566.02 1993-09-27,3543.11,3589.49,3539.47,3567.70,244920000,3567.70 1993-09-24,3539.75,3568.54,3507.90,3543.11,248270000,3543.11 1993-09-23,3547.02,3567.70,3513.48,3539.75,276660000,3539.75 1993-09-22,3537.24,3577.20,3516.56,3547.02,288960000,3547.02 1993-09-21,3575.80,3592.57,3501.47,3537.24,301740000,3537.24 1993-09-20,3613.25,3632.81,3567.98,3575.80,228040000,3575.80 1993-09-17,3630.85,3637.28,3580.83,3613.25,369600000,3613.25 1993-09-16,3633.65,3651.25,3601.79,3630.85,229700000,3630.85 1993-09-15,3615.76,3644.82,3573.84,3633.65,294410000,3633.65 1993-09-14,3634.21,3639.51,3590.61,3615.76,258620000,3615.76 1993-09-13,3621.63,3655.16,3607.66,3634.21,244970000,3634.21 1993-09-10,3589.49,3636.16,3576.64,3621.63,269950000,3621.63 1993-09-09,3588.93,3616.04,3556.52,3589.49,258070000,3589.49 1993-09-08,3607.10,3623.31,3561.27,3588.93,283100000,3588.93 1993-09-07,3633.93,3649.02,3592.57,3607.10,229500000,3607.10 1993-09-03,3626.10,3651.53,3603.75,3633.93,197160000,3633.93 1993-09-02,3645.10,3660.19,3610.17,3626.10,259870000,3626.10 1993-09-01,3651.25,3665.50,3619.67,3645.10,245040000,3645.10 1993-08-31,3643.99,3662.99,3619.67,3651.25,252830000,3651.25 1993-08-30,3640.63,3667.46,3621.63,3643.99,194180000,3643.99 1993-08-27,3648.18,3656.28,3606.54,3640.63,196140000,3640.63 1993-08-26,3652.09,3681.71,3620.23,3648.18,247800000,3648.18 1993-08-25,3638.96,3674.17,3620.51,3652.09,301640000,3652.09 1993-08-24,3605.98,3648.18,3590.89,3638.96,270700000,3638.96 1993-08-23,3615.48,3630.57,3578.87,3605.98,212500000,3605.98 1993-08-20,3612.13,3633.37,3580.55,3615.48,276800000,3615.48 1993-08-19,3604.86,3632.25,3581.11,3612.13,293330000,3612.13 1993-08-18,3586.98,3638.96,3577.48,3604.86,312940000,3604.86 1993-08-17,3579.15,3611.29,3554.00,3586.98,261320000,3586.98 1993-08-16,3569.65,3606.54,3547.86,3579.15,229190000,3579.15 1993-08-13,3569.09,3594.52,3547.58,3569.65,214370000,3569.65 1993-08-12,3583.35,3607.66,3537.24,3569.09,278530000,3569.09 1993-08-11,3572.73,3607.94,3550.93,3583.35,268330000,3583.35 1993-08-10,3576.08,3599.83,3547.02,3572.73,255520000,3572.73 1993-08-09,3560.43,3599.83,3541.15,3576.08,232750000,3576.08 1993-08-06,3548.97,3583.35,3536.12,3560.43,221150000,3560.43 1993-08-05,3552.05,3574.12,3523.54,3548.97,249650000,3548.97 1993-08-04,3561.27,3579.99,3530.25,3552.05,230040000,3552.05 1993-08-03,3560.99,3588.10,3530.81,3561.27,254540000,3561.27 1993-08-02,3539.47,3578.32,3524.94,3560.99,230380000,3560.99 1993-07-30,3567.42,3581.11,3515.72,3539.47,254420000,3539.47 1993-07-29,3553.45,3593.41,3531.37,3567.42,261240000,3567.42 1993-07-28,3565.46,3588.38,3524.38,3553.45,270530000,3553.45 1993-07-27,3567.70,3604.86,3533.60,3565.46,256750000,3565.46 1993-07-26,3546.74,3584.74,3541.43,3567.70,223280000,3567.70 1993-07-23,3525.22,3569.37,3508.17,3546.74,222170000,3546.74 1993-07-22,3555.40,3566.86,3514.32,3525.22,249630000,3525.22 1993-07-21,3544.78,3573.84,3516.84,3555.40,278590000,3555.40 1993-07-20,3535.28,3567.98,3500.63,3544.78,275130000,3544.78 1993-07-19,3528.29,3563.23,3502.87,3535.28,216370000,3535.28 1993-07-16,3550.93,3571.61,3505.94,3528.29,263100000,3528.29 1993-07-15,3542.55,3573.01,3509.85,3550.93,277810000,3550.93 1993-07-14,3515.44,3562.39,3507.34,3542.55,285890000,3542.55 1993-07-13,3524.38,3544.22,3491.13,3515.44,236720000,3515.44 1993-07-12,3521.06,3545.97,3495.04,3524.38,202310000,3524.38 1993-07-09,3514.42,3544.03,3490.89,3521.06,235210000,3521.06 1993-07-08,3475.67,3532.41,3462.38,3514.42,282910000,3514.42 1993-07-07,3449.93,3495.32,3443.28,3475.67,253170000,3475.67 1993-07-06,3483.97,3502.52,3443.28,3449.93,233420000,3449.93 1993-07-02,3510.54,3511.65,3468.47,3483.97,220750000,3483.97 1993-07-01,3516.08,3542.10,3487.29,3510.54,292040000,3510.54 1993-06-30,3518.85,3543.48,3493.11,3516.08,281120000,3516.08 1993-06-29,3530.20,3544.87,3491.44,3518.85,276310000,3518.85 1993-06-28,3490.89,3542.10,3486.74,3530.20,242090000,3530.20 1993-06-25,3490.61,3512.76,3473.18,3490.89,210430000,3490.89 1993-06-24,3466.81,3504.73,3449.10,3490.61,267450000,3490.61 1993-06-23,3497.53,3514.14,3445.77,3466.81,278260000,3466.81 1993-06-22,3510.82,3530.47,3474.28,3497.53,259530000,3497.53 1993-06-21,3494.77,3531.86,3477.05,3510.82,223650000,3510.82 1993-06-18,3521.89,3539.88,3478.44,3494.77,300500000,3494.77 1993-06-17,3511.65,3539.61,3488.68,3521.89,239810000,3521.89 1993-06-16,3492.00,3527.43,3460.17,3511.65,264500000,3511.65 1993-06-15,3514.69,3531.86,3471.24,3492.00,234110000,3492.00 1993-06-14,3505.01,3538.22,3486.74,3514.69,210440000,3514.69 1993-06-11,3491.72,3536.01,3479.27,3505.01,255200000,3505.01 1993-06-10,3511.93,3538.22,3461.83,3491.72,231760000,3491.72 1993-06-09,3510.54,3541.54,3490.89,3511.93,249030000,3511.93 1993-06-08,3532.13,3543.48,3494.21,3510.54,238170000,3510.54 1993-06-07,3545.14,3570.33,3510.82,3532.13,236930000,3532.13 1993-06-04,3544.87,3563.13,3516.63,3545.14,226440000,3545.14 1993-06-03,3553.45,3569.50,3516.08,3544.87,285770000,3544.87 1993-06-02,3552.34,3576.14,3530.47,3553.45,287120000,3553.45 1993-06-01,3527.43,3577.25,3518.02,3552.34,229690000,3552.34 1993-05-28,3554.83,3563.41,3503.62,3527.43,207820000,3527.43 1993-05-27,3540.16,3582.23,3523.28,3554.83,300810000,3554.83 1993-05-26,3516.63,3558.98,3498.64,3540.16,274230000,3540.16 1993-05-25,3507.78,3534.35,3486.46,3516.63,222090000,3516.63 1993-05-24,3492.83,3526.60,3472.35,3507.78,197990000,3507.78 1993-05-21,3523.28,3532.96,3468.47,3492.83,279120000,3492.83 1993-05-20,3500.03,3539.88,3475.39,3523.28,289160000,3523.28 1993-05-19,3444.39,3511.10,3405.09,3500.03,342420000,3500.03 1993-05-18,3449.93,3468.47,3409.79,3444.39,264300000,3444.39 1993-05-17,3443.01,3465.98,3421.42,3449.93,227580000,3449.93 1993-05-14,3447.99,3472.62,3421.14,3443.01,252910000,3443.01 1993-05-13,3482.31,3486.74,3428.89,3447.99,289860000,3447.99 1993-05-12,3468.75,3501.69,3441.07,3482.31,255680000,3482.31 1993-05-11,3443.28,3481.76,3421.42,3468.75,218480000,3468.75 1993-05-10,3437.19,3485.36,3420.31,3443.28,235580000,3443.28 1993-05-07,3441.90,3468.47,3413.67,3437.19,223570000,3437.19 1993-05-06,3449.10,3475.67,3418.93,3441.90,255460000,3441.90 1993-05-05,3446.19,3478.44,3420.86,3449.10,270960000,3449.10 1993-05-04,3446.46,3477.26,3424.04,3446.19,268310000,3446.19 1993-05-03,3427.55,3462.94,3402.42,3446.46,220860000,3446.46 1993-04-30,3425.12,3466.18,3405.39,3427.55,247460000,3427.55 1993-04-29,3413.50,3444.57,3377.57,3425.12,249760000,3425.12 1993-04-28,3415.93,3445.65,3372.16,3413.50,267980000,3413.50 1993-04-27,3398.37,3433.76,3364.06,3415.93,284140000,3415.93 1993-04-26,3413.77,3442.14,3369.46,3398.37,281180000,3398.37 1993-04-23,3429.17,3448.08,3385.67,3413.77,259810000,3413.77 1993-04-22,3439.44,3488.33,3399.99,3429.17,310390000,3429.17 1993-04-21,3443.49,3480.77,3401.34,3439.44,287300000,3439.44 1993-04-20,3466.99,3486.71,3400.26,3443.49,317990000,3443.49 1993-04-19,3478.61,3499.41,3436.73,3466.99,244710000,3466.99 1993-04-16,3455.92,3498.60,3437.54,3478.61,305160000,3478.61 1993-04-15,3455.64,3484.28,3419.17,3455.92,259500000,3455.92 1993-04-14,3444.03,3482.93,3424.85,3455.64,257340000,3455.64 1993-04-13,3428.09,3469.42,3408.37,3444.03,286690000,3444.03 1993-04-12,3396.48,3452.67,3391.08,3428.09,259610000,3428.09 1993-04-08,3397.02,3429.44,3357.58,3396.48,282470000,3396.48 1993-04-07,3377.57,3417.55,3355.41,3397.02,296290000,3397.02 1993-04-06,3379.19,3417.55,3339.75,3377.57,289640000,3377.57 1993-04-05,3370.81,3411.61,3338.39,3379.19,238630000,3379.19 1993-04-02,3439.44,3439.44,3344.88,3370.81,323330000,3370.81 1993-04-01,3435.11,3466.45,3419.98,3439.44,231950000,3439.44 1993-03-31,3457.27,3484.82,3424.85,3435.11,275710000,3435.11 1993-03-30,3455.10,3481.58,3422.14,3457.27,233330000,3457.27 1993-03-29,3439.98,3487.52,3431.87,3455.10,199890000,3455.10 1993-03-26,3461.32,3484.28,3428.63,3439.98,219130000,3439.98 1993-03-25,3445.38,3485.36,3429.44,3461.32,250040000,3461.32 1993-03-24,3461.86,3489.14,3417.55,3445.38,271980000,3445.38 1993-03-23,3463.48,3488.60,3438.08,3461.86,231900000,3461.86 1993-03-22,3471.58,3483.20,3429.71,3463.48,231900000,3463.48 1993-03-19,3465.64,3493.20,3446.46,3471.58,295510000,3471.58 1993-03-18,3427.01,3486.17,3427.01,3465.64,240490000,3465.64 1993-03-17,3442.95,3458.35,3408.91,3426.74,237850000,3426.74 1993-03-16,3442.41,3466.72,3423.77,3442.95,217730000,3442.95 1993-03-15,3427.82,3460.51,3412.96,3442.41,192690000,3442.41 1993-03-12,3447.81,3447.81,3385.40,3427.82,244740000,3427.82 1993-03-11,3478.34,3493.74,3437.27,3457.00,250720000,3457.00 1993-03-10,3472.12,3497.25,3432.68,3478.34,255190000,3478.34 1993-03-09,3469.42,3495.63,3443.76,3472.12,290120000,3472.12 1993-03-08,3404.58,3476.99,3401.34,3469.42,274560000,3469.42 1993-03-05,3398.91,3447.81,3373.25,3404.58,247130000,3404.58 1993-03-04,3404.04,3423.77,3372.43,3398.91,230780000,3398.91 1993-03-03,3400.53,3437.00,3368.92,3404.04,272290000,3404.04 1993-03-02,3355.41,3406.21,3334.07,3400.53,269640000,3400.53 1993-03-01,3370.81,3404.58,3336.23,3355.41,232090000,3355.41 1993-02-26,3365.14,3396.21,3336.23,3370.81,234160000,3370.81 1993-02-25,3356.50,3387.02,3326.78,3365.14,252790000,3365.14 1993-02-24,3323.27,3371.89,3311.92,3356.50,298940000,3356.50 1993-02-23,3342.99,3373.52,3296.79,3323.27,321050000,3323.27 1993-02-22,3322.18,3367.30,3297.06,3342.99,311510000,3342.99 1993-02-19,3302.19,3347.04,3270.04,3322.18,307960000,3322.18 1993-02-18,3312.19,3362.98,3262.48,3302.19,309570000,3302.19 1993-02-17,3309.49,3338.12,3273.56,3312.19,287240000,3312.19 1993-02-16,3391.62,3391.62,3285.98,3309.49,325350000,3309.49 1993-02-12,3422.69,3436.19,3378.11,3392.43,215750000,3392.43 1993-02-11,3412.42,3455.64,3395.94,3422.69,252780000,3422.69 1993-02-10,3414.58,3438.08,3379.19,3412.42,248480000,3412.42 1993-02-09,3437.54,3449.16,3394.86,3414.58,233670000,3414.58 1993-02-08,3442.14,3472.94,3408.91,3437.54,240350000,3437.54 1993-02-05,3416.74,3463.21,3391.62,3442.14,320960000,3442.14 1993-02-04,3373.79,3441.33,3367.03,3416.74,346480000,3416.74 1993-02-03,3328.67,3397.83,3322.73,3373.79,342530000,3373.79 1993-02-02,3332.18,3355.68,3300.30,3328.67,269250000,3328.67 1993-02-01,3310.03,3343.80,3300.30,3332.18,238260000,3332.18 1993-01-29,3306.25,3331.10,3287.06,3310.03,247010000,3310.03 1993-01-28,3291.39,3327.86,3270.58,3306.25,255550000,3306.25 1993-01-27,3298.95,3318.67,3260.05,3291.39,276880000,3291.39 1993-01-26,3292.20,3331.91,3272.47,3298.95,311450000,3298.95 1993-01-25,3256.81,3324.89,3243.84,3292.20,288010000,3292.20 1993-01-22,3253.02,3292.74,3225.74,3256.81,293250000,3256.81 1993-01-21,3241.95,3269.77,3219.25,3253.02,257350000,3253.02 1993-01-20,3255.99,3278.96,3231.41,3241.95,267740000,3241.95 1993-01-19,3274.91,3299.49,3239.52,3255.99,283110000,3255.99 1993-01-18,3271.12,3296.52,3244.65,3274.91,195980000,3274.91 1993-01-15,3267.88,3300.03,3238.70,3271.12,306140000,3271.12 1993-01-14,3263.56,3297.06,3230.87,3267.88,280020000,3267.88 1993-01-13,3264.64,3283.01,3225.47,3263.56,245020000,3263.56 1993-01-12,3262.75,3287.06,3229.79,3264.64,239250000,3264.64 1993-01-11,3251.67,3284.09,3228.98,3262.75,217150000,3262.75 1993-01-08,3268.96,3280.31,3221.68,3251.67,262620000,3251.67 1993-01-07,3305.16,3333.51,3250.30,3268.96,303140000,3268.96 1993-01-06,3307.87,3330.29,3276.53,3305.16,282850000,3305.16 1993-01-05,3309.22,3338.12,3279.23,3307.87,240550000,3307.87 1993-01-04,3301.11,3335.69,3282.74,3309.22,199680000,3309.22 1992-12-31,3321.10,3340.29,3294.36,3301.11,165910000,3301.11 1992-12-30,3310.84,3340.54,3298.93,3321.10,183870000,3321.10 1992-12-29,3333.26,3364.87,3295.71,3310.84,213660000,3310.84 1992-12-28,3326.24,3352.17,3297.33,3333.26,143800000,3333.26 1992-12-24,3313.54,3339.48,3303.27,3326.24,95240000,3326.24 1992-12-23,3321.10,3350.55,3293.01,3313.54,227980000,3313.54 1992-12-22,3312.46,3347.04,3286.52,3321.10,249670000,3321.10 1992-12-21,3313.27,3335.15,3280.85,3312.46,224680000,3312.46 1992-12-18,3269.23,3325.97,3261.94,3313.27,371080000,3313.27 1992-12-17,3255.18,3289.22,3229.79,3269.23,248590000,3269.23 1992-12-16,3284.36,3303.00,3238.70,3255.18,241910000,3255.18 1992-12-15,3292.20,3313.27,3260.32,3284.36,225880000,3284.36 1992-12-14,3304.08,3324.89,3279.50,3292.20,183510000,3292.20 1992-12-11,3312.19,3324.89,3280.85,3304.08,164450000,3304.08 1992-12-10,3323.81,3335.69,3285.17,3312.19,240570000,3312.19 1992-12-09,3322.18,3345.42,3295.98,3323.81,229980000,3323.81 1992-12-08,3307.33,3331.64,3288.41,3322.18,234300000,3322.18 1992-12-07,3288.68,3320.56,3274.37,3307.33,217700000,3307.33 1992-12-04,3276.53,3312.46,3261.40,3288.68,227410000,3288.68 1992-12-03,3286.25,3302.73,3252.48,3276.53,238200000,3276.53 1992-12-02,3294.36,3310.84,3265.18,3286.25,241860000,3286.25 1992-12-01,3305.16,3321.64,3268.15,3294.36,259020000,3294.36 1992-11-30,3282.20,3326.51,3270.31,3305.16,230190000,3305.16 1992-11-27,3266.26,3304.62,3259.24,3282.20,106010000,3282.20 1992-11-25,3248.70,3285.71,3243.57,3266.26,206700000,3266.26 1992-11-24,3223.04,3277.88,3209.26,3248.70,241520000,3248.70 1992-11-23,3227.36,3251.13,3196.83,3223.04,190490000,3223.04 1992-11-20,3209.53,3249.78,3197.64,3227.36,256340000,3227.36 1992-11-19,3207.37,3231.14,3190.35,3209.53,218700000,3209.53 1992-11-18,3193.32,3227.09,3176.84,3207.37,218660000,3207.37 1992-11-17,3205.74,3223.31,3178.19,3193.32,185460000,3193.32 1992-11-16,3233.03,3241.41,3191.16,3205.74,173500000,3205.74 1992-11-13,3239.79,3252.48,3211.69,3233.03,192320000,3233.03 1992-11-12,3240.33,3264.91,3214.39,3239.79,224580000,3239.79 1992-11-11,3225.47,3258.70,3203.31,3240.33,240160000,3240.33 1992-11-10,3240.87,3268.15,3212.50,3225.47,221990000,3225.47 1992-11-09,3240.06,3268.69,3220.33,3240.87,197490000,3240.87 1992-11-06,3243.84,3264.64,3216.82,3240.06,204870000,3240.06 1992-11-05,3223.04,3259.78,3203.58,3243.84,219580000,3243.84 1992-11-04,3252.48,3274.10,3211.15,3223.04,193980000,3223.04 1992-11-03,3262.21,3285.44,3226.82,3252.48,209740000,3252.48 1992-11-02,3226.28,3274.64,3211.42,3262.21,201620000,3262.21 1992-10-30,3246.27,3260.59,3208.45,3226.28,196740000,3226.28 1992-10-29,3251.40,3268.96,3224.39,3246.27,206300000,3246.27 1992-10-28,3235.73,3262.48,3210.34,3251.40,203040000,3251.40 1992-10-27,3244.11,3270.31,3210.88,3235.73,201650000,3235.73 1992-10-26,3207.64,3256.00,3190.08,3244.11,187950000,3244.11 1992-10-23,3200.88,3233.57,3175.76,3207.64,197400000,3207.64 1992-10-22,3187.10,3221.14,3162.79,3200.88,216080000,3200.88 1992-10-21,3186.02,3211.69,3163.33,3187.10,218990000,3187.10 1992-10-20,3188.45,3223.31,3166.30,3186.02,258220000,3186.02 1992-10-19,3174.41,3211.15,3154.14,3188.45,218670000,3188.45 1992-10-16,3174.68,3203.85,3123.89,3174.41,234480000,3174.41 1992-10-15,3195.48,3207.37,3147.66,3174.68,206990000,3174.68 1992-10-14,3201.42,3225.74,3167.11,3195.48,175440000,3195.48 1992-10-13,3174.41,3222.77,3159.28,3201.42,184120000,3201.42 1992-10-12,3140.10,3186.29,3140.10,3174.41,126590000,3174.41 1992-10-09,3176.03,3176.57,3120.37,3136.58,178910000,3136.58 1992-10-08,3152.25,3195.48,3135.77,3176.03,203780000,3176.03 1992-10-07,3178.19,3200.88,3136.85,3152.25,183100000,3152.25 1992-10-06,3179.00,3205.20,3147.93,3178.19,196660000,3178.19 1992-10-05,3197.10,3197.10,3087.41,3179.00,284380000,3179.00 1992-10-02,3254.37,3259.51,3193.59,3200.61,187400000,3200.61 1992-10-01,3271.66,3291.39,3237.35,3254.37,203670000,3254.37 1992-09-30,3266.80,3291.66,3247.89,3271.66,184220000,3271.66 1992-09-29,3276.26,3295.98,3247.08,3266.80,170350000,3266.80 1992-09-28,3250.32,3283.01,3226.55,3276.26,157480000,3276.26 1992-09-25,3287.87,3292.20,3226.82,3250.32,213650000,3250.32 1992-09-24,3278.69,3310.84,3267.07,3287.87,187770000,3287.87 1992-09-23,3280.85,3302.19,3252.48,3278.69,204350000,3278.69 1992-09-22,3320.83,3327.05,3270.58,3280.85,186990000,3280.85 1992-09-21,3327.05,3341.91,3295.71,3320.83,153900000,3320.83 1992-09-18,3315.70,3340.56,3297.87,3327.05,236080000,3327.05 1992-09-17,3319.21,3347.04,3292.20,3315.70,188270000,3315.70 1992-09-16,3327.32,3353.52,3288.95,3319.21,229380000,3319.21 1992-09-15,3372.98,3372.98,3317.86,3327.32,200220000,3327.32 1992-09-14,3326.51,3391.35,3326.51,3376.22,250900000,3376.22 1992-09-11,3305.16,3327.32,3285.44,3305.70,180640000,3305.70 1992-09-10,3271.39,3318.94,3261.67,3305.16,221970000,3305.16 1992-09-09,3260.59,3284.09,3244.92,3271.39,172890000,3271.39 1992-09-08,3281.93,3292.20,3245.73,3260.59,160930000,3260.59 1992-09-04,3292.20,3306.23,3265.16,3281.93,124340000,3281.93 1992-09-03,3290.31,3325.95,3268.94,3292.20,212540000,3292.20 1992-09-02,3266.26,3301.90,3249.76,3290.31,187010000,3290.31 1992-09-01,3257.35,3279.21,3239.77,3266.26,172650000,3266.26 1992-08-31,3267.61,3287.04,3244.90,3257.35,160230000,3257.35 1992-08-28,3254.64,3280.56,3237.88,3267.61,152230000,3267.61 1992-08-27,3246.81,3285.69,3237.06,3254.64,178490000,3254.64 1992-08-26,3232.22,3261.38,3217.07,3246.81,171840000,3246.81 1992-08-25,3228.17,3253.00,3200.86,3232.22,201630000,3232.22 1992-08-24,3254.09,3258.41,3207.08,3228.17,165130000,3228.17 1992-08-21,3304.89,3330.27,3243.55,3254.09,202640000,3254.09 1992-08-20,3307.06,3326.22,3285.69,3304.89,183390000,3304.89 1992-08-19,3329.48,3347.56,3302.44,3307.06,186710000,3307.06 1992-08-18,3324.89,3343.80,3309.22,3329.48,169880000,3329.48 1992-08-17,3328.94,3350.28,3310.03,3324.89,152750000,3324.89 1992-08-14,3313.27,3342.16,3300.82,3328.94,166180000,3328.94 1992-08-13,3320.83,3347.29,3294.07,3313.27,185700000,3313.27 1992-08-12,3331.10,3349.72,3304.88,3320.83,176440000,3320.83 1992-08-11,3337.58,3356.48,3304.34,3331.10,173810000,3331.10 1992-08-10,3332.18,3350.26,3305.14,3337.58,142440000,3337.58 1992-08-07,3340.56,3378.38,3318.40,3332.18,188340000,3332.18 1992-08-06,3365.14,3374.33,3327.05,3340.56,181390000,3340.56 1992-08-05,3384.32,3391.35,3347.58,3365.14,172410000,3365.14 1992-08-04,3395.40,3405.12,3367.03,3384.32,166740000,3384.32 1992-08-03,3393.78,3413.23,3365.14,3395.40,164360000,3395.40 1992-07-31,3391.89,3414.85,3371.89,3393.78,172920000,3393.78 1992-07-30,3379.19,3409.16,3351.07,3391.89,193280000,3391.89 1992-07-29,3345.13,3399.70,3345.13,3379.19,275760000,3379.19 1992-07-28,3282.20,3345.67,3277.59,3334.07,217950000,3334.07 1992-07-27,3285.71,3311.38,3265.99,3282.20,164680000,3282.20 1992-07-24,3290.04,3305.68,3261.94,3285.71,163870000,3285.71 1992-07-23,3277.61,3308.39,3255.43,3290.04,175460000,3290.04 1992-07-22,3308.41,3310.28,3262.19,3277.61,190130000,3277.61 1992-07-21,3303.00,3335.94,3292.45,3308.41,173800000,3308.41 1992-07-20,3318.38,3318.38,3271.11,3303.00,165730000,3303.00 1992-07-17,3359.74,3359.74,3308.14,3331.64,187520000,3331.64 1992-07-16,3345.42,3375.66,3318.65,3361.63,206040000,3361.63 1992-07-15,3358.39,3381.87,3319.73,3345.42,206550000,3345.42 1992-07-14,3337.31,3371.88,3315.95,3358.39,195310000,3358.39 1992-07-13,3330.56,3357.55,3315.41,3337.31,148820000,3337.31 1992-07-10,3324.08,3355.93,3304.88,3330.56,164750000,3330.56 1992-07-09,3293.28,3345.40,3292.45,3324.08,207970000,3324.08 1992-07-08,3295.17,3322.98,3258.70,3293.28,200020000,3293.28 1992-07-07,3339.21,3360.80,3285.69,3295.17,218740000,3295.17 1992-07-06,3330.29,3367.57,3295.96,3339.21,186410000,3339.21 1992-07-02,3354.10,3385.43,3303.30,3330.29,220130000,3330.29 1992-07-01,3318.52,3366.43,3305.45,3354.10,214240000,3354.10 1992-06-30,3319.86,3347.71,3295.01,3318.52,195520000,3318.52 1992-06-29,3282.41,3330.32,3278.16,3319.86,176710000,3319.86 1992-06-26,3284.01,3303.04,3254.89,3282.41,154430000,3282.41 1992-06-25,3290.70,3319.62,3261.31,3284.01,182310000,3284.01 1992-06-24,3285.62,3317.75,3262.11,3290.70,193850000,3290.70 1992-06-23,3280.80,3312.13,3263.45,3285.62,189170000,3285.62 1992-06-22,3285.35,3298.22,3242.32,3280.80,169340000,3280.80 1992-06-19,3274.12,3313.20,3264.79,3285.35,233440000,3285.35 1992-06-18,3287.76,3313.74,3245.53,3274.12,215080000,3274.12 1992-06-17,3329.49,3347.98,3271.21,3287.76,227650000,3287.76 1992-06-16,3354.90,3379.01,3321.76,3329.49,178850000,3329.49 1992-06-15,3354.36,3371.79,3327.11,3354.90,159100000,3354.90 1992-06-12,3351.51,3397.68,3339.62,3354.36,181830000,3354.36 1992-06-11,3343.22,3374.61,3301.51,3351.51,192940000,3351.51 1992-06-10,3369.92,3385.76,3328.99,3343.22,206380000,3343.22 1992-06-09,3404.14,3412.98,3350.25,3369.92,190780000,3369.92 1992-06-08,3398.69,3422.83,3370.21,3404.14,161130000,3404.14 1992-06-05,3399.73,3424.64,3356.98,3398.69,199050000,3398.69 1992-06-04,3406.99,3428.02,3376.43,3399.73,204360000,3399.73 1992-06-03,3396.10,3431.13,3378.76,3406.99,215730000,3406.99 1992-06-02,3413.21,3435.27,3380.84,3396.10,200660000,3396.10 1992-06-01,3396.88,3424.39,3365.02,3413.21,180780000,3413.21 1992-05-29,3398.43,3433.98,3384.20,3396.88,202730000,3396.88 1992-05-28,3370.44,3408.31,3354.91,3398.43,195230000,3398.43 1992-05-27,3364.21,3396.65,3337.29,3370.44,179980000,3370.44 1992-05-26,3386.77,3410.91,3338.84,3364.21,196950000,3364.21 1992-05-22,3378.71,3408.49,3364.08,3386.77,146640000,3386.77 1992-05-21,3393.84,3402.88,3354.80,3378.71,182190000,3378.71 1992-05-20,3397.99,3421.42,3376.04,3393.84,198170000,3393.84 1992-05-19,3376.03,3413.37,3350.41,3397.99,187030000,3397.99 1992-05-18,3353.09,3398.24,3349.93,3376.03,149830000,3376.03 1992-05-15,3368.88,3380.30,3330.43,3353.09,192040000,3353.09 1992-05-14,3391.98,3397.46,3347.59,3368.88,187700000,3368.88 1992-05-13,3385.12,3414.17,3362.93,3391.98,171610000,3391.98 1992-05-12,3397.58,3414.81,3361.51,3385.12,192810000,3385.12 1992-05-11,3369.41,3410.11,3363.82,3397.58,155730000,3397.58 1992-05-08,3363.37,3388.41,3344.59,3369.41,168670000,3369.41 1992-05-07,3369.41,3390.65,3343.25,3363.37,168910000,3363.37 1992-05-06,3359.35,3398.70,3346.60,3369.41,199070000,3369.41 1992-05-05,3378.13,3393.78,3346.15,3359.35,198860000,3359.35 1992-05-04,3340.79,3394.68,3340.79,3378.13,174520000,3378.13 1992-05-01,3359.12,3375.67,3316.64,3336.09,177360000,3336.09 1992-04-30,3333.18,3377.01,3314.40,3359.12,223160000,3359.12 1992-04-29,3307.92,3353.75,3295.39,3333.18,199740000,3333.18 1992-04-28,3304.56,3329.83,3273.03,3307.92,186740000,3307.92 1992-04-27,3324.46,3340.79,3284.66,3304.56,172820000,3304.56 1992-04-24,3348.61,3381.48,3305.23,3324.46,198740000,3324.46 1992-04-23,3338.77,3376.34,3298.52,3348.61,235740000,3348.61 1992-04-22,3343.25,3366.72,3309.48,3338.77,218790000,3338.77 1992-04-21,3336.31,3366.50,3305.68,3343.25,214400000,3343.25 1992-04-20,3366.50,3375.67,3300.98,3336.31,191910000,3336.31 1992-04-16,3353.76,3387.97,3321.33,3366.50,232480000,3366.50 1992-04-15,3306.13,3370.08,3296.51,3353.76,228400000,3353.76 1992-04-14,3269.90,3336.54,3259.39,3306.13,232040000,3306.13 1992-04-13,3255.37,3293.60,3230.77,3269.90,143100000,3269.90 1992-04-10,3227.64,3280.86,3227.64,3255.37,199450000,3255.37 1992-04-09,3181.35,3245.08,3171.06,3224.96,231330000,3224.96 1992-04-08,3213.55,3221.38,3141.77,3181.35,249210000,3181.35 1992-04-07,3275.49,3291.81,3207.51,3213.55,205110000,3213.55 1992-04-06,3249.11,3295.84,3238.37,3275.49,179330000,3275.49 1992-04-03,3234.12,3271.91,3201.92,3249.11,188530000,3249.11 1992-04-02,3249.33,3277.06,3209.08,3234.12,185110000,3234.12 1992-04-01,3235.47,3262.52,3202.37,3249.33,186260000,3249.33 1992-03-31,3235.24,3272.81,3216.46,3235.47,182200000,3235.47 1992-03-30,3231.44,3260.06,3215.79,3235.24,133980000,3235.24 1992-03-27,3267.67,3272.58,3218.92,3231.44,166140000,3231.44 1992-03-26,3259.39,3288.91,3245.08,3267.67,176690000,3267.67 1992-03-25,3260.96,3290.47,3238.15,3259.39,192080000,3259.39 1992-03-24,3272.14,3296.96,3242.84,3260.96,191580000,3260.96 1992-03-23,3276.39,3288.68,3249.33,3272.14,156620000,3272.14 1992-03-20,3261.40,3292.48,3240.83,3276.39,246170000,3276.39 1992-03-19,3254.25,3286.22,3240.38,3261.40,197240000,3261.40 1992-03-18,3256.04,3281.98,3230.10,3254.25,190800000,3254.25 1992-03-17,3236.36,3272.58,3222.27,3256.04,187240000,3256.04 1992-03-16,3235.91,3249.11,3201.25,3236.36,151280000,3236.36 1992-03-13,3208.63,3252.23,3203.71,3235.91,176000000,3235.91 1992-03-12,3208.63,3232.33,3176.21,3208.63,180240000,3208.63 1992-03-11,3230.99,3242.17,3189.85,3208.63,185320000,3208.63 1992-03-10,3215.12,3259.17,3207.29,3230.99,194530000,3230.99 1992-03-09,3221.60,3242.62,3188.95,3215.12,160620000,3215.12 1992-03-06,3241.50,3262.97,3204.61,3221.60,185040000,3221.60 1992-03-05,3268.56,3283.54,3226.74,3241.50,205730000,3241.50 1992-03-04,3290.25,3318.42,3256.04,3268.56,206770000,3268.56 1992-03-03,3275.27,3313.28,3258.50,3290.25,200860000,3290.25 1992-03-02,3267.67,3298.97,3242.39,3275.27,180380000,3275.27 1992-02-28,3269.45,3304.11,3247.09,3267.67,202130000,3267.67 1992-02-27,3283.32,3300.54,3251.79,3269.45,215050000,3269.45 1992-02-26,3257.83,3305.01,3246.20,3283.32,240690000,3283.32 1992-02-25,3282.42,3293.60,3226.74,3257.83,208400000,3257.83 1992-02-24,3280.19,3305.01,3253.58,3282.42,177470000,3282.42 1992-02-21,3280.64,3307.47,3242.17,3280.19,258700000,3280.19 1992-02-20,3230.32,3304.34,3224.28,3280.64,270550000,3280.64 1992-02-19,3224.73,3259.17,3199.02,3230.32,232900000,3230.32 1992-02-18,3245.97,3280.19,3195.66,3224.73,234270000,3224.73 1992-02-14,3246.65,3271.91,3208.63,3245.97,214840000,3245.97 1992-02-13,3276.83,3296.73,3226.07,3246.65,229360000,3246.65 1992-02-12,3251.57,3291.37,3233.68,3276.83,230230000,3276.83 1992-02-11,3245.08,3277.28,3222.49,3251.57,200110000,3251.57 1992-02-10,3225.40,3269.00,3208.85,3245.08,184390000,3245.08 1992-02-07,3255.59,3283.09,3199.91,3225.40,230950000,3225.40 1992-02-06,3257.60,3285.55,3224.95,3255.59,238210000,3255.59 1992-02-05,3272.81,3299.87,3233.68,3257.60,261960000,3257.60 1992-02-04,3234.12,3283.09,3208.63,3272.81,231530000,3272.81 1992-02-03,3223.39,3261.40,3193.42,3234.12,182150000,3234.12 1992-01-31,3244.86,3274.37,3207.96,3223.39,197060000,3223.39 1992-01-30,3224.96,3269.68,3200.58,3244.86,194670000,3244.86 1992-01-29,3272.14,3313.51,3204.16,3224.96,248900000,3224.96 1992-01-28,3240.61,3298.30,3230.99,3272.14,217070000,3272.14 1992-01-27,3232.78,3267.44,3216.23,3240.61,190430000,3240.61 1992-01-24,3226.74,3264.31,3203.71,3232.78,213600000,3232.78 1992-01-23,3255.81,3279.52,3205.95,3226.74,229680000,3226.74 1992-01-22,3223.39,3272.80,3190.96,3255.81,225030000,3255.81 1992-01-21,3254.03,3275.49,3194.09,3223.39,218650000,3223.39 1992-01-20,3264.98,3283.32,3230.99,3254.03,180870000,3254.03 1992-01-17,3249.55,3297.63,3224.28,3264.98,284560000,3264.98 1992-01-16,3258.50,3289.13,3200.80,3249.55,333750000,3249.55 1992-01-15,3246.20,3299.19,3207.73,3258.50,312400000,3258.50 1992-01-14,3185.60,3255.81,3167.93,3246.20,264540000,3246.20 1992-01-13,3199.46,3215.56,3161.67,3185.60,200270000,3185.60 1992-01-10,3209.53,3235.91,3165.92,3199.46,236060000,3199.46 1992-01-09,3203.94,3246.64,3173.75,3209.53,291780000,3209.53 1992-01-08,3204.83,3245.53,3164.58,3203.94,289690000,3203.94 1992-01-07,3200.13,3224.73,3165.25,3204.83,251280000,3204.83 1992-01-06,3201.48,3230.32,3166.37,3200.13,241980000,3200.13 1992-01-03,3172.41,3221.38,3156.30,3201.48,219170000,3201.48 1992-01-02,3168.83,3184.70,3119.86,3172.41,203610000,3172.41 1991-12-31,3163.91,3204.61,3121.20,3168.83,247670000,3168.83 1991-12-30,3101.52,3174.64,3090.79,3163.91,245450000,3163.91 1991-12-27,3082.96,3121.65,3063.73,3101.52,157940000,3101.52 1991-12-26,3050.98,3101.97,3036.23,3082.96,149200000,3082.96 1991-12-24,3022.58,3087.88,3015.65,3050.98,162300000,3050.98 1991-12-23,2934.48,3037.57,2919.05,3022.58,228730000,3022.58 1991-12-20,2914.36,2965.79,2907.65,2934.48,313810000,2934.48 1991-12-19,2908.09,2927.10,2881.48,2914.36,199830000,2914.36 1991-12-18,2902.28,2921.29,2870.30,2908.09,192350000,2908.09 1991-12-17,2919.05,2936.27,2886.40,2902.28,191280000,2902.28 1991-12-16,2914.36,2946.33,2900.49,2919.05,173010000,2919.05 1991-12-13,2895.13,2936.72,2893.34,2914.36,195790000,2914.36 1991-12-12,2865.38,2911.67,2861.14,2895.13,192930000,2895.13 1991-12-11,2863.82,2889.53,2832.29,2865.38,207410000,2865.38 1991-12-10,2871.65,2891.10,2841.23,2863.82,191800000,2863.82 1991-12-09,2886.40,2913.46,2856.22,2871.65,174700000,2871.65 1991-12-06,2889.09,2924.87,2854.65,2886.40,198170000,2886.40 1991-12-05,2911.67,2923.75,2874.77,2889.09,165660000,2889.09 1991-12-04,2929.56,2945.66,2892.22,2911.67,186380000,2911.67 1991-12-03,2935.38,2958.18,2904.74,2929.56,187160000,2929.56 1991-12-02,2894.68,2941.64,2855.32,2935.38,188050000,2935.38 1991-11-29,2900.04,2913.46,2877.46,2894.68,77420000,2894.68 1991-11-27,2916.14,2929.11,2883.72,2900.04,159790000,2900.04 1991-11-26,2902.06,2942.31,2861.14,2916.14,213650000,2916.14 1991-11-25,2902.73,2921.96,2870.30,2902.06,173520000,2902.06 1991-11-22,2932.69,2940.30,2880.81,2902.73,188110000,2902.73 1991-11-21,2930.01,2953.94,2902.28,2932.69,195060000,2932.69 1991-11-20,2931.57,2973.61,2912.12,2930.01,192670000,2930.01 1991-11-19,2960.20,2960.20,2883.72,2931.57,243880000,2931.57 1991-11-18,2943.20,2990.61,2923.30,2972.72,238170000,2972.72 1991-11-15,3063.51,3069.54,2936.05,2943.20,236000000,2943.20 1991-11-14,3065.30,3084.97,3037.34,3063.51,200030000,3063.51 1991-11-13,3054.11,3075.58,3023.70,3065.30,184080000,3065.30 1991-11-12,3042.26,3078.71,3028.62,3054.11,198600000,3054.11 1991-11-11,3045.62,3057.69,3025.27,3042.26,128910000,3042.26 1991-11-08,3054.11,3080.95,3034.66,3045.62,183260000,3045.62 1991-11-07,3038.46,3066.19,3020.35,3054.11,205440000,3054.11 1991-11-06,3031.31,3056.57,3010.51,3038.46,167370000,3038.46 1991-11-05,3045.62,3062.84,3015.88,3031.31,171950000,3031.31 1991-11-04,3056.35,3061.27,3019.01,3045.62,155530000,3045.62 1991-11-01,3069.10,3091.91,3031.75,3056.35,205750000,3056.35 1991-10-31,3071.78,3091.01,3045.62,3069.10,179490000,3069.10 1991-10-30,3061.94,3090.12,3038.24,3071.78,195340000,3071.78 1991-10-29,3045.62,3077.82,3020.13,3061.94,192700000,3061.94 1991-10-28,3004.92,3055.23,3001.57,3045.62,160220000,3045.62 1991-10-25,3016.32,3034.44,2983.01,3004.92,167260000,3004.92 1991-10-24,3040.92,3047.63,2991.73,3016.32,178990000,3016.32 1991-10-23,3039.80,3065.52,3015.21,3040.92,185340000,3040.92 1991-10-22,3060.38,3084.53,3020.57,3039.80,194120000,3039.80 1991-10-21,3077.15,3085.20,3042.49,3060.38,153770000,3060.38 1991-10-18,3053.00,3089.45,3045.62,3077.15,204030000,3077.15 1991-10-17,3061.72,3077.15,3027.06,3053.00,202780000,3053.00 1991-10-16,3041.37,3082.29,3016.10,3061.72,225290000,3061.72 1991-10-15,3019.45,3057.69,3000.22,3041.37,213440000,3041.37 1991-10-14,2983.68,3026.39,2975.85,3019.45,130110000,3019.45 1991-10-11,2976.52,3000.89,2957.51,2983.68,146560000,2983.68 1991-10-10,2946.33,2985.47,2930.23,2976.52,164120000,2976.52 1991-10-09,2963.77,2984.79,2925.54,2946.33,186590000,2946.33 1991-10-08,2942.75,2983.68,2927.77,2963.77,170000000,2963.77 1991-10-07,2961.76,2973.17,2926.21,2942.75,148430000,2942.75 1991-10-04,2984.79,3007.16,2956.17,2961.76,163930000,2961.76 1991-10-03,3012.52,3021.24,2972.50,2984.79,174230000,2984.79 1991-10-02,3018.34,3040.25,2992.40,3012.52,166290000,3012.52 1991-10-01,3016.77,3043.60,3002.46,3018.34,163520000,3018.34 1991-09-30,3006.04,3032.87,2982.78,3016.77,146740000,3016.77 1991-09-27,3017.22,3040.70,2989.49,3006.04,160430000,3006.04 1991-09-26,3021.02,3040.70,2996.87,3017.22,160190000,3017.22 1991-09-25,3029.07,3048.52,3004.92,3021.02,153800000,3021.02 1991-09-24,3010.51,3043.38,2995.97,3029.07,170300000,3029.07 1991-09-23,3019.23,3037.79,2997.76,3010.51,145530000,3010.51 1991-09-20,3024.37,3045.39,3002.46,3019.23,241340000,3019.23 1991-09-19,3017.89,3050.76,3002.91,3024.37,210770000,3024.37 1991-09-18,3013.19,3025.49,2993.52,3017.89,141280000,3017.89 1991-09-17,3015.21,3036.00,2992.62,3013.19,168310000,3013.19 1991-09-16,2985.69,3023.03,2973.61,3015.21,171960000,3015.21 1991-09-13,3007.83,3021.47,2963.10,2985.69,167800000,2985.69 1991-09-12,2987.03,3023.26,2977.64,3007.83,160310000,3007.83 1991-09-11,2982.56,3004.70,2964.67,2987.03,147910000,2987.03 1991-09-10,3007.16,3012.97,2967.80,2982.56,146730000,2982.56 1991-09-09,3011.63,3025.49,2987.70,3007.16,109250000,3007.16 1991-09-06,3008.50,3033.32,2987.48,3011.63,166410000,3011.63 1991-09-05,3008.50,3031.98,2989.71,3008.50,162250000,3008.50 1991-09-04,3017.67,3034.66,2990.83,3008.50,156770000,3008.50 1991-09-03,3043.60,3066.64,3013.64,3017.67,153550000,3017.67 1991-08-30,3049.64,3059.26,3024.82,3043.60,125830000,3043.60 1991-08-29,3055.23,3068.65,3030.86,3049.64,150180000,3049.64 1991-08-28,3026.16,3064.85,3018.11,3055.23,169590000,3055.23 1991-08-27,3039.36,3047.41,3007.83,3026.16,143920000,3026.16 1991-08-26,3040.25,3057.02,3020.80,3039.36,128400000,3039.36 1991-08-23,3007.38,3065.97,2999.11,3040.25,187010000,3040.25 1991-08-22,3001.79,3029.96,2989.94,3007.38,172900000,3007.38 1991-08-21,2941.64,3009.17,2941.64,3001.79,231720000,3001.79 1991-08-20,2898.03,2937.39,2886.85,2913.69,184090000,2913.69 1991-08-19,2924.42,2924.42,2836.31,2898.03,229590000,2898.03 1991-08-16,2998.43,3013.64,2945.89,2968.02,188360000,2968.02 1991-08-15,3005.37,3029.96,2985.24,2998.43,174310000,2998.43 1991-08-14,3008.72,3036.67,2988.60,3005.37,195890000,3005.37 1991-08-13,3001.34,3041.14,2989.27,3008.72,211890000,3008.72 1991-08-12,2996.20,3013.42,2974.06,3001.34,145280000,3001.34 1991-08-09,3013.86,3036.45,2986.81,2996.20,143610000,2996.20 1991-08-08,3026.61,3045.17,2995.30,3013.86,163620000,3013.86 1991-08-07,3027.28,3050.54,3008.50,3026.61,170820000,3026.61 1991-08-06,2989.04,3034.88,2970.48,3027.28,174340000,3027.28 1991-08-05,3006.26,3019.68,2978.76,2989.04,125790000,2989.04 1991-08-02,3017.67,3042.26,2994.41,3006.26,162050000,3006.26 1991-08-01,3024.82,3037.12,2997.76,3017.67,169920000,3017.67 1991-07-31,3016.32,3039.58,2999.11,3024.82,166650000,3024.82 1991-07-30,2985.24,3029.07,2983.68,3016.32,168950000,3016.32 1991-07-29,2972.50,2996.20,2957.07,2985.24,135240000,2985.24 1991-07-26,2980.10,2994.86,2953.26,2972.50,127690000,2972.50 1991-07-25,2966.23,2999.11,2947.23,2980.10,145510000,2980.10 1991-07-24,2983.23,3003.13,2950.80,2966.23,158530000,2966.23 1991-07-23,3012.97,3038.24,2972.94,2983.23,160010000,2983.23 1991-07-22,3016.32,3034.44,2990.83,3012.97,148880000,3012.97 1991-07-19,3016.32,3036.23,2989.49,3016.32,187290000,3016.32 1991-07-18,2978.76,3026.61,2970.93,3016.32,199470000,3016.32 1991-07-17,2983.90,3011.18,2961.54,2978.76,194150000,2978.76 1991-07-16,2990.61,3012.52,2962.88,2983.90,182740000,2983.90 1991-07-15,2980.77,3007.38,2965.79,2990.61,159340000,2990.61 1991-07-12,2959.75,3003.35,2942.98,2980.77,173060000,2980.77 1991-07-11,2944.77,2975.63,2933.36,2959.75,157680000,2959.75 1991-07-10,2947.23,2990.83,2927.77,2944.77,178170000,2944.77 1991-07-09,2961.99,2980.10,2934.03,2947.23,151430000,2947.23 1991-07-08,2932.47,2966.23,2897.36,2961.99,138210000,2961.99 1991-07-05,2934.70,2953.26,2917.71,2932.47,69790000,2932.47 1991-07-03,2957.07,2957.07,2915.03,2934.70,139290000,2934.70 1991-07-02,2958.41,2987.03,2939.62,2972.72,157140000,2972.72 1991-07-01,2911.67,2971.15,2911.67,2958.41,166880000,2958.41 1991-06-28,2934.03,2934.03,2879.25,2906.75,162670000,2906.75 1991-06-27,2913.01,2946.56,2909.21,2934.93,155820000,2934.93 1991-06-26,2910.11,2934.03,2879.25,2913.01,186830000,2913.01 1991-06-25,2913.01,2938.51,2887.97,2910.11,155450000,2910.11 1991-06-24,2957.29,2957.29,2904.29,2913.01,137700000,2913.01 1991-06-21,2953.94,2977.64,2937.84,2965.56,193110000,2965.56 1991-06-20,2955.50,2969.81,2927.33,2953.94,163780000,2953.94 1991-06-19,2978.31,2978.31,2933.59,2955.50,156070000,2955.50 1991-06-18,2993.96,3022.14,2970.48,2986.81,154900000,2986.81 1991-06-17,3000.45,3021.69,2977.86,2993.96,133910000,2993.96 1991-06-14,2967.58,3014.98,2967.58,3000.45,167530000,3000.45 1991-06-13,2961.99,2982.11,2942.53,2965.12,144870000,2965.12 1991-06-12,2985.91,2987.25,2928.89,2961.99,165720000,2961.99 1991-06-11,2975.40,3012.08,2963.10,2985.91,161240000,2985.91 1991-06-10,2976.74,2992.84,2958.41,2975.40,127420000,2975.40 1991-06-07,2994.86,3005.14,2954.61,2976.74,167830000,2976.74 1991-06-06,3005.37,3027.06,2975.63,2994.86,168050000,2994.86 1991-06-05,3027.95,3042.93,2989.49,3005.37,186300000,3005.37 1991-06-04,3035.33,3042.04,2992.62,3027.95,180170000,3027.95 1991-06-03,3027.50,3057.47,3000.67,3035.33,173710000,3035.33 1991-05-31,3000.45,3044.50,2972.94,3027.50,231680000,3027.50 1991-05-30,2969.59,3022.81,2950.58,3000.45,234090000,3000.45 1991-05-29,2958.86,2987.92,2940.74,2969.59,188150000,2969.59 1991-05-28,2913.91,2965.12,2903.85,2958.86,161950000,2958.86 1991-05-24,2900.04,2931.13,2893.78,2913.91,124500000,2913.91 1991-05-23,2910.33,2935.38,2881.04,2900.04,173080000,2900.04 1991-05-22,2906.08,2930.01,2881.93,2910.33,159310000,2910.33 1991-05-21,2892.22,2931.80,2875.00,2906.08,186860000,2906.08 1991-05-20,2886.63,2910.78,2872.76,2892.22,109510000,2892.22 1991-05-17,2894.01,2908.54,2860.02,2886.63,174210000,2886.63 1991-05-16,2865.38,2905.64,2863.82,2894.01,154460000,2894.01 1991-05-15,2886.85,2901.83,2834.53,2865.38,193110000,2865.38 1991-05-14,2922.85,2922.85,2870.08,2886.85,207910000,2886.85 1991-05-13,2920.17,2945.44,2896.24,2924.42,129620000,2924.42 1991-05-10,2971.15,2986.14,2906.08,2920.17,172730000,2920.17 1991-05-09,2930.90,2983.68,2926.88,2971.15,180210000,2971.15 1991-05-08,2917.49,2945.21,2898.70,2930.90,157240000,2930.90 1991-05-07,2941.64,2962.66,2906.53,2917.49,153290000,2917.49 1991-05-06,2938.86,2956.84,2911.45,2941.64,128360000,2941.64 1991-05-03,2938.61,2959.90,2906.93,2938.86,158160000,2938.86 1991-05-02,2930.20,2966.34,2917.33,2938.61,187090000,2938.61 1991-05-01,2887.87,2945.30,2882.43,2930.20,181900000,2930.20 1991-04-30,2876.98,2929.21,2859.41,2887.87,204930000,2887.87 1991-04-29,2912.38,2941.09,2869.55,2876.98,149860000,2876.98 1991-04-26,2921.04,2934.90,2888.61,2912.38,154550000,2912.38 1991-04-25,2949.51,2958.42,2905.20,2921.04,166940000,2921.04 1991-04-24,2930.45,2965.10,2913.37,2949.51,166800000,2949.51 1991-04-23,2927.72,2957.92,2905.94,2930.45,167840000,2930.45 1991-04-22,2962.13,2962.13,2911.63,2927.72,164410000,2927.72 1991-04-19,2999.26,3000.25,2943.56,2965.59,195510000,2965.59 1991-04-18,3004.46,3027.72,2976.24,2999.26,217410000,2999.26 1991-04-17,2986.88,3030.45,2963.12,3004.46,246930000,3004.46 1991-04-16,2933.17,2995.79,2912.13,2986.88,214480000,2986.88 1991-04-15,2920.79,2957.18,2896.29,2933.17,161800000,2933.17 1991-04-12,2905.45,2946.53,2884.16,2920.79,198610000,2920.79 1991-04-11,2877.72,2937.62,2877.72,2905.45,196570000,2905.45 1991-04-10,2873.02,2902.48,2848.51,2874.50,167940000,2874.50 1991-04-09,2918.56,2932.42,2863.36,2873.02,169940000,2873.02 1991-04-08,2896.78,2929.21,2877.72,2918.56,138580000,2918.56 1991-04-05,2924.50,2949.26,2876.98,2896.78,187410000,2896.78 1991-04-04,2926.73,2959.41,2899.75,2924.50,198120000,2924.50 1991-04-03,2945.05,2970.54,2915.84,2926.73,213720000,2926.73 1991-04-02,2881.19,2951.98,2878.22,2945.05,189530000,2945.05 1991-04-01,2913.86,2919.31,2868.32,2881.19,144010000,2881.19 1991-03-28,2917.57,2942.08,2893.32,2913.86,150750000,2913.86 1991-03-27,2914.85,2956.93,2886.14,2917.57,201830000,2917.57 1991-03-26,2865.84,2924.01,2848.02,2914.85,198720000,2914.85 1991-03-25,2858.91,2897.52,2837.87,2865.84,153920000,2865.84 1991-03-22,2855.45,2879.95,2829.21,2858.91,160890000,2858.91 1991-03-21,2872.03,2907.92,2841.58,2855.45,199830000,2855.45 1991-03-20,2867.82,2897.03,2840.84,2872.03,196810000,2872.03 1991-03-19,2908.17,2908.17,2840.84,2867.82,177070000,2867.82 1991-03-18,2948.27,2960.64,2899.75,2929.95,163100000,2929.95 1991-03-15,2952.23,2966.58,2918.81,2948.27,237660000,2948.27 1991-03-14,2955.20,3000.00,2925.74,2952.23,231000000,2952.23 1991-03-13,2922.52,2967.82,2910.89,2955.20,176000000,2955.20 1991-03-12,2939.36,2962.13,2906.68,2922.52,176440000,2922.52 1991-03-11,2955.20,2975.50,2923.27,2939.36,161600000,2939.36 1991-03-08,2963.37,3003.47,2934.90,2955.20,206850000,2955.20 1991-03-07,2973.27,2998.51,2948.51,2963.37,197060000,2963.37 1991-03-06,2972.52,3017.82,2957.67,2973.27,262290000,2973.27 1991-03-05,2914.11,2995.54,2913.86,2972.52,253700000,2972.52 1991-03-04,2909.90,2950.74,2897.03,2914.11,199830000,2914.11 1991-03-01,2882.18,2923.51,2846.78,2909.90,221510000,2909.90 1991-02-28,2889.11,2923.51,2858.42,2882.18,223010000,2882.18 1991-02-27,2864.60,2915.35,2839.85,2889.11,211410000,2889.11 1991-02-26,2887.87,2895.30,2840.10,2864.60,164170000,2864.60 1991-02-25,2889.36,2935.89,2865.35,2887.87,193820000,2887.87 1991-02-22,2891.83,2945.79,2860.40,2889.36,218760000,2889.36 1991-02-21,2899.01,2927.72,2871.29,2891.83,180770000,2891.83 1991-02-20,2923.76,2923.76,2879.46,2899.01,185680000,2899.01 1991-02-19,2934.65,2955.20,2895.30,2932.18,189900000,2932.18 1991-02-15,2877.23,2947.28,2868.07,2934.65,222370000,2934.65 1991-02-14,2909.16,2942.08,2852.48,2877.23,230750000,2877.23 1991-02-13,2874.75,2918.32,2848.51,2909.16,209960000,2909.16 1991-02-12,2902.23,2923.02,2848.27,2874.75,256160000,2874.75 1991-02-11,2830.69,2910.64,2822.52,2902.23,265930000,2902.23 1991-02-08,2810.64,2847.28,2787.13,2830.69,187830000,2830.69 1991-02-07,2830.94,2875.50,2790.59,2810.64,292190000,2810.64 1991-02-06,2788.37,2844.80,2760.15,2830.94,276940000,2830.94 1991-02-05,2772.28,2805.20,2742.82,2788.37,290570000,2788.37 1991-02-04,2730.69,2791.83,2714.85,2772.28,250750000,2772.28 1991-02-01,2736.39,2764.60,2694.31,2730.69,246670000,2730.69 1991-01-31,2713.12,2747.28,2691.58,2736.39,204240000,2736.39 1991-01-30,2662.62,2725.99,2654.70,2713.12,226790000,2713.12 1991-01-29,2654.46,2677.23,2627.23,2662.62,155740000,2662.62 1991-01-28,2659.41,2688.61,2635.15,2654.46,141270000,2654.46 1991-01-25,2643.07,2679.46,2623.27,2659.41,194350000,2659.41 1991-01-24,2619.06,2667.33,2615.10,2643.07,223150000,2643.07 1991-01-23,2603.22,2645.54,2584.65,2619.06,169440000,2619.06 1991-01-22,2629.21,2645.05,2586.39,2603.22,175590000,2603.22 1991-01-21,2646.29,2646.29,2602.97,2629.21,136290000,2629.21 1991-01-18,2623.51,2663.37,2600.25,2646.78,226770000,2646.78 1991-01-17,2571.78,2635.40,2571.78,2623.51,318890000,2623.51 1991-01-16,2490.59,2525.25,2475.99,2508.91,134560000,2508.91 1991-01-15,2483.91,2504.46,2470.05,2490.59,109980000,2490.59 1991-01-14,2500.99,2500.99,2447.03,2483.91,120830000,2483.91 1991-01-11,2498.76,2516.09,2472.77,2501.49,123050000,2501.49 1991-01-10,2470.30,2512.13,2467.08,2498.76,124510000,2498.76 1991-01-09,2509.41,2562.38,2456.19,2470.30,191100000,2470.30 1991-01-08,2522.77,2544.06,2493.07,2509.41,143390000,2509.41 1991-01-07,2563.37,2563.37,2514.11,2522.77,130610000,2522.77 1991-01-04,2573.51,2601.98,2540.84,2566.09,140820000,2566.09 1991-01-03,2610.64,2622.28,2567.57,2573.51,141450000,2573.51 1991-01-02,2633.66,2651.73,2600.99,2610.64,126280000,2610.64 1990-12-31,2629.21,2641.09,2611.14,2633.66,114130000,2633.66 1990-12-28,2625.50,2639.11,2607.92,2629.21,111030000,2629.21 1990-12-27,2637.13,2652.23,2616.58,2625.50,102900000,2625.50 1990-12-26,2621.29,2653.96,2613.37,2637.13,78730000,2637.13 1990-12-24,2633.66,2638.12,2609.65,2621.29,57200000,2621.29 1990-12-21,2629.46,2662.62,2619.55,2633.66,233400000,2633.66 1990-12-20,2626.73,2645.81,2591.58,2629.46,174700000,2629.46 1990-12-19,2626.73,2648.51,2602.48,2626.73,180380000,2626.73 1990-12-18,2593.32,2639.36,2583.17,2626.73,176460000,2626.73 1990-12-17,2593.81,2600.74,2563.61,2593.32,118560000,2593.32 1990-12-14,2614.36,2617.82,2572.03,2593.81,150880000,2593.81 1990-12-13,2622.28,2640.59,2598.76,2614.36,162110000,2614.36 1990-12-12,2586.14,2630.69,2578.22,2622.28,182270000,2622.28 1990-12-11,2596.78,2606.93,2565.59,2586.14,145330000,2586.14 1990-12-10,2590.10,2609.40,2566.58,2596.78,138650000,2596.78 1990-12-07,2602.48,2618.07,2571.78,2590.10,164950000,2590.10 1990-12-06,2610.40,2656.44,2589.36,2602.48,256380000,2602.48 1990-12-05,2579.70,2615.84,2558.42,2610.40,205820000,2610.40 1990-12-04,2565.59,2592.08,2534.65,2579.70,185820000,2579.70 1990-12-03,2559.65,2589.60,2543.56,2565.59,177010000,2565.59 1990-11-30,2518.81,2577.23,2498.51,2559.65,192350000,2559.65 1990-11-29,2535.15,2544.31,2501.23,2518.81,140920000,2518.81 1990-11-28,2543.81,2564.60,2521.04,2535.15,145490000,2535.15 1990-11-27,2533.17,2562.62,2516.09,2543.81,147590000,2543.81 1990-11-26,2527.23,2541.58,2489.85,2533.17,131540000,2533.17 1990-11-23,2539.36,2557.92,2521.04,2527.23,63350000,2527.23 1990-11-21,2530.20,2552.23,2502.72,2539.36,140660000,2539.36 1990-11-20,2565.35,2574.50,2524.01,2530.20,161170000,2530.20 1990-11-19,2550.25,2580.69,2543.07,2565.35,140950000,2565.35 1990-11-16,2545.05,2570.79,2522.28,2550.25,165440000,2550.25 1990-11-15,2559.65,2567.33,2528.71,2545.05,151370000,2545.05 1990-11-14,2535.40,2581.19,2522.77,2559.65,179310000,2559.65 1990-11-13,2540.35,2559.90,2512.38,2535.40,160240000,2535.40 1990-11-12,2490.10,2550.99,2490.10,2540.35,161390000,2540.35 1990-11-09,2443.81,2500.74,2438.61,2488.61,145160000,2488.61 1990-11-08,2440.84,2468.81,2415.84,2443.81,155570000,2443.81 1990-11-07,2485.15,2490.35,2430.94,2440.84,149130000,2440.84 1990-11-06,2502.23,2516.83,2471.53,2485.15,141130000,2485.15 1990-11-05,2490.84,2519.06,2472.77,2502.23,147510000,2502.23 1990-11-02,2454.95,2501.73,2447.28,2490.84,168700000,2490.84 1990-11-01,2442.33,2473.02,2415.59,2454.95,159270000,2454.95 1990-10-31,2448.02,2475.99,2419.55,2442.33,156060000,2442.33 1990-10-30,2430.20,2462.87,2400.50,2448.02,153450000,2448.02 1990-10-29,2436.14,2470.30,2407.67,2430.20,133980000,2430.20 1990-10-26,2482.18,2482.18,2429.21,2436.14,130190000,2436.14 1990-10-25,2504.21,2525.99,2464.11,2484.41,141460000,2484.41 1990-10-24,2494.06,2523.02,2470.54,2504.21,149290000,2504.21 1990-10-23,2516.09,2527.97,2480.20,2494.06,146300000,2494.06 1990-10-22,2520.79,2535.40,2476.73,2516.09,152650000,2516.09 1990-10-19,2453.47,2536.88,2453.47,2520.79,221480000,2520.79 1990-10-18,2391.83,2461.63,2391.83,2452.72,204110000,2452.72 1990-10-17,2381.19,2418.56,2358.17,2387.87,161260000,2387.87 1990-10-16,2416.34,2434.41,2366.83,2381.19,149570000,2381.19 1990-10-15,2398.02,2451.24,2354.95,2416.34,164980000,2416.34 1990-10-12,2365.10,2428.71,2349.75,2398.02,187940000,2398.02 1990-10-11,2407.92,2427.23,2344.31,2365.10,180060000,2365.10 1990-10-10,2445.54,2472.03,2388.36,2407.92,167890000,2407.92 1990-10-09,2514.60,2514.60,2437.87,2445.54,145610000,2445.54 1990-10-08,2510.64,2548.02,2507.18,2523.76,99470000,2523.76 1990-10-05,2516.83,2544.55,2453.47,2510.64,153380000,2510.64 1990-10-04,2489.36,2528.22,2464.85,2516.83,145410000,2516.83 1990-10-03,2505.20,2534.65,2470.79,2489.36,135490000,2489.36 1990-10-02,2515.84,2565.35,2487.62,2505.20,188360000,2505.20 1990-10-01,2452.48,2534.65,2446.53,2515.84,202210000,2515.84 1990-09-28,2427.48,2465.59,2367.82,2452.48,201010000,2452.48 1990-09-27,2459.65,2492.33,2396.29,2427.48,182690000,2427.48 1990-09-26,2485.64,2496.04,2435.40,2459.65,155570000,2459.65 1990-09-25,2452.97,2501.24,2437.38,2485.64,155940000,2485.64 1990-09-24,2498.02,2498.02,2438.12,2452.97,162210000,2452.97 1990-09-21,2518.32,2538.37,2479.95,2512.38,201050000,2512.38 1990-09-20,2549.01,2549.01,2495.54,2518.32,145100000,2518.32 1990-09-19,2571.29,2594.55,2534.41,2557.43,147530000,2557.43 1990-09-18,2567.33,2587.87,2524.26,2571.29,141130000,2571.29 1990-09-17,2564.11,2585.89,2537.13,2567.33,110600000,2567.33 1990-09-14,2582.67,2585.15,2545.54,2564.11,133390000,2564.11 1990-09-13,2625.74,2629.21,2570.54,2582.67,123370000,2582.67 1990-09-12,2612.62,2639.11,2592.33,2625.74,129890000,2625.74 1990-09-11,2615.59,2635.64,2586.88,2612.62,113220000,2612.62 1990-09-10,2619.55,2665.35,2600.99,2615.59,119730000,2615.59 1990-09-07,2596.29,2635.89,2577.72,2619.55,123800000,2619.55 1990-09-06,2628.22,2633.17,2575.99,2596.29,125620000,2596.29 1990-09-05,2613.37,2643.07,2588.61,2628.22,120610000,2628.22 1990-09-04,2614.36,2618.07,2573.02,2613.37,92940000,2613.37 1990-08-31,2593.32,2624.50,2569.31,2614.36,96480000,2614.36 1990-08-30,2632.43,2641.34,2578.47,2593.32,120890000,2593.32 1990-08-29,2614.85,2651.24,2596.53,2632.43,134240000,2632.43 1990-08-28,2611.63,2629.95,2582.92,2614.85,127660000,2614.85 1990-08-27,2590.59,2645.05,2590.59,2611.63,160150000,2611.63 1990-08-24,2483.42,2555.69,2480.45,2532.92,199040000,2532.92 1990-08-23,2539.60,2539.60,2459.41,2483.42,250440000,2483.42 1990-08-22,2603.96,2630.69,2553.22,2560.15,175550000,2560.15 1990-08-21,2645.53,2645.53,2566.09,2603.96,194630000,2603.96 1990-08-20,2644.80,2679.21,2632.43,2656.44,129630000,2656.44 1990-08-17,2679.21,2679.21,2598.02,2644.80,212560000,2644.80 1990-08-16,2746.53,2746.53,2676.24,2681.44,138850000,2681.44 1990-08-15,2747.77,2778.71,2736.38,2748.27,135210000,2748.27 1990-08-14,2746.78,2773.02,2720.54,2747.77,130320000,2747.77 1990-08-13,2716.58,2752.23,2676.73,2746.78,122820000,2746.78 1990-08-10,2758.91,2763.61,2692.82,2716.58,145340000,2716.58 1990-08-09,2734.90,2774.26,2716.58,2758.91,155810000,2758.91 1990-08-08,2710.64,2763.37,2691.34,2734.90,190400000,2734.90 1990-08-07,2716.34,2763.86,2676.24,2710.64,231580000,2710.64 1990-08-06,2758.42,2758.42,2683.17,2716.34,240400000,2716.34 1990-08-03,2863.86,2863.86,2722.03,2809.65,292360000,2809.65 1990-08-02,2899.26,2903.71,2833.17,2864.60,253090000,2864.60 1990-08-01,2905.20,2931.19,2875.00,2899.26,176810000,2899.26 1990-07-31,2917.33,2940.10,2878.47,2905.20,173810000,2905.20 1990-07-30,2898.51,2922.52,2861.14,2917.33,146470000,2917.33 1990-07-27,2920.79,2938.36,2877.72,2898.51,149070000,2898.51 1990-07-26,2930.94,2945.79,2888.12,2920.79,155040000,2920.79 1990-07-25,2922.52,2946.53,2896.78,2930.94,163530000,2930.94 1990-07-24,2904.70,2939.60,2866.83,2922.52,181920000,2922.52 1990-07-23,2961.14,2961.39,2833.17,2904.70,209030000,2904.70 1990-07-20,2993.81,3019.31,2953.71,2961.14,177810000,2961.14 1990-07-19,2981.68,3006.19,2948.27,2993.81,161990000,2993.81 1990-07-18,2999.75,3009.65,2963.61,2981.68,168760000,2981.68 1990-07-17,2999.75,3024.26,2970.05,2999.75,176790000,2999.75 1990-07-16,2980.20,3017.08,2971.78,2999.75,149450000,2999.75 1990-07-13,2969.80,3012.38,2956.68,2980.20,215600000,2980.20 1990-07-12,2932.67,2980.69,2917.82,2969.80,211510000,2969.80 1990-07-11,2890.84,2942.33,2890.10,2932.67,162220000,2932.67 1990-07-10,2914.11,2928.22,2882.18,2890.84,147630000,2890.84 1990-07-09,2904.95,2927.97,2890.84,2914.11,119390000,2914.11 1990-07-06,2879.21,2919.80,2867.57,2904.95,111730000,2904.95 1990-07-05,2906.44,2906.44,2863.61,2879.21,128320000,2879.21 1990-07-03,2899.26,2925.74,2891.09,2911.63,130050000,2911.63 1990-07-02,2880.69,2908.66,2869.80,2899.26,130200000,2899.26 1990-06-29,2878.71,2901.98,2865.84,2880.69,145510000,2880.69 1990-06-28,2862.13,2896.04,2850.50,2878.71,136120000,2878.71 1990-06-27,2842.33,2878.96,2821.53,2862.13,146620000,2862.13 1990-06-26,2845.05,2882.92,2832.67,2842.33,141420000,2842.33 1990-06-25,2857.18,2882.18,2834.90,2845.05,133100000,2845.05 1990-06-22,2901.73,2931.93,2848.02,2857.18,172570000,2857.18 1990-06-21,2895.30,2916.58,2870.05,2901.73,138570000,2901.73 1990-06-20,2893.56,2914.60,2868.81,2895.30,137420000,2895.30 1990-06-19,2882.18,2907.92,2866.58,2893.56,134930000,2893.56 1990-06-18,2930.45,2930.45,2877.48,2882.18,133470000,2882.18 1990-06-15,2928.22,2947.77,2902.72,2935.89,205130000,2935.89 1990-06-14,2929.95,2943.56,2902.97,2928.22,135770000,2928.22 1990-06-13,2933.42,2956.93,2910.15,2929.95,158910000,2929.95 1990-06-12,2892.57,2947.52,2877.97,2933.42,157100000,2933.42 1990-06-11,2862.38,2901.98,2852.97,2892.57,119550000,2892.57 1990-06-08,2897.33,2908.50,2850.73,2862.38,142600000,2862.38 1990-06-07,2911.65,2930.58,2880.34,2897.33,160360000,2897.33 1990-06-06,2925.00,2936.65,2891.99,2911.65,164030000,2911.65 1990-06-05,2935.19,2956.55,2911.89,2925.00,199720000,2925.00 1990-06-04,2900.97,2943.69,2883.98,2935.19,175520000,2935.19 1990-06-01,2876.66,2919.90,2868.69,2900.97,187860000,2900.97 1990-05-31,2878.56,2900.62,2854.64,2876.66,165690000,2876.66 1990-05-30,2870.49,2908.21,2853.89,2878.56,199540000,2878.56 1990-05-29,2820.92,2876.19,2812.62,2870.49,137410000,2870.49 1990-05-25,2855.55,2856.50,2806.69,2820.92,120250000,2820.92 1990-05-24,2856.26,2878.08,2828.04,2855.55,155140000,2855.55 1990-05-23,2852.23,2869.07,2824.95,2856.26,172330000,2856.26 1990-05-22,2844.68,2877.13,2828.51,2852.23,203350000,2852.23 1990-05-21,2819.91,2859.72,2802.08,2844.68,166280000,2844.68 1990-05-18,2831.71,2838.43,2804.63,2819.91,162520000,2819.91 1990-05-17,2819.68,2856.25,2811.57,2831.71,164770000,2831.71 1990-05-16,2822.45,2841.44,2800.23,2819.68,159810000,2819.68 1990-05-15,2821.53,2840.74,2798.15,2822.45,165730000,2822.45 1990-05-14,2801.58,2857.87,2793.75,2821.53,225410000,2821.53 1990-05-11,2743.02,2810.36,2743.02,2801.58,234040000,2801.58 1990-05-10,2732.88,2755.63,2716.44,2738.51,158460000,2738.51 1990-05-09,2733.56,2745.50,2710.14,2732.88,152220000,2732.88 1990-05-08,2721.62,2739.41,2710.36,2733.56,144230000,2733.56 1990-05-07,2710.36,2739.19,2698.87,2721.62,132760000,2721.62 1990-05-04,2696.17,2718.92,2682.43,2710.36,140550000,2710.36 1990-05-03,2689.64,2716.22,2682.88,2696.17,145560000,2696.17 1990-05-02,2668.92,2697.30,2659.01,2689.64,141610000,2689.64 1990-05-01,2656.76,2687.39,2651.35,2668.92,149020000,2668.92 1990-04-30,2645.05,2667.79,2627.70,2656.76,122750000,2656.76 1990-04-27,2676.58,2687.39,2639.19,2645.05,130630000,2645.05 1990-04-26,2666.44,2691.89,2650.22,2676.58,141330000,2676.58 1990-04-25,2654.50,2685.36,2649.32,2666.44,133480000,2666.44 1990-04-24,2666.67,2686.04,2643.69,2654.50,137360000,2654.50 1990-04-23,2690.77,2690.77,2650.90,2666.67,136150000,2666.67 1990-04-20,2711.94,2722.07,2668.47,2695.95,174260000,2695.95 1990-04-19,2732.88,2742.12,2700.00,2711.94,152930000,2711.94 1990-04-18,2765.77,2775.68,2722.75,2732.88,147130000,2732.88 1990-04-17,2763.06,2774.77,2738.29,2765.77,127990000,2765.77 1990-04-16,2751.80,2793.47,2748.87,2763.06,142810000,2763.06 1990-04-12,2729.73,2763.96,2729.50,2751.80,142470000,2751.80 1990-04-11,2731.08,2751.35,2713.29,2729.73,141080000,2729.73 1990-04-10,2722.07,2741.67,2707.88,2731.08,136020000,2731.08 1990-04-09,2717.12,2737.39,2701.35,2722.07,114970000,2722.07 1990-04-06,2721.17,2732.43,2695.50,2717.12,137490000,2717.12 1990-04-05,2719.37,2746.17,2709.01,2721.17,144170000,2721.17 1990-04-04,2736.71,2755.86,2708.56,2719.37,159540000,2719.37 1990-04-03,2700.45,2747.30,2699.55,2736.71,154310000,2736.71 1990-04-02,2707.21,2708.78,2668.69,2700.45,124360000,2700.45 1990-03-30,2727.70,2736.71,2692.34,2707.21,139340000,2707.21 1990-03-29,2743.69,2753.38,2711.49,2727.70,132190000,2727.70 1990-03-28,2736.94,2755.63,2716.21,2743.69,142300000,2743.69 1990-03-27,2707.66,2738.96,2691.89,2736.94,131610000,2736.94 1990-03-26,2704.28,2735.81,2697.97,2707.66,116110000,2707.66 1990-03-23,2695.72,2722.75,2688.06,2704.28,132070000,2704.28 1990-03-22,2727.93,2734.01,2674.32,2695.72,175930000,2695.72 1990-03-21,2738.74,2759.68,2718.24,2727.93,130990000,2727.93 1990-03-20,2755.63,2775.00,2724.10,2738.74,177320000,2738.74 1990-03-19,2741.22,2761.71,2706.53,2755.63,142300000,2755.63 1990-03-16,2699.32,2745.50,2699.32,2741.22,222520000,2741.22 1990-03-15,2687.84,2714.86,2677.93,2695.72,144410000,2695.72 1990-03-14,2674.55,2705.18,2662.39,2687.84,145060000,2687.84 1990-03-13,2686.71,2699.55,2657.88,2674.55,145440000,2674.55 1990-03-12,2683.33,2698.65,2661.94,2686.71,114790000,2686.71 1990-03-09,2696.17,2705.63,2665.54,2683.33,150410000,2683.33 1990-03-08,2669.59,2705.18,2661.26,2696.17,170900000,2696.17 1990-03-07,2676.80,2696.85,2656.08,2669.59,163580000,2669.59 1990-03-06,2649.55,2684.46,2638.06,2676.80,143640000,2676.80 1990-03-05,2660.36,2675.22,2636.71,2649.55,140110000,2649.55 1990-03-02,2635.59,2669.82,2630.18,2660.36,164330000,2660.36 1990-03-01,2627.25,2655.63,2607.88,2635.59,157930000,2635.59 1990-02-28,2617.12,2652.48,2603.60,2627.25,184410000,2627.25 1990-02-27,2602.48,2637.84,2592.12,2617.12,152590000,2617.12 1990-02-26,2564.19,2606.30,2560.13,2602.48,148910000,2602.48 1990-02-23,2574.77,2591.44,2540.99,2564.19,148490000,2564.19 1990-02-22,2583.56,2622.30,2568.02,2574.77,184320000,2574.77 1990-02-21,2596.85,2602.48,2556.31,2583.56,159240000,2583.56 1990-02-20,2619.14,2619.14,2579.05,2596.85,147300000,2596.85 1990-02-16,2649.55,2669.37,2623.65,2635.59,166840000,2635.59 1990-02-15,2624.32,2658.78,2614.86,2649.55,174630000,2649.55 1990-02-14,2624.10,2643.69,2608.11,2624.32,138530000,2624.32 1990-02-13,2619.14,2639.19,2592.57,2624.10,144490000,2624.10 1990-02-12,2648.20,2652.48,2610.59,2619.14,118390000,2619.14 1990-02-09,2644.37,2666.67,2628.15,2648.20,146910000,2648.20 1990-02-08,2640.09,2674.32,2622.30,2644.37,176240000,2644.37 1990-02-07,2606.31,2651.35,2579.28,2640.09,186710000,2640.09 1990-02-06,2622.52,2629.50,2588.29,2606.31,134070000,2606.31 1990-02-05,2602.70,2633.56,2592.12,2622.52,130950000,2622.52 1990-02-02,2586.26,2623.65,2577.03,2602.70,164400000,2602.70 1990-02-01,2590.54,2611.49,2571.85,2586.26,154580000,2586.26 1990-01-31,2546.85,2600.90,2546.85,2590.54,189660000,2590.54 1990-01-30,2553.38,2576.13,2513.06,2543.24,186030000,2543.24 1990-01-29,2559.23,2583.56,2522.97,2553.38,150770000,2553.38 1990-01-26,2561.04,2591.67,2516.89,2559.23,198190000,2559.23 1990-01-25,2604.50,2628.83,2546.17,2561.04,172270000,2561.04 1990-01-24,2615.32,2619.59,2534.23,2604.50,207830000,2604.50 1990-01-23,2600.45,2639.64,2584.01,2615.32,179300000,2615.32 1990-01-22,2677.90,2683.33,2595.27,2600.45,148380000,2600.45 1990-01-19,2666.38,2696.89,2657.85,2677.90,185590000,2677.90 1990-01-18,2659.13,2678.11,2625.85,2666.38,178590000,2666.38 1990-01-17,2692.62,2711.39,2643.77,2659.13,170470000,2659.13 1990-01-16,2669.37,2698.38,2634.17,2692.62,186070000,2692.62 1990-01-15,2689.21,2698.11,2656.36,2669.37,140590000,2669.37 1990-01-12,2735.92,2735.92,2675.98,2689.21,183880000,2689.21 1990-01-11,2750.64,2783.27,2748.29,2760.67,154390000,2760.67 1990-01-10,2766.00,2772.82,2725.47,2750.64,175990000,2750.64 1990-01-09,2794.37,2810.79,2760.03,2766.00,155210000,2766.00 1990-01-08,2773.25,2803.97,2753.41,2794.37,140110000,2794.37 1990-01-05,2796.08,2810.15,2758.11,2773.25,158530000,2773.25 1990-01-04,2809.73,2821.46,2766.42,2796.08,177000000,2796.08 1990-01-03,2810.15,2834.04,2786.26,2809.73,192330000,2809.73 1990-01-02,2753.20,2811.65,2732.51,2810.15,162070000,2810.15 1989-12-29,2732.30,2763.01,2726.96,2753.20,145940000,2753.20 1989-12-28,2724.40,2742.53,2709.04,2732.30,128030000,2732.30 1989-12-27,2709.26,2739.12,2700.30,2724.40,133740000,2724.40 1989-12-26,2711.39,2728.88,2694.75,2709.26,77610000,2709.26 1989-12-22,2691.13,2721.20,2682.59,2711.39,120980000,2711.39 1989-12-21,2687.93,2714.16,2671.72,2691.13,175150000,2691.13 1989-12-20,2695.61,2719.07,2667.02,2687.93,176520000,2687.93 1989-12-19,2697.53,2720.14,2658.70,2695.61,186060000,2695.61 1989-12-18,2739.55,2755.55,2679.82,2697.53,184750000,2697.53 1989-12-15,2753.63,2763.65,2703.92,2739.55,240390000,2739.55 1989-12-14,2761.09,2771.33,2732.08,2753.63,178700000,2753.63 1989-12-13,2752.13,2784.77,2737.20,2761.09,184660000,2761.09 1989-12-12,2728.24,2764.51,2716.51,2752.13,176820000,2752.13 1989-12-11,2731.44,2742.75,2705.63,2728.24,147130000,2728.24 1989-12-08,2720.78,2750.85,2716.51,2731.44,144910000,2731.44 1989-12-07,2736.77,2756.83,2702.00,2720.78,161980000,2720.78 1989-12-06,2741.68,2754.91,2722.70,2736.77,145850000,2736.77 1989-12-05,2753.63,2773.89,2731.23,2741.68,154640000,2741.68 1989-12-04,2747.65,2772.18,2731.02,2753.63,150360000,2753.63 1989-12-01,2706.27,2763.87,2705.42,2747.65,199200000,2747.65 1989-11-30,2688.78,2718.22,2681.95,2706.27,153200000,2706.27 1989-11-29,2702.01,2713.10,2677.47,2688.78,147270000,2688.78 1989-11-28,2694.97,2715.02,2677.26,2702.01,153770000,2702.01 1989-11-27,2675.55,2713.95,2663.40,2694.97,149390000,2694.97 1989-11-24,2657.00,2686.01,2657.00,2675.55,86290000,2675.55 1989-11-22,2639.29,2668.30,2629.91,2656.78,145730000,2656.78 1989-11-21,2632.04,2654.22,2614.97,2639.29,147900000,2639.29 1989-11-20,2652.66,2659.56,2615.40,2632.04,128170000,2632.04 1989-11-17,2635.66,2665.37,2623.15,2652.66,151020000,2652.66 1989-11-16,2632.58,2650.61,2613.52,2635.66,148370000,2635.66 1989-11-15,2610.25,2641.60,2600.00,2632.58,155130000,2632.58 1989-11-14,2626.43,2640.57,2597.13,2610.25,143170000,2610.25 1989-11-13,2625.61,2648.36,2602.05,2626.43,140750000,2626.43 1989-11-10,2603.69,2635.86,2603.07,2625.61,131800000,2625.61 1989-11-09,2623.36,2634.84,2595.90,2603.69,143390000,2603.69 1989-11-08,2597.13,2644.26,2594.67,2623.36,170150000,2623.36 1989-11-07,2582.17,2608.81,2563.11,2597.13,163000000,2597.13 1989-11-06,2621.72,2621.72,2574.59,2582.17,135480000,2582.17 1989-11-03,2631.56,2650.82,2612.91,2629.51,131500000,2629.51 1989-11-02,2645.90,2653.69,2607.58,2631.56,152440000,2631.56 1989-11-01,2645.08,2665.78,2622.95,2645.90,154240000,2645.90 1989-10-31,2606.97,2662.09,2606.97,2645.08,176100000,2645.08 1989-10-30,2596.72,2627.05,2588.11,2603.48,126630000,2603.48 1989-10-27,2613.73,2621.11,2573.56,2596.72,170330000,2596.72 1989-10-26,2653.28,2657.99,2597.74,2613.73,175240000,2613.73 1989-10-25,2659.22,2684.84,2627.66,2653.28,155650000,2653.28 1989-10-24,2662.91,2680.74,2570.28,2659.22,237960000,2659.22 1989-10-23,2689.14,2704.71,2648.77,2662.91,135860000,2662.91 1989-10-20,2683.20,2703.07,2660.25,2689.14,164830000,2689.14 1989-10-19,2650.61,2707.58,2650.61,2683.20,198120000,2683.20 1989-10-18,2638.73,2664.34,2610.66,2643.65,166900000,2643.65 1989-10-17,2657.38,2665.37,2588.73,2638.73,224070000,2638.73 1989-10-16,2569.26,2667.42,2496.93,2657.38,416290000,2657.38 1989-10-13,2759.84,2773.36,2545.49,2569.26,251170000,2569.26 1989-10-12,2744.06,2785.25,2744.06,2759.84,160120000,2759.84 1989-10-11,2785.33,2790.98,2750.82,2773.36,164070000,2773.36 1989-10-10,2791.41,2809.08,2766.53,2785.33,147560000,2785.33 1989-10-09,2785.52,2804.52,2766.32,2791.41,86810000,2791.41 1989-10-06,2773.56,2808.13,2765.58,2785.52,172520000,2785.52 1989-10-05,2771.09,2797.11,2747.15,2773.56,177890000,2773.56 1989-10-04,2754.56,2785.52,2738.79,2771.09,194590000,2771.09 1989-10-03,2713.72,2765.96,2708.97,2754.56,182550000,2754.56 1989-10-02,2692.82,2724.16,2677.05,2713.72,127410000,2713.72 1989-09-29,2694.91,2721.12,2675.72,2692.82,155300000,2692.82 1989-09-28,2673.06,2709.16,2657.86,2694.91,164240000,2694.91 1989-09-27,2663.94,2685.03,2636.78,2673.06,158400000,2673.06 1989-09-26,2659.19,2688.64,2652.93,2663.94,158350000,2663.94 1989-09-25,2681.61,2685.41,2647.61,2659.19,121130000,2659.19 1989-09-22,2680.28,2696.62,2667.55,2681.61,133350000,2681.61 1989-09-21,2683.89,2707.83,2665.65,2680.28,146930000,2680.28 1989-09-20,2687.31,2703.46,2672.49,2683.89,136640000,2683.89 1989-09-19,2687.50,2709.35,2675.91,2687.31,141610000,2687.31 1989-09-18,2674.58,2694.91,2662.61,2687.50,136940000,2687.50 1989-09-15,2664.89,2695.67,2643.05,2674.58,234870000,2674.58 1989-09-14,2679.52,2690.16,2647.61,2664.89,149250000,2664.89 1989-09-13,2707.26,2725.87,2671.35,2679.52,175330000,2679.52 1989-09-12,2704.41,2726.06,2689.59,2707.26,142140000,2707.26 1989-09-11,2709.54,2720.74,2677.05,2704.41,126020000,2704.41 1989-09-08,2706.88,2728.72,2679.33,2709.54,154090000,2709.54 1989-09-07,2719.79,2748.10,2692.06,2706.88,160160000,2706.88 1989-09-06,2744.68,2752.09,2697.95,2719.79,161800000,2719.79 1989-09-05,2752.09,2768.24,2731.76,2744.68,145180000,2744.68 1989-09-01,2737.27,2766.91,2726.82,2752.09,133300000,2752.09 1989-08-31,2728.15,2744.68,2717.90,2737.27,144820000,2737.27 1989-08-30,2726.63,2753.61,2705.36,2728.15,174350000,2728.15 1989-08-29,2743.36,2757.60,2704.98,2726.63,175210000,2726.63 1989-08-28,2732.36,2748.10,2710.74,2743.36,131180000,2743.36 1989-08-25,2734.64,2758.73,2715.48,2732.36,165930000,2732.36 1989-08-24,2678.11,2738.43,2672.23,2734.64,225520000,2734.64 1989-08-23,2650.99,2683.61,2641.20,2678.11,159640000,2678.11 1989-08-22,2647.00,2659.71,2619.71,2650.99,141930000,2650.99 1989-08-21,2687.97,2693.29,2640.74,2647.00,136800000,2647.00 1989-08-18,2679.63,2697.29,2665.97,2687.97,145810000,2687.97 1989-08-17,2693.29,2703.72,2663.13,2679.63,157560000,2679.63 1989-08-16,2687.78,2712.25,2680.58,2693.29,150060000,2693.29 1989-08-15,2677.92,2705.24,2665.02,2687.78,148770000,2687.78 1989-08-14,2683.99,2702.96,2654.97,2677.92,142010000,2677.92 1989-08-11,2712.63,2747.53,2668.06,2683.99,197550000,2683.99 1989-08-10,2686.08,2732.93,2669.58,2712.63,198660000,2712.63 1989-08-09,2699.17,2725.15,2678.11,2686.08,209900000,2686.08 1989-08-08,2694.99,2718.51,2676.97,2699.17,200340000,2699.17 1989-08-07,2653.45,2701.82,2643.59,2694.99,197580000,2694.99 1989-08-04,2661.61,2679.44,2629.17,2653.45,169750000,2653.45 1989-08-03,2657.44,2676.97,2640.74,2661.61,168690000,2661.61 1989-08-02,2641.12,2668.44,2626.33,2657.44,181760000,2657.44 1989-08-01,2660.66,2687.03,2628.98,2641.12,225280000,2641.12 1989-07-31,2635.24,2668.25,2615.52,2660.66,166650000,2660.66 1989-07-28,2635.43,2656.68,2615.71,2635.24,180610000,2635.24 1989-07-27,2613.05,2649.28,2604.70,2635.43,213680000,2635.43 1989-07-26,2583.08,2621.21,2563.73,2613.05,188270000,2613.05 1989-07-25,2584.98,2610.39,2565.63,2583.08,179270000,2583.08 1989-07-24,2607.36,2607.55,2574.36,2584.98,136260000,2584.98 1989-07-21,2575.49,2613.81,2558.23,2607.36,174880000,2607.36 1989-07-20,2584.41,2616.46,2566.58,2575.49,204590000,2575.49 1989-07-19,2546.47,2590.48,2546.47,2584.41,215740000,2584.41 1989-07-18,2553.49,2560.70,2531.68,2544.76,152350000,2544.76 1989-07-17,2554.82,2565.82,2535.85,2553.49,131960000,2553.49 1989-07-14,2538.32,2563.16,2512.52,2554.82,183480000,2554.82 1989-07-13,2532.63,2553.30,2517.83,2538.32,153820000,2538.32 1989-07-12,2514.61,2543.25,2504.93,2532.63,160550000,2532.63 1989-07-11,2503.41,2537.37,2503.41,2514.61,171590000,2514.61 1989-07-10,2487.86,2513.47,2482.74,2502.66,131870000,2502.66 1989-07-07,2462.44,2503.22,2456.56,2487.86,166430000,2487.86 1989-07-06,2456.56,2475.53,2446.51,2462.44,140450000,2462.44 1989-07-05,2452.77,2467.18,2431.53,2456.56,127710000,2456.56 1989-07-03,2440.06,2461.49,2434.37,2452.77,68870000,2452.77 1989-06-30,2458.27,2466.05,2412.94,2440.06,170490000,2440.06 1989-06-29,2500.00,2500.00,2451.25,2458.27,167100000,2458.27 1989-06-28,2526.37,2531.87,2485.77,2504.74,158470000,2504.74 1989-06-27,2511.38,2544.95,2507.40,2526.37,171090000,2526.37 1989-06-26,2531.87,2536.99,2500.57,2511.38,143600000,2511.38 1989-06-23,2490.14,2536.04,2490.14,2531.87,198720000,2531.87 1989-06-22,2464.91,2489.75,2452.77,2481.98,176510000,2481.98 1989-06-21,2472.88,2489.38,2450.87,2464.91,168830000,2464.91 1989-06-20,2479.89,2496.02,2463.96,2472.88,167650000,2472.88 1989-06-19,2486.38,2497.15,2465.10,2479.89,130720000,2479.89 1989-06-16,2475.00,2495.52,2461.57,2486.38,244510000,2486.38 1989-06-15,2503.36,2505.97,2460.82,2475.00,179480000,2475.00 1989-06-14,2503.54,2520.71,2486.01,2503.36,170540000,2503.36 1989-06-13,2518.84,2520.71,2484.70,2503.54,164870000,2503.54 1989-06-12,2513.42,2528.17,2484.70,2518.84,151460000,2518.84 1989-06-09,2516.91,2533.64,2494.85,2513.42,173240000,2513.42 1989-06-08,2512.32,2534.38,2499.81,2516.91,212310000,2516.91 1989-06-07,2496.32,2526.65,2493.38,2512.32,213710000,2512.32 1989-06-06,2480.70,2507.54,2471.32,2496.32,187570000,2496.32 1989-06-05,2517.83,2523.71,2476.84,2480.70,163420000,2480.70 1989-06-02,2492.46,2530.88,2492.46,2517.83,229140000,2517.83 1989-06-01,2480.15,2504.23,2469.67,2490.63,223160000,2490.63 1989-05-31,2475.55,2497.06,2462.68,2480.15,162530000,2480.15 1989-05-30,2493.77,2510.66,2459.74,2475.55,151780000,2475.55 1989-05-26,2482.59,2501.83,2473.06,2493.77,143120000,2493.77 1989-05-25,2483.87,2498.72,2467.56,2482.59,154470000,2482.59 1989-05-24,2478.01,2494.68,2458.03,2483.87,178600000,2483.87 1989-05-23,2501.83,2501.83,2467.19,2478.01,187690000,2478.01 1989-05-22,2501.10,2521.63,2481.30,2502.02,185010000,2502.02 1989-05-19,2470.12,2509.34,2468.29,2501.10,242410000,2501.10 1989-05-18,2462.43,2482.77,2448.86,2470.12,177480000,2470.12 1989-05-17,2453.45,2478.74,2439.70,2462.43,191210000,2462.43 1989-05-16,2463.89,2469.76,2439.88,2453.45,173100000,2453.45 1989-05-15,2439.70,2474.89,2432.37,2463.89,179350000,2463.89 1989-05-12,2408.54,2447.95,2408.54,2439.70,221490000,2439.70 1989-05-11,2374.45,2393.51,2365.83,2382.88,151620000,2382.88 1989-05-10,2371.33,2387.83,2361.25,2374.45,146000000,2374.45 1989-05-09,2376.47,2390.03,2356.85,2371.33,150090000,2371.33 1989-05-08,2381.96,2387.28,2356.30,2376.47,135130000,2376.47 1989-05-05,2384.90,2415.69,2371.88,2381.96,180810000,2381.96 1989-05-04,2393.70,2399.01,2373.35,2384.90,153130000,2384.90 1989-05-03,2402.86,2410.56,2382.51,2393.70,171690000,2393.70 1989-05-02,2414.96,2434.38,2394.61,2402.86,172560000,2402.86 1989-05-01,2418.80,2420.45,2390.03,2414.96,138050000,2414.96 1989-04-28,2418.99,2430.17,2403.59,2418.80,158390000,2418.80 1989-04-27,2389.10,2433.10,2387.83,2418.99,191170000,2418.99 1989-04-26,2386.85,2404.14,2373.90,2389.10,146090000,2389.10 1989-04-25,2402.68,2421.55,2378.85,2386.85,165430000,2386.85 1989-04-24,2409.46,2416.06,2385.08,2402.68,142100000,2402.68 1989-04-21,2377.38,2412.57,2373.35,2409.46,187310000,2409.46 1989-04-20,2386.91,2399.19,2356.85,2377.38,175970000,2377.38 1989-04-19,2379.40,2398.46,2369.50,2386.91,191510000,2386.91 1989-04-18,2351.36,2386.00,2351.36,2379.40,208650000,2379.40 1989-04-17,2337.06,2348.42,2324.23,2337.79,128540000,2337.79 1989-04-14,2308.83,2342.93,2308.83,2337.06,169780000,2337.06 1989-04-13,2319.65,2321.85,2289.59,2296.00,141590000,2296.00 1989-04-12,2311.58,2332.84,2304.44,2319.65,165200000,2319.65 1989-04-11,2301.87,2321.48,2295.27,2311.58,146830000,2311.58 1989-04-10,2304.80,2316.35,2293.62,2301.87,123990000,2301.87 1989-04-07,2291.97,2314.88,2282.07,2304.80,156950000,2304.80 1989-04-06,2304.80,2305.72,2282.81,2291.97,146530000,2291.97 1989-04-05,2298.20,2315.80,2286.84,2304.80,165880000,2304.80 1989-04-04,2304.80,2314.88,2282.44,2298.20,160680000,2298.20 1989-04-03,2293.62,2317.45,2284.09,2304.80,164660000,2304.80 1989-03-31,2281.34,2303.34,2277.49,2293.62,170960000,2293.62 1989-03-30,2281.52,2296.92,2264.30,2281.34,159950000,2281.34 1989-03-29,2275.54,2293.62,2262.65,2281.52,144240000,2281.52 1989-03-28,2258.93,2287.86,2258.93,2275.54,146420000,2275.54 1989-03-27,2243.04,2264.29,2234.46,2257.86,112960000,2257.86 1989-03-23,2263.21,2274.82,2235.89,2243.04,153750000,2243.04 1989-03-22,2266.25,2276.61,2247.14,2263.21,146570000,2263.21 1989-03-21,2262.50,2284.82,2259.64,2266.25,142010000,2266.25 1989-03-20,2286.25,2286.25,2249.46,2262.50,151260000,2262.50 1989-03-17,2307.68,2307.68,2267.86,2292.14,242900000,2292.14 1989-03-16,2320.54,2351.07,2315.36,2340.71,196040000,2340.71 1989-03-15,2306.25,2332.86,2300.71,2320.54,167070000,2320.54 1989-03-14,2306.25,2322.68,2296.79,2306.25,139970000,2306.25 1989-03-13,2282.68,2319.64,2282.68,2306.25,140460000,2306.25 1989-03-10,2291.43,2295.54,2261.61,2282.14,146830000,2282.14 1989-03-09,2295.54,2306.61,2282.86,2291.43,143160000,2291.43 1989-03-08,2290.71,2316.79,2280.00,2295.54,167620000,2295.54 1989-03-07,2294.82,2308.57,2278.93,2290.71,172500000,2290.71 1989-03-06,2274.29,2302.50,2270.36,2294.82,168880000,2294.82 1989-03-03,2265.71,2281.79,2255.00,2274.29,151790000,2274.29 1989-03-02,2243.04,2274.82,2239.82,2265.71,161980000,2265.71 1989-03-01,2258.39,2277.50,2234.82,2243.04,177210000,2243.04 1989-02-28,2250.36,2269.82,2242.68,2258.39,147430000,2258.39 1989-02-27,2245.54,2260.18,2232.14,2250.36,139900000,2250.36 1989-02-24,2289.46,2291.79,2242.68,2245.54,160680000,2245.54 1989-02-23,2283.93,2295.71,2266.96,2289.46,150370000,2289.46 1989-02-22,2326.43,2327.50,2276.43,2283.93,163140000,2283.93 1989-02-21,2324.82,2340.89,2311.79,2326.43,141950000,2326.43 1989-02-17,2311.43,2339.11,2301.96,2324.82,159520000,2324.82 1989-02-16,2303.93,2326.07,2293.04,2311.43,177450000,2311.43 1989-02-15,2281.25,2309.64,2275.71,2303.93,154220000,2303.93 1989-02-14,2282.50,2308.04,2274.82,2281.25,150610000,2281.25 1989-02-13,2286.07,2295.71,2266.07,2282.50,143520000,2282.50 1989-02-10,2322.32,2322.32,2278.93,2286.07,173560000,2286.07 1989-02-09,2343.21,2347.68,2308.39,2323.04,224220000,2323.04 1989-02-08,2347.14,2369.29,2332.86,2343.21,189420000,2343.21 1989-02-07,2321.07,2363.75,2314.64,2347.14,217260000,2347.14 1989-02-06,2331.25,2338.04,2307.67,2321.07,150980000,2321.07 1989-02-03,2333.75,2348.75,2319.29,2331.25,172980000,2331.25 1989-02-02,2338.21,2352.86,2319.64,2333.75,183430000,2333.75 1989-02-01,2342.32,2355.00,2319.29,2338.21,215640000,2338.21 1989-01-31,2324.11,2350.18,2302.68,2342.32,194050000,2342.32 1989-01-30,2322.86,2336.61,2304.82,2324.11,167830000,2324.11 1989-01-27,2295.18,2349.64,2295.18,2322.86,254870000,2322.86 1989-01-26,2265.89,2303.57,2252.86,2291.07,212250000,2291.07 1989-01-25,2256.43,2277.68,2242.32,2265.89,183610000,2265.89 1989-01-24,2218.39,2264.82,2214.82,2256.43,189620000,2256.43 1989-01-23,2235.36,2254.64,2214.29,2218.39,141640000,2218.39 1989-01-20,2239.11,2249.46,2221.25,2235.36,166120000,2235.36 1989-01-19,2238.75,2254.64,2225.71,2239.11,192030000,2239.11 1989-01-18,2214.64,2247.32,2202.50,2238.75,187450000,2238.75 1989-01-17,2224.64,2227.50,2203.75,2214.64,143930000,2214.64 1989-01-16,2226.07,2236.25,2215.36,2224.64,117380000,2224.64 1989-01-13,2222.32,2235.00,2210.54,2226.07,132320000,2226.07 1989-01-12,2206.43,2239.11,2200.71,2222.32,183000000,2222.32 1989-01-11,2193.21,2211.96,2185.71,2206.43,148950000,2206.43 1989-01-10,2199.46,2213.75,2182.32,2193.21,140420000,2193.21 1989-01-09,2194.29,2209.11,2185.00,2199.46,163180000,2199.46 1989-01-06,2190.54,2213.75,2182.32,2194.29,161330000,2194.29 1989-01-05,2177.68,2205.18,2173.04,2190.54,174040000,2190.54 1989-01-04,2146.61,2183.39,2146.61,2177.68,149700000,2177.68 1989-01-03,2168.39,2168.39,2127.14,2144.64,128500000,2144.64 1988-12-30,2182.68,2193.75,2162.50,2168.57,127210000,2168.57 1988-12-29,2166.43,2193.04,2165.18,2182.68,131290000,2182.68 1988-12-28,2162.68,2179.64,2153.57,2166.43,110630000,2166.43 1988-12-27,2168.93,2179.29,2156.43,2162.68,87490000,2162.68 1988-12-23,2160.36,2176.79,2157.86,2168.93,81760000,2168.93 1988-12-22,2164.64,2176.43,2151.43,2160.36,150510000,2160.36 1988-12-21,2166.07,2178.57,2146.07,2164.64,147250000,2164.64 1988-12-20,2172.68,2192.68,2161.25,2166.07,161090000,2166.07 1988-12-19,2150.71,2179.64,2141.07,2172.68,162250000,2172.68 1988-12-16,2133.00,2155.00,2131.25,2150.71,196480000,2150.71 1988-12-15,2134.25,2146.87,2120.91,2133.00,136820000,2133.00 1988-12-14,2143.49,2149.71,2121.44,2134.25,132350000,2134.25 1988-12-13,2139.58,2151.14,2119.31,2143.49,132340000,2143.49 1988-12-12,2143.49,2165.18,2133.89,2139.58,124160000,2139.58 1988-12-09,2141.71,2157.00,2131.40,2143.49,133770000,2143.49 1988-12-08,2153.63,2162.70,2133.18,2141.71,124150000,2141.71 1988-12-07,2149.36,2167.50,2136.38,2153.63,148360000,2153.63 1988-12-06,2123.76,2158.96,2117.18,2149.36,158340000,2149.36 1988-12-05,2092.64,2135.49,2092.64,2123.76,144660000,2123.76 1988-12-02,2101.88,2105.80,2075.39,2092.28,124610000,2092.28 1988-12-01,2114.51,2120.02,2095.48,2101.88,129380000,2101.88 1988-11-30,2101.53,2126.60,2095.48,2114.51,157810000,2114.51 1988-11-29,2081.44,2112.73,2072.37,2101.53,127420000,2101.53 1988-11-28,2074.68,2095.48,2062.23,2081.44,123480000,2081.44 1988-11-25,2085.53,2085.53,2062.77,2074.68,72090000,2074.68 1988-11-23,2077.70,2103.49,2071.48,2092.28,112010000,2092.28 1988-11-22,2065.97,2086.77,2052.63,2077.70,127000000,2077.70 1988-11-21,2062.41,2070.06,2036.81,2065.97,120430000,2065.97 1988-11-18,2052.45,2070.41,2047.12,2062.41,119320000,2062.41 1988-11-17,2038.58,2064.19,2033.25,2052.45,141280000,2052.45 1988-11-16,2077.17,2081.43,2026.67,2038.58,161710000,2038.58 1988-11-15,2065.08,2088.02,2060.28,2077.17,115170000,2077.17 1988-11-14,2067.03,2084.81,2050.85,2065.08,142900000,2065.08 1988-11-11,2107.04,2107.04,2063.48,2067.03,135500000,2067.03 1988-11-10,2118.24,2132.82,2103.31,2114.69,128920000,2114.69 1988-11-09,2127.49,2134.25,2100.82,2118.24,153140000,2118.24 1988-11-08,2124.64,2146.87,2119.67,2127.49,141660000,2127.49 1988-11-07,2143.14,2143.14,2113.62,2124.64,133870000,2124.64 1988-11-04,2170.34,2173.90,2139.58,2145.80,143580000,2145.80 1988-11-03,2156.83,2185.99,2153.45,2170.34,152980000,2170.34 1988-11-02,2150.96,2167.67,2131.40,2156.83,161300000,2156.83 1988-11-01,2148.65,2165.36,2132.82,2150.96,151250000,2150.96 1988-10-31,2149.89,2161.63,2125.36,2148.65,143460000,2148.65 1988-10-28,2140.83,2166.43,2135.67,2149.89,146300000,2149.89 1988-10-27,2165.18,2165.54,2120.90,2140.83,196540000,2140.83 1988-10-26,2173.36,2182.61,2148.47,2165.18,181550000,2165.18 1988-10-25,2170.34,2188.66,2156.83,2173.36,155190000,2173.36 1988-10-24,2183.50,2195.06,2162.16,2170.34,170590000,2170.34 1988-10-21,2181.19,2193.28,2152.56,2183.50,195410000,2183.50 1988-10-20,2137.27,2183.68,2129.80,2181.19,189580000,2181.19 1988-10-19,2159.85,2173.01,2110.95,2137.27,186350000,2137.27 1988-10-18,2140.47,2163.41,2124.29,2159.85,162500000,2159.85 1988-10-17,2133.18,2150.60,2120.02,2140.47,119290000,2140.47 1988-10-14,2133.36,2153.80,2118.77,2133.18,160240000,2133.18 1988-10-13,2126.24,2149.54,2114.33,2133.36,154530000,2133.36 1988-10-12,2146.34,2146.34,2113.44,2126.24,154840000,2126.24 1988-10-11,2158.96,2164.83,2137.09,2156.47,140900000,2156.47 1988-10-10,2150.25,2167.85,2139.05,2158.96,124660000,2158.96 1988-10-07,2112.02,2157.72,2112.02,2150.25,216390000,2150.25 1988-10-06,2106.51,2118.07,2092.64,2107.75,153570000,2107.75 1988-10-05,2102.06,2119.84,2082.33,2106.51,175130000,2106.51 1988-10-04,2105.26,2119.49,2090.68,2102.06,157760000,2102.06 1988-10-03,2112.91,2116.82,2083.39,2105.26,130380000,2105.26 1988-09-30,2119.31,2140.29,2104.02,2112.91,175750000,2112.91 1988-09-29,2085.53,2123.76,2084.46,2119.31,155790000,2119.31 1988-09-28,2082.33,2096.37,2070.23,2085.53,113720000,2085.53 1988-09-27,2085.17,2095.30,2069.88,2082.33,113010000,2082.33 1988-09-26,2090.68,2098.33,2075.75,2085.17,116420000,2085.17 1988-09-23,2080.01,2097.79,2070.41,2090.68,145100000,2090.68 1988-09-22,2090.50,2097.08,2066.68,2080.01,150670000,2080.01 1988-09-21,2087.48,2103.31,2078.77,2090.50,127400000,2090.50 1988-09-20,2081.08,2097.26,2073.26,2087.48,142220000,2087.48 1988-09-19,2096.55,2096.55,2066.86,2081.08,135770000,2081.08 1988-09-16,2092.28,2113.26,2077.70,2098.15,211110000,2098.15 1988-09-15,2100.64,2112.55,2084.28,2092.28,161210000,2092.28 1988-09-14,2083.04,2111.66,2079.13,2100.64,177220000,2100.64 1988-09-13,2072.37,2088.19,2055.30,2083.04,162490000,2083.04 1988-09-12,2068.81,2088.55,2057.43,2072.37,114880000,2072.37 1988-09-09,2063.12,2088.73,2038.94,2068.81,141540000,2068.81 1988-09-08,2065.79,2079.30,2052.10,2063.12,149380000,2063.12 1988-09-07,2065.26,2084.10,2052.98,2065.79,139590000,2065.79 1988-09-06,2054.59,2074.68,2046.41,2065.26,122250000,2065.26 1988-09-02,2022.40,2064.72,2022.40,2054.59,159840000,2054.59 1988-09-01,2027.56,2027.56,1988.44,2002.31,144090000,2002.31 1988-08-31,2038.23,2052.45,2022.94,2031.65,130480000,2031.65 1988-08-30,2041.43,2052.63,2028.63,2038.23,108720000,2038.23 1988-08-29,2019.56,2047.47,2019.56,2041.43,99280000,2041.43 1988-08-26,2010.85,2027.38,2002.13,2017.43,89240000,2017.43 1988-08-25,2022.05,2022.05,1990.40,2010.85,127640000,2010.85 1988-08-24,1990.04,2028.98,1990.04,2026.67,127800000,2026.67 1988-08-23,1990.22,2008.36,1978.66,1989.33,119540000,1989.33 1988-08-22,2016.00,2027.56,1987.02,1990.22,122250000,1990.22 1988-08-19,2027.03,2048.89,2011.38,2016.00,122370000,2016.00 1988-08-18,2025.96,2046.59,2014.22,2027.03,139820000,2027.03 1988-08-17,2021.51,2042.50,2003.38,2025.96,169500000,2025.96 1988-08-16,2004.27,2043.56,1993.78,2021.51,162790000,2021.51 1988-08-15,2037.52,2040.72,1998.76,2004.27,128560000,2004.27 1988-08-12,2039.30,2046.41,2019.38,2037.52,176960000,2037.52 1988-08-11,2034.14,2050.68,2014.05,2039.30,173000000,2039.30 1988-08-10,2078.41,2078.41,2023.65,2034.14,200950000,2034.14 1988-08-09,2107.40,2110.95,2061.17,2079.13,200710000,2079.13 1988-08-08,2119.13,2134.60,2103.13,2107.40,148800000,2107.40 1988-08-05,2126.60,2128.73,2105.44,2119.13,113400000,2119.13 1988-08-04,2134.07,2147.23,2117.71,2126.60,157240000,2126.60 1988-08-03,2131.22,2147.94,2115.40,2134.07,203590000,2134.07 1988-08-02,2130.51,2151.85,2112.20,2131.22,166660000,2131.22 1988-08-01,2128.73,2146.16,2111.84,2130.51,138170000,2130.51 1988-07-29,2084.28,2133.01,2084.28,2128.73,192340000,2128.73 1988-07-28,2053.70,2089.26,2047.30,2082.33,154570000,2082.33 1988-07-27,2073.97,2089.97,2047.30,2053.70,135890000,2053.70 1988-07-26,2071.83,2089.79,2059.57,2073.97,121960000,2073.97 1988-07-25,2060.99,2082.68,2048.54,2071.83,215140000,2071.83 1988-07-22,2086.59,2092.46,2050.32,2060.99,148880000,2060.99 1988-07-21,2110.60,2113.62,2077.17,2086.59,149460000,2086.59 1988-07-20,2097.26,2119.31,2091.39,2110.60,151990000,2110.60 1988-07-19,2117.89,2127.67,2081.08,2097.26,144110000,2097.26 1988-07-18,2129.45,2132.47,2099.40,2117.89,156210000,2117.89 1988-07-15,2113.62,2140.11,2099.57,2129.45,199710000,2129.45 1988-07-14,2104.37,2125.71,2089.26,2113.62,172410000,2113.62 1988-07-13,2092.64,2114.15,2073.44,2104.37,218930000,2104.37 1988-07-12,2111.31,2121.44,2077.52,2092.64,161650000,2092.64 1988-07-11,2106.15,2126.07,2098.68,2111.31,123300000,2111.31 1988-07-08,2122.69,2133.53,2099.40,2106.15,136070000,2106.15 1988-07-07,2130.16,2136.02,2101.35,2122.69,156100000,2122.69 1988-07-06,2158.61,2169.45,2107.40,2130.16,189630000,2130.16 1988-07-05,2131.58,2162.52,2117.71,2158.61,171790000,2158.61 1988-07-01,2141.71,2151.14,2118.95,2131.58,238330000,2131.58 1988-06-30,2121.98,2147.22,2112.38,2141.71,227410000,2141.71 1988-06-29,2130.87,2144.91,2106.15,2121.98,159590000,2121.98 1988-06-28,2108.46,2139.94,2100.11,2130.87,152370000,2130.87 1988-06-27,2142.96,2147.76,2101.17,2108.46,264410000,2108.46 1988-06-24,2148.29,2165.36,2133.53,2142.96,179880000,2142.96 1988-06-23,2152.20,2169.10,2131.58,2148.29,185770000,2148.29 1988-06-22,2131.05,2160.10,2131.05,2152.20,217510000,2152.20 1988-06-21,2083.93,2115.75,2072.55,2109.17,155060000,2109.17 1988-06-20,2100.11,2100.11,2072.72,2083.93,116750000,2083.93 1988-06-17,2094.24,2116.47,2070.06,2104.02,343920000,2104.02 1988-06-16,2120.73,2120.73,2081.97,2094.24,161550000,2094.24 1988-06-15,2124.47,2137.45,2109.53,2131.40,150260000,2131.40 1988-06-14,2111.13,2148.12,2111.13,2124.47,227150000,2124.47 1988-06-13,2101.71,2114.15,2084.64,2099.40,125310000,2099.40 1988-06-10,2093.35,2123.58,2084.81,2101.71,155710000,2101.71 1988-06-09,2102.95,2119.31,2081.79,2093.35,235160000,2093.35 1988-06-08,2055.83,2113.62,2055.83,2102.95,310030000,2102.95 1988-06-07,2075.21,2082.86,2042.85,2054.59,168710000,2054.59 1988-06-06,2071.31,2083.93,2049.08,2075.21,152460000,2075.21 1988-06-03,2052.45,2080.73,2040.00,2071.31,189600000,2071.31 1988-06-02,2064.01,2073.26,2030.94,2052.45,193540000,2052.45 1988-06-01,2031.12,2076.28,2021.34,2064.01,234560000,2064.01 1988-05-31,1959.38,2034.50,1959.38,2031.12,247610000,2031.12 1988-05-27,1966.70,1970.84,1944.35,1956.44,133590000,1956.44 1988-05-26,1961.37,1981.15,1951.28,1966.70,164260000,1966.70 1988-05-25,1962.53,1984.58,1952.42,1961.37,138310000,1961.37 1988-05-24,1941.48,1967.67,1938.16,1962.53,139930000,1962.53 1988-05-23,1952.59,1962.37,1927.22,1941.48,102640000,1941.48 1988-05-20,1958.72,1978.78,1940.48,1952.59,120600000,1952.59 1988-05-19,1951.09,1963.86,1921.58,1958.72,165160000,1958.72 1988-05-18,1986.41,1992.87,1941.31,1951.09,209420000,1951.09 1988-05-17,2007.63,2026.69,1982.10,1986.41,133850000,1986.41 1988-05-16,1990.55,2012.60,1980.27,2007.63,155010000,2007.63 1988-05-13,1971.65,2001.49,1971.65,1990.55,147240000,1990.55 1988-05-12,1965.85,1986.07,1960.54,1968.00,143880000,1968.00 1988-05-11,1988.56,1988.56,1950.27,1965.85,176720000,1965.85 1988-05-10,1997.35,2020.23,1984.42,2003.64,131200000,2003.64 1988-05-09,2007.46,2013.59,1984.08,1997.35,166320000,1997.35 1988-05-06,2013.59,2013.59,1997.84,2007.46,129080000,2007.46 1988-05-05,2036.31,2038.46,2008.95,2020.23,171840000,2020.23 1988-05-04,2058.36,2067.14,2029.51,2036.31,141320000,2036.31 1988-05-03,2043.27,2071.95,2036.64,2058.36,176920000,2058.36 1988-05-02,2032.33,2050.40,2019.89,2043.27,136470000,2043.27 1988-04-29,2041.28,2047.91,2014.09,2032.33,135620000,2032.33 1988-04-28,2047.91,2057.53,2026.03,2041.28,128680000,2041.28 1988-04-27,2044.76,2066.64,2033.16,2047.91,133810000,2047.91 1988-04-26,2035.97,2062.83,2023.04,2044.76,152300000,2044.76 1988-04-25,2015.09,2048.57,2011.60,2035.97,156950000,2035.97 1988-04-22,1987.40,2029.01,1985.58,2015.09,152520000,2015.09 1988-04-21,1985.41,2030.50,1968.00,1987.40,168440000,1987.40 1988-04-20,1999.50,2015.42,1975.46,1985.41,147590000,1985.41 1988-04-19,2008.12,2047.08,1990.55,1999.50,161910000,1999.50 1988-04-18,2013.93,2023.04,1985.74,2008.12,144650000,2008.12 1988-04-15,2005.64,2031.33,1969.99,2013.93,234160000,2013.93 1988-04-14,2083.22,2083.22,1998.18,2005.64,211810000,2005.64 1988-04-13,2110.08,2121.35,2082.56,2107.10,185120000,2107.10 1988-04-12,2095.99,2120.69,2085.38,2110.08,146400000,2110.08 1988-04-11,2090.19,2110.08,2075.27,2095.99,146370000,2095.99 1988-04-08,2062.17,2103.78,2051.06,2090.19,169300000,2090.19 1988-04-07,2061.67,2084.22,2042.94,2062.17,177840000,2062.17 1988-04-06,1997.51,2067.47,1987.67,2061.67,189760000,2061.67 1988-04-05,1980.60,2011.27,1969.99,1997.51,135290000,1997.51 1988-04-04,1988.06,2013.26,1969.50,1980.60,182240000,1980.60 1988-03-31,1978.12,2000.66,1957.89,1988.06,139870000,1988.06 1988-03-30,1998.34,2017.57,1973.81,1978.12,151810000,1978.12 1988-03-29,1979.77,2018.57,1979.61,1998.34,152680000,1998.34 1988-03-28,1978.95,1990.88,1951.26,1979.77,142820000,1979.77 1988-03-25,2023.87,2031.00,1973.81,1978.95,163170000,1978.95 1988-03-24,2052.22,2052.22,2011.44,2023.87,184910000,2023.87 1988-03-23,2066.15,2085.05,2047.41,2067.64,167370000,2067.64 1988-03-22,2067.14,2082.89,2052.06,2066.15,142000000,2066.15 1988-03-21,2081.23,2081.23,2050.56,2067.14,128830000,2067.14 1988-03-18,2086.04,2110.91,2067.64,2087.37,245750000,2087.37 1988-03-17,2064.32,2093.17,2057.03,2086.04,211920000,2086.04 1988-03-16,2047.41,2070.62,2027.02,2064.32,153590000,2064.32 1988-03-15,2050.07,2062.17,2030.17,2047.41,133170000,2047.41 1988-03-14,2034.98,2056.70,2023.04,2050.07,131890000,2050.07 1988-03-11,2026.03,2049.07,1996.52,2034.98,200020000,2034.98 1988-03-10,2074.27,2081.40,2020.72,2026.03,197260000,2026.03 1988-03-09,2081.07,2094.16,2064.49,2074.27,210900000,2074.27 1988-03-08,2056.37,2090.02,2055.04,2081.07,237680000,2081.07 1988-03-07,2057.86,2069.30,2034.15,2056.37,152980000,2056.37 1988-03-04,2063.49,2076.76,2033.49,2057.86,201410000,2057.86 1988-03-03,2071.29,2085.38,2048.41,2063.49,203310000,2063.49 1988-03-02,2070.47,2094.50,2058.19,2071.29,199630000,2071.29 1988-03-01,2071.62,2086.87,2048.57,2070.47,199990000,2070.47 1988-02-29,2023.21,2074.60,2017.24,2071.62,236050000,2071.62 1988-02-26,2017.57,2034.81,2005.14,2023.21,158060000,2023.21 1988-02-25,2039.95,2078.08,2006.96,2017.57,213490000,2017.57 1988-02-24,2039.12,2061.34,2022.88,2039.95,212730000,2039.95 1988-02-23,2040.29,2057.03,2017.24,2039.12,192260000,2039.12 1988-02-22,2014.59,2051.72,1998.67,2040.29,178930000,2040.29 1988-02-19,1986.41,2018.90,1973.31,2014.59,180300000,2014.59 1988-02-18,2000.99,2011.94,1972.81,1986.41,151430000,1986.41 1988-02-17,2005.97,2026.19,1982.59,2000.99,176830000,2000.99 1988-02-16,1983.26,2010.44,1969.83,2005.97,135380000,2005.97 1988-02-12,1961.54,1995.69,1958.06,1983.26,177190000,1983.26 1988-02-11,1962.04,1982.43,1942.81,1961.54,200760000,1961.54 1988-02-10,1916.78,1967.84,1916.78,1962.04,187980000,1962.04 1988-02-09,1895.72,1921.58,1885.78,1914.46,162350000,1914.46 1988-02-08,1910.48,1911.14,1878.15,1895.72,168850000,1895.72 1988-02-05,1923.57,1940.32,1906.32,1910.48,161310000,1910.48 1988-02-04,1924.57,1941.48,1902.85,1923.57,186490000,1923.57 1988-02-03,1952.92,1971.98,1907.00,1924.57,237270000,1924.57 1988-02-02,1944.63,1965.02,1921.09,1952.92,164920000,1952.92 1988-02-01,1958.22,1985.41,1935.84,1944.63,210660000,1944.63 1988-01-29,1930.04,1967.67,1921.09,1958.22,211880000,1958.22 1988-01-28,1911.14,1944.13,1904.34,1930.04,166430000,1930.04 1988-01-27,1920.59,1951.76,1889.42,1911.14,176360000,1911.14 1988-01-26,1946.45,1957.73,1906.50,1920.59,138380000,1920.59 1988-01-25,1903.51,1960.54,1897.05,1946.45,275250000,1946.45 1988-01-22,1879.31,1911.80,1876.16,1903.51,147050000,1903.51 1988-01-21,1879.14,1903.35,1845.99,1879.31,158080000,1879.31 1988-01-20,1934.85,1934.85,1858.59,1879.14,181660000,1879.14 1988-01-19,1963.86,1977.29,1923.41,1936.34,153550000,1936.34 1988-01-18,1956.07,1977.45,1938.99,1963.86,135100000,1963.86 1988-01-15,1942.47,1988.40,1942.47,1956.07,197940000,1956.07 1988-01-14,1924.73,1940.15,1894.06,1916.11,140570000,1916.11 1988-01-13,1928.55,1959.55,1884.95,1924.73,154020000,1924.73 1988-01-12,1945.13,1950.76,1877.98,1928.55,165730000,1928.55 1988-01-11,1911.31,1985.25,1886.94,1945.13,158980000,1945.13 1988-01-08,2051.89,2058.69,1898.04,1911.31,197300000,1911.31 1988-01-07,2037.80,2061.51,2004.64,2051.89,175360000,2051.89 1988-01-06,2031.50,2058.19,2012.77,2037.80,169730000,2037.80 1988-01-05,2021.39,2075.27,2021.39,2031.50,209520000,2031.50 1988-01-04,1950.76,2030.01,1950.76,2015.25,181810000,2015.25 1987-12-31,1950.10,1951.26,1912.63,1938.83,170140000,1938.83 1987-12-30,1926.89,1966.18,1925.73,1950.10,149230000,1950.10 1987-12-29,1942.97,1951.76,1918.10,1926.89,111580000,1926.89 1987-12-28,1966.18,1966.18,1921.92,1942.97,131220000,1942.97 1987-12-24,2005.64,2013.10,1985.74,1999.67,108800000,1999.67 1987-12-23,1978.45,2019.56,1977.62,2005.64,203110000,2005.64 1987-12-22,1990.38,1999.67,1949.27,1978.45,192650000,1978.45 1987-12-21,1975.30,2008.45,1959.56,1990.38,161790000,1990.38 1987-12-18,1924.73,1982.92,1924.73,1975.30,276220000,1975.30 1987-12-17,1974.47,1987.23,1917.44,1924.40,191780000,1924.40 1987-12-16,1941.48,1984.08,1918.44,1974.47,193820000,1974.47 1987-12-15,1932.86,1969.00,1916.28,1941.48,214970000,1941.48 1987-12-14,1867.04,1942.31,1860.41,1932.86,187680000,1932.86 1987-12-11,1855.44,1887.93,1838.36,1867.04,151680000,1867.04 1987-12-10,1902.52,1923.57,1835.71,1855.44,188960000,1855.44 1987-12-09,1868.37,1924.90,1846.65,1902.52,231430000,1902.52 1987-12-08,1812.17,1870.69,1794.60,1868.37,227310000,1868.37 1987-12-07,1766.74,1818.14,1765.75,1812.17,146660000,1812.17 1987-12-04,1776.53,1794.60,1733.92,1766.74,184800000,1766.74 1987-12-03,1848.97,1859.08,1772.21,1776.53,204160000,1776.53 1987-12-02,1842.34,1871.52,1825.27,1848.97,148890000,1848.97 1987-12-01,1833.55,1877.98,1829.08,1842.34,149870000,1842.34 1987-11-30,1867.37,1867.37,1795.26,1833.55,268910000,1833.55 1987-11-27,1946.95,1955.24,1907.00,1910.48,86360000,1910.48 1987-11-25,1963.53,1982.59,1935.68,1946.95,139780000,1946.95 1987-11-24,1936.84,1985.25,1936.84,1963.53,199520000,1963.53 1987-11-23,1913.63,1931.86,1889.26,1923.08,143160000,1923.08 1987-11-20,1895.39,1926.39,1853.61,1913.63,189170000,1913.63 1987-11-19,1939.16,1941.98,1881.80,1895.39,157140000,1895.39 1987-11-18,1922.25,1951.92,1888.93,1939.16,158260000,1939.16 1987-11-17,1939.99,1939.99,1888.76,1922.25,148240000,1922.25 1987-11-16,1935.01,1979.28,1921.75,1949.10,164340000,1949.10 1987-11-13,1960.21,1973.81,1923.08,1935.01,174920000,1935.01 1987-11-12,1934.84,1983.92,1934.84,1960.21,206280000,1960.21 1987-11-11,1881.96,1927.72,1881.96,1899.20,147850000,1899.20 1987-11-10,1900.20,1911.97,1845.99,1878.15,184310000,1878.15 1987-11-09,1941.81,1941.81,1881.96,1900.20,160690000,1900.20 1987-11-06,1985.41,2023.54,1938.83,1959.05,228290000,1959.05 1987-11-05,1945.29,2011.94,1920.42,1985.41,226000000,1985.41 1987-11-04,1963.53,1980.60,1913.50,1945.29,202500000,1945.29 1987-11-03,1988.40,1988.40,1891.74,1963.53,227800000,1963.53 1987-11-02,1993.53,2027.52,1957.23,2014.09,176000000,2014.09 1987-10-30,1965.68,2049.07,1965.68,1993.53,303400000,1993.53 1987-10-29,1849.30,1971.98,1849.30,1938.33,258100000,1938.33 1987-10-28,1846.49,1904.51,1767.74,1846.82,279400000,1846.82 1987-10-27,1806.70,1904.68,1806.70,1846.49,260200000,1846.49 1987-10-26,1881.80,1881.80,1774.04,1793.93,308800000,1793.93 1987-10-23,1950.43,1993.87,1898.54,1950.76,245600000,1950.76 1987-10-22,2004.97,2004.97,1837.86,1950.43,392200000,1950.43 1987-10-21,1951.76,2081.07,1951.76,2027.85,449600000,2027.85 1987-10-20,1738.74,2067.47,1616.21,1841.01,608100000,1841.01 1987-10-19,2164.16,2164.16,1677.55,1738.74,604300000,1738.74 1987-10-16,2355.09,2396.21,2207.73,2246.73,338500000,2246.73 1987-10-15,2412.70,2439.78,2345.63,2355.09,263200000,2355.09 1987-10-14,2485.15,2485.15,2400.46,2412.70,207400000,2412.70 1987-10-13,2471.44,2528.39,2456.92,2508.16,172900000,2508.16 1987-10-12,2482.21,2504.90,2433.91,2471.44,141900000,2471.44 1987-10-09,2516.64,2531.66,2472.26,2482.21,158300000,2482.21 1987-10-08,2551.08,2561.36,2491.51,2516.64,198700000,2516.64 1987-10-07,2548.63,2570.99,2511.75,2551.08,186300000,2551.08 1987-10-06,2632.83,2632.83,2542.59,2548.63,175600000,2548.63 1987-10-05,2640.99,2658.78,2610.97,2640.18,159700000,2640.18 1987-10-02,2639.20,2662.37,2622.06,2640.99,189100000,2640.99 1987-10-01,2596.28,2648.99,2593.18,2639.20,193200000,2639.20 1987-09-30,2590.57,2613.58,2563.64,2596.28,183100000,2596.28 1987-09-29,2601.50,2627.61,2569.03,2590.57,173500000,2590.57 1987-09-28,2574.58,2634.95,2574.58,2601.50,188100000,2601.50 1987-09-25,2566.42,2584.04,2543.73,2570.17,138000000,2570.17 1987-09-24,2585.67,2603.95,2552.06,2566.42,162200000,2566.42 1987-09-23,2568.05,2602.15,2554.83,2585.67,220300000,2585.67 1987-09-22,2492.82,2572.62,2468.99,2568.05,209500000,2568.05 1987-09-21,2524.64,2559.73,2479.77,2492.82,170100000,2492.82 1987-09-18,2527.90,2554.83,2514.03,2524.64,188100000,2524.64 1987-09-17,2530.19,2557.28,2508.00,2527.90,150700000,2527.90 1987-09-16,2566.58,2585.18,2522.52,2530.19,195700000,2530.19 1987-09-15,2610.48,2610.48,2560.22,2566.58,136200000,2566.58 1987-09-14,2608.74,2634.57,2587.85,2613.04,154400000,2613.04 1987-09-11,2576.05,2625.95,2575.41,2608.74,178000000,2608.74 1987-09-10,2549.43,2595.50,2549.43,2576.05,179800000,2576.05 1987-09-09,2545.12,2570.63,2522.80,2549.27,164900000,2549.27 1987-09-08,2561.38,2571.43,2493.78,2545.12,242900000,2545.12 1987-09-04,2599.49,2617.19,2556.28,2561.38,129100000,2561.38 1987-09-03,2602.04,2642.22,2560.11,2599.49,165200000,2599.49 1987-09-02,2610.97,2631.06,2567.76,2602.04,199900000,2602.04 1987-09-01,2662.95,2695.47,2594.07,2610.97,193500000,2610.97 1987-08-31,2639.35,2679.53,2623.57,2662.95,165800000,2662.95 1987-08-28,2675.06,2680.32,2632.02,2639.35,156300000,2639.35 1987-08-27,2701.85,2705.52,2661.35,2675.06,163600000,2675.06 1987-08-26,2722.42,2742.03,2686.54,2701.85,196200000,2701.85 1987-08-25,2697.07,2746.65,2694.83,2722.42,213500000,2722.42 1987-08-24,2709.50,2730.55,2678.89,2697.07,149400000,2697.07 1987-08-21,2706.79,2735.49,2689.09,2709.50,189600000,2709.50 1987-08-20,2665.97,2714.60,2665.97,2706.79,196600000,2706.79 1987-08-19,2654.66,2676.18,2628.19,2665.82,180900000,2665.82 1987-08-18,2691.01,2691.01,2626.59,2654.66,198400000,2654.66 1987-08-17,2685.43,2713.97,2674.43,2700.57,166100000,2700.57 1987-08-14,2691.49,2713.33,2660.08,2685.43,196100000,2685.43 1987-08-13,2669.32,2714.92,2656.57,2691.49,217100000,2691.49 1987-08-12,2680.48,2700.73,2648.60,2669.32,235800000,2669.32 1987-08-11,2635.84,2691.96,2635.52,2680.48,278100000,2680.48 1987-08-10,2592.00,2640.15,2587.85,2635.84,187200000,2635.84 1987-08-07,2594.23,2611.93,2576.21,2592.00,212700000,2592.00 1987-08-06,2566.65,2600.92,2551.82,2594.23,192000000,2594.23 1987-08-05,2546.72,2586.58,2540.98,2566.65,192700000,2566.65 1987-08-04,2557.08,2568.72,2525.99,2546.72,166500000,2546.72 1987-08-03,2572.07,2585.30,2536.67,2557.08,207800000,2557.08 1987-07-31,2567.44,2588.33,2551.02,2572.07,181900000,2572.07 1987-07-30,2539.54,2576.85,2527.42,2567.44,208000000,2567.44 1987-07-29,2519.77,2548.47,2501.59,2539.54,196200000,2539.54 1987-07-28,2493.94,2537.15,2489.32,2519.77,172600000,2519.77 1987-07-27,2485.33,2511.64,2468.75,2493.94,152000000,2493.94 1987-07-24,2471.94,2494.90,2462.53,2485.33,158400000,2485.33 1987-07-23,2470.18,2492.67,2447.07,2471.94,163700000,2471.94 1987-07-22,2467.95,2488.68,2448.50,2470.18,174700000,2470.18 1987-07-21,2487.82,2500.16,2444.67,2467.95,186600000,2467.95 1987-07-20,2510.04,2512.28,2476.88,2487.82,168100000,2487.82 1987-07-17,2496.97,2533.64,2485.65,2510.04,210000000,2510.04 1987-07-16,2483.74,2511.48,2471.78,2496.97,210900000,2496.97 1987-07-15,2481.35,2502.23,2455.20,2483.74,202300000,2483.74 1987-07-14,2452.97,2492.98,2442.60,2481.35,185900000,2481.35 1987-07-13,2455.99,2470.34,2427.14,2452.97,152500000,2452.97 1987-07-10,2451.21,2470.50,2435.91,2455.99,172100000,2455.99 1987-07-09,2463.97,2478.48,2441.17,2451.21,195400000,2451.21 1987-07-08,2449.78,2476.24,2432.56,2463.97,207500000,2463.97 1987-07-07,2429.53,2467.63,2425.06,2449.78,200700000,2449.78 1987-07-06,2436.70,2460.30,2412.95,2429.53,155000000,2429.53 1987-07-02,2415.66,2446.27,2415.66,2436.70,154900000,2436.70 1987-07-01,2418.53,2430.80,2391.26,2409.76,157000000,2409.76 1987-06-30,2446.91,2456.31,2401.15,2418.53,165500000,2418.53 1987-06-29,2436.86,2460.30,2423.79,2446.91,142500000,2446.91 1987-06-26,2451.05,2453.92,2423.63,2436.86,150500000,2436.86 1987-06-25,2430.33,2460.14,2430.33,2451.05,173500000,2451.05 1987-06-24,2439.73,2454.08,2415.34,2428.41,153800000,2428.41 1987-06-23,2445.51,2466.04,2421.72,2439.73,194200000,2439.73 1987-06-22,2420.85,2457.29,2417.40,2445.51,178200000,2445.51 1987-06-19,2408.13,2431.85,2395.26,2420.85,220500000,2420.85 1987-06-18,2407.35,2419.91,2386.46,2408.13,168600000,2408.13 1987-06-17,2407.35,2427.29,2390.70,2407.35,184700000,2407.35 1987-06-16,2391.54,2415.36,2376.10,2407.35,157800000,2407.35 1987-06-15,2377.73,2409.44,2374.39,2391.54,156900000,2391.54 1987-06-12,2360.74,2399.42,2360.74,2377.73,175100000,2377.73 1987-06-11,2353.61,2380.46,2341.93,2360.13,138900000,2360.13 1987-06-10,2352.70,2389.71,2328.58,2353.61,197400000,2353.61 1987-06-09,2351.64,2366.05,2331.77,2352.70,164200000,2352.70 1987-06-08,2326.15,2362.71,2306.89,2351.64,136400000,2351.64 1987-06-05,2337.08,2346.33,2312.35,2326.15,129100000,2326.15 1987-06-04,2320.69,2343.45,2308.71,2337.08,140300000,2337.08 1987-06-03,2283.37,2330.10,2283.37,2320.69,164200000,2320.69 1987-06-02,2288.23,2306.43,2260.62,2278.22,153400000,2278.22 1987-06-01,2291.57,2319.78,2277.00,2288.23,149300000,2288.23 1987-05-29,2310.68,2332.39,2281.10,2291.57,153500000,2291.57 1987-05-28,2295.81,2323.57,2265.93,2310.68,153800000,2310.68 1987-05-27,2297.94,2320.24,2274.27,2295.81,171400000,2295.81 1987-05-26,2252.88,2305.52,2252.88,2297.94,152500000,2297.94 1987-05-22,2225.77,2258.42,2220.15,2243.20,135800000,2243.20 1987-05-21,2215.87,2256.06,2212.77,2225.77,164800000,2225.77 1987-05-20,2221.28,2248.08,2188.53,2215.87,206800000,2215.87 1987-05-19,2258.66,2280.46,2205.40,2221.28,175400000,2221.28 1987-05-18,2272.52,2282.91,2227.05,2258.66,174200000,2258.66 1987-05-15,2324.48,2324.48,2266.60,2272.52,180800000,2272.52 1987-05-14,2329.68,2349.31,2307.16,2325.49,152000000,2325.49 1987-05-13,2322.60,2346.85,2302.11,2329.68,171000000,2329.68 1987-05-12,2307.30,2333.14,2289.84,2322.60,155300000,2322.60 1987-05-11,2322.30,2380.77,2297.92,2307.30,203700000,2307.30 1987-05-08,2334.66,2357.24,2303.13,2322.30,161900000,2322.30 1987-05-07,2342.19,2368.61,2315.77,2334.66,215200000,2334.66 1987-05-06,2338.07,2369.89,2309.94,2342.19,196600000,2342.19 1987-05-05,2294.60,2348.01,2294.60,2338.07,192300000,2338.07 1987-05-04,2280.40,2305.96,2255.26,2286.22,140600000,2286.22 1987-05-01,2286.36,2312.22,2256.68,2280.40,160100000,2280.40 1987-04-30,2254.26,2314.20,2250.00,2286.36,183100000,2286.36 1987-04-29,2231.96,2283.24,2228.27,2254.26,173600000,2254.26 1987-04-28,2230.54,2270.74,2214.06,2231.96,180100000,2231.96 1987-04-27,2235.37,2264.35,2180.54,2230.54,222700000,2230.54 1987-04-24,2279.55,2279.55,2221.59,2235.37,178000000,2235.37 1987-04-23,2285.94,2318.61,2255.82,2280.97,173900000,2280.97 1987-04-22,2337.07,2353.13,2282.10,2285.94,185900000,2285.94 1987-04-21,2270.60,2341.05,2240.91,2337.07,191300000,2337.07 1987-04-20,2275.99,2300.57,2252.56,2270.60,139100000,2270.60 1987-04-16,2282.95,2320.88,2264.63,2275.99,189600000,2275.99 1987-04-15,2252.98,2307.53,2243.32,2282.95,198200000,2282.95 1987-04-14,2287.07,2293.89,2213.64,2252.98,266500000,2252.98 1987-04-13,2338.78,2355.68,2278.41,2287.07,181000000,2287.07 1987-04-10,2339.20,2358.66,2305.11,2338.78,169500000,2338.78 1987-04-09,2372.16,2383.81,2320.60,2339.20,180300000,2339.20 1987-04-08,2360.94,2396.16,2342.61,2372.16,179800000,2372.16 1987-04-07,2405.54,2428.41,2352.84,2360.94,186400000,2360.94 1987-04-06,2390.34,2425.00,2384.80,2405.54,173700000,2405.54 1987-04-03,2320.45,2402.41,2307.67,2390.34,213400000,2390.34 1987-04-02,2316.05,2347.59,2299.29,2320.45,183000000,2320.45 1987-04-01,2304.69,2325.14,2271.16,2316.05,182600000,2316.05 1987-03-31,2278.41,2315.48,2271.31,2304.69,171800000,2304.69 1987-03-30,2303.41,2303.41,2230.26,2278.41,208400000,2278.41 1987-03-27,2372.59,2386.65,2326.99,2335.80,184400000,2335.80 1987-03-26,2363.49,2399.57,2359.38,2372.59,196000000,2372.59 1987-03-25,2369.18,2383.52,2344.46,2363.49,171300000,2363.49 1987-03-24,2363.78,2387.36,2348.01,2369.18,189900000,2369.18 1987-03-23,2333.52,2373.01,2322.44,2363.78,189100000,2363.78 1987-03-20,2299.57,2342.05,2295.03,2333.52,234000000,2333.52 1987-03-19,2286.93,2310.65,2270.17,2299.57,166100000,2299.57 1987-03-18,2284.80,2315.20,2262.22,2286.93,198100000,2286.93 1987-03-17,2248.44,2287.78,2238.21,2284.80,177300000,2284.80 1987-03-16,2258.66,2263.64,2224.86,2248.44,134900000,2248.44 1987-03-13,2267.34,2282.39,2245.03,2258.66,150900000,2258.66 1987-03-12,2268.98,2288.15,2250.14,2267.34,174500000,2267.34 1987-03-11,2280.09,2302.17,2256.47,2268.98,186900000,2268.98 1987-03-10,2260.12,2289.93,2246.48,2280.09,174800000,2280.09 1987-03-09,2279.67,2279.67,2238.61,2260.12,165400000,2260.12 1987-03-06,2276.43,2298.23,2256.47,2280.23,181600000,2280.23 1987-03-05,2257.45,2295.70,2253.94,2276.43,205400000,2276.43 1987-03-04,2226.52,2270.11,2226.24,2257.45,198400000,2257.45 1987-03-03,2220.47,2240.44,2209.93,2226.52,149200000,2226.52 1987-03-02,2223.99,2242.55,2209.08,2220.47,156700000,2220.47 1987-02-27,2216.68,2237.91,2204.87,2223.99,142800000,2223.99 1987-02-26,2226.24,2239.31,2196.71,2216.68,165800000,2216.68 1987-02-25,2223.28,2248.59,2209.36,2226.24,184100000,2226.24 1987-02-24,2216.54,2244.09,2202.62,2223.28,151300000,2223.28 1987-02-23,2235.24,2249.86,2186.30,2216.54,170500000,2216.54 1987-02-20,2244.09,2260.12,2220.89,2235.24,175800000,2235.24 1987-02-19,2237.63,2263.22,2212.32,2244.09,181500000,2244.09 1987-02-18,2237.49,2266.45,2213.16,2237.63,218200000,2237.63 1987-02-17,2184.90,2242.41,2184.90,2237.49,187800000,2237.49 1987-02-13,2165.78,2201.35,2148.76,2183.35,184400000,2183.35 1987-02-12,2171.96,2203.18,2146.09,2165.78,200400000,2165.78 1987-02-11,2158.04,2182.51,2145.53,2171.96,172400000,2171.96 1987-02-10,2176.74,2183.63,2134.42,2158.04,168300000,2158.04 1987-02-09,2186.87,2195.73,2157.90,2176.74,143300000,2176.74 1987-02-06,2201.49,2213.30,2176.32,2186.87,184100000,2186.87 1987-02-05,2191.23,2223.28,2174.63,2201.49,256700000,2201.49 1987-02-04,2168.45,2198.40,2154.67,2191.23,222400000,2191.23 1987-02-03,2179.42,2201.21,2159.73,2168.45,198100000,2168.45 1987-02-02,2158.04,2193.62,2142.15,2179.42,177400000,2179.42 1987-01-30,2160.01,2173.51,2127.67,2158.04,163400000,2158.04 1987-01-29,2163.39,2193.34,2139.20,2160.01,205300000,2160.01 1987-01-28,2150.45,2181.10,2136.39,2163.39,195800000,2163.39 1987-01-27,2110.24,2160.85,2110.24,2150.45,192300000,2150.45 1987-01-26,2101.52,2125.42,2079.72,2107.28,138900000,2107.28 1987-01-23,2145.67,2214.57,2062.85,2101.52,302400000,2101.52 1987-01-22,2094.07,2151.86,2083.66,2145.67,188700000,2145.67 1987-01-21,2104.47,2123.88,2079.02,2094.07,184200000,2094.07 1987-01-20,2102.50,2131.61,2082.54,2104.47,224800000,2104.47 1987-01-19,2076.63,2112.49,2051.32,2102.50,162800000,2102.50 1987-01-16,2070.73,2099.69,2054.56,2076.63,218400000,2076.63 1987-01-15,2035.01,2091.25,2030.79,2070.73,253100000,2070.73 1987-01-14,2012.94,2046.26,2003.94,2035.01,214200000,2035.01 1987-01-13,2009.42,2027.14,1994.52,2012.94,170900000,2012.94 1987-01-12,2005.91,2022.08,1987.63,2009.42,184200000,2009.42 1987-01-09,2002.25,2021.65,1988.61,2005.91,193000000,2005.91 1987-01-08,1993.95,2014.20,1975.96,2002.25,194500000,2002.25 1987-01-07,1974.83,2003.09,1965.69,1993.95,190900000,1993.95 1987-01-06,1971.32,1993.81,1961.90,1974.83,189300000,1974.83 1987-01-05,1936.59,1980.74,1936.59,1971.32,181900000,1971.32 1987-01-02,1897.36,1933.49,1897.36,1927.31,91880000,1927.31 1986-12-31,1908.61,1920.42,1885.40,1895.95,139200000,1895.95 1986-12-30,1912.12,1920.70,1894.69,1908.61,126200000,1908.61 1986-12-29,1930.40,1931.38,1904.53,1912.12,99800000,1912.12 1986-12-26,1926.88,1939.12,1919.71,1930.40,48860000,1930.40 1986-12-24,1914.37,1937.57,1910.01,1926.88,95410000,1926.88 1986-12-23,1926.18,1933.77,1902.28,1914.37,188700000,1914.37 1986-12-22,1928.85,1938.84,1907.76,1926.18,157600000,1926.18 1986-12-19,1912.82,1935.18,1899.89,1928.85,244700000,1928.85 1986-12-18,1918.31,1927.02,1900.17,1912.82,155400000,1912.82 1986-12-17,1936.16,1937.57,1909.45,1918.31,148800000,1918.31 1986-12-16,1922.81,1942.91,1912.40,1936.16,157000000,1936.16 1986-12-15,1912.26,1925.34,1887.09,1922.81,148200000,1922.81 1986-12-12,1923.65,1932.09,1904.39,1912.26,126600000,1912.26 1986-12-11,1932.93,1947.41,1904.81,1923.65,136000000,1923.65 1986-12-10,1916.90,1943.05,1908.32,1932.93,139700000,1932.93 1986-12-09,1930.26,1939.82,1909.87,1916.90,128700000,1916.90 1986-12-08,1925.06,1946.71,1906.92,1930.26,159000000,1930.26 1986-12-05,1939.68,1950.22,1911.70,1925.06,139800000,1925.06 1986-12-04,1947.27,1963.30,1930.26,1939.68,156900000,1939.68 1986-12-03,1955.57,1971.74,1933.91,1947.27,200100000,1947.27 1986-12-02,1914.93,1958.80,1914.93,1955.57,230400000,1955.57 1986-12-01,1914.23,1915.91,1880.48,1912.54,133800000,1912.54 1986-11-28,1916.76,1923.51,1903.82,1914.23,93530000,1914.23 1986-11-26,1912.12,1926.46,1895.11,1916.76,152000000,1916.76 1986-11-25,1906.07,1922.81,1890.04,1912.12,154600000,1912.12 1986-11-24,1893.56,1921.40,1879.08,1906.07,150800000,1906.07 1986-11-21,1860.66,1901.86,1853.07,1893.56,200700000,1893.56 1986-11-20,1826.63,1866.28,1823.12,1860.66,158100000,1860.66 1986-11-19,1817.21,1838.02,1797.10,1826.63,183300000,1826.63 1986-11-18,1860.52,1864.31,1806.52,1817.21,185300000,1817.21 1986-11-17,1873.59,1879.92,1846.74,1860.52,133300000,1860.52 1986-11-14,1862.20,1883.57,1848.28,1873.59,172100000,1873.59 1986-11-13,1893.70,1901.01,1857.28,1862.20,164000000,1862.20 1986-11-12,1895.95,1909.31,1876.97,1893.70,162200000,1893.70 1986-11-11,1892.29,1904.95,1882.45,1895.95,118500000,1895.95 1986-11-10,1886.53,1901.01,1871.20,1892.29,120200000,1892.29 1986-11-07,1891.59,1899.47,1870.78,1886.53,142300000,1886.53 1986-11-06,1899.04,1907.48,1868.95,1891.59,165300000,1891.59 1986-11-05,1892.44,1911.14,1876.55,1899.04,183200000,1899.04 1986-11-04,1894.26,1902.00,1873.88,1892.44,163200000,1892.44 1986-11-03,1877.71,1902.28,1870.78,1894.26,138200000,1894.26 1986-10-31,1878.37,1891.73,1858.13,1877.71,147200000,1877.71 1986-10-30,1862.77,1894.69,1862.77,1878.37,194200000,1878.37 1986-10-29,1845.47,1863.33,1834.51,1851.80,164400000,1851.80 1986-10-28,1841.82,1863.47,1830.99,1845.47,145900000,1845.47 1986-10-27,1832.36,1850.11,1817.49,1841.82,133200000,1841.82 1986-10-24,1834.93,1851.66,1821.71,1832.36,137500000,1832.36 1986-10-23,1808.35,1845.05,1806.95,1834.93,150900000,1834.93 1986-10-22,1805.68,1821.29,1793.59,1808.35,114000000,1808.35 1986-10-21,1811.02,1822.98,1792.04,1805.68,110000000,1805.68 1986-10-20,1826.63,1826.63,1793.87,1811.02,109000000,1811.02 1986-10-17,1836.19,1844.91,1817.07,1837.04,124100000,1837.04 1986-10-16,1831.69,1852.64,1819.18,1836.19,156900000,1836.19 1986-10-15,1800.20,1835.77,1792.18,1831.69,144300000,1831.69 1986-10-14,1798.37,1816.51,1783.32,1800.20,116800000,1800.20 1986-10-13,1793.17,1806.95,1781.50,1798.37,54990000,1798.37 1986-10-10,1796.82,1806.38,1780.93,1793.17,105100000,1793.17 1986-10-09,1803.85,1824.24,1785.85,1796.82,153400000,1796.82 1986-10-08,1784.45,1812.43,1772.22,1803.85,141700000,1803.85 1986-10-07,1784.45,1799.35,1765.19,1784.45,125100000,1784.45 1986-10-06,1774.18,1794.85,1763.36,1784.45,88250000,1784.45 1986-10-03,1781.21,1806.38,1761.25,1774.18,128100000,1774.18 1986-10-02,1782.90,1796.54,1767.72,1781.21,128100000,1781.21 1986-10-01,1767.58,1805.82,1762.65,1782.90,143600000,1782.90 1986-09-30,1755.20,1790.35,1750.14,1767.58,124900000,1767.58 1986-09-29,1768.98,1768.98,1732.99,1755.20,115600000,1755.20 1986-09-26,1768.56,1788.10,1750.14,1769.69,115300000,1769.69 1986-09-25,1803.15,1803.15,1753.80,1768.56,134300000,1768.56 1986-09-24,1797.81,1820.02,1786.28,1803.29,134600000,1803.29 1986-09-23,1793.45,1809.76,1778.54,1797.81,132600000,1797.81 1986-09-22,1762.65,1797.81,1761.67,1793.45,126100000,1793.45 1986-09-19,1774.18,1783.04,1747.61,1762.65,153900000,1762.65 1986-09-18,1769.40,1789.93,1748.03,1774.18,132200000,1774.18 1986-09-17,1778.54,1799.35,1757.87,1769.40,141000000,1769.40 1986-09-16,1767.58,1785.01,1739.60,1778.54,131200000,1778.54 1986-09-15,1758.72,1786.98,1746.20,1767.58,155600000,1767.58 1986-09-12,1792.89,1805.40,1733.55,1758.72,240500000,1758.72 1986-09-11,1868.67,1868.67,1780.79,1792.89,237600000,1792.89 1986-09-10,1884.14,1897.50,1863.05,1879.50,140300000,1879.50 1986-09-09,1888.64,1909.45,1874.02,1884.14,137500000,1884.14 1986-09-08,1899.75,1907.06,1866.84,1888.64,153300000,1888.64 1986-09-05,1919.71,1933.35,1890.19,1899.75,180600000,1899.75 1986-09-04,1881.33,1927.87,1877.25,1919.71,189400000,1919.71 1986-09-03,1870.36,1888.22,1852.78,1881.33,154300000,1881.33 1986-09-02,1898.34,1913.39,1857.42,1870.36,135500000,1870.36 1986-08-29,1900.17,1913.53,1883.44,1898.34,125300000,1898.34 1986-08-28,1904.53,1912.26,1882.73,1900.17,125100000,1900.17 1986-08-27,1904.25,1918.59,1887.80,1904.53,143300000,1904.53 1986-08-26,1871.77,1911.28,1870.50,1904.25,156600000,1904.25 1986-08-25,1887.80,1893.42,1860.52,1871.77,104400000,1871.77 1986-08-22,1881.19,1899.04,1868.11,1887.80,118100000,1887.80 1986-08-21,1881.33,1899.47,1864.31,1881.19,135200000,1881.19 1986-08-20,1862.91,1889.34,1849.97,1881.33,156600000,1881.33 1986-08-19,1869.52,1880.20,1846.88,1862.91,109300000,1862.91 1986-08-18,1855.60,1875.14,1842.66,1869.52,112800000,1869.52 1986-08-15,1844.91,1863.61,1829.02,1855.60,123500000,1855.60 1986-08-14,1844.49,1859.81,1832.54,1844.91,123800000,1844.91 1986-08-13,1835.49,1860.66,1822.98,1844.49,156400000,1844.49 1986-08-12,1811.16,1840.55,1804.42,1835.49,131700000,1835.49 1986-08-11,1782.62,1824.66,1779.25,1811.16,125600000,1811.16 1986-08-08,1786.28,1799.78,1769.69,1782.62,106300000,1782.62 1986-08-07,1779.53,1802.02,1766.17,1786.28,122400000,1786.28 1986-08-06,1777.00,1788.67,1759.84,1779.53,127500000,1779.53 1986-08-05,1769.97,1800.20,1766.87,1777.00,153100000,1777.00 1986-08-04,1763.64,1785.15,1730.60,1769.97,130000000,1769.97 1986-08-01,1775.31,1788.80,1753.09,1763.64,114900000,1763.64 1986-07-31,1779.39,1794.29,1764.20,1775.31,112700000,1775.31 1986-07-30,1766.87,1794.15,1741.56,1779.39,146700000,1779.39 1986-07-29,1773.90,1788.95,1752.95,1766.87,115700000,1766.87 1986-07-28,1810.04,1815.24,1760.26,1773.90,128000000,1773.90 1986-07-25,1791.62,1821.57,1791.06,1810.04,132000000,1810.04 1986-07-24,1798.37,1806.81,1778.68,1791.62,134700000,1791.62 1986-07-23,1795.13,1813.70,1780.09,1798.37,133300000,1798.37 1986-07-22,1779.11,1810.46,1769.12,1795.13,138500000,1795.13 1986-07-21,1777.98,1792.60,1763.92,1779.11,106300000,1779.11 1986-07-18,1781.78,1807.37,1754.64,1777.98,149700000,1777.98 1986-07-17,1774.18,1802.73,1762.09,1781.78,132400000,1781.78 1986-07-16,1768.70,1794.29,1759.70,1774.18,160800000,1774.18 1986-07-15,1793.45,1805.54,1760.12,1768.70,184000000,1768.70 1986-07-14,1816.65,1816.65,1785.29,1793.45,123200000,1793.45 1986-07-11,1831.83,1840.97,1810.88,1821.43,124500000,1821.43 1986-07-10,1826.07,1842.94,1799.07,1831.83,146200000,1831.83 1986-07-09,1820.73,1838.58,1807.65,1826.07,142900000,1826.07 1986-07-08,1834.36,1834.36,1794.99,1820.73,174100000,1820.73 1986-07-07,1895.53,1895.53,1834.08,1838.86,138200000,1838.86 1986-07-03,1909.03,1918.59,1887.23,1900.87,108300000,1900.87 1986-07-02,1903.54,1922.67,1891.31,1909.03,150000000,1909.03 1986-07-01,1892.72,1911.28,1878.52,1903.54,147700000,1903.54 1986-06-30,1885.26,1908.62,1876.12,1892.72,135100000,1892.72 1986-06-27,1880.20,1898.90,1871.34,1885.26,123800000,1885.26 1986-06-26,1885.05,1897.22,1867.41,1880.20,134100000,1880.20 1986-06-25,1875.55,1903.36,1870.32,1885.05,161800000,1885.05 1986-06-24,1864.26,1891.80,1853.94,1875.55,140600000,1875.55 1986-06-23,1879.54,1883.40,1853.39,1864.26,123800000,1864.26 1986-06-20,1855.86,1882.85,1847.64,1879.54,149100000,1879.54 1986-06-19,1868.94,1883.12,1851.46,1855.86,129000000,1855.86 1986-06-18,1865.78,1881.33,1843.75,1868.94,117000000,1868.94 1986-06-17,1871.77,1886.98,1853.94,1865.78,123100000,1865.78 1986-06-16,1874.19,1890.61,1863.29,1871.77,112100000,1871.77 1986-06-13,1843.92,1883.21,1843.92,1874.19,141200000,1874.19 1986-06-12,1846.07,1851.86,1826.29,1838.13,109100000,1838.13 1986-06-11,1837.19,1854.68,1825.75,1846.07,127400000,1846.07 1986-06-10,1840.15,1852.80,1816.07,1837.19,125000000,1837.19 1986-06-09,1880.25,1880.25,1833.83,1840.15,123300000,1840.15 1986-06-06,1879.44,1894.38,1866.12,1885.90,110900000,1885.90 1986-06-05,1863.29,1880.79,1851.18,1879.44,110900000,1879.44 1986-06-04,1870.43,1882.00,1846.34,1863.29,117000000,1863.29 1986-06-03,1861.95,1875.54,1845.67,1870.43,114700000,1870.43 1986-06-02,1876.71,1886.17,1845.53,1861.95,120600000,1861.95 1986-05-30,1882.35,1898.22,1857.95,1876.71,151200000,1876.71 1986-05-29,1878.28,1892.97,1857.42,1882.35,135700000,1882.35 1986-05-28,1853.03,1891.79,1851.92,1878.28,159600000,1878.28 1986-05-27,1823.48,1856.56,1823.48,1853.03,121200000,1853.03 1986-05-23,1806.30,1842.14,1804.69,1823.29,130200000,1823.29 1986-05-22,1775.17,1813.74,1774.18,1806.30,144900000,1806.30 1986-05-21,1783.98,1798.61,1766.62,1775.17,117100000,1775.17 1986-05-20,1758.18,1788.44,1752.48,1783.98,113000000,1783.98 1986-05-19,1759.80,1769.84,1746.53,1758.18,85840000,1758.18 1986-05-16,1774.68,1775.67,1749.88,1759.80,113500000,1759.80 1986-05-15,1808.28,1808.78,1766.99,1774.68,131600000,1774.68 1986-05-14,1785.34,1815.23,1775.55,1808.28,132100000,1808.28 1986-05-13,1787.33,1804.07,1772.32,1785.34,119200000,1785.34 1986-05-12,1789.43,1804.32,1774.80,1787.33,125400000,1787.33 1986-05-09,1786.21,1797.12,1767.73,1789.43,137400000,1789.43 1986-05-08,1775.30,1797.87,1768.48,1786.21,136000000,1786.21 1986-05-07,1787.95,1790.05,1755.21,1775.30,129900000,1775.30 1986-05-06,1793.77,1803.32,1775.92,1787.95,121200000,1787.95 1986-05-05,1774.68,1800.35,1770.96,1793.77,102400000,1793.77 1986-05-02,1777.78,1795.88,1763.14,1774.68,126300000,1774.68 1986-05-01,1783.98,1796.88,1761.04,1777.78,146500000,1777.78 1986-04-30,1825.89,1831.23,1777.90,1783.98,147500000,1783.98 1986-04-29,1843.75,1856.15,1813.12,1825.89,148800000,1825.89 1986-04-28,1835.57,1852.66,1817.71,1843.75,123900000,1843.75 1986-04-25,1831.72,1848.46,1813.74,1835.57,142300000,1835.57 1986-04-24,1829.61,1848.46,1818.95,1831.72,146600000,1831.72 1986-04-23,1830.98,1841.27,1803.94,1829.61,149700000,1829.61 1986-04-22,1855.90,1866.44,1815.97,1830.98,161500000,1830.98 1986-04-21,1840.40,1864.21,1829.86,1855.90,136100000,1855.90 1986-04-18,1855.03,1870.16,1830.98,1840.40,153600000,1840.40 1986-04-17,1847.97,1870.16,1831.72,1855.03,161400000,1855.03 1986-04-16,1814.73,1859.62,1814.73,1847.97,173800000,1847.97 1986-04-15,1805.31,1822.05,1789.68,1809.65,123700000,1809.65 1986-04-14,1790.18,1811.38,1781.00,1805.31,106700000,1805.31 1986-04-11,1794.30,1812.50,1779.14,1790.18,139400000,1790.18 1986-04-10,1778.62,1807.83,1768.20,1794.30,184800000,1794.30 1986-04-09,1769.76,1807.71,1754.19,1778.62,156300000,1778.62 1986-04-08,1737.07,1779.57,1737.07,1769.76,146300000,1769.76 1986-04-07,1739.22,1749.04,1712.52,1735.51,129800000,1735.51 1986-04-04,1766.40,1772.87,1728.45,1739.22,147300000,1739.22 1986-04-03,1795.26,1809.27,1753.71,1766.40,148200000,1766.40 1986-04-02,1790.11,1803.64,1769.76,1795.26,145300000,1795.26 1986-04-01,1818.61,1829.02,1777.54,1790.11,167400000,1790.11 1986-03-31,1821.72,1841.83,1803.16,1818.61,134400000,1818.61 1986-03-27,1810.70,1849.74,1806.51,1821.72,178100000,1821.72 1986-03-26,1778.50,1817.41,1775.98,1810.70,161500000,1810.70 1986-03-25,1782.93,1794.30,1762.09,1778.50,139300000,1778.50 1986-03-24,1768.56,1796.22,1763.29,1782.93,143800000,1782.93 1986-03-21,1804.24,1821.24,1764.85,1768.56,199100000,1768.56 1986-03-20,1787.95,1820.76,1784.36,1804.24,148000000,1804.24 1986-03-19,1789.87,1806.99,1773.47,1787.95,150000000,1787.95 1986-03-18,1776.86,1806.75,1763.65,1789.87,148000000,1789.87 1986-03-17,1790.59,1790.59,1758.38,1776.86,137500000,1776.86 1986-03-14,1753.71,1799.93,1745.21,1792.74,181900000,1792.74 1986-03-13,1745.45,1768.80,1729.53,1753.71,171500000,1753.71 1986-03-12,1746.05,1773.35,1733.48,1745.45,210300000,1745.45 1986-03-11,1704.26,1752.17,1704.26,1746.05,187300000,1746.05 1986-03-10,1699.83,1715.16,1688.70,1702.95,129900000,1702.95 1986-03-07,1696.60,1713.48,1682.83,1699.83,163200000,1699.83 1986-03-06,1686.66,1711.21,1681.75,1696.60,159000000,1696.60 1986-03-05,1686.42,1695.40,1663.07,1686.66,154600000,1686.66 1986-03-04,1696.67,1718.63,1679.72,1686.42,174500000,1686.42 1986-03-03,1709.06,1714.33,1684.63,1696.67,142700000,1696.67 1986-02-28,1713.99,1732.57,1687.50,1709.06,191700000,1709.06 1986-02-27,1696.90,1728.90,1683.37,1713.99,181700000,1713.99 1986-02-26,1692.66,1714.79,1679.59,1696.90,158000000,1696.90 1986-02-25,1698.28,1709.52,1674.08,1692.66,148000000,1692.66 1986-02-24,1697.71,1709.75,1678.67,1698.28,144700000,1698.28 1986-02-21,1672.82,1702.75,1668.69,1697.71,177600000,1697.71 1986-02-20,1658.26,1675.46,1641.97,1672.82,139700000,1672.82 1986-02-19,1678.78,1689.22,1651.03,1658.26,152000000,1658.26 1986-02-18,1664.45,1685.55,1649.43,1678.78,160200000,1678.78 1986-02-14,1645.07,1668.69,1636.12,1664.45,155600000,1664.45 1986-02-13,1629.93,1649.31,1616.86,1645.07,136500000,1645.07 1986-02-12,1622.82,1640.48,1611.70,1629.93,136400000,1629.93 1986-02-11,1626.38,1637.50,1613.30,1622.82,141300000,1622.82 1986-02-10,1613.42,1633.14,1605.16,1626.38,129900000,1626.38 1986-02-07,1600.69,1622.82,1576.83,1613.42,144400000,1613.42 1986-02-06,1593.12,1616.51,1587.50,1600.69,146100000,1600.69 1986-02-05,1593.23,1601.83,1576.26,1593.12,134300000,1593.12 1986-02-04,1594.27,1611.47,1575.46,1593.23,175700000,1593.23 1986-02-03,1570.99,1600.11,1564.33,1594.27,145300000,1594.27 1986-01-31,1552.18,1582.91,1548.17,1570.99,143500000,1570.99 1986-01-30,1558.94,1572.59,1545.76,1552.18,125300000,1552.18 1986-01-29,1556.42,1578.10,1548.05,1558.94,193800000,1558.94 1986-01-28,1537.61,1561.35,1530.50,1556.42,145700000,1556.42 1986-01-27,1529.93,1548.17,1524.43,1537.61,122900000,1537.61 1986-01-24,1511.24,1537.39,1507.68,1529.93,128900000,1529.93 1986-01-23,1502.29,1519.39,1491.74,1511.24,130300000,1511.24 1986-01-22,1514.45,1525.57,1494.84,1502.29,131200000,1502.29 1986-01-21,1529.13,1535.89,1502.87,1514.45,128300000,1514.45 1986-01-20,1536.01,1536.01,1516.86,1529.13,85340000,1529.13 1986-01-17,1541.63,1552.52,1519.72,1536.70,132100000,1536.70 1986-01-16,1527.29,1547.71,1517.09,1541.63,130500000,1541.63 1986-01-15,1519.04,1535.32,1512.96,1527.29,122400000,1527.29 1986-01-14,1520.53,1530.62,1508.03,1519.04,113900000,1519.04 1986-01-13,1513.53,1526.83,1502.29,1520.53,108700000,1520.53 1986-01-10,1518.23,1530.96,1500.57,1513.53,122800000,1513.53 1986-01-09,1526.61,1530.85,1495.64,1518.23,176500000,1518.23 1986-01-08,1565.71,1578.10,1516.63,1526.61,180300000,1526.61 1986-01-07,1547.59,1573.74,1544.50,1565.71,153000000,1565.71 1986-01-06,1549.20,1557.00,1537.04,1547.59,99610000,1547.59 1986-01-03,1537.73,1557.11,1534.98,1549.20,105000000,1549.20 1986-01-02,1546.67,1551.95,1523.74,1537.73,98960000,1537.73 1985-12-31,1550.46,1562.84,1537.50,1546.67,112700000,1546.67 1985-12-30,1543.00,1557.34,1534.98,1550.46,91970000,1550.46 1985-12-27,1527.29,1548.85,1527.29,1543.00,81560000,1543.00 1985-12-26,1519.15,1532.57,1514.68,1526.49,62050000,1526.49 1985-12-24,1528.78,1532.45,1508.83,1519.15,78300000,1519.15 1985-12-23,1543.00,1547.82,1516.63,1528.78,107900000,1528.78 1985-12-20,1543.92,1564.56,1535.67,1543.00,170300000,1543.00 1985-12-19,1542.43,1552.98,1532.00,1543.92,130200000,1543.92 1985-12-18,1544.50,1560.44,1528.44,1542.43,137900000,1542.43 1985-12-17,1553.10,1568.81,1536.35,1544.50,155200000,1544.50 1985-12-16,1535.21,1570.87,1528.90,1553.10,176000000,1553.10 1985-12-13,1511.24,1546.44,1502.75,1535.21,177900000,1535.21 1985-12-12,1511.70,1523.51,1496.79,1511.24,170500000,1511.24 1985-12-11,1499.20,1520.30,1492.09,1511.70,178500000,1511.70 1985-12-10,1497.02,1514.91,1483.94,1499.20,156500000,1499.20 1985-12-09,1478.10,1504.13,1478.10,1497.02,144000000,1497.02 1985-12-06,1482.91,1488.30,1464.79,1477.18,125500000,1477.18 1985-12-05,1484.40,1504.01,1477.98,1482.91,181000000,1482.91 1985-12-04,1459.06,1488.76,1457.45,1484.40,153200000,1484.40 1985-12-03,1457.91,1466.40,1450.34,1459.06,109700000,1459.06 1985-12-02,1472.13,1476.26,1451.26,1457.91,103500000,1457.91 1985-11-29,1475.69,1486.93,1463.99,1472.13,84060000,1472.13 1985-11-27,1456.77,1483.83,1454.01,1475.69,143700000,1475.69 1985-11-26,1456.65,1470.07,1447.25,1456.77,123100000,1456.77 1985-11-25,1464.33,1467.09,1449.43,1456.65,91710000,1456.65 1985-11-22,1462.27,1475.57,1451.61,1464.33,133800000,1464.33 1985-11-21,1439.79,1466.06,1439.79,1462.27,150300000,1462.27 1985-11-20,1438.99,1451.49,1429.24,1439.22,105100000,1439.22 1985-11-19,1440.02,1452.18,1430.05,1438.99,126100000,1438.99 1985-11-18,1435.09,1447.25,1422.25,1440.02,108400000,1440.02 1985-11-15,1439.22,1450.57,1425.69,1435.09,130200000,1435.09 1985-11-14,1427.75,1443.81,1420.64,1439.22,124900000,1439.22 1985-11-13,1433.60,1439.79,1419.38,1427.75,109700000,1427.75 1985-11-12,1431.88,1446.10,1421.10,1433.60,170800000,1433.60 1985-11-11,1404.36,1432.57,1402.41,1431.88,126500000,1431.88 1985-11-08,1399.54,1410.44,1391.06,1404.36,115000000,1404.36 1985-11-07,1403.44,1410.11,1389.91,1399.54,119000000,1399.54 1985-11-06,1396.67,1411.01,1386.47,1403.44,129500000,1403.44 1985-11-05,1389.68,1402.52,1380.28,1396.67,119200000,1396.67 1985-11-04,1390.25,1398.51,1377.06,1389.68,104900000,1389.68 1985-11-01,1374.31,1393.58,1367.78,1390.25,129400000,1390.25 1985-10-31,1375.57,1383.60,1362.61,1374.31,121500000,1374.31 1985-10-30,1368.73,1384.63,1361.01,1375.57,120400000,1375.57 1985-10-29,1359.99,1377.69,1356.18,1368.73,110600000,1368.73 1985-10-28,1356.52,1364.02,1346.55,1359.99,97880000,1359.99 1985-10-25,1362.34,1366.71,1351.59,1356.52,101800000,1356.52 1985-10-24,1367.16,1374.55,1355.29,1362.34,123100000,1362.34 1985-10-23,1364.36,1373.43,1357.08,1367.16,121700000,1367.16 1985-10-22,1364.14,1374.66,1356.18,1364.36,111300000,1364.36 1985-10-21,1368.84,1375.67,1357.75,1364.14,95680000,1364.14 1985-10-18,1369.29,1383.40,1358.87,1368.84,107100000,1368.84 1985-10-17,1368.50,1378.36,1356.85,1369.29,140500000,1369.29 1985-10-16,1350.81,1371.30,1346.21,1368.50,117400000,1368.50 1985-10-15,1354.73,1364.14,1343.53,1350.81,110400000,1350.81 1985-10-14,1339.94,1356.18,1336.58,1354.73,78540000,1354.73 1985-10-11,1328.07,1343.41,1323.70,1339.94,96370000,1339.94 1985-10-10,1326.72,1333.33,1318.44,1328.07,90910000,1328.07 1985-10-09,1325.49,1336.81,1320.23,1326.72,99140000,1326.72 1985-10-08,1324.37,1333.89,1316.20,1325.49,97170000,1325.49 1985-10-07,1328.74,1335.91,1315.19,1324.37,95550000,1324.37 1985-10-04,1333.11,1335.01,1321.12,1328.74,101200000,1328.74 1985-10-03,1333.67,1345.43,1323.81,1333.11,127500000,1333.11 1985-10-02,1340.95,1351.59,1327.96,1333.67,147300000,1333.67 1985-10-01,1328.63,1343.97,1323.48,1340.95,130200000,1340.95 1985-09-30,1320.79,1336.81,1318.55,1328.63,103600000,1328.63 1985-09-26,1312.05,1325.27,1301.97,1320.79,106100000,1320.79 1985-09-25,1321.12,1330.20,1306.00,1312.05,92120000,1312.05 1985-09-24,1316.31,1334.57,1301.86,1321.12,97870000,1321.12 1985-09-23,1305.78,1323.59,1305.78,1316.31,104800000,1316.31 1985-09-20,1306.79,1313.40,1294.47,1297.94,101400000,1297.94 1985-09-19,1300.40,1312.95,1291.22,1306.79,100300000,1306.79 1985-09-18,1298.16,1307.57,1283.71,1300.40,105700000,1300.40 1985-09-17,1309.14,1314.52,1291.22,1298.16,111900000,1298.16 1985-09-16,1307.68,1315.75,1301.08,1309.14,66700000,1309.14 1985-09-13,1312.39,1320.12,1296.71,1307.68,111400000,1307.68 1985-09-12,1319.44,1327.40,1307.01,1312.39,107100000,1312.39 1985-09-11,1333.45,1334.01,1314.85,1319.44,100400000,1319.44 1985-09-10,1339.27,1346.55,1324.82,1333.45,104700000,1333.45 1985-09-09,1335.69,1348.23,1326.61,1339.27,89850000,1339.27 1985-09-06,1325.83,1341.40,1323.92,1335.69,95040000,1335.69 1985-09-05,1326.72,1333.00,1318.66,1325.83,94480000,1325.83 1985-09-04,1329.19,1334.12,1318.21,1326.72,85510000,1326.72 1985-09-03,1334.01,1337.14,1322.80,1329.19,81190000,1329.19 1985-08-30,1335.13,1342.41,1325.27,1334.01,81620000,1334.01 1985-08-29,1331.09,1340.05,1325.16,1335.13,85660000,1335.13 1985-08-28,1322.47,1334.79,1316.98,1331.09,88530000,1331.09 1985-08-27,1317.65,1328.63,1315.19,1322.47,82140000,1322.47 1985-08-26,1318.32,1324.26,1309.81,1317.65,70290000,1317.65 1985-08-23,1318.10,1322.92,1310.48,1318.32,75270000,1318.32 1985-08-22,1329.53,1334.68,1313.51,1318.10,90600000,1318.10 1985-08-21,1323.70,1333.67,1319.11,1329.53,94880000,1329.53 1985-08-20,1312.50,1328.07,1311.83,1323.70,91230000,1323.70 1985-08-19,1312.72,1319.22,1307.57,1312.50,67930000,1312.50 1985-08-16,1317.76,1321.57,1305.89,1312.72,87910000,1312.72 1985-08-15,1316.98,1324.71,1308.13,1317.76,86100000,1317.76 1985-08-14,1315.30,1326.05,1311.38,1316.98,85780000,1316.98 1985-08-13,1314.29,1325.49,1303.65,1315.30,80300000,1315.30 1985-08-12,1320.79,1324.37,1309.14,1314.29,77340000,1314.29 1985-08-09,1329.86,1331.88,1317.65,1320.79,81750000,1320.79 1985-08-08,1325.04,1334.79,1318.32,1329.86,102900000,1329.86 1985-08-07,1325.16,1331.21,1316.31,1325.04,100000000,1325.04 1985-08-06,1346.89,1350.02,1322.92,1325.16,104000000,1325.16 1985-08-05,1352.71,1352.71,1336.92,1346.89,79610000,1346.89 1985-08-02,1355.62,1360.10,1345.43,1353.05,87860000,1353.05 1985-08-01,1347.45,1361.90,1342.97,1355.62,121500000,1355.62 1985-07-31,1346.10,1357.41,1340.05,1347.45,124200000,1347.45 1985-07-30,1343.86,1352.60,1334.90,1346.10,102300000,1346.10 1985-07-29,1357.08,1358.09,1338.93,1343.86,95960000,1343.86 1985-07-26,1353.61,1365.59,1345.21,1357.08,107000000,1357.08 1985-07-25,1348.90,1359.88,1338.60,1353.61,123300000,1353.61 1985-07-24,1351.81,1359.21,1335.69,1348.90,128600000,1348.90 1985-07-23,1357.64,1372.20,1344.76,1351.81,143600000,1351.81 1985-07-22,1359.54,1362.12,1346.89,1357.64,93540000,1357.64 1985-07-19,1350.92,1363.35,1346.44,1359.54,114800000,1359.54 1985-07-18,1357.97,1363.26,1345.32,1350.92,131400000,1350.92 1985-07-17,1347.89,1365.93,1346.21,1357.97,159900000,1357.97 1985-07-16,1335.46,1351.93,1331.54,1347.89,132500000,1347.89 1985-07-15,1338.60,1347.67,1326.95,1335.46,103900000,1335.46 1985-07-12,1337.70,1345.99,1326.39,1338.60,120300000,1338.60 1985-07-11,1332.89,1343.64,1326.16,1337.70,122800000,1337.70 1985-07-10,1321.91,1336.81,1315.30,1332.89,108200000,1332.89 1985-07-09,1328.41,1333.67,1313.40,1321.91,99060000,1321.91 1985-07-08,1334.45,1336.47,1318.88,1328.41,83670000,1328.41 1985-07-05,1326.39,1340.61,1324.93,1334.45,62450000,1334.45 1985-07-03,1334.01,1337.59,1320.23,1326.39,98410000,1326.39 1985-07-02,1337.14,1343.75,1329.19,1334.01,111100000,1334.01 1985-07-01,1335.46,1342.18,1322.58,1337.14,96080000,1337.14 1985-06-28,1332.21,1341.17,1326.16,1335.46,105200000,1335.46 1985-06-27,1323.81,1338.71,1321.80,1332.21,106700000,1332.21 1985-06-26,1323.03,1329.19,1314.74,1323.81,94130000,1323.81 1985-06-25,1320.56,1338.82,1314.07,1323.03,115700000,1323.03 1985-06-24,1324.48,1326.72,1307.80,1320.56,96040000,1320.56 1985-06-21,1299.73,1326.05,1293.79,1324.48,125400000,1324.48 1985-06-20,1297.38,1305.44,1287.75,1299.73,87500000,1299.73 1985-06-19,1304.77,1312.72,1293.57,1297.38,108300000,1297.38 1985-06-18,1298.39,1312.39,1293.68,1304.77,106900000,1304.77 1985-06-17,1300.96,1303.99,1288.75,1298.39,82170000,1298.39 1985-06-14,1290.10,1305.44,1288.88,1300.96,93090000,1300.96 1985-06-13,1306.34,1308.13,1285.39,1290.10,107000000,1290.10 1985-06-12,1313.84,1318.21,1300.74,1306.34,97700000,1306.34 1985-06-11,1318.44,1323.81,1308.02,1313.84,102100000,1313.84 1985-06-10,1316.42,1322.58,1307.24,1318.44,87940000,1318.44 1985-06-07,1327.28,1331.99,1312.95,1316.42,99630000,1316.42 1985-06-06,1320.56,1330.53,1311.94,1327.28,117200000,1327.28 1985-06-05,1315.30,1331.77,1312.61,1320.56,143900000,1320.56 1985-06-04,1310.93,1321.24,1304.44,1315.30,115400000,1315.30 1985-06-03,1315.41,1325.04,1304.21,1310.93,125000000,1310.93 1985-05-31,1305.78,1320.79,1298.72,1315.41,134100000,1315.41 1985-05-30,1302.98,1314.18,1293.91,1305.78,108300000,1305.78 1985-05-29,1301.52,1308.36,1292.79,1302.98,96540000,1302.98 1985-05-28,1301.97,1312.84,1293.23,1301.52,90600000,1301.52 1985-05-24,1296.71,1305.67,1291.11,1301.97,85970000,1301.97 1985-05-23,1303.76,1307.80,1290.99,1296.71,101000000,1296.71 1985-05-22,1308.92,1308.92,1294.35,1303.76,101400000,1303.76 1985-05-21,1304.88,1316.08,1297.49,1309.70,130200000,1309.70 1985-05-20,1292.23,1310.37,1292.23,1304.88,146300000,1304.88 1985-05-17,1278.05,1295.83,1271.42,1285.34,124600000,1285.34 1985-05-16,1273.52,1285.11,1270.10,1278.05,99420000,1278.05 1985-05-15,1273.30,1283.57,1265.46,1273.52,106100000,1273.52 1985-05-14,1277.50,1288.65,1267.67,1273.30,97360000,1273.30 1985-05-13,1274.18,1283.57,1268.77,1277.50,85830000,1277.50 1985-05-10,1261.59,1282.46,1261.59,1274.18,140300000,1274.18 1985-05-09,1249.78,1265.57,1246.58,1260.27,111000000,1260.27 1985-05-08,1252.75,1258.94,1239.51,1249.78,101300000,1249.78 1985-05-07,1247.79,1261.37,1243.15,1252.75,100200000,1252.75 1985-05-06,1247.24,1256.40,1241.39,1247.79,85650000,1247.79 1985-05-03,1242.27,1253.86,1238.30,1247.24,94870000,1247.24 1985-05-02,1242.05,1251.21,1235.53,1242.27,107700000,1242.27 1985-05-01,1258.06,1262.81,1239.07,1242.05,101600000,1242.05 1985-04-30,1259.72,1266.23,1245.80,1258.06,111800000,1258.06 1985-04-29,1275.18,1277.94,1257.40,1259.72,88860000,1259.72 1985-04-26,1284.78,1290.30,1270.54,1275.18,86570000,1275.18 1985-04-25,1278.49,1289.20,1272.53,1284.78,108600000,1284.78 1985-04-24,1278.71,1286.44,1269.88,1278.49,99600000,1278.49 1985-04-23,1266.56,1282.91,1261.15,1278.71,108900000,1278.71 1985-04-22,1266.56,1273.63,1257.62,1266.56,79930000,1266.56 1985-04-19,1265.13,1272.53,1258.50,1266.56,81110000,1266.56 1985-04-18,1272.31,1281.91,1260.82,1265.13,100600000,1265.13 1985-04-17,1269.55,1277.50,1263.47,1272.31,96020000,1272.31 1985-04-16,1266.78,1276.61,1256.96,1269.55,98480000,1269.55 1985-04-15,1265.68,1272.42,1257.84,1266.78,80660000,1266.78 1985-04-12,1263.69,1270.43,1257.29,1265.68,86220000,1265.68 1985-04-11,1259.94,1274.85,1257.18,1263.69,108400000,1263.69 1985-04-10,1253.86,1269.10,1252.10,1259.94,108200000,1259.94 1985-04-09,1252.98,1262.04,1246.58,1253.86,83980000,1253.86 1985-04-08,1259.05,1267.01,1246.02,1252.98,79960000,1252.98 1985-04-04,1258.06,1264.24,1248.34,1259.05,86910000,1259.05 1985-04-03,1265.68,1268.11,1251.55,1258.06,95480000,1258.06 1985-04-02,1272.75,1280.15,1261.48,1265.68,101700000,1265.68 1985-04-01,1266.78,1276.28,1260.49,1272.75,89900000,1272.75 1985-03-29,1260.71,1270.65,1255.85,1266.78,101400000,1266.78 1985-03-28,1264.91,1275.51,1256.63,1260.71,99780000,1260.71 1985-03-27,1259.72,1270.87,1255.96,1264.91,101000000,1264.91 1985-03-26,1259.94,1267.56,1252.10,1259.72,89930000,1259.72 1985-03-25,1267.45,1268.33,1252.87,1259.94,74040000,1259.94 1985-03-22,1268.22,1277.39,1261.70,1267.45,99250000,1267.45 1985-03-21,1265.24,1278.93,1257.62,1268.22,95930000,1268.22 1985-03-20,1271.09,1277.39,1257.84,1265.24,107500000,1265.24 1985-03-19,1249.67,1274.18,1245.69,1271.09,119200000,1271.09 1985-03-18,1247.35,1260.93,1242.82,1249.67,94020000,1249.67 1985-03-15,1260.05,1266.89,1245.14,1247.35,105200000,1247.35 1985-03-14,1261.70,1269.21,1254.20,1260.05,103400000,1260.05 1985-03-13,1271.75,1278.27,1257.62,1261.70,101700000,1261.70 1985-03-12,1268.55,1279.48,1262.48,1271.75,92840000,1271.75 1985-03-11,1269.66,1277.05,1260.93,1268.55,84110000,1268.55 1985-03-08,1271.53,1280.81,1264.13,1269.66,96390000,1269.66 1985-03-07,1280.37,1283.24,1265.46,1271.53,112100000,1271.53 1985-03-06,1291.85,1296.93,1275.51,1280.37,116900000,1280.37 1985-03-05,1289.53,1300.02,1281.03,1291.85,116400000,1291.85 1985-03-04,1299.36,1304.55,1283.13,1289.53,102100000,1289.53 1985-03-01,1284.01,1309.96,1282.69,1299.36,139900000,1299.36 1985-02-28,1281.03,1288.32,1271.42,1284.01,100700000,1284.01 1985-02-27,1286.11,1295.27,1274.40,1281.03,107700000,1281.03 1985-02-26,1277.50,1293.18,1272.31,1286.11,114200000,1286.11 1985-02-25,1275.84,1283.13,1263.91,1277.50,89740000,1277.50 1985-02-22,1279.04,1286.55,1269.99,1275.84,93680000,1275.84 1985-02-21,1283.13,1287.10,1272.64,1279.04,104000000,1279.04 1985-02-20,1280.59,1292.51,1272.53,1283.13,118200000,1283.13 1985-02-19,1282.02,1287.43,1273.52,1280.59,90400000,1280.59 1985-02-15,1287.88,1296.27,1275.07,1282.02,106500000,1282.02 1985-02-14,1297.92,1307.53,1283.68,1287.88,139700000,1287.88 1985-02-13,1276.61,1304.66,1274.51,1297.92,142500000,1297.92 1985-02-12,1276.06,1283.13,1266.34,1276.61,111100000,1276.61 1985-02-11,1289.97,1291.74,1268.66,1276.06,104000000,1276.06 1985-02-08,1290.08,1297.15,1281.36,1289.97,116500000,1289.97 1985-02-07,1280.59,1297.04,1279.81,1290.08,151700000,1290.08 1985-02-06,1285.23,1294.50,1275.07,1280.59,141000000,1280.59 1985-02-05,1290.08,1301.13,1278.60,1285.23,143900000,1285.23 1985-02-04,1277.72,1294.94,1268.99,1290.08,113700000,1290.08 1985-02-01,1286.11,1286.11,1269.77,1277.72,105400000,1277.72 1985-01-31,1287.88,1293.40,1272.64,1286.77,132500000,1286.77 1985-01-30,1292.62,1305.10,1278.93,1287.88,170000000,1287.88 1985-01-29,1277.83,1295.49,1266.89,1292.62,115700000,1292.62 1985-01-28,1276.06,1290.97,1264.24,1277.83,128400000,1277.83 1985-01-25,1270.43,1284.67,1262.04,1276.06,122400000,1276.06 1985-01-24,1274.73,1287.99,1264.58,1270.43,160700000,1270.43 1985-01-23,1259.50,1278.27,1252.54,1274.73,144400000,1274.73 1985-01-22,1261.37,1277.27,1252.87,1259.50,174800000,1259.50 1985-01-21,1227.36,1266.45,1226.70,1261.37,146800000,1261.37 1985-01-18,1228.69,1237.63,1219.52,1227.36,104700000,1227.36 1985-01-17,1230.68,1234.65,1219.74,1228.69,113600000,1228.69 1985-01-16,1230.79,1241.17,1220.74,1230.68,135500000,1230.68 1985-01-15,1234.54,1243.71,1223.06,1230.79,155300000,1230.79 1985-01-14,1218.09,1238.18,1210.36,1234.54,124900000,1234.54 1985-01-11,1223.50,1229.35,1210.91,1218.09,107600000,1218.09 1985-01-10,1202.74,1225.93,1195.56,1223.50,124700000,1223.50 1985-01-09,1191.70,1209.47,1190.26,1202.74,99230000,1202.74 1985-01-08,1190.59,1199.54,1184.08,1191.70,92110000,1191.70 1985-01-07,1184.96,1198.32,1182.86,1190.59,86190000,1190.59 1985-01-04,1189.82,1192.69,1178.67,1184.96,77480000,1184.96 1985-01-03,1198.87,1207.93,1185.18,1189.82,88880000,1189.82 1985-01-02,1211.57,1212.46,1194.35,1198.87,67820000,1198.87 1984-12-31,1204.17,1215.55,1199.20,1211.57,80260000,1211.57 1984-12-28,1202.52,1210.47,1196.11,1204.17,77070000,1204.17 1984-12-27,1208.92,1214.22,1199.09,1202.52,70100000,1202.52 1984-12-26,1210.14,1213.69,1201.74,1208.92,46700000,1208.92 1984-12-24,1199.20,1214.44,1199.20,1210.14,55550000,1210.14 1984-12-21,1203.29,1210.14,1186.84,1198.98,101200000,1198.98 1984-12-20,1208.04,1219.52,1198.87,1203.29,93220000,1203.29 1984-12-19,1211.57,1223.61,1201.52,1208.04,139600000,1208.04 1984-12-18,1182.31,1213.23,1182.31,1211.57,169000000,1211.57 1984-12-17,1175.91,1182.31,1164.53,1176.79,89490000,1176.79 1984-12-14,1168.84,1187.28,1165.64,1175.91,95060000,1175.91 1984-12-13,1175.13,1183.52,1162.65,1168.84,80850000,1168.84 1984-12-12,1178.33,1183.97,1170.38,1175.13,78710000,1175.13 1984-12-11,1172.26,1183.86,1167.51,1178.33,80240000,1178.33 1984-12-10,1163.21,1179.00,1154.70,1172.26,81140000,1172.26 1984-12-07,1170.49,1177.78,1160.00,1163.21,81000000,1163.21 1984-12-06,1171.60,1178.67,1159.23,1170.49,96560000,1170.49 1984-12-05,1185.07,1187.17,1166.85,1171.60,88700000,1171.60 1984-12-04,1182.42,1192.58,1178.67,1185.07,81250000,1185.07 1984-12-03,1188.94,1192.25,1173.37,1182.42,95300000,1182.42 1984-11-30,1193.46,1197.77,1181.10,1188.94,77580000,1188.94 1984-11-29,1205.39,1206.60,1188.16,1193.46,75860000,1193.46 1984-11-28,1220.19,1224.71,1203.51,1205.39,86300000,1205.39 1984-11-27,1212.35,1226.92,1204.62,1220.19,95470000,1220.19 1984-11-26,1220.30,1224.49,1206.16,1212.35,76520000,1212.35 1984-11-23,1204.28,1224.49,1204.28,1220.30,73910000,1220.30 1984-11-21,1195.12,1207.05,1185.07,1201.52,81620000,1201.52 1984-11-20,1185.29,1202.41,1184.30,1195.12,83240000,1195.12 1984-11-19,1187.94,1197.44,1180.76,1185.29,69730000,1185.29 1984-11-16,1206.16,1213.01,1186.73,1187.94,83140000,1187.94 1984-11-15,1206.93,1214.22,1198.54,1206.16,81530000,1206.16 1984-11-14,1206.60,1215.88,1198.98,1206.93,73940000,1206.93 1984-11-13,1219.19,1222.17,1203.07,1206.60,69790000,1206.60 1984-11-12,1218.97,1223.72,1209.25,1219.19,55610000,1219.19 1984-11-09,1228.69,1238.63,1216.65,1218.97,83620000,1218.97 1984-11-08,1233.22,1237.52,1220.30,1228.69,88580000,1228.69 1984-11-07,1244.15,1245.69,1223.72,1233.22,110800000,1233.22 1984-11-06,1229.24,1247.46,1227.03,1244.15,101200000,1244.15 1984-11-05,1216.65,1233.11,1212.57,1229.24,84730000,1229.24 1984-11-02,1217.09,1225.82,1208.26,1216.65,96810000,1216.65 1984-11-01,1207.38,1224.38,1204.51,1217.09,107300000,1217.09 1984-10-31,1217.31,1219.63,1201.52,1207.38,91890000,1207.38 1984-10-30,1201.41,1224.60,1200.42,1217.31,95200000,1217.31 1984-10-29,1204.95,1207.49,1195.01,1201.41,63200000,1201.41 1984-10-26,1211.02,1213.45,1197.77,1204.95,83900000,1204.95 1984-10-25,1216.43,1223.61,1206.05,1211.02,92760000,1211.02 1984-10-24,1213.01,1223.06,1205.17,1216.43,91620000,1216.43 1984-10-23,1217.20,1226.70,1206.71,1213.01,92260000,1213.01 1984-10-22,1225.93,1230.34,1210.80,1217.20,81020000,1217.20 1984-10-19,1225.38,1246.02,1213.56,1225.93,186900000,1225.93 1984-10-18,1195.89,1226.70,1185.73,1225.38,149500000,1225.38 1984-10-17,1197.77,1208.59,1185.62,1195.89,99740000,1195.89 1984-10-16,1202.96,1209.36,1192.25,1197.77,82930000,1197.77 1984-10-15,1190.70,1209.58,1186.73,1202.96,87590000,1202.96 1984-10-12,1183.08,1198.43,1181.10,1190.70,92190000,1190.70 1984-10-11,1177.23,1189.93,1170.61,1183.08,87020000,1183.08 1984-10-10,1175.13,1182.97,1158.24,1177.23,94270000,1177.23 1984-10-09,1177.89,1188.16,1171.93,1175.13,76840000,1175.13 1984-10-08,1182.53,1183.08,1170.49,1177.89,46360000,1177.89 1984-10-05,1187.39,1196.33,1176.57,1182.53,82950000,1182.53 1984-10-04,1182.86,1195.01,1181.10,1187.39,76700000,1187.39 1984-10-03,1191.36,1195.78,1174.69,1182.86,92400000,1182.86 1984-10-02,1198.98,1207.38,1188.60,1191.36,89360000,1191.36 1984-10-01,1206.71,1208.15,1192.36,1198.98,73630000,1198.98 1984-09-28,1216.76,1217.98,1200.09,1206.71,78950000,1206.71 1984-09-27,1212.12,1225.27,1211.35,1216.76,88880000,1216.76 1984-09-26,1207.16,1222.06,1199.98,1212.12,100200000,1212.12 1984-09-25,1205.06,1216.87,1192.80,1207.16,86250000,1207.16 1984-09-24,1201.74,1216.43,1196.00,1205.06,76380000,1205.06 1984-09-21,1216.54,1231.01,1197.00,1201.74,120600000,1201.74 1984-09-20,1213.01,1221.73,1202.52,1216.54,92030000,1216.54 1984-09-19,1226.26,1234.10,1206.05,1213.01,119900000,1213.01 1984-09-18,1237.08,1239.95,1221.18,1226.26,107700000,1226.26 1984-09-17,1237.52,1248.01,1226.26,1237.08,88790000,1237.08 1984-09-14,1228.25,1248.23,1227.92,1237.52,137400000,1237.52 1984-09-13,1200.31,1232.11,1196.00,1228.25,110500000,1228.25 1984-09-12,1197.99,1206.60,1189.82,1200.31,77980000,1200.31 1984-09-11,1202.52,1221.07,1196.33,1197.99,101300000,1197.99 1984-09-10,1207.38,1214.33,1191.81,1202.52,74410000,1202.52 1984-09-07,1218.86,1226.59,1201.63,1207.38,84110000,1207.38 1984-09-06,1209.03,1226.04,1208.70,1218.86,91920000,1218.86 1984-09-05,1212.35,1215.88,1199.65,1209.03,69250000,1209.03 1984-09-04,1222.39,1222.39,1206.93,1212.35,62110000,1212.35 1984-08-31,1223.28,1226.70,1213.89,1224.38,57460000,1224.38 1984-08-30,1226.92,1231.89,1218.64,1223.28,70840000,1223.28 1984-08-29,1232.11,1243.04,1222.50,1226.92,90660000,1226.92 1984-08-28,1227.92,1236.20,1220.85,1232.11,70560000,1232.11 1984-08-27,1234.76,1234.76,1219.08,1227.92,57660000,1227.92 1984-08-24,1232.44,1240.72,1227.14,1236.53,69640000,1236.53 1984-08-23,1231.78,1241.94,1221.51,1232.44,83130000,1232.44 1984-08-22,1239.73,1250.55,1225.82,1231.78,116000000,1231.78 1984-08-21,1216.98,1247.35,1216.65,1239.73,128100000,1239.73 1984-08-20,1211.90,1221.18,1203.62,1216.98,75450000,1216.98 1984-08-17,1209.14,1222.06,1205.94,1211.90,71500000,1211.90 1984-08-16,1198.98,1218.42,1196.78,1209.14,93610000,1209.14 1984-08-15,1214.11,1219.74,1195.56,1198.98,91880000,1198.98 1984-08-14,1220.08,1230.45,1208.70,1214.11,81470000,1214.11 1984-08-13,1218.09,1226.15,1204.39,1220.08,77960000,1220.08 1984-08-10,1224.05,1253.75,1214.66,1218.09,171000000,1218.09 1984-08-09,1196.11,1231.45,1189.49,1224.05,131100000,1224.05 1984-08-08,1204.62,1215.44,1191.70,1196.11,121200000,1196.11 1984-08-07,1202.96,1216.98,1184.96,1204.62,127900000,1204.62 1984-08-06,1202.08,1230.90,1191.14,1202.96,203000000,1202.96 1984-08-03,1176.13,1213.34,1176.13,1202.08,236500000,1202.08 1984-08-02,1138.14,1171.38,1138.14,1166.08,172800000,1166.08 1984-08-01,1115.28,1139.58,1114.95,1134.61,127500000,1134.61 1984-07-31,1109.98,1123.56,1104.90,1115.28,86910000,1115.28 1984-07-30,1114.62,1121.69,1103.25,1109.98,72330000,1109.98 1984-07-27,1107.55,1124.23,1101.59,1114.62,101350000,1114.62 1984-07-26,1096.95,1113.18,1093.42,1107.55,90410000,1107.55 1984-07-25,1086.57,1106.45,1078.95,1096.95,90520000,1096.95 1984-07-24,1096.62,1103.91,1083.59,1086.57,74370000,1086.57 1984-07-23,1101.37,1102.58,1083.37,1096.62,77990000,1096.62 1984-07-20,1102.92,1109.10,1092.42,1101.37,79090000,1101.37 1984-07-19,1111.64,1114.07,1098.28,1102.92,85230000,1102.92 1984-07-18,1122.90,1125.44,1106.01,1111.64,76640000,1111.64 1984-07-17,1116.83,1128.53,1110.87,1122.90,82890000,1122.90 1984-07-16,1109.87,1120.25,1100.82,1116.83,73420000,1116.83 1984-07-13,1104.57,1118.04,1101.92,1109.87,75480000,1109.87 1984-07-12,1108.55,1116.72,1096.18,1104.57,86050000,1104.57 1984-07-11,1126.88,1127.87,1106.23,1108.55,89540000,1108.55 1984-07-10,1134.05,1139.47,1119.92,1126.88,74010000,1126.88 1984-07-09,1122.57,1138.69,1112.63,1134.05,74830000,1134.05 1984-07-06,1124.56,1127.10,1112.19,1122.57,65850000,1122.57 1984-07-05,1134.28,1138.47,1122.24,1124.56,66100000,1124.56 1984-07-03,1130.08,1139.13,1124.01,1134.28,69960000,1134.28 1984-07-02,1132.40,1137.81,1120.25,1130.08,69230000,1130.08 1984-06-29,1126.55,1143.33,1124.56,1132.40,90770000,1132.40 1984-06-28,1116.72,1131.62,1112.74,1126.55,77660000,1126.55 1984-06-27,1122.79,1130.08,1109.98,1116.72,78400000,1116.72 1984-06-26,1130.52,1133.61,1116.83,1122.79,82600000,1122.79 1984-06-25,1131.07,1140.68,1124.01,1130.52,72850000,1130.52 1984-06-22,1127.21,1139.02,1118.93,1131.07,98400000,1131.07 1984-06-21,1131.63,1143.44,1115.17,1127.21,123380000,1127.21 1984-06-20,1115.83,1135.16,1097.73,1131.63,99090000,1131.63 1984-06-19,1109.65,1123.12,1105.79,1115.83,98000000,1115.83 1984-06-18,1086.90,1114.29,1079.39,1109.65,94900000,1109.65 1984-06-15,1097.61,1106.34,1083.59,1086.90,85460000,1086.90 1984-06-14,1110.53,1113.96,1089.55,1097.61,79120000,1097.61 1984-06-13,1110.53,1120.91,1103.80,1110.53,67510000,1110.53 1984-06-12,1115.61,1119.92,1101.92,1110.53,84660000,1110.53 1984-06-11,1130.96,1130.96,1112.63,1115.61,69050000,1115.61 1984-06-08,1132.44,1137.82,1123.81,1131.25,67840000,1131.25 1984-06-07,1133.84,1139.12,1125.11,1132.44,82120000,1132.44 1984-06-06,1124.89,1144.83,1117.89,1133.84,83440000,1133.84 1984-06-05,1131.57,1133.62,1117.13,1124.89,84840000,1124.89 1984-06-04,1125.32,1143.53,1125.32,1131.57,96740000,1131.57 1984-06-01,1106.25,1127.26,1106.25,1124.35,96040000,1124.35 1984-05-31,1102.59,1113.90,1095.15,1104.85,81890000,1104.85 1984-05-30,1101.24,1116.59,1083.19,1102.59,105660000,1102.59 1984-05-29,1107.10,1113.80,1093.80,1101.24,69060000,1101.24 1984-05-25,1103.43,1114.32,1096.84,1107.10,78190000,1107.10 1984-05-24,1113.80,1117.15,1096.31,1103.43,99040000,1103.43 1984-05-23,1116.62,1125.63,1109.19,1113.80,82690000,1113.80 1984-05-22,1125.31,1126.99,1105.95,1116.62,88030000,1116.62 1984-05-21,1133.79,1139.13,1121.23,1125.31,73380000,1125.31 1984-05-18,1142.27,1147.82,1125.73,1133.79,81270000,1133.79 1984-05-17,1153.16,1154.10,1134.84,1142.27,90310000,1142.27 1984-05-16,1150.86,1159.86,1146.88,1153.16,89210000,1153.16 1984-05-15,1151.07,1160.80,1143.43,1150.86,88250000,1150.86 1984-05-14,1157.14,1160.49,1141.96,1151.07,64900000,1151.07 1984-05-11,1167.19,1168.24,1145.31,1157.14,82780000,1157.14 1984-05-10,1165.52,1176.61,1158.71,1167.19,101810000,1167.19 1984-05-09,1176.30,1182.47,1157.45,1165.52,100590000,1165.52 1984-05-08,1166.56,1181.11,1159.97,1176.30,81610000,1176.30 1984-05-07,1165.31,1170.96,1157.87,1166.56,72760000,1166.56 1984-05-04,1181.53,1185.41,1158.92,1165.31,98580000,1165.31 1984-05-03,1186.56,1192.73,1174.10,1181.53,91910000,1181.53 1984-05-02,1183.00,1194.41,1174.10,1186.56,107080000,1186.56 1984-05-01,1170.75,1188.86,1167.40,1183.00,110550000,1183.00 1984-04-30,1169.07,1177.45,1160.07,1170.75,72740000,1170.75 1984-04-27,1175.25,1180.49,1163.32,1169.07,88530000,1169.07 1984-04-26,1163.53,1182.06,1162.79,1175.25,98000000,1175.25 1984-04-25,1162.90,1170.33,1153.69,1163.53,83520000,1163.53 1984-04-24,1149.50,1170.54,1144.37,1162.90,87060000,1162.90 1984-04-23,1158.08,1164.78,1146.04,1149.50,73080000,1149.50 1984-04-19,1156.51,1162.79,1145.41,1158.08,75860000,1158.08 1984-04-18,1164.57,1167.71,1151.07,1156.51,85040000,1156.51 1984-04-17,1160.28,1173.99,1156.83,1164.57,98150000,1164.57 1984-04-16,1150.13,1162.90,1139.55,1160.28,73870000,1160.28 1984-04-13,1157.14,1169.28,1144.58,1150.13,99620000,1150.13 1984-04-12,1130.97,1159.55,1121.02,1157.14,96330000,1157.14 1984-04-11,1138.30,1145.10,1127.20,1130.97,80280000,1130.97 1984-04-10,1133.90,1147.93,1131.28,1138.30,78990000,1138.30 1984-04-09,1132.22,1141.86,1123.64,1133.90,71570000,1133.90 1984-04-06,1130.55,1138.18,1117.25,1132.22,86620000,1132.22 1984-04-05,1148.56,1157.87,1128.35,1130.55,101750000,1130.55 1984-04-04,1148.76,1156.83,1141.02,1148.56,92860000,1148.56 1984-04-03,1153.16,1159.13,1140.39,1148.76,87980000,1148.76 1984-04-02,1164.89,1175.36,1145.94,1153.16,85680000,1153.16 1984-03-30,1170.75,1173.68,1157.87,1164.89,71590000,1164.89 1984-03-29,1174.62,1184.25,1165.52,1170.75,81470000,1170.75 1984-03-28,1154.31,1176.61,1151.80,1174.62,104870000,1174.62 1984-03-27,1152.95,1162.27,1145.62,1154.31,73670000,1154.31 1984-03-26,1154.84,1161.96,1146.25,1152.95,69070000,1152.95 1984-03-23,1155.88,1161.54,1145.31,1154.84,79760000,1154.84 1984-03-22,1170.85,1170.85,1150.75,1155.88,87340000,1155.88 1984-03-21,1175.77,1181.95,1165.62,1170.85,87170000,1170.85 1984-03-20,1171.38,1184.15,1166.25,1175.77,86460000,1175.77 1984-03-19,1179.02,1179.02,1163.00,1171.38,64060000,1171.38 1984-03-16,1176.19,1197.24,1176.19,1184.36,118000000,1184.36 1984-03-15,1166.04,1177.24,1159.23,1167.40,79520000,1167.40 1984-03-14,1164.78,1173.68,1155.67,1166.04,77250000,1166.04 1984-03-13,1156.09,1176.51,1156.09,1164.78,102600000,1164.78 1984-03-12,1139.76,1160.80,1136.52,1155.36,84470000,1155.36 1984-03-09,1147.09,1149.29,1132.54,1139.76,73170000,1139.76 1984-03-08,1143.63,1155.46,1136.10,1147.09,80630000,1147.09 1984-03-07,1152.53,1153.27,1131.70,1143.63,90080000,1143.63 1984-03-06,1165.20,1171.59,1148.24,1152.53,83590000,1152.53 1984-03-05,1171.48,1174.31,1158.50,1165.20,69870000,1165.20 1984-03-02,1163.21,1181.01,1163.21,1171.48,108270000,1171.48 1984-03-01,1154.63,1166.46,1146.25,1159.44,82010000,1159.44 1984-02-29,1157.14,1171.38,1146.46,1154.63,92810000,1154.63 1984-02-28,1177.45,1177.45,1150.34,1157.14,91010000,1157.14 1984-02-27,1165.10,1186.66,1156.41,1179.96,99140000,1179.96 1984-02-24,1137.04,1167.09,1137.04,1165.10,102620000,1165.10 1984-02-23,1134.21,1142.38,1114.95,1134.63,100220000,1134.63 1984-02-22,1139.34,1145.83,1128.66,1134.21,90080000,1134.21 1984-02-21,1148.87,1153.79,1134.00,1139.34,71890000,1139.34 1984-02-17,1154.94,1164.36,1141.23,1148.87,76600000,1148.87 1984-02-16,1158.71,1164.99,1143.74,1154.94,81750000,1154.94 1984-02-15,1163.84,1175.67,1154.31,1158.71,94870000,1158.71 1984-02-14,1150.13,1170.54,1147.09,1163.84,91800000,1163.84 1984-02-13,1160.70,1164.05,1139.97,1150.13,78460000,1150.13 1984-02-10,1152.74,1167.92,1149.92,1160.70,92220000,1160.70 1984-02-09,1156.30,1167.29,1139.03,1152.74,128190000,1152.74 1984-02-08,1180.49,1188.76,1151.28,1156.30,96890000,1156.30 1984-02-07,1174.31,1187.29,1161.12,1180.49,107640000,1180.49 1984-02-06,1193.15,1193.15,1167.92,1174.31,109090000,1174.31 1984-02-03,1213.88,1226.55,1192.00,1197.03,109100000,1197.03 1984-02-02,1212.31,1223.93,1198.49,1213.88,111330000,1213.88 1984-02-01,1220.58,1226.34,1203.31,1212.31,107100000,1212.31 1984-01-31,1221.52,1231.68,1209.59,1220.58,113510000,1220.58 1984-01-30,1230.00,1239.64,1212.42,1221.52,103120000,1221.52 1984-01-27,1229.69,1238.69,1218.91,1230.00,103720000,1230.00 1984-01-26,1231.89,1242.57,1222.78,1229.69,111100000,1229.69 1984-01-25,1242.88,1255.44,1227.39,1231.89,113470000,1231.89 1984-01-24,1244.45,1251.57,1234.61,1242.88,103050000,1242.88 1984-01-23,1259.11,1259.42,1240.05,1244.45,82010000,1244.45 1984-01-20,1266.02,1270.94,1252.30,1259.11,93360000,1259.11 1984-01-19,1269.37,1276.17,1259.32,1266.02,98340000,1266.02 1984-01-18,1271.46,1280.36,1261.93,1269.37,109010000,1269.37 1984-01-17,1267.59,1275.75,1260.89,1271.46,92750000,1271.46 1984-01-16,1270.10,1275.96,1259.53,1267.59,93790000,1267.59 1984-01-13,1279.31,1289.57,1262.98,1270.10,101790000,1270.10 1984-01-12,1277.32,1287.90,1271.78,1279.31,99410000,1279.31 1984-01-11,1278.48,1284.13,1267.59,1277.32,98660000,1277.32 1984-01-10,1286.22,1295.44,1273.97,1278.48,109570000,1278.48 1984-01-09,1286.64,1295.33,1275.86,1286.22,107100000,1286.22 1984-01-06,1282.24,1293.66,1271.78,1286.64,137590000,1286.64 1984-01-05,1269.05,1290.72,1268.74,1282.24,159990000,1282.24 1984-01-04,1252.74,1271.36,1246.55,1269.05,112980000,1269.05 1984-01-03,1258.64,1264.13,1247.46,1252.74,71340000,1252.74 1983-12-30,1260.16,1265.24,1253.15,1258.64,71840000,1258.64 1983-12-29,1263.21,1273.88,1256.30,1260.16,86560000,1260.16 1983-12-28,1263.72,1268.90,1254.17,1263.21,85660000,1263.21 1983-12-27,1250.51,1267.28,1249.80,1263.72,63800000,1263.72 1983-12-23,1253.66,1259.25,1241.97,1250.51,62710000,1250.51 1983-12-22,1254.98,1265.24,1246.65,1253.66,106260000,1253.66 1983-12-21,1241.97,1260.26,1240.24,1254.98,108080000,1254.98 1983-12-20,1244.61,1251.93,1236.79,1241.97,83740000,1241.97 1983-12-19,1242.17,1254.88,1238.21,1244.61,75180000,1244.61 1983-12-16,1236.79,1248.27,1231.40,1242.17,81030000,1242.17 1983-12-15,1246.65,1250.20,1231.20,1236.79,88300000,1236.79 1983-12-14,1255.89,1261.38,1241.77,1246.65,85430000,1246.65 1983-12-13,1261.59,1267.17,1250.81,1255.89,93500000,1255.89 1983-12-12,1260.06,1269.11,1248.78,1261.59,77340000,1261.59 1983-12-09,1261.89,1268.09,1252.03,1260.06,98280000,1260.06 1983-12-08,1273.78,1278.15,1256.91,1261.89,96530000,1261.89 1983-12-07,1269.31,1282.42,1263.21,1273.78,105670000,1273.78 1983-12-06,1270.53,1281.30,1262.80,1269.31,89690000,1269.31 1983-12-05,1265.24,1275.41,1256.40,1270.53,88330000,1270.53 1983-12-02,1275.10,1281.30,1259.76,1265.24,93960000,1265.24 1983-12-01,1276.02,1285.47,1265.45,1275.10,106970000,1275.10 1983-11-30,1287.19,1296.95,1271.04,1276.02,120130000,1276.02 1983-11-29,1269.82,1290.95,1264.22,1287.19,100460000,1287.19 1983-11-28,1277.44,1279.78,1263.11,1269.82,78210000,1269.82 1983-11-25,1275.61,1282.22,1268.80,1277.44,57820000,1277.44 1983-11-23,1275.81,1284.55,1265.04,1275.61,108080000,1275.61 1983-11-22,1268.80,1287.80,1262.91,1275.81,117550000,1275.81 1983-11-21,1251.02,1272.36,1248.17,1268.80,97740000,1268.80 1983-11-18,1254.67,1260.77,1240.35,1251.02,88280000,1251.02 1983-11-17,1251.32,1262.09,1243.19,1254.67,80740000,1254.67 1983-11-16,1247.95,1260.47,1242.07,1251.32,83380000,1251.32 1983-11-15,1254.07,1260.87,1242.28,1247.95,77840000,1247.95 1983-11-14,1250.20,1265.04,1244.61,1254.07,86880000,1254.07 1983-11-11,1235.87,1253.56,1230.79,1250.20,74270000,1250.20 1983-11-10,1232.52,1245.83,1226.83,1235.87,88730000,1235.87 1983-11-09,1214.94,1235.47,1212.20,1232.52,83100000,1232.52 1983-11-08,1214.84,1222.05,1208.74,1214.94,64900000,1214.94 1983-11-07,1218.29,1226.52,1209.35,1214.84,69400000,1214.84 1983-11-04,1227.13,1227.74,1211.89,1218.29,72080000,1218.29 1983-11-03,1237.30,1242.68,1222.76,1227.13,85350000,1227.13 1983-11-02,1229.27,1244.11,1220.83,1237.30,95210000,1237.30 1983-11-01,1225.20,1233.94,1210.47,1229.27,84460000,1229.27 1983-10-31,1223.48,1236.48,1214.63,1225.20,79460000,1225.20 1983-10-28,1242.07,1248.68,1217.07,1223.48,81180000,1223.48 1983-10-27,1243.80,1249.09,1230.49,1242.07,79570000,1242.07 1983-10-26,1252.44,1259.15,1238.62,1243.80,79570000,1243.80 1983-10-25,1248.98,1263.41,1245.22,1252.44,82530000,1252.44 1983-10-24,1248.88,1252.54,1227.74,1248.98,85420000,1248.98 1983-10-21,1251.52,1260.77,1231.61,1248.88,91640000,1248.88 1983-10-20,1246.75,1258.74,1241.06,1251.52,86000000,1251.52 1983-10-19,1250.81,1255.28,1229.37,1246.75,107790000,1246.75 1983-10-18,1268.70,1272.76,1245.53,1250.81,91080000,1250.81 1983-10-17,1263.52,1278.66,1256.20,1268.70,77730000,1268.70 1983-10-14,1261.38,1270.12,1251.83,1263.52,71600000,1263.52 1983-10-13,1259.65,1270.63,1250.51,1261.38,67750000,1261.38 1983-10-12,1265.14,1273.07,1252.95,1259.65,75630000,1259.65 1983-10-11,1284.65,1285.26,1261.89,1265.14,79510000,1265.14 1983-10-10,1272.15,1286.69,1261.59,1284.65,67050000,1284.65 1983-10-07,1268.80,1280.28,1262.60,1272.15,103630000,1272.15 1983-10-06,1250.20,1272.15,1246.95,1268.80,118270000,1268.80 1983-10-05,1236.69,1254.88,1228.96,1250.20,101710000,1250.20 1983-10-04,1231.30,1247.56,1225.71,1236.69,90270000,1236.69 1983-10-03,1233.13,1237.70,1216.26,1231.30,77230000,1231.30 1983-09-30,1240.14,1242.89,1224.59,1233.13,70860000,1233.13 1983-09-29,1241.97,1252.03,1236.08,1240.14,73730000,1240.14 1983-09-28,1247.97,1253.45,1234.35,1241.97,75820000,1241.97 1983-09-27,1259.25,1259.25,1239.33,1247.97,81100000,1247.97 1983-09-26,1255.59,1270.73,1247.56,1260.77,86400000,1260.77 1983-09-23,1257.52,1265.55,1246.24,1255.59,93180000,1255.59 1983-09-22,1243.29,1261.28,1236.79,1257.52,97050000,1257.52 1983-09-21,1249.19,1255.89,1236.79,1243.29,91280000,1243.29 1983-09-20,1233.94,1257.01,1233.64,1249.19,103050000,1249.19 1983-09-19,1225.71,1242.68,1221.24,1233.94,85630000,1233.94 1983-09-16,1215.04,1232.72,1210.16,1225.71,75530000,1225.71 1983-09-15,1229.47,1232.83,1213.01,1215.04,70420000,1215.04 1983-09-14,1224.09,1233.94,1218.80,1229.47,73370000,1229.47 1983-09-13,1229.07,1233.43,1214.63,1224.09,73970000,1224.09 1983-09-12,1239.74,1262.80,1225.00,1229.07,114020000,1229.07 1983-09-09,1246.14,1252.74,1233.33,1239.74,77990000,1239.74 1983-09-08,1244.11,1252.95,1232.83,1246.14,79250000,1246.14 1983-09-07,1238.72,1253.96,1229.27,1244.11,94240000,1244.11 1983-09-06,1222.05,1244.11,1222.05,1238.72,87500000,1238.72 1983-09-02,1206.81,1221.34,1204.17,1215.45,59300000,1215.45 1983-09-01,1216.16,1221.24,1197.36,1206.81,76120000,1206.81 1983-08-31,1196.04,1219.82,1191.16,1216.16,80800000,1216.16 1983-08-30,1194.11,1204.37,1187.20,1196.04,62370000,1196.04 1983-08-29,1192.07,1198.37,1178.15,1194.11,53030000,1194.11 1983-08-26,1185.06,1196.95,1174.59,1192.07,61650000,1192.07 1983-08-25,1184.25,1195.22,1173.27,1185.06,70140000,1185.06 1983-08-24,1192.89,1199.80,1179.67,1184.25,72200000,1184.25 1983-08-23,1203.15,1205.49,1186.38,1192.89,66800000,1192.89 1983-08-22,1194.21,1216.26,1191.36,1203.15,76420000,1203.15 1983-08-19,1192.48,1200.51,1183.64,1194.21,58950000,1194.21 1983-08-18,1206.54,1215.45,1188.52,1192.48,82280000,1192.48 1983-08-17,1190.45,1212.09,1186.28,1206.54,87800000,1206.54 1983-08-16,1193.50,1199.70,1180.49,1190.45,71780000,1190.45 1983-08-15,1186.69,1208.74,1186.69,1193.50,83200000,1193.50 1983-08-12,1174.39,1189.63,1169.82,1182.83,71840000,1182.83 1983-08-11,1175.98,1185.87,1165.55,1174.39,70630000,1174.39 1983-08-10,1168.27,1182.19,1157.25,1175.98,82900000,1175.98 1983-08-09,1163.06,1177.28,1152.14,1168.27,81420000,1168.27 1983-08-08,1180.19,1180.19,1157.55,1163.06,71460000,1163.06 1983-08-05,1183.09,1191.91,1173.58,1183.29,67850000,1183.29 1983-08-04,1197.82,1200.52,1166.57,1183.09,100870000,1183.09 1983-08-03,1188.00,1203.73,1179.29,1197.82,80370000,1197.82 1983-08-02,1194.21,1202.52,1183.89,1188.00,74460000,1188.00 1983-08-01,1199.22,1204.33,1183.79,1194.21,77210000,1194.21 1983-07-29,1216.35,1216.75,1188.10,1199.22,95240000,1199.22 1983-07-28,1230.47,1236.58,1211.74,1216.35,78410000,1216.35 1983-07-27,1243.69,1258.51,1225.86,1230.47,99290000,1230.47 1983-07-26,1232.87,1250.00,1226.46,1243.69,91280000,1243.69 1983-07-25,1231.17,1239.78,1217.45,1232.87,73680000,1232.87 1983-07-22,1229.37,1238.18,1220.45,1231.17,68850000,1231.17 1983-07-21,1227.86,1238.48,1217.35,1229.37,101830000,1229.37 1983-07-20,1206.03,1230.57,1206.03,1227.86,109310000,1227.86 1983-07-19,1189.90,1205.13,1188.40,1197.12,74030000,1197.12 1983-07-18,1192.31,1197.62,1179.79,1189.90,69110000,1189.90 1983-07-15,1204.33,1205.73,1187.10,1192.31,63160000,1192.31 1983-07-14,1197.82,1215.04,1195.11,1204.33,83500000,1204.33 1983-07-13,1198.52,1205.83,1189.40,1197.82,68900000,1197.82 1983-07-12,1215.54,1218.35,1194.11,1198.52,70220000,1198.52 1983-07-11,1207.23,1221.96,1205.53,1215.54,61610000,1215.54 1983-07-08,1210.44,1218.95,1201.52,1207.23,66520000,1207.23 1983-07-07,1220.65,1227.26,1203.33,1210.44,97130000,1210.44 1983-07-06,1208.53,1224.46,1202.72,1220.65,85670000,1220.65 1983-07-05,1217.25,1217.25,1200.22,1208.53,67320000,1208.53 1983-07-01,1221.96,1231.07,1213.94,1225.26,65110000,1225.26 1983-06-30,1213.84,1229.27,1209.54,1221.96,76310000,1221.96 1983-06-29,1209.23,1222.16,1201.22,1213.84,81580000,1213.84 1983-06-28,1229.47,1237.68,1205.83,1209.23,82730000,1209.23 1983-06-27,1241.69,1246.29,1221.85,1229.47,69360000,1229.47 1983-06-24,1241.79,1250.20,1229.87,1241.69,80810000,1241.69 1983-06-23,1245.69,1250.60,1231.67,1241.79,89590000,1241.79 1983-06-22,1247.40,1258.21,1234.27,1245.69,110270000,1245.69 1983-06-21,1239.18,1253.00,1228.27,1247.40,102880000,1247.40 1983-06-20,1242.19,1258.61,1230.77,1239.18,84270000,1239.18 1983-06-17,1248.30,1260.72,1232.87,1242.19,93630000,1242.19 1983-06-16,1237.28,1259.82,1236.08,1248.30,124560000,1248.30 1983-06-15,1227.26,1240.18,1216.85,1237.28,93410000,1237.28 1983-06-14,1220.55,1237.28,1214.64,1227.26,97710000,1227.26 1983-06-13,1199.12,1223.46,1199.12,1220.55,90700000,1220.55 1983-06-10,1189.00,1204.53,1187.30,1196.11,78470000,1196.11 1983-06-09,1185.50,1196.71,1176.78,1189.00,87440000,1189.00 1983-06-08,1194.91,1199.52,1179.59,1185.50,96600000,1185.50 1983-06-07,1214.24,1218.15,1193.21,1194.91,88550000,1194.91 1983-06-06,1213.04,1223.26,1203.83,1214.24,87670000,1214.24 1983-06-03,1211.44,1222.46,1204.23,1213.04,83110000,1213.04 1983-06-02,1202.21,1218.15,1195.01,1211.44,89750000,1211.44 1983-06-01,1199.98,1208.30,1187.69,1202.21,84460000,1202.21 1983-05-31,1216.14,1217.59,1191.95,1199.98,73910000,1199.98 1983-05-27,1223.49,1229.20,1209.95,1216.14,76290000,1216.14 1983-05-26,1229.01,1237.04,1215.17,1223.49,94980000,1223.49 1983-05-25,1219.04,1234.04,1207.62,1229.01,121050000,1229.01 1983-05-24,1200.56,1224.07,1199.21,1219.04,109850000,1219.04 1983-05-23,1190.02,1205.40,1174.25,1200.56,84960000,1200.56 1983-05-20,1191.37,1197.27,1179.08,1190.02,73150000,1190.02 1983-05-19,1203.56,1208.49,1186.15,1191.37,83260000,1191.37 1983-05-18,1205.79,1225.04,1196.98,1203.56,99780000,1203.56 1983-05-17,1202.98,1211.88,1193.30,1205.79,79510000,1205.79 1983-05-16,1209.95,1209.95,1190.21,1202.98,76250000,1202.98 1983-05-13,1214.40,1228.04,1209.17,1218.75,83110000,1218.75 1983-05-12,1219.72,1226.59,1204.82,1214.40,84060000,1214.40 1983-05-11,1229.68,1234.42,1210.72,1219.72,99820000,1219.72 1983-05-10,1228.23,1240.03,1220.49,1229.68,104010000,1229.68 1983-05-09,1232.59,1241.29,1219.04,1228.23,93670000,1228.23 1983-05-06,1219.72,1244.49,1217.69,1232.59,128200000,1232.59 1983-05-05,1212.65,1225.81,1202.40,1219.72,107860000,1219.72 1983-05-04,1208.01,1227.94,1198.63,1212.65,101690000,1212.65 1983-05-03,1204.33,1214.11,1188.37,1208.01,89550000,1208.01 1983-05-02,1225.43,1225.43,1197.27,1204.33,88170000,1204.33 1983-04-29,1219.52,1235.49,1208.59,1226.20,105750000,1226.20 1983-04-28,1208.40,1226.97,1201.04,1219.52,94410000,1219.52 1983-04-27,1209.46,1225.04,1197.37,1208.40,118140000,1208.40 1983-04-26,1187.21,1210.82,1177.92,1209.46,91210000,1209.46 1983-04-25,1196.30,1206.75,1183.24,1187.21,90150000,1187.21 1983-04-22,1188.27,1204.62,1184.21,1196.30,92270000,1196.30 1983-04-21,1191.47,1202.11,1180.92,1188.27,106170000,1188.27 1983-04-20,1174.54,1197.56,1170.47,1191.47,110240000,1191.47 1983-04-19,1183.24,1187.98,1166.22,1174.54,91210000,1174.54 1983-04-18,1171.34,1187.89,1164.57,1183.24,88560000,1183.24 1983-04-15,1165.25,1177.05,1159.06,1171.34,89590000,1171.34 1983-04-14,1156.64,1171.05,1146.67,1165.25,90160000,1165.25 1983-04-13,1145.32,1165.34,1142.22,1156.64,100520000,1156.64 1983-04-12,1141.83,1151.80,1134.09,1145.32,79900000,1145.32 1983-04-11,1127.23,1144.54,1127.23,1141.83,81440000,1141.83 1983-04-08,1117.65,1128.87,1109.52,1124.71,67710000,1124.71 1983-04-07,1113.49,1123.36,1106.71,1117.65,69480000,1117.65 1983-04-06,1120.16,1122.48,1102.17,1113.49,77140000,1113.49 1983-04-05,1127.61,1137.58,1116.39,1120.16,76810000,1120.16 1983-04-04,1130.03,1133.03,1115.13,1127.61,66010000,1127.61 1983-03-31,1143.29,1158.48,1125.29,1130.03,100570000,1130.03 1983-03-30,1131.19,1146.67,1129.64,1143.29,75800000,1143.29 1983-03-29,1133.32,1142.80,1125.39,1131.19,65300000,1131.19 1983-03-28,1140.09,1145.80,1126.84,1133.32,58510000,1133.32 1983-03-25,1145.90,1153.83,1132.64,1140.09,77330000,1140.09 1983-03-24,1140.87,1154.41,1134.48,1145.90,92340000,1145.90 1983-03-23,1122.97,1147.83,1121.81,1140.87,94980000,1140.87 1983-03-22,1125.29,1135.74,1118.61,1122.97,79610000,1122.97 1983-03-21,1117.74,1130.32,1109.33,1125.29,72160000,1125.29 1983-03-18,1116.97,1128.00,1109.71,1117.74,75110000,1117.74 1983-03-17,1116.00,1123.55,1108.07,1116.97,70290000,1116.97 1983-03-16,1124.52,1134.77,1111.46,1116.00,83570000,1116.00 1983-03-15,1114.45,1126.84,1109.62,1124.52,62410000,1124.52 1983-03-14,1117.74,1124.61,1105.07,1114.45,61890000,1114.45 1983-03-11,1120.94,1127.61,1107.97,1117.74,67240000,1117.74 1983-03-10,1132.64,1145.22,1116.49,1120.94,95410000,1120.94 1983-03-09,1119.78,1136.42,1112.04,1132.64,84250000,1132.64 1983-03-08,1141.74,1143.00,1117.55,1119.78,79410000,1119.78 1983-03-07,1140.96,1149.67,1128.19,1141.74,84020000,1141.74 1983-03-04,1138.06,1146.28,1125.58,1140.96,90930000,1140.96 1983-03-03,1135.06,1151.12,1128.39,1138.06,114440000,1138.06 1983-03-02,1130.71,1144.45,1121.90,1135.06,112600000,1135.06 1983-03-01,1112.16,1139.22,1110.20,1130.71,103750000,1130.71 1983-02-28,1120.94,1128.58,1105.26,1112.16,83750000,1112.16 1983-02-25,1121.81,1135.26,1115.13,1120.94,100970000,1120.94 1983-02-24,1100.62,1126.74,1100.62,1121.81,113220000,1121.81 1983-02-23,1080.40,1100.14,1077.69,1096.94,84100000,1096.94 1983-02-22,1092.82,1097.72,1074.01,1080.40,84080000,1080.40 1983-02-18,1088.91,1099.42,1079.99,1092.82,77420000,1092.82 1983-02-17,1087.43,1096.35,1075.52,1088.91,74930000,1088.91 1983-02-16,1093.10,1103.70,1083.43,1087.43,82100000,1087.43 1983-02-15,1097.10,1107.61,1086.22,1093.10,89040000,1093.10 1983-02-14,1086.50,1103.33,1080.64,1097.10,72640000,1097.10 1983-02-11,1087.75,1100.82,1080.17,1086.50,86700000,1086.50 1983-02-10,1067.88,1094.83,1067.88,1087.75,93510000,1087.75 1983-02-09,1075.33,1081.59,1058.13,1067.42,84520000,1067.42 1983-02-08,1087.10,1091.70,1068.71,1075.33,76580000,1075.33 1983-02-07,1077.91,1097.04,1073.77,1087.10,86030000,1087.10 1983-02-04,1064.66,1081.13,1056.75,1077.91,87000000,1077.91 1983-02-03,1062.64,1075.06,1057.03,1064.66,78890000,1064.66 1983-02-02,1059.79,1070.09,1046.82,1062.64,77220000,1062.64 1983-02-01,1075.70,1082.78,1057.58,1059.79,82750000,1059.79 1983-01-31,1064.75,1079.75,1055.83,1075.70,67140000,1075.70 1983-01-28,1063.65,1080.57,1056.66,1064.75,89490000,1064.75 1983-01-27,1037.99,1068.16,1037.35,1063.65,88120000,1063.65 1983-01-26,1042.03,1050.31,1027.78,1037.99,73720000,1037.99 1983-01-25,1030.17,1048.93,1028.61,1042.03,79740000,1042.03 1983-01-24,1039.28,1039.28,1013.43,1030.17,90800000,1030.17 1983-01-21,1070.46,1070.46,1045.16,1052.98,77110000,1052.98 1983-01-20,1068.06,1080.39,1060.15,1070.82,82790000,1070.82 1983-01-19,1079.65,1082.97,1057.12,1068.06,80900000,1068.06 1983-01-18,1084.81,1089.22,1068.06,1079.65,78380000,1079.65 1983-01-17,1080.85,1098.60,1077.35,1084.81,89210000,1084.81 1983-01-14,1073.95,1089.04,1070.36,1080.85,86480000,1080.85 1983-01-13,1083.61,1091.06,1068.80,1073.95,77030000,1073.95 1983-01-12,1083.79,1105.13,1075.88,1083.61,109850000,1083.61 1983-01-11,1092.35,1097.50,1076.07,1083.79,98250000,1083.79 1983-01-10,1076.07,1099.98,1065.12,1092.35,101890000,1092.35 1983-01-07,1070.92,1091.34,1063.19,1076.07,127290000,1076.07 1983-01-06,1044.89,1081.95,1042.40,1070.92,129410000,1070.92 1983-01-05,1046.08,1056.75,1033.94,1044.89,95390000,1044.89 1983-01-04,1027.04,1047.46,1020.24,1046.08,75530000,1046.08 1983-01-03,1046.54,1057.21,1022.17,1027.04,59080000,1027.04 1982-12-31,1047.37,1055.56,1041.84,1046.54,42110000,1046.54 1982-12-30,1059.60,1066.13,1043.60,1047.37,56380000,1047.37 1982-12-29,1058.87,1069.35,1050.68,1059.60,54810000,1059.60 1982-12-28,1070.55,1077.91,1053.44,1058.87,58610000,1058.87 1982-12-27,1045.07,1076.07,1043.60,1070.55,64690000,1070.55 1982-12-23,1035.04,1051.51,1032.19,1045.07,62880000,1045.07 1982-12-22,1030.26,1047.19,1021.62,1035.04,83470000,1035.04 1982-12-21,1004.51,1036.33,998.53,1030.26,78010000,1030.26 1982-12-20,1011.50,1022.63,998.44,1004.51,62210000,1004.51 1982-12-17,990.25,1018.12,989.24,1011.50,76010000,1011.50 1982-12-16,992.64,1004.42,983.35,990.25,73680000,990.25 1982-12-15,1009.38,1013.52,985.74,992.64,81030000,992.64 1982-12-14,1024.28,1047.28,1006.99,1009.38,98380000,1009.38 1982-12-13,1018.76,1030.91,1013.34,1024.28,63140000,1024.28 1982-12-10,1027.96,1038.36,1009.47,1018.76,86430000,1018.76 1982-12-09,1047.09,1049.39,1020.79,1027.96,90320000,1027.96 1982-12-08,1056.94,1069.72,1041.30,1047.09,97430000,1047.09 1982-12-07,1055.65,1071.10,1045.07,1056.94,111620000,1056.94 1982-12-06,1031.36,1061.26,1020.88,1055.65,83880000,1055.65 1982-12-03,1033.11,1046.82,1027.04,1031.36,71540000,1031.36 1982-12-02,1031.09,1047.37,1027.04,1033.11,77600000,1033.11 1982-12-01,1039.28,1055.00,1025.57,1031.09,107850000,1031.09 1982-11-30,1002.85,1042.40,998.34,1039.28,93470000,1039.28 1982-11-29,1007.36,1014.72,993.84,1002.85,61080000,1002.85 1982-11-26,1000.00,1012.60,998.53,1007.36,38810000,1007.36 1982-11-24,990.99,1007.36,988.23,1000.00,67220000,1000.00 1982-11-23,1000.00,1007.63,986.66,990.99,72920000,990.99 1982-11-22,1021.25,1024.01,997.42,1000.00,74960000,1000.00 1982-11-19,1032.10,1042.86,1017.11,1021.25,70310000,1021.25 1982-11-18,1027.50,1040.47,1020.05,1032.10,77620000,1032.10 1982-11-17,1012.05,1032.74,1012.05,1027.50,84440000,1027.50 1982-11-16,1019.68,1019.68,993.10,1008.00,102910000,1008.00 1982-11-15,1032.56,1032.56,1012.60,1021.43,78900000,1021.43 1982-11-12,1054.73,1060.52,1035.60,1039.92,95080000,1039.92 1982-11-11,1044.52,1057.03,1030.35,1054.73,78410000,1054.73 1982-11-10,1060.25,1078.27,1037.71,1044.52,113240000,1044.52 1982-11-09,1037.44,1065.86,1034.86,1060.25,111220000,1060.25 1982-11-08,1048.57,1048.57,1029.25,1037.44,75240000,1037.44 1982-11-05,1050.22,1061.17,1040.65,1051.78,96550000,1051.78 1982-11-04,1065.49,1078.46,1042.59,1050.22,149350000,1050.22 1982-11-03,1022.08,1068.16,1021.71,1065.49,137010000,1065.49 1982-11-02,1007.45,1036.98,1007.45,1022.08,104770000,1022.08 1982-11-01,991.72,1009.01,983.72,1005.70,73530000,1005.70 1982-10-29,990.99,999.45,977.92,991.72,74830000,991.72 1982-10-28,1006.35,1011.87,989.33,990.99,73590000,990.99 1982-10-27,1006.07,1019.87,996.87,1006.35,81670000,1006.35 1982-10-26,995.13,1011.13,975.90,1006.07,102080000,1006.07 1982-10-25,1018.76,1018.76,991.91,995.13,83720000,995.13 1982-10-22,1036.98,1051.88,1024.37,1031.46,101120000,1031.46 1982-10-21,1034.12,1049.12,1018.40,1036.98,122460000,1036.98 1982-10-20,1013.80,1035.23,1005.98,1034.12,98680000,1034.12 1982-10-19,1019.22,1031.09,1001.66,1013.80,100850000,1013.80 1982-10-18,993.10,1023.45,991.63,1019.22,83790000,1019.22 1982-10-15,996.87,1003.86,981.88,993.10,80290000,993.10 1982-10-14,1015.18,1020.97,991.17,996.87,107530000,996.87 1982-10-13,1003.68,1033.57,991.63,1015.18,139800000,1015.18 1982-10-12,1012.79,1026.95,992.00,1003.68,126310000,1003.68 1982-10-11,991.54,1027.59,991.54,1012.79,138530000,1012.79 1982-10-08,965.97,992.92,961.64,986.85,122250000,986.85 1982-10-07,950.24,972.87,950.24,965.97,147070000,965.97 1982-10-06,907.74,946.38,907.74,944.26,93570000,944.26 1982-10-05,903.61,917.77,899.47,907.19,69770000,907.19 1982-10-04,907.74,908.57,892.02,903.61,55650000,903.61 1982-10-01,896.25,910.87,892.02,907.74,65000000,907.74 1982-09-30,906.27,908.20,891.28,896.25,62610000,896.25 1982-09-29,919.33,920.71,901.12,906.27,62550000,906.27 1982-09-28,920.90,930.74,916.02,919.33,65900000,919.33 1982-09-27,919.52,925.04,909.86,920.90,44840000,920.90 1982-09-24,925.77,926.42,913.45,919.52,54600000,919.52 1982-09-23,927.61,933.50,915.38,925.77,68260000,925.77 1982-09-22,934.79,951.16,924.67,927.61,113150000,927.61 1982-09-21,916.30,937.09,913.91,934.79,82920000,934.79 1982-09-20,916.94,921.45,904.71,916.30,58520000,916.30 1982-09-17,927.80,931.29,912.71,916.94,63950000,916.94 1982-09-16,930.46,938.47,922.46,927.80,78900000,927.80 1982-09-15,923.01,933.13,915.56,930.46,69680000,930.46 1982-09-14,918.69,933.13,914.92,923.01,83070000,923.01 1982-09-13,906.82,921.08,898.36,918.69,59520000,918.69 1982-09-10,912.53,912.90,897.08,906.82,71080000,906.82 1982-09-09,915.75,925.31,906.27,912.53,73090000,912.53 1982-09-08,914.28,927.34,906.82,915.75,77960000,915.75 1982-09-07,925.13,928.35,906.92,914.28,68960000,914.28 1982-09-03,913.54,940.49,913.54,925.13,130910000,925.13 1982-09-02,895.05,913.17,888.70,909.40,74740000,909.40 1982-09-01,901.31,911.33,890.91,895.05,82830000,895.05 1982-08-31,893.30,910.96,887.97,901.31,86360000,901.31 1982-08-30,883.47,895.42,872.42,893.30,59560000,893.30 1982-08-27,892.41,893.84,874.14,883.47,74410000,883.47 1982-08-26,884.89,908.96,882.61,892.41,137330000,892.41 1982-08-25,874.90,900.97,867.87,884.89,106200000,884.89 1982-08-24,891.17,893.36,869.01,874.90,121650000,874.90 1982-08-23,869.29,894.22,861.68,891.17,110310000,891.17 1982-08-20,840.85,871.19,840.85,869.29,95890000,869.29 1982-08-19,829.43,848.93,824.49,838.57,78270000,838.57 1982-08-18,831.24,858.54,826.10,829.43,132690000,829.43 1982-08-17,796.14,832.76,796.14,831.24,92860000,831.24 1982-08-16,788.53,803.84,788.53,792.43,55420000,792.43 1982-08-13,776.92,790.62,774.54,788.05,44720000,788.05 1982-08-12,777.21,786.15,773.59,776.92,50080000,776.92 1982-08-11,779.30,783.96,772.17,777.21,49040000,777.21 1982-08-10,780.35,789.10,775.68,779.30,52680000,779.30 1982-08-09,784.34,784.34,769.98,780.35,54560000,780.35 1982-08-06,795.85,798.99,781.77,784.34,48660000,784.34 1982-08-05,803.46,804.41,789.76,795.85,54700000,795.85 1982-08-04,815.35,815.35,800.89,803.46,53440000,803.46 1982-08-03,822.11,831.43,815.26,816.40,60480000,816.40 1982-08-02,808.60,824.11,807.84,822.11,53460000,822.11 1982-07-30,812.21,817.64,806.13,808.60,39270000,808.60 1982-07-29,811.83,817.54,801.46,812.21,55680000,812.21 1982-07-28,822.77,823.44,807.65,811.83,53830000,811.83 1982-07-27,825.44,831.05,818.02,822.77,45740000,822.77 1982-07-26,830.57,833.24,820.59,825.44,37740000,825.44 1982-07-23,832.00,838.47,824.68,830.57,47280000,830.57 1982-07-22,832.19,839.71,823.71,832.00,53870000,832.00 1982-07-21,833.43,843.80,828.20,832.19,66770000,832.19 1982-07-20,826.10,837.71,820.02,833.43,61060000,833.43 1982-07-19,828.67,836.66,822.68,826.10,53030000,826.10 1982-07-16,827.34,837.33,819.92,828.67,58740000,828.67 1982-07-15,828.39,836.57,821.25,827.34,61090000,827.34 1982-07-14,824.20,831.62,815.26,828.39,58160000,828.39 1982-07-13,824.87,832.95,816.97,824.20,66170000,824.20 1982-07-12,814.69,830.10,814.69,824.87,74690000,824.87 1982-07-09,804.98,818.59,803.37,814.12,65870000,814.12 1982-07-08,799.66,807.17,787.39,804.98,63270000,804.98 1982-07-07,798.90,804.70,793.19,799.66,46920000,799.66 1982-07-06,796.99,802.89,789.19,798.90,44350000,798.90 1982-07-02,803.18,803.18,792.52,796.99,43760000,796.99 1982-07-01,811.93,814.88,800.04,803.27,47900000,803.27 1982-06-30,812.21,821.63,807.84,811.93,65280000,811.93 1982-06-29,811.93,818.40,805.18,812.21,46990000,812.21 1982-06-28,803.08,816.69,800.51,811.93,40700000,811.93 1982-06-25,810.41,812.12,800.61,803.08,38740000,803.08 1982-06-24,813.17,821.63,805.56,810.41,55860000,810.41 1982-06-23,799.66,815.35,795.76,813.17,62710000,813.17 1982-06-22,789.95,801.46,787.67,799.66,55290000,799.66 1982-06-21,788.62,797.85,784.25,789.95,50370000,789.95 1982-06-18,791.48,793.57,784.53,788.62,53800000,788.62 1982-06-17,796.90,797.56,787.01,791.48,49230000,791.48 1982-06-16,801.27,809.17,793.85,796.90,56280000,796.90 1982-06-15,801.85,805.18,793.38,801.27,44970000,801.27 1982-06-14,809.74,810.22,798.61,801.85,40100000,801.85 1982-06-11,803.37,815.92,803.37,809.74,68610000,809.74 1982-06-10,795.57,803.37,790.53,798.71,50950000,798.71 1982-06-09,802.23,804.03,789.76,795.57,55770000,795.57 1982-06-08,804.03,809.84,799.28,802.23,46820000,802.23 1982-06-07,804.98,809.93,797.09,804.03,44630000,804.03 1982-06-04,816.50,818.87,802.42,804.98,44110000,804.98 1982-06-03,816.88,824.30,810.79,816.50,48450000,816.50 1982-06-02,814.97,822.39,810.88,816.88,49220000,816.88 1982-06-01,819.54,822.96,811.92,814.97,41650000,814.97 1982-05-28,824.96,828.86,815.54,819.54,43900000,819.54 1982-05-27,828.77,832.19,821.06,824.96,44730000,824.96 1982-05-26,834.57,836.85,824.20,828.77,51250000,828.77 1982-05-25,836.38,845.32,832.38,834.57,44010000,834.57 1982-05-24,835.90,840.09,830.10,836.38,38510000,836.38 1982-05-21,832.48,841.23,829.24,835.90,45260000,835.90 1982-05-20,835.90,839.71,827.62,832.48,48330000,832.48 1982-05-19,840.85,845.41,832.57,835.90,48840000,835.90 1982-05-18,845.32,848.08,836.66,840.85,48970000,840.85 1982-05-17,857.21,857.21,842.94,845.32,45600000,845.32 1982-05-14,859.11,864.54,853.88,857.78,49900000,857.78 1982-05-13,865.77,869.86,855.88,859.11,58230000,859.11 1982-05-12,865.87,874.52,858.92,865.77,59210000,865.77 1982-05-11,860.92,870.62,857.31,865.87,54680000,865.87 1982-05-10,869.20,870.24,857.97,860.92,46300000,860.92 1982-05-07,863.20,876.52,859.78,869.20,67130000,869.20 1982-05-06,856.35,867.96,856.35,863.20,67540000,863.20 1982-05-05,854.45,861.97,848.74,854.45,58860000,854.45 1982-05-04,849.03,860.16,848.17,854.45,58720000,854.45 1982-05-03,848.36,852.74,837.52,849.03,46490000,849.03 1982-04-30,844.94,852.55,841.70,848.36,48200000,848.36 1982-04-29,852.64,852.93,840.09,844.94,51330000,844.94 1982-04-28,857.50,861.49,845.99,852.64,50530000,852.64 1982-04-27,865.58,868.34,853.50,857.50,56480000,857.50 1982-04-26,862.16,871.19,856.45,865.58,60500000,865.58 1982-04-23,853.12,865.37,851.79,862.16,71840000,862.16 1982-04-22,843.70,857.02,843.70,853.12,64470000,853.12 1982-04-21,840.56,847.70,835.81,843.42,57820000,843.42 1982-04-20,846.08,848.93,836.38,840.56,54610000,840.56 1982-04-19,843.42,854.26,838.66,846.08,58470000,846.08 1982-04-16,839.61,848.36,836.85,843.42,55890000,843.42 1982-04-15,838.09,842.85,832.38,839.61,45700000,839.61 1982-04-14,841.04,844.46,831.91,838.09,45150000,838.09 1982-04-13,841.32,847.89,836.19,841.04,48660000,841.04 1982-04-12,842.94,847.32,836.38,841.32,46520000,841.32 1982-04-08,836.35,847.51,833.33,842.94,60190000,842.94 1982-04-07,839.33,845.03,832.48,836.35,53130000,836.35 1982-04-06,835.33,842.85,827.91,839.33,43200000,839.33 1982-04-05,838.57,843.89,830.96,835.33,46900000,835.33 1982-04-02,833.24,843.23,831.53,838.57,59800000,838.57 1982-04-01,822.77,836.66,820.49,833.24,57100000,833.24 1982-03-31,824.49,830.57,818.40,822.77,43300000,822.77 1982-03-30,823.82,829.72,816.97,824.49,43900000,824.49 1982-03-29,817.92,826.77,813.17,823.82,37100000,823.82 1982-03-26,827.44,827.44,814.12,817.92,42400000,817.92 1982-03-25,823.34,833.71,818.59,827.63,51970000,827.63 1982-03-24,826.67,831.81,819.92,823.34,49380000,823.34 1982-03-23,819.54,830.67,817.54,826.67,67130000,826.67 1982-03-22,805.65,824.01,804.79,819.54,57610000,819.54 1982-03-19,805.27,811.64,799.75,805.65,46250000,805.65 1982-03-18,795.85,808.41,795.00,805.27,54270000,805.27 1982-03-17,798.33,802.70,791.29,795.85,48900000,795.85 1982-03-16,800.99,808.41,795.57,798.33,48900000,798.33 1982-03-15,797.37,805.18,789.38,800.99,43370000,800.99 1982-03-12,805.56,806.32,792.05,797.37,49600000,797.37 1982-03-11,804.89,814.88,800.51,805.56,52960000,805.56 1982-03-10,803.84,815.26,797.85,804.89,59440000,804.89 1982-03-09,795.47,810.79,786.15,803.84,76060000,803.84 1982-03-08,807.36,819.82,794.52,795.47,67330000,795.47 1982-03-05,807.55,814.97,799.28,807.36,67440000,807.36 1982-03-04,815.16,819.82,800.70,807.55,74340000,807.55 1982-03-03,825.82,826.01,808.69,815.16,70230000,815.16 1982-03-02,828.39,840.66,821.54,825.82,63800000,825.82 1982-03-01,824.39,834.28,818.21,828.39,53010000,828.39 1982-02-26,825.82,831.24,817.83,824.39,43840000,824.39 1982-02-25,826.77,837.42,820.78,825.82,54160000,825.82 1982-02-24,812.98,829.72,806.51,826.77,64800000,826.77 1982-02-23,811.26,817.73,802.23,812.98,60100000,812.98 1982-02-22,824.30,835.81,809.55,811.26,58310000,811.26 1982-02-19,828.96,833.33,818.59,824.30,51340000,824.30 1982-02-18,827.63,836.95,824.01,828.96,60810000,828.96 1982-02-17,831.34,836.95,822.68,827.63,47660000,827.63 1982-02-16,833.81,834.67,817.26,831.34,48880000,831.34 1982-02-12,834.67,841.32,829.24,833.81,37070000,833.81 1982-02-11,836.66,841.42,827.25,834.67,46730000,834.67 1982-02-10,830.57,842.09,829.34,836.66,46620000,836.66 1982-02-09,833.43,838.47,824.11,830.57,54420000,830.57 1982-02-08,849.70,849.70,830.86,833.43,48500000,833.43 1982-02-05,847.03,858.26,842.94,851.03,53350000,851.03 1982-02-04,845.03,852.74,835.71,847.03,53300000,847.03 1982-02-03,852.55,858.26,841.89,845.03,49560000,845.03 1982-02-02,851.69,860.83,846.46,852.55,45020000,852.55 1982-02-01,866.34,866.34,848.08,851.69,47720000,851.69 1982-01-29,864.25,876.71,859.78,871.10,73400000,871.10 1982-01-28,845.32,867.20,845.32,864.25,66690000,864.25 1982-01-27,841.51,848.08,832.67,842.66,50060000,842.66 1982-01-26,842.75,849.79,836.76,841.51,44870000,841.51 1982-01-25,845.03,846.75,832.57,842.75,43170000,842.75 1982-01-22,848.27,853.31,839.80,845.03,44370000,845.03 1982-01-21,845.89,856.64,842.85,848.27,48610000,848.27 1982-01-20,847.41,853.50,838.95,845.89,48860000,845.89 1982-01-19,855.12,861.97,845.22,847.41,45070000,847.41 1982-01-18,847.60,857.78,838.47,855.12,44920000,855.12 1982-01-15,842.28,852.64,840.37,847.60,43310000,847.60 1982-01-14,838.95,848.36,834.09,842.28,42940000,842.28 1982-01-13,847.70,855.31,835.14,838.95,49130000,838.95 1982-01-12,850.46,856.07,842.66,847.70,49800000,847.70 1982-01-11,866.53,872.43,848.55,850.46,51900000,850.46 1982-01-08,861.78,872.15,858.92,866.53,42050000,866.53 1982-01-07,861.02,865.39,851.22,861.78,43410000,861.78 1982-01-06,865.30,868.72,853.41,861.02,51510000,861.02 1982-01-05,882.52,882.61,862.82,865.30,47510000,865.30 1982-01-04,875.00,887.37,871.86,882.52,36760000,882.52 1981-12-31,873.10,880.33,868.91,875.00,40780000,875.00 1981-12-30,868.25,879.76,865.96,873.10,42960000,873.10 1981-12-29,870.34,875.67,864.44,868.25,35300000,868.25 1981-12-28,873.38,878.04,867.77,870.34,28320000,870.34 1981-12-24,869.67,876.14,866.15,873.38,23940000,873.38 1981-12-23,871.96,877.28,865.39,869.67,42910000,869.67 1981-12-22,873.10,878.81,867.77,871.96,48320000,871.96 1981-12-21,875.76,879.57,868.63,873.10,41290000,873.10 1981-12-18,870.53,880.71,867.39,875.76,50940000,875.76 1981-12-17,868.72,874.71,862.82,870.53,47230000,870.53 1981-12-16,875.95,878.42,865.11,868.72,42770000,868.72 1981-12-15,871.48,880.33,867.77,875.95,44130000,875.95 1981-12-14,882.52,882.52,868.72,871.48,44740000,871.48 1981-12-11,892.03,897.45,883.37,886.51,45850000,886.51 1981-12-10,888.22,897.74,885.18,892.03,47020000,892.03 1981-12-09,881.75,891.46,879.19,888.22,44810000,888.22 1981-12-08,886.99,889.36,875.29,881.75,45140000,881.75 1981-12-07,892.69,897.17,883.37,886.99,45720000,886.99 1981-12-04,885.75,898.50,885.75,892.69,55040000,892.69 1981-12-03,882.61,888.32,875.86,883.85,43770000,883.85 1981-12-02,890.22,892.41,879.28,882.61,44510000,882.61 1981-12-01,888.98,896.12,881.37,890.22,53980000,890.22 1981-11-30,885.94,892.79,878.14,888.98,47580000,888.98 1981-11-27,878.14,890.89,875.76,885.94,32770000,885.94 1981-11-25,870.72,884.99,870.72,878.14,58570000,878.14 1981-11-24,851.79,873.29,850.17,870.24,53200000,870.24 1981-11-23,852.93,860.92,848.17,851.79,45250000,851.79 1981-11-20,844.75,858.16,841.80,852.93,52010000,852.93 1981-11-19,844.08,850.08,834.57,844.75,48890000,844.75 1981-11-18,850.17,854.26,839.99,844.08,49980000,844.08 1981-11-17,845.03,853.50,841.23,850.17,43190000,850.17 1981-11-16,853.79,853.79,839.04,845.03,43740000,845.03 1981-11-13,860.54,865.20,851.79,855.88,45550000,855.88 1981-11-12,857.12,869.01,854.07,860.54,55720000,860.54 1981-11-11,853.98,860.83,849.03,857.12,41920000,857.12 1981-11-10,855.21,865.58,849.12,853.98,53940000,853.98 1981-11-09,852.45,861.49,844.65,855.21,48310000,855.21 1981-11-06,859.11,861.21,847.89,852.45,43270000,852.45 1981-11-05,866.82,874.14,856.93,859.11,50860000,859.11 1981-11-04,868.72,876.05,859.30,866.82,53450000,866.82 1981-11-03,866.82,873.19,859.87,868.72,54620000,868.72 1981-11-02,855.97,872.53,855.97,866.82,65100000,866.82 1981-10-30,832.95,854.83,826.96,852.55,59570000,852.55 1981-10-29,837.61,842.47,826.58,832.95,40070000,832.95 1981-10-28,838.38,847.89,832.29,837.61,48100000,837.61 1981-10-27,830.96,846.94,828.01,838.38,53030000,838.38 1981-10-26,837.99,837.99,823.63,830.96,38210000,830.96 1981-10-23,847.60,847.60,833.14,837.99,41990000,837.99 1981-10-22,851.03,854.07,840.85,848.27,40630000,848.27 1981-10-21,851.88,861.97,846.46,851.03,48490000,851.03 1981-10-20,847.13,860.06,844.75,851.88,51530000,851.88 1981-10-19,851.69,853.88,840.09,847.13,41590000,847.13 1981-10-16,856.26,860.73,846.37,851.69,37800000,851.69 1981-10-15,850.65,861.49,845.61,856.26,42830000,856.26 1981-10-14,865.58,866.53,848.46,850.65,40260000,850.65 1981-10-13,869.48,876.05,859.59,865.58,43360000,865.58 1981-10-12,873.00,877.76,862.25,869.48,30030000,869.48 1981-10-09,878.14,885.84,866.34,873.00,50060000,873.00 1981-10-08,868.72,881.66,862.63,878.14,47090000,878.14 1981-10-07,856.26,871.58,853.98,868.72,50030000,868.72 1981-10-06,859.87,870.81,848.74,856.26,45460000,856.26 1981-10-05,860.73,873.95,854.83,859.87,51290000,859.87 1981-10-02,852.26,866.34,848.65,860.73,54540000,860.73 1981-10-01,849.98,855.88,840.47,852.26,41600000,852.26 1981-09-30,847.89,854.36,839.61,849.98,40700000,849.98 1981-09-29,842.56,858.83,837.80,847.89,49800000,847.89 1981-09-28,824.01,844.65,807.46,842.56,61320000,842.56 1981-09-25,834.47,834.47,815.37,824.01,54390000,824.01 1981-09-24,840.94,850.65,832.00,835.14,48880000,835.14 1981-09-23,845.70,847.51,827.25,840.94,52700000,840.94 1981-09-22,846.56,855.40,838.18,845.70,46830000,845.70 1981-09-21,836.19,851.69,829.43,846.56,44570000,846.56 1981-09-18,840.09,845.51,829.43,836.19,47350000,836.19 1981-09-17,851.59,858.26,837.33,840.09,48300000,840.09 1981-09-16,858.35,858.44,845.98,851.59,43660000,851.59 1981-09-15,866.15,872.53,856.74,858.35,38580000,858.35 1981-09-14,872.81,876.24,860.06,866.15,34040000,866.15 1981-09-11,862.44,875.48,857.21,872.81,42170000,872.81 1981-09-10,853.88,868.82,853.12,862.44,47430000,862.44 1981-09-09,851.12,861.30,844.94,853.88,43910000,853.88 1981-09-08,861.68,863.39,843.13,851.12,47340000,851.12 1981-09-04,867.01,869.96,856.16,861.68,42760000,861.68 1981-09-03,884.23,888.70,865.11,867.01,41730000,867.01 1981-09-02,882.71,892.41,879.28,884.23,37570000,884.23 1981-09-01,881.47,889.36,873.10,882.71,45110000,882.71 1981-08-31,892.22,900.88,879.09,881.47,40360000,881.47 1981-08-28,889.08,898.78,884.80,892.22,38020000,892.22 1981-08-27,899.26,900.49,883.66,889.08,43900000,889.08 1981-08-26,901.83,908.39,893.65,899.26,39980000,899.26 1981-08-25,900.11,904.30,887.46,901.83,54600000,901.83 1981-08-24,917.43,917.43,896.97,900.11,46750000,900.11 1981-08-21,928.37,930.65,917.14,920.57,37670000,920.57 1981-08-20,926.46,935.31,923.52,928.37,38270000,928.37 1981-08-19,924.37,932.08,918.38,926.46,39390000,926.46 1981-08-18,926.75,932.74,916.38,924.37,47270000,924.37 1981-08-17,936.93,939.40,924.37,926.75,40840000,926.75 1981-08-14,944.35,947.77,933.79,936.93,42580000,936.93 1981-08-13,945.21,952.91,938.55,944.35,42460000,944.35 1981-08-12,949.30,955.86,942.26,945.21,53650000,945.21 1981-08-11,943.68,955.48,939.50,949.30,52600000,949.30 1981-08-10,942.54,948.82,935.88,943.68,38370000,943.68 1981-08-07,952.91,954.15,938.45,942.54,38370000,942.54 1981-08-06,953.58,961.47,947.30,952.91,52070000,952.91 1981-08-05,945.97,958.81,942.16,953.58,54290000,953.58 1981-08-04,946.25,951.39,937.40,945.97,39460000,945.97 1981-08-03,952.34,955.48,940.45,946.25,39650000,946.25 1981-07-31,945.11,956.72,943.40,952.34,43480000,952.34 1981-07-30,937.40,948.25,934.36,945.11,41560000,945.11 1981-07-29,939.40,947.30,933.50,937.40,37610000,937.40 1981-07-28,945.87,948.15,934.65,939.40,38160000,939.40 1981-07-27,937.12,950.82,937.12,945.87,39610000,945.87 1981-07-24,928.56,941.78,926.94,936.74,38880000,936.74 1981-07-23,924.66,932.84,918.66,928.56,41790000,928.56 1981-07-22,934.46,942.07,922.37,924.66,47500000,924.66 1981-07-21,940.54,944.35,927.23,934.46,47280000,934.46 1981-07-20,954.81,954.81,937.02,940.54,40240000,940.54 1981-07-17,955.48,964.80,949.30,958.90,42780000,958.90 1981-07-16,954.15,960.52,947.11,955.48,39010000,955.48 1981-07-15,948.25,960.33,945.49,954.15,48950000,954.15 1981-07-14,954.34,956.53,941.50,948.25,45230000,948.25 1981-07-13,955.67,962.42,949.87,954.34,38100000,954.34 1981-07-10,959.00,963.38,950.15,955.67,39950000,955.67 1981-07-09,953.48,963.18,950.06,959.00,45510000,959.00 1981-07-08,954.15,961.28,944.06,953.48,46000000,953.48 1981-07-07,949.30,962.90,943.49,954.15,53560000,954.15 1981-07-06,957.95,957.95,941.97,949.30,44590000,949.30 1981-07-02,967.66,972.70,954.72,959.19,45100000,959.19 1981-07-01,976.88,978.98,963.28,967.66,49080000,967.66 1981-06-30,984.59,988.01,972.69,976.88,41550000,976.88 1981-06-29,992.87,996.39,981.16,984.59,37930000,984.59 1981-06-26,996.77,1001.81,988.49,992.87,39240000,992.87 1981-06-25,999.33,1007.99,992.58,996.77,43920000,996.77 1981-06-24,1006.66,1008.09,993.15,999.33,46650000,999.33 1981-06-23,994.20,1008.94,990.01,1006.66,51840000,1006.66 1981-06-22,996.19,1004.19,988.96,994.20,41790000,994.20 1981-06-19,995.15,1002.85,988.77,996.19,46430000,996.19 1981-06-18,1006.56,1011.80,990.96,995.15,48400000,995.15 1981-06-17,1003.33,1010.84,992.01,1006.56,55470000,1006.56 1981-06-16,1011.99,1017.50,997.90,1003.33,57780000,1003.33 1981-06-15,1006.85,1023.02,1006.85,1011.99,63350000,1011.99 1981-06-12,1007.42,1017.22,996.77,1006.28,60790000,1006.28 1981-06-11,993.88,1010.57,989.89,1007.42,59530000,1007.42 1981-06-10,994.44,1003.71,985.91,993.88,53200000,993.88 1981-06-09,995.64,1004.45,987.76,994.44,44600000,994.44 1981-06-08,993.79,1003.52,990.54,995.64,41580000,995.64 1981-06-05,986.74,999.44,981.18,993.79,47180000,993.79 1981-06-04,989.71,996.66,980.25,986.74,48940000,986.74 1981-06-03,987.48,993.14,976.82,989.71,54700000,989.71 1981-06-02,997.96,1003.15,984.70,987.48,53930000,987.48 1981-06-01,991.75,1010.48,988.97,997.96,62170000,997.96 1981-05-29,994.25,1003.15,985.44,991.75,51580000,991.75 1981-05-28,993.14,1002.97,982.66,994.25,59500000,994.25 1981-05-27,983.96,998.70,978.76,993.14,58730000,993.14 1981-05-26,971.72,987.20,965.69,983.96,42760000,983.96 1981-05-22,976.59,982.62,966.59,971.72,40710000,971.72 1981-05-21,976.86,984.06,969.11,976.59,46820000,976.59 1981-05-20,980.01,984.87,971.36,976.86,42370000,976.86 1981-05-19,985.77,988.29,972.26,980.01,42220000,980.01 1981-05-18,985.95,994.42,978.84,985.77,42510000,985.77 1981-05-15,973.07,990.09,971.72,985.95,45460000,985.95 1981-05-14,967.76,979.02,963.08,973.07,42750000,973.07 1981-05-13,970.82,978.12,961.82,967.76,42600000,967.76 1981-05-12,963.44,973.70,956.68,970.82,40440000,970.82 1981-05-11,976.40,979.47,959.83,963.44,37640000,963.44 1981-05-08,978.39,983.88,972.71,976.40,41860000,976.40 1981-05-07,973.34,981.99,969.29,978.39,42590000,978.39 1981-05-06,972.44,983.16,969.47,973.34,47100000,973.34 1981-05-05,979.11,979.38,964.52,972.44,49000000,972.44 1981-05-04,985.41,985.41,971.90,979.11,40430000,979.11 1981-05-01,997.75,1005.22,987.12,995.59,48360000,995.59 1981-04-30,1004.32,1010.90,991.89,997.75,47970000,997.75 1981-04-29,1016.93,1018.37,996.58,1004.32,53340000,1004.32 1981-04-28,1024.05,1029.63,1009.37,1016.93,58210000,1016.93 1981-04-27,1020.35,1030.98,1013.87,1024.05,51080000,1024.05 1981-04-24,1010.27,1024.68,1004.32,1020.35,60000000,1020.35 1981-04-23,1007.02,1022.33,1001.89,1010.27,64200000,1010.27 1981-04-22,1005.94,1013.96,996.13,1007.02,60660000,1007.02 1981-04-21,1015.94,1020.98,1001.44,1005.94,60280000,1005.94 1981-04-20,1005.58,1020.71,995.14,1015.94,51020000,1015.94 1981-04-16,1001.71,1012.79,995.23,1005.58,52950000,1005.58 1981-04-15,989.10,1004.41,987.03,1001.71,56040000,1001.71 1981-04-14,993.16,998.56,981.81,989.10,48350000,989.10 1981-04-13,1000.27,1003.51,987.66,993.16,49860000,993.16 1981-04-10,998.83,1009.01,990.63,1000.27,58130000,1000.27 1981-04-09,993.43,1004.50,984.87,998.83,59520000,998.83 1981-04-08,992.89,1000.45,987.84,993.43,48000000,993.43 1981-04-07,994.24,1004.41,987.03,992.89,44540000,992.89 1981-04-06,1004.59,1004.59,986.67,994.24,43190000,994.24 1981-04-03,1009.01,1017.02,1000.72,1007.11,48680000,1007.11 1981-04-02,1014.14,1020.62,1002.07,1009.01,52570000,1009.01 1981-04-01,1003.87,1020.62,1002.16,1014.14,54880000,1014.14 1981-03-31,996.58,1011.44,996.58,1003.87,50980000,1003.87 1981-03-30,994.78,1005.04,987.21,992.16,33500000,992.16 1981-03-27,1005.76,1008.29,990.00,994.78,46930000,994.78 1981-03-26,1015.22,1021.79,1000.81,1005.76,60370000,1005.76 1981-03-25,996.13,1016.48,992.71,1015.22,56320000,1015.22 1981-03-24,1004.23,1015.58,992.35,996.13,66400000,996.13 1981-03-23,992.80,1008.92,988.56,1004.23,57880000,1004.23 1981-03-20,986.58,1002.07,981.27,992.80,61980000,992.80 1981-03-19,994.06,1001.71,981.18,986.58,62440000,986.58 1981-03-18,992.53,1003.33,984.15,994.06,55740000,994.06 1981-03-17,1002.79,1011.08,986.22,992.53,65920000,992.53 1981-03-16,985.77,1005.40,979.38,1002.79,49940000,1002.79 1981-03-13,989.82,1002.70,981.09,985.77,68290000,985.77 1981-03-12,967.67,991.35,966.05,989.82,54640000,989.82 1981-03-11,972.67,978.30,959.11,967.67,47390000,967.67 1981-03-10,976.42,987.60,968.47,972.67,56610000,972.67 1981-03-09,964.62,981.22,962.79,976.42,46180000,976.42 1981-03-06,964.62,972.13,955.71,964.62,43940000,964.62 1981-03-05,971.44,977.11,961.39,964.62,45380000,964.62 1981-03-04,966.02,980.70,959.47,971.44,47260000,971.44 1981-03-03,977.99,982.01,961.65,966.02,48730000,966.02 1981-03-02,974.58,983.75,964.36,977.99,47710000,977.99 1981-02-27,966.81,980.87,960.60,974.58,53210000,974.58 1981-02-26,954.40,972.22,953.00,966.81,60300000,966.81 1981-02-25,946.10,958.51,932.22,954.40,45710000,954.40 1981-02-24,945.23,955.63,938.77,946.10,43960000,946.10 1981-02-23,936.09,952.22,930.64,945.23,39590000,945.23 1981-02-20,933.36,942.41,926.11,936.09,41900000,936.09 1981-02-19,947.10,952.05,930.29,933.36,41630000,933.36 1981-02-18,939.68,950.34,935.15,947.10,40410000,947.10 1981-02-17,931.57,944.28,930.38,939.68,37940000,939.68 1981-02-13,936.60,940.19,926.45,931.57,33360000,931.57 1981-02-12,942.49,947.53,933.02,936.60,34700000,936.60 1981-02-11,948.63,954.44,938.99,942.49,37770000,942.49 1981-02-10,947.18,955.12,940.02,948.63,40820000,948.63 1981-02-09,952.30,958.53,943.26,947.18,38330000,947.18 1981-02-06,946.76,959.98,944.20,952.30,45820000,952.30 1981-02-05,941.98,952.22,936.09,946.76,45320000,946.76 1981-02-04,941.38,948.21,933.28,941.98,45520000,941.98 1981-02-03,932.25,944.37,925.77,941.38,45950000,941.38 1981-02-02,947.10,947.10,923.89,932.25,44070000,932.25 1981-01-30,948.89,960.24,940.61,947.27,41160000,947.27 1981-01-29,942.58,955.63,937.12,948.89,38170000,948.89 1981-01-28,949.49,956.91,939.68,942.58,36690000,942.58 1981-01-27,938.91,954.69,935.92,949.49,42260000,949.49 1981-01-26,940.19,947.70,930.89,938.91,35380000,938.91 1981-01-23,940.44,947.10,934.30,940.19,37220000,940.19 1981-01-22,946.25,951.28,934.13,940.44,39880000,940.44 1981-01-21,950.68,954.01,938.48,946.25,39190000,946.25 1981-01-20,970.99,975.94,948.55,950.68,41750000,950.68 1981-01-19,973.29,980.38,965.36,970.99,36470000,970.99 1981-01-16,969.97,980.29,964.85,973.29,43260000,973.29 1981-01-15,966.47,975.17,959.30,969.97,39640000,969.97 1981-01-14,965.10,978.07,960.75,966.47,41390000,966.47 1981-01-13,968.77,971.25,956.48,965.10,40890000,965.10 1981-01-12,968.69,983.87,964.76,968.77,48760000,968.77 1981-01-09,965.70,977.05,957.76,968.69,50190000,968.69 1981-01-08,980.89,986.01,959.13,965.70,55350000,965.70 1981-01-07,986.35,986.35,962.63,980.89,92890000,980.89 1981-01-06,992.66,1013.14,986.26,1004.69,67400000,1004.69 1981-01-05,976.28,996.93,976.28,992.66,58710000,992.66 1981-01-02,963.99,975.68,958.70,972.78,28870000,972.78 1980-12-31,962.03,971.50,955.55,963.99,41210000,963.99 1980-12-30,960.58,969.54,952.99,962.03,39750000,962.03 1980-12-29,966.38,974.57,956.40,960.58,36060000,960.58 1980-12-26,963.05,969.37,958.45,966.38,16130000,966.38 1980-12-24,958.28,968.17,950.85,963.05,29490000,963.05 1980-12-23,958.79,971.25,949.49,958.28,55260000,958.28 1980-12-22,937.20,962.17,934.64,958.79,51950000,958.79 1980-12-19,930.20,945.31,924.57,937.20,50770000,937.20 1980-12-18,928.50,948.38,925.00,930.20,69570000,930.20 1980-12-17,918.09,933.96,913.05,928.50,50800000,928.50 1980-12-16,911.60,922.35,902.47,918.09,41630000,918.09 1980-12-15,917.15,927.65,907.85,911.60,39700000,911.60 1980-12-12,908.45,923.12,906.48,917.15,39530000,917.15 1980-12-11,916.21,918.52,894.45,908.45,60220000,908.45 1980-12-10,934.04,943.52,914.16,916.21,49860000,916.21 1980-12-09,933.70,944.28,921.59,934.04,53220000,934.04 1980-12-08,951.19,951.19,928.33,933.70,53390000,933.70 1980-12-05,970.48,972.61,951.45,956.23,51990000,956.23 1980-12-04,972.27,984.22,963.31,970.48,51170000,970.48 1980-12-03,974.40,981.57,963.57,972.27,43430000,972.27 1980-12-02,969.45,979.69,954.95,974.40,52340000,974.40 1980-12-01,991.13,991.13,966.38,969.45,48180000,969.45 1980-11-28,989.68,998.72,980.38,993.34,34240000,993.34 1980-11-26,982.68,1000.77,979.86,989.68,55340000,989.68 1980-11-25,978.75,993.52,973.04,982.68,55840000,982.68 1980-11-24,988.14,988.14,967.66,978.75,51120000,978.75 1980-11-21,1000.17,1004.69,984.30,989.93,55950000,989.93 1980-11-20,991.04,1004.61,984.90,1000.17,60180000,1000.17 1980-11-19,997.95,1009.39,983.36,991.04,69230000,991.04 1980-11-18,986.26,1005.20,985.92,997.95,70380000,997.95 1980-11-17,986.35,990.78,968.94,986.26,50260000,986.26 1980-11-14,982.42,997.35,973.21,986.35,71630000,986.35 1980-11-13,964.93,984.64,962.20,982.42,69340000,982.42 1980-11-12,944.03,968.86,943.77,964.93,58500000,964.93 1980-11-11,933.79,951.19,933.02,944.03,41520000,944.03 1980-11-10,932.42,940.44,926.71,933.79,35720000,933.79 1980-11-07,935.41,940.53,926.11,932.42,40070000,932.42 1980-11-06,950.43,950.43,932.08,935.41,48890000,935.41 1980-11-05,950.34,982.59,950.34,953.16,84080000,953.16 1980-11-03,924.49,941.30,924.49,937.20,35820000,937.20 1980-10-31,917.75,929.35,911.60,924.49,40110000,924.49 1980-10-30,929.18,932.51,915.02,917.75,39060000,917.75 1980-10-29,932.59,941.64,925.68,929.18,37200000,929.18 1980-10-28,931.74,937.54,922.78,932.59,40300000,932.59 1980-10-27,943.60,944.62,930.12,931.74,34430000,931.74 1980-10-24,939.51,947.35,931.06,943.60,41050000,943.60 1980-10-23,955.12,958.28,936.69,939.51,49200000,939.51 1980-10-22,954.44,961.77,947.87,955.12,43060000,955.12 1980-10-21,960.84,968.69,949.91,954.44,51220000,954.44 1980-10-20,956.14,964.42,946.59,960.84,40910000,960.84 1980-10-17,958.70,966.04,946.42,956.14,43920000,956.14 1980-10-16,972.44,987.29,956.57,958.70,65450000,958.70 1980-10-15,962.20,975.94,959.73,972.44,48260000,972.44 1980-10-14,959.90,971.67,957.08,962.20,48830000,962.20 1980-10-13,950.68,963.65,946.50,959.90,31360000,959.90 1980-10-10,958.96,965.70,946.25,950.68,44040000,950.68 1980-10-09,963.99,971.08,953.07,958.96,43980000,958.96 1980-10-08,960.67,971.42,955.29,963.99,46580000,963.99 1980-10-07,965.70,973.04,955.55,960.67,50310000,960.67 1980-10-06,950.85,969.62,950.85,965.70,50130000,965.70 1980-10-03,942.24,957.85,938.40,950.68,47510000,950.68 1980-10-02,939.42,948.21,931.31,942.24,46160000,942.24 1980-10-01,932.42,945.14,923.04,939.42,48720000,939.42 1980-09-30,921.93,937.20,921.59,932.42,40290000,932.42 1980-09-29,934.81,934.81,918.00,921.93,46410000,921.93 1980-09-26,952.65,952.65,934.98,940.10,49460000,940.10 1980-09-25,964.76,972.61,953.07,955.97,49510000,955.97 1980-09-24,962.03,972.78,952.73,964.76,56860000,964.76 1980-09-23,974.57,980.72,957.94,962.03,64390000,962.03 1980-09-22,963.74,977.05,955.29,974.57,53140000,974.57 1980-09-19,956.48,972.70,950.77,963.74,53780000,963.74 1980-09-18,961.26,972.01,950.26,956.48,63390000,956.48 1980-09-17,945.90,966.98,943.69,961.26,63990000,961.26 1980-09-16,937.63,953.07,935.32,945.90,57290000,945.90 1980-09-15,936.52,942.58,926.96,937.63,44630000,937.63 1980-09-12,941.30,945.48,932.51,936.52,47180000,936.52 1980-09-11,938.48,947.78,934.39,941.30,44770000,941.30 1980-09-10,934.73,946.16,930.63,938.48,51430000,938.48 1980-09-09,928.58,936.09,919.03,934.73,44460000,934.73 1980-09-08,940.96,945.48,925.34,928.58,42050000,928.58 1980-09-05,948.81,950.68,937.03,940.96,37990000,940.96 1980-09-04,953.16,964.85,942.92,948.81,59030000,948.81 1980-09-03,940.78,955.20,939.85,953.16,52370000,953.16 1980-09-02,932.59,944.80,928.16,940.78,35290000,940.78 1980-08-29,930.38,936.43,923.04,932.59,33510000,932.59 1980-08-28,943.09,944.03,927.22,930.38,39890000,930.38 1980-08-27,953.24,953.24,939.68,943.09,44000000,943.09 1980-08-26,956.23,964.59,949.91,953.41,41700000,953.41 1980-08-25,958.19,961.35,947.70,956.23,35400000,956.23 1980-08-22,955.03,969.45,952.73,958.19,58210000,958.19 1980-08-21,945.31,958.53,943.94,955.03,50770000,955.03 1980-08-20,939.85,948.98,934.47,945.31,42560000,945.31 1980-08-19,948.63,952.13,937.37,939.85,41930000,939.85 1980-08-18,961.95,961.95,944.97,948.63,41890000,948.63 1980-08-15,962.63,972.35,956.31,966.72,47780000,966.72 1980-08-14,949.23,965.36,943.69,962.63,47700000,962.63 1980-08-13,952.39,958.79,944.45,949.23,44350000,949.23 1980-08-12,964.08,969.97,948.72,952.39,52050000,952.39 1980-08-11,954.69,966.89,950.43,964.08,44690000,964.08 1980-08-08,950.94,965.87,949.74,954.69,58860000,954.69 1980-08-07,938.23,953.75,935.84,950.94,61820000,950.94 1980-08-06,929.78,941.04,923.63,938.23,45050000,938.23 1980-08-05,931.06,938.82,924.23,929.78,45510000,929.78 1980-08-04,931.48,935.24,918.52,931.06,41550000,931.06 1980-08-01,935.32,940.02,924.83,931.48,46440000,931.48 1980-07-31,936.18,939.51,918.77,935.32,54610000,935.32 1980-07-30,931.91,946.93,926.54,936.18,58060000,936.18 1980-07-29,925.43,935.15,921.33,931.91,44840000,931.91 1980-07-28,918.09,927.73,911.69,925.43,35330000,925.43 1980-07-25,925.34,925.34,913.23,918.09,36250000,918.09 1980-07-24,928.58,933.79,919.97,926.11,42420000,926.11 1980-07-23,927.30,937.71,920.99,928.58,45890000,928.58 1980-07-22,928.67,940.78,922.18,927.30,52230000,927.30 1980-07-21,923.98,933.28,916.38,928.67,42750000,928.67 1980-07-18,915.10,930.80,914.42,923.98,58040000,923.98 1980-07-17,904.44,916.64,902.05,915.10,48850000,915.10 1980-07-16,901.54,912.97,898.21,904.44,49140000,904.44 1980-07-15,905.55,916.04,899.23,901.54,60920000,901.54 1980-07-14,891.13,908.28,887.20,905.55,45500000,905.55 1980-07-11,885.92,895.22,880.80,891.13,38310000,891.13 1980-07-10,897.27,900.34,883.28,885.92,43730000,885.92 1980-07-09,897.35,908.87,892.58,897.27,52010000,897.27 1980-07-08,898.21,904.86,891.38,897.35,45830000,897.35 1980-07-07,888.91,900.77,886.86,898.21,42540000,898.21 1980-07-03,876.02,890.78,874.83,888.91,47230000,888.91 1980-07-02,872.27,880.46,867.06,876.02,42950000,876.02 1980-07-01,867.92,876.02,862.63,872.27,34340000,872.27 1980-06-30,880.89,880.89,864.33,867.92,29910000,867.92 1980-06-27,883.45,889.08,874.49,881.83,33110000,881.83 1980-06-26,887.54,896.33,880.03,883.45,45110000,883.45 1980-06-25,877.30,892.49,874.91,887.54,46500000,887.54 1980-06-24,873.81,881.31,867.15,877.30,37730000,877.30 1980-06-23,869.71,879.61,864.85,873.81,34180000,873.81 1980-06-20,870.90,875.09,863.31,869.71,36530000,869.71 1980-06-19,881.91,886.01,869.62,870.90,38280000,870.90 1980-06-18,879.27,885.32,870.14,881.91,41960000,881.91 1980-06-17,877.73,887.63,872.35,879.27,41990000,879.27 1980-06-16,876.37,883.19,868.77,877.73,36190000,877.73 1980-06-13,872.61,883.96,866.81,876.37,41880000,876.37 1980-06-12,872.70,881.40,863.05,872.61,47300000,872.61 1980-06-11,863.99,876.88,860.24,872.70,43800000,872.70 1980-06-10,860.67,870.73,855.20,863.99,42030000,863.99 1980-06-09,861.52,867.66,855.72,860.67,36820000,860.67 1980-06-06,858.70,867.06,853.07,861.52,37230000,861.52 1980-06-05,858.02,868.60,853.50,858.70,49070000,858.70 1980-06-04,843.77,860.49,842.75,858.02,44180000,858.02 1980-06-03,847.35,851.96,840.70,843.77,33150000,843.77 1980-06-02,850.85,857.94,842.92,847.35,32710000,847.35 1980-05-30,846.25,853.24,835.07,850.85,34820000,850.85 1980-05-29,860.32,863.65,844.71,846.25,42000000,846.25 1980-05-28,857.76,866.13,850.09,860.32,38580000,860.32 1980-05-27,854.10,864.42,851.28,857.76,40810000,857.76 1980-05-23,843.34,858.62,843.34,854.10,45790000,854.10 1980-05-22,831.06,848.63,828.84,842.92,41040000,842.92 1980-05-21,832.51,836.43,821.50,831.06,34830000,831.06 1980-05-20,830.89,837.12,825.60,832.51,31800000,832.51 1980-05-19,826.88,835.75,820.65,830.89,30970000,830.89 1980-05-16,822.53,829.52,819.11,826.88,31710000,826.88 1980-05-15,819.62,829.35,816.04,822.53,41120000,822.53 1980-05-14,816.89,827.73,813.74,819.62,40840000,819.62 1980-05-13,805.20,820.39,803.07,816.89,35460000,816.89 1980-05-12,805.80,810.32,795.82,805.20,28220000,805.20 1980-05-09,815.10,815.10,802.47,805.80,30280000,805.80 1980-05-08,821.25,827.47,811.01,815.19,39280000,815.19 1980-05-07,816.04,828.67,810.49,821.25,42600000,821.25 1980-05-06,816.30,827.65,808.28,816.04,40160000,816.04 1980-05-05,810.92,819.20,803.58,816.30,34090000,816.30 1980-05-02,808.79,815.70,802.99,810.92,28040000,810.92 1980-05-01,817.06,820.22,803.24,808.79,32480000,808.79 1980-04-30,811.09,818.52,801.02,817.06,30850000,817.06 1980-04-29,805.46,816.21,802.65,811.09,27940000,811.09 1980-04-28,803.58,814.68,798.72,805.46,30600000,805.46 1980-04-25,797.10,806.74,786.35,803.58,28590000,803.58 1980-04-24,789.25,804.95,785.24,797.10,35790000,797.10 1980-04-23,789.85,801.11,784.13,789.25,42620000,789.25 1980-04-22,771.33,793.43,771.33,789.85,47920000,789.85 1980-04-21,763.40,769.62,751.37,759.13,27560000,759.13 1980-04-18,768.86,775.94,760.32,763.40,26880000,763.40 1980-04-17,771.25,776.37,762.12,768.86,32770000,768.86 1980-04-16,783.36,794.88,769.80,771.25,39730000,771.25 1980-04-15,784.90,792.41,778.84,783.36,26670000,783.36 1980-04-14,791.55,791.81,779.52,784.90,23060000,784.90 1980-04-11,791.47,800.85,786.52,791.55,29960000,791.55 1980-04-10,785.92,796.42,783.02,791.47,33940000,791.47 1980-04-09,775.00,790.02,772.44,785.92,33020000,785.92 1980-04-08,768.34,779.61,759.81,775.00,31700000,775.00 1980-04-07,784.13,784.39,765.44,768.34,29130000,768.34 1980-04-03,787.80,791.98,778.24,784.13,27970000,784.13 1980-04-02,784.47,796.40,779.95,787.80,35210000,787.80 1980-04-01,785.75,792.15,776.28,784.47,32230000,784.47 1980-03-31,777.65,790.87,772.18,785.75,35840000,785.75 1980-03-28,759.98,784.39,756.57,777.65,46720000,777.65 1980-03-27,762.12,767.41,729.95,759.98,63680000,759.98 1980-03-26,767.83,781.66,758.79,762.12,37370000,762.12 1980-03-25,765.44,777.47,758.36,767.83,43790000,767.83 1980-03-24,784.98,784.98,761.69,765.44,39230000,765.44 1980-03-21,789.08,794.71,779.52,785.15,32220000,785.15 1980-03-20,800.94,804.61,785.92,789.08,32580000,789.08 1980-03-19,801.62,812.12,794.97,800.94,36520000,800.94 1980-03-18,788.65,806.66,780.97,801.62,47340000,801.62 1980-03-17,811.26,811.26,784.98,788.65,37020000,788.65 1980-03-14,809.56,819.11,800.68,811.69,35180000,811.69 1980-03-13,819.54,825.26,806.57,809.56,33070000,809.56 1980-03-12,826.45,829.86,808.70,819.54,37990000,819.54 1980-03-11,818.94,831.91,817.58,826.45,41350000,826.45 1980-03-10,820.56,828.84,807.25,818.94,43750000,818.94 1980-03-07,828.07,832.51,813.23,820.56,50950000,820.56 1980-03-06,844.88,848.12,822.44,828.07,49610000,828.07 1980-03-05,856.48,868.69,840.78,844.88,49240000,844.88 1980-03-04,854.35,859.90,842.75,856.48,44310000,856.48 1980-03-03,863.14,868.26,851.37,854.35,38690000,854.35 1980-02-29,854.44,866.55,850.85,863.14,38810000,863.14 1980-02-28,855.12,865.10,847.27,854.44,40330000,854.44 1980-02-27,864.25,875.26,850.09,855.12,46430000,855.12 1980-02-26,859.81,869.45,853.24,864.25,40000000,864.25 1980-02-25,868.77,868.94,854.61,859.81,39140000,859.81 1980-02-22,868.52,877.47,855.80,868.77,48210000,868.77 1980-02-21,886.86,891.13,863.99,868.52,51530000,868.52 1980-02-20,876.02,891.30,872.44,886.86,44340000,886.86 1980-02-19,883.96,883.96,869.37,876.02,39480000,876.02 1980-02-15,892.92,892.92,875.09,884.98,46680000,884.98 1980-02-14,903.84,912.03,886.86,893.77,50540000,893.77 1980-02-13,898.98,918.17,896.59,903.84,65230000,903.84 1980-02-12,889.59,901.37,880.97,898.98,48090000,898.98 1980-02-11,895.73,902.39,884.04,889.59,58660000,889.59 1980-02-08,885.49,901.11,879.86,895.73,57860000,895.73 1980-02-07,881.83,897.27,878.24,885.49,57690000,885.49 1980-02-06,876.62,888.05,867.92,881.83,51950000,881.83 1980-02-05,875.09,880.89,868.17,876.62,41880000,876.62 1980-02-04,881.48,887.37,870.48,875.09,43070000,875.09 1980-02-01,875.85,886.64,866.30,881.48,46610000,881.48 1980-01-31,881.91,897.87,873.04,875.85,65900000,875.85 1980-01-30,874.40,886.09,870.14,881.91,51170000,881.91 1980-01-29,878.50,885.67,864.59,874.40,55480000,874.40 1980-01-28,876.11,884.56,866.64,878.50,53620000,878.50 1980-01-25,879.95,882.25,869.03,876.11,47100000,876.11 1980-01-24,877.56,891.38,874.15,879.95,59070000,879.95 1980-01-23,866.21,883.02,859.39,877.56,50730000,877.56 1980-01-22,872.78,879.95,861.95,866.21,50620000,866.21 1980-01-21,867.15,880.03,863.65,872.78,48040000,872.78 1980-01-18,863.57,873.21,855.29,867.15,47150000,867.15 1980-01-17,865.19,872.95,857.00,863.57,54170000,863.57 1980-01-16,868.60,881.14,862.12,865.19,67700000,865.19 1980-01-15,863.57,873.81,855.89,868.60,52320000,868.60 1980-01-14,858.53,870.65,854.95,863.57,52930000,863.57 1980-01-11,858.96,868.17,848.89,858.53,52890000,858.53 1980-01-10,850.09,866.72,848.89,858.96,55980000,858.96 1980-01-09,851.71,865.70,846.76,850.09,65260000,850.09 1980-01-08,832.00,853.67,828.84,851.71,53390000,851.71 1980-01-07,828.84,839.85,824.74,832.00,44500000,832.00 1980-01-04,820.31,833.53,819.03,828.84,39130000,828.84 1980-01-03,824.57,827.73,809.04,820.31,50480000,820.31 1980-01-02,838.74,841.21,822.35,824.57,40610000,824.57 1979-12-31,838.91,843.17,834.39,838.74,31530000,838.74 1979-12-28,840.10,843.43,834.64,838.91,34430000,838.91 1979-12-27,838.14,842.83,834.47,840.10,31410000,840.10 1979-12-26,839.16,843.09,833.74,838.14,24960000,838.14 1979-12-24,838.91,842.32,833.19,839.16,19150000,839.16 1979-12-21,843.34,847.35,834.56,838.91,36160000,838.91 1979-12-20,838.91,848.55,835.32,843.34,40380000,843.34 1979-12-19,838.65,842.75,830.46,838.91,41780000,838.91 1979-12-18,844.62,849.15,835.32,838.65,43310000,838.65 1979-12-17,842.75,851.54,838.05,844.62,43830000,844.62 1979-12-14,836.09,846.93,833.28,842.75,41800000,842.75 1979-12-13,835.67,840.53,830.03,836.09,36690000,836.09 1979-12-12,833.70,840.87,830.20,835.67,34630000,835.67 1979-12-11,833.87,841.47,828.41,833.70,36160000,833.70 1979-12-10,833.19,837.29,826.62,833.87,32270000,833.87 1979-12-07,835.07,844.71,829.35,833.19,42370000,833.19 1979-12-06,828.41,837.46,826.19,835.07,37510000,835.07 1979-12-05,824.91,837.37,824.15,828.41,39300000,828.41 1979-12-04,819.62,828.33,818.09,824.91,33510000,824.91 1979-12-03,822.35,825.51,814.76,819.62,29030000,819.62 1979-11-30,830.80,830.80,819.88,822.35,30480000,822.35 1979-11-29,830.46,838.57,826.45,831.74,33550000,831.74 1979-11-28,825.85,835.92,818.09,830.46,39690000,830.46 1979-11-27,828.75,837.29,820.73,825.85,45140000,825.85 1979-11-26,813.82,833.11,813.82,828.75,47940000,828.75 1979-11-23,807.42,815.96,804.86,811.77,23300000,811.77 1979-11-21,809.22,810.49,793.60,807.42,37020000,807.42 1979-11-20,815.27,820.14,805.12,809.22,35010000,809.22 1979-11-19,815.70,822.95,810.07,815.27,33090000,815.27 1979-11-16,821.33,822.61,812.54,815.70,30060000,815.70 1979-11-15,816.55,827.56,813.57,821.33,32380000,821.33 1979-11-14,814.08,823.04,805.03,816.55,30970000,816.55 1979-11-13,821.93,825.85,811.52,814.08,29240000,814.08 1979-11-12,806.48,823.72,805.63,821.93,26640000,821.93 1979-11-09,799.91,812.29,799.91,806.48,30060000,806.48 1979-11-08,796.67,804.27,792.24,797.61,26270000,797.61 1979-11-07,805.20,805.20,793.43,796.67,30830000,796.67 1979-11-06,812.63,813.40,804.61,806.48,21960000,806.48 1979-11-05,818.94,819.37,808.45,812.63,20470000,812.63 1979-11-02,820.14,824.74,814.42,818.94,23670000,818.94 1979-11-01,815.70,823.63,809.73,820.14,25880000,820.14 1979-10-31,823.81,826.88,812.88,815.70,27780000,815.70 1979-10-30,808.62,824.66,805.80,823.81,28890000,823.81 1979-10-29,809.30,815.53,804.86,808.62,22720000,808.62 1979-10-26,808.46,814.68,801.62,809.30,29660000,809.30 1979-10-25,808.36,816.38,803.07,808.46,28440000,808.46 1979-10-24,806.83,816.64,803.24,808.36,31480000,808.36 1979-10-23,809.13,816.38,801.96,806.83,32910000,806.83 1979-10-22,813.91,813.91,795.99,809.13,45240000,809.13 1979-10-19,829.18,829.18,812.46,814.68,42430000,814.68 1979-10-18,830.72,838.74,826.71,830.12,29590000,830.12 1979-10-17,829.52,840.53,827.39,830.72,29650000,830.72 1979-10-16,831.06,838.51,825.68,829.52,33770000,829.52 1979-10-15,838.99,840.36,823.89,831.06,34850000,831.06 1979-10-12,844.62,852.90,835.67,838.99,36390000,838.99 1979-10-11,849.32,854.69,834.98,844.62,47530000,844.62 1979-10-10,855.03,855.03,826.54,849.32,81620000,849.32 1979-10-09,879.35,879.35,854.10,857.59,55560000,857.59 1979-10-08,897.61,900.26,882.59,884.04,32610000,884.04 1979-10-05,890.10,904.86,889.59,897.61,48250000,897.61 1979-10-04,885.15,895.82,882.25,890.10,38800000,890.10 1979-10-03,885.32,891.98,879.35,885.15,36470000,885.15 1979-10-02,872.95,889.16,868.77,885.32,38310000,885.32 1979-10-01,877.73,877.73,866.55,872.95,24980000,872.95 1979-09-28,887.46,889.93,875.00,878.58,35950000,878.58 1979-09-27,886.35,892.32,880.55,887.46,33110000,887.46 1979-09-26,886.18,898.63,883.02,886.35,37700000,886.35 1979-09-25,885.84,889.68,875.00,886.18,32410000,886.18 1979-09-24,893.94,896.59,882.85,885.84,33790000,885.84 1979-09-21,893.69,902.13,886.52,893.94,52380000,893.94 1979-09-20,876.45,894.62,870.99,893.69,45100000,893.69 1979-09-19,874.15,883.36,870.39,876.45,35370000,876.45 1979-09-18,881.31,882.00,869.45,874.15,38750000,874.15 1979-09-17,879.10,890.02,877.39,881.31,37610000,881.31 1979-09-14,870.73,884.56,868.60,879.10,41980000,879.10 1979-09-13,870.90,876.37,864.93,870.73,35240000,870.73 1979-09-12,869.71,874.91,862.97,870.90,39350000,870.90 1979-09-11,876.88,880.80,864.93,869.71,42530000,869.71 1979-09-10,874.15,881.06,870.14,876.88,32980000,876.88 1979-09-07,867.32,877.39,863.32,874.15,34360000,874.15 1979-09-06,866.13,874.74,862.63,867.32,30330000,867.32 1979-09-05,871.08,871.08,857.85,866.13,41650000,866.13 1979-09-04,887.63,887.63,871.16,872.61,33350000,872.61 1979-08-31,883.70,890.10,881.14,887.63,26370000,887.63 1979-08-30,884.90,887.63,879.52,883.70,29300000,883.70 1979-08-29,884.64,888.23,879.52,884.90,30810000,884.90 1979-08-28,885.41,889.68,881.40,884.64,29430000,884.64 1979-08-27,880.20,891.81,877.47,885.41,32050000,885.41 1979-08-24,880.38,883.87,872.18,880.20,32730000,880.20 1979-08-23,885.84,888.40,877.22,880.38,35710000,880.38 1979-08-22,886.01,890.02,879.44,885.84,38450000,885.84 1979-08-21,886.52,892.32,880.63,886.01,38860000,886.01 1979-08-20,883.36,890.27,878.07,886.52,32300000,886.52 1979-08-17,884.04,888.31,877.05,883.36,31630000,883.36 1979-08-16,885.84,893.60,878.75,884.04,47000000,884.04 1979-08-15,876.71,888.23,871.50,885.84,46130000,885.84 1979-08-14,875.26,880.72,868.69,876.71,40910000,876.71 1979-08-13,867.15,878.58,867.15,875.26,41980000,875.26 1979-08-10,858.28,869.54,852.30,867.06,36740000,867.06 1979-08-09,863.14,864.51,855.12,858.28,34630000,858.28 1979-08-08,859.81,870.14,857.42,863.14,44970000,863.14 1979-08-07,848.55,863.99,848.04,859.81,45410000,859.81 1979-08-06,846.16,850.77,839.08,848.55,27190000,848.55 1979-08-03,847.95,850.51,843.32,846.16,28160000,846.16 1979-08-02,850.34,855.03,844.28,847.95,37720000,847.95 1979-08-01,846.42,852.30,841.38,850.34,36570000,850.34 1979-07-31,838.74,849.06,837.80,846.42,34360000,846.42 1979-07-30,839.76,842.49,833.45,838.74,28640000,838.74 1979-07-27,839.76,842.66,833.28,839.76,27760000,839.76 1979-07-26,839.51,843.17,833.96,839.76,32270000,839.76 1979-07-25,829.78,840.78,829.18,839.51,34890000,839.51 1979-07-24,825.51,833.28,822.61,829.78,29690000,829.78 1979-07-23,828.07,829.69,819.97,825.51,26860000,825.51 1979-07-20,827.30,832.08,822.70,828.07,26360000,828.07 1979-07-19,828.58,834.04,822.78,827.30,26780000,827.30 1979-07-18,828.50,830.97,818.00,828.58,35950000,828.58 1979-07-17,834.90,836.35,824.66,828.50,34270000,828.50 1979-07-16,833.53,838.57,828.92,834.90,26620000,834.90 1979-07-13,836.86,837.88,827.47,833.53,33080000,833.53 1979-07-12,843.86,844.62,834.22,836.86,31780000,836.86 1979-07-11,849.40,849.40,839.16,843.86,36650000,843.86 1979-07-10,852.99,857.00,845.73,850.34,39730000,850.34 1979-07-09,846.16,856.57,844.28,852.99,42460000,852.99 1979-07-06,835.75,847.27,834.22,846.16,38570000,846.16 1979-07-05,835.58,840.02,830.97,835.75,30290000,835.75 1979-07-03,834.04,838.99,829.27,835.58,31670000,835.58 1979-07-02,840.61,840.61,830.46,834.04,32060000,834.04 1979-06-29,843.04,848.12,837.20,841.98,34690000,841.98 1979-06-28,840.52,848.84,836.97,843.04,38470000,843.04 1979-06-27,837.66,846.15,834.20,840.52,36720000,840.52 1979-06-26,844.25,849.19,834.46,837.66,34680000,837.66 1979-06-25,849.10,850.83,839.66,844.25,31330000,844.25 1979-06-22,843.64,853.06,842.34,849.10,36410000,849.10 1979-06-21,839.83,847.80,837.40,843.64,36490000,843.64 1979-06-20,839.40,843.56,836.11,839.83,33790000,839.83 1979-06-19,839.40,843.99,835.85,839.40,30780000,839.40 1979-06-18,843.30,845.20,836.28,839.40,30970000,839.40 1979-06-15,842.34,847.11,837.40,843.30,40740000,843.30 1979-06-14,842.17,844.07,834.29,842.34,37850000,842.34 1979-06-13,845.29,850.31,840.00,842.17,40740000,842.17 1979-06-12,837.58,851.61,837.14,845.29,45450000,845.29 1979-06-11,835.15,839.66,830.73,837.58,28270000,837.58 1979-06-08,836.97,839.48,831.25,835.15,31470000,835.15 1979-06-07,835.50,842.78,833.16,836.97,43380000,836.97 1979-06-06,831.34,841.04,829.26,835.50,39830000,835.50 1979-06-05,821.90,834.46,820.25,831.34,35050000,831.34 1979-06-04,821.21,825.36,817.83,821.90,24040000,821.90 1979-06-01,822.33,826.14,817.74,821.21,24560000,821.21 1979-05-31,822.16,827.01,815.14,822.33,30300000,822.33 1979-05-30,832.47,832.47,820.17,822.16,29250000,822.16 1979-05-29,836.28,837.75,829.26,832.55,27040000,832.55 1979-05-25,837.66,840.26,831.86,836.28,27810000,836.28 1979-05-24,837.40,842.69,832.38,837.66,25710000,837.66 1979-05-23,845.37,851.26,836.19,837.40,30390000,837.40 1979-05-22,842.43,848.41,837.23,845.37,30400000,845.37 1979-05-21,841.91,847.80,836.28,842.43,25550000,842.43 1979-05-18,842.95,848.32,837.40,841.91,26590000,841.91 1979-05-17,828.48,845.03,827.44,842.95,30550000,842.95 1979-05-16,825.88,832.47,821.03,828.48,28350000,828.48 1979-05-15,825.02,832.12,821.55,825.88,26190000,825.88 1979-05-14,830.56,834.03,823.02,825.02,22450000,825.02 1979-05-11,828.92,834.11,824.76,830.56,24010000,830.56 1979-05-10,838.62,839.92,827.53,828.92,25230000,828.92 1979-05-09,834.89,842.26,829.09,838.62,27670000,838.62 1979-05-08,833.42,838.10,823.63,834.89,32720000,834.89 1979-05-07,846.07,846.07,832.03,833.42,30480000,833.42 1979-05-04,857.59,859.23,845.89,847.54,30630000,847.54 1979-05-03,855.51,863.22,852.74,857.59,30870000,857.59 1979-05-02,855.51,860.27,849.97,855.51,30510000,855.51 1979-05-01,854.90,861.40,850.83,855.51,31040000,855.51 1979-04-30,856.64,859.49,847.28,854.90,26440000,854.90 1979-04-27,860.79,860.79,852.39,856.64,29610000,856.64 1979-04-26,867.46,869.02,858.71,860.97,32400000,860.97 1979-04-25,866.86,872.31,863.22,867.46,31750000,867.46 1979-04-24,860.10,873.35,858.54,866.86,35540000,866.86 1979-04-23,856.98,863.31,852.39,860.10,25610000,860.10 1979-04-20,855.25,861.57,848.93,856.98,28830000,856.98 1979-04-19,860.27,865.73,852.91,855.25,31150000,855.25 1979-04-18,857.93,865.90,856.38,860.27,29510000,860.27 1979-04-17,860.45,865.64,853.95,857.93,29260000,857.93 1979-04-16,868.42,868.42,856.81,860.45,28050000,860.45 1979-04-12,871.71,875.78,865.21,870.50,26780000,870.50 1979-04-11,878.72,884.62,868.68,871.71,32900000,871.71 1979-04-10,873.70,882.54,869.80,878.72,31900000,878.72 1979-04-09,875.69,879.07,869.46,873.70,27230000,873.70 1979-04-06,877.60,884.01,871.88,875.69,34710000,875.69 1979-04-05,869.80,880.02,866.68,877.60,34520000,877.60 1979-04-04,868.33,878.38,867.12,869.80,41940000,869.80 1979-04-03,855.25,870.67,854.21,868.33,33530000,868.33 1979-04-02,859.93,859.93,849.27,855.25,28990000,855.25 1979-03-30,866.77,870.58,858.11,862.18,29970000,862.18 1979-03-29,866.25,873.53,860.19,866.77,28510000,866.77 1979-03-28,871.36,876.99,863.83,866.25,39920000,866.25 1979-03-27,854.82,872.49,852.91,871.36,32940000,871.36 1979-03-26,859.75,860.01,851.52,854.82,23430000,854.82 1979-03-23,861.31,867.20,855.08,859.75,33570000,859.75 1979-03-22,857.76,867.46,856.03,861.31,34380000,861.31 1979-03-21,850.31,859.23,844.68,857.76,31120000,857.76 1979-03-20,857.59,858.89,847.45,850.31,27180000,850.31 1979-03-19,852.82,864.95,852.65,857.59,34620000,857.59 1979-03-16,847.02,856.72,843.21,852.82,31770000,852.82 1979-03-15,845.37,853.17,841.39,847.02,29370000,847.02 1979-03-14,846.93,852.56,841.74,845.37,24630000,845.37 1979-03-13,844.68,855.60,840.78,846.93,31170000,846.93 1979-03-12,842.86,846.33,833.85,844.68,25740000,844.68 1979-03-09,844.85,851.44,840.00,842.86,33410000,842.86 1979-03-08,834.29,846.41,831.69,844.85,32000000,844.85 1979-03-07,826.58,841.04,825.28,834.29,28930000,834.29 1979-03-06,827.36,831.34,821.55,826.58,24490000,826.58 1979-03-05,818.00,832.55,818.00,827.36,25690000,827.36 1979-03-02,815.84,820.69,811.50,815.75,23130000,815.75 1979-03-01,808.82,818.17,807.26,815.84,23830000,815.84 1979-02-28,807.00,811.76,802.23,808.82,25090000,808.82 1979-02-27,821.12,821.12,803.53,807.00,31470000,807.00 1979-02-26,823.28,826.40,818.35,821.12,22620000,821.12 1979-02-23,828.57,828.83,819.99,823.28,22750000,823.28 1979-02-22,834.55,834.98,825.10,828.57,26290000,828.57 1979-02-21,834.55,841.56,830.91,834.55,26050000,834.55 1979-02-20,827.01,836.19,824.15,834.55,22010000,834.55 1979-02-16,829.09,831.69,823.54,827.01,21110000,827.01 1979-02-15,829.78,831.25,822.68,829.09,22550000,829.09 1979-02-14,830.21,836.88,825.71,829.78,27220000,829.78 1979-02-13,826.14,836.19,826.14,830.21,28470000,830.21 1979-02-12,822.23,827.62,816.61,824.84,20610000,824.84 1979-02-09,818.87,826.49,817.05,822.23,24320000,822.23 1979-02-08,816.01,823.02,812.89,818.87,23360000,818.87 1979-02-07,822.85,823.46,810.81,816.01,28450000,816.01 1979-02-06,823.98,828.48,819.21,822.85,23570000,822.85 1979-02-05,830.65,830.65,819.13,823.98,26490000,823.98 1979-02-02,840.87,843.38,832.47,834.63,25350000,834.63 1979-02-01,839.22,843.99,832.55,840.87,27930000,840.87 1979-01-31,851.78,853.52,835.67,839.22,30330000,839.22 1979-01-30,855.77,861.83,848.75,851.78,26910000,851.78 1979-01-29,859.75,862.96,851.61,855.77,24170000,855.77 1979-01-26,854.64,865.04,853.26,859.75,34230000,859.75 1979-01-25,846.41,858.11,843.90,854.64,31440000,854.64 1979-01-24,846.85,856.81,840.61,846.41,31730000,846.41 1979-01-23,838.53,851.35,835.67,846.85,30130000,846.85 1979-01-22,837.49,841.74,829.95,838.53,24390000,838.53 1979-01-19,839.14,846.67,833.94,837.49,26800000,837.49 1979-01-18,834.20,843.73,829.35,839.14,27260000,839.14 1979-01-17,835.59,839.05,825.80,834.20,25310000,834.20 1979-01-16,848.06,848.06,833.25,835.59,30340000,835.59 1979-01-15,836.28,851.00,831.69,848.67,27520000,848.67 1979-01-12,830.04,843.38,830.04,836.28,37120000,836.28 1979-01-11,824.93,829.44,817.31,828.05,24580000,828.05 1979-01-10,831.43,833.68,821.47,824.93,24990000,824.93 1979-01-09,828.14,836.80,825.80,831.43,27340000,831.43 1979-01-08,830.73,832.12,821.38,828.14,21440000,828.14 1979-01-05,826.14,837.23,823.89,830.73,28890000,830.73 1979-01-04,817.39,832.55,815.92,826.14,33290000,826.14 1979-01-03,811.42,822.68,811.42,817.39,29180000,817.39 1979-01-02,805.01,813.06,798.51,811.42,18340000,811.42 1978-12-29,805.96,812.20,800.50,805.01,30030000,805.01 1978-12-28,808.56,813.06,802.75,805.96,25440000,805.96 1978-12-27,815.32,815.32,804.57,808.56,23580000,808.56 1978-12-26,808.47,819.13,804.66,816.01,21470000,816.01 1978-12-22,795.05,811.16,795.05,808.47,23790000,808.47 1978-12-21,793.66,801.63,790.11,794.79,28670000,794.79 1978-12-20,789.85,797.90,785.69,793.66,26520000,793.66 1978-12-19,787.51,795.30,782.92,789.85,25960000,789.85 1978-12-18,794.87,794.87,781.01,787.51,32900000,787.51 1978-12-15,812.54,813.76,801.80,805.35,23620000,805.35 1978-12-14,809.86,814.97,804.40,812.54,20840000,812.54 1978-12-13,814.97,819.21,806.48,809.86,22480000,809.86 1978-12-12,817.65,821.90,811.50,814.97,22210000,814.97 1978-12-11,811.85,821.29,808.73,817.65,21000000,817.65 1978-12-08,816.09,819.56,807.95,811.85,18560000,811.85 1978-12-07,821.90,826.49,812.98,816.09,21170000,816.09 1978-12-06,820.51,829.87,815.23,821.90,29680000,821.90 1978-12-05,806.83,821.81,805.01,820.51,25670000,820.51 1978-12-04,811.50,814.80,802.23,806.83,22020000,806.83 1978-12-01,801.98,815.06,801.98,811.50,26830000,811.50 1978-11-30,790.11,800.94,786.64,799.03,19900000,799.03 1978-11-29,801.89,801.89,788.63,790.11,21160000,790.11 1978-11-28,813.84,817.91,802.67,804.14,22740000,804.14 1978-11-27,810.12,817.22,806.31,813.84,19790000,813.84 1978-11-24,807.00,812.98,803.36,810.12,14590000,810.12 1978-11-22,804.05,810.98,799.46,807.00,20010000,807.00 1978-11-21,805.61,810.55,799.98,804.05,20750000,804.05 1978-11-20,797.73,811.24,797.47,805.61,24440000,805.61 1978-11-17,794.18,804.49,792.19,797.73,25170000,797.73 1978-11-16,785.60,797.38,785.26,794.18,21340000,794.18 1978-11-15,785.26,798.08,782.66,785.60,26280000,785.60 1978-11-14,792.01,795.22,779.11,785.26,30610000,785.26 1978-11-13,806.83,806.83,790.71,792.01,20960000,792.01 1978-11-10,803.97,812.02,799.55,807.09,16750000,807.09 1978-11-09,807.61,815.75,798.86,803.97,23320000,803.97 1978-11-08,800.07,809.60,790.97,807.61,23560000,807.61 1978-11-07,808.13,808.13,793.92,800.07,25320000,800.07 1978-11-06,823.11,825.88,812.63,814.88,20450000,814.88 1978-11-03,816.96,829.00,809.51,823.11,25990000,823.11 1978-11-02,827.79,831.34,811.07,816.96,41030000,816.96 1978-11-01,805.53,831.69,805.53,827.79,50450000,827.79 1978-10-31,811.85,818.26,789.67,792.45,42720000,792.45 1978-10-30,806.05,814.36,782.05,811.85,59480000,811.85 1978-10-27,821.12,825.54,804.49,806.05,40360000,806.05 1978-10-26,830.21,835.41,816.61,821.12,31990000,821.12 1978-10-25,832.55,842.86,822.85,830.21,31380000,830.21 1978-10-24,839.66,846.93,830.35,832.55,28880000,832.55 1978-10-23,838.01,845.89,825.80,839.66,36090000,839.66 1978-10-20,846.41,847.37,830.47,838.01,43670000,838.01 1978-10-19,859.67,862.87,844.42,846.41,31810000,846.41 1978-10-18,866.34,871.19,853.60,859.67,32940000,859.67 1978-10-17,872.49,872.49,858.11,866.34,37870000,866.34 1978-10-16,894.84,894.84,874.39,875.17,24600000,875.17 1978-10-13,896.74,902.20,891.55,897.09,21920000,897.09 1978-10-12,901.42,909.39,892.84,896.74,30170000,896.74 1978-10-11,891.63,902.29,885.14,901.42,21740000,901.42 1978-10-10,893.19,899.26,887.56,891.63,25470000,891.63 1978-10-09,880.02,894.92,877.86,893.19,19720000,893.19 1978-10-06,876.47,885.14,873.79,880.02,27380000,880.02 1978-10-05,873.96,883.32,869.63,876.47,27820000,876.47 1978-10-04,867.90,875.52,860.10,873.96,25090000,873.96 1978-10-03,871.36,876.30,865.56,867.90,22540000,867.90 1978-10-02,865.82,874.48,863.13,871.36,18700000,871.36 1978-09-29,861.31,870.84,858.89,865.82,23610000,865.82 1978-09-28,860.19,864.43,854.90,861.31,24390000,861.31 1978-09-27,868.16,875.43,858.45,860.19,28370000,860.19 1978-09-26,862.35,872.66,859.67,868.16,26330000,868.16 1978-09-25,862.44,865.47,856.20,862.35,20970000,862.35 1978-09-22,861.14,868.16,855.42,862.44,27960000,862.44 1978-09-21,857.16,865.38,850.92,861.14,33640000,861.14 1978-09-20,861.57,870.50,853.95,857.16,35080000,857.16 1978-09-19,870.15,873.87,859.06,861.57,31660000,861.57 1978-09-18,878.55,884.88,866.86,870.15,35860000,870.15 1978-09-15,886.17,886.17,874.05,878.55,37290000,878.55 1978-09-14,899.60,900.21,885.48,887.04,37400000,887.04 1978-09-13,906.44,913.29,896.83,899.60,43340000,899.60 1978-09-12,907.74,910.26,899.43,906.44,34400000,906.44 1978-09-11,907.74,917.24,904.80,907.74,39670000,907.74 1978-09-08,895.62,909.91,895.62,907.74,42170000,907.74 1978-09-07,895.79,903.15,889.55,893.71,40310000,893.71 1978-09-06,887.91,902.03,887.91,895.79,42600000,895.79 1978-09-05,879.33,889.73,876.91,886.61,32170000,886.61 1978-09-01,876.82,884.88,871.36,879.33,35070000,879.33 1978-08-31,880.72,883.66,871.36,876.82,33850000,876.82 1978-08-30,880.20,888.17,873.61,880.72,37750000,880.72 1978-08-29,884.88,887.13,875.95,880.20,33780000,880.20 1978-08-28,895.53,895.70,882.62,884.88,31760000,884.88 1978-08-25,897.35,902.55,890.59,895.53,36190000,895.53 1978-08-24,897.00,904.80,890.94,897.35,38500000,897.35 1978-08-23,892.41,904.28,890.94,897.00,39630000,897.00 1978-08-22,888.95,896.05,881.15,892.41,29620000,892.41 1978-08-21,896.83,900.38,884.88,888.95,29440000,888.95 1978-08-18,900.12,909.22,892.93,896.83,34650000,896.83 1978-08-17,894.66,911.21,894.66,900.12,45270000,900.12 1978-08-16,887.13,898.30,884.88,894.58,36120000,894.58 1978-08-15,888.17,891.37,879.16,887.13,29760000,887.13 1978-08-14,890.85,899.17,884.27,888.17,32320000,888.17 1978-08-11,885.48,895.70,880.20,890.85,33550000,890.85 1978-08-10,891.63,898.39,880.20,885.48,39760000,885.48 1978-08-09,889.21,903.67,886.61,891.63,48800000,891.63 1978-08-08,885.05,891.55,877.51,889.21,34290000,889.21 1978-08-07,888.43,896.22,881.41,885.05,33350000,885.05 1978-08-04,886.87,895.79,879.33,888.43,37910000,888.43 1978-08-03,883.49,905.15,881.84,886.87,66370000,886.87 1978-08-02,860.71,884.88,857.50,883.49,47470000,883.49 1978-08-01,862.27,868.16,855.34,860.71,34810000,860.71 1978-07-31,856.29,866.34,852.56,862.27,33990000,862.27 1978-07-28,850.57,860.27,844.77,856.29,33390000,856.29 1978-07-27,847.19,857.16,843.04,850.57,33970000,850.57 1978-07-26,839.57,852.47,839.05,847.19,36830000,847.19 1978-07-25,831.60,841.65,827.18,839.57,25400000,839.57 1978-07-24,833.42,835.07,823.46,831.60,23280000,831.60 1978-07-21,838.62,842.00,828.83,833.42,26060000,833.42 1978-07-20,840.70,849.45,835.24,838.62,33350000,838.62 1978-07-19,829.00,842.52,828.05,840.70,30850000,840.70 1978-07-18,839.05,840.00,826.75,829.00,22860000,829.00 1978-07-17,839.83,848.58,835.59,839.05,29180000,839.05 1978-07-14,824.76,841.22,823.02,839.83,28370000,839.83 1978-07-13,824.93,827.88,818.09,824.76,23620000,824.76 1978-07-12,821.29,829.18,819.39,824.93,26640000,824.93 1978-07-11,816.79,826.32,814.62,821.29,27470000,821.29 1978-07-10,812.46,819.56,808.13,816.79,22470000,816.79 1978-07-07,807.17,816.18,805.79,812.46,23480000,812.46 1978-07-06,805.79,810.72,800.94,807.17,24990000,807.17 1978-07-05,812.62,812.62,802.15,805.79,23730000,805.79 1978-07-03,818.95,818.95,809.71,812.89,11560000,812.89 1978-06-30,821.64,823.20,815.06,818.95,18100000,818.95 1978-06-29,819.91,827.88,816.79,821.64,21660000,821.64 1978-06-28,817.31,824.24,811.59,819.91,23260000,819.91 1978-06-27,812.28,820.95,807.95,817.31,29280000,817.31 1978-06-26,823.02,824.15,810.03,812.28,29250000,812.28 1978-06-23,827.70,832.55,821.12,823.02,28530000,823.02 1978-06-22,824.93,831.77,822.16,827.70,27160000,827.70 1978-06-21,830.04,830.82,820.34,824.93,29100000,824.93 1978-06-20,838.62,840.44,828.40,830.04,27920000,830.04 1978-06-19,836.97,841.04,829.87,838.62,25500000,838.62 1978-06-16,844.25,846.85,834.98,836.97,27690000,836.97 1978-06-15,854.21,854.21,842.17,844.25,29280000,844.25 1978-06-14,856.98,865.82,850.57,854.56,37290000,854.56 1978-06-13,856.72,859.75,848.15,856.98,30760000,856.98 1978-06-12,859.23,866.94,853.34,856.72,24440000,856.72 1978-06-09,862.09,867.20,854.30,859.23,32470000,859.23 1978-06-08,861.92,871.88,856.46,862.09,39380000,862.09 1978-06-07,866.51,868.94,855.51,861.92,33060000,861.92 1978-06-06,863.83,879.33,863.22,866.51,51970000,866.51 1978-06-05,848.41,865.47,848.41,863.83,39580000,863.83 1978-06-02,840.70,849.79,838.62,847.54,31860000,847.54 1978-06-01,840.61,845.81,835.24,840.70,28750000,840.70 1978-05-31,834.20,846.85,832.99,840.61,29070000,840.61 1978-05-30,831.69,837.32,826.40,834.20,21040000,834.20 1978-05-26,835.41,836.37,827.79,831.69,21410000,831.69 1978-05-25,837.92,843.04,830.99,835.41,28410000,835.41 1978-05-24,842.86,842.86,829.87,837.92,31450000,837.92 1978-05-23,855.42,856.12,842.17,845.29,33230000,845.29 1978-05-22,846.85,857.76,842.34,855.42,28680000,855.42 1978-05-19,850.92,855.16,840.87,846.85,34360000,846.85 1978-05-18,858.37,863.57,848.67,850.92,42270000,850.92 1978-05-17,854.30,865.64,847.89,858.37,45490000,858.37 1978-05-16,848.15,861.05,848.15,854.30,48170000,854.30 1978-05-15,840.70,848.84,834.72,846.76,33890000,846.76 1978-05-12,834.20,847.54,834.11,840.70,46600000,840.70 1978-05-11,822.16,835.33,821.12,834.20,36630000,834.20 1978-05-10,822.07,829.61,817.22,822.16,33330000,822.16 1978-05-09,824.58,829.44,817.65,822.07,30860000,822.07 1978-05-08,829.09,837.14,822.77,824.58,34680000,824.58 1978-05-05,824.41,837.32,820.86,829.09,42680000,829.09 1978-05-04,828.83,829.09,813.84,824.41,37520000,824.41 1978-05-03,840.18,841.82,826.58,828.83,37560000,828.83 1978-05-02,844.33,847.54,833.42,840.18,41400000,840.18 1978-05-01,837.32,849.45,832.81,844.33,37020000,844.33 1978-04-28,826.92,838.79,822.16,837.32,32850000,837.32 1978-04-27,836.37,836.37,822.77,826.92,35470000,826.92 1978-04-26,833.59,846.15,828.48,836.97,44430000,836.97 1978-04-25,828.83,845.81,828.83,833.59,55800000,833.59 1978-04-24,812.80,827.36,810.38,826.06,34510000,826.06 1978-04-21,814.54,818.95,807.17,812.80,31540000,812.80 1978-04-20,810.38,825.10,810.38,814.54,43230000,814.54 1978-04-19,803.27,812.72,797.56,808.04,35060000,808.04 1978-04-18,810.12,814.97,798.15,803.27,38950000,803.27 1978-04-17,803.45,824.24,803.45,810.12,63510000,810.12 1978-04-14,780.41,797.73,780.41,795.13,52280000,795.13 1978-04-13,766.29,777.29,764.47,775.21,31580000,775.21 1978-04-12,770.18,772.96,764.30,766.29,26210000,766.29 1978-04-11,773.65,775.38,766.20,770.18,24300000,770.18 1978-04-10,769.58,776.16,766.11,773.65,25740000,773.65 1978-04-07,763.95,772.00,760.83,769.58,25160000,769.58 1978-04-06,763.08,768.10,759.62,763.95,27360000,763.95 1978-04-05,755.37,764.47,753.21,763.08,27260000,763.08 1978-04-04,751.04,757.19,748.79,755.37,20130000,755.37 1978-04-03,756.67,756.67,747.05,751.04,20230000,751.04 1978-03-31,759.62,761.78,753.12,757.36,20130000,757.36 1978-03-30,761.78,764.03,756.15,759.62,20460000,759.62 1978-03-29,758.84,765.42,755.80,761.78,25450000,761.78 1978-03-28,753.21,760.22,749.91,758.84,21600000,758.84 1978-03-27,756.50,758.14,750.52,753.21,18870000,753.21 1978-03-23,757.54,760.91,752.69,756.50,21290000,756.50 1978-03-22,762.82,764.38,754.50,757.54,21950000,757.54 1978-03-21,773.82,774.69,760.91,762.82,24410000,762.82 1978-03-20,768.88,777.81,768.88,773.82,28360000,773.82 1978-03-17,762.82,770.79,760.31,768.71,28470000,768.71 1978-03-16,758.58,764.03,754.42,762.82,25400000,762.82 1978-03-15,762.56,763.60,754.24,758.58,23340000,758.58 1978-03-14,759.96,764.99,752.86,762.56,24300000,762.56 1978-03-13,758.58,766.63,756.41,759.96,24070000,759.96 1978-03-10,750.09,760.91,750.09,758.58,27090000,758.58 1978-03-09,750.87,755.46,746.45,750.00,21820000,750.00 1978-03-08,746.79,752.86,743.76,750.87,22030000,750.87 1978-03-07,742.72,748.70,739.78,746.79,19900000,746.79 1978-03-06,746.97,746.97,740.12,742.72,17230000,742.72 1978-03-03,746.45,751.30,742.72,747.31,20120000,747.31 1978-03-02,743.33,749.13,739.78,746.45,20280000,746.45 1978-03-01,742.12,747.92,736.75,743.33,21010000,743.33 1978-02-28,748.35,748.61,739.17,742.12,19750000,742.12 1978-02-27,756.24,761.26,746.62,748.35,19990000,748.35 1978-02-24,750.95,760.40,750.78,756.24,22510000,756.24 1978-02-23,749.05,752.51,742.98,750.95,18720000,750.95 1978-02-22,749.31,753.55,746.71,749.05,18450000,749.05 1978-02-21,752.69,753.90,745.24,749.31,21890000,749.31 1978-02-17,753.29,759.96,748.18,752.69,18500000,752.69 1978-02-16,760.14,760.14,749.65,753.29,21570000,753.29 1978-02-15,765.16,767.07,758.32,761.69,20170000,761.69 1978-02-14,773.91,773.91,762.65,765.16,20470000,765.16 1978-02-13,775.99,777.37,770.44,774.43,16810000,774.43 1978-02-10,777.81,781.01,772.61,775.99,19480000,775.99 1978-02-09,782.66,783.00,774.43,777.81,17940000,777.81 1978-02-08,778.85,787.42,776.68,782.66,21300000,782.66 1978-02-07,768.62,780.23,768.62,778.85,14730000,778.85 1978-02-06,770.96,772.96,764.21,768.62,11630000,768.62 1978-02-03,775.38,776.59,766.98,770.96,19400000,770.96 1978-02-02,774.34,781.88,770.88,775.38,23050000,775.38 1978-02-01,769.92,777.89,764.81,774.34,22240000,774.34 1978-01-31,772.44,778.59,762.91,769.92,19870000,769.92 1978-01-30,764.12,774.95,761.09,772.44,17400000,772.44 1978-01-27,763.34,768.54,759.44,764.12,17600000,764.12 1978-01-26,772.44,775.81,761.00,763.34,19600000,763.34 1978-01-25,771.57,777.72,768.02,772.44,18690000,772.44 1978-01-24,770.70,776.42,765.68,771.57,18690000,771.57 1978-01-23,776.94,777.98,766.55,770.70,19380000,770.70 1978-01-20,778.67,780.15,772.52,776.94,7580000,776.94 1978-01-19,786.30,790.02,777.03,778.67,21500000,778.67 1978-01-18,779.02,788.20,776.25,786.30,21390000,786.30 1978-01-17,771.74,781.26,770.62,779.02,19360000,779.02 1978-01-16,775.73,777.81,767.41,771.74,18760000,771.74 1978-01-13,778.15,784.04,773.65,775.73,18010000,775.73 1978-01-12,775.90,785.00,772.78,778.15,22730000,778.15 1978-01-11,781.53,785.95,771.74,775.90,22880000,775.90 1978-01-10,784.56,790.89,777.55,781.53,25180000,781.53 1978-01-09,790.89,790.89,778.41,784.56,27990000,784.56 1978-01-06,803.36,803.36,788.29,793.49,26150000,793.49 1978-01-05,813.58,822.77,802.58,804.92,23570000,804.92 1978-01-04,817.48,817.48,804.92,813.58,24090000,813.58 1978-01-03,830.47,830.47,815.06,817.74,17720000,817.74 1977-12-30,830.39,835.15,825.80,831.17,23560000,831.17 1977-12-29,829.70,834.37,823.63,830.39,23610000,830.39 1977-12-28,829.70,833.33,822.77,829.70,19630000,829.70 1977-12-27,829.87,833.77,823.46,829.70,16750000,829.70 1977-12-23,822.16,832.64,822.16,829.87,20080000,829.87 1977-12-22,815.32,825.62,815.32,821.81,28100000,821.81 1977-12-21,806.22,817.83,805.35,813.93,24510000,813.93 1977-12-20,807.95,810.46,800.42,806.22,23250000,806.22 1977-12-19,815.32,817.31,806.13,807.95,21150000,807.95 1977-12-16,817.91,821.55,812.37,815.32,20270000,815.32 1977-12-15,822.68,825.10,815.23,817.91,21610000,817.91 1977-12-14,815.23,823.63,811.42,822.68,22110000,822.68 1977-12-13,815.75,818.61,809.94,815.23,19190000,815.23 1977-12-12,815.23,820.51,811.76,815.75,18180000,815.75 1977-12-09,806.91,819.04,806.65,815.23,19210000,815.23 1977-12-08,807.43,815.49,804.14,806.91,20400000,806.91 1977-12-07,806.91,812.54,802.06,807.43,21050000,807.43 1977-12-06,819.91,819.91,804.23,806.91,23770000,806.91 1977-12-05,823.98,826.84,818.78,821.03,19160000,821.03 1977-12-02,825.71,830.56,819.30,823.98,21160000,823.98 1977-12-01,829.70,832.81,823.02,825.71,24220000,825.71 1977-11-30,827.27,831.77,821.29,829.70,22670000,829.70 1977-11-29,839.48,839.48,824.24,827.27,22950000,827.27 1977-11-28,844.42,846.67,836.71,839.57,21570000,839.57 1977-11-25,843.30,847.63,838.70,844.42,17910000,844.42 1977-11-23,842.52,847.11,836.28,843.30,29150000,843.30 1977-11-22,836.11,846.15,834.63,842.52,28600000,842.52 1977-11-21,835.76,840.18,829.18,836.11,20110000,836.11 1977-11-18,831.86,840.26,829.18,835.76,23930000,835.76 1977-11-17,837.06,838.88,827.53,831.86,25110000,831.86 1977-11-16,842.78,846.24,834.03,837.06,24950000,837.06 1977-11-15,838.36,846.85,831.86,842.78,27740000,842.78 1977-11-14,845.89,849.01,834.46,838.36,23220000,838.36 1977-11-11,837.66,850.05,837.66,845.89,35260000,845.89 1977-11-10,818.43,836.11,814.10,832.55,31980000,832.55 1977-11-09,816.27,821.29,810.20,818.43,21330000,818.43 1977-11-08,816.44,821.29,810.81,816.27,19210000,816.27 1977-11-07,809.94,820.17,808.56,816.44,21270000,816.44 1977-11-04,802.67,814.02,802.41,809.94,21700000,809.94 1977-11-03,800.85,805.87,794.53,802.67,18090000,802.67 1977-11-02,806.91,809.51,797.73,800.85,20760000,800.85 1977-11-01,816.01,816.01,804.40,806.91,17170000,806.91 1977-10-31,822.68,824.93,813.93,818.35,17070000,818.35 1977-10-28,818.61,826.49,814.54,822.68,18050000,822.68 1977-10-27,813.41,825.71,809.42,818.61,21920000,818.61 1977-10-26,801.54,816.01,795.56,813.41,24860000,813.41 1977-10-25,802.32,805.35,792.79,801.54,23590000,801.54 1977-10-24,808.30,810.90,800.85,802.32,19210000,802.32 1977-10-21,814.80,815.75,804.57,808.30,20230000,808.30 1977-10-20,812.20,819.65,804.66,814.80,20520000,814.80 1977-10-19,820.51,823.20,809.08,812.20,22030000,812.20 1977-10-18,820.34,826.84,815.84,820.51,20130000,820.51 1977-10-17,821.64,824.93,813.76,820.34,17340000,820.34 1977-10-14,818.17,826.66,814.02,821.64,20410000,821.64 1977-10-13,823.98,824.67,811.42,818.17,23870000,818.17 1977-10-12,830.65,830.65,818.60,823.98,22440000,823.98 1977-10-11,840.26,841.39,830.47,832.29,17870000,832.29 1977-10-10,840.35,844.33,834.46,840.26,10580000,840.26 1977-10-07,842.08,845.98,836.11,840.35,16250000,840.35 1977-10-06,837.32,845.20,834.98,842.08,18490000,842.08 1977-10-05,842.00,843.73,832.38,837.32,18300000,837.32 1977-10-04,851.96,855.57,839.57,842.00,20850000,842.00 1977-10-03,847.11,853.60,842.08,851.96,19460000,851.96 1977-09-30,840.09,848.84,839.14,847.11,21170000,847.11 1977-09-29,834.72,843.56,832.55,840.09,21160000,840.09 1977-09-28,835.85,841.56,830.30,834.72,17960000,834.72 1977-09-27,841.65,845.55,831.95,835.85,19080000,835.85 1977-09-26,839.14,844.16,831.51,841.65,18230000,841.65 1977-09-23,839.41,844.77,834.81,839.14,18760000,839.14 1977-09-22,840.96,844.25,833.16,839.41,16660000,839.41 1977-09-21,851.78,856.29,838.79,840.96,22200000,840.96 1977-09-20,851.52,855.16,846.67,851.78,19030000,851.78 1977-09-19,856.81,857.42,848.23,851.52,16890000,851.52 1977-09-16,860.79,865.38,853.52,856.81,18340000,856.81 1977-09-15,858.71,866.16,855.51,860.79,18230000,860.79 1977-09-14,854.56,861.49,850.49,858.71,17330000,858.71 1977-09-13,854.38,859.58,848.49,854.56,14900000,854.56 1977-09-12,857.04,860.71,847.71,854.38,18700000,854.38 1977-09-09,865.47,865.47,853.17,857.04,18100000,857.04 1977-09-08,876.39,879.76,866.25,869.16,18290000,869.16 1977-09-07,873.27,878.98,869.80,876.39,18070000,876.39 1977-09-06,872.31,877.43,866.77,873.27,16130000,873.27 1977-09-02,864.86,873.79,862.44,872.31,15620000,872.31 1977-09-01,861.49,869.80,858.71,864.86,18820000,864.86 1977-08-31,858.89,862.87,850.92,861.49,19080000,861.49 1977-08-30,864.09,867.55,855.51,858.89,18220000,858.89 1977-08-29,855.77,866.77,855.77,864.09,15280000,864.09 1977-08-26,854.12,857.76,844.42,855.42,18480000,855.42 1977-08-25,862.87,863.13,851.18,854.12,19400000,854.12 1977-08-24,865.56,869.63,858.80,862.87,18170000,862.87 1977-08-23,867.29,875.61,862.70,865.56,20290000,865.56 1977-08-22,863.48,871.45,856.55,867.29,17870000,867.29 1977-08-19,864.26,870.06,856.64,863.48,20800000,863.48 1977-08-18,864.69,873.96,860.36,864.26,21040000,864.26 1977-08-17,869.28,872.75,859.58,864.69,20920000,864.69 1977-08-16,874.13,877.17,865.99,869.28,19340000,869.28 1977-08-15,871.10,877.60,864.09,874.13,15750000,874.13 1977-08-12,877.43,879.24,866.86,871.10,16870000,871.10 1977-08-11,887.04,891.46,876.04,877.43,21740000,877.43 1977-08-10,879.42,887.65,875.69,887.04,18280000,887.04 1977-08-09,879.42,884.53,873.70,879.42,19900000,879.42 1977-08-08,888.17,888.17,877.43,879.42,15870000,879.42 1977-08-05,888.17,894.84,884.36,888.69,19940000,888.69 1977-08-04,886.00,891.89,880.11,888.17,18870000,888.17 1977-08-03,887.39,888.95,877.25,886.00,21710000,886.00 1977-08-02,891.81,893.97,884.27,887.39,17910000,887.39 1977-08-01,890.07,900.03,886.17,891.81,17920000,891.81 1977-07-29,889.99,892.24,878.81,890.07,20350000,890.07 1977-07-28,888.43,893.71,879.76,889.99,26340000,889.99 1977-07-27,907.31,907.31,884.27,888.43,26440000,888.43 1977-07-26,914.24,914.33,902.98,908.18,21390000,908.18 1977-07-25,923.42,923.94,911.73,914.24,20430000,914.24 1977-07-22,921.78,927.84,916.75,923.42,23110000,923.42 1977-07-21,920.48,926.20,914.67,921.78,26880000,921.78 1977-07-20,919.27,927.75,915.45,920.48,29380000,920.48 1977-07-19,910.60,921.86,908.26,919.27,31930000,919.27 1977-07-18,905.95,915.02,901.25,910.60,29890000,910.60 1977-07-15,902.99,910.62,899.68,905.95,29120000,905.95 1977-07-13,903.41,906.80,896.29,902.99,23160000,902.99 1977-07-12,905.53,906.26,898.58,903.41,22470000,903.41 1977-07-11,907.99,910.96,900.27,905.53,19790000,905.53 1977-07-08,909.51,914.94,904.17,907.99,23820000,907.99 1977-07-07,907.73,913.42,903.49,909.51,21740000,909.51 1977-07-06,913.59,915.37,904.94,907.73,21230000,907.73 1977-07-05,912.65,919.01,907.90,913.59,16850000,913.59 1977-07-01,916.30,918.25,907.48,912.65,18160000,912.65 1977-06-30,913.33,920.88,909.09,916.30,19410000,916.30 1977-06-29,915.62,917.73,906.63,913.33,19000000,913.33 1977-06-28,924.10,926.98,914.01,915.62,22670000,915.62 1977-06-27,929.70,931.73,920.12,924.10,19870000,924.10 1977-06-24,925.37,933.77,924.02,929.70,27490000,929.70 1977-06-23,926.31,930.46,922.45,925.37,24330000,925.37 1977-06-22,928.60,930.89,921.13,926.31,25070000,926.31 1977-06-21,924.27,934.36,923.51,928.60,29730000,928.60 1977-06-20,920.45,926.98,916.89,924.27,22950000,924.27 1977-06-17,920.45,924.78,915.79,920.45,21960000,920.45 1977-06-16,917.57,924.53,910.53,920.45,24310000,920.45 1977-06-15,922.57,925.03,914.43,917.57,22640000,917.57 1977-06-14,912.40,924.27,912.14,922.57,25390000,922.57 1977-06-13,910.79,917.15,906.21,912.40,20250000,912.40 1977-06-10,909.85,915.20,904.77,910.79,20630000,910.79 1977-06-09,912.99,914.69,904.34,909.85,19940000,909.85 1977-06-08,908.67,918.25,906.21,912.99,22200000,912.99 1977-06-07,903.04,910.79,896.79,908.67,21110000,908.67 1977-06-06,912.23,916.13,901.03,903.04,18930000,903.04 1977-06-03,903.15,915.88,901.03,912.23,20330000,912.23 1977-06-02,906.55,912.91,899.42,903.15,18620000,903.15 1977-06-01,898.66,909.35,896.46,906.55,18320000,906.55 1977-05-31,898.83,904.77,892.55,898.66,17800000,898.66 1977-05-27,908.07,909.60,896.29,898.83,15730000,898.83 1977-05-26,903.24,910.45,899.17,908.07,18620000,908.07 1977-05-25,912.40,916.72,901.46,903.24,20710000,903.24 1977-05-24,917.06,917.83,906.55,912.40,20050000,912.40 1977-05-23,928.17,928.17,915.03,917.06,18290000,917.06 1977-05-20,936.48,937.16,925.71,930.46,18950000,930.46 1977-05-19,941.91,945.13,933.34,936.48,21280000,936.48 1977-05-18,936.48,947.34,935.46,941.91,27800000,941.91 1977-05-17,932.50,939.45,925.20,936.48,22290000,936.48 1977-05-16,928.34,938.43,926.73,932.50,21170000,932.50 1977-05-13,925.54,932.58,923.17,928.34,19780000,928.34 1977-05-12,926.90,930.04,917.74,925.54,21980000,925.54 1977-05-11,936.14,937.84,923.85,926.90,18980000,926.90 1977-05-10,933.09,941.40,930.55,936.14,21090000,936.14 1977-05-09,936.74,938.52,928.77,933.09,15230000,933.09 1977-05-06,943.27,943.27,932.24,936.74,19370000,936.74 1977-05-05,940.72,949.46,934.53,943.44,23450000,943.44 1977-05-04,934.19,944.96,929.44,940.72,23330000,940.72 1977-05-03,931.22,939.70,929.27,934.19,21950000,934.19 1977-05-02,926.90,934.02,923.00,931.22,17970000,931.22 1977-04-29,927.32,931.99,922.32,926.90,18330000,926.90 1977-04-28,923.76,931.14,919.78,927.32,18370000,927.32 1977-04-27,915.62,928.34,913.08,923.76,20590000,923.76 1977-04-26,914.60,922.74,910.36,915.62,20040000,915.62 1977-04-25,924.02,924.02,910.45,914.60,20440000,914.60 1977-04-22,935.13,935.13,923.59,927.07,20700000,927.07 1977-04-21,942.59,949.37,933.43,935.80,22740000,935.80 1977-04-20,938.77,948.69,933.43,942.59,25090000,942.59 1977-04-19,942.76,944.28,934.79,938.77,19510000,938.77 1977-04-18,947.76,951.32,939.28,942.76,17830000,942.76 1977-04-15,947.00,953.10,941.74,947.76,20230000,947.76 1977-04-14,943.69,956.07,943.69,947.00,30490000,947.00 1977-04-13,937.16,942.76,927.49,938.18,21800000,938.18 1977-04-12,924.69,940.98,924.69,937.16,23760000,937.16 1977-04-11,918.88,928.85,916.47,924.10,17650000,924.10 1977-04-07,914.73,921.21,910.57,918.88,17260000,918.88 1977-04-06,916.14,922.12,910.07,914.73,16600000,914.73 1977-04-05,915.56,920.88,909.74,916.14,18330000,916.14 1977-04-04,927.36,929.36,913.48,915.56,16250000,915.56 1977-04-01,919.55,930.27,919.55,927.36,17050000,927.36 1977-03-31,921.21,926.86,914.15,919.13,16510000,919.13 1977-03-30,932.01,935.84,917.64,921.21,18810000,921.21 1977-03-29,926.11,936.67,925.78,932.01,17030000,932.01 1977-03-28,928.86,931.27,920.71,926.11,16710000,926.11 1977-03-25,935.67,937.50,925.12,928.86,16550000,928.86 1977-03-24,942.32,944.48,931.93,935.67,19650000,935.67 1977-03-23,950.96,954.37,940.16,942.32,19360000,942.32 1977-03-22,953.54,955.95,944.65,950.96,18660000,950.96 1977-03-21,961.02,961.44,949.47,953.54,18040000,953.54 1977-03-18,964.84,967.50,956.95,961.02,19840000,961.02 1977-03-17,968.00,970.08,958.78,964.84,20700000,964.84 1977-03-16,965.01,971.58,961.44,968.00,22140000,968.00 1977-03-15,958.36,970.33,958.19,965.01,23940000,965.01 1977-03-14,947.72,960.19,944.73,958.36,19290000,958.36 1977-03-11,946.73,952.96,942.90,947.72,18230000,947.72 1977-03-10,942.90,948.89,938.00,946.73,18620000,946.73 1977-03-09,950.96,950.96,938.66,942.90,19680000,942.90 1977-03-08,955.12,960.36,949.47,952.04,19520000,952.04 1977-03-07,953.46,958.61,949.22,955.12,17410000,955.12 1977-03-04,948.64,956.28,947.39,953.46,18950000,953.46 1977-03-03,942.07,951.88,940.16,948.64,17560000,948.64 1977-03-02,944.73,949.97,938.50,942.07,18010000,942.07 1977-03-01,936.42,948.47,936.25,944.73,19480000,944.73 1977-02-28,933.43,938.50,928.61,936.42,16220000,936.42 1977-02-25,932.60,938.75,926.20,933.43,17610000,933.43 1977-02-24,938.25,940.24,927.69,932.60,19730000,932.60 1977-02-23,939.91,943.82,934.59,938.25,18240000,938.25 1977-02-22,940.24,946.06,933.84,939.91,17730000,939.91 1977-02-18,943.73,944.73,935.09,940.24,18040000,940.24 1977-02-17,948.30,950.71,939.58,943.73,19040000,943.73 1977-02-16,944.32,957.28,941.24,948.30,23430000,948.30 1977-02-15,938.33,948.39,937.08,944.32,21620000,944.32 1977-02-14,931.52,939.91,926.11,938.33,19230000,938.33 1977-02-11,937.92,940.91,926.03,931.52,20510000,931.52 1977-02-10,933.84,943.57,930.60,937.92,22340000,937.92 1977-02-09,942.24,944.98,928.27,933.84,23640000,933.84 1977-02-08,946.31,952.79,938.66,942.24,24040000,942.24 1977-02-07,947.89,954.70,941.82,946.31,20700000,946.31 1977-02-04,947.14,955.70,941.90,947.89,23130000,947.89 1977-02-03,952.79,954.95,941.99,947.14,23790000,947.14 1977-02-02,958.36,963.76,949.97,952.79,25700000,952.79 1977-02-01,954.37,962.02,950.05,958.36,23700000,958.36 1977-01-31,957.53,958.03,944.90,954.37,22920000,954.37 1977-01-28,954.54,961.85,949.38,957.53,22700000,957.53 1977-01-27,958.53,963.93,950.47,954.54,24360000,954.54 1977-01-26,965.92,968.33,953.13,958.53,27840000,958.53 1977-01-25,963.60,973.57,959.36,965.92,26340000,965.92 1977-01-24,962.43,968.83,956.87,963.60,22890000,963.60 1977-01-21,959.03,967.42,953.87,962.43,23930000,962.43 1977-01-20,968.67,973.82,954.70,959.03,26520000,959.03 1977-01-19,962.43,972.16,959.69,968.67,27120000,968.67 1977-01-18,967.25,970.08,958.53,962.43,24380000,962.43 1977-01-17,972.16,972.99,961.10,967.25,21060000,967.25 1977-01-14,976.15,979.22,967.00,972.16,24480000,972.16 1977-01-13,968.25,979.55,966.51,976.15,24780000,976.15 1977-01-12,976.23,976.23,962.52,968.25,22670000,968.25 1977-01-11,986.87,991.11,972.16,976.65,24100000,976.65 1977-01-10,983.13,990.69,979.31,986.87,20860000,986.87 1977-01-07,979.89,987.03,975.40,983.13,21720000,983.13 1977-01-06,978.06,989.03,974.07,979.89,23920000,979.89 1977-01-05,987.87,990.69,974.07,978.06,25010000,978.06 1977-01-04,999.75,1001.99,985.70,987.87,22740000,987.87 1977-01-03,1004.65,1007.81,994.18,999.75,21280000,999.75 1976-12-31,999.09,1006.32,997.34,1004.65,19170000,1004.65 1976-12-30,994.93,1005.49,991.69,999.09,23700000,999.09 1976-12-29,1000.08,1003.49,990.94,994.93,21910000,994.93 1976-12-28,996.09,1006.82,992.77,1000.08,25790000,1000.08 1976-12-27,985.62,997.92,982.71,996.09,20130000,996.09 1976-12-23,984.54,991.61,978.47,985.62,24560000,985.62 1976-12-22,978.39,993.35,977.73,984.54,26970000,984.54 1976-12-21,972.41,981.05,966.17,978.39,24390000,978.39 1976-12-20,979.06,981.96,969.00,972.41,20690000,972.41 1976-12-17,981.30,990.53,976.23,979.06,23870000,979.06 1976-12-16,983.79,988.20,973.90,981.30,23920000,981.30 1976-12-15,980.63,989.11,974.82,983.79,28300000,983.79 1976-12-14,974.24,983.13,966.92,980.63,25130000,980.63 1976-12-13,973.15,980.14,967.50,974.24,24830000,974.24 1976-12-10,970.74,978.31,965.59,973.15,25960000,973.15 1976-12-09,963.26,976.31,962.35,970.74,31800000,970.74 1976-12-08,960.69,966.01,953.54,963.26,24560000,963.26 1976-12-07,961.77,968.67,957.03,960.69,26140000,960.69 1976-12-06,950.55,966.59,948.72,961.77,24830000,961.77 1976-12-03,946.64,956.28,943.07,950.55,22640000,950.55 1976-12-02,949.38,956.62,944.07,946.64,23300000,946.64 1976-12-01,947.22,954.12,942.24,949.38,21960000,949.38 1976-11-30,950.05,952.13,941.41,947.22,17030000,947.22 1976-11-29,956.62,959.86,947.14,950.05,18750000,950.05 1976-11-26,950.96,959.28,947.97,956.62,15000000,956.62 1976-11-24,949.30,956.20,941.74,950.96,20420000,950.96 1976-11-23,955.87,958.94,945.98,949.30,19090000,949.30 1976-11-22,948.80,959.94,945.81,955.87,20930000,955.87 1976-11-19,950.13,957.86,942.49,948.80,24550000,948.80 1976-11-18,938.08,953.46,935.51,950.13,24000000,950.13 1976-11-17,935.34,943.90,930.44,938.08,19900000,938.08 1976-11-16,935.42,946.73,931.77,935.34,21020000,935.34 1976-11-15,927.69,937.25,921.63,935.42,16710000,935.42 1976-11-12,931.43,933.93,920.21,927.69,15550000,927.69 1976-11-11,924.04,932.85,917.97,931.43,13230000,931.43 1976-11-10,930.77,936.92,917.89,924.04,18890000,924.04 1976-11-09,933.68,939.33,924.45,930.77,19210000,930.77 1976-11-08,941.41,941.41,928.94,933.68,16520000,933.68 1976-11-05,960.44,962.93,940.24,943.07,20780000,943.07 1976-11-04,956.53,967.75,951.30,960.44,21700000,960.44 1976-11-03,960.44,960.44,944.73,956.53,19350000,956.53 1976-11-01,964.93,971.99,957.61,966.09,18390000,966.09 1976-10-29,952.63,966.26,947.47,964.93,17030000,964.93 1976-10-28,956.12,962.35,948.72,952.63,16920000,952.63 1976-10-27,948.14,959.77,944.56,956.12,15790000,956.12 1976-10-26,938.00,951.63,937.17,948.14,15490000,948.14 1976-10-25,938.75,942.65,932.51,938.00,13310000,938.00 1976-10-22,944.90,946.56,932.26,938.75,17870000,938.75 1976-10-21,954.87,960.77,942.74,944.90,17980000,944.90 1976-10-20,949.97,958.86,944.40,954.87,15860000,954.87 1976-10-19,946.56,953.87,938.66,949.97,16200000,949.97 1976-10-18,937.00,950.13,936.59,946.56,15710000,946.56 1976-10-15,935.92,942.74,928.27,937.00,16210000,937.00 1976-10-14,947.56,947.56,931.02,935.92,18610000,935.92 1976-10-13,932.35,950.38,932.01,948.30,21690000,948.30 1976-10-12,940.82,946.31,928.27,932.35,18210000,932.35 1976-10-11,948.88,948.88,934.26,940.82,14620000,940.82 1976-10-08,965.09,969.25,949.72,952.38,16740000,952.38 1976-10-07,959.69,968.50,951.71,965.09,19830000,965.09 1976-10-06,966.76,968.33,949.88,959.69,20870000,959.69 1976-10-05,977.98,979.97,960.69,966.76,19200000,966.76 1976-10-04,979.89,983.21,971.83,977.98,12630000,977.98 1976-10-01,990.19,995.60,974.40,979.89,20620000,979.89 1976-09-30,991.19,995.84,983.79,990.19,14700000,990.19 1976-09-29,994.93,1001.25,985.54,991.19,18090000,991.19 1976-09-28,1013.13,1014.38,992.11,994.93,20440000,994.93 1976-09-27,1009.31,1016.54,1004.40,1013.13,17430000,1013.13 1976-09-24,1010.80,1014.13,1001.75,1009.31,17400000,1009.31 1976-09-23,1014.05,1019.78,1005.32,1010.80,24210000,1010.80 1976-09-22,1014.79,1026.26,1009.56,1014.05,32970000,1014.05 1976-09-21,994.51,1016.54,993.60,1014.79,30300000,1014.79 1976-09-20,995.10,1002.74,990.69,994.51,21730000,994.51 1976-09-17,987.95,1000.50,986.62,995.10,28270000,995.10 1976-09-16,979.31,989.44,974.82,987.95,19620000,987.95 1976-09-15,978.64,983.96,971.24,979.31,17570000,979.31 1976-09-14,983.29,983.96,973.57,978.64,15550000,978.64 1976-09-13,988.36,994.02,980.30,983.29,16100000,983.29 1976-09-10,986.87,991.86,981.05,988.36,16930000,988.36 1976-09-09,992.94,993.43,983.05,986.87,16540000,986.87 1976-09-08,996.59,1001.41,987.87,992.94,19750000,992.94 1976-09-07,989.11,998.67,985.12,996.59,16310000,996.59 1976-09-03,984.79,991.19,979.22,989.11,13280000,989.11 1976-09-02,985.95,993.10,980.14,984.79,18920000,984.79 1976-09-01,973.74,987.95,971.24,985.95,18640000,985.95 1976-08-31,968.92,979.97,966.84,973.74,15480000,973.74 1976-08-30,963.93,972.91,961.44,968.92,11140000,968.92 1976-08-27,960.44,967.50,954.12,963.93,12120000,963.93 1976-08-26,970.83,975.90,958.28,960.44,15270000,960.44 1976-08-25,962.93,973.82,956.37,970.83,17400000,970.83 1976-08-24,971.49,977.14,960.77,962.93,16740000,962.93 1976-08-23,974.07,975.73,962.18,971.49,15450000,971.49 1976-08-20,982.63,982.63,970.99,974.07,14920000,974.07 1976-08-19,995.01,995.84,979.31,983.88,17230000,983.88 1976-08-18,999.34,1004.74,992.60,995.01,17150000,995.01 1976-08-17,992.77,1002.41,990.44,999.34,18500000,999.34 1976-08-16,990.19,997.51,986.95,992.77,16210000,992.77 1976-08-13,987.12,994.35,983.05,990.19,13930000,990.19 1976-08-12,986.79,992.10,979.22,987.12,15560000,987.12 1976-08-11,993.43,1000.00,984.46,986.79,18710000,986.79 1976-08-10,983.46,995.68,981.13,993.43,16690000,993.43 1976-08-09,986.00,987.53,979.06,983.46,11700000,983.46 1976-08-06,986.68,989.90,978.70,986.00,13930000,986.00 1976-08-05,992.28,995.76,983.28,986.68,15530000,986.68 1976-08-04,990.33,998.73,986.42,992.28,20650000,992.28 1976-08-03,982.26,992.96,978.70,990.33,18500000,990.33 1976-08-02,984.64,988.97,977.43,982.26,13870000,982.26 1976-07-30,979.29,987.95,974.71,984.64,14830000,984.64 1976-07-29,981.33,985.74,974.20,979.29,13330000,979.29 1976-07-28,984.13,984.89,974.71,981.33,16000000,981.33 1976-07-27,991.51,994.99,981.92,984.13,15580000,984.13 1976-07-26,990.91,997.20,985.91,991.51,13530000,991.51 1976-07-23,991.08,997.71,985.43,990.91,15870000,990.91 1976-07-22,989.44,995.99,982.97,991.08,15600000,991.08 1976-07-21,988.29,996.77,984.20,989.44,18350000,989.44 1976-07-20,990.83,994.43,983.06,988.29,18810000,988.29 1976-07-19,993.21,999.10,986.08,990.83,18200000,990.83 1976-07-16,997.30,997.30,985.43,993.21,20450000,993.21 1976-07-15,1005.16,1006.79,993.21,997.46,20400000,997.46 1976-07-14,1006.06,1012.20,997.95,1005.16,23840000,1005.16 1976-07-13,1011.21,1017.93,1001.64,1006.06,27550000,1006.06 1976-07-12,1003.11,1015.72,998.94,1011.21,23750000,1011.21 1976-07-09,991.98,1007.53,989.60,1003.11,23500000,1003.11 1976-07-08,991.16,998.85,987.15,991.98,21710000,991.98 1976-07-07,991.81,994.43,982.56,991.16,18470000,991.16 1976-07-06,999.84,1003.85,989.19,991.81,16130000,991.81 1976-07-02,994.84,1003.85,991.00,999.84,16730000,999.84 1976-07-01,1002.78,1009.00,990.26,994.84,21130000,994.84 1976-06-30,1000.65,1011.79,995.99,1002.78,23830000,1002.78 1976-06-29,997.38,1004.50,992.47,1000.65,19620000,1000.65 1976-06-28,999.84,1006.30,993.45,997.38,17490000,997.38 1976-06-25,1003.77,1008.35,995.58,999.84,17830000,999.84 1976-06-24,996.56,1009.09,994.52,1003.77,19850000,1003.77 1976-06-23,997.63,1002.05,987.23,996.56,17530000,996.56 1976-06-22,1007.45,1011.87,995.74,997.63,21150000,997.63 1976-06-21,1001.88,1010.97,997.54,1007.45,18930000,1007.45 1976-06-18,1003.19,1012.93,996.97,1001.88,25720000,1001.88 1976-06-17,988.62,1007.86,988.38,1003.19,27810000,1003.19 1976-06-16,985.92,995.66,979.94,988.62,21620000,988.62 1976-06-15,991.24,994.19,981.42,985.92,18440000,985.92 1976-06-14,979.78,995.17,979.78,991.24,21250000,991.24 1976-06-11,964.39,980.52,963.98,978.80,19470000,978.80 1976-06-10,958.09,967.99,956.12,964.39,16100000,964.39 1976-06-09,959.97,965.54,954.98,958.09,14560000,958.09 1976-06-08,958.09,968.48,956.45,959.97,16660000,959.97 1976-06-07,963.90,965.62,951.70,958.09,14510000,958.09 1976-06-04,973.80,973.97,961.28,963.90,15960000,963.90 1976-06-03,975.93,983.14,971.02,973.80,18900000,973.80 1976-06-02,973.13,979.37,968.57,975.93,16120000,975.93 1976-06-01,975.23,981.26,969.27,973.13,13880000,973.13 1976-05-28,965.57,978.60,962.92,975.23,16860000,975.23 1976-05-27,968.63,970.48,955.84,965.57,15310000,965.57 1976-05-26,971.69,976.43,963.48,968.63,16750000,968.63 1976-05-25,971.53,976.99,961.95,971.69,18770000,971.69 1976-05-24,988.82,988.82,969.03,971.53,16560000,971.53 1976-05-21,997.27,999.03,986.41,990.75,18730000,990.75 1976-05-20,988.90,1001.05,985.76,997.27,22560000,997.27 1976-05-19,989.45,996.14,983.99,988.90,18450000,988.90 1976-05-18,987.64,994.80,984.41,989.45,17410000,989.45 1976-05-17,992.60,993.47,982.05,987.64,14720000,987.64 1976-05-14,1000.24,1000.24,988.74,992.60,16800000,992.60 1976-05-13,1005.67,1008.66,997.48,1001.10,16730000,1001.10 1976-05-12,1006.61,1012.52,999.53,1005.67,18510000,1005.67 1976-05-11,1007.48,1015.82,1001.42,1006.61,23590000,1006.61 1976-05-10,996.22,1010.39,994.10,1007.48,22760000,1007.48 1976-05-07,989.53,999.53,984.97,996.22,17810000,996.22 1976-05-06,986.46,995.43,981.50,989.53,16200000,989.53 1976-05-05,993.70,997.09,982.53,986.46,14970000,986.46 1976-05-04,990.32,998.03,982.21,993.70,17240000,993.70 1976-05-03,995.83,995.83,981.74,990.32,15180000,990.32 1976-04-30,1002.13,1007.01,993.31,996.85,14530000,996.85 1976-04-29,1000.70,1010.39,996.62,1002.13,17740000,1002.13 1976-04-28,995.51,1002.36,987.09,1000.70,15790000,1000.70 1976-04-27,1002.76,1008.42,993.15,995.51,17760000,995.51 1976-04-26,1000.71,1005.20,991.03,1002.76,15520000,1002.76 1976-04-23,1007.71,1008.89,995.36,1000.71,17000000,1000.71 1976-04-22,1011.02,1017.71,1003.70,1007.71,20220000,1007.71 1976-04-21,1003.46,1016.85,1000.31,1011.02,26600000,1011.02 1976-04-20,998.51,1008.19,998.51,1003.46,23500000,1003.46 1976-04-19,980.48,991.18,979.16,988.11,16500000,988.11 1976-04-15,974.65,984.81,969.30,980.48,15100000,980.48 1976-04-14,984.26,990.24,972.76,974.65,18440000,974.65 1976-04-13,971.27,985.99,969.54,984.26,15990000,984.26 1976-04-12,968.28,978.90,963.00,971.27,16030000,971.27 1976-04-09,977.09,981.58,964.34,968.28,19050000,968.28 1976-04-08,986.22,987.80,968.99,977.09,20860000,977.09 1976-04-07,1001.65,1004.80,983.08,986.22,20190000,986.22 1976-04-06,1004.09,1015.35,998.90,1001.65,24170000,1001.65 1976-04-05,992.99,1008.74,992.99,1004.09,21940000,1004.09 1976-04-02,994.10,996.54,982.13,991.58,17420000,991.58 1976-04-01,999.45,1003.31,987.72,994.10,17910000,994.10 1976-03-31,992.13,1000.79,988.35,999.45,17520000,999.45 1976-03-30,997.40,1000.31,985.04,992.13,17930000,992.13 1976-03-29,1003.46,1007.40,993.78,997.40,16100000,997.40 1976-03-26,1002.13,1009.68,997.64,1003.46,18510000,1003.46 1976-03-25,1009.21,1014.72,997.72,1002.13,22510000,1002.13 1976-03-24,1001.65,1018.03,1001.65,1009.21,32610000,1009.21 1976-03-23,982.29,997.01,978.12,995.43,22450000,995.43 1976-03-22,979.85,988.27,977.64,982.29,19410000,982.29 1976-03-19,979.85,985.36,970.80,979.85,18090000,979.85 1976-03-18,985.99,988.98,971.35,979.85,20330000,979.85 1976-03-17,983.47,995.59,981.03,985.99,26190000,985.99 1976-03-16,974.50,986.62,970.09,983.47,22780000,983.47 1976-03-15,986.85,986.85,969.69,974.50,19570000,974.50 1976-03-12,1003.31,1006.61,984.49,987.64,26020000,987.64 1976-03-11,995.28,1008.42,992.76,1003.31,27300000,1003.31 1976-03-10,993.70,1003.15,987.17,995.28,24900000,995.28 1976-03-09,988.74,1005.67,987.88,993.70,31770000,993.70 1976-03-08,973.08,991.73,973.08,988.74,25060000,988.74 1976-03-05,970.64,981.03,965.37,972.92,23030000,972.92 1976-03-04,978.83,984.26,967.18,970.64,24410000,970.64 1976-03-03,985.12,988.99,973.00,978.83,25450000,978.83 1976-03-02,975.36,991.11,974.26,985.12,25590000,985.12 1976-03-01,972.61,981.19,964.18,975.36,22070000,975.36 1976-02-27,978.83,980.71,962.30,972.61,26940000,972.61 1976-02-26,994.57,1000.94,975.99,978.83,34320000,978.83 1976-02-25,993.55,1002.83,983.39,994.57,34680000,994.57 1976-02-24,985.28,1001.65,983.00,993.55,34380000,993.55 1976-02-23,987.80,993.39,977.25,985.28,31460000,985.28 1976-02-20,977.80,996.93,977.80,987.80,44510000,987.80 1976-02-19,961.74,979.85,961.74,975.76,39210000,975.76 1976-02-18,950.57,965.68,946.16,960.09,29900000,960.09 1976-02-17,958.36,963.48,946.63,950.57,25460000,950.57 1976-02-13,966.78,968.99,953.56,958.36,23870000,958.36 1976-02-12,971.90,978.12,963.00,966.78,28610000,966.78 1976-02-11,968.75,980.24,965.76,971.90,32300000,971.90 1976-02-10,957.18,971.74,953.09,968.75,27660000,968.75 1976-02-09,954.90,967.18,948.44,957.18,25340000,957.18 1976-02-06,964.81,965.60,948.84,954.90,27360000,954.90 1976-02-05,976.62,980.71,961.98,964.81,33780000,964.81 1976-02-04,972.61,981.66,966.94,976.62,38270000,976.62 1976-02-03,971.35,979.69,960.80,972.61,34080000,972.61 1976-02-02,975.28,976.54,962.06,971.35,24000000,971.35 1976-01-30,968.75,985.99,966.07,975.28,38510000,975.28 1976-01-29,951.35,970.80,948.13,968.75,29800000,968.75 1976-01-28,957.81,963.08,942.38,951.35,27370000,951.35 1976-01-27,961.51,973.16,950.80,957.81,32070000,957.81 1976-01-26,953.95,969.22,953.87,961.51,34470000,961.51 1976-01-23,943.48,958.38,940.57,953.95,33640000,953.95 1976-01-22,946.24,949.62,933.96,943.48,27420000,943.48 1976-01-21,949.86,954.97,934.35,946.24,34470000,946.24 1976-01-20,943.72,954.03,935.77,949.86,36690000,949.86 1976-01-19,929.63,946.08,923.80,943.72,29450000,943.72 1976-01-16,924.51,935.22,917.98,929.63,25940000,929.63 1976-01-15,929.63,940.26,921.21,924.51,38450000,924.51 1976-01-14,912.94,932.62,908.22,929.63,30340000,929.63 1976-01-13,922.39,930.26,909.40,912.94,34530000,912.94 1976-01-12,911.13,925.93,905.38,922.39,30440000,922.39 1976-01-09,907.98,916.88,903.73,911.13,26510000,911.13 1976-01-08,898.69,916.64,893.89,907.98,29030000,907.98 1976-01-07,890.82,908.69,886.41,898.69,33170000,898.69 1976-01-06,878.70,894.99,878.70,890.82,31270000,890.82 1976-01-05,858.71,879.80,858.63,877.83,21960000,877.83 1976-01-02,852.41,860.44,848.63,858.71,10300000,858.71 1975-12-31,852.41,859.65,848.71,852.41,16970000,852.41 1975-12-30,856.66,860.75,847.13,852.41,16040000,852.41 1975-12-29,859.81,866.11,853.59,856.66,17070000,856.66 1975-12-26,851.94,860.91,850.20,859.81,10020000,859.81 1975-12-24,845.01,854.93,845.01,851.94,11150000,851.94 1975-12-23,838.63,847.84,833.36,843.75,17750000,843.75 1975-12-22,844.38,847.29,835.33,838.63,15340000,838.63 1975-12-19,852.09,854.30,841.39,844.38,17720000,844.38 1975-12-18,846.27,857.13,843.12,852.09,18040000,852.09 1975-12-17,844.30,852.17,840.37,846.27,16560000,846.27 1975-12-16,836.59,849.73,833.91,844.30,18350000,844.30 1975-12-15,832.81,841.23,828.72,836.59,13960000,836.59 1975-12-12,832.73,836.74,825.53,832.81,13100000,832.81 1975-12-11,833.99,840.13,828.87,832.73,15300000,832.73 1975-12-10,824.15,835.72,820.92,833.99,15680000,833.99 1975-12-09,821.63,827.53,814.47,824.15,16040000,824.15 1975-12-08,818.80,826.43,812.81,821.63,14150000,821.63 1975-12-05,829.11,833.60,816.99,818.80,14050000,818.80 1975-12-04,825.49,833.67,818.17,829.11,16380000,829.11 1975-12-03,836.67,836.67,822.10,825.49,21320000,825.49 1975-12-02,856.34,856.66,841.70,843.20,17930000,843.20 1975-12-01,860.67,865.95,853.04,856.34,16050000,856.34 1975-11-28,858.55,865.24,854.06,860.67,12870000,860.67 1975-11-26,855.40,863.90,851.07,858.55,18780000,858.55 1975-11-25,845.64,859.10,845.56,855.40,17490000,855.40 1975-11-24,840.76,849.10,833.83,845.64,13930000,845.64 1975-11-21,843.51,848.39,834.62,840.76,14110000,840.76 1975-11-20,848.24,853.35,838.87,843.51,16460000,843.51 1975-11-19,855.24,857.53,842.25,848.24,16820000,848.24 1975-11-18,856.66,865.79,851.78,855.24,20760000,855.24 1975-11-17,853.67,862.56,847.61,856.66,17660000,856.66 1975-11-14,851.23,857.92,845.32,853.67,16460000,853.67 1975-11-13,852.25,863.11,848.47,851.23,25070000,851.23 1975-11-12,838.55,855.64,838.40,852.25,23960000,852.25 1975-11-11,835.48,843.28,831.63,838.55,14640000,838.55 1975-11-10,835.80,840.99,824.62,835.48,14910000,835.48 1975-11-07,840.92,843.83,830.29,835.80,15930000,835.80 1975-11-06,836.27,845.40,827.93,840.92,18600000,840.92 1975-11-05,830.13,843.91,829.50,836.27,17390000,836.27 1975-11-04,825.72,834.07,821.08,830.13,11570000,830.13 1975-11-03,836.04,836.82,822.26,825.72,11400000,825.72 1975-10-31,839.42,842.49,829.97,836.04,12910000,836.04 1975-10-30,838.63,847.29,832.97,839.42,15080000,839.42 1975-10-29,850.83,850.83,834.86,838.63,16110000,838.63 1975-10-28,838.48,853.67,837.53,851.46,17060000,851.46 1975-10-27,840.52,845.17,831.31,838.48,13100000,838.48 1975-10-24,855.16,857.76,837.22,840.52,18120000,840.52 1975-10-23,849.57,859.57,844.46,855.16,17900000,855.16 1975-10-22,846.82,855.09,840.37,849.57,16060000,849.57 1975-10-21,842.25,855.71,841.23,846.82,20800000,846.82 1975-10-20,832.18,844.14,828.24,842.25,13250000,842.25 1975-10-17,837.85,841.23,824.46,832.18,15650000,832.18 1975-10-16,837.22,851.46,833.60,837.85,18910000,837.85 1975-10-15,835.25,843.91,828.01,837.22,14440000,837.22 1975-10-14,837.77,852.41,830.13,835.25,19960000,835.25 1975-10-13,823.91,838.95,818.48,837.77,12020000,837.77 1975-10-10,824.54,832.57,817.14,823.91,14880000,823.91 1975-10-09,823.91,834.93,817.30,824.54,17770000,824.54 1975-10-08,816.51,829.35,809.82,823.91,17800000,823.91 1975-10-07,819.66,821.79,806.12,816.51,13530000,816.51 1975-10-06,813.21,826.83,811.32,819.66,15470000,819.66 1975-10-03,794.71,816.12,794.71,813.21,16360000,813.21 1975-10-02,784.16,799.28,781.72,794.55,14290000,794.55 1975-10-01,793.88,799.35,780.54,784.16,14070000,784.16 1975-09-30,804.44,804.44,789.66,793.88,12520000,793.88 1975-09-29,818.60,820.56,803.43,805.23,10580000,805.23 1975-09-26,820.24,827.28,811.33,818.60,12570000,818.60 1975-09-25,826.19,828.85,812.89,820.24,12890000,820.24 1975-09-24,820.24,836.83,820.24,826.19,16060000,826.19 1975-09-23,820.40,824.31,807.96,819.85,12800000,819.85 1975-09-22,829.79,835.65,817.58,820.40,14750000,820.40 1975-09-19,816.72,834.72,816.72,829.79,20830000,829.79 1975-09-18,799.05,817.19,797.64,814.61,14560000,814.61 1975-09-17,795.13,804.52,792.01,799.05,12190000,799.05 1975-09-16,803.19,809.76,792.79,795.13,13090000,795.13 1975-09-15,809.23,811.25,799.05,803.19,8670000,803.19 1975-09-12,812.66,823.69,806.63,809.23,12230000,809.23 1975-09-11,817.66,820.32,808.12,812.66,11100000,812.66 1975-09-10,825.33,825.33,809.53,817.66,14780000,817.66 1975-09-09,840.11,849.03,826.58,827.75,15790000,827.75 1975-09-08,835.97,843.95,830.18,840.11,11500000,840.11 1975-09-05,838.31,843.63,830.26,835.97,11680000,835.97 1975-09-04,832.29,843.55,827.21,838.31,12810000,838.31 1975-09-03,823.69,834.64,815.94,832.29,12260000,832.29 1975-09-02,835.34,840.19,821.26,823.69,11460000,823.69 1975-08-29,829.47,844.02,828.69,835.34,15480000,835.34 1975-08-28,809.92,831.59,809.92,829.47,14530000,829.47 1975-08-27,803.11,809.61,797.09,807.20,11100000,807.20 1975-08-26,812.34,815.55,799.98,803.11,11350000,803.11 1975-08-25,804.76,817.43,803.19,812.34,11250000,812.34 1975-08-22,791.69,806.95,789.97,804.76,13050000,804.76 1975-08-21,793.26,801.31,785.75,791.69,16610000,791.69 1975-08-20,805.46,805.46,789.58,793.26,18630000,793.26 1975-08-19,822.75,824.23,806.56,808.51,14990000,808.51 1975-08-18,825.64,833.31,819.38,822.75,10810000,822.75 1975-08-15,817.04,830.73,814.06,825.64,10610000,825.64 1975-08-14,820.56,824.08,812.73,817.04,12460000,817.04 1975-08-13,828.54,831.20,817.43,820.56,12000000,820.56 1975-08-12,823.76,838.63,823.29,828.54,14510000,828.54 1975-08-11,817.74,825.33,809.92,823.76,12350000,823.76 1975-08-08,815.79,826.19,812.66,817.74,11660000,817.74 1975-08-07,813.67,824.86,809.84,815.79,12390000,815.79 1975-08-06,810.15,820.40,804.60,813.67,16280000,813.67 1975-08-05,818.05,824.94,806.95,810.15,15470000,810.15 1975-08-04,826.50,826.81,813.52,818.05,12620000,818.05 1975-08-01,831.51,833.78,822.20,826.50,13320000,826.50 1975-07-31,831.66,843.09,828.77,831.51,14540000,831.51 1975-07-30,824.86,837.69,819.15,831.66,16150000,831.66 1975-07-29,827.83,840.74,820.32,824.86,19000000,824.86 1975-07-28,834.09,836.91,821.96,827.83,14850000,827.83 1975-07-25,840.27,846.92,829.40,834.09,15110000,834.09 1975-07-24,836.67,847.78,829.24,840.27,20550000,840.27 1975-07-23,846.76,853.41,834.64,836.67,20150000,836.67 1975-07-22,854.74,854.97,838.70,846.76,20660000,846.76 1975-07-21,862.41,867.88,852.00,854.74,16690000,854.74 1975-07-18,864.28,867.02,854.27,862.41,16870000,862.41 1975-07-17,872.11,877.35,858.73,864.28,21420000,864.28 1975-07-16,881.81,888.53,868.59,872.11,25250000,872.11 1975-07-15,875.86,888.85,874.14,881.81,28340000,881.81 1975-07-14,871.09,880.71,865.22,875.86,21900000,875.86 1975-07-11,871.87,881.49,862.80,871.09,22210000,871.09 1975-07-10,871.87,884.46,868.19,871.87,28880000,871.87 1975-07-09,858.65,875.00,858.65,871.87,26350000,871.87 1975-07-08,861.08,863.97,850.52,857.79,18990000,857.79 1975-07-07,871.79,873.36,859.04,861.08,15850000,861.08 1975-07-03,870.38,877.42,863.50,871.79,19000000,871.79 1975-07-02,876.25,876.25,861.62,870.38,18530000,870.38 1975-07-01,878.99,884.86,869.60,877.42,20390000,877.42 1975-06-30,873.12,884.62,867.96,878.99,19430000,878.99 1975-06-27,874.14,880.48,867.18,873.12,18820000,873.12 1975-06-26,872.73,883.37,866.55,874.14,24560000,874.14 1975-06-25,869.06,878.05,861.94,872.73,21610000,872.73 1975-06-24,864.83,878.44,861.00,869.06,26620000,869.06 1975-06-23,855.44,867.10,846.92,864.83,20720000,864.83 1975-06-20,847.86,864.67,847.86,855.44,26260000,855.44 1975-06-19,827.83,848.64,826.11,845.35,21450000,845.35 1975-06-18,828.61,834.01,818.99,827.83,15590000,827.83 1975-06-17,834.56,843.09,824.00,828.61,19440000,828.61 1975-06-16,824.47,837.77,821.34,834.56,16660000,834.56 1975-06-13,819.31,829.01,811.23,824.47,16300000,824.47 1975-06-12,824.55,831.43,815.39,819.31,15970000,819.31 1975-06-11,822.12,833.54,819.85,824.55,18230000,824.55 1975-06-10,829.08,829.08,813.75,822.12,21130000,822.12 1975-06-09,839.64,844.49,827.99,830.10,20670000,830.10 1975-06-06,842.15,849.73,833.15,839.64,22230000,839.64 1975-06-05,839.96,845.04,829.94,842.15,21610000,842.15 1975-06-04,846.14,850.83,834.17,839.96,24900000,839.96 1975-06-03,846.61,855.44,839.57,846.14,26560000,846.14 1975-06-02,835.73,853.49,835.73,846.61,28240000,846.61 1975-05-30,817.43,836.20,817.43,832.29,22670000,832.29 1975-05-29,817.04,823.53,808.12,815.00,18570000,815.00 1975-05-28,826.11,832.84,812.81,817.04,21850000,817.04 1975-05-27,831.90,837.53,820.09,826.11,17050000,826.11 1975-05-23,818.91,835.50,818.28,831.90,17870000,831.90 1975-05-22,818.68,828.54,807.96,818.91,17610000,818.91 1975-05-21,830.26,830.26,815.24,818.68,17640000,818.68 1975-05-20,837.69,843.79,827.52,830.49,18310000,830.49 1975-05-19,837.61,843.71,823.22,837.69,17870000,837.69 1975-05-16,848.80,849.03,831.35,837.61,16630000,837.61 1975-05-15,858.73,868.58,847.15,848.80,27690000,848.80 1975-05-14,850.13,866.00,846.84,858.73,29050000,858.73 1975-05-13,847.47,857.87,840.19,850.13,24950000,850.13 1975-05-12,850.13,857.32,841.99,847.47,22410000,847.47 1975-05-09,840.50,856.77,839.41,850.13,28440000,850.13 1975-05-08,836.44,845.20,828.07,840.50,22980000,840.50 1975-05-07,834.72,842.69,822.67,836.44,22250000,836.44 1975-05-06,855.60,860.06,832.68,834.72,25410000,834.72 1975-05-05,848.48,860.06,839.72,855.60,22370000,855.60 1975-05-02,832.21,853.25,832.21,848.48,25210000,848.48 1975-05-01,821.34,837.22,817.82,830.96,20660000,830.96 1975-04-30,803.04,823.22,796.93,821.34,18060000,821.34 1975-04-29,810.00,817.04,797.79,803.04,17740000,803.04 1975-04-28,811.80,820.56,803.50,810.00,17850000,810.00 1975-04-25,803.66,819.77,800.77,811.80,20260000,811.80 1975-04-24,802.49,810.15,792.32,803.66,19050000,803.66 1975-04-23,814.14,815.94,798.97,802.49,20040000,802.49 1975-04-22,815.86,828.93,811.17,814.14,26120000,814.14 1975-04-21,808.43,821.57,803.74,815.86,23960000,815.86 1975-04-18,819.46,822.12,802.25,808.43,26610000,808.43 1975-04-17,815.71,835.18,813.75,819.46,32650000,819.46 1975-04-16,815.08,819.77,800.30,815.71,22970000,815.71 1975-04-15,806.95,822.43,801.31,815.08,29620000,815.08 1975-04-14,790.83,811.48,790.83,806.95,26800000,806.95 1975-04-11,781.29,792.94,775.81,789.50,20160000,789.50 1975-04-10,769.40,788.25,769.40,781.29,24990000,781.29 1975-04-09,749.22,771.04,748.44,767.99,18120000,767.99 1975-04-08,742.88,755.38,741.00,749.22,14320000,749.22 1975-04-07,747.26,749.84,736.62,742.88,13860000,742.88 1975-04-04,752.19,755.40,740.69,747.26,14170000,747.26 1975-04-03,760.56,763.22,749.06,752.19,13920000,752.19 1975-04-02,761.58,770.96,754.77,760.56,15600000,760.56 1975-04-01,768.15,771.12,756.49,761.58,14480000,761.58 1975-03-31,770.26,779.72,764.39,768.15,16270000,768.15 1975-03-27,766.19,778.63,763.45,770.26,18300000,770.26 1975-03-26,750.94,769.97,750.94,766.19,18580000,766.19 1975-03-25,743.43,753.29,731.46,747.89,18500000,747.89 1975-03-24,752.50,752.50,737.48,743.43,17810000,743.43 1975-03-21,764.00,768.93,753.13,763.06,15940000,763.06 1975-03-20,769.48,779.65,758.29,764.00,20960000,764.00 1975-03-19,776.83,776.83,761.19,769.48,19030000,769.48 1975-03-18,786.53,796.93,776.60,779.41,29180000,779.41 1975-03-17,773.47,789.42,771.35,786.53,26780000,786.53 1975-03-14,762.98,779.57,761.81,773.47,24840000,773.47 1975-03-13,763.69,766.97,752.58,762.98,18620000,762.98 1975-03-12,770.89,774.33,756.73,763.69,21560000,763.69 1975-03-11,776.13,784.73,765.64,770.89,31280000,770.89 1975-03-10,770.10,779.41,761.58,776.13,25890000,776.13 1975-03-07,761.81,775.66,759.62,770.10,25930000,770.10 1975-03-06,761.81,764.71,761.81,761.81,21780000,761.81 1975-03-05,757.74,766.97,745.54,752.82,24120000,752.82 1975-03-04,753.83,773.23,753.83,757.74,34140000,757.74 1975-03-03,739.05,756.49,737.64,753.13,24100000,753.13 1975-02-28,731.15,741.94,724.50,739.05,17560000,739.05 1975-02-27,728.10,738.50,725.13,731.15,16430000,731.15 1975-02-26,719.18,731.77,713.70,728.10,18790000,728.10 1975-02-25,732.79,732.79,714.57,719.18,20910000,719.18 1975-02-24,749.77,750.16,733.49,736.94,19150000,736.94 1975-02-21,745.38,757.35,742.49,749.77,24440000,749.77 1975-02-20,736.39,749.53,731.38,745.38,22260000,745.38 1975-02-19,731.30,740.61,721.92,736.39,21930000,736.39 1975-02-18,734.20,742.10,722.39,731.30,23990000,731.30 1975-02-14,726.92,739.52,719.81,734.20,23290000,734.20 1975-02-13,718.48,738.27,718.48,726.92,35160000,726.92 1975-02-12,707.60,716.83,700.64,715.03,19790000,715.03 1975-02-11,708.39,711.67,697.83,707.60,16470000,707.60 1975-02-10,711.91,717.85,702.75,708.39,16120000,708.39 1975-02-07,714.17,715.97,697.51,711.91,19060000,711.91 1975-02-06,717.85,731.54,710.81,714.17,32020000,714.17 1975-02-05,708.07,721.45,699.78,717.85,25830000,717.85 1975-02-04,711.44,713.47,695.24,708.07,25040000,708.07 1975-02-03,703.69,717.62,696.50,711.44,25400000,711.44 1975-01-31,696.42,709.56,690.16,703.69,24640000,703.69 1975-01-30,705.96,717.30,693.13,696.42,29740000,696.42 1975-01-29,694.77,712.22,686.95,705.96,27410000,705.96 1975-01-28,692.66,705.10,689.69,694.77,31760000,694.77 1975-01-27,678.43,698.69,678.43,692.66,32130000,692.66 1975-01-24,656.76,671.46,652.69,666.61,20670000,666.61 1975-01-23,652.61,666.61,647.45,656.76,17960000,656.76 1975-01-22,641.90,654.02,634.39,652.61,15330000,652.61 1975-01-21,647.45,656.60,637.91,641.90,14780000,641.90 1975-01-20,644.63,650.19,635.09,647.45,13450000,647.45 1975-01-17,655.74,657.70,641.90,644.63,14260000,644.63 1975-01-16,653.39,660.12,648.08,655.74,17110000,655.74 1975-01-15,648.70,657.15,640.25,653.39,16580000,653.39 1975-01-14,654.18,657.93,644.01,648.70,16610000,648.70 1975-01-13,658.79,669.27,651.36,654.18,19780000,654.18 1975-01-10,650.11,666.69,650.11,658.79,25890000,658.79 1975-01-09,635.40,646.90,627.58,645.26,16340000,645.26 1975-01-08,641.19,646.28,632.12,635.40,15600000,635.40 1975-01-07,637.20,645.42,630.24,641.19,14890000,641.19 1975-01-06,634.54,646.43,631.88,637.20,17550000,637.20 1975-01-03,632.04,642.60,623.67,634.54,15270000,634.54 1975-01-02,619.13,637.12,619.13,632.04,14800000,632.04 1974-12-31,603.25,619.84,602.86,616.24,20970000,616.24 1974-12-30,602.16,607.24,595.04,603.25,18520000,603.25 1974-12-27,604.74,608.26,597.47,602.16,13060000,602.16 1974-12-26,598.40,610.37,597.07,604.74,11810000,604.74 1974-12-24,589.64,602.16,589.57,598.40,9540000,598.40 1974-12-23,598.48,598.95,583.70,589.64,18040000,589.64 1974-12-20,604.43,607.01,594.49,598.48,15840000,598.48 1974-12-19,603.49,611.00,596.21,604.43,15900000,604.43 1974-12-18,597.62,610.84,597.62,603.49,18050000,603.49 1974-12-17,586.83,599.42,582.45,597.54,16880000,597.54 1974-12-16,592.77,598.09,584.25,586.83,15370000,586.83 1974-12-13,596.37,602.00,586.67,592.77,14000000,592.77 1974-12-12,595.35,604.27,586.67,596.37,15390000,596.37 1974-12-11,593.87,606.15,589.17,595.35,15700000,595.35 1974-12-10,582.21,602.08,582.21,593.87,15690000,593.87 1974-12-09,577.60,587.14,570.01,579.94,14660000,579.94 1974-12-06,587.06,588.00,572.12,577.60,15500000,577.60 1974-12-05,598.64,604.11,585.11,587.06,12890000,587.06 1974-12-04,596.61,606.77,592.07,598.64,12580000,598.64 1974-12-03,603.02,603.33,590.82,596.61,13620000,596.61 1974-12-02,616.08,616.08,599.58,603.02,11140000,603.02 1974-11-29,619.29,623.90,610.92,618.66,7400000,618.66 1974-11-27,617.26,633.45,612.64,619.29,14810000,619.29 1974-11-26,611.94,625.08,606.85,617.26,13600000,617.26 1974-11-25,615.30,620.70,604.43,611.94,11300000,611.94 1974-11-22,609.59,625.31,609.59,615.30,13020000,615.30 1974-11-21,609.59,616.55,599.81,608.57,13820000,608.57 1974-11-20,614.05,622.81,605.76,609.59,12430000,609.59 1974-11-19,624.92,627.42,609.75,614.05,15720000,614.05 1974-11-18,641.11,641.11,621.71,624.92,15230000,624.92 1974-11-15,658.40,660.04,642.60,647.61,12480000,647.61 1974-11-14,659.18,671.31,635.55,658.40,13540000,658.40 1974-11-13,659.18,666.22,647.29,659.18,16040000,659.18 1974-11-12,672.64,675.06,656.45,659.18,15040000,659.18 1974-11-11,667.16,675.69,660.51,672.64,13220000,672.64 1974-11-08,671.93,676.55,661.53,667.16,15890000,667.16 1974-11-07,669.12,681.79,660.75,671.93,17150000,671.93 1974-11-06,674.75,692.82,666.07,669.12,23930000,669.12 1974-11-05,657.23,676.63,651.83,674.75,15960000,674.75 1974-11-04,664.19,664.19,647.37,657.23,12740000,657.23 1974-11-01,665.52,673.03,655.74,665.28,13470000,665.28 1974-10-31,673.03,685.62,659.18,665.52,18840000,665.52 1974-10-30,659.34,681.40,655.19,673.03,20130000,673.03 1974-10-29,638.77,661.53,638.77,659.34,15610000,659.34 1974-10-28,636.19,639.63,624.06,633.84,10540000,633.84 1974-10-25,636.26,648.00,629.93,636.19,12650000,636.19 1974-10-24,643.85,643.85,624.30,636.26,14910000,636.26 1974-10-23,660.51,660.51,637.83,645.03,14200000,645.03 1974-10-22,669.82,680.07,658.56,662.86,18930000,662.86 1974-10-21,654.88,674.12,645.65,669.82,14500000,669.82 1974-10-18,651.44,669.51,646.04,654.88,16460000,654.88 1974-10-17,642.29,657.31,635.48,651.44,14470000,651.44 1974-10-16,658.40,660.51,636.97,642.29,14790000,642.29 1974-10-15,673.50,679.21,652.38,658.40,17390000,658.40 1974-10-14,659.73,689.30,659.73,673.50,19770000,673.50 1974-10-11,648.08,665.91,638.14,658.17,20090000,658.17 1974-10-10,634.00,664.03,634.00,648.08,26360000,648.08 1974-10-09,602.63,633.37,591.91,631.02,18820000,631.02 1974-10-08,607.56,615.93,596.21,602.63,15460000,602.63 1974-10-07,587.77,610.45,587.77,607.56,15000000,607.56 1974-10-04,587.61,593.71,573.22,584.56,15910000,584.56 1974-10-03,600.75,600.75,582.21,587.61,13150000,587.61 1974-10-02,604.82,613.89,596.84,601.53,12230000,601.53 1974-10-01,607.87,613.27,589.57,604.82,16890000,604.82 1974-09-30,619.37,619.37,598.80,607.87,15000000,607.87 1974-09-27,637.98,643.62,619.37,621.95,12320000,621.95 1974-09-26,648.39,648.39,633.60,637.98,9060000,637.98 1974-09-25,654.10,671.46,643.77,649.95,17620000,649.95 1974-09-24,662.08,662.08,648.78,654.10,9840000,654.10 1974-09-23,670.76,678.19,657.78,663.72,12130000,663.72 1974-09-20,674.05,680.54,659.34,670.76,16250000,670.76 1974-09-19,659.34,679.83,659.34,674.05,17000000,674.05 1974-09-18,648.78,654.57,635.09,651.91,11760000,651.91 1974-09-17,642.76,662.16,642.76,648.78,13730000,648.78 1974-09-16,627.19,645.89,617.73,639.79,18370000,639.79 1974-09-13,641.74,643.77,624.37,627.19,16070000,627.19 1974-09-12,654.72,655.04,637.44,641.74,16920000,641.74 1974-09-11,658.17,665.60,650.58,654.72,11820000,654.72 1974-09-10,662.94,669.51,652.22,658.17,11980000,658.17 1974-09-09,676.71,676.71,660.59,662.94,11160000,662.94 1974-09-06,670.76,685.00,663.56,677.88,15130000,677.88 1974-09-05,649.95,673.50,649.95,670.76,14210000,670.76 1974-09-04,657.46,657.46,638.38,648.00,16930000,648.00 1974-09-03,678.58,686.48,662.23,663.33,12750000,663.33 1974-08-30,661.14,681.71,661.14,678.58,16230000,678.58 1974-08-29,666.61,669.51,651.60,656.84,13690000,656.84 1974-08-28,671.54,681.79,663.56,666.61,16670000,666.61 1974-08-27,688.13,690.86,668.02,671.54,12970000,671.54 1974-08-26,686.80,697.12,671.46,688.13,14630000,688.13 1974-08-23,704.63,710.73,683.90,686.80,13590000,686.80 1974-08-22,711.59,713.94,694.15,704.63,15690000,704.63 1974-08-21,726.85,730.05,709.25,711.59,11650000,711.59 1974-08-20,721.84,736.31,717.46,726.85,13820000,726.85 1974-08-19,731.15,731.15,715.35,721.84,11670000,721.84 1974-08-16,737.88,744.45,728.65,731.54,10510000,731.54 1974-08-15,740.54,749.14,732.24,737.88,11130000,737.88 1974-08-14,755.01,755.01,735.37,740.54,11750000,740.54 1974-08-13,767.29,768.54,750.55,756.44,10140000,756.44 1974-08-12,777.30,780.04,762.83,767.29,7780000,767.29 1974-08-09,784.89,787.47,771.90,777.30,10160000,777.30 1974-08-08,797.56,803.43,779.02,784.89,16060000,784.89 1974-08-07,773.78,798.89,770.81,797.56,13380000,797.56 1974-08-06,766.97,790.99,766.97,773.78,15770000,773.78 1974-08-05,752.58,768.46,747.97,760.40,11230000,760.40 1974-08-02,751.10,758.45,745.31,752.58,10110000,752.58 1974-08-01,757.43,764.16,745.62,751.10,11470000,751.10 1974-07-31,765.57,767.44,754.38,757.43,10960000,757.43 1974-07-30,770.89,775.03,758.84,765.57,11360000,765.57 1974-07-29,780.74,780.74,764.55,770.89,11560000,770.89 1974-07-26,795.68,798.03,781.52,784.57,10420000,784.57 1974-07-25,805.77,807.65,790.05,795.68,13310000,795.68 1974-07-24,797.72,809.76,791.54,805.77,12870000,805.77 1974-07-23,790.36,805.62,789.82,797.72,12910000,797.72 1974-07-22,787.94,795.53,779.49,790.36,9290000,790.36 1974-07-19,789.19,796.62,780.43,787.94,11080000,787.94 1974-07-18,784.97,803.04,781.45,789.19,13980000,789.19 1974-07-17,775.97,788.56,765.80,784.97,11320000,784.97 1974-07-16,785.20,785.20,771.82,775.97,9920000,775.97 1974-07-15,787.23,800.92,777.85,786.61,13560000,786.61 1974-07-12,770.03,790.68,770.03,787.23,17770000,787.23 1974-07-11,762.12,769.76,753.13,759.62,14640000,759.62 1974-07-10,772.29,779.18,759.54,762.12,13490000,762.12 1974-07-09,770.57,782.85,764.63,772.29,15580000,772.29 1974-07-08,788.41,788.41,765.33,770.57,15510000,770.57 1974-07-05,792.87,796.31,786.22,791.77,7400000,791.77 1974-07-03,790.68,798.58,785.12,792.87,13430000,792.87 1974-07-02,806.24,808.75,788.25,790.68,13460000,790.68 1974-07-01,802.41,811.95,797.48,806.24,10270000,806.24 1974-06-28,803.66,808.20,796.46,802.41,12010000,802.41 1974-06-27,816.96,817.27,800.77,803.66,12650000,803.66 1974-06-26,828.85,830.41,815.47,816.96,11410000,816.96 1974-06-25,817.66,832.53,817.66,828.85,11920000,828.85 1974-06-24,815.39,822.43,808.90,816.33,9960000,816.33 1974-06-21,820.79,822.59,810.15,815.39,11830000,815.39 1974-06-20,826.11,831.20,818.13,820.79,11990000,820.79 1974-06-19,830.26,833.54,821.26,826.11,10550000,826.11 1974-06-18,833.23,838.55,826.50,830.26,10110000,830.26 1974-06-17,843.09,843.24,829.47,833.23,9680000,833.23 1974-06-14,850.67,850.67,837.84,843.09,10030000,843.09 1974-06-13,848.56,861.00,843.79,852.08,11540000,852.08 1974-06-12,852.08,853.80,837.92,848.56,11150000,848.56 1974-06-11,859.67,865.54,848.09,852.08,12380000,852.08 1974-06-10,853.72,864.60,846.14,859.67,13540000,859.67 1974-06-07,845.59,863.27,845.59,853.72,19020000,853.72 1974-06-06,830.18,847.54,824.08,845.35,13360000,845.35 1974-06-05,828.69,839.41,819.23,830.18,13680000,830.18 1974-06-04,821.81,837.06,821.81,828.69,16040000,828.69 1974-06-03,802.17,822.36,799.83,821.26,12490000,821.26 1974-05-31,803.58,808.04,792.32,802.17,10810000,802.17 1974-05-30,795.37,808.28,788.80,803.58,13580000,803.58 1974-05-29,814.30,817.27,793.02,795.37,12300000,795.37 1974-05-28,816.65,824.55,809.14,814.30,10580000,814.30 1974-05-24,806.24,824.31,806.24,816.65,13740000,816.65 1974-05-23,802.57,811.33,796.15,805.23,14770000,805.23 1974-05-22,809.53,818.84,800.14,802.57,15450000,802.57 1974-05-21,812.42,822.67,803.04,809.53,12190000,809.53 1974-05-20,818.84,826.19,807.49,812.42,10550000,812.42 1974-05-17,833.31,833.31,813.75,818.84,13870000,818.84 1974-05-16,846.06,853.41,833.15,835.34,12090000,835.34 1974-05-15,847.86,853.02,839.25,846.06,11240000,846.06 1974-05-14,845.59,856.07,842.30,847.86,10880000,847.86 1974-05-13,850.44,854.82,838.70,845.59,11290000,845.59 1974-05-10,865.77,870.38,846.84,850.44,15270000,850.44 1974-05-09,850.99,870.07,849.19,865.77,14710000,865.77 1974-05-08,847.15,856.93,843.01,850.99,11850000,850.99 1974-05-07,844.88,855.84,840.50,847.15,10710000,847.15 1974-05-06,845.90,847.47,834.32,844.88,9450000,844.88 1974-05-03,851.06,852.78,839.88,845.90,11080000,845.90 1974-05-02,853.88,865.85,845.90,851.06,13620000,851.06 1974-05-01,836.75,861.08,832.77,853.88,15120000,853.88 1974-04-30,835.42,844.49,829.63,836.75,10980000,836.75 1974-04-29,834.64,839.80,824.70,835.42,10170000,835.42 1974-04-26,827.68,841.29,823.22,834.64,13250000,834.64 1974-04-25,832.37,835.11,818.68,827.68,15870000,827.68 1974-04-24,845.98,847.23,828.22,832.37,16010000,832.37 1974-04-23,858.57,859.51,843.55,845.98,14110000,845.98 1974-04-22,859.90,864.28,852.39,858.57,10520000,858.57 1974-04-19,868.90,868.90,856.15,859.90,10710000,859.90 1974-04-18,867.41,875.94,862.64,869.92,12470000,869.92 1974-04-17,861.23,874.45,856.38,867.41,14020000,867.41 1974-04-16,845.74,863.58,845.74,861.23,14530000,861.23 1974-04-15,844.81,852.00,839.33,843.79,10130000,843.79 1974-04-11,843.71,849.97,837.77,844.81,9970000,844.81 1974-04-10,846.84,855.52,840.27,843.71,11160000,843.71 1974-04-09,839.96,852.55,836.12,846.84,11330000,846.84 1974-04-08,847.23,847.23,834.25,839.96,10740000,839.96 1974-04-05,858.57,858.57,842.46,847.54,11670000,847.54 1974-04-04,858.03,865.46,852.32,858.89,11650000,858.89 1974-04-03,846.61,860.45,844.65,858.03,11500000,858.03 1974-04-02,843.48,853.18,839.17,846.61,12010000,846.61 1974-04-01,846.68,856.38,839.72,843.48,11470000,843.48 1974-03-29,854.35,858.57,842.38,846.68,12150000,846.68 1974-03-28,867.18,867.18,850.59,854.35,14940000,854.35 1974-03-27,883.68,887.83,869.76,871.17,11690000,871.17 1974-03-26,881.02,890.18,875.16,883.68,11840000,883.68 1974-03-25,878.13,884.78,866.79,881.02,10540000,881.02 1974-03-22,875.47,884.31,868.43,878.13,11930000,878.13 1974-03-21,872.34,887.12,870.23,875.47,12950000,875.47 1974-03-20,867.57,878.60,863.03,872.34,12960000,872.34 1974-03-19,874.22,875.70,861.86,867.57,12800000,867.57 1974-03-18,887.83,889.86,870.38,874.22,14010000,874.22 1974-03-15,889.78,893.38,878.68,887.83,14500000,887.83 1974-03-14,891.66,904.02,885.17,889.78,19770000,889.78 1974-03-13,887.12,900.81,881.88,891.66,16820000,891.66 1974-03-12,888.45,895.57,877.50,887.12,17250000,887.12 1974-03-11,878.05,893.30,865.93,888.45,18470000,888.45 1974-03-08,869.06,880.94,858.81,878.05,16210000,878.05 1974-03-07,879.85,880.24,865.07,869.06,14500000,869.06 1974-03-06,872.42,885.25,866.47,879.85,19140000,879.85 1974-03-05,860.40,880.40,860.40,872.42,21980000,872.42 1974-03-04,851.92,854.97,841.76,853.18,12270000,853.18 1974-03-01,860.53,861.62,845.90,851.92,12880000,851.92 1974-02-28,863.42,868.19,851.85,860.53,13680000,860.53 1974-02-27,859.51,871.40,855.76,863.42,18730000,863.42 1974-02-26,851.38,861.78,843.09,859.51,15860000,859.51 1974-02-25,855.99,859.20,843.79,851.38,12900000,851.38 1974-02-22,846.84,862.41,843.01,855.99,16360000,855.99 1974-02-21,831.04,849.66,830.18,846.84,13930000,846.84 1974-02-20,819.54,834.87,814.22,831.04,11670000,831.04 1974-02-19,820.32,840.50,816.65,819.54,15940000,819.54 1974-02-15,809.92,825.72,808.12,820.32,12640000,820.32 1974-02-14,806.87,816.57,802.17,809.92,12230000,809.92 1974-02-13,806.63,816.18,803.04,806.87,10990000,806.87 1974-02-12,803.90,811.72,795.68,806.63,12920000,806.63 1974-02-11,820.40,821.26,802.24,803.90,12930000,803.90 1974-02-08,828.46,831.90,817.82,820.40,12990000,820.40 1974-02-07,824.62,833.93,819.38,828.46,11750000,828.46 1974-02-06,820.64,831.35,817.51,824.62,11610000,824.62 1974-02-05,821.50,829.87,811.95,820.64,12820000,820.64 1974-02-04,838.63,838.63,816.49,821.50,14380000,821.50 1974-02-01,855.55,856.55,838.02,843.94,12480000,843.94 1974-01-31,862.32,868.85,852.01,855.55,14020000,855.55 1974-01-30,853.09,869.77,853.09,862.32,16790000,862.32 1974-01-29,853.01,858.86,844.48,852.32,12850000,852.32 1974-01-28,859.39,862.16,847.32,853.01,13410000,853.01 1974-01-25,863.08,869.16,850.71,859.39,14860000,859.39 1974-01-24,871.00,875.85,853.47,863.08,15980000,863.08 1974-01-23,863.47,878.69,859.01,871.00,16890000,871.00 1974-01-22,854.63,871.62,850.71,863.47,17330000,863.47 1974-01-21,855.47,858.86,835.79,854.63,15630000,854.63 1974-01-18,872.16,873.15,850.86,855.47,16470000,855.47 1974-01-17,856.32,878.54,856.32,872.16,21040000,872.16 1974-01-16,846.40,861.16,842.48,856.09,14930000,856.09 1974-01-15,840.18,855.78,834.64,846.40,13250000,846.40 1974-01-14,841.48,855.63,833.26,840.18,14610000,840.18 1974-01-11,823.11,847.63,819.88,841.48,15140000,841.48 1974-01-10,834.79,845.17,816.57,823.11,16120000,823.11 1974-01-09,853.01,853.01,831.41,834.79,18070000,834.79 1974-01-08,876.85,880.77,857.70,861.78,18080000,861.78 1974-01-07,880.23,883.99,866.31,876.85,19070000,876.85 1974-01-04,880.69,890.38,868.08,880.23,21700000,880.23 1974-01-03,858.86,886.69,858.86,880.69,24850000,880.69 1974-01-02,850.86,859.16,841.41,855.32,12060000,855.32 1973-12-31,848.02,857.09,836.18,850.86,23470000,850.86 1973-12-28,851.01,857.63,839.94,848.02,21310000,848.02 1973-12-27,839.02,858.93,839.02,851.01,22720000,851.01 1973-12-26,820.19,844.10,820.19,837.56,18620000,837.56 1973-12-24,818.73,820.73,805.73,814.81,11540000,814.81 1973-12-21,828.11,830.72,809.81,818.73,18680000,818.73 1973-12-20,829.57,841.64,820.50,828.11,17340000,828.11 1973-12-19,829.49,847.86,820.96,829.57,20670000,829.57 1973-12-18,811.12,834.72,807.12,829.49,19490000,829.49 1973-12-17,815.65,821.42,804.20,811.12,12930000,811.12 1973-12-14,800.43,823.57,793.51,815.65,20000000,815.65 1973-12-13,810.73,821.57,794.43,800.43,18130000,800.43 1973-12-12,828.64,828.64,805.27,810.73,18190000,810.73 1973-12-11,851.14,861.09,830.80,834.18,20100000,834.18 1973-12-10,838.05,857.31,829.17,851.14,18590000,851.14 1973-12-07,815.47,846.63,815.47,838.05,23230000,838.05 1973-12-06,788.31,816.68,786.50,814.12,23260000,814.12 1973-12-05,803.21,806.82,783.56,788.31,19180000,788.31 1973-12-04,806.52,817.73,795.68,803.21,19030000,803.21 1973-12-03,820.51,820.51,798.31,806.52,17900000,806.52 1973-11-30,835.11,836.02,819.39,822.25,15380000,822.25 1973-11-29,839.78,846.93,824.28,835.11,18870000,835.11 1973-11-28,817.73,843.47,814.80,839.78,19990000,839.78 1973-11-27,824.95,833.16,810.36,817.73,19750000,817.73 1973-11-26,844.15,844.15,816.60,824.95,19830000,824.95 1973-11-23,854.98,861.45,847.46,854.00,11470000,854.00 1973-11-21,844.90,869.21,839.78,854.98,24260000,854.98 1973-11-20,862.43,862.43,836.17,844.90,23960000,844.90 1973-11-19,889.75,889.75,860.78,862.66,16700000,862.66 1973-11-16,874.55,905.10,869.21,891.33,22510000,891.33 1973-11-15,869.88,886.82,859.27,874.55,24530000,874.55 1973-11-14,891.03,899.53,865.37,869.88,22710000,869.88 1973-11-13,897.65,902.47,876.88,891.03,20310000,891.03 1973-11-12,908.41,910.82,885.54,897.65,19250000,897.65 1973-11-09,932.65,932.95,902.92,908.41,17320000,908.41 1973-11-08,923.92,946.79,923.92,932.65,19650000,932.65 1973-11-07,913.08,929.64,909.69,920.08,16570000,920.08 1973-11-06,919.40,933.77,909.69,913.08,16430000,913.08 1973-11-05,932.87,932.87,912.55,919.40,17150000,919.40 1973-11-02,948.83,951.31,929.11,935.28,16340000,935.28 1973-11-01,956.58,963.80,941.83,948.83,16920000,948.83 1973-10-31,968.54,973.13,951.31,956.58,17890000,956.58 1973-10-30,984.80,985.93,963.65,968.54,17580000,968.54 1973-10-29,987.06,997.59,979.98,984.80,17960000,984.80 1973-10-26,974.49,992.62,972.61,987.06,17800000,987.06 1973-10-25,971.85,981.26,957.10,974.49,15580000,974.49 1973-10-24,966.51,977.50,960.79,971.85,15840000,971.85 1973-10-23,960.57,976.44,944.46,966.51,17230000,966.51 1973-10-22,963.73,970.42,951.08,960.57,14290000,960.57 1973-10-19,959.74,974.04,954.55,963.73,17880000,963.73 1973-10-18,962.52,974.34,950.11,959.74,19210000,959.74 1973-10-17,967.41,976.67,956.35,962.52,18600000,962.52 1973-10-16,967.04,971.63,951.76,967.41,18780000,967.41 1973-10-15,977.80,977.80,960.19,967.04,16160000,967.04 1973-10-12,976.07,991.80,972.00,978.63,22730000,978.63 1973-10-11,960.57,981.19,957.71,976.07,20740000,976.07 1973-10-10,974.19,980.28,953.79,960.57,19010000,960.57 1973-10-09,977.65,984.65,964.63,974.19,19440000,974.19 1973-10-08,971.25,983.22,955.82,977.65,18990000,977.65 1973-10-05,955.90,975.92,950.78,971.25,18820000,971.25 1973-10-04,964.55,969.30,949.50,955.90,19730000,955.90 1973-10-03,956.80,971.78,952.14,964.55,22040000,964.55 1973-10-02,948.83,961.54,943.93,956.80,20770000,956.80 1973-10-01,947.10,954.09,937.69,948.83,15830000,948.83 1973-09-28,953.27,954.92,937.54,947.10,16300000,947.10 1973-09-27,949.50,964.55,942.50,953.27,23660000,953.27 1973-09-26,940.55,954.55,935.43,949.50,21130000,949.50 1973-09-25,936.71,947.02,927.53,940.55,21530000,940.55 1973-09-24,927.90,940.70,924.37,936.71,19490000,936.71 1973-09-21,920.53,934.38,911.72,927.90,23760000,927.90 1973-09-20,910.37,925.42,909.54,920.53,25960000,920.53 1973-09-19,891.26,915.41,891.26,910.37,24570000,910.37 1973-09-18,892.99,900.14,882.38,891.26,16400000,891.26 1973-09-17,886.36,900.29,884.86,892.99,15100000,892.99 1973-09-14,880.57,889.15,873.34,886.36,13760000,886.36 1973-09-13,881.32,888.09,874.17,880.57,11670000,880.57 1973-09-12,885.76,889.75,874.77,881.32,12040000,881.32 1973-09-11,891.33,892.46,878.61,885.76,12690000,885.76 1973-09-10,898.63,903.45,888.62,891.33,11620000,891.33 1973-09-07,901.04,905.70,892.61,898.63,14930000,898.63 1973-09-06,899.08,908.04,894.04,901.04,15670000,901.04 1973-09-05,895.39,903.52,887.94,899.08,14580000,899.08 1973-09-04,887.57,900.25,885.69,895.39,14210000,895.39 1973-08-31,882.53,890.95,876.51,887.57,10530000,887.57 1973-08-30,883.43,892.31,877.48,882.53,12100000,882.53 1973-08-29,872.07,890.35,870.56,883.43,15690000,883.43 1973-08-28,870.71,877.63,865.37,872.07,11810000,872.07 1973-08-27,863.49,874.32,860.02,870.71,9740000,870.71 1973-08-24,864.46,873.12,856.56,863.49,11200000,863.49 1973-08-23,853.48,869.81,853.48,864.46,11390000,864.46 1973-08-22,857.84,860.55,845.50,851.90,10770000,851.90 1973-08-21,867.40,869.96,855.51,857.84,11480000,857.84 1973-08-20,871.84,875.08,862.73,867.40,8970000,867.40 1973-08-17,872.74,877.18,864.69,871.84,11110000,871.84 1973-08-16,874.17,886.44,867.62,872.74,12990000,872.74 1973-08-15,870.71,879.82,863.71,874.17,12040000,874.17 1973-08-14,883.20,887.42,867.70,870.71,11740000,870.71 1973-08-13,892.38,892.91,878.09,883.20,11330000,883.20 1973-08-10,901.49,903.52,887.12,892.38,10870000,892.38 1973-08-09,902.02,910.60,893.96,901.49,12880000,901.49 1973-08-08,911.95,913.23,897.43,902.02,12440000,902.02 1973-08-07,912.78,920.38,905.25,911.95,13510000,911.95 1973-08-06,908.87,918.50,900.96,912.78,12320000,912.78 1973-08-03,910.14,913.91,900.36,908.87,9940000,908.87 1973-08-02,912.18,917.37,899.46,910.14,16080000,910.14 1973-08-01,924.37,924.37,907.28,912.18,13530000,912.18 1973-07-31,933.77,941.15,923.39,926.40,13530000,926.40 1973-07-30,936.71,942.35,926.32,933.77,11170000,933.77 1973-07-27,934.53,942.28,925.65,936.71,12910000,936.71 1973-07-26,933.02,944.08,924.74,934.53,18410000,934.53 1973-07-25,918.72,942.58,917.22,933.02,22220000,933.02 1973-07-24,913.15,922.19,903.67,918.72,16280000,918.72 1973-07-23,910.90,921.88,907.36,913.15,15580000,913.15 1973-07-20,906.68,918.05,902.54,910.90,16300000,910.90 1973-07-19,905.40,916.47,893.66,906.68,18650000,906.68 1973-07-18,898.03,911.20,889.90,905.40,17020000,905.40 1973-07-17,897.58,911.80,892.84,898.03,18750000,898.03 1973-07-16,885.99,900.44,881.32,897.58,12920000,897.58 1973-07-13,901.94,902.77,883.05,885.99,11390000,885.99 1973-07-12,908.19,910.82,895.39,901.94,16400000,901.94 1973-07-11,889.90,911.80,889.90,908.19,18730000,908.19 1973-07-10,879.06,894.64,879.06,888.32,15090000,888.32 1973-07-09,870.11,879.74,863.94,877.26,11560000,877.26 1973-07-06,874.32,878.09,865.82,870.11,9980000,870.11 1973-07-05,874.17,879.74,867.10,874.32,10500000,874.32 1973-07-03,880.57,882.53,868.75,874.17,10560000,874.17 1973-07-02,890.20,890.20,876.66,880.57,9830000,880.57 1973-06-29,894.64,900.59,886.59,891.71,10770000,891.71 1973-06-28,884.63,897.88,880.87,894.64,12760000,894.64 1973-06-27,879.44,888.09,872.44,884.63,12660000,884.63 1973-06-26,869.13,881.85,864.46,879.44,14040000,879.44 1973-06-25,879.82,880.72,865.67,869.13,11670000,869.13 1973-06-22,875.23,897.58,875.23,879.82,18470000,879.82 1973-06-21,884.71,887.49,871.84,873.65,11630000,873.65 1973-06-20,881.55,890.65,876.28,884.71,10600000,884.71 1973-06-19,875.08,889.52,868.08,881.55,12970000,881.55 1973-06-18,887.34,887.34,869.36,875.08,11460000,875.08 1973-06-15,899.68,899.68,882.60,888.55,11970000,888.55 1973-06-14,915.49,922.49,899.61,902.92,13210000,902.92 1973-06-13,927.00,935.58,912.48,915.49,15700000,915.49 1973-06-12,915.11,930.01,912.85,927.00,13840000,927.00 1973-06-11,920.00,924.67,911.05,915.11,9940000,915.11 1973-06-08,909.62,926.85,908.19,920.00,14050000,920.00 1973-06-07,898.18,913.68,896.37,909.62,14160000,909.62 1973-06-06,900.81,908.87,891.71,898.18,13080000,898.18 1973-06-05,885.91,905.63,883.43,900.81,14080000,900.81 1973-06-04,893.96,894.42,880.72,885.91,11230000,885.91 1973-06-01,901.41,902.32,887.27,893.96,10410000,893.96 1973-05-31,908.87,912.03,895.62,901.41,12190000,901.41 1973-05-30,924.37,924.37,906.01,908.87,11730000,908.87 1973-05-29,930.84,934.08,921.36,925.57,11300000,925.57 1973-05-25,924.44,938.82,915.64,930.84,19270000,930.84 1973-05-24,895.02,926.48,890.35,924.44,17310000,924.44 1973-05-23,892.46,904.80,884.18,895.02,14950000,895.02 1973-05-22,886.51,905.93,884.86,892.46,18020000,892.46 1973-05-21,894.79,894.79,875.45,886.51,20690000,886.51 1973-05-18,908.79,908.79,889.00,895.17,17080000,895.17 1973-05-17,917.14,919.93,907.59,911.72,13060000,911.72 1973-05-16,917.44,927.83,907.66,917.14,13800000,917.14 1973-05-15,909.69,920.83,894.49,917.44,18530000,917.44 1973-05-14,925.27,925.27,906.31,909.69,13520000,909.69 1973-05-11,939.12,939.12,924.14,927.98,12980000,927.98 1973-05-10,949.05,950.63,934.75,939.34,13520000,939.34 1973-05-09,956.58,965.16,945.29,949.05,16050000,949.05 1973-05-08,950.71,961.24,940.92,956.58,13730000,956.58 1973-05-07,953.87,956.80,941.98,950.71,12500000,950.71 1973-05-04,945.67,962.67,944.31,953.87,19510000,953.87 1973-05-03,932.34,950.03,915.04,945.67,17760000,945.67 1973-05-02,921.21,938.37,920.23,932.34,14380000,932.34 1973-05-01,921.43,929.03,905.40,921.21,15380000,921.21 1973-04-30,922.19,929.18,907.51,921.43,14820000,921.43 1973-04-27,937.76,941.38,918.05,922.19,13730000,922.19 1973-04-26,930.54,944.24,919.78,937.76,16210000,937.76 1973-04-25,940.77,941.60,925.42,930.54,15960000,930.54 1973-04-24,955.37,958.68,938.37,940.77,13830000,940.77 1973-04-23,963.20,966.51,951.23,955.37,12580000,955.37 1973-04-19,958.31,970.95,953.79,963.20,14560000,963.20 1973-04-18,953.43,961.47,944.39,958.31,13890000,958.31 1973-04-17,956.73,959.29,947.62,953.43,12830000,953.43 1973-04-16,959.36,965.53,950.03,956.73,11350000,956.73 1973-04-13,964.03,967.56,950.71,959.36,14390000,959.36 1973-04-12,967.41,975.32,956.73,964.03,16360000,964.03 1973-04-11,960.49,970.50,953.94,967.41,14890000,967.41 1973-04-10,950.71,966.74,950.71,960.49,16770000,960.49 1973-04-09,931.07,950.63,927.45,947.55,13740000,947.55 1973-04-06,923.46,937.31,921.43,931.07,13890000,931.07 1973-04-05,925.05,929.03,914.81,923.46,12750000,923.46 1973-04-04,927.75,935.66,919.55,925.05,11890000,925.05 1973-04-03,936.18,936.71,920.45,927.75,12910000,927.75 1973-04-02,951.01,951.84,932.72,936.18,10640000,936.18 1973-03-30,959.14,961.69,944.84,951.01,13740000,951.01 1973-03-29,948.00,962.82,941.75,959.14,16050000,959.14 1973-03-28,944.91,955.82,936.94,948.00,15850000,948.00 1973-03-27,930.16,948.52,930.16,944.91,17500000,944.91 1973-03-26,922.71,931.74,914.28,927.90,14980000,927.90 1973-03-23,925.20,934.53,911.12,922.71,18470000,922.71 1973-03-22,937.46,937.46,919.25,925.20,17130000,925.20 1973-03-21,949.43,958.84,934.90,938.37,16080000,938.37 1973-03-20,952.06,956.80,941.15,949.43,13250000,949.43 1973-03-19,962.45,962.45,946.79,952.06,12460000,952.06 1973-03-16,969.82,973.21,957.41,963.05,15130000,963.05 1973-03-15,978.85,982.47,966.21,969.82,14450000,969.82 1973-03-14,976.07,982.31,972.00,978.85,14460000,978.85 1973-03-13,969.75,980.13,966.29,976.07,14210000,976.07 1973-03-12,972.23,979.00,965.68,969.75,13810000,969.75 1973-03-09,976.44,978.03,963.58,972.23,14070000,972.23 1973-03-08,979.98,985.25,973.59,976.44,15100000,976.44 1973-03-07,979.00,984.80,966.74,979.98,19310000,979.98 1973-03-06,966.89,982.39,966.44,979.00,17710000,979.00 1973-03-05,961.32,972.00,955.67,966.89,13720000,966.89 1973-03-02,949.65,962.97,937.69,961.32,17710000,961.32 1973-03-01,955.07,967.04,947.17,949.65,18210000,949.65 1973-02-28,947.92,958.31,938.82,955.07,17950000,955.07 1973-02-27,953.79,963.12,943.26,947.92,16130000,947.92 1973-02-26,959.89,962.90,943.78,953.79,15860000,953.79 1973-02-23,971.78,973.81,957.10,959.89,15450000,959.89 1973-02-22,974.34,978.63,963.05,971.78,14570000,971.78 1973-02-21,983.59,988.79,970.27,974.34,14880000,974.34 1973-02-20,979.23,991.04,975.69,983.59,14020000,983.59 1973-02-16,973.13,981.86,965.76,979.23,13320000,979.23 1973-02-15,979.91,984.12,966.29,973.13,13940000,973.13 1973-02-14,996.76,997.97,974.11,979.91,16520000,979.91 1973-02-13,991.65,1019.94,991.65,996.76,25320000,996.76 1973-02-12,980.81,996.24,980.81,991.57,16130000,991.57 1973-02-09,967.19,983.14,964.93,979.46,19260000,979.46 1973-02-08,968.32,973.81,954.17,967.19,18440000,967.19 1973-02-07,979.91,989.16,965.53,968.32,17960000,968.32 1973-02-06,978.40,986.00,972.23,979.91,15720000,979.91 1973-02-05,980.81,987.06,974.11,978.40,14580000,978.40 1973-02-02,985.78,992.32,975.02,980.81,17470000,980.81 1973-02-01,999.02,1008.58,983.14,985.78,20670000,985.78 1973-01-31,992.93,1004.06,988.11,999.02,14870000,999.02 1973-01-30,996.47,1005.34,989.09,992.93,15270000,992.93 1973-01-29,1003.54,1008.80,988.18,996.47,14680000,996.47 1973-01-26,1004.59,1008.50,989.46,1003.54,21130000,1003.54 1973-01-24,1018.66,1025.74,998.57,1004.59,20870000,1004.59 1973-01-23,1018.81,1024.68,1007.22,1018.66,19060000,1018.66 1973-01-22,1026.19,1034.69,1014.52,1018.81,15570000,1018.81 1973-01-19,1029.12,1031.68,1014.00,1026.19,17020000,1026.19 1973-01-18,1029.12,1039.96,1024.01,1029.12,17810000,1029.12 1973-01-17,1024.31,1036.35,1020.32,1029.12,17680000,1029.12 1973-01-16,1025.59,1033.34,1014.37,1024.31,19170000,1024.31 1973-01-15,1039.36,1053.28,1022.88,1025.59,21520000,1025.59 1973-01-12,1051.70,1059.90,1033.41,1039.36,22230000,1039.36 1973-01-11,1046.06,1067.20,1039.28,1051.70,25050000,1051.70 1973-01-10,1047.11,1053.28,1040.94,1046.06,20880000,1046.06 1973-01-09,1047.86,1053.21,1040.49,1047.11,16830000,1047.11 1973-01-08,1047.49,1053.58,1040.86,1047.86,16840000,1047.86 1973-01-05,1039.81,1053.43,1037.40,1047.49,19330000,1047.49 1973-01-04,1043.80,1047.86,1027.62,1039.81,20230000,1039.81 1973-01-03,1032.21,1049.59,1032.21,1043.80,20620000,1043.80 1973-01-02,1022.88,1038.98,1022.88,1031.68,17090000,1031.68 1972-12-29,1008.58,1027.39,1008.58,1020.02,27550000,1020.02 1972-12-27,1006.70,1014.22,1001.13,1007.68,19100000,1007.68 1972-12-26,1004.21,1010.91,999.85,1006.70,11120000,1006.70 1972-12-22,1000.00,1010.01,996.84,1004.21,12540000,1004.21 1972-12-21,1004.82,1010.91,996.09,1000.00,18290000,1000.00 1972-12-20,1009.18,1014.98,1001.88,1004.82,18490000,1004.82 1972-12-19,1013.25,1017.99,1004.06,1009.18,17000000,1009.18 1972-12-18,1022.05,1022.05,1004.29,1013.25,17540000,1013.25 1972-12-15,1025.06,1034.69,1018.59,1027.24,18300000,1027.24 1972-12-14,1030.48,1035.45,1020.09,1025.06,17930000,1025.06 1972-12-13,1033.19,1036.65,1025.14,1030.48,16540000,1030.48 1972-12-12,1036.27,1042.44,1029.65,1033.19,17040000,1033.19 1972-12-11,1033.19,1041.32,1029.80,1036.27,17230000,1036.27 1972-12-08,1033.26,1039.21,1027.17,1033.19,18030000,1033.19 1972-12-07,1027.54,1037.85,1025.36,1033.26,19320000,1033.26 1972-12-06,1022.95,1031.16,1018.29,1027.54,18610000,1027.54 1972-12-05,1027.02,1030.85,1017.46,1022.95,17800000,1022.95 1972-12-04,1023.93,1033.19,1021.45,1027.02,19730000,1027.02 1972-12-01,1018.21,1031.53,1016.56,1023.93,22570000,1023.93 1972-11-30,1018.81,1025.81,1010.54,1018.21,19340000,1018.21 1972-11-29,1019.34,1023.63,1011.89,1018.81,17380000,1018.81 1972-11-28,1017.76,1026.79,1012.57,1019.34,19210000,1019.34 1972-11-27,1025.21,1026.87,1008.65,1017.76,18190000,1017.76 1972-11-24,1020.54,1029.73,1014.15,1025.21,15760000,1025.21 1972-11-22,1013.25,1026.87,1009.93,1020.54,24510000,1020.54 1972-11-21,1005.04,1017.61,1002.86,1013.25,22110000,1013.25 1972-11-20,1005.57,1011.14,997.14,1005.04,16680000,1005.04 1972-11-17,1003.69,1012.34,998.57,1005.57,20220000,1005.57 1972-11-16,998.42,1008.13,991.57,1003.69,19580000,1003.69 1972-11-15,1003.16,1013.55,993.08,998.42,23270000,998.42 1972-11-14,997.07,1006.92,991.12,1003.16,20200000,1003.16 1972-11-13,995.26,1004.89,988.49,997.07,17210000,997.07 1972-11-10,988.26,1007.15,986.08,995.26,24360000,995.26 1972-11-09,983.74,992.32,973.89,988.26,17040000,988.26 1972-11-08,984.80,998.42,978.63,983.74,24620000,983.74 1972-11-06,984.12,993.38,977.05,984.80,21330000,984.80 1972-11-03,973.06,988.94,969.22,984.12,22510000,984.12 1972-11-02,968.54,977.80,961.77,973.06,20690000,973.06 1972-11-01,955.52,975.24,955.30,968.54,21360000,968.54 1972-10-31,946.42,958.53,944.39,955.52,15450000,955.52 1972-10-30,946.42,950.71,936.56,946.42,11820000,946.42 1972-10-27,950.56,956.20,941.07,946.42,15470000,946.42 1972-10-26,951.38,962.45,946.27,950.56,20790000,950.56 1972-10-25,952.51,958.46,944.99,951.38,17430000,951.38 1972-10-24,951.31,957.10,941.30,952.51,15240000,952.51 1972-10-23,945.21,958.31,945.21,951.31,14190000,951.31 1972-10-20,932.12,946.72,927.98,942.81,15740000,942.81 1972-10-19,932.34,939.27,926.70,932.12,13850000,932.12 1972-10-18,926.48,940.85,925.80,932.34,17290000,932.34 1972-10-17,921.66,931.29,917.07,926.48,13410000,926.48 1972-10-16,930.46,934.53,919.25,921.66,10940000,921.66 1972-10-13,937.46,940.17,923.77,930.46,12870000,930.46 1972-10-12,946.42,947.10,932.42,937.46,13130000,937.46 1972-10-11,951.84,956.05,941.60,946.42,11900000,946.42 1972-10-10,948.75,960.49,946.34,951.84,13310000,951.84 1972-10-09,945.36,952.21,941.00,948.75,7940000,948.75 1972-10-06,941.30,954.39,930.39,945.36,16630000,945.36 1972-10-05,951.31,955.67,937.54,941.30,17730000,941.30 1972-10-04,954.47,964.10,947.85,951.31,16640000,951.31 1972-10-03,953.27,959.96,948.22,954.47,13090000,954.47 1972-10-02,953.27,959.59,945.44,953.27,12440000,953.27 1972-09-29,955.15,965.08,949.05,953.27,16250000,953.27 1972-09-28,947.25,956.88,939.87,955.15,14710000,955.15 1972-09-27,936.56,949.05,932.95,947.25,14620000,947.25 1972-09-26,935.73,942.13,927.15,936.56,13150000,936.56 1972-09-25,943.03,947.47,933.10,935.73,10920000,935.73 1972-09-22,939.49,948.98,934.38,943.03,12570000,943.03 1972-09-21,940.25,945.44,932.72,939.49,11940000,939.49 1972-09-20,943.18,946.12,934.75,940.25,11980000,940.25 1972-09-19,945.36,952.44,939.12,943.18,13330000,943.18 1972-09-18,947.32,951.16,938.67,945.36,8880000,945.36 1972-09-15,947.55,952.29,940.62,947.32,11690000,947.32 1972-09-14,949.88,955.30,942.05,947.55,12500000,947.55 1972-09-13,946.04,954.09,941.30,949.88,13070000,949.88 1972-09-12,955.00,957.86,940.62,946.04,13560000,946.04 1972-09-11,961.24,964.55,951.08,955.00,10710000,955.00 1972-09-08,962.45,968.24,957.33,961.24,10980000,961.24 1972-09-07,963.43,968.02,957.41,962.45,11090000,962.45 1972-09-06,969.37,970.35,958.91,963.43,12010000,963.43 1972-09-05,970.05,977.35,964.63,969.37,10630000,969.37 1972-09-01,963.73,975.62,962.30,970.05,11600000,970.05 1972-08-31,957.86,966.89,953.57,963.73,12340000,963.73 1972-08-30,954.70,964.03,951.16,957.86,12470000,957.86 1972-08-29,956.95,961.62,945.29,954.70,12300000,954.70 1972-08-28,959.36,964.33,952.59,956.95,10720000,956.95 1972-08-25,958.38,964.86,949.80,959.36,13840000,959.36 1972-08-24,970.35,974.56,955.98,958.38,18280000,958.38 1972-08-23,973.51,980.36,962.60,970.35,18670000,970.35 1972-08-22,967.19,979.76,963.88,973.51,18560000,973.51 1972-08-21,965.83,974.19,958.16,967.19,14290000,967.19 1972-08-18,961.39,972.23,957.48,965.83,16150000,965.83 1972-08-17,964.25,971.25,955.60,961.39,14360000,961.39 1972-08-16,969.97,974.94,958.46,964.25,14950000,964.25 1972-08-15,973.51,978.33,962.30,969.97,16670000,969.97 1972-08-14,964.18,980.21,964.18,973.51,18870000,973.51 1972-08-11,952.89,966.59,948.75,964.18,16570000,964.18 1972-08-10,951.16,958.84,945.29,952.89,15260000,952.89 1972-08-09,952.44,958.99,943.86,951.16,15730000,951.16 1972-08-08,953.12,958.01,944.31,952.44,14550000,952.44 1972-08-07,951.76,959.36,945.67,953.12,13220000,953.12 1972-08-04,947.70,957.10,942.28,951.76,15700000,951.76 1972-08-03,941.15,953.19,939.12,947.70,19970000,947.70 1972-08-02,931.07,944.61,931.07,941.15,17920000,941.15 1972-08-01,924.74,935.36,922.03,930.46,15540000,930.46 1972-07-31,926.70,932.72,917.37,924.74,11120000,924.74 1972-07-28,926.85,933.93,920.15,926.70,13050000,926.70 1972-07-27,932.57,938.37,923.62,926.85,13870000,926.85 1972-07-26,934.45,940.92,927.60,932.57,14130000,932.57 1972-07-25,935.36,946.79,930.24,934.45,17180000,934.45 1972-07-24,922.19,941.98,922.19,935.36,18020000,935.36 1972-07-21,910.45,923.24,903.90,920.45,14010000,920.45 1972-07-20,916.69,919.40,905.55,910.45,15050000,910.45 1972-07-19,911.72,927.00,909.69,916.69,17880000,916.69 1972-07-18,914.96,917.97,900.06,911.72,16820000,911.72 1972-07-17,922.26,928.43,912.70,914.96,13170000,914.96 1972-07-14,916.99,927.83,911.88,922.26,13910000,922.26 1972-07-13,923.69,926.02,912.93,916.99,14740000,916.99 1972-07-12,925.87,934.15,919.33,923.69,16150000,923.69 1972-07-11,932.27,934.90,921.81,925.87,12830000,925.87 1972-07-10,938.06,943.03,928.73,932.27,11700000,932.27 1972-07-07,942.13,948.15,932.34,938.06,12900000,938.06 1972-07-06,934.90,955.45,934.90,942.13,19520000,942.13 1972-07-05,928.66,939.64,926.25,933.47,14710000,933.47 1972-07-03,929.03,935.05,922.71,928.66,8140000,928.66 1972-06-30,926.25,935.81,921.21,929.03,12860000,929.03 1972-06-29,930.84,932.95,917.75,926.25,14610000,926.25 1972-06-28,935.28,938.14,925.80,930.84,12140000,930.84 1972-06-27,936.41,943.33,928.96,935.28,13750000,935.28 1972-06-26,942.50,942.50,928.13,936.41,12720000,936.41 1972-06-23,950.71,957.25,939.27,944.69,13940000,944.69 1972-06-22,951.61,956.58,940.02,950.71,13410000,950.71 1972-06-21,948.22,959.96,943.63,951.61,15510000,951.61 1972-06-20,941.83,952.14,940.10,948.22,14970000,948.22 1972-06-19,945.06,947.62,935.43,941.83,11660000,941.83 1972-06-16,945.97,949.88,936.94,945.06,13010000,945.06 1972-06-15,946.79,956.05,940.25,945.97,16940000,945.97 1972-06-14,938.29,954.24,936.11,946.79,18320000,946.79 1972-06-13,936.71,943.33,928.88,938.29,15710000,938.29 1972-06-12,934.45,943.63,930.39,936.71,13390000,936.71 1972-06-09,941.30,942.88,930.01,934.45,12790000,934.45 1972-06-08,944.08,953.19,938.82,941.30,13820000,941.30 1972-06-07,951.46,952.51,938.52,944.08,15220000,944.08 1972-06-06,954.39,961.02,946.87,951.46,15980000,951.46 1972-06-05,961.39,964.48,948.52,954.39,13450000,954.39 1972-06-02,960.72,967.72,954.24,961.39,15400000,961.39 1972-06-01,960.72,966.36,954.85,960.72,14910000,960.72 1972-05-31,970.88,970.88,955.52,960.72,15230000,960.72 1972-05-30,971.25,979.46,966.51,971.18,15810000,971.18 1972-05-26,969.07,977.42,963.80,971.25,15730000,971.25 1972-05-25,965.46,975.54,960.57,969.07,16480000,969.07 1972-05-24,962.30,973.06,958.76,965.46,17870000,965.46 1972-05-23,965.31,970.05,956.20,962.30,16410000,962.30 1972-05-22,961.54,972.00,958.76,965.31,16030000,965.31 1972-05-19,951.23,967.56,950.11,961.54,19580000,961.54 1972-05-18,941.15,955.67,939.95,951.23,17370000,951.23 1972-05-17,939.27,944.61,932.95,941.15,13600000,941.15 1972-05-16,942.20,947.17,934.83,939.27,14070000,939.27 1972-05-15,941.83,948.45,936.63,942.20,13600000,942.20 1972-05-12,934.83,947.40,934.23,941.83,13990000,941.83 1972-05-11,931.07,941.15,925.87,934.83,12900000,934.83 1972-05-10,925.12,938.06,922.03,931.07,13870000,931.07 1972-05-09,937.54,937.54,917.37,925.12,19910000,925.12 1972-05-08,941.23,943.18,930.01,937.84,11250000,937.84 1972-05-05,937.31,948.30,932.57,941.23,13210000,941.23 1972-05-04,933.47,942.43,927.60,937.31,14790000,937.31 1972-05-03,935.20,947.32,927.90,933.47,15900000,933.47 1972-05-02,942.28,947.32,930.61,935.20,15370000,935.20 1972-05-01,954.17,956.95,938.59,942.28,12880000,942.28 1972-04-28,945.97,959.74,944.46,954.17,14160000,954.17 1972-04-27,946.94,954.92,940.70,945.97,15740000,945.97 1972-04-26,946.49,954.39,938.29,946.94,17710000,946.94 1972-04-25,957.48,959.14,943.63,946.49,17030000,946.49 1972-04-24,963.80,966.59,950.93,957.48,14650000,957.48 1972-04-21,966.29,974.64,959.21,963.80,18200000,963.80 1972-04-20,964.78,971.33,954.17,966.29,18190000,966.29 1972-04-19,968.92,975.92,959.36,964.78,19180000,964.78 1972-04-18,966.59,977.72,961.62,968.92,19410000,968.92 1972-04-17,967.72,972.16,959.36,966.59,15390000,966.59 1972-04-14,965.53,973.06,959.59,967.72,17460000,967.72 1972-04-13,966.96,973.28,960.42,965.53,17990000,965.53 1972-04-12,962.60,976.44,960.64,966.96,24690000,966.96 1972-04-11,958.08,967.79,951.23,962.60,19930000,962.60 1972-04-10,962.60,970.57,953.42,958.08,19470000,958.08 1972-04-07,959.44,965.91,950.26,962.60,19900000,962.60 1972-04-06,954.55,968.24,951.76,959.44,22830000,959.44 1972-04-05,943.41,958.99,943.33,954.55,22960000,954.55 1972-04-04,940.92,948.52,933.62,943.41,18110000,943.41 1972-04-03,940.70,948.75,935.66,940.92,14990000,940.92 1972-03-30,933.02,943.78,929.79,940.70,14360000,940.70 1972-03-29,937.01,940.17,925.87,933.02,13860000,933.02 1972-03-28,939.72,947.02,932.65,937.01,15380000,937.01 1972-03-27,942.28,946.57,933.77,939.72,12180000,939.72 1972-03-24,944.69,950.03,937.91,942.28,15390000,942.28 1972-03-23,933.93,949.20,932.34,944.69,18380000,944.69 1972-03-22,934.00,938.59,926.78,933.93,15400000,933.93 1972-03-21,940.32,940.32,925.95,934.00,18610000,934.00 1972-03-20,942.88,951.84,937.31,941.15,16420000,941.15 1972-03-17,936.71,949.88,931.52,942.88,16040000,942.88 1972-03-16,937.31,942.88,927.68,936.71,16700000,936.71 1972-03-15,934.00,945.44,929.18,937.31,19460000,937.31 1972-03-14,928.66,938.82,925.35,934.00,22370000,934.00 1972-03-13,939.87,941.23,924.22,928.66,16730000,928.66 1972-03-10,942.81,948.60,932.95,939.87,19690000,939.87 1972-03-09,945.59,950.78,937.61,942.81,21460000,942.81 1972-03-08,946.87,953.57,937.09,945.59,21290000,945.59 1972-03-07,950.18,956.20,940.40,946.87,22640000,946.87 1972-03-06,942.43,957.03,940.47,950.18,21000000,950.18 1972-03-03,933.77,948.00,930.69,942.43,20420000,942.43 1972-03-02,935.43,943.78,927.90,933.77,22200000,933.77 1972-03-01,928.13,943.03,924.14,935.43,23670000,935.43 1972-02-29,924.29,932.34,916.24,928.13,20320000,928.13 1972-02-28,922.79,930.31,917.14,924.29,18200000,924.29 1972-02-25,912.70,927.75,909.39,922.79,18180000,922.79 1972-02-24,911.88,919.25,906.61,912.70,16000000,912.70 1972-02-23,913.46,919.85,906.98,911.88,16770000,911.88 1972-02-22,917.52,922.86,909.17,913.46,16670000,913.46 1972-02-18,922.03,925.35,911.12,917.52,16590000,917.52 1972-02-17,922.94,933.25,916.84,922.03,22330000,922.03 1972-02-16,914.51,928.58,911.65,922.94,20670000,922.94 1972-02-15,910.90,920.98,906.46,914.51,17770000,914.51 1972-02-14,917.59,921.96,906.01,910.90,15840000,910.90 1972-02-11,921.28,924.82,910.52,917.59,17850000,917.59 1972-02-10,918.72,931.89,914.89,921.28,23460000,921.28 1972-02-09,907.13,921.81,905.18,918.72,19850000,918.72 1972-02-08,903.97,910.97,898.18,907.13,17390000,907.13 1972-02-07,906.68,913.61,898.93,903.97,16930000,903.97 1972-02-04,903.15,912.10,897.50,906.68,17890000,906.68 1972-02-03,905.85,910.97,896.30,903.15,19880000,903.15 1972-02-02,901.79,913.76,896.15,905.85,24070000,905.85 1972-02-01,902.17,906.23,894.34,901.79,19600000,901.79 1972-01-31,906.38,911.20,897.05,902.17,18250000,902.17 1972-01-28,899.83,913.23,896.60,906.38,25000000,906.38 1972-01-27,889.15,902.92,887.87,899.83,20360000,899.83 1972-01-26,894.72,897.65,883.43,889.15,14940000,889.15 1972-01-25,896.82,902.17,887.49,894.72,17570000,894.72 1972-01-24,907.44,911.20,893.81,896.82,15640000,896.82 1972-01-21,910.30,913.91,898.93,907.44,18810000,907.44 1972-01-20,914.96,922.19,906.76,910.30,20210000,910.30 1972-01-19,917.22,922.34,904.58,914.96,18800000,914.96 1972-01-18,911.12,923.99,908.94,917.22,21070000,917.22 1972-01-17,906.68,914.51,902.77,911.12,15860000,911.12 1972-01-14,905.18,910.82,899.16,906.68,14960000,906.68 1972-01-13,910.82,912.93,899.98,905.18,16410000,905.18 1972-01-12,912.10,922.03,906.01,910.82,20970000,910.82 1972-01-11,907.96,919.02,903.67,912.10,17970000,912.10 1972-01-10,910.37,914.43,898.48,907.96,15320000,907.96 1972-01-07,908.49,916.47,903.37,910.37,17140000,910.37 1972-01-06,904.43,913.83,901.87,908.49,21100000,908.49 1972-01-05,893.06,910.07,893.06,904.43,21350000,904.43 1972-01-04,889.30,897.73,882.75,892.23,15190000,892.23 1972-01-03,890.20,898.71,884.63,889.30,12570000,889.30 1971-12-31,889.07,895.77,884.48,890.20,14040000,890.20 1971-12-30,893.66,898.78,883.05,889.07,13810000,889.07 1971-12-29,889.98,902.47,886.59,893.66,17150000,893.66 1971-12-28,881.47,892.84,877.18,889.98,15090000,889.98 1971-12-27,881.17,889.83,875.68,881.47,11890000,881.47 1971-12-23,884.86,889.98,873.34,881.17,16000000,881.17 1971-12-22,888.32,893.81,878.54,884.86,18930000,884.86 1971-12-21,885.01,896.22,875.30,888.32,20460000,888.32 1971-12-20,876.28,895.17,876.28,885.01,23810000,885.01 1971-12-17,871.39,879.29,865.29,873.80,18270000,873.80 1971-12-16,863.76,878.69,863.26,871.39,21070000,871.39 1971-12-15,855.14,867.84,849.81,863.76,16890000,863.76 1971-12-14,858.79,864.92,851.12,855.14,16070000,855.14 1971-12-13,856.75,868.28,852.22,858.79,17020000,858.79 1971-12-10,852.15,861.86,847.69,856.75,17510000,856.75 1971-12-09,854.85,858.43,844.55,852.15,14710000,852.15 1971-12-08,857.40,861.71,847.91,854.85,16650000,854.85 1971-12-07,855.72,862.44,845.28,857.40,15250000,857.40 1971-12-06,859.59,872.59,852.58,855.72,17480000,855.72 1971-12-03,848.79,864.05,845.58,859.59,16760000,859.59 1971-12-02,846.01,854.70,837.47,848.79,17780000,848.79 1971-12-01,831.34,851.85,831.12,846.01,21040000,846.01 1971-11-30,829.73,837.03,819.22,831.34,18320000,831.34 1971-11-29,816.59,838.57,815.79,829.73,18910000,829.73 1971-11-26,799.87,818.12,799.87,816.59,10870000,816.59 1971-11-24,797.97,807.90,793.88,798.63,11870000,798.63 1971-11-23,803.15,807.10,790.67,797.97,16840000,797.97 1971-11-22,810.67,817.03,800.89,803.15,11390000,803.15 1971-11-19,815.35,817.98,804.83,810.67,12420000,810.67 1971-11-18,822.14,829.66,813.81,815.35,13010000,815.35 1971-11-17,818.71,825.79,812.13,822.14,12840000,822.14 1971-11-16,810.53,823.89,806.59,818.71,13300000,818.71 1971-11-15,812.94,820.68,806.66,810.53,9370000,810.53 1971-11-12,814.91,821.12,802.21,812.94,14540000,812.94 1971-11-11,826.15,827.91,810.82,814.91,13310000,814.91 1971-11-10,837.91,842.22,821.85,826.15,13410000,826.15 1971-11-09,837.54,845.72,832.21,837.91,12080000,837.91 1971-11-08,840.39,843.60,832.51,837.54,8520000,837.54 1971-11-05,843.17,845.94,832.94,840.39,10780000,840.39 1971-11-04,842.58,855.21,838.49,843.17,15750000,843.17 1971-11-03,828.34,845.87,828.34,842.58,14590000,842.58 1971-11-02,825.86,833.53,814.69,827.98,13330000,827.98 1971-11-01,839.00,840.25,823.21,825.86,10960000,825.86 1971-10-29,837.62,843.03,831.85,839.00,11710000,839.00 1971-10-28,836.38,844.63,827.83,837.62,15530000,837.62 1971-10-27,845.36,846.31,832.29,836.38,13480000,836.38 1971-10-26,848.50,857.26,842.95,845.36,13390000,845.36 1971-10-25,852.37,854.63,843.38,848.50,7340000,848.50 1971-10-22,854.85,863.90,848.57,852.37,14560000,852.37 1971-10-21,855.65,861.05,846.45,854.85,14990000,854.85 1971-10-20,868.43,873.39,851.20,855.65,16340000,855.65 1971-10-19,872.44,874.34,860.11,868.43,13040000,868.43 1971-10-18,874.58,880.40,868.87,872.44,10420000,872.44 1971-10-15,878.36,881.64,868.50,874.58,13120000,874.58 1971-10-14,888.80,889.16,875.22,878.36,12870000,878.36 1971-10-13,893.55,897.12,885.22,888.80,13540000,888.80 1971-10-12,891.94,899.61,888.29,893.55,14340000,893.55 1971-10-11,893.91,896.39,886.32,891.94,7800000,891.94 1971-10-08,901.80,902.82,890.55,893.91,13870000,893.91 1971-10-07,900.55,910.56,896.10,901.80,17780000,901.80 1971-10-06,891.14,902.38,886.90,900.55,15630000,900.55 1971-10-05,895.66,898.66,885.81,891.14,12360000,891.14 1971-10-04,893.98,904.42,892.01,895.66,14570000,895.66 1971-10-01,887.19,898.44,884.49,893.98,13400000,893.98 1971-09-30,883.83,894.13,878.14,887.19,13490000,887.19 1971-09-29,884.42,890.41,877.70,883.83,8580000,883.83 1971-09-28,883.47,891.50,877.77,884.42,11250000,884.42 1971-09-27,889.31,891.72,877.48,883.47,10220000,883.47 1971-09-24,891.28,900.26,886.24,889.31,13460000,889.31 1971-09-23,893.55,899.39,884.64,891.28,13250000,891.28 1971-09-22,903.40,904.94,891.72,893.55,14250000,893.55 1971-09-21,905.15,907.78,897.78,903.40,10640000,903.40 1971-09-20,908.22,911.29,900.19,905.15,9540000,905.15 1971-09-17,903.11,912.16,901.07,908.22,11020000,908.22 1971-09-16,904.86,908.81,898.66,903.11,10550000,903.11 1971-09-15,901.65,907.71,896.25,904.86,11080000,904.86 1971-09-14,909.39,911.73,898.58,901.65,11410000,901.65 1971-09-13,911.00,915.67,903.91,909.39,10000000,909.39 1971-09-10,915.89,916.84,904.42,911.00,11380000,911.00 1971-09-09,920.93,925.23,912.38,915.89,15790000,915.89 1971-09-08,916.47,925.67,911.87,920.93,14230000,920.93 1971-09-07,912.75,925.67,909.75,916.47,17080000,916.47 1971-09-03,900.63,914.06,899.53,912.75,14040000,912.75 1971-09-02,899.02,905.37,893.84,900.63,10690000,900.63 1971-09-01,898.07,906.25,894.20,899.02,10770000,899.02 1971-08-31,901.43,903.84,892.01,898.07,10430000,898.07 1971-08-30,908.15,912.53,898.51,901.43,11140000,901.43 1971-08-27,906.10,915.45,902.02,908.15,12490000,908.15 1971-08-26,908.37,914.06,898.88,906.10,13990000,906.10 1971-08-25,904.13,917.79,901.80,908.37,18280000,908.37 1971-08-24,892.38,909.02,892.09,904.13,18700000,904.13 1971-08-23,880.99,897.20,880.99,892.38,13040000,892.38 1971-08-20,880.77,887.27,874.93,880.91,11890000,880.91 1971-08-19,886.17,889.68,873.90,880.77,14190000,880.77 1971-08-18,899.90,901.36,882.08,886.17,20680000,886.17 1971-08-17,888.95,908.66,885.29,899.90,26790000,899.90 1971-08-16,882.59,906.32,882.59,888.95,31730000,888.95 1971-08-13,859.01,864.41,851.64,856.02,9960000,856.02 1971-08-12,848.57,863.46,848.57,859.01,15910000,859.01 1971-08-11,839.59,851.12,836.96,846.38,11370000,846.38 1971-08-10,842.65,846.82,834.92,839.59,9460000,839.59 1971-08-09,850.61,853.46,839.52,842.65,8110000,842.65 1971-08-06,849.45,855.94,844.70,850.61,9490000,850.61 1971-08-05,844.92,855.72,841.19,849.45,12100000,849.45 1971-08-04,850.03,857.70,840.10,844.92,15410000,844.92 1971-08-03,864.92,865.87,845.94,850.03,13490000,850.03 1971-08-02,858.43,871.86,857.70,864.92,11870000,864.92 1971-07-30,861.42,868.50,854.41,858.43,12970000,858.43 1971-07-29,872.01,873.03,856.97,861.42,14570000,861.42 1971-07-28,880.70,882.16,868.36,872.01,13940000,872.01 1971-07-27,888.87,891.28,877.04,880.70,11560000,880.70 1971-07-26,887.78,895.15,882.96,888.87,9930000,888.87 1971-07-23,886.68,893.03,880.33,887.78,12370000,887.78 1971-07-22,890.84,893.55,882.74,886.68,12570000,886.68 1971-07-21,892.30,896.54,886.61,890.84,11920000,890.84 1971-07-20,886.39,896.90,885.15,892.30,12540000,892.30 1971-07-19,888.51,893.47,879.23,886.39,11430000,886.39 1971-07-16,888.87,898.73,884.71,888.51,13870000,888.51 1971-07-15,891.21,901.43,885.00,888.87,13080000,888.87 1971-07-14,892.38,895.88,882.52,891.21,14360000,891.21 1971-07-13,903.40,906.47,888.80,892.38,13540000,892.38 1971-07-12,901.80,908.81,896.47,903.40,12020000,903.40 1971-07-09,900.99,908.73,896.69,901.80,12640000,901.80 1971-07-08,895.88,906.10,894.20,900.99,13920000,900.99 1971-07-07,892.30,903.18,888.87,895.88,14520000,895.88 1971-07-06,890.19,896.83,885.29,892.30,10440000,892.30 1971-07-02,893.03,895.52,885.73,890.19,9960000,890.19 1971-07-01,891.14,899.39,886.24,893.03,13090000,893.03 1971-06-30,882.30,895.66,881.28,891.14,15410000,891.14 1971-06-29,873.10,887.63,871.20,882.30,14460000,882.30 1971-06-28,876.68,879.53,866.82,873.10,9810000,873.10 1971-06-25,877.26,882.45,870.04,876.68,10580000,876.68 1971-06-24,879.45,885.44,872.01,877.26,11360000,877.26 1971-06-23,874.42,886.61,870.04,879.45,12640000,879.45 1971-06-22,876.53,884.56,866.31,874.42,15200000,874.42 1971-06-21,889.16,890.48,872.74,876.53,16490000,876.53 1971-06-18,906.25,906.47,887.63,889.16,15040000,889.16 1971-06-17,908.59,915.08,902.16,906.25,13980000,906.25 1971-06-16,907.20,915.52,901.29,908.59,14300000,908.59 1971-06-15,907.71,915.23,899.39,907.20,13550000,907.20 1971-06-14,916.47,917.79,904.13,907.71,11530000,907.71 1971-06-11,915.96,923.70,909.68,916.47,12270000,916.47 1971-06-10,912.46,921.00,907.78,915.96,12450000,915.96 1971-06-09,915.01,919.54,905.74,912.46,14250000,912.46 1971-06-08,923.06,925.89,911.95,915.01,13610000,915.01 1971-06-07,922.15,928.54,917.44,923.06,13800000,923.06 1971-06-04,921.30,926.78,915.40,922.15,14400000,922.15 1971-06-03,919.62,929.60,914.63,921.30,18790000,921.30 1971-06-02,913.65,925.31,911.96,919.62,17740000,919.62 1971-06-01,907.81,918.49,903.74,913.65,11930000,913.65 1971-05-28,905.78,912.24,900.58,907.81,11760000,907.81 1971-05-27,906.41,911.96,899.94,905.78,12610000,905.78 1971-05-26,906.69,914.91,901.07,906.41,13550000,906.41 1971-05-25,913.15,913.86,898.61,906.69,16050000,906.69 1971-05-24,921.87,923.69,911.05,913.15,12060000,913.15 1971-05-21,923.41,927.84,917.30,921.87,12090000,921.87 1971-05-20,920.04,931.42,917.93,923.41,11740000,923.41 1971-05-19,918.56,926.64,913.93,920.04,17640000,920.04 1971-05-18,921.30,926.64,909.99,918.56,17640000,918.56 1971-05-17,935.15,935.15,916.60,921.30,15980000,921.30 1971-05-14,936.34,942.03,930.37,936.06,16430000,936.06 1971-05-13,937.46,944.63,928.12,936.34,17640000,936.34 1971-05-12,937.25,943.86,930.65,937.46,15140000,937.46 1971-05-11,932.55,943.79,927.63,937.25,17730000,937.25 1971-05-10,936.97,938.87,925.24,932.55,12810000,932.55 1971-05-07,937.39,941.96,927.35,936.97,16490000,936.97 1971-05-06,939.92,948.85,933.53,937.39,19300000,937.39 1971-05-05,938.45,943.02,929.45,939.92,17270000,939.92 1971-05-04,932.41,942.38,927.42,938.45,17310000,938.45 1971-05-03,941.75,942.17,923.83,932.41,16120000,932.41 1971-04-30,948.15,951.31,936.20,941.75,17490000,941.75 1971-04-29,950.82,957.35,941.75,948.15,20340000,948.15 1971-04-28,947.09,958.12,941.82,950.82,24820000,950.82 1971-04-27,944.00,953.63,935.22,947.09,21250000,947.09 1971-04-26,947.79,953.20,937.46,944.00,18860000,944.00 1971-04-23,940.63,952.92,934.87,947.79,20150000,947.79 1971-04-22,941.33,947.65,932.97,940.63,19270000,940.63 1971-04-21,944.42,949.20,933.39,941.33,17040000,941.33 1971-04-20,948.85,952.43,940.49,944.42,17880000,944.42 1971-04-19,940.21,953.49,939.01,948.85,17730000,948.85 1971-04-16,938.17,945.55,932.55,940.21,18280000,940.21 1971-04-15,932.55,945.69,930.44,938.17,22540000,938.17 1971-04-14,927.28,937.96,921.51,932.55,19440000,932.55 1971-04-13,926.64,935.99,921.51,927.28,23200000,927.28 1971-04-12,920.39,932.83,917.02,926.64,19410000,926.64 1971-04-08,918.49,925.94,911.68,920.39,17590000,920.39 1971-04-07,912.73,925.59,908.94,918.49,22270000,918.49 1971-04-06,905.07,917.79,901.77,912.73,19990000,912.73 1971-04-05,903.04,909.99,897.48,905.07,16040000,905.07 1971-04-02,903.88,910.06,898.96,903.04,14520000,903.04 1971-04-01,904.37,910.06,898.75,903.88,13470000,903.88 1971-03-31,903.39,910.98,898.33,904.37,17610000,904.37 1971-03-30,903.48,909.99,896.78,903.39,15430000,903.39 1971-03-29,903.48,909.78,896.29,903.48,13650000,903.48 1971-03-26,900.81,910.32,895.95,903.48,15560000,903.48 1971-03-25,899.37,903.96,889.03,900.81,15870000,900.81 1971-03-24,908.89,910.05,896.77,899.37,15770000,899.37 1971-03-23,910.60,915.32,902.31,908.89,16470000,908.89 1971-03-22,912.92,917.78,905.53,910.60,14290000,910.60 1971-03-19,916.83,921.69,908.61,912.92,15150000,912.92 1971-03-18,914.02,922.30,910.46,916.83,17910000,916.83 1971-03-17,914.64,918.06,904.16,914.02,17070000,914.02 1971-03-16,908.20,920.93,908.06,914.64,22270000,914.64 1971-03-15,898.34,911.21,895.33,908.20,18920000,908.20 1971-03-12,899.44,903.14,892.25,898.34,14680000,898.34 1971-03-11,895.88,906.76,890.81,899.44,19830000,899.44 1971-03-10,899.10,902.59,891.50,895.88,17220000,895.88 1971-03-09,898.62,906.15,892.25,899.10,20490000,899.10 1971-03-08,898.00,905.19,891.43,898.62,19340000,898.62 1971-03-05,891.36,903.61,889.24,898.00,22430000,898.00 1971-03-04,882.39,894.92,878.01,891.36,17350000,891.36 1971-03-03,883.01,888.55,876.85,882.39,14680000,882.39 1971-03-02,882.53,887.94,875.27,883.01,14870000,883.01 1971-03-01,878.83,887.46,873.22,882.53,13020000,882.53 1971-02-26,881.98,886.36,870.55,878.83,17250000,878.83 1971-02-25,875.62,887.53,871.92,881.98,16200000,881.98 1971-02-24,870.00,881.37,868.29,875.62,15930000,875.62 1971-02-23,868.98,875.62,861.99,870.00,15080000,870.00 1971-02-22,877.05,877.05,863.29,868.98,15840000,868.98 1971-02-19,885.06,886.50,875.00,878.56,17860000,878.56 1971-02-18,887.87,891.16,877.67,885.06,16650000,885.06 1971-02-17,890.06,894.78,879.38,887.87,18720000,887.87 1971-02-16,888.83,898.14,882.26,890.06,21350000,890.06 1971-02-12,885.34,894.03,881.30,888.83,18470000,888.83 1971-02-11,881.09,891.02,878.77,885.34,19260000,885.34 1971-02-10,879.79,884.99,869.04,881.09,19040000,881.09 1971-02-09,882.12,889.17,874.79,879.79,28250000,879.79 1971-02-08,876.57,885.47,870.41,882.12,25590000,882.12 1971-02-05,874.79,882.67,868.22,876.57,20480000,876.57 1971-02-04,876.23,880.07,868.29,874.79,20860000,874.79 1971-02-03,874.59,880.61,866.51,876.23,21680000,876.23 1971-02-02,877.81,882.39,868.09,874.59,22030000,874.59 1971-02-01,868.50,882.19,866.03,877.81,20650000,877.81 1971-01-29,865.14,873.49,860.15,868.50,20960000,868.50 1971-01-28,860.83,869.11,853.92,865.14,18840000,865.14 1971-01-27,866.79,867.47,853.85,860.83,20640000,860.83 1971-01-26,865.62,873.84,859.19,866.79,21380000,866.79 1971-01-25,861.31,870.48,855.28,865.62,19050000,865.62 1971-01-22,854.74,866.58,854.46,861.31,21680000,861.31 1971-01-21,849.95,859.60,845.08,854.74,19060000,854.74 1971-01-20,849.47,856.24,842.96,849.95,18330000,849.95 1971-01-19,847.82,853.78,841.87,849.47,15800000,849.47 1971-01-18,845.70,854.39,841.25,847.82,15400000,847.82 1971-01-15,843.31,853.37,838.72,845.70,18010000,845.70 1971-01-14,841.11,849.26,832.97,843.31,17600000,843.31 1971-01-13,844.19,853.44,835.57,841.11,19070000,841.11 1971-01-12,837.21,849.19,834.68,844.19,17820000,844.19 1971-01-11,837.01,841.46,828.31,837.21,14720000,837.21 1971-01-08,837.83,843.31,831.94,837.01,14100000,837.01 1971-01-07,837.97,843.78,832.42,837.83,16460000,837.83 1971-01-06,835.77,843.92,831.67,837.97,16960000,837.97 1971-01-05,830.57,840.09,827.35,835.77,12600000,835.77 1971-01-04,838.92,839.06,826.53,830.57,10010000,830.57 1970-12-31,841.32,844.95,832.56,838.92,13390000,838.92 1970-12-30,842.00,848.23,836.05,841.32,19140000,841.32 1970-12-29,830.91,844.19,828.04,842.00,17750000,842.00 1970-12-28,828.38,834.75,824.07,830.91,12290000,830.91 1970-12-24,823.11,831.67,820.65,828.38,12140000,828.38 1970-12-23,822.77,830.16,816.54,823.11,15400000,823.11 1970-12-22,821.54,828.93,815.65,822.77,14510000,822.77 1970-12-21,822.77,828.45,815.31,821.54,12690000,821.54 1970-12-18,822.15,828.79,815.51,822.77,14360000,822.77 1970-12-17,819.07,826.94,815.85,822.15,13660000,822.15 1970-12-16,819.62,823.52,810.17,819.07,14240000,819.07 1970-12-15,823.18,826.12,813.25,819.62,13420000,819.62 1970-12-14,825.92,832.28,818.66,823.18,13810000,823.18 1970-12-11,821.06,831.67,818.18,825.92,15790000,825.92 1970-12-10,815.24,824.75,811.68,821.06,14610000,821.06 1970-12-09,815.10,819.96,806.27,815.24,13550000,815.24 1970-12-08,818.66,822.49,809.69,815.10,14370000,815.10 1970-12-07,816.06,823.59,810.24,818.66,15530000,818.66 1970-12-04,808.53,819.07,801.34,816.06,15980000,816.06 1970-12-03,802.64,816.88,801.48,808.53,20480000,808.53 1970-12-02,794.29,805.72,787.86,802.64,17960000,802.64 1970-12-01,794.09,805.65,787.45,794.29,20170000,794.29 1970-11-30,781.35,797.51,780.26,794.09,17700000,794.09 1970-11-27,774.71,783.61,771.15,781.35,10130000,781.35 1970-11-25,772.73,780.94,768.48,774.71,13490000,774.71 1970-11-24,767.52,775.60,762.60,772.73,12560000,772.73 1970-11-23,761.57,773.41,759.79,767.52,12720000,767.52 1970-11-20,755.82,764.10,752.19,761.57,10920000,761.57 1970-11-19,754.24,760.47,749.52,755.82,9280000,755.82 1970-11-18,760.47,761.77,751.78,754.24,9850000,754.24 1970-11-17,760.13,768.48,756.37,760.47,9450000,760.47 1970-11-16,759.79,764.99,752.46,760.13,9160000,760.13 1970-11-13,767.94,767.94,755.61,759.79,11890000,759.79 1970-11-12,779.50,781.76,765.88,768.00,12520000,768.00 1970-11-11,777.38,788.75,776.29,779.50,13520000,779.50 1970-11-10,777.66,783.00,773.34,777.38,12030000,777.38 1970-11-09,771.97,782.38,769.85,777.66,10890000,777.66 1970-11-06,771.56,777.38,765.81,771.97,9970000,771.97 1970-11-05,770.81,775.94,765.68,771.56,10800000,771.56 1970-11-04,768.07,777.25,764.92,770.81,12180000,770.81 1970-11-03,758.01,771.50,756.02,768.07,11760000,768.07 1970-11-02,755.61,762.25,750.68,758.01,9470000,758.01 1970-10-30,753.56,759.38,748.36,755.61,10520000,755.61 1970-10-29,755.96,760.34,749.45,753.56,10440000,753.56 1970-10-28,754.45,759.31,746.71,755.96,10660000,755.96 1970-10-27,756.43,759.38,750.21,754.45,9680000,754.45 1970-10-26,759.38,764.24,753.42,756.43,9200000,756.43 1970-10-23,757.87,764.03,753.90,759.38,10270000,759.38 1970-10-22,759.65,763.28,753.22,757.87,9000000,757.87 1970-10-21,758.83,769.24,756.64,759.65,11330000,759.65 1970-10-20,756.50,764.03,750.82,758.83,10630000,758.83 1970-10-19,763.35,766.09,753.29,756.50,9890000,756.50 1970-10-16,767.87,771.70,759.10,763.35,11300000,763.35 1970-10-15,762.73,773.27,760.88,767.87,11250000,767.87 1970-10-14,760.06,767.25,754.72,762.73,9920000,762.73 1970-10-13,764.24,767.11,754.38,760.06,9500000,760.06 1970-10-12,768.69,770.47,758.42,764.24,8570000,764.24 1970-10-09,777.04,780.46,764.72,768.69,13980000,768.69 1970-10-08,783.68,789.29,773.48,777.04,14500000,777.04 1970-10-07,782.45,788.47,771.22,783.68,15610000,783.68 1970-10-06,776.70,791.07,773.62,782.45,20240000,782.45 1970-10-05,766.16,780.53,763.76,776.70,19760000,776.70 1970-10-02,760.68,769.72,756.43,766.16,15420000,766.16 1970-10-01,760.68,764.79,754.38,760.68,9700000,760.68 1970-09-30,760.88,766.91,754.79,760.68,14830000,760.68 1970-09-29,758.97,766.09,749.66,760.88,17880000,760.88 1970-09-28,761.77,764.65,750.68,758.97,14390000,758.97 1970-09-25,759.31,767.39,754.65,761.77,20470000,761.77 1970-09-24,754.38,764.99,749.04,759.31,21340000,759.31 1970-09-23,747.47,762.32,744.25,754.38,16940000,754.38 1970-09-22,751.92,753.15,741.51,747.47,12110000,747.47 1970-09-21,758.49,763.96,748.22,751.92,12540000,751.92 1970-09-18,757.67,766.29,751.92,758.49,15900000,758.49 1970-09-17,754.31,766.29,751.57,757.67,15530000,757.67 1970-09-16,750.55,759.45,744.18,754.31,12090000,754.31 1970-09-15,757.05,757.05,745.14,750.55,9830000,750.55 1970-09-14,761.84,766.84,751.37,757.12,11900000,757.12 1970-09-11,760.75,767.32,755.48,761.84,12140000,761.84 1970-09-10,766.43,768.69,754.65,760.75,11900000,760.75 1970-09-09,773.14,776.97,759.31,766.43,16250000,766.43 1970-09-08,771.15,778.27,759.99,773.14,17110000,773.14 1970-09-04,765.27,775.12,761.91,771.15,15360000,771.15 1970-09-03,756.64,770.33,755.89,765.27,14110000,765.27 1970-09-02,758.15,760.13,748.43,756.64,9710000,756.64 1970-09-01,764.58,766.16,754.93,758.15,10960000,758.15 1970-08-31,765.81,770.67,759.86,764.58,10740000,764.58 1970-08-28,759.79,772.04,756.37,765.81,13820000,765.81 1970-08-27,760.47,766.84,752.53,759.79,12440000,759.79 1970-08-26,758.97,769.78,755.34,760.47,15970000,760.47 1970-08-25,759.58,764.17,747.47,758.97,17520000,758.97 1970-08-24,747.19,765.68,747.19,759.58,18910000,759.58 1970-08-21,729.60,748.84,728.78,745.41,13420000,745.41 1970-08-20,723.99,732.82,717.76,729.60,10170000,729.60 1970-08-19,716.66,728.92,715.09,723.99,9870000,723.99 1970-08-18,709.47,721.11,709.47,716.66,9500000,716.66 1970-08-17,710.84,713.92,704.41,709.06,6940000,709.06 1970-08-14,707.35,715.84,704.75,710.84,7850000,710.84 1970-08-13,710.64,713.51,702.83,707.35,8640000,707.35 1970-08-12,712.55,716.87,707.83,710.64,7440000,710.64 1970-08-11,713.92,716.73,706.39,712.55,7330000,712.55 1970-08-10,725.01,725.01,709.95,713.92,7580000,713.92 1970-08-07,722.82,731.93,718.03,725.70,9370000,725.70 1970-08-06,724.81,728.92,716.86,722.82,7560000,722.82 1970-08-05,725.90,732.06,719.67,724.81,7660000,724.81 1970-08-04,722.96,728.85,714.88,725.90,8310000,725.90 1970-08-03,734.12,734.67,718.65,722.96,7650000,722.96 1970-07-31,734.73,743.36,728.23,734.12,11640000,734.12 1970-07-30,735.56,740.07,728.78,734.73,10430000,734.73 1970-07-29,731.45,742.40,729.39,735.56,12580000,735.56 1970-07-28,730.08,735.49,724.40,731.45,9040000,731.45 1970-07-27,730.22,735.01,724.53,730.08,7460000,730.08 1970-07-24,732.68,736.58,722.96,730.22,9520000,730.22 1970-07-23,724.67,737.88,718.44,732.68,12460000,732.68 1970-07-22,722.07,735.01,716.25,724.67,12460000,724.67 1970-07-21,733.91,734.12,717.96,722.07,9940000,722.07 1970-07-20,735.08,743.36,728.64,733.91,11660000,733.91 1970-07-17,725.49,739.46,725.49,735.08,13870000,735.08 1970-07-16,712.14,730.76,712.14,723.44,12200000,723.44 1970-07-15,703.04,716.32,699.48,711.66,8860000,711.66 1970-07-14,702.22,707.69,696.40,703.04,7360000,703.04 1970-07-13,700.10,709.34,696.19,702.22,7450000,702.22 1970-07-10,692.77,704.41,689.69,700.10,10160000,700.10 1970-07-09,682.09,697.63,681.48,692.77,12820000,692.77 1970-07-08,669.36,684.08,666.00,682.09,10970000,682.09 1970-07-07,675.66,679.90,665.32,669.36,10470000,669.36 1970-07-06,689.14,689.90,671.69,675.66,9340000,675.66 1970-07-02,687.64,697.02,684.76,689.14,8440000,689.14 1970-07-01,683.53,692.02,678.26,687.64,8610000,687.64 1970-06-30,682.91,692.36,679.08,683.53,9280000,683.53 1970-06-29,687.84,691.13,679.15,682.91,8770000,682.91 1970-06-26,693.59,700.51,686.06,687.84,9160000,687.84 1970-06-25,692.29,701.60,686.40,693.59,8200000,693.59 1970-06-24,698.11,705.37,685.31,692.29,12630000,692.29 1970-06-23,716.11,716.66,696.40,698.11,10790000,698.11 1970-06-22,720.43,723.17,707.15,716.11,8700000,716.11 1970-06-19,713.65,728.23,713.65,720.43,10980000,720.43 1970-06-18,704.68,718.92,696.95,712.69,8870000,712.69 1970-06-17,706.26,715.36,699.55,704.68,9870000,704.68 1970-06-16,687.36,711.80,686.88,706.26,11330000,706.26 1970-06-15,684.21,694.82,679.83,687.36,6920000,687.36 1970-06-12,684.42,688.66,674.90,684.21,8890000,684.21 1970-06-11,694.35,695.44,677.85,684.42,7770000,684.42 1970-06-10,700.16,703.24,690.03,694.35,7240000,694.35 1970-06-09,700.23,705.64,695.17,700.16,7050000,700.16 1970-06-08,695.03,709.75,689.83,700.23,8040000,700.23 1970-06-05,706.53,707.56,687.91,695.03,12450000,695.03 1970-06-04,713.86,723.92,704.41,706.53,14380000,706.53 1970-06-03,709.61,721.73,702.22,713.86,16600000,713.86 1970-06-02,710.36,719.13,698.32,709.61,13480000,709.61 1970-06-01,700.44,715.64,694.14,710.36,15020000,710.36 1970-05-29,684.15,703.86,673.06,700.44,14630000,700.44 1970-05-28,666.96,690.92,666.96,684.15,18910000,684.15 1970-05-27,631.98,668.81,631.98,663.20,17460000,663.20 1970-05-26,641.36,649.64,627.46,631.16,17030000,631.16 1970-05-25,660.80,660.80,639.10,641.36,12660000,641.36 1970-05-22,665.25,675.11,653.27,662.17,12170000,662.17 1970-05-21,676.55,676.62,654.37,665.25,16710000,665.25 1970-05-20,690.72,690.72,674.56,676.55,13020000,676.55 1970-05-19,702.81,704.20,689.62,691.40,9480000,691.40 1970-05-18,702.22,709.74,695.35,702.81,8280000,702.81 1970-05-15,684.79,705.58,680.37,702.22,14570000,702.22 1970-05-14,693.57,693.57,673.51,684.79,13920000,684.79 1970-05-13,703.80,703.80,686.64,693.84,10720000,693.84 1970-05-12,710.07,715.15,699.31,704.59,10850000,704.59 1970-05-11,717.73,721.03,707.04,710.07,6650000,710.07 1970-05-08,723.07,725.51,713.04,717.73,6930000,717.73 1970-05-07,718.39,730.33,713.37,723.07,9530000,723.07 1970-05-06,709.74,731.19,707.76,718.39,14380000,718.39 1970-05-05,714.56,720.63,704.46,709.74,10580000,709.74 1970-05-04,732.38,732.38,710.40,714.56,11450000,714.56 1970-05-01,736.07,740.76,723.60,733.63,8290000,733.63 1970-04-30,737.39,745.58,728.48,736.07,9880000,736.07 1970-04-29,724.33,740.03,716.74,737.39,15800000,737.39 1970-04-28,735.15,740.76,720.70,724.33,12620000,724.33 1970-04-27,747.29,750.46,731.72,735.15,10240000,735.15 1970-04-24,750.59,754.42,742.21,747.29,10410000,747.29 1970-04-23,760.63,760.63,745.45,750.59,11050000,750.59 1970-04-22,772.51,774.35,758.51,762.61,10780000,762.61 1970-04-21,775.87,783.00,769.87,772.51,8490000,772.51 1970-04-20,775.94,780.56,769.67,775.87,8280000,775.87 1970-04-17,775.87,781.22,766.96,775.94,10990000,775.94 1970-04-16,782.60,787.22,773.03,775.87,10250000,775.87 1970-04-15,780.56,788.87,777.06,782.60,9410000,782.60 1970-04-14,785.90,787.35,772.90,780.56,10840000,780.56 1970-04-13,790.46,793.82,782.07,785.90,8810000,785.90 1970-04-10,792.50,797.25,785.04,790.46,10020000,790.46 1970-04-09,791.64,798.84,786.96,792.50,9060000,792.50 1970-04-08,791.64,796.00,787.42,791.64,9070000,791.64 1970-04-07,791.18,797.12,785.70,791.64,8490000,791.64 1970-04-06,791.84,796.07,786.30,791.18,8380000,791.18 1970-04-03,792.37,796.40,787.02,791.84,9920000,791.84 1970-04-02,792.04,797.91,787.02,792.37,10520000,792.37 1970-04-01,785.57,795.67,784.05,792.04,9810000,792.04 1970-03-31,784.65,789.20,778.38,785.57,8370000,785.57 1970-03-30,791.05,792.37,779.17,784.65,9600000,784.65 1970-03-26,790.13,797.45,785.24,791.05,11350000,791.05 1970-03-25,775.67,803.26,775.67,790.13,17500000,790.13 1970-03-24,764.52,776.99,764.52,773.76,8840000,773.76 1970-03-23,763.66,768.41,757.99,763.60,7330000,763.60 1970-03-20,764.98,768.55,758.91,763.66,7910000,763.66 1970-03-19,767.95,773.76,761.55,764.98,8930000,764.98 1970-03-18,767.42,775.67,763.93,767.95,9790000,767.95 1970-03-17,765.05,773.36,759.17,767.42,9090000,767.42 1970-03-16,772.11,772.84,760.16,765.05,8910000,765.05 1970-03-13,776.47,779.30,768.02,772.11,9560000,772.11 1970-03-12,778.12,781.55,771.77,776.47,9140000,776.47 1970-03-11,779.70,785.84,774.29,778.12,9180000,778.12 1970-03-10,778.31,785.37,772.18,779.70,9450000,779.70 1970-03-09,784.12,785.57,773.56,778.31,9760000,778.31 1970-03-06,787.55,789.93,779.37,784.12,10980000,784.12 1970-03-05,788.15,795.54,783.13,787.55,11370000,787.55 1970-03-04,787.42,795.54,782.27,788.15,11850000,788.15 1970-03-03,780.23,790.52,775.08,787.42,11700000,787.42 1970-03-02,777.59,790.52,774.49,780.23,12270000,780.23 1970-02-27,764.45,784.19,762.61,777.59,12890000,777.59 1970-02-26,768.28,770.53,755.48,764.45,11540000,764.45 1970-02-25,754.42,772.70,749.47,768.28,13210000,768.28 1970-02-24,757.46,761.68,748.88,754.42,10810000,754.42 1970-02-20,757.92,764.45,749.34,757.46,10790000,757.46 1970-02-19,756.80,766.90,751.58,757.92,12890000,757.92 1970-02-18,747.43,762.61,745.45,756.80,11950000,756.80 1970-02-17,753.70,757.13,741.09,747.43,10140000,747.43 1970-02-16,753.30,761.09,748.02,753.70,19780000,753.70 1970-02-13,755.61,758.65,745.97,753.30,11060000,753.30 1970-02-12,757.33,762.28,748.88,755.61,10010000,755.61 1970-02-11,746.63,760.69,739.90,757.33,12260000,757.33 1970-02-10,755.68,758.51,743.20,746.63,10110000,746.63 1970-02-09,752.77,764.92,750.40,755.68,10830000,755.68 1970-02-06,750.26,758.71,744.98,752.77,10150000,752.77 1970-02-05,754.49,756.73,743.33,750.26,9430000,750.26 1970-02-04,757.46,765.97,748.09,754.49,11040000,754.49 1970-02-03,746.44,764.45,738.78,757.46,16050000,757.46 1970-02-02,744.06,756.47,739.37,746.44,13440000,746.44 1970-01-30,748.35,756.20,739.11,744.06,12320000,744.06 1970-01-29,758.84,760.69,743.73,748.35,12210000,748.35 1970-01-28,763.99,769.87,755.74,758.84,10510000,758.84 1970-01-27,768.88,773.03,757.92,763.99,9630000,763.99 1970-01-26,775.54,777.52,762.54,768.88,10670000,768.88 1970-01-23,786.10,789.40,774.35,775.54,11000000,775.54 1970-01-22,782.27,793.16,777.39,786.10,11050000,786.10 1970-01-21,777.85,788.61,773.96,782.27,9880000,782.27 1970-01-20,776.07,783.13,770.72,777.85,11050000,777.85 1970-01-19,782.60,784.52,772.18,776.07,9500000,776.07 1970-01-16,785.04,791.97,778.25,782.60,11940000,782.60 1970-01-15,787.16,791.25,777.98,785.04,11120000,785.04 1970-01-14,788.01,796.73,780.36,787.16,10380000,787.16 1970-01-13,790.52,796.79,782.47,788.01,9870000,788.01 1970-01-12,798.11,799.23,786.30,790.52,8900000,790.52 1970-01-09,802.07,805.70,794.35,798.11,9380000,798.11 1970-01-08,801.81,809.33,796.92,802.07,10670000,802.07 1970-01-07,803.66,808.47,796.20,801.81,10010000,801.81 1970-01-06,811.31,814.08,798.71,803.66,11460000,803.66 1970-01-05,809.20,819.23,804.84,811.31,11490000,811.31 1970-01-02,800.36,813.56,797.32,809.20,8050000,809.20 1969-12-31,794.68,806.69,792.24,800.36,19380000,800.36 1969-12-30,792.37,799.63,786.30,794.68,15790000,794.68 1969-12-29,797.65,803.19,787.62,792.37,12500000,792.37 1969-12-26,794.15,802.47,790.85,797.65,6750000,797.65 1969-12-24,783.79,799.63,782.67,794.15,11670000,794.15 1969-12-23,785.97,789.66,776.27,783.79,13890000,783.79 1969-12-22,789.86,796.13,781.48,785.97,12680000,785.97 1969-12-19,783.79,798.18,780.76,789.86,15420000,789.86 1969-12-18,769.93,788.87,764.45,783.79,15950000,783.79 1969-12-17,773.83,780.16,765.71,769.93,12840000,769.93 1969-12-16,784.05,787.42,770.46,773.83,11880000,773.83 1969-12-15,786.69,791.97,779.63,784.05,11100000,784.05 1969-12-12,783.53,794.61,780.23,786.69,11630000,786.69 1969-12-11,783.99,791.25,778.38,783.53,10430000,783.53 1969-12-10,783.79,791.51,773.76,783.99,12590000,783.99 1969-12-09,785.04,794.42,778.18,783.79,12290000,783.79 1969-12-08,793.03,797.32,781.48,785.04,9990000,785.04 1969-12-05,796.53,804.05,788.94,793.03,11150000,793.03 1969-12-04,793.36,801.15,783.86,796.53,13230000,796.53 1969-12-03,801.35,804.78,789.93,793.36,11300000,793.36 1969-12-02,805.04,808.34,794.94,801.35,9940000,801.35 1969-12-01,812.30,816.39,802.20,805.04,9950000,805.04 1969-11-28,810.52,818.57,805.37,812.30,8550000,812.30 1969-11-26,807.29,814.15,800.36,810.52,10630000,810.52 1969-11-25,812.90,818.37,803.92,807.29,11560000,807.29 1969-11-24,823.13,825.96,808.01,812.90,10940000,812.90 1969-11-21,831.18,832.43,820.35,823.13,9840000,823.13 1969-11-20,839.96,840.28,823.98,831.18,12010000,831.18 1969-11-19,845.17,848.60,835.93,839.96,11240000,839.96 1969-11-18,842.53,848.67,836.99,845.17,11010000,845.17 1969-11-17,849.26,851.04,837.45,842.53,10120000,842.53 1969-11-14,849.85,854.74,842.00,849.26,10580000,849.26 1969-11-13,855.99,858.90,844.64,849.85,12090000,849.85 1969-11-12,859.75,863.98,851.70,855.99,12480000,855.99 1969-11-11,863.05,866.62,853.62,859.75,10080000,859.75 1969-11-10,860.48,871.77,856.65,863.05,12490000,863.05 1969-11-07,855.20,867.28,850.38,860.48,13280000,860.48 1969-11-06,854.08,859.82,846.49,855.20,11110000,855.20 1969-11-05,853.48,862.59,847.54,854.08,12110000,854.08 1969-11-04,854.54,859.82,841.67,853.48,12340000,853.48 1969-11-03,855.99,860.68,847.41,854.54,11140000,854.54 1969-10-31,850.51,860.61,845.04,855.99,13100000,855.99 1969-10-30,848.34,854.28,839.82,850.51,12820000,850.51 1969-10-29,855.86,858.83,845.37,848.34,12380000,848.34 1969-10-28,860.28,865.23,851.90,855.86,12410000,855.86 1969-10-27,862.26,866.95,852.56,860.28,12160000,860.28 1969-10-24,855.73,868.00,851.31,862.26,15430000,862.26 1969-10-23,860.35,863.38,845.23,855.73,14780000,855.73 1969-10-22,846.88,864.37,844.90,860.35,19320000,860.35 1969-10-21,839.23,850.78,834.94,846.88,16460000,846.88 1969-10-20,836.06,844.18,829.59,839.23,13540000,839.23 1969-10-17,838.77,845.23,829.73,836.06,13740000,836.06 1969-10-16,830.06,848.14,825.50,838.77,19500000,838.77 1969-10-15,832.43,837.12,823.13,830.06,15740000,830.06 1969-10-14,821.21,839.49,821.21,832.43,19950000,832.43 1969-10-13,806.96,820.88,804.51,819.30,13620000,819.30 1969-10-10,803.79,813.23,799.89,806.96,12210000,806.96 1969-10-09,802.20,808.94,793.95,803.79,10420000,803.79 1969-10-08,806.23,809.79,797.65,802.20,10370000,802.20 1969-10-07,809.40,813.23,803.13,806.23,10050000,806.23 1969-10-06,808.41,814.94,802.73,809.40,9180000,809.40 1969-10-03,811.84,819.76,803.59,808.41,12410000,808.41 1969-10-02,806.89,815.87,797.78,811.84,11430000,811.84 1969-10-01,813.09,814.48,803.37,806.89,9090000,806.89 1969-09-30,818.04,821.67,808.54,813.09,9180000,813.09 1969-09-29,824.18,826.03,811.05,818.04,10170000,818.04 1969-09-26,829.92,832.83,820.09,824.18,9680000,824.18 1969-09-25,834.68,838.50,826.49,829.92,10690000,829.92 1969-09-24,834.81,840.48,829.53,834.68,11320000,834.68 1969-09-23,831.77,841.80,827.28,834.81,13030000,834.81 1969-09-22,830.39,835.80,823.79,831.77,9280000,831.77 1969-09-19,831.57,837.32,825.30,830.39,12270000,830.39 1969-09-18,826.56,836.66,822.80,831.57,11170000,831.57 1969-09-17,831.64,835.47,821.61,826.56,10980000,826.56 1969-09-16,830.45,836.85,824.84,831.64,11160000,831.64 1969-09-15,824.25,835.73,821.28,830.45,10680000,830.45 1969-09-12,825.77,830.65,818.37,824.25,10800000,824.25 1969-09-11,828.01,838.50,821.94,825.77,12370000,825.77 1969-09-10,815.67,831.71,813.69,828.01,11490000,828.01 1969-09-09,811.84,822.20,804.45,815.67,10980000,815.67 1969-09-08,819.50,820.55,808.67,811.84,8310000,811.84 1969-09-05,825.30,826.82,816.46,819.50,8890000,819.50 1969-09-04,835.67,835.67,822.20,825.30,9380000,825.30 1969-09-03,837.78,841.61,829.86,835.67,8760000,835.67 1969-09-02,836.72,845.96,831.31,837.78,8560000,837.78 1969-08-29,828.41,839.96,825.37,836.72,8850000,836.72 1969-08-28,824.78,832.23,822.14,828.41,7730000,828.41 1969-08-27,823.52,830.39,819.43,824.78,9100000,824.78 1969-08-26,830.39,830.39,818.84,823.52,8910000,823.52 1969-08-25,837.25,841.54,828.01,831.44,8410000,831.44 1969-08-22,834.87,843.72,829.33,837.25,10140000,837.25 1969-08-21,833.22,839.69,828.60,834.87,8420000,834.87 1969-08-20,833.69,837.91,827.55,833.22,9680000,833.22 1969-08-19,827.68,841.28,824.97,833.69,12640000,833.69 1969-08-18,820.88,830.39,816.46,827.68,9420000,827.68 1969-08-15,813.23,825.17,810.52,820.88,10210000,820.88 1969-08-14,809.13,818.11,805.37,813.23,9690000,813.23 1969-08-13,812.96,815.07,800.62,809.13,9910000,809.13 1969-08-12,819.83,821.54,810.39,812.96,7870000,812.96 1969-08-11,824.46,826.76,816.33,819.83,6680000,819.83 1969-08-08,826.27,830.27,819.87,824.46,8760000,824.46 1969-08-07,825.88,832.02,820.26,826.27,9450000,826.27 1969-08-06,821.23,831.63,817.67,825.88,11100000,825.88 1969-08-05,822.58,827.30,813.40,821.23,8940000,821.23 1969-08-04,826.59,835.06,817.61,822.58,10700000,822.58 1969-08-01,815.60,833.63,815.60,826.59,15070000,826.59 1969-07-31,803.58,819.87,800.67,815.47,14160000,815.47 1969-07-30,801.96,809.40,788.07,803.58,15580000,803.58 1969-07-29,806.23,817.86,798.41,801.96,13630000,801.96 1969-07-28,818.06,819.48,803.26,806.23,11800000,806.23 1969-07-25,826.53,830.08,814.83,818.06,9800000,818.06 1969-07-24,827.95,834.22,821.10,826.53,9750000,826.53 1969-07-23,834.02,836.48,821.35,827.95,11680000,827.95 1969-07-22,845.92,851.54,831.76,834.02,9780000,834.02 1969-07-18,853.09,853.54,839.06,845.92,8590000,845.92 1969-07-17,849.34,863.04,845.79,853.09,10450000,853.09 1969-07-16,841.13,854.64,840.29,849.34,10470000,849.34 1969-07-15,843.14,847.60,832.79,841.13,11110000,841.13 1969-07-14,852.25,855.93,841.07,843.14,8310000,843.14 1969-07-11,847.79,858.91,844.49,852.25,11730000,852.25 1969-07-10,861.04,861.04,844.30,847.79,11450000,847.79 1969-07-09,870.35,871.06,857.94,861.62,9320000,861.62 1969-07-08,880.82,880.82,866.47,870.35,9320000,870.35 1969-07-07,886.12,893.87,879.27,883.21,9970000,883.21 1969-07-03,880.69,891.55,877.71,886.12,10110000,886.12 1969-07-02,875.90,884.69,872.87,880.69,11350000,880.69 1969-07-01,873.19,881.27,867.83,875.90,9890000,875.90 1969-06-30,869.76,880.69,867.18,873.19,8640000,873.19 1969-06-27,870.28,876.49,863.56,869.76,9020000,869.76 1969-06-26,874.10,876.16,862.78,870.28,10310000,870.28 1969-06-25,877.20,884.69,870.41,874.10,10490000,874.10 1969-06-24,870.86,883.73,869.25,877.20,11460000,877.20 1969-06-23,876.16,880.75,862.46,870.86,12900000,870.86 1969-06-20,882.37,888.77,873.32,876.16,11360000,876.16 1969-06-19,887.09,889.54,877.46,882.37,11160000,882.37 1969-06-18,885.73,897.10,882.30,887.09,11290000,887.09 1969-06-17,891.16,893.29,876.55,885.73,12210000,885.73 1969-06-16,894.84,902.79,888.83,891.16,10400000,891.16 1969-06-13,892.58,902.28,886.89,894.84,13070000,894.84 1969-06-12,904.60,906.22,890.71,892.58,11790000,892.58 1969-06-11,912.49,913.39,899.24,904.60,13640000,904.60 1969-06-10,918.05,922.83,909.32,912.49,10660000,912.49 1969-06-09,924.77,925.48,911.91,918.05,10650000,918.05 1969-06-06,930.71,936.14,921.41,924.77,12520000,924.77 1969-06-05,928.84,937.24,925.35,930.71,12350000,930.71 1969-06-04,930.78,936.47,925.87,928.84,10840000,928.84 1969-06-03,933.17,937.56,925.74,930.78,11190000,930.78 1969-06-02,937.56,938.73,927.68,933.17,9180000,933.17 1969-05-29,936.92,944.29,931.62,937.56,11770000,937.56 1969-05-28,938.66,941.96,928.58,936.92,11330000,936.92 1969-05-27,946.94,950.23,934.33,938.66,10580000,938.66 1969-05-26,947.45,954.05,942.22,946.94,9030000,946.94 1969-05-23,950.04,953.92,942.48,947.45,10900000,947.45 1969-05-22,951.78,963.09,946.10,950.04,13710000,950.04 1969-05-21,949.26,956.18,941.31,951.78,12100000,951.78 1969-05-20,959.02,959.86,944.35,949.26,10280000,949.26 1969-05-19,967.30,968.98,954.56,959.02,9790000,959.02 1969-05-16,965.16,971.56,959.80,967.30,12280000,967.30 1969-05-15,968.85,973.18,958.51,965.16,11930000,965.16 1969-05-14,962.97,974.92,959.86,968.85,14360000,968.85 1969-05-13,957.86,967.62,954.37,962.97,12910000,962.97 1969-05-12,961.61,964.97,951.14,957.86,10550000,957.86 1969-05-09,963.68,971.11,955.86,961.61,12530000,961.61 1969-05-08,959.60,970.14,954.76,963.68,13050000,963.68 1969-05-07,962.06,967.36,953.08,959.60,14030000,959.60 1969-05-06,958.95,968.23,954.05,962.06,14700000,962.06 1969-05-05,957.17,965.43,951.07,958.95,13300000,958.95 1969-05-02,949.22,961.68,945.41,957.17,13070000,957.17 1969-05-01,950.18,958.69,942.74,949.22,14380000,949.22 1969-04-30,934.10,956.28,933.97,950.18,19350000,950.18 1969-04-29,925.08,937.60,922.28,934.10,14730000,934.10 1969-04-28,924.00,930.73,917.13,925.08,11120000,925.08 1969-04-25,921.20,929.65,916.24,924.00,12480000,924.00 1969-04-24,917.64,925.65,911.60,921.20,11340000,921.20 1969-04-23,918.59,927.43,913.13,917.64,12220000,917.64 1969-04-22,917.51,922.09,908.81,918.59,10250000,918.59 1969-04-21,924.82,928.19,913.76,917.51,10010000,917.51 1969-04-18,924.12,932.26,916.94,924.82,10850000,924.82 1969-04-17,923.49,930.80,917.90,924.12,9360000,924.12 1969-04-16,931.94,932.89,920.69,923.49,9680000,923.49 1969-04-15,932.64,937.28,924.63,931.94,9610000,931.94 1969-04-14,933.46,938.36,926.73,932.64,8990000,932.64 1969-04-11,932.89,939.12,927.17,933.46,10650000,933.46 1969-04-10,929.97,941.28,927.87,932.89,12200000,932.89 1969-04-09,923.17,933.59,920.63,929.97,12530000,929.97 1969-04-08,918.78,927.81,913.89,923.17,9360000,923.17 1969-04-07,926.09,926.09,911.03,918.78,9430000,918.78 1969-04-03,930.92,933.66,921.39,927.30,10300000,927.30 1969-04-02,933.08,936.90,924.57,930.92,10110000,930.92 1969-04-01,935.48,942.23,928.38,933.08,12360000,933.08 1969-03-28,930.88,941.38,928.02,935.48,12430000,935.48 1969-03-27,923.30,936.16,921.74,930.88,11900000,930.88 1969-03-26,917.08,926.84,914.72,923.30,11030000,923.30 1969-03-25,917.08,923.05,911.30,917.08,9820000,917.08 1969-03-24,920.00,924.04,912.48,917.08,8110000,917.08 1969-03-21,920.13,926.16,913.35,920.00,9830000,920.00 1969-03-20,912.11,924.79,911.24,920.13,10260000,920.13 1969-03-19,907.38,917.52,903.53,912.11,9740000,912.11 1969-03-18,904.03,913.97,902.16,907.38,11210000,907.38 1969-03-17,904.28,909.00,895.76,904.03,9150000,904.03 1969-03-14,907.14,911.36,899.55,904.28,8640000,904.28 1969-03-13,916.77,916.77,903.97,907.14,10030000,907.14 1969-03-12,920.93,926.22,912.67,917.52,8720000,917.52 1969-03-11,917.14,928.77,914.53,920.93,9870000,920.93 1969-03-10,911.18,920.87,906.51,917.14,8920000,917.14 1969-03-07,913.54,914.59,900.67,911.18,10830000,911.18 1969-03-06,923.11,923.79,908.94,913.54,9670000,913.54 1969-03-05,919.51,929.89,916.65,923.11,11370000,923.11 1969-03-04,908.63,922.55,908.50,919.51,9320000,919.51 1969-03-03,905.21,914.04,902.04,908.63,8260000,908.63 1969-02-28,903.03,911.74,900.17,905.21,8990000,905.21 1969-02-27,905.77,908.88,897.07,903.03,9670000,903.03 1969-02-26,899.80,912.11,895.39,905.77,9540000,905.77 1969-02-25,903.97,914.41,896.32,899.80,9540000,899.80 1969-02-24,916.65,918.95,900.17,903.97,12730000,903.97 1969-02-20,925.10,928.46,913.04,916.65,10990000,916.65 1969-02-19,930.82,936.91,923.23,925.10,10390000,925.10 1969-02-18,937.53,937.53,923.11,930.82,12490000,930.82 1969-02-17,951.95,954.87,935.11,937.72,11670000,937.72 1969-02-14,952.70,959.16,945.67,951.95,11460000,951.95 1969-02-13,949.09,957.73,942.57,952.70,12010000,952.70 1969-02-12,948.97,954.00,942.81,949.09,11530000,949.09 1969-02-11,947.85,954.00,941.94,948.97,12320000,948.97 1969-02-07,946.67,954.00,940.39,947.85,12780000,947.85 1969-02-06,945.98,954.07,939.46,946.67,12570000,946.67 1969-02-05,945.11,952.32,938.53,945.98,13750000,945.98 1969-02-04,946.85,951.27,938.59,945.11,12550000,945.11 1969-02-03,946.05,953.01,936.41,946.85,12510000,946.85 1969-01-31,942.13,950.71,937.28,946.05,12020000,946.05 1969-01-30,938.09,947.23,934.36,942.13,13010000,942.13 1969-01-29,938.40,943.62,931.94,938.09,11470000,938.09 1969-01-28,937.47,944.49,930.88,938.40,12070000,938.40 1969-01-27,938.59,944.37,932.00,937.47,11020000,937.47 1969-01-24,940.20,946.85,932.93,938.59,12520000,938.59 1969-01-23,934.17,945.98,932.56,940.20,13140000,940.20 1969-01-22,929.82,938.46,925.16,934.17,11480000,934.17 1969-01-21,931.25,936.29,923.92,929.82,10910000,929.82 1969-01-20,935.54,939.40,927.09,931.25,10950000,931.25 1969-01-17,938.59,944.06,930.20,935.54,11590000,935.54 1969-01-16,931.75,945.55,930.07,938.59,13120000,938.59 1969-01-15,928.33,940.51,924.23,931.75,11810000,931.75 1969-01-14,923.11,931.56,918.32,928.33,10700000,928.33 1969-01-13,925.53,930.63,917.14,923.11,11160000,923.11 1969-01-10,927.46,937.22,921.31,925.53,12680000,925.53 1969-01-09,921.25,935.67,918.64,927.46,12100000,927.46 1969-01-08,925.72,932.19,915.53,921.25,13840000,921.25 1969-01-07,936.66,939.33,915.84,925.72,15740000,925.72 1969-01-06,951.89,956.05,932.93,936.66,12720000,936.66 1969-01-03,947.73,960.16,942.94,951.89,12750000,951.89 1969-01-02,943.75,956.36,940.39,947.73,9800000,947.73 1968-12-31,945.11,950.46,936.66,943.75,13130000,943.75 1968-12-30,952.51,955.87,938.90,945.11,12080000,945.11 1968-12-27,954.25,961.96,947.54,952.51,11200000,952.51 1968-12-26,952.32,961.52,948.47,954.25,9670000,954.25 1968-12-24,953.75,961.28,945.11,952.32,11540000,952.32 1968-12-23,966.99,969.05,949.47,953.75,12970000,953.75 1968-12-20,975.14,983.90,962.83,966.99,15910000,966.99 1968-12-19,970.91,980.11,954.62,975.14,19630000,975.14 1968-12-17,976.32,978.80,962.46,970.91,14700000,970.91 1968-12-16,981.29,989.12,970.60,976.32,15950000,976.32 1968-12-13,977.13,990.99,972.03,981.29,16740000,981.29 1968-12-12,977.69,987.20,969.05,977.13,18160000,977.13 1968-12-10,979.36,986.01,971.06,977.69,14500000,977.69 1968-12-09,978.24,987.01,971.41,979.36,15800000,979.36 1968-12-06,977.69,986.39,970.10,978.24,15320000,978.24 1968-12-05,985.21,989.31,969.67,977.69,19330000,977.69 1968-12-03,983.34,990.99,973.83,985.21,15460000,985.21 1968-12-02,985.08,994.65,974.76,983.34,15390000,983.34 1968-11-29,976.32,989.56,971.59,985.08,14390000,985.08 1968-11-27,979.49,984.96,969.17,976.32,16550000,976.32 1968-11-26,971.35,986.20,969.11,979.49,16360000,979.49 1968-11-25,967.06,977.13,961.46,971.35,14490000,971.35 1968-11-22,965.13,973.89,958.23,967.06,15420000,967.06 1968-11-21,966.75,971.35,953.69,965.13,18320000,965.13 1968-11-19,963.70,972.40,957.48,966.75,15120000,966.75 1968-11-18,965.88,970.85,957.11,963.70,14390000,963.70 1968-11-15,963.89,972.59,956.24,965.88,15040000,965.88 1968-11-14,967.43,972.90,957.86,963.89,14900000,963.89 1968-11-13,964.20,973.83,958.98,967.43,15660000,967.43 1968-11-12,958.98,972.15,953.75,964.20,17250000,964.20 1968-11-08,950.65,965.07,947.41,958.98,14250000,958.98 1968-11-07,949.47,957.55,938.59,950.65,11660000,950.65 1968-11-06,946.23,959.97,941.01,949.47,12640000,949.47 1968-11-04,948.41,952.01,936.54,946.23,10930000,946.23 1968-11-01,952.39,961.15,941.88,948.41,14480000,948.41 1968-10-31,951.08,965.00,944.06,952.39,17650000,952.39 1968-10-29,957.73,961.96,945.67,951.08,12340000,951.08 1968-10-28,961.28,966.50,951.45,957.73,11740000,957.73 1968-10-25,956.68,966.81,950.96,961.28,14150000,961.28 1968-10-24,963.14,967.37,949.34,956.68,18300000,956.68 1968-10-22,967.49,970.41,957.92,963.14,13970000,963.14 1968-10-21,967.49,974.27,959.54,967.49,14380000,967.49 1968-10-18,958.91,971.72,955.06,967.49,15130000,967.49 1968-10-17,955.31,969.29,952.51,958.91,21060000,958.91 1968-10-15,949.96,960.47,946.05,955.31,13410000,955.31 1968-10-14,949.59,955.37,942.50,949.96,11980000,949.96 1968-10-11,949.78,955.18,942.96,949.59,12650000,949.59 1968-10-10,956.24,958.66,944.24,949.78,17000000,949.78 1968-10-08,956.68,963.33,950.58,956.24,14000000,956.24 1968-10-07,952.95,961.03,946.98,956.68,12420000,956.68 1968-10-04,949.47,957.30,943.93,952.95,15350000,952.95 1968-10-03,942.32,954.81,940.39,949.47,21110000,949.47 1968-10-01,935.79,948.66,932.93,942.32,15560000,942.32 1968-09-30,933.80,941.45,926.59,935.79,13610000,935.79 1968-09-27,933.24,938.40,926.09,933.80,13860000,933.80 1968-09-26,938.28,945.86,928.08,933.24,18950000,933.24 1968-09-24,930.45,942.69,926.22,938.28,15210000,938.28 1968-09-23,924.42,934.05,920.93,930.45,11550000,930.45 1968-09-20,923.98,930.01,917.14,924.42,14190000,924.42 1968-09-19,923.05,933.43,916.27,923.98,17910000,923.98 1968-09-17,921.37,929.08,916.77,923.05,13920000,923.05 1968-09-16,917.21,927.46,912.98,921.37,13260000,921.37 1968-09-13,915.65,923.36,909.12,917.21,13070000,917.21 1968-09-12,919.38,923.26,908.07,915.65,14630000,915.65 1968-09-10,924.98,931.32,914.41,919.38,11430000,919.38 1968-09-09,921.25,932.31,916.89,924.98,11890000,924.98 1968-09-06,917.52,928.27,912.54,921.25,13180000,921.25 1968-09-05,906.95,921.87,904.03,917.52,12980000,917.52 1968-09-04,900.36,911.18,896.26,906.95,10040000,906.95 1968-09-03,896.01,904.96,892.59,900.36,8620000,900.36 1968-08-30,894.33,902.35,891.29,896.01,8190000,896.01 1968-08-29,893.65,900.73,886.69,894.33,10940000,894.33 1968-08-27,896.13,901.48,888.18,893.65,9710000,893.65 1968-08-26,892.34,902.23,890.04,896.13,9740000,896.13 1968-08-23,888.30,899.37,883.83,892.34,9890000,892.34 1968-08-22,888.67,894.95,878.85,888.30,15140000,888.30 1968-08-20,887.68,894.64,879.97,888.67,10640000,888.67 1968-08-19,885.89,893.15,880.66,887.68,9900000,887.68 1968-08-16,879.51,889.44,877.17,885.89,9940000,885.89 1968-08-15,884.68,892.32,874.76,879.51,12710000,879.51 1968-08-13,881.02,890.82,877.71,884.68,12730000,884.68 1968-08-12,869.65,884.20,867.66,881.02,10420000,881.02 1968-08-09,870.37,876.26,863.33,869.65,8390000,869.65 1968-08-08,876.92,882.82,866.58,870.37,12920000,870.37 1968-08-06,872.53,881.38,868.86,876.92,9620000,876.92 1968-08-05,871.27,879.33,865.86,872.53,8850000,872.53 1968-08-02,878.07,879.27,865.19,871.27,9860000,871.27 1968-08-01,883.00,892.02,874.94,878.07,14380000,878.07 1968-07-30,883.36,890.64,876.99,883.00,10250000,883.00 1968-07-29,888.47,893.59,877.23,883.36,10940000,883.36 1968-07-26,885.47,895.21,878.55,888.47,11690000,888.47 1968-07-25,898.10,901.29,880.41,885.47,16140000,885.47 1968-07-23,900.32,904.48,889.68,898.10,13570000,898.10 1968-07-22,913.92,914.52,894.31,900.32,13530000,900.32 1968-07-19,917.95,924.21,907.60,913.92,14620000,913.92 1968-07-18,921.20,926.55,911.93,917.95,17420000,917.95 1968-07-16,923.72,928.84,913.56,921.20,13380000,921.20 1968-07-15,922.46,929.32,915.24,923.72,13390000,923.72 1968-07-12,922.82,929.92,914.88,922.46,14810000,922.46 1968-07-11,920.42,933.83,915.78,922.82,20290000,922.82 1968-07-09,912.60,924.87,908.63,920.42,16540000,920.42 1968-07-08,903.51,920.00,901.89,912.60,16860000,912.60 1968-07-03,896.84,907.18,893.29,903.51,14390000,903.51 1968-07-02,896.35,902.97,889.62,896.84,13350000,896.84 1968-07-01,897.80,904.05,889.68,896.35,11280000,896.35 1968-06-28,898.76,905.14,892.26,897.80,12040000,897.80 1968-06-27,901.41,909.23,891.78,898.76,15370000,898.76 1968-06-25,901.83,908.08,895.09,901.41,13200000,901.41 1968-06-24,900.93,908.14,895.09,901.83,12320000,901.83 1968-06-21,898.28,907.96,891.48,900.93,13450000,900.93 1968-06-20,900.20,909.29,892.63,898.28,16290000,898.28 1968-06-18,903.45,909.17,895.09,900.20,13630000,900.20 1968-06-17,913.62,917.35,898.40,903.45,12570000,903.45 1968-06-14,913.86,918.91,904.48,913.62,14690000,913.62 1968-06-13,917.95,924.93,908.93,913.86,21350000,913.86 1968-06-11,913.38,924.81,909.41,917.95,15700000,917.95 1968-06-10,914.88,922.94,907.54,913.38,14640000,913.38 1968-06-07,910.13,920.84,906.28,914.88,17320000,914.88 1968-06-06,907.42,918.01,901.71,910.13,16130000,910.13 1968-06-05,916.63,922.10,904.05,907.42,15590000,907.42 1968-06-04,905.38,923.00,902.43,916.63,18030000,916.63 1968-06-03,899.00,912.12,896.23,905.38,14970000,905.38 1968-05-31,895.21,907.96,891.72,899.00,13090000,899.00 1968-05-29,896.78,903.69,889.44,895.21,14100000,895.21 1968-05-28,891.60,901.95,886.97,896.78,13850000,896.78 1968-05-27,895.28,898.76,885.53,891.60,12720000,891.60 1968-05-24,893.15,900.49,886.67,895.28,13300000,895.28 1968-05-23,896.79,901.47,888.23,893.15,12840000,893.15 1968-05-22,896.32,906.73,891.82,896.79,14200000,896.79 1968-05-21,894.19,902.39,886.33,896.32,13160000,896.32 1968-05-20,898.98,902.10,887.54,894.19,11180000,894.19 1968-05-17,903.72,905.92,891.18,898.98,11830000,898.98 1968-05-16,907.82,913.08,898.17,903.72,13030000,903.72 1968-05-15,908.06,914.64,900.08,907.82,13180000,907.82 1968-05-14,909.96,915.28,900.89,908.06,13160000,908.06 1968-05-13,912.91,918.34,903.90,909.96,11860000,909.96 1968-05-10,911.35,920.48,906.38,912.91,11700000,912.91 1968-05-09,918.86,921.81,904.82,911.35,12890000,911.35 1968-05-08,919.90,927.42,911.52,918.86,13120000,918.86 1968-05-07,914.53,926.78,910.54,919.90,13920000,919.90 1968-05-06,919.21,922.79,903.61,914.53,12160000,914.53 1968-05-03,918.05,935.68,913.49,919.21,17990000,919.21 1968-05-02,913.20,923.43,906.90,918.05,14260000,918.05 1968-05-01,912.22,919.85,902.51,913.20,14440000,913.20 1968-04-30,908.34,918.11,901.70,912.22,14380000,912.22 1968-04-29,906.03,914.01,900.72,908.34,12030000,908.34 1968-04-26,905.57,912.27,898.00,906.03,13500000,906.03 1968-04-25,898.46,912.56,895.98,905.57,14430000,905.57 1968-04-24,897.48,904.65,889.68,898.46,14810000,898.46 1968-04-23,891.99,904.47,890.43,897.48,14010000,897.48 1968-04-22,897.65,897.88,881.24,891.99,11720000,891.99 1968-04-19,908.40,908.40,890.72,897.65,14560000,897.65 1968-04-18,908.17,916.78,901.24,909.21,15890000,909.21 1968-04-17,906.78,912.74,896.84,908.17,14090000,908.17 1968-04-16,910.19,917.36,899.33,906.78,15680000,906.78 1968-04-15,905.69,916.03,893.61,910.19,14220000,910.19 1968-04-11,892.63,908.29,886.56,905.69,14230000,905.69 1968-04-10,884.42,905.74,884.07,892.63,20410000,892.63 1968-04-08,865.81,888.35,865.18,884.42,13010000,884.42 1968-04-05,872.52,877.31,862.11,865.81,12570000,865.81 1968-04-04,869.11,879.68,862.46,872.52,14340000,872.52 1968-04-03,863.96,883.38,859.45,869.11,19290000,869.11 1968-04-02,861.25,869.63,852.12,863.96,14520000,863.96 1968-04-01,849.23,870.90,849.23,861.25,17730000,861.25 1968-03-29,835.12,845.87,831.48,840.67,9000000,840.67 1968-03-28,836.57,841.08,830.67,835.12,8000000,835.12 1968-03-27,831.54,841.42,830.33,836.57,8970000,836.57 1968-03-26,827.27,836.17,823.62,831.54,8670000,831.54 1968-03-25,826.05,831.25,819.87,827.27,6700000,827.27 1968-03-22,825.13,831.48,817.61,826.05,9900000,826.05 1968-03-21,830.85,836.40,822.58,825.13,8580000,825.13 1968-03-20,832.99,836.63,826.34,830.85,7390000,830.85 1968-03-19,840.09,842.35,829.63,832.99,7410000,832.99 1968-03-18,837.55,854.25,836.28,840.09,10800000,840.09 1968-03-15,830.91,843.39,825.01,837.55,11210000,837.55 1968-03-14,841.54,841.54,824.26,830.91,11640000,830.91 1968-03-13,843.22,847.72,836.22,842.23,8990000,842.23 1968-03-12,843.04,847.55,834.72,843.22,9250000,843.22 1968-03-11,835.24,846.63,833.56,843.04,9520000,843.04 1968-03-08,836.22,840.38,828.59,835.24,7410000,835.24 1968-03-07,837.21,843.62,830.33,836.22,8630000,836.22 1968-03-06,827.03,841.37,826.46,837.21,9900000,837.21 1968-03-05,830.56,837.44,821.72,827.03,11440000,827.03 1968-03-04,840.44,842.75,828.02,830.56,10590000,830.56 1968-03-01,840.50,845.24,836.05,840.44,8610000,840.44 1968-02-29,844.72,847.03,835.76,840.50,7700000,840.50 1968-02-28,846.68,853.33,841.71,844.72,8020000,844.72 1968-02-27,841.77,848.59,835.93,846.68,7600000,846.68 1968-02-26,849.80,850.79,836.40,841.77,7810000,841.77 1968-02-23,849.23,857.78,844.43,849.80,8810000,849.80 1968-02-21,843.10,855.05,840.50,849.23,9170000,849.23 1968-02-20,838.65,847.67,836.05,843.10,8800000,843.10 1968-02-19,836.34,843.97,830.50,838.65,7270000,838.65 1968-02-16,839.23,841.66,830.85,836.34,9070000,836.34 1968-02-15,837.38,846.16,833.62,839.23,9770000,839.23 1968-02-14,831.77,841.94,826.46,837.38,11390000,837.38 1968-02-13,840.04,843.68,828.36,831.77,10830000,831.77 1968-02-09,850.32,851.65,834.84,840.04,11850000,840.04 1968-02-08,859.92,863.27,847.84,850.32,9660000,850.32 1968-02-07,861.25,867.78,855.93,859.92,8380000,859.92 1968-02-06,861.13,867.31,854.83,861.25,8560000,861.25 1968-02-05,863.56,867.66,854.77,861.13,8980000,861.13 1968-02-02,861.36,871.30,856.22,863.56,10120000,863.56 1968-02-01,855.47,864.89,850.55,861.36,10590000,861.36 1968-01-31,859.57,863.90,850.50,855.47,9410000,855.47 1968-01-30,863.67,867.95,852.92,859.57,10110000,859.57 1968-01-29,865.06,873.04,858.53,863.67,9950000,863.67 1968-01-26,864.25,873.79,859.51,865.06,9980000,865.06 1968-01-25,862.23,871.24,853.44,864.25,12410000,864.25 1968-01-24,864.77,870.20,854.83,862.23,10570000,862.23 1968-01-23,871.71,875.06,860.15,864.77,11030000,864.77 1968-01-22,880.32,881.24,866.68,871.71,10630000,871.71 1968-01-19,882.80,889.27,876.21,880.32,11950000,880.32 1968-01-18,883.78,893.49,879.33,882.80,13840000,882.80 1968-01-17,887.14,890.89,877.48,883.78,12910000,883.78 1968-01-16,892.74,896.56,882.34,887.14,12340000,887.14 1968-01-15,898.98,903.03,888.93,892.74,12640000,892.74 1968-01-12,899.79,906.58,891.07,898.98,13080000,898.98 1968-01-11,903.95,911.35,895.28,899.79,13220000,899.79 1968-01-10,908.29,911.87,897.94,903.95,11670000,903.95 1968-01-09,908.92,921.87,903.26,908.29,13720000,908.29 1968-01-08,901.24,915.63,896.27,908.92,14260000,908.92 1968-01-05,899.39,908.06,893.55,901.24,11880000,901.24 1968-01-04,904.13,908.23,889.51,899.39,13440000,899.39 1968-01-03,906.84,916.15,899.56,904.13,12650000,904.13 1968-01-02,905.11,914.30,897.54,906.84,11080000,906.84 1967-12-29,897.83,910.37,893.44,905.11,14950000,905.11 1967-12-28,894.94,902.97,886.73,897.83,12530000,897.83 1967-12-27,888.12,900.14,884.59,894.94,12690000,894.94 1967-12-26,887.37,893.96,881.93,888.12,9150000,888.12 1967-12-22,888.35,894.94,880.95,887.37,9570000,887.37 1967-12-21,886.90,897.71,883.78,888.35,11010000,888.35 1967-12-20,881.36,892.86,876.33,886.90,11390000,886.90 1967-12-19,881.65,886.96,875.69,881.36,10610000,881.36 1967-12-18,880.61,889.91,874.94,881.65,10320000,881.65 1967-12-15,883.44,890.43,875.87,880.61,11530000,880.61 1967-12-14,882.34,891.47,878.53,883.44,12310000,883.44 1967-12-13,881.30,887.77,881.14,882.34,12480000,882.34 1967-12-12,882.05,887.54,873.32,881.30,10860000,881.30 1967-12-11,887.25,892.16,876.96,882.05,10500000,882.05 1967-12-08,892.22,895.92,883.55,887.25,10710000,887.25 1967-12-07,892.28,901.76,887.94,892.22,12490000,892.22 1967-12-06,888.12,896.50,884.19,892.28,11940000,892.28 1967-12-05,883.50,895.80,881.24,888.12,12940000,888.12 1967-12-04,879.16,888.35,876.33,883.50,11740000,883.50 1967-12-01,875.81,882.69,868.76,879.16,9740000,879.16 1967-11-30,883.15,887.48,872.63,875.81,8860000,875.81 1967-11-29,884.88,894.88,878.24,883.15,11400000,883.15 1967-11-28,882.11,890.43,876.62,884.88,11040000,884.88 1967-11-27,877.60,887.77,873.21,882.11,10040000,882.11 1967-11-24,874.02,882.80,867.26,877.60,9470000,877.60 1967-11-22,870.95,884.54,865.87,874.02,12180000,874.02 1967-11-21,857.78,876.68,857.49,870.95,12300000,870.95 1967-11-20,862.11,862.58,839.40,857.78,12750000,857.78 1967-11-17,859.74,869.28,853.96,862.11,10050000,862.11 1967-11-16,855.18,867.49,852.12,859.74,10570000,859.74 1967-11-15,852.40,860.44,845.01,855.18,10000000,855.18 1967-11-14,859.74,864.60,849.23,852.40,10350000,852.40 1967-11-13,862.81,872.98,855.06,859.74,10130000,859.74 1967-11-10,856.97,868.93,854.83,862.81,9960000,862.81 1967-11-09,849.57,862.86,846.28,856.97,8890000,856.97 1967-11-08,855.29,870.67,847.61,849.57,12630000,849.57 1967-11-06,856.62,860.61,844.89,855.29,10320000,855.29 1967-11-03,864.83,867.95,853.10,856.62,8800000,856.62 1967-11-02,867.08,878.87,860.55,864.83,10760000,864.83 1967-11-01,879.74,880.95,863.44,867.08,10930000,867.08 1967-10-31,886.62,890.72,876.21,879.74,12020000,879.74 1967-10-30,888.18,894.07,880.37,886.62,10250000,886.62 1967-10-27,890.89,896.15,882.98,888.18,9880000,888.18 1967-10-26,886.73,896.04,881.99,890.89,9920000,890.89 1967-10-25,888.18,893.44,877.31,886.73,10300000,886.73 1967-10-24,894.65,903.84,885.52,888.18,11110000,888.18 1967-10-23,896.73,900.43,883.03,894.65,9680000,894.65 1967-10-20,903.72,906.96,891.35,896.73,9510000,896.73 1967-10-19,903.49,914.41,899.68,903.72,11620000,903.72 1967-10-18,904.36,910.48,896.15,903.49,10500000,903.49 1967-10-17,908.52,912.97,896.73,904.36,10290000,904.36 1967-10-16,918.17,922.97,905.46,908.52,9080000,908.52 1967-10-13,913.20,924.41,908.58,918.17,9040000,918.17 1967-10-12,920.25,922.56,909.79,913.20,7770000,913.20 1967-10-11,926.61,929.73,916.61,920.25,11230000,920.25 1967-10-10,933.31,940.07,921.35,926.61,12000000,926.61 1967-10-09,928.74,940.36,924.47,933.31,11180000,933.31 1967-10-06,927.13,935.74,921.58,928.74,9830000,928.74 1967-10-05,921.29,931.46,917.88,927.13,8490000,927.13 1967-10-04,924.47,932.33,916.32,921.29,11520000,921.29 1967-10-03,921.00,930.77,916.49,924.47,10320000,924.47 1967-10-02,926.66,930.42,915.92,921.00,9240000,921.00 1967-09-29,929.38,933.77,919.85,926.66,9710000,926.66 1967-09-28,933.14,937.30,925.05,929.38,10470000,929.38 1967-09-27,937.18,942.61,927.88,933.14,8810000,933.14 1967-09-26,943.08,951.57,934.12,937.18,10940000,937.18 1967-09-25,934.35,949.66,931.75,943.08,10910000,943.08 1967-09-22,930.48,940.48,923.95,934.35,11160000,934.35 1967-09-21,929.79,938.22,924.12,930.48,11290000,930.48 1967-09-20,930.07,936.89,922.50,929.79,10980000,929.79 1967-09-19,938.74,944.64,926.95,930.07,11540000,930.07 1967-09-18,933.48,944.58,929.73,938.74,11620000,938.74 1967-09-15,929.44,938.51,923.25,933.48,10270000,933.48 1967-09-14,923.77,939.38,923.72,929.44,12220000,929.44 1967-09-13,911.75,928.40,911.64,923.77,12400000,923.77 1967-09-12,909.62,916.84,905.05,911.75,9930000,911.75 1967-09-11,907.54,916.20,902.68,909.62,9170000,909.62 1967-09-08,908.17,914.41,901.24,907.54,9300000,907.54 1967-09-07,906.96,913.49,901.64,908.17,8910000,908.17 1967-09-06,904.13,913.55,899.27,906.96,9550000,906.96 1967-09-05,901.18,909.91,895.69,904.13,8320000,904.13 1967-09-01,901.29,906.84,894.19,901.18,7460000,901.18 1967-08-31,893.72,906.38,893.09,901.29,8840000,901.29 1967-08-30,894.76,900.72,888.64,893.72,7200000,893.72 1967-08-29,894.71,900.20,887.94,894.76,6350000,894.76 1967-08-28,894.07,902.16,887.83,894.71,6270000,894.71 1967-08-25,898.46,900.49,888.81,894.07,7250000,894.07 1967-08-24,905.11,910.54,896.09,898.46,7740000,898.46 1967-08-23,907.48,910.14,896.44,905.11,8760000,905.11 1967-08-22,912.27,916.15,903.61,907.48,7940000,907.48 1967-08-21,919.04,921.64,907.48,912.27,8600000,912.27 1967-08-18,918.23,925.51,912.79,919.04,8250000,919.04 1967-08-17,915.68,923.89,912.85,918.23,8790000,918.23 1967-08-16,919.15,921.64,910.83,915.68,8220000,915.68 1967-08-15,916.32,924.93,912.85,919.15,8710000,919.15 1967-08-14,920.65,922.16,909.96,916.32,7990000,916.32 1967-08-11,925.22,928.11,915.57,920.65,8250000,920.65 1967-08-10,926.72,933.14,920.77,925.22,9040000,925.22 1967-08-09,922.45,931.75,919.09,926.72,10100000,926.72 1967-08-08,920.37,927.88,916.67,922.45,8970000,922.45 1967-08-07,923.77,930.65,915.34,920.37,10160000,920.37 1967-08-04,921.98,931.06,917.65,923.77,11130000,923.77 1967-08-03,922.27,929.67,908.11,921.98,13440000,921.98 1967-08-02,913.55,931.29,913.55,922.27,13510000,922.27 1967-08-01,904.24,917.19,900.25,912.97,12290000,912.97 1967-07-31,901.53,912.85,896.67,904.24,10330000,904.24 1967-07-28,903.14,910.31,896.15,901.53,10900000,901.53 1967-07-27,903.14,912.79,896.96,903.14,12400000,903.14 1967-07-26,901.29,908.17,895.75,903.14,11160000,903.14 1967-07-25,904.53,909.56,895.52,901.29,9890000,901.29 1967-07-24,909.56,912.68,897.48,904.53,9580000,904.53 1967-07-21,908.69,918.69,903.03,909.56,11710000,909.56 1967-07-20,903.32,913.83,896.79,908.69,11160000,908.69 1967-07-19,896.09,908.75,892.63,903.32,12850000,903.32 1967-07-18,882.74,899.79,879.39,896.09,12060000,896.09 1967-07-17,882.05,891.30,875.35,882.74,10390000,882.74 1967-07-14,878.53,889.62,872.52,882.05,10880000,882.05 1967-07-13,878.70,885.81,873.04,878.53,10730000,878.53 1967-07-12,879.45,885.40,870.55,878.70,11240000,878.70 1967-07-11,875.52,886.15,870.90,879.45,12400000,879.45 1967-07-10,869.05,880.37,866.04,875.52,12130000,875.52 1967-07-07,864.02,874.42,860.32,869.05,11540000,869.05 1967-07-06,864.94,871.24,858.70,864.02,10170000,864.02 1967-07-05,859.69,871.01,857.43,864.94,9170000,864.94 1967-07-03,860.26,864.60,853.21,859.69,6040000,859.69 1967-06-30,861.94,867.83,855.58,860.26,7850000,860.26 1967-06-29,868.87,873.67,859.45,861.94,9940000,861.94 1967-06-28,869.39,875.17,864.14,868.87,9310000,868.87 1967-06-27,872.11,875.87,864.14,869.39,8780000,869.39 1967-06-26,877.37,884.30,866.91,872.11,9040000,872.11 1967-06-23,875.69,883.32,870.95,877.37,9130000,877.37 1967-06-22,877.66,881.13,868.82,875.69,9550000,875.69 1967-06-21,880.61,886.90,872.52,877.66,9760000,877.66 1967-06-20,884.54,890.72,876.44,880.61,10350000,880.61 1967-06-19,885.00,890.03,877.43,884.54,8570000,884.54 1967-06-16,883.26,892.80,879.68,885.00,10740000,885.00 1967-06-15,880.61,891.24,873.32,883.26,11240000,883.26 1967-06-14,886.15,890.78,876.39,880.61,10960000,880.61 1967-06-13,878.93,892.68,875.75,886.15,11570000,886.15 1967-06-12,874.89,884.77,870.49,878.93,10230000,878.93 1967-06-09,873.20,881.94,865.08,874.89,9650000,874.89 1967-06-08,869.19,875.17,861.64,873.20,8300000,873.20 1967-06-07,862.71,877.14,860.57,869.19,10170000,869.19 1967-06-06,848.33,868.46,848.33,862.71,9230000,862.71 1967-06-05,858.41,858.41,836.92,847.77,11110000,847.77 1967-06-02,864.98,870.82,857.46,863.31,8070000,863.31 1967-06-01,852.56,869.60,850.56,864.98,9040000,864.98 1967-05-31,864.64,864.64,850.39,852.56,8870000,852.56 1967-05-29,870.32,871.60,860.24,864.98,6590000,864.98 1967-05-26,870.71,875.22,863.31,870.32,7810000,870.32 1967-05-25,862.42,876.50,860.36,870.71,8960000,870.71 1967-05-24,868.71,870.49,857.18,862.42,10290000,862.42 1967-05-23,871.05,875.72,862.03,868.71,9810000,868.71 1967-05-22,874.55,876.61,863.75,871.05,9600000,871.05 1967-05-19,877.34,881.24,867.59,874.55,10560000,874.55 1967-05-18,882.24,885.13,873.27,877.34,10290000,877.34 1967-05-17,885.80,891.37,878.40,882.24,9560000,882.24 1967-05-16,882.41,891.76,877.90,885.80,10700000,885.80 1967-05-15,890.03,892.26,878.67,882.41,8320000,882.41 1967-05-12,896.21,900.67,885.86,890.03,10470000,890.03 1967-05-11,894.10,901.56,888.25,896.21,10320000,896.21 1967-05-10,899.89,902.23,888.47,894.10,10410000,894.10 1967-05-09,909.63,915.87,897.05,899.89,10830000,899.89 1967-05-08,905.96,915.31,899.44,909.63,10330000,909.63 1967-05-05,901.95,910.91,898.05,905.96,10630000,905.96 1967-05-04,896.77,906.57,892.65,901.95,12850000,901.95 1967-05-03,891.65,900.95,886.41,896.77,11550000,896.77 1967-05-02,892.93,898.39,886.19,891.65,10260000,891.65 1967-05-01,897.05,900.50,887.81,892.93,9410000,892.93 1967-04-28,894.82,903.73,891.20,897.05,11200000,897.05 1967-04-27,889.03,898.33,882.74,894.82,10250000,894.82 1967-04-26,891.20,898.50,883.96,889.03,10560000,889.03 1967-04-25,887.53,894.93,880.73,891.20,10420000,891.20 1967-04-24,883.18,894.82,877.84,887.53,10250000,887.53 1967-04-21,878.62,888.30,873.61,883.18,10210000,883.18 1967-04-20,873.94,882.18,869.04,878.62,9690000,878.62 1967-04-19,873.00,882.07,868.76,873.94,10860000,873.94 1967-04-18,866.59,876.73,861.92,873.00,10500000,873.00 1967-04-17,859.74,874.83,857.91,866.59,9070000,866.59 1967-04-14,848.83,865.03,847.05,859.74,8810000,859.74 1967-04-13,844.65,852.84,840.81,848.83,7610000,848.83 1967-04-12,847.66,852.67,841.48,844.65,7750000,844.65 1967-04-11,842.43,852.39,838.98,847.66,7710000,847.66 1967-04-10,852.84,852.84,839.76,842.43,8110000,842.43 1967-04-07,861.25,866.59,850.22,853.34,9090000,853.34 1967-04-06,861.19,867.59,856.51,861.25,9470000,861.25 1967-04-05,859.19,867.26,855.23,861.19,8810000,861.19 1967-04-04,859.97,865.65,852.17,859.19,8750000,859.19 1967-04-03,865.98,868.43,854.45,859.97,8530000,859.97 1967-03-31,869.99,874.28,861.19,865.98,8130000,865.98 1967-03-30,871.10,875.39,863.92,869.99,8340000,869.99 1967-03-29,875.28,880.40,866.31,871.10,8430000,871.10 1967-03-28,873.72,882.13,868.37,875.28,8940000,875.28 1967-03-27,876.67,883.41,869.15,873.72,9260000,873.72 1967-03-23,870.55,882.29,868.82,876.67,9500000,876.67 1967-03-22,866.59,875.11,857.68,870.55,8820000,870.55 1967-03-21,870.43,879.18,861.25,866.59,9820000,866.59 1967-03-20,869.77,877.28,862.36,870.43,9040000,870.43 1967-03-17,868.49,876.50,861.80,869.77,10020000,869.77 1967-03-16,854.51,872.33,854.51,868.49,12170000,868.49 1967-03-15,844.27,856.90,842.65,854.06,10830000,854.06 1967-03-14,844.82,850.33,836.86,844.27,10260000,844.27 1967-03-13,848.50,853.56,840.59,844.82,9910000,844.82 1967-03-10,845.43,864.25,845.43,848.50,14900000,848.50 1967-03-09,843.32,850.72,836.53,844.15,10480000,844.15 1967-03-08,841.76,851.00,836.36,843.32,11070000,843.32 1967-03-07,842.20,847.10,835.30,841.76,9810000,841.76 1967-03-06,846.60,851.45,837.86,842.20,10400000,842.20 1967-03-03,846.71,853.51,841.04,846.60,11100000,846.60 1967-03-02,843.49,852.62,840.87,846.71,11900000,846.71 1967-03-01,839.37,852.12,836.47,843.49,11510000,843.49 1967-02-28,836.64,844.27,827.95,839.37,9970000,839.37 1967-02-27,847.33,849.44,830.46,836.64,10210000,836.64 1967-02-24,846.77,854.79,839.64,847.33,9830000,847.33 1967-02-23,844.10,851.67,837.31,846.77,10010000,846.77 1967-02-21,847.88,851.39,840.03,844.10,9030000,844.10 1967-02-20,850.84,853.90,839.81,847.88,8640000,847.88 1967-02-17,851.56,856.35,845.88,850.84,8530000,850.84 1967-02-16,855.79,863.42,846.60,851.56,8490000,851.56 1967-02-15,856.90,863.47,850.22,855.79,10480000,855.79 1967-02-14,853.34,862.64,848.39,856.90,9760000,856.90 1967-02-13,855.73,860.52,848.72,853.34,7570000,853.34 1967-02-10,857.52,861.36,847.72,855.73,8850000,855.73 1967-02-09,860.97,871.71,854.06,857.52,10970000,857.52 1967-02-08,852.51,865.37,850.11,860.97,11220000,860.97 1967-02-07,855.12,857.68,847.27,852.51,6400000,852.51 1967-02-06,857.46,862.53,849.72,855.12,10680000,855.12 1967-02-03,853.12,864.09,849.78,857.46,12010000,857.46 1967-02-02,848.39,857.68,842.20,853.12,10720000,853.12 1967-02-01,849.89,854.51,842.54,848.39,9580000,848.39 1967-01-31,848.11,857.02,844.82,849.89,11540000,849.89 1967-01-30,844.04,854.57,840.48,848.11,10250000,848.11 1967-01-27,838.70,850.17,836.14,844.04,9690000,844.04 1967-01-26,840.59,848.27,830.18,838.70,10630000,838.70 1967-01-25,847.72,852.67,837.69,840.59,10260000,840.59 1967-01-24,847.72,853.12,836.30,847.72,10430000,847.72 1967-01-23,847.16,856.68,841.43,847.72,10830000,847.72 1967-01-20,846.44,851.39,838.59,847.16,9530000,847.16 1967-01-19,847.49,853.73,840.81,846.44,10230000,846.44 1967-01-18,843.65,853.34,839.14,847.49,11390000,847.49 1967-01-17,833.24,848.72,830.57,843.65,11590000,843.65 1967-01-16,835.13,842.48,828.12,833.24,10280000,833.24 1967-01-13,829.95,838.47,821.15,835.13,10000000,835.13 1967-01-12,822.49,839.25,819.76,829.95,12830000,829.95 1967-01-11,814.14,827.11,798.71,822.49,13230000,822.49 1967-01-10,813.47,820.93,808.18,814.14,8120000,814.14 1967-01-09,808.74,818.87,803.34,813.47,9180000,813.47 1967-01-06,805.51,816.53,801.67,808.74,7830000,808.74 1967-01-05,791.64,807.90,791.64,805.51,7320000,805.51 1967-01-04,786.41,795.54,776.16,791.14,6150000,791.14 1967-01-03,785.69,800.55,782.34,786.41,6100000,786.41 1966-12-30,786.35,794.59,779.34,785.69,11330000,785.69 1966-12-29,788.58,792.70,781.51,786.35,7900000,786.35 1966-12-28,792.20,799.38,785.96,788.58,7160000,788.58 1966-12-27,799.10,802.61,788.25,792.20,6280000,792.20 1966-12-23,801.67,806.51,793.09,799.10,7350000,799.10 1966-12-22,797.43,807.18,793.87,801.67,8560000,801.67 1966-12-21,794.59,802.00,789.69,797.43,7690000,797.43 1966-12-20,798.99,800.66,789.42,794.59,6830000,794.59 1966-12-19,807.18,807.46,792.70,798.99,7340000,798.99 1966-12-16,809.18,813.02,802.22,807.18,6980000,807.18 1966-12-15,817.98,820.82,804.45,809.18,7150000,809.18 1966-12-14,816.70,823.66,810.63,817.98,7470000,817.98 1966-12-13,820.54,827.22,812.08,816.70,9650000,816.70 1966-12-12,813.02,826.67,810.52,820.54,9530000,820.54 1966-12-09,812.80,818.20,804.95,813.02,7650000,813.02 1966-12-08,808.01,818.81,805.95,812.80,8370000,812.80 1966-12-07,797.43,812.41,795.43,808.01,8980000,808.01 1966-12-06,791.59,800.94,788.25,797.43,7670000,797.43 1966-12-05,789.47,795.54,784.35,791.59,6470000,791.59 1966-12-02,789.75,794.82,783.51,789.47,6230000,789.47 1966-12-01,791.59,797.93,785.63,789.75,8480000,789.75 1966-11-30,795.26,796.21,784.79,791.59,7230000,791.59 1966-11-29,801.16,803.28,791.59,795.26,7320000,795.26 1966-11-28,803.34,808.24,793.59,801.16,7630000,801.16 1966-11-25,796.82,807.68,793.87,803.34,6810000,803.34 1966-11-23,794.98,804.78,789.36,796.82,7350000,796.82 1966-11-22,798.16,799.55,785.46,794.98,6430000,794.98 1966-11-21,807.73,807.73,791.09,798.16,7450000,798.16 1966-11-18,816.03,817.81,804.95,809.40,6900000,809.40 1966-11-17,820.87,825.61,808.90,816.03,8900000,816.03 1966-11-16,815.31,827.33,812.69,820.87,10350000,820.87 1966-11-15,813.75,819.48,808.12,815.31,7190000,815.31 1966-11-14,819.09,823.10,808.29,813.75,6540000,813.75 1966-11-11,816.87,822.32,810.46,819.09,6690000,819.09 1966-11-10,809.91,822.38,807.18,816.87,8870000,816.87 1966-11-09,802.22,815.64,799.72,809.91,8390000,809.91 1966-11-07,805.06,809.85,796.38,802.22,6120000,802.22 1966-11-04,804.34,809.57,793.54,805.06,6530000,805.06 1966-11-03,807.29,812.24,798.32,804.34,5860000,804.34 1966-11-02,809.63,815.92,801.61,807.29,6740000,807.29 1966-11-01,807.07,814.30,800.33,809.63,6480000,809.63 1966-10-31,807.96,812.91,797.04,807.07,5860000,807.07 1966-10-28,809.57,816.64,801.44,807.96,6420000,807.96 1966-10-27,801.11,814.97,800.77,809.57,6670000,809.57 1966-10-26,793.09,809.29,792.31,801.11,6760000,801.11 1966-10-25,787.75,796.60,780.34,793.09,6190000,793.09 1966-10-24,787.30,796.10,781.73,787.75,5780000,787.75 1966-10-21,783.68,791.36,777.17,787.30,5690000,787.30 1966-10-20,785.35,796.04,778.11,783.68,6840000,783.68 1966-10-19,791.87,799.22,779.84,785.35,6460000,785.35 1966-10-18,778.89,795.65,777.44,791.87,7180000,791.87 1966-10-17,771.71,789.14,770.82,778.89,5570000,778.89 1966-10-14,772.93,782.90,765.14,771.71,5610000,771.71 1966-10-13,778.17,791.09,768.81,772.93,8680000,772.93 1966-10-12,758.63,780.12,752.89,778.17,6910000,778.17 1966-10-11,754.51,771.43,752.44,758.63,8430000,758.63 1966-10-10,744.32,758.07,735.74,754.51,9630000,754.51 1966-10-07,749.61,756.84,739.64,744.32,8140000,744.32 1966-10-06,755.45,759.52,744.09,749.61,8110000,749.61 1966-10-05,763.19,768.04,751.72,755.45,5880000,755.45 1966-10-04,757.96,767.53,750.33,763.19,8910000,763.19 1966-10-03,774.22,778.11,756.79,757.96,6490000,757.96 1966-09-30,772.66,779.34,763.91,774.22,6170000,774.22 1966-09-29,780.95,783.18,768.26,772.66,6110000,772.66 1966-09-28,794.09,795.60,777.33,780.95,5990000,780.95 1966-09-27,792.70,805.45,789.53,794.09,6300000,794.09 1966-09-26,790.97,797.32,784.46,792.70,4960000,792.70 1966-09-23,797.77,800.11,787.36,790.97,4560000,790.97 1966-09-22,793.59,801.83,785.69,797.77,5760000,797.77 1966-09-21,806.01,806.73,792.53,793.59,5360000,793.59 1966-09-20,810.85,813.08,801.22,806.01,4560000,806.01 1966-09-19,814.30,818.54,804.00,810.85,4920000,810.85 1966-09-16,814.30,822.93,808.35,814.30,5150000,814.30 1966-09-15,806.23,821.26,804.62,814.30,6140000,814.30 1966-09-14,795.48,809.02,789.58,806.23,6250000,806.23 1966-09-13,790.59,803.11,789.25,795.48,6870000,795.48 1966-09-12,775.61,795.32,775.61,790.59,6780000,790.59 1966-09-09,774.88,781.01,767.92,775.55,5280000,775.55 1966-09-08,777.39,782.46,763.36,774.88,6660000,774.88 1966-09-07,782.34,787.30,771.77,777.39,5530000,777.39 1966-09-06,787.69,795.15,778.84,782.34,4350000,782.34 1966-09-02,792.09,796.26,776.72,787.69,6080000,787.69 1966-09-01,788.41,798.94,782.12,792.09,6250000,792.09 1966-08-31,777.44,796.49,777.44,788.41,8690000,788.41 1966-08-30,767.03,781.62,759.52,775.72,11230000,775.72 1966-08-29,780.56,781.06,763.97,767.03,10900000,767.03 1966-08-26,792.37,792.53,776.22,780.56,8190000,780.56 1966-08-25,799.55,806.23,789.08,792.37,6760000,792.37 1966-08-24,790.20,805.45,790.20,799.55,7050000,799.55 1966-08-23,792.03,801.78,781.90,790.14,9830000,790.14 1966-08-22,804.62,807.79,786.85,792.03,8690000,792.03 1966-08-19,810.74,816.75,801.50,804.62,7070000,804.62 1966-08-18,819.59,821.15,804.73,810.74,7000000,810.74 1966-08-17,823.83,827.28,813.69,819.59,6630000,819.59 1966-08-16,834.79,834.79,820.04,823.83,6130000,823.83 1966-08-15,840.53,845.65,831.79,834.85,5680000,834.85 1966-08-12,837.91,847.66,834.68,840.53,6230000,840.53 1966-08-11,838.53,843.65,830.56,837.91,5700000,837.91 1966-08-10,844.82,846.71,835.02,838.53,5290000,838.53 1966-08-09,849.05,853.11,841.09,844.82,6270000,844.82 1966-08-08,852.39,854.78,842.42,849.05,4900000,849.05 1966-08-05,851.50,860.57,845.71,852.39,5500000,852.39 1966-08-04,841.70,858.57,841.20,851.50,6880000,851.50 1966-08-03,832.90,847.99,832.90,841.70,6220000,841.70 1966-08-02,835.18,840.97,827.28,832.57,5710000,832.57 1966-08-01,846.60,846.60,830.84,835.18,5880000,835.18 1966-07-29,854.06,857.46,843.76,847.38,5150000,847.38 1966-07-28,856.23,862.75,850.50,854.06,5680000,854.06 1966-07-27,852.17,863.30,850.55,856.23,6070000,856.23 1966-07-26,852.83,861.19,846.88,852.17,7610000,852.17 1966-07-25,869.15,870.43,850.50,852.83,7050000,852.83 1966-07-22,873.99,877.50,864.97,869.15,6540000,869.15 1966-07-21,874.49,880.34,866.98,873.99,6200000,873.99 1966-07-20,884.07,887.08,872.60,874.49,5470000,874.49 1966-07-19,888.41,889.81,876.55,884.07,5960000,884.07 1966-07-18,889.36,892.98,882.18,888.41,5110000,888.41 1966-07-15,887.80,896.65,883.74,889.36,6090000,889.36 1966-07-14,881.40,892.48,878.17,887.80,5950000,887.80 1966-07-13,886.19,887.58,875.33,881.40,5580000,881.40 1966-07-12,893.09,896.65,882.46,886.19,5180000,886.19 1966-07-11,894.04,901.16,888.64,893.09,6200000,893.09 1966-07-08,891.64,898.44,885.57,894.04,6100000,894.04 1966-07-07,888.86,898.21,883.90,891.64,7200000,891.64 1966-07-06,875.27,893.20,872.43,888.86,6860000,888.86 1966-07-05,877.06,884.13,869.09,875.27,4610000,875.27 1966-07-01,870.10,884.02,869.93,877.06,5200000,877.06 1966-06-30,871.60,876.33,858.90,870.10,7250000,870.10 1966-06-29,880.90,884.29,869.15,871.60,6020000,871.60 1966-06-28,888.97,890.81,874.83,880.90,6280000,880.90 1966-06-27,897.16,904.06,887.47,888.97,5330000,888.97 1966-06-24,896.43,904.17,888.41,897.16,7140000,897.16 1966-06-23,901.00,908.51,893.48,896.43,7930000,896.43 1966-06-22,894.98,904.62,892.59,901.00,7800000,901.00 1966-06-21,892.76,900.44,889.36,894.98,6860000,894.98 1966-06-20,894.26,898.21,887.24,892.76,5940000,892.76 1966-06-17,897.16,900.55,889.75,894.26,6580000,894.26 1966-06-16,901.11,903.61,890.92,897.16,6870000,897.16 1966-06-15,903.17,910.35,897.82,901.11,8520000,901.11 1966-06-14,897.60,907.18,891.53,903.17,7600000,903.17 1966-06-13,891.75,904.67,891.64,897.60,7600000,897.60 1966-06-10,882.62,896.77,880.84,891.75,8240000,891.75 1966-06-09,879.34,887.30,874.05,882.62,5810000,882.62 1966-06-08,877.33,883.68,872.16,879.34,4580000,879.34 1966-06-07,881.68,882.62,870.32,877.33,5040000,877.33 1966-06-06,887.86,888.95,876.22,881.68,4260000,881.68 1966-06-03,882.73,890.86,879.73,887.86,4430000,887.86 1966-06-02,883.63,890.64,878.34,882.73,5080000,882.73 1966-06-01,884.07,888.53,877.33,883.63,5290000,883.63 1966-05-31,897.04,899.61,881.73,884.07,5770000,884.07 1966-05-27,891.75,899.77,885.85,897.04,4790000,897.04 1966-05-26,890.42,900.33,886.80,891.75,6080000,891.75 1966-05-25,888.41,894.98,881.29,890.42,5820000,890.42 1966-05-24,882.46,898.38,882.12,888.41,7210000,888.41 1966-05-23,876.89,889.86,873.49,882.46,7080000,882.46 1966-05-20,872.99,880.06,863.53,876.89,6430000,876.89 1966-05-19,878.50,887.86,869.65,872.99,8640000,872.99 1966-05-18,864.42,883.96,864.42,878.50,9310000,878.50 1966-05-17,867.53,876.83,859.13,864.14,9870000,864.14 1966-05-16,876.11,881.73,862.86,867.53,9260000,867.53 1966-05-13,884.85,884.85,868.65,876.11,8970000,876.11 1966-05-12,895.43,900.00,878.84,885.57,8210000,885.57 1966-05-11,895.48,908.40,892.70,895.43,7470000,895.43 1966-05-10,886.80,904.39,886.35,895.48,9050000,895.48 1966-05-09,902.83,903.39,883.18,886.80,9290000,886.80 1966-05-06,899.77,909.18,882.90,902.83,13110000,902.83 1966-05-05,914.86,919.65,897.55,899.77,10100000,899.77 1966-05-04,921.77,923.38,906.23,914.86,9740000,914.86 1966-05-03,931.95,932.12,919.20,921.77,8020000,921.77 1966-05-02,933.68,939.64,926.61,931.95,7070000,931.95 1966-04-29,937.41,942.09,930.23,933.68,7220000,933.68 1966-04-28,944.54,945.54,927.22,937.41,8310000,937.41 1966-04-27,947.21,951.28,937.58,944.54,7950000,944.54 1966-04-26,950.55,955.56,943.20,947.21,7540000,947.21 1966-04-25,949.83,957.51,942.09,950.55,7270000,950.55 1966-04-22,954.73,957.23,944.09,949.83,8650000,949.83 1966-04-21,951.28,961.91,946.82,954.73,9560000,954.73 1966-04-20,941.75,957.01,941.75,951.28,10530000,951.28 1966-04-19,941.98,946.99,934.02,941.64,8820000,941.64 1966-04-18,947.77,953.22,936.91,941.98,9150000,941.98 1966-04-15,945.48,957.40,941.70,947.77,10270000,947.77 1966-04-14,938.36,953.67,936.52,945.48,12980000,945.48 1966-04-13,937.24,945.32,930.01,938.36,10440000,938.36 1966-04-12,942.42,947.10,932.51,937.24,10500000,937.24 1966-04-11,945.76,950.77,937.69,942.42,9310000,942.42 1966-04-07,945.26,952.39,939.53,945.76,9650000,945.76 1966-04-06,944.71,951.22,937.58,945.26,9040000,945.26 1966-04-05,937.86,951.44,935.91,944.71,10560000,944.71 1966-04-04,931.29,945.48,930.51,937.86,9360000,937.86 1966-04-01,924.77,936.30,921.77,931.29,9050000,931.29 1966-03-31,919.76,929.12,916.31,924.77,6690000,924.77 1966-03-30,928.00,928.00,915.31,919.76,7980000,919.76 1966-03-29,932.62,937.19,922.88,929.39,8300000,929.39 1966-03-28,929.95,940.36,928.61,932.62,8640000,932.62 1966-03-25,928.61,936.52,925.38,929.95,7750000,929.95 1966-03-24,929.00,933.35,923.37,928.61,7880000,928.61 1966-03-23,934.52,935.91,924.88,929.00,6720000,929.00 1966-03-22,929.28,942.92,929.28,934.52,8910000,934.52 1966-03-21,922.88,935.52,921.65,929.17,7230000,929.17 1966-03-18,919.32,928.95,914.58,922.88,6450000,922.88 1966-03-17,916.03,922.99,912.58,919.32,5460000,919.32 1966-03-16,911.08,922.27,909.13,916.03,7330000,916.03 1966-03-15,917.09,919.15,905.40,911.08,9440000,911.08 1966-03-14,927.95,930.01,914.36,917.09,7400000,917.09 1966-03-11,929.23,937.30,924.72,927.95,7000000,927.95 1966-03-10,929.84,941.42,924.10,929.23,10310000,929.23 1966-03-09,919.98,933.51,918.98,929.84,7980000,929.84 1966-03-08,917.78,928.95,909.57,919.98,10120000,919.98 1966-03-07,932.34,932.46,914.81,917.78,9370000,917.78 1966-03-04,936.35,943.31,928.89,932.34,9000000,932.34 1966-03-03,932.01,941.25,922.27,936.35,9900000,936.35 1966-03-02,938.19,943.09,927.78,932.01,10470000,932.01 1966-03-01,951.89,955.17,935.52,938.19,11030000,938.19 1966-02-28,953.00,960.41,948.21,951.89,9910000,951.89 1966-02-25,950.66,962.30,946.10,953.00,8140000,953.00 1966-02-24,960.13,962.19,946.60,950.66,7860000,950.66 1966-02-23,966.48,967.87,955.12,960.13,8080000,960.13 1966-02-21,975.22,977.11,962.80,966.48,8510000,966.48 1966-02-18,975.27,982.07,966.31,975.22,8470000,975.22 1966-02-17,982.40,985.85,969.93,975.27,9330000,975.27 1966-02-16,981.57,987.80,976.22,982.40,9180000,982.40 1966-02-15,987.69,990.81,977.61,981.57,8750000,981.57 1966-02-14,989.03,995.60,983.24,987.69,8360000,987.69 1966-02-11,990.81,997.99,984.96,989.03,8150000,989.03 1966-02-10,995.15,1000.27,986.74,990.81,9790000,990.81 1966-02-09,991.03,1001.11,987.63,995.15,9760000,995.15 1966-02-08,989.69,998.71,979.28,991.03,10560000,991.03 1966-02-07,986.35,996.71,981.84,989.69,8000000,989.69 1966-02-04,981.23,991.53,976.00,986.35,7560000,986.35 1966-02-03,982.29,991.59,976.33,981.23,8160000,981.23 1966-02-02,975.89,985.35,967.81,982.29,8130000,982.29 1966-02-01,983.51,987.47,969.43,975.89,9090000,975.89 1966-01-31,985.35,992.53,979.67,983.51,7800000,983.51 1966-01-28,990.36,994.59,979.95,985.35,9000000,985.35 1966-01-27,990.92,997.49,985.02,990.36,8970000,990.36 1966-01-26,991.64,999.16,984.13,990.92,9910000,990.92 1966-01-25,991.42,998.21,986.52,991.64,9300000,991.64 1966-01-24,988.14,999.22,984.63,991.42,8780000,991.42 1966-01-21,987.80,993.20,980.62,988.14,9180000,988.14 1966-01-20,991.14,997.77,983.90,987.80,8670000,987.80 1966-01-19,994.20,1000.55,985.30,991.14,10230000,991.14 1966-01-18,989.75,1000.50,984.68,994.20,9790000,994.20 1966-01-17,987.30,996.60,984.02,989.75,9430000,989.75 1966-01-14,985.69,994.09,982.07,987.30,9210000,987.30 1966-01-13,983.96,992.65,980.23,985.69,8860000,985.69 1966-01-12,986.85,992.59,980.45,983.96,8530000,983.96 1966-01-11,985.41,993.04,980.34,986.85,8910000,986.85 1966-01-10,986.13,991.92,980.56,985.41,7720000,985.41 1966-01-07,985.46,991.59,978.61,986.13,7600000,986.13 1966-01-06,981.62,992.26,979.00,985.46,7880000,985.46 1966-01-05,969.26,984.85,968.76,981.62,9650000,981.62 1966-01-04,968.54,978.50,963.02,969.26,7540000,969.26 1966-01-03,969.26,974.55,961.91,968.54,5950000,968.54 1965-12-31,963.69,976.61,962.58,969.26,7240000,969.26 1965-12-30,960.30,969.76,957.62,963.69,7060000,963.69 1965-12-29,957.96,969.15,953.67,960.30,7610000,960.30 1965-12-28,959.79,966.09,950.05,957.96,7280000,957.96 1965-12-27,966.36,972.49,958.29,959.79,5950000,959.79 1965-12-23,965.86,972.93,959.35,966.36,6870000,966.36 1965-12-22,959.46,974.16,956.34,965.86,9720000,965.86 1965-12-21,952.22,964.86,950.05,959.46,8230000,959.46 1965-12-20,957.85,960.69,947.16,952.22,7350000,952.22 1965-12-17,959.13,966.09,952.61,957.85,9490000,957.85 1965-12-16,958.74,967.14,953.78,959.13,9950000,959.13 1965-12-15,954.06,964.81,947.99,958.74,9560000,958.74 1965-12-14,951.55,959.85,948.05,954.06,9920000,954.06 1965-12-13,952.72,959.52,946.54,951.55,8660000,951.55 1965-12-10,949.55,957.51,945.71,952.72,8740000,952.72 1965-12-09,946.60,955.67,942.59,949.55,9150000,949.55 1965-12-08,951.33,959.63,943.42,946.60,10120000,946.60 1965-12-07,939.53,958.63,938.80,951.33,9340000,951.33 1965-12-06,946.10,946.15,924.44,939.53,11440000,939.53 1965-12-03,944.59,950.94,939.36,946.10,8160000,946.10 1965-12-02,947.60,951.11,938.80,944.59,9070000,944.59 1965-12-01,946.71,953.00,941.81,947.60,10140000,947.60 1965-11-30,946.93,950.89,937.24,946.71,8990000,946.71 1965-11-29,948.16,954.84,942.48,946.93,8760000,946.93 1965-11-26,948.94,953.56,943.76,948.16,6970000,948.16 1965-11-24,948.94,956.06,942.98,948.94,7870000,948.94 1965-11-23,946.38,953.28,941.87,948.94,7150000,948.94 1965-11-22,952.72,954.95,941.48,946.38,6370000,946.38 1965-11-19,950.50,958.51,946.88,952.72,6850000,952.72 1965-11-18,956.57,958.24,945.26,950.50,7040000,950.50 1965-11-17,956.51,963.14,950.66,956.57,9120000,956.57 1965-11-16,955.90,962.08,950.27,956.51,8380000,956.51 1965-11-15,956.29,963.91,951.39,955.90,8310000,955.90 1965-11-12,953.28,961.80,949.44,956.29,7780000,956.29 1965-11-11,951.22,955.84,946.15,953.28,5430000,953.28 1965-11-10,951.72,957.34,946.60,951.22,4860000,951.22 1965-11-09,953.95,959.13,945.76,951.72,6680000,951.72 1965-11-08,959.46,961.74,948.60,953.95,7000000,953.95 1965-11-05,961.85,967.42,953.89,959.46,7310000,959.46 1965-11-04,961.13,969.98,956.23,961.85,8380000,961.85 1965-11-03,958.96,965.97,953.06,961.13,7520000,961.13 1965-11-01,960.82,964.36,953.61,958.96,6340000,958.96 1965-10-29,959.11,966.47,955.38,960.82,7240000,960.82 1965-10-28,959.50,965.21,952.75,959.11,7230000,959.11 1965-10-27,956.32,967.46,954.83,959.50,7670000,959.50 1965-10-26,948.14,959.44,945.95,956.32,6750000,956.32 1965-10-25,952.42,958.95,944.30,948.14,7090000,948.14 1965-10-22,950.28,959.39,946.71,952.42,8960000,952.42 1965-10-21,948.47,957.36,944.90,950.28,9170000,950.28 1965-10-20,947.76,953.57,941.72,948.47,8200000,948.47 1965-10-19,945.84,955.49,943.15,947.76,8620000,947.76 1965-10-18,940.68,952.31,939.31,945.84,8180000,945.84 1965-10-15,937.50,945.07,934.15,940.68,7470000,940.68 1965-10-14,941.01,946.22,933.87,937.50,8580000,937.50 1965-10-13,941.12,945.84,935.74,941.01,9470000,941.01 1965-10-12,942.65,947.92,936.73,941.12,9470000,941.12 1965-10-11,938.32,948.30,936.40,942.65,9600000,942.65 1965-10-08,934.42,944.08,932.50,938.32,7670000,938.32 1965-10-07,936.84,941.83,930.75,934.42,6670000,934.42 1965-10-06,938.70,942.49,927.29,936.84,6010000,936.84 1965-10-05,930.86,942.49,930.14,938.70,6980000,938.70 1965-10-04,929.65,935.57,924.05,930.86,5590000,930.86 1965-10-01,930.58,936.07,923.23,929.65,7470000,929.65 1965-09-30,932.39,939.20,927.40,930.58,8670000,930.58 1965-09-29,935.85,944.96,927.89,932.39,10600000,932.39 1965-09-28,937.88,943.42,928.66,935.85,8750000,935.85 1965-09-27,929.54,944.74,927.89,937.88,6820000,937.88 1965-09-24,927.45,933.65,918.89,929.54,7810000,929.54 1965-09-23,931.62,938.37,922.95,927.45,9990000,927.45 1965-09-22,926.52,936.62,922.35,931.62,8290000,931.62 1965-09-21,931.18,936.73,923.45,926.52,7750000,926.52 1965-09-20,928.99,937.00,924.27,931.18,7040000,931.18 1965-09-17,931.18,934.59,922.57,928.99,6610000,928.99 1965-09-16,922.95,935.46,922.73,931.18,7410000,931.18 1965-09-15,916.59,927.89,913.41,922.95,6220000,922.95 1965-09-14,920.92,928.22,913.57,916.59,7830000,916.59 1965-09-13,918.95,927.62,913.41,920.92,7020000,920.92 1965-09-10,917.47,924.00,911.65,918.95,6650000,918.95 1965-09-09,913.68,923.12,911.81,917.47,7360000,917.47 1965-09-08,910.11,918.45,905.67,913.68,6240000,913.68 1965-09-07,907.97,915.22,904.30,910.11,5750000,910.11 1965-09-03,900.46,910.28,900.46,907.97,6010000,907.97 1965-09-02,893.60,903.03,892.17,900.40,6470000,900.40 1965-09-01,893.10,897.93,886.96,893.60,5890000,893.60 1965-08-31,895.63,900.84,888.22,893.10,5170000,893.10 1965-08-30,895.96,899.69,890.52,895.63,4400000,895.63 1965-08-27,896.18,901.88,891.95,895.96,5570000,895.96 1965-08-26,890.85,899.25,886.74,896.18,6010000,896.18 1965-08-25,887.12,895.79,884.38,890.85,6240000,890.85 1965-08-24,887.07,893.05,883.50,887.12,4740000,887.12 1965-08-23,889.92,893.65,883.94,887.07,4470000,887.07 1965-08-20,891.79,894.97,884.71,889.92,4170000,889.92 1965-08-19,894.37,900.13,889.43,891.79,5000000,891.79 1965-08-18,894.26,901.39,890.30,894.37,5850000,894.37 1965-08-17,891.13,898.37,888.11,894.26,4520000,894.26 1965-08-16,888.82,896.89,886.41,891.13,5270000,891.13 1965-08-13,881.96,891.95,880.48,888.82,5430000,888.82 1965-08-12,881.47,886.90,876.86,881.96,5160000,881.96 1965-08-11,878.89,885.42,876.48,881.47,5030000,881.47 1965-08-10,879.77,883.39,875.43,878.89,4690000,878.89 1965-08-09,882.51,887.40,876.31,879.77,4540000,879.77 1965-08-06,881.63,886.57,875.38,882.51,4200000,882.51 1965-08-05,883.88,886.96,878.34,881.63,4920000,881.63 1965-08-04,881.20,888.11,878.40,883.88,4830000,883.88 1965-08-03,881.85,885.04,874.78,881.20,4640000,881.20 1965-08-02,881.74,888.11,876.48,881.85,4220000,881.85 1965-07-30,875.49,885.31,875.49,881.74,5200000,881.74 1965-07-29,867.92,877.85,864.62,874.23,4690000,874.23 1965-07-28,863.53,873.18,858.42,867.92,4760000,867.92 1965-07-27,867.26,872.09,860.78,863.53,4190000,863.53 1965-07-26,863.97,870.66,858.75,867.26,3790000,867.26 1965-07-23,861.77,869.40,859.58,863.97,3600000,863.97 1965-07-22,865.01,868.08,857.71,861.77,3310000,861.77 1965-07-21,868.79,872.58,860.95,865.01,4350000,865.01 1965-07-20,880.26,882.02,866.82,868.79,4670000,868.79 1965-07-19,880.43,884.54,876.09,880.26,3220000,880.26 1965-07-16,880.98,885.91,875.98,880.43,3520000,880.43 1965-07-15,883.23,889.98,878.62,880.98,4420000,880.98 1965-07-14,876.97,886.24,874.23,883.23,4100000,883.23 1965-07-13,877.96,881.03,872.47,876.97,3260000,876.97 1965-07-12,879.49,883.99,874.39,877.96,3690000,877.96 1965-07-09,877.85,885.04,874.72,879.49,4800000,879.49 1965-07-08,870.77,880.59,867.20,877.85,4380000,877.85 1965-07-07,873.18,874.61,866.71,870.77,3020000,870.77 1965-07-06,875.16,879.60,870.00,873.18,3400000,873.18 1965-07-02,871.59,878.40,866.76,875.16,4260000,875.16 1965-07-01,868.03,873.84,861.88,871.59,4520000,871.59 1965-06-30,856.94,873.35,856.94,868.03,6930000,868.03 1965-06-29,840.59,856.45,832.74,851.40,10450000,851.40 1965-06-28,854.36,858.86,838.78,840.59,7650000,840.59 1965-06-25,857.76,861.99,849.75,854.36,5790000,854.36 1965-06-24,870.22,870.93,854.64,857.76,5840000,857.76 1965-06-23,875.43,879.38,868.25,870.22,3580000,870.22 1965-06-22,874.12,882.18,871.48,875.43,3330000,875.43 1965-06-21,879.17,881.47,868.79,874.12,3280000,874.12 1965-06-18,883.06,888.22,875.10,879.17,4330000,879.17 1965-06-17,878.07,888.44,876.20,883.06,5220000,883.06 1965-06-16,874.57,886.13,873.40,878.07,6290000,878.07 1965-06-15,868.71,876.75,859.13,874.57,8450000,874.57 1965-06-14,881.70,885.43,863.87,868.71,5920000,868.71 1965-06-11,876.49,886.55,874.52,881.70,5350000,881.70 1965-06-10,879.84,887.56,869.35,876.49,7470000,876.49 1965-06-09,889.05,893.79,875.90,879.84,7070000,879.84 1965-06-08,902.15,903.16,886.71,889.05,4660000,889.05 1965-06-07,900.87,907.47,889.90,902.15,4680000,902.15 1965-06-04,899.22,905.02,894.69,900.87,4530000,900.87 1965-06-03,904.06,913.11,896.40,899.22,5720000,899.22 1965-06-02,908.53,910.08,894.75,904.06,6790000,904.06 1965-06-01,918.04,921.85,907.04,908.53,4830000,908.53 1965-05-28,913.22,920.69,910.89,918.04,4270000,918.04 1965-05-27,917.16,918.20,904.82,913.22,5520000,913.22 1965-05-26,921.00,927.48,915.09,917.16,5330000,917.16 1965-05-25,914.21,924.58,912.55,921.00,4950000,921.00 1965-05-24,922.01,924.27,910.89,914.21,4790000,914.21 1965-05-21,927.27,928.02,918.66,922.01,4660000,922.01 1965-05-20,932.12,934.17,922.41,927.27,5750000,927.27 1965-05-19,930.62,936.87,926.97,932.12,5860000,932.12 1965-05-18,930.67,932.82,924.36,930.62,5130000,930.62 1965-05-17,939.62,941.52,928.07,930.67,4980000,930.67 1965-05-14,938.87,944.82,933.82,939.62,5860000,939.62 1965-05-13,934.17,942.37,933.52,938.87,6460000,938.87 1965-05-12,930.92,938.12,928.72,934.17,6310000,934.17 1965-05-11,931.47,934.87,925.62,930.92,5150000,930.92 1965-05-10,932.52,937.22,926.62,931.47,5600000,931.47 1965-05-07,933.52,937.07,927.07,932.52,5820000,932.52 1965-05-06,932.22,938.12,928.02,933.52,6340000,933.52 1965-05-05,928.22,936.37,924.91,932.22,6350000,932.22 1965-05-04,922.11,931.07,919.71,928.22,5720000,928.22 1965-05-03,922.31,926.97,916.66,922.11,5340000,922.11 1965-04-30,918.71,925.42,915.36,922.31,5190000,922.31 1965-04-29,918.86,923.01,914.91,918.71,5510000,918.71 1965-04-28,918.16,923.56,914.01,918.86,5680000,918.86 1965-04-27,916.86,924.96,915.76,918.16,6310000,918.16 1965-04-26,916.41,920.11,910.21,916.86,5410000,916.86 1965-04-23,915.06,921.51,912.26,916.41,5860000,916.41 1965-04-22,910.71,917.51,908.31,915.06,5990000,915.06 1965-04-21,911.96,915.31,903.81,910.71,5590000,910.71 1965-04-20,912.76,919.01,908.01,911.96,6480000,911.96 1965-04-19,911.91,917.41,907.91,912.76,5700000,912.76 1965-04-15,912.86,917.01,905.71,911.91,5830000,911.91 1965-04-14,908.01,916.51,905.96,912.86,6580000,912.86 1965-04-13,906.36,912.41,902.21,908.01,6690000,908.01 1965-04-12,901.29,909.51,899.90,906.36,6040000,906.36 1965-04-09,897.90,905.77,895.93,901.29,6580000,901.29 1965-04-08,892.94,900.41,890.72,897.90,5770000,897.90 1965-04-07,891.90,895.84,888.27,892.94,4430000,892.94 1965-04-06,893.23,896.13,888.51,891.90,4610000,891.90 1965-04-05,893.38,898.69,889.00,893.23,4920000,893.23 1965-04-02,890.33,897.31,888.71,893.38,5060000,893.38 1965-04-01,889.05,894.95,886.84,890.33,4890000,890.33 1965-03-31,889.05,893.72,885.51,889.05,4470000,889.05 1965-03-30,887.82,892.99,885.27,889.05,4270000,889.05 1965-03-29,891.66,896.43,884.68,887.82,4590000,887.82 1965-03-26,898.34,900.60,888.51,891.66,5020000,891.66 1965-03-25,900.56,904.88,895.74,898.34,5460000,898.34 1965-03-24,898.69,904.39,896.13,900.56,5420000,900.56 1965-03-23,896.12,902.32,893.82,898.69,4820000,898.69 1965-03-22,895.79,901.14,892.87,896.12,4920000,896.12 1965-03-19,896.55,900.43,892.20,895.79,5040000,895.79 1965-03-18,899.37,902.67,893.35,896.55,4990000,896.55 1965-03-17,898.90,904.01,894.45,899.37,5120000,899.37 1965-03-16,899.85,904.58,894.83,898.90,5480000,898.90 1965-03-15,900.33,907.88,896.89,899.85,6000000,899.85 1965-03-12,896.51,905.16,894.50,900.33,6370000,900.33 1965-03-11,892.39,900.71,890.24,896.51,5770000,896.51 1965-03-10,894.07,898.13,888.81,892.39,5100000,892.39 1965-03-09,896.84,900.71,890.72,894.07,5210000,894.07 1965-03-08,895.98,901.81,891.30,896.84,5250000,896.84 1965-03-05,897.75,898.61,886.28,895.98,6120000,895.98 1965-03-04,900.76,905.25,894.45,897.75,7300000,897.75 1965-03-03,901.91,906.95,896.27,900.76,6600000,900.76 1965-03-02,899.76,905.73,896.17,901.91,5730000,901.91 1965-03-01,903.48,907.40,895.55,899.76,5780000,899.76 1965-02-26,899.90,908.26,897.08,903.48,5800000,903.48 1965-02-25,897.84,904.82,894.64,899.90,6680000,899.90 1965-02-24,891.96,900.76,891.30,897.84,7160000,897.84 1965-02-23,885.61,895.84,884.60,891.96,5880000,891.96 1965-02-19,883.69,890.24,880.25,885.61,5560000,885.61 1965-02-18,882.93,888.52,878.53,883.69,6060000,883.69 1965-02-17,881.35,889.10,877.86,882.93,5510000,882.93 1965-02-16,885.32,887.90,877.48,881.35,5000000,881.35 1965-02-15,888.47,895.26,882.60,885.32,5760000,885.32 1965-02-12,881.88,891.15,881.45,888.47,4960000,888.47 1965-02-11,892.92,897.70,879.97,881.88,5800000,881.88 1965-02-10,901.24,905.54,890.77,892.92,7210000,892.92 1965-02-09,897.89,905.40,896.12,901.24,5690000,901.24 1965-02-08,901.57,901.86,889.96,897.89,6010000,897.89 1965-02-05,904.06,906.93,897.70,901.57,5690000,901.57 1965-02-04,906.30,911.80,900.33,904.06,6230000,904.06 1965-02-03,903.77,909.75,898.99,906.30,6130000,906.30 1965-02-02,903.68,907.21,898.61,903.77,5460000,903.77 1965-02-01,902.86,908.26,897.99,903.68,5690000,903.68 1965-01-29,900.95,907.79,898.32,902.86,6940000,902.86 1965-01-28,899.52,906.26,895.79,900.95,6730000,900.95 1965-01-27,897.84,904.44,894.26,899.52,6010000,899.52 1965-01-26,896.46,901.86,892.30,897.84,5760000,897.84 1965-01-25,893.59,900.71,890.82,896.46,5370000,896.46 1965-01-22,893.26,898.70,888.43,893.59,5430000,893.59 1965-01-21,895.31,897.46,887.81,893.26,4780000,893.26 1965-01-20,896.27,901.43,891.92,895.31,5550000,895.31 1965-01-19,895.21,902.10,891.10,896.27,5550000,896.27 1965-01-18,891.15,898.90,889.86,895.21,5550000,895.21 1965-01-15,887.18,895.12,884.65,891.15,5340000,891.15 1965-01-14,886.85,892.30,881.59,887.18,5810000,887.18 1965-01-13,885.89,891.77,883.22,886.85,6160000,886.85 1965-01-12,883.22,889.34,880.97,885.89,5400000,885.89 1965-01-11,882.60,887.42,877.43,883.22,5440000,883.22 1965-01-08,884.36,888.62,878.87,882.60,5340000,882.60 1965-01-07,879.68,887.52,876.95,884.36,5080000,884.36 1965-01-06,875.86,885.08,875.04,879.68,4850000,879.68 1965-01-05,869.78,879.87,868.69,875.86,4110000,875.86 1965-01-04,874.13,877.19,865.10,869.78,3930000,869.78 1964-12-31,868.78,879.78,868.78,874.13,6470000,874.13 1964-12-30,862.18,871.51,861.56,868.69,5610000,868.69 1964-12-29,867.01,868.78,858.26,862.18,4450000,862.18 1964-12-28,868.16,871.98,863.09,867.01,3990000,867.01 1964-12-24,868.02,872.89,863.57,868.16,3600000,868.16 1964-12-23,870.36,876.05,863.19,868.02,4470000,868.02 1964-12-22,869.74,876.38,865.86,870.36,4520000,870.36 1964-12-21,868.73,875.62,866.10,869.74,4470000,869.74 1964-12-18,863.57,872.22,862.95,868.73,4630000,868.73 1964-12-17,860.08,867.30,857.50,863.57,4850000,863.57 1964-12-16,857.45,865.34,854.87,860.08,4610000,860.08 1964-12-15,860.65,862.71,850.19,857.45,5340000,857.45 1964-12-14,864.34,868.78,857.40,860.65,4340000,860.65 1964-12-11,863.14,869.31,860.22,864.34,4530000,864.34 1964-12-10,863.81,869.16,858.46,863.14,4790000,863.14 1964-12-09,870.69,873.13,861.61,863.81,5120000,863.81 1964-12-08,873.99,878.44,867.35,870.69,4990000,870.69 1964-12-07,871.17,881.35,871.17,873.99,4770000,873.99 1964-12-04,870.79,875.09,866.44,870.93,4340000,870.93 1964-12-03,867.25,876.86,867.25,870.79,4250000,870.79 1964-12-02,864.43,871.84,861.08,867.16,4930000,867.16 1964-12-01,875.43,877.96,863.04,864.43,4940000,864.43 1964-11-30,882.12,885.22,871.46,875.43,4890000,875.43 1964-11-27,882.40,886.80,874.47,882.12,4070000,882.12 1964-11-25,887.61,890.00,880.16,882.40,4800000,882.40 1964-11-24,889.29,891.49,881.11,887.61,5070000,887.61 1964-11-23,890.72,894.83,882.88,889.29,4860000,889.29 1964-11-20,888.71,896.41,884.51,890.72,5210000,890.72 1964-11-19,891.71,892.97,882.07,888.71,5570000,888.71 1964-11-18,885.39,897.00,884.69,891.71,6560000,891.71 1964-11-17,880.19,892.18,880.19,885.39,5920000,885.39 1964-11-16,874.11,883.52,870.22,880.10,4870000,880.10 1964-11-13,874.62,878.46,870.73,874.11,4860000,874.11 1964-11-12,873.59,880.00,870.41,874.62,5250000,874.62 1964-11-11,870.64,876.17,866.80,873.59,3790000,873.59 1964-11-10,874.57,878.32,867.60,870.64,5020000,870.64 1964-11-09,876.87,880.00,871.34,874.57,4560000,874.57 1964-11-06,873.54,879.35,869.33,876.87,4810000,876.87 1964-11-05,873.82,879.26,869.10,873.54,4380000,873.54 1964-11-04,875.51,881.27,870.41,873.82,4720000,873.82 1964-11-02,873.08,878.13,867.64,875.51,4430000,875.51 1964-10-30,871.86,876.91,868.91,873.08,4120000,873.08 1964-10-29,871.16,876.87,867.83,871.86,4390000,871.86 1964-10-28,875.98,879.58,867.79,871.16,4890000,871.16 1964-10-27,877.01,880.33,872.75,875.98,4470000,875.98 1964-10-26,877.62,883.33,873.45,877.01,5230000,877.01 1964-10-23,877.01,879.91,872.14,877.62,3830000,877.62 1964-10-22,879.72,883.33,872.51,877.01,4670000,877.01 1964-10-21,881.50,886.28,876.49,879.72,5170000,879.72 1964-10-20,876.21,884.87,873.97,881.50,5140000,881.50 1964-10-19,873.54,879.82,870.41,876.21,5010000,876.21 1964-10-16,868.44,877.71,866.80,873.54,5140000,873.54 1964-10-15,875.18,876.40,861.42,868.44,6500000,868.44 1964-10-14,876.21,880.00,872.00,875.18,4530000,875.18 1964-10-13,877.57,881.88,871.95,876.21,5400000,876.21 1964-10-12,878.08,881.50,874.76,877.57,4110000,877.57 1964-10-09,874.90,881.78,872.65,878.08,5290000,878.08 1964-10-08,873.78,879.40,869.56,874.90,5060000,874.90 1964-10-07,875.14,879.02,871.34,873.78,5090000,873.78 1964-10-06,877.15,881.17,872.05,875.14,4820000,875.14 1964-10-05,872.65,882.39,871.48,877.15,4850000,877.15 1964-10-02,872.00,876.21,867.36,872.65,4370000,872.65 1964-10-01,875.37,878.23,869.80,872.00,4470000,872.00 1964-09-30,875.74,880.24,872.19,875.37,4720000,875.37 1964-09-29,875.46,880.14,871.30,875.74,5070000,875.74 1964-09-28,874.71,879.40,869.24,875.46,4810000,875.46 1964-09-25,872.98,879.26,868.72,874.71,6170000,874.71 1964-09-24,871.95,876.96,867.04,872.98,5840000,872.98 1964-09-23,872.47,876.77,867.88,871.95,5920000,871.95 1964-09-22,871.58,877.43,868.67,872.47,5250000,872.47 1964-09-21,866.47,875.00,866.47,871.58,5310000,871.58 1964-09-18,868.67,873.92,860.20,865.12,6160000,865.12 1964-09-17,864.18,873.17,862.87,868.67,6380000,868.67 1964-09-16,862.54,867.64,857.35,864.18,4230000,864.18 1964-09-15,866.24,871.30,860.95,862.54,5690000,862.54 1964-09-14,867.13,872.84,862.35,866.24,5370000,866.24 1964-09-11,859.50,870.64,857.06,867.13,5630000,867.13 1964-09-10,855.57,863.06,852.66,859.50,5470000,859.50 1964-09-09,851.91,860.01,850.56,855.57,5690000,855.57 1964-09-08,848.31,855.61,847.61,851.91,4090000,851.91 1964-09-04,846.02,850.84,843.58,848.31,4210000,848.31 1964-09-03,845.08,848.97,841.24,846.02,4310000,846.02 1964-09-02,844.00,849.62,840.96,845.08,4800000,845.08 1964-09-01,838.48,846.06,836.56,844.00,4650000,844.00 1964-08-31,839.09,842.83,834.59,838.48,3340000,838.48 1964-08-28,835.25,841.94,833.98,839.09,3760000,839.09 1964-08-27,829.21,837.40,826.91,835.25,3560000,835.25 1964-08-26,832.20,834.87,826.59,829.21,3300000,829.21 1964-08-25,837.31,839.09,830.29,832.20,3780000,832.20 1964-08-24,838.62,843.21,834.83,837.31,3790000,837.31 1964-08-21,838.71,842.60,835.39,838.62,3620000,838.62 1964-08-20,841.76,844.19,835.44,838.71,3840000,838.71 1964-08-19,842.83,847.19,838.24,841.76,4160000,841.76 1964-08-18,840.21,845.64,837.17,842.83,4180000,842.83 1964-08-17,838.81,844.77,836.18,840.21,3780000,840.21 1964-08-14,838.52,844.00,834.92,838.81,4080000,838.81 1964-08-13,834.08,842.41,833.14,838.52,4600000,838.52 1964-08-12,828.08,837.54,827.29,834.08,4140000,834.08 1964-08-11,829.35,832.95,825.56,828.08,3450000,828.08 1964-08-10,829.16,834.08,825.18,829.35,3050000,829.35 1964-08-07,823.40,831.60,822.75,829.16,3190000,829.16 1964-08-06,833.05,835.90,822.56,823.40,3940000,823.40 1964-08-05,832.77,835.44,820.78,833.05,6160000,833.05 1964-08-04,840.35,840.91,829.96,832.77,4780000,832.77 1964-08-03,841.10,844.28,837.45,840.35,3780000,840.35 1964-07-31,839.37,844.80,836.89,841.10,4220000,841.10 1964-07-30,838.67,843.86,836.14,839.37,4530000,839.37 1964-07-29,837.35,842.93,834.31,838.67,4050000,838.67 1964-07-28,841.05,842.27,833.47,837.35,3860000,837.35 1964-07-27,845.64,849.53,838.95,841.05,4090000,841.05 1964-07-24,846.48,850.32,842.88,845.64,4210000,845.64 1964-07-23,847.65,851.54,842.93,846.48,4560000,846.48 1964-07-22,846.95,851.45,841.71,847.65,4570000,847.65 1964-07-21,849.39,851.49,841.85,846.95,4570000,846.95 1964-07-20,851.35,855.19,847.00,849.39,4390000,849.39 1964-07-17,847.47,854.11,845.45,851.35,4640000,851.35 1964-07-16,844.80,850.04,842.04,847.47,4640000,847.47 1964-07-15,843.63,849.06,839.27,844.80,4610000,844.80 1964-07-14,845.55,849.53,839.60,843.63,4760000,843.63 1964-07-13,847.51,851.54,841.90,845.55,4800000,845.55 1964-07-10,845.13,852.52,841.99,847.51,5420000,847.51 1964-07-09,845.45,849.85,841.01,845.13,5040000,845.13 1964-07-08,844.94,849.34,839.98,845.45,4760000,845.45 1964-07-07,844.24,849.15,841.66,844.94,5240000,844.94 1964-07-06,841.47,848.64,838.01,844.24,5080000,844.24 1964-07-02,838.06,844.75,836.04,841.47,5230000,841.47 1964-07-01,831.50,839.88,829.30,838.06,5320000,838.06 1964-06-30,830.94,834.64,826.31,831.50,4360000,831.50 1964-06-29,830.99,835.90,827.01,830.94,4380000,830.94 1964-06-26,827.48,833.05,825.09,830.99,4440000,830.99 1964-06-25,827.01,832.39,823.40,827.48,5010000,827.48 1964-06-24,822.70,831.17,819.80,827.01,4840000,827.01 1964-06-23,826.38,830.05,820.55,822.70,4060000,822.70 1964-06-22,825.25,831.97,823.30,826.38,4540000,826.38 1964-06-19,823.98,828.11,819.94,825.25,4050000,825.25 1964-06-18,823.35,829.42,820.62,823.98,4730000,823.98 1964-06-17,818.16,826.45,817.63,823.35,5340000,823.35 1964-06-16,813.56,821.22,812.63,818.16,4590000,818.16 1964-06-15,809.39,816.79,808.11,813.56,4110000,813.56 1964-06-12,811.25,814.22,806.52,809.39,3840000,809.39 1964-06-11,807.53,815.15,806.65,811.25,3620000,811.25 1964-06-10,805.54,812.10,803.99,807.53,4170000,807.53 1964-06-09,800.31,808.15,796.90,805.54,4470000,805.54 1964-06-08,806.03,808.95,798.50,800.31,4010000,800.31 1964-06-05,802.48,810.37,801.78,806.03,4240000,806.03 1964-06-04,811.79,813.38,800.75,802.48,4880000,802.48 1964-06-03,813.78,818.16,809.84,811.79,3990000,811.79 1964-06-02,818.56,820.34,811.87,813.78,4180000,813.78 1964-06-01,820.56,824.94,815.82,818.56,4300000,818.56 1964-05-28,817.94,824.14,814.80,820.56,4560000,820.56 1964-05-27,818.92,822.20,812.63,817.94,4450000,817.94 1964-05-26,820.25,824.01,816.88,818.92,4290000,818.92 1964-05-25,820.87,825.47,816.39,820.25,3990000,820.25 1964-05-22,819.80,824.81,816.57,820.87,4640000,820.87 1964-05-21,820.11,826.45,816.08,819.80,5350000,819.80 1964-05-20,817.28,824.10,815.15,820.11,4790000,820.11 1964-05-19,821.31,823.26,813.96,817.28,4360000,817.28 1964-05-18,826.23,829.33,819.18,821.31,4590000,821.31 1964-05-15,824.45,829.15,821.22,826.23,5070000,826.23 1964-05-14,825.78,828.62,819.63,824.45,4720000,824.45 1964-05-13,827.38,832.78,822.24,825.78,5890000,825.78 1964-05-12,827.07,832.25,824.41,827.38,5200000,827.38 1964-05-11,828.57,832.21,824.10,827.07,4490000,827.07 1964-05-08,830.17,834.55,825.12,828.57,4910000,828.57 1964-05-07,828.18,836.06,824.19,830.17,5600000,830.17 1964-05-06,826.63,832.34,822.55,828.18,5560000,828.18 1964-05-05,823.83,829.28,817.23,826.63,5340000,826.63 1964-05-04,817.10,828.09,816.39,823.83,5360000,823.83 1964-05-01,810.77,819.40,808.55,817.10,5990000,817.10 1964-04-30,812.81,816.88,807.18,810.77,5690000,810.77 1964-04-29,816.70,821.97,810.32,812.81,6200000,812.81 1964-04-28,811.87,820.11,809.04,816.70,4790000,816.70 1964-04-27,814.89,817.68,807.71,811.87,5070000,811.87 1964-04-24,821.66,823.79,813.51,814.89,5610000,814.89 1964-04-23,823.57,830.04,819.32,821.66,6690000,821.66 1964-04-22,826.45,828.09,820.25,823.57,5390000,823.57 1964-04-21,824.54,830.70,820.47,826.45,5750000,826.45 1964-04-20,827.33,829.81,821.49,824.54,5560000,824.54 1964-04-17,825.65,831.63,822.51,827.33,6030000,827.33 1964-04-16,825.43,830.12,821.22,825.65,5240000,825.65 1964-04-15,822.95,828.62,820.38,825.43,5270000,825.43 1964-04-14,821.31,826.63,818.12,822.95,5120000,822.95 1964-04-13,821.75,826.71,818.21,821.31,5330000,821.31 1964-04-10,821.35,825.34,819.14,821.75,4990000,821.75 1964-04-09,824.19,827.51,819.54,821.35,5300000,821.35 1964-04-08,822.77,828.09,818.87,824.19,5380000,824.19 1964-04-07,824.76,829.42,819.18,822.77,5900000,822.77 1964-04-06,822.99,828.88,820.51,824.76,5840000,824.76 1964-04-03,820.87,828.49,818.43,822.99,5990000,822.99 1964-04-02,816.08,825.12,815.20,820.87,6840000,820.87 1964-04-01,813.29,819.23,809.79,816.08,5510000,816.08 1964-03-31,815.29,817.94,810.37,813.29,5270000,813.29 1964-03-30,815.91,819.98,812.18,815.29,6060000,815.29 1964-03-26,813.16,819.45,811.39,815.91,5760000,815.91 1964-03-25,811.43,816.35,808.60,813.16,5420000,813.16 1964-03-24,813.60,816.92,808.95,811.43,5210000,811.43 1964-03-23,814.93,817.72,809.93,813.60,4940000,813.60 1964-03-20,819.36,820.47,810.81,814.93,5020000,814.93 1964-03-19,820.25,824.72,815.91,819.36,5670000,819.36 1964-03-18,818.16,824.23,814.67,820.25,5890000,820.25 1964-03-17,816.48,821.80,812.58,818.16,5480000,818.16 1964-03-16,816.22,821.35,813.25,816.48,5140000,816.48 1964-03-13,814.22,819.85,810.94,816.22,5660000,816.22 1964-03-12,813.87,818.08,809.22,814.22,5290000,814.22 1964-03-11,809.39,817.01,807.84,813.87,6180000,813.87 1964-03-10,807.18,811.96,803.37,809.39,5500000,809.39 1964-03-09,806.03,812.14,803.41,807.18,5510000,807.18 1964-03-06,803.77,809.13,801.16,806.03,4790000,806.03 1964-03-05,804.70,807.93,799.78,803.77,4680000,803.77 1964-03-04,805.72,810.19,800.80,804.70,5250000,804.70 1964-03-03,802.75,809.75,801.33,805.72,5350000,805.72 1964-03-02,800.14,807.22,798.05,802.75,5690000,802.75 1964-02-28,797.04,802.35,793.80,800.14,4980000,800.14 1964-02-27,799.38,803.46,795.44,797.04,5420000,797.04 1964-02-26,796.59,802.00,793.80,799.38,5350000,799.38 1964-02-25,797.12,800.54,792.96,796.59,5010000,796.59 1964-02-24,796.99,802.93,793.32,797.12,5630000,797.12 1964-02-20,794.91,800.93,791.41,796.99,4690000,796.99 1964-02-19,795.40,800.27,791.32,794.91,4280000,794.91 1964-02-18,796.19,800.67,791.32,795.40,4660000,795.40 1964-02-17,794.56,800.40,791.45,796.19,4780000,796.19 1964-02-14,794.42,798.85,789.95,794.56,4360000,794.56 1964-02-13,794.82,799.07,789.99,794.42,4820000,794.42 1964-02-12,792.16,798.14,790.39,794.82,4650000,794.82 1964-02-11,788.71,795.04,786.58,792.16,4040000,792.16 1964-02-10,791.59,797.17,786.76,788.71,4150000,788.71 1964-02-07,786.41,795.40,784.37,791.59,4710000,791.59 1964-02-06,783.04,789.42,780.69,786.41,4110000,786.41 1964-02-05,783.30,789.82,777.99,783.04,4010000,783.04 1964-02-04,784.72,787.78,778.96,783.30,4320000,783.30 1964-02-03,785.34,789.90,780.25,784.72,4140000,784.72 1964-01-31,783.44,789.77,780.34,785.34,4000000,785.34 1964-01-30,782.60,788.35,778.88,783.44,4230000,783.44 1964-01-29,787.78,790.04,779.72,782.60,4450000,782.60 1964-01-28,785.34,791.63,781.75,787.78,4720000,787.78 1964-01-27,783.04,790.39,780.43,785.34,5240000,785.34 1964-01-24,782.86,787.65,778.12,783.04,5080000,783.04 1964-01-23,781.31,787.60,777.95,782.86,5380000,782.86 1964-01-22,776.44,786.89,774.45,781.31,5430000,781.31 1964-01-21,773.03,779.54,767.80,776.44,4800000,776.44 1964-01-20,775.69,780.47,769.82,773.03,5570000,773.03 1964-01-17,776.13,779.41,770.59,775.69,5600000,775.69 1964-01-16,774.71,781.71,770.95,776.13,6200000,776.13 1964-01-15,774.49,779.63,768.55,774.71,6750000,774.71 1964-01-14,773.12,778.88,770.46,774.49,6500000,774.49 1964-01-13,774.33,777.86,768.38,773.12,5440000,773.12 1964-01-10,776.55,778.81,770.38,774.33,5260000,774.33 1964-01-09,774.46,780.59,770.29,776.55,5180000,776.55 1964-01-08,771.73,777.25,768.94,774.46,5380000,774.46 1964-01-07,769.51,776.12,766.12,771.73,5700000,771.73 1964-01-06,767.68,773.77,764.77,769.51,5480000,769.51 1964-01-03,766.08,771.73,763.77,767.68,5550000,767.68 1964-01-02,762.95,770.73,760.34,766.08,4680000,766.08 1963-12-31,759.90,767.55,758.64,762.95,6730000,762.95 1963-12-30,762.95,764.12,756.64,759.90,4930000,759.90 1963-12-27,760.21,767.77,758.51,762.95,4360000,762.95 1963-12-26,756.86,764.47,754.91,760.21,3700000,760.21 1963-12-24,758.30,763.16,752.82,756.86,3970000,756.86 1963-12-23,762.08,765.03,754.43,758.30,4540000,758.30 1963-12-20,763.86,767.29,757.91,762.08,4600000,762.08 1963-12-19,767.21,769.81,760.73,763.86,4410000,763.86 1963-12-18,766.38,773.07,762.43,767.21,6000000,767.21 1963-12-17,761.64,769.51,758.99,766.38,5140000,766.38 1963-12-16,760.17,765.03,756.12,761.64,4280000,761.64 1963-12-13,757.43,762.82,756.25,760.17,4290000,760.17 1963-12-12,757.21,761.60,754.30,757.43,4220000,757.43 1963-12-11,759.25,762.03,754.04,757.21,4400000,757.21 1963-12-10,759.08,764.25,754.95,759.25,4560000,759.25 1963-12-09,760.25,764.29,755.43,759.08,4430000,759.08 1963-12-06,763.86,767.21,757.12,760.25,4830000,760.25 1963-12-05,755.51,766.21,753.69,763.86,5190000,763.86 1963-12-04,751.82,758.51,747.17,755.51,4790000,755.51 1963-12-03,751.91,756.82,747.26,751.82,4520000,751.82 1963-12-02,750.52,757.95,746.78,751.91,4770000,751.91 1963-11-29,741.00,752.39,738.56,750.52,4810000,750.52 1963-11-27,743.52,746.91,735.87,741.00,5210000,741.00 1963-11-26,732.96,746.60,732.96,743.52,9320000,743.52 1963-11-22,732.65,739.00,710.83,711.49,6630000,711.49 1963-11-21,742.06,744.69,730.57,732.65,5670000,732.65 1963-11-20,736.65,747.51,733.44,742.06,5330000,742.06 1963-11-19,734.85,743.13,731.64,736.65,4430000,736.65 1963-11-18,740.00,743.09,731.08,734.85,4730000,734.85 1963-11-15,747.04,749.22,737.90,740.00,4790000,740.00 1963-11-14,751.11,753.30,744.42,747.04,4610000,747.04 1963-11-13,750.21,753.77,745.88,751.11,4710000,751.11 1963-11-12,753.77,756.82,748.36,750.21,4610000,750.21 1963-11-11,750.81,756.56,749.95,753.77,3970000,753.77 1963-11-08,745.66,753.47,744.63,750.81,4570000,750.81 1963-11-07,744.03,750.21,740.99,745.66,4320000,745.66 1963-11-06,749.22,749.82,738.41,744.03,5600000,744.03 1963-11-04,753.73,757.12,746.09,749.22,5440000,749.22 1963-11-01,755.23,759.56,750.30,753.73,5240000,753.73 1963-10-31,755.19,759.00,749.78,755.23,5030000,755.23 1963-10-30,760.50,762.78,751.80,755.19,5170000,755.19 1963-10-29,759.39,767.24,755.49,760.50,6100000,760.50 1963-10-28,755.61,765.70,752.95,759.39,7150000,759.39 1963-10-25,751.80,759.90,748.62,755.61,6390000,755.61 1963-10-24,746.48,755.91,744.12,751.80,6280000,751.80 1963-10-23,747.21,752.10,742.40,746.48,5830000,746.48 1963-10-22,752.31,753.60,742.70,747.21,6420000,747.21 1963-10-21,750.60,757.12,747.25,752.31,5450000,752.31 1963-10-18,750.77,755.36,747.94,750.60,5830000,750.60 1963-10-17,748.45,755.83,746.99,750.77,6790000,750.77 1963-10-16,742.19,750.42,740.04,748.45,5570000,748.45 1963-10-15,741.84,746.43,738.97,742.19,4550000,742.19 1963-10-14,741.76,744.98,738.03,741.84,4270000,741.84 1963-10-11,740.56,746.05,737.60,741.76,4740000,741.76 1963-10-10,739.83,743.52,733.69,740.56,4470000,740.56 1963-10-09,743.90,747.16,737.90,739.83,5520000,739.83 1963-10-08,743.86,748.97,739.23,743.90,4920000,743.90 1963-10-07,745.06,749.91,740.90,743.86,4050000,743.86 1963-10-04,744.25,750.98,741.72,745.06,5120000,745.06 1963-10-03,737.94,746.86,736.61,744.25,4510000,744.25 1963-10-02,738.33,742.06,734.64,737.94,3780000,737.94 1963-10-01,732.79,742.57,732.49,738.33,4420000,738.33 1963-09-30,737.98,739.83,728.63,732.79,3730000,732.79 1963-09-27,736.95,741.33,731.55,737.98,4350000,737.98 1963-09-26,743.69,745.28,734.68,736.95,5100000,736.95 1963-09-25,745.96,753.04,739.31,743.69,6340000,743.69 1963-09-24,740.43,748.54,737.13,745.96,5520000,745.96 1963-09-23,743.60,746.99,736.65,740.43,5140000,740.43 1963-09-20,743.22,749.27,740.64,743.60,5310000,743.60 1963-09-19,737.86,744.63,736.48,743.22,4080000,743.22 1963-09-18,740.13,744.08,734.98,737.86,5070000,737.86 1963-09-17,738.46,744.50,736.83,740.13,4950000,740.13 1963-09-16,740.13,744.68,736.61,738.46,4740000,738.46 1963-09-13,740.26,744.42,737.25,740.13,5230000,740.13 1963-09-12,740.34,744.46,735.45,740.26,5560000,740.26 1963-09-11,737.43,746.18,736.87,740.34,6670000,740.34 1963-09-10,732.92,740.34,730.56,737.43,5310000,737.43 1963-09-09,735.37,739.27,730.09,732.92,5020000,732.92 1963-09-06,737.98,742.66,733.22,735.37,7160000,735.37 1963-09-05,732.92,739.87,729.49,737.98,5700000,737.98 1963-09-04,732.02,737.60,728.89,732.92,6070000,732.92 1963-09-03,729.32,735.50,728.76,732.02,5570000,732.02 1963-08-30,726.40,731.68,724.00,729.32,4560000,729.32 1963-08-29,725.07,730.09,723.27,726.40,5110000,726.40 1963-08-28,719.88,728.72,719.67,725.07,5120000,725.07 1963-08-27,724.17,725.16,717.95,719.88,4080000,719.88 1963-08-26,723.14,728.38,721.00,724.17,4700000,724.17 1963-08-23,718.47,726.02,718.21,723.14,4880000,723.14 1963-08-22,715.72,720.57,712.59,718.47,4540000,718.47 1963-08-21,717.27,719.80,713.49,715.72,3820000,715.72 1963-08-20,718.81,721.34,714.39,717.27,3660000,717.27 1963-08-19,719.32,723.57,715.72,718.81,3650000,718.81 1963-08-16,718.55,722.93,714.91,719.32,4130000,719.32 1963-08-15,714.95,721.51,712.63,718.55,4980000,718.55 1963-08-14,711.13,717.39,707.61,714.95,4420000,714.95 1963-08-13,710.27,714.31,707.83,711.13,4450000,711.13 1963-08-12,708.39,714.09,705.51,710.27,4770000,710.27 1963-08-09,704.18,709.84,701.48,708.39,4050000,708.39 1963-08-08,703.92,707.36,699.85,704.18,3460000,704.18 1963-08-07,707.06,710.62,701.78,703.92,3790000,703.92 1963-08-06,702.55,709.42,700.92,707.06,3760000,707.06 1963-08-05,697.83,704.83,697.10,702.55,3370000,702.55 1963-08-02,694.87,700.54,693.11,697.83,2940000,697.83 1963-08-01,695.43,699.21,691.23,694.87,3410000,694.87 1963-07-31,696.42,701.99,693.03,695.43,3960000,695.43 1963-07-30,690.71,698.30,690.07,696.42,3550000,696.42 1963-07-29,689.38,693.20,686.68,690.71,2840000,690.71 1963-07-26,687.71,691.44,684.58,689.38,2510000,689.38 1963-07-25,690.88,696.20,685.95,687.71,3710000,687.71 1963-07-24,687.84,693.41,685.99,690.88,2810000,690.88 1963-07-23,688.74,694.83,685.74,687.84,3500000,687.84 1963-07-22,693.89,696.16,684.41,688.74,3700000,688.74 1963-07-19,695.90,697.53,689.21,693.89,3340000,693.89 1963-07-18,699.72,703.20,693.93,695.90,3710000,695.90 1963-07-17,702.12,705.73,697.10,699.72,3940000,699.72 1963-07-16,703.28,706.28,699.76,702.12,3000000,702.12 1963-07-15,707.70,708.86,700.58,703.28,3290000,703.28 1963-07-12,709.76,712.55,705.21,707.70,3660000,707.70 1963-07-11,712.12,715.98,707.87,709.76,4100000,709.76 1963-07-10,714.09,716.28,708.90,712.12,3730000,712.12 1963-07-09,710.66,717.22,709.07,714.09,3830000,714.09 1963-07-08,716.45,717.22,708.64,710.66,3290000,710.66 1963-07-05,713.36,719.02,712.20,716.45,2910000,716.45 1963-07-03,708.94,716.19,708.51,713.36,4030000,713.36 1963-07-02,701.35,711.35,699.93,708.94,3540000,708.94 1963-07-01,706.88,709.11,698.86,701.35,3360000,701.35 1963-06-28,706.03,710.79,702.89,706.88,3020000,706.88 1963-06-27,708.99,712.93,702.42,706.03,4540000,706.03 1963-06-26,716.32,716.49,706.46,708.99,4500000,708.99 1963-06-25,718.42,722.07,713.83,716.32,4120000,716.32 1963-06-24,720.78,723.87,715.64,718.42,3700000,718.42 1963-06-21,718.85,724.81,716.06,720.78,4190000,720.78 1963-06-20,719.84,722.76,711.95,718.85,4970000,718.85 1963-06-19,718.90,723.27,715.98,719.84,3970000,719.84 1963-06-18,718.21,722.50,714.99,718.90,3910000,718.90 1963-06-17,722.03,723.61,716.11,718.21,3510000,718.21 1963-06-14,721.43,725.72,718.34,722.03,3840000,722.03 1963-06-13,723.36,727.09,719.92,721.43,4690000,721.43 1963-06-12,718.38,727.60,717.05,723.36,5210000,723.36 1963-06-11,716.49,721.94,714.00,718.38,4390000,718.38 1963-06-10,722.41,722.88,711.65,716.49,4690000,716.49 1963-06-07,726.87,730.31,719.41,722.41,5110000,722.41 1963-06-06,725.93,730.78,721.81,726.87,4990000,726.87 1963-06-05,726.49,732.97,722.46,725.93,5860000,725.93 1963-06-04,726.27,730.01,721.30,726.49,5970000,726.49 1963-06-03,726.96,731.59,723.57,726.27,5400000,726.27 1963-05-31,722.50,730.43,721.85,726.96,4680000,726.96 1963-05-29,717.95,725.59,717.22,722.50,4320000,722.50 1963-05-28,718.25,722.16,714.26,717.95,3860000,717.95 1963-05-27,720.53,721.98,714.52,718.25,3760000,718.25 1963-05-24,721.38,724.56,716.66,720.53,4320000,720.53 1963-05-23,722.84,725.67,718.12,721.38,4400000,721.38 1963-05-22,724.04,728.76,720.18,722.84,5560000,722.84 1963-05-21,720.18,727.26,717.48,724.04,5570000,724.04 1963-05-20,724.81,726.19,716.45,720.18,4710000,720.18 1963-05-17,722.84,727.13,720.01,724.81,4410000,724.81 1963-05-16,724.34,728.63,719.75,722.84,5640000,722.84 1963-05-15,719.84,727.69,717.22,724.34,5650000,724.34 1963-05-14,723.01,724.94,717.95,719.84,4740000,719.84 1963-05-13,723.30,727.13,720.53,723.01,4920000,723.01 1963-05-10,721.97,726.02,718.62,723.30,5260000,723.30 1963-05-09,718.54,726.48,717.20,721.97,5600000,721.97 1963-05-08,712.55,720.96,710.96,718.54,5140000,718.54 1963-05-07,713.77,716.78,708.16,712.55,4140000,712.55 1963-05-06,718.08,721.84,711.68,713.77,4090000,713.77 1963-05-03,721.09,723.77,716.53,718.08,4760000,718.08 1963-05-02,719.67,724.69,717.32,721.09,4480000,721.09 1963-05-01,717.70,723.89,716.40,719.67,5060000,719.67 1963-04-30,715.11,721.46,711.93,717.70,4680000,717.70 1963-04-29,717.16,719.54,712.05,715.11,3980000,715.11 1963-04-26,718.33,721.59,714.77,717.16,4490000,717.16 1963-04-25,717.74,721.92,712.68,718.33,5070000,718.33 1963-04-24,714.98,720.96,713.89,717.74,5910000,717.74 1963-04-23,711.01,717.53,707.83,714.98,5220000,714.98 1963-04-22,711.68,717.07,708.70,711.01,5180000,711.01 1963-04-19,708.16,713.72,705.32,711.68,4660000,711.68 1963-04-18,710.25,713.31,705.44,708.16,4770000,708.16 1963-04-17,710.92,715.23,705.19,710.25,5220000,710.25 1963-04-16,711.38,716.74,706.32,710.92,5570000,710.92 1963-04-15,708.45,716.61,705.94,711.38,5930000,711.38 1963-04-11,704.35,711.34,700.09,708.45,5250000,708.45 1963-04-10,706.03,710.50,698.25,704.35,5880000,704.35 1963-04-09,706.03,709.83,701.05,706.03,5090000,706.03 1963-04-08,702.43,709.46,700.84,706.03,5940000,706.03 1963-04-05,697.12,703.77,693.18,702.43,5240000,702.43 1963-04-04,690.76,699.12,690.76,697.12,5300000,697.12 1963-04-03,684.27,692.81,683.23,690.51,4660000,690.51 1963-04-02,685.86,691.18,682.14,684.27,4360000,684.27 1963-04-01,682.52,689.34,680.55,685.86,3890000,685.86 1963-03-29,682.47,685.74,678.92,682.52,3390000,682.52 1963-03-28,684.73,687.37,680.80,682.47,3890000,682.47 1963-03-27,680.38,686.95,679.17,684.73,4270000,684.73 1963-03-26,678.17,684.23,676.79,680.38,4100000,680.38 1963-03-25,677.83,682.31,674.94,678.17,3700000,678.17 1963-03-22,675.57,680.68,673.19,677.83,3820000,677.83 1963-03-21,677.12,680.01,673.15,675.57,3220000,675.57 1963-03-20,672.06,679.34,671.10,677.12,3690000,677.12 1963-03-19,673.56,675.95,669.17,672.06,3180000,672.06 1963-03-18,676.33,678.92,671.14,673.56,3250000,673.56 1963-03-15,673.73,679.30,671.72,676.33,3400000,676.33 1963-03-14,677.66,680.09,671.97,673.73,3540000,673.73 1963-03-13,675.20,680.93,673.56,677.66,4120000,677.66 1963-03-12,674.02,678.17,671.31,675.20,3350000,675.20 1963-03-11,672.43,677.83,670.01,674.02,3180000,674.02 1963-03-08,671.43,675.57,668.38,672.43,3360000,672.43 1963-03-07,668.08,675.03,667.12,671.43,3350000,671.43 1963-03-06,667.16,669.80,662.02,668.08,3100000,668.08 1963-03-05,667.04,672.85,663.02,667.16,3280000,667.16 1963-03-04,659.72,670.30,659.22,667.04,3650000,667.04 1963-03-01,662.94,667.63,656.66,659.72,3920000,659.72 1963-02-28,670.80,672.64,661.27,662.94,4090000,662.94 1963-02-27,675.28,678.12,669.05,670.80,3680000,670.80 1963-02-26,674.61,679.21,671.31,675.28,3670000,675.28 1963-02-25,681.64,682.06,673.15,674.61,3680000,674.61 1963-02-21,682.06,684.94,675.87,681.64,3980000,681.64 1963-02-20,686.07,686.07,678.79,682.06,4120000,682.06 1963-02-19,688.96,690.51,683.73,686.83,4130000,686.83 1963-02-18,686.07,694.27,685.15,688.96,4700000,688.96 1963-02-15,684.86,689.67,680.89,686.07,4410000,686.07 1963-02-14,681.72,688.71,679.59,684.86,5640000,684.86 1963-02-13,676.62,684.82,674.48,681.72,4960000,681.72 1963-02-12,674.74,678.08,669.84,676.62,3710000,676.62 1963-02-11,679.92,681.85,672.98,674.74,3880000,674.74 1963-02-08,679.09,682.31,673.90,679.92,3890000,679.92 1963-02-07,682.52,686.32,676.49,679.09,4240000,679.09 1963-02-06,681.30,686.74,678.25,682.52,4340000,682.52 1963-02-05,682.01,683.65,672.60,681.30,4050000,681.30 1963-02-04,683.19,687.20,678.92,682.01,3670000,682.01 1963-02-01,682.85,686.57,679.21,683.19,4280000,683.19 1963-01-31,678.58,685.24,675.28,682.85,4270000,682.85 1963-01-30,683.73,684.48,675.82,678.58,3740000,678.58 1963-01-29,682.89,686.91,678.29,683.73,4360000,683.73 1963-01-28,679.71,686.53,678.50,682.89,4720000,682.89 1963-01-25,676.99,683.81,673.31,679.71,4770000,679.71 1963-01-24,677.58,681.09,673.94,676.99,4810000,676.99 1963-01-23,675.53,680.38,674.02,677.58,4820000,677.58 1963-01-22,675.24,679.13,671.81,675.53,4810000,675.53 1963-01-21,672.52,676.74,668.42,675.24,4090000,675.24 1963-01-18,672.98,679.09,669.55,672.52,4760000,672.52 1963-01-17,669.00,676.07,665.07,672.98,5230000,672.98 1963-01-16,675.36,676.03,666.70,669.00,4260000,669.00 1963-01-15,675.74,680.80,672.14,675.36,5930000,675.36 1963-01-14,671.60,678.46,669.38,675.74,5000000,675.74 1963-01-11,669.51,673.61,665.91,671.60,4410000,671.60 1963-01-10,668.00,673.73,666.54,669.51,4520000,669.51 1963-01-09,669.88,674.23,665.95,668.00,5110000,668.00 1963-01-08,662.14,672.18,661.10,669.88,5410000,669.88 1963-01-07,662.23,666.70,657.83,662.14,4440000,662.14 1963-01-04,657.42,665.66,656.25,662.23,5400000,662.23 1963-01-03,646.79,659.17,646.62,657.42,4570000,657.42 1963-01-02,652.10,654.53,643.57,646.79,2540000,646.79 1962-12-31,651.43,654.53,648.05,652.10,5420000,652.10 1962-12-28,650.56,653.90,647.21,651.43,4140000,651.43 1962-12-27,651.64,655.07,648.42,650.56,3670000,650.56 1962-12-26,647.71,654.40,647.33,651.64,3370000,651.64 1962-12-24,646.41,651.48,643.65,647.71,3180000,647.71 1962-12-21,648.55,651.81,643.40,646.41,3470000,646.41 1962-12-20,647.00,652.69,645.20,648.55,4220000,648.55 1962-12-19,640.14,648.63,636.88,647.00,4000000,647.00 1962-12-18,645.49,646.75,638.09,640.14,3620000,640.14 1962-12-17,648.09,650.97,643.03,645.49,3590000,645.49 1962-12-14,645.20,650.35,641.02,648.09,3280000,648.09 1962-12-13,647.33,651.94,641.73,645.20,3380000,645.20 1962-12-12,645.16,653.02,643.49,647.33,3760000,647.33 1962-12-11,645.08,648.46,638.88,645.16,3700000,645.16 1962-12-10,652.10,655.07,642.73,645.08,4270000,645.08 1962-12-07,651.73,655.83,646.87,652.10,3900000,652.10 1962-12-06,653.99,657.00,646.92,651.73,4600000,651.73 1962-12-05,651.48,658.78,649.68,653.99,6280000,653.99 1962-12-04,646.41,654.61,644.07,651.48,5210000,651.48 1962-12-03,649.30,651.22,642.06,646.41,3810000,646.41 1962-11-30,652.61,655.03,645.70,649.30,4570000,649.30 1962-11-29,651.85,655.95,646.54,652.61,5810000,652.61 1962-11-28,648.05,654.86,646.50,651.85,5980000,651.85 1962-11-27,642.06,650.39,639.72,648.05,5500000,648.05 1962-11-26,644.87,651.27,638.34,642.06,5650000,642.06 1962-11-23,637.25,649.26,635.50,644.87,5660000,644.87 1962-11-21,632.94,640.36,630.18,637.25,5100000,637.25 1962-11-20,626.21,634.91,624.20,632.94,4290000,632.94 1962-11-19,630.98,633.36,624.03,626.21,3410000,626.21 1962-11-16,629.14,633.82,623.87,630.98,4000000,630.98 1962-11-15,630.48,636.25,626.67,629.14,5050000,629.14 1962-11-14,623.11,632.99,619.77,630.48,5090000,630.48 1962-11-13,624.41,628.47,618.85,623.11,4550000,623.11 1962-11-12,617.38,627.25,617.38,624.41,5090000,624.41 1962-11-09,609.14,617.51,605.33,616.13,4340000,616.13 1962-11-08,615.75,619.68,606.84,609.14,4160000,609.14 1962-11-07,610.48,620.06,605.58,615.75,4580000,615.75 1962-11-05,604.58,614.45,602.66,610.48,4320000,610.48 1962-11-02,597.13,609.43,592.87,604.58,5470000,604.58 1962-11-01,589.77,599.60,582.66,597.13,3400000,597.13 1962-10-31,588.98,594.79,586.13,589.77,3090000,589.77 1962-10-30,579.35,591.49,578.94,588.98,3830000,588.98 1962-10-29,576.13,586.59,576.13,579.35,4280000,579.35 1962-10-26,570.86,573.54,564.88,569.02,2580000,569.02 1962-10-25,575.84,575.84,562.79,570.86,3950000,570.86 1962-10-24,558.06,578.52,549.65,576.68,6720000,576.68 1962-10-23,568.60,573.96,556.18,558.06,6110000,558.06 1962-10-22,573.29,573.41,563.16,568.60,5690000,568.60 1962-10-19,581.15,582.78,570.44,573.29,4650000,573.29 1962-10-18,587.68,588.01,579.44,581.15,3280000,581.15 1962-10-17,589.35,590.52,581.91,587.68,3240000,587.68 1962-10-16,589.69,594.12,587.01,589.35,2860000,589.35 1962-10-15,586.47,592.28,584.08,589.69,2640000,589.69 1962-10-12,586.47,589.02,582.83,586.47,2020000,586.47 1962-10-11,588.14,590.69,584.08,586.47,2460000,586.47 1962-10-10,587.18,594.00,586.26,588.14,3040000,588.14 1962-10-09,586.09,589.35,582.70,587.18,2340000,587.18 1962-10-08,586.59,589.90,583.24,586.09,1950000,586.09 1962-10-05,582.41,588.47,581.11,586.59,2730000,586.59 1962-10-04,578.52,583.37,575.38,582.41,2530000,582.41 1962-10-03,578.73,584.37,576.09,578.52,2610000,578.52 1962-10-02,571.95,582.66,570.78,578.73,3000000,578.73 1962-10-01,578.98,579.90,569.23,571.95,3090000,571.95 1962-09-28,574.12,582.70,573.20,578.98,2850000,578.98 1962-09-27,578.48,581.99,572.16,574.12,3540000,574.12 1962-09-26,588.22,591.28,576.30,578.48,3550000,578.48 1962-09-25,582.91,590.52,578.73,588.22,3620000,588.22 1962-09-24,589.06,589.06,578.73,582.91,5000000,582.91 1962-09-21,601.32,601.32,589.52,591.78,4280000,591.78 1962-09-20,607.09,608.93,600.31,601.65,3350000,601.65 1962-09-19,607.09,609.89,603.66,607.09,2950000,607.09 1962-09-18,607.63,612.44,604.83,607.09,3690000,607.09 1962-09-17,605.84,611.57,603.45,607.63,3330000,607.63 1962-09-14,603.99,607.93,601.28,605.84,2880000,605.84 1962-09-13,606.34,609.77,601.94,603.99,3100000,603.99 1962-09-12,603.99,608.97,601.28,606.34,3100000,606.34 1962-09-11,602.03,607.88,599.23,603.99,3040000,603.99 1962-09-10,600.86,603.66,595.38,602.03,2520000,602.03 1962-09-07,600.81,606.34,598.26,600.86,2890000,600.86 1962-09-06,599.14,603.32,594.08,600.81,3180000,600.81 1962-09-05,602.45,604.96,596.42,599.14,3050000,599.14 1962-09-04,609.18,612.44,601.28,602.45,2970000,602.45 1962-08-31,602.32,610.19,600.27,609.18,2830000,609.18 1962-08-30,603.24,606.80,599.85,602.32,2260000,602.32 1962-08-29,605.25,606.42,598.81,603.24,2900000,603.24 1962-08-28,612.57,613.11,602.95,605.25,3180000,605.25 1962-08-27,613.74,616.84,609.27,612.57,3140000,612.57 1962-08-24,616.00,617.67,608.81,613.74,2890000,613.74 1962-08-23,615.54,622.02,612.32,616.00,4770000,616.00 1962-08-22,608.64,617.63,606.42,615.54,4520000,615.54 1962-08-21,612.86,614.66,605.79,608.64,3730000,608.64 1962-08-20,610.02,615.67,608.09,612.86,4580000,612.86 1962-08-17,606.71,611.98,604.62,610.02,3430000,610.02 1962-08-16,606.76,611.15,602.74,606.71,4180000,606.71 1962-08-15,601.94,610.90,601.94,606.76,4880000,606.76 1962-08-14,595.29,603.91,593.03,601.90,3640000,601.90 1962-08-13,592.32,597.51,590.65,595.29,2670000,595.29 1962-08-10,591.19,595.67,587.55,592.32,2470000,592.32 1962-08-09,590.94,595.17,588.43,591.19,2670000,591.19 1962-08-08,588.35,592.11,582.12,590.94,3080000,590.94 1962-08-07,593.24,593.66,585.71,588.35,2970000,588.35 1962-08-06,596.38,598.56,590.27,593.24,3110000,593.24 1962-08-03,593.83,598.35,591.11,596.38,5990000,596.38 1962-08-02,591.36,596.55,588.26,593.83,3410000,593.83 1962-08-01,597.64,597.64,588.68,591.36,3100000,591.36 1962-07-31,591.78,601.15,591.78,597.93,4190000,597.93 1962-07-30,585.00,593.03,583.87,591.44,3200000,591.44 1962-07-27,579.61,586.80,577.14,585.00,2890000,585.00 1962-07-26,574.67,582.87,574.08,579.61,2790000,579.61 1962-07-25,574.12,576.55,568.10,574.67,2910000,574.67 1962-07-24,577.47,579.31,572.03,574.12,2560000,574.12 1962-07-23,577.18,582.24,574.50,577.47,2770000,577.47 1962-07-20,573.16,579.86,570.78,577.18,2610000,577.18 1962-07-19,571.24,578.68,568.98,573.16,3090000,573.16 1962-07-18,577.39,577.39,568.02,571.24,3620000,571.24 1962-07-17,588.10,588.77,576.59,577.85,3500000,577.85 1962-07-16,590.19,591.23,582.41,588.10,3130000,588.10 1962-07-13,590.27,592.99,583.87,590.19,3380000,590.19 1962-07-12,589.06,596.59,586.68,590.27,5370000,590.27 1962-07-11,586.01,590.94,580.36,589.06,4250000,589.06 1962-07-10,583.50,599.02,583.50,586.01,7120000,586.01 1962-07-09,576.17,582.28,569.65,580.82,2950000,580.82 1962-07-06,582.58,582.58,571.28,576.17,3110000,576.17 1962-07-05,579.48,586.30,577.39,583.87,3350000,583.87 1962-07-03,573.75,582.99,570.53,579.48,3920000,579.48 1962-07-02,561.28,576.63,557.31,573.75,3450000,573.75 1962-06-29,557.35,569.06,555.22,561.28,4720000,561.28 1962-06-28,541.49,559.32,541.49,557.35,5440000,557.35 1962-06-27,535.76,539.28,528.73,536.98,3890000,536.98 1962-06-26,536.77,548.61,533.46,535.76,4630000,535.76 1962-06-25,539.19,541.24,524.55,536.77,7090000,536.77 1962-06-22,550.49,551.99,537.56,539.19,5640000,539.19 1962-06-21,561.87,561.87,549.15,550.49,4560000,550.49 1962-06-20,571.61,574.59,561.28,563.08,3360000,563.08 1962-06-19,574.21,575.21,566.59,571.61,2680000,571.61 1962-06-18,578.18,583.08,567.05,574.21,4580000,574.21 1962-06-15,563.00,579.90,556.09,578.18,7130000,578.18 1962-06-14,574.04,579.14,560.28,563.00,6240000,563.00 1962-06-13,580.94,586.42,572.20,574.04,5850000,574.04 1962-06-12,593.83,593.83,580.11,580.94,4690000,580.94 1962-06-11,601.61,603.20,592.66,595.17,2870000,595.17 1962-06-08,602.20,607.30,598.64,601.61,2560000,601.61 1962-06-07,603.91,608.14,599.27,602.20,2760000,602.20 1962-06-06,595.50,611.82,595.50,603.91,4190000,603.91 1962-06-05,593.68,603.37,584.12,594.96,6140000,594.96 1962-06-04,608.82,608.82,591.37,593.68,5380000,593.68 1962-06-01,613.36,616.54,603.58,611.05,5760000,611.05 1962-05-31,605.73,625.00,605.73,613.36,10710000,613.36 1962-05-29,576.93,613.11,553.75,603.96,14750000,603.96 1962-05-28,609.77,609.77,573.55,576.93,9350000,576.93 1962-05-25,622.56,625.94,606.18,611.88,6380000,611.88 1962-05-24,626.52,634.24,619.84,622.56,5250000,622.56 1962-05-23,636.34,637.83,622.56,626.52,5450000,626.52 1962-05-22,648.59,649.33,634.57,636.34,3640000,636.34 1962-05-21,650.70,652.14,645.09,648.59,2260000,648.59 1962-05-18,649.79,653.63,644.55,650.70,2490000,650.70 1962-05-17,654.04,654.33,644.01,649.79,2950000,649.79 1962-05-16,655.36,660.23,650.12,654.04,3360000,654.04 1962-05-15,647.56,660.64,647.56,655.36,4780000,655.36 1962-05-14,640.63,649.13,626.85,646.20,5990000,646.20 1962-05-11,647.23,653.79,637.45,640.63,4510000,640.63 1962-05-10,654.70,656.06,641.50,647.23,4730000,647.23 1962-05-09,663.90,664.15,652.31,654.70,3670000,654.70 1962-05-08,670.99,672.68,661.38,663.90,3020000,663.90 1962-05-07,671.20,675.74,666.41,670.99,2530000,670.99 1962-05-04,675.49,676.77,666.79,671.20,3010000,671.20 1962-05-03,669.96,679.20,668.93,675.49,3320000,675.49 1962-05-02,671.24,677.35,666.08,669.96,3780000,669.96 1962-05-01,665.33,673.59,655.44,671.24,5100000,671.24 1962-04-30,672.20,678.64,661.48,665.33,4150000,665.33 1962-04-27,678.68,685.84,668.40,672.20,4140000,672.20 1962-04-26,683.69,687.82,676.29,678.68,3650000,678.68 1962-04-25,693.00,694.13,681.55,683.69,3340000,683.69 1962-04-24,694.61,698.42,690.29,693.00,3040000,693.00 1962-04-23,694.25,700.04,690.37,694.61,3240000,694.61 1962-04-19,691.01,696.80,688.63,694.25,3100000,694.25 1962-04-18,688.43,696.03,686.77,691.01,3350000,691.01 1962-04-17,684.06,690.93,681.31,688.43,2940000,688.43 1962-04-16,687.90,690.65,681.18,684.06,3070000,684.06 1962-04-13,685.67,691.86,679.08,687.90,3470000,687.90 1962-04-12,694.37,694.37,683.49,685.67,3320000,685.67 1962-04-11,695.46,703.68,693.40,694.90,3240000,694.90 1962-04-10,692.96,697.85,688.75,695.46,2880000,695.46 1962-04-09,699.63,701.17,691.30,692.96,3020000,692.96 1962-04-06,700.88,705.42,697.73,699.63,2730000,699.63 1962-04-05,696.88,703.35,693.32,700.88,3130000,700.88 1962-04-04,700.60,705.05,695.26,696.88,3290000,696.88 1962-04-03,705.42,707.52,697.61,700.60,3350000,700.60 1962-04-02,706.95,709.74,702.91,705.42,2790000,705.42 1962-03-30,711.28,712.17,703.27,706.95,2950000,706.95 1962-03-29,712.25,716.94,709.58,711.28,2870000,711.28 1962-03-28,707.28,714.64,705.70,712.25,2940000,712.25 1962-03-27,710.67,713.34,704.12,707.28,3090000,707.28 1962-03-26,716.46,717.88,708.69,710.67,3040000,710.67 1962-03-23,716.70,720.18,713.02,716.46,3050000,716.46 1962-03-22,716.62,720.18,713.38,716.70,3130000,716.70 1962-03-21,719.66,722.49,713.59,716.62,3360000,716.62 1962-03-20,720.38,723.17,716.78,719.66,3060000,719.66 1962-03-19,722.27,725.28,717.39,720.38,3220000,720.38 1962-03-16,723.54,727.14,719.29,722.27,3060000,722.27 1962-03-15,720.95,726.65,718.08,723.54,3250000,723.54 1962-03-14,716.58,724.67,715.89,720.95,3670000,720.95 1962-03-13,714.68,719.66,711.56,716.58,3200000,716.58 1962-03-12,714.44,718.44,709.62,714.68,3280000,714.68 1962-03-09,713.75,718.28,710.96,714.44,3340000,714.44 1962-03-08,706.63,715.25,704.57,713.75,3210000,713.75 1962-03-07,708.17,710.63,703.88,706.63,2890000,706.63 1962-03-06,709.99,712.94,704.81,708.17,2870000,708.17 1962-03-05,711.00,714.15,706.02,709.99,3020000,709.99 1962-03-02,711.81,715.61,707.64,711.00,2980000,711.00 1962-03-01,708.05,715.89,706.67,711.81,2960000,711.81 1962-02-28,709.22,713.75,704.93,708.05,3030000,708.05 1962-02-27,706.22,712.98,704.16,709.22,3110000,709.22 1962-02-26,709.54,711.77,702.91,706.22,2910000,706.22 1962-02-23,713.02,713.71,705.09,709.54,3230000,709.54 1962-02-21,717.55,720.14,710.43,713.02,3310000,713.02 1962-02-20,714.36,719.61,711.24,717.55,3300000,717.55 1962-02-19,716.46,720.14,711.28,714.36,3350000,714.36 1962-02-16,717.27,721.39,713.22,716.46,3700000,716.46 1962-02-15,713.67,720.79,711.77,717.27,3470000,717.27 1962-02-14,714.32,716.90,709.14,713.67,3630000,713.67 1962-02-13,714.92,718.72,711.32,714.32,3400000,714.32 1962-02-12,714.27,718.52,711.81,714.92,2620000,714.92 1962-02-09,716.82,718.40,709.34,714.27,3370000,714.27 1962-02-08,715.73,719.86,712.45,716.82,3810000,716.82 1962-02-07,710.39,717.35,708.94,715.73,4140000,715.73 1962-02-06,706.14,713.22,702.06,710.39,3650000,710.39 1962-02-05,706.55,710.84,702.34,706.14,3890000,706.14 1962-02-02,702.54,709.34,699.11,706.55,3950000,706.55 1962-02-01,700.00,707.36,696.07,702.54,4260000,702.54 1962-01-31,694.09,702.75,692.27,700.00,3840000,700.00 1962-01-30,689.92,698.38,687.82,694.09,3520000,694.09 1962-01-29,692.19,695.71,686.89,689.92,3050000,689.92 1962-01-26,696.52,698.13,689.11,692.19,3330000,692.19 1962-01-25,698.17,703.80,694.17,696.52,3560000,696.52 1962-01-24,698.54,701.69,689.52,698.17,3760000,698.17 1962-01-23,701.98,704.40,694.57,698.54,3350000,698.54 1962-01-22,700.72,706.27,698.05,701.98,3810000,701.98 1962-01-19,696.03,703.35,694.29,700.72,3800000,700.72 1962-01-18,697.41,700.12,690.21,696.03,3460000,696.03 1962-01-17,705.29,707.03,694.86,697.41,3780000,697.41 1962-01-16,709.50,711.20,700.97,705.29,3650000,705.29 1962-01-15,711.73,715.00,706.18,709.50,3450000,709.50 1962-01-12,710.67,717.71,707.92,711.73,3730000,711.73 1962-01-11,706.02,713.10,702.26,710.67,3390000,710.67 1962-01-10,707.64,711.81,701.69,706.02,3300000,706.02 1962-01-09,708.98,714.96,703.88,707.64,3600000,707.64 1962-01-08,714.84,715.69,698.42,708.98,4620000,708.98 1962-01-05,722.53,725.60,709.74,714.84,4630000,714.84 1962-01-04,726.01,733.77,718.00,722.53,4450000,722.53 1962-01-03,724.71,729.61,720.22,726.01,3590000,726.01 1962-01-02,731.14,734.38,721.39,724.71,3120000,724.71 1961-12-29,731.51,734.99,726.41,731.14,5370000,731.14 1961-12-28,731.43,738.79,728.88,731.51,4530000,731.51 1961-12-27,723.34,734.54,723.34,731.43,4170000,731.43 1961-12-26,720.87,727.42,717.92,723.09,3180000,723.09 1961-12-22,720.10,725.08,714.60,720.87,3390000,720.87 1961-12-21,722.57,725.64,717.27,720.10,3440000,720.10 1961-12-20,722.41,728.19,718.32,722.57,3640000,722.57 1961-12-19,727.66,727.66,719.25,722.41,3440000,722.41 1961-12-18,729.40,734.91,724.43,727.71,3810000,727.71 1961-12-15,730.94,734.58,725.72,729.40,3710000,729.40 1961-12-14,734.91,737.82,727.34,730.94,4350000,730.94 1961-12-13,734.02,739.88,730.58,734.91,4890000,734.91 1961-12-12,732.56,739.36,728.23,734.02,4680000,734.02 1961-12-11,728.23,736.40,725.84,732.56,4360000,732.56 1961-12-08,726.45,732.92,722.24,728.23,4010000,728.23 1961-12-07,730.09,732.96,723.42,726.45,3900000,726.45 1961-12-06,731.31,735.80,725.04,730.09,4200000,730.09 1961-12-05,731.22,734.91,726.82,731.31,4330000,731.31 1961-12-04,728.80,737.62,725.16,731.22,4560000,731.22 1961-12-01,721.60,731.99,719.74,728.80,4420000,728.80 1961-11-30,727.18,727.50,717.88,721.60,4210000,721.60 1961-11-29,728.07,732.11,722.57,727.18,4550000,727.18 1961-11-28,731.99,735.19,724.23,728.07,4360000,728.07 1961-11-27,732.60,738.38,726.94,731.99,4700000,731.99 1961-11-24,730.42,735.92,726.61,732.60,4020000,732.60 1961-11-22,729.32,734.18,724.95,730.42,4500000,730.42 1961-11-21,730.09,737.58,724.06,729.32,4890000,729.32 1961-11-20,729.53,735.59,725.32,730.09,4190000,730.09 1961-11-17,733.33,736.00,724.83,729.53,3960000,729.53 1961-11-16,734.34,737.54,725.84,733.33,3980000,733.33 1961-11-15,732.56,741.30,730.86,734.34,4660000,734.34 1961-11-14,728.43,736.65,724.35,732.56,4750000,732.56 1961-11-13,724.83,732.48,721.27,728.43,4540000,728.43 1961-11-10,722.28,727.46,718.28,724.83,4180000,724.83 1961-11-09,723.74,726.82,717.75,722.28,4680000,722.28 1961-11-08,714.68,726.73,714.68,723.74,6090000,723.74 1961-11-06,709.26,717.47,707.11,714.60,4340000,714.60 1961-11-03,706.83,712.62,702.62,709.26,4070000,709.26 1961-11-02,703.84,710.35,701.29,706.83,3890000,706.83 1961-11-01,703.92,708.09,700.12,703.84,3210000,703.84 1961-10-31,701.09,706.67,699.35,703.92,3350000,703.92 1961-10-30,698.74,704.57,696.35,701.09,3430000,701.09 1961-10-27,700.68,703.60,694.94,698.74,3200000,698.74 1961-10-26,700.72,704.81,694.82,700.68,3330000,700.68 1961-10-25,697.24,706.47,695.55,700.72,3590000,700.72 1961-10-24,698.98,704.00,693.77,697.24,3430000,697.24 1961-10-23,705.62,708.73,695.55,698.98,3440000,698.98 1961-10-20,704.85,708.77,700.52,705.62,3470000,705.62 1961-10-19,704.20,710.43,700.48,704.85,3850000,704.85 1961-10-18,701.98,708.37,699.63,704.20,3520000,704.20 1961-10-17,703.15,706.18,698.62,701.98,3110000,701.98 1961-10-16,703.31,707.84,699.23,703.15,2840000,703.15 1961-10-13,705.50,708.77,700.12,703.31,3090000,703.31 1961-10-12,705.62,709.54,701.13,705.50,3060000,705.50 1961-10-11,706.67,710.59,701.69,705.62,3670000,705.62 1961-10-10,705.42,709.62,700.56,706.67,3430000,706.67 1961-10-09,708.25,712.05,700.93,705.42,2920000,705.42 1961-10-06,708.49,714.07,704.40,708.25,3470000,708.25 1961-10-05,703.31,711.89,701.13,708.49,3920000,708.49 1961-10-04,698.66,706.75,698.13,703.31,3380000,703.31 1961-10-03,699.83,703.03,693.12,698.66,2680000,698.66 1961-10-02,701.21,704.97,695.63,699.83,2800000,699.83 1961-09-29,700.28,704.93,694.25,701.21,3060000,701.21 1961-09-28,701.13,706.18,696.80,700.28,3000000,700.28 1961-09-27,693.20,703.47,691.58,701.13,3440000,701.13 1961-09-26,691.86,700.44,689.07,693.20,3320000,693.20 1961-09-25,701.57,702.99,688.87,691.86,3700000,691.86 1961-09-22,706.31,707.48,698.70,701.57,3070000,701.57 1961-09-21,707.32,713.22,703.43,706.31,3340000,706.31 1961-09-20,702.54,709.22,699.87,707.32,2700000,707.32 1961-09-19,711.24,712.98,700.52,702.54,3260000,702.54 1961-09-18,716.30,716.94,705.62,711.24,3550000,711.24 1961-09-15,715.00,720.06,710.23,716.30,3130000,716.30 1961-09-14,722.20,723.22,713.14,715.00,2920000,715.00 1961-09-13,722.61,727.66,718.81,722.20,3110000,722.20 1961-09-12,714.36,725.88,713.99,722.61,2950000,722.61 1961-09-11,720.91,721.39,710.47,714.36,2790000,714.36 1961-09-08,726.53,727.30,717.71,720.91,3430000,720.91 1961-09-07,726.01,733.53,723.05,726.53,3900000,726.53 1961-09-06,719.61,728.76,719.61,726.01,3440000,726.01 1961-09-05,721.19,726.01,716.26,718.72,3000000,718.72 1961-09-01,719.94,724.95,716.30,721.19,2710000,721.19 1961-08-31,716.90,723.13,713.75,719.94,2920000,719.94 1961-08-30,714.15,720.06,711.08,716.90,3220000,716.90 1961-08-29,716.01,718.52,709.78,714.15,3160000,714.15 1961-08-28,716.70,722.24,712.33,716.01,3150000,716.01 1961-08-25,714.03,720.10,712.01,716.70,3050000,716.70 1961-08-24,719.41,719.41,709.54,714.03,3090000,714.03 1961-08-23,725.76,726.86,717.27,720.46,3550000,720.46 1961-08-22,724.75,730.17,720.34,725.76,3640000,725.76 1961-08-21,723.54,728.35,719.49,724.75,3880000,724.75 1961-08-18,721.84,727.54,719.25,723.54,4030000,723.54 1961-08-17,718.20,725.80,715.53,721.84,4130000,721.84 1961-08-16,716.18,720.67,712.62,718.20,3430000,718.20 1961-08-15,718.93,722.85,714.15,716.18,3320000,716.18 1961-08-14,722.61,724.02,714.48,718.93,3120000,718.93 1961-08-11,720.49,726.57,717.31,722.61,3260000,722.61 1961-08-10,717.57,722.98,713.46,720.49,3570000,720.49 1961-08-09,720.22,722.31,713.86,717.57,3710000,717.57 1961-08-08,719.58,725.78,715.91,720.22,4050000,720.22 1961-08-07,720.69,723.14,712.95,719.58,3560000,719.58 1961-08-04,715.71,723.57,715.08,720.69,3710000,720.69 1961-08-03,710.46,720.41,709.04,715.71,3650000,715.71 1961-08-02,713.94,719.86,707.93,710.46,4300000,710.46 1961-08-01,705.37,716.03,702.21,713.94,3990000,713.94 1961-07-31,705.13,709.75,700.51,705.37,3170000,705.37 1961-07-28,702.80,709.75,700.00,705.13,3610000,705.13 1961-07-27,694.19,705.96,693.40,702.80,4170000,702.80 1961-07-26,687.63,697.98,687.63,694.19,4070000,694.19 1961-07-25,682.14,688.89,679.66,686.37,3010000,686.37 1961-07-24,682.81,687.16,678.27,682.14,2490000,682.14 1961-07-21,682.97,686.84,679.10,682.81,2360000,682.81 1961-07-20,682.74,686.21,678.31,682.97,2530000,682.97 1961-07-19,679.30,685.22,674.80,682.74,2940000,682.74 1961-07-18,684.59,687.95,677.44,679.30,3010000,679.30 1961-07-17,690.95,693.48,683.49,684.59,2690000,684.59 1961-07-14,685.90,693.68,682.58,690.95,2760000,690.95 1961-07-13,690.79,690.83,683.17,685.90,2670000,685.90 1961-07-12,694.47,696.28,687.28,690.79,3070000,690.79 1961-07-11,693.16,698.18,690.95,694.47,3160000,694.47 1961-07-10,692.73,698.49,689.33,693.16,3180000,693.16 1961-07-07,694.27,697.90,689.61,692.73,3030000,692.73 1961-07-06,692.77,698.97,690.36,694.27,3470000,694.27 1961-07-05,689.81,696.76,688.34,692.77,3270000,692.77 1961-07-03,683.96,691.50,681.91,689.81,2180000,689.81 1961-06-30,681.95,687.16,678.23,683.96,2380000,683.96 1961-06-29,684.59,687.28,679.62,681.95,2560000,681.95 1961-06-28,683.88,690.04,681.20,684.59,2830000,684.59 1961-06-27,681.16,687.16,676.30,683.88,3090000,683.88 1961-06-26,688.66,689.96,679.22,681.16,2690000,681.16 1961-06-23,685.62,692.81,683.64,688.66,2720000,688.66 1961-06-22,686.09,689.96,680.13,685.62,2880000,685.62 1961-06-21,687.87,691.42,683.13,686.09,3210000,686.09 1961-06-20,680.68,691.03,679.50,687.87,3280000,687.87 1961-06-19,685.50,686.53,673.49,680.68,3980000,680.68 1961-06-16,691.27,691.98,681.16,685.50,3380000,685.50 1961-06-15,695.81,699.72,689.69,691.27,3220000,691.27 1961-06-14,694.15,700.47,691.42,695.81,3430000,695.81 1961-06-13,696.76,698.93,690.24,694.15,3030000,694.15 1961-06-12,700.90,702.29,693.20,696.76,3260000,696.76 1961-06-09,701.69,705.88,697.39,700.90,3520000,700.90 1961-06-08,700.86,704.46,695.26,701.69,3810000,701.69 1961-06-07,703.79,708.05,697.70,700.86,3980000,700.86 1961-06-06,703.43,708.88,699.21,703.79,4250000,703.79 1961-06-05,697.70,708.57,695.33,703.43,4150000,703.43 1961-06-02,695.37,700.82,691.54,697.70,3670000,697.70 1961-06-01,696.72,700.86,691.39,695.37,3770000,695.37 1961-05-31,696.28,703.04,692.65,696.72,4320000,696.72 1961-05-26,690.16,699.48,686.13,696.28,3780000,696.28 1961-05-25,696.52,699.13,687.55,690.16,3760000,690.16 1961-05-24,700.59,702.56,689.77,696.52,3970000,696.52 1961-05-23,702.44,707.34,697.31,700.59,3660000,700.59 1961-05-22,705.96,714.69,697.74,702.44,4070000,702.44 1961-05-19,701.14,708.88,698.38,705.96,4200000,705.96 1961-05-18,705.52,709.00,697.70,701.14,4610000,701.14 1961-05-17,697.74,708.49,695.18,705.52,5520000,705.52 1961-05-16,692.37,700.35,690.52,697.74,5110000,697.74 1961-05-15,687.91,696.44,684.47,692.37,4840000,692.37 1961-05-12,686.49,691.54,683.41,687.91,4840000,687.91 1961-05-11,686.61,689.81,682.06,686.49,5170000,686.49 1961-05-10,686.92,690.67,682.93,686.61,5450000,686.61 1961-05-09,689.06,692.73,683.49,686.92,5380000,686.92 1961-05-08,690.67,695.41,685.15,689.06,5170000,689.06 1961-05-05,692.25,697.31,687.59,690.67,4980000,690.67 1961-05-04,688.90,696.16,686.49,692.25,5350000,692.25 1961-05-03,682.34,691.54,682.10,688.90,4940000,688.90 1961-05-02,677.05,685.34,674.68,682.34,4110000,682.34 1961-05-01,678.71,683.17,672.98,677.05,3710000,677.05 1961-04-28,679.54,683.96,673.34,678.71,3710000,678.71 1961-04-27,682.18,686.76,675.78,679.54,4450000,679.54 1961-04-26,683.09,688.98,678.94,682.18,4980000,682.18 1961-04-25,672.66,686.72,672.59,683.09,4670000,683.09 1961-04-24,684.16,684.16,671.64,672.66,4590000,672.66 1961-04-21,684.24,689.41,678.79,685.26,4340000,685.26 1961-04-20,686.21,689.02,679.77,684.24,4810000,684.24 1961-04-19,690.60,690.67,679.58,686.21,4870000,686.21 1961-04-18,696.72,697.43,687.63,690.60,4830000,690.60 1961-04-17,693.72,700.75,689.29,696.72,5860000,696.72 1961-04-14,692.02,698.45,688.07,693.72,5240000,693.72 1961-04-13,690.16,696.12,685.54,692.02,4770000,692.02 1961-04-12,694.11,697.39,686.96,690.16,4870000,690.16 1961-04-11,692.06,700.31,687.87,694.11,5230000,694.11 1961-04-10,684.16,695.77,684.16,692.06,5550000,692.06 1961-04-07,679.34,687.76,676.52,683.68,5100000,683.68 1961-04-06,677.32,682.58,673.39,679.34,4910000,679.34 1961-04-05,678.73,680.98,671.79,677.32,5430000,677.32 1961-04-04,677.59,683.11,673.81,678.73,7080000,678.73 1961-04-03,676.63,684.29,672.98,677.59,6470000,677.59 1961-03-30,676.41,682.01,673.13,676.63,5610000,676.63 1961-03-29,669.58,679.19,667.64,676.41,5330000,676.41 1961-03-28,671.03,674.96,665.73,669.58,4630000,669.58 1961-03-27,672.48,675.30,667.22,671.03,4190000,671.03 1961-03-24,675.45,677.28,668.59,672.48,4390000,672.48 1961-03-23,679.38,680.48,671.79,675.45,2170000,675.45 1961-03-22,678.73,685.32,675.19,679.38,5840000,679.38 1961-03-21,678.84,682.92,672.44,678.73,5800000,678.73 1961-03-20,676.48,684.07,674.12,678.84,5780000,678.84 1961-03-17,670.80,681.63,670.80,676.48,5960000,676.48 1961-03-16,662.88,674.19,660.36,670.38,5610000,670.38 1961-03-15,661.08,665.96,656.36,662.88,4900000,662.88 1961-03-14,664.44,667.11,657.85,661.08,4900000,661.08 1961-03-13,663.56,668.52,659.48,664.44,5080000,664.44 1961-03-10,663.33,667.91,658.57,663.56,5950000,663.56 1961-03-09,666.15,670.08,660.40,663.33,6010000,663.33 1961-03-08,667.14,670.54,660.70,666.15,5910000,666.15 1961-03-07,674.46,674.84,662.76,667.14,5540000,667.14 1961-03-06,671.57,678.23,668.78,674.46,5650000,674.46 1961-03-03,669.39,676.14,666.61,671.57,5530000,671.57 1961-03-02,663.03,671.53,661.01,669.39,5300000,669.39 1961-03-01,662.08,666.27,657.12,663.03,4970000,663.03 1961-02-28,660.44,667.03,657.16,662.08,5830000,662.08 1961-02-27,655.60,662.11,652.59,660.44,5470000,660.44 1961-02-24,654.42,659.56,650.99,655.60,5330000,655.60 1961-02-23,652.40,657.46,648.55,654.42,5620000,654.42 1961-02-21,653.65,657.54,649.00,652.40,5070000,652.40 1961-02-20,651.67,657.27,649.04,653.65,4680000,653.65 1961-02-17,651.86,656.21,647.90,651.67,4640000,651.67 1961-02-16,648.89,656.36,646.64,651.86,5070000,651.86 1961-02-15,642.91,651.94,641.46,648.89,5200000,648.89 1961-02-14,637.04,646.37,635.44,642.91,4490000,642.91 1961-02-13,639.67,640.89,632.81,637.04,3560000,637.04 1961-02-10,645.12,645.99,635.55,639.67,4840000,639.67 1961-02-09,648.85,651.56,641.57,645.12,5590000,645.12 1961-02-08,643.94,651.41,641.04,648.85,4940000,648.85 1961-02-07,645.65,647.48,637.99,643.94,4020000,643.94 1961-02-06,652.97,653.65,642.07,645.65,3890000,645.65 1961-02-03,653.62,657.20,647.37,652.97,5210000,652.97 1961-02-02,649.39,655.56,646.41,653.62,4900000,653.62 1961-02-01,648.20,652.82,643.67,649.39,4380000,649.39 1961-01-31,650.64,655.18,644.24,648.20,4690000,648.20 1961-01-30,643.59,653.96,642.33,650.64,5190000,650.64 1961-01-27,638.87,648.17,636.47,643.59,4510000,643.59 1961-01-26,637.72,641.84,632.66,638.87,4110000,638.87 1961-01-25,638.79,643.10,633.76,637.72,4470000,637.72 1961-01-24,639.82,642.22,634.87,638.79,4280000,638.79 1961-01-23,634.37,642.68,634.07,639.82,4450000,639.82 1961-01-20,632.39,637.76,630.41,634.37,3270000,634.37 1961-01-19,634.10,637.15,628.77,632.39,4740000,632.39 1961-01-18,628.96,636.39,626.48,634.10,4390000,634.10 1961-01-17,633.19,634.26,625.49,628.96,3830000,628.96 1961-01-16,633.65,639.17,629.91,633.19,4510000,633.19 1961-01-13,628.50,636.20,626.48,633.65,4520000,633.65 1961-01-12,627.21,633.23,623.28,628.50,4270000,628.50 1961-01-11,625.72,631.85,622.37,627.21,4370000,627.21 1961-01-10,624.42,630.90,620.96,625.72,4840000,625.72 1961-01-09,621.64,627.93,620.12,624.42,4210000,624.42 1961-01-06,622.67,624.58,615.66,621.64,3620000,621.64 1961-01-05,621.49,628.35,619.24,622.67,4130000,622.67 1961-01-04,610.25,623.36,608.46,621.49,3840000,621.49 1961-01-03,615.89,616.65,606.09,610.25,2770000,610.25 1960-12-30,616.19,620.80,612.76,615.89,5300000,615.89 1960-12-29,615.75,620.37,612.42,616.19,4340000,616.19 1960-12-28,613.38,618.60,610.76,615.75,3620000,615.75 1960-12-27,613.23,617.78,609.65,613.38,3270000,613.38 1960-12-23,613.31,617.52,608.28,613.23,3580000,613.23 1960-12-22,615.42,619.67,610.65,613.31,3820000,613.31 1960-12-21,614.82,621.33,610.42,615.42,4060000,615.42 1960-12-20,615.56,619.82,610.94,614.82,3340000,614.82 1960-12-19,617.78,621.07,612.50,615.56,3630000,615.56 1960-12-16,610.76,620.37,609.06,617.78,3770000,617.78 1960-12-15,612.68,616.42,607.21,610.76,3660000,610.76 1960-12-14,611.72,618.34,608.24,612.68,3880000,612.68 1960-12-13,611.94,615.49,606.80,611.72,3500000,611.72 1960-12-12,610.90,615.31,606.87,611.94,3020000,611.94 1960-12-09,605.17,612.86,601.88,610.90,4460000,610.90 1960-12-08,604.62,608.61,601.14,605.17,3540000,605.17 1960-12-07,597.11,606.84,595.93,604.62,3660000,604.62 1960-12-06,593.49,599.44,591.34,597.11,3360000,597.11 1960-12-05,596.00,597.52,590.79,593.49,3290000,593.49 1960-12-02,594.56,600.14,592.12,596.00,3140000,596.00 1960-12-01,597.22,598.18,589.82,594.56,3090000,594.56 1960-11-30,602.40,602.99,595.15,597.22,3080000,597.22 1960-11-29,605.43,606.98,599.03,602.40,3630000,602.40 1960-11-28,606.47,611.31,602.25,605.43,3860000,605.43 1960-11-25,602.47,608.57,600.18,606.47,3190000,606.47 1960-11-23,601.10,605.10,597.00,602.47,3000000,602.47 1960-11-22,604.54,608.02,598.55,601.10,3430000,601.10 1960-11-21,603.62,607.87,600.44,604.54,3090000,604.54 1960-11-18,602.18,608.02,599.96,603.62,2760000,603.62 1960-11-17,604.77,606.58,598.89,602.18,2450000,602.18 1960-11-16,606.87,611.61,602.29,604.77,3110000,604.77 1960-11-15,604.80,608.83,598.66,606.87,2990000,606.87 1960-11-14,608.61,610.09,600.66,604.80,2660000,604.80 1960-11-11,611.79,611.79,604.43,608.61,2730000,608.61 1960-11-10,602.25,614.09,600.48,612.01,4030000,612.01 1960-11-09,597.63,603.62,587.35,602.25,3450000,602.25 1960-11-07,596.07,604.32,593.52,597.63,3540000,597.63 1960-11-04,590.82,599.40,589.71,596.07,3050000,596.07 1960-11-03,588.23,592.60,584.65,590.82,2580000,590.82 1960-11-02,585.24,592.97,584.35,588.23,2780000,588.23 1960-11-01,580.36,589.42,579.43,585.24,2600000,585.24 1960-10-31,577.92,582.28,573.11,580.36,2460000,580.36 1960-10-28,580.95,582.10,575.18,577.92,2490000,577.92 1960-10-27,575.18,583.80,575.07,580.95,2900000,580.95 1960-10-26,566.60,577.66,566.60,575.18,3020000,575.18 1960-10-25,571.93,575.73,564.23,566.05,3030000,566.05 1960-10-24,577.55,578.18,566.64,571.93,4420000,571.93 1960-10-21,582.69,584.61,575.40,577.55,3090000,577.55 1960-10-20,587.01,589.71,580.62,582.69,2910000,582.69 1960-10-19,588.75,590.64,582.32,587.01,2410000,587.01 1960-10-18,593.34,594.71,585.61,588.75,2220000,588.75 1960-10-17,596.48,600.03,590.45,593.34,2280000,593.34 1960-10-14,591.49,599.51,590.45,596.48,2470000,596.48 1960-10-13,585.83,594.30,584.87,591.49,2220000,591.49 1960-10-12,588.75,590.90,583.72,585.83,1890000,585.83 1960-10-11,587.31,593.01,585.02,588.75,2350000,588.75 1960-10-10,586.42,591.49,583.17,587.31,2030000,587.31 1960-10-07,583.69,590.82,581.28,586.42,2530000,586.42 1960-10-06,579.54,589.20,579.54,583.69,2510000,583.69 1960-10-05,573.15,580.36,569.04,578.88,2650000,578.88 1960-10-04,577.81,578.73,569.74,573.15,2270000,573.15 1960-10-03,580.14,582.98,574.26,577.81,2220000,577.81 1960-09-30,572.22,582.47,572.22,580.14,3370000,580.14 1960-09-29,569.08,575.77,565.49,570.59,2850000,570.59 1960-09-28,574.81,579.40,565.53,569.08,3520000,569.08 1960-09-27,577.14,581.80,570.85,574.81,3170000,574.81 1960-09-26,584.76,584.76,573.29,577.14,3930000,577.14 1960-09-23,592.15,592.64,583.61,585.20,2580000,585.20 1960-09-22,594.26,596.70,588.57,592.15,1970000,592.15 1960-09-21,589.31,597.85,589.31,594.26,2930000,594.26 1960-09-20,586.76,592.08,581.91,588.20,3660000,588.20 1960-09-19,601.18,601.18,585.72,586.76,3790000,586.76 1960-09-16,602.69,606.61,598.22,602.18,2340000,602.18 1960-09-15,605.69,607.24,598.26,602.69,2870000,602.69 1960-09-14,611.79,614.01,604.43,605.69,2530000,605.69 1960-09-13,609.35,614.34,606.47,611.79,2180000,611.79 1960-09-12,614.12,615.05,606.73,609.35,2160000,609.35 1960-09-09,611.42,617.41,609.87,614.12,2750000,614.12 1960-09-08,612.27,615.79,607.39,611.42,2670000,611.42 1960-09-07,620.85,621.85,611.35,612.27,2850000,612.27 1960-09-06,625.22,627.58,618.97,620.85,2580000,620.85 1960-09-02,626.10,629.17,622.07,625.22,2680000,625.22 1960-09-01,625.99,630.95,622.78,626.10,3460000,626.10 1960-08-31,626.40,628.73,620.93,625.99,3130000,625.99 1960-08-30,634.46,636.35,624.44,626.40,2890000,626.40 1960-08-29,636.13,639.31,631.76,634.46,2780000,634.46 1960-08-26,637.16,640.34,632.13,636.13,2780000,636.13 1960-08-25,641.56,643.71,634.24,637.16,2680000,637.16 1960-08-24,638.29,645.30,636.68,641.56,3500000,641.56 1960-08-23,631.25,640.40,631.25,638.29,3560000,638.29 1960-08-22,629.27,634.55,625.53,630.71,2760000,630.71 1960-08-19,625.82,631.42,624.64,629.27,2570000,629.27 1960-08-18,626.54,629.31,622.70,625.82,2890000,625.82 1960-08-17,625.43,628.98,621.62,626.54,3090000,626.54 1960-08-16,624.17,628.98,622.19,625.43,2710000,625.43 1960-08-15,626.18,628.41,621.15,624.17,2450000,624.17 1960-08-12,622.88,630.53,622.34,626.18,3160000,626.18 1960-08-11,617.52,624.85,616.27,622.88,3070000,622.88 1960-08-10,615.69,620.54,612.67,617.52,2810000,617.52 1960-08-09,614.79,619.10,610.95,615.69,2700000,615.69 1960-08-08,614.29,618.57,609.15,614.79,2960000,614.79 1960-08-05,609.23,617.88,606.60,614.29,3000000,614.29 1960-08-04,608.69,611.24,600.28,609.23,2840000,609.23 1960-08-03,613.68,614.94,605.67,608.69,2470000,608.69 1960-08-02,617.85,622.34,610.09,613.68,2090000,613.68 1960-08-01,616.73,622.37,613.36,617.85,2440000,617.85 1960-07-29,605.67,618.35,605.24,616.73,2730000,616.73 1960-07-28,601.76,610.88,599.53,605.67,3020000,605.67 1960-07-27,606.75,611.96,600.35,601.76,2560000,601.76 1960-07-26,601.68,612.78,600.50,606.75,2720000,606.75 1960-07-25,609.87,612.17,597.30,601.68,2840000,601.68 1960-07-22,616.63,617.60,605.45,609.87,2850000,609.87 1960-07-21,624.13,626.76,614.22,616.63,2510000,616.63 1960-07-20,624.78,629.23,620.72,624.13,2370000,624.13 1960-07-19,626.00,629.52,621.22,624.78,2490000,624.78 1960-07-18,630.24,632.93,623.85,626.00,2350000,626.00 1960-07-15,631.32,635.16,627.47,630.24,2140000,630.24 1960-07-14,632.11,637.14,629.34,631.32,2480000,631.32 1960-07-13,634.12,638.18,629.16,632.11,2590000,632.11 1960-07-12,640.44,642.24,631.64,634.12,2860000,634.12 1960-07-11,646.91,649.17,637.60,640.44,2920000,640.44 1960-07-08,644.89,650.10,641.52,646.91,3010000,646.91 1960-07-07,640.37,646.83,638.21,644.89,3050000,644.89 1960-07-06,640.91,645.22,636.45,640.37,2970000,640.37 1960-07-05,641.30,645.11,636.27,640.91,2780000,640.91 1960-07-01,640.62,644.71,636.60,641.30,2620000,641.30 1960-06-30,638.39,644.39,634.91,640.62,2940000,640.62 1960-06-29,637.46,642.78,634.37,638.39,3160000,638.39 1960-06-28,642.49,644.75,634.66,637.46,3120000,637.46 1960-06-27,647.01,650.75,640.33,642.49,2960000,642.49 1960-06-24,647.41,650.32,641.91,647.01,3220000,647.01 1960-06-23,645.36,651.97,642.52,647.41,3620000,647.41 1960-06-22,644.93,649.06,639.22,645.36,3600000,645.36 1960-06-21,647.52,650.89,640.55,644.93,3860000,644.93 1960-06-20,650.89,654.09,642.02,647.52,3970000,647.52 1960-06-17,648.27,655.24,644.79,650.89,3920000,650.89 1960-06-16,649.42,653.95,644.00,648.27,3540000,648.27 1960-06-15,654.88,657.32,647.37,649.42,3630000,649.42 1960-06-14,655.85,660.05,650.71,654.88,3430000,654.88 1960-06-13,654.88,661.45,650.61,655.85,3180000,655.85 1960-06-10,656.42,659.55,650.68,654.88,2940000,654.88 1960-06-09,650.35,663.64,647.41,656.42,3820000,656.42 1960-06-08,645.58,652.83,642.49,650.35,3800000,650.35 1960-06-07,637.85,647.98,637.85,645.58,3710000,645.58 1960-06-06,628.98,639.43,627.19,636.92,3220000,636.92 1960-06-03,627.87,634.33,624.92,628.98,3340000,628.98 1960-06-02,624.89,631.28,620.76,627.87,3730000,627.87 1960-06-01,625.50,629.88,620.61,624.89,3770000,624.89 1960-05-31,624.78,631.28,622.66,625.50,3750000,625.50 1960-05-27,622.79,628.81,620.86,624.78,3040000,624.78 1960-05-26,621.28,626.78,618.20,622.79,3720000,622.79 1960-05-25,621.39,625.66,616.87,621.28,3440000,621.28 1960-05-24,623.66,626.89,617.71,621.39,3240000,621.39 1960-05-23,625.24,629.34,620.34,623.66,2530000,623.66 1960-05-20,624.68,631.44,621.60,625.24,3170000,625.24 1960-05-19,623.00,628.08,618.62,624.68,3700000,624.68 1960-05-18,621.63,630.21,617.71,623.00,5240000,623.00 1960-05-17,617.39,624.92,613.30,621.63,4080000,621.63 1960-05-16,616.03,621.84,611.76,617.39,3530000,617.39 1960-05-13,607.87,618.20,607.31,616.03,3750000,616.03 1960-05-12,606.54,612.70,603.81,607.87,3220000,607.87 1960-05-11,604.82,608.88,601.70,606.54,2900000,606.54 1960-05-10,607.48,610.14,602.86,604.82,2870000,604.82 1960-05-09,607.62,612.74,604.19,607.48,2670000,607.48 1960-05-06,608.32,611.41,603.56,607.62,2560000,607.62 1960-05-05,610.99,613.79,605.80,608.32,2670000,608.32 1960-05-04,607.73,613.47,606.05,610.99,2870000,610.99 1960-05-03,599.61,610.14,598.73,607.73,2910000,607.73 1960-05-02,601.70,605.52,596.61,599.61,2930000,599.61 1960-04-29,604.33,607.85,598.35,601.70,2850000,601.70 1960-04-28,609.96,612.22,599.27,604.33,3190000,604.33 1960-04-27,610.92,616.76,606.89,609.96,3020000,609.96 1960-04-26,611.13,613.76,606.65,610.92,2940000,610.92 1960-04-25,616.32,617.00,607.71,611.13,2980000,611.13 1960-04-22,619.15,622.64,614.47,616.32,2850000,616.32 1960-04-21,618.71,621.92,615.19,619.15,2700000,619.15 1960-04-20,625.68,625.68,615.94,618.71,3150000,618.71 1960-04-19,630.77,634.97,624.86,626.40,3080000,626.40 1960-04-18,630.12,637.16,626.33,630.77,3200000,630.77 1960-04-14,626.50,632.54,624.62,630.12,2730000,630.12 1960-04-13,626.50,630.15,623.39,626.50,2730000,626.50 1960-04-12,624.89,628.62,621.41,626.50,2470000,626.50 1960-04-11,628.10,631.28,622.40,624.89,2520000,624.89 1960-04-08,629.03,632.07,624.14,628.10,2820000,628.10 1960-04-07,628.31,634.08,626.91,629.03,3070000,629.03 1960-04-06,622.64,631.35,622.64,628.31,3450000,628.31 1960-04-05,618.54,624.69,616.56,622.19,2840000,622.19 1960-04-04,615.98,621.68,613.35,618.54,2450000,618.54 1960-04-01,616.59,619.94,612.94,615.98,2260000,615.98 1960-03-31,619.94,622.74,614.75,616.59,2690000,616.59 1960-03-30,620.35,623.56,616.28,619.94,2450000,619.94 1960-03-29,621.78,623.97,617.68,620.35,2320000,620.35 1960-03-28,622.47,625.68,618.81,621.78,2500000,621.78 1960-03-25,624.00,625.95,619.29,622.47,2640000,622.47 1960-03-24,622.06,627.86,621.51,624.00,2940000,624.00 1960-03-23,618.09,624.35,616.25,622.06,3020000,622.06 1960-03-22,617.00,622.09,614.20,618.09,2490000,618.09 1960-03-21,616.42,620.52,613.99,617.00,2500000,617.00 1960-03-18,615.09,620.69,613.52,616.42,2620000,616.42 1960-03-17,616.73,618.61,610.85,615.09,2140000,615.09 1960-03-16,612.18,620.90,611.74,616.73,2960000,616.73 1960-03-15,606.79,614.68,605.52,612.18,2690000,612.18 1960-03-14,605.83,610.17,602.96,606.79,2530000,606.79 1960-03-11,602.31,608.70,599.61,605.83,2770000,605.83 1960-03-10,607.16,609.72,600.40,602.31,3350000,602.31 1960-03-09,599.10,608.29,596.20,607.16,3580000,607.16 1960-03-08,604.02,607.88,596.64,599.10,3370000,599.10 1960-03-07,609.79,614.61,601.59,604.02,2900000,604.02 1960-03-04,612.05,613.55,600.36,609.79,4060000,609.79 1960-03-03,621.37,622.64,610.03,612.05,3160000,612.05 1960-03-02,626.87,628.34,618.95,621.37,3110000,621.37 1960-03-01,630.12,632.65,623.77,626.87,2920000,626.87 1960-02-29,632.00,635.31,627.56,630.12,2990000,630.12 1960-02-26,628.51,636.30,627.76,632.00,3380000,632.00 1960-02-25,623.73,630.22,621.65,628.51,3600000,628.51 1960-02-24,626.19,627.90,620.79,623.73,2740000,623.73 1960-02-23,628.45,633.50,624.04,626.19,2960000,626.19 1960-02-19,622.19,630.26,621.31,628.45,3230000,628.45 1960-02-18,615.29,625.95,615.29,622.19,3800000,622.19 1960-02-17,611.33,615.33,603.34,613.55,4210000,613.55 1960-02-16,617.58,619.29,608.94,611.33,3270000,611.33 1960-02-15,622.23,624.31,615.94,617.58,2780000,617.58 1960-02-12,618.57,623.70,617.38,622.23,2230000,622.23 1960-02-11,623.36,626.09,617.34,618.57,2610000,618.57 1960-02-10,628.45,631.79,620.25,623.36,2440000,623.36 1960-02-09,619.43,630.53,617.72,628.45,2860000,628.45 1960-02-08,626.50,626.50,610.17,619.43,3350000,619.43 1960-02-05,631.14,632.10,623.63,626.77,2530000,626.77 1960-02-04,630.97,634.53,627.11,631.14,2600000,631.14 1960-02-03,636.92,640.30,629.03,630.97,3020000,630.97 1960-02-02,628.04,638.86,628.04,636.92,3080000,636.92 1960-02-01,622.62,630.75,619.68,626.20,2820000,626.20 1960-01-29,629.84,631.51,619.51,622.62,3060000,622.62 1960-01-28,637.67,638.27,627.77,629.84,2630000,629.84 1960-01-27,639.84,643.05,633.89,637.67,2460000,637.67 1960-01-26,639.07,642.81,633.49,639.84,3060000,639.84 1960-01-25,645.85,648.83,637.20,639.07,2790000,639.07 1960-01-22,645.43,650.92,643.33,645.85,2690000,645.85 1960-01-21,643.69,649.51,641.40,645.43,2700000,645.43 1960-01-20,645.07,650.13,641.57,643.69,2720000,643.69 1960-01-19,653.86,654.97,642.58,645.07,3100000,645.07 1960-01-18,659.68,662.06,651.70,653.86,3020000,653.86 1960-01-15,660.53,666.38,656.25,659.68,3400000,659.68 1960-01-14,656.44,663.14,655.13,660.53,3560000,660.53 1960-01-13,660.43,664.68,653.11,656.44,3470000,656.44 1960-01-12,667.16,667.39,655.49,660.43,3760000,660.43 1960-01-11,675.73,676.74,663.67,667.16,3470000,667.16 1960-01-08,677.66,680.86,671.38,675.73,3290000,675.73 1960-01-07,682.62,683.05,674.98,677.66,3310000,677.66 1960-01-06,685.47,687.36,678.34,682.62,3730000,682.62 1960-01-05,679.06,687.14,677.43,685.47,3710000,685.47 1960-01-04,679.36,688.21,677.39,679.06,3990000,679.06 1959-12-31,676.97,682.72,676.32,679.36,3810000,679.36 1959-12-30,672.23,679.49,672.00,676.97,3680000,676.97 1959-12-29,669.77,675.01,667.13,672.23,3020000,672.23 1959-12-28,670.69,674.41,665.96,669.77,2830000,669.77 1959-12-24,670.18,674.69,666.93,670.69,2320000,670.69 1959-12-23,671.82,675.73,667.75,670.18,2890000,670.18 1959-12-22,675.92,677.34,669.90,671.82,2930000,671.82 1959-12-21,676.65,681.54,673.05,675.92,3290000,675.92 1959-12-18,673.90,679.52,671.35,676.65,3230000,676.65 1959-12-17,675.20,678.54,671.54,673.90,3040000,673.90 1959-12-16,673.78,679.20,671.41,675.20,3270000,675.20 1959-12-15,675.07,681.00,671.63,673.78,3450000,673.78 1959-12-14,670.50,678.26,669.02,675.07,3100000,675.07 1959-12-11,672.74,674.72,667.28,670.50,2910000,670.50 1959-12-10,671.26,676.96,668.80,672.74,3170000,672.74 1959-12-09,675.39,678.03,668.76,671.26,3430000,671.26 1959-12-08,665.67,679.36,665.07,675.39,3870000,675.39 1959-12-07,664.00,670.44,661.83,665.67,3620000,665.67 1959-12-04,662.96,668.04,659.87,664.00,3590000,664.00 1959-12-03,661.29,666.05,658.48,662.96,3280000,662.96 1959-12-02,664.38,668.48,658.64,661.29,3490000,661.29 1959-12-01,659.97,668.70,659.97,664.38,3990000,664.38 1959-11-30,652.52,661.23,651.55,659.18,3670000,659.18 1959-11-27,651.10,655.58,647.92,652.52,3030000,652.52 1959-11-25,649.69,655.55,646.69,651.10,3550000,651.10 1959-11-24,646.75,653.66,644.86,649.69,3650000,649.69 1959-11-23,645.46,651.51,641.77,646.75,3400000,646.75 1959-11-20,643.32,649.97,641.42,645.46,2960000,645.46 1959-11-19,641.99,648.36,639.63,643.32,3230000,643.32 1959-11-18,635.62,644.96,634.77,641.99,3660000,641.99 1959-11-17,634.46,639.60,630.99,635.62,3570000,635.62 1959-11-16,641.71,644.48,632.72,634.46,3710000,634.46 1959-11-13,644.26,647.38,640.01,641.71,3050000,641.71 1959-11-12,647.32,650.88,642.78,644.26,3600000,644.26 1959-11-11,648.14,649.94,644.96,647.32,2820000,647.32 1959-11-10,650.92,652.08,644.86,648.14,3020000,648.14 1959-11-09,650.92,658.86,648.27,650.92,3700000,650.92 1959-11-06,647.57,654.38,644.92,650.92,3450000,650.92 1959-11-05,645.74,651.61,641.99,647.57,3170000,647.57 1959-11-04,645.46,651.96,641.01,645.74,3940000,645.74 1959-11-02,646.60,650.85,642.24,645.46,3320000,645.46 1959-10-30,645.11,649.40,641.68,646.60,3560000,646.60 1959-10-29,643.60,648.65,638.78,645.11,3890000,645.11 1959-10-28,642.18,647.04,637.55,643.60,3920000,643.60 1959-10-27,637.61,645.87,636.19,642.18,4160000,642.18 1959-10-26,633.07,641.14,633.07,637.61,3580000,637.61 1959-10-23,625.59,634.42,624.84,633.07,2880000,633.07 1959-10-22,632.69,635.75,624.55,625.59,3060000,625.59 1959-10-21,635.37,637.99,630.64,632.69,2730000,632.69 1959-10-20,639.66,642.18,634.01,635.37,2740000,635.37 1959-10-19,643.22,643.88,634.93,639.66,2470000,639.66 1959-10-16,637.67,646.53,637.67,643.22,2760000,643.22 1959-10-15,634.27,640.51,632.91,637.48,2190000,637.48 1959-10-14,637.83,639.50,632.28,634.27,2320000,634.27 1959-10-13,638.55,642.34,635.46,637.83,2530000,637.83 1959-10-12,636.98,641.27,635.56,638.55,1750000,638.55 1959-10-09,633.04,638.74,631.62,636.98,2540000,636.98 1959-10-08,635.37,637.42,631.24,633.04,2510000,633.04 1959-10-07,636.06,638.46,631.90,635.37,2380000,635.37 1959-10-06,637.01,639.06,631.87,636.06,2330000,636.06 1959-10-05,636.57,640.76,634.58,637.01,2100000,637.01 1959-10-02,633.60,639.22,630.77,636.57,2270000,636.57 1959-10-01,631.68,635.72,625.40,633.60,2660000,633.60 1959-09-30,640.10,640.16,628.94,631.68,2850000,631.68 1959-09-29,636.47,643.60,635.72,640.10,3220000,640.10 1959-09-28,632.59,638.93,629.35,636.47,2640000,636.47 1959-09-25,632.85,637.73,628.18,632.59,3280000,632.59 1959-09-24,625.06,635.28,625.06,632.85,3480000,632.85 1959-09-23,617.21,626.73,617.21,624.02,3010000,624.02 1959-09-22,618.15,624.24,613.30,616.45,3000000,616.45 1959-09-21,625.59,625.59,613.71,618.15,3240000,618.15 1959-09-18,629.00,629.60,621.97,625.78,2530000,625.78 1959-09-17,632.41,636.19,627.64,629.00,2090000,629.00 1959-09-16,630.80,636.16,629.47,632.41,2180000,632.41 1959-09-15,633.79,634.83,624.49,630.80,2830000,630.80 1959-09-14,637.36,641.08,632.31,633.79,2590000,633.79 1959-09-11,633.38,641.33,632.34,637.36,2640000,637.36 1959-09-10,637.67,641.30,630.45,633.38,2520000,633.38 1959-09-09,642.69,644.74,631.43,637.67,3030000,637.67 1959-09-08,651.74,651.74,636.98,642.69,2940000,642.69 1959-09-04,645.90,653.91,645.37,652.18,2300000,652.18 1959-09-03,655.80,655.93,644.51,645.90,2330000,645.90 1959-09-02,655.90,659.87,652.15,655.80,2370000,655.80 1959-09-01,664.41,664.95,652.74,655.90,2430000,655.90 1959-08-31,663.06,667.72,660.25,664.41,2140000,664.41 1959-08-28,663.34,666.71,659.75,663.06,1930000,663.06 1959-08-27,657.60,665.61,657.60,663.34,2550000,663.34 1959-08-26,655.96,660.34,652.84,657.57,2210000,657.57 1959-08-25,653.22,659.56,651.07,655.96,1960000,655.96 1959-08-24,655.39,657.82,650.57,653.22,1860000,653.22 1959-08-21,655.02,658.86,651.89,655.39,2000000,655.39 1959-08-20,647.01,657.29,647.01,655.02,2450000,655.02 1959-08-19,649.31,649.31,639.34,646.53,3050000,646.53 1959-08-18,658.42,659.15,649.50,650.79,2280000,650.79 1959-08-17,658.74,663.02,656.18,658.42,1980000,658.42 1959-08-14,655.43,661.42,654.61,658.74,1990000,658.74 1959-08-13,655.14,658.48,651.99,655.43,2020000,655.43 1959-08-12,658.07,662.46,653.41,655.14,2700000,655.14 1959-08-11,653.79,661.76,651.14,658.07,2980000,658.07 1959-08-10,665.14,665.14,647.93,653.79,4190000,653.79 1959-08-07,671.98,676.11,666.71,668.57,2580000,668.57 1959-08-06,672.33,676.11,669.36,671.98,2610000,671.98 1959-08-05,675.76,675.76,667.82,672.33,2630000,672.33 1959-08-04,678.10,679.71,673.40,676.30,2530000,676.30 1959-08-03,674.88,683.90,673.90,678.10,2410000,678.10 1959-07-31,673.37,677.28,670.50,674.88,2270000,674.88 1959-07-30,673.18,678.67,668.29,673.37,3240000,673.37 1959-07-29,672.04,677.12,668.48,673.18,3460000,673.18 1959-07-28,669.08,675.76,666.62,672.04,3190000,672.04 1959-07-27,663.72,671.92,663.34,669.08,2910000,669.08 1959-07-24,664.63,668.10,661.29,663.72,2720000,663.72 1959-07-23,664.38,668.23,661.26,664.63,3310000,664.63 1959-07-22,661.48,667.69,660.06,664.38,3310000,664.38 1959-07-21,654.54,663.78,652.62,661.48,2950000,661.48 1959-07-20,657.13,659.87,651.83,654.54,2500000,654.54 1959-07-17,658.29,659.81,653.69,657.13,2510000,657.13 1959-07-16,660.57,662.93,655.46,658.29,3170000,658.29 1959-07-15,657.70,663.91,655.90,660.57,3280000,660.57 1959-07-14,657.35,661.13,653.53,657.70,3230000,657.70 1959-07-13,663.56,665.45,655.05,657.35,3360000,657.35 1959-07-10,663.09,667.34,659.24,663.56,3600000,663.56 1959-07-09,663.81,667.12,658.89,663.09,3560000,663.09 1959-07-08,663.21,668.26,658.23,663.81,4010000,663.81 1959-07-07,660.09,665.89,656.31,663.21,3840000,663.21 1959-07-06,654.76,663.31,653.79,660.09,3720000,660.09 1959-07-02,650.88,659.18,650.22,654.76,3610000,654.76 1959-07-01,643.60,654.01,643.60,650.88,3150000,650.88 1959-06-30,643.06,647.29,639.69,643.60,3200000,643.60 1959-06-29,639.25,646.41,638.33,643.06,3000000,643.06 1959-06-26,637.23,643.51,635.02,639.25,3100000,639.25 1959-06-25,634.27,640.23,631.87,637.23,3250000,637.23 1959-06-24,630.73,636.91,628.53,634.27,3180000,634.27 1959-06-23,631.71,635.62,627.61,630.73,2600000,630.73 1959-06-22,629.76,637.42,627.86,631.71,2630000,631.71 1959-06-19,629.41,633.73,625.12,629.76,2260000,629.76 1959-06-18,628.05,633.87,627.20,629.41,3150000,629.41 1959-06-17,621.40,629.82,619.00,628.05,2850000,628.05 1959-06-16,624.59,626.60,618.28,621.40,2440000,621.40 1959-06-15,627.42,629.73,621.02,624.59,2410000,624.59 1959-06-12,627.49,632.03,623.54,627.42,2580000,627.42 1959-06-11,627.17,634.14,624.62,627.49,3120000,627.49 1959-06-10,620.45,630.67,620.45,627.17,3310000,627.17 1959-06-09,621.62,624.81,613.11,617.62,3490000,617.62 1959-06-08,629.98,632.03,620.33,621.62,2970000,621.62 1959-06-05,630.54,633.95,625.97,629.98,2800000,629.98 1959-06-04,637.39,639.78,628.94,630.54,3210000,630.54 1959-06-03,637.45,642.46,634.36,637.39,2910000,637.39 1959-06-02,643.10,643.10,632.85,637.45,3120000,637.45 1959-06-01,643.79,648.65,640.32,643.51,2730000,643.51 1959-05-29,639.58,647.24,637.25,643.79,2790000,643.79 1959-05-28,636.68,643.09,635.59,639.58,2970000,639.58 1959-05-27,632.38,639.22,631.99,636.68,2940000,636.68 1959-05-26,632.35,636.28,629.41,632.38,2910000,632.38 1959-05-25,634.74,639.64,630.59,632.35,3260000,632.35 1959-05-22,631.65,637.37,630.38,634.74,3030000,634.74 1959-05-21,631.87,634.38,626.84,631.65,3230000,631.65 1959-05-20,635.44,636.77,628.99,631.87,3550000,631.87 1959-05-19,633.53,639.19,631.20,635.44,3170000,635.44 1959-05-18,634.53,636.62,629.90,633.53,2970000,633.53 1959-05-15,637.04,640.92,632.44,634.53,3510000,634.53 1959-05-14,633.05,640.10,631.02,637.04,3660000,637.04 1959-05-13,627.66,635.38,625.51,633.05,3540000,633.05 1959-05-12,625.03,630.90,622.97,627.66,3550000,627.66 1959-05-11,621.36,627.66,620.58,625.03,3860000,625.03 1959-05-08,615.73,625.81,615.73,621.36,3930000,621.36 1959-05-07,624.39,624.45,611.68,615.64,4530000,615.64 1959-05-06,625.90,630.84,621.73,624.39,4110000,624.39 1959-05-05,625.06,629.05,622.88,625.90,3360000,625.90 1959-05-04,625.06,629.87,622.18,625.06,3060000,625.06 1959-05-01,623.75,628.11,620.49,625.06,3020000,625.06 1959-04-30,625.87,628.69,620.91,623.75,3510000,623.75 1959-04-29,628.87,629.75,622.60,625.87,3470000,625.87 1959-04-28,629.87,633.95,625.24,628.87,3920000,628.87 1959-04-27,627.39,635.29,624.60,629.87,3850000,629.87 1959-04-24,623.27,630.26,622.60,627.39,3790000,627.39 1959-04-23,625.15,627.39,618.94,623.27,3310000,623.27 1959-04-22,629.23,631.62,622.69,625.15,3430000,625.15 1959-04-21,627.08,632.17,623.42,629.23,3650000,629.23 1959-04-20,624.06,630.69,622.54,627.08,3610000,627.08 1959-04-17,618.34,626.66,618.34,624.06,3870000,624.06 1959-04-16,612.50,620.58,611.41,617.58,3790000,617.58 1959-04-15,609.53,615.07,608.65,612.50,3680000,612.50 1959-04-14,607.76,611.98,605.44,609.53,3320000,609.53 1959-04-13,605.97,610.81,603.47,607.76,3140000,607.76 1959-04-10,605.50,609.52,603.56,605.97,3000000,605.97 1959-04-09,606.44,609.11,602.12,605.50,2830000,605.50 1959-04-08,610.34,612.28,605.15,606.44,3260000,606.44 1959-04-07,611.16,612.66,606.08,610.34,3020000,610.34 1959-04-06,611.93,616.42,608.26,611.16,3510000,611.16 1959-04-03,607.52,614.39,607.52,611.93,3680000,611.93 1959-04-02,602.97,610.25,602.97,607.52,3220000,607.52 1959-04-01,601.71,606.97,599.65,602.94,2980000,602.94 1959-03-31,602.65,605.73,599.21,601.71,2820000,601.71 1959-03-30,606.58,608.64,600.98,602.65,2940000,602.65 1959-03-26,606.47,608.61,601.50,606.58,2900000,606.58 1959-03-25,606.73,611.16,603.82,606.47,3280000,606.47 1959-03-24,605.56,608.67,602.36,606.73,3000000,606.73 1959-03-23,610.37,612.78,603.38,605.56,3700000,605.56 1959-03-20,610.02,614.16,605.85,610.37,3770000,610.37 1959-03-19,610.87,613.92,605.64,610.02,4150000,610.02 1959-03-18,612.69,617.15,609.14,610.87,4530000,610.87 1959-03-17,607.93,615.83,607.93,612.69,4730000,612.69 1959-03-16,614.69,615.80,605.82,607.88,4420000,607.88 1959-03-13,613.75,618.80,610.78,614.69,4880000,614.69 1959-03-12,611.49,616.10,608.55,613.75,4690000,613.75 1959-03-11,611.14,614.34,608.08,611.49,4160000,611.49 1959-03-10,609.96,614.39,605.44,611.14,3920000,611.14 1959-03-09,609.52,615.01,606.14,609.96,3530000,609.96 1959-03-06,611.87,613.16,605.20,609.52,3930000,609.52 1959-03-05,611.84,614.57,608.32,611.87,3930000,611.87 1959-03-04,610.78,615.77,606.20,611.84,4150000,611.84 1959-03-03,605.03,613.04,604.29,610.78,4790000,610.78 1959-03-02,603.50,608.82,600.89,605.03,4210000,605.03 1959-02-27,602.00,606.53,599.77,603.50,4300000,603.50 1959-02-26,601.18,604.44,596.84,602.00,3930000,602.00 1959-02-25,602.91,605.35,597.86,601.18,3780000,601.18 1959-02-24,602.21,607.61,599.57,602.91,4340000,602.91 1959-02-20,595.04,603.91,594.93,602.21,4190000,602.21 1959-02-19,589.58,597.48,589.58,595.04,4160000,595.04 1959-02-18,586.71,590.76,583.62,588.82,3480000,588.82 1959-02-17,587.91,591.58,583.83,586.71,3190000,586.71 1959-02-16,587.97,593.14,584.39,587.91,3480000,587.91 1959-02-13,581.89,589.91,580.01,587.97,3070000,587.97 1959-02-12,584.03,586.73,579.98,581.89,2630000,581.89 1959-02-11,582.65,588.17,581.63,584.03,3000000,584.03 1959-02-10,574.72,583.89,574.72,582.65,2960000,582.65 1959-02-09,581.36,581.36,571.73,574.46,3130000,574.46 1959-02-06,586.12,587.56,580.54,582.33,3010000,582.33 1959-02-05,589.38,591.14,584.06,586.12,3140000,586.12 1959-02-04,592.34,594.16,587.50,589.38,3170000,589.38 1959-02-03,592.23,595.60,589.35,592.34,3220000,592.34 1959-02-02,593.96,597.66,589.14,592.23,3610000,592.23 1959-01-30,590.40,597.60,590.35,593.96,3600000,593.96 1959-01-29,588.53,594.19,585.88,590.40,3470000,590.40 1959-01-28,594.66,596.37,584.71,588.53,4190000,588.53 1959-01-27,592.37,597.31,589.47,594.66,3480000,594.66 1959-01-26,596.07,599.77,591.11,592.37,3980000,592.37 1959-01-23,595.69,598.36,591.40,596.07,3600000,596.07 1959-01-22,597.66,601.74,593.96,595.69,4250000,595.69 1959-01-21,595.69,600.51,593.28,597.66,3940000,597.66 1959-01-20,594.40,598.45,590.99,595.69,3680000,595.69 1959-01-19,595.75,598.57,590.32,594.40,3840000,594.40 1959-01-16,594.81,599.89,590.38,595.75,4300000,595.75 1959-01-15,591.64,598.10,589.88,594.81,4500000,594.81 1959-01-14,590.70,593.28,586.85,591.64,4090000,591.64 1959-01-13,592.64,595.04,587.47,590.70,3790000,590.70 1959-01-12,592.72,597.31,589.61,592.64,4320000,592.64 1959-01-09,588.14,594.84,588.00,592.72,4760000,592.72 1959-01-08,583.15,590.11,580.54,588.14,4030000,588.14 1959-01-07,591.37,592.58,581.07,583.15,4140000,583.15 1959-01-06,590.17,593.52,584.88,591.37,3690000,591.37 1959-01-05,587.59,594.31,585.24,590.17,4210000,590.17 1959-01-02,583.65,590.38,580.80,587.59,3380000,587.59 1958-12-31,581.80,587.44,579.25,583.65,3970000,583.65 1958-12-30,577.31,584.59,577.13,581.80,3900000,581.80 1958-12-29,572.73,580.63,572.73,577.31,3790000,577.31 1958-12-24,566.39,573.64,564.27,572.73,3050000,572.73 1958-12-23,571.23,573.26,564.15,566.39,2870000,566.39 1958-12-22,573.17,574.84,568.12,571.23,3030000,571.23 1958-12-19,572.38,577.90,570.38,573.17,3540000,573.17 1958-12-18,569.38,575.52,568.24,572.38,3900000,572.38 1958-12-17,565.18,573.29,561.51,569.38,3900000,569.38 1958-12-16,563.98,568.29,562.25,565.18,3970000,565.18 1958-12-15,562.27,566.24,559.96,563.98,3340000,563.98 1958-12-12,563.07,565.01,559.43,562.27,3140000,562.27 1958-12-11,564.98,569.50,561.57,563.07,4250000,563.07 1958-12-10,558.13,566.50,558.05,564.98,4340000,564.98 1958-12-09,556.08,561.51,555.58,558.13,3790000,558.13 1958-12-08,556.75,559.54,553.70,556.08,3590000,556.08 1958-12-05,559.10,560.37,554.85,556.75,3360000,556.75 1958-12-04,558.81,563.19,556.40,559.10,3630000,559.10 1958-12-03,558.57,560.95,554.55,558.81,3460000,558.81 1958-12-02,560.07,562.98,555.37,558.57,3320000,558.57 1958-12-01,557.46,563.30,555.52,560.07,3800000,560.07 1958-11-28,550.41,559.04,550.41,557.46,4120000,557.46 1958-11-26,542.40,551.50,542.40,549.15,4090000,549.15 1958-11-25,544.89,546.95,538.43,540.52,3940000,540.52 1958-11-24,554.88,554.88,543.07,544.89,4770000,544.89 1958-11-21,566.24,566.50,558.16,559.57,3950000,559.57 1958-11-20,565.97,569.70,563.21,566.24,4320000,566.24 1958-11-19,564.89,568.68,562.10,565.97,4090000,565.97 1958-11-18,567.44,569.06,560.48,564.89,3820000,564.89 1958-11-17,564.68,572.05,561.54,567.44,4540000,567.44 1958-11-14,560.75,566.91,559.07,564.68,4390000,564.68 1958-11-13,562.39,564.42,557.43,560.75,4200000,560.75 1958-11-12,561.13,565.53,558.19,562.39,4440000,562.39 1958-11-11,557.72,563.60,556.93,561.13,4040000,561.13 1958-11-10,554.26,560.10,552.64,557.72,3730000,557.72 1958-11-07,554.85,558.22,550.85,554.26,3700000,554.26 1958-11-06,550.76,559.43,550.76,554.85,4890000,554.85 1958-11-05,545.16,552.35,543.34,550.68,4080000,550.68 1958-11-03,543.22,547.15,540.28,545.16,3240000,545.16 1958-10-31,543.31,546.27,539.31,543.22,3920000,543.22 1958-10-30,542.72,546.83,540.69,543.31,4360000,543.31 1958-10-29,536.88,544.92,536.85,542.72,4790000,542.72 1958-10-28,535.00,538.26,530.94,536.88,3670000,536.88 1958-10-27,539.52,541.22,533.09,535.00,3980000,535.00 1958-10-24,540.72,543.16,536.43,539.52,3770000,539.52 1958-10-23,542.31,544.07,537.76,540.72,3610000,540.72 1958-10-22,543.72,545.04,538.96,542.31,3500000,542.31 1958-10-21,544.19,546.54,540.28,543.72,4010000,543.72 1958-10-20,546.36,548.36,541.57,544.19,4560000,544.19 1958-10-17,541.07,548.97,541.07,546.36,5360000,546.36 1958-10-16,536.14,541.37,529.42,540.11,4560000,540.11 1958-10-15,541.72,545.68,533.65,536.14,4810000,536.14 1958-10-14,545.95,549.71,540.22,541.72,5110000,541.72 1958-10-13,543.36,549.30,542.95,545.95,4550000,545.95 1958-10-10,539.61,545.74,538.17,543.36,4610000,543.36 1958-10-09,539.31,541.46,535.85,539.61,3670000,539.61 1958-10-08,539.40,542.28,535.97,539.31,3680000,539.31 1958-10-07,536.29,540.96,534.12,539.40,3570000,539.40 1958-10-06,533.73,539.37,533.21,536.29,3570000,536.29 1958-10-03,532.09,536.82,531.53,533.73,3830000,533.73 1958-10-02,530.94,535.14,528.83,532.09,3750000,532.09 1958-10-01,532.09,533.91,527.68,530.94,3780000,530.94 1958-09-30,529.04,535.00,528.68,532.09,4160000,532.09 1958-09-29,526.83,531.74,525.54,529.04,3680000,529.04 1958-09-26,525.83,529.59,523.31,526.83,3420000,526.83 1958-09-25,528.15,530.68,523.34,525.83,4490000,525.83 1958-09-24,525.89,530.18,523.57,528.15,3120000,528.15 1958-09-23,524.01,528.62,520.87,525.89,3950000,525.89 1958-09-22,526.48,528.39,522.19,524.01,3490000,524.01 1958-09-19,522.34,527.74,521.05,526.48,3880000,526.48 1958-09-18,525.89,526.77,520.52,522.34,3460000,522.34 1958-09-17,526.57,529.45,522.43,525.89,3790000,525.89 1958-09-16,523.40,529.09,522.72,526.57,3940000,526.57 1958-09-15,519.43,524.57,517.47,523.40,3040000,523.40 1958-09-12,520.43,523.57,517.06,519.43,3100000,519.43 1958-09-11,516.20,521.72,515.32,520.43,3300000,520.43 1958-09-10,518.64,520.43,514.59,516.20,2820000,516.20 1958-09-09,515.23,521.31,515.23,518.64,3480000,518.64 1958-09-08,512.77,517.47,511.77,515.23,3030000,515.23 1958-09-05,513.44,515.35,510.45,512.77,2520000,512.77 1958-09-04,513.71,516.59,511.07,513.44,3100000,513.44 1958-09-03,511.77,516.03,510.15,513.71,3240000,513.71 1958-09-02,508.63,513.09,508.39,511.77,2930000,511.77 1958-08-29,507.72,510.18,505.60,508.63,2260000,508.63 1958-08-28,510.24,510.24,505.49,507.72,2540000,507.72 1958-08-27,509.63,513.33,508.19,510.39,3250000,510.39 1958-08-26,508.28,510.95,506.72,509.63,2910000,509.63 1958-08-25,508.28,510.62,505.37,508.28,2610000,508.28 1958-08-22,507.10,509.66,505.54,508.28,2660000,508.28 1958-08-21,503.96,508.89,503.05,507.10,2500000,507.10 1958-08-20,503.64,506.51,501.73,503.96,2460000,503.96 1958-08-19,502.67,506.13,501.26,503.64,2250000,503.64 1958-08-18,505.75,505.75,499.82,502.67,2390000,502.67 1958-08-15,510.30,510.36,504.66,506.13,2960000,506.13 1958-08-14,509.22,512.00,507.48,510.30,3370000,510.30 1958-08-13,508.19,511.24,505.31,509.22,2790000,509.22 1958-08-12,512.42,512.47,506.78,508.19,2600000,508.19 1958-08-11,510.13,514.44,508.69,512.42,2870000,512.42 1958-08-08,506.60,513.47,506.60,510.13,3650000,510.13 1958-08-07,503.11,507.84,501.46,506.10,3200000,506.10 1958-08-06,506.95,508.51,500.32,503.11,3440000,503.11 1958-08-05,510.33,511.01,503.49,506.95,4210000,506.95 1958-08-04,505.43,512.27,505.22,510.33,4000000,510.33 1958-08-01,502.99,507.39,501.64,505.43,3380000,505.43 1958-07-31,504.37,508.39,501.49,502.99,4440000,502.99 1958-07-30,501.38,505.10,497.38,504.37,3680000,504.37 1958-07-29,502.81,504.52,498.73,501.38,3310000,501.38 1958-07-28,501.76,504.43,498.67,502.81,3940000,502.81 1958-07-25,497.12,502.64,496.71,501.76,4430000,501.76 1958-07-24,494.06,498.50,492.42,497.12,3740000,497.12 1958-07-23,494.89,497.21,490.86,494.06,3550000,494.06 1958-07-22,493.36,496.74,490.01,494.89,3420000,494.89 1958-07-21,487.10,494.36,487.10,493.36,3440000,493.36 1958-07-18,485.70,489.89,483.43,486.55,3350000,486.55 1958-07-17,481.00,487.60,478.00,485.70,3180000,485.70 1958-07-16,478.88,485.87,478.88,481.00,3240000,481.00 1958-07-15,476.89,479.82,472.07,478.82,3090000,478.82 1958-07-14,482.55,482.55,475.74,476.89,2540000,476.89 1958-07-11,478.97,484.23,478.94,482.85,2400000,482.85 1958-07-10,477.59,480.35,475.01,478.97,2510000,478.97 1958-07-09,480.00,482.79,476.92,477.59,2630000,477.59 1958-07-08,481.85,482.99,478.12,480.00,2430000,480.00 1958-07-07,480.17,483.76,478.88,481.85,2510000,481.85 1958-07-03,480.15,482.26,478.03,480.17,2630000,480.17 1958-07-02,478.82,481.61,476.86,480.15,2370000,480.15 1958-07-01,478.18,480.64,476.83,478.82,2600000,478.82 1958-06-30,475.42,479.59,474.33,478.18,2820000,478.18 1958-06-27,474.01,478.09,473.22,475.42,2800000,475.42 1958-06-26,471.54,475.68,470.07,474.01,2910000,474.01 1958-06-25,470.43,473.39,468.05,471.54,2720000,471.54 1958-06-24,471.66,472.42,467.37,470.43,2560000,470.43 1958-06-23,473.60,474.60,469.46,471.66,2340000,471.66 1958-06-20,471.57,475.36,470.81,473.60,2590000,473.60 1958-06-19,476.65,478.03,470.93,471.57,2690000,471.57 1958-06-18,478.97,479.70,474.21,476.65,2640000,476.65 1958-06-17,476.56,482.11,475.36,478.97,2950000,478.97 1958-06-16,474.77,477.97,473.16,476.56,2870000,476.56 1958-06-13,471.57,476.56,471.57,474.77,3100000,474.77 1958-06-12,467.93,472.98,467.23,471.42,2760000,471.42 1958-06-11,468.19,470.04,465.58,467.93,2570000,467.93 1958-06-10,469.46,470.37,466.32,468.19,2390000,468.19 1958-06-09,469.60,471.60,467.17,469.46,2380000,469.46 1958-06-06,468.55,471.75,467.49,469.60,2680000,469.60 1958-06-05,468.58,469.84,465.38,468.55,2600000,468.55 1958-06-04,468.14,470.69,466.37,468.58,2690000,468.58 1958-06-03,466.11,469.66,465.35,468.14,2780000,468.14 1958-06-02,462.70,468.61,462.70,466.11,2770000,466.11 1958-05-29,460.44,463.85,459.91,462.70,2350000,462.70 1958-05-28,460.68,462.85,458.97,460.44,2260000,460.44 1958-05-27,461.06,462.53,457.92,460.68,2180000,460.68 1958-05-26,461.03,463.47,459.39,461.06,2500000,461.06 1958-05-23,460.24,463.32,459.21,461.03,2570000,461.03 1958-05-22,458.50,463.20,457.10,460.24,2950000,460.24 1958-05-21,459.83,461.62,456.83,458.50,2580000,458.50 1958-05-20,455.98,460.74,455.30,459.83,2500000,459.83 1958-05-19,457.10,458.06,454.16,455.98,1910000,455.98 1958-05-16,457.86,459.47,455.57,457.10,2030000,457.10 1958-05-15,455.45,459.00,453.84,457.86,2470000,457.86 1958-05-14,459.86,460.79,454.57,455.45,3060000,455.45 1958-05-13,460.74,462.03,457.62,459.86,2940000,459.86 1958-05-12,462.56,463.70,459.41,460.74,2780000,460.74 1958-05-09,462.50,465.14,460.44,462.56,2760000,462.56 1958-05-08,462.88,464.35,460.38,462.50,2790000,462.50 1958-05-07,463.67,465.17,461.12,462.88,2770000,462.88 1958-05-06,461.12,465.32,460.09,463.67,3110000,463.67 1958-05-05,459.56,462.38,457.39,461.12,2670000,461.12 1958-05-02,457.01,460.56,455.66,459.56,2290000,459.56 1958-05-01,455.86,460.21,454.95,457.01,2630000,457.01 1958-04-30,451.78,457.39,451.19,455.86,2900000,455.86 1958-04-29,454.42,454.42,449.78,451.78,2190000,451.78 1958-04-28,454.92,458.33,452.66,454.51,2400000,454.51 1958-04-25,453.42,457.10,451.13,454.92,3020000,454.92 1958-04-24,450.11,455.51,449.34,453.42,2870000,453.42 1958-04-23,449.55,451.87,445.88,450.11,2720000,450.11 1958-04-22,450.72,452.34,448.37,449.55,2440000,449.55 1958-04-21,449.31,452.49,448.34,450.72,2550000,450.72 1958-04-18,445.09,450.75,445.03,449.31,2700000,449.31 1958-04-17,444.35,446.14,442.35,445.09,2500000,445.09 1958-04-16,447.58,447.85,442.53,444.35,2240000,444.35 1958-04-15,443.76,448.96,442.62,447.58,2590000,447.58 1958-04-14,441.24,444.88,440.06,443.76,2180000,443.76 1958-04-11,441.06,442.65,438.83,441.24,2060000,441.24 1958-04-10,441.88,442.94,438.77,441.06,2000000,441.06 1958-04-09,442.59,445.20,440.97,441.88,2040000,441.88 1958-04-08,440.09,444.79,439.59,442.59,2190000,442.59 1958-04-07,440.50,441.97,437.25,440.09,2090000,440.09 1958-04-03,441.21,442.97,437.98,440.50,2130000,440.50 1958-04-02,445.47,447.29,440.06,441.21,2390000,441.21 1958-04-01,446.76,447.82,443.29,445.47,2070000,445.47 1958-03-31,448.61,450.05,445.56,446.76,2050000,446.76 1958-03-28,448.64,450.17,446.64,448.61,1930000,448.61 1958-03-27,449.70,451.81,447.02,448.64,2140000,448.64 1958-03-26,450.96,451.46,447.61,449.70,1990000,449.70 1958-03-25,453.75,454.31,449.52,450.96,2210000,450.96 1958-03-24,452.49,455.36,450.25,453.75,2580000,453.75 1958-03-21,449.46,453.57,447.79,452.49,2430000,452.49 1958-03-20,449.96,452.57,447.76,449.46,2280000,449.46 1958-03-19,447.38,452.37,446.91,449.96,2410000,449.96 1958-03-18,448.23,448.84,443.41,447.38,2070000,447.38 1958-03-17,453.04,453.25,447.08,448.23,2130000,448.23 1958-03-14,454.10,454.75,450.52,453.04,2150000,453.04 1958-03-13,454.60,456.80,451.87,454.10,2830000,454.10 1958-03-12,455.92,456.83,452.72,454.60,2420000,454.60 1958-03-11,451.90,457.27,450.58,455.92,2640000,455.92 1958-03-10,451.49,453.45,448.96,451.90,1980000,451.90 1958-03-07,450.96,452.81,448.58,451.49,2130000,451.49 1958-03-06,446.58,452.43,446.05,450.96,2470000,450.96 1958-03-05,445.06,448.14,442.56,446.58,2020000,446.58 1958-03-04,443.38,447.11,443.03,445.06,2010000,445.06 1958-03-03,439.92,444.56,439.24,443.38,1810000,443.38 1958-02-28,437.80,441.15,436.66,439.92,1580000,439.92 1958-02-27,440.42,441.18,436.13,437.80,1670000,437.80 1958-02-26,437.42,442.24,437.42,440.42,1880000,440.42 1958-02-25,437.19,438.13,434.04,436.89,1920000,436.89 1958-02-24,439.62,440.80,436.16,437.19,1570000,437.19 1958-02-21,439.74,441.42,437.33,439.62,1700000,439.62 1958-02-20,443.06,445.53,438.89,439.74,2060000,439.74 1958-02-19,442.71,446.47,441.44,443.06,2070000,443.06 1958-02-18,442.27,444.32,439.89,442.71,1680000,442.71 1958-02-17,444.44,445.47,441.03,442.27,1700000,442.27 1958-02-14,440.24,445.76,439.54,444.44,2070000,444.44 1958-02-13,441.21,445.29,439.27,440.24,1880000,440.24 1958-02-12,442.35,443.29,438.13,441.21,2030000,441.21 1958-02-11,445.94,447.61,440.97,442.35,2110000,442.35 1958-02-10,448.52,448.52,443.68,445.94,1900000,445.94 1958-02-07,453.07,453.07,446.73,448.76,2220000,448.76 1958-02-06,454.89,455.30,450.14,453.13,2210000,453.13 1958-02-05,458.39,458.39,453.34,454.89,2480000,454.89 1958-02-04,453.98,459.77,451.63,458.65,2970000,458.65 1958-02-03,450.02,455.10,449.52,453.98,2490000,453.98 1958-01-31,449.72,451.46,446.70,450.02,2030000,450.02 1958-01-30,451.16,453.63,448.46,449.72,2150000,449.72 1958-01-29,448.67,452.51,447.02,451.16,2220000,451.16 1958-01-28,448.46,450.22,445.41,448.67,2030000,448.67 1958-01-27,450.66,451.40,446.61,448.46,2320000,448.46 1958-01-24,447.93,452.28,446.32,450.66,2830000,450.66 1958-01-23,445.70,449.02,444.18,447.93,1910000,447.93 1958-01-22,446.64,449.58,444.67,445.70,2390000,445.70 1958-01-21,447.29,449.17,445.11,446.64,2160000,446.64 1958-01-20,444.12,449.43,444.00,447.29,2310000,447.29 1958-01-17,445.23,445.67,440.62,444.12,2200000,444.12 1958-01-16,445.20,453.25,444.18,445.23,3950000,445.23 1958-01-15,441.80,446.26,440.36,445.20,2080000,445.20 1958-01-14,439.71,444.88,439.36,441.80,2010000,441.80 1958-01-13,438.68,441.27,434.37,439.71,1860000,439.71 1958-01-10,443.09,443.09,436.83,438.68,2010000,438.68 1958-01-09,446.61,448.40,442.27,443.24,2180000,443.24 1958-01-08,447.79,449.61,443.97,446.61,2230000,446.61 1958-01-07,442.56,448.23,440.18,447.79,2220000,447.79 1958-01-06,444.56,447.87,441.62,442.56,2500000,442.56 1958-01-03,439.27,446.08,438.60,444.56,2440000,444.56 1958-01-02,435.69,441.39,435.45,439.27,1800000,439.27 1957-12-31,432.43,438.54,432.43,435.69,5070000,435.69 1957-12-30,432.90,434.04,428.35,431.78,3750000,431.78 1957-12-27,434.16,437.39,431.52,432.90,2620000,432.90 1957-12-26,429.58,436.13,429.58,434.16,2280000,434.16 1957-12-24,428.08,432.22,426.67,429.11,2220000,429.11 1957-12-23,427.20,430.40,423.86,428.08,2790000,428.08 1957-12-20,431.26,434.13,425.94,427.20,2500000,427.20 1957-12-19,426.18,432.90,424.62,431.26,2740000,431.26 1957-12-18,425.65,431.93,424.15,426.18,2750000,426.18 1957-12-17,433.22,433.22,424.85,425.65,2820000,425.65 1957-12-16,440.30,440.30,432.05,433.40,2350000,433.40 1957-12-13,438.48,443.00,437.27,440.48,2310000,440.48 1957-12-12,439.36,441.94,436.31,438.48,2330000,438.48 1957-12-11,439.24,441.53,435.87,439.36,2240000,439.36 1957-12-10,443.03,443.03,436.34,439.24,2360000,439.24 1957-12-09,447.20,447.49,441.21,443.76,2230000,443.76 1957-12-06,449.55,450.69,445.29,447.20,2350000,447.20 1957-12-05,448.87,451.81,446.52,449.55,2020000,449.55 1957-12-04,446.55,451.55,446.03,448.87,2220000,448.87 1957-12-03,446.91,448.99,444.00,446.55,2060000,446.55 1957-12-02,449.87,452.16,444.18,446.91,2430000,446.91 1957-11-29,446.03,452.49,445.76,449.87,2740000,449.87 1957-11-27,439.51,448.02,439.51,446.03,3330000,446.03 1957-11-26,444.38,448.49,434.43,435.34,3650000,435.34 1957-11-25,442.68,446.11,439.01,444.38,2600000,444.38 1957-11-22,439.80,445.64,437.74,442.68,2850000,442.68 1957-11-21,434.51,443.21,434.51,439.80,2900000,439.80 1957-11-20,431.73,435.22,427.32,433.37,2400000,433.37 1957-11-19,434.96,435.84,427.23,431.73,2240000,431.73 1957-11-18,439.35,439.48,432.49,434.96,2110000,434.96 1957-11-15,434.50,442.82,434.50,439.35,3510000,439.35 1957-11-14,430.07,434.94,426.89,427.94,2450000,427.94 1957-11-13,429.75,432.61,426.51,430.07,2120000,430.07 1957-11-12,434.94,435.96,428.70,429.75,2050000,429.75 1957-11-11,434.12,437.16,432.37,434.94,1540000,434.94 1957-11-08,438.65,438.65,432.11,434.12,2140000,434.12 1957-11-07,435.82,440.49,432.14,438.91,2580000,438.91 1957-11-06,434.04,440.60,434.01,435.82,2550000,435.82 1957-11-04,434.71,435.20,425.46,434.04,2380000,434.04 1957-11-01,438.76,438.76,431.50,434.71,2060000,434.71 1957-10-31,440.28,446.06,439.03,441.04,2170000,441.04 1957-10-30,435.76,441.74,435.38,440.28,2060000,440.28 1957-10-29,432.14,439.61,431.59,435.76,1860000,435.76 1957-10-28,435.00,435.00,429.37,432.14,1800000,432.14 1957-10-25,436.40,436.95,428.90,435.15,2400000,435.15 1957-10-24,437.13,443.38,434.15,436.40,4030000,436.40 1957-10-23,425.46,438.59,425.46,437.13,4600000,437.13 1957-10-22,423.06,426.48,416.15,419.79,5090000,419.79 1957-10-21,433.83,434.36,421.20,423.06,4670000,423.06 1957-10-18,436.87,439.70,432.69,433.83,2670000,433.83 1957-10-17,442.24,442.24,433.86,436.87,3060000,436.87 1957-10-16,447.90,450.09,442.97,443.93,2050000,443.93 1957-10-15,443.78,450.93,443.61,447.90,2620000,447.90 1957-10-14,441.16,446.06,437.74,443.78,2770000,443.78 1957-10-11,441.71,443.58,434.15,441.16,4460000,441.16 1957-10-10,451.31,451.31,439.44,441.71,3300000,441.71 1957-10-09,450.56,456.51,450.12,451.40,2120000,451.40 1957-10-08,452.42,454.87,446.82,450.56,3190000,450.56 1957-10-07,461.70,462.14,451.81,452.42,2490000,452.42 1957-10-04,465.82,466.02,460.71,461.70,1520000,461.70 1957-10-03,465.03,466.84,461.67,465.82,1590000,465.82 1957-10-02,461.79,468.15,461.79,465.03,1760000,465.03 1957-10-01,456.30,461.91,455.55,460.80,1680000,460.80 1957-09-30,456.89,459.28,454.70,456.30,1520000,456.30 1957-09-27,457.01,462.40,454.20,456.89,1750000,456.89 1957-09-26,456.95,460.60,452.98,457.01,2130000,457.01 1957-09-25,462.87,463.57,452.19,456.95,2770000,456.95 1957-09-24,458.96,466.02,457.30,462.87,2840000,462.87 1957-09-23,465.97,465.97,457.15,458.96,3160000,458.96 1957-09-20,474.55,474.55,466.75,468.42,2340000,468.42 1957-09-19,478.60,479.59,475.01,476.12,1520000,476.12 1957-09-18,478.28,481.08,476.88,478.60,1540000,478.60 1957-09-17,478.08,480.44,474.17,478.28,1490000,478.28 1957-09-16,481.02,481.05,476.30,478.08,1290000,478.08 1957-09-13,480.56,483.68,478.72,481.02,1620000,481.02 1957-09-12,474.40,482.31,473.99,480.56,2010000,480.56 1957-09-11,470.23,475.30,467.10,474.40,2130000,474.40 1957-09-10,474.28,476.53,468.77,470.23,1870000,470.23 1957-09-09,478.49,478.49,472.77,474.28,1420000,474.28 1957-09-06,479.51,481.87,477.06,478.63,1320000,478.63 1957-09-05,481.64,481.64,476.76,479.51,1420000,479.51 1957-09-04,486.13,486.19,481.35,482.60,1260000,482.60 1957-09-03,484.35,487.59,481.32,486.13,1490000,486.13 1957-08-30,476.71,484.82,476.71,484.35,1600000,484.35 1957-08-29,477.79,478.19,471.98,476.06,1630000,476.06 1957-08-28,477.55,482.75,476.38,477.79,1840000,477.79 1957-08-27,470.84,479.36,470.84,477.55,2250000,477.55 1957-08-26,475.74,476.44,469.03,470.14,2680000,470.14 1957-08-23,481.46,481.73,474.81,475.74,1960000,475.74 1957-08-22,485.14,485.29,479.77,481.46,1500000,481.46 1957-08-21,483.86,488.23,482.10,485.14,1720000,485.14 1957-08-20,478.95,485.49,474.52,483.86,2700000,483.86 1957-08-19,487.68,487.68,478.16,478.95,2040000,478.95 1957-08-16,487.30,490.42,485.37,488.20,1470000,488.20 1957-08-15,485.93,490.28,482.10,487.30,2040000,487.30 1957-08-14,492.14,493.55,484.32,485.93,2040000,485.93 1957-08-13,492.32,495.68,489.96,492.14,1580000,492.14 1957-08-12,496.23,496.23,489.90,492.32,1650000,492.32 1957-08-09,496.87,498.59,493.46,496.78,1570000,496.78 1957-08-08,498.48,500.90,495.03,496.87,1690000,496.87 1957-08-07,494.13,499.59,490.25,498.48,2460000,498.48 1957-08-06,500.72,500.72,493.55,494.13,1910000,494.13 1957-08-05,505.10,505.57,498.62,500.78,1790000,500.78 1957-08-02,506.21,508.66,501.98,505.10,1610000,505.10 1957-08-01,508.52,509.98,504.69,506.21,1660000,506.21 1957-07-31,508.93,512.69,507.26,508.52,1830000,508.52 1957-07-30,508.25,510.44,504.90,508.93,1780000,508.93 1957-07-29,514.59,515.64,507.00,508.25,1990000,508.25 1957-07-26,516.69,517.97,512.89,514.59,1710000,514.59 1957-07-25,515.78,518.26,514.15,516.69,1800000,516.69 1957-07-24,515.61,518.24,512.46,515.78,1730000,515.78 1957-07-23,515.32,517.65,513.33,515.61,1840000,515.61 1957-07-22,515.73,518.24,513.62,515.32,1950000,515.32 1957-07-19,515.64,517.94,512.08,515.73,1930000,515.73 1957-07-18,515.11,519.34,513.33,515.64,2130000,515.64 1957-07-17,517.42,518.64,513.13,515.11,2060000,515.11 1957-07-16,520.16,523.11,516.28,517.42,2510000,517.42 1957-07-15,520.77,522.91,516.60,520.16,2480000,520.16 1957-07-12,517.97,521.94,514.88,520.77,2240000,520.77 1957-07-11,519.81,522.20,515.00,517.97,2830000,517.97 1957-07-10,516.37,521.68,515.11,519.81,2880000,519.81 1957-07-09,518.41,520.22,513.51,516.37,2450000,516.37 1957-07-08,516.89,521.71,515.32,518.41,2840000,518.41 1957-07-05,513.42,518.70,513.42,516.89,2240000,516.89 1957-07-03,507.99,515.23,507.99,513.25,2720000,513.25 1957-07-02,503.29,509.36,502.86,507.55,2450000,507.55 1957-07-01,503.29,506.18,500.75,503.29,1840000,503.29 1957-06-28,503.03,506.53,500.81,503.29,1770000,503.29 1957-06-27,500.78,504.29,498.36,503.03,1800000,503.03 1957-06-26,501.98,504.75,498.24,500.78,1870000,500.78 1957-06-25,497.69,504.69,497.69,501.98,2000000,501.98 1957-06-24,500.00,500.99,492.87,497.08,2040000,497.08 1957-06-21,503.56,504.52,497.81,500.00,1970000,500.00 1957-06-20,505.92,507.87,501.31,503.56,2050000,503.56 1957-06-19,511.32,512.69,505.28,505.92,2220000,505.92 1957-06-18,513.19,515.20,506.68,511.32,2440000,511.32 1957-06-17,511.79,516.81,510.38,513.19,2220000,513.19 1957-06-14,511.58,514.38,508.93,511.79,2090000,511.79 1957-06-13,509.66,514.27,508.23,511.58,2630000,511.58 1957-06-12,509.48,513.36,507.76,509.66,2600000,509.66 1957-06-11,504.93,511.70,504.93,509.48,2850000,509.48 1957-06-10,505.63,507.87,497.78,503.76,2050000,503.76 1957-06-07,504.55,508.14,502.88,505.63,2380000,505.63 1957-06-06,502.07,506.39,501.13,504.55,2300000,504.55 1957-06-05,502.97,504.37,499.38,502.07,1940000,502.07 1957-06-04,503.76,506.68,499.53,502.97,2200000,502.97 1957-06-03,504.93,507.96,500.46,503.76,2050000,503.76 1957-05-31,502.18,507.76,501.57,504.93,2050000,504.93 1957-05-29,498.10,503.56,498.10,502.18,2270000,502.18 1957-05-28,499.21,499.62,494.42,497.72,2070000,497.72 1957-05-27,504.02,505.07,497.89,499.21,2290000,499.21 1957-05-24,504.02,506.94,502.15,504.02,2340000,504.02 1957-05-23,504.43,506.04,500.90,504.02,2110000,504.02 1957-05-22,506.04,506.82,502.36,504.43,2060000,504.43 1957-05-21,505.98,507.90,503.32,506.04,2370000,506.04 1957-05-20,505.60,508.75,503.82,505.98,2300000,505.98 1957-05-17,504.84,508.87,503.58,505.60,2510000,505.60 1957-05-16,501.98,507.06,501.16,504.84,2690000,504.84 1957-05-15,500.46,504.87,498.27,501.98,2590000,501.98 1957-05-14,502.21,504.43,498.16,500.46,2580000,500.46 1957-05-13,498.51,503.93,498.51,502.21,2720000,502.21 1957-05-10,496.76,500.46,495.15,498.30,2430000,498.30 1957-05-09,496.73,499.21,494.80,496.76,2520000,496.76 1957-05-08,494.68,498.13,493.34,496.73,2590000,496.73 1957-05-07,496.32,497.78,492.29,494.68,2300000,494.68 1957-05-06,497.54,500.29,494.86,496.32,2210000,496.32 1957-05-03,498.56,501.34,495.00,497.54,2390000,497.54 1957-05-02,495.76,501.13,494.98,498.56,2860000,498.56 1957-05-01,494.36,498.04,493.05,495.76,2310000,495.76 1957-04-30,493.95,496.49,491.62,494.36,2200000,494.36 1957-04-29,491.50,496.67,490.77,493.95,2290000,493.95 1957-04-26,492.29,493.92,488.41,491.50,2380000,491.50 1957-04-25,493.66,496.03,490.19,492.29,2640000,492.29 1957-04-24,491.88,497.22,489.87,493.66,2990000,493.66 1957-04-23,488.79,494.10,487.12,491.88,2840000,491.88 1957-04-22,488.03,491.59,485.90,488.79,2560000,488.79 1957-04-18,485.02,489.43,483.51,488.03,2480000,488.03 1957-04-17,484.32,487.47,482.22,485.02,2290000,485.02 1957-04-16,485.84,487.15,482.69,484.32,1890000,484.32 1957-04-15,486.72,488.53,483.62,485.84,2010000,485.84 1957-04-12,484.70,488.76,482.78,486.72,2370000,486.72 1957-04-11,485.17,486.86,481.75,484.70,2350000,484.70 1957-04-10,482.66,486.98,482.02,485.17,2920000,485.17 1957-04-09,479.04,484.32,478.40,482.66,2400000,482.66 1957-04-08,477.61,480.44,475.86,479.04,1950000,479.04 1957-04-05,477.43,479.45,475.68,477.61,1830000,477.61 1957-04-04,478.31,479.62,475.45,477.43,1820000,477.43 1957-04-03,477.55,481.08,476.73,478.31,2160000,478.31 1957-04-02,474.98,478.40,473.70,477.55,2300000,477.55 1957-04-01,474.81,476.82,473.09,474.98,1620000,474.98 1957-03-29,475.01,477.32,473.14,474.81,1650000,474.81 1957-03-28,473.12,476.88,472.27,475.01,1930000,475.01 1957-03-27,472.24,475.10,471.01,473.12,1710000,473.12 1957-03-26,471.51,474.02,468.91,472.24,1660000,472.24 1957-03-25,472.94,474.05,469.70,471.51,1590000,471.51 1957-03-22,474.02,475.57,471.04,472.94,1610000,472.94 1957-03-21,473.93,475.98,471.36,474.02,1630000,474.02 1957-03-20,473.93,476.38,472.85,473.93,1830000,473.93 1957-03-19,472.30,475.22,471.01,473.93,1540000,473.93 1957-03-18,474.28,474.66,470.17,472.30,1450000,472.30 1957-03-15,473.93,476.12,471.19,474.28,1600000,474.28 1957-03-14,472.53,475.45,471.39,473.93,1580000,473.93 1957-03-13,470.31,474.37,469.88,472.53,1840000,472.53 1957-03-12,469.50,471.45,466.69,470.31,1600000,470.31 1957-03-11,471.63,472.06,467.37,469.50,1650000,469.50 1957-03-08,474.17,474.40,470.40,471.63,1630000,471.63 1957-03-07,474.87,477.58,472.62,474.17,1830000,474.17 1957-03-06,472.88,475.77,470.43,474.87,1840000,474.87 1957-03-05,471.48,475.13,471.04,472.88,1860000,472.88 1957-03-04,468.91,472.97,468.15,471.48,1890000,471.48 1957-03-01,464.62,469.76,463.66,468.91,1700000,468.91 1957-02-28,466.26,468.50,463.51,464.62,1620000,464.62 1957-02-27,467.72,469.00,463.95,466.26,1620000,466.26 1957-02-26,466.90,470.34,465.76,467.72,1580000,467.72 1957-02-25,466.93,469.00,463.40,466.90,1710000,466.90 1957-02-21,469.00,470.08,465.15,466.93,1680000,466.93 1957-02-20,466.84,471.10,465.99,469.00,1790000,469.00 1957-02-19,467.40,469.23,463.63,466.84,1670000,466.84 1957-02-18,468.07,471.22,465.21,467.40,1800000,467.40 1957-02-15,461.56,468.83,459.37,468.07,2060000,468.07 1957-02-14,462.14,467.04,459.69,461.56,2220000,461.56 1957-02-13,454.87,462.70,454.87,462.14,2380000,462.14 1957-02-12,457.44,459.87,453.07,454.82,2550000,454.82 1957-02-11,465.50,465.50,456.01,457.44,2740000,457.44 1957-02-08,468.71,468.88,463.19,466.29,2120000,466.29 1957-02-07,470.81,473.93,467.42,468.71,1840000,468.71 1957-02-06,469.96,472.02,466.40,470.81,2110000,470.81 1957-02-05,476.18,476.18,466.65,469.96,2610000,469.96 1957-02-04,477.22,479.54,475.49,477.19,1750000,477.19 1957-02-01,479.16,479.76,474.43,477.22,1680000,477.22 1957-01-31,480.53,483.02,478.04,479.16,1920000,479.16 1957-01-30,476.92,481.95,476.42,480.53,1950000,480.53 1957-01-29,474.59,478.31,473.19,476.92,1800000,476.92 1957-01-28,478.34,478.48,473.14,474.59,1700000,474.59 1957-01-25,481.30,481.76,475.19,478.34,2010000,478.34 1957-01-24,479.93,483.57,478.34,481.30,1910000,481.30 1957-01-23,477.49,481.24,475.25,479.93,1920000,479.93 1957-01-22,475.90,480.45,475.71,477.49,1920000,477.49 1957-01-21,477.46,478.29,471.06,475.90,2740000,475.90 1957-01-18,484.01,486.42,476.23,477.46,2400000,477.46 1957-01-17,485.05,486.91,481.08,484.01,2140000,484.01 1957-01-16,484.75,488.28,483.19,485.05,2210000,485.05 1957-01-15,489.29,490.41,482.94,484.75,2370000,484.75 1957-01-14,493.81,494.49,487.65,489.29,2350000,489.29 1957-01-11,495.51,497.78,492.11,493.81,2340000,493.81 1957-01-10,493.21,498.00,492.74,495.51,2470000,495.51 1957-01-09,493.86,496.90,490.77,493.21,2330000,493.21 1957-01-08,495.20,497.20,491.29,493.86,2230000,493.86 1957-01-07,498.22,500.90,491.78,495.20,2500000,495.20 1957-01-04,499.20,502.57,496.24,498.22,2710000,498.22 1957-01-03,496.03,501.56,494.16,499.20,2260000,499.20 1957-01-02,499.47,501.01,492.06,496.03,1960000,496.03 1956-12-31,496.41,501.56,494.96,499.47,3680000,499.47 1956-12-28,496.38,498.68,493.89,496.41,2790000,496.41 1956-12-27,496.74,499.39,494.79,496.38,2420000,496.38 1956-12-26,494.38,500.32,494.00,496.74,2440000,496.74 1956-12-21,490.44,496.22,489.10,494.38,2380000,494.38 1956-12-20,493.81,494.57,489.29,490.44,2060000,490.44 1956-12-19,495.09,497.15,492.19,493.81,1900000,493.81 1956-12-18,493.75,497.70,491.97,495.09,2370000,495.09 1956-12-17,492.08,497.26,490.82,493.75,2500000,493.75 1956-12-14,490.47,493.75,488.69,492.08,2450000,492.08 1956-12-13,487.51,492.77,486.03,490.47,2370000,490.47 1956-12-12,490.36,491.75,486.06,487.51,2180000,487.51 1956-12-11,493.18,494.44,487.68,490.36,2210000,490.36 1956-12-10,494.79,498.95,492.14,493.18,2600000,493.18 1956-12-07,492.74,497.09,491.21,494.79,2400000,494.79 1956-12-06,488.55,495.18,487.32,492.74,2470000,492.74 1956-12-05,481.38,490.71,480.61,488.55,2360000,488.55 1956-12-04,480.61,483.82,479.08,481.38,2180000,481.38 1956-12-03,474.26,482.80,474.26,480.61,2570000,480.61 1956-11-30,467.09,474.59,467.09,472.78,2300000,472.78 1956-11-29,466.10,468.10,460.41,466.62,2440000,466.62 1956-11-28,470.18,472.81,465.20,466.10,2190000,466.10 1956-11-27,470.29,472.18,467.25,470.18,2130000,470.18 1956-11-26,472.56,476.89,468.73,470.29,2230000,470.29 1956-11-23,467.91,473.69,466.73,472.56,1880000,472.56 1956-11-21,470.07,472.37,466.16,467.91,2310000,467.91 1956-11-20,474.56,475.66,468.16,470.07,2240000,470.07 1956-11-19,480.67,481.05,472.54,474.56,2560000,474.56 1956-11-16,480.20,483.51,478.15,480.67,1820000,480.67 1956-11-15,482.36,486.28,479.11,480.20,2210000,480.20 1956-11-14,486.69,487.27,479.96,482.36,2290000,482.36 1956-11-13,487.05,490.71,484.99,486.69,2140000,486.69 1956-11-12,485.35,488.91,483.60,487.05,1600000,487.05 1956-11-09,488.72,490.50,483.57,485.35,1690000,485.35 1956-11-08,491.15,491.32,483.21,488.72,1970000,488.72 1956-11-07,495.37,500.52,490.22,491.15,2650000,491.15 1956-11-05,490.47,497.70,488.72,495.37,2830000,495.37 1956-11-02,487.62,493.40,486.42,490.47,2180000,490.47 1956-11-01,480.23,488.72,480.23,487.62,1890000,487.62 1956-10-31,486.47,486.47,476.83,479.85,2280000,479.85 1956-10-30,486.94,488.58,483.40,486.47,1830000,486.47 1956-10-29,486.06,494.11,484.83,486.94,2420000,486.94 1956-10-26,481.08,487.07,480.91,486.06,1800000,486.06 1956-10-25,482.67,483.30,478.29,481.08,1580000,481.08 1956-10-24,485.05,485.90,481.05,482.67,1640000,482.67 1956-10-23,485.27,487.05,483.19,485.05,1390000,485.05 1956-10-22,486.12,487.98,483.95,485.27,1430000,485.27 1956-10-19,486.31,489.46,484.45,486.12,1720000,486.12 1956-10-18,484.66,487.35,481.57,486.31,1640000,486.31 1956-10-17,487.57,488.83,482.47,484.66,1640000,484.66 1956-10-16,489.40,490.58,485.10,487.57,1580000,487.57 1956-10-15,490.19,493.01,487.76,489.40,1610000,489.40 1956-10-12,488.06,490.93,486.36,490.19,1330000,490.19 1956-10-11,487.32,491.18,485.90,488.06,1760000,488.06 1956-10-10,481.32,487.54,480.37,487.32,1620000,487.32 1956-10-09,483.38,483.68,479.22,481.32,1220000,481.32 1956-10-08,482.39,486.47,481.54,483.38,1450000,483.38 1956-10-05,481.24,483.62,478.86,482.39,1580000,482.39 1956-10-04,482.04,483.98,478.37,481.24,1600000,481.24 1956-10-03,476.97,484.06,476.97,482.04,2180000,482.04 1956-10-02,468.73,477.11,468.73,475.41,2400000,475.41 1956-10-01,475.25,475.38,463.83,468.70,2600000,468.70 1956-09-28,479.76,481.13,474.23,475.25,1720000,475.25 1956-09-27,481.60,485.21,477.85,479.76,1770000,479.76 1956-09-26,481.08,483.46,474.86,481.60,2370000,481.60 1956-09-25,487.70,488.31,479.57,481.08,2100000,481.08 1956-09-24,490.33,492.08,486.53,487.70,1840000,487.70 1956-09-21,488.00,493.86,488.00,490.33,2110000,490.33 1956-09-20,488.72,489.40,482.86,487.13,2150000,487.13 1956-09-19,493.45,494.66,487.68,488.72,2040000,488.72 1956-09-18,498.76,499.12,490.50,493.45,2200000,493.45 1956-09-17,500.32,502.40,496.49,498.76,1940000,498.76 1956-09-14,499.69,503.39,497.94,500.32,2110000,500.32 1956-09-13,499.97,502.92,497.56,499.69,2000000,499.69 1956-09-12,502.16,504.43,498.43,499.97,1930000,499.97 1956-09-11,505.56,505.63,499.26,502.16,1920000,502.16 1956-09-10,506.76,509.79,503.92,505.56,1860000,505.56 1956-09-07,509.49,509.55,504.39,506.76,1690000,506.76 1956-09-06,509.82,512.25,507.74,509.49,1550000,509.49 1956-09-05,507.66,512.68,507.34,509.82,2130000,509.82 1956-09-04,502.04,508.32,501.17,507.66,1790000,507.66 1956-08-31,495.96,503.51,495.96,502.04,1620000,502.04 1956-08-30,499.91,499.91,492.19,495.96,2050000,495.96 1956-08-29,503.05,504.25,498.85,500.90,1530000,500.90 1956-08-28,505.70,507.74,502.26,503.05,1400000,503.05 1956-08-27,507.91,510.28,504.58,505.70,1420000,505.70 1956-08-24,507.06,510.77,505.83,507.91,1530000,507.91 1956-08-23,502.34,508.95,502.23,507.06,1590000,507.06 1956-08-22,505.43,507.72,501.60,502.34,1570000,502.34 1956-08-21,509.25,509.25,500.84,505.43,2440000,505.43 1956-08-20,515.79,516.26,510.12,511.24,1770000,511.24 1956-08-17,517.19,518.52,514.13,515.79,1720000,515.79 1956-08-16,517.70,519.42,514.73,517.19,1790000,517.19 1956-08-15,517.27,521.11,516.01,517.70,2000000,517.70 1956-08-14,514.40,519.23,512.77,517.27,1790000,517.27 1956-08-13,517.38,518.25,512.08,514.40,1730000,514.40 1956-08-10,519.04,519.67,513.15,517.38,2040000,517.38 1956-08-09,518.74,523.24,517.13,519.04,2550000,519.04 1956-08-08,515.88,521.41,515.33,518.74,2480000,518.74 1956-08-07,513.88,518.30,511.67,515.88,2180000,515.88 1956-08-06,518.85,518.85,509.65,513.88,2280000,513.88 1956-08-03,520.95,522.72,517.51,520.27,2210000,520.27 1956-08-02,518.69,523.33,516.83,520.95,2530000,520.95 1956-08-01,517.81,521.50,515.55,518.69,2230000,518.69 1956-07-31,513.42,519.97,512.85,517.81,2520000,517.81 1956-07-30,512.30,515.22,508.59,513.42,2100000,513.42 1956-07-27,515.85,516.50,507.85,512.30,2240000,512.30 1956-07-26,514.13,517.62,513.20,515.85,2060000,515.85 1956-07-25,513.17,516.80,511.67,514.13,2220000,514.13 1956-07-24,513.61,516.78,511.26,513.17,2040000,513.17 1956-07-23,514.57,516.01,511.65,513.61,1970000,513.61 1956-07-20,513.86,516.37,512.36,514.57,2020000,514.57 1956-07-19,513.39,515.96,511.65,513.86,1950000,513.86 1956-07-18,514.43,517.59,511.73,513.39,2530000,513.39 1956-07-17,512.98,516.78,510.91,514.43,2520000,514.43 1956-07-16,511.10,515.19,510.17,512.98,2260000,512.98 1956-07-13,507.44,512.36,506.46,511.10,2020000,511.10 1956-07-12,509.65,511.05,505.26,507.44,2180000,507.44 1956-07-11,508.34,511.92,507.20,509.65,2520000,509.65 1956-07-10,506.52,510.72,504.85,508.34,2450000,508.34 1956-07-09,504.14,509.08,503.24,506.52,2180000,506.52 1956-07-06,500.54,506.24,500.08,504.14,2180000,504.14 1956-07-05,495.74,502.51,494.67,500.54,2240000,500.54 1956-07-03,491.92,496.97,491.02,495.74,1840000,495.74 1956-07-02,492.78,493.65,488.36,491.92,1610000,491.92 1956-06-29,492.50,494.82,489.85,492.78,1780000,492.78 1956-06-28,492.04,494.34,488.91,492.50,1900000,492.50 1956-06-27,489.37,494.16,488.85,492.04,2090000,492.04 1956-06-26,486.43,490.77,484.83,489.37,1730000,489.37 1956-06-25,487.95,489.74,485.34,486.43,1500000,486.43 1956-06-22,488.26,491.46,486.12,487.95,1630000,487.95 1956-06-21,485.06,490.45,485.06,488.26,1820000,488.26 1956-06-20,484.52,487.05,482.70,485.00,1670000,485.00 1956-06-19,483.91,486.38,481.18,484.52,1430000,484.52 1956-06-18,485.91,487.30,482.90,483.91,1440000,483.91 1956-06-15,485.52,487.58,484.15,485.91,1550000,485.91 1956-06-14,487.08,488.02,483.99,485.52,1670000,485.52 1956-06-13,485.49,489.69,484.45,487.08,1760000,487.08 1956-06-12,479.41,486.10,478.70,485.49,1900000,485.49 1956-06-11,476.15,481.22,476.15,479.41,2000000,479.41 1956-06-08,480.83,480.83,467.99,475.29,3630000,475.29 1956-06-07,480.54,485.20,480.14,482.99,1630000,482.99 1956-06-06,483.19,483.36,477.95,480.54,1460000,480.54 1956-06-05,483.22,485.82,481.73,483.19,1650000,483.19 1956-06-04,480.63,484.60,479.48,483.22,1500000,483.22 1956-06-01,478.05,481.52,475.54,480.63,1440000,480.63 1956-05-31,477.68,483.53,476.43,478.05,2020000,478.05 1956-05-29,470.43,478.99,470.43,477.68,2430000,477.68 1956-05-28,472.49,474.16,463.85,468.81,2780000,468.81 1956-05-25,473.51,477.79,469.31,472.49,2570000,472.49 1956-05-24,480.16,481.81,471.71,473.51,2600000,473.51 1956-05-23,484.13,487.60,479.38,480.16,2140000,480.16 1956-05-22,490.08,490.08,481.86,484.13,2290000,484.13 1956-05-21,496.13,496.13,488.93,491.62,1940000,491.62 1956-05-18,496.63,500.65,494.75,496.39,2020000,496.39 1956-05-17,492.69,497.93,492.22,496.63,1970000,496.63 1956-05-16,494.83,497.67,490.97,492.69,2080000,492.69 1956-05-15,497.28,497.86,490.73,494.83,2650000,494.83 1956-05-14,501.25,505.79,496.00,497.28,2440000,497.28 1956-05-11,501.56,503.18,497.57,501.25,2450000,501.25 1956-05-10,508.16,509.44,499.86,501.56,2850000,501.56 1956-05-09,509.13,511.74,506.05,508.16,2550000,508.16 1956-05-08,512.89,513.62,508.03,509.13,2440000,509.13 1956-05-07,516.44,518.50,511.74,512.89,2550000,512.89 1956-05-04,514.03,519.80,513.49,516.44,2860000,516.44 1956-05-03,512.78,516.57,511.43,514.03,2640000,514.03 1956-05-02,513.96,515.08,510.93,512.78,2440000,512.78 1956-05-01,516.12,516.88,511.24,513.96,2500000,513.96 1956-04-30,512.03,518.42,511.19,516.12,2730000,516.12 1956-04-27,507.95,513.98,507.95,512.03,2760000,512.03 1956-04-26,503.86,508.92,503.86,507.12,2630000,507.12 1956-04-25,503.36,505.48,500.99,503.02,2270000,503.02 1956-04-24,507.28,508.95,501.77,503.36,2500000,503.36 1956-04-23,507.20,510.77,506.00,507.28,2440000,507.28 1956-04-20,504.33,508.66,503.91,507.20,2320000,507.20 1956-04-19,506.55,507.95,502.45,504.33,2210000,504.33 1956-04-18,507.95,511.03,504.61,506.55,2470000,506.55 1956-04-17,509.15,511.11,505.81,507.95,2330000,507.95 1956-04-16,509.99,512.83,506.99,509.15,2310000,509.15 1956-04-13,509.15,511.61,506.73,509.99,2450000,509.99 1956-04-12,512.70,515.03,508.27,509.15,2700000,509.15 1956-04-11,510.04,514.61,508.89,512.70,2440000,512.70 1956-04-10,516.72,516.72,508.24,510.04,2590000,510.04 1956-04-09,521.05,524.37,517.40,518.52,2760000,518.52 1956-04-06,516.57,522.12,516.28,521.05,2600000,521.05 1956-04-05,518.65,522.86,514.90,516.57,2950000,516.57 1956-04-04,515.91,519.88,513.54,518.65,2760000,518.65 1956-04-03,515.10,519.85,513.33,515.91,2760000,515.91 1956-04-02,511.79,519.10,510.67,515.10,3120000,515.10 1956-03-29,510.25,515.86,509.36,511.79,3480000,511.79 1956-03-28,508.68,511.61,506.21,510.25,2610000,510.25 1956-03-27,512.39,512.39,507.77,508.68,2540000,508.68 1956-03-26,513.03,515.05,509.81,512.42,2720000,512.42 1956-03-23,510.94,515.15,510.25,513.03,2980000,513.03 1956-03-22,507.92,512.21,505.85,510.94,2650000,510.94 1956-03-21,512.62,513.70,506.33,507.92,2930000,507.92 1956-03-20,509.76,514.69,507.13,512.62,2960000,512.62 1956-03-19,507.60,511.57,506.36,509.76,2570000,509.76 1956-03-16,507.50,509.61,504.67,507.60,3120000,507.60 1956-03-15,504.01,509.19,504.01,507.50,3270000,507.50 1956-03-14,499.36,505.60,499.36,503.88,3140000,503.88 1956-03-13,500.24,502.32,496.45,499.33,2790000,499.33 1956-03-12,497.84,502.03,496.59,500.24,3110000,500.24 1956-03-09,492.63,499.09,492.63,497.84,3430000,497.84 1956-03-08,491.26,493.95,489.82,492.36,2500000,492.36 1956-03-07,491.41,492.75,489.21,491.26,2380000,491.26 1956-03-06,491.68,494.42,489.77,491.41,2770000,491.41 1956-03-05,488.84,493.29,488.57,491.68,3090000,491.68 1956-03-02,486.69,491.07,485.88,488.84,2860000,488.84 1956-03-01,483.65,487.98,483.63,486.69,2410000,486.69 1956-02-29,485.71,491.09,482.77,483.65,3900000,483.65 1956-02-28,485.00,487.03,482.48,485.71,2540000,485.71 1956-02-27,485.66,488.06,482.50,485.00,2440000,485.00 1956-02-24,481.55,487.30,481.55,485.66,2890000,485.66 1956-02-23,477.03,482.75,477.03,481.50,2900000,481.50 1956-02-21,476.46,478.20,474.19,476.93,2240000,476.93 1956-02-20,477.05,480.21,473.28,476.46,2530000,476.46 1956-02-17,469.61,477.91,469.12,477.05,2840000,477.05 1956-02-16,470.64,471.79,467.80,469.61,1750000,469.61 1956-02-15,469.25,476.02,469.25,470.64,3000000,470.64 1956-02-14,467.17,468.24,463.89,465.72,1590000,465.72 1956-02-13,467.66,469.56,465.60,467.17,1420000,467.17 1956-02-10,467.22,470.25,465.14,467.66,1770000,467.66 1956-02-09,471.23,471.45,465.50,467.22,2080000,467.22 1956-02-08,476.56,478.52,470.08,471.23,2170000,471.23 1956-02-07,478.57,479.18,474.16,476.56,2060000,476.56 1956-02-06,477.44,481.80,475.88,478.57,2230000,478.57 1956-02-03,473.43,479.10,472.26,477.44,2110000,477.44 1956-02-02,473.28,475.51,470.54,473.43,1900000,473.43 1956-02-01,470.74,475.41,470.69,473.28,2010000,473.28 1956-01-31,467.56,471.99,466.78,470.74,1900000,470.74 1956-01-30,466.56,470.10,465.23,467.56,1830000,467.56 1956-01-27,466.82,468.73,463.33,466.56,1950000,466.56 1956-01-26,470.71,471.62,465.38,466.82,1840000,466.82 1956-01-25,467.93,472.57,467.93,470.71,1950000,470.71 1956-01-24,463.91,469.78,463.91,467.88,2160000,467.88 1956-01-23,464.40,465.85,458.21,462.35,2720000,462.35 1956-01-20,468.49,472.11,463.16,464.40,2430000,464.40 1956-01-19,472.89,473.43,466.60,468.49,2500000,468.49 1956-01-18,477.73,479.69,472.40,472.89,2110000,472.89 1956-01-17,476.24,480.55,475.12,477.73,2050000,477.73 1956-01-16,481.50,481.50,475.19,476.24,2260000,476.24 1956-01-13,481.80,484.41,479.96,481.80,2120000,481.80 1956-01-12,478.71,483.70,478.71,481.80,2330000,481.80 1956-01-11,476.12,481.33,475.85,478.42,2310000,478.42 1956-01-10,479.69,479.69,472.65,476.12,2640000,476.12 1956-01-09,485.68,487.91,478.62,479.74,2700000,479.74 1956-01-06,484.02,488.18,483.78,485.68,2570000,485.68 1956-01-05,484.00,487.25,482.31,484.02,2110000,484.02 1956-01-04,485.78,487.79,481.01,484.00,2290000,484.00 1956-01-03,488.40,490.92,484.27,485.78,2390000,485.78 1955-12-30,484.71,490.33,484.71,488.40,2820000,488.40 1955-12-29,484.22,487.18,482.77,484.56,2190000,484.56 1955-12-28,485.81,487.13,483.41,484.22,1990000,484.22 1955-12-27,486.59,488.91,484.00,485.81,2010000,485.81 1955-12-23,486.08,489.31,484.83,486.59,2090000,486.59 1955-12-22,485.49,489.45,484.56,486.08,2650000,486.08 1955-12-21,481.87,487.37,481.87,485.49,2540000,485.49 1955-12-20,481.80,483.87,478.59,481.84,2280000,481.84 1955-12-19,482.08,485.22,480.69,481.80,2380000,481.80 1955-12-16,480.72,484.17,479.87,482.08,2310000,482.08 1955-12-15,480.84,483.38,478.32,480.72,2260000,480.72 1955-12-14,484.29,485.48,479.70,480.84,2670000,480.84 1955-12-13,483.72,487.04,482.41,484.29,2430000,484.29 1955-12-12,487.42,487.42,482.41,483.72,2510000,483.72 1955-12-09,487.80,490.37,486.14,487.64,2660000,487.64 1955-12-08,486.35,489.68,484.83,487.80,2970000,487.80 1955-12-07,486.73,489.11,484.81,486.35,2480000,486.35 1955-12-06,487.16,490.56,485.55,486.73,2540000,486.73 1955-12-05,483.15,488.71,483.15,487.16,2440000,487.16 1955-12-02,481.39,483.88,478.87,482.72,2400000,482.72 1955-12-01,483.26,485.48,480.01,481.39,2370000,481.39 1955-11-30,482.60,485.95,481.53,483.26,2900000,483.26 1955-11-29,480.96,484.03,479.13,482.60,2370000,482.60 1955-11-28,482.88,485.81,479.87,480.96,2460000,480.96 1955-11-25,482.62,485.40,480.98,482.88,2190000,482.88 1955-11-23,481.91,485.97,480.72,482.62,2550000,482.62 1955-11-22,477.30,483.38,477.25,481.91,2270000,481.91 1955-11-21,482.91,483.48,476.42,477.30,1960000,477.30 1955-11-18,485.26,485.74,478.89,482.91,2320000,482.91 1955-11-17,487.38,488.99,484.17,485.26,2310000,485.26 1955-11-16,487.07,490.75,483.60,487.38,2460000,487.38 1955-11-15,484.88,490.35,480.84,487.07,2560000,487.07 1955-11-14,479.20,486.69,479.20,484.88,2760000,484.88 1955-11-11,472.52,478.01,472.21,476.54,2000000,476.54 1955-11-10,473.90,478.70,471.48,472.52,2550000,472.52 1955-11-09,470.58,476.68,469.29,473.90,2580000,473.90 1955-11-07,467.35,472.45,466.73,470.58,2230000,470.58 1955-11-04,461.97,468.70,461.03,467.35,2430000,467.35 1955-11-03,455.99,463.09,455.99,461.97,2260000,461.97 1955-11-02,454.89,456.18,452.12,454.92,1610000,454.92 1955-11-01,454.87,456.84,452.86,454.89,1590000,454.89 1955-10-31,454.85,458.31,453.84,454.87,1800000,454.87 1955-10-28,453.77,456.59,451.21,454.85,1720000,454.85 1955-10-27,455.72,458.97,452.31,453.77,1830000,453.77 1955-10-26,458.40,459.34,454.51,455.72,1660000,455.72 1955-10-25,460.82,463.02,457.48,458.40,1950000,458.40 1955-10-24,458.47,462.38,458.35,460.82,1820000,460.82 1955-10-21,457.66,460.39,455.49,458.47,1710000,458.47 1955-10-20,454.39,460.66,454.39,457.66,2160000,457.66 1955-10-19,448.76,454.44,448.76,453.09,1760000,453.09 1955-10-18,446.13,450.43,444.82,448.58,1550000,448.58 1955-10-17,444.68,450.75,443.68,446.13,1480000,446.13 1955-10-14,444.91,446.90,440.59,444.68,1640000,444.68 1955-10-13,445.58,451.30,443.68,444.91,1980000,444.91 1955-10-12,442.46,448.16,442.46,445.58,1900000,445.58 1955-10-11,441.14,444.04,433.19,438.59,3590000,438.59 1955-10-10,452.97,452.97,440.17,441.14,3100000,441.14 1955-10-07,458.19,458.74,451.05,454.41,2150000,454.41 1955-10-06,461.14,461.79,456.61,458.19,1690000,458.19 1955-10-05,458.85,464.60,458.79,461.14,1920000,461.14 1955-10-04,455.70,461.79,455.35,458.85,2020000,458.85 1955-10-03,465.40,465.40,454.85,455.70,2720000,455.70 1955-09-30,468.68,469.68,464.14,466.62,2140000,466.62 1955-09-29,472.61,474.08,467.37,468.68,2560000,468.68 1955-09-28,467.49,475.13,467.49,472.61,3780000,472.61 1955-09-27,456.22,467.42,456.22,465.93,5500000,465.93 1955-09-26,463.59,463.59,446.74,455.56,7720000,455.56 1955-09-23,485.96,489.94,483.44,487.45,2540000,487.45 1955-09-22,485.98,489.51,484.12,485.96,2550000,485.96 1955-09-21,483.67,488.02,482.97,485.98,2460000,485.98 1955-09-20,483.80,485.05,480.84,483.67,2090000,483.67 1955-09-19,483.67,487.79,482.42,483.80,2390000,483.80 1955-09-16,481.56,485.32,480.02,483.67,2540000,483.67 1955-09-15,482.90,485.73,480.04,481.56,2890000,481.56 1955-09-14,480.93,485.71,479.61,482.90,2570000,482.90 1955-09-13,476.51,482.76,475.54,480.93,2580000,480.93 1955-09-12,474.59,478.44,473.02,476.51,2520000,476.51 1955-09-09,475.06,476.87,472.48,474.59,2480000,474.59 1955-09-08,475.20,476.97,472.96,475.06,2470000,475.06 1955-09-07,476.24,478.50,473.00,475.20,2380000,475.20 1955-09-06,472.84,478.80,472.84,476.24,2360000,476.24 1955-09-02,469.63,473.52,469.47,472.53,1700000,472.53 1955-09-01,468.18,471.51,467.36,469.63,1860000,469.63 1955-08-31,464.80,469.51,464.80,468.18,1850000,468.18 1955-08-30,464.37,466.41,462.70,464.67,1740000,464.67 1955-08-29,463.70,466.62,463.08,464.37,1910000,464.37 1955-08-26,461.27,465.30,460.68,463.70,2200000,463.70 1955-08-25,459.39,462.93,458.40,461.27,2120000,461.27 1955-08-24,457.38,462.68,457.38,459.39,2140000,459.39 1955-08-23,452.55,457.88,451.17,457.35,1890000,457.35 1955-08-22,453.57,454.41,450.76,452.55,1430000,452.55 1955-08-19,452.53,454.66,450.67,453.57,1400000,453.57 1955-08-18,452.85,454.86,451.13,452.53,1560000,452.53 1955-08-17,453.26,454.66,449.88,452.85,1570000,452.85 1955-08-16,456.09,457.17,451.92,453.26,1520000,453.26 1955-08-15,457.01,458.87,453.84,456.09,1230000,456.09 1955-08-12,455.18,458.99,454.93,457.01,1530000,457.01 1955-08-11,450.29,456.22,449.75,455.18,1620000,455.18 1955-08-10,448.84,452.44,447.39,450.29,1580000,450.29 1955-08-09,453.30,453.30,445.67,448.84,2240000,448.84 1955-08-08,456.40,459.28,453.05,454.05,1730000,454.05 1955-08-05,454.18,458.44,453.62,456.40,1690000,456.40 1955-08-04,458.92,458.92,452.37,454.18,2210000,454.18 1955-08-03,460.82,463.60,459.17,460.98,2190000,460.98 1955-08-02,460.25,463.02,457.11,460.82,2260000,460.82 1955-08-01,465.85,467.48,458.71,460.25,2190000,460.25 1955-07-29,466.46,468.75,463.45,465.85,2070000,465.85 1955-07-28,468.45,470.74,463.26,466.46,2090000,466.46 1955-07-27,468.41,471.35,465.71,468.45,2170000,468.45 1955-07-26,468.02,471.73,465.14,468.41,2340000,468.41 1955-07-25,464.69,470.53,464.35,468.02,2500000,468.02 1955-07-22,461.07,466.28,460.73,464.69,2500000,464.69 1955-07-21,458.10,462.86,457.65,461.07,2530000,461.07 1955-07-20,456.72,459.89,454.34,458.10,2080000,458.10 1955-07-19,460.07,460.86,453.39,456.72,2300000,456.72 1955-07-18,460.23,463.45,458.08,460.07,2160000,460.07 1955-07-15,458.49,463.15,457.94,460.23,2230000,460.23 1955-07-14,457.40,460.71,454.82,458.49,1980000,458.49 1955-07-13,462.97,464.96,456.06,457.40,2360000,457.40 1955-07-12,464.24,468.99,460.62,462.97,2630000,462.97 1955-07-11,461.18,466.10,460.32,464.24,2420000,464.24 1955-07-08,460.23,465.08,456.68,461.18,2450000,461.18 1955-07-07,467.41,469.06,458.28,460.23,3300000,460.23 1955-07-06,460.89,471.15,460.89,467.41,3140000,467.41 1955-07-05,454.80,462.22,454.80,459.42,2680000,459.42 1955-07-01,451.38,456.11,449.50,453.82,2540000,453.82 1955-06-30,449.70,453.48,448.70,451.38,2370000,451.38 1955-06-29,449.02,451.13,444.74,449.70,2180000,449.70 1955-06-28,449.86,452.28,446.12,449.02,2180000,449.02 1955-06-27,448.93,451.53,446.64,449.86,2250000,449.86 1955-06-24,448.82,450.99,445.15,448.93,2410000,448.93 1955-06-23,447.37,451.49,445.67,448.82,2900000,448.82 1955-06-22,446.80,450.45,445.24,447.37,3010000,447.37 1955-06-21,444.38,448.52,443.27,446.80,2720000,446.80 1955-06-20,444.08,446.53,443.13,444.38,2490000,444.38 1955-06-17,442.48,445.04,440.96,444.08,2340000,444.08 1955-06-16,441.93,445.42,440.51,442.48,2760000,442.48 1955-06-15,438.45,443.47,438.45,441.93,2650000,441.93 1955-06-14,440.17,443.45,437.45,438.20,2860000,438.20 1955-06-13,437.72,442.23,437.65,440.17,2770000,440.17 1955-06-10,435.07,438.94,433.60,437.72,2470000,437.72 1955-06-09,436.95,439.80,434.32,435.07,2960000,435.07 1955-06-08,434.55,439.26,433.26,436.95,3300000,436.95 1955-06-07,431.49,437.99,430.93,434.55,3230000,434.55 1955-06-06,428.53,433.19,427.37,431.49,2560000,431.49 1955-06-03,425.88,430.25,425.88,428.53,2590000,428.53 1955-06-02,424.88,428.13,422.86,425.80,2610000,425.80 1955-06-01,424.86,426.75,422.48,424.88,2510000,424.88 1955-05-31,425.66,427.06,422.84,424.86,1990000,424.86 1955-05-27,424.95,427.71,423.68,425.66,2220000,425.66 1955-05-26,421.77,426.08,421.48,424.95,2260000,424.95 1955-05-25,420.39,423.44,419.63,421.77,2100000,421.77 1955-05-24,420.32,422.39,417.16,420.39,1650000,420.39 1955-05-23,422.89,425.22,419.75,420.32,1900000,420.32 1955-05-20,419.72,423.84,418.64,422.89,2240000,422.89 1955-05-19,417.83,421.57,417.16,419.72,2380000,419.72 1955-05-18,414.12,418.83,413.95,417.83,2010000,417.83 1955-05-17,415.01,417.05,412.60,414.12,1900000,414.12 1955-05-16,419.57,421.02,412.73,415.01,2160000,415.01 1955-05-13,418.20,421.98,417.03,419.57,1860000,419.57 1955-05-12,420.29,421.24,414.43,418.20,2830000,418.20 1955-05-11,423.80,425.02,419.03,420.29,2120000,420.29 1955-05-10,424.32,425.69,419.85,423.80,2150000,423.80 1955-05-09,423.84,426.32,422.43,424.32,2090000,424.32 1955-05-06,423.39,425.71,421.57,423.84,2250000,423.84 1955-05-05,422.54,425.56,421.22,423.39,2270000,423.39 1955-05-04,422.78,424.65,419.18,422.54,2220000,422.54 1955-05-03,426.30,426.84,420.81,422.78,2630000,422.78 1955-05-02,425.65,428.27,424.00,426.30,2220000,426.30 1955-04-29,423.19,426.99,422.82,425.65,2230000,425.65 1955-04-28,428.10,428.92,421.96,423.19,2550000,423.19 1955-04-27,430.64,432.07,425.41,428.10,2660000,428.10 1955-04-26,427.62,432.76,427.62,430.64,2720000,430.64 1955-04-25,425.52,428.34,420.52,426.86,2720000,426.86 1955-04-22,428.45,430.27,423.24,425.52,2800000,425.52 1955-04-21,428.62,431.18,425.54,428.45,2810000,428.45 1955-04-20,427.88,430.85,426.04,428.62,3090000,428.62 1955-04-19,428.42,429.25,425.30,427.88,2700000,427.88 1955-04-18,425.45,430.03,425.02,428.42,3080000,428.42 1955-04-15,422.46,427.23,421.71,425.45,3180000,425.45 1955-04-14,421.57,424.52,419.05,422.46,2890000,422.46 1955-04-13,420.94,424.19,419.87,421.57,2820000,421.57 1955-04-12,418.77,422.85,418.12,420.94,2770000,420.94 1955-04-11,418.20,420.89,416.27,418.77,2680000,418.77 1955-04-07,416.42,419.79,415.84,418.20,2330000,418.20 1955-04-06,415.90,419.33,414.75,416.42,2500000,416.42 1955-04-05,412.97,416.84,411.84,415.90,2100000,415.90 1955-04-04,413.84,416.71,412.10,412.97,2500000,412.97 1955-04-01,409.78,414.80,409.78,413.84,2660000,413.84 1955-03-31,410.13,413.21,407.96,409.70,2680000,409.70 1955-03-30,413.73,414.82,409.07,410.13,3410000,410.13 1955-03-29,412.91,415.10,411.39,413.73,2770000,413.73 1955-03-28,414.77,416.16,411.87,412.91,2540000,412.91 1955-03-25,414.49,416.64,412.06,414.77,2540000,414.77 1955-03-24,411.39,416.42,411.39,414.49,3170000,414.49 1955-03-23,405.68,411.32,405.68,410.87,2730000,410.87 1955-03-22,402.40,405.68,401.28,404.47,1910000,404.47 1955-03-21,404.75,406.16,401.64,402.40,2020000,402.40 1955-03-18,405.23,408.09,402.88,404.75,2050000,404.75 1955-03-17,403.14,406.14,401.41,405.23,2200000,405.23 1955-03-16,399.60,405.94,399.60,403.14,2900000,403.14 1955-03-15,391.36,399.67,391.18,399.28,3160000,399.28 1955-03-14,400.06,400.06,387.50,391.36,4220000,391.36 1955-03-11,406.66,406.66,398.56,401.08,3040000,401.08 1955-03-10,404.90,410.06,404.90,406.83,2760000,406.83 1955-03-09,409.13,409.22,400.84,404.90,3590000,404.90 1955-03-08,416.27,416.27,408.52,409.13,3160000,409.13 1955-03-07,419.68,420.85,415.69,416.84,2630000,416.84 1955-03-04,418.33,421.83,416.53,419.68,2770000,419.68 1955-03-03,417.18,420.61,416.25,418.33,3330000,418.33 1955-03-02,413.95,418.33,413.95,417.18,3370000,417.18 1955-03-01,411.87,416.10,411.24,413.71,2830000,413.71 1955-02-28,409.50,413.62,408.18,411.87,2620000,411.87 1955-02-25,410.30,411.17,406.35,409.50,2540000,409.50 1955-02-24,411.48,412.65,407.63,410.30,2920000,410.30 1955-02-23,411.28,413.04,409.72,411.48,3030000,411.48 1955-02-21,411.63,414.21,409.57,411.28,3010000,411.28 1955-02-18,410.41,414.62,409.07,411.63,3660000,411.63 1955-02-17,409.98,412.78,408.55,410.41,3030000,410.41 1955-02-16,411.95,414.27,408.91,409.98,3660000,409.98 1955-02-15,411.39,414.69,409.54,411.95,3510000,411.95 1955-02-14,413.99,415.42,410.26,411.39,2950000,411.39 1955-02-11,412.89,416.55,410.74,413.99,3260000,413.99 1955-02-10,410.41,414.90,410.41,412.89,3460000,412.89 1955-02-09,405.70,411.34,405.20,410.32,3360000,410.32 1955-02-08,409.59,410.78,403.73,405.70,3400000,405.70 1955-02-07,409.76,412.93,407.20,409.59,3610000,409.59 1955-02-04,405.85,411.17,405.09,409.76,3370000,409.76 1955-02-03,407.11,408.20,403.51,405.85,2890000,405.85 1955-02-02,409.70,410.17,405.42,407.11,3210000,407.11 1955-02-01,408.83,411.63,406.72,409.70,3320000,409.70 1955-01-31,404.68,410.61,404.27,408.83,3500000,408.83 1955-01-28,402.60,406.38,400.67,404.68,3290000,404.68 1955-01-27,401.97,406.98,400.21,402.60,3500000,402.60 1955-01-26,398.19,405.31,398.19,401.97,3860000,401.97 1955-01-25,396.00,397.85,392.14,397.00,3230000,397.00 1955-01-24,395.90,397.89,394.09,396.00,2910000,396.00 1955-01-21,393.03,397.64,392.50,395.90,2690000,395.90 1955-01-20,392.31,394.35,390.66,393.03,2210000,393.03 1955-01-19,391.19,395.81,391.19,392.31,2760000,392.31 1955-01-18,388.20,391.76,385.65,390.98,3020000,390.98 1955-01-17,396.54,396.75,387.54,388.20,3360000,388.20 1955-01-14,398.34,399.70,394.88,396.54,2630000,396.54 1955-01-13,399.78,402.12,396.28,398.34,3350000,398.34 1955-01-12,400.25,401.86,396.60,399.78,3400000,399.78 1955-01-11,400.89,402.88,398.02,400.25,3680000,400.25 1955-01-10,397.72,402.24,397.72,400.89,4300000,400.89 1955-01-07,391.91,396.88,391.91,395.60,4030000,395.60 1955-01-06,397.19,397.19,387.09,391.89,5300000,391.89 1955-01-05,405.39,405.39,396.41,397.24,4640000,397.24 1955-01-04,408.89,409.21,401.84,406.17,4420000,406.17 1955-01-03,404.39,412.47,403.58,408.89,4570000,408.89 1954-12-31,401.97,407.17,401.48,404.39,3840000,404.39 1954-12-30,401.97,404.41,399.42,401.97,3590000,401.97 1954-12-29,398.51,404.21,398.17,401.97,4430000,401.97 1954-12-28,393.88,399.61,392.06,398.51,3660000,398.51 1954-12-27,397.15,397.77,392.33,393.88,2970000,393.88 1954-12-23,397.07,398.85,395.28,397.15,3310000,397.15 1954-12-22,398.11,399.97,395.73,397.07,3460000,397.07 1954-12-21,397.32,400.04,395.35,398.11,3630000,398.11 1954-12-20,394.94,399.59,393.31,397.32,3770000,397.32 1954-12-17,393.14,396.34,391.85,394.94,3730000,394.94 1954-12-16,389.28,394.54,389.28,393.14,3390000,393.14 1954-12-15,387.03,389.96,385.03,388.92,2740000,388.92 1954-12-14,389.79,390.98,386.56,387.03,2650000,387.03 1954-12-13,390.08,391.87,387.73,389.79,2750000,389.79 1954-12-10,391.53,393.54,388.41,390.08,3250000,390.08 1954-12-09,393.08,393.56,388.75,391.53,3300000,391.53 1954-12-08,393.88,395.43,390.85,393.08,4150000,393.08 1954-12-07,392.48,395.67,390.32,393.88,3820000,393.88 1954-12-06,389.77,394.01,389.77,392.48,3960000,392.48 1954-12-03,385.63,391.74,385.58,389.60,3790000,389.60 1954-12-02,384.04,388.05,382.80,385.63,3190000,385.63 1954-12-01,386.77,388.68,381.81,384.04,3100000,384.04 1954-11-30,388.51,391.21,385.67,386.77,3440000,386.77 1954-11-29,387.79,390.72,385.90,388.51,3300000,388.51 1954-11-26,384.63,388.96,384.06,387.79,3010000,387.79 1954-11-24,382.74,387.05,382.47,384.63,3990000,384.63 1954-11-23,379.47,384.29,378.65,382.74,3690000,382.74 1954-11-22,378.01,381.21,376.82,379.47,3000000,379.47 1954-11-19,377.44,380.34,375.29,378.01,3130000,378.01 1954-11-18,379.69,381.32,376.29,377.44,3530000,377.44 1954-11-17,379.39,382.06,377.46,379.69,3830000,379.69 1954-11-16,376.74,380.77,373.85,379.39,3260000,379.39 1954-11-15,377.10,379.20,374.04,376.74,3080000,376.74 1954-11-12,374.91,379.73,374.19,377.10,3720000,377.10 1954-11-11,371.88,375.89,371.47,374.91,2960000,374.91 1954-11-10,371.07,374.00,368.88,371.88,2070000,371.88 1954-11-09,369.46,372.83,368.52,371.07,3240000,371.07 1954-11-08,366.00,371.60,365.28,369.46,3180000,369.46 1954-11-05,366.95,368.31,363.90,366.00,2950000,366.00 1954-11-04,361.99,368.50,361.99,366.95,3140000,366.95 1954-11-03,355.45,363.30,355.45,361.50,2700000,361.50 1954-11-01,352.14,354.90,350.16,353.96,1790000,353.96 1954-10-29,354.56,354.71,350.72,352.14,1900000,352.14 1954-10-28,355.73,357.55,353.60,354.56,2190000,354.56 1954-10-27,356.32,358.00,354.01,355.73,2030000,355.73 1954-10-26,356.34,358.29,354.73,356.32,2010000,356.32 1954-10-25,358.61,360.82,355.15,356.34,2340000,356.34 1954-10-22,358.08,360.31,356.81,358.61,2080000,358.61 1954-10-21,357.42,360.46,356.60,358.08,2320000,358.08 1954-10-20,354.75,358.72,354.69,357.42,2380000,357.42 1954-10-19,354.35,356.34,353.11,354.75,1900000,354.75 1954-10-18,353.20,355.64,351.84,354.35,1790000,354.35 1954-10-15,354.69,355.64,351.54,353.20,2250000,353.20 1954-10-14,358.91,359.74,353.94,354.69,2540000,354.69 1954-10-13,359.57,360.71,357.51,358.91,2070000,358.91 1954-10-12,361.12,361.12,357.95,359.57,1620000,359.57 1954-10-11,363.77,364.98,360.37,361.43,2100000,361.43 1954-10-08,363.79,366.04,362.35,363.77,2120000,363.77 1954-10-07,364.43,366.40,362.30,363.79,1810000,363.79 1954-10-06,363.37,366.02,362.43,364.43,2570000,364.43 1954-10-05,362.73,365.11,361.75,363.37,2300000,363.37 1954-10-04,359.88,364.21,359.35,362.73,2000000,362.73 1954-10-01,360.46,361.62,358.59,359.88,1850000,359.88 1954-09-30,361.73,362.98,358.95,360.46,1840000,360.46 1954-09-29,363.32,364.21,360.39,361.73,1810000,361.73 1954-09-28,362.26,366.02,361.12,363.32,1800000,363.32 1954-09-27,361.67,364.00,361.03,362.26,2190000,362.26 1954-09-24,359.63,362.90,357.97,361.67,2340000,361.67 1954-09-23,358.36,361.71,357.08,359.63,2340000,359.63 1954-09-22,356.40,359.46,356.13,358.36,2260000,358.36 1954-09-21,353.48,356.91,352.24,356.40,1770000,356.40 1954-09-20,355.32,357.32,353.11,353.48,2060000,353.48 1954-09-17,352.37,356.40,352.22,355.32,2250000,355.32 1954-09-16,350.63,353.43,349.06,352.37,1880000,352.37 1954-09-15,351.78,353.45,348.59,350.63,2110000,350.63 1954-09-14,351.10,353.92,350.06,351.78,2120000,351.78 1954-09-13,347.83,352.29,347.83,351.10,2030000,351.10 1954-09-10,346.73,349.38,345.50,347.83,1870000,347.83 1954-09-09,346.07,347.47,344.22,346.73,1700000,346.73 1954-09-08,345.37,348.25,344.92,346.07,1970000,346.07 1954-09-07,343.10,346.34,341.82,345.37,1860000,345.37 1954-09-03,341.15,343.80,340.23,343.10,1630000,343.10 1954-09-02,338.41,342.76,338.41,341.15,1600000,341.15 1954-09-01,335.80,340.42,334.97,338.13,1790000,338.13 1954-08-31,340.44,340.44,333.21,335.80,2640000,335.80 1954-08-30,344.48,345.07,339.53,341.25,1950000,341.25 1954-08-27,343.35,346.37,342.29,344.48,1740000,344.48 1954-08-26,344.60,345.35,341.10,343.35,2060000,343.35 1954-08-25,346.32,347.49,341.97,344.60,2280000,344.60 1954-08-24,347.64,348.19,344.26,346.32,2000000,346.32 1954-08-23,350.38,351.08,347.00,347.64,2020000,347.64 1954-08-20,349.89,352.20,348.59,350.38,2110000,350.38 1954-08-19,348.51,352.27,347.05,349.89,2320000,349.89 1954-08-18,348.38,350.00,344.77,348.51,2390000,348.51 1954-08-17,349.61,351.86,347.05,348.38,2900000,348.38 1954-08-16,346.64,350.91,346.11,349.61,2760000,349.61 1954-08-13,345.84,347.98,343.52,346.64,2500000,346.64 1954-08-12,346.41,348.53,344.31,345.84,2680000,345.84 1954-08-11,343.56,347.92,343.12,346.41,3440000,346.41 1954-08-10,340.87,345.60,340.61,343.56,2890000,343.56 1954-08-09,343.06,343.71,338.70,340.87,2280000,340.87 1954-08-06,347.02,347.02,339.64,343.06,3350000,343.06 1954-08-05,349.74,350.42,345.90,347.79,3150000,347.79 1954-08-04,349.61,351.50,345.75,349.74,3620000,349.74 1954-08-03,349.57,351.44,347.05,349.61,2970000,349.61 1954-08-02,347.92,351.29,346.22,349.57,2850000,349.57 1954-07-30,346.15,349.21,345.22,347.92,2800000,347.92 1954-07-29,345.11,347.77,344.01,346.15,2710000,346.15 1954-07-28,344.69,346.83,342.72,345.11,2740000,345.11 1954-07-27,343.39,346.41,342.06,344.69,2690000,344.69 1954-07-26,343.48,345.05,341.42,343.39,2110000,343.39 1954-07-23,342.97,344.92,341.51,343.48,2520000,343.48 1954-07-22,339.98,344.54,338.94,342.97,2890000,342.97 1954-07-21,337.62,341.06,336.46,339.98,2510000,339.98 1954-07-20,338.64,339.09,334.80,337.62,2580000,337.62 1954-07-19,339.96,340.87,336.96,338.64,2370000,338.64 1954-07-16,341.06,342.12,338.03,339.96,2540000,339.96 1954-07-15,340.44,343.01,339.17,341.06,3000000,341.06 1954-07-14,340.04,341.25,337.37,340.44,2520000,340.44 1954-07-13,340.91,342.82,338.53,340.04,2430000,340.04 1954-07-12,341.25,343.59,339.43,340.91,2330000,340.91 1954-07-09,339.81,342.91,337.62,341.25,2240000,341.25 1954-07-08,340.34,341.63,337.64,339.81,2080000,339.81 1954-07-07,341.12,343.20,338.15,340.34,2380000,340.34 1954-07-06,337.71,342.10,337.71,341.12,2560000,341.12 1954-07-02,334.12,338.64,333.00,337.66,1980000,337.66 1954-07-01,333.53,335.44,330.68,334.12,1860000,334.12 1954-06-30,336.90,337.96,332.20,333.53,1950000,333.53 1954-06-29,336.12,338.78,330.95,336.90,2580000,336.90 1954-06-28,332.53,337.30,331.29,336.12,1890000,336.12 1954-06-25,332.20,335.09,330.19,332.53,2060000,332.53 1954-06-24,330.72,333.84,329.58,332.20,2260000,332.20 1954-06-23,329.51,331.54,326.81,330.72,2090000,330.72 1954-06-22,328.56,330.99,327.40,329.51,2100000,329.51 1954-06-21,327.91,330.19,326.33,328.56,1820000,328.56 1954-06-18,327.21,329.07,325.73,327.91,1580000,327.91 1954-06-17,327.28,329.49,325.88,327.21,1810000,327.21 1954-06-16,325.21,328.67,325.00,327.28,2070000,327.28 1954-06-15,322.65,325.80,322.04,325.21,1630000,325.21 1954-06-14,322.09,323.54,320.67,322.65,1420000,322.65 1954-06-11,320.12,323.29,319.19,322.09,1630000,322.09 1954-06-10,319.27,321.85,318.20,320.12,1610000,320.12 1954-06-09,321.00,321.26,315.66,319.27,2360000,319.27 1954-06-08,327.92,327.92,319.94,321.00,2540000,321.00 1954-06-07,327.63,329.54,326.50,327.96,1520000,327.96 1954-06-04,328.63,329.84,326.54,327.63,1720000,327.63 1954-06-03,328.36,330.35,327.35,328.63,1810000,328.63 1954-06-02,328.67,330.45,327.06,328.36,1930000,328.36 1954-06-01,327.49,329.48,326.21,328.67,1850000,328.67 1954-05-28,326.37,328.57,324.83,327.49,1940000,327.49 1954-05-27,327.11,328.93,325.50,326.37,2230000,326.37 1954-05-26,325.02,328.26,324.26,327.11,2180000,327.11 1954-05-25,326.09,326.80,323.27,325.02,2050000,325.02 1954-05-24,326.09,327.94,324.59,326.09,2330000,326.09 1954-05-21,323.88,327.43,323.82,326.09,2620000,326.09 1954-05-20,323.21,325.42,322.40,323.88,2070000,323.88 1954-05-19,324.14,325.64,321.79,323.21,2170000,323.21 1954-05-18,323.33,326.29,322.90,324.14,2250000,324.14 1954-05-17,322.50,324.69,321.10,323.33,2040000,323.33 1954-05-14,320.39,323.39,319.39,322.50,1970000,322.50 1954-05-13,321.61,323.80,319.21,320.39,2340000,320.39 1954-05-12,319.74,322.70,318.68,321.61,2210000,321.61 1954-05-11,321.32,322.03,318.22,319.74,1770000,319.74 1954-05-10,321.30,322.66,320.02,321.32,1800000,321.32 1954-05-07,320.41,323.13,319.54,321.30,2070000,321.30 1954-05-06,317.93,321.53,316.80,320.41,1980000,320.41 1954-05-05,319.82,320.94,316.45,317.93,2020000,317.93 1954-05-04,319.35,321.65,316.84,319.82,1990000,319.82 1954-05-03,319.33,320.94,317.37,319.35,1870000,319.35 1954-04-30,318.22,321.71,317.24,319.33,2450000,319.33 1954-04-29,314.02,319.76,314.02,318.22,2150000,318.22 1954-04-28,313.49,315.01,309.37,313.75,2120000,313.75 1954-04-27,314.54,315.74,310.91,313.49,1970000,313.49 1954-04-26,313.37,316.23,312.35,314.54,2150000,314.54 1954-04-23,311.48,314.34,311.16,313.37,1990000,313.37 1954-04-22,310.91,312.54,309.05,311.48,1750000,311.48 1954-04-21,311.89,313.94,309.92,310.91,1870000,310.91 1954-04-20,311.78,314.38,310.02,311.89,1860000,311.89 1954-04-19,313.77,316.15,310.65,311.78,2430000,311.78 1954-04-15,311.76,314.44,310.71,313.77,2200000,313.77 1954-04-14,308.98,312.96,308.38,311.76,2330000,311.76 1954-04-13,309.19,310.93,307.58,308.98,2020000,308.98 1954-04-12,309.39,310.77,307.44,309.19,1790000,309.19 1954-04-09,307.79,310.32,307.20,309.39,2360000,309.39 1954-04-08,305.82,309.57,305.82,307.79,2300000,307.79 1954-04-07,304.26,306.45,301.70,305.41,1830000,305.41 1954-04-06,307.04,308.50,302.78,304.26,2120000,304.26 1954-04-05,306.67,308.46,305.27,307.04,1710000,307.04 1954-04-02,306.27,307.95,304.52,306.67,1830000,306.67 1954-04-01,303.51,307.30,303.18,306.27,2270000,306.27 1954-03-31,301.01,305.15,301.01,303.51,2690000,303.51 1954-03-30,300.06,302.57,299.47,300.89,2130000,300.89 1954-03-29,299.08,301.46,297.66,300.06,1870000,300.06 1954-03-26,296.67,300.10,296.67,299.08,1550000,299.08 1954-03-25,296.89,297.68,294.76,296.40,1720000,296.40 1954-03-24,299.02,299.73,295.59,296.89,1900000,296.89 1954-03-23,301.60,302.49,298.39,299.02,2180000,299.02 1954-03-22,301.44,302.80,299.49,301.60,1800000,301.60 1954-03-19,300.12,302.65,300.12,301.44,1930000,301.44 1954-03-18,298.31,301.44,297.99,300.10,2020000,300.10 1954-03-17,298.09,299.22,296.14,298.31,1740000,298.31 1954-03-16,298.88,300.50,297.34,298.09,1540000,298.09 1954-03-15,299.71,300.12,296.81,298.88,1680000,298.88 1954-03-12,300.83,302.17,298.76,299.71,1980000,299.71 1954-03-11,299.59,301.68,298.76,300.83,2050000,300.83 1954-03-10,299.45,300.95,298.01,299.59,1870000,299.59 1954-03-09,298.64,300.50,297.09,299.45,1630000,299.45 1954-03-08,299.45,300.66,297.44,298.64,1650000,298.64 1954-03-05,297.48,300.68,296.50,299.45,2030000,299.45 1954-03-04,297.03,298.80,295.37,297.48,1830000,297.48 1954-03-03,297.48,299.65,295.79,297.03,2240000,297.03 1954-03-02,296.55,298.66,294.78,297.48,1980000,297.48 1954-03-01,294.54,297.80,294.23,296.55,2040000,296.55 1954-02-26,291.41,295.19,290.78,294.54,1910000,294.54 1954-02-25,289.54,292.04,289.06,291.41,1470000,291.41 1954-02-24,290.03,290.42,287.84,289.54,1350000,289.54 1954-02-23,291.07,291.98,289.00,290.03,1470000,290.03 1954-02-19,291.51,292.59,289.87,291.07,1510000,291.07 1954-02-18,290.11,292.67,289.08,291.51,1500000,291.51 1954-02-17,289.61,290.92,287.37,290.11,1740000,290.11 1954-02-16,292.55,292.95,288.61,289.61,1870000,289.61 1954-02-15,293.99,294.92,291.93,292.55,2080000,292.55 1954-02-12,292.45,294.78,291.90,293.99,1730000,293.99 1954-02-11,292.95,294.84,291.27,292.45,1860000,292.45 1954-02-10,293.79,294.50,292.00,292.95,1790000,292.95 1954-02-09,293.58,294.84,291.94,293.79,1880000,293.79 1954-02-08,293.97,294.92,292.20,293.58,2180000,293.58 1954-02-05,294.03,295.43,292.53,293.97,2030000,293.97 1954-02-04,292.32,295.10,292.06,294.03,2040000,294.03 1954-02-03,291.17,292.99,289.20,292.32,1690000,292.32 1954-02-02,291.84,291.88,289.75,291.17,1420000,291.17 1954-02-01,292.39,293.50,290.46,291.84,1740000,291.84 1954-01-29,291.51,293.81,290.86,292.39,1950000,292.39 1954-01-28,292.22,293.12,289.81,291.51,1730000,291.51 1954-01-27,292.85,294.56,291.53,292.22,2020000,292.22 1954-01-26,290.40,293.44,290.11,292.85,2120000,292.85 1954-01-25,289.65,291.29,288.27,290.40,1860000,290.40 1954-01-22,289.48,290.86,288.18,289.65,1890000,289.65 1954-01-21,289.14,290.66,287.68,289.48,1780000,289.48 1954-01-20,288.27,290.15,287.58,289.14,1960000,289.14 1954-01-19,286.03,289.14,285.24,288.27,1840000,288.27 1954-01-18,286.72,287.78,284.69,286.03,1580000,286.03 1954-01-15,284.49,288.10,284.49,286.72,2180000,286.72 1954-01-14,283.03,285.67,282.83,284.49,1530000,284.49 1954-01-13,281.51,284.37,281.12,283.03,1420000,283.03 1954-01-12,279.87,282.54,279.46,281.51,1250000,281.51 1954-01-11,281.51,281.67,278.91,279.87,1220000,279.87 1954-01-08,282.60,283.01,280.39,281.51,1260000,281.51 1954-01-07,283.96,284.86,281.83,282.60,1540000,282.60 1954-01-06,284.19,285.67,283.05,283.96,1460000,283.96 1954-01-05,282.89,285.34,282.65,284.19,1520000,284.19 1954-01-04,280.90,283.48,279.72,282.89,1310000,282.89 1953-12-31,280.43,282.18,279.52,280.90,2490000,280.90 1953-12-30,278.30,281.08,277.92,280.43,2050000,280.43 1953-12-29,279.74,279.74,275.91,278.30,2140000,278.30 1953-12-28,280.92,281.25,278.81,279.91,1570000,279.91 1953-12-24,279.84,281.69,279.15,280.92,1270000,280.92 1953-12-23,279.99,281.11,278.14,279.84,1570000,279.84 1953-12-22,282.85,282.85,278.95,279.99,1720000,279.99 1953-12-21,283.54,284.69,282.38,282.99,1690000,282.99 1953-12-18,282.67,284.35,281.71,283.54,1550000,283.54 1953-12-17,282.87,284.55,281.57,282.67,1600000,282.67 1953-12-16,279.52,283.88,279.36,282.87,1880000,282.87 1953-12-15,279.26,280.27,277.49,279.52,1450000,279.52 1953-12-14,279.91,280.98,278.18,279.26,1540000,279.26 1953-12-11,279.89,280.76,278.38,279.91,1440000,279.91 1953-12-10,281.12,281.53,278.93,279.89,1420000,279.89 1953-12-09,281.45,282.54,279.78,281.12,1410000,281.12 1953-12-08,282.00,282.48,279.34,281.45,1390000,281.45 1953-12-07,282.71,283.50,281.20,282.00,1410000,282.00 1953-12-04,283.25,284.11,281.55,282.71,1390000,282.71 1953-12-03,282.81,285.20,282.10,283.25,1740000,283.25 1953-12-02,281.10,283.74,280.33,282.81,1850000,282.81 1953-12-01,281.37,282.08,279.46,281.10,1580000,281.10 1953-11-30,280.23,282.46,279.80,281.37,1960000,281.37 1953-11-27,277.78,280.78,277.19,280.23,1600000,280.23 1953-11-25,277.13,278.87,276.40,277.78,1540000,277.78 1953-11-24,275.42,277.61,274.26,277.13,1470000,277.13 1953-11-23,276.05,276.58,273.80,275.42,1410000,275.42 1953-11-20,276.09,277.47,274.79,276.05,1300000,276.05 1953-11-19,274.51,277.02,274.16,276.09,1420000,276.09 1953-11-18,273.88,275.52,273.05,274.51,1250000,274.51 1953-11-17,275.58,275.58,273.01,273.88,1250000,273.88 1953-11-16,277.53,278.57,275.48,275.93,1490000,275.93 1953-11-13,276.23,278.08,275.16,277.53,1540000,277.53 1953-11-12,275.89,277.65,274.63,276.23,1390000,276.23 1953-11-10,277.86,277.86,275.06,275.89,1340000,275.89 1953-11-09,278.83,279.93,276.80,278.26,1440000,278.26 1953-11-06,279.09,280.25,277.57,278.83,1700000,278.83 1953-11-05,276.82,280.33,276.80,279.09,1720000,279.09 1953-11-04,276.72,277.72,274.83,276.82,1480000,276.82 1953-11-02,275.81,278.18,274.83,276.72,1340000,276.72 1953-10-30,276.31,277.04,274.87,275.81,1400000,275.81 1953-10-29,274.14,276.94,273.92,276.31,1610000,276.31 1953-10-28,273.35,274.69,272.13,274.14,1260000,274.14 1953-10-27,274.33,274.33,271.85,273.35,1170000,273.35 1953-10-26,275.34,276.56,273.88,274.43,1340000,274.43 1953-10-23,274.89,276.52,274.12,275.34,1330000,275.34 1953-10-22,273.74,275.77,272.97,274.89,1330000,274.89 1953-10-21,273.90,274.61,272.30,273.74,1320000,273.74 1953-10-20,273.31,275.16,272.36,273.90,1280000,273.90 1953-10-19,272.80,273.78,271.14,273.31,1190000,273.31 1953-10-16,271.22,273.94,271.02,272.80,1620000,272.80 1953-10-15,267.51,271.81,267.41,271.22,1710000,271.22 1953-10-14,266.09,268.22,265.64,267.51,1290000,267.51 1953-10-13,267.04,267.69,265.36,266.09,1130000,266.09 1953-10-09,266.72,267.69,265.52,267.04,900000,267.04 1953-10-08,266.53,267.97,265.96,266.72,960000,266.72 1953-10-07,264.26,266.86,263.57,266.53,1010000,266.53 1953-10-06,265.25,265.25,262.45,264.26,1100000,264.26 1953-10-05,266.70,267.59,264.52,265.48,930000,265.48 1953-10-02,265.68,267.59,265.32,266.70,890000,266.70 1953-10-01,264.04,266.47,263.79,265.68,940000,265.68 1953-09-30,264.77,265.38,262.94,264.04,940000,264.04 1953-09-29,264.79,266.61,263.90,264.77,1170000,264.77 1953-09-28,263.31,265.86,263.16,264.79,1150000,264.79 1953-09-25,262.45,264.06,261.78,263.31,910000,263.31 1953-09-24,262.35,263.83,261.36,262.45,1020000,262.45 1953-09-23,261.40,263.83,261.40,262.35,1240000,262.35 1953-09-22,258.01,261.89,257.85,261.28,1300000,261.28 1953-09-21,258.78,260.00,257.36,258.01,1070000,258.01 1953-09-18,259.84,259.84,257.65,258.78,1190000,258.78 1953-09-17,259.07,261.30,258.42,259.88,1290000,259.88 1953-09-16,257.97,260.95,257.97,259.07,1570000,259.07 1953-09-15,255.49,258.68,254.36,257.67,2850000,257.67 1953-09-14,259.71,260.20,255.29,255.49,2550000,255.49 1953-09-11,262.37,262.37,258.94,259.71,1930000,259.71 1953-09-10,265.38,265.38,262.58,262.88,1010000,262.88 1953-09-09,265.42,266.23,264.56,265.48,860000,265.48 1953-09-08,264.34,266.23,264.04,265.42,740000,265.42 1953-09-04,263.61,265.09,262.70,264.34,770000,264.34 1953-09-03,263.96,264.65,262.50,263.61,900000,263.61 1953-09-02,262.54,265.21,262.43,263.96,1110000,263.96 1953-09-01,261.22,263.23,260.32,262.54,1580000,262.54 1953-08-31,265.70,265.70,260.83,261.22,2190000,261.22 1953-08-28,265.68,266.86,264.89,265.74,1060000,265.74 1953-08-27,266.51,267.45,264.65,265.68,1290000,265.68 1953-08-26,267.45,269.17,266.27,266.51,1060000,266.51 1953-08-25,268.70,268.83,265.92,267.45,1470000,267.45 1953-08-24,271.93,271.99,268.06,268.70,1320000,268.70 1953-08-21,271.73,272.80,270.81,271.93,850000,271.93 1953-08-20,271.50,272.66,270.41,271.73,860000,271.73 1953-08-19,273.01,273.01,270.06,271.50,1400000,271.50 1953-08-18,275.04,275.91,273.13,273.29,1030000,273.29 1953-08-17,275.71,276.13,273.92,275.04,910000,275.04 1953-08-14,276.74,277.33,274.89,275.71,1000000,275.71 1953-08-13,276.42,278.30,275.75,276.74,1040000,276.74 1953-08-12,275.30,276.92,273.98,276.42,990000,276.42 1953-08-11,275.32,276.05,273.72,275.30,940000,275.30 1953-08-10,275.54,276.48,274.39,275.32,1090000,275.32 1953-08-07,275.77,276.46,274.20,275.54,950000,275.54 1953-08-06,275.08,276.54,274.63,275.77,1200000,275.77 1953-08-05,275.40,275.40,273.19,275.08,1080000,275.08 1953-08-04,276.13,276.46,274.28,275.68,1000000,275.68 1953-08-03,275.38,277.19,274.71,276.13,1160000,276.13 1953-07-31,272.82,275.85,272.58,275.38,1320000,275.38 1953-07-30,270.49,273.41,270.49,272.82,1200000,272.82 1953-07-29,269.13,271.16,268.83,270.43,1000000,270.43 1953-07-28,268.46,269.52,267.30,269.13,1080000,269.13 1953-07-27,269.76,270.71,267.83,268.46,1210000,268.46 1953-07-24,269.94,270.92,268.79,269.76,890000,269.76 1953-07-23,269.39,271.14,268.89,269.94,1000000,269.94 1953-07-22,268.99,270.23,267.95,269.39,900000,269.39 1953-07-21,269.74,269.90,268.28,268.99,850000,268.99 1953-07-20,270.94,270.94,268.85,269.74,830000,269.74 1953-07-17,269.41,271.59,268.95,270.96,840000,270.96 1953-07-16,268.75,270.17,268.48,269.41,790000,269.41 1953-07-15,268.06,270.02,267.73,268.75,840000,268.75 1953-07-14,268.52,269.19,266.96,268.06,1030000,268.06 1953-07-13,271.06,271.16,268.08,268.52,1120000,268.52 1953-07-10,271.32,271.93,270.31,271.06,860000,271.06 1953-07-09,272.19,272.38,270.98,271.32,910000,271.32 1953-07-08,272.13,272.82,271.06,272.19,950000,272.19 1953-07-07,270.88,272.60,270.17,272.13,1030000,272.13 1953-07-06,270.53,271.71,269.94,270.88,820000,270.88 1953-07-03,270.23,271.44,269.41,270.53,830000,270.53 1953-07-02,269.39,271.20,269.15,270.23,1030000,270.23 1953-07-01,268.26,269.90,267.51,269.39,910000,269.39 1953-06-30,268.20,269.03,267.06,268.26,820000,268.26 1953-06-29,269.05,269.70,267.26,268.20,800000,268.20 1953-06-26,268.93,269.70,268.01,269.05,830000,269.05 1953-06-25,267.85,270.31,267.85,268.93,1160000,268.93 1953-06-24,268.48,269.11,266.80,267.79,1030000,267.79 1953-06-23,267.26,269.15,266.68,268.48,1050000,268.48 1953-06-22,265.88,268.70,265.88,267.26,1030000,267.26 1953-06-19,265.86,266.53,264.24,265.80,890000,265.80 1953-06-18,265.74,267.20,264.93,265.86,1010000,265.86 1953-06-17,262.88,266.57,262.88,265.74,1150000,265.74 1953-06-16,263.87,264.10,260.75,262.88,1370000,262.88 1953-06-15,265.78,266.41,263.12,263.87,1090000,263.87 1953-06-12,264.99,266.86,264.59,265.78,920000,265.78 1953-06-11,263.39,266.68,263.39,264.99,1220000,264.99 1953-06-10,263.39,264.18,260.89,263.35,1960000,263.35 1953-06-09,267.91,268.14,262.90,263.39,2200000,263.39 1953-06-08,268.32,269.46,267.28,267.91,1000000,267.91 1953-06-05,267.63,269.33,266.57,268.32,1160000,268.32 1953-06-04,269.60,269.98,266.17,267.63,1400000,267.63 1953-06-03,269.84,271.77,268.99,269.60,1050000,269.60 1953-06-02,268.40,270.41,267.00,269.84,1450000,269.84 1953-06-01,272.28,272.64,267.91,268.40,1490000,268.40 1953-05-29,271.48,273.07,270.88,272.28,920000,272.28 1953-05-28,273.76,273.76,270.65,271.48,1240000,271.48 1953-05-27,276.37,276.58,273.53,273.96,1330000,273.96 1953-05-26,277.43,277.43,275.12,276.37,1160000,276.37 1953-05-25,278.16,278.73,276.82,277.47,1180000,277.47 1953-05-22,278.51,279.28,276.72,278.16,1350000,278.16 1953-05-21,278.04,279.84,277.63,278.51,1590000,278.51 1953-05-20,275.91,278.53,275.12,278.04,1690000,278.04 1953-05-19,276.92,277.04,274.81,275.91,1120000,275.91 1953-05-18,277.90,278.14,275.75,276.92,1080000,276.92 1953-05-15,277.96,279.18,276.70,277.90,1200000,277.90 1953-05-14,276.80,278.71,276.25,277.96,1210000,277.96 1953-05-13,277.09,277.59,275.10,276.80,1120000,276.80 1953-05-12,278.79,278.91,276.29,277.09,1080000,277.09 1953-05-11,278.22,279.78,277.59,278.79,1010000,278.79 1953-05-08,277.43,278.55,275.85,278.22,1220000,278.22 1953-05-07,278.14,278.65,276.54,277.43,1110000,277.43 1953-05-06,278.22,279.32,276.94,278.14,1110000,278.14 1953-05-05,278.34,280.01,277.31,278.22,1290000,278.22 1953-05-04,275.66,279.46,275.52,278.34,1520000,278.34 1953-05-01,274.75,276.33,273.59,275.66,1200000,275.66 1953-04-30,275.38,276.07,273.31,274.75,1140000,274.75 1953-04-29,273.96,276.37,273.31,275.38,1310000,275.38 1953-04-28,272.70,274.59,271.32,273.96,1330000,273.96 1953-04-27,271.30,274.14,271.30,272.70,1400000,272.70 1953-04-24,270.73,272.30,269.25,271.26,1780000,271.26 1953-04-23,273.51,273.51,270.15,270.73,1920000,270.73 1953-04-22,275.48,275.93,272.86,273.55,1390000,273.55 1953-04-21,275.99,277.88,274.67,275.48,1250000,275.48 1953-04-20,274.41,276.62,272.80,275.99,1520000,275.99 1953-04-17,276.74,276.86,273.70,274.41,1430000,274.41 1953-04-16,277.35,278.51,275.97,276.74,1310000,276.74 1953-04-15,276.01,278.79,276.01,277.35,1580000,277.35 1953-04-14,274.73,276.76,273.86,275.85,1480000,275.85 1953-04-13,275.50,276.46,274.10,274.73,1280000,274.73 1953-04-10,276.23,276.52,274.28,275.50,1360000,275.50 1953-04-09,276.84,278.08,274.83,276.23,1520000,276.23 1953-04-08,275.38,278.85,275.38,276.84,1860000,276.84 1953-04-07,274.10,276.33,271.99,275.16,2500000,275.16 1953-04-06,279.42,279.42,272.40,274.10,3050000,274.10 1953-04-02,280.09,281.81,279.26,280.03,1720000,280.03 1953-04-01,279.87,281.47,277.53,280.09,2240000,280.09 1953-03-31,282.73,282.73,277.57,279.87,3120000,279.87 1953-03-30,286.16,286.16,281.59,283.07,2740000,283.07 1953-03-27,286.60,288.63,285.97,287.33,1640000,287.33 1953-03-26,287.98,289.08,285.63,286.60,2000000,286.60 1953-03-25,288.83,290.78,287.47,287.98,2320000,287.98 1953-03-24,287.39,289.18,286.72,288.83,1970000,288.83 1953-03-23,289.69,289.69,286.74,287.39,1750000,287.39 1953-03-20,289.97,291.01,288.63,289.69,1730000,289.69 1953-03-19,290.32,291.09,288.49,289.97,1840000,289.97 1953-03-18,290.64,291.96,289.26,290.32,2110000,290.32 1953-03-17,289.52,291.78,289.10,290.64,2110000,290.64 1953-03-16,289.04,290.52,288.08,289.52,1770000,289.52 1953-03-13,288.00,289.59,286.76,289.04,1760000,289.04 1953-03-12,288.02,289.14,286.70,288.00,1780000,288.00 1953-03-11,285.22,288.75,284.94,288.02,1890000,288.02 1953-03-10,284.90,285.97,283.17,285.22,1530000,285.22 1953-03-09,284.82,285.99,283.88,284.90,1600000,284.90 1953-03-06,283.86,285.28,283.01,284.82,1690000,284.82 1953-03-05,283.70,284.84,282.46,283.86,1540000,283.86 1953-03-04,284.71,286.09,282.52,283.70,2010000,283.70 1953-03-03,284.71,286.40,283.84,285.99,1850000,285.99 1953-03-02,284.27,285.67,283.09,284.71,1760000,284.71 1953-02-27,284.35,285.40,282.32,284.27,1990000,284.27 1953-02-26,284.45,285.95,283.27,284.35,2290000,284.35 1953-02-25,282.99,285.22,281.93,284.45,2360000,284.45 1953-02-24,282.04,285.04,282.04,282.99,2300000,282.99 1953-02-20,281.55,283.29,280.74,281.89,1400000,281.89 1953-02-19,281.14,283.01,280.51,281.55,1390000,281.55 1953-02-18,281.51,281.96,279.72,281.14,1220000,281.14 1953-02-17,282.18,282.73,280.23,281.51,1290000,281.51 1953-02-16,283.11,284.25,281.71,282.18,1330000,282.18 1953-02-13,281.57,283.86,281.10,283.11,1350000,283.11 1953-02-11,281.67,283.05,280.53,281.57,1240000,281.57 1953-02-10,281.96,283.50,280.84,281.67,1350000,281.67 1953-02-09,282.85,283.31,279.93,281.96,1780000,281.96 1953-02-06,286.20,286.42,282.14,282.85,1870000,282.85 1953-02-05,289.04,289.04,285.16,286.20,1900000,286.20 1953-02-04,290.19,290.84,288.33,289.08,1660000,289.08 1953-02-03,290.03,290.88,287.90,290.19,1560000,290.19 1953-02-02,289.77,290.94,288.00,290.03,1890000,290.03 1953-01-30,287.96,290.46,287.54,289.77,1760000,289.77 1953-01-29,287.39,289.12,286.44,287.96,1830000,287.96 1953-01-28,286.81,288.21,285.87,287.39,1640000,287.39 1953-01-27,286.54,287.96,285.75,286.81,1550000,286.81 1953-01-26,286.89,287.68,285.12,286.54,1420000,286.54 1953-01-23,287.84,288.59,285.77,286.89,1340000,286.89 1953-01-22,287.60,288.87,286.70,287.84,1380000,287.84 1953-01-21,288.00,288.63,286.56,287.60,1300000,287.60 1953-01-20,286.97,289.16,286.28,288.00,1490000,288.00 1953-01-19,287.17,287.98,285.30,286.97,1360000,286.97 1953-01-16,288.18,288.90,285.12,287.17,1710000,287.17 1953-01-15,287.37,288.85,286.40,288.18,1450000,288.18 1953-01-14,286.85,288.47,285.63,287.37,1370000,287.37 1953-01-13,285.24,288.63,285.10,286.85,1680000,286.85 1953-01-12,287.52,287.88,284.29,285.24,1500000,285.24 1953-01-09,290.36,290.46,286.09,287.52,2080000,287.52 1953-01-08,290.76,292.02,289.48,290.36,1780000,290.36 1953-01-07,291.96,291.96,288.69,290.76,1760000,290.76 1953-01-06,293.79,294.25,290.25,292.18,2080000,292.18 1953-01-05,292.14,295.06,291.51,293.79,2130000,293.79 1953-01-02,291.90,293.56,290.30,292.14,1450000,292.14 1952-12-31,292.00,293.50,290.86,291.90,2050000,291.90 1952-12-30,289.65,292.83,289.46,292.00,2070000,292.00 1952-12-29,288.23,290.74,287.66,289.65,1820000,289.65 1952-12-26,287.37,289.10,285.67,288.23,1290000,288.23 1952-12-24,286.99,288.59,285.69,287.37,1510000,287.37 1952-12-23,288.02,289.18,286.22,286.99,2100000,286.99 1952-12-22,286.52,288.85,285.55,288.02,2100000,288.02 1952-12-19,285.36,287.15,284.55,286.52,2050000,286.52 1952-12-18,285.67,286.68,284.41,285.36,1860000,285.36 1952-12-17,286.16,286.95,284.55,285.67,1700000,285.67 1952-12-16,285.99,287.58,285.00,286.16,1980000,286.16 1952-12-15,285.20,287.13,284.45,285.99,1940000,285.99 1952-12-12,284.57,286.18,283.76,285.20,2030000,285.20 1952-12-11,284.55,285.69,283.48,284.57,1790000,284.57 1952-12-10,285.12,286.03,282.77,284.55,1880000,284.55 1952-12-09,283.62,286.32,283.25,285.12,2120000,285.12 1952-12-08,282.06,284.37,281.45,283.62,1790000,283.62 1952-12-05,281.63,283.03,280.68,282.06,1510000,282.06 1952-12-04,282.89,283.82,281.10,281.63,1570000,281.63 1952-12-03,283.78,284.69,282.00,282.89,1610000,282.89 1952-12-02,283.70,284.65,281.89,283.78,1610000,283.78 1952-12-01,283.66,285.20,282.58,283.70,2100000,283.70 1952-11-28,282.44,284.65,281.59,283.66,2160000,283.66 1952-11-26,280.90,283.13,279.93,282.44,1920000,282.44 1952-11-25,281.08,282.32,279.99,280.90,1930000,280.90 1952-11-24,279.32,281.59,278.67,281.08,2100000,281.08 1952-11-21,279.50,280.31,278.16,279.32,1760000,279.32 1952-11-20,280.05,280.80,278.02,279.50,1740000,279.50 1952-11-19,278.04,281.16,277.78,280.05,2350000,280.05 1952-11-18,274.45,279.03,274.20,278.04,2250000,278.04 1952-11-17,273.27,275.16,272.44,274.45,1490000,274.45 1952-11-14,272.54,274.10,271.22,273.27,1700000,273.27 1952-11-13,271.97,273.68,271.16,272.54,1330000,272.54 1952-11-12,273.47,274.28,271.30,271.97,1490000,271.97 1952-11-10,273.47,274.39,272.11,273.47,1360000,273.47 1952-11-07,272.58,274.77,271.89,273.47,1540000,273.47 1952-11-06,271.30,273.82,268.89,272.58,1390000,272.58 1952-11-05,270.65,274.77,270.65,271.30,2030000,271.30 1952-11-03,269.23,271.53,268.79,270.23,1670000,270.23 1952-10-31,265.78,269.96,265.78,269.23,1760000,269.23 1952-10-30,265.46,266.57,264.54,265.72,1090000,265.72 1952-10-29,265.72,266.72,264.65,265.46,1020000,265.46 1952-10-28,265.90,266.80,264.87,265.72,1080000,265.72 1952-10-27,265.46,266.65,264.73,265.90,1000000,265.90 1952-10-24,263.87,266.31,263.39,265.46,1060000,265.46 1952-10-23,263.06,264.93,262.01,263.87,1260000,263.87 1952-10-22,265.64,265.64,262.60,263.06,1160000,263.06 1952-10-21,266.63,267.18,265.09,265.84,990000,265.84 1952-10-20,267.30,268.06,265.37,266.63,1050000,266.63 1952-10-17,265.21,268.36,265.21,267.30,1360000,267.30 1952-10-16,267.12,267.45,263.33,264.87,1730000,264.87 1952-10-15,270.43,270.59,266.09,267.12,1730000,267.12 1952-10-14,270.61,271.59,269.48,270.43,1130000,270.43 1952-10-10,270.98,271.81,269.94,270.61,1070000,270.61 1952-10-09,271.40,272.36,270.15,270.98,1090000,270.98 1952-10-08,269.88,271.91,269.52,271.40,1260000,271.40 1952-10-07,270.00,271.04,268.97,269.88,950000,269.88 1952-10-06,270.55,271.20,269.29,270.00,1070000,270.00 1952-10-03,270.75,271.85,269.52,270.55,980000,270.55 1952-10-02,270.17,271.55,269.72,270.75,1040000,270.75 1952-10-01,270.61,271.08,269.21,270.17,1060000,270.17 1952-09-30,271.73,272.21,269.98,270.61,1120000,270.61 1952-09-29,271.95,272.76,270.51,271.73,970000,271.73 1952-09-26,272.42,273.33,271.14,271.95,1180000,271.95 1952-09-25,272.26,273.74,271.44,272.42,1210000,272.42 1952-09-24,271.65,273.19,271.06,272.26,1390000,272.26 1952-09-23,270.77,272.24,269.48,271.65,1240000,271.65 1952-09-22,270.55,272.09,269.56,270.77,1160000,270.77 1952-09-19,269.72,271.26,268.62,270.55,1150000,270.55 1952-09-18,270.43,271.12,268.81,269.72,1030000,269.72 1952-09-17,269.03,271.18,268.89,270.43,1000000,270.43 1952-09-16,268.38,269.74,267.08,269.03,1140000,269.03 1952-09-15,271.02,271.14,267.91,268.38,1100000,268.38 1952-09-12,272.11,272.46,269.66,271.02,1040000,271.02 1952-09-11,271.65,273.25,270.90,272.11,970000,272.11 1952-09-10,273.01,273.01,269.56,271.65,1590000,271.65 1952-09-09,275.87,276.29,273.13,273.53,1310000,273.53 1952-09-08,276.50,277.55,275.38,275.87,1170000,275.87 1952-09-05,276.76,277.43,275.18,276.50,1040000,276.50 1952-09-04,277.15,278.10,276.03,276.76,1120000,276.76 1952-09-03,276.40,278.16,275.95,277.15,1200000,277.15 1952-09-02,275.10,277.25,275.10,276.40,970000,276.40 1952-08-29,274.41,275.93,274.12,275.04,890000,275.04 1952-08-28,273.84,275.28,273.35,274.41,980000,274.41 1952-08-27,273.17,274.33,272.72,273.84,930000,273.84 1952-08-26,273.57,274.37,272.28,273.17,890000,273.17 1952-08-25,274.43,274.61,272.86,273.57,840000,273.57 1952-08-22,274.45,275.24,273.74,274.43,910000,274.43 1952-08-21,274.35,275.24,273.43,274.45,800000,274.45 1952-08-20,274.14,275.62,273.41,274.35,960000,274.35 1952-08-19,274.31,275.06,272.95,274.14,980000,274.14 1952-08-18,277.19,277.19,273.90,274.31,1090000,274.31 1952-08-15,277.75,278.61,276.54,277.37,890000,277.37 1952-08-14,277.88,278.75,277.04,277.75,930000,277.75 1952-08-13,278.14,278.81,276.62,277.88,990000,277.88 1952-08-12,280.03,280.03,277.39,278.14,1110000,278.14 1952-08-11,279.84,281.47,279.15,280.29,1160000,280.29 1952-08-08,279.38,280.92,278.49,279.84,1170000,279.84 1952-08-07,279.07,280.09,278.34,279.38,1180000,279.38 1952-08-06,279.50,280.21,277.88,279.07,1140000,279.07 1952-08-05,279.87,280.03,277.96,279.50,1050000,279.50 1952-08-04,279.80,280.51,278.59,279.87,950000,279.87 1952-08-01,279.56,280.49,278.81,279.80,1050000,279.80 1952-07-31,279.24,280.25,278.34,279.56,1230000,279.56 1952-07-30,278.57,280.07,277.78,279.24,1240000,279.24 1952-07-29,277.94,279.40,277.17,278.57,1010000,278.57 1952-07-28,277.71,278.95,276.92,277.94,1030000,277.94 1952-07-25,279.26,279.76,277.02,277.71,1130000,277.71 1952-07-24,277.63,280.05,277.63,279.26,1270000,279.26 1952-07-23,275.95,278.28,275.64,277.63,1020000,277.63 1952-07-22,274.91,276.54,274.14,275.95,910000,275.95 1952-07-21,273.90,275.54,273.17,274.91,780000,274.91 1952-07-18,275.62,275.85,273.11,273.90,1020000,273.90 1952-07-17,276.76,277.17,274.95,275.62,1010000,275.62 1952-07-16,276.76,278.02,275.83,276.76,1120000,276.76 1952-07-15,275.08,277.35,274.81,276.76,1220000,276.76 1952-07-14,274.22,276.07,274.06,275.08,1090000,275.08 1952-07-11,272.58,274.89,272.28,274.22,1040000,274.22 1952-07-10,273.25,273.80,271.73,272.58,1010000,272.58 1952-07-09,274.43,275.62,272.93,273.25,1120000,273.25 1952-07-08,274.20,275.10,273.51,274.43,850000,274.43 1952-07-07,274.95,275.58,273.27,274.20,1080000,274.20 1952-07-03,274.87,275.64,273.59,274.95,1150000,274.95 1952-07-02,275.46,276.09,273.86,274.87,1320000,274.87 1952-07-01,274.26,276.25,273.94,275.46,1450000,275.46 1952-06-30,272.44,274.97,272.30,274.26,1380000,274.26 1952-06-27,271.24,272.95,270.77,272.44,1210000,272.44 1952-06-26,270.45,271.85,269.88,271.24,1190000,271.24 1952-06-25,269.92,270.98,268.75,270.45,1230000,270.45 1952-06-24,269.50,270.47,268.81,269.92,1200000,269.92 1952-06-23,270.19,271.28,268.64,269.50,1200000,269.50 1952-06-20,269.54,270.84,268.89,270.19,1190000,270.19 1952-06-19,269.09,270.59,268.40,269.54,1320000,269.54 1952-06-18,268.03,269.48,267.63,269.09,1270000,269.09 1952-06-17,267.83,268.68,266.80,268.03,920000,268.03 1952-06-16,268.56,269.15,267.28,267.83,980000,267.83 1952-06-13,267.91,269.17,267.28,268.56,1130000,268.56 1952-06-12,267.93,269.03,266.90,267.91,1370000,267.91 1952-06-11,267.67,268.52,266.33,267.93,1190000,267.93 1952-06-10,269.15,269.15,266.76,267.67,1220000,267.67 1952-06-09,268.03,269.92,267.67,269.15,1270000,269.15 1952-06-06,266.29,268.95,266.21,268.03,1520000,268.03 1952-06-05,263.77,266.80,263.77,266.29,1410000,266.29 1952-06-04,262.09,264.20,261.91,263.67,1200000,263.67 1952-06-03,262.31,262.82,260.83,262.09,940000,262.09 1952-06-02,262.94,264.61,261.48,262.31,1190000,262.31 1952-05-29,262.78,263.51,261.62,262.94,1100000,262.94 1952-05-28,263.92,264.54,262.25,262.78,1130000,262.78 1952-05-27,264.22,265.17,262.82,263.92,1040000,263.92 1952-05-26,263.23,264.87,262.62,264.22,940000,264.22 1952-05-23,263.33,264.59,262.54,263.27,1150000,263.27 1952-05-22,261.78,264.02,261.54,263.33,1360000,263.33 1952-05-21,261.26,262.78,260.89,261.78,1210000,261.78 1952-05-20,260.06,262.66,259.51,261.26,1150000,261.26 1952-05-19,259.88,261.12,259.15,260.06,780000,260.06 1952-05-16,260.10,260.93,259.00,259.82,910000,259.82 1952-05-15,260.99,261.07,258.66,260.10,1050000,260.10 1952-05-14,261.99,262.62,260.26,260.99,950000,260.99 1952-05-13,261.72,263.04,260.87,261.99,890000,261.99 1952-05-12,262.50,262.86,260.83,261.72,800000,261.72 1952-05-09,262.39,263.47,260.99,262.74,960000,262.74 1952-05-08,261.99,263.77,261.58,262.39,1230000,262.39 1952-05-07,261.01,262.70,259.96,261.99,1120000,261.99 1952-05-06,261.54,262.29,260.02,261.01,1120000,261.01 1952-05-05,260.55,261.95,259.35,261.54,860000,261.54 1952-05-02,257.67,260.93,257.67,260.00,1300000,260.00 1952-05-01,257.44,257.44,254.70,256.35,1400000,256.35 1952-04-30,259.34,259.39,257.06,257.63,1000000,257.63 1952-04-29,259.95,260.52,258.19,259.34,1170000,259.34 1952-04-28,260.27,260.96,258.65,259.95,980000,259.95 1952-04-25,258.86,260.08,257.88,259.80,1240000,259.80 1952-04-24,259.97,260.26,257.04,258.86,1580000,258.86 1952-04-23,261.10,261.56,259.41,259.97,1090000,259.97 1952-04-22,261.63,263.03,260.64,261.10,1240000,261.10 1952-04-21,260.14,262.50,259.60,261.63,1110000,261.63 1952-04-18,259.85,261.88,258.84,260.52,1240000,260.52 1952-04-17,261.48,261.60,258.40,259.85,1620000,259.85 1952-04-16,261.29,263.05,260.03,261.48,1400000,261.48 1952-04-15,264.10,264.29,260.33,261.29,1720000,261.29 1952-04-14,266.29,267.11,263.24,264.10,1790000,264.10 1952-04-10,265.04,266.96,264.31,265.75,1130000,265.75 1952-04-09,265.29,266.09,263.89,265.04,980000,265.04 1952-04-08,263.38,265.88,262.57,265.29,1090000,265.29 1952-04-07,265.31,265.31,262.44,263.38,1230000,263.38 1952-04-04,266.80,266.86,264.45,265.62,1190000,265.62 1952-04-03,267.03,267.87,265.81,266.80,1280000,266.80 1952-04-02,267.22,268.08,265.79,267.03,1260000,267.03 1952-04-01,269.46,269.81,266.42,267.22,1720000,267.22 1952-03-31,269.00,270.40,267.17,269.46,1680000,269.46 1952-03-28,265.21,267.76,265.06,266.96,1560000,266.96 1952-03-27,263.87,265.88,263.20,265.21,1370000,265.21 1952-03-26,264.28,265.06,262.82,263.87,1030000,263.87 1952-03-25,265.52,265.52,263.72,264.28,1060000,264.28 1952-03-24,265.69,266.48,264.58,265.60,1040000,265.60 1952-03-21,265.33,267.05,264.93,265.62,1290000,265.62 1952-03-20,264.37,266.23,263.70,265.33,1240000,265.33 1952-03-19,264.10,265.16,262.80,264.37,1090000,264.37 1952-03-18,264.08,265.08,262.59,264.10,1170000,264.10 1952-03-17,264.43,265.48,263.26,264.08,1150000,264.08 1952-03-14,264.24,265.46,262.50,264.05,1350000,264.05 1952-03-13,263.78,265.62,262.65,264.24,1270000,264.24 1952-03-12,262.76,264.56,261.75,263.78,1310000,263.78 1952-03-11,262.76,263.80,261.25,262.76,1210000,262.76 1952-03-10,264.14,264.64,262.32,262.76,1170000,262.76 1952-03-07,264.03,264.89,262.53,263.87,1410000,263.87 1952-03-06,264.66,265.04,262.72,264.03,1210000,264.03 1952-03-05,263.95,266.17,263.61,264.66,1380000,264.66 1952-03-04,260.35,264.24,260.35,263.95,1570000,263.95 1952-03-03,260.27,261.17,258.95,260.08,1020000,260.08 1952-02-29,260.49,261.46,259.36,260.08,1000000,260.08 1952-02-28,259.68,261.79,259.28,260.49,1150000,260.49 1952-02-27,259.30,260.49,257.44,259.68,1260000,259.68 1952-02-26,260.58,260.98,258.69,259.30,1080000,259.30 1952-02-25,261.40,262.86,259.89,260.58,1200000,260.58 1952-02-21,258.49,261.63,258.49,259.60,1360000,259.60 1952-02-20,261.37,261.46,257.46,258.49,1970000,258.49 1952-02-19,265.14,265.14,260.93,261.37,1630000,261.37 1952-02-18,266.30,266.94,264.35,265.35,1140000,265.35 1952-02-15,265.88,267.57,265.29,266.27,1200000,266.27 1952-02-14,266.21,266.67,264.54,265.88,1340000,265.88 1952-02-13,268.37,268.37,265.52,266.21,1300000,266.21 1952-02-11,269.83,269.88,267.57,268.45,1140000,268.45 1952-02-08,268.35,270.48,267.61,269.85,1350000,269.85 1952-02-07,268.77,269.50,267.05,268.35,1170000,268.35 1952-02-06,269.04,270.27,267.38,268.77,1310000,268.77 1952-02-05,269.79,270.17,266.80,269.04,1590000,269.04 1952-02-04,272.51,272.64,268.79,269.79,1640000,269.79 1952-02-01,270.69,272.91,269.94,271.68,1350000,271.68 1952-01-31,270.71,272.18,268.05,270.69,1810000,270.69 1952-01-30,274.00,275.38,270.53,270.71,1880000,270.71 1952-01-29,274.17,275.44,272.91,274.00,1730000,274.00 1952-01-28,273.69,275.13,273.00,274.17,1590000,274.17 1952-01-25,273.90,275.07,272.43,273.41,1650000,273.41 1952-01-24,274.27,275.19,272.68,273.90,1570000,273.90 1952-01-23,275.40,275.95,273.44,274.27,1680000,274.27 1952-01-22,274.10,276.26,273.58,275.40,1920000,275.40 1952-01-21,272.93,274.55,272.32,274.10,1730000,274.10 1952-01-18,271.91,272.69,271.03,272.10,1740000,272.10 1952-01-17,271.13,273.00,270.53,271.91,1590000,271.91 1952-01-16,270.46,272.28,269.27,271.13,1430000,271.13 1952-01-15,271.59,272.09,269.44,270.46,1340000,270.46 1952-01-14,270.73,272.70,270.36,271.59,1510000,271.59 1952-01-11,269.46,271.20,268.74,270.31,1760000,270.31 1952-01-10,268.14,271.09,268.14,269.46,1520000,269.46 1952-01-09,268.66,270.04,266.34,268.08,1370000,268.08 1952-01-08,270.34,270.98,268.14,268.66,1390000,268.66 1952-01-07,271.26,272.60,269.94,270.34,1540000,270.34 1952-01-04,270.38,271.95,269.73,271.03,1480000,271.03 1952-01-03,269.86,271.28,268.58,270.38,1220000,270.38 1952-01-02,269.23,271.01,268.24,269.86,1070000,269.86 1951-12-31,268.52,270.00,267.84,269.23,1440000,269.23 1951-12-28,266.74,269.02,266.30,268.18,1470000,268.18 1951-12-27,264.06,267.26,263.85,266.74,1460000,266.74 1951-12-26,265.79,266.67,263.26,264.06,1520000,264.06 1951-12-24,265.94,266.69,264.91,265.79,680000,265.79 1951-12-21,267.45,267.78,265.37,266.34,1250000,266.34 1951-12-20,267.61,268.91,266.42,267.45,1340000,267.45 1951-12-19,266.61,268.93,265.92,267.61,1510000,267.61 1951-12-18,265.79,267.45,265.14,266.61,1290000,266.61 1951-12-17,265.48,266.71,264.50,265.79,1220000,265.79 1951-12-14,265.81,267.07,264.60,265.71,1360000,265.71 1951-12-13,266.09,266.92,264.56,265.81,1380000,265.81 1951-12-12,265.77,267.24,264.33,266.09,1280000,266.09 1951-12-11,267.38,267.68,265.14,265.77,1360000,265.77 1951-12-10,266.90,268.45,266.07,267.38,1340000,267.38 1951-12-07,266.23,268.95,265.96,266.99,1990000,266.99 1951-12-06,263.85,266.90,263.85,266.23,1840000,266.23 1951-12-05,264.29,265.21,262.71,263.72,1330000,263.72 1951-12-04,263.24,265.19,262.48,264.29,1280000,264.29 1951-12-03,262.29,264.77,261.73,263.24,1220000,263.24 1951-11-30,258.96,261.92,258.68,261.27,1530000,261.27 1951-11-29,258.64,259.93,257.29,258.96,1070000,258.96 1951-11-28,259.46,260.43,258.12,258.64,1150000,258.64 1951-11-27,257.47,260.36,257.47,259.46,1310000,259.46 1951-11-26,255.95,258.38,255.20,257.44,1180000,257.44 1951-11-23,258.72,258.89,255.93,256.95,1210000,256.95 1951-11-21,259.30,260.15,258.16,258.72,1090000,258.72 1951-11-20,259.70,260.04,257.57,259.30,1130000,259.30 1951-11-19,260.82,261.36,258.77,259.70,1030000,259.70 1951-11-16,260.91,261.06,259.00,260.39,1140000,260.39 1951-11-15,261.27,262.29,260.32,260.91,1200000,260.91 1951-11-14,260.41,262.01,259.85,261.27,1220000,261.27 1951-11-13,261.29,262.18,259.39,260.41,1160000,260.41 1951-11-09,257.81,261.21,257.81,259.91,1470000,259.91 1951-11-08,257.14,258.35,254.91,257.14,1410000,257.14 1951-11-07,259.76,260.37,256.58,257.14,1490000,257.14 1951-11-05,259.57,262.10,258.59,259.76,1130000,259.76 1951-11-02,264.06,264.37,261.01,261.94,1230000,261.94 1951-11-01,262.35,265.82,261.86,264.06,1430000,264.06 1951-10-31,260.52,263.15,258.44,262.35,1490000,262.35 1951-10-30,260.43,263.46,259.69,260.52,1530000,260.52 1951-10-29,258.53,261.12,256.39,260.43,1780000,260.43 1951-10-26,264.17,264.26,260.08,262.27,1710000,262.27 1951-10-25,264.95,266.20,262.66,264.17,1360000,264.17 1951-10-24,263.50,266.79,263.22,264.95,1670000,264.95 1951-10-23,262.29,264.80,259.76,263.50,2110000,263.50 1951-10-22,265.90,265.90,259.46,262.29,2690000,262.29 1951-10-19,273.51,274.10,269.23,269.68,1990000,269.68 1951-10-18,273.53,274.75,272.22,273.51,1450000,273.51 1951-10-17,274.40,275.24,272.86,273.53,1460000,273.53 1951-10-16,275.74,276.02,272.50,274.40,1730000,274.40 1951-10-15,275.13,276.93,274.25,275.74,1720000,275.74 1951-10-11,272.76,274.68,271.80,274.10,1760000,274.10 1951-10-10,273.38,274.47,271.46,272.76,1320000,272.76 1951-10-09,275.14,275.26,272.65,273.38,1750000,273.38 1951-10-08,275.53,276.59,274.23,275.14,1860000,275.14 1951-10-05,275.35,277.02,274.21,275.63,2080000,275.63 1951-10-04,275.87,276.93,274.49,275.35,1810000,275.35 1951-10-03,274.34,277.30,274.29,275.87,2780000,275.87 1951-10-02,272.56,275.42,272.13,274.34,1870000,274.34 1951-10-01,271.16,273.25,270.23,272.56,1330000,272.56 1951-09-28,271.31,272.24,269.66,271.16,1390000,271.16 1951-09-27,272.24,272.93,269.77,271.31,1540000,271.31 1951-09-26,272.24,273.67,270.88,272.24,1520000,272.24 1951-09-25,270.77,273.51,270.05,272.24,1740000,272.24 1951-09-24,271.83,271.83,269.08,270.77,1630000,270.77 1951-09-21,274.10,274.10,270.21,272.11,2180000,272.11 1951-09-20,274.27,276.02,272.58,274.10,2100000,274.10 1951-09-19,274.38,276.09,273.08,274.27,2070000,274.27 1951-09-18,275.09,275.63,271.91,274.38,2030000,274.38 1951-09-17,276.06,277.12,274.12,275.09,1800000,275.09 1951-09-14,276.37,277.51,274.01,276.06,2170000,276.06 1951-09-13,275.31,277.15,274.34,276.37,2350000,276.37 1951-09-12,273.88,276.56,273.32,275.31,2180000,275.31 1951-09-11,275.25,276.24,272.63,273.88,2040000,273.88 1951-09-10,273.89,276.63,273.62,275.25,2190000,275.25 1951-09-07,272.28,274.54,271.53,273.89,1970000,273.89 1951-09-06,272.48,273.98,271.23,272.28,2150000,272.28 1951-09-05,270.63,273.11,270.25,272.48,1850000,272.48 1951-09-04,270.25,272.28,269.49,270.63,1520000,270.63 1951-08-31,269.94,271.64,268.58,270.25,1530000,270.25 1951-08-30,268.18,270.68,267.98,269.94,1950000,269.94 1951-08-29,265.56,268.62,265.39,268.18,1520000,268.18 1951-08-28,265.59,266.81,264.42,265.56,1280000,265.56 1951-08-27,266.30,267.06,264.54,265.59,1080000,265.59 1951-08-24,265.65,267.53,264.94,266.30,1210000,266.30 1951-08-23,264.07,266.26,262.89,265.65,1230000,265.65 1951-08-22,265.30,265.56,262.80,264.07,1130000,264.07 1951-08-21,266.19,267.66,264.47,265.30,1400000,265.30 1951-08-20,266.17,267.42,264.98,266.19,1130000,266.19 1951-08-17,265.48,267.44,264.54,266.17,1620000,266.17 1951-08-16,264.27,266.63,263.78,265.48,1750000,265.48 1951-08-15,262.88,264.72,262.04,264.27,1340000,264.27 1951-08-14,263.06,263.98,261.57,262.88,1180000,262.88 1951-08-13,261.92,264.76,261.26,263.06,1320000,263.06 1951-08-10,262.69,263.26,260.67,261.92,1260000,261.92 1951-08-09,263.73,264.43,261.77,262.69,1500000,262.69 1951-08-08,264.94,265.52,262.24,263.73,1410000,263.73 1951-08-07,265.21,266.52,263.85,264.94,1810000,264.94 1951-08-06,262.98,265.72,261.88,265.21,1600000,265.21 1951-08-03,262.89,264.78,261.25,262.98,1570000,262.98 1951-08-02,260.05,264.05,260.05,262.89,2130000,262.89 1951-08-01,257.86,260.72,256.81,259.89,1680000,259.89 1951-07-31,260.30,260.30,256.64,257.86,1550000,257.86 1951-07-30,259.23,262.21,258.89,260.70,1600000,260.70 1951-07-27,259.09,259.87,256.92,259.23,1450000,259.23 1951-07-26,258.11,259.94,256.46,259.09,1480000,259.09 1951-07-25,258.94,260.79,257.33,258.11,1870000,258.11 1951-07-24,255.68,259.40,255.36,258.94,1740000,258.94 1951-07-23,253.73,256.35,253.44,255.68,1320000,255.68 1951-07-20,253.75,255.48,252.78,253.73,1390000,253.73 1951-07-19,253.67,254.56,252.24,253.75,1120000,253.75 1951-07-18,253.89,255.18,252.84,253.67,1370000,253.67 1951-07-17,252.31,254.18,251.05,253.89,1280000,253.89 1951-07-16,254.32,254.98,251.72,252.31,1200000,252.31 1951-07-13,252.59,255.36,252.39,254.32,1320000,254.32 1951-07-12,250.97,253.11,250.70,252.59,1050000,252.59 1951-07-11,250.00,251.75,249.31,250.97,970000,250.97 1951-07-10,250.65,251.41,249.09,250.00,990000,250.00 1951-07-09,250.01,252.10,249.20,250.65,1110000,250.65 1951-07-06,250.27,251.30,248.78,250.01,1170000,250.01 1951-07-05,247.01,250.90,247.01,250.27,1410000,250.27 1951-07-03,244.07,246.77,244.07,245.92,1250000,245.92 1951-07-02,242.64,244.92,241.06,243.98,1350000,243.98 1951-06-29,244.00,244.36,240.72,242.64,1730000,242.64 1951-06-28,246.84,247.22,242.57,244.00,1940000,244.00 1951-06-27,246.28,247.98,244.90,246.84,1360000,246.84 1951-06-26,245.30,247.44,244.29,246.28,1260000,246.28 1951-06-25,245.99,245.99,241.84,245.30,2440000,245.30 1951-06-22,250.21,250.21,246.66,247.86,1340000,247.86 1951-06-21,251.57,251.57,249.20,250.43,1100000,250.43 1951-06-20,253.53,254.47,251.41,251.86,1120000,251.86 1951-06-19,253.80,254.54,251.70,253.53,1100000,253.53 1951-06-18,254.03,255.23,252.55,253.80,1050000,253.80 1951-06-15,252.46,255.05,252.26,254.03,1370000,254.03 1951-06-14,250.21,253.11,250.21,252.46,1300000,252.46 1951-06-13,250.57,251.35,248.73,250.03,1060000,250.03 1951-06-12,251.56,252.64,249.75,250.57,1200000,250.57 1951-06-11,250.39,252.77,249.76,251.56,1220000,251.56 1951-06-08,250.81,251.27,249.19,250.39,1000000,250.39 1951-06-07,249.64,251.73,249.24,250.81,1340000,250.81 1951-06-06,247.66,250.73,247.66,249.64,1200000,249.64 1951-06-05,246.79,248.15,244.91,247.59,1180000,247.59 1951-06-04,249.14,249.14,246.11,246.79,1100000,246.79 1951-06-01,249.65,250.15,247.85,249.33,9810000,249.33 1951-05-31,248.44,251.68,248.32,249.65,1220000,249.65 1951-05-29,247.03,249.52,246.43,248.44,1190000,248.44 1951-05-28,245.83,248.20,245.60,247.03,1240000,247.03 1951-05-25,245.78,247.57,244.84,245.27,1210000,245.27 1951-05-24,246.94,246.94,241.89,245.78,2580000,245.78 1951-05-23,249.30,249.79,246.58,247.03,1540000,247.03 1951-05-22,249.98,251.72,248.49,249.30,1440000,249.30 1951-05-21,250.63,251.36,248.03,249.98,1580000,249.98 1951-05-18,254.57,255.03,250.01,250.10,1660000,250.10 1951-05-17,252.40,255.49,252.40,254.57,1370000,254.57 1951-05-16,252.08,254.19,250.81,252.14,1660000,252.14 1951-05-15,256.08,256.24,251.02,252.08,2020000,252.08 1951-05-14,257.26,258.10,255.45,256.08,1250000,256.08 1951-05-11,260.07,260.93,257.91,258.56,1640000,258.56 1951-05-10,261.49,261.83,259.14,260.07,1660000,260.07 1951-05-09,261.10,262.82,260.24,261.49,1960000,261.49 1951-05-08,261.23,262.05,259.31,261.10,1600000,261.10 1951-05-07,261.76,262.48,259.60,261.23,1580000,261.23 1951-05-04,263.13,264.44,261.74,262.77,2050000,262.77 1951-05-03,261.27,263.69,260.31,263.13,2060000,263.13 1951-05-02,260.71,262.41,259.70,261.27,1900000,261.27 1951-05-01,259.13,261.80,258.23,260.71,1760000,260.71 1951-04-30,259.08,260.83,257.99,259.13,1790000,259.13 1951-04-27,257.33,259.95,257.33,258.96,2120000,258.96 1951-04-26,254.92,257.98,254.92,257.13,1800000,257.13 1951-04-25,254.19,255.38,252.53,254.75,1520000,254.75 1951-04-24,255.12,255.67,253.48,254.19,1420000,254.19 1951-04-23,255.02,255.92,253.94,255.12,1160000,255.12 1951-04-20,254.92,255.51,253.44,254.82,940000,254.82 1951-04-19,256.01,256.53,253.99,254.92,1520000,254.92 1951-04-18,255.34,257.30,254.53,256.01,1780000,256.01 1951-04-17,254.85,256.06,253.88,255.34,1470000,255.34 1951-04-16,256.18,257.03,254.05,254.85,1730000,254.85 1951-04-13,251.76,255.31,251.76,254.75,2120000,254.75 1951-04-12,249.76,252.10,249.37,251.66,1530000,251.66 1951-04-11,250.42,250.57,247.70,249.76,1420000,249.76 1951-04-10,250.57,251.88,249.52,250.42,1280000,250.42 1951-04-09,250.28,251.46,249.62,250.57,1110000,250.57 1951-04-06,250.32,252.22,250.06,250.83,1450000,250.83 1951-04-05,247.75,250.91,247.75,250.32,1790000,250.32 1951-04-04,246.02,247.80,244.98,247.31,1300000,247.31 1951-04-03,246.63,247.69,245.46,246.02,1220000,246.02 1951-04-02,247.82,247.82,245.02,246.63,1280000,246.63 1951-03-30,246.95,249.25,246.95,248.53,1150000,248.53 1951-03-29,246.19,248.28,245.95,246.90,1300000,246.90 1951-03-28,248.74,249.15,245.34,246.19,1770000,246.19 1951-03-27,249.13,250.81,248.18,248.74,1250000,248.74 1951-03-26,248.14,249.79,247.04,249.13,1230000,249.13 1951-03-22,249.37,251.57,249.04,250.52,1290000,250.52 1951-03-21,247.87,250.39,247.45,249.37,1310000,249.37 1951-03-20,248.08,248.64,246.53,247.87,1020000,247.87 1951-03-19,249.03,249.45,246.45,248.08,1120000,248.08 1951-03-16,245.88,249.33,245.88,248.62,1660000,248.62 1951-03-15,243.95,245.80,242.06,244.85,2070000,244.85 1951-03-14,245.88,246.56,243.13,243.95,2110000,243.95 1951-03-13,249.35,249.35,244.61,245.88,2330000,245.88 1951-03-12,252.00,252.00,248.70,249.89,1640000,249.89 1951-03-09,252.81,254.27,251.98,252.75,1610000,252.75 1951-03-08,252.45,253.68,251.55,252.81,1440000,252.81 1951-03-07,251.55,253.41,250.71,252.45,1770000,252.45 1951-03-06,251.82,252.37,250.43,251.55,1490000,251.55 1951-03-05,253.43,253.43,250.23,251.82,1690000,251.82 1951-03-02,252.80,254.42,252.22,253.61,1570000,253.61 1951-03-01,252.05,253.73,250.96,252.80,1610000,252.80 1951-02-28,251.34,253.14,249.70,252.05,1640000,252.05 1951-02-27,253.18,253.73,250.81,251.34,1680000,251.34 1951-02-26,252.93,254.47,251.57,253.18,1650000,253.18 1951-02-23,252.28,253.59,251.21,252.18,1540000,252.18 1951-02-21,251.12,253.53,250.77,252.28,1670000,252.28 1951-02-20,251.67,252.15,248.78,251.12,2010000,251.12 1951-02-19,254.70,255.08,251.29,251.67,1910000,251.67 1951-02-16,253.61,255.58,253.10,254.90,1860000,254.90 1951-02-15,255.10,255.30,253.13,253.61,1700000,253.61 1951-02-14,255.71,256.34,253.34,255.10,2050000,255.10 1951-02-13,254.80,257.06,254.34,255.71,2400000,255.71 1951-02-09,253.34,255.58,253.08,254.24,2550000,254.24 1951-02-08,252.70,254.27,250.92,253.34,2120000,253.34 1951-02-07,254.47,254.47,251.69,252.70,2020000,252.70 1951-02-06,255.17,255.30,252.25,254.62,2370000,254.62 1951-02-05,253.92,256.06,252.91,255.17,2680000,255.17 1951-02-02,250.76,253.71,250.66,252.78,3030000,252.78 1951-02-01,248.83,251.17,247.04,250.76,2380000,250.76 1951-01-31,249.58,250.56,247.43,248.83,2340000,248.83 1951-01-30,248.64,250.46,247.49,249.58,2480000,249.58 1951-01-29,247.36,249.48,246.50,248.64,2630000,248.64 1951-01-26,242.22,245.42,241.86,244.51,2230000,244.51 1951-01-25,244.08,244.08,240.11,242.22,2520000,242.22 1951-01-24,245.30,246.28,243.45,244.36,1990000,244.36 1951-01-23,244.33,245.87,242.40,245.30,2080000,245.30 1951-01-22,246.91,247.48,242.70,244.33,2570000,244.33 1951-01-19,247.39,248.62,245.45,246.76,3170000,246.76 1951-01-18,248.01,249.07,245.60,247.39,3490000,247.39 1951-01-17,246.65,248.95,243.76,248.01,3880000,248.01 1951-01-16,245.02,247.64,244.76,246.65,3740000,246.65 1951-01-15,243.61,245.75,241.47,245.02,2830000,245.02 1951-01-12,244.72,245.87,242.77,243.81,2950000,243.81 1951-01-11,240.40,245.20,240.35,244.72,3490000,244.72 1951-01-10,243.50,244.61,239.12,240.40,3270000,240.40 1951-01-09,242.29,245.10,242.02,243.50,3800000,243.50 1951-01-08,240.68,243.05,239.62,242.29,2780000,242.29 1951-01-05,240.86,242.60,240.15,240.96,3390000,240.96 1951-01-04,238.99,241.71,237.64,240.86,3390000,240.86 1951-01-03,239.92,241.29,237.43,238.99,3370000,238.99 1951-01-02,235.41,240.46,234.93,239.92,3030000,239.92 1950-12-29,235.34,236.52,233.63,235.42,3440000,235.42 1950-12-28,234.21,236.25,233.02,235.34,3560000,235.34 1950-12-27,230.30,234.64,230.30,234.21,2940000,234.21 1950-12-26,231.54,232.41,228.44,229.65,2660000,229.65 1950-12-22,230.43,232.94,229.65,231.54,2720000,231.54 1950-12-21,231.20,232.02,229.06,230.43,3990000,230.43 1950-12-20,231.54,232.27,229.10,231.20,3510000,231.20 1950-12-19,231.01,233.05,229.77,231.54,3650000,231.54 1950-12-18,228.58,233.27,228.58,231.01,4500000,231.01 1950-12-15,225.89,226.57,223.19,224.70,2420000,224.70 1950-12-14,228.82,229.47,224.98,225.89,2660000,225.89 1950-12-13,229.27,230.35,227.42,228.82,2030000,228.82 1950-12-12,229.19,231.13,228.13,229.27,2140000,229.27 1950-12-11,227.30,230.78,227.05,229.19,2600000,229.19 1950-12-08,225.94,227.33,224.23,226.74,2310000,226.74 1950-12-07,226.16,227.35,224.41,225.94,1810000,225.94 1950-12-06,225.44,228.10,224.78,226.16,2010000,226.16 1950-12-05,222.33,225.97,222.01,225.44,1940000,225.44 1950-12-04,225.23,225.23,221.31,222.33,2510000,222.33 1950-12-01,227.60,230.42,227.05,228.89,1870000,228.89 1950-11-30,226.42,229.70,225.97,227.60,2080000,227.60 1950-11-29,227.78,227.78,223.82,226.42,2770000,226.42 1950-11-28,231.34,231.34,227.40,228.61,2970000,228.61 1950-11-27,235.06,236.09,232.75,234.96,1740000,234.96 1950-11-24,233.81,236.63,233.81,235.47,2620000,235.47 1950-11-22,231.16,234.26,230.37,233.81,2730000,233.81 1950-11-21,231.53,232.64,229.99,231.16,2010000,231.16 1950-11-20,231.64,233.55,230.48,231.53,2250000,231.53 1950-11-17,228.94,231.01,228.29,230.27,2130000,230.27 1950-11-16,229.52,229.75,226.70,228.94,1760000,228.94 1950-11-15,229.54,230.45,227.98,229.52,1620000,229.52 1950-11-14,229.44,230.17,227.58,229.54,1780000,229.54 1950-11-13,229.29,230.83,227.98,229.44,1630000,229.44 1950-11-10,227.17,229.90,226.74,229.29,1640000,229.29 1950-11-09,224.25,228.01,224.23,227.17,1760000,227.17 1950-11-08,222.86,226.55,222.86,224.25,1850000,224.25 1950-11-06,224.91,224.91,220.59,222.52,2580000,222.52 1950-11-03,227.25,229.44,226.21,228.10,1560000,228.10 1950-11-02,225.69,228.74,225.64,227.25,1580000,227.25 1950-11-01,225.01,226.75,223.07,225.69,1780000,225.69 1950-10-31,226.42,227.32,223.59,225.01,2010000,225.01 1950-10-30,228.56,230.05,225.87,226.42,1790000,226.42 1950-10-27,226.65,228.92,225.77,228.28,1800000,228.28 1950-10-26,230.85,230.85,225.44,226.65,3000000,226.65 1950-10-25,231.39,232.75,230.40,231.49,1930000,231.49 1950-10-24,230.62,231.87,229.55,231.39,1790000,231.39 1950-10-23,230.88,232.02,229.95,230.62,1850000,230.62 1950-10-20,230.83,231.41,229.07,230.33,1840000,230.33 1950-10-19,230.60,232.01,229.62,230.83,2250000,230.83 1950-10-18,229.26,231.54,229.26,230.60,2410000,230.60 1950-10-17,227.50,229.74,227.42,229.22,2010000,229.22 1950-10-16,227.63,228.38,225.39,227.50,1630000,227.50 1950-10-13,228.97,229.97,227.53,228.54,2030000,228.54 1950-10-11,227.60,229.92,226.59,228.97,2200000,228.97 1950-10-10,230.02,230.33,226.79,227.60,1870000,227.60 1950-10-09,231.81,232.47,228.49,230.02,2330000,230.02 1950-10-06,229.85,232.50,229.57,231.74,2360000,231.74 1950-10-05,231.15,232.17,229.16,229.85,2490000,229.85 1950-10-04,228.89,232.31,228.21,231.15,2920000,231.15 1950-10-03,228.94,230.86,228.01,228.89,2480000,228.89 1950-10-02,226.46,229.57,226.46,228.94,2200000,228.94 1950-09-29,225.93,227.40,225.32,226.36,1800000,226.36 1950-09-28,225.74,227.69,225.09,225.93,2200000,225.93 1950-09-27,222.84,226.06,222.00,225.74,2360000,225.74 1950-09-26,226.06,226.49,222.26,222.84,2280000,222.84 1950-09-25,226.64,227.51,224.77,226.06,2020000,226.06 1950-09-22,226.01,228.17,225.61,226.64,2510000,226.64 1950-09-21,224.33,226.49,223.58,226.01,1650000,226.01 1950-09-20,225.78,226.49,223.00,224.33,2100000,224.33 1950-09-19,226.78,226.85,224.40,225.78,1590000,225.78 1950-09-18,225.85,227.89,225.45,226.78,2040000,226.78 1950-09-15,224.48,226.32,223.13,225.85,2410000,225.85 1950-09-14,223.42,225.19,222.71,224.48,2350000,224.48 1950-09-13,221.18,224.22,221.18,223.42,2600000,223.42 1950-09-12,218.17,221.19,218.17,220.81,1680000,220.81 1950-09-11,220.03,220.77,217.44,218.10,1860000,218.10 1950-09-08,218.52,220.94,218.52,220.03,1960000,220.03 1950-09-07,218.20,219.20,217.15,218.33,1340000,218.33 1950-09-06,219.52,219.52,217.38,218.20,1300000,218.20 1950-09-05,218.42,220.71,217.88,220.02,1250000,220.02 1950-09-01,217.12,219.00,217.12,218.42,1290000,218.42 1950-08-31,217.05,217.79,216.21,216.87,1140000,216.87 1950-08-30,218.29,218.83,216.43,217.05,1490000,217.05 1950-08-29,218.55,220.20,217.86,218.29,1890000,218.29 1950-08-28,218.10,219.29,216.81,218.55,1300000,218.55 1950-08-25,219.45,219.45,217.10,218.10,1610000,218.10 1950-08-24,221.51,222.17,220.34,221.13,1620000,221.13 1950-08-23,219.79,221.93,219.48,221.51,1580000,221.51 1950-08-22,220.21,220.81,218.91,219.79,1550000,219.79 1950-08-21,219.23,222.12,218.87,220.21,1840000,220.21 1950-08-18,217.76,219.88,217.26,219.23,1780000,219.23 1950-08-17,215.82,218.94,215.82,217.76,2170000,217.76 1950-08-16,215.31,216.58,214.65,215.78,1770000,215.78 1950-08-15,215.31,216.24,214.11,215.31,1330000,215.31 1950-08-14,215.03,216.10,213.98,215.31,1280000,215.31 1950-08-11,216.64,216.89,214.41,215.03,1680000,215.03 1950-08-10,216.97,217.48,215.56,216.64,1870000,216.64 1950-08-09,215.44,217.45,214.16,216.97,1760000,216.97 1950-08-08,215.82,217.53,214.76,215.44,2180000,215.44 1950-08-07,212.66,216.21,212.48,215.82,1850000,215.82 1950-08-04,211.26,213.14,210.41,212.66,1600000,212.66 1950-08-03,211.26,212.28,209.55,211.26,1660000,211.26 1950-08-02,211.87,213.71,209.78,211.26,1980000,211.26 1950-08-01,209.56,212.98,209.56,211.87,1970000,211.87 1950-07-31,208.21,209.85,207.19,209.40,1590000,209.40 1950-07-28,206.76,209.56,206.76,208.21,2050000,208.21 1950-07-27,204.39,207.77,204.39,206.37,2300000,206.37 1950-07-26,203.83,205.68,201.91,204.39,2460000,204.39 1950-07-25,206.57,206.57,202.99,203.83,2770000,203.83 1950-07-24,207.65,208.66,205.64,206.95,2300000,206.95 1950-07-21,207.73,208.89,205.51,207.65,2810000,207.65 1950-07-20,205.13,208.62,204.41,207.73,3160000,207.73 1950-07-19,202.08,205.61,202.08,205.13,2430000,205.13 1950-07-18,198.00,202.42,198.00,201.88,1820000,201.88 1950-07-17,199.47,199.47,196.44,197.63,1520000,197.63 1950-07-14,197.89,201.48,197.89,199.83,1900000,199.83 1950-07-13,199.09,199.69,195.40,197.46,2660000,197.46 1950-07-12,203.83,203.83,197.44,199.09,3200000,199.09 1950-07-11,208.09,209.39,203.83,204.60,3250000,204.60 1950-07-10,208.59,209.42,206.31,208.09,1960000,208.09 1950-07-07,210.85,211.75,207.78,208.59,1870000,208.59 1950-07-06,210.03,212.19,209.46,210.85,1570000,210.85 1950-07-05,208.35,210.92,207.27,210.03,1400000,210.03 1950-07-03,209.11,209.48,205.92,208.35,1550000,208.35 1950-06-30,206.72,211.96,206.03,209.11,2660000,209.11 1950-06-29,214.68,214.74,206.33,206.72,3040000,206.72 1950-06-28,212.39,216.99,212.39,214.68,2600000,214.68 1950-06-27,213.91,217.13,206.33,212.22,4860000,212.22 1950-06-26,220.75,220.75,213.03,213.91,3950000,213.91 1950-06-23,224.51,225.55,223.57,224.35,1700000,224.35 1950-06-22,222.53,225.00,222.47,224.51,1830000,224.51 1950-06-21,220.81,223.07,220.81,222.53,1750000,222.53 1950-06-20,222.09,222.19,218.99,220.72,1470000,220.72 1950-06-19,222.71,223.94,221.49,222.09,1290000,222.09 1950-06-16,222.46,223.67,221.89,222.71,1180000,222.71 1950-06-15,223.32,224.97,221.79,222.46,1530000,222.46 1950-06-14,226.02,226.02,222.76,223.32,1650000,223.32 1950-06-13,228.09,228.09,225.58,226.44,1790000,226.44 1950-06-12,226.86,229.20,226.40,228.38,1790000,228.38 1950-06-09,225.52,227.82,225.16,226.86,2130000,226.86 1950-06-08,223.68,226.21,223.57,225.52,1780000,225.52 1950-06-07,223.46,225.17,221.82,223.68,1750000,223.68 1950-06-06,221.76,224.32,218.66,223.46,2250000,223.46 1950-06-05,223.71,224.12,221.13,221.76,1630000,221.76 1950-06-02,223.23,224.34,222.53,223.71,1450000,223.71 1950-06-01,223.42,224.06,222.40,223.23,1580000,223.23 1950-05-31,222.47,224.18,222.40,223.42,1530000,223.42 1950-05-29,221.71,223.11,221.16,222.47,1110000,222.47 1950-05-26,222.44,223.11,221.22,221.93,1330000,221.93 1950-05-25,222.57,223.10,220.74,222.44,1480000,222.44 1950-05-24,222.47,224.24,221.83,222.57,1850000,222.57 1950-05-23,221.55,222.82,220.85,222.47,1460000,222.47 1950-05-22,222.41,223.14,220.95,221.55,1620000,221.55 1950-05-19,220.63,222.79,220.23,222.11,2110000,222.11 1950-05-18,220.60,221.52,219.70,220.63,5240000,220.63 1950-05-17,219.70,221.48,219.39,220.60,2020000,220.60 1950-05-16,218.04,220.05,217.86,219.70,1730000,219.70 1950-05-15,217.78,218.90,216.87,218.04,1220000,218.04 1950-05-12,218.72,218.96,216.37,217.61,1790000,217.61 1950-05-11,218.64,219.32,217.26,218.72,1750000,218.72 1950-05-10,217.41,219.64,217.41,218.64,1880000,218.64 1950-05-09,216.71,217.86,216.00,217.40,1720000,217.40 1950-05-08,217.03,217.76,215.72,216.71,1680000,216.71 1950-05-05,214.87,216.30,214.14,215.72,1800000,215.72 1950-05-04,216.26,216.71,214.25,214.87,2150000,214.87 1950-05-03,214.87,217.13,214.30,216.26,2120000,216.26 1950-05-02,215.81,216.46,214.30,214.87,2250000,214.87 1950-05-01,214.33,216.35,214.06,215.81,2390000,215.81 1950-04-28,212.44,214.29,212.16,213.56,2190000,213.56 1950-04-27,211.72,213.21,210.76,212.44,2070000,212.44 1950-04-26,212.55,213.05,210.51,211.72,1880000,211.72 1950-04-25,212.58,213.65,211.50,212.55,1830000,212.55 1950-04-24,213.90,214.17,211.02,212.58,2310000,212.58 1950-04-21,213.72,215.09,212.85,214.14,2710000,214.14 1950-04-20,215.21,215.65,212.67,213.72,2590000,213.72 1950-04-19,215.05,216.32,214.22,215.21,2950000,215.21 1950-04-18,214.41,216.04,213.59,215.05,3320000,215.05 1950-04-17,214.48,215.27,213.18,214.41,2520000,214.41 1950-04-14,214.14,216.17,214.14,215.31,2750000,215.31 1950-04-13,213.94,215.40,213.36,214.13,2410000,214.13 1950-04-12,211.47,214.35,211.18,213.94,2010000,213.94 1950-04-11,212.29,213.40,210.15,211.47,2010000,211.47 1950-04-10,212.55,213.60,211.47,212.29,2070000,212.29 1950-04-06,210.34,212.68,210.26,212.10,2000000,212.10 1950-04-05,209.05,210.76,208.70,210.34,1430000,210.34 1950-04-04,208.44,210.19,208.15,209.05,2010000,209.05 1950-04-03,206.37,208.82,205.93,208.44,1570000,208.44 1950-03-31,206.43,207.54,205.28,206.05,1880000,206.05 1950-03-30,208.40,208.42,205.53,206.43,2370000,206.43 1950-03-29,209.50,209.58,207.77,208.40,2090000,208.40 1950-03-28,209.10,210.08,207.74,209.50,1780000,209.50 1950-03-27,210.62,211.22,208.74,209.10,1930000,209.10 1950-03-24,209.62,210.22,208.01,209.78,1570000,209.78 1950-03-23,209.31,210.67,208.61,209.62,2020000,209.62 1950-03-22,208.27,209.72,207.76,209.31,2010000,209.31 1950-03-21,207.78,209.16,207.38,208.27,1400000,208.27 1950-03-20,208.09,209.11,207.40,207.78,1430000,207.78 1950-03-17,207.89,208.92,206.81,207.57,1600000,207.57 1950-03-16,207.46,209.43,206.92,207.89,2060000,207.89 1950-03-15,204.85,207.80,204.85,207.46,1830000,207.46 1950-03-14,203.09,205.10,202.71,204.70,1140000,204.70 1950-03-13,202.96,203.91,202.09,203.09,1060000,203.09 1950-03-10,202.33,202.88,201.14,202.44,1260000,202.44 1950-03-09,203.71,203.95,201.97,202.33,1330000,202.33 1950-03-08,203.69,204.42,202.69,203.71,1360000,203.71 1950-03-07,204.88,204.89,202.33,203.69,1590000,203.69 1950-03-06,204.71,205.65,204.20,204.88,1470000,204.88 1950-03-03,203.54,204.85,203.09,204.48,1520000,204.48 1950-03-02,203.62,204.52,202.96,203.54,1340000,203.54 1950-03-01,203.44,204.02,202.15,203.62,1410000,203.62 1950-02-28,204.33,204.53,202.82,203.44,1310000,203.44 1950-02-27,204.15,204.85,203.46,204.33,1410000,204.33 1950-02-24,203.32,204.87,203.22,204.15,1710000,204.15 1950-02-23,203.35,203.95,202.31,203.32,1310000,203.32 1950-02-21,203.47,203.93,202.55,203.35,1260000,203.35 1950-02-20,203.97,204.26,202.53,203.47,1420000,203.47 1950-02-17,201.69,203.49,201.13,203.17,1940000,203.17 1950-02-16,201.93,202.49,200.59,201.69,1920000,201.69 1950-02-15,202.02,202.60,200.63,201.93,1730000,201.93 1950-02-14,203.32,203.32,200.75,202.02,2210000,202.02 1950-02-10,203.80,204.87,202.69,203.49,1790000,203.49 1950-02-09,202.71,204.67,202.24,203.80,1810000,203.80 1950-02-08,203.43,203.43,201.60,202.71,1470000,202.71 1950-02-07,204.40,204.40,202.59,203.53,1360000,203.53 1950-02-06,205.03,205.39,203.58,204.59,1490000,204.59 1950-02-03,204.11,205.39,203.55,204.53,2210000,204.53 1950-02-02,201.89,204.55,201.35,204.11,2040000,204.11 1950-02-01,201.79,202.96,201.36,201.89,1810000,201.89 1950-01-31,201.39,202.51,200.82,201.79,1690000,201.79 1950-01-30,200.08,201.93,199.66,201.39,1640000,201.39 1950-01-27,198.53,199.58,197.69,199.08,1250000,199.08 1950-01-26,198.39,199.22,197.54,198.53,1150000,198.53 1950-01-25,199.32,199.32,196.64,198.39,1700000,198.39 1950-01-24,200.42,200.42,198.78,199.62,1250000,199.62 1950-01-23,200.97,201.39,199.43,200.42,1340000,200.42 1950-01-20,199.80,200.86,199.14,200.13,1440000,200.13 1950-01-19,199.50,200.49,198.49,199.80,1170000,199.80 1950-01-18,198.78,200.74,198.35,199.50,1570000,199.50 1950-01-17,197.17,200.08,197.14,198.78,1790000,198.78 1950-01-16,196.92,197.75,195.57,197.17,1460000,197.17 1950-01-13,197.93,197.93,193.94,196.81,3330000,196.81 1950-01-12,201.61,202.08,197.53,197.93,2970000,197.93 1950-01-11,201.17,202.42,200.52,201.61,2630000,201.61 1950-01-10,201.98,202.04,200.13,201.17,2160000,201.17 1950-01-09,201.94,202.92,200.86,201.98,2520000,201.98 1950-01-06,200.57,201.62,199.84,200.96,2010000,200.96 1950-01-05,200.20,201.76,199.69,200.57,2550000,200.57 1950-01-04,198.89,200.55,198.26,200.20,1890000,200.20 1950-01-03,200.13,200.20,197.73,198.89,1260000,198.89 1949-12-30,199.39,200.91,198.97,200.52,2090000,200.52 1949-12-29,199.59,200.26,198.75,199.39,1820000,199.39 1949-12-28,198.28,200.19,198.10,199.59,1560000,199.59 1949-12-27,198.88,199.58,197.73,198.28,1560000,198.28 1949-12-23,198.52,199.73,197.88,198.88,1470000,198.88 1949-12-22,196.49,198.91,196.49,198.52,1630000,198.52 1949-12-21,197.22,197.64,195.79,196.45,1270000,196.45 1949-12-20,198.17,198.28,196.55,197.22,1330000,197.22 1949-12-19,197.98,199.15,197.46,198.17,1420000,198.17 1949-12-16,198.05,199.13,196.90,197.88,1960000,197.88 1949-12-15,197.51,198.59,196.34,198.05,2070000,198.05 1949-12-14,196.81,198.10,196.12,197.51,2210000,197.51 1949-12-13,196.17,197.22,195.22,196.81,2080000,196.81 1949-12-12,194.68,196.57,194.39,196.17,1780000,196.17 1949-12-09,194.45,194.99,193.54,194.35,1500000,194.35 1949-12-08,194.21,195.32,193.61,194.45,1720000,194.45 1949-12-07,194.59,194.59,192.59,194.21,1630000,194.21 1949-12-06,194.74,195.25,193.91,194.64,1430000,194.64 1949-12-05,194.43,195.54,193.69,194.74,1830000,194.74 1949-12-02,192.71,194.16,191.94,193.63,2020000,193.63 1949-12-01,191.55,193.11,191.12,192.71,1470000,192.71 1949-11-30,191.62,192.35,190.68,191.55,1320000,191.55 1949-11-29,192.24,192.54,190.54,191.62,1310000,191.62 1949-11-28,193.23,193.43,191.72,192.24,1080000,192.24 1949-11-25,193.52,194.34,192.27,192.78,1270000,192.78 1949-11-23,193.23,194.35,192.48,193.52,1460000,193.52 1949-11-22,192.35,193.65,191.69,193.23,1400000,193.23 1949-11-21,193.62,193.84,191.72,192.35,1180000,192.35 1949-11-18,191.77,193.97,191.77,193.41,1690000,193.41 1949-11-17,189.37,191.82,189.27,191.34,1410000,191.34 1949-11-16,187.98,190.13,187.83,189.37,1210000,189.37 1949-11-15,189.25,189.25,186.98,187.98,1250000,187.98 1949-11-14,190.46,191.08,188.71,189.27,1270000,189.27 1949-11-10,190.60,191.07,189.65,190.42,1170000,190.42 1949-11-09,190.89,192.43,190.06,190.60,1510000,190.60 1949-11-07,191.37,192.05,190.41,190.89,1170000,190.89 1949-11-04,192.19,192.31,190.57,191.29,1390000,191.29 1949-11-03,192.96,193.19,191.34,192.19,1370000,192.19 1949-11-02,191.23,193.63,191.15,192.96,1570000,192.96 1949-11-01,189.54,191.74,189.25,191.23,1300000,191.23 1949-10-31,190.36,191.08,189.15,189.54,1140000,189.54 1949-10-28,190.36,191.44,189.47,190.16,1480000,190.16 1949-10-27,189.08,191.12,188.96,190.36,1760000,190.36 1949-10-26,187.70,189.41,187.30,189.08,1620000,189.08 1949-10-25,186.54,188.01,186.38,187.70,1190000,187.70 1949-10-24,186.20,187.01,185.58,186.54,1240000,186.54 1949-10-21,186.64,186.97,185.62,186.20,1290000,186.20 1949-10-20,187.04,187.65,185.87,186.64,1270000,186.64 1949-10-19,186.12,187.34,185.81,187.04,1370000,187.04 1949-10-18,184.72,186.56,184.72,186.12,1220000,186.12 1949-10-17,186.06,186.06,183.94,184.72,1130000,184.72 1949-10-14,186.78,187.26,185.47,186.43,1190000,186.43 1949-10-13,186.74,187.91,186.29,186.78,1790000,186.78 1949-10-11,185.15,187.04,184.75,186.74,1660000,186.74 1949-10-10,185.36,185.55,184.49,185.15,1120000,185.15 1949-10-07,185.37,185.62,183.92,185.27,1280000,185.27 1949-10-06,184.80,185.99,184.53,185.37,1520000,185.37 1949-10-05,184.13,185.38,184.00,184.80,1470000,184.80 1949-10-04,182.68,184.39,182.68,184.13,1310000,184.13 1949-10-03,181.98,183.05,180.90,182.67,770000,182.67 1949-09-30,182.43,183.16,181.71,182.51,1100000,182.51 1949-09-29,181.31,183.42,181.00,182.43,1380000,182.43 1949-09-28,180.06,182.09,180.06,181.31,1300000,181.31 1949-09-27,180.54,180.54,178.61,179.63,1070000,179.63 1949-09-26,181.30,182.25,180.36,180.86,1020000,180.86 1949-09-23,180.83,181.74,180.17,181.30,1290000,181.30 1949-09-22,180.02,181.37,179.87,180.83,1280000,180.83 1949-09-21,178.04,180.42,177.71,180.02,1150000,180.02 1949-09-20,180.91,180.91,177.63,178.04,1350000,178.04 1949-09-19,182.13,182.13,180.18,181.42,1300000,181.42 1949-09-16,182.16,182.76,181.34,182.32,1160000,182.32 1949-09-15,182.71,182.71,181.00,182.16,1160000,182.16 1949-09-14,183.29,184.09,182.61,183.14,1700000,183.14 1949-09-13,181.27,183.51,181.27,183.29,1720000,183.29 1949-09-12,180.24,181.60,180.17,181.15,1080000,181.15 1949-09-09,180.53,180.86,179.89,180.24,770000,180.24 1949-09-08,180.21,181.30,179.99,180.53,940000,180.53 1949-09-07,179.20,180.54,178.91,180.21,850000,180.21 1949-09-06,179.38,179.85,178.65,179.20,640000,179.20 1949-09-02,179.52,179.91,178.97,179.38,750000,179.38 1949-09-01,178.66,180.20,178.54,179.52,840000,179.52 1949-08-31,178.69,179.05,177.77,178.66,720000,178.66 1949-08-30,177.75,179.04,177.60,178.69,590000,178.69 1949-08-29,179.08,179.08,177.45,177.75,640000,177.75 1949-08-26,179.01,179.69,178.42,179.24,660000,179.24 1949-08-25,178.78,179.52,178.44,179.01,730000,179.01 1949-08-24,178.51,179.15,177.86,178.78,720000,178.78 1949-08-23,180.18,180.18,178.28,178.51,840000,178.51 1949-08-22,181.16,181.33,180.06,180.53,710000,180.53 1949-08-19,182.02,182.38,180.83,181.16,850000,181.16 1949-08-18,181.59,182.67,181.44,182.02,1180000,182.02 1949-08-17,180.00,181.78,179.80,181.59,1440000,181.59 1949-08-16,178.97,180.40,178.71,180.00,840000,180.00 1949-08-15,179.29,179.71,178.55,178.97,720000,178.97 1949-08-12,180.02,180.10,178.62,179.29,770000,179.29 1949-08-11,180.60,180.98,179.48,180.02,1030000,180.02 1949-08-10,179.52,180.96,179.23,180.60,1280000,180.60 1949-08-09,180.35,180.35,178.86,179.52,1140000,179.52 1949-08-08,179.18,181.15,179.18,180.54,1660000,180.54 1949-08-05,177.06,179.38,176.77,179.07,1440000,179.07 1949-08-04,177.19,177.44,176.51,177.06,910000,177.06 1949-08-03,177.56,177.91,176.72,177.19,1270000,177.19 1949-08-02,176.84,177.78,176.35,177.56,800000,177.56 1949-08-01,175.92,177.17,175.68,176.84,860000,176.84 1949-07-29,176.26,176.54,175.30,175.92,640000,175.92 1949-07-28,176.46,176.84,175.57,176.26,790000,176.26 1949-07-27,176.37,177.04,175.93,176.46,1030000,176.46 1949-07-26,175.12,176.65,174.86,176.37,1310000,176.37 1949-07-25,174.53,175.99,174.28,175.12,860000,175.12 1949-07-22,174.59,174.95,173.85,174.53,730000,174.53 1949-07-21,175.49,175.49,174.15,174.59,780000,174.59 1949-07-20,175.31,176.14,174.86,175.60,1380000,175.60 1949-07-19,174.04,175.60,173.93,175.31,1590000,175.31 1949-07-18,173.48,174.40,173.20,174.04,810000,174.04 1949-07-15,173.59,173.89,172.64,173.48,800000,173.48 1949-07-14,173.24,174.02,172.47,173.59,1170000,173.59 1949-07-13,171.78,173.34,171.59,173.24,1050000,173.24 1949-07-12,170.81,171.96,170.52,171.78,870000,171.78 1949-07-11,170.92,171.41,170.10,170.81,680000,170.81 1949-07-08,171.01,171.53,170.41,170.92,640000,170.92 1949-07-07,170.68,171.27,169.95,171.01,890000,171.01 1949-07-06,169.02,170.83,168.77,170.68,1410000,170.68 1949-07-05,168.08,169.48,167.90,169.02,630000,169.02 1949-07-01,167.42,168.61,166.94,168.08,720000,168.08 1949-06-30,166.76,167.96,166.72,167.42,580000,167.42 1949-06-29,165.75,167.05,165.24,166.76,590000,166.76 1949-06-28,166.52,166.52,164.65,165.75,790000,165.75 1949-06-27,166.99,167.82,166.29,166.79,670000,166.79 1949-06-24,166.77,167.49,166.39,166.99,570000,166.99 1949-06-23,165.74,167.30,165.74,166.77,730000,166.77 1949-06-22,165.71,165.97,165.09,165.64,550000,165.64 1949-06-21,165.49,166.65,165.09,165.71,770000,165.71 1949-06-20,163.78,165.68,163.46,165.49,780000,165.49 1949-06-17,163.94,164.30,162.95,163.78,540000,163.78 1949-06-16,164.58,165.03,163.50,163.94,680000,163.94 1949-06-15,162.10,164.81,162.10,164.58,950000,164.58 1949-06-14,161.60,162.51,160.62,161.86,1120000,161.86 1949-06-13,163.90,163.90,160.95,161.60,1350000,161.60 1949-06-10,165.53,165.53,164.14,164.61,800000,164.61 1949-06-09,165.76,166.28,165.19,165.73,600000,165.73 1949-06-08,165.29,166.39,164.96,165.76,790000,165.76 1949-06-07,165.15,165.96,164.32,165.29,1040000,165.29 1949-06-06,167.24,167.35,164.27,165.15,1380000,165.15 1949-06-03,168.15,168.31,166.77,167.24,700000,167.24 1949-06-02,167.98,168.98,167.59,168.15,670000,168.15 1949-06-01,168.36,168.54,166.53,167.98,1140000,167.98 1949-05-31,171.53,171.60,168.14,168.36,1240000,168.36 1949-05-27,171.95,172.07,170.95,171.53,690000,171.53 1949-05-26,171.84,172.79,171.51,171.95,700000,171.95 1949-05-25,171.49,172.07,170.57,171.84,880000,171.84 1949-05-24,172.32,172.43,171.06,171.49,840000,171.49 1949-05-23,173.43,173.43,172.10,172.32,720000,172.32 1949-05-20,174.14,174.18,172.86,173.49,740000,173.49 1949-05-19,174.92,175.12,173.76,174.14,840000,174.14 1949-05-18,175.32,175.61,174.39,174.92,750000,174.92 1949-05-17,175.76,176.07,174.86,175.32,780000,175.32 1949-05-16,175.20,176.26,175.17,175.76,1030000,175.76 1949-05-13,174.70,175.40,174.26,174.82,780000,174.82 1949-05-12,174.40,175.17,174.14,174.70,790000,174.70 1949-05-11,174.37,175.11,173.75,174.40,790000,174.40 1949-05-10,175.17,175.32,173.97,174.37,730000,174.37 1949-05-09,175.39,175.75,174.70,175.17,610000,175.17 1949-05-06,176.24,176.24,174.74,175.50,780000,175.50 1949-05-05,176.63,177.18,175.91,176.33,920000,176.33 1949-05-04,175.09,177.04,175.09,176.63,1180000,176.63 1949-05-03,174.53,175.32,173.86,175.00,830000,175.00 1949-05-02,174.16,175.06,173.93,174.53,740000,174.53 1949-04-29,173.89,174.48,173.52,174.06,810000,174.06 1949-04-28,174.56,174.65,173.58,173.89,770000,173.89 1949-04-27,174.21,175.24,173.92,174.56,830000,174.56 1949-04-26,173.64,174.60,173.02,174.21,870000,174.21 1949-04-25,173.76,174.38,173.05,173.64,740000,173.64 1949-04-22,173.24,173.77,172.64,173.42,890000,173.42 1949-04-21,175.49,175.49,173.08,173.24,1310000,173.24 1949-04-20,176.73,176.79,175.38,175.69,970000,175.69 1949-04-19,177.16,177.50,176.39,176.73,830000,176.73 1949-04-18,177.07,177.71,176.47,177.16,890000,177.16 1949-04-14,176.81,177.30,176.18,176.62,800000,176.62 1949-04-13,176.99,177.69,172.26,176.81,920000,176.81 1949-04-12,176.54,177.46,175.61,176.99,860000,176.99 1949-04-11,176.75,177.14,175.94,176.54,720000,176.54 1949-04-08,176.04,176.62,175.34,176.44,850000,176.44 1949-04-07,176.71,176.94,175.43,176.04,850000,176.04 1949-04-06,177.04,177.53,176.19,176.71,930000,176.71 1949-04-05,176.59,177.67,175.94,177.04,900000,177.04 1949-04-04,176.88,177.78,176.15,176.59,920000,176.59 1949-04-01,177.04,177.04,175.86,176.28,850000,176.28 1949-03-31,178.43,178.43,176.87,177.10,980000,177.10 1949-03-30,178.39,179.19,177.69,178.45,1850000,178.45 1949-03-29,176.81,178.90,176.81,178.39,1800000,178.39 1949-03-28,175.82,176.72,175.35,175.99,700000,175.99 1949-03-25,176.41,176.49,175.29,175.83,630000,175.83 1949-03-24,176.20,177.37,176.13,176.41,920000,176.41 1949-03-23,174.83,176.54,174.32,176.20,960000,176.20 1949-03-22,175.61,175.85,174.34,174.83,840000,174.83 1949-03-21,176.07,176.47,175.27,175.61,620000,175.61 1949-03-18,176.33,176.78,175.73,176.29,670000,176.29 1949-03-17,175.53,176.67,175.17,176.33,760000,176.33 1949-03-16,176.02,176.08,174.87,175.53,670000,175.53 1949-03-15,176.82,176.82,175.43,176.02,740000,176.02 1949-03-14,176.96,177.66,176.35,176.98,800000,176.98 1949-03-11,175.64,176.87,175.41,176.52,1070000,176.52 1949-03-10,175.76,176.20,175.03,175.64,630000,175.64 1949-03-09,176.09,176.29,175.22,175.76,640000,175.76 1949-03-08,175.55,176.62,175.30,176.09,940000,176.09 1949-03-07,174.93,175.82,174.30,175.55,840000,175.55 1949-03-04,173.76,174.06,172.59,173.66,730000,173.66 1949-03-03,173.82,174.44,173.17,173.76,600000,173.76 1949-03-02,174.18,174.34,173.15,173.82,690000,173.82 1949-03-01,173.36,174.61,173.36,174.18,720000,174.18 1949-02-28,171.63,173.38,171.63,173.06,740000,173.06 1949-02-25,171.48,172.11,170.56,171.10,830000,171.10 1949-02-24,172.76,172.76,171.19,171.48,880000,171.48 1949-02-23,174.19,174.60,173.07,173.23,770000,173.23 1949-02-21,174.53,174.67,173.63,174.19,560000,174.19 1949-02-18,174.82,175.62,174.11,174.71,700000,174.71 1949-02-17,173.45,175.55,173.45,174.82,960000,174.82 1949-02-16,172.48,173.92,172.27,173.28,700000,173.28 1949-02-15,172.16,172.86,171.27,172.48,610000,172.48 1949-02-14,171.93,173.17,171.57,172.16,700000,172.16 1949-02-11,172.41,172.69,171.03,171.93,880000,171.93 1949-02-10,174.61,174.80,172.23,172.41,980000,172.41 1949-02-09,173.71,175.20,173.57,174.61,880000,174.61 1949-02-08,174.37,174.37,172.91,173.71,960000,173.71 1949-02-07,175.60,176.76,173.79,174.43,1330000,174.43 1949-02-04,180.09,180.32,177.69,177.92,1060000,177.92 1949-02-03,180.27,180.88,179.57,180.09,770000,180.09 1949-02-02,180.39,180.94,179.63,180.27,720000,180.27 1949-02-01,179.12,180.55,178.92,180.39,730000,180.39 1949-01-31,179.35,179.73,178.46,179.12,610000,179.12 1949-01-28,179.48,179.48,177.88,178.82,840000,178.82 1949-01-27,179.88,180.30,178.58,179.52,840000,179.52 1949-01-26,179.65,181.31,178.96,179.88,1040000,179.88 1949-01-25,180.83,181.05,179.06,179.65,820000,179.65 1949-01-24,181.54,182.28,180.51,180.83,850000,180.83 1949-01-21,181.43,181.89,180.69,181.00,770000,181.00 1949-01-20,181.12,181.85,180.44,181.43,820000,181.43 1949-01-19,180.55,181.47,179.75,181.12,760000,181.12 1949-01-18,180.14,181.55,180.09,180.55,770000,180.55 1949-01-17,179.15,180.48,177.99,180.14,720000,180.14 1949-01-14,180.17,180.20,178.19,178.80,930000,178.80 1949-01-13,180.69,181.06,179.79,180.17,700000,180.17 1949-01-12,180.76,181.66,180.21,180.69,710000,180.69 1949-01-11,180.57,181.00,179.73,180.76,710000,180.76 1949-01-10,181.41,181.47,179.78,180.57,770000,180.57 1949-01-07,180.47,182.50,180.47,181.31,1400000,181.31 1949-01-06,177.16,180.59,177.16,180.22,1150000,180.22 1949-01-05,175.50,177.76,175.50,177.08,800000,177.08 1949-01-04,175.03,175.97,174.56,175.49,640000,175.49 1949-01-03,176.99,176.99,174.37,175.03,980000,175.03 1948-12-31,177.92,178.50,176.81,177.30,1550000,177.30 1948-12-30,177.58,179.15,177.10,177.92,1390000,177.92 1948-12-29,175.98,177.85,175.88,177.58,1380000,177.58 1948-12-28,177.37,177.37,175.19,175.98,1650000,175.98 1948-12-27,177.42,178.35,176.63,177.40,1060000,177.40 1948-12-24,176.49,177.82,176.04,177.42,970000,177.42 1948-12-23,176.39,177.29,175.70,176.49,1080000,176.49 1948-12-22,176.35,176.93,175.62,176.39,1000000,176.39 1948-12-21,176.84,177.49,175.92,176.35,1000000,176.35 1948-12-20,175.69,177.60,175.14,176.84,980000,176.84 1948-12-17,175.83,176.78,175.17,175.92,1010000,175.92 1948-12-16,176.20,176.59,175.20,175.83,1010000,175.83 1948-12-15,176.59,177.26,175.78,176.20,920000,176.20 1948-12-14,177.34,177.73,175.86,176.59,1000000,176.59 1948-12-13,177.49,178.43,176.67,177.34,1180000,177.34 1948-12-10,175.75,176.79,175.17,176.41,1040000,176.41 1948-12-09,176.29,176.86,175.44,175.75,1220000,175.75 1948-12-08,176.67,176.98,175.25,176.29,1140000,176.29 1948-12-07,176.26,177.25,175.39,176.67,1160000,176.67 1948-12-06,176.22,177.12,175.59,176.26,1180000,176.26 1948-12-03,173.61,175.34,173.20,175.00,1100000,175.00 1948-12-02,173.22,174.88,173.15,173.61,1210000,173.61 1948-12-01,171.67,174.02,171.67,173.22,1320000,173.22 1948-11-30,171.99,172.49,170.35,171.20,1200000,171.20 1948-11-29,172.90,173.55,171.72,171.99,1010000,171.99 1948-11-26,173.40,174.14,172.38,173.16,1040000,173.16 1948-11-24,175.88,175.88,172.96,173.40,1290000,173.40 1948-11-23,176.33,176.72,175.17,176.17,1010000,176.17 1948-11-22,177.42,177.80,175.75,176.33,890000,176.33 1948-11-19,176.07,177.96,175.99,176.98,990000,176.98 1948-11-18,176.07,176.89,175.52,176.07,780000,176.07 1948-11-17,176.20,176.92,175.14,176.07,980000,176.07 1948-11-16,176.01,177.42,175.44,176.20,1060000,176.20 1948-11-15,174.37,176.56,174.37,176.01,1030000,176.01 1948-11-12,173.48,175.47,173.37,173.93,1110000,173.93 1948-11-10,173.94,174.93,172.13,173.48,2100000,173.48 1948-11-09,178.19,178.60,173.54,173.94,2260000,173.94 1948-11-08,178.94,179.85,177.46,178.19,1130000,178.19 1948-11-05,184.42,184.42,178.11,178.38,2530000,178.38 1948-11-04,182.92,185.79,182.92,184.54,1530000,184.54 1948-11-03,183.08,183.08,179.65,182.46,3240000,182.46 1948-11-01,188.62,190.45,188.39,189.76,1220000,189.76 1948-10-29,187.73,188.60,186.99,188.28,860000,188.28 1948-10-28,189.28,189.59,187.29,187.73,970000,187.73 1948-10-27,189.76,190.06,188.11,189.28,970000,189.28 1948-10-26,189.52,190.88,188.97,189.76,1140000,189.76 1948-10-25,190.19,190.53,188.54,189.52,1100000,189.52 1948-10-22,186.70,190.08,186.70,189.76,1800000,189.76 1948-10-21,186.51,187.16,185.49,186.44,1200000,186.44 1948-10-20,186.18,187.00,185.62,186.51,1180000,186.51 1948-10-19,185.33,186.58,185.15,186.18,1030000,186.18 1948-10-18,184.93,186.22,184.63,185.33,1030000,185.33 1948-10-15,184.52,185.26,183.76,184.62,910000,184.62 1948-10-14,183.84,185.46,183.65,184.52,980000,184.52 1948-10-13,182.41,184.25,182.30,183.84,830000,183.84 1948-10-11,182.09,182.76,181.71,182.41,510000,182.41 1948-10-08,182.52,182.99,181.55,182.02,630000,182.02 1948-10-07,181.72,183.10,181.58,182.52,800000,182.52 1948-10-06,181.23,182.34,180.91,181.72,710000,181.72 1948-10-05,181.70,181.89,180.52,181.23,550000,181.23 1948-10-04,180.78,182.19,180.74,181.70,610000,181.70 1948-10-01,178.30,180.08,178.22,179.87,680000,179.87 1948-09-30,179.04,179.71,177.95,178.30,700000,178.30 1948-09-29,177.59,179.53,177.59,179.04,810000,179.04 1948-09-28,175.99,177.91,175.84,177.54,910000,177.54 1948-09-27,178.32,178.32,175.84,175.99,1210000,175.99 1948-09-24,178.77,179.71,178.49,179.28,650000,179.28 1948-09-23,179.16,179.22,178.22,178.77,550000,178.77 1948-09-22,178.61,179.70,178.11,179.16,850000,179.16 1948-09-21,177.37,178.89,176.94,178.61,920000,178.61 1948-09-20,179.93,179.93,176.96,177.37,1260000,177.37 1948-09-17,180.69,180.78,179.60,180.06,680000,180.06 1948-09-16,180.62,181.10,179.84,180.69,580000,180.69 1948-09-15,180.63,181.47,179.85,180.62,710000,180.62 1948-09-14,179.41,181.12,179.41,180.63,710000,180.63 1948-09-13,180.51,180.51,178.87,179.38,680000,179.38 1948-09-10,180.33,181.26,179.04,180.61,970000,180.61 1948-09-09,182.83,182.83,179.74,180.33,2000000,180.33 1948-09-08,184.88,184.88,182.63,182.90,880000,182.90 1948-09-07,184.35,185.64,183.68,185.36,910000,185.36 1948-09-03,184.39,184.90,183.49,184.35,660000,184.35 1948-09-02,183.60,184.88,183.16,184.39,900000,184.39 1948-09-01,181.71,183.99,181.44,183.60,920000,183.60 1948-08-31,182.09,182.47,181.18,181.71,610000,181.71 1948-08-30,183.21,183.95,181.89,182.09,690000,182.09 1948-08-27,182.52,183.55,182.38,183.21,540000,183.21 1948-08-26,182.41,182.99,181.93,182.52,540000,182.52 1948-08-25,182.58,183.01,181.89,182.41,520000,182.41 1948-08-24,181.75,182.99,181.67,182.58,620000,182.58 1948-08-23,183.52,183.52,181.45,181.75,630000,181.75 1948-08-20,182.57,183.92,182.50,183.60,710000,183.60 1948-08-19,182.12,182.78,181.45,182.57,580000,182.57 1948-08-18,182.15,183.21,181.76,182.12,640000,182.12 1948-08-17,180.75,182.63,180.75,182.15,680000,182.15 1948-08-16,179.63,180.62,179.46,180.30,470000,180.30 1948-08-13,179.63,180.44,178.99,179.63,510000,179.63 1948-08-12,179.27,180.17,178.51,179.63,630000,179.63 1948-08-11,179.88,179.88,177.40,179.27,1310000,179.27 1948-08-10,182.26,182.26,179.91,180.02,840000,180.02 1948-08-09,183.01,183.75,182.02,182.26,670000,182.26 1948-08-06,182.92,183.44,181.89,183.01,680000,183.01 1948-08-05,183.06,184.54,182.45,182.92,880000,182.92 1948-08-04,180.98,183.29,180.82,183.06,870000,183.06 1948-08-03,181.13,181.72,180.24,180.98,720000,180.98 1948-08-02,181.33,182.61,180.61,181.13,710000,181.13 1948-07-30,182.56,182.56,180.04,181.33,1310000,181.33 1948-07-29,185.15,185.28,183.19,183.57,750000,183.57 1948-07-28,186.09,187.00,184.92,185.15,840000,185.15 1948-07-27,184.17,186.37,183.81,186.09,870000,186.09 1948-07-26,185.31,185.83,183.81,184.17,720000,184.17 1948-07-23,185.29,186.36,184.74,185.31,820000,185.31 1948-07-22,184.44,185.90,184.19,185.29,850000,185.29 1948-07-21,183.57,185.96,183.39,184.44,1200000,184.44 1948-07-20,181.27,184.41,181.27,183.57,1470000,183.57 1948-07-19,184.76,184.76,179.58,181.20,2570000,181.20 1948-07-16,187.70,188.34,184.98,185.90,1760000,185.90 1948-07-15,190.66,190.69,187.62,187.70,1620000,187.70 1948-07-14,190.36,191.13,189.41,190.66,1340000,190.66 1948-07-13,191.47,191.65,190.08,190.36,1200000,190.36 1948-07-12,191.62,192.38,190.95,191.47,1300000,191.47 1948-07-09,190.58,192.09,189.98,191.62,1370000,191.62 1948-07-08,190.06,191.16,189.73,190.58,1000000,190.58 1948-07-07,190.55,191.04,189.31,190.06,920000,190.06 1948-07-06,190.06,191.37,189.54,190.55,950000,190.55 1948-07-02,189.03,190.45,188.46,190.06,920000,190.06 1948-07-01,189.46,189.85,188.43,189.03,820000,189.03 1948-06-30,188.49,190.03,187.73,189.46,990000,189.46 1948-06-29,187.90,189.19,187.50,188.49,820000,188.49 1948-06-28,189.66,189.66,186.56,187.90,1210000,187.90 1948-06-25,190.87,191.06,188.95,190.00,1150000,190.00 1948-06-24,190.73,191.87,190.00,190.87,1560000,190.87 1948-06-23,189.66,191.32,189.42,190.73,1760000,190.73 1948-06-22,189.71,190.31,188.41,189.66,1410000,189.66 1948-06-21,191.65,192.08,189.52,189.71,1750000,189.71 1948-06-18,192.15,192.19,190.56,191.65,1250000,191.65 1948-06-17,192.34,192.99,191.12,192.15,1520000,192.15 1948-06-16,193.16,193.19,191.06,192.34,1580000,192.34 1948-06-15,192.86,193.93,191.62,193.16,1630000,193.16 1948-06-14,192.96,194.49,192.14,192.86,1750000,192.86 1948-06-11,192.50,193.65,191.48,192.96,1520000,192.96 1948-06-10,192.56,193.28,191.06,192.50,1700000,192.50 1948-06-09,192.16,193.54,191.86,192.56,1880000,192.56 1948-06-08,190.31,192.59,190.31,192.16,1520000,192.16 1948-06-07,190.18,190.74,188.87,190.13,930000,190.13 1948-06-04,191.05,191.31,189.56,190.18,1100000,190.18 1948-06-03,191.32,192.09,190.40,191.05,1300000,191.05 1948-06-02,191.18,192.18,190.30,191.32,1300000,191.32 1948-06-01,190.74,192.00,190.29,191.18,1310000,191.18 1948-05-28,190.97,191.48,189.49,190.74,1240000,190.74 1948-05-27,191.06,192.31,190.39,190.97,1830000,190.97 1948-05-26,189.71,191.57,189.06,191.06,1840000,191.06 1948-05-25,189.82,190.77,188.55,189.71,1810000,189.71 1948-05-24,190.00,190.67,188.98,189.82,1560000,189.82 1948-05-21,189.26,191.44,189.17,189.78,2680000,189.78 1948-05-20,188.28,190.00,187.52,189.26,2480000,189.26 1948-05-19,188.56,189.44,187.46,188.28,1850000,188.28 1948-05-18,190.44,191.01,188.16,188.56,2480000,188.56 1948-05-17,190.25,191.00,188.37,190.44,3050000,190.44 1948-05-14,185.01,188.93,185.01,188.60,3840000,188.60 1948-05-13,183.95,185.40,183.32,184.82,2030000,184.82 1948-05-12,183.75,184.39,182.49,183.95,1530000,183.95 1948-05-11,182.94,184.25,182.21,183.75,1750000,183.75 1948-05-10,182.50,183.46,181.68,182.94,1440000,182.94 1948-05-07,181.68,183.20,181.68,182.29,1670000,182.29 1948-05-06,180.94,182.14,180.16,181.65,1310000,181.65 1948-05-05,181.44,182.05,180.56,180.94,1240000,180.94 1948-05-04,181.09,182.43,180.70,181.44,1460000,181.44 1948-05-03,180.28,181.71,179.47,181.09,1150000,181.09 1948-04-30,180.65,181.64,179.69,180.51,1450000,180.51 1948-04-29,181.01,181.47,179.33,180.65,1480000,180.65 1948-04-28,180.97,182.01,180.16,181.01,1400000,181.01 1948-04-27,181.32,181.87,180.07,180.97,1420000,180.97 1948-04-26,183.09,183.09,180.93,181.32,1410000,181.32 1948-04-23,182.98,184.48,182.67,183.78,2470000,183.78 1948-04-22,181.37,183.40,180.88,182.98,2330000,182.98 1948-04-21,180.72,181.79,179.49,181.37,1670000,181.37 1948-04-20,181.05,181.87,179.98,180.72,1700000,180.72 1948-04-19,180.38,181.42,179.90,181.05,1530000,181.05 1948-04-16,180.27,181.69,179.90,180.63,2140000,180.63 1948-04-15,179.13,180.94,178.60,180.27,1650000,180.27 1948-04-14,179.45,179.91,178.59,179.13,1030000,179.13 1948-04-13,179.05,179.89,178.58,179.45,950000,179.45 1948-04-12,179.48,180.19,178.26,179.05,1030000,179.05 1948-04-09,178.80,179.91,178.40,179.16,1380000,179.16 1948-04-08,178.33,179.38,177.91,178.80,1060000,178.80 1948-04-07,178.77,179.14,177.70,178.33,1160000,178.33 1948-04-06,177.92,179.31,177.62,178.77,1310000,178.77 1948-04-05,177.45,178.27,177.06,177.92,1040000,177.92 1948-04-02,177.61,178.10,175.96,177.32,1080000,177.32 1948-04-01,177.20,178.14,176.08,177.61,1490000,177.61 1948-03-31,175.63,177.61,175.63,177.20,1780000,177.20 1948-03-30,173.65,175.38,173.30,175.23,1060000,175.23 1948-03-29,173.95,174.33,172.55,173.65,760000,173.65 1948-03-25,173.62,174.63,173.08,174.05,1040000,174.05 1948-03-24,173.50,174.45,172.84,173.62,1040000,173.62 1948-03-23,173.66,174.26,172.71,173.50,1160000,173.50 1948-03-22,173.12,175.23,173.05,173.66,2040000,173.66 1948-03-19,166.92,169.75,166.50,169.67,1160000,169.67 1948-03-18,166.24,168.02,166.07,166.92,890000,166.92 1948-03-17,165.39,166.60,165.03,166.24,930000,166.24 1948-03-16,167.21,167.21,165.03,165.39,940000,165.39 1948-03-15,167.62,168.16,167.09,167.62,690000,167.62 1948-03-12,167.21,167.54,166.51,166.99,690000,166.99 1948-03-11,167.48,168.27,166.67,167.21,820000,167.21 1948-03-10,166.76,167.74,166.04,167.48,730000,167.48 1948-03-09,167.54,167.54,166.04,166.76,660000,166.76 1948-03-08,168.94,169.13,167.46,167.71,740000,167.71 1948-03-05,168.13,168.64,167.20,168.35,630000,168.35 1948-03-04,168.61,168.92,167.69,168.13,580000,168.13 1948-03-03,168.75,169.28,168.04,168.61,760000,168.61 1948-03-02,168.14,169.18,167.78,168.75,780000,168.75 1948-03-01,167.46,168.62,167.46,168.14,770000,168.14 1948-02-27,167.56,167.56,165.92,166.80,770000,166.80 1948-02-26,168.39,168.71,167.17,167.56,620000,167.56 1948-02-25,167.80,169.01,167.72,168.39,710000,168.39 1948-02-24,167.60,168.24,166.81,167.80,640000,167.80 1948-02-20,167.86,167.96,166.38,167.44,700000,167.44 1948-02-19,168.04,168.98,167.34,167.86,680000,167.86 1948-02-18,167.89,168.36,167.23,168.04,610000,168.04 1948-02-17,168.30,169.23,167.47,167.89,720000,167.89 1948-02-16,166.86,168.96,166.86,168.30,830000,168.30 1948-02-13,165.69,167.23,164.99,166.33,930000,166.33 1948-02-11,165.65,166.41,164.07,165.69,1490000,165.69 1948-02-10,168.92,168.92,165.26,165.65,1460000,165.65 1948-02-09,169.79,170.83,169.33,169.82,660000,169.82 1948-02-06,169.18,169.67,167.95,168.81,920000,168.81 1948-02-05,170.43,170.43,168.13,169.18,1200000,169.18 1948-02-04,173.39,173.39,170.41,170.95,1200000,170.95 1948-02-03,174.92,175.03,173.54,173.95,700000,173.95 1948-02-02,175.05,176.05,174.57,174.92,770000,174.92 1948-01-30,174.47,175.58,173.61,174.76,890000,174.76 1948-01-29,173.39,175.06,173.39,174.47,1060000,174.47 1948-01-28,171.68,173.49,171.68,172.97,860000,172.97 1948-01-27,171.18,172.66,170.83,171.42,830000,171.42 1948-01-26,171.67,172.41,170.70,171.18,650000,171.18 1948-01-23,172.15,173.04,171.36,171.97,790000,171.97 1948-01-22,173.33,173.33,171.37,172.15,1110000,172.15 1948-01-21,175.27,176.10,173.32,173.53,1190000,173.53 1948-01-20,175.95,176.13,174.62,175.27,710000,175.27 1948-01-19,177.24,177.34,175.21,175.95,1050000,175.95 1948-01-16,177.03,177.71,176.28,177.15,760000,177.15 1948-01-15,177.49,178.06,176.54,177.03,780000,177.03 1948-01-14,177.49,178.16,176.50,177.37,820000,177.37 1948-01-13,179.29,179.29,177.25,177.49,950000,177.49 1948-01-12,180.20,180.62,178.70,179.33,1000000,179.33 1948-01-09,180.60,181.40,179.74,180.09,980000,180.09 1948-01-08,179.83,181.04,179.35,180.60,900000,180.60 1948-01-07,179.12,180.40,178.48,179.83,820000,179.83 1948-01-06,179.53,179.88,177.78,179.12,1030000,179.12 1948-01-05,181.04,181.69,179.19,179.53,1090000,179.53 1948-01-02,181.16,181.53,180.01,181.04,710000,181.04 1947-12-31,180.56,181.82,180.29,181.16,1540000,181.16 1947-12-30,178.58,180.93,178.43,180.56,1380000,180.56 1947-12-29,179.23,179.81,177.93,178.58,1190000,178.58 1947-12-26,180.71,180.71,178.90,179.28,930000,179.28 1947-12-24,180.71,181.49,179.72,180.84,1190000,180.84 1947-12-23,180.21,181.25,179.61,180.71,1360000,180.71 1947-12-22,181.06,181.78,179.98,180.21,1450000,180.21 1947-12-19,179.44,180.64,178.62,180.09,1250000,180.09 1947-12-18,179.81,180.53,179.03,179.44,1130000,179.44 1947-12-17,179.44,180.23,178.69,179.81,1250000,179.81 1947-12-16,179.69,180.25,178.91,179.44,1090000,179.44 1947-12-15,179.34,180.56,178.74,179.69,1430000,179.69 1947-12-12,177.37,178.92,176.82,178.37,1220000,178.37 1947-12-11,177.58,177.98,176.44,177.37,940000,177.37 1947-12-10,177.47,178.22,176.89,177.58,1120000,177.58 1947-12-09,176.71,177.98,176.00,177.47,1100000,177.47 1947-12-08,175.74,177.35,175.19,176.71,960000,176.71 1947-12-05,178.57,178.57,175.46,176.10,1290000,176.10 1947-12-04,179.63,179.83,178.16,178.79,970000,178.79 1947-12-03,180.57,180.57,179.18,179.63,930000,179.63 1947-12-02,180.61,181.77,180.20,180.76,890000,180.76 1947-12-01,179.40,181.09,179.09,180.61,800000,180.61 1947-11-28,180.94,181.15,179.30,179.51,930000,179.51 1947-11-26,181.35,182.39,180.67,180.94,910000,180.94 1947-11-25,181.98,182.43,180.92,181.35,870000,181.35 1947-11-24,182.33,183.06,181.23,181.98,790000,181.98 1947-11-21,183.17,183.97,182.23,182.61,980000,182.61 1947-11-20,182.71,183.68,181.15,183.17,960000,183.17 1947-11-19,181.71,182.98,181.69,182.71,1050000,182.71 1947-11-18,180.40,181.99,180.12,181.71,930000,181.71 1947-11-17,180.26,180.95,179.57,180.40,750000,180.40 1947-11-14,180.00,181.00,179.67,180.05,780000,180.05 1947-11-13,180.96,180.96,179.60,180.00,790000,180.00 1947-11-12,182.21,182.56,180.56,181.04,900000,181.04 1947-11-10,181.49,182.70,181.17,182.21,720000,182.21 1947-11-07,182.00,182.45,181.12,181.54,760000,181.54 1947-11-06,181.89,182.33,180.61,182.00,850000,182.00 1947-11-05,182.65,183.57,181.61,181.89,1050000,181.89 1947-11-03,182.48,183.51,181.85,182.65,760000,182.65 1947-10-31,181.32,182.40,180.43,181.81,800000,181.81 1947-10-30,183.04,183.04,179.93,181.32,1390000,181.32 1947-10-29,183.21,184.70,182.47,183.06,1140000,183.06 1947-10-28,183.27,184.24,182.72,183.21,930000,183.21 1947-10-27,182.73,183.70,181.76,183.27,850000,183.27 1947-10-24,184.47,184.47,181.55,182.53,1650000,182.53 1947-10-23,184.36,185.30,183.71,184.50,1190000,184.50 1947-10-22,185.09,185.89,184.00,184.36,1260000,184.36 1947-10-21,185.29,186.01,184.05,185.09,1400000,185.09 1947-10-20,184.27,186.24,184.27,185.29,1770000,185.29 1947-10-17,183.54,184.39,182.40,183.52,1270000,183.52 1947-10-16,183.28,184.56,182.71,183.54,1400000,183.54 1947-10-15,182.73,184.27,182.25,183.28,1930000,183.28 1947-10-14,180.49,183.14,180.47,182.73,1810000,182.73 1947-10-10,180.11,181.34,179.63,180.44,1120000,180.44 1947-10-09,178.78,180.37,178.56,180.11,790000,180.11 1947-10-08,180.01,180.56,178.26,178.78,1130000,178.78 1947-10-07,180.08,180.49,179.33,180.01,880000,180.01 1947-10-06,179.44,180.61,179.03,180.08,930000,180.08 1947-10-03,178.47,180.31,178.26,179.53,1270000,179.53 1947-10-02,178.10,178.96,177.50,178.47,850000,178.47 1947-10-01,177.49,178.87,176.89,178.10,1160000,178.10 1947-09-30,175.85,177.70,175.36,177.49,960000,177.49 1947-09-29,174.86,176.44,174.74,175.85,740000,175.85 1947-09-26,175.29,175.57,174.42,174.86,640000,174.86 1947-09-25,176.39,176.84,174.92,175.29,770000,175.29 1947-09-24,176.04,176.79,175.27,176.39,570000,176.39 1947-09-23,178.02,178.25,175.54,176.04,880000,176.04 1947-09-22,178.12,178.76,177.36,178.02,670000,178.02 1947-09-19,178.31,178.61,177.03,178.12,750000,178.12 1947-09-18,178.73,179.27,177.68,178.31,940000,178.31 1947-09-17,176.86,179.37,176.86,178.73,1260000,178.73 1947-09-16,175.30,177.01,174.73,176.70,740000,176.70 1947-09-15,175.92,175.99,174.82,175.30,500000,175.30 1947-09-12,176.16,176.67,174.98,175.92,600000,175.92 1947-09-11,176.24,177.11,175.31,176.16,800000,176.16 1947-09-10,175.32,176.61,174.70,176.24,740000,176.24 1947-09-09,175.14,176.07,174.02,175.32,750000,175.32 1947-09-08,176.97,176.97,174.79,175.14,830000,175.14 1947-09-05,177.27,177.51,175.69,177.13,720000,177.13 1947-09-04,178.84,178.84,176.57,177.27,870000,177.27 1947-09-03,179.81,180.08,178.55,179.09,650000,179.09 1947-09-02,178.85,180.56,178.75,179.81,650000,179.81 1947-08-29,177.70,179.15,177.63,178.85,580000,178.85 1947-08-28,177.88,178.64,177.22,177.70,580000,177.70 1947-08-27,177.73,178.24,177.14,177.88,480000,177.88 1947-08-26,177.57,178.05,176.54,177.73,620000,177.73 1947-08-25,179.74,179.78,177.33,177.57,810000,177.57 1947-08-22,179.42,180.29,179.34,179.74,580000,179.74 1947-08-21,179.01,179.77,178.50,179.42,580000,179.42 1947-08-20,179.75,180.10,178.76,179.01,600000,179.01 1947-08-19,180.44,180.64,179.23,179.75,600000,179.75 1947-08-18,181.04,181.43,179.98,180.44,710000,180.44 1947-08-15,179.87,181.58,179.44,181.04,880000,181.04 1947-08-14,179.80,180.43,178.64,179.87,690000,179.87 1947-08-13,179.94,180.71,179.17,179.80,690000,179.80 1947-08-12,179.14,180.76,179.14,179.94,690000,179.94 1947-08-11,180.13,180.16,178.22,178.98,720000,178.98 1947-08-08,181.99,181.99,179.77,180.13,790000,180.13 1947-08-07,182.35,182.57,181.03,182.11,660000,182.11 1947-08-06,183.08,183.48,181.85,182.35,660000,182.35 1947-08-05,182.51,184.05,182.27,183.08,750000,183.08 1947-08-04,183.69,183.69,182.01,182.51,730000,182.51 1947-08-01,183.18,184.38,182.35,183.81,770000,183.81 1947-07-31,181.17,183.56,181.17,183.18,840000,183.18 1947-07-30,182.05,182.33,179.77,180.91,1170000,180.91 1947-07-29,184.95,185.28,181.47,182.05,1390000,182.05 1947-07-28,186.38,187.51,184.76,184.95,1090000,184.95 1947-07-25,186.85,187.66,185.59,186.38,1150000,186.38 1947-07-24,185.08,187.36,185.08,186.85,1570000,186.85 1947-07-23,183.86,185.59,183.86,184.95,1070000,184.95 1947-07-22,183.52,184.41,182.73,183.78,780000,183.78 1947-07-21,184.60,184.86,183.02,183.52,850000,183.52 1947-07-18,183.83,184.87,182.51,184.60,920000,184.60 1947-07-17,185.46,185.92,183.43,183.83,1110000,183.83 1947-07-16,185.38,186.23,184.05,185.46,1070000,185.46 1947-07-15,185.60,186.24,184.23,185.38,1180000,185.38 1947-07-14,184.77,187.15,184.64,185.60,1660000,185.60 1947-07-11,183.14,185.52,183.14,184.77,1590000,184.77 1947-07-10,181.72,183.24,180.82,182.80,1020000,182.80 1947-07-09,182.66,183.29,181.12,181.72,1040000,181.72 1947-07-08,182.04,183.74,181.53,182.66,1390000,182.66 1947-07-07,181.73,182.61,180.62,182.04,1050000,182.04 1947-07-03,179.88,182.07,179.18,181.73,1250000,181.73 1947-07-02,180.33,181.17,179.33,179.88,1180000,179.88 1947-07-01,177.48,180.42,177.48,180.33,1090000,180.33 1947-06-30,176.56,177.66,175.82,177.30,670000,177.30 1947-06-27,176.58,177.20,175.77,176.56,650000,176.56 1947-06-26,175.73,177.15,175.44,176.58,820000,176.58 1947-06-25,174.54,176.19,173.93,175.73,830000,175.73 1947-06-24,177.44,177.55,174.13,174.54,1090000,174.54 1947-06-23,176.44,178.08,176.22,177.44,950000,177.44 1947-06-20,176.14,177.52,175.54,176.44,1130000,176.44 1947-06-19,174.94,176.81,174.43,176.14,1010000,176.14 1947-06-18,174.98,176.42,174.25,174.94,910000,174.94 1947-06-17,175.81,176.11,174.28,174.98,670000,174.98 1947-06-16,175.49,177.23,174.26,175.81,990000,175.81 1947-06-13,173.78,176.02,173.26,175.49,960000,175.49 1947-06-12,174.68,175.30,173.24,173.78,1040000,173.78 1947-06-11,171.50,174.78,171.50,174.68,1350000,174.68 1947-06-10,169.88,171.36,169.10,171.10,650000,171.10 1947-06-09,170.28,170.71,169.26,169.88,550000,169.88 1947-06-06,169.41,170.62,168.54,170.28,660000,170.28 1947-06-05,169.56,170.16,168.90,169.41,520000,169.41 1947-06-04,170.35,171.35,169.16,169.56,820000,169.56 1947-06-03,168.00,170.69,168.00,170.35,690000,170.35 1947-06-02,168.66,168.66,167.43,168.00,520000,168.00 1947-05-29,168.06,169.78,168.06,169.25,900000,169.25 1947-05-28,166.64,168.90,166.64,168.06,890000,168.06 1947-05-27,166.29,166.53,164.59,166.17,660000,166.17 1947-05-26,166.97,167.22,165.86,166.29,540000,166.29 1947-05-23,166.73,167.68,166.06,166.95,680000,166.95 1947-05-22,165.81,167.56,165.81,166.73,950000,166.73 1947-05-21,163.59,166.03,162.98,165.77,1030000,165.77 1947-05-20,163.55,164.81,162.99,163.59,920000,163.59 1947-05-19,163.21,164.43,161.38,163.55,1860000,163.55 1947-05-16,167.88,168.02,164.46,164.96,1430000,164.96 1947-05-15,166.96,168.42,166.96,167.88,770000,167.88 1947-05-14,167.34,167.34,165.93,166.68,1050000,166.68 1947-05-13,169.17,169.17,167.07,167.34,1210000,167.34 1947-05-12,171.67,171.69,169.76,169.80,700000,169.80 1947-05-09,171.56,172.21,170.52,171.54,720000,171.54 1947-05-08,172.49,172.87,171.20,171.56,670000,171.56 1947-05-07,172.77,173.14,172.08,172.49,600000,172.49 1947-05-06,173.83,173.83,171.89,172.77,750000,172.77 1947-05-05,174.00,175.08,173.58,174.21,740000,174.21 1947-05-02,171.91,174.45,171.85,173.45,950000,173.45 1947-05-01,170.64,172.65,170.62,171.91,920000,171.91 1947-04-30,168.76,170.85,168.76,170.64,780000,170.64 1947-04-29,168.85,169.47,167.42,168.70,840000,168.70 1947-04-28,169.13,170.00,168.56,168.85,590000,168.85 1947-04-25,170.19,170.38,168.60,168.93,780000,168.93 1947-04-24,170.87,171.20,169.81,170.19,620000,170.19 1947-04-23,170.94,171.71,169.92,170.87,700000,170.87 1947-04-22,169.50,171.25,169.24,170.94,890000,170.94 1947-04-21,169.32,171.47,169.32,169.50,1160000,169.50 1947-04-18,168.01,168.68,166.49,166.77,970000,166.77 1947-04-17,168.22,168.91,167.49,168.01,760000,168.01 1947-04-16,166.82,168.85,166.60,168.22,900000,168.22 1947-04-15,166.69,168.09,165.39,166.82,1450000,166.82 1947-04-14,170.42,170.42,166.17,166.69,2200000,166.69 1947-04-11,173.98,174.76,172.90,173.43,860000,173.43 1947-04-10,173.44,174.78,173.44,173.98,680000,173.98 1947-04-09,173.29,173.72,172.39,173.40,850000,173.40 1947-04-08,175.39,175.52,172.68,173.29,1020000,173.29 1947-04-07,176.16,176.16,174.82,175.39,630000,175.39 1947-04-03,177.21,177.21,175.60,176.52,680000,176.52 1947-04-02,177.45,178.28,176.87,177.32,680000,177.32 1947-04-01,177.20,177.74,176.18,177.45,770000,177.45 1947-03-31,178.36,178.58,177.01,177.20,720000,177.20 1947-03-28,179.19,179.68,178.18,178.63,830000,178.63 1947-03-27,177.67,179.51,177.67,179.19,1140000,179.19 1947-03-26,175.29,177.31,174.61,177.10,940000,177.10 1947-03-25,176.40,176.66,175.05,175.29,660000,175.29 1947-03-24,177.27,177.61,176.18,176.40,580000,176.40 1947-03-21,175.37,177.12,175.37,176.90,710000,176.90 1947-03-20,175.78,176.06,174.76,175.37,630000,175.37 1947-03-19,175.11,176.90,175.11,175.78,760000,175.78 1947-03-18,173.35,175.22,173.26,174.95,660000,174.95 1947-03-17,172.53,174.15,172.53,173.35,640000,173.35 1947-03-14,173.95,173.95,171.94,172.58,820000,172.58 1947-03-13,174.68,175.32,173.95,174.35,650000,174.35 1947-03-12,173.83,175.62,173.43,174.68,950000,174.68 1947-03-11,175.18,175.20,173.09,173.83,1190000,173.83 1947-03-10,175.84,176.36,174.73,175.18,830000,175.18 1947-03-07,181.19,181.19,176.87,177.05,1210000,177.05 1947-03-06,181.16,182.48,180.60,181.88,1020000,181.88 1947-03-05,179.77,181.56,179.32,181.16,990000,181.16 1947-03-04,179.43,180.31,178.46,179.77,680000,179.77 1947-03-03,179.29,179.84,178.29,179.43,690000,179.43 1947-02-28,178.91,179.73,177.75,178.90,690000,178.90 1947-02-27,177.67,179.35,177.67,178.91,960000,178.91 1947-02-26,179.02,179.02,176.34,177.22,1350000,177.22 1947-02-25,181.40,181.92,178.86,179.31,1280000,179.31 1947-02-24,182.26,182.47,181.03,181.40,810000,181.40 1947-02-21,181.22,182.76,181.22,182.26,860000,182.26 1947-02-20,180.78,181.40,179.12,180.74,1000000,180.74 1947-02-19,181.85,181.85,179.85,180.78,980000,180.78 1947-02-18,182.20,182.91,181.26,181.93,870000,181.93 1947-02-17,181.36,182.74,180.89,182.20,870000,182.20 1947-02-14,182.18,182.23,180.62,181.64,940000,181.64 1947-02-13,184.06,184.25,181.64,182.18,1340000,182.18 1947-02-11,183.57,184.43,181.81,184.06,1300000,184.06 1947-02-10,184.49,184.96,183.12,183.57,1300000,183.57 1947-02-07,181.57,184.18,181.33,183.74,1980000,183.74 1947-02-06,182.27,182.27,180.72,181.57,1120000,181.57 1947-02-05,182.28,183.12,181.45,182.52,1180000,182.52 1947-02-04,181.92,183.15,181.44,182.28,1350000,182.28 1947-02-03,180.88,182.37,180.57,181.92,1360000,181.92 1947-01-31,179.74,181.34,179.49,180.44,1310000,180.44 1947-01-30,180.17,181.18,179.33,179.74,1340000,179.74 1947-01-29,178.68,180.47,178.03,180.17,1530000,180.17 1947-01-28,177.28,178.98,177.17,178.68,1080000,178.68 1947-01-27,175.35,177.55,175.05,177.28,900000,177.28 1947-01-24,175.13,175.94,174.49,175.49,950000,175.49 1947-01-23,173.77,175.35,173.59,175.13,880000,175.13 1947-01-22,173.51,174.19,172.81,173.77,670000,173.77 1947-01-21,173.95,173.95,172.64,173.51,700000,173.51 1947-01-20,175.46,175.46,173.69,174.06,810000,174.06 1947-01-17,172.58,174.87,172.58,174.76,850000,174.76 1947-01-16,172.10,172.39,170.13,171.95,1050000,171.95 1947-01-15,172.63,173.46,171.70,172.10,770000,172.10 1947-01-14,172.49,173.24,171.31,172.63,850000,172.63 1947-01-13,174.50,174.50,170.99,172.49,1590000,172.49 1947-01-10,178.43,178.84,176.59,177.43,1060000,177.43 1947-01-09,178.06,179.06,177.94,178.43,720000,178.43 1947-01-08,177.49,178.43,176.54,178.06,790000,178.06 1947-01-07,178.43,179.25,177.12,177.49,980000,177.49 1947-01-06,176.99,179.04,176.99,178.43,980000,178.43 1947-01-03,176.39,177.16,174.71,176.76,880000,176.76 1947-01-02,177.20,177.83,176.04,176.39,750000,176.39 1946-12-31,176.23,177.89,175.79,177.20,1820000,177.20 1946-12-30,175.77,177.00,175.15,176.23,1400000,176.23 1946-12-27,175.21,176.17,173.88,175.66,1290000,175.66 1946-12-26,176.79,176.79,174.54,175.21,1150000,175.21 1946-12-24,177.36,177.51,176.25,176.95,950000,176.95 1946-12-23,178.32,178.54,176.85,177.36,1170000,177.36 1946-12-20,177.29,178.58,176.82,177.85,1470000,177.85 1946-12-19,175.28,178.06,175.28,177.29,1740000,177.29 1946-12-18,174.47,175.62,173.62,174.84,1110000,174.84 1946-12-17,174.85,175.42,173.93,174.47,1020000,174.47 1946-12-16,174.73,175.93,174.18,174.85,1010000,174.85 1946-12-13,173.91,174.41,172.57,173.90,1000000,173.90 1946-12-12,175.75,175.75,173.17,173.91,1060000,173.91 1946-12-11,175.92,176.67,174.80,176.07,1230000,176.07 1946-12-10,175.76,177.21,174.84,175.92,1730000,175.92 1946-12-09,173.43,176.48,173.43,175.76,2840000,175.76 1946-12-06,169.95,170.92,169.20,170.39,1060000,170.39 1946-12-05,170.33,170.66,168.63,169.95,1000000,169.95 1946-12-04,168.05,170.98,167.48,170.33,1440000,170.33 1946-12-03,167.50,168.60,166.20,168.05,960000,168.05 1946-12-02,169.07,169.07,166.74,167.50,810000,167.50 1946-11-29,168.34,170.25,168.23,169.78,1010000,169.78 1946-11-27,167.35,169.18,167.35,168.34,1070000,168.34 1946-11-26,165.31,167.81,165.31,166.94,1080000,166.94 1946-11-25,165.10,165.99,164.37,165.23,790000,165.23 1946-11-22,164.12,164.49,162.29,163.55,1200000,163.55 1946-11-21,165.98,165.98,163.50,164.12,1380000,164.12 1946-11-20,167.88,167.99,166.20,166.91,970000,166.91 1946-11-19,167.91,168.35,166.28,167.88,910000,167.88 1946-11-18,169.03,169.11,167.23,167.91,770000,167.91 1946-11-15,170.88,171.48,168.89,169.67,930000,169.67 1946-11-14,169.84,171.45,169.16,170.88,960000,170.88 1946-11-13,170.52,170.52,168.02,169.84,1050000,169.84 1946-11-12,171.80,173.48,170.41,170.87,1370000,170.87 1946-11-08,169.75,171.78,169.75,170.79,1000000,170.79 1946-11-07,168.88,170.59,167.50,169.60,1140000,169.60 1946-11-06,174.40,175.00,168.38,168.88,2000000,168.88 1946-11-04,173.03,175.78,173.03,174.40,1830000,174.40 1946-11-01,169.50,172.33,169.50,171.76,1670000,171.76 1946-10-31,164.71,169.68,164.71,169.15,1700000,169.15 1946-10-30,164.21,165.32,160.49,164.20,1940000,164.20 1946-10-29,166.04,166.62,163.98,164.21,1240000,164.21 1946-10-28,168.44,168.48,165.98,166.04,1000000,166.04 1946-10-25,169.96,169.96,167.84,168.76,920000,168.76 1946-10-24,170.67,170.90,169.14,169.98,860000,169.98 1946-10-23,171.25,171.27,168.68,170.67,950000,170.67 1946-10-22,171.93,172.34,170.16,171.25,870000,171.25 1946-10-21,171.34,172.59,170.63,171.93,840000,171.93 1946-10-18,171.76,172.51,170.32,171.65,920000,171.65 1946-10-17,173.61,173.61,170.47,171.76,1310000,171.76 1946-10-16,175.94,177.05,174.03,174.35,1650000,174.35 1946-10-15,173.05,176.52,173.05,175.94,2370000,175.94 1946-10-14,167.97,170.60,167.53,169.86,1290000,169.86 1946-10-11,165.60,168.59,165.60,167.97,1470000,167.97 1946-10-10,163.12,165.53,161.61,164.94,2220000,164.94 1946-10-09,166.53,166.53,162.80,163.12,2020000,163.12 1946-10-08,168.87,170.00,167.00,167.34,1260000,167.34 1946-10-07,169.00,169.83,167.82,168.87,950000,168.87 1946-10-04,171.13,171.13,169.06,169.80,920000,169.80 1946-10-03,172.72,173.10,171.13,171.64,920000,171.64 1946-10-02,171.47,173.39,171.40,172.72,960000,172.72 1946-10-01,172.42,172.42,170.43,171.47,890000,171.47 1946-09-30,173.56,173.56,170.44,172.42,1060000,172.42 1946-09-27,174.96,175.18,173.35,174.09,980000,174.09 1946-09-26,172.95,175.45,171.59,174.96,1300000,174.96 1946-09-25,169.43,173.44,169.43,172.95,1800000,172.95 1946-09-24,166.56,169.75,164.21,168.89,2230000,168.89 1946-09-23,169.06,172.15,166.09,166.56,2120000,166.56 1946-09-20,165.17,170.13,164.77,169.06,2820000,169.06 1946-09-19,169.05,169.05,164.09,165.17,2890000,165.17 1946-09-18,173.43,173.43,168.40,169.07,2100000,169.07 1946-09-17,174.45,174.82,172.13,173.66,1390000,173.66 1946-09-16,173.39,176.26,173.02,174.45,1490000,174.45 1946-09-13,171.70,173.99,170.87,173.39,1720000,173.39 1946-09-12,172.13,173.34,170.00,171.70,2010000,171.70 1946-09-11,167.80,173.20,167.80,172.13,2870000,172.13 1946-09-10,172.03,172.89,166.56,167.30,3300000,167.30 1946-09-09,177.52,177.52,170.53,172.03,2840000,172.03 1946-09-06,181.18,181.67,178.43,179.96,1670000,179.96 1946-09-05,177.96,181.81,177.96,181.18,2360000,181.18 1946-09-04,178.68,178.93,173.64,176.72,3620000,176.72 1946-09-03,188.21,188.21,177.49,178.68,2910000,178.68 1946-08-30,190.47,190.49,187.44,189.19,1170000,189.19 1946-08-29,190.03,192.50,189.71,190.47,1060000,190.47 1946-08-28,191.04,191.28,187.26,190.03,2100000,190.03 1946-08-27,195.46,195.46,190.03,191.04,1790000,191.04 1946-08-26,197.75,198.97,196.47,196.99,760000,196.99 1946-08-23,196.91,198.69,196.91,197.75,770000,197.75 1946-08-22,198.05,198.05,194.53,196.66,1540000,196.66 1946-08-21,201.27,202.49,199.70,200.00,840000,200.00 1946-08-20,200.22,201.54,200.22,201.27,700000,201.27 1946-08-19,200.69,201.18,198.90,200.19,660000,200.19 1946-08-16,201.38,201.38,200.14,200.69,690000,200.69 1946-08-15,203.81,203.81,202.30,202.49,620000,202.49 1946-08-14,204.52,205.01,203.59,203.99,800000,203.99 1946-08-13,203.36,204.94,203.28,204.52,930000,204.52 1946-08-12,203.57,203.90,202.81,203.36,700000,203.36 1946-08-09,204.10,204.46,203.16,203.57,910000,203.57 1946-08-08,203.13,204.56,203.13,204.10,890000,204.10 1946-08-07,201.35,203.08,201.18,202.96,880000,202.96 1946-08-06,201.93,202.05,200.47,201.35,730000,201.35 1946-08-05,202.82,203.03,201.39,201.93,700000,201.93 1946-08-02,202.26,203.38,201.70,202.82,750000,202.82 1946-08-01,201.56,202.97,201.32,202.26,830000,202.26 1946-07-31,199.40,202.15,198.78,201.56,1020000,201.56 1946-07-30,198.22,200.13,198.15,199.40,810000,199.40 1946-07-29,197.63,199.11,197.46,198.22,720000,198.22 1946-07-26,196.47,198.53,196.47,197.63,980000,197.63 1946-07-25,195.37,197.58,195.28,196.25,900000,196.25 1946-07-24,195.22,196.30,194.33,195.37,1170000,195.37 1946-07-23,199.83,199.83,194.79,195.22,1690000,195.22 1946-07-22,201.13,201.60,199.89,200.54,690000,200.54 1946-07-19,201.86,202.06,200.68,201.13,650000,201.13 1946-07-18,202.25,203.46,201.47,201.86,730000,201.86 1946-07-17,200.85,202.79,200.85,202.25,920000,202.25 1946-07-16,200.86,201.44,199.48,200.71,1180000,200.71 1946-07-15,204.20,204.42,200.31,200.86,1170000,200.86 1946-07-12,205.49,205.49,202.85,204.20,1130000,204.20 1946-07-11,207.52,207.52,205.96,206.30,990000,206.30 1946-07-10,207.43,208.17,206.84,207.56,910000,207.56 1946-07-09,206.62,207.91,206.16,207.43,790000,207.43 1946-07-08,206.72,207.40,206.37,206.62,680000,206.62 1946-07-05,207.06,207.40,206.47,206.72,490000,206.72 1946-07-03,206.64,207.50,206.36,207.06,650000,207.06 1946-07-02,206.47,207.43,205.56,206.64,760000,206.64 1946-07-01,205.79,208.59,205.79,206.47,1570000,206.47 1946-06-28,205.03,206.41,204.32,205.62,1010000,205.62 1946-06-27,202.83,205.68,202.83,205.03,1200000,205.03 1946-06-26,202.54,202.98,200.52,202.10,1020000,202.10 1946-06-25,203.56,203.83,202.11,202.54,880000,202.54 1946-06-24,203.09,204.65,202.68,203.56,990000,203.56 1946-06-21,200.52,203.42,198.98,203.09,1340000,203.09 1946-06-20,205.65,205.65,200.31,200.52,1310000,200.52 1946-06-19,206.93,206.93,205.24,205.74,1010000,205.74 1946-06-18,210.01,210.01,207.42,207.71,1150000,207.71 1946-06-17,210.36,211.16,209.65,210.13,1020000,210.13 1946-06-14,210.56,211.46,209.73,210.36,980000,210.36 1946-06-13,209.26,211.25,209.26,210.56,1150000,210.56 1946-06-12,209.05,209.34,207.52,208.96,970000,208.96 1946-06-11,210.68,211.14,208.92,209.05,1090000,209.05 1946-06-10,209.96,211.44,209.73,210.68,1010000,210.68 1946-06-07,209.50,210.40,208.63,209.96,1020000,209.96 1946-06-06,209.78,210.03,208.33,209.50,980000,209.50 1946-06-05,210.03,211.42,209.30,209.78,1170000,209.78 1946-06-04,211.37,211.37,209.03,210.03,1210000,210.03 1946-06-03,212.28,212.48,210.90,211.47,1210000,211.47 1946-05-31,212.50,213.29,210.97,212.28,1310000,212.28 1946-05-29,211.70,213.36,210.34,212.50,2000000,212.50 1946-05-28,209.42,212.18,209.29,211.70,2220000,211.70 1946-05-27,208.41,210.34,208.41,209.42,1730000,209.42 1946-05-24,208.05,208.26,205.96,207.69,1210000,207.69 1946-05-23,208.00,209.15,207.21,208.05,1350000,208.05 1946-05-22,207.25,208.38,207.00,208.00,1610000,208.00 1946-05-21,207.13,208.53,206.58,207.25,1250000,207.25 1946-05-20,205.80,207.42,205.05,207.13,910000,207.13 1946-05-17,206.17,207.04,205.50,206.56,980000,206.56 1946-05-16,205.07,206.53,204.38,206.17,1140000,206.17 1946-05-15,206.69,206.82,204.23,205.07,1020000,205.07 1946-05-14,207.34,207.47,205.88,206.69,1140000,206.69 1946-05-13,208.06,208.40,206.63,207.34,1250000,207.34 1946-05-10,204.09,207.84,204.09,207.10,1820000,207.10 1946-05-09,204.17,204.68,202.37,204.07,1070000,204.07 1946-05-08,203.51,205.05,202.35,204.17,1210000,204.17 1946-05-07,200.65,203.97,199.94,203.51,1350000,203.51 1946-05-06,202.00,202.00,199.26,200.65,1080000,200.65 1946-05-03,204.31,204.31,202.53,203.25,1020000,203.25 1946-05-02,205.67,206.25,204.47,204.98,1000000,204.98 1946-05-01,206.59,206.59,205.07,205.67,980000,205.67 1946-04-30,206.09,207.23,205.53,206.77,1000000,206.77 1946-04-29,206.13,206.97,205.07,206.09,1000000,206.09 1946-04-26,204.60,205.21,203.13,204.59,1210000,204.59 1946-04-25,205.60,205.60,203.09,204.60,1390000,204.60 1946-04-24,207.31,208.12,205.81,206.13,1500000,206.13 1946-04-23,207.99,208.19,206.01,207.31,1380000,207.31 1946-04-22,208.06,208.94,207.33,207.99,1210000,207.99 1946-04-18,207.93,209.10,207.27,208.31,1500000,208.31 1946-04-17,207.97,209.36,206.97,207.93,1530000,207.93 1946-04-16,206.28,208.51,206.28,207.97,1460000,207.97 1946-04-15,206.02,206.36,204.57,206.01,1170000,206.01 1946-04-12,206.93,207.89,206.16,206.96,1240000,206.96 1946-04-11,207.90,207.90,206.05,206.93,1210000,206.93 1946-04-10,208.03,208.93,207.20,208.02,1580000,208.02 1946-04-09,205.43,208.54,205.43,208.03,1710000,208.03 1946-04-08,204.98,206.00,204.31,205.43,1250000,205.43 1946-04-05,204.77,205.18,202.88,204.04,1660000,204.04 1946-04-04,203.25,205.79,203.25,204.77,2130000,204.77 1946-04-03,199.83,203.29,199.81,203.12,1560000,203.12 1946-04-02,199.19,200.16,198.98,199.83,1040000,199.83 1946-04-01,199.75,199.97,198.47,199.19,1050000,199.19 1946-03-29,198.23,200.36,198.23,199.56,1230000,199.56 1946-03-28,198.73,198.92,197.27,198.18,900000,198.18 1946-03-27,199.81,199.81,197.83,198.73,1000000,198.73 1946-03-26,200.55,201.85,200.04,200.56,1440000,200.56 1946-03-25,198.27,200.80,198.27,200.55,1640000,200.55 1946-03-22,196.70,198.20,195.92,197.19,1180000,197.19 1946-03-21,195.53,197.00,195.10,196.70,1210000,196.70 1946-03-20,194.09,195.90,193.63,195.53,1280000,195.53 1946-03-19,195.33,196.23,193.77,194.09,1050000,194.09 1946-03-18,194.05,195.86,194.05,195.33,1070000,195.33 1946-03-15,189.98,192.14,189.71,191.66,1060000,191.66 1946-03-14,190.36,191.76,189.32,189.98,1090000,189.98 1946-03-13,192.87,192.87,188.86,190.36,1620000,190.36 1946-03-12,192.89,193.86,192.39,193.52,720000,193.52 1946-03-11,194.45,194.73,192.34,192.89,880000,192.89 1946-03-08,192.08,194.40,192.08,193.70,970000,193.70 1946-03-07,190.30,191.93,190.30,191.50,900000,191.50 1946-03-06,190.49,190.77,189.39,190.28,890000,190.28 1946-03-05,188.91,191.16,188.91,190.49,1050000,190.49 1946-03-04,188.73,188.87,186.77,188.46,970000,188.46 1946-03-01,190.09,190.58,188.90,189.42,820000,189.42 1946-02-28,189.06,190.64,188.19,190.09,1180000,190.09 1946-02-27,187.34,189.56,187.34,189.06,1400000,189.06 1946-02-26,187.23,188.09,184.05,186.02,2650000,186.02 1946-02-25,194.04,194.04,186.87,187.23,2400000,187.23 1946-02-21,193.05,196.30,193.05,195.62,1590000,195.62 1946-02-20,195.06,195.06,191.17,192.38,2150000,192.38 1946-02-19,200.42,200.42,194.90,196.13,2300000,196.13 1946-02-18,204.13,204.13,200.84,201.63,1560000,201.63 1946-02-15,201.06,203.56,201.06,203.09,1780000,203.09 1946-02-14,198.74,201.18,198.45,199.75,1290000,199.75 1946-02-13,200.81,200.81,197.65,198.74,1690000,198.74 1946-02-11,202.30,202.72,200.59,201.14,1440000,201.14 1946-02-08,205.09,205.60,203.62,204.38,1260000,204.38 1946-02-07,205.48,205.73,203.63,205.09,1490000,205.09 1946-02-06,206.61,207.24,205.15,205.48,1750000,205.48 1946-02-05,205.84,206.84,204.55,206.61,1670000,206.61 1946-02-04,206.97,207.49,205.05,205.84,1660000,205.84 1946-02-01,204.67,206.06,203.69,205.79,1560000,205.79 1946-01-31,204.84,205.22,203.07,204.67,1690000,204.67 1946-01-30,205.35,206.59,203.37,204.84,2280000,204.84 1946-01-29,204.62,206.49,203.75,205.35,2910000,205.35 1946-01-28,202.10,205.50,202.10,204.62,3490000,204.62 1946-01-25,200.04,200.13,198.17,199.50,1760000,199.50 1946-01-24,198.84,200.86,198.68,200.04,2210000,200.04 1946-01-23,197.35,199.48,197.20,198.84,2050000,198.84 1946-01-22,196.63,198.00,195.63,197.35,1530000,197.35 1946-01-21,198.03,198.03,195.52,196.63,1680000,196.63 1946-01-18,203.49,203.70,200.78,202.18,3230000,202.18 1946-01-17,203.81,205.03,202.95,203.49,2200000,203.49 1946-01-16,202.97,204.50,201.93,203.81,2100000,203.81 1946-01-15,201.93,204.02,201.73,202.97,2720000,202.97 1946-01-14,200.25,202.59,200.25,201.93,2740000,201.93 1946-01-11,199.16,200.86,198.67,200.04,2250000,200.04 1946-01-10,197.33,199.78,197.17,199.16,2470000,199.16 1946-01-09,195.16,198.40,195.16,197.33,2930000,197.33 1946-01-08,192.04,194.98,192.04,194.65,2160000,194.65 1946-01-07,191.47,192.40,190.87,191.77,1230000,191.77 1946-01-04,191.25,191.81,190.27,190.90,1080000,190.90 1946-01-03,191.66,191.97,189.77,191.25,1390000,191.25 1946-01-02,192.65,192.65,191.15,191.66,1050000,191.66 1945-12-31,192.84,193.47,192.07,192.91,1010000,192.91 1945-12-28,192.31,192.95,191.58,192.43,1090000,192.43 1945-12-27,192.76,193.89,191.76,192.31,1330000,192.31 1945-12-26,191.59,193.45,191.59,192.76,1420000,192.76 1945-12-21,189.36,189.67,187.51,189.07,940000,189.07 1945-12-20,190.22,190.22,188.84,189.36,800000,189.36 1945-12-19,190.98,191.43,190.11,190.62,980000,190.62 1945-12-18,190.37,191.78,189.33,190.98,1360000,190.98 1945-12-17,192.87,192.87,189.80,190.37,1990000,190.37 1945-12-14,193.52,193.86,192.50,193.34,1130000,193.34 1945-12-13,193.96,194.62,192.84,193.52,1220000,193.52 1945-12-12,195.39,195.39,193.18,193.96,1680000,193.96 1945-12-11,195.64,196.47,194.34,195.82,1690000,195.82 1945-12-10,195.18,196.59,194.76,195.64,2140000,195.64 1945-12-07,193.84,194.78,193.18,194.08,2050000,194.08 1945-12-06,193.08,194.62,192.70,193.84,2290000,193.84 1945-12-05,193.06,193.67,191.75,193.08,1860000,193.08 1945-12-04,193.65,194.12,192.17,193.06,2310000,193.06 1945-12-03,192.40,194.36,192.16,193.65,2610000,193.65 1945-11-30,189.77,191.84,189.77,191.46,1820000,191.46 1945-11-29,189.99,190.22,188.80,189.58,1750000,189.58 1945-11-28,190.45,191.47,189.58,189.99,1800000,189.99 1945-11-27,188.79,190.90,188.79,190.45,1830000,190.45 1945-11-26,186.44,188.55,186.44,188.16,1530000,188.16 1945-11-23,189.26,189.26,187.34,187.82,1350000,187.82 1945-11-21,191.47,191.47,188.97,189.54,1910000,189.54 1945-11-20,191.51,192.83,190.69,192.12,2180000,192.12 1945-11-19,192.27,192.50,190.20,191.51,2020000,191.51 1945-11-16,191.13,192.95,191.02,192.13,2340000,192.13 1945-11-15,189.77,191.60,189.58,191.13,2010000,191.13 1945-11-14,190.56,190.61,188.82,189.77,1610000,189.77 1945-11-13,191.37,192.46,190.23,190.56,2500000,190.56 1945-11-09,191.72,192.46,190.68,191.46,1830000,191.46 1945-11-08,192.04,192.78,190.79,191.72,1960000,191.72 1945-11-07,190.13,192.76,190.13,192.04,2380000,192.04 1945-11-05,188.58,189.69,188.02,189.50,1650000,189.50 1945-11-02,188.84,189.40,187.54,188.62,1840000,188.62 1945-11-01,187.02,189.33,187.02,188.84,2210000,188.84 1945-10-31,184.16,186.74,183.59,186.60,2060000,186.60 1945-10-30,184.24,184.61,182.88,184.16,1170000,184.16 1945-10-29,185.39,186.02,183.90,184.24,1260000,184.24 1945-10-26,184.54,186.01,184.09,185.39,1300000,185.39 1945-10-25,183.72,185.13,183.43,184.54,1230000,184.54 1945-10-24,185.52,185.52,183.02,183.72,1370000,183.72 1945-10-23,187.06,187.52,184.76,186.15,1370000,186.15 1945-10-22,185.60,187.26,185.29,187.06,1140000,187.06 1945-10-19,186.78,187.50,185.12,185.34,1730000,185.34 1945-10-18,186.10,187.55,185.68,186.78,1670000,186.78 1945-10-17,185.49,186.72,184.92,186.10,1800000,186.10 1945-10-16,185.51,185.98,184.42,185.49,1630000,185.49 1945-10-15,185.72,186.32,185.00,185.51,1630000,185.51 1945-10-11,186.05,186.10,184.83,185.72,1560000,185.72 1945-10-10,185.43,186.52,185.07,186.05,1700000,186.05 1945-10-09,185.46,185.95,184.26,185.43,1640000,185.43 1945-10-08,184.77,186.02,184.66,185.46,1780000,185.46 1945-10-05,183.06,184.48,182.80,183.94,1420000,183.94 1945-10-04,183.33,183.75,182.32,183.06,1340000,183.06 1945-10-03,183.85,184.20,182.32,183.33,1430000,183.33 1945-10-02,183.37,185.05,183.13,183.85,1800000,183.85 1945-10-01,181.93,183.92,181.93,183.37,1990000,183.37 1945-09-28,178.83,180.31,178.83,180.11,1380000,180.11 1945-09-27,178.95,179.36,177.82,178.57,1060000,178.57 1945-09-26,179.41,179.41,178.12,178.95,1040000,178.95 1945-09-25,179.51,180.42,178.89,179.42,1190000,179.42 1945-09-24,179.49,179.79,178.71,179.51,890000,179.51 1945-09-21,180.22,180.80,178.87,179.69,1340000,179.69 1945-09-20,179.51,180.72,178.92,180.22,1500000,180.22 1945-09-19,178.32,180.06,178.32,179.51,1690000,179.51 1945-09-18,175.19,177.76,175.19,177.58,1160000,177.58 1945-09-17,175.11,175.11,173.30,174.75,900000,174.75 1945-09-14,178.59,178.59,177.20,177.74,1020000,177.74 1945-09-13,178.99,179.33,178.21,178.59,1170000,178.59 1945-09-12,177.77,179.33,177.55,178.99,1340000,178.99 1945-09-11,177.03,178.04,176.33,177.77,1130000,177.77 1945-09-10,176.99,177.78,176.62,177.03,1110000,177.03 1945-09-07,175.96,177.57,175.76,176.61,1330000,176.61 1945-09-06,174.24,176.14,174.17,175.96,1380000,175.96 1945-09-05,173.90,174.49,173.23,174.24,980000,174.24 1945-09-04,174.29,174.86,173.52,173.90,1070000,173.90 1945-08-31,172.73,174.54,172.73,174.29,1110000,174.29 1945-08-30,172.09,172.58,171.46,172.37,890000,172.37 1945-08-29,172.32,172.51,171.34,172.09,920000,172.09 1945-08-28,171.96,172.93,171.43,172.32,1260000,172.32 1945-08-27,170.11,172.26,170.11,171.96,1570000,171.96 1945-08-24,167.64,170.04,167.54,169.89,1320000,169.89 1945-08-23,164.99,167.94,164.99,167.64,1190000,167.64 1945-08-22,163.38,164.94,163.35,164.54,760000,164.54 1945-08-21,163.11,163.88,162.28,163.38,1160000,163.38 1945-08-20,164.38,164.82,162.68,163.11,1320000,163.11 1945-08-17,164.79,166.08,164.01,164.38,1210000,164.38 1945-08-14,164.11,165.22,164.04,164.79,910000,164.79 1945-08-13,165.02,165.02,162.81,164.11,970000,164.11 1945-08-10,164.55,166.54,164.07,165.14,1690000,165.14 1945-08-09,161.83,164.82,161.14,164.55,1460000,164.55 1945-08-08,161.55,162.74,161.17,161.83,700000,161.83 1945-08-07,162.87,162.87,161.16,161.55,980000,161.55 1945-08-06,163.06,163.69,162.66,163.19,490000,163.19 1945-08-03,162.49,163.23,162.27,163.06,510000,163.06 1945-08-02,162.72,163.08,161.82,162.49,600000,162.49 1945-08-01,162.88,163.21,162.27,162.72,650000,162.72 1945-07-31,162.21,163.36,162.21,162.88,870000,162.88 1945-07-30,160.92,162.51,160.88,162.09,910000,162.09 1945-07-27,160.91,161.34,159.95,160.92,920000,160.92 1945-07-26,162.44,162.91,160.71,160.91,1440000,160.91 1945-07-25,162.10,162.63,162.10,162.44,620000,162.44 1945-07-24,161.65,162.00,160.98,161.73,640000,161.73 1945-07-23,162.50,162.82,161.49,161.65,760000,161.65 1945-07-20,162.81,163.22,162.04,162.50,650000,162.50 1945-07-19,161.95,163.39,161.95,162.81,780000,162.81 1945-07-18,162.43,162.87,160.62,161.69,1450000,161.69 1945-07-17,165.22,165.22,162.29,162.43,1560000,162.43 1945-07-16,166.67,167.08,165.46,165.82,790000,165.82 1945-07-13,166.85,167.41,166.29,166.67,960000,166.67 1945-07-12,166.59,167.24,165.51,166.85,970000,166.85 1945-07-11,167.09,167.49,166.16,166.59,810000,166.59 1945-07-10,166.60,167.79,166.60,167.09,940000,167.09 1945-07-09,164.67,166.76,164.64,166.55,800000,166.55 1945-07-06,164.26,165.07,163.47,164.67,960000,164.67 1945-07-05,165.36,165.36,164.02,164.26,920000,164.26 1945-07-03,165.91,166.39,165.35,165.73,860000,165.73 1945-07-02,165.39,166.75,165.39,165.91,1380000,165.91 1945-06-29,166.22,166.24,163.78,164.57,2020000,164.57 1945-06-28,168.78,168.80,165.70,166.22,2940000,166.22 1945-06-27,168.92,169.27,168.36,168.78,1690000,168.78 1945-06-26,168.59,169.55,168.40,168.92,2140000,168.92 1945-06-25,168.24,168.90,167.97,168.59,1890000,168.59 1945-06-22,168.14,168.69,167.48,167.90,1850000,167.90 1945-06-21,167.74,168.84,167.53,168.14,2100000,168.14 1945-06-20,167.23,168.01,166.81,167.74,1680000,167.74 1945-06-19,166.94,167.80,166.50,167.23,1560000,167.23 1945-06-18,167.54,167.72,166.67,166.94,1930000,166.94 1945-06-15,167.08,168.10,166.92,167.64,1900000,167.64 1945-06-14,166.75,167.47,166.51,167.08,1850000,167.08 1945-06-13,166.39,167.10,166.07,166.75,1590000,166.75 1945-06-12,166.25,166.78,165.89,166.39,1320000,166.39 1945-06-11,166.85,167.20,166.09,166.25,1490000,166.25 1945-06-08,167.16,167.67,166.54,166.83,1710000,166.83 1945-06-07,167.29,167.63,166.58,167.16,1300000,167.16 1945-06-06,168.13,168.16,166.58,167.29,1520000,167.29 1945-06-05,168.08,168.80,167.54,168.13,1510000,168.13 1945-06-04,167.96,168.49,167.36,168.08,1540000,168.08 1945-06-01,168.30,168.51,167.47,168.08,1430000,168.08 1945-05-31,169.08,169.41,167.90,168.30,1220000,168.30 1945-05-29,168.21,169.53,168.06,169.08,1600000,169.08 1945-05-28,166.45,168.75,166.45,168.21,1570000,168.21 1945-05-25,164.41,165.55,164.38,165.12,1300000,165.12 1945-05-24,164.50,164.81,163.73,164.41,960000,164.41 1945-05-23,165.72,165.72,163.80,164.50,1310000,164.50 1945-05-22,165.99,166.61,165.47,165.91,1050000,165.91 1945-05-21,166.44,166.93,165.61,165.99,1080000,165.99 1945-05-18,165.20,166.47,165.19,166.17,1430000,166.17 1945-05-17,164.50,165.85,164.23,165.20,1370000,165.20 1945-05-16,164.00,165.07,163.76,164.50,1210000,164.50 1945-05-15,163.45,164.31,163.07,164.00,1010000,164.00 1945-05-14,163.96,164.41,163.16,163.45,980000,163.45 1945-05-11,163.09,163.82,162.60,163.21,1070000,163.21 1945-05-10,164.56,164.56,162.68,163.09,1510000,163.09 1945-05-09,166.42,166.72,165.06,165.24,1490000,165.24 1945-05-08,166.53,167.25,165.62,166.42,1580000,166.42 1945-05-07,166.71,167.25,165.76,166.53,1950000,166.53 1945-05-04,165.84,166.61,165.40,166.27,1410000,166.27 1945-05-03,165.03,166.02,164.77,165.84,1340000,165.84 1945-05-02,165.09,165.38,164.45,165.03,1140000,165.03 1945-05-01,165.44,166.18,164.49,165.09,1530000,165.09 1945-04-30,164.71,165.71,164.10,165.44,1500000,165.44 1945-04-27,163.22,164.27,163.12,163.94,1360000,163.94 1945-04-26,163.78,163.78,162.06,163.22,1370000,163.22 1945-04-25,164.31,164.46,163.17,163.91,1420000,163.91 1945-04-24,163.58,164.62,163.33,164.31,1830000,164.31 1945-04-23,163.20,164.08,162.88,163.58,1380000,163.58 1945-04-20,163.18,163.67,162.46,162.83,1130000,162.83 1945-04-19,163.83,164.45,162.72,163.18,1680000,163.18 1945-04-18,162.60,164.17,162.35,163.83,1710000,163.83 1945-04-17,162.43,163.72,162.15,162.60,2070000,162.60 1945-04-16,160.57,162.76,160.57,162.43,2500000,162.43 1945-04-13,158.48,159.95,157.73,159.75,1800000,159.75 1945-04-12,158.06,159.14,157.89,158.48,1060000,158.48 1945-04-11,156.59,158.17,156.59,158.06,1060000,158.06 1945-04-10,156.10,156.82,155.54,156.51,760000,156.51 1945-04-09,156.33,156.71,155.91,156.10,570000,156.10 1945-04-06,154.99,155.95,154.70,155.85,610000,155.85 1945-04-05,155.96,156.26,154.77,154.99,680000,154.99 1945-04-04,156.20,156.41,155.69,155.96,520000,155.96 1945-04-03,155.94,156.97,155.94,156.20,730000,156.20 1945-04-02,154.51,156.05,154.51,155.86,650000,155.86 1945-03-29,153.79,154.46,153.48,154.06,660000,154.06 1945-03-28,152.89,154.08,152.89,153.79,720000,153.79 1945-03-27,152.27,153.51,151.77,152.78,1110000,152.78 1945-03-26,153.62,153.62,151.74,152.27,1390000,152.27 1945-03-23,155.07,156.00,154.68,155.45,680000,155.45 1945-03-22,155.30,155.73,154.82,155.07,830000,155.07 1945-03-21,156.10,156.10,154.08,155.30,1340000,155.30 1945-03-20,157.71,157.71,156.14,156.37,920000,156.37 1945-03-19,158.75,158.88,157.36,157.89,1070000,157.89 1945-03-16,158.53,159.42,158.41,158.92,880000,158.92 1945-03-15,157.84,158.95,157.84,158.53,800000,158.53 1945-03-14,157.59,158.16,157.29,157.83,750000,157.83 1945-03-13,157.88,158.24,156.94,157.59,760000,157.59 1945-03-12,157.33,158.38,157.33,157.88,920000,157.88 1945-03-09,158.29,158.29,155.96,156.34,2060000,156.34 1945-03-08,161.34,161.34,158.31,158.86,1860000,158.86 1945-03-07,161.50,162.21,160.96,161.52,1400000,161.52 1945-03-06,160.68,162.22,160.56,161.50,1690000,161.50 1945-03-05,159.71,160.85,159.56,160.68,1190000,160.68 1945-03-02,160.72,160.76,159.63,159.95,1770000,159.95 1945-03-01,160.40,161.15,160.11,160.72,2090000,160.72 1945-02-28,159.51,160.85,159.51,160.40,1960000,160.40 1945-02-27,158.41,159.47,158.23,159.30,1190000,159.30 1945-02-26,158.69,158.91,157.45,158.41,1260000,158.41 1945-02-23,159.66,159.80,158.55,158.99,1320000,158.99 1945-02-21,159.57,160.17,158.04,159.66,1720000,159.66 1945-02-20,159.01,159.86,158.69,159.57,1770000,159.57 1945-02-19,158.23,159.54,157.92,159.01,1880000,159.01 1945-02-16,158.24,158.82,157.57,158.23,1900000,158.23 1945-02-15,157.08,158.37,157.06,158.24,1870000,158.24 1945-02-14,156.37,157.81,156.37,157.08,2060000,157.08 1945-02-13,154.90,156.49,154.90,156.34,1800000,156.34 1945-02-09,155.48,155.48,154.25,154.75,1180000,154.75 1945-02-08,155.71,156.17,155.19,155.54,1530000,155.54 1945-02-07,155.50,156.07,155.13,155.71,1500000,155.71 1945-02-06,155.35,156.00,155.18,155.50,1600000,155.50 1945-02-05,154.76,155.76,154.56,155.35,1800000,155.35 1945-02-02,153.79,154.71,153.30,154.45,1870000,154.45 1945-02-01,153.67,154.15,153.22,153.79,1560000,153.79 1945-01-31,153.45,153.93,152.62,153.67,1180000,153.67 1945-01-30,154.06,154.58,153.31,153.45,1530000,153.45 1945-01-29,154.13,154.25,153.30,154.06,1370000,154.06 1945-01-26,152.53,153.57,152.53,153.30,1260000,153.30 1945-01-25,151.39,152.62,151.39,152.26,970000,152.26 1945-01-24,151.36,152.15,150.53,151.35,1010000,151.35 1945-01-23,152.03,152.97,151.23,151.36,1370000,151.36 1945-01-22,152.41,152.41,151.10,152.03,1470000,152.03 1945-01-19,154.58,154.58,153.37,153.84,1610000,153.84 1945-01-18,155.33,155.50,153.95,154.61,1630000,154.61 1945-01-17,154.60,155.99,154.53,155.33,1830000,155.33 1945-01-16,154.76,155.04,153.96,154.60,1210000,154.60 1945-01-15,155.58,155.72,154.30,154.76,2010000,154.76 1945-01-12,155.85,156.22,154.99,155.42,1750000,155.42 1945-01-11,155.67,156.68,155.32,155.85,2210000,155.85 1945-01-10,155.01,155.95,154.38,155.67,2110000,155.67 1945-01-09,154.85,155.72,154.52,155.01,2260000,155.01 1945-01-08,153.69,155.04,153.69,154.85,2000000,154.85 1945-01-05,154.42,155.02,153.79,154.00,1800000,154.00 1945-01-04,154.31,155.00,153.72,154.42,1830000,154.42 1945-01-03,153.02,154.61,153.02,154.31,2160000,154.31 1945-01-02,152.32,152.83,151.63,152.58,1340000,152.58 1944-12-29,150.48,152.53,150.48,151.93,1890000,151.93 1944-12-28,148.71,150.73,148.62,150.47,1230000,150.47 1944-12-27,149.46,149.46,147.93,148.71,1580000,148.71 1944-12-26,150.36,150.36,149.41,149.66,1000000,149.66 1944-12-22,150.28,151.04,150.04,150.43,1280000,150.43 1944-12-21,150.59,150.73,149.88,150.28,950000,150.28 1944-12-20,151.39,151.39,150.15,150.59,1480000,150.59 1944-12-19,151.53,151.90,150.84,151.62,1280000,151.62 1944-12-18,152.28,152.28,151.15,151.53,980000,151.53 1944-12-15,150.93,152.75,150.93,152.28,2140000,152.28 1944-12-14,150.64,151.02,150.11,150.80,1390000,150.80 1944-12-13,151.20,151.34,150.43,150.64,1130000,150.64 1944-12-12,151.62,151.75,150.69,151.20,1160000,151.20 1944-12-11,151.31,152.14,150.65,151.62,1500000,151.62 1944-12-08,149.23,150.68,149.07,150.48,1680000,150.48 1944-12-07,148.77,149.64,148.55,149.23,1350000,149.23 1944-12-06,148.58,149.14,148.03,148.77,1090000,148.77 1944-12-05,148.22,149.23,148.05,148.58,1480000,148.58 1944-12-04,147.50,148.41,147.21,148.22,1430000,148.22 1944-12-01,147.33,147.65,146.76,147.30,930000,147.30 1944-11-30,147.81,148.06,147.06,147.33,990000,147.33 1944-11-29,147.14,148.07,146.89,147.81,1160000,147.81 1944-11-28,146.92,147.40,146.62,147.14,870000,147.14 1944-11-27,146.63,147.21,146.30,146.92,740000,146.92 1944-11-24,146.92,147.04,145.99,146.40,680000,146.40 1944-11-22,147.03,147.59,146.74,146.92,770000,146.92 1944-11-21,146.34,147.27,146.34,147.03,860000,147.03 1944-11-20,146.02,146.56,145.71,146.33,690000,146.33 1944-11-17,145.67,146.15,145.33,145.77,710000,145.77 1944-11-16,145.64,146.15,145.17,145.67,850000,145.67 1944-11-15,145.60,146.04,145.22,145.64,820000,145.64 1944-11-14,146.90,146.90,145.36,145.60,1100000,145.60 1944-11-13,148.08,148.22,146.78,146.97,920000,146.97 1944-11-10,147.75,148.39,147.64,148.08,1120000,148.08 1944-11-09,147.52,148.02,146.98,147.75,850000,147.75 1944-11-08,147.92,147.92,146.82,147.52,730000,147.52 1944-11-06,147.37,148.19,147.06,147.92,870000,147.92 1944-11-03,147.53,147.59,146.87,147.16,730000,147.16 1944-11-02,146.73,147.69,146.71,147.53,790000,147.53 1944-11-01,146.53,147.05,146.38,146.73,710000,146.73 1944-10-31,146.28,147.01,146.12,146.53,680000,146.53 1944-10-30,146.50,146.68,145.80,146.28,610000,146.28 1944-10-27,145.83,146.46,145.33,146.29,830000,146.29 1944-10-26,146.37,146.65,145.47,145.83,930000,145.83 1944-10-25,146.58,146.82,146.03,146.37,640000,146.37 1944-10-24,146.58,146.86,145.98,146.58,850000,146.58 1944-10-23,148.35,148.46,146.37,146.58,1030000,146.58 1944-10-20,148.55,148.70,147.96,148.21,750000,148.21 1944-10-19,148.87,149.18,148.21,148.55,830000,148.55 1944-10-18,148.47,149.18,148.47,148.87,910000,148.87 1944-10-17,148.09,148.58,147.85,148.39,670000,148.39 1944-10-16,148.59,148.67,147.97,148.09,580000,148.09 1944-10-13,148.79,149.03,148.48,148.70,680000,148.70 1944-10-11,148.25,149.00,148.19,148.79,720000,148.79 1944-10-10,148.06,148.56,147.68,148.25,600000,148.25 1944-10-09,148.86,148.86,147.98,148.06,610000,148.06 1944-10-06,148.62,149.20,148.51,148.84,800000,148.84 1944-10-05,147.89,148.95,147.78,148.62,1000000,148.62 1944-10-04,146.93,148.06,146.93,147.89,820000,147.89 1944-10-03,146.92,147.29,146.49,146.91,750000,146.91 1944-10-02,146.73,147.30,146.41,146.92,820000,146.92 1944-09-29,146.11,146.47,145.70,146.31,750000,146.31 1944-09-28,146.28,146.49,145.67,146.11,640000,146.11 1944-09-27,146.52,146.76,146.03,146.28,480000,146.28 1944-09-26,146.77,147.08,146.32,146.52,600000,146.52 1944-09-25,146.07,147.06,146.07,146.77,790000,146.77 1944-09-22,145.43,145.95,145.33,145.60,550000,145.60 1944-09-21,145.85,146.09,145.31,145.43,560000,145.43 1944-09-20,145.62,146.29,145.42,145.85,700000,145.85 1944-09-19,144.75,145.97,144.75,145.62,720000,145.62 1944-09-18,144.36,144.85,144.24,144.75,350000,144.75 1944-09-15,143.36,144.24,143.36,144.08,640000,144.08 1944-09-14,143.44,143.44,142.65,142.96,730000,142.96 1944-09-13,144.88,145.05,143.87,143.94,880000,143.94 1944-09-12,144.40,145.09,144.40,144.88,550000,144.88 1944-09-11,143.64,144.56,143.64,144.30,570000,144.30 1944-09-08,143.58,144.28,143.10,143.51,630000,143.51 1944-09-07,144.08,144.08,142.53,143.58,1480000,143.58 1944-09-06,146.44,146.44,144.26,144.42,1470000,144.42 1944-09-05,147.16,147.45,146.44,146.56,870000,146.56 1944-09-01,146.99,147.47,146.73,147.16,640000,147.16 1944-08-31,147.28,147.42,146.77,146.99,610000,146.99 1944-08-30,147.12,147.69,146.93,147.28,900000,147.28 1944-08-29,146.87,147.40,146.70,147.12,620000,147.12 1944-08-28,147.02,147.17,146.53,146.87,550000,146.87 1944-08-25,147.11,147.38,146.42,147.02,600000,147.02 1944-08-24,147.87,147.88,146.81,147.11,770000,147.11 1944-08-23,147.81,148.18,147.49,147.87,790000,147.87 1944-08-22,148.44,148.44,147.59,147.81,800000,147.81 1944-08-21,148.96,149.27,148.31,148.52,830000,148.52 1944-08-18,148.46,149.28,148.42,148.96,1150000,148.96 1944-08-17,147.62,148.58,147.62,148.46,1240000,148.46 1944-08-16,146.45,147.42,146.40,147.30,860000,147.30 1944-08-15,146.77,146.83,146.06,146.45,780000,146.45 1944-08-14,146.56,146.99,146.45,146.77,690000,146.77 1944-08-11,145.82,146.63,145.82,146.27,940000,146.27 1944-08-10,144.95,145.81,144.95,145.65,1020000,145.65 1944-08-09,144.97,145.25,144.48,144.90,960000,144.90 1944-08-08,145.32,145.69,144.70,144.97,1270000,144.97 1944-08-07,145.07,145.75,144.75,145.32,1070000,145.32 1944-08-04,146.29,146.49,145.20,145.30,1120000,145.30 1944-08-03,146.77,146.99,146.08,146.29,800000,146.29 1944-08-02,146.50,147.07,146.50,146.77,800000,146.77 1944-08-01,146.11,146.92,145.92,146.39,750000,146.39 1944-07-31,146.14,146.59,145.86,146.11,580000,146.11 1944-07-28,146.68,146.68,145.88,146.14,560000,146.14 1944-07-27,146.64,147.08,146.07,146.74,690000,146.74 1944-07-26,146.74,147.59,146.40,146.64,830000,146.64 1944-07-25,145.91,146.87,145.91,146.74,830000,146.74 1944-07-24,145.58,146.37,145.26,145.77,1010000,145.77 1944-07-21,148.01,148.01,146.42,146.77,1430000,146.77 1944-07-20,149.01,149.57,148.11,148.27,1340000,148.27 1944-07-19,148.10,149.46,147.98,149.01,1140000,149.01 1944-07-18,149.01,149.01,147.74,148.10,1280000,148.10 1944-07-17,150.49,150.49,148.71,149.28,1480000,149.28 1944-07-14,150.08,150.86,149.86,150.34,1090000,150.34 1944-07-13,150.42,150.80,149.66,150.08,1380000,150.08 1944-07-12,150.18,150.84,149.69,150.42,1420000,150.42 1944-07-11,150.50,150.80,149.53,150.18,1350000,150.18 1944-07-10,150.03,150.88,149.97,150.50,1840000,150.50 1944-07-07,149.07,149.61,148.61,149.36,1280000,149.36 1944-07-06,149.66,150.12,148.69,149.07,1710000,149.07 1944-07-05,149.32,150.42,149.17,149.66,2440000,149.66 1944-07-03,148.46,149.50,148.42,149.32,1560000,149.32 1944-06-30,148.07,148.82,147.93,148.38,1750000,148.38 1944-06-29,147.93,148.54,147.25,148.07,1890000,148.07 1944-06-28,148.48,148.52,147.40,147.93,1750000,147.93 1944-06-27,148.12,149.00,147.76,148.48,2180000,148.48 1944-06-26,147.48,148.46,147.40,148.12,1720000,148.12 1944-06-23,147.65,147.94,147.15,147.50,1300000,147.50 1944-06-22,147.90,148.32,147.18,147.65,1280000,147.65 1944-06-21,148.63,148.95,147.30,147.90,1520000,147.90 1944-06-20,148.42,149.15,147.79,148.63,1620000,148.63 1944-06-19,147.46,149.07,147.46,148.42,2370000,148.42 1944-06-16,145.94,147.57,145.94,146.96,2520000,146.96 1944-06-15,145.03,146.38,144.73,145.86,1850000,145.86 1944-06-14,145.05,145.60,144.26,145.03,1440000,145.03 1944-06-13,144.13,145.55,144.13,145.05,2330000,145.05 1944-06-12,142.90,144.31,142.90,144.08,2240000,144.08 1944-06-09,141.93,142.37,141.58,142.06,850000,142.06 1944-06-08,142.12,142.60,141.61,141.93,860000,141.93 1944-06-07,142.21,142.77,141.76,142.12,860000,142.12 1944-06-06,141.62,143.01,140.90,142.21,1790000,142.21 1944-06-05,142.34,142.53,141.49,141.62,860000,141.62 1944-06-02,142.14,142.52,141.80,142.07,820000,142.07 1944-06-01,142.24,142.92,141.95,142.14,1190000,142.14 1944-05-31,141.53,142.44,141.28,142.24,1180000,142.24 1944-05-29,141.24,141.68,140.97,141.53,810000,141.53 1944-05-26,140.38,141.20,140.31,141.03,840000,141.03 1944-05-25,140.48,140.69,139.89,140.38,800000,140.38 1944-05-24,139.91,140.98,139.91,140.48,1090000,140.48 1944-05-23,139.43,140.24,139.19,139.87,770000,139.87 1944-05-22,139.37,139.74,139.13,139.43,700000,139.43 1944-05-19,139.20,139.69,139.00,139.34,790000,139.34 1944-05-18,138.99,139.54,138.63,139.20,940000,139.20 1944-05-17,138.41,139.09,138.38,138.99,820000,138.99 1944-05-16,138.60,138.89,138.23,138.41,540000,138.41 1944-05-15,138.60,138.84,138.41,138.60,340000,138.60 1944-05-12,138.93,139.38,138.22,138.51,750000,138.51 1944-05-11,138.76,139.14,138.50,138.93,620000,138.93 1944-05-10,138.65,139.03,138.41,138.76,650000,138.76 1944-05-09,138.65,139.07,138.29,138.65,620000,138.65 1944-05-08,138.87,139.08,138.38,138.65,590000,138.65 1944-05-05,137.85,139.00,137.83,138.75,790000,138.75 1944-05-04,137.83,138.14,137.52,137.85,510000,137.85 1944-05-03,137.15,138.12,137.14,137.83,630000,137.83 1944-05-02,137.06,137.53,136.77,137.15,570000,137.15 1944-05-01,136.23,137.12,136.18,137.06,570000,137.06 1944-04-28,136.07,136.50,135.77,136.21,560000,136.21 1944-04-27,135.69,136.53,135.69,136.07,520000,136.07 1944-04-26,135.18,135.93,135.18,135.67,490000,135.67 1944-04-25,135.00,135.41,134.75,135.11,550000,135.11 1944-04-24,136.19,136.22,134.91,135.00,690000,135.00 1944-04-21,136.20,136.61,135.96,136.17,480000,136.17 1944-04-20,135.74,136.59,135.74,136.20,530000,136.20 1944-04-19,136.07,136.15,135.09,135.48,900000,135.48 1944-04-18,137.76,137.76,135.99,136.07,1190000,136.07 1944-04-17,138.06,138.25,137.64,137.77,540000,137.77 1944-04-14,137.65,137.95,137.52,137.69,480000,137.69 1944-04-13,137.93,137.93,137.33,137.65,660000,137.65 1944-04-12,138.74,138.86,137.88,137.98,720000,137.98 1944-04-11,139.11,139.16,138.50,138.74,730000,138.74 1944-04-10,139.10,139.45,138.80,139.11,570000,139.11 1944-04-06,138.31,139.24,138.31,138.91,760000,138.91 1944-04-05,138.06,138.63,137.95,138.17,770000,138.17 1944-04-04,138.01,138.39,137.67,138.06,570000,138.06 1944-04-03,138.66,138.66,137.70,138.01,690000,138.01 1944-03-31,138.60,139.29,138.50,138.84,800000,138.84 1944-03-30,137.74,138.89,137.74,138.60,680000,138.60 1944-03-29,137.88,138.17,136.98,137.45,1110000,137.45 1944-03-28,139.12,139.36,137.64,137.88,1340000,137.88 1944-03-27,139.19,139.67,138.99,139.12,690000,139.12 1944-03-24,138.95,139.60,138.81,139.28,840000,139.28 1944-03-23,139.98,140.33,138.81,138.95,1170000,138.95 1944-03-22,140.20,140.77,139.83,139.98,1570000,139.98 1944-03-21,139.89,140.47,139.63,140.20,1460000,140.20 1944-03-20,140.28,140.28,139.53,139.89,1200000,139.89 1944-03-17,140.91,141.10,140.24,140.80,1350000,140.80 1944-03-16,140.71,141.43,140.44,140.91,1590000,140.91 1944-03-15,140.37,141.00,140.08,140.71,1190000,140.71 1944-03-14,140.75,140.75,139.90,140.37,1010000,140.37 1944-03-13,140.44,141.37,140.33,141.00,1620000,141.00 1944-03-10,139.33,140.34,139.14,140.01,1150000,140.01 1944-03-09,139.50,139.70,138.89,139.33,930000,139.33 1944-03-08,138.34,139.89,138.34,139.50,1690000,139.50 1944-03-07,137.48,138.67,137.48,138.33,1210000,138.33 1944-03-06,136.79,137.46,136.75,137.21,750000,137.21 1944-03-03,136.69,136.97,136.38,136.59,760000,136.59 1944-03-02,136.44,136.91,136.33,136.69,710000,136.69 1944-03-01,136.30,136.75,135.86,136.44,630000,136.44 1944-02-29,136.79,136.91,136.02,136.30,870000,136.30 1944-02-28,136.58,137.01,136.36,136.79,750000,136.79 1944-02-25,136.58,136.74,136.11,136.56,900000,136.56 1944-02-24,136.51,137.00,136.25,136.58,1160000,136.58 1944-02-23,135.71,136.63,135.52,136.51,940000,136.51 1944-02-21,135.91,136.11,135.52,135.71,590000,135.71 1944-02-18,136.58,136.74,135.81,136.08,670000,136.08 1944-02-17,136.04,136.77,135.74,136.58,900000,136.58 1944-02-16,136.19,136.73,135.64,136.04,870000,136.04 1944-02-15,135.39,136.36,135.28,136.19,1030000,136.19 1944-02-14,135.41,135.71,135.00,135.39,550000,135.39 1944-02-11,135.55,136.08,135.19,135.41,850000,135.41 1944-02-10,135.03,135.74,134.80,135.55,860000,135.55 1944-02-09,135.06,135.44,134.55,135.03,630000,135.03 1944-02-08,134.36,135.24,134.36,135.06,610000,135.06 1944-02-07,135.11,135.11,134.10,134.22,570000,134.22 1944-02-04,135.89,135.89,134.75,135.04,600000,135.04 1944-02-03,137.08,137.16,135.76,136.24,960000,136.24 1944-02-02,137.45,137.45,136.79,137.08,900000,137.08 1944-02-01,137.40,137.69,137.09,137.45,860000,137.45 1944-01-31,137.15,137.85,136.83,137.40,630000,137.40 1944-01-28,136.65,137.37,136.65,137.19,620000,137.19 1944-01-27,136.71,137.10,136.38,136.59,600000,136.59 1944-01-26,137.77,137.77,136.59,136.71,780000,136.71 1944-01-25,137.97,138.21,137.59,137.97,690000,137.97 1944-01-24,138.24,138.50,137.70,137.97,690000,137.97 1944-01-21,138.16,138.32,137.69,138.07,810000,138.07 1944-01-20,137.83,138.49,137.79,138.16,730000,138.16 1944-01-19,137.87,138.28,137.20,137.83,640000,137.83 1944-01-18,138.10,138.22,137.51,137.87,820000,137.87 1944-01-17,138.40,138.60,137.78,138.10,820000,138.10 1944-01-14,137.36,138.31,137.21,138.15,940000,138.15 1944-01-13,137.86,137.86,136.99,137.36,680000,137.36 1944-01-12,138.47,138.71,137.74,137.94,710000,137.94 1944-01-11,137.97,138.89,137.97,138.47,1000000,138.47 1944-01-10,138.09,138.21,137.40,137.80,720000,137.80 1944-01-07,138.34,138.65,137.67,138.08,830000,138.08 1944-01-06,138.65,138.80,137.98,138.34,840000,138.34 1944-01-05,137.78,138.88,137.78,138.65,1160000,138.65 1944-01-04,135.92,137.23,135.91,137.15,730000,137.15 1944-01-03,135.89,136.47,135.51,135.92,520000,135.92 1943-12-31,136.20,136.73,135.54,135.89,990000,135.89 1943-12-30,135.00,136.37,135.00,136.20,1140000,136.20 1943-12-29,135.04,135.51,134.08,134.61,1000000,134.61 1943-12-28,136.08,136.08,134.81,135.04,920000,135.04 1943-12-27,136.24,136.60,135.67,136.14,650000,136.14 1943-12-24,136.07,136.47,135.75,136.24,510000,136.24 1943-12-23,136.15,136.57,135.77,136.07,580000,136.07 1943-12-22,135.86,136.53,135.65,136.15,560000,136.15 1943-12-21,136.10,136.49,135.51,135.86,660000,135.86 1943-12-20,135.89,136.56,135.47,136.10,860000,136.10 1943-12-17,135.19,135.90,134.92,135.44,880000,135.44 1943-12-16,134.18,135.47,133.96,135.19,760000,135.19 1943-12-15,134.19,134.53,133.69,134.18,660000,134.18 1943-12-14,134.74,134.74,133.72,134.19,680000,134.19 1943-12-13,135.28,135.81,134.37,134.80,730000,134.80 1943-12-10,134.05,135.47,133.96,135.04,870000,135.04 1943-12-09,134.42,134.89,133.57,134.05,860000,134.05 1943-12-08,133.64,134.85,133.64,134.42,1320000,134.42 1943-12-07,132.45,133.46,132.21,133.37,880000,133.37 1943-12-06,131.87,133.07,131.71,132.45,820000,132.45 1943-12-03,131.67,132.32,131.42,131.91,560000,131.91 1943-12-02,130.75,132.06,130.75,131.67,720000,131.67 1943-12-01,129.76,131.16,129.76,130.68,710000,130.68 1943-11-30,129.95,130.34,128.94,129.57,710000,129.57 1943-11-29,131.25,131.34,129.86,129.95,700000,129.95 1943-11-26,132.10,132.25,131.06,131.33,600000,131.33 1943-11-24,132.45,132.86,131.76,132.10,710000,132.10 1943-11-23,132.65,132.93,132.26,132.45,540000,132.45 1943-11-22,132.94,133.10,132.30,132.65,610000,132.65 1943-11-19,130.96,132.51,130.96,132.30,910000,132.30 1943-11-18,130.24,131.29,130.08,130.79,620000,130.79 1943-11-17,131.18,131.19,129.86,130.24,830000,130.24 1943-11-16,131.56,131.91,130.86,131.18,620000,131.18 1943-11-15,131.76,132.13,131.08,131.56,680000,131.56 1943-11-12,132.68,133.07,131.63,132.15,800000,132.15 1943-11-10,132.11,133.37,132.11,132.68,930000,132.68 1943-11-09,131.68,132.48,130.84,131.85,1510000,131.85 1943-11-08,135.03,135.03,131.42,131.68,2340000,131.68 1943-11-05,136.30,136.49,135.23,135.47,800000,135.47 1943-11-04,137.35,137.94,136.10,136.30,1150000,136.30 1943-11-03,138.50,138.96,137.19,137.35,1070000,137.35 1943-11-01,138.27,138.79,137.85,138.50,650000,138.50 1943-10-29,138.97,139.06,138.02,138.29,670000,138.29 1943-10-28,139.35,139.74,138.84,138.97,720000,138.97 1943-10-27,138.69,139.65,138.55,139.35,880000,139.35 1943-10-26,138.22,139.08,138.19,138.69,900000,138.69 1943-10-25,138.29,138.66,137.88,138.22,650000,138.22 1943-10-22,138.00,138.53,137.84,138.25,560000,138.25 1943-10-21,138.72,138.72,137.74,138.00,590000,138.00 1943-10-20,138.71,139.21,138.43,138.88,610000,138.88 1943-10-19,138.40,138.93,138.11,138.71,610000,138.71 1943-10-18,138.40,138.87,138.06,138.40,540000,138.40 1943-10-15,137.30,138.30,137.30,137.90,560000,137.90 1943-10-14,136.48,137.30,136.34,137.01,470000,137.01 1943-10-13,136.61,136.91,135.92,136.48,590000,136.48 1943-10-11,137.10,137.21,136.38,136.61,480000,136.61 1943-10-08,136.39,137.17,136.21,136.74,560000,136.74 1943-10-07,137.43,137.43,136.01,136.39,850000,136.39 1943-10-06,139.15,139.15,137.71,137.84,720000,137.84 1943-10-05,139.63,139.76,138.87,139.27,490000,139.27 1943-10-04,140.17,140.17,139.36,139.63,500000,139.63 1943-10-01,140.12,140.63,139.87,140.33,560000,140.33 1943-09-30,139.75,140.48,139.55,140.12,570000,140.12 1943-09-29,139.27,139.95,139.06,139.75,470000,139.75 1943-09-28,139.41,139.98,139.04,139.27,610000,139.27 1943-09-27,140.14,140.14,139.11,139.41,620000,139.41 1943-09-24,140.30,140.61,139.79,140.21,640000,140.21 1943-09-23,141.09,141.18,139.75,140.30,670000,140.30 1943-09-22,141.49,141.68,140.61,141.09,660000,141.09 1943-09-21,141.75,141.87,141.03,141.49,740000,141.49 1943-09-20,141.42,142.50,141.42,141.75,1100000,141.75 1943-09-17,138.42,139.71,138.42,139.60,890000,139.60 1943-09-16,137.62,138.43,137.50,138.36,530000,138.36 1943-09-15,137.53,138.21,137.31,137.62,600000,137.62 1943-09-14,137.82,137.98,137.24,137.53,440000,137.53 1943-09-13,138.04,138.17,137.52,137.82,510000,137.82 1943-09-10,137.75,138.26,137.50,137.96,760000,137.96 1943-09-09,136.92,138.12,136.92,137.75,1090000,137.75 1943-09-08,137.59,137.72,136.37,136.91,800000,136.91 1943-09-07,137.33,137.75,137.17,137.59,350000,137.59 1943-09-03,137.11,137.43,136.53,137.18,400000,137.18 1943-09-02,137.12,137.48,136.67,137.11,490000,137.11 1943-09-01,136.65,137.48,136.65,137.12,570000,137.12 1943-08-31,135.95,137.01,135.95,136.62,610000,136.62 1943-08-30,135.79,136.10,135.30,135.73,340000,135.73 1943-08-27,136.25,136.26,135.64,135.83,420000,135.83 1943-08-26,135.90,136.40,135.81,136.25,440000,136.25 1943-08-25,135.60,136.25,135.54,135.90,460000,135.90 1943-08-24,135.05,136.04,135.00,135.60,480000,135.60 1943-08-23,135.81,135.81,134.40,135.05,720000,135.05 1943-08-20,138.31,138.31,136.80,136.93,540000,136.93 1943-08-19,138.45,138.83,137.93,138.34,470000,138.34 1943-08-18,137.59,138.83,137.59,138.45,560000,138.45 1943-08-17,137.08,137.93,136.96,137.54,550000,137.54 1943-08-16,137.23,137.74,136.78,137.08,490000,137.08 1943-08-13,136.44,137.49,136.40,137.39,440000,137.39 1943-08-12,136.79,137.05,136.15,136.44,450000,136.44 1943-08-11,136.23,137.15,136.21,136.79,620000,136.79 1943-08-10,135.33,136.44,135.33,136.23,650000,136.23 1943-08-09,135.38,136.08,134.75,135.18,560000,135.18 1943-08-06,136.76,136.80,135.36,135.58,620000,135.58 1943-08-05,136.87,137.17,136.33,136.76,540000,136.76 1943-08-04,136.20,137.54,136.20,136.87,730000,136.87 1943-08-03,134.04,136.00,134.04,135.64,1200000,135.64 1943-08-02,135.95,136.50,133.87,134.00,1350000,134.00 1943-07-30,139.41,139.66,136.87,137.25,1230000,137.25 1943-07-29,138.28,139.90,138.28,139.41,1020000,139.41 1943-07-28,138.75,139.08,136.72,137.64,1850000,137.64 1943-07-27,142.07,142.07,138.65,138.75,1790000,138.75 1943-07-26,143.65,143.65,141.73,142.07,1460000,142.07 1943-07-23,143.77,144.18,143.31,143.80,910000,143.80 1943-07-22,143.94,144.13,143.38,143.77,820000,143.77 1943-07-21,143.93,144.22,143.33,143.94,770000,143.94 1943-07-20,144.74,144.79,143.50,143.93,990000,143.93 1943-07-19,144.72,145.31,144.39,144.74,830000,144.74 1943-07-16,144.87,145.67,144.41,144.75,1040000,144.75 1943-07-15,145.82,146.41,144.76,144.87,1220000,144.87 1943-07-14,145.30,146.26,145.08,145.82,1680000,145.82 1943-07-13,144.62,145.54,144.37,145.30,1390000,145.30 1943-07-12,144.23,144.79,143.94,144.62,1050000,144.62 1943-07-09,143.64,144.32,143.34,144.18,1050000,144.18 1943-07-08,143.41,144.09,143.15,143.64,960000,143.64 1943-07-07,143.76,143.82,142.83,143.41,710000,143.41 1943-07-06,143.70,144.41,143.46,143.76,960000,143.76 1943-07-02,143.58,144.05,143.17,143.68,890000,143.68 1943-07-01,143.38,144.02,142.98,143.58,1150000,143.58 1943-06-30,142.62,143.57,142.50,143.38,940000,143.38 1943-06-29,143.00,143.30,142.06,142.62,810000,142.62 1943-06-28,142.88,143.70,142.44,143.00,1030000,143.00 1943-06-25,140.96,142.49,140.96,142.27,1150000,142.27 1943-06-24,140.04,141.06,139.70,140.86,730000,140.86 1943-06-23,139.30,140.43,139.30,140.04,830000,140.04 1943-06-22,138.79,139.30,138.07,139.03,700000,139.03 1943-06-21,139.52,139.52,138.34,138.79,720000,138.79 1943-06-18,139.85,140.22,139.27,139.68,680000,139.68 1943-06-17,139.78,140.41,139.49,139.85,740000,139.85 1943-06-16,139.39,140.55,139.26,139.78,880000,139.78 1943-06-15,139.09,139.58,138.21,139.39,1010000,139.39 1943-06-14,140.91,140.91,138.86,139.09,1350000,139.09 1943-06-11,141.68,142.01,141.11,141.44,840000,141.44 1943-06-10,141.49,142.42,141.21,141.68,910000,141.68 1943-06-09,141.44,141.71,140.45,141.49,810000,141.49 1943-06-08,141.82,141.91,140.56,141.44,1080000,141.44 1943-06-07,142.99,142.99,141.50,141.82,1210000,141.82 1943-06-04,142.75,143.04,141.82,142.28,1260000,142.28 1943-06-03,142.39,143.05,141.51,142.75,1180000,142.75 1943-06-02,142.43,143.17,141.85,142.39,1310000,142.39 1943-06-01,142.06,142.90,141.72,142.43,1260000,142.43 1943-05-28,140.82,141.58,140.30,141.18,1050000,141.18 1943-05-27,140.38,141.54,140.13,140.82,1470000,140.82 1943-05-26,139.24,140.82,139.24,140.38,1320000,140.38 1943-05-25,138.84,139.37,138.06,139.17,890000,139.17 1943-05-24,138.78,139.14,138.41,138.84,790000,138.84 1943-05-21,138.84,139.25,138.10,138.90,920000,138.90 1943-05-20,139.15,140.09,138.60,138.84,1300000,138.84 1943-05-19,138.05,139.39,138.04,139.15,1490000,139.15 1943-05-18,136.98,138.39,136.92,138.05,930000,138.05 1943-05-17,137.31,137.43,136.30,136.98,850000,136.98 1943-05-14,137.85,137.85,136.13,136.82,1630000,136.82 1943-05-13,138.24,138.55,137.56,137.88,1030000,137.88 1943-05-12,138.36,138.96,137.83,138.24,1430000,138.24 1943-05-11,138.64,138.75,137.54,138.36,1790000,138.36 1943-05-10,138.36,139.30,138.12,138.64,2520000,138.64 1943-05-07,138.85,139.04,136.99,137.27,2150000,137.27 1943-05-06,138.34,139.13,137.97,138.85,2080000,138.85 1943-05-05,138.18,138.79,137.54,138.34,2470000,138.34 1943-05-04,137.43,138.71,137.27,138.18,2810000,138.18 1943-05-03,136.20,137.69,136.08,137.43,2350000,137.43 1943-04-30,135.24,136.17,135.01,135.48,1360000,135.48 1943-04-29,134.14,135.49,134.11,135.24,1340000,135.24 1943-04-28,134.39,134.61,133.46,134.14,880000,134.14 1943-04-27,134.34,134.75,133.75,134.39,830000,134.39 1943-04-26,134.34,134.89,133.91,134.34,1130000,134.34 1943-04-22,134.00,134.75,133.70,134.20,1250000,134.20 1943-04-21,133.17,134.31,133.17,134.00,1140000,134.00 1943-04-20,133.46,133.64,132.68,133.09,730000,133.09 1943-04-19,133.59,134.23,133.20,133.46,910000,133.46 1943-04-16,133.49,133.71,132.40,133.07,900000,133.07 1943-04-15,132.85,134.19,132.85,133.49,1390000,133.49 1943-04-14,131.38,132.90,131.38,132.49,1090000,132.49 1943-04-13,131.27,131.49,129.79,131.18,1410000,131.18 1943-04-12,131.63,132.86,131.11,131.27,1270000,131.27 1943-04-09,134.02,134.02,131.01,131.22,2520000,131.22 1943-04-08,136.00,136.68,135.18,135.52,1810000,135.52 1943-04-07,136.73,136.73,135.14,136.00,2100000,136.00 1943-04-06,136.44,137.45,136.09,136.93,2460000,136.93 1943-04-05,135.62,137.10,135.62,136.44,2650000,136.44 1943-04-02,136.44,136.44,135.08,135.67,1660000,135.67 1943-04-01,136.57,137.04,135.94,136.56,1740000,136.56 1943-03-31,136.82,137.07,135.86,136.57,1540000,136.57 1943-03-30,136.10,137.20,135.52,136.82,1940000,136.82 1943-03-29,134.75,136.41,134.75,136.10,2000000,136.10 1943-03-26,133.22,134.51,133.21,133.96,2140000,133.96 1943-03-25,130.91,133.30,130.91,133.22,2120000,133.22 1943-03-24,129.98,131.00,129.74,130.62,1160000,130.62 1943-03-23,129.46,130.47,129.46,129.98,1190000,129.98 1943-03-22,129.13,129.65,128.67,129.44,850000,129.44 1943-03-19,129.66,129.95,129.09,129.25,1070000,129.25 1943-03-18,129.49,130.00,129.07,129.66,870000,129.66 1943-03-17,130.22,130.22,128.86,129.49,1270000,129.49 1943-03-16,130.64,130.83,129.91,130.33,1030000,130.33 1943-03-15,130.73,130.95,130.03,130.64,1370000,130.64 1943-03-12,130.48,131.39,130.07,130.73,1970000,130.73 1943-03-11,129.16,130.74,128.95,130.48,1430000,130.48 1943-03-10,129.76,129.76,128.49,129.16,930000,129.16 1943-03-09,130.52,130.52,128.68,129.80,1420000,129.80 1943-03-08,130.74,131.23,130.14,130.56,1250000,130.56 1943-03-05,130.38,130.93,129.75,130.61,1210000,130.61 1943-03-04,130.03,131.20,129.97,130.38,2010000,130.38 1943-03-03,128.60,130.20,128.51,130.03,2020000,130.03 1943-03-02,129.18,129.18,127.91,128.60,1330000,128.60 1943-03-01,130.11,130.61,129.13,129.44,2000000,129.44 1943-02-26,130.04,130.25,129.20,129.71,1440000,129.71 1943-02-25,129.58,130.43,129.28,130.04,1780000,130.04 1943-02-24,128.78,130.00,128.39,129.58,1690000,129.58 1943-02-23,127.80,129.06,127.34,128.78,1430000,128.78 1943-02-19,127.06,127.25,125.82,126.67,900000,126.67 1943-02-18,128.29,128.29,126.82,127.06,1040000,127.06 1943-02-17,128.31,128.88,127.86,128.41,1100000,128.41 1943-02-16,128.60,128.88,127.70,128.31,1180000,128.31 1943-02-15,128.00,129.15,128.00,128.60,1840000,128.60 1943-02-11,127.01,127.54,126.53,127.09,1410000,127.09 1943-02-10,126.30,127.55,126.21,127.01,1500000,127.01 1943-02-09,125.57,126.59,125.38,126.30,920000,126.30 1943-02-08,125.81,126.10,125.19,125.57,730000,125.57 1943-02-05,125.07,126.00,124.71,125.75,880000,125.75 1943-02-04,125.56,125.57,124.69,125.07,800000,125.07 1943-02-03,125.88,126.10,124.84,125.56,830000,125.56 1943-02-02,125.86,126.38,125.51,125.88,1050000,125.88 1943-02-01,125.58,126.15,124.87,125.86,1090000,125.86 1943-01-29,124.38,125.71,124.23,125.41,1230000,125.41 1943-01-28,124.08,124.57,123.41,124.38,990000,124.38 1943-01-27,124.31,124.47,122.92,124.08,1030000,124.08 1943-01-26,123.74,124.59,123.63,124.31,1040000,124.31 1943-01-25,122.38,123.94,122.30,123.74,800000,123.74 1943-01-22,121.79,122.92,121.50,121.99,880000,121.99 1943-01-21,120.63,122.00,120.63,121.79,810000,121.79 1943-01-20,120.48,120.86,119.71,120.55,520000,120.55 1943-01-19,121.56,121.59,120.25,120.48,770000,120.48 1943-01-18,121.60,121.93,121.24,121.56,710000,121.56 1943-01-15,120.86,121.84,120.86,121.58,1000000,121.58 1943-01-14,120.25,121.03,120.09,120.79,680000,120.79 1943-01-13,119.98,120.59,119.80,120.25,630000,120.25 1943-01-12,119.95,120.52,119.54,119.98,630000,119.98 1943-01-11,119.51,120.41,119.51,119.95,810000,119.95 1943-01-08,119.37,119.71,118.92,119.26,800000,119.26 1943-01-07,119.66,119.95,118.84,119.37,710000,119.37 1943-01-06,119.70,120.31,119.40,119.66,550000,119.66 1943-01-05,120.25,120.62,119.50,119.70,670000,119.70 1943-01-04,119.93,120.82,119.75,120.25,620000,120.25 1942-12-31,119.56,120.19,119.08,119.40,1050000,119.40 1942-12-30,118.40,119.83,118.28,119.56,1120000,119.56 1942-12-29,118.50,118.95,117.30,118.40,1440000,118.40 1942-12-28,119.71,119.96,118.22,118.50,1200000,118.50 1942-12-24,119.07,119.67,118.56,119.27,800000,119.27 1942-12-23,118.49,119.58,118.24,119.07,920000,119.07 1942-12-22,118.66,119.23,118.09,118.49,780000,118.49 1942-12-21,118.75,119.35,118.12,118.66,770000,118.66 1942-12-18,118.68,119.76,118.41,118.97,1090000,118.97 1942-12-17,117.06,119.07,116.60,118.68,1310000,118.68 1942-12-16,116.31,117.38,116.08,117.06,910000,117.06 1942-12-15,115.83,116.64,115.65,116.31,700000,116.31 1942-12-14,115.82,116.13,115.21,115.83,690000,115.83 1942-12-11,116.00,116.55,115.16,115.70,640000,115.70 1942-12-10,115.93,116.38,115.41,116.00,570000,116.00 1942-12-09,115.76,116.38,115.35,115.93,620000,115.93 1942-12-08,115.03,116.05,115.03,115.76,620000,115.76 1942-12-07,115.24,115.57,114.71,115.00,500000,115.00 1942-12-04,115.19,115.42,114.41,115.02,530000,115.02 1942-12-03,115.16,115.87,114.76,115.19,630000,115.19 1942-12-02,114.61,115.61,114.43,115.16,540000,115.16 1942-12-01,114.50,115.12,114.08,114.61,560000,114.61 1942-11-30,114.95,115.03,114.01,114.50,470000,114.50 1942-11-27,114.13,115.12,114.08,114.86,530000,114.86 1942-11-25,114.10,114.66,113.55,114.13,570000,114.13 1942-11-24,114.46,114.61,113.46,114.10,640000,114.10 1942-11-23,115.27,115.27,114.03,114.46,630000,114.46 1942-11-20,114.55,115.67,114.37,115.27,660000,115.27 1942-11-19,114.64,114.95,114.24,114.55,500000,114.55 1942-11-18,114.53,115.08,114.12,114.64,510000,114.64 1942-11-17,115.70,116.24,114.42,114.53,670000,114.53 1942-11-16,116.24,116.32,115.41,115.70,520000,115.70 1942-11-13,116.46,116.76,115.80,116.26,670000,116.26 1942-11-12,116.30,117.14,115.63,116.46,710000,116.46 1942-11-10,117.14,117.14,115.96,116.30,770000,116.30 1942-11-09,116.92,118.18,116.61,117.30,1210000,117.30 1942-11-06,114.87,116.25,114.80,116.12,860000,116.12 1942-11-05,114.56,115.29,114.23,114.87,600000,114.87 1942-11-04,114.68,115.55,114.29,114.56,770000,114.56 1942-11-02,114.07,115.09,114.02,114.68,760000,114.68 1942-10-30,113.13,113.64,112.80,113.50,520000,113.50 1942-10-29,113.11,113.47,112.59,113.13,460000,113.13 1942-10-28,113.86,113.87,112.57,113.11,500000,113.11 1942-10-27,115.06,115.06,113.50,113.86,630000,113.86 1942-10-26,115.01,115.61,114.74,115.29,630000,115.29 1942-10-23,114.94,115.52,114.45,114.88,730000,114.88 1942-10-22,115.09,115.22,114.15,114.94,550000,114.94 1942-10-21,115.22,116.01,114.61,115.09,700000,115.09 1942-10-20,114.17,115.47,114.17,115.22,670000,115.22 1942-10-19,113.40,113.89,113.13,113.64,400000,113.64 1942-10-16,113.27,113.79,112.71,113.55,510000,113.55 1942-10-15,114.56,114.56,113.11,113.27,600000,113.27 1942-10-14,115.01,115.24,113.99,114.69,660000,114.69 1942-10-13,114.93,115.80,114.68,115.01,860000,115.01 1942-10-09,113.60,114.67,113.45,113.93,1050000,113.93 1942-10-08,112.01,113.86,112.01,113.60,1090000,113.60 1942-10-07,111.53,112.11,111.25,111.86,660000,111.86 1942-10-06,111.93,112.09,111.16,111.53,700000,111.53 1942-10-05,111.34,112.29,111.03,111.93,790000,111.93 1942-10-02,109.68,111.02,109.68,110.83,900000,110.83 1942-10-01,109.16,109.90,109.16,109.65,560000,109.65 1942-09-30,109.24,109.37,108.70,109.11,340000,109.11 1942-09-29,109.56,109.75,109.01,109.24,430000,109.24 1942-09-28,109.32,109.98,109.29,109.56,400000,109.56 1942-09-25,109.11,109.72,108.89,109.37,680000,109.37 1942-09-24,108.27,109.42,108.18,109.11,850000,109.11 1942-09-23,107.59,108.40,107.45,108.27,700000,108.27 1942-09-22,107.27,107.83,107.16,107.59,520000,107.59 1942-09-21,107.22,107.45,107.01,107.27,320000,107.27 1942-09-18,106.72,107.59,106.72,107.47,420000,107.47 1942-09-17,106.66,106.96,106.44,106.66,410000,106.66 1942-09-16,106.49,106.93,106.19,106.66,380000,106.66 1942-09-15,106.17,106.82,106.17,106.49,390000,106.49 1942-09-14,106.20,106.32,105.92,106.15,310000,106.15 1942-09-11,106.36,106.36,105.58,106.03,380000,106.03 1942-09-10,107.17,107.17,106.30,106.38,350000,106.38 1942-09-09,107.62,107.80,106.97,107.26,360000,107.26 1942-09-08,106.76,107.88,106.76,107.62,400000,107.62 1942-09-04,106.34,106.70,106.09,106.39,310000,106.39 1942-09-03,106.49,106.50,106.07,106.34,280000,106.34 1942-09-02,106.28,106.68,106.05,106.49,270000,106.49 1942-09-01,106.33,106.52,105.76,106.28,290000,106.28 1942-08-31,106.41,106.81,106.08,106.33,250000,106.33 1942-08-28,106.03,106.64,105.92,106.23,300000,106.23 1942-08-27,105.55,106.20,105.49,106.03,270000,106.03 1942-08-26,106.28,106.28,105.37,105.55,360000,105.55 1942-08-25,107.11,107.11,106.23,106.51,350000,106.51 1942-08-24,107.30,107.73,106.94,107.25,380000,107.25 1942-08-21,106.83,107.25,106.53,107.07,370000,107.07 1942-08-20,107.21,107.21,106.46,106.83,310000,106.83 1942-08-19,107.55,107.88,106.67,107.28,500000,107.28 1942-08-18,106.96,107.72,106.96,107.55,560000,107.55 1942-08-17,106.38,107.04,106.21,106.68,290000,106.68 1942-08-14,105.75,106.65,105.75,106.15,380000,106.15 1942-08-13,105.47,105.86,105.08,105.70,320000,105.70 1942-08-12,105.42,105.81,105.00,105.47,280000,105.47 1942-08-11,105.01,105.67,105.01,105.42,260000,105.42 1942-08-10,104.90,105.18,104.55,104.91,210000,104.91 1942-08-07,104.80,105.33,104.50,105.05,210000,105.05 1942-08-06,104.85,105.07,104.55,104.80,250000,104.80 1942-08-05,105.30,105.30,104.50,104.85,290000,104.85 1942-08-04,106.08,106.21,105.43,105.55,320000,105.55 1942-08-03,105.90,106.44,105.67,106.08,280000,106.08 1942-07-31,105.37,106.27,105.37,105.72,310000,105.72 1942-07-30,105.44,105.73,104.79,105.24,250000,105.24 1942-07-29,106.34,106.34,105.30,105.44,290000,105.44 1942-07-28,106.66,106.82,106.22,106.48,270000,106.48 1942-07-27,106.53,106.97,106.32,106.66,260000,106.66 1942-07-24,106.65,106.65,105.84,106.37,260000,106.37 1942-07-23,107.88,107.88,106.45,106.65,330000,106.65 1942-07-22,108.36,108.94,107.69,108.03,440000,108.03 1942-07-21,107.98,108.68,107.94,108.36,280000,108.36 1942-07-20,107.69,108.26,107.50,107.98,210000,107.98 1942-07-17,108.91,108.92,107.68,107.82,280000,107.82 1942-07-16,108.89,109.21,108.17,108.91,270000,108.91 1942-07-15,108.72,109.49,108.50,108.89,390000,108.89 1942-07-14,108.22,108.89,107.40,108.72,370000,108.72 1942-07-13,108.69,108.69,107.79,108.22,280000,108.22 1942-07-10,108.75,108.99,107.68,108.66,440000,108.66 1942-07-09,107.94,109.26,107.60,108.75,840000,108.75 1942-07-08,105.76,108.01,105.48,107.94,580000,107.94 1942-07-07,106.10,106.34,105.32,105.76,330000,105.76 1942-07-06,104.92,106.30,104.92,106.10,420000,106.10 1942-07-03,103.84,104.77,103.84,104.49,360000,104.49 1942-07-02,102.69,103.89,102.27,103.73,340000,103.73 1942-07-01,103.29,103.29,102.28,102.69,210000,102.69 1942-06-30,103.17,103.61,102.93,103.34,250000,103.34 1942-06-29,102.68,103.57,102.68,103.17,260000,103.17 1942-06-26,102.71,103.09,102.27,102.54,290000,102.54 1942-06-25,102.67,103.06,101.94,102.71,250000,102.71 1942-06-24,103.03,103.24,102.43,102.67,240000,102.67 1942-06-23,102.77,103.44,102.73,103.03,210000,103.03 1942-06-22,103.52,103.52,102.11,102.77,310000,102.77 1942-06-19,105.52,105.52,104.55,104.77,290000,104.77 1942-06-18,106.29,106.63,105.49,105.70,350000,105.70 1942-06-17,104.68,106.38,104.68,106.29,390000,106.29 1942-06-16,104.41,104.94,104.18,104.51,280000,104.51 1942-06-15,104.08,104.54,103.99,104.41,260000,104.41 1942-06-12,104.32,104.32,103.27,103.77,220000,103.77 1942-06-11,104.19,104.69,103.94,104.49,280000,104.49 1942-06-10,104.90,104.90,103.70,104.19,310000,104.19 1942-06-09,105.55,106.34,104.83,105.09,400000,105.09 1942-06-08,104.71,105.86,104.71,105.55,360000,105.55 1942-06-05,103.61,105.26,103.60,104.41,490000,104.41 1942-06-04,102.25,103.87,102.25,103.61,520000,103.61 1942-06-03,101.30,102.33,101.01,102.15,330000,102.15 1942-06-02,101.37,101.67,100.93,101.30,320000,101.30 1942-06-01,100.96,101.84,100.96,101.37,310000,101.37 1942-05-29,100.99,101.29,100.43,100.88,250000,100.88 1942-05-28,101.09,101.50,100.52,100.99,350000,100.99 1942-05-27,99.41,101.21,99.31,101.09,430000,101.09 1942-05-26,99.18,100.00,99.02,99.41,290000,99.41 1942-05-25,99.25,99.47,98.68,99.18,230000,99.18 1942-05-22,99.72,99.95,98.83,99.18,330000,99.18 1942-05-21,98.13,100.21,98.11,99.72,560000,99.72 1942-05-20,97.96,98.50,97.22,98.13,410000,98.13 1942-05-19,98.65,98.84,97.70,97.96,380000,97.96 1942-05-18,98.63,99.16,98.24,98.65,220000,98.65 1942-05-15,97.38,98.27,97.38,97.98,260000,97.98 1942-05-14,97.21,97.37,96.39,97.13,280000,97.13 1942-05-13,98.19,98.19,96.92,97.21,340000,97.21 1942-05-12,99.20,99.35,98.31,98.56,250000,98.56 1942-05-11,98.70,99.49,98.45,99.20,290000,99.20 1942-05-08,97.77,98.57,97.65,97.91,310000,97.91 1942-05-07,96.93,98.11,96.93,97.77,340000,97.77 1942-05-06,97.29,97.35,96.19,96.71,270000,96.71 1942-05-05,96.70,97.74,96.54,97.29,270000,97.29 1942-05-04,96.44,97.15,96.34,96.70,260000,96.70 1942-05-01,95.35,96.29,95.08,95.83,300000,95.83 1942-04-30,94.71,95.76,94.71,95.35,280000,95.35 1942-04-29,92.92,95.18,92.74,94.65,410000,94.65 1942-04-28,93.69,93.69,92.69,92.92,310000,92.92 1942-04-27,94.31,94.89,93.66,93.89,280000,93.89 1942-04-24,94.80,94.80,93.59,94.13,390000,94.13 1942-04-23,96.91,96.91,94.84,94.98,430000,94.98 1942-04-22,97.51,97.64,96.79,97.20,260000,97.20 1942-04-21,97.25,98.02,97.16,97.51,270000,97.51 1942-04-20,96.92,97.47,96.63,97.25,240000,97.25 1942-04-17,97.61,97.61,95.80,96.05,420000,96.05 1942-04-16,98.06,98.46,97.61,97.87,260000,97.87 1942-04-15,97.89,98.75,97.50,98.06,350000,98.06 1942-04-14,99.21,99.21,97.77,97.89,560000,97.89 1942-04-13,99.45,99.78,99.25,99.44,240000,99.44 1942-04-10,99.69,100.15,99.31,99.74,300000,99.74 1942-04-09,100.56,100.56,99.51,99.69,350000,99.69 1942-04-08,101.89,101.97,100.89,101.23,300000,101.23 1942-04-07,102.50,102.75,101.73,101.89,310000,101.89 1942-04-06,101.11,102.69,101.05,102.50,340000,102.50 1942-04-02,100.19,101.31,100.19,100.89,370000,100.89 1942-04-01,99.53,100.19,99.32,99.95,280000,99.95 1942-03-31,100.04,100.21,99.25,99.53,280000,99.53 1942-03-30,100.00,100.54,99.76,100.04,230000,100.04 1942-03-27,101.00,101.00,99.78,100.00,310000,100.00 1942-03-26,101.48,101.54,100.73,101.05,300000,101.05 1942-03-25,102.09,102.16,101.39,101.48,320000,101.48 1942-03-24,101.20,102.43,101.02,102.09,360000,102.09 1942-03-23,100.82,101.58,100.81,101.20,280000,101.20 1942-03-20,101.25,101.31,100.43,100.75,280000,100.75 1942-03-19,101.64,101.82,100.91,101.25,280000,101.25 1942-03-18,102.54,102.73,101.26,101.64,340000,101.64 1942-03-17,100.82,102.70,100.82,102.54,470000,102.54 1942-03-16,99.64,100.81,99.50,100.68,320000,100.68 1942-03-13,99.23,100.39,98.93,99.73,340000,99.73 1942-03-12,99.21,100.25,98.32,99.23,460000,99.23 1942-03-11,101.14,101.14,99.11,99.21,410000,99.21 1942-03-10,102.09,102.32,101.17,101.49,340000,101.49 1942-03-09,102.31,102.88,101.56,102.09,310000,102.09 1942-03-06,104.08,104.08,102.03,102.10,640000,102.10 1942-03-05,105.59,105.59,104.37,104.55,450000,104.55 1942-03-04,106.97,107.04,105.69,105.99,380000,105.99 1942-03-03,105.75,107.16,105.48,106.97,410000,106.97 1942-03-02,106.49,106.49,105.33,105.75,330000,105.75 1942-02-27,106.16,106.93,106.16,106.58,360000,106.58 1942-02-26,105.64,106.24,105.40,105.88,350000,105.88 1942-02-25,106.00,106.30,105.41,105.64,340000,105.64 1942-02-24,105.54,106.73,105.54,106.00,390000,106.00 1942-02-20,105.57,105.57,104.78,105.10,330000,105.10 1942-02-19,105.35,106.03,104.93,105.57,350000,105.57 1942-02-18,105.40,105.70,104.67,105.35,340000,105.35 1942-02-17,107.05,107.05,105.20,105.40,390000,105.40 1942-02-16,107.30,107.96,106.70,107.31,380000,107.31 1942-02-13,106.51,107.01,106.12,106.73,320000,106.73 1942-02-11,106.75,107.19,106.00,106.51,420000,106.51 1942-02-10,107.81,107.81,106.21,106.75,640000,106.75 1942-02-09,108.92,108.92,107.92,108.12,400000,108.12 1942-02-06,110.44,110.53,109.30,109.47,430000,109.47 1942-02-05,110.80,110.97,110.09,110.44,440000,110.44 1942-02-04,109.99,111.04,109.91,110.80,500000,110.80 1942-02-03,109.47,110.29,109.38,109.99,370000,109.99 1942-02-02,109.11,109.68,109.08,109.47,330000,109.47 1942-01-30,109.90,110.20,109.23,109.41,380000,109.41 1942-01-29,110.15,110.39,109.50,109.90,420000,109.90 1942-01-28,110.68,110.99,109.69,110.15,460000,110.15 1942-01-27,110.67,111.20,110.31,110.68,550000,110.68 1942-01-26,109.52,111.00,109.52,110.67,600000,110.67 1942-01-23,108.94,109.44,108.39,109.12,430000,109.12 1942-01-22,109.06,109.16,108.30,108.94,430000,108.94 1942-01-21,110.12,110.12,108.71,109.06,580000,109.06 1942-01-20,110.81,111.21,110.24,110.45,490000,110.45 1942-01-19,110.68,111.34,109.98,110.81,430000,110.81 1942-01-16,112.59,112.64,111.01,111.25,480000,111.25 1942-01-15,112.59,113.02,112.17,112.59,450000,112.59 1942-01-14,112.44,113.29,112.05,112.59,610000,112.59 1942-01-13,110.90,112.61,110.90,112.44,730000,112.44 1942-01-12,110.54,111.48,110.10,110.65,490000,110.65 1942-01-09,111.55,111.97,110.45,111.02,660000,111.02 1942-01-08,112.91,112.91,111.20,111.55,530000,111.55 1942-01-07,113.93,113.93,112.62,113.10,630000,113.10 1942-01-06,114.22,114.96,113.22,113.99,800000,113.99 1942-01-05,113.75,114.76,113.20,114.22,720000,114.22 1942-01-02,110.96,113.00,110.07,112.77,580000,112.77 1941-12-31,111.32,111.99,109.75,110.96,1750000,110.96 1941-12-30,107.56,112.04,107.45,111.32,2560000,111.32 1941-12-29,107.54,108.94,106.36,107.56,2930000,107.56 1941-12-26,106.67,107.86,105.92,106.95,1410000,106.95 1941-12-24,106.34,107.56,105.52,106.67,1380000,106.67 1941-12-23,106.59,107.21,105.57,106.34,1420000,106.34 1941-12-22,107.81,108.83,106.23,106.59,1460000,106.59 1941-12-19,108.21,109.52,107.61,108.28,1270000,108.28 1941-12-18,109.36,109.67,107.18,108.21,1310000,108.21 1941-12-17,110.86,111.05,108.68,109.36,1220000,109.36 1941-12-16,111.15,112.30,110.29,110.86,1230000,110.86 1941-12-15,110.73,112.01,109.97,111.15,1110000,111.15 1941-12-12,110.91,111.76,109.53,110.58,1120000,110.58 1941-12-11,109.01,111.73,108.38,110.91,1400000,110.91 1941-12-10,109.27,109.76,106.87,109.01,2090000,109.01 1941-12-09,112.52,112.73,107.56,109.27,2560000,109.27 1941-12-08,115.46,115.46,111.53,112.52,2030000,112.52 1941-12-05,116.44,116.44,115.09,115.90,980000,115.90 1941-12-04,116.65,117.54,115.96,116.60,1130000,116.60 1941-12-03,115.57,117.00,115.24,116.65,1090000,116.65 1941-12-02,113.60,115.79,113.60,115.57,1180000,115.57 1941-12-01,114.23,114.89,113.06,113.59,840000,113.59 1941-11-28,115.64,115.68,114.10,114.66,870000,114.66 1941-11-27,115.93,116.49,115.00,115.64,810000,115.64 1941-11-26,116.96,116.98,115.61,115.93,850000,115.93 1941-11-25,117.30,117.60,116.38,116.96,840000,116.96 1941-11-24,117.04,118.19,116.89,117.30,820000,117.30 1941-11-21,116.68,117.50,116.07,117.05,850000,117.05 1941-11-19,115.87,116.90,115.47,116.68,800000,116.68 1941-11-18,116.20,116.62,115.20,115.87,680000,115.87 1941-11-17,116.72,117.03,115.69,116.20,630000,116.20 1941-11-14,115.75,117.30,115.75,116.81,840000,116.81 1941-11-13,115.44,116.34,114.91,115.67,830000,115.67 1941-11-12,117.16,117.16,115.03,115.44,1020000,115.44 1941-11-10,118.26,118.41,117.24,117.45,630000,117.45 1941-11-07,118.84,118.84,117.64,118.33,700000,118.33 1941-11-06,119.80,119.80,118.41,118.84,670000,118.84 1941-11-05,118.87,120.34,118.84,119.85,920000,119.85 1941-11-03,118.11,119.32,118.11,118.87,600000,118.87 1941-10-31,119.17,119.17,117.40,117.82,640000,117.82 1941-10-30,119.37,119.65,118.57,119.18,550000,119.18 1941-10-29,119.60,119.96,118.99,119.37,550000,119.37 1941-10-28,119.43,120.07,119.03,119.60,560000,119.60 1941-10-27,120.04,120.04,119.11,119.43,480000,119.43 1941-10-24,120.62,121.69,120.62,121.18,710000,121.18 1941-10-23,120.56,120.84,119.77,120.47,540000,120.47 1941-10-22,121.07,121.19,120.25,120.56,490000,120.56 1941-10-21,120.13,121.27,119.83,121.07,580000,121.07 1941-10-20,120.10,120.75,119.64,120.13,620000,120.13 1941-10-17,118.52,119.56,117.88,119.15,670000,119.15 1941-10-16,120.04,120.04,118.43,118.52,840000,118.52 1941-10-15,121.36,121.36,120.19,120.52,480000,120.52 1941-10-14,122.63,122.80,121.62,121.82,440000,121.82 1941-10-10,122.53,123.06,122.01,122.46,490000,122.46 1941-10-09,124.08,124.08,122.18,122.53,720000,122.53 1941-10-08,124.42,124.52,123.61,124.13,440000,124.13 1941-10-07,125.83,125.86,124.08,124.42,600000,124.42 1941-10-06,126.10,126.20,125.50,125.83,490000,125.83 1941-10-03,126.15,126.44,125.57,126.06,420000,126.06 1941-10-02,126.85,127.06,126.08,126.15,470000,126.15 1941-10-01,126.82,127.20,126.39,126.85,370000,126.85 1941-09-30,126.49,127.31,126.49,126.82,460000,126.82 1941-09-29,126.03,126.54,125.76,126.05,400000,126.05 1941-09-26,126.38,126.68,125.55,125.81,490000,125.81 1941-09-25,127.54,127.71,125.33,126.38,1170000,126.38 1941-09-24,128.03,128.79,127.35,127.54,550000,127.54 1941-09-23,127.64,128.50,127.59,128.03,490000,128.03 1941-09-22,127.54,128.08,127.25,127.64,420000,127.64 1941-09-19,128.77,128.81,127.74,127.95,580000,127.95 1941-09-18,129.32,130.00,128.54,128.77,790000,128.77 1941-09-17,127.43,129.48,127.27,129.32,890000,129.32 1941-09-16,127.20,127.71,126.85,127.43,610000,127.43 1941-09-15,127.28,127.54,126.95,127.20,460000,127.20 1941-09-12,127.15,127.72,126.87,127.18,520000,127.18 1941-09-11,126.53,127.45,126.31,127.15,690000,127.15 1941-09-10,127.43,127.48,126.37,126.53,520000,126.53 1941-09-09,127.51,128.38,127.16,127.43,870000,127.43 1941-09-08,127.26,127.94,126.99,127.51,620000,127.51 1941-09-05,127.51,127.54,126.88,127.17,580000,127.17 1941-09-04,127.88,127.88,127.21,127.51,540000,127.51 1941-09-03,128.31,128.56,127.54,127.91,460000,127.91 1941-09-02,127.77,128.62,127.77,128.31,520000,128.31 1941-08-29,127.77,127.88,127.05,127.43,350000,127.43 1941-08-28,127.25,127.95,127.25,127.77,400000,127.77 1941-08-27,126.60,127.37,126.60,127.08,430000,127.08 1941-08-26,126.08,126.82,126.08,126.56,460000,126.56 1941-08-25,125.91,126.25,125.50,125.86,330000,125.86 1941-08-22,125.99,126.12,125.39,125.84,360000,125.84 1941-08-21,126.01,126.42,125.72,125.99,390000,125.99 1941-08-20,125.57,126.42,125.48,126.01,490000,126.01 1941-08-19,125.62,125.91,125.20,125.57,390000,125.57 1941-08-18,125.20,125.96,125.20,125.62,400000,125.62 1941-08-15,125.96,125.97,124.66,124.90,390000,124.90 1941-08-14,125.65,126.43,125.57,125.96,420000,125.96 1941-08-13,125.81,126.10,125.42,125.65,420000,125.65 1941-08-12,126.01,126.24,125.30,125.81,430000,125.81 1941-08-11,126.40,126.61,125.63,126.01,450000,126.01 1941-08-08,128.09,128.27,127.31,127.48,550000,127.48 1941-08-07,128.10,128.57,127.68,128.09,500000,128.09 1941-08-06,128.14,128.55,127.62,128.10,580000,128.10 1941-08-05,128.17,128.54,127.61,128.14,640000,128.14 1941-08-04,128.21,128.56,127.61,128.17,630000,128.17 1941-08-01,128.68,128.68,127.64,128.22,680000,128.22 1941-07-31,128.95,129.45,128.43,128.79,850000,128.79 1941-07-30,129.19,129.34,128.07,128.95,750000,128.95 1941-07-29,130.06,130.33,128.93,129.19,960000,129.19 1941-07-28,128.70,130.37,128.65,130.06,940000,130.06 1941-07-25,128.59,128.92,127.74,128.06,810000,128.06 1941-07-24,129.16,129.40,128.39,128.59,620000,128.59 1941-07-23,129.58,129.71,128.79,129.16,630000,129.16 1941-07-22,129.51,131.10,129.22,129.58,1350000,129.58 1941-07-21,127.98,129.57,127.78,129.51,910000,129.51 1941-07-18,127.14,127.89,126.92,127.69,420000,127.69 1941-07-17,127.83,127.88,126.75,127.14,460000,127.14 1941-07-16,128.19,128.70,127.62,127.83,640000,127.83 1941-07-15,127.89,128.68,127.53,128.19,700000,128.19 1941-07-14,127.80,128.17,127.44,127.89,560000,127.89 1941-07-11,127.78,128.70,127.35,127.90,810000,127.90 1941-07-10,127.63,128.36,127.05,127.78,840000,127.78 1941-07-09,127.64,128.77,127.12,127.63,1100000,127.63 1941-07-08,126.16,128.00,126.07,127.64,1380000,127.64 1941-07-07,124.54,126.24,124.54,126.16,900000,126.16 1941-07-03,123.58,124.43,123.43,124.04,470000,124.04 1941-07-02,122.85,123.90,122.78,123.58,390000,123.58 1941-07-01,123.14,123.37,122.54,122.85,350000,122.85 1941-06-30,123.40,123.58,122.87,123.14,270000,123.14 1941-06-27,123.96,124.03,123.22,123.46,410000,123.46 1941-06-26,123.52,124.13,123.42,123.96,530000,123.96 1941-06-25,123.24,123.83,122.85,123.52,430000,123.52 1941-06-24,123.97,124.03,122.88,123.24,440000,123.24 1941-06-23,123.41,125.14,123.41,123.97,760000,123.97 1941-06-20,123.30,123.30,121.85,122.19,360000,122.19 1941-06-19,123.50,123.73,122.61,123.48,460000,123.48 1941-06-18,123.17,124.31,123.17,123.50,580000,123.50 1941-06-17,122.14,123.21,122.14,123.12,400000,123.12 1941-06-16,122.04,122.58,121.72,121.95,340000,121.95 1941-06-13,122.88,122.88,121.75,122.31,440000,122.31 1941-06-12,122.18,123.48,122.17,122.98,560000,122.98 1941-06-11,121.89,122.64,121.46,122.18,540000,122.18 1941-06-10,120.61,122.48,120.61,121.89,830000,121.89 1941-06-09,118.99,120.27,118.99,120.16,440000,120.16 1941-06-06,118.13,118.26,117.78,118.00,330000,118.00 1941-06-05,117.68,118.60,117.59,118.13,610000,118.13 1941-06-04,117.38,117.98,116.89,117.68,430000,117.68 1941-06-03,116.32,117.85,116.32,117.38,420000,117.38 1941-06-02,115.76,116.45,115.52,116.18,260000,116.18 1941-05-29,116.16,116.80,115.84,116.23,350000,116.23 1941-05-28,115.95,116.50,115.56,116.16,340000,116.16 1941-05-27,115.73,116.31,115.33,115.95,390000,115.95 1941-05-26,116.28,116.28,115.51,115.73,300000,115.73 1941-05-23,116.81,117.16,116.22,116.73,260000,116.73 1941-05-22,117.82,117.98,116.56,116.81,400000,116.81 1941-05-21,117.65,118.45,117.34,117.82,540000,117.82 1941-05-20,116.31,117.78,116.31,117.65,470000,117.65 1941-05-19,116.11,116.36,115.92,116.15,220000,116.15 1941-05-16,115.73,116.38,115.36,115.86,290000,115.86 1941-05-15,117.01,117.37,115.54,115.73,500000,115.73 1941-05-14,117.21,117.36,116.67,117.01,320000,117.01 1941-05-13,117.14,117.93,116.88,117.21,430000,117.21 1941-05-12,117.54,117.83,116.85,117.14,440000,117.14 1941-05-09,116.34,116.90,116.18,116.46,400000,116.46 1941-05-08,116.76,116.76,115.97,116.34,440000,116.34 1941-05-07,117.10,117.49,116.53,116.87,560000,116.87 1941-05-06,116.02,117.63,116.02,117.10,910000,117.10 1941-05-05,115.55,116.20,114.97,115.84,420000,115.84 1941-05-02,115.41,116.34,115.41,115.72,400000,115.72 1941-05-01,115.54,115.64,114.78,115.30,310000,115.30 1941-04-30,116.73,116.78,115.36,115.54,410000,115.54 1941-04-29,116.63,117.48,116.45,116.73,510000,116.73 1941-04-28,116.43,116.86,115.96,116.63,310000,116.63 1941-04-25,117.35,117.56,116.45,116.58,430000,116.58 1941-04-24,116.61,117.85,116.61,117.35,490000,117.35 1941-04-23,115.78,116.82,115.33,116.59,480000,116.59 1941-04-22,116.06,117.03,115.36,115.78,440000,115.78 1941-04-21,116.15,116.39,115.49,116.06,430000,116.06 1941-04-18,117.74,117.74,116.11,116.28,490000,116.28 1941-04-17,118.60,118.75,117.78,118.16,400000,118.16 1941-04-16,118.59,119.01,117.65,118.60,440000,118.60 1941-04-15,118.89,119.61,118.24,118.59,450000,118.59 1941-04-14,118.60,119.05,118.01,118.89,460000,118.89 1941-04-10,119.85,120.45,119.40,119.66,360000,119.66 1941-04-09,120.72,120.72,119.56,119.85,590000,119.85 1941-04-08,122.94,122.94,121.00,121.21,740000,121.21 1941-04-07,124.11,124.11,123.36,123.64,360000,123.64 1941-04-04,124.65,125.28,124.23,124.64,700000,124.64 1941-04-03,123.74,124.93,123.74,124.65,940000,124.65 1941-04-02,123.26,123.55,122.66,123.43,450000,123.43 1941-04-01,122.87,123.57,122.87,123.26,430000,123.26 1941-03-31,122.37,123.02,122.32,122.72,440000,122.72 1941-03-28,123.33,123.70,122.47,122.68,440000,122.68 1941-03-27,122.84,123.75,122.84,123.33,550000,123.33 1941-03-26,122.78,123.21,122.55,122.70,530000,122.70 1941-03-25,122.39,123.00,121.98,122.78,450000,122.78 1941-03-24,121.92,122.62,121.82,122.39,370000,122.39 1941-03-21,123.39,123.39,122.26,122.47,470000,122.47 1941-03-20,123.55,123.92,123.26,123.60,490000,123.60 1941-03-19,123.92,124.35,123.24,123.55,540000,123.55 1941-03-18,123.46,124.10,123.02,123.92,410000,123.92 1941-03-17,123.40,124.12,123.18,123.46,380000,123.46 1941-03-14,122.56,123.12,122.42,122.75,320000,122.75 1941-03-13,123.19,123.27,122.35,122.56,340000,122.56 1941-03-12,123.27,124.04,122.73,123.19,460000,123.19 1941-03-11,123.64,124.20,123.03,123.27,510000,123.27 1941-03-10,121.48,123.71,121.48,123.64,620000,123.64 1941-03-07,121.63,122.25,121.34,121.59,350000,121.59 1941-03-06,120.30,121.68,120.10,121.63,480000,121.63 1941-03-05,121.15,121.15,119.98,120.30,290000,120.30 1941-03-04,120.88,121.44,120.62,121.16,310000,121.16 1941-03-03,121.65,121.65,120.58,120.88,330000,120.88 1941-02-28,121.87,122.69,121.60,121.97,410000,121.97 1941-02-27,122.22,122.22,121.22,121.87,310000,121.87 1941-02-26,122.40,122.90,121.99,122.39,380000,122.39 1941-02-25,121.60,122.77,121.60,122.40,360000,122.40 1941-02-24,120.44,121.74,120.44,121.49,350000,121.49 1941-02-21,119.99,120.64,119.60,120.24,300000,120.24 1941-02-20,118.84,120.52,118.84,119.99,450000,119.99 1941-02-19,118.71,118.71,117.43,117.94,470000,117.94 1941-02-18,119.18,119.65,118.53,118.98,320000,118.98 1941-02-17,118.70,119.73,118.70,119.18,360000,119.18 1941-02-14,120.74,120.74,117.57,117.66,930000,117.66 1941-02-13,122.06,122.06,120.57,121.10,640000,121.10 1941-02-11,123.80,123.80,122.51,122.61,420000,122.61 1941-02-10,124.71,125.13,123.93,124.19,300000,124.19 1941-02-07,124.58,124.58,123.57,124.30,340000,124.30 1941-02-06,124.25,125.27,124.25,124.76,420000,124.76 1941-02-05,122.77,124.55,122.77,124.14,490000,124.14 1941-02-04,122.67,123.29,122.29,122.63,350000,122.63 1941-02-03,123.28,123.75,122.40,122.67,490000,122.67 1941-01-31,124.05,124.85,123.86,124.13,470000,124.13 1941-01-30,125.96,125.96,123.94,124.05,780000,124.05 1941-01-29,127.93,127.93,125.76,126.00,600000,126.00 1941-01-28,129.03,129.27,128.42,128.60,470000,128.60 1941-01-27,128.96,129.47,128.54,129.03,360000,129.03 1941-01-24,128.34,128.92,127.68,128.52,410000,128.52 1941-01-23,128.65,129.15,127.74,128.34,470000,128.34 1941-01-22,128.20,129.03,127.98,128.65,520000,128.65 1941-01-21,129.24,129.51,127.83,128.20,580000,128.20 1941-01-20,129.75,129.99,128.78,129.24,380000,129.24 1941-01-17,129.93,130.20,128.73,129.54,580000,129.54 1941-01-16,131.36,131.36,129.82,129.93,610000,129.93 1941-01-15,132.43,132.43,131.20,131.51,400000,131.51 1941-01-14,133.11,133.11,132.17,132.44,470000,132.44 1941-01-13,133.49,133.85,132.92,133.25,480000,133.25 1941-01-10,133.39,134.27,133.14,133.59,750000,133.59 1941-01-09,133.02,133.94,132.79,133.39,860000,133.39 1941-01-08,133.02,133.74,132.35,133.02,640000,133.02 1941-01-07,132.83,133.50,132.19,133.02,530000,133.02 1941-01-06,132.42,133.68,132.42,132.83,720000,132.83 1941-01-03,130.57,132.19,130.24,132.01,510000,132.01 1941-01-02,131.13,131.88,130.39,130.57,530000,130.57 1940-12-31,131.04,131.86,130.40,131.13,1070000,131.13 1940-12-30,130.18,131.85,130.18,131.04,1180000,131.04 1940-12-27,129.02,130.11,128.55,129.51,1270000,129.51 1940-12-26,128.89,129.70,128.42,129.02,840000,129.02 1940-12-24,128.41,129.47,128.08,128.89,830000,128.89 1940-12-23,128.89,129.29,127.83,128.41,820000,128.41 1940-12-20,128.84,129.66,128.19,128.87,830000,128.87 1940-12-19,129.42,129.43,128.19,128.84,790000,128.84 1940-12-18,130.53,130.92,129.31,129.42,780000,129.42 1940-12-17,131.07,131.34,130.09,130.53,700000,130.53 1940-12-16,132.28,132.28,130.74,131.07,660000,131.07 1940-12-13,132.14,133.00,131.56,132.35,960000,132.35 1940-12-12,131.76,132.53,131.24,132.14,780000,132.14 1940-12-11,131.37,132.50,131.24,131.76,810000,131.76 1940-12-10,131.46,131.97,130.69,131.37,610000,131.37 1940-12-09,131.29,132.22,130.91,131.46,630000,131.46 1940-12-06,129.96,130.86,129.62,130.33,540000,130.33 1940-12-05,130.75,130.81,129.54,129.96,600000,129.96 1940-12-04,130.78,131.21,129.99,130.75,650000,130.75 1940-12-03,130.93,131.23,130.25,130.78,450000,130.78 1940-12-02,131.00,131.96,130.54,130.93,480000,130.93 1940-11-29,130.14,130.78,129.49,130.03,530000,130.03 1940-11-28,129.78,130.57,129.13,130.14,470000,130.14 1940-11-27,131.45,131.45,129.29,129.78,850000,129.78 1940-11-26,131.96,132.72,131.28,131.94,590000,131.94 1940-11-25,131.47,132.76,131.35,131.96,520000,131.96 1940-11-22,132.22,133.36,131.29,131.74,710000,131.74 1940-11-20,134.08,134.08,131.72,132.22,810000,132.22 1940-11-19,134.74,134.99,133.51,134.48,700000,134.48 1940-11-18,134.73,135.47,134.36,134.74,570000,134.74 1940-11-15,136.97,137.44,135.24,135.59,1050000,135.59 1940-11-14,136.61,137.78,136.20,136.97,1380000,136.97 1940-11-13,137.41,137.61,135.77,136.61,1070000,136.61 1940-11-12,138.12,138.50,136.56,137.41,1450000,137.41 1940-11-08,137.75,138.77,135.76,136.64,1750000,136.64 1940-11-07,131.98,138.13,131.93,137.75,2080000,137.75 1940-11-06,135.00,135.00,131.47,131.98,1210000,131.98 1940-11-04,134.85,135.83,133.81,135.21,1240000,135.21 1940-11-01,134.61,135.84,134.13,134.41,1260000,134.41 1940-10-31,133.06,135.10,133.06,134.61,1340000,134.61 1940-10-30,132.19,133.43,131.90,132.98,670000,132.98 1940-10-29,131.77,132.80,131.66,132.19,590000,132.19 1940-10-28,132.26,132.27,130.96,131.77,470000,131.77 1940-10-25,131.36,131.71,130.38,131.16,520000,131.16 1940-10-24,132.29,132.29,131.06,131.36,540000,131.36 1940-10-23,131.98,132.79,131.26,132.40,810000,132.40 1940-10-22,131.37,132.44,131.04,131.98,540000,131.98 1940-10-21,132.18,132.28,131.13,131.37,370000,131.37 1940-10-18,132.49,132.90,131.92,132.45,590000,132.45 1940-10-17,131.97,132.84,131.20,132.49,650000,132.49 1940-10-16,131.48,132.69,131.05,131.97,660000,131.97 1940-10-15,130.73,131.63,129.47,131.48,550000,131.48 1940-10-14,131.04,131.49,130.32,130.73,400000,130.73 1940-10-11,130.39,131.62,130.20,131.04,400000,131.04 1940-10-10,130.54,131.22,130.09,130.39,380000,130.39 1940-10-09,131.31,131.31,130.11,130.54,450000,130.54 1940-10-08,133.31,133.31,131.20,131.31,500000,131.31 1940-10-07,133.90,134.54,133.31,133.51,390000,133.51 1940-10-04,134.48,134.48,133.37,133.79,470000,133.79 1940-10-03,134.97,135.86,134.59,135.09,780000,135.09 1940-10-02,134.33,135.41,133.70,134.97,770000,134.97 1940-10-01,133.04,135.04,133.04,134.33,810000,134.33 1940-09-30,132.32,133.07,132.10,132.64,400000,132.64 1940-09-27,132.98,132.98,131.38,131.76,560000,131.76 1940-09-26,134.00,134.00,133.00,133.50,440000,133.50 1940-09-25,134.44,134.58,133.40,134.15,600000,134.15 1940-09-24,135.10,135.48,133.89,134.44,710000,134.44 1940-09-23,132.98,135.31,132.98,135.10,980000,135.10 1940-09-20,131.34,131.95,130.77,131.61,380000,131.61 1940-09-19,131.28,132.03,130.83,131.34,470000,131.34 1940-09-18,130.43,131.67,129.91,131.28,480000,131.28 1940-09-17,129.44,130.89,129.44,130.43,400000,130.43 1940-09-16,128.89,130.04,128.89,129.44,290000,129.44 1940-09-13,127.87,128.37,127.22,127.74,270000,127.74 1940-09-12,129.32,129.32,127.46,127.87,400000,127.87 1940-09-11,129.61,131.21,129.07,129.36,450000,129.36 1940-09-10,129.73,130.53,129.18,129.61,360000,129.61 1940-09-09,130.98,130.98,129.36,129.73,590000,129.73 1940-09-06,134.10,134.19,132.71,133.12,710000,133.12 1940-09-05,132.31,134.54,132.31,134.10,1250000,134.10 1940-09-04,129.74,132.25,128.89,132.16,780000,132.16 1940-09-03,129.42,130.59,129.12,129.74,550000,129.74 1940-08-30,126.98,129.18,126.98,128.88,560000,128.88 1940-08-29,126.87,127.37,126.49,126.87,270000,126.87 1940-08-28,125.81,127.37,125.81,126.87,380000,126.87 1940-08-27,125.71,125.76,124.95,125.33,220000,125.33 1940-08-26,125.48,126.04,125.34,125.71,160000,125.71 1940-08-23,126.34,126.34,124.81,125.34,290000,125.34 1940-08-22,125.62,126.97,125.62,126.46,440000,126.46 1940-08-21,123.95,125.38,123.95,125.07,360000,125.07 1940-08-20,122.52,123.41,122.52,123.17,240000,123.17 1940-08-19,121.98,122.37,121.70,122.06,130000,122.06 1940-08-16,122.50,122.50,120.90,121.28,310000,121.28 1940-08-15,122.73,123.46,122.73,123.04,220000,123.04 1940-08-14,122.98,123.17,122.00,122.25,270000,122.25 1940-08-13,126.42,126.42,122.64,122.98,640000,122.98 1940-08-12,126.99,127.55,126.50,127.26,290000,127.26 1940-08-09,125.44,126.81,125.44,126.40,310000,126.40 1940-08-08,125.12,125.48,124.87,125.13,210000,125.13 1940-08-07,125.27,125.47,124.61,125.12,240000,125.12 1940-08-06,126.28,126.28,125.11,125.27,290000,125.27 1940-08-05,126.36,126.73,125.57,126.44,280000,126.44 1940-08-02,126.13,126.97,125.77,126.37,300000,126.37 1940-08-01,126.14,126.86,125.57,126.13,330000,126.13 1940-07-31,125.97,127.18,125.47,126.14,560000,126.14 1940-07-30,123.58,126.18,123.58,125.97,670000,125.97 1940-07-29,122.45,123.38,122.16,123.15,260000,123.15 1940-07-26,121.93,122.75,121.70,122.05,270000,122.05 1940-07-25,121.64,122.09,121.19,121.93,250000,121.93 1940-07-24,122.23,122.30,121.49,121.64,200000,121.64 1940-07-23,122.06,122.53,121.49,122.23,250000,122.23 1940-07-22,121.87,122.47,121.62,122.06,230000,122.06 1940-07-19,122.93,122.93,122.01,122.18,260000,122.18 1940-07-18,122.82,123.22,122.52,123.00,220000,123.00 1940-07-17,123.12,123.91,122.34,122.82,380000,122.82 1940-07-16,121.82,123.73,121.82,123.12,440000,123.12 1940-07-15,121.48,122.13,121.29,121.72,230000,121.72 1940-07-12,121.58,121.95,121.32,121.63,260000,121.63 1940-07-11,121.49,122.30,121.28,121.58,330000,121.58 1940-07-10,121.60,121.82,120.83,121.49,280000,121.49 1940-07-09,121.63,122.33,121.36,121.60,300000,121.60 1940-07-08,121.59,122.04,121.39,121.63,230000,121.63 1940-07-05,121.02,121.96,121.02,121.51,280000,121.51 1940-07-03,120.96,121.68,120.14,120.96,380000,120.96 1940-07-02,121.12,122.01,120.71,120.96,320000,120.96 1940-07-01,121.77,121.77,120.79,121.12,270000,121.12 1940-06-28,121.82,124.42,121.82,122.06,1170000,122.06 1940-06-27,120.01,121.23,120.01,120.69,440000,120.69 1940-06-26,120.74,120.74,118.67,119.73,640000,119.73 1940-06-25,123.76,123.99,120.78,121.05,700000,121.05 1940-06-24,122.83,124.05,122.60,123.76,470000,123.76 1940-06-21,122.35,123.07,121.89,122.61,330000,122.61 1940-06-20,123.79,123.79,121.96,122.35,590000,122.35 1940-06-19,123.21,124.51,122.50,123.86,560000,123.86 1940-06-18,122.80,125.31,122.35,123.21,720000,123.21 1940-06-17,123.36,123.73,119.18,122.80,1210000,122.80 1940-06-14,119.91,122.95,118.96,122.27,950000,122.27 1940-06-13,121.46,122.10,119.37,119.91,880000,119.91 1940-06-12,117.41,122.38,117.41,121.46,1360000,121.46 1940-06-11,113.24,116.38,113.24,115.97,760000,115.97 1940-06-10,114.42,114.42,110.41,111.84,970000,111.84 1940-06-07,114.60,116.58,114.60,115.67,470000,115.67 1940-06-06,113.25,114.80,113.05,114.48,430000,114.48 1940-06-05,115.12,115.12,112.30,113.25,670000,113.25 1940-06-04,114.75,116.25,114.75,115.79,410000,115.79 1940-06-03,115.67,116.44,114.35,114.73,450000,114.73 1940-05-31,115.24,117.15,115.13,116.22,530000,116.22 1940-05-29,114.26,116.66,114.08,115.24,660000,115.24 1940-05-28,114.76,114.76,110.51,114.26,1260000,114.26 1940-05-27,115.07,117.71,115.07,116.35,790000,116.35 1940-05-24,114.71,116.15,113.37,113.94,870000,113.94 1940-05-23,114.75,117.84,112.78,114.71,1640000,114.71 1940-05-22,114.13,116.50,112.43,114.75,2130000,114.75 1940-05-21,120.52,120.52,110.61,114.13,3940000,114.13 1940-05-20,122.43,124.98,121.68,122.43,1240000,122.43 1940-05-17,130.43,131.21,122.93,124.20,3080000,124.20 1940-05-16,129.08,131.35,127.54,130.43,2350000,130.43 1940-05-15,128.27,131.17,125.76,129.08,3770000,129.08 1940-05-14,136.85,136.85,128.11,128.27,3680000,128.27 1940-05-13,144.42,144.42,137.25,137.63,2560000,137.63 1940-05-10,148.17,148.48,144.51,144.77,2090000,144.77 1940-05-09,147.96,148.60,147.65,148.17,850000,148.17 1940-05-08,147.74,148.70,147.49,147.96,690000,147.96 1940-05-07,147.33,148.22,146.89,147.74,580000,147.74 1940-05-06,147.55,148.12,147.05,147.33,530000,147.33 1940-05-03,147.76,148.70,146.42,147.65,1070000,147.65 1940-05-02,147.15,148.18,147.15,147.76,650000,147.76 1940-05-01,148.14,148.14,146.84,147.13,810000,147.13 1940-04-30,148.41,149.06,147.98,148.43,590000,148.43 1940-04-29,148.12,148.88,148.02,148.41,570000,148.41 1940-04-26,148.56,148.72,147.37,147.73,850000,147.73 1940-04-25,148.45,149.22,148.07,148.56,820000,148.56 1940-04-24,148.93,149.45,148.20,148.45,850000,148.45 1940-04-23,148.01,149.18,147.77,148.93,880000,148.93 1940-04-22,147.67,148.68,147.45,148.01,870000,148.01 1940-04-19,147.15,147.31,145.86,146.80,1160000,146.80 1940-04-18,148.35,148.64,146.76,147.15,1210000,147.15 1940-04-17,148.18,149.12,147.77,148.35,900000,148.35 1940-04-16,149.72,150.24,147.43,148.18,1510000,148.18 1940-04-15,149.66,150.67,149.20,149.72,1260000,149.72 1940-04-12,149.98,150.09,148.68,149.20,830000,149.20 1940-04-11,149.59,150.96,149.49,149.98,890000,149.98 1940-04-10,150.31,150.55,149.12,149.59,1290000,149.59 1940-04-09,151.29,152.01,149.16,150.31,2140000,150.31 1940-04-08,151.10,152.09,150.63,151.29,1260000,151.29 1940-04-05,150.41,151.32,149.94,150.36,1260000,150.36 1940-04-04,149.65,151.15,149.56,150.41,2000000,150.41 1940-04-03,147.92,149.74,147.56,149.65,1730000,149.65 1940-04-02,147.72,148.37,147.48,147.92,840000,147.92 1940-04-01,147.95,148.44,147.49,147.72,750000,147.72 1940-03-29,147.25,148.04,146.82,147.54,840000,147.54 1940-03-28,147.47,148.16,146.92,147.25,1020000,147.25 1940-03-27,146.24,147.83,146.24,147.47,1190000,147.47 1940-03-26,146.25,146.56,145.49,145.86,620000,145.86 1940-03-25,146.73,146.96,146.15,146.25,600000,146.25 1940-03-21,146.91,147.20,146.38,146.73,580000,146.73 1940-03-20,146.43,147.30,146.34,146.91,650000,146.91 1940-03-19,145.61,146.85,145.61,146.43,650000,146.43 1940-03-18,145.76,146.18,145.08,145.59,510000,145.59 1940-03-15,148.11,148.21,146.34,146.53,880000,146.53 1940-03-14,148.32,148.57,147.63,148.11,660000,148.11 1940-03-13,148.37,148.92,147.69,148.32,630000,148.32 1940-03-12,148.15,149.45,147.93,148.37,880000,148.37 1940-03-11,148.14,148.65,147.57,148.15,590000,148.15 1940-03-08,148.32,148.80,147.76,148.07,750000,148.07 1940-03-07,147.97,148.67,147.83,148.32,690000,148.32 1940-03-06,147.08,148.37,147.08,147.97,860000,147.97 1940-03-05,146.43,147.15,146.41,146.89,570000,146.89 1940-03-04,146.33,146.77,146.00,146.43,460000,146.43 1940-03-01,146.54,146.79,145.85,146.23,600000,146.23 1940-02-29,146.56,147.21,146.10,146.54,620000,146.54 1940-02-28,146.17,147.16,146.07,146.56,570000,146.56 1940-02-27,146.44,147.10,145.90,146.17,510000,146.17 1940-02-26,146.72,146.82,145.81,146.44,440000,146.44 1940-02-23,148.17,148.17,146.93,147.35,650000,147.35 1940-02-21,148.65,149.04,148.02,148.34,780000,148.34 1940-02-20,148.46,148.95,147.51,148.65,810000,148.65 1940-02-19,148.72,148.95,147.93,148.46,630000,148.46 1940-02-16,148.46,148.60,147.38,148.20,680000,148.20 1940-02-15,148.33,149.19,148.20,148.46,750000,148.46 1940-02-14,148.78,148.83,147.65,148.33,650000,148.33 1940-02-13,148.84,149.64,148.38,148.78,580000,148.78 1940-02-09,148.54,150.04,148.54,148.94,1100000,148.94 1940-02-08,146.63,148.50,146.32,148.40,870000,148.40 1940-02-07,145.93,146.97,145.84,146.63,490000,146.63 1940-02-06,145.00,146.00,144.79,145.93,540000,145.93 1940-02-05,145.58,145.58,144.69,145.00,410000,145.00 1940-02-02,145.23,145.97,144.83,145.33,520000,145.33 1940-02-01,145.33,145.57,144.73,145.23,460000,145.23 1940-01-31,145.63,145.91,145.12,145.33,610000,145.33 1940-01-30,146.26,146.37,145.19,145.63,550000,145.63 1940-01-29,146.51,147.05,145.86,146.26,490000,146.26 1940-01-26,146.29,147.16,146.00,146.61,600000,146.61 1940-01-25,147.00,147.29,146.04,146.29,540000,146.29 1940-01-24,145.71,147.11,145.71,147.00,710000,147.00 1940-01-23,145.13,145.97,144.85,145.49,510000,145.49 1940-01-22,145.64,145.66,144.57,145.13,440000,145.13 1940-01-19,145.61,146.75,145.52,145.86,640000,145.86 1940-01-18,145.81,146.44,144.77,145.61,610000,145.61 1940-01-17,145.67,146.71,145.30,145.81,470000,145.81 1940-01-16,144.65,146.11,144.37,145.67,530000,145.67 1940-01-15,145.19,145.95,143.06,144.65,860000,144.65 1940-01-12,148.23,148.35,145.76,145.96,1110000,145.96 1940-01-11,150.15,150.64,148.22,148.23,850000,148.23 1940-01-10,149.84,150.47,149.35,150.15,600000,150.15 1940-01-09,151.21,151.21,149.45,149.84,670000,149.84 1940-01-08,151.19,152.11,151.08,151.34,630000,151.34 1940-01-05,152.43,152.89,151.27,151.54,760000,151.54 1940-01-04,152.80,153.26,152.06,152.43,860000,152.43 1940-01-03,151.86,153.29,151.86,152.80,1020000,152.80 1940-01-02,150.45,151.79,150.45,151.43,580000,151.43 1939-12-29,149.48,150.70,149.06,149.99,1140000,149.99 1939-12-28,148.52,150.10,148.24,149.48,1080000,149.48 1939-12-27,149.27,149.51,147.66,148.52,1150000,148.52 1939-12-26,149.85,150.11,148.83,149.27,720000,149.27 1939-12-22,149.10,149.97,148.87,149.59,720000,149.59 1939-12-21,149.13,149.90,148.59,149.10,740000,149.10 1939-12-20,148.93,149.86,148.41,149.13,910000,149.13 1939-12-19,149.22,149.59,148.35,148.93,750000,148.93 1939-12-18,149.36,149.80,148.69,149.22,730000,149.22 1939-12-15,148.93,150.11,148.74,149.64,700000,149.64 1939-12-14,148.94,150.09,148.25,148.93,890000,148.93 1939-12-13,147.12,149.29,147.12,148.94,1060000,148.94 1939-12-12,147.05,147.59,146.43,146.93,610000,146.93 1939-12-11,147.93,148.27,146.67,147.05,570000,147.05 1939-12-08,148.57,148.57,147.50,147.86,580000,147.86 1939-12-07,148.78,149.59,147.98,148.70,1010000,148.70 1939-12-06,146.83,148.99,146.83,148.78,990000,148.78 1939-12-05,146.34,147.29,146.05,146.49,590000,146.49 1939-12-04,146.62,146.79,145.74,146.34,430000,146.34 1939-12-01,145.69,146.94,145.51,146.54,610000,146.54 1939-11-30,146.73,146.73,144.85,145.69,880000,145.69 1939-11-29,148.31,149.18,146.82,146.89,780000,146.89 1939-11-28,148.59,149.65,148.02,148.31,620000,148.31 1939-11-27,148.64,149.05,147.98,148.59,520000,148.59 1939-11-24,150.34,150.46,148.12,148.47,820000,148.47 1939-11-22,150.67,150.67,149.62,150.34,570000,150.34 1939-11-21,151.69,152.11,150.72,150.98,560000,150.98 1939-11-20,151.53,152.58,151.02,151.69,750000,151.69 1939-11-17,151.15,152.21,150.55,151.00,770000,151.00 1939-11-16,149.53,151.42,149.27,151.15,830000,151.15 1939-11-15,149.77,150.48,149.23,149.53,640000,149.53 1939-11-14,149.07,150.53,148.98,149.77,780000,149.77 1939-11-13,149.09,149.70,148.55,149.07,650000,149.07 1939-11-10,148.75,149.33,147.74,149.09,1090000,149.09 1939-11-09,150.35,150.87,148.53,148.75,1200000,148.75 1939-11-08,151.43,151.43,149.81,150.35,1070000,150.35 1939-11-06,152.35,152.35,150.76,151.46,1270000,151.46 1939-11-03,151.56,153.18,150.04,152.64,1820000,152.64 1939-11-02,151.60,152.20,150.47,151.56,850000,151.56 1939-11-01,151.88,152.26,150.64,151.60,790000,151.60 1939-10-31,153.21,153.24,151.32,151.88,1010000,151.88 1939-10-30,153.12,153.60,152.39,153.21,640000,153.21 1939-10-27,154.05,154.34,152.30,153.46,1060000,153.46 1939-10-26,155.48,155.95,153.84,154.05,1680000,154.05 1939-10-25,154.07,155.95,153.98,155.48,1690000,155.48 1939-10-24,153.71,154.76,153.04,154.07,1160000,154.07 1939-10-23,153.86,154.56,153.19,153.71,970000,153.71 1939-10-20,153.36,153.87,152.55,153.00,790000,153.00 1939-10-19,153.54,154.42,152.78,153.36,1160000,153.36 1939-10-18,154.56,155.28,153.23,153.54,1400000,153.54 1939-10-17,151.29,154.81,151.29,154.56,1840000,154.56 1939-10-16,150.38,151.34,149.95,150.84,490000,150.84 1939-10-13,151.34,152.40,150.43,150.85,740000,150.85 1939-10-11,150.66,151.89,150.49,151.34,630000,151.34 1939-10-10,149.92,152.02,149.92,150.66,950000,150.66 1939-10-09,149.60,150.51,148.91,149.89,620000,149.89 1939-10-06,150.48,153.06,149.61,150.61,1330000,150.61 1939-10-05,150.25,151.68,149.72,150.48,910000,150.48 1939-10-04,150.23,151.20,148.73,150.25,980000,150.25 1939-10-03,151.41,152.20,149.29,150.23,1000000,150.23 1939-10-02,152.36,152.36,150.68,151.41,840000,151.41 1939-09-29,150.89,150.89,148.92,150.16,1130000,150.16 1939-09-28,153.08,153.13,150.41,151.12,1570000,151.12 1939-09-27,153.54,154.92,152.01,153.08,2340000,153.08 1939-09-26,152.64,154.27,151.77,153.54,1710000,153.54 1939-09-25,152.99,153.91,152.05,152.64,1230000,152.64 1939-09-22,153.48,154.76,151.97,152.57,1660000,152.57 1939-09-21,152.25,154.56,151.49,153.48,1730000,153.48 1939-09-20,152.14,154.96,151.57,152.25,2140000,152.25 1939-09-19,148.46,152.83,148.46,152.14,1830000,152.14 1939-09-18,150.57,150.57,147.35,147.78,1730000,147.78 1939-09-15,153.71,155.57,152.56,154.03,1590000,154.03 1939-09-14,154.10,155.54,151.96,153.71,2010000,153.71 1939-09-13,155.92,157.77,152.74,154.10,3760000,154.10 1939-09-12,155.12,157.30,151.78,155.92,4170000,155.92 1939-09-11,150.91,156.34,150.85,155.12,4680000,155.12 1939-09-08,148.32,152.58,148.08,150.04,3510000,150.04 1939-09-07,148.04,150.52,146.74,148.32,2600000,148.32 1939-09-06,148.12,150.76,146.08,148.04,3940000,148.04 1939-09-05,142.38,150.07,142.38,148.12,5930000,148.12 1939-09-01,134.41,136.03,127.51,135.25,1970000,135.25 1939-08-31,135.76,135.76,133.38,134.41,460000,134.41 1939-08-30,137.39,138.07,135.76,136.16,500000,136.16 1939-08-29,135.91,137.84,135.91,137.39,480000,137.39 1939-08-28,136.39,136.40,132.68,134.66,670000,134.66 1939-08-25,131.33,134.53,130.58,133.73,690000,133.73 1939-08-24,131.82,132.42,128.60,131.33,1290000,131.33 1939-08-23,134.80,134.80,131.49,131.82,790000,131.82 1939-08-22,133.07,135.84,133.07,135.07,860000,135.07 1939-08-21,133.93,133.93,132.11,132.81,850000,132.81 1939-08-18,138.15,138.15,134.83,135.54,840000,135.54 1939-08-17,138.47,138.89,137.38,138.33,440000,138.33 1939-08-16,139.86,139.86,137.61,138.47,640000,138.47 1939-08-15,140.76,142.35,140.76,141.29,660000,141.29 1939-08-14,138.75,140.54,138.75,140.18,550000,140.18 1939-08-11,137.25,138.93,136.38,137.29,700000,137.29 1939-08-10,138.83,138.83,136.62,137.25,700000,137.25 1939-08-09,140.58,140.58,139.14,139.75,470000,139.75 1939-08-08,140.76,141.93,140.55,141.10,450000,141.10 1939-08-07,142.11,142.38,140.31,140.76,520000,140.76 1939-08-04,144.06,144.06,141.26,141.73,900000,141.73 1939-08-03,144.26,145.75,143.79,144.24,1010000,144.24 1939-08-02,143.36,144.90,142.69,144.26,1030000,144.26 1939-08-01,143.26,143.89,142.45,143.36,580000,143.36 1939-07-31,144.00,144.04,142.77,143.26,520000,143.26 1939-07-28,144.51,145.04,143.48,144.11,810000,144.11 1939-07-27,143.82,144.92,143.08,144.51,820000,144.51 1939-07-26,143.10,144.39,142.41,143.82,890000,143.82 1939-07-25,144.18,145.72,142.83,143.10,1230000,143.10 1939-07-24,144.71,144.89,143.38,144.18,1070000,144.18 1939-07-21,141.88,144.28,141.88,143.46,1270000,143.46 1939-07-20,142.64,143.24,141.05,141.24,810000,141.24 1939-07-19,143.60,143.60,141.70,142.64,1020000,142.64 1939-07-18,142.96,144.74,142.96,143.76,1890000,143.76 1939-07-17,138.48,143.20,138.48,142.58,1750000,142.58 1939-07-14,138.02,138.41,137.24,137.57,540000,137.57 1939-07-13,137.34,139.05,137.34,138.02,950000,138.02 1939-07-12,134.67,137.24,134.67,136.98,910000,136.98 1939-07-11,133.84,135.06,133.84,134.56,430000,134.56 1939-07-10,133.24,134.21,133.22,133.79,280000,133.79 1939-07-07,133.58,133.84,132.93,133.22,330000,133.22 1939-07-06,133.68,134.31,132.98,133.58,410000,133.58 1939-07-05,132.74,133.94,132.74,133.68,350000,133.68 1939-07-03,131.73,132.22,131.18,131.93,240000,131.93 1939-06-30,130.05,131.16,128.97,130.63,600000,130.63 1939-06-29,131.81,131.81,129.71,130.05,820000,130.05 1939-06-28,135.06,135.06,132.76,132.83,540000,132.83 1939-06-27,135.09,135.77,134.01,135.42,480000,135.42 1939-06-26,136.77,136.77,134.83,135.09,500000,135.09 1939-06-23,136.88,137.95,136.48,137.42,480000,137.42 1939-06-22,137.61,137.63,136.34,136.88,450000,136.88 1939-06-21,137.57,138.04,136.87,137.61,470000,137.61 1939-06-20,136.72,137.97,136.72,137.57,490000,137.57 1939-06-19,135.72,137.02,135.72,136.40,350000,136.40 1939-06-16,134.41,135.36,133.79,134.67,400000,134.67 1939-06-15,137.03,137.03,134.26,134.41,580000,134.41 1939-06-14,138.02,138.02,136.44,137.50,400000,137.50 1939-06-13,139.09,139.09,137.38,138.20,530000,138.20 1939-06-12,139.95,139.95,138.34,139.13,420000,139.13 1939-06-09,138.61,140.75,138.61,140.09,790000,140.09 1939-06-08,138.71,138.84,137.53,138.49,410000,138.49 1939-06-07,138.36,139.79,138.17,138.71,530000,138.71 1939-06-06,137.06,138.84,136.98,138.36,600000,138.36 1939-06-05,137.12,137.36,136.34,137.06,350000,137.06 1939-06-02,136.29,137.42,136.29,136.74,400000,136.74 1939-06-01,137.36,137.36,135.52,136.20,600000,136.20 1939-05-31,137.80,139.23,137.52,138.18,670000,138.18 1939-05-29,136.80,137.91,136.42,137.80,600000,137.80 1939-05-26,135.53,136.76,135.22,136.09,620000,136.09 1939-05-25,135.11,137.16,135.11,135.53,1010000,135.53 1939-05-24,132.09,135.14,132.09,135.04,1010000,135.04 1939-05-23,132.45,132.88,131.49,131.77,420000,131.77 1939-05-22,131.22,132.54,130.50,132.45,420000,132.45 1939-05-19,129.43,130.90,129.22,130.38,400000,130.38 1939-05-18,129.09,130.28,128.79,129.43,420000,129.43 1939-05-17,129.77,129.77,128.35,129.09,530000,129.09 1939-05-16,132.56,132.56,129.79,129.86,620000,129.86 1939-05-15,132.40,133.68,132.35,132.65,340000,132.65 1939-05-12,132.79,132.79,131.74,132.16,340000,132.16 1939-05-11,132.82,133.26,131.85,132.92,400000,132.92 1939-05-10,133.67,134.66,132.63,132.82,690000,132.82 1939-05-09,132.11,134.02,132.11,133.67,710000,133.67 1939-05-08,131.74,132.22,130.70,131.67,350000,131.67 1939-05-05,131.86,132.12,130.76,131.47,330000,131.47 1939-05-04,132.30,133.24,131.30,131.86,660000,131.86 1939-05-03,129.60,132.64,129.60,132.30,740000,132.30 1939-05-02,128.31,130.13,128.31,129.32,450000,129.32 1939-05-01,128.45,128.55,127.53,127.83,280000,127.83 1939-04-28,129.78,131.42,127.58,128.38,730000,128.38 1939-04-27,128.56,130.21,128.49,129.78,540000,129.78 1939-04-26,127.36,129.06,126.44,128.56,580000,128.56 1939-04-25,127.34,128.53,127.02,127.36,420000,127.36 1939-04-24,128.55,129.03,127.20,127.34,410000,127.34 1939-04-21,128.41,129.62,127.97,128.71,390000,128.71 1939-04-20,127.87,129.59,127.87,128.41,520000,128.41 1939-04-19,125.63,127.61,125.63,127.01,440000,127.01 1939-04-18,127.02,127.02,124.81,125.38,440000,125.38 1939-04-17,128.01,128.01,126.15,127.34,520000,127.34 1939-04-14,126.58,126.58,124.52,126.20,620000,126.20 1939-04-13,126.29,129.32,126.29,127.51,860000,127.51 1939-04-12,125.15,127.51,125.15,126.15,1070000,126.15 1939-04-11,124.03,124.42,120.04,123.75,1660000,123.75 1939-04-10,121.44,124.27,120.82,124.03,1650000,124.03 1939-04-06,129.23,129.23,125.49,126.32,1310000,126.32 1939-04-05,129.80,131.38,128.64,130.34,880000,130.34 1939-04-04,131.09,131.09,127.16,129.80,1530000,129.80 1939-04-03,132.83,135.57,130.49,132.25,1470000,132.25 1939-03-31,136.69,138.01,131.35,131.84,2890000,131.84 1939-03-30,139.75,140.55,136.41,136.69,990000,136.69 1939-03-29,139.33,140.55,138.84,139.75,470000,139.75 1939-03-28,139.98,139.98,138.46,139.33,680000,139.33 1939-03-27,141.55,143.14,140.91,141.14,570000,141.14 1939-03-24,141.13,142.80,141.13,141.82,650000,141.82 1939-03-23,139.51,142.17,139.42,140.33,830000,140.33 1939-03-22,141.97,141.97,138.42,139.51,1440000,139.51 1939-03-21,142.67,144.31,142.67,143.41,690000,143.41 1939-03-20,141.68,143.14,140.57,141.28,950000,141.28 1939-03-17,146.13,146.13,142.99,143.89,1470000,143.89 1939-03-16,147.66,148.17,146.45,147.54,670000,147.54 1939-03-15,150.28,150.28,147.16,147.66,1110000,147.66 1939-03-14,150.79,151.39,149.91,151.10,690000,151.10 1939-03-13,151.58,151.58,150.20,150.79,650000,150.79 1939-03-10,151.33,152.71,151.22,152.28,1210000,152.28 1939-03-09,151.42,152.42,150.52,151.33,1360000,151.33 1939-03-08,149.37,151.56,149.17,151.42,1050000,151.42 1939-03-07,148.86,149.88,148.86,149.37,570000,149.37 1939-03-06,149.49,150.23,148.37,148.84,840000,148.84 1939-03-03,147.31,148.89,147.31,148.76,1020000,148.76 1939-03-02,147.15,147.19,146.34,146.96,600000,146.96 1939-03-01,147.30,147.88,146.62,147.15,640000,147.15 1939-02-28,146.76,148.16,146.76,147.30,1060000,147.30 1939-02-27,146.82,147.32,146.10,146.62,750000,146.62 1939-02-24,143.46,145.69,143.46,145.44,970000,145.44 1939-02-23,142.64,143.63,142.45,142.93,460000,142.93 1939-02-21,142.74,143.13,142.05,142.64,470000,142.64 1939-02-20,144.54,144.54,142.48,142.74,690000,142.74 1939-02-17,145.39,146.03,144.69,144.95,680000,144.95 1939-02-16,144.60,146.12,144.50,145.39,850000,145.39 1939-02-15,144.13,144.95,143.83,144.60,500000,144.60 1939-02-14,144.48,144.48,143.49,144.13,420000,144.13 1939-02-10,143.99,144.01,142.70,143.68,450000,143.68 1939-02-09,145.43,145.56,143.83,143.99,550000,143.99 1939-02-08,144.45,145.55,144.45,145.43,610000,145.43 1939-02-07,145.03,145.11,143.50,144.10,570000,144.10 1939-02-06,145.07,146.43,144.78,145.03,1040000,145.03 1939-02-03,144.34,144.50,143.02,143.55,540000,143.55 1939-02-02,142.59,144.49,142.59,144.34,700000,144.34 1939-02-01,143.47,143.47,141.92,142.43,580000,142.43 1939-01-31,142.52,144.74,142.52,143.76,1120000,143.76 1939-01-30,139.32,141.80,139.32,141.56,790000,141.56 1939-01-27,136.84,139.27,136.84,138.90,1060000,138.90 1939-01-26,139.58,139.58,136.10,136.42,1540000,136.42 1939-01-25,141.35,141.68,139.37,140.72,900000,140.72 1939-01-24,141.32,142.83,139.62,141.35,1700000,141.35 1939-01-23,144.13,144.13,141.00,141.32,1870000,141.32 1939-01-20,149.47,149.75,148.77,149.11,740000,149.11 1939-01-19,148.99,149.88,148.35,149.47,890000,149.47 1939-01-18,148.93,149.56,148.55,148.99,630000,148.99 1939-01-17,148.26,149.23,147.49,148.93,820000,148.93 1939-01-16,148.26,148.71,147.70,148.26,670000,148.26 1939-01-13,147.33,147.84,146.03,146.52,850000,146.52 1939-01-12,148.65,149.43,146.17,147.33,1360000,147.33 1939-01-11,150.18,150.18,148.45,148.65,920000,148.65 1939-01-10,150.19,151.32,150.04,150.48,710000,150.48 1939-01-09,151.07,151.07,149.23,150.19,1100000,150.19 1939-01-06,153.18,153.55,152.42,152.87,950000,152.87 1939-01-05,154.85,155.47,153.02,153.18,1570000,153.18 1939-01-04,153.64,155.19,153.14,154.85,1500000,154.85 1939-01-03,154.76,154.99,153.16,153.64,1150000,153.64 1938-12-30,153.62,154.94,153.52,154.36,1400000,154.36 1938-12-29,152.06,153.85,152.06,153.62,1880000,153.62 1938-12-28,150.43,151.95,149.56,151.45,2160000,151.45 1938-12-27,151.38,151.74,150.04,150.43,1340000,150.43 1938-12-23,150.53,152.02,150.52,151.39,1220000,151.39 1938-12-22,149.58,150.79,149.28,150.53,1040000,150.53 1938-12-21,150.46,150.72,149.06,149.58,1060000,149.58 1938-12-20,150.38,151.29,149.69,150.46,940000,150.46 1938-12-19,150.36,151.77,149.72,150.38,1100000,150.38 1938-12-16,151.82,152.21,150.52,150.89,1150000,150.89 1938-12-15,151.83,153.16,151.44,151.82,1800000,151.82 1938-12-14,149.59,152.08,149.38,151.83,1970000,151.83 1938-12-13,148.65,150.16,148.60,149.59,1090000,149.59 1938-12-12,148.31,149.71,148.23,148.65,900000,148.65 1938-12-09,147.63,148.31,146.92,147.39,700000,147.39 1938-12-08,148.73,148.79,147.35,147.63,740000,147.63 1938-12-07,148.33,149.98,148.30,148.73,1110000,148.73 1938-12-06,147.47,149.27,147.01,148.33,990000,148.33 1938-12-05,147.50,147.88,146.44,147.47,680000,147.47 1938-12-02,148.50,148.50,146.68,147.57,820000,147.57 1938-12-01,149.82,150.20,148.17,148.63,860000,148.63 1938-11-30,147.68,149.97,147.68,149.82,980000,149.82 1938-11-29,146.38,147.85,146.38,147.07,820000,147.07 1938-11-28,147.93,147.93,145.21,146.14,1240000,146.14 1938-11-25,149.88,151.13,149.79,150.10,810000,150.10 1938-11-23,149.56,151.00,149.27,149.88,1000000,149.88 1938-11-22,150.14,150.14,148.90,149.56,880000,149.56 1938-11-21,150.38,151.03,149.15,150.26,940000,150.26 1938-11-18,152.78,153.19,149.16,149.93,1420000,149.93 1938-11-17,151.54,153.18,151.34,152.78,1000000,152.78 1938-11-16,154.66,155.60,151.41,151.54,1800000,151.54 1938-11-15,155.33,155.33,153.17,154.66,1470000,154.66 1938-11-14,157.57,157.57,155.16,155.61,1650000,155.61 1938-11-10,158.08,158.90,156.79,157.47,2180000,157.47 1938-11-09,155.62,158.39,155.62,158.08,3100000,158.08 1938-11-07,152.12,155.56,152.02,154.91,1760000,154.91 1938-11-04,152.31,153.08,151.44,152.10,1200000,152.10 1938-11-03,152.21,153.13,151.72,152.31,1070000,152.31 1938-11-02,151.39,152.64,150.68,152.21,780000,152.21 1938-11-01,151.73,152.83,150.93,151.39,1280000,151.39 1938-10-31,151.07,152.17,150.28,151.73,1090000,151.73 1938-10-28,152.69,152.82,150.75,151.07,1560000,151.07 1938-10-27,152.40,153.93,151.46,152.69,2000000,152.69 1938-10-26,153.52,153.52,151.28,152.40,1700000,152.40 1938-10-25,154.12,155.22,153.46,154.17,1500000,154.17 1938-10-24,154.11,155.38,153.52,154.12,1680000,154.12 1938-10-21,151.52,153.01,151.36,152.15,1720000,152.15 1938-10-20,150.02,151.90,149.46,151.52,1620000,151.52 1938-10-19,152.10,153.02,149.41,150.02,2430000,150.02 1938-10-18,150.81,152.37,148.68,152.10,2410000,152.10 1938-10-17,151.96,153.15,150.46,150.81,2520000,150.81 1938-10-14,152.46,153.19,150.96,151.45,1950000,151.45 1938-10-13,150.05,152.93,150.05,152.46,2360000,152.46 1938-10-11,149.55,150.40,148.21,149.41,1530000,149.41 1938-10-10,149.75,150.57,148.70,149.55,1660000,149.55 1938-10-07,148.10,149.43,147.29,148.41,1470000,148.41 1938-10-06,148.32,150.48,147.70,148.10,2450000,148.10 1938-10-05,144.59,148.51,144.59,148.32,2240000,148.32 1938-10-04,144.29,144.83,143.26,144.23,950000,144.23 1938-10-03,143.13,145.21,142.64,144.29,1460000,144.29 1938-09-30,139.61,142.05,139.61,141.45,1900000,141.45 1938-09-29,134.58,137.45,134.58,137.16,1230000,137.16 1938-09-28,130.19,134.54,127.85,133.68,1570000,133.68 1938-09-27,129.91,132.49,129.62,130.19,770000,130.19 1938-09-26,131.82,131.82,127.88,129.91,1230000,129.91 1938-09-23,136.07,136.07,133.71,134.08,720000,134.08 1938-09-22,138.17,138.17,136.81,137.35,470000,137.35 1938-09-21,138.41,140.20,137.57,139.29,1030000,139.29 1938-09-20,137.11,139.49,137.11,138.41,1200000,138.41 1938-09-19,133.49,135.24,133.49,134.10,830000,134.10 1938-09-16,135.53,135.53,134.06,134.85,670000,134.85 1938-09-15,134.47,136.97,134.47,136.22,1140000,136.22 1938-09-14,134.19,136.91,130.38,132.93,2820000,132.93 1938-09-13,140.19,141.95,133.90,134.19,1700000,134.19 1938-09-12,138.29,140.67,138.16,140.19,600000,140.19 1938-09-09,141.39,141.39,139.20,139.90,700000,139.90 1938-09-08,142.90,142.90,141.63,142.19,570000,142.19 1938-09-07,141.47,143.42,141.05,143.08,890000,143.08 1938-09-06,142.48,142.80,141.10,141.47,420000,141.47 1938-09-02,138.52,141.48,138.52,141.38,550000,141.38 1938-09-01,139.27,139.45,137.65,138.36,510000,138.36 1938-08-31,138.30,139.80,138.30,139.27,460000,139.27 1938-08-30,137.08,138.89,137.08,138.26,630000,138.26 1938-08-29,139.56,139.56,136.64,137.06,1250000,137.06 1938-08-26,144.07,144.61,142.69,142.94,820000,142.94 1938-08-25,143.53,144.36,142.57,144.07,830000,144.07 1938-08-24,143.70,145.30,143.28,143.53,1240000,143.53 1938-08-23,141.03,144.00,141.03,143.70,1100000,143.70 1938-08-22,141.20,141.61,140.12,140.92,400000,140.92 1938-08-19,139.33,142.05,139.18,141.13,830000,141.13 1938-08-18,139.03,139.76,138.38,139.33,450000,139.33 1938-08-17,138.58,140.89,138.58,139.03,600000,139.03 1938-08-16,137.09,139.38,137.09,138.44,610000,138.44 1938-08-15,136.45,138.20,136.45,136.98,590000,136.98 1938-08-12,138.31,138.31,135.38,136.51,1480000,136.51 1938-08-11,142.40,142.75,139.13,139.32,1100000,139.32 1938-08-10,143.21,143.67,141.80,142.40,810000,142.40 1938-08-09,143.87,143.87,141.59,143.21,830000,143.21 1938-08-08,145.67,145.89,143.75,144.33,910000,144.33 1938-08-05,142.34,144.76,142.34,144.47,1170000,144.47 1938-08-04,141.73,142.76,141.04,142.13,610000,142.13 1938-08-03,141.97,143.40,141.10,141.73,820000,141.73 1938-08-02,140.37,142.50,139.90,141.97,820000,141.97 1938-08-01,140.96,140.96,139.83,140.37,590000,140.37 1938-07-29,142.20,143.57,140.93,141.20,1200000,141.20 1938-07-28,140.24,142.50,139.51,142.20,1070000,142.20 1938-07-27,143.33,144.03,139.39,140.24,1970000,140.24 1938-07-26,144.18,144.18,142.48,143.33,1250000,143.33 1938-07-25,144.24,146.31,144.23,144.91,2110000,144.91 1938-07-22,141.92,143.13,141.20,142.25,1220000,142.25 1938-07-21,141.84,143.51,140.52,141.92,1810000,141.92 1938-07-20,143.67,143.97,141.09,141.84,2510000,141.84 1938-07-19,141.27,144.12,141.27,143.67,2940000,143.67 1938-07-18,138.53,140.78,137.70,140.39,1560000,140.39 1938-07-15,135.81,138.17,135.52,137.30,930000,137.30 1938-07-14,136.90,137.85,135.22,135.81,1160000,135.81 1938-07-13,137.49,140.52,136.46,136.90,2620000,136.90 1938-07-12,134.56,138.22,133.84,137.49,1620000,137.49 1938-07-11,136.20,136.72,133.97,134.56,1090000,134.56 1938-07-08,136.76,136.76,134.51,135.66,1570000,135.66 1938-07-07,137.78,140.05,136.44,137.45,2770000,137.45 1938-07-06,136.52,138.20,134.57,137.78,1820000,137.78 1938-07-05,138.50,138.50,135.19,136.52,1700000,136.52 1938-07-01,133.88,137.13,133.53,136.53,2030000,136.53 1938-06-30,135.87,138.19,133.24,133.88,2580000,133.88 1938-06-29,130.38,136.13,130.36,135.87,2660000,135.87 1938-06-28,130.48,132.28,129.44,130.38,1290000,130.38 1938-06-27,131.94,132.98,129.79,130.48,2110000,130.48 1938-06-24,127.54,130.71,127.54,129.06,2290000,129.06 1938-06-23,123.99,128.49,123.71,127.40,2400000,127.40 1938-06-22,121.34,124.74,120.65,123.99,1710000,123.99 1938-06-21,119.01,122.36,119.01,121.34,1460000,121.34 1938-06-20,115.31,118.92,115.31,118.61,1090000,118.61 1938-06-17,113.97,114.51,112.82,113.06,330000,113.06 1938-06-16,113.24,114.30,112.93,113.97,340000,113.97 1938-06-15,112.88,114.18,112.88,113.24,340000,113.24 1938-06-14,111.87,113.06,111.54,112.78,350000,112.78 1938-06-13,113.37,113.37,111.75,111.87,330000,111.87 1938-06-10,115.74,116.08,114.29,114.47,410000,114.47 1938-06-09,113.79,116.03,113.79,115.74,590000,115.74 1938-06-08,113.12,114.04,112.78,113.75,280000,113.75 1938-06-07,113.19,114.51,112.84,113.12,370000,113.12 1938-06-06,112.01,114.27,112.01,113.19,470000,113.19 1938-06-03,110.52,110.52,109.35,109.71,290000,109.71 1938-06-02,110.61,111.94,110.35,110.68,480000,110.68 1938-06-01,107.74,110.87,107.58,110.61,540000,110.61 1938-05-31,108.50,108.50,106.94,107.74,400000,107.74 1938-05-27,108.28,108.55,106.44,107.98,760000,107.98 1938-05-26,110.60,111.30,108.14,108.28,780000,108.28 1938-05-25,112.24,112.24,110.43,110.60,560000,110.60 1938-05-24,113.97,114.66,112.26,112.35,420000,112.35 1938-05-23,113.25,114.27,112.88,113.97,330000,113.97 1938-05-20,115.28,115.48,114.08,114.99,440000,114.99 1938-05-19,117.02,117.08,114.92,115.28,490000,115.28 1938-05-18,116.36,117.49,116.31,117.02,400000,117.02 1938-05-17,115.38,116.65,114.75,116.36,410000,116.36 1938-05-16,117.11,117.11,115.19,115.38,400000,115.38 1938-05-13,118.41,118.41,116.30,116.87,610000,116.87 1938-05-12,118.52,119.67,117.88,118.55,600000,118.55 1938-05-11,117.93,119.70,117.78,118.52,980000,118.52 1938-05-10,119.43,120.28,117.75,117.93,1040000,117.93 1938-05-09,117.21,119.81,116.36,119.43,1020000,119.43 1938-05-06,113.46,117.44,113.27,117.16,1020000,117.16 1938-05-05,113.88,115.42,112.86,113.46,690000,113.46 1938-05-04,112.71,114.32,111.69,113.88,550000,113.88 1938-05-03,110.75,113.12,110.75,112.71,470000,112.71 1938-05-02,110.55,110.55,109.40,110.09,350000,110.09 1938-04-29,111.88,111.88,109.83,111.66,540000,111.66 1938-04-28,114.83,114.83,111.73,111.98,540000,111.98 1938-04-27,114.75,116.22,114.75,115.25,430000,115.25 1938-04-26,115.70,115.70,113.51,113.94,450000,113.94 1938-04-25,116.86,116.86,115.40,116.23,400000,116.23 1938-04-22,115.74,119.67,115.74,118.52,1120000,118.52 1938-04-21,114.90,115.98,114.05,115.40,600000,115.40 1938-04-20,115.50,115.50,112.47,114.90,780000,114.90 1938-04-19,118.46,118.46,116.00,116.34,570000,116.34 1938-04-18,121.00,121.54,118.45,118.99,860000,118.99 1938-04-14,114.85,117.57,113.56,116.82,1010000,116.82 1938-04-13,113.88,116.29,113.79,114.85,640000,114.85 1938-04-12,112.93,114.15,111.60,113.88,600000,113.88 1938-04-11,115.32,115.71,112.43,112.93,1100000,112.93 1938-04-08,106.89,110.23,106.89,109.57,830000,109.57 1938-04-07,106.29,106.93,104.78,105.43,330000,105.43 1938-04-06,107.90,107.90,105.72,106.29,480000,106.29 1938-04-05,105.58,108.67,104.85,108.36,690000,108.36 1938-04-04,106.11,106.79,104.47,105.58,690000,105.58 1938-04-01,100.95,103.37,100.95,103.02,860000,103.02 1938-03-31,100.97,102.86,97.46,98.95,1270000,98.95 1938-03-30,101.92,103.89,100.17,100.97,1670000,100.97 1938-03-29,105.87,105.87,101.56,101.92,1720000,101.92 1938-03-28,106.63,108.55,105.68,107.25,1250000,107.25 1938-03-25,114.37,114.37,108.12,108.57,1680000,108.57 1938-03-24,114.38,115.97,112.73,114.64,890000,114.64 1938-03-23,115.95,115.95,112.78,114.38,1470000,114.38 1938-03-22,120.29,120.35,116.47,117.11,690000,117.11 1938-03-21,120.43,122.48,120.09,120.29,540000,120.29 1938-03-18,121.92,121.92,117.20,118.41,1580000,118.41 1938-03-17,122.87,124.60,121.90,122.03,640000,122.03 1938-03-16,126.10,126.10,121.84,122.87,1020000,122.87 1938-03-15,124.52,127.44,124.52,127.24,760000,127.24 1938-03-14,122.85,124.53,122.85,123.68,430000,123.68 1938-03-11,123.89,123.89,121.93,122.44,770000,122.44 1938-03-10,125.67,126.35,124.52,124.71,460000,124.71 1938-03-09,125.33,126.83,124.57,125.67,560000,125.67 1938-03-08,125.38,125.85,122.81,125.33,740000,125.33 1938-03-07,127.63,127.63,125.19,125.38,620000,125.38 1938-03-04,128.22,129.57,127.37,127.78,490000,127.78 1938-03-03,128.75,128.75,127.39,128.22,470000,128.22 1938-03-02,130.47,130.68,129.19,129.38,410000,129.38 1938-03-01,129.64,131.03,128.84,130.47,530000,130.47 1938-02-28,130.89,130.89,128.63,129.64,560000,129.64 1938-02-25,130.85,132.66,129.85,131.58,900000,131.58 1938-02-24,132.05,132.05,130.47,130.85,720000,130.85 1938-02-23,130.69,132.86,130.69,132.41,1300000,132.41 1938-02-21,127.60,130.19,127.60,129.49,760000,129.49 1938-02-18,127.59,128.74,125.61,126.29,770000,126.29 1938-02-17,125.03,128.35,125.03,127.59,860000,127.59 1938-02-16,124.93,125.35,123.39,124.90,470000,124.90 1938-02-15,125.97,127.00,124.60,124.93,520000,124.93 1938-02-14,125.04,126.44,125.04,125.97,400000,125.97 1938-02-11,125.54,126.53,124.45,124.94,390000,124.94 1938-02-10,125.00,127.23,124.56,125.54,630000,125.54 1938-02-09,125.52,126.98,124.65,125.00,750000,125.00 1938-02-08,122.39,125.76,122.39,125.52,770000,125.52 1938-02-07,122.88,123.15,120.88,121.39,510000,121.39 1938-02-04,118.49,120.91,117.13,120.52,810000,120.52 1938-02-03,121.49,121.49,117.78,118.49,1090000,118.49 1938-02-02,123.97,125.00,122.74,123.06,580000,123.06 1938-02-01,122.69,124.71,122.69,123.97,690000,123.97 1938-01-31,120.14,122.28,120.09,121.87,760000,121.87 1938-01-28,121.57,122.32,118.94,120.66,1190000,120.66 1938-01-27,123.23,124.54,120.44,121.57,1210000,121.57 1938-01-26,126.10,126.10,121.86,123.23,1620000,123.23 1938-01-25,129.47,129.47,127.97,128.33,540000,128.33 1938-01-24,130.00,130.52,129.13,129.89,540000,129.89 1938-01-21,132.33,133.23,130.56,130.69,790000,130.69 1938-01-20,130.39,132.54,130.39,132.33,820000,132.33 1938-01-19,131.53,131.68,128.68,130.09,1000000,130.09 1938-01-18,132.49,132.98,130.88,131.53,780000,131.53 1938-01-17,134.31,134.70,132.19,132.49,930000,132.49 1938-01-14,131.60,132.37,130.29,131.84,850000,131.84 1938-01-13,133.22,133.40,131.27,131.60,970000,131.60 1938-01-12,134.35,134.95,132.94,133.22,1210000,133.22 1938-01-11,133.55,134.63,132.36,134.35,1510000,134.35 1938-01-10,130.84,134.27,130.81,133.55,1830000,133.55 1938-01-07,128.97,129.51,127.30,128.21,1050000,128.21 1938-01-06,125.38,129.23,125.38,128.97,1210000,128.97 1938-01-05,124.61,127.27,124.17,124.66,1150000,124.66 1938-01-04,121.69,124.96,121.69,124.61,940000,124.61 1938-01-03,120.85,123.07,119.60,120.57,920000,120.57 1937-12-31,121.49,121.49,119.65,120.85,780000,120.85 1937-12-30,120.71,122.63,120.71,121.56,910000,121.56 1937-12-29,118.93,121.00,117.71,120.15,2460000,120.15 1937-12-28,122.51,122.51,118.31,118.93,2380000,118.93 1937-12-27,126.59,126.59,122.96,123.45,1360000,123.45 1937-12-24,127.63,128.60,126.85,127.36,840000,127.36 1937-12-23,128.53,128.53,126.50,127.63,1060000,127.63 1937-12-22,129.98,130.52,127.99,128.55,1160000,128.55 1937-12-21,129.08,130.76,128.60,129.98,1280000,129.98 1937-12-20,127.29,130.38,127.29,129.08,1400000,129.08 1937-12-17,125.75,126.29,124.44,124.98,790000,124.98 1937-12-16,124.52,126.92,124.52,125.75,1030000,125.75 1937-12-15,123.50,125.63,123.33,124.19,930000,124.19 1937-12-14,122.83,124.25,121.85,123.50,900000,123.50 1937-12-13,125.86,125.86,122.18,122.83,1020000,122.83 1937-12-10,128.15,128.27,125.49,126.72,1080000,126.72 1937-12-09,129.80,130.37,127.62,128.15,1080000,128.15 1937-12-08,128.31,131.15,128.22,129.80,1520000,129.80 1937-12-07,126.21,128.56,124.85,128.31,970000,128.31 1937-12-06,127.79,128.36,125.76,126.21,840000,126.21 1937-12-03,125.52,129.40,125.52,127.55,1560000,127.55 1937-12-02,122.11,125.38,120.21,125.14,940000,125.14 1937-12-01,123.48,124.09,121.41,122.11,700000,122.11 1937-11-30,121.58,125.43,121.49,123.48,1150000,123.48 1937-11-29,123.39,123.39,120.37,121.58,1150000,121.58 1937-11-26,114.37,118.78,114.37,118.26,1180000,118.26 1937-11-24,115.78,116.17,112.72,113.64,990000,113.64 1937-11-23,114.19,117.08,112.54,115.78,1640000,115.78 1937-11-22,119.28,119.28,113.77,114.19,1520000,114.19 1937-11-19,124.32,124.32,117.98,118.13,1890000,118.13 1937-11-18,127.54,127.73,124.35,125.48,900000,125.48 1937-11-17,127.98,129.94,127.02,127.54,760000,127.54 1937-11-16,129.22,129.63,125.34,127.98,1270000,127.98 1937-11-15,133.05,134.36,129.08,129.22,1450000,129.22 1937-11-12,132.16,135.70,131.64,133.09,1880000,133.09 1937-11-10,128.63,132.59,128.63,132.16,1920000,132.16 1937-11-09,124.07,127.11,124.07,126.16,1050000,126.16 1937-11-08,124.93,124.93,121.61,123.98,1380000,123.98 1937-11-05,128.84,132.31,128.35,128.92,1250000,128.92 1937-11-04,130.14,130.17,126.67,128.84,1470000,128.84 1937-11-03,135.49,135.49,129.56,130.14,1740000,130.14 1937-11-01,137.01,137.01,135.00,135.94,1030000,135.94 1937-10-29,136.46,141.22,136.46,138.48,2800000,138.48 1937-10-28,132.58,138.31,132.58,135.22,2460000,135.22 1937-10-27,132.78,134.01,130.48,132.26,1060000,132.26 1937-10-26,134.43,136.79,131.77,132.78,1820000,132.78 1937-10-25,127.15,135.12,124.56,134.43,2340000,134.43 1937-10-22,135.48,135.66,131.74,132.26,2110000,132.26 1937-10-21,134.56,137.82,132.09,135.48,3640000,135.48 1937-10-20,126.87,135.48,126.87,134.56,4340000,134.56 1937-10-19,125.73,127.61,115.84,126.85,7290000,126.85 1937-10-18,136.30,137.00,125.14,125.73,3230000,125.73 1937-10-15,136.54,138.14,133.95,135.48,2540000,135.48 1937-10-14,138.20,140.88,136.09,136.54,1680000,136.54 1937-10-13,138.79,140.94,134.79,138.20,2570000,138.20 1937-10-11,143.66,143.66,137.71,138.79,1750000,138.79 1937-10-08,146.59,148.26,143.00,144.03,1150000,144.03 1937-10-07,147.18,150.47,145.76,146.59,1190000,146.59 1937-10-06,144.08,147.62,141.63,147.18,1790000,147.18 1937-10-05,149.97,149.97,143.01,144.08,1680000,144.08 1937-10-04,154.08,154.63,151.84,152.19,630000,152.19 1937-10-01,154.57,155.11,152.50,153.89,680000,153.89 1937-09-30,154.70,157.12,153.97,154.57,1050000,154.57 1937-09-29,153.16,155.24,150.09,154.70,1350000,154.70 1937-09-28,152.03,155.22,151.41,153.16,1310000,153.16 1937-09-27,147.47,152.49,146.25,152.03,2210000,152.03 1937-09-24,151.58,151.58,146.22,147.38,2480000,147.38 1937-09-23,157.45,157.51,153.79,153.98,890000,153.98 1937-09-22,156.56,158.89,156.55,157.45,740000,157.45 1937-09-21,155.96,159.26,155.96,156.56,980000,156.56 1937-09-20,156.92,156.92,152.36,155.56,1550000,155.56 1937-09-17,164.19,164.19,161.59,162.15,810000,162.15 1937-09-16,162.85,165.37,162.29,164.75,890000,164.75 1937-09-15,162.90,165.16,161.26,162.85,1140000,162.85 1937-09-14,160.00,164.37,160.00,162.90,1510000,162.90 1937-09-13,159.96,163.12,154.94,158.00,2560000,158.00 1937-09-10,166.36,166.87,157.35,157.98,2320000,157.98 1937-09-09,164.88,168.06,164.88,166.36,1410000,166.36 1937-09-08,164.39,166.06,162.17,163.37,2260000,163.37 1937-09-07,170.29,170.29,163.18,164.39,1870000,164.39 1937-09-03,171.82,174.03,171.82,172.17,690000,172.17 1937-09-02,172.71,172.71,169.75,170.84,1200000,170.84 1937-09-01,176.11,176.11,172.89,173.08,820000,173.08 1937-08-31,177.88,179.10,177.29,177.41,500000,177.41 1937-08-30,176.10,178.26,176.10,177.88,460000,177.88 1937-08-27,178.52,179.23,175.09,175.91,890000,175.91 1937-08-26,180.71,180.71,177.57,178.52,970000,178.52 1937-08-25,182.39,183.00,181.39,181.70,500000,181.70 1937-08-24,181.88,182.87,180.80,182.39,560000,182.39 1937-08-23,183.74,184.20,181.31,181.88,580000,181.88 1937-08-20,185.28,185.28,182.30,182.95,800000,182.95 1937-08-19,186.97,186.97,184.75,185.28,760000,185.28 1937-08-18,188.68,189.10,187.30,187.39,700000,187.39 1937-08-17,189.18,189.18,188.12,188.68,660000,188.68 1937-08-16,189.94,189.94,188.60,189.34,620000,189.34 1937-08-13,187.62,189.76,187.35,189.29,1040000,189.29 1937-08-12,186.72,188.30,186.39,187.62,790000,187.62 1937-08-11,186.98,187.31,185.93,186.72,570000,186.72 1937-08-10,186.75,187.67,186.23,186.98,690000,186.98 1937-08-09,186.41,187.33,186.06,186.75,750000,186.75 1937-08-06,186.09,186.56,185.16,185.43,680000,185.43 1937-08-05,186.80,187.22,185.76,186.09,800000,186.09 1937-08-04,185.91,187.31,185.38,186.80,900000,186.80 1937-08-03,186.91,187.14,185.43,185.91,900000,185.91 1937-08-02,185.61,187.28,185.35,186.91,790000,186.91 1937-07-30,183.01,184.66,182.92,184.01,620000,184.01 1937-07-29,182.57,183.61,182.07,183.01,610000,183.01 1937-07-28,184.24,184.54,182.17,182.57,870000,182.57 1937-07-27,184.42,184.73,183.43,184.24,740000,184.24 1937-07-26,184.85,185.15,183.72,184.42,900000,184.42 1937-07-23,182.96,184.75,182.70,183.78,910000,183.78 1937-07-22,182.35,184.13,182.14,182.96,960000,182.96 1937-07-21,183.32,183.94,181.87,182.35,980000,182.35 1937-07-20,182.06,183.90,182.01,183.32,1200000,183.32 1937-07-19,180.11,182.39,180.11,182.06,950000,182.06 1937-07-16,179.71,180.45,178.65,179.53,700000,179.53 1937-07-15,178.57,180.09,177.78,179.71,740000,179.71 1937-07-14,178.24,180.17,177.83,178.57,1040000,178.57 1937-07-13,178.70,179.53,177.50,178.24,850000,178.24 1937-07-12,176.72,179.16,176.69,178.70,1020000,178.70 1937-07-09,177.70,178.36,176.65,177.40,850000,177.40 1937-07-08,177.74,178.38,176.49,177.70,1030000,177.70 1937-07-07,176.80,178.88,176.25,177.74,1410000,177.74 1937-07-06,173.18,177.08,173.18,176.80,1410000,176.80 1937-07-02,170.13,172.49,169.58,172.22,840000,172.22 1937-07-01,169.32,171.28,169.13,170.13,670000,170.13 1937-06-30,167.11,170.02,167.00,169.32,690000,169.32 1937-06-29,166.71,168.10,166.11,167.11,550000,167.11 1937-06-28,168.45,168.99,166.26,166.71,730000,166.71 1937-06-25,170.08,170.98,169.10,169.59,580000,169.59 1937-06-24,169.01,170.46,168.79,170.08,550000,170.08 1937-06-23,168.22,169.72,168.22,169.01,550000,169.01 1937-06-22,167.98,169.42,167.59,168.20,530000,168.20 1937-06-21,168.60,168.79,167.28,167.98,420000,167.98 1937-06-18,167.74,169.37,167.05,168.79,690000,168.79 1937-06-17,165.86,167.95,163.31,167.74,1260000,167.74 1937-06-16,167.40,167.59,165.49,165.86,700000,165.86 1937-06-15,165.51,168.10,164.69,167.40,930000,167.40 1937-06-14,168.45,168.45,163.73,165.51,1310000,165.51 1937-06-11,172.59,172.59,170.33,170.77,720000,170.77 1937-06-10,173.47,174.06,172.53,172.82,570000,172.82 1937-06-09,174.33,175.00,173.12,173.47,620000,173.47 1937-06-08,173.88,174.91,173.25,174.33,600000,174.33 1937-06-07,175.00,175.40,173.56,173.88,590000,173.88 1937-06-04,172.82,175.39,172.19,175.14,780000,175.14 1937-06-03,172.63,173.09,171.56,172.82,550000,172.82 1937-06-02,172.25,173.73,172.25,172.63,540000,172.63 1937-06-01,172.69,172.69,170.72,171.59,750000,171.59 1937-05-28,174.19,175.22,174.04,174.71,560000,174.71 1937-05-27,173.70,175.03,173.22,174.19,600000,174.19 1937-05-26,173.79,174.47,172.62,173.70,580000,173.70 1937-05-25,175.59,176.11,173.30,173.79,840000,173.79 1937-05-24,175.00,176.25,174.51,175.59,680000,175.59 1937-05-21,173.59,174.59,173.12,173.83,770000,173.83 1937-05-20,170.00,173.99,170.00,173.59,1230000,173.59 1937-05-19,169.97,170.85,169.11,169.75,790000,169.75 1937-05-18,167.84,170.55,166.20,169.97,1200000,169.97 1937-05-17,169.60,169.98,167.64,167.84,600000,167.84 1937-05-14,167.46,169.89,166.58,169.15,1230000,169.15 1937-05-13,171.43,171.43,166.88,167.46,1770000,167.46 1937-05-12,172.55,173.72,171.81,172.24,670000,172.24 1937-05-11,173.04,173.28,171.59,172.55,750000,172.55 1937-05-10,175.19,175.19,172.78,173.04,780000,173.04 1937-05-07,175.81,176.91,175.50,175.89,820000,175.89 1937-05-06,174.67,176.05,174.06,175.81,760000,175.81 1937-05-05,176.30,176.81,174.41,174.67,770000,174.67 1937-05-04,175.20,176.69,175.20,176.30,870000,176.30 1937-05-03,174.42,175.58,174.16,174.59,640000,174.59 1937-04-30,171.51,174.66,171.51,174.27,1450000,174.27 1937-04-29,170.13,172.88,169.37,170.52,2030000,170.52 1937-04-28,173.78,173.78,168.77,170.13,2530000,170.13 1937-04-27,172.36,175.18,172.36,174.52,1410000,174.52 1937-04-26,175.33,175.33,171.20,171.97,2020000,171.97 1937-04-23,181.70,182.60,178.00,178.54,1200000,178.54 1937-04-22,183.60,184.33,181.28,181.70,1180000,181.70 1937-04-21,181.44,184.05,181.39,183.60,1250000,183.60 1937-04-20,180.82,182.63,180.28,181.44,1130000,181.44 1937-04-19,180.51,181.38,179.76,180.82,820000,180.82 1937-04-16,181.19,182.27,179.70,180.75,1070000,180.75 1937-04-15,181.93,182.25,180.69,181.19,940000,181.19 1937-04-14,182.10,183.34,181.27,181.93,1480000,181.93 1937-04-13,180.59,183.43,180.59,182.10,1590000,182.10 1937-04-12,178.26,180.12,176.39,179.74,1130000,179.74 1937-04-09,178.18,180.38,175.86,178.94,1730000,178.94 1937-04-08,178.07,179.94,176.72,178.18,1920000,178.18 1937-04-07,182.13,182.13,177.68,178.07,2290000,178.07 1937-04-06,184.19,184.66,182.06,182.98,1250000,182.98 1937-04-05,183.54,185.09,183.39,184.19,980000,184.19 1937-04-02,184.43,184.43,180.89,182.75,1640000,182.75 1937-04-01,186.41,186.63,184.37,185.19,1210000,185.19 1937-03-31,186.77,187.99,185.77,186.41,1660000,186.41 1937-03-30,184.09,186.93,183.64,186.77,1230000,186.77 1937-03-29,184.95,185.75,183.79,184.09,870000,184.09 1937-03-25,184.32,186.11,183.73,184.08,1250000,184.08 1937-03-24,181.87,184.97,181.63,184.32,1430000,184.32 1937-03-23,179.93,182.96,179.93,181.87,1600000,181.87 1937-03-22,182.83,182.83,179.28,179.82,2030000,179.82 1937-03-19,184.73,185.94,183.72,184.56,1740000,184.56 1937-03-18,187.52,187.52,183.72,184.73,2280000,184.73 1937-03-17,189.95,190.52,188.15,188.50,2120000,188.50 1937-03-16,189.41,191.29,188.88,189.95,1750000,189.95 1937-03-15,190.58,190.81,188.59,189.41,1770000,189.41 1937-03-12,192.22,192.27,189.39,191.24,2290000,191.24 1937-03-11,194.40,195.33,191.77,192.22,2740000,192.22 1937-03-10,193.29,195.59,192.77,194.40,2820000,194.40 1937-03-09,192.69,194.89,191.65,193.29,2390000,193.29 1937-03-08,194.15,195.20,191.53,192.69,3180000,192.69 1937-03-05,192.17,195.17,192.17,194.14,2830000,194.14 1937-03-04,192.91,193.95,190.98,191.63,2730000,191.63 1937-03-03,190.29,193.86,190.29,192.91,3570000,192.91 1937-03-02,187.68,190.41,187.64,189.91,2300000,189.91 1937-03-01,187.30,188.48,186.00,187.68,1660000,187.68 1937-02-26,186.68,187.93,185.82,187.17,1780000,187.17 1937-02-25,187.35,188.31,186.19,186.68,2230000,186.68 1937-02-24,186.50,187.88,185.15,187.35,2080000,187.35 1937-02-23,189.36,189.36,185.96,186.50,2870000,186.50 1937-02-19,188.07,190.42,187.71,189.37,2730000,189.37 1937-02-18,187.98,188.90,186.82,188.07,2130000,188.07 1937-02-17,188.18,189.39,187.30,187.98,2580000,187.98 1937-02-16,188.39,189.20,187.05,188.18,2220000,188.18 1937-02-15,189.58,189.58,187.45,188.39,1960000,188.39 1937-02-11,189.35,191.39,188.69,190.29,2920000,190.29 1937-02-10,187.68,189.83,187.58,189.35,2920000,189.35 1937-02-09,187.82,188.79,186.74,187.68,2590000,187.68 1937-02-08,187.11,188.66,186.68,187.82,2990000,187.82 1937-02-05,188.39,189.07,184.85,186.01,3320000,186.01 1937-02-04,188.69,189.64,187.65,188.39,2390000,188.39 1937-02-03,188.20,189.94,187.48,188.69,2450000,188.69 1937-02-02,186.61,189.13,186.13,188.20,2430000,188.20 1937-02-01,185.74,187.77,185.10,186.61,2360000,186.61 1937-01-29,183.41,185.41,182.34,184.74,1970000,184.74 1937-01-28,183.97,185.59,182.77,183.41,2340000,183.41 1937-01-27,183.19,184.32,182.15,183.97,1940000,183.97 1937-01-26,185.62,185.68,182.64,183.19,2180000,183.19 1937-01-25,186.69,186.97,185.02,185.62,2220000,185.62 1937-01-22,186.90,187.80,185.01,186.53,2680000,186.53 1937-01-21,185.96,187.49,184.98,186.90,2990000,186.90 1937-01-20,184.10,186.88,184.10,185.96,3270000,185.96 1937-01-19,184.95,185.16,183.22,184.02,2620000,184.02 1937-01-18,185.73,185.93,183.74,184.95,2860000,184.95 1937-01-15,183.71,185.40,183.55,184.53,2900000,184.53 1937-01-14,183.01,184.66,182.53,183.71,3260000,183.71 1937-01-13,183.30,184.01,182.25,183.01,3680000,183.01 1937-01-12,183.26,184.49,182.08,183.30,3570000,183.30 1937-01-11,182.75,183.82,181.77,183.26,3080000,183.26 1937-01-08,181.77,183.58,181.36,182.95,3220000,182.95 1937-01-07,179.32,182.11,179.32,181.77,3060000,181.77 1937-01-06,179.07,179.90,178.17,178.92,1920000,178.92 1937-01-05,177.72,179.66,177.64,179.07,1870000,179.07 1937-01-04,178.39,178.39,176.96,177.72,1510000,177.72 1936-12-31,180.57,181.77,179.34,179.90,1760000,179.90 1936-12-30,178.02,181.13,178.02,180.57,2310000,180.57 1936-12-29,177.12,178.48,176.26,177.60,2280000,177.60 1936-12-28,178.60,179.52,176.71,177.12,1790000,177.12 1936-12-24,178.36,179.54,177.75,178.60,1610000,178.60 1936-12-23,177.30,179.00,176.70,178.36,1870000,178.36 1936-12-22,176.14,178.20,176.14,177.30,1670000,177.30 1936-12-21,177.61,178.28,175.31,175.85,1760000,175.85 1936-12-18,180.78,181.10,179.03,179.42,1910000,179.42 1936-12-17,181.58,182.18,180.35,180.78,1950000,180.78 1936-12-16,181.97,182.57,180.87,181.58,1950000,181.58 1936-12-15,181.87,183.30,181.30,181.97,2480000,181.97 1936-12-14,180.92,182.67,180.74,181.87,2880000,181.87 1936-12-11,182.18,182.33,180.76,181.10,2610000,181.10 1936-12-10,181.16,182.77,180.67,182.18,2440000,182.18 1936-12-09,180.57,181.77,179.93,181.16,1860000,181.16 1936-12-08,180.13,181.29,179.95,180.57,1620000,180.57 1936-12-07,181.05,181.49,179.74,180.13,1680000,180.13 1936-12-04,181.29,182.34,180.36,180.97,2160000,180.97 1936-12-03,180.25,181.92,179.90,181.29,2040000,181.29 1936-12-02,181.89,181.89,179.66,180.25,2320000,180.25 1936-12-01,183.22,183.59,181.56,182.05,2230000,182.05 1936-11-30,183.32,184.03,181.87,183.22,2140000,183.22 1936-11-27,180.91,183.27,180.91,182.81,2280000,182.81 1936-11-25,181.11,181.49,179.68,180.78,1860000,180.78 1936-11-24,178.84,181.51,178.84,181.11,1920000,181.11 1936-11-23,181.78,181.78,177.91,178.62,2160000,178.62 1936-11-20,182.21,182.35,180.24,180.74,1820000,180.74 1936-11-19,184.26,184.26,181.63,182.21,2440000,182.21 1936-11-18,184.90,186.39,183.73,184.44,2920000,184.44 1936-11-17,182.94,185.55,182.94,184.90,3270000,184.90 1936-11-16,181.45,183.39,181.00,182.65,2380000,182.65 1936-11-13,183.15,184.28,181.39,182.24,2480000,182.24 1936-11-12,184.01,185.52,182.26,183.15,2580000,183.15 1936-11-10,183.65,185.24,182.82,184.01,2700000,184.01 1936-11-09,183.38,184.77,182.39,183.65,3140000,183.65 1936-11-06,182.25,183.53,180.68,181.60,2720000,181.60 1936-11-05,180.66,183.31,180.57,182.25,3620000,182.25 1936-11-04,177.00,181.15,177.00,180.66,3290000,180.66 1936-11-02,177.19,177.74,175.35,176.67,1600000,176.67 1936-10-30,176.31,178.09,176.20,177.15,1680000,177.15 1936-10-29,174.84,176.60,174.61,176.31,1710000,176.31 1936-10-28,174.47,176.61,174.47,174.84,1630000,174.84 1936-10-27,172.89,174.90,172.89,174.36,1310000,174.36 1936-10-26,174.74,174.74,172.16,172.30,1480000,172.30 1936-10-23,174.90,176.23,174.64,175.60,1510000,175.60 1936-10-22,176.70,177.01,174.50,174.90,1980000,174.90 1936-10-21,176.78,177.63,175.81,176.70,1630000,176.70 1936-10-20,177.42,177.82,175.98,176.78,1670000,176.78 1936-10-19,177.63,178.44,176.66,177.42,1890000,177.42 1936-10-16,175.33,177.31,175.33,176.66,2050000,176.66 1936-10-15,175.57,176.32,174.13,175.22,1790000,175.22 1936-10-14,176.29,176.79,175.03,175.57,1640000,175.57 1936-10-13,176.05,177.68,175.87,176.29,2070000,176.29 1936-10-09,174.93,176.45,174.23,175.19,2240000,175.19 1936-10-08,174.59,175.49,173.41,174.93,2230000,174.93 1936-10-07,174.42,175.92,173.94,174.59,3030000,174.59 1936-10-06,172.93,174.82,172.93,174.42,2260000,174.42 1936-10-05,172.44,174.04,172.04,172.81,2080000,172.81 1936-10-02,168.63,170.94,168.63,170.76,1930000,170.76 1936-10-01,167.82,168.83,167.54,168.26,1100000,168.26 1936-09-30,168.48,169.55,167.47,167.82,1350000,167.82 1936-09-29,168.79,169.85,168.01,168.48,1380000,168.48 1936-09-28,168.07,169.62,167.72,168.79,1450000,168.79 1936-09-25,169.03,169.03,165.91,166.36,1160000,166.36 1936-09-24,169.01,169.79,168.10,169.14,1190000,169.14 1936-09-23,169.47,170.72,168.68,169.01,1480000,169.01 1936-09-22,168.90,170.47,168.37,169.47,1550000,169.47 1936-09-21,168.93,170.25,168.34,168.90,1770000,168.90 1936-09-18,166.25,168.36,166.10,167.76,1270000,167.76 1936-09-17,165.16,166.51,164.82,166.25,770000,166.25 1936-09-16,166.44,166.75,164.97,165.16,1040000,165.16 1936-09-15,166.86,167.14,165.41,166.44,1130000,166.44 1936-09-14,167.98,167.98,166.11,166.86,1010000,166.86 1936-09-11,169.00,169.38,167.59,168.59,1400000,168.59 1936-09-10,168.50,169.59,168.05,169.00,1550000,169.00 1936-09-09,169.55,169.73,168.07,168.50,1570000,168.50 1936-09-08,168.32,170.02,168.32,169.55,1720000,169.55 1936-09-04,166.24,167.62,166.01,167.04,1180000,167.04 1936-09-03,166.65,167.25,165.64,166.24,1050000,166.24 1936-09-02,166.35,167.89,166.15,166.65,1350000,166.65 1936-09-01,166.29,167.21,165.24,166.35,1140000,166.35 1936-08-31,166.91,167.25,165.84,166.29,1150000,166.29 1936-08-28,166.77,168.02,166.31,166.78,1380000,166.78 1936-08-27,163.32,166.94,163.21,166.77,1340000,166.77 1936-08-26,164.34,165.00,162.98,163.32,910000,163.32 1936-08-25,163.78,165.23,163.60,164.34,800000,164.34 1936-08-24,162.90,164.64,162.90,163.78,800000,163.78 1936-08-21,164.69,164.69,160.52,160.80,1480000,160.80 1936-08-20,166.04,166.70,165.23,165.59,960000,165.59 1936-08-19,165.42,166.87,165.26,166.04,1010000,166.04 1936-08-18,165.38,166.37,164.89,165.42,790000,165.42 1936-08-17,165.86,167.01,164.66,165.38,830000,165.38 1936-08-14,167.64,167.80,165.40,165.75,1070000,165.75 1936-08-13,169.05,169.59,167.30,167.64,1400000,167.64 1936-08-12,167.86,169.63,167.50,169.05,1260000,169.05 1936-08-11,168.80,169.08,167.20,167.86,1100000,167.86 1936-08-10,169.10,170.15,168.15,168.80,1340000,168.80 1936-08-07,165.71,168.63,165.34,168.01,1670000,168.01 1936-08-06,165.07,166.24,164.17,165.71,1170000,165.71 1936-08-05,165.41,166.57,163.91,165.07,1280000,165.07 1936-08-04,165.32,165.91,164.41,165.41,1050000,165.41 1936-08-03,165.42,166.53,164.63,165.32,1010000,165.32 1936-07-31,165.98,167.27,164.32,164.86,1160000,164.86 1936-07-30,165.67,167.05,165.13,165.98,1510000,165.98 1936-07-29,167.01,167.83,165.13,165.67,1950000,165.67 1936-07-28,166.92,168.23,165.98,167.01,1900000,167.01 1936-07-27,165.56,167.63,165.51,166.92,1830000,166.92 1936-07-24,164.61,165.31,164.00,164.37,1320000,164.37 1936-07-23,164.49,165.06,163.46,164.61,1340000,164.61 1936-07-22,165.23,166.06,163.99,164.49,1450000,164.49 1936-07-21,164.43,165.81,163.75,165.23,1590000,165.23 1936-07-20,164.42,165.48,163.84,164.43,1420000,164.43 1936-07-17,163.64,165.07,163.02,163.55,1560000,163.55 1936-07-16,163.24,164.38,162.27,163.64,1480000,163.64 1936-07-15,162.80,164.42,162.28,163.24,1980000,163.24 1936-07-14,161.35,163.22,160.99,162.80,1660000,162.80 1936-07-13,160.72,162.14,160.33,161.35,1440000,161.35 1936-07-10,158.07,160.67,158.07,160.07,1690000,160.07 1936-07-09,156.20,158.17,156.05,157.71,1290000,157.71 1936-07-08,155.60,156.76,154.85,156.20,870000,156.20 1936-07-07,156.87,156.87,154.86,155.60,970000,155.60 1936-07-06,158.11,158.86,156.73,157.11,850000,157.11 1936-07-03,157.51,159.13,156.93,158.11,1020000,158.11 1936-07-02,158.38,159.55,156.87,157.51,1070000,157.51 1936-07-01,157.69,159.16,156.82,158.38,970000,158.38 1936-06-30,158.01,158.76,157.11,157.69,820000,157.69 1936-06-29,158.46,159.66,157.58,158.01,770000,158.01 1936-06-26,158.64,159.54,157.86,158.21,890000,158.21 1936-06-25,160.66,161.00,158.27,158.64,1340000,158.64 1936-06-24,158.94,161.15,158.56,160.66,1240000,160.66 1936-06-23,159.13,160.25,158.24,158.94,970000,158.94 1936-06-22,157.40,159.66,157.40,159.13,990000,159.13 1936-06-19,157.38,157.46,156.11,156.53,830000,156.53 1936-06-18,156.97,158.05,156.54,157.38,940000,157.38 1936-06-17,156.70,157.96,156.47,156.97,1220000,156.97 1936-06-16,155.09,156.94,154.88,156.70,1120000,156.70 1936-06-15,154.64,155.81,154.57,155.09,720000,155.09 1936-06-12,155.16,155.91,153.55,153.71,1000000,153.71 1936-06-11,153.02,155.38,152.65,155.16,1090000,155.16 1936-06-10,152.90,153.87,152.44,153.02,1040000,153.02 1936-06-09,151.44,153.12,151.44,152.90,880000,152.90 1936-06-08,150.40,152.01,150.40,151.39,690000,151.39 1936-06-05,149.39,149.95,148.52,149.26,640000,149.26 1936-06-04,151.10,151.10,149.22,149.39,770000,149.39 1936-06-03,151.97,152.38,151.20,151.53,640000,151.53 1936-06-02,152.84,153.22,151.30,151.97,760000,151.97 1936-06-01,152.64,154.02,152.62,152.84,790000,152.84 1936-05-29,151.77,152.92,151.53,152.64,740000,152.64 1936-05-28,152.57,152.91,151.49,151.77,760000,151.77 1936-05-27,152.26,153.57,151.44,152.57,1220000,152.57 1936-05-26,150.83,152.48,150.48,152.26,1140000,152.26 1936-05-25,150.65,151.62,150.31,150.83,690000,150.83 1936-05-22,148.80,150.26,148.61,149.58,680000,149.58 1936-05-21,148.94,150.21,148.46,148.80,670000,148.80 1936-05-20,147.49,149.28,147.30,148.94,690000,148.94 1936-05-19,149.56,149.56,147.21,147.49,910000,147.49 1936-05-18,151.42,152.44,150.09,150.35,990000,150.35 1936-05-15,151.49,152.43,150.56,151.60,990000,151.60 1936-05-14,149.00,151.97,149.00,151.49,1390000,151.49 1936-05-13,146.92,148.38,146.92,147.90,590000,147.90 1936-05-12,146.85,148.16,146.10,146.70,600000,146.70 1936-05-11,147.85,148.85,146.44,146.85,680000,146.85 1936-05-08,147.14,147.33,145.68,146.87,780000,146.87 1936-05-07,149.73,149.96,146.29,147.14,1010000,147.14 1936-05-06,148.56,150.52,148.52,149.73,1130000,149.73 1936-05-05,147.69,149.97,147.69,148.56,1180000,148.56 1936-05-04,146.41,147.63,144.18,146.96,1070000,146.96 1936-05-01,145.67,147.86,145.67,147.07,1160000,147.07 1936-04-30,143.65,146.20,141.53,145.67,2310000,145.67 1936-04-29,146.75,147.23,143.20,143.65,1790000,143.65 1936-04-28,147.05,147.79,144.80,146.75,2230000,146.75 1936-04-27,151.81,151.81,145.96,147.05,2300000,147.05 1936-04-24,151.08,152.51,149.63,151.54,1660000,151.54 1936-04-23,154.92,155.16,149.63,151.08,2060000,151.08 1936-04-22,153.60,155.59,153.60,154.92,1200000,154.92 1936-04-21,152.40,154.09,151.29,153.36,1880000,153.36 1936-04-20,156.07,156.73,152.10,152.40,1660000,152.40 1936-04-17,158.49,159.22,157.32,157.78,1160000,157.78 1936-04-16,159.61,160.33,157.93,158.49,1150000,158.49 1936-04-15,158.41,160.27,157.92,159.61,1320000,159.61 1936-04-14,160.76,161.10,157.51,158.41,1940000,158.41 1936-04-13,160.48,161.26,159.71,160.76,1450000,160.76 1936-04-09,160.97,161.44,159.46,160.26,1650000,160.26 1936-04-08,160.94,162.54,160.34,160.97,1650000,160.97 1936-04-07,161.99,162.33,160.42,160.94,1580000,160.94 1936-04-06,161.50,163.07,161.18,161.99,2030000,161.99 1936-04-03,160.43,161.84,159.80,160.09,1560000,160.09 1936-04-02,159.12,161.55,159.12,160.43,2190000,160.43 1936-04-01,157.04,159.42,157.04,158.96,1690000,158.96 1936-03-31,155.37,157.01,155.06,156.34,1040000,156.34 1936-03-30,155.54,156.73,155.16,155.37,950000,155.37 1936-03-27,157.73,157.82,155.01,155.52,1550000,155.52 1936-03-26,157.88,159.53,157.08,157.73,1870000,157.73 1936-03-25,156.56,158.74,155.81,157.88,1910000,157.88 1936-03-24,157.62,158.76,156.23,156.56,1900000,156.56 1936-03-23,156.42,158.22,156.20,157.62,1680000,157.62 1936-03-20,157.40,158.81,156.69,157.42,1890000,157.42 1936-03-19,155.85,158.22,155.85,157.40,2020000,157.40 1936-03-18,156.34,157.30,155.04,155.82,1750000,155.82 1936-03-17,153.85,156.73,153.85,156.34,2240000,156.34 1936-03-16,154.07,154.73,152.14,153.25,1840000,153.25 1936-03-13,153.13,153.46,149.65,150.42,2660000,150.42 1936-03-12,156.63,156.63,152.35,153.13,2920000,153.13 1936-03-11,155.37,157.95,155.37,156.85,2190000,156.85 1936-03-10,153.50,155.87,153.35,155.37,2320000,155.37 1936-03-09,156.86,156.86,153.33,153.50,2750000,153.50 1936-03-06,157.52,159.87,157.27,158.75,2890000,158.75 1936-03-05,156.70,158.56,156.03,157.52,2590000,157.52 1936-03-04,156.19,158.24,155.45,156.70,2980000,156.70 1936-03-03,154.08,156.61,154.08,156.19,2700000,156.19 1936-03-02,152.15,154.54,151.65,154.08,1980000,154.08 1936-02-28,152.64,153.94,151.61,152.53,2460000,152.53 1936-02-27,150.59,153.02,150.59,152.64,2320000,152.64 1936-02-26,150.78,151.10,149.08,149.81,2040000,149.81 1936-02-25,152.74,153.25,149.99,150.78,2390000,150.78 1936-02-24,153.74,153.75,152.00,152.74,2200000,152.74 1936-02-21,154.43,155.14,153.05,153.74,3010000,153.74 1936-02-20,153.09,155.14,152.30,154.43,3460000,154.43 1936-02-19,153.36,155.69,152.54,153.09,4580000,153.09 1936-02-18,151.40,153.76,151.23,153.36,3530000,153.36 1936-02-17,152.40,153.57,150.43,151.40,4720000,151.40 1936-02-14,152.53,153.01,150.86,151.97,2600000,151.97 1936-02-13,152.25,153.67,151.48,152.53,2920000,152.53 1936-02-11,151.15,153.16,150.80,152.25,3350000,152.25 1936-02-10,150.40,151.88,149.72,151.15,2460000,151.15 1936-02-07,150.86,151.67,149.50,150.17,2570000,150.17 1936-02-06,150.60,151.97,150.14,150.86,2750000,150.86 1936-02-05,150.94,151.94,150.07,150.60,2920000,150.60 1936-02-04,150.62,151.77,149.92,150.94,3010000,150.94 1936-02-03,149.58,151.05,148.32,150.62,2320000,150.62 1936-01-31,146.98,150.00,146.79,149.49,3230000,149.49 1936-01-30,147.71,148.50,146.25,146.98,3010000,146.98 1936-01-29,146.94,148.50,146.33,147.71,2680000,147.71 1936-01-28,147.30,147.84,146.38,146.94,2290000,146.94 1936-01-27,147.01,148.30,146.73,147.30,3100000,147.30 1936-01-24,146.97,147.91,146.15,146.59,2540000,146.59 1936-01-23,145.99,147.70,145.80,146.97,2940000,146.97 1936-01-22,143.79,146.36,143.79,145.99,2150000,145.99 1936-01-21,144.06,144.29,142.77,143.50,1330000,143.50 1936-01-20,144.93,145.23,143.60,144.06,1810000,144.06 1936-01-17,145.92,146.58,144.64,145.81,2350000,145.81 1936-01-16,145.66,146.73,145.03,145.92,3110000,145.92 1936-01-15,146.32,147.13,145.02,145.66,4630000,145.66 1936-01-14,146.52,146.89,145.41,146.32,2790000,146.32 1936-01-13,146.73,147.45,145.67,146.52,2600000,146.52 1936-01-10,145.68,148.02,145.68,147.08,3270000,147.08 1936-01-09,146.16,146.83,144.63,145.66,3000000,145.66 1936-01-08,144.92,147.29,144.62,146.16,2530000,146.16 1936-01-07,143.11,145.22,142.05,144.92,3080000,144.92 1936-01-06,144.08,145.35,141.55,143.11,3730000,143.11 1936-01-03,144.13,145.28,143.49,144.69,2830000,144.69 1936-01-02,144.13,145.22,143.34,144.13,2240000,144.13 1935-12-31,143.00,145.02,142.93,144.13,2440000,144.13 1935-12-30,141.35,143.37,141.35,143.00,1630000,143.00 1935-12-27,141.54,142.83,140.67,141.58,2130000,141.58 1935-12-26,141.53,142.64,140.87,141.54,2340000,141.54 1935-12-24,140.58,141.88,140.04,141.53,1710000,141.53 1935-12-23,140.19,141.42,139.75,140.58,1920000,140.58 1935-12-20,138.94,140.00,138.46,139.50,1410000,139.50 1935-12-19,139.95,139.95,138.33,138.94,1260000,138.94 1935-12-18,140.60,141.73,139.71,140.10,1690000,140.10 1935-12-17,139.11,140.89,138.90,140.60,1390000,140.60 1935-12-16,140.38,141.28,138.91,139.11,1400000,139.11 1935-12-13,141.34,142.12,139.56,140.16,1890000,140.16 1935-12-12,142.84,143.46,140.86,141.34,2140000,141.34 1935-12-11,142.31,143.90,141.63,142.84,2130000,142.84 1935-12-10,144.10,144.32,141.61,142.31,2340000,142.31 1935-12-09,144.47,145.07,143.06,144.10,2510000,144.10 1935-12-06,143.72,144.78,143.09,143.48,2370000,143.48 1935-12-05,144.04,145.09,143.12,143.72,2260000,143.72 1935-12-04,143.58,145.13,143.29,144.04,2960000,144.04 1935-12-03,140.72,143.71,140.60,143.58,1930000,143.58 1935-12-02,142.35,142.95,140.38,140.72,1520000,140.72 1935-11-29,143.38,144.27,141.15,142.34,2170000,142.34 1935-11-27,142.59,144.30,141.94,143.38,1860000,143.38 1935-11-26,144.72,145.25,141.80,142.59,2330000,142.59 1935-11-25,146.12,147.50,143.89,144.72,3370000,144.72 1935-11-22,147.37,148.10,143.48,144.61,3920000,144.61 1935-11-21,146.65,147.83,145.96,147.37,3280000,147.37 1935-11-20,148.44,149.42,145.98,146.65,3820000,146.65 1935-11-19,147.06,148.81,146.93,148.44,2880000,148.44 1935-11-18,147.31,148.94,146.35,147.06,3200000,147.06 1935-11-15,145.59,147.40,145.10,146.32,2940000,146.32 1935-11-14,143.85,146.39,143.85,145.59,3950000,145.59 1935-11-13,142.56,143.97,141.60,143.59,2050000,143.59 1935-11-12,144.36,144.60,142.20,142.56,2140000,142.56 1935-11-08,143.40,145.40,142.80,144.25,3350000,144.25 1935-11-07,142.90,145.28,142.15,143.40,2790000,143.40 1935-11-06,141.19,143.48,141.19,142.90,3080000,142.90 1935-11-04,141.20,141.78,139.99,141.07,1750000,141.07 1935-11-01,140.07,141.77,140.07,141.31,2040000,141.31 1935-10-31,139.35,140.52,138.85,139.74,1810000,139.74 1935-10-30,140.49,140.56,138.40,139.35,2150000,139.35 1935-10-29,140.78,141.23,139.49,140.49,1710000,140.49 1935-10-28,141.47,142.08,139.86,140.78,2110000,140.78 1935-10-25,139.58,141.89,139.58,140.68,2470000,140.68 1935-10-24,139.58,140.84,138.41,139.42,2160000,139.42 1935-10-23,138.77,140.46,138.32,139.58,2760000,139.58 1935-10-22,138.96,140.08,137.84,138.77,2840000,138.77 1935-10-21,137.11,139.50,137.11,138.96,2870000,138.96 1935-10-18,135.57,136.11,134.54,135.13,1450000,135.13 1935-10-17,135.68,136.76,135.10,135.57,1610000,135.57 1935-10-16,136.26,137.15,134.83,135.68,2240000,135.68 1935-10-15,135.03,137.11,134.85,136.26,2570000,136.26 1935-10-14,133.56,135.25,133.17,135.03,1590000,135.03 1935-10-11,133.03,134.56,133.03,133.56,2060000,133.56 1935-10-10,131.14,133.09,131.14,132.99,1860000,132.99 1935-10-09,130.06,130.81,129.51,130.59,880000,130.59 1935-10-08,130.77,131.30,129.85,130.06,1180000,130.06 1935-10-07,130.35,131.35,130.24,130.77,950000,130.77 1935-10-04,129.05,130.59,128.82,129.76,1420000,129.76 1935-10-03,128.06,129.41,126.95,129.05,1490000,129.05 1935-10-02,130.43,130.43,127.56,128.06,2190000,128.06 1935-10-01,131.92,133.19,131.18,131.51,1420000,131.51 1935-09-30,131.75,132.60,131.17,131.92,1260000,131.92 1935-09-27,131.06,132.12,130.74,131.48,1120000,131.48 1935-09-26,131.52,131.67,129.95,131.06,1090000,131.06 1935-09-25,131.02,132.45,130.99,131.52,1080000,131.52 1935-09-24,130.26,131.68,130.26,131.02,1010000,131.02 1935-09-23,128.97,130.66,128.97,129.55,1010000,129.55 1935-09-20,130.38,130.38,127.98,128.42,2220000,128.42 1935-09-19,134.11,134.49,131.10,131.44,1920000,131.44 1935-09-18,133.11,135.34,133.07,134.11,1940000,134.11 1935-09-17,132.91,133.78,131.86,133.11,1330000,133.11 1935-09-16,133.40,133.86,131.91,132.91,1490000,132.91 1935-09-13,133.33,134.67,132.88,133.52,1730000,133.52 1935-09-12,134.01,134.72,132.63,133.33,1880000,133.33 1935-09-11,133.22,135.05,132.90,134.01,2590000,134.01 1935-09-10,132.48,134.06,131.50,133.22,1980000,133.22 1935-09-09,131.86,133.36,131.13,132.48,2000000,132.48 1935-09-06,129.34,131.34,128.94,130.75,2150000,130.75 1935-09-05,128.46,130.34,128.29,129.34,1890000,129.34 1935-09-04,127.27,128.70,126.43,128.46,1000000,128.46 1935-09-03,127.89,128.47,126.81,127.27,900000,127.27 1935-08-30,126.95,127.70,126.76,127.35,830000,127.35 1935-08-29,126.61,127.62,126.57,126.95,900000,126.95 1935-08-28,126.81,127.32,125.65,126.61,1390000,126.61 1935-08-27,128.99,129.97,126.27,126.81,2160000,126.81 1935-08-26,127.93,129.53,127.61,128.99,1430000,128.99 1935-08-23,128.52,129.59,127.82,128.93,1890000,128.93 1935-08-22,127.66,129.49,127.33,128.52,1670000,128.52 1935-08-21,126.59,128.25,126.59,127.66,1750000,127.66 1935-08-20,126.33,126.68,124.97,126.31,1980000,126.31 1935-08-19,127.96,128.39,126.07,126.33,2070000,126.33 1935-08-16,127.47,128.03,126.51,127.63,1710000,127.63 1935-08-15,128.27,128.72,127.07,127.47,1580000,127.47 1935-08-14,128.09,128.94,127.35,128.27,1950000,128.27 1935-08-13,128.00,128.85,127.15,128.09,2630000,128.09 1935-08-12,127.94,128.84,127.44,128.00,2430000,128.00 1935-08-09,125.98,127.80,125.72,127.27,2190000,127.27 1935-08-08,125.61,126.59,125.16,125.98,1430000,125.98 1935-08-07,125.64,126.54,125.18,125.61,1390000,125.61 1935-08-06,126.07,126.96,125.00,125.64,1770000,125.64 1935-08-05,125.90,126.62,125.31,126.07,1740000,126.07 1935-08-02,125.85,126.13,124.28,124.93,1520000,124.93 1935-08-01,126.23,126.88,125.19,125.85,1890000,125.85 1935-07-31,125.57,127.04,125.00,126.23,1910000,126.23 1935-07-30,126.56,126.78,125.03,125.57,1680000,125.57 1935-07-29,125.27,126.89,125.10,126.56,1750000,126.56 1935-07-26,123.80,124.45,123.37,124.02,990000,124.02 1935-07-25,124.60,125.27,123.19,123.80,1330000,123.80 1935-07-24,124.14,124.93,123.83,124.60,1310000,124.60 1935-07-23,124.10,125.36,123.58,124.14,1730000,124.14 1935-07-22,122.69,124.34,122.67,124.10,1370000,124.10 1935-07-19,123.41,123.88,121.94,122.33,1150000,122.33 1935-07-18,122.91,124.24,122.60,123.41,1500000,123.41 1935-07-17,122.34,123.49,122.25,122.91,1360000,122.91 1935-07-16,121.72,122.56,121.00,122.34,900000,122.34 1935-07-15,121.88,122.74,121.40,121.72,950000,121.72 1935-07-12,121.93,122.63,121.29,122.20,1100000,122.20 1935-07-11,122.69,122.90,121.14,121.93,1000000,121.93 1935-07-10,122.15,123.14,121.97,122.69,1150000,122.69 1935-07-09,122.55,123.34,121.74,122.15,1350000,122.15 1935-07-08,121.02,122.68,120.69,122.55,1310000,122.55 1935-07-05,119.02,120.75,119.02,120.61,880000,120.61 1935-07-03,118.69,118.98,117.80,118.81,720000,118.81 1935-07-02,118.82,119.70,118.32,118.69,1200000,118.69 1935-07-01,118.21,119.30,117.97,118.82,680000,118.82 1935-06-28,117.69,118.83,117.69,118.36,760000,118.36 1935-06-27,117.64,118.50,116.91,117.56,740000,117.56 1935-06-26,118.73,119.49,117.51,117.64,960000,117.64 1935-06-25,119.64,119.64,117.85,118.73,1140000,118.73 1935-06-24,120.75,121.30,119.67,120.04,1120000,120.04 1935-06-21,117.80,120.04,117.80,119.48,1520000,119.48 1935-06-20,117.47,117.47,115.85,117.24,1000000,117.24 1935-06-19,119.32,119.76,117.47,118.12,1630000,118.12 1935-06-18,118.67,119.71,118.67,119.32,890000,119.32 1935-06-17,119.17,119.33,118.21,118.67,910000,118.67 1935-06-14,117.89,119.67,117.64,119.00,1280000,119.00 1935-06-13,117.14,118.40,116.49,117.89,860000,117.89 1935-06-12,117.08,118.53,116.27,117.14,1290000,117.14 1935-06-11,115.89,117.53,115.77,117.08,1150000,117.08 1935-06-10,114.72,116.12,114.04,115.89,630000,115.89 1935-06-07,113.54,114.27,113.15,114.01,590000,114.01 1935-06-06,113.92,114.89,113.27,113.54,680000,113.54 1935-06-05,113.58,115.08,112.96,113.92,1100000,113.92 1935-06-04,111.95,113.73,111.95,113.58,870000,113.58 1935-06-03,110.15,111.84,110.15,111.45,600000,111.45 1935-05-31,111.85,112.62,110.40,110.64,1120000,110.64 1935-05-29,113.67,113.67,111.37,111.85,1500000,111.85 1935-05-28,116.74,117.62,112.99,113.76,2310000,113.76 1935-05-27,115.90,117.12,115.32,116.74,820000,116.74 1935-05-24,116.81,117.43,115.91,116.17,1180000,116.17 1935-05-23,116.24,117.51,116.20,116.81,1290000,116.81 1935-05-22,115.56,116.69,115.07,116.24,1150000,116.24 1935-05-21,114.67,116.31,114.57,115.56,1140000,115.56 1935-05-20,114.58,115.27,114.18,114.67,970000,114.67 1935-05-17,116.58,117.09,115.28,115.81,1820000,115.81 1935-05-16,114.67,117.30,114.67,116.58,2420000,116.58 1935-05-15,114.18,115.11,113.87,114.61,1050000,114.61 1935-05-14,114.23,115.03,113.71,114.18,1210000,114.18 1935-05-13,114.08,114.93,113.36,114.23,1130000,114.23 1935-05-10,113.10,114.50,112.84,113.67,1580000,113.67 1935-05-09,112.63,113.92,112.11,113.10,1660000,113.10 1935-05-08,110.18,112.74,110.18,112.63,1400000,112.63 1935-05-07,110.53,110.68,109.23,109.79,810000,109.79 1935-05-06,110.83,111.60,110.22,110.53,1030000,110.53 1935-05-03,109.04,110.93,109.04,110.49,950000,110.49 1935-05-02,108.71,109.47,107.82,108.84,880000,108.84 1935-05-01,109.45,110.26,108.52,108.71,820000,108.71 1935-04-30,109.91,110.61,108.75,109.45,860000,109.45 1935-04-29,109.68,110.40,108.65,109.91,890000,109.91 1935-04-26,110.47,111.33,109.23,110.37,1520000,110.37 1935-04-25,109.45,111.52,108.94,110.47,1640000,110.47 1935-04-24,110.06,110.75,109.08,109.45,1280000,109.45 1935-04-23,110.27,110.70,109.56,110.06,1230000,110.06 1935-04-22,109.76,110.91,109.42,110.27,1380000,110.27 1935-04-18,105.68,108.33,105.68,107.97,820000,107.97 1935-04-17,106.33,106.67,105.24,105.43,850000,105.43 1935-04-16,105.93,106.67,105.44,106.33,740000,106.33 1935-04-15,105.42,106.44,105.05,105.93,1110000,105.93 1935-04-12,104.03,104.69,103.59,104.45,840000,104.45 1935-04-11,104.06,104.59,103.57,104.03,730000,104.03 1935-04-10,104.32,105.06,103.74,104.06,990000,104.06 1935-04-09,102.65,104.46,102.58,104.32,860000,104.32 1935-04-08,103.04,103.40,102.31,102.65,710000,102.65 1935-04-05,101.35,102.87,101.35,102.53,1210000,102.53 1935-04-04,100.39,101.38,100.34,101.13,560000,101.13 1935-04-03,101.00,101.11,99.75,100.39,530000,100.39 1935-04-02,101.23,101.86,100.84,101.00,530000,101.00 1935-04-01,100.81,101.59,100.67,101.23,440000,101.23 1935-03-29,100.59,101.33,100.26,100.78,460000,100.78 1935-03-28,100.35,101.54,99.69,100.59,610000,100.59 1935-03-27,98.97,100.72,98.87,100.35,460000,100.35 1935-03-26,99.50,99.80,98.61,98.97,440000,98.97 1935-03-25,99.84,99.99,98.63,99.50,460000,99.50 1935-03-22,99.72,100.88,99.10,100.68,780000,100.68 1935-03-21,98.29,100.55,98.03,99.72,890000,99.72 1935-03-20,98.31,99.11,97.75,98.29,490000,98.29 1935-03-19,97.05,98.61,97.05,98.31,510000,98.31 1935-03-18,97.62,97.62,95.95,97.01,590000,97.01 1935-03-15,96.71,98.51,96.47,98.21,770000,98.21 1935-03-14,98.02,98.50,96.49,96.71,810000,96.71 1935-03-13,97.66,98.52,96.81,98.02,1080000,98.02 1935-03-12,99.39,99.62,97.60,97.66,1050000,97.66 1935-03-11,101.18,101.60,99.24,99.39,800000,99.39 1935-03-08,101.27,102.37,101.27,101.58,440000,101.58 1935-03-07,100.22,101.37,100.13,101.17,540000,101.17 1935-03-06,100.09,101.94,98.77,100.22,1290000,100.22 1935-03-05,102.29,102.29,100.00,100.09,900000,100.09 1935-03-04,103.16,103.16,102.24,102.58,420000,102.58 1935-03-01,102.38,103.59,102.03,103.27,640000,103.27 1935-02-28,102.55,103.27,102.14,102.38,570000,102.38 1935-02-27,102.24,102.86,101.27,102.55,930000,102.55 1935-02-26,103.14,103.60,102.08,102.24,950000,102.24 1935-02-25,103.25,103.57,102.33,103.14,740000,103.14 1935-02-21,104.97,105.47,104.28,104.86,700000,104.86 1935-02-20,105.89,106.25,104.60,104.97,970000,104.97 1935-02-19,107.17,107.36,105.59,105.89,1100000,105.89 1935-02-18,104.54,108.29,103.64,107.17,1910000,107.17 1935-02-15,103.43,105.07,103.43,104.67,730000,104.67 1935-02-14,102.69,103.31,102.56,103.05,410000,103.05 1935-02-13,102.42,103.06,102.18,102.69,390000,102.69 1935-02-11,102.66,102.67,101.65,102.42,360000,102.42 1935-02-08,101.16,102.58,101.16,102.35,590000,102.35 1935-02-07,100.23,101.34,100.02,101.00,520000,101.00 1935-02-06,100.74,100.90,99.95,100.23,560000,100.23 1935-02-05,101.40,101.40,100.46,100.74,560000,100.74 1935-02-04,102.17,102.17,101.35,101.56,350000,101.56 1935-02-01,101.69,102.05,101.10,101.53,490000,101.53 1935-01-31,101.05,102.12,101.05,101.69,530000,101.69 1935-01-30,100.69,101.39,100.38,101.00,430000,101.00 1935-01-29,101.51,101.58,100.24,100.69,580000,100.69 1935-01-28,102.31,102.31,101.03,101.51,690000,101.51 1935-01-25,102.44,103.12,102.32,102.86,520000,102.86 1935-01-24,102.85,102.85,102.01,102.44,440000,102.44 1935-01-23,102.77,103.43,102.43,102.88,620000,102.88 1935-01-22,103.35,103.64,102.60,102.77,590000,102.77 1935-01-21,102.96,103.93,102.57,103.35,690000,103.35 1935-01-18,101.92,102.63,101.58,102.36,690000,102.36 1935-01-17,101.54,102.30,101.04,101.92,740000,101.92 1935-01-16,100.49,101.95,100.40,101.54,670000,101.54 1935-01-15,102.76,103.20,99.54,100.49,1370000,100.49 1935-01-14,102.39,103.37,102.39,102.76,550000,102.76 1935-01-11,104.87,105.49,102.50,103.35,1380000,103.35 1935-01-10,105.05,105.65,104.41,104.87,780000,104.87 1935-01-09,105.03,105.68,104.28,105.05,900000,105.05 1935-01-08,105.88,106.22,104.56,105.03,1190000,105.03 1935-01-07,105.56,106.71,105.24,105.88,1290000,105.88 1935-01-04,105.14,105.43,104.18,104.69,970000,104.69 1935-01-03,104.51,105.63,104.12,105.14,1070000,105.14 1935-01-02,104.04,104.93,103.05,104.51,880000,104.51 1934-12-31,103.90,104.46,103.36,104.04,1020000,104.04 1934-12-28,100.57,103.29,100.57,103.15,1280000,103.15 1934-12-27,100.35,101.41,99.58,100.26,1630000,100.26 1934-12-26,100.69,101.32,100.05,100.35,1050000,100.35 1934-12-24,99.73,101.00,99.52,100.69,810000,100.69 1934-12-21,99.59,100.38,98.99,99.90,920000,99.90 1934-12-20,99.78,100.01,98.93,99.59,880000,99.59 1934-12-19,100.88,100.88,99.40,99.78,980000,99.78 1934-12-18,100.92,101.37,100.41,101.00,820000,101.00 1934-12-17,100.84,101.66,100.45,100.92,900000,100.92 1934-12-14,100.68,101.30,100.34,100.69,940000,100.69 1934-12-13,100.97,102.02,100.39,100.68,1000000,100.68 1934-12-12,100.81,101.62,100.52,100.97,790000,100.97 1934-12-11,102.76,103.58,100.50,100.81,1280000,100.81 1934-12-10,102.83,103.52,102.18,102.76,850000,102.76 1934-12-07,103.47,103.90,102.75,103.16,1020000,103.16 1934-12-06,103.42,104.23,102.91,103.47,1420000,103.47 1934-12-05,102.69,104.08,102.69,103.42,1640000,103.42 1934-12-04,101.92,102.93,101.59,102.57,950000,102.57 1934-12-03,102.77,102.77,101.74,101.92,750000,101.92 1934-11-30,102.75,103.36,101.94,102.94,800000,102.94 1934-11-28,102.38,103.47,101.90,102.75,1160000,102.75 1934-11-27,103.08,103.12,101.80,102.38,1010000,102.38 1934-11-26,102.40,103.51,102.16,103.08,1410000,103.08 1934-11-23,100.17,101.99,100.17,101.62,1130000,101.62 1934-11-22,99.47,100.48,98.93,99.93,770000,99.93 1934-11-21,99.90,100.43,98.95,99.47,810000,99.47 1934-11-20,99.89,100.14,98.96,99.90,870000,99.90 1934-11-19,99.45,100.68,99.24,99.89,980000,99.89 1934-11-16,99.72,100.08,98.70,99.39,1030000,99.39 1934-11-15,99.42,100.80,99.34,99.72,1540000,99.72 1934-11-14,99.19,99.81,98.49,99.42,960000,99.42 1934-11-13,99.21,99.98,98.49,99.19,1130000,99.19 1934-11-09,97.26,99.34,96.97,99.02,1230000,99.02 1934-11-08,97.55,98.31,96.83,97.26,840000,97.26 1934-11-07,96.06,97.81,95.31,97.55,1110000,97.55 1934-11-05,94.95,96.17,94.83,96.06,760000,96.06 1934-11-02,93.83,94.94,93.83,94.42,650000,94.42 1934-11-01,93.36,93.98,92.79,93.46,540000,93.46 1934-10-31,93.05,94.04,92.90,93.36,420000,93.36 1934-10-30,92.59,93.46,92.59,93.05,430000,93.05 1934-10-29,92.86,93.60,92.37,92.53,430000,92.53 1934-10-26,93.86,93.86,92.20,93.01,870000,93.01 1934-10-25,95.60,96.15,94.05,94.19,1030000,94.19 1934-10-24,94.65,95.71,93.96,95.60,770000,95.60 1934-10-23,94.78,95.17,94.19,94.65,540000,94.65 1934-10-22,95.02,95.79,94.65,94.78,570000,94.78 1934-10-19,95.33,95.33,94.39,94.90,530000,94.90 1934-10-18,95.29,96.03,94.63,95.34,660000,95.34 1934-10-17,95.25,96.36,94.83,95.29,660000,95.29 1934-10-16,94.16,95.81,94.15,95.25,680000,95.25 1934-10-15,94.90,95.37,94.01,94.16,510000,94.16 1934-10-11,93.94,96.04,93.94,95.50,1400000,95.50 1934-10-10,91.78,94.01,91.78,93.75,990000,93.75 1934-10-09,92.50,93.03,91.31,91.71,770000,91.71 1934-10-08,92.85,93.21,92.16,92.50,450000,92.50 1934-10-05,91.74,93.58,91.74,92.96,870000,92.96 1934-10-04,91.04,91.44,89.84,91.01,610000,91.01 1934-10-03,90.88,91.82,90.66,91.04,410000,91.04 1934-10-02,90.41,91.44,90.30,90.88,370000,90.88 1934-10-01,92.17,92.17,90.14,90.41,620000,90.41 1934-09-28,93.40,93.52,92.24,92.49,510000,92.49 1934-09-27,92.44,94.02,92.23,93.40,800000,93.40 1934-09-26,92.72,93.12,92.05,92.44,800000,92.44 1934-09-25,90.45,92.79,89.91,92.72,840000,92.72 1934-09-24,91.08,91.50,89.97,90.45,510000,90.45 1934-09-21,89.65,91.34,89.65,91.10,710000,91.10 1934-09-20,89.34,89.93,88.76,89.35,490000,89.35 1934-09-19,87.91,89.58,87.91,89.34,560000,89.34 1934-09-18,86.69,87.84,86.57,87.37,530000,87.37 1934-09-17,87.34,87.41,85.72,86.69,650000,86.69 1934-09-14,89.25,89.25,86.64,86.83,840000,86.83 1934-09-13,89.62,90.45,89.12,89.44,420000,89.44 1934-09-12,89.25,90.14,89.14,89.62,400000,89.62 1934-09-11,89.27,89.75,88.42,89.25,630000,89.25 1934-09-10,90.83,91.32,89.04,89.27,700000,89.27 1934-09-07,91.82,92.52,90.50,90.99,690000,90.99 1934-09-06,93.65,94.05,91.67,91.82,600000,91.82 1934-09-05,92.64,93.96,92.64,93.65,480000,93.65 1934-09-04,92.59,92.59,91.74,92.30,310000,92.30 1934-08-31,92.76,93.05,92.05,92.86,400000,92.86 1934-08-30,93.59,93.59,92.01,92.76,650000,92.76 1934-08-29,94.19,95.59,93.64,93.69,760000,93.69 1934-08-28,94.46,94.48,93.55,94.19,400000,94.19 1934-08-27,95.31,95.31,94.25,94.46,530000,94.46 1934-08-24,94.05,95.55,93.85,95.48,750000,95.48 1934-08-23,94.32,94.97,93.64,94.05,750000,94.05 1934-08-22,92.68,94.95,92.68,94.32,1300000,94.32 1934-08-21,90.87,92.70,90.87,92.57,580000,92.57 1934-08-20,90.86,91.02,90.08,90.44,280000,90.44 1934-08-17,91.69,92.25,91.00,91.12,480000,91.12 1934-08-16,91.08,92.51,91.08,91.69,610000,91.69 1934-08-15,91.12,91.70,90.66,91.00,580000,91.00 1934-08-14,91.80,91.98,90.82,91.12,530000,91.12 1934-08-13,89.79,92.56,89.69,91.80,810000,91.80 1934-08-10,91.34,91.47,89.39,89.66,770000,89.66 1934-08-09,88.97,91.80,87.19,91.34,1420000,91.34 1934-08-08,87.47,89.28,87.16,88.97,690000,88.97 1934-08-07,88.11,89.10,86.70,87.47,610000,87.47 1934-08-06,88.43,88.51,86.32,88.11,780000,88.11 1934-08-03,90.87,91.08,89.82,90.14,470000,90.14 1934-08-02,90.57,91.12,89.75,90.87,560000,90.87 1934-08-01,88.55,90.96,88.55,90.57,780000,90.57 1934-07-31,88.17,88.51,87.17,88.05,360000,88.05 1934-07-30,88.72,88.96,86.90,88.17,810000,88.17 1934-07-27,86.64,88.86,86.64,87.84,2210000,87.84 1934-07-26,91.32,91.32,84.58,85.51,3340000,85.51 1934-07-25,91.01,92.08,90.09,91.57,1350000,91.57 1934-07-24,91.98,92.91,90.63,91.01,1600000,91.01 1934-07-23,94.62,95.17,91.96,91.98,1880000,91.98 1934-07-20,97.20,97.20,94.43,94.74,1240000,94.74 1934-07-19,98.26,98.70,96.92,97.24,610000,97.24 1934-07-18,97.18,98.45,97.18,98.26,490000,98.26 1934-07-17,97.04,97.75,96.50,96.79,620000,96.79 1934-07-16,98.51,98.51,96.91,97.04,590000,97.04 1934-07-13,98.32,99.08,97.66,98.82,530000,98.82 1934-07-12,98.67,99.01,97.93,98.32,470000,98.32 1934-07-11,98.12,99.35,98.12,98.67,650000,98.67 1934-07-10,97.04,98.63,97.02,98.07,650000,98.07 1934-07-09,97.15,97.54,96.54,97.04,320000,97.04 1934-07-06,96.56,97.80,96.56,97.32,460000,97.32 1934-07-05,95.19,96.92,95.19,96.44,440000,96.44 1934-07-03,94.80,95.13,94.25,94.77,400000,94.77 1934-07-02,95.71,95.71,94.59,94.80,410000,94.80 1934-06-29,96.84,96.84,95.59,95.75,440000,95.75 1934-06-28,96.94,97.88,96.18,97.14,640000,97.14 1934-06-27,97.33,98.31,96.74,96.94,630000,96.94 1934-06-26,95.79,97.53,95.46,97.33,620000,97.33 1934-06-25,96.59,97.03,95.49,95.79,490000,95.79 1934-06-22,97.50,97.87,95.48,95.93,930000,95.93 1934-06-21,98.25,98.62,97.39,97.50,530000,97.50 1934-06-20,99.02,99.10,97.94,98.25,550000,98.25 1934-06-19,100.42,101.11,98.75,99.02,850000,99.02 1934-06-18,99.85,100.70,99.32,100.42,610000,100.42 1934-06-15,97.23,99.29,97.23,98.70,730000,98.70 1934-06-14,98.49,98.49,96.92,97.15,630000,97.15 1934-06-13,98.78,99.92,98.32,98.75,880000,98.75 1934-06-12,97.82,99.60,97.77,98.78,950000,98.78 1934-06-11,98.70,98.70,97.40,97.82,750000,97.82 1934-06-08,94.82,98.55,94.82,98.44,1610000,98.44 1934-06-07,94.77,95.24,94.04,94.72,470000,94.72 1934-06-06,94.66,95.68,94.27,94.77,670000,94.77 1934-06-05,92.74,94.94,92.74,94.66,740000,94.66 1934-06-04,91.84,93.04,91.84,92.73,360000,92.73 1934-06-01,93.71,93.71,91.70,91.79,630000,91.79 1934-05-31,94.78,94.78,93.71,94.00,440000,94.00 1934-05-29,95.56,95.85,94.85,95.32,380000,95.32 1934-05-28,95.32,96.33,95.32,95.56,620000,95.56 1934-05-25,93.37,94.96,93.25,94.50,540000,94.50 1934-05-24,92.86,94.08,92.57,93.37,500000,93.37 1934-05-23,93.61,93.74,92.23,92.86,660000,92.86 1934-05-22,95.76,96.29,93.26,93.61,830000,93.61 1934-05-21,95.13,95.96,94.81,95.76,380000,95.76 1934-05-18,95.98,96.57,94.62,95.17,910000,95.17 1934-05-17,92.73,96.17,92.63,95.98,1290000,95.98 1934-05-16,92.84,93.83,91.95,92.73,720000,92.73 1934-05-15,91.81,93.65,91.47,92.84,890000,92.84 1934-05-14,92.22,92.95,89.10,91.81,1680000,91.81 1934-05-11,93.91,95.19,92.99,93.18,1000000,93.18 1934-05-10,95.59,95.59,92.16,93.91,2130000,93.91 1934-05-09,97.16,97.81,95.38,95.71,1030000,95.71 1934-05-08,95.51,97.73,94.47,97.16,1860000,97.16 1934-05-07,98.20,98.71,94.30,95.51,2360000,95.51 1934-05-04,99.02,100.66,99.02,99.29,840000,99.29 1934-05-03,98.82,100.06,98.36,98.94,1110000,98.94 1934-05-02,100.62,101.36,98.47,98.82,1340000,98.82 1934-05-01,100.49,101.20,99.55,100.62,1340000,100.62 1934-04-30,102.72,102.72,100.31,100.49,1490000,100.49 1934-04-27,103.56,104.30,103.12,103.65,840000,103.65 1934-04-26,105.05,105.51,102.95,103.56,1640000,103.56 1934-04-25,105.31,105.55,104.53,105.05,960000,105.05 1934-04-24,105.92,106.19,104.70,105.31,1270000,105.31 1934-04-23,106.34,106.73,105.31,105.92,1110000,105.92 1934-04-20,105.52,107.00,105.08,106.55,1890000,106.55 1934-04-19,105.45,106.18,104.34,105.52,1330000,105.52 1934-04-18,104.58,106.26,104.58,105.45,1540000,105.45 1934-04-17,103.57,104.82,103.34,104.46,940000,104.46 1934-04-16,105.04,105.31,102.88,103.57,1290000,103.57 1934-04-13,104.80,105.72,104.42,104.98,1180000,104.98 1934-04-12,105.16,105.82,104.30,104.80,1330000,104.80 1934-04-11,105.05,106.23,104.64,105.16,1550000,105.16 1934-04-10,103.95,105.51,103.95,105.05,1410000,105.05 1934-04-09,103.60,104.07,102.92,103.54,850000,103.54 1934-04-06,103.37,104.30,102.86,103.97,1010000,103.97 1934-04-05,103.19,104.09,102.47,103.37,1420000,103.37 1934-04-04,102.74,103.91,102.21,103.19,1560000,103.19 1934-04-03,101.96,103.00,101.18,102.74,1340000,102.74 1934-04-02,101.85,102.82,101.41,101.96,1370000,101.96 1934-03-29,99.18,100.83,99.18,100.31,1020000,100.31 1934-03-28,98.76,99.84,98.60,99.02,840000,99.02 1934-03-27,99.32,99.32,97.41,98.76,1590000,98.76 1934-03-26,100.92,102.67,100.70,100.95,1280000,100.95 1934-03-23,100.53,100.53,99.47,99.80,760000,99.80 1934-03-22,99.33,100.94,98.87,100.54,1030000,100.54 1934-03-21,100.73,100.73,98.45,99.33,1070000,99.33 1934-03-20,99.68,101.82,98.75,101.01,1540000,101.01 1934-03-19,101.04,101.04,98.99,99.68,1510000,99.68 1934-03-16,102.21,103.26,101.46,102.72,1170000,102.72 1934-03-15,103.54,103.73,101.43,102.21,1340000,102.21 1934-03-14,104.00,104.69,103.31,103.54,1360000,103.54 1934-03-13,104.23,104.89,103.54,104.00,1280000,104.00 1934-03-12,102.77,104.61,102.66,104.23,1260000,104.23 1934-03-09,103.21,103.91,102.13,102.44,1370000,102.44 1934-03-08,101.59,103.44,100.78,103.21,1700000,103.21 1934-03-07,103.84,104.59,101.12,101.59,1730000,101.59 1934-03-06,104.94,104.94,103.40,103.84,810000,103.84 1934-03-05,105.56,105.89,103.79,105.02,950000,105.02 1934-03-02,103.74,105.99,103.74,105.79,1480000,105.79 1934-03-01,103.46,103.81,101.93,103.18,1240000,103.18 1934-02-28,103.67,105.37,103.09,103.46,1320000,103.46 1934-02-27,103.12,104.55,102.63,103.67,1270000,103.67 1934-02-26,104.49,104.49,102.21,103.12,2190000,103.12 1934-02-23,108.50,109.36,105.72,106.14,2290000,106.14 1934-02-21,108.14,109.39,107.55,108.50,1900000,108.50 1934-02-20,107.53,108.68,107.24,108.14,1220000,108.14 1934-02-19,109.07,109.57,107.04,107.53,2350000,107.53 1934-02-16,108.30,109.96,107.60,108.61,2770000,108.61 1934-02-15,106.92,109.04,106.92,108.30,2980000,108.30 1934-02-14,106.10,107.21,104.64,106.78,1940000,106.78 1934-02-13,105.47,107.35,104.78,106.10,2060000,106.10 1934-02-09,108.45,108.76,104.29,106.09,3340000,106.09 1934-02-08,107.95,109.09,106.05,108.45,3200000,108.45 1934-02-07,110.20,110.20,106.53,107.95,4500000,107.95 1934-02-06,110.74,111.25,108.88,110.24,4330000,110.24 1934-02-05,109.50,111.93,109.50,110.74,4940000,110.74 1934-02-02,108.95,109.69,107.67,108.31,2870000,108.31 1934-02-01,107.94,110.35,107.94,108.95,4710000,108.95 1934-01-31,108.99,109.17,106.81,107.22,3110000,107.22 1934-01-30,107.91,110.06,107.91,108.99,4240000,108.99 1934-01-29,106.11,108.42,106.11,107.90,2780000,107.90 1934-01-26,106.85,107.93,105.85,106.38,2510000,106.38 1934-01-25,107.02,107.52,105.44,106.85,2270000,106.85 1934-01-24,106.62,108.20,106.26,107.02,3370000,107.02 1934-01-23,105.09,107.00,104.47,106.62,2380000,106.62 1934-01-22,105.52,106.92,104.34,105.09,2660000,105.09 1934-01-19,103.46,106.19,103.46,105.60,3540000,105.60 1934-01-18,103.50,104.48,102.50,103.30,2130000,103.30 1934-01-17,103.40,104.87,102.38,103.50,2850000,103.50 1934-01-16,103.19,104.60,102.66,103.40,3440000,103.40 1934-01-15,99.50,103.48,99.50,103.19,3740000,103.19 1934-01-12,99.38,99.98,98.24,98.73,1600000,98.73 1934-01-11,99.77,100.49,98.77,99.38,1700000,99.38 1934-01-10,97.78,99.99,97.78,99.77,1420000,99.77 1934-01-09,97.09,98.53,97.09,97.57,870000,97.57 1934-01-08,96.94,97.93,96.26,96.73,720000,96.73 1934-01-05,98.78,99.39,96.97,97.23,1060000,97.23 1934-01-04,99.09,99.13,96.48,98.78,1190000,98.78 1934-01-03,100.36,100.83,97.75,99.09,1380000,99.09 1934-01-02,99.90,101.94,99.61,100.36,1270000,100.36 1933-12-29,99.29,99.73,97.85,98.67,1130000,98.67 1933-12-28,97.16,100.04,97.16,99.29,1480000,99.29 1933-12-27,96.30,98.21,95.16,96.80,3080000,96.80 1933-12-26,97.76,97.76,95.56,96.30,1300000,96.30 1933-12-22,95.93,99.90,95.93,98.87,2420000,98.87 1933-12-21,95.28,96.16,94.78,95.50,1020000,95.50 1933-12-20,97.25,97.96,93.70,95.28,2160000,95.28 1933-12-19,97.20,97.99,96.30,97.25,1030000,97.25 1933-12-18,98.06,98.42,95.77,97.20,1340000,97.20 1933-12-15,101.44,101.67,99.44,99.95,1170000,99.95 1933-12-14,100.69,102.92,100.58,101.44,1560000,101.44 1933-12-13,101.64,101.98,99.94,100.69,1330000,100.69 1933-12-12,101.94,103.03,101.06,101.64,1650000,101.64 1933-12-11,102.92,103.97,101.63,101.94,2450000,101.94 1933-12-08,102.04,102.47,100.30,101.04,1330000,101.04 1933-12-07,101.28,103.01,101.07,102.04,1680000,102.04 1933-12-06,101.99,102.72,100.70,101.28,1440000,101.28 1933-12-05,99.20,102.44,99.20,101.99,2020000,101.99 1933-12-04,99.07,99.41,98.19,98.89,670000,98.89 1933-12-01,98.41,100.08,98.41,98.89,810000,98.89 1933-11-29,96.57,98.51,96.57,98.14,750000,98.14 1933-11-28,95.77,97.79,95.59,96.23,1010000,96.23 1933-11-27,99.28,99.45,95.32,95.77,1560000,95.77 1933-11-24,98.59,100.81,98.09,99.52,1420000,99.52 1933-11-23,100.07,100.29,97.20,98.59,1370000,98.59 1933-11-22,100.29,101.61,98.80,100.07,1570000,100.07 1933-11-21,101.28,101.94,99.67,100.29,1800000,100.29 1933-11-20,98.67,101.83,98.52,101.28,1900000,101.28 1933-11-17,99.01,100.59,97.54,98.09,2320000,98.09 1933-11-16,94.36,99.34,94.12,99.01,2580000,99.01 1933-11-15,95.50,96.35,93.27,94.36,1350000,94.36 1933-11-14,95.98,98.26,94.73,95.50,2170000,95.50 1933-11-13,96.10,97.15,95.25,95.98,1090000,95.98 1933-11-10,96.40,97.21,94.60,95.06,1370000,95.06 1933-11-09,95.54,98.34,95.46,96.40,2900000,96.40 1933-11-08,92.50,96.05,91.82,95.54,1800000,95.54 1933-11-06,93.09,93.14,91.67,92.50,690000,92.50 1933-11-03,90.54,93.92,89.96,93.60,1500000,93.60 1933-11-02,89.62,91.38,89.17,90.54,1120000,90.54 1933-11-01,88.16,89.92,86.83,89.62,1140000,89.62 1933-10-31,88.43,89.44,86.50,88.16,1130000,88.16 1933-10-30,92.01,93.99,88.05,88.43,1470000,88.43 1933-10-27,92.02,94.11,90.83,93.22,1110000,93.22 1933-10-26,93.54,93.95,91.29,92.02,1220000,92.02 1933-10-25,91.35,95.23,91.23,93.54,2880000,93.54 1933-10-24,88.13,91.67,87.10,91.35,2110000,91.35 1933-10-23,86.25,90.54,86.25,88.13,2130000,88.13 1933-10-20,84.38,88.41,83.57,86.63,2700000,86.63 1933-10-19,88.62,88.62,84.26,84.38,2900000,84.38 1933-10-18,92.67,92.72,88.47,88.95,1730000,88.95 1933-10-17,90.49,93.47,88.69,92.67,2480000,92.67 1933-10-16,94.93,94.93,89.35,90.49,2670000,90.49 1933-10-13,98.77,98.77,95.14,95.36,1270000,95.36 1933-10-11,98.77,99.94,97.54,98.85,1030000,98.85 1933-10-10,99.72,100.20,98.05,98.77,1140000,98.77 1933-10-09,98.20,100.58,98.14,99.72,1250000,99.72 1933-10-06,98.05,99.18,95.92,97.54,1460000,97.54 1933-10-05,98.60,99.34,96.95,98.05,1660000,98.05 1933-10-04,94.89,99.21,94.89,98.60,2140000,98.60 1933-10-03,92.99,94.43,91.93,93.55,930000,93.55 1933-10-02,94.82,95.32,92.69,92.99,960000,92.99 1933-09-29,94.66,97.21,93.94,94.24,1640000,94.24 1933-09-28,93.18,95.30,92.89,94.66,1440000,94.66 1933-09-27,96.91,96.91,92.44,93.18,2320000,93.18 1933-09-26,98.03,100.23,96.84,97.41,1430000,97.41 1933-09-25,99.34,99.34,96.46,98.03,1310000,98.03 1933-09-22,97.56,99.93,95.73,99.06,3320000,99.06 1933-09-21,102.29,102.29,97.15,97.56,3650000,97.56 1933-09-20,105.71,105.71,102.26,103.99,2420000,103.99 1933-09-19,105.30,106.25,102.44,105.74,2820000,105.74 1933-09-18,105.32,107.68,104.36,105.30,2720000,105.30 1933-09-15,104.66,106.14,102.14,102.63,2450000,102.63 1933-09-14,103.81,106.53,103.81,104.66,2900000,104.66 1933-09-13,102.90,104.13,102.90,103.65,740000,103.65 1933-09-12,103.59,104.90,102.33,102.84,2240000,102.84 1933-09-11,99.42,103.74,99.26,103.59,1920000,103.59 1933-09-08,99.20,100.41,98.16,99.58,1300000,99.58 1933-09-07,100.33,101.12,98.82,99.20,1070000,99.20 1933-09-06,100.22,100.90,97.74,100.33,1890000,100.33 1933-09-05,103.34,103.34,99.80,100.22,1250000,100.22 1933-09-01,102.41,103.89,101.86,103.66,1220000,103.66 1933-08-31,102.35,103.31,101.48,102.41,1140000,102.41 1933-08-30,103.59,104.13,100.38,102.35,2170000,102.35 1933-08-29,104.72,105.39,100.23,103.59,3120000,103.59 1933-08-28,105.07,105.53,103.02,104.72,2120000,104.72 1933-08-25,102.84,105.60,102.84,105.07,3330000,105.07 1933-08-24,100.38,102.77,99.52,101.41,1730000,101.41 1933-08-23,101.34,102.75,99.58,100.38,2580000,100.38 1933-08-22,100.17,101.71,99.02,101.34,1960000,101.34 1933-08-21,98.57,100.86,98.57,100.17,1560000,100.17 1933-08-18,99.30,100.77,96.81,98.32,2090000,98.32 1933-08-17,94.44,99.49,93.59,99.30,2470000,99.30 1933-08-16,96.28,96.28,92.95,94.44,1800000,94.44 1933-08-15,96.53,97.53,95.72,96.63,910000,96.63 1933-08-14,97.40,97.40,94.63,96.53,1220000,96.53 1933-08-11,97.58,98.68,96.28,97.47,1340000,97.47 1933-08-10,99.06,100.14,96.48,97.58,2820000,97.58 1933-08-09,96.17,99.39,96.17,99.06,2560000,99.06 1933-08-08,93.16,96.10,93.16,95.84,1230000,95.84 1933-08-07,92.62,93.32,91.63,92.55,770000,92.55 1933-08-04,93.45,93.45,92.03,92.62,500000,92.62 1933-08-03,94.84,95.86,93.21,94.10,1510000,94.10 1933-08-02,92.70,95.27,91.97,94.84,1730000,94.84 1933-08-01,90.77,93.23,89.61,92.70,1780000,92.70 1933-07-31,94.18,94.18,87.75,90.77,3090000,90.77 1933-07-28,95.90,95.90,93.75,94.54,1390000,94.54 1933-07-27,95.05,97.28,94.12,96.03,2460000,96.03 1933-07-26,92.83,95.50,92.23,95.05,2040000,95.05 1933-07-25,94.28,96.27,91.77,92.83,3540000,92.83 1933-07-24,90.63,94.75,90.63,94.28,3420000,94.28 1933-07-21,96.26,98.69,84.45,88.71,9570000,88.71 1933-07-20,103.58,105.65,94.76,96.26,8120000,96.26 1933-07-19,108.67,109.23,102.32,103.58,7450000,103.58 1933-07-18,108.27,110.53,106.98,108.67,6590000,108.67 1933-07-17,106.22,110.30,106.22,108.27,6380000,108.27 1933-07-14,105.51,107.63,103.94,105.04,5230000,105.04 1933-07-13,104.55,107.77,104.54,105.51,7450000,105.51 1933-07-12,103.08,105.46,101.87,104.55,5190000,104.55 1933-07-11,104.08,105.10,101.97,103.08,5240000,103.08 1933-07-10,105.15,105.87,103.12,104.08,4840000,104.08 1933-07-07,104.98,107.51,103.23,105.35,6970000,105.35 1933-07-06,102.73,105.56,101.21,104.98,6540000,104.98 1933-07-05,103.77,104.70,101.02,102.73,5800000,102.73 1933-07-03,101.64,104.99,101.64,103.77,6720000,103.77 1933-06-30,96.99,98.69,95.50,98.14,3630000,98.14 1933-06-29,97.74,99.23,95.90,96.99,4590000,96.99 1933-06-28,98.74,100.48,96.69,97.74,5510000,97.74 1933-06-27,98.49,100.27,98.01,98.74,5640000,98.74 1933-06-26,95.93,99.10,95.93,98.49,4530000,98.49 1933-06-23,92.93,95.59,91.93,95.53,3310000,95.53 1933-06-22,95.91,97.79,91.69,92.93,4370000,92.93 1933-06-21,95.23,97.34,94.41,95.91,3890000,95.91 1933-06-20,95.99,98.34,94.57,95.23,5540000,95.23 1933-06-19,92.86,96.36,92.86,95.99,5480000,95.99 1933-06-16,88.87,91.11,86.48,89.22,5710000,89.22 1933-06-15,93.94,93.94,88.17,88.87,4890000,88.87 1933-06-14,94.79,96.29,91.41,94.06,5550000,94.06 1933-06-13,96.75,97.92,94.21,94.79,6300000,94.79 1933-06-12,94.42,97.10,94.16,96.75,5810000,96.75 1933-06-09,93.52,95.03,91.64,94.29,5310000,94.29 1933-06-08,92.98,95.15,91.59,93.52,6360000,93.52 1933-06-07,91.90,94.38,91.04,92.98,6640000,92.98 1933-06-06,91.89,93.83,90.66,91.90,6220000,91.90 1933-06-05,90.02,92.37,89.14,91.89,5010000,91.89 1933-06-02,89.10,92.66,88.97,92.21,6880000,92.21 1933-06-01,88.11,90.57,87.37,89.10,4750000,89.10 1933-05-31,90.02,91.05,87.72,88.11,6080000,88.11 1933-05-29,89.61,91.33,87.87,90.02,6950000,90.02 1933-05-26,83.73,86.98,83.47,86.42,4350000,86.42 1933-05-25,84.29,85.48,82.70,83.73,4010000,83.73 1933-05-24,83.53,85.47,83.53,84.29,4710000,84.29 1933-05-23,80.56,83.49,80.56,83.06,3140000,83.06 1933-05-22,80.21,81.08,78.61,79.94,2220000,79.94 1933-05-19,82.57,83.20,80.65,81.75,3280000,81.75 1933-05-18,82.64,84.13,80.70,82.57,4110000,82.57 1933-05-17,81.33,84.18,81.33,82.64,4790000,82.64 1933-05-16,79.70,82.25,79.54,81.29,3290000,81.29 1933-05-15,80.85,81.23,79.06,79.70,3150000,79.70 1933-05-12,82.48,82.75,80.13,82.14,4560000,82.14 1933-05-11,81.18,83.61,81.18,82.48,6160000,82.48 1933-05-10,77.95,81.01,77.95,80.78,3820000,80.78 1933-05-09,76.63,78.03,75.61,77.23,2230000,77.23 1933-05-08,77.61,79.67,76.01,76.63,3200000,76.63 1933-05-05,79.16,81.27,78.81,79.78,5000000,79.78 1933-05-04,77.37,79.80,76.19,79.16,4590000,79.16 1933-05-03,77.29,78.92,75.69,77.37,4640000,77.37 1933-05-02,77.79,78.37,75.66,77.29,3900000,77.29 1933-05-01,77.66,79.98,76.91,77.79,6050000,77.79 1933-04-28,71.71,73.34,69.78,73.10,2160000,73.10 1933-04-27,72.64,73.06,70.72,71.71,1880000,71.71 1933-04-26,72.45,73.58,70.86,72.64,2920000,72.64 1933-04-25,73.69,73.70,70.77,72.45,3500000,72.45 1933-04-24,72.32,74.84,72.32,73.69,4810000,73.69 1933-04-21,72.27,72.80,68.64,69.78,5220000,69.78 1933-04-20,69.78,75.20,69.78,72.27,7130000,72.27 1933-04-19,63.56,68.70,63.56,68.31,5090000,68.31 1933-04-18,61.59,63.31,60.74,62.65,1440000,62.65 1933-04-17,62.75,62.75,60.93,61.59,1010000,61.59 1933-04-13,60.35,63.31,60.35,62.69,1660000,62.69 1933-04-12,61.08,61.08,59.68,60.26,750000,60.26 1933-04-11,62.11,62.65,60.71,61.15,1440000,61.15 1933-04-10,59.98,62.23,59.98,62.11,1760000,62.11 1933-04-07,58.80,60.06,58.18,58.78,950000,58.78 1933-04-06,57.73,59.56,57.73,58.80,1230000,58.80 1933-04-05,56.53,58.69,56.53,57.50,1150000,57.50 1933-04-04,55.69,56.61,55.00,56.09,720000,56.09 1933-04-03,55.66,56.62,55.26,55.69,600000,55.69 1933-03-31,56.49,57.05,54.94,55.40,880000,55.40 1933-03-30,56.81,57.17,56.10,56.49,620000,56.49 1933-03-29,57.90,57.90,56.57,56.81,640000,56.81 1933-03-28,56.53,58.02,56.12,57.92,600000,57.92 1933-03-27,57.62,57.62,56.31,56.53,500000,56.53 1933-03-24,58.06,58.41,56.90,57.93,640000,57.93 1933-03-23,57.69,59.91,57.69,58.06,980000,58.06 1933-03-22,57.58,58.48,56.35,56.86,990000,56.86 1933-03-21,59.85,59.85,57.23,57.58,1210000,57.58 1933-03-20,60.56,61.33,59.72,59.90,780000,59.90 1933-03-17,62.54,62.54,60.32,60.73,1730000,60.73 1933-03-16,62.10,64.56,62.05,62.95,3300000,62.95 1933-03-15,57.11,62.55,57.11,62.10,3070000,62.10 1933-03-03,52.54,55.44,51.54,53.84,1410000,53.84 1933-03-02,52.54,53.01,50.25,52.54,1000000,52.54 1933-03-01,51.39,52.97,50.81,52.54,790000,52.54 1933-02-28,50.16,52.12,49.83,51.39,910000,51.39 1933-02-27,50.93,52.13,49.68,50.16,1250000,50.16 1933-02-24,51.94,54.13,51.13,53.84,1070000,53.84 1933-02-23,53.60,53.60,51.65,51.94,1330000,51.94 1933-02-21,54.26,54.84,53.52,53.99,690000,53.99 1933-02-20,55.61,55.61,53.82,54.26,860000,54.26 1933-02-17,55.49,56.78,55.15,56.37,650000,56.37 1933-02-16,56.63,56.63,54.69,55.49,1080000,55.49 1933-02-15,56.57,57.59,56.08,56.71,750000,56.71 1933-02-14,58.19,58.19,56.04,56.57,1540000,56.57 1933-02-10,60.06,60.06,58.81,59.11,720000,59.11 1933-02-09,59.17,60.85,59.17,60.09,1080000,60.09 1933-02-08,58.38,59.21,57.85,58.87,720000,58.87 1933-02-07,58.07,58.67,57.50,58.38,590000,58.38 1933-02-06,57.55,58.27,56.65,58.07,670000,58.07 1933-02-03,58.03,58.46,57.11,58.11,910000,58.11 1933-02-02,58.90,58.90,57.45,58.03,1250000,58.03 1933-02-01,60.89,60.89,58.63,59.08,1190000,59.08 1933-01-31,60.77,61.34,60.48,60.90,660000,60.90 1933-01-30,60.71,61.05,60.09,60.77,480000,60.77 1933-01-27,61.73,61.98,60.03,61.43,970000,61.43 1933-01-26,62.33,62.79,61.61,61.73,810000,61.73 1933-01-25,61.30,62.66,60.84,62.33,750000,62.33 1933-01-24,61.46,61.99,60.67,61.30,490000,61.30 1933-01-23,61.79,62.10,60.55,61.46,660000,61.46 1933-01-20,61.02,62.68,60.90,61.63,710000,61.63 1933-01-19,60.37,61.99,60.37,61.02,620000,61.02 1933-01-18,61.75,62.03,60.07,60.36,690000,60.36 1933-01-17,61.62,62.09,60.93,61.75,660000,61.75 1933-01-16,63.09,63.87,61.38,61.62,870000,61.62 1933-01-13,63.09,63.94,62.12,63.18,830000,63.18 1933-01-12,63.81,64.80,62.84,63.09,920000,63.09 1933-01-11,64.35,65.28,63.62,63.81,1620000,63.81 1933-01-10,62.31,64.57,61.83,64.35,1150000,64.35 1933-01-09,62.96,63.64,61.90,62.31,930000,62.31 1933-01-06,62.25,63.85,62.07,62.96,1140000,62.96 1933-01-05,62.35,63.39,61.58,62.25,1140000,62.25 1933-01-04,59.54,62.62,59.54,62.35,1090000,62.35 1933-01-03,59.93,60.17,58.87,59.29,490000,59.29 1932-12-30,59.12,60.84,58.82,60.26,1050000,60.26 1932-12-29,57.85,59.38,57.39,59.12,1610000,59.12 1932-12-28,57.60,59.49,57.10,57.85,1600000,57.85 1932-12-27,57.98,58.57,56.95,57.60,800000,57.60 1932-12-23,56.55,57.30,56.07,56.80,930000,56.80 1932-12-22,58.97,59.29,56.24,56.55,1300000,56.55 1932-12-21,58.78,59.65,58.27,58.97,730000,58.97 1932-12-20,60.08,60.19,58.28,58.78,1000000,58.78 1932-12-19,60.11,61.51,59.82,60.08,920000,60.08 1932-12-16,61.16,61.40,59.75,60.52,920000,60.52 1932-12-15,61.93,62.89,60.98,61.16,1180000,61.16 1932-12-14,60.35,62.11,59.19,61.93,1020000,61.93 1932-12-13,61.38,61.38,59.98,60.35,730000,60.35 1932-12-12,61.25,62.50,60.68,61.48,920000,61.48 1932-12-09,60.05,61.90,59.28,61.58,1180000,61.58 1932-12-08,59.77,60.51,58.97,60.05,710000,60.05 1932-12-07,59.58,60.97,59.12,59.77,1190000,59.77 1932-12-06,56.95,59.96,56.95,59.58,1110000,59.58 1932-12-05,55.83,58.06,55.58,56.53,730000,56.53 1932-12-02,57.50,57.50,55.70,55.91,690000,55.91 1932-12-01,56.35,58.40,56.02,58.02,760000,58.02 1932-11-30,58.77,59.33,55.94,56.35,1090000,56.35 1932-11-29,59.17,59.74,58.31,58.77,530000,58.77 1932-11-28,58.89,59.71,58.10,59.17,540000,59.17 1932-11-25,59.47,59.54,57.47,58.78,1000000,58.78 1932-11-23,62.60,62.60,59.10,59.47,1200000,59.47 1932-11-22,63.65,64.40,62.86,63.16,540000,63.16 1932-11-21,64.14,64.68,63.23,63.65,610000,63.65 1932-11-18,62.99,64.73,62.66,62.96,730000,62.96 1932-11-17,63.24,63.83,62.18,62.99,710000,62.99 1932-11-16,65.26,65.26,62.56,63.24,950000,63.24 1932-11-15,65.57,66.17,63.54,65.26,1050000,65.26 1932-11-14,67.88,67.88,64.87,65.57,1310000,65.57 1932-11-11,65.54,68.27,65.41,68.03,2630000,68.03 1932-11-10,61.67,65.61,61.44,65.54,1570000,65.54 1932-11-09,64.58,65.42,61.02,61.67,1270000,61.67 1932-11-07,63.22,65.43,63.22,64.58,1610000,64.58 1932-11-04,58.99,62.07,58.99,61.53,970000,61.53 1932-11-03,58.53,59.06,57.21,58.28,1020000,58.28 1932-11-02,60.22,61.13,57.96,58.53,1100000,58.53 1932-11-01,61.57,61.57,59.86,60.22,520000,60.22 1932-10-31,62.09,62.19,61.06,61.90,390000,61.90 1932-10-28,61.86,63.51,61.81,63.09,690000,63.09 1932-10-27,61.36,62.83,60.77,61.86,720000,61.86 1932-10-26,60.32,61.73,59.03,61.36,860000,61.36 1932-10-25,61.03,61.69,59.70,60.32,600000,60.32 1932-10-24,60.85,61.58,60.07,61.03,550000,61.03 1932-10-21,63.64,63.64,60.71,61.01,1240000,61.01 1932-10-20,65.74,66.13,63.92,64.40,1060000,64.40 1932-10-19,63.49,66.06,63.35,65.74,1300000,65.74 1932-10-18,62.69,64.82,62.06,63.49,1020000,63.49 1932-10-17,64.07,64.07,62.21,62.69,770000,62.69 1932-10-14,60.27,65.45,60.27,63.84,2030000,63.84 1932-10-13,61.66,62.54,58.84,59.76,1230000,59.76 1932-10-11,59.07,62.52,59.07,61.66,1750000,61.66 1932-10-10,61.17,62.57,57.67,58.47,2280000,58.47 1932-10-07,66.28,66.89,62.16,62.67,2300000,62.67 1932-10-06,66.07,67.08,64.67,66.28,1940000,66.28 1932-10-05,70.92,70.92,65.90,66.07,2950000,66.07 1932-10-04,71.21,72.63,70.45,71.16,1240000,71.16 1932-10-03,72.09,72.32,69.88,71.21,1000000,71.21 1932-09-30,71.53,72.00,69.75,71.56,1160000,71.56 1932-09-29,73.52,74.36,71.24,71.53,1340000,71.53 1932-09-28,71.49,74.07,71.40,73.52,1380000,73.52 1932-09-27,71.06,73.42,69.98,71.49,1400000,71.49 1932-09-26,74.83,75.67,70.41,71.06,2080000,71.06 1932-09-23,72.71,75.16,72.42,73.92,2200000,73.92 1932-09-22,75.16,76.01,72.14,72.71,3690000,72.71 1932-09-21,69.46,75.53,69.46,75.16,4350000,75.16 1932-09-20,65.06,67.65,64.68,67.49,1250000,67.49 1932-09-19,66.44,67.40,64.82,65.06,1260000,65.06 1932-09-16,67.94,69.84,66.11,67.10,1910000,67.10 1932-09-15,65.88,68.58,64.27,67.94,3140000,67.94 1932-09-14,69.85,72.41,65.54,65.88,3250000,65.88 1932-09-13,71.54,71.54,66.38,69.85,5100000,69.85 1932-09-12,76.54,76.68,70.81,72.33,4050000,72.33 1932-09-09,77.49,79.91,75.69,76.19,4040000,76.19 1932-09-08,79.93,81.39,76.92,77.49,5370000,77.49 1932-09-07,77.28,80.28,76.78,79.93,4150000,79.93 1932-09-06,78.33,80.36,76.66,77.28,4360000,77.28 1932-09-02,74.00,77.12,74.00,76.77,3490000,76.77 1932-09-01,73.16,74.55,71.92,73.67,2420000,73.67 1932-08-31,74.30,74.44,71.11,73.16,3000000,73.16 1932-08-30,75.22,76.73,73.59,74.30,3300000,74.30 1932-08-29,75.61,77.01,74.25,75.22,3930000,75.22 1932-08-26,73.31,75.41,71.28,74.43,3120000,74.43 1932-08-25,73.55,75.88,72.54,73.31,4170000,73.31 1932-08-24,72.13,74.01,70.82,73.55,3690000,73.55 1932-08-23,70.87,73.80,70.69,72.13,4570000,72.13 1932-08-22,67.50,71.11,67.50,70.87,3180000,70.87 1932-08-19,67.93,69.47,66.10,66.84,2170000,66.84 1932-08-18,67.50,68.52,65.65,67.93,1790000,67.93 1932-08-17,68.91,70.56,65.62,67.50,2870000,67.50 1932-08-16,67.16,70.54,67.16,68.91,3610000,68.91 1932-08-15,63.19,66.72,62.93,66.51,1910000,66.51 1932-08-12,68.90,69.06,62.45,63.11,3710000,63.11 1932-08-11,69.39,71.62,66.95,68.90,4400000,68.90 1932-08-10,67.08,71.34,65.65,69.39,4430000,69.39 1932-08-09,67.71,69.53,65.36,67.08,3840000,67.08 1932-08-08,66.56,71.49,64.86,67.71,5460000,67.71 1932-08-05,59.73,63.42,59.73,62.60,2680000,62.60 1932-08-04,58.22,62.13,57.90,59.63,3520000,59.63 1932-08-03,53.16,58.69,52.99,58.22,2400000,58.22 1932-08-02,54.94,55.57,52.40,53.16,1440000,53.16 1932-08-01,54.26,56.92,53.59,54.94,2110000,54.94 1932-07-29,52.61,54.68,51.52,53.89,2100000,53.89 1932-07-28,51.34,53.84,50.67,52.61,2730000,52.61 1932-07-27,49.04,51.71,48.18,51.34,1700000,51.34 1932-07-26,49.78,50.41,48.49,49.04,1500000,49.04 1932-07-25,48.01,50.23,48.01,49.78,1550000,49.78 1932-07-22,46.50,48.31,46.35,47.69,1450000,47.69 1932-07-21,45.43,46.86,45.12,46.50,930000,46.50 1932-07-20,44.22,45.56,44.22,45.43,630000,45.43 1932-07-19,44.07,44.51,43.53,43.79,470000,43.79 1932-07-18,45.29,45.61,43.83,44.07,610000,44.07 1932-07-15,44.34,45.82,43.74,45.47,810000,45.47 1932-07-14,44.88,45.85,43.91,44.34,1000000,44.34 1932-07-13,42.68,45.05,42.35,44.88,980000,44.88 1932-07-12,42.99,43.65,42.36,42.68,700000,42.68 1932-07-11,41.63,43.03,40.92,42.99,600000,42.99 1932-07-08,41.81,42.61,40.56,41.22,720000,41.22 1932-07-07,44.08,44.26,41.63,41.81,780000,41.81 1932-07-06,43.47,44.50,42.31,44.08,730000,44.08 1932-07-05,44.39,44.43,42.53,43.47,610000,43.47 1932-07-01,42.84,44.63,42.64,44.39,610000,44.39 1932-06-30,43.66,44.44,42.41,42.84,630000,42.84 1932-06-29,43.18,44.21,42.54,43.66,630000,43.66 1932-06-28,42.93,44.30,42.31,43.18,830000,43.18 1932-06-27,44.76,44.82,42.52,42.93,770000,42.93 1932-06-24,46.83,47.57,44.55,44.84,770000,44.84 1932-06-23,46.27,47.47,46.15,46.83,470000,46.83 1932-06-22,46.58,46.66,45.43,46.27,610000,46.27 1932-06-21,47.80,48.42,46.47,46.58,500000,46.58 1932-06-20,47.55,48.66,47.41,47.80,390000,47.80 1932-06-17,50.34,50.36,47.44,47.56,790000,47.56 1932-06-16,50.62,51.43,49.73,50.34,850000,50.34 1932-06-15,49.37,51.43,49.37,50.62,1160000,50.62 1932-06-14,48.11,49.70,47.59,49.00,760000,49.00 1932-06-13,48.26,48.97,47.12,48.11,570000,48.11 1932-06-10,45.32,49.52,45.22,48.94,1270000,48.94 1932-06-09,45.20,47.55,44.45,45.32,1190000,45.32 1932-06-08,47.21,47.21,45.01,45.20,990000,45.20 1932-06-07,49.32,49.74,47.18,47.47,830000,47.47 1932-06-06,50.63,50.63,48.54,49.32,960000,49.32 1932-06-03,47.35,50.29,47.35,48.40,1890000,48.40 1932-06-02,44.93,47.74,43.49,47.25,1870000,47.25 1932-06-01,44.74,48.60,44.13,44.93,1840000,44.93 1932-05-31,46.93,46.93,44.27,44.74,1480000,44.74 1932-05-27,49.94,49.94,47.17,47.47,900000,47.47 1932-05-26,49.10,50.72,47.02,49.99,1850000,49.99 1932-05-25,50.79,50.79,48.65,49.10,1300000,49.10 1932-05-24,52.98,53.20,50.59,50.85,980000,50.85 1932-05-23,53.04,54.34,52.61,52.98,560000,52.98 1932-05-20,53.14,55.50,52.97,53.31,770000,53.31 1932-05-19,52.81,53.88,51.79,53.14,680000,53.14 1932-05-18,54.04,54.68,52.28,52.81,680000,52.81 1932-05-17,53.96,55.65,52.16,54.04,930000,54.04 1932-05-16,52.48,54.63,50.21,53.96,1310000,53.96 1932-05-13,55.33,55.33,53.23,53.46,870000,53.46 1932-05-12,57.71,57.71,54.91,55.62,920000,55.62 1932-05-11,57.68,59.52,57.47,57.83,690000,57.83 1932-05-10,57.04,58.94,56.68,57.68,740000,57.68 1932-05-09,58.04,58.74,56.29,57.04,640000,57.04 1932-05-06,54.58,59.76,54.58,59.01,1630000,59.01 1932-05-05,54.88,55.74,52.73,54.10,1000000,54.10 1932-05-04,54.15,55.21,52.33,54.88,1320000,54.88 1932-05-03,55.37,56.12,53.80,54.15,900000,54.15 1932-05-02,56.11,56.28,54.20,55.37,780000,55.37 1932-04-29,57.81,57.81,55.37,55.93,1160000,55.93 1932-04-28,61.28,61.36,57.98,58.24,930000,58.24 1932-04-27,59.71,62.15,59.40,61.28,1120000,61.28 1932-04-26,58.92,61.01,58.51,59.71,790000,59.71 1932-04-25,59.22,60.51,58.06,58.92,640000,58.92 1932-04-22,61.39,61.39,58.26,58.88,920000,58.88 1932-04-21,59.46,62.71,59.04,62.01,1110000,62.01 1932-04-20,59.75,60.81,58.70,59.46,990000,59.46 1932-04-19,60.85,61.45,58.91,59.75,1030000,59.75 1932-04-18,63.21,63.21,60.57,60.85,850000,60.85 1932-04-15,63.27,66.51,62.21,64.49,1540000,64.49 1932-04-14,61.18,63.84,59.10,63.27,1720000,63.27 1932-04-13,62.33,63.74,60.66,61.18,1100000,61.18 1932-04-12,62.04,64.13,60.62,62.33,1550000,62.33 1932-04-11,64.48,64.54,60.76,62.04,1700000,62.04 1932-04-08,65.73,65.73,61.98,62.90,2130000,62.90 1932-04-07,66.46,68.29,65.23,66.20,1800000,66.20 1932-04-06,68.07,68.93,65.85,66.46,3000000,66.46 1932-04-05,70.67,70.67,67.29,68.07,1480000,68.07 1932-04-04,71.30,71.84,68.32,71.19,1610000,71.19 1932-04-01,73.28,74.38,71.21,72.18,1530000,72.18 1932-03-31,77.15,77.80,72.49,73.28,1480000,73.28 1932-03-30,75.50,77.64,75.08,77.15,1010000,77.15 1932-03-29,75.09,76.98,74.68,75.50,1110000,75.50 1932-03-28,75.69,75.79,73.55,75.09,1350000,75.09 1932-03-24,78.64,79.58,77.49,77.99,840000,77.99 1932-03-23,79.55,80.08,78.23,78.64,840000,78.64 1932-03-22,79.90,80.59,77.79,79.55,1080000,79.55 1932-03-21,78.09,80.19,77.32,79.90,890000,79.90 1932-03-18,80.59,80.59,77.63,78.82,1410000,78.82 1932-03-17,79.11,81.55,77.57,80.87,1770000,80.87 1932-03-16,81.02,81.84,78.76,79.11,1460000,79.11 1932-03-15,81.12,82.44,79.66,81.02,1470000,81.02 1932-03-14,84.30,84.30,80.44,81.12,2030000,81.12 1932-03-11,85.70,85.70,83.26,83.61,1260000,83.61 1932-03-10,86.94,87.47,85.44,86.25,1050000,86.25 1932-03-09,88.78,89.87,86.57,86.94,1330000,86.94 1932-03-08,87.16,89.87,86.90,88.78,1640000,88.78 1932-03-07,88.49,89.78,86.80,87.16,1580000,87.16 1932-03-04,86.13,87.87,84.54,86.11,1510000,86.11 1932-03-03,86.28,88.35,85.47,86.13,1720000,86.13 1932-03-02,82.10,86.50,82.10,86.28,1760000,86.28 1932-03-01,81.44,82.20,80.50,81.87,730000,81.87 1932-02-29,82.02,83.89,80.84,81.44,880000,81.44 1932-02-26,82.05,83.53,81.37,82.09,890000,82.09 1932-02-25,82.73,82.92,80.13,82.05,1040000,82.05 1932-02-24,80.26,83.32,79.57,82.73,1080000,82.73 1932-02-23,83.59,84.03,79.85,80.26,1280000,80.26 1932-02-19,85.26,89.84,85.26,85.98,2430000,85.98 1932-02-18,82.24,85.74,81.45,85.13,1680000,85.13 1932-02-17,85.75,87.18,81.67,82.24,2190000,82.24 1932-02-16,82.18,86.51,80.49,85.75,2500000,85.75 1932-02-15,85.36,85.36,80.88,82.18,1980000,82.18 1932-02-11,74.27,79.62,74.27,78.60,2560000,78.60 1932-02-10,72.38,73.98,70.64,71.80,1300000,71.80 1932-02-09,73.45,74.50,71.85,72.38,1160000,72.38 1932-02-08,74.45,75.15,72.31,73.45,1150000,73.45 1932-02-05,77.50,77.50,74.71,75.00,1080000,75.00 1932-02-04,78.26,78.88,77.15,77.66,680000,77.66 1932-02-03,77.82,78.96,76.77,78.26,810000,78.26 1932-02-02,79.63,80.74,77.61,77.82,1120000,77.82 1932-02-01,76.32,80.62,76.32,79.63,1520000,79.63 1932-01-29,76.73,77.14,74.19,76.55,1530000,76.55 1932-01-28,77.82,78.03,75.85,76.73,1120000,76.73 1932-01-27,79.20,79.20,76.66,77.82,1280000,77.82 1932-01-26,78.92,80.79,78.92,79.76,760000,79.76 1932-01-25,77.98,79.94,77.42,78.66,830000,78.66 1932-01-22,83.42,83.51,78.56,78.81,1560000,78.81 1932-01-21,83.57,85.03,82.70,83.42,1240000,83.42 1932-01-20,81.10,83.79,80.45,83.57,1210000,83.57 1932-01-19,81.45,82.79,80.35,81.10,1090000,81.10 1932-01-18,84.44,85.32,81.29,81.45,1380000,81.45 1932-01-15,85.35,86.59,83.24,85.88,1640000,85.88 1932-01-14,84.70,87.78,84.70,85.35,2650000,85.35 1932-01-13,79.96,84.67,79.96,84.36,2070000,84.36 1932-01-12,80.44,82.08,78.84,79.39,1360000,79.39 1932-01-11,79.98,82.20,77.23,80.44,1800000,80.44 1932-01-08,78.03,82.11,76.74,81.80,1970000,81.80 1932-01-07,76.31,80.17,76.11,78.03,2180000,78.03 1932-01-06,73.02,77.16,73.02,76.31,1840000,76.31 1932-01-05,71.59,72.78,69.85,71.24,1420000,71.24 1932-01-04,74.06,74.06,70.91,71.59,1510000,71.59 1931-12-31,77.14,79.92,76.92,77.90,1510000,77.90 1931-12-30,75.84,77.86,75.12,77.14,2110000,77.14 1931-12-29,73.84,77.81,73.54,75.84,2440000,75.84 1931-12-28,75.84,76.27,72.41,73.84,2000000,73.84 1931-12-24,76.02,77.45,75.14,75.84,1110000,75.84 1931-12-23,79.55,80.17,75.42,76.02,1560000,76.02 1931-12-22,78.08,80.32,77.26,79.55,1400000,79.55 1931-12-21,80.75,81.76,77.55,78.08,1930000,78.08 1931-12-18,73.79,81.10,72.62,80.69,3620000,80.69 1931-12-17,76.33,76.33,71.79,73.79,2940000,73.79 1931-12-16,78.60,80.00,75.93,76.49,1960000,76.49 1931-12-15,77.22,79.44,75.50,78.60,2630000,78.60 1931-12-14,78.93,82.57,76.15,77.22,2890000,77.22 1931-12-11,82.46,83.11,79.26,79.63,2350000,79.63 1931-12-10,84.14,84.15,80.75,82.46,2660000,82.46 1931-12-09,86.50,86.52,82.49,84.14,2260000,84.14 1931-12-08,90.11,90.98,85.81,86.50,1600000,86.50 1931-12-07,90.14,92.60,89.16,90.11,1460000,90.11 1931-12-04,89.70,91.97,85.75,86.76,1920000,86.76 1931-12-03,87.90,90.59,86.28,89.70,1800000,89.70 1931-12-02,91.17,93.06,87.39,87.90,1890000,87.90 1931-12-01,93.38,93.38,87.78,91.17,2030000,91.17 1931-11-30,90.02,95.77,89.35,93.87,2000000,93.87 1931-11-27,93.79,93.79,90.65,91.55,1820000,91.55 1931-11-25,98.54,98.54,93.67,94.15,1500000,94.15 1931-11-24,96.60,100.10,96.53,98.61,1250000,98.61 1931-11-23,97.42,98.83,95.00,96.60,1350000,96.60 1931-11-20,100.99,100.99,96.45,97.96,2040000,97.96 1931-11-19,101.69,103.81,99.83,101.25,1510000,101.25 1931-11-18,105.86,105.86,101.21,101.69,1670000,101.69 1931-11-17,104.76,108.02,103.76,106.16,1460000,106.16 1931-11-16,106.35,107.86,103.43,104.76,1510000,104.76 1931-11-13,111.95,112.39,106.71,107.33,1790000,107.33 1931-11-12,112.01,114.61,110.86,111.95,1440000,111.95 1931-11-11,113.98,114.63,110.38,112.01,1490000,112.01 1931-11-10,116.58,116.58,112.24,113.98,1750000,113.98 1931-11-09,115.60,119.15,114.47,116.79,3050000,116.79 1931-11-06,108.58,113.28,106.43,112.72,2280000,112.72 1931-11-05,108.33,110.68,107.45,108.58,1520000,108.58 1931-11-04,104.50,108.85,103.19,108.33,1480000,108.33 1931-11-02,105.43,107.76,103.94,104.50,1460000,104.50 1931-10-30,100.75,104.51,100.75,103.97,1560000,103.97 1931-10-29,100.52,101.66,98.19,100.66,1340000,100.66 1931-10-28,104.25,104.50,99.20,100.52,1770000,100.52 1931-10-27,106.31,106.31,102.43,104.25,1390000,104.25 1931-10-26,109.36,109.36,105.69,106.37,1190000,106.37 1931-10-23,105.02,109.17,104.58,108.88,1330000,108.88 1931-10-22,108.39,108.58,104.09,105.02,1390000,105.02 1931-10-21,108.65,109.69,103.86,108.39,2240000,108.39 1931-10-20,104.69,109.59,104.69,108.65,2510000,108.65 1931-10-19,102.28,104.19,100.87,103.45,860000,103.45 1931-10-16,98.71,103.19,98.24,102.49,1420000,102.49 1931-10-15,97.45,102.67,97.45,98.71,1380000,98.71 1931-10-14,100.24,102.50,96.01,97.27,1640000,97.27 1931-10-13,105.37,105.37,99.74,100.24,1250000,100.24 1931-10-09,105.79,108.98,102.79,104.46,3220000,104.46 1931-10-08,98.19,106.43,98.19,105.79,2870000,105.79 1931-10-07,99.34,103.84,96.79,97.32,2820000,97.32 1931-10-06,87.51,100.49,87.51,99.34,4310000,99.34 1931-10-05,92.14,92.14,85.51,86.48,3190000,86.48 1931-10-02,95.66,100.03,93.64,96.88,2530000,96.88 1931-10-01,96.61,98.51,92.88,95.66,3640000,95.66 1931-09-30,99.80,102.39,95.76,96.61,3210000,96.61 1931-09-29,104.39,104.64,99.02,99.80,2900000,99.80 1931-09-28,107.36,108.80,103.58,104.39,1490000,104.39 1931-09-25,107.79,112.64,104.73,109.86,2850000,109.86 1931-09-24,115.99,116.95,106.64,107.79,3050000,107.79 1931-09-23,110.77,117.75,110.77,115.99,2930000,115.99 1931-09-22,110.83,112.65,108.12,109.40,2050000,109.40 1931-09-21,111.74,114.59,104.79,110.83,4400000,110.83 1931-09-18,121.27,121.27,114.47,115.08,2900000,115.08 1931-09-17,119.26,123.28,117.29,121.76,2420000,121.76 1931-09-16,120.59,123.10,118.41,119.26,1980000,119.26 1931-09-15,121.30,123.03,118.70,120.59,2170000,120.59 1931-09-14,123.00,123.00,119.12,121.30,2450000,121.30 1931-09-11,127.30,129.47,124.50,128.23,1970000,128.23 1931-09-10,128.43,130.45,126.04,127.30,1510000,127.30 1931-09-09,129.19,130.67,126.36,128.43,2020000,128.43 1931-09-08,131.57,131.57,127.91,129.19,2040000,129.19 1931-09-04,133.14,133.82,131.44,132.62,1200000,132.62 1931-09-03,136.54,136.54,132.21,133.14,2130000,133.14 1931-09-02,140.08,140.08,136.62,137.31,960000,137.31 1931-09-01,139.41,140.54,138.51,140.13,540000,140.13 1931-08-31,142.07,142.07,138.96,139.41,740000,139.41 1931-08-28,138.82,142.11,138.82,140.78,930000,140.78 1931-08-27,139.93,140.75,137.88,138.66,830000,138.66 1931-08-26,136.65,140.32,135.98,139.93,840000,139.93 1931-08-25,137.62,139.22,135.69,136.65,860000,136.65 1931-08-24,137.76,137.99,135.62,137.62,820000,137.62 1931-08-21,141.93,142.49,137.35,138.60,1310000,138.60 1931-08-20,141.72,143.93,140.96,141.93,1070000,141.93 1931-08-19,141.26,142.61,140.04,141.72,1080000,141.72 1931-08-18,140.98,144.43,139.36,141.26,1710000,141.26 1931-08-17,144.27,144.27,140.34,140.98,1320000,140.98 1931-08-14,140.82,145.05,140.82,144.15,1830000,144.15 1931-08-13,137.63,141.30,137.03,140.22,1380000,140.22 1931-08-12,140.16,140.99,137.03,137.63,1260000,137.63 1931-08-11,134.26,141.42,133.80,140.16,1600000,140.16 1931-08-10,134.85,134.85,132.79,134.26,710000,134.26 1931-08-07,133.77,135.72,132.96,135.13,740000,135.13 1931-08-06,134.10,134.93,132.55,133.77,910000,133.77 1931-08-05,135.83,135.83,133.59,134.10,820000,134.10 1931-08-04,137.50,137.77,134.85,136.50,720000,136.50 1931-08-03,136.65,139.35,136.36,137.50,880000,137.50 1931-07-31,136.93,138.12,133.70,135.39,1220000,135.39 1931-07-30,136.19,138.05,134.33,136.93,1350000,136.93 1931-07-29,139.26,139.26,134.99,136.19,1580000,136.19 1931-07-28,139.65,142.12,139.65,141.53,650000,141.53 1931-07-27,138.24,140.16,137.72,139.64,570000,139.64 1931-07-24,142.41,142.41,138.20,139.01,1070000,139.01 1931-07-23,142.52,143.77,140.81,142.63,790000,142.63 1931-07-22,145.88,145.88,142.11,142.52,990000,142.52 1931-07-21,144.48,147.69,144.21,146.70,1150000,146.70 1931-07-20,142.75,145.00,142.75,144.48,710000,144.48 1931-07-17,141.99,144.84,141.44,142.61,1270000,142.61 1931-07-16,137.86,142.30,137.30,141.99,1520000,141.99 1931-07-15,140.13,140.13,134.39,137.86,2610000,137.86 1931-07-14,142.43,143.19,139.67,140.85,1110000,140.85 1931-07-13,143.44,143.44,139.59,142.43,1280000,142.43 1931-07-10,144.91,148.50,143.46,146.97,1290000,146.97 1931-07-09,143.83,145.97,142.24,144.91,1510000,144.91 1931-07-08,145.92,147.24,141.36,143.83,2360000,143.83 1931-07-07,152.80,155.39,144.65,145.92,3010000,145.92 1931-07-06,154.08,154.08,151.20,152.80,1050000,152.80 1931-07-03,152.21,156.74,152.21,155.26,2050000,155.26 1931-07-02,152.66,154.84,150.72,151.48,1330000,151.48 1931-07-01,150.18,153.86,147.44,152.66,1710000,152.66 1931-06-30,152.67,153.67,148.63,150.18,1950000,150.18 1931-06-29,156.59,156.59,151.30,152.67,2140000,152.67 1931-06-26,150.75,155.50,150.75,154.04,3120000,154.04 1931-06-25,151.60,156.33,148.79,150.36,4320000,150.36 1931-06-24,144.56,153.42,144.56,151.60,5070000,151.60 1931-06-23,145.82,146.71,141.41,143.89,2600000,143.89 1931-06-22,140.08,147.97,140.08,145.82,4590000,145.82 1931-06-19,130.56,131.86,128.64,130.31,1150000,130.31 1931-06-18,133.58,133.58,130.09,130.56,1150000,130.56 1931-06-17,135.47,135.93,132.91,133.68,920000,133.68 1931-06-16,135.26,136.39,132.93,135.47,1120000,135.47 1931-06-15,137.03,138.58,134.82,135.26,1270000,135.26 1931-06-12,136.57,138.16,133.98,136.98,1590000,136.98 1931-06-11,136.82,138.47,134.24,136.57,1750000,136.57 1931-06-10,132.97,137.30,132.04,136.82,1800000,136.82 1931-06-09,135.92,138.88,132.08,132.97,1890000,132.97 1931-06-08,129.91,136.40,127.96,135.92,1710000,135.92 1931-06-05,134.73,138.89,131.69,133.33,2850000,133.33 1931-06-04,130.37,136.10,128.35,134.73,3170000,134.73 1931-06-03,121.70,130.64,120.79,130.37,3310000,130.37 1931-06-02,122.77,126.20,119.89,121.70,3320000,121.70 1931-06-01,128.40,128.40,121.76,122.77,3100000,122.77 1931-05-29,131.81,134.60,127.30,128.46,2050000,128.46 1931-05-28,130.76,134.16,128.72,131.81,2090000,131.81 1931-05-27,133.11,134.59,127.95,130.76,2510000,130.76 1931-05-26,132.87,136.38,130.75,133.11,2410000,133.11 1931-05-25,137.43,137.43,132.15,132.87,1880000,132.87 1931-05-22,139.54,141.37,136.93,139.49,1560000,139.49 1931-05-21,137.74,141.07,135.19,139.54,2350000,139.54 1931-05-20,138.86,142.49,136.18,137.74,2320000,137.74 1931-05-19,139.52,141.93,136.05,138.86,2780000,138.86 1931-05-18,142.95,143.09,138.54,139.52,2540000,139.52 1931-05-15,146.64,147.23,141.84,144.49,2380000,144.49 1931-05-14,149.63,150.61,146.02,146.64,1770000,146.64 1931-05-13,150.24,152.63,147.55,149.63,1670000,149.63 1931-05-12,151.56,152.11,148.28,150.24,1310000,150.24 1931-05-11,151.31,153.37,148.19,151.56,1650000,151.56 1931-05-08,148.88,155.65,147.43,154.41,2660000,154.41 1931-05-07,149.73,152.57,146.77,148.88,1690000,148.88 1931-05-06,148.99,150.54,145.65,149.73,1500000,149.73 1931-05-05,150.50,153.19,147.88,148.99,1580000,148.99 1931-05-04,147.49,151.26,146.80,150.50,1360000,150.50 1931-05-01,151.19,153.82,144.91,145.58,2870000,145.58 1931-04-30,143.61,152.50,142.12,151.19,3340000,151.19 1931-04-29,147.59,147.59,141.78,143.61,3180000,143.61 1931-04-28,149.78,151.09,144.52,147.95,2860000,147.95 1931-04-27,151.98,152.98,146.31,149.78,3650000,149.78 1931-04-24,157.43,159.45,153.55,155.76,2600000,155.76 1931-04-23,156.37,159.53,153.13,157.43,3820000,157.43 1931-04-22,158.83,160.06,155.61,156.37,2670000,156.37 1931-04-21,163.41,164.06,157.82,158.83,1990000,158.83 1931-04-20,162.37,164.42,159.45,163.41,1560000,163.41 1931-04-17,162.59,164.34,158.50,160.23,2550000,160.23 1931-04-16,164.66,165.64,161.63,162.59,2330000,162.59 1931-04-15,167.64,167.64,163.89,164.66,2050000,164.66 1931-04-14,171.07,173.24,167.11,168.43,1940000,168.43 1931-04-13,168.03,171.61,167.11,171.07,1630000,171.07 1931-04-10,168.77,171.06,166.96,168.72,1570000,168.72 1931-04-09,169.54,171.43,167.66,168.77,1940000,168.77 1931-04-08,167.03,171.49,166.34,169.54,2050000,169.54 1931-04-07,169.72,170.44,166.10,167.03,2190000,167.03 1931-04-06,172.43,174.69,169.44,169.72,1460000,169.72 1931-04-02,170.82,173.15,168.30,169.89,2510000,169.89 1931-04-01,172.36,173.72,169.18,170.82,2270000,170.82 1931-03-31,172.56,176.50,171.09,172.36,2410000,172.36 1931-03-30,174.06,175.42,170.64,172.56,3190000,172.56 1931-03-27,181.70,182.02,176.63,177.30,2950000,177.30 1931-03-26,184.20,185.56,180.85,181.70,2550000,181.70 1931-03-25,186.00,187.18,183.20,184.20,2100000,184.20 1931-03-24,184.32,186.86,181.65,186.00,1880000,186.00 1931-03-23,185.24,186.38,182.05,184.32,1990000,184.32 1931-03-20,186.56,189.31,185.15,187.72,2740000,187.72 1931-03-19,184.06,188.42,184.06,186.56,3530000,186.56 1931-03-18,180.61,184.53,179.62,183.95,2100000,183.95 1931-03-17,183.61,185.82,179.94,180.61,2800000,180.61 1931-03-16,180.76,184.11,180.32,183.61,2130000,183.61 1931-03-13,180.14,180.47,175.89,178.91,2380000,178.91 1931-03-12,181.91,182.96,178.57,180.14,2490000,180.14 1931-03-11,183.63,185.01,180.51,181.91,2290000,181.91 1931-03-10,185.38,188.10,182.49,183.63,3240000,183.63 1931-03-09,183.85,186.51,181.80,185.38,2850000,185.38 1931-03-06,184.69,186.62,178.49,179.73,3860000,179.73 1931-03-05,180.96,185.18,179.41,184.69,2730000,184.69 1931-03-04,183.76,184.65,179.39,180.96,3090000,180.96 1931-03-03,184.38,186.56,182.00,183.76,2940000,183.76 1931-03-02,189.66,191.93,183.53,184.38,3320000,184.38 1931-02-27,192.23,194.53,188.92,190.34,3730000,190.34 1931-02-26,190.72,195.95,189.81,192.23,4620000,192.23 1931-02-25,194.36,195.17,188.75,190.72,4390000,190.72 1931-02-24,191.32,196.96,190.19,194.36,5350000,194.36 1931-02-20,184.86,189.55,184.86,188.22,3830000,188.22 1931-02-19,181.51,185.35,181.51,184.46,2480000,184.46 1931-02-18,179.55,184.69,179.22,181.10,2840000,181.10 1931-02-17,182.88,186.29,178.70,179.55,3990000,179.55 1931-02-16,180.68,184.77,180.68,182.88,3170000,182.88 1931-02-13,181.88,184.50,179.14,180.99,2750000,180.99 1931-02-11,181.20,185.89,179.14,181.88,4700000,181.88 1931-02-10,177.72,184.12,176.83,181.20,4760000,181.20 1931-02-09,173.24,178.58,173.24,177.72,4130000,177.72 1931-02-06,169.38,171.84,168.55,169.88,1660000,169.88 1931-02-05,171.13,171.31,167.16,169.38,1490000,169.38 1931-02-04,169.71,172.13,168.89,171.13,1520000,171.13 1931-02-03,168.71,170.77,167.59,169.71,1190000,169.71 1931-02-02,167.55,169.32,165.60,168.71,1160000,168.71 1931-01-30,168.87,172.42,168.15,169.34,2210000,169.34 1931-01-29,166.84,169.82,164.81,168.87,1650000,168.87 1931-01-28,170.44,170.44,165.69,166.84,1620000,166.84 1931-01-27,171.19,172.33,168.91,170.82,1600000,170.82 1931-01-26,169.80,172.12,168.03,171.19,1540000,171.19 1931-01-23,168.87,172.97,168.87,171.84,2870000,171.84 1931-01-22,164.76,168.78,164.25,168.46,1860000,168.46 1931-01-21,165.82,167.18,163.29,164.76,1410000,164.76 1931-01-20,162.06,166.42,162.06,165.82,1330000,165.82 1931-01-19,162.89,163.18,160.09,161.45,1120000,161.45 1931-01-16,162.82,165.55,161.52,164.94,1320000,164.94 1931-01-15,167.46,167.72,161.95,162.82,1930000,162.82 1931-01-14,165.95,168.20,164.90,167.46,1280000,167.46 1931-01-13,167.99,168.42,164.76,165.95,1710000,165.95 1931-01-12,171.71,172.12,167.23,167.99,1500000,167.99 1931-01-09,173.04,175.66,169.68,170.18,2800000,170.18 1931-01-08,171.86,173.62,170.02,173.04,1710000,173.04 1931-01-07,172.66,175.32,171.07,171.86,2140000,171.86 1931-01-06,170.71,173.48,168.43,172.66,1910000,172.66 1931-01-05,172.12,173.30,167.77,170.71,2090000,170.71 1931-01-02,164.58,170.09,161.46,169.84,2030000,169.84 1930-12-31,163.09,167.99,162.48,164.58,1940000,164.58 1930-12-30,160.16,165.34,159.68,163.09,3430000,163.09 1930-12-29,160.30,162.60,158.41,160.16,2790000,160.16 1930-12-26,165.20,166.96,160.63,161.18,1800000,161.18 1930-12-24,163.57,168.00,163.57,165.20,1580000,165.20 1930-12-23,162.42,165.93,160.22,162.93,2450000,162.93 1930-12-22,169.42,170.02,162.15,162.42,2100000,162.42 1930-12-19,166.71,170.43,164.96,168.99,2270000,168.99 1930-12-18,165.60,171.64,164.99,166.71,3290000,166.71 1930-12-17,157.51,166.83,154.45,165.60,5010000,165.60 1930-12-16,163.34,166.04,156.44,157.51,4160000,157.51 1930-12-15,163.34,166.13,160.66,163.34,3440000,163.34 1930-12-12,170.31,173.08,167.99,168.68,2030000,168.68 1930-12-11,173.02,173.02,166.97,170.31,2890000,170.31 1930-12-10,176.50,178.10,170.21,173.98,3150000,173.98 1930-12-09,176.09,178.21,173.88,176.50,2120000,176.50 1930-12-08,177.98,177.98,174.27,176.09,1980000,176.09 1930-12-05,180.99,181.70,177.26,181.11,1590000,181.11 1930-12-04,184.06,184.06,179.75,180.99,1590000,180.99 1930-12-03,186.82,187.07,183.30,184.11,1220000,184.11 1930-12-02,185.48,187.96,183.36,186.82,1580000,186.82 1930-12-01,183.39,186.33,182.32,185.48,1100000,185.48 1930-11-28,183.06,183.06,178.88,180.91,1740000,180.91 1930-11-26,185.47,186.98,181.93,183.11,1950000,183.11 1930-11-25,188.27,191.28,185.17,185.47,2150000,185.47 1930-11-24,188.04,189.08,184.32,188.27,1630000,188.27 1930-11-21,187.09,191.28,185.32,190.30,2250000,190.30 1930-11-20,187.57,191.04,185.76,187.09,2630000,187.09 1930-11-19,183.42,188.61,182.21,187.57,2480000,187.57 1930-11-18,180.50,184.16,177.63,183.42,2020000,183.42 1930-11-17,185.13,185.13,178.86,180.50,2140000,180.50 1930-11-14,180.38,184.64,177.69,184.03,2640000,184.03 1930-11-13,177.33,183.08,174.96,180.38,3450000,180.38 1930-11-12,173.30,177.50,168.58,177.33,3420000,177.33 1930-11-11,171.60,176.93,169.38,173.30,3330000,173.30 1930-11-10,173.14,177.07,168.32,171.60,4420000,171.60 1930-11-07,180.72,181.00,172.85,174.38,2370000,174.38 1930-11-06,179.81,182.40,177.80,180.72,2450000,180.72 1930-11-05,185.39,185.47,178.78,179.81,2150000,179.81 1930-11-03,184.89,187.23,183.12,185.39,1260000,185.39 1930-10-31,188.00,188.00,181.64,183.35,2250000,183.35 1930-10-30,190.55,190.55,185.99,188.07,1910000,188.07 1930-10-29,194.35,194.35,189.33,190.73,1670000,190.73 1930-10-28,195.09,198.59,193.28,194.95,2020000,194.95 1930-10-27,193.34,195.73,189.17,195.09,1810000,195.09 1930-10-24,189.07,195.79,189.07,195.09,2760000,195.09 1930-10-23,184.98,190.95,184.75,188.10,2670000,188.10 1930-10-22,186.40,188.34,181.53,184.98,2740000,184.98 1930-10-21,193.32,193.95,184.22,186.40,2430000,186.40 1930-10-20,187.07,194.44,187.07,193.32,2140000,193.32 1930-10-17,195.30,195.30,186.74,187.37,2660000,187.37 1930-10-16,200.13,200.13,194.78,196.62,1860000,196.62 1930-10-15,196.70,201.64,193.40,200.26,2380000,200.26 1930-10-14,193.05,198.01,186.99,196.70,3390000,196.70 1930-10-10,192.00,198.86,186.70,198.50,6300000,198.50 1930-10-09,199.96,199.96,190.17,192.00,5050000,192.00 1930-10-08,203.62,205.21,198.61,200.56,2070000,200.56 1930-10-07,202.76,207.04,198.51,203.62,3570000,203.62 1930-10-06,209.01,209.01,201.90,202.76,2370000,202.76 1930-10-03,211.13,216.89,211.13,214.18,2050000,214.18 1930-10-02,214.14,214.76,206.25,211.04,2320000,211.04 1930-10-01,205.92,215.32,205.92,214.14,3160000,214.14 1930-09-30,208.14,209.95,201.95,204.90,4500000,204.90 1930-09-29,212.52,216.96,207.30,208.14,3760000,208.14 1930-09-26,217.75,220.21,211.31,213.27,3710000,213.27 1930-09-25,222.10,223.89,215.31,217.75,3070000,217.75 1930-09-24,226.75,228.87,218.08,222.10,3440000,222.10 1930-09-23,222.78,227.30,221.82,226.75,1920000,226.75 1930-09-22,229.29,229.29,222.00,222.78,2330000,222.78 1930-09-19,233.52,233.52,226.39,229.02,2950000,229.02 1930-09-18,237.45,237.45,233.47,234.18,1380000,234.18 1930-09-17,237.22,239.31,236.51,237.74,1190000,237.74 1930-09-16,236.62,237.75,232.85,237.22,1770000,237.22 1930-09-15,239.96,239.96,234.95,236.62,1560000,236.62 1930-09-12,242.88,244.42,239.49,241.17,1910000,241.17 1930-09-11,245.09,245.23,241.67,242.88,1740000,242.88 1930-09-10,244.29,247.21,243.30,245.09,2480000,245.09 1930-09-09,242.84,245.48,241.55,244.29,1940000,244.29 1930-09-08,243.64,246.08,241.78,242.84,2240000,242.84 1930-09-05,236.09,240.93,236.09,240.37,1650000,240.37 1930-09-04,237.45,239.65,234.35,236.04,1520000,236.04 1930-09-03,240.42,242.40,236.71,237.45,1750000,237.45 1930-09-02,240.42,242.77,238.51,240.42,1770000,240.42 1930-08-29,237.79,241.35,236.75,240.42,1860000,240.42 1930-08-28,237.93,239.33,235.19,237.79,1440000,237.79 1930-08-27,235.47,239.54,235.38,237.93,2200000,237.93 1930-08-26,231.52,236.30,230.73,235.47,1750000,235.47 1930-08-25,234.42,236.46,230.68,231.52,1600000,231.52 1930-08-22,231.27,234.04,229.64,232.63,1340000,232.63 1930-08-21,232.98,234.91,229.21,231.27,1710000,231.27 1930-08-20,230.68,235.26,229.84,232.98,1820000,232.98 1930-08-19,227.79,233.46,227.43,230.68,1860000,230.68 1930-08-18,228.02,229.08,224.42,227.79,1410000,227.79 1930-08-15,221.08,229.44,219.82,228.55,2110000,228.55 1930-08-14,220.35,224.38,219.24,221.08,1530000,221.08 1930-08-13,217.24,221.35,214.49,220.35,2290000,220.35 1930-08-12,223.74,223.74,216.48,217.24,2090000,217.24 1930-08-11,222.59,226.05,220.09,224.13,1750000,224.13 1930-08-08,231.73,231.73,222.24,222.82,3310000,222.82 1930-08-07,234.38,234.39,230.50,232.69,1450000,232.69 1930-08-06,237.99,237.99,233.67,234.38,1320000,234.38 1930-08-05,238.16,240.95,237.22,238.47,1220000,238.47 1930-08-04,234.50,238.57,233.26,238.16,1200000,238.16 1930-08-01,233.99,235.78,231.86,233.57,1090000,233.57 1930-07-31,231.08,235.19,229.09,233.99,2160000,233.99 1930-07-30,238.40,239.93,230.53,231.08,2510000,231.08 1930-07-29,240.81,241.53,237.00,238.40,1860000,238.40 1930-07-28,240.31,243.65,239.04,240.81,2430000,240.81 1930-07-25,235.51,238.58,233.77,237.48,1360000,237.48 1930-07-24,239.33,239.51,234.65,235.51,1480000,235.51 1930-07-23,234.94,241.76,234.94,239.33,2530000,239.33 1930-07-22,229.29,235.29,228.81,234.30,2080000,234.30 1930-07-21,236.58,236.58,228.72,229.29,1950000,229.29 1930-07-18,239.07,242.01,236.47,240.57,2750000,240.57 1930-07-17,235.63,240.27,234.03,239.07,2500000,239.07 1930-07-16,233.79,236.47,230.59,235.63,2590000,235.63 1930-07-15,234.21,237.19,231.73,233.79,3090000,233.79 1930-07-14,229.23,234.54,229.02,234.21,2740000,234.21 1930-07-11,227.39,228.65,223.97,224.86,1530000,224.86 1930-07-10,222.04,228.35,219.18,227.39,2170000,227.39 1930-07-09,219.11,223.52,219.11,222.04,1360000,222.04 1930-07-08,218.33,220.22,214.64,219.08,1560000,219.08 1930-07-07,221.31,221.31,216.33,218.33,1480000,218.33 1930-07-03,225.25,226.26,219.94,222.46,1380000,222.46 1930-07-02,223.03,227.24,222.14,225.25,1230000,225.25 1930-07-01,226.34,229.53,221.92,223.03,2280000,223.03 1930-06-30,219.12,226.85,219.06,226.34,1840000,226.34 1930-06-27,220.58,222.84,213.97,218.78,2080000,218.78 1930-06-26,215.58,222.11,214.25,220.58,2270000,220.58 1930-06-25,211.84,216.80,207.74,215.58,3400000,215.58 1930-06-24,219.58,222.89,211.07,211.84,2870000,211.84 1930-06-23,215.30,221.26,209.16,219.58,3840000,219.58 1930-06-20,228.97,232.69,219.70,221.92,5660000,221.92 1930-06-19,219.83,229.83,219.83,228.97,3760000,228.97 1930-06-18,226.29,226.29,212.27,218.84,6430000,218.84 1930-06-17,230.05,234.94,224.37,228.57,5020000,228.57 1930-06-16,242.18,242.18,228.94,230.05,5660000,230.05 1930-06-13,247.18,251.63,243.27,249.69,2230000,249.69 1930-06-12,249.08,250.90,241.00,247.18,3900000,247.18 1930-06-11,257.24,257.24,243.90,249.08,4480000,249.08 1930-06-10,250.78,257.72,247.62,257.29,4770000,257.29 1930-06-09,257.82,259.60,249.51,250.78,4650000,250.78 1930-06-06,268.59,268.69,263.29,263.93,2160000,263.93 1930-06-05,272.44,272.65,266.90,268.59,2390000,268.59 1930-06-04,271.18,274.03,269.54,272.44,1690000,272.44 1930-06-03,274.45,274.69,270.01,271.18,1750000,271.18 1930-06-02,275.07,276.86,273.03,274.45,1710000,274.45 1930-05-29,273.84,276.66,273.05,275.07,2200000,275.07 1930-05-28,272.43,275.17,270.64,273.84,2410000,273.84 1930-05-27,272.14,274.72,270.54,272.43,2260000,272.43 1930-05-26,271.33,276.18,270.64,272.14,2250000,272.14 1930-05-23,267.01,272.14,267.01,270.01,2160000,270.01 1930-05-22,265.52,268.65,262.53,266.89,1860000,266.89 1930-05-21,267.10,268.94,262.67,265.52,2080000,265.52 1930-05-20,265.87,268.40,260.76,267.10,3530000,267.10 1930-05-19,272.36,272.36,264.63,265.87,2410000,265.87 1930-05-16,269.91,272.96,268.54,271.52,2090000,271.52 1930-05-15,274.35,274.35,268.45,269.91,2680000,269.91 1930-05-14,274.17,277.22,272.22,274.40,3180000,274.40 1930-05-13,270.16,276.09,269.51,274.17,2700000,274.17 1930-05-12,272.01,275.11,268.56,270.16,3030000,270.16 1930-05-09,263.93,269.08,261.64,267.29,3010000,267.29 1930-05-08,263.69,266.11,257.74,263.93,3760000,263.93 1930-05-07,268.81,272.15,262.20,263.69,4300000,263.69 1930-05-06,259.68,270.34,259.04,268.81,4760000,268.81 1930-05-05,258.31,262.84,249.82,259.68,8280000,259.68 1930-05-02,274.59,276.81,264.93,266.56,5990000,266.56 1930-05-01,279.23,281.95,273.00,274.59,4640000,274.59 1930-04-30,278.43,283.51,275.97,279.23,4550000,279.23 1930-04-29,276.94,280.71,272.24,278.43,5410000,278.43 1930-04-28,285.46,286.12,275.71,276.94,4850000,276.94 1930-04-25,286.18,289.28,283.68,285.76,4730000,285.76 1930-04-24,288.78,290.58,283.74,286.18,5230000,286.18 1930-04-23,290.01,293.27,286.25,288.78,5570000,288.78 1930-04-22,288.23,291.39,284.28,290.01,4590000,290.01 1930-04-21,294.07,295.88,287.24,288.23,4490000,288.23 1930-04-17,292.20,296.05,290.38,294.07,3940000,294.07 1930-04-16,293.26,297.25,290.27,292.20,4400000,292.20 1930-04-15,293.18,295.69,289.34,293.26,4220000,293.26 1930-04-14,293.43,295.81,289.72,293.18,4150000,293.18 1930-04-11,292.19,296.35,288.42,292.65,5630000,292.65 1930-04-10,291.15,295.98,289.18,292.19,5680000,292.19 1930-04-09,288.36,293.36,287.37,291.15,5190000,291.15 1930-04-08,290.19,291.89,285.96,288.36,4690000,288.36 1930-04-07,289.96,293.43,287.03,290.19,5490000,290.19 1930-04-04,285.77,291.44,284.92,288.35,5930000,288.35 1930-04-03,285.27,288.17,282.29,285.77,4630000,285.77 1930-04-02,287.11,290.15,283.59,285.27,5300000,285.27 1930-04-01,286.10,290.15,283.64,287.11,5400000,287.11 1930-03-31,283.85,289.13,282.85,286.10,5160000,286.10 1930-03-28,281.63,287.06,280.83,283.85,5070000,283.85 1930-03-27,283.22,286.10,279.98,281.63,4710000,281.63 1930-03-26,280.50,285.38,279.31,283.22,5030000,283.22 1930-03-25,279.11,284.01,278.21,280.50,4530000,280.50 1930-03-24,276.43,280.92,275.03,279.11,4130000,279.11 1930-03-21,279.41,284.08,276.78,280.55,4630000,280.55 1930-03-20,277.88,282.23,275.25,279.41,3260000,279.41 1930-03-19,277.27,281.05,274.91,277.88,4340000,277.88 1930-03-18,274.26,279.79,273.90,277.27,4250000,277.27 1930-03-17,270.25,274.84,268.94,274.26,3640000,274.26 1930-03-14,273.47,275.82,270.38,271.34,3950000,271.34 1930-03-13,272.13,274.77,269.60,273.47,3850000,273.47 1930-03-12,276.25,277.06,270.01,272.13,4470000,272.13 1930-03-11,276.85,278.76,274.25,276.25,2640000,276.25 1930-03-10,275.46,279.40,273.71,276.85,3990000,276.85 1930-03-07,274.51,278.48,272.84,275.57,3640000,275.57 1930-03-06,270.59,276.05,269.01,274.51,3360000,274.51 1930-03-05,273.51,276.10,269.03,270.59,3720000,270.59 1930-03-04,271.11,275.19,269.16,273.51,3460000,273.51 1930-03-03,273.24,274.47,269.59,271.11,3630000,271.11 1930-02-28,269.39,272.55,267.41,271.11,3210000,271.11 1930-02-27,269.06,272.13,267.43,269.39,3310000,269.39 1930-02-26,262.94,269.92,262.94,269.06,3020000,269.06 1930-02-25,262.47,264.64,259.78,262.80,2630000,262.80 1930-02-24,265.81,266.33,261.40,262.47,2320000,262.47 1930-02-21,263.41,266.68,262.01,265.81,2570000,265.81 1930-02-20,268.46,269.72,262.43,263.41,3660000,263.41 1930-02-19,270.73,273.35,267.09,268.46,3490000,268.46 1930-02-18,270.54,274.41,268.98,270.73,3800000,270.73 1930-02-17,269.25,271.62,265.29,270.54,3290000,270.54 1930-02-14,272.27,274.20,268.60,271.52,3510000,271.52 1930-02-13,271.05,275.00,268.97,272.27,3670000,272.27 1930-02-11,268.56,272.67,267.00,271.05,3320000,271.05 1930-02-10,269.78,271.78,266.37,268.56,3170000,268.56 1930-02-07,268.56,271.62,265.36,267.82,3390000,267.82 1930-02-06,272.06,273.59,266.96,268.56,3710000,268.56 1930-02-05,268.85,274.01,268.85,272.06,4360000,272.06 1930-02-04,266.54,270.00,264.41,268.48,3230000,268.48 1930-02-03,268.41,271.54,264.84,266.54,3800000,266.54 1930-01-31,263.28,268.71,262.81,267.14,3740000,267.14 1930-01-30,262.18,266.30,260.48,263.28,3640000,263.28 1930-01-29,257.90,263.73,257.38,262.18,3250000,262.18 1930-01-28,260.93,261.89,256.70,257.90,2910000,257.90 1930-01-27,259.06,262.57,257.24,260.93,3460000,260.93 1930-01-24,253.52,258.98,252.98,256.31,3480000,256.31 1930-01-23,250.19,254.39,249.62,253.52,3230000,253.52 1930-01-22,249.58,251.85,248.60,250.19,2310000,250.19 1930-01-21,247.31,250.62,246.25,249.58,2230000,249.58 1930-01-20,246.84,248.92,244.86,247.31,1700000,247.31 1930-01-17,248.99,249.88,244.50,246.33,2680000,246.33 1930-01-16,251.54,253.49,248.16,248.99,3040000,248.99 1930-01-15,250.44,252.57,247.76,251.54,2630000,251.54 1930-01-14,249.62,252.39,248.98,250.44,1880000,250.44 1930-01-13,248.71,250.83,246.82,249.62,1460000,249.62 1930-01-10,249.68,252.91,248.80,250.03,2400000,250.03 1930-01-09,245.70,250.52,245.67,249.68,2400000,249.68 1930-01-08,246.50,248.04,243.80,245.70,1640000,245.70 1930-01-07,248.10,249.40,243.80,246.50,2030000,246.50 1930-01-06,248.85,250.37,245.49,248.10,2170000,248.10 1930-01-03,244.20,248.71,243.00,247.19,2070000,247.19 1930-01-02,248.48,252.29,241.78,244.20,2930000,244.20 1929-12-31,241.90,249.24,241.90,248.48,2680000,248.48 1929-12-30,238.43,242.95,235.95,241.06,4160000,241.06 1929-12-27,240.96,246.35,239.13,240.66,3350000,240.66 1929-12-26,234.07,242.62,233.89,240.96,2580000,240.96 1929-12-24,232.65,237.94,231.96,234.07,1000000,234.07 1929-12-23,235.42,236.37,226.39,232.65,3490000,232.65 1929-12-20,240.42,241.92,227.20,230.89,5550000,230.89 1929-12-19,246.84,247.14,238.80,240.42,3410000,240.42 1929-12-18,249.58,250.51,245.03,246.84,2290000,246.84 1929-12-17,245.88,250.23,243.63,249.58,2440000,249.58 1929-12-16,253.02,253.17,244.34,245.88,2590000,245.88 1929-12-13,243.14,251.79,239.58,249.60,4390000,249.60 1929-12-12,258.44,258.56,241.40,243.14,4510000,243.14 1929-12-11,262.20,264.23,256.45,258.44,3900000,258.44 1929-12-10,259.18,263.98,255.52,262.20,3650000,262.20 1929-12-09,263.46,267.56,257.41,259.18,5020000,259.18 1929-12-06,251.51,261.52,250.27,260.12,4720000,260.12 1929-12-05,254.64,256.45,249.55,251.51,4380000,251.51 1929-12-04,249.61,256.63,248.05,254.64,4440000,254.64 1929-12-03,241.70,251.13,241.38,249.61,3810000,249.61 1929-12-02,238.95,243.39,236.13,241.70,2510000,241.70 1929-11-27,235.35,240.66,233.59,238.95,2430000,238.95 1929-11-26,243.44,243.97,234.51,235.35,3630000,235.35 1929-11-25,245.74,246.06,237.41,243.44,3020000,243.44 1929-11-22,248.49,250.75,243.36,245.74,2930000,245.74 1929-11-21,241.23,249.57,238.61,248.49,3140000,248.49 1929-11-20,235.18,243.48,235.18,241.23,2830000,241.23 1929-11-19,227.56,234.56,222.93,234.02,2720000,234.02 1929-11-18,228.73,233.36,224.71,227.56,2750000,227.56 1929-11-15,222.50,232.77,222.50,228.73,4340000,228.73 1929-11-14,205.61,219.49,205.61,217.28,5570000,217.28 1929-11-13,209.74,211.92,195.35,198.69,7760000,198.69 1929-11-12,220.39,222.56,208.09,209.74,6450000,209.74 1929-11-11,235.13,235.13,219.34,220.39,3640000,220.39 1929-11-08,238.19,245.28,234.63,236.53,3220000,236.53 1929-11-07,232.13,242.10,217.84,238.19,7180000,238.19 1929-11-06,252.20,252.20,228.35,232.13,5920000,232.13 1929-11-04,269.75,269.75,255.43,257.68,6200000,257.68 1929-10-31,264.97,281.54,264.97,273.51,7150000,273.51 1929-10-30,230.98,260.93,230.98,258.47,10730000,258.47 1929-10-29,252.38,252.38,212.33,230.07,16410000,230.07 1929-10-28,295.18,295.18,256.75,260.64,9210000,260.64 1929-10-25,299.47,306.02,295.59,301.22,5920000,301.22 1929-10-24,305.85,312.76,272.32,299.47,12900000,299.47 1929-10-23,326.51,329.94,303.84,305.85,6370000,305.85 1929-10-22,322.03,333.01,322.03,326.51,4130000,326.51 1929-10-21,323.87,328.28,314.55,320.91,6090000,320.91 1929-10-18,341.86,343.12,332.16,333.29,3510000,333.29 1929-10-17,336.13,343.24,332.11,341.86,3860000,341.86 1929-10-16,346.99,346.99,335.12,336.13,4090000,336.13 1929-10-15,350.97,354.09,345.58,347.24,3110000,347.24 1929-10-14,352.69,358.20,348.94,350.97,2760000,350.97 1929-10-11,352.86,358.77,349.64,352.69,3960000,352.69 1929-10-10,346.66,355.63,345.63,352.86,4000000,352.86 1929-10-09,345.00,349.03,338.86,346.66,3160000,346.66 1929-10-08,345.72,349.67,340.86,345.00,3760000,345.00 1929-10-07,341.36,348.54,338.86,345.72,4260000,345.72 1929-10-04,329.95,333.28,320.45,325.17,5620000,325.17 1929-10-03,344.50,345.30,327.71,329.95,4750000,329.95 1929-10-02,342.57,350.19,339.45,344.50,3370000,344.50 1929-10-01,343.45,345.67,335.99,342.57,4530000,342.57 1929-09-30,347.17,349.37,341.06,343.45,3210000,343.45 1929-09-27,354.63,354.63,343.26,344.87,4590000,344.87 1929-09-26,352.57,358.16,349.73,355.95,4000000,355.95 1929-09-25,352.61,355.42,344.85,352.57,4960000,352.57 1929-09-24,359.00,363.67,350.84,352.61,4410000,352.61 1929-09-23,361.16,365.03,355.63,359.00,4390000,359.00 1929-09-20,369.97,371.10,360.44,362.05,4880000,362.05 1929-09-19,370.90,375.20,367.70,369.97,4130000,369.97 1929-09-18,368.52,374.03,365.65,370.90,4040000,370.90 1929-09-17,372.39,374.96,366.89,368.52,4290000,368.52 1929-09-16,367.01,373.63,364.80,372.39,4180000,372.39 1929-09-13,366.35,369.67,359.70,366.85,5070000,366.85 1929-09-12,370.91,375.52,363.11,366.35,5020000,366.35 1929-09-11,367.29,375.05,366.22,370.91,4790000,370.91 1929-09-10,374.93,379.16,364.46,367.29,4520000,367.29 1929-09-09,377.56,380.57,373.49,374.93,4860000,374.93 1929-09-06,369.77,378.71,369.46,376.29,5120000,376.29 1929-09-05,379.61,382.01,367.35,369.77,5560000,369.77 1929-09-04,380.12,380.12,376.33,379.61,4690000,379.61 1929-09-03,380.33,386.10,378.23,381.17,4440000,381.17 1929-08-30,376.18,383.96,376.16,380.33,4570000,380.33 1929-08-29,372.06,378.76,370.79,376.18,3480000,376.18 1929-08-28,373.79,377.56,370.34,372.06,3960000,372.06 1929-08-27,374.46,378.16,371.76,373.79,3900000,373.79 1929-08-26,375.44,380.18,372.09,374.46,4430000,374.46 1929-08-23,369.96,378.66,369.96,374.61,4800000,374.61 1929-08-22,365.55,373.45,365.39,369.95,3440000,369.95 1929-08-21,367.67,374.67,363.41,365.55,4720000,365.55 1929-08-20,366.31,372.59,366.31,367.67,4640000,367.67 1929-08-19,360.70,367.78,355.68,365.20,3980000,365.20 1929-08-16,356.84,364.39,356.84,361.49,4800000,361.49 1929-08-15,354.86,358.65,351.68,354.42,3410000,354.42 1929-08-14,354.03,361.55,352.05,354.86,4200000,354.86 1929-08-13,351.13,357.88,348.24,354.03,4100000,354.03 1929-08-12,345.71,354.36,345.71,351.13,3610000,351.13 1929-08-09,344.89,344.89,336.13,337.99,5020000,337.99 1929-08-08,348.44,354.17,347.79,352.10,2830000,352.10 1929-08-07,351.39,353.27,344.67,348.44,3160000,348.44 1929-08-06,352.50,354.52,346.98,351.39,3800000,351.39 1929-08-05,355.62,358.66,350.68,352.50,3860000,352.50 1929-08-02,350.56,358.31,349.77,353.08,4030000,353.08 1929-08-01,347.70,353.30,346.39,350.56,3320000,350.56 1929-07-31,343.12,349.79,342.65,347.70,3410000,347.70 1929-07-30,339.21,346.04,339.10,343.12,2690000,343.12 1929-07-29,343.73,344.93,336.36,339.21,2760000,339.21 1929-07-26,344.67,349.45,341.95,345.47,3550000,345.47 1929-07-25,343.04,348.15,340.09,344.67,3480000,344.67 1929-07-24,345.48,349.30,341.95,343.04,3780000,343.04 1929-07-23,341.37,347.85,339.65,345.48,3780000,345.48 1929-07-22,345.87,347.85,339.32,341.37,3680000,341.37 1929-07-19,344.59,349.19,343.15,345.20,4200000,345.20 1929-07-18,345.63,347.69,343.40,344.59,3730000,344.59 1929-07-17,344.24,349.79,341.41,345.63,4360000,345.63 1929-07-16,341.93,347.98,339.98,344.24,4500000,344.24 1929-07-15,345.94,347.04,340.05,341.93,4290000,341.93 1929-07-12,343.34,350.26,343.34,346.37,4760000,346.37 1929-07-11,343.30,347.12,340.12,343.04,4210000,343.04 1929-07-10,345.57,347.64,340.19,343.30,4210000,343.30 1929-07-09,346.55,349.29,342.00,345.57,4250000,345.57 1929-07-08,344.66,350.09,342.45,346.55,3520000,346.55 1929-07-05,341.99,348.67,340.84,344.27,3750000,344.27 1929-07-03,340.28,345.84,337.50,341.99,4690000,341.99 1929-07-02,335.22,343.07,333.48,340.28,4590000,340.28 1929-07-01,333.79,339.09,332.23,335.22,4090000,335.22 1929-06-28,328.91,335.25,328.15,331.65,3950000,331.65 1929-06-27,328.60,333.66,325.68,328.91,3910000,328.91 1929-06-26,326.16,332.75,325.13,328.60,4030000,328.60 1929-06-25,321.15,327.95,319.27,326.16,2930000,326.16 1929-06-24,322.23,325.73,319.91,321.15,3030000,321.15 1929-06-21,317.73,323.46,316.32,320.68,3190000,320.68 1929-06-20,316.41,320.43,314.32,317.73,2760000,317.73 1929-06-19,319.67,321.26,314.62,316.41,3060000,316.41 1929-06-18,319.33,323.30,317.64,319.67,3340000,319.67 1929-06-17,314.26,322.43,313.58,319.33,3210000,319.33 1929-06-14,313.05,317.39,311.76,313.68,3240000,313.68 1929-06-13,306.80,314.21,306.80,313.05,3160000,313.05 1929-06-12,306.64,309.29,304.25,306.68,2130000,306.68 1929-06-11,303.27,307.60,301.22,306.64,2140000,306.64 1929-06-10,305.12,307.60,301.86,303.27,2200000,303.27 1929-06-07,307.72,312.00,304.75,307.46,3080000,307.46 1929-06-06,307.68,310.50,305.33,307.72,2930000,307.72 1929-06-05,310.57,311.97,305.42,307.68,3340000,307.68 1929-06-04,304.33,311.44,304.33,310.57,3410000,310.57 1929-06-03,299.12,307.07,298.53,304.20,3020000,304.20 1929-05-31,296.76,300.27,290.02,297.41,3300000,297.41 1929-05-29,298.87,302.32,295.18,296.76,2980000,296.76 1929-05-28,293.42,300.08,291.80,298.87,3940000,298.87 1929-05-27,304.19,304.19,291.82,293.42,4350000,293.42 1929-05-24,308.09,313.30,304.32,305.64,3270000,305.64 1929-05-23,300.83,309.51,300.42,308.09,3810000,308.09 1929-05-22,311.89,311.89,300.54,300.83,4840000,300.83 1929-05-21,312.70,316.41,308.32,314.09,4410000,314.09 1929-05-20,321.48,322.65,312.18,312.70,3810000,312.70 1929-05-17,320.09,325.64,318.81,321.38,3330000,321.38 1929-05-16,319.35,321.89,314.51,320.09,3440000,320.09 1929-05-15,320.79,324.38,317.93,319.35,3350000,319.35 1929-05-14,316.49,322.33,315.17,320.79,3630000,320.79 1929-05-13,324.49,324.49,313.56,316.49,4630000,316.49 1929-05-10,321.49,328.00,321.49,325.70,3920000,325.70 1929-05-09,323.51,324.87,317.09,321.17,3660000,321.17 1929-05-08,321.91,325.90,318.87,323.51,3470000,323.51 1929-05-07,326.16,327.55,320.60,321.91,3490000,321.91 1929-05-06,327.08,331.01,323.01,326.16,3810000,326.16 1929-05-03,322.33,329.11,322.33,325.56,4530000,325.56 1929-05-02,320.13,324.60,317.73,321.52,4180000,321.52 1929-05-01,319.29,323.99,317.90,320.13,4690000,320.13 1929-04-30,314.02,321.09,314.02,319.29,4320000,319.29 1929-04-29,315.55,315.55,309.62,313.84,3270000,313.84 1929-04-26,314.28,319.31,311.00,314.15,4010000,314.15 1929-04-25,315.66,317.23,312.37,314.28,3340000,314.28 1929-04-24,316.62,320.00,313.56,315.66,4070000,315.66 1929-04-23,315.33,320.10,314.20,316.62,4130000,316.62 1929-04-22,311.98,318.26,311.98,315.33,3570000,315.33 1929-04-19,311.87,313.81,308.67,310.58,3060000,310.58 1929-04-18,309.91,315.22,309.63,311.87,3770000,311.87 1929-04-17,304.19,311.19,304.16,309.91,3500000,309.91 1929-04-16,302.43,305.51,299.30,304.19,2370000,304.19 1929-04-15,304.41,305.55,301.54,302.43,2640000,302.43 1929-04-12,304.09,309.79,303.61,305.43,3410000,305.43 1929-04-11,300.67,307.90,299.40,304.09,3100000,304.09 1929-04-10,299.13,304.60,295.71,300.67,3280000,300.67 1929-04-09,301.49,306.29,297.17,299.13,3630000,299.13 1929-04-08,302.81,305.70,299.52,301.49,2720000,301.49 1929-04-05,305.37,307.97,301.39,303.04,3410000,303.04 1929-04-04,300.35,306.99,295.79,305.37,3330000,305.37 1929-04-03,303.49,307.70,298.58,300.35,3700000,300.35 1929-04-02,300.40,305.20,298.07,303.49,3780000,303.49 1929-04-01,304.21,304.21,294.11,300.40,4160000,300.40 1929-03-28,303.22,311.13,302.93,308.85,5100000,308.85 1929-03-27,296.51,305.87,293.70,303.22,5620000,303.22 1929-03-26,297.50,300.60,281.51,296.51,8250000,296.51 1929-03-25,306.21,311.55,294.34,297.50,5860000,297.50 1929-03-22,314.63,316.94,307.50,310.26,4830000,310.26 1929-03-21,316.44,319.31,313.12,314.63,4460000,314.63 1929-03-20,317.53,320.06,313.27,316.44,5190000,316.44 1929-03-19,317.59,321.28,315.23,317.53,4450000,317.53 1929-03-18,320.00,321.70,315.49,317.59,5020000,317.59 1929-03-15,316.26,322.75,315.92,319.70,5890000,319.70 1929-03-14,311.02,317.98,311.02,316.26,4630000,316.26 1929-03-13,306.79,312.30,306.79,310.29,3330000,310.29 1929-03-12,305.75,312.76,305.20,306.14,3060000,306.14 1929-03-11,311.61,312.96,305.20,305.75,3630000,305.75 1929-03-08,308.99,313.25,304.78,311.59,3950000,311.59 1929-03-07,305.20,310.39,303.05,308.99,3630000,308.99 1929-03-06,310.20,313.45,302.93,305.20,4490000,305.20 1929-03-05,313.86,316.17,308.22,310.20,4430000,310.20 1929-03-04,319.12,320.22,312.85,313.86,4560000,313.86 1929-03-01,317.79,324.40,317.79,321.18,6020000,321.18 1929-02-28,314.53,319.69,312.91,317.41,4970000,317.41 1929-02-27,311.25,317.03,309.71,314.53,4370000,314.53 1929-02-26,311.24,313.49,307.04,311.25,3740000,311.25 1929-02-25,310.06,315.08,308.10,311.24,3510000,311.24 1929-02-21,305.99,311.31,303.45,310.06,3400000,310.06 1929-02-20,301.10,307.55,301.05,305.99,2910000,305.99 1929-02-19,300.74,305.58,299.00,301.10,3210000,301.10 1929-02-18,295.85,301.68,293.40,300.74,3480000,300.74 1929-02-15,306.49,309.79,299.38,300.41,3900000,300.41 1929-02-14,308.07,308.29,300.60,306.49,3730000,306.49 1929-02-13,310.35,316.06,307.15,308.07,4530000,308.07 1929-02-11,301.53,311.24,299.58,310.35,3890000,310.35 1929-02-08,305.75,309.26,298.03,301.53,4550000,301.53 1929-02-07,312.56,312.56,302.40,305.75,5210000,305.75 1929-02-06,322.06,323.31,313.32,317.18,4680000,317.18 1929-02-05,319.05,324.51,317.28,322.06,4070000,322.06 1929-02-04,319.76,323.74,316.91,319.05,4050000,319.05 1929-02-01,317.51,324.16,315.64,319.68,4970000,319.68 1929-01-31,312.60,319.96,311.34,317.51,4680000,317.51 1929-01-30,312.60,316.15,308.47,312.60,4130000,312.60 1929-01-29,314.04,316.33,309.23,312.60,4290000,312.60 1929-01-28,314.56,319.58,310.44,314.04,4980000,314.04 1929-01-25,311.28,319.36,311.28,315.13,5510000,315.13 1929-01-24,310.33,314.01,305.94,309.39,4500000,309.39 1929-01-23,307.06,315.49,306.46,310.33,4920000,310.33 1929-01-22,304.64,310.08,303.05,307.06,5120000,307.06 1929-01-21,305.96,308.22,302.36,304.64,4900000,304.64 1929-01-18,303.95,308.05,301.05,304.14,4940000,304.14 1929-01-17,302.66,306.96,301.09,303.95,4260000,303.95 1929-01-16,297.66,304.36,297.00,302.66,3670000,302.66 1929-01-15,304.06,306.09,295.78,297.66,4180000,297.66 1929-01-14,301.25,306.26,299.06,304.06,3920000,304.06 1929-01-11,301.58,305.85,298.68,301.66,4240000,301.66 1929-01-10,300.83,305.20,299.60,301.58,4020000,301.58 1929-01-09,296.98,303.04,296.37,300.83,4050000,300.83 1929-01-08,297.70,300.87,292.89,296.98,3850000,296.98 1929-01-07,301.85,301.85,293.35,297.70,4800000,297.70 1929-01-04,305.72,307.51,299.92,304.75,5530000,304.75 1929-01-03,307.01,311.46,302.90,305.72,5100000,305.72 1929-01-02,300.31,308.66,300.31,307.01,5410000,307.01 1928-12-31,297.28,301.61,291.99,300.00,4890000,300.00 1928-12-28,290.95,297.79,283.68,296.52,4800000,296.52 1928-12-27,286.13,291.39,281.55,290.95,3570000,290.95 1928-12-26,287.89,292.53,283.94,286.13,3620000,286.13 1928-12-24,285.94,291.17,284.30,287.89,3700000,287.89 1928-12-21,282.01,288.39,281.31,286.53,3460000,286.53 1928-12-20,280.50,285.60,277.91,282.01,3810000,282.01 1928-12-19,275.41,282.84,275.09,280.50,3400000,280.50 1928-12-18,270.23,276.41,269.61,275.41,2270000,275.41 1928-12-17,270.72,272.27,266.21,270.23,2230000,270.23 1928-12-14,266.99,275.45,266.99,272.26,3010000,272.26 1928-12-13,266.82,269.53,260.51,266.88,3270000,266.88 1928-12-12,269.34,272.74,264.95,266.82,3990000,266.82 1928-12-11,263.95,270.41,263.71,269.34,3920000,269.34 1928-12-10,257.33,266.22,254.36,263.95,5220000,263.95 1928-12-07,279.79,284.44,269.58,271.05,6190000,271.05 1928-12-06,290.68,292.56,278.66,279.79,5410000,279.79 1928-12-05,291.30,294.20,289.91,290.68,4380000,290.68 1928-12-04,289.23,295.61,287.61,291.30,4920000,291.30 1928-12-03,290.80,291.05,283.89,289.23,4490000,289.23 1928-11-30,295.62,299.07,288.82,293.38,6410000,293.38 1928-11-28,292.39,299.35,290.68,295.62,6370000,295.62 1928-11-27,291.16,294.75,289.28,292.39,5280000,292.39 1928-11-26,288.22,296.10,288.14,291.16,5320000,291.16 1928-11-23,290.34,295.17,284.40,288.22,6940000,288.22 1928-11-22,281.28,292.12,281.28,290.34,5840000,290.34 1928-11-21,283.90,288.71,276.91,280.53,6170000,280.53 1928-11-20,278.78,288.13,278.05,283.90,6440000,283.90 1928-11-19,277.48,280.68,272.98,278.78,5100000,278.78 1928-11-16,271.48,278.65,271.48,276.66,6730000,276.66 1928-11-15,268.60,271.63,266.48,269.42,4730000,269.42 1928-11-14,269.89,272.94,266.80,268.60,5410000,268.60 1928-11-13,269.67,272.03,264.88,269.89,5240000,269.89 1928-11-12,265.08,272.47,264.42,269.67,5680000,269.67 1928-11-09,261.11,266.24,259.37,263.05,4950000,263.05 1928-11-08,260.68,265.26,258.96,261.11,4850000,261.11 1928-11-07,258.48,263.97,258.48,260.68,4830000,260.68 1928-11-05,254.16,259.68,253.89,257.58,3740000,257.58 1928-11-02,255.23,256.99,252.46,254.38,3490000,254.38 1928-11-01,252.16,256.59,251.56,255.23,3450000,255.23 1928-10-31,253.70,256.16,248.76,252.16,3490000,252.16 1928-10-30,257.13,259.00,252.39,253.70,3450000,253.70 1928-10-29,255.51,259.76,255.03,257.13,3690000,257.13 1928-10-26,256.48,259.16,250.00,251.44,4520000,251.44 1928-10-25,257.03,260.03,254.93,256.48,4210000,256.48 1928-10-24,256.04,260.39,249.09,257.03,4550000,257.03 1928-10-23,253.60,258.60,252.73,256.04,4160000,256.04 1928-10-22,253.75,257.32,250.08,253.60,3860000,253.60 1928-10-19,251.88,259.19,250.35,256.59,4560000,256.59 1928-10-18,250.87,255.24,249.65,251.88,4400000,251.88 1928-10-17,249.43,253.60,247.74,250.87,3960000,250.87 1928-10-16,249.85,255.27,247.92,249.43,4530000,249.43 1928-10-15,249.13,252.70,247.33,249.85,4040000,249.85 1928-10-11,246.53,250.14,245.57,247.69,3970000,247.69 1928-10-10,241.73,249.06,241.57,246.53,4170000,246.53 1928-10-09,239.55,242.86,236.79,241.73,3820000,241.73 1928-10-08,240.17,243.33,237.72,239.55,3940000,239.55 1928-10-05,240.00,243.08,238.22,240.44,4360000,240.44 1928-10-04,237.75,242.53,237.72,240.00,4330000,240.00 1928-10-03,238.14,239.14,233.60,237.75,4060000,237.75 1928-10-02,240.01,241.54,235.42,238.14,3850000,238.14 1928-10-01,239.43,242.46,238.24,240.01,3500000,240.01 statsmodels-0.12.2/statsmodels/sandbox/examples/ex_cusum.py000066400000000000000000000056141400612667500241730ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Apr 02 11:41:25 2010 Author: josef-pktd """ import numpy as np from numpy.testing import assert_almost_equal import matplotlib.pyplot as plt import statsmodels.api as sm from statsmodels.stats.diagnostic import recursive_olsresiduals from statsmodels.stats.diagnostic import ( breaks_hansen, breaks_cusumolsresid) #examples from ex_onewaygls.py #choose example #-------------- example = ['null', 'smalldiff', 'mediumdiff', 'largediff'][1] example_size = [20, 100][1] example_groups = ['2', '2-2'][1] #'2-2': 4 groups, # groups 0 and 1 and groups 2 and 3 have identical parameters in DGP #generate example #---------------- #np.random.seed(87654589) nobs = example_size x1 = 0.1+np.random.randn(nobs) y1 = 10 + 15*x1 + 2*np.random.randn(nobs) x1 = sm.add_constant(x1, prepend=False) #assert_almost_equal(x1, np.vander(x1[:,0],2), 16) #res1 = sm.OLS(y1, x1).fit() #print res1.params #print np.polyfit(x1[:,0], y1, 1) #assert_almost_equal(res1.params, np.polyfit(x1[:,0], y1, 1), 14) #print res1.summary(xname=['x1','const1']) #regression 2 x2 = 0.1+np.random.randn(nobs) if example == 'null': y2 = 10 + 15*x2 + 2*np.random.randn(nobs) # if H0 is true elif example == 'smalldiff': y2 = 11 + 16*x2 + 2*np.random.randn(nobs) elif example == 'mediumdiff': y2 = 12 + 16*x2 + 2*np.random.randn(nobs) else: y2 = 19 + 17*x2 + 2*np.random.randn(nobs) x2 = sm.add_constant(x2, prepend=False) # stack x = np.concatenate((x1,x2),0) y = np.concatenate((y1,y2)) if example_groups == '2': groupind = (np.arange(2*nobs)>nobs-1).astype(int) else: groupind = np.mod(np.arange(2*nobs),4) groupind.sort() #x = np.column_stack((x,x*groupind[:,None])) res1 = sm.OLS(y, x).fit() skip = 8 rresid, rparams, rypred, rresid_standardized, rresid_scaled, rcusum, rcusumci = \ recursive_olsresiduals(res1, skip) print(rcusum) print(rresid_scaled[skip-1:]) assert_almost_equal(rparams[-1], res1.params) plt.plot(rcusum) plt.plot(rcusumci[0]) plt.plot(rcusumci[1]) plt.figure() plt.plot(rresid) plt.plot(np.abs(rresid)) print('cusum test reject:') print(((rcusum[1:]>rcusumci[1]) | (rcusum[1:] nsubj//4: nobs_i = 6 #generate exogenous variables X = np.random.standard_normal((nobs_i, nx)) Z = np.random.standard_normal((nobs_i, nz-1)) Z = np.column_stack((np.ones(nobs_i), Z)) noise = 0.1 * np.random.randn(nobs_i) #sig_e = 0.1 #generate endogenous variable Y = np.dot(X, beta) + np.dot(Z, gamma_re) + noise #add random effect design matrix also to fixed effects to #capture the mean #this seems to be necessary to force mean of RE to zero !? #(It's not required for estimation but interpretation of random #effects covariance matrix changes - still need to check details. X = np.hstack((X,Z)) # create units and append to list new_unit = Unit(Y, X, Z) units.append(new_unit) m = OneWayMixed(units) import time t0 = time.time() m.initialize() res = m.fit(maxiter=100, rtol=1.0e-5, params_rtol=1e-6, params_atol=1e-6) t1 = time.time() print('time for initialize and fit', t1-t0) print('number of iterations', m.iterations) #print(dir(m) #print(vars(m) print('\nestimates for fixed effects') print(m.a) print(m.params) bfixed_cov = m.cov_fixed() print('beta fixed standard errors') print(np.sqrt(np.diag(bfixed_cov))) print(m.bse) b_re = m.params_random_units print('RE mean:', b_re.mean(0)) print('RE columns std', b_re.std(0)) print('np.cov(b_re, rowvar=0), sample statistic') print(np.cov(b_re, rowvar=0)) print('std of above') print(np.sqrt(np.diag(np.cov(b_re, rowvar=0)))) print('m.cov_random()') print(m.cov_random()) print('std of above') print(res.std_random()) print(np.sqrt(np.diag(m.cov_random()))) print('\n(non)convergence of llf') print(m.history['llf'][-4:]) print('convergence of parameters') #print(np.diff(np.vstack(m.history[-4:])[:,1:],axis=0) print(np.diff(np.vstack(m.history['params'][-4:]),axis=0)) print('convergence of D') print(np.diff(np.array(m.history['D'][-4:]), axis=0)) #zdotb = np.array([np.dot(unit.Z, unit.b) for unit in m.units]) zb = np.array([(unit.Z * unit.b[None,:]).sum(0) for unit in m.units]) '''if Z is not included in X: >>> np.dot(b_re.T, b_re)/100 array([[ 0.03270611, -0.00916051], [-0.00916051, 0.26432783]]) >>> m.cov_random() array([[ 0.0348722 , -0.00909159], [-0.00909159, 0.26846254]]) >>> #note cov_random does not subtract mean! ''' print('\nchecking the random effects distribution and prediction') gamma_re_true = np.array(gamma_re_true) print('mean of random effect true', gamma_re_true.mean(0)) print('mean from fixed effects ', m.params[-2:]) print('mean of estimated RE ', b_re.mean(0)) print('') absmean_true = np.abs(gamma_re_true).mean(0) mape = ((m.params[-2:] + b_re) / gamma_re_true - 1).mean(0)*100 mean_abs_perc = np.abs((m.params[-2:] + b_re) - gamma_re_true).mean(0) \ / absmean_true*100 median_abs_perc = np.median(np.abs((m.params[-2:] + b_re) - gamma_re_true), 0) \ / absmean_true*100 rmse_perc = ((m.params[-2:] + b_re) - gamma_re_true).std(0) \ / absmean_true*100 print('mape ', mape) print('mean_abs_perc ', mean_abs_perc) print('median_abs_perc', median_abs_perc) print('rmse_perc (std)', rmse_perc) #from numpy.testing import assert_almost_equal #assert is for n_units=100 in original example #I changed random number generation, so this will not work anymore #assert_almost_equal(rmse_perc, [ 34.14783884, 11.6031684 ], decimal=8) #now returns res print(res.llf) #based on MLE, does not include constant print(res.tvalues) print(res.pvalues) print(res.t_test([1,-1,0,0,0,0])) print('test mean of both random effects variables is zero') print(res.f_test([[0,0,0,0,1,0], [0,0,0,0,0,1]])) plots = res.plot_random_univariate(bins=50) fig = res.plot_scatter_pairs(0, 1) import matplotlib.pyplot as plt plt.show() statsmodels-0.12.2/statsmodels/sandbox/examples/ex_mixed_lls_re.py000066400000000000000000000124371400612667500255060ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Example using OneWayMixed Created on Sat Dec 03 10:15:55 2011 Author: Josef Perktold This example constructs a linear model with individual specific random effects, and uses OneWayMixed to estimate it. This is a variation on ex_mixed_lls_0.py. Here we only have a single individual specific constant, that is just a random effect without exogenous regressors. """ import numpy as np from statsmodels.sandbox.panel.mixed import OneWayMixed, Unit examples = ['ex1'] if 'ex1' in examples: #np.random.seed(54321) np.random.seed(978326) nsubj = 2000 units = [] nobs_i = 4 #number of observations per unit, changed below nx = 0 #number fixed effects nz = 1 ##number random effects beta = np.ones(nx) gamma = 0.5 * np.ones(nz) #mean of random effect gamma[0] = 0 gamma_re_true = [] for i in range(nsubj): #create data for one unit #random effect/coefficient gamma_re = gamma + 0.2 * np.random.standard_normal(nz) #store true parameter for checking gamma_re_true.append(gamma_re) #for testing unbalanced case, let's change nobs per unit if i > nsubj//4: nobs_i = 6 #generate exogenous variables X = np.random.standard_normal((nobs_i, nx)) Z = np.random.standard_normal((nobs_i, nz-1)) Z = np.column_stack((np.ones(nobs_i), Z)) noise = 0.1 * np.random.randn(nobs_i) #sig_e = 0.1 #generate endogenous variable Y = np.dot(X, beta) + np.dot(Z, gamma_re) + noise #add random effect design matrix also to fixed effects to #capture the mean #this seems to be necessary to force mean of RE to zero !? #(It's not required for estimation but interpretation of random #effects covariance matrix changes - still need to check details. X = np.hstack((X,Z)) # create units and append to list new_unit = Unit(Y, X, Z) units.append(new_unit) m = OneWayMixed(units) import time t0 = time.time() m.initialize() res = m.fit(maxiter=100, rtol=1.0e-5, params_rtol=1e-6, params_atol=1e-6) t1 = time.time() print('time for initialize and fit', t1-t0) print('number of iterations', m.iterations) #print dir(m) #print vars(m) print('\nestimates for fixed effects') print(m.a) print(m.params) bfixed_cov = m.cov_fixed() print('beta fixed standard errors') print(np.sqrt(np.diag(bfixed_cov))) print(m.bse) b_re = m.params_random_units print('RE mean:', b_re.mean(0)) print('RE columns std', b_re.std(0)) print('np.cov(b_re, rowvar=0), sample statistic') print(np.cov(b_re, rowvar=0)) print('std of above') #need atleast_1d or diag raises exception print(np.sqrt(np.diag(np.atleast_1d(np.cov(b_re, rowvar=0))))) print('m.cov_random()') print(m.cov_random()) print('std of above') print(res.std_random()) print(np.sqrt(np.diag(m.cov_random()))) print('\n(non)convergence of llf') print(m.history['llf'][-4:]) print('convergence of parameters') #print np.diff(np.vstack(m.history[-4:])[:,1:],axis=0) print(np.diff(np.vstack(m.history['params'][-4:]),axis=0)) print('convergence of D') print(np.diff(np.array(m.history['D'][-4:]), axis=0)) #zdotb = np.array([np.dot(unit.Z, unit.b) for unit in m.units]) zb = np.array([(unit.Z * unit.b[None,:]).sum(0) for unit in m.units]) '''if Z is not included in X: >>> np.dot(b_re.T, b_re)/100 array([[ 0.03270611, -0.00916051], [-0.00916051, 0.26432783]]) >>> m.cov_random() array([[ 0.0348722 , -0.00909159], [-0.00909159, 0.26846254]]) >>> #note cov_random does not subtract mean! ''' print('\nchecking the random effects distribution and prediction') gamma_re_true = np.array(gamma_re_true) print('mean of random effect true', gamma_re_true.mean(0)) print('mean from fixed effects ', m.params[-2:]) print('mean of estimated RE ', b_re.mean(0)) print() absmean_true = np.abs(gamma_re_true).mean(0) mape = ((m.params[-2:] + b_re) / gamma_re_true - 1).mean(0)*100 mean_abs_perc = np.abs((m.params[-2:] + b_re) - gamma_re_true).mean(0) \ / absmean_true*100 median_abs_perc = np.median(np.abs((m.params[-2:] + b_re) - gamma_re_true), 0) \ / absmean_true*100 rmse_perc = ((m.params[-2:] + b_re) - gamma_re_true).std(0) \ / absmean_true*100 print('mape ', mape) print('mean_abs_perc ', mean_abs_perc) print('median_abs_perc', median_abs_perc) print('rmse_perc (std)', rmse_perc) #from numpy.testing import assert_almost_equal #assert is for n_units=100 in original example #I changed random number generation, so this will not work anymore #assert_almost_equal(rmse_perc, [ 34.14783884, 11.6031684 ], decimal=8) #now returns res print('llf', res.llf) #based on MLE, does not include constant print('tvalues', res.tvalues) print('pvalues', res.pvalues) print(res.t_test([1])) print('test mean of both random effects variables is zero') print(res.f_test([[1]])) plots = res.plot_random_univariate(bins=50) #fig = res.plot_scatter_pairs(0, 1) #no pairs import matplotlib.pyplot as plt plt.show() statsmodels-0.12.2/statsmodels/sandbox/examples/ex_mixed_lls_timecorr.py000066400000000000000000000172421400612667500267230ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Example using OneWayMixed with within group intertemporal correlation Created on Sat Dec 03 10:15:55 2011 Author: Josef Perktold This example constructs a linear model with individual specific random effects, and uses OneWayMixed to estimate it. This is a variation on ex_mixed_lls_0.py. Here we use time dummies as random effects (all except 1st time period). I think, this should allow for (almost) arbitrary intertemporal correlation. The assumption is that each unit can have different constants, however the intertemporal covariance matrix is the same for all units. One caveat, to avoid singular matrices, we have to treat one time period differently. Estimation requires that the number of units is larger than the number of time periods. Also, it requires that we have the same number of periods for each unit. I needed to remove the first observation from the time dummies to avoid a singular matrix. So, interpretation of time effects should be relative to first observation. (I did not check the math.) TODO: Note, I do not already have constant in X. Constant for first time observation is missing. Do I need all dummies in exog_fe, Z, but not in exog_re, Z? Tried this and it works. In the error decomposition we also have the noise variable, I guess this works like constant, so we get full rank (square) with only T-1 time dummies. But we do not get correlation with the noise, or do we? conditional? -> sample correlation of estimated random effects looks a bit high, upward bias? or still some problems with initial condition? correlation from estimated cov_random looks good. Since we include the time dummies also in the fixed effect, we can have arbitrary trends, different constants in each period. Intertemporal correlation in data generating process, DGP, to see if the results correctly estimate it. used AR(1) as example, but only starting at second period. (?) Note: we do not impose AR structure in the estimation """ import numpy as np from statsmodels.sandbox.panel.mixed import OneWayMixed, Unit examples = ['ex1'] if 'ex1' in examples: #np.random.seed(54321) #np.random.seed(978326) nsubj = 200 units = [] nobs_i = 8 #number of observations per unit, changed below nx = 1 #number fixed effects nz = nobs_i - 1 ##number random effects beta = np.ones(nx) gamma = 0.5 * np.ones(nz) #mean of random effect #gamma[0] = 0 gamma_re_true = [] for i in range(nsubj): #create data for one unit #random effect/coefficient use_correlated = True if not use_correlated: gamma_re = gamma + 0.2 * np.random.standard_normal(nz) else: #coefficients are AR(1) for all but first time periods from scipy import linalg as splinalg rho = 0.6 corr_re = splinalg.toeplitz(rho**np.arange(nz)) rvs = np.random.multivariate_normal(np.zeros(nz), corr_re) gamma_re = gamma + 0.2 * rvs #store true parameter for checking gamma_re_true.append(gamma_re) #generate exogenous variables X = np.random.standard_normal((nobs_i, nx)) #try Z should be time dummies time_dummies = (np.arange(nobs_i)[:, None] == np.arange(nobs_i)[None, :]).astype(float) Z = time_dummies[:,1:] # Z = np.random.standard_normal((nobs_i, nz-1)) # Z = np.column_stack((np.ones(nobs_i), Z)) noise = 0.1 * np.random.randn(nobs_i) #sig_e = 0.1 #generate endogenous variable Y = np.dot(X, beta) + np.dot(Z, gamma_re) + noise #add random effect design matrix also to fixed effects to #capture the mean #this seems to be necessary to force mean of RE to zero !? #(It's not required for estimation but interpretation of random #effects covariance matrix changes - still need to check details. #X = np.hstack((X,Z)) X = np.hstack((X, time_dummies)) # create units and append to list new_unit = Unit(Y, X, Z) units.append(new_unit) m = OneWayMixed(units) import time t0 = time.time() m.initialize() res = m.fit(maxiter=100, rtol=1.0e-5, params_rtol=1e-6, params_atol=1e-6) t1 = time.time() print('time for initialize and fit', t1-t0) print('number of iterations', m.iterations) #print dir(m) #print vars(m) print('\nestimates for fixed effects') print(m.a) print(m.params) bfixed_cov = m.cov_fixed() print('beta fixed standard errors') print(np.sqrt(np.diag(bfixed_cov))) print(m.bse) b_re = m.params_random_units print('RE mean:', b_re.mean(0)) print('RE columns std', b_re.std(0)) print('np.cov(b_re, rowvar=0), sample statistic') print(np.cov(b_re, rowvar=0)) print('sample correlation of estimated random effects') print(np.corrcoef(b_re, rowvar=0)) print('std of above') #need atleast_1d or diag raises exception print(np.sqrt(np.diag(np.atleast_1d(np.cov(b_re, rowvar=0))))) print('m.cov_random()') print(m.cov_random()) print('correlation from above') print(res.cov_random()/ res.std_random()[:,None] /res.std_random()) print('std of above') print(res.std_random()) print(np.sqrt(np.diag(m.cov_random()))) print('\n(non)convergence of llf') print(m.history['llf'][-4:]) print('convergence of parameters') #print np.diff(np.vstack(m.history[-4:])[:,1:],axis=0) print(np.diff(np.vstack(m.history['params'][-4:]),axis=0)) print('convergence of D') print(np.diff(np.array(m.history['D'][-4:]), axis=0)) #zdotb = np.array([np.dot(unit.Z, unit.b) for unit in m.units]) zb = np.array([(unit.Z * unit.b[None,:]).sum(0) for unit in m.units]) '''if Z is not included in X: >>> np.dot(b_re.T, b_re)/100 array([[ 0.03270611, -0.00916051], [-0.00916051, 0.26432783]]) >>> m.cov_random() array([[ 0.0348722 , -0.00909159], [-0.00909159, 0.26846254]]) >>> #note cov_random does not subtract mean! ''' print('\nchecking the random effects distribution and prediction') gamma_re_true = np.array(gamma_re_true) print('mean of random effect true', gamma_re_true.mean(0)) print('mean from fixed effects ', m.params[-2:]) print('mean of estimated RE ', b_re.mean(0)) print() absmean_true = np.abs(gamma_re_true).mean(0) mape = ((m.params[-nz:] + b_re) / gamma_re_true - 1).mean(0)*100 mean_abs_perc = np.abs((m.params[-nz:] + b_re) - gamma_re_true).mean(0) \ / absmean_true*100 median_abs_perc = np.median(np.abs((m.params[-nz:] + b_re) - gamma_re_true), 0) \ / absmean_true*100 rmse_perc = ((m.params[-nz:] + b_re) - gamma_re_true).std(0) \ / absmean_true*100 print('mape ', mape) print('mean_abs_perc ', mean_abs_perc) print('median_abs_perc', median_abs_perc) print('rmse_perc (std)', rmse_perc) #from numpy.testing import assert_almost_equal #assert is for n_units=100 in original example #I changed random number generation, so this will not work anymore #assert_almost_equal(rmse_perc, [ 34.14783884, 11.6031684 ], decimal=8) #now returns res print('llf', res.llf) #based on MLE, does not include constant print('tvalues', res.tvalues) print('pvalues', res.pvalues) rmat = np.zeros(len(res.params)) rmat[-nz:] = 1 print('t_test mean of random effects variables are zero') print(res.t_test(rmat)) print('f_test mean of both random effects variables is zero (joint hypothesis)') print(res.f_test(rmat)) plots = res.plot_random_univariate() #(bins=50) fig = res.plot_scatter_all_pairs() import matplotlib.pyplot as plt plt.show() statsmodels-0.12.2/statsmodels/sandbox/examples/ex_onewaygls.py000066400000000000000000000153731400612667500250520ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Example: Test for equality of coefficients across groups/regressions Created on Sat Mar 27 22:36:51 2010 Author: josef-pktd """ import numpy as np from scipy import stats #from numpy.testing import assert_almost_equal import statsmodels.api as sm from statsmodels.sandbox.regression.onewaygls import OneWayLS #choose example #-------------- example = ['null', 'diff'][1] #null: identical coefficients across groups example_size = [10, 100][0] example_size = [(10,2), (100,2)][0] example_groups = ['2', '2-2'][1] #'2-2': 4 groups, # groups 0 and 1 and groups 2 and 3 have identical parameters in DGP #generate example #---------------- np.random.seed(87654589) nobs, nvars = example_size x1 = np.random.normal(size=(nobs, nvars)) y1 = 10 + np.dot(x1,[15.]*nvars) + 2*np.random.normal(size=nobs) x1 = sm.add_constant(x1, prepend=False) #assert_almost_equal(x1, np.vander(x1[:,0],2), 16) #res1 = sm.OLS(y1, x1).fit() #print res1.params #print np.polyfit(x1[:,0], y1, 1) #assert_almost_equal(res1.params, np.polyfit(x1[:,0], y1, 1), 14) #print res1.summary(xname=['x1','const1']) #regression 2 x2 = np.random.normal(size=(nobs,nvars)) if example == 'null': y2 = 10 + np.dot(x2,[15.]*nvars) + 2*np.random.normal(size=nobs) # if H0 is true else: y2 = 19 + np.dot(x2,[17.]*nvars) + 2*np.random.normal(size=nobs) x2 = sm.add_constant(x2, prepend=False) # stack x = np.concatenate((x1,x2),0) y = np.concatenate((y1,y2)) if example_groups == '2': groupind = (np.arange(2*nobs)>nobs-1).astype(int) else: groupind = np.mod(np.arange(2*nobs),4) groupind.sort() #x = np.column_stack((x,x*groupind[:,None])) def print_results(res): groupind = res.groups #res.fitjoint() #not really necessary, because called by ftest_summary ft = res.ftest_summary() #print ft[0] #skip because table is nicer print('\nTable of F-tests for overall or pairwise equality of coefficients') ## print 'hypothesis F-statistic p-value df_denom df_num reject' ## for row in ft[1]: ## print row, ## if row[1][1]<0.05: ## print '*' ## else: ## print '' from statsmodels.iolib import SimpleTable print(SimpleTable([(['%r' % (row[0],)] + list(row[1]) + ['*']*(row[1][1]>0.5).item() ) for row in ft[1]], headers=['pair', 'F-statistic','p-value','df_denom', 'df_num'])) print('Notes: p-values are not corrected for many tests') print(' (no Bonferroni correction)') print(' * : reject at 5% uncorrected confidence level') print('Null hypothesis: all or pairwise coefficient are the same') print('Alternative hypothesis: all coefficients are different') print('\nComparison with stats.f_oneway') print(stats.f_oneway(*[y[groupind==gr] for gr in res.unique])) print('\nLikelihood Ratio Test') print('likelihood ratio p-value df') print(res.lr_test()) print('Null model: pooled all coefficients are the same across groups,') print('Alternative model: all coefficients are allowed to be different') print('not verified but looks close to f-test result') print('\nOLS parameters by group from individual, separate ols regressions') for group in sorted(res.olsbygroup): r = res.olsbygroup[group] print(group, r.params) print('\nCheck for heteroscedasticity, ') print('variance and standard deviation for individual regressions') print(' '*12, ' '.join('group %-10s' %(gr) for gr in res.unique)) print('variance ', res.sigmabygroup) print('standard dev', np.sqrt(res.sigmabygroup)) #now added to class def print_results2(res): groupind = res.groups #res.fitjoint() #not really necessary, because called by ftest_summary ft = res.ftest_summary() txt = '' #print ft[0] #skip because table is nicer templ = \ '''Table of F-tests for overall or pairwise equality of coefficients' %(tab)s Notes: p-values are not corrected for many tests (no Bonferroni correction) * : reject at 5%% uncorrected confidence level Null hypothesis: all or pairwise coefficient are the same' Alternative hypothesis: all coefficients are different' Comparison with stats.f_oneway %(statsfow)s Likelihood Ratio Test %(lrtest)s Null model: pooled all coefficients are the same across groups,' Alternative model: all coefficients are allowed to be different' not verified but looks close to f-test result' OLS parameters by group from individual, separate ols regressions' %(olsbg)s for group in sorted(res.olsbygroup): r = res.olsbygroup[group] print group, r.params Check for heteroscedasticity, ' variance and standard deviation for individual regressions' %(grh)s variance ', res.sigmabygroup standard dev', np.sqrt(res.sigmabygroup) ''' from statsmodels.iolib import SimpleTable resvals = {} resvals['tab'] = str(SimpleTable([(['%r' % (row[0],)] + list(row[1]) + ['*']*(row[1][1]>0.5).item() ) for row in ft[1]], headers=['pair', 'F-statistic','p-value','df_denom', 'df_num'])) resvals['statsfow'] = str(stats.f_oneway(*[y[groupind==gr] for gr in res.unique])) #resvals['lrtest'] = str(res.lr_test()) resvals['lrtest'] = str(SimpleTable([res.lr_test()], headers=['likelihood ratio', 'p-value', 'df'] )) resvals['olsbg'] = str(SimpleTable([[group] + res.olsbygroup[group].params.tolist() for group in sorted(res.olsbygroup)])) resvals['grh'] = str(SimpleTable(np.vstack([res.sigmabygroup, np.sqrt(res.sigmabygroup)]), headers=res.unique.tolist())) return templ % resvals #get results for example #----------------------- print('\nTest for equality of coefficients for all exogenous variables') print('-------------------------------------------------------------') res = OneWayLS(y,x, groups=groupind.astype(int)) print_results(res) print('\n\nOne way ANOVA, constant is the only regressor') print('---------------------------------------------') print('this is the same as scipy.stats.f_oneway') res = OneWayLS(y,np.ones(len(y)), groups=groupind) print_results(res) print('\n\nOne way ANOVA, constant is the only regressor with het is true') print('--------------------------------------------------------------') print('this is the similar to scipy.stats.f_oneway,') print('but variance is not assumed to be the same across groups') res = OneWayLS(y,np.ones(len(y)), groups=groupind.astype(str), het=True) print_results(res) print(res.print_summary()) #(res) statsmodels-0.12.2/statsmodels/sandbox/examples/ex_random_panel.py000066400000000000000000000135641400612667500255010ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri May 18 13:05:47 2012 Author: Josef Perktold moved example from main of random_panel """ import numpy as np from statsmodels.sandbox.panel.panel_short import ShortPanelGLS, ShortPanelGLS2 from statsmodels.sandbox.panel.random_panel import PanelSample import statsmodels.sandbox.panel.correlation_structures as cs import statsmodels.stats.sandwich_covariance as sw #from statsmodels.stats.sandwich_covariance import ( # S_hac_groupsum, weights_bartlett, _HCCM2) from statsmodels.stats.moment_helpers import se_cov cov_nw_panel2 = sw.cov_nw_groupsum examples = ['ex1'] if 'ex1' in examples: nobs = 100 nobs_i = 5 n_groups = nobs // nobs_i k_vars = 3 # dgp = PanelSample(nobs, k_vars, n_groups, corr_structure=cs.corr_equi, # corr_args=(0.6,)) # dgp = PanelSample(nobs, k_vars, n_groups, corr_structure=cs.corr_ar, # corr_args=([1, -0.95],)) dgp = PanelSample(nobs, k_vars, n_groups, corr_structure=cs.corr_arma, corr_args=([1], [1., -0.9],), seed=377769) print('seed', dgp.seed) y = dgp.generate_panel() noise = y - dgp.y_true print(np.corrcoef(y.reshape(-1,n_groups, order='F'))) print(np.corrcoef(noise.reshape(-1,n_groups, order='F'))) mod = ShortPanelGLS2(y, dgp.exog, dgp.groups) res = mod.fit() print(res.params) print(res.bse) #Now what? #res.resid is of transformed model #np.corrcoef(res.resid.reshape(-1,n_groups, order='F')) y_pred = np.dot(mod.exog, res.params) resid = y - y_pred print(np.corrcoef(resid.reshape(-1,n_groups, order='F'))) print(resid.std()) err = y_pred - dgp.y_true print(err.std()) #OLS standard errors are too small mod.res_pooled.params mod.res_pooled.bse #heteroscedasticity robust does not help mod.res_pooled.HC1_se #compare with cluster robust se print(sw.se_cov(sw.cov_cluster(mod.res_pooled, dgp.groups.astype(int)))) #not bad, pretty close to panel estimator #and with Newey-West Hac print(sw.se_cov(sw.cov_nw_panel(mod.res_pooled, 4, mod.group.groupidx))) #too small, assuming no bugs, #see Peterson assuming it refers to same kind of model print(dgp.cov) mod2 = ShortPanelGLS(y, dgp.exog, dgp.groups) res2 = mod2.fit_iterative(2) print(res2.params) print(res2.bse) #both implementations produce the same results: from numpy.testing import assert_almost_equal assert_almost_equal(res.params, res2.params, decimal=12) assert_almost_equal(res.bse, res2.bse, decimal=13) mod5 = ShortPanelGLS(y, dgp.exog, dgp.groups) res5 = mod5.fit_iterative(5) print(res5.params) print(res5.bse) #fitting once is the same as OLS #note: I need to create new instance, otherwise it continuous fitting mod1 = ShortPanelGLS(y, dgp.exog, dgp.groups) res1 = mod1.fit_iterative(1) res_ols = mod1._fit_ols() assert_almost_equal(res1.params, res_ols.params, decimal=12) assert_almost_equal(res1.bse, res_ols.bse, decimal=13) #cov_hac_panel with uniform_kernel is the same as cov_cluster for balanced #panel with full length kernel #I fixe default correction to be equal mod2._fit_ols() cov_clu = sw.cov_cluster(mod2.res_pooled, dgp.groups.astype(int)) clubse = se_cov(cov_clu) cov_uni = sw.cov_nw_panel(mod2.res_pooled, 4, mod2.group.groupidx, weights_func=sw.weights_uniform, use_correction='cluster') assert_almost_equal(cov_uni, cov_clu, decimal=7) #without correction cov_clu2 = sw.cov_cluster(mod2.res_pooled, dgp.groups.astype(int), use_correction=False) cov_uni2 = sw.cov_nw_panel(mod2.res_pooled, 4, mod2.group.groupidx, weights_func=sw.weights_uniform, use_correction=False) assert_almost_equal(cov_uni2, cov_clu2, decimal=8) cov_white = sw.cov_white_simple(mod2.res_pooled) cov_pnw0 = sw.cov_nw_panel(mod2.res_pooled, 0, mod2.group.groupidx, use_correction='hac') assert_almost_equal(cov_pnw0, cov_white, decimal=13) time = np.tile(np.arange(nobs_i), n_groups) #time = mod2.group.group_int cov_pnw1 = sw.cov_nw_panel(mod2.res_pooled, 4, mod2.group.groupidx) cov_pnw2 = cov_nw_panel2(mod2.res_pooled, 4, time) #s = sw.group_sums(x, time) c2, ct, cg = sw.cov_cluster_2groups(mod2.res_pooled, time, dgp.groups.astype(int), use_correction=False) ct_nw0 = cov_nw_panel2(mod2.res_pooled, 0, time, weights_func=sw.weights_uniform, use_correction=False) cg_nw0 = cov_nw_panel2(mod2.res_pooled, 0, dgp.groups.astype(int), weights_func=sw.weights_uniform, use_correction=False) assert_almost_equal(ct_nw0, ct, decimal=13) assert_almost_equal(cg_nw0, cg, decimal=13) #pnw2 0 lags assert_almost_equal(cov_clu2, cg, decimal=13) assert_almost_equal(cov_uni2, cg, decimal=8) #pnw all lags import pandas as pa #pandas.DataFrame does not do inplace append se = pa.DataFrame(res_ols.bse[None,:], index=['OLS']) se = se.append(pa.DataFrame(res5.bse[None,:], index=['PGLSit5'])) clbse = sw.se_cov(sw.cov_cluster(mod.res_pooled, dgp.groups.astype(int))) se = se.append(pa.DataFrame(clbse[None,:], index=['OLSclu'])) pnwse = sw.se_cov(sw.cov_nw_panel(mod.res_pooled, 4, mod.group.groupidx)) se = se.append(pa.DataFrame(pnwse[None,:], index=['OLSpnw'])) print(se) #list(se.index) from statsmodels.iolib.table import SimpleTable headers = [str(i) for i in se.columns] stubs=list(se.index) # print SimpleTable(np.round(np.asarray(se), 4), # headers=headers, # stubs=stubs) print(SimpleTable(np.asarray(se), headers=headers, stubs=stubs, txt_fmt=dict(data_fmts=['%10.4f']), title='Standard Errors')) statsmodels-0.12.2/statsmodels/sandbox/examples/example_crossval.py000066400000000000000000000040041400612667500257020ustar00rootroot00000000000000 import numpy as np from statsmodels.sandbox.tools import cross_val if __name__ == '__main__': #A: josef-pktd import statsmodels.api as sm #from statsmodels.datasets.longley import load from statsmodels.datasets.stackloss import load data = load(as_pandas=False) data.exog = sm.tools.add_constant(data.exog, prepend=False) resols = sm.OLS(data.endog, data.exog).fit() print('\n OLS leave 1 out') for inidx, outidx in cross_val.LeaveOneOut(len(data.endog)): res = sm.OLS(data.endog[inidx], data.exog[inidx,:]).fit() print(data.endog[outidx], res.model.predict(res.params, data.exog[outidx,:], end=' ')) print(data.endog[outidx] - res.model.predict(res.params, data.exog[outidx,:])) print('\n OLS leave 2 out') resparams = [] for inidx, outidx in cross_val.LeavePOut(len(data.endog), 2): res = sm.OLS(data.endog[inidx], data.exog[inidx,:]).fit() #print data.endog[outidx], res.model.predict(data.exog[outidx,:]), #print ((data.endog[outidx] - res.model.predict(data.exog[outidx,:]))**2).sum() resparams.append(res.params) resparams = np.array(resparams) print(resparams) doplots = 1 if doplots: import matplotlib.pyplot as plt from matplotlib.font_manager import FontProperties plt.figure() figtitle = 'Leave2out parameter estimates' t = plt.gcf().text(0.5, 0.95, figtitle, horizontalalignment='center', fontproperties=FontProperties(size=16)) for i in range(resparams.shape[1]): plt.subplot(4, 2, i+1) plt.hist(resparams[:,i], bins = 10) #plt.title("Leave2out parameter estimates") plt.show() for inidx, outidx in cross_val.KStepAhead(20,2): #note the following were broken because KStepAhead returns now a slice by default print(inidx) print(np.ones(20)[inidx].sum(), np.arange(20)[inidx][-4:]) print(outidx) print(np.nonzero(np.ones(20)[outidx])[0][()]) statsmodels-0.12.2/statsmodels/sandbox/examples/example_gam.py000066400000000000000000000043611400612667500246200ustar00rootroot00000000000000'''original example for checking how far GAM works Note: uncomment plt.show() to display graphs ''' import time import numpy as np import numpy.random as R import matplotlib.pyplot as plt import scipy.stats from statsmodels.sandbox.gam import AdditiveModel from statsmodels.sandbox.gam import Model as GAM #? from statsmodels.genmod.families import family example = 2 # 1,2 or 3 standardize = lambda x: (x - x.mean()) / x.std() demean = lambda x: (x - x.mean()) nobs = 150 x1 = R.standard_normal(nobs) x1.sort() x2 = R.standard_normal(nobs) x2.sort() y = R.standard_normal((nobs,)) f1 = lambda x1: (x1 + x1**2 - 3 - 1 * x1**3 + 0.1 * np.exp(-x1/4.)) f2 = lambda x2: (x2 + x2**2 - 0.1 * np.exp(x2/4.)) z = standardize(f1(x1)) + standardize(f2(x2)) z = standardize(z) * 2 # 0.1 y += z d = np.array([x1,x2]).T if example == 1: print("normal") m = AdditiveModel(d) m.fit(y) x = np.linspace(-2,2,50) print(m) y_pred = m.results.predict(d) plt.figure() plt.plot(y, '.') plt.plot(z, 'b-', label='true') plt.plot(y_pred, 'r-', label='AdditiveModel') plt.legend() plt.title('gam.AdditiveModel') if example == 2: print("binomial") f = family.Binomial() b = np.asarray([scipy.stats.bernoulli.rvs(p) for p in f.link.inverse(y)]) b.shape = y.shape m = GAM(b, d, family=f) toc = time.time() m.fit(b) tic = time.time() print(tic-toc) if example == 3: print("Poisson") f = family.Poisson() y = y/y.max() * 3 yp = f.link.inverse(y) p = np.asarray([scipy.stats.poisson.rvs(p) for p in f.link.inverse(y)], float) p.shape = y.shape m = GAM(p, d, family=f) toc = time.time() m.fit(p) tic = time.time() print(tic-toc) plt.figure() plt.plot(x1, standardize(m.smoothers[0](x1)), 'r') plt.plot(x1, standardize(f1(x1)), linewidth=2) plt.figure() plt.plot(x2, standardize(m.smoothers[1](x2)), 'r') plt.plot(x2, standardize(f2(x2)), linewidth=2) plt.show() ## pylab.figure(num=1) ## pylab.plot(x1, standardize(m.smoothers[0](x1)), 'b') ## pylab.plot(x1, standardize(f1(x1)), linewidth=2) ## pylab.figure(num=2) ## pylab.plot(x2, standardize(m.smoothers[1](x2)), 'b') ## pylab.plot(x2, standardize(f2(x2)), linewidth=2) ## pylab.show() statsmodels-0.12.2/statsmodels/sandbox/examples/example_gam_0.py000066400000000000000000000105031400612667500250320ustar00rootroot00000000000000'''first examples for gam and PolynomialSmoother used for debugging This example was written as a test case. The data generating process is chosen so the parameters are well identified and estimated. Note: uncomment plt.show() to display graphs ''' import time import numpy as np import numpy.random as R import matplotlib.pyplot as plt import scipy.stats from statsmodels.sandbox.gam import AdditiveModel from statsmodels.sandbox.gam import Model as GAM #? from statsmodels.genmod import families example = 2 #3 # 1,2 or 3 #np.random.seed(987654) standardize = lambda x: (x - x.mean()) / x.std() demean = lambda x: (x - x.mean()) nobs = 500 lb, ub = -1., 1. #for Poisson #lb, ub = -0.75, 2 #0.75 #for Binomial x1 = R.uniform(lb, ub, nobs) #R.standard_normal(nobs) x1 = np.linspace(lb, ub, nobs) x1.sort() x2 = R.uniform(lb, ub, nobs) # #x2 = R.standard_normal(nobs) x2.sort() #x2 = np.cos(x2) x2 = x2 + np.exp(x2/2.) #x2 = np.log(x2-x2.min()+0.1) y = 0.5 * R.uniform(lb, ub, nobs) #R.standard_normal((nobs,)) f1 = lambda x1: (2*x1 - 0.5 * x1**2 - 0.75 * x1**3) # + 0.1 * np.exp(-x1/4.)) f2 = lambda x2: (x2 - 1* x2**2) # - 0.75 * np.exp(x2)) z = standardize(f1(x1)) + standardize(f2(x2)) z = standardize(z) + 1 # 0.1 #try this z = f1(x1) + f2(x2) #z = demean(z) z -= np.median(z) print('z.std()', z.std()) #z = standardize(z) + 0.2 # with standardize I get better values, but I do not know what the true params are print(z.mean(), z.min(), z.max()) #y += z #noise y = z d = np.array([x1,x2]).T if example == 1: print("normal") m = AdditiveModel(d) m.fit(y) x = np.linspace(-2,2,50) print(m) if example == 2: print("binomial") mod_name = 'Binomial' f = families.Binomial() #b = np.asarray([scipy.stats.bernoulli.rvs(p) for p in f.link.inverse(y)]) b = np.asarray([scipy.stats.bernoulli.rvs(p) for p in f.link.inverse(z)]) b.shape = y.shape m = GAM(b, d, family=f) toc = time.time() m.fit(b) tic = time.time() print(tic-toc) #for plotting yp = f.link.inverse(y) p = b if example == 3: print("Poisson") f = families.Poisson() #y = y/y.max() * 3 yp = f.link.inverse(z) p = np.asarray([scipy.stats.poisson.rvs(val) for val in f.link.inverse(z)], float) p.shape = y.shape m = GAM(p, d, family=f) toc = time.time() m.fit(p) tic = time.time() print(tic-toc) if example > 1: y_pred = m.results.mu# + m.results.alpha#m.results.predict(d) plt.figure() plt.subplot(2,2,1) plt.plot(p, '.') plt.plot(yp, 'b-', label='true') plt.plot(y_pred, 'r-', label='GAM') plt.legend(loc='upper left') plt.title('gam.GAM ' + mod_name) counter = 2 for ii, xx in zip(['z', 'x1', 'x2'], [z, x1, x2]): sortidx = np.argsort(xx) #plt.figure() plt.subplot(2, 2, counter) plt.plot(xx[sortidx], p[sortidx], '.') plt.plot(xx[sortidx], yp[sortidx], 'b.', label='true') plt.plot(xx[sortidx], y_pred[sortidx], 'r.', label='GAM') plt.legend(loc='upper left') plt.title('gam.GAM ' + mod_name + ' ' + ii) counter += 1 # counter = 2 # for ii, xx in zip(['z', 'x1', 'x2'], [z, x1, x2]): # #plt.figure() # plt.subplot(2, 2, counter) # plt.plot(xx, p, '.') # plt.plot(xx, yp, 'b-', label='true') # plt.plot(xx, y_pred, 'r-', label='GAM') # plt.legend(loc='upper left') # plt.title('gam.GAM Poisson ' + ii) # counter += 1 plt.figure() plt.plot(z, 'b-', label='true' ) plt.plot(np.log(m.results.mu), 'r-', label='GAM') plt.title('GAM Poisson, raw') plt.figure() plt.plot(x1, standardize(m.smoothers[0](x1)), 'r') plt.plot(x1, standardize(f1(x1)), linewidth=2) plt.figure() plt.plot(x2, standardize(m.smoothers[1](x2)), 'r') plt.plot(x2, standardize(f2(x2)), linewidth=2) ##y_pred = m.results.predict(d) ##plt.figure() ##plt.plot(z, p, '.') ##plt.plot(z, yp, 'b-', label='true') ##plt.plot(z, y_pred, 'r-', label='AdditiveModel') ##plt.legend() ##plt.title('gam.AdditiveModel') #plt.show() ## pylab.figure(num=1) ## pylab.plot(x1, standardize(m.smoothers[0](x1)), 'b') ## pylab.plot(x1, standardize(f1(x1)), linewidth=2) ## pylab.figure(num=2) ## pylab.plot(x2, standardize(m.smoothers[1](x2)), 'b') ## pylab.plot(x2, standardize(f2(x2)), linewidth=2) ## pylab.show() statsmodels-0.12.2/statsmodels/sandbox/examples/example_maxent.py000066400000000000000000000024041400612667500253440ustar00rootroot00000000000000""" This is an example of using scipy.maxentropy to solve Jaynes' dice problem See Golan, Judge, and Miller Section 2.3 """ from scipy import maxentropy import numpy as np samplespace = [1., 2., 3., 4., 5., 6.] def sump(x): return x in samplespace def meanp(x): return np.mean(x) # Set the constraints # 1) We have a proper probability # 2) The mean is equal to... F = [sump, meanp] model = maxentropy.model(F, samplespace) # set the desired feature expectations K = np.ones((5,2)) K[:,1] = [2.,3.,3.5,4.,5.] model.verbose = False for i in range(K.shape[0]): model.fit(K[i]) # Output the distribution print("\nFitted model parameters are:\n" + str(model.params)) print("\nFitted distribution is:") p = model.probdist() for j in range(len(model.samplespace)): x = model.samplespace[j] print("y = %-15s\tx = %-15s" %(str(K[i,1])+":",str(x) + ":") + \ " p(x) = "+str(p[j])) # Now show how well the constraints are satisfied: print() print("Desired constraints:") print("\tsum_{i}p_{i}= 1") print("\tE[X] = %-15s" % str(K[i,1])) print() print("Actual expectations under the fitted model:") print("\tsum_{i}p_{i} =", np.sum(p)) print("\tE[X] = " + str(np.sum(p*np.arange(1,7)))) statsmodels-0.12.2/statsmodels/sandbox/examples/example_mle.py000066400000000000000000000040551400612667500246310ustar00rootroot00000000000000'''Examples to compare MLE with OLS TODO: compare standard error of parameter estimates ''' from scipy import optimize import numpy as np import statsmodels.api as sm from statsmodels.datasets.longley import load print('\nExample 1: Artificial Data') print('--------------------------\n') np.random.seed(54321) X = np.random.rand(40,2) X = sm.add_constant(X, prepend=False) beta = np.array((3.5, 5.7, 150)) Y = np.dot(X,beta) + np.random.standard_normal(40) mod2 = sm.OLS(Y,X) res2 = mod2.fit() f2 = lambda params: -1*mod2.loglike(params) resfmin = optimize.fmin(f2, np.ones(3), ftol=1e-10) print('OLS') print(res2.params) print('MLE') print(resfmin) print('\nExample 2: Longley Data, high multicollinearity') print('-----------------------------------------------\n') data = load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) mod = sm.OLS(data.endog, data.exog) f = lambda params: -1*mod.loglike(params) score = lambda params: -1*mod.score(params) #now you're set up to try and minimize or root find, but I couldn't get this one to work #note that if you want to get the results, it's also a property of mod, so you can do res = mod.fit() #print mod.results.params print('OLS') print(res.params) print('MLE') #resfmin2 = optimize.fmin(f, mod.results.params*0.9, maxfun=5000, maxiter=5000, xtol=1e-10, ftol= 1e-10) resfmin2 = optimize.fmin(f, np.ones(7), maxfun=5000, maxiter=5000, xtol=1e-10, ftol= 1e-10) print(resfmin2) # there is not a unique solution? Is this due to the multicollinearity? Improved with use of analytically # defined score function? #check X'X matrix xtxi = np.linalg.inv(np.dot(data.exog.T,data.exog)) eval, evec = np.linalg.eig(xtxi) print('Eigenvalues') print(eval) # look at correlation print('correlation matrix') print(np.corrcoef(data.exog[:,:-1], rowvar=0)) #exclude constant # --> conclusion high multicollinearity # compare print('with matrix formula') print(np.dot(xtxi,np.dot(data.exog.T, data.endog[:,np.newaxis])).ravel()) print('with pinv') print(np.dot(np.linalg.pinv(data.exog), data.endog[:,np.newaxis]).ravel()) statsmodels-0.12.2/statsmodels/sandbox/examples/example_nbin.py000066400000000000000000000315561400612667500250100ustar00rootroot00000000000000# -*- coding: utf-8 -*- ''' Author: Vincent Arel-Bundock Date: 2012-08-25 This example file implements 5 variations of the negative binomial regression model for count data: NB-P, NB-1, NB-2, geometric and left-truncated. The NBin class inherits from the GenericMaximumLikelihood statsmodels class which provides automatic numerical differentiation for the score and hessian. NB-1, NB-2 and geometric are implemented as special cases of the NB-P model described in Greene (2008) Functional forms for the negative binomial model for count data. Economics Letters, v99n3. Tests are included to check how NB-1, NB-2 and geometric coefficient estimates compare to equivalent models in R. Results usually agree up to the 4th digit. The NB-P and left-truncated model results have not been compared to other implementations. Note that NB-P appears to only have been implemented in the LIMDEP software. ''' from urllib.request import urlopen import numpy as np from numpy.testing import assert_almost_equal from scipy.special import digamma from scipy.stats import nbinom import pandas import patsy from statsmodels.base.model import GenericLikelihoodModel from statsmodels.base.model import GenericLikelihoodModelResults #### Negative Binomial Log-likelihoods #### def _ll_nbp(y, X, beta, alph, Q): r''' Negative Binomial Log-likelihood -- type P References: Greene, W. 2008. "Functional forms for the negative binomial model for count data". Economics Letters. Volume 99, Number 3, pp.585-590. Hilbe, J.M. 2011. "Negative binomial regression". Cambridge University Press. Following notation in Greene (2008), with negative binomial heterogeneity parameter :math:`\alpha`: .. math:: \lambda_i = exp(X\beta)\\ \theta = 1 / \alpha \\ g_i = \theta \lambda_i^Q \\ w_i = g_i/(g_i + \lambda_i) \\ r_i = \theta / (\theta+\lambda_i) \\ ln \mathcal{L}_i = ln \Gamma(y_i+g_i) - ln \Gamma(1+y_i) + g_iln (r_i) + y_i ln(1-r_i) ''' mu = np.exp(np.dot(X, beta)) size = 1/alph*mu**Q prob = size/(size+mu) ll = nbinom.logpmf(y, size, prob) return ll def _ll_nb1(y, X, beta, alph): '''Negative Binomial regression (type 1 likelihood)''' ll = _ll_nbp(y, X, beta, alph, Q=1) return ll def _ll_nb2(y, X, beta, alph): '''Negative Binomial regression (type 2 likelihood)''' ll = _ll_nbp(y, X, beta, alph, Q=0) return ll def _ll_geom(y, X, beta): '''Geometric regression''' ll = _ll_nbp(y, X, beta, alph=1, Q=0) return ll def _ll_nbt(y, X, beta, alph, C=0): r''' Negative Binomial (truncated) Truncated densities for count models (Cameron & Trivedi, 2005, 680): .. math:: f(y|\beta, y \geq C+1) = \frac{f(y|\beta)}{1-F(C|\beta)} ''' Q = 0 mu = np.exp(np.dot(X, beta)) size = 1/alph*mu**Q prob = size/(size+mu) ll = nbinom.logpmf(y, size, prob) - np.log(1 - nbinom.cdf(C, size, prob)) return ll #### Model Classes #### class NBin(GenericLikelihoodModel): ''' Negative Binomial regression Parameters ---------- endog : array_like 1-d array of the response variable. exog : array_like `exog` is an n x p array where n is the number of observations and p is the number of regressors including the intercept if one is included in the data. ll_type: str log-likelihood type `nb2`: Negative Binomial type-2 (most common) `nb1`: Negative Binomial type-1 `nbp`: Negative Binomial type-P (Greene, 2008) `nbt`: Left-truncated Negative Binomial (type-2) `geom`: Geometric regression model C: int Cut-point for `nbt` model ''' def __init__(self, endog, exog, ll_type='nb2', C=0, **kwds): self.exog = np.array(exog) self.endog = np.array(endog) self.C = C super(NBin, self).__init__(endog, exog, **kwds) # Check user input if ll_type not in ['nb2', 'nb1', 'nbp', 'nbt', 'geom']: raise NameError('Valid ll_type are: nb2, nb1, nbp, nbt, geom') self.ll_type = ll_type # Starting values (assumes first column of exog is constant) if ll_type == 'geom': self.start_params_default = np.zeros(self.exog.shape[1]) elif ll_type == 'nbp': # Greene recommends starting NB-P at NB-2 start_mod = NBin(endog, exog, 'nb2') start_res = start_mod.fit(disp=False) self.start_params_default = np.append(start_res.params, 0) else: self.start_params_default = np.append(np.zeros(self.exog.shape[1]), .5) self.start_params_default[0] = np.log(self.endog.mean()) # Define loglik based on ll_type argument if ll_type == 'nb1': self.ll_func = _ll_nb1 elif ll_type == 'nb2': self.ll_func = _ll_nb2 elif ll_type == 'geom': self.ll_func = _ll_geom elif ll_type == 'nbp': self.ll_func = _ll_nbp elif ll_type == 'nbt': self.ll_func = _ll_nbt def nloglikeobs(self, params): alph = params[-1] beta = params[:self.exog.shape[1]] if self.ll_type == 'geom': return -self.ll_func(self.endog, self.exog, beta) elif self.ll_type == 'nbt': return -self.ll_func(self.endog, self.exog, beta, alph, self.C) elif self.ll_type == 'nbp': Q = params[-2] return -self.ll_func(self.endog, self.exog, beta, alph, Q) else: return -self.ll_func(self.endog, self.exog, beta, alph) def fit(self, start_params=None, maxiter=10000, maxfun=5000, **kwds): if start_params is None: countfit = super(NBin, self).fit(start_params=self.start_params_default, maxiter=maxiter, maxfun=maxfun, **kwds) else: countfit = super(NBin, self).fit(start_params=start_params, maxiter=maxiter, maxfun=maxfun, **kwds) countfit = CountResults(self, countfit) return countfit class CountResults(GenericLikelihoodModelResults): def __init__(self, model, mlefit): self.model = model self.__dict__.update(mlefit.__dict__) def summary(self, yname=None, xname=None, title=None, alpha=.05, yname_list=None): top_left = [('Dep. Variable:', None), ('Model:', [self.model.__class__.__name__]), ('Method:', ['MLE']), ('Date:', None), ('Time:', None), ('Converged:', ["%s" % self.mle_retvals['converged']])] top_right = [('No. Observations:', None), ('Log-Likelihood:', None), ] if title is None: title = self.model.__class__.__name__ + ' ' + "Regression Results" #boiler plate from statsmodels.iolib.summary import Summary smry = Summary() # for top of table smry.add_table_2cols(self, gleft=top_left, gright=top_right, #[], yname=yname, xname=xname, title=title) # for parameters, etc smry.add_table_params(self, yname=yname_list, xname=xname, alpha=alpha, use_t=True) return smry #### Score function for NB-P #### def _score_nbp(y, X, beta, thet, Q): r''' Negative Binomial Score -- type P likelihood from Greene (2007) .. math:: \lambda_i = exp(X\beta)\\ g_i = \theta \lambda_i^Q \\ w_i = g_i/(g_i + \lambda_i) \\ r_i = \theta / (\theta+\lambda_i) \\ A_i = \left [ \Psi(y_i+g_i) - \Psi(g_i) + ln w_i \right ] \\ B_i = \left [ g_i (1-w_i) - y_iw_i \right ] \\ \partial ln \mathcal{L}_i / \partial \begin{pmatrix} \lambda_i \\ \theta \\ Q \end{pmatrix}= [A_i+B_i] \begin{pmatrix} Q/\lambda_i \\ 1/\theta \\ ln(\lambda_i) \end{pmatrix} -B_i \begin{pmatrix} 1/\lambda_i\\ 0 \\ 0 \end{pmatrix} \\ \frac{\partial \lambda}{\partial \beta} = \lambda_i \mathbf{x}_i \\ \frac{\partial \mathcal{L}_i}{\partial \beta} = \left (\frac{\partial\mathcal{L}_i}{\partial \lambda_i} \right ) \frac{\partial \lambda_i}{\partial \beta} ''' lamb = np.exp(np.dot(X, beta)) g = thet * lamb**Q w = g / (g + lamb) r = thet / (thet+lamb) A = digamma(y+g) - digamma(g) + np.log(w) B = g*(1-w) - y*w dl = (A+B) * Q/lamb - B * 1/lamb dt = (A+B) * 1/thet dq = (A+B) * np.log(lamb) db = X * (dl * lamb)[:,np.newaxis] sc = np.array([dt.sum(), dq.sum()]) sc = np.concatenate([db.sum(axis=0), sc]) return sc #### Tests #### medpar = pandas.read_csv(urlopen('https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/csv/COUNT/medpar.csv')) mdvis = pandas.read_csv(urlopen('https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/csv/COUNT/mdvis.csv')) # NB-2 ''' # R v2.15.1 library(MASS) library(COUNT) data(medpar) f <- los~factor(type)+hmo+white mod <- glm.nb(f, medpar) summary(mod) Call: glm.nb(formula = f, data = medpar, init.theta = 2.243376203, link = log) Deviance Residuals: Min 1Q Median 3Q Max -2.4671 -0.9090 -0.2693 0.4320 3.8668 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 2.31028 0.06745 34.253 < 2e-16 *** factor(type)2 0.22125 0.05046 4.385 1.16e-05 *** factor(type)3 0.70616 0.07600 9.292 < 2e-16 *** hmo -0.06796 0.05321 -1.277 0.202 white -0.12907 0.06836 -1.888 0.059 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for Negative Binomial(2.2434) family taken to be 1) Null deviance: 1691.1 on 1494 degrees of freedom Residual deviance: 1568.1 on 1490 degrees of freedom AIC: 9607 Number of Fisher Scoring iterations: 1 Theta: 2.2434 Std. Err.: 0.0997 2 x log-likelihood: -9594.9530 ''' def test_nb2(): y, X = patsy.dmatrices('los ~ C(type) + hmo + white', medpar) y = np.array(y)[:,0] nb2 = NBin(y,X,'nb2').fit(maxiter=10000, maxfun=5000) assert_almost_equal(nb2.params, [2.31027893349935, 0.221248978197356, 0.706158824346228, -0.067955221930748, -0.129065442248951, 0.4457567], decimal=2) # NB-1 ''' # R v2.15.1 # COUNT v1.2.3 library(COUNT) data(medpar) f <- los~factor(type)+hmo+white ml.nb1(f, medpar) Estimate SE Z LCL UCL (Intercept) 2.34918407 0.06023641 38.9994023 2.23112070 2.46724744 factor(type)2 0.16175471 0.04585569 3.5274735 0.07187757 0.25163186 factor(type)3 0.41879257 0.06553258 6.3906006 0.29034871 0.54723643 hmo -0.04533566 0.05004714 -0.9058592 -0.14342805 0.05275673 white -0.12951295 0.06071130 -2.1332593 -0.24850710 -0.01051880 alpha 4.57898241 0.22015968 20.7984603 4.14746943 5.01049539 ''' #def test_nb1(): #y, X = patsy.dmatrices('los ~ C(type) + hmo + white', medpar) #y = np.array(y)[:,0] ## TODO: Test fails with some of the other optimization methods #nb1 = NBin(y,X,'nb1').fit(method='ncg', maxiter=10000, maxfun=5000) #assert_almost_equal(nb1.params, #[2.34918407014186, 0.161754714412848, 0.418792569970658, # -0.0453356614650342, -0.129512952033423, 4.57898241219275], #decimal=2) # NB-Geometric ''' MASS v7.3-20 R v2.15.1 library(MASS) data(medpar) f <- los~factor(type)+hmo+white mod <- glm(f, family=negative.binomial(1), data=medpar) summary(mod) Call: glm(formula = f, family = negative.binomial(1), data = medpar) Deviance Residuals: Min 1Q Median 3Q Max -1.7942 -0.6545 -0.1896 0.3044 2.6844 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.30849 0.07071 32.649 < 2e-16 *** factor(type)2 0.22121 0.05283 4.187 2.99e-05 *** factor(type)3 0.70599 0.08092 8.724 < 2e-16 *** hmo -0.06779 0.05521 -1.228 0.2197 white -0.12709 0.07169 -1.773 0.0765 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for Negative Binomial(1) family taken to be 0.5409721) Null deviance: 872.29 on 1494 degrees of freedom Residual deviance: 811.95 on 1490 degrees of freedom AIC: 9927.3 Number of Fisher Scoring iterations: 5 ''' #def test_geom(): #y, X = patsy.dmatrices('los ~ C(type) + hmo + white', medpar) #y = np.array(y)[:,0] ## TODO: remove alph from geom params #geom = NBin(y,X,'geom').fit(maxiter=10000, maxfun=5000) #assert_almost_equal(geom.params, #[2.3084850946241, 0.221206159108742, 0.705986369841159, # -0.0677871843613577, -0.127088772164963], #decimal=4) test_nb2() statsmodels-0.12.2/statsmodels/sandbox/examples/example_pca.py000066400000000000000000000010051400612667500246070ustar00rootroot00000000000000#!/usr/bin/env python import numpy as np from statsmodels.sandbox.pca import Pca x=np.random.randn(1000) y=x*2.3+5+np.random.randn(1000) z=x*3.1+2.1*y+np.random.randn(1000)/2 #create the Pca object - requires a p x N array as the input p=Pca((x,y,z)) print('energies:',p.getEnergies()) print('vecs:',p.getEigenvectors()) print('projected data',p.project(vals=np.ones((3,10)))) #p.plot2d() #requires matplotlib #from matplotlib import pyplot as plt #plt.show() #necessary for script #p.plot3d() #requires mayavi statsmodels-0.12.2/statsmodels/sandbox/examples/example_pca_regression.py000066400000000000000000000067551400612667500270700ustar00rootroot00000000000000'''Example: Principal Component Regression * simulate model with 2 factors and 4 explanatory variables * use pca to extract factors from data, * run OLS on factors, * use information criteria to choose "best" model Warning: pca sorts factors by explaining variance in explanatory variables, which are not necessarily the most important factors for explaining the endogenous variable. # try out partial correlation for dropping (or adding) factors # get algorithm for partial least squares as an alternative to PCR ''' import numpy as np import statsmodels.api as sm from statsmodels.iolib.table import SimpleTable from statsmodels.sandbox.tools import pca from statsmodels.sandbox.tools.cross_val import LeaveOneOut # Example: principal component regression nobs = 1000 f0 = np.c_[np.random.normal(size=(nobs,2)), np.ones((nobs,1))] f2xcoef = np.c_[np.repeat(np.eye(2),2,0),np.arange(4)[::-1]].T f2xcoef = np.array([[ 1., 1., 0., 0.], [ 0., 0., 1., 1.], [ 3., 2., 1., 0.]]) f2xcoef = np.array([[ 0.1, 3., 1., 0.], [ 0., 0., 1.5, 0.1], [ 3., 2., 1., 0.]]) x0 = np.dot(f0, f2xcoef) x0 += 0.1*np.random.normal(size=x0.shape) ytrue = np.dot(f0,[1., 1., 1.]) y0 = ytrue + 0.1*np.random.normal(size=ytrue.shape) xred, fact, eva, eve = pca(x0, keepdim=0) print(eve) print(fact[:5]) print(f0[:5]) res = sm.OLS(y0, sm.add_constant(x0, prepend=False)).fit() print('OLS on original data') print(res.params) print(res.aic) print(res.rsquared) #print 'OLS on Factors' #for k in range(x0.shape[1]): # xred, fact, eva, eve = pca(x0, keepdim=k, normalize=1) # fact_wconst = sm.add_constant(fact) # res = sm.OLS(y0, fact_wconst).fit() # print 'k =', k # print res.params # print 'aic: ', res.aic # print 'bic: ', res.bic # print 'llf: ', res.llf # print 'R2 ', res.rsquared # print 'R2 adj', res.rsquared_adj print('OLS on Factors') results = [] xred, fact, eva, eve = pca(x0, keepdim=0, normalize=1) for k in range(0, x0.shape[1]+1): #xred, fact, eva, eve = pca(x0, keepdim=k, normalize=1) # this is faster and same result fact_wconst = sm.add_constant(fact[:,:k], prepend=False) res = sm.OLS(y0, fact_wconst).fit() ## print 'k =', k ## print res.params ## print 'aic: ', res.aic ## print 'bic: ', res.bic ## print 'llf: ', res.llf ## print 'R2 ', res.rsquared ## print 'R2 adj', res.rsquared_adj prederr2 = 0. for inidx, outidx in LeaveOneOut(len(y0)): resl1o = sm.OLS(y0[inidx], fact_wconst[inidx,:]).fit() #print data.endog[outidx], res.model.predict(data.exog[outidx,:]), prederr2 += (y0[outidx] - resl1o.predict(fact_wconst[outidx,:]))**2. results.append([k, res.aic, res.bic, res.rsquared_adj, prederr2]) results = np.array(results) print(results) print('best result for k, by AIC, BIC, R2_adj, L1O') print(np.r_[(np.argmin(results[:,1:3],0), np.argmax(results[:,3],0), np.argmin(results[:,-1],0))]) headers = 'k, AIC, BIC, R2_adj, L1O'.split(', ') numformat = ['%6d'] + ['%10.3f']*4 #'%10.4f' txt_fmt1 = dict(data_fmts = numformat) tabl = SimpleTable(results, headers, None, txt_fmt=txt_fmt1) print("PCA regression on simulated data,") print("DGP: 2 factors and 4 explanatory variables") print(tabl) print("Notes: k is number of components of PCA,") print(" constant is added additionally") print(" k=0 means regression on constant only") print(" L1O: sum of squared prediction errors for leave-one-out") statsmodels-0.12.2/statsmodels/sandbox/examples/example_sysreg.py000066400000000000000000000176261400612667500254000ustar00rootroot00000000000000"""Example: statsmodels.sandbox.sysreg """ #TODO: this is going to change significantly once we have a panel data structure from statsmodels.compat.python import lmap, asbytes import numpy as np import statsmodels.api as sm from statsmodels.sandbox.sysreg import SUR, Sem2SLS from statsmodels.sandbox.regression.gmm import IV2SLS #for Python 3 compatibility # Seemingly Unrelated Regressions (SUR) Model # This example uses the subset of the Grunfeld data in Greene's Econometric # Analysis Chapter 14 (5th Edition) grun_data = sm.datasets.grunfeld.load(as_pandas=False) firms = ['General Motors', 'Chrysler', 'General Electric', 'Westinghouse', 'US Steel'] #for Python 3 compatibility firms = lmap(asbytes, firms) grun_exog = grun_data.exog grun_endog = grun_data.endog # Right now takes SUR takes a list of arrays # The array alternates between the LHS of an equation and RHS side of an # equation # This is very likely to change grun_sys = [] for i in firms: index = grun_exog['firm'] == i grun_sys.append(grun_endog[index]) exog = grun_exog[index][['value','capital']].view(float).reshape(-1,2) exog = sm.add_constant(exog, prepend=True) grun_sys.append(exog) # Note that the results in Greene (5th edition) uses a slightly different # version of the Grunfeld data. To reproduce Table 14.1 the following changes # are necessary. grun_sys[-2][5] = 261.6 grun_sys[-2][-3] = 645.2 grun_sys[-1][11,2] = 232.6 grun_mod = SUR(grun_sys) grun_res = grun_mod.fit() print("Results for the 2-step GLS") print("Compare to Greene Table 14.1, 5th edition") print(grun_res.params) # or you can do an iterative fit # you have to define a new model though this will be fixed # TODO: note the above print("Results for iterative GLS (equivalent to MLE)") print("Compare to Greene Table 14.3") #TODO: these are slightly off, could be a convergence issue # or might use a different default DOF correction? grun_imod = SUR(grun_sys) grun_ires = grun_imod.fit(igls=True) print(grun_ires.params) # Two-Stage Least Squares for Simultaneous Equations #TODO: we are going to need *some kind* of formula framework # This follows the simple macroeconomic model given in # Greene Example 15.1 (5th Edition) # The data however is from statsmodels and is not the same as # Greene's # The model is # consumption: c_{t} = \alpha_{0} + \alpha_{1}y_{t} + \alpha_{2}c_{t-1} + \epsilon_{t1} # investment: i_{t} = \beta_{0} + \beta_{1}r_{t} + \beta_{2}\left(y_{t}-y_{t-1}\right) + \epsilon_{t2} # demand: y_{t} = c_{t} + I_{t} + g_{t} # See Greene's Econometric Analysis for more information # Load the data macrodata = sm.datasets.macrodata.load(as_pandas=False).data # Not needed, but make sure the data is sorted macrodata = np.sort(macrodata, order=['year','quarter']) # Impose the demand restriction y = macrodata['realcons'] + macrodata['realinv'] + macrodata['realgovt'] # Build the system macro_sys = [] # First equation LHS macro_sys.append(macrodata['realcons'][1:]) # leave off first date # First equation RHS exog1 = np.column_stack((y[1:],macrodata['realcons'][:-1])) #TODO: it might be nice to have "lag" and "lead" functions exog1 = sm.add_constant(exog1, prepend=True) macro_sys.append(exog1) # Second equation LHS macro_sys.append(macrodata['realinv'][1:]) # Second equation RHS exog2 = np.column_stack((macrodata['tbilrate'][1:], np.diff(y))) exog2 = sm.add_constant(exog2, prepend=True) macro_sys.append(exog2) # We need to say that y_{t} in the RHS of equation 1 is an endogenous regressor # We will call these independent endogenous variables # Right now, we use a dictionary to declare these indep_endog = {0 : [1]} # We also need to create a design of our instruments # This will be done automatically in the future instruments = np.column_stack((macrodata[['realgovt', 'tbilrate']][1:].view(float).reshape(-1,2),macrodata['realcons'][:-1], y[:-1])) instruments = sm.add_constant(instruments, prepend=True) macro_mod = Sem2SLS(macro_sys, indep_endog=indep_endog, instruments=instruments) # Right now this only returns parameters macro_params = macro_mod.fit() print("The parameters for the first equation are correct.") print("The parameters for the second equation are not.") print(macro_params) #TODO: Note that the above is incorrect, because we have no way of telling the # model that *part* of the y_{t} - y_{t-1} is an independent endogenous variable # To correct for this we would have to do the following y_instrumented = macro_mod.wexog[0][:,1] whitened_ydiff = y_instrumented - y[:-1] wexog = np.column_stack((macrodata['tbilrate'][1:],whitened_ydiff)) wexog = sm.add_constant(wexog, prepend=True) correct_params = sm.GLS(macrodata['realinv'][1:], wexog).fit().params print("If we correctly instrument everything, then these are the parameters") print("for the second equation") print(correct_params) print("Compare to output of R script statsmodels/sandbox/tests/macrodata.s") print('\nUsing IV2SLS') miv = IV2SLS(macro_sys[0], macro_sys[1], instruments) resiv = miv.fit() print("equation 1") print(resiv.params) miv2 = IV2SLS(macro_sys[2], macro_sys[3], instruments) resiv2 = miv2.fit() print("equation 2") print(resiv2.params) ### Below is the same example using Greene's data ### run_greene = 0 if run_greene: try: data3 = np.genfromtxt('/home/skipper/school/MetricsII/Greene \ TableF5-1.txt', names=True) except: raise ValueError("Based on Greene TableF5-1. You should download it " "from his web site and edit this script accordingly.") # Example 15.1 in Greene 5th Edition # c_t = constant + y_t + c_t-1 # i_t = constant + r_t + (y_t - y_t-1) # y_t = c_t + i_t + g_t sys3 = [] sys3.append(data3['realcons'][1:]) # have to leave off a beg. date # impose 3rd equation on y y = data3['realcons'] + data3['realinvs'] + data3['realgovt'] exog1 = np.column_stack((y[1:],data3['realcons'][:-1])) exog1 = sm.add_constant(exog1, prepend=False) sys3.append(exog1) sys3.append(data3['realinvs'][1:]) exog2 = np.column_stack((data3['tbilrate'][1:], np.diff(y))) # realint is missing 1st observation exog2 = sm.add_constant(exog2, prepend=False) sys3.append(exog2) indep_endog = {0 : [0]} # need to be able to say that y_1 is an instrument.. instruments = np.column_stack((data3[['realgovt', 'tbilrate']][1:].view(float).reshape(-1,2),data3['realcons'][:-1], y[:-1])) instruments = sm.add_constant(instruments, prepend=False) sem_mod = Sem2SLS(sys3, indep_endog = indep_endog, instruments=instruments) sem_params = sem_mod.fit() # first equation is right, but not second? # should y_t in the diff be instrumented? # how would R know this in the script? # well, let's check... y_instr = sem_mod.wexog[0][:,0] wyd = y_instr - y[:-1] wexog = np.column_stack((data3['tbilrate'][1:],wyd)) wexog = sm.add_constant(wexog, prepend=False) params = sm.GLS(data3['realinvs'][1:], wexog).fit().params print("These are the simultaneous equation estimates for Greene's \ example 13-1 (Also application 13-1 in 6th edition.") print(sem_params) print("The first set of parameters is correct. The second set is not.") print("Compare to the solution manual at \ http://pages.stern.nyu.edu/~wgreene/Text/econometricanalysis.htm") print("The reason is the restriction on (y_t - y_1)") print("Compare to R script GreeneEx15_1.s") print("Somehow R carries y.1 in yd to know that it needs to be \ instrumented") print("If we replace our estimate with the instrumented one") print(params) print("We get the right estimate") print("Without a formula framework we have to be able to do restrictions.") # yep!, but how in the world does R know this when we just fed it yd?? # must be implicit in the formula framework... # we are going to need to keep the two equations separate and use # a restrictions matrix. Ugh, is a formula framework really, necessary to get # around this? statsmodels-0.12.2/statsmodels/sandbox/examples/gspc_table.csv000066400000000000000000030742421400612667500246170ustar00rootroot00000000000000Date,Open,High,Low,Close,Volume,Adj Close 2010-02-12,1075.95,1077.81,1062.97,1075.51,4160680000,1075.51 2010-02-11,1067.10,1080.04,1060.59,1078.47,4400870000,1078.47 2010-02-10,1069.68,1073.67,1059.34,1068.13,4251450000,1068.13 2010-02-09,1060.06,1079.28,1060.06,1070.52,5114260000,1070.52 2010-02-08,1065.51,1071.20,1056.51,1056.74,4089820000,1056.74 2010-02-05,1064.12,1067.13,1044.50,1066.19,6438900000,1066.19 2010-02-04,1097.25,1097.25,1062.78,1063.11,5859690000,1063.11 2010-02-03,1100.67,1102.72,1093.97,1097.28,4285450000,1097.28 2010-02-02,1090.05,1104.73,1087.96,1103.32,4749540000,1103.32 2010-02-01,1073.89,1089.38,1073.89,1089.19,4077610000,1089.19 2010-01-29,1087.61,1096.45,1071.59,1073.87,5412850000,1073.87 2010-01-28,1096.93,1100.22,1078.46,1084.53,5452400000,1084.53 2010-01-27,1091.94,1099.51,1083.11,1097.50,5319120000,1097.50 2010-01-26,1095.80,1103.69,1089.86,1092.17,4731910000,1092.17 2010-01-25,1092.40,1102.97,1092.40,1096.78,4481390000,1096.78 2010-01-22,1115.49,1115.49,1090.18,1091.76,6208650000,1091.76 2010-01-21,1138.68,1141.58,1114.84,1116.48,6874289600,1116.48 2010-01-20,1147.95,1147.95,1129.25,1138.04,4810560000,1138.04 2010-01-19,1136.03,1150.45,1135.77,1150.23,4724830000,1150.23 2010-01-15,1147.72,1147.77,1131.39,1136.03,4758730000,1136.03 2010-01-14,1145.68,1150.41,1143.80,1148.46,3915200000,1148.46 2010-01-13,1137.31,1148.40,1133.18,1145.68,4170360000,1145.68 2010-01-12,1143.81,1143.81,1131.77,1136.22,4716160000,1136.22 2010-01-11,1145.96,1149.74,1142.02,1146.98,4255780000,1146.98 2010-01-08,1140.52,1145.39,1136.22,1144.98,4389590000,1144.98 2010-01-07,1136.27,1142.46,1131.32,1141.69,5270680000,1141.69 2010-01-06,1135.71,1139.19,1133.95,1137.14,4972660000,1137.14 2010-01-05,1132.66,1136.63,1129.66,1136.52,2491020000,1136.52 2010-01-04,1116.56,1133.87,1116.56,1132.99,3991400000,1132.99 2009-12-31,1126.60,1127.64,1114.81,1115.10,2076990000,1115.10 2009-12-30,1125.53,1126.42,1121.94,1126.42,2277300000,1126.42 2009-12-29,1128.55,1130.38,1126.08,1126.20,2491020000,1126.20 2009-12-28,1127.53,1130.38,1123.51,1127.78,2716400000,1127.78 2009-12-24,1121.08,1126.48,1121.08,1126.48,1267710000,1126.48 2009-12-23,1118.84,1121.58,1116.00,1120.59,3166870000,1120.59 2009-12-22,1114.51,1120.27,1114.51,1118.02,3641130000,1118.02 2009-12-21,1105.31,1117.68,1105.31,1114.05,3977340000,1114.05 2009-12-18,1097.86,1103.74,1093.88,1102.47,6325890000,1102.47 2009-12-17,1106.36,1106.36,1095.88,1096.08,7615070400,1096.08 2009-12-16,1108.61,1116.21,1107.96,1109.18,4829820000,1109.18 2009-12-15,1114.11,1114.11,1105.35,1107.93,5045100000,1107.93 2009-12-14,1107.84,1114.76,1107.84,1114.11,4548490000,1114.11 2009-12-11,1103.96,1108.50,1101.34,1106.41,3791090000,1106.41 2009-12-10,1098.69,1106.25,1098.69,1102.35,3996490000,1102.35 2009-12-09,1091.07,1097.04,1085.89,1095.95,4115410000,1095.95 2009-12-08,1103.04,1103.04,1088.61,1091.94,4748030000,1091.94 2009-12-07,1105.52,1110.72,1100.83,1103.25,4103360000,1103.25 2009-12-04,1100.43,1119.13,1096.52,1105.98,5781140000,1105.98 2009-12-03,1110.59,1117.28,1098.74,1099.92,4810030000,1099.92 2009-12-02,1109.03,1115.58,1105.29,1109.24,3941340000,1109.24 2009-12-01,1098.89,1112.28,1098.89,1108.86,4249310000,1108.86 2009-11-30,1091.07,1097.24,1086.25,1095.63,3895520000,1095.63 2009-11-27,1105.47,1105.47,1083.74,1091.49,2362910000,1091.49 2009-11-25,1106.49,1111.18,1104.75,1110.63,3036350000,1110.63 2009-11-24,1105.83,1107.56,1097.63,1105.65,3700820000,1105.65 2009-11-23,1094.86,1112.38,1094.86,1106.24,3827920000,1106.24 2009-11-20,1094.66,1094.66,1086.81,1091.38,3751230000,1091.38 2009-11-19,1106.44,1106.44,1088.40,1094.90,4178030000,1094.90 2009-11-18,1109.44,1111.10,1102.70,1109.80,4293340000,1109.80 2009-11-17,1109.22,1110.52,1102.19,1110.32,3824070000,1110.32 2009-11-16,1094.13,1113.69,1094.13,1109.30,4565850000,1109.30 2009-11-13,1087.59,1097.79,1085.33,1093.48,3792610000,1093.48 2009-11-12,1098.31,1101.97,1084.90,1087.24,4160250000,1087.24 2009-11-11,1096.04,1105.37,1093.81,1098.51,4286700000,1098.51 2009-11-10,1091.86,1096.42,1087.40,1093.01,4394770000,1093.01 2009-11-09,1072.31,1093.19,1072.31,1093.08,4460030000,1093.08 2009-11-06,1064.95,1071.48,1059.32,1069.30,4277130000,1069.30 2009-11-05,1047.30,1066.65,1047.30,1066.63,4848350000,1066.63 2009-11-04,1047.14,1061.00,1045.15,1046.50,5635510000,1046.50 2009-11-03,1040.92,1046.36,1033.94,1045.41,5487500000,1045.41 2009-11-02,1036.18,1052.18,1029.38,1042.88,6202640000,1042.88 2009-10-30,1065.41,1065.41,1033.38,1036.19,6512420000,1036.19 2009-10-29,1043.69,1066.83,1043.69,1066.11,5595040000,1066.11 2009-10-28,1061.51,1063.26,1042.19,1042.63,6600350000,1042.63 2009-10-27,1067.54,1072.48,1060.62,1063.41,5337380000,1063.41 2009-10-26,1080.36,1091.75,1065.23,1066.95,6363380000,1066.95 2009-10-23,1095.62,1095.83,1075.49,1079.60,4767460000,1079.60 2009-10-22,1080.96,1095.21,1074.31,1092.91,5192410000,1092.91 2009-10-21,1090.36,1101.36,1080.77,1081.40,5616290000,1081.40 2009-10-20,1098.64,1098.64,1086.16,1091.06,5396930000,1091.06 2009-10-19,1088.22,1100.17,1086.48,1097.91,4619240000,1097.91 2009-10-16,1094.67,1094.67,1081.53,1087.68,4894740000,1087.68 2009-10-15,1090.36,1096.56,1086.41,1096.56,5369780000,1096.56 2009-10-14,1078.68,1093.17,1078.68,1092.02,5406420000,1092.02 2009-10-13,1074.96,1075.30,1066.71,1073.19,4320480000,1073.19 2009-10-12,1071.63,1079.46,1071.63,1076.19,3710430000,1076.19 2009-10-09,1065.28,1071.51,1063.00,1071.49,3763780000,1071.49 2009-10-08,1060.03,1070.67,1060.03,1065.48,4988400000,1065.48 2009-10-07,1053.65,1058.02,1050.10,1057.58,4238220000,1057.58 2009-10-06,1042.02,1060.55,1042.02,1054.72,5029840000,1054.72 2009-10-05,1026.87,1042.58,1025.92,1040.46,4313310000,1040.46 2009-10-02,1029.71,1030.60,1019.95,1025.21,5583240000,1025.21 2009-10-01,1054.91,1054.91,1029.45,1029.85,5791450000,1029.85 2009-09-30,1061.02,1063.40,1046.47,1057.08,5998860000,1057.08 2009-09-29,1063.69,1069.62,1057.83,1060.61,4949900000,1060.61 2009-09-28,1045.38,1065.13,1045.38,1062.98,3726950000,1062.98 2009-09-25,1049.48,1053.47,1041.17,1044.38,4507090000,1044.38 2009-09-24,1062.56,1066.29,1045.85,1050.78,5505610000,1050.78 2009-09-23,1072.69,1080.15,1060.39,1060.87,5531930000,1060.87 2009-09-22,1066.35,1073.81,1066.35,1071.66,5246600000,1071.66 2009-09-21,1067.14,1067.28,1057.46,1064.66,4615280000,1064.66 2009-09-18,1066.60,1071.52,1064.27,1068.30,5607970000,1068.30 2009-09-17,1067.87,1074.77,1061.20,1065.49,6668110000,1065.49 2009-09-16,1053.99,1068.76,1052.87,1068.76,6793529600,1068.76 2009-09-15,1049.03,1056.04,1043.42,1052.63,6185620000,1052.63 2009-09-14,1040.15,1049.74,1035.00,1049.34,4979610000,1049.34 2009-09-11,1043.92,1048.18,1038.40,1042.73,4922600000,1042.73 2009-09-10,1032.99,1044.14,1028.04,1044.14,5191380000,1044.14 2009-09-09,1025.36,1036.34,1023.97,1033.37,5202550000,1033.37 2009-09-08,1018.67,1026.07,1018.67,1025.39,5235160000,1025.39 2009-09-04,1003.84,1016.48,1001.65,1016.40,4097370000,1016.40 2009-09-03,996.12,1003.43,992.25,1003.24,4624280000,1003.24 2009-09-02,996.07,1000.34,991.97,994.75,5842730000,994.75 2009-09-01,1019.52,1028.45,996.28,998.04,6862360000,998.04 2009-08-31,1025.21,1025.21,1014.62,1020.62,5004560000,1020.62 2009-08-28,1031.62,1039.47,1023.13,1028.93,5785780000,1028.93 2009-08-27,1027.81,1033.33,1016.20,1030.98,5785880000,1030.98 2009-08-26,1027.35,1032.47,1021.57,1028.12,5080060000,1028.12 2009-08-25,1026.63,1037.75,1026.21,1028.00,5768740000,1028.00 2009-08-24,1026.59,1035.82,1022.48,1025.57,6302450000,1025.57 2009-08-21,1009.06,1027.59,1009.06,1026.13,5885550000,1026.13 2009-08-20,996.41,1008.92,996.39,1007.37,4893160000,1007.37 2009-08-19,986.88,999.61,980.62,996.46,4257000000,996.46 2009-08-18,980.62,991.20,980.62,989.67,4198970000,989.67 2009-08-17,998.18,998.18,978.51,979.73,4088570000,979.73 2009-08-14,1012.23,1012.60,994.60,1004.09,4940750000,1004.09 2009-08-13,1005.86,1013.14,1000.82,1012.73,5250660000,1012.73 2009-08-12,994.00,1012.78,993.36,1005.81,5498170000,1005.81 2009-08-11,1005.77,1005.77,992.40,994.35,5773160000,994.35 2009-08-10,1008.89,1010.12,1000.99,1007.10,5406080000,1007.10 2009-08-07,999.83,1018.00,999.83,1010.48,6827089600,1010.48 2009-08-06,1004.06,1008.00,992.49,997.08,6753380000,997.08 2009-08-05,1005.41,1006.64,994.31,1002.72,7242120000,1002.72 2009-08-04,1001.41,1007.12,996.68,1005.65,5713700000,1005.65 2009-08-03,990.22,1003.61,990.22,1002.63,5603440000,1002.63 2009-07-31,986.80,993.18,982.85,987.48,5139070000,987.48 2009-07-30,976.01,996.68,976.01,986.75,6035180000,986.75 2009-07-29,977.66,977.76,968.65,975.15,5178770000,975.15 2009-07-28,981.48,982.35,969.35,979.62,5490350000,979.62 2009-07-27,978.63,982.49,972.29,982.18,4631290000,982.18 2009-07-24,972.16,979.79,965.95,979.26,4458300000,979.26 2009-07-23,954.07,979.42,953.27,976.29,5761650000,976.29 2009-07-22,953.40,959.83,947.75,954.07,4634100000,954.07 2009-07-21,951.97,956.53,943.22,954.58,5309300000,954.58 2009-07-20,942.07,951.62,940.99,951.13,4853150000,951.13 2009-07-17,940.56,941.89,934.65,940.38,5141380000,940.38 2009-07-16,930.17,943.96,927.45,940.74,4898640000,940.74 2009-07-15,910.15,933.95,910.15,932.68,5238830000,932.68 2009-07-14,900.77,905.84,896.50,905.84,4149030000,905.84 2009-07-13,879.57,901.05,875.32,901.05,4499440000,901.05 2009-07-10,880.03,883.57,872.81,879.13,3912080000,879.13 2009-07-09,881.28,887.86,878.45,882.68,4347170000,882.68 2009-07-08,881.90,886.80,869.32,879.56,5721780000,879.56 2009-07-07,898.60,898.60,879.93,881.03,4673300000,881.03 2009-07-06,894.27,898.72,886.36,898.72,4712580000,898.72 2009-07-02,921.24,921.24,896.42,896.42,3931000000,896.42 2009-07-01,920.82,931.92,920.82,923.33,3919400000,923.33 2009-06-30,927.15,930.01,912.86,919.32,4627570000,919.32 2009-06-29,919.86,927.99,916.18,927.23,4211760000,927.23 2009-06-26,918.84,922.00,913.03,918.90,6076660000,918.90 2009-06-25,899.45,921.42,896.27,920.26,4911240000,920.26 2009-06-24,896.31,910.85,896.31,900.94,4636720000,900.94 2009-06-23,893.46,898.69,888.86,895.10,5071020000,895.10 2009-06-22,918.13,918.13,893.04,893.04,4903940000,893.04 2009-06-19,919.96,927.09,915.80,921.23,5713390000,921.23 2009-06-18,910.86,921.93,907.94,918.37,4684010000,918.37 2009-06-17,911.89,918.44,903.78,910.71,5523650000,910.71 2009-06-16,925.60,928.00,911.60,911.97,4951200000,911.97 2009-06-15,942.45,942.45,919.65,923.72,4697880000,923.72 2009-06-12,943.44,946.30,935.66,946.21,4528120000,946.21 2009-06-11,939.04,956.23,939.04,944.89,5500840000,944.89 2009-06-10,942.73,949.77,927.97,939.15,5379420000,939.15 2009-06-09,940.35,946.92,936.15,942.43,4439950000,942.43 2009-06-08,938.12,946.33,926.44,939.14,4483430000,939.14 2009-06-05,945.67,951.69,934.13,940.09,5277910000,940.09 2009-06-04,932.49,942.47,929.32,942.46,5352890000,942.46 2009-06-03,942.51,942.51,923.85,931.76,5323770000,931.76 2009-06-02,942.87,949.38,938.46,944.74,5987340000,944.74 2009-06-01,923.26,947.77,923.26,942.87,6370440000,942.87 2009-05-29,907.02,920.02,903.56,919.14,6050420000,919.14 2009-05-28,892.96,909.45,887.60,906.83,5738980000,906.83 2009-05-27,909.95,913.84,891.87,893.06,5698800000,893.06 2009-05-26,887.00,911.76,881.46,910.33,5667050000,910.33 2009-05-22,888.68,896.65,883.75,887.00,5155320000,887.00 2009-05-21,900.42,900.42,879.61,888.33,6019840000,888.33 2009-05-20,908.62,924.60,901.37,903.47,8205060000,903.47 2009-05-19,909.67,916.39,905.22,908.13,6616270000,908.13 2009-05-18,886.07,910.00,886.07,909.71,5702150000,909.71 2009-05-15,892.76,896.97,878.94,882.88,5439720000,882.88 2009-05-14,884.24,898.36,882.52,893.07,6134870000,893.07 2009-05-13,905.40,905.40,882.80,883.92,7091820000,883.92 2009-05-12,910.52,915.57,896.46,908.35,6871750400,908.35 2009-05-11,922.99,922.99,908.68,909.24,6150600000,909.24 2009-05-08,909.03,930.17,909.03,929.23,8163280000,929.23 2009-05-07,919.58,929.58,901.36,907.39,9120100000,907.39 2009-05-06,903.95,920.28,903.95,919.53,8555040000,919.53 2009-05-05,906.10,907.70,897.34,903.80,6882860000,903.80 2009-05-04,879.21,907.85,879.21,907.24,7038840000,907.24 2009-05-01,872.74,880.48,866.10,877.52,5312170000,877.52 2009-04-30,876.59,888.70,868.51,872.81,6862540000,872.81 2009-04-29,856.85,882.06,856.85,873.64,6101620000,873.64 2009-04-28,854.48,864.48,847.12,855.16,6328000000,855.16 2009-04-27,862.82,868.83,854.65,857.51,5613460000,857.51 2009-04-24,853.91,871.80,853.91,866.23,7114440000,866.23 2009-04-23,844.62,852.87,835.45,851.92,6563100000,851.92 2009-04-22,847.26,861.78,840.57,843.55,7327860000,843.55 2009-04-21,831.25,850.09,826.83,850.08,7436489600,850.08 2009-04-20,868.27,868.27,832.39,832.39,6973960000,832.39 2009-04-17,865.18,875.63,860.87,869.60,7352009600,869.60 2009-04-16,854.54,870.35,847.04,865.30,6598670000,865.30 2009-04-15,839.44,852.93,835.58,852.06,6241100000,852.06 2009-04-14,856.88,856.88,840.25,841.50,7569840000,841.50 2009-04-13,855.33,864.31,845.35,858.73,6434890000,858.73 2009-04-09,829.29,856.91,829.29,856.56,7600710400,856.56 2009-04-08,816.76,828.42,814.84,825.16,5938460000,825.16 2009-04-07,834.12,834.12,814.53,815.55,5155580000,815.55 2009-04-06,839.75,839.75,822.79,835.48,6210000000,835.48 2009-04-03,835.13,842.50,826.70,842.50,5855640000,842.50 2009-04-02,814.53,845.61,814.53,834.38,7542809600,834.38 2009-04-01,793.59,813.62,783.32,811.08,6034140000,811.08 2009-03-31,790.88,810.48,790.88,797.87,6089100000,797.87 2009-03-30,809.07,809.07,779.81,787.53,5912660000,787.53 2009-03-27,828.68,828.68,813.43,815.94,5600210000,815.94 2009-03-26,814.06,832.98,814.06,832.86,6992960000,832.86 2009-03-25,806.81,826.78,791.37,813.88,7687180000,813.88 2009-03-24,820.60,823.65,805.48,806.12,6767980000,806.12 2009-03-23,772.31,823.37,772.31,822.92,7715769600,822.92 2009-03-20,784.58,788.91,766.20,768.54,7643720000,768.54 2009-03-19,797.92,803.24,781.82,784.04,9033870400,784.04 2009-03-18,776.01,803.04,765.64,794.35,9098449600,794.35 2009-03-17,753.88,778.12,749.93,778.12,6156800000,778.12 2009-03-16,758.84,774.53,753.37,753.89,7883540000,753.89 2009-03-13,751.97,758.29,742.46,756.55,6787089600,756.55 2009-03-12,720.89,752.63,714.76,750.74,7326630400,750.74 2009-03-11,719.59,731.92,713.85,721.36,7287809600,721.36 2009-03-10,679.28,719.60,679.28,719.60,8618329600,719.60 2009-03-09,680.76,695.27,672.88,676.53,7277320000,676.53 2009-03-06,684.04,699.09,666.79,683.38,7331830400,683.38 2009-03-05,708.27,708.27,677.93,682.55,7507249600,682.55 2009-03-04,698.60,724.12,698.60,712.87,7673620000,712.87 2009-03-03,704.44,711.67,692.30,696.33,7583230400,696.33 2009-03-02,729.57,729.57,699.70,700.82,7868289600,700.82 2009-02-27,749.93,751.27,734.52,735.09,8926480000,735.09 2009-02-26,765.76,779.42,751.75,752.83,7599969600,752.83 2009-02-25,770.64,780.12,752.89,764.90,7483640000,764.90 2009-02-24,744.69,775.49,744.69,773.14,7234489600,773.14 2009-02-23,773.25,777.85,742.37,743.33,6509300000,743.33 2009-02-20,775.87,778.69,754.25,770.05,8210590400,770.05 2009-02-19,787.91,797.58,777.03,778.94,5746940000,778.94 2009-02-18,791.06,796.17,780.43,788.42,5740710000,788.42 2009-02-17,818.61,818.61,789.17,789.17,5907820000,789.17 2009-02-13,833.95,839.43,825.21,826.84,5296650000,826.84 2009-02-12,829.91,835.48,808.06,835.19,6476460000,835.19 2009-02-11,827.41,838.22,822.30,833.74,5926460000,833.74 2009-02-10,866.87,868.05,822.99,827.16,6770169600,827.16 2009-02-09,868.24,875.01,861.65,869.89,5574370000,869.89 2009-02-06,846.09,870.75,845.42,868.60,6484100000,868.60 2009-02-05,831.75,850.55,819.91,845.85,6624030000,845.85 2009-02-04,837.77,851.85,829.18,832.23,6420450000,832.23 2009-02-03,825.69,842.60,821.98,838.51,5886310000,838.51 2009-02-02,823.09,830.78,812.87,825.44,5673270000,825.44 2009-01-30,845.69,851.66,821.67,825.88,5350580000,825.88 2009-01-29,868.89,868.89,844.15,845.14,5067060000,845.14 2009-01-28,845.73,877.86,845.73,874.09,6199180000,874.09 2009-01-27,837.30,850.45,835.40,845.71,5353260000,845.71 2009-01-26,832.50,852.53,827.69,836.57,6039940000,836.57 2009-01-23,822.16,838.61,806.07,831.95,5832160000,831.95 2009-01-22,839.74,839.74,811.29,827.50,5843830000,827.50 2009-01-21,806.77,841.72,804.30,840.24,6467830000,840.24 2009-01-20,849.64,849.64,804.47,805.22,6375230000,805.22 2009-01-16,844.45,858.13,830.66,850.12,6786040000,850.12 2009-01-15,841.99,851.59,817.04,843.74,7807350400,843.74 2009-01-14,867.28,867.28,836.93,842.62,5407880000,842.62 2009-01-13,869.79,877.02,862.02,871.79,5017470000,871.79 2009-01-12,890.40,890.40,864.32,870.26,4725050000,870.26 2009-01-09,909.91,911.93,888.31,890.35,4716500000,890.35 2009-01-08,905.73,910.00,896.81,909.73,4991550000,909.73 2009-01-07,927.45,927.45,902.37,906.65,4704940000,906.65 2009-01-06,931.17,943.85,927.28,934.70,5392620000,934.70 2009-01-05,929.17,936.63,919.53,927.45,5413910000,927.45 2009-01-02,902.99,934.73,899.35,931.80,4048270000,931.80 2008-12-31,890.59,910.32,889.67,903.25,4172940000,903.25 2008-12-30,870.58,891.12,870.58,890.64,3627800000,890.64 2008-12-29,872.37,873.70,857.07,869.42,3323430000,869.42 2008-12-26,869.51,873.74,866.52,872.80,1880050000,872.80 2008-12-24,863.87,869.79,861.44,868.15,1546550000,868.15 2008-12-23,874.31,880.44,860.10,863.16,4051970000,863.16 2008-12-22,887.20,887.37,857.09,871.63,4869850000,871.63 2008-12-19,886.96,905.47,883.02,887.88,6705310000,887.88 2008-12-18,905.98,911.02,877.44,885.28,5675000000,885.28 2008-12-17,908.16,918.85,895.94,904.42,5907380000,904.42 2008-12-16,871.53,914.66,871.53,913.18,6009780000,913.18 2008-12-15,881.07,884.63,857.72,868.57,4982390000,868.57 2008-12-12,871.79,883.24,851.35,879.73,5959590000,879.73 2008-12-11,898.35,904.63,868.73,873.59,5513840000,873.59 2008-12-10,892.17,908.27,885.45,899.24,5942130000,899.24 2008-12-09,906.48,916.26,885.38,888.67,5693110000,888.67 2008-12-08,882.71,918.57,882.71,909.70,6553600000,909.70 2008-12-05,844.43,879.42,818.41,876.07,6165370000,876.07 2008-12-04,869.75,875.60,833.60,845.22,5860390000,845.22 2008-12-03,843.60,873.12,827.60,870.74,6221880000,870.74 2008-12-02,817.94,850.54,817.94,848.81,6170100000,848.81 2008-12-01,888.61,888.61,815.69,816.21,6052010000,816.21 2008-11-28,886.89,896.25,881.21,896.24,2740860000,896.24 2008-11-26,852.90,887.68,841.37,887.68,5793260000,887.68 2008-11-25,853.40,868.94,834.99,857.39,6952700000,857.39 2008-11-24,801.20,865.60,801.20,851.81,7879440000,851.81 2008-11-21,755.84,801.20,741.02,800.03,9495900000,800.03 2008-11-20,805.87,820.52,747.78,752.44,9093740000,752.44 2008-11-19,859.03,864.57,806.18,806.58,6548600000,806.58 2008-11-18,852.34,865.90,826.84,859.12,6679470000,859.12 2008-11-17,873.23,882.29,848.98,850.75,4927490000,850.75 2008-11-14,904.36,916.88,869.88,873.29,5881030000,873.29 2008-11-13,853.13,913.01,818.69,911.29,7849120000,911.29 2008-11-12,893.39,893.39,850.48,852.30,5764180000,852.30 2008-11-11,917.15,917.15,884.90,898.95,4998340000,898.95 2008-11-10,936.75,951.95,907.47,919.21,4572000000,919.21 2008-11-07,907.44,931.46,906.90,930.99,4931640000,930.99 2008-11-06,952.40,952.40,899.73,904.88,6102230000,904.88 2008-11-05,1001.84,1001.84,949.86,952.77,5426640000,952.77 2008-11-04,971.31,1007.51,971.31,1005.75,5531290000,1005.75 2008-11-03,968.67,975.57,958.82,966.30,4492280000,966.30 2008-10-31,953.11,984.38,944.59,968.75,6394350000,968.75 2008-10-30,939.38,963.23,928.50,954.09,6175830000,954.09 2008-10-29,939.51,969.97,922.26,930.09,7077800000,930.09 2008-10-28,848.92,940.51,845.27,940.51,7096950400,940.51 2008-10-27,874.28,893.78,846.75,848.92,5558050000,848.92 2008-10-24,895.22,896.30,852.85,876.77,6550050000,876.77 2008-10-23,899.08,922.83,858.44,908.11,7184180000,908.11 2008-10-22,951.67,951.67,875.81,896.78,6147980000,896.78 2008-10-21,980.40,985.44,952.47,955.05,5121830000,955.05 2008-10-20,943.51,985.40,943.51,985.40,5175640000,985.40 2008-10-17,942.29,984.64,918.74,940.55,6581780000,940.55 2008-10-16,909.53,947.71,865.83,946.43,7984500000,946.43 2008-10-15,994.60,994.60,903.99,907.84,6542330000,907.84 2008-10-14,1009.97,1044.31,972.07,998.01,8161990400,998.01 2008-10-13,912.75,1006.93,912.75,1003.35,7263369600,1003.35 2008-10-10,902.31,936.36,839.80,899.22,11456230400,899.22 2008-10-09,988.42,1005.25,909.19,909.92,6819000000,909.92 2008-10-08,988.91,1021.06,970.97,984.94,8716329600,984.94 2008-10-07,1057.60,1072.91,996.23,996.23,7069209600,996.23 2008-10-06,1097.56,1097.56,1007.97,1056.89,7956020000,1056.89 2008-10-03,1115.16,1153.82,1098.14,1099.23,6716120000,1099.23 2008-10-02,1160.64,1160.64,1111.43,1114.28,6285640000,1114.28 2008-10-01,1164.17,1167.03,1140.77,1161.06,5782130000,1161.06 2008-09-30,1113.78,1168.03,1113.78,1166.36,4937680000,1166.36 2008-09-29,1209.07,1209.07,1106.42,1106.42,7305060000,1106.42 2008-09-26,1204.47,1215.77,1187.54,1213.27,5383610000,1213.27 2008-09-25,1187.87,1220.03,1187.87,1209.18,5877640000,1209.18 2008-09-24,1188.79,1197.41,1179.79,1185.87,4820360000,1185.87 2008-09-23,1207.61,1221.15,1187.06,1188.22,5185730000,1188.22 2008-09-22,1255.37,1255.37,1205.61,1207.09,5332130000,1207.09 2008-09-19,1213.11,1265.12,1213.11,1255.08,9387169600,1255.08 2008-09-18,1157.08,1211.14,1133.50,1206.51,10082689600,1206.51 2008-09-17,1210.34,1210.34,1155.88,1156.39,9431870400,1156.39 2008-09-16,1188.31,1214.84,1169.28,1213.60,9459830400,1213.60 2008-09-15,1250.92,1250.92,1192.70,1192.70,8279510400,1192.70 2008-09-12,1245.88,1255.09,1233.81,1251.70,6273260000,1251.70 2008-09-11,1229.04,1249.98,1211.54,1249.05,6869249600,1249.05 2008-09-10,1227.50,1243.90,1221.60,1232.04,6543440000,1232.04 2008-09-09,1267.98,1268.66,1224.51,1224.51,7380630400,1224.51 2008-09-08,1249.50,1274.42,1247.12,1267.79,7351340000,1267.79 2008-09-05,1233.21,1244.94,1217.23,1242.31,5017080000,1242.31 2008-09-04,1271.80,1271.80,1232.83,1236.83,5212500000,1236.83 2008-09-03,1276.61,1280.60,1265.59,1274.98,5056980000,1274.98 2008-09-02,1287.83,1303.04,1272.20,1277.58,4783560000,1277.58 2008-08-29,1296.49,1297.59,1282.74,1282.83,3288120000,1282.83 2008-08-28,1283.79,1300.68,1283.79,1300.68,3854280000,1300.68 2008-08-27,1271.29,1285.05,1270.03,1281.66,3499610000,1281.66 2008-08-26,1267.03,1275.65,1263.21,1271.51,3587570000,1271.51 2008-08-25,1290.47,1290.47,1264.87,1266.84,3420600000,1266.84 2008-08-22,1277.59,1293.09,1277.59,1292.20,3741070000,1292.20 2008-08-21,1271.07,1281.40,1265.22,1277.72,4032590000,1277.72 2008-08-20,1267.34,1276.01,1261.16,1274.54,4555030000,1274.54 2008-08-19,1276.65,1276.65,1263.11,1266.69,4159760000,1266.69 2008-08-18,1298.14,1300.22,1274.51,1278.60,3829290000,1278.60 2008-08-15,1293.85,1302.05,1290.74,1298.20,4041820000,1298.20 2008-08-14,1282.11,1300.11,1276.84,1292.93,4064000000,1292.93 2008-08-13,1288.64,1294.03,1274.86,1285.83,4787600000,1285.83 2008-08-12,1304.79,1304.79,1285.64,1289.59,4711290000,1289.59 2008-08-11,1294.42,1313.15,1291.41,1305.32,5067310000,1305.32 2008-08-08,1266.29,1297.85,1262.11,1296.32,4966810000,1296.32 2008-08-07,1286.51,1286.51,1264.29,1266.07,5319380000,1266.07 2008-08-06,1283.99,1291.67,1276.00,1289.19,4873420000,1289.19 2008-08-05,1254.87,1284.88,1254.67,1284.88,1219310000,1284.88 2008-08-04,1253.27,1260.49,1247.45,1249.01,4562280000,1249.01 2008-08-01,1269.42,1270.52,1254.54,1260.31,4684870000,1260.31 2008-07-31,1281.37,1284.93,1265.97,1267.38,5346050000,1267.38 2008-07-30,1264.52,1284.33,1264.52,1284.26,5631330000,1284.26 2008-07-29,1236.38,1263.20,1236.38,1263.20,5414240000,1263.20 2008-07-28,1257.76,1260.09,1234.37,1234.37,4282960000,1234.37 2008-07-25,1253.51,1263.23,1251.75,1257.76,4672560000,1257.76 2008-07-24,1283.22,1283.22,1251.48,1252.54,6127980000,1252.54 2008-07-23,1278.87,1291.17,1276.06,1282.19,6705830000,1282.19 2008-07-22,1257.08,1277.42,1248.83,1277.00,6180230000,1277.00 2008-07-21,1261.82,1267.74,1255.70,1260.00,4630640000,1260.00 2008-07-18,1258.22,1262.23,1251.81,1260.68,5653280000,1260.68 2008-07-17,1246.31,1262.31,1241.49,1260.32,7365209600,1260.32 2008-07-16,1214.65,1245.52,1211.39,1245.36,6738630400,1245.36 2008-07-15,1226.83,1234.35,1200.44,1214.91,7363640000,1214.91 2008-07-14,1241.61,1253.50,1225.01,1228.30,5434860000,1228.30 2008-07-11,1248.66,1257.27,1225.35,1239.49,6742200000,1239.49 2008-07-10,1245.25,1257.65,1236.76,1253.39,5840430000,1253.39 2008-07-09,1273.38,1277.36,1244.57,1244.69,5181000000,1244.69 2008-07-08,1251.84,1274.17,1242.84,1273.70,6034110000,1273.70 2008-07-07,1262.90,1273.95,1240.68,1252.31,5265420000,1252.31 2008-07-03,1262.96,1271.48,1252.01,1262.90,3247590000,1262.90 2008-07-02,1285.82,1292.17,1261.51,1261.52,5276090000,1261.52 2008-07-01,1276.69,1285.31,1260.68,1284.91,5846290000,1284.91 2008-06-30,1278.06,1290.31,1274.86,1280.00,5032330000,1280.00 2008-06-27,1283.60,1289.45,1272.00,1278.38,6208260000,1278.38 2008-06-26,1316.29,1316.29,1283.15,1283.15,5231280000,1283.15 2008-06-25,1314.54,1335.63,1314.54,1321.97,4825640000,1321.97 2008-06-24,1317.23,1326.02,1304.42,1314.29,4705050000,1314.29 2008-06-23,1319.77,1323.78,1315.31,1318.00,4186370000,1318.00 2008-06-20,1341.02,1341.02,1314.46,1317.93,5324900000,1317.93 2008-06-19,1336.89,1347.66,1330.50,1342.83,4811670000,1342.83 2008-06-18,1349.59,1349.59,1333.40,1337.81,4573570000,1337.81 2008-06-17,1360.71,1366.59,1350.54,1350.93,3801960000,1350.93 2008-06-16,1358.85,1364.70,1352.07,1360.14,3706940000,1360.14 2008-06-13,1341.81,1360.03,1341.71,1360.03,4080420000,1360.03 2008-06-12,1335.78,1353.03,1331.29,1339.87,4734240000,1339.87 2008-06-11,1357.09,1357.09,1335.47,1335.49,4779980000,1335.49 2008-06-10,1358.98,1366.84,1351.56,1358.44,4635070000,1358.44 2008-06-09,1360.83,1370.63,1350.62,1361.76,4404570000,1361.76 2008-06-06,1400.06,1400.06,1359.90,1360.68,4771660000,1360.68 2008-06-05,1377.48,1404.05,1377.48,1404.05,4350790000,1404.05 2008-06-04,1376.26,1388.18,1371.74,1377.20,4338640000,1377.20 2008-06-03,1386.42,1393.12,1370.12,1377.65,4396380000,1377.65 2008-06-02,1399.62,1399.62,1377.79,1385.67,3714320000,1385.67 2008-05-30,1398.36,1404.46,1398.08,1400.38,3845630000,1400.38 2008-05-29,1390.50,1406.32,1388.59,1398.26,3894440000,1398.26 2008-05-28,1386.54,1391.25,1378.16,1390.84,3927240000,1390.84 2008-05-27,1375.97,1387.40,1373.07,1385.35,3588860000,1385.35 2008-05-23,1392.20,1392.20,1373.72,1375.93,3516380000,1375.93 2008-05-22,1390.83,1399.07,1390.23,1394.35,3955960000,1394.35 2008-05-21,1414.06,1419.12,1388.81,1390.71,4517990000,1390.71 2008-05-20,1424.49,1424.49,1409.09,1413.40,3854320000,1413.40 2008-05-19,1425.28,1440.24,1421.63,1426.63,3683970000,1426.63 2008-05-16,1423.89,1425.82,1414.35,1425.35,3842590000,1425.35 2008-05-15,1408.36,1424.40,1406.87,1423.57,3836480000,1423.57 2008-05-14,1405.65,1420.19,1405.65,1408.66,3979370000,1408.66 2008-05-13,1404.40,1406.30,1396.26,1403.04,4018590000,1403.04 2008-05-12,1389.40,1404.06,1386.20,1403.58,3370630000,1403.58 2008-05-09,1394.90,1394.90,1384.11,1388.28,3518620000,1388.28 2008-05-08,1394.29,1402.35,1389.39,1397.68,3827550000,1397.68 2008-05-07,1417.49,1419.54,1391.16,1392.57,4075860000,1392.57 2008-05-06,1405.60,1421.57,1397.10,1418.26,3924100000,1418.26 2008-05-05,1415.34,1415.34,1404.37,1407.49,3410090000,1407.49 2008-05-02,1409.16,1422.72,1406.25,1413.90,3953030000,1413.90 2008-05-01,1385.97,1410.07,1383.07,1409.34,4448780000,1409.34 2008-04-30,1391.22,1404.57,1384.25,1385.59,4508890000,1385.59 2008-04-29,1395.61,1397.00,1386.70,1390.94,3815320000,1390.94 2008-04-28,1397.96,1402.90,1394.40,1396.37,3607000000,1396.37 2008-04-25,1387.88,1399.11,1379.98,1397.84,3891150000,1397.84 2008-04-24,1380.52,1397.72,1371.09,1388.82,4461660000,1388.82 2008-04-23,1378.40,1387.87,1372.24,1379.93,4103610000,1379.93 2008-04-22,1386.43,1386.43,1369.84,1375.94,3821900000,1375.94 2008-04-21,1387.72,1390.23,1379.25,1388.17,3420570000,1388.17 2008-04-18,1369.00,1395.90,1369.00,1390.33,4222380000,1390.33 2008-04-17,1363.37,1368.60,1357.25,1365.56,3713880000,1365.56 2008-04-16,1337.02,1365.49,1337.02,1364.71,4260370000,1364.71 2008-04-15,1331.72,1337.72,1324.35,1334.43,3581230000,1334.43 2008-04-14,1332.20,1335.64,1326.16,1328.32,3565020000,1328.32 2008-04-11,1357.98,1357.98,1331.21,1332.83,3723790000,1332.83 2008-04-10,1355.37,1367.24,1350.11,1360.55,3686150000,1360.55 2008-04-09,1365.50,1368.39,1349.97,1354.49,3556670000,1354.49 2008-04-08,1370.16,1370.16,1360.62,1365.54,3602500000,1365.54 2008-04-07,1373.69,1386.74,1369.02,1372.54,3747780000,1372.54 2008-04-04,1369.85,1380.91,1362.83,1370.40,3703100000,1370.40 2008-04-03,1365.69,1375.66,1358.68,1369.31,3920100000,1369.31 2008-04-02,1369.96,1377.95,1361.55,1367.53,4320440000,1367.53 2008-04-01,1326.41,1370.18,1326.41,1370.18,4745120000,1370.18 2008-03-31,1315.92,1328.52,1312.81,1322.70,4188990000,1322.70 2008-03-28,1327.02,1334.87,1312.95,1315.22,3686980000,1315.22 2008-03-27,1340.34,1345.62,1325.66,1325.76,4037930000,1325.76 2008-03-26,1352.45,1352.45,1336.41,1341.13,4055670000,1341.13 2008-03-25,1349.07,1357.47,1341.21,1352.99,4145120000,1352.99 2008-03-24,1330.29,1359.68,1330.29,1349.88,4499000000,1349.88 2008-03-20,1299.67,1330.67,1295.22,1329.51,6145220000,1329.51 2008-03-19,1330.97,1341.51,1298.42,1298.42,1203830000,1298.42 2008-03-18,1277.16,1330.74,1277.16,1330.74,5335630000,1330.74 2008-03-17,1283.21,1287.50,1256.98,1276.60,5683010000,1276.60 2008-03-14,1316.05,1321.47,1274.86,1288.14,5153780000,1288.14 2008-03-13,1305.26,1321.68,1282.11,1315.48,5073360000,1315.48 2008-03-12,1321.13,1333.26,1307.86,1308.77,4414280000,1308.77 2008-03-11,1274.40,1320.65,1274.40,1320.65,5109080000,1320.65 2008-03-10,1293.16,1295.01,1272.66,1273.37,4261240000,1273.37 2008-03-07,1301.53,1313.24,1282.43,1293.37,4565410000,1293.37 2008-03-06,1332.20,1332.20,1303.42,1304.34,4323460000,1304.34 2008-03-05,1327.69,1344.19,1320.22,1333.70,4277710000,1333.70 2008-03-04,1329.58,1331.03,1307.39,1326.75,4757180000,1326.75 2008-03-03,1330.45,1335.13,1320.04,1331.34,4117570000,1331.34 2008-02-29,1364.07,1364.07,1325.42,1330.63,4426730000,1330.63 2008-02-28,1378.16,1378.16,1363.16,1367.68,3938580000,1367.68 2008-02-27,1378.95,1388.34,1372.00,1380.02,3904700000,1380.02 2008-02-26,1371.76,1387.34,1363.29,1381.29,4096060000,1381.29 2008-02-25,1352.75,1374.36,1346.03,1371.80,3866350000,1371.80 2008-02-22,1344.22,1354.30,1327.04,1353.11,3572660000,1353.11 2008-02-21,1362.21,1367.94,1339.34,1342.53,3696660000,1342.53 2008-02-20,1348.39,1363.71,1336.55,1360.03,3870520000,1360.03 2008-02-19,1355.86,1367.28,1345.05,1348.78,3613550000,1348.78 2008-02-15,1347.52,1350.00,1338.13,1349.99,3583300000,1349.99 2008-02-14,1367.33,1368.16,1347.31,1348.86,3644760000,1348.86 2008-02-13,1353.12,1369.23,1350.78,1367.21,3856420000,1367.21 2008-02-12,1340.55,1362.10,1339.36,1348.86,4044640000,1348.86 2008-02-11,1331.92,1341.40,1320.32,1339.13,3593140000,1339.13 2008-02-08,1336.88,1341.22,1321.06,1331.29,3768490000,1331.29 2008-02-07,1324.01,1347.16,1316.75,1336.91,4589160000,1336.91 2008-02-06,1339.48,1351.96,1324.34,1326.45,4008120000,1326.45 2008-02-05,1380.28,1380.28,1336.64,1336.64,4315740000,1336.64 2008-02-04,1395.38,1395.38,1379.69,1380.82,3495780000,1380.82 2008-02-01,1378.60,1396.02,1375.93,1395.42,4650770000,1395.42 2008-01-31,1351.98,1385.62,1334.08,1378.55,4970290000,1378.55 2008-01-30,1362.22,1385.86,1352.95,1355.81,4742760000,1355.81 2008-01-29,1355.94,1364.93,1350.19,1362.30,4232960000,1362.30 2008-01-28,1330.70,1353.97,1322.26,1353.96,4100930000,1353.96 2008-01-25,1357.32,1368.56,1327.50,1330.61,4882250000,1330.61 2008-01-24,1340.13,1355.15,1334.31,1352.07,5735300000,1352.07 2008-01-23,1310.41,1339.09,1270.05,1338.60,3241680000,1338.60 2008-01-22,1312.94,1322.09,1274.29,1310.50,6544690000,1310.50 2008-01-18,1333.90,1350.28,1312.51,1325.19,6004840000,1325.19 2008-01-17,1374.79,1377.72,1330.67,1333.25,5303130000,1333.25 2008-01-16,1377.41,1391.99,1364.27,1373.20,5440620000,1373.20 2008-01-15,1411.88,1411.88,1380.60,1380.95,4601640000,1380.95 2008-01-14,1402.91,1417.89,1402.91,1416.25,3682090000,1416.25 2008-01-11,1419.91,1419.91,1394.83,1401.02,4495840000,1401.02 2008-01-10,1406.78,1429.09,1395.31,1420.33,5170490000,1420.33 2008-01-09,1390.25,1409.19,1378.70,1409.13,5351030000,1409.13 2008-01-08,1415.71,1430.28,1388.30,1390.19,4705390000,1390.19 2008-01-07,1414.07,1423.87,1403.45,1416.18,4221260000,1416.18 2008-01-04,1444.01,1444.01,1411.19,1411.63,4166000000,1411.63 2008-01-03,1447.55,1456.80,1443.73,1447.16,3429500000,1447.16 2008-01-02,1467.97,1471.77,1442.07,1447.16,3452650000,1447.16 2007-12-31,1475.25,1475.83,1465.13,1468.36,2440880000,1468.36 2007-12-28,1479.83,1488.01,1471.70,1478.49,2420510000,1478.49 2007-12-27,1495.05,1495.05,1475.86,1476.27,2365770000,1476.27 2007-12-26,1495.12,1498.85,1488.20,1497.66,2010500000,1497.66 2007-12-24,1484.55,1497.63,1484.55,1496.45,1267420000,1496.45 2007-12-21,1463.19,1485.40,1463.19,1484.46,4508590000,1484.46 2007-12-20,1456.42,1461.53,1447.22,1460.12,3526890000,1460.12 2007-12-19,1454.70,1464.42,1445.31,1453.00,3401300000,1453.00 2007-12-18,1445.92,1460.16,1435.65,1454.98,3723690000,1454.98 2007-12-17,1465.05,1465.05,1445.43,1445.90,3569030000,1445.90 2007-12-14,1486.19,1486.67,1467.78,1467.95,3401050000,1467.95 2007-12-13,1483.27,1489.40,1469.21,1488.41,3635170000,1488.41 2007-12-12,1487.58,1511.96,1468.23,1486.59,4482120000,1486.59 2007-12-11,1516.68,1523.57,1475.99,1477.65,4080180000,1477.65 2007-12-10,1505.11,1518.27,1504.96,1515.96,2911760000,1515.96 2007-12-07,1508.60,1510.63,1502.66,1504.66,3177710000,1504.66 2007-12-06,1484.59,1508.02,1482.19,1507.34,3568570000,1507.34 2007-12-05,1465.22,1486.09,1465.22,1485.01,3663660000,1485.01 2007-12-04,1471.34,1471.34,1460.66,1462.79,3343620000,1462.79 2007-12-03,1479.63,1481.16,1470.08,1472.42,3323250000,1472.42 2007-11-30,1471.83,1488.94,1470.89,1481.14,4422200000,1481.14 2007-11-29,1467.41,1473.81,1458.36,1469.72,3524730000,1469.72 2007-11-28,1432.95,1471.62,1432.95,1469.02,4508020000,1469.02 2007-11-27,1409.59,1429.49,1407.43,1428.23,4320720000,1428.23 2007-11-26,1440.74,1446.09,1406.10,1407.22,3706470000,1407.22 2007-11-23,1417.62,1440.86,1417.62,1440.70,1612720000,1440.70 2007-11-21,1434.71,1436.40,1415.64,1416.77,4076230000,1416.77 2007-11-20,1434.51,1452.64,1419.28,1439.70,4875150000,1439.70 2007-11-19,1456.70,1456.70,1430.42,1433.27,4119650000,1433.27 2007-11-16,1453.09,1462.18,1443.99,1458.74,4168870000,1458.74 2007-11-15,1468.04,1472.67,1443.49,1451.15,3941010000,1451.15 2007-11-14,1483.40,1492.14,1466.47,1470.58,4031470000,1470.58 2007-11-13,1441.35,1481.37,1441.35,1481.05,4141310000,1481.05 2007-11-12,1453.66,1464.94,1438.53,1439.18,4192520000,1439.18 2007-11-09,1467.59,1474.09,1448.51,1453.70,4587050000,1453.70 2007-11-08,1475.27,1482.50,1450.31,1474.77,5439720000,1474.77 2007-11-07,1515.46,1515.46,1475.04,1475.62,4353160000,1475.62 2007-11-06,1505.33,1520.77,1499.07,1520.27,3879160000,1520.27 2007-11-05,1505.61,1510.84,1489.95,1502.17,3819330000,1502.17 2007-11-02,1511.07,1513.15,1492.53,1509.65,4285990000,1509.65 2007-11-01,1545.79,1545.79,1506.66,1508.44,4241470000,1508.44 2007-10-31,1532.15,1552.76,1529.40,1549.38,3953070000,1549.38 2007-10-30,1539.42,1539.42,1529.55,1531.02,3212520000,1531.02 2007-10-29,1536.92,1544.67,1536.43,1540.98,3124480000,1540.98 2007-10-26,1522.17,1535.53,1520.18,1535.28,3612120000,1535.28 2007-10-25,1516.15,1523.24,1500.46,1514.40,4183960000,1514.40 2007-10-24,1516.61,1517.23,1489.56,1515.88,4003300000,1515.88 2007-10-23,1509.30,1520.01,1503.61,1519.59,3309120000,1519.59 2007-10-22,1497.79,1508.06,1490.40,1506.33,3471830000,1506.33 2007-10-19,1540.00,1540.00,1500.26,1500.63,4160970000,1500.63 2007-10-18,1539.29,1542.79,1531.76,1540.08,3203210000,1540.08 2007-10-17,1544.44,1550.66,1526.01,1541.24,3638070000,1541.24 2007-10-16,1547.81,1547.81,1536.29,1538.53,3234560000,1538.53 2007-10-15,1562.25,1564.74,1540.81,1548.71,3139290000,1548.71 2007-10-12,1555.41,1563.03,1554.09,1561.80,2788690000,1561.80 2007-10-11,1564.72,1576.09,1546.72,1554.41,3911260000,1554.41 2007-10-10,1564.98,1565.42,1555.46,1562.47,3044760000,1562.47 2007-10-09,1553.18,1565.26,1551.82,1565.15,2932040000,1565.15 2007-10-08,1556.51,1556.51,1549.00,1552.58,2040650000,1552.58 2007-10-05,1543.84,1561.91,1543.84,1557.59,2919030000,1557.59 2007-10-04,1539.91,1544.02,1537.63,1542.84,2690430000,1542.84 2007-10-03,1545.80,1545.84,1536.34,1539.59,3065320000,1539.59 2007-10-02,1546.96,1548.01,1540.37,1546.63,3101910000,1546.63 2007-10-01,1527.29,1549.02,1527.25,1547.04,3281990000,1547.04 2007-09-28,1531.24,1533.74,1521.99,1526.75,2925350000,1526.75 2007-09-27,1527.32,1532.46,1525.81,1531.38,2872180000,1531.38 2007-09-26,1518.62,1529.39,1518.62,1525.42,3237390000,1525.42 2007-09-25,1516.34,1518.27,1507.13,1517.21,3187770000,1517.21 2007-09-24,1525.75,1530.18,1516.15,1517.73,3131310000,1517.73 2007-09-21,1518.75,1530.89,1518.75,1525.75,3679460000,1525.75 2007-09-20,1528.69,1529.14,1516.42,1518.75,2957700000,1518.75 2007-09-19,1519.75,1538.74,1519.75,1529.03,3846750000,1529.03 2007-09-18,1476.63,1519.89,1476.63,1519.78,3708940000,1519.78 2007-09-17,1484.24,1484.24,1471.82,1476.65,2598390000,1476.65 2007-09-14,1483.95,1485.99,1473.18,1484.25,2641740000,1484.25 2007-09-13,1471.47,1489.58,1471.47,1483.95,2877080000,1483.95 2007-09-12,1471.10,1479.50,1465.75,1471.56,2885720000,1471.56 2007-09-11,1451.69,1472.48,1451.69,1471.49,3015330000,1471.49 2007-09-10,1453.50,1462.25,1439.29,1451.70,2835720000,1451.70 2007-09-07,1478.55,1478.55,1449.07,1453.55,3191080000,1453.55 2007-09-06,1472.03,1481.49,1467.41,1478.55,2459590000,1478.55 2007-09-05,1488.76,1488.76,1466.34,1472.29,2991600000,1472.29 2007-09-04,1473.96,1496.40,1472.15,1489.42,2766600000,1489.42 2007-08-31,1457.61,1481.47,1457.61,1473.99,2731610000,1473.99 2007-08-30,1463.67,1468.43,1451.25,1457.64,2582960000,1457.64 2007-08-29,1432.01,1463.76,1432.01,1463.76,2824070000,1463.76 2007-08-28,1466.72,1466.72,1432.01,1432.36,3078090000,1432.36 2007-08-27,1479.36,1479.36,1465.98,1466.79,2406180000,1466.79 2007-08-24,1462.34,1479.40,1460.54,1479.37,2541400000,1479.37 2007-08-23,1464.05,1472.06,1453.88,1462.50,3084390000,1462.50 2007-08-22,1447.03,1464.86,1447.03,1464.07,3309120000,1464.07 2007-08-21,1445.55,1455.32,1439.76,1447.12,3012150000,1447.12 2007-08-20,1445.94,1451.75,1430.54,1445.55,3321340000,1445.55 2007-08-17,1411.26,1450.33,1411.26,1445.94,3570040000,1445.94 2007-08-16,1406.64,1415.97,1370.60,1411.27,6509300000,1411.27 2007-08-15,1426.15,1440.78,1404.36,1406.70,4290930000,1406.70 2007-08-14,1452.87,1456.74,1426.20,1426.54,3814630000,1426.54 2007-08-13,1453.42,1466.29,1451.54,1452.92,3696280000,1452.92 2007-08-10,1453.09,1462.02,1429.74,1453.64,5345780000,1453.64 2007-08-09,1497.21,1497.21,1453.09,1453.09,5889600000,1453.09 2007-08-08,1476.22,1503.89,1476.22,1497.49,5499560000,1497.49 2007-08-07,1467.62,1488.30,1455.80,1476.71,4909390000,1476.71 2007-08-06,1433.04,1467.67,1427.39,1467.67,5067200000,1467.67 2007-08-03,1472.18,1473.23,1432.80,1433.06,4272110000,1433.06 2007-08-02,1465.46,1476.43,1460.58,1472.20,4368850000,1472.20 2007-08-01,1455.18,1468.38,1439.59,1465.81,5256780000,1465.81 2007-07-31,1473.90,1488.30,1454.25,1455.27,4524520000,1455.27 2007-07-30,1458.93,1477.88,1454.32,1473.91,4128780000,1473.91 2007-07-27,1482.44,1488.53,1458.95,1458.95,4784650000,1458.95 2007-07-26,1518.09,1518.09,1465.30,1482.66,4472550000,1482.66 2007-07-25,1511.03,1524.31,1503.73,1518.09,4283200000,1518.09 2007-07-24,1541.57,1541.57,1508.62,1511.04,4115830000,1511.04 2007-07-23,1534.06,1547.23,1534.06,1541.57,3102700000,1541.57 2007-07-20,1553.19,1553.19,1529.20,1534.10,3745780000,1534.10 2007-07-19,1546.13,1555.20,1546.13,1553.08,3251450000,1553.08 2007-07-18,1549.20,1549.20,1533.67,1546.17,3609220000,1546.17 2007-07-17,1549.52,1555.32,1547.74,1549.37,3007140000,1549.37 2007-07-16,1552.50,1555.90,1546.69,1549.52,2704110000,1549.52 2007-07-13,1547.68,1555.10,1544.85,1552.50,2801120000,1552.50 2007-07-12,1518.74,1547.92,1518.74,1547.70,3489600000,1547.70 2007-07-11,1509.93,1519.34,1506.10,1518.76,3082920000,1518.76 2007-07-10,1531.85,1531.85,1510.01,1510.12,3244280000,1510.12 2007-07-09,1530.43,1534.26,1527.45,1531.85,2715330000,1531.85 2007-07-06,1524.96,1532.40,1520.47,1530.44,2441520000,1530.44 2007-07-05,1524.86,1526.57,1517.72,1525.40,2622950000,1525.40 2007-07-03,1519.12,1526.01,1519.12,1524.87,1560790000,1524.87 2007-07-02,1504.66,1519.45,1504.66,1519.43,2644990000,1519.43 2007-06-29,1505.70,1517.53,1493.61,1503.35,3165410000,1503.35 2007-06-28,1506.32,1514.84,1503.41,1505.71,3006710000,1505.71 2007-06-27,1492.62,1506.80,1484.18,1506.34,3398150000,1506.34 2007-06-26,1497.68,1506.12,1490.54,1492.89,3398530000,1492.89 2007-06-25,1502.56,1514.29,1492.68,1497.74,3287250000,1497.74 2007-06-22,1522.19,1522.19,1500.74,1502.56,4284320000,1502.56 2007-06-21,1512.50,1522.90,1504.75,1522.19,3161110000,1522.19 2007-06-20,1533.68,1537.32,1512.36,1512.84,3286900000,1512.84 2007-06-19,1531.02,1535.85,1525.67,1533.70,2873590000,1533.70 2007-06-18,1532.90,1535.44,1529.31,1531.05,2480240000,1531.05 2007-06-15,1522.97,1538.71,1522.97,1532.91,3406030000,1532.91 2007-06-14,1515.58,1526.45,1515.58,1522.97,2813630000,1522.97 2007-06-13,1492.65,1515.70,1492.65,1515.67,3077930000,1515.67 2007-06-12,1509.12,1511.33,1492.97,1493.00,3056200000,1493.00 2007-06-11,1507.64,1515.53,1503.35,1509.12,2525280000,1509.12 2007-06-08,1490.71,1507.76,1487.41,1507.67,2993460000,1507.67 2007-06-07,1517.36,1517.36,1490.37,1490.72,3538470000,1490.72 2007-06-06,1530.57,1530.57,1514.13,1517.38,2964190000,1517.38 2007-06-05,1539.12,1539.12,1525.62,1530.95,2939450000,1530.95 2007-06-04,1536.28,1540.53,1532.31,1539.18,2738930000,1539.18 2007-06-01,1530.62,1540.56,1530.62,1536.34,2927020000,1536.34 2007-05-31,1530.19,1535.56,1528.26,1530.62,3335530000,1530.62 2007-05-30,1517.60,1530.23,1510.06,1530.23,2980210000,1530.23 2007-05-29,1515.55,1521.80,1512.02,1518.11,2571790000,1518.11 2007-05-25,1507.50,1517.41,1507.50,1515.73,2316250000,1515.73 2007-05-24,1522.10,1529.31,1505.18,1507.51,3365530000,1507.51 2007-05-23,1524.09,1532.43,1521.90,1522.28,3084260000,1522.28 2007-05-22,1525.10,1529.24,1522.05,1524.12,2860500000,1524.12 2007-05-21,1522.75,1529.87,1522.71,1525.10,3465360000,1525.10 2007-05-18,1512.74,1522.75,1512.74,1522.75,2959050000,1522.75 2007-05-17,1514.01,1517.14,1509.29,1512.75,2868640000,1512.75 2007-05-16,1500.75,1514.15,1500.75,1514.14,2915350000,1514.14 2007-05-15,1503.11,1514.83,1500.43,1501.19,3071020000,1501.19 2007-05-14,1505.76,1510.90,1498.34,1503.15,2776130000,1503.15 2007-05-11,1491.47,1506.24,1491.47,1505.85,2720780000,1505.85 2007-05-10,1512.33,1512.33,1491.42,1491.47,3031240000,1491.47 2007-05-09,1507.32,1513.80,1503.77,1512.58,2935550000,1512.58 2007-05-08,1509.36,1509.36,1500.66,1507.72,2795720000,1507.72 2007-05-07,1505.57,1511.00,1505.54,1509.48,2545090000,1509.48 2007-05-04,1502.35,1510.34,1501.80,1505.62,2761930000,1505.62 2007-05-03,1495.56,1503.34,1495.56,1502.39,3007970000,1502.39 2007-05-02,1486.13,1499.10,1486.13,1495.92,3189800000,1495.92 2007-05-01,1482.37,1487.27,1476.70,1486.30,3400350000,1486.30 2007-04-30,1494.07,1497.16,1482.29,1482.37,3093420000,1482.37 2007-04-27,1494.21,1497.32,1488.67,1494.07,2732810000,1494.07 2007-04-26,1495.27,1498.02,1491.17,1494.25,3211800000,1494.25 2007-04-25,1480.28,1496.59,1480.28,1495.42,3252590000,1495.42 2007-04-24,1480.93,1483.82,1473.74,1480.41,3119750000,1480.41 2007-04-23,1484.33,1487.32,1480.19,1480.93,2575020000,1480.93 2007-04-20,1470.69,1484.74,1470.69,1484.35,3329940000,1484.35 2007-04-19,1472.48,1474.23,1464.47,1470.73,2913610000,1470.73 2007-04-18,1471.47,1476.57,1466.41,1472.50,2971330000,1472.50 2007-04-17,1468.47,1474.35,1467.15,1471.48,2920570000,1471.48 2007-04-16,1452.84,1468.62,1452.84,1468.33,2870140000,1468.33 2007-04-13,1447.80,1453.11,1444.15,1452.85,2690020000,1452.85 2007-04-12,1438.87,1448.02,1433.91,1447.80,2770570000,1447.80 2007-04-11,1448.23,1448.39,1436.15,1438.87,2950190000,1438.87 2007-04-10,1444.58,1448.73,1443.99,1448.39,2510110000,1448.39 2007-04-09,1443.77,1448.10,1443.28,1444.61,2349410000,1444.61 2007-04-05,1438.94,1444.88,1436.67,1443.76,2357230000,1443.76 2007-04-04,1437.75,1440.16,1435.08,1439.37,2616320000,1439.37 2007-04-03,1424.27,1440.57,1424.27,1437.77,2921760000,1437.77 2007-04-02,1420.83,1425.49,1416.37,1424.55,2875880000,1424.55 2007-03-30,1422.52,1429.22,1408.90,1420.86,2903960000,1420.86 2007-03-29,1417.17,1426.24,1413.27,1422.53,2854710000,1422.53 2007-03-28,1428.35,1428.35,1414.07,1417.23,3000440000,1417.23 2007-03-27,1437.49,1437.49,1425.54,1428.61,2673040000,1428.61 2007-03-26,1436.11,1437.65,1423.28,1437.50,2754660000,1437.50 2007-03-23,1434.54,1438.89,1433.21,1436.11,2619020000,1436.11 2007-03-22,1435.04,1437.66,1429.88,1434.54,3129970000,1434.54 2007-03-21,1410.92,1437.77,1409.75,1435.04,3184770000,1435.04 2007-03-20,1402.04,1411.53,1400.70,1410.94,2795940000,1410.94 2007-03-19,1386.95,1403.20,1386.95,1402.06,2777180000,1402.06 2007-03-16,1392.28,1397.51,1383.63,1386.95,3393640000,1386.95 2007-03-15,1387.11,1395.73,1385.16,1392.28,2821900000,1392.28 2007-03-14,1377.86,1388.09,1363.98,1387.17,3758350000,1387.17 2007-03-13,1406.23,1406.23,1377.71,1377.95,3485570000,1377.95 2007-03-12,1402.80,1409.34,1398.40,1406.60,2664000000,1406.60 2007-03-09,1401.89,1410.15,1397.30,1402.84,2623050000,1402.84 2007-03-08,1391.88,1407.93,1391.88,1401.89,3014850000,1401.89 2007-03-07,1395.02,1401.16,1390.64,1391.97,3141350000,1391.97 2007-03-06,1374.06,1397.90,1374.06,1395.41,3358160000,1395.41 2007-03-05,1387.11,1391.86,1373.97,1374.12,3480520000,1374.12 2007-03-02,1403.16,1403.40,1386.87,1387.17,3312260000,1387.17 2007-03-01,1406.80,1409.46,1380.87,1403.17,3874910000,1403.17 2007-02-28,1398.64,1415.89,1396.65,1406.82,3925250000,1406.82 2007-02-27,1449.25,1449.25,1389.42,1399.04,4065230000,1399.04 2007-02-26,1451.04,1456.95,1445.48,1449.37,2822170000,1449.37 2007-02-23,1456.22,1456.22,1448.36,1451.19,2579950000,1451.19 2007-02-22,1457.29,1461.57,1450.51,1456.38,1950770000,1456.38 2007-02-21,1459.60,1459.60,1452.02,1457.63,2606980000,1457.63 2007-02-20,1455.53,1460.53,1449.20,1459.68,2337860000,1459.68 2007-02-16,1456.77,1456.77,1451.57,1455.54,2399450000,1455.54 2007-02-15,1455.15,1457.97,1453.19,1456.81,2490920000,1456.81 2007-02-14,1443.91,1457.65,1443.91,1455.30,2699290000,1455.30 2007-02-13,1433.22,1444.41,1433.22,1444.26,2652150000,1444.26 2007-02-12,1438.00,1439.11,1431.44,1433.37,2395680000,1433.37 2007-02-09,1448.25,1452.45,1433.44,1438.06,2951810000,1438.06 2007-02-08,1449.99,1450.45,1442.81,1448.31,2816180000,1448.31 2007-02-07,1447.41,1452.99,1446.44,1450.02,2618820000,1450.02 2007-02-06,1446.98,1450.19,1443.40,1448.00,2608710000,1448.00 2007-02-05,1448.33,1449.38,1443.85,1446.99,2439430000,1446.99 2007-02-02,1445.94,1449.33,1444.49,1448.39,2569450000,1448.39 2007-02-01,1437.90,1446.64,1437.90,1445.94,2914890000,1445.94 2007-01-31,1428.65,1441.61,1424.78,1438.24,2976690000,1438.24 2007-01-30,1420.61,1428.82,1420.61,1428.82,2706250000,1428.82 2007-01-29,1422.03,1426.94,1418.46,1420.62,2730480000,1420.62 2007-01-26,1423.90,1427.27,1416.96,1422.18,2626620000,1422.18 2007-01-25,1440.12,1440.69,1422.34,1423.90,2994330000,1423.90 2007-01-24,1427.96,1440.14,1427.96,1440.13,2783180000,1440.13 2007-01-23,1422.95,1431.33,1421.66,1427.99,2975070000,1427.99 2007-01-22,1430.47,1431.39,1420.40,1422.95,2540120000,1422.95 2007-01-19,1426.35,1431.57,1425.19,1430.50,2777480000,1430.50 2007-01-18,1430.59,1432.96,1424.21,1426.37,2822430000,1426.37 2007-01-17,1431.77,1435.27,1428.57,1430.62,2690270000,1430.62 2007-01-16,1430.73,1433.93,1428.62,1431.90,2599530000,1431.90 2007-01-12,1423.82,1431.23,1422.58,1430.73,2686480000,1430.73 2007-01-11,1414.84,1427.12,1414.84,1423.82,2857870000,1423.82 2007-01-10,1408.70,1415.99,1405.32,1414.85,2764660000,1414.85 2007-01-09,1412.84,1415.61,1405.42,1412.11,3038380000,1412.11 2007-01-08,1409.26,1414.98,1403.97,1412.84,2763340000,1412.84 2007-01-05,1418.34,1418.34,1405.75,1409.71,2919400000,1409.71 2007-01-04,1416.60,1421.84,1408.43,1418.34,3004460000,1418.34 2007-01-03,1418.03,1429.42,1407.86,1416.60,3429160000,1416.60 2006-12-29,1424.71,1427.00,1416.84,1418.30,1678200000,1418.30 2006-12-28,1426.77,1427.26,1422.05,1424.73,1508570000,1424.73 2006-12-27,1416.63,1427.72,1416.63,1426.84,1667370000,1426.84 2006-12-26,1410.75,1417.91,1410.45,1416.90,1310310000,1416.90 2006-12-22,1418.10,1418.82,1410.28,1410.76,1647590000,1410.76 2006-12-21,1423.20,1426.40,1415.90,1418.30,2322410000,1418.30 2006-12-20,1425.51,1429.05,1423.51,1423.53,2387630000,1423.53 2006-12-19,1422.42,1428.30,1414.88,1425.55,2717060000,1425.55 2006-12-18,1427.08,1431.81,1420.65,1422.48,2568140000,1422.48 2006-12-15,1425.48,1431.63,1425.48,1427.09,3229580000,1427.09 2006-12-14,1413.16,1427.23,1413.16,1425.49,2729700000,1425.49 2006-12-13,1411.32,1416.64,1411.05,1413.21,2552260000,1413.21 2006-12-12,1413.00,1413.78,1404.75,1411.56,2738170000,1411.56 2006-12-11,1409.81,1415.60,1408.56,1413.04,2289900000,1413.04 2006-12-08,1407.27,1414.09,1403.67,1409.84,2440460000,1409.84 2006-12-07,1412.86,1418.27,1406.80,1407.29,2743150000,1407.29 2006-12-06,1414.40,1415.93,1411.05,1412.90,2725280000,1412.90 2006-12-05,1409.10,1415.27,1408.78,1414.76,2755700000,1414.76 2006-12-04,1396.67,1411.23,1396.67,1409.12,2766320000,1409.12 2006-12-01,1400.63,1402.46,1385.93,1396.71,2800980000,1396.71 2006-11-30,1399.47,1406.30,1393.83,1400.63,4006230000,1400.63 2006-11-29,1386.11,1401.14,1386.11,1399.48,2790970000,1399.48 2006-11-28,1381.61,1387.91,1377.83,1386.72,2639750000,1386.72 2006-11-27,1400.95,1400.95,1381.44,1381.96,2711210000,1381.96 2006-11-24,1405.94,1405.94,1399.25,1400.95,832550000,1400.95 2006-11-22,1402.69,1407.89,1402.26,1406.09,2237710000,1406.09 2006-11-21,1400.43,1403.49,1399.99,1402.81,2597940000,1402.81 2006-11-20,1401.17,1404.37,1397.85,1400.50,2546710000,1400.50 2006-11-17,1399.76,1401.21,1394.55,1401.20,2726100000,1401.20 2006-11-16,1396.53,1403.76,1396.53,1399.76,2835730000,1399.76 2006-11-15,1392.91,1401.35,1392.13,1396.57,2831130000,1396.57 2006-11-14,1384.36,1394.49,1379.07,1393.22,3027480000,1393.22 2006-11-13,1380.58,1387.61,1378.80,1384.42,2386340000,1384.42 2006-11-10,1378.33,1381.04,1375.60,1380.90,2290200000,1380.90 2006-11-09,1385.43,1388.92,1377.31,1378.33,3012050000,1378.33 2006-11-08,1382.50,1388.61,1379.33,1385.72,2814820000,1385.72 2006-11-07,1379.75,1388.19,1379.19,1382.84,2636390000,1382.84 2006-11-06,1364.27,1381.40,1364.27,1379.78,2533550000,1379.78 2006-11-03,1367.31,1371.68,1360.98,1364.30,2419730000,1364.30 2006-11-02,1367.44,1368.39,1362.21,1367.34,2646180000,1367.34 2006-11-01,1377.76,1381.95,1366.26,1367.81,2821160000,1367.81 2006-10-31,1377.93,1381.21,1372.19,1377.94,2803030000,1377.94 2006-10-30,1377.30,1381.22,1373.46,1377.93,2770440000,1377.93 2006-10-27,1388.89,1388.89,1375.85,1377.34,2458450000,1377.34 2006-10-26,1382.21,1389.45,1379.47,1389.08,2793350000,1389.08 2006-10-25,1377.36,1383.61,1376.00,1382.22,2953540000,1382.22 2006-10-24,1377.02,1377.78,1372.42,1377.38,2876890000,1377.38 2006-10-23,1368.58,1377.40,1363.94,1377.02,2480430000,1377.02 2006-10-20,1366.94,1368.66,1362.10,1368.60,2526410000,1368.60 2006-10-19,1365.95,1368.09,1362.06,1366.96,2619830000,1366.96 2006-10-18,1363.93,1372.87,1360.95,1365.80,2658840000,1365.80 2006-10-17,1369.05,1369.05,1356.87,1364.05,2519620000,1364.05 2006-10-16,1365.61,1370.20,1364.48,1369.06,2305920000,1369.06 2006-10-13,1362.82,1366.63,1360.50,1365.62,2482920000,1365.62 2006-10-12,1349.94,1363.76,1349.94,1362.83,2514350000,1362.83 2006-10-11,1353.28,1353.97,1343.57,1349.95,2521000000,1349.95 2006-10-10,1350.62,1354.23,1348.60,1353.42,2376140000,1353.42 2006-10-09,1349.58,1352.69,1346.55,1350.66,1935170000,1350.66 2006-10-06,1353.22,1353.22,1344.21,1349.59,2523000000,1349.59 2006-10-05,1349.84,1353.79,1347.75,1353.22,2817240000,1353.22 2006-10-04,1333.81,1350.20,1331.48,1350.20,3019880000,1350.20 2006-10-03,1331.32,1338.31,1327.10,1334.11,2682690000,1334.11 2006-10-02,1335.82,1338.54,1330.28,1331.32,2154480000,1331.32 2006-09-29,1339.15,1339.88,1335.64,1335.85,2273430000,1335.85 2006-09-28,1336.56,1340.28,1333.75,1338.88,2397820000,1338.88 2006-09-27,1336.12,1340.08,1333.54,1336.59,2749190000,1336.59 2006-09-26,1326.35,1336.60,1325.30,1336.35,2673350000,1336.35 2006-09-25,1314.78,1329.35,1311.58,1326.37,2710240000,1326.37 2006-09-22,1318.03,1318.03,1310.94,1314.78,2162880000,1314.78 2006-09-21,1324.89,1328.19,1315.45,1318.03,2627440000,1318.03 2006-09-20,1318.28,1328.53,1318.28,1325.18,2543070000,1325.18 2006-09-19,1321.17,1322.04,1312.17,1317.64,2390850000,1317.64 2006-09-18,1319.85,1324.87,1318.16,1321.18,2325080000,1321.18 2006-09-15,1316.28,1324.65,1316.28,1319.66,3198030000,1319.66 2006-09-14,1318.00,1318.00,1313.25,1316.28,2351220000,1316.28 2006-09-13,1312.74,1319.92,1311.12,1318.07,2597220000,1318.07 2006-09-12,1299.53,1314.28,1299.53,1313.00,2791580000,1313.00 2006-09-11,1298.86,1302.36,1290.93,1299.54,2506430000,1299.54 2006-09-08,1294.02,1300.14,1294.02,1298.92,2132890000,1298.92 2006-09-07,1300.21,1301.25,1292.13,1294.02,2325850000,1294.02 2006-09-06,1313.04,1313.04,1299.28,1300.26,2329870000,1300.26 2006-09-05,1310.94,1314.67,1308.82,1313.25,2114480000,1313.25 2006-09-01,1303.80,1312.03,1303.80,1311.01,1800520000,1311.01 2006-08-31,1304.25,1306.11,1302.45,1303.82,1974540000,1303.82 2006-08-30,1303.70,1306.74,1302.15,1305.37,2060690000,1305.37 2006-08-29,1301.57,1305.02,1295.29,1304.28,2093720000,1304.28 2006-08-28,1295.09,1305.02,1293.97,1301.78,1834920000,1301.78 2006-08-25,1295.92,1298.88,1292.39,1295.09,1667580000,1295.09 2006-08-24,1292.97,1297.23,1291.40,1296.06,1930320000,1296.06 2006-08-23,1298.73,1301.50,1289.82,1292.99,1893670000,1292.99 2006-08-22,1297.52,1302.49,1294.44,1298.82,1908740000,1298.82 2006-08-21,1302.30,1302.30,1295.51,1297.52,1759240000,1297.52 2006-08-18,1297.48,1302.30,1293.57,1302.30,2033910000,1302.30 2006-08-17,1295.37,1300.78,1292.71,1297.48,2458340000,1297.48 2006-08-16,1285.27,1296.21,1285.27,1295.43,2554570000,1295.43 2006-08-15,1268.19,1286.23,1268.19,1285.58,2334100000,1285.58 2006-08-14,1266.67,1278.90,1266.67,1268.21,2118020000,1268.21 2006-08-11,1271.64,1271.64,1262.08,1266.74,2004540000,1266.74 2006-08-10,1265.72,1272.55,1261.30,1271.81,2402190000,1271.81 2006-08-09,1271.13,1283.74,1264.73,1265.95,2555180000,1265.95 2006-08-08,1275.67,1282.75,1268.37,1271.48,2457840000,1271.48 2006-08-07,1279.31,1279.31,1273.00,1275.77,2045660000,1275.77 2006-08-04,1280.26,1292.92,1273.82,1279.36,2530970000,1279.36 2006-08-03,1278.22,1283.96,1271.25,1280.27,2728440000,1280.27 2006-08-02,1270.73,1283.42,1270.73,1277.41,2610750000,1277.41 2006-08-01,1278.53,1278.66,1265.71,1270.92,2527690000,1270.92 2006-07-31,1278.53,1278.66,1274.31,1276.66,2461300000,1276.66 2006-07-28,1263.15,1280.42,1263.15,1278.55,2480420000,1278.55 2006-07-27,1268.20,1275.85,1261.92,1263.20,2776710000,1263.20 2006-07-26,1268.87,1273.89,1261.94,1268.40,2667710000,1268.40 2006-07-25,1260.91,1272.39,1257.19,1268.88,2563930000,1268.88 2006-07-24,1240.25,1262.50,1240.25,1260.91,2312720000,1260.91 2006-07-21,1249.12,1250.96,1238.72,1240.29,2704090000,1240.29 2006-07-20,1259.81,1262.56,1249.13,1249.13,2345580000,1249.13 2006-07-19,1236.74,1261.81,1236.74,1259.81,2701980000,1259.81 2006-07-18,1234.48,1239.86,1224.54,1236.86,2481750000,1236.86 2006-07-17,1236.20,1240.07,1231.49,1234.49,2146410000,1234.49 2006-07-14,1242.29,1242.70,1228.45,1236.20,2467120000,1236.20 2006-07-13,1258.58,1258.58,1241.43,1242.28,2545760000,1242.28 2006-07-12,1272.39,1273.31,1257.29,1258.60,2250450000,1258.60 2006-07-11,1267.26,1273.64,1259.65,1272.43,2310850000,1272.43 2006-07-10,1265.46,1274.06,1264.46,1267.34,1854590000,1267.34 2006-07-07,1274.08,1275.38,1263.13,1265.48,1988150000,1265.48 2006-07-06,1270.58,1278.32,1270.58,1274.08,2009160000,1274.08 2006-07-05,1280.05,1280.05,1265.91,1270.91,2165070000,1270.91 2006-07-03,1270.06,1280.38,1270.06,1280.19,1114470000,1280.19 2006-06-30,1272.86,1276.30,1270.20,1270.20,3049560000,1270.20 2006-06-29,1245.94,1272.88,1245.94,1272.87,2621250000,1272.87 2006-06-28,1238.99,1247.06,1237.59,1246.00,2085490000,1246.00 2006-06-27,1250.55,1253.37,1238.94,1239.20,2203130000,1239.20 2006-06-26,1244.50,1250.92,1243.68,1250.56,1878580000,1250.56 2006-06-23,1245.59,1253.13,1241.43,1244.50,2017270000,1244.50 2006-06-22,1251.92,1251.92,1241.53,1245.60,2148180000,1245.60 2006-06-21,1240.09,1257.96,1240.09,1252.20,2361230000,1252.20 2006-06-20,1240.12,1249.01,1238.87,1240.12,2232950000,1240.12 2006-06-19,1251.54,1255.93,1237.17,1240.13,2517200000,1240.13 2006-06-16,1256.16,1256.27,1246.33,1251.54,2783390000,1251.54 2006-06-15,1230.01,1258.64,1230.01,1256.16,2775480000,1256.16 2006-06-14,1223.66,1231.46,1219.29,1230.04,2667990000,1230.04 2006-06-13,1236.08,1243.37,1222.52,1223.69,3215770000,1223.69 2006-06-12,1252.27,1255.22,1236.43,1237.44,2247010000,1237.44 2006-06-09,1257.93,1262.58,1250.03,1252.30,2214000000,1252.30 2006-06-08,1256.08,1259.85,1235.18,1257.93,3543790000,1257.93 2006-06-07,1263.61,1272.47,1255.77,1256.15,2644170000,1256.15 2006-06-06,1265.23,1269.88,1254.46,1263.85,2697650000,1263.85 2006-06-05,1288.16,1288.16,1264.66,1265.29,2313470000,1265.29 2006-06-02,1285.71,1290.68,1280.22,1288.22,2295540000,1288.22 2006-06-01,1270.05,1285.71,1269.19,1285.71,2360160000,1285.71 2006-05-31,1259.38,1270.09,1259.38,1270.09,2692160000,1270.09 2006-05-30,1280.04,1280.04,1259.87,1259.87,2176190000,1259.87 2006-05-26,1272.71,1280.54,1272.50,1280.16,1814020000,1280.16 2006-05-25,1258.41,1273.26,1258.41,1272.88,2372730000,1272.88 2006-05-24,1256.56,1264.53,1245.34,1258.57,2999030000,1258.57 2006-05-23,1262.06,1273.67,1256.15,1256.58,2605250000,1256.58 2006-05-22,1267.03,1268.77,1252.98,1262.07,2773010000,1262.07 2006-05-19,1261.81,1272.15,1256.28,1267.03,2982300000,1267.03 2006-05-18,1270.25,1274.89,1261.75,1261.81,2537490000,1261.81 2006-05-17,1291.73,1291.73,1267.31,1270.32,2830200000,1270.32 2006-05-16,1294.50,1297.88,1288.51,1292.08,2386210000,1292.08 2006-05-15,1291.19,1294.81,1284.51,1294.50,2505660000,1294.50 2006-05-12,1305.88,1305.88,1290.38,1291.24,2567970000,1291.24 2006-05-11,1322.63,1322.63,1303.45,1305.92,2531520000,1305.92 2006-05-10,1324.57,1325.51,1317.44,1322.85,2268550000,1322.85 2006-05-09,1324.66,1326.60,1322.48,1325.14,2157290000,1325.14 2006-05-08,1325.76,1326.70,1322.87,1324.66,2151300000,1324.66 2006-05-05,1312.25,1326.53,1312.25,1325.76,2294760000,1325.76 2006-05-04,1307.85,1315.14,1307.85,1312.25,2431450000,1312.25 2006-05-03,1313.21,1313.47,1303.92,1308.12,2395230000,1308.12 2006-05-02,1305.19,1313.66,1305.19,1313.21,2403470000,1313.21 2006-05-01,1310.61,1317.21,1303.46,1305.19,2437040000,1305.19 2006-04-28,1309.72,1316.04,1306.16,1310.61,2419920000,1310.61 2006-04-27,1305.41,1315.00,1295.57,1309.72,2772010000,1309.72 2006-04-26,1301.74,1310.97,1301.74,1305.41,2502690000,1305.41 2006-04-25,1308.11,1310.79,1299.17,1301.74,2366380000,1301.74 2006-04-24,1311.28,1311.28,1303.79,1308.11,2117330000,1308.11 2006-04-21,1311.46,1317.67,1306.59,1311.28,2392630000,1311.28 2006-04-20,1309.93,1318.16,1306.38,1311.46,2512920000,1311.46 2006-04-19,1307.65,1310.39,1302.79,1309.93,2447310000,1309.93 2006-04-18,1285.33,1309.02,1285.33,1307.28,2595440000,1307.28 2006-04-17,1289.12,1292.45,1280.74,1285.33,1794650000,1285.33 2006-04-13,1288.12,1292.09,1283.37,1289.12,1891940000,1289.12 2006-04-12,1286.57,1290.93,1286.45,1288.12,1938100000,1288.12 2006-04-11,1296.60,1300.71,1282.96,1286.57,2232880000,1286.57 2006-04-10,1295.51,1300.74,1293.17,1296.62,1898320000,1296.62 2006-04-07,1309.04,1314.07,1294.18,1295.50,2082470000,1295.50 2006-04-06,1311.56,1311.99,1302.44,1309.04,2281680000,1309.04 2006-04-05,1305.93,1312.81,1304.82,1311.56,2420020000,1311.56 2006-04-04,1297.81,1307.55,1294.71,1305.93,2147660000,1305.93 2006-04-03,1302.88,1309.19,1296.65,1297.81,2494080000,1297.81 2006-03-31,1300.25,1303.00,1294.87,1294.87,2236710000,1294.87 2006-03-30,1302.89,1310.15,1296.72,1300.25,2294560000,1300.25 2006-03-29,1293.23,1305.60,1293.23,1302.89,2143540000,1302.89 2006-03-28,1301.61,1306.24,1291.84,1293.23,2148580000,1293.23 2006-03-27,1302.95,1303.74,1299.09,1301.61,2029700000,1301.61 2006-03-24,1301.67,1306.53,1298.89,1302.95,2326070000,1302.95 2006-03-23,1305.04,1305.04,1298.11,1301.67,1980940000,1301.67 2006-03-22,1297.23,1305.97,1295.81,1305.04,2039810000,1305.04 2006-03-21,1305.08,1310.88,1295.82,1297.23,2147370000,1297.23 2006-03-20,1307.25,1310.00,1303.59,1305.08,1976830000,1305.08 2006-03-17,1305.33,1309.79,1305.32,1307.25,2549620000,1307.25 2006-03-16,1303.02,1310.45,1303.02,1305.33,2292180000,1305.33 2006-03-15,1297.48,1304.40,1294.97,1303.02,2293000000,1303.02 2006-03-14,1284.13,1298.14,1282.67,1297.48,2165270000,1297.48 2006-03-13,1281.58,1287.37,1281.58,1284.13,2070330000,1284.13 2006-03-10,1272.23,1284.37,1271.11,1281.42,2123450000,1281.42 2006-03-09,1278.47,1282.74,1272.23,1272.23,2140110000,1272.23 2006-03-08,1275.88,1280.33,1268.42,1278.47,2442870000,1278.47 2006-03-07,1278.26,1278.26,1271.11,1275.88,2268050000,1275.88 2006-03-06,1287.23,1288.23,1275.67,1278.26,2280190000,1278.26 2006-03-03,1289.14,1297.33,1284.20,1287.23,2152950000,1287.23 2006-03-02,1291.24,1291.24,1283.21,1289.14,2494590000,1289.14 2006-03-01,1280.66,1291.80,1280.66,1291.24,2308320000,1291.24 2006-02-28,1294.12,1294.12,1278.66,1280.66,2370860000,1280.66 2006-02-27,1289.43,1297.57,1289.43,1294.12,1975320000,1294.12 2006-02-24,1287.79,1292.11,1285.62,1289.43,1933010000,1289.43 2006-02-23,1292.67,1293.84,1285.14,1287.79,2144210000,1287.79 2006-02-22,1283.03,1294.17,1283.03,1292.67,2222380000,1292.67 2006-02-21,1287.24,1291.92,1281.33,1283.03,2104320000,1283.03 2006-02-17,1289.38,1289.47,1284.07,1287.24,2128260000,1287.24 2006-02-16,1280.00,1289.39,1280.00,1289.38,2251490000,1289.38 2006-02-15,1275.53,1281.00,1271.06,1280.00,2317590000,1280.00 2006-02-14,1262.86,1278.21,1260.80,1275.53,2437940000,1275.53 2006-02-13,1266.99,1266.99,1258.34,1262.86,1850080000,1262.86 2006-02-10,1263.82,1269.89,1254.98,1266.99,2290050000,1266.99 2006-02-09,1265.65,1274.56,1262.80,1263.78,2441920000,1263.78 2006-02-08,1254.78,1266.47,1254.78,1265.65,2456860000,1265.65 2006-02-07,1265.02,1265.78,1253.61,1254.78,2366370000,1254.78 2006-02-06,1264.03,1267.04,1261.62,1265.02,2132360000,1265.02 2006-02-03,1270.84,1270.87,1261.02,1264.03,2282210000,1264.03 2006-02-02,1282.46,1282.46,1267.72,1270.84,2565300000,1270.84 2006-02-01,1280.08,1283.33,1277.57,1282.46,2589410000,1282.46 2006-01-31,1285.20,1285.20,1276.85,1280.08,2708310000,1280.08 2006-01-30,1283.72,1287.94,1283.51,1285.19,2282730000,1285.19 2006-01-27,1273.83,1286.38,1273.83,1283.72,2623620000,1283.72 2006-01-26,1264.68,1276.44,1264.68,1273.83,2856780000,1273.83 2006-01-25,1266.86,1271.87,1259.42,1264.68,2617060000,1264.68 2006-01-24,1263.82,1271.47,1263.82,1266.86,2608720000,1266.86 2006-01-23,1261.49,1268.19,1261.49,1263.82,2256070000,1263.82 2006-01-20,1285.04,1285.04,1260.92,1261.49,2845810000,1261.49 2006-01-19,1277.93,1287.79,1277.93,1285.04,2444020000,1285.04 2006-01-18,1282.93,1282.93,1272.08,1277.93,2233200000,1277.93 2006-01-17,1287.61,1287.61,1278.61,1283.03,2179970000,1283.03 2006-01-13,1286.06,1288.96,1282.78,1287.61,2206510000,1287.61 2006-01-12,1294.18,1294.18,1285.04,1286.06,2318350000,1286.06 2006-01-11,1289.72,1294.90,1288.12,1294.18,2406130000,1294.18 2006-01-10,1290.15,1290.15,1283.76,1289.69,2373080000,1289.69 2006-01-09,1285.45,1290.78,1284.82,1290.15,2301490000,1290.15 2006-01-06,1273.48,1286.09,1273.48,1285.45,2446560000,1285.45 2006-01-05,1273.46,1276.91,1270.30,1273.48,2433340000,1273.48 2006-01-04,1268.80,1275.37,1267.74,1273.46,2515330000,1273.46 2006-01-03,1248.29,1270.22,1245.74,1268.80,2554570000,1268.80 2005-12-30,1254.42,1254.42,1246.59,1248.29,1443500000,1248.29 2005-12-29,1258.17,1260.61,1254.18,1254.42,1382540000,1254.42 2005-12-28,1256.54,1261.10,1256.54,1258.17,1422360000,1258.17 2005-12-27,1268.66,1271.83,1256.54,1256.54,1540470000,1256.54 2005-12-23,1268.12,1269.76,1265.92,1268.66,1285810000,1268.66 2005-12-22,1262.79,1268.19,1262.50,1268.12,1888500000,1268.12 2005-12-21,1259.62,1269.37,1259.62,1262.79,2065170000,1262.79 2005-12-20,1259.92,1263.86,1257.21,1259.62,1996690000,1259.62 2005-12-19,1267.32,1270.51,1259.28,1259.92,2208810000,1259.92 2005-12-16,1270.94,1275.24,1267.32,1267.32,2584190000,1267.32 2005-12-15,1272.74,1275.17,1267.74,1270.94,2180590000,1270.94 2005-12-14,1267.43,1275.80,1267.07,1272.74,2145520000,1272.74 2005-12-13,1260.43,1272.11,1258.56,1267.43,2390020000,1267.43 2005-12-12,1259.37,1263.86,1255.52,1260.43,1876550000,1260.43 2005-12-09,1255.84,1263.08,1254.24,1259.37,1896290000,1259.37 2005-12-08,1257.37,1263.36,1250.91,1255.84,2178300000,1255.84 2005-12-07,1263.70,1264.85,1253.02,1257.37,2093830000,1257.37 2005-12-06,1262.09,1272.89,1262.09,1263.70,2110740000,1263.70 2005-12-05,1265.08,1265.08,1258.12,1262.09,2325840000,1262.09 2005-12-02,1264.67,1266.85,1261.42,1265.08,2125580000,1265.08 2005-12-01,1249.48,1266.17,1249.48,1264.67,2614830000,1264.67 2005-11-30,1257.48,1260.93,1249.39,1249.48,2374690000,1249.48 2005-11-29,1257.46,1266.18,1257.46,1257.48,2268340000,1257.48 2005-11-28,1268.25,1268.44,1257.17,1257.46,2016900000,1257.46 2005-11-25,1265.61,1268.78,1265.54,1268.25,724940000,1268.25 2005-11-23,1261.23,1270.64,1259.51,1265.61,1985400000,1265.61 2005-11-22,1254.85,1261.90,1251.40,1261.23,2291420000,1261.23 2005-11-21,1248.27,1255.89,1246.90,1254.85,2117350000,1254.85 2005-11-18,1242.80,1249.58,1240.71,1248.27,2453290000,1248.27 2005-11-17,1231.21,1242.96,1231.21,1242.80,2298040000,1242.80 2005-11-16,1229.01,1232.24,1227.18,1231.21,2121580000,1231.21 2005-11-15,1233.76,1237.94,1226.41,1229.01,2359370000,1229.01 2005-11-14,1234.72,1237.20,1231.78,1233.76,1899780000,1233.76 2005-11-11,1230.96,1235.70,1230.72,1234.72,1773140000,1234.72 2005-11-10,1220.65,1232.41,1215.05,1230.96,2378460000,1230.96 2005-11-09,1218.59,1226.59,1216.53,1220.65,2214460000,1220.65 2005-11-08,1222.81,1222.81,1216.08,1218.59,1965050000,1218.59 2005-11-07,1220.14,1224.18,1217.29,1222.81,1987580000,1222.81 2005-11-04,1219.94,1222.52,1214.45,1220.14,2050510000,1220.14 2005-11-03,1214.76,1224.70,1214.76,1219.94,2716630000,1219.94 2005-11-02,1202.76,1215.17,1201.07,1214.76,2648090000,1214.76 2005-11-01,1207.01,1207.34,1201.66,1202.76,2457850000,1202.76 2005-10-31,1198.41,1211.43,1198.41,1207.01,2567470000,1207.01 2005-10-28,1178.90,1198.41,1178.90,1198.41,2379400000,1198.41 2005-10-27,1191.38,1192.65,1178.89,1178.90,2395370000,1178.90 2005-10-26,1196.54,1204.01,1191.38,1191.38,2467750000,1191.38 2005-10-25,1199.38,1201.30,1189.29,1196.54,2312470000,1196.54 2005-10-24,1179.59,1199.39,1179.59,1199.38,2197790000,1199.38 2005-10-21,1177.80,1186.46,1174.92,1179.59,2470920000,1179.59 2005-10-20,1195.76,1197.30,1173.30,1177.80,2617250000,1177.80 2005-10-19,1178.14,1195.76,1170.55,1195.76,2703590000,1195.76 2005-10-18,1190.10,1190.10,1178.13,1178.14,2197010000,1178.14 2005-10-17,1186.57,1191.21,1184.48,1190.10,2054570000,1190.10 2005-10-14,1176.84,1187.13,1175.44,1186.57,2188940000,1186.57 2005-10-13,1177.68,1179.56,1168.20,1176.84,2351150000,1176.84 2005-10-12,1184.87,1190.02,1173.65,1177.68,2491280000,1177.68 2005-10-11,1187.33,1193.10,1183.16,1184.87,2299040000,1184.87 2005-10-10,1195.90,1196.52,1186.12,1187.33,2195990000,1187.33 2005-10-07,1191.49,1199.71,1191.46,1195.90,2126080000,1195.90 2005-10-06,1196.39,1202.14,1181.92,1191.49,2792030000,1191.49 2005-10-05,1214.47,1214.47,1196.25,1196.39,2546780000,1196.39 2005-10-04,1226.70,1229.88,1214.02,1214.47,2341420000,1214.47 2005-10-03,1228.81,1233.34,1225.15,1226.70,2097490000,1226.70 2005-09-30,1227.68,1229.57,1225.22,1228.81,2097520000,1228.81 2005-09-29,1216.89,1228.70,1211.54,1227.68,2176120000,1227.68 2005-09-28,1215.66,1220.98,1212.72,1216.89,2106980000,1216.89 2005-09-27,1215.63,1220.17,1211.11,1215.66,1976270000,1215.66 2005-09-26,1215.29,1222.56,1211.84,1215.63,2022220000,1215.63 2005-09-23,1214.62,1218.83,1209.80,1215.29,1973020000,1215.29 2005-09-22,1210.20,1216.64,1205.35,1214.62,2424720000,1214.62 2005-09-21,1221.34,1221.52,1209.89,1210.20,2548150000,1210.20 2005-09-20,1231.02,1236.49,1220.07,1221.34,2319250000,1221.34 2005-09-19,1237.91,1237.91,1227.65,1231.02,2076540000,1231.02 2005-09-16,1228.42,1237.95,1228.42,1237.91,3152470000,1237.91 2005-09-15,1227.16,1231.88,1224.85,1227.73,2079340000,1227.73 2005-09-14,1231.20,1234.74,1226.16,1227.16,1986750000,1227.16 2005-09-13,1240.57,1240.57,1231.20,1231.20,2082360000,1231.20 2005-09-12,1241.48,1242.60,1239.15,1240.56,1938050000,1240.56 2005-09-09,1231.67,1243.13,1231.67,1241.48,1992560000,1241.48 2005-09-08,1236.36,1236.36,1229.51,1231.67,1955380000,1231.67 2005-09-07,1233.39,1237.06,1230.93,1236.36,2067700000,1236.36 2005-09-06,1218.02,1233.61,1218.02,1233.39,1932090000,1233.39 2005-09-02,1221.59,1224.45,1217.75,1218.02,1640160000,1218.02 2005-09-01,1220.33,1227.29,1216.18,1221.59,2229860000,1221.59 2005-08-31,1208.41,1220.36,1204.40,1220.33,2365510000,1220.33 2005-08-30,1212.28,1212.28,1201.07,1208.41,1916470000,1208.41 2005-08-29,1205.10,1214.28,1201.53,1212.28,1599450000,1212.28 2005-08-26,1212.40,1212.40,1204.23,1205.10,1541090000,1205.10 2005-08-25,1209.59,1213.73,1209.57,1212.37,1571110000,1212.37 2005-08-24,1217.57,1224.15,1209.37,1209.59,1930800000,1209.59 2005-08-23,1221.73,1223.04,1214.44,1217.59,1678620000,1217.59 2005-08-22,1219.71,1228.96,1216.47,1221.73,1621330000,1221.73 2005-08-19,1219.02,1225.08,1219.02,1219.71,1558790000,1219.71 2005-08-18,1220.24,1222.64,1215.93,1219.02,1808170000,1219.02 2005-08-17,1219.34,1225.63,1218.07,1220.24,1859150000,1220.24 2005-08-16,1233.87,1233.87,1219.05,1219.34,1820410000,1219.34 2005-08-15,1230.40,1236.24,1226.20,1233.87,1562880000,1233.87 2005-08-12,1237.81,1237.81,1225.87,1230.39,1709300000,1230.39 2005-08-11,1229.13,1237.81,1228.33,1237.81,1941560000,1237.81 2005-08-10,1231.38,1242.69,1226.58,1229.13,2172320000,1229.13 2005-08-09,1223.13,1234.11,1223.13,1231.38,1897520000,1231.38 2005-08-08,1226.42,1232.28,1222.67,1223.13,1804140000,1223.13 2005-08-05,1235.86,1235.86,1225.62,1226.42,1930280000,1226.42 2005-08-04,1245.04,1245.04,1235.15,1235.86,1981220000,1235.86 2005-08-03,1244.12,1245.86,1240.57,1245.04,1999980000,1245.04 2005-08-02,1235.35,1244.69,1235.35,1244.12,2043120000,1244.12 2005-08-01,1234.18,1239.10,1233.80,1235.35,1716870000,1235.35 2005-07-29,1243.72,1245.04,1234.18,1234.18,1789600000,1234.18 2005-07-28,1236.79,1245.15,1235.81,1243.72,2001680000,1243.72 2005-07-27,1231.16,1237.64,1230.15,1236.79,1945800000,1236.79 2005-07-26,1229.03,1234.42,1229.03,1231.16,1934180000,1231.16 2005-07-25,1233.68,1238.36,1228.15,1229.03,1717580000,1229.03 2005-07-22,1227.04,1234.19,1226.15,1233.68,1766990000,1233.68 2005-07-21,1235.20,1235.83,1224.70,1227.04,2129840000,1227.04 2005-07-20,1229.35,1236.56,1222.91,1235.20,2063340000,1235.20 2005-07-19,1221.13,1230.34,1221.13,1229.35,2041280000,1229.35 2005-07-18,1227.92,1227.92,1221.13,1221.13,1582100000,1221.13 2005-07-15,1226.50,1229.53,1223.50,1227.92,1716400000,1227.92 2005-07-14,1223.29,1233.16,1223.29,1226.50,2048710000,1226.50 2005-07-13,1222.21,1224.46,1219.64,1223.29,1812500000,1223.29 2005-07-12,1219.44,1225.54,1216.60,1222.21,1932010000,1222.21 2005-07-11,1211.86,1220.03,1211.86,1219.44,1846300000,1219.44 2005-07-08,1197.87,1212.73,1197.20,1211.86,1900810000,1211.86 2005-07-07,1194.94,1198.46,1183.55,1197.87,1952440000,1197.87 2005-07-06,1204.99,1206.11,1194.78,1194.94,1883470000,1194.94 2005-07-05,1194.44,1206.34,1192.49,1204.99,1805820000,1204.99 2005-07-01,1191.33,1197.89,1191.33,1194.44,1593820000,1194.44 2005-06-30,1199.85,1203.27,1190.51,1191.33,2109490000,1191.33 2005-06-29,1201.57,1204.07,1198.70,1199.85,1769280000,1199.85 2005-06-28,1190.69,1202.54,1190.69,1201.57,1772410000,1201.57 2005-06-27,1191.57,1194.33,1188.30,1190.69,1738620000,1190.69 2005-06-24,1200.73,1200.90,1191.45,1191.57,2418800000,1191.57 2005-06-23,1213.88,1216.45,1200.72,1200.73,2029920000,1200.73 2005-06-22,1213.61,1219.59,1211.69,1213.88,1823250000,1213.88 2005-06-21,1216.10,1217.13,1211.86,1213.61,1720700000,1213.61 2005-06-20,1216.96,1219.10,1210.65,1216.10,1714530000,1216.10 2005-06-17,1210.93,1219.55,1210.93,1216.96,2407370000,1216.96 2005-06-16,1206.55,1212.10,1205.47,1210.96,1776040000,1210.96 2005-06-15,1203.91,1208.08,1198.66,1206.58,1840440000,1206.58 2005-06-14,1200.82,1207.53,1200.18,1203.91,1698150000,1203.91 2005-06-13,1198.11,1206.03,1194.51,1200.82,1661350000,1200.82 2005-06-10,1200.93,1202.79,1192.64,1198.11,1664180000,1198.11 2005-06-09,1194.67,1201.86,1191.09,1200.93,1824120000,1200.93 2005-06-08,1197.26,1201.97,1193.33,1194.67,1715490000,1194.67 2005-06-07,1197.51,1208.85,1197.26,1197.26,1851370000,1197.26 2005-06-06,1196.02,1198.78,1192.75,1197.51,1547120000,1197.51 2005-06-03,1204.29,1205.09,1194.55,1196.02,1627520000,1196.02 2005-06-02,1202.27,1204.67,1198.42,1204.29,1813790000,1204.29 2005-06-01,1191.50,1205.64,1191.03,1202.22,1810100000,1202.22 2005-05-31,1198.78,1198.78,1191.50,1191.50,1840680000,1191.50 2005-05-27,1197.62,1199.56,1195.28,1198.78,1381430000,1198.78 2005-05-26,1190.01,1198.95,1190.01,1197.62,1654110000,1197.62 2005-05-25,1194.07,1194.07,1185.96,1190.01,1742180000,1190.01 2005-05-24,1193.86,1195.29,1189.87,1194.07,1681000000,1194.07 2005-05-23,1189.28,1197.44,1188.76,1193.86,1681170000,1193.86 2005-05-20,1191.08,1191.22,1185.19,1189.28,1631750000,1189.28 2005-05-19,1185.56,1191.09,1184.49,1191.08,1775860000,1191.08 2005-05-18,1173.80,1187.90,1173.80,1185.56,2266320000,1185.56 2005-05-17,1165.69,1174.35,1159.86,1173.80,1887260000,1173.80 2005-05-16,1154.05,1165.75,1153.64,1165.69,1856860000,1165.69 2005-05-13,1159.36,1163.75,1146.18,1154.05,2188590000,1154.05 2005-05-12,1171.11,1173.37,1157.76,1159.36,1995290000,1159.36 2005-05-11,1166.22,1171.77,1157.71,1171.11,1834970000,1171.11 2005-05-10,1178.84,1178.84,1162.98,1166.22,1889660000,1166.22 2005-05-09,1171.35,1178.87,1169.38,1178.84,1857020000,1178.84 2005-05-06,1172.63,1177.75,1170.50,1171.35,1707200000,1171.35 2005-05-05,1175.65,1178.62,1166.77,1172.63,1997100000,1172.63 2005-05-04,1161.17,1176.01,1161.17,1175.65,2306480000,1175.65 2005-05-03,1162.16,1166.89,1156.71,1161.17,2167020000,1161.17 2005-05-02,1156.85,1162.87,1154.71,1162.16,1980040000,1162.16 2005-04-29,1143.22,1156.97,1139.19,1156.85,2362360000,1156.85 2005-04-28,1156.38,1156.38,1143.22,1143.22,2182270000,1143.22 2005-04-27,1151.74,1159.87,1144.42,1156.38,2151520000,1156.38 2005-04-26,1162.10,1164.80,1151.83,1151.83,1959740000,1151.83 2005-04-25,1152.12,1164.05,1152.12,1162.10,1795030000,1162.10 2005-04-22,1159.95,1159.95,1142.95,1152.12,2045880000,1152.12 2005-04-21,1137.50,1159.95,1137.50,1159.95,2308560000,1159.95 2005-04-20,1152.78,1155.50,1136.15,1137.50,2217050000,1137.50 2005-04-19,1145.98,1154.67,1145.98,1152.78,2142700000,1152.78 2005-04-18,1142.62,1148.92,1139.80,1145.98,2180670000,1145.98 2005-04-15,1162.05,1162.05,1141.92,1142.62,2689960000,1142.62 2005-04-14,1173.79,1174.67,1161.70,1162.05,2355040000,1162.05 2005-04-13,1187.76,1187.76,1171.40,1173.79,2049740000,1173.79 2005-04-12,1181.21,1190.17,1170.85,1187.76,1979830000,1187.76 2005-04-11,1181.20,1184.07,1178.69,1181.21,1525310000,1181.21 2005-04-08,1191.14,1191.75,1181.13,1181.20,1661330000,1181.20 2005-04-07,1184.07,1191.88,1183.81,1191.14,1900620000,1191.14 2005-04-06,1181.39,1189.34,1181.39,1184.07,1797400000,1184.07 2005-04-05,1176.12,1183.56,1176.12,1181.39,1870800000,1181.39 2005-04-04,1172.79,1178.61,1167.72,1176.12,2079770000,1176.12 2005-04-01,1180.59,1189.80,1169.91,1172.92,2168690000,1172.92 2005-03-31,1181.41,1184.53,1179.49,1180.59,2214230000,1180.59 2005-03-30,1165.36,1181.54,1165.36,1181.41,2097110000,1181.41 2005-03-29,1174.28,1179.39,1163.69,1165.36,2223250000,1165.36 2005-03-28,1171.42,1179.91,1171.42,1174.28,1746220000,1174.28 2005-03-24,1172.53,1180.11,1171.42,1171.42,1721720000,1171.42 2005-03-23,1171.71,1176.26,1168.70,1172.53,2246870000,1172.53 2005-03-22,1183.78,1189.59,1171.63,1171.71,2114470000,1171.71 2005-03-21,1189.65,1189.65,1178.82,1183.78,1819440000,1183.78 2005-03-18,1190.21,1191.98,1182.78,1189.65,2344370000,1189.65 2005-03-17,1188.07,1193.28,1186.34,1190.21,1581930000,1190.21 2005-03-16,1197.75,1197.75,1185.61,1188.07,1653190000,1188.07 2005-03-15,1206.83,1210.54,1197.75,1197.75,1513530000,1197.75 2005-03-14,1200.08,1206.83,1199.51,1206.83,1437430000,1206.83 2005-03-11,1209.25,1213.04,1198.15,1200.08,1449820000,1200.08 2005-03-10,1207.01,1211.23,1201.41,1209.25,1604020000,1209.25 2005-03-09,1219.43,1219.43,1206.66,1207.01,1704970000,1207.01 2005-03-08,1225.31,1225.69,1218.57,1219.43,1523090000,1219.43 2005-03-07,1222.12,1229.11,1222.12,1225.31,1488830000,1225.31 2005-03-04,1210.47,1224.76,1210.47,1222.12,1636820000,1222.12 2005-03-03,1210.08,1215.72,1204.45,1210.47,1616240000,1210.47 2005-03-02,1210.41,1215.79,1204.22,1210.08,1568540000,1210.08 2005-03-01,1203.60,1212.25,1203.60,1210.41,1708060000,1210.41 2005-02-28,1211.37,1211.37,1198.13,1203.60,1795480000,1203.60 2005-02-25,1200.20,1212.15,1199.61,1211.37,1523680000,1211.37 2005-02-24,1190.80,1200.42,1187.80,1200.20,1518750000,1200.20 2005-02-23,1184.16,1193.52,1184.16,1190.80,1501090000,1190.80 2005-02-22,1201.59,1202.48,1184.16,1184.16,1744940000,1184.16 2005-02-18,1200.75,1202.92,1197.35,1201.59,1551200000,1201.59 2005-02-17,1210.34,1211.33,1200.74,1200.75,1580120000,1200.75 2005-02-16,1210.12,1212.44,1205.06,1210.34,1490100000,1210.34 2005-02-15,1206.14,1212.44,1205.52,1210.12,1527080000,1210.12 2005-02-14,1205.30,1206.93,1203.59,1206.14,1290180000,1206.14 2005-02-11,1197.01,1208.38,1193.28,1205.30,1562300000,1205.30 2005-02-10,1191.99,1198.75,1191.54,1197.01,1491670000,1197.01 2005-02-09,1202.30,1203.83,1191.54,1191.99,1511040000,1191.99 2005-02-08,1201.72,1205.11,1200.16,1202.30,1416170000,1202.30 2005-02-07,1203.03,1204.15,1199.27,1201.72,1347270000,1201.72 2005-02-04,1189.89,1203.47,1189.67,1203.03,1648160000,1203.03 2005-02-03,1193.19,1193.19,1185.64,1189.89,1554460000,1189.89 2005-02-02,1189.41,1195.25,1188.92,1193.19,1561740000,1193.19 2005-02-01,1181.27,1190.39,1180.95,1189.41,1681980000,1189.41 2005-01-31,1171.36,1182.07,1171.36,1181.27,1679800000,1181.27 2005-01-28,1174.55,1175.61,1166.25,1171.36,1641800000,1171.36 2005-01-27,1174.07,1177.50,1170.15,1174.55,1600600000,1174.55 2005-01-26,1168.41,1175.96,1168.41,1174.07,1635900000,1174.07 2005-01-25,1163.75,1174.30,1163.75,1168.41,1610400000,1168.41 2005-01-24,1167.87,1173.03,1163.75,1163.75,1494600000,1163.75 2005-01-21,1175.41,1179.45,1167.82,1167.87,1643500000,1167.87 2005-01-20,1184.63,1184.63,1173.42,1175.41,1692000000,1175.41 2005-01-19,1195.98,1195.98,1184.41,1184.63,1498700000,1184.63 2005-01-18,1184.52,1195.98,1180.10,1195.98,1596800000,1195.98 2005-01-14,1177.45,1185.21,1177.45,1184.52,1335400000,1184.52 2005-01-13,1187.70,1187.70,1175.81,1177.45,1510300000,1177.45 2005-01-12,1182.99,1187.92,1175.64,1187.70,1562100000,1187.70 2005-01-11,1190.25,1190.25,1180.43,1182.99,1488800000,1182.99 2005-01-10,1186.19,1194.78,1184.80,1190.25,1490400000,1190.25 2005-01-07,1187.89,1192.20,1182.16,1186.19,1477900000,1186.19 2005-01-06,1183.74,1191.63,1183.27,1187.89,1569100000,1187.89 2005-01-05,1188.05,1192.73,1183.72,1183.74,1738900000,1183.74 2005-01-04,1202.08,1205.84,1185.39,1188.05,1721000000,1188.05 2005-01-03,1211.92,1217.80,1200.32,1202.08,1510800000,1202.08 2004-12-31,1213.55,1217.33,1211.65,1211.92,786900000,1211.92 2004-12-30,1213.45,1216.47,1213.41,1213.55,829800000,1213.55 2004-12-29,1213.54,1213.85,1210.95,1213.45,925900000,1213.45 2004-12-28,1204.92,1213.54,1204.92,1213.54,983000000,1213.54 2004-12-27,1210.13,1214.13,1204.92,1204.92,922000000,1204.92 2004-12-23,1209.57,1213.66,1208.71,1210.13,956100000,1210.13 2004-12-22,1205.45,1211.42,1203.85,1209.57,1390800000,1209.57 2004-12-21,1194.65,1205.93,1194.65,1205.45,1483700000,1205.45 2004-12-20,1194.20,1203.43,1193.36,1194.65,1422800000,1194.65 2004-12-17,1203.21,1203.21,1193.49,1194.20,2335000000,1194.20 2004-12-16,1205.72,1207.97,1198.41,1203.21,1793900000,1203.21 2004-12-15,1203.38,1206.61,1199.44,1205.72,1695800000,1205.72 2004-12-14,1198.68,1205.29,1197.84,1203.38,1544400000,1203.38 2004-12-13,1188.00,1198.74,1188.00,1198.68,1436100000,1198.68 2004-12-10,1189.24,1191.45,1185.24,1188.00,1443700000,1188.00 2004-12-09,1182.81,1190.51,1173.79,1189.24,1624700000,1189.24 2004-12-08,1177.07,1184.05,1177.07,1182.81,1525200000,1182.81 2004-12-07,1190.25,1192.17,1177.07,1177.07,1533900000,1177.07 2004-12-06,1191.17,1192.41,1185.18,1190.25,1354400000,1190.25 2004-12-03,1190.33,1197.46,1187.71,1191.17,1566700000,1191.17 2004-12-02,1191.37,1194.80,1186.72,1190.33,1774900000,1190.33 2004-12-01,1173.78,1191.37,1173.78,1191.37,1772800000,1191.37 2004-11-30,1178.57,1178.66,1173.81,1173.82,1553500000,1173.82 2004-11-29,1182.65,1186.94,1172.37,1178.57,1378500000,1178.57 2004-11-26,1181.76,1186.62,1181.08,1182.65,504580000,1182.65 2004-11-24,1176.94,1182.46,1176.94,1181.76,1149600000,1181.76 2004-11-23,1177.24,1179.52,1171.41,1176.94,1428300000,1176.94 2004-11-22,1170.34,1178.18,1167.89,1177.24,1392700000,1177.24 2004-11-19,1183.55,1184.00,1169.19,1170.34,1526600000,1170.34 2004-11-18,1181.94,1184.90,1180.15,1183.55,1456700000,1183.55 2004-11-17,1175.43,1188.46,1175.43,1181.94,1684200000,1181.94 2004-11-16,1183.81,1183.81,1175.32,1175.43,1364400000,1175.43 2004-11-15,1184.17,1184.48,1179.85,1183.81,1453300000,1183.81 2004-11-12,1173.48,1184.17,1171.43,1184.17,1531600000,1184.17 2004-11-11,1162.91,1174.80,1162.91,1173.48,1393000000,1173.48 2004-11-10,1164.08,1169.25,1162.51,1162.91,1504300000,1162.91 2004-11-09,1164.89,1168.96,1162.48,1164.08,1450800000,1164.08 2004-11-08,1166.17,1166.77,1162.32,1164.89,1358700000,1164.89 2004-11-05,1161.67,1170.87,1160.66,1166.17,1724400000,1166.17 2004-11-04,1143.20,1161.67,1142.34,1161.67,1782700000,1161.67 2004-11-03,1130.54,1147.57,1130.54,1143.20,1767500000,1143.20 2004-11-02,1130.51,1140.48,1128.12,1130.56,1659000000,1130.56 2004-11-01,1130.20,1133.41,1127.60,1130.51,1395900000,1130.51 2004-10-29,1127.44,1131.40,1124.62,1130.20,1500800000,1130.20 2004-10-28,1125.34,1130.67,1120.60,1127.44,1628200000,1127.44 2004-10-27,1111.09,1126.29,1107.43,1125.40,1741900000,1125.40 2004-10-26,1094.81,1111.10,1094.81,1111.09,1685400000,1111.09 2004-10-25,1095.74,1096.81,1090.29,1094.80,1380500000,1094.80 2004-10-22,1106.49,1108.14,1095.47,1095.74,1469600000,1095.74 2004-10-21,1103.66,1108.87,1098.47,1106.49,1673000000,1106.49 2004-10-20,1103.23,1104.09,1094.25,1103.66,1685700000,1103.66 2004-10-19,1114.02,1117.96,1103.15,1103.23,1737500000,1103.23 2004-10-18,1108.20,1114.46,1103.33,1114.02,1373300000,1114.02 2004-10-15,1103.29,1113.17,1102.14,1108.20,1645100000,1108.20 2004-10-14,1113.65,1114.96,1102.06,1103.29,1489500000,1103.29 2004-10-13,1121.84,1127.01,1109.63,1113.65,1546200000,1113.65 2004-10-12,1124.39,1124.39,1115.77,1121.84,1320100000,1121.84 2004-10-11,1122.14,1126.20,1122.14,1124.39,943800000,1124.39 2004-10-08,1130.65,1132.92,1120.19,1122.14,1291600000,1122.14 2004-10-07,1142.05,1142.05,1130.50,1130.65,1447500000,1130.65 2004-10-06,1134.48,1142.05,1132.94,1142.05,1416700000,1142.05 2004-10-05,1135.17,1137.87,1132.03,1134.48,1418400000,1134.48 2004-10-04,1131.50,1140.13,1131.50,1135.17,1534000000,1135.17 2004-10-01,1114.58,1131.64,1114.58,1131.50,1582200000,1131.50 2004-09-30,1114.80,1116.31,1109.68,1114.58,1748000000,1114.58 2004-09-29,1110.06,1114.80,1107.42,1114.80,1402900000,1114.80 2004-09-28,1103.52,1111.77,1101.29,1110.06,1396600000,1110.06 2004-09-27,1110.11,1110.11,1103.24,1103.52,1263500000,1103.52 2004-09-24,1108.36,1113.81,1108.36,1110.11,1255400000,1110.11 2004-09-23,1113.56,1113.61,1108.05,1108.36,1286300000,1108.36 2004-09-22,1129.30,1129.30,1112.67,1113.56,1379900000,1113.56 2004-09-21,1122.20,1131.54,1122.20,1129.30,1325000000,1129.30 2004-09-20,1128.55,1128.55,1120.34,1122.20,1197600000,1122.20 2004-09-17,1123.50,1130.14,1123.50,1128.55,1422600000,1128.55 2004-09-16,1120.37,1126.06,1120.37,1123.50,1113900000,1123.50 2004-09-15,1128.33,1128.33,1119.82,1120.37,1256000000,1120.37 2004-09-14,1125.82,1129.46,1124.72,1128.33,1204500000,1128.33 2004-09-13,1123.92,1129.78,1123.35,1125.82,1299800000,1125.82 2004-09-10,1118.38,1125.26,1114.39,1123.92,1261200000,1123.92 2004-09-09,1116.27,1121.30,1113.62,1118.38,1371300000,1118.38 2004-09-08,1121.30,1123.05,1116.27,1116.27,1246300000,1116.27 2004-09-07,1113.63,1124.08,1113.63,1121.30,1214400000,1121.30 2004-09-03,1118.31,1120.80,1113.57,1113.63,924170000,1113.63 2004-09-02,1105.91,1119.11,1105.60,1118.31,1118400000,1118.31 2004-09-01,1104.24,1109.24,1099.18,1105.91,1142100000,1105.91 2004-08-31,1099.15,1104.24,1094.72,1104.24,1138200000,1104.24 2004-08-30,1107.77,1107.77,1099.15,1099.15,843100000,1099.15 2004-08-27,1105.09,1109.68,1104.62,1107.77,845400000,1107.77 2004-08-26,1104.96,1106.78,1102.46,1105.09,1023600000,1105.09 2004-08-25,1096.19,1106.29,1093.24,1104.96,1192200000,1104.96 2004-08-24,1095.68,1100.94,1092.82,1096.19,1092500000,1096.19 2004-08-23,1098.35,1101.40,1094.73,1095.68,1021900000,1095.68 2004-08-20,1091.23,1100.26,1089.57,1098.35,1199900000,1098.35 2004-08-19,1095.17,1095.17,1086.28,1091.23,1249400000,1091.23 2004-08-18,1081.71,1095.17,1078.93,1095.17,1282500000,1095.17 2004-08-17,1079.34,1086.78,1079.34,1081.71,1267800000,1081.71 2004-08-16,1064.80,1080.66,1064.80,1079.34,1206200000,1079.34 2004-08-13,1063.23,1067.58,1060.72,1064.80,1175100000,1064.80 2004-08-12,1075.79,1075.79,1062.82,1063.23,1405100000,1063.23 2004-08-11,1079.04,1079.04,1065.92,1075.79,1410400000,1075.79 2004-08-10,1065.22,1079.04,1065.22,1079.04,1245600000,1079.04 2004-08-09,1063.97,1069.46,1063.97,1065.22,1086000000,1065.22 2004-08-06,1080.70,1080.70,1062.23,1063.97,1521000000,1063.97 2004-08-05,1098.63,1098.79,1079.98,1080.70,1397400000,1080.70 2004-08-04,1099.69,1102.45,1092.40,1098.63,1369200000,1098.63 2004-08-03,1106.62,1106.62,1099.26,1099.69,1338300000,1099.69 2004-08-02,1101.72,1108.60,1097.34,1106.62,1276000000,1106.62 2004-07-30,1100.43,1103.73,1096.96,1101.72,1298200000,1101.72 2004-07-29,1095.42,1103.51,1095.42,1100.43,1530100000,1100.43 2004-07-28,1094.83,1098.84,1082.17,1095.42,1554300000,1095.42 2004-07-27,1084.07,1096.65,1084.07,1094.83,1610800000,1094.83 2004-07-26,1086.20,1089.82,1078.78,1084.07,1413400000,1084.07 2004-07-23,1096.84,1096.84,1083.56,1086.20,1337500000,1086.20 2004-07-22,1093.88,1099.66,1084.16,1096.84,1680800000,1096.84 2004-07-21,1108.67,1116.27,1093.88,1093.88,1679500000,1093.88 2004-07-20,1100.90,1108.88,1099.10,1108.67,1445800000,1108.67 2004-07-19,1101.39,1105.52,1096.55,1100.90,1319900000,1100.90 2004-07-16,1106.69,1112.17,1101.07,1101.39,1450300000,1101.39 2004-07-15,1111.47,1114.63,1106.67,1106.69,1408700000,1106.69 2004-07-14,1115.14,1119.60,1107.83,1111.47,1462000000,1111.47 2004-07-13,1114.35,1116.30,1112.99,1115.14,1199700000,1115.14 2004-07-12,1112.81,1116.11,1106.71,1114.35,1114600000,1114.35 2004-07-09,1109.11,1115.57,1109.11,1112.81,1186300000,1112.81 2004-07-08,1118.33,1119.12,1108.72,1109.11,1401100000,1109.11 2004-07-07,1116.21,1122.37,1114.92,1118.33,1328600000,1118.33 2004-07-06,1125.38,1125.38,1113.21,1116.21,1283300000,1116.21 2004-07-02,1128.94,1129.15,1123.26,1125.38,1085000000,1125.38 2004-07-01,1140.84,1140.84,1123.06,1128.94,1495700000,1128.94 2004-06-30,1136.20,1144.20,1133.62,1140.84,1473800000,1140.84 2004-06-29,1133.35,1138.26,1131.81,1136.20,1375000000,1136.20 2004-06-28,1134.43,1142.60,1131.72,1133.35,1354600000,1133.35 2004-06-25,1140.65,1145.97,1134.24,1134.43,1812900000,1134.43 2004-06-24,1144.06,1146.34,1139.94,1140.65,1394900000,1140.65 2004-06-23,1134.41,1145.15,1131.73,1144.06,1444200000,1144.06 2004-06-22,1130.30,1135.05,1124.37,1134.41,1382300000,1134.41 2004-06-21,1135.02,1138.05,1129.64,1130.30,1123900000,1130.30 2004-06-18,1132.05,1138.96,1129.83,1135.02,1500600000,1135.02 2004-06-17,1133.56,1133.56,1126.89,1132.05,1296700000,1132.05 2004-06-16,1132.01,1135.28,1130.55,1133.56,1168400000,1133.56 2004-06-15,1125.29,1137.36,1125.29,1132.01,1345900000,1132.01 2004-06-14,1136.47,1136.47,1122.16,1125.29,1179400000,1125.29 2004-06-10,1131.33,1136.47,1131.33,1136.47,1160600000,1136.47 2004-06-09,1142.18,1142.18,1131.17,1131.33,1276800000,1131.33 2004-06-08,1140.42,1142.18,1135.45,1142.18,1190300000,1142.18 2004-06-07,1122.50,1140.54,1122.50,1140.42,1211800000,1140.42 2004-06-04,1116.64,1129.17,1116.64,1122.50,1115300000,1122.50 2004-06-03,1124.99,1125.31,1116.57,1116.64,1232400000,1116.64 2004-06-02,1121.20,1128.10,1118.64,1124.99,1251700000,1124.99 2004-06-01,1120.68,1122.70,1113.32,1121.20,1238000000,1121.20 2004-05-28,1121.28,1122.69,1118.10,1120.68,1172600000,1120.68 2004-05-27,1114.94,1123.95,1114.86,1121.28,1447500000,1121.28 2004-05-26,1113.05,1116.71,1109.91,1114.94,1369400000,1114.94 2004-05-25,1095.41,1113.80,1090.74,1113.05,1545700000,1113.05 2004-05-24,1093.56,1101.28,1091.77,1095.41,1227500000,1095.41 2004-05-21,1089.19,1099.64,1089.19,1093.56,1258600000,1093.56 2004-05-20,1088.68,1092.62,1085.43,1089.19,1211000000,1089.19 2004-05-19,1091.49,1105.93,1088.49,1088.68,1548600000,1088.68 2004-05-18,1084.10,1094.10,1084.10,1091.49,1353000000,1091.49 2004-05-17,1095.70,1095.70,1079.36,1084.10,1430100000,1084.10 2004-05-14,1096.44,1102.10,1088.24,1095.70,1335900000,1095.70 2004-05-13,1097.28,1102.77,1091.76,1096.44,1411100000,1096.44 2004-05-12,1095.45,1097.55,1076.32,1097.28,1697600000,1097.28 2004-05-11,1087.12,1095.69,1087.12,1095.45,1533800000,1095.45 2004-05-10,1098.70,1098.70,1079.63,1087.12,1918400000,1087.12 2004-05-07,1113.99,1117.30,1098.63,1098.70,1653600000,1098.70 2004-05-06,1121.53,1121.53,1106.30,1113.99,1509300000,1113.99 2004-05-05,1119.55,1125.07,1117.90,1121.53,1469000000,1121.53 2004-05-04,1117.49,1127.74,1112.89,1119.55,1662100000,1119.55 2004-05-03,1107.30,1118.72,1107.30,1117.49,1571600000,1117.49 2004-04-30,1113.89,1119.26,1107.23,1107.30,1634700000,1107.30 2004-04-29,1122.41,1128.80,1108.04,1113.89,1859000000,1113.89 2004-04-28,1138.11,1138.11,1121.70,1122.41,1855600000,1122.41 2004-04-27,1135.53,1146.56,1135.53,1138.11,1518000000,1138.11 2004-04-26,1140.60,1145.08,1132.91,1135.53,1290600000,1135.53 2004-04-23,1139.93,1141.92,1134.81,1140.60,1396100000,1140.60 2004-04-22,1124.09,1142.77,1121.95,1139.93,1826700000,1139.93 2004-04-21,1118.15,1125.72,1116.03,1124.09,1738100000,1124.09 2004-04-20,1135.82,1139.26,1118.09,1118.15,1508500000,1118.15 2004-04-19,1134.56,1136.18,1129.84,1135.82,1194900000,1135.82 2004-04-16,1128.84,1136.80,1126.90,1134.61,1487800000,1134.61 2004-04-15,1128.17,1134.08,1120.75,1128.84,1568700000,1128.84 2004-04-14,1129.44,1132.52,1122.15,1128.17,1547700000,1128.17 2004-04-13,1145.20,1147.78,1127.70,1129.44,1423200000,1129.44 2004-04-12,1139.32,1147.29,1139.32,1145.20,1102400000,1145.20 2004-04-08,1140.53,1148.97,1134.52,1139.32,1199800000,1139.32 2004-04-07,1148.16,1148.16,1138.41,1140.53,1458800000,1140.53 2004-04-06,1150.57,1150.57,1143.30,1148.16,1397700000,1148.16 2004-04-05,1141.81,1150.57,1141.64,1150.57,1413700000,1150.57 2004-04-02,1132.17,1144.81,1132.17,1141.81,1629200000,1141.81 2004-04-01,1126.21,1135.67,1126.20,1132.17,1560700000,1132.17 2004-03-31,1127.00,1130.83,1121.46,1126.21,1560700000,1126.21 2004-03-30,1122.47,1127.60,1119.66,1127.00,1332400000,1127.00 2004-03-29,1108.06,1124.37,1108.06,1122.47,1405500000,1122.47 2004-03-26,1109.19,1115.27,1106.13,1108.06,1319100000,1108.06 2004-03-25,1091.33,1110.38,1091.33,1109.19,1471700000,1109.19 2004-03-24,1093.95,1098.32,1087.16,1091.33,1527800000,1091.33 2004-03-23,1095.40,1101.52,1091.57,1093.95,1458200000,1093.95 2004-03-22,1109.78,1109.78,1089.54,1095.40,1452300000,1095.40 2004-03-19,1122.32,1122.72,1109.69,1109.78,1457400000,1109.78 2004-03-18,1123.75,1125.50,1113.25,1122.32,1369200000,1122.32 2004-03-17,1110.70,1125.76,1110.70,1123.75,1490100000,1123.75 2004-03-16,1104.49,1113.76,1102.61,1110.70,1500700000,1110.70 2004-03-15,1120.57,1120.57,1103.36,1104.49,1600600000,1104.49 2004-03-12,1106.78,1120.63,1106.78,1120.57,1388500000,1120.57 2004-03-11,1123.89,1125.96,1105.87,1106.78,1889900000,1106.78 2004-03-10,1140.58,1141.45,1122.53,1123.89,1648400000,1123.89 2004-03-09,1147.20,1147.32,1136.84,1140.58,1499400000,1140.58 2004-03-08,1156.86,1159.94,1146.97,1147.20,1254400000,1147.20 2004-03-05,1154.87,1163.23,1148.77,1156.86,1398200000,1156.86 2004-03-04,1151.03,1154.97,1149.81,1154.87,1265800000,1154.87 2004-03-03,1149.10,1152.44,1143.78,1151.03,1334500000,1151.03 2004-03-02,1155.97,1156.54,1147.31,1149.10,1476000000,1149.10 2004-03-01,1144.94,1157.45,1144.94,1155.97,1497100000,1155.97 2004-02-27,1145.80,1151.68,1141.80,1144.94,1540400000,1144.94 2004-02-26,1143.67,1147.23,1138.62,1144.91,1383900000,1144.91 2004-02-25,1139.09,1145.24,1138.96,1143.67,1360700000,1143.67 2004-02-24,1140.99,1144.54,1134.43,1139.09,1543600000,1139.09 2004-02-23,1144.11,1146.69,1136.98,1140.99,1380400000,1140.99 2004-02-20,1147.06,1149.81,1139.00,1144.11,1479600000,1144.11 2004-02-19,1151.82,1158.57,1146.85,1147.06,1562800000,1147.06 2004-02-18,1156.99,1157.40,1149.54,1151.82,1382400000,1151.82 2004-02-17,1145.81,1158.98,1145.81,1156.99,1396500000,1156.99 2004-02-13,1152.11,1156.88,1143.24,1145.81,1329200000,1145.81 2004-02-12,1157.76,1157.76,1151.44,1152.11,1464300000,1152.11 2004-02-11,1145.54,1158.89,1142.33,1157.76,1699300000,1157.76 2004-02-10,1139.81,1147.02,1138.70,1145.54,1403900000,1145.54 2004-02-09,1142.76,1144.46,1139.21,1139.81,1303500000,1139.81 2004-02-06,1128.59,1142.79,1128.39,1142.76,1477600000,1142.76 2004-02-05,1126.52,1131.17,1124.44,1128.59,1566600000,1128.59 2004-02-04,1136.03,1136.03,1124.74,1126.52,1634800000,1126.52 2004-02-03,1135.26,1137.44,1131.33,1136.03,1476900000,1136.03 2004-02-02,1131.13,1142.45,1127.87,1135.26,1599200000,1135.26 2004-01-30,1134.11,1134.17,1127.73,1131.13,1635000000,1131.13 2004-01-29,1128.48,1134.39,1122.38,1134.11,1921900000,1134.11 2004-01-28,1144.05,1149.14,1126.50,1128.48,1842000000,1128.48 2004-01-27,1155.37,1155.37,1144.05,1144.05,1673100000,1144.05 2004-01-26,1141.55,1155.38,1141.00,1155.37,1480600000,1155.37 2004-01-23,1143.94,1150.31,1136.85,1141.55,1561200000,1141.55 2004-01-22,1147.62,1150.51,1143.01,1143.94,1693700000,1143.94 2004-01-21,1138.77,1149.21,1134.62,1147.62,1757600000,1147.62 2004-01-20,1139.83,1142.93,1135.40,1138.77,1698200000,1138.77 2004-01-16,1132.05,1139.83,1132.05,1139.83,1721100000,1139.83 2004-01-15,1130.52,1137.11,1124.54,1132.05,1695000000,1132.05 2004-01-14,1121.22,1130.75,1121.22,1130.52,1514600000,1130.52 2004-01-13,1127.23,1129.07,1115.19,1121.22,1595900000,1121.22 2004-01-12,1121.86,1127.85,1120.90,1127.23,1510200000,1127.23 2004-01-09,1131.92,1131.92,1120.90,1121.86,1720700000,1121.86 2004-01-08,1126.33,1131.92,1124.91,1131.92,1868400000,1131.92 2004-01-07,1123.67,1126.33,1116.45,1126.33,1704900000,1126.33 2004-01-06,1122.22,1124.46,1118.44,1123.67,1494500000,1123.67 2004-01-05,1108.48,1122.22,1108.48,1122.22,1578200000,1122.22 2004-01-02,1111.92,1118.85,1105.08,1108.48,1153200000,1108.48 2003-12-31,1109.64,1112.56,1106.21,1111.92,1027500000,1111.92 2003-12-30,1109.48,1109.75,1106.41,1109.64,1012600000,1109.64 2003-12-29,1095.89,1109.48,1095.89,1109.48,1058800000,1109.48 2003-12-26,1094.04,1098.47,1094.04,1095.89,356070000,1095.89 2003-12-24,1096.02,1096.40,1092.73,1094.04,518060000,1094.04 2003-12-23,1092.94,1096.95,1091.73,1096.02,1145300000,1096.02 2003-12-22,1088.66,1092.94,1086.14,1092.94,1251700000,1092.94 2003-12-19,1089.18,1091.06,1084.19,1088.66,1657300000,1088.66 2003-12-18,1076.48,1089.50,1076.48,1089.18,1579900000,1089.18 2003-12-17,1075.13,1076.54,1071.14,1076.48,1441700000,1076.48 2003-12-16,1068.04,1075.94,1068.04,1075.13,1547900000,1075.13 2003-12-15,1074.14,1082.79,1068.00,1068.04,1520800000,1068.04 2003-12-12,1071.21,1074.76,1067.64,1074.14,1223100000,1074.14 2003-12-11,1059.05,1073.63,1059.05,1071.21,1441100000,1071.21 2003-12-10,1060.18,1063.02,1053.41,1059.05,1444000000,1059.05 2003-12-09,1069.30,1071.94,1059.16,1060.18,1465500000,1060.18 2003-12-08,1061.50,1069.59,1060.93,1069.30,1218900000,1069.30 2003-12-05,1069.72,1069.72,1060.09,1061.50,1265900000,1061.50 2003-12-04,1064.73,1070.37,1063.15,1069.72,1463100000,1069.72 2003-12-03,1066.62,1074.30,1064.63,1064.73,1441700000,1064.73 2003-12-02,1070.12,1071.22,1065.22,1066.62,1383200000,1066.62 2003-12-01,1058.20,1070.47,1058.20,1070.12,1375000000,1070.12 2003-11-28,1058.45,1060.63,1056.77,1058.20,487220000,1058.20 2003-11-26,1053.89,1058.45,1048.28,1058.45,1097700000,1058.45 2003-11-25,1052.08,1058.05,1049.31,1053.89,1333700000,1053.89 2003-11-24,1035.28,1052.08,1035.28,1052.08,1302800000,1052.08 2003-11-21,1033.65,1037.57,1031.20,1035.28,1273800000,1035.28 2003-11-20,1042.44,1046.48,1033.42,1033.65,1326700000,1033.65 2003-11-19,1034.15,1043.95,1034.15,1042.44,1326200000,1042.44 2003-11-18,1043.63,1048.77,1034.00,1034.15,1354300000,1034.15 2003-11-17,1050.35,1050.35,1035.28,1043.63,1374300000,1043.63 2003-11-14,1058.41,1063.65,1048.11,1050.35,1356100000,1050.35 2003-11-13,1058.56,1059.62,1052.96,1058.41,1383000000,1058.41 2003-11-12,1046.57,1059.10,1046.57,1058.53,1349300000,1058.53 2003-11-11,1047.11,1048.23,1043.46,1046.57,1162500000,1046.57 2003-11-10,1053.21,1053.65,1045.58,1047.11,1243600000,1047.11 2003-11-07,1058.05,1062.39,1052.17,1053.21,1440500000,1053.21 2003-11-06,1051.81,1058.94,1046.93,1058.05,1453900000,1058.05 2003-11-05,1053.25,1054.54,1044.88,1051.81,1401800000,1051.81 2003-11-04,1059.02,1059.02,1051.70,1053.25,1417600000,1053.25 2003-11-03,1050.71,1061.44,1050.71,1059.02,1378200000,1059.02 2003-10-31,1046.94,1053.09,1046.94,1050.71,1498900000,1050.71 2003-10-30,1048.11,1052.81,1043.82,1046.94,1629700000,1046.94 2003-10-29,1046.79,1049.83,1043.35,1048.11,1562600000,1048.11 2003-10-28,1031.13,1046.79,1031.13,1046.79,1629200000,1046.79 2003-10-27,1028.91,1037.75,1028.91,1031.13,1371800000,1031.13 2003-10-24,1033.77,1033.77,1018.32,1028.91,1420300000,1028.91 2003-10-23,1030.36,1035.44,1025.89,1033.77,1604300000,1033.77 2003-10-22,1046.03,1046.03,1028.39,1030.36,1647200000,1030.36 2003-10-21,1044.68,1048.57,1042.59,1046.03,1498000000,1046.03 2003-10-20,1039.32,1044.69,1036.13,1044.68,1172600000,1044.68 2003-10-17,1050.07,1051.89,1036.57,1039.32,1352000000,1039.32 2003-10-16,1046.76,1052.94,1044.04,1050.07,1417700000,1050.07 2003-10-15,1049.48,1053.79,1043.15,1046.76,1521100000,1046.76 2003-10-14,1045.35,1049.49,1040.84,1049.48,1271900000,1049.48 2003-10-13,1038.06,1048.90,1038.06,1045.35,1040500000,1045.35 2003-10-10,1038.73,1040.84,1035.74,1038.06,1108100000,1038.06 2003-10-09,1033.78,1048.28,1033.78,1038.73,1578700000,1038.73 2003-10-08,1039.25,1040.06,1030.96,1033.78,1262500000,1033.78 2003-10-07,1034.35,1039.25,1026.27,1039.25,1279500000,1039.25 2003-10-06,1029.85,1036.48,1029.15,1034.35,1025800000,1034.35 2003-10-03,1020.24,1039.31,1020.24,1029.85,1570500000,1029.85 2003-10-02,1018.22,1021.87,1013.38,1020.24,1269300000,1020.24 2003-10-01,995.97,1018.22,995.97,1018.22,1566300000,1018.22 2003-09-30,1006.58,1006.58,990.36,995.97,1590500000,995.97 2003-09-29,996.85,1006.89,995.31,1006.58,1366500000,1006.58 2003-09-26,1003.27,1003.45,996.08,996.85,1472500000,996.85 2003-09-25,1009.38,1015.97,1003.26,1003.27,1530000000,1003.27 2003-09-24,1029.03,1029.83,1008.93,1009.38,1556000000,1009.38 2003-09-23,1022.82,1030.12,1021.54,1029.03,1301700000,1029.03 2003-09-22,1036.30,1036.30,1018.30,1022.82,1278800000,1022.82 2003-09-19,1039.58,1040.29,1031.89,1036.30,1518600000,1036.30 2003-09-18,1025.97,1040.16,1025.75,1039.58,1498800000,1039.58 2003-09-17,1029.32,1031.34,1024.53,1025.97,1338210000,1025.97 2003-09-16,1014.81,1029.66,1014.81,1029.32,1403200000,1029.32 2003-09-15,1018.63,1019.79,1013.59,1014.81,1151300000,1014.81 2003-09-12,1016.42,1019.65,1007.71,1018.63,1236700000,1018.63 2003-09-11,1010.92,1020.88,1010.92,1016.42,1335900000,1016.42 2003-09-10,1023.17,1023.17,1009.74,1010.92,1582100000,1010.92 2003-09-09,1031.64,1031.64,1021.14,1023.17,1414800000,1023.17 2003-09-08,1021.39,1032.41,1021.39,1031.64,1299300000,1031.64 2003-09-05,1027.97,1029.21,1018.19,1021.39,1465200000,1021.39 2003-09-04,1026.27,1029.17,1022.19,1027.97,1453900000,1027.97 2003-09-03,1021.99,1029.34,1021.99,1026.27,1675600000,1026.27 2003-09-02,1008.01,1022.59,1005.73,1021.99,1470500000,1021.99 2003-08-29,1002.84,1008.85,999.52,1008.01,945100000,1008.01 2003-08-28,996.79,1004.12,991.42,1002.84,1165200000,1002.84 2003-08-27,996.73,998.05,993.33,996.79,1051400000,996.79 2003-08-26,993.71,997.93,983.57,996.73,1178700000,996.73 2003-08-25,993.06,993.71,987.91,993.71,971700000,993.71 2003-08-22,1003.27,1011.01,992.62,993.06,1308900000,993.06 2003-08-21,1000.30,1009.53,999.33,1003.27,1407100000,1003.27 2003-08-20,1002.35,1003.54,996.62,1000.30,1210800000,1000.30 2003-08-19,999.74,1003.30,995.30,1002.35,1300600000,1002.35 2003-08-18,990.67,1000.35,990.67,999.74,1127600000,999.74 2003-08-15,990.51,992.39,987.10,990.67,636370000,990.67 2003-08-14,984.03,991.91,980.36,990.51,1186800000,990.51 2003-08-13,990.35,992.50,980.85,984.03,1208800000,984.03 2003-08-12,980.59,990.41,979.90,990.35,1132300000,990.35 2003-08-11,977.59,985.46,974.21,980.59,1022200000,980.59 2003-08-08,974.12,980.57,973.83,977.59,1086600000,977.59 2003-08-07,967.08,974.89,963.82,974.12,1389300000,974.12 2003-08-06,965.46,975.74,960.84,967.08,1491000000,967.08 2003-08-05,982.82,982.82,964.97,965.46,1351700000,965.46 2003-08-04,980.15,985.75,966.79,982.82,1318700000,982.82 2003-08-01,990.31,990.31,978.86,980.15,1390600000,980.15 2003-07-31,987.49,1004.59,987.49,990.31,1608000000,990.31 2003-07-30,989.28,992.62,985.96,987.49,1391900000,987.49 2003-07-29,996.52,998.64,984.15,989.28,1508900000,989.28 2003-07-28,998.68,1000.68,993.59,996.52,1328600000,996.52 2003-07-25,981.60,998.71,977.49,998.68,1397500000,998.68 2003-07-24,988.61,998.89,981.07,981.60,1559000000,981.60 2003-07-23,988.11,989.86,979.79,988.61,1362700000,988.61 2003-07-22,978.80,990.29,976.08,988.11,1439700000,988.11 2003-07-21,993.32,993.32,975.63,978.80,1254200000,978.80 2003-07-18,981.73,994.25,981.71,993.32,1365200000,993.32 2003-07-17,994.00,994.00,978.60,981.73,1661400000,981.73 2003-07-16,1000.42,1003.47,989.30,994.09,1662000000,994.09 2003-07-15,1003.86,1009.61,996.67,1000.42,1518600000,1000.42 2003-07-14,998.14,1015.41,998.14,1003.86,1448900000,1003.86 2003-07-11,988.70,1000.86,988.70,998.14,1212700000,998.14 2003-07-10,1002.21,1002.21,983.63,988.70,1465700000,988.70 2003-07-09,1007.84,1010.43,998.17,1002.21,1618000000,1002.21 2003-07-08,1004.42,1008.92,998.73,1007.84,1565700000,1007.84 2003-07-07,985.70,1005.56,985.70,1004.42,1429100000,1004.42 2003-07-03,993.75,995.00,983.34,985.70,775900000,985.70 2003-07-02,982.32,993.78,982.32,993.75,1519300000,993.75 2003-07-01,974.50,983.26,962.10,982.32,1460200000,982.32 2003-06-30,976.22,983.61,973.60,974.50,1587200000,974.50 2003-06-27,985.82,988.88,974.29,976.22,1267800000,976.22 2003-06-26,975.32,986.53,973.80,985.82,1387400000,985.82 2003-06-25,983.45,991.64,974.86,975.32,1459200000,975.32 2003-06-24,981.64,987.84,979.08,983.45,1388300000,983.45 2003-06-23,995.69,995.69,977.40,981.64,1398100000,981.64 2003-06-20,994.70,1002.09,993.36,995.69,1698000000,995.69 2003-06-19,1010.09,1011.22,993.08,994.70,1530100000,994.70 2003-06-18,1011.66,1015.12,1004.61,1010.09,1488900000,1010.09 2003-06-17,1010.74,1015.33,1007.04,1011.66,1479700000,1011.66 2003-06-16,988.61,1010.86,988.61,1010.74,1345900000,1010.74 2003-06-13,998.51,1000.92,984.27,988.61,1271600000,988.61 2003-06-12,997.48,1002.74,991.27,998.51,1553100000,998.51 2003-06-11,984.84,997.48,981.61,997.48,1520000000,997.48 2003-06-10,975.93,984.84,975.93,984.84,1275400000,984.84 2003-06-09,987.76,987.76,972.59,975.93,1307000000,975.93 2003-06-06,990.14,1007.69,986.01,987.76,1837200000,987.76 2003-06-05,986.24,990.14,978.13,990.14,1693100000,990.14 2003-06-04,971.56,987.85,970.72,986.24,1618700000,986.24 2003-06-03,967.00,973.02,964.47,971.56,1450200000,971.56 2003-06-02,963.59,979.11,963.59,967.00,1662500000,967.00 2003-05-30,949.64,965.38,949.64,963.59,1688800000,963.59 2003-05-29,953.22,962.08,946.23,949.64,1685800000,949.64 2003-05-28,951.48,959.39,950.12,953.22,1559000000,953.22 2003-05-27,933.22,952.76,927.33,951.48,1532000000,951.48 2003-05-23,931.87,935.20,927.42,933.22,1201000000,933.22 2003-05-22,923.42,935.30,922.54,931.87,1448500000,931.87 2003-05-21,919.73,923.85,914.91,923.42,1457800000,923.42 2003-05-20,920.77,925.34,912.05,919.73,1505300000,919.73 2003-05-19,944.30,944.30,920.23,920.77,1375700000,920.77 2003-05-16,946.67,948.65,938.60,944.30,1505500000,944.30 2003-05-15,939.28,948.23,938.79,946.67,1508700000,946.67 2003-05-14,942.30,947.29,935.24,939.28,1401800000,939.28 2003-05-13,945.11,947.51,938.91,942.30,1418100000,942.30 2003-05-12,933.41,946.84,929.30,945.11,1378800000,945.11 2003-05-09,920.27,933.77,920.27,933.41,1326100000,933.41 2003-05-08,929.62,929.62,919.72,920.27,1379600000,920.27 2003-05-07,934.39,937.22,926.41,929.62,1531900000,929.62 2003-05-06,926.55,939.61,926.38,934.39,1649600000,934.39 2003-05-05,930.08,933.88,924.55,926.55,1446300000,926.55 2003-05-02,916.30,930.56,912.35,930.08,1554300000,930.08 2003-05-01,916.92,919.68,902.83,916.30,1397500000,916.30 2003-04-30,917.84,922.01,911.70,916.92,1788510000,916.92 2003-04-29,914.84,924.24,911.10,917.84,1525600000,917.84 2003-04-28,898.81,918.15,898.81,914.84,1273000000,914.84 2003-04-25,911.43,911.43,897.52,898.81,1335800000,898.81 2003-04-24,919.02,919.02,906.69,911.43,1648100000,911.43 2003-04-23,911.37,919.74,909.89,919.02,1667200000,919.02 2003-04-22,892.01,911.74,886.70,911.37,1631200000,911.37 2003-04-21,893.58,898.01,888.17,892.01,1118700000,892.01 2003-04-17,879.91,893.83,879.20,893.58,1430600000,893.58 2003-04-16,890.81,896.77,877.93,879.91,1587600000,879.91 2003-04-15,885.23,891.27,881.85,890.81,1460200000,890.81 2003-04-14,868.30,885.26,868.30,885.23,1131000000,885.23 2003-04-11,871.58,883.34,865.92,868.30,1141600000,868.30 2003-04-10,865.99,871.78,862.76,871.58,1275300000,871.58 2003-04-09,878.29,887.35,865.72,865.99,1293700000,865.99 2003-04-08,879.93,883.11,874.68,878.29,1235400000,878.29 2003-04-07,878.85,904.89,878.85,879.93,1494000000,879.93 2003-04-04,876.45,882.73,874.23,878.85,1241200000,878.85 2003-04-03,880.90,885.89,876.12,876.45,1339500000,876.45 2003-04-02,858.48,884.57,858.48,880.90,1589800000,880.90 2003-04-01,848.18,861.28,847.85,858.48,1461600000,858.48 2003-03-31,863.50,863.50,843.68,848.18,1495500000,848.18 2003-03-28,868.52,869.88,860.83,863.50,1227000000,863.50 2003-03-27,869.95,874.15,858.09,868.52,1232900000,868.52 2003-03-26,874.74,875.80,866.47,869.95,1319700000,869.95 2003-03-25,864.23,879.87,862.59,874.74,1333400000,874.74 2003-03-24,895.79,895.79,862.02,864.23,1293000000,864.23 2003-03-21,875.84,895.90,875.84,895.79,1883710000,895.79 2003-03-20,874.02,879.60,859.01,875.67,1439100000,875.67 2003-03-19,866.45,874.99,861.21,874.02,1473400000,874.02 2003-03-18,862.79,866.94,857.36,866.45,1555100000,866.45 2003-03-17,833.27,862.79,827.17,862.79,1700420000,862.79 2003-03-14,831.89,841.39,828.26,833.27,1541900000,833.27 2003-03-13,804.19,832.02,804.19,831.90,1816300000,831.90 2003-03-12,800.73,804.19,788.90,804.19,1620000000,804.19 2003-03-11,807.48,814.25,800.30,800.73,1427700000,800.73 2003-03-10,828.89,828.89,806.57,807.48,1255000000,807.48 2003-03-07,822.10,829.55,811.23,828.89,1368500000,828.89 2003-03-06,829.85,829.85,819.85,822.10,1299200000,822.10 2003-03-05,821.99,829.87,819.00,829.85,1332700000,829.85 2003-03-04,834.81,835.43,821.96,821.99,1256600000,821.99 2003-03-03,841.15,852.34,832.74,834.81,1208900000,834.81 2003-02-28,837.28,847.00,837.28,841.15,1373300000,841.15 2003-02-27,827.55,842.19,827.55,837.28,1287800000,837.28 2003-02-26,838.57,840.10,826.68,827.55,1374400000,827.55 2003-02-25,832.58,839.55,818.54,838.57,1483700000,838.57 2003-02-24,848.17,848.17,832.16,832.58,1229200000,832.58 2003-02-21,837.10,852.28,831.48,848.17,1398200000,848.17 2003-02-20,845.13,849.37,836.56,837.10,1194100000,837.10 2003-02-19,851.17,851.17,838.79,845.13,1075600000,845.13 2003-02-18,834.89,852.87,834.89,851.17,1250800000,851.17 2003-02-14,817.37,834.89,815.03,834.89,1404600000,834.89 2003-02-13,818.68,821.25,806.29,817.37,1489300000,817.37 2003-02-12,829.20,832.12,818.49,818.68,1260500000,818.68 2003-02-11,835.97,843.02,825.09,829.20,1307000000,829.20 2003-02-10,829.69,837.16,823.53,835.97,1238200000,835.97 2003-02-07,838.15,845.73,826.70,829.69,1276800000,829.69 2003-02-06,843.59,844.23,833.25,838.15,1430900000,838.15 2003-02-05,848.20,861.63,842.11,843.59,1450800000,843.59 2003-02-04,860.32,860.32,840.19,848.20,1451600000,848.20 2003-02-03,855.70,864.64,855.70,860.32,1258500000,860.32 2003-01-31,844.61,858.33,840.34,855.70,1578530000,855.70 2003-01-30,864.36,865.48,843.74,844.61,1510300000,844.61 2003-01-29,858.54,868.72,845.86,864.36,1595400000,864.36 2003-01-28,847.48,860.76,847.48,858.54,1459100000,858.54 2003-01-27,861.40,863.95,844.25,847.48,1435900000,847.48 2003-01-24,887.34,887.34,859.71,861.40,1574800000,861.40 2003-01-23,878.36,890.25,876.89,887.34,1744550000,887.34 2003-01-22,887.62,889.74,877.64,878.36,1560800000,878.36 2003-01-21,901.78,906.00,887.62,887.62,1335200000,887.62 2003-01-17,914.60,914.60,899.02,901.78,1358200000,901.78 2003-01-16,918.22,926.03,911.98,914.60,1534600000,914.60 2003-01-15,931.66,932.59,916.70,918.22,1432100000,918.22 2003-01-14,926.26,931.66,921.72,931.66,1379400000,931.66 2003-01-13,927.57,935.05,922.05,926.26,1396300000,926.26 2003-01-10,927.58,932.89,917.66,927.57,1485400000,927.57 2003-01-09,909.93,928.31,909.93,927.57,1560300000,927.57 2003-01-08,922.93,922.93,908.32,909.93,1467600000,909.93 2003-01-07,929.01,930.81,919.93,922.93,1545200000,922.93 2003-01-06,908.59,931.77,908.59,929.01,1435900000,929.01 2003-01-03,909.03,911.25,903.07,908.59,1130800000,908.59 2003-01-02,879.82,909.03,879.82,909.03,1229200000,909.03 2002-12-31,879.39,881.93,869.45,879.82,1088500000,879.82 2002-12-30,875.40,882.10,870.23,879.39,1057800000,879.39 2002-12-27,889.66,890.46,873.62,875.40,758400000,875.40 2002-12-26,892.47,903.89,887.48,889.66,721100000,889.66 2002-12-24,897.38,897.38,892.29,892.47,458310000,892.47 2002-12-23,895.74,902.43,892.26,897.38,1112100000,897.38 2002-12-20,884.25,897.79,884.25,895.76,1782730000,895.76 2002-12-19,890.02,899.19,880.32,884.25,1385900000,884.25 2002-12-18,902.99,902.99,887.82,891.12,1446200000,891.12 2002-12-17,910.40,911.22,901.74,902.99,1251800000,902.99 2002-12-16,889.48,910.42,889.48,910.40,1271600000,910.40 2002-12-13,901.58,901.58,888.48,889.48,1330800000,889.48 2002-12-12,904.96,908.37,897.00,901.58,1255300000,901.58 2002-12-11,904.45,909.94,896.48,904.96,1285100000,904.96 2002-12-10,892.00,904.95,892.00,904.45,1286600000,904.45 2002-12-09,912.23,912.23,891.97,892.00,1320800000,892.00 2002-12-06,906.55,915.48,895.96,912.23,1241100000,912.23 2002-12-05,917.58,921.49,905.90,906.55,1250200000,906.55 2002-12-04,920.75,925.25,909.51,917.58,1588900000,917.58 2002-12-03,934.53,934.53,918.73,920.75,1488400000,920.75 2002-12-02,936.31,954.28,927.72,934.53,1612000000,934.53 2002-11-29,938.87,941.82,935.58,936.31,643460000,936.31 2002-11-27,913.31,940.41,913.31,938.87,1350300000,938.87 2002-11-26,932.87,932.87,912.10,913.31,1543600000,913.31 2002-11-25,930.55,937.15,923.31,932.87,1574000000,932.87 2002-11-22,933.76,937.28,928.41,930.55,1626800000,930.55 2002-11-21,914.15,935.13,914.15,933.76,2415100000,933.76 2002-11-20,896.74,915.01,894.93,914.15,1517300000,914.15 2002-11-19,900.36,905.45,893.09,896.74,1337400000,896.74 2002-11-18,909.83,915.91,899.48,900.36,1282600000,900.36 2002-11-15,904.27,910.21,895.35,909.83,1400100000,909.83 2002-11-14,882.53,904.27,882.53,904.27,1519000000,904.27 2002-11-13,882.95,892.51,872.05,882.53,1463400000,882.53 2002-11-12,876.19,894.30,876.19,882.95,1377100000,882.95 2002-11-11,894.74,894.74,874.63,876.19,1113000000,876.19 2002-11-08,902.65,910.11,891.62,894.74,1446500000,894.74 2002-11-07,923.76,923.76,898.68,902.65,1466900000,902.65 2002-11-06,915.39,925.66,905.00,923.76,1674000000,923.76 2002-11-05,908.35,915.83,904.91,915.39,1354100000,915.39 2002-11-04,900.96,924.58,900.96,908.35,1645900000,908.35 2002-11-01,885.76,903.42,877.71,900.96,1450400000,900.96 2002-10-31,890.71,898.83,879.75,885.76,1641300000,885.76 2002-10-30,882.15,895.28,879.19,890.71,1422300000,890.71 2002-10-29,890.23,890.64,867.91,882.15,1529700000,882.15 2002-10-28,897.65,907.44,886.15,890.23,1382600000,890.23 2002-10-25,882.50,897.71,877.03,897.65,1340400000,897.65 2002-10-24,896.14,902.94,879.00,882.50,1700570000,882.50 2002-10-23,890.16,896.14,873.82,896.14,1593900000,896.14 2002-10-22,899.72,899.72,882.40,890.16,1549200000,890.16 2002-10-21,884.39,900.69,873.06,899.72,1447000000,899.72 2002-10-18,879.20,886.68,866.58,884.39,1423100000,884.39 2002-10-17,860.02,885.35,860.02,879.20,1780390000,879.20 2002-10-16,881.27,881.27,856.28,860.02,1585000000,860.02 2002-10-15,841.44,881.27,841.44,881.27,1956000000,881.27 2002-10-14,835.32,844.39,828.37,841.44,1200300000,841.44 2002-10-11,803.92,843.27,803.92,835.32,1854130000,835.32 2002-10-10,776.76,806.51,768.63,803.92,2090230000,803.92 2002-10-09,798.55,798.55,775.80,776.76,1885030000,776.76 2002-10-08,785.28,808.86,779.50,798.55,1938430000,798.55 2002-10-07,800.58,808.21,782.96,785.28,1576500000,785.28 2002-10-04,818.95,825.90,794.10,800.58,1835930000,800.58 2002-10-03,827.91,840.02,817.25,818.95,1674500000,818.95 2002-10-02,843.77,851.93,826.50,827.91,1668900000,827.91 2002-10-01,815.28,847.93,812.82,847.91,1780900000,847.91 2002-09-30,827.37,827.37,800.20,815.28,1721870000,815.28 2002-09-27,854.95,854.95,826.84,827.37,1507300000,827.37 2002-09-26,839.66,856.60,839.66,854.95,1650000000,854.95 2002-09-25,819.27,844.22,818.46,839.66,1651500000,839.66 2002-09-24,833.70,833.70,817.38,819.29,1670240000,819.29 2002-09-23,845.39,845.39,825.76,833.70,1381100000,833.70 2002-09-20,843.32,849.32,839.09,845.39,1792800000,845.39 2002-09-19,869.46,869.46,843.09,843.32,1524000000,843.32 2002-09-18,873.52,878.45,857.39,869.46,1501000000,869.46 2002-09-17,891.10,902.68,872.38,873.52,1448600000,873.52 2002-09-16,889.81,891.84,878.91,891.10,1001400000,891.10 2002-09-13,886.91,892.75,877.05,889.81,1271000000,889.81 2002-09-12,909.45,909.45,884.84,886.91,1191600000,886.91 2002-09-11,910.63,924.02,908.47,909.45,846600000,909.45 2002-09-10,902.96,909.89,900.50,909.58,1186400000,909.58 2002-09-09,893.92,907.34,882.92,902.96,1130600000,902.96 2002-09-06,879.15,899.07,879.15,893.92,1184500000,893.92 2002-09-05,893.40,893.40,870.50,879.15,1401300000,879.15 2002-09-04,878.02,896.10,875.73,893.40,1372100000,893.40 2002-09-03,916.07,916.07,877.51,878.02,1289800000,878.02 2002-08-30,917.80,928.15,910.17,916.07,929900000,916.07 2002-08-29,917.87,924.59,903.33,917.80,1271100000,917.80 2002-08-28,934.82,934.82,913.21,917.87,1146600000,917.87 2002-08-27,947.95,955.82,930.36,934.82,1307700000,934.82 2002-08-26,940.86,950.80,930.42,947.95,1016900000,947.95 2002-08-23,962.70,962.70,937.17,940.86,1071500000,940.86 2002-08-22,949.36,965.00,946.43,962.70,1373000000,962.70 2002-08-21,937.43,951.59,931.32,949.36,1353100000,949.36 2002-08-20,950.70,950.70,931.86,937.43,1308500000,937.43 2002-08-19,928.77,951.17,927.21,950.70,1299800000,950.70 2002-08-16,930.25,935.38,916.21,928.77,1265300000,928.77 2002-08-15,919.62,933.29,918.17,930.25,1505100000,930.25 2002-08-14,884.21,920.21,876.20,919.62,1533800000,919.62 2002-08-13,903.80,911.71,883.62,884.21,1297700000,884.21 2002-08-12,908.64,908.64,892.38,903.80,1036500000,903.80 2002-08-09,898.73,913.95,890.77,908.64,1294900000,908.64 2002-08-08,876.77,905.84,875.17,905.46,1646700000,905.46 2002-08-07,859.57,878.74,854.15,876.77,1490400000,876.77 2002-08-06,834.60,874.44,834.60,859.57,1514100000,859.57 2002-08-05,864.24,864.24,833.44,834.60,1425500000,834.60 2002-08-02,884.40,884.72,853.95,864.24,1538100000,864.24 2002-08-01,911.62,911.62,882.48,884.66,1672200000,884.66 2002-07-31,902.78,911.64,889.88,911.62,2049360000,911.62 2002-07-30,898.96,909.81,884.70,902.78,1826090000,902.78 2002-07-29,852.84,898.96,852.84,898.96,1778650000,898.96 2002-07-26,838.68,852.85,835.92,852.84,1796100000,852.84 2002-07-25,843.42,853.83,816.11,838.68,2424700000,838.68 2002-07-24,797.71,844.32,775.68,843.43,2775560000,843.43 2002-07-23,819.85,827.69,796.13,797.70,2441020000,797.70 2002-07-22,847.76,854.13,813.26,819.85,2248060000,819.85 2002-07-19,881.56,881.56,842.07,847.75,2654100000,847.75 2002-07-18,905.45,907.80,880.60,881.56,1736300000,881.56 2002-07-17,901.05,926.52,895.03,906.04,2566500000,906.04 2002-07-16,917.93,918.65,897.13,900.94,1843700000,900.94 2002-07-15,921.39,921.39,876.46,917.93,2574800000,917.93 2002-07-12,927.37,934.31,913.71,921.39,1607400000,921.39 2002-07-11,920.47,929.16,900.94,927.37,2080480000,927.37 2002-07-10,952.83,956.34,920.29,920.47,1816900000,920.47 2002-07-09,976.98,979.63,951.71,952.83,1348900000,952.83 2002-07-08,989.03,993.56,972.91,976.98,1184400000,976.98 2002-07-05,953.99,989.07,953.99,989.03,699400000,989.03 2002-07-03,948.09,954.30,934.87,953.99,1527800000,953.99 2002-07-02,968.65,968.65,945.54,948.09,1823000000,948.09 2002-07-01,989.82,994.46,967.43,968.65,1425500000,968.65 2002-06-28,990.64,1001.79,988.31,989.82,2117000000,989.82 2002-06-27,973.53,990.67,963.74,990.64,1908600000,990.64 2002-06-26,976.14,977.43,952.92,973.53,2014290000,973.53 2002-06-25,992.72,1005.88,974.21,976.14,1513700000,976.14 2002-06-24,989.14,1002.11,970.85,992.72,1552600000,992.72 2002-06-21,1006.29,1006.29,985.65,989.14,1497200000,989.14 2002-06-20,1019.99,1023.33,1004.59,1006.29,1389700000,1006.29 2002-06-19,1037.14,1037.61,1017.88,1019.99,1336100000,1019.99 2002-06-18,1036.17,1040.83,1030.92,1037.14,1193100000,1037.14 2002-06-17,1007.27,1036.17,1007.27,1036.17,1236600000,1036.17 2002-06-14,1009.56,1009.56,981.63,1007.27,1549000000,1007.27 2002-06-13,1020.26,1023.47,1008.12,1009.56,1405500000,1009.56 2002-06-12,1013.26,1021.85,1002.58,1020.26,1795720000,1020.26 2002-06-11,1030.74,1039.04,1012.94,1013.60,1212400000,1013.60 2002-06-10,1027.53,1038.18,1025.45,1030.74,1226200000,1030.74 2002-06-07,1029.15,1033.02,1012.49,1027.53,1341300000,1027.53 2002-06-06,1049.90,1049.90,1026.91,1029.15,1601500000,1029.15 2002-06-05,1040.69,1050.11,1038.84,1049.90,1300100000,1049.90 2002-06-04,1040.68,1046.06,1030.52,1040.69,1466600000,1040.69 2002-06-03,1067.14,1070.74,1039.90,1040.68,1324300000,1040.68 2002-05-31,1064.66,1079.93,1064.66,1067.14,1277300000,1067.14 2002-05-30,1067.66,1069.50,1054.26,1064.66,1286600000,1064.66 2002-05-29,1074.55,1074.83,1067.66,1067.66,1081800000,1067.66 2002-05-28,1083.82,1085.98,1070.31,1074.55,996500000,1074.55 2002-05-24,1097.08,1097.08,1082.19,1083.82,885400000,1083.82 2002-05-23,1086.02,1097.10,1080.55,1097.08,1192900000,1097.08 2002-05-22,1079.88,1086.02,1075.64,1086.02,1136300000,1086.02 2002-05-21,1091.88,1099.55,1079.08,1079.88,1200500000,1079.88 2002-05-20,1106.59,1106.59,1090.61,1091.88,989800000,1091.88 2002-05-17,1098.23,1106.59,1096.77,1106.59,1274400000,1106.59 2002-05-16,1091.07,1099.29,1089.17,1098.23,1256600000,1098.23 2002-05-15,1097.28,1104.23,1088.94,1091.07,1420200000,1091.07 2002-05-14,1074.56,1097.71,1074.56,1097.28,1414500000,1097.28 2002-05-13,1054.99,1074.84,1053.90,1074.56,1088600000,1074.56 2002-05-10,1073.01,1075.43,1053.93,1054.99,1171900000,1054.99 2002-05-09,1088.85,1088.85,1072.23,1073.01,1153000000,1073.01 2002-05-08,1049.49,1088.92,1049.49,1088.85,1502000000,1088.85 2002-05-07,1052.67,1058.67,1048.96,1049.49,1354700000,1049.49 2002-05-06,1073.43,1075.96,1052.65,1052.67,1122600000,1052.67 2002-05-03,1084.56,1084.56,1068.89,1073.43,1284500000,1073.43 2002-05-02,1086.46,1091.42,1079.46,1084.56,1364000000,1084.56 2002-05-01,1076.92,1088.32,1065.29,1086.46,1451400000,1086.46 2002-04-30,1065.45,1082.62,1063.46,1076.92,1628600000,1076.92 2002-04-29,1076.32,1078.95,1063.62,1065.45,1314700000,1065.45 2002-04-26,1091.48,1096.77,1076.31,1076.32,1374200000,1076.32 2002-04-25,1093.14,1094.36,1084.81,1091.48,1517400000,1091.48 2002-04-24,1100.96,1108.46,1092.51,1093.14,1373200000,1093.14 2002-04-23,1107.83,1111.17,1098.94,1100.96,1388500000,1100.96 2002-04-22,1125.17,1125.17,1105.62,1107.83,1181800000,1107.83 2002-04-19,1124.47,1128.82,1122.59,1125.17,1185000000,1125.17 2002-04-18,1126.07,1130.49,1109.29,1124.47,1359300000,1124.47 2002-04-17,1128.37,1133.00,1123.37,1126.07,1376900000,1126.07 2002-04-16,1102.55,1129.40,1102.55,1128.37,1341300000,1128.37 2002-04-15,1111.01,1114.86,1099.41,1102.55,1120400000,1102.55 2002-04-12,1103.69,1112.77,1102.74,1111.01,1282100000,1111.01 2002-04-11,1130.47,1130.47,1102.42,1103.69,1505600000,1103.69 2002-04-10,1117.80,1131.76,1117.80,1130.47,1447900000,1130.47 2002-04-09,1125.29,1128.29,1116.73,1117.80,1235400000,1117.80 2002-04-08,1122.73,1125.41,1111.79,1125.29,1095300000,1125.29 2002-04-05,1126.34,1133.31,1119.49,1122.73,1110200000,1122.73 2002-04-04,1125.40,1130.45,1120.06,1126.34,1283800000,1126.34 2002-04-03,1136.76,1138.85,1119.68,1125.40,1219700000,1125.40 2002-04-02,1146.54,1146.54,1135.71,1136.76,1176700000,1136.76 2002-04-01,1147.39,1147.84,1132.87,1146.54,1050900000,1146.54 2002-03-28,1144.58,1154.45,1144.58,1147.39,1147600000,1147.39 2002-03-27,1138.49,1146.95,1135.33,1144.58,1180100000,1144.58 2002-03-26,1131.87,1147.00,1131.61,1138.49,1223600000,1138.49 2002-03-25,1148.70,1151.04,1131.87,1131.87,1057900000,1131.87 2002-03-22,1153.59,1156.49,1144.60,1148.70,1243300000,1148.70 2002-03-21,1151.85,1155.10,1139.48,1153.59,1339200000,1153.59 2002-03-20,1170.29,1170.29,1151.61,1151.85,1304900000,1151.85 2002-03-19,1165.55,1173.94,1165.55,1170.29,1255000000,1170.29 2002-03-18,1166.16,1172.73,1159.14,1165.55,1169500000,1165.55 2002-03-15,1153.04,1166.48,1153.04,1166.16,1493900000,1166.16 2002-03-14,1154.09,1157.83,1151.08,1153.04,1208800000,1153.04 2002-03-13,1165.58,1165.58,1151.01,1154.09,1354000000,1154.09 2002-03-12,1168.26,1168.26,1154.34,1165.58,1304400000,1165.58 2002-03-11,1164.31,1173.03,1159.58,1168.26,1210200000,1168.26 2002-03-08,1157.54,1172.76,1157.54,1164.31,1412000000,1164.31 2002-03-07,1162.77,1167.94,1150.69,1157.54,1517400000,1157.54 2002-03-06,1146.14,1165.29,1145.11,1162.77,1541300000,1162.77 2002-03-05,1153.84,1157.74,1144.78,1146.14,1549300000,1146.14 2002-03-04,1131.78,1153.84,1130.93,1153.84,1594300000,1153.84 2002-03-01,1106.73,1131.79,1106.73,1131.78,1456500000,1131.78 2002-02-28,1109.89,1121.57,1106.73,1106.73,1392200000,1106.73 2002-02-27,1109.38,1123.06,1102.26,1109.89,1393800000,1109.89 2002-02-26,1109.43,1115.05,1101.72,1109.38,1309200000,1109.38 2002-02-25,1089.84,1112.71,1089.84,1109.43,1367400000,1109.43 2002-02-22,1080.95,1093.93,1074.39,1089.84,1411000000,1089.84 2002-02-21,1097.98,1101.50,1080.24,1080.95,1381600000,1080.95 2002-02-20,1083.34,1098.32,1074.36,1097.98,1438900000,1097.98 2002-02-19,1104.18,1104.18,1082.24,1083.34,1189900000,1083.34 2002-02-15,1116.48,1117.09,1103.23,1104.18,1359200000,1104.18 2002-02-14,1118.51,1124.72,1112.30,1116.48,1272500000,1116.48 2002-02-13,1107.50,1120.56,1107.50,1118.51,1215900000,1118.51 2002-02-12,1111.94,1112.68,1102.98,1107.50,1094200000,1107.50 2002-02-11,1096.22,1112.01,1094.68,1111.94,1159400000,1111.94 2002-02-08,1080.17,1096.30,1079.91,1096.22,1371900000,1096.22 2002-02-07,1083.51,1094.03,1078.44,1080.17,1441600000,1080.17 2002-02-06,1090.02,1093.58,1077.78,1083.51,1665800000,1083.51 2002-02-05,1094.44,1100.96,1082.58,1090.02,1778300000,1090.02 2002-02-04,1122.20,1122.20,1092.25,1094.44,1437600000,1094.44 2002-02-01,1130.20,1130.20,1118.51,1122.20,1367200000,1122.20 2002-01-31,1113.57,1130.21,1113.30,1130.20,1557000000,1130.20 2002-01-30,1100.64,1113.79,1081.66,1113.57,2019600000,1113.57 2002-01-29,1133.06,1137.47,1098.74,1100.64,1812000000,1100.64 2002-01-28,1133.28,1138.63,1126.66,1133.06,1186800000,1133.06 2002-01-25,1132.15,1138.31,1127.82,1133.28,1345100000,1133.28 2002-01-24,1128.18,1139.50,1128.18,1132.15,1552800000,1132.15 2002-01-23,1119.31,1131.94,1117.43,1128.18,1479200000,1128.18 2002-01-22,1127.58,1135.26,1117.91,1119.31,1311600000,1119.31 2002-01-18,1138.88,1138.88,1124.45,1127.58,1333300000,1127.58 2002-01-17,1127.57,1139.27,1127.57,1138.88,1380100000,1138.88 2002-01-16,1146.19,1146.19,1127.49,1127.57,1482500000,1127.57 2002-01-15,1138.41,1148.81,1136.88,1146.19,1386900000,1146.19 2002-01-14,1145.60,1145.60,1138.15,1138.41,1286400000,1138.41 2002-01-11,1156.55,1159.41,1145.45,1145.60,1211900000,1145.60 2002-01-10,1155.14,1159.93,1150.85,1156.55,1299000000,1156.55 2002-01-09,1160.71,1174.26,1151.89,1155.14,1452000000,1155.14 2002-01-08,1164.89,1167.60,1157.46,1160.71,1258800000,1160.71 2002-01-07,1172.51,1176.97,1163.55,1164.89,1308300000,1164.89 2002-01-04,1165.27,1176.55,1163.42,1172.51,1513000000,1172.51 2002-01-03,1154.67,1165.27,1154.01,1165.27,1398900000,1165.27 2002-01-02,1148.08,1154.67,1136.23,1154.67,1171000000,1154.67 2001-12-31,1161.02,1161.16,1148.04,1148.08,943600000,1148.08 2001-12-28,1157.13,1164.64,1157.13,1161.02,917400000,1161.02 2001-12-27,1149.37,1157.13,1149.37,1157.13,876300000,1157.13 2001-12-26,1144.65,1159.18,1144.65,1149.37,791100000,1149.37 2001-12-24,1144.89,1147.83,1144.62,1144.65,439670000,1144.65 2001-12-21,1139.93,1147.46,1139.93,1144.89,1694000000,1144.89 2001-12-20,1149.56,1151.42,1139.93,1139.93,1490500000,1139.93 2001-12-19,1142.92,1152.44,1134.75,1149.56,1484900000,1149.56 2001-12-18,1134.36,1145.10,1134.36,1142.92,1354000000,1142.92 2001-12-17,1123.09,1137.30,1122.66,1134.36,1260400000,1134.36 2001-12-14,1119.38,1128.28,1114.53,1123.09,1306800000,1123.09 2001-12-13,1137.07,1137.07,1117.85,1119.38,1511500000,1119.38 2001-12-12,1136.76,1141.58,1126.01,1137.07,1449700000,1137.07 2001-12-11,1139.93,1150.89,1134.32,1136.76,1367200000,1136.76 2001-12-10,1158.31,1158.31,1139.66,1139.93,1218700000,1139.93 2001-12-07,1167.10,1167.10,1152.66,1158.31,1248200000,1158.31 2001-12-06,1170.35,1173.35,1164.43,1167.10,1487900000,1167.10 2001-12-05,1143.77,1173.62,1143.77,1170.35,1765300000,1170.35 2001-12-04,1129.90,1144.80,1128.86,1144.80,1318500000,1144.80 2001-12-03,1139.45,1139.45,1125.78,1129.90,1202900000,1129.90 2001-11-30,1140.20,1143.57,1135.89,1139.45,1343600000,1139.45 2001-11-29,1128.52,1140.40,1125.51,1140.20,1375700000,1140.20 2001-11-28,1149.50,1149.50,1128.29,1128.52,1423700000,1128.52 2001-11-27,1157.42,1163.38,1140.81,1149.50,1288000000,1149.50 2001-11-26,1150.34,1157.88,1146.17,1157.42,1129800000,1157.42 2001-11-23,1137.03,1151.05,1135.90,1150.34,410300000,1150.34 2001-11-21,1142.66,1142.66,1129.78,1137.03,1029300000,1137.03 2001-11-20,1151.06,1152.45,1142.17,1142.66,1330200000,1142.66 2001-11-19,1138.65,1151.06,1138.65,1151.06,1316800000,1151.06 2001-11-16,1142.24,1143.52,1129.92,1138.65,1337400000,1138.65 2001-11-15,1141.21,1146.46,1135.06,1142.24,1454500000,1142.24 2001-11-14,1139.09,1148.28,1132.87,1141.21,1443400000,1141.21 2001-11-13,1118.33,1139.14,1118.33,1139.09,1370100000,1139.09 2001-11-12,1120.31,1121.71,1098.32,1118.33,991600000,1118.33 2001-11-09,1118.54,1123.02,1111.13,1120.31,1093800000,1120.31 2001-11-08,1115.80,1135.75,1115.42,1118.54,1517500000,1118.54 2001-11-07,1118.86,1126.62,1112.98,1115.80,1411300000,1115.80 2001-11-06,1102.84,1119.73,1095.36,1118.86,1356000000,1118.86 2001-11-05,1087.20,1106.72,1087.20,1102.84,1267700000,1102.84 2001-11-02,1084.10,1089.63,1075.58,1087.20,1121900000,1087.20 2001-11-01,1059.78,1085.61,1054.31,1084.10,1317400000,1084.10 2001-10-31,1059.79,1074.79,1057.55,1059.78,1352500000,1059.78 2001-10-30,1078.30,1078.30,1053.61,1059.79,1297400000,1059.79 2001-10-29,1104.61,1104.61,1078.30,1078.30,1106100000,1078.30 2001-10-26,1100.09,1110.61,1094.24,1104.61,1244500000,1104.61 2001-10-25,1085.20,1100.09,1065.64,1100.09,1364400000,1100.09 2001-10-24,1084.78,1090.26,1079.98,1085.20,1336200000,1085.20 2001-10-23,1089.90,1098.99,1081.53,1084.78,1317300000,1084.78 2001-10-22,1073.48,1090.57,1070.79,1089.90,1105700000,1089.90 2001-10-19,1068.61,1075.52,1057.24,1073.48,1294900000,1073.48 2001-10-18,1077.09,1077.94,1064.54,1068.61,1262900000,1068.61 2001-10-17,1097.54,1107.12,1076.57,1077.09,1452200000,1077.09 2001-10-16,1089.98,1101.66,1087.13,1097.54,1210500000,1097.54 2001-10-15,1091.65,1091.65,1078.19,1089.98,1024700000,1089.98 2001-10-12,1097.43,1097.43,1072.15,1091.65,1331400000,1091.65 2001-10-11,1080.99,1099.16,1080.99,1097.43,1704580000,1097.43 2001-10-10,1056.75,1081.62,1052.76,1080.99,1312400000,1080.99 2001-10-09,1062.44,1063.37,1053.83,1056.75,1227800000,1056.75 2001-10-08,1071.37,1071.37,1056.88,1062.44,979000000,1062.44 2001-10-05,1069.62,1072.35,1053.50,1071.38,1301700000,1071.38 2001-10-04,1072.28,1084.12,1067.82,1069.63,1609100000,1069.63 2001-10-03,1051.33,1075.38,1041.48,1072.28,1650600000,1072.28 2001-10-02,1038.55,1051.33,1034.47,1051.33,1289800000,1051.33 2001-10-01,1040.94,1040.94,1026.76,1038.55,1175600000,1038.55 2001-09-28,1018.61,1040.94,1018.61,1040.94,1631500000,1040.94 2001-09-27,1007.04,1018.92,998.24,1018.61,1467000000,1018.61 2001-09-26,1012.27,1020.29,1002.62,1007.04,1519100000,1007.04 2001-09-25,1003.45,1017.14,998.33,1012.27,1613800000,1012.27 2001-09-24,965.80,1008.44,965.80,1003.45,1746600000,1003.45 2001-09-21,984.54,984.54,944.75,965.80,2317300000,965.80 2001-09-20,1016.10,1016.10,984.49,984.54,2004800000,984.54 2001-09-19,1032.74,1038.91,984.62,1016.10,2120550000,1016.10 2001-09-18,1038.77,1046.42,1029.25,1032.74,1650410000,1032.74 2001-09-17,1092.54,1092.54,1037.46,1038.77,2330830000,1038.77 2001-09-10,1085.78,1096.94,1073.15,1092.54,1276600000,1092.54 2001-09-07,1106.40,1106.40,1082.12,1085.78,1424300000,1085.78 2001-09-06,1131.74,1131.74,1105.83,1106.40,1359700000,1106.40 2001-09-05,1132.94,1135.52,1114.86,1131.74,1384500000,1131.74 2001-09-04,1133.58,1155.40,1129.06,1132.94,1178300000,1132.94 2001-08-31,1129.03,1141.83,1126.38,1133.58,920100000,1133.58 2001-08-30,1148.60,1151.75,1124.87,1129.03,1157000000,1129.03 2001-08-29,1161.51,1166.97,1147.38,1148.56,963700000,1148.56 2001-08-28,1179.21,1179.66,1161.17,1161.51,987100000,1161.51 2001-08-27,1184.93,1186.85,1178.07,1179.21,842600000,1179.21 2001-08-24,1162.09,1185.15,1162.09,1184.93,1043600000,1184.93 2001-08-23,1165.31,1169.86,1160.96,1162.09,986200000,1162.09 2001-08-22,1157.26,1168.56,1153.34,1165.31,1110800000,1165.31 2001-08-21,1171.41,1179.85,1156.56,1157.26,1041600000,1157.26 2001-08-20,1161.97,1171.41,1160.94,1171.41,897100000,1171.41 2001-08-17,1181.66,1181.66,1156.07,1161.97,974300000,1161.97 2001-08-16,1178.02,1181.80,1166.08,1181.66,1055400000,1181.66 2001-08-15,1186.73,1191.21,1177.61,1178.02,1065600000,1178.02 2001-08-14,1191.29,1198.79,1184.26,1186.73,964600000,1186.73 2001-08-13,1190.16,1193.82,1185.12,1191.29,837600000,1191.29 2001-08-10,1183.43,1193.33,1169.55,1190.16,960900000,1190.16 2001-08-09,1183.53,1184.71,1174.68,1183.43,1104200000,1183.43 2001-08-08,1204.40,1206.79,1181.27,1183.53,1124600000,1183.53 2001-08-07,1200.47,1207.56,1195.64,1204.40,1012000000,1204.40 2001-08-06,1214.35,1214.35,1197.35,1200.48,811700000,1200.48 2001-08-03,1220.75,1220.75,1205.31,1214.35,939900000,1214.35 2001-08-02,1215.93,1226.27,1215.31,1220.75,1218300000,1220.75 2001-08-01,1211.23,1223.04,1211.23,1215.93,1340300000,1215.93 2001-07-31,1204.52,1222.74,1204.52,1211.23,1129200000,1211.23 2001-07-30,1205.82,1209.05,1200.41,1204.52,909100000,1204.52 2001-07-27,1202.93,1209.26,1195.99,1205.82,1015300000,1205.82 2001-07-26,1190.49,1204.18,1182.65,1202.93,1213900000,1202.93 2001-07-25,1171.65,1190.52,1171.28,1190.49,1280700000,1190.49 2001-07-24,1191.03,1191.03,1165.54,1171.65,1198700000,1171.65 2001-07-23,1210.85,1215.22,1190.50,1191.03,986900000,1191.03 2001-07-20,1215.02,1215.69,1207.04,1210.85,1170900000,1210.85 2001-07-19,1207.71,1225.04,1205.80,1215.02,1343500000,1215.02 2001-07-18,1214.44,1214.44,1198.33,1207.71,1316300000,1207.71 2001-07-17,1202.45,1215.36,1196.14,1214.44,1238100000,1214.44 2001-07-16,1215.68,1219.63,1200.05,1202.45,1039800000,1202.45 2001-07-13,1208.14,1218.54,1203.61,1215.68,1121700000,1215.68 2001-07-12,1180.18,1210.25,1180.18,1208.14,1394000000,1208.14 2001-07-11,1181.52,1184.93,1168.46,1180.18,1384100000,1180.18 2001-07-10,1198.78,1203.43,1179.93,1181.52,1263800000,1181.52 2001-07-09,1190.59,1201.76,1189.75,1198.78,1045700000,1198.78 2001-07-06,1219.24,1219.24,1188.74,1190.59,1056700000,1190.59 2001-07-05,1234.45,1234.45,1219.15,1219.24,934900000,1219.24 2001-07-03,1236.71,1236.71,1229.43,1234.45,622110000,1234.45 2001-07-02,1224.42,1239.78,1224.03,1236.72,1128300000,1236.72 2001-06-29,1226.20,1237.29,1221.14,1224.38,1832360000,1224.38 2001-06-28,1211.07,1234.44,1211.07,1226.20,1327300000,1226.20 2001-06-27,1216.76,1219.92,1207.29,1211.07,1162100000,1211.07 2001-06-26,1218.60,1220.70,1204.64,1216.76,1198900000,1216.76 2001-06-25,1225.35,1231.50,1213.60,1218.60,1050100000,1218.60 2001-06-22,1237.04,1237.73,1221.41,1225.35,1189200000,1225.35 2001-06-21,1223.14,1240.24,1220.25,1237.04,1546820000,1237.04 2001-06-20,1212.58,1225.61,1210.07,1223.14,1350100000,1223.14 2001-06-19,1208.43,1226.11,1207.71,1212.58,1184900000,1212.58 2001-06-18,1214.36,1221.23,1208.33,1208.43,1111600000,1208.43 2001-06-15,1219.87,1221.50,1203.03,1214.36,1635550000,1214.36 2001-06-14,1241.60,1241.60,1218.90,1219.87,1242900000,1219.87 2001-06-13,1255.85,1259.75,1241.59,1241.60,1063600000,1241.60 2001-06-12,1254.39,1261.00,1235.75,1255.85,1136500000,1255.85 2001-06-11,1264.96,1264.96,1249.23,1254.39,870100000,1254.39 2001-06-08,1276.96,1277.11,1259.99,1264.96,726200000,1264.96 2001-06-07,1270.03,1277.08,1265.08,1276.96,1089600000,1276.96 2001-06-06,1283.57,1283.85,1269.01,1270.03,1061900000,1270.03 2001-06-05,1267.11,1286.62,1267.11,1283.57,1116800000,1283.57 2001-06-04,1260.67,1267.17,1256.36,1267.11,836500000,1267.11 2001-06-01,1255.82,1265.34,1246.88,1260.67,1015000000,1260.67 2001-05-31,1248.08,1261.91,1248.07,1255.82,1226600000,1255.82 2001-05-30,1267.93,1267.93,1245.96,1248.08,1158600000,1248.08 2001-05-29,1277.89,1278.42,1265.41,1267.93,1026000000,1267.93 2001-05-25,1293.17,1293.17,1276.42,1277.89,828100000,1277.89 2001-05-24,1289.05,1295.04,1281.22,1293.17,1100700000,1293.17 2001-05-23,1309.38,1309.38,1288.70,1289.05,1134800000,1289.05 2001-05-22,1312.83,1315.93,1306.89,1309.38,1260400000,1309.38 2001-05-21,1291.96,1312.95,1287.87,1312.83,1174900000,1312.83 2001-05-18,1288.49,1292.06,1281.15,1291.96,1130800000,1291.96 2001-05-17,1284.99,1296.48,1282.65,1288.49,1355600000,1288.49 2001-05-16,1249.44,1286.39,1243.02,1284.99,1405300000,1284.99 2001-05-15,1248.92,1257.45,1245.36,1249.44,1071800000,1249.44 2001-05-14,1245.67,1249.68,1241.02,1248.92,858200000,1248.92 2001-05-11,1255.18,1259.84,1240.79,1245.67,906200000,1245.67 2001-05-10,1255.54,1268.14,1254.56,1255.18,1056700000,1255.18 2001-05-09,1261.20,1261.65,1247.83,1255.54,1132400000,1255.54 2001-05-08,1266.71,1267.01,1253.00,1261.20,1006300000,1261.20 2001-05-07,1266.61,1270.00,1259.19,1263.51,949000000,1263.51 2001-05-04,1248.58,1267.51,1232.00,1266.61,1082100000,1266.61 2001-05-03,1267.43,1267.43,1239.88,1248.58,1137900000,1248.58 2001-05-02,1266.44,1272.93,1257.70,1267.43,1342200000,1267.43 2001-05-01,1249.46,1266.47,1243.55,1266.44,1181300000,1266.44 2001-04-30,1253.05,1269.30,1243.99,1249.46,1266800000,1249.46 2001-04-27,1234.52,1253.07,1234.52,1253.05,1091300000,1253.05 2001-04-26,1228.75,1248.30,1228.75,1234.52,1345200000,1234.52 2001-04-25,1209.47,1232.36,1207.38,1228.75,1203600000,1228.75 2001-04-24,1224.36,1233.54,1208.89,1209.47,1216500000,1209.47 2001-04-23,1242.98,1242.98,1217.47,1224.36,1012600000,1224.36 2001-04-20,1253.70,1253.70,1234.41,1242.98,1338700000,1242.98 2001-04-19,1238.16,1253.71,1233.39,1253.69,1486800000,1253.69 2001-04-18,1191.81,1248.42,1191.81,1238.16,1918900000,1238.16 2001-04-17,1179.68,1192.25,1168.90,1191.81,1109600000,1191.81 2001-04-16,1183.50,1184.64,1167.38,1179.68,913900000,1179.68 2001-04-12,1165.89,1183.51,1157.73,1183.50,1102000000,1183.50 2001-04-11,1168.38,1182.24,1160.26,1165.89,1290300000,1165.89 2001-04-10,1137.59,1173.92,1137.59,1168.38,1349600000,1168.38 2001-04-09,1128.43,1146.13,1126.38,1137.59,1062800000,1137.59 2001-04-06,1151.44,1151.44,1119.29,1128.43,1266800000,1128.43 2001-04-05,1103.25,1151.47,1103.25,1151.44,1368000000,1151.44 2001-04-04,1106.46,1117.50,1091.99,1103.25,1425590000,1103.25 2001-04-03,1145.87,1145.87,1100.19,1106.46,1386100000,1106.46 2001-04-02,1160.33,1169.51,1137.51,1145.87,1254900000,1145.87 2001-03-30,1147.95,1162.80,1143.83,1160.33,1280800000,1160.33 2001-03-29,1153.29,1161.69,1136.26,1147.95,1234500000,1147.95 2001-03-28,1182.17,1182.17,1147.83,1153.29,1333400000,1153.29 2001-03-27,1152.69,1183.35,1150.96,1182.17,1314200000,1182.17 2001-03-26,1139.83,1160.02,1139.83,1152.69,1114000000,1152.69 2001-03-23,1117.58,1141.83,1117.58,1139.83,1364900000,1139.83 2001-03-22,1122.14,1124.27,1081.19,1117.58,1723950000,1117.58 2001-03-21,1142.62,1149.39,1118.74,1122.14,1346300000,1122.14 2001-03-20,1170.81,1180.56,1142.19,1142.62,1235900000,1142.62 2001-03-19,1150.53,1173.50,1147.18,1170.81,1126200000,1170.81 2001-03-16,1173.56,1173.56,1148.64,1150.53,1543560000,1150.53 2001-03-15,1166.71,1182.04,1166.71,1173.56,1259500000,1173.56 2001-03-14,1197.66,1197.66,1155.35,1166.71,1397400000,1166.71 2001-03-13,1180.16,1197.83,1171.50,1197.66,1360900000,1197.66 2001-03-12,1233.42,1233.42,1176.78,1180.16,1229000000,1180.16 2001-03-09,1264.74,1264.74,1228.42,1233.42,1085900000,1233.42 2001-03-08,1261.89,1266.50,1257.60,1264.74,1114100000,1264.74 2001-03-07,1253.80,1263.86,1253.80,1261.89,1132200000,1261.89 2001-03-06,1241.41,1267.42,1241.41,1253.80,1091800000,1253.80 2001-03-05,1234.18,1242.55,1234.04,1241.41,929200000,1241.41 2001-03-02,1241.23,1251.01,1219.74,1234.18,1294000000,1234.18 2001-03-01,1239.94,1241.36,1214.50,1241.23,1294900000,1241.23 2001-02-28,1257.94,1263.47,1229.65,1239.94,1225300000,1239.94 2001-02-27,1267.65,1272.76,1252.26,1257.94,1114100000,1257.94 2001-02-26,1245.86,1267.69,1241.71,1267.65,1130800000,1267.65 2001-02-23,1252.82,1252.82,1215.44,1245.86,1231300000,1245.86 2001-02-22,1255.27,1259.94,1228.33,1252.82,1365900000,1252.82 2001-02-21,1278.94,1282.97,1253.16,1255.27,1208500000,1255.27 2001-02-20,1301.53,1307.16,1278.44,1278.94,1112200000,1278.94 2001-02-16,1326.61,1326.61,1293.18,1301.53,1257200000,1301.53 2001-02-15,1315.92,1331.29,1315.92,1326.61,1153700000,1326.61 2001-02-14,1318.80,1320.73,1304.72,1315.92,1150300000,1315.92 2001-02-13,1330.31,1336.62,1317.51,1318.80,1075200000,1318.80 2001-02-12,1314.76,1330.96,1313.64,1330.31,1039100000,1330.31 2001-02-09,1332.53,1332.53,1309.98,1314.76,1075500000,1314.76 2001-02-08,1341.10,1350.32,1332.42,1332.53,1107200000,1332.53 2001-02-07,1352.26,1352.26,1334.26,1340.89,1158300000,1340.89 2001-02-06,1354.31,1363.55,1350.04,1352.26,1059600000,1352.26 2001-02-05,1349.47,1354.56,1344.48,1354.31,1013000000,1354.31 2001-02-02,1373.47,1376.38,1348.72,1349.47,1048400000,1349.47 2001-02-01,1366.01,1373.50,1359.34,1373.47,1118800000,1373.47 2001-01-31,1373.73,1383.37,1364.66,1366.01,1295300000,1366.01 2001-01-30,1364.17,1375.68,1356.20,1373.73,1149800000,1373.73 2001-01-29,1354.92,1365.54,1350.36,1364.17,1053100000,1364.17 2001-01-26,1357.51,1357.51,1342.75,1354.95,1098000000,1354.95 2001-01-25,1364.30,1367.35,1354.63,1357.51,1258000000,1357.51 2001-01-24,1360.40,1369.75,1357.28,1364.30,1309000000,1364.30 2001-01-23,1342.90,1362.90,1339.63,1360.40,1232600000,1360.40 2001-01-22,1342.54,1353.62,1333.84,1342.90,1164000000,1342.90 2001-01-19,1347.97,1354.55,1336.74,1342.54,1407800000,1342.54 2001-01-18,1329.89,1352.71,1327.41,1347.97,1445000000,1347.97 2001-01-17,1326.65,1346.92,1325.41,1329.47,1349100000,1329.47 2001-01-16,1318.32,1327.81,1313.33,1326.65,1205700000,1326.65 2001-01-12,1326.82,1333.21,1311.59,1318.55,1276000000,1318.55 2001-01-11,1313.27,1332.19,1309.72,1326.82,1411200000,1326.82 2001-01-10,1300.80,1313.76,1287.28,1313.27,1296500000,1313.27 2001-01-09,1295.86,1311.72,1295.14,1300.80,1191300000,1300.80 2001-01-08,1298.35,1298.35,1276.29,1295.86,1115500000,1295.86 2001-01-05,1333.34,1334.77,1294.95,1298.35,1430800000,1298.35 2001-01-04,1347.56,1350.24,1329.14,1333.34,2131000000,1333.34 2001-01-03,1283.27,1347.76,1274.62,1347.56,1880700000,1347.56 2001-01-02,1320.28,1320.28,1276.05,1283.27,1129400000,1283.27 2000-12-29,1334.22,1340.10,1317.51,1320.28,1035500000,1320.28 2000-12-28,1328.92,1335.93,1325.78,1334.22,1015300000,1334.22 2000-12-27,1315.19,1332.03,1310.96,1328.92,1092700000,1328.92 2000-12-26,1305.97,1315.94,1301.64,1315.19,806500000,1315.19 2000-12-22,1274.86,1305.97,1274.86,1305.95,1087100000,1305.95 2000-12-21,1264.74,1285.31,1254.07,1274.86,1449900000,1274.86 2000-12-20,1305.60,1305.60,1261.16,1264.74,1421600000,1264.74 2000-12-19,1322.96,1346.44,1305.20,1305.60,1324900000,1305.60 2000-12-18,1312.15,1332.32,1312.15,1322.74,1189900000,1322.74 2000-12-15,1340.93,1340.93,1305.38,1312.15,1561100000,1312.15 2000-12-14,1359.99,1359.99,1340.48,1340.93,1061300000,1340.93 2000-12-13,1371.18,1385.82,1358.48,1359.99,1195100000,1359.99 2000-12-12,1380.20,1380.27,1370.27,1371.18,1083400000,1371.18 2000-12-11,1369.89,1389.05,1364.14,1380.20,1202400000,1380.20 2000-12-08,1343.55,1380.33,1343.55,1369.89,1358300000,1369.89 2000-12-07,1351.46,1353.50,1339.26,1343.55,1128000000,1343.55 2000-12-06,1376.54,1376.54,1346.15,1351.46,1399300000,1351.46 2000-12-05,1324.97,1376.56,1324.97,1376.54,900300000,1376.54 2000-12-04,1315.18,1332.06,1310.23,1324.97,1103000000,1324.97 2000-12-01,1314.95,1334.67,1307.02,1315.23,1195200000,1315.23 2000-11-30,1341.91,1341.91,1294.90,1314.95,1186530000,1314.95 2000-11-29,1336.09,1352.38,1329.28,1341.93,402100000,1341.93 2000-11-28,1348.97,1358.81,1334.97,1336.09,1028200000,1336.09 2000-11-27,1341.77,1362.50,1341.77,1348.97,946100000,1348.97 2000-11-24,1322.36,1343.83,1322.36,1341.77,404870000,1341.77 2000-11-22,1347.35,1347.35,1321.89,1322.36,963200000,1322.36 2000-11-21,1342.62,1355.87,1333.62,1347.35,1137100000,1347.35 2000-11-20,1367.72,1367.72,1341.67,1342.62,955800000,1342.62 2000-11-17,1372.32,1384.85,1355.55,1367.72,1070400000,1367.72 2000-11-16,1389.81,1394.76,1370.39,1372.32,956300000,1372.32 2000-11-15,1382.95,1395.96,1374.75,1389.81,1066800000,1389.81 2000-11-14,1351.26,1390.06,1351.26,1382.95,1118800000,1382.95 2000-11-13,1365.98,1365.98,1328.62,1351.26,1129300000,1351.26 2000-11-10,1400.14,1400.14,1365.97,1365.98,962500000,1365.98 2000-11-09,1409.28,1409.28,1369.68,1400.14,1111000000,1400.14 2000-11-08,1431.87,1437.28,1408.78,1409.28,909300000,1409.28 2000-11-07,1432.19,1436.22,1423.26,1431.87,880900000,1431.87 2000-11-06,1428.76,1438.46,1427.72,1432.19,930900000,1432.19 2000-11-03,1428.32,1433.21,1420.92,1426.69,997700000,1426.69 2000-11-02,1421.22,1433.40,1421.22,1428.32,1167700000,1428.32 2000-11-01,1429.40,1429.60,1410.45,1421.22,1206800000,1421.22 2000-10-31,1398.66,1432.22,1398.66,1429.40,1366400000,1429.40 2000-10-30,1379.58,1406.36,1376.86,1398.66,1186500000,1398.66 2000-10-27,1364.44,1384.57,1364.13,1379.58,1086300000,1379.58 2000-10-26,1364.90,1372.72,1337.81,1364.44,1303800000,1364.44 2000-10-25,1398.13,1398.13,1362.21,1364.90,1315600000,1364.90 2000-10-24,1395.78,1415.64,1388.13,1398.13,1158600000,1398.13 2000-10-23,1396.93,1406.96,1387.75,1395.78,1046800000,1395.78 2000-10-20,1388.76,1408.47,1382.19,1396.93,1177400000,1396.93 2000-10-19,1342.13,1389.93,1342.13,1388.76,1297900000,1388.76 2000-10-18,1349.97,1356.65,1305.79,1342.13,1441700000,1342.13 2000-10-17,1374.62,1380.99,1342.34,1349.97,1161500000,1349.97 2000-10-16,1374.17,1379.48,1365.06,1374.62,1005400000,1374.62 2000-10-13,1329.78,1374.17,1327.08,1374.17,1223900000,1374.17 2000-10-12,1364.59,1374.93,1328.06,1329.78,1388600000,1329.78 2000-10-11,1387.02,1387.02,1349.67,1364.59,1387500000,1364.59 2000-10-10,1402.03,1408.83,1383.85,1387.02,1044000000,1387.02 2000-10-09,1408.99,1409.69,1392.48,1402.03,716600000,1402.03 2000-10-06,1436.28,1443.30,1397.06,1408.99,1150100000,1408.99 2000-10-05,1434.32,1444.17,1431.80,1436.28,1176100000,1436.28 2000-10-04,1426.46,1439.99,1416.31,1434.32,1167400000,1434.32 2000-10-03,1436.23,1454.82,1425.28,1426.46,1098100000,1426.46 2000-10-02,1436.52,1445.60,1429.83,1436.23,1051200000,1436.23 2000-09-29,1458.29,1458.29,1436.29,1436.51,1197100000,1436.51 2000-09-28,1426.57,1461.69,1425.78,1458.29,1206200000,1458.29 2000-09-27,1427.21,1437.22,1419.44,1426.57,1174700000,1426.57 2000-09-26,1439.03,1448.04,1425.25,1427.21,1106600000,1427.21 2000-09-25,1448.72,1457.42,1435.93,1439.03,982400000,1439.03 2000-09-22,1449.05,1449.05,1421.88,1448.72,1185500000,1448.72 2000-09-21,1451.34,1452.77,1436.30,1449.05,1105400000,1449.05 2000-09-20,1459.90,1460.49,1430.95,1451.34,1104000000,1451.34 2000-09-19,1444.51,1461.16,1444.51,1459.90,1024900000,1459.90 2000-09-18,1465.81,1467.77,1441.92,1444.51,962500000,1444.51 2000-09-15,1480.87,1480.96,1460.22,1465.81,1268400000,1465.81 2000-09-14,1484.91,1494.16,1476.73,1480.87,1014000000,1480.87 2000-09-13,1481.99,1487.45,1473.61,1484.91,1068300000,1484.91 2000-09-12,1489.26,1496.93,1479.67,1481.99,991200000,1481.99 2000-09-11,1494.50,1506.76,1483.01,1489.26,899300000,1489.26 2000-09-08,1502.51,1502.51,1489.88,1494.50,961000000,1494.50 2000-09-07,1492.25,1505.34,1492.25,1502.51,985500000,1502.51 2000-09-06,1507.08,1512.61,1492.12,1492.25,995100000,1492.25 2000-09-05,1520.77,1520.77,1504.21,1507.08,838500000,1507.08 2000-09-01,1517.68,1530.09,1515.53,1520.77,767700000,1520.77 2000-08-31,1502.59,1525.21,1502.59,1517.68,1056600000,1517.68 2000-08-30,1509.84,1510.49,1500.09,1502.59,818400000,1502.59 2000-08-29,1514.09,1514.81,1505.46,1509.84,795600000,1509.84 2000-08-28,1506.45,1523.95,1506.45,1514.09,733600000,1514.09 2000-08-25,1508.31,1513.47,1505.09,1506.45,685600000,1506.45 2000-08-24,1505.97,1511.16,1501.25,1508.31,837100000,1508.31 2000-08-23,1498.13,1507.20,1489.52,1505.97,871000000,1505.97 2000-08-22,1499.48,1508.45,1497.42,1498.13,818800000,1498.13 2000-08-21,1491.72,1502.84,1491.13,1499.48,731600000,1499.48 2000-08-18,1496.07,1499.47,1488.99,1491.72,821400000,1491.72 2000-08-17,1479.85,1499.32,1479.85,1496.07,922400000,1496.07 2000-08-16,1484.43,1496.09,1475.74,1479.85,929800000,1479.85 2000-08-15,1491.56,1493.12,1482.74,1484.43,895900000,1484.43 2000-08-14,1471.84,1491.64,1468.56,1491.56,783800000,1491.56 2000-08-11,1460.25,1475.72,1453.06,1471.84,835500000,1471.84 2000-08-10,1472.87,1475.15,1459.89,1460.25,940800000,1460.25 2000-08-09,1482.80,1490.33,1471.16,1472.87,1054000000,1472.87 2000-08-08,1479.32,1484.52,1472.61,1482.80,992200000,1482.80 2000-08-07,1462.93,1480.80,1460.72,1479.32,854800000,1479.32 2000-08-04,1452.56,1462.93,1451.31,1462.93,956000000,1462.93 2000-08-03,1438.70,1454.19,1425.43,1452.56,1095600000,1452.56 2000-08-02,1438.10,1451.59,1433.49,1438.70,994500000,1438.70 2000-08-01,1430.83,1443.54,1428.96,1438.10,938700000,1438.10 2000-07-31,1419.89,1437.65,1418.71,1430.83,952600000,1430.83 2000-07-28,1449.62,1456.68,1413.89,1419.89,980000000,1419.89 2000-07-27,1452.42,1464.91,1445.33,1449.62,1156400000,1449.62 2000-07-26,1474.47,1474.47,1452.42,1452.42,1235800000,1452.42 2000-07-25,1464.29,1476.23,1464.29,1474.47,969400000,1474.47 2000-07-24,1480.19,1485.88,1463.80,1464.29,880300000,1464.29 2000-07-21,1495.57,1495.57,1477.91,1480.19,968300000,1480.19 2000-07-20,1481.96,1501.92,1481.96,1495.57,1064600000,1495.57 2000-07-19,1493.74,1495.63,1479.92,1481.96,909400000,1481.96 2000-07-18,1510.49,1510.49,1491.35,1493.74,908300000,1493.74 2000-07-17,1509.98,1517.32,1505.26,1510.49,906000000,1510.49 2000-07-14,1495.84,1509.99,1494.56,1509.98,960600000,1509.98 2000-07-13,1492.92,1501.39,1489.65,1495.84,1026800000,1495.84 2000-07-12,1480.88,1497.69,1480.88,1492.92,1001200000,1492.92 2000-07-11,1475.62,1488.77,1470.48,1480.88,980500000,1480.88 2000-07-10,1478.90,1486.56,1474.76,1475.62,838700000,1475.62 2000-07-07,1456.67,1484.12,1456.67,1478.90,931700000,1478.90 2000-07-06,1446.23,1461.65,1439.56,1456.67,947300000,1456.67 2000-07-05,1469.54,1469.54,1442.45,1446.23,1019300000,1446.23 2000-07-03,1454.60,1469.58,1450.85,1469.54,451900000,1469.54 2000-06-30,1442.39,1454.68,1438.71,1454.60,1459700000,1454.60 2000-06-29,1454.82,1455.14,1434.63,1442.39,1110900000,1442.39 2000-06-28,1450.55,1467.63,1450.55,1454.82,1095100000,1454.82 2000-06-27,1455.31,1463.35,1450.55,1450.55,1042500000,1450.55 2000-06-26,1441.48,1459.66,1441.48,1455.31,889000000,1455.31 2000-06-23,1452.18,1459.94,1438.31,1441.48,847600000,1441.48 2000-06-22,1479.13,1479.13,1448.03,1452.18,1022700000,1452.18 2000-06-21,1475.95,1482.19,1468.00,1479.13,1009600000,1479.13 2000-06-20,1486.00,1487.32,1470.18,1475.95,1031500000,1475.95 2000-06-19,1464.46,1488.93,1459.05,1486.00,921700000,1486.00 2000-06-16,1478.73,1480.77,1460.42,1464.46,1250800000,1464.46 2000-06-15,1470.54,1482.04,1464.62,1478.73,1011400000,1478.73 2000-06-14,1469.44,1483.62,1467.71,1470.54,929700000,1470.54 2000-06-13,1446.00,1470.42,1442.38,1469.44,935900000,1469.44 2000-06-12,1456.95,1462.93,1445.99,1446.00,774100000,1446.00 2000-06-09,1461.67,1472.67,1454.96,1456.95,786000000,1456.95 2000-06-08,1471.36,1475.65,1456.49,1461.67,854300000,1461.67 2000-06-07,1457.84,1474.64,1455.06,1471.36,854600000,1471.36 2000-06-06,1467.63,1471.36,1454.74,1457.84,950100000,1457.84 2000-06-05,1477.26,1477.28,1464.68,1467.63,838600000,1467.63 2000-06-02,1448.81,1483.23,1448.81,1477.26,1162400000,1477.26 2000-06-01,1420.60,1448.81,1420.60,1448.81,960100000,1448.81 2000-05-31,1422.44,1434.49,1415.50,1420.60,960500000,1420.60 2000-05-30,1378.02,1422.45,1378.02,1422.45,844200000,1422.45 2000-05-26,1381.52,1391.42,1369.75,1378.02,722600000,1378.02 2000-05-25,1399.05,1411.65,1373.93,1381.52,984500000,1381.52 2000-05-24,1373.86,1401.75,1361.09,1399.05,1152300000,1399.05 2000-05-23,1400.72,1403.77,1373.43,1373.86,869900000,1373.86 2000-05-22,1406.95,1410.55,1368.73,1400.72,869000000,1400.72 2000-05-19,1437.21,1437.21,1401.74,1406.95,853700000,1406.95 2000-05-18,1447.80,1458.04,1436.59,1437.21,807900000,1437.21 2000-05-17,1466.04,1466.04,1441.67,1447.80,820500000,1447.80 2000-05-16,1452.36,1470.40,1450.76,1466.04,955500000,1466.04 2000-05-15,1420.96,1452.39,1416.54,1452.36,854600000,1452.36 2000-05-12,1407.81,1430.13,1407.81,1420.96,858200000,1420.96 2000-05-11,1383.05,1410.26,1383.05,1407.81,953600000,1407.81 2000-05-10,1412.14,1412.14,1375.14,1383.05,1006400000,1383.05 2000-05-09,1424.17,1430.28,1401.85,1412.14,896600000,1412.14 2000-05-08,1432.63,1432.63,1417.05,1424.17,787600000,1424.17 2000-05-05,1409.57,1436.03,1405.08,1432.63,805500000,1432.63 2000-05-04,1415.10,1420.99,1404.94,1409.57,925800000,1409.57 2000-05-03,1446.29,1446.29,1398.36,1415.10,991600000,1415.10 2000-05-02,1468.25,1468.25,1445.22,1446.29,1011500000,1446.29 2000-05-01,1452.43,1481.51,1452.43,1468.25,966300000,1468.25 2000-04-28,1464.92,1473.62,1448.15,1452.43,984600000,1452.43 2000-04-27,1460.99,1469.21,1434.81,1464.92,1111000000,1464.92 2000-04-26,1477.44,1482.94,1456.98,1460.99,999600000,1460.99 2000-04-25,1429.86,1477.67,1429.86,1477.44,1071100000,1477.44 2000-04-24,1434.54,1434.54,1407.13,1429.86,868700000,1429.86 2000-04-20,1427.47,1435.49,1422.08,1434.54,896200000,1434.54 2000-04-19,1441.61,1447.69,1424.26,1427.47,1001400000,1427.47 2000-04-18,1401.44,1441.61,1397.81,1441.61,1109400000,1441.61 2000-04-17,1356.56,1401.53,1346.50,1401.44,1204700000,1401.44 2000-04-14,1440.51,1440.51,1339.40,1356.56,1279700000,1356.56 2000-04-13,1467.17,1477.52,1439.34,1440.51,1032000000,1440.51 2000-04-12,1500.59,1509.08,1466.15,1467.17,1175900000,1467.17 2000-04-11,1504.46,1512.80,1486.78,1500.59,971400000,1500.59 2000-04-10,1516.35,1527.19,1503.35,1504.46,853700000,1504.46 2000-04-07,1501.34,1518.68,1501.34,1516.35,891600000,1516.35 2000-04-06,1487.37,1511.76,1487.37,1501.34,1008000000,1501.34 2000-04-05,1494.73,1506.55,1478.05,1487.37,1110300000,1487.37 2000-04-04,1505.98,1526.45,1416.41,1494.73,1515460000,1494.73 2000-04-03,1498.58,1507.19,1486.96,1505.97,1021700000,1505.97 2000-03-31,1487.92,1519.81,1484.38,1498.58,1227400000,1498.58 2000-03-30,1508.52,1517.38,1474.63,1487.92,1193400000,1487.92 2000-03-29,1507.73,1521.45,1497.45,1508.52,1061900000,1508.52 2000-03-28,1523.86,1527.36,1507.09,1507.73,959100000,1507.73 2000-03-27,1527.46,1534.63,1518.46,1523.86,901000000,1523.86 2000-03-24,1527.35,1552.87,1516.83,1527.46,1052200000,1527.46 2000-03-23,1500.64,1532.50,1492.39,1527.35,1078300000,1527.35 2000-03-22,1493.87,1505.08,1487.33,1500.64,1075000000,1500.64 2000-03-21,1456.63,1493.92,1446.06,1493.87,1065900000,1493.87 2000-03-20,1464.47,1470.30,1448.49,1456.63,920800000,1456.63 2000-03-17,1458.47,1477.33,1453.32,1464.47,1295100000,1464.47 2000-03-16,1392.15,1458.47,1392.15,1458.47,1482300000,1458.47 2000-03-15,1359.15,1397.99,1356.99,1392.14,1302800000,1392.14 2000-03-14,1383.62,1395.15,1359.15,1359.15,1094000000,1359.15 2000-03-13,1395.07,1398.39,1364.84,1383.62,1016100000,1383.62 2000-03-10,1401.69,1413.46,1392.07,1395.07,1138800000,1395.07 2000-03-09,1366.70,1401.82,1357.88,1401.69,1123000000,1401.69 2000-03-08,1355.62,1373.79,1346.62,1366.70,1203000000,1366.70 2000-03-07,1391.28,1399.21,1349.99,1355.62,1314100000,1355.62 2000-03-06,1409.17,1409.74,1384.75,1391.28,1029000000,1391.28 2000-03-03,1381.76,1410.88,1381.76,1409.17,1150300000,1409.17 2000-03-02,1379.19,1386.56,1370.35,1381.76,1198600000,1381.76 2000-03-01,1366.42,1383.46,1366.42,1379.19,1274100000,1379.19 2000-02-29,1348.05,1369.63,1348.05,1366.42,1204300000,1366.42 2000-02-28,1333.36,1360.82,1325.07,1348.05,1026500000,1348.05 2000-02-25,1353.43,1362.14,1329.15,1333.36,1065200000,1333.36 2000-02-24,1360.69,1364.80,1329.88,1353.43,1215000000,1353.43 2000-02-23,1352.17,1370.11,1342.44,1360.69,993700000,1360.69 2000-02-22,1346.09,1358.11,1331.88,1352.17,980000000,1352.17 2000-02-18,1388.26,1388.59,1345.32,1346.09,1042300000,1346.09 2000-02-17,1387.67,1399.88,1380.07,1388.26,1034800000,1388.26 2000-02-16,1402.05,1404.55,1385.58,1387.67,1018800000,1387.67 2000-02-15,1389.94,1407.72,1376.25,1402.05,1092100000,1402.05 2000-02-14,1387.12,1394.93,1380.53,1389.94,927300000,1389.94 2000-02-11,1416.83,1416.83,1378.89,1387.12,1025700000,1387.12 2000-02-10,1411.70,1422.10,1406.43,1416.83,1058800000,1416.83 2000-02-09,1441.72,1444.55,1411.65,1411.71,1050500000,1411.71 2000-02-08,1424.24,1441.83,1424.24,1441.72,1047700000,1441.72 2000-02-07,1424.37,1427.15,1413.33,1424.24,918100000,1424.24 2000-02-04,1424.97,1435.91,1420.63,1424.37,1045100000,1424.37 2000-02-03,1409.12,1425.78,1398.52,1424.97,1146500000,1424.97 2000-02-02,1409.28,1420.61,1403.49,1409.12,1038600000,1409.12 2000-02-01,1394.46,1412.49,1384.79,1409.28,981000000,1409.28 2000-01-31,1360.16,1394.48,1350.14,1394.46,993800000,1394.46 2000-01-28,1398.56,1398.56,1356.20,1360.16,1095800000,1360.16 2000-01-27,1404.09,1418.86,1370.99,1398.56,1129500000,1398.56 2000-01-26,1410.03,1412.73,1400.16,1404.09,1117300000,1404.09 2000-01-25,1401.53,1414.26,1388.49,1410.03,1073700000,1410.03 2000-01-24,1441.36,1454.09,1395.42,1401.53,1115800000,1401.53 2000-01-21,1445.57,1453.18,1439.60,1441.36,1209800000,1441.36 2000-01-20,1455.90,1465.71,1438.54,1445.57,1100700000,1445.57 2000-01-19,1455.14,1461.39,1448.68,1455.90,1087800000,1455.90 2000-01-18,1465.15,1465.15,1451.30,1455.14,1056700000,1455.14 2000-01-14,1449.68,1473.00,1449.68,1465.15,1085900000,1465.15 2000-01-13,1432.25,1454.20,1432.25,1449.68,1030400000,1449.68 2000-01-12,1438.56,1442.60,1427.08,1432.25,974600000,1432.25 2000-01-11,1457.60,1458.66,1434.42,1438.56,1014000000,1438.56 2000-01-10,1441.47,1464.36,1441.47,1457.60,1064800000,1457.60 2000-01-07,1403.45,1441.47,1400.73,1441.47,1225200000,1441.47 2000-01-06,1402.11,1411.90,1392.10,1403.45,1092300000,1403.45 2000-01-05,1399.42,1413.27,1377.68,1402.11,1085500000,1402.11 2000-01-04,1455.22,1455.22,1397.43,1399.42,1009000000,1399.42 2000-01-03,1469.25,1478.00,1438.36,1455.22,931800000,1455.22 1999-12-31,1464.47,1472.42,1458.19,1469.25,374050000,1469.25 1999-12-30,1463.46,1473.10,1462.60,1464.47,554680000,1464.47 1999-12-29,1457.66,1467.47,1457.66,1463.46,567860000,1463.46 1999-12-28,1457.09,1462.68,1452.78,1457.66,655400000,1457.66 1999-12-27,1458.34,1463.19,1450.83,1457.10,722600000,1457.10 1999-12-23,1436.13,1461.44,1436.13,1458.34,728600000,1458.34 1999-12-22,1433.43,1440.02,1429.13,1436.13,850000000,1436.13 1999-12-21,1418.09,1436.47,1414.80,1433.43,963500000,1433.43 1999-12-20,1421.03,1429.16,1411.10,1418.09,904600000,1418.09 1999-12-17,1418.78,1431.77,1418.78,1421.03,1349800000,1421.03 1999-12-16,1413.32,1423.11,1408.35,1418.78,1070300000,1418.78 1999-12-15,1403.17,1417.40,1396.20,1413.33,1033900000,1413.33 1999-12-14,1415.22,1418.30,1401.59,1403.17,1027800000,1403.17 1999-12-13,1417.04,1421.58,1410.10,1415.22,977600000,1415.22 1999-12-10,1408.11,1421.58,1405.65,1417.04,987200000,1417.04 1999-12-09,1403.88,1418.43,1391.47,1408.11,1122100000,1408.11 1999-12-08,1409.17,1415.66,1403.88,1403.88,957000000,1403.88 1999-12-07,1423.33,1426.81,1409.17,1409.17,1085800000,1409.17 1999-12-06,1433.30,1434.15,1418.25,1423.33,916800000,1423.33 1999-12-03,1409.04,1447.42,1409.04,1433.30,1006400000,1433.30 1999-12-02,1397.72,1409.04,1397.72,1409.04,900700000,1409.04 1999-12-01,1388.91,1400.12,1387.38,1397.72,884000000,1397.72 1999-11-30,1407.83,1410.59,1386.95,1388.91,951500000,1388.91 1999-11-29,1416.62,1416.62,1404.15,1407.83,866100000,1407.83 1999-11-26,1417.08,1425.24,1416.14,1416.62,312120000,1416.62 1999-11-24,1404.64,1419.71,1399.17,1417.08,734800000,1417.08 1999-11-23,1420.94,1423.91,1402.20,1404.64,926100000,1404.64 1999-11-22,1422.00,1425.00,1412.40,1420.94,873500000,1420.94 1999-11-19,1424.94,1424.94,1417.54,1422.00,893800000,1422.00 1999-11-18,1410.71,1425.31,1410.71,1424.94,1022800000,1424.94 1999-11-17,1420.07,1423.44,1410.69,1410.71,960000000,1410.71 1999-11-16,1394.39,1420.36,1394.39,1420.07,942200000,1420.07 1999-11-15,1396.06,1398.58,1392.28,1394.39,795700000,1394.39 1999-11-12,1381.46,1396.12,1368.54,1396.06,900200000,1396.06 1999-11-11,1373.46,1382.12,1372.19,1381.46,891300000,1381.46 1999-11-10,1365.28,1379.18,1359.98,1373.46,984700000,1373.46 1999-11-09,1377.01,1383.81,1361.45,1365.28,854300000,1365.28 1999-11-08,1370.23,1380.78,1365.87,1377.01,806800000,1377.01 1999-11-05,1362.64,1387.48,1362.64,1370.23,1007300000,1370.23 1999-11-04,1354.93,1369.41,1354.93,1362.64,981700000,1362.64 1999-11-03,1347.74,1360.33,1347.74,1354.93,914400000,1354.93 1999-11-02,1354.12,1369.32,1346.41,1347.74,904500000,1347.74 1999-11-01,1362.93,1367.30,1354.05,1354.12,861000000,1354.12 1999-10-29,1342.44,1373.17,1342.44,1362.93,1120500000,1362.93 1999-10-28,1296.71,1342.47,1296.71,1342.44,1135100000,1342.44 1999-10-27,1281.91,1299.39,1280.48,1296.71,950100000,1296.71 1999-10-26,1293.63,1303.46,1281.86,1281.91,878300000,1281.91 1999-10-25,1301.65,1301.68,1286.07,1293.63,777000000,1293.63 1999-10-22,1283.61,1308.81,1283.61,1301.65,959200000,1301.65 1999-10-21,1289.43,1289.43,1265.61,1283.61,1012500000,1283.61 1999-10-20,1261.32,1289.44,1261.32,1289.43,928800000,1289.43 1999-10-19,1254.13,1279.32,1254.13,1261.32,905700000,1261.32 1999-10-18,1247.41,1254.13,1233.70,1254.13,818700000,1254.13 1999-10-15,1283.42,1283.42,1245.39,1247.41,912600000,1247.41 1999-10-14,1285.55,1289.63,1267.62,1283.42,892300000,1283.42 1999-10-13,1313.04,1313.04,1282.80,1285.55,821500000,1285.55 1999-10-12,1335.21,1335.21,1311.80,1313.04,778300000,1313.04 1999-10-11,1336.02,1339.23,1332.96,1335.21,655900000,1335.21 1999-10-08,1317.64,1336.61,1311.88,1336.02,897300000,1336.02 1999-10-07,1325.40,1328.05,1314.13,1317.64,827800000,1317.64 1999-10-06,1301.35,1325.46,1301.35,1325.40,895200000,1325.40 1999-10-05,1304.60,1316.41,1286.44,1301.35,965700000,1301.35 1999-10-04,1282.81,1304.60,1282.81,1304.60,803300000,1304.60 1999-10-01,1282.71,1283.17,1265.78,1282.81,896200000,1282.81 1999-09-30,1268.37,1291.31,1268.37,1282.71,1017600000,1282.71 1999-09-29,1282.20,1288.83,1268.16,1268.37,856000000,1268.37 1999-09-28,1283.31,1285.55,1256.26,1282.20,885400000,1282.20 1999-09-27,1277.36,1295.03,1277.36,1283.31,780600000,1283.31 1999-09-24,1280.41,1281.17,1263.84,1277.36,872800000,1277.36 1999-09-23,1310.51,1315.25,1277.30,1280.41,890800000,1280.41 1999-09-22,1307.58,1316.18,1297.81,1310.51,822200000,1310.51 1999-09-21,1335.52,1335.53,1301.97,1307.58,817300000,1307.58 1999-09-20,1335.42,1338.38,1330.61,1335.53,568000000,1335.53 1999-09-17,1318.48,1337.59,1318.48,1335.42,861900000,1335.42 1999-09-16,1317.97,1322.51,1299.97,1318.48,739000000,1318.48 1999-09-15,1336.29,1347.21,1317.97,1317.97,787300000,1317.97 1999-09-14,1344.13,1344.18,1330.61,1336.29,734500000,1336.29 1999-09-13,1351.66,1351.66,1341.70,1344.13,657900000,1344.13 1999-09-10,1347.66,1357.62,1346.20,1351.66,808500000,1351.66 1999-09-09,1344.15,1347.66,1333.91,1347.66,773900000,1347.66 1999-09-08,1350.45,1355.18,1337.36,1344.15,791200000,1344.15 1999-09-07,1357.24,1361.39,1349.59,1350.45,715300000,1350.45 1999-09-03,1319.11,1357.74,1319.11,1357.24,663200000,1357.24 1999-09-02,1331.07,1331.07,1304.88,1319.11,687100000,1319.11 1999-09-01,1320.41,1331.18,1320.39,1331.07,708200000,1331.07 1999-08-31,1324.02,1333.27,1306.96,1320.41,861700000,1320.41 1999-08-30,1348.27,1350.70,1322.80,1324.02,597900000,1324.02 1999-08-27,1362.01,1365.63,1347.35,1348.27,570050000,1348.27 1999-08-26,1381.79,1381.79,1361.53,1362.01,719000000,1362.01 1999-08-25,1363.50,1382.84,1359.20,1381.79,864600000,1381.79 1999-08-24,1360.22,1373.32,1353.63,1363.50,732700000,1363.50 1999-08-23,1336.61,1360.24,1336.61,1360.22,682600000,1360.22 1999-08-20,1323.59,1336.61,1323.59,1336.61,661200000,1336.61 1999-08-19,1332.84,1332.84,1315.35,1323.59,684200000,1323.59 1999-08-18,1344.16,1344.16,1332.13,1332.84,682800000,1332.84 1999-08-17,1330.77,1344.16,1328.76,1344.16,691500000,1344.16 1999-08-16,1327.68,1331.05,1320.51,1330.77,583550000,1330.77 1999-08-13,1298.16,1327.72,1298.16,1327.68,691700000,1327.68 1999-08-12,1301.93,1313.61,1298.06,1298.16,745600000,1298.16 1999-08-11,1281.43,1301.93,1281.43,1301.93,792300000,1301.93 1999-08-10,1297.80,1298.62,1267.73,1281.43,836200000,1281.43 1999-08-09,1300.29,1306.68,1295.99,1297.80,684300000,1297.80 1999-08-06,1313.71,1316.74,1293.19,1300.29,698900000,1300.29 1999-08-05,1305.33,1313.71,1287.23,1313.71,859300000,1313.71 1999-08-04,1322.18,1330.16,1304.50,1305.33,789300000,1305.33 1999-08-03,1328.05,1336.13,1314.91,1322.18,739600000,1322.18 1999-08-02,1328.72,1344.69,1325.21,1328.05,649550000,1328.05 1999-07-30,1341.03,1350.92,1328.49,1328.72,736800000,1328.72 1999-07-29,1365.40,1365.40,1332.82,1341.03,770100000,1341.03 1999-07-28,1362.84,1370.53,1355.54,1365.40,690900000,1365.40 1999-07-27,1347.75,1368.70,1347.75,1362.84,723800000,1362.84 1999-07-26,1356.94,1358.61,1346.20,1347.76,613450000,1347.76 1999-07-23,1360.97,1367.41,1349.91,1356.94,630580000,1356.94 1999-07-22,1379.29,1379.29,1353.98,1360.97,771700000,1360.97 1999-07-21,1377.10,1386.66,1372.63,1379.29,785500000,1379.29 1999-07-20,1407.65,1407.65,1375.15,1377.10,754800000,1377.10 1999-07-19,1418.78,1420.33,1404.56,1407.65,642330000,1407.65 1999-07-16,1409.62,1418.78,1407.07,1418.78,714100000,1418.78 1999-07-15,1398.17,1409.84,1398.17,1409.62,818800000,1409.62 1999-07-14,1393.56,1400.05,1386.51,1398.17,756100000,1398.17 1999-07-13,1399.10,1399.10,1386.84,1393.56,736000000,1393.56 1999-07-12,1403.28,1406.82,1394.70,1399.10,685300000,1399.10 1999-07-09,1394.42,1403.28,1394.42,1403.28,701000000,1403.28 1999-07-08,1395.86,1403.25,1386.69,1394.42,830600000,1394.42 1999-07-07,1388.12,1395.88,1384.95,1395.86,791200000,1395.86 1999-07-06,1391.22,1405.29,1387.08,1388.12,722900000,1388.12 1999-07-02,1380.96,1391.22,1379.57,1391.22,613570000,1391.22 1999-07-01,1372.71,1382.80,1360.80,1380.96,843400000,1380.96 1999-06-30,1351.45,1372.93,1338.78,1372.71,1117000000,1372.71 1999-06-29,1331.35,1351.51,1328.40,1351.45,820100000,1351.45 1999-06-28,1315.31,1333.68,1315.31,1331.35,652910000,1331.35 1999-06-25,1315.78,1329.13,1312.64,1315.31,623460000,1315.31 1999-06-24,1333.06,1333.06,1308.47,1315.78,690400000,1315.78 1999-06-23,1335.87,1335.88,1322.55,1333.06,731800000,1333.06 1999-06-22,1349.00,1351.12,1335.52,1335.88,716500000,1335.88 1999-06-21,1342.84,1349.06,1337.63,1349.00,686600000,1349.00 1999-06-18,1339.90,1344.48,1333.52,1342.84,914500000,1342.84 1999-06-17,1330.41,1343.54,1322.75,1339.90,700300000,1339.90 1999-06-16,1301.16,1332.83,1301.16,1330.41,806800000,1330.41 1999-06-15,1294.00,1310.76,1294.00,1301.16,696600000,1301.16 1999-06-14,1293.64,1301.99,1292.20,1294.00,669400000,1294.00 1999-06-11,1302.82,1311.97,1287.88,1293.64,698200000,1293.64 1999-06-10,1318.64,1318.64,1293.28,1302.82,716500000,1302.82 1999-06-09,1317.33,1326.01,1314.73,1318.64,662000000,1318.64 1999-06-08,1334.52,1334.52,1312.83,1317.33,685900000,1317.33 1999-06-07,1327.75,1336.42,1325.89,1334.52,664300000,1334.52 1999-06-04,1299.54,1327.75,1299.54,1327.75,694500000,1327.75 1999-06-03,1294.81,1304.15,1294.20,1299.54,719600000,1299.54 1999-06-02,1294.26,1297.10,1277.47,1294.81,728000000,1294.81 1999-06-01,1301.84,1301.84,1281.44,1294.26,683800000,1294.26 1999-05-28,1281.41,1304.00,1281.41,1301.84,649960000,1301.84 1999-05-27,1304.76,1304.76,1277.31,1281.41,811400000,1281.41 1999-05-26,1284.40,1304.85,1278.43,1304.76,870800000,1304.76 1999-05-25,1306.65,1317.52,1284.38,1284.40,826700000,1284.40 1999-05-24,1330.29,1333.02,1303.53,1306.65,754700000,1306.65 1999-05-21,1338.83,1340.88,1326.19,1330.29,686600000,1330.29 1999-05-20,1344.23,1350.49,1338.83,1338.83,752200000,1338.83 1999-05-19,1333.32,1344.23,1327.05,1344.23,801100000,1344.23 1999-05-18,1339.49,1345.44,1323.46,1333.32,753400000,1333.32 1999-05-17,1337.80,1339.95,1321.19,1339.49,665500000,1339.49 1999-05-14,1367.56,1367.56,1332.63,1337.80,727800000,1337.80 1999-05-13,1364.00,1375.98,1364.00,1367.56,796900000,1367.56 1999-05-12,1355.61,1367.36,1333.10,1364.00,825500000,1364.00 1999-05-11,1340.30,1360.00,1340.30,1355.61,836100000,1355.61 1999-05-10,1345.00,1352.01,1334.00,1340.30,773300000,1340.30 1999-05-07,1332.05,1345.99,1332.05,1345.00,814900000,1345.00 1999-05-06,1347.31,1348.36,1322.56,1332.05,875400000,1332.05 1999-05-05,1332.00,1347.32,1317.44,1347.31,913500000,1347.31 1999-05-04,1354.63,1354.64,1330.64,1332.00,933100000,1332.00 1999-05-03,1335.18,1354.63,1329.01,1354.63,811400000,1354.63 1999-04-30,1342.83,1351.83,1314.58,1335.18,936500000,1335.18 1999-04-29,1350.91,1356.75,1336.81,1342.83,1003600000,1342.83 1999-04-28,1362.80,1368.62,1348.29,1350.91,951700000,1350.91 1999-04-27,1360.04,1371.56,1356.55,1362.80,891700000,1362.80 1999-04-26,1356.85,1363.56,1353.72,1360.04,712000000,1360.04 1999-04-23,1358.83,1363.65,1348.45,1356.85,744900000,1356.85 1999-04-22,1336.12,1358.84,1336.12,1358.82,927900000,1358.82 1999-04-21,1306.17,1336.12,1301.84,1336.12,920000000,1336.12 1999-04-20,1289.48,1306.30,1284.21,1306.17,985400000,1306.17 1999-04-19,1319.00,1340.10,1284.48,1289.48,1214400000,1289.48 1999-04-16,1322.86,1325.03,1311.40,1319.00,1002300000,1319.00 1999-04-15,1328.44,1332.41,1308.38,1322.85,1089800000,1322.85 1999-04-14,1349.82,1357.24,1326.41,1328.44,952000000,1328.44 1999-04-13,1358.64,1362.38,1344.03,1349.82,810900000,1349.82 1999-04-12,1348.35,1358.69,1333.48,1358.63,810800000,1358.63 1999-04-09,1343.98,1351.22,1335.24,1348.35,716100000,1348.35 1999-04-08,1326.89,1344.08,1321.60,1343.98,850500000,1343.98 1999-04-07,1317.89,1329.58,1312.59,1326.89,816400000,1326.89 1999-04-06,1321.12,1326.76,1311.07,1317.89,787500000,1317.89 1999-04-05,1293.72,1321.12,1293.72,1321.12,695800000,1321.12 1999-04-01,1286.37,1294.54,1282.56,1293.72,703000000,1293.72 1999-03-31,1300.75,1313.60,1285.87,1286.37,924300000,1286.37 1999-03-30,1310.17,1310.17,1295.47,1300.75,729000000,1300.75 1999-03-29,1282.80,1311.76,1282.80,1310.17,747900000,1310.17 1999-03-26,1289.99,1289.99,1277.25,1282.80,707200000,1282.80 1999-03-25,1268.59,1289.99,1268.59,1289.99,784200000,1289.99 1999-03-24,1262.14,1269.02,1256.43,1268.59,761900000,1268.59 1999-03-23,1297.01,1297.01,1257.46,1262.14,811300000,1262.14 1999-03-22,1299.29,1303.84,1294.26,1297.01,658200000,1297.01 1999-03-19,1316.55,1323.82,1298.92,1299.29,914700000,1299.29 1999-03-18,1297.82,1317.62,1294.75,1316.55,831000000,1316.55 1999-03-17,1306.38,1306.55,1292.63,1297.82,752300000,1297.82 1999-03-16,1307.26,1311.11,1302.29,1306.38,751900000,1306.38 1999-03-15,1294.59,1307.47,1291.03,1307.26,727200000,1307.26 1999-03-12,1297.68,1304.42,1289.17,1294.59,825800000,1294.59 1999-03-11,1286.84,1306.43,1286.84,1297.68,904800000,1297.68 1999-03-10,1279.84,1287.02,1275.16,1286.84,841900000,1286.84 1999-03-09,1282.73,1293.74,1275.11,1279.84,803700000,1279.84 1999-03-08,1275.47,1282.74,1271.58,1282.73,714600000,1282.73 1999-03-05,1246.64,1275.73,1246.64,1275.47,834900000,1275.47 1999-03-04,1227.70,1247.74,1227.70,1246.64,770900000,1246.64 1999-03-03,1225.50,1231.63,1216.03,1227.70,751700000,1227.70 1999-03-02,1236.16,1248.31,1221.87,1225.50,753600000,1225.50 1999-03-01,1238.33,1238.70,1221.88,1236.16,699500000,1236.16 1999-02-26,1245.02,1246.73,1226.24,1238.33,784600000,1238.33 1999-02-25,1253.41,1253.41,1225.01,1245.02,740500000,1245.02 1999-02-24,1271.18,1283.84,1251.94,1253.41,782000000,1253.41 1999-02-23,1272.14,1280.38,1263.36,1271.18,781100000,1271.18 1999-02-22,1239.22,1272.22,1239.22,1272.14,718500000,1272.14 1999-02-19,1237.28,1247.91,1232.03,1239.22,700000000,1239.22 1999-02-18,1224.03,1239.13,1220.70,1237.28,742400000,1237.28 1999-02-17,1241.87,1249.31,1220.92,1224.03,735100000,1224.03 1999-02-16,1230.13,1252.17,1230.13,1241.87,653760000,1241.87 1999-02-12,1254.04,1254.04,1225.53,1230.13,691500000,1230.13 1999-02-11,1223.55,1254.05,1223.19,1254.04,815800000,1254.04 1999-02-10,1216.14,1226.78,1211.89,1223.55,721400000,1223.55 1999-02-09,1243.77,1243.97,1215.63,1216.14,736000000,1216.14 1999-02-08,1239.40,1246.93,1231.98,1243.77,705400000,1243.77 1999-02-05,1248.49,1251.86,1232.28,1239.40,872000000,1239.40 1999-02-04,1272.07,1272.23,1248.36,1248.49,854400000,1248.49 1999-02-03,1261.99,1276.04,1255.27,1272.07,876500000,1272.07 1999-02-02,1273.00,1273.49,1247.56,1261.99,845500000,1261.99 1999-02-01,1279.64,1283.75,1271.31,1273.00,799400000,1273.00 1999-01-29,1265.37,1280.37,1255.18,1279.64,917000000,1279.64 1999-01-28,1243.17,1266.40,1243.17,1265.37,848800000,1265.37 1999-01-27,1252.31,1262.61,1242.82,1243.17,893800000,1243.17 1999-01-26,1233.98,1253.25,1233.98,1252.31,896400000,1252.31 1999-01-25,1225.19,1233.98,1219.46,1233.98,723900000,1233.98 1999-01-22,1235.16,1236.41,1217.97,1225.19,785900000,1225.19 1999-01-21,1256.62,1256.94,1232.19,1235.16,871800000,1235.16 1999-01-20,1252.00,1274.07,1251.54,1256.62,905700000,1256.62 1999-01-19,1243.26,1253.27,1234.91,1252.00,785500000,1252.00 1999-01-15,1212.19,1243.26,1212.19,1243.26,798100000,1243.26 1999-01-14,1234.40,1236.81,1209.54,1212.19,797200000,1212.19 1999-01-13,1239.51,1247.75,1205.46,1234.40,931500000,1234.40 1999-01-12,1263.88,1264.45,1238.29,1239.51,800200000,1239.51 1999-01-11,1275.09,1276.22,1253.34,1263.88,818000000,1263.88 1999-01-08,1269.73,1278.24,1261.82,1275.09,937800000,1275.09 1999-01-07,1272.34,1272.34,1257.68,1269.73,863000000,1269.73 1999-01-06,1244.78,1272.50,1244.78,1272.34,986900000,1272.34 1999-01-05,1228.10,1246.11,1228.10,1244.78,775000000,1244.78 1999-01-04,1229.23,1248.81,1219.10,1228.10,877000000,1228.10 1998-12-31,1231.93,1237.18,1224.96,1229.23,719200000,1229.23 1998-12-30,1241.81,1244.93,1231.20,1231.93,594220000,1231.93 1998-12-29,1225.49,1241.86,1220.78,1241.81,586490000,1241.81 1998-12-28,1226.27,1231.52,1221.17,1225.49,531560000,1225.49 1998-12-24,1228.54,1229.72,1224.85,1226.27,246980000,1226.27 1998-12-23,1203.57,1229.89,1203.57,1228.54,697500000,1228.54 1998-12-22,1202.84,1209.22,1192.72,1203.57,680500000,1203.57 1998-12-21,1188.03,1210.88,1188.03,1202.84,744800000,1202.84 1998-12-18,1179.98,1188.89,1178.27,1188.03,839600000,1188.03 1998-12-17,1161.94,1180.03,1161.94,1179.98,739400000,1179.98 1998-12-16,1162.83,1166.29,1154.69,1161.94,725500000,1161.94 1998-12-15,1141.20,1162.83,1141.20,1162.83,777900000,1162.83 1998-12-14,1166.46,1166.46,1136.89,1141.20,741800000,1141.20 1998-12-11,1165.02,1167.89,1153.19,1166.46,688900000,1166.46 1998-12-10,1183.49,1183.77,1163.75,1165.02,748600000,1165.02 1998-12-09,1181.38,1185.22,1175.89,1183.49,694200000,1183.49 1998-12-08,1187.70,1193.53,1172.78,1181.38,727700000,1181.38 1998-12-07,1176.74,1188.96,1176.71,1187.70,671200000,1187.70 1998-12-04,1150.14,1176.74,1150.14,1176.74,709700000,1176.74 1998-12-03,1171.25,1176.99,1149.61,1150.14,799100000,1150.14 1998-12-02,1175.28,1175.28,1157.76,1171.25,727400000,1171.25 1998-12-01,1163.63,1175.89,1150.31,1175.28,789200000,1175.28 1998-11-30,1192.33,1192.72,1163.63,1163.63,687900000,1163.63 1998-11-27,1186.87,1192.97,1186.83,1192.33,256950000,1192.33 1998-11-25,1182.99,1187.16,1179.37,1186.87,583580000,1186.87 1998-11-24,1188.21,1191.30,1181.81,1182.99,766200000,1182.99 1998-11-23,1163.55,1188.21,1163.55,1188.21,774100000,1188.21 1998-11-20,1152.61,1163.55,1152.61,1163.55,721200000,1163.55 1998-11-19,1144.48,1155.10,1144.42,1152.61,671000000,1152.61 1998-11-18,1139.32,1144.52,1133.07,1144.48,652510000,1144.48 1998-11-17,1135.87,1151.71,1129.67,1139.32,705200000,1139.32 1998-11-16,1125.72,1138.72,1125.72,1135.87,615580000,1135.87 1998-11-13,1117.69,1126.34,1116.76,1125.72,602270000,1125.72 1998-11-12,1120.97,1126.57,1115.55,1117.69,662300000,1117.69 1998-11-11,1128.26,1136.25,1117.40,1120.97,715700000,1120.97 1998-11-10,1130.20,1135.37,1122.80,1128.26,671300000,1128.26 1998-11-09,1141.01,1141.01,1123.17,1130.20,592990000,1130.20 1998-11-06,1133.85,1141.30,1131.18,1141.01,683100000,1141.01 1998-11-05,1118.67,1133.88,1109.55,1133.85,770200000,1133.85 1998-11-04,1110.84,1127.18,1110.59,1118.67,861100000,1118.67 1998-11-03,1111.60,1115.02,1106.42,1110.84,704300000,1110.84 1998-11-02,1098.67,1114.44,1098.67,1111.60,753800000,1111.60 1998-10-30,1085.93,1103.78,1085.93,1098.67,785000000,1098.67 1998-10-29,1068.09,1086.11,1065.95,1085.93,699400000,1085.93 1998-10-28,1065.34,1072.79,1059.65,1068.09,677500000,1068.09 1998-10-27,1072.32,1087.08,1063.06,1065.34,764500000,1065.34 1998-10-26,1070.67,1081.23,1068.17,1072.32,609910000,1072.32 1998-10-23,1078.48,1078.48,1067.43,1070.67,637640000,1070.67 1998-10-22,1069.92,1080.43,1061.47,1078.48,754900000,1078.48 1998-10-21,1063.93,1073.61,1058.08,1069.92,745100000,1069.92 1998-10-20,1062.39,1084.06,1060.61,1063.93,958200000,1063.93 1998-10-19,1056.42,1065.21,1054.23,1062.39,738600000,1062.39 1998-10-16,1047.49,1062.65,1047.49,1056.42,1042200000,1056.42 1998-10-15,1005.53,1053.09,1000.12,1047.49,937600000,1047.49 1998-10-14,994.80,1014.42,987.80,1005.53,791200000,1005.53 1998-10-13,997.71,1000.78,987.55,994.80,733300000,994.80 1998-10-12,984.39,1010.71,984.39,997.71,691100000,997.71 1998-10-09,959.44,984.42,953.04,984.39,878100000,984.39 1998-10-08,970.68,970.68,923.32,959.44,1114600000,959.44 1998-10-07,984.59,995.66,957.15,970.68,977000000,970.68 1998-10-06,988.56,1008.77,974.81,984.59,845700000,984.59 1998-10-05,1002.60,1002.60,964.72,988.56,817500000,988.56 1998-10-02,986.39,1005.45,971.69,1002.60,902900000,1002.60 1998-10-01,1017.01,1017.01,981.29,986.39,899700000,986.39 1998-09-30,1049.02,1049.02,1015.73,1017.01,800100000,1017.01 1998-09-29,1048.69,1056.31,1039.88,1049.02,760100000,1049.02 1998-09-28,1044.75,1061.46,1042.23,1048.69,690500000,1048.69 1998-09-25,1042.72,1051.89,1028.49,1044.75,736800000,1044.75 1998-09-24,1066.09,1066.11,1033.04,1042.72,805900000,1042.72 1998-09-23,1029.63,1066.09,1029.63,1066.09,899700000,1066.09 1998-09-22,1023.89,1033.89,1021.96,1029.63,694900000,1029.63 1998-09-21,1020.09,1026.02,993.82,1023.89,609880000,1023.89 1998-09-18,1018.87,1022.01,1011.86,1020.09,794700000,1020.09 1998-09-17,1045.48,1045.48,1016.05,1018.87,694500000,1018.87 1998-09-16,1037.68,1046.07,1029.31,1045.48,797500000,1045.48 1998-09-15,1029.72,1037.90,1021.42,1037.68,724600000,1037.68 1998-09-14,1009.06,1038.38,1009.06,1029.72,714400000,1029.72 1998-09-11,980.19,1009.06,969.71,1009.06,819100000,1009.06 1998-09-10,1006.20,1006.20,968.64,980.19,880300000,980.19 1998-09-09,1023.46,1027.72,1004.56,1006.20,704300000,1006.20 1998-09-08,973.89,1023.46,973.89,1023.46,814800000,1023.46 1998-09-04,982.26,991.41,956.51,973.89,780300000,973.89 1998-09-03,990.47,990.47,969.32,982.26,880500000,982.26 1998-09-02,994.26,1013.19,988.40,990.48,894600000,990.48 1998-09-01,957.28,1000.71,939.98,994.26,1216600000,994.26 1998-08-31,1027.14,1033.47,957.28,957.28,917500000,957.28 1998-08-28,1042.59,1051.80,1021.04,1027.14,840300000,1027.14 1998-08-27,1084.19,1084.19,1037.61,1042.59,938600000,1042.59 1998-08-26,1092.85,1092.85,1075.91,1084.19,674100000,1084.19 1998-08-25,1088.14,1106.64,1085.53,1092.85,664900000,1092.85 1998-08-24,1081.24,1093.82,1081.24,1088.14,558100000,1088.14 1998-08-21,1091.60,1091.60,1054.92,1081.24,725700000,1081.24 1998-08-20,1098.06,1098.79,1089.55,1091.60,621630000,1091.60 1998-08-19,1101.20,1106.32,1094.93,1098.06,633630000,1098.06 1998-08-18,1083.67,1101.72,1083.67,1101.20,690600000,1101.20 1998-08-17,1062.75,1083.67,1055.08,1083.67,584380000,1083.67 1998-08-14,1074.91,1083.92,1057.22,1062.75,644030000,1062.75 1998-08-13,1084.22,1091.50,1074.91,1074.91,660700000,1074.91 1998-08-12,1068.98,1084.70,1068.98,1084.22,711700000,1084.22 1998-08-11,1083.14,1083.14,1054.00,1068.98,774400000,1068.98 1998-08-10,1089.45,1092.82,1081.76,1083.14,579180000,1083.14 1998-08-07,1089.63,1102.54,1084.72,1089.45,759100000,1089.45 1998-08-06,1081.43,1090.95,1074.94,1089.63,768400000,1089.63 1998-08-05,1072.12,1084.80,1057.35,1081.43,851600000,1081.43 1998-08-04,1112.44,1119.73,1071.82,1072.12,852600000,1072.12 1998-08-03,1120.67,1121.79,1110.39,1112.44,620400000,1112.44 1998-07-31,1142.95,1142.97,1114.30,1120.67,645910000,1120.67 1998-07-30,1125.21,1143.07,1125.21,1142.95,687400000,1142.95 1998-07-29,1130.24,1138.56,1121.98,1125.21,644350000,1125.21 1998-07-28,1147.27,1147.27,1119.44,1130.24,703600000,1130.24 1998-07-27,1140.80,1147.27,1128.19,1147.27,619990000,1147.27 1998-07-24,1139.75,1150.14,1129.11,1140.80,698600000,1140.80 1998-07-23,1164.08,1164.35,1139.75,1139.75,741600000,1139.75 1998-07-22,1165.07,1167.67,1155.20,1164.08,739800000,1164.08 1998-07-21,1184.10,1187.37,1163.05,1165.07,659700000,1165.07 1998-07-20,1186.75,1190.58,1179.19,1184.10,560580000,1184.10 1998-07-17,1183.99,1188.10,1182.42,1186.75,618030000,1186.75 1998-07-16,1174.81,1184.02,1170.40,1183.99,677800000,1183.99 1998-07-15,1177.58,1181.48,1174.73,1174.81,723900000,1174.81 1998-07-14,1165.19,1179.76,1165.19,1177.58,700300000,1177.58 1998-07-13,1164.33,1166.98,1160.21,1165.19,574880000,1165.19 1998-07-10,1158.57,1166.93,1150.88,1164.33,576080000,1164.33 1998-07-09,1166.38,1166.38,1156.03,1158.56,663600000,1158.56 1998-07-08,1154.66,1166.89,1154.66,1166.38,607230000,1166.38 1998-07-07,1157.33,1159.81,1152.85,1154.66,624890000,1154.66 1998-07-06,1146.42,1157.33,1145.03,1157.33,514750000,1157.33 1998-07-02,1148.56,1148.56,1142.99,1146.42,510210000,1146.42 1998-07-01,1133.84,1148.56,1133.84,1148.56,701600000,1148.56 1998-06-30,1138.49,1140.80,1131.98,1133.84,757200000,1133.84 1998-06-29,1133.20,1145.15,1133.20,1138.49,564350000,1138.49 1998-06-26,1129.28,1136.83,1129.28,1133.20,520050000,1133.20 1998-06-25,1132.88,1142.04,1127.60,1129.28,669900000,1129.28 1998-06-24,1119.49,1134.40,1115.10,1132.88,714900000,1132.88 1998-06-23,1103.21,1119.49,1103.21,1119.49,657100000,1119.49 1998-06-22,1100.65,1109.01,1099.42,1103.21,531550000,1103.21 1998-06-19,1106.37,1111.25,1097.10,1100.65,715500000,1100.65 1998-06-18,1107.11,1109.36,1103.71,1106.37,590440000,1106.37 1998-06-17,1087.59,1112.87,1087.58,1107.11,744400000,1107.11 1998-06-16,1077.01,1087.59,1074.67,1087.59,664600000,1087.59 1998-06-15,1098.84,1098.84,1077.01,1077.01,595820000,1077.01 1998-06-12,1094.58,1098.84,1080.83,1098.84,633300000,1098.84 1998-06-11,1112.28,1114.20,1094.28,1094.58,627470000,1094.58 1998-06-10,1118.41,1126.00,1110.27,1112.28,609410000,1112.28 1998-06-09,1115.72,1119.92,1111.31,1118.41,563610000,1118.41 1998-06-08,1113.86,1119.70,1113.31,1115.72,543390000,1115.72 1998-06-05,1095.10,1113.88,1094.83,1113.86,558440000,1113.86 1998-06-04,1082.73,1095.93,1078.10,1094.83,577470000,1094.83 1998-06-03,1093.22,1097.43,1081.09,1082.73,584480000,1082.73 1998-06-02,1090.98,1098.71,1089.67,1093.22,590930000,1093.22 1998-06-01,1090.82,1097.85,1084.22,1090.98,537660000,1090.98 1998-05-29,1097.60,1104.16,1090.82,1090.82,556780000,1090.82 1998-05-28,1092.23,1099.73,1089.06,1097.60,588900000,1097.60 1998-05-27,1094.02,1094.44,1074.39,1092.23,682040000,1092.23 1998-05-26,1110.47,1116.79,1094.01,1094.02,541410000,1094.02 1998-05-22,1114.64,1116.89,1107.99,1110.47,444070000,1110.47 1998-05-21,1119.06,1124.45,1111.94,1114.64,551970000,1114.64 1998-05-20,1109.52,1119.08,1107.51,1119.06,587240000,1119.06 1998-05-19,1105.82,1113.50,1105.82,1109.52,566020000,1109.52 1998-05-18,1108.73,1112.44,1097.99,1105.82,519100000,1105.82 1998-05-15,1117.37,1118.66,1107.11,1108.73,621990000,1108.73 1998-05-14,1118.86,1124.03,1112.43,1117.37,578380000,1117.37 1998-05-13,1115.79,1122.22,1114.93,1118.86,600010000,1118.86 1998-05-12,1106.64,1115.96,1102.78,1115.79,604420000,1115.79 1998-05-11,1108.14,1119.13,1103.72,1106.64,560840000,1106.64 1998-05-08,1095.14,1111.42,1094.53,1108.14,567890000,1108.14 1998-05-07,1104.92,1105.58,1094.59,1095.14,582240000,1095.14 1998-05-06,1115.50,1118.39,1104.64,1104.92,606540000,1104.92 1998-05-05,1122.07,1122.07,1111.16,1115.50,583630000,1115.50 1998-05-04,1121.00,1130.52,1121.00,1122.07,551700000,1122.07 1998-05-01,1111.75,1121.02,1111.75,1121.00,581970000,1121.00 1998-04-30,1094.63,1116.97,1094.63,1111.75,695600000,1111.75 1998-04-29,1085.11,1098.24,1084.65,1094.62,638790000,1094.62 1998-04-28,1086.54,1095.94,1081.49,1085.11,678600000,1085.11 1998-04-27,1107.90,1107.90,1076.70,1086.54,685960000,1086.54 1998-04-24,1119.58,1122.81,1104.77,1107.90,633890000,1107.90 1998-04-23,1130.54,1130.54,1117.49,1119.58,653190000,1119.58 1998-04-22,1126.67,1132.98,1126.29,1130.54,696740000,1130.54 1998-04-21,1123.65,1129.65,1119.54,1126.67,675640000,1126.67 1998-04-20,1122.72,1124.88,1118.43,1123.65,595190000,1123.65 1998-04-17,1108.17,1122.72,1104.95,1122.72,672290000,1122.72 1998-04-16,1119.32,1119.32,1105.27,1108.17,699570000,1108.17 1998-04-15,1115.75,1119.90,1112.24,1119.32,685020000,1119.32 1998-04-14,1109.69,1115.95,1109.48,1115.75,613730000,1115.75 1998-04-13,1110.67,1110.75,1100.60,1109.69,564480000,1109.69 1998-04-09,1101.65,1111.45,1101.65,1110.67,548940000,1110.67 1998-04-08,1109.55,1111.60,1098.21,1101.65,616330000,1101.65 1998-04-07,1121.38,1121.38,1102.44,1109.55,670760000,1109.55 1998-04-06,1122.70,1131.99,1121.37,1121.38,625810000,1121.38 1998-04-03,1120.01,1126.36,1118.12,1122.70,653880000,1122.70 1998-04-02,1108.15,1121.01,1107.89,1120.01,674340000,1120.01 1998-04-01,1101.75,1109.19,1095.29,1108.15,677310000,1108.15 1998-03-31,1093.55,1110.13,1093.55,1101.75,674930000,1101.75 1998-03-30,1095.44,1099.10,1090.02,1093.60,497400000,1093.60 1998-03-27,1100.80,1107.18,1091.14,1095.44,582190000,1095.44 1998-03-26,1101.93,1106.28,1097.00,1100.80,606770000,1100.80 1998-03-25,1105.65,1113.07,1092.84,1101.93,676550000,1101.93 1998-03-24,1095.55,1106.75,1095.55,1105.65,605720000,1105.65 1998-03-23,1099.16,1101.16,1094.25,1095.55,631350000,1095.55 1998-03-20,1089.74,1101.04,1089.39,1099.16,717310000,1099.16 1998-03-19,1085.52,1089.74,1084.30,1089.74,598240000,1089.74 1998-03-18,1080.45,1085.52,1077.77,1085.52,632690000,1085.52 1998-03-17,1079.27,1080.52,1073.29,1080.45,680960000,1080.45 1998-03-16,1068.61,1079.46,1068.61,1079.27,548980000,1079.27 1998-03-13,1069.92,1075.86,1066.57,1068.61,597800000,1068.61 1998-03-12,1068.47,1071.87,1063.54,1069.92,594940000,1069.92 1998-03-11,1064.25,1069.18,1064.22,1068.47,655260000,1068.47 1998-03-10,1052.31,1064.59,1052.31,1064.25,631920000,1064.25 1998-03-09,1055.69,1058.55,1050.02,1052.31,624700000,1052.31 1998-03-06,1035.05,1055.69,1035.05,1055.69,665500000,1055.69 1998-03-05,1047.33,1047.33,1030.87,1035.05,648270000,1035.05 1998-03-04,1052.02,1052.02,1042.74,1047.33,644280000,1047.33 1998-03-03,1047.70,1052.02,1043.41,1052.02,612360000,1052.02 1998-03-02,1049.34,1053.98,1044.70,1047.70,591470000,1047.70 1998-02-27,1048.67,1051.66,1044.40,1049.34,574480000,1049.34 1998-02-26,1042.90,1048.68,1039.85,1048.67,646280000,1048.67 1998-02-25,1030.56,1045.79,1030.56,1042.90,611350000,1042.90 1998-02-24,1038.14,1038.73,1028.89,1030.56,589880000,1030.56 1998-02-23,1034.21,1038.68,1031.76,1038.14,550730000,1038.14 1998-02-20,1028.28,1034.21,1022.69,1034.21,594300000,1034.21 1998-02-19,1032.08,1032.93,1026.62,1028.28,581820000,1028.28 1998-02-18,1022.76,1032.08,1021.70,1032.08,606000000,1032.08 1998-02-17,1020.09,1028.02,1020.09,1022.76,605890000,1022.76 1998-02-13,1024.14,1024.14,1017.71,1020.09,531940000,1020.09 1998-02-12,1020.01,1026.30,1008.55,1024.14,611480000,1024.14 1998-02-11,1019.01,1020.71,1016.38,1020.01,599300000,1020.01 1998-02-10,1010.74,1022.15,1010.71,1019.01,642800000,1019.01 1998-02-09,1012.46,1015.33,1006.28,1010.74,524810000,1010.74 1998-02-06,1003.54,1013.07,1003.36,1012.46,569650000,1012.46 1998-02-05,1006.90,1013.51,1000.27,1003.54,703980000,1003.54 1998-02-04,1006.00,1009.52,999.43,1006.90,695420000,1006.90 1998-02-03,1001.27,1006.13,996.90,1006.00,692120000,1006.00 1998-02-02,980.28,1002.48,980.28,1001.27,724320000,1001.27 1998-01-30,985.49,987.41,979.63,980.28,613380000,980.28 1998-01-29,977.46,992.65,975.21,985.49,750760000,985.49 1998-01-28,969.02,978.63,969.02,977.46,708470000,977.46 1998-01-27,956.95,973.23,956.26,969.02,679140000,969.02 1998-01-26,957.59,963.04,954.24,956.95,555080000,956.95 1998-01-23,963.04,966.44,950.86,957.59,635770000,957.59 1998-01-22,970.81,970.81,959.49,963.04,646570000,963.04 1998-01-21,978.60,978.60,963.29,970.81,626160000,970.81 1998-01-20,961.51,978.60,961.48,978.60,644790000,978.60 1998-01-16,950.73,965.12,950.73,961.51,670080000,961.51 1998-01-15,957.94,957.94,950.27,950.73,569050000,950.73 1998-01-14,952.12,958.12,948.00,957.94,603280000,957.94 1998-01-13,939.21,952.14,939.21,952.12,646740000,952.12 1998-01-12,927.69,939.25,912.83,939.21,705450000,939.21 1998-01-09,956.05,956.05,921.72,927.69,746420000,927.69 1998-01-08,964.00,964.00,955.04,956.05,652140000,956.05 1998-01-07,966.58,966.58,952.67,964.00,667390000,964.00 1998-01-06,977.07,977.07,962.68,966.58,618360000,966.58 1998-01-05,975.04,982.63,969.00,977.07,628070000,977.07 1998-01-02,970.43,975.04,965.73,975.04,366730000,975.04 1997-12-31,970.84,975.02,967.41,970.43,467280000,970.43 1997-12-30,953.35,970.84,953.35,970.84,499500000,970.84 1997-12-29,936.46,953.95,936.46,953.35,443160000,953.35 1997-12-26,932.70,939.99,932.70,936.46,154900000,936.46 1997-12-24,939.13,942.88,932.70,932.70,265980000,932.70 1997-12-23,953.70,954.51,938.91,939.13,515070000,939.13 1997-12-22,946.78,956.73,946.25,953.70,530670000,953.70 1997-12-19,955.30,955.30,924.92,946.78,793200000,946.78 1997-12-18,965.54,965.54,950.55,955.30,618870000,955.30 1997-12-17,968.04,974.30,964.25,965.54,618900000,965.54 1997-12-16,963.39,973.00,963.39,968.04,623320000,968.04 1997-12-15,953.39,965.96,953.39,963.39,597150000,963.39 1997-12-12,954.94,961.32,947.00,953.39,579280000,953.39 1997-12-11,969.79,969.79,951.89,954.94,631770000,954.94 1997-12-10,975.78,975.78,962.68,969.79,602290000,969.79 1997-12-09,982.37,982.37,973.81,975.78,539130000,975.78 1997-12-08,983.79,985.67,979.57,982.37,490320000,982.37 1997-12-05,973.10,986.25,969.10,983.79,563590000,983.79 1997-12-04,976.77,983.36,971.37,973.10,633470000,973.10 1997-12-03,971.68,980.81,966.16,976.77,624610000,976.77 1997-12-02,974.78,976.20,969.83,971.68,576120000,971.68 1997-12-01,955.40,974.77,955.40,974.77,590300000,974.77 1997-11-28,951.64,959.13,951.64,955.40,189070000,955.40 1997-11-26,950.82,956.47,950.82,951.64,487750000,951.64 1997-11-25,946.67,954.47,944.71,950.82,587890000,950.82 1997-11-24,963.09,963.09,945.22,946.67,514920000,946.67 1997-11-21,958.98,964.55,954.60,963.09,611000000,963.09 1997-11-20,944.59,961.83,944.59,958.98,602610000,958.98 1997-11-19,938.23,947.28,934.83,944.59,542720000,944.59 1997-11-18,946.20,947.65,937.43,938.23,521380000,938.23 1997-11-17,928.35,949.66,928.35,946.20,576540000,946.20 1997-11-14,916.66,930.44,915.34,928.35,635760000,928.35 1997-11-13,905.96,917.79,900.61,916.66,653960000,916.66 1997-11-12,923.78,923.88,905.34,905.96,585340000,905.96 1997-11-11,921.13,928.29,919.63,923.78,435660000,923.78 1997-11-10,927.51,935.90,920.26,921.13,464140000,921.13 1997-11-07,938.03,938.03,915.39,927.51,569980000,927.51 1997-11-06,942.76,942.85,934.16,938.03,522890000,938.03 1997-11-05,940.76,949.62,938.16,942.76,565680000,942.76 1997-11-04,938.99,941.40,932.66,940.76,541590000,940.76 1997-11-03,914.62,939.02,914.62,938.99,564740000,938.99 1997-10-31,903.68,919.93,903.68,914.62,638070000,914.62 1997-10-30,919.16,923.28,903.68,903.68,712230000,903.68 1997-10-29,921.85,935.24,913.88,919.16,777660000,919.16 1997-10-28,876.99,923.09,855.27,921.85,1202550000,921.85 1997-10-27,941.64,941.64,876.73,876.99,693730000,876.99 1997-10-24,950.69,960.04,937.55,941.64,677630000,941.64 1997-10-23,968.49,968.49,944.16,950.69,673270000,950.69 1997-10-22,972.28,972.61,965.66,968.49,613490000,968.49 1997-10-21,955.61,972.56,955.61,972.28,582310000,972.28 1997-10-20,944.16,955.72,941.43,955.61,483880000,955.61 1997-10-17,955.23,955.23,931.58,944.16,624980000,944.16 1997-10-16,965.72,973.38,950.77,955.25,597010000,955.25 1997-10-15,970.28,970.28,962.75,965.72,505310000,965.72 1997-10-14,968.10,972.86,961.87,970.28,510330000,970.28 1997-10-13,966.98,973.46,966.95,968.10,354800000,968.10 1997-10-10,970.62,970.62,963.42,966.98,500680000,966.98 1997-10-09,973.84,974.72,963.34,970.62,551840000,970.62 1997-10-08,983.12,983.12,968.65,973.84,573110000,973.84 1997-10-07,972.69,983.12,971.95,983.12,551970000,983.12 1997-10-06,965.03,974.16,965.03,972.69,495620000,972.69 1997-10-03,960.46,975.47,955.13,965.03,623370000,965.03 1997-10-02,955.41,960.46,952.94,960.46,474760000,960.46 1997-10-01,947.28,956.71,947.28,955.41,598660000,955.41 1997-09-30,953.34,955.17,947.28,947.28,587500000,947.28 1997-09-29,945.22,953.96,941.94,953.34,477100000,953.34 1997-09-26,937.91,946.44,937.91,945.22,505340000,945.22 1997-09-25,944.48,947.00,937.38,937.91,524880000,937.91 1997-09-24,951.93,959.78,944.07,944.48,639460000,944.48 1997-09-23,955.43,955.78,948.07,951.93,522930000,951.93 1997-09-22,950.51,960.59,950.51,955.43,490900000,955.43 1997-09-19,947.29,952.35,943.90,950.51,631040000,950.51 1997-09-18,943.00,958.19,943.00,947.29,566830000,947.29 1997-09-17,945.64,950.29,941.99,943.00,590550000,943.00 1997-09-16,919.77,947.66,919.77,945.64,636380000,945.64 1997-09-15,923.91,928.90,919.41,919.77,468030000,919.77 1997-09-12,912.59,925.05,906.70,923.91,544150000,923.91 1997-09-11,919.03,919.03,902.56,912.59,575020000,912.59 1997-09-10,933.62,933.62,918.76,919.03,517620000,919.03 1997-09-09,931.20,938.90,927.28,933.62,502200000,933.62 1997-09-08,929.05,936.50,929.05,931.20,466430000,931.20 1997-09-05,930.87,940.37,924.05,929.05,536400000,929.05 1997-09-04,927.86,933.36,925.59,930.87,559310000,930.87 1997-09-03,927.58,935.90,926.87,927.86,549060000,927.86 1997-09-02,899.47,927.58,899.47,927.58,491870000,927.58 1997-08-29,903.67,907.28,896.82,899.47,413910000,899.47 1997-08-28,913.70,915.90,898.65,903.67,486300000,903.67 1997-08-27,913.02,916.23,903.83,913.70,492150000,913.70 1997-08-26,920.16,922.47,911.72,913.02,449110000,913.02 1997-08-25,923.55,930.93,917.29,920.16,388990000,920.16 1997-08-22,925.05,925.05,905.42,923.54,460160000,923.54 1997-08-21,939.35,939.47,921.35,925.05,499000000,925.05 1997-08-20,926.01,939.35,924.58,939.35,521270000,939.35 1997-08-19,912.49,926.01,912.49,926.01,545630000,926.01 1997-08-18,900.81,912.57,893.34,912.49,514330000,912.49 1997-08-15,924.77,924.77,900.81,900.81,537820000,900.81 1997-08-14,922.02,930.07,916.92,924.77,530460000,924.77 1997-08-13,926.53,935.77,916.54,922.02,587210000,922.02 1997-08-12,937.00,942.99,925.66,926.53,499310000,926.53 1997-08-11,933.54,938.50,925.39,937.00,480340000,937.00 1997-08-08,951.19,951.19,925.74,933.54,563420000,933.54 1997-08-07,960.32,964.17,950.87,951.19,576030000,951.19 1997-08-06,952.37,962.43,949.45,960.32,565200000,960.32 1997-08-05,950.30,954.21,948.92,952.37,525710000,952.37 1997-08-04,947.14,953.18,943.60,950.30,456000000,950.30 1997-08-01,954.29,955.35,939.04,947.14,513750000,947.14 1997-07-31,952.29,957.73,948.89,954.31,547830000,954.31 1997-07-30,942.29,953.98,941.98,952.29,568470000,952.29 1997-07-29,936.45,942.96,932.56,942.29,544540000,942.29 1997-07-28,938.79,942.97,935.19,936.45,466920000,936.45 1997-07-25,940.30,945.65,936.09,938.79,521510000,938.79 1997-07-24,936.56,941.51,926.91,940.30,571020000,940.30 1997-07-23,933.98,941.80,933.98,936.56,616930000,936.56 1997-07-22,912.94,934.38,912.94,933.98,579590000,933.98 1997-07-21,915.30,915.38,907.12,912.94,459500000,912.94 1997-07-18,931.61,931.61,912.90,915.30,589710000,915.30 1997-07-17,936.59,936.96,927.90,931.61,629250000,931.61 1997-07-16,925.76,939.32,925.76,936.59,647390000,936.59 1997-07-15,918.38,926.15,914.52,925.76,598370000,925.76 1997-07-14,916.68,921.78,912.02,918.38,485960000,918.38 1997-07-11,913.78,919.74,913.11,916.68,500050000,916.68 1997-07-10,907.54,916.54,904.31,913.78,551340000,913.78 1997-07-09,918.75,922.03,902.48,907.54,589110000,907.54 1997-07-08,912.20,918.76,911.56,918.75,526010000,918.75 1997-07-07,916.92,923.26,909.69,912.20,518780000,912.20 1997-07-03,904.03,917.82,904.03,916.92,374680000,916.92 1997-07-02,891.03,904.05,891.03,904.03,526970000,904.03 1997-07-01,885.14,893.88,884.54,891.03,544190000,891.03 1997-06-30,887.30,892.62,879.82,885.14,561540000,885.14 1997-06-27,883.68,894.70,883.68,887.30,472540000,887.30 1997-06-26,888.99,893.21,879.32,883.68,499780000,883.68 1997-06-25,896.34,902.09,882.24,888.99,603040000,888.99 1997-06-24,878.62,896.75,878.62,896.34,542650000,896.34 1997-06-23,898.70,898.70,878.43,878.62,492940000,878.62 1997-06-20,897.99,901.77,897.77,898.70,653110000,898.70 1997-06-19,889.06,900.09,888.99,897.99,536940000,897.99 1997-06-18,894.42,894.42,887.03,889.06,491740000,889.06 1997-06-17,893.90,897.60,886.19,894.42,543010000,894.42 1997-06-16,893.27,895.17,891.21,893.90,414280000,893.90 1997-06-13,883.48,894.69,883.48,893.27,575810000,893.27 1997-06-12,869.57,884.34,869.01,883.46,592730000,883.46 1997-06-11,865.27,870.66,865.15,869.57,513740000,869.57 1997-06-10,862.91,870.05,862.18,865.27,526980000,865.27 1997-06-09,858.01,865.14,858.01,862.91,465810000,862.91 1997-06-06,843.43,859.24,843.36,858.01,488940000,858.01 1997-06-05,840.11,848.89,840.11,843.43,452610000,843.43 1997-06-04,845.48,845.55,838.82,840.11,466690000,840.11 1997-06-03,846.36,850.56,841.51,845.48,527120000,845.48 1997-06-02,848.28,851.34,844.61,846.36,435950000,846.36 1997-05-30,844.08,851.87,831.87,848.28,537200000,848.28 1997-05-29,847.21,848.96,842.61,844.08,462600000,844.08 1997-05-28,849.71,850.95,843.21,847.21,487340000,847.21 1997-05-27,847.03,851.53,840.96,849.71,436150000,849.71 1997-05-23,835.66,848.49,835.66,847.03,417030000,847.03 1997-05-22,839.35,841.91,833.86,835.66,426940000,835.66 1997-05-21,841.66,846.87,835.22,839.35,540730000,839.35 1997-05-20,833.27,841.96,826.41,841.66,450850000,841.66 1997-05-19,829.75,835.92,828.87,833.27,345140000,833.27 1997-05-16,841.88,841.88,829.15,829.75,486780000,829.75 1997-05-15,836.04,842.45,833.34,841.88,458170000,841.88 1997-05-14,833.13,841.29,833.13,836.04,504960000,836.04 1997-05-13,837.66,838.49,829.12,833.13,489760000,833.13 1997-05-12,824.78,838.56,824.78,837.66,459370000,837.66 1997-05-09,820.26,827.69,815.78,824.78,455690000,824.78 1997-05-08,815.62,829.09,811.84,820.26,534120000,820.26 1997-05-07,827.76,827.76,814.70,815.62,500580000,815.62 1997-05-06,830.24,832.29,824.70,827.76,603680000,827.76 1997-05-05,812.97,830.29,811.80,830.29,549410000,830.29 1997-05-02,798.53,812.99,798.53,812.97,499770000,812.97 1997-05-01,801.34,802.95,793.21,798.53,460380000,798.53 1997-04-30,794.05,804.13,791.21,801.34,556070000,801.34 1997-04-29,772.96,794.44,772.96,794.05,547690000,794.05 1997-04-28,765.37,773.89,763.30,772.96,404470000,772.96 1997-04-25,771.18,771.18,764.63,765.37,414350000,765.37 1997-04-24,773.64,779.89,769.72,771.18,493640000,771.18 1997-04-23,774.61,778.19,771.90,773.64,489350000,773.64 1997-04-22,760.37,774.64,759.90,774.61,507500000,774.61 1997-04-21,766.34,767.39,756.38,760.37,397300000,760.37 1997-04-18,761.77,767.93,761.77,766.34,468940000,766.34 1997-04-17,763.53,768.55,760.49,761.77,503760000,761.77 1997-04-16,754.72,763.53,751.99,763.53,498820000,763.53 1997-04-15,743.73,754.72,743.73,754.72,507370000,754.72 1997-04-14,737.65,743.73,733.54,743.73,406800000,743.73 1997-04-11,758.34,758.34,737.64,737.65,444380000,737.65 1997-04-10,760.60,763.73,757.65,758.34,421790000,758.34 1997-04-09,766.12,769.53,759.15,760.60,451500000,760.60 1997-04-08,762.13,766.25,758.36,766.12,450790000,766.12 1997-04-07,757.90,764.82,757.90,762.13,453790000,762.13 1997-04-04,750.32,757.90,744.04,757.90,544580000,757.90 1997-04-03,750.11,751.04,744.40,750.32,498010000,750.32 1997-04-02,759.64,759.65,747.59,750.11,478210000,750.11 1997-04-01,757.12,761.49,751.26,759.64,515770000,759.64 1997-03-31,773.88,773.88,756.13,757.12,555880000,757.12 1997-03-27,790.50,792.58,767.32,773.88,476790000,773.88 1997-03-26,789.07,794.89,786.77,790.50,506670000,790.50 1997-03-25,790.89,798.11,788.39,789.07,487520000,789.07 1997-03-24,784.10,791.01,780.79,790.89,451970000,790.89 1997-03-21,782.65,786.44,782.65,784.10,638760000,784.10 1997-03-20,785.77,786.29,778.04,782.65,497480000,782.65 1997-03-19,789.66,791.59,780.03,785.77,535580000,785.77 1997-03-18,795.71,797.18,785.47,789.66,467330000,789.66 1997-03-17,793.17,796.28,782.98,795.71,495260000,795.71 1997-03-14,789.56,796.88,789.56,793.17,491540000,793.17 1997-03-13,804.26,804.26,789.44,789.56,507560000,789.56 1997-03-12,811.34,811.34,801.07,804.26,490200000,804.26 1997-03-11,813.65,814.90,810.77,811.34,493250000,811.34 1997-03-10,804.97,813.66,803.66,813.65,468780000,813.65 1997-03-07,798.56,808.19,798.56,804.97,508270000,804.97 1997-03-06,801.99,804.11,797.50,798.56,540310000,798.56 1997-03-05,790.95,801.99,790.95,801.99,532500000,801.99 1997-03-04,795.31,798.93,789.98,790.95,537890000,790.95 1997-03-03,790.82,795.31,785.66,795.31,437220000,795.31 1997-02-28,795.07,795.70,788.50,790.82,508280000,790.82 1997-02-27,805.68,805.68,795.06,795.07,464660000,795.07 1997-02-26,812.10,812.70,798.13,805.68,573920000,805.68 1997-02-25,810.28,812.85,807.65,812.03,527450000,812.03 1997-02-24,801.77,810.64,798.42,810.28,462450000,810.28 1997-02-21,802.80,804.94,799.99,801.77,478450000,801.77 1997-02-20,812.49,812.49,800.35,802.80,492220000,802.80 1997-02-19,816.29,817.68,811.20,812.49,519350000,812.49 1997-02-18,808.48,816.29,806.34,816.29,474110000,816.29 1997-02-14,811.82,812.20,808.15,808.48,491540000,808.48 1997-02-13,802.77,812.93,802.77,811.82,593710000,811.82 1997-02-12,789.59,802.77,789.59,802.77,563890000,802.77 1997-02-11,785.43,789.60,780.95,789.59,483090000,789.59 1997-02-10,789.56,793.46,784.69,785.43,471590000,785.43 1997-02-07,780.15,789.72,778.19,789.56,540910000,789.56 1997-02-06,778.28,780.35,774.45,780.15,519660000,780.15 1997-02-05,789.26,792.71,773.43,778.28,580520000,778.28 1997-02-04,786.73,789.28,783.68,789.26,506530000,789.26 1997-02-03,786.16,787.14,783.12,786.73,463600000,786.73 1997-01-31,784.17,791.86,784.17,786.16,578550000,786.16 1997-01-30,772.50,784.17,772.50,784.17,524160000,784.17 1997-01-29,765.02,772.70,765.02,772.50,498390000,772.50 1997-01-28,765.02,776.32,761.75,765.02,541580000,765.02 1997-01-27,770.52,771.43,764.18,765.02,445760000,765.02 1997-01-24,777.56,778.21,768.17,770.52,542920000,770.52 1997-01-23,786.23,794.67,776.64,777.56,685070000,777.56 1997-01-22,782.72,786.23,779.56,786.23,589230000,786.23 1997-01-21,776.70,783.72,772.00,782.72,571280000,782.72 1997-01-20,776.17,780.08,774.19,776.70,440470000,776.70 1997-01-17,769.75,776.37,769.72,776.17,534640000,776.17 1997-01-16,767.20,772.05,765.25,769.75,537290000,769.75 1997-01-15,768.86,770.95,763.72,767.20,524990000,767.20 1997-01-14,759.51,772.04,759.51,768.86,531600000,768.86 1997-01-13,759.50,762.85,756.69,759.51,445400000,759.51 1997-01-10,754.85,759.65,746.92,759.50,545850000,759.50 1997-01-09,748.41,757.68,748.41,754.85,555370000,754.85 1997-01-08,753.23,755.72,747.71,748.41,557510000,748.41 1997-01-07,747.65,753.26,742.18,753.23,538220000,753.23 1997-01-06,748.03,753.31,743.82,747.65,531350000,747.65 1997-01-03,737.01,748.24,737.01,748.03,452970000,748.03 1997-01-02,740.74,742.81,729.55,737.01,463230000,737.01 1996-12-31,753.85,753.95,740.74,740.74,399760000,740.74 1996-12-30,756.79,759.20,752.73,753.85,339060000,753.85 1996-12-27,755.82,758.75,754.82,756.79,253810000,756.79 1996-12-26,751.03,757.07,751.02,755.82,254630000,755.82 1996-12-24,746.92,751.03,746.92,751.03,165140000,751.03 1996-12-23,748.87,750.40,743.28,746.92,343280000,746.92 1996-12-20,745.76,755.41,745.76,748.87,654340000,748.87 1996-12-19,731.54,746.06,731.54,745.76,526410000,745.76 1996-12-18,726.04,732.76,726.04,731.54,500490000,731.54 1996-12-17,720.98,727.67,716.69,726.04,519840000,726.04 1996-12-16,728.64,732.68,719.40,720.98,447560000,720.98 1996-12-13,729.33,731.40,721.97,728.64,458540000,728.64 1996-12-12,740.73,744.86,729.30,729.30,492920000,729.30 1996-12-11,747.54,747.54,732.75,740.73,494210000,740.73 1996-12-10,749.76,753.43,747.02,747.54,446120000,747.54 1996-12-09,739.60,749.76,739.60,749.76,381570000,749.76 1996-12-06,744.38,744.38,726.89,739.60,500860000,739.60 1996-12-05,745.10,747.65,742.61,744.38,483710000,744.38 1996-12-04,748.28,748.40,738.46,745.10,498240000,745.10 1996-12-03,756.56,761.75,747.58,748.28,516160000,748.28 1996-12-02,757.02,757.03,751.49,756.56,412520000,756.56 1996-11-29,755.00,758.27,755.00,757.02,14990000,757.02 1996-11-27,755.96,757.30,753.18,755.00,377780000,755.00 1996-11-26,757.03,762.12,752.83,755.96,527380000,755.96 1996-11-25,748.73,757.05,747.99,757.03,475260000,757.03 1996-11-22,742.75,748.73,742.75,748.73,525210000,748.73 1996-11-21,743.95,745.20,741.08,742.75,464430000,742.75 1996-11-20,742.16,746.99,740.40,743.95,497900000,743.95 1996-11-19,737.02,742.18,736.87,742.16,461980000,742.16 1996-11-18,737.62,739.24,734.39,737.02,388520000,737.02 1996-11-15,735.88,741.92,735.15,737.62,529100000,737.62 1996-11-14,731.13,735.99,729.20,735.88,480350000,735.88 1996-11-13,729.56,732.11,728.03,731.13,429840000,731.13 1996-11-12,731.87,733.04,728.20,729.56,471740000,729.56 1996-11-11,730.82,732.60,729.94,731.87,353960000,731.87 1996-11-08,727.65,730.82,725.22,730.82,402320000,730.82 1996-11-07,724.59,729.49,722.23,727.65,502530000,727.65 1996-11-06,714.14,724.60,712.83,724.59,509600000,724.59 1996-11-05,706.73,714.56,706.73,714.14,486660000,714.14 1996-11-04,703.77,707.02,702.84,706.73,398790000,706.73 1996-11-01,705.27,708.60,701.30,703.77,465510000,703.77 1996-10-31,700.90,706.61,700.35,705.27,482840000,705.27 1996-10-30,701.50,703.44,700.05,700.90,437770000,700.90 1996-10-29,697.26,703.25,696.22,701.50,443890000,701.50 1996-10-28,700.92,705.40,697.25,697.26,383620000,697.26 1996-10-25,702.29,704.11,700.53,700.92,367640000,700.92 1996-10-24,707.27,708.25,702.11,702.29,418970000,702.29 1996-10-23,706.57,707.31,700.98,707.27,442170000,707.27 1996-10-22,709.85,709.85,704.55,706.57,410790000,706.57 1996-10-21,710.82,714.10,707.71,709.85,414630000,709.85 1996-10-18,706.99,711.04,706.11,710.82,473020000,710.82 1996-10-17,705.00,708.52,704.76,706.99,478550000,706.99 1996-10-16,702.57,704.42,699.15,704.41,441410000,704.41 1996-10-15,703.54,708.07,699.07,702.57,458980000,702.57 1996-10-14,700.66,705.16,700.66,703.54,322000000,703.54 1996-10-11,694.61,700.67,694.61,700.66,396050000,700.66 1996-10-10,696.74,696.82,693.34,694.61,394950000,694.61 1996-10-09,700.64,702.36,694.42,696.74,408450000,696.74 1996-10-08,703.34,705.76,699.88,700.64,435070000,700.64 1996-10-07,701.46,704.17,701.39,703.34,380750000,703.34 1996-10-04,692.78,701.74,692.78,701.46,463940000,701.46 1996-10-03,694.01,694.81,691.78,692.78,386500000,692.78 1996-10-02,689.08,694.82,689.08,694.01,440130000,694.01 1996-10-01,687.31,689.54,684.44,689.08,421550000,689.08 1996-09-30,686.19,690.11,686.03,687.33,388570000,687.33 1996-09-27,685.86,687.11,683.73,686.19,414760000,686.19 1996-09-26,685.83,690.15,683.77,685.86,500870000,685.86 1996-09-25,685.61,688.26,684.92,685.83,451710000,685.83 1996-09-24,686.48,690.88,683.54,685.61,460150000,685.61 1996-09-23,687.03,687.03,681.01,686.48,297760000,686.48 1996-09-20,683.00,687.07,683.00,687.03,519420000,687.03 1996-09-19,681.47,684.07,679.06,683.00,398580000,683.00 1996-09-18,682.94,683.77,679.75,681.47,396600000,681.47 1996-09-17,683.98,685.80,679.96,682.94,449850000,682.94 1996-09-16,680.54,686.48,680.53,683.98,430080000,683.98 1996-09-13,671.15,681.39,671.15,680.54,488360000,680.54 1996-09-12,667.28,673.07,667.28,671.15,398820000,671.15 1996-09-11,663.81,667.73,661.79,667.28,376880000,667.28 1996-09-10,663.76,665.57,661.55,663.81,372960000,663.81 1996-09-09,655.68,663.77,655.68,663.76,311530000,663.76 1996-09-06,649.44,658.21,649.44,655.68,348710000,655.68 1996-09-05,655.61,655.61,648.89,649.44,361430000,649.44 1996-09-04,654.72,655.82,652.93,655.61,351290000,655.61 1996-09-03,651.99,655.13,643.97,654.72,345740000,654.72 1996-08-30,657.40,657.71,650.52,651.99,258380000,651.99 1996-08-29,664.81,664.81,655.35,657.40,321120000,657.40 1996-08-28,666.40,667.41,664.39,664.81,296440000,664.81 1996-08-27,663.88,666.40,663.50,666.40,310520000,666.40 1996-08-26,667.03,667.03,662.36,663.88,281430000,663.88 1996-08-23,670.68,670.68,664.93,667.03,308010000,667.03 1996-08-22,665.07,670.68,664.88,670.68,354950000,670.68 1996-08-21,665.69,665.69,662.16,665.07,348820000,665.07 1996-08-20,666.58,666.99,665.15,665.69,334960000,665.69 1996-08-19,665.21,667.12,665.00,666.58,294080000,666.58 1996-08-16,662.28,666.34,662.26,665.21,337650000,665.21 1996-08-15,662.05,664.18,660.64,662.28,323950000,662.28 1996-08-14,660.20,662.42,658.47,662.05,343460000,662.05 1996-08-13,665.77,665.77,659.13,660.20,362470000,660.20 1996-08-12,662.10,665.77,658.95,665.77,312170000,665.77 1996-08-09,662.59,665.37,660.31,662.10,327280000,662.10 1996-08-08,664.16,664.17,661.28,662.59,334570000,662.59 1996-08-07,662.38,664.61,660.00,664.16,394340000,664.16 1996-08-06,660.23,662.75,656.83,662.38,347290000,662.38 1996-08-05,662.49,663.64,659.03,660.23,307240000,660.23 1996-08-02,650.02,662.49,650.02,662.49,442080000,662.49 1996-08-01,639.95,650.66,639.49,650.02,439110000,650.02 1996-07-31,635.26,640.54,633.74,639.95,403560000,639.95 1996-07-30,630.91,635.26,629.22,635.26,341090000,635.26 1996-07-29,635.90,635.90,630.90,630.91,281560000,630.91 1996-07-26,631.17,636.23,631.17,635.90,349900000,635.90 1996-07-25,626.65,633.57,626.65,631.17,405390000,631.17 1996-07-24,626.19,629.10,616.43,626.65,463030000,626.65 1996-07-23,633.79,637.70,625.65,626.87,421900000,626.87 1996-07-22,638.73,638.73,630.38,633.77,327300000,633.77 1996-07-19,643.51,643.51,635.50,638.73,408070000,638.73 1996-07-18,634.07,644.44,633.29,643.56,474460000,643.56 1996-07-17,628.37,636.61,628.37,634.07,513830000,634.07 1996-07-16,629.80,631.99,605.88,628.37,682980000,628.37 1996-07-15,646.19,646.19,629.69,629.80,419020000,629.80 1996-07-12,645.67,647.64,640.21,646.19,396740000,646.19 1996-07-11,656.06,656.06,639.52,645.67,520470000,645.67 1996-07-10,654.75,656.27,648.39,656.06,421350000,656.06 1996-07-09,652.54,656.60,652.54,654.75,400170000,654.75 1996-07-08,657.44,657.65,651.13,652.54,367560000,652.54 1996-07-05,672.40,672.40,657.41,657.44,181470000,657.44 1996-07-03,673.61,673.64,670.21,672.40,336260000,672.40 1996-07-02,675.88,675.88,672.55,673.61,388000000,673.61 1996-07-01,670.63,675.88,670.63,675.88,345750000,675.88 1996-06-28,668.55,672.68,668.55,670.63,470460000,670.63 1996-06-27,664.39,668.90,661.56,668.55,405580000,668.55 1996-06-26,668.48,668.49,663.67,664.39,386520000,664.39 1996-06-25,668.85,670.65,667.29,668.48,391900000,668.48 1996-06-24,666.84,671.07,666.84,668.85,333840000,668.85 1996-06-21,662.10,666.84,662.10,666.84,520340000,666.84 1996-06-20,661.96,664.96,658.75,662.10,441060000,662.10 1996-06-19,662.06,665.62,661.21,661.96,383610000,661.96 1996-06-18,665.16,666.36,661.34,662.06,373290000,662.06 1996-06-17,665.85,668.27,664.09,665.16,298410000,665.16 1996-06-14,667.92,668.40,664.35,665.85,390630000,665.85 1996-06-13,669.04,670.54,665.49,667.92,397620000,667.92 1996-06-12,670.97,673.67,668.77,669.04,397190000,669.04 1996-06-11,672.16,676.72,669.94,670.97,405390000,670.97 1996-06-10,673.31,673.61,670.15,672.16,337480000,672.16 1996-06-07,673.03,673.31,662.48,673.31,445710000,673.31 1996-06-06,678.44,680.32,673.02,673.03,466940000,673.03 1996-06-05,672.56,678.45,672.09,678.44,380360000,678.44 1996-06-04,667.68,672.60,667.68,672.56,386040000,672.56 1996-06-03,669.12,669.12,665.19,667.68,318470000,667.68 1996-05-31,671.70,673.46,667.00,669.12,351750000,669.12 1996-05-30,667.93,673.51,664.56,671.70,381960000,671.70 1996-05-29,672.23,673.73,666.09,667.93,346730000,667.93 1996-05-28,678.51,679.98,671.52,672.23,341480000,672.23 1996-05-24,676.00,679.72,676.00,678.51,329150000,678.51 1996-05-23,678.42,681.10,673.45,676.00,431850000,676.00 1996-05-22,672.76,678.42,671.23,678.42,423670000,678.42 1996-05-21,673.15,675.56,672.26,672.76,409610000,672.76 1996-05-20,668.91,673.66,667.64,673.15,385000000,673.15 1996-05-17,664.85,669.84,664.85,668.91,429140000,668.91 1996-05-16,665.42,667.11,662.79,664.85,392070000,664.85 1996-05-15,665.60,669.82,664.46,665.42,447790000,665.42 1996-05-14,661.51,666.96,661.51,665.60,460440000,665.60 1996-05-13,652.09,662.16,652.09,661.51,394180000,661.51 1996-05-10,645.44,653.00,645.44,652.09,428370000,652.09 1996-05-09,644.77,647.95,643.18,645.44,404310000,645.44 1996-05-08,638.26,644.79,630.07,644.77,495460000,644.77 1996-05-07,640.81,641.40,636.96,638.26,410770000,638.26 1996-05-06,641.63,644.64,636.19,640.81,375820000,640.81 1996-05-03,643.38,648.45,640.23,641.63,434010000,641.63 1996-05-02,654.58,654.58,642.13,643.38,442960000,643.38 1996-05-01,654.17,656.44,652.26,654.58,404620000,654.58 1996-04-30,654.16,654.59,651.05,654.17,393390000,654.17 1996-04-29,653.46,654.71,651.60,654.16,344030000,654.16 1996-04-26,652.87,656.43,651.96,653.46,402530000,653.46 1996-04-25,650.17,654.18,647.06,652.87,462120000,652.87 1996-04-24,651.58,653.37,648.25,650.17,494220000,650.17 1996-04-23,647.89,651.59,647.70,651.58,452690000,651.58 1996-04-22,645.07,650.91,645.07,647.89,395370000,647.89 1996-04-19,643.61,647.32,643.61,645.07,435690000,645.07 1996-04-18,641.61,644.66,640.76,643.61,415150000,643.61 1996-04-17,645.00,645.00,638.71,641.61,465200000,641.61 1996-04-16,642.49,645.57,642.15,645.00,453310000,645.00 1996-04-15,636.71,642.49,636.71,642.49,346370000,642.49 1996-04-12,631.18,637.14,631.18,636.71,413270000,636.71 1996-04-11,633.50,635.26,624.14,631.18,519710000,631.18 1996-04-10,642.19,642.78,631.76,633.50,475150000,633.50 1996-04-09,644.24,646.33,640.84,642.19,426790000,642.19 1996-04-08,655.86,655.86,638.04,644.24,411810000,644.24 1996-04-04,655.88,656.68,654.89,655.86,383400000,655.86 1996-04-03,655.26,655.89,651.81,655.88,386620000,655.88 1996-04-02,653.73,655.27,652.81,655.26,406640000,655.26 1996-04-01,645.50,653.87,645.50,653.73,392120000,653.73 1996-03-29,648.94,650.96,644.89,645.50,413510000,645.50 1996-03-28,648.91,649.58,646.36,648.94,370750000,648.94 1996-03-27,652.97,653.94,647.60,648.91,406280000,648.91 1996-03-26,650.04,654.31,648.15,652.97,400090000,652.97 1996-03-25,650.62,655.50,648.82,650.04,336700000,650.04 1996-03-22,649.19,652.08,649.19,650.62,329390000,650.62 1996-03-21,649.98,651.54,648.10,649.19,367180000,649.19 1996-03-20,651.69,653.13,645.57,649.98,409780000,649.98 1996-03-19,652.65,656.18,649.80,651.69,438300000,651.69 1996-03-18,641.43,652.65,641.43,652.65,437100000,652.65 1996-03-15,640.87,642.87,638.35,641.43,529970000,641.43 1996-03-14,638.55,644.17,638.55,640.87,492630000,640.87 1996-03-13,637.09,640.52,635.19,638.55,413030000,638.55 1996-03-12,640.02,640.02,628.82,637.09,454980000,637.09 1996-03-11,633.50,640.41,629.95,640.02,449500000,640.02 1996-03-08,653.65,653.65,627.63,633.50,546550000,633.50 1996-03-07,652.00,653.65,649.54,653.65,425790000,653.65 1996-03-06,655.79,656.97,651.61,652.00,428220000,652.00 1996-03-05,650.81,655.80,648.77,655.79,445700000,655.79 1996-03-04,644.37,653.54,644.37,650.81,417270000,650.81 1996-03-01,640.43,644.38,635.00,644.37,471480000,644.37 1996-02-29,644.75,646.95,639.01,640.43,453170000,640.43 1996-02-28,647.24,654.39,643.99,644.75,447790000,644.75 1996-02-27,650.46,650.62,643.87,647.24,431340000,647.24 1996-02-26,659.08,659.08,650.16,650.46,399330000,650.46 1996-02-23,658.86,663.00,652.25,659.08,443130000,659.08 1996-02-22,648.10,659.75,648.10,658.86,485470000,658.86 1996-02-21,640.65,648.11,640.65,648.10,431220000,648.10 1996-02-20,647.98,647.98,638.79,640.65,395910000,640.65 1996-02-16,651.32,651.42,646.99,647.98,445570000,647.98 1996-02-15,655.58,656.84,651.15,651.32,415320000,651.32 1996-02-14,660.51,661.53,654.36,655.58,421790000,655.58 1996-02-13,661.45,664.23,657.92,660.51,441540000,660.51 1996-02-12,656.37,662.95,656.34,661.45,397890000,661.45 1996-02-09,656.07,661.08,653.64,656.37,477640000,656.37 1996-02-08,649.93,656.54,647.93,656.07,474970000,656.07 1996-02-07,646.33,649.93,645.59,649.93,462730000,649.93 1996-02-06,641.43,646.67,639.68,646.33,465940000,646.33 1996-02-05,635.84,641.43,633.71,641.43,377760000,641.43 1996-02-02,638.46,639.26,634.29,635.84,420020000,635.84 1996-02-01,636.02,638.46,634.54,638.46,461430000,638.46 1996-01-31,630.15,636.18,629.48,636.02,472210000,636.02 1996-01-30,624.22,630.29,624.22,630.15,464350000,630.15 1996-01-29,621.62,624.22,621.42,624.22,363330000,624.22 1996-01-26,617.03,621.70,615.26,621.62,385700000,621.62 1996-01-25,619.96,620.15,616.62,617.03,453270000,617.03 1996-01-24,612.79,619.96,612.79,619.96,476380000,619.96 1996-01-23,613.40,613.40,610.65,612.79,416910000,612.79 1996-01-22,611.83,613.45,610.95,613.40,398040000,613.40 1996-01-19,608.24,612.92,606.76,611.83,497720000,611.83 1996-01-18,606.37,608.27,604.12,608.24,450410000,608.24 1996-01-17,608.44,609.93,604.70,606.37,458720000,606.37 1996-01-16,599.82,608.44,599.05,608.44,425220000,608.44 1996-01-15,601.81,603.43,598.47,599.82,306180000,599.82 1996-01-12,602.69,604.80,597.46,601.81,383400000,601.81 1996-01-11,598.48,602.71,597.54,602.69,408800000,602.69 1996-01-10,609.45,609.45,597.29,598.48,496830000,598.48 1996-01-09,618.46,619.15,608.21,609.45,417400000,609.45 1996-01-08,616.71,618.46,616.49,618.46,130360000,618.46 1996-01-05,617.70,617.70,612.02,616.71,437110000,616.71 1996-01-04,621.32,624.49,613.96,617.70,512580000,617.70 1996-01-03,620.73,623.25,619.56,621.32,468950000,621.32 1996-01-02,615.93,620.74,613.17,620.73,364180000,620.73 1995-12-29,614.12,615.93,612.36,615.93,321250000,615.93 1995-12-28,614.53,615.50,612.40,614.12,288660000,614.12 1995-12-27,614.30,615.73,613.75,614.53,252300000,614.53 1995-12-26,611.96,614.50,611.96,614.30,217280000,614.30 1995-12-22,610.49,613.50,610.45,611.95,289600000,611.95 1995-12-21,605.94,610.52,605.94,610.49,415810000,610.49 1995-12-20,611.93,614.27,605.93,605.94,437680000,605.94 1995-12-19,606.81,611.94,605.05,611.93,478280000,611.93 1995-12-18,616.34,616.34,606.13,606.81,426270000,606.81 1995-12-15,616.92,617.72,614.46,616.34,636800000,616.34 1995-12-14,621.69,622.88,616.13,616.92,465300000,616.92 1995-12-13,618.78,622.02,618.27,621.69,415290000,621.69 1995-12-12,619.52,619.55,617.68,618.78,349860000,618.78 1995-12-11,617.48,620.90,617.14,619.52,342070000,619.52 1995-12-08,616.17,617.82,614.32,617.48,327900000,617.48 1995-12-07,620.18,620.19,615.21,616.17,379260000,616.17 1995-12-06,617.68,621.11,616.69,620.18,417780000,620.18 1995-12-05,613.68,618.48,613.14,617.68,437360000,617.68 1995-12-04,606.98,613.83,606.84,613.68,405480000,613.68 1995-12-01,605.37,608.11,605.37,606.98,393310000,606.98 1995-11-30,607.64,608.69,605.37,605.37,440050000,605.37 1995-11-29,606.45,607.66,605.47,607.64,398280000,607.64 1995-11-28,601.32,606.45,599.02,606.45,408860000,606.45 1995-11-27,599.97,603.35,599.97,601.32,359130000,601.32 1995-11-24,598.40,600.24,598.40,599.97,125870000,599.97 1995-11-22,600.24,600.71,598.40,598.40,404980000,598.40 1995-11-21,596.85,600.28,595.42,600.24,408320000,600.24 1995-11-20,600.07,600.40,596.17,596.85,333150000,596.85 1995-11-17,597.34,600.14,597.30,600.07,437200000,600.07 1995-11-16,593.96,597.91,593.52,597.34,423280000,597.34 1995-11-15,589.29,593.97,588.36,593.96,376100000,593.96 1995-11-14,592.30,592.30,588.98,589.29,354420000,589.29 1995-11-13,592.72,593.72,590.58,592.30,295840000,592.30 1995-11-10,593.26,593.26,590.39,592.72,298690000,592.72 1995-11-09,591.71,593.90,590.89,593.26,380760000,593.26 1995-11-08,586.32,591.71,586.32,591.71,359780000,591.71 1995-11-07,588.46,588.46,584.24,586.32,364680000,586.32 1995-11-06,590.57,590.64,588.31,588.46,309100000,588.46 1995-11-03,589.72,590.57,588.65,590.57,348500000,590.57 1995-11-02,584.22,589.72,584.22,589.72,397070000,589.72 1995-11-01,581.50,584.24,581.04,584.22,378090000,584.22 1995-10-31,583.25,586.71,581.50,581.50,377390000,581.50 1995-10-30,579.70,583.79,579.70,583.25,319160000,583.25 1995-10-27,576.72,579.71,573.21,579.70,379230000,579.70 1995-10-26,582.47,582.63,572.53,576.72,464270000,576.72 1995-10-25,586.54,587.19,581.41,582.47,433620000,582.47 1995-10-24,585.06,587.31,584.75,586.54,415540000,586.54 1995-10-23,587.46,587.46,583.73,585.06,330750000,585.06 1995-10-20,590.65,590.66,586.78,587.46,389360000,587.46 1995-10-19,587.44,590.66,586.34,590.65,406620000,590.65 1995-10-18,586.78,589.77,586.27,587.44,411270000,587.44 1995-10-17,583.03,586.78,581.90,586.78,356380000,586.78 1995-10-16,584.50,584.86,582.63,583.03,300750000,583.03 1995-10-13,583.10,587.39,583.10,584.50,374680000,584.50 1995-10-12,579.46,583.12,579.46,583.10,344060000,583.10 1995-10-11,577.52,579.52,577.08,579.46,340740000,579.46 1995-10-10,578.37,578.37,571.55,577.52,412710000,577.52 1995-10-09,582.49,582.49,576.35,578.37,275320000,578.37 1995-10-06,582.63,584.54,582.10,582.49,313680000,582.49 1995-10-05,581.47,582.63,579.58,582.63,367480000,582.63 1995-10-04,582.34,582.34,579.91,581.47,339380000,581.47 1995-10-03,581.72,582.34,578.48,582.34,385940000,582.34 1995-10-02,584.41,585.05,580.54,581.72,304990000,581.72 1995-09-29,585.87,587.61,584.00,584.41,335250000,584.41 1995-09-28,581.04,585.88,580.69,585.87,367720000,585.87 1995-09-27,581.41,581.42,574.68,581.04,411300000,581.04 1995-09-26,581.81,584.66,580.65,581.41,363630000,581.41 1995-09-25,581.73,582.14,579.50,581.81,273120000,581.81 1995-09-22,583.00,583.00,578.25,581.73,370790000,581.73 1995-09-21,586.77,586.79,580.91,583.00,367100000,583.00 1995-09-20,584.20,586.77,584.18,586.77,400050000,586.77 1995-09-19,582.78,584.24,580.75,584.20,371170000,584.20 1995-09-18,583.35,583.37,579.36,582.77,326090000,582.77 1995-09-15,583.61,585.07,581.79,583.35,459370000,583.35 1995-09-14,578.77,583.99,578.77,583.61,382880000,583.61 1995-09-13,576.51,579.72,575.47,578.77,384380000,578.77 1995-09-12,573.91,576.51,573.11,576.51,344540000,576.51 1995-09-11,572.68,575.15,572.68,573.91,296840000,573.91 1995-09-08,570.29,572.68,569.27,572.68,317940000,572.68 1995-09-07,570.17,571.11,569.23,570.29,321720000,570.29 1995-09-06,569.17,570.53,569.00,570.17,369540000,570.17 1995-09-05,563.86,569.20,563.84,569.17,332670000,569.17 1995-09-01,561.88,564.62,561.01,563.84,256730000,563.84 1995-08-31,561.09,562.36,560.49,561.88,300920000,561.88 1995-08-30,560.00,561.52,559.49,560.92,329840000,560.92 1995-08-29,559.05,560.01,555.71,560.00,311290000,560.00 1995-08-28,560.10,562.22,557.99,559.05,267860000,559.05 1995-08-25,557.46,561.31,557.46,560.10,255990000,560.10 1995-08-24,557.14,558.63,555.20,557.46,299200000,557.46 1995-08-23,559.52,560.00,557.08,557.14,291890000,557.14 1995-08-22,558.11,559.52,555.87,559.52,290890000,559.52 1995-08-21,559.21,563.34,557.89,558.11,303200000,558.11 1995-08-18,559.04,561.24,558.34,559.21,320490000,559.21 1995-08-17,559.97,559.97,557.42,559.04,354460000,559.04 1995-08-16,558.57,559.98,557.37,559.97,390170000,559.97 1995-08-15,559.74,559.98,555.22,558.57,330070000,558.57 1995-08-14,555.11,559.74,554.76,559.74,264920000,559.74 1995-08-11,557.45,558.50,553.04,555.11,267850000,555.11 1995-08-10,559.71,560.63,556.05,557.45,306660000,557.45 1995-08-09,560.39,561.59,559.29,559.71,303390000,559.71 1995-08-08,560.03,561.53,558.32,560.39,306090000,560.39 1995-08-07,558.94,561.24,558.94,560.03,277050000,560.03 1995-08-04,558.75,559.57,557.91,558.94,314740000,558.94 1995-08-03,558.80,558.80,554.10,558.75,353110000,558.75 1995-08-02,559.64,565.62,557.87,558.80,374330000,558.80 1995-08-01,562.06,562.11,556.67,559.64,332210000,559.64 1995-07-31,562.93,563.49,560.06,562.06,291950000,562.06 1995-07-28,565.22,565.40,562.04,562.93,311590000,562.93 1995-07-27,561.61,565.33,561.61,565.22,356570000,565.22 1995-07-26,561.10,563.78,560.85,561.61,393470000,561.61 1995-07-25,556.63,561.75,556.34,561.10,373200000,561.10 1995-07-24,553.62,557.21,553.62,556.63,315300000,556.63 1995-07-21,553.34,554.73,550.91,553.62,431830000,553.62 1995-07-20,550.98,554.43,549.10,553.54,383380000,553.54 1995-07-19,556.58,558.46,542.51,550.98,489850000,550.98 1995-07-18,562.55,562.72,556.86,558.46,372230000,558.46 1995-07-17,560.34,562.94,559.45,562.72,322540000,562.72 1995-07-14,561.00,561.00,556.41,559.89,312930000,559.89 1995-07-13,560.89,562.00,559.07,561.00,387500000,561.00 1995-07-12,555.27,561.56,554.27,560.89,416360000,560.89 1995-07-11,556.78,557.19,553.80,554.78,376770000,554.78 1995-07-10,556.37,558.48,555.77,557.19,409700000,557.19 1995-07-07,553.90,556.57,553.05,556.37,466540000,556.37 1995-07-06,547.26,553.99,546.59,553.99,420500000,553.99 1995-07-05,547.09,549.98,546.28,547.26,357850000,547.26 1995-07-03,544.75,547.10,544.43,547.09,117900000,547.09 1995-06-30,543.87,546.82,543.51,544.75,311650000,544.75 1995-06-29,544.73,546.25,540.79,543.87,313080000,543.87 1995-06-28,542.43,546.33,540.72,544.73,368060000,544.73 1995-06-27,544.11,547.07,542.19,542.43,346950000,542.43 1995-06-26,549.71,549.79,544.06,544.13,296720000,544.13 1995-06-23,551.07,551.07,548.23,549.71,321660000,549.71 1995-06-22,543.98,551.07,543.98,551.07,421000000,551.07 1995-06-21,544.98,545.93,543.90,543.98,398210000,543.98 1995-06-20,545.22,545.44,543.43,544.98,382370000,544.98 1995-06-19,539.83,545.22,539.83,545.22,322990000,545.22 1995-06-16,537.51,539.98,537.12,539.83,442740000,539.83 1995-06-15,536.48,539.07,535.56,537.12,334700000,537.12 1995-06-14,536.05,536.48,533.83,536.47,330770000,536.47 1995-06-13,530.88,536.23,530.88,536.05,339660000,536.05 1995-06-12,527.94,532.54,527.94,530.88,289920000,530.88 1995-06-09,532.35,532.35,526.00,527.94,327570000,527.94 1995-06-08,533.13,533.56,531.65,532.35,289880000,532.35 1995-06-07,535.55,535.55,531.66,533.13,327790000,533.13 1995-06-06,535.60,537.09,535.14,535.55,340490000,535.55 1995-06-05,532.51,537.73,532.47,535.60,337520000,535.60 1995-06-02,533.49,536.91,529.55,532.51,366000000,532.51 1995-06-01,533.40,534.21,530.05,533.49,345920000,533.49 1995-05-31,523.70,533.41,522.17,533.40,358180000,533.40 1995-05-30,523.65,525.58,521.38,523.58,283020000,523.58 1995-05-26,528.59,528.59,522.51,523.65,291220000,523.65 1995-05-25,528.37,529.04,524.89,528.59,341820000,528.59 1995-05-24,528.59,531.91,525.57,528.61,391770000,528.61 1995-05-23,523.65,528.59,523.65,528.59,362690000,528.59 1995-05-22,519.19,524.34,519.19,523.65,285600000,523.65 1995-05-19,519.58,519.58,517.07,519.19,354010000,519.19 1995-05-18,526.88,526.88,519.58,519.58,351900000,519.58 1995-05-17,528.19,528.42,525.38,527.07,347930000,527.07 1995-05-16,527.74,529.08,526.45,528.19,366180000,528.19 1995-05-15,525.55,527.74,525.00,527.74,316240000,527.74 1995-05-12,524.37,527.05,523.30,525.55,361000000,525.55 1995-05-11,524.33,524.89,522.70,524.37,339900000,524.37 1995-05-10,523.74,524.40,521.53,524.36,381990000,524.36 1995-05-09,523.96,525.99,521.79,523.56,361300000,523.56 1995-05-08,520.09,525.15,519.14,523.96,291810000,523.96 1995-05-05,520.75,522.35,518.28,520.12,342380000,520.12 1995-05-04,520.48,525.40,519.44,520.54,434990000,520.54 1995-05-03,514.93,520.54,514.86,520.48,392370000,520.48 1995-05-02,514.23,515.18,513.03,514.86,302560000,514.86 1995-05-01,514.76,515.60,513.42,514.26,296830000,514.26 1995-04-28,513.64,515.29,510.90,514.71,320440000,514.71 1995-04-27,512.70,513.62,511.63,513.55,350850000,513.55 1995-04-26,511.99,513.04,510.47,512.66,350810000,512.66 1995-04-25,512.80,513.54,511.32,512.10,351790000,512.10 1995-04-24,508.49,513.02,507.44,512.89,326280000,512.89 1995-04-21,505.63,508.49,505.63,508.49,403250000,508.49 1995-04-20,504.92,506.50,503.44,505.29,368450000,505.29 1995-04-19,505.37,505.89,501.19,504.92,378050000,504.92 1995-04-18,506.43,507.65,504.12,505.37,344680000,505.37 1995-04-17,509.23,512.03,505.43,506.13,333930000,506.13 1995-04-13,507.19,509.83,507.17,509.23,301580000,509.23 1995-04-12,505.59,507.17,505.07,507.17,327880000,507.17 1995-04-11,507.24,508.85,505.29,505.53,310660000,505.53 1995-04-10,506.30,507.01,504.61,507.01,260980000,507.01 1995-04-07,506.13,507.19,503.59,506.42,314760000,506.42 1995-04-06,505.63,507.10,505.00,506.08,320460000,506.08 1995-04-05,505.27,505.57,503.17,505.57,315170000,505.57 1995-04-04,501.85,505.26,501.85,505.24,330580000,505.24 1995-04-03,500.70,501.91,500.20,501.85,296430000,501.85 1995-03-31,501.94,502.22,495.70,500.71,353060000,500.71 1995-03-30,503.17,504.66,501.00,502.22,362940000,502.22 1995-03-29,503.92,508.15,500.96,503.12,385940000,503.12 1995-03-28,503.19,503.91,501.83,503.90,320360000,503.90 1995-03-27,500.97,503.20,500.93,503.20,296270000,503.20 1995-03-24,496.07,500.97,496.07,500.97,358370000,500.97 1995-03-23,495.67,496.77,494.19,495.95,318530000,495.95 1995-03-22,495.07,495.67,493.67,495.67,313120000,495.67 1995-03-21,496.15,499.19,494.04,495.07,367110000,495.07 1995-03-20,495.52,496.61,495.27,496.14,301740000,496.14 1995-03-17,495.43,496.67,494.95,495.52,417380000,495.52 1995-03-16,491.87,495.74,491.78,495.41,336670000,495.41 1995-03-15,492.89,492.89,490.83,491.88,309540000,491.88 1995-03-14,490.05,493.69,490.05,492.89,346160000,492.89 1995-03-13,489.57,491.28,489.35,490.05,275280000,490.05 1995-03-10,483.16,490.37,483.16,489.57,382940000,489.57 1995-03-09,483.14,483.74,482.05,483.16,319320000,483.16 1995-03-08,482.12,484.08,481.57,483.14,349780000,483.14 1995-03-07,485.63,485.63,479.70,482.12,355550000,482.12 1995-03-06,485.42,485.70,481.52,485.63,298870000,485.63 1995-03-03,485.13,485.42,483.07,485.42,330840000,485.42 1995-03-02,485.65,485.71,483.19,485.13,330030000,485.13 1995-03-01,487.39,487.83,484.92,485.65,362600000,485.65 1995-02-28,483.81,487.44,483.77,487.39,317220000,487.39 1995-02-27,488.26,488.26,483.18,483.81,285790000,483.81 1995-02-24,486.82,488.28,485.70,488.11,302930000,488.11 1995-02-23,485.07,489.19,485.07,486.91,394280000,486.91 1995-02-22,482.74,486.15,482.45,485.07,339460000,485.07 1995-02-21,481.95,483.26,481.94,482.72,308090000,482.72 1995-02-17,485.15,485.22,481.97,481.97,347970000,481.97 1995-02-16,484.56,485.22,483.05,485.22,360990000,485.22 1995-02-15,482.55,485.54,481.77,484.54,378040000,484.54 1995-02-14,481.65,482.94,480.89,482.55,300720000,482.55 1995-02-13,481.46,482.86,481.07,481.65,256270000,481.65 1995-02-10,480.19,481.96,479.53,481.46,295600000,481.46 1995-02-09,481.19,482.00,479.91,480.19,325570000,480.19 1995-02-08,480.81,482.60,480.40,481.19,318430000,481.19 1995-02-07,481.14,481.32,479.69,480.81,314660000,480.81 1995-02-06,478.64,481.95,478.36,481.14,325660000,481.14 1995-02-03,472.78,479.91,472.78,478.65,441000000,478.65 1995-02-02,470.40,472.79,469.95,472.79,322110000,472.79 1995-02-01,470.42,472.75,469.29,470.40,395310000,470.40 1995-01-31,468.51,471.03,468.18,470.42,411590000,470.42 1995-01-30,470.39,470.52,467.49,468.51,318550000,468.51 1995-01-27,468.32,471.36,468.32,470.39,339510000,470.39 1995-01-26,467.44,468.62,466.90,468.32,304730000,468.32 1995-01-25,465.86,469.51,464.40,467.44,342610000,467.44 1995-01-24,465.81,466.88,465.47,465.86,315430000,465.86 1995-01-23,464.78,466.23,461.14,465.82,325830000,465.82 1995-01-20,466.95,466.99,463.99,464.78,378190000,464.78 1995-01-19,469.72,469.72,466.40,466.95,297220000,466.95 1995-01-18,470.05,470.43,468.03,469.71,344660000,469.71 1995-01-17,469.38,470.15,468.19,470.05,331520000,470.05 1995-01-16,465.97,470.39,465.97,469.38,315810000,469.38 1995-01-13,461.64,466.43,461.64,465.97,336740000,465.97 1995-01-12,461.64,461.93,460.63,461.64,313040000,461.64 1995-01-11,461.68,463.61,458.65,461.66,346310000,461.66 1995-01-10,460.90,464.59,460.90,461.68,352450000,461.68 1995-01-09,460.67,461.77,459.74,460.83,278790000,460.83 1995-01-06,460.38,462.49,459.47,460.68,308070000,460.68 1995-01-05,460.73,461.30,459.75,460.34,309050000,460.34 1995-01-04,459.13,460.72,457.56,460.71,319510000,460.71 1995-01-03,459.21,459.27,457.20,459.11,262450000,459.11 1994-12-30,461.17,462.12,459.24,459.27,256260000,459.27 1994-12-29,460.92,461.81,460.36,461.17,250650000,461.17 1994-12-28,462.47,462.49,459.00,460.86,246260000,460.86 1994-12-27,459.85,462.73,459.85,462.47,211180000,462.47 1994-12-23,459.70,461.32,459.39,459.83,196540000,459.83 1994-12-22,459.62,461.21,459.33,459.68,340330000,459.68 1994-12-21,457.24,461.70,457.17,459.61,379130000,459.61 1994-12-20,458.08,458.45,456.37,457.10,326530000,457.10 1994-12-19,458.78,458.78,456.64,457.91,271850000,457.91 1994-12-16,455.35,458.80,455.35,458.80,481860000,458.80 1994-12-15,454.97,456.84,454.50,455.34,332790000,455.34 1994-12-14,450.05,456.16,450.05,454.97,355000000,454.97 1994-12-13,449.52,451.69,449.43,450.15,307110000,450.15 1994-12-12,446.95,449.48,445.62,449.47,285730000,449.47 1994-12-09,445.45,446.98,442.88,446.96,336440000,446.96 1994-12-08,451.23,452.06,444.59,445.45,362290000,445.45 1994-12-07,453.11,453.11,450.01,451.23,283490000,451.23 1994-12-06,453.29,453.93,450.35,453.11,298930000,453.11 1994-12-05,453.30,455.04,452.06,453.32,258490000,453.32 1994-12-02,448.92,453.31,448.00,453.30,284750000,453.30 1994-12-01,453.55,453.91,447.97,448.92,285920000,448.92 1994-11-30,455.17,457.13,453.27,453.69,298650000,453.69 1994-11-29,454.23,455.17,452.14,455.17,286620000,455.17 1994-11-28,452.26,454.19,451.04,454.16,265480000,454.16 1994-11-25,449.94,452.87,449.94,452.29,118290000,452.29 1994-11-23,450.01,450.61,444.18,449.93,430760000,449.93 1994-11-22,457.95,458.03,450.08,450.09,387270000,450.09 1994-11-21,461.69,463.41,457.55,458.30,293030000,458.30 1994-11-18,463.60,463.84,460.25,461.47,356730000,461.47 1994-11-17,465.71,465.83,461.47,463.57,323190000,463.57 1994-11-16,465.06,466.25,464.28,465.62,296980000,465.62 1994-11-15,466.04,468.51,462.95,465.03,336450000,465.03 1994-11-14,462.44,466.29,462.35,466.04,260380000,466.04 1994-11-11,464.17,464.17,461.45,462.35,220800000,462.35 1994-11-10,465.40,467.79,463.73,464.37,280910000,464.37 1994-11-09,465.65,469.95,463.46,465.40,337780000,465.40 1994-11-08,463.08,467.54,463.07,465.65,290860000,465.65 1994-11-07,462.31,463.56,461.25,463.07,255030000,463.07 1994-11-04,467.96,469.28,462.28,462.28,280560000,462.28 1994-11-03,466.50,468.64,466.40,467.91,285170000,467.91 1994-11-02,468.41,470.92,466.36,466.51,331360000,466.51 1994-11-01,472.26,472.26,467.64,468.42,314940000,468.42 1994-10-31,473.76,474.74,472.33,472.35,302820000,472.35 1994-10-28,465.84,473.78,465.80,473.77,381450000,473.77 1994-10-27,462.68,465.85,462.62,465.85,327790000,465.85 1994-10-26,461.55,463.77,461.22,462.62,322570000,462.62 1994-10-25,460.83,461.95,458.26,461.53,326110000,461.53 1994-10-24,464.89,466.37,460.80,460.83,282800000,460.83 1994-10-21,466.69,466.69,463.83,464.89,315310000,464.89 1994-10-20,470.37,470.37,465.39,466.85,331460000,466.85 1994-10-19,467.69,471.43,465.96,470.28,317030000,470.28 1994-10-18,469.02,469.19,466.54,467.66,259730000,467.66 1994-10-17,469.11,469.88,468.16,468.96,238490000,468.96 1994-10-14,467.78,469.53,466.11,469.10,251770000,469.10 1994-10-13,465.56,471.30,465.56,467.79,337900000,467.79 1994-10-12,465.78,466.70,464.79,465.47,269550000,465.47 1994-10-11,459.04,466.34,459.04,465.79,355540000,465.79 1994-10-10,455.12,459.29,455.12,459.04,213110000,459.04 1994-10-07,452.37,455.67,452.13,455.10,284230000,455.10 1994-10-06,453.52,454.49,452.13,452.36,272620000,452.36 1994-10-05,454.59,454.59,449.27,453.52,359670000,453.52 1994-10-04,461.77,462.46,454.03,454.59,325620000,454.59 1994-10-03,462.69,463.31,460.33,461.74,269130000,461.74 1994-09-30,462.27,465.30,461.91,462.71,291900000,462.71 1994-09-29,464.84,464.84,461.51,462.24,302280000,462.24 1994-09-28,462.10,465.55,462.10,464.84,330020000,464.84 1994-09-27,460.82,462.75,459.83,462.05,290330000,462.05 1994-09-26,459.65,460.87,459.31,460.82,272530000,460.82 1994-09-23,461.27,462.14,459.01,459.67,300060000,459.67 1994-09-22,461.45,463.22,460.96,461.27,305210000,461.27 1994-09-21,463.42,464.01,458.47,461.46,351830000,461.46 1994-09-20,470.83,470.83,463.36,463.36,326050000,463.36 1994-09-19,471.21,473.15,470.68,470.85,277110000,470.85 1994-09-16,474.81,474.81,470.06,471.19,410750000,471.19 1994-09-15,468.80,474.81,468.79,474.81,281920000,474.81 1994-09-14,467.55,468.86,466.82,468.80,297480000,468.80 1994-09-13,466.27,468.76,466.27,467.51,293370000,467.51 1994-09-12,468.18,468.42,466.15,466.21,244680000,466.21 1994-09-09,473.13,473.13,466.55,468.18,293360000,468.18 1994-09-08,470.96,473.40,470.86,473.14,295010000,473.14 1994-09-07,471.86,472.41,470.20,470.99,290330000,470.99 1994-09-06,471.00,471.92,469.64,471.86,199670000,471.86 1994-09-02,473.20,474.89,470.67,470.99,216150000,470.99 1994-09-01,475.49,475.49,471.74,473.17,282830000,473.17 1994-08-31,476.07,477.59,474.43,475.49,354650000,475.49 1994-08-30,474.59,476.61,473.56,476.07,294520000,476.07 1994-08-29,473.89,477.14,473.89,474.59,266080000,474.59 1994-08-26,468.08,474.65,468.08,473.80,305120000,473.80 1994-08-25,469.07,470.12,467.64,468.08,284230000,468.08 1994-08-24,464.51,469.05,464.51,469.03,310510000,469.03 1994-08-23,462.39,466.58,462.39,464.51,307240000,464.51 1994-08-22,463.61,463.61,461.46,462.32,235870000,462.32 1994-08-19,463.25,464.37,461.81,463.68,276630000,463.68 1994-08-18,465.10,465.10,462.30,463.17,287330000,463.17 1994-08-17,465.11,465.91,464.57,465.17,309250000,465.17 1994-08-16,461.22,465.20,459.89,465.01,306640000,465.01 1994-08-15,461.97,463.34,461.21,461.23,223210000,461.23 1994-08-12,458.88,462.27,458.88,461.94,249280000,461.94 1994-08-11,460.31,461.41,456.88,458.88,275690000,458.88 1994-08-10,457.98,460.48,457.98,460.30,279500000,460.30 1994-08-09,457.89,458.16,456.66,457.92,259140000,457.92 1994-08-08,457.08,458.30,457.01,457.89,217680000,457.89 1994-08-05,458.34,458.34,456.08,457.09,230270000,457.09 1994-08-04,461.45,461.49,458.40,458.40,289150000,458.40 1994-08-03,460.65,461.46,459.51,461.45,283840000,461.45 1994-08-02,461.01,462.77,459.70,460.56,294740000,460.56 1994-08-01,458.28,461.01,458.08,461.01,258180000,461.01 1994-07-29,454.25,459.33,454.25,458.26,269560000,458.26 1994-07-28,452.57,454.93,452.30,454.24,245990000,454.24 1994-07-27,453.36,453.38,451.36,452.57,251680000,452.57 1994-07-26,454.25,454.25,452.78,453.36,232670000,453.36 1994-07-25,453.10,454.32,452.76,454.25,213470000,454.25 1994-07-22,452.61,454.03,452.33,453.11,261600000,453.11 1994-07-21,451.60,453.22,451.00,452.61,292120000,452.61 1994-07-20,453.89,454.16,450.69,451.60,267840000,451.60 1994-07-19,455.22,455.30,453.86,453.86,251530000,453.86 1994-07-18,454.41,455.71,453.26,455.22,227460000,455.22 1994-07-15,453.28,454.33,452.80,454.16,275860000,454.16 1994-07-14,448.73,454.33,448.73,453.41,322330000,453.41 1994-07-13,448.03,450.06,447.97,448.73,265840000,448.73 1994-07-12,448.02,448.16,444.65,447.95,252250000,447.95 1994-07-11,449.56,450.24,445.27,448.06,222970000,448.06 1994-07-08,448.38,449.75,446.53,449.55,236520000,449.55 1994-07-07,446.15,448.64,446.15,448.38,259740000,448.38 1994-07-06,446.29,447.28,444.18,446.13,236230000,446.13 1994-07-05,446.20,447.62,445.14,446.37,195410000,446.37 1994-07-01,444.27,446.45,443.58,446.20,199030000,446.20 1994-06-30,447.63,448.61,443.66,444.27,293410000,444.27 1994-06-29,446.05,449.83,446.04,447.63,264430000,447.63 1994-06-28,447.36,448.47,443.08,446.07,267740000,446.07 1994-06-27,442.78,447.76,439.83,447.31,250080000,447.31 1994-06-24,449.63,449.63,442.51,442.80,261260000,442.80 1994-06-23,453.09,454.16,449.43,449.63,256480000,449.63 1994-06-22,451.40,453.91,451.40,453.09,251110000,453.09 1994-06-21,455.48,455.48,449.45,451.34,298730000,451.34 1994-06-20,458.45,458.45,454.46,455.48,229520000,455.48 1994-06-17,461.93,462.16,458.44,458.45,373450000,458.45 1994-06-16,460.61,461.93,459.80,461.93,256390000,461.93 1994-06-15,462.38,463.23,459.95,460.61,269740000,460.61 1994-06-14,459.10,462.52,459.10,462.37,288550000,462.37 1994-06-13,458.67,459.36,457.18,459.10,243640000,459.10 1994-06-10,457.86,459.48,457.36,458.67,222480000,458.67 1994-06-09,457.06,457.87,455.86,457.86,252870000,457.86 1994-06-08,458.21,459.74,455.43,457.06,256000000,457.06 1994-06-07,458.88,459.46,457.65,458.21,234680000,458.21 1994-06-06,460.13,461.87,458.85,458.88,259080000,458.88 1994-06-03,457.65,460.86,456.27,460.13,271490000,460.13 1994-06-02,457.62,458.50,457.26,457.65,271630000,457.65 1994-06-01,456.50,458.29,453.99,457.63,279910000,457.63 1994-05-31,457.32,457.61,455.16,456.50,216700000,456.50 1994-05-27,457.03,457.33,454.67,457.33,186430000,457.33 1994-05-26,456.33,457.77,455.79,457.06,255740000,457.06 1994-05-25,454.84,456.34,452.20,456.34,254420000,456.34 1994-05-24,453.21,456.77,453.21,454.81,280040000,454.81 1994-05-23,454.92,454.92,451.79,453.20,249420000,453.20 1994-05-20,456.48,456.48,454.22,454.92,295180000,454.92 1994-05-19,453.69,456.88,453.00,456.48,303680000,456.48 1994-05-18,449.39,454.45,448.87,453.69,337670000,453.69 1994-05-17,444.49,449.37,443.70,449.37,311280000,449.37 1994-05-16,444.15,445.82,443.62,444.49,234700000,444.49 1994-05-13,443.62,444.72,441.21,444.14,252070000,444.14 1994-05-12,441.50,444.80,441.50,443.75,272770000,443.75 1994-05-11,446.03,446.03,440.78,441.49,277400000,441.49 1994-05-10,442.37,446.84,442.37,446.01,297660000,446.01 1994-05-09,447.82,447.82,441.84,442.32,250870000,442.32 1994-05-06,451.37,451.37,445.64,447.82,291910000,447.82 1994-05-05,451.72,452.82,450.72,451.38,255690000,451.38 1994-05-04,453.04,453.11,449.87,451.72,267940000,451.72 1994-05-03,453.06,453.98,450.51,453.03,288270000,453.03 1994-05-02,450.91,453.57,449.05,453.02,296130000,453.02 1994-04-29,449.07,451.35,447.91,450.91,293970000,450.91 1994-04-28,451.84,452.23,447.97,449.10,325200000,449.10 1994-04-26,452.71,452.79,450.66,451.87,288120000,451.87 1994-04-25,447.64,452.71,447.58,452.71,262320000,452.71 1994-04-22,448.73,449.96,447.16,447.63,295710000,447.63 1994-04-21,441.96,449.14,441.96,448.73,378770000,448.73 1994-04-20,442.54,445.01,439.40,441.96,366540000,441.96 1994-04-19,442.54,444.82,438.83,442.54,323280000,442.54 1994-04-18,446.27,447.87,441.48,442.46,271470000,442.46 1994-04-15,446.38,447.85,445.81,446.18,309550000,446.18 1994-04-14,446.26,447.55,443.57,446.38,275130000,446.38 1994-04-13,447.63,448.57,442.62,446.26,278030000,446.26 1994-04-12,449.83,450.80,447.33,447.57,257990000,447.57 1994-04-11,447.12,450.34,447.10,449.87,243180000,449.87 1994-04-08,450.89,450.89,445.51,447.10,264090000,447.10 1994-04-07,448.11,451.10,446.38,450.88,289280000,450.88 1994-04-06,448.29,449.63,444.98,448.05,302000000,448.05 1994-04-05,439.14,448.29,439.14,448.29,365990000,448.29 1994-04-04,445.66,445.66,435.86,438.92,344390000,438.92 1994-03-31,445.55,447.16,436.16,445.77,403580000,445.77 1994-03-30,452.48,452.49,445.55,445.55,390520000,445.55 1994-03-29,460.00,460.32,452.43,452.48,305360000,452.48 1994-03-28,460.58,461.12,456.10,460.00,287350000,460.00 1994-03-25,464.35,465.29,460.58,460.58,249640000,460.58 1994-03-24,468.57,468.57,462.41,464.35,303740000,464.35 1994-03-23,468.89,470.38,468.52,468.54,281500000,468.54 1994-03-22,468.40,470.47,467.88,468.80,282240000,468.80 1994-03-21,471.06,471.06,467.23,468.54,247380000,468.54 1994-03-18,470.89,471.09,467.83,471.06,462240000,471.06 1994-03-17,469.42,471.05,468.62,470.90,303930000,470.90 1994-03-16,467.04,469.85,465.48,469.42,307640000,469.42 1994-03-15,467.39,468.99,466.04,467.01,303750000,467.01 1994-03-14,466.44,467.60,466.08,467.39,260150000,467.39 1994-03-11,463.86,466.61,462.54,466.44,303890000,466.44 1994-03-10,467.08,467.29,462.46,463.90,369370000,463.90 1994-03-09,465.94,467.42,463.40,467.06,309810000,467.06 1994-03-08,466.92,467.79,465.02,465.88,298110000,465.88 1994-03-07,464.74,468.07,464.74,466.91,285590000,466.91 1994-03-04,463.03,466.16,462.41,464.74,311850000,464.74 1994-03-03,464.81,464.83,462.50,463.01,291790000,463.01 1994-03-02,464.40,464.87,457.49,464.81,361130000,464.81 1994-03-01,467.19,467.43,462.02,464.44,304450000,464.44 1994-02-28,466.07,469.16,466.07,467.14,268690000,467.14 1994-02-25,464.33,466.48,464.33,466.07,273680000,466.07 1994-02-24,470.65,470.65,464.26,464.26,342940000,464.26 1994-02-23,471.48,472.41,469.47,470.69,309910000,470.69 1994-02-22,467.69,471.65,467.58,471.46,270900000,471.46 1994-02-18,470.29,471.09,466.07,467.69,293210000,467.69 1994-02-17,472.79,475.12,468.44,470.34,340030000,470.34 1994-02-16,472.53,474.16,471.94,472.79,295450000,472.79 1994-02-15,470.23,473.41,470.23,472.52,306790000,472.52 1994-02-14,470.18,471.99,469.05,470.23,263190000,470.23 1994-02-11,468.93,471.13,466.89,470.18,213740000,470.18 1994-02-10,472.81,473.13,468.91,468.93,327250000,468.93 1994-02-09,471.05,473.41,471.05,472.77,332670000,472.77 1994-02-08,471.76,472.33,469.50,471.05,318180000,471.05 1994-02-07,469.81,472.09,467.57,471.76,348270000,471.76 1994-02-04,480.68,481.02,469.28,469.81,378380000,469.81 1994-02-03,481.96,481.96,478.71,480.71,318350000,480.71 1994-02-02,479.62,482.23,479.57,482.00,328960000,482.00 1994-02-01,481.60,481.64,479.18,479.62,322510000,479.62 1994-01-31,478.70,482.85,478.70,481.61,322870000,481.61 1994-01-28,477.05,479.75,477.05,478.70,313140000,478.70 1994-01-27,473.20,477.52,473.20,477.05,346500000,477.05 1994-01-26,470.92,473.44,470.72,473.20,304660000,473.20 1994-01-25,471.97,472.56,470.27,470.92,326120000,470.92 1994-01-24,474.72,475.20,471.49,471.97,296900000,471.97 1994-01-21,474.98,475.56,473.72,474.72,346350000,474.72 1994-01-20,474.30,475.00,473.42,474.98,310450000,474.98 1994-01-19,474.25,474.70,472.21,474.30,311370000,474.30 1994-01-18,473.30,475.19,473.29,474.25,308840000,474.25 1994-01-17,474.91,474.91,472.84,473.30,233980000,473.30 1994-01-14,472.50,475.32,472.50,474.91,304920000,474.91 1994-01-13,474.17,474.17,471.80,472.47,277970000,472.47 1994-01-12,474.13,475.06,472.14,474.17,310690000,474.17 1994-01-11,475.27,475.28,473.27,474.13,305490000,474.13 1994-01-10,469.90,475.27,469.55,475.27,319490000,475.27 1994-01-07,467.09,470.26,467.03,469.90,324920000,469.90 1994-01-06,467.55,469.00,467.02,467.12,365960000,467.12 1994-01-05,466.89,467.82,465.92,467.55,400030000,467.55 1994-01-04,465.44,466.89,464.44,466.89,326600000,466.89 1994-01-03,466.51,466.94,464.36,465.44,270140000,465.44 1993-12-31,468.66,470.75,466.45,466.45,168590000,466.45 1993-12-30,470.58,470.58,468.09,468.64,195860000,468.64 1993-12-29,470.88,471.29,469.87,470.58,269570000,470.58 1993-12-28,470.61,471.05,469.43,470.94,200960000,470.94 1993-12-27,467.40,470.55,467.35,470.54,171200000,470.54 1993-12-23,467.30,468.97,467.30,467.38,227240000,467.38 1993-12-22,465.08,467.38,465.08,467.32,272440000,467.32 1993-12-21,465.84,465.92,464.03,465.30,273370000,465.30 1993-12-20,466.38,466.90,465.53,465.85,255900000,465.85 1993-12-17,463.34,466.38,463.34,466.38,363750000,466.38 1993-12-16,461.86,463.98,461.86,463.34,284620000,463.34 1993-12-15,463.06,463.69,461.84,461.84,331770000,461.84 1993-12-14,465.73,466.12,462.46,463.06,275050000,463.06 1993-12-13,463.93,465.71,462.71,465.70,256580000,465.70 1993-12-10,464.18,464.87,462.66,463.93,245620000,463.93 1993-12-09,466.29,466.54,463.87,464.18,287570000,464.18 1993-12-08,465.88,466.73,465.42,466.29,314460000,466.29 1993-12-07,466.43,466.77,465.44,466.76,285690000,466.76 1993-12-06,464.89,466.89,464.40,466.43,292370000,466.43 1993-12-03,463.13,464.89,462.67,464.89,268360000,464.89 1993-12-02,461.89,463.22,461.45,463.11,256370000,463.11 1993-12-01,461.93,464.47,461.63,461.89,293870000,461.89 1993-11-30,461.90,463.62,460.45,461.79,286660000,461.79 1993-11-29,463.06,464.83,461.83,461.90,272710000,461.90 1993-11-26,462.36,463.63,462.36,463.06,90220000,463.06 1993-11-24,461.03,462.90,461.03,462.36,230630000,462.36 1993-11-23,459.13,461.77,458.47,461.03,260400000,461.03 1993-11-22,462.60,462.60,457.08,459.13,280130000,459.13 1993-11-19,463.59,463.60,460.03,462.60,302970000,462.60 1993-11-18,464.83,464.88,461.73,463.62,313490000,463.62 1993-11-17,466.74,467.24,462.73,464.81,316940000,464.81 1993-11-16,463.75,466.74,462.97,466.74,303980000,466.74 1993-11-15,465.39,466.13,463.01,463.75,251030000,463.75 1993-11-12,462.64,465.84,462.64,465.39,326240000,465.39 1993-11-11,463.72,464.96,462.49,462.64,283820000,462.64 1993-11-10,460.40,463.72,459.57,463.72,283450000,463.72 1993-11-09,460.21,463.42,460.21,460.33,276360000,460.33 1993-11-08,459.57,461.54,458.78,460.21,234340000,460.21 1993-11-05,457.49,459.63,454.36,459.57,336890000,459.57 1993-11-04,463.02,463.16,457.26,457.49,323430000,457.49 1993-11-03,468.44,468.61,460.95,463.02,342110000,463.02 1993-11-02,469.10,469.10,466.20,468.44,304780000,468.44 1993-11-01,467.83,469.11,467.33,469.10,256030000,469.10 1993-10-29,467.72,468.20,467.37,467.83,270570000,467.83 1993-10-28,464.52,468.76,464.52,467.73,301220000,467.73 1993-10-27,464.30,464.61,463.36,464.61,279830000,464.61 1993-10-26,464.20,464.32,462.65,464.30,284530000,464.30 1993-10-25,463.27,464.49,462.05,464.20,260310000,464.20 1993-10-22,465.36,467.82,463.27,463.27,301440000,463.27 1993-10-21,466.06,466.64,464.38,465.36,289600000,465.36 1993-10-20,466.21,466.87,464.54,466.07,305670000,466.07 1993-10-19,468.41,468.64,464.80,466.21,304400000,466.21 1993-10-18,469.50,470.04,468.02,468.45,329580000,468.45 1993-10-15,466.83,471.10,466.83,469.50,366110000,469.50 1993-10-14,461.55,466.83,461.55,466.83,352530000,466.83 1993-10-13,461.12,461.98,460.76,461.49,290930000,461.49 1993-10-12,461.04,462.47,460.73,461.12,263970000,461.12 1993-10-11,460.31,461.87,460.31,460.88,183060000,460.88 1993-10-08,459.18,460.99,456.40,460.31,243600000,460.31 1993-10-07,460.71,461.13,459.08,459.18,255210000,459.18 1993-10-06,461.24,462.60,460.26,460.74,277070000,460.74 1993-10-05,461.34,463.15,459.45,461.20,294570000,461.20 1993-10-04,461.28,461.80,460.02,461.34,229380000,461.34 1993-10-01,458.93,461.48,458.35,461.28,256880000,461.28 1993-09-30,460.11,460.56,458.28,458.93,280980000,458.93 1993-09-29,461.60,462.17,459.51,460.11,277690000,460.11 1993-09-28,461.84,462.08,460.91,461.53,243320000,461.53 1993-09-27,457.63,461.81,457.63,461.80,244920000,461.80 1993-09-24,457.74,458.56,456.92,457.63,248270000,457.63 1993-09-23,456.25,458.69,456.25,457.74,275350000,457.74 1993-09-22,452.94,456.92,452.94,456.20,298960000,456.20 1993-09-21,455.05,455.80,449.64,452.95,300310000,452.95 1993-09-20,458.84,459.91,455.00,455.05,231130000,455.05 1993-09-17,459.43,459.43,457.09,458.83,381370000,458.83 1993-09-16,461.54,461.54,459.00,459.43,229700000,459.43 1993-09-15,459.90,461.96,456.31,461.60,294410000,461.60 1993-09-14,461.93,461.93,458.15,459.90,258650000,459.90 1993-09-13,461.70,463.38,461.41,462.06,244970000,462.06 1993-09-10,457.49,461.86,457.49,461.72,269950000,461.72 1993-09-09,456.65,458.11,455.17,457.50,258070000,457.50 1993-09-08,458.52,458.53,453.75,456.65,283100000,456.65 1993-09-07,461.34,462.07,457.95,458.52,229500000,458.52 1993-09-03,461.30,462.05,459.91,461.34,197160000,461.34 1993-09-02,463.13,463.54,461.07,461.30,259870000,461.30 1993-09-01,463.55,463.80,461.77,463.15,245040000,463.15 1993-08-31,461.90,463.56,461.29,463.56,252830000,463.56 1993-08-30,460.54,462.58,460.28,461.90,194180000,461.90 1993-08-27,461.05,461.05,459.19,460.54,196140000,460.54 1993-08-26,460.04,462.87,458.82,461.04,254070000,461.04 1993-08-25,459.75,462.04,459.30,460.13,301650000,460.13 1993-08-24,455.23,459.77,455.04,459.77,270700000,459.77 1993-08-23,456.12,456.12,454.29,455.23,212500000,455.23 1993-08-20,456.51,456.68,454.60,456.16,276800000,456.16 1993-08-19,456.01,456.76,455.20,456.43,293330000,456.43 1993-08-18,453.21,456.99,453.21,456.04,312940000,456.04 1993-08-17,452.38,453.70,451.96,453.13,261320000,453.13 1993-08-16,450.25,453.41,450.25,452.38,233640000,452.38 1993-08-13,448.97,450.25,448.97,450.14,214370000,450.14 1993-08-12,450.47,451.63,447.53,448.96,278530000,448.96 1993-08-11,449.60,451.00,449.60,450.46,268330000,450.46 1993-08-10,450.71,450.71,449.10,449.45,255520000,449.45 1993-08-09,448.68,451.51,448.31,450.72,232750000,450.72 1993-08-06,448.13,449.26,447.87,448.68,221170000,448.68 1993-08-05,448.55,449.61,446.94,448.13,261900000,448.13 1993-08-04,449.27,449.72,447.93,448.54,230040000,448.54 1993-08-03,450.15,450.43,447.59,449.27,253110000,449.27 1993-08-02,448.13,450.15,448.03,450.15,230380000,450.15 1993-07-30,450.19,450.22,446.98,448.13,254420000,448.13 1993-07-29,447.19,450.77,447.19,450.24,261240000,450.24 1993-07-28,448.25,448.61,446.59,447.19,273100000,447.19 1993-07-27,449.00,449.44,446.76,448.24,256750000,448.24 1993-07-26,447.06,449.50,447.04,449.09,222580000,449.09 1993-07-23,444.54,447.10,444.54,447.10,222170000,447.10 1993-07-22,447.18,447.23,443.72,444.51,249630000,444.51 1993-07-21,447.28,447.50,445.84,447.18,278590000,447.18 1993-07-20,446.03,447.63,443.71,447.31,277420000,447.31 1993-07-19,445.75,446.78,444.83,446.03,216370000,446.03 1993-07-16,449.07,449.08,445.66,445.75,263100000,445.75 1993-07-15,450.09,450.12,447.26,449.22,277810000,449.22 1993-07-14,448.08,451.12,448.08,450.08,297430000,450.08 1993-07-13,449.00,450.70,448.07,448.09,236720000,448.09 1993-07-12,448.13,449.11,447.71,448.98,202310000,448.98 1993-07-09,448.64,448.94,446.74,448.11,235210000,448.11 1993-07-08,442.84,448.64,442.84,448.64,282910000,448.64 1993-07-07,441.40,443.63,441.40,442.83,253170000,442.83 1993-07-06,445.86,446.87,441.42,441.43,234810000,441.43 1993-07-02,449.02,449.02,445.20,445.84,220750000,445.84 1993-07-01,450.54,451.15,448.71,449.02,292040000,449.02 1993-06-30,450.69,451.47,450.15,450.53,281120000,450.53 1993-06-29,451.89,451.90,449.67,450.69,276310000,450.69 1993-06-28,447.60,451.90,447.60,451.85,242090000,451.85 1993-06-25,446.62,448.64,446.62,447.60,210430000,447.60 1993-06-24,443.04,447.21,442.50,446.62,267450000,446.62 1993-06-23,445.96,445.96,443.19,443.19,278260000,443.19 1993-06-22,446.25,446.29,444.94,445.93,259530000,445.93 1993-06-21,443.68,446.22,443.68,446.22,223650000,446.22 1993-06-18,448.54,448.59,443.68,443.68,300500000,443.68 1993-06-17,447.43,448.98,446.91,448.54,239810000,448.54 1993-06-16,446.27,447.43,443.61,447.43,267500000,447.43 1993-06-15,447.73,448.28,446.18,446.27,234110000,446.27 1993-06-14,447.26,448.64,447.23,447.71,210440000,447.71 1993-06-11,445.38,448.19,445.38,447.26,256750000,447.26 1993-06-10,445.78,446.22,444.09,445.38,232600000,445.38 1993-06-09,444.71,447.39,444.66,445.78,249030000,445.78 1993-06-08,447.65,447.65,444.31,444.71,240640000,444.71 1993-06-07,450.07,450.75,447.32,447.69,236920000,447.69 1993-06-04,452.43,452.43,448.92,450.06,226440000,450.06 1993-06-03,453.84,453.85,451.12,452.49,285570000,452.49 1993-06-02,453.83,454.53,452.68,453.85,295560000,453.85 1993-06-01,450.23,455.63,450.23,453.83,229690000,453.83 1993-05-28,452.41,452.41,447.67,450.19,207820000,450.19 1993-05-27,453.44,454.55,451.14,452.41,300810000,452.41 1993-05-26,448.85,453.51,448.82,453.44,274230000,453.44 1993-05-25,448.00,449.04,447.70,448.85,222090000,448.85 1993-05-24,445.84,448.44,445.26,448.00,197990000,448.00 1993-05-21,450.59,450.59,444.89,445.84,279120000,445.84 1993-05-20,447.57,450.59,447.36,450.59,289160000,450.59 1993-05-19,440.32,447.86,436.86,447.57,342420000,447.57 1993-05-18,440.39,441.26,437.95,440.32,264300000,440.32 1993-05-17,439.56,440.38,437.83,440.37,227580000,440.37 1993-05-14,439.22,439.82,438.10,439.56,252910000,439.56 1993-05-13,444.75,444.75,439.23,439.23,293920000,439.23 1993-05-12,444.32,445.16,442.87,444.80,255680000,444.80 1993-05-11,442.80,444.57,441.52,444.36,218480000,444.36 1993-05-10,442.34,445.42,442.05,442.80,235580000,442.80 1993-05-07,443.28,443.70,441.69,442.31,223570000,442.31 1993-05-06,444.60,444.81,442.90,443.26,255460000,443.26 1993-05-05,443.98,446.09,443.76,444.52,274240000,444.52 1993-05-04,442.58,445.19,442.45,444.05,268310000,444.05 1993-05-03,440.19,442.59,438.25,442.46,224970000,442.46 1993-04-30,438.89,442.29,438.89,440.19,247460000,440.19 1993-04-29,438.02,438.96,435.59,438.89,249760000,438.89 1993-04-28,438.01,438.80,436.68,438.02,267980000,438.02 1993-04-27,433.52,438.02,433.14,438.01,284140000,438.01 1993-04-26,437.03,438.35,432.30,433.54,283260000,433.54 1993-04-23,439.49,439.49,436.82,437.03,259810000,437.03 1993-04-22,443.55,445.73,439.46,439.46,310390000,439.46 1993-04-21,445.09,445.77,443.08,443.63,287300000,443.63 1993-04-20,447.46,447.46,441.81,445.10,317990000,445.10 1993-04-19,448.94,449.14,445.85,447.46,244710000,447.46 1993-04-16,448.41,449.39,447.67,448.94,305160000,448.94 1993-04-15,448.60,449.11,446.39,448.40,259500000,448.40 1993-04-14,449.22,450.00,448.02,448.66,257340000,448.66 1993-04-13,448.41,450.40,447.66,449.22,286690000,449.22 1993-04-12,441.84,448.37,441.84,448.37,259690000,448.37 1993-04-08,442.71,443.77,440.02,441.84,284370000,441.84 1993-04-07,441.16,442.73,440.50,442.73,300000000,442.73 1993-04-06,442.29,443.38,439.48,441.16,293680000,441.16 1993-04-05,441.42,442.43,440.53,442.29,296080000,442.29 1993-04-02,450.28,450.28,440.71,441.39,323330000,441.39 1993-04-01,451.67,452.63,449.60,450.30,234530000,450.30 1993-03-31,451.97,454.88,451.67,451.67,279190000,451.67 1993-03-30,450.79,452.06,449.63,451.97,231190000,451.97 1993-03-29,447.76,452.81,447.75,450.77,199970000,450.77 1993-03-26,450.91,452.09,447.69,447.78,226650000,447.78 1993-03-25,448.09,451.75,447.93,450.88,251530000,450.88 1993-03-24,448.71,450.90,446.10,448.07,274300000,448.07 1993-03-23,448.88,449.80,448.30,448.76,232730000,448.76 1993-03-22,450.17,450.17,446.08,448.88,233190000,448.88 1993-03-19,451.90,453.32,449.91,450.18,339660000,450.18 1993-03-18,448.36,452.39,448.36,451.89,241180000,451.89 1993-03-17,451.36,451.36,447.99,448.31,241270000,448.31 1993-03-16,451.43,452.36,451.01,451.37,218820000,451.37 1993-03-15,449.83,451.43,449.40,451.43,195930000,451.43 1993-03-12,453.70,453.70,447.04,449.83,255420000,449.83 1993-03-11,456.35,456.76,453.48,453.72,257060000,453.72 1993-03-10,454.40,456.34,452.70,456.33,255610000,456.33 1993-03-09,454.67,455.52,453.68,454.40,290670000,454.40 1993-03-08,446.12,454.71,446.12,454.71,275290000,454.71 1993-03-05,447.34,449.59,445.56,446.11,253480000,446.11 1993-03-04,449.26,449.52,446.72,447.34,234220000,447.34 1993-03-03,447.90,450.00,447.73,449.26,277380000,449.26 1993-03-02,442.00,447.91,441.07,447.90,269750000,447.90 1993-03-01,443.38,444.18,441.34,442.01,232460000,442.01 1993-02-26,442.34,443.77,440.98,443.38,234160000,443.38 1993-02-25,440.70,442.34,439.67,442.34,252860000,442.34 1993-02-24,434.76,440.87,434.68,440.87,316750000,440.87 1993-02-23,435.34,436.84,432.41,434.80,329060000,434.80 1993-02-22,434.21,436.49,433.53,435.24,311570000,435.24 1993-02-19,431.93,434.26,431.68,434.22,310700000,434.22 1993-02-18,433.30,437.79,428.25,431.90,311180000,431.90 1993-02-17,433.93,433.97,430.92,433.30,302210000,433.30 1993-02-16,444.53,444.53,433.47,433.91,332850000,433.91 1993-02-12,447.66,447.70,444.58,444.58,216810000,444.58 1993-02-11,446.21,449.36,446.21,447.66,257190000,447.66 1993-02-10,445.33,446.37,444.24,446.23,251910000,446.23 1993-02-09,448.04,448.04,444.52,445.33,240410000,445.33 1993-02-08,448.94,450.04,447.70,447.85,243400000,447.85 1993-02-05,449.56,449.56,446.95,448.93,324710000,448.93 1993-02-04,447.20,449.86,447.20,449.56,351140000,449.56 1993-02-03,442.56,447.35,442.56,447.20,345410000,447.20 1993-02-02,442.52,442.87,440.76,442.55,271560000,442.55 1993-02-01,438.78,442.52,438.78,442.52,238570000,442.52 1993-01-29,438.67,438.93,436.91,438.78,247200000,438.78 1993-01-28,438.13,439.14,437.30,438.66,256980000,438.66 1993-01-27,439.95,440.04,436.82,438.11,277020000,438.11 1993-01-26,440.05,442.66,439.54,439.95,314110000,439.95 1993-01-25,436.11,440.53,436.11,440.01,288740000,440.01 1993-01-22,435.49,437.81,435.49,436.11,293320000,436.11 1993-01-21,433.37,435.75,432.48,435.49,257620000,435.49 1993-01-20,435.14,436.23,433.37,433.37,268790000,433.37 1993-01-19,436.84,437.70,434.59,435.13,283240000,435.13 1993-01-18,437.13,437.13,435.92,436.84,196030000,436.84 1993-01-15,435.87,439.49,435.84,437.15,309720000,437.15 1993-01-14,433.08,435.96,433.08,435.94,281040000,435.94 1993-01-13,431.03,433.44,429.99,433.03,245360000,433.03 1993-01-12,430.95,431.39,428.19,431.04,239410000,431.04 1993-01-11,429.04,431.04,429.01,430.95,217150000,430.95 1993-01-08,430.73,430.73,426.88,429.05,263470000,429.05 1993-01-07,434.52,435.46,429.76,430.73,304850000,430.73 1993-01-06,434.34,435.17,432.52,434.52,295240000,434.52 1993-01-05,435.38,435.40,433.55,434.34,240350000,434.34 1993-01-04,435.70,437.32,434.48,435.38,201210000,435.38 1992-12-31,438.82,439.59,435.71,435.71,165910000,435.71 1992-12-30,437.98,439.37,437.12,438.82,183930000,438.82 1992-12-29,439.15,442.65,437.60,437.98,213660000,437.98 1992-12-28,439.77,439.77,437.26,439.15,143970000,439.15 1992-12-24,439.03,439.81,439.03,439.77,95240000,439.77 1992-12-23,440.29,441.11,439.03,439.03,234140000,439.03 1992-12-22,440.70,441.64,438.25,440.31,250430000,440.31 1992-12-21,441.26,441.26,439.65,440.70,224680000,440.70 1992-12-18,435.46,441.29,435.46,441.28,389300000,441.28 1992-12-17,431.52,435.44,431.46,435.43,251640000,435.43 1992-12-16,432.58,434.22,430.88,431.52,242130000,431.52 1992-12-15,432.82,433.66,431.92,432.57,227770000,432.57 1992-12-14,433.73,435.26,432.83,432.84,187040000,432.84 1992-12-11,434.64,434.64,433.34,433.73,164510000,433.73 1992-12-10,435.66,435.66,432.65,434.64,240640000,434.64 1992-12-09,436.99,436.99,433.98,435.65,230060000,435.65 1992-12-08,435.31,436.99,434.68,436.99,234330000,436.99 1992-12-07,432.06,435.31,432.06,435.31,217700000,435.31 1992-12-04,429.93,432.89,429.74,432.06,234960000,432.06 1992-12-03,429.98,430.99,428.80,429.91,238050000,429.91 1992-12-02,430.78,430.87,428.61,429.89,247010000,429.89 1992-12-01,431.35,431.47,429.20,430.78,259050000,430.78 1992-11-30,430.19,431.53,429.36,431.35,230150000,431.35 1992-11-27,429.19,431.93,429.17,430.16,106020000,430.16 1992-11-25,427.59,429.41,427.58,429.19,207700000,429.19 1992-11-24,425.14,429.31,424.83,427.59,241540000,427.59 1992-11-23,426.65,426.65,424.95,425.12,192530000,425.12 1992-11-20,423.61,426.98,423.61,426.65,257460000,426.65 1992-11-19,422.86,423.61,422.50,423.61,218720000,423.61 1992-11-18,419.27,423.49,419.24,422.85,219080000,422.85 1992-11-17,420.63,420.97,418.31,419.27,187660000,419.27 1992-11-16,422.44,422.44,420.35,420.68,173600000,420.68 1992-11-13,422.89,422.91,421.04,422.43,192950000,422.43 1992-11-12,422.20,423.10,421.70,422.87,226010000,422.87 1992-11-11,418.62,422.33,418.40,422.20,243750000,422.20 1992-11-10,418.59,419.71,417.98,418.62,223180000,418.62 1992-11-09,417.58,420.13,416.79,418.59,197560000,418.59 1992-11-06,418.35,418.35,417.01,417.58,205310000,417.58 1992-11-05,417.08,418.40,415.58,418.34,219730000,418.34 1992-11-04,419.91,421.07,416.61,417.11,194400000,417.11 1992-11-03,422.75,422.81,418.59,419.92,208140000,419.92 1992-11-02,418.66,422.75,418.12,422.75,203280000,422.75 1992-10-30,420.86,421.13,418.54,418.68,201930000,418.68 1992-10-29,420.15,421.16,419.83,420.86,206550000,420.86 1992-10-28,418.49,420.13,417.56,420.13,203910000,420.13 1992-10-27,418.18,419.20,416.97,418.49,201730000,418.49 1992-10-26,414.09,418.17,413.71,418.16,188060000,418.16 1992-10-23,414.90,416.23,413.68,414.10,199060000,414.10 1992-10-22,415.67,416.81,413.10,414.90,216400000,414.90 1992-10-21,415.53,416.15,414.54,415.67,219100000,415.67 1992-10-20,414.98,417.98,414.49,415.48,258210000,415.48 1992-10-19,411.73,414.98,410.66,414.98,222150000,414.98 1992-10-16,409.60,411.73,407.43,411.73,235920000,411.73 1992-10-15,409.34,411.03,407.92,409.60,213590000,409.60 1992-10-14,409.30,411.52,407.86,409.37,175900000,409.37 1992-10-13,407.44,410.64,406.83,409.30,186650000,409.30 1992-10-12,402.66,407.44,402.66,407.44,126670000,407.44 1992-10-09,407.75,407.75,402.42,402.66,178940000,402.66 1992-10-08,404.29,408.04,404.29,407.75,205000000,407.75 1992-10-07,407.17,408.60,403.91,404.25,184380000,404.25 1992-10-06,407.57,408.56,404.84,407.18,203500000,407.18 1992-10-05,410.47,410.47,396.80,407.57,286550000,407.57 1992-10-02,416.29,416.35,410.45,410.47,188030000,410.47 1992-10-01,417.80,418.67,415.46,416.29,204780000,416.29 1992-09-30,416.79,418.58,416.67,417.80,184470000,417.80 1992-09-29,416.62,417.38,415.34,416.80,170750000,416.80 1992-09-28,414.35,416.62,413.00,416.62,158760000,416.62 1992-09-25,418.47,418.63,412.71,414.35,213670000,414.35 1992-09-24,417.46,419.01,417.46,418.47,187960000,418.47 1992-09-23,417.14,417.88,416.00,417.44,205700000,417.44 1992-09-22,422.14,422.14,417.13,417.14,188810000,417.14 1992-09-21,422.90,422.90,421.18,422.14,153940000,422.14 1992-09-18,419.92,422.93,419.92,422.93,237440000,422.93 1992-09-17,419.92,421.43,419.62,419.93,188270000,419.93 1992-09-16,419.71,422.44,417.77,419.92,231450000,419.92 1992-09-15,425.22,425.22,419.54,419.77,211860000,419.77 1992-09-14,419.65,425.27,419.65,425.27,250940000,425.27 1992-09-11,419.95,420.58,419.13,419.58,180560000,419.58 1992-09-10,416.34,420.52,416.34,419.95,221990000,419.95 1992-09-09,414.44,416.44,414.44,416.36,178800000,416.36 1992-09-08,417.08,417.18,414.30,414.44,161440000,414.44 1992-09-04,417.98,418.62,416.76,417.08,124380000,417.08 1992-09-03,417.98,420.31,417.49,417.98,212500000,417.98 1992-09-02,416.07,418.28,415.31,417.98,187480000,417.98 1992-09-01,414.03,416.07,413.35,416.07,172680000,416.07 1992-08-31,414.87,415.29,413.76,414.03,161480000,414.03 1992-08-28,413.54,414.95,413.38,414.84,152260000,414.84 1992-08-27,413.51,415.83,413.51,413.53,178600000,413.53 1992-08-26,411.65,413.61,410.53,413.51,171860000,413.51 1992-08-25,410.73,411.64,408.30,411.61,202760000,411.61 1992-08-24,414.80,414.80,410.07,410.72,165690000,410.72 1992-08-21,418.27,420.35,413.58,414.85,204800000,414.85 1992-08-20,418.19,418.85,416.93,418.26,183420000,418.26 1992-08-19,421.34,421.62,418.19,418.19,187070000,418.19 1992-08-18,420.74,421.40,419.78,421.34,171750000,421.34 1992-08-17,419.89,421.89,419.44,420.74,152830000,420.74 1992-08-14,417.74,420.40,417.74,419.91,166820000,419.91 1992-08-13,417.78,419.88,416.40,417.73,185750000,417.73 1992-08-12,418.89,419.75,416.43,417.78,176560000,417.78 1992-08-11,419.45,419.72,416.53,418.90,173940000,418.90 1992-08-10,418.87,419.42,417.04,419.42,142480000,419.42 1992-08-07,420.59,423.45,418.51,418.88,190640000,418.88 1992-08-06,422.19,422.36,420.26,420.59,181440000,420.59 1992-08-05,424.35,424.35,421.92,422.19,172450000,422.19 1992-08-04,425.09,425.14,423.10,424.36,166760000,424.36 1992-08-03,424.19,425.09,422.84,425.09,164460000,425.09 1992-07-31,423.92,424.80,422.46,424.21,172920000,424.21 1992-07-30,422.20,423.94,421.57,423.92,193410000,423.92 1992-07-29,417.52,423.02,417.52,422.23,275850000,422.23 1992-07-28,411.55,417.55,411.55,417.52,218060000,417.52 1992-07-27,411.60,412.67,411.27,411.54,164700000,411.54 1992-07-24,412.07,412.07,409.93,411.60,163890000,411.60 1992-07-23,410.93,412.08,409.81,412.08,175490000,412.08 1992-07-22,413.74,413.74,409.95,410.93,190160000,410.93 1992-07-21,413.75,414.92,413.10,413.76,173760000,413.76 1992-07-20,415.62,415.62,410.72,413.75,165760000,413.75 1992-07-17,417.54,417.54,412.96,415.62,192120000,415.62 1992-07-16,417.04,417.93,414.79,417.54,206900000,417.54 1992-07-15,417.68,417.81,416.29,417.10,206560000,417.10 1992-07-14,414.86,417.69,414.33,417.68,195570000,417.68 1992-07-13,414.62,415.86,413.93,414.87,148870000,414.87 1992-07-10,414.23,415.88,413.34,414.62,164770000,414.62 1992-07-09,410.28,414.69,410.26,414.23,207980000,414.23 1992-07-08,409.15,410.28,407.20,410.28,201030000,410.28 1992-07-07,413.83,415.33,408.58,409.16,226050000,409.16 1992-07-06,411.77,413.84,410.46,413.84,186920000,413.84 1992-07-02,412.88,415.71,410.07,411.77,220200000,411.77 1992-07-01,408.20,412.88,408.20,412.88,214250000,412.88 1992-06-30,408.94,409.63,407.85,408.14,195530000,408.14 1992-06-29,403.47,408.96,403.47,408.94,176750000,408.94 1992-06-26,403.12,403.51,401.94,403.45,154430000,403.45 1992-06-25,403.83,405.53,402.01,403.12,182960000,403.12 1992-06-24,404.05,404.76,403.26,403.84,193870000,403.84 1992-06-23,403.40,405.41,403.40,404.04,189190000,404.04 1992-06-22,403.64,403.64,399.92,403.40,169370000,403.40 1992-06-19,400.96,404.23,400.96,403.67,233460000,403.67 1992-06-18,402.26,402.68,400.51,400.96,225600000,400.96 1992-06-17,408.33,408.33,401.98,402.26,227760000,402.26 1992-06-16,410.29,411.40,408.32,408.32,194400000,408.32 1992-06-15,409.76,411.68,408.13,410.29,164080000,410.29 1992-06-12,409.08,411.86,409.08,409.76,181860000,409.76 1992-06-11,407.25,409.05,406.11,409.05,204780000,409.05 1992-06-10,410.06,410.10,406.81,407.25,210750000,407.25 1992-06-09,413.40,413.56,409.30,410.06,191170000,410.06 1992-06-08,413.48,413.95,412.03,413.36,161240000,413.36 1992-06-05,413.26,413.85,410.97,413.48,199050000,413.48 1992-06-04,414.60,414.98,412.97,413.26,204450000,413.26 1992-06-03,413.50,416.54,413.04,414.59,215770000,414.59 1992-06-02,417.30,417.30,413.50,413.50,202560000,413.50 1992-06-01,415.35,417.30,412.44,417.30,180800000,417.30 1992-05-29,416.74,418.36,415.35,415.35,204010000,415.35 1992-05-28,412.17,416.77,411.81,416.74,195300000,416.74 1992-05-27,411.41,412.68,411.06,412.17,182240000,412.17 1992-05-26,414.02,414.02,410.23,411.41,197700000,411.41 1992-05-22,412.61,414.82,412.60,414.02,146710000,414.02 1992-05-21,415.40,415.41,411.57,412.60,184860000,412.60 1992-05-20,416.37,416.83,415.37,415.39,198180000,415.39 1992-05-19,412.82,416.51,412.26,416.37,187130000,416.37 1992-05-18,410.13,413.34,410.13,412.81,151380000,412.81 1992-05-15,413.14,413.14,409.85,410.09,192740000,410.09 1992-05-14,416.45,416.52,411.82,413.14,189150000,413.14 1992-05-13,416.29,417.04,415.86,416.45,175850000,416.45 1992-05-12,418.49,418.68,414.69,416.29,192870000,416.29 1992-05-11,416.05,418.75,416.05,418.49,155730000,418.49 1992-05-08,415.87,416.85,414.41,416.05,168720000,416.05 1992-05-07,416.79,416.84,415.38,415.85,168980000,415.85 1992-05-06,416.84,418.48,416.40,416.79,199950000,416.79 1992-05-05,416.91,418.53,415.77,416.84,200550000,416.84 1992-05-04,412.54,417.84,412.54,416.91,174540000,416.91 1992-05-01,414.95,415.21,409.87,412.53,177390000,412.53 1992-04-30,412.02,414.95,412.02,414.95,223590000,414.95 1992-04-29,409.11,412.31,409.11,412.02,206780000,412.02 1992-04-28,408.45,409.69,406.33,409.11,189220000,409.11 1992-04-27,409.03,409.60,407.64,408.45,172900000,408.45 1992-04-24,411.60,412.48,408.74,409.02,199310000,409.02 1992-04-23,409.81,411.60,406.86,411.60,235860000,411.60 1992-04-22,410.26,411.30,409.23,409.81,218850000,409.81 1992-04-21,410.16,411.09,408.20,410.26,214460000,410.26 1992-04-20,416.05,416.05,407.93,410.18,191980000,410.18 1992-04-16,416.28,416.28,413.40,416.04,233230000,416.04 1992-04-15,412.39,416.28,412.39,416.28,229710000,416.28 1992-04-14,406.08,413.86,406.08,412.39,231130000,412.39 1992-04-13,404.28,406.08,403.90,406.08,143140000,406.08 1992-04-10,400.59,405.12,400.59,404.29,199530000,404.29 1992-04-09,394.50,401.04,394.50,400.64,231430000,400.64 1992-04-08,398.05,398.05,392.41,394.50,249280000,394.50 1992-04-07,405.59,405.75,397.97,398.06,205210000,398.06 1992-04-06,401.54,405.93,401.52,405.59,179910000,405.59 1992-04-03,400.50,401.59,398.21,401.55,188580000,401.55 1992-04-02,404.17,404.63,399.28,400.50,185210000,400.50 1992-04-01,403.67,404.50,400.75,404.23,186530000,404.23 1992-03-31,403.00,405.21,402.22,403.69,182360000,403.69 1992-03-30,403.50,404.30,402.97,403.00,133990000,403.00 1992-03-27,407.86,407.86,402.87,403.50,166140000,403.50 1992-03-26,407.52,409.44,406.75,407.86,176720000,407.86 1992-03-25,408.88,409.87,407.52,407.52,192650000,407.52 1992-03-24,409.91,411.43,407.99,408.88,191610000,408.88 1992-03-23,411.29,411.29,408.87,409.91,157050000,409.91 1992-03-20,409.80,411.30,408.53,411.30,246210000,411.30 1992-03-19,409.15,410.57,409.12,409.80,197310000,409.80 1992-03-18,409.58,410.84,408.23,409.15,191720000,409.15 1992-03-17,406.39,409.72,406.39,409.58,187250000,409.58 1992-03-16,405.85,406.40,403.55,406.39,155950000,406.39 1992-03-13,403.92,406.69,403.92,405.84,177900000,405.84 1992-03-12,404.03,404.72,401.94,403.89,180310000,403.89 1992-03-11,406.88,407.02,402.64,404.03,186330000,404.03 1992-03-10,405.21,409.16,405.21,406.89,203000000,406.89 1992-03-09,404.45,405.64,404.25,405.21,160650000,405.21 1992-03-06,406.51,407.51,403.65,404.44,185190000,404.44 1992-03-05,409.33,409.33,405.42,406.51,205770000,406.51 1992-03-04,412.86,413.27,409.33,409.33,206860000,409.33 1992-03-03,412.45,413.78,411.88,412.85,200890000,412.85 1992-03-02,412.68,413.74,411.52,412.45,180380000,412.45 1992-02-28,413.86,416.07,411.80,412.70,202320000,412.70 1992-02-27,415.35,415.99,413.47,413.86,215110000,413.86 1992-02-26,410.48,415.35,410.48,415.35,241500000,415.35 1992-02-25,412.27,412.27,408.02,410.45,210350000,410.45 1992-02-24,411.46,412.94,410.34,412.27,177540000,412.27 1992-02-21,413.90,414.26,409.72,411.43,261650000,411.43 1992-02-20,408.26,413.90,408.26,413.90,270650000,413.90 1992-02-19,407.38,408.70,406.54,408.26,232970000,408.26 1992-02-18,412.48,413.27,406.34,407.38,234300000,407.38 1992-02-14,413.69,413.84,411.20,412.48,215110000,412.48 1992-02-13,417.13,417.77,412.07,413.69,229360000,413.69 1992-02-12,413.77,418.08,413.36,417.13,237630000,417.13 1992-02-11,413.77,414.38,412.24,413.76,200130000,413.76 1992-02-10,411.07,413.77,411.07,413.77,184410000,413.77 1992-02-07,413.82,415.29,408.04,411.09,231120000,411.09 1992-02-06,413.87,414.55,411.93,413.82,242050000,413.82 1992-02-05,413.88,416.17,413.18,413.84,262440000,413.84 1992-02-04,409.60,413.85,409.28,413.85,233680000,413.85 1992-02-03,408.79,409.95,407.45,409.53,185290000,409.53 1992-01-31,411.65,412.63,408.64,408.78,197620000,408.78 1992-01-30,410.34,412.17,409.26,411.62,194680000,411.62 1992-01-29,414.96,417.83,409.17,410.34,248940000,410.34 1992-01-28,414.98,416.41,414.54,414.96,218400000,414.96 1992-01-27,415.44,416.84,414.48,414.99,190970000,414.99 1992-01-24,414.96,417.27,414.29,415.48,213630000,415.48 1992-01-23,418.13,419.78,414.36,414.96,234580000,414.96 1992-01-22,412.65,418.13,412.49,418.13,228140000,418.13 1992-01-21,416.36,416.39,411.32,412.64,218750000,412.64 1992-01-20,418.86,418.86,415.80,416.36,180900000,416.36 1992-01-17,418.20,419.45,416.00,418.86,287370000,418.86 1992-01-16,420.77,420.85,415.37,418.21,336240000,418.21 1992-01-15,420.45,421.18,418.79,420.77,314830000,420.77 1992-01-14,414.34,420.44,414.32,420.44,265900000,420.44 1992-01-13,415.05,415.36,413.54,414.34,200270000,414.34 1992-01-10,417.62,417.62,413.31,415.10,236130000,415.10 1992-01-09,418.09,420.50,415.85,417.61,292350000,417.61 1992-01-08,417.36,420.23,415.02,418.10,290750000,418.10 1992-01-07,417.96,417.96,415.20,417.40,252780000,417.40 1992-01-06,419.31,419.44,416.92,417.96,251210000,417.96 1992-01-03,417.27,419.79,416.16,419.34,224270000,419.34 1992-01-02,417.03,417.27,411.04,417.26,207570000,417.26 1991-12-31,415.14,418.32,412.73,417.09,247080000,417.09 1991-12-30,406.49,415.14,406.49,415.14,245600000,415.14 1991-12-27,404.84,406.58,404.59,406.46,157950000,406.46 1991-12-26,399.33,404.92,399.31,404.84,149230000,404.84 1991-12-24,396.82,401.79,396.82,399.33,162640000,399.33 1991-12-23,387.05,397.44,386.96,396.82,228900000,396.82 1991-12-20,382.52,388.24,382.52,387.04,316140000,387.04 1991-12-19,383.46,383.46,380.64,382.52,199330000,382.52 1991-12-18,382.74,383.51,380.88,383.48,192410000,383.48 1991-12-17,384.46,385.05,382.60,382.74,191310000,382.74 1991-12-16,384.48,385.84,384.37,384.46,173080000,384.46 1991-12-13,381.55,385.04,381.55,384.47,194470000,384.47 1991-12-12,377.70,381.62,377.70,381.55,192950000,381.55 1991-12-11,377.90,379.42,374.78,377.70,207430000,377.70 1991-12-10,378.26,379.57,376.64,377.90,192920000,377.90 1991-12-09,379.09,381.42,377.67,378.26,174760000,378.26 1991-12-06,377.39,382.39,375.41,379.10,199160000,379.10 1991-12-05,380.07,380.07,376.58,377.39,166350000,377.39 1991-12-04,380.96,381.51,378.07,380.07,187960000,380.07 1991-12-03,381.40,381.48,379.92,380.96,187230000,380.96 1991-12-02,375.11,381.40,371.36,381.40,188410000,381.40 1991-11-29,376.55,376.55,374.65,375.22,76830000,375.22 1991-11-27,377.96,378.11,375.98,376.55,167720000,376.55 1991-11-26,375.34,378.29,371.63,377.96,213810000,377.96 1991-11-25,376.14,377.07,374.00,375.34,175870000,375.34 1991-11-22,380.05,380.05,374.52,376.14,188240000,376.14 1991-11-21,378.53,381.12,377.41,380.06,195130000,380.06 1991-11-20,379.42,381.51,377.84,378.53,192760000,378.53 1991-11-19,385.24,385.24,374.90,379.42,243880000,379.42 1991-11-18,382.62,385.40,379.70,385.24,241940000,385.24 1991-11-15,397.15,397.16,382.62,382.62,239690000,382.62 1991-11-14,397.41,398.22,395.85,397.15,200030000,397.15 1991-11-13,396.74,397.42,394.01,397.41,184480000,397.41 1991-11-12,393.12,397.13,393.12,396.74,198610000,396.74 1991-11-11,392.90,393.57,392.32,393.12,128920000,393.12 1991-11-08,393.72,396.43,392.42,392.89,183260000,392.89 1991-11-07,389.97,393.72,389.97,393.72,205480000,393.72 1991-11-06,388.71,389.97,387.58,389.97,167440000,389.97 1991-11-05,390.28,392.17,388.19,388.71,172090000,388.71 1991-11-04,391.29,391.29,388.09,390.28,155660000,390.28 1991-11-01,392.46,395.10,389.67,391.32,205780000,391.32 1991-10-31,392.96,392.96,391.58,392.45,179680000,392.45 1991-10-30,391.48,393.11,390.78,392.96,195400000,392.96 1991-10-29,389.52,391.70,386.88,391.48,192810000,391.48 1991-10-28,384.20,389.52,384.20,389.52,161630000,389.52 1991-10-25,385.07,386.13,382.97,384.20,167310000,384.20 1991-10-24,387.94,388.32,383.45,385.07,179040000,385.07 1991-10-23,387.83,389.08,386.52,387.94,185390000,387.94 1991-10-22,390.02,391.20,387.40,387.83,194160000,387.83 1991-10-21,392.49,392.49,388.96,390.02,154140000,390.02 1991-10-18,391.92,392.80,391.77,392.50,204090000,392.50 1991-10-17,392.79,393.81,390.32,391.92,206030000,391.92 1991-10-16,391.01,393.29,390.14,392.80,225380000,392.80 1991-10-15,386.47,391.50,385.95,391.01,213540000,391.01 1991-10-14,381.45,386.47,381.45,386.47,130120000,386.47 1991-10-11,380.55,381.46,379.90,381.45,148850000,381.45 1991-10-10,376.80,380.55,376.11,380.55,164240000,380.55 1991-10-09,380.57,380.57,376.35,376.80,186710000,376.80 1991-10-08,379.50,381.23,379.18,380.67,177120000,380.67 1991-10-07,381.22,381.27,379.07,379.50,148430000,379.50 1991-10-04,384.47,385.19,381.24,381.25,164000000,381.25 1991-10-03,388.23,388.23,384.47,384.47,174360000,384.47 1991-10-02,389.20,390.03,387.62,388.26,166380000,388.26 1991-10-01,387.86,389.56,387.86,389.20,163570000,389.20 1991-09-30,385.91,388.29,384.32,387.86,146780000,387.86 1991-09-27,386.49,389.09,384.87,385.90,160660000,385.90 1991-09-26,386.87,388.39,385.30,386.49,158980000,386.49 1991-09-25,387.72,388.25,385.99,386.88,153910000,386.88 1991-09-24,385.92,388.13,384.46,387.71,170350000,387.71 1991-09-23,387.90,388.55,385.76,385.92,145940000,385.92 1991-09-20,387.56,388.82,386.49,387.92,254520000,387.92 1991-09-19,386.94,389.42,386.27,387.56,211010000,387.56 1991-09-18,385.49,386.94,384.28,386.94,141340000,386.94 1991-09-17,385.78,387.13,384.97,385.50,168340000,385.50 1991-09-16,383.59,385.79,382.77,385.78,172560000,385.78 1991-09-13,387.16,387.95,382.85,383.59,169630000,383.59 1991-09-12,385.09,387.34,385.09,387.34,160420000,387.34 1991-09-11,384.56,385.60,383.59,385.09,148000000,385.09 1991-09-10,388.57,388.63,383.78,384.56,143390000,384.56 1991-09-09,389.11,389.34,387.88,388.57,115100000,388.57 1991-09-06,389.14,390.71,387.36,389.10,166560000,389.10 1991-09-05,389.97,390.97,388.49,389.14,162380000,389.14 1991-09-04,392.15,392.62,388.68,389.97,157520000,389.97 1991-09-03,395.43,397.62,392.10,392.15,153600000,392.15 1991-08-30,396.47,396.47,393.60,395.43,143440000,395.43 1991-08-29,396.65,396.82,395.14,396.47,154150000,396.47 1991-08-28,393.06,396.64,393.05,396.64,169890000,396.64 1991-08-27,393.85,393.87,391.77,393.06,144670000,393.06 1991-08-26,394.17,394.39,392.75,393.85,130570000,393.85 1991-08-23,391.33,395.34,390.69,394.17,188870000,394.17 1991-08-22,390.59,391.98,390.21,391.33,173090000,391.33 1991-08-21,379.55,390.59,379.55,390.59,232690000,390.59 1991-08-20,376.47,380.35,376.47,379.43,184260000,379.43 1991-08-19,385.58,385.58,374.09,376.47,230350000,376.47 1991-08-16,389.33,390.41,383.16,385.58,189480000,385.58 1991-08-15,389.91,391.92,389.29,389.33,174690000,389.33 1991-08-14,389.62,391.85,389.13,389.90,124230000,389.90 1991-08-13,388.02,392.12,388.02,389.62,212760000,389.62 1991-08-12,387.11,388.17,385.90,388.02,145440000,388.02 1991-08-09,389.32,389.89,387.04,387.12,143740000,387.12 1991-08-08,390.56,391.80,388.15,389.32,163890000,389.32 1991-08-07,390.62,391.59,389.86,390.56,172220000,390.56 1991-08-06,385.06,390.80,384.29,390.62,174460000,390.62 1991-08-05,387.17,387.17,384.48,385.06,128050000,385.06 1991-08-02,387.12,389.56,386.05,387.18,162270000,387.18 1991-08-01,387.81,387.95,386.48,387.12,170610000,387.12 1991-07-31,386.69,387.81,386.19,387.81,166830000,387.81 1991-07-30,383.15,386.92,383.15,386.69,169010000,386.69 1991-07-29,380.93,383.15,380.45,383.15,136000000,383.15 1991-07-26,380.96,381.76,379.81,380.93,127760000,380.93 1991-07-25,378.64,381.13,378.15,380.96,145800000,380.96 1991-07-24,379.42,380.46,378.29,378.64,158700000,378.64 1991-07-23,382.88,384.86,379.39,379.42,160190000,379.42 1991-07-22,384.21,384.55,381.84,382.88,149050000,382.88 1991-07-19,385.38,385.83,383.65,384.22,190700000,384.22 1991-07-18,381.18,385.37,381.18,385.37,200930000,385.37 1991-07-17,381.50,382.86,381.13,381.18,195460000,381.18 1991-07-16,382.39,382.94,380.80,381.54,182990000,381.54 1991-07-15,380.28,383.00,380.24,382.39,161750000,382.39 1991-07-12,376.97,381.41,375.79,380.25,174770000,380.25 1991-07-11,375.73,377.68,375.51,376.97,157930000,376.97 1991-07-10,376.11,380.35,375.20,375.74,178290000,375.74 1991-07-09,377.94,378.58,375.37,376.11,151820000,376.11 1991-07-08,374.09,377.94,370.92,377.94,138330000,377.94 1991-07-05,373.34,375.51,372.17,374.08,69910000,374.08 1991-07-03,377.47,377.47,372.08,373.33,140580000,373.33 1991-07-02,377.92,377.93,376.62,377.47,157290000,377.47 1991-07-01,371.18,377.92,371.18,377.92,167480000,377.92 1991-06-28,374.40,374.40,367.98,371.16,163770000,371.16 1991-06-27,371.59,374.40,371.59,374.40,163080000,374.40 1991-06-26,370.65,372.73,368.34,371.59,187170000,371.59 1991-06-25,370.94,372.62,369.56,370.65,155710000,370.65 1991-06-24,377.74,377.74,370.73,370.94,137940000,370.94 1991-06-21,375.42,377.75,375.33,377.75,193310000,377.75 1991-06-20,375.09,376.29,373.87,375.42,163980000,375.42 1991-06-19,378.57,378.57,374.36,375.09,156440000,375.09 1991-06-18,380.13,381.83,377.99,378.59,155200000,378.59 1991-06-17,382.30,382.31,380.13,380.13,134230000,380.13 1991-06-14,377.63,382.30,377.63,382.29,167950000,382.29 1991-06-13,376.65,377.90,376.08,377.63,145650000,377.63 1991-06-12,381.05,381.05,374.46,376.65,166140000,376.65 1991-06-11,378.57,381.63,378.57,381.05,161610000,381.05 1991-06-10,379.43,379.75,377.95,378.57,127720000,378.57 1991-06-07,383.63,383.63,378.76,379.43,169570000,379.43 1991-06-06,385.10,385.85,383.13,383.63,168260000,383.63 1991-06-05,387.74,388.23,384.45,385.09,186560000,385.09 1991-06-04,388.06,388.06,385.14,387.74,180450000,387.74 1991-06-03,389.81,389.81,386.97,388.06,173990000,388.06 1991-05-31,386.96,389.85,385.01,389.83,232040000,389.83 1991-05-30,382.79,388.17,382.50,386.96,234440000,386.96 1991-05-29,381.94,383.66,381.37,382.79,188450000,382.79 1991-05-28,377.49,382.10,377.12,381.94,162350000,381.94 1991-05-24,374.97,378.08,374.97,377.49,124640000,377.49 1991-05-23,376.19,378.07,373.55,374.96,173080000,374.96 1991-05-22,375.35,376.50,374.40,376.19,159310000,376.19 1991-05-21,372.28,376.66,372.28,375.35,176620000,375.35 1991-05-20,372.39,373.65,371.26,372.28,109510000,372.28 1991-05-17,372.19,373.01,369.44,372.39,174210000,372.39 1991-05-16,368.57,372.51,368.57,372.19,154460000,372.19 1991-05-15,371.55,372.47,365.83,368.57,193110000,368.57 1991-05-14,375.51,375.53,370.82,371.62,207890000,371.62 1991-05-13,375.74,377.02,374.62,376.76,129620000,376.76 1991-05-10,383.26,383.91,375.61,375.74,172730000,375.74 1991-05-09,378.51,383.56,378.51,383.25,180460000,383.25 1991-05-08,377.33,379.26,376.21,378.51,157240000,378.51 1991-05-07,380.08,380.91,377.31,377.32,153290000,377.32 1991-05-06,380.78,380.78,377.86,380.08,129110000,380.08 1991-05-03,380.52,381.00,378.82,380.80,158150000,380.80 1991-05-02,380.29,382.14,379.82,380.52,187090000,380.52 1991-05-01,375.35,380.46,375.27,380.29,181900000,380.29 1991-04-30,373.66,377.86,373.01,375.34,206230000,375.34 1991-04-29,379.01,380.96,373.66,373.66,149860000,373.66 1991-04-26,379.25,380.11,376.77,379.02,154550000,379.02 1991-04-25,382.89,382.89,378.43,379.25,166940000,379.25 1991-04-24,381.76,383.02,379.99,382.76,166800000,382.76 1991-04-23,380.95,383.55,379.67,381.76,167840000,381.76 1991-04-22,384.19,384.19,380.16,380.95,164410000,380.95 1991-04-19,388.46,388.46,383.90,384.20,195520000,384.20 1991-04-18,390.45,390.97,388.13,388.46,217410000,388.46 1991-04-17,387.62,391.26,387.30,390.45,246930000,390.45 1991-04-16,381.19,387.62,379.64,387.62,214480000,387.62 1991-04-15,380.40,382.32,378.78,381.19,161800000,381.19 1991-04-12,377.65,381.07,376.89,380.40,198610000,380.40 1991-04-11,373.15,379.53,373.15,377.63,196570000,377.63 1991-04-10,373.57,374.83,371.21,373.15,167940000,373.15 1991-04-09,378.65,379.02,373.11,373.56,169940000,373.56 1991-04-08,375.35,378.76,374.69,378.66,138580000,378.66 1991-04-05,379.78,381.12,374.15,375.36,187410000,375.36 1991-04-04,378.94,381.88,377.05,379.77,198120000,379.77 1991-04-03,379.50,381.56,378.49,378.94,213720000,378.94 1991-04-02,371.30,379.50,371.30,379.50,189530000,379.50 1991-04-01,375.22,375.22,370.27,371.30,144010000,371.30 1991-03-28,375.35,376.60,374.40,375.22,150750000,375.22 1991-03-27,376.28,378.48,374.73,375.35,201830000,375.35 1991-03-26,369.83,376.30,369.37,376.30,198720000,376.30 1991-03-25,367.48,371.31,367.46,369.83,153920000,369.83 1991-03-22,366.58,368.22,365.58,367.48,160890000,367.48 1991-03-21,367.94,371.01,366.51,366.58,199830000,366.58 1991-03-20,366.59,368.85,365.80,367.92,196810000,367.92 1991-03-19,372.11,372.11,366.54,366.59,177070000,366.59 1991-03-18,373.59,374.09,369.46,372.11,163100000,372.11 1991-03-15,373.50,374.58,370.21,373.59,237650000,373.59 1991-03-14,374.59,378.28,371.76,373.50,232070000,373.50 1991-03-13,370.03,374.65,370.03,374.57,176000000,374.57 1991-03-12,372.96,374.35,369.55,370.03,176440000,370.03 1991-03-11,374.94,375.10,372.52,372.96,161600000,372.96 1991-03-08,375.91,378.69,374.43,374.95,206850000,374.95 1991-03-07,376.16,377.49,375.58,375.91,197060000,375.91 1991-03-06,376.72,379.66,375.02,376.17,262290000,376.17 1991-03-05,369.33,377.89,369.33,376.72,253700000,376.72 1991-03-04,370.47,371.99,369.07,369.33,199830000,369.33 1991-03-01,367.07,370.47,363.73,370.47,221510000,370.47 1991-02-28,367.73,369.91,365.95,367.07,223010000,367.07 1991-02-27,362.81,368.38,362.81,367.74,211410000,367.74 1991-02-26,367.26,367.26,362.19,362.81,164170000,362.81 1991-02-25,365.65,370.19,365.16,367.26,193820000,367.26 1991-02-22,364.97,370.96,364.23,365.65,218760000,365.65 1991-02-21,365.14,366.79,364.50,364.97,180770000,364.97 1991-02-20,369.37,369.37,364.38,365.14,185680000,365.14 1991-02-19,369.06,370.11,367.05,369.39,189900000,369.39 1991-02-15,364.23,369.49,364.23,369.06,228480000,369.06 1991-02-14,369.02,370.26,362.77,364.22,230750000,364.22 1991-02-13,365.50,369.49,364.64,369.02,209960000,369.02 1991-02-12,368.58,370.54,365.50,365.50,256160000,365.50 1991-02-11,359.36,368.58,359.32,368.58,265350000,368.58 1991-02-08,356.52,359.35,356.02,359.35,187830000,359.35 1991-02-07,358.07,363.43,355.53,356.52,292190000,356.52 1991-02-06,351.26,358.07,349.58,358.07,276940000,358.07 1991-02-05,348.34,351.84,347.21,351.26,290570000,351.26 1991-02-04,343.05,348.71,342.96,348.34,250750000,348.34 1991-02-01,343.91,344.90,340.37,343.05,246670000,343.05 1991-01-31,340.92,343.93,340.47,343.93,204520000,343.93 1991-01-30,335.80,340.91,335.71,340.91,226790000,340.91 1991-01-29,336.03,336.03,334.26,335.84,155740000,335.84 1991-01-28,336.06,337.41,335.81,336.03,141270000,336.03 1991-01-25,334.78,336.92,334.20,336.07,194350000,336.07 1991-01-24,330.21,335.83,330.19,334.78,223150000,334.78 1991-01-23,328.30,331.04,327.93,330.21,168620000,330.21 1991-01-22,331.06,331.26,327.83,328.31,177060000,328.31 1991-01-21,332.23,332.23,328.87,331.06,136290000,331.06 1991-01-18,327.93,332.23,327.08,332.23,226770000,332.23 1991-01-17,316.25,327.97,316.25,327.97,319080000,327.97 1991-01-16,313.73,316.94,312.94,316.17,134560000,316.17 1991-01-15,312.49,313.73,311.84,313.73,110000000,313.73 1991-01-14,315.23,315.23,309.35,312.49,120830000,312.49 1991-01-11,314.53,315.24,313.59,315.23,123050000,315.23 1991-01-10,311.51,314.77,311.51,314.53,124510000,314.53 1991-01-09,314.90,320.73,310.93,311.49,191100000,311.49 1991-01-08,315.44,316.97,313.79,314.90,143390000,314.90 1991-01-07,320.97,320.97,315.44,315.44,130610000,315.44 1991-01-04,321.91,322.35,318.87,321.00,140820000,321.00 1991-01-03,326.46,326.53,321.90,321.91,141450000,321.91 1991-01-02,330.20,330.75,326.45,326.45,126280000,326.45 1990-12-31,328.71,330.23,327.50,330.22,114130000,330.22 1990-12-28,328.29,328.72,327.24,328.72,111030000,328.72 1990-12-27,330.85,331.04,328.23,328.29,102900000,328.29 1990-12-26,329.89,331.69,329.89,330.85,78730000,330.85 1990-12-24,331.74,331.74,329.16,329.90,57200000,329.90 1990-12-21,330.12,332.47,330.12,331.75,233400000,331.75 1990-12-20,330.20,330.74,326.94,330.12,174700000,330.12 1990-12-19,330.04,330.80,329.39,330.20,180380000,330.20 1990-12-18,326.02,330.43,325.75,330.05,176460000,330.05 1990-12-17,326.82,326.82,324.46,326.02,118560000,326.02 1990-12-14,329.34,329.34,325.16,326.82,151010000,326.82 1990-12-13,330.14,330.58,328.77,329.34,162110000,329.34 1990-12-12,326.44,330.36,326.44,330.19,182270000,330.19 1990-12-11,328.88,328.88,325.65,326.44,145330000,326.44 1990-12-10,327.75,328.97,326.15,328.89,138650000,328.89 1990-12-07,329.09,329.39,326.39,327.75,164950000,327.75 1990-12-06,329.94,333.98,328.37,329.07,256380000,329.07 1990-12-05,326.36,329.92,325.66,329.92,205820000,329.92 1990-12-04,324.11,326.77,321.97,326.35,185820000,326.35 1990-12-03,322.23,324.90,322.23,324.10,177000000,324.10 1990-11-30,316.42,323.02,315.42,322.22,192350000,322.22 1990-11-29,317.95,317.95,315.03,316.42,140920000,316.42 1990-11-28,318.11,319.96,317.62,317.95,145490000,317.95 1990-11-27,316.51,318.69,315.80,318.10,147590000,318.10 1990-11-26,315.08,316.51,311.48,316.51,131540000,316.51 1990-11-23,316.03,317.30,315.06,315.10,63350000,315.10 1990-11-21,315.31,316.15,312.42,316.03,140660000,316.03 1990-11-20,319.34,319.34,315.31,315.31,161170000,315.31 1990-11-19,317.15,319.39,317.15,319.34,140950000,319.34 1990-11-16,317.02,318.80,314.99,317.12,165440000,317.12 1990-11-15,320.40,320.40,316.13,317.02,151370000,317.02 1990-11-14,317.66,321.70,317.23,320.40,179310000,320.40 1990-11-13,319.48,319.48,317.26,317.67,160240000,317.67 1990-11-12,313.74,319.77,313.73,319.48,161390000,319.48 1990-11-09,307.61,313.78,307.61,313.74,145160000,313.74 1990-11-08,306.01,309.77,305.03,307.61,155570000,307.61 1990-11-07,311.62,311.62,305.79,306.01,149130000,306.01 1990-11-06,314.59,314.76,311.43,311.62,142660000,311.62 1990-11-05,311.85,314.61,311.41,314.59,147510000,314.59 1990-11-02,307.02,311.94,306.88,311.85,168700000,311.85 1990-11-01,303.99,307.27,301.61,307.02,159270000,307.02 1990-10-31,304.06,305.70,302.33,304.00,156060000,304.00 1990-10-30,301.88,304.36,299.44,304.06,153450000,304.06 1990-10-29,304.74,307.41,300.69,301.88,133980000,301.88 1990-10-26,310.17,310.17,304.71,304.71,130190000,304.71 1990-10-25,312.60,313.71,309.70,310.17,141460000,310.17 1990-10-24,312.36,313.51,310.74,312.60,149290000,312.60 1990-10-23,314.76,315.06,312.06,312.36,146300000,312.36 1990-10-22,312.48,315.83,310.47,314.76,152650000,314.76 1990-10-19,305.74,312.48,305.74,312.48,221480000,312.48 1990-10-18,298.75,305.74,298.75,305.74,204110000,305.74 1990-10-17,298.92,301.50,297.79,298.76,161260000,298.76 1990-10-16,303.23,304.34,298.12,298.92,149570000,298.92 1990-10-15,300.03,304.79,296.41,303.23,164980000,303.23 1990-10-12,295.45,301.68,295.22,300.03,187940000,300.03 1990-10-11,300.39,301.45,294.51,295.46,180060000,295.46 1990-10-10,305.09,306.43,299.21,300.39,169190000,300.39 1990-10-09,313.46,313.46,305.09,305.10,145610000,305.10 1990-10-08,311.50,315.03,311.50,313.48,99470000,313.48 1990-10-05,312.69,314.79,305.76,311.50,153380000,311.50 1990-10-04,311.40,313.40,308.59,312.69,145410000,312.69 1990-10-03,315.21,316.26,310.70,311.40,135490000,311.40 1990-10-02,314.94,319.69,314.94,315.21,188360000,315.21 1990-10-01,306.10,314.94,306.10,314.94,202210000,314.94 1990-09-28,300.97,306.05,295.98,306.05,201010000,306.05 1990-09-27,305.06,307.47,299.10,300.97,182690000,300.97 1990-09-26,308.26,308.28,303.05,305.06,155570000,305.06 1990-09-25,305.46,308.27,304.23,308.26,155940000,308.26 1990-09-24,311.30,311.30,303.58,304.59,164070000,304.59 1990-09-21,311.53,312.17,307.98,311.32,201050000,311.32 1990-09-20,316.60,316.60,310.55,311.48,145100000,311.48 1990-09-19,318.60,319.35,316.25,316.60,147530000,316.60 1990-09-18,317.77,318.85,314.27,318.60,141130000,318.60 1990-09-17,316.83,318.05,315.21,317.77,110600000,317.77 1990-09-14,318.65,318.65,314.76,316.83,133390000,316.83 1990-09-13,322.51,322.51,318.02,318.65,123390000,318.65 1990-09-12,321.04,322.55,319.60,322.54,129890000,322.54 1990-09-11,321.63,322.18,319.60,321.04,113220000,321.04 1990-09-10,323.42,326.53,320.31,321.63,119730000,321.63 1990-09-07,320.46,324.18,319.71,323.40,123800000,323.40 1990-09-06,324.39,324.39,319.37,320.46,125620000,320.46 1990-09-05,323.09,324.52,320.99,324.39,120610000,324.39 1990-09-04,322.56,323.09,319.11,323.09,92940000,323.09 1990-08-31,318.71,322.57,316.59,322.56,96480000,322.56 1990-08-30,324.19,324.57,317.82,318.71,120890000,318.71 1990-08-29,321.34,325.83,320.87,324.19,134240000,324.19 1990-08-28,321.44,322.20,320.25,321.34,127660000,321.34 1990-08-27,311.55,323.11,311.55,321.44,160150000,321.44 1990-08-24,307.06,311.65,306.18,311.51,199040000,311.51 1990-08-23,316.55,316.55,306.56,307.06,250440000,307.06 1990-08-22,321.86,324.15,316.55,316.55,175550000,316.55 1990-08-21,328.51,328.51,318.78,321.86,194630000,321.86 1990-08-20,327.83,329.90,327.07,328.51,129630000,328.51 1990-08-17,332.36,332.36,324.63,327.83,212560000,327.83 1990-08-16,340.06,340.06,332.39,332.39,138850000,332.39 1990-08-15,339.39,341.92,339.38,340.06,136710000,340.06 1990-08-14,338.84,340.96,337.19,339.39,130320000,339.39 1990-08-13,335.39,338.88,332.02,338.84,122820000,338.84 1990-08-10,339.90,339.90,334.22,335.52,145340000,335.52 1990-08-09,338.35,340.56,337.56,339.94,155810000,339.94 1990-08-08,334.83,339.21,334.83,338.35,190400000,338.35 1990-08-07,334.43,338.63,332.22,334.83,231580000,334.83 1990-08-06,344.86,344.86,333.27,334.43,240400000,334.43 1990-08-03,351.48,351.48,338.20,344.86,295880000,344.86 1990-08-02,355.52,355.52,349.73,351.48,253090000,351.48 1990-08-01,356.15,357.35,353.82,355.52,178260000,355.52 1990-07-31,355.55,357.54,353.91,356.15,175380000,356.15 1990-07-30,353.44,355.55,351.15,355.55,146470000,355.55 1990-07-27,355.90,355.94,352.14,353.44,149070000,353.44 1990-07-26,357.09,357.47,353.95,355.91,155040000,355.91 1990-07-25,355.79,357.52,354.80,357.09,163530000,357.09 1990-07-24,355.31,356.09,351.46,355.79,181920000,355.79 1990-07-23,361.61,361.61,350.09,355.31,209030000,355.31 1990-07-20,365.32,366.64,361.58,361.61,177810000,361.61 1990-07-19,364.22,365.32,361.29,365.32,161990000,365.32 1990-07-18,367.52,367.52,362.95,364.22,168760000,364.22 1990-07-17,368.95,369.40,364.99,367.52,176790000,367.52 1990-07-16,367.31,369.78,367.31,368.95,149430000,368.95 1990-07-13,365.45,369.68,365.45,367.31,215600000,367.31 1990-07-12,361.23,365.46,360.57,365.44,213180000,365.44 1990-07-11,356.49,361.23,356.49,361.23,162220000,361.23 1990-07-10,359.52,359.74,356.41,356.49,147630000,356.49 1990-07-09,358.42,360.05,358.11,359.52,119390000,359.52 1990-07-06,355.69,359.02,354.64,358.42,111730000,358.42 1990-07-05,360.16,360.16,354.86,355.68,128320000,355.68 1990-07-03,359.54,360.73,359.44,360.16,130050000,360.16 1990-07-02,358.02,359.58,357.54,359.54,130200000,359.54 1990-06-29,357.64,359.09,357.30,358.02,145510000,358.02 1990-06-28,355.16,357.63,355.16,357.63,136120000,357.63 1990-06-27,352.06,355.89,351.23,355.14,146620000,355.14 1990-06-26,352.32,356.09,351.85,352.06,141420000,352.06 1990-06-25,355.42,356.41,351.91,352.31,133100000,352.31 1990-06-22,360.52,363.20,355.31,355.43,172570000,355.43 1990-06-21,359.10,360.88,357.63,360.47,138570000,360.47 1990-06-20,358.47,359.91,357.00,359.10,137420000,359.10 1990-06-19,356.88,358.90,356.18,358.47,134930000,358.47 1990-06-18,362.91,362.91,356.88,356.88,133470000,356.88 1990-06-15,362.89,363.14,360.71,362.91,205130000,362.91 1990-06-14,364.90,364.90,361.64,362.90,135770000,362.90 1990-06-13,366.25,367.09,364.51,364.90,158910000,364.90 1990-06-12,361.63,367.27,361.15,366.25,157100000,366.25 1990-06-11,358.71,361.63,357.70,361.63,119550000,361.63 1990-06-08,363.15,363.49,357.68,358.71,142600000,358.71 1990-06-07,365.92,365.92,361.60,363.15,160360000,363.15 1990-06-06,366.64,366.64,364.42,364.96,164030000,364.96 1990-06-05,367.40,368.78,365.49,366.64,199720000,366.64 1990-06-04,363.16,367.85,362.43,367.40,175520000,367.40 1990-06-01,361.26,363.52,361.21,363.16,187860000,363.16 1990-05-31,360.86,361.84,360.23,361.23,165690000,361.23 1990-05-30,360.65,362.26,360.00,360.86,199540000,360.86 1990-05-29,354.58,360.65,354.55,360.65,137410000,360.65 1990-05-25,358.41,358.41,354.32,354.58,120250000,354.58 1990-05-24,359.29,359.56,357.87,358.41,155140000,358.41 1990-05-23,358.43,359.29,356.99,359.29,172330000,359.29 1990-05-22,358.00,360.50,356.09,358.43,203350000,358.43 1990-05-21,354.64,359.07,353.78,358.00,166280000,358.00 1990-05-18,354.47,354.64,352.52,354.64,162520000,354.64 1990-05-17,354.00,356.92,354.00,354.47,164770000,354.47 1990-05-16,354.27,354.68,351.95,354.00,159810000,354.00 1990-05-15,354.75,355.09,352.84,354.28,165730000,354.28 1990-05-14,352.00,358.41,351.95,354.75,225410000,354.75 1990-05-11,343.82,352.31,343.82,352.00,234040000,352.00 1990-05-10,342.87,344.98,342.77,343.82,158460000,343.82 1990-05-09,342.01,343.08,340.90,342.86,152220000,342.86 1990-05-08,340.53,342.03,340.17,342.01,144230000,342.01 1990-05-07,338.39,341.07,338.11,340.53,132760000,340.53 1990-05-04,335.58,338.46,335.17,338.39,140550000,338.39 1990-05-03,334.48,337.02,334.47,335.57,145560000,335.57 1990-05-02,332.25,334.48,332.15,334.48,141610000,334.48 1990-05-01,330.80,332.83,330.80,332.25,149020000,332.25 1990-04-30,329.11,331.31,327.76,330.80,122750000,330.80 1990-04-27,332.92,333.57,328.71,329.11,130630000,329.11 1990-04-26,332.03,333.76,330.67,332.92,141330000,332.92 1990-04-25,330.36,332.74,330.36,332.03,133480000,332.03 1990-04-24,331.05,332.97,329.71,330.36,137360000,330.36 1990-04-23,335.12,335.12,330.09,331.05,136150000,331.05 1990-04-20,338.09,338.52,333.41,335.12,174260000,335.12 1990-04-19,340.72,340.72,337.59,338.09,152930000,338.09 1990-04-18,344.68,345.33,340.11,340.72,147130000,340.72 1990-04-17,344.74,345.19,342.06,344.68,127990000,344.68 1990-04-16,344.34,347.30,344.10,344.74,142810000,344.74 1990-04-12,341.92,344.79,341.91,344.34,142470000,344.34 1990-04-11,342.07,343.00,341.26,341.92,141080000,341.92 1990-04-10,341.37,342.41,340.62,342.07,136020000,342.07 1990-04-09,340.08,341.83,339.88,341.37,114970000,341.37 1990-04-06,340.73,341.73,338.94,340.08,137490000,340.08 1990-04-05,341.09,342.85,340.63,340.73,144170000,340.73 1990-04-04,343.64,344.12,340.40,341.09,159530000,341.09 1990-04-03,338.70,343.76,338.70,343.64,154310000,343.64 1990-04-02,339.94,339.94,336.33,338.70,124360000,338.70 1990-03-30,340.79,341.41,338.21,339.94,139340000,339.94 1990-03-29,342.00,342.07,339.77,340.79,132190000,340.79 1990-03-28,341.50,342.58,340.60,342.00,142300000,342.00 1990-03-27,337.63,341.50,337.03,341.50,131610000,341.50 1990-03-26,337.22,339.74,337.22,337.63,116110000,337.63 1990-03-23,335.69,337.58,335.69,337.22,132070000,337.22 1990-03-22,339.74,339.77,333.62,335.69,175930000,335.69 1990-03-21,341.57,342.34,339.56,339.74,130990000,339.74 1990-03-20,343.53,344.49,340.87,341.57,177320000,341.57 1990-03-19,341.91,343.76,339.12,343.53,142300000,343.53 1990-03-16,338.07,341.91,338.07,341.91,222520000,341.91 1990-03-15,336.87,338.91,336.87,338.07,144410000,338.07 1990-03-14,336.00,337.63,334.93,336.87,145060000,336.87 1990-03-13,338.67,338.67,335.36,336.00,145440000,336.00 1990-03-12,337.93,339.08,336.14,338.67,114790000,338.67 1990-03-09,340.12,340.27,336.84,337.93,150410000,337.93 1990-03-08,336.95,340.66,336.95,340.27,170900000,340.27 1990-03-07,337.93,338.84,336.33,336.95,163580000,336.95 1990-03-06,333.74,337.93,333.57,337.93,143640000,337.93 1990-03-05,335.54,336.38,333.49,333.74,140110000,333.74 1990-03-02,332.74,335.54,332.72,335.54,164330000,335.54 1990-03-01,331.89,334.40,331.08,332.74,157930000,332.74 1990-02-28,330.26,333.48,330.16,331.89,184400000,331.89 1990-02-27,328.68,331.94,328.47,330.26,152590000,330.26 1990-02-26,324.16,328.67,323.98,328.67,148900000,328.67 1990-02-23,325.70,326.15,322.10,324.15,148490000,324.15 1990-02-22,327.67,330.98,325.70,325.70,184320000,325.70 1990-02-21,327.91,328.17,324.47,327.67,159240000,327.67 1990-02-20,332.72,332.72,326.26,327.99,147300000,327.99 1990-02-16,334.89,335.64,332.42,332.72,166840000,332.72 1990-02-15,332.01,335.21,331.61,334.89,174620000,334.89 1990-02-14,331.02,333.20,330.64,332.01,138530000,332.01 1990-02-13,330.08,331.61,327.92,331.02,144490000,331.02 1990-02-12,333.62,333.62,329.97,330.08,118390000,330.08 1990-02-09,333.02,334.60,332.41,333.62,146910000,333.62 1990-02-08,333.75,336.09,332.00,332.96,176240000,332.96 1990-02-07,329.66,333.76,326.55,333.75,186710000,333.75 1990-02-06,331.85,331.86,328.20,329.66,134070000,329.66 1990-02-05,330.92,332.16,330.45,331.85,130950000,331.85 1990-02-02,328.79,332.10,328.09,330.92,164400000,330.92 1990-02-01,329.08,329.86,327.76,328.79,154580000,328.79 1990-01-31,322.98,329.08,322.98,329.08,189660000,329.08 1990-01-30,325.20,325.73,319.83,322.98,186030000,322.98 1990-01-29,325.80,327.31,321.79,325.20,150770000,325.20 1990-01-26,326.09,328.58,321.44,325.80,198190000,325.80 1990-01-25,330.26,332.33,325.33,326.08,172270000,326.08 1990-01-24,331.61,331.71,324.17,330.26,207830000,330.26 1990-01-23,330.38,332.76,328.67,331.61,179300000,331.61 1990-01-22,339.14,339.96,330.28,330.38,148380000,330.38 1990-01-19,338.19,340.48,338.19,339.15,185590000,339.15 1990-01-18,337.40,338.38,333.98,338.19,178590000,338.19 1990-01-17,340.77,342.01,336.26,337.40,170470000,337.40 1990-01-16,337.00,340.75,333.37,340.75,186070000,340.75 1990-01-15,339.93,339.94,336.57,337.00,140590000,337.00 1990-01-12,348.53,348.53,339.49,339.93,183880000,339.93 1990-01-11,347.31,350.14,347.31,348.53,154390000,348.53 1990-01-10,349.62,349.62,344.32,347.31,175990000,347.31 1990-01-09,353.83,354.17,349.61,349.62,155210000,349.62 1990-01-08,352.20,354.24,350.54,353.79,140110000,353.79 1990-01-05,355.67,355.67,351.35,352.20,158530000,352.20 1990-01-04,358.76,358.76,352.89,355.67,177000000,355.67 1990-01-03,359.69,360.59,357.89,358.76,192330000,358.76 1990-01-02,353.40,359.69,351.98,359.69,162070000,359.69 1989-12-29,350.68,353.41,350.67,353.40,145940000,353.40 1989-12-28,348.80,350.68,348.76,350.67,128030000,350.67 1989-12-27,346.84,349.12,346.81,348.81,133740000,348.81 1989-12-26,347.42,347.87,346.53,346.81,77610000,346.81 1989-12-22,344.78,347.53,344.76,347.42,120980000,347.42 1989-12-21,342.84,345.03,342.84,344.78,175150000,344.78 1989-12-20,342.50,343.70,341.79,342.84,176520000,342.84 1989-12-19,343.69,343.74,339.63,342.46,186060000,342.46 1989-12-18,350.14,350.88,342.19,343.69,184750000,343.69 1989-12-15,350.97,351.86,346.08,350.14,240390000,350.14 1989-12-14,352.74,352.75,350.08,350.93,178700000,350.93 1989-12-13,351.70,354.10,351.65,352.75,184660000,352.75 1989-12-12,348.56,352.21,348.41,351.73,176820000,351.73 1989-12-11,348.68,348.74,346.39,348.56,147130000,348.56 1989-12-08,347.60,349.60,347.59,348.69,144910000,348.69 1989-12-07,348.55,349.84,346.00,347.59,161980000,347.59 1989-12-06,349.58,349.94,347.91,348.55,145850000,348.55 1989-12-05,351.41,352.24,349.58,349.58,154640000,349.58 1989-12-04,350.63,351.51,350.32,351.41,150360000,351.41 1989-12-01,346.01,351.88,345.99,350.63,199200000,350.63 1989-11-30,343.60,346.50,343.57,345.99,153200000,345.99 1989-11-29,345.77,345.77,343.36,343.60,147270000,343.60 1989-11-28,345.61,346.33,344.41,345.77,153770000,345.77 1989-11-27,343.98,346.24,343.97,345.61,149390000,345.61 1989-11-24,341.92,344.24,341.91,343.97,86290000,343.97 1989-11-22,339.59,341.92,339.59,341.91,145730000,341.91 1989-11-21,339.35,340.21,337.53,339.59,147900000,339.59 1989-11-20,341.61,341.90,338.29,339.35,128170000,339.35 1989-11-17,340.58,342.24,339.85,341.61,151020000,341.61 1989-11-16,340.54,341.02,338.93,340.58,148370000,340.58 1989-11-15,338.00,340.54,337.14,340.54,155130000,340.54 1989-11-14,339.55,340.41,337.06,337.99,143170000,337.99 1989-11-13,339.08,340.51,337.93,339.55,140750000,339.55 1989-11-10,336.57,339.10,336.57,339.10,131800000,339.10 1989-11-09,338.15,338.73,336.21,336.57,143390000,336.57 1989-11-08,334.81,339.41,334.81,338.15,170150000,338.15 1989-11-07,332.61,334.82,330.91,334.81,163000000,334.81 1989-11-06,337.61,337.62,332.33,332.61,135480000,332.61 1989-11-03,338.48,339.67,337.37,337.62,131500000,337.62 1989-11-02,341.20,341.20,336.61,338.48,152440000,338.48 1989-11-01,340.36,341.74,339.79,341.20,154240000,341.20 1989-10-31,335.08,340.86,335.07,340.36,176100000,340.36 1989-10-30,335.06,337.04,334.48,335.07,126630000,335.07 1989-10-27,337.93,337.97,333.26,335.06,170330000,335.06 1989-10-26,342.50,342.50,337.20,337.93,175240000,337.93 1989-10-25,343.70,344.51,341.96,342.50,155650000,342.50 1989-10-24,344.83,344.83,335.13,343.70,237960000,343.70 1989-10-23,347.11,348.19,344.22,344.83,135860000,344.83 1989-10-20,347.04,347.57,344.47,347.16,164830000,347.16 1989-10-19,341.76,348.82,341.76,347.13,198120000,347.13 1989-10-18,341.16,343.39,339.03,341.76,166900000,341.76 1989-10-17,342.84,342.85,335.69,341.16,224070000,341.16 1989-10-16,333.65,342.87,327.12,342.85,416290000,342.85 1989-10-13,355.39,355.53,332.81,333.65,251170000,333.65 1989-10-12,356.99,356.99,354.91,355.39,160120000,355.39 1989-10-11,359.13,359.13,356.08,356.99,164070000,356.99 1989-10-10,359.80,360.44,358.11,359.13,147560000,359.13 1989-10-09,358.76,359.86,358.06,359.80,86810000,359.80 1989-10-06,356.97,359.05,356.97,358.78,172520000,358.78 1989-10-05,356.94,357.63,356.28,356.97,177890000,356.97 1989-10-04,354.71,357.49,354.71,356.94,194590000,356.94 1989-10-03,350.87,354.73,350.85,354.71,182550000,354.71 1989-10-02,349.15,350.99,348.35,350.87,127410000,350.87 1989-09-29,348.60,350.31,348.12,349.15,155300000,349.15 1989-09-28,345.10,348.61,345.10,348.60,164240000,348.60 1989-09-27,344.33,345.47,342.85,345.10,158400000,345.10 1989-09-26,344.23,347.02,344.13,344.33,158350000,344.33 1989-09-25,347.05,347.05,343.70,344.23,121130000,344.23 1989-09-22,345.70,347.57,345.69,347.05,133350000,347.05 1989-09-21,346.47,348.46,344.96,345.70,146930000,345.70 1989-09-20,346.55,347.27,346.18,346.47,136640000,346.47 1989-09-19,346.73,348.17,346.44,346.55,141610000,346.55 1989-09-18,345.06,346.84,344.60,346.73,136940000,346.73 1989-09-15,343.16,345.06,341.37,345.06,234860000,345.06 1989-09-14,345.46,345.61,342.55,343.16,149250000,343.16 1989-09-13,348.70,350.10,345.46,345.46,175330000,345.46 1989-09-12,347.66,349.46,347.50,348.70,142140000,348.70 1989-09-11,348.76,348.76,345.91,347.66,126020000,347.66 1989-09-08,348.35,349.18,345.74,348.76,154090000,348.76 1989-09-07,349.24,350.31,348.15,348.35,160160000,348.35 1989-09-06,352.56,352.56,347.98,349.24,161800000,349.24 1989-09-05,353.73,354.13,351.82,352.56,145180000,352.56 1989-09-01,351.45,353.90,350.88,353.73,133300000,353.73 1989-08-31,350.65,351.45,350.21,351.45,144820000,351.45 1989-08-30,349.84,352.27,348.66,350.65,174350000,350.65 1989-08-29,352.09,352.12,348.86,349.84,175210000,349.84 1989-08-28,350.52,352.09,349.08,352.09,131180000,352.09 1989-08-25,351.52,352.73,350.09,350.52,165930000,350.52 1989-08-24,344.70,351.52,344.70,351.52,225520000,351.52 1989-08-23,341.19,344.80,341.19,344.70,159640000,344.70 1989-08-22,340.67,341.25,339.00,341.19,141930000,341.19 1989-08-21,346.03,346.25,340.55,340.67,136800000,340.67 1989-08-18,344.45,346.03,343.89,346.03,145810000,346.03 1989-08-17,345.66,346.39,342.97,344.45,157560000,344.45 1989-08-16,344.71,346.37,344.71,345.66,150060000,345.66 1989-08-15,343.06,345.03,343.05,344.71,148770000,344.71 1989-08-14,344.71,345.44,341.96,343.06,142010000,343.06 1989-08-11,348.28,351.18,344.01,344.74,197550000,344.74 1989-08-10,346.94,349.78,345.31,348.25,198660000,348.25 1989-08-09,349.30,351.00,346.86,346.94,209900000,346.94 1989-08-08,349.41,349.84,348.28,349.35,200340000,349.35 1989-08-07,343.92,349.42,343.91,349.41,197580000,349.41 1989-08-04,344.74,345.42,342.60,343.92,169750000,343.92 1989-08-03,344.34,345.22,343.81,344.74,168690000,344.74 1989-08-02,343.75,344.34,342.47,344.34,181760000,344.34 1989-08-01,346.08,347.99,342.93,343.75,225280000,343.75 1989-07-31,342.13,346.08,342.02,346.08,166650000,346.08 1989-07-28,341.94,342.96,341.30,342.15,180610000,342.15 1989-07-27,338.05,342.00,338.05,341.99,213680000,341.99 1989-07-26,333.88,338.05,333.19,338.05,188270000,338.05 1989-07-25,333.67,336.29,332.60,333.88,179270000,333.88 1989-07-24,335.90,335.90,333.44,333.67,136260000,333.67 1989-07-21,333.50,335.91,332.46,335.90,174880000,335.90 1989-07-20,335.74,337.40,333.22,333.51,204590000,333.51 1989-07-19,331.37,335.73,331.35,335.73,215740000,335.73 1989-07-18,332.42,332.44,330.75,331.35,152350000,331.35 1989-07-17,331.78,333.02,331.02,332.44,131960000,332.44 1989-07-14,329.96,331.89,327.13,331.84,183480000,331.84 1989-07-13,329.81,330.37,329.08,329.95,153820000,329.95 1989-07-12,328.78,330.39,327.92,329.81,160550000,329.81 1989-07-11,327.07,330.42,327.07,328.78,171590000,328.78 1989-07-10,324.93,327.07,324.91,327.07,131870000,327.07 1989-07-07,321.55,325.87,321.08,324.91,166430000,324.91 1989-07-06,320.64,321.55,320.45,321.55,140450000,321.55 1989-07-05,319.23,321.22,317.26,320.64,127710000,320.64 1989-07-03,317.98,319.27,317.27,319.23,68870000,319.23 1989-06-30,319.67,319.97,314.38,317.98,170490000,317.98 1989-06-29,325.81,325.81,319.54,319.68,167100000,319.68 1989-06-28,328.44,328.44,324.30,325.81,158470000,325.81 1989-06-27,326.60,329.19,326.59,328.44,171090000,328.44 1989-06-26,328.00,328.15,326.31,326.60,143600000,326.60 1989-06-23,322.32,328.00,322.32,328.00,198720000,328.00 1989-06-22,320.48,322.34,320.20,322.32,176510000,322.32 1989-06-21,321.25,321.87,319.25,320.48,168830000,320.48 1989-06-20,321.89,322.78,321.03,321.25,167650000,321.25 1989-06-19,321.35,321.89,320.40,321.89,130720000,321.89 1989-06-16,319.96,321.36,318.69,321.35,244510000,321.35 1989-06-15,323.83,323.83,319.21,320.08,179480000,320.08 1989-06-14,323.91,324.89,322.80,323.83,170540000,323.83 1989-06-13,326.24,326.24,322.96,323.91,164870000,323.91 1989-06-12,326.69,326.69,323.73,326.24,151460000,326.24 1989-06-09,326.75,327.32,325.16,326.69,173240000,326.69 1989-06-08,326.95,327.37,325.92,326.75,212310000,326.75 1989-06-07,324.24,327.39,324.24,326.95,213710000,326.95 1989-06-06,322.03,324.48,321.27,324.24,187570000,324.24 1989-06-05,325.52,325.93,322.02,322.03,163420000,322.03 1989-06-02,321.97,325.63,321.97,325.52,229140000,325.52 1989-06-01,320.51,322.57,320.01,321.97,223160000,321.97 1989-05-31,319.05,321.30,318.68,320.52,162530000,320.52 1989-05-30,321.59,322.53,317.83,319.05,151780000,319.05 1989-05-26,319.17,321.59,319.14,321.59,143120000,321.59 1989-05-25,319.14,319.60,318.42,319.17,154470000,319.17 1989-05-24,318.32,319.14,317.58,319.14,178600000,319.14 1989-05-23,321.98,321.98,318.20,318.32,187690000,318.32 1989-05-22,321.24,323.06,320.45,321.98,185010000,321.98 1989-05-19,317.97,321.38,317.97,321.24,242410000,321.24 1989-05-18,317.48,318.52,316.54,317.97,177480000,317.97 1989-05-17,315.28,317.94,315.11,317.48,191210000,317.48 1989-05-16,316.16,316.16,314.99,315.28,173100000,315.28 1989-05-15,313.84,316.16,313.84,316.16,179350000,316.16 1989-05-12,306.95,313.84,306.95,313.84,221490000,313.84 1989-05-11,305.80,307.34,305.80,306.95,151620000,306.95 1989-05-10,305.19,306.25,304.85,305.80,146000000,305.80 1989-05-09,306.00,306.99,304.06,305.19,150090000,305.19 1989-05-08,307.61,307.61,304.74,306.00,135130000,306.00 1989-05-05,307.77,310.69,306.98,307.61,180810000,307.61 1989-05-04,308.16,308.40,307.32,307.77,153130000,307.77 1989-05-03,308.12,308.52,307.11,308.16,171690000,308.16 1989-05-02,309.13,310.45,308.12,308.12,172560000,308.12 1989-05-01,309.64,309.64,307.40,309.12,138050000,309.12 1989-04-28,309.58,309.65,308.48,309.64,158390000,309.64 1989-04-27,306.93,310.45,306.93,309.58,191170000,309.58 1989-04-26,306.78,307.30,306.07,306.93,146090000,306.93 1989-04-25,308.69,309.65,306.74,306.75,165430000,306.75 1989-04-24,309.61,309.61,307.83,308.69,142100000,308.69 1989-04-21,306.19,309.61,306.19,309.61,187310000,309.61 1989-04-20,307.15,307.96,304.53,306.19,175970000,306.19 1989-04-19,306.02,307.68,305.36,307.15,191510000,307.15 1989-04-18,301.72,306.25,301.72,306.02,208650000,306.02 1989-04-17,301.36,302.01,300.71,301.72,128540000,301.72 1989-04-14,296.40,301.38,296.40,301.36,169780000,301.36 1989-04-13,298.99,299.00,296.27,296.40,141590000,296.40 1989-04-12,298.49,299.81,298.49,298.99,165200000,298.99 1989-04-11,297.11,298.87,297.11,298.49,146830000,298.49 1989-04-10,297.16,297.94,296.85,297.11,123990000,297.11 1989-04-07,295.29,297.62,294.35,297.16,156950000,297.16 1989-04-06,296.22,296.24,294.52,295.29,146530000,295.29 1989-04-05,295.31,296.43,295.28,296.24,165880000,296.24 1989-04-04,296.40,296.40,294.72,295.31,160680000,295.31 1989-04-03,294.87,297.04,294.62,296.39,164660000,296.39 1989-03-31,292.52,294.96,292.52,294.87,170960000,294.87 1989-03-30,292.35,293.80,291.50,292.52,159950000,292.52 1989-03-29,291.59,292.75,291.42,292.35,144240000,292.35 1989-03-28,290.57,292.32,290.57,291.59,146420000,291.59 1989-03-27,288.98,290.57,288.07,290.57,112960000,290.57 1989-03-23,290.49,291.51,288.56,288.98,153750000,288.98 1989-03-22,291.33,291.46,289.90,290.49,146570000,290.49 1989-03-21,289.92,292.38,289.92,291.33,142010000,291.33 1989-03-20,292.69,292.69,288.56,289.92,151260000,289.92 1989-03-17,299.44,299.44,291.08,292.69,242900000,292.69 1989-03-16,296.67,299.99,296.66,299.44,196040000,299.44 1989-03-15,295.14,296.78,295.14,296.67,167070000,296.67 1989-03-14,295.32,296.29,294.63,295.14,139970000,295.14 1989-03-13,292.88,296.18,292.88,295.32,140460000,295.32 1989-03-10,293.93,293.93,291.60,292.88,146830000,292.88 1989-03-09,294.08,294.69,293.85,293.93,143160000,293.93 1989-03-08,293.87,295.62,293.51,294.08,167620000,294.08 1989-03-07,294.81,295.16,293.50,293.87,172500000,293.87 1989-03-06,291.20,294.81,291.18,294.81,168880000,294.81 1989-03-03,289.94,291.18,289.44,291.18,151790000,291.18 1989-03-02,287.11,290.32,287.11,289.95,161980000,289.95 1989-03-01,288.86,290.28,286.46,287.11,177210000,287.11 1989-02-28,287.82,289.42,287.63,288.86,147430000,288.86 1989-02-27,287.13,288.12,286.26,287.82,139900000,287.82 1989-02-24,292.05,292.05,287.13,287.13,160680000,287.13 1989-02-23,290.91,292.05,289.83,292.05,150370000,292.05 1989-02-22,295.98,295.98,290.76,290.91,163140000,290.91 1989-02-21,296.76,297.04,295.16,295.98,141950000,295.98 1989-02-17,294.81,297.12,294.69,296.76,159520000,296.76 1989-02-16,294.24,295.15,294.22,294.81,177450000,294.81 1989-02-15,291.81,294.42,291.49,294.24,154220000,294.24 1989-02-14,292.54,294.37,291.41,291.81,150610000,291.81 1989-02-13,292.02,293.07,290.88,292.54,143520000,292.54 1989-02-10,296.06,296.06,291.96,292.02,173560000,292.02 1989-02-09,298.65,298.79,295.16,296.06,224220000,296.06 1989-02-08,299.62,300.57,298.41,298.65,189420000,298.65 1989-02-07,296.04,300.34,295.78,299.63,217260000,299.63 1989-02-06,296.97,296.99,294.96,296.04,150980000,296.04 1989-02-03,296.84,297.66,296.15,296.97,172980000,296.97 1989-02-02,297.09,297.92,295.81,296.84,183430000,296.84 1989-02-01,297.47,298.33,296.22,297.09,215640000,297.09 1989-01-31,294.99,297.51,293.57,297.47,194050000,297.47 1989-01-30,293.82,295.13,293.54,294.99,167830000,294.99 1989-01-27,291.69,296.08,291.69,293.82,254870000,293.82 1989-01-26,289.14,292.62,288.13,291.69,212250000,291.69 1989-01-25,288.49,289.15,287.97,289.14,183610000,289.14 1989-01-24,284.50,288.49,284.50,288.49,189620000,288.49 1989-01-23,287.85,287.98,284.50,284.50,141640000,284.50 1989-01-20,286.90,287.04,285.75,286.63,166120000,286.63 1989-01-19,286.53,287.90,286.14,286.91,192030000,286.91 1989-01-18,283.55,286.87,282.65,286.53,187450000,286.53 1989-01-17,284.14,284.14,283.06,283.55,143930000,283.55 1989-01-16,283.87,284.88,283.63,284.14,117380000,284.14 1989-01-13,283.17,284.12,282.71,283.87,132320000,283.87 1989-01-12,282.01,284.63,282.01,283.17,183000000,283.17 1989-01-11,280.38,282.01,280.21,282.01,148950000,282.01 1989-01-10,280.98,281.58,279.44,280.38,140420000,280.38 1989-01-09,280.67,281.89,280.32,280.98,163180000,280.98 1989-01-06,280.01,282.06,280.01,280.67,161330000,280.67 1989-01-05,279.43,281.51,279.43,280.01,174040000,280.01 1989-01-04,275.31,279.75,275.31,279.43,149700000,279.43 1989-01-03,277.72,277.72,273.81,275.31,128500000,275.31 1988-12-30,279.39,279.78,277.72,277.72,127210000,277.72 1988-12-29,277.08,279.42,277.08,279.40,131290000,279.40 1988-12-28,276.83,277.55,276.17,277.08,110630000,277.08 1988-12-27,277.87,278.09,276.74,276.83,87490000,276.83 1988-12-23,276.87,277.99,276.87,277.87,81760000,277.87 1988-12-22,277.38,277.89,276.86,276.87,150510000,276.87 1988-12-21,277.47,277.83,276.30,277.38,147250000,277.38 1988-12-20,278.91,280.45,277.47,277.47,161090000,277.47 1988-12-19,276.29,279.31,275.61,278.91,162250000,278.91 1988-12-16,274.28,276.29,274.28,276.29,196480000,276.29 1988-12-15,275.32,275.62,274.01,274.28,136820000,274.28 1988-12-14,276.31,276.31,274.58,275.31,132350000,275.31 1988-12-13,276.52,276.52,274.58,276.31,132340000,276.31 1988-12-12,277.03,278.82,276.52,276.52,124160000,276.52 1988-12-09,276.57,277.82,276.34,277.03,133770000,277.03 1988-12-08,278.13,278.13,276.55,276.59,124150000,276.59 1988-12-07,277.59,279.01,277.34,278.13,148360000,278.13 1988-12-06,274.93,277.89,274.62,277.59,158340000,277.59 1988-12-05,274.93,275.62,271.81,274.93,144660000,274.93 1988-12-02,272.49,272.49,270.47,271.81,124610000,271.81 1988-12-01,273.68,273.70,272.27,272.49,129380000,272.49 1988-11-30,270.91,274.36,270.90,273.70,157810000,273.70 1988-11-29,268.60,271.31,268.13,270.91,127420000,270.91 1988-11-28,267.22,268.98,266.97,268.64,123480000,268.64 1988-11-25,268.99,269.00,266.47,267.23,72090000,267.23 1988-11-23,267.22,269.56,267.21,269.00,112010000,269.00 1988-11-22,266.19,267.85,265.42,267.21,127000000,267.21 1988-11-21,266.35,266.47,263.41,266.22,120430000,266.22 1988-11-18,264.60,266.62,264.60,266.47,119320000,266.47 1988-11-17,264.61,265.63,263.45,264.60,141280000,264.60 1988-11-16,268.41,268.41,262.85,263.82,161710000,263.82 1988-11-15,267.73,268.75,267.72,268.34,115170000,268.34 1988-11-14,267.93,269.25,266.79,267.72,142900000,267.72 1988-11-11,273.65,273.69,267.92,267.92,135500000,267.92 1988-11-10,273.32,274.37,272.98,273.69,128920000,273.69 1988-11-09,275.14,275.15,272.15,273.33,153140000,273.33 1988-11-08,273.95,275.80,273.93,275.15,141660000,275.15 1988-11-07,276.30,276.31,273.62,273.93,133870000,273.93 1988-11-04,279.11,279.20,276.31,276.31,143580000,276.31 1988-11-03,279.04,280.37,279.04,279.20,152980000,279.20 1988-11-02,279.07,279.45,277.08,279.06,161300000,279.06 1988-11-01,278.97,279.57,278.01,279.06,151250000,279.06 1988-10-31,278.54,279.39,277.14,278.97,143460000,278.97 1988-10-28,277.29,279.48,277.28,278.53,146300000,278.53 1988-10-27,281.35,281.38,276.00,277.28,196540000,277.28 1988-10-26,282.37,282.52,280.54,281.38,181550000,281.38 1988-10-25,282.28,282.84,281.87,282.38,155190000,282.38 1988-10-24,283.63,283.95,282.28,282.28,170590000,282.28 1988-10-21,282.88,283.66,281.16,283.66,195410000,283.66 1988-10-20,276.97,282.88,276.93,282.88,189580000,282.88 1988-10-19,279.40,280.53,274.41,276.97,186350000,276.97 1988-10-18,276.43,279.39,276.41,279.38,162500000,279.38 1988-10-17,275.48,276.65,275.01,276.41,119290000,276.41 1988-10-14,275.27,277.01,274.08,275.50,160240000,275.50 1988-10-13,273.95,275.83,273.39,275.22,154530000,275.22 1988-10-12,277.91,277.93,273.05,273.98,154840000,273.98 1988-10-11,278.15,278.24,276.33,277.93,140900000,277.93 1988-10-10,278.06,278.69,277.10,278.24,124660000,278.24 1988-10-07,272.38,278.07,272.37,278.07,216390000,278.07 1988-10-06,271.87,272.39,271.30,272.39,153570000,272.39 1988-10-05,270.63,272.45,270.08,271.86,175130000,271.86 1988-10-04,271.37,271.79,270.34,270.62,157760000,270.62 1988-10-03,271.89,271.91,268.84,271.38,130380000,271.38 1988-09-30,272.55,274.87,271.66,271.91,175750000,271.91 1988-09-29,269.09,273.02,269.08,272.59,155790000,272.59 1988-09-28,268.22,269.08,267.77,269.08,113720000,269.08 1988-09-27,268.89,269.36,268.01,268.26,113010000,268.26 1988-09-26,269.77,269.80,268.61,268.88,116420000,268.88 1988-09-23,269.16,270.31,268.28,269.76,145100000,269.76 1988-09-22,270.19,270.58,268.26,269.18,150670000,269.18 1988-09-21,269.76,270.64,269.48,270.16,127400000,270.16 1988-09-20,268.83,270.07,268.50,269.73,142220000,269.73 1988-09-19,270.64,270.65,267.41,268.82,135770000,268.82 1988-09-16,268.13,270.81,267.33,270.65,211110000,270.65 1988-09-15,269.30,269.78,268.03,268.13,161210000,268.13 1988-09-14,267.50,269.47,267.41,269.31,177220000,269.31 1988-09-13,266.45,267.43,265.22,267.43,162490000,267.43 1988-09-12,266.85,267.64,266.22,266.47,114880000,266.47 1988-09-09,265.88,268.26,263.66,266.84,141540000,266.84 1988-09-08,265.87,266.54,264.88,265.88,149380000,265.88 1988-09-07,265.62,266.98,264.93,265.87,139590000,265.87 1988-09-06,264.42,265.94,264.40,265.59,122250000,265.59 1988-09-02,258.35,264.90,258.35,264.48,159840000,264.48 1988-09-01,261.52,261.52,256.98,258.35,144090000,258.35 1988-08-31,262.51,263.80,261.21,261.52,130480000,261.52 1988-08-30,262.33,263.18,261.53,262.51,108720000,262.51 1988-08-29,259.68,262.56,259.68,262.33,99280000,262.33 1988-08-26,259.18,260.15,258.87,259.68,89240000,259.68 1988-08-25,261.10,261.13,257.56,259.18,127640000,259.18 1988-08-24,257.16,261.13,257.09,261.13,127800000,261.13 1988-08-23,256.99,257.86,256.53,257.09,119540000,257.09 1988-08-22,260.24,260.71,256.94,256.98,122250000,256.98 1988-08-19,261.05,262.27,260.23,260.24,122370000,260.24 1988-08-18,260.76,262.76,260.75,261.03,139820000,261.03 1988-08-17,260.57,261.84,259.33,260.77,169500000,260.77 1988-08-16,258.68,262.61,257.50,260.56,162790000,260.56 1988-08-15,262.49,262.55,258.68,258.69,128560000,258.69 1988-08-12,262.70,262.94,261.37,262.55,176960000,262.55 1988-08-11,261.92,262.77,260.34,262.75,173000000,262.75 1988-08-10,266.43,266.49,261.03,261.90,200950000,261.90 1988-08-09,270.00,270.20,265.06,266.49,200710000,266.49 1988-08-08,271.13,272.47,269.93,269.98,148800000,269.98 1988-08-05,271.70,271.93,270.08,271.15,113400000,271.15 1988-08-04,273.00,274.20,271.77,271.93,157240000,271.93 1988-08-03,272.03,273.42,271.15,272.98,203590000,272.98 1988-08-02,272.19,273.68,270.37,272.06,166660000,272.06 1988-08-01,272.03,272.80,271.21,272.21,138170000,272.21 1988-07-29,266.04,272.02,266.02,272.02,192340000,272.02 1988-07-28,262.52,266.55,262.50,266.02,154570000,266.02 1988-07-27,265.18,265.83,262.48,262.50,135890000,262.50 1988-07-26,264.70,266.09,264.32,265.19,121960000,265.19 1988-07-25,263.49,265.17,263.03,264.68,215140000,264.68 1988-07-22,266.65,266.66,263.29,263.50,148880000,263.50 1988-07-21,269.99,270.00,266.66,266.66,149460000,266.66 1988-07-20,268.52,270.24,268.47,270.00,151990000,270.00 1988-07-19,270.49,271.21,267.01,268.47,144110000,268.47 1988-07-18,271.99,272.05,268.66,270.51,156210000,270.51 1988-07-15,270.23,272.06,269.53,272.05,199710000,272.05 1988-07-14,269.33,270.69,268.58,270.26,172410000,270.26 1988-07-13,267.87,269.46,266.12,269.32,218930000,269.32 1988-07-12,270.54,270.70,266.96,267.85,161650000,267.85 1988-07-11,270.03,271.64,270.02,270.55,123300000,270.55 1988-07-08,271.76,272.31,269.86,270.02,136070000,270.02 1988-07-07,272.00,272.05,269.31,271.78,156100000,271.78 1988-07-06,275.80,276.36,269.92,272.02,189630000,272.02 1988-07-05,271.78,275.81,270.51,275.81,171790000,275.81 1988-07-01,273.50,273.80,270.78,271.78,238330000,271.78 1988-06-30,271.00,273.51,270.97,273.50,227410000,273.50 1988-06-29,272.32,273.01,269.49,270.98,159590000,270.98 1988-06-28,269.07,272.80,269.06,272.31,152370000,272.31 1988-06-27,273.78,273.79,268.85,269.06,264410000,269.06 1988-06-24,274.81,275.19,273.53,273.78,179880000,273.78 1988-06-23,275.62,275.89,274.26,274.82,185770000,274.82 1988-06-22,271.69,276.88,271.67,275.66,217510000,275.66 1988-06-21,268.95,271.67,267.52,271.67,155060000,271.67 1988-06-20,270.67,270.68,268.59,268.94,116750000,268.94 1988-06-17,269.79,270.77,268.09,270.68,343920000,270.68 1988-06-16,274.44,274.45,268.76,269.77,161550000,269.77 1988-06-15,274.29,274.45,272.75,274.45,150260000,274.45 1988-06-14,271.58,276.14,271.44,274.30,227150000,274.30 1988-06-13,271.28,271.94,270.53,271.43,125310000,271.43 1988-06-10,270.22,273.21,270.20,271.26,155710000,271.26 1988-06-09,271.50,272.29,270.19,270.20,235160000,270.20 1988-06-08,265.32,272.01,265.17,271.52,310030000,271.52 1988-06-07,267.02,267.28,264.50,265.17,168710000,265.17 1988-06-06,266.46,267.05,264.97,267.05,152460000,267.05 1988-06-03,265.34,267.11,264.42,266.45,189600000,266.45 1988-06-02,266.65,266.71,264.12,265.33,193540000,265.33 1988-06-01,262.16,267.43,262.10,266.69,234560000,266.69 1988-05-31,253.44,262.16,253.42,262.16,247610000,262.16 1988-05-27,254.62,254.63,252.74,253.42,133590000,253.42 1988-05-26,253.75,254.98,253.52,254.63,164260000,254.63 1988-05-25,253.52,255.34,253.51,253.76,138310000,253.76 1988-05-24,250.84,253.51,250.83,253.51,139930000,253.51 1988-05-23,253.00,253.02,249.82,250.83,102640000,250.83 1988-05-20,252.61,253.70,251.79,253.02,120600000,253.02 1988-05-19,251.36,252.57,248.85,252.57,165160000,252.57 1988-05-18,255.40,255.67,250.73,251.35,209420000,251.35 1988-05-17,258.72,260.20,255.35,255.39,133850000,255.39 1988-05-16,256.75,258.71,256.28,258.71,155010000,258.71 1988-05-13,253.88,256.83,253.85,256.78,147240000,256.78 1988-05-12,253.32,254.87,253.31,253.85,143880000,253.85 1988-05-11,257.60,257.62,252.32,253.31,176720000,253.31 1988-05-10,256.53,258.30,255.93,257.62,131200000,257.62 1988-05-09,257.47,258.22,255.45,256.54,166320000,256.54 1988-05-06,258.80,260.31,257.03,257.48,129080000,257.48 1988-05-05,260.30,260.32,258.13,258.79,171840000,258.79 1988-05-04,263.05,263.23,260.31,260.32,141320000,260.32 1988-05-03,261.55,263.70,261.55,263.00,176920000,263.00 1988-05-02,261.36,261.56,259.99,261.56,136470000,261.56 1988-04-29,262.59,262.61,259.97,261.33,135620000,261.33 1988-04-28,263.79,263.80,262.22,262.61,128680000,262.61 1988-04-27,263.94,265.09,263.45,263.80,133810000,263.80 1988-04-26,262.45,265.06,262.18,263.93,152300000,263.93 1988-04-25,260.15,263.29,260.14,262.51,156950000,262.51 1988-04-22,256.45,261.16,256.42,260.14,152520000,260.14 1988-04-21,256.15,260.44,254.71,256.42,168440000,256.42 1988-04-20,257.91,258.54,256.12,256.13,147590000,256.13 1988-04-19,259.24,262.38,257.91,257.92,161910000,257.92 1988-04-18,259.75,259.81,258.03,259.21,144650000,259.21 1988-04-15,259.74,260.39,255.97,259.77,234160000,259.77 1988-04-14,271.55,271.57,259.37,259.75,211810000,259.75 1988-04-13,271.33,271.70,269.23,271.58,185120000,271.58 1988-04-12,269.88,272.05,269.66,271.37,146400000,271.37 1988-04-11,269.43,270.41,268.61,270.16,146370000,270.16 1988-04-08,266.15,270.22,266.11,269.43,169300000,269.43 1988-04-07,265.51,267.32,265.22,266.16,177840000,266.16 1988-04-06,258.52,265.50,258.22,265.49,189760000,265.49 1988-04-05,256.10,258.52,256.03,258.51,135290000,258.51 1988-04-04,258.89,259.06,255.68,256.09,182240000,256.09 1988-03-31,258.03,259.03,256.16,258.89,139870000,258.89 1988-03-30,260.06,261.59,257.92,258.07,151810000,258.07 1988-03-29,258.11,260.86,258.06,260.07,152690000,260.07 1988-03-28,258.50,258.51,256.07,258.06,142820000,258.06 1988-03-25,263.34,263.44,258.12,258.51,163170000,258.51 1988-03-24,268.91,268.91,262.48,263.35,184910000,263.35 1988-03-23,268.81,269.79,268.01,268.91,167370000,268.91 1988-03-22,268.73,269.61,267.90,268.84,142000000,268.84 1988-03-21,271.10,271.12,267.42,268.74,128830000,268.74 1988-03-18,271.22,272.64,269.76,271.12,245750000,271.12 1988-03-17,268.66,271.22,268.65,271.22,211920000,271.22 1988-03-16,266.11,268.68,264.81,268.65,153590000,268.65 1988-03-15,266.34,266.41,264.92,266.13,133170000,266.13 1988-03-14,264.93,266.55,264.52,266.37,131890000,266.37 1988-03-11,263.85,264.94,261.27,264.94,200020000,264.94 1988-03-10,269.07,269.35,263.80,263.84,197260000,263.84 1988-03-09,269.46,270.76,268.65,269.06,210900000,269.06 1988-03-08,267.38,270.06,267.38,269.43,237680000,269.43 1988-03-07,267.28,267.69,265.94,267.38,152980000,267.38 1988-03-04,267.87,268.40,264.72,267.30,201410000,267.30 1988-03-03,267.98,268.40,266.82,267.88,203310000,267.88 1988-03-02,267.23,268.75,267.00,267.98,199630000,267.98 1988-03-01,267.82,267.95,265.39,267.22,199990000,267.22 1988-02-29,262.46,267.82,262.46,267.82,236050000,267.82 1988-02-26,261.56,263.00,261.38,262.46,158060000,262.46 1988-02-25,264.39,267.75,261.05,261.58,213490000,261.58 1988-02-24,265.01,266.25,263.87,264.43,212730000,264.43 1988-02-23,265.62,266.12,263.11,265.02,192260000,265.02 1988-02-22,261.60,266.06,260.88,265.64,178930000,265.64 1988-02-19,257.90,261.61,257.62,261.61,180300000,261.61 1988-02-18,258.82,259.60,256.90,257.91,151430000,257.91 1988-02-17,259.94,261.47,257.83,259.21,176830000,259.21 1988-02-16,257.61,259.84,256.57,259.83,135380000,259.83 1988-02-12,255.95,258.86,255.85,257.63,177190000,257.63 1988-02-11,256.63,257.77,255.12,255.95,200760000,255.95 1988-02-10,251.74,256.92,251.72,256.66,187980000,256.66 1988-02-09,249.11,251.72,248.66,251.72,162350000,251.72 1988-02-08,250.95,250.96,247.82,249.10,168850000,249.10 1988-02-05,252.22,253.85,250.90,250.96,161310000,250.96 1988-02-04,252.20,253.03,250.34,252.21,186490000,252.21 1988-02-03,255.56,256.98,250.56,252.21,237270000,252.21 1988-02-02,255.05,256.08,252.80,255.57,164920000,255.57 1988-02-01,257.05,258.27,254.93,255.04,210660000,255.04 1988-01-29,253.31,257.07,252.70,257.07,211880000,257.07 1988-01-28,249.39,253.66,249.38,253.29,166430000,253.29 1988-01-27,249.58,253.02,248.50,249.38,176360000,249.38 1988-01-26,252.13,252.17,249.10,249.57,138380000,249.57 1988-01-25,246.53,252.87,246.50,252.17,275250000,252.17 1988-01-22,243.14,246.50,243.14,246.50,147050000,246.50 1988-01-21,242.65,244.25,240.17,243.14,158080000,243.14 1988-01-20,249.31,249.32,241.14,242.63,181660000,242.63 1988-01-19,251.84,253.33,248.75,249.32,153550000,249.32 1988-01-18,252.05,252.86,249.98,251.88,135100000,251.88 1988-01-15,246.02,253.65,245.88,252.05,197940000,252.05 1988-01-14,245.83,247.00,243.97,245.88,140570000,245.88 1988-01-13,245.41,249.25,241.41,245.81,154020000,245.81 1988-01-12,247.44,247.49,240.46,245.42,165730000,245.42 1988-01-11,243.38,247.51,241.07,247.49,158980000,247.49 1988-01-08,261.05,261.07,242.95,243.40,197300000,243.40 1988-01-07,258.87,261.32,256.18,261.07,175360000,261.07 1988-01-06,258.64,259.79,257.18,258.89,169730000,258.89 1988-01-05,255.95,261.78,255.95,258.63,209520000,258.63 1988-01-04,247.10,256.44,247.08,255.94,181810000,255.94 1987-12-31,247.84,247.86,245.22,247.08,170140000,247.08 1987-12-30,244.63,248.06,244.59,247.86,149230000,247.86 1987-12-29,245.58,245.88,244.28,244.59,111580000,244.59 1987-12-28,252.01,252.02,244.19,245.57,131220000,245.57 1987-12-24,253.13,253.16,251.68,252.03,108800000,252.03 1987-12-23,249.96,253.35,249.95,253.16,203110000,253.16 1987-12-22,249.56,249.97,247.01,249.95,192650000,249.95 1987-12-21,249.14,250.25,248.30,249.54,161790000,249.54 1987-12-18,243.01,249.18,243.01,249.16,276220000,249.16 1987-12-17,248.08,248.60,242.96,242.98,191780000,242.98 1987-12-16,242.81,248.11,242.80,248.08,193820000,248.08 1987-12-15,242.19,245.59,241.31,242.81,214970000,242.81 1987-12-14,235.30,242.34,235.04,242.19,187680000,242.19 1987-12-11,233.60,235.48,233.35,235.32,151680000,235.32 1987-12-10,238.89,240.05,233.40,233.57,188960000,233.57 1987-12-09,234.91,240.09,233.83,238.89,231430000,238.89 1987-12-08,228.77,234.92,228.69,234.91,227310000,234.91 1987-12-07,223.98,228.77,223.92,228.76,146660000,228.76 1987-12-04,225.20,225.77,221.24,223.92,184800000,223.92 1987-12-03,233.46,233.90,225.21,225.21,204160000,225.21 1987-12-02,232.01,234.56,230.31,233.45,148890000,233.45 1987-12-01,230.32,234.02,230.30,232.00,149870000,232.00 1987-11-30,240.27,240.34,225.75,230.30,268910000,230.30 1987-11-27,244.11,244.12,240.34,240.34,86360000,240.34 1987-11-25,246.42,246.54,244.08,244.10,139780000,244.10 1987-11-24,242.98,247.90,242.98,246.39,199520000,246.39 1987-11-23,242.00,242.99,240.50,242.99,143160000,242.99 1987-11-20,240.04,242.01,235.89,242.00,189170000,242.00 1987-11-19,245.54,245.55,239.70,240.05,157140000,240.05 1987-11-18,243.09,245.55,240.67,245.55,158270000,245.55 1987-11-17,246.73,246.76,240.81,243.04,148240000,243.04 1987-11-16,245.69,249.54,244.98,246.76,164340000,246.76 1987-11-13,248.54,249.42,245.64,245.64,174920000,245.64 1987-11-12,241.93,249.90,241.90,248.52,206280000,248.52 1987-11-11,239.01,243.86,239.00,241.90,147850000,241.90 1987-11-10,243.14,243.17,237.64,239.00,184310000,239.00 1987-11-09,250.41,250.41,243.01,243.17,160690000,243.17 1987-11-06,254.49,257.21,249.68,250.41,228290000,250.41 1987-11-05,248.93,256.09,247.72,254.48,226000000,254.48 1987-11-04,250.81,251.00,246.34,248.96,202500000,248.96 1987-11-03,255.75,255.75,242.78,250.82,227800000,250.82 1987-11-02,251.73,255.75,249.15,255.75,176000000,255.75 1987-10-30,244.77,254.04,244.77,251.79,303400000,251.79 1987-10-29,233.31,246.69,233.28,244.77,258100000,244.77 1987-10-28,233.19,238.58,226.26,233.28,279400000,233.28 1987-10-27,227.67,237.81,227.67,233.19,260200000,233.19 1987-10-26,248.20,248.22,227.26,227.67,308800000,227.67 1987-10-23,248.29,250.70,242.76,248.22,245600000,248.22 1987-10-22,258.24,258.38,242.99,248.25,392200000,248.25 1987-10-21,236.83,259.27,236.83,258.38,449600000,258.38 1987-10-20,225.06,245.62,216.46,236.83,608100000,236.83 1987-10-19,282.70,282.70,224.83,224.84,604300000,224.84 1987-10-16,298.08,298.92,281.52,282.70,338500000,282.70 1987-10-15,305.21,305.23,298.07,298.08,263200000,298.08 1987-10-14,314.52,314.52,304.78,305.23,207400000,305.23 1987-10-13,309.39,314.53,309.39,314.52,172900000,314.52 1987-10-12,311.07,311.07,306.76,309.39,141900000,309.39 1987-10-09,314.16,315.04,310.97,311.07,158300000,311.07 1987-10-08,318.54,319.34,312.02,314.16,198700000,314.16 1987-10-07,319.22,319.39,315.78,318.54,186300000,318.54 1987-10-06,328.08,328.08,319.17,319.22,175600000,319.22 1987-10-05,328.07,328.57,326.09,328.08,159700000,328.08 1987-10-02,327.33,328.94,327.22,328.07,189100000,328.07 1987-10-01,321.83,327.34,321.83,327.33,193200000,327.33 1987-09-30,321.69,322.53,320.16,321.83,183100000,321.83 1987-09-29,323.20,324.63,320.27,321.69,173500000,321.69 1987-09-28,320.16,325.33,320.16,323.20,188100000,323.20 1987-09-25,319.72,320.55,318.10,320.16,138000000,320.16 1987-09-24,321.09,322.01,319.12,319.72,162200000,319.72 1987-09-23,319.49,321.83,319.12,321.19,220300000,321.19 1987-09-22,310.54,319.51,308.69,319.50,209500000,319.50 1987-09-21,314.92,317.66,310.12,310.54,170100000,310.54 1987-09-18,314.98,316.99,314.86,314.86,188100000,314.86 1987-09-17,314.94,316.08,313.45,314.93,150700000,314.93 1987-09-16,317.75,319.50,314.61,314.86,195700000,314.86 1987-09-15,323.07,323.08,317.63,317.74,136200000,317.74 1987-09-14,322.02,323.81,320.40,323.08,154400000,323.08 1987-09-11,317.14,322.45,317.13,321.98,178000000,321.98 1987-09-10,313.92,317.59,313.92,317.13,179800000,317.13 1987-09-09,313.60,315.41,312.29,313.92,164900000,313.92 1987-09-08,316.68,316.70,308.56,313.56,242900000,313.56 1987-09-04,320.21,322.03,316.53,316.70,129100000,316.70 1987-09-03,321.47,324.29,317.39,320.21,165200000,320.21 1987-09-02,323.40,324.53,318.76,321.68,199900000,321.68 1987-09-01,329.81,332.18,322.83,323.40,193500000,323.40 1987-08-31,327.03,330.09,326.99,329.80,165800000,329.80 1987-08-28,331.37,331.38,327.03,327.04,156300000,327.04 1987-08-27,334.56,334.57,331.10,331.38,163600000,331.38 1987-08-26,336.77,337.39,334.46,334.57,196200000,334.57 1987-08-25,333.37,337.89,333.33,336.77,213500000,336.77 1987-08-24,335.89,335.90,331.92,333.33,149400000,333.33 1987-08-21,334.85,336.37,334.30,335.90,189600000,335.90 1987-08-20,331.49,335.19,329.83,334.84,196600000,334.84 1987-08-19,329.26,329.89,326.54,329.83,180900000,329.83 1987-08-18,334.10,334.11,326.43,329.25,198400000,329.25 1987-08-17,333.98,335.43,332.88,334.11,166100000,334.11 1987-08-14,334.63,336.08,332.63,333.99,196100000,333.99 1987-08-13,332.38,335.52,332.38,334.65,217100000,334.65 1987-08-12,333.32,334.57,331.06,332.39,235800000,332.39 1987-08-11,328.02,333.40,328.00,333.33,278100000,333.33 1987-08-10,322.98,328.00,322.95,328.00,187200000,328.00 1987-08-07,322.10,324.15,321.82,323.00,212700000,323.00 1987-08-06,318.49,322.09,317.50,322.09,192000000,322.09 1987-08-05,316.25,319.74,316.23,318.45,192700000,318.45 1987-08-04,317.59,318.25,314.51,316.23,166500000,316.23 1987-08-03,318.62,320.26,316.52,317.57,207800000,317.57 1987-07-31,318.05,318.85,317.56,318.66,181900000,318.66 1987-07-30,315.69,318.53,315.65,318.05,208000000,318.05 1987-07-29,312.34,315.65,311.73,315.65,196200000,315.65 1987-07-28,310.65,312.33,310.28,312.33,172600000,312.33 1987-07-27,309.30,310.70,308.61,310.65,152000000,310.65 1987-07-24,307.82,309.28,307.78,309.27,158400000,309.27 1987-07-23,308.50,309.63,306.10,307.81,163700000,307.81 1987-07-22,308.56,309.12,307.22,308.47,174700000,308.47 1987-07-21,311.36,312.41,307.51,308.55,186600000,308.55 1987-07-20,314.56,314.59,311.24,311.39,168100000,311.39 1987-07-17,312.71,314.59,312.38,314.59,210000000,314.59 1987-07-16,311.00,312.83,310.42,312.70,210900000,312.70 1987-07-15,310.67,312.08,309.07,310.42,202300000,310.42 1987-07-14,307.67,310.69,307.46,310.68,185900000,310.68 1987-07-13,308.41,308.41,305.49,307.63,152500000,307.63 1987-07-10,307.55,308.40,306.96,308.37,172100000,308.37 1987-07-09,308.30,309.56,307.42,307.52,195400000,307.52 1987-07-08,307.41,308.48,306.01,308.29,207500000,308.29 1987-07-07,304.91,308.63,304.73,307.40,200700000,307.40 1987-07-06,305.64,306.75,304.23,304.92,155000000,304.92 1987-07-02,302.96,306.34,302.94,305.63,154900000,305.63 1987-07-01,303.99,304.00,302.53,302.94,157000000,302.94 1987-06-30,307.89,308.00,303.01,304.00,165500000,304.00 1987-06-29,307.15,308.15,306.75,307.90,142500000,307.90 1987-06-26,308.94,308.96,306.36,307.16,150500000,307.16 1987-06-25,306.87,309.44,306.86,308.96,173500000,308.96 1987-06-24,308.44,308.91,306.32,306.86,153800000,306.86 1987-06-23,309.66,310.27,307.48,308.43,194200000,308.43 1987-06-22,306.98,310.20,306.97,309.65,178200000,309.65 1987-06-19,305.71,306.97,305.55,306.97,220500000,306.97 1987-06-18,304.78,306.13,303.38,305.69,168600000,305.69 1987-06-17,304.77,305.74,304.03,304.81,184700000,304.81 1987-06-16,303.12,304.86,302.60,304.76,157800000,304.76 1987-06-15,301.62,304.11,301.62,303.14,156900000,303.14 1987-06-12,298.77,302.26,298.73,301.62,175100000,301.62 1987-06-11,297.50,298.94,297.47,298.73,138900000,298.73 1987-06-10,297.28,300.81,295.66,297.47,197400000,297.47 1987-06-09,296.72,297.59,295.90,297.28,164200000,297.28 1987-06-08,293.46,297.03,291.55,296.72,136400000,296.72 1987-06-05,295.11,295.11,292.80,293.45,129100000,293.45 1987-06-04,293.46,295.09,292.76,295.09,140300000,295.09 1987-06-03,288.56,293.47,288.56,293.47,164200000,293.47 1987-06-02,289.82,290.94,286.93,288.46,153400000,288.46 1987-06-01,290.12,291.96,289.23,289.83,149300000,289.83 1987-05-29,290.77,292.87,289.70,290.10,153500000,290.10 1987-05-28,288.73,291.50,286.33,290.76,153800000,290.76 1987-05-27,289.07,290.78,288.19,288.73,171400000,288.73 1987-05-26,282.16,289.11,282.16,289.11,152500000,289.11 1987-05-22,280.17,283.33,280.17,282.16,135800000,282.16 1987-05-21,278.23,282.31,278.21,280.17,164800000,280.17 1987-05-20,279.62,280.89,277.01,278.21,206800000,278.21 1987-05-19,286.66,287.39,278.83,279.62,175400000,279.62 1987-05-18,287.43,287.43,282.57,286.65,174200000,286.65 1987-05-15,294.23,294.24,287.11,287.43,180800000,287.43 1987-05-14,293.98,295.10,292.95,294.24,152000000,294.24 1987-05-13,293.31,294.54,290.74,293.98,171000000,293.98 1987-05-12,291.57,293.30,290.18,293.30,155300000,293.30 1987-05-11,293.37,298.69,291.55,291.57,203700000,291.57 1987-05-08,294.73,296.18,291.73,293.37,161900000,293.37 1987-05-07,295.45,296.80,294.07,294.71,215200000,294.71 1987-05-06,295.35,296.19,293.60,295.47,196600000,295.47 1987-05-05,289.36,295.40,289.34,295.34,192300000,295.34 1987-05-04,288.02,289.99,286.39,289.36,140600000,289.36 1987-05-01,286.99,289.71,286.52,288.03,160100000,288.03 1987-04-30,284.58,290.08,284.57,288.36,183100000,288.36 1987-04-29,282.58,286.42,282.58,284.57,173600000,284.57 1987-04-28,281.83,285.95,281.83,282.51,180100000,282.51 1987-04-27,281.52,284.45,276.22,281.83,222700000,281.83 1987-04-24,286.81,286.82,281.18,281.52,178000000,281.52 1987-04-23,287.19,289.12,284.28,286.82,173900000,286.82 1987-04-22,293.05,293.46,286.98,287.19,185900000,287.19 1987-04-21,285.88,293.07,282.89,293.07,191300000,293.07 1987-04-20,286.91,288.36,284.55,286.09,139100000,286.09 1987-04-16,284.45,289.57,284.44,286.91,189600000,286.91 1987-04-15,279.17,285.14,279.16,284.44,198200000,284.44 1987-04-14,285.61,285.62,275.67,279.16,266500000,279.16 1987-04-13,292.48,293.36,285.62,285.62,181000000,285.62 1987-04-10,292.82,293.74,290.94,292.49,169500000,292.49 1987-04-09,297.25,297.71,291.50,292.86,180300000,292.86 1987-04-08,296.72,299.20,295.18,297.26,179800000,297.26 1987-04-07,301.94,303.65,296.67,296.69,186400000,296.69 1987-04-06,300.46,302.21,300.41,301.95,173700000,301.95 1987-04-03,293.64,301.30,292.30,300.41,213400000,300.41 1987-04-02,292.41,294.47,292.02,293.63,183000000,293.63 1987-04-01,291.59,292.38,288.34,292.38,182600000,292.38 1987-03-31,289.21,291.87,289.07,291.70,171800000,291.70 1987-03-30,296.10,296.13,286.69,289.20,208400000,289.20 1987-03-27,300.96,301.41,296.06,296.13,184400000,296.13 1987-03-26,300.39,302.72,300.38,300.93,196000000,300.93 1987-03-25,301.52,301.85,299.36,300.38,171300000,300.38 1987-03-24,301.17,301.92,300.14,301.64,189900000,301.64 1987-03-23,298.16,301.17,297.50,301.16,189100000,301.16 1987-03-20,294.08,298.17,294.08,298.17,234000000,298.17 1987-03-19,292.73,294.46,292.26,294.08,166100000,294.08 1987-03-18,292.49,294.58,290.87,292.78,198100000,292.78 1987-03-17,288.09,292.47,287.96,292.47,177300000,292.47 1987-03-16,289.88,289.89,286.64,288.23,134900000,288.23 1987-03-13,291.22,291.79,289.88,289.89,150900000,289.89 1987-03-12,290.33,291.91,289.66,291.22,174500000,291.22 1987-03-11,290.87,292.51,289.33,290.31,186900000,290.31 1987-03-10,288.30,290.87,287.89,290.86,174800000,290.86 1987-03-09,290.66,290.66,287.12,288.30,165400000,288.30 1987-03-06,290.52,290.67,288.77,290.66,181600000,290.66 1987-03-05,288.62,291.24,288.60,290.52,205400000,290.52 1987-03-04,284.12,288.62,284.12,288.62,198400000,288.62 1987-03-03,283.00,284.19,282.92,284.12,149200000,284.12 1987-03-02,284.17,284.83,282.30,283.00,156700000,283.00 1987-02-27,282.96,284.55,282.77,284.20,142800000,284.20 1987-02-26,284.00,284.40,280.73,282.96,165800000,282.96 1987-02-25,282.88,285.35,282.14,284.00,184100000,284.00 1987-02-24,282.38,283.33,281.45,282.88,151300000,282.88 1987-02-23,285.48,285.50,279.37,282.38,170500000,282.38 1987-02-20,285.57,285.98,284.31,285.48,175800000,285.48 1987-02-19,285.42,286.24,283.84,285.57,181500000,285.57 1987-02-18,285.49,287.55,282.97,285.42,218200000,285.42 1987-02-17,279.70,285.49,279.70,285.49,187800000,285.49 1987-02-13,275.62,280.91,275.01,279.70,184400000,279.70 1987-02-12,277.54,278.04,273.89,275.62,200400000,275.62 1987-02-11,275.07,277.71,274.71,277.54,172400000,277.54 1987-02-10,278.16,278.16,273.49,275.07,168300000,275.07 1987-02-09,280.04,280.04,277.24,278.16,143300000,278.16 1987-02-06,281.16,281.79,279.87,280.04,184100000,280.04 1987-02-05,279.64,282.26,278.66,281.16,256700000,281.16 1987-02-04,275.99,279.65,275.35,279.64,222400000,279.64 1987-02-03,276.45,277.83,275.84,275.99,198100000,275.99 1987-02-02,274.08,277.35,273.16,276.45,177400000,276.45 1987-01-30,274.24,274.24,271.38,274.08,163400000,274.08 1987-01-29,275.40,276.85,272.54,274.24,205300000,274.24 1987-01-28,273.75,275.71,273.03,275.40,195800000,275.40 1987-01-27,269.61,274.31,269.61,273.75,192300000,273.75 1987-01-26,270.10,270.40,267.73,269.61,138900000,269.61 1987-01-23,273.91,280.96,268.41,270.10,302400000,270.10 1987-01-22,267.84,274.05,267.32,273.91,188700000,273.91 1987-01-21,269.04,270.87,267.35,267.84,184200000,267.84 1987-01-20,269.34,271.03,267.65,269.04,224800000,269.04 1987-01-19,266.26,269.34,264.00,269.34,162800000,269.34 1987-01-16,265.46,267.24,264.31,266.28,218400000,266.28 1987-01-15,262.65,266.68,262.64,265.49,253100000,265.49 1987-01-14,259.95,262.72,259.62,262.64,214200000,262.64 1987-01-13,260.30,260.45,259.21,259.95,170900000,259.95 1987-01-12,258.72,261.36,257.92,260.30,184200000,260.30 1987-01-09,257.26,259.20,256.11,258.73,193000000,258.73 1987-01-08,255.36,257.28,254.97,257.28,194500000,257.28 1987-01-07,252.78,255.72,252.65,255.33,190900000,255.33 1987-01-06,252.20,253.99,252.14,252.78,189300000,252.78 1987-01-05,246.45,252.57,246.45,252.19,181900000,252.19 1987-01-02,242.17,246.45,242.17,246.45,91880000,246.45 1986-12-31,243.37,244.03,241.28,242.17,139200000,242.17 1986-12-30,244.66,244.67,243.04,243.37,126200000,243.37 1986-12-29,246.90,246.92,244.31,244.67,99800000,244.67 1986-12-26,246.75,247.09,246.73,246.92,48860000,246.92 1986-12-24,246.34,247.22,246.02,246.75,95410000,246.75 1986-12-23,248.75,248.75,245.85,246.34,188700000,246.34 1986-12-22,249.73,249.73,247.45,248.75,157600000,248.75 1986-12-19,246.79,249.96,245.89,249.73,244700000,249.73 1986-12-18,247.56,247.81,246.45,246.78,155400000,246.78 1986-12-17,250.01,250.04,247.19,247.56,148800000,247.56 1986-12-16,248.21,250.04,247.40,250.04,157000000,250.04 1986-12-15,247.31,248.23,244.92,248.21,148200000,248.21 1986-12-12,248.17,248.31,247.02,247.35,126600000,247.35 1986-12-11,250.97,250.98,247.15,248.17,136000000,248.17 1986-12-10,249.28,251.53,248.94,250.96,139700000,250.96 1986-12-09,251.16,251.27,249.25,249.28,128700000,249.28 1986-12-08,251.16,252.36,248.82,251.16,159000000,251.16 1986-12-05,253.05,253.89,250.71,251.17,139800000,251.17 1986-12-04,253.85,254.42,252.88,253.04,156900000,253.04 1986-12-03,254.00,254.87,253.24,253.85,200100000,253.85 1986-12-02,249.06,254.00,249.05,254.00,230400000,254.00 1986-12-01,249.22,249.22,245.72,249.05,133800000,249.05 1986-11-28,248.82,249.22,248.07,249.22,93530000,249.22 1986-11-26,248.14,248.90,247.73,248.77,152000000,248.77 1986-11-25,247.44,248.18,246.30,248.17,154600000,248.17 1986-11-24,245.86,248.00,245.21,247.45,150800000,247.45 1986-11-21,242.03,246.38,241.97,245.86,200700000,245.86 1986-11-20,237.66,242.05,237.66,242.05,158100000,242.05 1986-11-19,236.77,237.94,235.51,237.66,183300000,237.66 1986-11-18,243.20,243.23,236.65,236.78,185300000,236.78 1986-11-17,244.50,244.80,242.29,243.21,133300000,243.21 1986-11-14,243.01,244.51,241.96,244.50,172100000,244.50 1986-11-13,246.63,246.66,242.98,243.02,164000000,243.02 1986-11-12,247.06,247.67,245.68,246.64,162200000,246.64 1986-11-11,246.15,247.10,246.12,247.08,118500000,247.08 1986-11-10,245.75,246.22,244.68,246.13,120200000,246.13 1986-11-07,245.85,246.13,244.92,245.77,142300000,245.77 1986-11-06,246.54,246.90,244.30,245.87,165300000,245.87 1986-11-05,246.09,247.05,245.21,246.58,183200000,246.58 1986-11-04,245.80,246.43,244.42,246.20,163200000,246.20 1986-11-03,243.97,245.80,243.93,245.80,138200000,245.80 1986-10-31,243.70,244.51,242.95,243.98,147200000,243.98 1986-10-30,240.97,244.08,240.94,243.71,194200000,243.71 1986-10-29,239.23,241.00,238.98,240.94,164400000,240.94 1986-10-28,238.81,240.58,238.77,239.26,145900000,239.26 1986-10-27,238.22,238.77,236.72,238.77,133200000,238.77 1986-10-24,239.30,239.65,238.25,238.26,137500000,238.26 1986-10-23,236.28,239.76,236.26,239.28,150900000,239.28 1986-10-22,235.89,236.64,235.82,236.26,114000000,236.26 1986-10-21,236.03,236.49,234.95,235.88,110000000,235.88 1986-10-20,238.84,238.84,234.78,235.97,109000000,235.97 1986-10-17,239.50,239.53,237.71,238.84,124100000,238.84 1986-10-16,238.83,240.18,238.80,239.53,156900000,239.53 1986-10-15,235.36,239.03,235.27,238.80,144300000,238.80 1986-10-14,235.90,236.37,234.37,235.37,116800000,235.37 1986-10-13,235.52,235.91,235.02,235.91,54990000,235.91 1986-10-10,235.84,236.27,235.31,235.48,105100000,235.48 1986-10-09,236.67,238.20,235.72,235.85,153400000,235.85 1986-10-08,234.41,236.84,233.68,236.68,141700000,236.68 1986-10-07,234.74,235.18,233.46,234.41,125100000,234.41 1986-10-06,233.71,235.34,233.17,234.78,88250000,234.78 1986-10-03,233.92,236.16,232.79,233.71,128100000,233.71 1986-10-02,233.60,234.33,232.77,233.92,128100000,233.92 1986-10-01,231.32,234.62,231.32,233.60,143600000,233.60 1986-09-30,229.91,233.01,229.91,231.32,124900000,231.32 1986-09-29,232.23,232.23,228.08,229.91,115600000,229.91 1986-09-26,231.83,233.68,230.64,232.23,115300000,232.23 1986-09-25,231.83,236.28,230.67,231.83,134300000,231.83 1986-09-24,235.66,237.06,235.53,236.28,134600000,236.28 1986-09-23,234.96,235.88,234.50,235.67,132600000,235.67 1986-09-22,232.20,234.93,232.20,234.93,126100000,234.93 1986-09-19,232.30,232.31,230.69,232.21,153900000,232.21 1986-09-18,231.67,232.87,230.57,232.31,132200000,232.31 1986-09-17,231.73,233.81,231.38,231.68,141000000,231.68 1986-09-16,231.93,231.94,228.32,231.72,131200000,231.72 1986-09-15,230.67,232.82,229.44,231.94,155600000,231.94 1986-09-12,235.18,235.45,228.74,230.67,240500000,230.67 1986-09-11,247.06,247.06,234.67,235.18,237600000,235.18 1986-09-10,247.67,247.76,246.11,247.06,140300000,247.06 1986-09-09,248.14,250.21,246.94,247.67,137500000,247.67 1986-09-08,250.47,250.47,247.02,248.14,153300000,248.14 1986-09-05,253.83,254.13,250.33,250.47,180600000,250.47 1986-09-04,250.08,254.01,250.03,253.83,189400000,253.83 1986-09-03,248.52,250.08,247.59,250.08,154300000,250.08 1986-09-02,252.93,253.30,248.14,248.52,135500000,248.52 1986-08-29,252.84,254.07,251.73,252.93,125300000,252.93 1986-08-28,253.30,253.67,251.91,252.84,125100000,252.84 1986-08-27,252.84,254.24,252.66,253.30,143300000,253.30 1986-08-26,247.81,252.91,247.81,252.84,156600000,252.84 1986-08-25,250.19,250.26,247.76,247.81,104400000,247.81 1986-08-22,249.67,250.61,249.27,250.19,118100000,250.19 1986-08-21,249.77,250.45,249.11,249.67,135200000,249.67 1986-08-20,246.53,249.77,246.51,249.77,156600000,249.77 1986-08-19,247.38,247.42,245.82,246.51,109300000,246.51 1986-08-18,247.15,247.83,245.48,247.38,112800000,247.38 1986-08-15,246.25,247.15,245.70,247.15,123500000,247.15 1986-08-14,245.67,246.79,245.53,246.25,123800000,246.25 1986-08-13,243.34,246.51,243.06,245.67,156400000,245.67 1986-08-12,240.68,243.37,240.35,243.34,131700000,243.34 1986-08-11,236.88,241.20,236.87,240.68,125600000,240.68 1986-08-08,237.04,238.06,236.37,236.88,106300000,236.88 1986-08-07,236.84,238.02,236.31,237.04,122400000,237.04 1986-08-06,237.03,237.35,235.48,236.84,127500000,236.84 1986-08-05,235.99,238.31,235.97,237.03,153100000,237.03 1986-08-04,234.91,236.86,231.92,235.99,130000000,235.99 1986-08-01,236.12,236.89,234.59,234.91,114900000,234.91 1986-07-31,236.59,236.92,235.89,236.12,112700000,236.12 1986-07-30,234.57,237.38,233.07,236.59,146700000,236.59 1986-07-29,235.72,236.01,234.40,234.55,115700000,234.55 1986-07-28,240.20,240.25,235.23,236.01,128000000,236.01 1986-07-25,237.99,240.36,237.95,240.22,132000000,240.22 1986-07-24,238.69,239.05,237.32,237.95,134700000,237.95 1986-07-23,238.19,239.25,238.17,238.67,133300000,238.67 1986-07-22,236.24,238.42,235.92,238.18,138500000,238.18 1986-07-21,236.36,236.45,235.53,236.24,106300000,236.24 1986-07-18,236.07,238.22,233.94,236.36,149700000,236.36 1986-07-17,235.01,236.65,235.01,236.07,132400000,236.07 1986-07-16,233.66,236.19,233.66,235.01,160800000,235.01 1986-07-15,238.09,238.12,233.60,233.66,184000000,233.66 1986-07-14,242.22,242.22,238.04,238.11,123200000,238.11 1986-07-11,243.01,243.48,241.68,242.22,124500000,242.22 1986-07-10,242.82,243.44,239.66,243.01,146200000,243.01 1986-07-09,241.59,243.07,241.46,242.82,142900000,242.82 1986-07-08,244.05,244.06,239.07,241.59,174100000,241.59 1986-07-07,251.79,251.81,243.63,244.05,138200000,244.05 1986-07-03,252.70,252.94,251.23,251.79,108300000,251.79 1986-07-02,252.04,253.20,251.79,252.70,150000000,252.70 1986-07-01,250.67,252.04,250.53,252.04,147700000,252.04 1986-06-30,249.60,251.81,249.60,250.84,135100000,250.84 1986-06-27,248.74,249.74,248.74,249.60,123800000,249.60 1986-06-26,248.93,249.43,247.72,248.74,134100000,248.74 1986-06-25,247.03,250.13,247.03,248.93,161800000,248.93 1986-06-24,245.26,248.26,244.53,247.03,140600000,247.03 1986-06-23,247.58,247.58,244.45,245.26,123800000,245.26 1986-06-20,244.06,247.60,243.98,247.58,149100000,247.58 1986-06-19,244.99,245.80,244.05,244.06,129000000,244.06 1986-06-18,244.35,245.25,242.57,244.99,117000000,244.99 1986-06-17,246.13,246.26,243.60,244.35,123100000,244.35 1986-06-16,245.73,246.50,245.17,246.13,112100000,246.13 1986-06-13,241.71,245.91,241.71,245.73,141200000,245.73 1986-06-12,241.24,241.64,240.70,241.49,109100000,241.49 1986-06-11,239.58,241.13,239.21,241.13,127400000,241.13 1986-06-10,239.96,240.08,238.23,239.58,125000000,239.58 1986-06-09,245.67,245.67,239.68,239.96,123300000,239.96 1986-06-06,245.65,246.07,244.43,245.67,110900000,245.67 1986-06-05,243.94,245.66,243.41,245.65,110900000,245.65 1986-06-04,245.51,246.30,242.59,243.94,117000000,243.94 1986-06-03,245.04,245.51,243.67,245.51,114700000,245.51 1986-06-02,246.04,247.74,243.83,245.04,120600000,245.04 1986-05-30,247.98,249.19,246.43,247.35,151200000,247.35 1986-05-29,246.63,248.32,245.29,247.98,135700000,247.98 1986-05-28,244.75,247.40,244.75,246.63,159600000,246.63 1986-05-27,241.35,244.76,241.35,244.75,121200000,244.75 1986-05-23,240.12,242.16,240.12,241.35,130200000,241.35 1986-05-22,235.45,240.25,235.45,240.12,144900000,240.12 1986-05-21,236.11,236.83,235.45,235.45,117100000,235.45 1986-05-20,233.20,236.12,232.58,236.11,113000000,236.11 1986-05-19,232.76,233.54,232.41,233.20,85840000,233.20 1986-05-16,234.43,234.43,232.26,232.76,113500000,232.76 1986-05-15,237.54,237.54,233.93,234.43,131600000,234.43 1986-05-14,236.41,237.54,235.85,237.54,132100000,237.54 1986-05-13,237.58,237.87,236.02,236.41,119200000,236.41 1986-05-12,237.85,238.53,237.02,237.58,125400000,237.58 1986-05-09,237.13,238.01,235.85,237.85,137400000,237.85 1986-05-08,236.08,237.96,236.08,237.13,136000000,237.13 1986-05-07,236.56,237.24,233.98,236.08,129900000,236.08 1986-05-06,237.73,238.28,236.26,237.24,121200000,237.24 1986-05-05,234.79,237.73,234.79,237.73,102400000,237.73 1986-05-02,235.16,236.52,234.15,234.79,126300000,234.79 1986-05-01,235.52,236.01,234.21,235.16,146500000,235.16 1986-04-30,240.52,240.52,235.26,235.52,147500000,235.52 1986-04-29,243.08,243.57,239.23,240.51,148800000,240.51 1986-04-28,242.29,243.08,241.23,243.08,123900000,243.08 1986-04-25,242.02,242.80,240.91,242.29,142300000,242.29 1986-04-24,241.75,243.13,241.65,242.02,146600000,242.02 1986-04-23,242.42,242.42,240.08,241.75,149700000,241.75 1986-04-22,244.74,245.47,241.30,242.42,161500000,242.42 1986-04-21,242.38,244.78,241.88,244.74,136100000,244.74 1986-04-18,243.03,243.47,241.74,242.38,153600000,242.38 1986-04-17,242.22,243.36,241.89,243.03,161400000,243.03 1986-04-16,237.73,242.57,237.73,242.22,173800000,242.22 1986-04-15,237.28,238.09,236.64,237.73,123700000,237.73 1986-04-14,235.97,237.48,235.43,237.28,106700000,237.28 1986-04-11,236.44,237.85,235.13,235.97,139400000,235.97 1986-04-10,233.75,236.54,233.75,236.44,184800000,236.44 1986-04-09,233.52,235.57,232.13,233.75,156300000,233.75 1986-04-08,228.63,233.70,228.63,233.52,146300000,233.52 1986-04-07,228.69,228.83,226.30,228.63,129800000,228.63 1986-04-04,232.47,232.56,228.32,228.69,147300000,228.69 1986-04-03,235.71,236.42,232.07,232.47,148200000,232.47 1986-04-02,235.14,235.71,233.40,235.71,145300000,235.71 1986-04-01,238.90,239.10,234.57,235.14,167400000,235.14 1986-03-31,238.97,239.86,238.08,238.90,134400000,238.90 1986-03-27,237.30,240.11,237.30,238.97,178100000,238.97 1986-03-26,234.72,237.79,234.71,237.30,161500000,237.30 1986-03-25,235.33,235.33,233.62,234.72,139300000,234.72 1986-03-24,233.34,235.33,232.92,235.33,143800000,235.33 1986-03-21,236.54,237.35,233.29,233.34,199100000,233.34 1986-03-20,235.60,237.09,235.60,236.54,148000000,236.54 1986-03-19,235.78,236.52,235.13,235.60,150000000,235.60 1986-03-18,234.67,236.52,234.14,235.78,148000000,235.78 1986-03-17,236.55,236.55,233.69,234.67,137500000,234.67 1986-03-14,233.19,236.55,232.58,236.55,181900000,236.55 1986-03-13,232.54,233.89,231.27,233.19,171500000,233.19 1986-03-12,231.69,234.70,231.68,232.54,210300000,232.54 1986-03-11,226.58,231.81,226.58,231.69,187300000,231.69 1986-03-10,225.57,226.98,225.36,226.58,129900000,226.58 1986-03-07,225.13,226.33,224.44,225.57,163200000,225.57 1986-03-06,224.39,225.50,224.13,225.13,159000000,225.13 1986-03-05,224.14,224.37,222.18,224.34,154600000,224.34 1986-03-04,225.42,227.33,223.94,224.38,174500000,224.38 1986-03-03,226.92,226.92,224.41,225.42,142700000,225.42 1986-02-28,226.77,227.92,225.42,226.92,191700000,226.92 1986-02-27,224.04,226.88,223.41,226.77,181700000,226.77 1986-02-26,223.72,224.59,223.15,224.04,158000000,224.04 1986-02-25,224.34,224.40,222.63,223.79,148000000,223.79 1986-02-24,224.58,225.29,223.31,224.34,144700000,224.34 1986-02-21,222.22,224.62,222.22,224.62,177600000,224.62 1986-02-20,219.76,222.22,219.22,222.22,139700000,222.22 1986-02-19,222.45,222.96,219.73,219.76,152000000,219.76 1986-02-18,219.76,222.45,219.26,222.45,160200000,222.45 1986-02-14,217.40,219.76,217.22,219.76,155600000,219.76 1986-02-13,215.97,217.41,215.38,217.40,136500000,217.40 1986-02-12,215.92,216.28,215.13,215.97,136400000,215.97 1986-02-11,216.24,216.67,215.54,215.92,141300000,215.92 1986-02-10,214.56,216.24,214.47,216.24,129900000,216.24 1986-02-07,213.47,215.27,211.13,214.56,144400000,214.56 1986-02-06,212.96,214.51,212.60,213.47,146100000,213.47 1986-02-05,212.84,213.03,211.21,212.96,134300000,212.96 1986-02-04,213.96,214.57,210.82,212.79,175700000,212.79 1986-02-03,211.78,214.18,211.60,213.96,145300000,213.96 1986-01-31,209.33,212.42,209.19,211.78,143500000,211.78 1986-01-30,210.29,211.54,209.15,209.33,125300000,209.33 1986-01-29,209.81,212.36,209.81,210.29,193800000,210.29 1986-01-28,207.42,209.82,207.40,209.81,145700000,209.81 1986-01-27,206.43,207.69,206.43,207.39,122900000,207.39 1986-01-24,204.25,206.43,204.25,206.43,128900000,206.43 1986-01-23,203.49,204.43,202.60,204.25,130300000,204.25 1986-01-22,205.79,206.03,203.41,203.49,131200000,203.49 1986-01-21,207.53,207.78,205.05,205.79,128300000,205.79 1986-01-20,208.43,208.43,206.62,207.53,85340000,207.53 1986-01-17,209.17,209.40,207.59,208.43,132100000,208.43 1986-01-16,208.26,209.18,207.61,209.17,130500000,209.17 1986-01-15,206.64,208.27,206.64,208.26,122400000,208.26 1986-01-14,206.72,207.37,206.06,206.64,113900000,206.64 1986-01-13,205.96,206.83,205.52,206.72,108700000,206.72 1986-01-10,206.11,207.33,205.52,205.96,122800000,205.96 1986-01-09,207.97,207.97,204.51,206.11,176500000,206.11 1986-01-08,213.80,214.57,207.49,207.97,180300000,207.97 1986-01-07,210.65,213.80,210.65,213.80,153000000,213.80 1986-01-06,210.88,210.98,209.93,210.65,99610000,210.65 1986-01-03,209.59,210.88,209.51,210.88,105000000,210.88 1986-01-02,211.28,211.28,208.93,209.59,98960000,209.59 1985-12-31,210.68,211.61,210.68,211.28,112700000,211.28 1985-12-30,209.61,210.70,209.17,210.68,91970000,210.68 1985-12-27,207.65,209.62,207.65,209.61,81560000,209.61 1985-12-26,207.14,207.76,207.05,207.65,62050000,207.65 1985-12-24,208.57,208.57,206.44,207.14,78300000,207.14 1985-12-23,210.57,210.94,208.44,208.57,107900000,208.57 1985-12-20,210.02,211.77,210.02,210.94,170300000,210.94 1985-12-19,209.81,210.13,209.25,210.02,130200000,210.02 1985-12-18,210.65,211.23,209.24,209.81,137900000,209.81 1985-12-17,212.02,212.45,210.58,210.65,155200000,210.65 1985-12-16,209.94,213.08,209.91,212.02,176000000,212.02 1985-12-13,206.73,210.31,206.73,209.94,177900000,209.94 1985-12-12,206.31,207.65,205.83,206.73,170500000,206.73 1985-12-11,204.39,206.68,204.17,206.31,178500000,206.31 1985-12-10,204.25,205.16,203.68,204.39,156500000,204.39 1985-12-09,202.99,204.65,202.98,204.25,144000000,204.25 1985-12-06,203.88,203.88,202.45,202.99,125500000,202.99 1985-12-05,204.23,205.86,203.79,203.88,181000000,203.88 1985-12-04,200.86,204.23,200.86,204.23,153200000,204.23 1985-12-03,200.46,200.98,200.10,200.86,109700000,200.86 1985-12-02,202.17,202.19,200.20,200.46,103500000,200.46 1985-11-29,202.54,203.40,201.92,202.17,84060000,202.17 1985-11-27,200.67,202.65,200.67,202.54,143700000,202.54 1985-11-26,200.35,201.16,200.11,200.67,123100000,200.67 1985-11-25,201.52,201.52,200.08,200.35,91710000,200.35 1985-11-22,201.41,202.01,201.05,201.52,133800000,201.52 1985-11-21,198.99,201.43,198.99,201.41,150300000,201.41 1985-11-20,198.67,199.20,198.52,198.99,105100000,198.99 1985-11-19,198.71,199.52,198.01,198.67,126100000,198.67 1985-11-18,198.11,198.71,197.51,198.71,108400000,198.71 1985-11-15,199.06,199.58,197.90,198.11,130200000,198.11 1985-11-14,197.10,199.19,196.88,199.06,124900000,199.06 1985-11-13,198.08,198.11,196.91,197.10,109700000,197.10 1985-11-12,197.28,198.66,196.97,198.08,170800000,198.08 1985-11-11,193.72,197.29,193.70,197.28,126500000,197.28 1985-11-08,192.62,193.97,192.53,193.72,115000000,193.72 1985-11-07,192.78,192.96,192.16,192.62,119000000,192.62 1985-11-06,192.37,193.01,191.83,192.76,129500000,192.76 1985-11-05,191.25,192.43,190.99,192.37,119200000,192.37 1985-11-04,191.45,191.96,190.66,191.25,104900000,191.25 1985-11-01,189.82,191.53,189.37,191.53,129400000,191.53 1985-10-31,190.07,190.15,189.35,189.82,121500000,189.82 1985-10-30,189.23,190.09,189.14,190.07,120400000,190.07 1985-10-29,187.76,189.78,187.76,189.23,110600000,189.23 1985-10-28,187.52,187.76,186.93,187.76,97880000,187.76 1985-10-25,188.50,188.51,187.32,187.52,101800000,187.52 1985-10-24,189.09,189.45,188.41,188.50,123100000,188.50 1985-10-23,188.04,189.09,188.04,189.09,121700000,189.09 1985-10-22,186.96,188.56,186.96,188.04,111300000,188.04 1985-10-21,187.04,187.30,186.79,186.96,95680000,186.96 1985-10-18,187.66,188.11,186.89,187.04,107100000,187.04 1985-10-17,187.98,188.52,187.42,187.66,140500000,187.66 1985-10-16,186.08,187.98,186.08,187.98,117400000,187.98 1985-10-15,186.37,187.16,185.66,186.08,110400000,186.08 1985-10-14,184.31,186.37,184.28,186.37,78540000,186.37 1985-10-11,182.78,184.28,182.61,184.28,96370000,184.28 1985-10-10,182.52,182.79,182.05,182.78,90910000,182.78 1985-10-09,181.87,183.27,181.87,182.52,99140000,182.52 1985-10-08,181.87,182.30,181.16,181.87,97170000,181.87 1985-10-07,183.22,183.22,181.30,181.87,95550000,181.87 1985-10-04,184.36,184.36,182.65,183.22,101200000,183.22 1985-10-03,184.06,185.17,183.59,184.36,127500000,184.36 1985-10-02,185.07,185.94,184.06,184.06,147300000,184.06 1985-10-01,182.06,185.08,182.02,185.07,130200000,185.07 1985-09-30,181.30,182.08,181.22,182.08,103600000,182.08 1985-09-26,180.66,181.29,179.45,181.29,106100000,181.29 1985-09-25,182.62,182.62,180.62,180.66,92120000,180.66 1985-09-24,184.30,184.30,182.42,182.62,97870000,182.62 1985-09-23,182.05,184.65,182.05,184.30,104800000,184.30 1985-09-20,183.39,183.99,182.04,182.05,101400000,182.05 1985-09-19,181.71,183.40,181.71,183.39,100300000,183.39 1985-09-18,181.36,181.83,180.81,181.71,105700000,181.71 1985-09-17,182.88,182.88,180.78,181.36,111900000,181.36 1985-09-16,182.91,182.91,182.45,182.88,66700000,182.88 1985-09-13,183.69,184.19,182.05,182.91,111400000,182.91 1985-09-12,185.03,185.21,183.49,183.69,107100000,183.69 1985-09-11,186.90,186.90,184.79,185.03,100400000,185.03 1985-09-10,188.25,188.26,186.50,186.90,104700000,186.90 1985-09-09,188.24,188.80,187.90,188.25,89850000,188.25 1985-09-06,187.27,188.43,187.27,188.24,95040000,188.24 1985-09-05,187.37,187.52,186.89,187.27,94480000,187.27 1985-09-04,187.91,187.92,186.97,187.37,85510000,187.37 1985-09-03,188.63,188.63,187.38,187.91,81190000,187.91 1985-08-30,188.93,189.13,188.00,188.63,81620000,188.63 1985-08-29,188.73,188.94,188.38,188.93,85660000,188.93 1985-08-28,188.10,188.83,187.90,188.83,88530000,188.83 1985-08-27,187.31,188.10,187.31,188.10,82140000,188.10 1985-08-26,187.17,187.44,186.46,187.31,70290000,187.31 1985-08-23,187.22,187.35,186.59,187.17,75270000,187.17 1985-08-22,189.11,189.23,187.20,187.36,90600000,187.36 1985-08-21,188.08,189.16,188.08,189.16,94880000,189.16 1985-08-20,186.38,188.27,186.38,188.08,91230000,188.08 1985-08-19,186.10,186.82,186.10,186.38,67930000,186.38 1985-08-16,187.26,187.26,186.10,186.10,87910000,186.10 1985-08-15,187.41,187.74,186.62,187.26,86100000,187.26 1985-08-14,187.30,187.87,187.30,187.41,85780000,187.41 1985-08-13,187.63,188.15,186.51,187.30,80300000,187.30 1985-08-12,188.32,188.32,187.43,187.63,77340000,187.63 1985-08-09,188.95,189.05,188.11,188.32,81750000,188.32 1985-08-08,187.68,188.96,187.68,188.95,102900000,188.95 1985-08-07,187.93,187.93,187.39,187.68,100000000,187.68 1985-08-06,190.62,190.72,187.87,187.93,104000000,187.93 1985-08-05,191.48,191.48,189.95,190.62,79610000,190.62 1985-08-02,192.11,192.11,191.27,191.48,87860000,191.48 1985-08-01,190.92,192.17,190.91,192.11,121500000,192.11 1985-07-31,189.93,191.33,189.93,190.92,124200000,190.92 1985-07-30,189.62,190.05,189.30,189.93,102300000,189.93 1985-07-29,192.40,192.42,189.53,189.60,95960000,189.60 1985-07-26,192.06,192.78,191.58,192.40,107000000,192.40 1985-07-25,191.58,192.23,191.17,192.06,123300000,192.06 1985-07-24,192.55,192.55,190.66,191.58,128600000,191.58 1985-07-23,194.35,194.98,192.28,192.55,143600000,192.55 1985-07-22,195.13,195.13,193.58,194.35,93540000,194.35 1985-07-19,194.38,195.13,194.28,195.13,114800000,195.13 1985-07-18,195.65,195.65,194.34,194.38,131400000,194.38 1985-07-17,194.86,196.07,194.72,195.65,159900000,195.65 1985-07-16,192.72,194.72,192.72,194.72,132500000,194.72 1985-07-15,193.29,193.84,192.55,192.72,103900000,192.72 1985-07-12,192.94,193.32,192.64,193.29,120300000,193.29 1985-07-11,192.37,192.95,192.28,192.94,122800000,192.94 1985-07-10,191.05,192.37,190.99,192.37,108200000,192.37 1985-07-09,191.93,191.93,190.81,191.05,99060000,191.05 1985-07-08,192.47,192.52,191.26,191.93,83670000,191.93 1985-07-05,191.45,192.67,191.45,192.52,62450000,192.52 1985-07-03,192.01,192.08,191.37,191.45,98410000,191.45 1985-07-02,192.43,192.63,191.84,192.01,111100000,192.01 1985-07-01,191.85,192.43,191.17,192.43,96080000,192.43 1985-06-28,191.23,191.85,191.04,191.85,105200000,191.85 1985-06-27,190.06,191.36,190.06,191.23,106700000,191.23 1985-06-26,189.74,190.26,189.44,190.06,94130000,190.06 1985-06-25,189.15,190.96,189.15,189.74,115700000,189.74 1985-06-24,188.77,189.61,187.84,189.15,96040000,189.15 1985-06-21,186.73,189.66,186.43,189.61,125400000,189.61 1985-06-20,186.63,186.74,185.97,186.73,87500000,186.73 1985-06-19,187.34,187.98,186.63,186.63,108300000,186.63 1985-06-18,186.53,187.65,186.51,187.34,106900000,187.34 1985-06-17,187.10,187.10,185.98,186.53,82170000,186.53 1985-06-14,185.33,187.10,185.33,187.10,93090000,187.10 1985-06-13,187.61,187.61,185.03,185.33,107000000,185.33 1985-06-12,189.04,189.04,187.59,187.61,97700000,187.61 1985-06-11,189.51,189.61,188.78,189.04,102100000,189.04 1985-06-10,189.68,189.68,188.82,189.51,87940000,189.51 1985-06-07,191.06,191.29,189.55,189.68,99630000,189.68 1985-06-06,189.75,191.06,189.13,191.06,117200000,191.06 1985-06-05,190.04,191.02,190.04,190.16,143900000,190.16 1985-06-04,189.32,190.27,188.88,190.04,115400000,190.04 1985-06-03,189.55,190.36,188.93,189.32,125000000,189.32 1985-05-31,187.75,189.59,187.45,189.55,134100000,189.55 1985-05-30,187.68,188.04,187.09,187.75,108300000,187.75 1985-05-29,187.86,187.86,187.11,187.68,96540000,187.68 1985-05-28,188.29,188.94,187.38,187.86,90600000,187.86 1985-05-24,187.60,188.29,187.29,188.29,85970000,188.29 1985-05-23,188.56,188.56,187.45,187.60,101000000,187.60 1985-05-22,189.64,189.64,187.71,188.56,101400000,188.56 1985-05-21,189.72,189.81,188.78,189.64,130200000,189.64 1985-05-20,187.42,189.98,187.42,189.72,146300000,189.72 1985-05-17,185.66,187.94,185.47,187.42,124600000,187.42 1985-05-16,184.54,185.74,184.54,185.66,99420000,185.66 1985-05-15,183.87,185.43,183.86,184.54,106100000,184.54 1985-05-14,184.61,185.17,183.65,183.87,97360000,183.87 1985-05-13,184.28,184.61,184.19,184.61,85830000,184.61 1985-05-10,181.92,184.74,181.92,184.28,140300000,184.28 1985-05-09,180.62,181.97,180.62,181.92,111000000,181.92 1985-05-08,180.76,180.76,179.96,180.62,101300000,180.62 1985-05-07,179.99,181.09,179.87,180.76,100200000,180.76 1985-05-06,180.08,180.56,179.82,179.99,85650000,179.99 1985-05-03,179.01,180.30,179.01,180.08,94870000,180.08 1985-05-02,178.37,179.01,178.37,179.01,107700000,179.01 1985-05-01,179.83,180.04,178.35,178.37,101600000,178.37 1985-04-30,180.63,180.63,178.86,179.83,111800000,179.83 1985-04-29,182.18,182.34,180.62,180.63,88860000,180.63 1985-04-26,183.43,183.61,182.11,182.18,86570000,182.18 1985-04-25,182.26,183.43,182.12,183.43,108600000,183.43 1985-04-24,181.88,182.27,181.74,182.26,99600000,182.26 1985-04-23,180.70,181.97,180.34,181.88,108900000,181.88 1985-04-22,181.11,181.23,180.25,180.70,79930000,180.70 1985-04-19,180.84,181.25,180.42,181.11,81110000,181.11 1985-04-18,181.68,182.56,180.75,180.84,100600000,180.84 1985-04-17,181.20,181.91,181.14,181.68,96020000,181.68 1985-04-16,180.92,181.78,180.19,181.20,98480000,181.20 1985-04-15,180.54,181.15,180.45,180.92,80660000,180.92 1985-04-12,180.19,180.55,180.06,180.54,86220000,180.54 1985-04-11,179.42,180.91,179.42,180.19,108400000,180.19 1985-04-10,178.21,179.90,178.21,179.42,108200000,179.42 1985-04-09,178.03,178.67,177.97,178.21,83980000,178.21 1985-04-08,179.03,179.46,177.86,178.03,79960000,178.03 1985-04-04,179.11,179.13,178.29,179.03,86910000,179.03 1985-04-03,180.53,180.53,178.64,179.11,95480000,179.11 1985-04-02,181.27,181.86,180.28,180.53,101700000,180.53 1985-04-01,180.66,181.27,180.43,181.27,89900000,181.27 1985-03-29,179.54,180.66,179.54,180.66,101400000,180.66 1985-03-28,179.54,180.60,179.43,179.54,99780000,179.54 1985-03-27,178.43,179.80,178.43,179.54,101000000,179.54 1985-03-26,177.97,178.86,177.88,178.43,89930000,178.43 1985-03-25,179.04,179.04,177.85,177.97,74040000,177.97 1985-03-22,179.35,179.92,178.86,179.04,99250000,179.04 1985-03-21,179.08,180.22,178.89,179.35,95930000,179.35 1985-03-20,179.54,179.78,178.79,179.08,107500000,179.08 1985-03-19,176.88,179.56,176.87,179.54,119200000,179.54 1985-03-18,176.53,177.66,176.53,176.88,94020000,176.88 1985-03-15,177.84,178.41,176.53,176.53,105200000,176.53 1985-03-14,178.19,178.53,177.61,177.84,103400000,177.84 1985-03-13,179.66,179.96,178.02,178.19,101700000,178.19 1985-03-12,178.79,180.14,178.70,179.66,92840000,179.66 1985-03-11,179.10,179.46,178.15,178.79,84110000,178.79 1985-03-08,179.51,179.97,179.07,179.10,96390000,179.10 1985-03-07,180.65,180.65,179.44,179.51,112100000,179.51 1985-03-06,182.23,182.25,180.59,180.65,116900000,180.65 1985-03-05,182.06,182.65,181.42,182.23,116400000,182.23 1985-03-04,183.23,183.41,181.40,182.06,102100000,182.06 1985-03-01,181.18,183.89,181.16,183.23,139900000,183.23 1985-02-28,180.71,181.21,180.33,181.18,100700000,181.18 1985-02-27,181.17,181.87,180.50,180.71,107700000,180.71 1985-02-26,179.23,181.58,179.16,181.17,114200000,181.17 1985-02-25,179.36,179.36,178.13,179.23,89740000,179.23 1985-02-22,180.19,180.41,179.23,179.36,93680000,179.36 1985-02-21,181.18,181.18,180.02,180.19,104000000,180.19 1985-02-20,181.33,182.10,180.64,181.18,118200000,181.18 1985-02-19,181.60,181.61,180.95,181.33,90400000,181.33 1985-02-15,182.41,182.65,181.23,181.60,106500000,181.60 1985-02-14,183.35,183.95,182.39,182.41,139700000,182.41 1985-02-13,180.56,183.86,180.50,183.35,142500000,183.35 1985-02-12,180.51,180.75,179.45,180.56,111100000,180.56 1985-02-11,182.19,182.19,180.11,180.51,104000000,180.51 1985-02-08,181.82,182.39,181.67,182.19,116500000,182.19 1985-02-07,180.43,181.96,180.43,181.82,151700000,181.82 1985-02-06,180.61,181.50,180.32,180.43,141000000,180.43 1985-02-05,180.35,181.53,180.07,180.61,143900000,180.61 1985-02-04,178.63,180.35,177.75,180.35,113700000,180.35 1985-02-01,179.63,179.63,178.44,178.63,105400000,178.63 1985-01-31,179.39,179.83,178.56,179.63,132500000,179.63 1985-01-30,179.18,180.27,179.05,179.39,170000000,179.39 1985-01-29,177.40,179.19,176.58,179.18,115700000,179.18 1985-01-28,177.35,178.19,176.56,177.40,128400000,177.40 1985-01-25,176.71,177.75,176.54,177.35,122400000,177.35 1985-01-24,177.30,178.16,176.56,176.71,160700000,176.71 1985-01-23,175.48,177.30,175.15,177.30,144400000,177.30 1985-01-22,175.23,176.63,175.14,175.48,174800000,175.48 1985-01-21,171.32,175.45,171.31,175.23,146800000,175.23 1985-01-18,170.73,171.42,170.66,171.32,104700000,171.32 1985-01-17,171.19,171.34,170.22,170.73,113600000,170.73 1985-01-16,170.81,171.94,170.41,171.19,135500000,171.19 1985-01-15,170.51,171.82,170.40,170.81,155300000,170.81 1985-01-14,167.91,170.55,167.58,170.51,124900000,170.51 1985-01-11,168.31,168.72,167.58,167.91,107600000,167.91 1985-01-10,165.18,168.31,164.99,168.31,124700000,168.31 1985-01-09,163.99,165.57,163.99,165.18,99230000,165.18 1985-01-08,164.24,164.59,163.91,163.99,92110000,163.99 1985-01-07,163.68,164.71,163.68,164.24,86190000,164.24 1985-01-04,164.55,164.55,163.36,163.68,77480000,163.68 1985-01-03,165.37,166.11,164.38,164.57,88880000,164.57 1985-01-02,167.20,167.20,165.19,165.37,67820000,165.37 1984-12-31,166.26,167.34,166.06,167.24,80260000,167.24 1984-12-28,165.75,166.32,165.67,166.26,77070000,166.26 1984-12-27,166.47,166.50,165.62,165.75,70100000,165.75 1984-12-26,166.76,166.76,166.29,166.47,46700000,166.47 1984-12-24,165.51,166.93,165.50,166.76,55550000,166.76 1984-12-21,166.34,166.38,164.62,165.51,101200000,165.51 1984-12-20,167.16,167.58,166.29,166.38,93220000,166.38 1984-12-19,168.11,169.03,166.84,167.16,139600000,167.16 1984-12-18,163.61,168.11,163.61,168.11,169000000,168.11 1984-12-17,162.69,163.63,162.44,163.61,89490000,163.61 1984-12-14,161.81,163.53,161.63,162.69,95060000,162.69 1984-12-13,162.63,162.92,161.54,161.81,80850000,161.81 1984-12-12,163.07,163.18,162.55,162.63,78710000,162.63 1984-12-11,162.83,163.18,162.56,163.07,80240000,163.07 1984-12-10,162.26,163.32,161.54,162.83,81140000,162.83 1984-12-07,162.76,163.31,162.26,162.26,81000000,162.26 1984-12-06,162.10,163.11,161.76,162.76,96560000,162.76 1984-12-05,163.38,163.40,161.93,162.10,88700000,162.10 1984-12-04,162.82,163.91,162.82,163.38,81250000,163.38 1984-12-03,163.58,163.58,162.29,162.82,95300000,162.82 1984-11-30,163.91,163.91,162.99,163.58,77580000,163.58 1984-11-29,165.02,165.02,163.78,163.91,75860000,163.91 1984-11-28,166.29,166.90,164.97,165.02,86300000,165.02 1984-11-27,165.55,166.85,165.07,166.29,95470000,166.29 1984-11-26,166.92,166.92,165.37,165.55,76520000,165.55 1984-11-23,164.52,166.92,164.52,166.92,73910000,166.92 1984-11-21,164.18,164.68,163.29,164.51,81620000,164.51 1984-11-20,163.10,164.47,163.10,164.18,83240000,164.18 1984-11-19,164.10,164.34,163.03,163.09,69730000,163.09 1984-11-16,165.89,166.24,164.09,164.10,83140000,164.10 1984-11-15,165.99,166.49,165.61,165.89,81530000,165.89 1984-11-14,165.97,166.43,165.39,165.99,73940000,165.99 1984-11-13,167.36,167.38,165.79,165.97,69790000,165.97 1984-11-12,167.65,167.65,166.67,167.36,55610000,167.36 1984-11-09,168.68,169.46,167.44,167.60,83620000,167.60 1984-11-08,169.19,169.27,168.27,168.68,88580000,168.68 1984-11-07,170.41,170.41,168.44,169.17,110800000,169.17 1984-11-06,168.58,170.41,168.58,170.41,101200000,170.41 1984-11-05,167.42,168.65,167.33,168.58,84730000,168.58 1984-11-02,167.49,167.95,167.24,167.42,96810000,167.42 1984-11-01,166.09,167.83,166.09,167.49,107300000,167.49 1984-10-31,166.74,166.95,165.99,166.09,91890000,166.09 1984-10-30,164.78,167.33,164.78,166.84,95200000,166.84 1984-10-29,165.29,165.29,164.67,164.78,63200000,164.78 1984-10-26,166.31,166.31,164.93,165.29,83900000,165.29 1984-10-25,167.20,167.62,166.17,166.31,92760000,166.31 1984-10-24,167.09,167.54,166.82,167.20,91620000,167.20 1984-10-23,167.36,168.27,166.83,167.09,92260000,167.09 1984-10-22,167.96,168.36,167.26,167.36,81020000,167.36 1984-10-19,168.08,169.62,167.31,167.96,186900000,167.96 1984-10-18,164.14,168.10,163.80,168.10,149500000,168.10 1984-10-17,164.78,165.04,163.71,164.14,99740000,164.14 1984-10-16,165.78,165.78,164.66,164.78,82930000,164.78 1984-10-15,164.18,166.15,164.09,165.77,87590000,165.77 1984-10-12,162.78,164.47,162.78,164.18,92190000,164.18 1984-10-11,162.11,162.87,162.00,162.78,87020000,162.78 1984-10-10,161.67,162.12,160.02,162.11,94270000,162.11 1984-10-09,162.13,162.84,161.62,161.67,76840000,161.67 1984-10-08,162.68,162.68,161.80,162.13,46360000,162.13 1984-10-05,162.92,163.32,162.51,162.68,82950000,162.68 1984-10-04,162.44,163.22,162.44,162.92,76700000,162.92 1984-10-03,163.59,163.59,162.20,162.44,92400000,162.44 1984-10-02,164.62,165.24,163.55,163.59,89360000,163.59 1984-10-01,166.10,166.10,164.48,164.62,73630000,164.62 1984-09-28,166.96,166.96,165.77,166.10,78950000,166.10 1984-09-27,166.75,167.18,166.33,166.96,88880000,166.96 1984-09-26,165.62,167.20,165.61,166.28,100200000,166.28 1984-09-25,165.28,165.97,164.45,165.62,86250000,165.62 1984-09-24,165.67,166.12,164.98,165.28,76380000,165.28 1984-09-21,167.47,168.67,165.66,165.67,120600000,165.67 1984-09-20,166.94,167.47,166.70,167.47,92030000,167.47 1984-09-19,167.65,168.76,166.89,166.94,119900000,166.94 1984-09-18,168.87,168.87,167.64,167.65,107700000,167.65 1984-09-17,168.78,169.37,167.99,168.87,88790000,168.87 1984-09-14,167.94,169.65,167.94,168.78,137400000,168.78 1984-09-13,164.68,167.94,164.68,167.94,110500000,167.94 1984-09-12,164.45,164.81,164.14,164.68,77980000,164.68 1984-09-11,165.22,166.17,164.28,164.45,101300000,164.45 1984-09-10,164.37,165.05,163.06,164.26,74410000,164.26 1984-09-07,165.65,166.31,164.22,164.37,84110000,164.37 1984-09-06,164.29,165.95,164.29,165.65,91920000,165.65 1984-09-05,164.88,164.88,163.84,164.29,69250000,164.29 1984-09-04,166.68,166.68,164.73,164.88,62110000,164.88 1984-08-31,166.60,166.68,165.78,166.68,57460000,166.68 1984-08-30,167.10,167.19,166.55,166.60,70840000,166.60 1984-08-29,167.40,168.21,167.03,167.09,90660000,167.09 1984-08-28,166.44,167.43,166.21,167.40,70560000,167.40 1984-08-27,167.51,167.51,165.81,166.44,57660000,166.44 1984-08-24,167.12,167.52,167.12,167.51,69640000,167.51 1984-08-23,167.06,167.78,166.61,167.12,83130000,167.12 1984-08-22,167.83,168.80,166.92,167.06,116000000,167.06 1984-08-21,164.94,168.22,164.93,167.83,128100000,167.83 1984-08-20,164.14,164.94,163.76,164.94,75450000,164.94 1984-08-17,164.30,164.61,163.78,164.14,71500000,164.14 1984-08-16,162.80,164.42,162.75,163.77,93610000,163.77 1984-08-15,164.42,164.42,162.75,162.80,91880000,162.80 1984-08-14,165.43,166.09,164.28,164.42,81470000,164.42 1984-08-13,164.84,165.49,163.98,165.43,77960000,165.43 1984-08-10,165.54,168.59,165.24,165.42,171000000,165.42 1984-08-09,161.75,165.88,161.47,165.54,131100000,165.54 1984-08-08,162.71,163.87,161.75,161.75,121200000,161.75 1984-08-07,162.60,163.58,160.81,162.72,127900000,162.72 1984-08-06,162.35,165.27,162.09,162.60,203000000,162.60 1984-08-03,160.28,162.56,158.00,162.35,236500000,162.35 1984-08-02,154.08,157.99,154.08,157.99,172800000,157.99 1984-08-01,150.66,154.08,150.66,154.08,127500000,154.08 1984-07-31,150.19,150.77,149.65,150.66,86910000,150.66 1984-07-30,151.19,151.19,150.14,150.19,72330000,150.19 1984-07-27,150.08,151.38,149.99,151.19,101350000,151.19 1984-07-26,148.83,150.16,148.83,150.08,90410000,150.08 1984-07-25,147.82,149.30,147.26,148.83,90520000,148.83 1984-07-24,148.95,149.28,147.78,147.82,74370000,147.82 1984-07-23,149.55,149.55,147.85,148.95,77990000,148.95 1984-07-20,150.37,150.58,149.07,149.55,79090000,149.55 1984-07-19,151.40,151.40,150.27,150.37,85230000,150.37 1984-07-18,152.38,152.38,151.11,151.40,76640000,151.40 1984-07-17,151.60,152.60,151.26,152.38,82890000,152.38 1984-07-16,150.88,151.60,150.01,151.60,73420000,151.60 1984-07-13,150.03,151.16,150.03,150.88,75480000,150.88 1984-07-12,150.56,151.06,149.63,150.03,86050000,150.03 1984-07-11,152.89,152.89,150.55,150.56,89540000,150.56 1984-07-10,153.36,153.53,152.57,152.89,74010000,152.89 1984-07-09,152.24,153.53,151.44,153.36,74830000,153.36 1984-07-06,152.76,152.76,151.63,152.24,65850000,152.24 1984-07-05,153.70,153.87,152.71,152.76,66100000,152.76 1984-07-03,153.20,153.86,153.10,153.70,69960000,153.70 1984-07-02,153.16,153.22,152.44,153.20,69230000,153.20 1984-06-29,152.84,154.08,152.82,153.18,90770000,153.18 1984-06-28,151.64,153.07,151.62,152.84,77660000,152.84 1984-06-27,152.71,152.88,151.30,151.64,78400000,151.64 1984-06-26,153.97,153.97,152.47,152.71,82600000,152.71 1984-06-25,154.46,154.67,153.86,153.97,72850000,153.97 1984-06-22,154.51,154.92,153.89,154.46,98400000,154.46 1984-06-21,154.84,155.64,154.05,154.51,123380000,154.51 1984-06-20,151.89,154.84,150.96,154.84,99090000,154.84 1984-06-19,151.73,153.00,151.73,152.61,98000000,152.61 1984-06-18,149.03,151.92,148.53,151.73,94900000,151.73 1984-06-15,150.49,150.71,149.02,149.03,85460000,149.03 1984-06-14,152.12,152.14,150.31,150.39,79120000,150.39 1984-06-13,152.19,152.85,151.86,152.13,67510000,152.13 1984-06-12,153.06,153.07,151.61,152.19,84660000,152.19 1984-06-11,155.17,155.17,153.00,153.06,69050000,153.06 1984-06-08,154.92,155.40,154.57,155.17,67840000,155.17 1984-06-07,155.01,155.11,154.36,154.92,82120000,154.92 1984-06-06,153.65,155.03,153.38,155.01,83440000,155.01 1984-06-05,154.34,154.34,153.28,153.65,84840000,153.65 1984-06-04,153.24,155.10,153.24,154.34,96740000,154.34 1984-06-01,150.55,153.24,150.55,153.24,96040000,153.24 1984-05-31,150.35,150.69,149.76,150.55,81890000,150.55 1984-05-30,150.29,151.43,148.68,150.35,105660000,150.35 1984-05-29,151.62,151.86,149.95,150.29,69060000,150.29 1984-05-25,151.23,152.02,150.85,151.62,78190000,151.62 1984-05-24,153.15,153.15,150.80,151.23,99040000,151.23 1984-05-23,153.88,154.02,153.10,153.15,82690000,153.15 1984-05-22,154.73,154.73,152.99,153.88,88030000,153.88 1984-05-21,155.78,156.11,154.63,154.73,73380000,154.73 1984-05-18,156.57,156.77,155.24,155.78,81270000,155.78 1984-05-17,157.99,157.99,156.15,156.57,90310000,156.57 1984-05-16,158.00,158.41,157.83,157.99,89210000,157.99 1984-05-15,157.50,158.27,157.29,158.00,88250000,158.00 1984-05-14,158.49,158.49,157.20,157.50,64900000,157.50 1984-05-11,160.00,160.00,157.42,158.49,82780000,158.49 1984-05-10,160.11,160.45,159.61,160.00,101810000,160.00 1984-05-09,160.52,161.31,159.39,160.11,100590000,160.11 1984-05-08,159.47,160.52,159.14,160.52,81610000,160.52 1984-05-07,159.11,159.48,158.63,159.47,72760000,159.47 1984-05-04,161.20,161.20,158.93,159.11,98580000,159.11 1984-05-03,161.90,161.90,160.95,161.20,91910000,161.20 1984-05-02,161.68,162.11,161.41,161.90,107080000,161.90 1984-05-01,160.05,161.69,160.05,161.68,110550000,161.68 1984-04-30,159.89,160.43,159.30,160.05,72740000,160.05 1984-04-27,160.30,160.69,159.77,159.89,88530000,159.89 1984-04-26,158.65,160.50,158.65,160.30,98000000,160.30 1984-04-25,158.07,158.77,157.80,158.65,83520000,158.65 1984-04-24,156.80,158.38,156.61,158.07,87060000,158.07 1984-04-23,158.02,158.05,156.79,156.80,73080000,156.80 1984-04-19,157.90,158.02,157.10,158.02,75860000,158.02 1984-04-18,158.97,158.97,157.64,157.90,85040000,157.90 1984-04-17,158.32,159.59,158.32,158.97,98150000,158.97 1984-04-16,157.31,158.35,156.49,158.32,73870000,158.32 1984-04-13,157.73,158.87,157.13,157.31,99620000,157.31 1984-04-12,155.00,157.74,154.17,157.73,96330000,157.73 1984-04-11,155.93,156.31,154.90,155.00,80280000,155.00 1984-04-10,155.45,156.57,155.45,155.87,78990000,155.87 1984-04-09,155.48,155.86,154.71,155.45,71570000,155.45 1984-04-06,155.04,155.48,154.12,155.48,86620000,155.48 1984-04-05,157.54,158.10,154.96,155.04,101750000,155.04 1984-04-04,157.66,158.11,157.29,157.54,92860000,157.54 1984-04-03,157.99,158.27,157.17,157.66,87980000,157.66 1984-04-02,159.18,159.87,157.63,157.98,85680000,157.98 1984-03-30,159.52,159.52,158.92,159.18,71590000,159.18 1984-03-29,159.88,160.46,159.52,159.52,81470000,159.52 1984-03-28,157.30,159.90,157.30,159.88,104870000,159.88 1984-03-27,156.67,157.30,156.61,157.30,73670000,157.30 1984-03-26,156.86,157.18,156.31,156.67,69070000,156.67 1984-03-23,156.69,156.92,156.02,156.86,79760000,156.86 1984-03-22,158.66,158.67,156.61,156.69,87340000,156.69 1984-03-21,158.86,159.26,158.59,158.66,87170000,158.66 1984-03-20,157.78,159.17,157.78,158.86,86460000,158.86 1984-03-19,159.27,159.27,157.28,157.78,64060000,157.78 1984-03-16,157.41,160.45,157.41,159.27,118000000,159.27 1984-03-15,156.78,158.05,156.73,157.41,79520000,157.41 1984-03-14,156.78,157.17,156.22,156.77,77250000,156.77 1984-03-13,156.34,157.93,156.34,156.78,102600000,156.78 1984-03-12,154.35,156.35,154.35,156.34,84470000,156.34 1984-03-09,155.12,155.19,153.77,154.35,73170000,154.35 1984-03-08,154.57,155.80,154.35,155.19,80630000,155.19 1984-03-07,156.25,156.25,153.81,154.57,90080000,154.57 1984-03-06,157.89,158.37,156.21,156.25,83590000,156.25 1984-03-05,159.24,159.24,157.59,157.89,69870000,157.89 1984-03-02,158.19,159.90,158.19,159.24,108270000,159.24 1984-03-01,157.06,158.19,156.77,158.19,82010000,158.19 1984-02-29,156.82,158.27,156.41,157.06,92810000,157.06 1984-02-28,159.30,159.30,156.59,156.82,91010000,156.82 1984-02-27,157.51,159.58,157.08,159.30,99140000,159.30 1984-02-24,154.31,157.51,154.29,157.51,102620000,157.51 1984-02-23,154.02,154.45,152.13,154.29,100220000,154.29 1984-02-22,154.52,155.10,153.94,154.31,90080000,154.31 1984-02-21,155.71,155.74,154.47,154.64,71890000,154.64 1984-02-17,156.13,156.80,155.51,155.74,76600000,155.74 1984-02-16,155.94,156.44,155.44,156.13,81750000,156.13 1984-02-15,156.61,157.48,156.10,156.25,94870000,156.25 1984-02-14,154.95,156.61,154.95,156.61,91800000,156.61 1984-02-13,156.30,156.32,154.13,154.95,78460000,154.95 1984-02-10,155.42,156.52,155.42,156.30,92220000,156.30 1984-02-09,155.85,156.17,154.30,155.42,128190000,155.42 1984-02-08,158.74,159.07,155.67,155.85,96890000,155.85 1984-02-07,157.91,158.81,157.01,158.74,107640000,158.74 1984-02-06,160.91,160.91,158.02,158.08,109090000,158.08 1984-02-03,163.44,163.98,160.82,160.91,109100000,160.91 1984-02-02,162.74,163.36,162.24,163.36,111330000,163.36 1984-02-01,163.41,164.00,162.27,162.74,107100000,162.74 1984-01-31,162.87,163.60,162.03,163.41,113510000,163.41 1984-01-30,164.40,164.67,162.40,162.87,103120000,162.87 1984-01-27,164.24,164.33,163.07,163.94,103720000,163.94 1984-01-26,164.84,165.55,164.12,164.24,111100000,164.24 1984-01-25,165.94,167.12,164.74,164.84,113470000,164.84 1984-01-24,164.87,166.35,164.84,165.94,103050000,165.94 1984-01-23,166.21,166.21,164.83,164.87,82010000,164.87 1984-01-20,167.04,167.06,165.87,166.21,93360000,166.21 1984-01-19,167.55,167.65,166.67,167.04,98340000,167.04 1984-01-18,167.83,168.34,167.02,167.55,109010000,167.55 1984-01-17,167.18,167.84,167.01,167.83,92750000,167.83 1984-01-16,167.02,167.55,166.77,167.18,93790000,167.18 1984-01-13,167.75,168.59,166.64,167.02,101790000,167.02 1984-01-12,167.79,168.40,167.68,167.75,99410000,167.75 1984-01-11,167.95,168.07,167.27,167.80,98660000,167.80 1984-01-10,168.90,169.54,167.87,167.95,109570000,167.95 1984-01-09,169.18,169.46,168.48,168.90,107100000,168.90 1984-01-06,168.81,169.31,168.49,169.28,137590000,169.28 1984-01-05,166.78,169.10,166.78,168.81,159990000,168.81 1984-01-04,164.09,166.78,164.04,166.78,112980000,166.78 1984-01-03,164.93,164.93,163.98,164.04,71340000,164.04 1983-12-30,164.86,165.05,164.58,164.93,71840000,164.93 1983-12-29,165.33,165.84,164.83,164.86,86560000,164.86 1983-12-28,164.69,165.34,164.30,165.34,85660000,165.34 1983-12-27,163.22,164.76,163.22,164.76,63800000,164.76 1983-12-23,163.27,163.31,162.90,163.22,62710000,163.22 1983-12-22,163.56,164.18,163.17,163.53,106260000,163.53 1983-12-21,162.00,163.57,161.99,163.56,108080000,163.56 1983-12-20,162.33,162.80,161.64,162.00,83740000,162.00 1983-12-19,162.34,162.88,162.27,162.32,75180000,162.32 1983-12-16,161.69,162.39,161.58,162.39,81030000,162.39 1983-12-15,163.33,163.33,161.66,161.66,88300000,161.66 1983-12-14,164.93,164.93,163.25,163.33,85430000,163.33 1983-12-13,165.62,165.63,164.85,164.93,93500000,164.93 1983-12-12,165.13,165.62,164.99,165.62,77340000,165.62 1983-12-09,165.20,165.29,164.50,165.08,98280000,165.08 1983-12-08,165.91,166.01,164.86,165.20,96530000,165.20 1983-12-07,165.47,166.34,165.35,165.91,105670000,165.91 1983-12-06,165.77,165.93,165.34,165.47,89690000,165.47 1983-12-05,165.44,165.79,164.71,165.76,88330000,165.76 1983-12-02,166.49,166.70,165.25,165.44,93960000,165.44 1983-12-01,166.37,166.77,166.08,166.49,106970000,166.49 1983-11-30,167.91,168.07,166.33,166.40,120130000,166.40 1983-11-29,166.54,167.92,166.17,167.91,100460000,167.91 1983-11-28,167.20,167.22,166.21,166.54,78210000,166.54 1983-11-25,167.02,167.20,166.73,167.18,57820000,167.18 1983-11-23,166.88,167.21,166.26,166.96,108080000,166.96 1983-11-22,166.05,167.26,166.05,166.84,117550000,166.84 1983-11-21,165.04,166.05,165.00,166.05,97740000,166.05 1983-11-18,166.08,166.13,164.50,165.09,88280000,165.09 1983-11-17,166.08,166.49,165.51,166.13,80740000,166.13 1983-11-16,165.36,166.41,165.34,166.08,83380000,166.08 1983-11-15,166.58,166.59,165.28,165.36,77840000,165.36 1983-11-14,166.29,167.58,166.27,166.58,86880000,166.58 1983-11-11,164.41,166.30,164.34,166.29,74270000,166.29 1983-11-10,163.99,164.71,163.97,164.41,88730000,164.41 1983-11-09,161.74,163.97,161.74,163.97,83100000,163.97 1983-11-08,161.91,162.15,161.63,161.76,64900000,161.76 1983-11-07,162.42,162.56,161.84,161.91,69400000,161.91 1983-11-04,162.68,163.45,162.22,162.44,72080000,162.44 1983-11-03,164.84,164.85,163.42,163.45,85350000,163.45 1983-11-02,165.21,165.21,163.55,164.84,95210000,164.84 1983-11-01,163.55,163.66,162.37,163.66,84460000,163.66 1983-10-31,163.37,164.58,162.86,163.55,79460000,163.55 1983-10-28,164.89,165.19,163.23,163.37,81180000,163.37 1983-10-27,165.31,165.38,164.41,164.84,79570000,164.84 1983-10-26,166.49,166.65,165.36,165.38,79570000,165.38 1983-10-25,166.00,167.15,166.00,166.47,82530000,166.47 1983-10-24,165.85,165.99,163.85,165.99,85420000,165.99 1983-10-21,166.97,167.23,164.98,165.95,91640000,165.95 1983-10-20,166.77,167.35,166.44,166.98,86000000,166.98 1983-10-19,167.81,167.81,165.67,166.73,107790000,166.73 1983-10-18,170.41,170.41,167.67,167.81,91080000,167.81 1983-10-17,169.85,171.18,169.63,170.43,77730000,170.43 1983-10-14,169.88,169.99,169.18,169.86,71600000,169.86 1983-10-13,169.63,170.12,169.13,169.87,67750000,169.87 1983-10-12,170.34,170.84,169.34,169.62,75630000,169.62 1983-10-11,172.59,172.59,170.34,170.34,79510000,170.34 1983-10-10,170.77,172.65,170.05,172.65,67050000,172.65 1983-10-07,170.32,171.10,170.31,170.80,103630000,170.80 1983-10-06,167.76,170.28,167.76,170.28,118270000,170.28 1983-10-05,166.29,167.74,165.92,167.74,101710000,167.74 1983-10-04,165.81,166.80,165.81,166.27,90270000,166.27 1983-10-03,165.99,166.07,164.93,165.81,77230000,165.81 1983-09-30,167.23,167.23,165.63,166.07,70860000,166.07 1983-09-29,168.02,168.35,167.23,167.23,73730000,167.23 1983-09-28,168.42,168.53,167.52,168.00,75820000,168.00 1983-09-27,170.02,170.02,167.95,168.43,81100000,168.43 1983-09-26,169.53,170.41,169.16,170.07,86400000,170.07 1983-09-23,169.76,170.17,168.88,169.51,93180000,169.51 1983-09-22,168.40,169.78,168.22,169.76,97050000,169.76 1983-09-21,169.27,169.30,168.21,168.41,91280000,168.41 1983-09-20,167.64,169.38,167.64,169.24,103050000,169.24 1983-09-19,166.27,168.09,166.26,167.62,85630000,167.62 1983-09-16,164.42,166.57,164.39,166.25,75530000,166.25 1983-09-15,165.39,165.58,164.38,164.38,70420000,164.38 1983-09-14,164.80,165.42,164.63,165.35,73370000,165.35 1983-09-13,165.48,165.48,164.17,164.80,73970000,164.80 1983-09-12,166.95,169.20,165.27,165.48,114020000,165.48 1983-09-09,167.77,167.77,166.91,166.92,77990000,166.92 1983-09-08,167.96,168.14,167.12,167.77,79250000,167.77 1983-09-07,167.90,168.48,167.46,167.96,94240000,167.96 1983-09-06,165.20,167.90,165.03,167.89,87500000,167.89 1983-09-02,164.25,165.07,164.21,165.00,59300000,165.00 1983-09-01,164.40,164.66,163.95,164.23,76120000,164.23 1983-08-31,162.55,164.40,162.32,164.40,80800000,164.40 1983-08-30,162.25,163.13,162.11,162.58,62370000,162.58 1983-08-29,162.14,162.32,160.97,162.25,53030000,162.25 1983-08-26,160.85,162.16,160.25,162.14,61650000,162.14 1983-08-25,161.27,161.28,159.96,160.84,70140000,160.84 1983-08-24,162.77,162.77,161.20,161.25,72200000,161.25 1983-08-23,164.33,164.33,162.54,162.77,66800000,162.77 1983-08-22,164.18,165.64,163.77,164.34,76420000,164.34 1983-08-19,163.58,164.27,163.22,163.98,58950000,163.98 1983-08-18,165.29,165.91,163.55,163.55,82280000,163.55 1983-08-17,163.58,165.40,163.43,165.29,87800000,165.29 1983-08-16,163.74,163.84,162.72,163.41,71780000,163.41 1983-08-15,162.22,164.76,162.22,163.70,83200000,163.70 1983-08-12,161.55,162.60,161.55,162.16,71840000,162.16 1983-08-11,161.55,162.14,161.41,161.54,70630000,161.54 1983-08-10,160.11,161.77,159.47,161.54,82900000,161.54 1983-08-09,159.20,160.14,158.50,160.13,81420000,160.13 1983-08-08,161.73,161.73,159.18,159.18,71460000,159.18 1983-08-05,161.33,161.88,160.89,161.74,67850000,161.74 1983-08-04,163.28,163.42,159.63,161.33,100870000,161.33 1983-08-03,162.01,163.44,161.52,163.44,80370000,163.44 1983-08-02,162.06,163.04,161.97,162.01,74460000,162.01 1983-08-01,162.34,162.78,161.55,162.04,77210000,162.04 1983-07-29,165.03,165.03,161.50,162.56,95240000,162.56 1983-07-28,167.32,167.79,164.99,165.04,78410000,165.04 1983-07-27,170.68,170.72,167.49,167.59,99290000,167.59 1983-07-26,169.62,170.63,169.26,170.53,91280000,170.53 1983-07-25,167.67,169.74,167.63,169.53,73680000,169.53 1983-07-22,168.51,169.08,168.40,168.89,68850000,168.89 1983-07-21,169.29,169.80,168.33,169.06,101830000,169.06 1983-07-20,164.89,169.29,164.89,169.29,109310000,169.29 1983-07-19,163.95,165.18,163.95,164.82,74030000,164.82 1983-07-18,164.28,164.29,163.30,163.95,69110000,163.95 1983-07-15,166.01,166.04,164.03,164.29,63160000,164.29 1983-07-14,165.61,166.96,165.61,166.01,83500000,166.01 1983-07-13,165.00,165.68,164.77,165.46,68900000,165.46 1983-07-12,168.05,168.05,165.51,165.53,70220000,165.53 1983-07-11,167.09,168.11,167.09,168.11,61610000,168.11 1983-07-08,167.56,167.98,166.95,167.08,66520000,167.08 1983-07-07,168.48,169.15,167.08,167.56,97130000,167.56 1983-07-06,166.71,168.88,166.49,168.48,85670000,168.48 1983-07-05,166.55,168.80,165.80,166.60,67320000,166.60 1983-07-01,168.11,168.64,167.77,168.64,65110000,168.64 1983-06-30,167.64,167.64,167.64,167.64,76310000,167.64 1983-06-29,165.78,166.64,165.43,166.64,81580000,166.64 1983-06-28,168.45,168.81,165.67,165.68,82730000,165.68 1983-06-27,170.40,170.46,168.32,168.46,69360000,168.46 1983-06-24,170.57,170.69,170.03,170.41,80810000,170.41 1983-06-23,170.99,171.00,170.13,170.57,89590000,170.57 1983-06-22,170.53,171.60,170.42,170.99,110270000,170.99 1983-06-21,169.03,170.60,168.25,170.53,102880000,170.53 1983-06-20,169.13,170.10,168.59,169.02,84270000,169.02 1983-06-17,169.11,169.64,168.60,169.13,93630000,169.13 1983-06-16,167.11,169.38,167.11,169.14,124560000,169.14 1983-06-15,165.52,167.12,165.07,167.12,93410000,167.12 1983-06-14,164.87,165.93,164.87,165.53,97710000,165.53 1983-06-13,162.70,164.84,162.70,164.84,90700000,164.84 1983-06-10,161.86,162.76,161.86,162.68,78470000,162.68 1983-06-09,161.37,161.92,160.80,161.83,87440000,161.83 1983-06-08,162.78,162.78,161.35,161.36,96600000,161.36 1983-06-07,164.84,164.93,162.77,162.77,88550000,162.77 1983-06-06,164.43,165.09,163.75,164.83,87670000,164.83 1983-06-03,163.96,164.79,163.96,164.42,83110000,164.42 1983-06-02,162.56,164.00,162.56,163.98,89750000,163.98 1983-06-01,162.38,162.64,161.33,162.55,84460000,162.55 1983-05-31,164.44,164.44,162.12,162.39,73910000,162.39 1983-05-27,165.49,165.49,164.33,164.46,76290000,164.46 1983-05-26,166.22,166.39,165.27,165.48,94980000,165.48 1983-05-25,165.54,166.21,164.79,166.21,121050000,166.21 1983-05-24,163.45,165.59,163.45,165.54,109850000,165.54 1983-05-23,162.06,163.50,160.29,163.43,84960000,163.43 1983-05-20,161.97,162.14,161.25,162.14,73150000,162.14 1983-05-19,163.27,163.61,161.98,161.99,83260000,161.99 1983-05-18,163.73,165.18,163.16,163.27,99780000,163.27 1983-05-17,163.40,163.71,162.55,163.71,79510000,163.71 1983-05-16,164.90,164.90,162.33,163.40,76250000,163.40 1983-05-13,164.26,165.23,164.26,164.91,83110000,164.91 1983-05-12,164.98,165.35,163.82,164.25,84060000,164.25 1983-05-11,165.95,166.30,164.53,164.96,99820000,164.96 1983-05-10,165.82,166.40,165.74,165.95,104010000,165.95 1983-05-09,166.10,166.46,164.90,165.81,93670000,165.81 1983-05-06,164.30,166.99,164.30,166.10,128200000,166.10 1983-05-05,163.35,164.30,163.35,164.28,107860000,164.28 1983-05-04,162.38,163.64,162.38,163.31,101690000,163.31 1983-05-03,162.10,162.35,160.80,162.34,89550000,162.34 1983-05-02,164.41,164.42,161.99,162.11,88170000,162.11 1983-04-29,162.97,164.43,162.72,164.43,105750000,164.43 1983-04-28,161.44,162.96,161.44,162.95,94410000,162.95 1983-04-27,161.85,162.77,160.76,161.44,118140000,161.44 1983-04-26,158.81,161.81,158.07,161.81,91210000,161.81 1983-04-25,160.43,160.83,158.72,158.81,90150000,158.81 1983-04-22,160.04,160.76,160.02,160.42,92270000,160.42 1983-04-21,160.73,161.08,159.96,160.05,106170000,160.05 1983-04-20,158.71,160.83,158.71,160.71,110240000,160.71 1983-04-19,159.74,159.74,158.54,158.71,91210000,158.71 1983-04-18,158.75,159.75,158.41,159.74,88560000,159.74 1983-04-15,158.11,158.75,158.11,158.75,89590000,158.75 1983-04-14,156.80,158.12,156.55,158.12,90160000,158.12 1983-04-13,155.82,157.22,155.82,156.77,100520000,156.77 1983-04-12,155.15,155.82,154.78,155.82,79900000,155.82 1983-04-11,152.87,155.14,152.87,155.14,81440000,155.14 1983-04-08,151.77,152.85,151.39,152.85,67710000,152.85 1983-04-07,151.04,151.76,150.81,151.76,69480000,151.76 1983-04-06,151.90,151.90,150.17,151.04,77140000,151.04 1983-04-05,153.04,153.92,151.81,151.90,76810000,151.90 1983-04-04,152.92,153.02,152.23,153.02,66010000,153.02 1983-03-31,153.41,155.02,152.86,152.96,100570000,152.96 1983-03-30,151.60,153.39,151.60,153.39,75800000,153.39 1983-03-29,151.85,152.46,151.42,151.59,65300000,151.59 1983-03-28,152.67,152.67,151.56,151.85,58510000,151.85 1983-03-25,153.37,153.71,152.30,152.67,77330000,152.67 1983-03-24,152.82,153.78,152.82,153.37,92340000,153.37 1983-03-23,150.65,152.98,150.65,152.81,94980000,152.81 1983-03-22,151.21,151.59,150.60,150.66,79610000,150.66 1983-03-21,149.82,151.20,149.32,151.19,72160000,151.19 1983-03-18,149.59,150.29,149.56,149.90,75110000,149.90 1983-03-17,149.80,149.80,149.12,149.59,70290000,149.59 1983-03-16,151.36,151.62,149.78,149.81,83570000,149.81 1983-03-15,150.83,151.37,150.40,151.37,62410000,151.37 1983-03-14,151.28,151.30,150.24,150.83,61890000,150.83 1983-03-11,151.75,151.75,150.65,151.24,67240000,151.24 1983-03-10,152.87,154.01,151.75,151.80,95410000,151.80 1983-03-09,151.25,152.87,150.84,152.87,84250000,152.87 1983-03-08,153.63,153.63,151.26,151.26,79410000,151.26 1983-03-07,153.67,154.00,152.65,153.67,84020000,153.67 1983-03-04,153.47,153.67,152.53,153.67,90930000,153.67 1983-03-03,152.31,154.16,152.31,153.48,114440000,153.48 1983-03-02,150.91,152.63,150.91,152.30,112600000,152.30 1983-03-01,148.07,150.88,148.07,150.88,103750000,150.88 1983-02-28,149.74,149.74,147.81,148.06,83750000,148.06 1983-02-25,149.60,150.88,149.60,149.74,100970000,149.74 1983-02-24,146.80,149.67,146.80,149.60,113220000,149.60 1983-02-23,145.47,146.79,145.40,146.79,84100000,146.79 1983-02-22,148.01,148.11,145.42,145.48,84080000,145.48 1983-02-18,147.44,148.29,147.21,148.00,77420000,148.00 1983-02-17,147.43,147.57,143.84,147.44,74930000,147.44 1983-02-16,148.31,148.66,147.41,147.43,82100000,147.43 1983-02-15,148.94,149.41,148.13,148.30,89040000,148.30 1983-02-14,147.71,149.14,147.40,148.93,72640000,148.93 1983-02-11,147.51,148.81,147.18,147.65,86700000,147.65 1983-02-10,145.04,147.75,145.04,147.50,93510000,147.50 1983-02-09,145.70,145.83,144.09,145.00,84520000,145.00 1983-02-08,146.93,147.21,145.52,145.70,76580000,145.70 1983-02-07,146.14,147.42,146.14,146.93,86030000,146.93 1983-02-04,144.26,146.14,144.14,146.14,87000000,146.14 1983-02-03,143.25,144.43,143.25,144.26,78890000,144.26 1983-02-02,142.95,143.52,141.90,143.23,77220000,143.23 1983-02-01,145.29,145.29,142.96,142.96,82750000,142.96 1983-01-31,144.51,145.30,143.93,145.30,67140000,145.30 1983-01-28,144.31,145.47,144.25,144.51,89490000,144.51 1983-01-27,141.54,144.30,141.54,144.27,88120000,144.27 1983-01-26,141.77,142.16,141.16,141.54,73720000,141.54 1983-01-25,139.98,141.75,139.98,141.75,79740000,141.75 1983-01-24,143.84,143.84,139.10,139.97,90800000,139.97 1983-01-21,146.30,146.30,143.25,143.85,77110000,143.85 1983-01-20,145.29,146.62,145.29,146.29,82790000,146.29 1983-01-19,146.40,146.45,144.51,145.27,80900000,145.27 1983-01-18,146.71,146.74,145.52,146.40,78380000,146.40 1983-01-17,146.65,147.90,146.64,146.72,89210000,146.72 1983-01-14,145.72,147.12,145.72,146.65,86480000,146.65 1983-01-13,146.67,146.94,145.67,145.73,77030000,145.73 1983-01-12,145.76,148.36,145.76,146.69,109850000,146.69 1983-01-11,146.79,146.83,145.38,145.78,98250000,145.78 1983-01-10,145.19,147.25,144.58,146.78,101890000,146.78 1983-01-07,145.27,146.46,145.15,145.18,127290000,145.18 1983-01-06,142.01,145.77,142.01,145.27,129410000,145.27 1983-01-05,141.35,142.60,141.15,141.96,95390000,141.96 1983-01-04,138.33,141.36,138.08,141.36,75530000,141.36 1983-01-03,140.65,141.33,138.20,138.34,59080000,138.34 1982-12-31,140.34,140.78,140.27,140.64,42110000,140.64 1982-12-30,141.24,141.68,140.22,140.33,56380000,140.33 1982-12-29,140.77,141.73,140.68,141.24,54810000,141.24 1982-12-28,142.18,142.34,140.75,140.77,58610000,140.77 1982-12-27,139.73,142.32,139.72,142.17,64690000,142.17 1982-12-23,138.84,139.94,138.84,139.72,62880000,139.72 1982-12-22,138.63,139.69,138.60,138.83,83470000,138.83 1982-12-21,136.24,139.27,136.07,138.61,78010000,138.61 1982-12-20,137.49,137.84,136.19,136.25,62210000,136.25 1982-12-17,135.35,137.71,135.35,137.49,76010000,137.49 1982-12-16,135.22,135.78,134.79,135.30,73680000,135.30 1982-12-15,137.40,137.40,135.12,135.24,81030000,135.24 1982-12-14,139.99,142.50,137.34,137.40,98380000,137.40 1982-12-13,139.57,140.12,139.50,139.95,63140000,139.95 1982-12-10,139.99,141.15,139.35,139.57,86430000,139.57 1982-12-09,141.80,141.80,139.92,140.00,90320000,140.00 1982-12-08,142.71,143.58,141.82,141.82,97430000,141.82 1982-12-07,141.79,143.68,141.79,142.72,111620000,142.72 1982-12-06,138.70,141.77,138.01,141.77,83880000,141.77 1982-12-03,138.87,139.59,138.59,138.69,71540000,138.69 1982-12-02,138.72,139.63,138.66,138.82,77600000,138.82 1982-12-01,138.56,140.37,138.35,138.72,107850000,138.72 1982-11-30,134.20,138.53,134.19,138.53,93470000,138.53 1982-11-29,134.89,135.29,133.69,134.20,61080000,134.20 1982-11-26,133.89,134.88,133.89,134.88,38810000,134.88 1982-11-24,132.92,133.88,132.92,133.88,67220000,133.88 1982-11-23,134.21,134.28,132.89,132.93,72920000,132.93 1982-11-22,137.03,137.10,134.21,134.22,74960000,134.22 1982-11-19,138.35,138.93,137.00,137.02,70310000,137.02 1982-11-18,137.93,138.78,137.47,138.34,77620000,138.34 1982-11-17,135.47,137.93,135.47,137.93,84440000,137.93 1982-11-16,136.97,136.97,134.05,135.42,102910000,135.42 1982-11-15,139.54,139.54,137.00,137.03,78900000,137.03 1982-11-12,141.75,141.85,139.53,139.53,95080000,139.53 1982-11-11,141.15,141.75,139.88,141.75,78410000,141.75 1982-11-10,143.04,144.36,140.80,141.16,113240000,141.16 1982-11-09,140.48,143.16,140.46,143.02,111220000,143.02 1982-11-08,142.12,142.12,139.98,140.44,75240000,140.44 1982-11-05,141.85,142.43,141.32,142.16,96550000,142.16 1982-11-04,142.85,143.99,141.65,141.85,149350000,141.85 1982-11-03,137.53,142.88,137.53,142.87,137010000,142.87 1982-11-02,135.48,138.51,135.48,137.49,104770000,137.49 1982-11-01,133.72,136.03,133.22,135.47,73530000,135.47 1982-10-29,133.54,134.02,132.64,133.72,74830000,133.72 1982-10-28,135.28,135.42,133.59,133.59,73590000,133.59 1982-10-27,134.48,135.92,134.48,135.29,81670000,135.29 1982-10-26,133.29,134.48,131.50,134.48,102080000,134.48 1982-10-25,138.81,138.81,133.32,133.32,83720000,133.32 1982-10-22,139.06,140.40,138.75,138.83,101120000,138.83 1982-10-21,139.23,140.27,137.63,139.06,122460000,139.06 1982-10-20,136.58,139.23,136.37,139.23,98680000,139.23 1982-10-19,136.73,137.96,135.72,136.58,100850000,136.58 1982-10-18,133.59,136.73,133.59,136.73,83790000,136.73 1982-10-15,134.55,134.61,133.28,133.57,80290000,133.57 1982-10-14,136.71,136.89,134.55,134.57,107530000,134.57 1982-10-13,134.42,137.97,134.14,136.71,139800000,136.71 1982-10-12,134.48,135.85,133.59,134.44,126310000,134.44 1982-10-11,131.06,135.53,131.06,134.47,138530000,134.47 1982-10-08,128.79,131.11,128.79,131.05,122250000,131.05 1982-10-07,125.99,128.96,125.99,128.80,147070000,128.80 1982-10-06,122.00,125.97,122.00,125.97,93570000,125.97 1982-10-05,121.60,122.73,121.60,121.98,69770000,121.98 1982-10-04,121.97,121.97,120.56,121.51,55650000,121.51 1982-10-01,120.40,121.97,120.15,121.97,65000000,121.97 1982-09-30,121.62,121.62,120.14,120.42,62610000,120.42 1982-09-29,123.24,123.24,121.28,121.63,62550000,121.63 1982-09-28,123.62,124.16,123.21,123.24,65900000,123.24 1982-09-27,123.32,123.62,122.75,123.62,44840000,123.62 1982-09-24,123.79,123.80,123.11,123.32,54600000,123.32 1982-09-23,123.99,124.19,122.96,123.81,68260000,123.81 1982-09-22,124.90,126.43,123.99,123.99,113150000,123.99 1982-09-21,122.51,124.91,122.51,124.88,82920000,124.88 1982-09-20,122.54,122.54,121.48,122.51,58520000,122.51 1982-09-17,123.76,123.76,122.34,122.55,63950000,122.55 1982-09-16,124.28,124.88,123.65,123.77,78900000,123.77 1982-09-15,123.09,124.81,122.72,124.29,69680000,124.29 1982-09-14,122.27,123.69,122.27,123.10,83070000,123.10 1982-09-13,120.94,122.24,120.25,122.24,59520000,122.24 1982-09-10,121.97,121.98,120.27,120.97,71080000,120.97 1982-09-09,122.19,123.22,121.90,121.97,73090000,121.97 1982-09-08,121.33,123.11,121.19,122.20,77960000,122.20 1982-09-07,122.68,122.68,121.19,121.37,68960000,121.37 1982-09-03,120.31,123.64,120.31,122.68,130910000,122.68 1982-09-02,118.24,120.32,117.84,120.29,74740000,120.29 1982-09-01,119.52,120.05,117.98,118.25,82830000,118.25 1982-08-31,117.65,119.60,117.65,119.51,86360000,119.51 1982-08-30,117.05,117.66,115.79,117.66,59560000,117.66 1982-08-27,117.38,118.56,116.63,117.11,74410000,117.11 1982-08-26,117.57,120.26,117.57,118.55,137330000,118.55 1982-08-25,115.35,118.12,115.11,117.58,106200000,117.58 1982-08-24,116.11,116.39,115.08,115.35,121650000,115.35 1982-08-23,113.02,116.11,112.65,116.11,110310000,116.11 1982-08-20,109.19,113.02,109.19,113.02,95890000,113.02 1982-08-19,108.53,109.86,108.34,109.16,78270000,109.16 1982-08-18,109.04,111.58,108.46,108.54,132690000,108.54 1982-08-17,105.40,109.04,104.09,109.04,92860000,109.04 1982-08-16,103.86,105.52,103.86,104.09,55420000,104.09 1982-08-13,102.42,103.85,102.40,103.85,44720000,103.85 1982-08-12,102.60,103.22,102.39,102.42,50080000,102.42 1982-08-11,102.83,103.01,102.48,102.60,49040000,102.60 1982-08-10,103.11,103.84,102.82,102.84,52680000,102.84 1982-08-09,103.69,103.69,102.20,103.08,54560000,103.08 1982-08-06,105.16,105.16,103.67,103.71,48660000,103.71 1982-08-05,106.10,106.10,104.76,105.16,54700000,105.16 1982-08-04,107.83,107.83,106.11,106.14,53440000,106.14 1982-08-03,108.98,109.43,107.81,107.83,60480000,107.83 1982-08-02,107.71,109.09,107.11,108.98,53460000,108.98 1982-07-30,107.35,107.95,107.01,107.09,39270000,107.09 1982-07-29,107.42,107.92,106.62,107.72,55680000,107.72 1982-07-28,109.42,109.42,107.53,107.74,53830000,107.74 1982-07-27,110.26,110.35,109.36,109.43,45740000,109.43 1982-07-26,110.66,111.16,110.29,110.36,37740000,110.36 1982-07-23,111.46,111.58,111.05,111.17,47280000,111.17 1982-07-22,110.95,112.02,110.94,111.48,53870000,111.48 1982-07-21,112.15,112.39,111.38,111.42,66770000,111.42 1982-07-20,111.11,111.56,110.35,111.54,61060000,111.54 1982-07-19,111.75,111.78,110.66,110.73,53030000,110.73 1982-07-16,110.16,111.48,110.16,111.07,58740000,111.07 1982-07-15,110.83,110.95,110.27,110.47,61090000,110.47 1982-07-14,109.68,110.44,109.08,110.44,58160000,110.44 1982-07-13,109.19,110.07,109.19,109.45,66170000,109.45 1982-07-12,109.48,109.62,108.89,109.57,74690000,109.57 1982-07-09,108.23,108.97,107.56,108.83,65870000,108.83 1982-07-08,106.85,107.53,105.57,107.53,63270000,107.53 1982-07-07,107.08,107.61,106.99,107.22,46920000,107.22 1982-07-06,107.27,107.67,106.74,107.29,44350000,107.29 1982-07-02,108.10,108.71,107.60,107.65,43760000,107.65 1982-07-01,109.52,109.63,108.62,108.71,47900000,108.71 1982-06-30,110.95,111.00,109.50,109.61,65280000,109.61 1982-06-29,110.26,110.57,109.68,110.21,46990000,110.21 1982-06-28,109.30,110.45,109.17,110.26,40700000,110.26 1982-06-25,109.56,109.83,109.09,109.14,38740000,109.14 1982-06-24,110.25,110.92,109.79,109.83,55860000,109.83 1982-06-23,108.59,110.14,108.09,110.14,62710000,110.14 1982-06-22,107.25,108.30,107.17,108.30,55290000,108.30 1982-06-21,107.28,107.88,107.01,107.20,50370000,107.20 1982-06-18,107.60,107.60,107.07,107.28,53800000,107.28 1982-06-17,108.01,108.85,107.48,107.60,49230000,107.60 1982-06-16,110.10,110.13,108.82,108.87,56280000,108.87 1982-06-15,109.63,109.96,108.98,109.69,44970000,109.69 1982-06-14,110.50,111.22,109.90,109.96,40100000,109.96 1982-06-11,111.11,111.48,109.65,111.24,68610000,111.24 1982-06-10,109.35,109.70,108.96,109.61,50950000,109.61 1982-06-09,109.46,109.63,108.53,108.99,55770000,108.99 1982-06-08,110.33,110.33,109.60,109.63,46820000,109.63 1982-06-07,109.59,110.59,109.42,110.12,44630000,110.12 1982-06-04,111.66,111.85,110.02,110.09,44110000,110.09 1982-06-03,112.04,112.48,111.45,111.86,48450000,111.86 1982-06-02,111.74,112.19,111.55,112.04,49220000,112.04 1982-06-01,111.97,112.07,111.66,111.68,41650000,111.68 1982-05-28,112.79,112.80,111.66,111.88,43900000,111.88 1982-05-27,113.11,113.12,112.58,112.66,44730000,112.66 1982-05-26,113.68,114.40,112.88,113.11,51250000,113.11 1982-05-25,115.50,115.51,114.40,114.40,44010000,114.40 1982-05-24,114.46,114.86,114.24,114.79,38510000,114.79 1982-05-21,115.03,115.13,114.60,114.89,45260000,114.89 1982-05-20,114.85,115.07,114.37,114.59,48330000,114.59 1982-05-19,115.61,115.96,114.82,114.89,48840000,114.89 1982-05-18,116.35,116.70,115.71,115.84,48970000,115.84 1982-05-17,117.62,118.02,116.66,116.71,45600000,116.71 1982-05-14,118.20,118.40,118.01,118.01,49900000,118.01 1982-05-13,119.08,119.20,118.13,118.22,58230000,118.22 1982-05-12,119.89,119.92,118.76,119.17,59210000,119.17 1982-05-11,118.54,119.59,118.32,119.42,54680000,119.42 1982-05-10,119.08,119.49,118.37,118.38,46300000,118.38 1982-05-07,119.08,119.89,118.71,119.47,67130000,119.47 1982-05-06,118.82,118.83,117.68,118.68,67540000,118.68 1982-05-05,117.85,118.05,117.31,117.67,58860000,117.67 1982-05-04,117.41,117.64,116.85,117.46,58720000,117.46 1982-05-03,115.96,116.82,115.91,116.82,46490000,116.82 1982-04-30,116.21,116.78,116.07,116.44,48200000,116.44 1982-04-29,116.40,117.24,116.11,116.14,51330000,116.14 1982-04-28,117.83,118.05,116.94,117.26,50530000,117.26 1982-04-27,119.07,119.26,117.73,118.00,56480000,118.00 1982-04-26,118.94,119.33,118.25,119.26,60500000,119.26 1982-04-23,118.02,118.64,117.19,118.64,71840000,118.64 1982-04-22,115.72,117.25,115.72,117.19,64470000,117.19 1982-04-21,115.48,115.87,115.30,115.72,57820000,115.72 1982-04-20,115.80,117.14,114.83,115.44,54610000,115.44 1982-04-19,116.81,118.16,115.83,116.70,58470000,116.70 1982-04-16,116.35,117.70,115.68,116.81,55890000,116.81 1982-04-15,115.83,116.86,115.02,116.35,45700000,116.35 1982-04-14,115.99,116.69,114.80,115.83,45150000,115.83 1982-04-13,116.00,117.12,115.16,115.99,48660000,115.99 1982-04-12,116.22,117.02,115.16,116.00,46520000,116.00 1982-04-08,115.46,116.94,114.94,116.22,60190000,116.22 1982-04-07,115.36,116.45,114.58,115.46,53130000,115.46 1982-04-06,114.73,115.92,113.70,115.36,43200000,115.36 1982-04-05,115.12,115.90,113.94,114.73,46900000,114.73 1982-04-02,113.79,115.79,113.65,115.12,59800000,115.12 1982-04-01,111.96,114.22,111.48,113.79,57100000,113.79 1982-03-31,112.27,113.17,111.32,111.96,43300000,111.96 1982-03-30,112.30,113.09,111.30,112.27,43900000,112.27 1982-03-29,111.94,112.82,110.90,112.30,37100000,112.30 1982-03-26,113.21,113.43,111.26,111.94,42400000,111.94 1982-03-25,112.97,114.26,112.02,113.21,51970000,113.21 1982-03-24,113.55,114.31,112.23,112.97,49380000,112.97 1982-03-23,112.77,114.51,112.29,113.55,67130000,113.55 1982-03-22,110.71,113.35,110.71,112.77,57610000,112.77 1982-03-19,110.30,111.59,109.64,110.61,46250000,110.61 1982-03-18,109.08,111.02,108.85,110.30,54270000,110.30 1982-03-17,109.28,110.10,108.11,109.08,48900000,109.08 1982-03-16,109.45,110.92,108.57,109.28,48900000,109.28 1982-03-15,108.61,109.99,107.47,109.45,43370000,109.45 1982-03-12,109.36,109.72,104.46,108.61,49600000,108.61 1982-03-11,109.41,110.87,108.38,109.36,52960000,109.36 1982-03-10,108.83,110.98,108.09,109.41,59440000,109.41 1982-03-09,107.34,109.88,106.17,108.83,76060000,108.83 1982-03-08,109.34,111.06,107.03,107.34,67330000,107.34 1982-03-05,109.88,110.90,108.31,109.34,67440000,109.34 1982-03-04,110.92,111.78,108.77,109.88,74340000,109.88 1982-03-03,112.51,112.51,109.98,110.92,70230000,110.92 1982-03-02,113.31,114.80,112.03,112.68,63800000,112.68 1982-03-01,113.11,114.32,111.86,113.31,53010000,113.31 1982-02-26,113.21,114.01,112.04,113.11,43840000,113.11 1982-02-25,113.47,114.86,112.44,113.21,54160000,113.21 1982-02-24,111.51,113.88,110.71,113.47,64800000,113.47 1982-02-23,111.59,112.46,110.03,111.51,60100000,111.51 1982-02-22,113.22,114.90,111.20,111.59,58310000,111.59 1982-02-19,113.82,114.58,112.33,113.22,51340000,113.22 1982-02-18,113.69,115.04,112.97,113.82,60810000,113.82 1982-02-17,114.06,115.09,112.97,113.69,47660000,113.69 1982-02-16,114.38,114.63,112.06,114.06,48880000,114.06 1982-02-12,114.43,115.39,113.70,114.38,37070000,114.38 1982-02-11,114.66,115.59,113.41,114.43,46730000,114.43 1982-02-10,113.68,115.62,113.45,114.66,46620000,114.66 1982-02-09,114.63,115.15,112.82,113.68,54420000,113.68 1982-02-08,117.04,117.04,114.20,114.63,48500000,114.63 1982-02-05,116.42,118.26,115.74,117.26,53350000,117.26 1982-02-04,116.48,117.49,114.88,116.42,53300000,116.42 1982-02-03,118.01,118.67,116.04,116.48,49560000,116.48 1982-02-02,117.78,119.15,116.91,118.01,45020000,118.01 1982-02-01,119.81,119.81,117.14,117.78,47720000,117.78 1982-01-29,118.92,121.38,118.64,120.40,73400000,120.40 1982-01-28,116.10,119.35,116.10,118.92,66690000,118.92 1982-01-27,115.19,116.60,114.38,115.74,50060000,115.74 1982-01-26,115.41,116.60,114.49,115.19,44870000,115.19 1982-01-25,115.38,115.93,113.63,115.41,43170000,115.41 1982-01-22,115.75,116.53,114.58,115.38,44370000,115.38 1982-01-21,115.27,116.92,114.60,115.75,48610000,115.75 1982-01-20,115.97,116.64,114.29,115.27,48860000,115.27 1982-01-19,117.22,118.15,115.52,115.97,45070000,115.97 1982-01-18,116.33,117.69,114.85,117.22,44920000,117.22 1982-01-15,115.54,117.14,115.10,116.33,43310000,116.33 1982-01-14,114.88,116.30,114.07,115.54,42940000,115.54 1982-01-13,116.30,117.46,114.24,114.88,49130000,114.88 1982-01-12,116.78,117.49,115.18,116.30,49800000,116.30 1982-01-11,119.55,120.34,116.47,116.78,51900000,116.78 1982-01-08,118.93,120.59,118.55,119.55,42050000,119.55 1982-01-07,119.18,119.88,117.70,118.93,43410000,118.93 1982-01-06,120.05,120.45,117.99,119.18,51510000,119.18 1982-01-05,122.61,122.61,119.57,120.05,47510000,120.05 1982-01-04,122.55,123.72,121.48,122.74,36760000,122.74 1981-12-31,122.30,123.42,121.57,122.55,40780000,122.55 1981-12-30,121.67,123.11,121.04,122.30,42960000,122.30 1981-12-29,122.27,122.90,121.12,121.67,35300000,121.67 1981-12-28,122.54,123.36,121.73,122.27,28320000,122.27 1981-12-24,122.31,123.06,121.57,122.54,23940000,122.54 1981-12-23,122.88,123.59,121.58,122.31,42910000,122.31 1981-12-22,123.34,124.17,122.19,122.88,48320000,122.88 1981-12-21,124.00,124.71,122.67,123.34,41290000,123.34 1981-12-18,123.12,124.87,122.56,124.00,50940000,124.00 1981-12-17,122.42,123.79,121.82,123.12,47230000,123.12 1981-12-16,122.99,123.66,121.73,122.42,42770000,122.42 1981-12-15,122.78,123.78,121.83,122.99,44130000,122.99 1981-12-14,124.37,124.37,122.17,122.78,44740000,122.78 1981-12-11,125.71,126.26,124.32,124.93,45850000,124.93 1981-12-10,125.48,126.54,124.60,125.71,47020000,125.71 1981-12-09,124.82,126.08,124.09,125.48,44810000,125.48 1981-12-08,125.19,125.75,123.52,124.82,45140000,124.82 1981-12-07,126.26,126.91,124.67,125.19,45720000,125.19 1981-12-04,125.12,127.32,125.12,126.26,55040000,126.26 1981-12-03,124.69,125.84,123.63,125.12,43770000,125.12 1981-12-02,126.10,126.45,124.18,124.69,44510000,124.69 1981-12-01,126.35,127.30,124.84,126.10,53980000,126.10 1981-11-30,125.09,126.97,124.18,126.35,47580000,126.35 1981-11-27,124.05,125.71,123.63,125.09,32770000,125.09 1981-11-25,123.51,125.29,123.07,124.05,58570000,124.05 1981-11-24,121.60,124.04,121.22,123.51,53200000,123.51 1981-11-23,121.71,123.09,120.76,121.60,45250000,121.60 1981-11-20,120.71,122.59,120.13,121.71,52010000,121.71 1981-11-19,120.26,121.67,119.42,120.71,48890000,120.71 1981-11-18,121.15,121.66,119.61,120.26,49980000,120.26 1981-11-17,120.24,121.78,119.50,121.15,43190000,121.15 1981-11-16,121.64,121.64,119.13,120.24,43740000,120.24 1981-11-13,123.19,123.61,121.06,121.67,45550000,121.67 1981-11-12,122.92,124.71,122.19,123.19,55720000,123.19 1981-11-11,122.70,123.82,121.51,122.92,41920000,122.92 1981-11-10,123.29,124.69,122.01,122.70,53940000,122.70 1981-11-09,122.67,124.13,121.59,123.29,48310000,123.29 1981-11-06,123.54,124.03,121.85,122.67,43270000,122.67 1981-11-05,124.74,125.80,122.98,123.54,50860000,123.54 1981-11-04,124.80,126.00,123.64,124.74,53450000,124.74 1981-11-03,124.20,125.52,123.14,124.80,54620000,124.80 1981-11-02,122.35,125.14,122.35,124.20,65100000,124.20 1981-10-30,119.06,122.53,118.43,121.89,59570000,121.89 1981-10-29,119.45,120.37,118.14,119.06,40070000,119.06 1981-10-28,119.29,120.96,118.39,119.45,48100000,119.45 1981-10-27,118.16,120.43,117.80,119.29,53030000,119.29 1981-10-26,118.60,119.00,116.81,118.16,38210000,118.16 1981-10-23,119.64,119.92,117.78,118.60,41990000,118.60 1981-10-22,120.10,120.78,118.48,119.64,40630000,119.64 1981-10-21,120.28,121.94,119.35,120.10,48490000,120.10 1981-10-20,118.98,121.29,118.78,120.28,51530000,120.28 1981-10-19,119.19,119.85,117.58,118.98,41590000,118.98 1981-10-16,119.71,120.46,118.38,119.19,37800000,119.19 1981-10-15,118.80,120.58,118.01,119.71,42830000,119.71 1981-10-14,120.78,120.97,118.38,118.80,40260000,118.80 1981-10-13,121.21,122.37,119.96,120.78,43360000,120.78 1981-10-12,121.45,122.37,120.17,121.21,30030000,121.21 1981-10-09,122.31,123.28,120.63,121.45,50060000,121.45 1981-10-08,121.31,123.08,120.23,122.31,47090000,122.31 1981-10-07,119.39,121.87,119.09,121.31,50030000,121.31 1981-10-06,119.51,121.39,118.08,119.39,45460000,119.39 1981-10-05,119.36,121.54,118.61,119.51,51290000,119.51 1981-10-02,117.08,120.16,117.07,119.36,54540000,119.36 1981-10-01,116.18,117.66,115.00,117.08,41600000,117.08 1981-09-30,115.94,117.05,114.60,116.18,40700000,116.18 1981-09-29,115.53,117.75,114.75,115.94,49800000,115.94 1981-09-28,112.77,115.83,110.19,115.53,61320000,115.53 1981-09-25,114.69,114.69,111.64,112.77,54390000,112.77 1981-09-24,115.65,117.47,114.32,115.01,48880000,115.01 1981-09-23,116.68,116.68,113.60,115.65,52700000,115.65 1981-09-22,117.24,118.19,115.93,116.68,46830000,116.68 1981-09-21,116.26,118.07,115.04,117.24,44570000,117.24 1981-09-18,117.15,117.69,115.18,116.26,47350000,116.26 1981-09-17,118.87,119.87,116.63,117.15,48300000,117.15 1981-09-16,119.77,120.00,117.89,118.87,43660000,118.87 1981-09-15,120.66,121.77,119.27,119.77,38580000,119.77 1981-09-14,121.61,122.00,119.67,120.66,34040000,120.66 1981-09-11,120.14,122.13,119.29,121.61,42170000,121.61 1981-09-10,118.40,122.18,118.33,120.14,47430000,120.14 1981-09-09,117.98,119.49,116.87,118.40,43910000,118.40 1981-09-08,120.07,120.12,116.85,117.98,47340000,117.98 1981-09-04,121.24,121.54,119.24,120.07,42760000,120.07 1981-09-03,123.49,124.16,120.82,121.24,41730000,121.24 1981-09-02,123.02,124.58,122.54,123.49,37570000,123.49 1981-09-01,122.79,123.92,121.59,123.02,45110000,123.02 1981-08-31,124.08,125.58,122.29,122.79,40360000,122.79 1981-08-28,123.51,125.09,122.85,124.08,38020000,124.08 1981-08-27,124.96,125.31,122.90,123.51,43900000,123.51 1981-08-26,125.13,126.17,123.99,124.96,39980000,124.96 1981-08-25,125.50,125.77,123.00,125.13,54600000,125.13 1981-08-24,128.59,128.59,125.02,125.50,46750000,125.50 1981-08-21,130.69,131.06,128.70,129.23,37670000,129.23 1981-08-20,130.49,131.74,129.84,130.69,38270000,130.69 1981-08-19,130.11,131.20,128.99,130.49,39390000,130.49 1981-08-18,131.22,131.73,129.10,130.11,47270000,130.11 1981-08-17,132.49,133.02,130.75,131.22,40840000,131.22 1981-08-14,133.51,134.33,131.91,132.49,42580000,132.49 1981-08-13,133.40,134.58,132.53,133.51,42460000,133.51 1981-08-12,133.85,135.18,132.73,133.40,53650000,133.40 1981-08-11,132.54,134.63,132.09,133.85,52600000,133.85 1981-08-10,131.75,133.32,130.83,132.54,38370000,132.54 1981-08-07,132.64,133.04,130.96,131.75,38370000,131.75 1981-08-06,132.67,134.04,131.74,132.64,52070000,132.64 1981-08-05,131.18,133.39,130.76,132.67,54290000,132.67 1981-08-04,130.48,131.66,129.43,131.18,39460000,131.18 1981-08-03,130.92,131.74,129.42,130.48,39650000,130.48 1981-07-31,130.01,131.78,129.60,130.92,43480000,130.92 1981-07-30,129.16,130.68,128.56,130.01,41560000,130.01 1981-07-29,129.14,130.09,128.37,129.16,37610000,129.16 1981-07-28,129.90,130.44,128.28,129.14,38160000,129.14 1981-07-27,128.46,130.61,128.43,129.90,39610000,129.90 1981-07-24,127.40,129.31,127.11,128.46,38880000,128.46 1981-07-23,127.13,128.26,125.96,127.40,41790000,127.40 1981-07-22,128.34,129.72,126.70,127.13,47500000,127.13 1981-07-21,128.72,129.60,127.08,128.34,47280000,128.34 1981-07-20,130.60,130.60,127.98,128.72,40240000,128.72 1981-07-17,130.34,131.60,129.49,130.76,42780000,130.76 1981-07-16,130.23,131.41,129.30,130.34,39010000,130.34 1981-07-15,129.65,131.59,128.89,130.23,48950000,130.23 1981-07-14,129.64,130.78,128.14,129.65,45230000,129.65 1981-07-13,129.37,130.82,128.79,129.64,38100000,129.64 1981-07-10,129.30,130.43,128.38,129.37,39950000,129.37 1981-07-09,128.32,130.08,127.57,129.30,45510000,129.30 1981-07-08,128.24,129.57,126.95,128.32,46000000,128.32 1981-07-07,127.37,129.60,126.39,128.24,53560000,128.24 1981-07-06,128.64,128.99,126.44,127.37,44590000,127.37 1981-07-02,129.77,130.48,127.84,128.64,45100000,128.64 1981-07-01,131.21,131.69,129.04,129.77,49080000,129.77 1981-06-30,131.89,132.67,130.31,131.21,41550000,131.21 1981-06-29,132.56,133.50,131.20,131.89,37930000,131.89 1981-06-26,132.81,133.75,131.71,132.56,39240000,132.56 1981-06-25,132.66,134.30,131.78,132.81,43920000,132.81 1981-06-24,133.35,133.90,131.65,132.66,46650000,132.66 1981-06-23,131.95,133.98,131.16,133.35,51840000,133.35 1981-06-22,132.27,133.54,131.10,131.95,41790000,131.95 1981-06-19,131.64,133.27,130.49,132.27,46430000,132.27 1981-06-18,133.32,133.98,130.94,131.64,48400000,131.64 1981-06-17,132.15,133.98,130.81,133.32,55470000,133.32 1981-06-16,133.61,134.00,131.29,132.15,57780000,132.15 1981-06-15,133.49,135.67,132.78,133.61,63350000,133.61 1981-06-12,133.75,135.09,132.40,133.49,60790000,133.49 1981-06-11,132.32,134.31,131.58,133.75,59530000,133.75 1981-06-10,131.97,133.49,131.04,132.32,53200000,132.32 1981-06-09,132.24,133.30,130.94,131.97,44600000,131.97 1981-06-08,132.22,133.68,131.29,132.24,41580000,132.24 1981-06-05,130.96,132.98,130.17,132.22,47180000,132.22 1981-06-04,130.71,132.21,129.72,130.96,48940000,130.96 1981-06-03,130.62,131.37,128.77,130.71,54700000,130.71 1981-06-02,132.41,132.96,129.84,130.62,53930000,130.62 1981-06-01,132.59,134.62,131.49,132.41,62170000,132.41 1981-05-29,133.45,134.36,131.52,132.59,51580000,132.59 1981-05-28,133.77,134.92,132.00,133.45,59500000,133.45 1981-05-27,132.77,134.65,131.85,133.77,58730000,133.77 1981-05-26,131.33,133.30,130.64,132.77,42760000,132.77 1981-05-22,131.75,132.65,130.42,131.33,40710000,131.33 1981-05-21,132.00,133.03,130.70,131.75,46820000,131.75 1981-05-20,132.09,133.03,130.59,132.00,42370000,132.00 1981-05-19,132.54,133.22,130.78,132.09,42220000,132.09 1981-05-18,132.17,133.65,131.49,132.54,42510000,132.54 1981-05-15,131.28,133.21,130.75,132.17,45460000,132.17 1981-05-14,130.55,132.15,129.91,131.28,42750000,131.28 1981-05-13,130.72,131.96,129.53,130.55,42600000,130.55 1981-05-12,129.71,131.17,128.78,130.72,40440000,130.72 1981-05-11,131.66,132.23,129.11,129.71,37640000,129.71 1981-05-08,131.67,132.69,130.84,131.66,41860000,131.66 1981-05-07,130.78,132.41,130.21,131.67,42590000,131.67 1981-05-06,130.32,132.38,130.09,130.78,47100000,130.78 1981-05-05,130.67,131.33,128.93,130.32,49000000,130.32 1981-05-04,131.78,131.78,129.61,130.67,40430000,130.67 1981-05-01,132.81,134.17,131.43,132.72,48360000,132.72 1981-04-30,133.05,134.44,131.85,132.81,47970000,132.81 1981-04-29,134.33,134.69,131.82,133.05,53340000,133.05 1981-04-28,135.48,136.09,133.10,134.33,58210000,134.33 1981-04-27,135.14,136.56,134.13,135.48,51080000,135.48 1981-04-24,133.94,136.00,132.88,135.14,60000000,135.14 1981-04-23,134.14,135.90,132.90,133.94,64200000,133.94 1981-04-22,134.23,135.54,132.72,134.14,60660000,134.14 1981-04-21,135.45,136.38,133.49,134.23,60280000,134.23 1981-04-20,134.70,136.25,133.19,135.45,51020000,135.45 1981-04-16,134.17,135.82,133.43,134.70,52950000,134.70 1981-04-15,132.68,134.79,132.20,134.17,56040000,134.17 1981-04-14,133.15,134.03,131.58,132.68,48350000,132.68 1981-04-13,134.51,134.91,132.24,133.15,49860000,133.15 1981-04-10,134.67,136.23,133.18,134.51,58130000,134.51 1981-04-09,134.31,135.80,132.59,134.67,59520000,134.67 1981-04-08,133.91,135.34,133.26,134.31,48000000,134.31 1981-04-07,133.93,135.27,132.96,133.91,44540000,133.91 1981-04-06,135.49,135.61,132.91,133.93,43190000,133.93 1981-04-03,136.32,137.04,134.67,135.49,48680000,135.49 1981-04-02,136.57,137.72,135.16,136.32,52570000,136.32 1981-04-01,136.00,137.56,135.04,136.57,54880000,136.57 1981-03-31,134.68,137.15,134.68,136.00,50980000,136.00 1981-03-30,134.65,135.87,133.51,134.28,33500000,134.28 1981-03-27,136.27,136.89,133.91,134.65,46930000,134.65 1981-03-26,137.11,138.38,135.29,136.27,60370000,136.27 1981-03-25,134.67,137.32,133.92,137.11,56320000,137.11 1981-03-24,135.69,137.40,134.10,134.67,66400000,134.67 1981-03-23,134.08,136.50,133.41,135.69,57880000,135.69 1981-03-20,133.46,135.29,132.50,134.08,61980000,134.08 1981-03-19,134.22,135.37,132.37,133.46,62440000,133.46 1981-03-18,133.92,135.66,132.80,134.22,55740000,134.22 1981-03-17,134.68,136.09,132.80,133.92,65920000,133.92 1981-03-16,133.11,135.35,132.10,134.68,49940000,134.68 1981-03-13,133.19,135.53,132.39,133.11,68290000,133.11 1981-03-12,129.95,133.56,129.76,133.19,54640000,133.19 1981-03-11,130.46,131.20,128.72,129.95,47390000,129.95 1981-03-10,131.12,132.64,129.72,130.46,56610000,130.46 1981-03-09,129.85,131.94,129.39,131.12,46180000,131.12 1981-03-06,129.93,131.18,128.56,129.85,43940000,129.85 1981-03-05,130.86,131.82,129.25,129.93,45380000,129.93 1981-03-04,130.56,132.07,129.57,130.86,47260000,130.86 1981-03-03,132.01,132.72,129.66,130.56,48730000,130.56 1981-03-02,131.27,132.96,130.15,132.01,47710000,132.01 1981-02-27,130.10,132.02,129.35,131.27,53210000,131.27 1981-02-26,128.52,130.93,128.02,130.10,60300000,130.10 1981-02-25,127.39,129.21,125.77,128.52,45710000,128.52 1981-02-24,127.35,128.76,126.49,127.39,43960000,127.39 1981-02-23,126.58,128.28,125.69,127.35,39590000,127.35 1981-02-20,126.61,127.65,124.66,126.58,41900000,126.58 1981-02-19,128.48,129.07,125.98,126.61,41630000,126.61 1981-02-18,127.81,129.25,127.09,128.48,40410000,128.48 1981-02-17,126.98,128.75,126.43,127.81,37940000,127.81 1981-02-13,127.48,128.34,126.04,126.98,33360000,126.98 1981-02-12,128.24,128.95,126.78,127.48,34700000,127.48 1981-02-11,129.24,129.92,127.60,128.24,37770000,128.24 1981-02-10,129.27,130.19,128.05,129.24,40820000,129.24 1981-02-09,130.60,131.39,128.61,129.27,38330000,129.27 1981-02-06,129.63,131.81,129.03,130.60,45820000,130.60 1981-02-05,128.59,130.49,127.99,129.63,45320000,129.63 1981-02-04,128.46,129.71,127.29,128.59,45520000,128.59 1981-02-03,126.91,128.92,125.89,128.46,45950000,128.46 1981-02-02,129.48,129.48,125.82,126.91,44070000,126.91 1981-01-30,130.24,131.65,128.61,129.55,41160000,129.55 1981-01-29,130.34,131.78,128.97,130.24,38170000,130.24 1981-01-28,131.12,132.41,129.82,130.34,36690000,130.34 1981-01-27,129.84,131.95,129.32,131.12,42260000,131.12 1981-01-26,130.23,131.18,128.57,129.84,35380000,129.84 1981-01-23,130.26,131.34,129.00,130.23,37220000,130.23 1981-01-22,131.36,132.08,129.23,130.26,39880000,130.26 1981-01-21,131.65,132.48,129.93,131.36,39190000,131.36 1981-01-20,134.37,135.30,131.26,131.65,41750000,131.65 1981-01-19,134.77,135.86,133.51,134.37,36470000,134.37 1981-01-16,134.22,135.91,133.35,134.77,43260000,134.77 1981-01-15,133.47,135.15,132.44,134.22,39640000,134.22 1981-01-14,133.29,135.25,132.65,133.47,41390000,133.47 1981-01-13,133.52,134.27,131.69,133.29,40890000,133.29 1981-01-12,133.48,135.88,132.79,133.52,48760000,133.52 1981-01-09,133.06,134.76,131.71,133.48,50190000,133.48 1981-01-08,135.08,136.10,131.96,133.06,55350000,133.06 1981-01-07,136.02,136.02,132.30,135.08,92890000,135.08 1981-01-06,137.97,140.32,135.78,138.12,67400000,138.12 1981-01-05,136.34,139.24,135.86,137.97,58710000,137.97 1981-01-02,135.76,137.10,134.61,136.34,28870000,136.34 1980-12-31,135.33,136.76,134.29,135.76,41210000,135.76 1980-12-30,135.03,136.51,134.04,135.33,39750000,135.33 1980-12-29,136.57,137.51,134.36,135.03,36060000,135.03 1980-12-26,135.88,137.02,135.20,136.57,16130000,136.57 1980-12-24,135.30,136.55,134.15,135.88,29490000,135.88 1980-12-23,135.78,137.48,134.01,135.30,55260000,135.30 1980-12-22,133.70,136.68,132.88,135.78,51950000,135.78 1980-12-19,133.00,134.00,131.80,133.70,50770000,133.70 1980-12-18,132.89,135.90,131.89,133.00,69570000,133.00 1980-12-17,130.60,133.59,130.22,132.89,50800000,132.89 1980-12-16,129.45,131.22,128.33,130.60,41630000,130.60 1980-12-15,129.23,131.33,128.64,129.45,39700000,129.45 1980-12-12,127.36,129.98,127.15,129.23,39530000,129.23 1980-12-11,128.26,128.73,125.32,127.36,60220000,127.36 1980-12-10,130.48,131.99,127.94,128.26,49860000,128.26 1980-12-09,130.61,131.92,128.77,130.48,53220000,130.48 1980-12-08,133.19,133.19,129.71,130.61,53390000,130.61 1980-12-05,136.37,136.37,132.91,134.03,51990000,134.03 1980-12-04,136.71,138.40,135.09,136.48,51170000,136.48 1980-12-03,136.97,138.09,135.43,136.71,43430000,136.71 1980-12-02,137.21,138.11,134.37,136.97,52340000,136.97 1980-12-01,140.52,140.66,136.75,137.21,48180000,137.21 1980-11-28,140.17,141.54,139.00,140.52,34240000,140.52 1980-11-26,139.33,141.96,138.60,140.17,55340000,140.17 1980-11-25,138.31,140.83,137.42,139.33,55840000,139.33 1980-11-24,139.11,139.36,136.36,138.31,51120000,138.31 1980-11-21,140.40,141.24,138.10,139.11,55950000,139.11 1980-11-20,139.06,141.24,137.79,140.40,60180000,140.40 1980-11-19,139.70,141.76,138.06,139.06,69230000,139.06 1980-11-18,137.91,140.92,137.91,139.70,70380000,139.70 1980-11-17,137.15,138.46,134.90,137.75,50260000,137.75 1980-11-14,136.49,138.96,135.12,137.15,71630000,137.15 1980-11-13,134.59,137.21,134.12,136.49,69340000,136.49 1980-11-12,131.33,135.12,131.33,134.59,58500000,134.59 1980-11-11,129.48,132.30,129.48,131.26,41520000,131.26 1980-11-10,129.18,130.51,128.19,129.48,35720000,129.48 1980-11-07,128.91,130.08,127.74,129.18,40070000,129.18 1980-11-06,131.30,131.30,128.23,128.91,48890000,128.91 1980-11-05,130.77,135.65,130.77,131.33,84080000,131.33 1980-11-03,127.47,129.85,127.23,129.04,35820000,129.04 1980-10-31,126.29,128.24,125.29,127.47,40110000,127.47 1980-10-30,127.91,128.71,125.78,126.29,39060000,126.29 1980-10-29,128.05,129.91,127.07,127.91,37200000,127.91 1980-10-28,127.88,128.86,126.36,128.05,40300000,128.05 1980-10-27,129.85,129.94,127.34,127.88,34430000,127.88 1980-10-24,129.53,130.55,128.04,129.85,41050000,129.85 1980-10-23,131.92,132.54,128.87,129.53,49200000,129.53 1980-10-22,131.84,132.97,130.62,131.92,43060000,131.92 1980-10-21,132.61,134.01,130.78,131.84,51220000,131.84 1980-10-20,131.52,133.21,130.04,132.61,40910000,132.61 1980-10-17,132.22,133.07,130.22,131.52,43920000,131.52 1980-10-16,133.70,135.88,131.64,132.22,65450000,132.22 1980-10-15,132.02,134.35,131.59,133.70,48260000,133.70 1980-10-14,132.03,133.57,131.16,132.02,48830000,132.02 1980-10-13,130.29,132.46,129.37,132.03,31360000,132.03 1980-10-10,131.04,132.15,129.58,130.29,44040000,130.29 1980-10-09,131.65,132.65,130.25,131.04,43980000,131.04 1980-10-08,131.00,132.78,130.28,131.65,46580000,131.65 1980-10-07,131.73,132.88,130.10,131.00,50310000,131.00 1980-10-06,129.35,132.38,129.35,131.73,50130000,131.73 1980-10-03,128.09,130.44,127.65,129.33,47510000,129.33 1980-10-02,127.13,128.82,126.04,128.09,46160000,128.09 1980-10-01,125.46,127.88,124.66,127.13,48720000,127.13 1980-09-30,123.54,126.09,123.54,125.46,40290000,125.46 1980-09-29,125.41,125.41,122.87,123.54,46410000,123.54 1980-09-26,128.17,128.17,125.29,126.35,49460000,126.35 1980-09-25,130.37,131.53,128.13,128.72,49510000,128.72 1980-09-24,129.43,131.34,128.45,130.37,56860000,130.37 1980-09-23,130.40,132.17,128.55,129.43,64390000,129.43 1980-09-22,129.25,130.99,127.89,130.40,53140000,130.40 1980-09-19,128.40,130.33,127.57,129.25,53780000,129.25 1980-09-18,128.87,130.38,127.63,128.40,63390000,128.40 1980-09-17,126.74,129.68,126.37,128.87,63990000,128.87 1980-09-16,125.67,127.78,125.15,126.74,57290000,126.74 1980-09-15,125.54,126.35,124.09,125.67,44630000,125.67 1980-09-12,125.66,126.75,124.72,125.54,47180000,125.54 1980-09-11,124.81,126.48,124.19,125.66,44770000,125.66 1980-09-10,124.07,125.95,123.60,124.81,51430000,124.81 1980-09-09,123.31,124.52,121.94,124.07,44460000,124.07 1980-09-08,124.88,125.67,122.78,123.31,42050000,123.31 1980-09-05,125.42,126.12,124.08,124.88,37990000,124.88 1980-09-04,126.12,127.70,124.42,125.42,59030000,125.42 1980-09-03,123.87,126.43,123.87,126.12,52370000,126.12 1980-09-02,122.38,124.36,121.79,123.74,35290000,123.74 1980-08-29,122.08,123.01,121.06,122.38,33510000,122.38 1980-08-28,123.52,123.91,121.61,122.08,39890000,122.08 1980-08-27,124.84,124.98,122.93,123.52,44000000,123.52 1980-08-26,125.16,126.29,124.01,124.84,41700000,124.84 1980-08-25,126.02,126.28,124.65,125.16,35400000,125.16 1980-08-22,125.46,127.78,125.18,126.02,58210000,126.02 1980-08-21,123.77,125.99,123.61,125.46,50770000,125.46 1980-08-20,122.60,124.27,121.91,123.77,42560000,123.77 1980-08-19,123.39,124.00,121.97,122.60,41930000,122.60 1980-08-18,125.28,125.28,122.82,123.39,41890000,123.39 1980-08-15,125.25,126.61,124.57,125.72,47780000,125.72 1980-08-14,123.28,125.62,122.68,125.25,47700000,125.25 1980-08-13,123.79,124.67,122.49,123.28,44350000,123.28 1980-08-12,124.78,125.78,123.29,123.79,52050000,123.79 1980-08-11,123.61,125.31,122.85,124.78,44690000,124.78 1980-08-08,123.30,125.23,122.82,123.61,58860000,123.61 1980-08-07,121.66,123.84,121.66,123.30,61820000,123.30 1980-08-06,120.74,122.01,119.94,121.55,45050000,121.55 1980-08-05,120.98,122.09,119.96,120.74,45510000,120.74 1980-08-04,121.21,121.63,119.42,120.98,41550000,120.98 1980-08-01,121.67,122.38,120.08,121.21,46440000,121.21 1980-07-31,122.23,122.34,119.40,121.67,54610000,121.67 1980-07-30,122.40,123.93,121.16,122.23,58060000,122.23 1980-07-29,121.43,122.99,120.76,122.40,44840000,122.40 1980-07-28,120.78,122.02,119.78,121.43,35330000,121.43 1980-07-25,121.79,121.96,119.94,120.78,36250000,120.78 1980-07-24,121.93,122.98,120.83,121.79,42420000,121.79 1980-07-23,122.19,123.26,120.93,121.93,45890000,121.93 1980-07-22,122.51,123.90,121.38,122.19,52230000,122.19 1980-07-21,122.04,123.15,120.85,122.51,42750000,122.51 1980-07-18,121.44,123.19,120.88,122.04,58040000,122.04 1980-07-17,119.63,121.84,119.43,121.44,48850000,121.44 1980-07-16,119.30,120.87,118.54,119.63,49140000,119.63 1980-07-15,120.01,121.56,118.85,119.30,60920000,119.30 1980-07-14,117.84,120.37,117.45,120.01,45500000,120.01 1980-07-11,116.95,118.38,116.29,117.84,38310000,117.84 1980-07-10,117.98,118.57,116.38,116.95,43730000,116.95 1980-07-09,117.84,119.52,117.10,117.98,52010000,117.98 1980-07-08,118.29,119.11,117.07,117.84,45830000,117.84 1980-07-07,117.46,118.85,116.96,118.29,42540000,118.29 1980-07-03,115.68,117.80,115.49,117.46,47230000,117.46 1980-07-02,114.93,116.44,114.36,115.68,42950000,115.68 1980-07-01,114.24,115.45,113.54,114.93,34340000,114.93 1980-06-30,116.00,116.04,113.55,114.24,29910000,114.24 1980-06-27,116.19,116.93,115.06,116.00,33110000,116.00 1980-06-26,116.72,117.98,115.58,116.19,45110000,116.19 1980-06-25,115.14,117.37,115.07,116.72,46500000,116.72 1980-06-24,114.51,115.75,113.76,115.14,37730000,115.14 1980-06-23,114.06,115.28,113.35,114.51,34180000,114.51 1980-06-20,114.66,114.90,113.12,114.06,36530000,114.06 1980-06-19,116.26,116.81,114.36,114.66,38280000,114.66 1980-06-18,116.03,116.84,114.77,116.26,41960000,116.26 1980-06-17,116.09,117.16,115.13,116.03,41990000,116.03 1980-06-16,115.81,116.80,114.78,116.09,36190000,116.09 1980-06-13,115.52,116.94,114.67,115.81,41880000,115.81 1980-06-12,116.02,117.01,114.28,115.52,47300000,115.52 1980-06-11,114.66,116.64,114.22,116.02,43800000,116.02 1980-06-10,113.71,115.50,113.17,114.66,42030000,114.66 1980-06-09,113.20,114.51,112.68,113.71,36820000,113.71 1980-06-06,112.78,114.01,112.11,113.20,37230000,113.20 1980-06-05,112.61,114.38,111.89,112.78,49070000,112.78 1980-06-04,110.51,113.45,110.22,112.61,44180000,112.61 1980-06-03,110.76,111.63,109.77,110.51,33150000,110.51 1980-06-02,111.24,112.15,110.06,110.76,32710000,110.76 1980-05-30,110.27,111.55,108.87,111.24,34820000,111.24 1980-05-29,112.06,112.64,109.86,110.27,42000000,110.27 1980-05-28,111.40,112.72,110.42,112.06,38580000,112.06 1980-05-27,110.62,112.30,110.35,111.40,40810000,111.40 1980-05-23,109.01,111.37,109.01,110.62,45790000,110.62 1980-05-22,107.72,109.73,107.34,109.01,41040000,109.01 1980-05-21,107.62,108.31,106.54,107.72,34830000,107.72 1980-05-20,107.67,108.39,106.75,107.62,31800000,107.62 1980-05-19,107.35,108.43,106.51,107.67,30970000,107.67 1980-05-16,106.99,107.89,106.25,107.35,31710000,107.35 1980-05-15,106.85,107.99,106.07,106.99,41120000,106.99 1980-05-14,106.30,107.89,106.00,106.85,40840000,106.85 1980-05-13,104.78,106.76,104.44,106.30,35460000,106.30 1980-05-12,104.72,105.48,103.50,104.78,28220000,104.78 1980-05-09,106.13,106.20,104.18,104.72,30280000,104.72 1980-05-08,107.18,108.02,105.50,106.13,39280000,106.13 1980-05-07,106.25,108.12,105.83,107.18,42600000,107.18 1980-05-06,106.38,107.83,105.36,106.25,40160000,106.25 1980-05-05,105.58,106.83,104.64,106.38,34090000,106.38 1980-05-02,105.46,106.25,104.61,105.58,28040000,105.58 1980-05-01,106.29,106.86,104.72,105.46,32480000,105.46 1980-04-30,105.86,106.72,104.50,106.29,30850000,106.29 1980-04-29,105.64,106.70,104.86,105.86,27940000,105.86 1980-04-28,105.16,106.79,104.64,105.64,30600000,105.64 1980-04-25,104.40,105.57,103.02,105.16,28590000,105.16 1980-04-24,103.73,105.43,102.93,104.40,35790000,104.40 1980-04-23,103.43,105.11,102.81,103.73,42620000,103.73 1980-04-22,100.81,104.02,100.81,103.43,47920000,103.43 1980-04-21,100.55,101.26,98.95,99.80,27560000,99.80 1980-04-18,101.05,102.07,99.97,100.55,26880000,100.55 1980-04-17,101.54,102.21,100.12,101.05,32770000,101.05 1980-04-16,102.63,104.42,101.13,101.54,39730000,101.54 1980-04-15,102.84,103.94,101.85,102.63,26670000,102.63 1980-04-14,103.79,103.92,102.08,102.84,23060000,102.84 1980-04-11,104.08,105.15,103.20,103.79,29960000,103.79 1980-04-10,103.11,105.00,102.81,104.08,33940000,104.08 1980-04-09,101.20,103.60,101.01,103.11,33020000,103.11 1980-04-08,100.19,101.88,99.23,101.20,31700000,101.20 1980-04-07,102.15,102.27,99.73,100.19,29130000,100.19 1980-04-03,102.68,103.34,101.31,102.15,27970000,102.15 1980-04-02,102.18,103.87,101.45,102.68,35210000,102.68 1980-04-01,102.09,103.28,100.85,102.18,32230000,102.18 1980-03-31,100.68,102.65,100.02,102.09,35840000,102.09 1980-03-28,98.22,101.43,97.72,100.68,46720000,100.68 1980-03-27,98.68,99.58,94.23,98.22,63680000,98.22 1980-03-26,99.19,101.22,98.10,98.68,37370000,98.68 1980-03-25,99.28,100.58,97.89,99.19,43790000,99.19 1980-03-24,102.18,102.18,98.88,99.28,39230000,99.28 1980-03-21,103.12,103.73,101.55,102.31,32220000,102.31 1980-03-20,104.31,105.17,102.52,103.12,32580000,103.12 1980-03-19,104.10,105.72,103.35,104.31,36520000,104.31 1980-03-18,102.26,104.71,101.14,104.10,47340000,104.10 1980-03-17,105.23,105.23,101.82,102.26,37020000,102.26 1980-03-14,105.62,106.49,104.01,105.43,35180000,105.43 1980-03-13,106.87,107.55,105.10,105.62,33070000,105.62 1980-03-12,107.78,108.40,105.42,106.87,37990000,106.87 1980-03-11,106.51,108.54,106.18,107.78,41350000,107.78 1980-03-10,106.90,107.86,104.92,106.51,43750000,106.51 1980-03-07,108.65,108.96,105.99,106.90,50950000,106.90 1980-03-06,111.13,111.29,107.85,108.65,49610000,108.65 1980-03-05,112.78,113.94,110.58,111.13,49240000,111.13 1980-03-04,112.50,113.41,110.83,112.78,44310000,112.78 1980-03-03,113.66,114.34,112.01,112.50,38690000,112.50 1980-02-29,112.35,114.12,111.77,113.66,38810000,113.66 1980-02-28,112.38,113.70,111.33,112.35,40330000,112.35 1980-02-27,113.98,115.12,111.91,112.38,46430000,112.38 1980-02-26,113.33,114.76,112.30,113.98,40000000,113.98 1980-02-25,114.93,114.93,112.62,113.33,39140000,113.33 1980-02-22,115.28,116.46,113.43,115.04,48210000,115.04 1980-02-21,116.47,117.90,114.44,115.28,51530000,115.28 1980-02-20,114.60,117.18,114.06,116.47,44340000,116.47 1980-02-19,115.41,115.67,113.35,114.60,39480000,114.60 1980-02-15,116.70,116.70,114.12,115.41,46680000,115.41 1980-02-14,118.44,119.30,116.04,116.72,50540000,116.72 1980-02-13,117.90,120.22,117.57,118.44,65230000,118.44 1980-02-12,117.12,118.41,115.75,117.90,48090000,117.90 1980-02-11,117.95,119.05,116.31,117.12,58660000,117.12 1980-02-08,116.28,118.66,115.72,117.95,57860000,117.95 1980-02-07,115.72,117.87,115.22,116.28,57690000,116.28 1980-02-06,114.66,116.57,113.65,115.72,51950000,115.72 1980-02-05,114.37,115.25,112.15,114.66,41880000,114.66 1980-02-04,115.12,116.01,113.83,114.37,43070000,114.37 1980-02-01,114.16,115.54,113.13,115.12,46610000,115.12 1980-01-31,115.20,117.17,113.78,114.16,65900000,114.16 1980-01-30,114.07,115.85,113.37,115.20,51170000,115.20 1980-01-29,114.85,115.77,113.03,114.07,55480000,114.07 1980-01-28,113.61,115.65,112.93,114.85,53620000,114.85 1980-01-25,113.70,114.45,112.36,113.61,47100000,113.61 1980-01-24,113.44,115.27,112.95,113.70,59070000,113.70 1980-01-23,111.51,113.93,110.93,113.44,50730000,113.44 1980-01-22,112.10,113.10,110.92,111.51,50620000,111.51 1980-01-21,111.07,112.90,110.66,112.10,48040000,112.10 1980-01-18,110.70,111.74,109.88,111.07,47150000,111.07 1980-01-17,111.05,112.01,109.81,110.70,54170000,110.70 1980-01-16,111.14,112.90,110.38,111.05,67700000,111.05 1980-01-15,110.38,111.93,109.45,111.14,52320000,111.14 1980-01-14,109.92,111.44,109.34,110.38,52930000,110.38 1980-01-11,109.89,111.16,108.89,109.92,52890000,109.92 1980-01-10,109.05,110.86,108.47,109.89,55980000,109.89 1980-01-09,108.95,111.09,108.41,109.05,65260000,109.05 1980-01-08,106.81,109.29,106.29,108.95,53390000,108.95 1980-01-07,106.52,107.80,105.80,106.81,44500000,106.81 1980-01-04,105.22,107.08,105.09,106.52,39130000,106.52 1980-01-03,105.76,106.08,103.26,105.22,50480000,105.22 1980-01-02,107.94,108.43,105.29,105.76,40610000,105.76 1979-12-31,107.84,108.53,107.26,107.94,31530000,107.94 1979-12-28,107.96,108.61,107.16,107.84,34430000,107.84 1979-12-27,107.78,108.50,107.14,107.96,31410000,107.96 1979-12-26,107.66,108.37,107.06,107.78,24960000,107.78 1979-12-24,107.59,108.08,106.80,107.66,19150000,107.66 1979-12-21,108.26,108.76,106.99,107.59,36160000,107.59 1979-12-20,108.20,109.24,107.40,108.26,40380000,108.26 1979-12-19,108.30,108.79,107.02,108.20,41780000,108.20 1979-12-18,109.33,109.83,107.83,108.30,43310000,108.30 1979-12-17,108.92,110.33,108.36,109.33,43830000,109.33 1979-12-14,107.67,109.49,107.37,108.92,41800000,108.92 1979-12-13,107.52,108.29,106.68,107.67,36690000,107.67 1979-12-12,107.49,108.32,106.78,107.52,34630000,107.52 1979-12-11,107.67,108.58,106.79,107.49,36160000,107.49 1979-12-10,107.52,108.27,106.65,107.67,32270000,107.67 1979-12-07,108.00,109.24,106.55,107.52,42370000,107.52 1979-12-06,107.25,108.47,106.71,108.00,37510000,108.00 1979-12-05,106.79,108.36,106.60,107.25,39300000,107.25 1979-12-04,105.83,107.25,105.66,106.79,33510000,106.79 1979-12-03,106.16,106.65,105.07,105.83,29030000,105.83 1979-11-30,106.81,107.16,105.56,106.16,30480000,106.16 1979-11-29,106.77,107.84,106.17,106.81,33550000,106.81 1979-11-28,106.38,107.55,105.29,106.77,39690000,106.77 1979-11-27,106.80,107.89,105.64,106.38,45140000,106.38 1979-11-26,104.83,107.44,104.83,106.80,47940000,106.80 1979-11-23,103.89,105.13,103.56,104.67,23300000,104.67 1979-11-21,103.69,104.23,102.04,103.89,37020000,103.89 1979-11-20,104.23,105.11,103.14,103.69,35010000,103.69 1979-11-19,103.79,105.08,103.17,104.23,33090000,104.23 1979-11-16,104.13,104.72,103.07,103.79,30060000,103.79 1979-11-15,103.39,104.94,103.10,104.13,32380000,104.13 1979-11-14,102.94,104.13,101.91,103.39,30970000,103.39 1979-11-13,103.51,104.21,102.42,102.94,29240000,102.94 1979-11-12,101.51,103.72,101.27,103.51,26640000,103.51 1979-11-09,100.58,102.18,100.58,101.51,30060000,101.51 1979-11-08,99.87,101.00,99.49,100.30,26270000,100.30 1979-11-07,100.97,100.97,99.42,99.87,30830000,99.87 1979-11-06,101.82,102.01,100.77,101.20,21960000,101.20 1979-11-05,102.51,102.66,101.24,101.82,20470000,101.82 1979-11-02,102.57,103.21,101.92,102.51,23670000,102.51 1979-11-01,101.82,103.07,101.10,102.57,25880000,102.57 1979-10-31,102.67,103.16,101.38,101.82,27780000,101.82 1979-10-30,100.71,102.83,100.41,102.67,28890000,102.67 1979-10-29,100.57,101.56,100.13,100.71,22720000,100.71 1979-10-26,100.00,101.31,99.59,100.57,29660000,100.57 1979-10-25,100.44,101.39,99.56,100.00,28440000,100.00 1979-10-24,100.28,101.45,99.66,100.44,31480000,100.44 1979-10-23,100.71,101.44,99.61,100.28,32910000,100.28 1979-10-22,101.38,101.38,99.06,100.71,45240000,100.71 1979-10-19,103.58,103.58,101.24,101.60,42430000,101.60 1979-10-18,103.39,104.62,102.92,103.61,29590000,103.61 1979-10-17,103.19,104.54,102.74,103.39,29650000,103.39 1979-10-16,103.36,104.37,102.52,103.19,33770000,103.19 1979-10-15,104.49,104.74,102.69,103.36,34850000,103.36 1979-10-12,105.05,106.20,104.01,104.49,36390000,104.49 1979-10-11,105.30,106.33,103.70,105.05,47530000,105.05 1979-10-10,106.23,106.23,102.31,105.30,81620000,105.30 1979-10-09,109.43,109.43,106.04,106.63,55560000,106.63 1979-10-08,111.27,111.83,109.65,109.88,32610000,109.88 1979-10-05,110.17,112.16,110.16,111.27,48250000,111.27 1979-10-04,109.59,110.81,109.14,110.17,38800000,110.17 1979-10-03,109.59,110.43,108.88,109.59,36470000,109.59 1979-10-02,108.56,110.08,108.03,109.59,38310000,109.59 1979-10-01,109.19,109.19,107.70,108.56,24980000,108.56 1979-09-28,110.21,110.67,108.70,109.32,35950000,109.32 1979-09-27,109.96,110.75,109.19,110.21,33110000,110.21 1979-09-26,109.68,111.25,109.37,109.96,37700000,109.96 1979-09-25,109.61,110.19,108.27,109.68,32410000,109.68 1979-09-24,110.47,110.90,109.16,109.61,33790000,109.61 1979-09-21,110.51,111.58,109.46,110.47,52380000,110.47 1979-09-20,108.28,110.69,107.59,110.51,45100000,110.51 1979-09-19,108.00,109.02,107.52,108.28,35370000,108.28 1979-09-18,108.84,109.00,107.32,108.00,38750000,108.00 1979-09-17,108.76,110.06,108.40,108.84,37610000,108.84 1979-09-14,107.85,109.48,107.42,108.76,41980000,108.76 1979-09-13,107.82,108.53,107.06,107.85,35240000,107.85 1979-09-12,107.51,108.41,106.72,107.82,39350000,107.82 1979-09-11,108.17,108.83,106.80,107.51,42530000,107.51 1979-09-10,107.66,108.71,107.21,108.17,32980000,108.17 1979-09-07,106.85,108.09,106.30,107.66,34360000,107.66 1979-09-06,106.40,107.61,105.97,106.85,30330000,106.85 1979-09-05,107.19,107.19,105.38,106.40,41650000,106.40 1979-09-04,109.32,109.41,107.22,107.44,33350000,107.44 1979-08-31,109.02,109.80,108.58,109.32,26370000,109.32 1979-08-30,109.02,109.59,108.40,109.02,29300000,109.02 1979-08-29,109.02,109.59,108.36,109.02,30810000,109.02 1979-08-28,109.14,109.65,108.47,109.02,29430000,109.02 1979-08-27,108.60,109.84,108.12,109.14,32050000,109.14 1979-08-24,108.63,109.11,107.65,108.60,32730000,108.60 1979-08-23,108.99,109.59,108.12,108.63,35710000,108.63 1979-08-22,108.91,109.56,108.09,108.99,38450000,108.99 1979-08-21,108.83,109.68,108.17,108.91,38860000,108.91 1979-08-20,108.30,109.32,107.69,108.83,32300000,108.83 1979-08-17,108.09,108.94,107.25,108.30,31630000,108.30 1979-08-16,108.25,109.18,107.38,108.09,47000000,108.09 1979-08-15,107.52,108.64,106.75,108.25,46130000,108.25 1979-08-14,107.42,108.03,106.60,107.52,40910000,107.52 1979-08-13,106.40,107.90,106.28,107.42,41980000,107.42 1979-08-10,105.49,106.79,104.81,106.40,36740000,106.40 1979-08-09,105.98,106.25,104.89,105.49,34630000,105.49 1979-08-08,105.65,106.84,105.20,105.98,44970000,105.98 1979-08-07,104.30,106.23,104.12,105.65,45410000,105.65 1979-08-06,104.04,104.66,103.27,104.30,27190000,104.30 1979-08-03,104.10,104.56,103.36,104.04,28160000,104.04 1979-08-02,104.17,105.02,103.59,104.10,37720000,104.10 1979-08-01,103.81,104.57,103.14,104.17,36570000,104.17 1979-07-31,103.15,104.26,102.89,103.81,34360000,103.81 1979-07-30,103.10,103.63,102.42,103.15,28640000,103.15 1979-07-27,103.10,103.50,102.29,103.10,27760000,103.10 1979-07-26,103.08,103.63,102.34,103.10,32270000,103.10 1979-07-25,101.97,103.44,101.85,103.08,34890000,103.08 1979-07-24,101.59,102.50,101.14,101.97,29690000,101.97 1979-07-23,101.82,102.13,100.84,101.59,26860000,101.59 1979-07-20,101.61,102.32,101.06,101.82,26360000,101.82 1979-07-19,101.69,102.42,101.04,101.61,26780000,101.61 1979-07-18,101.83,102.06,100.35,101.69,35950000,101.69 1979-07-17,102.74,103.06,101.27,101.83,34270000,101.83 1979-07-16,102.32,103.20,101.81,102.74,26620000,102.74 1979-07-13,102.69,102.99,101.49,102.32,33080000,102.32 1979-07-12,103.64,103.72,102.22,102.69,31780000,102.69 1979-07-11,104.20,104.34,102.87,103.64,36650000,103.64 1979-07-10,104.47,105.17,103.52,104.20,39730000,104.20 1979-07-09,103.62,105.07,103.36,104.47,42460000,104.47 1979-07-06,102.43,103.91,102.12,103.62,38570000,103.62 1979-07-05,102.09,102.88,101.59,102.43,30290000,102.43 1979-07-03,101.99,102.57,101.31,102.09,31670000,102.09 1979-07-02,102.91,103.00,101.45,101.99,32060000,101.99 1979-06-29,102.80,103.67,102.04,102.91,34690000,102.91 1979-06-28,102.27,103.46,101.91,102.80,38470000,102.80 1979-06-27,101.66,102.95,101.29,102.27,36720000,102.27 1979-06-26,102.09,102.09,101.22,101.66,34680000,101.66 1979-06-25,102.64,102.91,101.45,102.09,31330000,102.09 1979-06-22,102.09,103.16,101.91,102.64,36410000,102.64 1979-06-21,101.63,102.74,101.20,102.09,36490000,102.09 1979-06-20,101.58,102.19,100.93,101.63,33790000,101.63 1979-06-19,101.56,102.28,100.91,101.58,30780000,101.58 1979-06-18,102.09,102.48,101.05,101.56,30970000,101.56 1979-06-15,102.20,102.78,101.38,102.09,40740000,102.09 1979-06-14,102.31,102.63,101.04,102.20,37850000,102.20 1979-06-13,102.85,103.58,101.83,102.31,40740000,102.31 1979-06-12,101.91,103.64,101.81,102.85,45450000,102.85 1979-06-11,101.49,102.24,100.91,101.91,28270000,101.91 1979-06-08,101.79,102.23,100.91,101.49,31470000,101.49 1979-06-07,101.30,102.54,101.15,101.79,43380000,101.79 1979-06-06,100.62,101.96,100.38,101.30,39830000,101.30 1979-06-05,99.32,101.07,99.17,100.62,35050000,100.62 1979-06-04,99.17,99.76,98.61,99.32,24040000,99.32 1979-06-01,99.08,99.70,98.57,99.17,24560000,99.17 1979-05-31,99.11,99.61,98.29,99.08,30300000,99.08 1979-05-30,100.05,100.25,98.79,99.11,29250000,99.11 1979-05-29,100.22,100.76,99.56,100.05,27040000,100.05 1979-05-25,99.93,100.68,99.52,100.22,27810000,100.22 1979-05-24,99.89,100.44,99.14,99.93,25710000,99.93 1979-05-23,100.51,101.31,99.63,99.89,30390000,99.89 1979-05-22,100.14,100.93,99.45,100.51,30400000,100.51 1979-05-21,99.93,100.75,99.37,100.14,25550000,100.14 1979-05-18,99.94,100.73,99.33,99.93,26590000,99.93 1979-05-17,98.42,100.22,98.29,99.94,30550000,99.94 1979-05-16,98.14,98.80,97.49,98.42,28350000,98.42 1979-05-15,98.06,98.90,97.60,98.14,26190000,98.14 1979-05-14,98.52,98.95,97.71,98.06,22450000,98.06 1979-05-11,98.52,99.03,97.92,98.52,24010000,98.52 1979-05-10,99.46,99.63,98.22,98.52,25230000,98.52 1979-05-09,99.17,100.01,98.50,99.46,27670000,99.46 1979-05-08,99.02,99.56,97.98,99.17,32720000,99.17 1979-05-07,100.37,100.37,98.78,99.02,30480000,99.02 1979-05-04,101.81,102.08,100.42,100.69,30630000,100.69 1979-05-03,101.72,102.57,101.25,101.81,30870000,101.81 1979-05-02,101.68,102.28,101.00,101.72,30510000,101.72 1979-05-01,101.76,102.50,101.22,101.68,31040000,101.68 1979-04-30,101.80,102.24,100.91,101.76,26440000,101.76 1979-04-27,102.01,102.32,101.04,101.80,29610000,101.80 1979-04-26,102.50,102.91,101.58,102.01,32400000,102.01 1979-04-25,102.20,103.07,101.79,102.50,31750000,102.50 1979-04-24,101.57,103.02,101.39,102.20,35540000,102.20 1979-04-23,101.23,102.00,100.68,101.57,25610000,101.57 1979-04-20,101.28,101.81,100.46,101.23,28830000,101.23 1979-04-19,101.70,102.40,100.88,101.28,31150000,101.28 1979-04-18,101.24,102.23,100.96,101.70,29510000,101.70 1979-04-17,101.12,101.94,100.65,101.24,29260000,101.24 1979-04-16,102.00,102.02,100.67,101.12,28050000,101.12 1979-04-12,102.31,102.77,101.51,102.00,26780000,102.00 1979-04-11,103.34,103.77,101.92,102.31,32900000,102.31 1979-04-10,102.87,103.83,102.42,103.34,31900000,103.34 1979-04-09,103.18,103.56,102.28,102.87,27230000,102.87 1979-04-06,103.26,103.95,102.58,103.18,34710000,103.18 1979-04-05,102.65,103.60,102.16,103.26,34520000,103.26 1979-04-04,102.40,103.73,102.16,102.65,41940000,102.65 1979-04-03,100.90,102.67,100.81,102.40,33530000,102.40 1979-04-02,101.56,101.56,100.14,100.90,28990000,100.90 1979-03-30,102.03,102.51,101.03,101.59,29970000,101.59 1979-03-29,102.12,102.78,101.43,102.03,28510000,102.03 1979-03-28,102.48,103.31,101.74,102.12,39920000,102.12 1979-03-27,101.04,102.71,100.81,102.48,32940000,102.48 1979-03-26,101.60,101.77,100.60,101.04,23430000,101.04 1979-03-23,101.67,102.37,101.02,101.60,33570000,101.60 1979-03-22,101.25,102.41,101.04,101.67,34380000,101.67 1979-03-21,100.50,101.48,99.87,101.25,31120000,101.25 1979-03-20,101.06,101.34,100.01,100.50,27180000,100.50 1979-03-19,100.69,101.94,100.35,101.06,34620000,101.06 1979-03-16,99.86,101.16,99.53,100.69,31770000,100.69 1979-03-15,99.71,100.57,99.11,99.86,29370000,99.86 1979-03-14,99.84,100.43,99.23,99.71,24630000,99.71 1979-03-13,99.67,100.66,99.13,99.84,31170000,99.84 1979-03-12,99.54,100.04,98.56,99.67,25740000,99.67 1979-03-09,99.58,100.58,99.12,99.54,33410000,99.54 1979-03-08,98.44,99.82,98.10,99.58,32000000,99.58 1979-03-07,97.87,99.23,97.67,98.44,28930000,98.44 1979-03-06,98.06,98.53,97.36,97.87,24490000,97.87 1979-03-05,97.03,98.64,97.03,98.06,25690000,98.06 1979-03-02,96.90,97.55,96.44,96.97,23130000,96.97 1979-03-01,96.28,97.28,95.98,96.90,23830000,96.90 1979-02-28,96.13,96.69,95.38,96.28,25090000,96.28 1979-02-27,97.65,97.65,95.69,96.13,31470000,96.13 1979-02-26,97.78,98.28,97.20,97.67,22620000,97.67 1979-02-23,98.33,98.50,97.29,97.78,22750000,97.78 1979-02-22,99.07,99.21,97.88,98.33,26290000,98.33 1979-02-21,99.42,100.07,98.69,99.07,26050000,99.07 1979-02-20,98.67,99.67,98.26,99.42,22010000,99.42 1979-02-16,98.73,99.23,98.11,98.67,21110000,98.67 1979-02-15,98.87,99.13,97.96,98.73,22550000,98.73 1979-02-14,98.93,99.64,98.21,98.87,27220000,98.87 1979-02-13,98.25,99.58,98.25,98.93,28470000,98.93 1979-02-12,97.87,98.55,97.05,98.20,20610000,98.20 1979-02-09,97.65,98.50,97.28,97.87,24320000,97.87 1979-02-08,97.16,98.11,96.82,97.65,23360000,97.65 1979-02-07,98.05,98.07,96.51,97.16,28450000,97.16 1979-02-06,98.09,98.74,97.48,98.05,23570000,98.05 1979-02-05,99.07,99.07,97.57,98.09,26490000,98.09 1979-02-02,99.96,100.52,99.10,99.50,25350000,99.50 1979-02-01,99.93,100.38,99.01,99.96,27930000,99.96 1979-01-31,101.05,101.41,99.47,99.93,30330000,99.93 1979-01-30,101.55,102.07,100.68,101.05,26910000,101.05 1979-01-29,101.86,102.33,100.99,101.55,24170000,101.55 1979-01-26,101.19,102.59,101.03,101.86,34230000,101.86 1979-01-25,100.16,101.66,99.99,101.19,31440000,101.19 1979-01-24,100.60,101.31,99.67,100.16,31730000,100.16 1979-01-23,99.90,101.05,99.35,100.60,30130000,100.60 1979-01-22,99.75,100.35,98.90,99.90,24390000,99.90 1979-01-19,99.72,100.57,99.22,99.75,26800000,99.75 1979-01-18,99.48,100.35,98.91,99.72,27260000,99.72 1979-01-17,99.46,100.00,98.33,99.48,25310000,99.48 1979-01-16,100.69,100.88,99.11,99.46,30340000,99.46 1979-01-15,99.93,101.13,99.58,100.69,27520000,100.69 1979-01-12,99.32,100.91,99.32,99.93,37120000,99.93 1979-01-11,98.77,99.41,97.95,99.10,24580000,99.10 1979-01-10,99.33,99.75,98.28,98.77,24990000,98.77 1979-01-09,98.80,99.96,98.62,99.33,27340000,99.33 1979-01-08,99.13,99.30,97.83,98.80,21440000,98.80 1979-01-05,98.58,99.79,98.25,99.13,28890000,99.13 1979-01-04,97.80,99.42,97.52,98.58,33290000,98.58 1979-01-03,96.81,98.54,96.81,97.80,29180000,97.80 1979-01-02,96.11,96.96,95.22,96.73,18340000,96.73 1978-12-29,96.28,97.03,95.48,96.11,30030000,96.11 1978-12-28,96.66,97.19,95.82,96.28,25440000,96.28 1978-12-27,97.51,97.51,96.15,96.66,23580000,96.66 1978-12-26,96.31,97.89,95.99,97.52,21470000,97.52 1978-12-22,94.77,96.62,94.77,96.31,23790000,96.31 1978-12-21,94.68,95.66,94.11,94.71,28670000,94.71 1978-12-20,94.24,95.20,93.70,94.68,26520000,94.68 1978-12-19,93.44,94.85,93.05,94.24,25960000,94.24 1978-12-18,94.33,94.33,92.64,93.44,32900000,93.44 1978-12-15,96.04,96.28,94.88,95.33,23620000,95.33 1978-12-14,96.06,96.44,95.20,96.04,20840000,96.04 1978-12-13,96.59,97.07,95.59,96.06,22480000,96.06 1978-12-12,97.11,97.58,96.27,96.59,22210000,96.59 1978-12-11,96.63,97.56,96.07,97.11,21000000,97.11 1978-12-08,97.08,97.48,96.14,96.63,18560000,96.63 1978-12-07,97.49,98.10,96.58,97.08,21170000,97.08 1978-12-06,97.44,98.58,96.83,97.49,29680000,97.49 1978-12-05,96.15,97.70,95.88,97.44,25670000,97.44 1978-12-04,96.28,96.96,95.37,96.15,22020000,96.15 1978-12-01,95.01,96.69,95.01,96.28,26830000,96.28 1978-11-30,93.75,94.94,93.29,94.70,19900000,94.70 1978-11-29,94.92,94.92,93.48,93.75,21160000,93.75 1978-11-28,95.99,96.51,94.88,95.15,22740000,95.15 1978-11-27,95.79,96.52,95.17,95.99,19790000,95.99 1978-11-24,95.48,96.17,94.98,95.79,14590000,95.79 1978-11-22,95.01,95.91,94.54,95.48,20010000,95.48 1978-11-21,95.25,95.83,94.49,95.01,20750000,95.01 1978-11-20,94.42,95.86,94.29,95.25,24440000,95.25 1978-11-17,93.71,95.03,93.59,94.42,25170000,94.42 1978-11-16,92.71,94.08,92.59,93.71,21340000,93.71 1978-11-15,92.49,94.00,92.29,92.71,26280000,92.71 1978-11-14,93.13,93.53,91.77,92.49,30610000,92.49 1978-11-13,94.77,94.90,92.96,93.13,20960000,93.13 1978-11-10,94.42,95.39,93.94,94.77,16750000,94.77 1978-11-09,94.45,95.50,93.81,94.42,23320000,94.42 1978-11-08,93.85,94.74,92.89,94.45,23560000,94.45 1978-11-07,94.75,94.75,93.14,93.85,25320000,93.85 1978-11-06,96.18,96.49,94.84,95.19,20450000,95.19 1978-11-03,95.61,96.98,94.78,96.18,25990000,96.18 1978-11-02,96.85,97.31,94.84,95.61,41030000,95.61 1978-11-01,94.13,97.41,94.13,96.85,50450000,96.85 1978-10-31,95.06,95.80,92.72,93.15,42720000,93.15 1978-10-30,94.59,95.49,91.65,95.06,59480000,95.06 1978-10-27,96.03,96.62,94.30,94.59,40360000,94.59 1978-10-26,97.31,97.71,95.59,96.03,31990000,96.03 1978-10-25,97.49,98.56,96.33,97.31,31380000,97.31 1978-10-24,98.18,98.95,97.13,97.49,28880000,97.49 1978-10-23,97.95,98.84,96.63,98.18,36090000,98.18 1978-10-20,99.26,99.26,97.12,97.95,43670000,97.95 1978-10-19,100.49,101.03,99.04,99.33,31810000,99.33 1978-10-18,101.26,101.76,99.89,100.49,32940000,100.49 1978-10-17,102.35,102.35,100.47,101.26,37870000,101.26 1978-10-16,104.63,104.63,102.43,102.61,24600000,102.61 1978-10-13,104.88,105.34,104.07,104.66,21920000,104.66 1978-10-12,105.39,106.23,104.42,104.88,30170000,104.88 1978-10-11,104.46,105.64,103.80,105.39,21740000,105.39 1978-10-10,104.59,105.36,103.90,104.46,25470000,104.46 1978-10-09,103.52,104.89,103.31,104.59,19720000,104.59 1978-10-06,103.27,104.23,102.82,103.52,27380000,103.52 1978-10-05,103.06,104.10,102.54,103.27,27820000,103.27 1978-10-04,102.60,103.36,101.76,103.06,25090000,103.06 1978-10-03,102.96,103.56,102.18,102.60,22540000,102.60 1978-10-02,102.54,103.42,102.13,102.96,18700000,102.96 1978-09-29,101.96,103.08,101.65,102.54,23610000,102.54 1978-09-28,101.66,102.38,100.94,101.96,24390000,101.96 1978-09-27,102.62,103.44,101.33,101.66,28370000,101.66 1978-09-26,101.86,103.15,101.58,102.62,26330000,102.62 1978-09-25,101.84,102.36,101.05,101.86,20970000,101.86 1978-09-22,101.90,102.69,101.13,101.84,27960000,101.84 1978-09-21,101.73,102.54,100.66,101.90,33640000,101.90 1978-09-20,102.53,103.29,101.28,101.73,35080000,101.73 1978-09-19,103.21,103.82,102.12,102.53,31660000,102.53 1978-09-18,104.12,105.03,102.75,103.21,35860000,103.21 1978-09-15,105.10,105.12,103.56,104.12,37290000,104.12 1978-09-14,106.34,106.62,104.77,105.10,37400000,105.10 1978-09-13,106.99,107.85,105.87,106.34,43340000,106.34 1978-09-12,106.98,107.48,106.02,106.99,34400000,106.99 1978-09-11,106.79,108.05,106.42,106.98,39670000,106.98 1978-09-08,105.50,107.19,105.50,106.79,42170000,106.79 1978-09-07,105.38,106.49,104.76,105.42,40310000,105.42 1978-09-06,104.51,106.19,104.51,105.38,42600000,105.38 1978-09-05,103.68,104.83,103.31,104.49,32170000,104.49 1978-09-01,103.29,104.27,102.73,103.68,35070000,103.68 1978-08-31,103.50,104.05,102.63,103.29,33850000,103.29 1978-08-30,103.39,104.26,102.70,103.50,37750000,103.50 1978-08-29,103.96,104.34,102.92,103.39,33780000,103.39 1978-08-28,104.90,105.14,103.61,103.96,31760000,103.96 1978-08-25,105.08,105.68,104.24,104.90,36190000,104.90 1978-08-24,104.91,105.86,104.29,105.08,38500000,105.08 1978-08-23,104.31,105.68,104.12,104.91,39630000,104.91 1978-08-22,103.89,104.79,103.14,104.31,29620000,104.31 1978-08-21,104.73,105.20,103.44,103.89,29440000,103.89 1978-08-18,105.08,105.98,104.23,104.73,34650000,104.73 1978-08-17,104.65,106.27,104.34,105.08,45270000,105.08 1978-08-16,103.85,105.15,103.41,104.65,36120000,104.65 1978-08-15,103.97,104.38,102.86,103.85,29760000,103.85 1978-08-14,103.96,104.98,103.40,103.97,32320000,103.97 1978-08-11,103.66,104.67,102.85,103.96,33550000,103.96 1978-08-10,104.50,105.11,103.10,103.66,39760000,103.66 1978-08-09,104.01,105.72,103.70,104.50,48800000,104.50 1978-08-08,103.55,104.35,102.60,104.01,34290000,104.01 1978-08-07,103.92,104.84,103.03,103.55,33350000,103.55 1978-08-04,103.51,104.67,102.75,103.92,37910000,103.92 1978-08-03,102.92,105.41,102.82,103.51,66370000,103.51 1978-08-02,100.66,103.21,100.18,102.92,47470000,102.92 1978-08-01,100.68,101.46,99.95,100.66,34810000,100.66 1978-07-31,100.00,101.18,99.37,100.68,33990000,100.68 1978-07-28,99.54,100.51,98.90,100.00,33390000,100.00 1978-07-27,99.08,100.17,98.60,99.54,33970000,99.54 1978-07-26,99.08,99.08,99.08,99.08,36830000,99.08 1978-07-25,97.72,98.73,97.20,98.44,25400000,98.44 1978-07-24,97.75,98.13,96.72,97.72,23280000,97.72 1978-07-21,98.03,98.57,97.02,97.75,26060000,97.75 1978-07-20,98.12,99.18,97.49,98.03,33350000,98.03 1978-07-19,96.87,98.41,96.71,98.12,30850000,98.12 1978-07-18,97.78,97.98,96.52,96.87,22860000,96.87 1978-07-17,97.58,98.84,97.24,97.78,29180000,97.78 1978-07-14,96.25,97.88,95.89,97.58,28370000,97.58 1978-07-13,96.24,96.66,95.42,96.25,23620000,96.25 1978-07-12,95.93,96.83,95.50,96.24,26640000,96.24 1978-07-11,95.27,96.49,94.92,95.93,27470000,95.93 1978-07-10,94.89,95.67,94.28,95.27,22470000,95.27 1978-07-07,94.32,95.32,94.02,94.89,23480000,94.89 1978-07-06,94.27,94.83,93.59,94.32,24990000,94.32 1978-07-05,95.09,95.20,93.78,94.27,23730000,94.27 1978-07-03,95.53,95.65,94.62,95.09,11560000,95.09 1978-06-30,95.57,95.96,94.87,95.53,18100000,95.53 1978-06-29,95.40,96.26,95.00,95.57,21660000,95.57 1978-06-28,94.98,95.79,94.44,95.40,23260000,95.40 1978-06-27,94.60,95.48,93.99,94.98,29280000,94.98 1978-06-26,95.85,96.06,94.31,94.60,29250000,94.60 1978-06-23,96.24,96.98,95.49,95.85,28530000,95.85 1978-06-22,96.01,96.76,95.52,96.24,27160000,96.24 1978-06-21,96.51,96.74,95.42,96.01,29100000,96.01 1978-06-20,97.49,97.78,96.15,96.51,27920000,96.51 1978-06-19,97.42,97.94,96.53,97.49,25500000,97.49 1978-06-16,98.34,98.59,97.10,97.42,27690000,97.42 1978-06-15,99.48,99.54,97.97,98.34,29280000,98.34 1978-06-14,99.57,100.68,98.89,99.48,37290000,99.48 1978-06-13,99.55,99.98,98.43,99.57,30760000,99.57 1978-06-12,99.93,100.60,99.16,99.55,24440000,99.55 1978-06-09,100.21,100.71,99.30,99.93,32470000,99.93 1978-06-08,100.12,101.21,99.55,100.21,39380000,100.21 1978-06-07,100.32,100.81,99.36,100.12,33060000,100.12 1978-06-06,99.95,101.84,99.90,100.32,51970000,100.32 1978-06-05,98.14,100.27,97.97,99.95,39580000,99.95 1978-06-02,97.35,98.52,97.01,98.14,31860000,98.14 1978-06-01,97.24,97.95,96.63,97.35,28750000,97.35 1978-05-31,96.86,97.97,96.50,97.24,29070000,97.24 1978-05-30,96.58,97.23,95.95,96.86,21040000,96.86 1978-05-26,96.80,97.14,96.01,96.58,21410000,96.58 1978-05-25,97.08,97.80,96.30,96.80,28410000,96.80 1978-05-24,97.74,97.74,96.27,97.08,31450000,97.08 1978-05-23,99.09,99.17,97.53,98.05,33230000,98.05 1978-05-22,98.12,99.43,97.65,99.09,28680000,99.09 1978-05-19,98.62,99.06,97.42,98.12,34360000,98.12 1978-05-18,99.60,100.04,98.19,98.62,42270000,98.62 1978-05-17,99.35,100.32,98.63,99.60,45490000,99.60 1978-05-16,98.76,100.16,98.61,99.35,48170000,99.35 1978-05-15,98.07,99.11,97.40,98.76,33890000,98.76 1978-05-12,97.20,98.89,97.14,98.07,46600000,98.07 1978-05-11,95.92,97.47,95.60,97.20,36630000,97.20 1978-05-10,95.90,96.69,95.35,95.92,33330000,95.92 1978-05-09,96.19,96.68,95.33,95.90,30860000,95.90 1978-05-08,96.53,97.50,95.82,96.19,34680000,96.19 1978-05-05,95.93,97.44,95.56,96.53,42680000,96.53 1978-05-04,96.26,96.43,94.57,95.93,37520000,95.93 1978-05-03,97.25,97.61,95.84,96.26,37560000,96.26 1978-05-02,97.67,98.11,96.44,97.25,41400000,97.25 1978-05-01,96.83,98.30,96.41,97.67,37020000,97.67 1978-04-28,95.86,97.10,95.24,96.83,32850000,96.83 1978-04-27,96.82,96.93,95.30,95.86,35470000,95.86 1978-04-26,96.64,97.75,95.96,96.82,44430000,96.82 1978-04-25,96.05,97.91,96.05,96.64,55800000,96.64 1978-04-24,94.34,96.00,94.08,95.77,34510000,95.77 1978-04-21,94.54,95.09,93.71,94.34,31540000,94.34 1978-04-20,93.97,95.71,93.97,94.54,43230000,94.54 1978-04-19,93.43,94.48,92.75,93.86,35060000,93.86 1978-04-18,94.45,94.72,92.87,93.43,38950000,93.43 1978-04-17,93.60,95.89,93.60,94.45,63510000,94.45 1978-04-14,91.40,93.31,91.40,92.92,52280000,92.92 1978-04-13,90.11,91.27,89.82,90.98,31580000,90.98 1978-04-12,90.25,90.78,89.65,90.11,26210000,90.11 1978-04-11,90.49,90.79,89.77,90.25,24300000,90.25 1978-04-10,90.17,90.88,89.73,90.49,25740000,90.49 1978-04-07,89.79,90.59,89.39,90.17,25160000,90.17 1978-04-06,89.64,90.46,89.31,89.79,27360000,89.79 1978-04-05,88.86,89.91,88.62,89.64,27260000,89.64 1978-04-04,88.46,89.18,88.16,88.86,20130000,88.86 1978-04-03,89.20,89.20,88.07,88.46,20230000,88.46 1978-03-31,89.41,89.64,88.68,89.21,20130000,89.21 1978-03-30,89.64,89.89,88.97,89.41,20460000,89.41 1978-03-29,89.50,90.17,89.14,89.64,25450000,89.64 1978-03-28,88.87,89.76,88.47,89.50,21600000,89.50 1978-03-27,89.36,89.50,88.51,88.87,18870000,88.87 1978-03-23,89.47,89.90,88.83,89.36,21290000,89.36 1978-03-22,89.79,90.07,88.99,89.47,21950000,89.47 1978-03-21,90.82,91.06,89.50,89.79,24410000,89.79 1978-03-20,90.20,91.35,90.10,90.82,28360000,90.82 1978-03-17,89.51,90.52,89.17,90.20,28470000,90.20 1978-03-16,89.12,89.77,88.58,89.51,25400000,89.51 1978-03-15,89.35,89.73,88.52,89.12,23340000,89.12 1978-03-14,88.95,89.62,88.21,89.35,24300000,89.35 1978-03-13,88.88,89.77,88.48,88.95,24070000,88.95 1978-03-10,87.89,89.25,87.82,88.88,27090000,88.88 1978-03-09,87.84,88.49,87.34,87.89,21820000,87.89 1978-03-08,87.36,88.08,86.97,87.84,22030000,87.84 1978-03-07,86.90,87.63,86.55,87.36,19900000,87.36 1978-03-06,87.45,87.52,86.48,86.90,17230000,86.90 1978-03-03,87.32,87.98,86.83,87.45,20120000,87.45 1978-03-02,87.19,87.81,86.69,87.32,20280000,87.32 1978-03-01,87.04,87.63,86.45,87.19,21010000,87.19 1978-02-28,87.72,87.76,86.58,87.04,19750000,87.04 1978-02-27,88.49,88.97,87.49,87.72,19990000,87.72 1978-02-24,87.66,88.87,87.66,88.49,22510000,88.49 1978-02-23,87.56,87.92,86.83,87.64,18720000,87.64 1978-02-22,87.59,88.15,87.19,87.56,18450000,87.56 1978-02-21,87.96,88.19,87.09,87.59,21890000,87.59 1978-02-17,88.08,88.70,87.55,87.96,18500000,87.96 1978-02-16,88.77,88.77,87.64,88.08,21570000,88.08 1978-02-15,89.04,89.40,88.30,88.83,20170000,88.83 1978-02-14,89.86,89.89,88.70,89.04,20470000,89.04 1978-02-13,90.08,90.30,89.38,89.86,16810000,89.86 1978-02-10,90.30,90.69,89.56,90.08,19480000,90.08 1978-02-09,90.83,90.96,89.84,90.30,17940000,90.30 1978-02-08,90.33,91.32,90.09,90.83,21300000,90.83 1978-02-07,89.50,90.53,89.38,90.33,14730000,90.33 1978-02-06,89.62,89.85,88.95,89.50,11630000,89.50 1978-02-03,90.13,90.32,89.19,89.62,19400000,89.62 1978-02-02,89.93,90.91,89.54,90.13,23050000,90.13 1978-02-01,89.25,90.24,88.82,89.93,22240000,89.93 1978-01-31,89.34,89.92,88.61,89.25,19870000,89.25 1978-01-30,88.58,89.67,88.26,89.34,17400000,89.34 1978-01-27,88.58,89.10,88.02,88.58,17600000,88.58 1978-01-26,89.39,89.79,88.31,88.58,19600000,88.58 1978-01-25,89.25,89.94,88.83,89.39,18690000,89.39 1978-01-24,89.24,89.80,88.67,89.25,18690000,89.25 1978-01-23,89.89,90.08,88.81,89.24,19380000,89.24 1978-01-20,90.09,90.27,89.41,89.89,7580000,89.89 1978-01-19,90.56,91.04,89.74,90.09,21500000,90.09 1978-01-18,89.88,90.86,89.59,90.56,21390000,90.56 1978-01-17,89.43,90.31,89.05,89.88,19360000,89.88 1978-01-16,89.69,90.11,88.88,89.43,18760000,89.43 1978-01-13,89.82,90.47,89.26,89.69,18010000,89.69 1978-01-12,89.74,90.60,89.25,89.82,22730000,89.82 1978-01-11,90.17,90.70,89.23,89.74,22880000,89.74 1978-01-10,90.64,91.29,89.72,90.17,25180000,90.17 1978-01-09,91.48,91.48,89.97,90.64,27990000,90.64 1978-01-06,92.66,92.66,91.05,91.62,26150000,91.62 1978-01-05,93.52,94.53,92.51,92.74,23570000,92.74 1978-01-04,93.82,94.10,92.57,93.52,24090000,93.52 1978-01-03,95.10,95.15,93.49,93.82,17720000,93.82 1977-12-30,94.94,95.67,94.44,95.10,23560000,95.10 1977-12-29,94.75,95.43,94.10,94.94,23610000,94.94 1977-12-28,94.69,95.20,93.99,94.75,19630000,94.75 1977-12-27,94.69,95.21,94.09,94.69,16750000,94.69 1977-12-23,93.80,94.99,93.75,94.69,20080000,94.69 1977-12-22,93.05,94.37,93.05,93.80,28100000,93.80 1977-12-21,92.50,93.58,92.20,93.05,24510000,93.05 1977-12-20,92.69,93.00,91.76,92.50,23250000,92.50 1977-12-19,93.40,93.71,92.42,92.69,21150000,92.69 1977-12-16,93.55,94.04,92.93,93.40,20270000,93.40 1977-12-15,94.03,94.42,93.23,93.55,21610000,93.55 1977-12-14,93.56,94.26,92.94,94.03,22110000,94.03 1977-12-13,93.63,94.04,92.90,93.56,19190000,93.56 1977-12-12,93.65,94.29,93.18,93.63,18180000,93.63 1977-12-09,92.96,94.11,92.77,93.65,19210000,93.65 1977-12-08,92.78,93.76,92.51,92.96,20400000,92.96 1977-12-07,92.83,93.39,92.15,92.78,21050000,92.78 1977-12-06,94.09,94.09,92.44,92.83,23770000,92.83 1977-12-05,94.67,95.01,93.91,94.27,19160000,94.27 1977-12-02,94.69,95.25,94.08,94.67,21160000,94.67 1977-12-01,94.83,95.45,94.23,94.69,24220000,94.69 1977-11-30,94.55,95.17,93.78,94.83,22670000,94.83 1977-11-29,96.04,96.09,94.28,94.55,22950000,94.55 1977-11-28,96.69,96.98,95.67,96.04,21570000,96.04 1977-11-25,96.49,97.11,95.86,96.69,17910000,96.69 1977-11-23,96.09,96.94,95.60,96.49,29150000,96.49 1977-11-22,95.25,96.52,95.05,96.09,28600000,96.09 1977-11-21,95.33,95.77,94.59,95.25,20110000,95.25 1977-11-18,95.16,95.88,94.70,95.33,23930000,95.33 1977-11-17,95.45,95.88,94.59,95.16,25110000,95.16 1977-11-16,95.93,96.47,95.06,95.45,24950000,95.45 1977-11-15,95.32,96.47,94.73,95.93,27740000,95.93 1977-11-14,95.98,96.38,94.91,95.32,23220000,95.32 1977-11-11,95.10,96.49,95.10,95.98,35260000,95.98 1977-11-10,92.98,95.10,92.69,94.71,31980000,94.71 1977-11-09,92.46,93.27,92.01,92.98,21330000,92.98 1977-11-08,92.29,92.97,91.82,92.46,19210000,92.46 1977-11-07,91.58,92.70,91.32,92.29,21270000,92.29 1977-11-04,90.76,91.97,90.72,91.58,21700000,91.58 1977-11-03,90.71,91.18,90.01,90.76,18090000,90.76 1977-11-02,91.35,91.59,90.29,90.71,20760000,90.71 1977-11-01,92.19,92.19,91.00,91.35,17170000,91.35 1977-10-31,92.61,93.03,91.85,92.34,17070000,92.34 1977-10-28,92.34,93.13,91.88,92.61,18050000,92.61 1977-10-27,92.10,93.15,91.54,92.34,21920000,92.34 1977-10-26,91.00,92.46,90.44,92.10,24860000,92.10 1977-10-25,91.63,91.71,90.20,91.00,23590000,91.00 1977-10-24,92.32,92.62,91.36,91.63,19210000,91.63 1977-10-21,92.67,92.99,91.80,92.32,20230000,92.32 1977-10-20,92.38,93.12,91.60,92.67,20520000,92.67 1977-10-19,93.46,93.71,92.07,92.38,22030000,92.38 1977-10-18,93.47,94.19,93.01,93.46,20130000,93.46 1977-10-17,93.56,94.03,92.87,93.47,17340000,93.47 1977-10-14,93.46,94.19,92.88,93.56,20410000,93.56 1977-10-13,94.04,94.32,92.89,93.46,23870000,93.46 1977-10-12,94.82,94.82,93.40,94.04,22440000,94.04 1977-10-11,95.75,95.97,94.73,94.93,17870000,94.93 1977-10-10,95.97,96.15,95.32,95.75,10580000,95.75 1977-10-07,96.05,96.51,95.48,95.97,16250000,95.97 1977-10-06,95.68,96.45,95.30,96.05,18490000,96.05 1977-10-05,96.03,96.36,95.20,95.68,18300000,95.68 1977-10-04,96.74,97.27,95.73,96.03,20850000,96.03 1977-10-03,96.53,97.11,95.86,96.74,19460000,96.74 1977-09-30,95.85,96.85,95.66,96.53,21170000,96.53 1977-09-29,95.31,96.28,95.09,95.85,21160000,95.85 1977-09-28,95.24,95.91,94.73,95.31,17960000,95.31 1977-09-27,95.38,96.01,94.76,95.24,19080000,95.24 1977-09-26,95.04,95.68,94.44,95.38,18230000,95.38 1977-09-23,95.09,95.69,94.60,95.04,18760000,95.04 1977-09-22,95.10,95.61,94.51,95.09,16660000,95.09 1977-09-21,95.89,96.52,94.83,95.10,22200000,95.10 1977-09-20,95.85,96.29,95.23,95.89,19030000,95.89 1977-09-19,96.48,96.59,95.46,95.85,16890000,95.85 1977-09-16,96.80,97.30,96.05,96.48,18340000,96.48 1977-09-15,96.55,97.31,96.15,96.80,18230000,96.80 1977-09-14,96.09,96.88,95.66,96.55,17330000,96.55 1977-09-13,96.03,96.56,95.48,96.09,14900000,96.09 1977-09-12,96.37,96.64,95.37,96.03,18700000,96.03 1977-09-09,97.10,97.10,95.97,96.37,18100000,96.37 1977-09-08,98.01,98.43,97.01,97.28,18290000,97.28 1977-09-07,97.71,98.38,97.33,98.01,18070000,98.01 1977-09-06,97.45,98.13,96.93,97.71,16130000,97.71 1977-09-02,96.83,97.76,96.51,97.45,15620000,97.45 1977-09-01,96.77,97.54,96.35,96.83,18820000,96.83 1977-08-31,96.38,97.00,95.59,96.77,19080000,96.77 1977-08-30,96.92,97.55,96.04,96.38,18220000,96.38 1977-08-29,96.06,97.25,95.93,96.92,15280000,96.92 1977-08-26,96.15,96.42,95.04,96.06,18480000,96.06 1977-08-25,97.18,97.18,95.81,96.15,19400000,96.15 1977-08-24,97.62,97.99,96.77,97.23,18170000,97.23 1977-08-23,97.79,98.52,97.18,97.62,20290000,97.62 1977-08-22,97.51,98.29,96.84,97.79,17870000,97.79 1977-08-19,97.68,98.29,96.78,97.51,20800000,97.51 1977-08-18,97.74,98.69,97.21,97.68,21040000,97.68 1977-08-17,97.73,98.40,97.12,97.74,20920000,97.74 1977-08-16,98.18,98.60,97.35,97.73,19340000,97.73 1977-08-15,97.88,98.56,97.14,98.18,15750000,98.18 1977-08-12,98.16,98.51,97.31,97.88,16870000,97.88 1977-08-11,98.92,99.45,97.90,98.16,21740000,98.16 1977-08-10,98.05,99.06,97.67,98.92,18280000,98.92 1977-08-09,97.99,98.63,97.48,98.05,19900000,98.05 1977-08-08,98.76,98.86,97.68,97.99,15870000,97.99 1977-08-05,98.74,99.44,98.31,98.76,19940000,98.76 1977-08-04,98.37,99.19,97.79,98.74,18870000,98.74 1977-08-03,98.50,98.86,97.53,98.37,21710000,98.37 1977-08-02,99.12,99.27,98.14,98.50,17910000,98.50 1977-08-01,98.85,99.84,98.46,99.12,17920000,99.12 1977-07-29,98.79,99.21,97.71,98.85,20350000,98.85 1977-07-28,98.64,99.36,97.78,98.79,26340000,98.79 1977-07-27,100.27,100.29,98.31,98.64,26440000,98.64 1977-07-26,100.85,100.92,99.72,100.27,21390000,100.27 1977-07-25,101.67,101.85,100.46,100.85,20430000,100.85 1977-07-22,101.59,102.28,101.02,101.67,23110000,101.67 1977-07-21,101.73,102.19,100.85,101.59,26880000,101.59 1977-07-20,101.79,102.57,101.14,101.73,29380000,101.73 1977-07-19,100.95,102.17,100.68,101.79,31930000,101.79 1977-07-18,100.18,101.40,99.94,100.95,29890000,100.95 1977-07-15,99.59,100.68,99.28,100.18,29120000,100.18 1977-07-13,99.45,99.99,98.83,99.59,23160000,99.59 1977-07-12,99.55,100.01,98.81,99.45,22470000,99.45 1977-07-11,99.79,100.16,98.90,99.55,19790000,99.55 1977-07-08,99.93,100.62,99.37,99.79,23820000,99.79 1977-07-07,99.58,100.30,99.12,99.93,21740000,99.93 1977-07-06,100.09,100.41,99.20,99.58,21230000,99.58 1977-07-05,100.10,100.72,99.62,100.09,16850000,100.09 1977-07-01,100.48,100.76,99.63,100.10,18160000,100.10 1977-06-30,100.11,100.88,99.68,100.48,19410000,100.48 1977-06-29,100.14,100.49,99.30,100.11,19000000,100.11 1977-06-28,100.98,101.36,99.87,100.14,22670000,100.14 1977-06-27,101.19,101.63,100.47,100.98,19870000,100.98 1977-06-24,100.62,101.65,100.41,101.19,27490000,101.19 1977-06-23,100.46,101.10,99.88,100.62,24330000,100.62 1977-06-22,100.74,101.07,99.90,100.46,25070000,100.46 1977-06-21,100.42,101.41,100.16,100.74,29730000,100.74 1977-06-20,99.97,100.76,99.56,100.42,22950000,100.42 1977-06-17,99.85,100.47,99.34,99.97,21960000,99.97 1977-06-16,99.61,100.33,98.91,99.85,24310000,99.85 1977-06-15,99.86,100.31,99.12,99.61,22640000,99.61 1977-06-14,98.76,100.12,98.76,99.86,25390000,99.86 1977-06-13,98.46,99.21,98.06,98.74,20250000,98.74 1977-06-10,98.14,98.86,97.68,98.46,20630000,98.46 1977-06-09,98.20,98.62,97.51,98.14,19940000,98.14 1977-06-08,97.73,98.75,97.49,98.20,22200000,98.20 1977-06-07,97.23,98.01,96.60,97.73,21110000,97.73 1977-06-06,97.69,98.26,96.89,97.23,18930000,97.23 1977-06-03,96.74,98.12,96.55,97.69,20330000,97.69 1977-06-02,96.93,97.53,96.23,96.74,18620000,96.74 1977-06-01,96.12,97.27,95.89,96.93,18320000,96.93 1977-05-31,96.27,96.75,95.52,96.12,17800000,96.12 1977-05-27,97.01,97.26,95.92,96.27,15730000,96.27 1977-05-26,96.77,97.47,96.20,97.01,18620000,97.01 1977-05-25,97.67,98.14,96.50,96.77,20710000,96.77 1977-05-24,98.15,98.25,97.00,97.67,20050000,97.67 1977-05-23,99.35,99.35,97.88,98.15,18290000,98.15 1977-05-20,99.88,100.12,98.91,99.45,18950000,99.45 1977-05-19,100.30,100.74,99.49,99.88,21280000,99.88 1977-05-18,99.77,100.93,99.58,100.30,27800000,100.30 1977-05-17,99.47,100.11,98.76,99.77,22290000,99.77 1977-05-16,99.03,99.98,98.79,99.47,21170000,99.47 1977-05-13,98.73,99.52,98.37,99.03,19780000,99.03 1977-05-12,98.78,99.25,97.91,98.73,21980000,98.73 1977-05-11,99.47,99.77,98.40,98.78,18980000,98.78 1977-05-10,99.18,100.09,98.82,99.47,21090000,99.47 1977-05-09,99.49,99.78,98.66,99.18,15230000,99.18 1977-05-06,100.11,100.20,98.95,99.49,19370000,99.49 1977-05-05,99.96,100.79,99.28,100.11,23450000,100.11 1977-05-04,99.43,100.56,98.90,99.96,23330000,99.96 1977-05-03,98.93,99.96,98.72,99.43,21950000,99.43 1977-05-02,98.44,99.26,97.97,98.93,17970000,98.93 1977-04-29,98.20,98.87,97.58,98.44,18330000,98.44 1977-04-28,97.96,98.77,97.47,98.20,18370000,98.20 1977-04-27,97.11,98.47,96.90,97.96,20590000,97.96 1977-04-26,97.15,97.94,96.53,97.11,20040000,97.11 1977-04-25,98.32,98.32,96.54,97.15,20440000,97.15 1977-04-22,99.67,99.67,98.08,98.44,20700000,98.44 1977-04-21,100.40,101.20,99.35,99.75,22740000,99.75 1977-04-20,100.07,100.98,99.49,100.40,25090000,100.40 1977-04-19,100.54,100.81,99.58,100.07,19510000,100.07 1977-04-18,101.04,101.36,100.09,100.54,17830000,100.54 1977-04-15,101.00,101.63,100.35,101.04,20230000,101.04 1977-04-14,100.42,102.07,100.42,101.00,30490000,101.00 1977-04-13,100.15,100.72,99.02,100.16,21800000,100.16 1977-04-12,98.97,100.58,98.97,100.15,23760000,100.15 1977-04-11,98.35,99.37,98.08,98.88,17650000,98.88 1977-04-07,97.91,98.65,97.48,98.35,17260000,98.35 1977-04-06,98.01,98.61,97.45,97.91,16600000,97.91 1977-04-05,98.23,98.60,97.43,98.01,18330000,98.01 1977-04-04,99.21,99.50,97.98,98.23,16250000,98.23 1977-04-01,98.42,99.57,98.38,99.21,17050000,99.21 1977-03-31,98.54,99.14,97.80,98.42,16510000,98.42 1977-03-30,99.69,99.99,98.18,98.54,18810000,98.54 1977-03-29,99.00,100.12,98.95,99.69,17030000,99.69 1977-03-28,99.06,99.54,98.35,99.00,16710000,99.00 1977-03-25,99.70,100.05,98.71,99.06,16550000,99.06 1977-03-24,100.20,100.60,99.26,99.70,19650000,99.70 1977-03-23,101.00,101.42,99.88,100.20,19360000,100.20 1977-03-22,101.31,101.58,100.35,101.00,18660000,101.00 1977-03-21,101.86,102.13,100.92,101.31,18040000,101.31 1977-03-18,102.08,102.61,101.39,101.86,19840000,101.86 1977-03-17,102.17,102.58,101.28,102.08,20700000,102.08 1977-03-16,101.98,102.70,101.52,102.17,22140000,102.17 1977-03-15,101.42,102.61,101.34,101.98,23940000,101.98 1977-03-14,100.65,101.75,100.24,101.42,19290000,101.42 1977-03-11,100.67,101.37,100.14,100.65,18230000,100.65 1977-03-10,100.10,100.96,99.49,100.67,18620000,100.67 1977-03-09,100.87,100.89,99.63,100.10,19680000,100.10 1977-03-08,101.25,101.85,100.48,100.87,19520000,100.87 1977-03-07,101.20,101.77,100.64,101.25,17410000,101.25 1977-03-04,100.88,101.67,100.52,101.20,18950000,101.20 1977-03-03,100.39,101.28,100.01,100.88,17560000,100.88 1977-03-02,100.66,101.24,99.97,100.39,18010000,100.39 1977-03-01,99.82,101.03,99.65,100.66,19480000,100.66 1977-02-28,99.48,100.06,98.91,99.82,16220000,99.82 1977-02-25,99.60,100.02,98.82,99.48,17610000,99.48 1977-02-24,100.19,100.42,99.18,99.60,19730000,99.60 1977-02-23,100.49,100.95,99.78,100.19,18240000,100.19 1977-02-22,100.49,101.22,99.94,100.49,17730000,100.49 1977-02-18,100.92,101.13,99.95,100.49,18040000,100.49 1977-02-17,101.50,101.76,100.43,100.92,19040000,100.92 1977-02-16,101.04,102.22,100.68,101.50,23430000,101.50 1977-02-15,100.74,101.67,100.35,101.04,21620000,101.04 1977-02-14,100.22,101.06,99.51,100.74,19230000,100.74 1977-02-11,100.82,101.18,99.74,100.22,20510000,100.22 1977-02-10,100.73,101.51,100.16,100.82,22340000,100.82 1977-02-09,101.60,101.88,100.12,100.73,23640000,100.73 1977-02-08,101.89,102.65,101.16,101.60,24040000,101.60 1977-02-07,101.88,102.43,101.25,101.89,20700000,101.89 1977-02-04,101.85,102.71,101.30,101.88,23130000,101.88 1977-02-03,102.36,102.57,101.28,101.85,23790000,101.85 1977-02-02,102.54,103.32,101.89,102.36,25700000,102.36 1977-02-01,102.03,103.06,101.57,102.54,23700000,102.54 1977-01-31,101.93,102.44,100.91,102.03,22920000,102.03 1977-01-28,101.79,102.61,101.08,101.93,22700000,101.93 1977-01-27,102.34,102.81,101.27,101.79,24360000,101.79 1977-01-26,103.13,103.48,101.84,102.34,27840000,102.34 1977-01-25,103.25,104.08,102.42,103.13,26340000,103.13 1977-01-24,103.32,104.06,102.50,103.25,22890000,103.25 1977-01-21,102.97,103.91,102.35,103.32,23930000,103.32 1977-01-20,103.85,104.45,102.50,102.97,26520000,102.97 1977-01-19,103.32,104.38,102.83,103.85,27120000,103.85 1977-01-18,103.73,104.29,102.71,103.32,24380000,103.32 1977-01-17,104.01,104.37,103.04,103.73,21060000,103.73 1977-01-14,104.20,104.71,103.37,104.01,24480000,104.01 1977-01-13,103.40,104.60,103.21,104.20,24780000,104.20 1977-01-12,104.12,104.18,102.75,103.40,22670000,103.40 1977-01-11,105.20,105.60,103.76,104.12,24100000,104.12 1977-01-10,105.01,105.75,104.46,105.20,20860000,105.20 1977-01-07,105.02,105.59,104.30,105.01,21720000,105.01 1977-01-06,104.76,105.86,104.40,105.02,23920000,105.02 1977-01-05,105.70,106.07,104.33,104.76,25010000,104.76 1977-01-04,107.00,107.31,105.40,105.70,22740000,105.70 1977-01-03,107.46,107.97,106.42,107.00,21280000,107.00 1976-12-31,106.88,107.82,106.55,107.46,19170000,107.46 1976-12-30,106.34,107.41,105.97,106.88,23700000,106.88 1976-12-29,106.77,107.17,105.83,106.34,21910000,106.34 1976-12-28,106.06,107.36,105.90,106.77,25790000,106.77 1976-12-27,104.84,106.31,104.58,106.06,20130000,106.06 1976-12-23,104.71,105.49,104.09,104.84,24560000,104.84 1976-12-22,104.22,105.59,104.03,104.71,26970000,104.71 1976-12-21,103.65,104.66,102.99,104.22,24390000,104.22 1976-12-20,104.26,104.63,103.21,103.65,20690000,103.65 1976-12-17,104.80,105.60,103.89,104.26,23870000,104.26 1976-12-16,105.14,105.53,104.07,104.80,23920000,104.80 1976-12-15,105.07,105.89,104.33,105.14,28300000,105.14 1976-12-14,104.63,105.44,103.80,105.07,25130000,105.07 1976-12-13,104.70,105.33,103.94,104.63,24830000,104.63 1976-12-10,104.51,105.36,103.90,104.70,25960000,104.70 1976-12-09,104.08,105.27,103.71,104.51,31800000,104.51 1976-12-08,103.49,104.40,102.94,104.08,24560000,104.08 1976-12-07,103.56,104.40,102.96,103.49,26140000,103.49 1976-12-06,102.76,104.15,102.53,103.56,24830000,103.56 1976-12-03,102.12,103.31,101.75,102.76,22640000,102.76 1976-12-02,102.49,103.30,101.70,102.12,23300000,102.12 1976-12-01,102.10,103.03,101.62,102.49,21960000,102.49 1976-11-30,102.44,102.72,101.46,102.10,17030000,102.10 1976-11-29,103.15,103.46,102.07,102.44,18750000,102.44 1976-11-26,102.41,103.51,102.13,103.15,15000000,103.15 1976-11-24,101.96,102.85,101.41,102.41,20420000,102.41 1976-11-23,102.59,102.90,101.50,101.96,19090000,101.96 1976-11-22,101.92,103.15,101.63,102.59,20930000,102.59 1976-11-19,101.89,102.77,101.17,101.92,24550000,101.92 1976-11-18,100.61,102.22,100.49,101.89,24000000,101.89 1976-11-17,100.04,101.32,99.64,100.61,19900000,100.61 1976-11-16,99.90,101.12,99.44,100.04,21020000,100.04 1976-11-15,99.24,100.16,98.53,99.90,16710000,99.90 1976-11-12,99.64,99.95,98.51,99.24,15550000,99.24 1976-11-11,98.81,99.89,98.35,99.64,13230000,99.64 1976-11-10,99.32,99.98,98.18,98.81,18890000,98.81 1976-11-09,99.60,100.21,98.38,99.32,19210000,99.32 1976-11-08,100.62,100.62,99.10,99.60,16520000,99.60 1976-11-05,102.41,102.70,100.48,100.82,20780000,100.82 1976-11-04,101.92,103.16,101.40,102.41,21700000,102.41 1976-11-03,102.49,102.49,100.73,101.92,19350000,101.92 1976-11-01,102.90,103.78,102.19,103.10,18390000,103.10 1976-10-29,101.61,103.10,101.15,102.90,17030000,102.90 1976-10-28,101.76,102.50,101.12,101.61,16920000,101.61 1976-10-27,101.06,102.12,100.61,101.76,15790000,101.76 1976-10-26,100.07,101.50,99.91,101.06,15490000,101.06 1976-10-25,99.96,100.60,99.21,100.07,13310000,100.07 1976-10-22,100.77,100.93,99.24,99.96,17870000,99.96 1976-10-21,101.74,102.32,100.49,100.77,17980000,100.77 1976-10-20,101.45,102.23,100.81,101.74,15860000,101.74 1976-10-19,101.47,102.04,100.42,101.45,16200000,101.45 1976-10-18,100.88,101.99,100.62,101.47,15710000,101.47 1976-10-15,100.85,101.50,100.02,100.88,16210000,100.88 1976-10-14,102.12,102.14,100.28,100.85,18610000,100.85 1976-10-13,100.81,102.44,100.54,102.12,21690000,102.12 1976-10-12,101.64,102.19,100.38,100.81,18210000,100.81 1976-10-11,102.48,102.48,100.98,101.64,14620000,101.64 1976-10-08,103.54,104.00,102.24,102.56,16740000,102.56 1976-10-07,102.97,103.90,102.16,103.54,19830000,103.54 1976-10-06,103.23,103.72,102.05,102.97,20870000,102.97 1976-10-05,104.03,104.25,102.51,103.23,19200000,103.23 1976-10-04,104.17,104.62,103.42,104.03,12630000,104.03 1976-10-01,105.24,105.75,103.60,104.17,20620000,104.17 1976-09-30,105.37,105.84,104.57,105.24,14700000,105.24 1976-09-29,105.92,106.45,104.83,105.37,18090000,105.37 1976-09-28,107.27,107.54,105.61,105.92,20440000,105.92 1976-09-27,106.80,107.70,106.35,107.27,17430000,107.27 1976-09-24,106.92,107.36,106.03,106.80,17400000,106.80 1976-09-23,107.46,107.96,106.40,106.92,24210000,106.92 1976-09-22,107.83,108.72,106.92,107.46,32970000,107.46 1976-09-21,106.32,108.13,106.09,107.83,30300000,107.83 1976-09-20,106.27,107.20,105.74,106.32,21730000,106.32 1976-09-17,105.34,106.81,105.14,106.27,28270000,106.27 1976-09-16,104.25,105.59,103.84,105.34,19620000,105.34 1976-09-15,103.94,104.70,103.28,104.25,17570000,104.25 1976-09-14,104.29,104.50,103.31,103.94,15550000,103.94 1976-09-13,104.65,105.29,103.88,104.29,16100000,104.29 1976-09-10,104.40,105.03,103.79,104.65,16930000,104.65 1976-09-09,104.94,105.12,103.91,104.40,16540000,104.40 1976-09-08,105.03,105.73,104.34,104.94,19750000,104.94 1976-09-07,104.30,105.31,103.93,105.03,16310000,105.03 1976-09-03,103.92,104.63,103.36,104.30,13280000,104.30 1976-09-02,104.06,104.84,103.47,103.92,18920000,103.92 1976-09-01,102.91,104.30,102.60,104.06,18640000,104.06 1976-08-31,102.07,103.38,101.94,102.91,15480000,102.91 1976-08-30,101.48,102.51,101.22,102.07,11140000,102.07 1976-08-27,101.32,101.90,100.55,101.48,12120000,101.48 1976-08-26,102.03,102.59,101.01,101.32,15270000,101.32 1976-08-25,101.27,102.41,100.43,102.03,17400000,102.03 1976-08-24,101.96,102.65,100.98,101.27,16740000,101.27 1976-08-23,102.37,102.49,101.04,101.96,15450000,101.96 1976-08-20,103.31,103.31,101.96,102.37,14920000,102.37 1976-08-19,104.56,104.74,103.01,103.39,17230000,103.39 1976-08-18,104.80,105.41,104.12,104.56,17150000,104.56 1976-08-17,104.43,105.25,103.98,104.80,18500000,104.80 1976-08-16,104.25,104.99,103.74,104.43,16210000,104.43 1976-08-13,104.22,104.79,103.61,104.25,13930000,104.25 1976-08-12,104.06,104.64,103.38,104.22,15560000,104.22 1976-08-11,104.41,105.24,103.73,104.06,18710000,104.06 1976-08-10,103.49,104.71,103.21,104.41,16690000,104.41 1976-08-09,103.79,104.02,103.01,103.49,11700000,103.49 1976-08-06,103.85,104.25,103.10,103.79,13930000,103.79 1976-08-05,104.43,104.76,103.48,103.85,15530000,103.85 1976-08-04,104.14,105.18,103.72,104.43,20650000,104.43 1976-08-03,103.19,104.49,102.79,104.14,18500000,104.14 1976-08-02,103.44,103.98,102.64,103.19,13870000,103.19 1976-07-30,102.93,103.88,102.47,103.44,14830000,103.44 1976-07-29,103.05,103.59,102.36,102.93,13330000,102.93 1976-07-28,103.48,103.58,102.31,103.05,16000000,103.05 1976-07-27,104.07,104.51,103.13,103.48,15580000,103.48 1976-07-26,104.06,104.69,103.46,104.07,13530000,104.07 1976-07-23,103.93,104.71,103.49,104.06,15870000,104.06 1976-07-22,103.82,104.42,103.15,103.93,15600000,103.93 1976-07-21,103.72,104.56,103.21,103.82,18350000,103.82 1976-07-20,104.29,104.57,103.05,103.72,18810000,103.72 1976-07-19,104.68,105.32,103.84,104.29,18200000,104.29 1976-07-16,105.20,105.27,103.87,104.68,20450000,104.68 1976-07-15,105.95,106.25,104.76,105.20,20400000,105.20 1976-07-14,105.67,106.61,105.05,105.95,23840000,105.95 1976-07-13,105.90,106.78,105.15,105.67,27550000,105.67 1976-07-12,104.98,106.30,104.74,105.90,23750000,105.90 1976-07-09,103.98,105.41,103.80,104.98,23500000,104.98 1976-07-08,103.83,104.75,103.44,103.98,21710000,103.98 1976-07-07,103.54,104.23,102.80,103.83,18470000,103.83 1976-07-06,104.11,104.67,103.19,103.54,16130000,103.54 1976-07-02,103.59,104.53,103.13,104.11,16730000,104.11 1976-07-01,104.28,104.98,103.14,103.59,21130000,103.59 1976-06-30,103.86,105.07,103.52,104.28,23830000,104.28 1976-06-29,103.43,104.33,102.95,103.86,19620000,103.86 1976-06-28,103.72,104.35,102.97,103.43,17490000,103.43 1976-06-25,103.79,104.54,103.17,103.72,17830000,103.72 1976-06-24,103.25,104.37,102.90,103.79,19850000,103.79 1976-06-23,103.47,103.90,102.40,103.25,17530000,103.25 1976-06-22,104.28,104.82,103.16,103.47,21150000,103.47 1976-06-21,103.76,104.73,103.18,104.28,18930000,104.28 1976-06-18,103.61,104.80,103.06,103.76,25720000,103.76 1976-06-17,102.01,104.12,101.97,103.61,27810000,103.61 1976-06-16,101.46,102.65,100.96,102.01,21620000,102.01 1976-06-15,101.95,102.39,100.84,101.46,18440000,101.46 1976-06-14,101.00,102.51,101.00,101.95,21250000,101.95 1976-06-11,99.56,101.22,99.38,100.92,19470000,100.92 1976-06-10,98.74,99.98,98.55,99.56,16100000,99.56 1976-06-09,98.80,99.49,98.23,98.74,14560000,98.74 1976-06-08,98.63,99.71,98.32,98.80,16660000,98.80 1976-06-07,99.15,99.39,97.97,98.63,14510000,98.63 1976-06-04,100.13,100.27,98.79,99.15,15960000,99.15 1976-06-03,100.22,101.10,99.68,100.13,18900000,100.13 1976-06-02,99.85,100.69,99.26,100.22,16120000,100.22 1976-06-01,100.18,100.74,99.36,99.85,13880000,99.85 1976-05-28,99.38,100.64,99.00,100.18,16860000,100.18 1976-05-27,99.34,99.77,98.26,99.38,15310000,99.38 1976-05-26,99.49,100.14,98.65,99.34,16750000,99.34 1976-05-25,99.44,100.02,98.48,99.49,18770000,99.49 1976-05-24,101.07,101.07,99.11,99.44,16560000,99.44 1976-05-21,102.00,102.34,100.81,101.26,18730000,101.26 1976-05-20,101.18,102.53,100.69,102.00,22560000,102.00 1976-05-19,101.26,102.01,100.55,101.18,18450000,101.18 1976-05-18,101.09,102.00,100.72,101.26,17410000,101.26 1976-05-17,101.34,101.71,100.41,101.09,14720000,101.09 1976-05-14,102.16,102.23,100.82,101.34,16800000,101.34 1976-05-13,102.77,103.03,101.73,102.16,16730000,102.16 1976-05-12,102.95,103.55,102.14,102.77,18510000,102.77 1976-05-11,103.10,103.99,102.39,102.95,23590000,102.95 1976-05-10,101.88,103.51,101.76,103.10,22760000,103.10 1976-05-07,101.16,102.27,100.77,101.88,17810000,101.88 1976-05-06,100.88,101.70,100.31,101.16,16200000,101.16 1976-05-05,101.46,101.92,100.45,100.88,14970000,100.88 1976-05-04,100.92,101.93,100.29,101.46,17240000,101.46 1976-05-03,101.64,101.73,100.14,100.92,15180000,100.92 1976-04-30,102.13,102.65,101.16,101.64,14530000,101.64 1976-04-29,102.13,102.97,101.45,102.13,17740000,102.13 1976-04-28,101.86,102.46,100.91,102.13,15790000,102.13 1976-04-27,102.43,103.18,101.51,101.86,17760000,101.86 1976-04-26,102.29,102.80,101.36,102.43,15520000,102.43 1976-04-23,102.98,103.21,101.70,102.29,17000000,102.29 1976-04-22,103.32,104.04,102.52,102.98,20220000,102.98 1976-04-21,102.87,104.03,102.30,103.32,26600000,103.32 1976-04-20,101.44,103.32,101.42,102.87,23500000,102.87 1976-04-19,100.67,101.83,100.32,101.44,16500000,101.44 1976-04-15,100.31,101.18,99.73,100.67,15100000,100.67 1976-04-14,101.05,101.77,99.98,100.31,18440000,100.31 1976-04-13,100.20,101.39,99.64,101.05,15990000,101.05 1976-04-12,100.35,101.30,99.57,100.20,16030000,100.20 1976-04-09,101.28,101.74,99.87,100.35,19050000,100.35 1976-04-08,102.21,102.38,100.53,101.28,20860000,101.28 1976-04-07,103.36,103.85,101.92,102.21,20190000,102.21 1976-04-06,103.51,104.63,102.93,103.36,24170000,103.36 1976-04-05,102.32,104.13,102.32,103.51,21940000,103.51 1976-04-02,102.24,102.76,101.23,102.25,17420000,102.25 1976-04-01,102.77,103.24,101.50,102.24,17910000,102.24 1976-03-31,102.01,103.08,101.60,102.77,17520000,102.77 1976-03-30,102.41,103.36,101.25,102.01,17930000,102.01 1976-03-29,102.85,103.36,101.99,102.41,16100000,102.41 1976-03-26,102.85,103.65,102.20,102.85,18510000,102.85 1976-03-25,103.42,104.00,102.19,102.85,22510000,102.85 1976-03-24,102.51,104.39,102.51,103.42,32610000,103.42 1976-03-23,100.71,102.54,100.32,102.24,22450000,102.24 1976-03-22,100.58,101.53,100.14,100.71,19410000,100.71 1976-03-19,100.45,101.23,99.70,100.58,18090000,100.58 1976-03-18,100.86,101.37,99.73,100.45,20330000,100.45 1976-03-17,100.92,102.01,100.28,100.86,26190000,100.86 1976-03-16,99.80,101.25,99.38,100.92,22780000,100.92 1976-03-15,100.86,100.90,99.24,99.80,19570000,99.80 1976-03-12,101.89,102.46,100.49,100.86,26020000,100.86 1976-03-11,100.94,102.41,100.62,101.89,27300000,101.89 1976-03-10,100.58,101.80,99.98,100.94,24900000,100.94 1976-03-09,100.19,101.90,99.95,100.58,31770000,100.58 1976-03-08,99.11,100.71,98.93,100.19,25060000,100.19 1976-03-05,98.92,99.88,98.23,99.11,23030000,99.11 1976-03-04,99.98,100.40,98.49,98.92,24410000,98.92 1976-03-03,100.58,100.97,99.23,99.98,25450000,99.98 1976-03-02,100.02,101.26,99.61,100.58,25590000,100.58 1976-03-01,99.71,100.64,98.67,100.02,22070000,100.02 1976-02-27,100.11,100.53,98.60,99.71,26940000,99.71 1976-02-26,101.69,102.36,99.74,100.11,34320000,100.11 1976-02-25,102.03,102.71,100.69,101.69,34680000,101.69 1976-02-24,101.61,102.92,101.03,102.03,34380000,102.03 1976-02-23,102.10,102.54,100.69,101.61,31460000,101.61 1976-02-20,101.41,103.07,101.18,102.10,44510000,102.10 1976-02-19,99.94,101.92,99.94,101.41,39210000,101.41 1976-02-18,99.05,100.43,98.50,99.85,29900000,99.85 1976-02-17,99.67,100.25,98.56,99.05,25460000,99.05 1976-02-13,100.25,100.66,99.01,99.67,23870000,99.67 1976-02-12,100.77,101.55,99.82,100.25,28610000,100.25 1976-02-11,100.47,101.80,100.10,100.77,32300000,100.77 1976-02-10,99.62,100.96,99.11,100.47,27660000,100.47 1976-02-09,99.46,100.66,98.77,99.62,25340000,99.62 1976-02-06,100.39,100.53,98.64,99.46,27360000,99.46 1976-02-05,101.91,102.30,100.06,100.39,33780000,100.39 1976-02-04,101.18,102.57,100.70,101.91,38270000,101.91 1976-02-03,100.87,101.97,99.58,101.18,34080000,101.18 1976-02-02,100.86,101.39,99.74,100.87,24000000,100.87 1976-01-30,100.11,101.99,99.94,100.86,38510000,100.86 1976-01-29,98.53,100.54,98.32,100.11,29800000,100.11 1976-01-28,99.07,99.64,97.66,98.53,27370000,98.53 1976-01-27,99.68,100.52,98.28,99.07,32070000,99.07 1976-01-26,99.21,100.75,98.92,99.68,34470000,99.68 1976-01-23,98.04,99.88,97.68,99.21,33640000,99.21 1976-01-22,98.24,98.79,97.07,98.04,27420000,98.04 1976-01-21,98.86,99.24,97.12,98.24,34470000,98.24 1976-01-20,98.32,99.44,97.43,98.86,36690000,98.86 1976-01-19,97.00,98.84,96.36,98.32,29450000,98.32 1976-01-16,96.61,97.73,95.84,97.00,25940000,97.00 1976-01-15,97.13,98.34,96.15,96.61,38450000,96.61 1976-01-14,95.57,97.47,94.91,97.13,30340000,97.13 1976-01-13,96.33,97.39,95.11,95.57,34530000,95.57 1976-01-12,94.95,96.76,94.38,96.33,30440000,96.33 1976-01-09,94.58,95.71,94.05,94.95,26510000,94.95 1976-01-08,93.95,95.47,93.41,94.58,29030000,94.58 1976-01-07,93.53,95.15,92.91,93.95,33170000,93.95 1976-01-06,92.58,94.18,92.37,93.53,31270000,93.53 1976-01-05,90.90,92.84,90.85,92.58,21960000,92.58 1976-01-02,90.19,91.18,89.81,90.90,10300000,90.90 1975-12-31,89.77,90.75,89.17,90.19,16970000,90.19 1975-12-30,90.13,90.55,89.20,89.77,16040000,89.77 1975-12-29,90.25,91.09,89.63,90.13,17070000,90.13 1975-12-26,89.46,90.45,89.25,90.25,10020000,90.25 1975-12-24,88.73,89.84,88.73,89.46,11150000,89.46 1975-12-23,88.14,89.23,87.64,88.73,17750000,88.73 1975-12-22,88.80,89.13,87.74,88.14,15340000,88.14 1975-12-19,89.43,89.81,88.39,88.80,17720000,88.80 1975-12-18,89.15,90.09,88.62,89.43,18040000,89.43 1975-12-17,88.93,89.80,88.46,89.15,16560000,89.15 1975-12-16,88.09,89.49,87.78,88.93,18350000,88.93 1975-12-15,87.83,88.64,87.32,88.09,13960000,88.09 1975-12-12,87.80,88.22,87.05,87.83,13100000,87.83 1975-12-11,88.08,88.79,87.41,87.80,15300000,87.80 1975-12-10,87.30,88.39,86.91,88.08,15680000,88.08 1975-12-09,87.07,87.80,86.16,87.30,16040000,87.30 1975-12-08,86.82,87.75,86.15,87.07,14150000,87.07 1975-12-05,87.84,88.38,86.54,86.82,14050000,86.82 1975-12-04,87.60,88.39,86.68,87.84,16380000,87.84 1975-12-03,88.83,88.83,87.08,87.60,21320000,87.60 1975-12-02,90.67,90.81,89.08,89.33,17930000,89.33 1975-12-01,91.24,91.90,90.33,90.67,16050000,90.67 1975-11-28,90.94,91.74,90.44,91.24,12870000,91.24 1975-11-26,90.71,91.58,90.17,90.94,18780000,90.94 1975-11-25,89.70,91.10,89.66,90.71,17490000,90.71 1975-11-24,89.53,90.17,88.65,89.70,13930000,89.70 1975-11-21,89.64,90.23,88.79,89.53,14110000,89.53 1975-11-20,89.98,90.68,89.09,89.64,16460000,89.64 1975-11-19,91.00,91.28,89.47,89.98,16820000,89.98 1975-11-18,91.46,92.30,90.60,91.00,20760000,91.00 1975-11-17,90.97,91.99,90.50,91.46,17660000,91.46 1975-11-14,91.04,91.59,90.19,90.97,16460000,90.97 1975-11-13,91.19,92.33,90.56,91.04,25070000,91.04 1975-11-12,89.87,91.63,89.80,91.19,23960000,91.19 1975-11-11,89.34,90.47,89.04,89.87,14640000,89.87 1975-11-10,89.33,89.98,88.35,89.34,14910000,89.34 1975-11-07,89.55,90.18,88.67,89.33,15930000,89.33 1975-11-06,89.15,90.15,88.16,89.55,18600000,89.55 1975-11-05,88.51,90.08,88.32,89.15,17390000,89.15 1975-11-04,88.09,89.03,87.63,88.51,11570000,88.51 1975-11-03,89.04,89.21,87.78,88.09,11400000,88.09 1975-10-31,89.31,89.80,88.35,89.04,12910000,89.04 1975-10-30,89.39,90.20,88.70,89.31,15080000,89.31 1975-10-29,90.51,90.61,88.89,89.39,16110000,89.39 1975-10-28,89.73,91.01,89.40,90.51,17060000,90.51 1975-10-27,89.83,90.40,88.85,89.73,13100000,89.73 1975-10-24,91.24,91.52,89.46,89.83,18120000,89.83 1975-10-23,90.71,91.75,90.09,91.24,17900000,91.24 1975-10-22,90.56,91.38,89.77,90.71,16060000,90.71 1975-10-21,89.82,91.43,89.79,90.56,20800000,90.56 1975-10-20,88.86,90.14,88.43,89.82,13250000,89.82 1975-10-17,89.37,89.87,88.08,88.86,15650000,88.86 1975-10-16,89.23,90.73,88.90,89.37,18910000,89.37 1975-10-15,89.28,90.07,88.50,89.23,14440000,89.23 1975-10-14,89.46,90.80,88.81,89.28,19960000,89.28 1975-10-13,88.21,89.67,87.73,89.46,12020000,89.46 1975-10-10,88.37,89.17,87.44,88.21,14880000,88.21 1975-10-09,87.94,89.42,87.60,88.37,17770000,88.37 1975-10-08,86.77,88.46,86.34,87.94,17800000,87.94 1975-10-07,86.88,87.32,85.56,86.77,13530000,86.77 1975-10-06,85.98,87.64,85.98,86.88,15470000,86.88 1975-10-03,83.88,86.21,83.88,85.95,16360000,85.95 1975-10-02,82.93,84.33,82.82,83.82,14290000,83.82 1975-10-01,83.87,85.45,82.57,82.93,14070000,82.93 1975-09-30,85.01,85.01,83.44,83.87,12520000,83.87 1975-09-29,86.19,86.38,84.74,85.03,10580000,85.03 1975-09-26,85.64,86.86,85.13,86.19,12570000,86.19 1975-09-25,85.74,86.41,84.79,85.64,12890000,85.64 1975-09-24,85.03,86.70,85.03,85.74,16060000,85.74 1975-09-23,85.07,85.51,83.80,84.94,12800000,84.94 1975-09-22,85.88,86.70,84.70,85.07,14750000,85.07 1975-09-19,84.26,86.39,84.26,85.88,20830000,85.88 1975-09-18,82.37,84.34,82.23,84.06,14560000,84.06 1975-09-17,82.09,82.93,81.57,82.37,12190000,82.37 1975-09-16,82.88,83.43,81.79,82.09,13090000,82.09 1975-09-15,83.30,83.49,82.29,82.88,8670000,82.88 1975-09-12,83.45,84.47,82.84,83.30,12230000,83.30 1975-09-11,83.79,84.30,82.88,83.45,11100000,83.45 1975-09-10,84.59,84.59,83.00,83.79,14780000,83.79 1975-09-09,85.89,86.73,84.37,84.60,15790000,84.60 1975-09-08,85.62,86.31,84.89,85.89,11500000,85.89 1975-09-05,86.20,86.49,85.19,85.62,11680000,85.62 1975-09-04,86.03,86.91,85.29,86.20,12810000,86.20 1975-09-03,85.48,86.38,84.62,86.03,12260000,86.03 1975-09-02,86.88,87.42,85.21,85.48,11460000,85.48 1975-08-29,86.40,87.73,86.10,86.88,15480000,86.88 1975-08-28,84.68,86.64,84.68,86.40,14530000,86.40 1975-08-27,83.96,84.79,83.35,84.43,11100000,84.43 1975-08-26,85.06,85.40,83.65,83.96,11350000,83.96 1975-08-25,84.28,85.58,84.06,85.06,11250000,85.06 1975-08-22,83.07,84.61,82.79,84.28,13050000,84.28 1975-08-21,83.22,84.15,82.21,83.07,16610000,83.07 1975-08-20,84.78,84.78,82.76,83.22,18630000,83.22 1975-08-19,86.20,86.47,84.66,84.95,14990000,84.95 1975-08-18,86.36,87.21,85.76,86.20,10810000,86.20 1975-08-15,85.60,86.76,85.33,86.36,10610000,86.36 1975-08-14,85.97,86.34,85.02,85.60,12460000,85.60 1975-08-13,87.12,87.41,85.61,85.97,12000000,85.97 1975-08-12,86.55,88.17,86.49,87.12,14510000,87.12 1975-08-11,86.02,86.89,85.34,86.55,12350000,86.55 1975-08-08,86.30,87.00,85.52,86.02,11660000,86.02 1975-08-07,86.25,87.24,85.69,86.30,12390000,86.30 1975-08-06,86.23,87.04,85.34,86.25,16280000,86.25 1975-08-05,87.15,87.81,85.89,86.23,15470000,86.23 1975-08-04,87.99,88.17,86.68,87.15,12620000,87.15 1975-08-01,88.75,89.04,87.46,87.99,13320000,87.99 1975-07-31,88.83,90.07,88.31,88.75,14540000,88.75 1975-07-30,88.19,89.49,87.68,88.83,16150000,88.83 1975-07-29,88.69,89.91,87.71,88.19,19000000,88.19 1975-07-28,89.29,89.68,88.02,88.69,14850000,88.69 1975-07-25,90.07,90.72,88.72,89.29,15110000,89.29 1975-07-24,90.18,90.95,88.90,90.07,20550000,90.07 1975-07-23,91.45,92.15,89.83,90.18,20150000,90.18 1975-07-22,92.44,92.49,90.63,91.45,20660000,91.45 1975-07-21,93.20,93.93,92.03,92.44,16690000,92.44 1975-07-18,93.63,93.96,92.39,93.20,16870000,93.20 1975-07-17,94.61,95.03,92.99,93.63,21420000,93.63 1975-07-16,95.61,96.37,94.20,94.61,25250000,94.61 1975-07-15,95.19,96.58,94.71,95.61,28340000,95.61 1975-07-14,94.66,95.76,94.04,95.19,21900000,95.19 1975-07-11,94.81,95.69,93.83,94.66,22210000,94.66 1975-07-10,94.80,96.19,94.25,94.81,28880000,94.81 1975-07-09,93.39,95.22,93.38,94.80,26350000,94.80 1975-07-08,93.54,94.03,92.51,93.39,18990000,93.39 1975-07-07,94.36,94.82,93.16,93.54,15850000,93.54 1975-07-03,94.18,95.04,93.49,94.36,19000000,94.36 1975-07-02,94.85,94.91,93.37,94.18,18530000,94.18 1975-07-01,95.19,95.73,94.13,94.85,20390000,94.85 1975-06-30,94.81,95.85,94.30,95.19,19430000,95.19 1975-06-27,94.81,95.66,94.10,94.81,18820000,94.81 1975-06-26,94.62,95.72,93.88,94.81,24560000,94.81 1975-06-25,94.19,95.29,93.53,94.62,21610000,94.62 1975-06-24,93.62,95.23,93.31,94.19,26620000,94.19 1975-06-23,92.61,93.98,91.81,93.62,20720000,93.62 1975-06-20,92.02,93.75,91.83,92.61,26260000,92.61 1975-06-19,90.39,92.37,90.12,92.02,21450000,92.02 1975-06-18,90.58,91.07,89.60,90.39,15590000,90.39 1975-06-17,91.46,92.22,90.17,90.58,19440000,90.58 1975-06-16,90.52,91.85,90.12,91.46,16660000,91.46 1975-06-13,90.08,91.06,89.30,90.52,16300000,90.52 1975-06-12,90.55,91.36,89.64,90.08,15970000,90.08 1975-06-11,90.44,91.67,90.00,90.55,18230000,90.55 1975-06-10,91.21,91.21,89.46,90.44,21130000,90.44 1975-06-09,92.48,92.87,90.91,91.21,20670000,91.21 1975-06-06,92.69,93.60,91.75,92.48,22230000,92.48 1975-06-05,92.60,93.16,91.41,92.69,21610000,92.69 1975-06-04,92.89,93.61,91.82,92.60,24900000,92.60 1975-06-03,92.58,93.76,91.88,92.89,26560000,92.89 1975-06-02,91.32,93.41,91.32,92.58,28240000,92.58 1975-05-30,89.87,91.62,89.87,91.15,22670000,91.15 1975-05-29,89.71,90.59,88.83,89.68,18570000,89.68 1975-05-28,90.34,91.14,89.07,89.71,21850000,89.71 1975-05-27,90.58,91.29,89.60,90.34,17050000,90.34 1975-05-23,89.39,91.02,89.30,90.58,17870000,90.58 1975-05-22,89.06,90.30,88.35,89.39,17610000,89.39 1975-05-21,90.07,90.25,88.47,89.06,17640000,89.06 1975-05-20,90.53,91.45,89.58,90.07,18310000,90.07 1975-05-19,90.43,91.07,88.98,90.53,17870000,90.53 1975-05-16,91.41,91.59,89.74,90.43,16630000,90.43 1975-05-15,92.27,93.51,90.94,91.41,27690000,91.41 1975-05-14,91.58,93.23,91.17,92.27,29050000,92.27 1975-05-13,90.61,92.26,89.99,91.58,24950000,91.58 1975-05-12,90.53,91.67,89.91,90.61,22410000,90.61 1975-05-09,89.56,91.24,89.33,90.53,28440000,90.53 1975-05-08,89.08,90.13,88.23,89.56,22980000,89.56 1975-05-07,88.64,89.75,87.60,89.08,22250000,89.08 1975-05-06,90.08,90.86,88.15,88.64,25410000,88.64 1975-05-05,89.22,90.82,88.26,90.08,22370000,90.08 1975-05-02,88.10,89.98,87.91,89.22,25210000,89.22 1975-05-01,87.30,89.10,86.94,88.10,20660000,88.10 1975-04-30,85.64,87.61,85.00,87.30,18060000,87.30 1975-04-29,86.23,86.79,85.04,85.64,17740000,85.64 1975-04-28,86.62,87.33,85.54,86.23,17850000,86.23 1975-04-25,86.04,87.50,85.62,86.62,20260000,86.62 1975-04-24,86.12,86.92,85.00,86.04,19050000,86.04 1975-04-23,87.09,87.42,85.65,86.12,20040000,86.12 1975-04-22,87.23,88.64,86.58,87.09,26120000,87.09 1975-04-21,86.30,87.99,85.92,87.23,23960000,87.23 1975-04-18,87.25,87.59,85.53,86.30,26610000,86.30 1975-04-17,86.60,88.79,86.43,87.25,32650000,87.25 1975-04-16,86.30,87.10,84.93,86.60,22970000,86.60 1975-04-15,85.60,87.24,85.03,86.30,29620000,86.30 1975-04-14,84.18,86.12,83.98,85.60,26800000,85.60 1975-04-11,83.77,84.68,82.93,84.18,20160000,84.18 1975-04-10,82.84,84.70,82.68,83.77,24990000,83.77 1975-04-09,80.99,83.22,80.91,82.84,18120000,82.84 1975-04-08,80.35,81.65,80.13,80.99,14320000,80.99 1975-04-07,80.88,81.11,79.66,80.35,13860000,80.35 1975-04-04,81.51,81.90,80.29,80.88,14170000,80.88 1975-04-03,82.43,82.84,80.88,81.51,13920000,81.51 1975-04-02,82.64,83.57,81.80,82.43,15600000,82.43 1975-04-01,83.36,83.59,81.98,82.64,14480000,82.64 1975-03-31,83.85,84.62,82.84,83.36,16270000,83.36 1975-03-27,83.59,84.88,83.04,83.85,18300000,83.85 1975-03-26,82.16,84.24,82.16,83.59,18580000,83.59 1975-03-25,81.42,82.67,80.08,82.06,18500000,82.06 1975-03-24,82.39,82.39,80.60,81.42,17810000,81.42 1975-03-21,83.61,84.11,82.52,83.39,15940000,83.39 1975-03-20,84.34,85.30,83.02,83.61,20960000,83.61 1975-03-19,85.13,85.17,83.43,84.34,19030000,84.34 1975-03-18,86.01,87.08,84.75,85.13,29180000,85.13 1975-03-17,84.76,86.52,84.39,86.01,26780000,86.01 1975-03-14,83.74,85.43,83.50,84.76,24840000,84.76 1975-03-13,83.59,84.26,82.52,83.74,18620000,83.74 1975-03-12,84.36,84.73,82.87,83.59,21560000,83.59 1975-03-11,84.95,85.89,83.80,84.36,31280000,84.36 1975-03-10,84.30,85.47,83.43,84.95,25890000,84.95 1975-03-07,83.69,85.14,83.25,84.30,25930000,84.30 1975-03-06,83.90,84.17,81.94,83.69,21780000,83.69 1975-03-05,83.56,84.71,82.16,83.90,24120000,83.90 1975-03-04,83.03,85.43,82.85,83.56,34140000,83.56 1975-03-03,81.59,83.46,81.32,83.03,24100000,83.03 1975-02-28,80.77,82.02,80.07,81.59,17560000,81.59 1975-02-27,80.37,81.64,80.06,80.77,16430000,80.77 1975-02-26,79.53,80.89,78.91,80.37,18790000,80.37 1975-02-25,81.09,81.09,79.05,79.53,20910000,79.53 1975-02-24,82.62,82.71,80.87,81.44,19150000,81.44 1975-02-21,82.21,83.56,81.72,82.62,24440000,82.62 1975-02-20,81.44,82.78,80.82,82.21,22260000,82.21 1975-02-19,80.93,81.94,79.83,81.44,21930000,81.44 1975-02-18,81.50,82.45,80.16,80.93,23990000,80.93 1975-02-14,81.01,82.33,80.13,81.50,23290000,81.50 1975-02-13,79.98,82.53,79.98,81.01,35160000,81.01 1975-02-12,78.58,80.21,77.94,79.92,19790000,79.92 1975-02-11,78.36,79.07,77.38,78.58,16470000,78.58 1975-02-10,78.63,79.40,77.77,78.36,16120000,78.36 1975-02-07,78.56,79.12,77.00,78.63,19060000,78.63 1975-02-06,78.95,80.72,78.09,78.56,32020000,78.56 1975-02-05,77.61,79.40,76.81,78.95,25830000,78.95 1975-02-04,77.82,78.37,76.00,77.61,25040000,77.61 1975-02-03,76.98,78.55,76.36,77.82,25400000,77.82 1975-01-31,76.21,77.72,75.41,76.98,24640000,76.98 1975-01-30,77.26,78.69,75.82,76.21,29740000,76.21 1975-01-29,76.03,78.03,75.23,77.26,27410000,77.26 1975-01-28,75.37,77.59,75.36,76.03,31760000,76.03 1975-01-27,73.76,76.03,73.76,75.37,32130000,75.37 1975-01-24,72.07,73.57,71.55,72.98,20670000,72.98 1975-01-23,71.74,73.11,71.09,72.07,17960000,72.07 1975-01-22,70.70,71.97,69.86,71.74,15330000,71.74 1975-01-21,71.08,72.04,70.25,70.70,14780000,70.70 1975-01-20,70.96,71.46,69.80,71.08,13450000,71.08 1975-01-17,72.05,72.36,70.56,70.96,14260000,70.96 1975-01-16,72.14,72.93,71.26,72.05,17110000,72.05 1975-01-15,71.68,72.77,70.45,72.14,16580000,72.14 1975-01-14,72.31,72.70,71.02,71.68,16610000,71.68 1975-01-13,72.61,73.81,71.83,72.31,19780000,72.31 1975-01-10,71.60,73.75,71.60,72.61,25890000,72.61 1975-01-09,70.04,71.42,69.04,71.17,16340000,71.17 1975-01-08,71.02,71.53,69.65,70.04,15600000,70.04 1975-01-07,71.07,71.75,69.92,71.02,14890000,71.02 1975-01-06,70.71,72.24,70.33,71.07,17550000,71.07 1975-01-03,70.23,71.64,69.29,70.71,15270000,70.71 1975-01-02,68.65,70.92,68.65,70.23,14800000,70.23 1974-12-31,67.16,69.04,67.15,68.56,20970000,68.56 1974-12-30,67.14,67.65,66.23,67.16,18520000,67.16 1974-12-27,67.44,67.99,66.49,67.14,13060000,67.14 1974-12-26,66.88,68.19,66.62,67.44,11810000,67.44 1974-12-24,65.96,67.25,65.86,66.88,9540000,66.88 1974-12-23,66.91,67.18,65.34,65.96,18040000,65.96 1974-12-20,67.65,67.93,66.36,66.91,15840000,66.91 1974-12-19,67.90,68.62,66.93,67.65,15900000,67.65 1974-12-18,67.58,69.01,67.30,67.90,18050000,67.90 1974-12-17,66.46,67.92,65.86,67.58,16880000,67.58 1974-12-16,67.07,67.74,66.02,66.46,15370000,66.46 1974-12-13,67.45,68.15,66.32,67.07,14000000,67.07 1974-12-12,67.67,68.61,66.56,67.45,15390000,67.45 1974-12-11,67.28,69.03,66.83,67.67,15700000,67.67 1974-12-10,65.88,68.17,65.88,67.28,15690000,67.28 1974-12-09,65.01,66.29,64.13,65.60,14660000,65.60 1974-12-06,66.13,66.20,64.40,65.01,15500000,65.01 1974-12-05,67.41,68.00,65.90,66.13,12890000,66.13 1974-12-04,67.17,68.32,66.61,67.41,12580000,67.41 1974-12-03,68.11,68.13,66.62,67.17,13620000,67.17 1974-12-02,69.80,69.80,67.81,68.11,11140000,68.11 1974-11-29,69.94,70.49,69.18,69.97,7400000,69.97 1974-11-27,69.47,71.31,69.17,69.94,14810000,69.94 1974-11-26,68.83,70.36,68.19,69.47,13600000,69.47 1974-11-25,68.90,69.68,67.79,68.83,11300000,68.83 1974-11-22,68.24,70.00,68.24,68.90,13020000,68.90 1974-11-21,67.90,68.94,66.85,68.18,13820000,68.18 1974-11-20,68.20,69.25,67.36,67.90,12430000,67.90 1974-11-19,69.27,69.71,67.66,68.20,15720000,68.20 1974-11-18,71.10,71.10,68.95,69.27,15230000,69.27 1974-11-15,73.06,73.27,71.41,71.91,12480000,71.91 1974-11-14,73.35,74.54,72.53,73.06,13540000,73.06 1974-11-13,73.67,74.25,72.32,73.35,16040000,73.35 1974-11-12,75.15,75.59,73.34,73.67,15040000,73.67 1974-11-11,74.91,75.70,74.04,75.15,13220000,75.15 1974-11-08,75.21,76.00,74.01,74.91,15890000,74.91 1974-11-07,74.75,76.30,73.85,75.21,17150000,75.21 1974-11-06,75.11,77.41,74.23,74.75,23930000,74.75 1974-11-05,73.08,75.36,72.49,75.11,15960000,75.11 1974-11-04,73.80,73.80,71.93,73.08,12740000,73.08 1974-11-01,73.90,74.85,72.68,73.88,13470000,73.88 1974-10-31,74.31,75.90,73.15,73.90,18840000,73.90 1974-10-30,72.83,75.45,72.40,74.31,20130000,74.31 1974-10-29,70.49,73.19,70.49,72.83,15610000,72.83 1974-10-28,70.12,70.67,68.89,70.09,10540000,70.09 1974-10-25,70.22,71.59,69.46,70.12,12650000,70.12 1974-10-24,70.98,70.98,68.80,70.22,14910000,70.22 1974-10-23,72.81,72.81,70.40,71.03,14200000,71.03 1974-10-22,73.50,75.09,72.55,73.13,18930000,73.13 1974-10-21,72.28,73.92,71.24,73.50,14500000,73.50 1974-10-18,71.20,73.34,71.20,72.28,16460000,72.28 1974-10-17,70.33,72.00,69.41,71.17,14470000,71.17 1974-10-16,71.44,71.98,69.54,70.33,14790000,70.33 1974-10-15,72.74,73.35,70.61,71.44,17390000,71.44 1974-10-14,71.17,74.43,71.17,72.74,19770000,72.74 1974-10-11,69.79,71.99,68.80,71.14,20090000,71.14 1974-10-10,68.30,71.48,68.30,69.79,26360000,69.79 1974-10-09,64.84,68.15,63.74,67.82,18820000,67.82 1974-10-08,64.95,66.07,63.95,64.84,15460000,64.84 1974-10-07,62.78,65.40,62.78,64.95,15000000,64.95 1974-10-04,62.28,63.23,60.96,62.34,15910000,62.34 1974-10-03,63.38,63.48,61.66,62.28,13150000,62.28 1974-10-02,63.39,64.62,62.74,63.38,12230000,63.38 1974-10-01,63.54,64.37,61.75,63.39,16890000,63.39 1974-09-30,64.85,64.85,62.52,63.54,15000000,63.54 1974-09-27,66.46,67.09,64.58,64.94,12320000,64.94 1974-09-26,67.40,67.40,65.79,66.46,9060000,66.46 1974-09-25,68.02,69.77,66.86,67.57,17620000,67.57 1974-09-24,69.03,69.03,67.42,68.02,9840000,68.02 1974-09-23,70.14,71.02,68.79,69.42,12130000,69.42 1974-09-20,70.09,71.12,68.62,70.14,16250000,70.14 1974-09-19,68.36,70.76,68.36,70.09,17000000,70.09 1974-09-18,67.38,68.14,65.92,67.72,11760000,67.72 1974-09-17,66.45,68.84,66.45,67.38,13730000,67.38 1974-09-16,65.20,66.92,64.15,66.26,18370000,66.26 1974-09-13,66.71,66.91,64.74,65.20,16070000,65.20 1974-09-12,68.54,68.54,66.22,66.71,16920000,66.71 1974-09-11,69.24,70.00,68.22,68.55,11820000,68.55 1974-09-10,69.72,70.47,68.55,69.24,11980000,69.24 1974-09-09,71.35,71.35,69.38,69.72,11160000,69.72 1974-09-06,70.87,72.42,70.08,71.42,15130000,71.42 1974-09-05,68.69,71.30,68.65,70.87,14210000,70.87 1974-09-04,69.85,69.85,67.64,68.69,16930000,68.69 1974-09-03,72.15,73.01,70.28,70.52,12750000,70.52 1974-08-30,70.22,72.68,70.22,72.15,16230000,72.15 1974-08-29,70.76,71.22,69.37,69.99,13690000,69.99 1974-08-28,70.94,72.17,70.13,70.76,16670000,70.76 1974-08-27,72.16,72.50,70.50,70.94,12970000,70.94 1974-08-26,71.55,73.17,70.42,72.16,14630000,72.16 1974-08-23,72.80,73.71,70.75,71.55,13590000,71.55 1974-08-22,73.51,74.05,71.61,72.80,15690000,72.80 1974-08-21,74.95,75.50,73.16,73.51,11650000,73.51 1974-08-20,74.57,76.11,73.82,74.95,13820000,74.95 1974-08-19,75.65,75.65,73.78,74.57,11670000,74.57 1974-08-16,76.30,77.02,75.29,75.67,10510000,75.67 1974-08-15,76.73,77.52,75.19,76.30,11130000,76.30 1974-08-14,76.73,76.73,76.73,76.73,11750000,76.73 1974-08-13,79.75,79.95,77.83,78.49,10140000,78.49 1974-08-12,80.86,81.26,79.30,79.75,7780000,79.75 1974-08-09,81.57,81.88,80.11,80.86,10160000,80.86 1974-08-08,82.65,83.53,80.86,81.57,16060000,81.57 1974-08-07,80.52,82.93,80.13,82.65,13380000,82.65 1974-08-06,79.78,82.65,79.78,80.52,15770000,80.52 1974-08-05,78.59,80.31,78.03,79.29,11230000,79.29 1974-08-02,78.75,79.39,77.84,78.59,10110000,78.59 1974-08-01,79.31,80.02,77.97,78.75,11470000,78.75 1974-07-31,80.50,80.82,78.96,79.31,10960000,79.31 1974-07-30,80.94,81.52,79.58,80.50,11360000,80.50 1974-07-29,82.02,82.02,80.22,80.94,11560000,80.94 1974-07-26,83.98,84.17,82.00,82.40,10420000,82.40 1974-07-25,84.99,85.67,83.13,83.98,13310000,83.98 1974-07-24,84.65,85.64,83.61,84.99,12870000,84.99 1974-07-23,83.81,85.63,83.67,84.65,12910000,84.65 1974-07-22,83.54,84.44,82.59,83.81,9290000,83.81 1974-07-19,83.78,84.67,82.87,83.54,11080000,83.54 1974-07-18,83.70,85.39,83.13,83.78,13980000,83.78 1974-07-17,82.81,84.13,81.70,83.70,11320000,83.70 1974-07-16,83.78,83.85,82.14,82.81,9920000,82.81 1974-07-15,83.15,84.89,82.65,83.78,13560000,83.78 1974-07-12,80.97,83.65,80.97,83.15,17770000,83.15 1974-07-11,79.99,81.08,79.08,79.89,14640000,79.89 1974-07-10,81.48,82.22,79.74,79.99,13490000,79.99 1974-07-09,81.09,82.50,80.35,81.48,15580000,81.48 1974-07-08,83.13,83.13,80.48,81.09,15510000,81.09 1974-07-05,84.25,84.45,83.17,83.66,7400000,83.66 1974-07-03,84.30,85.15,83.46,84.25,13430000,84.25 1974-07-02,86.02,86.26,83.98,84.30,13460000,84.30 1974-07-01,86.00,86.89,85.32,86.02,10270000,86.02 1974-06-28,86.31,86.78,85.13,86.00,12010000,86.00 1974-06-27,87.61,87.61,85.88,86.31,12650000,86.31 1974-06-26,88.98,89.12,87.30,87.61,11410000,87.61 1974-06-25,87.69,89.48,87.67,88.98,11920000,88.98 1974-06-24,87.46,88.38,86.70,87.69,9960000,87.69 1974-06-21,88.21,88.31,86.77,87.46,11830000,87.46 1974-06-20,88.84,89.35,87.80,88.21,11990000,88.21 1974-06-19,89.45,89.80,88.39,88.84,10550000,88.84 1974-06-18,90.04,90.53,88.92,89.45,10110000,89.45 1974-06-17,91.30,91.34,89.63,90.04,9680000,90.04 1974-06-14,92.23,92.23,90.73,91.30,10030000,91.30 1974-06-13,92.06,93.33,91.48,92.34,11540000,92.34 1974-06-12,92.28,92.61,90.89,92.06,11150000,92.06 1974-06-11,93.10,93.57,91.76,92.28,12380000,92.28 1974-06-10,92.55,93.64,91.53,93.10,13540000,93.10 1974-06-07,91.96,93.76,91.74,92.55,19020000,92.55 1974-06-06,90.31,92.31,89.71,91.96,13360000,91.96 1974-06-05,90.14,91.42,89.04,90.31,13680000,90.31 1974-06-04,89.10,91.13,89.09,90.14,16040000,90.14 1974-06-03,87.28,89.40,86.78,89.10,12490000,89.10 1974-05-31,87.43,88.02,86.19,87.28,10810000,87.28 1974-05-30,86.89,88.09,85.87,87.43,13580000,87.43 1974-05-29,88.37,88.84,86.52,86.89,12300000,86.89 1974-05-28,88.58,89.37,87.69,88.37,10580000,88.37 1974-05-24,87.29,89.27,87.20,88.58,13740000,88.58 1974-05-23,87.09,87.98,86.12,87.29,14770000,87.29 1974-05-22,87.91,88.79,86.72,87.09,15450000,87.09 1974-05-21,87.86,88.98,87.19,87.91,12190000,87.91 1974-05-20,88.21,89.09,87.19,87.86,10550000,87.86 1974-05-17,89.53,89.53,87.67,88.21,13870000,88.21 1974-05-16,90.45,91.31,89.36,89.72,12090000,89.72 1974-05-15,90.69,91.22,89.65,90.45,11240000,90.45 1974-05-14,90.66,91.68,90.05,90.69,10880000,90.69 1974-05-13,91.47,91.72,89.91,90.66,11290000,90.66 1974-05-10,92.96,93.57,91.03,91.47,15270000,91.47 1974-05-09,91.64,93.49,91.27,92.96,14710000,92.96 1974-05-08,91.46,92.34,90.71,91.64,11850000,91.64 1974-05-07,91.12,92.36,90.69,91.46,10710000,91.46 1974-05-06,91.29,91.60,90.13,91.12,9450000,91.12 1974-05-03,92.09,92.27,90.59,91.29,11080000,91.29 1974-05-02,92.22,93.59,91.46,92.09,13620000,92.09 1974-05-01,90.31,93.03,89.82,92.22,15120000,92.22 1974-04-30,90.00,91.09,89.38,90.31,10980000,90.31 1974-04-29,90.18,90.78,89.02,90.00,10170000,90.00 1974-04-26,89.57,91.10,89.06,90.18,13250000,90.18 1974-04-25,90.30,90.53,88.62,89.57,15870000,89.57 1974-04-24,91.81,91.82,89.91,90.30,16010000,90.30 1974-04-23,93.38,93.51,91.53,91.81,14110000,91.81 1974-04-22,93.75,94.12,92.71,93.38,10520000,93.38 1974-04-19,94.77,94.77,93.20,93.75,10710000,93.75 1974-04-18,94.36,95.42,93.75,94.78,12470000,94.78 1974-04-17,93.66,95.04,93.12,94.36,14020000,94.36 1974-04-16,92.05,94.06,92.05,93.66,14530000,93.66 1974-04-15,92.12,92.94,91.49,92.05,10130000,92.05 1974-04-11,92.40,92.92,91.55,92.12,9970000,92.12 1974-04-10,92.61,93.52,91.89,92.40,11160000,92.40 1974-04-09,92.03,93.28,91.61,92.61,11330000,92.61 1974-04-08,93.00,93.00,91.50,92.03,10740000,92.03 1974-04-05,94.24,94.24,92.55,93.01,11670000,93.01 1974-04-04,94.33,95.14,93.55,94.33,11650000,94.33 1974-04-03,93.35,94.70,92.94,94.33,11500000,94.33 1974-04-02,93.25,94.15,92.59,93.35,12010000,93.35 1974-04-01,93.98,94.68,92.82,93.25,11470000,93.25 1974-03-29,94.82,95.12,93.44,93.98,12150000,93.98 1974-03-28,96.20,96.20,94.36,94.82,14940000,94.82 1974-03-27,97.95,98.26,96.32,96.59,11690000,96.59 1974-03-26,97.64,98.66,97.11,97.95,11840000,97.95 1974-03-25,97.27,98.02,95.69,97.64,10540000,97.64 1974-03-22,97.34,98.04,96.35,97.27,11930000,97.27 1974-03-21,97.57,98.59,96.82,97.34,12950000,97.34 1974-03-20,97.23,98.22,96.67,97.57,12960000,97.57 1974-03-19,98.05,98.20,96.63,97.23,12800000,97.23 1974-03-18,99.28,99.71,97.62,98.05,14010000,98.05 1974-03-15,99.65,99.99,98.22,99.28,14500000,99.28 1974-03-14,99.74,101.05,98.80,99.65,19770000,99.65 1974-03-13,99.15,100.73,98.72,99.74,16820000,99.74 1974-03-12,98.88,100.02,97.97,99.15,17250000,99.15 1974-03-11,97.78,99.40,96.38,98.88,18470000,98.88 1974-03-08,96.94,98.28,95.77,97.78,16210000,97.78 1974-03-07,97.98,98.20,96.37,96.94,14500000,96.94 1974-03-06,97.32,98.57,96.54,97.98,19140000,97.98 1974-03-05,95.98,98.17,95.98,97.32,21980000,97.32 1974-03-04,95.53,95.95,94.19,95.53,12270000,95.53 1974-03-01,96.22,96.40,94.81,95.53,12880000,95.53 1974-02-28,96.40,96.98,95.20,96.22,13680000,96.22 1974-02-27,96.00,97.43,95.49,96.40,18730000,96.40 1974-02-26,95.03,96.38,94.20,96.00,15860000,96.00 1974-02-25,95.39,95.96,94.24,95.03,12900000,95.03 1974-02-22,94.71,96.19,94.08,95.39,16360000,95.39 1974-02-21,93.44,95.19,93.20,94.71,13930000,94.71 1974-02-20,92.12,93.92,91.34,93.44,11670000,93.44 1974-02-19,92.27,94.44,91.68,92.12,15940000,92.12 1974-02-15,90.95,92.98,90.62,92.27,12640000,92.27 1974-02-14,90.98,91.89,90.17,90.95,12230000,90.95 1974-02-13,90.94,92.13,90.37,90.98,10990000,90.98 1974-02-12,90.66,91.60,89.53,90.94,12920000,90.94 1974-02-11,92.33,92.54,90.26,90.66,12930000,90.66 1974-02-08,93.30,93.79,91.87,92.33,12990000,92.33 1974-02-07,93.26,94.09,92.43,93.30,11750000,93.30 1974-02-06,93.00,94.09,92.37,93.26,11610000,93.26 1974-02-05,93.29,94.17,92.26,93.00,12820000,93.00 1974-02-04,94.89,94.89,92.74,93.29,14380000,93.29 1974-02-01,96.57,96.63,94.66,95.32,12480000,95.32 1974-01-31,97.06,98.06,96.11,96.57,14020000,96.57 1974-01-30,96.02,97.90,96.02,97.06,16790000,97.06 1974-01-29,96.09,96.81,94.97,96.01,12850000,96.01 1974-01-28,96.63,97.32,95.37,96.09,13410000,96.09 1974-01-25,96.82,97.64,95.68,96.63,14860000,96.63 1974-01-24,97.07,97.75,95.49,96.82,15980000,96.82 1974-01-23,96.55,98.11,95.88,97.07,16890000,97.07 1974-01-22,95.40,97.41,94.92,96.55,17330000,96.55 1974-01-21,95.56,95.96,93.23,95.40,15630000,95.40 1974-01-18,97.30,97.63,95.00,95.56,16470000,95.56 1974-01-17,95.67,98.35,95.67,97.30,21040000,97.30 1974-01-16,94.23,96.20,93.78,95.67,14930000,95.67 1974-01-15,93.42,95.26,92.84,94.23,13250000,94.23 1974-01-14,93.66,95.24,92.35,93.42,14610000,93.42 1974-01-11,92.39,94.57,91.75,93.66,15140000,93.66 1974-01-10,93.42,94.63,91.62,92.39,16120000,92.39 1974-01-09,95.40,95.40,92.63,93.42,18070000,93.42 1974-01-08,98.07,98.26,95.58,96.12,18080000,96.12 1974-01-07,98.90,99.31,96.86,98.07,19070000,98.07 1974-01-04,99.80,100.70,97.70,98.90,21700000,98.90 1974-01-03,98.02,100.94,98.02,99.80,24850000,99.80 1974-01-02,97.55,98.38,96.25,97.68,12060000,97.68 1973-12-31,97.54,98.30,95.95,97.55,23470000,97.55 1973-12-28,97.74,98.76,96.41,97.54,21310000,97.54 1973-12-27,96.00,98.53,96.00,97.74,22720000,97.74 1973-12-26,93.87,96.52,93.87,95.74,18620000,95.74 1973-12-24,93.54,93.77,91.68,92.90,11540000,92.90 1973-12-21,94.55,95.11,92.70,93.54,18680000,93.54 1973-12-20,94.82,96.26,93.51,94.55,17340000,94.55 1973-12-19,94.74,96.83,93.81,94.82,20670000,94.82 1973-12-18,92.75,95.41,92.18,94.74,19490000,94.74 1973-12-17,93.29,94.00,91.87,92.75,12930000,92.75 1973-12-14,92.38,94.53,91.05,93.29,20000000,93.29 1973-12-13,93.57,94.68,91.64,92.38,18130000,92.38 1973-12-12,95.52,95.52,92.90,93.57,18190000,93.57 1973-12-11,97.95,99.09,95.62,96.04,20100000,96.04 1973-12-10,96.51,98.58,95.44,97.95,18590000,97.95 1973-12-07,94.49,97.58,94.49,96.51,23230000,96.51 1973-12-06,92.16,94.89,91.68,94.42,23260000,94.42 1973-12-05,93.59,93.93,91.55,92.16,19180000,92.16 1973-12-04,93.90,95.23,92.60,93.59,19030000,93.59 1973-12-03,95.83,95.83,92.92,93.90,17900000,93.90 1973-11-30,97.31,97.55,95.40,95.96,15380000,95.96 1973-11-29,97.65,98.72,96.01,97.31,18870000,97.31 1973-11-28,95.70,98.40,95.22,97.65,19990000,97.65 1973-11-27,96.58,97.70,94.88,95.70,19750000,95.70 1973-11-26,98.64,98.64,95.79,96.58,19830000,96.58 1973-11-23,99.76,100.49,98.59,99.44,11470000,99.44 1973-11-21,98.66,101.33,97.87,99.76,24260000,99.76 1973-11-20,100.65,100.65,97.64,98.66,23960000,98.66 1973-11-19,103.65,103.65,100.37,100.71,16700000,100.71 1973-11-16,102.43,105.41,101.77,103.88,22510000,103.88 1973-11-15,102.45,103.85,100.69,102.43,24530000,102.43 1973-11-14,104.36,105.25,101.87,102.45,22710000,102.45 1973-11-13,104.44,105.42,102.91,104.36,20310000,104.36 1973-11-12,105.30,105.75,103.12,104.44,19250000,104.44 1973-11-09,107.02,107.27,104.77,105.30,17320000,105.30 1973-11-08,106.10,108.45,106.10,107.02,19650000,107.02 1973-11-07,104.96,106.72,104.53,105.80,16570000,105.80 1973-11-06,105.52,107.00,104.52,104.96,16430000,104.96 1973-11-05,106.97,106.97,104.87,105.52,17150000,105.52 1973-11-02,107.69,108.35,106.33,107.07,16340000,107.07 1973-11-01,108.29,109.20,106.88,107.69,16920000,107.69 1973-10-31,109.33,109.82,107.64,108.29,17890000,108.29 1973-10-30,111.15,111.30,108.95,109.33,17580000,109.33 1973-10-29,111.38,112.56,110.52,111.15,17960000,111.15 1973-10-26,110.50,112.31,110.08,111.38,17800000,111.38 1973-10-25,110.27,111.33,108.85,110.50,15580000,110.50 1973-10-24,109.75,110.98,109.03,110.27,15840000,110.27 1973-10-23,109.16,110.91,107.40,109.75,17230000,109.75 1973-10-22,110.22,110.56,108.18,109.16,14290000,109.16 1973-10-19,110.01,111.56,109.30,110.22,17880000,110.22 1973-10-18,109.97,111.43,108.97,110.01,19210000,110.01 1973-10-17,110.19,111.41,109.19,109.97,18600000,109.97 1973-10-16,110.05,110.80,108.50,110.19,18780000,110.19 1973-10-15,111.32,111.32,109.29,110.05,16160000,110.05 1973-10-12,111.09,112.82,110.52,111.44,22730000,111.44 1973-10-11,109.22,111.77,108.96,111.09,20740000,111.09 1973-10-10,110.13,111.31,108.51,109.22,19010000,109.22 1973-10-09,110.23,111.19,109.05,110.13,19440000,110.13 1973-10-08,109.85,110.93,108.02,110.23,18990000,110.23 1973-10-05,108.41,110.46,107.76,109.85,18820000,109.85 1973-10-04,108.78,109.53,107.30,108.41,19730000,108.41 1973-10-03,108.79,109.95,107.74,108.78,22040000,108.78 1973-10-02,108.21,109.46,107.48,108.79,20770000,108.79 1973-10-01,108.43,108.98,107.08,108.21,15830000,108.21 1973-09-28,109.08,109.42,107.48,108.43,16300000,108.43 1973-09-27,108.83,110.45,108.02,109.08,23660000,109.08 1973-09-26,108.05,109.61,107.43,108.83,21130000,108.83 1973-09-25,107.36,108.79,106.50,108.05,21530000,108.05 1973-09-24,107.20,108.36,106.21,107.36,19490000,107.36 1973-09-21,106.76,108.02,105.43,107.20,23760000,107.20 1973-09-20,105.88,107.55,105.32,106.76,25960000,106.76 1973-09-19,103.80,106.43,103.80,105.88,24570000,105.88 1973-09-18,104.15,104.62,102.41,103.77,16400000,103.77 1973-09-17,104.44,105.41,103.21,104.15,15100000,104.15 1973-09-14,103.36,104.75,102.66,104.44,13760000,104.44 1973-09-13,103.06,104.09,102.37,103.36,11670000,103.36 1973-09-12,103.22,103.98,102.15,103.06,12040000,103.06 1973-09-11,103.85,104.09,102.13,103.22,12690000,103.22 1973-09-10,104.76,105.12,103.33,103.85,11620000,103.85 1973-09-07,105.15,105.87,104.04,104.76,14930000,104.76 1973-09-06,104.64,105.95,104.05,105.15,15670000,105.15 1973-09-05,104.51,105.33,103.60,104.64,14580000,104.64 1973-09-04,104.25,105.35,103.60,104.51,14210000,104.51 1973-08-31,103.88,104.72,103.15,104.25,10530000,104.25 1973-08-30,104.03,104.84,103.29,103.88,12100000,103.88 1973-08-29,103.02,104.92,102.69,104.03,15690000,104.03 1973-08-28,102.42,103.66,102.06,103.02,11810000,103.02 1973-08-27,101.62,102.82,101.09,102.42,9740000,102.42 1973-08-24,101.91,102.65,100.88,101.62,11200000,101.62 1973-08-23,100.62,102.50,100.62,101.91,11390000,101.91 1973-08-22,100.89,101.39,99.74,100.53,10770000,100.53 1973-08-21,101.61,102.10,100.51,100.89,11480000,100.89 1973-08-20,102.31,102.54,101.11,101.61,8970000,101.61 1973-08-17,102.29,102.98,101.38,102.31,11110000,102.31 1973-08-16,103.01,103.97,101.85,102.29,12990000,102.29 1973-08-15,102.71,103.79,101.92,103.01,12040000,103.01 1973-08-14,103.71,104.29,102.34,102.71,11740000,102.71 1973-08-13,104.77,104.83,103.13,103.71,11330000,103.71 1973-08-10,105.61,106.03,104.21,104.77,10870000,104.77 1973-08-09,105.55,106.65,104.89,105.61,12880000,105.61 1973-08-08,106.55,106.73,105.04,105.55,12440000,105.55 1973-08-07,106.73,107.57,105.87,106.55,13510000,106.55 1973-08-06,106.49,107.54,105.45,106.73,12320000,106.73 1973-08-03,106.67,107.17,105.68,106.49,9940000,106.49 1973-08-02,106.83,107.38,105.51,106.67,16080000,106.67 1973-08-01,108.17,108.17,106.29,106.83,13530000,106.83 1973-07-31,109.25,110.09,107.89,108.22,13530000,108.22 1973-07-30,109.59,110.12,108.24,109.25,11170000,109.25 1973-07-27,109.85,110.49,108.70,109.59,12910000,109.59 1973-07-26,109.64,111.04,108.51,109.85,18410000,109.85 1973-07-25,108.14,110.76,107.92,109.64,22220000,109.64 1973-07-24,107.52,108.63,106.31,108.14,16280000,108.14 1973-07-23,107.14,108.42,106.54,107.52,15580000,107.52 1973-07-20,106.55,108.02,105.95,107.14,16300000,107.14 1973-07-19,106.35,107.58,105.06,106.55,18650000,106.55 1973-07-18,105.72,107.05,104.73,106.35,17020000,106.35 1973-07-17,105.67,107.28,104.99,105.72,18750000,105.72 1973-07-16,104.09,106.01,103.42,105.67,12920000,105.67 1973-07-13,105.50,105.80,103.66,104.09,11390000,104.09 1973-07-12,105.80,106.62,104.38,105.50,16400000,105.50 1973-07-11,103.64,106.21,103.64,105.80,18730000,105.80 1973-07-10,102.26,104.20,102.26,103.52,15090000,103.52 1973-07-09,101.28,102.45,100.44,102.14,11560000,102.14 1973-07-06,101.78,102.22,100.67,101.28,9980000,101.28 1973-07-05,101.87,102.48,100.80,101.78,10500000,101.78 1973-07-03,102.90,103.02,101.14,101.87,10560000,101.87 1973-07-02,104.10,104.10,102.44,102.90,9830000,102.90 1973-06-29,104.69,105.30,103.68,104.26,10770000,104.26 1973-06-28,103.62,105.17,103.18,104.69,12760000,104.69 1973-06-27,103.30,104.23,102.29,103.62,12660000,103.62 1973-06-26,102.25,103.78,101.45,103.30,14040000,103.30 1973-06-25,103.64,103.64,101.71,102.25,11670000,102.25 1973-06-22,103.21,105.66,103.07,103.70,18470000,103.70 1973-06-21,104.44,104.77,102.84,103.21,11630000,103.21 1973-06-20,103.99,105.13,103.51,104.44,10600000,104.44 1973-06-19,103.60,104.96,102.46,103.99,12970000,103.99 1973-06-18,104.96,104.96,103.08,103.60,11460000,103.60 1973-06-15,106.21,106.21,104.37,105.10,11970000,105.10 1973-06-14,107.60,108.27,105.83,106.40,13210000,106.40 1973-06-13,108.29,109.52,107.08,107.60,15700000,107.60 1973-06-12,106.70,108.78,106.40,108.29,13840000,108.29 1973-06-11,107.03,107.79,106.11,106.70,9940000,106.70 1973-06-08,105.84,107.75,105.60,107.03,14050000,107.03 1973-06-07,104.31,106.39,104.19,105.84,14160000,105.84 1973-06-06,104.62,105.78,103.60,104.31,13080000,104.31 1973-06-05,102.97,105.27,102.61,104.62,14080000,104.62 1973-06-04,103.93,103.98,102.33,102.97,11230000,102.97 1973-06-01,104.95,105.04,103.31,103.93,10410000,103.93 1973-05-31,105.91,106.30,104.35,104.95,12190000,104.95 1973-05-30,107.51,107.64,105.48,105.91,11730000,105.91 1973-05-29,107.94,108.58,106.77,107.51,11300000,107.51 1973-05-25,107.14,108.86,106.08,107.94,19270000,107.94 1973-05-24,104.07,107.44,103.59,107.14,17310000,107.14 1973-05-23,103.58,105.10,102.82,104.07,14950000,104.07 1973-05-22,102.73,105.04,102.58,103.58,18020000,103.58 1973-05-21,103.77,103.77,101.36,102.73,20690000,102.73 1973-05-18,105.41,105.41,103.18,103.86,17080000,103.86 1973-05-17,106.43,106.82,105.15,105.56,13060000,105.56 1973-05-16,106.57,107.61,105.49,106.43,13800000,106.43 1973-05-15,105.90,107.16,104.12,106.57,18530000,106.57 1973-05-14,107.74,107.74,105.52,105.90,13520000,105.90 1973-05-11,109.49,109.49,107.70,108.17,12980000,108.17 1973-05-10,110.44,110.86,108.86,109.54,13520000,109.54 1973-05-09,111.25,112.25,109.97,110.44,16050000,110.44 1973-05-08,110.53,111.72,109.46,111.25,13730000,111.25 1973-05-07,111.00,111.38,109.68,110.53,12500000,110.53 1973-05-04,110.22,111.99,109.89,111.00,19510000,111.00 1973-05-03,108.43,110.64,106.81,110.22,17760000,110.22 1973-05-02,107.10,109.06,106.95,108.43,14380000,108.43 1973-05-01,106.97,108.00,105.34,107.10,15380000,107.10 1973-04-30,107.23,107.90,105.44,106.97,14820000,106.97 1973-04-27,108.89,109.28,106.76,107.23,13730000,107.23 1973-04-26,108.34,109.66,107.14,108.89,16210000,108.89 1973-04-25,109.82,109.82,107.79,108.34,15960000,108.34 1973-04-24,111.57,111.89,109.64,109.99,13830000,109.99 1973-04-23,112.17,112.66,110.91,111.57,12580000,111.57 1973-04-19,111.54,112.93,111.06,112.17,14560000,112.17 1973-04-18,110.94,112.03,109.99,111.54,13890000,111.54 1973-04-17,111.44,111.81,110.19,110.94,12830000,110.94 1973-04-16,112.08,112.61,110.91,111.44,11350000,111.44 1973-04-13,112.58,112.91,111.23,112.08,14390000,112.08 1973-04-12,112.68,113.65,111.83,112.58,16360000,112.58 1973-04-11,112.21,113.27,111.21,112.68,14890000,112.68 1973-04-10,110.92,112.85,110.92,112.21,16770000,112.21 1973-04-09,109.28,111.24,108.74,110.86,13740000,110.86 1973-04-06,108.52,110.04,108.22,109.28,13890000,109.28 1973-04-05,108.77,109.15,107.44,108.52,12750000,108.52 1973-04-04,109.24,109.96,108.10,108.77,11890000,108.77 1973-04-03,110.18,110.35,108.47,109.24,12910000,109.24 1973-04-02,111.52,111.70,109.68,110.18,10640000,110.18 1973-03-30,112.71,112.87,110.89,111.52,13740000,111.52 1973-03-29,111.62,113.22,111.07,112.71,16050000,112.71 1973-03-28,111.56,112.47,110.54,111.62,15850000,111.62 1973-03-27,109.95,112.07,109.95,111.56,17500000,111.56 1973-03-26,108.88,110.40,108.29,109.84,14980000,109.84 1973-03-23,108.84,109.97,107.41,108.88,18470000,108.88 1973-03-22,110.39,110.39,108.19,108.84,17130000,108.84 1973-03-21,111.95,112.81,110.17,110.49,16080000,110.49 1973-03-20,112.17,112.68,111.02,111.95,13250000,111.95 1973-03-19,113.50,113.50,111.65,112.17,12460000,112.17 1973-03-16,114.12,114.62,112.84,113.54,15130000,113.54 1973-03-15,114.98,115.47,113.77,114.12,14450000,114.12 1973-03-14,114.48,115.61,113.97,114.98,14460000,114.98 1973-03-13,113.86,115.05,113.32,114.48,14210000,114.48 1973-03-12,113.79,114.80,113.25,113.86,13810000,113.86 1973-03-09,114.23,114.55,112.93,113.79,14070000,113.79 1973-03-08,114.45,115.23,113.57,114.23,15100000,114.23 1973-03-07,114.10,115.12,112.83,114.45,19310000,114.45 1973-03-06,112.68,114.71,112.57,114.10,17710000,114.10 1973-03-05,112.28,113.43,111.33,112.68,13720000,112.68 1973-03-02,111.05,112.62,109.45,112.28,17710000,112.28 1973-03-01,111.68,112.98,110.68,111.05,18210000,111.05 1973-02-28,110.90,112.21,109.80,111.68,17950000,111.68 1973-02-27,112.19,112.90,110.50,110.90,16130000,110.90 1973-02-26,113.16,113.26,111.15,112.19,15860000,112.19 1973-02-23,114.44,114.67,112.77,113.16,15450000,113.16 1973-02-22,114.69,115.20,113.44,114.44,14570000,114.44 1973-02-21,115.40,116.01,114.13,114.69,14880000,114.69 1973-02-20,114.98,116.26,114.57,115.40,14020000,115.40 1973-02-16,114.45,115.47,113.73,114.98,13320000,114.98 1973-02-15,115.10,115.68,113.70,114.45,13940000,114.45 1973-02-14,116.78,116.92,114.52,115.10,16520000,115.10 1973-02-13,116.09,118.98,116.09,116.78,25320000,116.78 1973-02-12,114.69,116.66,114.69,116.06,16130000,116.06 1973-02-09,113.16,115.20,113.08,114.68,19260000,114.68 1973-02-08,113.66,114.05,111.85,113.16,18440000,113.16 1973-02-07,114.45,115.48,113.24,113.66,17960000,113.66 1973-02-06,114.23,115.33,113.45,114.45,15720000,114.45 1973-02-05,114.35,115.15,113.62,114.23,14580000,114.23 1973-02-02,114.76,115.40,113.45,114.35,17470000,114.35 1973-02-01,116.03,117.01,114.26,114.76,20670000,114.76 1973-01-31,115.83,116.84,115.05,116.03,14870000,116.03 1973-01-30,116.01,117.11,115.26,115.83,15270000,115.83 1973-01-29,116.45,117.18,115.13,116.01,14680000,116.01 1973-01-26,116.73,117.29,114.97,116.45,21130000,116.45 1973-01-24,118.22,119.04,116.09,116.73,20870000,116.73 1973-01-23,118.21,119.00,116.84,118.22,19060000,118.22 1973-01-22,118.78,119.63,117.72,118.21,15570000,118.21 1973-01-19,118.85,119.45,117.46,118.78,17020000,118.78 1973-01-18,118.68,119.93,118.15,118.85,17810000,118.85 1973-01-17,118.14,119.35,117.61,118.68,17680000,118.68 1973-01-16,118.44,119.17,117.04,118.14,19170000,118.14 1973-01-15,119.30,120.82,118.04,118.44,21520000,118.44 1973-01-12,120.24,121.27,118.69,119.30,22230000,119.30 1973-01-11,119.43,121.74,119.01,120.24,25050000,120.24 1973-01-10,119.73,120.44,118.78,119.43,20880000,119.43 1973-01-09,119.85,120.40,118.89,119.73,16830000,119.73 1973-01-08,119.87,120.55,119.04,119.85,16840000,119.85 1973-01-05,119.40,120.71,118.88,119.87,19330000,119.87 1973-01-04,119.57,120.17,118.12,119.40,20230000,119.40 1973-01-03,119.10,120.45,118.69,119.57,20620000,119.57 1973-01-02,118.06,119.90,118.06,119.10,17090000,119.10 1972-12-29,116.93,118.77,116.70,118.05,27550000,118.05 1972-12-27,116.30,117.55,115.89,116.93,19100000,116.93 1972-12-26,115.83,116.87,115.54,116.30,11120000,116.30 1972-12-22,115.11,116.40,114.78,115.83,12540000,115.83 1972-12-21,115.95,116.60,114.63,115.11,18290000,115.11 1972-12-20,116.34,117.13,115.38,115.95,18490000,115.95 1972-12-19,116.90,117.37,115.69,116.34,17000000,116.34 1972-12-18,117.88,117.88,115.89,116.90,17540000,116.90 1972-12-15,118.24,119.25,117.37,118.26,18300000,118.26 1972-12-14,118.56,119.19,117.63,118.24,17930000,118.24 1972-12-13,118.66,119.23,117.77,118.56,16540000,118.56 1972-12-12,119.12,119.79,118.09,118.66,17040000,118.66 1972-12-11,118.86,119.78,118.24,119.12,17230000,119.12 1972-12-08,118.60,119.54,117.92,118.86,18030000,118.86 1972-12-07,118.01,119.17,117.57,118.60,19320000,118.60 1972-12-06,117.58,118.56,116.90,118.01,18610000,118.01 1972-12-05,117.77,118.42,116.89,117.58,17800000,117.58 1972-12-04,117.38,118.54,116.99,117.77,19730000,117.77 1972-12-01,116.67,118.18,116.29,117.38,22570000,117.38 1972-11-30,116.52,117.39,115.74,116.67,19340000,116.67 1972-11-29,116.47,117.14,115.56,116.52,17380000,116.52 1972-11-28,116.72,117.48,115.78,116.47,19210000,116.47 1972-11-27,117.27,117.55,115.66,116.72,18190000,116.72 1972-11-24,116.90,117.91,116.19,117.27,15760000,117.27 1972-11-22,116.21,117.61,115.67,116.90,24510000,116.90 1972-11-21,115.53,116.84,115.04,116.21,22110000,116.21 1972-11-20,115.49,116.25,114.57,115.53,16680000,115.53 1972-11-17,115.13,116.23,114.44,115.49,20220000,115.49 1972-11-16,114.50,115.57,113.73,115.13,19580000,115.13 1972-11-15,114.95,116.07,113.87,114.50,23270000,114.50 1972-11-14,113.90,115.41,113.36,114.95,20200000,114.95 1972-11-13,113.73,114.75,112.91,113.90,17210000,113.90 1972-11-10,113.50,115.15,112.85,113.73,24360000,113.73 1972-11-09,113.35,114.11,112.08,113.50,17040000,113.50 1972-11-08,113.98,115.23,112.77,113.35,24620000,113.35 1972-11-06,114.22,115.17,112.91,113.98,21330000,113.98 1972-11-03,113.23,114.81,112.71,114.22,22510000,114.22 1972-11-02,112.67,113.81,111.96,113.23,20690000,113.23 1972-11-01,111.58,113.31,111.32,112.67,21360000,112.67 1972-10-31,110.59,112.05,110.40,111.58,15450000,111.58 1972-10-30,110.62,111.19,109.66,110.59,11820000,110.59 1972-10-27,110.99,111.62,109.99,110.62,15470000,110.62 1972-10-26,110.72,112.26,110.26,110.99,20790000,110.99 1972-10-25,110.81,111.56,109.96,110.72,17430000,110.72 1972-10-24,110.35,111.34,109.38,110.81,15240000,110.81 1972-10-23,109.51,111.10,109.51,110.35,14190000,110.35 1972-10-20,108.05,109.79,107.59,109.24,15740000,109.24 1972-10-19,108.19,108.81,107.40,108.05,13850000,108.05 1972-10-18,107.50,109.11,107.36,108.19,17290000,108.19 1972-10-17,106.77,108.04,106.27,107.50,13410000,107.50 1972-10-16,107.92,108.40,106.38,106.77,10940000,106.77 1972-10-13,108.60,108.88,107.17,107.92,12870000,107.92 1972-10-12,109.50,109.69,108.03,108.60,13130000,108.60 1972-10-11,109.99,110.51,108.77,109.50,11900000,109.50 1972-10-10,109.90,111.11,109.32,109.99,13310000,109.99 1972-10-09,109.62,110.44,109.28,109.90,7940000,109.90 1972-10-06,108.89,110.49,107.78,109.62,16630000,109.62 1972-10-05,110.09,110.52,108.49,108.89,17730000,108.89 1972-10-04,110.30,111.35,109.58,110.09,16640000,110.09 1972-10-03,110.16,110.90,109.47,110.30,13090000,110.30 1972-10-02,110.55,110.98,109.49,110.16,12440000,110.16 1972-09-29,110.35,110.55,108.05,110.55,16250000,110.55 1972-09-28,109.66,110.75,108.75,110.35,14710000,110.35 1972-09-27,108.12,109.92,107.79,109.66,14620000,109.66 1972-09-26,108.05,108.97,107.35,108.12,13150000,108.12 1972-09-25,108.52,109.09,107.67,108.05,10920000,108.05 1972-09-22,108.43,109.20,107.72,108.52,12570000,108.52 1972-09-21,108.60,109.13,107.75,108.43,11940000,108.43 1972-09-20,108.55,109.12,107.84,108.60,11980000,108.60 1972-09-19,108.61,109.57,108.08,108.55,13330000,108.55 1972-09-18,108.81,109.22,107.86,108.61,8880000,108.61 1972-09-15,108.93,109.49,108.10,108.81,11690000,108.81 1972-09-14,108.90,109.64,108.21,108.93,12500000,108.93 1972-09-13,108.47,109.36,107.84,108.90,13070000,108.90 1972-09-12,109.51,109.84,107.81,108.47,13560000,108.47 1972-09-11,110.15,110.57,109.01,109.51,10710000,109.51 1972-09-08,110.29,110.90,109.67,110.15,10980000,110.15 1972-09-07,110.55,111.06,109.71,110.29,11090000,110.29 1972-09-06,111.23,111.38,110.04,110.55,12010000,110.55 1972-09-05,111.51,112.08,110.75,111.23,10630000,111.23 1972-09-01,111.09,112.12,110.70,111.51,11600000,111.51 1972-08-31,110.57,111.52,110.08,111.09,12340000,111.09 1972-08-30,110.41,111.33,109.90,110.57,12470000,110.57 1972-08-29,110.23,111.02,109.26,110.41,12300000,110.41 1972-08-28,110.67,111.24,109.71,110.23,10720000,110.23 1972-08-25,111.02,111.53,109.78,110.67,13840000,110.67 1972-08-24,112.26,112.81,110.62,111.02,18280000,111.02 1972-08-23,112.41,113.27,111.30,112.26,18670000,112.26 1972-08-22,111.72,113.16,111.28,112.41,18560000,112.41 1972-08-21,111.76,112.74,110.75,111.72,14290000,111.72 1972-08-18,111.34,112.53,110.81,111.76,16150000,111.76 1972-08-17,111.66,112.41,110.72,111.34,14360000,111.34 1972-08-16,112.06,112.80,110.87,111.66,14950000,111.66 1972-08-15,112.55,113.04,111.27,112.06,16670000,112.06 1972-08-14,111.95,113.45,111.66,112.55,18870000,112.55 1972-08-11,111.05,112.40,110.52,111.95,16570000,111.95 1972-08-10,110.86,111.68,110.09,111.05,15260000,111.05 1972-08-09,110.69,111.57,109.98,110.86,15730000,110.86 1972-08-08,110.61,111.32,109.67,110.69,14550000,110.69 1972-08-07,110.43,111.38,109.69,110.61,13220000,110.61 1972-08-04,110.14,111.12,109.37,110.43,15700000,110.43 1972-08-03,109.29,110.88,108.90,110.14,19970000,110.14 1972-08-02,108.40,109.85,108.12,109.29,17920000,109.29 1972-08-01,107.39,108.85,107.06,108.40,15540000,108.40 1972-07-31,107.38,108.06,106.60,107.39,11120000,107.39 1972-07-28,107.28,108.03,106.52,107.38,13050000,107.38 1972-07-27,107.53,108.31,106.61,107.28,13870000,107.28 1972-07-26,107.60,108.42,106.79,107.53,14130000,107.53 1972-07-25,107.92,108.88,107.06,107.60,17180000,107.60 1972-07-24,106.66,108.67,106.63,107.92,18020000,107.92 1972-07-21,105.81,107.05,104.99,106.66,14010000,106.66 1972-07-20,106.14,106.68,105.12,105.81,15050000,105.81 1972-07-19,105.83,107.36,105.47,106.14,17880000,106.14 1972-07-18,105.88,106.40,104.43,105.83,16820000,105.83 1972-07-17,106.80,107.37,105.55,105.88,13170000,105.88 1972-07-14,106.28,107.58,105.77,106.80,13910000,106.80 1972-07-13,106.89,107.30,105.62,106.28,14740000,106.28 1972-07-12,107.32,108.15,106.42,106.89,16150000,106.89 1972-07-11,108.11,108.35,106.87,107.32,12830000,107.32 1972-07-10,108.69,109.16,107.62,108.11,11700000,108.11 1972-07-07,109.04,109.66,108.16,108.69,12900000,108.69 1972-07-06,108.28,110.27,108.28,109.04,19520000,109.04 1972-07-05,107.49,108.80,107.14,108.10,14710000,108.10 1972-07-03,107.14,107.95,106.72,107.49,8140000,107.49 1972-06-30,106.82,107.91,106.40,107.14,12860000,107.14 1972-06-29,107.02,107.47,105.94,106.82,14610000,106.82 1972-06-28,107.37,107.87,106.49,107.02,12140000,107.02 1972-06-27,107.48,108.29,106.70,107.37,13750000,107.37 1972-06-26,108.23,108.23,106.68,107.48,12720000,107.48 1972-06-23,108.68,109.33,107.69,108.27,13940000,108.27 1972-06-22,108.79,109.26,107.62,108.68,13410000,108.68 1972-06-21,108.56,109.66,107.98,108.79,15510000,108.79 1972-06-20,108.11,109.12,107.64,108.56,14970000,108.56 1972-06-19,108.36,108.78,107.37,108.11,11660000,108.11 1972-06-16,108.44,108.94,107.54,108.36,13010000,108.36 1972-06-15,108.39,109.52,107.78,108.44,16940000,108.44 1972-06-14,107.55,109.15,107.38,108.39,18320000,108.39 1972-06-13,107.01,108.03,106.38,107.55,15710000,107.55 1972-06-12,106.86,107.92,106.29,107.01,13390000,107.01 1972-06-09,107.28,107.68,106.30,106.86,12790000,106.86 1972-06-08,107.65,108.52,106.90,107.28,13820000,107.28 1972-06-07,108.21,108.52,106.91,107.65,15220000,107.65 1972-06-06,108.82,109.32,107.71,108.21,15980000,108.21 1972-06-05,109.73,109.92,108.28,108.82,13450000,108.82 1972-06-02,109.69,110.51,108.93,109.73,15400000,109.73 1972-06-01,109.53,110.35,108.97,109.69,14910000,109.69 1972-05-31,110.35,110.52,108.92,109.53,15230000,109.53 1972-05-30,110.66,111.48,109.78,110.35,15810000,110.35 1972-05-26,110.46,111.31,109.84,110.66,15730000,110.66 1972-05-25,110.31,111.20,109.67,110.46,16480000,110.46 1972-05-24,109.78,111.07,109.39,110.31,17870000,110.31 1972-05-23,109.69,110.46,108.91,109.78,16410000,109.78 1972-05-22,108.98,110.37,108.79,109.69,16030000,109.69 1972-05-19,107.94,109.59,107.74,108.98,19580000,108.98 1972-05-18,106.89,108.39,106.72,107.94,17370000,107.94 1972-05-17,106.66,107.38,106.02,106.89,13600000,106.89 1972-05-16,106.86,107.55,106.13,106.66,14070000,106.66 1972-05-15,106.38,107.45,106.06,106.86,13600000,106.86 1972-05-12,105.77,107.02,105.49,106.38,13990000,106.38 1972-05-11,105.42,106.45,104.90,105.77,12900000,105.77 1972-05-10,104.74,106.10,104.43,105.42,13870000,105.42 1972-05-09,106.06,106.06,103.83,104.74,19910000,104.74 1972-05-08,106.63,106.81,105.36,106.14,11250000,106.14 1972-05-05,106.25,107.33,105.70,106.63,13210000,106.63 1972-05-04,105.99,106.81,105.14,106.25,14790000,106.25 1972-05-03,106.08,107.24,105.44,105.99,15900000,105.99 1972-05-02,106.69,107.37,105.55,106.08,15370000,106.08 1972-05-01,107.67,108.00,106.30,106.69,12880000,106.69 1972-04-28,107.05,108.28,106.70,107.67,14160000,107.67 1972-04-27,106.89,107.89,106.42,107.05,15740000,107.05 1972-04-26,107.12,107.89,106.18,106.89,17710000,106.89 1972-04-25,108.19,108.29,106.70,107.12,17030000,107.12 1972-04-24,108.89,109.19,107.62,108.19,14650000,108.19 1972-04-21,109.04,109.92,108.30,108.89,18200000,108.89 1972-04-20,109.20,109.69,108.08,109.04,18190000,109.04 1972-04-19,109.77,110.35,108.71,109.20,19180000,109.20 1972-04-18,109.51,110.64,109.02,109.77,19410000,109.77 1972-04-17,109.84,110.22,108.77,109.51,15390000,109.51 1972-04-14,109.91,110.56,109.07,109.84,17460000,109.84 1972-04-13,110.18,110.79,109.37,109.91,17990000,109.91 1972-04-12,109.76,111.11,109.36,110.18,24690000,110.18 1972-04-11,109.45,110.38,108.76,109.76,19930000,109.76 1972-04-10,109.62,110.54,108.89,109.45,19470000,109.45 1972-04-07,109.53,110.15,108.53,109.62,19900000,109.62 1972-04-06,109.00,110.29,108.53,109.53,22830000,109.53 1972-04-05,108.12,109.64,107.96,109.00,22960000,109.00 1972-04-04,107.48,108.62,106.77,108.12,18110000,108.12 1972-04-03,107.20,108.26,106.75,107.48,14990000,107.48 1972-03-30,106.49,107.67,106.07,107.20,14360000,107.20 1972-03-29,107.17,107.41,105.98,106.49,13860000,106.49 1972-03-28,107.30,108.08,106.22,107.17,15380000,107.17 1972-03-27,107.52,108.00,106.53,107.30,12180000,107.30 1972-03-24,107.75,108.36,106.95,107.52,15390000,107.52 1972-03-23,106.84,108.33,106.67,107.75,18380000,107.75 1972-03-22,106.69,107.52,106.00,106.84,15400000,106.84 1972-03-21,107.59,107.68,105.86,106.69,18610000,106.69 1972-03-20,107.92,108.81,107.18,107.59,16420000,107.59 1972-03-17,107.50,108.61,106.89,107.92,16040000,107.92 1972-03-16,107.75,108.22,106.55,107.50,16700000,107.50 1972-03-15,107.61,108.55,107.09,107.75,19460000,107.75 1972-03-14,107.33,108.20,106.71,107.61,22370000,107.61 1972-03-13,108.38,108.52,106.71,107.33,16730000,107.33 1972-03-10,108.94,109.37,107.77,108.38,19690000,108.38 1972-03-09,108.96,109.75,108.19,108.94,21460000,108.94 1972-03-08,108.87,109.68,108.04,108.96,21290000,108.96 1972-03-07,108.77,109.72,108.02,108.87,22640000,108.87 1972-03-06,107.94,109.40,107.64,108.77,21000000,108.77 1972-03-03,107.32,108.51,106.78,107.94,20420000,107.94 1972-03-02,107.35,108.39,106.63,107.32,22200000,107.32 1972-03-01,106.57,108.13,106.21,107.35,23670000,107.35 1972-02-29,106.19,107.16,105.45,106.57,20320000,106.57 1972-02-28,106.18,107.04,105.37,106.19,18200000,106.19 1972-02-25,105.45,106.73,105.04,106.18,18180000,106.18 1972-02-24,105.38,106.24,104.76,105.45,16000000,105.45 1972-02-23,105.29,106.18,104.72,105.38,16770000,105.38 1972-02-22,105.28,106.18,104.65,105.29,16670000,105.29 1972-02-18,105.59,106.01,104.47,105.28,16590000,105.28 1972-02-17,105.62,106.65,104.96,105.59,22330000,105.59 1972-02-16,105.03,106.25,104.65,105.62,20670000,105.62 1972-02-15,104.59,105.59,104.10,105.03,17770000,105.03 1972-02-14,105.08,105.53,104.03,104.59,15840000,104.59 1972-02-11,105.59,105.91,104.45,105.08,17850000,105.08 1972-02-10,105.55,106.69,104.97,105.59,23460000,105.59 1972-02-09,104.74,106.03,104.36,105.55,19850000,105.55 1972-02-08,104.54,105.22,103.90,104.74,17390000,104.74 1972-02-07,104.86,105.46,103.97,104.54,16930000,104.54 1972-02-04,104.64,105.48,104.05,104.86,17890000,104.86 1972-02-03,104.68,105.43,103.85,104.64,19880000,104.64 1972-02-02,104.01,105.41,103.50,104.68,24070000,104.68 1972-02-01,103.94,104.57,103.10,104.01,19600000,104.01 1972-01-31,104.16,104.88,103.30,103.94,18250000,103.94 1972-01-28,103.50,104.98,103.22,104.16,25000000,104.16 1972-01-27,102.50,103.93,102.20,103.50,20360000,103.50 1972-01-26,102.70,103.31,101.81,102.50,14940000,102.50 1972-01-25,102.57,103.59,101.63,102.70,17570000,102.70 1972-01-24,103.65,104.03,102.20,102.57,15640000,102.57 1972-01-21,103.88,104.40,102.75,103.65,18810000,103.65 1972-01-20,103.88,105.00,103.32,103.88,20210000,103.88 1972-01-19,104.05,104.61,102.83,103.88,18800000,103.88 1972-01-18,103.70,104.85,103.35,104.05,21070000,104.05 1972-01-17,103.39,104.24,102.80,103.70,15860000,103.70 1972-01-14,102.99,103.89,102.41,103.39,14960000,103.39 1972-01-13,103.59,103.80,102.29,102.99,16410000,102.99 1972-01-12,103.65,104.66,103.05,103.59,20970000,103.59 1972-01-11,103.32,104.30,102.85,103.65,17970000,103.65 1972-01-10,103.47,103.97,102.44,103.32,15320000,103.32 1972-01-07,103.51,104.29,102.38,103.47,17140000,103.47 1972-01-06,103.06,104.20,102.66,103.51,21100000,103.51 1972-01-05,102.09,103.69,101.90,103.06,21350000,103.06 1972-01-04,101.67,102.59,100.87,102.09,15190000,102.09 1972-01-03,102.09,102.85,101.19,101.67,12570000,101.67 1971-12-31,102.09,102.09,102.09,102.09,14040000,102.09 1971-12-30,101.78,101.78,101.78,101.78,13810000,101.78 1971-12-29,102.21,102.21,102.21,102.21,17150000,102.21 1971-12-28,101.95,101.95,101.95,101.95,15090000,101.95 1971-12-27,100.95,100.95,100.95,100.95,11890000,100.95 1971-12-23,100.74,100.74,100.74,100.74,16000000,100.74 1971-12-22,101.18,101.18,101.18,101.18,18930000,101.18 1971-12-21,101.80,101.80,101.80,101.80,20460000,101.80 1971-12-20,101.55,101.55,101.55,101.55,23810000,101.55 1971-12-17,100.26,100.26,100.26,100.26,18270000,100.26 1971-12-16,99.74,99.74,99.74,99.74,21070000,99.74 1971-12-15,98.54,98.54,98.54,98.54,16890000,98.54 1971-12-14,97.67,97.67,97.67,97.67,16070000,97.67 1971-12-13,97.97,97.97,97.97,97.97,17020000,97.97 1971-12-10,97.69,97.69,97.69,97.69,17510000,97.69 1971-12-09,96.96,96.96,96.96,96.96,14710000,96.96 1971-12-08,96.87,97.65,96.08,96.92,16650000,96.92 1971-12-07,96.51,97.35,95.40,96.87,15250000,96.87 1971-12-06,97.06,98.17,96.07,96.51,17480000,96.51 1971-12-03,95.84,97.57,95.36,97.06,16760000,97.06 1971-12-02,95.44,96.59,94.73,95.84,17780000,95.84 1971-12-01,93.99,96.12,93.95,95.44,21040000,95.44 1971-11-30,93.41,94.43,92.51,93.99,18320000,93.99 1971-11-29,92.04,94.90,92.04,93.41,18910000,93.41 1971-11-26,90.33,92.19,90.27,91.94,10870000,91.94 1971-11-24,90.16,91.14,89.73,90.33,11870000,90.33 1971-11-23,90.79,91.10,89.34,90.16,16840000,90.16 1971-11-22,91.61,92.12,90.51,90.79,11390000,90.79 1971-11-19,92.13,92.38,90.95,91.61,12420000,91.61 1971-11-18,92.85,93.62,91.88,92.13,13010000,92.13 1971-11-17,92.71,93.35,91.80,92.85,12840000,92.85 1971-11-16,91.81,93.15,91.21,92.71,13300000,92.71 1971-11-15,92.12,92.69,91.38,91.81,9370000,91.81 1971-11-12,92.12,92.90,90.93,92.12,14540000,92.12 1971-11-11,93.41,93.54,91.64,92.12,13310000,92.12 1971-11-10,94.46,94.84,93.10,93.41,13410000,93.41 1971-11-09,94.39,95.31,93.94,94.46,12080000,94.46 1971-11-08,94.46,94.97,93.78,94.39,8520000,94.39 1971-11-05,94.79,95.01,93.64,94.46,10780000,94.46 1971-11-04,94.91,96.08,94.37,94.79,15750000,94.79 1971-11-03,93.27,95.31,93.27,94.91,14590000,94.91 1971-11-02,92.80,93.73,91.84,93.18,13330000,93.18 1971-11-01,94.23,94.43,92.48,92.80,10960000,92.80 1971-10-29,93.96,94.71,93.28,94.23,11710000,94.23 1971-10-28,93.79,94.75,92.96,93.96,15530000,93.96 1971-10-27,94.74,94.99,93.39,93.79,13480000,93.79 1971-10-26,95.02,95.02,94.38,94.74,13390000,94.74 1971-10-25,95.57,95.76,94.57,95.10,7340000,95.10 1971-10-22,95.60,96.83,94.97,95.57,14560000,95.57 1971-10-21,95.65,96.33,94.59,95.60,14990000,95.60 1971-10-20,97.00,97.45,95.23,95.65,16340000,95.65 1971-10-19,97.35,97.66,96.05,97.00,13040000,97.00 1971-10-18,97.79,98.33,96.98,97.35,10420000,97.35 1971-10-15,98.13,98.45,97.03,97.79,13120000,97.79 1971-10-14,99.03,99.25,97.74,98.13,12870000,98.13 1971-10-13,99.57,100.08,98.61,99.03,13540000,99.03 1971-10-12,99.21,100.20,98.62,99.57,14340000,99.57 1971-10-11,99.36,99.62,98.58,99.21,7800000,99.21 1971-10-08,100.02,100.30,98.87,99.36,13870000,99.36 1971-10-07,99.82,100.96,99.42,100.02,17780000,100.02 1971-10-06,99.11,100.13,98.49,99.82,15630000,99.82 1971-10-05,99.21,99.78,98.34,99.11,12360000,99.11 1971-10-04,98.93,100.04,98.62,99.21,14570000,99.21 1971-10-01,98.34,99.49,97.96,98.93,13400000,98.93 1971-09-30,97.90,98.97,97.48,98.34,13490000,98.34 1971-09-29,97.88,98.51,97.29,97.90,8580000,97.90 1971-09-28,97.62,98.55,97.12,97.88,11250000,97.88 1971-09-27,98.15,98.41,96.97,97.62,10220000,97.62 1971-09-24,98.38,99.35,97.78,98.15,13460000,98.15 1971-09-23,98.47,99.12,97.61,98.38,13250000,98.38 1971-09-22,99.34,99.72,98.15,98.47,14250000,98.47 1971-09-21,99.68,100.08,98.71,99.34,10640000,99.34 1971-09-20,99.96,100.40,99.14,99.68,9540000,99.68 1971-09-17,99.66,100.52,99.26,99.96,11020000,99.96 1971-09-16,99.77,100.35,99.07,99.66,10550000,99.66 1971-09-15,99.34,100.24,98.79,99.77,11080000,99.77 1971-09-14,100.07,100.35,98.99,99.34,11410000,99.34 1971-09-13,100.42,100.84,99.49,100.07,10000000,100.07 1971-09-10,100.80,101.01,99.69,100.42,11380000,100.42 1971-09-09,101.34,101.88,100.38,100.80,15790000,100.80 1971-09-08,101.15,101.94,100.52,101.34,14230000,101.34 1971-09-07,100.69,102.25,100.43,101.15,17080000,101.15 1971-09-03,99.29,100.93,99.10,100.69,14040000,100.69 1971-09-02,99.07,99.80,98.52,99.29,10690000,99.29 1971-09-01,99.03,99.84,98.50,99.07,10770000,99.07 1971-08-31,99.52,99.76,98.32,99.03,10430000,99.03 1971-08-30,100.48,100.89,99.17,99.52,11140000,99.52 1971-08-27,100.24,101.22,99.76,100.48,12490000,100.48 1971-08-26,100.41,101.12,99.40,100.24,13990000,100.24 1971-08-25,100.40,101.51,99.77,100.41,18280000,100.41 1971-08-24,99.25,101.02,99.15,100.40,18700000,100.40 1971-08-23,98.33,99.96,98.09,99.25,13040000,99.25 1971-08-20,98.16,98.94,97.52,98.33,11890000,98.33 1971-08-19,98.60,99.07,97.35,98.16,14190000,98.16 1971-08-18,99.99,100.19,98.06,98.60,20680000,98.60 1971-08-17,98.76,101.00,98.49,99.99,26790000,99.99 1971-08-16,97.90,100.96,97.90,98.76,31730000,98.76 1971-08-13,96.00,96.53,95.19,95.69,9960000,95.69 1971-08-12,94.81,96.50,94.81,96.00,15910000,96.00 1971-08-11,93.54,95.06,93.35,94.66,11370000,94.66 1971-08-10,93.53,94.13,92.81,93.54,9460000,93.54 1971-08-09,94.25,94.55,93.17,93.53,8110000,93.53 1971-08-06,94.09,94.91,93.63,94.25,9490000,94.25 1971-08-05,93.89,94.89,93.33,94.09,12100000,94.09 1971-08-04,94.51,95.34,93.35,93.89,15410000,93.89 1971-08-03,95.96,96.11,94.06,94.51,13490000,94.51 1971-08-02,95.58,96.76,95.22,95.96,11870000,95.96 1971-07-30,96.02,96.78,95.08,95.58,12970000,95.58 1971-07-29,97.07,97.22,95.37,96.02,14570000,96.02 1971-07-28,97.78,98.15,96.51,97.07,13940000,97.07 1971-07-27,98.14,98.99,97.42,97.78,11560000,97.78 1971-07-26,98.94,99.47,96.67,98.14,9930000,98.14 1971-07-23,99.11,99.60,98.26,98.94,12370000,98.94 1971-07-22,99.28,99.82,98.50,99.11,12570000,99.11 1971-07-21,99.32,100.00,98.74,99.28,11920000,99.28 1971-07-20,98.93,100.01,98.60,99.32,12540000,99.32 1971-07-19,99.11,99.57,98.11,98.93,11430000,98.93 1971-07-16,99.28,100.35,98.64,99.11,13870000,99.11 1971-07-15,99.22,100.48,98.76,99.28,13080000,99.28 1971-07-14,99.50,99.83,98.23,99.22,14360000,99.22 1971-07-13,100.82,101.06,99.07,99.50,13540000,99.50 1971-07-12,100.69,101.52,100.19,100.82,12020000,100.82 1971-07-09,100.34,101.33,99.86,100.69,12640000,100.69 1971-07-08,100.04,101.03,99.59,100.34,13920000,100.34 1971-07-07,99.76,100.83,99.25,100.04,14520000,100.04 1971-07-06,99.78,100.35,99.10,99.76,10440000,99.76 1971-07-02,99.78,100.31,99.09,99.78,9960000,99.78 1971-07-01,99.16,100.65,99.16,99.78,13090000,99.78 1971-06-30,98.82,100.29,98.68,98.70,15410000,98.70 1971-06-29,97.74,99.39,97.61,98.82,14460000,98.82 1971-06-28,97.99,98.48,97.02,97.74,9810000,97.74 1971-06-25,98.13,98.66,97.33,97.99,10580000,97.99 1971-06-24,98.41,99.00,97.59,98.13,11360000,98.13 1971-06-23,97.59,98.95,97.36,98.41,12640000,98.41 1971-06-22,97.87,98.66,96.92,97.59,15200000,97.59 1971-06-21,98.97,99.18,97.22,97.87,16490000,97.87 1971-06-18,100.50,100.63,98.65,98.97,15040000,98.97 1971-06-17,100.52,101.37,99.87,100.50,13980000,100.50 1971-06-16,100.32,101.29,99.68,100.52,14300000,100.52 1971-06-15,100.22,101.10,99.45,100.32,13550000,100.32 1971-06-14,101.07,101.28,99.78,100.22,11530000,100.22 1971-06-11,100.64,101.71,100.18,101.07,12270000,101.07 1971-06-10,100.29,101.23,99.78,100.64,12450000,100.64 1971-06-09,100.32,100.97,99.28,100.29,14250000,100.29 1971-06-08,101.09,101.50,99.91,100.32,13610000,100.32 1971-06-07,101.30,102.02,100.55,101.09,13800000,101.09 1971-06-04,101.01,101.88,100.43,101.30,14400000,101.30 1971-06-03,100.96,102.07,100.30,101.01,18790000,101.01 1971-06-02,100.20,101.53,99.89,100.96,17740000,100.96 1971-06-01,99.63,100.76,99.22,100.20,11930000,100.20 1971-05-28,99.40,100.17,98.68,99.63,11760000,99.63 1971-05-27,99.59,100.14,98.78,99.40,12610000,99.40 1971-05-26,99.47,100.49,98.93,99.59,13550000,99.59 1971-05-25,100.13,100.39,98.73,99.47,16050000,99.47 1971-05-24,100.99,101.24,99.72,100.13,12060000,100.13 1971-05-21,101.31,101.84,100.41,100.99,12090000,100.99 1971-05-20,101.07,102.17,100.61,101.31,11740000,101.31 1971-05-19,100.83,101.75,100.30,101.07,17640000,101.07 1971-05-18,100.69,101.62,99.68,100.83,17640000,100.83 1971-05-17,102.08,102.08,100.25,100.69,15980000,100.69 1971-05-14,102.69,103.17,101.65,102.21,16430000,102.21 1971-05-13,102.90,103.57,101.98,102.69,17640000,102.69 1971-05-12,102.62,103.57,102.12,102.90,15140000,102.90 1971-05-11,102.36,103.37,101.50,102.62,17730000,102.62 1971-05-10,102.87,103.15,101.71,102.36,12810000,102.36 1971-05-07,103.23,103.50,101.86,102.87,16490000,102.87 1971-05-06,103.78,104.42,102.80,103.23,19300000,103.23 1971-05-05,103.79,104.28,102.68,103.78,17270000,103.78 1971-05-04,103.29,104.36,102.71,103.79,17310000,103.79 1971-05-03,103.95,104.11,102.37,103.29,16120000,103.29 1971-04-30,104.63,104.96,103.25,103.95,17490000,103.95 1971-04-29,104.77,105.58,103.90,104.63,20340000,104.63 1971-04-28,104.59,105.60,103.85,104.77,24820000,104.77 1971-04-27,103.94,105.07,103.23,104.59,21250000,104.59 1971-04-26,104.05,104.83,103.19,103.94,18860000,103.94 1971-04-23,103.56,104.63,102.79,104.05,20150000,104.05 1971-04-22,103.36,104.27,102.58,103.56,19270000,103.56 1971-04-21,103.61,104.16,102.55,103.36,17040000,103.36 1971-04-20,104.01,104.58,103.06,103.61,17880000,103.61 1971-04-19,103.49,104.63,103.09,104.01,17730000,104.01 1971-04-16,103.52,104.18,102.68,103.49,18280000,103.49 1971-04-15,103.37,104.40,102.76,103.52,22540000,103.52 1971-04-14,102.98,104.01,102.28,103.37,19440000,103.37 1971-04-13,102.88,103.96,102.25,102.98,23200000,102.98 1971-04-12,102.10,103.54,101.75,102.88,19410000,102.88 1971-04-08,101.98,102.86,101.30,102.10,17590000,102.10 1971-04-07,101.51,102.87,101.13,101.98,22270000,101.98 1971-04-06,100.79,102.11,100.30,101.51,19990000,101.51 1971-04-05,100.56,101.41,99.88,100.79,16040000,100.79 1971-04-02,100.39,101.23,99.86,100.56,14520000,100.56 1971-04-01,100.31,100.99,99.63,100.39,13470000,100.39 1971-03-31,100.26,101.05,99.69,100.31,17610000,100.31 1971-03-30,100.03,100.86,99.41,100.26,15430000,100.26 1971-03-29,99.95,100.74,99.36,100.03,13650000,100.03 1971-03-26,99.61,100.65,99.18,99.95,15560000,99.95 1971-03-25,99.62,100.03,98.36,99.61,15870000,99.61 1971-03-24,100.28,100.63,99.15,99.62,15770000,99.62 1971-03-23,100.62,101.06,99.62,100.28,16470000,100.28 1971-03-22,101.01,101.46,100.08,100.62,14290000,100.62 1971-03-19,101.19,101.74,100.35,101.01,15150000,101.01 1971-03-18,101.12,102.03,100.43,101.19,17910000,101.19 1971-03-17,101.21,101.66,99.98,101.12,17070000,101.12 1971-03-16,100.71,101.94,100.36,101.21,22270000,101.21 1971-03-15,99.57,101.15,99.12,100.71,18920000,100.71 1971-03-12,99.39,100.09,98.64,99.57,14680000,99.57 1971-03-11,99.30,100.29,98.57,99.39,19830000,99.39 1971-03-10,99.46,100.10,98.63,99.30,17220000,99.30 1971-03-09,99.38,100.31,98.72,99.46,20490000,99.46 1971-03-08,98.96,99.44,98.42,99.38,19340000,99.38 1971-03-05,97.92,99.49,97.82,98.96,22430000,98.96 1971-03-04,96.95,98.38,96.90,97.92,17350000,97.92 1971-03-03,96.98,97.54,96.30,96.95,14680000,96.95 1971-03-02,97.00,97.60,96.32,96.98,14870000,96.98 1971-03-01,96.75,97.48,96.11,97.00,13020000,97.00 1971-02-26,96.96,97.54,95.84,96.75,17250000,96.75 1971-02-25,96.73,97.71,96.08,96.96,16200000,96.96 1971-02-24,96.09,97.34,95.86,96.73,15930000,96.73 1971-02-23,95.72,96.67,94.92,96.09,15080000,96.09 1971-02-22,96.65,96.65,94.97,95.72,15840000,95.72 1971-02-19,97.56,97.79,96.25,96.74,17860000,96.74 1971-02-18,98.20,98.60,96.96,97.56,16650000,97.56 1971-02-17,98.66,99.32,97.32,98.20,18720000,98.20 1971-02-16,98.43,99.59,97.85,98.66,21350000,98.66 1971-02-12,97.91,98.96,97.56,98.43,18470000,98.43 1971-02-11,97.39,98.49,96.99,97.91,19260000,97.91 1971-02-10,97.51,97.97,96.23,97.39,19040000,97.39 1971-02-09,97.45,98.50,96.90,97.51,28250000,97.51 1971-02-08,96.93,98.04,96.13,97.45,25590000,97.45 1971-02-05,96.62,97.58,95.84,96.93,20480000,96.93 1971-02-04,96.63,97.26,95.69,96.62,20860000,96.62 1971-02-03,96.43,97.19,95.58,96.63,21680000,96.63 1971-02-02,96.42,97.19,95.60,96.43,22030000,96.43 1971-02-01,95.88,97.05,95.38,96.42,20650000,96.42 1971-01-29,95.21,96.49,94.79,95.88,20960000,95.88 1971-01-28,94.89,95.78,94.12,95.21,18840000,95.21 1971-01-27,95.59,95.78,93.96,94.89,20640000,94.89 1971-01-26,95.28,96.36,94.69,95.59,21380000,95.59 1971-01-25,94.88,95.93,94.16,95.28,19050000,95.28 1971-01-22,94.19,95.53,93.96,94.88,21680000,94.88 1971-01-21,93.78,94.69,93.15,94.19,19060000,94.19 1971-01-20,93.76,94.53,93.07,93.78,18330000,93.78 1971-01-19,93.41,94.28,92.85,93.76,15800000,93.76 1971-01-18,93.03,94.11,92.63,93.41,15400000,93.41 1971-01-15,92.80,93.94,92.25,93.03,18010000,93.03 1971-01-14,92.56,93.36,91.67,92.80,17600000,92.80 1971-01-13,92.72,93.66,91.88,92.56,19070000,92.56 1971-01-12,91.98,93.28,91.63,92.72,17820000,92.72 1971-01-11,92.19,92.67,90.99,91.98,14720000,91.98 1971-01-08,92.38,93.02,91.60,92.19,14100000,92.19 1971-01-07,92.35,93.26,91.75,92.38,16460000,92.38 1971-01-06,91.80,93.00,91.50,92.35,16960000,92.35 1971-01-05,91.15,92.28,90.69,91.80,12600000,91.80 1971-01-04,92.15,92.19,90.64,91.15,10010000,91.15 1970-12-31,92.27,92.79,91.36,92.15,13390000,92.15 1970-12-30,92.08,92.99,91.60,92.27,19140000,92.27 1970-12-29,91.09,92.38,90.73,92.08,17750000,92.08 1970-12-28,90.61,91.49,90.28,91.09,12290000,91.09 1970-12-24,90.10,91.08,89.81,90.61,12140000,90.61 1970-12-23,90.04,90.86,89.35,90.10,15400000,90.10 1970-12-22,89.94,90.84,89.35,90.04,14510000,90.04 1970-12-21,90.22,90.77,89.36,89.94,12690000,89.94 1970-12-18,90.04,90.77,89.42,90.22,14360000,90.22 1970-12-17,89.72,90.61,89.31,90.04,13660000,90.04 1970-12-16,89.66,90.22,88.77,89.72,14240000,89.72 1970-12-15,89.80,90.32,88.93,89.66,13420000,89.66 1970-12-14,90.26,90.81,89.28,89.80,13810000,89.80 1970-12-11,89.92,90.93,89.44,90.26,15790000,90.26 1970-12-10,89.54,90.87,89.01,89.92,14610000,89.92 1970-12-09,89.47,90.03,88.48,89.54,13550000,89.54 1970-12-08,89.94,90.47,88.87,89.47,14370000,89.47 1970-12-07,89.46,90.39,88.76,89.94,15530000,89.94 1970-12-04,88.90,89.89,88.12,89.46,15980000,89.46 1970-12-03,88.48,89.87,88.11,88.90,20480000,88.90 1970-12-02,87.47,88.83,86.72,88.48,17960000,88.48 1970-12-01,87.20,88.61,86.11,87.47,20170000,87.47 1970-11-30,85.93,87.60,85.79,87.20,17700000,87.20 1970-11-27,85.09,86.21,84.67,85.93,10130000,85.93 1970-11-25,84.78,85.70,84.35,85.09,13490000,85.09 1970-11-24,84.24,85.18,83.59,84.78,12560000,84.78 1970-11-23,83.72,84.92,83.47,84.24,12720000,84.24 1970-11-20,82.91,84.06,82.49,83.72,10920000,83.72 1970-11-19,82.79,83.48,82.23,82.91,9280000,82.91 1970-11-18,83.47,83.53,82.41,82.79,9850000,82.79 1970-11-17,83.24,84.17,82.81,83.47,9450000,83.47 1970-11-16,83.37,83.75,82.34,83.24,9160000,83.24 1970-11-13,84.15,84.33,82.92,83.37,11890000,83.37 1970-11-12,85.03,85.54,83.81,84.15,12520000,84.15 1970-11-11,84.79,86.24,84.69,85.03,13520000,85.03 1970-11-10,84.67,85.69,84.18,84.79,12030000,84.79 1970-11-09,84.22,85.27,83.82,84.67,10890000,84.67 1970-11-06,84.10,84.73,83.55,84.22,9970000,84.22 1970-11-05,84.39,84.79,83.53,84.10,10800000,84.10 1970-11-04,84.22,85.26,83.82,84.39,12180000,84.39 1970-11-03,83.51,84.77,83.21,84.22,11760000,84.22 1970-11-02,83.25,83.99,82.66,83.51,9470000,83.51 1970-10-30,83.36,83.80,82.52,83.25,10520000,83.25 1970-10-29,83.43,84.10,82.82,83.36,10440000,83.36 1970-10-28,83.12,83.81,82.29,83.43,10660000,83.43 1970-10-27,83.31,83.73,82.52,83.12,9680000,83.12 1970-10-26,83.77,84.26,82.89,83.31,9200000,83.31 1970-10-23,83.38,84.30,82.91,83.77,10270000,83.77 1970-10-22,83.66,84.04,82.77,83.38,9000000,83.38 1970-10-21,83.64,84.72,83.21,83.66,11330000,83.66 1970-10-20,83.15,84.19,82.62,83.64,10630000,83.64 1970-10-19,84.28,84.29,82.81,83.15,9890000,83.15 1970-10-16,84.65,85.21,83.83,84.28,11300000,84.28 1970-10-15,84.19,85.28,83.82,84.65,11250000,84.65 1970-10-14,84.06,84.83,83.42,84.19,9920000,84.19 1970-10-13,84.17,84.70,83.24,84.06,9500000,84.06 1970-10-12,85.05,85.05,83.58,84.17,8570000,84.17 1970-10-09,85.95,86.25,84.54,85.08,13980000,85.08 1970-10-08,86.89,87.37,85.55,85.95,14500000,85.95 1970-10-07,86.85,87.47,85.55,86.89,15610000,86.89 1970-10-06,86.47,87.75,86.04,86.85,20240000,86.85 1970-10-05,85.16,86.99,85.01,86.47,19760000,86.47 1970-10-02,84.32,85.56,84.06,85.16,15420000,85.16 1970-10-01,84.30,84.70,83.46,84.32,9700000,84.32 1970-09-30,83.86,84.99,82.78,84.30,14830000,84.30 1970-09-29,83.91,84.57,83.11,83.86,17880000,83.86 1970-09-28,82.83,84.56,82.61,83.91,14390000,83.91 1970-09-25,81.66,83.60,81.41,82.83,20470000,82.83 1970-09-24,81.91,82.24,80.82,81.66,21340000,81.66 1970-09-23,81.86,83.15,81.52,81.91,16940000,81.91 1970-09-22,81.91,82.24,80.82,81.86,12110000,81.86 1970-09-21,82.62,83.15,81.52,81.91,12540000,81.91 1970-09-18,82.29,83.50,81.77,82.62,15900000,82.62 1970-09-17,81.79,83.09,81.51,82.29,15530000,82.29 1970-09-16,81.36,82.57,80.61,81.79,12090000,81.79 1970-09-15,82.07,82.11,80.75,81.36,9830000,81.36 1970-09-14,82.52,83.13,81.43,82.07,11900000,82.07 1970-09-11,82.30,83.19,81.81,82.52,12140000,82.52 1970-09-10,82.79,82.98,81.62,82.30,11900000,82.30 1970-09-09,83.04,83.78,81.90,82.79,16250000,82.79 1970-09-08,82.83,83.69,81.48,83.04,17110000,83.04 1970-09-04,82.09,83.42,81.79,82.83,15360000,82.83 1970-09-03,80.96,82.63,80.88,82.09,14110000,82.09 1970-09-02,80.95,81.35,79.95,80.96,9710000,80.96 1970-09-01,81.52,81.80,80.43,80.95,10960000,80.95 1970-08-31,81.86,82.33,80.95,81.52,10740000,81.52 1970-08-28,81.08,82.47,80.69,81.86,13820000,81.86 1970-08-27,81.21,81.91,80.13,81.08,12440000,81.08 1970-08-26,81.12,82.26,80.60,81.21,15970000,81.21 1970-08-25,80.99,81.81,79.69,81.12,17520000,81.12 1970-08-24,79.41,81.62,79.41,80.99,18910000,80.99 1970-08-21,77.84,79.60,77.46,79.24,13420000,79.24 1970-08-20,76.96,77.99,76.30,77.84,10170000,77.84 1970-08-19,76.20,77.58,76.01,76.96,9870000,76.96 1970-08-18,75.33,76.79,75.30,76.20,9500000,76.20 1970-08-17,75.18,75.79,74.52,75.33,6940000,75.33 1970-08-14,74.76,75.74,74.39,75.18,7850000,75.18 1970-08-13,75.42,75.69,74.13,74.76,8640000,74.76 1970-08-12,75.82,76.24,75.04,75.42,7440000,75.42 1970-08-11,76.20,76.33,75.16,75.82,7330000,75.82 1970-08-10,77.28,77.40,75.72,76.20,7580000,76.20 1970-08-07,77.08,78.09,76.46,77.28,9370000,77.28 1970-08-06,77.18,77.68,76.39,77.08,7560000,77.08 1970-08-05,77.19,77.86,76.59,77.18,7660000,77.18 1970-08-04,77.02,77.56,76.12,77.19,8310000,77.19 1970-08-03,78.05,78.24,76.56,77.02,7650000,77.02 1970-07-31,78.07,79.03,77.44,78.05,11640000,78.05 1970-07-30,78.04,78.66,77.36,78.07,10430000,78.07 1970-07-29,77.77,78.81,77.28,78.04,12580000,78.04 1970-07-28,77.65,78.35,76.96,77.77,9040000,77.77 1970-07-27,77.82,78.27,77.07,77.65,7460000,77.65 1970-07-24,78.00,78.48,76.96,77.82,9520000,77.82 1970-07-23,77.03,78.51,76.46,78.00,12460000,78.00 1970-07-22,76.98,78.20,76.22,77.03,12460000,77.03 1970-07-21,77.79,77.94,76.39,76.98,9940000,76.98 1970-07-20,77.69,78.72,77.04,77.79,11660000,77.79 1970-07-17,76.37,78.23,76.37,77.69,13870000,77.69 1970-07-16,75.23,77.09,75.12,76.34,12200000,76.34 1970-07-15,74.42,75.68,74.06,75.23,8860000,75.23 1970-07-14,74.55,75.04,73.78,74.42,7360000,74.42 1970-07-13,74.45,75.37,73.83,74.55,7450000,74.55 1970-07-10,74.06,75.21,73.49,74.45,10160000,74.45 1970-07-09,73.00,74.77,72.88,74.06,12820000,74.06 1970-07-08,71.23,73.30,70.99,73.00,10970000,73.00 1970-07-07,71.78,72.32,70.69,71.23,10470000,71.23 1970-07-06,72.92,73.12,71.38,71.78,9340000,71.78 1970-07-02,72.94,73.92,72.43,72.92,8440000,72.92 1970-07-01,72.72,73.66,72.11,72.94,8610000,72.94 1970-06-30,72.89,73.89,72.25,72.72,9280000,72.72 1970-06-29,73.47,73.86,72.34,72.89,8770000,72.89 1970-06-26,74.02,74.68,73.09,73.47,9160000,73.47 1970-06-25,73.97,74.93,73.30,74.02,8200000,74.02 1970-06-24,74.76,75.42,73.40,73.97,12630000,73.97 1970-06-23,76.64,76.83,74.52,74.76,10790000,74.76 1970-06-22,77.05,77.43,75.61,76.64,8700000,76.64 1970-06-19,76.51,78.05,76.31,77.05,10980000,77.05 1970-06-18,76.00,77.17,74.99,76.51,8870000,76.51 1970-06-17,76.15,78.04,75.63,76.00,9870000,76.00 1970-06-16,74.58,76.76,74.21,76.15,11330000,76.15 1970-06-15,73.88,75.27,73.67,74.58,6920000,74.58 1970-06-12,74.45,74.84,73.25,73.88,8890000,73.88 1970-06-11,75.48,75.52,73.96,74.45,7770000,74.45 1970-06-10,76.25,76.62,74.92,75.48,7240000,75.48 1970-06-09,76.29,79.96,75.58,76.25,7050000,76.25 1970-06-08,76.17,77.37,75.30,76.29,8040000,76.29 1970-06-05,77.36,77.48,75.25,76.17,12450000,76.17 1970-06-04,78.52,79.42,76.99,77.36,14380000,77.36 1970-06-03,77.84,79.22,76.97,78.52,16600000,78.52 1970-06-02,77.84,78.73,76.51,77.84,13480000,77.84 1970-06-01,76.55,78.40,75.84,77.84,15020000,77.84 1970-05-29,74.61,76.92,73.53,76.55,14630000,76.55 1970-05-28,72.77,75.44,72.59,74.61,18910000,74.61 1970-05-27,69.37,73.22,69.37,72.77,17460000,72.77 1970-05-26,70.25,71.17,68.61,69.29,17030000,69.29 1970-05-25,72.16,72.16,69.92,70.25,12660000,70.25 1970-05-22,72.16,73.42,71.42,72.25,12170000,72.25 1970-05-21,73.51,73.51,70.94,72.16,16710000,72.16 1970-05-20,75.35,75.35,73.25,73.52,13020000,73.52 1970-05-19,76.96,77.20,75.21,75.46,9480000,75.46 1970-05-18,76.90,77.68,76.07,76.96,8280000,76.96 1970-05-15,75.44,77.42,74.59,76.90,14570000,76.90 1970-05-14,76.53,76.64,74.03,75.44,13920000,75.44 1970-05-13,77.75,77.75,75.92,76.53,10720000,76.53 1970-05-12,78.60,79.15,77.06,77.85,10850000,77.85 1970-05-11,79.44,79.72,78.29,78.60,6650000,78.60 1970-05-08,79.83,80.15,78.71,79.44,6930000,79.44 1970-05-07,79.47,80.60,78.89,79.83,9530000,79.83 1970-05-06,78.60,80.91,78.23,79.47,14380000,79.47 1970-05-05,79.37,79.83,78.02,78.60,10580000,78.60 1970-05-04,81.28,81.28,78.85,79.37,11450000,79.37 1970-05-01,81.52,82.32,80.27,81.44,8290000,81.44 1970-04-30,81.81,82.57,80.76,81.52,9880000,81.52 1970-04-29,80.27,83.23,79.31,81.81,15800000,81.81 1970-04-28,81.46,82.16,79.86,80.27,12620000,80.27 1970-04-27,82.77,83.08,81.08,81.46,10240000,81.46 1970-04-24,83.04,83.62,81.96,82.77,10410000,82.77 1970-04-23,84.27,84.30,82.61,83.04,11050000,83.04 1970-04-22,85.38,85.51,83.84,84.27,10780000,84.27 1970-04-21,85.83,86.54,84.99,85.38,8490000,85.38 1970-04-20,85.67,86.36,84.99,85.83,8280000,85.83 1970-04-17,85.88,86.36,84.75,85.67,10990000,85.67 1970-04-16,86.73,87.13,85.51,85.88,10250000,85.88 1970-04-15,86.89,87.71,86.53,86.73,9410000,86.73 1970-04-14,87.64,87.73,86.01,86.89,10840000,86.89 1970-04-13,88.24,88.67,87.15,87.64,8810000,87.64 1970-04-10,88.53,89.14,87.82,88.24,10020000,88.24 1970-04-09,88.49,89.32,87.96,88.53,9060000,88.53 1970-04-08,88.52,89.09,87.83,88.49,9070000,88.49 1970-04-07,88.76,89.31,87.94,88.52,8490000,88.52 1970-04-06,89.39,89.61,88.15,88.76,8380000,88.76 1970-04-03,89.79,90.16,88.81,89.39,9920000,89.39 1970-04-02,90.07,90.70,89.28,89.79,10520000,89.79 1970-04-01,89.63,90.62,89.30,90.07,9810000,90.07 1970-03-31,89.63,90.17,88.85,89.63,8370000,89.63 1970-03-30,89.92,90.41,88.91,89.63,9600000,89.63 1970-03-26,89.77,90.65,89.18,89.92,11350000,89.92 1970-03-25,88.11,91.07,88.11,89.77,17500000,89.77 1970-03-24,86.99,88.43,86.90,87.98,8840000,87.98 1970-03-23,87.06,87.64,86.19,86.99,7330000,86.99 1970-03-20,87.42,87.77,86.43,87.06,7910000,87.06 1970-03-19,87.54,88.20,86.88,87.42,8930000,87.42 1970-03-18,87.29,88.28,86.93,87.54,9790000,87.54 1970-03-17,86.91,87.86,86.36,87.29,9090000,87.29 1970-03-16,87.86,87.97,86.39,86.91,8910000,86.91 1970-03-13,88.33,89.43,87.29,87.86,9560000,87.86 1970-03-12,88.69,89.09,87.68,88.33,9140000,88.33 1970-03-11,88.75,89.58,88.11,88.69,9180000,88.69 1970-03-10,88.51,89.41,87.89,88.75,9450000,88.75 1970-03-09,89.43,89.43,87.94,88.51,9760000,88.51 1970-03-06,90.00,90.36,88.84,89.44,10980000,89.44 1970-03-05,90.04,90.99,89.38,90.00,11370000,90.00 1970-03-04,90.23,91.05,89.32,90.04,11850000,90.04 1970-03-03,89.71,90.67,88.96,90.23,11700000,90.23 1970-03-02,89.50,90.80,88.92,89.71,12270000,89.71 1970-02-27,88.90,90.33,88.42,89.50,12890000,89.50 1970-02-26,89.35,89.63,87.63,88.90,11540000,88.90 1970-02-25,87.99,89.80,87.11,89.35,13210000,89.35 1970-02-24,88.03,88.91,87.28,87.99,10810000,87.99 1970-02-20,87.76,88.74,86.87,88.03,10790000,88.03 1970-02-19,87.44,88.70,86.94,87.76,12890000,87.76 1970-02-18,86.37,88.07,86.19,87.44,11950000,87.44 1970-02-17,86.47,87.08,85.57,86.37,10140000,86.37 1970-02-16,86.54,87.30,85.80,86.47,19780000,86.47 1970-02-13,86.73,87.30,85.71,86.54,11060000,86.54 1970-02-12,86.94,87.54,85.93,86.73,10010000,86.73 1970-02-11,86.10,87.38,85.30,86.94,12260000,86.94 1970-02-10,87.01,87.40,85.58,86.10,10110000,86.10 1970-02-09,86.33,87.85,86.16,87.01,10830000,87.01 1970-02-06,85.90,86.88,85.23,86.33,10150000,86.33 1970-02-05,86.24,86.62,84.95,85.90,9430000,85.90 1970-02-04,86.77,87.66,85.59,86.24,11040000,86.24 1970-02-03,85.75,87.54,84.64,86.77,16050000,86.77 1970-02-02,85.02,86.76,84.76,85.75,13440000,85.75 1970-01-30,85.69,86.33,84.42,85.02,12320000,85.02 1970-01-29,86.79,87.09,85.02,85.69,12210000,85.69 1970-01-28,87.62,88.24,86.44,86.79,10510000,86.79 1970-01-27,88.17,88.54,86.92,87.62,9630000,87.62 1970-01-26,89.23,89.23,87.49,88.17,10670000,88.17 1970-01-23,90.04,90.45,88.74,89.37,11000000,89.37 1970-01-22,89.95,90.80,89.20,90.04,11050000,90.04 1970-01-21,89.83,90.61,89.20,89.95,9880000,89.95 1970-01-20,89.65,90.45,88.64,89.83,11050000,89.83 1970-01-19,90.72,90.72,89.14,89.65,9500000,89.65 1970-01-16,91.68,92.49,90.36,90.92,11940000,90.92 1970-01-15,91.65,92.35,90.73,91.68,11120000,91.68 1970-01-14,91.92,92.40,90.88,91.65,10380000,91.65 1970-01-13,91.70,92.61,90.99,91.92,9870000,91.92 1970-01-12,92.40,92.67,91.20,91.70,8900000,91.70 1970-01-09,92.68,93.25,91.82,92.40,9380000,92.40 1970-01-08,92.63,93.47,91.99,92.68,10670000,92.68 1970-01-07,92.82,93.38,91.93,92.63,10010000,92.63 1970-01-06,93.46,93.81,92.13,92.82,11460000,92.82 1970-01-05,93.00,94.25,92.53,93.46,11490000,93.46 1970-01-02,92.06,93.54,91.79,93.00,8050000,93.00 1969-12-31,91.60,92.94,91.15,92.06,19380000,92.06 1969-12-30,91.25,92.20,90.47,91.60,15790000,91.60 1969-12-29,91.89,92.49,90.66,91.25,12500000,91.25 1969-12-26,91.18,92.30,90.94,91.89,6750000,91.89 1969-12-24,90.23,91.89,89.93,91.18,11670000,91.18 1969-12-23,90.58,91.13,89.40,90.23,13890000,90.23 1969-12-22,91.38,92.03,90.10,90.58,12680000,90.58 1969-12-19,90.61,92.34,90.33,91.38,15420000,91.38 1969-12-18,89.20,91.15,88.62,90.61,15950000,90.61 1969-12-17,89.72,90.32,88.94,89.20,12840000,89.20 1969-12-16,90.54,91.05,89.23,89.72,11880000,89.72 1969-12-15,90.81,91.42,89.96,90.54,11100000,90.54 1969-12-12,90.52,91.67,90.05,90.81,11630000,90.81 1969-12-11,90.48,91.37,89.74,90.52,10430000,90.52 1969-12-10,90.55,91.22,89.33,90.48,12590000,90.48 1969-12-09,90.84,91.79,89.93,90.55,12290000,90.55 1969-12-08,91.73,92.05,90.29,90.84,9990000,90.84 1969-12-05,91.95,92.91,91.14,91.73,11150000,91.73 1969-12-04,91.65,92.45,90.36,91.95,13230000,91.95 1969-12-03,92.65,93.05,91.25,91.65,11300000,91.65 1969-12-02,93.22,93.54,91.95,92.65,9940000,92.65 1969-12-01,93.81,94.47,92.78,93.22,9950000,93.22 1969-11-28,93.27,94.41,92.88,93.81,8550000,93.81 1969-11-26,92.94,93.85,92.24,93.27,10630000,93.27 1969-11-25,93.24,94.17,92.38,92.94,11560000,92.94 1969-11-24,94.32,94.43,92.63,93.24,10940000,93.24 1969-11-21,94.91,95.34,93.87,94.32,9840000,94.32 1969-11-20,95.90,95.94,94.12,94.91,12010000,94.91 1969-11-19,96.39,96.95,95.36,95.90,11240000,95.90 1969-11-18,96.41,97.00,95.57,96.39,11010000,96.39 1969-11-17,97.07,97.36,95.82,96.41,10120000,96.41 1969-11-14,97.42,97.44,96.36,97.07,10580000,97.07 1969-11-13,97.89,98.34,96.54,97.42,12090000,97.42 1969-11-12,98.07,98.72,97.28,97.89,12480000,97.89 1969-11-11,98.33,98.79,97.45,98.07,10080000,98.07 1969-11-10,98.26,99.23,97.65,98.33,12490000,98.33 1969-11-07,97.67,99.01,97.18,98.26,13280000,98.26 1969-11-06,97.64,98.31,96.80,97.67,11110000,97.67 1969-11-05,97.21,98.39,96.75,97.64,12110000,97.64 1969-11-04,97.15,97.82,95.84,97.21,12340000,97.21 1969-11-03,97.12,97.82,96.19,97.15,11140000,97.15 1969-10-31,96.93,98.03,96.33,97.12,13100000,97.12 1969-10-30,96.81,97.47,95.61,96.93,12820000,96.93 1969-10-29,97.66,97.92,96.26,96.81,12380000,96.81 1969-10-28,97.97,98.55,97.02,97.66,12410000,97.66 1969-10-27,98.12,98.78,97.49,97.97,12160000,97.97 1969-10-24,97.46,98.83,96.97,98.12,15430000,98.12 1969-10-23,97.83,98.39,96.46,97.46,14780000,97.46 1969-10-22,97.20,98.61,96.56,97.83,19320000,97.83 1969-10-21,96.46,97.84,95.86,97.20,16460000,97.20 1969-10-20,96.26,97.17,95.29,96.46,13540000,96.46 1969-10-17,96.37,97.24,95.38,96.26,13740000,96.26 1969-10-16,95.72,97.54,95.05,96.37,19500000,96.37 1969-10-15,95.70,96.56,94.65,95.72,15740000,95.72 1969-10-14,94.55,96.53,94.32,95.70,19950000,95.70 1969-10-13,93.56,94.86,93.20,94.55,13620000,94.55 1969-10-10,93.03,94.19,92.60,93.56,12210000,93.56 1969-10-09,92.67,93.55,91.75,93.03,10420000,93.03 1969-10-08,93.09,93.56,92.04,92.67,10370000,92.67 1969-10-07,93.38,94.03,92.59,93.09,10050000,93.09 1969-10-06,93.19,93.99,92.50,93.38,9180000,93.38 1969-10-03,93.24,94.39,92.65,93.19,12410000,93.19 1969-10-02,92.52,93.63,91.66,93.24,11430000,93.24 1969-10-01,93.12,93.51,92.12,92.52,9090000,92.52 1969-09-30,93.41,94.05,92.55,93.12,9180000,93.12 1969-09-29,94.16,94.45,92.62,93.41,10170000,93.41 1969-09-26,94.77,95.23,93.53,94.16,9680000,94.16 1969-09-25,95.50,95.92,94.28,94.77,10690000,94.77 1969-09-24,95.63,96.20,94.75,95.50,11320000,95.50 1969-09-23,95.63,96.62,94.86,95.63,13030000,95.63 1969-09-22,95.19,96.13,94.58,95.63,9280000,95.63 1969-09-19,94.90,95.92,94.35,95.19,12270000,95.19 1969-09-18,94.76,95.53,94.05,94.90,11170000,94.90 1969-09-17,94.95,95.70,94.04,94.76,10980000,94.76 1969-09-16,94.87,95.73,94.06,94.95,11160000,94.95 1969-09-15,94.13,95.61,93.73,94.87,10680000,94.87 1969-09-12,94.22,95.04,93.26,94.13,10800000,94.13 1969-09-11,94.95,95.77,93.72,94.22,12370000,94.22 1969-09-10,93.38,95.35,93.23,94.95,11490000,94.95 1969-09-09,92.70,93.94,91.77,93.38,10980000,93.38 1969-09-08,93.64,93.76,92.35,92.70,8310000,92.70 1969-09-05,94.20,94.51,93.09,93.64,8890000,93.64 1969-09-04,94.98,95.20,93.66,94.20,9380000,94.20 1969-09-03,95.54,96.11,94.38,94.98,8760000,94.98 1969-09-02,95.51,96.31,94.85,95.54,8560000,95.54 1969-08-29,94.89,95.51,94.46,95.51,8850000,95.51 1969-08-28,94.49,95.38,94.04,94.89,7730000,94.89 1969-08-27,94.30,95.16,93.76,94.49,9100000,94.49 1969-08-26,94.93,95.04,93.65,94.30,8910000,94.30 1969-08-25,95.92,96.13,94.52,94.93,8410000,94.93 1969-08-22,95.35,96.43,94.91,95.92,10140000,95.92 1969-08-21,95.07,95.87,94.56,95.35,8420000,95.35 1969-08-20,95.07,95.64,94.25,95.07,9680000,95.07 1969-08-19,94.57,95.18,93.95,95.07,12640000,95.07 1969-08-18,94.00,95.00,93.51,94.57,9420000,94.57 1969-08-15,93.34,94.50,92.92,94.00,10210000,94.00 1969-08-14,92.70,93.87,92.32,93.34,9690000,93.34 1969-08-13,92.63,93.26,91.48,92.70,9910000,92.70 1969-08-12,93.36,93.66,92.19,92.63,7870000,92.63 1969-08-11,93.94,94.24,92.77,93.36,6680000,93.36 1969-08-08,93.99,94.63,93.29,93.94,8760000,93.94 1969-08-07,93.92,94.77,93.17,93.99,9450000,93.99 1969-08-06,93.41,94.76,93.02,93.92,11100000,93.92 1969-08-05,92.99,94.02,92.13,93.41,8940000,93.41 1969-08-04,93.47,94.42,92.29,92.99,10700000,92.99 1969-08-01,91.92,94.19,91.92,93.47,15070000,93.47 1969-07-31,89.96,92.40,89.96,91.83,14160000,91.83 1969-07-30,89.48,90.82,88.04,89.93,15580000,89.93 1969-07-29,90.21,91.56,89.06,89.48,13630000,89.48 1969-07-28,91.91,91.91,89.83,90.21,11800000,90.21 1969-07-25,92.80,93.28,91.54,92.06,9800000,92.06 1969-07-24,93.12,93.87,92.29,92.80,9750000,92.80 1969-07-23,93.52,93.99,92.07,93.12,11680000,93.12 1969-07-22,94.95,95.45,93.15,93.52,9780000,93.52 1969-07-18,95.76,95.84,94.18,94.95,8590000,94.95 1969-07-17,95.18,96.71,95.07,95.76,10450000,95.76 1969-07-16,94.24,95.83,94.22,95.18,10470000,95.18 1969-07-15,94.55,95.00,93.11,94.24,11110000,94.24 1969-07-14,95.77,96.17,94.20,94.55,8310000,94.55 1969-07-11,95.38,96.65,94.81,95.77,11730000,95.77 1969-07-10,96.88,97.04,95.03,95.38,11450000,95.38 1969-07-09,97.63,97.85,96.33,96.88,9320000,96.88 1969-07-08,98.98,98.98,97.15,97.63,9320000,97.63 1969-07-07,99.61,100.33,98.45,99.03,9970000,99.03 1969-07-03,98.94,100.25,98.62,99.61,10110000,99.61 1969-07-02,98.08,99.50,97.81,98.94,11350000,98.94 1969-07-01,97.71,98.66,97.13,98.08,9890000,98.08 1969-06-30,97.33,98.64,96.82,97.71,8640000,97.71 1969-06-27,97.25,98.15,96.65,97.33,9020000,97.33 1969-06-26,97.01,97.91,95.97,97.25,10310000,97.25 1969-06-25,97.32,98.30,96.56,97.01,10490000,97.01 1969-06-24,96.29,98.04,96.29,97.32,11460000,97.32 1969-06-23,96.67,97.17,95.21,96.23,12900000,96.23 1969-06-20,97.24,98.22,96.29,96.67,11360000,96.67 1969-06-19,97.81,98.38,96.61,97.24,11160000,97.24 1969-06-18,97.95,99.20,97.45,97.81,11290000,97.81 1969-06-17,98.32,98.71,96.88,97.95,12210000,97.95 1969-06-16,98.65,99.64,97.91,98.32,10400000,98.32 1969-06-13,98.26,99.51,97.59,98.65,13070000,98.65 1969-06-12,99.05,99.78,97.96,98.26,11790000,98.26 1969-06-11,100.42,100.71,99.02,99.05,13640000,99.05 1969-06-10,101.20,101.76,100.02,100.42,10660000,100.42 1969-06-09,102.12,102.16,100.54,101.20,10650000,101.20 1969-06-06,102.76,103.41,101.68,102.12,12520000,102.12 1969-06-05,102.59,103.45,102.05,102.76,12350000,102.76 1969-06-04,102.63,103.45,102.07,102.59,10840000,102.59 1969-06-03,102.94,103.60,102.09,102.63,11190000,102.63 1969-06-02,103.46,103.75,102.40,102.94,9180000,102.94 1969-05-29,103.26,104.27,102.76,103.46,11770000,103.46 1969-05-28,103.57,103.91,102.29,103.26,11330000,103.26 1969-05-27,104.36,104.68,103.12,103.57,10580000,103.57 1969-05-26,104.59,105.14,103.80,104.36,9030000,104.36 1969-05-23,104.60,105.32,103.78,104.59,10900000,104.59 1969-05-22,104.47,105.66,103.92,104.60,13710000,104.60 1969-05-21,104.04,105.03,103.37,104.47,12100000,104.47 1969-05-20,104.97,105.16,103.56,104.04,10280000,104.04 1969-05-19,105.94,106.15,104.52,104.97,9790000,104.97 1969-05-16,105.85,106.59,105.18,105.94,12280000,105.94 1969-05-15,106.16,106.69,105.08,105.85,11930000,105.85 1969-05-14,105.34,106.74,105.07,106.16,14360000,106.16 1969-05-13,104.89,105.91,104.31,105.34,12910000,105.34 1969-05-12,105.05,105.65,104.12,104.89,10550000,104.89 1969-05-09,105.10,106.01,104.35,105.05,12530000,105.05 1969-05-08,104.67,105.74,104.10,105.10,13050000,105.10 1969-05-07,104.86,105.59,103.83,104.67,14030000,104.67 1969-05-06,104.37,105.50,103.84,104.86,14700000,104.86 1969-05-05,104.00,105.08,103.48,104.37,13300000,104.37 1969-05-02,103.51,104.63,102.98,104.00,13070000,104.00 1969-05-01,103.69,104.59,102.74,103.51,14380000,103.51 1969-04-30,102.79,104.56,102.50,103.69,19350000,103.69 1969-04-29,102.03,103.31,101.51,102.79,14730000,102.79 1969-04-28,101.72,102.65,100.97,102.03,11120000,102.03 1969-04-25,101.27,102.29,100.81,101.72,12480000,101.72 1969-04-24,100.80,101.80,100.21,101.27,11340000,101.27 1969-04-23,100.78,101.77,100.15,100.80,12220000,100.80 1969-04-22,100.56,101.29,99.52,100.78,10250000,100.78 1969-04-21,101.24,101.68,100.11,100.56,10010000,100.56 1969-04-18,100.78,102.09,100.30,101.24,10850000,101.24 1969-04-17,100.63,101.41,99.99,100.78,9360000,100.78 1969-04-16,101.53,101.78,100.16,100.63,9680000,100.63 1969-04-15,101.57,102.15,100.76,101.53,9610000,101.53 1969-04-14,101.65,102.40,101.02,101.57,8990000,101.57 1969-04-11,101.55,102.28,100.97,101.65,10650000,101.65 1969-04-10,101.02,102.22,100.73,101.55,12200000,101.55 1969-04-09,100.14,101.44,99.88,101.02,12530000,101.02 1969-04-08,99.89,101.27,99.35,100.14,9360000,100.14 1969-04-07,100.63,100.63,99.08,99.89,9430000,99.89 1969-04-03,100.78,101.30,99.87,100.68,10300000,100.68 1969-04-02,101.42,101.65,100.61,100.78,10110000,100.78 1969-04-01,101.51,102.45,100.84,101.42,12360000,101.42 1969-03-28,101.10,102.35,100.73,101.51,12430000,101.51 1969-03-27,100.39,101.81,100.03,101.10,11900000,101.10 1969-03-26,99.66,100.86,99.24,100.39,11030000,100.39 1969-03-25,99.50,100.30,98.88,99.66,9820000,99.66 1969-03-24,99.63,100.16,98.85,99.50,8110000,99.50 1969-03-21,99.84,100.37,98.88,99.63,9830000,99.63 1969-03-20,99.21,100.39,98.90,99.84,10260000,99.84 1969-03-19,98.49,99.70,98.03,99.21,9740000,99.21 1969-03-18,98.25,99.41,97.83,98.49,11210000,98.49 1969-03-17,98.00,98.71,97.06,98.25,9150000,98.25 1969-03-14,98.39,98.70,97.40,98.00,8640000,98.00 1969-03-13,99.05,99.35,97.82,98.39,10030000,98.39 1969-03-12,99.32,99.87,98.35,99.05,8720000,99.05 1969-03-11,98.99,100.14,98.58,99.32,9870000,99.32 1969-03-10,98.65,99.47,97.87,98.99,8920000,98.99 1969-03-07,98.70,99.13,97.32,98.65,10830000,98.65 1969-03-06,99.71,99.93,98.11,98.70,9670000,98.70 1969-03-05,99.32,100.48,98.95,99.71,11370000,99.71 1969-03-04,98.38,99.76,98.17,99.32,9320000,99.32 1969-03-03,98.13,99.08,97.61,98.38,8260000,98.38 1969-02-28,98.14,99.02,97.53,98.13,8990000,98.13 1969-02-27,98.45,99.00,97.50,98.14,9670000,98.14 1969-02-26,97.98,99.10,97.36,98.45,9540000,98.45 1969-02-25,98.60,99.65,97.50,97.98,9540000,97.98 1969-02-24,99.79,100.07,98.09,98.60,12730000,98.60 1969-02-20,100.65,101.03,99.29,99.79,10990000,99.79 1969-02-19,101.40,102.07,100.30,100.65,10390000,100.65 1969-02-18,102.27,102.27,100.58,101.40,12490000,101.40 1969-02-17,103.61,104.03,102.04,102.44,11670000,102.44 1969-02-14,103.71,104.37,102.88,103.61,11460000,103.61 1969-02-13,103.63,104.36,102.86,103.71,12010000,103.71 1969-02-12,103.65,104.34,102.98,103.63,11530000,103.63 1969-02-11,103.53,104.61,102.96,103.65,12320000,103.65 1969-02-07,103.54,104.22,102.50,103.53,12780000,103.53 1969-02-06,103.20,104.30,102.55,103.54,12570000,103.54 1969-02-05,102.92,103.84,102.26,103.20,13750000,103.20 1969-02-04,102.89,103.59,102.15,102.92,12550000,102.92 1969-02-03,103.01,103.75,102.04,102.89,12510000,102.89 1969-01-31,102.55,103.64,102.08,103.01,12020000,103.01 1969-01-30,102.51,103.33,101.73,102.55,13010000,102.55 1969-01-29,102.41,103.31,101.69,102.51,11470000,102.51 1969-01-28,102.40,103.30,101.56,102.41,12070000,102.41 1969-01-27,102.38,103.15,101.64,102.40,11020000,102.40 1969-01-24,102.43,103.23,101.71,102.38,12520000,102.38 1969-01-23,101.98,103.21,101.57,102.43,13140000,102.43 1969-01-22,101.63,102.55,101.06,101.98,11480000,101.98 1969-01-21,101.69,102.40,100.88,101.63,10910000,101.63 1969-01-20,102.03,102.60,101.00,101.69,10950000,101.69 1969-01-17,102.18,103.06,101.32,102.03,11590000,102.03 1969-01-16,101.62,103.25,101.27,102.18,13120000,102.18 1969-01-15,101.13,102.48,100.78,101.62,11810000,101.62 1969-01-14,100.44,101.63,99.04,101.13,10700000,101.13 1969-01-13,100.93,101.35,96.63,100.44,11160000,100.44 1969-01-10,101.22,102.14,100.32,100.93,12680000,100.93 1969-01-09,100.80,102.09,100.35,101.22,12100000,101.22 1969-01-08,101.22,102.12,100.14,100.80,13840000,100.80 1969-01-07,102.47,102.68,100.15,101.22,15740000,101.22 1969-01-06,103.99,104.36,101.94,102.47,12720000,102.47 1969-01-03,103.93,104.87,103.17,103.99,12750000,103.99 1969-01-02,103.86,104.85,103.21,103.93,9800000,103.93 1968-12-31,103.80,104.61,102.98,103.86,13130000,103.86 1968-12-30,104.74,104.99,103.09,103.80,12080000,103.80 1968-12-27,105.15,105.87,104.20,104.74,11200000,104.74 1968-12-26,105.04,106.03,104.29,105.15,9670000,105.15 1968-12-24,105.21,105.95,104.37,105.04,11540000,105.04 1968-12-23,106.34,106.68,104.61,105.21,12970000,105.21 1968-12-20,106.97,107.98,105.73,106.34,15910000,106.34 1968-12-19,106.66,107.67,105.10,106.97,19630000,106.97 1968-12-17,107.10,107.65,105.86,106.66,14700000,106.66 1968-12-16,107.58,108.40,106.40,107.10,15950000,107.10 1968-12-13,107.32,108.50,106.56,107.58,16740000,107.58 1968-12-12,107.39,108.43,106.33,107.32,18160000,107.32 1968-12-10,107.66,108.33,106.68,107.39,14500000,107.39 1968-12-09,107.93,108.77,106.89,107.66,15800000,107.66 1968-12-06,107.67,108.91,106.85,107.93,15320000,107.93 1968-12-05,108.02,108.90,106.71,107.67,19330000,107.67 1968-12-03,108.12,108.74,107.02,108.02,15460000,108.02 1968-12-02,108.37,109.37,107.15,108.12,15390000,108.12 1968-11-29,107.76,109.09,107.32,108.37,14390000,108.37 1968-11-27,107.26,108.55,106.59,107.76,16550000,107.76 1968-11-26,106.48,107.93,106.11,107.26,16360000,107.26 1968-11-25,106.30,107.29,105.47,106.48,14490000,106.48 1968-11-22,105.97,106.89,105.21,106.30,15420000,106.30 1968-11-21,106.14,106.77,104.85,105.97,18320000,105.97 1968-11-19,105.92,106.84,105.06,106.14,15120000,106.14 1968-11-18,105.78,106.74,105.05,105.92,14390000,105.92 1968-11-15,105.20,106.44,104.61,105.78,15040000,105.78 1968-11-14,105.13,106.01,104.34,105.20,14900000,105.20 1968-11-13,104.62,105.76,104.08,105.13,15660000,105.13 1968-11-12,103.95,105.28,103.51,104.62,17250000,104.62 1968-11-08,103.50,104.59,102.96,103.95,14250000,103.95 1968-11-07,103.27,104.47,102.31,103.50,11660000,103.50 1968-11-06,103.10,104.41,102.45,103.27,12640000,103.27 1968-11-04,103.06,103.69,101.85,103.10,10930000,103.10 1968-11-01,103.41,104.30,102.36,103.06,14480000,103.06 1968-10-31,103.30,104.57,102.43,103.41,17650000,103.41 1968-10-29,103.90,104.50,102.65,103.30,12340000,103.30 1968-10-28,104.20,104.89,103.16,103.90,11740000,103.90 1968-10-25,103.84,104.81,103.14,104.20,14150000,104.20 1968-10-24,104.57,105.15,103.15,103.84,18300000,103.84 1968-10-22,104.99,105.48,103.84,104.57,13970000,104.57 1968-10-21,104.82,105.78,104.09,104.99,14380000,104.99 1968-10-18,104.01,105.34,103.54,104.82,15130000,104.82 1968-10-17,103.81,105.01,103.81,104.01,21060000,104.01 1968-10-15,103.32,104.25,102.66,103.53,13410000,103.53 1968-10-14,103.18,104.03,102.48,103.32,11980000,103.32 1968-10-11,103.29,103.90,102.39,103.18,12650000,103.18 1968-10-10,103.74,104.30,102.61,103.29,17000000,103.29 1968-10-08,103.70,104.45,102.84,103.74,14000000,103.74 1968-10-07,103.71,104.40,102.93,103.70,12420000,103.70 1968-10-04,103.22,104.35,102.65,103.71,15350000,103.71 1968-10-03,102.86,104.13,102.34,103.22,21110000,103.22 1968-10-01,102.67,103.58,101.80,102.86,15560000,102.86 1968-09-30,102.31,103.29,101.71,102.67,13610000,102.67 1968-09-27,102.36,103.07,101.36,102.31,13860000,102.31 1968-09-26,102.59,103.63,101.59,102.36,18950000,102.36 1968-09-24,102.24,103.21,101.59,102.59,15210000,102.59 1968-09-23,101.66,102.82,101.20,102.24,11550000,102.24 1968-09-20,101.59,102.37,100.81,101.66,14190000,101.66 1968-09-19,101.50,102.53,100.84,101.59,17910000,101.59 1968-09-17,101.24,102.18,100.64,101.50,13920000,101.50 1968-09-16,100.86,102.01,100.33,101.24,13260000,101.24 1968-09-13,100.52,101.53,99.89,100.86,13070000,100.86 1968-09-12,100.73,101.40,99.70,100.52,14630000,100.52 1968-09-10,101.23,101.81,100.12,100.73,11430000,100.73 1968-09-09,101.20,102.09,100.47,101.23,11890000,101.23 1968-09-06,100.74,101.88,100.23,101.20,13180000,101.20 1968-09-05,100.02,101.34,99.63,100.74,12980000,100.74 1968-09-04,99.32,100.49,98.95,100.02,10040000,100.02 1968-09-03,98.86,99.89,98.31,99.32,8620000,99.32 1968-08-30,98.74,99.52,98.20,98.86,8190000,98.86 1968-08-29,98.81,99.49,97.90,98.74,10940000,98.74 1968-08-27,98.94,99.61,98.16,98.81,9710000,98.81 1968-08-26,98.69,99.67,98.29,98.94,9740000,98.94 1968-08-23,98.70,99.57,97.71,98.69,9890000,98.69 1968-08-22,98.96,99.58,97.71,98.70,15140000,98.70 1968-08-20,99.00,99.65,98.08,98.96,10640000,98.96 1968-08-19,98.68,99.64,98.16,99.00,9900000,99.00 1968-08-16,98.07,99.21,97.62,98.68,9940000,98.68 1968-08-15,98.53,99.36,97.48,98.07,12710000,98.07 1968-08-13,98.01,99.20,97.68,98.53,12730000,98.53 1968-08-12,97.01,98.49,96.72,98.01,10420000,98.01 1968-08-09,97.04,97.56,96.11,97.01,8390000,97.01 1968-08-08,97.25,98.32,96.58,97.04,12920000,97.04 1968-08-06,96.85,97.82,96.42,97.25,9620000,97.25 1968-08-05,96.63,97.51,95.95,96.85,8850000,96.85 1968-08-02,97.28,97.47,95.79,96.63,9860000,96.63 1968-08-01,97.74,98.82,96.78,97.28,14380000,97.28 1968-07-30,97.65,98.62,96.84,97.74,10250000,97.74 1968-07-29,98.34,98.78,96.89,97.65,10940000,97.65 1968-07-26,97.94,99.14,97.22,98.34,11690000,98.34 1968-07-25,99.21,100.07,97.43,97.94,16140000,97.94 1968-07-23,99.33,99.93,97.89,99.21,13570000,99.21 1968-07-22,100.46,100.88,98.51,99.33,13530000,99.33 1968-07-19,101.44,101.82,99.80,100.46,14620000,100.46 1968-07-18,101.70,102.65,100.49,101.44,17420000,101.44 1968-07-16,102.26,102.72,100.97,101.70,13380000,101.70 1968-07-15,102.34,103.15,101.44,102.26,13390000,102.26 1968-07-12,102.39,103.24,101.39,102.34,14810000,102.34 1968-07-11,102.23,103.67,101.41,102.39,20290000,102.39 1968-07-09,101.94,102.93,101.19,102.23,16540000,102.23 1968-07-08,100.91,102.76,100.72,101.94,16860000,101.94 1968-07-03,99.74,101.36,99.60,100.91,14390000,100.91 1968-07-02,99.40,100.60,98.60,99.74,13350000,99.74 1968-07-01,99.58,100.33,98.77,99.40,11280000,99.40 1968-06-28,99.98,100.63,98.91,99.58,12040000,99.58 1968-06-27,100.08,101.01,99.11,99.98,15370000,99.98 1968-06-25,100.39,101.10,99.28,100.08,13200000,100.08 1968-06-24,100.66,101.48,99.66,100.39,12320000,100.39 1968-06-21,101.51,101.59,99.80,100.66,13450000,100.66 1968-06-20,99.99,101.60,99.52,101.51,16290000,101.51 1968-06-18,100.13,101.09,99.43,99.99,13630000,99.99 1968-06-17,101.13,101.71,99.43,100.13,12570000,100.13 1968-06-14,101.25,101.82,99.98,101.13,14690000,101.13 1968-06-13,101.66,102.84,100.55,101.25,21350000,101.25 1968-06-11,101.41,102.40,100.74,101.66,15700000,101.66 1968-06-10,101.27,102.25,100.42,101.41,14640000,101.41 1968-06-07,100.65,101.89,100.24,101.27,17320000,101.27 1968-06-06,99.89,101.59,99.50,100.65,16130000,100.65 1968-06-05,100.38,101.13,99.26,99.89,15590000,99.89 1968-06-04,99.99,101.26,99.32,100.38,18030000,100.38 1968-06-03,98.72,100.62,98.72,99.99,14970000,99.99 1968-05-31,97.92,99.40,97.66,98.68,13090000,98.68 1968-05-29,97.62,98.74,97.01,97.92,14100000,97.92 1968-05-28,96.99,98.20,96.41,97.62,13850000,97.62 1968-05-27,97.15,97.81,96.29,96.99,12720000,96.99 1968-05-24,96.97,97.73,96.21,97.15,13300000,97.15 1968-05-23,97.18,97.79,96.38,96.97,12840000,96.97 1968-05-22,96.93,98.17,96.47,97.18,14200000,97.18 1968-05-21,96.45,97.52,95.92,96.93,13160000,96.93 1968-05-20,96.90,97.41,95.80,96.45,11180000,96.45 1968-05-17,97.60,97.81,96.11,96.90,11830000,96.90 1968-05-16,98.07,98.69,97.05,97.60,13030000,97.60 1968-05-15,98.12,98.79,97.32,98.07,13180000,98.07 1968-05-14,98.19,98.85,97.33,98.12,13160000,98.12 1968-05-13,98.50,99.10,97.52,98.19,11860000,98.19 1968-05-10,98.39,99.30,97.76,98.50,11700000,98.50 1968-05-09,98.91,99.47,97.68,98.39,12890000,98.39 1968-05-08,98.90,99.74,98.25,98.91,13120000,98.91 1968-05-07,98.35,99.59,97.86,98.90,13920000,98.90 1968-05-06,98.66,99.11,97.27,98.35,12160000,98.35 1968-05-03,98.59,100.19,97.98,98.66,17990000,98.66 1968-05-02,97.97,99.18,97.53,98.59,14260000,98.59 1968-05-01,97.46,98.61,96.84,97.97,14440000,97.97 1968-04-30,97.97,98.17,96.58,97.46,14380000,97.46 1968-04-29,97.21,98.61,96.81,97.97,12030000,97.97 1968-04-26,96.62,97.83,96.22,97.21,13500000,97.21 1968-04-25,96.92,97.48,95.68,96.62,14430000,96.62 1968-04-24,96.62,97.81,95.98,96.92,14810000,96.92 1968-04-23,95.68,97.48,95.68,96.62,14010000,96.62 1968-04-22,95.85,96.07,94.22,95.32,11720000,95.32 1968-04-19,97.08,97.08,95.15,95.85,14560000,95.85 1968-04-18,96.81,97.89,96.12,97.08,15890000,97.08 1968-04-17,96.62,97.40,95.76,96.81,14090000,96.81 1968-04-16,96.59,97.54,95.72,96.62,15680000,96.62 1968-04-15,96.53,97.36,95.33,96.59,14220000,96.59 1968-04-11,95.67,96.93,94.81,96.53,14230000,96.53 1968-04-10,94.95,97.11,94.74,95.67,20410000,95.67 1968-04-08,93.29,95.45,93.11,94.95,13010000,94.95 1968-04-05,93.84,94.51,92.67,93.29,12570000,93.29 1968-04-04,93.47,94.59,92.63,93.84,14340000,93.84 1968-04-03,92.64,95.13,92.24,93.47,19290000,93.47 1968-04-02,92.48,93.44,91.39,92.64,14520000,92.64 1968-04-01,91.11,93.55,91.11,92.48,17730000,92.48 1968-03-29,89.57,90.92,89.21,90.20,9000000,90.20 1968-03-28,89.66,90.40,89.05,89.57,8000000,89.57 1968-03-27,88.93,90.20,88.88,89.66,8970000,89.66 1968-03-26,88.33,89.50,88.10,88.93,8670000,88.93 1968-03-25,88.42,88.88,87.65,88.33,6700000,88.33 1968-03-22,88.33,89.14,87.50,88.42,9900000,88.42 1968-03-21,88.98,89.48,88.05,88.33,8580000,88.33 1968-03-20,88.99,89.65,88.48,88.98,7390000,88.98 1968-03-19,89.59,90.05,88.61,88.99,7410000,88.99 1968-03-18,89.11,91.09,89.11,89.59,10800000,89.59 1968-03-15,88.32,89.75,87.61,89.10,11210000,89.10 1968-03-14,89.75,89.75,87.81,88.32,11640000,88.32 1968-03-13,90.23,90.71,89.40,90.03,8990000,90.03 1968-03-12,90.13,90.78,89.39,90.23,9250000,90.23 1968-03-11,89.03,90.56,88.81,90.13,9520000,90.13 1968-03-08,89.10,89.57,88.23,89.03,7410000,89.03 1968-03-07,89.26,89.98,88.44,89.10,8630000,89.10 1968-03-06,87.72,89.76,87.64,89.26,9900000,89.26 1968-03-05,87.92,88.72,86.99,87.72,11440000,87.72 1968-03-04,89.11,89.33,87.52,87.92,10590000,87.92 1968-03-01,89.36,89.82,88.58,89.11,8610000,89.11 1968-02-29,90.08,90.24,88.93,89.36,7700000,89.36 1968-02-28,90.53,91.19,89.71,90.08,8020000,90.08 1968-02-27,90.18,90.91,89.56,90.53,7600000,90.53 1968-02-26,90.89,91.08,89.67,90.18,7810000,90.18 1968-02-23,91.24,91.80,90.28,90.89,8810000,90.89 1968-02-21,91.24,91.87,90.54,91.24,9170000,91.24 1968-02-20,90.31,91.34,89.95,91.24,8800000,91.24 1968-02-19,89.96,90.87,89.42,90.31,7270000,90.31 1968-02-16,90.30,90.62,89.28,89.96,9070000,89.96 1968-02-15,90.30,90.30,90.30,90.30,9770000,90.30 1968-02-14,89.07,90.60,88.66,90.14,11390000,90.14 1968-02-13,89.86,90.46,86.73,89.07,10830000,89.07 1968-02-09,90.90,91.00,89.23,89.86,11850000,89.86 1968-02-08,92.06,92.40,90.60,90.90,9660000,90.90 1968-02-07,91.90,92.74,91.48,92.06,8380000,92.06 1968-02-06,91.87,92.52,91.15,91.90,8560000,91.90 1968-02-05,92.27,92.72,91.24,91.87,8980000,91.87 1968-02-02,92.56,93.44,91.69,92.27,10120000,92.27 1968-02-01,92.24,93.14,91.57,92.56,10590000,92.56 1968-01-31,92.89,93.26,91.27,92.24,9410000,92.24 1968-01-30,93.35,93.71,92.18,92.89,10110000,92.89 1968-01-29,93.45,94.38,92.71,93.35,9950000,93.35 1968-01-26,93.30,94.34,92.77,93.45,9980000,93.45 1968-01-25,93.17,94.11,91.96,93.30,12410000,93.30 1968-01-24,93.66,94.12,92.45,93.17,10570000,93.17 1968-01-23,94.03,94.66,92.88,93.66,11030000,93.66 1968-01-22,95.24,95.40,93.55,94.03,10630000,94.03 1968-01-19,95.56,96.22,94.60,95.24,11950000,95.24 1968-01-18,95.64,96.66,95.01,95.56,13840000,95.56 1968-01-17,95.82,96.41,94.78,95.64,12910000,95.64 1968-01-16,96.42,96.91,95.32,95.82,12340000,95.82 1968-01-15,96.72,97.46,95.85,96.42,12640000,96.42 1968-01-12,96.62,97.44,95.87,96.72,13080000,96.72 1968-01-11,96.52,97.82,95.88,96.62,13220000,96.62 1968-01-10,96.50,97.26,95.66,96.52,11670000,96.52 1968-01-09,96.62,97.84,95.89,96.50,13720000,96.50 1968-01-08,95.94,97.40,95.54,96.62,14260000,96.62 1968-01-05,95.36,96.66,94.97,95.94,11880000,95.94 1968-01-04,95.67,96.23,94.31,95.36,13440000,95.36 1968-01-03,96.11,96.95,95.04,95.67,12650000,95.67 1968-01-02,96.47,97.33,95.31,96.11,11080000,96.11 1967-12-29,95.89,96.90,95.85,96.47,14950000,96.47 1967-12-28,95.91,96.65,94.91,95.89,12530000,95.89 1967-12-27,95.26,96.42,94.82,95.91,12690000,95.91 1967-12-26,95.20,96.02,94.61,95.26,9150000,95.26 1967-12-22,95.38,96.11,94.61,95.20,9570000,95.20 1967-12-21,95.15,96.25,94.69,95.38,11010000,95.38 1967-12-20,94.63,95.75,94.17,95.15,11390000,95.15 1967-12-19,94.77,95.41,94.00,94.63,10610000,94.63 1967-12-18,95.03,95.88,94.17,94.77,10320000,94.77 1967-12-15,95.47,96.20,94.51,95.03,11530000,95.03 1967-12-14,95.34,96.35,94.85,95.47,12310000,95.47 1967-12-13,95.01,96.00,94.58,95.34,12480000,95.34 1967-12-12,95.12,95.78,94.34,95.01,10860000,95.01 1967-12-11,95.42,95.99,94.50,95.12,10500000,95.12 1967-12-08,95.53,96.25,94.78,95.42,10710000,95.42 1967-12-07,95.64,96.67,95.04,95.53,12490000,95.53 1967-12-06,95.23,96.16,94.10,95.64,11940000,95.64 1967-12-05,95.10,96.27,94.52,95.23,12940000,95.23 1967-12-04,94.50,95.68,94.09,95.10,11740000,95.10 1967-12-01,94.00,94.95,93.41,94.50,9740000,94.50 1967-11-30,94.47,94.94,93.49,94.00,8860000,94.00 1967-11-29,94.49,95.51,93.85,94.47,11400000,94.47 1967-11-28,94.17,95.08,93.57,94.49,11040000,94.49 1967-11-27,93.90,94.80,93.32,94.17,10040000,94.17 1967-11-24,93.65,94.46,92.74,93.90,9470000,93.90 1967-11-22,93.10,94.41,92.70,93.65,12180000,93.65 1967-11-21,91.65,93.71,91.64,93.10,12300000,93.10 1967-11-20,92.38,92.38,90.09,91.65,12750000,91.65 1967-11-17,92.60,93.62,92.02,92.82,10050000,92.82 1967-11-16,91.76,93.28,91.50,92.60,10570000,92.60 1967-11-15,91.39,92.25,90.44,91.76,10000000,91.76 1967-11-14,91.97,92.49,90.81,91.39,10350000,91.39 1967-11-13,92.21,93.23,91.46,91.97,10130000,91.97 1967-11-10,91.59,92.84,91.29,92.21,9960000,92.21 1967-11-09,91.14,92.25,90.61,91.59,8890000,91.59 1967-11-08,91.48,93.07,90.80,91.14,12630000,91.14 1967-11-06,91.78,92.23,90.39,91.48,10320000,91.48 1967-11-03,92.34,92.90,91.33,91.78,8800000,91.78 1967-11-02,92.71,93.69,91.85,92.34,10760000,92.34 1967-11-01,93.30,94.21,92.45,92.71,10930000,92.71 1967-10-31,94.79,95.25,93.29,93.30,12020000,93.30 1967-10-30,94.96,95.67,94.14,94.79,10250000,94.79 1967-10-27,94.94,95.79,94.31,94.96,9880000,94.96 1967-10-26,94.52,95.56,93.99,94.94,9920000,94.94 1967-10-25,94.42,95.18,93.47,94.52,10300000,94.52 1967-10-24,94.96,95.98,94.05,94.42,11110000,94.42 1967-10-23,95.38,95.69,93.92,94.96,9680000,94.96 1967-10-20,95.43,96.12,94.62,95.38,9510000,95.38 1967-10-19,95.25,96.46,94.86,95.43,11620000,95.43 1967-10-18,95.00,95.82,94.34,95.25,10500000,95.25 1967-10-17,95.25,95.92,94.19,95.00,10290000,95.00 1967-10-16,96.00,96.55,94.85,95.25,9080000,95.25 1967-10-13,95.75,96.69,95.16,96.00,9040000,96.00 1967-10-12,96.37,96.70,95.32,95.75,7770000,95.75 1967-10-11,96.84,97.34,95.70,96.37,11230000,96.37 1967-10-10,97.51,98.15,96.38,96.84,12000000,96.84 1967-10-09,97.26,98.25,96.70,97.51,11180000,97.51 1967-10-06,96.67,97.83,96.34,97.26,9830000,97.26 1967-10-05,96.43,97.25,95.89,96.67,8490000,96.67 1967-10-04,96.65,97.47,95.94,96.43,11520000,96.43 1967-10-03,96.32,97.23,95.75,96.65,10320000,96.65 1967-10-02,96.71,97.25,95.82,96.32,9240000,96.32 1967-09-29,96.79,97.37,96.06,96.71,9710000,96.71 1967-09-28,96.79,97.59,96.19,96.79,10470000,96.79 1967-09-27,96.76,97.54,96.00,96.79,8810000,96.79 1967-09-26,97.59,98.20,96.40,96.76,10940000,96.76 1967-09-25,97.00,98.31,96.74,97.59,10910000,97.59 1967-09-22,96.75,97.61,96.11,97.00,11160000,97.00 1967-09-21,96.13,97.50,95.67,96.75,11290000,96.75 1967-09-20,96.17,96.84,95.39,96.13,10980000,96.13 1967-09-19,96.53,97.35,95.84,96.17,11540000,96.17 1967-09-18,96.27,97.31,95.73,96.53,11620000,96.53 1967-09-15,96.20,96.94,95.47,96.27,10270000,96.27 1967-09-14,95.99,97.40,95.59,96.20,12220000,96.20 1967-09-13,94.99,96.62,94.80,95.99,12400000,95.99 1967-09-12,94.54,95.48,94.01,94.99,9930000,94.99 1967-09-11,94.36,95.26,93.88,94.54,9170000,94.54 1967-09-08,94.33,95.04,93.70,94.36,9300000,94.36 1967-09-07,94.39,94.95,93.70,94.33,8910000,94.33 1967-09-06,94.21,95.06,93.72,94.39,9550000,94.39 1967-09-05,93.68,94.70,93.36,94.21,8320000,94.21 1967-09-01,93.64,94.21,93.00,93.68,7460000,93.68 1967-08-31,93.07,94.19,92.84,93.64,8840000,93.64 1967-08-30,92.88,93.67,92.43,93.07,7200000,93.07 1967-08-29,92.64,93.58,92.17,92.88,6350000,92.88 1967-08-28,92.70,93.31,92.01,92.64,6270000,92.64 1967-08-25,93.09,93.38,92.04,92.70,7250000,92.70 1967-08-24,93.61,94.28,92.77,93.09,7740000,93.09 1967-08-23,93.74,94.15,92.77,93.61,8760000,93.61 1967-08-22,94.25,94.72,93.35,93.74,7940000,93.74 1967-08-21,94.78,95.22,93.79,94.25,8600000,94.25 1967-08-18,94.63,95.40,94.16,94.78,8250000,94.78 1967-08-17,94.55,95.33,94.11,94.63,8790000,94.63 1967-08-16,94.77,95.15,93.93,94.55,8220000,94.55 1967-08-15,94.64,95.54,94.18,94.77,8710000,94.77 1967-08-14,95.15,95.40,94.02,94.64,7990000,94.64 1967-08-11,95.53,95.98,94.62,95.15,8250000,95.15 1967-08-10,95.78,96.67,95.05,95.53,9040000,95.53 1967-08-09,95.69,96.47,95.11,95.78,10100000,95.78 1967-08-08,95.58,96.28,95.04,95.69,8970000,95.69 1967-08-07,95.83,96.43,95.02,95.58,10160000,95.58 1967-08-04,95.66,96.54,95.15,95.83,11130000,95.83 1967-08-03,95.78,96.36,94.42,95.66,13440000,95.66 1967-08-02,95.37,96.64,95.03,95.78,13510000,95.78 1967-08-01,94.75,95.84,94.20,95.37,12290000,95.37 1967-07-31,94.49,95.51,94.01,94.75,10330000,94.75 1967-07-28,94.35,95.23,93.77,94.49,10900000,94.49 1967-07-27,94.06,95.19,93.51,94.35,12400000,94.35 1967-07-26,93.24,94.71,93.12,94.06,11160000,94.06 1967-07-25,93.73,94.56,93.03,93.24,9890000,93.24 1967-07-24,94.04,94.68,92.91,93.73,9580000,93.73 1967-07-21,93.85,94.92,93.24,94.04,11710000,94.04 1967-07-20,93.65,94.49,93.01,93.85,11160000,93.85 1967-07-19,93.50,94.40,92.83,93.65,12850000,93.65 1967-07-18,92.75,94.05,92.30,93.50,12060000,93.50 1967-07-17,92.74,93.53,92.10,92.75,10390000,92.75 1967-07-14,92.42,93.35,91.87,92.74,10880000,92.74 1967-07-13,92.40,93.17,91.82,92.42,10730000,92.42 1967-07-12,92.48,93.10,91.62,92.40,11240000,92.40 1967-07-11,92.05,93.16,91.58,92.48,12400000,92.48 1967-07-10,91.69,92.80,91.11,92.05,12130000,92.05 1967-07-07,91.32,92.28,90.76,91.69,11540000,91.69 1967-07-06,91.36,92.03,90.64,91.32,10170000,91.32 1967-07-05,90.91,91.91,90.56,91.36,9170000,91.36 1967-07-03,90.64,91.32,90.12,90.91,6040000,90.91 1967-06-30,90.64,90.64,90.64,90.64,7850000,90.64 1967-06-29,90.85,90.85,90.85,90.85,9940000,90.85 1967-06-28,91.31,91.31,91.31,91.31,9310000,91.31 1967-06-27,91.30,91.30,91.30,91.30,8780000,91.30 1967-06-26,91.64,91.64,91.64,91.64,9040000,91.64 1967-06-23,92.00,92.00,92.00,92.00,9130000,92.00 1967-06-22,91.97,91.97,91.97,91.97,9550000,91.97 1967-06-21,92.20,92.20,92.20,92.20,9760000,92.20 1967-06-20,92.48,92.48,92.48,92.48,10350000,92.48 1967-06-19,92.51,92.51,92.51,92.51,8570000,92.51 1967-06-16,92.49,93.28,91.98,92.54,10740000,92.54 1967-06-15,92.40,93.26,91.76,92.49,11240000,92.49 1967-06-14,92.62,93.21,91.81,92.40,10960000,92.40 1967-06-13,92.04,93.27,91.65,92.62,11570000,92.62 1967-06-12,91.56,92.66,91.12,92.04,10230000,92.04 1967-06-09,91.40,92.26,90.77,91.56,9650000,91.56 1967-06-08,90.91,91.78,90.24,91.40,8300000,91.40 1967-06-07,90.23,91.75,89.92,90.91,10170000,90.91 1967-06-06,88.48,90.59,88.48,90.23,9230000,90.23 1967-06-05,89.56,89.56,87.19,88.43,11110000,88.43 1967-06-02,90.23,90.90,89.27,89.79,8070000,89.79 1967-06-01,89.08,90.76,88.81,90.23,9040000,90.23 1967-05-31,90.39,90.39,88.71,89.08,8870000,89.08 1967-05-29,90.98,91.22,89.92,90.49,6590000,90.49 1967-05-26,91.19,91.70,90.34,90.98,7810000,90.98 1967-05-25,90.18,91.84,90.04,91.19,8960000,91.19 1967-05-24,91.23,91.36,89.68,90.18,10290000,90.18 1967-05-23,91.67,92.07,90.58,91.23,9810000,91.23 1967-05-22,92.07,92.40,90.83,91.67,9600000,91.67 1967-05-19,92.53,92.86,91.40,92.07,10560000,92.07 1967-05-18,92.78,93.30,91.98,92.53,10290000,92.53 1967-05-17,93.14,93.75,92.34,92.78,9560000,92.78 1967-05-16,92.71,93.85,92.19,93.14,10700000,93.14 1967-05-15,93.48,93.75,92.27,92.71,8320000,92.71 1967-05-12,93.75,94.45,92.94,93.48,10470000,93.48 1967-05-11,93.35,94.37,92.90,93.75,10320000,93.75 1967-05-10,93.60,94.04,92.51,93.35,10410000,93.35 1967-05-09,94.58,95.25,93.28,93.60,10830000,93.60 1967-05-08,94.44,95.22,93.71,94.58,10330000,94.58 1967-05-05,94.32,95.14,93.64,94.44,10630000,94.44 1967-05-04,93.91,94.92,93.41,94.32,12850000,94.32 1967-05-03,93.67,94.48,92.94,93.91,11550000,93.91 1967-05-02,93.84,94.42,93.06,93.67,10260000,93.67 1967-05-01,94.01,94.60,93.08,93.84,9410000,93.84 1967-04-28,93.81,94.77,93.33,94.01,11200000,94.01 1967-04-27,93.02,94.25,92.41,93.81,10250000,93.81 1967-04-26,93.11,93.99,92.44,93.02,10560000,93.02 1967-04-25,92.62,93.57,92.01,93.11,10420000,93.11 1967-04-24,92.30,93.45,91.78,92.62,10250000,92.62 1967-04-21,92.11,92.90,91.48,92.30,10210000,92.30 1967-04-20,91.94,92.61,91.21,92.11,9690000,92.11 1967-04-19,91.86,92.73,91.25,91.94,10860000,91.94 1967-04-18,91.07,92.31,90.70,91.86,10500000,91.86 1967-04-17,90.43,91.78,90.18,91.07,9070000,91.07 1967-04-14,89.46,91.08,89.26,90.43,8810000,90.43 1967-04-13,88.78,89.86,88.49,89.46,7610000,89.46 1967-04-12,88.88,89.54,88.36,88.78,7750000,88.78 1967-04-11,88.24,89.34,87.92,88.88,7710000,88.88 1967-04-10,89.32,89.32,87.86,88.24,8110000,88.24 1967-04-07,89.94,90.60,88.96,89.36,9090000,89.36 1967-04-06,89.79,90.74,89.44,89.94,9470000,89.94 1967-04-05,89.22,90.31,88.92,89.79,8810000,89.79 1967-04-04,89.24,89.93,88.45,89.22,8750000,89.22 1967-04-03,90.20,90.37,88.76,89.24,8530000,89.24 1967-03-31,90.70,91.15,89.75,90.20,8130000,90.20 1967-03-30,90.73,91.32,90.06,90.70,8340000,90.70 1967-03-29,90.91,91.45,90.17,90.73,8430000,90.73 1967-03-28,90.87,91.62,90.23,90.91,8940000,90.91 1967-03-27,90.94,91.72,90.19,90.87,9260000,90.87 1967-03-23,90.25,91.51,90.04,90.94,9500000,90.94 1967-03-22,90.00,90.70,89.17,90.25,8820000,90.25 1967-03-21,90.20,91.05,89.52,90.00,9820000,90.00 1967-03-20,90.25,90.87,89.35,90.20,9040000,90.20 1967-03-17,90.09,90.84,89.39,90.25,10020000,90.25 1967-03-16,89.19,90.66,89.09,90.09,12170000,90.09 1967-03-15,88.35,89.60,88.00,89.19,10830000,89.19 1967-03-14,88.43,89.07,87.58,88.35,10260000,88.35 1967-03-13,88.89,89.41,87.93,88.43,9910000,88.43 1967-03-10,88.53,90.37,88.46,88.89,14900000,88.89 1967-03-09,88.27,89.04,87.70,88.53,10480000,88.53 1967-03-08,88.16,89.10,87.69,88.27,11070000,88.27 1967-03-07,88.10,88.74,87.34,88.16,9810000,88.16 1967-03-06,88.29,89.08,87.46,88.10,10400000,88.10 1967-03-03,88.16,89.00,87.51,88.29,11100000,88.29 1967-03-02,87.68,88.85,87.39,88.16,11900000,88.16 1967-03-01,86.78,88.36,86.67,87.68,11510000,87.68 1967-02-28,86.46,87.26,85.61,86.78,9970000,86.78 1967-02-27,87.41,87.61,85.68,86.46,10210000,86.46 1967-02-24,87.45,88.16,86.76,87.41,9830000,87.41 1967-02-23,87.34,88.00,86.64,87.45,10010000,87.45 1967-02-21,87.40,88.01,86.80,87.34,9030000,87.34 1967-02-20,87.89,88.13,86.65,87.40,8640000,87.40 1967-02-17,87.86,88.40,87.25,87.89,8530000,87.89 1967-02-16,88.27,88.80,87.43,87.86,8490000,87.86 1967-02-15,88.17,89.00,87.62,88.27,10480000,88.27 1967-02-14,87.58,88.74,87.15,88.17,9760000,88.17 1967-02-13,87.63,88.19,86.95,87.58,7570000,87.58 1967-02-10,87.36,88.19,86.79,87.63,8850000,87.63 1967-02-09,87.72,88.57,86.99,87.36,10970000,87.36 1967-02-08,86.95,88.25,86.64,87.72,11220000,87.72 1967-02-07,87.18,87.52,86.48,86.95,6400000,86.95 1967-02-06,87.36,87.98,86.61,87.18,10680000,87.18 1967-02-03,86.73,87.97,86.51,87.36,12010000,87.36 1967-02-02,86.43,87.31,85.87,86.73,10720000,86.73 1967-02-01,86.61,87.04,85.68,86.43,9580000,86.43 1967-01-31,86.66,87.46,86.06,86.61,11540000,86.61 1967-01-30,86.16,87.35,85.84,86.66,10250000,86.66 1967-01-27,85.81,86.76,85.34,86.16,9690000,86.16 1967-01-26,85.85,86.66,84.87,85.81,10630000,85.81 1967-01-25,86.51,87.02,85.47,85.85,10260000,85.85 1967-01-24,86.39,87.00,85.29,86.51,10430000,86.51 1967-01-23,86.07,88.17,85.64,86.39,10830000,86.39 1967-01-20,85.82,86.47,85.07,86.07,9530000,86.07 1967-01-19,85.79,86.61,85.17,85.82,10230000,85.82 1967-01-18,85.24,86.36,84.90,85.79,11390000,85.79 1967-01-17,84.31,85.81,84.03,85.24,11590000,85.24 1967-01-16,84.53,85.28,83.73,84.31,10280000,84.31 1967-01-13,83.91,84.90,83.10,84.53,10000000,84.53 1967-01-12,83.47,84.80,83.11,83.91,12830000,83.91 1967-01-11,82.81,83.92,81.37,83.47,13230000,83.47 1967-01-10,82.81,83.54,82.22,82.81,8120000,82.81 1967-01-09,82.18,83.31,81.78,82.81,9180000,82.81 1967-01-06,81.60,82.79,81.32,82.18,7830000,82.18 1967-01-05,80.55,81.93,80.50,81.60,7320000,81.60 1967-01-04,80.38,81.01,79.43,80.55,6150000,80.55 1967-01-03,80.33,81.61,79.59,80.38,6100000,80.38 1966-12-30,80.37,81.14,79.66,80.33,11330000,80.33 1966-12-29,80.61,81.08,79.84,80.37,7900000,80.37 1966-12-28,81.00,81.67,80.29,80.61,7160000,80.61 1966-12-27,81.47,81.84,80.55,81.00,6280000,81.00 1966-12-23,81.69,82.22,80.97,81.47,7350000,81.47 1966-12-22,81.38,82.34,81.00,81.69,8560000,81.69 1966-12-21,80.96,81.91,80.42,81.38,7690000,81.38 1966-12-20,81.27,81.69,80.31,80.96,6830000,80.96 1966-12-19,81.58,82.06,80.56,81.27,7340000,81.27 1966-12-16,81.64,82.21,80.94,81.58,6980000,81.58 1966-12-15,82.64,82.89,81.20,81.64,7150000,81.64 1966-12-14,82.73,83.35,81.97,82.64,7470000,82.64 1966-12-13,83.00,83.88,82.28,82.73,9650000,82.73 1966-12-12,82.14,83.54,81.94,83.00,9530000,83.00 1966-12-09,82.05,82.68,81.33,82.14,7650000,82.14 1966-12-08,81.72,82.72,81.34,82.05,8370000,82.05 1966-12-07,80.84,82.19,80.59,81.72,8980000,81.72 1966-12-06,80.24,81.29,79.95,80.84,7670000,80.84 1966-12-05,80.13,80.81,79.60,80.24,6470000,80.24 1966-12-02,80.08,81.29,79.49,80.13,6230000,80.13 1966-12-01,80.45,81.04,79.66,80.08,8480000,80.08 1966-11-30,80.42,80.90,79.62,80.45,7230000,80.45 1966-11-29,80.71,81.16,79.94,80.42,7320000,80.42 1966-11-28,80.85,81.38,79.96,80.71,7630000,80.71 1966-11-25,80.21,81.37,79.83,80.85,6810000,80.85 1966-11-23,79.67,80.85,79.39,80.21,7350000,80.21 1966-11-22,80.09,80.32,78.89,79.67,6430000,79.67 1966-11-21,81.09,81.09,79.51,80.09,7450000,80.09 1966-11-18,81.80,82.05,80.79,81.26,6900000,81.26 1966-11-17,82.37,82.80,81.24,81.80,8900000,81.80 1966-11-16,81.69,83.01,81.55,82.37,10350000,82.37 1966-11-15,81.37,82.07,80.82,81.69,7190000,81.69 1966-11-14,81.94,82.18,80.81,81.37,6540000,81.37 1966-11-11,81.89,82.36,81.27,81.94,6690000,81.94 1966-11-10,81.38,82.43,81.00,81.89,8870000,81.89 1966-11-09,80.73,81.90,80.46,81.38,8390000,81.38 1966-11-07,80.81,81.48,80.16,80.73,6120000,80.73 1966-11-04,80.56,81.21,79.64,80.81,6530000,80.81 1966-11-03,80.88,81.35,79.98,80.56,5860000,80.56 1966-11-02,80.81,81.68,80.30,80.88,6740000,80.88 1966-11-01,80.20,81.18,79.79,80.81,6480000,80.81 1966-10-31,80.24,80.82,79.34,80.20,5860000,80.20 1966-10-28,80.23,80.91,79.49,80.24,6420000,80.24 1966-10-27,79.58,80.72,79.28,80.23,6670000,80.23 1966-10-26,78.90,80.29,78.70,79.58,6760000,79.58 1966-10-25,78.42,79.22,77.56,78.90,6190000,78.90 1966-10-24,78.19,79.20,77.73,78.42,5780000,78.42 1966-10-21,77.84,78.62,77.16,78.19,5690000,78.19 1966-10-20,78.05,78.96,77.26,77.84,6840000,77.84 1966-10-19,78.68,79.34,77.54,78.05,6460000,78.05 1966-10-18,77.47,79.08,77.35,78.68,7180000,78.68 1966-10-17,76.60,78.41,76.48,77.47,5570000,77.47 1966-10-14,76.89,77.80,76.01,76.60,5610000,76.60 1966-10-13,77.04,78.45,76.22,76.89,8680000,76.89 1966-10-12,74.91,77.26,74.37,77.04,6910000,77.04 1966-10-11,74.53,76.20,74.22,74.91,8430000,74.91 1966-10-10,73.20,74.97,72.28,74.53,9630000,74.53 1966-10-07,74.05,74.67,72.77,73.20,8140000,73.20 1966-10-06,74.69,75.09,73.47,74.05,8110000,74.05 1966-10-05,75.10,76.10,74.31,74.69,5880000,74.69 1966-10-04,74.90,75.76,73.91,75.10,8910000,75.10 1966-10-03,76.56,76.98,74.71,74.90,6490000,74.90 1966-09-30,76.31,77.09,75.45,76.56,6170000,76.56 1966-09-29,77.11,77.28,75.85,76.31,6110000,76.31 1966-09-28,78.10,78.36,76.70,77.11,5990000,77.11 1966-09-27,77.86,79.10,77.56,78.10,6300000,78.10 1966-09-26,77.67,78.34,76.88,77.86,4960000,77.86 1966-09-23,77.94,78.43,77.15,77.67,4560000,77.67 1966-09-22,77.71,78.41,76.81,77.94,5760000,77.94 1966-09-21,79.04,79.15,77.52,77.71,5360000,77.71 1966-09-20,79.59,79.90,78.57,79.04,4560000,79.04 1966-09-19,79.99,80.50,79.02,79.59,4920000,79.59 1966-09-16,80.08,80.81,79.33,79.99,5150000,79.99 1966-09-15,79.13,80.60,78.87,80.08,6140000,80.08 1966-09-14,78.32,79.43,77.73,79.13,6250000,79.13 1966-09-13,77.91,79.16,77.66,78.32,6870000,78.32 1966-09-12,76.47,78.34,76.47,77.91,6780000,77.91 1966-09-09,76.05,76.94,75.43,76.29,5280000,76.29 1966-09-08,76.37,76.95,75.03,76.05,6660000,76.05 1966-09-07,76.96,77.26,75.77,76.37,5530000,76.37 1966-09-06,77.42,78.16,76.55,76.96,4350000,76.96 1966-09-02,77.70,78.20,76.27,77.42,6080000,77.42 1966-09-01,77.10,78.50,76.66,77.70,6250000,77.70 1966-08-31,75.98,78.06,75.98,77.10,8690000,77.10 1966-08-30,74.53,76.46,73.91,75.86,11230000,75.86 1966-08-29,76.24,76.24,74.18,74.53,10900000,74.53 1966-08-26,77.85,77.85,76.10,76.41,8190000,76.41 1966-08-25,79.07,79.79,77.80,78.06,6760000,78.06 1966-08-24,78.11,79.63,77.92,79.07,7050000,79.07 1966-08-23,78.24,79.24,77.05,78.11,9830000,78.11 1966-08-22,79.62,79.88,77.58,78.24,8690000,78.24 1966-08-19,80.16,80.78,79.24,79.62,7070000,79.62 1966-08-18,81.18,81.38,79.60,80.16,7000000,80.16 1966-08-17,81.63,81.90,80.53,81.18,6630000,81.18 1966-08-16,82.71,82.71,81.26,81.63,6130000,81.63 1966-08-15,83.17,83.69,82.39,82.74,5680000,82.74 1966-08-12,83.02,83.88,82.57,83.17,6230000,83.17 1966-08-11,83.11,83.53,82.34,83.02,5700000,83.02 1966-08-10,83.49,83.83,82.69,83.11,5290000,83.11 1966-08-09,83.75,84.36,83.04,83.49,6270000,83.49 1966-08-08,84.00,84.31,82.97,83.75,4900000,83.75 1966-08-05,83.93,84.70,83.43,84.00,5500000,84.00 1966-08-04,83.15,84.54,83.07,83.93,6880000,83.93 1966-08-03,82.33,83.71,82.30,83.15,6220000,83.15 1966-08-02,82.31,83.04,81.77,82.33,5710000,82.33 1966-08-01,83.50,83.50,81.98,82.31,5880000,82.31 1966-07-29,83.77,84.30,83.10,83.60,5150000,83.60 1966-07-28,84.10,84.76,83.44,83.77,5680000,83.77 1966-07-27,83.70,84.83,83.50,84.10,6070000,84.10 1966-07-26,83.83,84.67,83.05,83.70,7610000,83.70 1966-07-25,85.41,85.57,83.56,83.83,7050000,83.83 1966-07-22,85.52,86.11,84.93,85.41,6540000,85.41 1966-07-21,85.51,86.24,84.77,85.52,6200000,85.52 1966-07-20,86.33,86.64,85.26,85.51,5470000,85.51 1966-07-19,86.99,87.17,85.75,86.33,5960000,86.33 1966-07-18,87.08,87.59,86.42,86.99,5110000,86.99 1966-07-15,86.82,87.68,86.44,87.08,6090000,87.08 1966-07-14,86.30,87.34,85.85,86.82,5950000,86.82 1966-07-13,86.88,87.06,85.83,86.30,5580000,86.30 1966-07-12,87.45,87.78,86.45,86.88,5180000,86.88 1966-07-11,87.61,88.19,86.97,87.45,6200000,87.45 1966-07-08,87.38,88.04,86.85,87.61,6100000,87.61 1966-07-07,87.06,88.02,86.67,87.38,7200000,87.38 1966-07-06,85.82,87.38,85.57,87.06,6860000,87.06 1966-07-05,85.61,86.41,85.09,85.82,4610000,85.82 1966-07-01,84.74,86.08,84.74,85.61,5200000,85.61 1966-06-30,84.86,85.37,83.75,84.74,7250000,84.74 1966-06-29,85.67,85.98,84.52,84.86,6020000,84.86 1966-06-28,86.08,86.43,85.00,85.67,6280000,85.67 1966-06-27,86.58,87.31,85.77,86.08,5330000,86.08 1966-06-24,86.50,87.31,85.68,86.58,7140000,86.58 1966-06-23,86.85,87.73,86.11,86.50,7930000,86.50 1966-06-22,86.71,87.38,86.15,86.85,7800000,86.85 1966-06-21,86.48,87.28,86.07,86.71,6860000,86.71 1966-06-20,86.51,87.03,85.84,86.48,5940000,86.48 1966-06-17,86.47,87.11,85.89,86.51,6580000,86.51 1966-06-16,86.73,87.18,85.88,86.47,6870000,86.47 1966-06-15,87.07,87.74,86.33,86.73,8520000,86.73 1966-06-14,86.83,87.57,86.02,87.07,7600000,87.07 1966-06-13,86.44,87.59,86.20,86.83,7600000,86.83 1966-06-10,85.50,86.97,85.32,86.44,8240000,86.44 1966-06-09,84.93,85.98,84.56,85.50,5810000,85.50 1966-06-08,84.83,85.43,84.31,84.93,4580000,84.93 1966-06-07,85.42,85.54,84.25,84.83,5040000,84.83 1966-06-06,86.06,86.28,85.03,85.42,4260000,85.42 1966-06-03,85.96,86.55,85.43,86.06,4430000,86.06 1966-06-02,86.10,86.85,85.55,85.96,5080000,85.96 1966-06-01,86.13,86.65,85.28,86.10,5290000,86.10 1966-05-31,87.33,87.65,85.80,86.13,5770000,86.13 1966-05-27,87.07,87.42,86.43,87.33,4790000,87.33 1966-05-26,87.07,87.88,86.54,87.07,6080000,87.07 1966-05-25,86.77,87.48,86.05,87.07,5820000,87.07 1966-05-24,86.20,87.70,86.19,86.77,7210000,86.77 1966-05-23,85.43,86.91,85.29,86.20,7080000,86.20 1966-05-20,85.02,85.79,84.21,85.43,6430000,85.43 1966-05-19,85.12,86.33,84.54,85.02,8640000,85.02 1966-05-18,83.72,85.64,83.72,85.12,9310000,85.12 1966-05-17,84.41,85.03,83.18,83.63,9870000,83.63 1966-05-16,85.47,86.04,83.90,84.41,9260000,84.41 1966-05-13,86.23,86.31,84.77,85.47,8970000,85.47 1966-05-12,87.23,87.49,85.72,86.23,8210000,86.23 1966-05-11,87.08,88.38,86.84,87.23,7470000,87.23 1966-05-10,86.32,87.88,86.12,87.08,9050000,87.08 1966-05-09,87.84,87.96,85.92,86.32,9290000,86.32 1966-05-06,87.93,88.52,86.24,87.84,13110000,87.84 1966-05-05,89.39,89.77,87.60,87.93,10100000,87.93 1966-05-04,89.85,90.11,88.54,89.39,9740000,89.39 1966-05-03,90.90,91.10,89.46,89.85,8020000,89.85 1966-05-02,91.06,91.75,90.43,90.90,7070000,90.90 1966-04-29,91.13,91.86,90.57,91.06,7220000,91.06 1966-04-28,91.76,91.92,90.24,91.13,8310000,91.13 1966-04-27,91.99,92.49,91.10,91.76,7950000,91.76 1966-04-26,92.08,92.77,91.47,91.99,7540000,91.99 1966-04-25,92.27,92.86,91.41,92.08,7270000,92.08 1966-04-22,92.42,92.87,91.60,92.27,8650000,92.27 1966-04-21,92.08,93.02,91.78,92.42,9560000,92.42 1966-04-20,91.57,92.75,91.34,92.08,10530000,92.08 1966-04-19,91.58,92.31,90.89,91.57,8820000,91.57 1966-04-18,91.99,92.59,91.09,91.58,9150000,91.58 1966-04-15,91.87,92.75,91.28,91.99,10270000,91.99 1966-04-14,91.54,92.80,91.12,91.87,12980000,91.87 1966-04-13,91.45,92.81,90.73,91.54,10440000,91.54 1966-04-12,91.79,92.51,90.92,91.45,10500000,91.45 1966-04-11,91.76,92.60,91.08,91.79,9310000,91.79 1966-04-07,91.56,92.42,90.99,91.76,9650000,91.76 1966-04-06,91.31,92.10,90.77,91.56,9040000,91.56 1966-04-05,90.76,92.04,90.47,91.31,10560000,91.31 1966-04-04,89.94,91.33,89.92,90.76,9360000,90.76 1966-04-01,89.23,90.37,88.96,89.94,9050000,89.94 1966-03-31,88.78,89.70,88.47,89.23,6690000,89.23 1966-03-30,89.27,89.57,88.31,88.78,7980000,88.78 1966-03-29,89.62,90.04,88.63,89.27,8300000,89.27 1966-03-28,89.54,90.41,89.15,89.62,8640000,89.62 1966-03-25,89.29,90.14,88.96,89.54,7750000,89.54 1966-03-24,89.13,89.80,88.68,89.29,7880000,89.29 1966-03-23,89.46,89.80,88.69,89.13,6720000,89.13 1966-03-22,89.20,90.28,89.01,89.46,8910000,89.46 1966-03-21,88.53,89.73,88.40,89.20,7230000,89.20 1966-03-18,88.17,89.23,87.82,88.53,6450000,88.53 1966-03-17,87.86,88.60,87.45,88.17,5460000,88.17 1966-03-16,87.35,88.55,87.09,87.86,7330000,87.86 1966-03-15,87.85,88.20,86.69,87.35,9440000,87.35 1966-03-14,88.85,88.92,87.56,87.85,7400000,87.85 1966-03-11,88.96,89.63,88.30,88.85,7000000,88.85 1966-03-10,88.96,90.14,88.36,88.96,10310000,88.96 1966-03-09,88.18,89.21,87.96,88.96,7980000,88.96 1966-03-08,88.04,89.00,87.17,88.18,10120000,88.18 1966-03-07,89.24,89.39,87.67,88.04,9370000,88.04 1966-03-04,89.47,90.25,88.72,89.24,9000000,89.24 1966-03-03,89.15,90.03,88.26,89.47,9900000,89.47 1966-03-02,90.06,90.65,88.70,89.15,10470000,89.15 1966-03-01,91.22,91.65,89.76,90.06,11030000,90.06 1966-02-28,91.14,91.95,90.65,91.22,9910000,91.22 1966-02-25,90.89,91.88,90.43,91.14,8140000,91.14 1966-02-24,91.48,91.81,90.45,90.89,7860000,90.89 1966-02-23,91.87,92.21,90.99,91.48,8080000,91.48 1966-02-21,92.41,92.83,91.35,91.87,8510000,91.87 1966-02-18,92.66,93.14,91.80,92.41,8470000,92.41 1966-02-17,93.16,93.58,92.11,92.66,9330000,92.66 1966-02-16,93.17,93.74,92.63,93.16,9180000,93.16 1966-02-15,93.53,94.04,92.67,93.17,8750000,93.17 1966-02-14,93.81,94.40,93.15,93.53,8360000,93.53 1966-02-11,93.83,94.52,93.25,93.81,8150000,93.81 1966-02-10,94.06,94.70,93.32,93.83,9790000,93.83 1966-02-09,93.55,94.72,93.29,94.06,9760000,94.06 1966-02-08,93.59,94.29,92.58,93.55,10560000,93.55 1966-02-07,93.26,94.22,92.85,93.59,8000000,93.59 1966-02-04,92.65,93.70,92.33,93.26,7560000,93.26 1966-02-03,92.53,93.67,92.11,92.65,8160000,92.65 1966-02-02,92.16,92.91,91.32,92.53,8130000,92.53 1966-02-01,92.88,93.36,91.61,92.16,9090000,92.16 1966-01-31,93.31,93.77,92.46,92.88,7800000,92.88 1966-01-28,93.67,94.15,92.84,93.31,9000000,93.31 1966-01-27,93.70,94.34,93.09,93.67,8970000,93.67 1966-01-26,93.85,94.53,93.18,93.70,9910000,93.70 1966-01-25,93.71,94.56,93.24,93.85,9300000,93.85 1966-01-24,93.47,94.41,93.07,93.71,8780000,93.71 1966-01-21,93.36,93.97,92.60,93.47,9180000,93.47 1966-01-20,93.69,94.33,92.87,93.36,8670000,93.36 1966-01-19,93.95,94.62,93.16,93.69,10230000,93.69 1966-01-18,93.77,94.64,93.23,93.95,9790000,93.95 1966-01-17,93.50,94.46,93.10,93.77,9430000,93.77 1966-01-14,93.36,94.14,92.98,93.50,9210000,93.50 1966-01-13,93.19,94.00,92.68,93.36,8860000,93.36 1966-01-12,93.41,93.98,92.80,93.19,8530000,93.19 1966-01-11,93.33,94.05,92.85,93.41,8910000,93.41 1966-01-10,93.14,93.94,92.75,93.33,7720000,93.33 1966-01-07,93.06,93.64,92.47,93.14,7600000,93.14 1966-01-06,92.85,93.65,92.51,93.06,7880000,93.06 1966-01-05,92.26,93.33,91.99,92.85,9650000,92.85 1966-01-04,92.18,93.04,91.68,92.26,7540000,92.26 1966-01-03,92.43,92.87,91.63,92.18,5950000,92.18 1965-12-31,92.20,93.05,91.82,92.43,7240000,92.43 1965-12-30,91.81,92.68,91.52,92.20,7060000,92.20 1965-12-29,91.53,92.39,91.14,91.81,7610000,91.81 1965-12-28,91.52,92.13,90.63,91.53,7280000,91.53 1965-12-27,92.19,92.71,91.28,91.52,5950000,91.52 1965-12-23,92.29,92.89,91.58,92.19,6870000,92.19 1965-12-22,92.01,93.07,91.53,92.29,9720000,92.29 1965-12-21,91.65,92.59,91.24,92.01,8230000,92.01 1965-12-20,92.08,92.35,91.09,91.65,7350000,91.65 1965-12-17,92.12,92.76,91.51,92.08,9490000,92.08 1965-12-16,92.02,92.95,91.53,92.12,9950000,92.12 1965-12-15,91.88,92.67,91.30,92.02,9560000,92.02 1965-12-14,91.83,92.59,91.35,91.88,9920000,91.88 1965-12-13,91.80,92.45,91.27,91.83,8660000,91.83 1965-12-10,91.56,92.28,91.14,91.80,8740000,91.80 1965-12-09,91.28,92.06,90.87,91.56,9150000,91.56 1965-12-08,91.39,92.24,90.84,91.28,10120000,91.28 1965-12-07,90.59,92.00,90.45,91.39,9340000,91.39 1965-12-06,91.20,91.20,89.20,90.59,11440000,90.59 1965-12-03,91.21,91.80,90.53,91.27,8160000,91.27 1965-12-02,91.50,91.95,90.69,91.21,9070000,91.21 1965-12-01,91.61,92.26,91.02,91.50,10140000,91.50 1965-11-30,91.80,92.14,90.81,91.61,8990000,91.61 1965-11-29,92.03,92.60,91.37,91.80,8760000,91.80 1965-11-26,91.94,92.65,91.39,92.03,6970000,92.03 1965-11-24,91.78,92.50,91.14,91.94,7870000,91.94 1965-11-23,91.64,92.24,91.15,91.78,7150000,91.78 1965-11-22,92.24,92.48,91.16,91.64,6370000,91.64 1965-11-19,92.22,92.88,91.73,92.24,6850000,92.24 1965-11-18,92.60,92.94,91.72,92.22,7040000,92.22 1965-11-17,92.41,93.28,91.85,92.60,9120000,92.60 1965-11-16,92.63,93.13,91.90,92.41,8380000,92.41 1965-11-15,92.55,93.30,92.04,92.63,8310000,92.63 1965-11-12,92.11,93.07,91.83,92.55,7780000,92.55 1965-11-11,91.83,92.37,91.31,92.11,5430000,92.11 1965-11-10,91.93,92.40,91.35,91.83,4860000,91.83 1965-11-09,92.23,92.65,91.47,91.93,6680000,91.93 1965-11-08,92.37,92.97,91.63,92.23,7000000,92.23 1965-11-05,92.46,92.92,91.78,92.37,7310000,92.37 1965-11-04,92.31,93.07,91.90,92.46,8380000,92.46 1965-11-03,92.23,92.79,91.62,92.31,7520000,92.31 1965-11-01,92.42,92.92,91.73,92.23,6340000,92.23 1965-10-29,92.21,92.94,91.83,92.42,7240000,92.42 1965-10-28,92.51,92.95,91.60,92.21,7230000,92.21 1965-10-27,92.20,93.19,91.95,92.51,7670000,92.51 1965-10-26,91.67,92.63,91.36,92.20,6750000,92.20 1965-10-25,91.98,92.72,91.34,91.67,7090000,91.67 1965-10-22,91.94,92.74,91.54,91.98,8960000,91.98 1965-10-21,91.78,92.51,91.42,91.94,9170000,91.94 1965-10-20,91.80,92.26,91.12,91.78,8200000,91.78 1965-10-19,91.68,92.45,91.35,91.80,8620000,91.80 1965-10-18,91.38,92.28,91.06,91.68,8180000,91.68 1965-10-15,91.19,92.09,90.76,91.38,7470000,91.38 1965-10-14,91.34,91.90,90.71,91.19,8580000,91.19 1965-10-13,91.35,91.81,90.73,91.34,9470000,91.34 1965-10-12,91.37,91.94,90.83,91.35,9470000,91.35 1965-10-11,90.85,91.84,90.73,91.37,9600000,91.37 1965-10-08,90.47,91.31,90.30,90.85,7670000,90.85 1965-10-07,90.54,91.09,90.09,90.47,6670000,90.47 1965-10-06,90.63,90.94,89.74,90.54,6010000,90.54 1965-10-05,90.08,91.02,89.92,90.63,6980000,90.63 1965-10-04,89.90,90.56,89.47,90.08,5590000,90.08 1965-10-01,89.96,90.48,89.30,89.90,7470000,89.90 1965-09-30,90.02,90.71,89.51,89.96,8670000,89.96 1965-09-29,90.43,91.11,89.56,90.02,10600000,90.02 1965-09-28,90.65,91.13,89.83,90.43,8750000,90.43 1965-09-27,90.65,90.65,90.65,90.65,6820000,90.65 1965-09-24,89.86,90.47,89.13,90.02,7810000,90.02 1965-09-23,90.22,90.78,89.43,89.86,9990000,89.86 1965-09-22,89.81,90.67,89.45,90.22,8290000,90.22 1965-09-21,90.08,90.66,89.43,89.81,7750000,89.81 1965-09-20,90.05,90.67,89.51,90.08,7040000,90.08 1965-09-17,90.02,90.47,89.32,90.05,6610000,90.05 1965-09-16,90.02,90.02,90.02,90.02,7410000,90.02 1965-09-15,89.03,89.96,88.71,89.52,6220000,89.52 1965-09-14,89.38,90.01,88.69,89.03,7830000,89.03 1965-09-13,89.12,89.91,88.77,89.38,7020000,89.38 1965-09-10,88.89,89.85,88.41,89.12,6650000,89.12 1965-09-09,88.66,89.46,88.35,88.89,7360000,88.89 1965-09-08,88.36,89.08,87.93,88.66,6240000,88.66 1965-09-07,88.06,88.77,87.76,88.36,5750000,88.36 1965-09-03,87.65,88.41,87.52,88.06,6010000,88.06 1965-09-02,87.17,87.96,86.98,87.65,6470000,87.65 1965-09-01,87.17,87.63,86.69,87.17,5890000,87.17 1965-08-31,87.21,87.79,86.78,87.17,5170000,87.17 1965-08-30,87.20,87.64,86.76,87.21,4400000,87.21 1965-08-27,87.14,87.74,86.81,87.20,5570000,87.20 1965-08-26,86.81,87.52,86.40,87.14,6010000,87.14 1965-08-25,86.71,87.27,86.33,86.81,6240000,86.81 1965-08-24,86.56,87.19,86.22,86.71,4740000,86.71 1965-08-23,86.69,87.10,86.22,86.56,4470000,86.56 1965-08-20,86.79,87.14,86.21,86.69,4170000,86.69 1965-08-19,86.99,87.48,86.49,86.79,5000000,86.79 1965-08-18,87.04,87.57,86.63,86.99,5850000,86.99 1965-08-17,86.87,87.42,86.48,87.04,4520000,87.04 1965-08-16,86.77,87.43,86.46,86.87,5270000,86.87 1965-08-13,86.38,87.14,86.09,86.77,5430000,86.77 1965-08-12,86.13,86.75,85.85,86.38,5160000,86.38 1965-08-11,85.87,86.48,85.64,86.13,5030000,86.13 1965-08-10,85.86,86.31,85.45,85.87,4690000,85.87 1965-08-09,86.07,86.54,85.52,85.86,4540000,85.86 1965-08-06,85.79,86.40,85.42,86.07,4200000,86.07 1965-08-05,85.79,86.28,85.43,85.79,4920000,85.79 1965-08-04,85.46,86.12,85.22,85.79,4830000,85.79 1965-08-03,85.42,85.81,84.80,85.46,4640000,85.46 1965-08-02,85.25,85.87,84.87,85.42,4220000,85.42 1965-07-30,84.68,85.64,84.64,85.25,5200000,85.25 1965-07-29,84.03,85.00,83.79,84.68,4690000,84.68 1965-07-28,83.87,84.52,83.30,84.03,4760000,84.03 1965-07-27,84.05,84.59,83.58,83.87,4190000,83.87 1965-07-26,84.07,84.47,83.49,84.05,3790000,84.05 1965-07-23,83.85,84.52,83.57,84.07,3600000,84.07 1965-07-22,84.07,84.45,83.53,83.85,3310000,83.85 1965-07-21,84.55,84.84,83.76,84.07,4350000,84.07 1965-07-20,85.63,85.85,84.39,84.55,4670000,84.55 1965-07-19,85.69,86.04,85.21,85.63,3220000,85.63 1965-07-16,85.72,86.14,85.26,85.69,3520000,85.69 1965-07-15,85.87,86.47,85.44,85.72,4420000,85.72 1965-07-14,85.59,86.23,85.18,85.87,4100000,85.87 1965-07-13,85.69,86.01,85.12,85.59,3260000,85.59 1965-07-12,85.71,86.08,85.24,85.69,3690000,85.69 1965-07-09,85.39,86.11,85.11,85.71,4800000,85.71 1965-07-08,84.67,85.60,84.29,85.39,4380000,85.39 1965-07-07,84.99,85.14,84.28,84.67,3020000,84.67 1965-07-06,85.16,85.63,84.57,84.99,3400000,84.99 1965-07-02,84.48,85.40,84.13,85.16,4260000,85.16 1965-07-01,84.12,84.64,83.57,84.48,4520000,84.48 1965-06-30,82.97,84.63,82.97,84.12,6930000,84.12 1965-06-29,81.60,83.04,80.73,82.41,10450000,82.41 1965-06-28,83.06,83.34,81.36,81.60,7650000,81.60 1965-06-25,83.56,83.83,82.60,83.06,5790000,83.06 1965-06-24,84.67,84.73,83.30,83.56,5840000,83.56 1965-06-23,85.21,85.59,84.52,84.67,3580000,84.67 1965-06-22,85.05,85.70,84.76,85.21,3330000,85.21 1965-06-21,85.34,85.64,84.53,85.05,3280000,85.05 1965-06-18,85.74,86.10,84.90,85.34,4330000,85.34 1965-06-17,85.20,86.22,84.98,85.74,5220000,85.74 1965-06-16,84.58,85.79,84.58,85.20,6290000,85.20 1965-06-15,84.01,84.86,83.01,84.49,8450000,84.49 1965-06-14,85.12,85.68,83.64,84.01,5920000,84.01 1965-06-11,84.73,85.68,84.50,85.12,5350000,85.12 1965-06-10,85.04,85.82,84.10,84.73,7470000,84.73 1965-06-09,85.93,86.37,84.75,85.04,7070000,85.04 1965-06-08,86.88,87.10,85.74,85.93,4660000,85.93 1965-06-07,87.11,87.45,86.04,86.88,4680000,86.88 1965-06-04,86.90,87.46,86.36,87.11,4530000,87.11 1965-06-03,87.09,88.05,86.58,86.90,5720000,86.90 1965-06-02,87.87,87.87,86.25,87.09,6790000,87.09 1965-06-01,88.42,88.80,87.88,88.72,4830000,88.72 1965-05-28,87.84,88.68,87.58,88.42,4270000,88.42 1965-05-27,88.30,88.36,87.24,87.84,5520000,87.84 1965-05-26,88.60,89.22,88.04,88.30,5330000,88.30 1965-05-25,88.09,88.96,87.82,88.60,4950000,88.60 1965-05-24,88.75,88.89,87.75,88.09,4790000,88.09 1965-05-21,89.18,89.41,88.40,88.75,4660000,88.75 1965-05-20,89.67,89.86,88.74,89.18,5750000,89.18 1965-05-19,89.46,90.15,89.17,89.67,5860000,89.67 1965-05-18,89.54,89.84,88.87,89.46,5130000,89.46 1965-05-17,90.10,90.44,89.24,89.54,4980000,89.54 1965-05-14,90.27,90.66,89.63,90.10,5860000,90.10 1965-05-13,89.94,90.68,89.68,90.27,6460000,90.27 1965-05-12,89.55,90.31,89.30,89.94,6310000,89.94 1965-05-11,89.66,89.98,89.05,89.55,5150000,89.55 1965-05-10,89.85,90.22,89.22,89.66,5600000,89.66 1965-05-07,89.92,90.30,89.33,89.85,5820000,89.85 1965-05-06,89.71,90.57,89.39,89.92,6340000,89.92 1965-05-05,89.51,90.40,89.14,89.71,6350000,89.71 1965-05-04,89.23,89.89,88.82,89.51,5720000,89.51 1965-05-03,89.11,89.68,88.62,89.23,5340000,89.23 1965-04-30,88.93,89.44,88.50,89.11,5190000,89.11 1965-04-29,89.00,89.43,88.47,88.93,5510000,88.93 1965-04-28,89.04,89.48,88.51,89.00,5680000,89.00 1965-04-27,88.89,89.64,88.71,89.04,6310000,89.04 1965-04-26,88.88,89.29,88.30,88.89,5410000,88.89 1965-04-23,88.78,89.41,88.48,88.88,5860000,88.88 1965-04-22,88.30,89.13,88.12,88.78,5990000,88.78 1965-04-21,88.46,88.82,87.70,88.30,5590000,88.30 1965-04-20,88.51,89.07,88.02,88.46,6480000,88.46 1965-04-19,88.15,88.90,87.90,88.51,5700000,88.51 1965-04-15,88.24,88.63,87.55,88.15,5830000,88.15 1965-04-14,88.04,88.65,87.71,88.24,6580000,88.24 1965-04-13,87.94,88.48,87.54,88.04,6690000,88.04 1965-04-12,87.56,88.36,87.31,87.94,6040000,87.94 1965-04-09,87.04,87.87,86.86,87.56,6580000,87.56 1965-04-08,86.55,87.35,86.34,87.04,5770000,87.04 1965-04-07,86.50,86.88,86.14,86.55,4430000,86.55 1965-04-06,86.53,86.91,86.08,86.50,4610000,86.50 1965-04-05,86.53,87.08,86.14,86.53,4920000,86.53 1965-04-02,86.32,86.89,86.08,86.53,5060000,86.53 1965-04-01,86.16,86.73,85.87,86.32,4890000,86.32 1965-03-31,86.20,86.64,85.83,86.16,4470000,86.16 1965-03-30,86.03,86.53,85.69,86.20,4270000,86.20 1965-03-29,86.20,86.66,85.65,86.03,4590000,86.03 1965-03-26,86.84,87.06,85.96,86.20,5020000,86.20 1965-03-25,87.09,87.50,86.55,86.84,5460000,86.84 1965-03-24,86.93,87.55,86.68,87.09,5420000,87.09 1965-03-23,86.83,87.34,86.45,86.93,4820000,86.93 1965-03-22,86.84,87.34,86.41,86.83,4920000,86.83 1965-03-19,86.81,87.37,86.43,86.84,5040000,86.84 1965-03-18,87.02,87.48,86.50,86.81,4990000,86.81 1965-03-17,87.13,87.51,86.63,87.02,5120000,87.02 1965-03-16,87.24,87.61,86.67,87.13,5480000,87.13 1965-03-15,87.21,87.92,86.82,87.24,6000000,87.24 1965-03-12,86.90,87.65,86.60,87.21,6370000,87.21 1965-03-11,86.54,87.29,86.17,86.90,5770000,86.90 1965-03-10,86.69,87.07,86.20,86.54,5100000,86.54 1965-03-09,86.83,87.27,86.33,86.69,5210000,86.69 1965-03-08,86.80,87.28,86.31,86.83,5250000,86.83 1965-03-05,86.98,87.26,86.00,86.80,6120000,86.80 1965-03-04,87.26,87.72,86.63,86.98,7300000,86.98 1965-03-03,87.40,87.83,86.88,87.26,6600000,87.26 1965-03-02,87.25,87.79,86.84,87.40,5730000,87.40 1965-03-01,87.43,87.93,86.92,87.25,5780000,87.25 1965-02-26,87.20,87.84,86.81,87.43,5800000,87.43 1965-02-25,87.17,87.70,86.70,87.20,6680000,87.20 1965-02-24,86.64,87.72,86.43,87.17,7160000,87.17 1965-02-23,86.21,87.01,86.03,86.64,5880000,86.64 1965-02-19,86.05,86.67,85.71,86.21,5560000,86.21 1965-02-18,85.77,86.48,85.47,86.05,6060000,86.05 1965-02-17,85.67,86.25,85.25,85.77,5510000,85.77 1965-02-16,86.07,86.31,85.33,85.67,5000000,85.67 1965-02-15,86.17,86.86,85.75,86.07,5760000,86.07 1965-02-12,85.54,86.48,85.54,86.17,4960000,86.17 1965-02-11,86.46,86.89,85.40,85.54,5800000,85.54 1965-02-10,87.24,87.70,86.20,86.46,7210000,86.46 1965-02-09,86.95,87.64,86.70,87.24,5690000,87.24 1965-02-08,87.00,87.00,85.95,86.95,6010000,86.95 1965-02-05,87.57,87.98,86.90,87.29,5690000,87.29 1965-02-04,87.63,88.06,87.06,87.57,6230000,87.57 1965-02-03,87.55,88.01,87.07,87.63,6130000,87.63 1965-02-02,87.58,87.94,87.03,87.55,5460000,87.55 1965-02-01,87.56,88.01,87.05,87.58,5690000,87.58 1965-01-29,87.48,88.19,87.18,87.56,6940000,87.56 1965-01-28,87.23,87.88,86.89,87.48,6730000,87.48 1965-01-27,86.94,87.67,86.70,87.23,6010000,87.23 1965-01-26,86.86,87.45,86.51,86.94,5760000,86.94 1965-01-25,86.74,87.27,86.39,86.86,5370000,86.86 1965-01-22,86.52,87.15,86.20,86.74,5430000,86.74 1965-01-21,86.60,86.90,86.02,86.52,4780000,86.52 1965-01-20,86.63,87.10,86.26,86.60,5550000,86.60 1965-01-19,86.49,87.09,86.15,86.63,5550000,86.63 1965-01-18,86.21,87.15,85.99,86.49,5550000,86.49 1965-01-15,85.84,86.52,85.60,86.21,5340000,86.21 1965-01-14,85.84,86.38,85.41,85.84,5810000,85.84 1965-01-13,85.61,86.27,85.35,85.84,6160000,85.84 1965-01-12,85.40,85.98,85.13,85.61,5400000,85.61 1965-01-11,85.37,85.81,84.90,85.40,5440000,85.40 1965-01-08,85.26,85.84,84.91,85.37,5340000,85.37 1965-01-07,84.89,85.62,84.66,85.26,5080000,85.26 1965-01-06,84.63,85.38,84.45,84.89,4850000,84.89 1965-01-05,84.23,85.02,84.02,84.63,4110000,84.63 1965-01-04,84.75,85.15,83.77,84.23,3930000,84.23 1964-12-31,84.30,85.18,84.18,84.75,6470000,84.75 1964-12-30,83.81,84.63,83.63,84.30,5610000,84.30 1964-12-29,84.07,84.35,83.38,83.81,4450000,83.81 1964-12-28,84.15,84.58,83.70,84.07,3990000,84.07 1964-12-24,84.15,84.59,83.74,84.15,3600000,84.15 1964-12-23,84.33,84.76,83.79,84.15,4470000,84.15 1964-12-22,84.38,84.88,83.94,84.33,4520000,84.33 1964-12-21,84.29,84.91,84.11,84.38,4470000,84.38 1964-12-18,83.90,84.65,83.73,84.29,4630000,84.29 1964-12-17,83.55,84.24,83.34,83.90,4850000,83.90 1964-12-16,83.22,83.94,83.00,83.55,4610000,83.55 1964-12-15,83.45,83.79,82.65,83.22,5340000,83.22 1964-12-14,83.66,84.17,83.10,83.45,4340000,83.45 1964-12-11,83.45,84.05,83.09,83.66,4530000,83.66 1964-12-10,83.46,83.96,82.98,83.45,4790000,83.45 1964-12-09,84.00,84.24,83.24,83.46,5120000,83.46 1964-12-08,84.33,84.71,83.69,84.00,4990000,84.00 1964-12-07,84.35,85.03,84.04,84.33,4770000,84.33 1964-12-04,84.35,84.35,84.35,84.35,4340000,84.35 1964-12-03,83.79,84.74,83.71,84.18,4250000,84.18 1964-12-02,83.55,84.23,83.12,83.79,4930000,83.79 1964-12-01,84.42,84.56,83.36,83.55,4940000,83.55 1964-11-30,85.16,85.41,84.10,84.42,4890000,84.42 1964-11-27,85.44,85.68,84.55,85.16,4070000,85.16 1964-11-25,85.73,86.18,85.10,85.44,4800000,85.44 1964-11-24,86.00,86.12,85.15,85.73,5070000,85.73 1964-11-23,86.28,86.59,85.48,86.00,4860000,86.00 1964-11-20,86.18,86.80,85.73,86.28,5210000,86.28 1964-11-19,86.22,86.57,85.60,86.18,5570000,86.18 1964-11-18,86.03,86.80,85.73,86.22,6560000,86.22 1964-11-17,85.65,86.55,85.48,86.03,5920000,86.03 1964-11-16,85.21,85.94,84.88,85.65,4870000,85.65 1964-11-13,85.19,85.68,84.76,85.21,4860000,85.21 1964-11-12,85.08,85.63,84.75,85.19,5250000,85.19 1964-11-11,84.84,85.30,84.49,85.08,3790000,85.08 1964-11-10,85.19,85.55,84.49,84.84,5020000,84.84 1964-11-09,85.23,85.72,84.93,85.19,4560000,85.19 1964-11-06,85.16,85.55,84.65,85.23,4810000,85.23 1964-11-05,85.14,85.62,84.72,85.16,4380000,85.16 1964-11-04,85.18,85.90,84.80,85.14,4720000,85.14 1964-11-02,84.86,85.54,84.51,85.18,4430000,85.18 1964-10-30,84.73,85.22,84.41,84.86,4120000,84.86 1964-10-29,84.69,85.15,84.36,84.73,4390000,84.73 1964-10-28,85.00,85.37,84.43,84.69,4890000,84.69 1964-10-27,85.00,85.40,84.61,85.00,4470000,85.00 1964-10-26,85.14,85.70,84.65,85.00,5230000,85.00 1964-10-23,84.94,85.42,84.57,85.14,3830000,85.14 1964-10-22,85.10,85.44,84.51,84.94,4670000,84.94 1964-10-21,85.18,85.64,84.77,85.10,5170000,85.10 1964-10-20,84.93,85.57,84.56,85.18,5140000,85.18 1964-10-19,84.83,85.36,84.47,84.93,5010000,84.93 1964-10-16,84.25,85.10,84.10,84.83,5140000,84.83 1964-10-15,84.79,84.99,83.65,84.25,6500000,84.25 1964-10-14,84.96,85.29,84.50,84.79,4530000,84.79 1964-10-13,85.24,85.57,84.63,84.96,5400000,84.96 1964-10-12,85.22,85.58,84.88,85.24,4110000,85.24 1964-10-09,85.04,85.60,84.72,85.22,5290000,85.22 1964-10-08,84.80,85.40,84.47,85.04,5060000,85.04 1964-10-07,84.79,85.25,84.42,84.80,5090000,84.80 1964-10-06,84.74,85.24,84.37,84.79,4820000,84.79 1964-10-05,84.36,85.25,84.20,84.74,4850000,84.74 1964-10-02,84.08,84.64,83.71,84.36,4370000,84.36 1964-10-01,84.18,84.53,83.74,84.08,4470000,84.08 1964-09-30,84.24,84.66,83.86,84.18,4720000,84.18 1964-09-29,84.28,84.80,83.84,84.24,5070000,84.24 1964-09-28,84.21,84.73,83.79,84.28,4810000,84.28 1964-09-25,84.00,84.62,83.56,84.21,6170000,84.21 1964-09-24,83.91,84.43,83.45,84.00,5840000,84.00 1964-09-23,83.89,84.37,83.45,83.91,5920000,83.91 1964-09-22,83.86,84.44,83.53,83.89,5250000,83.89 1964-09-21,83.48,84.32,83.41,83.86,5310000,83.86 1964-09-18,83.79,84.29,83.03,83.48,6160000,83.48 1964-09-17,83.24,84.18,83.17,83.79,6380000,83.79 1964-09-16,83.00,83.52,82.57,83.24,4230000,83.24 1964-09-15,83.22,83.68,82.69,83.00,5690000,83.00 1964-09-14,83.45,83.89,82.88,83.22,5370000,83.22 1964-09-11,83.10,83.84,82.79,83.45,5630000,83.45 1964-09-10,83.05,83.50,82.60,83.10,5470000,83.10 1964-09-09,82.87,83.51,82.54,83.05,5690000,83.05 1964-09-08,82.76,83.24,82.46,82.87,4090000,82.87 1964-09-04,82.56,83.03,82.31,82.76,4210000,82.76 1964-09-03,82.31,82.83,82.04,82.56,4310000,82.56 1964-09-02,82.18,82.76,81.95,82.31,4800000,82.31 1964-09-01,81.83,82.50,81.57,82.18,4650000,82.18 1964-08-31,81.99,82.48,81.46,81.83,3340000,81.83 1964-08-28,81.70,82.29,81.54,81.99,3760000,81.99 1964-08-27,81.32,81.94,81.07,81.70,3560000,81.70 1964-08-26,81.44,81.74,80.99,81.32,3300000,81.32 1964-08-25,81.91,82.13,81.20,81.44,3780000,81.44 1964-08-24,82.07,82.48,81.64,81.91,3790000,81.91 1964-08-21,81.94,82.43,81.64,82.07,3620000,82.07 1964-08-20,82.32,82.57,81.60,81.94,3840000,81.94 1964-08-19,82.40,82.80,81.99,82.32,4160000,82.32 1964-08-18,82.36,82.79,82.01,82.40,4180000,82.40 1964-08-17,82.35,82.85,82.02,82.36,3780000,82.36 1964-08-14,82.41,82.83,82.03,82.35,4080000,82.35 1964-08-13,82.17,82.87,81.98,82.41,4600000,82.41 1964-08-12,81.76,82.53,81.60,82.17,4140000,82.17 1964-08-11,81.78,82.25,81.45,81.76,3450000,81.76 1964-08-10,81.86,82.23,81.43,81.78,3050000,81.78 1964-08-07,81.34,82.20,81.19,81.86,3190000,81.86 1964-08-06,82.09,82.45,81.20,81.34,3940000,81.34 1964-08-05,81.96,82.41,80.80,82.09,6160000,82.09 1964-08-04,83.00,83.02,81.68,81.96,4780000,81.96 1964-08-03,83.18,83.49,82.65,83.00,3780000,83.00 1964-07-31,83.09,83.57,82.72,83.18,4220000,83.18 1964-07-30,82.92,83.50,82.63,83.09,4530000,83.09 1964-07-29,82.85,83.30,82.47,82.92,4050000,82.92 1964-07-28,83.08,83.30,82.40,82.85,3860000,82.85 1964-07-27,83.46,83.82,82.82,83.08,4090000,83.08 1964-07-24,83.48,83.92,83.07,83.46,4210000,83.46 1964-07-23,83.52,83.91,83.06,83.48,4560000,83.48 1964-07-22,83.54,83.95,82.96,83.52,4570000,83.52 1964-07-21,83.74,83.99,83.06,83.54,4570000,83.54 1964-07-20,84.01,84.33,83.44,83.74,4390000,83.74 1964-07-17,83.64,84.33,83.37,84.01,4640000,84.01 1964-07-16,83.34,83.98,83.06,83.64,4640000,83.64 1964-07-15,83.06,83.67,82.72,83.34,4610000,83.34 1964-07-14,83.31,83.71,82.72,83.06,4760000,83.06 1964-07-13,83.36,83.86,82.92,83.31,4800000,83.31 1964-07-10,83.22,83.99,82.87,83.36,5420000,83.36 1964-07-09,83.12,83.64,82.74,83.22,5040000,83.22 1964-07-08,83.12,83.56,82.58,83.12,4760000,83.12 1964-07-07,82.98,83.53,82.60,83.12,5240000,83.12 1964-07-06,82.60,83.38,82.37,82.98,5080000,82.98 1964-07-02,82.27,82.98,82.09,82.60,5230000,82.60 1964-07-01,81.69,82.51,81.46,82.27,5320000,82.27 1964-06-30,81.64,82.07,81.19,81.69,4360000,81.69 1964-06-29,81.46,82.10,81.10,81.64,4380000,81.64 1964-06-26,81.21,81.78,80.86,81.46,4440000,81.46 1964-06-25,81.06,81.73,80.75,81.21,5010000,81.21 1964-06-24,80.77,81.45,80.41,81.06,4840000,81.06 1964-06-23,81.11,81.43,80.50,80.77,4060000,80.77 1964-06-22,80.89,81.54,80.66,81.11,4540000,81.11 1964-06-19,80.79,81.23,80.39,80.89,4050000,80.89 1964-06-18,80.81,81.34,80.43,80.79,4730000,80.79 1964-06-17,80.40,81.13,80.22,80.81,5340000,80.81 1964-06-16,79.97,80.72,79.85,80.40,4590000,80.40 1964-06-15,79.60,80.33,79.39,79.97,4110000,79.97 1964-06-12,79.73,80.05,79.19,79.60,3840000,79.60 1964-06-11,79.44,80.13,79.24,79.73,3620000,79.73 1964-06-10,79.14,79.84,79.02,79.44,4170000,79.44 1964-06-09,78.64,79.39,78.15,79.14,4470000,79.14 1964-06-08,79.02,79.44,78.44,78.64,4010000,78.64 1964-06-05,78.67,79.45,78.50,79.02,4240000,79.02 1964-06-04,79.49,79.75,78.44,78.67,4880000,78.67 1964-06-03,79.70,80.12,79.27,79.49,3990000,79.49 1964-06-02,80.11,80.60,79.50,79.70,4180000,79.70 1964-06-01,80.37,80.83,79.83,80.11,4300000,80.11 1964-05-28,80.26,80.75,79.88,80.37,4560000,80.37 1964-05-27,80.39,80.72,79.78,80.26,4450000,80.26 1964-05-26,80.56,80.94,80.12,80.39,4290000,80.39 1964-05-25,80.73,81.16,80.21,80.56,3990000,80.56 1964-05-22,80.94,81.15,80.36,80.73,4640000,80.73 1964-05-21,80.66,81.49,80.36,80.94,5350000,80.94 1964-05-20,80.30,81.02,80.09,80.66,4790000,80.66 1964-05-19,80.72,81.04,79.96,80.30,4360000,80.30 1964-05-18,81.10,81.47,80.42,80.72,4590000,80.72 1964-05-15,80.86,81.45,80.49,81.10,5070000,81.10 1964-05-14,80.97,81.28,80.37,80.86,4720000,80.86 1964-05-13,81.16,81.65,80.66,80.97,5890000,80.97 1964-05-12,80.90,81.81,80.66,81.16,5200000,81.16 1964-05-11,81.00,81.51,80.58,80.90,4490000,80.90 1964-05-08,81.00,81.00,81.00,81.00,4910000,81.00 1964-05-07,81.06,81.72,80.67,81.15,5600000,81.15 1964-05-06,80.88,81.57,80.53,81.06,5560000,81.06 1964-05-05,80.47,81.20,79.99,80.88,5340000,80.88 1964-05-04,80.17,81.01,79.87,80.47,5360000,80.47 1964-05-01,79.46,80.47,79.46,80.17,5990000,80.17 1964-04-30,79.70,80.08,79.08,79.46,5690000,79.46 1964-04-29,79.90,80.60,79.29,79.70,6200000,79.70 1964-04-28,79.35,80.26,79.14,79.90,4790000,79.90 1964-04-27,79.75,80.01,78.90,79.35,5070000,79.35 1964-04-24,80.38,80.62,79.45,79.75,5610000,79.75 1964-04-23,80.49,81.20,80.09,80.38,6690000,80.38 1964-04-22,80.54,80.92,80.06,80.49,5390000,80.49 1964-04-21,80.50,80.98,80.05,80.54,5750000,80.54 1964-04-20,80.55,81.04,80.11,80.50,5560000,80.50 1964-04-17,80.20,80.98,79.99,80.55,6030000,80.55 1964-04-16,80.09,80.62,79.73,80.20,5240000,80.20 1964-04-15,79.99,80.50,79.63,80.09,5270000,80.09 1964-04-14,79.77,80.37,79.46,79.99,5120000,79.99 1964-04-13,79.85,80.30,79.42,79.77,5330000,79.77 1964-04-10,79.70,80.26,79.43,79.85,4990000,79.85 1964-04-09,79.75,80.23,79.36,79.70,5300000,79.70 1964-04-08,79.74,80.17,79.26,79.75,5380000,79.75 1964-04-07,80.02,80.44,79.41,79.74,5900000,79.74 1964-04-06,79.94,80.45,79.55,80.02,5840000,80.02 1964-04-03,79.70,80.37,79.45,79.94,5990000,79.94 1964-04-02,79.24,80.09,79.13,79.70,6840000,79.70 1964-04-01,78.98,79.58,78.67,79.24,5510000,79.24 1964-03-31,79.14,79.51,78.57,78.98,5270000,78.98 1964-03-30,79.19,79.67,78.75,79.14,6060000,79.14 1964-03-26,78.98,79.58,78.67,79.19,5760000,79.19 1964-03-25,78.79,79.33,78.17,78.98,5420000,78.98 1964-03-24,78.93,79.34,78.51,78.79,5210000,78.79 1964-03-23,78.92,79.33,78.45,78.93,4940000,78.93 1964-03-20,79.30,79.35,78.92,78.92,5020000,78.92 1964-03-19,79.38,79.85,78.94,79.30,5670000,79.30 1964-03-18,79.32,79.89,78.90,79.38,5890000,79.38 1964-03-17,79.14,79.65,78.77,79.32,5480000,79.32 1964-03-16,79.14,79.60,78.72,79.14,5140000,79.14 1964-03-13,79.08,79.59,78.74,79.14,5660000,79.14 1964-03-12,78.95,79.41,78.55,79.08,5290000,79.08 1964-03-11,78.59,79.42,78.45,78.95,6180000,78.95 1964-03-10,78.33,78.90,77.95,78.59,5500000,78.59 1964-03-09,78.31,78.88,77.95,78.33,5510000,78.33 1964-03-06,78.06,78.60,77.85,78.31,4790000,78.31 1964-03-05,78.07,78.44,77.58,78.06,4680000,78.06 1964-03-04,78.22,78.70,77.70,78.07,5250000,78.07 1964-03-03,77.97,78.66,77.69,78.22,5350000,78.22 1964-03-02,77.80,78.38,77.50,77.97,5690000,77.97 1964-02-28,77.62,78.06,77.20,77.80,4980000,77.80 1964-02-27,77.87,78.29,77.38,77.62,5420000,77.62 1964-02-26,77.68,78.13,77.33,77.87,5350000,77.87 1964-02-25,77.68,78.31,77.19,77.68,5010000,77.68 1964-02-24,77.62,78.16,77.27,77.68,5630000,77.68 1964-02-20,77.55,77.99,77.16,77.62,4690000,77.62 1964-02-19,77.47,77.98,77.13,77.55,4280000,77.55 1964-02-18,77.46,77.90,77.00,77.47,4660000,77.47 1964-02-17,77.48,77.93,77.04,77.46,4780000,77.46 1964-02-14,77.52,77.82,77.02,77.48,4360000,77.48 1964-02-13,77.57,77.93,77.10,77.52,4820000,77.52 1964-02-12,77.33,77.88,77.14,77.57,4650000,77.57 1964-02-11,77.05,77.65,76.81,77.33,4040000,77.33 1964-02-10,77.18,77.77,76.83,77.05,4150000,77.05 1964-02-07,76.93,77.51,76.66,77.18,4710000,77.18 1964-02-06,76.75,77.26,76.47,76.93,4110000,76.93 1964-02-05,76.88,77.28,76.36,76.75,4010000,76.75 1964-02-04,76.97,77.31,76.46,76.88,4320000,76.88 1964-02-03,77.04,77.55,76.53,76.97,4140000,76.97 1964-01-31,76.70,77.37,76.39,77.04,4000000,77.04 1964-01-30,76.63,77.20,76.26,76.70,4230000,76.70 1964-01-29,77.10,77.36,76.33,76.63,4450000,76.63 1964-01-28,77.08,77.56,76.63,77.10,4720000,77.10 1964-01-27,77.11,77.78,76.64,77.08,5240000,77.08 1964-01-24,77.09,77.56,76.58,77.11,5080000,77.11 1964-01-23,77.03,77.62,76.67,77.09,5380000,77.09 1964-01-22,76.62,77.62,76.45,77.03,5430000,77.03 1964-01-21,76.41,76.99,75.87,76.62,4800000,76.62 1964-01-20,76.56,77.19,76.02,76.41,5570000,76.41 1964-01-17,76.55,77.09,76.02,76.56,5600000,76.56 1964-01-16,76.64,77.21,76.05,76.55,6200000,76.55 1964-01-15,76.36,77.06,75.96,76.64,6750000,76.64 1964-01-14,76.22,76.85,75.88,76.36,6500000,76.36 1964-01-13,76.24,76.71,75.78,76.22,5440000,76.22 1964-01-10,76.28,76.67,75.74,76.24,5260000,76.24 1964-01-09,76.00,76.64,75.60,76.28,5180000,76.28 1964-01-08,75.69,76.35,75.39,76.00,5380000,76.00 1964-01-07,75.67,76.24,75.25,75.69,5700000,75.69 1964-01-06,75.50,76.12,75.18,75.67,5480000,75.67 1964-01-03,75.43,76.04,75.09,75.50,5550000,75.50 1964-01-02,75.02,75.79,74.82,75.43,4680000,75.43 1963-12-31,74.56,75.36,74.40,75.02,6730000,75.02 1963-12-30,74.44,74.94,74.13,74.56,4930000,74.56 1963-12-27,74.32,74.91,74.09,74.44,4360000,74.44 1963-12-26,73.97,74.63,73.74,74.32,3700000,74.32 1963-12-24,73.81,74.48,73.44,73.97,3970000,73.97 1963-12-23,74.28,74.45,73.49,73.81,4540000,73.81 1963-12-20,74.40,74.75,73.85,74.28,4600000,74.28 1963-12-19,74.63,74.92,74.08,74.40,4410000,74.40 1963-12-18,74.74,75.21,74.25,74.63,6000000,74.63 1963-12-17,74.30,75.08,74.07,74.74,5140000,74.74 1963-12-16,74.06,74.66,73.78,74.30,4280000,74.30 1963-12-13,73.91,74.39,73.68,74.06,4290000,74.06 1963-12-12,73.90,74.31,73.58,73.91,4220000,73.91 1963-12-11,73.99,74.37,73.58,73.90,4400000,73.90 1963-12-10,73.96,74.48,73.40,73.99,4560000,73.99 1963-12-09,74.00,74.41,73.56,73.96,4430000,73.96 1963-12-06,74.28,74.63,73.62,74.00,4830000,74.00 1963-12-05,73.80,74.57,73.45,74.28,5190000,74.28 1963-12-04,73.62,74.18,73.21,73.80,4790000,73.80 1963-12-03,73.66,74.01,73.14,73.62,4520000,73.62 1963-12-02,73.23,74.08,73.02,73.66,4770000,73.66 1963-11-29,72.25,73.47,72.05,73.23,4810000,73.23 1963-11-27,72.38,72.78,71.76,72.25,5210000,72.25 1963-11-26,71.40,72.74,71.40,72.38,9320000,72.38 1963-11-22,71.62,72.17,69.48,69.61,6630000,69.61 1963-11-21,72.56,72.86,71.40,71.62,5670000,71.62 1963-11-20,71.90,73.14,71.49,72.56,5330000,72.56 1963-11-19,71.83,72.61,71.42,71.90,4430000,71.90 1963-11-18,72.35,72.52,71.42,71.83,4730000,71.83 1963-11-15,72.95,73.20,72.09,72.35,4790000,72.35 1963-11-14,73.29,73.53,72.63,72.95,4610000,72.95 1963-11-13,73.23,73.67,72.89,73.29,4710000,73.29 1963-11-12,73.23,73.23,73.23,73.23,4610000,73.23 1963-11-11,73.52,73.52,73.52,73.52,3970000,73.52 1963-11-08,73.06,73.66,72.80,73.36,4570000,73.36 1963-11-07,72.81,73.48,72.58,73.06,4320000,73.06 1963-11-06,73.45,73.47,72.33,72.81,5600000,72.81 1963-11-04,73.83,74.27,73.09,73.45,5440000,73.45 1963-11-01,74.01,74.44,73.47,73.83,5240000,73.83 1963-10-31,73.80,74.35,73.25,74.01,5030000,74.01 1963-10-30,74.46,74.59,73.43,73.80,5170000,73.80 1963-10-29,74.48,75.18,73.97,74.46,6100000,74.46 1963-10-28,74.01,75.15,73.75,74.48,7150000,74.48 1963-10-25,73.28,74.41,73.06,74.01,6390000,74.01 1963-10-24,73.00,73.73,72.74,73.28,6280000,73.28 1963-10-23,72.96,73.55,72.59,73.00,5830000,73.00 1963-10-22,73.38,73.55,72.48,72.96,6420000,72.96 1963-10-21,73.32,73.87,73.03,73.38,5450000,73.38 1963-10-18,73.26,73.74,72.85,73.32,5830000,73.32 1963-10-17,72.97,73.77,72.84,73.26,6790000,73.26 1963-10-16,72.40,73.20,72.08,72.97,5570000,72.97 1963-10-15,72.30,72.79,71.99,72.40,4550000,72.40 1963-10-14,72.27,72.43,71.85,72.30,4270000,72.30 1963-10-11,72.20,72.71,71.87,72.27,4740000,72.27 1963-10-10,71.87,72.52,71.60,72.20,4470000,72.20 1963-10-09,71.98,71.98,71.60,71.87,5520000,71.87 1963-10-08,72.70,73.14,72.24,72.60,4920000,72.60 1963-10-07,72.85,73.27,72.39,72.70,4050000,72.70 1963-10-04,72.83,73.19,72.46,72.85,5120000,72.85 1963-10-03,72.30,73.10,72.10,72.83,4510000,72.83 1963-10-02,72.22,72.67,71.92,72.30,3780000,72.30 1963-10-01,71.70,72.65,71.57,72.22,4420000,72.22 1963-09-30,72.13,72.37,71.28,71.70,3730000,71.70 1963-09-27,72.27,72.60,71.60,72.13,4350000,72.13 1963-09-26,72.89,73.07,72.01,72.27,5100000,72.27 1963-09-25,73.30,73.87,72.58,72.89,6340000,72.89 1963-09-24,72.96,73.67,72.59,73.30,5520000,73.30 1963-09-23,73.30,73.53,72.62,72.96,5140000,72.96 1963-09-20,73.22,73.71,72.92,73.30,5310000,73.30 1963-09-19,72.80,73.47,72.61,73.22,4080000,73.22 1963-09-18,73.12,73.44,72.51,72.80,5070000,72.80 1963-09-17,73.07,73.64,72.79,73.12,4950000,73.12 1963-09-16,73.17,73.63,72.80,73.07,4740000,73.07 1963-09-13,73.15,73.59,72.82,73.17,5230000,73.17 1963-09-12,73.20,73.60,72.72,73.15,5560000,73.15 1963-09-11,72.99,73.79,72.83,73.20,6670000,73.20 1963-09-10,72.58,73.27,72.25,72.99,5310000,72.99 1963-09-09,72.84,73.23,72.26,72.58,5020000,72.58 1963-09-06,73.00,73.51,72.51,72.84,7160000,72.84 1963-09-05,72.64,73.19,72.15,73.00,5700000,73.00 1963-09-04,72.66,73.18,72.32,72.64,6070000,72.64 1963-09-03,72.50,73.09,72.30,72.66,5570000,72.66 1963-08-30,72.16,72.71,71.88,72.50,4560000,72.50 1963-08-29,72.04,72.56,71.83,72.16,5110000,72.16 1963-08-28,71.52,72.39,71.49,72.04,5120000,72.04 1963-08-27,71.91,72.04,71.27,71.52,4080000,71.52 1963-08-26,71.76,72.30,71.57,71.91,4700000,71.91 1963-08-23,71.54,72.14,71.33,71.76,4880000,71.76 1963-08-22,71.29,71.81,70.95,71.54,4540000,71.54 1963-08-21,71.38,71.73,71.00,71.29,3820000,71.29 1963-08-20,71.44,71.91,71.03,71.38,3660000,71.38 1963-08-19,71.49,71.92,71.15,71.44,3650000,71.44 1963-08-16,71.38,71.95,71.05,71.49,4130000,71.49 1963-08-15,71.07,71.71,70.81,71.38,4980000,71.38 1963-08-14,70.79,71.32,70.39,71.07,4420000,71.07 1963-08-13,70.59,71.09,70.32,70.79,4450000,70.79 1963-08-12,70.48,71.00,70.19,70.59,4770000,70.59 1963-08-09,70.02,70.65,69.83,70.48,4050000,70.48 1963-08-08,69.96,70.31,69.58,70.02,3460000,70.02 1963-08-07,70.17,70.53,69.69,69.96,3790000,69.96 1963-08-06,69.71,70.40,69.57,70.17,3760000,70.17 1963-08-05,69.30,69.97,69.20,69.71,3370000,69.71 1963-08-02,69.07,69.56,68.86,69.30,2940000,69.30 1963-08-01,69.13,69.47,68.64,69.07,3410000,69.07 1963-07-31,69.24,69.83,68.91,69.13,3960000,69.13 1963-07-30,68.67,69.45,68.58,69.24,3550000,69.24 1963-07-29,68.54,68.96,68.32,68.67,2840000,68.67 1963-07-26,68.26,68.76,68.03,68.54,2510000,68.54 1963-07-25,68.28,68.92,68.02,68.26,3710000,68.26 1963-07-24,67.91,68.54,67.76,68.28,2810000,68.28 1963-07-23,67.90,68.57,67.65,67.91,3500000,67.91 1963-07-22,68.35,68.60,67.54,67.90,3700000,67.90 1963-07-19,68.49,68.70,67.90,68.35,3340000,68.35 1963-07-18,68.93,69.27,68.34,68.49,3710000,68.49 1963-07-17,69.14,69.53,68.68,68.93,3940000,68.93 1963-07-16,69.20,69.51,68.85,69.14,3000000,69.14 1963-07-15,69.64,69.73,68.97,69.20,3290000,69.20 1963-07-12,69.76,70.13,69.36,69.64,3660000,69.64 1963-07-11,69.89,70.30,69.52,69.76,4100000,69.76 1963-07-10,70.04,70.31,69.56,69.89,3730000,69.89 1963-07-09,69.74,70.39,69.55,70.04,3830000,70.04 1963-07-08,70.22,70.35,69.47,69.74,3290000,69.74 1963-07-05,69.94,70.48,69.78,70.22,2910000,70.22 1963-07-03,69.46,70.28,69.42,69.94,4030000,69.94 1963-07-02,68.86,69.72,68.74,69.46,3540000,69.46 1963-07-01,69.37,69.53,68.58,68.86,3360000,68.86 1963-06-28,69.07,69.68,68.93,69.37,3020000,69.37 1963-06-27,69.41,69.81,68.78,69.07,4540000,69.07 1963-06-26,70.04,70.10,69.17,69.41,4500000,69.41 1963-06-25,70.20,70.51,69.75,70.04,4120000,70.04 1963-06-24,70.25,70.67,69.84,70.20,3700000,70.20 1963-06-21,70.01,70.57,69.79,70.25,4190000,70.25 1963-06-20,70.09,70.36,69.31,70.01,4970000,70.01 1963-06-19,70.02,70.47,69.75,70.09,3970000,70.09 1963-06-18,69.95,70.43,69.63,70.02,3910000,70.02 1963-06-17,69.95,69.95,69.95,69.95,3510000,69.95 1963-06-14,70.23,70.60,69.87,70.25,3840000,70.25 1963-06-13,70.41,70.85,69.98,70.23,4690000,70.23 1963-06-12,70.03,70.81,69.91,70.41,5210000,70.41 1963-06-11,69.94,70.41,69.58,70.03,4390000,70.03 1963-06-10,70.41,70.51,69.57,69.94,4690000,69.94 1963-06-07,70.58,70.98,70.10,70.41,5110000,70.41 1963-06-06,70.53,70.95,70.11,70.58,4990000,70.58 1963-06-05,70.70,71.17,70.17,70.53,5860000,70.53 1963-06-04,70.69,71.08,70.20,70.70,5970000,70.70 1963-06-03,70.80,71.24,70.39,70.69,5400000,70.69 1963-05-31,70.33,71.14,70.27,70.80,4680000,70.80 1963-05-29,70.01,70.65,69.86,70.33,4320000,70.33 1963-05-28,69.87,70.41,69.55,70.01,3860000,70.01 1963-05-27,70.02,70.27,69.48,69.87,3760000,69.87 1963-05-24,70.10,70.44,69.66,70.02,4320000,70.02 1963-05-23,70.14,70.53,69.79,70.10,4400000,70.10 1963-05-22,70.14,70.68,69.82,70.14,5560000,70.14 1963-05-21,69.96,70.51,69.62,70.14,5570000,70.14 1963-05-20,70.29,70.48,69.59,69.96,4710000,69.96 1963-05-17,70.25,70.63,69.83,70.29,4410000,70.29 1963-05-16,70.43,70.81,69.91,70.25,5640000,70.25 1963-05-15,70.21,70.77,69.87,70.43,5650000,70.43 1963-05-14,70.48,70.73,69.92,70.21,4740000,70.21 1963-05-13,70.52,70.89,70.11,70.48,4920000,70.48 1963-05-10,70.35,70.81,69.99,70.52,5260000,70.52 1963-05-09,70.01,70.74,69.86,70.35,5600000,70.35 1963-05-08,69.44,70.24,69.23,70.01,5140000,70.01 1963-05-07,69.53,69.92,69.03,69.44,4140000,69.44 1963-05-06,70.03,70.31,69.32,69.53,4090000,69.53 1963-05-03,70.17,70.51,69.78,70.03,4760000,70.03 1963-05-02,69.97,70.50,69.75,70.17,4480000,70.17 1963-05-01,69.80,70.43,69.61,69.97,5060000,69.97 1963-04-30,69.65,70.18,69.26,69.80,4680000,69.80 1963-04-29,69.70,70.04,69.26,69.65,3980000,69.65 1963-04-26,69.76,70.11,69.23,69.70,4490000,69.70 1963-04-25,69.72,70.08,69.25,69.76,5070000,69.76 1963-04-24,69.53,70.12,69.34,69.72,5910000,69.72 1963-04-23,69.30,69.83,68.95,69.53,5220000,69.53 1963-04-22,69.23,69.82,69.01,69.30,5180000,69.30 1963-04-19,68.89,69.46,68.60,69.23,4660000,69.23 1963-04-18,68.92,69.34,68.56,68.89,4770000,68.89 1963-04-17,69.14,69.37,68.47,68.92,5220000,68.92 1963-04-16,69.09,69.61,68.66,69.14,5570000,69.14 1963-04-15,68.77,69.56,68.58,69.09,5930000,69.09 1963-04-11,68.29,69.07,67.97,68.77,5250000,68.77 1963-04-10,68.45,68.89,67.66,68.29,5880000,68.29 1963-04-09,68.52,68.84,68.03,68.45,5090000,68.45 1963-04-08,68.28,68.91,68.05,68.52,5940000,68.52 1963-04-05,67.85,68.46,67.46,68.28,5240000,68.28 1963-04-04,67.36,68.12,67.28,67.85,5300000,67.85 1963-04-03,66.84,67.55,66.63,67.36,4660000,67.36 1963-04-02,66.85,67.36,66.51,66.84,4360000,66.84 1963-04-01,66.57,67.18,66.23,66.85,3890000,66.85 1963-03-29,66.58,66.90,66.23,66.57,3390000,66.57 1963-03-28,66.68,67.01,66.32,66.58,3890000,66.58 1963-03-27,66.40,66.93,66.21,66.68,4270000,66.68 1963-03-26,66.21,66.73,66.01,66.40,4100000,66.40 1963-03-25,66.19,66.60,65.92,66.21,3700000,66.21 1963-03-22,65.85,66.44,65.68,66.19,3820000,66.19 1963-03-21,65.95,66.25,65.60,65.85,3220000,65.85 1963-03-20,65.47,66.15,65.30,65.95,3690000,65.95 1963-03-19,65.61,65.85,65.19,65.47,3180000,65.47 1963-03-18,65.93,66.17,65.36,65.61,3250000,65.61 1963-03-15,65.60,66.22,65.39,65.93,3400000,65.93 1963-03-14,65.91,66.21,65.39,65.60,3540000,65.60 1963-03-13,65.67,66.27,65.54,65.91,4120000,65.91 1963-03-12,65.51,65.97,65.26,65.67,3350000,65.67 1963-03-11,65.33,65.86,65.11,65.51,3180000,65.51 1963-03-08,65.26,65.74,65.03,65.33,3360000,65.33 1963-03-07,64.85,65.60,64.81,65.26,3350000,65.26 1963-03-06,64.74,65.06,64.31,64.85,3100000,64.85 1963-03-05,64.72,65.27,64.41,64.74,3280000,64.74 1963-03-04,64.10,65.08,63.88,64.72,3650000,64.72 1963-03-01,64.29,64.75,63.80,64.10,3920000,64.10 1963-02-28,65.01,65.14,64.08,64.29,4090000,64.29 1963-02-27,65.47,65.74,64.86,65.01,3680000,65.01 1963-02-26,65.46,65.86,65.06,65.47,3670000,65.47 1963-02-25,65.92,66.09,65.24,65.46,3680000,65.46 1963-02-21,65.83,66.23,65.36,65.92,3980000,65.92 1963-02-20,66.20,66.28,65.44,65.83,4120000,65.83 1963-02-19,66.52,66.67,65.92,66.20,4130000,66.20 1963-02-18,66.41,66.96,66.10,66.52,4700000,66.52 1963-02-15,66.35,66.74,65.96,66.41,4410000,66.41 1963-02-14,66.15,66.75,65.93,66.35,5640000,66.35 1963-02-13,65.83,66.53,65.56,66.15,4960000,66.15 1963-02-12,65.76,66.01,65.16,65.83,3710000,65.83 1963-02-11,66.17,66.41,65.50,65.76,3880000,65.76 1963-02-08,66.17,66.45,65.65,66.17,3890000,66.17 1963-02-07,66.40,66.81,65.91,66.17,4240000,66.17 1963-02-06,66.11,66.76,65.88,66.40,4340000,66.40 1963-02-05,66.17,66.35,65.38,66.11,4050000,66.11 1963-02-04,66.31,66.66,65.89,66.17,3670000,66.17 1963-02-01,66.31,66.31,66.31,66.31,4280000,66.31 1963-01-31,65.85,66.45,65.51,66.20,4270000,66.20 1963-01-30,66.23,66.33,65.55,65.85,3740000,65.85 1963-01-29,66.24,66.58,65.83,66.23,4360000,66.23 1963-01-28,65.92,66.59,65.77,66.24,4720000,66.24 1963-01-25,65.75,66.23,65.38,65.92,4770000,65.92 1963-01-24,65.62,66.09,65.33,65.75,4810000,65.75 1963-01-23,65.44,65.91,65.23,65.62,4820000,65.62 1963-01-22,65.28,65.80,65.03,65.44,4810000,65.44 1963-01-21,65.18,65.52,64.64,65.28,4090000,65.28 1963-01-18,65.13,65.70,64.86,65.18,4760000,65.18 1963-01-17,64.67,65.40,64.35,65.13,5230000,65.13 1963-01-16,65.11,65.25,64.42,64.67,4260000,64.67 1963-01-15,65.20,65.62,64.82,65.11,5930000,65.11 1963-01-14,64.85,65.50,64.61,65.20,5000000,65.20 1963-01-11,64.71,65.10,64.31,64.85,4410000,64.85 1963-01-10,64.59,65.16,64.33,64.71,4520000,64.71 1963-01-09,64.74,65.22,64.32,64.59,5110000,64.59 1963-01-08,64.12,64.98,64.00,64.74,5410000,64.74 1963-01-07,64.13,64.59,63.67,64.12,4440000,64.12 1963-01-04,63.72,64.45,63.57,64.13,5400000,64.13 1963-01-03,62.69,63.89,62.67,63.72,4570000,63.72 1963-01-02,63.10,63.39,62.32,62.69,2540000,62.69 1962-12-31,62.96,63.43,62.68,63.10,5420000,63.10 1962-12-28,62.93,63.25,62.53,62.96,4140000,62.96 1962-12-27,63.02,63.41,62.67,62.93,3670000,62.93 1962-12-26,62.63,63.32,62.56,63.02,3370000,63.02 1962-12-24,62.64,63.03,62.19,62.63,3180000,62.63 1962-12-21,62.82,63.13,62.26,62.64,3470000,62.64 1962-12-20,62.58,63.28,62.44,62.82,4220000,62.82 1962-12-19,62.07,62.81,61.72,62.58,4000000,62.58 1962-12-18,62.37,62.66,61.78,62.07,3620000,62.07 1962-12-17,62.57,62.95,62.14,62.37,3590000,62.37 1962-12-14,62.42,62.83,61.96,62.57,3280000,62.57 1962-12-13,62.63,63.07,62.09,62.42,3380000,62.42 1962-12-12,62.32,63.16,62.13,62.63,3760000,62.63 1962-12-11,62.27,62.58,61.72,62.32,3700000,62.32 1962-12-10,63.06,63.35,61.96,62.27,4270000,62.27 1962-12-07,62.93,63.43,62.45,63.06,3900000,63.06 1962-12-06,62.39,63.36,62.28,62.93,4600000,62.93 1962-12-05,62.64,63.50,62.37,62.39,6280000,62.39 1962-12-04,61.94,62.93,61.77,62.64,5210000,62.64 1962-12-03,62.26,62.45,61.28,61.94,3810000,61.94 1962-11-30,62.41,62.78,61.78,62.26,4570000,62.26 1962-11-29,62.12,62.72,61.69,62.41,5810000,62.41 1962-11-28,61.73,62.48,61.51,62.12,5980000,62.12 1962-11-27,61.36,62.04,60.98,61.73,5500000,61.73 1962-11-26,61.54,62.13,60.95,61.36,5650000,61.36 1962-11-23,60.81,62.03,60.66,61.54,5660000,61.54 1962-11-21,60.45,61.18,60.19,60.81,5100000,60.81 1962-11-20,59.82,60.63,59.57,60.45,4290000,60.45 1962-11-19,60.16,60.42,59.46,59.82,3410000,59.82 1962-11-16,59.97,60.46,59.46,60.16,4000000,60.16 1962-11-15,60.16,60.67,59.74,59.97,5050000,59.97 1962-11-14,59.46,60.41,59.18,60.16,5090000,60.16 1962-11-13,59.59,60.06,59.06,59.46,4550000,59.46 1962-11-12,58.78,60.00,58.59,59.59,5090000,59.59 1962-11-09,58.32,58.99,57.90,58.78,4340000,58.78 1962-11-08,58.71,59.12,58.09,58.32,4160000,58.32 1962-11-07,58.35,59.11,57.76,58.71,4580000,58.71 1962-11-05,57.75,58.70,57.69,58.35,4320000,58.35 1962-11-02,57.12,58.19,56.78,57.75,5470000,57.75 1962-11-01,56.52,57.31,55.90,57.12,3400000,57.12 1962-10-31,56.54,57.00,56.19,56.52,3090000,56.52 1962-10-30,55.72,56.84,55.52,56.54,3830000,56.54 1962-10-29,55.34,56.38,55.34,55.72,4280000,55.72 1962-10-26,54.69,54.96,54.08,54.54,2580000,54.54 1962-10-25,55.17,55.17,53.82,54.69,3950000,54.69 1962-10-24,53.49,55.44,52.55,55.21,6720000,55.21 1962-10-23,54.96,55.19,53.24,53.49,6110000,53.49 1962-10-22,55.48,55.48,54.38,54.96,5690000,54.96 1962-10-19,56.34,56.54,55.34,55.59,4650000,55.59 1962-10-18,56.89,57.02,56.18,56.34,3280000,56.34 1962-10-17,57.08,57.23,56.37,56.89,3240000,56.89 1962-10-16,57.27,57.63,56.87,57.08,2860000,57.08 1962-10-15,56.95,57.50,56.66,57.27,2640000,57.27 1962-10-12,57.05,57.21,56.66,56.95,2020000,56.95 1962-10-11,57.24,57.46,56.78,57.05,2460000,57.05 1962-10-10,57.20,57.83,56.96,57.24,3040000,57.24 1962-10-09,57.07,57.40,56.71,57.20,2340000,57.20 1962-10-08,57.07,57.41,56.68,57.07,1950000,57.07 1962-10-05,56.70,57.30,56.55,57.07,2730000,57.07 1962-10-04,56.16,56.84,55.90,56.70,2530000,56.70 1962-10-03,56.10,56.71,55.84,56.16,2610000,56.16 1962-10-02,55.49,56.46,55.31,56.10,3000000,56.10 1962-10-01,56.27,56.31,55.26,55.49,3090000,55.49 1962-09-28,55.77,56.58,55.59,56.27,2850000,56.27 1962-09-27,56.15,56.55,55.53,55.77,3540000,55.77 1962-09-26,56.96,57.29,55.92,56.15,3550000,56.15 1962-09-25,56.63,57.22,56.12,56.96,3620000,56.96 1962-09-24,57.45,57.45,56.30,56.63,5000000,56.63 1962-09-21,58.54,58.64,57.43,57.69,4280000,57.69 1962-09-20,58.95,59.29,58.33,58.54,3350000,58.54 1962-09-19,59.03,59.26,58.59,58.95,2950000,58.95 1962-09-18,59.08,59.54,58.77,59.03,3690000,59.03 1962-09-17,58.89,59.42,58.65,59.08,3330000,59.08 1962-09-14,58.70,59.14,58.40,58.89,2880000,58.89 1962-09-13,58.84,59.18,58.46,58.70,3100000,58.70 1962-09-12,58.59,59.06,58.40,58.84,3100000,58.84 1962-09-11,58.45,58.93,58.17,58.59,3040000,58.59 1962-09-10,58.38,58.64,57.88,58.45,2520000,58.45 1962-09-07,58.36,58.90,58.09,58.38,2890000,58.38 1962-09-06,58.12,58.60,57.72,58.36,3180000,58.36 1962-09-05,58.56,58.77,57.95,58.12,3050000,58.12 1962-09-04,59.12,59.49,58.44,58.56,2970000,58.56 1962-08-31,58.68,59.25,58.45,59.12,2830000,59.12 1962-08-30,58.66,59.06,58.39,58.68,2260000,58.68 1962-08-29,58.79,58.96,58.17,58.66,2900000,58.66 1962-08-28,59.55,59.61,58.66,58.79,3180000,58.79 1962-08-27,59.58,59.94,59.24,59.55,3140000,59.55 1962-08-24,59.70,59.92,59.18,59.58,2890000,59.58 1962-08-23,59.78,60.33,59.47,59.70,4770000,59.70 1962-08-22,59.12,59.93,58.91,59.78,4520000,59.78 1962-08-21,59.37,59.66,58.90,59.12,3730000,59.12 1962-08-20,59.01,59.72,58.90,59.37,4580000,59.37 1962-08-17,58.64,59.24,58.43,59.01,3430000,59.01 1962-08-16,58.66,59.11,58.24,58.64,4180000,58.64 1962-08-15,58.25,59.11,58.22,58.66,4880000,58.66 1962-08-14,57.63,58.43,57.41,58.25,3640000,58.25 1962-08-13,57.55,57.90,57.22,57.63,2670000,57.63 1962-08-10,57.57,57.85,57.16,57.55,2470000,57.55 1962-08-09,57.51,57.88,57.19,57.57,2670000,57.57 1962-08-08,57.36,57.64,56.76,57.51,3080000,57.51 1962-08-07,57.75,57.81,57.07,57.36,2970000,57.36 1962-08-06,58.12,58.35,57.54,57.75,3110000,57.75 1962-08-03,57.98,58.32,57.63,58.12,5990000,58.12 1962-08-02,57.75,58.20,57.38,57.98,3410000,57.98 1962-08-01,58.23,58.30,57.51,57.75,3100000,57.75 1962-07-31,57.83,58.58,57.74,58.23,4190000,58.23 1962-07-30,57.20,57.98,57.08,57.83,3200000,57.83 1962-07-27,56.77,57.36,56.56,57.20,2890000,57.20 1962-07-26,56.46,57.18,56.16,56.77,2790000,56.77 1962-07-25,56.36,56.67,55.78,56.46,2910000,56.46 1962-07-24,56.80,56.93,56.14,56.36,2560000,56.36 1962-07-23,56.81,57.32,56.53,56.80,2770000,56.80 1962-07-20,56.42,57.09,56.27,56.81,2610000,56.81 1962-07-19,56.20,56.95,55.96,56.42,3090000,56.42 1962-07-18,56.78,56.81,55.86,56.20,3620000,56.20 1962-07-17,57.83,57.96,56.68,56.78,3500000,56.78 1962-07-16,57.83,58.10,57.18,57.83,3130000,57.83 1962-07-13,58.03,58.18,57.23,57.83,3380000,57.83 1962-07-12,57.73,58.67,57.59,58.03,5370000,58.03 1962-07-11,57.20,57.95,56.77,57.73,4250000,57.73 1962-07-10,56.99,58.36,56.99,57.20,7120000,57.20 1962-07-09,56.17,56.73,55.54,56.55,2950000,56.55 1962-07-06,56.73,56.73,55.64,56.17,3110000,56.17 1962-07-05,56.49,57.10,56.15,56.81,3350000,56.81 1962-07-03,55.86,56.74,55.57,56.49,3920000,56.49 1962-07-02,54.75,56.02,54.47,55.86,3450000,55.86 1962-06-29,54.41,55.47,54.20,54.75,4720000,54.75 1962-06-28,52.98,54.64,52.98,54.41,5440000,54.41 1962-06-27,52.32,52.83,51.77,52.60,3890000,52.60 1962-06-26,52.45,53.58,52.10,52.32,4630000,52.32 1962-06-25,52.68,52.96,51.35,52.45,7090000,52.45 1962-06-22,53.59,53.78,52.48,52.68,5640000,52.68 1962-06-21,54.78,54.78,53.50,53.59,4560000,53.59 1962-06-20,55.54,55.92,54.66,54.78,3360000,54.78 1962-06-19,55.74,55.88,54.98,55.54,2680000,55.54 1962-06-18,55.89,56.53,54.97,55.74,4580000,55.74 1962-06-15,54.33,55.96,53.66,55.89,7130000,55.89 1962-06-14,55.50,56.00,54.12,54.33,6240000,54.33 1962-06-13,56.34,56.80,55.24,55.50,5850000,55.50 1962-06-12,57.66,57.66,56.23,56.34,4690000,56.34 1962-06-11,58.45,58.58,57.51,57.82,2870000,57.82 1962-06-08,58.40,58.97,58.14,58.45,2560000,58.45 1962-06-07,58.39,58.90,58.00,58.40,2760000,58.40 1962-06-06,57.64,59.17,57.64,58.39,4190000,58.39 1962-06-05,57.27,58.42,56.33,57.57,6140000,57.57 1962-06-04,59.12,59.12,57.14,57.27,5380000,57.27 1962-06-01,59.63,59.96,58.52,59.38,5760000,59.38 1962-05-31,58.80,60.82,58.80,59.63,10710000,59.63 1962-05-29,55.50,58.29,53.13,58.08,14750000,58.08 1962-05-28,59.15,59.15,55.42,55.50,9350000,55.50 1962-05-25,60.62,60.98,59.00,59.47,6380000,59.47 1962-05-24,61.11,61.79,60.36,60.62,5250000,60.62 1962-05-23,62.34,62.42,60.90,61.11,5450000,61.11 1962-05-22,63.59,63.69,62.26,62.34,3640000,62.34 1962-05-21,63.82,64.00,63.21,63.59,2260000,63.59 1962-05-18,63.93,64.14,63.29,63.82,2490000,63.82 1962-05-17,64.27,64.41,63.38,63.93,2950000,63.93 1962-05-16,64.29,64.88,63.82,64.27,3360000,64.27 1962-05-15,63.41,64.87,63.41,64.29,4780000,64.29 1962-05-14,62.65,63.31,61.11,63.10,5990000,63.10 1962-05-11,63.57,64.10,62.44,62.65,4510000,62.65 1962-05-10,64.26,64.39,62.99,63.57,4730000,63.57 1962-05-09,65.17,65.17,64.02,64.26,3670000,64.26 1962-05-08,66.02,66.13,64.88,65.17,3020000,65.17 1962-05-07,66.24,66.56,65.66,66.02,2530000,66.02 1962-05-04,66.53,66.80,65.80,66.24,3010000,66.24 1962-05-03,65.99,66.93,65.81,66.53,3320000,66.53 1962-05-02,65.70,66.67,65.56,65.99,3780000,65.99 1962-05-01,65.24,65.94,63.76,65.70,5100000,65.70 1962-04-30,66.30,66.90,64.95,65.24,4150000,65.24 1962-04-27,67.05,67.61,65.99,66.30,4140000,66.30 1962-04-26,67.71,67.97,66.92,67.05,3650000,67.05 1962-04-25,68.46,68.58,67.53,67.71,3340000,67.71 1962-04-24,68.53,68.91,68.16,68.46,3040000,68.46 1962-04-23,68.59,69.01,68.17,68.53,3240000,68.53 1962-04-19,68.27,68.90,68.07,68.59,3100000,68.59 1962-04-18,67.90,68.72,67.83,68.27,3350000,68.27 1962-04-17,67.60,68.20,67.24,67.90,2940000,67.90 1962-04-16,67.90,68.19,67.21,67.60,3070000,67.60 1962-04-13,67.90,68.11,67.03,67.90,3470000,67.90 1962-04-12,68.41,68.43,67.47,67.90,3320000,67.90 1962-04-11,68.56,69.26,68.24,68.41,3240000,68.41 1962-04-10,68.31,68.80,67.94,68.56,2880000,68.56 1962-04-09,68.84,69.02,68.09,68.31,3020000,68.31 1962-04-06,68.91,69.42,68.58,68.84,2730000,68.84 1962-04-05,68.49,69.09,68.12,68.91,3130000,68.91 1962-04-04,68.81,69.22,68.33,68.49,3290000,68.49 1962-04-03,69.37,69.53,68.53,68.81,3350000,68.81 1962-04-02,69.55,69.82,69.13,69.37,2790000,69.37 1962-03-30,70.01,70.09,69.16,69.55,2950000,69.55 1962-03-29,70.04,70.50,69.81,70.01,2870000,70.01 1962-03-28,69.70,70.33,69.54,70.04,2940000,70.04 1962-03-27,69.89,70.20,69.41,69.70,3090000,69.70 1962-03-26,70.45,70.63,69.73,69.89,3040000,69.89 1962-03-23,70.40,70.78,70.12,70.45,3050000,70.45 1962-03-22,70.51,70.84,70.14,70.40,3130000,70.40 1962-03-21,70.66,70.93,70.16,70.51,3360000,70.51 1962-03-20,70.85,71.08,70.40,70.66,3060000,70.66 1962-03-19,70.94,71.31,70.53,70.85,3220000,70.85 1962-03-16,71.06,71.34,70.67,70.94,3060000,70.94 1962-03-15,70.91,71.44,70.59,71.06,3250000,71.06 1962-03-14,70.60,71.25,70.48,70.91,3670000,70.91 1962-03-13,70.40,70.86,70.06,70.60,3200000,70.60 1962-03-12,70.42,70.76,70.02,70.40,3280000,70.40 1962-03-09,70.19,70.71,70.00,70.42,3340000,70.42 1962-03-08,69.69,70.37,69.40,70.19,3210000,70.19 1962-03-07,69.78,70.07,69.37,69.69,2890000,69.69 1962-03-06,70.01,70.24,69.46,69.78,2870000,69.78 1962-03-05,70.16,70.48,69.65,70.01,3020000,70.01 1962-03-02,70.16,70.16,69.75,70.16,2980000,70.16 1962-03-01,69.96,70.60,69.76,70.20,2960000,70.20 1962-02-28,69.89,70.42,69.57,69.96,3030000,69.96 1962-02-27,69.76,70.32,69.48,69.89,3110000,69.89 1962-02-26,70.16,70.33,69.44,69.76,2910000,69.76 1962-02-23,70.32,70.57,69.73,70.16,3230000,70.16 1962-02-21,70.66,70.97,70.12,70.32,3310000,70.32 1962-02-20,70.41,70.91,70.13,70.66,3300000,70.66 1962-02-19,70.59,70.96,70.12,70.41,3350000,70.41 1962-02-16,70.74,71.13,70.27,70.59,3700000,70.59 1962-02-15,70.42,71.06,70.23,70.74,3470000,70.74 1962-02-14,70.45,70.79,70.03,70.42,3630000,70.42 1962-02-13,70.46,70.89,70.07,70.45,3400000,70.45 1962-02-12,70.48,70.81,70.14,70.46,2620000,70.46 1962-02-09,70.58,70.83,69.93,70.48,3370000,70.48 1962-02-08,70.42,70.95,70.16,70.58,3810000,70.58 1962-02-07,69.96,70.67,69.78,70.42,4140000,70.42 1962-02-06,69.88,70.32,69.41,69.96,3650000,69.96 1962-02-05,69.81,70.30,69.42,69.88,3890000,69.88 1962-02-02,69.26,70.02,69.02,69.81,3950000,69.81 1962-02-01,68.84,69.65,68.56,69.26,4260000,69.26 1962-01-31,68.17,69.09,68.12,68.84,3840000,68.84 1962-01-30,67.90,68.65,67.62,68.17,3520000,68.17 1962-01-29,68.13,68.50,67.55,67.90,3050000,67.90 1962-01-26,68.35,68.67,67.83,68.13,3330000,68.13 1962-01-25,68.40,69.05,68.10,68.35,3560000,68.35 1962-01-24,68.29,68.68,67.55,68.40,3760000,68.40 1962-01-23,68.81,68.96,68.00,68.29,3350000,68.29 1962-01-22,68.75,69.37,68.45,68.81,3810000,68.81 1962-01-19,68.39,70.08,68.14,68.75,3800000,68.75 1962-01-18,68.32,68.73,67.75,68.39,3460000,68.39 1962-01-17,69.07,69.31,68.13,68.32,3780000,68.32 1962-01-16,69.47,69.61,68.68,69.07,3650000,69.07 1962-01-15,69.61,69.96,69.06,69.47,3450000,69.47 1962-01-12,69.37,70.17,69.23,69.61,3730000,69.61 1962-01-11,68.96,69.54,68.57,69.37,3390000,69.37 1962-01-10,69.15,69.58,68.62,68.96,3300000,68.96 1962-01-09,69.12,69.93,68.83,69.15,3600000,69.15 1962-01-08,69.66,69.84,68.17,69.12,4620000,69.12 1962-01-05,70.64,70.84,69.35,69.66,4630000,69.66 1962-01-04,71.13,71.62,70.45,70.64,4450000,70.64 1962-01-03,70.96,71.48,70.38,71.13,3590000,71.13 1962-01-02,71.55,71.96,70.71,70.96,3120000,70.96 1961-12-29,71.55,71.55,71.55,71.55,5370000,71.55 1961-12-28,71.69,71.69,71.69,71.69,4530000,71.69 1961-12-27,71.65,71.65,71.65,71.65,4170000,71.65 1961-12-26,71.02,71.02,71.02,71.02,3180000,71.02 1961-12-22,70.91,70.91,70.91,70.91,3390000,70.91 1961-12-21,70.86,70.86,70.86,70.86,3440000,70.86 1961-12-20,71.12,71.12,71.12,71.12,3640000,71.12 1961-12-19,71.26,71.26,71.26,71.26,3440000,71.26 1961-12-18,71.76,71.76,71.76,71.76,3810000,71.76 1961-12-15,72.01,72.01,72.01,72.01,3710000,72.01 1961-12-14,71.98,71.98,71.98,71.98,4350000,71.98 1961-12-13,72.53,72.53,72.53,72.53,4890000,72.53 1961-12-12,72.64,72.64,72.64,72.64,4680000,72.64 1961-12-11,72.39,72.39,72.39,72.39,4360000,72.39 1961-12-08,72.04,72.04,72.04,72.04,4010000,72.04 1961-12-07,71.70,71.70,71.70,71.70,3900000,71.70 1961-12-06,71.99,71.99,71.99,71.99,4200000,71.99 1961-12-05,71.93,71.93,71.93,71.93,4330000,71.93 1961-12-04,72.01,72.01,72.01,72.01,4560000,72.01 1961-12-01,71.78,71.78,71.78,71.78,4420000,71.78 1961-11-30,71.32,71.32,71.32,71.32,4210000,71.32 1961-11-29,71.70,71.70,71.70,71.70,4550000,71.70 1961-11-28,71.75,71.75,71.75,71.75,4360000,71.75 1961-11-27,71.85,71.85,71.85,71.85,4700000,71.85 1961-11-24,71.84,71.84,71.84,71.84,4020000,71.84 1961-11-22,71.70,71.70,71.70,71.70,4500000,71.70 1961-11-21,71.78,71.78,71.78,71.78,4890000,71.78 1961-11-20,71.72,71.72,71.72,71.72,4190000,71.72 1961-11-17,71.62,71.62,71.62,71.62,3960000,71.62 1961-11-16,71.62,71.62,71.62,71.62,3980000,71.62 1961-11-15,71.67,71.67,71.67,71.67,4660000,71.67 1961-11-14,71.66,71.66,71.66,71.66,4750000,71.66 1961-11-13,71.27,71.27,71.27,71.27,4540000,71.27 1961-11-10,71.07,71.07,71.07,71.07,4180000,71.07 1961-11-09,70.77,70.77,70.77,70.77,4680000,70.77 1961-11-08,70.87,70.87,70.87,70.87,6090000,70.87 1961-11-06,70.01,70.01,70.01,70.01,4340000,70.01 1961-11-03,69.47,69.47,69.47,69.47,4070000,69.47 1961-11-02,69.11,69.11,69.11,69.11,3890000,69.11 1961-11-01,68.73,68.73,68.73,68.73,3210000,68.73 1961-10-31,68.62,68.62,68.62,68.62,3350000,68.62 1961-10-30,68.42,68.42,68.42,68.42,3430000,68.42 1961-10-27,68.34,68.34,68.34,68.34,3200000,68.34 1961-10-26,68.46,68.46,68.46,68.46,3330000,68.46 1961-10-25,68.34,68.34,68.34,68.34,3590000,68.34 1961-10-24,67.98,67.98,67.98,67.98,3430000,67.98 1961-10-23,68.06,68.06,68.06,68.06,3440000,68.06 1961-10-20,68.00,68.00,68.00,68.00,3470000,68.00 1961-10-19,68.45,68.45,68.45,68.45,3850000,68.45 1961-10-18,68.21,68.21,68.21,68.21,3520000,68.21 1961-10-17,67.87,67.87,67.87,67.87,3110000,67.87 1961-10-16,67.85,67.85,67.85,67.85,2840000,67.85 1961-10-13,68.04,68.04,68.04,68.04,3090000,68.04 1961-10-12,68.16,68.16,68.16,68.16,3060000,68.16 1961-10-11,68.17,68.17,68.17,68.17,3670000,68.17 1961-10-10,68.11,68.11,68.11,68.11,3430000,68.11 1961-10-09,67.94,67.94,67.94,67.94,2920000,67.94 1961-10-06,66.97,66.97,66.97,66.97,3470000,66.97 1961-10-05,67.77,67.77,67.77,67.77,3920000,67.77 1961-10-04,67.18,67.18,67.18,67.18,3380000,67.18 1961-10-03,66.73,66.73,66.73,66.73,2680000,66.73 1961-10-02,66.77,66.77,66.77,66.77,2800000,66.77 1961-09-29,66.73,66.73,66.73,66.73,3060000,66.73 1961-09-28,66.58,66.58,66.58,66.58,3000000,66.58 1961-09-27,66.47,66.47,66.47,66.47,3440000,66.47 1961-09-26,65.78,65.78,65.78,65.78,3320000,65.78 1961-09-25,65.77,65.77,65.77,65.77,3700000,65.77 1961-09-22,66.72,66.72,66.72,66.72,3070000,66.72 1961-09-21,66.99,66.99,66.99,66.99,3340000,66.99 1961-09-20,66.96,66.96,66.96,66.96,2700000,66.96 1961-09-19,66.08,66.08,66.08,66.08,3260000,66.08 1961-09-18,67.21,67.21,67.21,67.21,3550000,67.21 1961-09-15,67.65,67.65,67.65,67.65,3130000,67.65 1961-09-14,67.53,67.53,67.53,67.53,2920000,67.53 1961-09-13,68.01,68.01,68.01,68.01,3110000,68.01 1961-09-12,67.96,67.96,67.96,67.96,2950000,67.96 1961-09-11,67.28,67.28,67.28,67.28,2790000,67.28 1961-09-08,67.88,67.88,67.88,67.88,3430000,67.88 1961-09-07,68.35,68.35,68.35,68.35,3900000,68.35 1961-09-06,68.46,68.46,68.46,68.46,3440000,68.46 1961-09-05,67.96,67.96,67.96,67.96,3000000,67.96 1961-09-01,68.19,68.19,68.19,68.19,2710000,68.19 1961-08-31,68.07,68.07,68.07,68.07,2920000,68.07 1961-08-30,67.81,67.81,67.81,67.81,3220000,67.81 1961-08-29,67.55,67.55,67.55,67.55,3160000,67.55 1961-08-28,67.70,67.70,67.70,67.70,3150000,67.70 1961-08-25,67.67,67.67,67.67,67.67,3050000,67.67 1961-08-24,67.59,67.59,67.59,67.59,3090000,67.59 1961-08-23,67.98,67.98,67.98,67.98,3550000,67.98 1961-08-22,68.44,68.44,68.44,68.44,3640000,68.44 1961-08-21,68.43,68.43,68.43,68.43,3880000,68.43 1961-08-18,68.29,68.29,68.29,68.29,4030000,68.29 1961-08-17,68.11,68.11,68.11,68.11,4130000,68.11 1961-08-16,67.73,67.73,67.73,67.73,3430000,67.73 1961-08-15,67.55,67.55,67.55,67.55,3320000,67.55 1961-08-14,67.72,67.72,67.72,67.72,3120000,67.72 1961-08-11,68.06,68.06,68.06,68.06,3260000,68.06 1961-08-10,67.95,67.95,67.95,67.95,3570000,67.95 1961-08-09,67.74,67.74,67.74,67.74,3710000,67.74 1961-08-08,67.82,67.82,67.82,67.82,4050000,67.82 1961-08-07,67.67,67.67,67.67,67.67,3560000,67.67 1961-08-04,67.68,67.68,67.68,67.68,3710000,67.68 1961-08-03,67.29,67.29,67.29,67.29,3650000,67.29 1961-08-02,66.94,66.94,66.94,66.94,4300000,66.94 1961-08-01,67.37,67.37,67.37,67.37,3990000,67.37 1961-07-31,66.76,66.76,66.76,66.76,3170000,66.76 1961-07-28,66.71,66.71,66.71,66.71,3610000,66.71 1961-07-27,66.61,66.61,66.61,66.61,4170000,66.61 1961-07-26,65.84,65.84,65.84,65.84,4070000,65.84 1961-07-25,65.23,65.23,65.23,65.23,3010000,65.23 1961-07-24,64.87,64.87,64.87,64.87,2490000,64.87 1961-07-21,64.86,64.86,64.86,64.86,2360000,64.86 1961-07-20,64.71,64.71,64.71,64.71,2530000,64.71 1961-07-19,64.70,64.70,64.70,64.70,2940000,64.70 1961-07-18,64.41,64.41,64.41,64.41,3010000,64.41 1961-07-17,64.79,64.79,64.79,64.79,2690000,64.79 1961-07-14,65.28,65.28,65.28,65.28,2760000,65.28 1961-07-13,64.86,64.86,64.86,64.86,2670000,64.86 1961-07-12,65.32,65.32,65.32,65.32,3070000,65.32 1961-07-11,65.69,65.69,65.69,65.69,3160000,65.69 1961-07-10,65.71,65.71,65.71,65.71,3180000,65.71 1961-07-07,65.77,65.77,65.77,65.77,3030000,65.77 1961-07-06,65.81,65.81,65.81,65.81,3470000,65.81 1961-07-05,65.63,65.63,65.63,65.63,3270000,65.63 1961-07-03,65.21,65.21,65.21,65.21,2180000,65.21 1961-06-30,64.64,64.64,64.64,64.64,2380000,64.64 1961-06-29,64.52,64.52,64.52,64.52,2560000,64.52 1961-06-28,64.59,64.59,64.59,64.59,2830000,64.59 1961-06-27,64.47,64.47,64.47,64.47,3090000,64.47 1961-06-26,64.47,64.47,64.47,64.47,2690000,64.47 1961-06-23,65.16,65.16,65.16,65.16,2720000,65.16 1961-06-22,64.90,64.90,64.90,64.90,2880000,64.90 1961-06-21,65.14,65.14,65.14,65.14,3210000,65.14 1961-06-20,65.15,65.15,65.15,65.15,3280000,65.15 1961-06-19,64.58,64.58,64.58,64.58,3980000,64.58 1961-06-16,65.18,65.18,65.18,65.18,3380000,65.18 1961-06-15,65.69,65.69,65.69,65.69,3220000,65.69 1961-06-14,65.98,65.98,65.98,65.98,3430000,65.98 1961-06-13,65.80,65.80,65.80,65.80,3030000,65.80 1961-06-12,66.15,66.15,66.15,66.15,3260000,66.15 1961-06-09,66.66,66.66,66.66,66.66,3520000,66.66 1961-06-08,66.67,66.67,66.67,66.67,3810000,66.67 1961-06-07,65.64,65.64,65.64,65.64,3980000,65.64 1961-06-06,66.89,66.89,66.89,66.89,4250000,66.89 1961-06-05,67.08,67.08,67.08,67.08,4150000,67.08 1961-06-02,66.73,66.73,66.73,66.73,3670000,66.73 1961-06-01,66.56,66.56,66.56,66.56,3770000,66.56 1961-05-31,66.56,66.56,66.56,66.56,4320000,66.56 1961-05-26,66.43,66.43,66.43,66.43,3780000,66.43 1961-05-25,66.01,66.01,66.01,66.01,3760000,66.01 1961-05-24,66.26,66.26,66.26,66.26,3970000,66.26 1961-05-23,66.68,66.68,66.68,66.68,3660000,66.68 1961-05-22,66.85,66.85,66.85,66.85,4070000,66.85 1961-05-19,67.27,67.27,67.27,67.27,4200000,67.27 1961-05-18,66.99,66.99,66.99,66.99,4610000,66.99 1961-05-17,67.39,67.39,67.39,67.39,5520000,67.39 1961-05-16,67.08,67.08,67.08,67.08,5110000,67.08 1961-05-15,66.83,66.83,66.83,66.83,4840000,66.83 1961-05-12,66.50,66.50,66.50,66.50,4840000,66.50 1961-05-11,66.39,66.39,66.39,66.39,5170000,66.39 1961-05-10,66.41,66.41,66.41,66.41,5450000,66.41 1961-05-09,66.47,66.47,66.47,66.47,5380000,66.47 1961-05-08,66.41,66.41,66.41,66.41,5170000,66.41 1961-05-05,66.52,66.52,66.52,66.52,4980000,66.52 1961-05-04,66.44,66.44,66.44,66.44,5350000,66.44 1961-05-03,66.18,66.18,66.18,66.18,4940000,66.18 1961-05-02,65.64,65.64,65.64,65.64,4110000,65.64 1961-05-01,65.17,65.17,65.17,65.17,3710000,65.17 1961-04-28,65.31,65.31,65.31,65.31,3710000,65.31 1961-04-27,65.46,65.46,65.46,65.46,4450000,65.46 1961-04-26,65.55,65.55,65.55,65.55,4980000,65.55 1961-04-25,65.30,65.30,65.30,65.30,4670000,65.30 1961-04-24,64.40,64.40,64.40,64.40,4590000,64.40 1961-04-21,65.77,65.77,65.77,65.77,4340000,65.77 1961-04-20,65.82,65.82,65.82,65.82,4810000,65.82 1961-04-19,65.81,65.81,65.81,65.81,4870000,65.81 1961-04-18,66.20,66.20,66.20,66.20,4830000,66.20 1961-04-17,68.68,68.68,68.68,68.68,5860000,68.68 1961-04-14,66.37,66.37,66.37,66.37,5240000,66.37 1961-04-13,66.26,66.26,66.26,66.26,4770000,66.26 1961-04-12,66.31,66.31,66.31,66.31,4870000,66.31 1961-04-11,66.62,66.62,66.62,66.62,5230000,66.62 1961-04-10,66.53,66.53,66.53,66.53,5550000,66.53 1961-04-07,65.96,65.96,65.96,65.96,5100000,65.96 1961-04-06,65.61,65.61,65.61,65.61,4910000,65.61 1961-04-05,65.46,65.46,65.46,65.46,5430000,65.46 1961-04-04,65.66,65.66,65.66,65.66,7080000,65.66 1961-04-03,65.60,65.60,65.60,65.60,6470000,65.60 1961-03-30,65.06,65.06,65.06,65.06,5610000,65.06 1961-03-29,64.93,64.93,64.93,64.93,5330000,64.93 1961-03-28,64.38,64.38,64.38,64.38,4630000,64.38 1961-03-27,64.35,64.35,64.35,64.35,4190000,64.35 1961-03-24,64.42,64.42,64.42,64.42,4390000,64.42 1961-03-23,64.53,64.53,64.53,64.53,2170000,64.53 1961-03-22,64.70,64.70,64.70,64.70,5840000,64.70 1961-03-21,64.74,64.74,64.74,64.74,5800000,64.74 1961-03-20,64.86,64.86,64.86,64.86,5780000,64.86 1961-03-17,64.00,64.00,64.00,64.00,5960000,64.00 1961-03-16,64.21,64.21,64.21,64.21,5610000,64.21 1961-03-15,63.57,63.57,63.57,63.57,4900000,63.57 1961-03-14,63.38,63.38,63.38,63.38,4900000,63.38 1961-03-13,63.66,63.66,63.66,63.66,5080000,63.66 1961-03-10,63.48,63.48,63.48,63.48,5950000,63.48 1961-03-09,63.50,63.50,63.50,63.50,6010000,63.50 1961-03-08,63.44,63.44,63.44,63.44,5910000,63.44 1961-03-07,63.47,63.47,63.47,63.47,5540000,63.47 1961-03-06,64.05,64.05,64.05,64.05,5650000,64.05 1961-03-03,63.95,63.95,63.95,63.95,5530000,63.95 1961-03-02,63.85,63.85,63.85,63.85,5300000,63.85 1961-03-01,63.43,63.43,63.43,63.43,4970000,63.43 1961-02-28,63.44,63.44,63.44,63.44,5830000,63.44 1961-02-27,63.30,63.30,63.30,63.30,5470000,63.30 1961-02-24,62.84,62.84,62.84,62.84,5330000,62.84 1961-02-23,62.59,62.59,62.59,62.59,5620000,62.59 1961-02-21,62.36,62.36,62.36,62.36,5070000,62.36 1961-02-20,62.32,62.32,62.32,62.32,4680000,62.32 1961-02-17,62.10,62.10,62.10,62.10,4640000,62.10 1961-02-16,62.30,62.30,62.30,62.30,5070000,62.30 1961-02-15,61.92,61.92,61.92,61.92,5200000,61.92 1961-02-14,61.41,61.41,61.41,61.41,4490000,61.41 1961-02-13,61.14,61.14,61.14,61.14,3560000,61.14 1961-02-10,61.50,61.50,61.50,61.50,4840000,61.50 1961-02-09,62.02,62.02,62.02,62.02,5590000,62.02 1961-02-08,62.21,62.21,62.21,62.21,4940000,62.21 1961-02-07,61.65,61.65,61.65,61.65,4020000,61.65 1961-02-06,61.76,61.76,61.76,61.76,3890000,61.76 1961-02-03,62.22,62.22,62.22,62.22,5210000,62.22 1961-02-02,62.30,62.30,62.30,62.30,4900000,62.30 1961-02-01,61.90,61.90,61.90,61.90,4380000,61.90 1961-01-31,61.78,61.78,61.78,61.78,4690000,61.78 1961-01-30,61.97,61.97,61.97,61.97,5190000,61.97 1961-01-27,61.24,61.24,61.24,61.24,4510000,61.24 1961-01-26,60.62,60.62,60.62,60.62,4110000,60.62 1961-01-25,60.53,60.53,60.53,60.53,4470000,60.53 1961-01-24,60.45,60.45,60.45,60.45,4280000,60.45 1961-01-23,60.29,60.29,60.29,60.29,4450000,60.29 1961-01-20,59.96,59.96,59.96,59.96,3270000,59.96 1961-01-19,59.77,59.77,59.77,59.77,4740000,59.77 1961-01-18,59.68,59.68,59.68,59.68,4390000,59.68 1961-01-17,59.64,59.64,59.64,59.64,3830000,59.64 1961-01-16,59.58,59.58,59.58,59.58,4510000,59.58 1961-01-13,59.60,59.60,59.60,59.60,4520000,59.60 1961-01-12,59.32,59.32,59.32,59.32,4270000,59.32 1961-01-11,59.14,59.14,59.14,59.14,4370000,59.14 1961-01-10,58.97,58.97,58.97,58.97,4840000,58.97 1961-01-09,58.81,58.81,58.81,58.81,4210000,58.81 1961-01-06,58.40,58.40,58.40,58.40,3620000,58.40 1961-01-05,58.57,58.57,58.57,58.57,4130000,58.57 1961-01-04,58.36,58.36,58.36,58.36,3840000,58.36 1961-01-03,57.57,57.57,57.57,57.57,2770000,57.57 1960-12-30,58.11,58.11,58.11,58.11,5300000,58.11 1960-12-29,58.05,58.05,58.05,58.05,4340000,58.05 1960-12-28,57.78,57.78,57.78,57.78,3620000,57.78 1960-12-27,57.52,57.52,57.52,57.52,3270000,57.52 1960-12-23,57.44,57.44,57.44,57.44,3580000,57.44 1960-12-22,57.39,57.39,57.39,57.39,3820000,57.39 1960-12-21,57.55,57.55,57.55,57.55,4060000,57.55 1960-12-20,57.09,57.09,57.09,57.09,3340000,57.09 1960-12-19,57.13,57.13,57.13,57.13,3630000,57.13 1960-12-16,57.20,57.20,57.20,57.20,3770000,57.20 1960-12-15,56.68,56.68,56.68,56.68,3660000,56.68 1960-12-14,56.84,56.84,56.84,56.84,3880000,56.84 1960-12-13,56.88,56.88,56.88,56.88,3500000,56.88 1960-12-12,56.85,56.85,56.85,56.85,3020000,56.85 1960-12-09,56.65,56.65,56.65,56.65,4460000,56.65 1960-12-08,56.15,56.15,56.15,56.15,3540000,56.15 1960-12-07,56.02,56.02,56.02,56.02,3660000,56.02 1960-12-06,55.47,55.47,55.47,55.47,3360000,55.47 1960-12-05,55.31,55.31,55.31,55.31,3290000,55.31 1960-12-02,55.39,55.39,55.39,55.39,3140000,55.39 1960-12-01,55.30,55.30,55.30,55.30,3090000,55.30 1960-11-30,55.54,55.54,55.54,55.54,3080000,55.54 1960-11-29,55.83,55.83,55.83,55.83,3630000,55.83 1960-11-28,56.03,56.03,56.03,56.03,3860000,56.03 1960-11-25,56.13,56.13,56.13,56.13,3190000,56.13 1960-11-23,55.80,55.80,55.80,55.80,3000000,55.80 1960-11-22,55.72,55.72,55.72,55.72,3430000,55.72 1960-11-21,55.93,55.93,55.93,55.93,3090000,55.93 1960-11-18,55.82,55.82,55.82,55.82,2760000,55.82 1960-11-17,55.55,55.55,55.55,55.55,2450000,55.55 1960-11-16,55.70,55.70,55.70,55.70,3110000,55.70 1960-11-15,55.81,55.81,55.81,55.81,2990000,55.81 1960-11-14,55.59,55.59,55.59,55.59,2660000,55.59 1960-11-11,55.87,55.87,55.87,55.87,2730000,55.87 1960-11-10,56.43,56.43,56.43,56.43,4030000,56.43 1960-11-09,55.35,55.35,55.35,55.35,3450000,55.35 1960-11-07,55.11,55.11,55.11,55.11,3540000,55.11 1960-11-04,54.90,54.90,54.90,54.90,3050000,54.90 1960-11-03,54.43,54.43,54.43,54.43,2580000,54.43 1960-11-02,54.22,54.22,54.22,54.22,2780000,54.22 1960-11-01,53.94,53.94,53.94,53.94,2600000,53.94 1960-10-31,53.39,53.39,53.39,53.39,2460000,53.39 1960-10-28,53.41,53.41,53.41,53.41,2490000,53.41 1960-10-27,53.62,53.62,53.62,53.62,2900000,53.62 1960-10-26,53.05,53.05,53.05,53.05,3020000,53.05 1960-10-25,52.20,52.20,52.20,52.20,3030000,52.20 1960-10-24,52.70,52.70,52.70,52.70,4420000,52.70 1960-10-21,53.72,53.72,53.72,53.72,3090000,53.72 1960-10-20,53.86,53.86,53.86,53.86,2910000,53.86 1960-10-19,54.25,54.25,54.25,54.25,2410000,54.25 1960-10-18,54.35,54.35,54.35,54.35,2220000,54.35 1960-10-17,54.63,54.63,54.63,54.63,2280000,54.63 1960-10-14,54.86,54.86,54.86,54.86,2470000,54.86 1960-10-13,54.57,54.57,54.57,54.57,2220000,54.57 1960-10-12,54.15,54.15,54.15,54.15,1890000,54.15 1960-10-11,54.22,54.22,54.22,54.22,2350000,54.22 1960-10-10,54.14,54.14,54.14,54.14,2030000,54.14 1960-10-07,54.03,54.03,54.03,54.03,2530000,54.03 1960-10-06,53.72,53.72,53.72,53.72,2510000,53.72 1960-10-05,53.39,53.39,53.39,53.39,2650000,53.39 1960-10-04,52.99,52.99,52.99,52.99,2270000,52.99 1960-10-03,53.36,53.36,53.36,53.36,2220000,53.36 1960-09-30,53.52,53.52,53.52,53.52,3370000,53.52 1960-09-29,52.62,52.62,52.62,52.62,2850000,52.62 1960-09-28,52.48,52.48,52.48,52.48,3520000,52.48 1960-09-27,52.94,52.94,52.94,52.94,3170000,52.94 1960-09-26,53.06,53.06,53.06,53.06,3930000,53.06 1960-09-23,53.90,53.90,53.90,53.90,2580000,53.90 1960-09-22,54.36,54.36,54.36,54.36,1970000,54.36 1960-09-21,54.57,54.57,54.57,54.57,2930000,54.57 1960-09-20,54.01,54.01,54.01,54.01,3660000,54.01 1960-09-19,53.86,53.86,53.86,53.86,3790000,53.86 1960-09-16,55.11,55.11,55.11,55.11,2340000,55.11 1960-09-15,55.22,55.22,55.22,55.22,2870000,55.22 1960-09-14,55.44,55.44,55.44,55.44,2530000,55.44 1960-09-13,55.83,55.83,55.83,55.83,2180000,55.83 1960-09-12,55.72,55.72,55.72,55.72,2160000,55.72 1960-09-09,56.11,56.11,56.11,56.11,2750000,56.11 1960-09-08,55.74,55.74,55.74,55.74,2670000,55.74 1960-09-07,55.79,55.79,55.79,55.79,2850000,55.79 1960-09-06,56.49,56.49,56.49,56.49,2580000,56.49 1960-09-02,57.00,57.00,57.00,57.00,2680000,57.00 1960-09-01,57.09,57.09,57.09,57.09,3460000,57.09 1960-08-31,56.96,56.96,56.96,56.96,3130000,56.96 1960-08-30,56.84,56.84,56.84,56.84,2890000,56.84 1960-08-29,57.44,57.44,57.44,57.44,2780000,57.44 1960-08-26,57.60,57.60,57.60,57.60,2780000,57.60 1960-08-25,57.79,57.79,57.79,57.79,2680000,57.79 1960-08-24,58.07,58.07,58.07,58.07,3500000,58.07 1960-08-23,57.75,57.75,57.75,57.75,3560000,57.75 1960-08-22,57.19,57.19,57.19,57.19,2760000,57.19 1960-08-19,57.01,57.01,57.01,57.01,2570000,57.01 1960-08-18,56.81,56.81,56.81,56.81,2890000,56.81 1960-08-17,56.84,56.84,56.84,56.84,3090000,56.84 1960-08-16,56.72,56.72,56.72,56.72,2710000,56.72 1960-08-15,56.61,56.61,56.61,56.61,2450000,56.61 1960-08-12,56.66,56.66,56.66,56.66,3160000,56.66 1960-08-11,56.28,56.28,56.28,56.28,3070000,56.28 1960-08-10,56.07,56.07,56.07,56.07,2810000,56.07 1960-08-09,55.84,55.84,55.84,55.84,2700000,55.84 1960-08-08,55.52,55.52,55.52,55.52,2960000,55.52 1960-08-05,55.44,55.44,55.44,55.44,3000000,55.44 1960-08-04,54.89,54.89,54.89,54.89,2840000,54.89 1960-08-03,54.72,54.72,54.72,54.72,2470000,54.72 1960-08-02,55.04,55.04,55.04,55.04,2090000,55.04 1960-08-01,55.53,55.53,55.53,55.53,2440000,55.53 1960-07-29,55.51,55.51,55.51,55.51,2730000,55.51 1960-07-28,54.57,54.57,54.57,54.57,3020000,54.57 1960-07-27,54.17,54.17,54.17,54.17,2560000,54.17 1960-07-26,54.51,54.51,54.51,54.51,2720000,54.51 1960-07-25,54.18,54.18,54.18,54.18,2840000,54.18 1960-07-22,54.72,54.72,54.72,54.72,2850000,54.72 1960-07-21,55.10,55.10,55.10,55.10,2510000,55.10 1960-07-20,55.61,55.61,55.61,55.61,2370000,55.61 1960-07-19,55.70,55.70,55.70,55.70,2490000,55.70 1960-07-18,55.70,55.70,55.70,55.70,2350000,55.70 1960-07-15,56.05,56.05,56.05,56.05,2140000,56.05 1960-07-14,56.12,56.12,56.12,56.12,2480000,56.12 1960-07-13,56.10,56.10,56.10,56.10,2590000,56.10 1960-07-12,56.25,56.25,56.25,56.25,2860000,56.25 1960-07-11,56.87,56.87,56.87,56.87,2920000,56.87 1960-07-08,57.38,57.38,57.38,57.38,3010000,57.38 1960-07-07,57.24,57.24,57.24,57.24,3050000,57.24 1960-07-06,56.94,56.94,56.94,56.94,2970000,56.94 1960-07-05,57.02,57.02,57.02,57.02,2780000,57.02 1960-07-01,57.06,57.06,57.06,57.06,2620000,57.06 1960-06-30,56.92,56.92,56.92,56.92,2940000,56.92 1960-06-29,56.94,56.94,56.94,56.94,3160000,56.94 1960-06-28,56.94,56.94,56.94,56.94,3120000,56.94 1960-06-27,57.33,57.33,57.33,57.33,2960000,57.33 1960-06-24,57.68,57.68,57.68,57.68,3220000,57.68 1960-06-23,57.59,57.59,57.59,57.59,3620000,57.59 1960-06-22,57.28,57.28,57.28,57.28,3600000,57.28 1960-06-21,57.11,57.11,57.11,57.11,3860000,57.11 1960-06-20,57.16,57.16,57.16,57.16,3970000,57.16 1960-06-17,57.44,57.44,57.44,57.44,3920000,57.44 1960-06-16,57.50,57.50,57.50,57.50,3540000,57.50 1960-06-15,57.57,57.57,57.57,57.57,3630000,57.57 1960-06-14,57.91,57.91,57.91,57.91,3430000,57.91 1960-06-13,57.99,57.99,57.99,57.99,3180000,57.99 1960-06-10,57.97,57.97,57.97,57.97,2940000,57.97 1960-06-09,58.00,58.00,58.00,58.00,3820000,58.00 1960-06-08,57.89,57.89,57.89,57.89,3800000,57.89 1960-06-07,57.43,57.43,57.43,57.43,3710000,57.43 1960-06-06,56.89,56.89,56.89,56.89,3220000,56.89 1960-06-03,56.23,56.23,56.23,56.23,3340000,56.23 1960-06-02,56.13,56.13,56.13,56.13,3730000,56.13 1960-06-01,55.89,55.89,55.89,55.89,3770000,55.89 1960-05-31,55.83,55.83,55.83,55.83,3750000,55.83 1960-05-27,55.74,55.74,55.74,55.74,3040000,55.74 1960-05-26,55.71,55.71,55.71,55.71,3720000,55.71 1960-05-25,55.67,55.67,55.67,55.67,3440000,55.67 1960-05-24,55.70,55.70,55.70,55.70,3240000,55.70 1960-05-23,55.76,55.76,55.76,55.76,2530000,55.76 1960-05-20,55.73,55.73,55.73,55.73,3170000,55.73 1960-05-19,55.68,55.68,55.68,55.68,3700000,55.68 1960-05-18,55.44,55.44,55.44,55.44,5240000,55.44 1960-05-17,55.46,55.46,55.46,55.46,4080000,55.46 1960-05-16,55.25,55.25,55.25,55.25,3530000,55.25 1960-05-13,55.30,55.30,55.30,55.30,3750000,55.30 1960-05-12,54.85,54.85,54.85,54.85,3220000,54.85 1960-05-11,54.57,54.57,54.57,54.57,2900000,54.57 1960-05-10,54.42,54.42,54.42,54.42,2870000,54.42 1960-05-09,54.80,54.80,54.80,54.80,2670000,54.80 1960-05-06,54.75,54.75,54.75,54.75,2560000,54.75 1960-05-05,54.86,54.86,54.86,54.86,2670000,54.86 1960-05-04,55.04,55.04,55.04,55.04,2870000,55.04 1960-05-03,54.83,54.83,54.83,54.83,2910000,54.83 1960-05-02,54.13,54.13,54.13,54.13,2930000,54.13 1960-04-29,54.37,54.37,54.37,54.37,2850000,54.37 1960-04-28,54.56,54.56,54.56,54.56,3190000,54.56 1960-04-27,55.04,55.04,55.04,55.04,3020000,55.04 1960-04-26,55.04,55.04,55.04,55.04,2940000,55.04 1960-04-25,54.86,54.86,54.86,54.86,2980000,54.86 1960-04-22,55.42,55.42,55.42,55.42,2850000,55.42 1960-04-21,55.59,55.59,55.59,55.59,2700000,55.59 1960-04-20,55.44,55.44,55.44,55.44,3150000,55.44 1960-04-19,56.13,56.13,56.13,56.13,3080000,56.13 1960-04-18,56.59,56.59,56.59,56.59,3200000,56.59 1960-04-14,56.43,56.43,56.43,56.43,2730000,56.43 1960-04-13,56.30,56.30,56.30,56.30,2730000,56.30 1960-04-12,56.30,56.30,56.30,56.30,2470000,56.30 1960-04-11,56.17,56.17,56.17,56.17,2520000,56.17 1960-04-08,56.39,56.39,56.39,56.39,2820000,56.39 1960-04-07,56.52,56.52,56.52,56.52,3070000,56.52 1960-04-06,56.51,56.51,56.51,56.51,3450000,56.51 1960-04-05,55.37,55.37,55.37,55.37,2840000,55.37 1960-04-04,55.54,55.54,55.54,55.54,2450000,55.54 1960-04-01,55.43,55.43,55.43,55.43,2260000,55.43 1960-03-31,55.34,55.34,55.34,55.34,2690000,55.34 1960-03-30,55.66,55.66,55.66,55.66,2450000,55.66 1960-03-29,55.78,55.78,55.78,55.78,2320000,55.78 1960-03-28,55.86,55.86,55.86,55.86,2500000,55.86 1960-03-25,55.98,55.98,55.98,55.98,2640000,55.98 1960-03-24,55.98,55.98,55.98,55.98,2940000,55.98 1960-03-23,55.74,55.74,55.74,55.74,3020000,55.74 1960-03-22,55.29,55.29,55.29,55.29,2490000,55.29 1960-03-21,55.07,55.07,55.07,55.07,2500000,55.07 1960-03-18,55.01,55.01,55.01,55.01,2620000,55.01 1960-03-17,54.96,54.96,54.96,54.96,2140000,54.96 1960-03-16,55.04,55.04,55.04,55.04,2960000,55.04 1960-03-15,54.74,54.74,54.74,54.74,2690000,54.74 1960-03-14,54.32,54.32,54.32,54.32,2530000,54.32 1960-03-11,54.24,54.24,54.24,54.24,2770000,54.24 1960-03-10,53.83,53.83,53.83,53.83,3350000,53.83 1960-03-09,54.04,54.04,54.04,54.04,3580000,54.04 1960-03-08,53.47,53.47,53.47,53.47,3370000,53.47 1960-03-07,54.02,54.02,54.02,54.02,2900000,54.02 1960-03-04,54.57,54.57,54.57,54.57,4060000,54.57 1960-03-03,54.78,54.78,54.78,54.78,3160000,54.78 1960-03-02,55.62,55.62,55.62,55.62,3110000,55.62 1960-03-01,56.01,56.01,56.01,56.01,2920000,56.01 1960-02-29,56.12,56.12,56.12,56.12,2990000,56.12 1960-02-26,56.16,56.16,56.16,56.16,3380000,56.16 1960-02-25,55.93,55.93,55.93,55.93,3600000,55.93 1960-02-24,55.74,55.74,55.74,55.74,2740000,55.74 1960-02-23,55.94,55.94,55.94,55.94,2960000,55.94 1960-02-19,56.24,56.24,56.24,56.24,3230000,56.24 1960-02-18,55.80,55.80,55.80,55.80,3800000,55.80 1960-02-17,55.03,55.03,55.03,55.03,4210000,55.03 1960-02-16,54.73,54.73,54.73,54.73,3270000,54.73 1960-02-15,55.17,55.17,55.17,55.17,2780000,55.17 1960-02-12,55.46,55.46,55.46,55.46,2230000,55.46 1960-02-11,55.18,55.18,55.18,55.18,2610000,55.18 1960-02-10,55.49,55.49,55.49,55.49,2440000,55.49 1960-02-09,55.84,55.84,55.84,55.84,2860000,55.84 1960-02-08,55.32,55.32,55.32,55.32,3350000,55.32 1960-02-05,55.98,55.98,55.98,55.98,2530000,55.98 1960-02-04,56.27,56.27,56.27,56.27,2600000,56.27 1960-02-03,56.32,56.32,56.32,56.32,3020000,56.32 1960-02-02,56.82,56.82,56.82,56.82,3080000,56.82 1960-02-01,55.96,55.96,55.96,55.96,2820000,55.96 1960-01-29,55.61,55.61,55.61,55.61,3060000,55.61 1960-01-28,56.13,56.13,56.13,56.13,2630000,56.13 1960-01-27,56.72,56.72,56.72,56.72,2460000,56.72 1960-01-26,56.86,56.86,56.86,56.86,3060000,56.86 1960-01-25,56.78,56.78,56.78,56.78,2790000,56.78 1960-01-22,57.38,57.38,57.38,57.38,2690000,57.38 1960-01-21,57.21,57.21,57.21,57.21,2700000,57.21 1960-01-20,57.07,57.07,57.07,57.07,2720000,57.07 1960-01-19,57.27,57.27,57.27,57.27,3100000,57.27 1960-01-18,57.89,57.89,57.89,57.89,3020000,57.89 1960-01-15,58.38,58.38,58.38,58.38,3400000,58.38 1960-01-14,58.40,58.40,58.40,58.40,3560000,58.40 1960-01-13,58.08,58.08,58.08,58.08,3470000,58.08 1960-01-12,58.41,58.41,58.41,58.41,3760000,58.41 1960-01-11,58.77,58.77,58.77,58.77,3470000,58.77 1960-01-08,59.50,59.50,59.50,59.50,3290000,59.50 1960-01-07,59.69,59.69,59.69,59.69,3310000,59.69 1960-01-06,60.13,60.13,60.13,60.13,3730000,60.13 1960-01-05,60.39,60.39,60.39,60.39,3710000,60.39 1960-01-04,59.91,59.91,59.91,59.91,3990000,59.91 1959-12-31,59.89,59.89,59.89,59.89,3810000,59.89 1959-12-30,59.77,59.77,59.77,59.77,3680000,59.77 1959-12-29,59.30,59.30,59.30,59.30,3020000,59.30 1959-12-28,58.98,58.98,58.98,58.98,2830000,58.98 1959-12-24,59.00,59.00,59.00,59.00,2320000,59.00 1959-12-23,58.96,58.96,58.96,58.96,2890000,58.96 1959-12-22,59.14,59.14,59.14,59.14,2930000,59.14 1959-12-21,59.21,59.21,59.21,59.21,3290000,59.21 1959-12-18,59.14,59.14,59.14,59.14,3230000,59.14 1959-12-17,58.86,58.86,58.86,58.86,3040000,58.86 1959-12-16,58.97,58.97,58.97,58.97,3270000,58.97 1959-12-15,58.90,58.90,58.90,58.90,3450000,58.90 1959-12-14,59.04,59.04,59.04,59.04,3100000,59.04 1959-12-11,58.88,58.88,58.88,58.88,2910000,58.88 1959-12-10,59.02,59.02,59.02,59.02,3170000,59.02 1959-12-09,58.97,58.97,58.97,58.97,3430000,58.97 1959-12-08,59.34,59.34,59.34,59.34,3870000,59.34 1959-12-07,58.96,58.96,58.96,58.96,3620000,58.96 1959-12-04,58.85,58.85,58.85,58.85,3590000,58.85 1959-12-03,58.73,58.73,58.73,58.73,3280000,58.73 1959-12-02,58.60,58.60,58.60,58.60,3490000,58.60 1959-12-01,58.70,58.70,58.70,58.70,3990000,58.70 1959-11-30,58.28,58.28,58.28,58.28,3670000,58.28 1959-11-27,57.70,57.70,57.70,57.70,3030000,57.70 1959-11-25,57.44,57.44,57.44,57.44,3550000,57.44 1959-11-24,57.35,57.35,57.35,57.35,3650000,57.35 1959-11-23,57.08,57.08,57.08,57.08,3400000,57.08 1959-11-20,56.97,56.97,56.97,56.97,2960000,56.97 1959-11-19,56.94,56.94,56.94,56.94,3230000,56.94 1959-11-18,56.99,56.99,56.99,56.99,3660000,56.99 1959-11-17,56.38,56.38,56.38,56.38,3570000,56.38 1959-11-16,56.22,56.22,56.22,56.22,3710000,56.22 1959-11-13,56.85,56.85,56.85,56.85,3050000,56.85 1959-11-12,57.17,57.17,57.17,57.17,3600000,57.17 1959-11-11,57.49,57.49,57.49,57.49,2820000,57.49 1959-11-10,57.48,57.48,57.48,57.48,3020000,57.48 1959-11-09,57.50,57.50,57.50,57.50,3700000,57.50 1959-11-06,57.60,57.60,57.60,57.60,3450000,57.60 1959-11-05,57.32,57.32,57.32,57.32,3170000,57.32 1959-11-04,57.26,57.26,57.26,57.26,3940000,57.26 1959-11-02,57.41,57.41,57.41,57.41,3320000,57.41 1959-10-30,57.52,57.52,57.52,57.52,3560000,57.52 1959-10-29,57.41,57.41,57.41,57.41,3890000,57.41 1959-10-28,57.46,57.46,57.46,57.46,3920000,57.46 1959-10-27,57.42,57.42,57.42,57.42,4160000,57.42 1959-10-26,56.94,56.94,56.94,56.94,3580000,56.94 1959-10-23,56.56,56.56,56.56,56.56,2880000,56.56 1959-10-22,56.00,56.00,56.00,56.00,3060000,56.00 1959-10-21,56.55,56.55,56.55,56.55,2730000,56.55 1959-10-20,56.66,56.66,56.66,56.66,2740000,56.66 1959-10-19,57.01,57.01,57.01,57.01,2470000,57.01 1959-10-16,57.33,57.33,57.33,57.33,2760000,57.33 1959-10-15,56.87,56.87,56.87,56.87,2190000,56.87 1959-10-14,56.71,56.71,56.71,56.71,2320000,56.71 1959-10-13,57.16,57.16,57.16,57.16,2530000,57.16 1959-10-12,57.32,57.32,57.32,57.32,1750000,57.32 1959-10-09,57.00,57.00,57.00,57.00,2540000,57.00 1959-10-08,56.81,56.81,56.81,56.81,2510000,56.81 1959-10-07,56.94,56.94,56.94,56.94,2380000,56.94 1959-10-06,57.09,57.09,57.09,57.09,2330000,57.09 1959-10-05,57.14,57.14,57.14,57.14,2100000,57.14 1959-10-02,57.20,57.20,57.20,57.20,2270000,57.20 1959-10-01,56.94,56.94,56.94,56.94,2660000,56.94 1959-09-30,56.88,56.88,56.88,56.88,2850000,56.88 1959-09-29,57.51,57.51,57.51,57.51,3220000,57.51 1959-09-28,57.15,57.15,57.15,57.15,2640000,57.15 1959-09-25,56.73,56.73,56.73,56.73,3280000,56.73 1959-09-24,56.78,56.78,56.78,56.78,3480000,56.78 1959-09-23,55.82,55.82,55.82,55.82,3010000,55.82 1959-09-22,55.14,55.14,55.14,55.14,3000000,55.14 1959-09-21,55.27,55.27,55.27,55.27,3240000,55.27 1959-09-18,56.19,56.19,56.19,56.19,2530000,56.19 1959-09-17,56.41,56.41,56.41,56.41,2090000,56.41 1959-09-16,56.72,56.72,56.72,56.72,2180000,56.72 1959-09-15,56.68,56.68,56.68,56.68,2830000,56.68 1959-09-14,56.99,56.99,56.99,56.99,2590000,56.99 1959-09-11,57.41,57.41,57.41,57.41,2640000,57.41 1959-09-10,56.99,56.99,56.99,56.99,2520000,56.99 1959-09-09,57.29,57.29,57.29,57.29,3030000,57.29 1959-09-08,57.70,57.70,57.70,57.70,2940000,57.70 1959-09-04,58.54,58.54,58.54,58.54,2300000,58.54 1959-09-03,58.26,58.26,58.26,58.26,2330000,58.26 1959-09-02,58.92,58.92,58.92,58.92,2370000,58.92 1959-09-01,58.87,58.87,58.87,58.87,2430000,58.87 1959-08-31,59.60,59.60,59.60,59.60,2140000,59.60 1959-08-28,59.60,59.60,59.60,59.60,1930000,59.60 1959-08-27,59.58,59.58,59.58,59.58,2550000,59.58 1959-08-26,59.07,59.07,59.07,59.07,2210000,59.07 1959-08-25,58.99,58.99,58.99,58.99,1960000,58.99 1959-08-24,58.87,58.87,58.87,58.87,1860000,58.87 1959-08-21,59.08,59.08,59.08,59.08,2000000,59.08 1959-08-20,59.14,59.14,59.14,59.14,2450000,59.14 1959-08-19,58.27,58.27,58.27,58.27,3050000,58.27 1959-08-18,58.62,58.62,58.62,58.62,2280000,58.62 1959-08-17,59.17,59.17,59.17,59.17,1980000,59.17 1959-08-14,59.29,59.29,59.29,59.29,1990000,59.29 1959-08-13,59.15,59.15,59.15,59.15,2020000,59.15 1959-08-12,59.25,59.25,59.25,59.25,2700000,59.25 1959-08-11,59.39,59.39,59.39,59.39,2980000,59.39 1959-08-10,58.62,58.62,58.62,58.62,4190000,58.62 1959-08-07,59.87,59.87,59.87,59.87,2580000,59.87 1959-08-06,60.24,60.24,60.24,60.24,2610000,60.24 1959-08-05,60.30,60.30,60.30,60.30,2630000,60.30 1959-08-04,60.61,60.61,60.61,60.61,2530000,60.61 1959-08-03,60.71,60.71,60.71,60.71,2410000,60.71 1959-07-31,60.51,60.51,60.51,60.51,2270000,60.51 1959-07-30,60.50,60.50,60.50,60.50,3240000,60.50 1959-07-29,60.62,60.62,60.62,60.62,3460000,60.62 1959-07-28,60.32,60.32,60.32,60.32,3190000,60.32 1959-07-27,60.02,60.02,60.02,60.02,2910000,60.02 1959-07-24,59.65,59.65,59.65,59.65,2720000,59.65 1959-07-23,59.67,59.67,59.67,59.67,3310000,59.67 1959-07-22,59.61,59.61,59.61,59.61,3310000,59.61 1959-07-21,59.41,59.41,59.41,59.41,2950000,59.41 1959-07-20,58.91,58.91,58.91,58.91,2500000,58.91 1959-07-17,59.19,59.19,59.19,59.19,2510000,59.19 1959-07-16,59.41,59.41,59.41,59.41,3170000,59.41 1959-07-15,59.59,59.59,59.59,59.59,3280000,59.59 1959-07-14,59.55,59.55,59.55,59.55,3230000,59.55 1959-07-13,59.41,59.41,59.41,59.41,3360000,59.41 1959-07-10,59.91,59.91,59.91,59.91,3600000,59.91 1959-07-09,59.97,59.97,59.97,59.97,3560000,59.97 1959-07-08,60.03,60.03,60.03,60.03,4010000,60.03 1959-07-07,60.01,60.01,60.01,60.01,3840000,60.01 1959-07-06,59.65,59.65,59.65,59.65,3720000,59.65 1959-07-02,59.28,59.28,59.28,59.28,3610000,59.28 1959-07-01,58.97,58.97,58.97,58.97,3150000,58.97 1959-06-30,58.47,58.47,58.47,58.47,3200000,58.47 1959-06-29,58.37,58.37,58.37,58.37,3000000,58.37 1959-06-26,57.98,57.98,57.98,57.98,3100000,57.98 1959-06-25,57.73,57.73,57.73,57.73,3250000,57.73 1959-06-24,57.41,57.41,57.41,57.41,3180000,57.41 1959-06-23,57.12,57.12,57.12,57.12,2600000,57.12 1959-06-22,57.13,57.13,57.13,57.13,2630000,57.13 1959-06-19,57.13,57.13,57.13,57.13,2260000,57.13 1959-06-18,57.05,57.05,57.05,57.05,3150000,57.05 1959-06-17,57.09,57.09,57.09,57.09,2850000,57.09 1959-06-16,56.56,56.56,56.56,56.56,2440000,56.56 1959-06-15,56.99,56.99,56.99,56.99,2410000,56.99 1959-06-12,57.29,57.29,57.29,57.29,2580000,57.29 1959-06-11,57.25,57.25,57.25,57.25,3120000,57.25 1959-06-10,57.19,57.19,57.19,57.19,3310000,57.19 1959-06-09,56.36,56.36,56.36,56.36,3490000,56.36 1959-06-08,56.76,56.76,56.76,56.76,2970000,56.76 1959-06-05,57.51,57.51,57.51,57.51,2800000,57.51 1959-06-04,57.63,57.63,57.63,57.63,3210000,57.63 1959-06-03,58.25,58.25,58.25,58.25,2910000,58.25 1959-06-02,58.23,58.23,58.23,58.23,3120000,58.23 1959-06-01,58.63,58.63,58.63,58.63,2730000,58.63 1959-05-29,58.68,58.68,58.68,58.68,2790000,58.68 1959-05-28,58.39,58.39,58.39,58.39,2970000,58.39 1959-05-27,58.19,58.19,58.19,58.19,2940000,58.19 1959-05-26,58.09,58.09,58.09,58.09,2910000,58.09 1959-05-25,58.18,58.18,58.18,58.18,3260000,58.18 1959-05-22,58.33,58.33,58.33,58.33,3030000,58.33 1959-05-21,58.14,58.14,58.14,58.14,3230000,58.14 1959-05-20,58.09,58.09,58.09,58.09,3550000,58.09 1959-05-19,58.32,58.32,58.32,58.32,3170000,58.32 1959-05-18,58.15,58.15,58.15,58.15,2970000,58.15 1959-05-15,58.16,58.16,58.16,58.16,3510000,58.16 1959-05-14,58.37,58.37,58.37,58.37,3660000,58.37 1959-05-13,57.97,57.97,57.97,57.97,3540000,57.97 1959-05-12,57.96,57.96,57.96,57.96,3550000,57.96 1959-05-11,57.96,57.96,57.96,57.96,3860000,57.96 1959-05-08,57.32,57.32,57.32,57.32,3930000,57.32 1959-05-07,56.88,56.88,56.88,56.88,4530000,56.88 1959-05-06,57.61,57.61,57.61,57.61,4110000,57.61 1959-05-05,57.75,57.75,57.75,57.75,3360000,57.75 1959-05-04,57.65,57.65,57.65,57.65,3060000,57.65 1959-05-01,57.65,57.65,57.65,57.65,3020000,57.65 1959-04-30,57.59,57.59,57.59,57.59,3510000,57.59 1959-04-29,57.69,57.69,57.69,57.69,3470000,57.69 1959-04-28,57.92,57.92,57.92,57.92,3920000,57.92 1959-04-27,58.14,58.14,58.14,58.14,3850000,58.14 1959-04-24,57.96,57.96,57.96,57.96,3790000,57.96 1959-04-23,57.60,57.60,57.60,57.60,3310000,57.60 1959-04-22,57.73,57.73,57.73,57.73,3430000,57.73 1959-04-21,58.11,58.11,58.11,58.11,3650000,58.11 1959-04-20,58.17,58.17,58.17,58.17,3610000,58.17 1959-04-17,57.92,57.92,57.92,57.92,3870000,57.92 1959-04-16,57.43,57.43,57.43,57.43,3790000,57.43 1959-04-15,56.96,56.96,56.96,56.96,3680000,56.96 1959-04-14,56.71,56.71,56.71,56.71,3320000,56.71 1959-04-13,56.43,56.43,56.43,56.43,3140000,56.43 1959-04-10,56.22,56.22,56.22,56.22,3000000,56.22 1959-04-09,56.17,56.17,56.17,56.17,2830000,56.17 1959-04-08,56.21,56.21,56.21,56.21,3260000,56.21 1959-04-07,56.48,56.48,56.48,56.48,3020000,56.48 1959-04-06,56.60,56.60,56.60,56.60,3510000,56.60 1959-04-03,56.44,56.44,56.44,56.44,3680000,56.44 1959-04-02,56.00,56.00,56.00,56.00,3220000,56.00 1959-04-01,55.69,55.69,55.69,55.69,2980000,55.69 1959-03-31,55.44,55.44,55.44,55.44,2820000,55.44 1959-03-30,55.45,55.45,55.45,55.45,2940000,55.45 1959-03-26,55.76,55.76,55.76,55.76,2900000,55.76 1959-03-25,55.88,55.88,55.88,55.88,3280000,55.88 1959-03-24,55.96,55.96,55.96,55.96,3000000,55.96 1959-03-23,55.87,55.87,55.87,55.87,3700000,55.87 1959-03-20,56.39,56.39,56.39,56.39,3770000,56.39 1959-03-19,56.34,56.34,56.34,56.34,4150000,56.34 1959-03-18,56.39,56.39,56.39,56.39,4530000,56.39 1959-03-17,56.52,56.52,56.52,56.52,4730000,56.52 1959-03-16,56.06,56.06,56.06,56.06,4420000,56.06 1959-03-13,56.67,56.67,56.67,56.67,4880000,56.67 1959-03-12,56.60,56.60,56.60,56.60,4690000,56.60 1959-03-11,56.35,56.35,56.35,56.35,4160000,56.35 1959-03-10,56.31,56.31,56.31,56.31,3920000,56.31 1959-03-09,56.15,56.15,56.15,56.15,3530000,56.15 1959-03-06,56.21,56.21,56.21,56.21,3930000,56.21 1959-03-05,56.43,56.43,56.43,56.43,3930000,56.43 1959-03-04,56.35,56.35,56.35,56.35,4150000,56.35 1959-03-03,56.25,56.25,56.25,56.25,4790000,56.25 1959-03-02,55.73,55.73,55.73,55.73,4210000,55.73 1959-02-27,55.41,55.41,55.41,55.41,4300000,55.41 1959-02-26,55.34,55.34,55.34,55.34,3930000,55.34 1959-02-25,55.24,55.24,55.24,55.24,3780000,55.24 1959-02-24,55.48,55.48,55.48,55.48,4340000,55.48 1959-02-20,55.52,55.52,55.52,55.52,4190000,55.52 1959-02-19,55.50,55.50,55.50,55.50,4160000,55.50 1959-02-18,54.30,54.30,54.30,54.30,3480000,54.30 1959-02-17,54.29,54.29,54.29,54.29,3190000,54.29 1959-02-16,54.50,54.50,54.50,54.50,3480000,54.50 1959-02-13,54.42,54.42,54.42,54.42,3070000,54.42 1959-02-12,54.00,54.00,54.00,54.00,2630000,54.00 1959-02-11,54.35,54.35,54.35,54.35,3000000,54.35 1959-02-10,54.32,54.32,54.32,54.32,2960000,54.32 1959-02-09,53.58,53.58,53.58,53.58,3130000,53.58 1959-02-06,54.37,54.37,54.37,54.37,3010000,54.37 1959-02-05,54.81,54.81,54.81,54.81,3140000,54.81 1959-02-04,55.06,55.06,55.06,55.06,3170000,55.06 1959-02-03,55.28,55.28,55.28,55.28,3220000,55.28 1959-02-02,55.21,55.21,55.21,55.21,3610000,55.21 1959-01-30,55.45,55.45,55.45,55.45,3600000,55.45 1959-01-29,55.20,55.20,55.20,55.20,3470000,55.20 1959-01-28,55.16,55.16,55.16,55.16,4190000,55.16 1959-01-27,55.78,55.78,55.78,55.78,3480000,55.78 1959-01-26,55.77,55.77,55.77,55.77,3980000,55.77 1959-01-23,56.00,56.00,56.00,56.00,3600000,56.00 1959-01-22,55.97,55.97,55.97,55.97,4250000,55.97 1959-01-21,56.04,56.04,56.04,56.04,3940000,56.04 1959-01-20,55.72,55.72,55.72,55.72,3680000,55.72 1959-01-19,55.68,55.68,55.68,55.68,3840000,55.68 1959-01-16,55.81,55.81,55.81,55.81,4300000,55.81 1959-01-15,55.83,55.83,55.83,55.83,4500000,55.83 1959-01-14,55.62,55.62,55.62,55.62,4090000,55.62 1959-01-13,55.47,55.47,55.47,55.47,3790000,55.47 1959-01-12,55.78,55.78,55.78,55.78,4320000,55.78 1959-01-09,55.77,55.77,55.77,55.77,4760000,55.77 1959-01-08,55.40,55.40,55.40,55.40,4030000,55.40 1959-01-07,54.89,54.89,54.89,54.89,4140000,54.89 1959-01-06,55.59,55.59,55.59,55.59,3690000,55.59 1959-01-05,55.66,55.66,55.66,55.66,4210000,55.66 1959-01-02,55.44,55.44,55.44,55.44,3380000,55.44 1958-12-31,55.21,55.21,55.21,55.21,3970000,55.21 1958-12-30,54.93,54.93,54.93,54.93,3900000,54.93 1958-12-29,54.74,54.74,54.74,54.74,3790000,54.74 1958-12-24,54.11,54.11,54.11,54.11,3050000,54.11 1958-12-23,53.42,53.42,53.42,53.42,2870000,53.42 1958-12-22,53.71,53.71,53.71,53.71,3030000,53.71 1958-12-19,54.07,54.07,54.07,54.07,3540000,54.07 1958-12-18,54.15,54.15,54.15,54.15,3900000,54.15 1958-12-17,53.92,53.92,53.92,53.92,3900000,53.92 1958-12-16,53.57,53.57,53.57,53.57,3970000,53.57 1958-12-15,53.37,53.37,53.37,53.37,3340000,53.37 1958-12-12,53.22,53.22,53.22,53.22,3140000,53.22 1958-12-11,53.35,53.35,53.35,53.35,4250000,53.35 1958-12-10,53.46,53.46,53.46,53.46,4340000,53.46 1958-12-09,52.82,52.82,52.82,52.82,3790000,52.82 1958-12-08,52.46,52.46,52.46,52.46,3590000,52.46 1958-12-05,52.46,52.46,52.46,52.46,3360000,52.46 1958-12-04,52.55,52.55,52.55,52.55,3630000,52.55 1958-12-03,52.53,52.53,52.53,52.53,3460000,52.53 1958-12-02,52.46,52.46,52.46,52.46,3320000,52.46 1958-12-01,52.69,52.69,52.69,52.69,3800000,52.69 1958-11-28,52.48,52.48,52.48,52.48,4120000,52.48 1958-11-26,51.90,51.90,51.90,51.90,4090000,51.90 1958-11-25,51.02,51.02,51.02,51.02,3940000,51.02 1958-11-24,52.03,52.03,52.03,52.03,4770000,52.03 1958-11-21,52.70,52.70,52.70,52.70,3950000,52.70 1958-11-20,53.21,53.21,53.21,53.21,4320000,53.21 1958-11-19,53.20,53.20,53.20,53.20,4090000,53.20 1958-11-18,53.13,53.13,53.13,53.13,3820000,53.13 1958-11-17,53.24,53.24,53.24,53.24,4540000,53.24 1958-11-14,53.09,53.09,53.09,53.09,4390000,53.09 1958-11-13,52.83,52.83,52.83,52.83,4200000,52.83 1958-11-12,53.05,53.05,53.05,53.05,4440000,53.05 1958-11-11,52.98,52.98,52.98,52.98,4040000,52.98 1958-11-10,52.57,52.57,52.57,52.57,3730000,52.57 1958-11-07,52.26,52.26,52.26,52.26,3700000,52.26 1958-11-06,52.45,52.45,52.45,52.45,4890000,52.45 1958-11-05,52.03,52.03,52.03,52.03,4080000,52.03 1958-11-03,51.56,51.56,51.56,51.56,3240000,51.56 1958-10-31,51.33,51.33,51.33,51.33,3920000,51.33 1958-10-30,51.27,51.27,51.27,51.27,4360000,51.27 1958-10-29,51.07,51.07,51.07,51.07,4790000,51.07 1958-10-28,50.58,50.58,50.58,50.58,3670000,50.58 1958-10-27,50.42,50.42,50.42,50.42,3980000,50.42 1958-10-24,50.81,50.81,50.81,50.81,3770000,50.81 1958-10-23,50.97,50.97,50.97,50.97,3610000,50.97 1958-10-22,51.07,51.07,51.07,51.07,3500000,51.07 1958-10-21,51.27,51.27,51.27,51.27,4010000,51.27 1958-10-20,51.27,51.27,51.27,51.27,4560000,51.27 1958-10-17,51.46,51.46,51.46,51.46,5360000,51.46 1958-10-16,50.94,50.94,50.94,50.94,4560000,50.94 1958-10-15,50.58,50.58,50.58,50.58,4810000,50.58 1958-10-14,51.26,51.26,51.26,51.26,5110000,51.26 1958-10-13,51.62,51.62,51.62,51.62,4550000,51.62 1958-10-10,51.39,51.39,51.39,51.39,4610000,51.39 1958-10-09,51.05,51.05,51.05,51.05,3670000,51.05 1958-10-08,51.06,51.06,51.06,51.06,3680000,51.06 1958-10-07,51.07,51.07,51.07,51.07,3570000,51.07 1958-10-06,51.07,51.07,51.07,51.07,3570000,51.07 1958-10-03,50.37,50.37,50.37,50.37,3830000,50.37 1958-10-02,50.17,50.17,50.17,50.17,3750000,50.17 1958-10-01,49.98,49.98,49.98,49.98,3780000,49.98 1958-09-30,50.06,50.06,50.06,50.06,4160000,50.06 1958-09-29,49.87,49.87,49.87,49.87,3680000,49.87 1958-09-26,49.66,49.66,49.66,49.66,3420000,49.66 1958-09-25,49.57,49.57,49.57,49.57,4490000,49.57 1958-09-24,49.78,49.78,49.78,49.78,3120000,49.78 1958-09-23,49.56,49.56,49.56,49.56,3950000,49.56 1958-09-22,49.20,49.20,49.20,49.20,3490000,49.20 1958-09-19,49.40,49.40,49.40,49.40,3880000,49.40 1958-09-18,49.38,49.38,49.38,49.38,3460000,49.38 1958-09-17,49.35,49.35,49.35,49.35,3790000,49.35 1958-09-16,49.35,49.35,49.35,49.35,3940000,49.35 1958-09-15,48.96,48.96,48.96,48.96,3040000,48.96 1958-09-12,48.53,48.53,48.53,48.53,3100000,48.53 1958-09-11,48.64,48.64,48.64,48.64,3300000,48.64 1958-09-10,48.31,48.31,48.31,48.31,2820000,48.31 1958-09-09,48.46,48.46,48.46,48.46,3480000,48.46 1958-09-08,48.13,48.13,48.13,48.13,3030000,48.13 1958-09-05,47.97,47.97,47.97,47.97,2520000,47.97 1958-09-04,48.10,48.10,48.10,48.10,3100000,48.10 1958-09-03,48.18,48.18,48.18,48.18,3240000,48.18 1958-09-02,48.00,48.00,48.00,48.00,2930000,48.00 1958-08-29,47.75,47.75,47.75,47.75,2260000,47.75 1958-08-28,47.66,47.66,47.66,47.66,2540000,47.66 1958-08-27,47.91,47.91,47.91,47.91,3250000,47.91 1958-08-26,47.90,47.90,47.90,47.90,2910000,47.90 1958-08-25,47.74,47.74,47.74,47.74,2610000,47.74 1958-08-22,47.73,47.73,47.73,47.73,2660000,47.73 1958-08-21,47.63,47.63,47.63,47.63,2500000,47.63 1958-08-20,47.32,47.32,47.32,47.32,2460000,47.32 1958-08-19,47.30,47.30,47.30,47.30,2250000,47.30 1958-08-18,47.22,47.22,47.22,47.22,2390000,47.22 1958-08-15,47.50,47.50,47.50,47.50,2960000,47.50 1958-08-14,47.91,47.91,47.91,47.91,3370000,47.91 1958-08-13,47.81,47.81,47.81,47.81,2790000,47.81 1958-08-12,47.73,47.73,47.73,47.73,2600000,47.73 1958-08-11,48.16,48.16,48.16,48.16,2870000,48.16 1958-08-08,48.05,48.05,48.05,48.05,3650000,48.05 1958-08-07,47.77,47.77,47.77,47.77,3200000,47.77 1958-08-06,47.46,47.46,47.46,47.46,3440000,47.46 1958-08-05,47.75,47.75,47.75,47.75,4210000,47.75 1958-08-04,47.94,47.94,47.94,47.94,4000000,47.94 1958-08-01,47.49,47.49,47.49,47.49,3380000,47.49 1958-07-31,47.19,47.19,47.19,47.19,4440000,47.19 1958-07-30,47.09,47.09,47.09,47.09,3680000,47.09 1958-07-29,46.96,46.96,46.96,46.96,3310000,46.96 1958-07-28,47.15,47.15,47.15,47.15,3940000,47.15 1958-07-25,46.97,46.97,46.97,46.97,4430000,46.97 1958-07-24,46.65,46.65,46.65,46.65,3740000,46.65 1958-07-23,46.40,46.40,46.40,46.40,3550000,46.40 1958-07-22,46.41,46.41,46.41,46.41,3420000,46.41 1958-07-21,46.33,46.33,46.33,46.33,3440000,46.33 1958-07-18,45.77,45.77,45.77,45.77,3350000,45.77 1958-07-17,45.55,45.55,45.55,45.55,3180000,45.55 1958-07-16,45.25,45.25,45.25,45.25,3240000,45.25 1958-07-15,45.11,45.11,45.11,45.11,3090000,45.11 1958-07-14,45.14,45.14,45.14,45.14,2540000,45.14 1958-07-11,45.72,45.72,45.72,45.72,2400000,45.72 1958-07-10,45.42,45.42,45.42,45.42,2510000,45.42 1958-07-09,45.25,45.25,45.25,45.25,2630000,45.25 1958-07-08,45.40,45.40,45.40,45.40,2430000,45.40 1958-07-07,45.62,45.62,45.62,45.62,2510000,45.62 1958-07-03,45.47,45.47,45.47,45.47,2630000,45.47 1958-07-02,45.32,45.32,45.32,45.32,2370000,45.32 1958-07-01,45.28,45.28,45.28,45.28,2600000,45.28 1958-06-30,45.24,45.24,45.24,45.24,2820000,45.24 1958-06-27,44.90,44.90,44.90,44.90,2800000,44.90 1958-06-26,44.84,44.84,44.84,44.84,2910000,44.84 1958-06-25,44.63,44.63,44.63,44.63,2720000,44.63 1958-06-24,44.52,44.52,44.52,44.52,2560000,44.52 1958-06-23,44.69,44.69,44.69,44.69,2340000,44.69 1958-06-20,44.85,44.85,44.85,44.85,2590000,44.85 1958-06-19,44.61,44.61,44.61,44.61,2690000,44.61 1958-06-18,45.34,45.34,45.34,45.34,2640000,45.34 1958-06-17,44.94,44.94,44.94,44.94,2950000,44.94 1958-06-16,45.18,45.18,45.18,45.18,2870000,45.18 1958-06-13,45.02,45.02,45.02,45.02,3100000,45.02 1958-06-12,44.75,44.75,44.75,44.75,2760000,44.75 1958-06-11,44.49,44.49,44.49,44.49,2570000,44.49 1958-06-10,44.48,44.48,44.48,44.48,2390000,44.48 1958-06-09,44.57,44.57,44.57,44.57,2380000,44.57 1958-06-06,44.64,44.64,44.64,44.64,2680000,44.64 1958-06-05,44.55,44.55,44.55,44.55,2600000,44.55 1958-06-04,44.50,44.50,44.50,44.50,2690000,44.50 1958-06-03,44.46,44.46,44.46,44.46,2780000,44.46 1958-06-02,44.31,44.31,44.31,44.31,2770000,44.31 1958-05-29,44.09,44.09,44.09,44.09,2350000,44.09 1958-05-28,43.85,43.85,43.85,43.85,2260000,43.85 1958-05-27,43.79,43.79,43.79,43.79,2180000,43.79 1958-05-26,43.85,43.85,43.85,43.85,2500000,43.85 1958-05-23,43.87,43.87,43.87,43.87,2570000,43.87 1958-05-22,43.78,43.78,43.78,43.78,2950000,43.78 1958-05-21,43.55,43.55,43.55,43.55,2580000,43.55 1958-05-20,43.61,43.61,43.61,43.61,2500000,43.61 1958-05-19,43.24,43.24,43.24,43.24,1910000,43.24 1958-05-16,43.36,43.36,43.36,43.36,2030000,43.36 1958-05-15,43.34,43.34,43.34,43.34,2470000,43.34 1958-05-14,43.12,43.12,43.12,43.12,3060000,43.12 1958-05-13,43.62,43.62,43.62,43.62,2940000,43.62 1958-05-12,43.75,43.75,43.75,43.75,2780000,43.75 1958-05-09,44.09,44.09,44.09,44.09,2760000,44.09 1958-05-08,43.99,43.99,43.99,43.99,2790000,43.99 1958-05-07,43.93,43.93,43.93,43.93,2770000,43.93 1958-05-06,44.01,44.01,44.01,44.01,3110000,44.01 1958-05-05,43.79,43.79,43.79,43.79,2670000,43.79 1958-05-02,43.69,43.69,43.69,43.69,2290000,43.69 1958-05-01,43.54,43.54,43.54,43.54,2630000,43.54 1958-04-30,43.44,43.44,43.44,43.44,2900000,43.44 1958-04-29,43.00,43.00,43.00,43.00,2190000,43.00 1958-04-28,43.22,43.22,43.22,43.22,2400000,43.22 1958-04-25,43.36,43.36,43.36,43.36,3020000,43.36 1958-04-24,43.14,43.14,43.14,43.14,2870000,43.14 1958-04-23,42.80,42.80,42.80,42.80,2720000,42.80 1958-04-22,42.80,42.80,42.80,42.80,2440000,42.80 1958-04-21,42.93,42.93,42.93,42.93,2550000,42.93 1958-04-18,42.71,42.71,42.71,42.71,2700000,42.71 1958-04-17,42.25,42.25,42.25,42.25,2500000,42.25 1958-04-16,42.10,42.10,42.10,42.10,2240000,42.10 1958-04-15,42.43,42.43,42.43,42.43,2590000,42.43 1958-04-14,42.00,42.00,42.00,42.00,2180000,42.00 1958-04-11,41.74,41.74,41.74,41.74,2060000,41.74 1958-04-10,41.70,41.70,41.70,41.70,2000000,41.70 1958-04-09,41.65,41.65,41.65,41.65,2040000,41.65 1958-04-08,41.43,41.43,41.43,41.43,2190000,41.43 1958-04-07,41.33,41.33,41.33,41.33,2090000,41.33 1958-04-03,41.48,41.48,41.48,41.48,2130000,41.48 1958-04-02,41.60,41.60,41.60,41.60,2390000,41.60 1958-04-01,41.93,41.93,41.93,41.93,2070000,41.93 1958-03-31,42.10,42.10,42.10,42.10,2050000,42.10 1958-03-28,42.20,42.20,42.20,42.20,1930000,42.20 1958-03-27,42.17,42.17,42.17,42.17,2140000,42.17 1958-03-26,42.30,42.30,42.30,42.30,1990000,42.30 1958-03-25,42.44,42.44,42.44,42.44,2210000,42.44 1958-03-24,42.58,42.58,42.58,42.58,2580000,42.58 1958-03-21,42.42,42.42,42.42,42.42,2430000,42.42 1958-03-20,42.11,42.11,42.11,42.11,2280000,42.11 1958-03-19,42.09,42.09,42.09,42.09,2410000,42.09 1958-03-18,41.89,41.89,41.89,41.89,2070000,41.89 1958-03-17,42.04,42.04,42.04,42.04,2130000,42.04 1958-03-14,42.33,42.33,42.33,42.33,2150000,42.33 1958-03-13,42.46,42.46,42.46,42.46,2830000,42.46 1958-03-12,42.41,42.41,42.41,42.41,2420000,42.41 1958-03-11,42.51,42.51,42.51,42.51,2640000,42.51 1958-03-10,42.21,42.21,42.21,42.21,1980000,42.21 1958-03-07,42.07,42.07,42.07,42.07,2130000,42.07 1958-03-06,42.00,42.00,42.00,42.00,2470000,42.00 1958-03-05,41.47,41.47,41.47,41.47,2020000,41.47 1958-03-04,41.35,41.35,41.35,41.35,2010000,41.35 1958-03-03,41.13,41.13,41.13,41.13,1810000,41.13 1958-02-28,40.84,40.84,40.84,40.84,1580000,40.84 1958-02-27,40.68,40.68,40.68,40.68,1670000,40.68 1958-02-26,40.92,40.92,40.92,40.92,1880000,40.92 1958-02-25,40.61,40.61,40.61,40.61,1920000,40.61 1958-02-24,40.65,40.65,40.65,40.65,1570000,40.65 1958-02-21,40.88,40.88,40.88,40.88,1700000,40.88 1958-02-20,40.91,40.91,40.91,40.91,2060000,40.91 1958-02-19,41.15,41.15,41.15,41.15,2070000,41.15 1958-02-18,41.17,41.17,41.17,41.17,1680000,41.17 1958-02-17,41.11,41.11,41.11,41.11,1700000,41.11 1958-02-14,41.33,41.33,41.33,41.33,2070000,41.33 1958-02-13,40.94,40.94,40.94,40.94,1880000,40.94 1958-02-12,40.93,40.93,40.93,40.93,2030000,40.93 1958-02-11,41.11,41.11,41.11,41.11,2110000,41.11 1958-02-10,41.48,41.48,41.48,41.48,1900000,41.48 1958-02-07,41.73,41.73,41.73,41.73,2220000,41.73 1958-02-06,42.10,42.10,42.10,42.10,2210000,42.10 1958-02-05,42.19,42.19,42.19,42.19,2480000,42.19 1958-02-04,42.46,42.46,42.46,42.46,2970000,42.46 1958-02-03,42.04,42.04,42.04,42.04,2490000,42.04 1958-01-31,41.70,41.70,41.70,41.70,2030000,41.70 1958-01-30,41.68,41.68,41.68,41.68,2150000,41.68 1958-01-29,41.88,41.88,41.88,41.88,2220000,41.88 1958-01-28,41.63,41.63,41.63,41.63,2030000,41.63 1958-01-27,41.59,41.59,41.59,41.59,2320000,41.59 1958-01-24,41.71,41.71,41.71,41.71,2830000,41.71 1958-01-23,41.36,41.36,41.36,41.36,1910000,41.36 1958-01-22,41.20,41.20,41.20,41.20,2390000,41.20 1958-01-21,41.30,41.30,41.30,41.30,2160000,41.30 1958-01-20,41.35,41.35,41.35,41.35,2310000,41.35 1958-01-17,41.10,41.10,41.10,41.10,2200000,41.10 1958-01-16,41.06,41.06,41.06,41.06,3950000,41.06 1958-01-15,40.99,40.99,40.99,40.99,2080000,40.99 1958-01-14,40.67,40.67,40.67,40.67,2010000,40.67 1958-01-13,40.49,40.49,40.49,40.49,1860000,40.49 1958-01-10,40.37,40.37,40.37,40.37,2010000,40.37 1958-01-09,40.75,40.75,40.75,40.75,2180000,40.75 1958-01-08,40.99,40.99,40.99,40.99,2230000,40.99 1958-01-07,41.00,41.00,41.00,41.00,2220000,41.00 1958-01-06,40.68,40.68,40.68,40.68,2500000,40.68 1958-01-03,40.87,40.87,40.87,40.87,2440000,40.87 1958-01-02,40.33,40.33,40.33,40.33,1800000,40.33 1957-12-31,39.99,39.99,39.99,39.99,5070000,39.99 1957-12-30,39.58,39.58,39.58,39.58,3750000,39.58 1957-12-27,39.78,39.78,39.78,39.78,2620000,39.78 1957-12-26,39.92,39.92,39.92,39.92,2280000,39.92 1957-12-24,39.52,39.52,39.52,39.52,2220000,39.52 1957-12-23,39.48,39.48,39.48,39.48,2790000,39.48 1957-12-20,39.48,39.48,39.48,39.48,2500000,39.48 1957-12-19,39.80,39.80,39.80,39.80,2740000,39.80 1957-12-18,39.38,39.38,39.38,39.38,2750000,39.38 1957-12-17,39.42,39.42,39.42,39.42,2820000,39.42 1957-12-16,40.12,40.12,40.12,40.12,2350000,40.12 1957-12-13,40.73,40.73,40.73,40.73,2310000,40.73 1957-12-12,40.55,40.55,40.55,40.55,2330000,40.55 1957-12-11,40.51,40.51,40.51,40.51,2240000,40.51 1957-12-10,40.56,40.56,40.56,40.56,2360000,40.56 1957-12-09,40.92,40.92,40.92,40.92,2230000,40.92 1957-12-06,41.31,41.31,41.31,41.31,2350000,41.31 1957-12-05,41.52,41.52,41.52,41.52,2020000,41.52 1957-12-04,41.54,41.54,41.54,41.54,2220000,41.54 1957-12-03,41.37,41.37,41.37,41.37,2060000,41.37 1957-12-02,41.36,41.36,41.36,41.36,2430000,41.36 1957-11-29,41.72,41.72,41.72,41.72,2740000,41.72 1957-11-27,41.25,41.25,41.25,41.25,3330000,41.25 1957-11-26,40.09,40.09,40.09,40.09,3650000,40.09 1957-11-25,41.18,41.18,41.18,41.18,2600000,41.18 1957-11-22,40.87,40.87,40.87,40.87,2850000,40.87 1957-11-21,40.48,40.48,40.48,40.48,2900000,40.48 1957-11-20,39.92,39.92,39.92,39.92,2400000,39.92 1957-11-19,39.81,39.81,39.81,39.81,2240000,39.81 1957-11-18,40.04,40.04,40.04,40.04,2110000,40.04 1957-11-15,40.37,40.37,40.37,40.37,3510000,40.37 1957-11-14,39.44,39.44,39.44,39.44,2450000,39.44 1957-11-13,39.55,39.55,39.55,39.55,2120000,39.55 1957-11-12,39.60,39.60,39.60,39.60,2050000,39.60 1957-11-11,40.18,40.18,40.18,40.18,1540000,40.18 1957-11-08,40.19,40.19,40.19,40.19,2140000,40.19 1957-11-07,40.67,40.67,40.67,40.67,2580000,40.67 1957-11-06,40.43,40.43,40.43,40.43,2550000,40.43 1957-11-04,40.37,40.37,40.37,40.37,2380000,40.37 1957-11-01,40.44,40.44,40.44,40.44,2060000,40.44 1957-10-31,41.06,41.06,41.06,41.06,2170000,41.06 1957-10-30,41.02,41.02,41.02,41.02,2060000,41.02 1957-10-29,40.69,40.69,40.69,40.69,1860000,40.69 1957-10-28,40.42,40.42,40.42,40.42,1800000,40.42 1957-10-25,40.59,40.59,40.59,40.59,2400000,40.59 1957-10-24,40.71,40.71,40.71,40.71,4030000,40.71 1957-10-23,40.73,40.73,40.73,40.73,4600000,40.73 1957-10-22,38.98,38.98,38.98,38.98,5090000,38.98 1957-10-21,39.15,39.15,39.15,39.15,4670000,39.15 1957-10-18,40.33,40.33,40.33,40.33,2670000,40.33 1957-10-17,40.65,40.65,40.65,40.65,3060000,40.65 1957-10-16,41.33,41.33,41.33,41.33,2050000,41.33 1957-10-15,41.67,41.67,41.67,41.67,2620000,41.67 1957-10-14,41.24,41.24,41.24,41.24,2770000,41.24 1957-10-11,40.94,40.94,40.94,40.94,4460000,40.94 1957-10-10,40.96,40.96,40.96,40.96,3300000,40.96 1957-10-09,41.99,41.99,41.99,41.99,2120000,41.99 1957-10-08,41.95,41.95,41.95,41.95,3190000,41.95 1957-10-07,42.22,42.22,42.22,42.22,2490000,42.22 1957-10-04,42.79,42.79,42.79,42.79,1520000,42.79 1957-10-03,43.14,43.14,43.14,43.14,1590000,43.14 1957-10-02,43.10,43.10,43.10,43.10,1760000,43.10 1957-10-01,42.76,42.76,42.76,42.76,1680000,42.76 1957-09-30,42.42,42.42,42.42,42.42,1520000,42.42 1957-09-27,42.55,42.55,42.55,42.55,1750000,42.55 1957-09-26,42.57,42.57,42.57,42.57,2130000,42.57 1957-09-25,42.98,42.98,42.98,42.98,2770000,42.98 1957-09-24,42.98,42.98,42.98,42.98,2840000,42.98 1957-09-23,42.69,42.69,42.69,42.69,3160000,42.69 1957-09-20,43.69,43.69,43.69,43.69,2340000,43.69 1957-09-19,44.40,44.40,44.40,44.40,1520000,44.40 1957-09-18,44.69,44.69,44.69,44.69,1540000,44.69 1957-09-17,44.64,44.64,44.64,44.64,1490000,44.64 1957-09-16,44.58,44.58,44.58,44.58,1290000,44.58 1957-09-13,44.80,44.80,44.80,44.80,1620000,44.80 1957-09-12,44.82,44.82,44.82,44.82,2010000,44.82 1957-09-11,44.26,44.26,44.26,44.26,2130000,44.26 1957-09-10,43.87,43.87,43.87,43.87,1870000,43.87 1957-09-09,44.28,44.28,44.28,44.28,1420000,44.28 1957-09-06,44.68,44.68,44.68,44.68,1320000,44.68 1957-09-05,44.82,44.82,44.82,44.82,1420000,44.82 1957-09-04,45.05,45.05,45.05,45.05,1260000,45.05 1957-09-03,45.44,45.44,45.44,45.44,1490000,45.44 1957-08-30,45.22,45.22,45.22,45.22,1600000,45.22 1957-08-29,44.46,44.46,44.46,44.46,1630000,44.46 1957-08-28,44.64,44.64,44.64,44.64,1840000,44.64 1957-08-27,44.61,44.61,44.61,44.61,2250000,44.61 1957-08-26,43.89,43.89,43.89,43.89,2680000,43.89 1957-08-23,44.51,44.51,44.51,44.51,1960000,44.51 1957-08-22,45.16,45.16,45.16,45.16,1500000,45.16 1957-08-21,45.49,45.49,45.49,45.49,1720000,45.49 1957-08-20,45.29,45.29,45.29,45.29,2700000,45.29 1957-08-19,44.91,44.91,44.91,44.91,2040000,44.91 1957-08-16,45.83,45.83,45.83,45.83,1470000,45.83 1957-08-15,45.75,45.75,45.75,45.75,2040000,45.75 1957-08-14,45.73,45.73,45.73,45.73,2040000,45.73 1957-08-13,46.30,46.30,46.30,46.30,1580000,46.30 1957-08-12,46.33,46.33,46.33,46.33,1650000,46.33 1957-08-09,46.92,46.92,46.92,46.92,1570000,46.92 1957-08-08,46.90,46.90,46.90,46.90,1690000,46.90 1957-08-07,47.03,47.03,47.03,47.03,2460000,47.03 1957-08-06,46.67,46.67,46.67,46.67,1910000,46.67 1957-08-05,47.26,47.26,47.26,47.26,1790000,47.26 1957-08-02,47.68,47.68,47.68,47.68,1610000,47.68 1957-08-01,47.79,47.79,47.79,47.79,1660000,47.79 1957-07-31,47.91,47.91,47.91,47.91,1830000,47.91 1957-07-30,47.92,47.92,47.92,47.92,1780000,47.92 1957-07-29,47.92,47.92,47.92,47.92,1990000,47.92 1957-07-26,48.45,48.45,48.45,48.45,1710000,48.45 1957-07-25,48.61,48.61,48.61,48.61,1800000,48.61 1957-07-24,48.61,48.61,48.61,48.61,1730000,48.61 1957-07-23,48.56,48.56,48.56,48.56,1840000,48.56 1957-07-22,48.47,48.47,48.47,48.47,1950000,48.47 1957-07-19,48.58,48.58,48.58,48.58,1930000,48.58 1957-07-18,48.53,48.53,48.53,48.53,2130000,48.53 1957-07-17,48.58,48.58,48.58,48.58,2060000,48.58 1957-07-16,48.88,48.88,48.88,48.88,2510000,48.88 1957-07-15,49.13,49.13,49.13,49.13,2480000,49.13 1957-07-12,49.08,49.08,49.08,49.08,2240000,49.08 1957-07-11,48.86,48.86,48.86,48.86,2830000,48.86 1957-07-10,49.00,49.00,49.00,49.00,2880000,49.00 1957-07-09,48.90,48.90,48.90,48.90,2450000,48.90 1957-07-08,48.90,48.90,48.90,48.90,2840000,48.90 1957-07-05,48.69,48.69,48.69,48.69,2240000,48.69 1957-07-03,48.46,48.46,48.46,48.46,2720000,48.46 1957-07-02,47.90,47.90,47.90,47.90,2450000,47.90 1957-07-01,47.43,47.43,47.43,47.43,1840000,47.43 1957-06-28,47.37,47.37,47.37,47.37,1770000,47.37 1957-06-27,47.26,47.26,47.26,47.26,1800000,47.26 1957-06-26,47.09,47.09,47.09,47.09,1870000,47.09 1957-06-25,47.15,47.15,47.15,47.15,2000000,47.15 1957-06-24,46.78,46.78,46.78,46.78,2040000,46.78 1957-06-21,47.15,47.15,47.15,47.15,1970000,47.15 1957-06-20,47.43,47.43,47.43,47.43,2050000,47.43 1957-06-19,47.72,47.72,47.72,47.72,2220000,47.72 1957-06-18,48.04,48.04,48.04,48.04,2440000,48.04 1957-06-17,48.24,48.24,48.24,48.24,2220000,48.24 1957-06-14,48.15,48.15,48.15,48.15,2090000,48.15 1957-06-13,48.14,48.14,48.14,48.14,2630000,48.14 1957-06-12,48.05,48.05,48.05,48.05,2600000,48.05 1957-06-11,47.94,47.94,47.94,47.94,2850000,47.94 1957-06-10,47.90,47.90,47.90,47.90,2050000,47.90 1957-06-07,47.85,47.85,47.85,47.85,2380000,47.85 1957-06-06,47.80,47.80,47.80,47.80,2300000,47.80 1957-06-05,47.27,47.27,47.27,47.27,1940000,47.27 1957-06-04,47.28,47.28,47.28,47.28,2200000,47.28 1957-06-03,47.37,47.37,47.37,47.37,2050000,47.37 1957-05-31,47.43,47.43,47.43,47.43,2050000,47.43 1957-05-29,47.11,47.11,47.11,47.11,2270000,47.11 1957-05-28,46.69,46.69,46.69,46.69,2070000,46.69 1957-05-27,46.78,46.78,46.78,46.78,2290000,46.78 1957-05-24,47.21,47.21,47.21,47.21,2340000,47.21 1957-05-23,47.15,47.15,47.15,47.15,2110000,47.15 1957-05-22,47.14,47.14,47.14,47.14,2060000,47.14 1957-05-21,47.33,47.33,47.33,47.33,2370000,47.33 1957-05-20,47.35,47.35,47.35,47.35,2300000,47.35 1957-05-17,47.15,47.15,47.15,47.15,2510000,47.15 1957-05-16,47.02,47.02,47.02,47.02,2690000,47.02 1957-05-15,46.83,46.83,46.83,46.83,2590000,46.83 1957-05-14,46.67,46.67,46.67,46.67,2580000,46.67 1957-05-13,46.88,46.88,46.88,46.88,2720000,46.88 1957-05-10,46.59,46.59,46.59,46.59,2430000,46.59 1957-05-09,46.36,46.36,46.36,46.36,2520000,46.36 1957-05-08,46.31,46.31,46.31,46.31,2590000,46.31 1957-05-07,46.13,46.13,46.13,46.13,2300000,46.13 1957-05-06,46.27,46.27,46.27,46.27,2210000,46.27 1957-05-03,46.34,46.34,46.34,46.34,2390000,46.34 1957-05-02,46.39,46.39,46.39,46.39,2860000,46.39 1957-05-01,46.02,46.02,46.02,46.02,2310000,46.02 1957-04-30,45.74,45.74,45.74,45.74,2200000,45.74 1957-04-29,45.73,45.73,45.73,45.73,2290000,45.73 1957-04-26,45.50,45.50,45.50,45.50,2380000,45.50 1957-04-25,45.56,45.56,45.56,45.56,2640000,45.56 1957-04-24,45.72,45.72,45.72,45.72,2990000,45.72 1957-04-23,45.65,45.65,45.65,45.65,2840000,45.65 1957-04-22,45.48,45.48,45.48,45.48,2560000,45.48 1957-04-18,45.41,45.41,45.41,45.41,2480000,45.41 1957-04-17,45.08,45.08,45.08,45.08,2290000,45.08 1957-04-16,45.02,45.02,45.02,45.02,1890000,45.02 1957-04-15,44.95,44.95,44.95,44.95,2010000,44.95 1957-04-12,44.98,44.98,44.98,44.98,2370000,44.98 1957-04-11,44.98,44.98,44.98,44.98,2350000,44.98 1957-04-10,44.98,44.98,44.98,44.98,2920000,44.98 1957-04-09,44.79,44.79,44.79,44.79,2400000,44.79 1957-04-08,44.39,44.39,44.39,44.39,1950000,44.39 1957-04-05,44.49,44.49,44.49,44.49,1830000,44.49 1957-04-04,44.44,44.44,44.44,44.44,1820000,44.44 1957-04-03,44.54,44.54,44.54,44.54,2160000,44.54 1957-04-02,44.42,44.42,44.42,44.42,2300000,44.42 1957-04-01,44.14,44.14,44.14,44.14,1620000,44.14 1957-03-29,44.11,44.11,44.11,44.11,1650000,44.11 1957-03-28,44.18,44.18,44.18,44.18,1930000,44.18 1957-03-27,44.09,44.09,44.09,44.09,1710000,44.09 1957-03-26,43.91,43.91,43.91,43.91,1660000,43.91 1957-03-25,43.88,43.88,43.88,43.88,1590000,43.88 1957-03-22,44.06,44.06,44.06,44.06,1610000,44.06 1957-03-21,44.11,44.11,44.11,44.11,1630000,44.11 1957-03-20,44.10,44.10,44.10,44.10,1830000,44.10 1957-03-19,44.04,44.04,44.04,44.04,1540000,44.04 1957-03-18,43.85,43.85,43.85,43.85,1450000,43.85 1957-03-15,44.05,44.05,44.05,44.05,1600000,44.05 1957-03-14,44.07,44.07,44.07,44.07,1580000,44.07 1957-03-13,44.04,44.04,44.04,44.04,1840000,44.04 1957-03-12,43.75,43.75,43.75,43.75,1600000,43.75 1957-03-11,43.78,43.78,43.78,43.78,1650000,43.78 1957-03-08,44.07,44.07,44.07,44.07,1630000,44.07 1957-03-07,44.21,44.21,44.21,44.21,1830000,44.21 1957-03-06,44.23,44.23,44.23,44.23,1840000,44.23 1957-03-05,44.22,44.22,44.22,44.22,1860000,44.22 1957-03-04,44.06,44.06,44.06,44.06,1890000,44.06 1957-03-01,43.74,43.74,43.74,43.74,1700000,43.74 1957-02-28,43.26,43.26,43.26,43.26,1620000,43.26 1957-02-27,43.41,43.41,43.41,43.41,1620000,43.41 1957-02-26,43.45,43.45,43.45,43.45,1580000,43.45 1957-02-25,43.38,43.38,43.38,43.38,1710000,43.38 1957-02-21,43.48,43.48,43.48,43.48,1680000,43.48 1957-02-20,43.63,43.63,43.63,43.63,1790000,43.63 1957-02-19,43.49,43.49,43.49,43.49,1670000,43.49 1957-02-18,43.46,43.46,43.46,43.46,1800000,43.46 1957-02-15,43.51,43.51,43.51,43.51,2060000,43.51 1957-02-14,42.99,42.99,42.99,42.99,2220000,42.99 1957-02-13,43.04,43.04,43.04,43.04,2380000,43.04 1957-02-12,42.39,42.39,42.39,42.39,2550000,42.39 1957-02-11,42.57,42.57,42.57,42.57,2740000,42.57 1957-02-08,43.32,43.32,43.32,43.32,2120000,43.32 1957-02-07,43.62,43.62,43.62,43.62,1840000,43.62 1957-02-06,43.82,43.82,43.82,43.82,2110000,43.82 1957-02-05,43.89,43.89,43.89,43.89,2610000,43.89 1957-02-04,44.53,44.53,44.53,44.53,1750000,44.53 1957-02-01,44.62,44.62,44.62,44.62,1680000,44.62 1957-01-31,44.72,44.72,44.72,44.72,1920000,44.72 1957-01-30,44.91,44.91,44.91,44.91,1950000,44.91 1957-01-29,44.71,44.71,44.71,44.71,1800000,44.71 1957-01-28,44.49,44.49,44.49,44.49,1700000,44.49 1957-01-25,44.82,44.82,44.82,44.82,2010000,44.82 1957-01-24,45.03,45.03,45.03,45.03,1910000,45.03 1957-01-23,44.87,44.87,44.87,44.87,1920000,44.87 1957-01-22,44.53,44.53,44.53,44.53,1920000,44.53 1957-01-21,44.40,44.40,44.40,44.40,2740000,44.40 1957-01-18,44.64,44.64,44.64,44.64,2400000,44.64 1957-01-17,45.22,45.22,45.22,45.22,2140000,45.22 1957-01-16,45.23,45.23,45.23,45.23,2210000,45.23 1957-01-15,45.18,45.18,45.18,45.18,2370000,45.18 1957-01-14,45.86,45.86,45.86,45.86,2350000,45.86 1957-01-11,46.18,46.18,46.18,46.18,2340000,46.18 1957-01-10,46.27,46.27,46.27,46.27,2470000,46.27 1957-01-09,46.16,46.16,46.16,46.16,2330000,46.16 1957-01-08,46.25,46.25,46.25,46.25,2230000,46.25 1957-01-07,46.42,46.42,46.42,46.42,2500000,46.42 1957-01-04,46.66,46.66,46.66,46.66,2710000,46.66 1957-01-03,46.60,46.60,46.60,46.60,2260000,46.60 1957-01-02,46.20,46.20,46.20,46.20,1960000,46.20 1956-12-31,46.67,46.67,46.67,46.67,3680000,46.67 1956-12-28,46.56,46.56,46.56,46.56,2790000,46.56 1956-12-27,46.35,46.35,46.35,46.35,2420000,46.35 1956-12-26,46.39,46.39,46.39,46.39,2440000,46.39 1956-12-21,46.37,46.37,46.37,46.37,2380000,46.37 1956-12-20,46.07,46.07,46.07,46.07,2060000,46.07 1956-12-19,46.43,46.43,46.43,46.43,1900000,46.43 1956-12-18,46.54,46.54,46.54,46.54,2370000,46.54 1956-12-17,46.54,46.54,46.54,46.54,2500000,46.54 1956-12-14,46.54,46.54,46.54,46.54,2450000,46.54 1956-12-13,46.50,46.50,46.50,46.50,2370000,46.50 1956-12-12,46.13,46.13,46.13,46.13,2180000,46.13 1956-12-11,46.48,46.48,46.48,46.48,2210000,46.48 1956-12-10,46.80,46.80,46.80,46.80,2600000,46.80 1956-12-07,47.04,47.04,47.04,47.04,2400000,47.04 1956-12-06,46.81,46.81,46.81,46.81,2470000,46.81 1956-12-05,46.39,46.39,46.39,46.39,2360000,46.39 1956-12-04,45.84,45.84,45.84,45.84,2180000,45.84 1956-12-03,45.98,45.98,45.98,45.98,2570000,45.98 1956-11-30,45.08,45.08,45.08,45.08,2300000,45.08 1956-11-29,44.38,44.38,44.38,44.38,2440000,44.38 1956-11-28,44.43,44.43,44.43,44.43,2190000,44.43 1956-11-27,44.91,44.91,44.91,44.91,2130000,44.91 1956-11-26,44.87,44.87,44.87,44.87,2230000,44.87 1956-11-23,45.14,45.14,45.14,45.14,1880000,45.14 1956-11-21,44.67,44.67,44.67,44.67,2310000,44.67 1956-11-20,44.89,44.89,44.89,44.89,2240000,44.89 1956-11-19,45.29,45.29,45.29,45.29,2560000,45.29 1956-11-16,45.74,45.74,45.74,45.74,1820000,45.74 1956-11-15,45.72,45.72,45.72,45.72,2210000,45.72 1956-11-14,46.01,46.01,46.01,46.01,2290000,46.01 1956-11-13,46.27,46.27,46.27,46.27,2140000,46.27 1956-11-12,46.49,46.49,46.49,46.49,1600000,46.49 1956-11-09,46.34,46.34,46.34,46.34,1690000,46.34 1956-11-08,46.73,46.73,46.73,46.73,1970000,46.73 1956-11-07,47.11,47.11,47.11,47.11,2650000,47.11 1956-11-05,47.60,47.60,47.60,47.60,2830000,47.60 1956-11-02,46.98,46.98,46.98,46.98,2180000,46.98 1956-11-01,46.52,46.52,46.52,46.52,1890000,46.52 1956-10-31,45.58,45.58,45.58,45.58,2280000,45.58 1956-10-30,46.37,46.37,46.37,46.37,1830000,46.37 1956-10-29,46.40,46.40,46.40,46.40,2420000,46.40 1956-10-26,46.27,46.27,46.27,46.27,1800000,46.27 1956-10-25,45.85,45.85,45.85,45.85,1580000,45.85 1956-10-24,45.93,45.93,45.93,45.93,1640000,45.93 1956-10-23,46.12,46.12,46.12,46.12,1390000,46.12 1956-10-22,46.23,46.23,46.23,46.23,1430000,46.23 1956-10-19,46.24,46.24,46.24,46.24,1720000,46.24 1956-10-18,46.34,46.34,46.34,46.34,1640000,46.34 1956-10-17,46.26,46.26,46.26,46.26,1640000,46.26 1956-10-16,46.62,46.62,46.62,46.62,1580000,46.62 1956-10-15,46.86,46.86,46.86,46.86,1610000,46.86 1956-10-12,47.00,47.00,47.00,47.00,1330000,47.00 1956-10-11,46.81,46.81,46.81,46.81,1760000,46.81 1956-10-10,46.84,46.84,46.84,46.84,1620000,46.84 1956-10-09,46.20,46.20,46.20,46.20,1220000,46.20 1956-10-08,46.43,46.43,46.43,46.43,1450000,46.43 1956-10-05,46.45,46.45,46.45,46.45,1580000,46.45 1956-10-04,46.29,46.29,46.29,46.29,1600000,46.29 1956-10-03,46.28,46.28,46.28,46.28,2180000,46.28 1956-10-02,45.52,45.52,45.52,45.52,2400000,45.52 1956-10-01,44.70,44.70,44.70,44.70,2600000,44.70 1956-09-28,45.35,45.35,45.35,45.35,1720000,45.35 1956-09-27,45.60,45.60,45.60,45.60,1770000,45.60 1956-09-26,45.82,45.82,45.82,45.82,2370000,45.82 1956-09-25,45.75,45.75,45.75,45.75,2100000,45.75 1956-09-24,46.40,46.40,46.40,46.40,1840000,46.40 1956-09-21,46.58,46.58,46.58,46.58,2110000,46.58 1956-09-20,46.21,46.21,46.21,46.21,2150000,46.21 1956-09-19,46.24,46.24,46.24,46.24,2040000,46.24 1956-09-18,46.79,46.79,46.79,46.79,2200000,46.79 1956-09-17,47.10,47.10,47.10,47.10,1940000,47.10 1956-09-14,47.21,47.21,47.21,47.21,2110000,47.21 1956-09-13,46.09,46.09,46.09,46.09,2000000,46.09 1956-09-12,47.05,47.05,47.05,47.05,1930000,47.05 1956-09-11,47.38,47.38,47.38,47.38,1920000,47.38 1956-09-10,47.56,47.56,47.56,47.56,1860000,47.56 1956-09-07,47.81,47.81,47.81,47.81,1690000,47.81 1956-09-06,48.10,48.10,48.10,48.10,1550000,48.10 1956-09-05,48.02,48.02,48.02,48.02,2130000,48.02 1956-09-04,47.89,47.89,47.89,47.89,1790000,47.89 1956-08-31,47.51,47.51,47.51,47.51,1620000,47.51 1956-08-30,46.94,46.94,46.94,46.94,2050000,46.94 1956-08-29,47.36,47.36,47.36,47.36,1530000,47.36 1956-08-28,47.57,47.57,47.57,47.57,1400000,47.57 1956-08-27,47.66,47.66,47.66,47.66,1420000,47.66 1956-08-24,47.95,47.95,47.95,47.95,1530000,47.95 1956-08-23,48.00,48.00,48.00,48.00,1590000,48.00 1956-08-22,47.42,47.42,47.42,47.42,1570000,47.42 1956-08-21,47.89,47.89,47.89,47.89,2440000,47.89 1956-08-20,48.25,48.25,48.25,48.25,1770000,48.25 1956-08-17,48.82,48.82,48.82,48.82,1720000,48.82 1956-08-16,48.88,48.88,48.88,48.88,1790000,48.88 1956-08-15,48.99,48.99,48.99,48.99,2000000,48.99 1956-08-14,48.00,48.00,48.00,48.00,1790000,48.00 1956-08-13,48.58,48.58,48.58,48.58,1730000,48.58 1956-08-10,49.09,49.09,49.09,49.09,2040000,49.09 1956-08-09,49.32,49.32,49.32,49.32,2550000,49.32 1956-08-08,49.36,49.36,49.36,49.36,2480000,49.36 1956-08-07,49.16,49.16,49.16,49.16,2180000,49.16 1956-08-06,48.96,48.96,48.96,48.96,2280000,48.96 1956-08-03,49.64,49.64,49.64,49.64,2210000,49.64 1956-08-02,49.64,49.64,49.64,49.64,2530000,49.64 1956-08-01,49.62,49.62,49.62,49.62,2230000,49.62 1956-07-31,49.39,49.39,49.39,49.39,2520000,49.39 1956-07-30,49.00,49.00,49.00,49.00,2100000,49.00 1956-07-27,49.08,49.08,49.08,49.08,2240000,49.08 1956-07-26,49.48,49.48,49.48,49.48,2060000,49.48 1956-07-25,49.44,49.44,49.44,49.44,2220000,49.44 1956-07-24,49.33,49.33,49.33,49.33,2040000,49.33 1956-07-23,49.33,49.33,49.33,49.33,1970000,49.33 1956-07-20,49.35,49.35,49.35,49.35,2020000,49.35 1956-07-19,49.32,49.32,49.32,49.32,1950000,49.32 1956-07-18,49.30,49.30,49.30,49.30,2530000,49.30 1956-07-17,49.31,49.31,49.31,49.31,2520000,49.31 1956-07-16,49.14,49.14,49.14,49.14,2260000,49.14 1956-07-13,48.72,48.72,48.72,48.72,2020000,48.72 1956-07-12,48.58,48.58,48.58,48.58,2180000,48.58 1956-07-11,48.69,48.69,48.69,48.69,2520000,48.69 1956-07-10,48.54,48.54,48.54,48.54,2450000,48.54 1956-07-09,48.25,48.25,48.25,48.25,2180000,48.25 1956-07-06,48.04,48.04,48.04,48.04,2180000,48.04 1956-07-05,47.80,47.80,47.80,47.80,2240000,47.80 1956-07-03,47.32,47.32,47.32,47.32,1840000,47.32 1956-07-02,46.93,46.93,46.93,46.93,1610000,46.93 1956-06-29,46.97,46.97,46.97,46.97,1780000,46.97 1956-06-28,47.13,47.13,47.13,47.13,1900000,47.13 1956-06-27,47.07,47.07,47.07,47.07,2090000,47.07 1956-06-26,46.72,46.72,46.72,46.72,1730000,46.72 1956-06-25,46.41,46.41,46.41,46.41,1500000,46.41 1956-06-22,46.59,46.59,46.59,46.59,1630000,46.59 1956-06-21,46.73,46.73,46.73,46.73,1820000,46.73 1956-06-20,46.41,46.41,46.41,46.41,1670000,46.41 1956-06-19,46.22,46.22,46.22,46.22,1430000,46.22 1956-06-18,46.17,46.17,46.17,46.17,1440000,46.17 1956-06-15,46.37,46.37,46.37,46.37,1550000,46.37 1956-06-14,46.31,46.31,46.31,46.31,1670000,46.31 1956-06-13,46.42,46.42,46.42,46.42,1760000,46.42 1956-06-12,46.36,46.36,46.36,46.36,1900000,46.36 1956-06-11,45.71,45.71,45.71,45.71,2000000,45.71 1956-06-08,45.14,45.14,45.14,45.14,3630000,45.14 1956-06-07,45.99,45.99,45.99,45.99,1630000,45.99 1956-06-06,45.63,45.63,45.63,45.63,1460000,45.63 1956-06-05,45.86,45.86,45.86,45.86,1650000,45.86 1956-06-04,45.85,45.85,45.85,45.85,1500000,45.85 1956-06-01,45.58,45.58,45.58,45.58,1440000,45.58 1956-05-31,45.20,45.20,45.20,45.20,2020000,45.20 1956-05-29,45.11,45.11,45.11,45.11,2430000,45.11 1956-05-28,44.10,44.10,44.10,44.10,2780000,44.10 1956-05-25,44.62,44.62,44.62,44.62,2570000,44.62 1956-05-24,44.60,44.60,44.60,44.60,2600000,44.60 1956-05-23,45.02,45.02,45.02,45.02,2140000,45.02 1956-05-22,45.26,45.26,45.26,45.26,2290000,45.26 1956-05-21,45.99,45.99,45.99,45.99,1940000,45.99 1956-05-18,46.39,46.39,46.39,46.39,2020000,46.39 1956-05-17,46.61,46.61,46.61,46.61,1970000,46.61 1956-05-16,46.05,46.05,46.05,46.05,2080000,46.05 1956-05-15,46.37,46.37,46.37,46.37,2650000,46.37 1956-05-14,46.86,46.86,46.86,46.86,2440000,46.86 1956-05-11,47.12,47.12,47.12,47.12,2450000,47.12 1956-05-10,47.16,47.16,47.16,47.16,2850000,47.16 1956-05-09,47.94,47.94,47.94,47.94,2550000,47.94 1956-05-08,48.02,48.02,48.02,48.02,2440000,48.02 1956-05-07,48.22,48.22,48.22,48.22,2550000,48.22 1956-05-04,48.51,48.51,48.51,48.51,2860000,48.51 1956-05-03,48.34,48.34,48.34,48.34,2640000,48.34 1956-05-02,48.17,48.17,48.17,48.17,2440000,48.17 1956-05-01,48.16,48.16,48.16,48.16,2500000,48.16 1956-04-30,48.38,48.38,48.38,48.38,2730000,48.38 1956-04-27,47.99,47.99,47.99,47.99,2760000,47.99 1956-04-26,47.49,47.49,47.49,47.49,2630000,47.49 1956-04-25,47.09,47.09,47.09,47.09,2270000,47.09 1956-04-24,47.26,47.26,47.26,47.26,2500000,47.26 1956-04-23,47.65,47.65,47.65,47.65,2440000,47.65 1956-04-20,47.76,47.76,47.76,47.76,2320000,47.76 1956-04-19,47.57,47.57,47.57,47.57,2210000,47.57 1956-04-18,47.74,47.74,47.74,47.74,2470000,47.74 1956-04-17,47.93,47.93,47.93,47.93,2330000,47.93 1956-04-16,47.96,47.96,47.96,47.96,2310000,47.96 1956-04-13,47.95,47.95,47.95,47.95,2450000,47.95 1956-04-12,48.02,48.02,48.02,48.02,2700000,48.02 1956-04-11,48.31,48.31,48.31,48.31,2440000,48.31 1956-04-10,47.93,47.93,47.93,47.93,2590000,47.93 1956-04-09,48.61,48.61,48.61,48.61,2760000,48.61 1956-04-06,48.85,48.85,48.85,48.85,2600000,48.85 1956-04-05,48.57,48.57,48.57,48.57,2950000,48.57 1956-04-04,48.80,48.80,48.80,48.80,2760000,48.80 1956-04-03,48.53,48.53,48.53,48.53,2760000,48.53 1956-04-02,48.70,48.70,48.70,48.70,3120000,48.70 1956-03-29,48.48,48.48,48.48,48.48,3480000,48.48 1956-03-28,48.51,48.51,48.51,48.51,2610000,48.51 1956-03-27,48.25,48.25,48.25,48.25,2540000,48.25 1956-03-26,48.62,48.62,48.62,48.62,2720000,48.62 1956-03-23,48.83,48.83,48.83,48.83,2980000,48.83 1956-03-22,48.72,48.72,48.72,48.72,2650000,48.72 1956-03-21,48.23,48.23,48.23,48.23,2930000,48.23 1956-03-20,48.87,48.87,48.87,48.87,2960000,48.87 1956-03-19,48.59,48.59,48.59,48.59,2570000,48.59 1956-03-16,48.14,48.14,48.14,48.14,3120000,48.14 1956-03-15,47.99,47.99,47.99,47.99,3270000,47.99 1956-03-14,47.53,47.53,47.53,47.53,3140000,47.53 1956-03-13,47.06,47.06,47.06,47.06,2790000,47.06 1956-03-12,47.13,47.13,47.13,47.13,3110000,47.13 1956-03-09,46.70,46.70,46.70,46.70,3430000,46.70 1956-03-08,46.12,46.12,46.12,46.12,2500000,46.12 1956-03-07,46.01,46.01,46.01,46.01,2380000,46.01 1956-03-06,46.04,46.04,46.04,46.04,2770000,46.04 1956-03-05,46.06,46.06,46.06,46.06,3090000,46.06 1956-03-02,45.81,45.81,45.81,45.81,2860000,45.81 1956-03-01,45.54,45.54,45.54,45.54,2410000,45.54 1956-02-29,45.34,45.34,45.34,45.34,3900000,45.34 1956-02-28,45.43,45.43,45.43,45.43,2540000,45.43 1956-02-27,45.27,45.27,45.27,45.27,2440000,45.27 1956-02-24,45.32,45.32,45.32,45.32,2890000,45.32 1956-02-23,44.95,44.95,44.95,44.95,2900000,44.95 1956-02-21,44.56,44.56,44.56,44.56,2240000,44.56 1956-02-20,44.45,44.45,44.45,44.45,2530000,44.45 1956-02-17,44.52,44.52,44.52,44.52,2840000,44.52 1956-02-16,43.82,43.82,43.82,43.82,1750000,43.82 1956-02-15,44.04,44.04,44.04,44.04,3000000,44.04 1956-02-14,43.42,43.42,43.42,43.42,1590000,43.42 1956-02-13,43.58,43.58,43.58,43.58,1420000,43.58 1956-02-10,43.64,43.64,43.64,43.64,1770000,43.64 1956-02-09,43.66,43.66,43.66,43.66,2080000,43.66 1956-02-08,44.16,44.16,44.16,44.16,2170000,44.16 1956-02-07,44.60,44.60,44.60,44.60,2060000,44.60 1956-02-06,44.81,44.81,44.81,44.81,2230000,44.81 1956-02-03,44.78,44.78,44.78,44.78,2110000,44.78 1956-02-02,44.22,44.22,44.22,44.22,1900000,44.22 1956-02-01,44.03,44.03,44.03,44.03,2010000,44.03 1956-01-31,43.82,43.82,43.82,43.82,1900000,43.82 1956-01-30,43.50,43.50,43.50,43.50,1830000,43.50 1956-01-27,43.35,43.35,43.35,43.35,1950000,43.35 1956-01-26,43.46,43.46,43.46,43.46,1840000,43.46 1956-01-25,43.72,43.72,43.72,43.72,1950000,43.72 1956-01-24,43.65,43.65,43.65,43.65,2160000,43.65 1956-01-23,43.11,43.11,43.11,43.11,2720000,43.11 1956-01-20,43.22,43.22,43.22,43.22,2430000,43.22 1956-01-19,43.72,43.72,43.72,43.72,2500000,43.72 1956-01-18,44.17,44.17,44.17,44.17,2110000,44.17 1956-01-17,44.47,44.47,44.47,44.47,2050000,44.47 1956-01-16,44.14,44.14,44.14,44.14,2260000,44.14 1956-01-13,44.67,44.67,44.67,44.67,2120000,44.67 1956-01-12,44.75,44.75,44.75,44.75,2330000,44.75 1956-01-11,44.38,44.38,44.38,44.38,2310000,44.38 1956-01-10,44.16,44.16,44.16,44.16,2640000,44.16 1956-01-09,44.51,44.51,44.51,44.51,2700000,44.51 1956-01-06,45.14,45.14,45.14,45.14,2570000,45.14 1956-01-05,44.95,44.95,44.95,44.95,2110000,44.95 1956-01-04,45.00,45.00,45.00,45.00,2290000,45.00 1956-01-03,45.16,45.16,45.16,45.16,2390000,45.16 1955-12-30,45.48,45.48,45.48,45.48,2820000,45.48 1955-12-29,45.15,45.15,45.15,45.15,2190000,45.15 1955-12-28,45.05,45.05,45.05,45.05,1990000,45.05 1955-12-27,45.22,45.22,45.22,45.22,2010000,45.22 1955-12-23,45.50,45.50,45.50,45.50,2090000,45.50 1955-12-22,45.41,45.41,45.41,45.41,2650000,45.41 1955-12-21,45.84,45.84,45.84,45.84,2540000,45.84 1955-12-20,44.95,44.95,44.95,44.95,2280000,44.95 1955-12-19,45.02,45.02,45.02,45.02,2380000,45.02 1955-12-16,45.13,45.13,45.13,45.13,2310000,45.13 1955-12-15,45.06,45.06,45.06,45.06,2260000,45.06 1955-12-14,45.07,45.07,45.07,45.07,2670000,45.07 1955-12-13,45.45,45.45,45.45,45.45,2430000,45.45 1955-12-12,45.42,45.42,45.42,45.42,2510000,45.42 1955-12-09,45.89,45.89,45.89,45.89,2660000,45.89 1955-12-08,45.82,45.82,45.82,45.82,2970000,45.82 1955-12-07,45.55,45.55,45.55,45.55,2480000,45.55 1955-12-06,45.70,45.70,45.70,45.70,2540000,45.70 1955-12-05,45.70,45.70,45.70,45.70,2440000,45.70 1955-12-02,45.44,45.44,45.44,45.44,2400000,45.44 1955-12-01,45.35,45.35,45.35,45.35,2370000,45.35 1955-11-30,45.51,45.51,45.51,45.51,2900000,45.51 1955-11-29,45.56,45.56,45.56,45.56,2370000,45.56 1955-11-28,45.38,45.38,45.38,45.38,2460000,45.38 1955-11-25,45.68,45.68,45.68,45.68,2190000,45.68 1955-11-23,45.72,45.72,45.72,45.72,2550000,45.72 1955-11-22,45.66,45.66,45.66,45.66,2270000,45.66 1955-11-21,45.22,45.22,45.22,45.22,1960000,45.22 1955-11-18,45.54,45.54,45.54,45.54,2320000,45.54 1955-11-17,45.59,45.59,45.59,45.59,2310000,45.59 1955-11-16,45.91,45.91,45.91,45.91,2460000,45.91 1955-11-15,46.21,46.21,46.21,46.21,2560000,46.21 1955-11-14,46.41,46.41,46.41,46.41,2760000,46.41 1955-11-11,45.24,45.24,45.24,45.24,2000000,45.24 1955-11-10,44.72,44.72,44.72,44.72,2550000,44.72 1955-11-09,44.61,44.61,44.61,44.61,2580000,44.61 1955-11-07,44.15,44.15,44.15,44.15,2230000,44.15 1955-11-04,43.96,43.96,43.96,43.96,2430000,43.96 1955-11-03,43.24,43.24,43.24,43.24,2260000,43.24 1955-11-02,42.35,42.35,42.35,42.35,1610000,42.35 1955-11-01,42.28,42.28,42.28,42.28,1590000,42.28 1955-10-31,42.34,42.34,42.34,42.34,1800000,42.34 1955-10-28,42.37,42.37,42.37,42.37,1720000,42.37 1955-10-27,42.34,42.34,42.34,42.34,1830000,42.34 1955-10-26,42.29,42.29,42.29,42.29,1660000,42.29 1955-10-25,42.63,42.63,42.63,42.63,1950000,42.63 1955-10-24,42.91,42.91,42.91,42.91,1820000,42.91 1955-10-21,42.59,42.59,42.59,42.59,1710000,42.59 1955-10-20,42.59,42.59,42.59,42.59,2160000,42.59 1955-10-19,42.07,42.07,42.07,42.07,1760000,42.07 1955-10-18,41.65,41.65,41.65,41.65,1550000,41.65 1955-10-17,41.35,41.35,41.35,41.35,1480000,41.35 1955-10-14,41.22,41.22,41.22,41.22,1640000,41.22 1955-10-13,41.39,41.39,41.39,41.39,1980000,41.39 1955-10-12,41.52,41.52,41.52,41.52,1900000,41.52 1955-10-11,40.80,40.80,40.80,40.80,3590000,40.80 1955-10-10,41.15,41.15,41.15,41.15,3100000,41.15 1955-10-07,42.38,42.38,42.38,42.38,2150000,42.38 1955-10-06,42.70,42.70,42.70,42.70,1690000,42.70 1955-10-05,42.99,42.99,42.99,42.99,1920000,42.99 1955-10-04,42.82,42.82,42.82,42.82,2020000,42.82 1955-10-03,42.49,42.49,42.49,42.49,2720000,42.49 1955-09-30,43.67,43.67,43.67,43.67,2140000,43.67 1955-09-29,44.03,44.03,44.03,44.03,2560000,44.03 1955-09-28,44.31,44.31,44.31,44.31,3780000,44.31 1955-09-27,43.58,43.58,43.58,43.58,5500000,43.58 1955-09-26,42.61,42.61,42.61,42.61,7720000,42.61 1955-09-23,45.63,45.63,45.63,45.63,2540000,45.63 1955-09-22,45.39,45.39,45.39,45.39,2550000,45.39 1955-09-21,45.39,45.39,45.39,45.39,2460000,45.39 1955-09-20,45.13,45.13,45.13,45.13,2090000,45.13 1955-09-19,45.16,45.16,45.16,45.16,2390000,45.16 1955-09-16,45.09,45.09,45.09,45.09,2540000,45.09 1955-09-15,44.75,44.75,44.75,44.75,2890000,44.75 1955-09-14,44.99,44.99,44.99,44.99,2570000,44.99 1955-09-13,44.80,44.80,44.80,44.80,2580000,44.80 1955-09-12,44.19,44.19,44.19,44.19,2520000,44.19 1955-09-09,43.89,43.89,43.89,43.89,2480000,43.89 1955-09-08,43.88,43.88,43.88,43.88,2470000,43.88 1955-09-07,43.85,43.85,43.85,43.85,2380000,43.85 1955-09-06,43.86,43.86,43.86,43.86,2360000,43.86 1955-09-02,43.60,43.60,43.60,43.60,1700000,43.60 1955-09-01,43.37,43.37,43.37,43.37,1860000,43.37 1955-08-31,43.18,43.18,43.18,43.18,1850000,43.18 1955-08-30,42.92,42.92,42.92,42.92,1740000,42.92 1955-08-29,42.96,42.96,42.96,42.96,1910000,42.96 1955-08-26,42.99,42.99,42.99,42.99,2200000,42.99 1955-08-25,42.80,42.80,42.80,42.80,2120000,42.80 1955-08-24,42.61,42.61,42.61,42.61,2140000,42.61 1955-08-23,42.55,42.55,42.55,42.55,1890000,42.55 1955-08-22,41.98,41.98,41.98,41.98,1430000,41.98 1955-08-19,42.02,42.02,42.02,42.02,1400000,42.02 1955-08-18,41.84,41.84,41.84,41.84,1560000,41.84 1955-08-17,41.90,41.90,41.90,41.90,1570000,41.90 1955-08-16,41.86,41.86,41.86,41.86,1520000,41.86 1955-08-15,42.17,42.17,42.17,42.17,1230000,42.17 1955-08-12,42.21,42.21,42.21,42.21,1530000,42.21 1955-08-11,42.13,42.13,42.13,42.13,1620000,42.13 1955-08-10,41.74,41.74,41.74,41.74,1580000,41.74 1955-08-09,41.75,41.75,41.75,41.75,2240000,41.75 1955-08-08,42.31,42.31,42.31,42.31,1730000,42.31 1955-08-05,42.56,42.56,42.56,42.56,1690000,42.56 1955-08-04,42.36,42.36,42.36,42.36,2210000,42.36 1955-08-03,43.09,43.09,43.09,43.09,2190000,43.09 1955-08-02,43.03,43.03,43.03,43.03,2260000,43.03 1955-08-01,42.93,42.93,42.93,42.93,2190000,42.93 1955-07-29,43.52,43.52,43.52,43.52,2070000,43.52 1955-07-28,43.50,43.50,43.50,43.50,2090000,43.50 1955-07-27,43.76,43.76,43.76,43.76,2170000,43.76 1955-07-26,43.58,43.58,43.58,43.58,2340000,43.58 1955-07-25,43.48,43.48,43.48,43.48,2500000,43.48 1955-07-22,43.00,43.00,43.00,43.00,2500000,43.00 1955-07-21,42.64,42.64,42.64,42.64,2530000,42.64 1955-07-20,42.23,42.23,42.23,42.23,2080000,42.23 1955-07-19,42.10,42.10,42.10,42.10,2300000,42.10 1955-07-18,42.36,42.36,42.36,42.36,2160000,42.36 1955-07-15,42.40,42.40,42.40,42.40,2230000,42.40 1955-07-14,42.25,42.25,42.25,42.25,1980000,42.25 1955-07-13,42.24,42.24,42.24,42.24,2360000,42.24 1955-07-12,42.75,42.75,42.75,42.75,2630000,42.75 1955-07-11,42.75,42.75,42.75,42.75,2420000,42.75 1955-07-08,42.64,42.64,42.64,42.64,2450000,42.64 1955-07-07,42.58,42.58,42.58,42.58,3300000,42.58 1955-07-06,43.18,43.18,43.18,43.18,3140000,43.18 1955-07-05,41.69,41.69,41.69,41.69,2680000,41.69 1955-07-01,41.19,41.19,41.19,41.19,2540000,41.19 1955-06-30,41.03,41.03,41.03,41.03,2370000,41.03 1955-06-29,40.79,40.79,40.79,40.79,2180000,40.79 1955-06-28,40.77,40.77,40.77,40.77,2180000,40.77 1955-06-27,40.99,40.99,40.99,40.99,2250000,40.99 1955-06-24,40.96,40.96,40.96,40.96,2410000,40.96 1955-06-23,40.75,40.75,40.75,40.75,2900000,40.75 1955-06-22,40.60,40.60,40.60,40.60,3010000,40.60 1955-06-21,40.51,40.51,40.51,40.51,2720000,40.51 1955-06-20,40.14,40.14,40.14,40.14,2490000,40.14 1955-06-17,40.10,40.10,40.10,40.10,2340000,40.10 1955-06-16,39.96,39.96,39.96,39.96,2760000,39.96 1955-06-15,39.89,39.89,39.89,39.89,2650000,39.89 1955-06-14,39.67,39.67,39.67,39.67,2860000,39.67 1955-06-13,39.62,39.62,39.62,39.62,2770000,39.62 1955-06-10,39.25,39.25,39.25,39.25,2470000,39.25 1955-06-09,39.01,39.01,39.01,39.01,2960000,39.01 1955-06-08,39.22,39.22,39.22,39.22,3300000,39.22 1955-06-07,39.96,39.96,39.96,39.96,3230000,39.96 1955-06-06,39.69,39.69,39.69,39.69,2560000,39.69 1955-06-03,38.37,38.37,38.37,38.37,2590000,38.37 1955-06-02,38.01,38.01,38.01,38.01,2610000,38.01 1955-06-01,37.96,37.96,37.96,37.96,2510000,37.96 1955-05-31,37.91,37.91,37.91,37.91,1990000,37.91 1955-05-27,37.93,37.93,37.93,37.93,2220000,37.93 1955-05-26,37.85,37.85,37.85,37.85,2260000,37.85 1955-05-25,37.60,37.60,37.60,37.60,2100000,37.60 1955-05-24,37.46,37.46,37.46,37.46,1650000,37.46 1955-05-23,37.48,37.48,37.48,37.48,1900000,37.48 1955-05-20,37.74,37.74,37.74,37.74,2240000,37.74 1955-05-19,37.49,37.49,37.49,37.49,2380000,37.49 1955-05-18,37.28,37.28,37.28,37.28,2010000,37.28 1955-05-17,36.97,36.97,36.97,36.97,1900000,36.97 1955-05-16,37.02,37.02,37.02,37.02,2160000,37.02 1955-05-13,37.44,37.44,37.44,37.44,1860000,37.44 1955-05-12,37.20,37.20,37.20,37.20,2830000,37.20 1955-05-11,37.42,37.42,37.42,37.42,2120000,37.42 1955-05-10,37.85,37.85,37.85,37.85,2150000,37.85 1955-05-09,37.93,37.93,37.93,37.93,2090000,37.93 1955-05-06,37.89,37.89,37.89,37.89,2250000,37.89 1955-05-05,37.82,37.82,37.82,37.82,2270000,37.82 1955-05-04,37.64,37.64,37.64,37.64,2220000,37.64 1955-05-03,37.70,37.70,37.70,37.70,2630000,37.70 1955-05-02,38.04,38.04,38.04,38.04,2220000,38.04 1955-04-29,37.96,37.96,37.96,37.96,2230000,37.96 1955-04-28,37.68,37.68,37.68,37.68,2550000,37.68 1955-04-27,38.11,38.11,38.11,38.11,2660000,38.11 1955-04-26,38.31,38.31,38.31,38.31,2720000,38.31 1955-04-25,38.11,38.11,38.11,38.11,2720000,38.11 1955-04-22,38.01,38.01,38.01,38.01,2800000,38.01 1955-04-21,38.32,38.32,38.32,38.32,2810000,38.32 1955-04-20,38.28,38.28,38.28,38.28,3090000,38.28 1955-04-19,38.22,38.22,38.22,38.22,2700000,38.22 1955-04-18,38.27,38.27,38.27,38.27,3080000,38.27 1955-04-15,37.96,37.96,37.96,37.96,3180000,37.96 1955-04-14,37.79,37.79,37.79,37.79,2890000,37.79 1955-04-13,37.71,37.71,37.71,37.71,2820000,37.71 1955-04-12,37.66,37.66,37.66,37.66,2770000,37.66 1955-04-11,37.44,37.44,37.44,37.44,2680000,37.44 1955-04-07,37.34,37.34,37.34,37.34,2330000,37.34 1955-04-06,37.17,37.17,37.17,37.17,2500000,37.17 1955-04-05,36.98,36.98,36.98,36.98,2100000,36.98 1955-04-04,36.83,36.83,36.83,36.83,2500000,36.83 1955-04-01,36.95,36.95,36.95,36.95,2660000,36.95 1955-03-31,36.58,36.58,36.58,36.58,2680000,36.58 1955-03-30,36.52,36.52,36.52,36.52,3410000,36.52 1955-03-29,36.85,36.85,36.85,36.85,2770000,36.85 1955-03-28,36.83,36.83,36.83,36.83,2540000,36.83 1955-03-25,36.96,36.96,36.96,36.96,2540000,36.96 1955-03-24,36.93,36.93,36.93,36.93,3170000,36.93 1955-03-23,36.64,36.64,36.64,36.64,2730000,36.64 1955-03-22,36.17,36.17,36.17,36.17,1910000,36.17 1955-03-21,35.95,35.95,35.95,35.95,2020000,35.95 1955-03-18,36.18,36.18,36.18,36.18,2050000,36.18 1955-03-17,36.12,36.12,36.12,36.12,2200000,36.12 1955-03-16,35.98,35.98,35.98,35.98,2900000,35.98 1955-03-15,35.71,35.71,35.71,35.71,3160000,35.71 1955-03-14,34.96,34.96,34.96,34.96,4220000,34.96 1955-03-11,35.82,35.82,35.82,35.82,3040000,35.82 1955-03-10,36.45,36.45,36.45,36.45,2760000,36.45 1955-03-09,36.22,36.22,36.22,36.22,3590000,36.22 1955-03-08,36.58,36.58,36.58,36.58,3160000,36.58 1955-03-07,37.28,37.28,37.28,37.28,2630000,37.28 1955-03-04,37.52,37.52,37.52,37.52,2770000,37.52 1955-03-03,37.29,37.29,37.29,37.29,3330000,37.29 1955-03-02,37.15,37.15,37.15,37.15,3370000,37.15 1955-03-01,36.83,36.83,36.83,36.83,2830000,36.83 1955-02-28,36.76,36.76,36.76,36.76,2620000,36.76 1955-02-25,36.57,36.57,36.57,36.57,2540000,36.57 1955-02-24,36.62,36.62,36.62,36.62,2920000,36.62 1955-02-23,36.82,36.82,36.82,36.82,3030000,36.82 1955-02-21,36.85,36.85,36.85,36.85,3010000,36.85 1955-02-18,36.89,36.89,36.89,36.89,3660000,36.89 1955-02-17,36.84,36.84,36.84,36.84,3030000,36.84 1955-02-16,36.77,36.77,36.77,36.77,3660000,36.77 1955-02-15,36.89,36.89,36.89,36.89,3510000,36.89 1955-02-14,36.89,36.89,36.89,36.89,2950000,36.89 1955-02-11,37.15,37.15,37.15,37.15,3260000,37.15 1955-02-10,37.08,37.08,37.08,37.08,3460000,37.08 1955-02-09,36.75,36.75,36.75,36.75,3360000,36.75 1955-02-08,36.46,36.46,36.46,36.46,3400000,36.46 1955-02-07,36.96,36.96,36.96,36.96,3610000,36.96 1955-02-04,36.96,36.96,36.96,36.96,3370000,36.96 1955-02-03,36.44,36.44,36.44,36.44,2890000,36.44 1955-02-02,36.61,36.61,36.61,36.61,3210000,36.61 1955-02-01,36.72,36.72,36.72,36.72,3320000,36.72 1955-01-31,36.63,36.63,36.63,36.63,3500000,36.63 1955-01-28,36.19,36.19,36.19,36.19,3290000,36.19 1955-01-27,35.99,35.99,35.99,35.99,3500000,35.99 1955-01-26,35.95,35.95,35.95,35.95,3860000,35.95 1955-01-25,35.51,35.51,35.51,35.51,3230000,35.51 1955-01-24,35.52,35.52,35.52,35.52,2910000,35.52 1955-01-21,35.44,35.44,35.44,35.44,2690000,35.44 1955-01-20,35.13,35.13,35.13,35.13,2210000,35.13 1955-01-19,34.96,34.96,34.96,34.96,2760000,34.96 1955-01-18,34.80,34.80,34.80,34.80,3020000,34.80 1955-01-17,34.58,34.58,34.58,34.58,3360000,34.58 1955-01-14,35.28,35.28,35.28,35.28,2630000,35.28 1955-01-13,35.43,35.43,35.43,35.43,3350000,35.43 1955-01-12,35.58,35.58,35.58,35.58,3400000,35.58 1955-01-11,35.68,35.68,35.68,35.68,3680000,35.68 1955-01-10,35.79,35.79,35.79,35.79,4300000,35.79 1955-01-07,35.33,35.33,35.33,35.33,4030000,35.33 1955-01-06,35.04,35.04,35.04,35.04,5300000,35.04 1955-01-05,35.52,35.52,35.52,35.52,4640000,35.52 1955-01-04,36.42,36.42,36.42,36.42,4420000,36.42 1955-01-03,36.75,36.75,36.75,36.75,4570000,36.75 1954-12-31,35.98,35.98,35.98,35.98,3840000,35.98 1954-12-30,35.74,35.74,35.74,35.74,3590000,35.74 1954-12-29,35.74,35.74,35.74,35.74,4430000,35.74 1954-12-28,35.43,35.43,35.43,35.43,3660000,35.43 1954-12-27,35.07,35.07,35.07,35.07,2970000,35.07 1954-12-23,35.37,35.37,35.37,35.37,3310000,35.37 1954-12-22,35.34,35.34,35.34,35.34,3460000,35.34 1954-12-21,35.38,35.38,35.38,35.38,3630000,35.38 1954-12-20,35.33,35.33,35.33,35.33,3770000,35.33 1954-12-17,35.92,35.92,35.92,35.92,3730000,35.92 1954-12-16,34.93,34.93,34.93,34.93,3390000,34.93 1954-12-15,34.56,34.56,34.56,34.56,2740000,34.56 1954-12-14,34.35,34.35,34.35,34.35,2650000,34.35 1954-12-13,34.59,34.59,34.59,34.59,2750000,34.59 1954-12-10,34.56,34.56,34.56,34.56,3250000,34.56 1954-12-09,34.69,34.69,34.69,34.69,3300000,34.69 1954-12-08,34.86,34.86,34.86,34.86,4150000,34.86 1954-12-07,34.92,34.92,34.92,34.92,3820000,34.92 1954-12-06,34.76,34.76,34.76,34.76,3960000,34.76 1954-12-03,34.49,34.49,34.49,34.49,3790000,34.49 1954-12-02,34.18,34.18,34.18,34.18,3190000,34.18 1954-12-01,33.99,33.99,33.99,33.99,3100000,33.99 1954-11-30,34.24,34.24,34.24,34.24,3440000,34.24 1954-11-29,34.54,34.54,34.54,34.54,3300000,34.54 1954-11-26,34.55,34.55,34.55,34.55,3010000,34.55 1954-11-24,34.22,34.22,34.22,34.22,3990000,34.22 1954-11-23,34.03,34.03,34.03,34.03,3690000,34.03 1954-11-22,33.58,33.58,33.58,33.58,3000000,33.58 1954-11-19,33.45,33.45,33.45,33.45,3130000,33.45 1954-11-18,33.44,33.44,33.44,33.44,3530000,33.44 1954-11-17,33.63,33.63,33.63,33.63,3830000,33.63 1954-11-16,33.57,33.57,33.57,33.57,3260000,33.57 1954-11-15,33.47,33.47,33.47,33.47,3080000,33.47 1954-11-12,33.54,33.54,33.54,33.54,3720000,33.54 1954-11-11,33.47,33.47,33.47,33.47,2960000,33.47 1954-11-10,33.18,33.18,33.18,33.18,2070000,33.18 1954-11-09,33.15,33.15,33.15,33.15,3240000,33.15 1954-11-08,33.02,33.02,33.02,33.02,3180000,33.02 1954-11-05,32.71,32.71,32.71,32.71,2950000,32.71 1954-11-04,32.82,32.82,32.82,32.82,3140000,32.82 1954-11-03,32.44,32.44,32.44,32.44,2700000,32.44 1954-11-01,31.79,31.79,31.79,31.79,1790000,31.79 1954-10-29,31.68,31.68,31.68,31.68,1900000,31.68 1954-10-28,31.88,31.88,31.88,31.88,2190000,31.88 1954-10-27,32.02,32.02,32.02,32.02,2030000,32.02 1954-10-26,31.94,31.94,31.94,31.94,2010000,31.94 1954-10-25,31.96,31.96,31.96,31.96,2340000,31.96 1954-10-22,32.13,32.13,32.13,32.13,2080000,32.13 1954-10-21,32.13,32.13,32.13,32.13,2320000,32.13 1954-10-20,32.17,32.17,32.17,32.17,2380000,32.17 1954-10-19,31.91,31.91,31.91,31.91,1900000,31.91 1954-10-18,31.83,31.83,31.83,31.83,1790000,31.83 1954-10-15,31.71,31.71,31.71,31.71,2250000,31.71 1954-10-14,31.88,31.88,31.88,31.88,2540000,31.88 1954-10-13,32.27,32.27,32.27,32.27,2070000,32.27 1954-10-12,32.28,32.28,32.28,32.28,1620000,32.28 1954-10-11,32.41,32.41,32.41,32.41,2100000,32.41 1954-10-08,32.67,32.67,32.67,32.67,2120000,32.67 1954-10-07,32.69,32.69,32.69,32.69,1810000,32.69 1954-10-06,32.76,32.76,32.76,32.76,2570000,32.76 1954-10-05,32.63,32.63,32.63,32.63,2300000,32.63 1954-10-04,32.47,32.47,32.47,32.47,2000000,32.47 1954-10-01,32.29,32.29,32.29,32.29,1850000,32.29 1954-09-30,32.31,32.31,32.31,32.31,1840000,32.31 1954-09-29,32.50,32.50,32.50,32.50,1810000,32.50 1954-09-28,32.69,32.69,32.69,32.69,1800000,32.69 1954-09-27,32.53,32.53,32.53,32.53,2190000,32.53 1954-09-24,32.40,32.40,32.40,32.40,2340000,32.40 1954-09-23,32.18,32.18,32.18,32.18,2340000,32.18 1954-09-22,32.00,32.00,32.00,32.00,2260000,32.00 1954-09-21,31.79,31.79,31.79,31.79,1770000,31.79 1954-09-20,31.57,31.57,31.57,31.57,2060000,31.57 1954-09-17,31.71,31.71,31.71,31.71,2250000,31.71 1954-09-16,31.46,31.46,31.46,31.46,1880000,31.46 1954-09-15,31.29,31.29,31.29,31.29,2110000,31.29 1954-09-14,31.28,31.28,31.28,31.28,2120000,31.28 1954-09-13,31.12,31.12,31.12,31.12,2030000,31.12 1954-09-10,30.84,30.84,30.84,30.84,1870000,30.84 1954-09-09,30.73,30.73,30.73,30.73,1700000,30.73 1954-09-08,30.68,30.68,30.68,30.68,1970000,30.68 1954-09-07,30.66,30.66,30.66,30.66,1860000,30.66 1954-09-03,30.50,30.50,30.50,30.50,1630000,30.50 1954-09-02,30.27,30.27,30.27,30.27,1600000,30.27 1954-09-01,30.04,30.04,30.04,30.04,1790000,30.04 1954-08-31,29.83,29.83,29.83,29.83,2640000,29.83 1954-08-30,30.35,30.35,30.35,30.35,1950000,30.35 1954-08-27,30.66,30.66,30.66,30.66,1740000,30.66 1954-08-26,30.57,30.57,30.57,30.57,2060000,30.57 1954-08-25,30.65,30.65,30.65,30.65,2280000,30.65 1954-08-24,30.87,30.87,30.87,30.87,2000000,30.87 1954-08-23,31.00,31.00,31.00,31.00,2020000,31.00 1954-08-20,31.21,31.21,31.21,31.21,2110000,31.21 1954-08-19,31.16,31.16,31.16,31.16,2320000,31.16 1954-08-18,31.09,31.09,31.09,31.09,2390000,31.09 1954-08-17,31.12,31.12,31.12,31.12,2900000,31.12 1954-08-16,31.05,31.05,31.05,31.05,2760000,31.05 1954-08-13,30.72,30.72,30.72,30.72,2500000,30.72 1954-08-12,30.59,30.59,30.59,30.59,2680000,30.59 1954-08-11,30.72,30.72,30.72,30.72,3440000,30.72 1954-08-10,30.37,30.37,30.37,30.37,2890000,30.37 1954-08-09,30.12,30.12,30.12,30.12,2280000,30.12 1954-08-06,30.38,30.38,30.38,30.38,3350000,30.38 1954-08-05,30.77,30.77,30.77,30.77,3150000,30.77 1954-08-04,30.90,30.90,30.90,30.90,3620000,30.90 1954-08-03,30.93,30.93,30.93,30.93,2970000,30.93 1954-08-02,30.99,30.99,30.99,30.99,2850000,30.99 1954-07-30,30.88,30.88,30.88,30.88,2800000,30.88 1954-07-29,30.69,30.69,30.69,30.69,2710000,30.69 1954-07-28,30.58,30.58,30.58,30.58,2740000,30.58 1954-07-27,30.52,30.52,30.52,30.52,2690000,30.52 1954-07-26,30.34,30.34,30.34,30.34,2110000,30.34 1954-07-23,30.31,30.31,30.31,30.31,2520000,30.31 1954-07-22,30.27,30.27,30.27,30.27,2890000,30.27 1954-07-21,30.03,30.03,30.03,30.03,2510000,30.03 1954-07-20,29.84,29.84,29.84,29.84,2580000,29.84 1954-07-19,29.98,29.98,29.98,29.98,2370000,29.98 1954-07-16,30.06,30.06,30.06,30.06,2540000,30.06 1954-07-15,30.19,30.19,30.19,30.19,3000000,30.19 1954-07-14,30.09,30.09,30.09,30.09,2520000,30.09 1954-07-13,30.02,30.02,30.02,30.02,2430000,30.02 1954-07-12,30.12,30.12,30.12,30.12,2330000,30.12 1954-07-09,30.14,30.14,30.14,30.14,2240000,30.14 1954-07-08,29.94,29.94,29.94,29.94,2080000,29.94 1954-07-07,29.94,29.94,29.94,29.94,2380000,29.94 1954-07-06,29.92,29.92,29.92,29.92,2560000,29.92 1954-07-02,29.59,29.59,29.59,29.59,1980000,29.59 1954-07-01,29.21,29.21,29.21,29.21,1860000,29.21 1954-06-30,29.21,29.21,29.21,29.21,1950000,29.21 1954-06-29,29.43,29.43,29.43,29.43,2580000,29.43 1954-06-28,29.28,29.28,29.28,29.28,1890000,29.28 1954-06-25,29.20,29.20,29.20,29.20,2060000,29.20 1954-06-24,29.26,29.26,29.26,29.26,2260000,29.26 1954-06-23,29.13,29.13,29.13,29.13,2090000,29.13 1954-06-22,29.08,29.08,29.08,29.08,2100000,29.08 1954-06-21,29.06,29.06,29.06,29.06,1820000,29.06 1954-06-18,29.04,29.04,29.04,29.04,1580000,29.04 1954-06-17,28.96,28.96,28.96,28.96,1810000,28.96 1954-06-16,29.04,29.04,29.04,29.04,2070000,29.04 1954-06-15,28.83,28.83,28.83,28.83,1630000,28.83 1954-06-14,28.62,28.62,28.62,28.62,1420000,28.62 1954-06-11,28.58,28.58,28.58,28.58,1630000,28.58 1954-06-10,28.34,28.34,28.34,28.34,1610000,28.34 1954-06-09,28.15,28.15,28.15,28.15,2360000,28.15 1954-06-08,28.34,28.34,28.34,28.34,2540000,28.34 1954-06-07,28.99,28.99,28.99,28.99,1520000,28.99 1954-06-04,29.10,29.10,29.10,29.10,1720000,29.10 1954-06-03,29.15,29.15,29.15,29.15,1810000,29.15 1954-06-02,29.16,29.16,29.16,29.16,1930000,29.16 1954-06-01,29.19,29.19,29.19,29.19,1850000,29.19 1954-05-28,29.19,29.19,29.19,29.19,1940000,29.19 1954-05-27,29.05,29.05,29.05,29.05,2230000,29.05 1954-05-26,29.17,29.17,29.17,29.17,2180000,29.17 1954-05-25,28.93,28.93,28.93,28.93,2050000,28.93 1954-05-24,29.00,29.00,29.00,29.00,2330000,29.00 1954-05-21,28.99,28.99,28.99,28.99,2620000,28.99 1954-05-20,28.82,28.82,28.82,28.82,2070000,28.82 1954-05-19,28.72,28.72,28.72,28.72,2170000,28.72 1954-05-18,28.85,28.85,28.85,28.85,2250000,28.85 1954-05-17,28.84,28.84,28.84,28.84,2040000,28.84 1954-05-14,28.80,28.80,28.80,28.80,1970000,28.80 1954-05-13,28.56,28.56,28.56,28.56,2340000,28.56 1954-05-12,28.72,28.72,28.72,28.72,2210000,28.72 1954-05-11,28.49,28.49,28.49,28.49,1770000,28.49 1954-05-10,28.62,28.62,28.62,28.62,1800000,28.62 1954-05-07,28.65,28.65,28.65,28.65,2070000,28.65 1954-05-06,28.51,28.51,28.51,28.51,1980000,28.51 1954-05-05,28.29,28.29,28.29,28.29,2020000,28.29 1954-05-04,28.28,28.28,28.28,28.28,1990000,28.28 1954-05-03,28.21,28.21,28.21,28.21,1870000,28.21 1954-04-30,28.26,28.26,28.26,28.26,2450000,28.26 1954-04-29,28.18,28.18,28.18,28.18,2150000,28.18 1954-04-28,27.76,27.76,27.76,27.76,2120000,27.76 1954-04-27,27.71,27.71,27.71,27.71,1970000,27.71 1954-04-26,27.88,27.88,27.88,27.88,2150000,27.88 1954-04-23,27.78,27.78,27.78,27.78,1990000,27.78 1954-04-22,27.68,27.68,27.68,27.68,1750000,27.68 1954-04-21,27.64,27.64,27.64,27.64,1870000,27.64 1954-04-20,27.75,27.75,27.75,27.75,1860000,27.75 1954-04-19,27.76,27.76,27.76,27.76,2430000,27.76 1954-04-15,27.94,27.94,27.94,27.94,2200000,27.94 1954-04-14,27.85,27.85,27.85,27.85,2330000,27.85 1954-04-13,27.64,27.64,27.64,27.64,2020000,27.64 1954-04-12,27.57,27.57,27.57,27.57,1790000,27.57 1954-04-09,27.38,27.38,27.38,27.38,2360000,27.38 1954-04-08,27.38,27.38,27.38,27.38,2300000,27.38 1954-04-07,27.11,27.11,27.11,27.11,1830000,27.11 1954-04-06,27.01,27.01,27.01,27.01,2120000,27.01 1954-04-05,27.26,27.26,27.26,27.26,1710000,27.26 1954-04-02,27.21,27.21,27.21,27.21,1830000,27.21 1954-04-01,27.17,27.17,27.17,27.17,2270000,27.17 1954-03-31,26.94,26.94,26.94,26.94,2690000,26.94 1954-03-30,26.69,26.69,26.69,26.69,2130000,26.69 1954-03-29,26.66,26.66,26.66,26.66,1870000,26.66 1954-03-26,26.56,26.56,26.56,26.56,1550000,26.56 1954-03-25,26.42,26.42,26.42,26.42,1720000,26.42 1954-03-24,26.47,26.47,26.47,26.47,1900000,26.47 1954-03-23,26.60,26.60,26.60,26.60,2180000,26.60 1954-03-22,26.79,26.79,26.79,26.79,1800000,26.79 1954-03-19,26.81,26.81,26.81,26.81,1930000,26.81 1954-03-18,26.73,26.73,26.73,26.73,2020000,26.73 1954-03-17,26.62,26.62,26.62,26.62,1740000,26.62 1954-03-16,26.56,26.56,26.56,26.56,1540000,26.56 1954-03-15,26.57,26.57,26.57,26.57,1680000,26.57 1954-03-12,26.69,26.69,26.69,26.69,1980000,26.69 1954-03-11,26.69,26.69,26.69,26.69,2050000,26.69 1954-03-10,26.57,26.57,26.57,26.57,1870000,26.57 1954-03-09,26.51,26.51,26.51,26.51,1630000,26.51 1954-03-08,26.45,26.45,26.45,26.45,1650000,26.45 1954-03-05,26.52,26.52,26.52,26.52,2030000,26.52 1954-03-04,26.41,26.41,26.41,26.41,1830000,26.41 1954-03-03,26.32,26.32,26.32,26.32,2240000,26.32 1954-03-02,26.32,26.32,26.32,26.32,1980000,26.32 1954-03-01,26.25,26.25,26.25,26.25,2040000,26.25 1954-02-26,26.15,26.15,26.15,26.15,1910000,26.15 1954-02-25,25.91,25.91,25.91,25.91,1470000,25.91 1954-02-24,25.83,25.83,25.83,25.83,1350000,25.83 1954-02-23,25.83,25.83,25.83,25.83,1470000,25.83 1954-02-19,25.92,25.92,25.92,25.92,1510000,25.92 1954-02-18,25.86,25.86,25.86,25.86,1500000,25.86 1954-02-17,25.86,25.86,25.86,25.86,1740000,25.86 1954-02-16,25.81,25.81,25.81,25.81,1870000,25.81 1954-02-15,26.04,26.04,26.04,26.04,2080000,26.04 1954-02-12,26.12,26.12,26.12,26.12,1730000,26.12 1954-02-11,26.06,26.06,26.06,26.06,1860000,26.06 1954-02-10,26.14,26.14,26.14,26.14,1790000,26.14 1954-02-09,26.17,26.17,26.17,26.17,1880000,26.17 1954-02-08,26.23,26.23,26.23,26.23,2180000,26.23 1954-02-05,26.30,26.30,26.30,26.30,2030000,26.30 1954-02-04,26.20,26.20,26.20,26.20,2040000,26.20 1954-02-03,26.01,26.01,26.01,26.01,1690000,26.01 1954-02-02,25.92,25.92,25.92,25.92,1420000,25.92 1954-02-01,25.99,25.99,25.99,25.99,1740000,25.99 1954-01-29,26.08,26.08,26.08,26.08,1950000,26.08 1954-01-28,26.02,26.02,26.02,26.02,1730000,26.02 1954-01-27,26.01,26.01,26.01,26.01,2020000,26.01 1954-01-26,26.09,26.09,26.09,26.09,2120000,26.09 1954-01-25,25.93,25.93,25.93,25.93,1860000,25.93 1954-01-22,25.85,25.85,25.85,25.85,1890000,25.85 1954-01-21,25.79,25.79,25.79,25.79,1780000,25.79 1954-01-20,25.75,25.75,25.75,25.75,1960000,25.75 1954-01-19,25.68,25.68,25.68,25.68,1840000,25.68 1954-01-18,25.43,25.43,25.43,25.43,1580000,25.43 1954-01-15,25.43,25.43,25.43,25.43,2180000,25.43 1954-01-14,25.19,25.19,25.19,25.19,1530000,25.19 1954-01-13,25.07,25.07,25.07,25.07,1420000,25.07 1954-01-12,24.93,24.93,24.93,24.93,1250000,24.93 1954-01-11,24.80,24.80,24.80,24.80,1220000,24.80 1954-01-08,24.93,24.93,24.93,24.93,1260000,24.93 1954-01-07,25.06,25.06,25.06,25.06,1540000,25.06 1954-01-06,25.14,25.14,25.14,25.14,1460000,25.14 1954-01-05,25.10,25.10,25.10,25.10,1520000,25.10 1954-01-04,24.95,24.95,24.95,24.95,1310000,24.95 1953-12-31,24.81,24.81,24.81,24.81,2490000,24.81 1953-12-30,24.76,24.76,24.76,24.76,2050000,24.76 1953-12-29,24.55,24.55,24.55,24.55,2140000,24.55 1953-12-28,24.71,24.71,24.71,24.71,1570000,24.71 1953-12-24,24.80,24.80,24.80,24.80,1270000,24.80 1953-12-23,24.69,24.69,24.69,24.69,1570000,24.69 1953-12-22,24.76,24.76,24.76,24.76,1720000,24.76 1953-12-21,24.95,24.95,24.95,24.95,1690000,24.95 1953-12-18,24.99,24.99,24.99,24.99,1550000,24.99 1953-12-17,24.94,24.94,24.94,24.94,1600000,24.94 1953-12-16,24.96,24.96,24.96,24.96,1880000,24.96 1953-12-15,24.71,24.71,24.71,24.71,1450000,24.71 1953-12-14,24.69,24.69,24.69,24.69,1540000,24.69 1953-12-11,24.76,24.76,24.76,24.76,1440000,24.76 1953-12-10,24.78,24.78,24.78,24.78,1420000,24.78 1953-12-09,24.84,24.84,24.84,24.84,1410000,24.84 1953-12-08,24.87,24.87,24.87,24.87,1390000,24.87 1953-12-07,24.95,24.95,24.95,24.95,1410000,24.95 1953-12-04,24.98,24.98,24.98,24.98,1390000,24.98 1953-12-03,24.97,24.97,24.97,24.97,1740000,24.97 1953-12-02,24.95,24.95,24.95,24.95,1850000,24.95 1953-12-01,24.78,24.78,24.78,24.78,1580000,24.78 1953-11-30,24.76,24.76,24.76,24.76,1960000,24.76 1953-11-27,24.66,24.66,24.66,24.66,1600000,24.66 1953-11-25,24.52,24.52,24.52,24.52,1540000,24.52 1953-11-24,24.50,24.50,24.50,24.50,1470000,24.50 1953-11-23,24.36,24.36,24.36,24.36,1410000,24.36 1953-11-20,24.44,24.44,24.44,24.44,1300000,24.44 1953-11-19,24.40,24.40,24.40,24.40,1420000,24.40 1953-11-18,24.29,24.29,24.29,24.29,1250000,24.29 1953-11-17,24.25,24.25,24.25,24.25,1250000,24.25 1953-11-16,24.38,24.38,24.38,24.38,1490000,24.38 1953-11-13,24.54,24.54,24.54,24.54,1540000,24.54 1953-11-12,24.46,24.46,24.46,24.46,1390000,24.46 1953-11-10,24.37,24.37,24.37,24.37,1340000,24.37 1953-11-09,24.66,24.66,24.66,24.66,1440000,24.66 1953-11-06,24.61,24.61,24.61,24.61,1700000,24.61 1953-11-05,24.64,24.64,24.64,24.64,1720000,24.64 1953-11-04,24.51,24.51,24.51,24.51,1480000,24.51 1953-11-02,24.66,24.66,24.66,24.66,1340000,24.66 1953-10-30,24.54,24.54,24.54,24.54,1400000,24.54 1953-10-29,24.58,24.58,24.58,24.58,1610000,24.58 1953-10-28,24.29,24.29,24.29,24.29,1260000,24.29 1953-10-27,24.26,24.26,24.26,24.26,1170000,24.26 1953-10-26,24.31,24.31,24.31,24.31,1340000,24.31 1953-10-23,24.35,24.35,24.35,24.35,1330000,24.35 1953-10-22,24.30,24.30,24.30,24.30,1330000,24.30 1953-10-21,24.19,24.19,24.19,24.19,1320000,24.19 1953-10-20,24.17,24.17,24.17,24.17,1280000,24.17 1953-10-19,24.16,24.16,24.16,24.16,1190000,24.16 1953-10-16,24.14,24.14,24.14,24.14,1620000,24.14 1953-10-15,23.95,23.95,23.95,23.95,1710000,23.95 1953-10-14,23.68,23.68,23.68,23.68,1290000,23.68 1953-10-13,23.57,23.57,23.57,23.57,1130000,23.57 1953-10-09,23.66,23.66,23.66,23.66,900000,23.66 1953-10-08,23.62,23.62,23.62,23.62,960000,23.62 1953-10-07,23.58,23.58,23.58,23.58,1010000,23.58 1953-10-06,23.39,23.39,23.39,23.39,1100000,23.39 1953-10-05,23.48,23.48,23.48,23.48,930000,23.48 1953-10-02,23.59,23.59,23.59,23.59,890000,23.59 1953-10-01,23.49,23.49,23.49,23.49,940000,23.49 1953-09-30,23.35,23.35,23.35,23.35,940000,23.35 1953-09-29,23.49,23.49,23.49,23.49,1170000,23.49 1953-09-28,23.45,23.45,23.45,23.45,1150000,23.45 1953-09-25,23.30,23.30,23.30,23.30,910000,23.30 1953-09-24,23.24,23.24,23.24,23.24,1020000,23.24 1953-09-23,23.23,23.23,23.23,23.23,1240000,23.23 1953-09-22,23.20,23.20,23.20,23.20,1300000,23.20 1953-09-21,22.88,22.88,22.88,22.88,1070000,22.88 1953-09-18,22.95,22.95,22.95,22.95,1190000,22.95 1953-09-17,23.07,23.07,23.07,23.07,1290000,23.07 1953-09-16,23.01,23.01,23.01,23.01,1570000,23.01 1953-09-15,22.90,22.90,22.90,22.90,2850000,22.90 1953-09-14,22.71,22.71,22.71,22.71,2550000,22.71 1953-09-11,23.14,23.14,23.14,23.14,1930000,23.14 1953-09-10,23.41,23.41,23.41,23.41,1010000,23.41 1953-09-09,23.65,23.65,23.65,23.65,860000,23.65 1953-09-08,23.61,23.61,23.61,23.61,740000,23.61 1953-09-04,23.57,23.57,23.57,23.57,770000,23.57 1953-09-03,23.51,23.51,23.51,23.51,900000,23.51 1953-09-02,23.56,23.56,23.56,23.56,1110000,23.56 1953-09-01,23.42,23.42,23.42,23.42,1580000,23.42 1953-08-31,23.32,23.32,23.32,23.32,2190000,23.32 1953-08-28,23.74,23.74,23.74,23.74,1060000,23.74 1953-08-27,23.79,23.79,23.79,23.79,1290000,23.79 1953-08-26,23.86,23.86,23.86,23.86,1060000,23.86 1953-08-25,23.93,23.93,23.93,23.93,1470000,23.93 1953-08-24,24.09,24.09,24.09,24.09,1320000,24.09 1953-08-21,24.35,24.35,24.35,24.35,850000,24.35 1953-08-20,24.29,24.29,24.29,24.29,860000,24.29 1953-08-19,24.31,24.31,24.31,24.31,1400000,24.31 1953-08-18,24.46,24.46,24.46,24.46,1030000,24.46 1953-08-17,24.56,24.56,24.56,24.56,910000,24.56 1953-08-14,24.62,24.62,24.62,24.62,1000000,24.62 1953-08-13,24.73,24.73,24.73,24.73,1040000,24.73 1953-08-12,24.78,24.78,24.78,24.78,990000,24.78 1953-08-11,24.72,24.72,24.72,24.72,940000,24.72 1953-08-10,24.75,24.75,24.75,24.75,1090000,24.75 1953-08-07,24.78,24.78,24.78,24.78,950000,24.78 1953-08-06,24.80,24.80,24.80,24.80,1200000,24.80 1953-08-05,24.68,24.68,24.68,24.68,1080000,24.68 1953-08-04,24.78,24.78,24.78,24.78,1000000,24.78 1953-08-03,24.84,24.84,24.84,24.84,1160000,24.84 1953-07-31,24.75,24.75,24.75,24.75,1320000,24.75 1953-07-30,24.49,24.49,24.49,24.49,1200000,24.49 1953-07-29,24.26,24.26,24.26,24.26,1000000,24.26 1953-07-28,24.11,24.11,24.11,24.11,1080000,24.11 1953-07-27,24.07,24.07,24.07,24.07,1210000,24.07 1953-07-24,24.23,24.23,24.23,24.23,890000,24.23 1953-07-23,24.23,24.23,24.23,24.23,1000000,24.23 1953-07-22,24.19,24.19,24.19,24.19,900000,24.19 1953-07-21,24.16,24.16,24.16,24.16,850000,24.16 1953-07-20,24.22,24.22,24.22,24.22,830000,24.22 1953-07-17,24.35,24.35,24.35,24.35,840000,24.35 1953-07-16,24.18,24.18,24.18,24.18,790000,24.18 1953-07-15,24.15,24.15,24.15,24.15,840000,24.15 1953-07-14,24.08,24.08,24.08,24.08,1030000,24.08 1953-07-13,24.17,24.17,24.17,24.17,1120000,24.17 1953-07-10,24.41,24.41,24.41,24.41,860000,24.41 1953-07-09,24.43,24.43,24.43,24.43,910000,24.43 1953-07-08,24.50,24.50,24.50,24.50,950000,24.50 1953-07-07,24.51,24.51,24.51,24.51,1030000,24.51 1953-07-06,24.38,24.38,24.38,24.38,820000,24.38 1953-07-03,24.36,24.36,24.36,24.36,830000,24.36 1953-07-02,24.31,24.31,24.31,24.31,1030000,24.31 1953-07-01,24.24,24.24,24.24,24.24,910000,24.24 1953-06-30,24.14,24.14,24.14,24.14,820000,24.14 1953-06-29,24.14,24.14,24.14,24.14,800000,24.14 1953-06-26,24.21,24.21,24.21,24.21,830000,24.21 1953-06-25,24.19,24.19,24.19,24.19,1160000,24.19 1953-06-24,24.09,24.09,24.09,24.09,1030000,24.09 1953-06-23,24.12,24.12,24.12,24.12,1050000,24.12 1953-06-22,23.96,23.96,23.96,23.96,1030000,23.96 1953-06-19,23.84,23.84,23.84,23.84,890000,23.84 1953-06-18,23.84,23.84,23.84,23.84,1010000,23.84 1953-06-17,23.85,23.85,23.85,23.85,1150000,23.85 1953-06-16,23.55,23.55,23.55,23.55,1370000,23.55 1953-06-15,23.62,23.62,23.62,23.62,1090000,23.62 1953-06-12,23.82,23.82,23.82,23.82,920000,23.82 1953-06-11,23.75,23.75,23.75,23.75,1220000,23.75 1953-06-10,23.54,23.54,23.54,23.54,1960000,23.54 1953-06-09,23.60,23.60,23.60,23.60,2200000,23.60 1953-06-08,24.01,24.01,24.01,24.01,1000000,24.01 1953-06-05,24.09,24.09,24.09,24.09,1160000,24.09 1953-06-04,24.03,24.03,24.03,24.03,1400000,24.03 1953-06-03,24.18,24.18,24.18,24.18,1050000,24.18 1953-06-02,24.22,24.22,24.22,24.22,1450000,24.22 1953-06-01,24.15,24.15,24.15,24.15,1490000,24.15 1953-05-29,24.54,24.54,24.54,24.54,920000,24.54 1953-05-28,24.46,24.46,24.46,24.46,1240000,24.46 1953-05-27,24.64,24.64,24.64,24.64,1330000,24.64 1953-05-26,24.87,24.87,24.87,24.87,1160000,24.87 1953-05-25,24.99,24.99,24.99,24.99,1180000,24.99 1953-05-22,25.03,25.03,25.03,25.03,1350000,25.03 1953-05-21,25.06,25.06,25.06,25.06,1590000,25.06 1953-05-20,24.93,24.93,24.93,24.93,1690000,24.93 1953-05-19,24.70,24.70,24.70,24.70,1120000,24.70 1953-05-18,24.75,24.75,24.75,24.75,1080000,24.75 1953-05-15,24.84,24.84,24.84,24.84,1200000,24.84 1953-05-14,24.85,24.85,24.85,24.85,1210000,24.85 1953-05-13,24.71,24.71,24.71,24.71,1120000,24.71 1953-05-12,24.74,24.74,24.74,24.74,1080000,24.74 1953-05-11,24.91,24.91,24.91,24.91,1010000,24.91 1953-05-08,24.90,24.90,24.90,24.90,1220000,24.90 1953-05-07,24.90,24.90,24.90,24.90,1110000,24.90 1953-05-06,25.00,25.00,25.00,25.00,1110000,25.00 1953-05-05,25.03,25.03,25.03,25.03,1290000,25.03 1953-05-04,25.00,25.00,25.00,25.00,1520000,25.00 1953-05-01,24.73,24.73,24.73,24.73,1200000,24.73 1953-04-30,24.62,24.62,24.62,24.62,1140000,24.62 1953-04-29,24.68,24.68,24.68,24.68,1310000,24.68 1953-04-28,24.52,24.52,24.52,24.52,1330000,24.52 1953-04-27,24.34,24.34,24.34,24.34,1400000,24.34 1953-04-24,24.20,24.20,24.20,24.20,1780000,24.20 1953-04-23,24.19,24.19,24.19,24.19,1920000,24.19 1953-04-22,24.46,24.46,24.46,24.46,1390000,24.46 1953-04-21,24.67,24.67,24.67,24.67,1250000,24.67 1953-04-20,24.73,24.73,24.73,24.73,1520000,24.73 1953-04-17,24.62,24.62,24.62,24.62,1430000,24.62 1953-04-16,24.91,24.91,24.91,24.91,1310000,24.91 1953-04-15,24.96,24.96,24.96,24.96,1580000,24.96 1953-04-14,24.86,24.86,24.86,24.86,1480000,24.86 1953-04-13,24.77,24.77,24.77,24.77,1280000,24.77 1953-04-10,24.82,24.82,24.82,24.82,1360000,24.82 1953-04-09,24.88,24.88,24.88,24.88,1520000,24.88 1953-04-08,24.93,24.93,24.93,24.93,1860000,24.93 1953-04-07,24.71,24.71,24.71,24.71,2500000,24.71 1953-04-06,24.61,24.61,24.61,24.61,3050000,24.61 1953-04-02,25.23,25.23,25.23,25.23,1720000,25.23 1953-04-01,25.25,25.25,25.25,25.25,2240000,25.25 1953-03-31,25.29,25.29,25.29,25.29,3120000,25.29 1953-03-30,25.61,25.61,25.61,25.61,2740000,25.61 1953-03-27,25.99,25.99,25.99,25.99,1640000,25.99 1953-03-26,25.95,25.95,25.95,25.95,2000000,25.95 1953-03-25,26.10,26.10,26.10,26.10,2320000,26.10 1953-03-24,26.17,26.17,26.17,26.17,1970000,26.17 1953-03-23,26.02,26.02,26.02,26.02,1750000,26.02 1953-03-20,26.18,26.18,26.18,26.18,1730000,26.18 1953-03-19,26.22,26.22,26.22,26.22,1840000,26.22 1953-03-18,26.24,26.24,26.24,26.24,2110000,26.24 1953-03-17,26.33,26.33,26.33,26.33,2110000,26.33 1953-03-16,26.22,26.22,26.22,26.22,1770000,26.22 1953-03-13,26.18,26.18,26.18,26.18,1760000,26.18 1953-03-12,26.13,26.13,26.13,26.13,1780000,26.13 1953-03-11,26.12,26.12,26.12,26.12,1890000,26.12 1953-03-10,25.91,25.91,25.91,25.91,1530000,25.91 1953-03-09,25.83,25.83,25.83,25.83,1600000,25.83 1953-03-06,25.84,25.84,25.84,25.84,1690000,25.84 1953-03-05,25.79,25.79,25.79,25.79,1540000,25.79 1953-03-04,25.78,25.78,25.78,25.78,2010000,25.78 1953-03-03,26.00,26.00,26.00,26.00,1850000,26.00 1953-03-02,25.93,25.93,25.93,25.93,1760000,25.93 1953-02-27,25.90,25.90,25.90,25.90,1990000,25.90 1953-02-26,25.95,25.95,25.95,25.95,2290000,25.95 1953-02-25,25.91,25.91,25.91,25.91,2360000,25.91 1953-02-24,25.75,25.75,25.75,25.75,2300000,25.75 1953-02-20,25.63,25.63,25.63,25.63,1400000,25.63 1953-02-19,25.57,25.57,25.57,25.57,1390000,25.57 1953-02-18,25.48,25.48,25.48,25.48,1220000,25.48 1953-02-17,25.50,25.50,25.50,25.50,1290000,25.50 1953-02-16,25.65,25.65,25.65,25.65,1330000,25.65 1953-02-13,25.74,25.74,25.74,25.74,1350000,25.74 1953-02-11,25.64,25.64,25.64,25.64,1240000,25.64 1953-02-10,25.62,25.62,25.62,25.62,1350000,25.62 1953-02-09,25.69,25.69,25.69,25.69,1780000,25.69 1953-02-06,26.51,26.51,26.51,26.51,1870000,26.51 1953-02-05,26.15,26.15,26.15,26.15,1900000,26.15 1953-02-04,26.42,26.42,26.42,26.42,1660000,26.42 1953-02-03,26.54,26.54,26.54,26.54,1560000,26.54 1953-02-02,26.51,26.51,26.51,26.51,1890000,26.51 1953-01-30,26.38,26.38,26.38,26.38,1760000,26.38 1953-01-29,26.20,26.20,26.20,26.20,1830000,26.20 1953-01-28,26.13,26.13,26.13,26.13,1640000,26.13 1953-01-27,26.05,26.05,26.05,26.05,1550000,26.05 1953-01-26,26.02,26.02,26.02,26.02,1420000,26.02 1953-01-23,26.07,26.07,26.07,26.07,1340000,26.07 1953-01-22,26.12,26.12,26.12,26.12,1380000,26.12 1953-01-21,26.09,26.09,26.09,26.09,1300000,26.09 1953-01-20,26.14,26.14,26.14,26.14,1490000,26.14 1953-01-19,26.01,26.01,26.01,26.01,1360000,26.01 1953-01-16,26.02,26.02,26.02,26.02,1710000,26.02 1953-01-15,26.13,26.13,26.13,26.13,1450000,26.13 1953-01-14,26.08,26.08,26.08,26.08,1370000,26.08 1953-01-13,26.02,26.02,26.02,26.02,1680000,26.02 1953-01-12,25.86,25.86,25.86,25.86,1500000,25.86 1953-01-09,26.08,26.08,26.08,26.08,2080000,26.08 1953-01-08,26.33,26.33,26.33,26.33,1780000,26.33 1953-01-07,26.37,26.37,26.37,26.37,1760000,26.37 1953-01-06,26.48,26.48,26.48,26.48,2080000,26.48 1953-01-05,26.66,26.66,26.66,26.66,2130000,26.66 1953-01-02,26.54,26.54,26.54,26.54,1450000,26.54 1952-12-31,26.57,26.57,26.57,26.57,2050000,26.57 1952-12-30,26.59,26.59,26.59,26.59,2070000,26.59 1952-12-29,26.40,26.40,26.40,26.40,1820000,26.40 1952-12-26,26.25,26.25,26.25,26.25,1290000,26.25 1952-12-24,26.21,26.21,26.21,26.21,1510000,26.21 1952-12-23,26.19,26.19,26.19,26.19,2100000,26.19 1952-12-22,26.30,26.30,26.30,26.30,2100000,26.30 1952-12-19,26.15,26.15,26.15,26.15,2050000,26.15 1952-12-18,26.03,26.03,26.03,26.03,1860000,26.03 1952-12-17,26.04,26.04,26.04,26.04,1700000,26.04 1952-12-16,26.07,26.07,26.07,26.07,1980000,26.07 1952-12-15,26.04,26.04,26.04,26.04,1940000,26.04 1952-12-12,26.04,26.04,26.04,26.04,2030000,26.04 1952-12-11,25.96,25.96,25.96,25.96,1790000,25.96 1952-12-10,25.98,25.98,25.98,25.98,1880000,25.98 1952-12-09,25.93,25.93,25.93,25.93,2120000,25.93 1952-12-08,25.76,25.76,25.76,25.76,1790000,25.76 1952-12-05,25.62,25.62,25.62,25.62,1510000,25.62 1952-12-04,25.61,25.61,25.61,25.61,1570000,25.61 1952-12-03,25.71,25.71,25.71,25.71,1610000,25.71 1952-12-02,25.74,25.74,25.74,25.74,1610000,25.74 1952-12-01,25.68,25.68,25.68,25.68,2100000,25.68 1952-11-28,25.66,25.66,25.66,25.66,2160000,25.66 1952-11-26,25.52,25.52,25.52,25.52,1920000,25.52 1952-11-25,25.36,25.36,25.36,25.36,1930000,25.36 1952-11-24,25.42,25.42,25.42,25.42,2100000,25.42 1952-11-21,25.27,25.27,25.27,25.27,1760000,25.27 1952-11-20,25.28,25.28,25.28,25.28,1740000,25.28 1952-11-19,25.33,25.33,25.33,25.33,2350000,25.33 1952-11-18,25.16,25.16,25.16,25.16,2250000,25.16 1952-11-17,24.80,24.80,24.80,24.80,1490000,24.80 1952-11-14,24.75,24.75,24.75,24.75,1700000,24.75 1952-11-13,24.71,24.71,24.71,24.71,1330000,24.71 1952-11-12,24.65,24.65,24.65,24.65,1490000,24.65 1952-11-10,24.77,24.77,24.77,24.77,1360000,24.77 1952-11-07,24.78,24.78,24.78,24.78,1540000,24.78 1952-11-06,24.77,24.77,24.77,24.77,1390000,24.77 1952-11-05,24.67,24.67,24.67,24.67,2030000,24.67 1952-11-03,24.60,24.60,24.60,24.60,1670000,24.60 1952-10-31,24.52,24.52,24.52,24.52,1760000,24.52 1952-10-30,24.15,24.15,24.15,24.15,1090000,24.15 1952-10-29,24.15,24.15,24.15,24.15,1020000,24.15 1952-10-28,24.13,24.13,24.13,24.13,1080000,24.13 1952-10-27,24.09,24.09,24.09,24.09,1000000,24.09 1952-10-24,24.03,24.03,24.03,24.03,1060000,24.03 1952-10-23,23.87,23.87,23.87,23.87,1260000,23.87 1952-10-22,23.80,23.80,23.80,23.80,1160000,23.80 1952-10-21,24.07,24.07,24.07,24.07,990000,24.07 1952-10-20,24.13,24.13,24.13,24.13,1050000,24.13 1952-10-17,24.20,24.20,24.20,24.20,1360000,24.20 1952-10-16,23.91,23.91,23.91,23.91,1730000,23.91 1952-10-15,24.06,24.06,24.06,24.06,1730000,24.06 1952-10-14,24.48,24.48,24.48,24.48,1130000,24.48 1952-10-10,24.55,24.55,24.55,24.55,1070000,24.55 1952-10-09,24.57,24.57,24.57,24.57,1090000,24.57 1952-10-08,24.58,24.58,24.58,24.58,1260000,24.58 1952-10-07,24.40,24.40,24.40,24.40,950000,24.40 1952-10-06,24.44,24.44,24.44,24.44,1070000,24.44 1952-10-03,24.50,24.50,24.50,24.50,980000,24.50 1952-10-02,24.52,24.52,24.52,24.52,1040000,24.52 1952-10-01,24.48,24.48,24.48,24.48,1060000,24.48 1952-09-30,24.54,24.54,24.54,24.54,1120000,24.54 1952-09-29,24.68,24.68,24.68,24.68,970000,24.68 1952-09-26,24.73,24.73,24.73,24.73,1180000,24.73 1952-09-25,24.81,24.81,24.81,24.81,1210000,24.81 1952-09-24,24.79,24.79,24.79,24.79,1390000,24.79 1952-09-23,24.70,24.70,24.70,24.70,1240000,24.70 1952-09-22,24.59,24.59,24.59,24.59,1160000,24.59 1952-09-19,24.57,24.57,24.57,24.57,1150000,24.57 1952-09-18,24.51,24.51,24.51,24.51,1030000,24.51 1952-09-17,24.58,24.58,24.58,24.58,1000000,24.58 1952-09-16,24.53,24.53,24.53,24.53,1140000,24.53 1952-09-15,24.45,24.45,24.45,24.45,1100000,24.45 1952-09-12,24.71,24.71,24.71,24.71,1040000,24.71 1952-09-11,24.72,24.72,24.72,24.72,970000,24.72 1952-09-10,24.69,24.69,24.69,24.69,1590000,24.69 1952-09-09,24.86,24.86,24.86,24.86,1310000,24.86 1952-09-08,25.11,25.11,25.11,25.11,1170000,25.11 1952-09-05,25.21,25.21,25.21,25.21,1040000,25.21 1952-09-04,25.24,25.24,25.24,25.24,1120000,25.24 1952-09-03,25.25,25.25,25.25,25.25,1200000,25.25 1952-09-02,25.15,25.15,25.15,25.15,970000,25.15 1952-08-29,25.03,25.03,25.03,25.03,890000,25.03 1952-08-28,24.97,24.97,24.97,24.97,980000,24.97 1952-08-27,24.94,24.94,24.94,24.94,930000,24.94 1952-08-26,24.83,24.83,24.83,24.83,890000,24.83 1952-08-25,24.87,24.87,24.87,24.87,840000,24.87 1952-08-22,24.99,24.99,24.99,24.99,910000,24.99 1952-08-21,24.98,24.98,24.98,24.98,800000,24.98 1952-08-20,24.95,24.95,24.95,24.95,960000,24.95 1952-08-19,24.89,24.89,24.89,24.89,980000,24.89 1952-08-18,24.94,24.94,24.94,24.94,1090000,24.94 1952-08-15,25.20,25.20,25.20,25.20,890000,25.20 1952-08-14,25.28,25.28,25.28,25.28,930000,25.28 1952-08-13,25.28,25.28,25.28,25.28,990000,25.28 1952-08-12,25.31,25.31,25.31,25.31,1110000,25.31 1952-08-11,25.52,25.52,25.52,25.52,1160000,25.52 1952-08-08,25.55,25.55,25.55,25.55,1170000,25.55 1952-08-07,25.52,25.52,25.52,25.52,1180000,25.52 1952-08-06,25.44,25.44,25.44,25.44,1140000,25.44 1952-08-05,25.46,25.46,25.46,25.46,1050000,25.46 1952-08-04,25.43,25.43,25.43,25.43,950000,25.43 1952-08-01,25.45,25.45,25.45,25.45,1050000,25.45 1952-07-31,25.40,25.40,25.40,25.40,1230000,25.40 1952-07-30,25.37,25.37,25.37,25.37,1240000,25.37 1952-07-29,25.26,25.26,25.26,25.26,1010000,25.26 1952-07-28,25.20,25.20,25.20,25.20,1030000,25.20 1952-07-25,25.16,25.16,25.16,25.16,1130000,25.16 1952-07-24,25.24,25.24,25.24,25.24,1270000,25.24 1952-07-23,25.11,25.11,25.11,25.11,1020000,25.11 1952-07-22,25.00,25.00,25.00,25.00,910000,25.00 1952-07-21,24.95,24.95,24.95,24.95,780000,24.95 1952-07-18,24.85,24.85,24.85,24.85,1020000,24.85 1952-07-17,25.05,25.05,25.05,25.05,1010000,25.05 1952-07-16,25.16,25.16,25.16,25.16,1120000,25.16 1952-07-15,25.16,25.16,25.16,25.16,1220000,25.16 1952-07-14,25.03,25.03,25.03,25.03,1090000,25.03 1952-07-11,24.98,24.98,24.98,24.98,1040000,24.98 1952-07-10,24.81,24.81,24.81,24.81,1010000,24.81 1952-07-09,24.86,24.86,24.86,24.86,1120000,24.86 1952-07-08,24.96,24.96,24.96,24.96,850000,24.96 1952-07-07,24.97,24.97,24.97,24.97,1080000,24.97 1952-07-03,25.05,25.05,25.05,25.05,1150000,25.05 1952-07-02,25.06,25.06,25.06,25.06,1320000,25.06 1952-07-01,25.12,25.12,25.12,25.12,1450000,25.12 1952-06-30,24.96,24.96,24.96,24.96,1380000,24.96 1952-06-27,24.83,24.83,24.83,24.83,1210000,24.83 1952-06-26,24.75,24.75,24.75,24.75,1190000,24.75 1952-06-25,24.66,24.66,24.66,24.66,1230000,24.66 1952-06-24,24.60,24.60,24.60,24.60,1200000,24.60 1952-06-23,24.56,24.56,24.56,24.56,1200000,24.56 1952-06-20,24.59,24.59,24.59,24.59,1190000,24.59 1952-06-19,24.51,24.51,24.51,24.51,1320000,24.51 1952-06-18,24.43,24.43,24.43,24.43,1270000,24.43 1952-06-17,24.33,24.33,24.33,24.33,920000,24.33 1952-06-16,24.30,24.30,24.30,24.30,980000,24.30 1952-06-13,24.37,24.37,24.37,24.37,1130000,24.37 1952-06-12,24.31,24.31,24.31,24.31,1370000,24.31 1952-06-11,24.31,24.31,24.31,24.31,1190000,24.31 1952-06-10,24.23,24.23,24.23,24.23,1220000,24.23 1952-06-09,24.37,24.37,24.37,24.37,1270000,24.37 1952-06-06,24.26,24.26,24.26,24.26,1520000,24.26 1952-06-05,24.10,24.10,24.10,24.10,1410000,24.10 1952-06-04,23.95,23.95,23.95,23.95,1200000,23.95 1952-06-03,23.78,23.78,23.78,23.78,940000,23.78 1952-06-02,23.80,23.80,23.80,23.80,1190000,23.80 1952-05-29,23.86,23.86,23.86,23.86,1100000,23.86 1952-05-28,23.84,23.84,23.84,23.84,1130000,23.84 1952-05-27,23.88,23.88,23.88,23.88,1040000,23.88 1952-05-26,23.94,23.94,23.94,23.94,940000,23.94 1952-05-23,23.89,23.89,23.89,23.89,1150000,23.89 1952-05-22,23.91,23.91,23.91,23.91,1360000,23.91 1952-05-21,23.78,23.78,23.78,23.78,1210000,23.78 1952-05-20,23.74,23.74,23.74,23.74,1150000,23.74 1952-05-19,23.61,23.61,23.61,23.61,780000,23.61 1952-05-16,23.56,23.56,23.56,23.56,910000,23.56 1952-05-15,23.60,23.60,23.60,23.60,1050000,23.60 1952-05-14,23.68,23.68,23.68,23.68,950000,23.68 1952-05-13,23.78,23.78,23.78,23.78,890000,23.78 1952-05-12,23.75,23.75,23.75,23.75,800000,23.75 1952-05-09,23.84,23.84,23.84,23.84,960000,23.84 1952-05-08,23.86,23.86,23.86,23.86,1230000,23.86 1952-05-07,23.81,23.81,23.81,23.81,1120000,23.81 1952-05-06,23.67,23.67,23.67,23.67,1120000,23.67 1952-05-05,23.66,23.66,23.66,23.66,860000,23.66 1952-05-02,23.56,23.56,23.56,23.56,1300000,23.56 1952-05-01,23.17,23.17,23.17,23.17,1400000,23.17 1952-04-30,23.32,23.32,23.32,23.32,1000000,23.32 1952-04-29,23.49,23.49,23.49,23.49,1170000,23.49 1952-04-28,23.55,23.55,23.55,23.55,980000,23.55 1952-04-25,23.54,23.54,23.54,23.54,1240000,23.54 1952-04-24,23.43,23.43,23.43,23.43,1580000,23.43 1952-04-23,23.48,23.48,23.48,23.48,1090000,23.48 1952-04-22,23.58,23.58,23.58,23.58,1240000,23.58 1952-04-21,23.69,23.69,23.69,23.69,1110000,23.69 1952-04-18,23.50,23.50,23.50,23.50,1240000,23.50 1952-04-17,23.41,23.41,23.41,23.41,1620000,23.41 1952-04-16,23.58,23.58,23.58,23.58,1400000,23.58 1952-04-15,23.65,23.65,23.65,23.65,1720000,23.65 1952-04-14,23.95,23.95,23.95,23.95,1790000,23.95 1952-04-10,24.11,24.11,24.11,24.11,1130000,24.11 1952-04-09,23.94,23.94,23.94,23.94,980000,23.94 1952-04-08,23.91,23.91,23.91,23.91,1090000,23.91 1952-04-07,23.80,23.80,23.80,23.80,1230000,23.80 1952-04-04,24.02,24.02,24.02,24.02,1190000,24.02 1952-04-03,24.12,24.12,24.12,24.12,1280000,24.12 1952-04-02,24.12,24.12,24.12,24.12,1260000,24.12 1952-04-01,24.18,24.18,24.18,24.18,1720000,24.18 1952-03-31,24.37,24.37,24.37,24.37,1680000,24.37 1952-03-28,24.18,24.18,24.18,24.18,1560000,24.18 1952-03-27,23.99,23.99,23.99,23.99,1370000,23.99 1952-03-26,23.78,23.78,23.78,23.78,1030000,23.78 1952-03-25,23.79,23.79,23.79,23.79,1060000,23.79 1952-03-24,23.93,23.93,23.93,23.93,1040000,23.93 1952-03-21,23.93,23.93,23.93,23.93,1290000,23.93 1952-03-20,23.89,23.89,23.89,23.89,1240000,23.89 1952-03-19,23.82,23.82,23.82,23.82,1090000,23.82 1952-03-18,23.87,23.87,23.87,23.87,1170000,23.87 1952-03-17,23.92,23.92,23.92,23.92,1150000,23.92 1952-03-14,23.75,23.75,23.75,23.75,1350000,23.75 1952-03-13,23.75,23.75,23.75,23.75,1270000,23.75 1952-03-12,23.73,23.73,23.73,23.73,1310000,23.73 1952-03-11,23.62,23.62,23.62,23.62,1210000,23.62 1952-03-10,23.60,23.60,23.60,23.60,1170000,23.60 1952-03-07,23.72,23.72,23.72,23.72,1410000,23.72 1952-03-06,23.69,23.69,23.69,23.69,1210000,23.69 1952-03-05,23.71,23.71,23.71,23.71,1380000,23.71 1952-03-04,23.68,23.68,23.68,23.68,1570000,23.68 1952-03-03,23.29,23.29,23.29,23.29,1020000,23.29 1952-02-29,23.26,23.26,23.26,23.26,1000000,23.26 1952-02-28,23.29,23.29,23.29,23.29,1150000,23.29 1952-02-27,23.18,23.18,23.18,23.18,1260000,23.18 1952-02-26,23.15,23.15,23.15,23.15,1080000,23.15 1952-02-25,23.23,23.23,23.23,23.23,1200000,23.23 1952-02-21,23.16,23.16,23.16,23.16,1360000,23.16 1952-02-20,23.09,23.09,23.09,23.09,1970000,23.09 1952-02-19,23.36,23.36,23.36,23.36,1630000,23.36 1952-02-18,23.74,23.74,23.74,23.74,1140000,23.74 1952-02-15,23.86,23.86,23.86,23.86,1200000,23.86 1952-02-14,23.87,23.87,23.87,23.87,1340000,23.87 1952-02-13,23.92,23.92,23.92,23.92,1300000,23.92 1952-02-11,24.11,24.11,24.11,24.11,1140000,24.11 1952-02-08,24.24,24.24,24.24,24.24,1350000,24.24 1952-02-07,24.11,24.11,24.11,24.11,1170000,24.11 1952-02-06,24.18,24.18,24.18,24.18,1310000,24.18 1952-02-05,24.11,24.11,24.11,24.11,1590000,24.11 1952-02-04,24.12,24.12,24.12,24.12,1640000,24.12 1952-02-01,24.30,24.30,24.30,24.30,1350000,24.30 1952-01-31,24.14,24.14,24.14,24.14,1810000,24.14 1952-01-30,24.23,24.23,24.23,24.23,1880000,24.23 1952-01-29,24.57,24.57,24.57,24.57,1730000,24.57 1952-01-28,24.61,24.61,24.61,24.61,1590000,24.61 1952-01-25,24.55,24.55,24.55,24.55,1650000,24.55 1952-01-24,24.56,24.56,24.56,24.56,1570000,24.56 1952-01-23,24.54,24.54,24.54,24.54,1680000,24.54 1952-01-22,24.66,24.66,24.66,24.66,1920000,24.66 1952-01-21,24.46,24.46,24.46,24.46,1730000,24.46 1952-01-18,24.25,24.25,24.25,24.25,1740000,24.25 1952-01-17,24.20,24.20,24.20,24.20,1590000,24.20 1952-01-16,24.09,24.09,24.09,24.09,1430000,24.09 1952-01-15,24.06,24.06,24.06,24.06,1340000,24.06 1952-01-14,24.16,24.16,24.16,24.16,1510000,24.16 1952-01-11,23.98,23.98,23.98,23.98,1760000,23.98 1952-01-10,23.86,23.86,23.86,23.86,1520000,23.86 1952-01-09,23.74,23.74,23.74,23.74,1370000,23.74 1952-01-08,23.82,23.82,23.82,23.82,1390000,23.82 1952-01-07,23.91,23.91,23.91,23.91,1540000,23.91 1952-01-04,23.92,23.92,23.92,23.92,1480000,23.92 1952-01-03,23.88,23.88,23.88,23.88,1220000,23.88 1952-01-02,23.80,23.80,23.80,23.80,1070000,23.80 1951-12-31,23.77,23.77,23.77,23.77,1440000,23.77 1951-12-28,23.69,23.69,23.69,23.69,1470000,23.69 1951-12-27,23.65,23.65,23.65,23.65,1460000,23.65 1951-12-26,23.44,23.44,23.44,23.44,1520000,23.44 1951-12-24,23.54,23.54,23.54,23.54,680000,23.54 1951-12-21,23.51,23.51,23.51,23.51,1250000,23.51 1951-12-20,23.57,23.57,23.57,23.57,1340000,23.57 1951-12-19,23.57,23.57,23.57,23.57,1510000,23.57 1951-12-18,23.49,23.49,23.49,23.49,1290000,23.49 1951-12-17,23.41,23.41,23.41,23.41,1220000,23.41 1951-12-14,23.37,23.37,23.37,23.37,1360000,23.37 1951-12-13,23.39,23.39,23.39,23.39,1380000,23.39 1951-12-12,23.37,23.37,23.37,23.37,1280000,23.37 1951-12-11,23.30,23.30,23.30,23.30,1360000,23.30 1951-12-10,23.42,23.42,23.42,23.42,1340000,23.42 1951-12-07,23.38,23.38,23.38,23.38,1990000,23.38 1951-12-06,23.34,23.34,23.34,23.34,1840000,23.34 1951-12-05,23.07,23.07,23.07,23.07,1330000,23.07 1951-12-04,23.14,23.14,23.14,23.14,1280000,23.14 1951-12-03,23.01,23.01,23.01,23.01,1220000,23.01 1951-11-30,22.88,22.88,22.88,22.88,1530000,22.88 1951-11-29,22.67,22.67,22.67,22.67,1070000,22.67 1951-11-28,22.61,22.61,22.61,22.61,1150000,22.61 1951-11-27,22.66,22.66,22.66,22.66,1310000,22.66 1951-11-26,22.43,22.43,22.43,22.43,1180000,22.43 1951-11-23,22.40,22.40,22.40,22.40,1210000,22.40 1951-11-21,22.64,22.64,22.64,22.64,1090000,22.64 1951-11-20,22.68,22.68,22.68,22.68,1130000,22.68 1951-11-19,22.73,22.73,22.73,22.73,1030000,22.73 1951-11-16,22.82,22.82,22.82,22.82,1140000,22.82 1951-11-15,22.84,22.84,22.84,22.84,1200000,22.84 1951-11-14,22.85,22.85,22.85,22.85,1220000,22.85 1951-11-13,22.79,22.79,22.79,22.79,1160000,22.79 1951-11-09,22.75,22.75,22.75,22.75,1470000,22.75 1951-11-08,22.47,22.47,22.47,22.47,1410000,22.47 1951-11-07,22.49,22.49,22.49,22.49,1490000,22.49 1951-11-05,22.82,22.82,22.82,22.82,1130000,22.82 1951-11-02,22.93,22.93,22.93,22.93,1230000,22.93 1951-11-01,23.10,23.10,23.10,23.10,1430000,23.10 1951-10-31,22.94,22.94,22.94,22.94,1490000,22.94 1951-10-30,22.66,22.66,22.66,22.66,1530000,22.66 1951-10-29,22.69,22.69,22.69,22.69,1780000,22.69 1951-10-26,22.81,22.81,22.81,22.81,1710000,22.81 1951-10-25,22.96,22.96,22.96,22.96,1360000,22.96 1951-10-24,23.03,23.03,23.03,23.03,1670000,23.03 1951-10-23,22.84,22.84,22.84,22.84,2110000,22.84 1951-10-22,22.75,22.75,22.75,22.75,2690000,22.75 1951-10-19,23.32,23.32,23.32,23.32,1990000,23.32 1951-10-18,23.67,23.67,23.67,23.67,1450000,23.67 1951-10-17,23.69,23.69,23.69,23.69,1460000,23.69 1951-10-16,23.77,23.77,23.77,23.77,1730000,23.77 1951-10-15,23.85,23.85,23.85,23.85,1720000,23.85 1951-10-11,23.70,23.70,23.70,23.70,1760000,23.70 1951-10-10,23.61,23.61,23.61,23.61,1320000,23.61 1951-10-09,23.65,23.65,23.65,23.65,1750000,23.65 1951-10-08,23.75,23.75,23.75,23.75,1860000,23.75 1951-10-05,23.78,23.78,23.78,23.78,2080000,23.78 1951-10-04,23.72,23.72,23.72,23.72,1810000,23.72 1951-10-03,23.79,23.79,23.79,23.79,2780000,23.79 1951-10-02,23.64,23.64,23.64,23.64,1870000,23.64 1951-10-01,23.47,23.47,23.47,23.47,1330000,23.47 1951-09-28,23.26,23.26,23.26,23.26,1390000,23.26 1951-09-27,23.27,23.27,23.27,23.27,1540000,23.27 1951-09-26,23.40,23.40,23.40,23.40,1520000,23.40 1951-09-25,23.38,23.38,23.38,23.38,1740000,23.38 1951-09-24,23.30,23.30,23.30,23.30,1630000,23.30 1951-09-21,23.40,23.40,23.40,23.40,2180000,23.40 1951-09-20,23.57,23.57,23.57,23.57,2100000,23.57 1951-09-19,23.59,23.59,23.59,23.59,2070000,23.59 1951-09-18,23.59,23.59,23.59,23.59,2030000,23.59 1951-09-17,23.62,23.62,23.62,23.62,1800000,23.62 1951-09-14,23.69,23.69,23.69,23.69,2170000,23.69 1951-09-13,23.71,23.71,23.71,23.71,2350000,23.71 1951-09-12,23.60,23.60,23.60,23.60,2180000,23.60 1951-09-11,23.50,23.50,23.50,23.50,2040000,23.50 1951-09-10,23.62,23.62,23.62,23.62,2190000,23.62 1951-09-07,23.53,23.53,23.53,23.53,1970000,23.53 1951-09-06,23.47,23.47,23.47,23.47,2150000,23.47 1951-09-05,23.42,23.42,23.42,23.42,1850000,23.42 1951-09-04,23.28,23.28,23.28,23.28,1520000,23.28 1951-08-31,23.28,23.28,23.28,23.28,1530000,23.28 1951-08-30,23.24,23.24,23.24,23.24,1950000,23.24 1951-08-29,23.08,23.08,23.08,23.08,1520000,23.08 1951-08-28,22.90,22.90,22.90,22.90,1280000,22.90 1951-08-27,22.85,22.85,22.85,22.85,1080000,22.85 1951-08-24,22.88,22.88,22.88,22.88,1210000,22.88 1951-08-23,22.90,22.90,22.90,22.90,1230000,22.90 1951-08-22,22.75,22.75,22.75,22.75,1130000,22.75 1951-08-21,22.83,22.83,22.83,22.83,1400000,22.83 1951-08-20,22.93,22.93,22.93,22.93,1130000,22.93 1951-08-17,22.94,22.94,22.94,22.94,1620000,22.94 1951-08-16,22.87,22.87,22.87,22.87,1750000,22.87 1951-08-15,22.79,22.79,22.79,22.79,1340000,22.79 1951-08-14,22.70,22.70,22.70,22.70,1180000,22.70 1951-08-13,22.80,22.80,22.80,22.80,1320000,22.80 1951-08-10,22.79,22.79,22.79,22.79,1260000,22.79 1951-08-09,22.84,22.84,22.84,22.84,1500000,22.84 1951-08-08,22.93,22.93,22.93,22.93,1410000,22.93 1951-08-07,23.03,23.03,23.03,23.03,1810000,23.03 1951-08-06,23.01,23.01,23.01,23.01,1600000,23.01 1951-08-03,22.85,22.85,22.85,22.85,1570000,22.85 1951-08-02,22.82,22.82,22.82,22.82,2130000,22.82 1951-08-01,22.51,22.51,22.51,22.51,1680000,22.51 1951-07-31,22.40,22.40,22.40,22.40,1550000,22.40 1951-07-30,22.63,22.63,22.63,22.63,1600000,22.63 1951-07-27,22.53,22.53,22.53,22.53,1450000,22.53 1951-07-26,22.47,22.47,22.47,22.47,1480000,22.47 1951-07-25,22.32,22.32,22.32,22.32,1870000,22.32 1951-07-24,22.44,22.44,22.44,22.44,1740000,22.44 1951-07-23,22.10,22.10,22.10,22.10,1320000,22.10 1951-07-20,21.88,21.88,21.88,21.88,1390000,21.88 1951-07-19,21.84,21.84,21.84,21.84,1120000,21.84 1951-07-18,21.88,21.88,21.88,21.88,1370000,21.88 1951-07-17,21.92,21.92,21.92,21.92,1280000,21.92 1951-07-16,21.73,21.73,21.73,21.73,1200000,21.73 1951-07-13,21.98,21.98,21.98,21.98,1320000,21.98 1951-07-12,21.80,21.80,21.80,21.80,1050000,21.80 1951-07-11,21.68,21.68,21.68,21.68,970000,21.68 1951-07-10,21.63,21.63,21.63,21.63,990000,21.63 1951-07-09,21.73,21.73,21.73,21.73,1110000,21.73 1951-07-06,21.64,21.64,21.64,21.64,1170000,21.64 1951-07-05,21.64,21.64,21.64,21.64,1410000,21.64 1951-07-03,21.23,21.23,21.23,21.23,1250000,21.23 1951-07-02,21.10,21.10,21.10,21.10,1350000,21.10 1951-06-29,20.96,20.96,20.96,20.96,1730000,20.96 1951-06-28,21.10,21.10,21.10,21.10,1940000,21.10 1951-06-27,21.37,21.37,21.37,21.37,1360000,21.37 1951-06-26,21.30,21.30,21.30,21.30,1260000,21.30 1951-06-25,21.29,21.29,21.29,21.29,2440000,21.29 1951-06-22,21.55,21.55,21.55,21.55,1340000,21.55 1951-06-21,21.78,21.78,21.78,21.78,1100000,21.78 1951-06-20,21.91,21.91,21.91,21.91,1120000,21.91 1951-06-19,22.02,22.02,22.02,22.02,1100000,22.02 1951-06-18,22.05,22.05,22.05,22.05,1050000,22.05 1951-06-15,22.04,22.04,22.04,22.04,1370000,22.04 1951-06-14,21.84,21.84,21.84,21.84,1300000,21.84 1951-06-13,21.55,21.55,21.55,21.55,1060000,21.55 1951-06-12,21.52,21.52,21.52,21.52,1200000,21.52 1951-06-11,21.61,21.61,21.61,21.61,1220000,21.61 1951-06-08,21.49,21.49,21.49,21.49,1000000,21.49 1951-06-07,21.56,21.56,21.56,21.56,1340000,21.56 1951-06-06,21.48,21.48,21.48,21.48,1200000,21.48 1951-06-05,21.33,21.33,21.33,21.33,1180000,21.33 1951-06-04,21.24,21.24,21.24,21.24,1100000,21.24 1951-06-01,21.48,21.48,21.48,21.48,9810000,21.48 1951-05-31,21.52,21.52,21.52,21.52,1220000,21.52 1951-05-29,21.35,21.35,21.35,21.35,1190000,21.35 1951-05-28,21.21,21.21,21.21,21.21,1240000,21.21 1951-05-25,21.03,21.03,21.03,21.03,1210000,21.03 1951-05-24,21.05,21.05,21.05,21.05,2580000,21.05 1951-05-23,21.16,21.16,21.16,21.16,1540000,21.16 1951-05-22,21.36,21.36,21.36,21.36,1440000,21.36 1951-05-21,21.46,21.46,21.46,21.46,1580000,21.46 1951-05-18,21.51,21.51,21.51,21.51,1660000,21.51 1951-05-17,21.91,21.91,21.91,21.91,1370000,21.91 1951-05-16,21.69,21.69,21.69,21.69,1660000,21.69 1951-05-15,21.76,21.76,21.76,21.76,2020000,21.76 1951-05-14,22.18,22.18,22.18,22.18,1250000,22.18 1951-05-11,22.33,22.33,22.33,22.33,1640000,22.33 1951-05-10,22.51,22.51,22.51,22.51,1660000,22.51 1951-05-09,22.64,22.64,22.64,22.64,1960000,22.64 1951-05-08,22.61,22.61,22.61,22.61,1600000,22.61 1951-05-07,22.63,22.63,22.63,22.63,1580000,22.63 1951-05-04,22.77,22.77,22.77,22.77,2050000,22.77 1951-05-03,22.81,22.81,22.81,22.81,2060000,22.81 1951-05-02,22.62,22.62,22.62,22.62,1900000,22.62 1951-05-01,22.53,22.53,22.53,22.53,1760000,22.53 1951-04-30,22.43,22.43,22.43,22.43,1790000,22.43 1951-04-27,22.39,22.39,22.39,22.39,2120000,22.39 1951-04-26,22.16,22.16,22.16,22.16,1800000,22.16 1951-04-25,21.97,21.97,21.97,21.97,1520000,21.97 1951-04-24,21.96,21.96,21.96,21.96,1420000,21.96 1951-04-23,22.05,22.05,22.05,22.05,1160000,22.05 1951-04-20,22.04,22.04,22.04,22.04,940000,22.04 1951-04-19,22.04,22.04,22.04,22.04,1520000,22.04 1951-04-18,22.13,22.13,22.13,22.13,1780000,22.13 1951-04-17,22.09,22.09,22.09,22.09,1470000,22.09 1951-04-16,22.04,22.04,22.04,22.04,1730000,22.04 1951-04-13,22.09,22.09,22.09,22.09,2120000,22.09 1951-04-12,21.83,21.83,21.83,21.83,1530000,21.83 1951-04-11,21.64,21.64,21.64,21.64,1420000,21.64 1951-04-10,21.65,21.65,21.65,21.65,1280000,21.65 1951-04-09,21.68,21.68,21.68,21.68,1110000,21.68 1951-04-06,21.72,21.72,21.72,21.72,1450000,21.72 1951-04-05,21.69,21.69,21.69,21.69,1790000,21.69 1951-04-04,21.40,21.40,21.40,21.40,1300000,21.40 1951-04-03,21.26,21.26,21.26,21.26,1220000,21.26 1951-04-02,21.32,21.32,21.32,21.32,1280000,21.32 1951-03-30,21.48,21.48,21.48,21.48,1150000,21.48 1951-03-29,21.33,21.33,21.33,21.33,1300000,21.33 1951-03-28,21.26,21.26,21.26,21.26,1770000,21.26 1951-03-27,21.51,21.51,21.51,21.51,1250000,21.51 1951-03-26,21.53,21.53,21.53,21.53,1230000,21.53 1951-03-22,21.73,21.73,21.73,21.73,1290000,21.73 1951-03-21,21.64,21.64,21.64,21.64,1310000,21.64 1951-03-20,21.52,21.52,21.52,21.52,1020000,21.52 1951-03-19,21.56,21.56,21.56,21.56,1120000,21.56 1951-03-16,21.64,21.64,21.64,21.64,1660000,21.64 1951-03-15,21.29,21.29,21.29,21.29,2070000,21.29 1951-03-14,21.25,21.25,21.25,21.25,2110000,21.25 1951-03-13,21.41,21.41,21.41,21.41,2330000,21.41 1951-03-12,21.70,21.70,21.70,21.70,1640000,21.70 1951-03-09,21.95,21.95,21.95,21.95,1610000,21.95 1951-03-08,21.95,21.95,21.95,21.95,1440000,21.95 1951-03-07,21.86,21.86,21.86,21.86,1770000,21.86 1951-03-06,21.79,21.79,21.79,21.79,1490000,21.79 1951-03-05,21.79,21.79,21.79,21.79,1690000,21.79 1951-03-02,21.93,21.93,21.93,21.93,1570000,21.93 1951-03-01,21.85,21.85,21.85,21.85,1610000,21.85 1951-02-28,21.80,21.80,21.80,21.80,1640000,21.80 1951-02-27,21.76,21.76,21.76,21.76,1680000,21.76 1951-02-26,21.93,21.93,21.93,21.93,1650000,21.93 1951-02-23,21.92,21.92,21.92,21.92,1540000,21.92 1951-02-21,21.86,21.86,21.86,21.86,1670000,21.86 1951-02-20,21.79,21.79,21.79,21.79,2010000,21.79 1951-02-19,21.83,21.83,21.83,21.83,1910000,21.83 1951-02-16,22.13,22.13,22.13,22.13,1860000,22.13 1951-02-15,22.00,22.00,22.00,22.00,1700000,22.00 1951-02-14,22.12,22.12,22.12,22.12,2050000,22.12 1951-02-13,22.18,22.18,22.18,22.18,2400000,22.18 1951-02-09,22.17,22.17,22.17,22.17,2550000,22.17 1951-02-08,22.09,22.09,22.09,22.09,2120000,22.09 1951-02-07,21.99,21.99,21.99,21.99,2020000,21.99 1951-02-06,22.12,22.12,22.12,22.12,2370000,22.12 1951-02-05,22.20,22.20,22.20,22.20,2680000,22.20 1951-02-02,21.96,21.96,21.96,21.96,3030000,21.96 1951-02-01,21.77,21.77,21.77,21.77,2380000,21.77 1951-01-31,21.66,21.66,21.66,21.66,2340000,21.66 1951-01-30,21.74,21.74,21.74,21.74,2480000,21.74 1951-01-29,21.67,21.67,21.67,21.67,2630000,21.67 1951-01-26,21.26,21.26,21.26,21.26,2230000,21.26 1951-01-25,21.03,21.03,21.03,21.03,2520000,21.03 1951-01-24,21.16,21.16,21.16,21.16,1990000,21.16 1951-01-23,21.26,21.26,21.26,21.26,2080000,21.26 1951-01-22,21.18,21.18,21.18,21.18,2570000,21.18 1951-01-19,21.36,21.36,21.36,21.36,3170000,21.36 1951-01-18,21.40,21.40,21.40,21.40,3490000,21.40 1951-01-17,21.55,21.55,21.55,21.55,3880000,21.55 1951-01-16,21.46,21.46,21.46,21.46,3740000,21.46 1951-01-15,21.30,21.30,21.30,21.30,2830000,21.30 1951-01-12,21.11,21.11,21.11,21.11,2950000,21.11 1951-01-11,21.19,21.19,21.19,21.19,3490000,21.19 1951-01-10,20.85,20.85,20.85,20.85,3270000,20.85 1951-01-09,21.12,21.12,21.12,21.12,3800000,21.12 1951-01-08,21.00,21.00,21.00,21.00,2780000,21.00 1951-01-05,20.87,20.87,20.87,20.87,3390000,20.87 1951-01-04,20.87,20.87,20.87,20.87,3390000,20.87 1951-01-03,20.69,20.69,20.69,20.69,3370000,20.69 1951-01-02,20.77,20.77,20.77,20.77,3030000,20.77 1950-12-29,20.43,20.43,20.43,20.43,3440000,20.43 1950-12-28,20.38,20.38,20.38,20.38,3560000,20.38 1950-12-27,20.30,20.30,20.30,20.30,2940000,20.30 1950-12-26,19.92,19.92,19.92,19.92,2660000,19.92 1950-12-22,20.07,20.07,20.07,20.07,2720000,20.07 1950-12-21,19.98,19.98,19.98,19.98,3990000,19.98 1950-12-20,19.97,19.97,19.97,19.97,3510000,19.97 1950-12-19,19.96,19.96,19.96,19.96,3650000,19.96 1950-12-18,19.85,19.85,19.85,19.85,4500000,19.85 1950-12-15,19.33,19.33,19.33,19.33,2420000,19.33 1950-12-14,19.43,19.43,19.43,19.43,2660000,19.43 1950-12-13,19.67,19.67,19.67,19.67,2030000,19.67 1950-12-12,19.68,19.68,19.68,19.68,2140000,19.68 1950-12-11,19.72,19.72,19.72,19.72,2600000,19.72 1950-12-08,19.40,19.40,19.40,19.40,2310000,19.40 1950-12-07,19.40,19.40,19.40,19.40,1810000,19.40 1950-12-06,19.45,19.45,19.45,19.45,2010000,19.45 1950-12-05,19.31,19.31,19.31,19.31,1940000,19.31 1950-12-04,19.00,19.00,19.00,19.00,2510000,19.00 1950-12-01,19.66,19.66,19.66,19.66,1870000,19.66 1950-11-30,19.51,19.51,19.51,19.51,2080000,19.51 1950-11-29,19.37,19.37,19.37,19.37,2770000,19.37 1950-11-28,19.56,19.56,19.56,19.56,2970000,19.56 1950-11-27,20.18,20.18,20.18,20.18,1740000,20.18 1950-11-24,20.32,20.32,20.32,20.32,2620000,20.32 1950-11-22,20.16,20.16,20.16,20.16,2730000,20.16 1950-11-21,19.88,19.88,19.88,19.88,2010000,19.88 1950-11-20,19.93,19.93,19.93,19.93,2250000,19.93 1950-11-17,19.86,19.86,19.86,19.86,2130000,19.86 1950-11-16,19.72,19.72,19.72,19.72,1760000,19.72 1950-11-15,19.82,19.82,19.82,19.82,1620000,19.82 1950-11-14,19.86,19.86,19.86,19.86,1780000,19.86 1950-11-13,20.01,20.01,20.01,20.01,1630000,20.01 1950-11-10,19.94,19.94,19.94,19.94,1640000,19.94 1950-11-09,19.79,19.79,19.79,19.79,1760000,19.79 1950-11-08,19.56,19.56,19.56,19.56,1850000,19.56 1950-11-06,19.36,19.36,19.36,19.36,2580000,19.36 1950-11-03,19.85,19.85,19.85,19.85,1560000,19.85 1950-11-02,19.73,19.73,19.73,19.73,1580000,19.73 1950-11-01,19.56,19.56,19.56,19.56,1780000,19.56 1950-10-31,19.53,19.53,19.53,19.53,2010000,19.53 1950-10-30,19.61,19.61,19.61,19.61,1790000,19.61 1950-10-27,19.77,19.77,19.77,19.77,1800000,19.77 1950-10-26,19.61,19.61,19.61,19.61,3000000,19.61 1950-10-25,20.05,20.05,20.05,20.05,1930000,20.05 1950-10-24,20.08,20.08,20.08,20.08,1790000,20.08 1950-10-23,19.96,19.96,19.96,19.96,1850000,19.96 1950-10-20,19.96,19.96,19.96,19.96,1840000,19.96 1950-10-19,20.02,20.02,20.02,20.02,2250000,20.02 1950-10-18,20.01,20.01,20.01,20.01,2410000,20.01 1950-10-17,19.89,19.89,19.89,19.89,2010000,19.89 1950-10-16,19.71,19.71,19.71,19.71,1630000,19.71 1950-10-13,19.85,19.85,19.85,19.85,2030000,19.85 1950-10-11,19.86,19.86,19.86,19.86,2200000,19.86 1950-10-10,19.78,19.78,19.78,19.78,1870000,19.78 1950-10-09,20.00,20.00,20.00,20.00,2330000,20.00 1950-10-06,20.12,20.12,20.12,20.12,2360000,20.12 1950-10-05,19.89,19.89,19.89,19.89,2490000,19.89 1950-10-04,20.00,20.00,20.00,20.00,2920000,20.00 1950-10-03,19.66,19.66,19.66,19.66,2480000,19.66 1950-10-02,19.69,19.69,19.69,19.69,2200000,19.69 1950-09-29,19.45,19.45,19.45,19.45,1800000,19.45 1950-09-28,19.42,19.42,19.42,19.42,2200000,19.42 1950-09-27,19.41,19.41,19.41,19.41,2360000,19.41 1950-09-26,19.14,19.14,19.14,19.14,2280000,19.14 1950-09-25,19.42,19.42,19.42,19.42,2020000,19.42 1950-09-22,19.44,19.44,19.44,19.44,2510000,19.44 1950-09-21,19.37,19.37,19.37,19.37,1650000,19.37 1950-09-20,19.21,19.21,19.21,19.21,2100000,19.21 1950-09-19,19.31,19.31,19.31,19.31,1590000,19.31 1950-09-18,19.37,19.37,19.37,19.37,2040000,19.37 1950-09-15,19.29,19.29,19.29,19.29,2410000,19.29 1950-09-14,19.18,19.18,19.18,19.18,2350000,19.18 1950-09-13,19.09,19.09,19.09,19.09,2600000,19.09 1950-09-12,18.87,18.87,18.87,18.87,1680000,18.87 1950-09-11,18.61,18.61,18.61,18.61,1860000,18.61 1950-09-08,18.75,18.75,18.75,18.75,1960000,18.75 1950-09-07,18.59,18.59,18.59,18.59,1340000,18.59 1950-09-06,18.54,18.54,18.54,18.54,1300000,18.54 1950-09-05,18.68,18.68,18.68,18.68,1250000,18.68 1950-09-01,18.55,18.55,18.55,18.55,1290000,18.55 1950-08-31,18.42,18.42,18.42,18.42,1140000,18.42 1950-08-30,18.43,18.43,18.43,18.43,1490000,18.43 1950-08-29,18.54,18.54,18.54,18.54,1890000,18.54 1950-08-28,18.53,18.53,18.53,18.53,1300000,18.53 1950-08-25,18.54,18.54,18.54,18.54,1610000,18.54 1950-08-24,18.79,18.79,18.79,18.79,1620000,18.79 1950-08-23,18.82,18.82,18.82,18.82,1580000,18.82 1950-08-22,18.68,18.68,18.68,18.68,1550000,18.68 1950-08-21,18.70,18.70,18.70,18.70,1840000,18.70 1950-08-18,18.68,18.68,18.68,18.68,1780000,18.68 1950-08-17,18.54,18.54,18.54,18.54,2170000,18.54 1950-08-16,18.34,18.34,18.34,18.34,1770000,18.34 1950-08-15,18.32,18.32,18.32,18.32,1330000,18.32 1950-08-14,18.29,18.29,18.29,18.29,1280000,18.29 1950-08-11,18.28,18.28,18.28,18.28,1680000,18.28 1950-08-10,18.48,18.48,18.48,18.48,1870000,18.48 1950-08-09,18.61,18.61,18.61,18.61,1760000,18.61 1950-08-08,18.46,18.46,18.46,18.46,2180000,18.46 1950-08-07,18.41,18.41,18.41,18.41,1850000,18.41 1950-08-04,18.14,18.14,18.14,18.14,1600000,18.14 1950-08-03,17.99,17.99,17.99,17.99,1660000,17.99 1950-08-02,17.95,17.95,17.95,17.95,1980000,17.95 1950-08-01,18.02,18.02,18.02,18.02,1970000,18.02 1950-07-31,17.84,17.84,17.84,17.84,1590000,17.84 1950-07-28,17.69,17.69,17.69,17.69,2050000,17.69 1950-07-27,17.50,17.50,17.50,17.50,2300000,17.50 1950-07-26,17.27,17.27,17.27,17.27,2460000,17.27 1950-07-25,17.23,17.23,17.23,17.23,2770000,17.23 1950-07-24,17.48,17.48,17.48,17.48,2300000,17.48 1950-07-21,17.59,17.59,17.59,17.59,2810000,17.59 1950-07-20,17.61,17.61,17.61,17.61,3160000,17.61 1950-07-19,17.36,17.36,17.36,17.36,2430000,17.36 1950-07-18,17.06,17.06,17.06,17.06,1820000,17.06 1950-07-17,16.68,16.68,16.68,16.68,1520000,16.68 1950-07-14,16.87,16.87,16.87,16.87,1900000,16.87 1950-07-13,16.69,16.69,16.69,16.69,2660000,16.69 1950-07-12,16.87,16.87,16.87,16.87,3200000,16.87 1950-07-11,17.32,17.32,17.32,17.32,3250000,17.32 1950-07-10,17.59,17.59,17.59,17.59,1960000,17.59 1950-07-07,17.67,17.67,17.67,17.67,1870000,17.67 1950-07-06,17.91,17.91,17.91,17.91,1570000,17.91 1950-07-05,17.81,17.81,17.81,17.81,1400000,17.81 1950-07-03,17.64,17.64,17.64,17.64,1550000,17.64 1950-06-30,17.69,17.69,17.69,17.69,2660000,17.69 1950-06-29,17.44,17.44,17.44,17.44,3040000,17.44 1950-06-28,18.11,18.11,18.11,18.11,2600000,18.11 1950-06-27,17.91,17.91,17.91,17.91,4860000,17.91 1950-06-26,18.11,18.11,18.11,18.11,3950000,18.11 1950-06-23,19.14,19.14,19.14,19.14,1700000,19.14 1950-06-22,19.16,19.16,19.16,19.16,1830000,19.16 1950-06-21,19.00,19.00,19.00,19.00,1750000,19.00 1950-06-20,18.83,18.83,18.83,18.83,1470000,18.83 1950-06-19,18.92,18.92,18.92,18.92,1290000,18.92 1950-06-16,18.97,18.97,18.97,18.97,1180000,18.97 1950-06-15,18.93,18.93,18.93,18.93,1530000,18.93 1950-06-14,18.98,18.98,18.98,18.98,1650000,18.98 1950-06-13,19.25,19.25,19.25,19.25,1790000,19.25 1950-06-12,19.40,19.40,19.40,19.40,1790000,19.40 1950-06-09,19.26,19.26,19.26,19.26,2130000,19.26 1950-06-08,19.14,19.14,19.14,19.14,1780000,19.14 1950-06-07,18.93,18.93,18.93,18.93,1750000,18.93 1950-06-06,18.88,18.88,18.88,18.88,2250000,18.88 1950-06-05,18.60,18.60,18.60,18.60,1630000,18.60 1950-06-02,18.79,18.79,18.79,18.79,1450000,18.79 1950-06-01,18.77,18.77,18.77,18.77,1580000,18.77 1950-05-31,18.78,18.78,18.78,18.78,1530000,18.78 1950-05-29,18.72,18.72,18.72,18.72,1110000,18.72 1950-05-26,18.67,18.67,18.67,18.67,1330000,18.67 1950-05-25,18.69,18.69,18.69,18.69,1480000,18.69 1950-05-24,18.69,18.69,18.69,18.69,1850000,18.69 1950-05-23,18.71,18.71,18.71,18.71,1460000,18.71 1950-05-22,18.60,18.60,18.60,18.60,1620000,18.60 1950-05-19,18.68,18.68,18.68,18.68,2110000,18.68 1950-05-18,18.56,18.56,18.56,18.56,5240000,18.56 1950-05-17,18.52,18.52,18.52,18.52,2020000,18.52 1950-05-16,18.44,18.44,18.44,18.44,1730000,18.44 1950-05-15,18.26,18.26,18.26,18.26,1220000,18.26 1950-05-12,18.18,18.18,18.18,18.18,1790000,18.18 1950-05-11,18.29,18.29,18.29,18.29,1750000,18.29 1950-05-10,18.29,18.29,18.29,18.29,1880000,18.29 1950-05-09,18.27,18.27,18.27,18.27,1720000,18.27 1950-05-08,18.27,18.27,18.27,18.27,1680000,18.27 1950-05-05,18.22,18.22,18.22,18.22,1800000,18.22 1950-05-04,18.12,18.12,18.12,18.12,2150000,18.12 1950-05-03,18.27,18.27,18.27,18.27,2120000,18.27 1950-05-02,18.11,18.11,18.11,18.11,2250000,18.11 1950-05-01,18.22,18.22,18.22,18.22,2390000,18.22 1950-04-28,17.96,17.96,17.96,17.96,2190000,17.96 1950-04-27,17.86,17.86,17.86,17.86,2070000,17.86 1950-04-26,17.76,17.76,17.76,17.76,1880000,17.76 1950-04-25,17.83,17.83,17.83,17.83,1830000,17.83 1950-04-24,17.83,17.83,17.83,17.83,2310000,17.83 1950-04-21,17.96,17.96,17.96,17.96,2710000,17.96 1950-04-20,17.93,17.93,17.93,17.93,2590000,17.93 1950-04-19,18.05,18.05,18.05,18.05,2950000,18.05 1950-04-18,18.03,18.03,18.03,18.03,3320000,18.03 1950-04-17,17.88,17.88,17.88,17.88,2520000,17.88 1950-04-14,17.96,17.96,17.96,17.96,2750000,17.96 1950-04-13,17.98,17.98,17.98,17.98,2410000,17.98 1950-04-12,17.94,17.94,17.94,17.94,2010000,17.94 1950-04-11,17.75,17.75,17.75,17.75,2010000,17.75 1950-04-10,17.85,17.85,17.85,17.85,2070000,17.85 1950-04-06,17.78,17.78,17.78,17.78,2000000,17.78 1950-04-05,17.63,17.63,17.63,17.63,1430000,17.63 1950-04-04,17.55,17.55,17.55,17.55,2010000,17.55 1950-04-03,17.53,17.53,17.53,17.53,1570000,17.53 1950-03-31,17.29,17.29,17.29,17.29,1880000,17.29 1950-03-30,17.30,17.30,17.30,17.30,2370000,17.30 1950-03-29,17.44,17.44,17.44,17.44,2090000,17.44 1950-03-28,17.53,17.53,17.53,17.53,1780000,17.53 1950-03-27,17.46,17.46,17.46,17.46,1930000,17.46 1950-03-24,17.56,17.56,17.56,17.56,1570000,17.56 1950-03-23,17.56,17.56,17.56,17.56,2020000,17.56 1950-03-22,17.55,17.55,17.55,17.55,2010000,17.55 1950-03-21,17.45,17.45,17.45,17.45,1400000,17.45 1950-03-20,17.44,17.44,17.44,17.44,1430000,17.44 1950-03-17,17.45,17.45,17.45,17.45,1600000,17.45 1950-03-16,17.49,17.49,17.49,17.49,2060000,17.49 1950-03-15,17.45,17.45,17.45,17.45,1830000,17.45 1950-03-14,17.25,17.25,17.25,17.25,1140000,17.25 1950-03-13,17.12,17.12,17.12,17.12,1060000,17.12 1950-03-10,17.09,17.09,17.09,17.09,1260000,17.09 1950-03-09,17.07,17.07,17.07,17.07,1330000,17.07 1950-03-08,17.19,17.19,17.19,17.19,1360000,17.19 1950-03-07,17.20,17.20,17.20,17.20,1590000,17.20 1950-03-06,17.32,17.32,17.32,17.32,1470000,17.32 1950-03-03,17.29,17.29,17.29,17.29,1520000,17.29 1950-03-02,17.23,17.23,17.23,17.23,1340000,17.23 1950-03-01,17.24,17.24,17.24,17.24,1410000,17.24 1950-02-28,17.22,17.22,17.22,17.22,1310000,17.22 1950-02-27,17.28,17.28,17.28,17.28,1410000,17.28 1950-02-24,17.28,17.28,17.28,17.28,1710000,17.28 1950-02-23,17.21,17.21,17.21,17.21,1310000,17.21 1950-02-21,17.17,17.17,17.17,17.17,1260000,17.17 1950-02-20,17.20,17.20,17.20,17.20,1420000,17.20 1950-02-17,17.15,17.15,17.15,17.15,1940000,17.15 1950-02-16,16.99,16.99,16.99,16.99,1920000,16.99 1950-02-15,17.06,17.06,17.06,17.06,1730000,17.06 1950-02-14,17.06,17.06,17.06,17.06,2210000,17.06 1950-02-10,17.24,17.24,17.24,17.24,1790000,17.24 1950-02-09,17.28,17.28,17.28,17.28,1810000,17.28 1950-02-08,17.21,17.21,17.21,17.21,1470000,17.21 1950-02-07,17.23,17.23,17.23,17.23,1360000,17.23 1950-02-06,17.32,17.32,17.32,17.32,1490000,17.32 1950-02-03,17.29,17.29,17.29,17.29,2210000,17.29 1950-02-02,17.23,17.23,17.23,17.23,2040000,17.23 1950-02-01,17.05,17.05,17.05,17.05,1810000,17.05 1950-01-31,17.05,17.05,17.05,17.05,1690000,17.05 1950-01-30,17.02,17.02,17.02,17.02,1640000,17.02 1950-01-27,16.82,16.82,16.82,16.82,1250000,16.82 1950-01-26,16.73,16.73,16.73,16.73,1150000,16.73 1950-01-25,16.74,16.74,16.74,16.74,1700000,16.74 1950-01-24,16.86,16.86,16.86,16.86,1250000,16.86 1950-01-23,16.92,16.92,16.92,16.92,1340000,16.92 1950-01-20,16.90,16.90,16.90,16.90,1440000,16.90 1950-01-19,16.87,16.87,16.87,16.87,1170000,16.87 1950-01-18,16.85,16.85,16.85,16.85,1570000,16.85 1950-01-17,16.86,16.86,16.86,16.86,1790000,16.86 1950-01-16,16.72,16.72,16.72,16.72,1460000,16.72 1950-01-13,16.67,16.67,16.67,16.67,3330000,16.67 1950-01-12,16.76,16.76,16.76,16.76,2970000,16.76 1950-01-11,17.09,17.09,17.09,17.09,2630000,17.09 1950-01-10,17.03,17.03,17.03,17.03,2160000,17.03 1950-01-09,17.08,17.08,17.08,17.08,2520000,17.08 1950-01-06,16.98,16.98,16.98,16.98,2010000,16.98 1950-01-05,16.93,16.93,16.93,16.93,2550000,16.93 1950-01-04,16.85,16.85,16.85,16.85,1890000,16.85 1950-01-03,16.66,16.66,16.66,16.66,1260000,16.66 statsmodels-0.12.2/statsmodels/sandbox/examples/run_all.py000066400000000000000000000023321400612667500237710ustar00rootroot00000000000000'''run all examples to make sure we do not get an exception Note: If an example contaings plt.show(), then all plot windows have to be closed manually, at least in my setup. uncomment plt.show() to show all plot windows ''' from statsmodels.compat.python import input stop_on_error = True filelist = ['example_pca.py', 'example_sysreg.py', 'example_mle.py', # 'example_gam.py', # exclude, currently we are not working on it 'example_pca_regression.py'] cont = input("""Are you sure you want to run all of the examples? This is done mainly to check that they are up to date. (y/n) >>> """) if 'y' in cont.lower(): for run_all_f in filelist: try: print("Executing example file", run_all_f) print("-----------------------" + "-"*len(run_all_f)) exec(open(run_all_f).read()) except: #f might be overwritten in the executed file print("*********************") print("ERROR in example file", run_all_f) print("**********************" + "*"*len(run_all_f)) if stop_on_error: raise #plt.show() #plt.close('all') #close does not work because I never get here without closing plots manually statsmodels-0.12.2/statsmodels/sandbox/examples/thirdparty/000077500000000000000000000000001400612667500241555ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/examples/thirdparty/ex_ratereturn.py000066400000000000000000000102631400612667500274200ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Playing with correlation of DJ-30 stock returns this uses pickled data that needs to be created with findow.py to see graphs, uncomment plt.show() Created on Sat Jan 30 16:30:18 2010 Author: josef-pktd """ import pickle import numpy as np import matplotlib.pyplot as plt import matplotlib as mpl import statsmodels.sandbox.tools as sbtools from statsmodels.graphics.correlation import plot_corr, plot_corr_grid try: with open('dj30rr', 'rb') as fd: rrdm = pickle.load(fd) except Exception: #blanket for any unpickling error print("Error with unpickling, a new pickle file can be created with findow_1") raise ticksym = rrdm.columns.tolist() rr = rrdm.values[1:400] rrcorr = np.corrcoef(rr, rowvar=0) plot_corr(rrcorr, xnames=ticksym) nvars = rrcorr.shape[0] plt.figure() plt.hist(rrcorr[np.triu_indices(nvars,1)]) plt.title('Correlation Coefficients') xreda, facta, evaa, evea = sbtools.pcasvd(rr) evallcs = (evaa).cumsum() print(evallcs/evallcs[-1]) xred, fact, eva, eve = sbtools.pcasvd(rr, keepdim=4) pcacorr = np.corrcoef(xred, rowvar=0) plot_corr(pcacorr, xnames=ticksym, title='Correlation PCA') resid = rr-xred residcorr = np.corrcoef(resid, rowvar=0) plot_corr(residcorr, xnames=ticksym, title='Correlation Residuals') plt.matshow(residcorr) plt.imshow(residcorr, cmap=plt.cm.jet, interpolation='nearest', extent=(0,30,0,30), vmin=-1.0, vmax=1.0) plt.colorbar() normcolor = (0,1) #False #True fig = plt.figure() ax = fig.add_subplot(2,2,1) plot_corr(rrcorr, xnames=ticksym, normcolor=normcolor, ax=ax) ax2 = fig.add_subplot(2,2,3) #pcacorr = np.corrcoef(xred, rowvar=0) plot_corr(pcacorr, xnames=ticksym, title='Correlation PCA', normcolor=normcolor, ax=ax2) ax3 = fig.add_subplot(2,2,4) plot_corr(residcorr, xnames=ticksym, title='Correlation Residuals', normcolor=normcolor, ax=ax3) images = [c for fig_ax in fig.axes for c in fig_ax.get_children() if isinstance(c, mpl.image.AxesImage)] print(images) print(ax.get_children()) #cax = fig.add_subplot(2,2,2) #[0.85, 0.1, 0.075, 0.8] fig. subplots_adjust(bottom=0.1, right=0.9, top=0.9) cax = fig.add_axes([0.9, 0.1, 0.025, 0.8]) fig.colorbar(images[0], cax=cax) fig.savefig('corrmatrixgrid.png', dpi=120) has_sklearn = True try: import sklearn # noqa:F401 except ImportError: has_sklearn = False print('sklearn not available') def cov2corr(cov): std_ = np.sqrt(np.diag(cov)) corr = cov / np.outer(std_, std_) return corr if has_sklearn: from sklearn.covariance import LedoitWolf, OAS, MCD lw = LedoitWolf(store_precision=False) lw.fit(rr, assume_centered=False) cov_lw = lw.covariance_ corr_lw = cov2corr(cov_lw) oas = OAS(store_precision=False) oas.fit(rr, assume_centered=False) cov_oas = oas.covariance_ corr_oas = cov2corr(cov_oas) mcd = MCD()#.fit(rr, reweight=None) mcd.fit(rr, assume_centered=False) cov_mcd = mcd.covariance_ corr_mcd = cov2corr(cov_mcd) titles = ['raw correlation', 'lw', 'oas', 'mcd'] normcolor = None fig = plt.figure() for i, c in enumerate([rrcorr, corr_lw, corr_oas, corr_mcd]): #for i, c in enumerate([np.cov(rr, rowvar=0), cov_lw, cov_oas, cov_mcd]): ax = fig.add_subplot(2,2,i+1) plot_corr(c, xnames=None, title=titles[i], normcolor=normcolor, ax=ax) images = [c for fig_ax in fig.axes for c in fig_ax.get_children() if isinstance(c, mpl.image.AxesImage)] fig. subplots_adjust(bottom=0.1, right=0.9, top=0.9) cax = fig.add_axes([0.9, 0.1, 0.025, 0.8]) fig.colorbar(images[0], cax=cax) corrli = [rrcorr, corr_lw, corr_oas, corr_mcd, pcacorr] diffssq = np.array([[((ci-cj)**2).sum() for ci in corrli] for cj in corrli]) diffsabs = np.array([[np.max(np.abs(ci-cj)) for ci in corrli] for cj in corrli]) print(diffssq) print('\nmaxabs') print(diffsabs) fig.savefig('corrmatrix_sklearn.png', dpi=120) fig2 = plot_corr_grid(corrli+[residcorr], ncols=3, titles=titles+['pca', 'pca-residual'], xnames=[], ynames=[]) fig2.savefig('corrmatrix_sklearn_2.png', dpi=120) #plt.show() #plt.close('all') statsmodels-0.12.2/statsmodels/sandbox/examples/thirdparty/findow_1.py000066400000000000000000000050111400612667500262320ustar00rootroot00000000000000# -*- coding: utf-8 -*- """A quick look at volatility of stock returns for 2009 Just an exercise to find my way around the pandas methods. Shows the daily rate of return, the square of it (volatility) and a 5 day moving average of the volatility. No guarantee for correctness. Assumes no missing values. colors of lines in graphs are not great uses DataFrame and WidePanel to hold data downloaded from yahoo using matplotlib. I have not figured out storage, so the download happens at each run of the script. Created on Sat Jan 30 16:30:18 2010 Author: josef-pktd """ import os from statsmodels.compat.python import lzip import numpy as np import matplotlib.finance as fin import matplotlib.pyplot as plt import datetime as dt import pandas as pd def getquotes(symbol, start, end): # Taken from the no-longer-existent pandas.examples.finance quotes = fin.quotes_historical_yahoo(symbol, start, end) dates, open, close, high, low, volume = lzip(*quotes) data = { 'open' : open, 'close' : close, 'high' : high, 'low' : low, 'volume' : volume } dates = pd.Index([dt.datetime.fromordinal(int(d)) for d in dates]) return pd.DataFrame(data, index=dates) start_date = dt.datetime(2007, 1, 1) end_date = dt.datetime(2009, 12, 31) dj30 = ['MMM', 'AA', 'AXP', 'T', 'BAC', 'BA', 'CAT', 'CVX', 'CSCO', 'KO', 'DD', 'XOM', 'GE', 'HPQ', 'HD', 'INTC', 'IBM', 'JNJ', 'JPM', 'KFT', 'MCD', 'MRK', 'MSFT', 'PFE', 'PG', 'TRV', 'UTX', 'VZ', 'WMT', 'DIS'] mysym = ['msft', 'ibm', 'goog'] indexsym = ['gspc', 'dji'] # download data dmall = {} for sy in dj30: dmall[sy] = getquotes(sy, start_date, end_date) # combine into WidePanel pawp = pd.WidePanel.fromDict(dmall) print(pawp.values.shape) # select closing prices paclose = pawp.getMinorXS('close') # take log and first difference over time paclose_ratereturn = paclose.apply(np.log).diff() if not os.path.exists('dj30rr'): #if pandas is updated, then sometimes unpickling fails, and need to save again paclose_ratereturn.save('dj30rr') plt.figure() paclose_ratereturn.plot() plt.title('daily rate of return') # square the returns paclose_ratereturn_vol = paclose_ratereturn.apply(lambda x:np.power(x,2)) plt.figure() plt.title('volatility (with 5 day moving average') paclose_ratereturn_vol.plot() # use convolution to get moving average paclose_ratereturn_vol_mov = paclose_ratereturn_vol.apply( lambda x:np.convolve(x,np.ones(5)/5.,'same')) paclose_ratereturn_vol_mov.plot() #plt.show() statsmodels-0.12.2/statsmodels/sandbox/examples/thirdparty/try_interchange.py000066400000000000000000000052021400612667500277130ustar00rootroot00000000000000# -*- coding: utf-8 -*- """groupmean, groupby in pandas, la and tabular from a scikits.timeseries after a question on the scipy-user mailing list I tried to do groupmeans, which in this case are duplicate dates, in the 3 packages. I'm using the versions that I had installed, which are all based on repository checkout, but are not fully up-to-date some brief comments * la.larry and pandas.DataFrame require unique labels/index so groups have to represented in a separate data structure * pandas is missing GroupBy in the docs, but the docstring is helpful * both la and pandas handle datetime objects as object arrays * tabular requires conversion to structured dtype, but easy helper functions or methods are available in scikits.timeseries and tabular * not too bad for a first try Created on Sat Jan 30 08:33:11 2010 Author: josef-pktd """ from statsmodels.compat.python import lrange import numpy as np import scikits.timeseries as ts import la import pandas import tabular as tb from finance import msft, ibm # hack to make it run as standalone s = ts.time_series([1,2,3,4,5], dates=ts.date_array(["2001-01","2001-01", "2001-02","2001-03","2001-03"],freq="M")) print('\nUsing la') dta = la.larry(s.data, label=[lrange(len(s.data))]) dat = la.larry(s.dates.tolist(), label=[lrange(len(s.data))]) s2 = ts.time_series(dta.group_mean(dat).x,dates=ts.date_array(dat.x,freq="M")) s2u = ts.remove_duplicated_dates(s2) print(repr(s)) print(dat) print(repr(s2)) print(repr(s2u)) print('\nUsing pandas') pdta = pandas.DataFrame(s.data, np.arange(len(s.data)), [1]) pa = pdta.groupby(dict(zip(np.arange(len(s.data)), s.dates.tolist()))).aggregate(np.mean) s3 = ts.time_series(pa.values.ravel(), dates=ts.date_array(pa.index.tolist(),freq="M")) print(pa) print(repr(s3)) print('\nUsing tabular') X = tb.tabarray(array=s.torecords(), dtype=s.torecords().dtype) tabx = X.aggregate(On=['_dates'], AggFuncDict={'_data':np.mean,'_mask':np.all}) s4 = ts.time_series(tabx['_data'],dates=ts.date_array(tabx['_dates'],freq="M")) print(tabx) print(repr(s4)) #after running pandas/examples/finance.py larmsft = la.larry(msft.values, [msft.index.tolist(), msft.columns.tolist()]) laribm = la.larry(ibm.values, [ibm.index.tolist(), ibm.columns.tolist()]) lar1 = la.larry(np.dstack((msft.values,ibm.values)), [ibm.index.tolist(), ibm.columns.tolist(), ['msft', 'ibm']]) print(lar1.mean(0)) y = la.larry([[1.0, 2.0], [3.0, 4.0]], [['a', 'b'], ['c', 'd']]) ysr = np.empty(y.x.shape[0],dtype=([('index','S1')]+[(i,np.float) for i in y.label[1]])) ysr['index'] = y.label[0] for i in ysr.dtype.names[1:]: ysr[i] = y[y.labelindex(i, axis=1)].x statsmodels-0.12.2/statsmodels/sandbox/examples/try_gmm_other.py000066400000000000000000000123101400612667500252110ustar00rootroot00000000000000 import numpy as np from scipy import stats from statsmodels.regression.linear_model import OLS from statsmodels.tools import tools from statsmodels.sandbox.regression.gmm import spec_hausman from statsmodels.sandbox.regression import gmm if __name__ == '__main__': examples = ['ivols', 'distquant'][:] if 'ivols' in examples: exampledata = ['ols', 'iv', 'ivfake'][1] nobs = nsample = 500 sige = 3 corrfactor = 0.025 x = np.linspace(0,10, nobs) X = tools.add_constant(np.column_stack((x, x**2)), prepend=False) beta = np.array([1, 0.1, 10]) def sample_ols(exog): endog = np.dot(exog, beta) + sige*np.random.normal(size=nobs) return endog, exog, None def sample_iv(exog): print('using iv example') X = exog.copy() e = sige * np.random.normal(size=nobs) endog = np.dot(X, beta) + e exog[:,0] = X[:,0] + corrfactor * e z0 = X[:,0] + np.random.normal(size=nobs) z1 = X.sum(1) + np.random.normal(size=nobs) z2 = X[:,1] z3 = (np.dot(X, np.array([2,1, 0])) + sige/2. * np.random.normal(size=nobs)) z4 = X[:,1] + np.random.normal(size=nobs) instrument = np.column_stack([z0, z1, z2, z3, z4, X[:,-1]]) return endog, exog, instrument def sample_ivfake(exog): X = exog e = sige * np.random.normal(size=nobs) endog = np.dot(X, beta) + e #X[:,0] += 0.01 * e #z1 = X.sum(1) + np.random.normal(size=nobs) #z2 = X[:,1] z3 = (np.dot(X, np.array([2,1, 0])) + sige/2. * np.random.normal(size=nobs)) z4 = X[:,1] + np.random.normal(size=nobs) instrument = np.column_stack([X[:,:2], z3, z4, X[:,-1]]) #last is constant return endog, exog, instrument if exampledata == 'ols': endog, exog, _ = sample_ols(X) instrument = exog elif exampledata == 'iv': endog, exog, instrument = sample_iv(X) elif exampledata == 'ivfake': endog, exog, instrument = sample_ivfake(X) #using GMM and IV2SLS classes #---------------------------- mod = gmm.IVGMM(endog, exog, instrument, nmoms=instrument.shape[1]) res = mod.fit() modgmmols = gmm.IVGMM(endog, exog, exog, nmoms=exog.shape[1]) resgmmols = modgmmols.fit() #the next is the same as IV2SLS, (Z'Z)^{-1} as weighting matrix modgmmiv = gmm.IVGMM(endog, exog, instrument, nmoms=instrument.shape[1]) #same as mod resgmmiv = modgmmiv.fitgmm(np.ones(exog.shape[1], float), weights=np.linalg.inv(np.dot(instrument.T, instrument))) modls = gmm.IV2SLS(endog, exog, instrument) resls = modls.fit() modols = OLS(endog, exog) resols = modols.fit() print('\nIV case') print('params') print('IV2SLS', resls.params) print('GMMIV ', resgmmiv) # .params print('GMM ', res.params) print('diff ', res.params - resls.params) print('OLS ', resols.params) print('GMMOLS', resgmmols.params) print('\nbse') print('IV2SLS', resls.bse) print('GMM ', res.bse) #bse currently only attached to model not results print('diff ', res.bse - resls.bse) print('%-diff', resls.bse / res.bse * 100 - 100) print('OLS ', resols.bse) print('GMMOLS', resgmmols.bse) #print 'GMMiv', modgmmiv.bse print("Hausman's specification test") print(resls.spec_hausman()) print(spec_hausman(resols.params, res.params, resols.cov_params(), res.cov_params())) print(spec_hausman(resgmmols.params, res.params, resgmmols.cov_params(), res.cov_params())) if 'distquant' in examples: #estimating distribution parameters from quantiles #------------------------------------------------- #example taken from distribution_estimators.py gparrvs = stats.genpareto.rvs(2, size=5000) x0p = [1., gparrvs.min()-5, 1] moddist = gmm.DistQuantilesGMM(gparrvs, None, None, distfn=stats.genpareto) #produces non-sense because optimal weighting matrix calculations do not #apply to this case #resgp = moddist.fit() #now with 'cov': LinAlgError: Singular matrix pit1, wit1 = moddist.fititer([1.5,0,1.5], maxiter=1) print(pit1) p1 = moddist.fitgmm([1.5,0,1.5]) print(p1) moddist2 = gmm.DistQuantilesGMM(gparrvs, None, None, distfn=stats.genpareto, pquant=np.linspace(0.01,0.99,10)) pit1a, wit1a = moddist2.fititer([1.5,0,1.5], maxiter=1) print(pit1a) p1a = moddist2.fitgmm([1.5,0,1.5]) print(p1a) #Note: pit1a and p1a are the same and almost the same (1e-5) as # fitquantilesgmm version (functions instead of class) res1b = moddist2.fitonce([1.5,0,1.5]) print(res1b.params) print(res1b.bse) #they look much too large print(np.sqrt(np.diag(res1b._cov_params))) statsmodels-0.12.2/statsmodels/sandbox/examples/try_multiols.py000066400000000000000000000023531400612667500251060ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun May 26 13:23:40 2013 Author: Josef Perktold, based on Enrico Giampieri's multiOLS """ #import numpy as np import pandas as pd import statsmodels.api as sm from statsmodels.sandbox.multilinear import multiOLS, multigroup data = sm.datasets.longley.load_pandas() df = data.exog df['TOTEMP'] = data.endog #This will perform the specified linear model on all the #other columns of the dataframe res0 = multiOLS('GNP + 1', df) #This select only a certain subset of the columns res = multiOLS('GNP + 0', df, ['GNPDEFL', 'TOTEMP', 'POP']) print(res.to_string()) url = "https://raw.githubusercontent.com/vincentarelbundock/" url = url + "Rdatasets/csv/HistData/Guerry.csv" df = pd.read_csv(url, index_col=1) #'dept') #evaluate the relationship between the various parameters whith the Wealth pvals = multiOLS('Wealth', df)['adj_pvals', '_f_test'] #define the groups groups = {} groups['crime'] = ['Crime_prop', 'Infanticide', 'Crime_parents', 'Desertion', 'Crime_pers'] groups['religion'] = ['Donation_clergy', 'Clergy', 'Donations'] groups['wealth'] = ['Commerce', 'Lottery', 'Instruction', 'Literacy'] #do the analysis of the significance res3 = multigroup(pvals < 0.05, groups) print(res3) statsmodels-0.12.2/statsmodels/sandbox/examples/try_quantile_regression.py000066400000000000000000000023571400612667500273240ustar00rootroot00000000000000'''Example to illustrate Quantile Regression Author: Josef Perktold ''' import numpy as np import matplotlib.pyplot as plt import statsmodels.api as sm from statsmodels.regression.quantile_regression import QuantReg sige = 5 nobs, k_vars = 500, 5 x = np.random.randn(nobs, k_vars) #x[:,0] = 1 y = x.sum(1) + sige * (np.random.randn(nobs)/2 + 1)**3 p = 0.5 exog = np.column_stack((np.ones(nobs), x)) res_qr = QuantReg(y, exog).fit(p) res_qr2 = QuantReg(y, exog).fit(0.25) res_qr3 = QuantReg(y, exog).fit(0.75) res_ols = sm.OLS(y, exog).fit() ##print 'ols ', res_ols.params ##print '0.25', res_qr2 ##print '0.5 ', res_qr ##print '0.75', res_qr3 params = [res_ols.params, res_qr2.params, res_qr.params, res_qr3.params] labels = ['ols', 'qr 0.25', 'qr 0.5', 'qr 0.75'] #sortidx = np.argsort(y) fitted_ols = np.dot(res_ols.model.exog, params[0]) sortidx = np.argsort(fitted_ols) x_sorted = res_ols.model.exog[sortidx] fitted_ols = np.dot(x_sorted, params[0]) plt.figure() plt.plot(y[sortidx], 'o', alpha=0.75) for lab, beta in zip(['ols', 'qr 0.25', 'qr 0.5', 'qr 0.75'], params): print('%-8s' % lab, np.round(beta, 4)) fitted = np.dot(x_sorted, beta) lw = 2 if lab == 'ols' else 1 plt.plot(fitted, lw=lw, label=lab) plt.legend() plt.show() statsmodels-0.12.2/statsmodels/sandbox/examples/try_quantile_regression1.py000066400000000000000000000021751400612667500274030ustar00rootroot00000000000000'''Example to illustrate Quantile Regression Author: Josef Perktold polynomial regression with systematic deviations above ''' import numpy as np import matplotlib.pyplot as plt from scipy import stats import statsmodels.api as sm from statsmodels.regression.quantile_regression import QuantReg sige = 0.1 nobs, k_vars = 500, 3 x = np.random.uniform(-1, 1, size=nobs) x.sort() exog = np.vander(x, k_vars+1)[:,::-1] mix = 0.1 * stats.norm.pdf(x[:,None], loc=np.linspace(-0.5, 0.75, 4), scale=0.01).sum(1) y = exog.sum(1) + mix + sige * (np.random.randn(nobs)/2 + 1)**3 p = 0.5 res_qr = QuantReg(y, exog).fit(p) res_qr2 = QuantReg(y, exog).fit(0.1) res_qr3 = QuantReg(y, exog).fit(0.75) res_ols = sm.OLS(y, exog).fit() params = [res_ols.params, res_qr2.params, res_qr.params, res_qr3.params] labels = ['ols', 'qr 0.1', 'qr 0.5', 'qr 0.75'] plt.figure() plt.plot(x, y, '.', alpha=0.5) for lab, beta in zip(['ols', 'qr 0.1', 'qr 0.5', 'qr 0.75'], params): print('%-8s' % lab, np.round(beta, 4)) fitted = np.dot(exog, beta) lw = 2 plt.plot(x, fitted, lw=lw, label=lab) plt.legend() plt.title('Quantile Regression') plt.show() statsmodels-0.12.2/statsmodels/sandbox/examples/try_smoothers.py000066400000000000000000000051371400612667500252640ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Tue Nov 01 15:17:52 2011 Author: Mike Author: Josef mainly script for checking Kernel Regression """ import numpy as np if __name__ == "__main__": #from statsmodels.sandbox.nonparametric import smoothers as s from statsmodels.sandbox.nonparametric import smoothers, kernels import matplotlib.pyplot as plt #from numpy import sin, array, random import time np.random.seed(500) nobs = 250 sig_fac = 0.5 #x = np.random.normal(size=nobs) x = np.random.uniform(-2, 2, size=nobs) #y = np.array([np.sin(i*5)/i + 2*i + (3+i)*np.random.normal() for i in x]) y = np.sin(x*5)/x + 2*x + sig_fac * (3+x)*np.random.normal(size=nobs) K = kernels.Biweight(0.25) K2 = kernels.CustomKernel(lambda x: (1 - x*x)**2, 0.25, domain = [-1.0, 1.0]) KS = smoothers.KernelSmoother(x, y, K) KS2 = smoothers.KernelSmoother(x, y, K2) KSx = np.arange(-3, 3, 0.1) start = time.time() KSy = KS.conf(KSx) KVar = KS.std(KSx) print(time.time() - start) # This should be significantly quicker... start = time.time() # KS2y = KS2.conf(KSx) # K2Var = KS2.std(KSx) # print(time.time() - start) # ...than this. KSConfIntx, KSConfInty = KS.conf(15) print("Norm const should be 0.9375") print(K2.norm_const) print("L2 Norms Should Match:") print(K.L2Norm) print(K2.L2Norm) print("Fit values should match:") #print zip(KSy, KS2y) print(KSy[28]) print(KS2y[28]) print("Var values should match:") #print zip(KVar, K2Var) print(KVar[39]) print(K2Var[39]) fig = plt.figure() ax = fig.add_subplot(221) ax.plot(x, y, "+") ax.plot(KSx, KSy, "-o") #ax.set_ylim(-20, 30) ax2 = fig.add_subplot(222) ax2.plot(KSx, KVar, "-o") ax3 = fig.add_subplot(223) ax3.plot(x, y, "+") ax3.plot(KSx, KS2y, "-o") #ax3.set_ylim(-20, 30) ax4 = fig.add_subplot(224) ax4.plot(KSx, K2Var, "-o") fig2 = plt.figure() ax5 = fig2.add_subplot(111) ax5.plot(x, y, "+") ax5.plot(KSConfIntx, KSConfInty, "-o") import statsmodels.nonparametric.smoothers_lowess as lo ys = lo.lowess(y, x) ax5.plot(ys[:,0], ys[:,1], 'b-') ys2 = lo.lowess(y, x, frac=0.25) ax5.plot(ys2[:,0], ys2[:,1], 'b--', lw=2) #need to sort for matplolib plot ? xind = np.argsort(x) pmod = smoothers.PolySmoother(5, x[xind]) pmod.fit(y[xind]) yp = pmod(x[xind]) ax5.plot(x[xind], yp, 'k-') ax5.set_title('Kernel regression, lowess - blue, polysmooth - black') #plt.show() statsmodels-0.12.2/statsmodels/sandbox/gam.py000066400000000000000000000360271400612667500212730ustar00rootroot00000000000000""" Generalized additive models Requirements for smoothers -------------------------- smooth(y, weights=xxx) : ? no return ? alias for fit predict(x=None) : smoothed values, fittedvalues or for new exog df_fit() : degress of freedom of fit ? Notes ----- - using PolySmoother works for AdditiveModel, and GAM with Poisson and Binomial - testfailure with Gamma, no other families tested - there is still an indeterminacy in the split up of the constant across components (smoothers) and alpha, sum, i.e. constant, looks good. - role of offset, that I have not tried to figure out yet Refactoring ----------- currently result is attached to model instead of other way around split up Result in class for AdditiveModel and for GAM, subclass GLMResults, needs verification that result statistics are appropriate how much inheritance, double inheritance? renamings and cleanup interface to other smoothers, scipy splines basic unittests as support for refactoring exist, but we should have a test case for gamma and the others. Advantage of PolySmoother is that we can benchmark against the parametric GLM results. """ # JP: # changes: use PolySmoother instead of crashing bspline # TODO: check/catalogue required interface of a smoother # TODO: replace default smoother by corresponding function to initialize # other smoothers # TODO: fix iteration, do not define class with iterator methods, use looping; # add maximum iteration and other optional stop criteria # fixed some of the dimension problems in PolySmoother, # now graph for example looks good # NOTE: example script is now in examples folder #update: I did some of the above, see module docstring import numpy as np from statsmodels.genmod import families from statsmodels.sandbox.nonparametric.smoothers import PolySmoother from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.tools.sm_exceptions import IterationLimitWarning, iteration_limit_doc import warnings DEBUG = False def default_smoother(x, s_arg=None): ''' ''' # _x = x.copy() # _x.sort() _x = np.sort(x) n = x.shape[0] # taken form smooth.spline in R #if n < 50: if n < 500: nknots = n else: a1 = np.log(50) / np.log(2) a2 = np.log(100) / np.log(2) a3 = np.log(140) / np.log(2) a4 = np.log(200) / np.log(2) if n < 200: nknots = 2**(a1 + (a2 - a1) * (n - 50)/150.) elif n < 800: nknots = 2**(a2 + (a3 - a2) * (n - 200)/600.) elif n < 3200: nknots = 2**(a3 + (a4 - a3) * (n - 800)/2400.) else: nknots = 200 + (n - 3200.)**0.2 knots = _x[np.linspace(0, n-1, nknots).astype(np.int32)] #s = SmoothingSpline(knots, x=x.copy()) #when I set order=2, I get nans in the GAM prediction if s_arg is None: order = 3 #what about knots? need smoother *args or **kwds else: order = s_arg s = PolySmoother(order, x=x.copy()) #TODO: change order, why copy? # s.gram(d=2) # s.target_df = 5 return s class Offset(object): def __init__(self, fn, offset): self.fn = fn self.offset = offset def __call__(self, *args, **kw): return self.fn(*args, **kw) + self.offset class Results(object): def __init__(self, Y, alpha, exog, smoothers, family, offset): self.nobs, self.k_vars = exog.shape #assumes exog is 2d #weird: If I put the previous line after the definition of self.mu, # then the attributed do not get added self.Y = Y self.alpha = alpha self.smoothers = smoothers self.offset = offset self.family = family self.exog = exog self.offset = offset self.mu = self.linkinversepredict(exog) #TODO: remove __call__ def __call__(self, exog): '''expected value ? check new GLM, same as mu for given exog maybe remove this ''' return self.linkinversepredict(exog) def linkinversepredict(self, exog): #TODO what's the name in GLM '''expected value ? check new GLM, same as mu for given exog ''' return self.family.link.inverse(self.predict(exog)) def predict(self, exog): '''predict response, sum of smoothed components TODO: What's this in the case of GLM, corresponds to X*beta ? ''' #note: sum is here over axis=0, #TODO: transpose in smoothed and sum over axis=1 #BUG: there is some inconsistent orientation somewhere #temporary hack, will not work for 1d #print dir(self) #print 'self.nobs, self.k_vars', self.nobs, self.k_vars exog_smoothed = self.smoothed(exog) #print 'exog_smoothed.shape', exog_smoothed.shape if exog_smoothed.shape[0] == self.k_vars: import warnings warnings.warn("old orientation, colvars, will go away", FutureWarning) return np.sum(self.smoothed(exog), axis=0) + self.alpha if exog_smoothed.shape[1] == self.k_vars: return np.sum(exog_smoothed, axis=1) + self.alpha else: raise ValueError('shape mismatch in predict') def smoothed(self, exog): '''get smoothed prediction for each component ''' #bug: with exog in predict I get a shape error #print 'smoothed', exog.shape, self.smoothers[0].predict(exog).shape #there was a mistake exog did not have column index i return np.array([self.smoothers[i].predict(exog[:,i]) + self.offset[i] #should not be a mistake because exog[:,i] is attached to smoother, but #it is for different exog #return np.array([self.smoothers[i].predict() + self.offset[i] for i in range(exog.shape[1])]).T def smoothed_demeaned(self, exog): components = self.smoothed(exog) means = components.mean(0) constant = means.sum() + self.alpha components_demeaned = components - means return components_demeaned, constant class AdditiveModel(object): '''additive model with non-parametric, smoothed components Parameters ---------- exog : ndarray smoothers : None or list of smoother instances smoother instances not yet checked weights : None or ndarray family : None or family instance I think only used because of shared results with GAM and subclassing. If None, then Gaussian is used. ''' def __init__(self, exog, smoothers=None, weights=None, family=None): self.exog = exog if weights is not None: self.weights = weights else: self.weights = np.ones(self.exog.shape[0]) self.smoothers = smoothers or [default_smoother(exog[:,i]) for i in range(exog.shape[1])] #TODO: why do we set here df, refactoring temporary? for i in range(exog.shape[1]): self.smoothers[i].df = 10 if family is None: self.family = families.Gaussian() else: self.family = family #self.family = families.Gaussian() def _iter__(self): '''initialize iteration ?, should be removed ''' self.iter = 0 self.dev = np.inf return self def next(self): '''internal calculation for one fit iteration BUG: I think this does not improve, what is supposed to improve offset does not seem to be used, neither an old alpha The smoothers keep coef/params from previous iteration ''' _results = self.results Y = self.results.Y mu = _results.predict(self.exog) #TODO offset is never used ? offset = np.zeros(self.exog.shape[1], np.float64) alpha = (Y * self.weights).sum() / self.weights.sum() for i in range(self.exog.shape[1]): tmp = self.smoothers[i].predict() #TODO: check what smooth needs to do #smooth (alias for fit, fit given x to new y and attach #print 'next shape', (Y - alpha - mu + tmp).shape bad = np.isnan(Y - alpha - mu + tmp).any() if bad: #temporary assert while debugging print(Y, alpha, mu, tmp) raise ValueError("nan encountered") #self.smoothers[i].smooth(Y - alpha - mu + tmp, self.smoothers[i].smooth(Y - mu + tmp, weights=self.weights) tmp2 = self.smoothers[i].predict() #fittedvalues of previous smooth/fit self.results.offset[i] = -(tmp2*self.weights).sum() / self.weights.sum() #self.offset used in smoothed if DEBUG: print(self.smoothers[i].params) mu += tmp2 - tmp #change setting offset here: tests still pass, offset equal to constant #in component ??? what's the effect of offset offset = self.results.offset #print self.iter #self.iter += 1 #missing incrementing of iter counter NOT return Results(Y, alpha, self.exog, self.smoothers, self.family, offset) def cont(self): '''condition to continue iteration loop Parameters ---------- tol Returns ------- cont : bool If true, then iteration should be continued. ''' self.iter += 1 #moved here to always count, not necessary if DEBUG: print(self.iter, self.results.Y.shape) print(self.results.predict(self.exog).shape, self.weights.shape) curdev = (((self.results.Y - self.results.predict(self.exog))**2) * self.weights).sum() if self.iter > self.maxiter: #kill it, no max iterationoption return False if np.fabs((self.dev - curdev) / curdev) < self.rtol: self.dev = curdev return False #self.iter += 1 self.dev = curdev return True def df_resid(self): '''degrees of freedom of residuals, ddof is sum of all smoothers df ''' return self.results.Y.shape[0] - np.array([self.smoothers[i].df_fit() for i in range(self.exog.shape[1])]).sum() def estimate_scale(self): '''estimate standard deviation of residuals ''' #TODO: remove use of self.results.__call__ return ((self.results.Y - self.results(self.exog))**2).sum() / self.df_resid() def fit(self, Y, rtol=1.0e-06, maxiter=30): '''fit the model to a given endogenous variable Y This needs to change for consistency with statsmodels ''' self.rtol = rtol self.maxiter = maxiter #iter(self) # what does this do? anything? self._iter__() mu = 0 alpha = (Y * self.weights).sum() / self.weights.sum() offset = np.zeros(self.exog.shape[1], np.float64) for i in range(self.exog.shape[1]): self.smoothers[i].smooth(Y - alpha - mu, weights=self.weights) tmp = self.smoothers[i].predict() offset[i] = (tmp * self.weights).sum() / self.weights.sum() tmp -= tmp.sum() mu += tmp self.results = Results(Y, alpha, self.exog, self.smoothers, self.family, offset) while self.cont(): self.results = self.next() if self.iter >= self.maxiter: warnings.warn(iteration_limit_doc, IterationLimitWarning) return self.results class Model(GLM, AdditiveModel): #class Model(AdditiveModel): #TODO: what does GLM do? Is it actually used ? #only used in __init__, dropping it does not change results #but where gets family attached now? - weird, it's Gaussian in this case now #also where is the link defined? #AdditiveModel overwrites family and sets it to Gaussian - corrected #I think both GLM and AdditiveModel subclassing is only used in __init__ #niter = 2 # def __init__(self, exog, smoothers=None, family=family.Gaussian()): # GLM.__init__(self, exog, family=family) # AdditiveModel.__init__(self, exog, smoothers=smoothers) # self.family = family def __init__(self, endog, exog, smoothers=None, family=families.Gaussian()): #self.family = family #TODO: inconsistent super __init__ AdditiveModel.__init__(self, exog, smoothers=smoothers, family=family) GLM.__init__(self, endog, exog, family=family) assert self.family is family #make sure we got the right family def next(self): _results = self.results Y = _results.Y if np.isnan(self.weights).all(): print("nanweights1") _results.mu = self.family.link.inverse(_results.predict(self.exog)) #eta = _results.predict(self.exog) #_results.mu = self.family.fitted(eta) weights = self.family.weights(_results.mu) if np.isnan(weights).all(): self.weights = weights print("nanweights2") self.weights = weights if DEBUG: print('deriv isnan', np.isnan(self.family.link.deriv(_results.mu)).any()) #Z = _results.predict(self.exog) + \ Z = _results.predict(self.exog) + \ self.family.link.deriv(_results.mu) * (Y - _results.mu) #- _results.alpha #?added alpha m = AdditiveModel(self.exog, smoothers=self.smoothers, weights=self.weights, family=self.family) #TODO: I do not know what the next two lines do, Z, Y ? which is endog? #Y is original endog, Z is endog for the next step in the iterative solver _results = m.fit(Z) self.history.append([Z, _results.predict(self.exog)]) _results.Y = Y _results.mu = self.family.link.inverse(_results.predict(self.exog)) self.iter += 1 self.results = _results return _results def estimate_scale(self, Y=None): """ Return Pearson\'s X^2 estimate of scale. """ if Y is None: Y = self.Y resid = Y - self.results.mu return (np.power(resid, 2) / self.family.variance(self.results.mu)).sum() \ / self.df_resid #TODO check this #/ AdditiveModel.df_resid(self) #what is the class doing here? def fit(self, Y, rtol=1.0e-06, maxiter=30): self.rtol = rtol self.maxiter = maxiter self.Y = np.asarray(Y, np.float64) self.history = [] #iter(self) self._iter__() #TODO code duplication with next? alpha = self.Y.mean() mu0 = self.family.starting_mu(Y) #Z = self.family.link(alpha) + self.family.link.deriv(alpha) * (Y - alpha) Z = self.family.link(alpha) + self.family.link.deriv(alpha) * (Y - mu0) m = AdditiveModel(self.exog, smoothers=self.smoothers, family=self.family) self.results = m.fit(Z) self.results.mu = self.family.link.inverse(self.results.predict(self.exog)) self.results.Y = Y while self.cont(): self.results = self.next() self.scale = self.results.scale = self.estimate_scale() if self.iter >= self.maxiter: import warnings warnings.warn(iteration_limit_doc, IterationLimitWarning) return self.results statsmodels-0.12.2/statsmodels/sandbox/infotheo.py000066400000000000000000000402341400612667500223350ustar00rootroot00000000000000""" Information Theoretic and Entropy Measures References ---------- Golan, As. 2008. "Information and Entropy Econometrics -- A Review and Synthesis." Foundations And Trends in Econometrics 2(1-2), 1-145. Golan, A., Judge, G., and Miller, D. 1996. Maximum Entropy Econometrics. Wiley & Sons, Chichester. """ #For MillerMadow correction #Miller, G. 1955. Note on the bias of information estimates. Info. Theory # Psychol. Prob. Methods II-B:95-100. #For ChaoShen method #Chao, A., and T.-J. Shen. 2003. Nonparametric estimation of Shannon's index of diversity when #there are unseen species in sample. Environ. Ecol. Stat. 10:429-443. #Good, I. J. 1953. The population frequencies of species and the estimation of population parameters. #Biometrika 40:237-264. #Horvitz, D.G., and D. J. Thompson. 1952. A generalization of sampling without replacement from a finute universe. J. Am. Stat. Assoc. 47:663-685. #For NSB method #Nemenman, I., F. Shafee, and W. Bialek. 2002. Entropy and inference, revisited. In: Dietterich, T., #S. Becker, Z. Gharamani, eds. Advances in Neural Information Processing Systems 14: 471-478. #Cambridge (Massachusetts): MIT Press. #For shrinkage method #Dougherty, J., Kohavi, R., and Sahami, M. (1995). Supervised and unsupervised discretization of #continuous features. In International Conference on Machine Learning. #Yang, Y. and Webb, G. I. (2003). Discretization for naive-bayes learning: managing discretization #bias and variance. Technical Report 2003/131 School of Computer Science and Software Engineer- #ing, Monash University. from statsmodels.compat.python import lzip, lmap from scipy import stats import numpy as np from matplotlib import pyplot as plt from scipy.special import logsumexp as sp_logsumexp #TODO: change these to use maxentutils so that over/underflow is handled #with the logsumexp. def logsumexp(a, axis=None): """ Compute the log of the sum of exponentials log(e^{a_1}+...e^{a_n}) of a Avoids numerical overflow. Parameters ---------- a : array_like The vector to exponentiate and sum axis : int, optional The axis along which to apply the operation. Defaults is None. Returns ------- sum(log(exp(a))) Notes ----- This function was taken from the mailing list http://mail.scipy.org/pipermail/scipy-user/2009-October/022931.html This should be superceded by the ufunc when it is finished. """ if axis is None: # Use the scipy.maxentropy version. return sp_logsumexp(a) a = np.asarray(a) shp = list(a.shape) shp[axis] = 1 a_max = a.max(axis=axis) s = np.log(np.exp(a - a_max.reshape(shp)).sum(axis=axis)) lse = a_max + s return lse def _isproperdist(X): """ Checks to see if `X` is a proper probability distribution """ X = np.asarray(X) if not np.allclose(np.sum(X), 1) or not np.all(X>=0) or not np.all(X<=1): return False else: return True def discretize(X, method="ef", nbins=None): """ Discretize `X` Parameters ---------- bins : int, optional Number of bins. Default is floor(sqrt(N)) method : str "ef" is equal-frequency binning "ew" is equal-width binning Examples -------- """ nobs = len(X) if nbins is None: nbins = np.floor(np.sqrt(nobs)) if method == "ef": discrete = np.ceil(nbins * stats.rankdata(X)/nobs) if method == "ew": width = np.max(X) - np.min(X) width = np.floor(width/nbins) svec, ivec = stats.fastsort(X) discrete = np.zeros(nobs) binnum = 1 base = svec[0] discrete[ivec[0]] = binnum for i in range(1,nobs): if svec[i] < base + width: discrete[ivec[i]] = binnum else: base = svec[i] binnum += 1 discrete[ivec[i]] = binnum return discrete #TODO: looks okay but needs more robust tests for corner cases def logbasechange(a,b): """ There is a one-to-one transformation of the entropy value from a log base b to a log base a : H_{b}(X)=log_{b}(a)[H_{a}(X)] Returns ------- log_{b}(a) """ return np.log(b)/np.log(a) def natstobits(X): """ Converts from nats to bits """ return logbasechange(np.e, 2) * X def bitstonats(X): """ Converts from bits to nats """ return logbasechange(2, np.e) * X #TODO: make this entropy, and then have different measures as #a method def shannonentropy(px, logbase=2): """ This is Shannon's entropy Parameters ---------- logbase, int or np.e The base of the log px : 1d or 2d array_like Can be a discrete probability distribution, a 2d joint distribution, or a sequence of probabilities. Returns ----- For log base 2 (bits) given a discrete distribution H(p) = sum(px * log2(1/px) = -sum(pk*log2(px)) = E[log2(1/p(X))] For log base 2 (bits) given a joint distribution H(px,py) = -sum_{k,j}*w_{kj}log2(w_{kj}) Notes ----- shannonentropy(0) is defined as 0 """ #TODO: have not defined the px,py case? px = np.asarray(px) if not np.all(px <= 1) or not np.all(px >= 0): raise ValueError("px does not define proper distribution") entropy = -np.sum(np.nan_to_num(px*np.log2(px))) if logbase != 2: return logbasechange(2,logbase) * entropy else: return entropy # Shannon's information content def shannoninfo(px, logbase=2): """ Shannon's information Parameters ---------- px : float or array_like `px` is a discrete probability distribution Returns ------- For logbase = 2 np.log2(px) """ px = np.asarray(px) if not np.all(px <= 1) or not np.all(px >= 0): raise ValueError("px does not define proper distribution") if logbase != 2: return - logbasechange(2,logbase) * np.log2(px) else: return - np.log2(px) def condentropy(px, py, pxpy=None, logbase=2): """ Return the conditional entropy of X given Y. Parameters ---------- px : array_like py : array_like pxpy : array_like, optional If pxpy is None, the distributions are assumed to be independent and conendtropy(px,py) = shannonentropy(px) logbase : int or np.e Returns ------- sum_{kj}log(q_{j}/w_{kj} where q_{j} = Y[j] and w_kj = X[k,j] """ if not _isproperdist(px) or not _isproperdist(py): raise ValueError("px or py is not a proper probability distribution") if pxpy is not None and not _isproperdist(pxpy): raise ValueError("pxpy is not a proper joint distribtion") if pxpy is None: pxpy = np.outer(py,px) condent = np.sum(pxpy * np.nan_to_num(np.log2(py/pxpy))) if logbase == 2: return condent else: return logbasechange(2, logbase) * condent def mutualinfo(px,py,pxpy, logbase=2): """ Returns the mutual information between X and Y. Parameters ---------- px : array_like Discrete probability distribution of random variable X py : array_like Discrete probability distribution of random variable Y pxpy : 2d array_like The joint probability distribution of random variables X and Y. Note that if X and Y are independent then the mutual information is zero. logbase : int or np.e, optional Default is 2 (bits) Returns ------- shannonentropy(px) - condentropy(px,py,pxpy) """ if not _isproperdist(px) or not _isproperdist(py): raise ValueError("px or py is not a proper probability distribution") if pxpy is not None and not _isproperdist(pxpy): raise ValueError("pxpy is not a proper joint distribtion") if pxpy is None: pxpy = np.outer(py,px) return shannonentropy(px, logbase=logbase) - condentropy(px,py,pxpy, logbase=logbase) def corrent(px,py,pxpy,logbase=2): """ An information theoretic correlation measure. Reflects linear and nonlinear correlation between two random variables X and Y, characterized by the discrete probability distributions px and py respectively. Parameters ---------- px : array_like Discrete probability distribution of random variable X py : array_like Discrete probability distribution of random variable Y pxpy : 2d array_like, optional Joint probability distribution of X and Y. If pxpy is None, X and Y are assumed to be independent. logbase : int or np.e, optional Default is 2 (bits) Returns ------- mutualinfo(px,py,pxpy,logbase=logbase)/shannonentropy(py,logbase=logbase) Notes ----- This is also equivalent to corrent(px,py,pxpy) = 1 - condent(px,py,pxpy)/shannonentropy(py) """ if not _isproperdist(px) or not _isproperdist(py): raise ValueError("px or py is not a proper probability distribution") if pxpy is not None and not _isproperdist(pxpy): raise ValueError("pxpy is not a proper joint distribtion") if pxpy is None: pxpy = np.outer(py,px) return mutualinfo(px,py,pxpy,logbase=logbase)/shannonentropy(py, logbase=logbase) def covent(px,py,pxpy,logbase=2): """ An information theoretic covariance measure. Reflects linear and nonlinear correlation between two random variables X and Y, characterized by the discrete probability distributions px and py respectively. Parameters ---------- px : array_like Discrete probability distribution of random variable X py : array_like Discrete probability distribution of random variable Y pxpy : 2d array_like, optional Joint probability distribution of X and Y. If pxpy is None, X and Y are assumed to be independent. logbase : int or np.e, optional Default is 2 (bits) Returns ------- condent(px,py,pxpy,logbase=logbase) + condent(py,px,pxpy, logbase=logbase) Notes ----- This is also equivalent to covent(px,py,pxpy) = condent(px,py,pxpy) + condent(py,px,pxpy) """ if not _isproperdist(px) or not _isproperdist(py): raise ValueError("px or py is not a proper probability distribution") if pxpy is not None and not _isproperdist(pxpy): raise ValueError("pxpy is not a proper joint distribtion") if pxpy is None: pxpy = np.outer(py,px) # FIXME: these should be `condentropy`, not `condent` return (condent(px, py, pxpy, logbase=logbase) # noqa:F821 See GH#5756 + condent(py, px, pxpy, logbase=logbase)) # noqa:F821 See GH#5756 #### Generalized Entropies #### def renyientropy(px,alpha=1,logbase=2,measure='R'): """ Renyi's generalized entropy Parameters ---------- px : array_like Discrete probability distribution of random variable X. Note that px is assumed to be a proper probability distribution. logbase : int or np.e, optional Default is 2 (bits) alpha : float or inf The order of the entropy. The default is 1, which in the limit is just Shannon's entropy. 2 is Renyi (Collision) entropy. If the string "inf" or numpy.inf is specified the min-entropy is returned. measure : str, optional The type of entropy measure desired. 'R' returns Renyi entropy measure. 'T' returns the Tsallis entropy measure. Returns ------- 1/(1-alpha)*log(sum(px**alpha)) In the limit as alpha -> 1, Shannon's entropy is returned. In the limit as alpha -> inf, min-entropy is returned. """ #TODO:finish returns #TODO:add checks for measure if not _isproperdist(px): raise ValueError("px is not a proper probability distribution") alpha = float(alpha) if alpha == 1: genent = shannonentropy(px) if logbase != 2: return logbasechange(2, logbase) * genent return genent elif 'inf' in str(alpha).lower() or alpha == np.inf: return -np.log(np.max(px)) # gets here if alpha != (1 or inf) px = px**alpha genent = np.log(px.sum()) if logbase == 2: return 1/(1-alpha) * genent else: return 1/(1-alpha) * logbasechange(2, logbase) * genent #TODO: before completing this, need to rethink the organization of # (relative) entropy measures, ie., all put into one function # and have kwdargs, etc.? def gencrossentropy(px,py,pxpy,alpha=1,logbase=2, measure='T'): """ Generalized cross-entropy measures. Parameters ---------- px : array_like Discrete probability distribution of random variable X py : array_like Discrete probability distribution of random variable Y pxpy : 2d array_like, optional Joint probability distribution of X and Y. If pxpy is None, X and Y are assumed to be independent. logbase : int or np.e, optional Default is 2 (bits) measure : str, optional The measure is the type of generalized cross-entropy desired. 'T' is the cross-entropy version of the Tsallis measure. 'CR' is Cressie-Read measure. """ if __name__ == "__main__": print("From Golan (2008) \"Information and Entropy Econometrics -- A Review \ and Synthesis") print("Table 3.1") # Examples from Golan (2008) X = [.2,.2,.2,.2,.2] Y = [.322,.072,.511,.091,.004] for i in X: print(shannoninfo(i)) for i in Y: print(shannoninfo(i)) print(shannonentropy(X)) print(shannonentropy(Y)) p = [1e-5,1e-4,.001,.01,.1,.15,.2,.25,.3,.35,.4,.45,.5] plt.subplot(111) plt.ylabel("Information") plt.xlabel("Probability") x = np.linspace(0,1,100001) plt.plot(x, shannoninfo(x)) # plt.show() plt.subplot(111) plt.ylabel("Entropy") plt.xlabel("Probability") x = np.linspace(0,1,101) plt.plot(x, lmap(shannonentropy, lzip(x,1-x))) # plt.show() # define a joint probability distribution # from Golan (2008) table 3.3 w = np.array([[0,0,1./3],[1/9.,1/9.,1/9.],[1/18.,1/9.,1/6.]]) # table 3.4 px = w.sum(0) py = w.sum(1) H_X = shannonentropy(px) H_Y = shannonentropy(py) H_XY = shannonentropy(w) H_XgivenY = condentropy(px,py,w) H_YgivenX = condentropy(py,px,w) # note that cross-entropy is not a distance measure as the following shows D_YX = logbasechange(2,np.e)*stats.entropy(px, py) D_XY = logbasechange(2,np.e)*stats.entropy(py, px) I_XY = mutualinfo(px,py,w) print("Table 3.3") print(H_X,H_Y, H_XY, H_XgivenY, H_YgivenX, D_YX, D_XY, I_XY) print("discretize functions") X=np.array([21.2,44.5,31.0,19.5,40.6,38.7,11.1,15.8,31.9,25.8,20.2,14.2, 24.0,21.0,11.3,18.0,16.3,22.2,7.8,27.8,16.3,35.1,14.9,17.1,28.2,16.4, 16.5,46.0,9.5,18.8,32.1,26.1,16.1,7.3,21.4,20.0,29.3,14.9,8.3,22.5, 12.8,26.9,25.5,22.9,11.2,20.7,26.2,9.3,10.8,15.6]) discX = discretize(X) #CF: R's infotheo #TODO: compare to pyentropy quantize? print print("Example in section 3.6 of Golan, using table 3.3") print("Bounding errors using Fano's inequality") print("H(P_{e}) + P_{e}log(K-1) >= H(X|Y)") print("or, a weaker inequality") print("P_{e} >= [H(X|Y) - 1]/log(K)") print("P(x) = %s" % px) print("X = 3 has the highest probability, so this is the estimate Xhat") pe = 1 - px[2] print("The probability of error Pe is 1 - p(X=3) = %0.4g" % pe) H_pe = shannonentropy([pe,1-pe]) print("H(Pe) = %0.4g and K=3" % H_pe) print("H(Pe) + Pe*log(K-1) = %0.4g >= H(X|Y) = %0.4g" % \ (H_pe+pe*np.log2(2), H_XgivenY)) print("or using the weaker inequality") print("Pe = %0.4g >= [H(X) - 1]/log(K) = %0.4g" % (pe, (H_X - 1)/np.log2(3))) print("Consider now, table 3.5, where there is additional information") print("The conditional probabilities of P(X|Y=y) are ") w2 = np.array([[0.,0.,1.],[1/3.,1/3.,1/3.],[1/6.,1/3.,1/2.]]) print(w2) # not a proper distribution? print("The probability of error given this information is") print("Pe = [H(X|Y) -1]/log(K) = %0.4g" % ((np.mean([0,shannonentropy(w2[1]),shannonentropy(w2[2])])-1)/np.log2(3))) print("such that more information lowers the error") ### Stochastic processes markovchain = np.array([[.553,.284,.163],[.465,.312,.223],[.420,.322,.258]]) statsmodels-0.12.2/statsmodels/sandbox/mcevaluate/000077500000000000000000000000001400612667500222735ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/mcevaluate/__init__.py000066400000000000000000000000001400612667500243720ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/mcevaluate/arma.py000066400000000000000000000107141400612667500235700ustar00rootroot00000000000000 import numpy as np from statsmodels.tsa.arima_process import arma_generate_sample from statsmodels.tsa.arma_mle import Arma #TODO: still refactoring problem with cov_x #copied from sandbox.tsa.arima.py def mcarma22(niter=10, nsample=1000, ar=None, ma=None, sig=0.5): '''run Monte Carlo for ARMA(2,2) DGP parameters currently hard coded also sample size `nsample` was not a self contained function, used instances from outer scope now corrected ''' #nsample = 1000 #ar = [1.0, 0, 0] if ar is None: ar = [1.0, -0.55, -0.1] #ma = [1.0, 0, 0] if ma is None: ma = [1.0, 0.3, 0.2] results = [] results_bse = [] for _ in range(niter): y2 = arma_generate_sample(ar,ma,nsample+1000, sig)[-nsample:] y2 -= y2.mean() arest2 = Arma(y2) rhohat2a, cov_x2a, infodict, mesg, ier = arest2.fit((2,2)) results.append(rhohat2a) err2a = arest2.geterrors(rhohat2a) sige2a = np.sqrt(np.dot(err2a,err2a)/nsample) #print('sige2a', sige2a, #print('cov_x2a.shape', cov_x2a.shape #results_bse.append(sige2a * np.sqrt(np.diag(cov_x2a))) if cov_x2a is not None: results_bse.append(sige2a * np.sqrt(np.diag(cov_x2a))) else: results_bse.append(np.nan + np.zeros_like(rhohat2a)) return np.r_[ar[1:], ma[1:]], np.array(results), np.array(results_bse) def mc_summary(res, rt=None): if rt is None: rt = np.zeros(res.shape[1]) nanrows = np.isnan(res).any(1) print('fractions of iterations with nans', nanrows.mean()) res = res[~nanrows] print('RMSE') print(np.sqrt(((res-rt)**2).mean(0))) print('mean bias') print((res-rt).mean(0)) print('median bias') print(np.median((res-rt),0)) print('median bias percent') print(np.median((res-rt)/rt*100,0)) print('median absolute error') print(np.median(np.abs(res-rt),0)) print('positive error fraction') print((res > rt).mean(0)) if __name__ == '__main__': #short version # true, est, bse = mcarma22(niter=50) # print(true # #print(est # print(est.mean(0) ''' niter 50, sample size=1000, 2 runs [-0.55 -0.1 0.3 0.2 ] [-0.542401 -0.09904305 0.30840599 0.2052473 ] [-0.55 -0.1 0.3 0.2 ] [-0.54681176 -0.09742921 0.2996297 0.20624258] niter=50, sample size=200, 3 runs [-0.55 -0.1 0.3 0.2 ] [-0.64669489 -0.01134491 0.19972259 0.20634019] [-0.55 -0.1 0.3 0.2 ] [-0.53141595 -0.10653234 0.32297968 0.20505973] [-0.55 -0.1 0.3 0.2 ] [-0.50244588 -0.125455 0.33867488 0.19498214] niter=50, sample size=100, 5 runs --> ar1 too low, ma1 too high [-0.55 -0.1 0.3 0.2 ] [-0.35715008 -0.23392766 0.48771794 0.21901059] [-0.55 -0.1 0.3 0.2 ] [-0.3554852 -0.21581914 0.51744748 0.24759245] [-0.55 -0.1 0.3 0.2 ] [-0.3737861 -0.24665911 0.48031939 0.17274438] [-0.55 -0.1 0.3 0.2 ] [-0.30015385 -0.27705506 0.56168199 0.21995759] [-0.55 -0.1 0.3 0.2 ] [-0.35879991 -0.22999604 0.4761953 0.19670835] new version, with burnin 1000 in DGP and demean [-0.55 -0.1 0.3 0.2 ] [-0.56770228 -0.00076025 0.25621825 0.24492449] [-0.55 -0.1 0.3 0.2 ] [-0.27598305 -0.2312364 0.57599134 0.23582417] [-0.55 -0.1 0.3 0.2 ] [-0.38059051 -0.17413628 0.45147109 0.20046776] [-0.55 -0.1 0.3 0.2 ] [-0.47789765 -0.08650743 0.3554441 0.24196087] ''' ar = [1.0, -0.55, -0.1] ma = [1.0, 0.3, 0.2] nsample = 200 run_mc = True#False if run_mc: for sig in [0.1, 0.5, 1.]: import time t0 = time.time() rt, res_rho, res_bse = mcarma22(niter=100, sig=sig) print('\nResults for Monte Carlo') print('true') print(rt) print('nsample =', nsample, 'sigma = ', sig) print('elapsed time for Monte Carlo', time.time()-t0) # 20 seconds for ARMA(2,2), 1000 iterations with 1000 observations #sige2a = np.sqrt(np.dot(err2a,err2a)/nsample) #print('\nbse of one sample' #print(sige2a * np.sqrt(np.diag(cov_x2a)) print('\nMC of rho versus true') mc_summary(res_rho, rt) print('\nMC of bse versus zero') # this implies inf in percent mc_summary(res_bse) print('\nMC of bse versus std') mc_summary(res_bse, res_rho.std(0)) statsmodels-0.12.2/statsmodels/sandbox/mcevaluate/mcresuts_arma1.txt000066400000000000000000000207561400612667500257740ustar00rootroot00000000000000MonteCarlo for Arma(2,2) fit with conditional least squares =========================================================== Comments: --------- scikits.statsmodels.tsa.arma_mle.Arma.fit((2,0,2)) niter=100 did not use seed some strange inf in median bias percent and positive error fraction equal to 1 Sample Size 1000 ---------------- Results for Monte Carlo true [-0.55 -0.1 0.3 0.2 ] nsample = 1000 sigma = 0.1 elapsed time for Monte Carlo 3.67199993134 MC of rho versus true fractions of iterations with nans 0.0 RMSE [ 0.20193839 0.1609546 0.19646184 0.03923539] mean bias [-0.00186601 0.00542719 -0.00533277 0.00676964] median bias [-0.00810009 0.01230101 -0.01806484 0.0026727 ] median bias percent [ 1.47274338 -12.30101426 -6.02161246 1.33634779] median absolute error [ 0.12849263 0.0892165 0.11939251 0.02566005] positive error fraction [ 0.49 0.52 0.48 0.54] MC of bse versus zero fractions of iterations with nans 0.0 RMSE [ 0.18967743 0.1526568 0.18747709 0.0399396 ] mean bias [ 0.18424688 0.14866981 0.18194085 0.03985427] median bias [ 0.18197743 0.14733603 0.17935651 0.03915853] median bias percent [ Inf Inf Inf Inf] median absolute error [ 0.18197743 0.14733603 0.17935651 0.03915853] positive error fraction [ 1. 1. 1. 1.] MC of bse versus std fractions of iterations with nans 0.0 RMSE [ 0.04840765 0.03674317 0.04747574 0.00287514] mean bias [-0.01768289 -0.01219327 -0.0144486 0.0012073 ] median bias [-0.01995233 -0.01352704 -0.01703294 0.00051156] median bias percent [-9.88082703 -8.40904072 -8.67304431 1.3236821 ] median absolute error [ 0.03143609 0.02330123 0.03006728 0.00095056] positive error fraction [ 0.31 0.31 0.35 0.65] Results for Monte Carlo true [-0.55 -0.1 0.3 0.2 ] nsample = 1000 sigma = 0.5 elapsed time for Monte Carlo 3.53200006485 MC of rho versus true fractions of iterations with nans 0.0 RMSE [ 0.23357913 0.18306959 0.23336364 0.04347842] mean bias [-0.01220215 0.01449933 -0.00740801 0.00400656] median bias [ 0.00474757 -0.00285192 -0.00179209 0.00881695] median bias percent [-0.86319392 2.85192134 -0.59736288 4.40847694] median absolute error [ 0.14260379 0.10966381 0.1388728 0.02879121] positive error fraction [ 0.51 0.49 0.5 0.59] MC of bse versus zero fractions of iterations with nans 0.0 RMSE [ 0.19115836 0.15300091 0.18899884 0.04041533] mean bias [ 0.18636096 0.14958803 0.18410379 0.04029974] median bias [ 0.17674161 0.14286746 0.17423869 0.03952101] median bias percent [ Inf Inf Inf Inf] median absolute error [ 0.17674161 0.14286746 0.17423869 0.03952101] positive error fraction [ 1. 1. 1. 1.] MC of bse versus std fractions of iterations with nans 0.0 RMSE [ 0.0633297 0.04599496 0.06512538 0.004277 ] mean bias [-0.04689923 -0.03290647 -0.04914224 -0.00299369] median bias [-0.05651859 -0.03962704 -0.05900734 -0.00377242] median bias percent [-24.22984657 -21.71410167 -25.29832734 -8.71360165] median absolute error [ 0.05810372 0.04048892 0.06100925 0.00383568] positive error fraction [ 0.13 0.11 0.11 0.1 ] Results for Monte Carlo true [-0.55 -0.1 0.3 0.2 ] nsample = 1000 sigma = 1.0 elapsed time for Monte Carlo 3.78200006485 MC of rho versus true fractions of iterations with nans 0.0 RMSE [ 0.23501983 0.18658536 0.23630675 0.04845701] mean bias [-0.0638577 0.0559638 -0.06116445 -0.00201522] median bias [-0.02571522 0.01710684 -0.02476506 -0.00040966] median bias percent [ 4.6754946 -17.10684152 -8.25501939 -0.20482813] median absolute error [ 0.13186172 0.11635244 0.1391435 0.03325726] positive error fraction [ 0.45 0.52 0.46 0.5 ] MC of bse versus zero fractions of iterations with nans 0.0 RMSE [ 0.2057234 0.16345869 0.20369599 0.04110316] mean bias [ 0.19816783 0.15783531 0.19595057 0.04093056] median bias [ 0.18616527 0.14688067 0.18394698 0.03953418] median bias percent [ Inf Inf Inf Inf] median absolute error [ 0.18616527 0.14688067 0.18394698 0.03953418] positive error fraction [ 1. 1. 1. 1.] MC of bse versus std fractions of iterations with nans 0.0 RMSE [ 0.06193706 0.04704427 0.06433453 0.00837719] mean bias [-0.02801022 -0.02015949 -0.03230322 -0.00748453] median bias [-0.04001279 -0.03111413 -0.04430681 -0.00888091] median bias percent [-17.69083491 -17.48036125 -19.41120455 -18.3432625 ] median absolute error [ 0.05454876 0.03993081 0.05735269 0.00892246] positive error fraction [ 0.24 0.21 0.2 0.07] Sample Size 200 --------------- Results for Monte Carlo true [-0.55 -0.1 0.3 0.2 ] nsample = 200 sigma = 0.1 elapsed time for Monte Carlo 3.76600003242 MC of rho versus true fractions of iterations with nans 0.0 RMSE [ 0.23797307 0.18908967 0.24248704 0.04532965] mean bias [-0.02240914 0.02006369 -0.02856247 0.00419784] median bias [ 0.0132667 -0.01695 -0.00779267 0.00943245] median bias percent [ -2.41212746 16.94999813 -2.5975563 4.71622452] median absolute error [ 0.14314755 0.10134399 0.13262758 0.02681113] positive error fraction [ 0.53 0.49 0.48 0.57] MC of bse versus zero fractions of iterations with nans 0.0 RMSE [ 0.18994719 0.1524025 0.18777651 0.0401027 ] mean bias [ 0.18437936 0.14841141 0.18216825 0.03997125] median bias [ 0.18044553 0.14526126 0.17764634 0.03921749] median bias percent [ Inf Inf Inf Inf] median absolute error [ 0.18044553 0.14526126 0.17764634 0.03921749] positive error fraction [ 1. 1. 1. 1.] MC of bse versus std fractions of iterations with nans 0.0 RMSE [ 0.0696006 0.05262689 0.07424492 0.00609829] mean bias [-0.05253626 -0.0396108 -0.05863073 -0.00516361] median bias [-0.0564701 -0.04276095 -0.06315264 -0.00591737] median bias percent [-23.83553085 -22.74250075 -26.22629031 -13.11041727] median absolute error [ 0.05851016 0.04572261 0.0646474 0.00594597] positive error fraction [ 0.11 0.13 0.1 0.04] Results for Monte Carlo true [-0.55 -0.1 0.3 0.2 ] nsample = 200 sigma = 0.5 elapsed time for Monte Carlo 3.86000013351 MC of rho versus true fractions of iterations with nans 0.0 RMSE [ 0.21997161 0.17584013 0.22184246 0.04268358] mean bias [-0.04259758 0.03350341 -0.05393998 -0.01056256] median bias [-0.02365517 0.01051654 -0.04060612 -0.00710624] median bias percent [ 4.3009406 -10.51654169 -13.53537431 -3.55312073] median absolute error [ 0.13186161 0.1056892 0.13501117 0.02523291] positive error fraction [ 0.45 0.55 0.42 0.42] MC of bse versus zero fractions of iterations with nans 0.0 RMSE [ 0.21373305 0.17013489 0.21176584 0.04080147] mean bias [ 0.20622114 0.16464733 0.20408995 0.04068523] median bias [ 0.19022777 0.15274254 0.1879751 0.03969161] median bias percent [ Inf Inf Inf Inf] median absolute error [ 0.19022777 0.15274254 0.1879751 0.03969161] positive error fraction [ 1. 1. 1. 1.] MC of bse versus std fractions of iterations with nans 0.0 RMSE [ 0.05697861 0.0435968 0.05757744 0.00314984] mean bias [-0.00958654 -0.00797153 -0.01109498 -0.00067079] median bias [-0.02557991 -0.01987633 -0.02720983 -0.00166441] median bias percent [-11.85310581 -11.5145739 -12.64485773 -4.02458691] median absolute error [ 0.03635737 0.0292344 0.03793175 0.00238808] positive error fraction [ 0.31 0.29 0.3 0.28] Results for Monte Carlo true [-0.55 -0.1 0.3 0.2 ] nsample = 200 sigma = 1.0 elapsed time for Monte Carlo 3.59400010109 MC of rho versus true fractions of iterations with nans 0.0 RMSE [ 0.22232599 0.17545665 0.21586404 0.04731953] mean bias [-0.02145001 0.02789994 -0.01930862 0.00418517] median bias [ 0.00685442 0.01411879 0.01616525 0.01340016] median bias percent [ -1.24625802 -14.11879188 5.38841584 6.70007966] median absolute error [ 0.1010917 0.09510124 0.10884815 0.02735024] positive error fraction [ 0.51 0.54 0.51 0.64] MC of bse versus zero fractions of iterations with nans 0.0 RMSE [ 0.19090008 0.15218083 0.18870297 0.04077881] mean bias [ 0.1863764 0.14894541 0.18407595 0.04063975] median bias [ 0.17861243 0.14324048 0.17665358 0.03948681] median bias percent [ Inf Inf Inf Inf] median absolute error [ 0.17861243 0.14324048 0.17665358 0.03948681] positive error fraction [ 1. 1. 1. 1.] MC of bse versus std fractions of iterations with nans 0.0 RMSE [ 0.05408839 0.03954405 0.0517791 0.00731427] mean bias [-0.03491242 -0.02427881 -0.03092279 -0.00649433] median bias [-0.04267639 -0.02998373 -0.03834516 -0.00764727] median bias percent [-19.2853791 -17.30920408 -17.83506488 -16.22449948] median absolute error [ 0.04673299 0.03434164 0.0433639 0.00769409] positive error fraction [ 0.13 0.14 0.16 0.07] statsmodels-0.12.2/statsmodels/sandbox/mle.py000066400000000000000000000031721400612667500212770ustar00rootroot00000000000000'''What's the origin of this file? It is not ours. Does not run because of missing mtx files, now included changes: JP corrections to imports so it runs, comment out print ''' import numpy as np from numpy import dot, outer, random from scipy import io, linalg, optimize from scipy.sparse import eye as speye import matplotlib.pyplot as plt def R(v): rq = dot(v.T,A*v)/dot(v.T,B*v) res = (A*v-rq*B*v)/linalg.norm(B*v) data.append(linalg.norm(res)) return rq def Rp(v): """ Gradient """ result = 2*(A*v-R(v)*B*v)/dot(v.T,B*v) #print "Rp: ", result return result def Rpp(v): """ Hessian """ result = 2*(A-R(v)*B-outer(B*v,Rp(v))-outer(Rp(v),B*v))/dot(v.T,B*v) #print "Rpp: ", result return result A = io.mmread('nos4.mtx') # clustered eigenvalues #B = io.mmread('bcsstm02.mtx.gz') #A = io.mmread('bcsstk06.mtx.gz') # clustered eigenvalues #B = io.mmread('bcsstm06.mtx.gz') n = A.shape[0] B = speye(n,n) random.seed(1) v_0=random.rand(n) print("try fmin_bfgs") full_output = 1 data=[] v,fopt, gopt, Hopt, func_calls, grad_calls, warnflag, allvecs = \ optimize.fmin_bfgs(R,v_0,fprime=Rp,full_output=full_output,retall=1) if warnflag == 0: plt.semilogy(np.arange(0,len(data)),data) print('Rayleigh quotient BFGS',R(v)) print("fmin_bfgs OK") print("try fmin_ncg") # # WARNING: the program may hangs if fmin_ncg is used # data=[] v,fopt, fcalls, gcalls, hcalls, warnflag, allvecs = \ optimize.fmin_ncg(R,v_0,fprime=Rp,fhess=Rpp,full_output=full_output,retall=1) if warnflag==0: plt.figure() plt.semilogy(np.arange(0,len(data)),data) print('Rayleigh quotient NCG',R(v)) statsmodels-0.12.2/statsmodels/sandbox/mlogitmath.lyx000066400000000000000000000145471400612667500230630ustar00rootroot00000000000000#LyX 1.6.2 created this file. For more info see http://www.lyx.org/ \lyxformat 345 \begin_document \begin_header \textclass article \use_default_options true \language english \inputencoding auto \font_roman default \font_sans default \font_typewriter default \font_default_family default \font_sc false \font_osf false \font_sf_scale 100 \font_tt_scale 100 \graphics default \paperfontsize default \use_hyperref false \papersize default \use_geometry false \use_amsmath 1 \use_esint 1 \cite_engine basic \use_bibtopic false \paperorientation portrait \secnumdepth 3 \tocdepth 3 \paragraph_separation indent \defskip medskip \quotes_language english \papercolumns 1 \papersides 1 \paperpagestyle default \tracking_changes false \output_changes false \author "" \author "" \end_header \begin_body \begin_layout Standard Notes on mlogit. \end_layout \begin_layout Standard Assume that \begin_inset Formula $J=3$ \end_inset , so that there are \begin_inset Formula $2$ \end_inset vectors of parameters for \begin_inset Formula $J-1$ \end_inset . For now the parameters are passed around as \begin_inset Formula \[ \left[\beta_{1}^{\prime}\beta_{2}^{\prime}\right]\] \end_inset \end_layout \begin_layout Standard So if \begin_inset Formula $K=3$ \end_inset (including the constant), then the matrix of parameters is \begin_inset Formula \[ \left[\begin{array}{cc} b_{10} & b_{20}\\ b_{11} & b_{21}\\ b_{12} & b_{22}\end{array}\right]^{\prime}\] \end_inset \end_layout \begin_layout Standard (changed to rows and added prime above, so this all changes and the score is also just transposed and flattend along the zero axis.) This is flattened along the zero axis for the sake of the solvers. So that it is passed internally as \begin_inset Formula \[ \left[\begin{array}{cccccc} b_{10} & b_{20} & b_{11} & b_{21} & b_{12} & b_{22}\end{array}\right]\] \end_inset Now the matrix of score vectors is \begin_inset Formula \[ \left[\begin{array}{cc} \frac{\partial\ln L}{\partial b_{10}} & \frac{\partial\ln L}{\partial b_{20}}\\ \frac{\partial\ln L}{\partial b_{11}} & \frac{\partial\ln L}{\partial b_{21}}\\ \frac{\partial\ln L}{\partial b_{12}} & \frac{\partial\ln L}{\partial b_{22}}\end{array}\right]\] \end_inset \end_layout \begin_layout Standard In Dhrymes notation, this would be column vectors \begin_inset Formula $\left(\partial\ln L/\partial\beta_{j}\right)^{\prime}\text{ for }j=1,2$ \end_inset in our example. So, our Jacobian is actually transposed vis-a-vis the more traditional notation. So that the solvers can handle this, though, it gets flattened but the score gets flattened along the first axis to make things easier, which is going to make things tricky. Now, in traditional notation, the Hessian would be \begin_inset Formula \[ \frac{\partial^{2}\ln L}{\partial\beta_{j}\partial\beta_{j}}=\frac{\partial}{\partial\beta_{j}}\vec{\left[\left(\frac{\partial\ln L}{\partial\beta_{j}}\right)\right]}\] \end_inset \end_layout \begin_layout Standard where \begin_inset Formula $\vec{}$ \end_inset denotes a vectorized matrix, i.e., for a \begin_inset Formula $n\times m$ \end_inset matrix \begin_inset Formula $X$ \end_inset , \begin_inset Formula $\vec{X}=\left(x_{\cdot1}^{\prime},x_{\cdot2}^{\prime},...,x_{\cdot m}^{\prime}\right)^{\prime}$ \end_inset such that \begin_inset Formula $x_{\cdot1}$ \end_inset is the first \begin_inset Formula $n$ \end_inset elements of column 1 of \begin_inset Formula $X$ \end_inset . This matrix is \begin_inset Formula $mn\times n$ \end_inset . In our case \begin_inset Formula $\ln L$ \end_inset is a scalar so \begin_inset Formula $m=1$ \end_inset , so each second derivative is \begin_inset Formula $n\times n$ \end_inset and \begin_inset Formula $n=K=3$ \end_inset in our example. Given our score \begin_inset Quotes eld \end_inset matrix, \begin_inset Quotes erd \end_inset our Hessian will look like \begin_inset Formula \[ H=\left[\begin{array}{cc} \frac{\partial\ln L}{\partial\beta_{1}\partial\beta_{1}} & \frac{\partial\ln L}{\partial\beta_{1}\partial\beta_{2}}\\ \frac{\partial\ln L}{\partial\beta_{2}\partial\beta_{1}} & \frac{\partial\ln L}{\partial\beta_{2}\partial\beta_{2}}\end{array}\right]\] \end_inset \begin_inset Formula \[ H=\left[\begin{array}{cccccc} \frac{\partial^{2}\ln L}{\partial b_{10}\partial b_{10}} & \frac{\partial^{2}\ln L}{\partial b_{10}\partial b_{11}} & \frac{\partial^{2}\ln L}{\partial b_{10}\partial b_{12}} & \frac{\partial^{2}\ln L}{\partial b_{10}\partial b_{20}} & \frac{\partial^{2}\ln L}{\partial b_{10}\partial b_{21}} & \frac{\partial^{2}\ln L}{\partial b_{10}\partial b_{22}}\\ \frac{\partial\ln L}{\partial b_{11}\partial b_{10}} & \frac{\partial\ln L}{\partial b_{11}\partial b_{11}} & \frac{\partial\ln L}{\partial b_{11}\partial b_{12}} & \frac{\partial\ln L}{\partial b_{11}\partial b_{20}} & \frac{\partial\ln L}{\partial b_{11}\partial b_{21}} & \frac{\partial\ln L}{\partial b_{11}\partial b_{22}}\\ \frac{\partial\ln L}{\partial b_{12}\partial b_{10}} & \frac{\partial\ln L}{\partial b_{12}\partial b_{11}} & \frac{\partial\ln L}{\partial b_{12}\partial b_{12}} & \frac{\partial\ln L}{\partial b_{12}\partial b_{20}} & \frac{\partial\ln L}{\partial b_{12}\partial b_{21}} & \frac{\partial\ln L}{\partial b_{12}\partial b_{22}}\\ \frac{\partial^{2}\ln L}{\partial b_{20}\partial b_{10}} & \frac{\partial^{2}\ln L}{\partial b_{20}\partial b_{11}} & \frac{\partial^{2}\ln L}{\partial b_{20}\partial b_{12}} & \frac{\partial^{2}\ln L}{\partial b_{20}\partial b_{20}} & \frac{\partial^{2}\ln L}{\partial b_{20}\partial b_{21}} & \frac{\partial^{2}\ln L}{\partial b_{20}\partial b_{22}}\\ \frac{\partial\ln L}{\partial b_{21}\partial b_{10}} & \frac{\partial\ln L}{\partial b_{21}\partial b_{11}} & \frac{\partial\ln L}{\partial b_{21}\partial b_{12}} & \frac{\partial\ln L}{\partial b_{21}\partial b_{20}} & \frac{\partial\ln L}{\partial b_{21}\partial b_{21}} & \frac{\partial\ln L}{\partial b_{21}\partial b_{22}}\\ \frac{\partial\ln L}{\partial b_{22}\partial b_{10}} & \frac{\partial\ln L}{\partial b_{22}\partial b_{11}} & \frac{\partial\ln L}{\partial b_{22}\partial b_{12}} & \frac{\partial\ln L}{\partial b_{22}\partial b_{20}} & \frac{\partial\ln L}{\partial b_{22}\partial b_{21}} & \frac{\partial\ln L}{\partial b_{22}\partial b_{22}}\end{array}\right]\] \end_inset \end_layout \begin_layout Standard But since our Jacobian is a row vector that alternate \end_layout \end_body \end_document statsmodels-0.12.2/statsmodels/sandbox/multilinear.py000066400000000000000000000331021400612667500230430ustar00rootroot00000000000000"""Analyze a set of multiple variables with a linear models multiOLS: take a model and test it on a series of variables defined over a pandas dataset, returning a summary for each variable multigroup: take a boolean vector and the definition of several groups of variables and test if the group has a fraction of true values higher than the rest. It allows to test if the variables in the group are significantly more significant than outside the group. """ from patsy import dmatrix import pandas as pd from statsmodels.api import OLS from statsmodels.api import stats import numpy as np import logging def _model2dataframe(model_endog, model_exog, model_type=OLS, **kwargs): """return a series containing the summary of a linear model All the exceding parameters will be redirected to the linear model """ # create the linear model and perform the fit model_result = model_type(model_endog, model_exog, **kwargs).fit() # keeps track of some global statistics statistics = pd.Series({'r2': model_result.rsquared, 'adj_r2': model_result.rsquared_adj}) # put them togher with the result for each term result_df = pd.DataFrame({'params': model_result.params, 'pvals': model_result.pvalues, 'std': model_result.bse, 'statistics': statistics}) # add the complexive results for f-value and the total p-value fisher_df = pd.DataFrame({'params': {'_f_test': model_result.fvalue}, 'pvals': {'_f_test': model_result.f_pvalue}}) # merge them and unstack to obtain a hierarchically indexed series res_series = pd.concat([result_df, fisher_df]).unstack() return res_series.dropna() def multiOLS(model, dataframe, column_list=None, method='fdr_bh', alpha=0.05, subset=None, model_type=OLS, **kwargs): """apply a linear model to several endogenous variables on a dataframe Take a linear model definition via formula and a dataframe that will be the environment of the model, and apply the linear model to a subset (or all) of the columns of the dataframe. It will return a dataframe with part of the information from the linear model summary. Parameters ---------- model : str formula description of the model dataframe : pandas.dataframe dataframe where the model will be evaluated column_list : list[str], optional Names of the columns to analyze with the model. If None (Default) it will perform the function on all the eligible columns (numerical type and not in the model definition) model_type : model class, optional The type of model to be used. The default is the linear model. Can be any linear model (OLS, WLS, GLS, etc..) method : str, optional the method used to perform the pvalue correction for multiple testing. default is the Benjamini/Hochberg, other available methods are: `bonferroni` : one-step correction `sidak` : on-step correction `holm-sidak` : `holm` : `simes-hochberg` : `hommel` : `fdr_bh` : Benjamini/Hochberg `fdr_by` : Benjamini/Yekutieli alpha : float, optional the significance level used for the pvalue correction (default 0.05) subset : bool array the selected rows to be used in the regression all the other parameters will be directed to the model creation. Returns ------- summary : pandas.DataFrame a dataframe containing an extract from the summary of the model obtained for each columns. It will give the model complexive f test result and p-value, and the regression value and standard deviarion for each of the regressors. The DataFrame has a hierachical column structure, divided as: - params: contains the parameters resulting from the models. Has an additional column named _f_test containing the result of the F test. - pval: the pvalue results of the models. Has the _f_test column for the significativity of the whole test. - adj_pval: the corrected pvalues via the multitest function. - std: uncertainties of the model parameters - statistics: contains the r squared statistics and the adjusted r squared. Notes ----- The main application of this function is on system biology to perform a linear model testing of a lot of different parameters, like the different genetic expression of several genes. See Also -------- statsmodels.stats.multitest contains several functions to perform the multiple p-value correction Examples -------- Using the longley data as dataframe example >>> import statsmodels.api as sm >>> data = sm.datasets.longley.load_pandas() >>> df = data.exog >>> df['TOTEMP'] = data.endog This will perform the specified linear model on all the other columns of the dataframe >>> multiOLS('GNP + 1', df) This select only a certain subset of the columns >>> multiOLS('GNP + 0', df, ['GNPDEFL', 'TOTEMP', 'POP']) It is possible to specify a trasformation also on the target column, conforming to the patsy formula specification >>> multiOLS('GNP + 0', df, ['I(GNPDEFL**2)', 'center(TOTEMP)']) It is possible to specify the subset of the dataframe on which perform the analysis >> multiOLS('GNP + 1', df, subset=df.GNPDEFL > 90) Even a single column name can be given without enclosing it in a list >>> multiOLS('GNP + 0', df, 'GNPDEFL') """ # data normalization # if None take all the numerical columns that are not present in the model # it's not waterproof but is a good enough criterion for everyday use if column_list is None: column_list = [name for name in dataframe.columns if dataframe[name].dtype != object and name not in model] # if it's a single string transform it in a single element list if isinstance(column_list, str): column_list = [column_list] if subset is not None: dataframe = dataframe.loc[subset] # perform each model and retrieve the statistics col_results = {} # as the model will use always the same endogenous variables # we can create them once and reuse model_exog = dmatrix(model, data=dataframe, return_type="dataframe") for col_name in column_list: # it will try to interpret the column name as a valid dataframe # index as it can be several times faster. If it fails it # interpret it as a patsy formula (for example for centering) try: model_endog = dataframe[col_name] except KeyError: model_endog = dmatrix(col_name + ' + 0', data=dataframe) # retrieve the result and store them res = _model2dataframe(model_endog, model_exog, model_type, **kwargs) col_results[col_name] = res # mangle them togheter and sort by complexive p-value summary = pd.DataFrame(col_results) # order by the p-value: the most useful model first! summary = summary.T.sort_values([('pvals', '_f_test')]) summary.index.name = 'endogenous vars' # implementing the pvalue correction method smt = stats.multipletests for (key1, key2) in summary: if key1 != 'pvals': continue p_values = summary[key1, key2] corrected = smt(p_values, method=method, alpha=alpha)[1] # extend the dataframe of results with the column # of the corrected p_values summary['adj_' + key1, key2] = corrected return summary def _test_group(pvalues, group_name, group, exact=True): """test if the objects in the group are different from the general set. The test is performed on the pvalues set (ad a pandas series) over the group specified via a fisher exact test. """ from scipy.stats import fisher_exact, chi2_contingency totals = 1.0 * len(pvalues) total_significant = 1.0 * np.sum(pvalues) cross_index = [c for c in group if c in pvalues.index] missing = [c for c in group if c not in pvalues.index] if missing: s = ('the test is not well defined if the group ' 'has elements not presents in the significativity ' 'array. group name: {}, missing elements: {}') logging.warning(s.format(group_name, missing)) # how many are significant and not in the group group_total = 1.0 * len(cross_index) group_sign = 1.0 * len([c for c in cross_index if pvalues[c]]) group_nonsign = 1.0 * (group_total - group_sign) # how many are significant and not outside the group extern_sign = 1.0 * (total_significant - group_sign) extern_nonsign = 1.0 * (totals - total_significant - group_nonsign) # make the fisher test or the chi squared test = fisher_exact if exact else chi2_contingency table = [[extern_nonsign, extern_sign], [group_nonsign, group_sign]] pvalue = test(np.array(table))[1] # is the group more represented or less? part = group_sign, group_nonsign, extern_sign, extern_nonsign #increase = (group_sign / group_total) > (total_significant / totals) increase = np.log((totals * group_sign) / (total_significant * group_total)) return pvalue, increase, part def multigroup(pvals, groups, exact=True, keep_all=True, alpha=0.05): """Test if the given groups are different from the total partition. Given a boolean array test if each group has a proportion of positives different than the complexive proportion. The test can be done as an exact Fisher test or approximated as a Chi squared test for more speed. Parameters ---------- pvals : pandas series of boolean the significativity of the variables under analysis groups : dict of list the name of each category of variables under exam. each one is a list of the variables included exact : bool, optional If True (default) use the fisher exact test, otherwise use the chi squared test for contingencies tables. For high number of elements in the array the fisher test can be significantly slower than the chi squared. keep_all : bool, optional if False it will drop those groups where the fraction of positive is below the expected result. If True (default) it will keep all the significant results. alpha : float, optional the significativity level for the pvalue correction on the whole set of groups (not inside the groups themselves). Returns ------- result_df: pandas dataframe for each group returns: pvals - the fisher p value of the test adj_pvals - the adjusted pvals increase - the log of the odd ratio between the internal significant ratio versus the external one _in_sign - significative elements inside the group _in_non - non significative elements inside the group _out_sign - significative elements outside the group _out_non - non significative elements outside the group Notes ----- This test allow to see if a category of variables is generally better suited to be described for the model. For example to see if a predictor gives more information on demographic or economical parameters, by creating two groups containing the endogenous variables of each category. This function is conceived for medical dataset with a lot of variables that can be easily grouped into functional groups. This is because The significativity of a group require a rather large number of composing elements. Examples -------- A toy example on a real dataset, the Guerry dataset from R >>> url = "https://raw.githubusercontent.com/vincentarelbundock/" >>> url = url + "Rdatasets/csv/HistData/Guerry.csv" >>> df = pd.read_csv(url, index_col='dept') evaluate the relationship between the various paramenters whith the Wealth >>> pvals = multiOLS('Wealth', df)['adj_pvals', '_f_test'] define the groups >>> groups = {} >>> groups['crime'] = ['Crime_prop', 'Infanticide', ... 'Crime_parents', 'Desertion', 'Crime_pers'] >>> groups['religion'] = ['Donation_clergy', 'Clergy', 'Donations'] >>> groups['wealth'] = ['Commerce', 'Lottery', 'Instruction', 'Literacy'] do the analysis of the significativity >>> multigroup(pvals < 0.05, groups) """ pvals = pd.Series(pvals) if not (set(pvals.unique()) <= set([False, True])): raise ValueError("the series should be binary") if hasattr(pvals.index, 'is_unique') and not pvals.index.is_unique: raise ValueError("series with duplicated index is not accepted") results = {'pvals': {}, 'increase': {}, '_in_sign': {}, '_in_non': {}, '_out_sign': {}, '_out_non': {}} for group_name, group_list in groups.items(): res = _test_group(pvals, group_name, group_list, exact) results['pvals'][group_name] = res[0] results['increase'][group_name] = res[1] results['_in_sign'][group_name] = res[2][0] results['_in_non'][group_name] = res[2][1] results['_out_sign'][group_name] = res[2][2] results['_out_non'][group_name] = res[2][3] result_df = pd.DataFrame(results).sort_values('pvals') if not keep_all: result_df = result_df[result_df.increase] smt = stats.multipletests corrected = smt(result_df['pvals'], method='fdr_bh', alpha=alpha)[1] result_df['adj_pvals'] = corrected return result_df statsmodels-0.12.2/statsmodels/sandbox/nonparametric/000077500000000000000000000000001400612667500230075ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/nonparametric/__init__.py000066400000000000000000000000301400612667500251110ustar00rootroot00000000000000# -*- coding: utf-8 -*- statsmodels-0.12.2/statsmodels/sandbox/nonparametric/densityorthopoly.py000066400000000000000000000424261400612667500270300ustar00rootroot00000000000000# -*- coding: utf-8 -*- # some cut and paste characters are not ASCII '''density estimation based on orthogonal polynomials Author: Josef Perktold Created: 2011-05017 License: BSD 2 versions work: based on Fourier, FPoly, and chebychev T, ChebyTPoly also hermite polynomials, HPoly, works other versions need normalization TODO: * check fourier case again: base is orthonormal, but needs offsetfact = 0 and does not integrate to 1, rescaled looks good * hermite: works but DensityOrthoPoly requires currently finite bounds I use it with offsettfactor 0.5 in example * not implemented methods: - add bonafide density correction - add transformation to domain of polynomial base - DONE possible problem: what is the behavior at the boundary, offsetfact requires more work, check different cases, add as option moved to polynomial class by default, as attribute * convert examples to test cases * need examples with large density on boundary, beta ? * organize poly classes in separate module, check new numpy.polynomials, polyvander * MISE measures, order selection, ... enhancements: * other polynomial bases: especially for open and half open support * wavelets * local or piecewise approximations ''' from scipy import stats, integrate, special import numpy as np sqr2 = np.sqrt(2.) class FPoly(object): '''Orthonormal (for weight=1) Fourier Polynomial on [0,1] orthonormal polynomial but density needs corfactor that I do not see what it is analytically parameterization on [0,1] from Sam Efromovich: Orthogonal series density estimation, 2010 John Wiley & Sons, Inc. WIREs Comp Stat 2010 2 467-476 ''' def __init__(self, order): self.order = order self.domain = (0, 1) self.intdomain = self.domain def __call__(self, x): if self.order == 0: return np.ones_like(x) else: return sqr2 * np.cos(np.pi * self.order * x) class F2Poly(object): '''Orthogonal (for weight=1) Fourier Polynomial on [0,pi] is orthogonal but first component does not square-integrate to 1 final result seems to need a correction factor of sqrt(pi) _corfactor = sqrt(pi) from integrating the density Parameterization on [0, pi] from Peter Hall, Cross-Validation and the Smoothing of Orthogonal Series Density Estimators, JOURNAL OF MULTIVARIATE ANALYSIS 21, 189-206 (1987) ''' def __init__(self, order): self.order = order self.domain = (0, np.pi) self.intdomain = self.domain self.offsetfactor = 0 def __call__(self, x): if self.order == 0: return np.ones_like(x) / np.sqrt(np.pi) else: return sqr2 * np.cos(self.order * x) / np.sqrt(np.pi) class ChebyTPoly(object): '''Orthonormal (for weight=1) Chebychev Polynomial on (-1,1) Notes ----- integration requires to stay away from boundary, offsetfactor > 0 maybe this implies that we cannot use it for densities that are > 0 at boundary ??? or maybe there is a mistake close to the boundary, sometimes integration works. ''' def __init__(self, order): self.order = order from scipy.special import chebyt self.poly = chebyt(order) self.domain = (-1, 1) self.intdomain = (-1+1e-6, 1-1e-6) #not sure if I need this, in integration nans are possible on the boundary self.offsetfactor = 0.01 #required for integration def __call__(self, x): if self.order == 0: return np.ones_like(x) / (1-x**2)**(1/4.) /np.sqrt(np.pi) else: return self.poly(x) / (1-x**2)**(1/4.) /np.sqrt(np.pi) *np.sqrt(2) logpi2 = np.log(np.pi)/2 class HPoly(object): '''Orthonormal (for weight=1) Hermite Polynomial, uses finite bounds for current use with DensityOrthoPoly domain is defined as [-6,6] ''' def __init__(self, order): self.order = order from scipy.special import hermite self.poly = hermite(order) self.domain = (-6, +6) self.offsetfactor = 0.5 # note this is def __call__(self, x): k = self.order lnfact = -(1./2)*(k*np.log(2.) + special.gammaln(k+1) + logpi2) - x*x/2 fact = np.exp(lnfact) return self.poly(x) * fact def polyvander(x, polybase, order=5): polyarr = np.column_stack([polybase(i)(x) for i in range(order)]) return polyarr def inner_cont(polys, lower, upper, weight=None): '''inner product of continuous function (with weight=1) Parameters ---------- polys : list of callables polynomial instances lower : float lower integration limit upper : float upper integration limit weight : callable or None weighting function Returns ------- innp : ndarray symmetric 2d square array with innerproduct of all function pairs err : ndarray numerical error estimate from scipy.integrate.quad, same dimension as innp Examples -------- >>> from scipy.special import chebyt >>> polys = [chebyt(i) for i in range(4)] >>> r, e = inner_cont(polys, -1, 1) >>> r array([[ 2. , 0. , -0.66666667, 0. ], [ 0. , 0.66666667, 0. , -0.4 ], [-0.66666667, 0. , 0.93333333, 0. ], [ 0. , -0.4 , 0. , 0.97142857]]) ''' n_polys = len(polys) innerprod = np.empty((n_polys, n_polys)) innerprod.fill(np.nan) interr = np.zeros((n_polys, n_polys)) for i in range(n_polys): for j in range(i+1): p1 = polys[i] p2 = polys[j] if weight is not None: innp, err = integrate.quad(lambda x: p1(x)*p2(x)*weight(x), lower, upper) else: innp, err = integrate.quad(lambda x: p1(x)*p2(x), lower, upper) innerprod[i,j] = innp interr[i,j] = err if not i == j: innerprod[j,i] = innp interr[j,i] = err return innerprod, interr def is_orthonormal_cont(polys, lower, upper, rtol=0, atol=1e-08): '''check whether functions are orthonormal Parameters ---------- polys : list of polynomials or function Returns ------- is_orthonormal : bool is False if the innerproducts are not close to 0 or 1 Notes ----- this stops as soon as the first deviation from orthonormality is found. Examples -------- >>> from scipy.special import chebyt >>> polys = [chebyt(i) for i in range(4)] >>> r, e = inner_cont(polys, -1, 1) >>> r array([[ 2. , 0. , -0.66666667, 0. ], [ 0. , 0.66666667, 0. , -0.4 ], [-0.66666667, 0. , 0.93333333, 0. ], [ 0. , -0.4 , 0. , 0.97142857]]) >>> is_orthonormal_cont(polys, -1, 1, atol=1e-6) False >>> polys = [ChebyTPoly(i) for i in range(4)] >>> r, e = inner_cont(polys, -1, 1) >>> r array([[ 1.00000000e+00, 0.00000000e+00, -9.31270888e-14, 0.00000000e+00], [ 0.00000000e+00, 1.00000000e+00, 0.00000000e+00, -9.47850712e-15], [ -9.31270888e-14, 0.00000000e+00, 1.00000000e+00, 0.00000000e+00], [ 0.00000000e+00, -9.47850712e-15, 0.00000000e+00, 1.00000000e+00]]) >>> is_orthonormal_cont(polys, -1, 1, atol=1e-6) True ''' for i in range(len(polys)): for j in range(i+1): p1 = polys[i] p2 = polys[j] innerprod = integrate.quad(lambda x: p1(x)*p2(x), lower, upper)[0] #print i,j, innerprod if not np.allclose(innerprod, i==j, rtol=rtol, atol=atol): return False return True #new versions class DensityOrthoPoly(object): '''Univariate density estimation by orthonormal series expansion Uses an orthonormal polynomial basis to approximate a univariate density. currently all arguments can be given to fit, I might change it to requiring arguments in __init__ instead. ''' def __init__(self, polybase=None, order=5): if polybase is not None: self.polybase = polybase self.polys = polys = [polybase(i) for i in range(order)] #try: #self.offsetfac = 0.05 #self.offsetfac = polys[0].offsetfactor #polys maybe not defined yet self._corfactor = 1 self._corshift = 0 def fit(self, x, polybase=None, order=5, limits=None): '''estimate the orthogonal polynomial approximation to the density ''' if polybase is None: polys = self.polys[:order] else: self.polybase = polybase self.polys = polys = [polybase(i) for i in range(order)] #move to init ? if not hasattr(self, 'offsetfac'): self.offsetfac = polys[0].offsetfactor xmin, xmax = x.min(), x.max() if limits is None: self.offset = offset = (xmax - xmin) * self.offsetfac limits = self.limits = (xmin - offset, xmax + offset) interval_length = limits[1] - limits[0] xinterval = xmax - xmin # need to cover (half-)open intervalls self.shrink = 1. / interval_length #xinterval/interval_length offset = (interval_length - xinterval ) / 2. self.shift = xmin - offset self.x = x = self._transform(x) coeffs = [(p(x)).mean() for p in polys] self.coeffs = coeffs self.polys = polys self._verify() #verify that it is a proper density return self #coeffs, polys def evaluate(self, xeval, order=None): xeval = self._transform(xeval) if order is None: order = len(self.polys) res = sum(c*p(xeval) for c, p in list(zip(self.coeffs, self.polys))[:order]) res = self._correction(res) return res def __call__(self, xeval): '''alias for evaluate, except no order argument''' return self.evaluate(xeval) def _verify(self): '''check for bona fide density correction currently only checks that density integrates to 1 ` non-negativity - NotImplementedYet ''' #watch out for circular/recursive usage #evaluate uses domain of data, we stay offset away from bounds intdomain = self.limits #self.polys[0].intdomain self._corfactor = 1./integrate.quad(self.evaluate, *intdomain)[0] #self._corshift = 0 #self._corfactor return self._corfactor def _correction(self, x): '''bona fide density correction affine shift of density to make it into a proper density ''' if self._corfactor != 1: x *= self._corfactor if self._corshift != 0: x += self._corshift return x def _transform(self, x): # limits=None): '''transform observation to the domain of the density uses shrink and shift attribute which are set in fit to stay ''' #use domain from first instance #class does not have domain self.polybase.domain[0] AttributeError domain = self.polys[0].domain ilen = (domain[1] - domain[0]) shift = self.shift - domain[0]/self.shrink/ilen shrink = self.shrink * ilen return (x - shift) * shrink #old version as a simple function def density_orthopoly(x, polybase, order=5, xeval=None): #polybase = legendre #chebyt #hermitenorm# #polybase = chebyt #polybase = FPoly #polybase = ChtPoly #polybase = hermite #polybase = HPoly if xeval is None: xeval = np.linspace(x.min(),x.max(),50) #polys = [legendre(i) for i in range(order)] polys = [polybase(i) for i in range(order)] #coeffs = [(p(x)*(1-x**2)**(-1/2.)).mean() for p in polys] #coeffs = [(p(x)*np.exp(-x*x)).mean() for p in polys] coeffs = [(p(x)).mean() for p in polys] res = sum(c*p(xeval) for c, p in zip(coeffs, polys)) #res *= (1-xeval**2)**(-1/2.) #res *= np.exp(-xeval**2./2) return res, xeval, coeffs, polys if __name__ == '__main__': examples = ['chebyt', 'fourier', 'hermite']#[2] nobs = 10000 import matplotlib.pyplot as plt from statsmodels.distributions.mixture_rvs import ( mixture_rvs, MixtureDistribution) #np.random.seed(12345) ## obs_dist = mixture_rvs([1/3.,2/3.], size=nobs, dist=[stats.norm, stats.norm], ## kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.75))) mix_kwds = (dict(loc=-0.5,scale=.5),dict(loc=1,scale=.2)) obs_dist = mixture_rvs([1/3.,2/3.], size=nobs, dist=[stats.norm, stats.norm], kwargs=mix_kwds) mix = MixtureDistribution() #obs_dist = np.random.randn(nobs)/4. #np.sqrt(2) if "chebyt_" in examples: # needed for Cheby example below #obs_dist = np.clip(obs_dist, -2, 2)/2.01 #chebyt [0,1] obs_dist = obs_dist[(obs_dist>-2) & (obs_dist<2)]/2.0 #/4. + 2/4.0 #fourier [0,1] #obs_dist = obs_dist[(obs_dist>-2) & (obs_dist<2)]/4. + 2/4.0 f_hat, grid, coeffs, polys = density_orthopoly(obs_dist, ChebyTPoly, order=20, xeval=None) #f_hat /= f_hat.sum() * (grid.max() - grid.min())/len(grid) f_hat0 = f_hat fint = integrate.trapz(f_hat, grid)# dx=(grid.max() - grid.min())/len(grid)) #f_hat -= fint/2. print('f_hat.min()', f_hat.min()) f_hat = (f_hat - f_hat.min()) #/ f_hat.max() - f_hat.min fint2 = integrate.trapz(f_hat, grid)# dx=(grid.max() - grid.min())/len(grid)) print('fint2', fint, fint2) f_hat /= fint2 # note that this uses a *huge* grid by default #f_hat, grid = kdensityfft(emp_dist, kernel="gauss", bw="scott") # check the plot doplot = 0 if doplot: plt.hist(obs_dist, bins=50, normed=True, color='red') plt.plot(grid, f_hat, lw=2, color='black') plt.plot(grid, f_hat0, lw=2, color='g') plt.show() for i,p in enumerate(polys[:5]): for j,p2 in enumerate(polys[:5]): print(i,j,integrate.quad(lambda x: p(x)*p2(x), -1,1)[0]) for p in polys: print(integrate.quad(lambda x: p(x)**2, -1,1)) #examples using the new class if "chebyt" in examples: dop = DensityOrthoPoly().fit(obs_dist, ChebyTPoly, order=20) grid = np.linspace(obs_dist.min(), obs_dist.max()) xf = dop(grid) #print('np.max(np.abs(xf - f_hat0))', np.max(np.abs(xf - f_hat0)) dopint = integrate.quad(dop, *dop.limits)[0] print('dop F integral', dopint) mpdf = mix.pdf(grid, [1/3.,2/3.], dist=[stats.norm, stats.norm], kwargs=mix_kwds) doplot = 1 if doplot: plt.figure() plt.hist(obs_dist, bins=50, normed=True, color='red') plt.plot(grid, xf, lw=2, color='black') plt.plot(grid, mpdf, lw=2, color='green') plt.title('using Chebychev polynomials') #plt.show() if "fourier" in examples: dop = DensityOrthoPoly() dop.offsetfac = 0.5 dop = dop.fit(obs_dist, F2Poly, order=30) grid = np.linspace(obs_dist.min(), obs_dist.max()) xf = dop(grid) #print(np.max(np.abs(xf - f_hat0)) dopint = integrate.quad(dop, *dop.limits)[0] print('dop F integral', dopint) mpdf = mix.pdf(grid, [1/3.,2/3.], dist=[stats.norm, stats.norm], kwargs=mix_kwds) doplot = 1 if doplot: plt.figure() plt.hist(obs_dist, bins=50, normed=True, color='red') plt.title('using Fourier polynomials') plt.plot(grid, xf, lw=2, color='black') plt.plot(grid, mpdf, lw=2, color='green') #plt.show() #check orthonormality: print(np.max(np.abs(inner_cont(dop.polys[:5], 0, 1)[0] -np.eye(5)))) if "hermite" in examples: dop = DensityOrthoPoly() dop.offsetfac = 0 dop = dop.fit(obs_dist, HPoly, order=20) grid = np.linspace(obs_dist.min(), obs_dist.max()) xf = dop(grid) #print(np.max(np.abs(xf - f_hat0)) dopint = integrate.quad(dop, *dop.limits)[0] print('dop F integral', dopint) mpdf = mix.pdf(grid, [1/3.,2/3.], dist=[stats.norm, stats.norm], kwargs=mix_kwds) doplot = 1 if doplot: plt.figure() plt.hist(obs_dist, bins=50, normed=True, color='red') plt.plot(grid, xf, lw=2, color='black') plt.plot(grid, mpdf, lw=2, color='green') plt.title('using Hermite polynomials') plt.show() #check orthonormality: print(np.max(np.abs(inner_cont(dop.polys[:5], 0, 1)[0] -np.eye(5)))) #check orthonormality hpolys = [HPoly(i) for i in range(5)] inn = inner_cont(hpolys, -6, 6)[0] print(np.max(np.abs(inn - np.eye(5)))) print((inn*100000).astype(int)) from scipy.special import hermite, chebyt htpolys = [hermite(i) for i in range(5)] innt = inner_cont(htpolys, -10, 10)[0] print((innt*100000).astype(int)) polysc = [chebyt(i) for i in range(4)] r, e = inner_cont(polysc, -1, 1, weight=lambda x: (1-x*x)**(-1/2.)) print(np.max(np.abs(r - np.diag(np.diag(r))))) statsmodels-0.12.2/statsmodels/sandbox/nonparametric/dgp_examples.py000066400000000000000000000135501400612667500260350ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Examples of non-linear functions for non-parametric regression Created on Sat Jan 05 20:21:22 2013 Author: Josef Perktold """ import numpy as np ## Functions def fg1(x): '''Fan and Gijbels example function 1 ''' return x + 2 * np.exp(-16 * x**2) def fg1eu(x): '''Eubank similar to Fan and Gijbels example function 1 ''' return x + 0.5 * np.exp(-50 * (x - 0.5)**2) def fg2(x): '''Fan and Gijbels example function 2 ''' return np.sin(2 * x) + 2 * np.exp(-16 * x**2) def func1(x): '''made up example with sin, square ''' return np.sin(x * 5) / x + 2. * x - 1. * x**2 ## Classes with Data Generating Processes doc = {'description': '''Base Class for Univariate non-linear example Does not work on it's own. needs additional at least self.func ''', 'ref': ''} class _UnivariateFunction(object): #Base Class for Univariate non-linear example. #Does not work on it's own. needs additionally at least self.func __doc__ = '''%(description)s Parameters ---------- nobs : int number of observations to simulate x : None or 1d array If x is given then it is used for the exogenous variable instead of creating a random sample distr_x : None or distribution instance Only used if x is None. The rvs method is used to create a random sample of the exogenous (explanatory) variable. distr_noise : None or distribution instance The rvs method is used to create a random sample of the errors. Attributes ---------- x : ndarray, 1-D exogenous or explanatory variable. x is sorted. y : ndarray, 1-D endogenous or response variable y_true : ndarray, 1-D expected values of endogenous or response variable, i.e. values of y without noise func : callable underlying function (defined by subclass) %(ref)s ''' #% doc def __init__(self, nobs=200, x=None, distr_x=None, distr_noise=None): if x is None: if distr_x is None: x = np.random.normal(loc=0, scale=self.s_x, size=nobs) else: x = distr_x.rvs(size=nobs) x.sort() self.x = x if distr_noise is None: noise = np.random.normal(loc=0, scale=self.s_noise, size=nobs) else: noise = distr_noise.rvs(size=nobs) if hasattr(self, 'het_scale'): noise *= self.het_scale(self.x) #self.func = fg1 self.y_true = y_true = self.func(x) self.y = y_true + noise def plot(self, scatter=True, ax=None): '''plot the mean function and optionally the scatter of the sample Parameters ---------- scatter : bool If true, then add scatterpoints of sample to plot. ax : None or matplotlib axis instance If None, then a matplotlib.pyplot figure is created, otherwise the given axis, ax, is used. Returns ------- Figure This is either the created figure instance or the one associated with ax if ax is given. ''' if ax is None: import matplotlib.pyplot as plt fig = plt.figure() ax = fig.add_subplot(1, 1, 1) if scatter: ax.plot(self.x, self.y, 'o', alpha=0.5) xx = np.linspace(self.x.min(), self.x.max(), 100) ax.plot(xx, self.func(xx), lw=2, color='b', label='dgp mean') return ax.figure doc = {'description': '''Fan and Gijbels example function 1 linear trend plus a hump ''', 'ref': ''' References ---------- Fan, Jianqing, and Irene Gijbels. 1992. "Variable Bandwidth and Local Linear Regression Smoothers." The Annals of Statistics 20 (4) (December): 2008-2036. doi:10.2307/2242378. '''} class UnivariateFanGijbels1(_UnivariateFunction): __doc__ = _UnivariateFunction.__doc__ % doc def __init__(self, nobs=200, x=None, distr_x=None, distr_noise=None): self.s_x = 1. self.s_noise = 0.7 self.func = fg1 super(self.__class__, self).__init__(nobs=nobs, x=x, distr_x=distr_x, distr_noise=distr_noise) doc['description'] =\ '''Fan and Gijbels example function 2 sin plus a hump ''' class UnivariateFanGijbels2(_UnivariateFunction): __doc__ = _UnivariateFunction.__doc__ % doc def __init__(self, nobs=200, x=None, distr_x=None, distr_noise=None): self.s_x = 1. self.s_noise = 0.5 self.func = fg2 super(self.__class__, self).__init__(nobs=nobs, x=x, distr_x=distr_x, distr_noise=distr_noise) class UnivariateFanGijbels1EU(_UnivariateFunction): ''' Eubank p.179f ''' def __init__(self, nobs=50, x=None, distr_x=None, distr_noise=None): if distr_x is None: from scipy import stats distr_x = stats.uniform self.s_noise = 0.15 self.func = fg1eu super(self.__class__, self).__init__(nobs=nobs, x=x, distr_x=distr_x, distr_noise=distr_noise) class UnivariateFunc1(_UnivariateFunction): ''' made up, with sin and quadratic trend ''' def __init__(self, nobs=200, x=None, distr_x=None, distr_noise=None): if x is None and distr_x is None: from scipy import stats distr_x = stats.uniform(-2, 4) else: nobs = x.shape[0] self.s_noise = 2. self.func = func1 super(UnivariateFunc1, self).__init__(nobs=nobs, x=x, distr_x=distr_x, distr_noise=distr_noise) def het_scale(self, x): return np.sqrt(np.abs(3+x)) statsmodels-0.12.2/statsmodels/sandbox/nonparametric/kde2.py000066400000000000000000000062001400612667500242040ustar00rootroot00000000000000# -*- coding: utf-8 -*- from statsmodels.compat.python import lzip import numpy as np from statsmodels.tools.validation import array_like from . import kernels #TODO: should this be a function? class KDE(object): """ Kernel Density Estimator Parameters ---------- x : array_like N-dimensional array from which the density is to be estimated kernel : Kernel Class Should be a class from * """ #TODO: amend docs for Nd case? def __init__(self, x, kernel=None): x = array_like(x, "x", maxdim=2, contiguous=True) if x.ndim == 1: x = x[:,None] nobs, n_series = x.shape if kernel is None: kernel = kernels.Gaussian() # no meaningful bandwidth yet if n_series > 1: if isinstance( kernel, kernels.CustomKernel ): kernel = kernels.NdKernel(n_series, kernels = kernel) self.kernel = kernel self.n = n_series #TODO change attribute self.x = x def density(self, x): return self.kernel.density(self.x, x) def __call__(self, x, h="scott"): return np.array([self.density(xx) for xx in x]) def evaluate(self, x, h="silverman"): density = self.kernel.density return np.array([density(xx) for xx in x]) if __name__ == "__main__": from numpy import random import matplotlib.pyplot as plt import statsmodels.nonparametric.bandwidths as bw from statsmodels.sandbox.nonparametric.testdata import kdetest # 1-D case random.seed(142) x = random.standard_t(4.2, size = 50) h = bw.bw_silverman(x) #NOTE: try to do it with convolution support = np.linspace(-10,10,512) kern = kernels.Gaussian(h = h) kde = KDE( x, kern) print(kde.density(1.015469)) print(0.2034675) Xs = np.arange(-10,10,0.1) fig = plt.figure() ax = fig.add_subplot(111) ax.plot(Xs, kde(Xs), "-") ax.set_ylim(-10, 10) ax.set_ylim(0,0.4) # 2-D case x = lzip(kdetest.faithfulData["eruptions"], kdetest.faithfulData["waiting"]) x = np.array(x) x = (x - x.mean(0))/x.std(0) nobs = x.shape[0] H = kdetest.Hpi kern = kernels.NdKernel( 2 ) kde = KDE( x, kern ) print(kde.density( np.matrix( [1,2 ]))) #.T plt.figure() plt.plot(x[:,0], x[:,1], 'o') n_grid = 50 xsp = np.linspace(x.min(0)[0], x.max(0)[0], n_grid) ysp = np.linspace(x.min(0)[1], x.max(0)[1], n_grid) # xsorted = np.sort(x) # xlow = xsorted[nobs/4] # xupp = xsorted[3*nobs/4] # xsp = np.linspace(xlow[0], xupp[0], n_grid) # ysp = np.linspace(xlow[1], xupp[1], n_grid) xr, yr = np.meshgrid(xsp, ysp) kde_vals = np.array([kde.density( np.matrix( [xi, yi ]) ) for xi, yi in zip(xr.ravel(), yr.ravel())]) plt.contour(xsp, ysp, kde_vals.reshape(n_grid, n_grid)) plt.show() # 5 D case # random.seed(142) # mu = [1.0, 4.0, 3.5, -2.4, 0.0] # sigma = np.matrix( # [[ 0.6 - 0.1*abs(i-j) if i != j else 1.0 for j in xrange(5)] for i in xrange(5)]) # x = random.multivariate_normal(mu, sigma, size = 100) # kern = kernel.Gaussian() # kde = KernelEstimate( x, kern ) statsmodels-0.12.2/statsmodels/sandbox/nonparametric/kdecovclass.py000066400000000000000000000130451400612667500256650ustar00rootroot00000000000000'''subclassing kde Author: josef pktd ''' import numpy as np from numpy.testing import assert_almost_equal, assert_ import scipy from scipy import stats import matplotlib.pylab as plt class gaussian_kde_set_covariance(stats.gaussian_kde): ''' from Anne Archibald in mailinglist: http://www.nabble.com/Width-of-the-gaussian-in-stats.kde.gaussian_kde---td19558924.html#a19558924 ''' def __init__(self, dataset, covariance): self.covariance = covariance scipy.stats.gaussian_kde.__init__(self, dataset) def _compute_covariance(self): self.inv_cov = np.linalg.inv(self.covariance) self._norm_factor = np.sqrt(np.linalg.det(2*np.pi*self.covariance)) * self.n class gaussian_kde_covfact(stats.gaussian_kde): def __init__(self, dataset, covfact = 'scotts'): self.covfact = covfact scipy.stats.gaussian_kde.__init__(self, dataset) def _compute_covariance_(self): '''not used''' self.inv_cov = np.linalg.inv(self.covariance) self._norm_factor = np.sqrt(np.linalg.det(2*np.pi*self.covariance)) * self.n def covariance_factor(self): if self.covfact in ['sc', 'scotts']: return self.scotts_factor() if self.covfact in ['si', 'silverman']: return self.silverman_factor() elif self.covfact: return float(self.covfact) else: raise ValueError('covariance factor has to be scotts, silverman or a number') def reset_covfact(self, covfact): self.covfact = covfact self.covariance_factor() self._compute_covariance() def plotkde(covfact): gkde.reset_covfact(covfact) kdepdf = gkde.evaluate(ind) plt.figure() # plot histgram of sample plt.hist(xn, bins=20, normed=1) # plot estimated density plt.plot(ind, kdepdf, label='kde', color="g") # plot data generating density plt.plot(ind, alpha * stats.norm.pdf(ind, loc=mlow) + (1-alpha) * stats.norm.pdf(ind, loc=mhigh), color="r", label='DGP: normal mix') plt.title('Kernel Density Estimation - ' + str(gkde.covfact)) plt.legend() def test_kde_1d(): np.random.seed(8765678) n_basesample = 500 xn = np.random.randn(n_basesample) xnmean = xn.mean() xnstd = xn.std(ddof=1) print(xnmean, xnstd) # get kde for original sample gkde = stats.gaussian_kde(xn) # evaluate the density function for the kde for some points xs = np.linspace(-7,7,501) kdepdf = gkde.evaluate(xs) normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd) print('MSE', np.sum((kdepdf - normpdf)**2)) print('axabserror', np.max(np.abs(kdepdf - normpdf))) intervall = xs[1] - xs[0] assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01) #assert_array_almost_equal(kdepdf, normpdf, decimal=2) print(gkde.integrate_gaussian(0.0, 1.0)) print(gkde.integrate_box_1d(-np.inf, 0.0)) print(gkde.integrate_box_1d(0.0, np.inf)) print(gkde.integrate_box_1d(-np.inf, xnmean)) print(gkde.integrate_box_1d(xnmean, np.inf)) assert_almost_equal(gkde.integrate_box_1d(xnmean, np.inf), 0.5, decimal=1) assert_almost_equal(gkde.integrate_box_1d(-np.inf, xnmean), 0.5, decimal=1) assert_almost_equal(gkde.integrate_box(xnmean, np.inf), 0.5, decimal=1) assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), 0.5, decimal=1) assert_almost_equal(gkde.integrate_kde(gkde), (kdepdf**2).sum()*intervall, decimal=2) assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2), (kdepdf*normpdf).sum()*intervall, decimal=2) ## assert_almost_equal(gkde.integrate_gaussian(0.0, 1.0), ## (kdepdf*normpdf).sum()*intervall, decimal=2) if __name__ == '__main__': # generate a sample n_basesample = 1000 np.random.seed(8765678) alpha = 0.6 #weight for (prob of) lower distribution mlow, mhigh = (-3,3) #mean locations for gaussian mixture xn = np.concatenate([mlow + np.random.randn(alpha * n_basesample), mhigh + np.random.randn((1-alpha) * n_basesample)]) # get kde for original sample #gkde = stats.gaussian_kde(xn) gkde = gaussian_kde_covfact(xn, 0.1) # evaluate the density function for the kde for some points ind = np.linspace(-7,7,101) kdepdf = gkde.evaluate(ind) plt.figure() # plot histgram of sample plt.hist(xn, bins=20, normed=1) # plot estimated density plt.plot(ind, kdepdf, label='kde', color="g") # plot data generating density plt.plot(ind, alpha * stats.norm.pdf(ind, loc=mlow) + (1-alpha) * stats.norm.pdf(ind, loc=mhigh), color="r", label='DGP: normal mix') plt.title('Kernel Density Estimation') plt.legend() gkde = gaussian_kde_covfact(xn, 'scotts') kdepdf = gkde.evaluate(ind) plt.figure() # plot histgram of sample plt.hist(xn, bins=20, normed=1) # plot estimated density plt.plot(ind, kdepdf, label='kde', color="g") # plot data generating density plt.plot(ind, alpha * stats.norm.pdf(ind, loc=mlow) + (1-alpha) * stats.norm.pdf(ind, loc=mhigh), color="r", label='DGP: normal mix') plt.title('Kernel Density Estimation') plt.legend() #plt.show() for cv in ['scotts', 'silverman', 0.05, 0.1, 0.5]: plotkde(cv) test_kde_1d() np.random.seed(8765678) n_basesample = 1000 xn = np.random.randn(n_basesample) xnmean = xn.mean() xnstd = xn.std(ddof=1) # get kde for original sample gkde = stats.gaussian_kde(xn) statsmodels-0.12.2/statsmodels/sandbox/nonparametric/kernel_extras.py000066400000000000000000000336721400612667500262420ustar00rootroot00000000000000""" Multivariate Conditional and Unconditional Kernel Density Estimation with Mixed Data Types References ---------- [1] Racine, J., Li, Q. Nonparametric econometrics: theory and practice. Princeton University Press. (2007) [2] Racine, Jeff. "Nonparametric Econometrics: A Primer," Foundation and Trends in Econometrics: Vol 3: No 1, pp1-88. (2008) http://dx.doi.org/10.1561/0800000009 [3] Racine, J., Li, Q. "Nonparametric Estimation of Distributions with Categorical and Continuous Data." Working Paper. (2000) [4] Racine, J. Li, Q. "Kernel Estimation of Multivariate Conditional Distributions Annals of Economics and Finance 5, 211-235 (2004) [5] Liu, R., Yang, L. "Kernel estimation of multivariate cumulative distribution function." Journal of Nonparametric Statistics (2008) [6] Li, R., Ju, G. "Nonparametric Estimation of Multivariate CDF with Categorical and Continuous Data." Working Paper [7] Li, Q., Racine, J. "Cross-validated local linear nonparametric regression" Statistica Sinica 14(2004), pp. 485-512 [8] Racine, J.: "Consistent Significance Testing for Nonparametric Regression" Journal of Business & Economics Statistics [9] Racine, J., Hart, J., Li, Q., "Testing the Significance of Categorical Predictor Variables in Nonparametric Regression Models", 2006, Econometric Reviews 25, 523-544 """ # TODO: make default behavior efficient=True above a certain n_obs import numpy as np from scipy import optimize from scipy.stats.mstats import mquantiles from statsmodels.nonparametric.api import KDEMultivariate, KernelReg from statsmodels.nonparametric._kernel_base import \ gpke, LeaveOneOut, _get_type_pos, _adjust_shape __all__ = ['SingleIndexModel', 'SemiLinear', 'TestFForm'] class TestFForm(object): """ Nonparametric test for functional form. Parameters ---------- endog : list Dependent variable (training set) exog : list of array_like objects The independent (right-hand-side) variables bw : array_like, str Bandwidths for exog or specify method for bandwidth selection fform : function The functional form ``y = g(b, x)`` to be tested. Takes as inputs the RHS variables `exog` and the coefficients ``b`` (betas) and returns a fitted ``y_hat``. var_type : str The type of the independent `exog` variables: - c: continuous - o: ordered - u: unordered estimator : function Must return the estimated coefficients b (betas). Takes as inputs ``(endog, exog)``. E.g. least square estimator:: lambda (x,y): np.dot(np.pinv(np.dot(x.T, x)), np.dot(x.T, y)) References ---------- See Racine, J.: "Consistent Significance Testing for Nonparametric Regression" Journal of Business & Economics Statistics. See chapter 12 in [1] pp. 355-357. """ def __init__(self, endog, exog, bw, var_type, fform, estimator, nboot=100): self.endog = endog self.exog = exog self.var_type = var_type self.fform = fform self.estimator = estimator self.nboot = nboot self.bw = KDEMultivariate(exog, bw=bw, var_type=var_type).bw self.sig = self._compute_sig() def _compute_sig(self): Y = self.endog X = self.exog b = self.estimator(Y, X) m = self.fform(X, b) n = np.shape(X)[0] resid = Y - m resid = resid - np.mean(resid) # center residuals self.test_stat = self._compute_test_stat(resid) sqrt5 = np.sqrt(5.) fct1 = (1 - sqrt5) / 2. fct2 = (1 + sqrt5) / 2. u1 = fct1 * resid u2 = fct2 * resid r = fct2 / sqrt5 I_dist = np.empty((self.nboot,1)) for j in range(self.nboot): u_boot = u2.copy() prob = np.random.uniform(0,1, size = (n,)) ind = prob < r u_boot[ind] = u1[ind] Y_boot = m + u_boot b_hat = self.estimator(Y_boot, X) m_hat = self.fform(X, b_hat) u_boot_hat = Y_boot - m_hat I_dist[j] = self._compute_test_stat(u_boot_hat) self.boots_results = I_dist sig = "Not Significant" if self.test_stat > mquantiles(I_dist, 0.9): sig = "*" if self.test_stat > mquantiles(I_dist, 0.95): sig = "**" if self.test_stat > mquantiles(I_dist, 0.99): sig = "***" return sig def _compute_test_stat(self, u): n = np.shape(u)[0] XLOO = LeaveOneOut(self.exog) uLOO = LeaveOneOut(u[:,None]).__iter__() ival = 0 S2 = 0 for i, X_not_i in enumerate(XLOO): u_j = next(uLOO) u_j = np.squeeze(u_j) # See Bootstrapping procedure on p. 357 in [1] K = gpke(self.bw, data=-X_not_i, data_predict=-self.exog[i, :], var_type=self.var_type, tosum=False) f_i = (u[i] * u_j * K) assert u_j.shape == K.shape ival += f_i.sum() # See eq. 12.7 on p. 355 in [1] S2 += (f_i**2).sum() # See Theorem 12.1 on p.356 in [1] assert np.size(ival) == 1 assert np.size(S2) == 1 ival *= 1. / (n * (n - 1)) ix_cont = _get_type_pos(self.var_type)[0] hp = self.bw[ix_cont].prod() S2 *= 2 * hp / (n * (n - 1)) T = n * ival * np.sqrt(hp / S2) return T class SingleIndexModel(KernelReg): """ Single index semiparametric model ``y = g(X * b) + e``. Parameters ---------- endog : array_like The dependent variable exog : array_like The independent variable(s) var_type : str The type of variables in X: - c: continuous - o: ordered - u: unordered Attributes ---------- b : array_like The linear coefficients b (betas) bw : array_like Bandwidths Methods ------- fit(): Computes the fitted values ``E[Y|X] = g(X * b)`` and the marginal effects ``dY/dX``. References ---------- See chapter on semiparametric models in [1] Notes ----- This model resembles the binary choice models. The user knows that X and b interact linearly, but ``g(X * b)`` is unknown. In the parametric binary choice models the user usually assumes some distribution of g() such as normal or logistic. """ def __init__(self, endog, exog, var_type): self.var_type = var_type self.K = len(var_type) self.var_type = self.var_type[0] self.endog = _adjust_shape(endog, 1) self.exog = _adjust_shape(exog, self.K) self.nobs = np.shape(self.exog)[0] self.data_type = self.var_type self.ckertype = 'gaussian' self.okertype = 'wangryzin' self.ukertype = 'aitchisonaitken' self.func = self._est_loc_linear self.b, self.bw = self._est_b_bw() def _est_b_bw(self): params0 = np.random.uniform(size=(self.K + 1, )) b_bw = optimize.fmin(self.cv_loo, params0, disp=0) b = b_bw[0:self.K] bw = b_bw[self.K:] bw = self._set_bw_bounds(bw) return b, bw def cv_loo(self, params): # See p. 254 in Textbook params = np.asarray(params) b = params[0 : self.K] bw = params[self.K:] LOO_X = LeaveOneOut(self.exog) LOO_Y = LeaveOneOut(self.endog).__iter__() L = 0 for i, X_not_i in enumerate(LOO_X): Y = next(LOO_Y) #print b.shape, np.dot(self.exog[i:i+1, :], b).shape, bw, G = self.func(bw, endog=Y, exog=-np.dot(X_not_i, b)[:,None], #data_predict=-b*self.exog[i, :])[0] data_predict=-np.dot(self.exog[i:i+1, :], b))[0] #print G.shape L += (self.endog[i] - G) ** 2 # Note: There might be a way to vectorize this. See p.72 in [1] return L / self.nobs def fit(self, data_predict=None): if data_predict is None: data_predict = self.exog else: data_predict = _adjust_shape(data_predict, self.K) N_data_predict = np.shape(data_predict)[0] mean = np.empty((N_data_predict,)) mfx = np.empty((N_data_predict, self.K)) for i in range(N_data_predict): mean_mfx = self.func(self.bw, self.endog, np.dot(self.exog, self.b)[:,None], data_predict=np.dot(data_predict[i:i+1, :],self.b)) mean[i] = mean_mfx[0] mfx_c = np.squeeze(mean_mfx[1]) mfx[i, :] = mfx_c return mean, mfx def __repr__(self): """Provide something sane to print.""" repr = "Single Index Model \n" repr += "Number of variables: K = " + str(self.K) + "\n" repr += "Number of samples: nobs = " + str(self.nobs) + "\n" repr += "Variable types: " + self.var_type + "\n" repr += "BW selection method: cv_ls" + "\n" repr += "Estimator type: local constant" + "\n" return repr class SemiLinear(KernelReg): """ Semiparametric partially linear model, ``Y = Xb + g(Z) + e``. Parameters ---------- endog : array_like The dependent variable exog : array_like The linear component in the regression exog_nonparametric : array_like The nonparametric component in the regression var_type : str The type of the variables in the nonparametric component; - c: continuous - o: ordered - u: unordered k_linear : int The number of variables that comprise the linear component. Attributes ---------- bw : array_like Bandwidths for the nonparametric component exog_nonparametric b : array_like Coefficients in the linear component nobs : int The number of observations. k_linear : int The number of variables that comprise the linear component. Methods ------- fit Returns the fitted mean and marginal effects dy/dz Notes ----- This model uses only the local constant regression estimator References ---------- See chapter on Semiparametric Models in [1] """ def __init__(self, endog, exog, exog_nonparametric, var_type, k_linear): self.endog = _adjust_shape(endog, 1) self.exog = _adjust_shape(exog, k_linear) self.K = len(var_type) self.exog_nonparametric = _adjust_shape(exog_nonparametric, self.K) self.k_linear = k_linear self.nobs = np.shape(self.exog)[0] self.var_type = var_type self.data_type = self.var_type self.ckertype = 'gaussian' self.okertype = 'wangryzin' self.ukertype = 'aitchisonaitken' self.func = self._est_loc_linear self.b, self.bw = self._est_b_bw() def _est_b_bw(self): """ Computes the (beta) coefficients and the bandwidths. Minimizes ``cv_loo`` with respect to ``b`` and ``bw``. """ params0 = np.random.uniform(size=(self.k_linear + self.K, )) b_bw = optimize.fmin(self.cv_loo, params0, disp=0) b = b_bw[0 : self.k_linear] bw = b_bw[self.k_linear:] #bw = self._set_bw_bounds(np.asarray(bw)) return b, bw def cv_loo(self, params): """ Similar to the cross validation leave-one-out estimator. Modified to reflect the linear components. Parameters ---------- params : array_like Vector consisting of the coefficients (b) and the bandwidths (bw). The first ``k_linear`` elements are the coefficients. Returns ------- L : float The value of the objective function References ---------- See p.254 in [1] """ params = np.asarray(params) b = params[0 : self.k_linear] bw = params[self.k_linear:] LOO_X = LeaveOneOut(self.exog) LOO_Y = LeaveOneOut(self.endog).__iter__() LOO_Z = LeaveOneOut(self.exog_nonparametric).__iter__() Xb = np.dot(self.exog, b)[:,None] L = 0 for ii, X_not_i in enumerate(LOO_X): Y = next(LOO_Y) Z = next(LOO_Z) Xb_j = np.dot(X_not_i, b)[:,None] Yx = Y - Xb_j G = self.func(bw, endog=Yx, exog=-Z, data_predict=-self.exog_nonparametric[ii, :])[0] lt = Xb[ii, :] #.sum() # linear term L += (self.endog[ii] - lt - G) ** 2 return L def fit(self, exog_predict=None, exog_nonparametric_predict=None): """Computes fitted values and marginal effects""" if exog_predict is None: exog_predict = self.exog else: exog_predict = _adjust_shape(exog_predict, self.k_linear) if exog_nonparametric_predict is None: exog_nonparametric_predict = self.exog_nonparametric else: exog_nonparametric_predict = _adjust_shape(exog_nonparametric_predict, self.K) N_data_predict = np.shape(exog_nonparametric_predict)[0] mean = np.empty((N_data_predict,)) mfx = np.empty((N_data_predict, self.K)) Y = self.endog - np.dot(exog_predict, self.b)[:,None] for i in range(N_data_predict): mean_mfx = self.func(self.bw, Y, self.exog_nonparametric, data_predict=exog_nonparametric_predict[i, :]) mean[i] = mean_mfx[0] mfx_c = np.squeeze(mean_mfx[1]) mfx[i, :] = mfx_c return mean, mfx def __repr__(self): """Provide something sane to print.""" repr = "Semiparamatric Partially Linear Model \n" repr += "Number of variables: K = " + str(self.K) + "\n" repr += "Number of samples: N = " + str(self.nobs) + "\n" repr += "Variable types: " + self.var_type + "\n" repr += "BW selection method: cv_ls" + "\n" repr += "Estimator type: local constant" + "\n" return repr statsmodels-0.12.2/statsmodels/sandbox/nonparametric/kernels.py000066400000000000000000000456601400612667500250370ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ This models contains the Kernels for Kernel smoothing. Hopefully in the future they may be reused/extended for other kernel based method References: ---------- Pointwise Kernel Confidence Bounds (smoothconf) http://fedc.wiwi.hu-berlin.de/xplore/ebooks/html/anr/anrhtmlframe62.html """ # pylint: disable-msg=C0103 # pylint: disable-msg=W0142 # pylint: disable-msg=E1101 # pylint: disable-msg=E0611 from statsmodels.compat.python import lzip, lfilter import numpy as np import scipy.integrate from scipy.special import factorial from numpy import exp, multiply, square, divide, subtract, inf class NdKernel(object): """Generic N-dimensial kernel Parameters ---------- n : int The number of series for kernel estimates kernels : list kernels Can be constructed from either a) a list of n kernels which will be treated as indepent marginals on a gaussian copula (specified by H) or b) a single univariate kernel which will be applied radially to the mahalanobis distance defined by H. In the case of the Gaussian these are both equivalent, and the second constructiong is prefered. """ def __init__(self, n, kernels = None, H = None): if kernels is None: kernels = Gaussian() self._kernels = kernels self.weights = None if H is None: H = np.matrix( np.identity(n)) self._H = H self._Hrootinv = np.linalg.cholesky( H.I ) def getH(self): """Getter for kernel bandwidth, H""" return self._H def setH(self, value): """Setter for kernel bandwidth, H""" self._H = value H = property(getH, setH, doc="Kernel bandwidth matrix") def density(self, xs, x): n = len(xs) #xs = self.in_domain( xs, xs, x )[0] if len(xs)>0: ## Need to do product of marginal distributions #w = np.sum([self(self._Hrootinv * (xx-x).T ) for xx in xs])/n #vectorized does not work: if self.weights is not None: w = np.mean(self((xs-x) * self._Hrootinv).T * self.weights)/sum(self.weights) else: w = np.mean(self((xs-x) * self._Hrootinv )) #transposed #w = np.mean([self(xd) for xd in ((xs-x) * self._Hrootinv)] ) #transposed return w else: return np.nan def _kernweight(self, x ): """returns the kernel weight for the independent multivariate kernel""" if isinstance( self._kernels, CustomKernel ): ## Radial case #d = x.T * x #x is matrix, 2d, element wise sqrt looks wrong #d = np.sqrt( x.T * x ) x = np.asarray(x) #d = np.sqrt( (x * x).sum(-1) ) d = (x * x).sum(-1) return self._kernels( np.asarray(d) ) def __call__(self, x): """ This simply returns the value of the kernel function at x Does the same as weight if the function is normalised """ return self._kernweight(x) class CustomKernel(object): """ Generic 1D Kernel object. Can be constructed by selecting a standard named Kernel, or providing a lambda expression and domain. The domain allows some algorithms to run faster for finite domain kernels. """ # MC: Not sure how this will look in the end - or even still exist. # Main purpose of this is to allow custom kernels and to allow speed up # from finite support. def __init__(self, shape, h = 1.0, domain = None, norm = None): """ shape should be a function taking and returning numeric type. For sanity it should always return positive or zero but this is not enforced in case you want to do weird things. Bear in mind that the statistical tests etc. may not be valid for non-positive kernels. The bandwidth of the kernel is supplied as h. You may specify a domain as a list of 2 values [min, max], in which case kernel will be treated as zero outside these values. This will speed up calculation. You may also specify the normalisation constant for the supplied Kernel. If you do this number will be stored and used as the normalisation without calculation. It is recommended you do this if you know the constant, to speed up calculation. In particular if the shape function provided is already normalised you should provide norm = 1.0. Warning: I think several calculations assume that the kernel is normalized. No tests for non-normalized kernel. """ self._normconst = norm # a value or None, if None, then calculate self.domain = domain self.weights = None if callable(shape): self._shape = shape else: raise TypeError("shape must be a callable object/function") self._h = h self._L2Norm = None self._kernel_var = None self._normal_reference_constant = None self._order = None def geth(self): """Getter for kernel bandwidth, h""" return self._h def seth(self, value): """Setter for kernel bandwidth, h""" self._h = value h = property(geth, seth, doc="Kernel Bandwidth") def in_domain(self, xs, ys, x): """ Returns the filtered (xs, ys) based on the Kernel domain centred on x """ # Disable black-list functions: filter used for speed instead of # list-comprehension # pylint: disable-msg=W0141 def isInDomain(xy): """Used for filter to check if point is in the domain""" u = (xy[0]-x)/self.h return np.all((u >= self.domain[0]) & (u <= self.domain[1])) if self.domain is None: return (xs, ys) else: filtered = lfilter(isInDomain, lzip(xs, ys)) if len(filtered) > 0: xs, ys = lzip(*filtered) return (xs, ys) else: return ([], []) def density(self, xs, x): """Returns the kernel density estimate for point x based on x-values xs """ xs = np.asarray(xs) n = len(xs) # before in_domain? if self.weights is not None: xs, weights = self.in_domain( xs, self.weights, x ) else: xs = self.in_domain( xs, xs, x )[0] xs = np.asarray(xs) #print 'len(xs)', len(xs), x if xs.ndim == 1: xs = xs[:,None] if len(xs)>0: h = self.h if self.weights is not None: w = 1 / h * np.sum(self((xs-x)/h).T * weights, axis=1) else: w = 1. / (h * n) * np.sum(self((xs-x)/h), axis=0) return w else: return np.nan def density_var(self, density, nobs): """approximate pointwise variance for kernel density not verified Parameters ---------- density : array_lie pdf of the kernel density nobs : int number of observations used in the KDE estimation Returns ------- kde_var : ndarray estimated variance of the density estimate Notes ----- This uses the asymptotic normal approximation to the distribution of the density estimate. """ return np.asarray(density) * self.L2Norm / self.h / nobs def density_confint(self, density, nobs, alpha=0.05): """approximate pointwise confidence interval for kernel density The confidence interval is centered at the estimated density and ignores the bias of the density estimate. not verified Parameters ---------- density : array_lie pdf of the kernel density nobs : int number of observations used in the KDE estimation Returns ------- conf_int : ndarray estimated confidence interval of the density estimate, lower bound in first column and upper bound in second column Notes ----- This uses the asymptotic normal approximation to the distribution of the density estimate. The lower bound can be negative for density values close to zero. """ from scipy import stats crit = stats.norm.isf(alpha / 2.) density = np.asarray(density) half_width = crit * np.sqrt(self.density_var(density, nobs)) conf_int = np.column_stack((density - half_width, density + half_width)) return conf_int def smooth(self, xs, ys, x): """Returns the kernel smoothing estimate for point x based on x-values xs and y-values ys. Not expected to be called by the user. """ xs, ys = self.in_domain(xs, ys, x) if len(xs)>0: w = np.sum(self((xs-x)/self.h)) #TODO: change the below to broadcasting when shape is sorted v = np.sum([yy*self((xx-x)/self.h) for xx, yy in zip(xs, ys)]) return v / w else: return np.nan def smoothvar(self, xs, ys, x): """Returns the kernel smoothing estimate of the variance at point x. """ xs, ys = self.in_domain(xs, ys, x) if len(xs) > 0: fittedvals = np.array([self.smooth(xs, ys, xx) for xx in xs]) sqresid = square( subtract(ys, fittedvals) ) w = np.sum(self((xs-x)/self.h)) v = np.sum([rr*self((xx-x)/self.h) for xx, rr in zip(xs, sqresid)]) return v / w else: return np.nan def smoothconf(self, xs, ys, x, alpha=0.05): """Returns the kernel smoothing estimate with confidence 1sigma bounds """ xs, ys = self.in_domain(xs, ys, x) if len(xs) > 0: fittedvals = np.array([self.smooth(xs, ys, xx) for xx in xs]) #fittedvals = self.smooth(xs, ys, x) # x or xs in Haerdle sqresid = square( subtract(ys, fittedvals) ) w = np.sum(self((xs-x)/self.h)) #var = sqresid.sum() / (len(sqresid) - 0) # nonlocal var ? JP just trying v = np.sum([rr*self((xx-x)/self.h) for xx, rr in zip(xs, sqresid)]) var = v / w sd = np.sqrt(var) K = self.L2Norm yhat = self.smooth(xs, ys, x) from scipy import stats crit = stats.norm.isf(alpha / 2) err = crit * sd * np.sqrt(K) / np.sqrt(w * self.h * self.norm_const) return (yhat - err, yhat, yhat + err) else: return (np.nan, np.nan, np.nan) @property def L2Norm(self): """Returns the integral of the square of the kernal from -inf to inf""" if self._L2Norm is None: L2Func = lambda x: (self.norm_const*self._shape(x))**2 if self.domain is None: self._L2Norm = scipy.integrate.quad(L2Func, -inf, inf)[0] else: self._L2Norm = scipy.integrate.quad(L2Func, self.domain[0], self.domain[1])[0] return self._L2Norm @property def norm_const(self): """ Normalising constant for kernel (integral from -inf to inf) """ if self._normconst is None: if self.domain is None: quadres = scipy.integrate.quad(self._shape, -inf, inf) else: quadres = scipy.integrate.quad(self._shape, self.domain[0], self.domain[1]) self._normconst = 1.0/(quadres[0]) return self._normconst @property def kernel_var(self): """Returns the second moment of the kernel""" if self._kernel_var is None: func = lambda x: x**2 * self.norm_const * self._shape(x) if self.domain is None: self._kernel_var = scipy.integrate.quad(func, -inf, inf)[0] else: self._kernel_var = scipy.integrate.quad(func, self.domain[0], self.domain[1])[0] return self._kernel_var def moments(self, n): if n > 2: msg = "Only first and second moment currently implemented" raise NotImplementedError(msg) if n == 1: return 0 if n == 2: return self.kernel_var @property def normal_reference_constant(self): """ Constant used for silverman normal reference asymtotic bandwidth calculation. C = 2((pi^(1/2)*(nu!)^3 R(k))/(2nu(2nu)!kap_nu(k)^2))^(1/(2nu+1)) nu = kernel order kap_nu = nu'th moment of kernel R = kernel roughness (square of L^2 norm) Note: L2Norm property returns square of norm. """ nu = self._order if not nu == 2: msg = "Only implemented for second order kernels" raise NotImplementedError(msg) if self._normal_reference_constant is None: C = np.pi**(.5) * factorial(nu)**3 * self.L2Norm C /= (2 * nu * factorial(2 * nu) * self.moments(nu)**2) C = 2*C**(1.0/(2*nu+1)) self._normal_reference_constant = C return self._normal_reference_constant def weight(self, x): """This returns the normalised weight at distance x""" return self.norm_const*self._shape(x) def __call__(self, x): """ This simply returns the value of the kernel function at x Does the same as weight if the function is normalised """ return self._shape(x) class Uniform(CustomKernel): def __init__(self, h=1.0): CustomKernel.__init__(self, shape=lambda x: 0.5 * np.ones(x.shape), h=h, domain=[-1.0, 1.0], norm = 1.0) self._L2Norm = 0.5 self._kernel_var = 1. / 3 self._order = 2 class Triangular(CustomKernel): def __init__(self, h=1.0): CustomKernel.__init__(self, shape=lambda x: 1 - abs(x), h=h, domain=[-1.0, 1.0], norm = 1.0) self._L2Norm = 2.0/3.0 self._kernel_var = 1. / 6 self._order = 2 class Epanechnikov(CustomKernel): def __init__(self, h=1.0): CustomKernel.__init__(self, shape=lambda x: 0.75*(1 - x*x), h=h, domain=[-1.0, 1.0], norm = 1.0) self._L2Norm = 0.6 self._kernel_var = 0.2 self._order = 2 class Biweight(CustomKernel): def __init__(self, h=1.0): CustomKernel.__init__(self, shape=lambda x: 0.9375*(1 - x*x)**2, h=h, domain=[-1.0, 1.0], norm = 1.0) self._L2Norm = 5.0/7.0 self._kernel_var = 1. / 7 self._order = 2 def smooth(self, xs, ys, x): """Returns the kernel smoothing estimate for point x based on x-values xs and y-values ys. Not expected to be called by the user. Special implementation optimized for Biweight. """ xs, ys = self.in_domain(xs, ys, x) if len(xs) > 0: w = np.sum(square(subtract(1, square(divide(subtract(xs, x), self.h))))) v = np.sum(multiply(ys, square(subtract(1, square(divide( subtract(xs, x), self.h)))))) return v / w else: return np.nan def smoothvar(self, xs, ys, x): """ Returns the kernel smoothing estimate of the variance at point x. """ xs, ys = self.in_domain(xs, ys, x) if len(xs) > 0: fittedvals = np.array([self.smooth(xs, ys, xx) for xx in xs]) rs = square(subtract(ys, fittedvals)) w = np.sum(square(subtract(1.0, square(divide(subtract(xs, x), self.h))))) v = np.sum(multiply(rs, square(subtract(1, square(divide( subtract(xs, x), self.h)))))) return v / w else: return np.nan def smoothconf_(self, xs, ys, x): """Returns the kernel smoothing estimate with confidence 1sigma bounds """ xs, ys = self.in_domain(xs, ys, x) if len(xs) > 0: fittedvals = np.array([self.smooth(xs, ys, xx) for xx in xs]) rs = square(subtract(ys, fittedvals)) w = np.sum(square(subtract(1.0, square(divide(subtract(xs, x), self.h))))) v = np.sum(multiply(rs, square(subtract(1, square(divide( subtract(xs, x), self.h)))))) var = v / w sd = np.sqrt(var) K = self.L2Norm yhat = self.smooth(xs, ys, x) err = sd * K / np.sqrt(0.9375 * w * self.h) return (yhat - err, yhat, yhat + err) else: return (np.nan, np.nan, np.nan) class Triweight(CustomKernel): def __init__(self, h=1.0): CustomKernel.__init__(self, shape=lambda x: 1.09375*(1 - x*x)**3, h=h, domain=[-1.0, 1.0], norm = 1.0) self._L2Norm = 350.0/429.0 self._kernel_var = 1. / 9 self._order = 2 class Gaussian(CustomKernel): """ Gaussian (Normal) Kernel K(u) = 1 / (sqrt(2*pi)) exp(-0.5 u**2) """ def __init__(self, h=1.0): CustomKernel.__init__(self, shape = lambda x: 0.3989422804014327 * np.exp(-x**2/2.0), h = h, domain = None, norm = 1.0) self._L2Norm = 1.0/(2.0*np.sqrt(np.pi)) self._kernel_var = 1.0 self._order = 2 def smooth(self, xs, ys, x): """Returns the kernel smoothing estimate for point x based on x-values xs and y-values ys. Not expected to be called by the user. Special implementation optimized for Gaussian. """ w = np.sum(exp(multiply(square(divide(subtract(xs, x), self.h)),-0.5))) v = np.sum(multiply(ys, exp(multiply(square(divide(subtract(xs, x), self.h)), -0.5)))) return v/w class Cosine(CustomKernel): """ Cosine Kernel K(u) = pi/4 cos(0.5 * pi * u) between -1.0 and 1.0 """ def __init__(self, h=1.0): CustomKernel.__init__(self, shape=lambda x: 0.78539816339744828 * np.cos(np.pi/2.0 * x), h=h, domain=[-1.0, 1.0], norm = 1.0) self._L2Norm = np.pi**2/16.0 self._kernel_var = 0.1894305308612978 # = 1 - 8 / np.pi**2 self._order = 2 class Cosine2(CustomKernel): """ Cosine2 Kernel K(u) = 1 + cos(2 * pi * u) between -0.5 and 0.5 Note: this is the same Cosine kernel that Stata uses """ def __init__(self, h=1.0): CustomKernel.__init__(self, shape=lambda x: 1 + np.cos(2.0 * np.pi * x) , h=h, domain=[-0.5, 0.5], norm = 1.0) self._L2Norm = 1.5 self._kernel_var = 0.03267274151216444 # = 1/12. - 0.5 / np.pi**2 self._order = 2 statsmodels-0.12.2/statsmodels/sandbox/nonparametric/smoothers.py000066400000000000000000000300101400612667500253760ustar00rootroot00000000000000""" This module contains scatterplot smoothers, that is classes who generate a smooth fit of a set of (x,y) pairs. """ # pylint: disable-msg=C0103 # pylint: disable-msg=W0142 # pylint: disable-msg=E0611 # pylint: disable-msg=E1101 import numpy as np from . import kernels class KernelSmoother(object): """ 1D Kernel Density Regression/Kernel Smoother Requires: x - array_like of x values y - array_like of y values Kernel - Kernel object, Default is Gaussian. """ def __init__(self, x, y, Kernel = None): if Kernel is None: Kernel = kernels.Gaussian() self.Kernel = Kernel self.x = np.array(x) self.y = np.array(y) def fit(self): pass def __call__(self, x): return np.array([self.predict(xx) for xx in x]) def predict(self, x): """ Returns the kernel smoothed prediction at x If x is a real number then a single value is returned. Otherwise an attempt is made to cast x to numpy.ndarray and an array of corresponding y-points is returned. """ if np.size(x) == 1: # if isinstance(x, numbers.Real): return self.Kernel.smooth(self.x, self.y, x) else: return np.array([self.Kernel.smooth(self.x, self.y, xx) for xx in np.array(x)]) def conf(self, x): """ Returns the fitted curve and 1-sigma upper and lower point-wise confidence. These bounds are based on variance only, and do not include the bias. If the bandwidth is much larger than the curvature of the underlying function then the bias could be large. x is the points on which you want to evaluate the fit and the errors. Alternatively if x is specified as a positive integer, then the fit and confidence bands points will be returned after every xth sample point - so they are closer together where the data is denser. """ if isinstance(x, int): sorted_x = np.array(self.x) sorted_x.sort() confx = sorted_x[::x] conffit = self.conf(confx) return (confx, conffit) else: return np.array([self.Kernel.smoothconf(self.x, self.y, xx) for xx in x]) def var(self, x): return np.array([self.Kernel.smoothvar(self.x, self.y, xx) for xx in x]) def std(self, x): return np.sqrt(self.var(x)) class PolySmoother(object): """ Polynomial smoother up to a given order. Fit based on weighted least squares. The x values can be specified at instantiation or when called. This is a 3 liner with OLS or WLS, see test. It's here as a test smoother for GAM """ #JP: heavily adjusted to work as plugin replacement for bspline # smoother in gam.py initialized by function default_smoother # Only fixed exceptions, I did not check whether it is statistically # correctand I think it is not, there are still be some dimension # problems, and there were some dimension problems initially. # TODO: undo adjustments and fix dimensions correctly # comment: this is just like polyfit with initialization options # and additional results (OLS on polynomial of x (x is 1d?)) def __init__(self, order, x=None): #order = 4 # set this because we get knots instead of order self.order = order #print order, x.shape self.coef = np.zeros((order+1,), np.float64) if x is not None: if x.ndim > 1: print('Warning: 2d x detected in PolySmoother init, shape:', x.shape) x=x[0,:] #check orientation self.X = np.array([x**i for i in range(order+1)]).T def df_fit(self): '''alias of df_model for backwards compatibility ''' return self.df_model() def df_model(self): """ Degrees of freedom used in the fit. """ return self.order + 1 def gram(self, d=None): #fake for spline imitation pass def smooth(self,*args, **kwds): '''alias for fit, for backwards compatibility, do we need it with different behavior than fit? ''' return self.fit(*args, **kwds) def df_resid(self): """ Residual degrees of freedom from last fit. """ return self.N - self.order - 1 def __call__(self, x=None): return self.predict(x=x) def predict(self, x=None): if x is not None: #if x.ndim > 1: x=x[0,:] #why this this should select column not row if x.ndim > 1: print('Warning: 2d x detected in PolySmoother predict, shape:', x.shape) x=x[:,0] #TODO: check and clean this up X = np.array([(x**i) for i in range(self.order+1)]) else: X = self.X #return np.squeeze(np.dot(X.T, self.coef)) #need to check what dimension this is supposed to be if X.shape[1] == self.coef.shape[0]: return np.squeeze(np.dot(X, self.coef))#[0] else: return np.squeeze(np.dot(X.T, self.coef))#[0] def fit(self, y, x=None, weights=None): self.N = y.shape[0] if y.ndim == 1: y = y[:,None] if weights is None or np.isnan(weights).all(): weights = 1 _w = 1 else: _w = np.sqrt(weights)[:,None] if x is None: if not hasattr(self, "X"): raise ValueError("x needed to fit PolySmoother") else: if x.ndim > 1: print('Warning: 2d x detected in PolySmoother predict, shape:', x.shape) #x=x[0,:] #TODO: check orientation, row or col self.X = np.array([(x**i) for i in range(self.order+1)]).T #print _w.shape X = self.X * _w _y = y * _w#[:,None] #self.coef = np.dot(L.pinv(X).T, _y[:,None]) #self.coef = np.dot(L.pinv(X), _y) self.coef = np.linalg.lstsq(X, _y, rcond=-1)[0] self.params = np.squeeze(self.coef) # comment out for now to remove dependency on _hbspline ##class SmoothingSpline(BSpline): ## ## penmax = 30. ## ## def fit(self, y, x=None, weights=None, pen=0.): ## banded = True ## ## if x is None: ## x = self.tau[(self.M-1):-(self.M-1)] # internal knots ## ## if pen == 0.: # cannot use cholesky for singular matrices ## banded = False ## ## if x.shape != y.shape: ## raise ValueError('x and y shape do not agree, by default x are the Bspline\'s internal knots') ## ## bt = self.basis(x) ## if pen >= self.penmax: ## pen = self.penmax ## ## if weights is None: ## weights = np.array(1.) ## ## wmean = weights.mean() ## _w = np.sqrt(weights / wmean) ## bt *= _w ## ## # throw out rows with zeros (this happens at boundary points!) ## ## mask = np.flatnonzero(1 - np.alltrue(np.equal(bt, 0), axis=0)) ## ## bt = bt[:, mask] ## y = y[mask] ## ## self.df_total = y.shape[0] ## ## if bt.shape[1] != y.shape[0]: ## raise ValueError("some x values are outside range of B-spline knots") ## bty = np.dot(bt, _w * y) ## self.N = y.shape[0] ## if not banded: ## self.btb = np.dot(bt, bt.T) ## _g = _band2array(self.g, lower=1, symmetric=True) ## self.coef, _, self.rank = L.lstsq(self.btb + pen*_g, bty)[0:3] ## self.rank = min(self.rank, self.btb.shape[0]) ## else: ## self.btb = np.zeros(self.g.shape, np.float64) ## nband, nbasis = self.g.shape ## for i in range(nbasis): ## for k in range(min(nband, nbasis-i)): ## self.btb[k, i] = (bt[i] * bt[i+k]).sum() ## ## bty.shape = (1, bty.shape[0]) ## self.chol, self.coef = solveh_banded(self.btb + ## pen*self.g, ## bty, lower=1) ## ## self.coef = np.squeeze(self.coef) ## self.resid = np.sqrt(wmean) * (y * _w - np.dot(self.coef, bt)) ## self.pen = pen ## ## def gcv(self): ## """ ## Generalized cross-validation score of current fit. ## """ ## ## norm_resid = (self.resid**2).sum() ## return norm_resid / (self.df_total - self.trace()) ## ## def df_resid(self): ## """ ## self.N - self.trace() ## ## where self.N is the number of observations of last fit. ## """ ## ## return self.N - self.trace() ## ## def df_fit(self): ## """ ## = self.trace() ## ## How many degrees of freedom used in the fit? ## """ ## return self.trace() ## ## def trace(self): ## """ ## Trace of the smoothing matrix S(pen) ## """ ## ## if self.pen > 0: ## _invband = _hbspline.invband(self.chol.copy()) ## tr = _trace_symbanded(_invband, self.btb, lower=1) ## return tr ## else: ## return self.rank ## ##class SmoothingSplineFixedDF(SmoothingSpline): ## """ ## Fit smoothing spline with approximately df degrees of freedom ## used in the fit, i.e. so that self.trace() is approximately df. ## ## In general, df must be greater than the dimension of the null space ## of the Gram inner product. For cubic smoothing splines, this means ## that df > 2. ## """ ## ## target_df = 5 ## ## def __init__(self, knots, order=4, coef=None, M=None, target_df=None): ## if target_df is not None: ## self.target_df = target_df ## BSpline.__init__(self, knots, order=order, coef=coef, M=M) ## self.target_reached = False ## ## def fit(self, y, x=None, df=None, weights=None, tol=1.0e-03): ## ## df = df or self.target_df ## ## apen, bpen = 0, 1.0e-03 ## olddf = y.shape[0] - self.m ## ## if not self.target_reached: ## while True: ## curpen = 0.5 * (apen + bpen) ## SmoothingSpline.fit(self, y, x=x, weights=weights, pen=curpen) ## curdf = self.trace() ## if curdf > df: ## apen, bpen = curpen, 2 * curpen ## else: ## apen, bpen = apen, curpen ## if apen >= self.penmax: ## raise ValueError("penalty too large, try setting penmax higher or decreasing df") ## if np.fabs(curdf - df) / df < tol: ## self.target_reached = True ## break ## else: ## SmoothingSpline.fit(self, y, x=x, weights=weights, pen=self.pen) ## ##class SmoothingSplineGCV(SmoothingSpline): ## ## """ ## Fit smoothing spline trying to optimize GCV. ## ## Try to find a bracketing interval for scipy.optimize.golden ## based on bracket. ## ## It is probably best to use target_df instead, as it is ## sometimes difficult to find a bracketing interval. ## ## """ ## ## def fit(self, y, x=None, weights=None, tol=1.0e-03, ## bracket=(0,1.0e-03)): ## ## def _gcv(pen, y, x): ## SmoothingSpline.fit(y, x=x, pen=np.exp(pen), weights=weights) ## a = self.gcv() ## return a ## ## a = golden(_gcv, args=(y,x), brack=(-100,20), tol=tol) ## ##def _trace_symbanded(a,b, lower=0): ## """ ## Compute the trace(a*b) for two upper or lower banded real symmetric matrices. ## """ ## ## if lower: ## t = _zero_triband(a * b, lower=1) ## return t[0].sum() + 2 * t[1:].sum() ## else: ## t = _zero_triband(a * b, lower=0) ## return t[-1].sum() + 2 * t[:-1].sum() ## ## ## ##def _zero_triband(a, lower=0): ## """ ## Zero out unnecessary elements of a real symmetric banded matrix. ## """ ## ## nrow, ncol = a.shape ## if lower: ## for i in range(nrow): a[i,(ncol-i):] = 0. ## else: ## for i in range(nrow): a[i,0:i] = 0. ## return a statsmodels-0.12.2/statsmodels/sandbox/nonparametric/testdata.py000066400000000000000000000067241400612667500252030ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Mar 04 07:36:28 2011 @author: Mike """ import numpy as np class kdetest(object): Hpi = np.matrix([[ 0.05163034, 0.5098923 ], [0.50989228, 8.8822365 ]]) faithfulData = dict( eruptions=[ 3.6, 1.8, 3.333, 2.283, 4.533, 2.883, 4.7, 3.6, 1.95, 4.35, 1.833, 3.917, 4.2, 1.75, 4.7, 2.167, 1.75, 4.8, 1.6, 4.25, 1.8, 1.75, 3.45, 3.067, 4.533, 3.6, 1.967, 4.083, 3.85, 4.433, 4.3, 4.467, 3.367, 4.033, 3.833, 2.017, 1.867, 4.833, 1.833, 4.783, 4.35, 1.883, 4.567, 1.75, 4.533, 3.317, 3.833, 2.1, 4.633, 2, 4.8, 4.716, 1.833, 4.833, 1.733, 4.883, 3.717, 1.667, 4.567, 4.317, 2.233, 4.5, 1.75, 4.8, 1.817, 4.4, 4.167, 4.7, 2.067, 4.7, 4.033, 1.967, 4.5, 4, 1.983, 5.067, 2.017, 4.567, 3.883, 3.6, 4.133, 4.333, 4.1, 2.633, 4.067, 4.933, 3.95, 4.517, 2.167, 4, 2.2, 4.333, 1.867, 4.817, 1.833, 4.3, 4.667, 3.75, 1.867, 4.9, 2.483, 4.367, 2.1, 4.5, 4.05, 1.867, 4.7, 1.783, 4.85, 3.683, 4.733, 2.3, 4.9, 4.417, 1.7, 4.633, 2.317, 4.6, 1.817, 4.417, 2.617, 4.067, 4.25, 1.967, 4.6, 3.767, 1.917, 4.5, 2.267, 4.65, 1.867, 4.167, 2.8, 4.333, 1.833, 4.383, 1.883, 4.933, 2.033, 3.733, 4.233, 2.233, 4.533, 4.817, 4.333, 1.983, 4.633, 2.017, 5.1, 1.8, 5.033, 4, 2.4, 4.6, 3.567, 4, 4.5, 4.083, 1.8, 3.967, 2.2, 4.15, 2, 3.833, 3.5, 4.583, 2.367, 5, 1.933, 4.617, 1.917, 2.083, 4.583, 3.333, 4.167, 4.333, 4.5, 2.417, 4, 4.167, 1.883, 4.583, 4.25, 3.767, 2.033, 4.433, 4.083, 1.833, 4.417, 2.183, 4.8, 1.833, 4.8, 4.1, 3.966, 4.233, 3.5, 4.366, 2.25, 4.667, 2.1, 4.35, 4.133, 1.867, 4.6, 1.783, 4.367, 3.85, 1.933, 4.5, 2.383, 4.7, 1.867, 3.833, 3.417, 4.233, 2.4, 4.8, 2, 4.15, 1.867, 4.267, 1.75, 4.483, 4, 4.117, 4.083, 4.267, 3.917, 4.55, 4.083, 2.417, 4.183, 2.217, 4.45, 1.883, 1.85, 4.283, 3.95, 2.333, 4.15, 2.35, 4.933, 2.9, 4.583, 3.833, 2.083, 4.367, 2.133, 4.35, 2.2, 4.45, 3.567, 4.5, 4.15, 3.817, 3.917, 4.45, 2, 4.283, 4.767, 4.533, 1.85, 4.25, 1.983, 2.25, 4.75, 4.117, 2.15, 4.417, 1.817, 4.467], waiting=[ 79, 54, 74, 62, 85, 55, 88, 85, 51, 85, 54, 84, 78, 47, 83, 52, 62, 84, 52, 79, 51, 47, 78, 69, 74, 83, 55, 76, 78, 79, 73, 77, 66, 80, 74, 52, 48, 80, 59, 90, 80, 58, 84, 58, 73, 83, 64, 53, 82, 59, 75, 90, 54, 80, 54, 83, 71, 64, 77, 81, 59, 84, 48, 82, 60, 92, 78, 78, 65, 73, 82, 56, 79, 71, 62, 76, 60, 78, 76, 83, 75, 82, 70, 65, 73, 88, 76, 80, 48, 86, 60, 90, 50, 78, 63, 72, 84, 75, 51, 82, 62, 88, 49, 83, 81, 47, 84, 52, 86, 81, 75, 59, 89, 79, 59, 81, 50, 85, 59, 87, 53, 69, 77, 56, 88, 81, 45, 82, 55, 90, 45, 83, 56, 89, 46, 82, 51, 86, 53, 79, 81, 60, 82, 77, 76, 59, 80, 49, 96, 53, 77, 77, 65, 81, 71, 70, 81, 93, 53, 89, 45, 86, 58, 78, 66, 76, 63, 88, 52, 93, 49, 57, 77, 68, 81, 81, 73, 50, 85, 74, 55, 77, 83, 83, 51, 78, 84, 46, 83, 55, 81, 57, 76, 84, 77, 81, 87, 77, 51, 78, 60, 82, 91, 53, 78, 46, 77, 84, 49, 83, 71, 80, 49, 75, 64, 76, 53, 94, 55, 76, 50, 82, 54, 75, 78, 79, 78, 78, 70, 79, 70, 54, 86, 50, 90, 54, 54, 77, 79, 64, 75, 47, 86, 63, 85, 82, 57, 82, 67, 74, 54, 83, 73, 73, 88, 80, 71, 83, 56, 79, 78, 84, 58, 83, 43, 60, 75, 81, 46, 90, 46, 74] ) statsmodels-0.12.2/statsmodels/sandbox/nonparametric/tests/000077500000000000000000000000001400612667500241515ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/nonparametric/tests/__init__.py000066400000000000000000000000001400612667500262500ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/nonparametric/tests/ex_gam_am_new.py000066400000000000000000000044411400612667500273140ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Example for gam.AdditiveModel and PolynomialSmoother This example was written as a test case. The data generating process is chosen so the parameters are well identified and estimated. Created on Fri Nov 04 13:45:43 2011 Author: Josef Perktold """ from statsmodels.compat.python import lrange import numpy as np from statsmodels.sandbox.gam import AdditiveModel from statsmodels.regression.linear_model import OLS np.random.seed(8765993) #seed is chosen for nice result, not randomly #other seeds are pretty off in the prediction #DGP: simple polynomial order = 3 sigma_noise = 0.5 nobs = 1000 #1000 #with 1000, OLS and Additivemodel agree in params at 2 decimals lb, ub = -3.5, 4#2.5 x1 = np.linspace(lb, ub, nobs) x2 = np.sin(2*x1) x = np.column_stack((x1/x1.max()*2, x2)) exog = (x[:,:,None]**np.arange(order+1)[None, None, :]).reshape(nobs, -1) idx = lrange((order+1)*2) del idx[order+1] exog_reduced = exog[:,idx] #remove duplicate constant y_true = exog.sum(1) / 2. z = y_true #alias check d = x y = y_true + sigma_noise * np.random.randn(nobs) example = 1 if example == 1: m = AdditiveModel(d) m.fit(y) y_pred = m.results.predict(d) for ss in m.smoothers: print(ss.params) res_ols = OLS(y, exog_reduced).fit() print(res_ols.params) #from numpy.testing import assert_almost_equal #assert_almost_equal(y_pred, res_ols.fittedvalues, 3) if example > 0: import matplotlib.pyplot as plt plt.figure() plt.plot(exog) y_pred = m.results.mu# + m.results.alpha #m.results.predict(d) plt.figure() plt.subplot(2,2,1) plt.plot(y, '.', alpha=0.25) plt.plot(y_true, 'k-', label='true') plt.plot(res_ols.fittedvalues, 'g-', label='OLS', lw=2, alpha=-.7) plt.plot(y_pred, 'r-', label='AM') plt.legend(loc='upper left') plt.title('gam.AdditiveModel') counter = 2 for ii, xx in zip(['z', 'x1', 'x2'], [z, x[:,0], x[:,1]]): sortidx = np.argsort(xx) #plt.figure() plt.subplot(2, 2, counter) plt.plot(xx[sortidx], y[sortidx], '.', alpha=0.25) plt.plot(xx[sortidx], y_true[sortidx], 'k.', label='true', lw=2) plt.plot(xx[sortidx], y_pred[sortidx], 'r.', label='AM') plt.legend(loc='upper left') plt.title('gam.AdditiveModel ' + ii) counter += 1 plt.show() statsmodels-0.12.2/statsmodels/sandbox/nonparametric/tests/ex_gam_new.py000066400000000000000000000071171400612667500266420ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Example for GAM with Poisson Model and PolynomialSmoother This example was written as a test case. The data generating process is chosen so the parameters are well identified and estimated. Created on Fri Nov 04 13:45:43 2011 Author: Josef Perktold """ from statsmodels.compat.python import lrange import time import numpy as np from scipy import stats from statsmodels.sandbox.gam import Model as GAM from statsmodels.genmod.families import family from statsmodels.genmod.generalized_linear_model import GLM np.seterr(all='raise') np.random.seed(8765993) #seed is chosen for nice result, not randomly #other seeds are pretty off in the prediction or end in overflow #DGP: simple polynomial order = 3 sigma_noise = 0.1 nobs = 1000 #lb, ub = -0.75, 3#1.5#0.75 #2.5 lb, ub = -3.5, 3 x1 = np.linspace(lb, ub, nobs) x2 = np.sin(2*x1) x = np.column_stack((x1/x1.max()*1, 1.*x2)) exog = (x[:,:,None]**np.arange(order+1)[None, None, :]).reshape(nobs, -1) idx = lrange((order+1)*2) del idx[order+1] exog_reduced = exog[:,idx] #remove duplicate constant y_true = exog.sum(1) #/ 4. z = y_true #alias check d = x y = y_true + sigma_noise * np.random.randn(nobs) example = 3 if example == 2: print("binomial") f = family.Binomial() mu_true = f.link.inverse(z) #b = np.asarray([scipy.stats.bernoulli.rvs(p) for p in f.link.inverse(y)]) b = np.asarray([stats.bernoulli.rvs(p) for p in f.link.inverse(z)]) b.shape = y.shape m = GAM(b, d, family=f) toc = time.time() m.fit(b) tic = time.time() print(tic-toc) #for plotting yp = f.link.inverse(y) p = b if example == 3: print("Poisson") f = family.Poisson() #y = y/y.max() * 3 yp = f.link.inverse(z) p = np.asarray([stats.poisson.rvs(val) for val in f.link.inverse(z)], float) p.shape = y.shape m = GAM(p, d, family=f) toc = time.time() m.fit(p) tic = time.time() print(tic-toc) for ss in m.smoothers: print(ss.params) if example > 1: import matplotlib.pyplot as plt plt.figure() for i in np.array(m.history[2:15:3]): plt.plot(i.T) plt.figure() plt.plot(exog) #plt.plot(p, '.', lw=2) plt.plot(y_true, lw=2) y_pred = m.results.mu # + m.results.alpha #m.results.predict(d) plt.figure() plt.subplot(2,2,1) plt.plot(p, '.') plt.plot(yp, 'b-', label='true') plt.plot(y_pred, 'r-', label='GAM') plt.legend(loc='upper left') plt.title('gam.GAM Poisson') counter = 2 for ii, xx in zip(['z', 'x1', 'x2'], [z, x[:,0], x[:,1]]): sortidx = np.argsort(xx) #plt.figure() plt.subplot(2, 2, counter) plt.plot(xx[sortidx], p[sortidx], 'k.', alpha=0.5) plt.plot(xx[sortidx], yp[sortidx], 'b.', label='true') plt.plot(xx[sortidx], y_pred[sortidx], 'r.', label='GAM') plt.legend(loc='upper left') plt.title('gam.GAM Poisson ' + ii) counter += 1 res = GLM(p, exog_reduced, family=f).fit() #plot component, compared to true component x1 = x[:,0] x2 = x[:,1] f1 = exog[:,:order+1].sum(1) - 1 #take out constant f2 = exog[:,order+1:].sum(1) - 1 plt.figure() #Note: need to correct for constant which is indeterminatedly distributed #plt.plot(x1, m.smoothers[0](x1)-m.smoothers[0].params[0]+1, 'r') #better would be subtract f(0) m.smoothers[0](np.array([0])) plt.plot(x1, f1, linewidth=2) plt.plot(x1, m.smoothers[0](x1)-m.smoothers[0].params[0], 'r') plt.figure() plt.plot(x2, f2, linewidth=2) plt.plot(x2, m.smoothers[1](x2)-m.smoothers[1].params[0], 'r') plt.show() statsmodels-0.12.2/statsmodels/sandbox/nonparametric/tests/ex_smoothers.py000066400000000000000000000024321400612667500272430ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Nov 04 10:51:39 2011 @author: josef """ import numpy as np from statsmodels.sandbox.nonparametric import smoothers from statsmodels.regression.linear_model import OLS, WLS #DGP: simple polynomial order = 3 sigma_noise = 0.5 nobs = 100 lb, ub = -1, 2 x = np.linspace(lb, ub, nobs) x = np.sin(x) exog = x[:,None]**np.arange(order+1) y_true = exog.sum(1) y = y_true + sigma_noise * np.random.randn(nobs) #xind = np.argsort(x) pmod = smoothers.PolySmoother(2, x) pmod.fit(y) #no return y_pred = pmod.predict(x) error = y - y_pred mse = (error*error).mean() print(mse) res_ols = OLS(y, exog[:,:3]).fit() print(np.squeeze(pmod.coef) - res_ols.params) weights = np.ones(nobs) weights[:nobs//3] = 0.1 weights[-nobs//5:] = 2 pmodw = smoothers.PolySmoother(2, x) pmodw.fit(y, weights=weights) #no return y_predw = pmodw.predict(x) error = y - y_predw mse = (error*error).mean() print(mse) res_wls = WLS(y, exog[:,:3], weights=weights).fit() print(np.squeeze(pmodw.coef) - res_wls.params) doplot = 1 if doplot: import matplotlib.pyplot as plt plt.plot(y, '.') plt.plot(y_true, 'b-', label='true') plt.plot(y_pred, '-', label='poly') plt.plot(y_predw, '-', label='poly -w') plt.legend(loc='upper left') plt.close() #plt.show() statsmodels-0.12.2/statsmodels/sandbox/nonparametric/tests/test_kernel_extras.py000066400000000000000000000066051400612667500304370ustar00rootroot00000000000000import numpy as np import numpy.testing as npt from statsmodels.sandbox.nonparametric.kernel_extras import SemiLinear class KernelExtrasTestBase(object): @classmethod def setup_class(cls): nobs = 60 np.random.seed(123456) cls.o = np.random.binomial(2, 0.7, size=(nobs, 1)) cls.o2 = np.random.binomial(3, 0.7, size=(nobs, 1)) cls.c1 = np.random.normal(size=(nobs, 1)) cls.c2 = np.random.normal(10, 1, size=(nobs, 1)) cls.c3 = np.random.normal(10, 2, size=(nobs, 1)) cls.noise = np.random.normal(size=(nobs, 1)) b0 = 0.3 b1 = 1.2 b2 = 3.7 # regression coefficients cls.y = b0 + b1 * cls.c1 + b2 * cls.c2 + cls.noise cls.y2 = b0 + b1 * cls.c1 + b2 * cls.c2 + cls.o + cls.noise # Italy data from R's np package (the first 50 obs) R>> data (Italy) cls.Italy_gdp = \ [8.556, 12.262, 9.587, 8.119, 5.537, 6.796, 8.638, 6.483, 6.212, 5.111, 6.001, 7.027, 4.616, 3.922, 4.688, 3.957, 3.159, 3.763, 3.829, 5.242, 6.275, 8.518, 11.542, 9.348, 8.02, 5.527, 6.865, 8.666, 6.672, 6.289, 5.286, 6.271, 7.94, 4.72, 4.357, 4.672, 3.883, 3.065, 3.489, 3.635, 5.443, 6.302, 9.054, 12.485, 9.896, 8.33, 6.161, 7.055, 8.717, 6.95] cls.Italy_year = \ [1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1953, 1953, 1953, 1953, 1953, 1953, 1953, 1953] # OECD panel data from NP R>> data(oecdpanel) cls.growth = \ [-0.0017584, 0.00740688, 0.03424461, 0.03848719, 0.02932506, 0.03769199, 0.0466038, 0.00199456, 0.03679607, 0.01917304, -0.00221, 0.00787269, 0.03441118, -0.0109228, 0.02043064, -0.0307962, 0.02008947, 0.00580313, 0.00344502, 0.04706358, 0.03585851, 0.01464953, 0.04525762, 0.04109222, -0.0087903, 0.04087915, 0.04551403, 0.036916, 0.00369293, 0.0718669, 0.02577732, -0.0130759, -0.01656641, 0.00676429, 0.08833017, 0.05092105, 0.02005877, 0.00183858, 0.03903173, 0.05832116, 0.0494571, 0.02078484, 0.09213897, 0.0070534, 0.08677202, 0.06830603, -0.00041, 0.0002856, 0.03421225, -0.0036825] cls.oecd = \ [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0] class TestSemiLinear(KernelExtrasTestBase): def test_basic(self): nobs = 300 np.random.seed(1234) C1 = np.random.normal(0,2, size=(nobs, )) C2 = np.random.normal(2, 1, size=(nobs, )) e = np.random.normal(size=(nobs, )) b1 = 1.3 b2 = -0.7 Y = b1 * C1 + np.exp(b2 * C2) + e model = SemiLinear(endog=[Y], exog=[C1], exog_nonparametric=[C2], var_type='c', k_linear=1) b_hat = np.squeeze(model.b) # Only tests for the linear part of the regression # Currently does not work well with the nonparametric part # Needs some more work npt.assert_allclose(b1, b_hat, rtol=0.1) statsmodels-0.12.2/statsmodels/sandbox/nonparametric/tests/test_smoothers.py000066400000000000000000000057761400612667500276240ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Nov 04 10:51:39 2011 Author: Josef Perktold License: BSD-3 """ import numpy as np from numpy.testing import assert_almost_equal, assert_equal from statsmodels.sandbox.nonparametric import smoothers from statsmodels.regression.linear_model import OLS, WLS class CheckSmoother(object): def test_predict(self): assert_almost_equal(self.res_ps.predict(self.x), self.res2.fittedvalues, decimal=13) assert_almost_equal(self.res_ps.predict(self.x[:10]), self.res2.fittedvalues[:10], decimal=13) def test_coef(self): #TODO: check dim of coef assert_almost_equal(self.res_ps.coef.ravel(), self.res2.params, decimal=14) def test_df(self): #TODO: make into attributes assert_equal(self.res_ps.df_model(), self.res2.df_model+1) #with const assert_equal(self.res_ps.df_fit(), self.res2.df_model+1) #alias assert_equal(self.res_ps.df_resid(), self.res2.df_resid) class BasePolySmoother(object): @classmethod def setup_class(cls): #DGP: simple polynomial order = 3 sigma_noise = 0.5 nobs = 100 lb, ub = -1, 2 cls.x = x = np.linspace(lb, ub, nobs) cls.exog = exog = x[:,None]**np.arange(order+1) y_true = exog.sum(1) np.random.seed(987567) cls.y = y = y_true + sigma_noise * np.random.randn(nobs) class TestPolySmoother1(BasePolySmoother, CheckSmoother): @classmethod def setup_class(cls): super(TestPolySmoother1, cls).setup_class() #initialize DGP y, x, exog = cls.y, cls.x, cls.exog #use order = 2 in regression pmod = smoothers.PolySmoother(2, x) pmod.fit(y) #no return cls.res_ps = pmod cls.res2 = OLS(y, exog[:,:2+1]).fit() class TestPolySmoother2(BasePolySmoother, CheckSmoother): @classmethod def setup_class(cls): super(TestPolySmoother2, cls).setup_class() #initialize DGP y, x, exog = cls.y, cls.x, cls.exog #use order = 3 in regression pmod = smoothers.PolySmoother(3, x) #pmod.fit(y) #no return pmod.smooth(y) #no return, use alias for fit cls.res_ps = pmod cls.res2 = OLS(y, exog[:,:3+1]).fit() class TestPolySmoother3(BasePolySmoother, CheckSmoother): @classmethod def setup_class(cls): super(TestPolySmoother3, cls).setup_class() #initialize DGP y, x, exog = cls.y, cls.x, cls.exog nobs = y.shape[0] weights = np.ones(nobs) weights[:nobs//3] = 0.1 weights[-nobs//5:] = 2 #use order = 2 in regression pmod = smoothers.PolySmoother(2, x) pmod.fit(y, weights=weights) #no return cls.res_ps = pmod cls.res2 = WLS(y, exog[:,:2+1], weights=weights).fit() if __name__ == '__main__': t1 = TestPolySmoother1() t1.test_predict() t1.test_coef() t1.test_df t3 = TestPolySmoother3() t3.test_predict() statsmodels-0.12.2/statsmodels/sandbox/nos4.mtx000066400000000000000000000222511400612667500215640ustar00rootroot00000000000000%%MatrixMarket matrix coordinate real symmetric 100 100 347 1 1 1.7155418000000e-01 2 1 3.5777088000000e-02 3 1 -1.0000000000000e-01 13 1 -7.1554176000000e-02 14 1 -3.5777088000000e-02 2 2 4.1788854000000e-01 12 2 -2.0000000000000e-01 13 2 -3.5777088000000e-02 14 2 -1.7888544000000e-02 3 3 3.4310835000000e-01 5 3 -1.0000000000000e-01 4 4 4.3577709000000e-01 14 4 -2.0000000000000e-01 5 5 3.4310835000000e-01 7 5 -1.0000000000000e-01 13 5 -7.1554176000000e-02 14 5 3.5777088000000e-02 17 5 -7.1554176000000e-02 18 5 -3.5777088000000e-02 6 6 4.3577709000000e-01 13 6 3.5777088000000e-02 14 6 -1.7888544000000e-02 16 6 -2.0000000000000e-01 17 6 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statsmodels-0.12.2/statsmodels/sandbox/panel/000077500000000000000000000000001400612667500212445ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/panel/__init__.py000066400000000000000000000000001400612667500233430ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/panel/correlation_structures.py000066400000000000000000000120231400612667500264400ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Correlation and Covariance Structures Created on Sat Dec 17 20:46:05 2011 Author: Josef Perktold License: BSD-3 Reference --------- quick reading of some section on mixed effects models in S-plus and of outline for GEE. """ import numpy as np from statsmodels.regression.linear_model import yule_walker from statsmodels.stats.moment_helpers import cov2corr def corr_equi(k_vars, rho): '''create equicorrelated correlation matrix with rho on off diagonal Parameters ---------- k_vars : int number of variables, correlation matrix will be (k_vars, k_vars) rho : float correlation between any two random variables Returns ------- corr : ndarray (k_vars, k_vars) correlation matrix ''' corr = np.empty((k_vars, k_vars)) corr.fill(rho) corr[np.diag_indices_from(corr)] = 1 return corr def corr_ar(k_vars, ar): '''create autoregressive correlation matrix This might be MA, not AR, process if used for residual process - check Parameters ---------- ar : array_like, 1d AR lag-polynomial including 1 for lag 0 ''' from scipy.linalg import toeplitz if len(ar) < k_vars: ar_ = np.zeros(k_vars) ar_[:len(ar)] = ar ar = ar_ return toeplitz(ar) def corr_arma(k_vars, ar, ma): '''create arma correlation matrix converts arma to autoregressive lag-polynomial with k_var lags ar and arma might need to be switched for generating residual process Parameters ---------- ar : array_like, 1d AR lag-polynomial including 1 for lag 0 ma : array_like, 1d MA lag-polynomial ''' from scipy.linalg import toeplitz from statsmodels.tsa.arima_process import arma2ar # TODO: flesh out the comment below about a bug in arma2ar ar = arma2ar(ar, ma, lags=k_vars)[:k_vars] # bug in arma2ar return toeplitz(ar) def corr2cov(corr, std): '''convert correlation matrix to covariance matrix Parameters ---------- corr : ndarray, (k_vars, k_vars) correlation matrix std : ndarray, (k_vars,) or scalar standard deviation for the vector of random variables. If scalar, then it is assumed that all variables have the same scale given by std. ''' if np.size(std) == 1: std = std*np.ones(corr.shape[0]) cov = corr * std[:, None] * std[None, :] # same as outer product return cov def whiten_ar(x, ar_coefs, order): """ Whiten a series of columns according to an AR(p) covariance structure. This drops the initial conditions (Cochran-Orcut ?) Uses loop, so for short ar polynomials only, use lfilter otherwise This needs to improve, option on method, full additional to conditional Parameters ---------- x : array_like, (nobs,) or (nobs, k_vars) The data to be whitened along axis 0 ar_coefs : ndarray coefficients of AR lag- polynomial, TODO: ar or ar_coefs? order : int Returns ------- x_new : ndarray transformed array """ rho = ar_coefs x = np.array(x, np.float64) _x = x.copy() # TODO: dimension handling is not DRY # I think previous code worked for 2d because of single index rows in np if x.ndim == 2: rho = rho[:, None] for i in range(order): _x[(i+1):] = _x[(i+1):] - rho[i] * x[0:-(i+1)] return _x[order:] def yule_walker_acov(acov, order=1, method="unbiased", df=None, inv=False): """ Estimate AR(p) parameters from acovf using Yule-Walker equation. Parameters ---------- acov : array_like, 1d auto-covariance order : int, optional The order of the autoregressive process. Default is 1. inv : bool If inv is True the inverse of R is also returned. Default is False. Returns ------- rho : ndarray The estimated autoregressive coefficients sigma TODO Rinv : ndarray inverse of the Toepliz matrix """ return yule_walker(acov, order=order, method=method, df=df, inv=inv, demean=False) class ARCovariance(object): ''' experimental class for Covariance of AR process classmethod? staticmethods? ''' def __init__(self, ar=None, ar_coefs=None, sigma=1.): if ar is not None: self.ar = ar self.ar_coefs = -ar[1:] self.k_lags = len(ar) elif ar_coefs is not None: self.arcoefs = ar_coefs self.ar = np.hstack(([1], -ar_coefs)) self.k_lags = len(self.ar) @classmethod def fit(cls, cov, order, **kwds): rho, sigma = yule_walker_acov(cov, order=order, **kwds) return cls(ar_coefs=rho) def whiten(self, x): return whiten_ar(x, self.ar_coefs, order=self.order) def corr(self, k_vars=None): if k_vars is None: k_vars = len(self.ar) # TODO: this could move into corr_arr return corr_ar(k_vars, self.ar) def cov(self, k_vars=None): return cov2corr(self.corr(k_vars=None), self.sigma) statsmodels-0.12.2/statsmodels/sandbox/panel/mixed.py000066400000000000000000000506521400612667500227340ustar00rootroot00000000000000""" Mixed effects models Author: Jonathan Taylor Author: Josef Perktold License: BSD-3 Notes ------ It's pretty slow if the model is misspecified, in my first example convergence in loglike is not reached within 2000 iterations. Added stop criteria based on convergence of parameters instead. With correctly specified model, convergence is fast, in 6 iterations in example. """ import numpy as np import numpy.linalg as L from statsmodels.base.model import LikelihoodModelResults from statsmodels.tools.decorators import cache_readonly class Unit(object): """ Individual experimental unit for EM implementation of (repeated measures) mixed effects model. \'Maximum Likelihood Computations with Repeated Measures: Application of the EM Algorithm\' Nan Laird; Nicholas Lange; Daniel Stram Journal of the American Statistical Association, Vol. 82, No. 397. (Mar., 1987), pp. 97-105. Parameters ---------- endog : ndarray, (nobs,) response, endogenous variable exog_fe : ndarray, (nobs, k_vars_fe) explanatory variables as regressors or fixed effects, should include exog_re to correct mean of random coefficients, see Notes exog_re : ndarray, (nobs, k_vars_re) explanatory variables or random effects or coefficients Notes ----- If the exog_re variables are not included in exog_fe, then the mean of the random constants or coefficients are not centered. The covariance matrix of the random parameter estimates are not centered in this case. (That's how it looks to me. JP) """ def __init__(self, endog, exog_fe, exog_re): self.Y = endog self.X = exog_fe self.Z = exog_re self.n = endog.shape[0] def _compute_S(self, D, sigma): """covariance of observations (nobs_i, nobs_i) (JP check) Display (3.3) from Laird, Lange, Stram (see help(Unit)) """ self.S = (np.identity(self.n) * sigma**2 + np.dot(self.Z, np.dot(D, self.Z.T))) def _compute_W(self): """inverse covariance of observations (nobs_i, nobs_i) (JP check) Display (3.2) from Laird, Lange, Stram (see help(Unit)) """ self.W = L.inv(self.S) def compute_P(self, Sinv): """projection matrix (nobs_i, nobs_i) (M in regression ?) (JP check, guessing) Display (3.10) from Laird, Lange, Stram (see help(Unit)) W - W X Sinv X' W' """ t = np.dot(self.W, self.X) self.P = self.W - np.dot(np.dot(t, Sinv), t.T) def _compute_r(self, alpha): """residual after removing fixed effects Display (3.5) from Laird, Lange, Stram (see help(Unit)) """ self.r = self.Y - np.dot(self.X, alpha) def _compute_b(self, D): """coefficients for random effects/coefficients Display (3.4) from Laird, Lange, Stram (see help(Unit)) D Z' W r """ self.b = np.dot(D, np.dot(np.dot(self.Z.T, self.W), self.r)) def fit(self, a, D, sigma): """ Compute unit specific parameters in Laird, Lange, Stram (see help(Unit)). Displays (3.2)-(3.5). """ self._compute_S(D, sigma) #random effect plus error covariance self._compute_W() #inv(S) self._compute_r(a) #residual after removing fixed effects/exogs self._compute_b(D) #? coefficients on random exog, Z ? def compute_xtwy(self): """ Utility function to compute X^tWY (transposed ?) for Unit instance. """ return np.dot(np.dot(self.W, self.Y), self.X) #is this transposed ? def compute_xtwx(self): """ Utility function to compute X^tWX for Unit instance. """ return np.dot(np.dot(self.X.T, self.W), self.X) def cov_random(self, D, Sinv=None): """ Approximate covariance of estimates of random effects. Just after Display (3.10) in Laird, Lange, Stram (see help(Unit)). D - D' Z' P Z D Notes ----- In example where the mean of the random coefficient is not zero, this is not a covariance but a non-centered moment. (proof by example) """ if Sinv is not None: self.compute_P(Sinv) t = np.dot(self.Z, D) return D - np.dot(np.dot(t.T, self.P), t) def logL(self, a, ML=False): """ Individual contributions to the log-likelihood, tries to return REML contribution by default though this requires estimated fixed effect a to be passed as an argument. no constant with pi included a is not used if ML=true (should be a=None in signature) If ML is false, then the residuals are calculated for the given fixed effects parameters a. """ if ML: return (np.log(L.det(self.W)) - (self.r * np.dot(self.W, self.r)).sum()) / 2. else: if a is None: raise ValueError('need fixed effect a for REML contribution to log-likelihood') r = self.Y - np.dot(self.X, a) return (np.log(L.det(self.W)) - (r * np.dot(self.W, r)).sum()) / 2. def deviance(self, ML=False): '''deviance defined as 2 times the negative loglikelihood ''' return - 2 * self.logL(ML=ML) class OneWayMixed(object): """ Model for EM implementation of (repeated measures) mixed effects model. \'Maximum Likelihood Computations with Repeated Measures: Application of the EM Algorithm\' Nan Laird; Nicholas Lange; Daniel Stram Journal of the American Statistical Association, Vol. 82, No. 397. (Mar., 1987), pp. 97-105. Parameters ---------- units : list of units the data for the individual units should be attached to the units response, fixed and random : formula expression, called as argument to Formula *available results and alias* (subject to renaming, and coversion to cached attributes) params() -> self.a : coefficient for fixed effects or exog cov_params() -> self.Sinv : covariance estimate of fixed effects/exog bse() : standard deviation of params cov_random -> self.D : estimate of random effects covariance params_random_units -> [self.units[...].b] : random coefficient for each unit *attributes* (others) self.m : number of units self.p : k_vars_fixed self.q : k_vars_random self.N : nobs (total) Notes ----- Fit returns a result instance, but not all results that use the inherited methods have been checked. Parameters need to change: drop formula and we require a naming convention for the units (currently Y,X,Z). - endog, exog_fe, endog_re ? logL does not include constant, e.g. sqrt(pi) llf is for MLE not for REML convergence criteria for iteration Currently convergence in the iterative solver is reached if either the loglikelihood *or* the fixed effects parameter do not change above tolerance. In some examples, the fixed effects parameters converged to 1e-5 within 150 iterations while the log likelihood did not converge within 2000 iterations. This might be the case if the fixed effects parameters are well estimated, but there are still changes in the random effects. If params_rtol and params_atol are set at a higher level, then the random effects might not be estimated to a very high precision. The above was with a misspecified model, without a constant. With a correctly specified model convergence is fast, within a few iterations (6 in example). """ def __init__(self, units): self.units = units self.m = len(self.units) self.n_units = self.m self.N = sum(unit.X.shape[0] for unit in self.units) self.nobs = self.N #alias for now # Determine size of fixed effects d = self.units[0].X self.p = d.shape[1] # d.shape = p self.k_exog_fe = self.p #alias for now self.a = np.zeros(self.p, np.float64) # Determine size of D, and sensible initial estimates # of sigma and D d = self.units[0].Z self.q = d.shape[1] # Z.shape = q self.k_exog_re = self.q #alias for now self.D = np.zeros((self.q,)*2, np.float64) self.sigma = 1. self.dev = np.inf #initialize for iterations, move it? def _compute_a(self): """fixed effects parameters Display (3.1) of Laird, Lange, Stram (see help(Mixed)). """ for unit in self.units: unit.fit(self.a, self.D, self.sigma) S = sum([unit.compute_xtwx() for unit in self.units]) Y = sum([unit.compute_xtwy() for unit in self.units]) self.Sinv = L.pinv(S) self.a = np.dot(self.Sinv, Y) def _compute_sigma(self, ML=False): """ Estimate sigma. If ML is True, return the ML estimate of sigma, else return the REML estimate. If ML, this is (3.6) in Laird, Lange, Stram (see help(Mixed)), otherwise it corresponds to (3.8). sigma is the standard deviation of the noise (residual) """ sigmasq = 0. for unit in self.units: if ML: W = unit.W else: unit.compute_P(self.Sinv) W = unit.P t = unit.r - np.dot(unit.Z, unit.b) sigmasq += np.power(t, 2).sum() sigmasq += self.sigma**2 * np.trace(np.identity(unit.n) - self.sigma**2 * W) self.sigma = np.sqrt(sigmasq / self.N) def _compute_D(self, ML=False): """ Estimate random effects covariance D. If ML is True, return the ML estimate of sigma, else return the REML estimate. If ML, this is (3.7) in Laird, Lange, Stram (see help(Mixed)), otherwise it corresponds to (3.9). """ D = 0. for unit in self.units: if ML: W = unit.W else: unit.compute_P(self.Sinv) W = unit.P D += np.multiply.outer(unit.b, unit.b) t = np.dot(unit.Z, self.D) D += self.D - np.dot(np.dot(t.T, W), t) self.D = D / self.m def cov_fixed(self): """ Approximate covariance of estimates of fixed effects. Just after Display (3.10) in Laird, Lange, Stram (see help(Mixed)). """ return self.Sinv #----------- alias (JP) move to results class ? def cov_random(self): """ Estimate random effects covariance D. If ML is True, return the ML estimate of sigma, else return the REML estimate. see _compute_D, alias for self.D """ return self.D @property def params(self): ''' estimated coefficients for exogeneous variables or fixed effects see _compute_a, alias for self.a ''' return self.a @property def params_random_units(self): '''random coefficients for each unit ''' return np.array([unit.b for unit in self.units]) def cov_params(self): ''' estimated covariance for coefficients for exogeneous variables or fixed effects see cov_fixed, and Sinv in _compute_a ''' return self.cov_fixed() @property def bse(self): ''' standard errors of estimated coefficients for exogeneous variables (fixed) ''' return np.sqrt(np.diag(self.cov_params())) #----------- end alias def deviance(self, ML=False): '''deviance defined as 2 times the negative loglikelihood ''' return -2 * self.logL(ML=ML) def logL(self, ML=False): """ Return log-likelihood, REML by default. """ #I do not know what the difference between REML and ML is here. logL = 0. for unit in self.units: logL += unit.logL(a=self.a, ML=ML) if not ML: logL += np.log(L.det(self.Sinv)) / 2 return logL def initialize(self): S = sum([np.dot(unit.X.T, unit.X) for unit in self.units]) Y = sum([np.dot(unit.X.T, unit.Y) for unit in self.units]) self.a = L.lstsq(S, Y, rcond=-1)[0] D = 0 t = 0 sigmasq = 0 for unit in self.units: unit.r = unit.Y - np.dot(unit.X, self.a) if self.q > 1: unit.b = L.lstsq(unit.Z, unit.r, rcond=-1)[0] else: Z = unit.Z.reshape((unit.Z.shape[0], 1)) unit.b = L.lstsq(Z, unit.r, rcond=-1)[0] sigmasq += (np.power(unit.Y, 2).sum() - (self.a * np.dot(unit.X.T, unit.Y)).sum() - (unit.b * np.dot(unit.Z.T, unit.r)).sum()) D += np.multiply.outer(unit.b, unit.b) t += L.pinv(np.dot(unit.Z.T, unit.Z)) #TODO: JP added df_resid check self.df_resid = (self.N - (self.m - 1) * self.q - self.p) sigmasq /= (self.N - (self.m - 1) * self.q - self.p) self.sigma = np.sqrt(sigmasq) self.D = (D - sigmasq * t) / self.m def cont(self, ML=False, rtol=1.0e-05, params_rtol=1e-5, params_atol=1e-4): '''convergence check for iterative estimation ''' self.dev, old = self.deviance(ML=ML), self.dev #self.history.append(np.hstack((self.dev, self.a))) self.history['llf'].append(self.dev) self.history['params'].append(self.a.copy()) self.history['D'].append(self.D.copy()) if np.fabs((self.dev - old) / self.dev) < rtol: #why is there times `*`? #print np.fabs((self.dev - old)), self.dev, old self.termination = 'llf' return False #break if parameters converged #TODO: check termination conditions, OR or AND if np.all(np.abs(self.a - self._a_old) < (params_rtol * self.a + params_atol)): self.termination = 'params' return False self._a_old = self.a.copy() return True def fit(self, maxiter=100, ML=False, rtol=1.0e-05, params_rtol=1e-6, params_atol=1e-6): #initialize for convergence criteria self._a_old = np.inf * self.a self.history = {'llf':[], 'params':[], 'D':[]} for i in range(maxiter): self._compute_a() #a, Sinv : params, cov_params of fixed exog self._compute_sigma(ML=ML) #sigma MLE or REML of sigma ? self._compute_D(ML=ML) #D : covariance of random effects, MLE or REML if not self.cont(ML=ML, rtol=rtol, params_rtol=params_rtol, params_atol=params_atol): break else: #if end of loop is reached without break self.termination = 'maxiter' print('Warning: maximum number of iterations reached') self.iterations = i results = OneWayMixedResults(self) #compatibility functions for fixed effects/exog results.scale = 1 results.normalized_cov_params = self.cov_params() return results class OneWayMixedResults(LikelihoodModelResults): '''Results class for OneWayMixed models ''' def __init__(self, model): #TODO: check, change initialization to more standard pattern self.model = model self.params = model.params #need to overwrite this because we do not have a standard #model.loglike yet #TODO: what todo about REML loglike, logL is not normalized @cache_readonly def llf(self): return self.model.logL(ML=True) @property def params_random_units(self): return self.model.params_random_units def cov_random(self): return self.model.cov_random() def mean_random(self, idx='lastexog'): if idx == 'lastexog': meanr = self.params[-self.model.k_exog_re:] elif isinstance(idx, list): if not len(idx) == self.model.k_exog_re: raise ValueError('length of idx different from k_exog_re') else: meanr = self.params[idx] else: meanr = np.zeros(self.model.k_exog_re) return meanr def std_random(self): return np.sqrt(np.diag(self.cov_random())) def plot_random_univariate(self, bins=None, use_loc=True): '''create plot of marginal distribution of random effects Parameters ---------- bins : int or bin edges option for bins in matplotlibs hist method. Current default is not very sophisticated. All distributions use the same setting for bins. use_loc : bool If True, then the distribution with mean given by the fixed effect is used. Returns ------- Figure figure with subplots Notes ----- What can make this fancier? Bin edges will not make sense if loc or scale differ across random effect distributions. ''' #outsource this import matplotlib.pyplot as plt from scipy.stats import norm as normal fig = plt.figure() k = self.model.k_exog_re if k > 3: rows, cols = int(np.ceil(k * 0.5)), 2 else: rows, cols = k, 1 if bins is None: #bins = self.model.n_units // 20 #TODO: just roughly, check #bins = np.sqrt(self.model.n_units) bins = 5 + 2 * self.model.n_units**(1./3.) if use_loc: loc = self.mean_random() else: loc = [0]*k scale = self.std_random() for ii in range(k): ax = fig.add_subplot(rows, cols, ii) freq, bins_, _ = ax.hist(loc[ii] + self.params_random_units[:,ii], bins=bins, normed=True) points = np.linspace(bins_[0], bins_[-1], 200) #ax.plot(points, normal.pdf(points, loc=loc, scale=scale)) #loc of sample is approx. zero, with Z appended to X #alternative, add fixed to mean ax.set_title('Random Effect %d Marginal Distribution' % ii) ax.plot(points, normal.pdf(points, loc=loc[ii], scale=scale[ii]), 'r') return fig def plot_scatter_pairs(self, idx1, idx2, title=None, ax=None): '''create scatter plot of two random effects Parameters ---------- idx1, idx2 : int indices of the two random effects to display, corresponding to columns of exog_re title : None or string If None, then a default title is added ax : None or matplotlib axis instance If None, then a figure with one axis is created and returned. If ax is not None, then the scatter plot is created on it, and this axis instance is returned. Returns ------- ax_or_fig : axis or figure instance see ax parameter Notes ----- Still needs ellipse from estimated parameters ''' import matplotlib.pyplot as plt if ax is None: fig = plt.figure() ax = fig.add_subplot(1,1,1) ax_or_fig = fig re1 = self.params_random_units[:,idx1] re2 = self.params_random_units[:,idx2] ax.plot(re1, re2, 'o', alpha=0.75) if title is None: title = 'Random Effects %d and %d' % (idx1, idx2) ax.set_title(title) ax_or_fig = ax return ax_or_fig def plot_scatter_all_pairs(self, title=None): from statsmodels.graphics.plot_grids import scatter_ellipse if self.model.k_exog_re < 2: raise ValueError('less than two variables available') return scatter_ellipse(self.params_random_units, #ell_kwds not implemented yet ell_kwds={'color':'r'}) # #note I have written this already as helper function, get it # import matplotlib.pyplot as plt # #from scipy.stats import norm as normal # fig = plt.figure() # k = self.model.k_exog_re # n_plots = k * (k - 1) // 2 # if n_plots > 3: # rows, cols = int(np.ceil(n_plots * 0.5)), 2 # else: # rows, cols = n_plots, 1 # # count = 1 # for ii in range(k): # for jj in range(ii): # ax = fig.add_subplot(rows, cols, count) # self.plot_scatter_pairs(ii, jj, title=None, ax=ax) # count += 1 # # return fig statsmodels-0.12.2/statsmodels/sandbox/panel/panel_short.py000066400000000000000000000176451400612667500241510ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Panel data analysis for short T and large N Created on Sat Dec 17 19:32:00 2011 Author: Josef Perktold License: BSD-3 starting from scratch before looking at references again just a stub to get the basic structure for group handling target outsource as much as possible for reuse Notes ----- this is the basic version using a loop over individuals which will be more widely applicable. Depending on the special cases, there will be faster implementations possible (sparse, kroneker, ...) the only two group specific methods or get_within_cov and whiten """ import numpy as np from statsmodels.regression.linear_model import OLS, GLS from statsmodels.tools.grouputils import GroupSorted def sum_outer_product_loop(x, group_iter): '''sum outerproduct dot(x_i, x_i.T) over individuals loop version ''' mom = 0 for g in group_iter(): x_g = x[g] #print 'x_g.shape', x_g.shape mom += np.outer(x_g, x_g) return mom def sum_outer_product_balanced(x, n_groups): '''sum outerproduct dot(x_i, x_i.T) over individuals where x_i is (nobs_i, 1), and result is (nobs_i, nobs_i) reshape-dot version, for x.ndim=1 only ''' xrs = x.reshape(-1, n_groups, order='F') return np.dot(xrs, xrs.T) #should be (nobs_i, nobs_i) #x.reshape(n_groups, nobs_i, k_vars) #, order='F') #... ? this is getting 3-dimensional dot, tensordot? #needs (n_groups, k_vars, k_vars) array with sum over groups #NOT #I only need this for x is 1d, i.e. residual def whiten_individuals_loop(x, transform, group_iter): '''apply linear transform for each individual loop version ''' #Note: figure out dimension of transformed variable #so we can pre-allocate x_new = [] for g in group_iter(): x_g = x[g] x_new.append(np.dot(transform, x_g)) return np.concatenate(x_new) #np.vstack(x_new) #or np.array(x_new) #check shape class ShortPanelGLS2(object): '''Short Panel with general intertemporal within correlation assumes data is stacked by individuals, panel is balanced and within correlation structure is identical across individuals. It looks like this can just inherit GLS and overwrite whiten ''' def __init__(self, endog, exog, group): self.endog = endog self.exog = exog self.group = GroupSorted(group) self.n_groups = self.group.n_groups #self.nobs_group = #list for unbalanced? def fit_ols(self): self.res_pooled = OLS(self.endog, self.exog).fit() return self.res_pooled #return or not def get_within_cov(self, resid): #central moment or not? mom = sum_outer_product_loop(resid, self.group.group_iter) return mom / self.n_groups #df correction ? def whiten_groups(self, x, cholsigmainv_i): #from scipy import sparse #use sparse wx = whiten_individuals_loop(x, cholsigmainv_i, self.group.group_iter) return wx def fit(self): res_pooled = self.fit_ols() #get starting estimate sigma_i = self.get_within_cov(res_pooled.resid) self.cholsigmainv_i = np.linalg.cholesky(np.linalg.pinv(sigma_i)).T wendog = self.whiten_groups(self.endog, self.cholsigmainv_i) wexog = self.whiten_groups(self.exog, self.cholsigmainv_i) #print wendog.shape, wexog.shape self.res1 = OLS(wendog, wexog).fit() return self.res1 class ShortPanelGLS(GLS): '''Short Panel with general intertemporal within correlation assumes data is stacked by individuals, panel is balanced and within correlation structure is identical across individuals. It looks like this can just inherit GLS and overwrite whiten ''' def __init__(self, endog, exog, group, sigma_i=None): self.group = GroupSorted(group) self.n_groups = self.group.n_groups #self.nobs_group = #list for unbalanced? nobs_i = len(endog) / self.n_groups #endog might later not be an ndarray #balanced only for now, #which is a requirement anyway in this case (full cov) #needs to change for parametrized sigma_i # if sigma_i is None: sigma_i = np.eye(int(nobs_i)) self.cholsigmainv_i = np.linalg.cholesky(np.linalg.pinv(sigma_i)).T #super is taking care of endog, exog and sigma super(self.__class__, self).__init__(endog, exog, sigma=None) def get_within_cov(self, resid): #central moment or not? mom = sum_outer_product_loop(resid, self.group.group_iter) return mom / self.n_groups #df correction ? def whiten_groups(self, x, cholsigmainv_i): #from scipy import sparse #use sparse wx = whiten_individuals_loop(x, cholsigmainv_i, self.group.group_iter) return wx def _fit_ols(self): #used as starting estimate in old explicity version self.res_pooled = OLS(self.endog, self.exog).fit() return self.res_pooled #return or not def _fit_old(self): #old explicit version res_pooled = self._fit_ols() #get starting estimate sigma_i = self.get_within_cov(res_pooled.resid) self.cholsigmainv_i = np.linalg.cholesky(np.linalg.pinv(sigma_i)).T wendog = self.whiten_groups(self.endog, self.cholsigmainv_i) wexog = self.whiten_groups(self.exog, self.cholsigmainv_i) self.res1 = OLS(wendog, wexog).fit() return self.res1 def whiten(self, x): #whiten x by groups, will be applied to endog and exog wx = whiten_individuals_loop(x, self.cholsigmainv_i, self.group.group_iter) return wx #copied from GLSHet and adjusted (boiler plate?) def fit_iterative(self, maxiter=3): """ Perform an iterative two-step procedure to estimate the GLS model. Parameters ---------- maxiter : int, optional the number of iterations Notes ----- maxiter=1: returns the estimated based on given weights maxiter=2: performs a second estimation with the updated weights, this is 2-step estimation maxiter>2: iteratively estimate and update the weights TODO: possible extension stop iteration if change in parameter estimates is smaller than x_tol Repeated calls to fit_iterative, will do one redundant pinv_wexog calculation. Calling fit_iterative(maxiter) once does not do any redundant recalculations (whitening or calculating pinv_wexog). """ #Note: in contrast to GLSHet, we do not have an auxiliary regression here # might be needed if there is more structure in cov_i #because we only have the loop we are not attaching the ols_pooled #initial estimate anymore compared to original version if maxiter < 1: raise ValueError('maxiter needs to be at least 1') import collections self.history = collections.defaultdict(list) #not really necessary for i in range(maxiter): #pinv_wexog is cached, delete it to force recalculation if hasattr(self, 'pinv_wexog'): del self.pinv_wexog #fit with current cov, GLS, i.e. OLS on whitened endog, exog results = self.fit() self.history['self_params'].append(results.params) if not i == maxiter-1: #skip for last iteration, could break instead #print 'ols', self.results_old = results #store previous results for debugging #get cov from residuals of previous regression sigma_i = self.get_within_cov(results.resid) self.cholsigmainv_i = np.linalg.cholesky(np.linalg.pinv(sigma_i)).T #calculate new whitened endog and exog self.initialize() #note results is the wrapper, results._results is the results instance #results._results.results_residual_regression = res_resid return results statsmodels-0.12.2/statsmodels/sandbox/panel/panelmod.py000066400000000000000000000343711400612667500234250ustar00rootroot00000000000000""" Sandbox Panel Estimators References ----------- Baltagi, Badi H. `Econometric Analysis of Panel Data.` 4th ed. Wiley, 2008. """ from functools import reduce import numpy as np from statsmodels.regression.linear_model import GLS __all__ = ["PanelModel"] from pandas import Panel def group(X): """ Returns unique numeric values for groups without sorting. Examples -------- >>> X = np.array(['a','a','b','c','b','c']) >>> group(X) >>> g array([ 0., 0., 1., 2., 1., 2.]) """ uniq_dict = {} group = np.zeros(len(X)) for i in range(len(X)): if not X[i] in uniq_dict: uniq_dict.update({X[i] : len(uniq_dict)}) group[i] = uniq_dict[X[i]] return group def repanel_cov(groups, sigmas): '''calculate error covariance matrix for random effects model Parameters ---------- groups : ndarray, (nobs, nre) or (nobs,) array of group/category observations sigma : ndarray, (nre+1,) array of standard deviations of random effects, last element is the standard deviation of the idiosyncratic error Returns ------- omega : ndarray, (nobs, nobs) covariance matrix of error omegainv : ndarray, (nobs, nobs) inverse covariance matrix of error omegainvsqrt : ndarray, (nobs, nobs) squareroot inverse covariance matrix of error such that omega = omegainvsqrt * omegainvsqrt.T Notes ----- This does not use sparse matrices and constructs nobs by nobs matrices. Also, omegainvsqrt is not sparse, i.e. elements are non-zero ''' if groups.ndim == 1: groups = groups[:,None] nobs, nre = groups.shape omega = sigmas[-1]*np.eye(nobs) for igr in range(nre): group = groups[:,igr:igr+1] groupuniq = np.unique(group) dummygr = sigmas[igr] * (group == groupuniq).astype(float) omega += np.dot(dummygr, dummygr.T) ev, evec = np.linalg.eigh(omega) #eig does not work omegainv = np.dot(evec, (1/ev * evec).T) omegainvhalf = evec/np.sqrt(ev) return omega, omegainv, omegainvhalf class PanelData(Panel): pass class PanelModel(object): """ An abstract statistical model class for panel (longitudinal) datasets. Parameters ---------- endog : array_like or str If a pandas object is used then endog should be the name of the endogenous variable as a string. # exog # panel_arr # time_arr panel_data : pandas.Panel object Notes ----- If a pandas object is supplied it is assumed that the major_axis is time and that the minor_axis has the panel variable. """ def __init__(self, endog=None, exog=None, panel=None, time=None, xtnames=None, equation=None, panel_data=None): if panel_data is None: # if endog == None and exog == None and panel == None and \ # time == None: # raise ValueError("If pandel_data is False then endog, exog, \ #panel_arr, and time_arr cannot be None.") self.initialize(endog, exog, panel, time, xtnames, equation) # elif aspandas != False: # if not isinstance(endog, str): # raise ValueError("If a pandas object is supplied then endog \ #must be a string containing the name of the endogenous variable") # if not isinstance(aspandas, Panel): # raise ValueError("Only pandas.Panel objects are supported") # self.initialize_pandas(endog, aspandas, panel_name) def initialize(self, endog, exog, panel, time, xtnames, equation): """ Initialize plain array model. See PanelModel """ #TODO: for now, we are going assume a constant, and then make the first #panel the base, add a flag for this.... # get names names = equation.split(" ") self.endog_name = names[0] exog_names = names[1:] # this makes the order matter in the array self.panel_name = xtnames[0] self.time_name = xtnames[1] novar = exog.var(0) == 0 if True in novar: cons_index = np.where(novar == 1)[0][0] # constant col. num exog_names.insert(cons_index, 'cons') self._cons_index = novar # used again in fit_fixed self.exog_names = exog_names self.endog = np.squeeze(np.asarray(endog)) exog = np.asarray(exog) self.exog = exog self.panel = np.asarray(panel) self.time = np.asarray(time) self.paneluniq = np.unique(panel) self.timeuniq = np.unique(time) #TODO: this structure can possibly be extracted somewhat to deal with #names in general #TODO: add some dimension checks, etc. # def initialize_pandas(self, endog, aspandas): # """ # Initialize pandas objects. # # See PanelModel. # """ # self.aspandas = aspandas # endog = aspandas[endog].values # self.endog = np.squeeze(endog) # exog_name = aspandas.columns.tolist() # exog_name.remove(endog) # self.exog = aspandas.filterItems(exog_name).values #TODO: can the above be simplified to slice notation? # if panel_name != None: # self.panel_name = panel_name # self.exog_name = exog_name # self.endog_name = endog # self.time_arr = aspandas.major_axis #TODO: is time always handled correctly in fromRecords? # self.panel_arr = aspandas.minor_axis #TODO: all of this might need to be refactored to explicitly rely (internally) # on the pandas LongPanel structure for speed and convenience. # not sure this part is finished... #TODO: does not conform to new initialize def initialize_pandas(self, panel_data, endog_name, exog_name): self.panel_data = panel_data endog = panel_data[endog_name].values # does this create a copy? self.endog = np.squeeze(endog) if exog_name is None: exog_name = panel_data.columns.tolist() exog_name.remove(endog_name) self.exog = panel_data.filterItems(exog_name).values # copy? self._exog_name = exog_name self._endog_name = endog_name self._timeseries = panel_data.major_axis # might not need these self._panelseries = panel_data.minor_axis #TODO: this could be pulled out and just have a by kwd that takes # the panel or time array #TODO: this also needs to be expanded for 'twoway' def _group_mean(self, X, index='oneway', counts=False, dummies=False): """ Get group means of X by time or by panel. index default is panel """ if index == 'oneway': Y = self.panel uniq = self.paneluniq elif index == 'time': Y = self.time uniq = self.timeuniq else: raise ValueError("index %s not understood" % index) print(Y, uniq, uniq[:,None], len(Y), len(uniq), len(uniq[:,None]), index) #TODO: use sparse matrices dummy = (Y == uniq[:,None]).astype(float) if X.ndim > 1: mean = np.dot(dummy,X)/dummy.sum(1)[:,None] else: mean = np.dot(dummy,X)/dummy.sum(1) if counts is False and dummies is False: return mean elif counts is True and dummies is False: return mean, dummy.sum(1) elif counts is True and dummies is True: return mean, dummy.sum(1), dummy elif counts is False and dummies is True: return mean, dummy #TODO: Use kwd arguments or have fit_method methods? def fit(self, model=None, method=None, effects='oneway'): """ method : LSDV, demeaned, MLE, GLS, BE, FE, optional model : between fixed random pooled [gmm] effects : oneway time twoway femethod : demeaned (only one implemented) WLS remethod : swar - amemiya nerlove walhus Notes ----- This is unfinished. None of the method arguments work yet. Only oneway effects should work. """ if method: # get rid of this with default method = method.lower() model = model.lower() if method and method not in ["lsdv", "demeaned", "mle", "gls", "be", "fe"]: # get rid of if method with default raise ValueError("%s not a valid method" % method) # if method == "lsdv": # self.fit_lsdv(model) if model == 'pooled': return GLS(self.endog, self.exog).fit() if model == 'between': return self._fit_btwn(method, effects) if model == 'fixed': return self._fit_fixed(method, effects) # def fit_lsdv(self, effects): # """ # Fit using least squares dummy variables. # # Notes # ----- # Should only be used for small `nobs`. # """ # pdummies = None # tdummies = None def _fit_btwn(self, method, effects): # group mean regression or WLS if effects != "twoway": endog = self._group_mean(self.endog, index=effects) exog = self._group_mean(self.exog, index=effects) else: raise ValueError("%s effects is not valid for the between " "estimator" % effects) befit = GLS(endog, exog).fit() return befit def _fit_fixed(self, method, effects): endog = self.endog exog = self.exog demeantwice = False if effects in ["oneway","twoways"]: if effects == "twoways": demeantwice = True effects = "oneway" endog_mean, counts = self._group_mean(endog, index=effects, counts=True) exog_mean = self._group_mean(exog, index=effects) counts = counts.astype(int) endog = endog - np.repeat(endog_mean, counts) exog = exog - np.repeat(exog_mean, counts, axis=0) if demeantwice or effects == "time": endog_mean, dummies = self._group_mean(endog, index="time", dummies=True) exog_mean = self._group_mean(exog, index="time") # This allows unbalanced panels endog = endog - np.dot(endog_mean, dummies) exog = exog - np.dot(dummies.T, exog_mean) fefit = GLS(endog, exog[:,-self._cons_index]).fit() #TODO: might fail with one regressor return fefit class SURPanel(PanelModel): pass class SEMPanel(PanelModel): pass class DynamicPanel(PanelModel): pass if __name__ == "__main__": import pandas from pandas import Panel import statsmodels.api as sm import numpy.lib.recfunctions as nprf data = sm.datasets.grunfeld.load(as_pandas=False) # Baltagi does not include American Steel endog = data.endog[:-20] fullexog = data.exog[:-20] # fullexog.sort(order=['firm','year']) panel_arr = nprf.append_fields(fullexog, 'investment', endog, float, usemask=False) panel_df = pandas.DataFrame(panel_arr) panel_panda = panel_df.set_index(['year', 'firm']).to_panel() # the most cumbersome way of doing it as far as preprocessing by hand exog = fullexog[['value','capital']].view(float).reshape(-1,2) exog = sm.add_constant(exog, prepend=False) panel = group(fullexog['firm']) year = fullexog['year'] panel_mod = PanelModel(endog, exog, panel, year, xtnames=['firm','year'], equation='invest value capital') # note that equation does not actually do anything but name the variables panel_ols = panel_mod.fit(model='pooled') panel_be = panel_mod.fit(model='between', effects='oneway') panel_fe = panel_mod.fit(model='fixed', effects='oneway') panel_bet = panel_mod.fit(model='between', effects='time') panel_fet = panel_mod.fit(model='fixed', effects='time') panel_fe2 = panel_mod.fit(model='fixed', effects='twoways') #see also Baltagi (3rd edt) 3.3 THE RANDOM EFFECTS MODEL p.35 #for explicit formulas for spectral decomposition #but this works also for unbalanced panel # #I also just saw: 9.4.2 The Random Effects Model p.176 which is #partially almost the same as I did # #this needs to use sparse matrices for larger datasets # #""" # #import numpy as np # groups = np.array([0,0,0,1,1,2,2,2]) nobs = groups.shape[0] groupuniq = np.unique(groups) periods = np.array([0,1,2,1,2,0,1,2]) perioduniq = np.unique(periods) dummygr = (groups[:,None] == groupuniq).astype(float) dummype = (periods[:,None] == perioduniq).astype(float) sigma = 1. sigmagr = np.sqrt(2.) sigmape = np.sqrt(3.) #dummyall = np.c_[sigma*np.ones((nobs,1)), sigmagr*dummygr, # sigmape*dummype] #exclude constant ? dummyall = np.c_[sigmagr*dummygr, sigmape*dummype] # omega is the error variance-covariance matrix for the stacked # observations omega = np.dot(dummyall, dummyall.T) + sigma* np.eye(nobs) print(omega) print(np.linalg.cholesky(omega)) ev, evec = np.linalg.eigh(omega) #eig does not work omegainv = np.dot(evec, (1/ev * evec).T) omegainv2 = np.linalg.inv(omega) omegacomp = np.dot(evec, (ev * evec).T) print(np.max(np.abs(omegacomp - omega))) #check #print(np.dot(omegainv,omega) print(np.max(np.abs(np.dot(omegainv,omega) - np.eye(nobs)))) omegainvhalf = evec/np.sqrt(ev) #not sure whether ev should not be column print(np.max(np.abs(np.dot(omegainvhalf,omegainvhalf.T) - omegainv))) # now we can use omegainvhalf in GLS (instead of the cholesky) sigmas2 = np.array([sigmagr, sigmape, sigma]) groups2 = np.column_stack((groups, periods)) omega_, omegainv_, omegainvhalf_ = repanel_cov(groups2, sigmas2) print(np.max(np.abs(omega_ - omega))) print(np.max(np.abs(omegainv_ - omegainv))) print(np.max(np.abs(omegainvhalf_ - omegainvhalf))) # notation Baltagi (3rd) section 9.4.1 (Fixed Effects Model) Pgr = reduce(np.dot,[dummygr, np.linalg.inv(np.dot(dummygr.T, dummygr)),dummygr.T]) Qgr = np.eye(nobs) - Pgr # within group effect: np.dot(Qgr, groups) # but this is not memory efficient, compared to groupstats print(np.max(np.abs(np.dot(Qgr, groups)))) statsmodels-0.12.2/statsmodels/sandbox/panel/random_panel.py000066400000000000000000000115211400612667500242550ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Generate a random process with panel structure Created on Sat Dec 17 22:15:27 2011 Author: Josef Perktold Notes ----- * written with unbalanced panels in mind, but not flexible enough yet * need more shortcuts and options for balanced panel * need to add random intercept or coefficients * only one-way (repeated measures) so far """ import numpy as np from . import correlation_structures as cs class PanelSample(object): '''data generating process for panel with within correlation allows various within correlation structures, but no random intercept yet Parameters ---------- nobs : int total number of observations k_vars : int number of explanatory variables to create in exog, including constant n_groups int number of groups in balanced sample exog : None or ndarray default is None, in which case a exog is created within : bool If True (default), then the exog vary within a group. If False, then only variation across groups is used. TODO: this option needs more work corr_structure : ndarray or ?? Default is np.eye. corr_args : tuple arguments for the corr_structure scale : float scale of noise, standard deviation of normal distribution seed : None or int If seed is given, then this is used to create the random numbers for the sample. Notes ----- The behavior for panel robust covariance estimators seems to differ by a large amount by whether exog have mostly within group or across group variation. I do not understand why this should be the case from the theory, and this would warrant more investigation. This is just used in one example so far and needs more usage to see what will be useful to add. ''' def __init__(self, nobs, k_vars, n_groups, exog=None, within=True, corr_structure=np.eye, corr_args=(), scale=1, seed=None): nobs_i = nobs//n_groups nobs = nobs_i * n_groups #make balanced self.nobs = nobs self.nobs_i = nobs_i self.n_groups = n_groups self.k_vars = k_vars self.corr_structure = corr_structure self.groups = np.repeat(np.arange(n_groups), nobs_i) self.group_indices = np.arange(n_groups+1) * nobs_i #check +1 if exog is None: if within: #t = np.tile(np.linspace(-1,1,nobs_i), n_groups) t = np.tile(np.linspace(0, 2, nobs_i), n_groups) #rs2 = np.random.RandomState(9876) #t = 1 + 0.3 * rs2.randn(nobs_i * n_groups) #mix within and across variation #t += np.repeat(np.linspace(-1,1,nobs_i), n_groups) else: #no within group variation, t = np.repeat(np.linspace(-1,1,nobs_i), n_groups) exog = t[:,None]**np.arange(k_vars) self.exog = exog #self.y_true = exog.sum(1) #all coefficients equal 1, #moved to make random coefficients #initialize self.y_true = None self.beta = None if seed is None: seed = np.random.randint(0, 999999) self.seed = seed self.random_state = np.random.RandomState(seed) #this makes overwriting difficult, move to method? self.std = scale * np.ones(nobs_i) corr = self.corr_structure(nobs_i, *corr_args) self.cov = cs.corr2cov(corr, self.std) self.group_means = np.zeros(n_groups) def get_y_true(self): if self.beta is None: self.y_true = self.exog.sum(1) else: self.y_true = np.dot(self.exog, self.beta) def generate_panel(self): ''' generate endog for a random panel dataset with within correlation ''' random = self.random_state if self.y_true is None: self.get_y_true() nobs_i = self.nobs_i n_groups = self.n_groups use_balanced = True if use_balanced: #much faster for balanced case noise = self.random_state.multivariate_normal(np.zeros(nobs_i), self.cov, size=n_groups).ravel() #need to add self.group_means noise += np.repeat(self.group_means, nobs_i) else: noise = np.empty(self.nobs, np.float64) noise.fill(np.nan) for ii in range(self.n_groups): #print ii, idx, idxupp = self.group_indices[ii:ii+2] #print idx, idxupp mean_i = self.group_means[ii] noise[idx:idxupp] = self.random_state.multivariate_normal( mean_i * np.ones(self.nobs_i), self.cov) endog = self.y_true + noise return endog statsmodels-0.12.2/statsmodels/sandbox/panel/sandwich_covariance_generic.py000066400000000000000000000073151400612667500273120ustar00rootroot00000000000000# -*- coding: utf-8 -*- """covariance with (nobs,nobs) loop and general kernel This is a general implementation that is not efficient for any special cases. kernel is currently only for one continuous variable and any number of categorical groups. No spatial example, continuous is interpreted as time Created on Wed Nov 30 08:20:44 2011 Author: Josef Perktold License: BSD-3 """ import numpy as np def kernel(d1, d2, r=None, weights=None): '''general product kernel hardcoded split for the example: cat1 is continuous (time), other categories are discrete weights is e.g. Bartlett for cat1 r is (0,1) indicator vector for boolean weights 1{d1_i == d2_i} returns boolean if no continuous weights are used ''' diff = d1 - d2 if (weights is None) or (r[0] == 0): #time is irrelevant or treated as categorical return np.all((r * diff) == 0) #return bool else: #time uses continuous kernel, all other categorical return weights[diff] * np.all((r[1:] * diff[1:]) == 0) def aggregate_cov(x, d, r=None, weights=None): '''sum of outer procuct over groups and time selected by r This is for a generic reference implementation, it uses a nobs-nobs double loop. Parameters ---------- x : ndarray, (nobs,) or (nobs, k_vars) data, for robust standard error calculation, this is array of x_i * u_i d : ndarray, (nobs, n_groups) integer group labels, each column contains group (or time) indices r : ndarray, (n_groups,) indicator for which groups to include. If r[i] is zero, then this group is ignored. If r[i] is not zero, then the cluster robust standard errors include this group. weights : ndarray weights if the first group dimension uses a HAC kernel Returns ------- cov : ndarray (k_vars, k_vars) or scalar covariance matrix aggregates over group kernels count : int number of terms added in sum, mainly returned for cross-checking Notes ----- This uses `kernel` to calculate the weighted distance between two observations. ''' nobs = x.shape[0] #either 1d or 2d with obs in rows #next is not needed yet # if x.ndim == 2: # kvars = x.shape[1] # else: # kvars = 1 count = 0 #count non-zero pairs for cross checking, not needed res = 0 * np.outer(x[0], x[0]) #get output shape for ii in range(nobs): for jj in range(nobs): w = kernel(d[ii], d[jj], r=r, weights=weights) if w: #true or non-zero res += w * np.outer(x[0], x[0]) count *= 1 return res, count def weights_bartlett(nlags): #with lag zero, nlags is the highest lag included return 1 - np.arange(nlags+1)/(nlags+1.) #------- examples, cases: hardcoded for d is time and two categorical groups def S_all_hac(x, d, nlags=1): '''HAC independent of categorical group membership ''' r = np.zeros(d.shape[1]) r[0] = 1 weights = weights_bartlett(nlags) return aggregate_cov(x, d, r=r, weights=weights) def S_within_hac(x, d, nlags=1, groupidx=1): '''HAC for observations within a categorical group ''' r = np.zeros(d.shape[1]) r[0] = 1 r[groupidx] = 1 weights = weights_bartlett(nlags) return aggregate_cov(x, d, r=r, weights=weights) def S_cluster(x, d, groupidx=[1]): r = np.zeros(d.shape[1]) r[groupidx] = 1 return aggregate_cov(x, d, r=r, weights=None) def S_white(x, d): '''simple white heteroscedasticity robust covariance note: calculating this way is very inefficient, just for cross-checking ''' r = np.ones(d.shape[1]) #only points on diagonal return aggregate_cov(x, d, r=r, weights=None) statsmodels-0.12.2/statsmodels/sandbox/panel/tests/000077500000000000000000000000001400612667500224065ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/panel/tests/__init__.py000066400000000000000000000000001400612667500245050ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/panel/tests/test_random_panel.py000066400000000000000000000124751400612667500264670ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Test for short_panel and panel sandwich Created on Fri May 18 13:05:47 2012 Author: Josef Perktold moved example from main of random_panel """ import numpy as np from numpy.testing import assert_almost_equal import numpy.testing as npt import statsmodels.tools.eval_measures as em from statsmodels.stats.moment_helpers import cov2corr, se_cov from statsmodels.regression.linear_model import OLS from statsmodels.sandbox.panel.panel_short import ShortPanelGLS, ShortPanelGLS2 from statsmodels.sandbox.panel.random_panel import PanelSample import statsmodels.sandbox.panel.correlation_structures as cs import statsmodels.stats.sandwich_covariance as sw def assert_maxabs(actual, expected, value): npt.assert_array_less(em.maxabs(actual, expected, None), value) def test_short_panel(): #this checks that some basic statistical properties are satisfied by the #results, not verified results against other packages #Note: the ranking of robust bse is different if within=True #I added within keyword to PanelSample to be able to use old example #if within is False, then there is no within group variation in exog. nobs = 100 nobs_i = 5 n_groups = nobs // nobs_i k_vars = 3 dgp = PanelSample(nobs, k_vars, n_groups, corr_structure=cs.corr_arma, corr_args=([1], [1., -0.9],), seed=377769, within=False) #print 'seed', dgp.seed y = dgp.generate_panel() noise = y - dgp.y_true #test dgp dgp_cov_e = np.array( [[ 1. , 0.9 , 0.81 , 0.729 , 0.6561], [ 0.9 , 1. , 0.9 , 0.81 , 0.729 ], [ 0.81 , 0.9 , 1. , 0.9 , 0.81 ], [ 0.729 , 0.81 , 0.9 , 1. , 0.9 ], [ 0.6561, 0.729 , 0.81 , 0.9 , 1. ]]) npt.assert_almost_equal(dgp.cov, dgp_cov_e, 13) cov_noise = np.cov(noise.reshape(-1,n_groups, order='F')) corr_noise = cov2corr(cov_noise) npt.assert_almost_equal(corr_noise, dgp.cov, 1) #estimate panel model mod2 = ShortPanelGLS(y, dgp.exog, dgp.groups) res2 = mod2.fit_iterative(2) #whitened residual should be uncorrelated corr_wresid = np.corrcoef(res2.wresid.reshape(-1,n_groups, order='F')) assert_maxabs(corr_wresid, np.eye(5), 0.1) #residual should have same correlation as dgp corr_resid = np.corrcoef(res2.resid.reshape(-1,n_groups, order='F')) assert_maxabs(corr_resid, dgp.cov, 0.1) assert_almost_equal(res2.resid.std(),1, decimal=0) y_pred = np.dot(mod2.exog, res2.params) assert_almost_equal(res2.fittedvalues, y_pred, 13) #compare with OLS res2_ols = mod2._fit_ols() npt.assert_(mod2.res_pooled is res2_ols) res2_ols = mod2.res_pooled #TODO: BUG: requires call to _fit_ols #fitting once is the same as OLS #note: I need to create new instance, otherwise it continuous fitting mod1 = ShortPanelGLS(y, dgp.exog, dgp.groups) res1 = mod1.fit_iterative(1) assert_almost_equal(res1.params, res2_ols.params, decimal=13) assert_almost_equal(res1.bse, res2_ols.bse, decimal=13) res_ols = OLS(y, dgp.exog).fit() assert_almost_equal(res1.params, res_ols.params, decimal=13) assert_almost_equal(res1.bse, res_ols.bse, decimal=13) #compare with old version mod_old = ShortPanelGLS2(y, dgp.exog, dgp.groups) res_old = mod_old.fit() assert_almost_equal(res2.params, res_old.params, decimal=13) assert_almost_equal(res2.bse, res_old.bse, decimal=13) mod5 = ShortPanelGLS(y, dgp.exog, dgp.groups) res5 = mod5.fit_iterative(5) #make sure it's different #npt.assert_array_less(0.009, em.maxabs(res5.bse, res2.bse)) cov_clu = sw.cov_cluster(mod2.res_pooled, dgp.groups.astype(int)) clubse = se_cov(cov_clu) pnwbse = se_cov(sw.cov_nw_panel(mod2.res_pooled, 4, mod2.group.groupidx)) bser = np.vstack((res2.bse, res5.bse, clubse, pnwbse)) bser_mean = np.mean(bser, axis=0) #cov_cluster close to robust and PanelGLS #is up to 24% larger than mean of bser #npt.assert_array_less(0, clubse / bser_mean - 1) npt.assert_array_less(clubse / bser_mean - 1, 0.25) #cov_nw_panel close to robust and PanelGLS npt.assert_array_less(pnwbse / bser_mean - 1, 0.1) #OLS underestimates bse, robust at least 60% larger npt.assert_array_less(0.6, bser_mean / res_ols.bse - 1) #cov_hac_panel with uniform_kernel is the same as cov_cluster for balanced #panel with full length kernel #I fixe default correction to be equal cov_uni = sw.cov_nw_panel(mod2.res_pooled, 4, mod2.group.groupidx, weights_func=sw.weights_uniform, use_correction='c') assert_almost_equal(cov_uni, cov_clu, decimal=13) #without correction cov_clu2 = sw.cov_cluster(mod2.res_pooled, dgp.groups.astype(int), use_correction=False) cov_uni2 = sw.cov_nw_panel(mod2.res_pooled, 4, mod2.group.groupidx, weights_func=sw.weights_uniform, use_correction=False) assert_almost_equal(cov_uni2, cov_clu2, decimal=13) cov_white = sw.cov_white_simple(mod2.res_pooled) cov_pnw0 = sw.cov_nw_panel(mod2.res_pooled, 0, mod2.group.groupidx, use_correction='hac') assert_almost_equal(cov_pnw0, cov_white, decimal=13) statsmodels-0.12.2/statsmodels/sandbox/pca.py000066400000000000000000000156041400612667500212700ustar00rootroot00000000000000#Copyright (c) 2008 Erik Tollerud (etolleru@uci.edu) import numpy as np class Pca(object): """ A basic class for Principal Component Analysis (PCA). p is the number of dimensions, while N is the number of data points """ _colors=('r','g','b','c','y','m','k') #defaults def __calc(self): A = self.A M=A-np.mean(A,axis=0) N=M/np.std(M,axis=0) self.M = M self.N = N self._eig = None def __init__(self,data,names=None): """ p X N matrix input """ A = np.array(data).T n,p = A.shape self.n,self.p = n,p if p > n: from warnings import warn warn('p > n - intentional?', RuntimeWarning) self.A = A self._origA=A.copy() self.__calc() self._colors= np.tile(self._colors,int((p-1)/len(self._colors))+1)[:p] if names is not None and len(names) != p: raise ValueError('names must match data dimension') self.names = None if names is None else tuple([str(x) for x in names]) def getCovarianceMatrix(self): """ returns the covariance matrix for the dataset """ return np.cov(self.N.T) def getEigensystem(self): """ returns a tuple of (eigenvalues,eigenvectors) for the data set. """ if self._eig is None: res = np.linalg.eig(self.getCovarianceMatrix()) sorti=np.argsort(res[0])[::-1] res=(res[0][sorti],res[1][:,sorti]) self._eig=res return self._eig def getEigenvalues(self): return self.getEigensystem()[0] def getEigenvectors(self): return self.getEigensystem()[1] def getEnergies(self): """ "energies" are just normalized eigenvectors """ v=self.getEigenvalues() return v/np.sum(v) def plot2d(self,ix=0,iy=1,clf=True): """ Generates a 2-dimensional plot of the data set and principle components using matplotlib. ix specifies which p-dimension to put on the x-axis of the plot and iy specifies which to put on the y-axis (0-indexed) """ import matplotlib.pyplot as plt x,y=self.N[:,ix],self.N[:,iy] if clf: plt.clf() plt.scatter(x,y) vals,evs=self.getEigensystem() #evx,evy=evs[:,ix],evs[:,iy] xl,xu=plt.xlim() yl,yu=plt.ylim() dx,dy=(xu-xl),(yu-yl) for val,vec,c in zip(vals,evs.T,self._colors): plt.arrow(0,0,val*vec[ix],val*vec[iy],head_width=0.05*(dx*dy/4)**0.5,fc=c,ec=c) #plt.arrow(0,0,vals[ix]*evs[ix,ix],vals[ix]*evs[iy,ix],head_width=0.05*(dx*dy/4)**0.5,fc='g',ec='g') #plt.arrow(0,0,vals[iy]*evs[ix,iy],vals[iy]*evs[iy,iy],head_width=0.05*(dx*dy/4)**0.5,fc='r',ec='r') if self.names is not None: plt.xlabel('$'+self.names[ix]+'/\\sigma$') plt.ylabel('$'+self.names[iy]+'/\\sigma$') def plot3d(self,ix=0,iy=1,iz=2,clf=True): """ Generates a 3-dimensional plot of the data set and principle components using mayavi. ix, iy, and iz specify which of the input p-dimensions to place on each of the x,y,z axes, respectively (0-indexed). """ import enthought.mayavi.mlab as M if clf: M.clf() z3=np.zeros(3) v=(self.getEigenvectors()*self.getEigenvalues()) M.quiver3d(z3,z3,z3,v[ix],v[iy],v[iz],scale_factor=5) M.points3d(self.N[:,ix],self.N[:,iy],self.N[:,iz],scale_factor=0.3) if self.names: M.axes(xlabel=self.names[ix]+'/sigma',ylabel=self.names[iy]+'/sigma',zlabel=self.names[iz]+'/sigma') else: M.axes() def sigclip(self,sigs): """ clips out all data points that are more than a certain number of standard deviations from the mean. sigs can be either a single value or a length-p sequence that specifies the number of standard deviations along each of the p dimensions. """ if np.isscalar(sigs): sigs=sigs*np.ones(self.N.shape[1]) sigs = sigs*np.std(self.N,axis=1) n = self.N.shape[0] m = np.all(np.abs(self.N) < sigs,axis=1) self.A=self.A[m] self.__calc() return n-sum(m) def reset(self): self.A = self._origA.copy() self.__calc() def project(self,vals=None,enthresh=None,nPCs=None,cumen=None): """ projects the normalized values onto the components enthresh, nPCs, and cumen determine how many PCs to use if vals is None, the normalized data vectors are the values to project. Otherwise, it should be convertable to a p x N array returns n,p(>threshold) dimension array """ nonnones = sum([e is not None for e in (enthresh, nPCs, cumen)]) if nonnones == 0: m = slice(None) elif nonnones > 1: raise ValueError("cannot specify more than one threshold") else: if enthresh is not None: m = self.energies() > enthresh elif nPCs is not None: m = slice(None,nPCs) elif cumen is not None: m = np.cumsum(self.energies()) < cumen else: raise RuntimeError('Should be unreachable') if vals is None: vals = self.N.T else: vals = np.array(vals,copy=False) if self.N.T.shape[0] != vals.shape[0]: raise ValueError("shape for vals does not match") proj = np.matrix(self.getEigenvectors()).T*vals return proj[m].T def deproject(self,A,normed=True): """ input is an n X q array, where q <= p output is p X n """ A=np.atleast_2d(A) n,q = A.shape p = self.A.shape[1] if q > p : raise ValueError("q > p") evinv=np.linalg.inv(np.matrix(self.getEigenvectors()).T) zs = np.zeros((n,p)) zs[:,:q]=A proj = evinv*zs.T if normed: return np.array(proj.T).T else: mns=np.mean(self.A,axis=0) sds=np.std(self.M,axis=0) return (np.array(proj.T)*sds+mns).T def subtractPC(self,pc,vals=None): """ pc can be a scalar or any sequence of pc indecies if vals is None, the source data is self.A, else whatever is in vals (which must be p x m) """ if vals is None: vals = self.A else: vals = vals.T if vals.shape[1]!= self.A.shape[1]: raise ValueError("vals do not have the correct number of components") pcs=self.project() zpcs=np.zeros_like(pcs) zpcs[:,pc]=pcs[:,pc] upc=self.deproject(zpcs,False) A = vals.T-upc B = A.T*np.std(self.M,axis=0) return B+np.mean(self.A,axis=0) statsmodels-0.12.2/statsmodels/sandbox/predict_functional.py000066400000000000000000000367371400612667500244130ustar00rootroot00000000000000""" A predict-like function that constructs means and pointwise or simultaneous confidence bands for the function f(x) = E[Y | X*=x, X1=x1, ...], where X* is the focus variable and X1, X2, ... are non-focus variables. This is especially useful when conducting a functional regression in which the role of x is modeled with b-splines or other basis functions. """ import pandas as pd import patsy import numpy as np import warnings from statsmodels.tools.sm_exceptions import ValueWarning from statsmodels.compat.pandas import Appender _predict_functional_doc =\ """ Predictions and contrasts of a fitted model as a function of a given covariate. The value of the focus variable varies along a sequence of its quantiles, calculated from the data used to fit the model. The other variables are held constant either at given values, or at values obtained by applying given summary functions to the data used to fit the model. Optionally, a second specification of the non-focus variables is provided and the contrast between the two specifications is returned. Parameters ---------- result : statsmodels result object A results object for the fitted model. focus_var : str The name of the 'focus variable'. summaries : dict-like A map from names of non-focus variables to summary functions. Each summary function is applied to the data used to fit the model, to obtain a value at which the variable is held fixed. values : dict-like Values at which a given non-focus variable is held fixed. summaries2 : dict-like A second set of summary functions used to define a contrast. values2 : dict-like A second set of fixed values used to define a contrast. alpha : float `1 - alpha` is the coverage probability. ci_method : str The method for constructing the confidence band, one of 'pointwise', 'scheffe', and 'simultaneous'. num_points : int The number of equally-spaced quantile points where the prediction is made. exog : array_like Explicitly provide points to cover with the confidence band. exog2 : array_like Explicitly provide points to contrast to `exog` in a functional confidence band. kwargs : Arguments passed to the `predict` method. Returns ------- pred : array_like The predicted mean values. cb : array_like An array with two columns, containing respectively the lower and upper limits of a confidence band. fvals : array_like The values of the focus variable at which the prediction is made. Notes ----- All variables in the model except for the focus variable should be included as a key in either `summaries` or `values` (unless `exog` is provided). If `summaries2` and `values2` are not provided, the returned value contains predicted conditional means for the outcome as the focus variable varies, with the other variables fixed as specified. If `summaries2` and/or `values2` is provided, two sets of predicted conditional means are calculated, and the returned value is the contrast between them. If `exog` is provided, then the rows should contain a sequence of values approximating a continuous path through the domain of the covariates. For example, if Z(s) is the covariate expressed as a function of s, then the rows of exog may approximate Z(g(s)) for some continuous function g. If `exog` is provided then neither of the summaries or values arguments should be provided. If `exog2` is also provided, then the returned value is a contrast between the functionas defined by `exog` and `exog2`. Examples -------- Fit a model using a formula in which the predictors are age (modeled with splines), ethnicity (which is categorical), gender, and income. Then we obtain the fitted mean values as a function of age for females with mean income and the most common ethnicity. >>> model = sm.OLS.from_formula('y ~ bs(age, df=4) + C(ethnicity) + gender + income', data) >>> result = model.fit() >>> mode = lambda x : x.value_counts().argmax() >>> summaries = {'income': np.mean, ethnicity=mode} >>> values = {'gender': 'female'} >>> pr, cb, x = predict_functional(result, 'age', summaries, values) Fit a model using arrays. Plot the means as a function of x3, holding x1 fixed at its mean value in the data used to fit the model, and holding x2 fixed at 1. >>> model = sm.OLS(y ,x) >>> result = model.fit() >>> summaries = {'x1': np.mean} >>> values = {'x2': 1} >>> pr, cb, x = predict_functional(result, 'x3', summaries, values) Fit a model usng a formula and construct a contrast comparing the female and male predicted mean functions. >>> model = sm.OLS.from_formula('y ~ bs(age, df=4) + gender', data) >>> result = model.fit() >>> values = {'gender': 'female'} >>> values2 = {'gender': 'male'} >>> pr, cb, x = predict_functional(result, 'age', values=values, values2=values2) """ def _make_exog_from_formula(result, focus_var, summaries, values, num_points): """ Create dataframes for exploring a fitted model as a function of one variable. This works for models fit with a formula. Returns ------- dexog : data frame A data frame in which the focus variable varies and the other variables are fixed at specified or computed values. fexog : data frame The data frame `dexog` processed through the model formula. """ model = result.model exog = model.data.frame if summaries is None: summaries = {} if values is None: values = {} if exog[focus_var].dtype is np.dtype('O'): raise ValueError('focus variable may not have object type') colnames = list(summaries.keys()) + list(values.keys()) + [focus_var] dtypes = [exog[x].dtype for x in colnames] # Check for variables whose values are not set either through # `values` or `summaries`. Since the model data frame can contain # extra variables not referenced in the formula RHS, this may not # be a problem, so just warn. There is no obvious way to extract # from a formula all the variable names that it references. varl = set(exog.columns.tolist()) - set([model.endog_names]) unmatched = varl - set(colnames) unmatched = list(unmatched) if len(unmatched) > 0: warnings.warn("%s in data frame but not in summaries or values." % ", ".join(["'%s'" % x for x in unmatched]), ValueWarning) # Initialize at zero so each column can be converted to any dtype. ix = range(num_points) fexog = pd.DataFrame(index=ix, columns=colnames) for d, x in zip(dtypes, colnames): fexog[x] = pd.Series(index=ix, dtype=d) # The values of the 'focus variable' are a sequence of percentiles pctls = np.linspace(0, 100, num_points).tolist() fvals = np.percentile(exog[focus_var], pctls) fvals = np.asarray(fvals) fexog.loc[:, focus_var] = fvals # The values of the other variables may be given by summary functions... for ky in summaries.keys(): fexog.loc[:, ky] = summaries[ky](exog.loc[:, ky]) # or they may be provided as given values. for ky in values.keys(): fexog.loc[:, ky] = values[ky] dexog = patsy.dmatrix(model.data.design_info, fexog, return_type='dataframe') return dexog, fexog, fvals def _make_exog_from_arrays(result, focus_var, summaries, values, num_points): """ Create dataframes for exploring a fitted model as a function of one variable. This works for models fit without a formula. Returns ------- exog : data frame A data frame in which the focus variable varies and the other variables are fixed at specified or computed values. """ model = result.model model_exog = model.exog exog_names = model.exog_names if summaries is None: summaries = {} if values is None: values = {} exog = np.zeros((num_points, model_exog.shape[1])) # Check for variables whose values are not set either through # `values` or `summaries`. colnames = list(values.keys()) + list(summaries.keys()) + [focus_var] unmatched = set(exog_names) - set(colnames) unmatched = list(unmatched) if len(unmatched) > 0: warnings.warn("%s in model but not in `summaries` or `values`." % ", ".join(["'%s'" % x for x in unmatched]), ValueWarning) # The values of the 'focus variable' are a sequence of percentiles pctls = np.linspace(0, 100, num_points).tolist() ix = exog_names.index(focus_var) fvals = np.percentile(model_exog[:, ix], pctls) exog[:, ix] = fvals # The values of the other variables may be given by summary functions... for ky in summaries.keys(): ix = exog_names.index(ky) exog[:, ix] = summaries[ky](model_exog[:, ix]) # or they may be provided as given values. for ky in values.keys(): ix = exog_names.index(ky) exog[:, ix] = values[ky] return exog, fvals def _make_exog(result, focus_var, summaries, values, num_points): # Branch depending on whether the model was fit with a formula. if hasattr(result.model.data, "frame"): dexog, fexog, fvals = _make_exog_from_formula(result, focus_var, summaries, values, num_points) else: exog, fvals = _make_exog_from_arrays(result, focus_var, summaries, values, num_points) dexog, fexog = exog, exog return dexog, fexog, fvals def _check_args(values, summaries, values2, summaries2): if values is None: values = {} if values2 is None: values2 = {} if summaries is None: summaries = {} if summaries2 is None: summaries2 = {} for (s,v) in (summaries, values), (summaries2, values2): ky = set(v.keys()) & set(s.keys()) ky = list(ky) if len(ky) > 0: raise ValueError("One or more variable names are contained in both `summaries` and `values`:" + ", ".join(ky)) return values, summaries, values2, summaries2 @Appender(_predict_functional_doc) def predict_functional(result, focus_var, summaries=None, values=None, summaries2=None, values2=None, alpha=0.05, ci_method="pointwise", linear=True, num_points=10, exog=None, exog2=None, **kwargs): if ci_method not in ("pointwise", "scheffe", "simultaneous"): raise ValueError('confidence band method must be one of ' '`pointwise`, `scheffe`, and `simultaneous`.') contrast = (values2 is not None) or (summaries2 is not None) if contrast and not linear: raise ValueError("`linear` must be True for computing contrasts") model = result.model if exog is not None: if any(x is not None for x in [summaries, summaries2, values, values2]): raise ValueError("if `exog` is provided then do not " "provide `summaries` or `values`") fexog = exog dexog = patsy.dmatrix(model.data.design_info, fexog, return_type='dataframe') fvals = exog[focus_var] if exog2 is not None: fexog2 = exog dexog2 = patsy.dmatrix(model.data.design_info, fexog2, return_type='dataframe') fvals2 = fvals else: values, summaries, values2, summaries2 = _check_args(values, summaries, values2, summaries2) dexog, fexog, fvals = _make_exog(result, focus_var, summaries, values, num_points) if len(summaries2) + len(values2) > 0: dexog2, fexog2, fvals2 = _make_exog(result, focus_var, summaries2, values2, num_points) from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod.generalized_estimating_equations import GEE if isinstance(result.model, (GLM, GEE)): kwargs_pred = kwargs.copy() kwargs_pred.update({"linear": True}) else: kwargs_pred = kwargs pred = result.predict(exog=fexog, **kwargs_pred) if contrast: pred2 = result.predict(exog=fexog2, **kwargs_pred) pred = pred - pred2 dexog = dexog - dexog2 if ci_method == 'pointwise': t_test = result.t_test(dexog) cb = t_test.conf_int(alpha=alpha) elif ci_method == 'scheffe': t_test = result.t_test(dexog) sd = t_test.sd cb = np.zeros((num_points, 2)) # Scheffe's method from scipy.stats.distributions import f as fdist df1 = result.model.exog.shape[1] df2 = result.model.exog.shape[0] - df1 qf = fdist.cdf(1 - alpha, df1, df2) fx = sd * np.sqrt(df1 * qf) cb[:, 0] = pred - fx cb[:, 1] = pred + fx elif ci_method == 'simultaneous': sigma, c = _glm_basic_scr(result, dexog, alpha) cb = np.zeros((dexog.shape[0], 2)) cb[:, 0] = pred - c*sigma cb[:, 1] = pred + c*sigma if not linear: # May need to support other models with link-like functions. link = result.family.link pred = link.inverse(pred) cb = link.inverse(cb) return pred, cb, fvals def _glm_basic_scr(result, exog, alpha): """ The basic SCR from (Sun et al. Annals of Statistics 2000). Computes simultaneous confidence regions (SCR). Parameters ---------- result : results instance The fitted GLM results instance exog : array_like The exog values spanning the interval alpha : float `1 - alpha` is the coverage probability. Returns ------- An array with two columns, containing the lower and upper confidence bounds, respectively. Notes ----- The rows of `exog` should be a sequence of covariate values obtained by taking one 'free variable' x and varying it over an interval. The matrix `exog` is thus the basis functions and any other covariates evaluated as x varies. """ model = result.model n = model.exog.shape[0] # Get the Hessian without recomputing. cov = result.cov_params() hess = np.linalg.inv(cov) # Proposition 3.1 of Sun et al. A = hess / n B = np.linalg.cholesky(A).T # Upper Cholesky triangle # The variance and SD of the linear predictor at each row of exog. sigma2 = (np.dot(exog, cov) * exog).sum(1) sigma = np.asarray(np.sqrt(sigma2)) # Calculate kappa_0 (formula 42 from Sun et al) bz = np.linalg.solve(B.T, exog.T).T bz /= np.sqrt(n) bz /= sigma[:, None] bzd = np.diff(bz, 1, axis=0) bzdn = (bzd**2).sum(1) kappa_0 = np.sqrt(bzdn).sum() from scipy.stats.distributions import norm # The root of this function is the multiplier for the confidence # band, see Sun et al. equation 35. def func(c): return kappa_0 * np.exp(-c**2/2) / np.pi + 2*(1 - norm.cdf(c)) - alpha from scipy.optimize import brentq c, rslt = brentq(func, 1, 10, full_output=True) if not rslt.converged: raise ValueError("Root finding error in basic SCR") return sigma, c statsmodels-0.12.2/statsmodels/sandbox/regression/000077500000000000000000000000001400612667500223255ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/regression/__init__.py000066400000000000000000000001441400612667500244350ustar00rootroot00000000000000 #from anova_nistcertified import anova_oneway, anova_ols #from predstd import wls_prediction_std statsmodels-0.12.2/statsmodels/sandbox/regression/anova_nistcertified.py000066400000000000000000000075231400612667500267260ustar00rootroot00000000000000'''calculating anova and verifying with NIST test data compares my implementations, stats.f_oneway and anova using statsmodels.OLS ''' from statsmodels.compat.python import lmap import os import numpy as np from scipy import stats import statsmodels.api as sm from .try_ols_anova import data2dummy filenameli = ['SiRstv.dat', 'SmLs01.dat', 'SmLs02.dat', 'SmLs03.dat', 'AtmWtAg.dat', 'SmLs04.dat', 'SmLs05.dat', 'SmLs06.dat', 'SmLs07.dat', 'SmLs08.dat', 'SmLs09.dat'] ##filename = 'SmLs03.dat' #'SiRstv.dat' #'SmLs09.dat'#, 'AtmWtAg.dat' #'SmLs07.dat' ##path = __file__ ##print(locals().keys() ###print(path def getnist(filename): here = os.path.dirname(__file__) fname = os.path.abspath(os.path.join(here, 'data', filename)) with open(fname, 'r') as fd: content = fd.read().split('\n') data = [line.split() for line in content[60:]] certified = [line.split() for line in content[40:48] if line] dataf = np.loadtxt(fname, skiprows=60) y,x = dataf.T y = y.astype(int) caty = np.unique(y) f = float(certified[0][-1]) R2 = float(certified[2][-1]) resstd = float(certified[4][-1]) dfbn = int(certified[0][-4]) dfwn = int(certified[1][-3]) # dfbn->dfwn is this correct prob = stats.f.sf(f,dfbn,dfwn) return y, x, np.array([f, prob, R2, resstd]), certified, caty def anova_oneway(y, x, seq=0): # new version to match NIST # no generalization or checking of arguments, tested only for 1d yrvs = y[:,np.newaxis] #- min(y) #subracting mean increases numerical accuracy for NIST test data sets xrvs = x[:,np.newaxis] - x.mean() #for 1d#- 1e12 trick for 'SmLs09.dat' from .try_catdata import groupsstats_dummy meang, varg, xdevmeangr, countg = groupsstats_dummy(yrvs[:, :1], xrvs[:, :1]) # TODO: the following does not work as replacement # from .try_catdata import groupsstats_dummy, groupstatsbin # gcount, gmean , meanarr, withinvar, withinvararr = groupstatsbin(y, x) sswn = np.dot(xdevmeangr.T,xdevmeangr) ssbn = np.dot((meang-xrvs.mean())**2, countg.T) nobs = yrvs.shape[0] ncat = meang.shape[1] dfbn = ncat - 1 dfwn = nobs - ncat msb = ssbn/float(dfbn) msw = sswn/float(dfwn) f = msb/msw prob = stats.f.sf(f,dfbn,dfwn) R2 = (ssbn/(sswn+ssbn)) #R-squared resstd = np.sqrt(msw) #residual standard deviation #print(f, prob def _fix2scalar(z): # return number if np.shape(z) == (1, 1): return z[0, 0] else: return z f, prob, R2, resstd = lmap(_fix2scalar, (f, prob, R2, resstd)) return f, prob, R2, resstd def anova_ols(y, x): X = sm.add_constant(data2dummy(x), prepend=False) res = sm.OLS(y, X).fit() return res.fvalue, res.f_pvalue, res.rsquared, np.sqrt(res.mse_resid) if __name__ == '__main__': print('\n using new ANOVA anova_oneway') print('f, prob, R2, resstd') for fn in filenameli: print(fn) y, x, cert, certified, caty = getnist(fn) res = anova_oneway(y, x) # TODO: figure out why these results are less accurate/precise # than others rtol = { "SmLs08.dat": .027, "SmLs07.dat": 1.7e-3, "SmLs09.dat": 1e-4 }.get(fn, 1e-7) np.testing.assert_allclose(np.array(res), cert, rtol=rtol) print('\n using stats ANOVA f_oneway') for fn in filenameli: print(fn) y, x, cert, certified, caty = getnist(fn) xlist = [x[y==ii] for ii in caty] res = stats.f_oneway(*xlist) print(np.array(res) - cert[:2]) print('\n using statsmodels.OLS') print('f, prob, R2, resstd') for fn in filenameli[:]: print(fn) y, x, cert, certified, caty = getnist(fn) res = anova_ols(x, y) print(np.array(res) - cert) statsmodels-0.12.2/statsmodels/sandbox/regression/ar_panel.py000066400000000000000000000067401400612667500244670ustar00rootroot00000000000000'''Paneldata model with fixed effect (constants) and AR(1) errors checking fast evaluation of groupar1filter quickly written to try out grouparfilter without python loops maybe the example has MA(1) not AR(1) errors, I'm not sure and changed this. results look good, I'm also differencing the dummy variable (constants) ??? e.g. nobs = 35 true 0.6, 10, 20, 30 (alpha, mean_0, mean_1, mean_2) estimate 0.369453125 [ 10.14646929 19.87135086 30.12706505] Currently minimizes ssr but could switch to minimize llf, i.e. conditional MLE. This should correspond to iterative FGLS, where data are AR(1) transformed similar to GLSAR ? Result statistic from GLS return by OLS on transformed data should be asymptotically correct (check) Could be extended to AR(p) errors, but then requires panel with larger T ''' import numpy as np from scipy import optimize from statsmodels.regression.linear_model import OLS class PanelAR1(object): def __init__(self, endog, exog=None, groups=None): #take this from a super class, no checking is done here nobs = endog.shape[0] self.endog = endog if exog is not None: self.exog = exog self.groups_start = (np.diff(groups)!=0) self.groups_valid = ~self.groups_start def ar1filter(self, xy, alpha): #print(alpha,) return (xy[1:] - alpha * xy[:-1])[self.groups_valid] def fit_conditional(self, alpha): y = self.ar1filter(self.endog, alpha) x = self.ar1filter(self.exog, alpha) res = OLS(y, x).fit() return res.ssr #res.llf def fit(self): alpha0 = 0.1 #startvalue func = self.fit_conditional fitres = optimize.fmin(func, alpha0) # fit_conditional only returns ssr for now alpha = fitres[0] y = self.ar1filter(self.endog, alpha) x = self.ar1filter(self.exog, alpha) reso = OLS(y, x).fit() return fitres, reso if __name__ == '__main__': #------------ development code for groupar1filter and example groups = np.array([0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2, 2,2,2,2,2,2,2,2]) nobs = len(groups) data0 = np.arange(nobs) data = np.arange(1,nobs+1) - 0.5*np.arange(nobs) + 0.1*np.random.randn(nobs) y00 = 0.5*np.random.randn(nobs+1) # I do not think a trend is handled yet data = np.arange(nobs) + y00[1:] + 0.2*y00[:-1] + 0.1*np.random.randn(nobs) #Are these AR(1) or MA(1) errors ??? data = y00[1:] + 0.6*y00[:-1] #+ 0.1*np.random.randn(nobs) group_codes = np.unique(groups) group_dummy = (groups[:,None] == group_codes).astype(int) groups_start = (np.diff(groups)!=0) groups_valid = (np.diff(groups)==0) #this applies to y with length for AR(1) #could use np.nonzero for index instead y = data + np.dot(group_dummy, np.array([10, 20, 30])) y0 = data0 + np.dot(group_dummy, np.array([10, 20, 30])) print(groups_valid) print(np.diff(y)[groups_valid]) alpha = 1 #test with 1 print((y0[1:] - alpha*y0[:-1])[groups_valid]) alpha = 0.2 #test with 1 print((y0[1:] - alpha*y0[:-1] + 0.001)[groups_valid]) #this is now AR(1) for each group separately #------------ #fitting the example exog = np.ones(nobs) exog = group_dummy mod = PanelAR1(y, exog, groups=groups) #mod = PanelAR1(data, exog, groups=groups) #data does not contain different means #print(mod.ar1filter(mod.endog, 1)) resa, reso = mod.fit() print(resa[0], reso.params) statsmodels-0.12.2/statsmodels/sandbox/regression/data/000077500000000000000000000000001400612667500232365ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/regression/data/AtmWtAg.dat000066400000000000000000000057671400612667500252530ustar00rootroot00000000000000NIST/ITL StRD Dataset Name: AtmWtAg (AtmWtAg.dat) File Format: ASCII Certified Values (lines 41 to 47) Data (lines 61 to 108) Procedure: Analysis of Variance Reference: Powell, L.J., Murphy, T.J. and Gramlich, J.W. (1982). "The Absolute Isotopic Abundance & Atomic Weight of a Reference Sample of Silver". NBS Journal of Research, 87, pp. 9-19. Data: 1 Factor 2 Treatments 24 Replicates/Cell 48 Observations 7 Constant Leading Digits Average Level of Difficulty Observed Data Model: 3 Parameters (mu, tau_1, tau_2) y_{ij} = mu + tau_i + epsilon_{ij} Certified Values: Source of Sums of Mean Variation df Squares Squares F Statistic Between Instrument 1 3.63834187500000E-09 3.63834187500000E-09 1.59467335677930E+01 Within Instrument 46 1.04951729166667E-08 2.28155932971014E-10 Certified R-Squared 2.57426544538321E-01 Certified Residual Standard Deviation 1.51048314446410E-05 Data: Instrument AgWt 1 107.8681568 1 107.8681465 1 107.8681572 1 107.8681785 1 107.8681446 1 107.8681903 1 107.8681526 1 107.8681494 1 107.8681616 1 107.8681587 1 107.8681519 1 107.8681486 1 107.8681419 1 107.8681569 1 107.8681508 1 107.8681672 1 107.8681385 1 107.8681518 1 107.8681662 1 107.8681424 1 107.8681360 1 107.8681333 1 107.8681610 1 107.8681477 2 107.8681079 2 107.8681344 2 107.8681513 2 107.8681197 2 107.8681604 2 107.8681385 2 107.8681642 2 107.8681365 2 107.8681151 2 107.8681082 2 107.8681517 2 107.8681448 2 107.8681198 2 107.8681482 2 107.8681334 2 107.8681609 2 107.8681101 2 107.8681512 2 107.8681469 2 107.8681360 2 107.8681254 2 107.8681261 2 107.8681450 2 107.8681368 statsmodels-0.12.2/statsmodels/sandbox/regression/data/Longley.dat000066400000000000000000000055371400612667500253530ustar00rootroot00000000000000NIST/ITL StRD Dataset Name: Longley (Longley.dat) File Format: ASCII Certified Values (lines 31 to 51) Data (lines 61 to 76) Procedure: Linear Least Squares Regression Reference: Longley, J. W. (1967). An Appraisal of Least Squares Programs for the Electronic Computer from the Viewpoint of the User. Journal of the American Statistical Association, 62, pp. 819-841. Data: 1 Response Variable (y) 6 Predictor Variable (x) 16 Observations Higher Level of Difficulty Observed Data Model: Polynomial Class 7 Parameters (B0,B1,...,B7) y = B0 + B1*x1 + B2*x2 + B3*x3 + B4*x4 + B5*x5 + B6*x6 + e Certified Regression Statistics Standard Deviation Parameter Estimate of Estimate B0 -3482258.63459582 890420.383607373 B1 15.0618722713733 84.9149257747669 B2 -0.358191792925910E-01 0.334910077722432E-01 B3 -2.02022980381683 0.488399681651699 B4 -1.03322686717359 0.214274163161675 B5 -0.511041056535807E-01 0.226073200069370 B6 1829.15146461355 455.478499142212 Residual Standard Deviation 304.854073561965 R-Squared 0.995479004577296 Certified Analysis of Variance Table Source of Degrees of Sums of Mean Variation Freedom Squares Squares F Statistic Regression 6 184172401.944494 30695400.3240823 330.285339234588 Residual 9 836424.055505915 92936.0061673238 Data: y x1 x2 x3 x4 x5 x6 60323 83.0 234289 2356 1590 107608 1947 61122 88.5 259426 2325 1456 108632 1948 60171 88.2 258054 3682 1616 109773 1949 61187 89.5 284599 3351 1650 110929 1950 63221 96.2 328975 2099 3099 112075 1951 63639 98.1 346999 1932 3594 113270 1952 64989 99.0 365385 1870 3547 115094 1953 63761 100.0 363112 3578 3350 116219 1954 66019 101.2 397469 2904 3048 117388 1955 67857 104.6 419180 2822 2857 118734 1956 68169 108.4 442769 2936 2798 120445 1957 66513 110.8 444546 4681 2637 121950 1958 68655 112.6 482704 3813 2552 123366 1959 69564 114.2 502601 3931 2514 125368 1960 69331 115.7 518173 4806 2572 127852 1961 70551 116.9 554894 4007 2827 130081 1962 statsmodels-0.12.2/statsmodels/sandbox/regression/data/SiRstv.dat000066400000000000000000000036331400612667500251670ustar00rootroot00000000000000NIST/ITL StRD Dataset Name: SiRstv (SiRstv.dat) File Format: ASCII Certified Values (lines 41 to 47) Data (lines 61 to 85) Procedure: Analysis of Variance Reference: Ehrstein, James and Croarkin, M. Carroll. Unpublished NIST dataset. Data: 1 Factor 5 Treatments 5 Replicates/Cell 25 Observations 3 Constant Leading Digits Lower Level of Difficulty Observed Data Model: 6 Parameters (mu,tau_1, ... , tau_5) y_{ij} = mu + tau_i + epsilon_{ij} Certified Values: Source of Sums of Mean Variation df Squares Squares F Statistic Between Instrument 4 5.11462616000000E-02 1.27865654000000E-02 1.18046237440255E+00 Within Instrument 20 2.16636560000000E-01 1.08318280000000E-02 Certified R-Squared 1.90999039051129E-01 Certified Residual Standard Deviation 1.04076068334656E-01 Data: Instrument Resistance 1 196.3052 1 196.1240 1 196.1890 1 196.2569 1 196.3403 2 196.3042 2 196.3825 2 196.1669 2 196.3257 2 196.0422 3 196.1303 3 196.2005 3 196.2889 3 196.0343 3 196.1811 4 196.2795 4 196.1748 4 196.1494 4 196.1485 4 195.9885 5 196.2119 5 196.1051 5 196.1850 5 196.0052 5 196.2090 statsmodels-0.12.2/statsmodels/sandbox/regression/data/SmLs01.dat000066400000000000000000000136471400612667500247620ustar00rootroot00000000000000NIST/ITL StRD Dataset Name: SmLs01 (SmLs01.dat) File Format: ASCII Certified Values (lines 41 to 47) Data (lines 61 to 249) Procedure: Analysis of Variance Reference: Simon, Stephen D. and Lesage, James P. (1989). "Assessing the Accuracy of ANOVA Calculations in Statistical Software". Computational Statistics & Data Analysis, 8, pp. 325-332. Data: 1 Factor 9 Treatments 21 Replicates/Cell 189 Observations 1 Constant Leading Digit Lower Level of Difficulty Generated Data Model: 10 Parameters (mu,tau_1, ... , tau_9) y_{ij} = mu + tau_i + epsilon_{ij} Certified Values: Source of Sums of Mean Variation df Squares Squares F Statistic Between Treatment 8 1.68000000000000E+00 2.10000000000000E-01 2.10000000000000E+01 Within Treatment 180 1.80000000000000E+00 1.00000000000000E-02 Certified R-Squared 4.82758620689655E-01 Certified Residual Standard Deviation 1.00000000000000E-01 Data: Treatment Response 1 1.4 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 2 1.3 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 3 1.5 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 4 1.3 4 1.2 4 1.4 4 1.2 4 1.4 4 1.2 4 1.4 4 1.2 4 1.4 4 1.2 4 1.4 4 1.2 4 1.4 4 1.2 4 1.4 4 1.2 4 1.4 4 1.2 4 1.4 4 1.2 4 1.4 5 1.5 5 1.4 5 1.6 5 1.4 5 1.6 5 1.4 5 1.6 5 1.4 5 1.6 5 1.4 5 1.6 5 1.4 5 1.6 5 1.4 5 1.6 5 1.4 5 1.6 5 1.4 5 1.6 5 1.4 5 1.6 6 1.3 6 1.2 6 1.4 6 1.2 6 1.4 6 1.2 6 1.4 6 1.2 6 1.4 6 1.2 6 1.4 6 1.2 6 1.4 6 1.2 6 1.4 6 1.2 6 1.4 6 1.2 6 1.4 6 1.2 6 1.4 7 1.5 7 1.4 7 1.6 7 1.4 7 1.6 7 1.4 7 1.6 7 1.4 7 1.6 7 1.4 7 1.6 7 1.4 7 1.6 7 1.4 7 1.6 7 1.4 7 1.6 7 1.4 7 1.6 7 1.4 7 1.6 8 1.3 8 1.2 8 1.4 8 1.2 8 1.4 8 1.2 8 1.4 8 1.2 8 1.4 8 1.2 8 1.4 8 1.2 8 1.4 8 1.2 8 1.4 8 1.2 8 1.4 8 1.2 8 1.4 8 1.2 8 1.4 9 1.5 9 1.4 9 1.6 9 1.4 9 1.6 9 1.4 9 1.6 9 1.4 9 1.6 9 1.4 9 1.6 9 1.4 9 1.6 9 1.4 9 1.6 9 1.4 9 1.6 9 1.4 9 1.6 9 1.4 9 1.6 statsmodels-0.12.2/statsmodels/sandbox/regression/data/SmLs02.dat000066400000000000000000001327411400612667500247600ustar00rootroot00000000000000NIST/ITL StRD Dataset Name: SmLs02 (SmLs02.dat) File Format: ASCII Certified Values (lines 41 to 47) Data (lines 61 to 1869) Procedure: Analysis of Variance Reference: Simon, Stephen D. and Lesage, James P. (1989). "Assessing the Accuracy of ANOVA Calculations in Statistical Software". Computational Statistics & Data Analysis, 8, pp. 325-332. Data: 1 Factor 9 Treatments 201 Replicates/Cell 1809 Observations 1 Constant Leading Digit Lower Level of Difficulty Generated Data Model: 10 Parameters (mu,tau_1, ... , tau_9) y_{ij} = mu + tau_i + epsilon_{ij} Certified Values: Source of Sums of Mean Variation df Squares Squares F Statistic Between Treatment 8 1.60800000000000E+01 2.01000000000000E+00 2.01000000000000E+02 Within Treatment 1800 1.80000000000000E+01 1.00000000000000E-02 Certified R-Squared 4.71830985915493E-01 Certified Residual Standard Deviation 1.00000000000000E-01 Data: Treatment Response 1 1.4 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 2 1.3 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 2 1.2 2 1.4 3 1.5 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 3 1.6 3 1.4 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(1989). "Assessing the Accuracy of ANOVA Calculations in Statistical Software". Computational Statistics & Data Analysis, 8, pp. 325-332. Data: 1 Factor 9 Treatments 2001 Replicates/Cell 18009 Observations 1 Constant Leading Digit Lower Level of Difficulty Generated Data Model: 10 Parameters (mu,tau_1, ... , tau_9) y_{ij} = mu + tau_i + epsilon_{ij} Certified Values: Source of Sums of Mean Variation df Squares Squares F Statistic Between Treatment 8 1.60080000000000E+02 2.00100000000000E+01 2.00100000000000E+03 Within Treatment 18000 1.80000000000000E+02 1.00000000000000E-02 Certified R-Squared 4.70712773465067E-01 Certified Residual Standard Deviation 1.00000000000000E-01 Data: Treatment Response 1 1.4 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 1 1.5 1 1.3 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Procedure: Analysis of Variance Reference: Simon, Stephen D. and Lesage, James P. (1989). "Assessing the Accuracy of ANOVA Calculations in Statistical Software". Computational Statistics & Data Analysis, 8, pp. 325-332. Data: 1 Factor 9 Treatments 21 Replicates/Cell 189 Observations 7 Constant Leading Digits Average Level of Difficulty Generated Data Model: 10 Parameters (mu,tau_1, ... , tau_9) y_{ij} = mu + tau_i + epsilon_{ij} Certified Values: Source of Sums of Mean Variation df Squares Squares F Statistic Between Treatment 8 1.68000000000000E+00 2.10000000000000E-01 2.10000000000000E+01 Within Treatment 180 1.80000000000000E+00 1.00000000000000E-02 Certified R-Squared 4.82758620689655E-01 Certified Residual Standard Deviation 1.00000000000000E-01 Data: Treatment Response 1 1000000.4 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 2 1000000.3 2 1000000.2 2 1000000.4 2 1000000.2 2 1000000.4 2 1000000.2 2 1000000.4 2 1000000.2 2 1000000.4 2 1000000.2 2 1000000.4 2 1000000.2 2 1000000.4 2 1000000.2 2 1000000.4 2 1000000.2 2 1000000.4 2 1000000.2 2 1000000.4 2 1000000.2 2 1000000.4 3 1000000.5 3 1000000.4 3 1000000.6 3 1000000.4 3 1000000.6 3 1000000.4 3 1000000.6 3 1000000.4 3 1000000.6 3 1000000.4 3 1000000.6 3 1000000.4 3 1000000.6 3 1000000.4 3 1000000.6 3 1000000.4 3 1000000.6 3 1000000.4 3 1000000.6 3 1000000.4 3 1000000.6 4 1000000.3 4 1000000.2 4 1000000.4 4 1000000.2 4 1000000.4 4 1000000.2 4 1000000.4 4 1000000.2 4 1000000.4 4 1000000.2 4 1000000.4 4 1000000.2 4 1000000.4 4 1000000.2 4 1000000.4 4 1000000.2 4 1000000.4 4 1000000.2 4 1000000.4 4 1000000.2 4 1000000.4 5 1000000.5 5 1000000.4 5 1000000.6 5 1000000.4 5 1000000.6 5 1000000.4 5 1000000.6 5 1000000.4 5 1000000.6 5 1000000.4 5 1000000.6 5 1000000.4 5 1000000.6 5 1000000.4 5 1000000.6 5 1000000.4 5 1000000.6 5 1000000.4 5 1000000.6 5 1000000.4 5 1000000.6 6 1000000.3 6 1000000.2 6 1000000.4 6 1000000.2 6 1000000.4 6 1000000.2 6 1000000.4 6 1000000.2 6 1000000.4 6 1000000.2 6 1000000.4 6 1000000.2 6 1000000.4 6 1000000.2 6 1000000.4 6 1000000.2 6 1000000.4 6 1000000.2 6 1000000.4 6 1000000.2 6 1000000.4 7 1000000.5 7 1000000.4 7 1000000.6 7 1000000.4 7 1000000.6 7 1000000.4 7 1000000.6 7 1000000.4 7 1000000.6 7 1000000.4 7 1000000.6 7 1000000.4 7 1000000.6 7 1000000.4 7 1000000.6 7 1000000.4 7 1000000.6 7 1000000.4 7 1000000.6 7 1000000.4 7 1000000.6 8 1000000.3 8 1000000.2 8 1000000.4 8 1000000.2 8 1000000.4 8 1000000.2 8 1000000.4 8 1000000.2 8 1000000.4 8 1000000.2 8 1000000.4 8 1000000.2 8 1000000.4 8 1000000.2 8 1000000.4 8 1000000.2 8 1000000.4 8 1000000.2 8 1000000.4 8 1000000.2 8 1000000.4 9 1000000.5 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 statsmodels-0.12.2/statsmodels/sandbox/regression/data/SmLs05.dat000066400000000000000000001510471400612667500247630ustar00rootroot00000000000000NIST/ITL StRD Dataset Name: SmLs05 (SmLs05.dat) File Format: ASCII Certified Values (lines 41 to 47) Data (lines 61 to 1869) Procedure: Analysis of Variance Reference: Simon, Stephen D. and Lesage, James P. (1989). "Assessing the Accuracy of ANOVA Calculations in Statistical Software". Computational Statistics & Data Analysis, 8, pp. 325-332. Data: 1 Factor 9 Treatments 201 Replicates/Cell 1809 Observations 7 Constant Leading Digits Average Level of Difficulty Generated Data Model: 10 Parameters (mu,tau_1, ... , tau_9) y_{ij} = mu + tau_i + epsilon_{ij} Certified Values: Source of Sums of Mean Variation df Squares Squares F Statistic Between Treatment 8 1.60800000000000E+01 2.01000000000000E+00 2.01000000000000E+02 Within Treatment 1800 1.80000000000000E+01 1.00000000000000E-02 Certified R-Squared 4.71830985915493E-01 Certified Residual Standard Deviation 1.00000000000000E-01 Data: Treatment Response 1 1000000.4 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 2 1000000.3 2 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1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 statsmodels-0.12.2/statsmodels/sandbox/regression/data/SmLs06.dat000066400000000000000000017765251400612667500250030ustar00rootroot00000000000000NIST/ITL StRD Dataset Name: SmLs06 (SmLs06.dat) File Format: ASCII Certified Values (lines 41 to 47) Data (lines 61 to 18069) Procedure: Analysis of Variance Reference: Simon, Stephen D. and Lesage, James P. (1989). "Assessing the Accuracy of ANOVA Calculations in Statistical Software". Computational Statistics & Data Analysis, 8, pp. 325-332. Data: 1 Factor 9 Treatments 2001 Replicates/Cell 18009 Observations 7 Constant Leading Digits Average Level of Difficulty Generated Data Model: 10 Parameters (mu,tau_1, ... , tau_9) y_{ij} = mu + tau_i + epsilon_{ij} Certified Values: Source of Sums of Mean Variation df Squares Squares F Statistic Between Treatment 8 1.60080000000000E+02 2.00100000000000E+01 2.00100000000000E+03 Within Treatment 18000 1.80000000000000E+02 1.00000000000000E-02 Certified R-Squared 4.70712773465067E-01 Certified Residual Standard Deviation 1.00000000000000E-01 Data: Treatment Response 1 1000000.4 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 1000000.5 1 1000000.3 1 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1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 9 1000000.4 9 1000000.6 statsmodels-0.12.2/statsmodels/sandbox/regression/data/SmLs07.dat000066400000000000000000000163251400612667500247640ustar00rootroot00000000000000NIST/ITL StRD Dataset Name: SmLs07 (SmLs07.dat) File Format: ASCII Certified Values (lines 41 to 47) Data (lines 61 to 249) Procedure: Analysis of Variance Reference: Simon, Stephen D. and Lesage, James P. (1989). "Assessing the Accuracy of ANOVA Calculations in Statistical Software". Computational Statistics & Data Analysis, 8, pp. 325-332. Data: 1 Factor 9 Treatments 21 Replicates/Cell 189 Observations 13 Constant Leading Digits Higher Level of Difficulty Generated Data Model: 10 Parameters (mu,tau_1, ... , tau_9) y_{ij} = mu + tau_i + epsilon_{ij} Certified Values: Source of Sums of Mean Variation df Squares Squares F Statistic Between Treatment 8 1.68000000000000E+00 2.10000000000000E-01 2.10000000000000E+01 Within Treatment 180 1.80000000000000E+00 1.00000000000000E-02 Certified R-Squared 4.82758620689655E-01 Certified Residual Standard Deviation 1.00000000000000E-01 Data: Treatment Response 1 1000000000000.4 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 2 1000000000000.3 2 1000000000000.2 2 1000000000000.4 2 1000000000000.2 2 1000000000000.4 2 1000000000000.2 2 1000000000000.4 2 1000000000000.2 2 1000000000000.4 2 1000000000000.2 2 1000000000000.4 2 1000000000000.2 2 1000000000000.4 2 1000000000000.2 2 1000000000000.4 2 1000000000000.2 2 1000000000000.4 2 1000000000000.2 2 1000000000000.4 2 1000000000000.2 2 1000000000000.4 3 1000000000000.5 3 1000000000000.4 3 1000000000000.6 3 1000000000000.4 3 1000000000000.6 3 1000000000000.4 3 1000000000000.6 3 1000000000000.4 3 1000000000000.6 3 1000000000000.4 3 1000000000000.6 3 1000000000000.4 3 1000000000000.6 3 1000000000000.4 3 1000000000000.6 3 1000000000000.4 3 1000000000000.6 3 1000000000000.4 3 1000000000000.6 3 1000000000000.4 3 1000000000000.6 4 1000000000000.3 4 1000000000000.2 4 1000000000000.4 4 1000000000000.2 4 1000000000000.4 4 1000000000000.2 4 1000000000000.4 4 1000000000000.2 4 1000000000000.4 4 1000000000000.2 4 1000000000000.4 4 1000000000000.2 4 1000000000000.4 4 1000000000000.2 4 1000000000000.4 4 1000000000000.2 4 1000000000000.4 4 1000000000000.2 4 1000000000000.4 4 1000000000000.2 4 1000000000000.4 5 1000000000000.5 5 1000000000000.4 5 1000000000000.6 5 1000000000000.4 5 1000000000000.6 5 1000000000000.4 5 1000000000000.6 5 1000000000000.4 5 1000000000000.6 5 1000000000000.4 5 1000000000000.6 5 1000000000000.4 5 1000000000000.6 5 1000000000000.4 5 1000000000000.6 5 1000000000000.4 5 1000000000000.6 5 1000000000000.4 5 1000000000000.6 5 1000000000000.4 5 1000000000000.6 6 1000000000000.3 6 1000000000000.2 6 1000000000000.4 6 1000000000000.2 6 1000000000000.4 6 1000000000000.2 6 1000000000000.4 6 1000000000000.2 6 1000000000000.4 6 1000000000000.2 6 1000000000000.4 6 1000000000000.2 6 1000000000000.4 6 1000000000000.2 6 1000000000000.4 6 1000000000000.2 6 1000000000000.4 6 1000000000000.2 6 1000000000000.4 6 1000000000000.2 6 1000000000000.4 7 1000000000000.5 7 1000000000000.4 7 1000000000000.6 7 1000000000000.4 7 1000000000000.6 7 1000000000000.4 7 1000000000000.6 7 1000000000000.4 7 1000000000000.6 7 1000000000000.4 7 1000000000000.6 7 1000000000000.4 7 1000000000000.6 7 1000000000000.4 7 1000000000000.6 7 1000000000000.4 7 1000000000000.6 7 1000000000000.4 7 1000000000000.6 7 1000000000000.4 7 1000000000000.6 8 1000000000000.3 8 1000000000000.2 8 1000000000000.4 8 1000000000000.2 8 1000000000000.4 8 1000000000000.2 8 1000000000000.4 8 1000000000000.2 8 1000000000000.4 8 1000000000000.2 8 1000000000000.4 8 1000000000000.2 8 1000000000000.4 8 1000000000000.2 8 1000000000000.4 8 1000000000000.2 8 1000000000000.4 8 1000000000000.2 8 1000000000000.4 8 1000000000000.2 8 1000000000000.4 9 1000000000000.5 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 statsmodels-0.12.2/statsmodels/sandbox/regression/data/SmLs08.dat000066400000000000000000001635341400612667500247720ustar00rootroot00000000000000NIST/ITL StRD Dataset Name: SmLs08 (SmLs08.dat) File Format: ASCII Certified Values (lines 41 to 47) Data (lines 61 to 1869) Procedure: Analysis of Variance Reference: Simon, Stephen D. and Lesage, James P. (1989). "Assessing the Accuracy of ANOVA Calculations in Statistical Software". Computational Statistics & Data Analysis, 8, pp. 325-332. Data: 1 Factor 9 Treatments 201 Replicates/Cell 1809 Observations 13 Constant Leading Digits Higher Level of Difficulty Generated Data Model: 10 Parameters (mu,tau_1, ... , tau_9) y_{ij} = mu + tau_i + epsilon_{ij} Certified Values: Source of Sums of Mean Variation df Squares Squares F Statistic Between Treatment 8 1.60800000000000E+01 2.01000000000000E+00 2.01000000000000E+02 Within Treatment 1800 1.80000000000000E+01 1.00000000000000E-02 Certified R-Squared 4.71830985915493E-01 Certified Residual Standard Deviation 1.00000000000000E-01 Data: Treatment Response 1 1000000000000.4 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 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1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 9 1000000000000.4 9 1000000000000.6 statsmodels-0.12.2/statsmodels/sandbox/regression/data/SmLs09.dat000066400000000000000000021501411400612667500247630ustar00rootroot00000000000000NIST/ITL StRD Dataset Name: SmLs09 (SmLs09.dat) File Format: ASCII Certified Values (lines 41 to 47) Data (lines 61 to 18069) Procedure: Analysis of Variance Reference: Simon, Stephen D. and Lesage, James P. (1989). "Assessing the Accuracy of ANOVA Calculations in Statistical Software". Computational Statistics & Data Analysis, 8, pp. 325-332. Data: 1 Factor 9 Treatments 2001 Replicates/Cell 18009 Observations 13 Constant Leading Digits Higher Level of Difficulty Generated Data Model: 10 Parameters (mu,tau_1, ... , tau_9) y_{ij} = mu + tau_i + epsilon_{ij} Certified Values: Source of Sums of Mean Variation df Squares Squares F Statistic Between Treatment 8 1.60080000000000E+02 2.00100000000000E+01 2.00100000000000E+03 Within Treatment 18000 1.80000000000000E+02 1.00000000000000E-02 Certified R-Squared 4.70712773465067E-01 Certified Residual Standard Deviation 1.00000000000000E-01 Data: Treatment Response 1 1000000000000.4 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 1000000000000.3 1 1000000000000.5 1 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1000000000000.6 statsmodels-0.12.2/statsmodels/sandbox/regression/example_kernridge.py000066400000000000000000000023201400612667500263610ustar00rootroot00000000000000 import numpy as np import matplotlib.pyplot as plt from .kernridgeregress_class import GaussProcess, kernel_euclid m,k = 50,4 upper = 6 scale = 10 xs = np.linspace(1,upper,m)[:,np.newaxis] #xs1 = xs1a*np.ones((1,4)) + 1/(1.0+np.exp(np.random.randn(m,k))) #xs1 /= np.std(xs1[::k,:],0) # normalize scale, could use cov to normalize ##y1true = np.sum(np.sin(xs1)+np.sqrt(xs1),1)[:,np.newaxis] xs1 = np.sin(xs)#[:,np.newaxis] y1true = np.sum(xs1 + 0.01*np.sqrt(np.abs(xs1)),1)[:,np.newaxis] y1 = y1true + 0.10 * np.random.randn(m,1) stride = 3 #use only some points as trainig points e.g 2 means every 2nd xstrain = xs1[::stride,:] ystrain = y1[::stride,:] xstrain = np.r_[xs1[:m/2,:], xs1[m/2+10:,:]] ystrain = np.r_[y1[:m/2,:], y1[m/2+10:,:]] index = np.hstack((np.arange(m/2), np.arange(m/2+10,m))) gp1 = GaussProcess(xstrain, ystrain, kernel=kernel_euclid, ridgecoeff=5*1e-4) yhatr1 = gp1.predict(xs1) plt.figure() plt.plot(y1true, y1,'bo',y1true, yhatr1,'r.') plt.title('euclid kernel: true y versus noisy y and estimated y') plt.figure() plt.plot(index,ystrain.ravel(),'bo-',y1true,'go-',yhatr1,'r.-') plt.title('euclid kernel: true (green), noisy (blue) and estimated (red) '+ 'observations') statsmodels-0.12.2/statsmodels/sandbox/regression/gmm.py000066400000000000000000001712041400612667500234640ustar00rootroot00000000000000'''Generalized Method of Moments, GMM, and Two-Stage Least Squares for instrumental variables IV2SLS Issues ------ * number of parameters, nparams, and starting values for parameters Where to put them? start was initially taken from global scope (bug) * When optimal weighting matrix cannot be calculated numerically In DistQuantilesGMM, we only have one row of moment conditions, not a moment condition for each observation, calculation for cov of moments breaks down. iter=1 works (weights is identity matrix) -> need method to do one iteration with an identity matrix or an analytical weighting matrix given as parameter. -> add result statistics for this case, e.g. cov_params, I have it in the standalone function (and in calc_covparams which is a copy of it), but not tested yet. DONE `fitonce` in DistQuantilesGMM, params are the same as in direct call to fitgmm move it to GMM class (once it's clearer for which cases I need this.) * GMM does not know anything about the underlying model, e.g. y = X beta + u or panel data model. It would be good if we can reuse methods from regressions, e.g. predict, fitted values, calculating the error term, and some result statistics. What's the best way to do this, multiple inheritance, outsourcing the functions, mixins or delegation (a model creates a GMM instance just for estimation). Unclear ------- * dof in Hausman - based on rank - differs between IV2SLS method and function used with GMM or (IV2SLS) - with GMM, covariance matrix difference has negative eigenvalues in iv example, ??? * jtest/jval - I'm not sure about the normalization (multiply or divide by nobs) in jtest. need a test case. Scaling of jval is irrelevant for estimation. jval in jtest looks to large in example, but I have no idea about the size * bse for fitonce look too large (no time for checking now) formula for calc_cov_params for the case without optimal weighting matrix is wrong. I do not have an estimate for omega in that case. And I'm confusing between weights and omega, which are *not* the same in this case. Author: josef-pktd License: BSD (3-clause) ''' from statsmodels.compat.python import lrange import numpy as np from scipy import optimize, stats from statsmodels.tools.numdiff import approx_fprime from statsmodels.base.model import (Model, LikelihoodModel, LikelihoodModelResults) from statsmodels.regression.linear_model import (OLS, RegressionResults, RegressionResultsWrapper) import statsmodels.stats.sandwich_covariance as smcov from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.tools import _ensure_2d DEBUG = 0 def maxabs(x): '''just a shortcut to np.abs(x).max() ''' return np.abs(x).max() class IV2SLS(LikelihoodModel): """ Instrumental variables estimation using Two-Stage Least-Squares (2SLS) Parameters ---------- endog : ndarray Endogenous variable, 1-dimensional or 2-dimensional array nobs by 1 exog : ndarray Explanatory variables, 1-dimensional or 2-dimensional array nobs by k instrument : ndarray Instruments for explanatory variables. Must contain both exog variables that are not being instrumented and instruments Notes ----- All variables in exog are instrumented in the calculations. If variables in exog are not supposed to be instrumented, then these variables must also to be included in the instrument array. Degrees of freedom in the calculation of the standard errors uses `df_resid = (nobs - k_vars)`. (This corresponds to the `small` option in Stata's ivreg2.) """ def __init__(self, endog, exog, instrument=None): self.instrument, self.instrument_names = _ensure_2d(instrument, True) super(IV2SLS, self).__init__(endog, exog) # where is this supposed to be handled # Note: Greene p.77/78 dof correction is not necessary (because only # asy results), but most packages do it anyway self.df_resid = self.exog.shape[0] - self.exog.shape[1] #self.df_model = float(self.rank - self.k_constant) self.df_model = float(self.exog.shape[1] - self.k_constant) def initialize(self): self.wendog = self.endog self.wexog = self.exog def whiten(self, X): """Not implemented""" pass def fit(self): '''estimate model using 2SLS IV regression Returns ------- results : instance of RegressionResults regression result Notes ----- This returns a generic RegressioResults instance as defined for the linear models. Parameter estimates and covariance are correct, but other results have not been tested yet, to see whether they apply without changes. ''' #Greene 5th edt., p.78 section 5.4 #move this maybe y,x,z = self.endog, self.exog, self.instrument # TODO: this uses "textbook" calculation, improve linalg ztz = np.dot(z.T, z) ztx = np.dot(z.T, x) self.xhatparams = xhatparams = np.linalg.solve(ztz, ztx) #print 'x.T.shape, xhatparams.shape', x.shape, xhatparams.shape F = xhat = np.dot(z, xhatparams) FtF = np.dot(F.T, F) self.xhatprod = FtF #store for Housman specification test Ftx = np.dot(F.T, x) Fty = np.dot(F.T, y) params = np.linalg.solve(FtF, Fty) Ftxinv = np.linalg.inv(Ftx) self.normalized_cov_params = np.dot(Ftxinv.T, np.dot(FtF, Ftxinv)) lfit = IVRegressionResults(self, params, normalized_cov_params=self.normalized_cov_params) lfit.exog_hat_params = xhatparams lfit.exog_hat = xhat # TODO: do we want to store this, might be large self._results_ols2nd = OLS(y, xhat).fit() return RegressionResultsWrapper(lfit) # copied from GLS, because I subclass currently LikelihoodModel and not GLS def predict(self, params, exog=None): """ Return linear predicted values from a design matrix. Parameters ---------- exog : array_like Design / exogenous data params : array_like, optional after fit has been called Parameters of a linear model Returns ------- An array of fitted values Notes ----- If the model as not yet been fit, params is not optional. """ if exog is None: exog = self.exog return np.dot(exog, params) class IVRegressionResults(RegressionResults): """ Results class for for an OLS model. Most of the methods and attributes are inherited from RegressionResults. The special methods that are only available for OLS are: - get_influence - outlier_test - el_test - conf_int_el See Also -------- RegressionResults """ @cache_readonly def fvalue(self): const_idx = self.model.data.const_idx # if constant is implicit or missing, return nan see #2444, #3544 if const_idx is None: return np.nan else: k_vars = len(self.params) restriction = np.eye(k_vars) idx_noconstant = lrange(k_vars) del idx_noconstant[const_idx] fval = self.f_test(restriction[idx_noconstant]).fvalue # without constant return fval def spec_hausman(self, dof=None): '''Hausman's specification test See Also -------- spec_hausman : generic function for Hausman's specification test ''' #use normalized cov_params for OLS endog, exog = self.model.endog, self.model.exog resols = OLS(endog, exog).fit() normalized_cov_params_ols = resols.model.normalized_cov_params # Stata `ivendog` does not use df correction for se #se2 = resols.mse_resid #* resols.df_resid * 1. / len(endog) se2 = resols.ssr / len(endog) params_diff = self.params - resols.params cov_diff = np.linalg.pinv(self.model.xhatprod) - normalized_cov_params_ols #TODO: the following is very inefficient, solves problem (svd) twice #use linalg.lstsq or svd directly #cov_diff will very often be in-definite (singular) if not dof: dof = np.linalg.matrix_rank(cov_diff) cov_diffpinv = np.linalg.pinv(cov_diff) H = np.dot(params_diff, np.dot(cov_diffpinv, params_diff))/se2 pval = stats.chi2.sf(H, dof) return H, pval, dof # copied from regression results with small changes, no llf def summary(self, yname=None, xname=None, title=None, alpha=.05): """Summarize the Regression Results Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Default is `var_##` for ## in p the number of regressors title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : class to hold summary results """ #TODO: import where we need it (for now), add as cached attributes from statsmodels.stats.stattools import (jarque_bera, omni_normtest, durbin_watson) jb, jbpv, skew, kurtosis = jarque_bera(self.wresid) omni, omnipv = omni_normtest(self.wresid) #TODO: reuse condno from somewhere else ? #condno = np.linalg.cond(np.dot(self.wexog.T, self.wexog)) wexog = self.model.wexog eigvals = np.linalg.linalg.eigvalsh(np.dot(wexog.T, wexog)) eigvals = np.sort(eigvals) #in increasing order condno = np.sqrt(eigvals[-1]/eigvals[0]) # TODO: check what is valid. # box-pierce, breusch-pagan, durbin's h are not with endogenous on rhs # use Cumby Huizinga 1992 instead self.diagn = dict(jb=jb, jbpv=jbpv, skew=skew, kurtosis=kurtosis, omni=omni, omnipv=omnipv, condno=condno, mineigval=eigvals[0]) #TODO not used yet #diagn_left_header = ['Models stats'] #diagn_right_header = ['Residual stats'] #TODO: requiring list/iterable is a bit annoying #need more control over formatting #TODO: default do not work if it's not identically spelled top_left = [('Dep. Variable:', None), ('Model:', None), ('Method:', ['Two Stage']), ('', ['Least Squares']), ('Date:', None), ('Time:', None), ('No. Observations:', None), ('Df Residuals:', None), #[self.df_resid]), #TODO: spelling ('Df Model:', None), #[self.df_model]) ] top_right = [('R-squared:', ["%#8.3f" % self.rsquared]), ('Adj. R-squared:', ["%#8.3f" % self.rsquared_adj]), ('F-statistic:', ["%#8.4g" % self.fvalue] ), ('Prob (F-statistic):', ["%#6.3g" % self.f_pvalue]), #('Log-Likelihood:', None), #["%#6.4g" % self.llf]), #('AIC:', ["%#8.4g" % self.aic]), #('BIC:', ["%#8.4g" % self.bic]) ] diagn_left = [('Omnibus:', ["%#6.3f" % omni]), ('Prob(Omnibus):', ["%#6.3f" % omnipv]), ('Skew:', ["%#6.3f" % skew]), ('Kurtosis:', ["%#6.3f" % kurtosis]) ] diagn_right = [('Durbin-Watson:', ["%#8.3f" % durbin_watson(self.wresid)]), ('Jarque-Bera (JB):', ["%#8.3f" % jb]), ('Prob(JB):', ["%#8.3g" % jbpv]), ('Cond. No.', ["%#8.3g" % condno]) ] if title is None: title = self.model.__class__.__name__ + ' ' + "Regression Results" #create summary table instance from statsmodels.iolib.summary import Summary smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, yname=yname, xname=xname, title=title) smry.add_table_params(self, yname=yname, xname=xname, alpha=alpha, use_t=True) smry.add_table_2cols(self, gleft=diagn_left, gright=diagn_right, yname=yname, xname=xname, title="") return smry ############# classes for Generalized Method of Moments GMM _gmm_options = '''\ Options for GMM --------------- Type of GMM ~~~~~~~~~~~ - one-step - iterated - CUE : not tested yet weight matrix ~~~~~~~~~~~~~ - `weights_method` : str, defines method for robust Options here are similar to :mod:`statsmodels.stats.robust_covariance` default is heteroscedasticity consistent, HC0 currently available methods are - `cov` : HC0, optionally with degrees of freedom correction - `hac` : - `iid` : untested, only for Z*u case, IV cases with u as error indep of Z - `ac` : not available yet - `cluster` : not connected yet - others from robust_covariance other arguments: - `wargs` : tuple or dict, required arguments for weights_method - `centered` : bool, indicates whether moments are centered for the calculation of the weights and covariance matrix, applies to all weight_methods - `ddof` : int degrees of freedom correction, applies currently only to `cov` - maxlag : int number of lags to include in HAC calculation , applies only to `hac` - others not yet, e.g. groups for cluster robust covariance matrix ~~~~~~~~~~~~~~~~~ The same options as for weight matrix also apply to the calculation of the estimate of the covariance matrix of the parameter estimates. The additional option is - `has_optimal_weights`: If true, then the calculation of the covariance matrix assumes that we have optimal GMM with :math:`W = S^{-1}`. Default is True. TODO: do we want to have a different default after `onestep`? ''' class GMM(Model): ''' Class for estimation by Generalized Method of Moments needs to be subclassed, where the subclass defined the moment conditions `momcond` Parameters ---------- endog : ndarray endogenous variable, see notes exog : ndarray array of exogenous variables, see notes instrument : ndarray array of instruments, see notes nmoms : None or int number of moment conditions, if None then it is set equal to the number of columns of instruments. Mainly needed to determine the shape or size of start parameters and starting weighting matrix. kwds : anything this is mainly if additional variables need to be stored for the calculations of the moment conditions Attributes ---------- results : instance of GMMResults currently just a storage class for params and cov_params without it's own methods bse : property return bse Notes ----- The GMM class only uses the moment conditions and does not use any data directly. endog, exog, instrument and kwds in the creation of the class instance are only used to store them for access in the moment conditions. Which of this are required and how they are used depends on the moment conditions of the subclass. Warning: Options for various methods have not been fully implemented and are still missing in several methods. TODO: currently onestep (maxiter=0) still produces an updated estimate of bse and cov_params. ''' results_class = 'GMMResults' def __init__(self, endog, exog, instrument, k_moms=None, k_params=None, missing='none', **kwds): ''' maybe drop and use mixin instead TODO: GMM does not really care about the data, just the moment conditions ''' instrument = self._check_inputs(instrument, endog) # attaches if needed super(GMM, self).__init__(endog, exog, missing=missing, instrument=instrument) # self.endog = endog # self.exog = exog # self.instrument = instrument self.nobs = endog.shape[0] if k_moms is not None: self.nmoms = k_moms elif instrument is not None: self.nmoms = instrument.shape[1] else: self.nmoms = np.nan if k_params is not None: self.k_params = k_params elif instrument is not None: self.k_params = exog.shape[1] else: self.k_params = np.nan self.__dict__.update(kwds) self.epsilon_iter = 1e-6 def _check_inputs(self, instrument, endog): if instrument is not None: offset = np.asarray(instrument) if offset.shape[0] != endog.shape[0]: raise ValueError("instrument is not the same length as endog") return instrument def _fix_param_names(self, params, param_names=None): # TODO: this is a temporary fix, need xnames = self.data.xnames if param_names is not None: if len(params) == len(param_names): self.data.xnames = param_names else: raise ValueError('param_names has the wrong length') else: if len(params) < len(xnames): # cut in front for poisson multiplicative self.data.xnames = xnames[-len(params):] elif len(params) > len(xnames): # use generic names self.data.xnames = ['p%2d' % i for i in range(len(params))] def set_param_names(self, param_names, k_params=None): """set the parameter names in the model Parameters ---------- param_names : list[str] param_names should have the same length as the number of params k_params : None or int If k_params is None, then the k_params attribute is used, unless it is None. If k_params is not None, then it will also set the k_params attribute. """ if k_params is not None: self.k_params = k_params else: k_params = self.k_params if k_params == len(param_names): self.data.xnames = param_names else: raise ValueError('param_names has the wrong length') def fit(self, start_params=None, maxiter=10, inv_weights=None, weights_method='cov', wargs=(), has_optimal_weights=True, optim_method='bfgs', optim_args=None): ''' Estimate parameters using GMM and return GMMResults TODO: weight and covariance arguments still need to be made consistent with similar options in other models, see RegressionResult.get_robustcov_results Parameters ---------- start_params : array (optional) starting value for parameters ub minimization. If None then fitstart method is called for the starting values. maxiter : int or 'cue' Number of iterations in iterated GMM. The onestep estimate can be obtained with maxiter=0 or 1. If maxiter is large, then the iteration will stop either at maxiter or on convergence of the parameters (TODO: no options for convergence criteria yet.) If `maxiter == 'cue'`, the the continuously updated GMM is calculated which updates the weight matrix during the minimization of the GMM objective function. The CUE estimation uses the onestep parameters as starting values. inv_weights : None or ndarray inverse of the starting weighting matrix. If inv_weights are not given then the method `start_weights` is used which depends on the subclass, for IV subclasses `inv_weights = z'z` where `z` are the instruments, otherwise an identity matrix is used. weights_method : str, defines method for robust Options here are similar to :mod:`statsmodels.stats.robust_covariance` default is heteroscedasticity consistent, HC0 currently available methods are - `cov` : HC0, optionally with degrees of freedom correction - `hac` : - `iid` : untested, only for Z*u case, IV cases with u as error indep of Z - `ac` : not available yet - `cluster` : not connected yet - others from robust_covariance wargs` : tuple or dict, required and optional arguments for weights_method - `centered` : bool, indicates whether moments are centered for the calculation of the weights and covariance matrix, applies to all weight_methods - `ddof` : int degrees of freedom correction, applies currently only to `cov` - `maxlag` : int number of lags to include in HAC calculation , applies only to `hac` - others not yet, e.g. groups for cluster robust has_optimal_weights: If true, then the calculation of the covariance matrix assumes that we have optimal GMM with :math:`W = S^{-1}`. Default is True. TODO: do we want to have a different default after `onestep`? optim_method : str, default is 'bfgs' numerical optimization method. Currently not all optimizers that are available in LikelihoodModels are connected. optim_args : dict keyword arguments for the numerical optimizer. Returns ------- results : instance of GMMResults this is also attached as attribute results Notes ----- Warning: One-step estimation, `maxiter` either 0 or 1, still has problems (at least compared to Stata's gmm). By default it uses a heteroscedasticity robust covariance matrix, but uses the assumption that the weight matrix is optimal. See options for cov_params in the results instance. The same options as for weight matrix also apply to the calculation of the estimate of the covariance matrix of the parameter estimates. ''' # TODO: add check for correct wargs keys # currently a misspelled key is not detected, # because I'm still adding options # TODO: check repeated calls to fit with different options # arguments are dictionaries, i.e. mutable # unit test if anything is stale or spilled over. #bug: where does start come from ??? start = start_params # alias for renaming if start is None: start = self.fitstart() #TODO: temporary hack if inv_weights is None: inv_weights if optim_args is None: optim_args = {} if 'disp' not in optim_args: optim_args['disp'] = 1 if maxiter == 0 or maxiter == 'cue': if inv_weights is not None: weights = np.linalg.pinv(inv_weights) else: # let start_weights handle the inv=False for maxiter=0 weights = self.start_weights(inv=False) params = self.fitgmm(start, weights=weights, optim_method=optim_method, optim_args=optim_args) weights_ = weights # temporary alias used in jval else: params, weights = self.fititer(start, maxiter=maxiter, start_invweights=inv_weights, weights_method=weights_method, wargs=wargs, optim_method=optim_method, optim_args=optim_args) # TODO weights returned by fititer is inv_weights - not true anymore # weights_ currently not necessary and used anymore weights_ = np.linalg.pinv(weights) if maxiter == 'cue': #we have params from maxiter= 0 as starting value # TODO: need to give weights options to gmmobjective_cu params = self.fitgmm_cu(params, optim_method=optim_method, optim_args=optim_args) # weights is stored as attribute weights = self._weights_cu #TODO: use Bunch instead ? options_other = {'weights_method':weights_method, 'has_optimal_weights':has_optimal_weights, 'optim_method':optim_method} # check that we have the right number of xnames self._fix_param_names(params, param_names=None) results = results_class_dict[self.results_class]( model = self, params = params, weights = weights, wargs = wargs, options_other = options_other, optim_args = optim_args) self.results = results # FIXME: remove, still keeping it temporarily return results def fitgmm(self, start, weights=None, optim_method='bfgs', optim_args=None): '''estimate parameters using GMM Parameters ---------- start : array_like starting values for minimization weights : ndarray weighting matrix for moment conditions. If weights is None, then the identity matrix is used Returns ------- paramest : ndarray estimated parameters Notes ----- todo: add fixed parameter option, not here ??? uses scipy.optimize.fmin ''' ## if not fixed is None: #fixed not defined in this version ## raise NotImplementedError # TODO: should start_weights only be in `fit` if weights is None: weights = self.start_weights(inv=False) if optim_args is None: optim_args = {} if optim_method == 'nm': optimizer = optimize.fmin elif optim_method == 'bfgs': optimizer = optimize.fmin_bfgs # TODO: add score optim_args['fprime'] = self.score #lambda params: self.score(params, weights) elif optim_method == 'ncg': optimizer = optimize.fmin_ncg optim_args['fprime'] = self.score elif optim_method == 'cg': optimizer = optimize.fmin_cg optim_args['fprime'] = self.score elif optim_method == 'fmin_l_bfgs_b': optimizer = optimize.fmin_l_bfgs_b optim_args['fprime'] = self.score elif optim_method == 'powell': optimizer = optimize.fmin_powell elif optim_method == 'slsqp': optimizer = optimize.fmin_slsqp else: raise ValueError('optimizer method not available') if DEBUG: print(np.linalg.det(weights)) #TODO: add other optimization options and results return optimizer(self.gmmobjective, start, args=(weights,), **optim_args) def fitgmm_cu(self, start, optim_method='bfgs', optim_args=None): '''estimate parameters using continuously updating GMM Parameters ---------- start : array_like starting values for minimization Returns ------- paramest : ndarray estimated parameters Notes ----- todo: add fixed parameter option, not here ??? uses scipy.optimize.fmin ''' ## if not fixed is None: #fixed not defined in this version ## raise NotImplementedError if optim_args is None: optim_args = {} if optim_method == 'nm': optimizer = optimize.fmin elif optim_method == 'bfgs': optimizer = optimize.fmin_bfgs optim_args['fprime'] = self.score_cu elif optim_method == 'ncg': optimizer = optimize.fmin_ncg else: raise ValueError('optimizer method not available') #TODO: add other optimization options and results return optimizer(self.gmmobjective_cu, start, args=(), **optim_args) def start_weights(self, inv=True): """Create identity matrix for starting weights""" return np.eye(self.nmoms) def gmmobjective(self, params, weights): ''' objective function for GMM minimization Parameters ---------- params : ndarray parameter values at which objective is evaluated weights : ndarray weighting matrix Returns ------- jval : float value of objective function ''' moms = self.momcond_mean(params) return np.dot(np.dot(moms, weights), moms) #moms = self.momcond(params) #return np.dot(np.dot(moms.mean(0),weights), moms.mean(0)) def gmmobjective_cu(self, params, weights_method='cov', wargs=()): ''' objective function for continuously updating GMM minimization Parameters ---------- params : ndarray parameter values at which objective is evaluated Returns ------- jval : float value of objective function ''' moms = self.momcond(params) inv_weights = self.calc_weightmatrix(moms, weights_method=weights_method, wargs=wargs) weights = np.linalg.pinv(inv_weights) self._weights_cu = weights # store if we need it later return np.dot(np.dot(moms.mean(0), weights), moms.mean(0)) def fititer(self, start, maxiter=2, start_invweights=None, weights_method='cov', wargs=(), optim_method='bfgs', optim_args=None): '''iterative estimation with updating of optimal weighting matrix stopping criteria are maxiter or change in parameter estimate less than self.epsilon_iter, with default 1e-6. Parameters ---------- start : ndarray starting value for parameters maxiter : int maximum number of iterations start_weights : array (nmoms, nmoms) initial weighting matrix; if None, then the identity matrix is used weights_method : {'cov', ...} method to use to estimate the optimal weighting matrix, see calc_weightmatrix for details Returns ------- params : ndarray estimated parameters weights : ndarray optimal weighting matrix calculated with final parameter estimates Notes ----- ''' self.history = [] momcond = self.momcond if start_invweights is None: w = self.start_weights(inv=True) else: w = start_invweights #call fitgmm function #args = (self.endog, self.exog, self.instrument) #args is not used in the method version winv_new = w for it in range(maxiter): winv = winv_new w = np.linalg.pinv(winv) #this is still calling function not method ## resgmm = fitgmm(momcond, (), start, weights=winv, fixed=None, ## weightsoptimal=False) resgmm = self.fitgmm(start, weights=w, optim_method=optim_method, optim_args=optim_args) moms = momcond(resgmm) # the following is S = cov_moments winv_new = self.calc_weightmatrix(moms, weights_method=weights_method, wargs=wargs, params=resgmm) if it > 2 and maxabs(resgmm - start) < self.epsilon_iter: #check rule for early stopping # TODO: set has_optimal_weights = True break start = resgmm return resgmm, w def calc_weightmatrix(self, moms, weights_method='cov', wargs=(), params=None): ''' calculate omega or the weighting matrix Parameters ---------- moms : ndarray moment conditions (nobs x nmoms) for all observations evaluated at a parameter value weights_method : str 'cov' If method='cov' is cov then the matrix is calculated as simple covariance of the moment conditions. see fit method for available aoptions for the weight and covariance matrix wargs : tuple or dict parameters that are required by some kernel methods to estimate the long-run covariance. Not used yet. Returns ------- w : array (nmoms, nmoms) estimate for the weighting matrix or covariance of the moment condition Notes ----- currently a constant cutoff window is used TODO: implement long-run cov estimators, kernel-based Newey-West Andrews Andrews-Moy???? References ---------- Greene Hansen, Bruce ''' nobs, k_moms = moms.shape # TODO: wargs are tuple or dict ? if DEBUG: print(' momcov wargs', wargs) centered = not ('centered' in wargs and not wargs['centered']) if not centered: # caller does not want centered moment conditions moms_ = moms else: moms_ = moms - moms.mean() # TODO: store this outside to avoid doing this inside optimization loop # TODO: subclasses need to be able to add weights_methods, and remove # IVGMM can have homoscedastic (OLS), # some options will not make sense in some cases # possible add all here and allow subclasses to define a list # TODO: should other weights_methods also have `ddof` if weights_method == 'cov': w = np.dot(moms_.T, moms_) if 'ddof' in wargs: # caller requests degrees of freedom correction if wargs['ddof'] == 'k_params': w /= (nobs - self.k_params) else: if DEBUG: print(' momcov ddof', wargs['ddof']) w /= (nobs - wargs['ddof']) else: # default: divide by nobs w /= nobs elif weights_method == 'flatkernel': #uniform cut-off window # This was a trial version, can use HAC with flatkernel if 'maxlag' not in wargs: raise ValueError('flatkernel requires maxlag') maxlag = wargs['maxlag'] h = np.ones(maxlag + 1) w = np.dot(moms_.T, moms_)/nobs for i in range(1,maxlag+1): w += (h[i] * np.dot(moms_[i:].T, moms_[:-i]) / (nobs-i)) elif weights_method == 'hac': maxlag = wargs['maxlag'] if 'kernel' in wargs: weights_func = wargs['kernel'] else: weights_func = smcov.weights_bartlett wargs['kernel'] = weights_func w = smcov.S_hac_simple(moms_, nlags=maxlag, weights_func=weights_func) w /= nobs #(nobs - self.k_params) elif weights_method == 'iid': # only when we have instruments and residual mom = Z * u # TODO: problem we do not have params in argument # I cannot keep everything in here w/o params as argument u = self.get_error(params) if centered: # Note: I'm not centering instruments, # should not we always center u? Ok, with centered as default u -= u.mean(0) #demean inplace, we do not need original u instrument = self.instrument w = np.dot(instrument.T, instrument).dot(np.dot(u.T, u)) / nobs if 'ddof' in wargs: # caller requests degrees of freedom correction if wargs['ddof'] == 'k_params': w /= (nobs - self.k_params) else: # assume ddof is a number if DEBUG: print(' momcov ddof', wargs['ddof']) w /= (nobs - wargs['ddof']) else: # default: divide by nobs w /= nobs else: raise ValueError('weight method not available') return w def momcond_mean(self, params): ''' mean of moment conditions, ''' momcond = self.momcond(params) self.nobs_moms, self.k_moms = momcond.shape return momcond.mean(0) def gradient_momcond(self, params, epsilon=1e-4, centered=True): '''gradient of moment conditions Parameters ---------- params : ndarray parameter at which the moment conditions are evaluated epsilon : float stepsize for finite difference calculation centered : bool This refers to the finite difference calculation. If `centered` is true, then the centered finite difference calculation is used. Otherwise the one-sided forward differences are used. TODO: looks like not used yet missing argument `weights` ''' momcond = self.momcond_mean # TODO: approx_fprime has centered keyword if centered: gradmoms = (approx_fprime(params, momcond, epsilon=epsilon) + approx_fprime(params, momcond, epsilon=-epsilon))/2 else: gradmoms = approx_fprime(params, momcond, epsilon=epsilon) return gradmoms def score(self, params, weights, epsilon=None, centered=True): """Score""" deriv = approx_fprime(params, self.gmmobjective, args=(weights,), centered=centered, epsilon=epsilon) return deriv def score_cu(self, params, epsilon=None, centered=True): """Score cu""" deriv = approx_fprime(params, self.gmmobjective_cu, args=(), centered=centered, epsilon=epsilon) return deriv # TODO: wrong superclass, I want tvalues, ... right now class GMMResults(LikelihoodModelResults): '''just a storage class right now''' use_t = False def __init__(self, *args, **kwds): self.__dict__.update(kwds) self.nobs = self.model.nobs self.df_resid = np.inf self.cov_params_default = self._cov_params() @cache_readonly def q(self): """Objective function at params""" return self.model.gmmobjective(self.params, self.weights) @cache_readonly def jval(self): """nobs_moms attached by momcond_mean""" return self.q * self.model.nobs_moms def _cov_params(self, **kwds): #TODO add options ???) # this should use by default whatever options have been specified in # fit # TODO: do not do this when we want to change options # if hasattr(self, '_cov_params'): # #replace with decorator later # return self._cov_params # set defaults based on fit arguments if 'wargs' not in kwds: # Note: we do not check the keys in wargs, use either all or nothing kwds['wargs'] = self.wargs if 'weights_method' not in kwds: kwds['weights_method'] = self.options_other['weights_method'] if 'has_optimal_weights' not in kwds: kwds['has_optimal_weights'] = self.options_other['has_optimal_weights'] gradmoms = self.model.gradient_momcond(self.params) moms = self.model.momcond(self.params) covparams = self.calc_cov_params(moms, gradmoms, **kwds) return covparams def calc_cov_params(self, moms, gradmoms, weights=None, use_weights=False, has_optimal_weights=True, weights_method='cov', wargs=()): '''calculate covariance of parameter estimates not all options tried out yet If weights matrix is given, then the formula use to calculate cov_params depends on whether has_optimal_weights is true. If no weights are given, then the weight matrix is calculated with the given method, and has_optimal_weights is assumed to be true. (API Note: The latter assumption could be changed if we allow for has_optimal_weights=None.) ''' nobs = moms.shape[0] if weights is None: #omegahat = self.model.calc_weightmatrix(moms, method=method, wargs=wargs) #has_optimal_weights = True #add other options, Barzen, ... longrun var estimators # TODO: this might still be inv_weights after fititer weights = self.weights else: pass #omegahat = weights #2 different names used, #TODO: this is wrong, I need an estimate for omega if use_weights: omegahat = weights else: omegahat = self.model.calc_weightmatrix( moms, weights_method=weights_method, wargs=wargs, params=self.params) if has_optimal_weights: #has_optimal_weights: # TOD0 make has_optimal_weights depend on convergence or iter >2 cov = np.linalg.inv(np.dot(gradmoms.T, np.dot(np.linalg.inv(omegahat), gradmoms))) else: gw = np.dot(gradmoms.T, weights) gwginv = np.linalg.inv(np.dot(gw, gradmoms)) cov = np.dot(np.dot(gwginv, np.dot(np.dot(gw, omegahat), gw.T)), gwginv) #cov /= nobs return cov/nobs @property def bse_(self): '''standard error of the parameter estimates ''' return self.get_bse() def get_bse(self, **kwds): '''standard error of the parameter estimates with options Parameters ---------- kwds : optional keywords options for calculating cov_params Returns ------- bse : ndarray estimated standard error of parameter estimates ''' return np.sqrt(np.diag(self.cov_params(**kwds))) def jtest(self): '''overidentification test I guess this is missing a division by nobs, what's the normalization in jval ? ''' jstat = self.jval nparams = self.params.size #self.nparams df = self.model.nmoms - nparams return jstat, stats.chi2.sf(jstat, df), df def compare_j(self, other): '''overidentification test for comparing two nested gmm estimates This assumes that some moment restrictions have been dropped in one of the GMM estimates relative to the other. Not tested yet We are comparing two separately estimated models, that use different weighting matrices. It is not guaranteed that the resulting difference is positive. TODO: Check in which cases Stata programs use the same weigths ''' jstat1 = self.jval k_moms1 = self.model.nmoms jstat2 = other.jval k_moms2 = other.model.nmoms jdiff = jstat1 - jstat2 df = k_moms1 - k_moms2 if df < 0: # possible nested in other way, TODO allow this or not # flip sign instead of absolute df = - df jdiff = - jdiff return jdiff, stats.chi2.sf(jdiff, df), df def summary(self, yname=None, xname=None, title=None, alpha=.05): """Summarize the Regression Results Parameters ---------- yname : str, optional Default is `y` xname : list[str], optional Default is `var_##` for ## in p the number of regressors title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float significance level for the confidence intervals Returns ------- smry : Summary instance this holds the summary tables and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary : class to hold summary results """ #TODO: add a summary text for options that have been used jvalue, jpvalue, jdf = self.jtest() top_left = [('Dep. Variable:', None), ('Model:', None), ('Method:', ['GMM']), ('Date:', None), ('Time:', None), ('No. Observations:', None), #('Df Residuals:', None), #[self.df_resid]), #TODO: spelling #('Df Model:', None), #[self.df_model]) ] top_right = [#('R-squared:', ["%#8.3f" % self.rsquared]), #('Adj. R-squared:', ["%#8.3f" % self.rsquared_adj]), ('Hansen J:', ["%#8.4g" % jvalue] ), ('Prob (Hansen J):', ["%#6.3g" % jpvalue]), #('F-statistic:', ["%#8.4g" % self.fvalue] ), #('Prob (F-statistic):', ["%#6.3g" % self.f_pvalue]), #('Log-Likelihood:', None), #["%#6.4g" % self.llf]), #('AIC:', ["%#8.4g" % self.aic]), #('BIC:', ["%#8.4g" % self.bic]) ] if title is None: title = self.model.__class__.__name__ + ' ' + "Results" # create summary table instance from statsmodels.iolib.summary import Summary smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, yname=yname, xname=xname, title=title) smry.add_table_params(self, yname=yname, xname=xname, alpha=alpha, use_t=self.use_t) return smry class IVGMM(GMM): ''' Basic class for instrumental variables estimation using GMM A linear function for the conditional mean is defined as default but the methods should be overwritten by subclasses, currently `LinearIVGMM` and `NonlinearIVGMM` are implemented as subclasses. See Also -------- LinearIVGMM NonlinearIVGMM ''' results_class = 'IVGMMResults' def fitstart(self): """Create array of zeros""" return np.zeros(self.exog.shape[1]) def start_weights(self, inv=True): """Starting weights""" zz = np.dot(self.instrument.T, self.instrument) nobs = self.instrument.shape[0] if inv: return zz / nobs else: return np.linalg.pinv(zz / nobs) def get_error(self, params): """Get error at params""" return self.endog - self.predict(params) def predict(self, params, exog=None): """Get prediction at params""" if exog is None: exog = self.exog return np.dot(exog, params) def momcond(self, params): """Error times instrument""" instrument = self.instrument return instrument * self.get_error(params)[:, None] class LinearIVGMM(IVGMM): """class for linear instrumental variables models estimated with GMM Uses closed form expression instead of nonlinear optimizers for each step of the iterative GMM. The model is assumed to have the following moment condition E( z * (y - x beta)) = 0 Where `y` is the dependent endogenous variable, `x` are the explanatory variables and `z` are the instruments. Variables in `x` that are exogenous need also be included in `z`. Notation Warning: our name `exog` stands for the explanatory variables, and includes both exogenous and explanatory variables that are endogenous, i.e. included endogenous variables Parameters ---------- endog : array_like dependent endogenous variable exog : array_like explanatory, right hand side variables, including explanatory variables that are endogenous instrument : array_like Instrumental variables, variables that are exogenous to the error in the linear model containing both included and excluded exogenous variables """ def fitgmm(self, start, weights=None, optim_method=None, **kwds): '''estimate parameters using GMM for linear model Uses closed form expression instead of nonlinear optimizers Parameters ---------- start : not used starting values for minimization, not used, only for consistency of method signature weights : ndarray weighting matrix for moment conditions. If weights is None, then the identity matrix is used optim_method : not used, optimization method, not used, only for consistency of method signature **kwds : keyword arguments not used, will be silently ignored (for compatibility with generic) Returns ------- paramest : ndarray estimated parameters ''' ## if not fixed is None: #fixed not defined in this version ## raise NotImplementedError # TODO: should start_weights only be in `fit` if weights is None: weights = self.start_weights(inv=False) y, x, z = self.endog, self.exog, self.instrument zTx = np.dot(z.T, x) zTy = np.dot(z.T, y) # normal equation, solved with pinv part0 = zTx.T.dot(weights) part1 = part0.dot(zTx) part2 = part0.dot(zTy) params = np.linalg.pinv(part1).dot(part2) return params def predict(self, params, exog=None): if exog is None: exog = self.exog return np.dot(exog, params) def gradient_momcond(self, params, **kwds): # **kwds for compatibility not used x, z = self.exog, self.instrument gradmoms = -np.dot(z.T, x) / self.nobs return gradmoms def score(self, params, weights, **kwds): # **kwds for compatibility, not used # Note: I coud use general formula with gradient_momcond instead x, z = self.exog, self.instrument nobs = z.shape[0] u = self.get_errors(params) score = -2 * np.dot(x.T, z).dot(weights.dot(np.dot(z.T, u))) score /= nobs * nobs return score class NonlinearIVGMM(IVGMM): """ Class for non-linear instrumental variables estimation wusing GMM The model is assumed to have the following moment condition E[ z * (y - f(X, beta)] = 0 Where `y` is the dependent endogenous variable, `x` are the explanatory variables and `z` are the instruments. Variables in `x` that are exogenous need also be included in z. `f` is a nonlinear function. Notation Warning: our name `exog` stands for the explanatory variables, and includes both exogenous and explanatory variables that are endogenous, i.e. included endogenous variables Parameters ---------- endog : array_like dependent endogenous variable exog : array_like explanatory, right hand side variables, including explanatory variables that are endogenous. instruments : array_like Instrumental variables, variables that are exogenous to the error in the linear model containing both included and excluded exogenous variables func : callable function for the mean or conditional expectation of the endogenous variable. The function will be called with parameters and the array of explanatory, right hand side variables, `func(params, exog)` Notes ----- This class uses numerical differences to obtain the derivative of the objective function. If the jacobian of the conditional mean function, `func` is available, then it can be used by subclassing this class and defining a method `jac_func`. TODO: check required signature of jac_error and jac_func """ # This should be reversed: # NonlinearIVGMM is IVGMM and need LinearIVGMM as special case (fit, predict) def fitstart(self): #might not make sense for more general functions return np.zeros(self.exog.shape[1]) def __init__(self, endog, exog, instrument, func, **kwds): self.func = func super(NonlinearIVGMM, self).__init__(endog, exog, instrument, **kwds) def predict(self, params, exog=None): if exog is None: exog = self.exog return self.func(params, exog) #---------- the following a semi-general versions, # TODO: move to higher class after testing def jac_func(self, params, weights, args=None, centered=True, epsilon=None): # TODO: Why are ther weights in the signature - copy-paste error? deriv = approx_fprime(params, self.func, args=(self.exog,), centered=centered, epsilon=epsilon) return deriv def jac_error(self, params, weights, args=None, centered=True, epsilon=None): jac_func = self.jac_func(params, weights, args=None, centered=True, epsilon=None) return -jac_func def score(self, params, weights, **kwds): # **kwds for compatibility not used # Note: I coud use general formula with gradient_momcond instead z = self.instrument nobs = z.shape[0] jac_u = self.jac_error(params, weights, args=None, epsilon=None, centered=True) x = -jac_u # alias, plays the same role as X in linear model u = self.get_error(params) score = -2 * np.dot(np.dot(x.T, z), weights).dot(np.dot(z.T, u)) score /= nobs * nobs return score class IVGMMResults(GMMResults): """Results class of IVGMM""" # this assumes that we have an additive error model `(y - f(x, params))` @cache_readonly def fittedvalues(self): """Fitted values""" return self.model.predict(self.params) @cache_readonly def resid(self): """Residuals""" return self.model.endog - self.fittedvalues @cache_readonly def ssr(self): """Sum of square errors""" return (self.resid * self.resid).sum(0) def spec_hausman(params_e, params_i, cov_params_e, cov_params_i, dof=None): '''Hausmans specification test Parameters ---------- params_e : ndarray efficient and consistent under Null hypothesis, inconsistent under alternative hypothesis params_i : ndarray consistent under Null hypothesis, consistent under alternative hypothesis cov_params_e : ndarray, 2d covariance matrix of parameter estimates for params_e cov_params_i : ndarray, 2d covariance matrix of parameter estimates for params_i example instrumental variables OLS estimator is `e`, IV estimator is `i` Notes ----- Todos,Issues - check dof calculations and verify for linear case - check one-sided hypothesis References ---------- Greene section 5.5 p.82/83 ''' params_diff = (params_i - params_e) cov_diff = cov_params_i - cov_params_e #TODO: the following is very inefficient, solves problem (svd) twice #use linalg.lstsq or svd directly #cov_diff will very often be in-definite (singular) if not dof: dof = np.linalg.matrix_rank(cov_diff) cov_diffpinv = np.linalg.pinv(cov_diff) H = np.dot(params_diff, np.dot(cov_diffpinv, params_diff)) pval = stats.chi2.sf(H, dof) evals = np.linalg.eigvalsh(cov_diff) return H, pval, dof, evals ########### class DistQuantilesGMM(GMM): ''' Estimate distribution parameters by GMM based on matching quantiles Currently mainly to try out different requirements for GMM when we cannot calculate the optimal weighting matrix. ''' def __init__(self, endog, exog, instrument, **kwds): #TODO: something wrong with super super(DistQuantilesGMM, self).__init__(endog, exog, instrument) #self.func = func self.epsilon_iter = 1e-5 self.distfn = kwds['distfn'] #done by super does not work yet #TypeError: super does not take keyword arguments self.endog = endog #make this optional for fit if 'pquant' not in kwds: self.pquant = pquant = np.array([0.01, 0.05,0.1,0.4,0.6,0.9,0.95,0.99]) else: self.pquant = pquant = kwds['pquant'] #TODO: vectorize this: use edf self.xquant = np.array([stats.scoreatpercentile(endog, p) for p in pquant*100]) self.nmoms = len(self.pquant) #TODOcopied from GMM, make super work self.endog = endog self.exog = exog self.instrument = instrument self.results = GMMResults(model=self) #self.__dict__.update(kwds) self.epsilon_iter = 1e-6 def fitstart(self): #todo: replace with or add call to distfn._fitstart # added but not used during testing, avoid Travis distfn = self.distfn if hasattr(distfn, '_fitstart'): start = distfn._fitstart(self.endog) else: start = [1]*distfn.numargs + [0.,1.] return np.asarray(start) def momcond(self, params): #drop distfn as argument #, mom2, quantile=None, shape=None '''moment conditions for estimating distribution parameters by matching quantiles, defines as many moment conditions as quantiles. Returns ------- difference : ndarray difference between theoretical and empirical quantiles Notes ----- This can be used for method of moments or for generalized method of moments. ''' #this check looks redundant/unused know if len(params) == 2: loc, scale = params elif len(params) == 3: shape, loc, scale = params else: #raise NotImplementedError pass #see whether this might work, seems to work for beta with 2 shape args #mom2diff = np.array(distfn.stats(*params)) - mom2 #if not quantile is None: pq, xq = self.pquant, self.xquant #ppfdiff = distfn.ppf(pq, alpha) cdfdiff = self.distfn.cdf(xq, *params) - pq #return np.concatenate([mom2diff, cdfdiff[:1]]) return np.atleast_2d(cdfdiff) def fitonce(self, start=None, weights=None, has_optimal_weights=False): '''fit without estimating an optimal weighting matrix and return results This is a convenience function that calls fitgmm and covparams with a given weight matrix or the identity weight matrix. This is useful if the optimal weight matrix is know (or is analytically given) or if an optimal weight matrix cannot be calculated. (Developer Notes: this function could go into GMM, but is needed in this class, at least at the moment.) Parameters ---------- Returns ------- results : GMMResult instance result instance with params and _cov_params attached See Also -------- fitgmm cov_params ''' if weights is None: weights = np.eye(self.nmoms) params = self.fitgmm(start=start) # TODO: rewrite this old hack, should use fitgmm or fit maxiter=0 self.results.params = params #required before call to self.cov_params self.results.wargs = {} #required before call to self.cov_params self.results.options_other = {'weights_method':'cov'} # TODO: which weights_method? There should not be any needed ? _cov_params = self.results.cov_params(weights=weights, has_optimal_weights=has_optimal_weights) self.results.weights = weights self.results.jval = self.gmmobjective(params, weights) self.results.options_other.update({'has_optimal_weights':has_optimal_weights}) return self.results results_class_dict = {'GMMResults': GMMResults, 'IVGMMResults': IVGMMResults, 'DistQuantilesGMM': GMMResults} #TODO: should be a default statsmodels-0.12.2/statsmodels/sandbox/regression/kernridgeregress_class.py000066400000000000000000000170571400612667500274430ustar00rootroot00000000000000'''Kernel Ridge Regression for local non-parametric regression''' import numpy as np from scipy import spatial as ssp import matplotlib.pylab as plt def kernel_rbf(x,y,scale=1, **kwds): #scale = kwds.get('scale',1) dist = ssp.minkowski_distance_p(x[:,np.newaxis,:],y[np.newaxis,:,:],2) return np.exp(-0.5/scale*(dist)) def kernel_euclid(x,y,p=2, **kwds): return ssp.minkowski_distance(x[:,np.newaxis,:],y[np.newaxis,:,:],p) class GaussProcess(object): '''class to perform kernel ridge regression (gaussian process) Warning: this class is memory intensive, it creates nobs x nobs distance matrix and its inverse, where nobs is the number of rows (observations). See sparse version for larger number of observations Notes ----- Todo: * normalize multidimensional x array on demand, either by var or cov * add confidence band * automatic selection or proposal of smoothing parameters Note: this is different from kernel smoothing regression, see for example https://en.wikipedia.org/wiki/Kernel_smoother In this version of the kernel ridge regression, the training points are fitted exactly. Needs a fast version for leave-one-out regression, for fitting each observation on all the other points. This version could be numerically improved for the calculation for many different values of the ridge coefficient. see also short summary by Isabelle Guyon (ETHZ) in a manuscript KernelRidge.pdf Needs verification and possibly additional statistical results or summary statistics for interpretation, but this is a problem with non-parametric, non-linear methods. Reference --------- Rasmussen, C.E. and C.K.I. Williams, 2006, Gaussian Processes for Machine Learning, the MIT Press, www.GaussianProcess.org/gpal, chapter 2 a short summary of the kernel ridge regression is at http://www.ics.uci.edu/~welling/teaching/KernelsICS273B/Kernel-Ridge.pdf ''' def __init__(self, x, y=None, kernel=kernel_rbf, scale=0.5, ridgecoeff = 1e-10, **kwds ): ''' Parameters ---------- x : 2d array (N,K) data array of explanatory variables, columns represent variables rows represent observations y : 2d array (N,1) (optional) endogenous variable that should be fitted or predicted can alternatively be specified as parameter to fit method kernel : function, default: kernel_rbf kernel: (x1,x2)->kernel matrix is a function that takes as parameter two column arrays and return the kernel or distance matrix scale : float (optional) smoothing parameter for the rbf kernel ridgecoeff : float (optional) coefficient that is multiplied with the identity matrix in the ridge regression Notes ----- After initialization, kernel matrix is calculated and if y is given as parameter then also the linear regression parameter and the fitted or estimated y values, yest, are calculated. yest is available as an attribute in this case. Both scale and the ridge coefficient smooth the fitted curve. ''' self.x = x self.kernel = kernel self.scale = scale self.ridgecoeff = ridgecoeff self.distxsample = kernel(x,x,scale=scale) self.Kinv = np.linalg.inv(self.distxsample + np.eye(*self.distxsample.shape)*ridgecoeff) if y is not None: self.y = y self.yest = self.fit(y) def fit(self,y): '''fit the training explanatory variables to a sample ouput variable''' self.parest = np.dot(self.Kinv, y) #self.kernel(y,y,scale=self.scale)) yhat = np.dot(self.distxsample,self.parest) return yhat ## print ds33.shape ## ds33_2 = kernel(x,x[::k,:],scale=scale) ## dsinv = np.linalg.inv(ds33+np.eye(*distxsample.shape)*ridgecoeff) ## B = np.dot(dsinv,y[::k,:]) def predict(self,x): '''predict new y values for a given array of explanatory variables''' self.xpredict = x distxpredict = self.kernel(x, self.x, scale=self.scale) self.ypredict = np.dot(distxpredict, self.parest) return self.ypredict def plot(self, y, plt=plt ): '''some basic plots''' #todo return proper graph handles plt.figure() plt.plot(self.x,self.y, 'bo-', self.x, self.yest, 'r.-') plt.title('sample (training) points') plt.figure() plt.plot(self.xpredict,y,'bo-',self.xpredict,self.ypredict,'r.-') plt.title('all points') def example1(): m,k = 500,4 upper = 6 scale=10 xs1a = np.linspace(1,upper,m)[:,np.newaxis] xs1 = xs1a*np.ones((1,4)) + 1/(1.0+np.exp(np.random.randn(m,k))) xs1 /= np.std(xs1[::k,:],0) # normalize scale, could use cov to normalize y1true = np.sum(np.sin(xs1)+np.sqrt(xs1),1)[:,np.newaxis] y1 = y1true + 0.250 * np.random.randn(m,1) stride = 2 #use only some points as trainig points e.g 2 means every 2nd gp1 = GaussProcess(xs1[::stride,:],y1[::stride,:], kernel=kernel_euclid, ridgecoeff=1e-10) yhatr1 = gp1.predict(xs1) plt.figure() plt.plot(y1true, y1,'bo',y1true, yhatr1,'r.') plt.title('euclid kernel: true y versus noisy y and estimated y') plt.figure() plt.plot(y1,'bo-',y1true,'go-',yhatr1,'r.-') plt.title('euclid kernel: true (green), noisy (blue) and estimated (red) '+ 'observations') gp2 = GaussProcess(xs1[::stride,:],y1[::stride,:], kernel=kernel_rbf, scale=scale, ridgecoeff=1e-1) yhatr2 = gp2.predict(xs1) plt.figure() plt.plot(y1true, y1,'bo',y1true, yhatr2,'r.') plt.title('rbf kernel: true versus noisy (blue) and estimated (red) observations') plt.figure() plt.plot(y1,'bo-',y1true,'go-',yhatr2,'r.-') plt.title('rbf kernel: true (green), noisy (blue) and estimated (red) '+ 'observations') #gp2.plot(y1) def example2(m=100, scale=0.01, stride=2): #m,k = 100,1 upper = 6 xs1 = np.linspace(1,upper,m)[:,np.newaxis] y1true = np.sum(np.sin(xs1**2),1)[:,np.newaxis]/xs1 y1 = y1true + 0.05*np.random.randn(m,1) ridgecoeff = 1e-10 #stride = 2 #use only some points as trainig points e.g 2 means every 2nd gp1 = GaussProcess(xs1[::stride,:],y1[::stride,:], kernel=kernel_euclid, ridgecoeff=1e-10) yhatr1 = gp1.predict(xs1) plt.figure() plt.plot(y1true, y1,'bo',y1true, yhatr1,'r.') plt.title('euclid kernel: true versus noisy (blue) and estimated (red) observations') plt.figure() plt.plot(y1,'bo-',y1true,'go-',yhatr1,'r.-') plt.title('euclid kernel: true (green), noisy (blue) and estimated (red) '+ 'observations') gp2 = GaussProcess(xs1[::stride,:],y1[::stride,:], kernel=kernel_rbf, scale=scale, ridgecoeff=1e-2) yhatr2 = gp2.predict(xs1) plt.figure() plt.plot(y1true, y1,'bo',y1true, yhatr2,'r.') plt.title('rbf kernel: true versus noisy (blue) and estimated (red) observations') plt.figure() plt.plot(y1,'bo-',y1true,'go-',yhatr2,'r.-') plt.title('rbf kernel: true (green), noisy (blue) and estimated (red) '+ 'observations') #gp2.plot(y1) if __name__ == '__main__': example2() #example2(m=1000, scale=0.01) #example2(m=100, scale=0.5) # oversmoothing #example2(m=2000, scale=0.005) # this looks good for rbf, zoom in #example2(m=200, scale=0.01,stride=4) example1() #plt.show() statsmodels-0.12.2/statsmodels/sandbox/regression/notes_runmnl.txt000066400000000000000000000026211400612667500256120ustar00rootroot00000000000000 access to data and parameters by branch and leaves -------------------------------------------------- * this could be used in a similar way in other system estimators * dictionary access to data per equation, branch, leaf * alternative dictionary of individual variables used in equations * memory: temporary copies while using linalg, or permanent copies * outsource acces into call-back function or method * with a parser the dictionaries could be created from a formula * similar applies for accessing parameters from the params array in optimization (MLE, GMM) when there are identical parameters across equations or leaves * in latest version use dictionary mapping coefficient/parameter names to index into params global/outer-scope variables ---------------------------- * for nested logit I need to access params and store, change probabilites from the branch * need variables in a scope outside of the recursion * nested function or save params and probs in instance attribute constraint estimation as alternative and extension -------------------------------------------------- * cross-equation and within equation restrictions on parameters could also be directly imposed, instead of relying on the dictionary * no idea yet on how to encode this * might be easier to use constraint optimizer and keep constraints (partially) separate from the parameterization in the likelihood calculations statsmodels-0.12.2/statsmodels/sandbox/regression/ols_anova_original.py000066400000000000000000000250271400612667500265520ustar00rootroot00000000000000''' convenience functions for ANOVA type analysis with OLS Note: statistical results of ANOVA are not checked, OLS is checked but not whether the reported results are the ones used in ANOVA ''' import numpy as np import numpy.lib.recfunctions from statsmodels.compat.python import lmap import statsmodels.api as sm dt_b = np.dtype([('breed', int), ('sex', int), ('litter', int), ('pen', int), ('pig', int), ('age', float), ('bage', float), ('y', float)]) ''' too much work using structured masked arrays dta = np.mafromtxt('dftest3.data', dtype=dt_b) dta_use = np.ma.column_stack[[dta[col] for col in 'y sex age'.split()]] ''' dta = np.genfromtxt('dftest3.data') print(dta.shape) mask = np.isnan(dta) print("rows with missing values", mask.any(1).sum()) vars = dict((v[0], (idx, v[1])) for idx, v in enumerate((('breed', int), ('sex', int), ('litter', int), ('pen', int), ('pig', int), ('age', float), ('bage', float), ('y', float)))) datavarnames = 'y sex age'.split() #possible to avoid temporary array ? dta_use = dta[:, [vars[col][0] for col in datavarnames]] keeprows = ~np.isnan(dta_use).any(1) print('number of complete observations', keeprows.sum()) dta_used = dta_use[keeprows,:] varsused = dict((k, [dta_used[:,idx], idx, vars[k][1]]) for idx, k in enumerate(datavarnames)) # use function for dummy #sexgroups = np.unique(dta_used[:,1]) #sexdummy = (dta_used[:,1][:, None] == sexgroups).astype(int) def data2dummy(x, returnall=False): '''convert array of categories to dummy variables by default drops dummy variable for last category uses ravel, 1d only''' x = x.ravel() groups = np.unique(x) if returnall: return (x[:, None] == groups).astype(int) else: return (x[:, None] == groups).astype(int)[:,:-1] def data2proddummy(x): '''creates product dummy variables from 2 columns of 2d array drops last dummy variable, but not from each category singular with simple dummy variable but not with constant quickly written, no safeguards ''' #brute force, assumes x is 2d #replace with encoding if possible groups = np.unique(lmap(tuple, x.tolist())) #includes singularity with additive factors return (x==groups[:,None,:]).all(-1).T.astype(int)[:,:-1] def data2groupcont(x1,x2): '''create dummy continuous variable Parameters ---------- x1 : 1d array label or group array x2 : 1d array (float) continuous variable Notes ----- useful for group specific slope coefficients in regression ''' if x2.ndim == 1: x2 = x2[:,None] dummy = data2dummy(x1, returnall=True) return dummy * x2 sexdummy = data2dummy(dta_used[:,1]) factors = ['sex'] for k in factors: varsused[k][0] = data2dummy(varsused[k][0]) products = [('sex', 'age')] for k in products: varsused[''.join(k)] = data2proddummy(np.c_[varsused[k[0]][0],varsused[k[1]][0]]) # make dictionary of variables with dummies as one variable #vars_to_use = {name: data or dummy variables} X_b0 = np.c_[sexdummy, dta_used[:,2], np.ones((dta_used.shape[0],1))] y_b0 = dta_used[:,0] res_b0 = sm.OLS(y_b0, X_b0).results print(res_b0.params) print(res_b0.ssr) anova_str0 = ''' ANOVA statistics (model sum of squares excludes constant) Source DF Sum Squares Mean Square F Value Pr > F Model %(df_model)i %(ess)f %(mse_model)f %(fvalue)f %(f_pvalue)f Error %(df_resid)i %(ssr)f %(mse_resid)f CTotal %(nobs)i %(uncentered_tss)f %(mse_total)f R squared %(rsquared)f ''' anova_str = ''' ANOVA statistics (model sum of squares includes constant) Source DF Sum Squares Mean Square F Value Pr > F Model %(df_model)i %(ssmwithmean)f %(mse_model)f %(fvalue)f %(f_pvalue)f Error %(df_resid)i %(ssr)f %(mse_resid)f CTotal %(nobs)i %(uncentered_tss)f %(mse_total)f R squared %(rsquared)f ''' #print(anova_str % dict([('df_model', res.df_model)]) #anovares = ['df_model' , 'df_resid' def anovadict(res): '''update regression results dictionary with ANOVA specific statistics not checked for completeness ''' ad = {} ad.update(res.__dict__) anova_attr = ['df_model', 'df_resid', 'ess', 'ssr','uncentered_tss', 'mse_model', 'mse_resid', 'mse_total', 'fvalue', 'f_pvalue', 'rsquared'] for key in anova_attr: ad[key] = getattr(res, key) ad['nobs'] = res.model.nobs ad['ssmwithmean'] = res.uncentered_tss - res.ssr return ad print(anova_str0 % anovadict(res_b0)) #the following leaves the constant in, not with NIST regression #but something fishy with res.ess negative in examples print(anova_str % anovadict(res_b0)) print('using sex only') X2 = np.c_[sexdummy, np.ones((dta_used.shape[0],1))] res2 = sm.OLS(y_b0, X2).results print(res2.params) print(res2.ssr) print(anova_str % anovadict(res2)) print('using age only') X3 = np.c_[ dta_used[:,2], np.ones((dta_used.shape[0],1))] res3 = sm.OLS(y_b0, X3).results print(res3.params) print(res3.ssr) print(anova_str % anovadict(res3)) def form2design(ss, data): '''convert string formula to data dictionary ss : str * I : add constant * varname : for simple varnames data is used as is * F:varname : create dummy variables for factor varname * P:varname1*varname2 : create product dummy variables for varnames * G:varname1*varname2 : create product between factor and continuous variable data : dict or structured array data set, access of variables by name as in dictionaries Returns ------- vars : dictionary dictionary of variables with converted dummy variables names : list list of names, product (P:) and grouped continuous variables (G:) have name by joining individual names sorted according to input Examples -------- >>> xx, n = form2design('I a F:b P:c*d G:c*f', testdata) >>> xx.keys() ['a', 'b', 'const', 'cf', 'cd'] >>> n ['const', 'a', 'b', 'cd', 'cf'] Notes ----- with sorted dict, separate name list would not be necessary ''' vars = {} names = [] for item in ss.split(): if item == 'I': vars['const'] = np.ones(data.shape[0]) names.append('const') elif ':' not in item: vars[item] = data[item] names.append(item) elif item[:2] == 'F:': v = item.split(':')[1] vars[v] = data2dummy(data[v]) names.append(v) elif item[:2] == 'P:': v = item.split(':')[1].split('*') vars[''.join(v)] = data2proddummy(np.c_[data[v[0]],data[v[1]]]) names.append(''.join(v)) elif item[:2] == 'G:': v = item.split(':')[1].split('*') vars[''.join(v)] = data2groupcont(data[v[0]], data[v[1]]) names.append(''.join(v)) else: raise ValueError('unknown expression in formula') return vars, names nobs = 1000 testdataint = np.random.randint(3, size=(nobs,4)).view([('a',int),('b',int),('c',int),('d',int)]) testdatacont = np.random.normal( size=(nobs,2)).view([('e',float), ('f',float)]) dt2 = numpy.lib.recfunctions.zip_descr((testdataint, testdatacont),flatten=True) # concatenate structured arrays testdata = np.empty((nobs,1), dt2) for name in testdataint.dtype.names: testdata[name] = testdataint[name] for name in testdatacont.dtype.names: testdata[name] = testdatacont[name] #print(form2design('a',testdata)) if 0: xx, n = form2design('F:a',testdata) print(xx) print(form2design('P:a*b',testdata)) print(data2proddummy((np.c_[testdata['a'],testdata['b']]))) xx, names = form2design('a F:b P:c*d',testdata) #xx, names = form2design('I a F:b F:c F:d P:c*d',testdata) xx, names = form2design('I a F:b P:c*d', testdata) xx, names = form2design('I a F:b P:c*d G:a*e f', testdata) X = np.column_stack([xx[nn] for nn in names]) # simple test version: all coefficients equal to one y = X.sum(1) + 0.01*np.random.normal(size=(nobs)) rest1 = sm.OLS(y,X).results print(rest1.params) print(anova_str % anovadict(rest1)) def dropname(ss, li): '''drop names from a list of strings, names to drop are in space delimited list does not change original list ''' newli = li[:] for item in ss.split(): newli.remove(item) return newli X = np.column_stack([xx[nn] for nn in dropname('ae f', names)]) # simple test version: all coefficients equal to one y = X.sum(1) + 0.01*np.random.normal(size=(nobs)) rest1 = sm.OLS(y,X).results print(rest1.params) print(anova_str % anovadict(rest1)) # Example: from Bruce # ------------------- # read data set and drop rows with missing data dta = np.genfromtxt('dftest3.data', dt_b,missing='.', usemask=True) print('missing', [dta.mask[k].sum() for k in dta.dtype.names]) m = dta.mask.view(bool) droprows = m.reshape(-1,len(dta.dtype.names)).any(1) # get complete data as plain structured array # maybe does not work with masked arrays dta_use_b1 = dta[~droprows,:].data print(dta_use_b1.shape) print(dta_use_b1.dtype) #Example b1: variables from Bruce's glm # prepare data and dummy variables xx_b1, names_b1 = form2design('I F:sex age', dta_use_b1) # create design matrix X_b1 = np.column_stack([xx_b1[nn] for nn in dropname('', names_b1)]) y_b1 = dta_use_b1['y'] # estimate using OLS rest_b1 = sm.OLS(y_b1, X_b1).results # print(results) print(rest_b1.params) print(anova_str % anovadict(rest_b1)) #compare with original version only in original version print(anova_str % anovadict(res_b0)) # Example: use all variables except pig identifier allexog = ' '.join(dta.dtype.names[:-1]) #'breed sex litter pen pig age bage' xx_b1a, names_b1a = form2design('I F:breed F:sex F:litter F:pen age bage', dta_use_b1) X_b1a = np.column_stack([xx_b1a[nn] for nn in dropname('', names_b1a)]) y_b1a = dta_use_b1['y'] rest_b1a = sm.OLS(y_b1a, X_b1a).results print(rest_b1a.params) print(anova_str % anovadict(rest_b1a)) for dropn in names_b1a: print('\nResults dropping', dropn) X_b1a_ = np.column_stack([xx_b1a[nn] for nn in dropname(dropn, names_b1a)]) y_b1a_ = dta_use_b1['y'] rest_b1a_ = sm.OLS(y_b1a_, X_b1a_).results #print(rest_b1a_.params print(anova_str % anovadict(rest_b1a_)) statsmodels-0.12.2/statsmodels/sandbox/regression/onewaygls.py000066400000000000000000000354331400612667500247170ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ F test for null hypothesis that coefficients in several regressions are the same * implemented by creating groupdummies*exog and testing appropriate contrast matrices * similar to test for structural change in all variables at predefined break points * allows only one group variable * currently tests for change in all exog variables * allows for heterogscedasticity, error variance varies across groups * does not work if there is a group with only a single observation TODO ---- * generalize anova structure, - structural break in only some variables - compare structural breaks in several exog versus constant only - fast way to construct comparisons * print anova style results * add all pairwise comparison tests (DONE) with and without Bonferroni correction * add additional test, likelihood-ratio, lagrange-multiplier, wald ? * test for heteroscedasticity, equality of variances - how? - like lagrange-multiplier in stattools heteroscedasticity tests * permutation or bootstrap test statistic or pvalues References ---------- Greene: section 7.4 Modeling and Testing for a Structural Break is not the same because I use a different normalization, which looks easier for more than 2 groups/subperiods after looking at Greene: * my version assumes that all groups are large enough to estimate the coefficients * in sections 7.4.2 and 7.5.3, predictive tests can also be used when there are insufficient (nobs>> res.contrasts.keys() [(0, 1), 1, 'all', 3, (1, 2), 2, (1, 3), (2, 3), (0, 3), (0, 2)] The keys are based on the original names or labels of the groups. TODO: keys can be numpy scalars and then the keys cannot be sorted ''' if not hasattr(self, 'weights'): self.fitbygroups() groupdummy = (self.groupsint[:,None] == self.uniqueint).astype(int) #order of dummy variables by variable - not used #dummyexog = self.exog[:,:,None]*groupdummy[:,None,1:] #order of dummy variables by grous - used dummyexog = self.exog[:,None,:]*groupdummy[:,1:,None] exog = np.c_[self.exog, dummyexog.reshape(self.exog.shape[0],-1)] #self.nobs ?? #Notes: I changed to drop first group from dummy #instead I want one full set dummies if self.het: weights = self.weights res = WLS(self.endog, exog, weights=weights).fit() else: res = OLS(self.endog, exog).fit() self.lsjoint = res contrasts = {} nvars = self.exog.shape[1] nparams = exog.shape[1] ndummies = nparams - nvars contrasts['all'] = np.c_[np.zeros((ndummies, nvars)), np.eye(ndummies)] for groupind, group in enumerate(self.unique[1:]): #need enumerate if groups != groupsint groupind = groupind + 1 contr = np.zeros((nvars, nparams)) contr[:,nvars*groupind:nvars*(groupind+1)] = np.eye(nvars) contrasts[group] = contr #save also for pairs, see next contrasts[(self.unique[0], group)] = contr #Note: I'm keeping some duplication for testing pairs = np.triu_indices(len(self.unique),1) for ind1,ind2 in zip(*pairs): #replace with group1, group2 in sorted(keys) if ind1 == 0: continue # need comparison with benchmark/normalization group separate g1 = self.unique[ind1] g2 = self.unique[ind2] group = (g1, g2) contr = np.zeros((nvars, nparams)) contr[:,nvars*ind1:nvars*(ind1+1)] = np.eye(nvars) contr[:,nvars*ind2:nvars*(ind2+1)] = -np.eye(nvars) contrasts[group] = contr self.contrasts = contrasts def fitpooled(self): '''fit the pooled model, which assumes there are no differences across groups ''' if self.het: if not hasattr(self, 'weights'): self.fitbygroups() weights = self.weights res = WLS(self.endog, self.exog, weights=weights).fit() else: res = OLS(self.endog, self.exog).fit() self.lspooled = res def ftest_summary(self): '''run all ftests on the joint model Returns ------- fres : str a string that lists the results of all individual f-tests summarytable : list of tuples contains (pair, (fvalue, pvalue,df_denom, df_num)) for each f-test Note ---- This are the raw results and not formatted for nice printing. ''' if not hasattr(self, 'lsjoint'): self.fitjoint() txt = [] summarytable = [] txt.append('F-test for equality of coefficients across groups') fres = self.lsjoint.f_test(self.contrasts['all']) txt.append(fres.__str__()) summarytable.append(('all',(fres.fvalue, fres.pvalue, fres.df_denom, fres.df_num))) # for group in self.unique[1:]: #replace with group1, group2 in sorted(keys) # txt.append('F-test for equality of coefficients between group' # ' %s and group %s' % (group, '0')) # fres = self.lsjoint.f_test(self.contrasts[group]) # txt.append(fres.__str__()) # summarytable.append((group,(fres.fvalue, fres.pvalue, fres.df_denom, fres.df_num))) pairs = np.triu_indices(len(self.unique),1) for ind1,ind2 in zip(*pairs): #replace with group1, group2 in sorted(keys) g1 = self.unique[ind1] g2 = self.unique[ind2] txt.append('F-test for equality of coefficients between group' ' %s and group %s' % (g1, g2)) group = (g1, g2) fres = self.lsjoint.f_test(self.contrasts[group]) txt.append(fres.__str__()) summarytable.append((group,(fres.fvalue, fres.pvalue, fres.df_denom, fres.df_num))) self.summarytable = summarytable return '\n'.join(txt), summarytable def print_summary(self, res): '''printable string of summary ''' groupind = res.groups #res.fitjoint() #not really necessary, because called by ftest_summary if hasattr(res, 'self.summarytable'): summtable = self.summarytable else: _, summtable = res.ftest_summary() txt = '' #print ft[0] #skip because table is nicer templ = \ '''Table of F-tests for overall or pairwise equality of coefficients' %(tab)s Notes: p-values are not corrected for many tests (no Bonferroni correction) * : reject at 5%% uncorrected confidence level Null hypothesis: all or pairwise coefficient are the same' Alternative hypothesis: all coefficients are different' Comparison with stats.f_oneway %(statsfow)s Likelihood Ratio Test %(lrtest)s Null model: pooled all coefficients are the same across groups,' Alternative model: all coefficients are allowed to be different' not verified but looks close to f-test result' OLS parameters by group from individual, separate ols regressions' %(olsbg)s for group in sorted(res.olsbygroup): r = res.olsbygroup[group] print group, r.params Check for heteroscedasticity, ' variance and standard deviation for individual regressions' %(grh)s variance ', res.sigmabygroup standard dev', np.sqrt(res.sigmabygroup) ''' from statsmodels.iolib import SimpleTable resvals = {} resvals['tab'] = str(SimpleTable([(['%r' % (row[0],)] + list(row[1]) + ['*']*(row[1][1]>0.5).item() ) for row in summtable], headers=['pair', 'F-statistic','p-value','df_denom', 'df_num'])) resvals['statsfow'] = str(stats.f_oneway(*[res.endog[groupind==gr] for gr in res.unique])) #resvals['lrtest'] = str(res.lr_test()) resvals['lrtest'] = str(SimpleTable([res.lr_test()], headers=['likelihood ratio', 'p-value', 'df'] )) resvals['olsbg'] = str(SimpleTable([[group] + res.olsbygroup[group].params.tolist() for group in sorted(res.olsbygroup)])) resvals['grh'] = str(SimpleTable(np.vstack([res.sigmabygroup, np.sqrt(res.sigmabygroup)]), headers=res.unique.tolist())) return templ % resvals # a variation of this has been added to RegressionResults as compare_lr def lr_test(self): r''' generic likelihood ratio test between nested models \begin{align} D & = -2(\ln(\text{likelihood for null model}) - \ln(\text{likelihood for alternative model})) \\ & = -2\ln\left( \frac{\text{likelihood for null model}}{\text{likelihood for alternative model}} \right). \end{align} is distributed as chisquare with df equal to difference in number of parameters or equivalently difference in residual degrees of freedom (sign?) TODO: put into separate function ''' if not hasattr(self, 'lsjoint'): self.fitjoint() if not hasattr(self, 'lspooled'): self.fitpooled() loglikejoint = self.lsjoint.llf loglikepooled = self.lspooled.llf lrstat = -2*(loglikepooled - loglikejoint) #??? check sign lrdf = self.lspooled.df_resid - self.lsjoint.df_resid lrpval = stats.chi2.sf(lrstat, lrdf) return lrstat, lrpval, lrdf statsmodels-0.12.2/statsmodels/sandbox/regression/penalized.py000066400000000000000000000417221400612667500246600ustar00rootroot00000000000000# -*- coding: utf-8 -*- """linear model with Theil prior probabilistic restrictions, generalized Ridge Created on Tue Dec 20 00:10:10 2011 Author: Josef Perktold License: BSD-3 open issues * selection of smoothing factor, strength of prior, cross validation * GLS, does this really work this way * None of inherited results have been checked yet, I'm not sure if any need to be adjusted or if only interpretation changes One question is which results are based on likelihood (residuals) and which are based on "posterior" as for example bse and cov_params * helper functions to construct priors? * increasing penalization for ordered regressors, e.g. polynomials * compare with random/mixed effects/coefficient, like estimated priors there is something fishy with the result instance, some things, e.g. normalized_cov_params, do not look like they update correctly as we search over lambda -> some stale state again ? I added df_model to result class using the hatmatrix, but df_model is defined in model instance not in result instance. -> not clear where refactoring should occur. df_resid does not get updated correctly. problem with definition of df_model, it has 1 subtracted for constant """ from statsmodels.compat.python import lrange import numpy as np from statsmodels.tools.decorators import cache_readonly from statsmodels.regression.linear_model import OLS, GLS, RegressionResults from statsmodels.regression.feasible_gls import atleast_2dcols class TheilGLS(GLS): r"""GLS with stochastic restrictions TheilGLS estimates the following linear model .. math:: y = X \beta + u using additional information given by a stochastic constraint .. math:: q = R \beta + v :math:`E(u) = 0`, :math:`cov(u) = \Sigma` :math:`cov(u, v) = \Sigma_p`, with full rank. u and v are assumed to be independent of each other. If :math:`E(v) = 0`, then the estimator is unbiased. Note: The explanatory variables are not rescaled, the parameter estimates not scale equivariant and fitted values are not scale invariant since scaling changes the relative penalization weights (for given \Sigma_p). Note: GLS is not tested yet, only Sigma is identity is tested Notes ----- The parameter estimates solves the moment equation: .. math:: (X' \Sigma X + \lambda R' \sigma^2 \Sigma_p^{-1} R) b = X' \Sigma y + \lambda R' \Sigma_p^{-1} q :math:`\lambda` is the penalization weight similar to Ridge regression. If lambda is zero, then the parameter estimate is the same as OLS. If lambda goes to infinity, then the restriction is imposed with equality. In the model `pen_weight` is used as name instead of $\lambda$ R does not have to be square. The number of rows of R can be smaller than the number of parameters. In this case not all linear combination of parameters are penalized. The stochastic constraint can be interpreted in several different ways: - The prior information represents parameter estimates from independent prior samples. - We can consider it just as linear restrictions that we do not want to impose without uncertainty. - With a full rank square restriction matrix R, the parameter estimate is the same as a Bayesian posterior mean for the case of an informative normal prior, normal likelihood and known error variance Sigma. If R is less than full rank, then it defines a partial prior. References ---------- Theil Goldberger Baum, Christopher slides for tgmixed in Stata (I do not remember what I used when I first wrote the code.) Parameters ---------- endog : array_like, 1-D dependent or endogenous variable exog : array_like, 1D or 2D array of explanatory or exogenous variables r_matrix : None or array_like, 2D array of linear restrictions for stochastic constraint. default is identity matrix that does not penalize constant, if constant is detected to be in `exog`. q_matrix : None or array_like mean of the linear restrictions. If None, the it is set to zeros. sigma_prior : None or array_like A fully specified sigma_prior is a square matrix with the same number of rows and columns as there are constraints (number of rows of r_matrix). If sigma_prior is None, a scalar or one-dimensional, then a diagonal matrix is created. sigma : None or array_like Sigma is the covariance matrix of the error term that is used in the same way as in GLS. """ def __init__(self, endog, exog, r_matrix=None, q_matrix=None, sigma_prior=None, sigma=None): super(TheilGLS, self).__init__(endog, exog, sigma=sigma) if r_matrix is not None: r_matrix = np.asarray(r_matrix) else: try: const_idx = self.data.const_idx except AttributeError: const_idx = None k_exog = exog.shape[1] r_matrix = np.eye(k_exog) if const_idx is not None: keep_idx = lrange(k_exog) del keep_idx[const_idx] r_matrix = r_matrix[keep_idx] # delete row for constant k_constraints, k_exog = r_matrix.shape self.r_matrix = r_matrix if k_exog != self.exog.shape[1]: raise ValueError('r_matrix needs to have the same number of columns' 'as exog') if q_matrix is not None: self.q_matrix = atleast_2dcols(q_matrix) else: self.q_matrix = np.zeros(k_constraints)[:, None] if self.q_matrix.shape != (k_constraints, 1): raise ValueError('q_matrix has wrong shape') if sigma_prior is not None: sigma_prior = np.asarray(sigma_prior) if np.size(sigma_prior) == 1: sigma_prior = np.diag(sigma_prior * np.ones(k_constraints)) #no numerical shortcuts are used for this case elif sigma_prior.ndim == 1: sigma_prior = np.diag(sigma_prior) else: sigma_prior = np.eye(k_constraints) if sigma_prior.shape != (k_constraints, k_constraints): raise ValueError('sigma_prior has wrong shape') self.sigma_prior = sigma_prior self.sigma_prior_inv = np.linalg.pinv(sigma_prior) #or inv def fit(self, pen_weight=1., cov_type='sandwich', use_t=True): """Estimate parameters and return results instance Parameters ---------- pen_weight : float penalization factor for the restriction, default is 1. cov_type : str, 'data-prior' or 'sandwich' 'data-prior' assumes that the stochastic restriction reflects a previous sample. The covariance matrix of the parameter estimate is in this case the same form as the one of GLS. The covariance matrix for cov_type='sandwich' treats the stochastic restriction (R and q) as fixed and has a sandwich form analogously to M-estimators. Returns ------- results : TheilRegressionResults instance Notes ----- cov_params for cov_type data-prior, is calculated as .. math:: \\sigma^2 A^{-1} cov_params for cov_type sandwich, is calculated as .. math:: \\sigma^2 A^{-1} (X'X) A^{-1} where :math:`A = X' \\Sigma X + \\lambda \\sigma^2 R' \\Simga_p^{-1} R` :math:`\\sigma^2` is an estimate of the error variance. :math:`\\sigma^2` inside A is replaced by the estimate from the initial GLS estimate. :math:`\\sigma^2` in cov_params is obtained from the residuals of the final estimate. The sandwich form of the covariance estimator is not robust to misspecified heteroscedasticity or autocorrelation. """ lambd = pen_weight #this does duplicate transformation, but I need resid not wresid res_gls = GLS(self.endog, self.exog, sigma=self.sigma).fit() self.res_gls = res_gls sigma2_e = res_gls.mse_resid r_matrix = self.r_matrix q_matrix = self.q_matrix sigma_prior_inv = self.sigma_prior_inv x = self.wexog y = self.wendog[:,None] #why are sigma2_e * lambd multiplied, not ratio? #larger lambd -> stronger prior (it's not the variance) # Bayesian: lambd is precision = 1/sigma2_prior #print('lambd inside fit', lambd xx = np.dot(x.T, x) xpx = xx + \ sigma2_e * lambd * np.dot(r_matrix.T, np.dot(sigma_prior_inv, r_matrix)) xpy = np.dot(x.T, y) + \ sigma2_e * lambd * np.dot(r_matrix.T, np.dot(sigma_prior_inv, q_matrix)) #xpy = xpy[:,None] xpxi = np.linalg.pinv(xpx, rcond=1e-15**2) #to match pinv(x) in OLS case xpxi_sandwich = xpxi.dot(xx).dot(xpxi) params = np.dot(xpxi, xpy) #or solve params = np.squeeze(params) # normalized_cov_params should have sandwich form xpxi @ xx @ xpxi if cov_type == 'sandwich': normalized_cov_params = xpxi_sandwich elif cov_type == 'data-prior': normalized_cov_params = xpxi #why attach it to self, i.e. model? else: raise ValueError("cov_type has to be 'sandwich' or 'data-prior'") self.normalized_cov_params = xpxi_sandwich self.xpxi = xpxi self.sigma2_e = sigma2_e lfit = TheilRegressionResults(self, params, normalized_cov_params=normalized_cov_params, use_t=use_t) lfit.penalization_factor = lambd return lfit def select_pen_weight(self, method='aicc', start_params=1., optim_args=None): """find penalization factor that minimizes gcv or an information criterion Parameters ---------- method : str the name of an attribute of the results class. Currently the following are available aic, aicc, bic, gc and gcv. start_params : float starting values for the minimization to find the penalization factor `lambd`. Not since there can be local minima, it is best to try different starting values. optim_args : None or dict optimization keyword arguments used with `scipy.optimize.fmin` Returns ------- min_pen_weight : float The penalization factor at which the target criterion is (locally) minimized. Notes ----- This uses `scipy.optimize.fmin` as optimizer. """ if optim_args is None: optim_args = {} #this does not make sense, since number of parameters stays unchanged # information criteria changes if we use df_model based on trace(hat_matrix) #need leave-one-out, gcv; or some penalization for weak priors #added extra penalization for lambd def get_ic(lambd): # this can be optimized more # for pure Ridge we can keep the eigenvector decomposition return getattr(self.fit(lambd), method) from scipy import optimize lambd = optimize.fmin(get_ic, start_params, **optim_args) return lambd #TODO: #I need the hatmatrix in the model if I want to do iterative fitting, e.g. GCV #move to model or use it from a results instance inside the model, # each call to fit returns results instance # note: we need to recalculate hatmatrix for each lambda, so keep in results is fine class TheilRegressionResults(RegressionResults): def __init__(self, *args, **kwds): super(TheilRegressionResults, self).__init__(*args, **kwds) # overwrite df_model and df_resid self.df_model = self.hatmatrix_trace() - 1 #assume constant self.df_resid = self.model.endog.shape[0] - self.df_model - 1 @cache_readonly def hatmatrix_diag(self): '''diagonal of hat matrix diag(X' xpxi X) where xpxi = (X'X + sigma2_e * lambd * sigma_prior)^{-1} Notes ----- uses wexog, so this includes weights or sigma - check this case not clear whether I need to multiply by sigmahalf, i.e. (W^{-0.5} X) (X' W X)^{-1} (W^{-0.5} X)' or (W X) (X' W X)^{-1} (W X)' projection y_hat = H y or in terms of transformed variables (W^{-0.5} y) might be wrong for WLS and GLS case ''' # TODO is this still correct with sandwich normalized_cov_params, I guess not xpxi = self.model.normalized_cov_params #something fishy with self.normalized_cov_params in result, does not update #print(self.model.wexog.shape, np.dot(xpxi, self.model.wexog.T).shape return (self.model.wexog * np.dot(xpxi, self.model.wexog.T).T).sum(1) #@cache_readonly def hatmatrix_trace(self): """trace of hat matrix """ return self.hatmatrix_diag.sum() ## #this does not update df_resid ## @property #needs to be property or attribute (no call) ## def df_model(self): ## return self.hatmatrix_trace() #Note: mse_resid uses df_resid not nobs-k_vars, which might differ if df_model, tr(H), is used #in paper for gcv ess/nobs is used instead of mse_resid @cache_readonly def gcv(self): return self.mse_resid / (1. - self.hatmatrix_trace() / self.nobs)**2 @cache_readonly def cv(self): return ((self.resid / (1. - self.hatmatrix_diag))**2).sum() / self.nobs @cache_readonly def aicc(self): aic = np.log(self.mse_resid) + 1 aic += 2 * (1. + self.hatmatrix_trace()) / (self.nobs - self.hatmatrix_trace() -2) return aic def test_compatibility(self): """Hypothesis test for the compatibility of prior mean with data """ # TODO: should we store the OLS results ? not needed so far, but maybe cache #params_ols = np.linalg.pinv(self.model.exog).dot(self.model.endog) #res = self.wald_test(self.model.r_matrix, q_matrix=self.model.q_matrix, use_f=False) #from scratch res_ols = OLS(self.model.endog, self.model.exog).fit() r_mat = self.model.r_matrix r_diff = self.model.q_matrix - r_mat.dot(res_ols.params)[:,None] ols_cov_r = res_ols.cov_params(r_matrix=r_mat) statistic = r_diff.T.dot(np.linalg.solve(ols_cov_r + self.model.sigma_prior, r_diff)) from scipy import stats df = np.linalg.matrix_rank(self.model.sigma_prior) # same as r_mat.shape[0] pvalue = stats.chi2.sf(statistic, df) # TODO: return results class return statistic, pvalue, df def share_data(self): """a measure for the fraction of the data in the estimation result The share of the prior information is `1 - share_data`. Returns ------- share : float between 0 and 1 share of data defined as the ration between effective degrees of freedom of the model and the number (TODO should be rank) of the explanatory variables. """ # this is hatmatrix_trace / self.exog.shape[1] # This needs to use rank of exog and not shape[1], # since singular exog is allowed return (self.df_model + 1) / self.model.rank # + 1 is for constant # contrast/restriction matrices, temporary location def coef_restriction_meandiff(n_coeffs, n_vars=None, position=0): reduced = np.eye(n_coeffs) - 1./n_coeffs if n_vars is None: return reduced else: full = np.zeros((n_coeffs, n_vars)) full[:, position:position+n_coeffs] = reduced return full def coef_restriction_diffbase(n_coeffs, n_vars=None, position=0, base_idx=0): reduced = -np.eye(n_coeffs) #make all rows, drop one row later reduced[:, base_idx] = 1 keep = lrange(n_coeffs) del keep[base_idx] reduced = np.take(reduced, keep, axis=0) if n_vars is None: return reduced else: full = np.zeros((n_coeffs-1, n_vars)) full[:, position:position+n_coeffs] = reduced return full def next_odd(d): return d + (1 - d % 2) def coef_restriction_diffseq(n_coeffs, degree=1, n_vars=None, position=0, base_idx=0): #check boundaries, returns "valid" ? if degree == 1: diff_coeffs = [-1, 1] n_points = 2 elif degree > 1: from scipy import misc n_points = next_odd(degree + 1) #next odd integer after degree+1 diff_coeffs = misc.central_diff_weights(n_points, ndiv=degree) dff = np.concatenate((diff_coeffs, np.zeros(n_coeffs - len(diff_coeffs)))) from scipy import linalg reduced = linalg.toeplitz(dff, np.zeros(n_coeffs - len(diff_coeffs) + 1)).T #reduced = np.kron(np.eye(n_coeffs-n_points), diff_coeffs) if n_vars is None: return reduced else: full = np.zeros((n_coeffs-1, n_vars)) full[:, position:position+n_coeffs] = reduced return full ## ## R = np.c_[np.zeros((n_groups, k_vars-1)), np.eye(n_groups)] ## r = np.zeros(n_groups) ## R = np.c_[np.zeros((n_groups-1, k_vars)), ## np.eye(n_groups-1)-1./n_groups * np.ones((n_groups-1, n_groups-1))] statsmodels-0.12.2/statsmodels/sandbox/regression/predstd.py000066400000000000000000000056711400612667500243550ustar00rootroot00000000000000'''Additional functions prediction standard errors and confidence intervals A: josef pktd ''' import numpy as np from scipy import stats def atleast_2dcol(x): ''' convert array_like to 2d from 1d or 0d not tested because not used ''' x = np.asarray(x) if (x.ndim == 1): x = x[:, None] elif (x.ndim == 0): x = np.atleast_2d(x) elif (x.ndim > 0): raise ValueError('too many dimensions') return x def wls_prediction_std(res, exog=None, weights=None, alpha=0.05): '''calculate standard deviation and confidence interval for prediction applies to WLS and OLS, not to general GLS, that is independently but not identically distributed observations Parameters ---------- res : regression result instance results of WLS or OLS regression required attributes see notes exog : array_like (optional) exogenous variables for points to predict weights : scalar or array_like (optional) weights as defined for WLS (inverse of variance of observation) alpha : float (default: alpha = 0.05) confidence level for two-sided hypothesis Returns ------- predstd : array_like, 1d standard error of prediction same length as rows of exog interval_l, interval_u : array_like lower und upper confidence bounds Notes ----- The result instance needs to have at least the following res.model.predict() : predicted values or res.fittedvalues : values used in estimation res.cov_params() : covariance matrix of parameter estimates If exog is 1d, then it is interpreted as one observation, i.e. a row vector. testing status: not compared with other packages References ---------- Greene p.111 for OLS, extended to WLS by analogy ''' # work around current bug: # fit does not attach results to model, predict broken #res.model.results covb = res.cov_params() if exog is None: exog = res.model.exog predicted = res.fittedvalues if weights is None: weights = res.model.weights else: exog = np.atleast_2d(exog) if covb.shape[1] != exog.shape[1]: raise ValueError('wrong shape of exog') predicted = res.model.predict(res.params, exog) if weights is None: weights = 1. else: weights = np.asarray(weights) if weights.size > 1 and len(weights) != exog.shape[0]: raise ValueError('weights and exog do not have matching shape') # full covariance: #predvar = res3.mse_resid + np.diag(np.dot(X2,np.dot(covb,X2.T))) # predication variance only predvar = res.mse_resid/weights + (exog * np.dot(covb, exog.T).T).sum(1) predstd = np.sqrt(predvar) tppf = stats.t.isf(alpha/2., res.df_resid) interval_u = predicted + tppf * predstd interval_l = predicted - tppf * predstd return predstd, interval_l, interval_u statsmodels-0.12.2/statsmodels/sandbox/regression/runmnl.py000066400000000000000000000273161400612667500242230ustar00rootroot00000000000000'''conditional logit and nested conditional logit nested conditional logit is supposed to be the random utility version (RU2 and maybe RU1) References: ----------- currently based on: Greene, Econometric Analysis, 5th edition and draft (?) Hess, Florian, 2002, Structural Choice analysis with nested logit models, The Stats Journal 2(3) pp 227-252 not yet used: Silberhorn Nadja, Yasemin Boztug, Lutz Hildebrandt, 2008, Estimation with the nested logit model: specifications and software particularities, OR Spectrum Koppelman, Frank S., and Chandra Bhat with technical support from Vaneet Sethi, Sriram Subramanian, Vincent Bernardin and Jian Zhang, 2006, A Self Instructing Course in Mode Choice Modeling: Multinomial and Nested Logit Models Author: josef-pktd License: BSD (simplified) ''' import numpy as np import numpy.lib.recfunctions as recf from scipy import optimize class TryCLogit(object): ''' Conditional Logit, data handling test Parameters ---------- endog : array (nobs,nchoices) dummy encoding of realized choices exog_bychoices : list of arrays explanatory variables, one array of exog for each choice. Variables with common coefficients have to be first in each array ncommon : int number of explanatory variables with common coefficients Notes ----- Utility for choice j is given by $V_j = X_j * beta + Z * gamma_j$ where X_j contains generic variables (terminology Hess) that have the same coefficient across choices, and Z are variables, like individual-specific variables that have different coefficients across variables. If there are choice specific constants, then they should be contained in Z. For identification, the constant of one choice should be dropped. ''' def __init__(self, endog, exog_bychoices, ncommon): self.endog = endog self.exog_bychoices = exog_bychoices self.ncommon = ncommon self.nobs, self.nchoices = endog.shape self.nchoices = len(exog_bychoices) #TODO: rename beta to params and include inclusive values for nested CL betaind = [exog_bychoices[ii].shape[1]-ncommon for ii in range(4)] zi = np.r_[[ncommon], ncommon + np.array(betaind).cumsum()] beta_indices = [np.r_[np.array([0, 1]),z[zi[ii]:zi[ii+1]]] for ii in range(len(zi)-1)] self.beta_indices = beta_indices #for testing only beta = np.arange(7) betaidx_bychoices = [beta[idx] for idx in beta_indices] def xbetas(self, params): '''these are the V_i ''' res = np.empty((self.nobs, self.nchoices)) for choiceind in range(self.nchoices): res[:,choiceind] = np.dot(self.exog_bychoices[choiceind], params[self.beta_indices[choiceind]]) return res def loglike(self, params): #normalization ? xb = self.xbetas(params) expxb = np.exp(xb) sumexpxb = expxb.sum(1)#[:,None] probs = expxb/expxb.sum(1)[:,None] #we do not really need this for all loglike = (self.endog * np.log(probs)).sum(1) #is this the same: YES #self.logliketest = (self.endog * xb).sum(1) - np.log(sumexpxb) #if self.endog where index then xb[self.endog] return -loglike.sum() #return sum for now not for each observation def fit(self, start_params=None): if start_params is None: start_params = np.zeros(6) # need better np.zeros(6) return optimize.fmin(self.loglike, start_params, maxfun=10000) class TryNCLogit(object): ''' Nested Conditional Logit (RUNMNL), data handling test unfinished, does not do anything yet ''' def __init__(self, endog, exog_bychoices, ncommon): self.endog = endog self.exog_bychoices = exog_bychoices self.ncommon = ncommon self.nobs, self.nchoices = endog.shape self.nchoices = len(exog_bychoices) #TODO rename beta to params and include inclusive values for nested CL betaind = [exog_bychoices[ii].shape[1]-ncommon for ii in range(4)] zi = np.r_[[ncommon], ncommon + np.array(betaind).cumsum()] beta_indices = [np.r_[np.array([0, 1]),z[zi[ii]:zi[ii+1]]] for ii in range(len(zi)-1)] self.beta_indices = beta_indices #for testing only beta = np.arange(7) betaidx_bychoices = [beta[idx] for idx in beta_indices] def xbetas(self, params): '''these are the V_i ''' res = np.empty((self.nobs, self.nchoices)) for choiceind in range(self.nchoices): res[:,choiceind] = np.dot(self.exog_bychoices[choiceind], params[self.beta_indices[choiceind]]) return res def loglike_leafbranch(self, params, tau): #normalization ? #check/change naming for tau xb = self.xbetas(params) expxb = np.exp(xb/tau) sumexpxb = expxb.sum(1)#[:,None] logsumexpxb = np.log(sumexpxb) #loglike = (self.endog * xb).sum(1) - logsumexpxb probs = expxb/sumexpxb[:,None] return probs, logsumexpxp # noqa:F821 See GH#5756 #if self.endog where index then xb[self.endog] #return -loglike.sum() #return sum for now not for each observation def loglike_branch(self, params, tau): #not yet sure how to keep track of branches during walking of tree ivs = [] for b in branches: # noqa:F821 See GH#5756 probs, iv = self.loglike_leafbranch(params, tau) ivs.append(iv) #ivs = np.array(ivs) #note ivs is (nobs,nbranchchoices) ivs = np.column_stack(ivs) # this way ? exptiv = np.exp(tau*ivs) sumexptiv = exptiv.sum(1) logsumexpxb = np.log(sumexpxb) # noqa:F821 See GH#5756 probs = exptiv/sumexptiv[:,None] ####### obsolete version to try out attaching data, ####### new in treewalkerclass.py, copy new version to replace this ####### problem with bzr I will disconnect history when copying testxb = 0 #global to class class RU2NMNL(object): '''Nested Multinomial Logit with Random Utility 2 parameterization ''' def __init__(self, endog, exog, tree, paramsind): self.endog = endog self.datadict = exog self.tree = tree self.paramsind = paramsind self.branchsum = '' self.probs = {} def calc_prob(self, tree, keys=None): '''walking a tree bottom-up based on dictionary ''' endog = self.endog datadict = self.datadict paramsind = self.paramsind branchsum = self.branchsum if isinstance(tree, tuple): #assumes leaves are int for choice index name, subtree = tree print(name, datadict[name]) print('subtree', subtree) keys = [] if testxb: branchsum = datadict[name] else: branchsum = name #0 for b in subtree: print(b) #branchsum += branch2(b) branchsum = branchsum + self.calc_prob(b, keys) print('branchsum', branchsum, keys) for k in keys: self.probs[k] = self.probs[k] + ['*' + name + '-prob'] else: keys.append(tree) self.probs[tree] = [tree + '-prob' + '(%s)' % ', '.join(self.paramsind[tree])] if testxb: leavessum = sum((datadict[bi] for bi in tree)) print('final branch with', tree, ''.join(tree), leavessum) #sum(tree) return leavessum #sum(xb[tree]) else: return ''.join(tree) #sum(tree) print('working on branch', tree, branchsum) return branchsum #Trying out ways to handle data #------------------------------ #travel data from Greene dta = np.genfromtxt('TableF23-2.txt', skip_header=1, names='Mode Ttme Invc Invt GC Hinc PSize'.split()) endog = dta['Mode'].reshape(-1,4).copy() #I do not want a view nobs, nchoices = endog.shape datafloat = dta.view(float).reshape(-1,7) exog = datafloat[:,1:].reshape(-1,6*nchoices).copy() #I do not want a view print(endog.sum(0)) varnames = dta.dtype.names print(varnames[1:]) modes = ['Air', 'Train', 'Bus', 'Car'] print(exog.mean(0).reshape(nchoices, -1)) # Greene Table 23.23 #try dummy encoding for individual-specific variables exog_choice_names = ['GC', 'Ttme'] exog_choice = np.column_stack([dta[name] for name in exog_choice_names]) exog_choice = exog_choice.reshape(-1,len(exog_choice_names)*nchoices) exog_choice = np.c_[endog, exog_choice] # add constant dummy exog_individual = dta['Hinc'][:,None] #exog2 = np.c_[exog_choice, exog_individual*endog] # we can also overwrite and select in original datafloat # e.g. Hinc*endog{choice) choice_index = np.arange(dta.shape[0]) % nchoices hinca = dta['Hinc']*(choice_index==0) dta2=recf.append_fields(dta, ['Hinca'],[hinca], usemask=False) #another version xi = [] for ii in range(4): xi.append(datafloat[choice_index==ii]) #one more dta1 = recf.append_fields(dta, ['Const'],[np.ones(dta.shape[0])], usemask=False) xivar = [['GC', 'Ttme', 'Const', 'Hinc'], ['GC', 'Ttme', 'Const'], ['GC', 'Ttme', 'Const'], ['GC', 'Ttme']] #need to drop one constant xi = [] for ii in range(4): xi.append(dta1[xivar[ii]][choice_index==ii]) #this does not change sequence of columns, bug report by Skipper I think ncommon = 2 betaind = [len(xi[ii].dtype.names)-ncommon for ii in range(4)] zi=np.r_[[ncommon], ncommon+np.array(betaind).cumsum()] z=np.arange(7) #what is n? betaindices = [np.r_[np.array([0, 1]),z[zi[ii]:zi[ii+1]]] for ii in range(len(zi)-1)] beta = np.arange(7) betai = [beta[idx] for idx in betaindices] #examples for TryCLogit #---------------------- #get exogs as float xifloat = [xx.view(float).reshape(nobs,-1) for xx in xi] clogit = TryCLogit(endog, xifloat, 2) debug = 0 if debug: res = optimize.fmin(clogit.loglike, np.ones(6)) #estimated parameters from Greene: tab2324 = [-0.15501, -0.09612, 0.01329, 5.2074, 3.8690, 3.1632] if debug: res2 = optimize.fmin(clogit.loglike, tab2324) res3 = optimize.fmin(clogit.loglike, np.zeros(6),maxfun=10000) #this has same numbers as Greene table 23.24, but different sequence #coefficient on GC is exactly 10% of Greene's #TODO: get better starting values ''' Optimization terminated successfully. Current function value: 199.128369 Iterations: 957 Function evaluations: 1456 array([-0.0961246 , -0.0155019 , 0.01328757, 5.20741244, 3.86905293, 3.16319074]) ''' res3corr = res3[[1, 0, 2, 3, 4, 5]] res3corr[0] *= 10 print(res3corr - tab2324) # diff 1e-5 to 1e-6 #199.128369 - 199.1284 #llf same up to print(precision of Greene print(clogit.fit()) tree0 = ('top', [('Fly',['Air']), ('Ground', ['Train', 'Car', 'Bus']) ]) datadict = dict(zip(['Air', 'Train', 'Bus', 'Car'], [xifloat[i]for i in range(4)])) #for testing only (mock that returns it's own name datadict = dict(zip(['Air', 'Train', 'Bus', 'Car'], ['Airdata', 'Traindata', 'Busdata', 'Cardata'])) datadict.update({'top' : [], 'Fly' : [], 'Ground': []}) paramsind = {'top' : [], 'Fly' : [], 'Ground': [], 'Air' : ['GC', 'Ttme', 'ConstA', 'Hinc'], 'Train' : ['GC', 'Ttme', 'ConstT'], 'Bus' : ['GC', 'Ttme', 'ConstB'], 'Car' : ['GC', 'Ttme'] } modru = RU2NMNL(endog, datadict, tree0, paramsind) print(modru.calc_prob(modru.tree)) print('\nmodru.probs') print(modru.probs) statsmodels-0.12.2/statsmodels/sandbox/regression/sympy_diff.py000066400000000000000000000033151400612667500250520ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sat Mar 13 07:56:22 2010 Author: josef-pktd """ import sympy as sy def pdf(x, mu, sigma): """Return the probability density function as an expression in x""" #x = sy.sympify(x) return 1/(sigma*sy.sqrt(2*sy.pi)) * sy.exp(-(x-mu)**2 / (2*sigma**2)) def cdf(x, mu, sigma): """Return the cumulative density function as an expression in x""" #x = sy.sympify(x) return (1+sy.erf((x-mu)/(sigma*sy.sqrt(2))))/2 mu = sy.Symbol('mu') sigma = sy.Symbol('sigma') sigma2 = sy.Symbol('sigma2') x = sy.Symbol('x') y = sy.Symbol('y') df = sy.Symbol('df') s = sy.Symbol('s') dldxnorm = sy.log(pdf(x, mu,sigma)).diff(x) print(sy.simplify(dldxnorm)) print(sy.diff(sy.log(sy.gamma((s+1)/2)),s)) print(sy.diff((df+1)/2. * sy.log(1+df/(df-2)), df)) #standard t distribution, not verified tllf1 = sy.log(sy.gamma((df+1)/2.)) - sy.log(sy.gamma(df/2.)) - 0.5*sy.log((df)*sy.pi) tllf2 = (df+1.)/2. * sy.log(1. + (y-mu)**2/(df)/sigma2) + 0.5 * sy.log(sigma2) tllf2std = (df+1.)/2. * sy.log(1. + y**2/df) + 0.5 tllf = tllf1 - tllf2 print(tllf1.diff(df)) print(tllf2.diff(y)) dlddf = (tllf1-tllf2).diff(df) print(dlddf) print(sy.cse(dlddf)) print('\n derivative of loglike of t distribution wrt df') for k,v in sy.cse(dlddf)[0]: print(k, '=', v) print(sy.cse(dlddf)[1][0]) print('\nstandard t distribution, dll_df, dll_dy') tllfstd = tllf1 - tllf2std print(tllfstd.diff(df)) print(tllfstd.diff(y)) print('\n') print(dlddf.subs(dict(y=1,mu=1,sigma2=1.5,df=10.0001))) print(dlddf.subs(dict(y=1,mu=1,sigma2=1.5,df=10.0001)).evalf()) # Note: derivatives of nested function does not work in sympy # at least not higher order derivatives (second or larger) # looks like print(failure statsmodels-0.12.2/statsmodels/sandbox/regression/tests/000077500000000000000000000000001400612667500234675ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/regression/tests/__init__.py000066400000000000000000000000001400612667500255660ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/regression/tests/griliches76.dta000066400000000000000000001763401400612667500263220ustar00rootroot00000000000000röWages of Very Young Men, Zvi Griliches, J.Pol.Ec. 1976_ÿß2ñ¿_ÿ0G230 Nov 2012 10:14þþþþþþþþþþþþþþþþþþþþrnssthˆšxà“ž@ª8jrns80˜‘ø’’©h™›0mrtmorfq€i€¢è‘hmrt80”ðbà…À¢H‘°¬ˆsmsa1moȬ È¬€n0q˜smsa80o›Àe°šà‰wàn˜med‰fžhœ¸šØ©€Š`iqtePrp¬`¬Pwø¬¸w@kww000Otx]0\Àh€¬£year00P“@}ð¯xqàjH£agešÈŽ§Ð¬@n¬X\¨age80¨Hwx˜ðrà˜  ps¬H¬xn høŽXa H}ì«‚s80 «šœ«š¨«š¤«š°«š¬«š¸«š´expr«š¼«šÄ«šÈ«š˜«€Ä«šÌ«šÎexpr80«›$«¤«¬«´«¼«Ä«tenure«Ü«ä«ì«ô«€´«ü«‚tenure80«›«› «’$«€Ì«€Ô«€ôlwÜ«€ä«€ì« «ŸL«†´«†4«†lw80…è«…È«¡ì«†Ô«¢0«ƒ,«ƒ<«êTS#RIDLT¶LDGO¾CINO¢RDVR%9.0g%9.0g«ƒ¬«%9.0g%9.0g%%9.0g%9.0g%9.0g%9.0g%9%9.0g%9.0g%9.0g%9.0g%9.%9.0g%9.0g%9.0g%9.0g%9.0%9.0g%9.0g%9.0g%9.0g%9.0g%9.0g%9.0g%9.0g%9.0g%9.0g%9.0g%9.0g%9.0g`°°%9.0gX%9.0g°%9.0gË æ %9.0gÐ%9.0g %9.0glay onXTI Snd Buf Size Ping Intrval Ping Timeout start memmax emWAN Quantum SizeWAN Threshol mSec  «0Û¸ÿ €ÿÿ ¡p«0ÚÈ/ .¬;è ¡ « @ÚÌ ÿ;ÑKÿÿ㢠钌Õ¸ÿÿ F` ¡Ð« ÚÐÂl bûû ¢« ÚÔ Stata ResulsF` ¢0« ÚØ c¥F` ¢P« ÚÜ fi ` ¢p« Úà lo F ¢«0Úä/¤ >l ¢°«  Û etnRDEVafpt€ ¢à«0ÛÄ>l £«0ÛÀ/œ £0« @Û¼ÿÿÿÿÿÿÿÿÿÿresidency in South ¡š¾Fˆesidency in South ¡š¾Fˆmarital status = 1 if married ¡š¾Fˆarital status = 1 if married ¡š¾Fˆreside metro area = 1 if urban ¡š¾Fˆeside metro area = 1 if urban ¡š¾Fˆmother's education, yearsrban ¡š¾Fˆiq scoreeducation, yearsrban ¡š¾Fˆscore on knowledge in world of work test¾Fˆcore on knowledge in world of work test¾Fˆcore on knowledge in world of work test¾Fˆcore on knowledge in world of work test¾Fˆcompleted years of schoolingf work test¾Fˆompleted years of schoolingf work test¾Fˆexperience, years schoolingf work test¾Fˆxperience, years schoolingf work test¾Fˆtenure, yearsars schoolingf work test¾Fˆenure, yearsars schoolingf work test¾Fˆlog wageearsars schoolingf work test¾Fˆog wageearsars schoolingf work test¾Fˆ€?€?€?AºB BˆB˜AøA@A@AD‹ì>ö(*A@Í̼@×£Ô@€?€?€?`AîB$B„B¸AB€AA;ß5A@€A®@?5Ö@€?€?€?`AØB8B†B AB`A`Au“Ø>\0A€?AR¸¶@HáÖ@€?€?€?@AÀBB„BAB@A@Aú~ª>‹lQA€?à@Zd¯@–CÏ@€?€?€?€?À@”BØA’BÐABA0A?5A˜nfA@@ @ü©½@¾ŸÊ@€?€?A¶BÀA„B€AðAA Aú~ª>åÐVA€?^º™@9´Ì@€?€?€?€?AäBHB’BðABAAq=š?Âñ@À@`ANbÐ@Pß@€?€?`AÞBB†B¸ABpApA ?…ëIA€?€?#Û¹@Ë¡á@€?€?€?€?@A¾B0B„B°AB@A@Ao@¶ó}A@€A•·@VÝ@€?€?PAC0B’BðABAA²¯? A @PAX9Ì@R¸Ú@€?€?€AÌB4BŠB°AB`A`AœÄA€?0A¨Æ·@˜nÚ@@AúB BŒB AðA`ApAHáº>²ƒ@€?@@HáÆ@ü©Ù@€?€?€? 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0,.1833651,66,3,9,1,1,0,1,0,1,20.451,1,0,4356,3.018032,1,9,2.197225,2.197225,1,.2,.04,2.0451 1,.0887311,66,17,1,0,0,1,0,0,0,84.525,3,1,4356,4.437047,1,1,0,0,1,.2,.04,8.4525002 0,.6091371,76,6,2,0,0,0,1,1,0,11.82,1,0,5776,2.469793,0,2,.6931472,.6931472,1,2.2,4.84,1.182 0,1,83,11,26,0,0,1,1,1,1,11.592,3,1,6889,2.450315,0,26,3.258096,3.258096,1,3.6,12.96,1.1592 0,.736508,69,10,10,0,0,0,1,0,0,18.9,0,0,4761,2.939162,0,10,2.302585,2.302585,1,.8,.64,1.89 0,.2228164,65,14,4,0,0,1,0,1,1,62.832,2,1,4225,4.140464,0,4,1.386294,1.386294,1,0,0,6.2832001 0,.9863014,65,12,2,1,0,1,1,0,0,7.3,0,1,4225,1.987874,0,2,.6931472,.6931472,1,0,0,.73000002 0,.1728608,75,12,11,11,0,0,1,0,0,40.495,2,0,5625,3.701179,0,11,2.397895,2.397895,1,2,4,4.0494999 0,.1715014,76,16,14,3,0,1,0,0,0,40.816,2,1,5776,3.709074,0,14,2.639057,2.639057,1,2.2,4.84,4.0816002 0,.5327869,71,12,5,1,0,0,1,0,0,12.2,2,0,5041,2.501436,0,5,1.609438,1.609438,1,1.2,1.44,1.22 0,.1316749,79,14,9,0,0,1,0,1,1,49.364,2,1,6241,3.899221,0,9,2.197225,2.197225,1,2.8,7.84,4.9363998 0,.7033898,85,8,4,1,0,1,1,1,1,3.54,2,1,7225,1.264127,0,4,1.386294,1.386294,1,4,16,.354 0,.3362475,70,17,9,1,0,1,0,0,0,2.974,1,1,4900,1.089908,0,9,2.197225,2.197225,1,1,1,.2974 0,.3362475,71,15,3,1,0,1,1,0,0,2.974,0,1,5041,1.089908,0,3,1.098612,1.098612,1,1.2,1.44,.2974 0,.6138589,71,14,2,2,0,1,0,0,0,35.544,2,1,5041,3.570771,0,2,.6931472,.6931472,1,1.2,1.44,3.5543999 0,0,85,12,9,0,0,1,0,0,0,0,1,1,7225,,0,9,2.197225,2.197225,1,4,16,0 0,0,81,12,6,0,0,1,1,0,0,0,2,1,6561,,0,6,1.791759,1.791759,1,3.2,10.24,0 0,.2421525,65,13,5,1,1,0,1,1,1,17.84,3,0,4225,2.881443,1,5,1.609438,1.609438,1,0,0,1.784 0,.4154981,76,14,14,1,0,0,1,0,0,28.881,1,0,5776,3.363184,0,14,2.639057,2.639057,1,2.2,4.84,2.8881001 0,.387822,67,14,2,3,0,1,0,0,0,35.671,1,1,4489,3.574338,0,2,.6931472,.6931472,1,.4,.16,3.5671001 0,0,66,12,9,4,0,1,1,0,0,21.837,2,1,4356,3.083606,0,9,2.197225,2.197225,1,.2,.04,2.1837 0,.2727273,67,12,4,2,0,0,1,0,0,22,1,0,4489,3.091043,1,4,1.386294,1.386294,1,.4,.16,2.2 0,0,65,14,0,0,0,0,0,1,0,49.72,1,0,4225,3.906407,1,0,,-4.60517,0,0,0,4.9720001 0,.5164319,75,12,10,0,0,1,1,1,1,21.3,2,1,5625,3.058707,0,10,2.302585,2.302585,1,2,4,2.1299999 0,.8695652,84,12,2,2,0,0,1,0,0,11.5,1,0,7056,2.442347,0,2,.6931472,.6931472,1,3.8,14.44,1.15 0,1,71,5,11,2,0,1,1,1,1,8.7,3,1,5041,2.163323,0,11,2.397895,2.397895,1,1.2,1.44,.86999998 0,1,83,8,3,0,0,0,1,1,0,9.024,1,0,6889,2.199888,0,3,1.098612,1.098612,1,3.6,12.96,.90240002 1,0,65,12,3,0,0,0,1,0,0,8.06,2,0,4225,2.086914,0,3,1.098612,1.098612,1,0,0,.80600004 0,.3057424,67,12,13,10,0,1,0,0,0,17.989,3,1,4489,2.88976,0,13,2.564949,2.564949,1,.4,.16,1.7989 0,.3643644,85,5,5,0,1,0,1,1,1,23.976,4,0,7225,3.177053,1,5,1.609438,1.609438,1,4,16,2.3976 0,.7215634,70,16,5,1,0,1,1,1,0,17.961,1,1,4900,2.888203,0,5,1.609438,1.609438,1,1,1,1.7961 0,1,83,6,2,0,0,0,0,0,1,4.95,2,0,6889,1.599388,1,2,.6931472,.6931472,1,3.6,12.96,.49499998 0,1,85,12,15,7,1,0,1,1,1,8.16,3,0,7225,2.099244,0,15,2.70805,2.70805,1,4,16,.81599998 0,.9745293,72,9,8,2,0,1,1,1,1,13.545,6,1,5184,2.606018,0,8,2.079442,2.079442,1,1.4,1.96,1.3545 0,.8374771,80,13,6,3,0,1,1,0,0,11.463,2,1,6400,2.439125,0,6,1.791759,1.791759,1,3,9,1.1463 0,1,67,3,14,2,0,0,1,1,1,8.5,2,0,4489,2.140066,1,14,2.639057,2.639057,1,.4,.16,.85 0,1,65,4,10,0,0,0,0,1,1,8.5,1,0,4225,2.140066,1,10,2.302585,2.302585,1,0,0,.85 statsmodels-0.12.2/statsmodels/sandbox/regression/tests/results_gmm_griliches.py000066400000000000000000000337511400612667500304440ustar00rootroot00000000000000'''Results for GMM estimation with Stata gmm autogenerated, but edited ''' import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch # gmm twostep est = dict( rank=13, N=758, Q=.0153053843867424, J=11.60148136515076, J_df=2, k_1=13, converged=1, has_xtinst=0, type=1, n_eq=1, k=13, n_moments=15, k_aux=13, k_eq_model=0, k_eq=13, cmdline="gmm (lw - {xb:s iq expr tenure rns smsa dyear*} - {b0}), instruments(expr tenure rns smsa dyear* med kww age mrt)", # noqa:E501 cmd="gmm", estat_cmd="gmm_estat", predict="gmm_p", marginsnotok="_ALL", eqnames="1", technique="gn", winit="Unadjusted", estimator="twostep", wmatrix="robust", vce="robust", vcetype="Robust", params="xb_s xb_iq xb_expr xb_tenure xb_rns xb_smsa xb_dyear_67 xb_dyear_68 xb_dyear_69 xb_dyear_70 xb_dyear_71 xb_dyear_73 b0", # noqa:E501 inst_1="expr tenure rns smsa dyear_67 dyear_68 dyear_69 dyear_70 dyear_71 dyear_73 med kww age mrt _cons", # noqa:E501 params_1="xb_s xb_iq xb_expr xb_tenure xb_rns xb_smsa xb_dyear_67 xb_dyear_68 xb_dyear_69 xb_dyear_70 xb_dyear_71 xb_dyear_73 b0", # noqa:E501 sexp_1="lw - ({xb_s} *s + {xb_iq} *iq + {xb_expr} *expr + {xb_tenure} *tenure + {xb_rns} *rns + {xb_smsa} *smsa + {xb_dyear_67} *dyear_67 + {xb_dyear_68} *dyear_68 + {xb_dyear_69} *dyear_69 + {xb_dyear_70} *dyear_70 + {xb_dyear_71} *dyear_71 + {xb_dyear_73} *dyear_73) - {b0}", # noqa:E501 properties="b V", ) params_table = np.array([ .17579576802018, .02085135579518, 8.4309034744314, 3.430065999e-17, .1349278616328, .21666367440756, np.nan, 1.9599639845401, 0, -.00928615655842, .00491818692744, -1.8881259893969, .05900903858228, -.01892562580544, .00035331268861, np.nan, 1.9599639845401, 0, .05028275907275, .00810402250669, 6.2046667603925, 5.481292387e-10, .03439916682973, .06616635131577, np.nan, 1.9599639845401, 0, .04252138311466, .00956014552889, 4.4477757149388, 8.676405373e-06, .02378384219108, .06125892403824, np.nan, 1.9599639845401, 0, -.10409306762507, .03372997947655, -3.0860696994324, .00202821272955, -.17020261259839, -.03798352265175, np.nan, 1.9599639845401, 0, .12475123236049, .03098732229429, 4.0258797186699, .00005676270037, .06401719668634, .18548526803464, np.nan, 1.9599639845401, 0, -.0530431735239, .05178756424595, -1.0242453819993, .30571938841786, -.15454493429301, .04845858724521, np.nan, 1.9599639845401, 0, .045954590377, .0500069437958, .91896418554698, .35811430537838, -.05205721843969, .14396639919369, np.nan, 1.9599639845401, 0, .15548006235586, .04801256009054, 3.238320599082, .00120235613037, .06137717377284, .24958295093889, np.nan, 1.9599639845401, 0, .16698745541498, .06133412154231, 2.7225865670836, .00647730609718, .04677478616864, .28720012466132, np.nan, 1.9599639845401, 0, .08464846645187, .05581696231774, 1.516536603515, .12938372202927, -.02475076941733, .19404770232108, np.nan, 1.9599639845401, 0, .0996068440051, .06123938652803, 1.6265160324477, .10383992558646, -.02042014802516, .21963383603536, np.nan, 1.9599639845401, 0, 4.0039243732137, .33647541282379, 11.899604608883, 1.189091957e-32, 3.3444446823958, 4.6634040640315, np.nan, 1.9599639845401, 0]).reshape(13, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['_cons'] * 13 cov = np.array([ .0004347790385, -.00007935266682, .00002810133321, .00001482865838, -.00017806902959, -6.657494262e-06, -.00011587283596, -.00018806600631, -.00012201035826, -.00008278800394, -.00031494508432, -.00063549805233, .00264135978484, -.00007935266682, .00002418856265, 4.931157962e-06, -.00001114070074, .00006618982562, -.0000220304377, 4.705098991e-07, .00003206383766, -.00002261417242, -.00006024150154, -.00001412826237, .00001471698858, -.00144299517314, .00002810133321, 4.931157962e-06, .00006567518079, -.00002036677634, .00005210753053, -.00003295500811, .00003592276303, .00008754309097, .00003052996731, .00001691178156, -.00008575591893, -.00013143657018, -.00094318538399, .00001482865838, -.00001114070074, -.00002036677634, .00009139638253, -.00003771101246, 7.851603106e-06, .00008478298315, .00006722294295, .00011231163007, .0001007216652, .00011202284802, .00009437878507, .00075643538833, -.00017806902959, .00006618982562, .00005210753053, -.00003771101246, .00113771151549, .0001300530702, .00018006693931, .00018772842105, -9.500874246e-06, .00001633701903, -.00005338908155, .00008260866257, -.00499436928105, -6.657494262e-06, -.0000220304377, -.00003295500811, 7.851603106e-06, .0001300530702, .00096021414297, .00005702363753, .00011167528598, .00025281311283, .00010653704891, .00030212216421, .000307795004, .00157107924026, -.00011587283596, 4.705098991e-07, .00003592276303, .00008478298315, .00018006693931, .00005702363753, .00268195181053, .00085892679447, .00091106709634, .00096277498668, .00090313286214, .00102719488714, .00034624154943, -.00018806600631, .00003206383766, .00008754309097, .00006722294295, .00018772842105, .00011167528598, .00085892679447, .0025006944278, .00092531815147, .00088200162521, .00082339570405, .00095012566921, -.0020631120951, -.00012201035826, -.00002261417242, .00003052996731, .00011231163007, -9.500874246e-06, .00025281311283, .00091106709634, .00092531815147, .00230520592645, .00118209509709, .00111002620771, .00129242901685, .00256100032752, -.00008278800394, -.00006024150154, .00001691178156, .0001007216652, .00001633701903, .00010653704891, .00096277498668, .00088200162521, .00118209509709, .00376187446537, .00124524263644, .00155856745623, .00599140534858, -.00031494508432, -.00001412826237, -.00008575591893, .00011202284802, -.00005338908155, .00030212216421, .00090313286214, .00082339570405, .00111002620771, .00124524263644, .00311553328238, .00184297728198, .00431291320555, -.00063549805233, .00001471698858, -.00013143657018, .00009437878507, .00008260866257, .000307795004, .00102719488714, .00095012566921, .00129242901685, .00155856745623, .00184297728198, .00375026246233, .00538820067052, .00264135978484, -.00144299517314, -.00094318538399, .00075643538833, -.00499436928105, .00157107924026, .00034624154943, -.0020631120951, .00256100032752, .00599140534858, .00431291320555, .00538820067052, .11321570343494]).reshape(13, 13) cov_colnames = ['_cons'] * 13 cov_rownames = ['_cons'] * 13 results_twostep = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) # begin gmm onestep est = dict( rank=13, N=758, Q=.0175043949471787, J=13.26833136996146, J_df=2, k_1=13, converged=1, has_xtinst=0, type=1, n_eq=1, k=13, n_moments=15, k_aux=13, k_eq_model=0, k_eq=13, cmdline="gmm (lw - {xb:s iq expr tenure rns smsa dyear*} - {b0}), instruments(expr tenure rns smsa dyear* med kww age mrt) onestep", # noqa:E501 cmd="gmm", estat_cmd="gmm_estat", predict="gmm_p", marginsnotok="_ALL", eqnames="1", technique="gn", winit="Unadjusted", estimator="onestep", wmatrix="robust", vce="robust", vcetype="Robust", params="xb_s xb_iq xb_expr xb_tenure xb_rns xb_smsa xb_dyear_67 xb_dyear_68 xb_dyear_69 xb_dyear_70 xb_dyear_71 xb_dyear_73 b0", # noqa:E501 inst_1="expr tenure rns smsa dyear_67 dyear_68 dyear_69 dyear_70 dyear_71 dyear_73 med kww age mrt _cons", # noqa:E501 params_1="xb_s xb_iq xb_expr xb_tenure xb_rns xb_smsa xb_dyear_67 xb_dyear_68 xb_dyear_69 xb_dyear_70 xb_dyear_71 xb_dyear_73 b0", # noqa:E501 sexp_1="lw - ({xb_s} *s + {xb_iq} *iq + {xb_expr} *expr + {xb_tenure} *tenure + {xb_rns} *rns + {xb_smsa} *smsa + {xb_dyear_67} *dyear_67 + {xb_dyear_68} *dyear_68 + {xb_dyear_69} *dyear_69 + {xb_dyear_70} *dyear_70 + {xb_dyear_71} *dyear_71 + {xb_dyear_73} *dyear_73) - {b0}", # noqa:E501 properties="b V", ) params_table = np.array([ .1724253119448, .02073946970972, 8.3138727440057, 9.262847838e-17, .13177669825528, .21307392563431, np.nan, 1.9599639845401, 0, -.00909883104783, .00488623921543, -1.8621337692816, .06258423710802, -.01867568392991, .00047802183425, np.nan, 1.9599639845401, 0, .04928948974112, .00804979771953, 6.1230718408647, 9.178828333e-10, .033512176128, .06506680335423, np.nan, 1.9599639845401, 0, .04221709210829, .00946363451925, 4.4609808232133, 8.158539147e-06, .0236687092877, .06076547492887, np.nan, 1.9599639845401, 0, -.10179345005432, .0337105276595, -3.0196338390938, .00253080446805, -.16786487016678, -.03572202994187, np.nan, 1.9599639845401, 0, .12611094948071, .0308113805617, 4.0929989887401, .00004258295784, .06572175326583, .18650014569559, np.nan, 1.9599639845401, 0, -.0596171062088, .05171372339438, -1.1528295062831, .24898037089783, -.16097414156825, .04173992915064, np.nan, 1.9599639845401, 0, .04867955998567, .04981322392381, .97724170714436, .32844950450919, -.04895256485883, .14631168483017, np.nan, 1.9599639845401, 0, .15281763323761, .04792849748935, 3.188450321681, .00143037585682, .05887950432536, .24675576214986, np.nan, 1.9599639845401, 0, .17443605153365, .06112514589814, 2.8537527227227, .00432061472141, .05463296702353, .29423913604377, np.nan, 1.9599639845401, 0, .0916659665856, .0554618025144, 1.6527765494425, .09837634840443, -.01703716886029, .20036910203149, np.nan, 1.9599639845401, 0, .09323976498299, .06084900556261, 1.5323137021041, .125445041459, -.02602209441479, .21250162438078, np.nan, 1.9599639845401, 0, 4.0335098954259, .33503289261392, 12.03914595954, 2.212341104e-33, 3.3768574922664, 4.6901622985855, np.nan, 1.9599639845401, 0]).reshape(13, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['_cons'] * 13 cov = np.array([ .00043012560384, -.00007821948168, .00002814664044, .00001470659469, -.00018137297337, -8.404214163e-06, -.000116495836, -.00019098604401, -.00012670601919, -.00008672920733, -.00031350033095, -.00062509206531, .00258704275396, -.00007821948168, .00002387533367, 4.911669728e-06, -.00001098678322, .00006618473561, -.00002158670034, 8.107545213e-07, .00003255315461, -.00002143051924, -.0000597535309, -.00001402380853, .00001385883996, -.00142630446035, .00002814664044, 4.911669728e-06, .00006479924333, -.00001977796199, .00005110284341, -.00003232809926, .00003557970376, .00008581782553, .00002961847494, .00001478700432, -.00008727552546, -.00012994173168, -.00094120116335, .00001470659469, -.00001098678322, -.00001977796199, .00008956037831, -.00003784800308, 7.059546860e-06, .00008151950631, .00006348047144, .00010852497856, .00009624187488, .00010823787214, .00009132957164, .00074787094553, -.00018137297337, .00006618473561, .00005110284341, -.00003784800308, .00113639967508, .00013313518183, .00019039509438, .0002000965573, 7.191780465e-06, .00002329093697, -.00005087978271, .00009086571425, -.00495748724374, -8.404214163e-06, -.00002158670034, -.00003232809926, 7.059546860e-06, .00013313518183, .00094934117212, .00006195450052, .00011810217311, .00025505395817, .00011081126685, .00030134673539, .00030676742472, .00155300401754, -.000116495836, 8.107545213e-07, .00003557970376, .00008151950631, .00019039509438, .00006195450052, .00267430918731, .00086135304709, .00092017339035, .00095567351479, .000887006474, .00102883960359, .0003167617596, -.00019098604401, .00003255315461, .00008581782553, .00006348047144, .0002000965573, .00011810217311, .00086135304709, .00248135727768, .0009302682109, .0008777378644, .00081079994623, .00094288525746, -.00207087031796, -.00012670601919, -.00002143051924, .00002961847494, .00010852497856, 7.191780465e-06, .00025505395817, .00092017339035, .0009302682109, .00229714087159, .00117701812554, .00109484405919, .00129252524238, .00250083573173, -.00008672920733, -.0000597535309, .00001478700432, .00009624187488, .00002329093697, .00011081126685, .00095567351479, .0008777378644, .00117701812554, .00373628346107, .00123495172035, .00154490399953, .00600809353679, -.00031350033095, -.00001402380853, -.00008727552546, .00010823787214, -.00005087978271, .00030134673539, .000887006474, .00081079994623, .00109484405919, .00123495172035, .00307601153815, .0018118788444, .00430884303498, -.00062509206531, .00001385883996, -.00012994173168, .00009132957164, .00009086571425, .00030676742472, .00102883960359, .00094288525746, .00129252524238, .00154490399953, .0018118788444, .00370260147796, .00534911865442, .00258704275396, -.00142630446035, -.00094120116335, .00074787094553, -.00495748724374, .00155300401754, .0003167617596, -.00207087031796, .00250083573173, .00600809353679, .00430884303498, .00534911865442, .11224703913325]).reshape(13, 13) cov_colnames = ['_cons'] * 13 cov_rownames = ['_cons'] * 13 results_onestep = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) statsmodels-0.12.2/statsmodels/sandbox/regression/tests/results_gmm_griliches_iter.py000066400000000000000000000157471400612667500314740ustar00rootroot00000000000000import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch est = dict( rank=13, N=758, Q=.0150568875809373, J=11.41312078635046, J_df=2, k_1=13, converged=1, has_xtinst=0, type=1, n_eq=1, k=13, n_moments=15, k_aux=13, k_eq_model=0, ic=6, k_eq=13, cmdline="gmm (lw - {xb:s iq expr tenure rns smsa dyear*} - {b0}) , instruments(expr tenure rns smsa dyear* med kww age mrt) igmm", # noqa:E501 cmd="gmm", estat_cmd="gmm_estat", predict="gmm_p", marginsnotok="_ALL", eqnames="1", technique="gn", winit="Unadjusted", estimator="igmm", wmatrix="robust", vce="robust", vcetype="Robust", params="xb_s xb_iq xb_expr xb_tenure xb_rns xb_smsa xb_dyear_67 xb_dyear_68 xb_dyear_69 xb_dyear_70 xb_dyear_71 xb_dyear_73 b0", # noqa:E501 inst_1="expr tenure rns smsa dyear_67 dyear_68 dyear_69 dyear_70 dyear_71 dyear_73 med kww age mrt _cons", # noqa:E501 params_1="xb_s xb_iq xb_expr xb_tenure xb_rns xb_smsa xb_dyear_67 xb_dyear_68 xb_dyear_69 xb_dyear_70 xb_dyear_71 xb_dyear_73 b0", # noqa:E501 sexp_1="lw - ({xb_s} *s + {xb_iq} *iq + {xb_expr} *expr + {xb_tenure} *tenure + {xb_rns} *rns + {xb_smsa} *smsa + {xb_dyear_67} *dyear_67 + {xb_dyear_68} *dyear_68 + {xb_dyear_69} *dyear_69 + {xb_dyear_70} *dyear_70 + {xb_dyear_71} *dyear_71 + {xb_dyear_73} *dyear_73) - {b0}", # noqa:E501 properties="b V", ) params_table = np.array([ .17587739850768, .02085563162829, 8.4330890400415, 3.366583555e-17, .1350011116414, .21675368537396, np.nan, 1.9599639845401, 0, -.00928586712743, .00491894287617, -1.88777697997, .05905589683705, -.01892681800673, .00035508375188, np.nan, 1.9599639845401, 0, .05031651549731, .00810558790493, 6.2076330659127, 5.378855978e-10, .03442985513012, .0662031758645, np.nan, 1.9599639845401, 0, .04246235782951, .00956418082077, 4.4397276280375, 9.007280073e-06, .02371690787918, .06120780777985, np.nan, 1.9599639845401, 0, -.1039476753865, .03373281188749, -3.0815004611293, .00205960157647, -.17006277178325, -.03783257898975, np.nan, 1.9599639845401, 0, .12477256813508, .03099244898605, 4.0259021864082, .0000567572801, .06402848432973, .18551665194043, np.nan, 1.9599639845401, 0, -.05297127223127, .0517946935923, -1.0227162003936, .30644204936546, -.15448700626247, .04854446179993, np.nan, 1.9599639845401, 0, .04564516152971, .05001865637643, .91256272831865, .36147256434055, -.05238960352318, .1436799265826, np.nan, 1.9599639845401, 0, .15574543741982, .04802004585645, 3.2433421218593, .00118136262363, .06162787700523, .24986299783442, np.nan, 1.9599639845401, 0, .16681173496168, .06134387289984, 2.7192892635594, .00654223677971, .0465799534058, .28704351651757, np.nan, 1.9599639845401, 0, .08417610675323, .05582688740597, 1.507805838092, .13160422753823, -.02524258193145, .19359479543791, np.nan, 1.9599639845401, 0, .09964580476612, .06124947866865, 1.6268841291727, .10376170930541, -.02040096749628, .21969257702853, np.nan, 1.9599639845401, 0, 4.0027753075622, .33649589464938, 11.895465505554, 1.249543428e-32, 3.3432554731038, 4.6622951420205, np.nan, 1.9599639845401, 0]).reshape(13, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['_cons'] * 13 cov = np.array([ .00043495737061, -.00007938790704, .00002809207919, .00001486824321, -.00017806650894, -6.696078938e-06, -.00011595347261, -.00018816769626, -.00012205118386, -.00008281236274, -.00031504876539, -.00063574245306, .00264272738846, -.00007938790704, .00002419599902, 4.932871670e-06, -.00001114848619, .00006618803917, -.00002202930782, 4.808220835e-07, .00003206765662, -.00002261059773, -.00006024105579, -.00001412126593, .00001474591556, -.00144330101198, .00002809207919, 4.932871670e-06, .00006570055528, -.0000203894891, .00005213529923, -.00003297805448, .00003595284891, .00008758906787, .00003058926358, .00001696423798, -.00008568569767, -.00013140753648, -.00094326672008, .00001486824321, -.00001114848619, -.0000203894891, .00009147355477, -.00003774547245, 7.828122784e-06, .00008484461309, .00006729820252, .00011236802193, .00010082715772, .00011217081931, .00009440153548, .00075659901252, -.00017806650894, .00006618803917, .00005213529923, -.00003774547245, .00113790259784, .00013005865302, .00018021354375, .00018779266096, -9.435310865e-06, .0000165483542, -.00005323328914, .00008265052168, -.00499436873124, -6.696078938e-06, -.00002202930782, -.00003297805448, 7.828122784e-06, .00013005865302, .00096053189415, .00005704546746, .00011160225767, .00025285680201, .00010656723202, .00030213005331, .00030792696913, .00157128168902, -.00011595347261, 4.808220835e-07, .00003595284891, .00008484461309, .00018021354375, .00005704546746, .00268269028432, .00085942321667, .00091151417222, .00096327250114, .00090372304081, .00102768195348, .00034563629591, -.00018816769626, .00003206765662, .00008758906787, .00006729820252, .00018779266096, .00011160225767, .00085942321667, .0025018659857, .00092591134763, .00088266305412, .0008241186538, .00095084381197, -.00206285154639, -.00012205118386, -.00002261059773, .00003058926358, .00011236802193, -9.435310865e-06, .00025285680201, .00091151417222, .00092591134763, .00230592480406, .00118265696692, .0011106470199, .00129290662149, .00256049741814, -.00008281236274, -.00006024105579, .00001696423798, .00010082715772, .0000165483542, .00010656723202, .00096327250114, .00088266305412, .00118265696692, .00376307074235, .00124584145426, .00155915431219, .00599086304364, -.00031504876539, -.00001412126593, -.00008568569767, .00011217081931, -.00005323328914, .00030213005331, .00090372304081, .0008241186538, .0011106470199, .00124584145426, .00311664135744, .0018437604357, .00431259131307, -.00063574245306, .00001474591556, -.00013140753648, .00009440153548, .00008265052168, .00030792696913, .00102768195348, .00095084381197, .00129290662149, .00155915431219, .0018437604357, .00375149863718, .00538769349865, .00264272738846, -.00144330101198, -.00094326672008, .00075659901252, -.00499436873124, .00157128168902, .00034563629591, -.00206285154639, .00256049741814, .00599086304364, .00431259131307, .00538769349865, .11322948711589]).reshape(13, 13) cov_colnames = ['_cons'] * 13 cov_rownames = ['_cons'] * 13 results = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) statsmodels-0.12.2/statsmodels/sandbox/regression/tests/results_gmm_poisson.py000066400000000000000000000613601400612667500301620ustar00rootroot00000000000000import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch est = dict( rank=8, N=3629, Q=4.59536484786e-20, J=1.66765790329e-16, J_df=0, k_1=8, converged=1, has_xtinst=0, type=1, n_eq=1, k=8, n_moments=8, k_aux=8, k_eq_model=0, k_eq=8, cmdline="gmm ( docvis - exp({xb:private medicaid aget aget2 educyr actlim totchr}+{b0})), instruments(incomet ssiratio aget aget2 educyr actlim totchr) onestep vce(robust)", # noqa:E501 cmd="gmm", estat_cmd="gmm_estat", predict="gmm_p", marginsnotok="_ALL", eqnames="1", technique="gn", winit="Unadjusted", estimator="onestep", wmatrix="robust", vce="robust", vcetype="Robust", params="xb_private xb_medicaid xb_aget xb_aget2 xb_educyr xb_actlim xb_totchr b0", # noqa:E501 inst_1="incomet ssiratio aget aget2 educyr actlim totchr _cons", params_1="xb_private xb_medicaid xb_aget xb_aget2 xb_educyr xb_actlim xb_totchr b0", # noqa:E501 sexp_1="docvis - exp( ({xb_private} *private + {xb_medicaid} *medicaid + {xb_aget} *aget + {xb_aget2} *aget2 + {xb_educyr} *educyr + {xb_actlim} *actlim + {xb_totchr} *totchr) + {b0} )", # noqa:E501 properties="b V", ) params_table = np.array([ .62093805844748, .35860052573857, 1.731559252928, .08335206643438, -.08190605683724, 1.3237821737322, np.nan, 1.9599639845401, 0, .68895699568302, .43817618784254, 1.5723286997298, .11587434043505, -.1698525513714, 1.5477665427374, np.nan, 1.9599639845401, 0, .25750627258076, .05009451793791, 5.1404082358855, 2.741421857e-07, .15932282159956, .35568972356197, np.nan, 1.9599639845401, 0, -.05352997420414, .01103202674353, -4.8522339048464, 1.220785200e-06, -.07515234929795, -.03190759911034, np.nan, 1.9599639845401, 0, .03106248018916, .01032090201131, 3.0096671933432, .00261534090329, .01083388395902, .05129107641931, np.nan, 1.9599639845401, 0, .14175365608301, .0494498280382, 2.8666157539212, .00414886404159, .04483377408643, .23867353807958, np.nan, 1.9599639845401, 0, .23128095221422, .01565221628818, 14.776243054406, 2.084750820e-49, .20060317201116, .26195873241727, np.nan, 1.9599639845401, 0, .34763567088735, .31615794015526, 1.0995633091379, .27152243570261, -.27202250524333, .96729384701803, np.nan, 1.9599639845401, 0 ]).reshape(8, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['_cons'] * 8 cov = np.array([ .12859433705998, .13265896898444, .00910916927048, -.00144786113189, -.00037337560793, -.00152379041042, -.00336772308907, -.09899309651531, .13265896898444, .19199837159222, .00979636564963, -.00135323134276, .00180599814286, -.00930935415071, -.00460031335865, -.13429156867927, .00910916927048, .00979636564963, .00250946072743, -.00052373946978, 5.155389870e-07, -.00016461502154, -.00025816911604, -.00869892550441, -.00144786113189, -.00135323134276, -.00052373946978, .00012170561407, 8.334416260e-06, -.00002526568199, .00003797456789, .00131001446811, -.00037337560793, .00180599814286, 5.155389870e-07, 8.334416260e-06, .00010652101833, -.00026856403693, -.00003344387872, -.00122933496346, -.00152379041042, -.00930935415071, -.00016461502154, -.00002526568199, -.00026856403693, .00244528549301, .00003610001892, .00527355381855, -.00336772308907, -.00460031335865, -.00025816911604, .00003797456789, -.00003344387872, .00003610001892, .00024499187473, .00300075896709, -.09899309651531, -.13429156867927, -.00869892550441, .00131001446811, -.00122933496346, .00527355381855, .00300075896709, .09995584312322 ]).reshape(8, 8) cov_colnames = ['_cons'] * 8 cov_rownames = ['_cons'] * 8 results_addonestep = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=8, N=3629, Q=6.09567389485e-33, J=2.21212005644e-29, J_df=0, k_1=8, converged=1, has_xtinst=0, type=1, n_eq=1, k=8, n_moments=8, k_aux=8, k_eq_model=0, k_eq=8, cmdline="gmm ( docvis - exp({xb:private medicaid aget aget2 educyr actlim totchr}+{b0})), instruments(incomet ssiratio aget aget2 educyr actlim totchr) twostep vce(robust)", # noqa:E501 cmd="gmm", estat_cmd="gmm_estat", predict="gmm_p", marginsnotok="_ALL", eqnames="1", technique="gn", winit="Unadjusted", estimator="twostep", wmatrix="robust", vce="robust", vcetype="Robust", params="xb_private xb_medicaid xb_aget xb_aget2 xb_educyr xb_actlim xb_totchr b0", # noqa:E501 inst_1="incomet ssiratio aget aget2 educyr actlim totchr _cons", params_1="xb_private xb_medicaid xb_aget xb_aget2 xb_educyr xb_actlim xb_totchr b0", # noqa:E501 sexp_1="docvis - exp( ({xb_private} *private + {xb_medicaid} *medicaid + {xb_aget} *aget + {xb_aget2} *aget2 + {xb_educyr} *educyr + {xb_actlim} *actlim + {xb_totchr} *totchr) + {b0} )", # noqa:E501 properties="b V", ) params_table = np.array([ .6209380584426, .35860052570457, 1.7315592530786, .08335206640755, -.08190605677548, 1.3237821736607, np.nan, 1.9599639845401, 0, .68895699501744, .43817618789764, 1.5723286980131, .11587434083298, -.16985255214498, 1.5477665421799, np.nan, 1.9599639845401, 0, .25750627271754, .05009451794125, 5.1404082382732, 2.741421823e-07, .15932282172979, .35568972370529, np.nan, 1.9599639845401, 0, -.05352997423123, .01103202674378, -4.8522339071944, 1.220785186e-06, -.07515234932551, -.03190759913694, np.nan, 1.9599639845401, 0, .03106248018903, .01032090201422, 3.0096671924822, .0026153409107, .01083388395319, .05129107642488, np.nan, 1.9599639845401, 0, .14175365616691, .04944982804302, 2.8666157553386, .00414886402301, .04483377416089, .23867353817294, np.nan, 1.9599639845401, 0, .23128095224221, .01565221628892, 14.776243055497, 2.084750786e-49, .20060317203771, .26195873244672, np.nan, 1.9599639845401, 0, .34763567064032, .31615794015859, 1.099563308345, .27152243604826, -.27202250549689, .96729384677754, np.nan, 1.9599639845401, 0 ]).reshape(8, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['_cons'] * 8 cov = np.array([ .12859433703559, .1326589689683, .00910916927021, -.00144786113188, -.00037337560766, -.00152379040753, -.00336772308885, -.09899309649807, .1326589689683, .1919983716405, .00979636565235, -.00135323134324, .00180599814488, -.00930935415256, -.00460031335946, -.13429156869395, .00910916927021, .00979636565235, .00250946072777, -.00052373946983, 5.155391569e-07, -.00016461502162, -.00025816911611, -.00869892550672, -.00144786113188, -.00135323134324, -.00052373946983, .00012170561408, 8.334416227e-06, -.00002526568198, .0000379745679, .00131001446858, -.00037337560766, .00180599814488, 5.155391569e-07, 8.334416227e-06, .00010652101839, -.00026856403706, -.00003344387875, -.00122933496459, -.00152379040753, -.00930935415256, -.00016461502162, -.00002526568198, -.00026856403706, .00244528549348, .00003610001887, .00527355381795, -.00336772308885, -.00460031335946, -.00025816911611, .0000379745679, -.00003344387875, .00003610001887, .00024499187475, .00300075896724, -.09899309649807, -.13429156869395, -.00869892550672, .00131001446858, -.00122933496459, .00527355381795, .00300075896724, .09995584312533 ]).reshape(8, 8) cov_colnames = ['_cons'] * 8 cov_rownames = ['_cons'] * 8 results_addtwostep = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=8, N=3629, Q=.0002538911897719, J=.9213711276820714, J_df=1, k_1=8, converged=1, has_xtinst=0, type=1, n_eq=1, k=8, n_moments=9, k_aux=8, k_eq_model=0, k_eq=8, cmdline="gmm ( (docvis / exp({xb:private medicaid aget aget2 educyr actlim totchr}+{b0})) - 1), instruments(income ssiratio medicaid aget aget2 educyr actlim totchr) onestep vce(robust)", # noqa:E501 cmd="gmm", estat_cmd="gmm_estat", predict="gmm_p", marginsnotok="_ALL", eqnames="1", technique="gn", winit="Unadjusted", estimator="onestep", wmatrix="robust", vce="robust", vcetype="Robust", params="xb_private xb_medicaid xb_aget xb_aget2 xb_educyr xb_actlim xb_totchr b0", # noqa:E501 inst_1="income ssiratio medicaid aget aget2 educyr actlim totchr _cons", params_1="xb_private xb_medicaid xb_aget xb_aget2 xb_educyr xb_actlim xb_totchr b0", # noqa:E501 sexp_1="(docvis / exp( ({xb_private} *private + {xb_medicaid} *medicaid + {xb_aget} *aget + {xb_aget2} *aget2 + {xb_educyr} *educyr + {xb_actlim} *actlim + {xb_totchr} *totchr) + {b0} )) - 1", # noqa:E501 properties="b V", ) params_table = np.array([ .67045580921478, .25039046077656, 2.6776411814389, .00741425985435, .17969952402034, 1.1612120944092, np.nan, 1.9599639845401, 0, .28551241628798, .10358919281318, 2.7561988710819, .00584774303307, .08248132918657, .4885435033894, np.nan, 1.9599639845401, 0, .2672004738793, .05203985579809, 5.1345352476769, 2.828420839e-07, .16520423075439, .36919671700421, np.nan, 1.9599639845401, 0, -.0560702624564, .01191485946838, -4.7059105149509, 2.527353692e-06, -.07942295789528, -.03271756701753, np.nan, 1.9599639845401, 0, .01448379701656, .00782559934942, 1.8508227127214, .06419506241955, -.00085409586574, .02982168989887, np.nan, 1.9599639845401, 0, .18130374188096, .0382173439987, 4.7440173206998, 2.095209222e-06, .10639912405874, .25620835970318, np.nan, 1.9599639845401, 0, .28146161235562, .01380395117777, 20.389931022715, 2.054354003e-92, .25440636520284, .30851685950839, np.nan, 1.9599639845401, 0, .51399857133918, .10262653035745, 5.0084375799215, 5.487366567e-07, .31285426798028, .71514287469808, np.nan, 1.9599639845401, 0 ]).reshape(8, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['_cons'] * 8 cov = np.array([ .0626953828479, .02323594786658, .00535172023578, -.00103050587759, -.00154311442856, .00154515839603, -.00043159973572, -.01570852578318, .02323594786658, .01073072086769, .00207768328305, -.00039713375955, -.00049396171685, .00027652302157, -.00020408147523, -.00701276303887, .00535172023578, .00207768328305, .00270814659149, -.00059652725999, -.00012298559534, .00021079055266, -.00004341699196, -.0031278522429, -.00103050587759, -.00039713375955, -.00059652725999, .00014196387615, .00002481291175, -.00006035908648, .00001093157006, .00059187926133, -.00154311442856, -.00049396171685, -.00012298559534, .00002481291175, .00006124000518, -.00001857594061, .00001436652009, .00008106194688, .00154515839603, .00027652302157, .00021079055266, -.00006035908648, -.00001857594061, .00146056538231, -.00016708887634, -.00074321753343, -.00043159973572, -.00020408147523, -.00004341699196, .00001093157006, .00001436652009, -.00016708887634, .00019054906812, -.00028024031412, -.01570852578318, -.00701276303887, -.0031278522429, .00059187926133, .00008106194688, -.00074321753343, -.00028024031412, .01053220473321 ]).reshape(8, 8) cov_colnames = ['_cons'] * 8 cov_rownames = ['_cons'] * 8 results_multonestep = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=8, N=3629, Q=.0002589826272982, J=.9398479544653281, J_df=1, k_1=8, converged=1, has_xtinst=0, type=1, n_eq=1, k=8, n_moments=9, k_aux=8, k_eq_model=0, k_eq=8, cmdline="gmm ( (docvis / exp({xb:private medicaid aget aget2 educyr actlim totchr}+{b0})) - 1), instruments(income ssiratio medicaid aget aget2 educyr actlim totchr) twostep vce(robust)", # noqa:E501 cmd="gmm", estat_cmd="gmm_estat", predict="gmm_p", marginsnotok="_ALL", eqnames="1", technique="gn", winit="Unadjusted", estimator="twostep", wmatrix="robust", vce="robust", vcetype="Robust", params="xb_private xb_medicaid xb_aget xb_aget2 xb_educyr xb_actlim xb_totchr b0", # noqa:E501 inst_1="income ssiratio medicaid aget aget2 educyr actlim totchr _cons", params_1="xb_private xb_medicaid xb_aget xb_aget2 xb_educyr xb_actlim xb_totchr b0", # noqa:E501 sexp_1="(docvis / exp( ({xb_private} *private + {xb_medicaid} *medicaid + {xb_aget} *aget + {xb_aget2} *aget2 + {xb_educyr} *educyr + {xb_actlim} *actlim + {xb_totchr} *totchr) + {b0} )) - 1", # noqa:E501 properties="b V", ) params_table = np.array([ .67815288158883, .25053953449054, 2.7067699433856, .00679413212727, .18710441728393, 1.1692013458937, np.nan, 1.9599639845401, 0, .28872837589732, .1032733938985, 2.7957672833051, .00517766683505, .08631624329503, .49114050849961, np.nan, 1.9599639845401, 0, .27067071818542, .05199695467114, 5.2055109745809, 1.934635127e-07, .16875855972422, .37258287664662, np.nan, 1.9599639845401, 0, -.05690856524563, .01189861686254, -4.7827882772482, 1.728801925e-06, -.08022942576205, -.03358770472921, np.nan, 1.9599639845401, 0, .01438118999252, .00783219080428, 1.8361644081315, .06633334485657, -.00096962190392, .02973200188896, np.nan, 1.9599639845401, 0, .18038262255626, .03826653224544, 4.7138481584715, 2.430818311e-06, .10538159754195, .25538364757056, np.nan, 1.9599639845401, 0, .28251027986119, .01378475918788, 20.494393555287, 2.415775858e-93, .25549264831739, .30952791140498, np.nan, 1.9599639845401, 0, .5077134442587, .10235830367214, 4.9601588346456, 7.043556343e-07, .30709485554269, .7083320329747, np.nan, 1.9599639845401, 0 ]).reshape(8, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['_cons'] * 8 cov = np.array([ .06277005834274, .02315710174743, .00533574120292, -.00102544979294, -.00154463417995, .0015508406274, -.00043796451278, -.01559999387335, .02315710174743, .01066539388732, .00206217803508, -.00039331197813, -.00049172930967, .00027603135609, -.00020644763374, -.00694810289238, .00533574120292, .00206217803508, .00270368329507, -.0005950942106, -.00012276584915, .00021462173623, -.00004681980342, -.00310767551047, -.00102544979294, -.00039331197813, -.0005950942106, .00014157708324, .00002474211336, -.00006134660609, .00001178280314, .00058658157366, -.00154463417995, -.00049172930967, -.00012276584915, .00002474211336, .00006134321279, -.00001855941375, .00001443470174, .0000776612477, .0015508406274, .00027603135609, .00021462173623, -.00006134660609, -.00001855941375, .00146432749009, -.00016643326394, -.00074847803836, -.00043796451278, -.00020644763374, -.00004681980342, .00001178280314, .00001443470174, -.00016643326394, .00019001958587, -.00027573517109, -.01559999387335, -.00694810289238, -.00310767551047, .00058658157366, .0000776612477, -.00074847803836, -.00027573517109, .01047722233064 ]).reshape(8, 8) cov_colnames = ['_cons'] * 8 cov_rownames = ['_cons'] * 8 results_multtwostep = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=8, N=3629, Q=.0002590497181628, J=.940091427212973, J_df=1, k_1=8, converged=1, has_xtinst=0, type=1, n_eq=1, k=8, n_moments=9, k_aux=8, k_eq_model=0, k_eq=8, cmdline="gmm ( (docvis / exp({xb:private medicaid aget aget2 educyr actlim totchr}+{b0})) - 1), instruments(income ssiratio medicaid aget aget2 educyr actlim totchr) twostep wmatrix(robust) vce(unadjusted) center", # noqa:E501 cmd="gmm", estat_cmd="gmm_estat", predict="gmm_p", marginsnotok="_ALL", eqnames="1", technique="gn", winit="Unadjusted", estimator="twostep", wmatrix="robust", vce="unadjusted", params="xb_private xb_medicaid xb_aget xb_aget2 xb_educyr xb_actlim xb_totchr b0", # noqa:E501 inst_1="income ssiratio medicaid aget aget2 educyr actlim totchr _cons", params_1="xb_private xb_medicaid xb_aget xb_aget2 xb_educyr xb_actlim xb_totchr b0", # noqa:E501 sexp_1="(docvis / exp( ({xb_private} *private + {xb_medicaid} *medicaid + {xb_aget} *aget + {xb_aget2} *aget2 + {xb_educyr} *educyr + {xb_actlim} *actlim + {xb_totchr} *totchr) + {b0} )) - 1", # noqa:E501 properties="b V", ) params_table = np.array([ .67815486150911, .25018082946574, 2.7106587781218, .00671496899138, .1878094461339, 1.1685002768843, np.nan, 1.9599639845401, 0, .28872920226215, .10311429027815, 2.8000891193967, .00510884999633, .08662890702558, .49082949749873, np.nan, 1.9599639845401, 0, .27067161407481, .0518802415232, 5.2172388972735, 1.816099638e-07, .16898820918009, .37235501896953, np.nan, 1.9599639845401, 0, -.05690878166227, .0118728670827, -4.7931793783164, 1.641587211e-06, -.08017917353758, -.03363838978695, np.nan, 1.9599639845401, 0, .01438116368432, .00781887593806, 1.8392878718448, .0658728559523, -.00094355155385, .0297058789225, np.nan, 1.9599639845401, 0, .18038238197017, .03819661477822, 4.7224703816696, 2.329970297e-06, .10551839267351, .25524637126682, np.nan, 1.9599639845401, 0, .28251055147828, .01376659609161, 20.521452768591, 1.385109204e-93, .25552851894901, .30949258400755, np.nan, 1.9599639845401, 0, .50771182444237, .10208891085993, 4.9732318639284, 6.584582712e-07, .30762123593598, .70780241294876, np.nan, 1.9599639845401, 0 ]).reshape(8, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['xb_private', 'xb_medicaid', 'xb_aget', 'xb_aget2', 'xb_educyr', 'xb_actlim', 'xb_totchr', 'b0'] cov = np.array([ .06259044743217, .02308524749042, .00531802921719, -.0010223122446, -.00154027662468, .00154945994717, -.00043816683551, -.01554486097815, .02308524749042, .01063255685957, .00205438168765, -.00039193802388, -.00049039628782, .0002760841411, -.0002064504141, -.00691934867666, .00531802921719, .00205438168765, .00269155946051, -.00059250696972, -.00012247118567, .00021403084056, -.00004749600121, -.00308951213731, -.0010223122446, -.00039193802388, -.00059250696972, .00014096497276, .00002468288871, -.00006115240604, .00001190303672, .00058327928125, -.00154027662468, -.00049039628782, -.00012247118567, .00002468288871, .00006113482093, -.00001854325518, .00001439868646, .00007784185009, .00154945994717, .0002760841411, .00021403084056, -.00006115240604, -.00001854325518, .00145898138052, -.00016596475072, -.00074697007542, -.00043816683551, -.0002064504141, -.00004749600121, .00001190303672, .00001439868646, -.00016596475072, .00018951916795, -.00027350320218, -.01554486097815, -.00691934867666, -.00308951213731, .00058327928125, .00007784185009, -.00074697007542, -.00027350320218, .01042214572057 ]).reshape(8, 8) cov_colnames = ['xb_private', 'xb_medicaid', 'xb_aget', 'xb_aget2', 'xb_educyr', 'xb_actlim', 'xb_totchr', 'b0'] cov_rownames = ['xb_private', 'xb_medicaid', 'xb_aget', 'xb_aget2', 'xb_educyr', 'xb_actlim', 'xb_totchr', 'b0'] results_multtwostepdefault = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( rank=8, N=3629, Q=.0002590497181628, J=.940091427212973, J_df=1, k_1=8, converged=1, has_xtinst=0, type=1, n_eq=1, k=8, n_moments=9, k_aux=8, k_eq_model=0, k_eq=8, cmdline="gmm ( (docvis / exp({xb:private medicaid aget aget2 educyr actlim totchr}+{b0})) - 1), instruments(income ssiratio medicaid aget aget2 educyr actlim totchr) twostep wmatrix(robust) center", # noqa:E501 cmd="gmm", estat_cmd="gmm_estat", predict="gmm_p", marginsnotok="_ALL", eqnames="1", technique="gn", winit="Unadjusted", estimator="twostep", wmatrix="robust", vce="robust", vcetype="Robust", params="xb_private xb_medicaid xb_aget xb_aget2 xb_educyr xb_actlim xb_totchr b0", # noqa:E501 inst_1="income ssiratio medicaid aget aget2 educyr actlim totchr _cons", params_1="xb_private xb_medicaid xb_aget xb_aget2 xb_educyr xb_actlim xb_totchr b0", # noqa:E501 sexp_1="(docvis / exp( ({xb_private} *private + {xb_medicaid} *medicaid + {xb_aget} *aget + {xb_aget2} *aget2 + {xb_educyr} *educyr + {xb_actlim} *actlim + {xb_totchr} *totchr) + {b0} )) - 1", # noqa:E501 properties="b V", ) params_table = np.array([ .67815486150911, .25053960844836, 2.7067770469869, .00679398676131, .18710625224955, 1.1692034707687, np.nan, 1.9599639845401, 0, .28872920226215, .10327332768441, 2.7957770775479, .00517750993835, .08631719943712, .49114120508719, np.nan, 1.9599639845401, 0, .27067161407481, .05199697557915, 5.2055261110869, 1.934477426e-07, .16875941463467, .37258381351495, np.nan, 1.9599639845401, 0, -.05690878166227, .01189862079945, -4.7828048831437, 1.728659059e-06, -.08022964989488, -.03358791342965, np.nan, 1.9599639845401, 0, .01438116368432, .00783219272776, 1.8361605982125, .06633390816397, -.00096965198207, .02973197935072, np.nan, 1.9599639845401, 0, .18038238197017, .03826654814775, 4.71383991244, 2.430916736e-06, .10538132578791, .25538343815243, np.nan, 1.9599639845401, 0, .28251055147828, .01378476509846, 20.494404471929, 2.415234157e-93, .25549290834996, .3095281946066, np.nan, 1.9599639845401, 0, .50771182444237, .10235828870929, 4.960143734762, 7.044103886e-07, .307093265053, .70833038383174, np.nan, 1.9599639845401, 0 ]).reshape(8, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = ['_cons'] * 8 cov = np.array([ .06277009540146, .02315708886727, .00533574465012, -.0010254503134, -.00154463481696, .00155084007911, -.00043796389511, -.01559997980204, .02315708886727, .01066538021101, .00206217721135, -.00039331175814, -.00049172883672, .00027603038575, -.00020644729789, -.00694809209467, .00533574465012, .00206217721135, .00270368546938, -.00059509464294, -.000122765895, .00021462183651, -.00004681968717, -.003107676362, -.0010254503134, -.00039331175814, -.00059509464294, .00014157717693, .00002474211983, -.00006134664668, .00001178278294, .00058658166731, -.00154463481696, -.00049172883672, -.000122765895, .00002474211983, .00006134324292, -.00001855938213, .00001443468876, .00007766055925, .00155084007911, .00027603038575, .00021462183651, -.00006134664668, -.00001855938213, .00146432870714, -.00016643336248, -.00074847778305, -.00043796389511, -.00020644729789, -.00004681968717, .00001178278294, .00001443468876, -.00016643336248, .00019001974882, -.00027573582025, -.01559997980204, -.00694809209467, -.003107676362, .00058658166731, .00007766055925, -.00074847778305, -.00027573582025, .0104772192675 ]).reshape(8, 8) cov_colnames = ['_cons'] * 8 cov_rownames = ['_cons'] * 8 results_multtwostepcenter = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) statsmodels-0.12.2/statsmodels/sandbox/regression/tests/results_ivreg2_griliches.py000066400000000000000000001075121400612667500310570ustar00rootroot00000000000000import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch param_names = [ 's', 'iq', 'expr', 'tenure', 'rns', 'smsa', 'dyear_67', 'dyear_68', 'dyear_69', 'dyear_70', 'dyear_71', 'dyear_73', '_cons'] est = dict( N=758, inexog_ct=10, exexog_ct=4, endog_ct=2, partial_ct=0, df_m=12, sdofminus=0, dofminus=0, r2=.2279825291623523, rmse=.3766456260250817, rss=107.5313411236999, mss=31.75480871825532, r2_a=.2155473484240278, F=37.63903370585436, Fp=1.04881083780e-68, Fdf1=12, Fdf2=745, yy=24652.2466174172, yyc=139.2861498419552, r2u=.9956380713371686, partialcons=0, cons=1, cdf=12.55161416131593, widstat=12.55161416131593, cd=.0675726199801665, idp=2.15251425210e-10, iddf=3, idstat=47.97804382236573, sarganp=.0013146751383334, sargandf=2, sargan=13.26833137393004, jp=.0013146751383334, jdf=2, j=13.26833137393004, ll=-335.4059158173529, rankV=13, rankxx=13, rankzz=15, r2c=.2279825291623523, hacsubtitleV="Statistics consistent for homoskedasticity only", hacsubtitleB="Estimates efficient for homoskedasticity only", title="IV (2SLS) estimation", predict="ivreg2_p", version="02.2.08", cmdline="ivreg2 lw expr tenure rns smsa dyear* (s iq=med kww age mrt)", cmd="ivreg2", model="iv", depvar="lw", partialsmall="small", exexog="med kww age mrt", inexog="expr tenure rns smsa dyear_67 dyear_68 dyear_69 dyear_70 dyear_71 dyear_73", # noqa:E501 insts="med kww age mrt expr tenure rns smsa dyear_67 dyear_68 dyear_69 dyear_70 dyear_71 dyear_73", # noqa:E501 instd="s iq", properties="b V", ) params_table = np.array([ .17242531190423, .02073807855911, 8.3144304527925, 9.219394861e-17, .13177942481982, .21307119898864, np.nan, 1.9599639845401, 0, -.00909883103476, .00470440157185, -1.9341101935687, .05309958088226, -.01831928868441, .00012162661488, np.nan, 1.9599639845401, 0, .04928948974574, .008154589406, 6.0443864542646, 1.499796319e-09, .03330678820126, .06527219129022, np.nan, 1.9599639845401, 0, .04221709210309, .00884287446052, 4.774136768712, 1.804797032e-06, .02488537664065, .05954880756552, np.nan, 1.9599639845401, 0, -.10179345001799, .03417647128271, -2.9784657747708, .00289695381119, -.16877810285078, -.03480879718521, np.nan, 1.9599639845401, 0, .12611094946923, .03092747922238, 4.0776342799379, .00004549625503, .06549420406076, .18672769487769, np.nan, 1.9599639845401, 0, -.05961710621535, .05529546018534, -1.0781555305902, .28096435347028, -.16799421668718, .04876000425648, np.nan, 1.9599639845401, 0, .04867955999401, .05201609347935, .93585574651683, .34934746462842, -.05327010984199, .15062922983, np.nan, 1.9599639845401, 0, .15281763322545, .0515629903814, 2.9637077309732, .0030395682829, .05175602914272, .25387923730817, np.nan, 1.9599639845401, 0, .17443605148569, .05975759031645, 2.9190610023255, .00351087511908, .05731332666255, .29155877630882, np.nan, 1.9599639845401, 0, .09166596656323, .05414400395495, 1.6930031003894, .09045487706511, -.01445433116727, .19778626429372, np.nan, 1.9599639845401, 0, .09323976497853, .0571819085978, 1.6305815469428, .10297864547348, -.01883471644041, .20531424639747, np.nan, 1.9599639845401, 0, 4.0335098946211, .31542152364325, 12.787681221092, 1.921209213e-37, 3.4152950683316, 4.6517247209107, np.nan, 1.9599639845401, 0]).reshape(13, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = param_names cov = np.array([ .00043006790232, -.00007669911732, .00003390383154, .00001947510761, -.00014211117725, .00001984430949, .00001313809086, -.00010726217801, -.0000934373525, .00003291577926, -.00026067342405, -.00058025280789, .00230075400852, -.00007669911732, .00002213139415, 4.388754481e-06, -8.774272042e-06, .00005855699916, -.00001627155824, -.00001175114527, .00001447038262, -.00001630144788, -.00007254738147, -.0000221423658, .00001715527313, -.00125964216852, .00003390383154, 4.388754481e-06, .00006649732838, -.00001561989737, .00003340985346, -6.286271714e-06, .00004284715305, .00006535720207, .00002474647562, 2.348670591e-06, -.00012774309302, -.00013889592824, -.00097053265371, .00001947510761, -8.774272042e-06, -.00001561989737, .00007819642872, -.00001656102532, -1.454183906e-06, .00006415542548, .0000658729123, .00007759572764, .00006755177717, .00006035533972, .00007925563165, .00048915076309, -.00014211117725, .00005855699916, .00003340985346, -.00001656102532, .00116803118934, .00009910080232, .00010687488928, .0000916567869, -.00004794231232, -.00018139826234, -.00013904727086, -.00016941373862, -.00453388036786, .00001984430949, -.00001627155824, -6.286271714e-06, -1.454183906e-06, .00009910080232, .00095650897105, 2.293607157e-06, -4.175180521e-06, .00008023363682, .0000277191399, .00011455631826, 7.627834100e-06, .00071035658346, .00001313809086, -.00001175114527, .00004284715305, .00006415542548, .00010687488928, 2.293607157e-06, .00305758791711, .00082806878751, .00084056268139, .00086879959596, .00072687243235, .00079702544855, .00005969922435, -.00010726217801, .00001447038262, .00006535720207, .0000658729123, .0000916567869, -4.175180521e-06, .00082806878751, .00270567398085, .00090000327564, .0008652672979, .00075215815711, .00093055832029, -.0011308128858, -.0000934373525, -.00001630144788, .00002474647562, .00007759572764, -.00004794231232, .00008023363682, .00084056268139, .00090000327564, .00265874197707, .00106768253686, .00097403133741, .00118960267354, .00179874271988, .00003291577926, -.00007254738147, 2.348670591e-06, .00006755177717, -.00018139826234, .0000277191399, .00086879959596, .0008652672979, .00106768253686, .00357096960043, .00115404290469, .00134956217212, .00598978065251, -.00026067342405, -.0000221423658, -.00012774309302, .00006035533972, -.00013904727086, .00011455631826, .00072687243235, .00075215815711, .00097403133741, .00115404290469, .00293157316427, .00171538928992, .0048030008792, -.00058025280789, .00001715527313, -.00013889592824, .00007925563165, -.00016941373862, 7.627834100e-06, .00079702544855, .00093055832029, .00118960267354, .00134956217212, .00171538928992, .00326977067089, .00483241607215, .00230075400852, -.00125964216852, -.00097053265371, .00048915076309, -.00453388036786, .00071035658346, .00005969922435, -.0011308128858, .00179874271988, .00598978065251, .0048030008792, .00483241607215, .09949073757743]).reshape(13, 13) cov_colnames = param_names cov_rownames = param_names results = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( N=758, inexog_ct=10, exexog_ct=4, endog_ct=2, partial_ct=0, df_m=12, sdofminus=0, dofminus=0, r2=.2279825291623523, rmse=.3766456260250817, rss=107.5313411236999, mss=31.75480871825532, r2_a=.2155473484240278, F=40.08955571761713, Fp=1.50331141073e-72, Fdf1=12, Fdf2=745, yy=24652.2466174172, yyc=139.2861498419552, r2u=.9956380713371686, partialcons=0, cons=1, cdf=12.55161416131593, widstat=11.46142788662503, cd=.0675726199801665, idp=6.77658650925e-09, iddf=3, idstat=40.92698219921901, jp=.0030253131145893, jdf=2, j=11.60148136780177, ll=-335.4059158173529, rankV=13, rankS=15, rankxx=13, rankzz=15, r2c=.2279825291623523, hacsubtitleV="Statistics robust to heteroskedasticity", hacsubtitleB="Estimates efficient for homoskedasticity only", title="IV (2SLS) estimation", predict="ivreg2_p", version="02.2.08", cmdline="ivreg2 lw expr tenure rns smsa dyear* (s iq=med kww age mrt), robust", # noqa:E501 cmd="ivreg2", model="iv", depvar="lw", vcetype="Robust", partialsmall="small", exexog="med kww age mrt", inexog="expr tenure rns smsa dyear_67 dyear_68 dyear_69 dyear_70 dyear_71 dyear_73", # noqa:E501 insts="med kww age mrt expr tenure rns smsa dyear_67 dyear_68 dyear_69 dyear_70 dyear_71 dyear_73", # noqa:E501 instd="s iq", properties="b V", ) params_table = np.array([ .17242531190423, .02073946970741, 8.3138727429773, 9.262847918e-17, .13177669821925, .21307392558922, np.nan, 1.9599639845401, 0, -.00909883103476, .00488623921475, -1.862133766863, .06258423744885, -.01867568391553, .000478021846, np.nan, 1.9599639845401, 0, .04928948974574, .00804979771814, 6.1230718424932, 9.178828239e-10, .03351217613534, .06506680335614, np.nan, 1.9599639845401, 0, .04221709210309, .00946363451747, 4.4609808235038, 8.158539136e-06, .02366870928599, .06076547492018, np.nan, 1.9599639845401, 0, -.10179345001799, .03371052765435, -3.0196338384772, .0025308044732, -.16786487012036, -.03572202991563, np.nan, 1.9599639845401, 0, .12611094946923, .03081138055695, 4.0929989889975, .0000425829578, .06572175326364, .18650014567481, np.nan, 1.9599639845401, 0, -.05961710621535, .05171372338658, -1.1528295065836, .24898037077447, -.16097414155951, .04173992912881, np.nan, 1.9599639845401, 0, .04867955999401, .04981322391886, .97724170740882, .32844950437829, -.04895256484079, .14631168482881, np.nan, 1.9599639845401, 0, .15281763322545, .04792849748217, 3.1884503219051, .00143037585571, .05887950432728, .24675576212361, np.nan, 1.9599639845401, 0, .17443605148569, .06112514588945, 2.8537527223437, .00432061472656, .0546329669926, .29423913597877, np.nan, 1.9599639845401, 0, .09166596656323, .05546180250571, 1.6527765492979, .09837634843385, -.01703716886563, .20036910199209, np.nan, 1.9599639845401, 0, .09323976497853, .06084900555321, 1.5323137022675, .12544504141872, -.02602209440084, .21250162435791, np.nan, 1.9599639845401, 0, 4.0335098946211, .33503289255951, 12.039145959093, 2.212341116e-33, 3.3768574915682, 4.6901622976741, np.nan, 1.9599639845401, 0]).reshape(13, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = param_names cov = np.array([ .00043012560374, -.00007821948167, .00002814664043, .00001470659468, -.0001813729733, -8.404214148e-06, -.00011649583596, -.000190986044, -.0001267060192, -.00008672920729, -.00031350033086, -.00062509206513, .00258704275336, -.00007821948167, .00002387533366, 4.911669726e-06, -.00001098678321, .00006618473559, -.00002158670033, 8.107545182e-07, .00003255315461, -.00002143051923, -.00005975353088, -.00001402380853, .00001385883995, -.00142630445991, .00002814664043, 4.911669726e-06, .0000647992433, -.00001977796198, .00005110284339, -.00003232809925, .00003557970375, .00008581782551, .00002961847493, .00001478700432, -.00008727552542, -.00012994173162, -.000941201163, .00001470659468, -.00001098678321, -.00001977796198, .00008956037828, -.00003784800305, 7.059546852e-06, .0000815195063, .00006348047141, .00010852497853, .00009624187487, .0001082378721, .0000913295716, .00074787094515, -.0001813729733, .00006618473559, .00005110284339, -.00003784800305, .00113639967473, .0001331351818, .00019039509428, .00020009655722, 7.191780470e-06, .00002329093699, -.00005087978262, .00009086571417, -.0049574872418, -8.404214148e-06, -.00002158670033, -.00003232809925, 7.059546852e-06, .0001331351818, .00094934117183, .00006195450043, .00011810217306, .00025505395801, .00011081126682, .0003013467353, .00030676742453, .00155300401661, -.00011649583596, 8.107545182e-07, .00003557970375, .0000815195063, .00019039509428, .00006195450043, .0026743091865, .00086135304687, .00092017339013, .00095567351458, .00088700647379, .00102883960334, .00031676175972, -.000190986044, .00003255315461, .00008581782551, .00006348047141, .00020009655722, .00011810217306, .00086135304687, .00248135727719, .00093026821071, .00087773786421, .00081079994607, .0009428852573, -.00207087031744, -.0001267060192, -.00002143051923, .00002961847493, .00010852497853, 7.191780470e-06, .00025505395801, .00092017339013, .00093026821071, .0022971408709, .00117701812528, .00109484405896, .00129252524214, .00250083573092, -.00008672920729, -.00005975353088, .00001478700432, .00009624187487, .00002329093699, .00011081126682, .00095567351458, .00087773786421, .00117701812528, .00373628346001, .00123495172003, .00154490399913, .00600809353497, -.00031350033086, -.00001402380853, -.00008727552542, .0001082378721, -.00005087978262, .0003013467353, .00088700647379, .00081079994607, .00109484405896, .00123495172003, .00307601153718, .00181187884386, .00430884303329, -.00062509206513, .00001385883995, -.00012994173162, .0000913295716, .00009086571417, .00030676742453, .00102883960334, .0009428852573, .00129252524214, .00154490399913, .00181187884386, .00370260147681, .00534911865268, .00258704275336, -.00142630445991, -.000941201163, .00074787094515, -.0049574872418, .00155300401661, .00031676175972, -.00207087031744, .00250083573092, .00600809353497, .00430884303329, .00534911865268, .11224703909679]).reshape(13, 13) cov_colnames = param_names cov_rownames = param_names results_robust = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( N=758, inexog_ct=10, exexog_ct=4, endog_ct=2, partial_ct=0, df_r=745, df_m=12, sdofminus=0, dofminus=0, r2=.2279825291623523, rmse=.3799175840045295, rss=107.5313411236999, mss=31.75480871825532, r2_a=.2155473484240278, F=37.63903370585438, Fp=1.04881083780e-68, Fdf1=12, Fdf2=745, yy=24652.2466174172, yyc=139.2861498419552, partialcons=0, cons=1, cdf=12.55161416131593, widstat=12.55161416131593, cd=.0675726199801665, idp=2.15251425210e-10, iddf=3, idstat=47.97804382236573, sarganp=.0013146751383334, sargandf=2, sargan=13.26833137393004, jp=.0013146751383334, jdf=2, j=13.26833137393004, ll=-335.4059158173529, rankV=13, rankxx=13, rankzz=15, r2c=.2279825291623523, r2u=.9956380713371686, hacsubtitleV="Statistics consistent for homoskedasticity only", hacsubtitleB="Estimates efficient for homoskedasticity only", title="IV (2SLS) estimation", predict="ivreg2_p", version="02.2.08", cmdline="ivreg2 lw expr tenure rns smsa dyear* (s iq=med kww age mrt), small", # noqa:E501 cmd="ivreg2", model="iv", depvar="lw", partialsmall="small", small="small", exexog="med kww age mrt", inexog="expr tenure rns smsa dyear_67 dyear_68 dyear_69 dyear_70 dyear_71 dyear_73", # noqa:E501 insts="med kww age mrt expr tenure rns smsa dyear_67 dyear_68 dyear_69 dyear_70 dyear_71 dyear_73", # noqa:E501 instd="s iq", properties="b V", ) params_table = np.array([ .17242531190423, .02091823230823, 8.2428242197305, 7.570254109e-16, .13135961443277, .2134910093757, 745, 1.9631533327653, 0, -.00909883103476, .00474526917577, -1.917453088061, .055562500369, -.01841452203205, .00021685996252, 745, 1.9631533327653, 0, .04928948974574, .00822542913447, 5.9923304839106, 3.219967401e-09, .03314171112698, .0654372683645, 745, 1.9631533327653, 0, .04221709210309, .00891969338965, 4.7330205488974, 2.647391010e-06, .02470636629795, .05972781790823, 745, 1.9631533327653, 0, -.10179345001799, .03447336568476, -2.9528143828148, .00324794122176, -.16946995275367, -.03411694728232, 745, 1.9631533327653, 0, .12611094946923, .03119614930755, 4.0425165370872, .00005838098525, .06486812498666, .18735377395179, 745, 1.9631533327653, 0, -.05961710621535, .05577581734252, -1.0688701493919, .28547438462206, -.16911358791902, .04987937548832, 745, 1.9631533327653, 0, .04867955999401, .05246796245209, .92779589141575, .35381393703187, -.05432309535722, .15168221534524, 745, 1.9631533327653, 0, .15281763322545, .0520109232025, 2.9381834394759, .00340336072573, .05071221600025, .25492305045064, 745, 1.9631533327653, 0, .17443605148569, .06027671044146, 2.8939212211172, .00391575116799, .0561036264944, .29276847647697, 745, 1.9631533327653, 0, .09166596656323, .05461435829744, 1.678422477547, .09368402236573, -.01555039294523, .19888232607168, 745, 1.9631533327653, 0, .09323976497853, .05767865351978, 1.6165385162217, .10640126701552, -.01999227590824, .20647180586531, 745, 1.9631533327653, 0, 4.0335098946211, .31816162176165, 12.677550083784, 1.723599587e-33, 3.4089098465017, 4.6581099427405, 745, 1.9631533327653, 0]).reshape(13, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = param_names cov = np.array([ .0004375724429, -.00007803749118, .00003449544203, .0000198149417, -.00014459096961, .00002019058603, .00001336734613, -.00010913386703, -.00009506780295, .00003349014856, -.00026522208782, -.00059037802467, .0023409013939, -.00007803749118, .00002251757955, 4.465336774e-06, -8.927380145e-06, .00005957879915, -.00001655549147, -.00001195619881, .00001472288594, -.00001658590268, -.00007381330893, -.00002252874265, .00001745462689, -.00128162250166, .00003449544203, 4.465336774e-06, .00006765768445, -.00001589245933, .00003399284419, -6.395965046e-06, .0000435948215, .00006649766331, .00002517829331, 2.389654105e-06, -.00012997216713, -.00014131961558, -.00098746812283, .0000198149417, -8.927380145e-06, -.00001589245933, .00007956093017, -.00001685000965, -1.479558927e-06, .00006527491612, .00006702237252, .00007894974705, .00006873053302, .00006140852014, .00008063861583, .00049768627977, -.00014459096961, .00005957879915, .00003399284419, -.00001685000965, .00118841294164, .00010083007806, .00010873982024, .00009325616707, -.00004877888958, -.00018456360114, -.00014147359908, -.00017236995151, -.00461299505884, .00002019058603, -.00001655549147, -6.395965046e-06, -1.479558927e-06, .00010083007806, .00097319973162, 2.333629833e-06, -4.248036020e-06, .00008163368686, .00002820282959, .00011655528757, 7.760937245e-06, .00072275206747, .00001336734613, -.00001195619881, .0000435948215, .00006527491612, .00010873982024, 2.333629833e-06, .00311094180023, .00084251830998, .00085523021811, .00088395985737, .00073955611238, .00081093327517, .00006074095578, -.00010913386703, .00001472288594, .00006649766331, .00006702237252, .00009325616707, -4.248036020e-06, .00084251830998, .00275288708387, .00091570803079, .00088036592189, .00076528306455, .00094679625072, -.00115054519119, -.00009506780295, -.00001658590268, .00002517829331, .00007894974705, -.00004877888958, .00008163368686, .00085523021811, .00091570803079, .00270513613238, .00108631323884, .00099102785739, .001210360841, .00183013017674, .00003349014856, -.00007381330893, 2.389654105e-06, .00006873053302, -.00018456360114, .00002820282959, .00088395985737, .00088036592189, .00108631323884, .00363328182164, .00117418056612, .00137311157915, .0060943003149, -.00026522208782, -.00002252874265, -.00012997216713, .00006140852014, -.00014147359908, .00011655528757, .00073955611238, .00076528306455, .00099102785739, .00117418056612, .00298272813224, .00174532225739, .0048868116328, -.00059037802467, .00001745462689, -.00014131961558, .00008063861583, -.00017236995151, 7.760937245e-06, .00081093327517, .00094679625072, .001210360841, .00137311157915, .00174532225739, .00332682707186, .00491674011099, .0023409013939, -.00128162250166, -.00098746812283, .00049768627977, -.00461299505884, .00072275206747, .00006074095578, -.00115054519119, .00183013017674, .0060943003149, .0048868116328, .00491674011099, .101226817562]).reshape(13, 13) cov_colnames = param_names cov_rownames = param_names # not autogenerated # calculated with `ivendog` after ivreg2 hausman = dict( df_r=743, df=2, WHFp=1.47099195224e-16, WHF=38.30408858936179, DWHp=4.12270104038e-16, DWH=70.84970589405181 ) results_small = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, hausman=hausman, **est ) est = dict( N=758, inexog_ct=10, exexog_ct=4, endog_ct=2, partial_ct=0, df_r=745, df_m=12, sdofminus=0, dofminus=0, r2=.2279825291623523, rmse=.3799175840045295, rss=107.5313411236999, mss=31.75480871825532, r2_a=.2155473484240278, F=40.08955571761724, Fp=1.50331141073e-72, Fdf1=12, Fdf2=745, yy=24652.2466174172, yyc=139.2861498419552, partialcons=0, cons=1, cdf=12.55161416131593, widstat=11.46142788662503, cd=.0675726199801665, idp=6.77658650925e-09, iddf=3, idstat=40.92698219921901, jp=.0030253131145893, jdf=2, j=11.60148136780177, ll=-335.4059158173529, rankV=13, rankS=15, rankxx=13, rankzz=15, r2c=.2279825291623523, r2u=.9956380713371686, hacsubtitleV="Statistics robust to heteroskedasticity", hacsubtitleB="Estimates efficient for homoskedasticity only", title="IV (2SLS) estimation", predict="ivreg2_p", version="02.2.08", cmdline="ivreg2 lw expr tenure rns smsa dyear* (s iq=med kww age mrt), small robust", # noqa:E501 cmd="ivreg2", model="iv", depvar="lw", vcetype="Robust", partialsmall="small", small="small", exexog="med kww age mrt", inexog="expr tenure rns smsa dyear_67 dyear_68 dyear_69 dyear_70 dyear_71 dyear_73", # noqa:E501 insts="med kww age mrt expr tenure rns smsa dyear_67 dyear_68 dyear_69 dyear_70 dyear_71 dyear_73", # noqa:E501 instd="s iq", properties="b V", ) params_table = np.array([ .17242531190423, .02091963554158, 8.2422713130704, 7.602390656e-16, .13135685967055, .21349376413792, 745, 1.9631533327653, 0, -.00909883103476, .00492868646034, -1.8460965427549, .06527471189517, -.01877459828554, .00057693621602, 745, 1.9631533327653, 0, .04928948974574, .00811972711081, 6.0703382112603, 2.032123371e-09, .03334922040701, .06522975908447, 745, 1.9631533327653, 0, .04221709210309, .0095458460509, 4.4225615915015, .00001120706314, .0234771326142, .06095705159197, 745, 1.9631533327653, 0, -.10179345001799, .0340033743578, -2.9936278954812, .00284801771574, -.16854728771377, -.03503961232222, 745, 1.9631533327653, 0, .12611094946923, .03107904208149, 4.057748920915, .00005477891606, .0650980244278, .18712387451065, 745, 1.9631533327653, 0, -.05961710621535, .05216296564028, -1.1429010119263, .25344683532742, -.16202100605898, .04278679362828, 745, 1.9631533327653, 0, .04867955999401, .05024595634484, .96882542467533, .33294671206223, -.04996095666234, .14732007665036, 745, 1.9631533327653, 0, .15281763322545, .04834485710231, 3.1609904834768, .00163599246861, .05790926588299, .24772600056791, 745, 1.9631533327653, 0, .17443605148569, .06165614610562, 2.8291753945643, .00479228267652, .05339558277297, .2954765201984, 745, 1.9631533327653, 0, .09166596656323, .05594360469515, 1.638542368922, .10173082236229, -.01815990744096, .20149184056742, 745, 1.9631533327653, 0, .09323976497853, .06137760691084, 1.5191169820938, .12915730016675, -.02725388858564, .21373341854271, 745, 1.9631533327653, 0, 4.0335098946211, .33794335658841, 11.935461419748, 3.577808889e-30, 3.3700752678487, 4.6969445213936, 745, 1.9631533327653, 0]).reshape(13, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = param_names cov = np.array([ .00043763115119, -.00007958438537, .00002863778986, .00001496321982, -.00018453787082, -8.550864865e-06, -.0001185286492, -.00019431868638, -.00012891699672, -.00008824260285, -.00031897080643, -.0006359997119, .00263218578127, -.00007958438537, .00002429195022, 4.997376715e-06, -.00001117849889, .00006733963701, -.00002196338101, 8.249019125e-07, .00003312119623, -.0000218044746, -.00006079620995, -.00001426851928, .00001410067206, -.00145119299411, .00002863778986, 4.997376715e-06, .00006592996835, -.00002012308078, .00005199457086, -.00003289221373, .00003620055764, .00008731531776, .00003013530738, .00001504503258, -.00008879845405, -.00013220917123, -.00095762480745, .00001496321982, -.00001117849889, -.00002012308078, .00009112317683, -.000038508438, 7.182733576e-06, .00008294199433, .00006458818434, .00011041870299, .00009792126329, .00011012658665, .00009292324197, .00076092104218, -.00018453787082, .00006733963701, .00005199457086, -.000038508438, .00115622946772, .00013545834604, .00019371742478, .000203588175, 7.317274626e-06, .00002369735603, -.00005176761775, .00009245129039, -.00504399373059, -8.550864865e-06, -.00002196338101, -.00003289221373, 7.182733576e-06, .00013545834604, .0009659068567, .00006303558567, .00012016301635, .00025950456399, .00011274488624, .00030660513471, .00031212041314, .00158010341555, -.0001185286492, 8.249019125e-07, .00003620055764, .00008294199433, .00019371742478, .00006303558567, .00272097498439, .0008763833685, .000936230107, .00097234969671, .0009024844391, .00104679250917, .00032228914613, -.00019431868638, .00003312119623, .00008731531776, .00006458818434, .000203588175, .00012016301635, .0008763833685, .00252465612901, .00094650107881, .0008930540954, .00082494813305, .00095933828863, -.00210700630956, -.00012891699672, -.0000218044746, .00003013530738, .00011041870299, 7.317274626e-06, .00025950456399, .000936230107, .00094650107881, .00233722520824, .0011975566966, .00111394872039, .00131507937389, .00254447447521, -.00008824260285, -.00006079620995, .00001504503258, .00009792126329, .00002369735603, .00011274488624, .00097234969671, .0008930540954, .0011975566966, .0038014803526, .00125650121313, .00157186205549, .00611293275102, -.00031897080643, -.00001426851928, -.00008879845405, .00011012658665, -.00005176761775, .00030660513471, .0009024844391, .00082494813305, .00111394872039, .00125650121313, .00312968690629, .00184349552167, .0043840308983, -.0006359997119, .00001410067206, -.00013220917123, .00009292324197, .00009245129039, .00031212041314, .00104679250917, .00095933828863, .00131507937389, .00157186205549, .00184349552167, .0037672106301, .00544245897816, .00263218578127, -.00145119299411, -.00095762480745, .00076092104218, -.00504399373059, .00158010341555, .00032228914613, -.00210700630956, .00254447447521, .00611293275102, .0043840308983, .00544245897816, .11420571226224]).reshape(13, 13) cov_colnames = param_names cov_rownames = param_names results_small_robust = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) est = dict( N=758, inexog_ct=10, exexog_ct=4, endog_ct=2, partial_ct=0, df_m=12, sdofminus=0, dofminus=0, r2=.2168305947462866, rmse=.3793562300139549, rss=109.0846511318037, mss=30.20149871015154, r2_a=.2042157855341463, F=41.97598961240392, Fp=1.89290505854e-75, Fdf1=12, Fdf2=745, yy=24652.2466174172, yyc=139.2861498419552, r2u=.995575062475047, partialcons=0, cons=1, cdf=12.55161416131593, widstat=11.46142788662503, cd=.0675726199801665, idp=6.77658650925e-09, iddf=3, idstat=40.92698219921901, jp=.0030253131145893, jdf=2, j=11.60148136780177, ll=-340.8414755627023, rankV=13, rankS=15, rankxx=13, rankzz=15, r2c=.2168305947462866, hacsubtitleV="Statistics robust to heteroskedasticity", hacsubtitleB="Estimates efficient for arbitrary heteroskedasticity", title="2-Step GMM estimation", predict="ivreg2_p", version="02.2.08", cmdline="ivreg2 lw expr tenure rns smsa dyear* (s iq=med kww age mrt), gmm2s robust", # noqa:E501 cmd="ivreg2", model="gmm2s", depvar="lw", vcetype="Robust", partialsmall="small", exexog="med kww age mrt", inexog="expr tenure rns smsa dyear_67 dyear_68 dyear_69 dyear_70 dyear_71 dyear_73", # noqa:E501 insts="med kww age mrt expr tenure rns smsa dyear_67 dyear_68 dyear_69 dyear_70 dyear_71 dyear_73", # noqa:E501 instd="s iq", properties="b V", ) params_table = np.array([ .17579576800916, .02067662557145, 8.5021498020418, 1.861114268e-17, .13527032656731, .21632120945101, np.nan, 1.9599639845401, 0, -.00928615655484, .00488241935929, -1.9019579989933, .05717664576009, -.01885552265647, .00028320954679, np.nan, 1.9599639845401, 0, .0502827590727, .00804384217519, 6.251087226427, 4.076051363e-10, .03451711811201, .06604840003339, np.nan, 1.9599639845401, 0, .04252138311207, .00945488880069, 4.4972906618407, 6.882486994e-06, .0239901415849, .06105262463925, np.nan, 1.9599639845401, 0, -.10409306761385, .03352385821237, -3.105044382255, .00190250475151, -.16979862233293, -.03838751289477, np.nan, 1.9599639845401, 0, .12475123235604, .03077474836143, 4.0536881371349, .00005041641801, .06443383393436, .18506863077773, np.nan, 1.9599639845401, 0, -.05304317352459, .05146091261443, -1.0307468490116, .30265954893659, -.15390470886044, .04781836181126, np.nan, 1.9599639845401, 0, .04595459037414, .04957352345681, .92699867126001, .35392722417214, -.05120773018796, .14311691093625, np.nan, 1.9599639845401, 0, .15548006234452, .04763105506, 3.264258206094, .00109751095685, .06212490988128, .24883521480777, np.nan, 1.9599639845401, 0, .16698745539298, .06100058345996, 2.7374730850337, .00619131861175, .04742850877554, .28654640201043, np.nan, 1.9599639845401, 0, .08464846645323, .05540348923564, 1.5278544297672, .12654868468826, -.02394037706648, .19323730997294, np.nan, 1.9599639845401, 0, .09960684400937, .06070338085689, 1.6408780302402, .10082273637942, -.01936959620995, .2185832842287, np.nan, 1.9599639845401, 0, 4.0039243729942, .33484233500232, 11.957640819123, 5.922056626e-33, 3.3476454558904, 4.6602032900981, np.nan, 1.9599639845401, 0]).reshape(13, 9) params_table_colnames = 'b se z pvalue ll ul df crit eform'.split() params_table_rownames = param_names cov = np.array([ .00042752284502, -.00007792910934, .00002799053689, .00001411255161, -.00017627354771, -6.164167361e-06, -.00011238067476, -.0001840592946, -.00012075971225, -.00008045016526, -.00030956302647, -.00062213915849, .0025864317125, -.00007792910934, .0000238380188, 4.908457545e-06, -.0000109083863, .00006550360735, -.00002187678826, 4.129956698e-08, .00003161755605, -.00002236410253, -.00006047183643, -.0000144130349, .00001326368633, -.00142544425011, .00002799053689, 4.908457545e-06, .00006470339694, -.00001976276105, .00005093819277, -.0000323622135, .00003452531659, .00008555059005, .0000288422901, .00001508898973, -.00008682961428, -.00013087868262, -.00093791708189, .00001411255161, -.0000109083863, -.00001976276105, .00008939492223, -.00003640760589, 7.669817608e-06, .00008322349071, .00006546263505, .00011054793547, .00009771882719, .00010901321979, .0000926582973, .00074577978354, -.00017627354771, .00006550360735, .00005093819277, -.00003640760589, .00112384906944, .00012782990916, .0001752536517, .00018281146997, -.00001062129812, .0000105829103, -.00005745271672, .00007901951626, -.00493822443862, -6.164167361e-06, -.00002187678826, -.0000323622135, 7.669817608e-06, .00012782990916, .00094708513671, .00005587818268, .0001108109152, .00024772966236, .00010526192189, .00029836672951, .0003020559345, .00155999842113, -.00011238067476, 4.129956698e-08, .00003452531659, .00008322349071, .0001752536517, .00005587818268, .00264822552711, .00084013008538, .00089372787896, .00094462335409, .00088393735147, .00100740924129, .00036769011237, -.0001840592946, .00003161755605, .00008555059005, .00006546263505, .00018281146997, .0001108109152, .00084013008538, .00245753422792, .00090550111616, .00086043845508, .00080197738555, .00092623266791, -.00204303139567, -.00012075971225, -.00002236410253, .0000288422901, .00011054793547, -.00001062129812, .00024772966236, .00089372787896, .00090550111616, .00226871740613, .00116169566043, .00108859648529, .00127118636737, .00254572878148, -.00008045016526, -.00006047183643, .00001508898973, .00009771882719, .0000105829103, .00010526192189, .00094462335409, .00086043845508, .00116169566043, .00372107118246, .00122563410541, .00153681917159, .00601243235865, -.00030956302647, -.0000144130349, -.00008682961428, .00010901321979, -.00005745271672, .00029836672951, .00088393735147, .00080197738555, .00108859648529, .00122563410541, .00306954661948, .00181011399651, .00430171295221, -.00062213915849, .00001326368633, -.00013087868262, .0000926582973, .00007901951626, .0003020559345, .00100740924129, .00092623266791, .00127118636737, .00153681917159, .00181011399651, .00368490044746, .00539258837124, .0025864317125, -.00142544425011, -.00093791708189, .00074577978354, -.00493822443862, .00155999842113, .00036769011237, -.00204303139567, .00254572878148, .00601243235865, .00430171295221, .00539258837124, .11211938930981]).reshape(13, 13) cov_colnames = param_names cov_rownames = param_names results_gmm2s_robust = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, **est ) statsmodels-0.12.2/statsmodels/sandbox/regression/tests/test_gmm.py000066400000000000000000000756351400612667500257000ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Oct 04 13:19:01 2013 Author: Josef Perktold """ from statsmodels.compat.python import lrange, lmap import os import copy import pytest import numpy as np from numpy.testing import assert_allclose, assert_equal import pandas as pd from statsmodels.tools.tools import add_constant from statsmodels.regression.linear_model import OLS import statsmodels.sandbox.regression.gmm as gmm def get_griliches76_data(): curdir = os.path.split(__file__)[0] path = os.path.join(curdir, 'griliches76.dta') griliches76_data = pd.read_stata(path) # create year dummies years = griliches76_data['year'].unique() N = griliches76_data.shape[0] for yr in years: griliches76_data['D_%i' % yr] = np.zeros(N) for i in range(N): if griliches76_data.loc[griliches76_data.index[i], 'year'] == yr: griliches76_data.loc[griliches76_data.index[i], 'D_%i' % yr] = 1 else: pass griliches76_data['const'] = 1 X = add_constant(griliches76_data[['s', 'iq', 'expr', 'tenure', 'rns', 'smsa', 'D_67', 'D_68', 'D_69', 'D_70', 'D_71', 'D_73']], #prepend=False) # for Stata comparison prepend=True) # for R comparison Z = add_constant(griliches76_data[['expr', 'tenure', 'rns', 'smsa', \ 'D_67', 'D_68', 'D_69', 'D_70', 'D_71', 'D_73', 'med', 'kww', 'age', 'mrt']]) Y = griliches76_data['lw'] return Y, X, Z # use module global to load only once yg_df, xg_df, zg_df = get_griliches76_data() endog = np.asarray(yg_df, dtype=float) # TODO: why is yg_df float32 exog, instrument = lmap(np.asarray, [xg_df, zg_df]) assert exog.dtype == np.float64 assert instrument.dtype == np.float64 # from R #----------------- varnames = np.array(["(Intercept)", "s", "iq", "expr", "tenure", "rns", "smsa", "D_67", "D_68", "D_69", "D_70", "D_71", "D_73"]) params = np.array([ 4.03350989, 0.17242531, -0.00909883, 0.04928949, 0.04221709, -0.10179345, 0.12611095, -0.05961711, 0.04867956, 0.15281763, 0.17443605, 0.09166597, 0.09323977]) bse = np.array([ 0.31816162, 0.02091823, 0.00474527, 0.00822543, 0.00891969, 0.03447337, 0.03119615, 0.05577582, 0.05246796, 0.05201092, 0.06027671, 0.05461436, 0.05767865]) tvalues = np.array([ 12.6775501, 8.2428242, -1.9174531, 5.9923305, 4.7330205, -2.9528144, 4.0425165, -1.0688701, 0.9277959, 2.9381834, 2.8939212, 1.6784225, 1.6165385]) pvalues = np.array([ 1.72360000e-33, 7.57025400e-16, 5.55625000e-02, 3.21996700e-09, 2.64739100e-06, 3.24794100e-03, 5.83809900e-05, 2.85474400e-01, 3.53813900e-01, 3.40336100e-03, 3.91575100e-03, 9.36840200e-02, 1.06401300e-01]) #----------------- def test_iv2sls_r(): mod = gmm.IV2SLS(endog, exog, instrument) res = mod.fit() # print(res.params) # print(res.params - params) n, k = exog.shape assert_allclose(res.params, params, rtol=1e-7, atol=1e-9) # TODO: check df correction #assert_allclose(res.bse * np.sqrt((n - k) / (n - k - 1.)), bse, assert_allclose(res.bse, bse, rtol=0, atol=3e-7) # GH 3849 assert not hasattr(mod, '_results') def test_ivgmm0_r(): n, k = exog.shape nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs w0 = np.linalg.inv(w0inv) mod = gmm.IVGMM(endog, exog, instrument) res = mod.fit(np.ones(exog.shape[1], float), maxiter=0, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-8, 'disp': 0}) assert_allclose(res.params, params, rtol=1e-4, atol=1e-4) # TODO : res.bse and bse are not the same, rtol=0.09 is large in this case #res.bse is still robust?, bse is not a sandwich ? assert_allclose(res.bse, bse, rtol=0.09, atol=0) score = res.model.score(res.params, w0) assert_allclose(score, np.zeros(score.shape), rtol=0, atol=5e-6) # atol=1e-8) ?? def test_ivgmm1_stata(): # copied constant to the beginning params_stata = np.array( [ 4.0335099 , 0.17242531, -0.00909883, 0.04928949, 0.04221709, -0.10179345, 0.12611095, -0.05961711, 0.04867956, 0.15281763, 0.17443605, 0.09166597, 0.09323976]) # robust bse with gmm onestep bse_stata = np.array( [ 0.33503289, 0.02073947, 0.00488624, 0.0080498 , 0.00946363, 0.03371053, 0.03081138, 0.05171372, 0.04981322, 0.0479285 , 0.06112515, 0.0554618 , 0.06084901]) n, k = exog.shape nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs w0 = np.linalg.inv(w0inv) start = OLS(endog, exog).fit().params mod = gmm.IVGMM(endog, exog, instrument) res = mod.fit(start, maxiter=1, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}) # move constant to end for Stata idx = lrange(len(params)) idx = idx[1:] + idx[:1] exog_st = exog[:, idx] class TestGMMOLS(object): @classmethod def setup_class(cls): exog = exog_st # with const at end res_ols = OLS(endog, exog).fit() # use exog as instrument nobs, k_instr = exog.shape w0inv = np.dot(exog.T, exog) / nobs #w0 = np.linalg.inv(w0inv) mod = gmm.IVGMM(endog, exog, exog) res = mod.fit(np.ones(exog.shape[1], float), maxiter=0, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}) cls.res1 = res cls.res2 = res_ols def test_basic(self): res1, res2 = self.res1, self.res2 # test both absolute and relative difference assert_allclose(res1.params, res2.params, rtol=5e-4, atol=0) assert_allclose(res1.params, res2.params, rtol=0, atol=1e-5) n = res1.model.exog.shape[0] dffac = 1#np.sqrt((n - 1.) / n) # currently different df in cov calculation assert_allclose(res1.bse * dffac, res2.HC0_se, rtol=5e-6, atol=0) assert_allclose(res1.bse * dffac, res2.HC0_se, rtol=0, atol=1e-7) @pytest.mark.xfail(reason="Not asserting anything meaningful", raises=NotImplementedError, strict=True) def test_other(self): res1, res2 = self.res1, self.res2 raise NotImplementedError class CheckGMM(object): params_tol = [5e-6, 5e-6] bse_tol = [5e-7, 5e-7] def test_basic(self): res1, res2 = self.res1, self.res2 # test both absolute and relative difference rtol, atol = self.params_tol assert_allclose(res1.params, res2.params, rtol=rtol, atol=0) assert_allclose(res1.params, res2.params, rtol=0, atol=atol) n = res1.model.exog.shape[0] dffac = 1 #np.sqrt((n - 1.) / n) # currently different df in cov calculation rtol, atol = self.bse_tol assert_allclose(res1.bse * dffac, res2.bse, rtol=rtol, atol=0) assert_allclose(res1.bse * dffac, res2.bse, rtol=0, atol=atol) def test_other(self): # TODO: separate Q and J tests res1, res2 = self.res1, self.res2 assert_allclose(res1.q, res2.Q, rtol=5e-6, atol=0) assert_allclose(res1.jval, res2.J, rtol=5e-5, atol=0) def test_hypothesis(self): res1, res2 = self.res1, self.res2 restriction = np.eye(len(res1.params)) res_t = res1.t_test(restriction) assert_allclose(res_t.tvalue, res1.tvalues, rtol=1e-12, atol=0) assert_allclose(res_t.pvalue, res1.pvalues, rtol=1e-12, atol=0) rtol, atol = self.bse_tol assert_allclose(res_t.tvalue, res2.tvalues, rtol=rtol*10, atol=atol) assert_allclose(res_t.pvalue, res2.pvalues, rtol=rtol*10, atol=atol) res_f = res1.f_test(restriction[:-1]) # without constant # comparison with fvalue is not possible, those are not defined # assert_allclose(res_f.fvalue, res1.fvalue, rtol=1e-12, atol=0) # assert_allclose(res_f.pvalue, res1.f_pvalue, rtol=1e-12, atol=0) # assert_allclose(res_f.fvalue, res2.F, rtol=1e-10, atol=0) # assert_allclose(res_f.pvalue, res2.Fp, rtol=1e-08, atol=0) # Smoke test for Wald res_wald = res1.wald_test(restriction[:-1]) @pytest.mark.smoke def test_summary(self): res1 = self.res1 summ = res1.summary() # len + 1 is for header line assert_equal(len(summ.tables[1]), len(res1.params) + 1) def test_use_t(self): # Copy to avoid cache res1 = copy.deepcopy(self.res1) res1.use_t = True summ = res1.summary() assert 'P>|t|' in str(summ) assert 'P>|z|' not in str(summ) class TestGMMSt1(CheckGMM): @classmethod def setup_class(cls): #cls.bse_tol = [5e-7, 5e-7] # compare to Stata default options, iterative GMM exog = exog_st # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs #w0 = np.linalg.inv(w0inv) mod = gmm.IVGMM(endog, exog, instrument) res10 = mod.fit(start, maxiter=10, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}, wargs={'centered':False}) cls.res1 = res10 from .results_gmm_griliches_iter import results cls.res2 = results class TestGMMStTwostep(CheckGMM): #compares has_optimal_weights=True with Stata's has_optimal_weights=False @classmethod def setup_class(cls): # compare to Stata default options, twostep GMM cls.params_tol = [5e-5, 5e-6] cls.bse_tol = [5e-6, 5e-7] exog = exog_st # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs #w0 = np.linalg.inv(w0inv) mod = gmm.IVGMM(endog, exog, instrument) res10 = mod.fit(start, maxiter=2, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}, wargs={'centered':False}) cls.res1 = res10 from .results_gmm_griliches import results_twostep as results cls.res2 = results class TestGMMStTwostepNO(CheckGMM): #with Stata default `has_optimal_weights=False` @classmethod def setup_class(cls): # compare to Stata default options, twostep GMM cls.params_tol = [5e-5, 5e-6] cls.bse_tol = [1e-6, 5e-5] exog = exog_st # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs #w0 = np.linalg.inv(w0inv) mod = gmm.IVGMM(endog, exog, instrument) res10 = mod.fit(start, maxiter=2, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}, wargs={'centered':False}, has_optimal_weights=False) cls.res1 = res10 from .results_gmm_griliches import results_twostep as results cls.res2 = results class TestGMMStOnestep(CheckGMM): @classmethod def setup_class(cls): # compare to Stata default options, onestep GMM cls.params_tol = [5e-4, 5e-5] cls.bse_tol = [7e-3, 5e-4] exog = exog_st # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs #w0 = np.linalg.inv(w0inv) mod = gmm.IVGMM(endog, exog, instrument) res = mod.fit(start, maxiter=0, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}) cls.res1 = res from .results_gmm_griliches import results_onestep as results cls.res2 = results def test_bse_other(self): res1, res2 = self.res1, self.res2 # try other versions for bse, # TODO: next two produce the same as before (looks like) bse = np.sqrt(np.diag((res1._cov_params(has_optimal_weights=False)))) #weights=res1.weights)))) # TODO: does not look different #assert_allclose(res1.bse, res2.bse, rtol=5e-06, atol=0) #nobs = instrument.shape[0] #w0inv = np.dot(instrument.T, instrument) / nobs q = self.res1.model.gmmobjective(self.res1.params, np.linalg.inv(self.res1.weights)) #assert_allclose(q, res2.Q, rtol=5e-6, atol=0) @pytest.mark.xfail(reason="q vs Q comparison fails", raises=AssertionError, strict=True) def test_other(self): super(TestGMMStOnestep, self).test_other() class TestGMMStOnestepNO(CheckGMM): # matches Stats's defaults wargs={'centered':False}, has_optimal_weights=False @classmethod def setup_class(cls): # compare to Stata default options, onestep GMM cls.params_tol = [1e-5, 1e-6] cls.bse_tol = [5e-6, 5e-7] exog = exog_st # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs #w0 = np.linalg.inv(w0inv) mod = gmm.IVGMM(endog, exog, instrument) res = mod.fit(start, maxiter=0, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}, wargs={'centered':False}, has_optimal_weights=False) cls.res1 = res from .results_gmm_griliches import results_onestep as results cls.res2 = results @pytest.mark.xfail(reason="q vs Q comparison fails", raises=AssertionError, strict=True) def test_other(self): super(TestGMMStOnestepNO, self).test_other() class TestGMMStOneiter(CheckGMM): @classmethod def setup_class(cls): # compare to Stata default options, onestep GMM # this uses maxiter=1, one iteration in loop cls.params_tol = [5e-4, 5e-5] cls.bse_tol = [7e-3, 5e-4] exog = exog_st # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs #w0 = np.linalg.inv(w0inv) mod = gmm.IVGMM(endog, exog, instrument) res = mod.fit(start, maxiter=1, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}) cls.res1 = res from .results_gmm_griliches import results_onestep as results cls.res2 = results @pytest.mark.xfail(reason="q vs Q comparison fails", raises=AssertionError, strict=True) def test_other(self): super(TestGMMStOneiter, self).test_other() def test_bse_other(self): res1, res2 = self.res1, self.res2 moms = res1.model.momcond(res1.params) w = res1.model.calc_weightmatrix(moms) # try other versions for bse, # TODO: next two produce the same as before (looks like) bse = np.sqrt(np.diag((res1._cov_params(has_optimal_weights=False, weights=res1.weights)))) # TODO: does not look different #assert_allclose(res1.bse, res2.bse, rtol=5e-06, atol=0) bse = np.sqrt(np.diag((res1._cov_params(has_optimal_weights=False)))) #use_weights=True #weights=w #assert_allclose(res1.bse, res2.bse, rtol=5e-06, atol=0) #This does not replicate Stata oneway either nobs = instrument.shape[0] w0inv = np.dot(instrument.T, instrument) / nobs q = self.res1.model.gmmobjective(self.res1.params, w)#self.res1.weights) #assert_allclose(q, res2.Q, rtol=5e-6, atol=0) class TestGMMStOneiterNO(CheckGMM): @classmethod def setup_class(cls): # compare to Stata default options, onestep GMM # this uses maxiter=1, one iteration in loop cls.params_tol = [1e-5, 1e-6] cls.bse_tol = [5e-6, 5e-7] exog = exog_st # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs #w0 = np.linalg.inv(w0inv) mod = gmm.IVGMM(endog, exog, instrument) res = mod.fit(start, maxiter=1, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}, wargs={'centered':False}, has_optimal_weights=False) cls.res1 = res from .results_gmm_griliches import results_onestep as results cls.res2 = results @pytest.mark.xfail(reason="q vs Q comparison fails", raises=AssertionError, strict=True) def test_other(self): super(TestGMMStOneiterNO, self).test_other() #------------ Crosscheck subclasses class TestGMMStOneiterNO_Linear(CheckGMM): @classmethod def setup_class(cls): # compare to Stata default options, onestep GMM # this uses maxiter=1, one iteration in loop cls.params_tol = [5e-9, 1e-9] cls.bse_tol = [5e-10, 1e-10] exog = exog_st # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs #w0 = np.linalg.inv(w0inv) mod = gmm.LinearIVGMM(endog, exog, instrument) res = mod.fit(start, maxiter=1, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-8, 'disp': 0}, wargs={'centered':False}, has_optimal_weights=False) cls.res1 = res mod = gmm.IVGMM(endog, exog, instrument) res = mod.fit(start, maxiter=1, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}, wargs={'centered':False}, has_optimal_weights=False) cls.res3 = res from .results_gmm_griliches import results_onestep as results cls.res2 = results @pytest.mark.xfail(reason="q vs Q comparison fails", raises=AssertionError, strict=True) def test_other(self): super(TestGMMStOneiterNO_Linear, self).test_other() class TestGMMStOneiterNO_Nonlinear(CheckGMM): @classmethod def setup_class(cls): # compare to Stata default options, onestep GMM # this uses maxiter=1, one iteration in loop cls.params_tol = [5e-5, 5e-6] cls.bse_tol = [5e-6, 1e-1] exog = exog_st # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs #w0 = np.linalg.inv(w0inv) def func(params, exog): return np.dot(exog, params) mod = gmm.NonlinearIVGMM(endog, exog, instrument, func) res = mod.fit(start, maxiter=1, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-8, 'disp': 0}, wargs={'centered':False}, has_optimal_weights=False) cls.res1 = res mod = gmm.IVGMM(endog, exog, instrument) res = mod.fit(start, maxiter=1, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}, wargs={'centered':False}, has_optimal_weights=False) cls.res3 = res from .results_gmm_griliches import results_onestep as results cls.res2 = results @pytest.mark.xfail(reason="q vs Q comparison fails", raises=AssertionError, strict=True) def test_other(self): super(TestGMMStOneiterNO_Nonlinear, self).test_other() def test_score(self): params = self.res1.params * 1.1 weights = self.res1.weights sc1 = self.res1.model.score(params, weights) sc2 = super(self.res1.model.__class__, self.res1.model).score(params, weights) assert_allclose(sc1, sc2, rtol=1e-6, atol=0) assert_allclose(sc1, sc2, rtol=0, atol=1e-7) # score at optimum sc1 = self.res1.model.score(self.res1.params, weights) assert_allclose(sc1, np.zeros(len(params)), rtol=0, atol=1e-8) class TestGMMStOneiterOLS_Linear(CheckGMM): @classmethod def setup_class(cls): # replicating OLS by GMM - high agreement cls.params_tol = [1e-11, 1e-12] cls.bse_tol = [1e-12, 1e-12] exog = exog_st # with const at end res_ols = OLS(endog, exog).fit() #Note: start is irrelevant but required start = np.ones(len(res_ols.params)) nobs, k_instr = instrument.shape w0inv = np.dot(exog.T, exog) / nobs #w0 = np.linalg.inv(w0inv) mod = gmm.LinearIVGMM(endog, exog, exog) res = mod.fit(start, maxiter=0, inv_weights=w0inv, #optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}, optim_args={'disp': 0}, weights_method='iid', wargs={'centered':False, 'ddof':'k_params'}, has_optimal_weights=True) # fix use of t distribution see #2495 comment res.use_t = True res.df_resid = res.nobs - len(res.params) cls.res1 = res #from .results_gmm_griliches import results_onestep as results #cls.res2 = results cls.res2 = res_ols @pytest.mark.xfail(reason="RegressionResults has no `Q` attribute", raises=AttributeError, strict=True) def test_other(self): super(TestGMMStOneiterOLS_Linear, self).test_other() # ------------------ class TestGMMSt2(object): # this looks like an old version, trying out different comparisons # of options with Stats @classmethod def setup_class(cls): # compare to Stata default options, iterative GMM exog = exog_st # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs #w0 = np.linalg.inv(w0inv) mod = gmm.IVGMM(endog, exog, instrument) res = mod.fit(start, maxiter=2, inv_weights=w0inv, wargs={'ddof':0, 'centered':False}, optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}) cls.res1 = res from .results_ivreg2_griliches import results_gmm2s_robust as results cls.res2 = results # TODO: remove after testing, compare bse from 1 iteration # see test_basic mod = gmm.IVGMM(endog, exog, instrument) res = mod.fit(start, maxiter=1, inv_weights=w0inv, wargs={'ddof':0, 'centered':False}, optim_method='bfgs', optim_args={'gtol':1e-6, 'disp': 0}) cls.res3 = res def test_basic(self): res1, res2 = self.res1, self.res2 # test both absolute and relative difference assert_allclose(res1.params, res2.params, rtol=5e-05, atol=0) assert_allclose(res1.params, res2.params, rtol=0, atol=5e-06) n = res1.model.exog.shape[0] # TODO: check df correction np.sqrt(745./758 )*res1.bse matches better dffact = np.sqrt(745. / 758 ) assert_allclose(res1.bse * dffact, res2.bse, rtol=5e-03, atol=0) assert_allclose(res1.bse * dffact, res2.bse, rtol=0, atol=5e-03) # try other versions for bse, # TODO: next two produce the same as before (looks like) bse = np.sqrt(np.diag((res1._cov_params(has_optimal_weights=True, weights=res1.weights)))) assert_allclose(res1.bse, res2.bse, rtol=5e-01, atol=0) bse = np.sqrt(np.diag((res1._cov_params(has_optimal_weights=True, weights=res1.weights, use_weights=True)))) assert_allclose(res1.bse, res2.bse, rtol=5e-02, atol=0) # TODO: resolve this # try bse from previous step, is closer to Stata # guess: Stata ivreg2 does not calc for bse update after final iteration # need better test case, bse difference is close to numerical optimization precision assert_allclose(self.res3.bse, res2.bse, rtol=5e-05, atol=0) assert_allclose(self.res3.bse, res2.bse, rtol=0, atol=5e-06) # TODO; tvalues are not available yet, no inheritance #assert_allclose(res1.tvalues, res2.tvalues, rtol=5e-10, atol=0) class CheckIV2SLS(object): def test_basic(self): res1, res2 = self.res1, self.res2 # test both absolute and relative difference assert_allclose(res1.params, res2.params, rtol=1e-9, atol=0) assert_allclose(res1.params, res2.params, rtol=0, atol=1e-10) n = res1.model.exog.shape[0] assert_allclose(res1.bse, res2.bse, rtol=1e-10, atol=0) assert_allclose(res1.bse, res2.bse, rtol=0, atol=1e-11) assert_allclose(res1.tvalues, res2.tvalues, rtol=5e-10, atol=0) def test_other(self): res1, res2 = self.res1, self.res2 assert_allclose(res1.rsquared, res2.r2, rtol=1e-7, atol=0) assert_allclose(res1.rsquared_adj, res2.r2_a, rtol=1e-7, atol=0) # TODO: why is fvalue different, IV2SLS uses inherited linear assert_allclose(res1.fvalue, res2.F, rtol=1e-10, atol=0) assert_allclose(res1.f_pvalue, res2.Fp, rtol=1e-8, atol=0) assert_allclose(np.sqrt(res1.mse_resid), res2.rmse, rtol=1e-10, atol=0) assert_allclose(res1.ssr, res2.rss, rtol=1e-10, atol=0) assert_allclose(res1.uncentered_tss, res2.yy, rtol=1e-10, atol=0) assert_allclose(res1.centered_tss, res2.yyc, rtol=1e-10, atol=0) assert_allclose(res1.ess, res2.mss, rtol=1e-9, atol=0) assert_equal(res1.df_model, res2.df_m) assert_equal(res1.df_resid, res2.df_r) # TODO: llf raise NotImplementedError #assert_allclose(res1.llf, res2.ll, rtol=1e-10, atol=0) def test_hypothesis(self): res1, res2 = self.res1, self.res2 restriction = np.eye(len(res1.params)) res_t = res1.t_test(restriction) assert_allclose(res_t.tvalue, res1.tvalues, rtol=1e-12, atol=0) assert_allclose(res_t.pvalue, res1.pvalues, rtol=1e-12, atol=0) res_f = res1.f_test(restriction[:-1]) # without constant # TODO res1.fvalue problem, see issue #1104 assert_allclose(res_f.fvalue, res1.fvalue, rtol=1e-12, atol=0) assert_allclose(res_f.pvalue, res1.f_pvalue, rtol=1e-10, atol=0) assert_allclose(res_f.fvalue, res2.F, rtol=1e-10, atol=0) assert_allclose(res_f.pvalue, res2.Fp, rtol=1e-08, atol=0) def test_hausman(self): res1, res2 = self.res1, self.res2 hausm = res1.spec_hausman() # hausman uses se2 = ssr / nobs, no df correction assert_allclose(hausm[0], res2.hausman['DWH'], rtol=1e-11, atol=0) assert_allclose(hausm[1], res2.hausman['DWHp'], rtol=1e-10, atol=1e-25) @pytest.mark.smoke def test_summary(self): res1 = self.res1 summ = res1.summary() assert_equal(len(summ.tables[1]), len(res1.params) + 1) class TestIV2SLSSt1(CheckIV2SLS): @classmethod def setup_class(cls): exog = exog_st # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape mod = gmm.IV2SLS(endog, exog, instrument) res = mod.fit() cls.res1 = res from .results_ivreg2_griliches import results_small as results cls.res2 = results # See GH #2720 def test_input_dimensions(self): rs = np.random.RandomState(1234) x = rs.randn(200, 2) z = rs.randn(200) x[:, 0] = np.sqrt(0.5) * x[:, 0] + np.sqrt(0.5) * z z = np.column_stack((x[:, [1]], z[:, None])) e = np.sqrt(0.5) * rs.randn(200) + np.sqrt(0.5) * x[:, 0] y_1d = y = x[:, 0] + x[:, 1] + e y_2d = y[:, None] y_series = pd.Series(y) y_df = pd.DataFrame(y_series) x_1d = x[:, 0] x_2d = x x_df = pd.DataFrame(x) x_df_single = x_df.iloc[:, [0]] x_series = x_df.iloc[:, 0] z_2d = z z_series = pd.Series(z[:, 1]) z_1d = z_series.values z_df = pd.DataFrame(z) ys = (y_df, y_series, y_2d, y_1d) xs = (x_2d, x_1d, x_df_single, x_df, x_series) zs = (z_1d, z_2d, z_series, z_df) res2 = gmm.IV2SLS(y_1d, x_2d, z_2d).fit() res1 = gmm.IV2SLS(y_1d, x_1d, z_1d).fit() res1_2sintr = gmm.IV2SLS(y_1d, x_1d, z_2d).fit() for _y in ys: for _x in xs: for _z in zs: x_1d = np.size(_x) == _x.shape[0] z_1d = np.size(_z) == _z.shape[0] if z_1d and not x_1d: continue res = gmm.IV2SLS(_y, _x, _z).fit() if z_1d: assert_allclose(res.params, res1.params) elif x_1d and not z_1d: assert_allclose(res.params, res1_2sintr.params) else: assert_allclose(res.params, res2.params) def test_noconstant(): exog = exog_st[:, :-1] # with const removed at end mod = gmm.IV2SLS(endog, exog, instrument) res = mod.fit() assert_equal(res.fvalue, np.nan) # smoke test summ = res.summary() assert_equal(len(summ.tables[1]), len(res.params) + 1) def test_gmm_basic(): # this currently tests mainly the param names, exog_names # see #4340 cd = np.array([1.5, 1.5, 1.7, 2.2, 2.0, 1.8, 1.8, 2.2, 1.9, 1.6, 1.8, 2.2, 2.0, 1.5, 1.1, 1.5, 1.4, 1.7, 1.42, 1.9]) dcd = np.array([0, 0.2 ,0.5, -0.2, -0.2, 0, 0.4, -0.3, -0.3, 0.2, 0.4, -0.2, -0.5, -0.4, 0.4, -0.1, 0.3, -0.28, 0.48, 0.2]) inst = np.column_stack((np.ones(len(cd)), cd)) class GMMbase(gmm.GMM): def momcond(self, params): p0, p1, p2, p3 = params endog = self.endog[:, None] exog = self.exog inst = self.instrument mom0 = (endog - p0 - p1 * exog) * inst mom1 = ((endog - p0 - p1 * exog)**2 - p2 * (exog**(2 * p3)) / 12) * inst g = np.column_stack((mom0, mom1)) return g beta0 = np.array([0.1, 0.1, 0.01, 1]) res = GMMbase(endog=dcd, exog=cd, instrument=inst, k_moms=4, k_params=4).fit(beta0, optim_args={'disp': 0}) summ = res.summary() assert_equal(len(summ.tables[1]), len(res.params) + 1) pnames = ['p%2d' % i for i in range(len(res.params))] assert_equal(res.model.exog_names, pnames) # check set_param_names method mod = GMMbase(endog=dcd, exog=cd, instrument=inst, k_moms=4, k_params=4) # use arbitrary names pnames = ['beta', 'gamma', 'psi', 'phi'] mod.set_param_names(pnames) res1 = mod.fit(beta0, optim_args={'disp': 0}) assert_equal(res1.model.exog_names, pnames) statsmodels-0.12.2/statsmodels/sandbox/regression/tests/test_gmm_poisson.py000066400000000000000000000320001400612667500274250ustar00rootroot00000000000000''' TestGMMMultTwostepDefault() has lower precision ''' from statsmodels.compat.python import lmap import numpy as np import pandas from scipy import stats import pytest from statsmodels.regression.linear_model import OLS from statsmodels.sandbox.regression import gmm from numpy.testing import assert_allclose, assert_equal def get_data(): import os curdir = os.path.split(__file__)[0] dt = pandas.read_csv(os.path.join(curdir, 'racd10data_with_transformed.csv')) # Transformations compared to original data ##dt3['income'] /= 10. ##dt3['aget'] = (dt3['age'] - dt3['age'].min()) / 5. ##dt3['aget2'] = dt3['aget']**2 # How do we do this with pandas mask = ~((np.asarray(dt['private']) == 1) & (dt['medicaid'] == 1)) mask = mask & (dt['docvis'] <= 70) dt3 = dt[mask] dt3['const'] = 1 # add constant return dt3 DATA = get_data() #------------- moment conditions for example def moment_exponential_add(params, exog, exp=True): if not np.isfinite(params).all(): print("invalid params", params) # moment condition without instrument if exp: predicted = np.exp(np.dot(exog, params)) #if not np.isfinite(predicted).all(): #print "invalid predicted", predicted #raise RuntimeError('invalid predicted') predicted = np.clip(predicted, 0, 1e100) # try to avoid inf else: predicted = np.dot(exog, params) return predicted def moment_exponential_mult(params, data, exp=True): # multiplicative error model endog = data[:,0] exog = data[:,1:] if not np.isfinite(params).all(): print("invalid params", params) # moment condition without instrument if exp: predicted = np.exp(np.dot(exog, params)) predicted = np.clip(predicted, 0, 1e100) # avoid inf resid = endog / predicted - 1 if not np.isfinite(resid).all(): print("invalid resid", resid) else: resid = endog - np.dot(exog, params) return resid #------------------- test classes # copied from test_gmm.py, with changes class CheckGMM(object): # default tolerance, overwritten by subclasses params_tol = [5e-6, 5e-6] bse_tol = [5e-7, 5e-7] q_tol = [5e-6, 1e-9] j_tol = [5e-5, 1e-9] def test_basic(self): res1, res2 = self.res1, self.res2 # test both absolute and relative difference rtol, atol = self.params_tol assert_allclose(res1.params, res2.params, rtol=rtol, atol=0) assert_allclose(res1.params, res2.params, rtol=0, atol=atol) rtol, atol = self.bse_tol assert_allclose(res1.bse, res2.bse, rtol=rtol, atol=0) assert_allclose(res1.bse, res2.bse, rtol=0, atol=atol) def test_other(self): res1, res2 = self.res1, self.res2 rtol, atol = self.q_tol assert_allclose(res1.q, res2.Q, rtol=atol, atol=rtol) rtol, atol = self.j_tol assert_allclose(res1.jval, res2.J, rtol=atol, atol=rtol) j, jpval, jdf = res1.jtest() # j and jval should be the same assert_allclose(res1.jval, res2.J, rtol=13, atol=13) #pvalue is not saved in Stata results pval = stats.chi2.sf(res2.J, res2.J_df) #assert_allclose(jpval, pval, rtol=1e-4, atol=1e-6) assert_allclose(jpval, pval, rtol=rtol, atol=atol) assert_equal(jdf, res2.J_df) @pytest.mark.smoke def test_summary(self): res1 = self.res1 summ = res1.summary() assert_equal(len(summ.tables[1]), len(res1.params) + 1) class TestGMMAddOnestep(CheckGMM): @classmethod def setup_class(cls): XLISTEXOG2 = 'aget aget2 educyr actlim totchr'.split() endog_name = 'docvis' exog_names = 'private medicaid'.split() + XLISTEXOG2 + ['const'] instrument_names = 'income ssiratio'.split() + XLISTEXOG2 + ['const'] endog = DATA[endog_name] exog = DATA[exog_names] instrument = DATA[instrument_names] asarray = lambda x: np.asarray(x, float) endog, exog, instrument = lmap(asarray, [endog, exog, instrument]) cls.bse_tol = [5e-6, 5e-7] q_tol = [0.04, 0] # compare to Stata default options, iterative GMM # with const at end start = OLS(np.log(endog+1), exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs mod = gmm.NonlinearIVGMM(endog, exog, instrument, moment_exponential_add) res0 = mod.fit(start, maxiter=0, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-8, 'disp': 0}, wargs={'centered':False}) cls.res1 = res0 from .results_gmm_poisson import results_addonestep as results cls.res2 = results class TestGMMAddTwostep(CheckGMM): @classmethod def setup_class(cls): XLISTEXOG2 = 'aget aget2 educyr actlim totchr'.split() endog_name = 'docvis' exog_names = 'private medicaid'.split() + XLISTEXOG2 + ['const'] instrument_names = 'income ssiratio'.split() + XLISTEXOG2 + ['const'] endog = DATA[endog_name] exog = DATA[exog_names] instrument = DATA[instrument_names] asarray = lambda x: np.asarray(x, float) endog, exog, instrument = lmap(asarray, [endog, exog, instrument]) cls.bse_tol = [5e-6, 5e-7] # compare to Stata default options, iterative GMM # with const at end start = OLS(np.log(endog+1), exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs mod = gmm.NonlinearIVGMM(endog, exog, instrument, moment_exponential_add) res0 = mod.fit(start, maxiter=2, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-8, 'disp': 0}, wargs={'centered':False}, has_optimal_weights=False) cls.res1 = res0 from .results_gmm_poisson import results_addtwostep as results cls.res2 = results class TestGMMMultOnestep(CheckGMM): #compares has_optimal_weights=True with Stata's has_optimal_weights=False @classmethod def setup_class(cls): # compare to Stata default options, twostep GMM XLISTEXOG2 = 'aget aget2 educyr actlim totchr'.split() endog_name = 'docvis' exog_names = 'private medicaid'.split() + XLISTEXOG2 + ['const'] instrument_names = 'income medicaid ssiratio'.split() + XLISTEXOG2 + ['const'] endog = DATA[endog_name] exog = DATA[exog_names] instrument = DATA[instrument_names] asarray = lambda x: np.asarray(x, float) endog, exog, instrument = lmap(asarray, [endog, exog, instrument]) # Need to add all data into exog endog_ = np.zeros(len(endog)) exog_ = np.column_stack((endog, exog)) cls.bse_tol = [5e-6, 5e-7] cls.q_tol = [0.04, 0] cls.j_tol = [0.04, 0] # compare to Stata default options, iterative GMM # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs mod = gmm.NonlinearIVGMM(endog_, exog_, instrument, moment_exponential_mult) res0 = mod.fit(start, maxiter=0, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-8, 'disp': 0}, wargs={'centered':False}, has_optimal_weights=False) cls.res1 = res0 from .results_gmm_poisson import results_multonestep as results cls.res2 = results class TestGMMMultTwostep(CheckGMM): #compares has_optimal_weights=True with Stata's has_optimal_weights=False @classmethod def setup_class(cls): # compare to Stata default options, twostep GMM XLISTEXOG2 = 'aget aget2 educyr actlim totchr'.split() endog_name = 'docvis' exog_names = 'private medicaid'.split() + XLISTEXOG2 + ['const'] instrument_names = 'income medicaid ssiratio'.split() + XLISTEXOG2 + ['const'] endog = DATA[endog_name] exog = DATA[exog_names] instrument = DATA[instrument_names] asarray = lambda x: np.asarray(x, float) endog, exog, instrument = lmap(asarray, [endog, exog, instrument]) # Need to add all data into exog endog_ = np.zeros(len(endog)) exog_ = np.column_stack((endog, exog)) cls.bse_tol = [5e-6, 5e-7] # compare to Stata default options, iterative GMM # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs mod = gmm.NonlinearIVGMM(endog_, exog_, instrument, moment_exponential_mult) res0 = mod.fit(start, maxiter=2, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-8, 'disp': 0}, wargs={'centered':False}, has_optimal_weights=False) cls.res1 = res0 from .results_gmm_poisson import results_multtwostep as results cls.res2 = results class TestGMMMultTwostepDefault(CheckGMM): # compares my defaults with the same options in Stata # agreement is not very high, maybe vce(unadjusted) is different after all @classmethod def setup_class(cls): # compare to Stata default options, twostep GMM XLISTEXOG2 = 'aget aget2 educyr actlim totchr'.split() endog_name = 'docvis' exog_names = 'private medicaid'.split() + XLISTEXOG2 + ['const'] instrument_names = 'income medicaid ssiratio'.split() + XLISTEXOG2 + ['const'] endog = DATA[endog_name] exog = DATA[exog_names] instrument = DATA[instrument_names] asarray = lambda x: np.asarray(x, float) endog, exog, instrument = lmap(asarray, [endog, exog, instrument]) # Need to add all data into exog endog_ = np.zeros(len(endog)) exog_ = np.column_stack((endog, exog)) cls.bse_tol = [0.004, 5e-4] cls.params_tol = [5e-5, 5e-5] # compare to Stata default options, iterative GMM # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs mod = gmm.NonlinearIVGMM(endog_, exog_, instrument, moment_exponential_mult) res0 = mod.fit(start, maxiter=2, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-8, 'disp': 0}, #wargs={'centered':True}, has_optimal_weights=True ) cls.res1 = res0 from .results_gmm_poisson import results_multtwostepdefault as results cls.res2 = results class TestGMMMultTwostepCenter(CheckGMM): #compares my defaults with the same options in Stata @classmethod def setup_class(cls): # compare to Stata default options, twostep GMM XLISTEXOG2 = 'aget aget2 educyr actlim totchr'.split() endog_name = 'docvis' exog_names = 'private medicaid'.split() + XLISTEXOG2 + ['const'] instrument_names = 'income medicaid ssiratio'.split() + XLISTEXOG2 + ['const'] endog = DATA[endog_name] exog = DATA[exog_names] instrument = DATA[instrument_names] asarray = lambda x: np.asarray(x, float) endog, exog, instrument = lmap(asarray, [endog, exog, instrument]) # Need to add all data into exog endog_ = np.zeros(len(endog)) exog_ = np.column_stack((endog, exog)) cls.bse_tol = [5e-4, 5e-5] cls.params_tol = [5e-5, 5e-5] q_tol = [5e-5, 1e-8] # compare to Stata default options, iterative GMM # with const at end start = OLS(endog, exog).fit().params nobs, k_instr = instrument.shape w0inv = np.dot(instrument.T, instrument) / nobs mod = gmm.NonlinearIVGMM(endog_, exog_, instrument, moment_exponential_mult) res0 = mod.fit(start, maxiter=2, inv_weights=w0inv, optim_method='bfgs', optim_args={'gtol':1e-8, 'disp': 0}, wargs={'centered':True}, has_optimal_weights=False ) cls.res1 = res0 from .results_gmm_poisson import results_multtwostepcenter as results cls.res2 = results def test_more(self): # from Stata `overid` J_df = 1 J_p = 0.332254330027383 J = 0.940091427212973 j, jpval, jdf = self.res1.jtest() assert_allclose(jpval, J_p, rtol=5e-5, atol=0) if __name__ == '__main__': tt = TestGMMAddOnestep() tt.setup_class() tt.test_basic() tt.test_other() tt = TestGMMAddTwostep() tt.setup_class() tt.test_basic() tt.test_other() tt = TestGMMMultOnestep() tt.setup_class() tt.test_basic() #tt.test_other() tt = TestGMMMultTwostep() tt.setup_class() tt.test_basic() tt.test_other() tt = TestGMMMultTwostepDefault() tt.setup_class() tt.test_basic() tt.test_other() tt = TestGMMMultTwostepCenter() tt.setup_class() tt.test_basic() tt.test_other() statsmodels-0.12.2/statsmodels/sandbox/regression/tools.py000066400000000000000000000310051400612667500240360ustar00rootroot00000000000000'''gradient/Jacobian of normal and t loglikelihood use chain rule normal derivative wrt mu, sigma and beta new version: loc-scale distributions, derivative wrt loc, scale also includes "standardized" t distribution (for use in GARCH) TODO: * use sympy for derivative of loglike wrt shape parameters it works for df of t distribution dlog(gamma(a))da = polygamma(0,a) check polygamma is available in scipy.special * get loc-scale example to work with mean = X*b * write some full unit test examples A: josef-pktd ''' import numpy as np from scipy import special from scipy.special import gammaln def norm_lls(y, params): '''normal loglikelihood given observations and mean mu and variance sigma2 Parameters ---------- y : ndarray, 1d normally distributed random variable params : ndarray, (nobs, 2) array of mean, variance (mu, sigma2) with observations in rows Returns ------- lls : ndarray contribution to loglikelihood for each observation ''' mu, sigma2 = params.T lls = -0.5*(np.log(2*np.pi) + np.log(sigma2) + (y-mu)**2/sigma2) return lls def norm_lls_grad(y, params): '''Jacobian of normal loglikelihood wrt mean mu and variance sigma2 Parameters ---------- y : ndarray, 1d normally distributed random variable params : ndarray, (nobs, 2) array of mean, variance (mu, sigma2) with observations in rows Returns ------- grad : array (nobs, 2) derivative of loglikelihood for each observation wrt mean in first column, and wrt variance in second column Notes ----- this is actually the derivative wrt sigma not sigma**2, but evaluated with parameter sigma2 = sigma**2 ''' mu, sigma2 = params.T dllsdmu = (y-mu)/sigma2 dllsdsigma2 = ((y-mu)**2/sigma2 - 1)/np.sqrt(sigma2) return np.column_stack((dllsdmu, dllsdsigma2)) def mean_grad(x, beta): '''gradient/Jacobian for d (x*beta)/ d beta ''' return x def normgrad(y, x, params): '''Jacobian of normal loglikelihood wrt mean mu and variance sigma2 Parameters ---------- y : ndarray, 1d normally distributed random variable with mean x*beta, and variance sigma2 x : ndarray, 2d explanatory variables, observation in rows, variables in columns params : array_like, (nvars + 1) array of coefficients and variance (beta, sigma2) Returns ------- grad : array (nobs, 2) derivative of loglikelihood for each observation wrt mean in first column, and wrt scale (sigma) in second column assume params = (beta, sigma2) Notes ----- TODO: for heteroscedasticity need sigma to be a 1d array ''' beta = params[:-1] sigma2 = params[-1]*np.ones((len(y),1)) dmudbeta = mean_grad(x, beta) mu = np.dot(x, beta) #print(beta, sigma2) params2 = np.column_stack((mu,sigma2)) dllsdms = norm_lls_grad(y,params2) grad = np.column_stack((dllsdms[:,:1]*dmudbeta, dllsdms[:,:1])) return grad def tstd_lls(y, params, df): '''t loglikelihood given observations and mean mu and variance sigma2 = 1 Parameters ---------- y : ndarray, 1d normally distributed random variable params : ndarray, (nobs, 2) array of mean, variance (mu, sigma2) with observations in rows df : int degrees of freedom of the t distribution Returns ------- lls : ndarray contribution to loglikelihood for each observation Notes ----- parametrized for garch ''' mu, sigma2 = params.T df = df*1.0 #lls = gammaln((df+1)/2.) - gammaln(df/2.) - 0.5*np.log((df-2)*np.pi) #lls -= (df+1)/2. * np.log(1. + (y-mu)**2/(df-2.)/sigma2) + 0.5 * np.log(sigma2) lls = gammaln((df+1)/2.) - gammaln(df/2.) - 0.5*np.log((df-2)*np.pi) lls -= (df+1)/2. * np.log(1. + (y-mu)**2/(df-2)/sigma2) + 0.5 * np.log(sigma2) return lls def norm_dlldy(y): '''derivative of log pdf of standard normal with respect to y ''' return -y def tstd_pdf(x, df): '''pdf for standardized (not standard) t distribution, variance is one ''' r = np.array(df*1.0) Px = np.exp(special.gammaln((r+1)/2.)-special.gammaln(r/2.))/np.sqrt((r-2)*np.pi) Px /= (1+(x**2)/(r-2))**((r+1)/2.) return Px def ts_lls(y, params, df): '''t loglikelihood given observations and mean mu and variance sigma2 = 1 Parameters ---------- y : ndarray, 1d normally distributed random variable params : ndarray, (nobs, 2) array of mean, variance (mu, sigma2) with observations in rows df : int degrees of freedom of the t distribution Returns ------- lls : ndarray contribution to loglikelihood for each observation Notes ----- parametrized for garch normalized/rescaled so that sigma2 is the variance >>> df = 10; sigma = 1. >>> stats.t.stats(df, loc=0., scale=sigma.*np.sqrt((df-2.)/df)) (array(0.0), array(1.0)) >>> sigma = np.sqrt(2.) >>> stats.t.stats(df, loc=0., scale=sigma*np.sqrt((df-2.)/df)) (array(0.0), array(2.0)) ''' print(y, params, df) mu, sigma2 = params.T df = df*1.0 #lls = gammaln((df+1)/2.) - gammaln(df/2.) - 0.5*np.log((df-2)*np.pi) #lls -= (df+1)/2. * np.log(1. + (y-mu)**2/(df-2.)/sigma2) + 0.5 * np.log(sigma2) lls = gammaln((df+1)/2.) - gammaln(df/2.) - 0.5*np.log((df)*np.pi) lls -= (df+1.)/2. * np.log(1. + (y-mu)**2/(df)/sigma2) + 0.5 * np.log(sigma2) return lls def ts_dlldy(y, df): '''derivative of log pdf of standard t with respect to y Parameters ---------- y : array_like data points of random variable at which loglike is evaluated df : array_like degrees of freedom,shape parameters of log-likelihood function of t distribution Returns ------- dlldy : ndarray derivative of loglikelihood wrt random variable y evaluated at the points given in y Notes ----- with mean 0 and scale 1, but variance is df/(df-2) ''' df = df*1. #(df+1)/2. / (1 + y**2/(df-2.)) * 2.*y/(df-2.) #return -(df+1)/(df-2.) / (1 + y**2/(df-2.)) * y return -(df+1)/(df) / (1 + y**2/(df)) * y def tstd_dlldy(y, df): '''derivative of log pdf of standardized t with respect to y Parameters ---------- y : array_like data points of random variable at which loglike is evaluated df : array_like degrees of freedom,shape parameters of log-likelihood function of t distribution Returns ------- dlldy : ndarray derivative of loglikelihood wrt random variable y evaluated at the points given in y Notes ----- parametrized for garch, standardized to variance=1 ''' #(df+1)/2. / (1 + y**2/(df-2.)) * 2.*y/(df-2.) return -(df+1)/(df-2.) / (1 + y**2/(df-2.)) * y #return (df+1)/(df) / (1 + y**2/(df)) * y def locscale_grad(y, loc, scale, dlldy, *args): '''derivative of log-likelihood with respect to location and scale Parameters ---------- y : array_like data points of random variable at which loglike is evaluated loc : float location parameter of distribution scale : float scale parameter of distribution dlldy : function derivative of loglikelihood fuction wrt. random variable x args : array_like shape parameters of log-likelihood function Returns ------- dlldloc : ndarray derivative of loglikelihood wrt location evaluated at the points given in y dlldscale : ndarray derivative of loglikelihood wrt scale evaluated at the points given in y ''' yst = (y-loc)/scale #ystandardized dlldloc = -dlldy(yst, *args) / scale dlldscale = -1./scale - dlldy(yst, *args) * (y-loc)/scale**2 return dlldloc, dlldscale if __name__ == '__main__': verbose = 0 if verbose: sig = 0.1 beta = np.ones(2) rvs = np.random.randn(10,3) x = rvs[:,1:] y = np.dot(x,beta) + sig*rvs[:,0] params = [1,1,1] print(normgrad(y, x, params)) dllfdbeta = (y-np.dot(x, beta))[:,None]*x #for sigma = 1 print(dllfdbeta) print(locscale_grad(y, np.dot(x, beta), 1, norm_dlldy)) print(y-np.dot(x, beta)) from scipy import stats, misc def llt(y,loc,scale,df): return np.log(stats.t.pdf(y, df, loc=loc, scale=scale)) def lltloc(loc,y,scale,df): return np.log(stats.t.pdf(y, df, loc=loc, scale=scale)) def lltscale(scale,y,loc,df): return np.log(stats.t.pdf(y, df, loc=loc, scale=scale)) def llnorm(y,loc,scale): return np.log(stats.norm.pdf(y, loc=loc, scale=scale)) def llnormloc(loc,y,scale): return np.log(stats.norm.pdf(y, loc=loc, scale=scale)) def llnormscale(scale,y,loc): return np.log(stats.norm.pdf(y, loc=loc, scale=scale)) if verbose: print('\ngradient of t') print(misc.derivative(llt, 1, dx=1e-6, n=1, args=(0,1,10), order=3)) print('t ', locscale_grad(1, 0, 1, tstd_dlldy, 10)) print('ts', locscale_grad(1, 0, 1, ts_dlldy, 10)) print(misc.derivative(llt, 1.5, dx=1e-10, n=1, args=(0,1,20), order=3),) print('ts', locscale_grad(1.5, 0, 1, ts_dlldy, 20)) print(misc.derivative(llt, 1.5, dx=1e-10, n=1, args=(0,2,20), order=3),) print('ts', locscale_grad(1.5, 0, 2, ts_dlldy, 20)) print(misc.derivative(llt, 1.5, dx=1e-10, n=1, args=(1,2,20), order=3),) print('ts', locscale_grad(1.5, 1, 2, ts_dlldy, 20)) print(misc.derivative(lltloc, 1, dx=1e-10, n=1, args=(1.5,2,20), order=3),) print(misc.derivative(lltscale, 2, dx=1e-10, n=1, args=(1.5,1,20), order=3)) y,loc,scale,df = 1.5, 1, 2, 20 print('ts', locscale_grad(y,loc,scale, ts_dlldy, 20)) print(misc.derivative(lltloc, loc, dx=1e-10, n=1, args=(y,scale,df), order=3),) print(misc.derivative(lltscale, scale, dx=1e-10, n=1, args=(y,loc,df), order=3)) print('\ngradient of norm') print(misc.derivative(llnorm, 1, dx=1e-6, n=1, args=(0,1), order=3)) print(locscale_grad(1, 0, 1, norm_dlldy)) y,loc,scale = 1.5, 1, 2 print('ts', locscale_grad(y,loc,scale, norm_dlldy)) print(misc.derivative(llnormloc, loc, dx=1e-10, n=1, args=(y,scale), order=3),) print(misc.derivative(llnormscale, scale, dx=1e-10, n=1, args=(y,loc), order=3)) y,loc,scale = 1.5, 0, 1 print('ts', locscale_grad(y,loc,scale, norm_dlldy)) print(misc.derivative(llnormloc, loc, dx=1e-10, n=1, args=(y,scale), order=3),) print(misc.derivative(llnormscale, scale, dx=1e-10, n=1, args=(y,loc), order=3)) #print('still something wrong with handling of scale and variance' #looks ok now print('\nloglike of t') print(tstd_lls(1, np.array([0,1]), 100), llt(1,0,1,100), 'differently standardized') print(tstd_lls(1, np.array([0,1]), 10), llt(1,0,1,10), 'differently standardized') print(ts_lls(1, np.array([0,1]), 10), llt(1,0,1,10)) print(tstd_lls(1, np.array([0,1.*10./8.]), 10), llt(1.,0,1.,10)) print(ts_lls(1, np.array([0,1]), 100), llt(1,0,1,100)) print(tstd_lls(1, np.array([0,1]), 10), llt(1,0,1.*np.sqrt(8/10.),10)) from numpy.testing import assert_almost_equal params =[(0, 1), (1.,1.), (0.,2.), ( 1., 2.)] yt = np.linspace(-2.,2.,11) for loc,scale in params: dlldlo = misc.derivative(llnormloc, loc, dx=1e-10, n=1, args=(yt,scale), order=3) dlldsc = misc.derivative(llnormscale, scale, dx=1e-10, n=1, args=(yt,loc), order=3) gr = locscale_grad(yt, loc, scale, norm_dlldy) assert_almost_equal(dlldlo, gr[0], 5, err_msg='deriv loc') assert_almost_equal(dlldsc, gr[1], 5, err_msg='deriv scale') for df in [3, 10, 100]: for loc,scale in params: dlldlo = misc.derivative(lltloc, loc, dx=1e-10, n=1, args=(yt,scale,df), order=3) dlldsc = misc.derivative(lltscale, scale, dx=1e-10, n=1, args=(yt,loc,df), order=3) gr = locscale_grad(yt, loc, scale, ts_dlldy, df) assert_almost_equal(dlldlo, gr[0], 4, err_msg='deriv loc') assert_almost_equal(dlldsc, gr[1], 4, err_msg='deriv scale') assert_almost_equal(ts_lls(yt, np.array([loc, scale**2]), df), llt(yt,loc,scale,df), 5, err_msg='loglike') assert_almost_equal(tstd_lls(yt, np.array([loc, scale**2]), df), llt(yt,loc,scale*np.sqrt((df-2.)/df),df), 5, err_msg='loglike') statsmodels-0.12.2/statsmodels/sandbox/regression/treewalkerclass.py000066400000000000000000000515421400612667500261010ustar00rootroot00000000000000''' Formulas -------- This follows mostly Greene notation (in slides) partially ignoring factors tau or mu for now, ADDED (if all tau==1, then runmnl==clogit) leaf k probability : Prob(k|j) = exp(b_k * X_k / mu_j)/ sum_{i in L(j)} (exp(b_i * X_i / mu_j) branch j probabilities : Prob(j) = exp(b_j * X_j + mu*IV_j )/ sum_{i in NB(j)} (exp(b_i * X_i + mu_i*IV_i) inclusive value of branch j : IV_j = log( sum_{i in L(j)} (exp(b_i * X_i / mu_j) ) this is the log of the denominator of the leaf probabilities L(j) : leaves at branch j, where k is child of j NB(j) : set of j and it's siblings Design ------ * splitting calculation transmission between returns and changes to instance.probs - probability for each leaf is in instance.probs - inclusive values and contribution of exog on branch level need to be added separately. handed up the tree through returns * question: should params array be accessed directly through `self.recursionparams[self.parinddict[name]]` or should the dictionary return the values of the params, e.g. `self.params_node_dict[name]`. The second would be easier for fixing tau=1 for degenerate branches. The easiest might be to do the latter only for the taus and default to 1 if the key ('tau_'+branchname) is not found. I also need to exclude tau for degenerate branches from params, but then I cannot change them from the outside for testing and experimentation. (?) * SAS manual describes restrictions on tau (though their model is a bit different), e.g. equal tau across sibling branches, fixed tau. The also allow linear and non-linear (? not sure) restriction on params, the regression coefficients. Related to previous issue, callback without access to the underlying array, where params_node_dict returns the actual params value would provide more flexibility to impose different kinds of restrictions. bugs/problems ------------- * singleton branches return zero to `top`, not a value I'm not sure what they are supposed to return, given the split between returns and instance.probs DONE * Why does 'Air' (singleton branch) get probability exactly 0.5 ? DONE TODO ---- * add tau, normalization for nested logit, currently tau is 1 (clogit) taus also needs to become part of params MOSTLY DONE * add effect of branch level explanatory variables DONE * write a generic multinomial logit that takes arbitrary probabilities, this would be the same for MNL, clogit and runmnl, delegate calculation of probabilities * test on actual data, - tau=1 replicate clogit numbers, - transport example from Greene tests 1-level tree and degenerate sub-trees - test example for multi-level trees ??? * starting values: Greene mentiones that the starting values for the nested version come from the (non-nested) MNL version. SPSS uses constant equal (? check transformation) to sample frequencies and zeros for slope coefficient as starting values for (non-nested) MNL * associated test statistics - (I do not think I will fight with the gradient or hessian of the log-like.) - basic MLE statistics can be generic - tests specific to the model (?) * nice printouts since I'm currently collecting a lot of information in the tree recursion and everything has names The only parts that are really necessary to get a functional nested logit are adding the taus (DONE) and the MLE wrapper class. The rest are enhancements. I added fake tau, one fixed tau for all branches. (OBSOLETE) It's not clear where the tau for leaf should be added either at original assignment of self.probs, or as part of the one-step-down probability correction in the bottom branches. The second would be cleaner (would make treatment of leaves and branches more symmetric, but requires that initial assignment in the leaf only does initialization. e.g self.probs = 1. ??? DONE added taus still todo: - tau for degenerate branches are not identified, set to 1 for MLE - rename parinddict to paramsinddict Author: Josef Perktold License : BSD (3-clause) ''' from statsmodels.compat.python import lrange import numpy as np from pprint import pprint def randintw(w, size=1): '''generate integer random variables given probabilties useful because it can be used as index into any array or sequence type Parameters ---------- w : 1d array_like sequence of weights, probabilites. The weights are normalized to add to one. size : int or tuple of ints shape of output array Returns ------- rvs : array of shape given by size random variables each distributed according to the same discrete distribution defined by (normalized) w. Examples -------- >>> np.random.seed(0) >>> randintw([0.4, 0.4, 0.2], size=(2,6)) array([[1, 1, 1, 1, 1, 1], [1, 2, 2, 0, 1, 1]]) >>> np.bincount(randintw([0.6, 0.4, 0.0], size=3000))/3000. array([ 0.59566667, 0.40433333]) ''' #from Charles Harris, numpy mailing list from numpy.random import random p = np.cumsum(w)/np.sum(w) rvs = p.searchsorted(random(np.prod(size))).reshape(size) return rvs def getbranches(tree): ''' walk tree to get list of branches Parameters ---------- tree : list of tuples tree as defined for RU2NMNL Returns ------- branch : list list of all branch names ''' if isinstance(tree, tuple): name, subtree = tree a = [name] for st in subtree: a.extend(getbranches(st)) return a return [] def getnodes(tree): ''' walk tree to get list of branches and list of leaves Parameters ---------- tree : list of tuples tree as defined for RU2NMNL Returns ------- branch : list list of all branch names leaves : list list of all leaves names ''' if isinstance(tree, tuple): name, subtree = tree ab = [name] al = [] #degenerate branches if len(subtree) == 1: adeg = [name] else: adeg = [] for st in subtree: b, l, d = getnodes(st) ab.extend(b) al.extend(l) adeg.extend(d) return ab, al, adeg return [], [tree], [] testxb = 2 #global to class to return strings instead of numbers class RU2NMNL(object): '''Nested Multinomial Logit with Random Utility 2 parameterization Parameters ---------- endog : ndarray not used in this part exog : dict_like dictionary access to data where keys correspond to branch and leaf names. The values are the data arrays for the exog in that node. tree : nested tuples and lists each branch, tree or subtree, is defined by a tuple (branch_name, [subtree1, subtree2, ..., subtreek]) Bottom branches have as subtrees the list of leaf names. paramsind : dictionary dictionary that maps branch and leaf names to the names of parameters, the coefficients for exogs) Methods ------- get_probs Attributes ---------- branches leaves paramsnames parinddict Notes ----- endog needs to be encoded so it is consistent with self.leaves, which defines the columns for the probability array. The ordering in leaves is determined by the ordering of the tree. In the dummy encoding of endog, the columns of endog need to have the same order as self.leaves. In the integer encoding, the integer for a choice has to correspond to the index in self.leaves. (This could be made more robust, by handling the endog encoding internally by leaf names, if endog is defined as categorical variable with associated category level names.) ''' def __init__(self, endog, exog, tree, paramsind): self.endog = endog self.datadict = exog self.tree = tree self.paramsind = paramsind self.branchsum = '' self.probs = {} self.probstxt = {} self.branchleaves = {} self.branchvalues = {} #just to keep track of returns by branches self.branchsums = {} self.bprobs = {} self.branches, self.leaves, self.branches_degenerate = getnodes(tree) self.nbranches = len(self.branches) #copied over but not quite sure yet #unique, parameter array names, #sorted alphabetically, order is/should be only internal self.paramsnames = (sorted(set([i for j in paramsind.values() for i in j])) + ['tau_%s' % bname for bname in self.branches]) self.nparams = len(self.paramsnames) #mapping coefficient names to indices to unique/parameter array self.paramsidx = dict((name, idx) for (idx,name) in enumerate(self.paramsnames)) #mapping branch and leaf names to index in parameter array self.parinddict = dict((k, [self.paramsidx[j] for j in v]) for k,v in self.paramsind.items()) self.recursionparams = 1. + np.arange(len(self.paramsnames)) #for testing that individual parameters are used in the right place self.recursionparams = np.zeros(len(self.paramsnames)) #self.recursionparams[2] = 1 self.recursionparams[-self.nbranches:] = 1 #values for tau's #self.recursionparams[-2] = 2 def get_probs(self, params): ''' obtain the probability array given an array of parameters This is the function that can be called by loglike or other methods that need the probabilities as function of the params. Parameters ---------- params : 1d array, (nparams,) coefficients and tau that parameterize the model. The required length can be obtained by nparams. (and will depend on the number of degenerate leaves - not yet) Returns ------- probs : ndarray, (nobs, nchoices) probabilites for all choices for each observation. The order is available by attribute leaves. See note in docstring of class ''' self.recursionparams = params self.calc_prob(self.tree) probs_array = np.array([self.probs[leaf] for leaf in self.leaves]) return probs_array #what's the ordering? Should be the same as sequence in tree. #TODO: need a check/assert that this sequence is the same as the # encoding in endog def calc_prob(self, tree, parent=None): '''walking a tree bottom-up based on dictionary ''' #0.5#2 #placeholder for now #should be tau=self.taus[name] but as part of params for optimization endog = self.endog datadict = self.datadict paramsind = self.paramsind branchsum = self.branchsum if isinstance(tree, tuple): #assumes leaves are int for choice index name, subtree = tree self.branchleaves[name] = [] #register branch in dictionary tau = self.recursionparams[self.paramsidx['tau_'+name]] if DEBUG: print('----------- starting next branch-----------') print(name, datadict[name], 'tau=', tau) print('subtree', subtree) branchvalue = [] if testxb == 2: branchsum = 0 elif testxb == 1: branchsum = datadict[name] else: branchsum = name for b in subtree: if DEBUG: print(b) bv = self.calc_prob(b, name) bv = np.exp(bv/tau) #this should not be here, when adding branch data branchvalue.append(bv) branchsum = branchsum + bv self.branchvalues[name] = branchvalue #keep track what was returned if DEBUG: print('----------- returning to branch-----------') print(name) print('branchsum in branch', name, branchsum) if parent: if DEBUG: print('parent', parent) self.branchleaves[parent].extend(self.branchleaves[name]) if 0: #not name == 'top': # not used anymore !!! ??? #if not name == 'top': #TODO: do I need this only on the lowest branches ? tmpsum = 0 for k in self.branchleaves[name]: #similar to this is now also in return branch values #depends on what will be returned tmpsum += self.probs[k] iv = np.log(tmpsum) for k in self.branchleaves[name]: self.probstxt[k] = self.probstxt[k] + ['*' + name + '-prob' + '(%s)' % ', '.join(self.paramsind[name])] #TODO: does this use the denominator twice now self.probs[k] = self.probs[k] / tmpsum if np.size(self.datadict[name])>0: #not used yet, might have to move one indentation level #self.probs[k] = self.probs[k] / tmpsum ## np.exp(-self.datadict[name] * ## np.sum(self.recursionparams[self.parinddict[name]])) if DEBUG: print('self.datadict[name], self.probs[k]') print(self.datadict[name], self.probs[k]) #if not name == 'top': # self.probs[k] = self.probs[k] * np.exp( iv) #walk one level down again to add branch probs to instance.probs self.bprobs[name] = [] for bidx, b in enumerate(subtree): if DEBUG: print('repr(b)', repr(b), bidx) #if len(b) == 1: #TODO: skip leaves, check this if not isinstance(b, tuple): # isinstance(b, str): #TODO: replace this with a check for branch (tuple) instead #this implies name is a bottom branch, #possible to add special things here self.bprobs[name].append(self.probs[b]) #TODO: need tau possibly here self.probs[b] = self.probs[b] / branchsum if DEBUG: print('*********** branchsum at bottom branch', branchsum) #self.bprobs[name].append(self.probs[b]) else: bname = b[0] branchsum2 = sum(self.branchvalues[name]) assert np.abs(branchsum - branchsum2).sum() < 1e-8 bprob = branchvalue[bidx]/branchsum self.bprobs[name].append(bprob) for k in self.branchleaves[bname]: if DEBUG: print('branchprob', bname, k, bprob, branchsum) #temporary hack with maximum to avoid zeros self.probs[k] = self.probs[k] * np.maximum(bprob, 1e-4) if DEBUG: print('working on branch', tree, branchsum) if testxb<2: return branchsum else: #this is the relevant part self.branchsums[name] = branchsum if np.size(self.datadict[name])>0: branchxb = np.sum(self.datadict[name] * self.recursionparams[self.parinddict[name]]) else: branchxb = 0 if not name=='top': tau = self.recursionparams[self.paramsidx['tau_'+name]] else: tau = 1 iv = branchxb + tau * branchsum #which tau: name or parent??? return branchxb + tau * np.log(branchsum) #iv #branchsum is now IV, TODO: add effect of branch variables else: tau = self.recursionparams[self.paramsidx['tau_'+parent]] if DEBUG: print('parent', parent) self.branchleaves[parent].append(tree) # register leave with parent self.probstxt[tree] = [tree + '-prob' + '(%s)' % ', '.join(self.paramsind[tree])] #this is not yet a prob, not normalized to 1, it is exp(x*b) leafprob = np.exp(np.sum(self.datadict[tree] * self.recursionparams[self.parinddict[tree]]) / tau) # fake tau for now, wrong spot ??? #it seems I get the same answer with and without tau here self.probs[tree] = leafprob #= 1 #try initialization only #TODO: where should I add tau in the leaves if testxb == 2: return np.log(leafprob) elif testxb == 1: leavessum = np.array(datadict[tree]) # sum((datadict[bi] for bi in datadict[tree])) if DEBUG: print('final branch with', tree, ''.join(tree), leavessum) #sum(tree) return leavessum #sum(xb[tree]) elif testxb == 0: return ''.join(tree) #sum(tree) if __name__ == '__main__': DEBUG = 0 endog = 5 # dummy place holder ############## Example similar to Greene #get pickled data #endog3, xifloat3 = pickle.load(open('xifloat2.pickle','rb')) tree0 = ('top', [('Fly',['Air']), ('Ground', ['Train', 'Car', 'Bus']) ]) ''' this is with real data from Greene's clogit example datadict = dict(zip(['Air', 'Train', 'Bus', 'Car'], [xifloat[i]for i in range(4)])) ''' #for testing only (mock that returns it's own name datadict = dict(zip(['Air', 'Train', 'Bus', 'Car'], ['Airdata', 'Traindata', 'Busdata', 'Cardata'])) if testxb: datadict = dict(zip(['Air', 'Train', 'Bus', 'Car'], np.arange(4))) datadict.update({'top' : [], 'Fly' : [], 'Ground': []}) paramsind = {'top' : [], 'Fly' : [], 'Ground': [], 'Air' : ['GC', 'Ttme', 'ConstA', 'Hinc'], 'Train' : ['GC', 'Ttme', 'ConstT'], 'Bus' : ['GC', 'Ttme', 'ConstB'], 'Car' : ['GC', 'Ttme'] } modru = RU2NMNL(endog, datadict, tree0, paramsind) modru.recursionparams[-1] = 2 modru.recursionparams[1] = 1 print('Example 1') print('---------\n') print(modru.calc_prob(modru.tree)) print('Tree') pprint(modru.tree) print('\nmodru.probs') pprint(modru.probs) ############## example with many layers tree2 = ('top', [('B1',['a','b']), ('B2', [('B21',['c', 'd']), ('B22',['e', 'f', 'g']) ] ), ('B3',['h'])]) #Note: dict looses ordering paramsind2 = { 'B1': [], 'a': ['consta', 'p'], 'b': ['constb', 'p'], 'B2': ['const2', 'x2'], 'B21': [], 'c': ['constc', 'p', 'time'], 'd': ['constd', 'p', 'time'], 'B22': ['x22'], 'e': ['conste', 'p', 'hince'], 'f': ['constf', 'p', 'hincf'], 'g': [ 'p', 'hincg'], 'B3': [], 'h': ['consth', 'p', 'h'], 'top': []} datadict2 = dict([i for i in zip('abcdefgh',lrange(8))]) datadict2.update({'top':1000, 'B1':100, 'B2':200, 'B21':21,'B22':22, 'B3':300}) ''' >>> pprint(datadict2) {'B1': 100, 'B2': 200, 'B21': 21, 'B22': 22, 'B3': 300, 'a': 0.5, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'top': 1000} ''' modru2 = RU2NMNL(endog, datadict2, tree2, paramsind2) modru2.recursionparams[-3] = 2 modru2.recursionparams[3] = 1 print('\n\nExample 2') print('---------\n') print(modru2.calc_prob(modru2.tree)) print('Tree') pprint(modru2.tree) print('\nmodru.probs') pprint(modru2.probs) print('sum of probs', sum(list(modru2.probs.values()))) print('branchvalues') print(modru2.branchvalues) print(modru.branchvalues) print('branch probabilities') print(modru.bprobs) print('degenerate branches') print(modru.branches_degenerate) ''' >>> modru.bprobs {'Fly': [], 'top': [0.0016714179077931082, 0.99832858209220687], 'Ground': []} >>> modru2.bprobs {'top': [0.25000000000000006, 0.62499999999999989, 0.12500000000000003], 'B22': [], 'B21': [], 'B1': [], 'B2': [0.40000000000000008, 0.59999999999999998], 'B3': []} ''' params1 = np.array([ 0., 1., 0., 0., 0., 0., 1., 1., 2.]) print(modru.get_probs(params1)) params2 = np.array([ 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 1., 1., 2., 1., 1.]) print(modru2.get_probs(params2)) #raises IndexError statsmodels-0.12.2/statsmodels/sandbox/regression/try_catdata.py000066400000000000000000000111411400612667500251740ustar00rootroot00000000000000''' Working with categorical data ============================= use of dummy variables, group statistics, within and between statistics examples for efficient matrix algebra dummy versions require that the number of unique groups or categories is not too large group statistics with scipy.ndimage can handle large number of observations and groups scipy.ndimage stats is missing count new: np.bincount can also be used for calculating values per label ''' from statsmodels.compat.python import lrange import numpy as np from scipy import ndimage #problem: ndimage does not allow axis argument, # calculates mean or var corresponding to axis=None in np.mean, np.var # useless for multivariate application def labelmeanfilter(y, x): # requires integer labels # from mailing list scipy-user 2009-02-11 labelsunique = np.arange(np.max(y)+1) labelmeans = np.array(ndimage.mean(x, labels=y, index=labelsunique)) # returns label means for each original observation return labelmeans[y] #groupcount: i.e. number of observation by group/label #np.array(ndimage.histogram(yrvs[:,0],0,10,1,labels=yrvs[:,0],index=np.unique(yrvs[:,0]))) def labelmeanfilter_nd(y, x): # requires integer labels # from mailing list scipy-user 2009-02-11 # adjusted for 2d x with column variables labelsunique = np.arange(np.max(y)+1) labmeansdata = [] labmeans = [] for xx in x.T: labelmeans = np.array(ndimage.mean(xx, labels=y, index=labelsunique)) labmeansdata.append(labelmeans[y]) labmeans.append(labelmeans) # group count: labelcount = np.array(ndimage.histogram(y, labelsunique[0], labelsunique[-1]+1, 1, labels=y, index=labelsunique)) # returns array of lable/group counts and of label/group means # and label/group means for each original observation return labelcount, np.array(labmeans), np.array(labmeansdata).T def labelmeanfilter_str(ys, x): # works also for string labels in ys, but requires 1D # from mailing list scipy-user 2009-02-11 unil, unilinv = np.unique(ys, return_index=False, return_inverse=True) labelmeans = np.array(ndimage.mean(x, labels=unilinv, index=np.arange(np.max(unil)+1))) arr3 = labelmeans[unilinv] return arr3 def groupstatsbin(factors, values): '''uses np.bincount, assumes factors/labels are integers ''' n = len(factors) ix,rind = np.unique(factors, return_inverse=1) gcount = np.bincount(rind) gmean = np.bincount(rind, weights=values)/ (1.0*gcount) meanarr = gmean[rind] withinvar = np.bincount(rind, weights=(values-meanarr)**2) / (1.0*gcount) withinvararr = withinvar[rind] return gcount, gmean , meanarr, withinvar, withinvararr def convertlabels(ys, indices=None): '''convert labels based on multiple variables or string labels to unique index labels 0,1,2,...,nk-1 where nk is the number of distinct labels ''' if indices is None: ylabel = ys else: idx = np.array(indices) if idx.size > 1 and ys.ndim == 2: ylabel = np.array(['@%s@' % ii[:2].tostring() for ii in ys])[:,np.newaxis] #alternative ## if ys[:,idx].dtype.kind == 'S': ## ylabel = nd.array([' '.join(ii[:2]) for ii in ys])[:,np.newaxis] else: # there might be a problem here ylabel = ys unil, unilinv = np.unique(ylabel, return_index=False, return_inverse=True) return unilinv, np.arange(len(unil)), unil def groupsstats_1d(y, x, labelsunique): '''use ndimage to get fast mean and variance''' labelmeans = np.array(ndimage.mean(x, labels=y, index=labelsunique)) labelvars = np.array(ndimage.var(x, labels=y, index=labelsunique)) return labelmeans, labelvars def cat2dummy(y, nonseq=0): if nonseq or (y.ndim == 2 and y.shape[1] > 1): ycat, uniques, unitransl = convertlabels(y, lrange(y.shape[1])) else: ycat = y.copy() ymin = y.min() uniques = np.arange(ymin,y.max()+1) if ycat.ndim == 1: ycat = ycat[:,np.newaxis] # this builds matrix nobs*ncat dummy = (ycat == uniques).astype(int) return dummy def groupsstats_dummy(y, x, nonseq=0): if x.ndim == 1: # use groupsstats_1d x = x[:,np.newaxis] dummy = cat2dummy(y, nonseq=nonseq) countgr = dummy.sum(0, dtype=float) meangr = np.dot(x.T,dummy)/countgr meandata = np.dot(dummy,meangr.T) # category/group means as array in shape of x xdevmeangr = x - meandata # deviation from category/group mean vargr = np.dot((xdevmeangr * xdevmeangr).T, dummy) / countgr return meangr, vargr, xdevmeangr, countgr statsmodels-0.12.2/statsmodels/sandbox/regression/try_ols_anova.py000066400000000000000000000217751400612667500255720ustar00rootroot00000000000000''' convenience functions for ANOVA type analysis with OLS Note: statistical results of ANOVA are not checked, OLS is checked but not whether the reported results are the ones used in ANOVA includes form2design for creating dummy variables TODO: * ... * ''' from statsmodels.compat.python import lmap import numpy as np #from scipy import stats import statsmodels.api as sm def data2dummy(x, returnall=False): '''convert array of categories to dummy variables by default drops dummy variable for last category uses ravel, 1d only''' x = x.ravel() groups = np.unique(x) if returnall: return (x[:, None] == groups).astype(int) else: return (x[:, None] == groups).astype(int)[:,:-1] def data2proddummy(x): '''creates product dummy variables from 2 columns of 2d array drops last dummy variable, but not from each category singular with simple dummy variable but not with constant quickly written, no safeguards ''' #brute force, assumes x is 2d #replace with encoding if possible groups = np.unique(lmap(tuple, x.tolist())) #includes singularity with additive factors return (x==groups[:,None,:]).all(-1).T.astype(int)[:,:-1] def data2groupcont(x1,x2): '''create dummy continuous variable Parameters ---------- x1 : 1d array label or group array x2 : 1d array (float) continuous variable Notes ----- useful for group specific slope coefficients in regression ''' if x2.ndim == 1: x2 = x2[:,None] dummy = data2dummy(x1, returnall=True) return dummy * x2 # Result strings #the second leaves the constant in, not with NIST regression #but something fishy with res.ess negative in examples ? #not checked if these are all the right ones anova_str0 = ''' ANOVA statistics (model sum of squares excludes constant) Source DF Sum Squares Mean Square F Value Pr > F Model %(df_model)i %(ess)f %(mse_model)f %(fvalue)f %(f_pvalue)f Error %(df_resid)i %(ssr)f %(mse_resid)f CTotal %(nobs)i %(uncentered_tss)f %(mse_total)f R squared %(rsquared)f ''' anova_str = ''' ANOVA statistics (model sum of squares includes constant) Source DF Sum Squares Mean Square F Value Pr > F Model %(df_model)i %(ssmwithmean)f %(mse_model)f %(fvalue)f %(f_pvalue)f Error %(df_resid)i %(ssr)f %(mse_resid)f CTotal %(nobs)i %(uncentered_tss)f %(mse_total)f R squared %(rsquared)f ''' def anovadict(res): '''update regression results dictionary with ANOVA specific statistics not checked for completeness ''' ad = {} ad.update(res.__dict__) #dict does not work with cached attributes anova_attr = ['df_model', 'df_resid', 'ess', 'ssr','uncentered_tss', 'mse_model', 'mse_resid', 'mse_total', 'fvalue', 'f_pvalue', 'rsquared'] for key in anova_attr: ad[key] = getattr(res, key) ad['nobs'] = res.model.nobs ad['ssmwithmean'] = res.uncentered_tss - res.ssr return ad def form2design(ss, data): '''convert string formula to data dictionary ss : str * I : add constant * varname : for simple varnames data is used as is * F:varname : create dummy variables for factor varname * P:varname1*varname2 : create product dummy variables for varnames * G:varname1*varname2 : create product between factor and continuous variable data : dict or structured array data set, access of variables by name as in dictionaries Returns ------- vars : dictionary dictionary of variables with converted dummy variables names : list list of names, product (P:) and grouped continuous variables (G:) have name by joining individual names sorted according to input Examples -------- >>> xx, n = form2design('I a F:b P:c*d G:c*f', testdata) >>> xx.keys() ['a', 'b', 'const', 'cf', 'cd'] >>> n ['const', 'a', 'b', 'cd', 'cf'] Notes ----- with sorted dict, separate name list would not be necessary ''' vars = {} names = [] for item in ss.split(): if item == 'I': vars['const'] = np.ones(data.shape[0]) names.append('const') elif ':' not in item: vars[item] = data[item] names.append(item) elif item[:2] == 'F:': v = item.split(':')[1] vars[v] = data2dummy(data[v]) names.append(v) elif item[:2] == 'P:': v = item.split(':')[1].split('*') vars[''.join(v)] = data2proddummy(np.c_[data[v[0]],data[v[1]]]) names.append(''.join(v)) elif item[:2] == 'G:': v = item.split(':')[1].split('*') vars[''.join(v)] = data2groupcont(data[v[0]], data[v[1]]) names.append(''.join(v)) else: raise ValueError('unknown expression in formula') return vars, names def dropname(ss, li): '''drop names from a list of strings, names to drop are in space delimited list does not change original list ''' newli = li[:] for item in ss.split(): newli.remove(item) return newli if __name__ == '__main__': # Test Example with created data # ------------------------------ nobs = 1000 testdataint = np.random.randint(3, size=(nobs,4)).view([('a',int),('b',int),('c',int),('d',int)]) testdatacont = np.random.normal( size=(nobs,2)).view([('e',float), ('f',float)]) import numpy.lib.recfunctions dt2 = numpy.lib.recfunctions.zip_descr((testdataint, testdatacont),flatten=True) # concatenate structured arrays testdata = np.empty((nobs,1), dt2) for name in testdataint.dtype.names: testdata[name] = testdataint[name] for name in testdatacont.dtype.names: testdata[name] = testdatacont[name] #print(form2design('a',testdata) if 0: # print(only when nobs is small, e.g. nobs=10 xx, n = form2design('F:a',testdata) print(xx) print(form2design('P:a*b',testdata)) print(data2proddummy((np.c_[testdata['a'],testdata['b']]))) xx, names = form2design('a F:b P:c*d',testdata) #xx, names = form2design('I a F:b F:c F:d P:c*d',testdata) xx, names = form2design('I a F:b P:c*d', testdata) xx, names = form2design('I a F:b P:c*d G:a*e f', testdata) X = np.column_stack([xx[nn] for nn in names]) # simple test version: all coefficients equal to one y = X.sum(1) + 0.01*np.random.normal(size=(nobs)) rest1 = sm.OLS(y,X).fit() #results print(rest1.params) print(anova_str % anovadict(rest1)) X = np.column_stack([xx[nn] for nn in dropname('ae f', names)]) # simple test version: all coefficients equal to one y = X.sum(1) + 0.01*np.random.normal(size=(nobs)) rest1 = sm.OLS(y,X).fit() print(rest1.params) print(anova_str % anovadict(rest1)) # Example: from Bruce # ------------------- #get data and clean it #^^^^^^^^^^^^^^^^^^^^^ # requires file 'dftest3.data' posted by Bruce # read data set and drop rows with missing data dt_b = np.dtype([('breed', int), ('sex', int), ('litter', int), ('pen', int), ('pig', int), ('age', float), ('bage', float), ('y', float)]) dta = np.genfromtxt('dftest3.data', dt_b,missing='.', usemask=True) print('missing', [dta.mask[k].sum() for k in dta.dtype.names]) m = dta.mask.view(bool) droprows = m.reshape(-1,len(dta.dtype.names)).any(1) # get complete data as plain structured array # maybe does not work with masked arrays dta_use_b1 = dta[~droprows,:].data print(dta_use_b1.shape) print(dta_use_b1.dtype) #Example b1: variables from Bruce's glm #^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ # prepare data and dummy variables xx_b1, names_b1 = form2design('I F:sex age', dta_use_b1) # create design matrix X_b1 = np.column_stack([xx_b1[nn] for nn in dropname('', names_b1)]) y_b1 = dta_use_b1['y'] # estimate using OLS rest_b1 = sm.OLS(y_b1, X_b1).fit() # print(results) print(rest_b1.params) print(anova_str % anovadict(rest_b1)) #compare with original version only in original version #print(anova_str % anovadict(res_b0)) # Example: use all variables except pig identifier #^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ allexog = ' '.join(dta.dtype.names[:-1]) #'breed sex litter pen pig age bage' xx_b1a, names_b1a = form2design('I F:breed F:sex F:litter F:pen age bage', dta_use_b1) X_b1a = np.column_stack([xx_b1a[nn] for nn in dropname('', names_b1a)]) y_b1a = dta_use_b1['y'] rest_b1a = sm.OLS(y_b1a, X_b1a).fit() print(rest_b1a.params) print(anova_str % anovadict(rest_b1a)) for dropn in names_b1a: print(('\nResults dropping', dropn)) X_b1a_ = np.column_stack([xx_b1a[nn] for nn in dropname(dropn, names_b1a)]) y_b1a_ = dta_use_b1['y'] rest_b1a_ = sm.OLS(y_b1a_, X_b1a_).fit() #print(rest_b1a_.params) print(anova_str % anovadict(rest_b1a_)) statsmodels-0.12.2/statsmodels/sandbox/regression/try_treewalker.py000066400000000000000000000104301400612667500257400ustar00rootroot00000000000000'''Trying out tree structure for nested logit sum is standing for likelihood calculations should collect and aggregate likelihood contributions bottom up ''' from statsmodels.compat.python import lrange import numpy as np tree = [[0,1],[[2,3],[4,5,6]],[7]] #singleton/degenerate branch needs to be list xb = 2*np.arange(8) testxb = 1 #0 def branch(tree): '''walking a tree bottom-up ''' if not isinstance(tree[0], int): #assumes leaves are int for choice index branchsum = 0 for b in tree: branchsum += branch(b) else: print(tree) print('final branch with', tree, sum(tree)) if testxb: return sum(xb[tree]) else: return sum(tree) print('working on branch', tree, branchsum) return branchsum print(branch(tree)) #new version that also keeps track of branch name and allows V_j for a branch # as in Greene, V_j + lamda * IV does not look the same as including the # explanatory variables in leaf X_j, V_j is linear in X, IV is logsumexp of X, testxb = 0#1#0 def branch2(tree): '''walking a tree bottom-up based on dictionary ''' if isinstance(tree, tuple): #assumes leaves are int for choice index name, subtree = tree print(name, data2[name]) print('subtree', subtree) if testxb: branchsum = data2[name] else: branchsum = name #0 for b in subtree: #branchsum += branch2(b) branchsum = branchsum + branch2(b) else: leavessum = sum((data2[bi] for bi in tree)) print('final branch with', tree, ''.join(tree), leavessum) #sum(tree) if testxb: return leavessum #sum(xb[tree]) else: return ''.join(tree) #sum(tree) print('working on branch', tree, branchsum) return branchsum tree = [[0,1],[[2,3],[4,5,6]],[7]] tree2 = ('top', [('B1',['a','b']), ('B2', [('B21',['c', 'd']), ('B22',['e', 'f', 'g']) ] ), ('B3',['h'])] ) data2 = dict([i for i in zip('abcdefgh',lrange(8))]) #data2.update({'top':1000, 'B1':100, 'B2':200, 'B21':300,'B22':400, 'B3':400}) data2.update({'top':1000, 'B1':100, 'B2':200, 'B21':21,'B22':22, 'B3':300}) #data2 #{'a': 0, 'c': 2, 'b': 1, 'e': 4, 'd': 3, 'g': 6, 'f': 5, 'h': 7, #'top': 1000, 'B22': 22, 'B21': 21, 'B1': 100, 'B2': 200, 'B3': 300} print('\n tree with dictionary data') print(branch2(tree2)) # results look correct for testxb=0 and 1 #parameters/coefficients map coefficient names to indices, list of indices into #a 1d params one for each leave and branch #Note: dict looses ordering paramsind = { 'B1': [], 'a': ['consta', 'p'], 'b': ['constb', 'p'], 'B2': ['const2', 'x2'], 'B21': [], 'c': ['consta', 'p', 'time'], 'd': ['consta', 'p', 'time'], 'B22': ['x22'], 'e': ['conste', 'p', 'hince'], 'f': ['constt', 'p', 'hincf'], 'g': [ 'p', 'hincg'], 'B3': [], 'h': ['consth', 'p', 'h'], 'top': []} #unique, parameter array names, #sorted alphabetically, order is/should be only internal paramsnames = sorted(set([i for j in paramsind.values() for i in j])) #mapping coefficient names to indices to unique/parameter array paramsidx = dict((name, idx) for (idx,name) in enumerate(paramsnames)) #mapping branch and leaf names to index in parameter array inddict = dict((k,[paramsidx[j] for j in v]) for k,v in paramsind.items()) ''' >>> paramsnames ['const2', 'consta', 'constb', 'conste', 'consth', 'constt', 'h', 'hince', 'hincf', 'hincg', 'p', 'time', 'x2', 'x22'] >>> parmasidx {'conste': 3, 'consta': 1, 'constb': 2, 'h': 6, 'time': 11, 'consth': 4, 'p': 10, 'constt': 5, 'const2': 0, 'x2': 12, 'x22': 13, 'hince': 7, 'hincg': 9, 'hincf': 8} >>> inddict {'a': [1, 10], 'c': [1, 10, 11], 'b': [2, 10], 'e': [3, 10, 7], 'd': [1, 10, 11], 'g': [10, 9], 'f': [5, 10, 8], 'h': [4, 10, 6], 'top': [], 'B22': [13], 'B21': [], 'B1': [], 'B2': [0, 12], 'B3': []} >>> paramsind {'a': ['consta', 'p'], 'c': ['consta', 'p', 'time'], 'b': ['constb', 'p'], 'e': ['conste', 'p', 'hince'], 'd': ['consta', 'p', 'time'], 'g': ['p', 'hincg'], 'f': ['constt', 'p', 'hincf'], 'h': ['consth', 'p', 'h'], 'top': [], 'B22': ['x22'], 'B21': [], 'B1': [], 'B2': ['const2', 'x2'], 'B3': []} ''' statsmodels-0.12.2/statsmodels/sandbox/rls.py000066400000000000000000000120171400612667500213200ustar00rootroot00000000000000"""Restricted least squares from pandas License: Simplified BSD """ import numpy as np from statsmodels.regression.linear_model import GLS, RegressionResults class RLS(GLS): """ Restricted general least squares model that handles linear constraints Parameters ---------- endog : array_like n length array containing the dependent variable exog : array_like n-by-p array of independent variables constr : array_like k-by-p array of linear constraints param : array_like or scalar p-by-1 array (or scalar) of constraint parameters sigma (None): scalar or array_like The weighting matrix of the covariance. No scaling by default (OLS). If sigma is a scalar, then it is converted into an n-by-n diagonal matrix with sigma as each diagonal element. If sigma is an n-length array, then it is assumed to be a diagonal matrix with the given sigma on the diagonal (WLS). Notes ----- endog = exog * beta + epsilon weights' * constr * beta = param See Greene and Seaks, "The Restricted Least Squares Estimator: A Pedagogical Note", The Review of Economics and Statistics, 1991. """ def __init__(self, endog, exog, constr, param=0., sigma=None): N, Q = exog.shape constr = np.asarray(constr) if constr.ndim == 1: K, P = 1, constr.shape[0] else: K, P = constr.shape if Q != P: raise Exception('Constraints and design do not align') self.ncoeffs = Q self.nconstraint = K self.constraint = constr if np.isscalar(param) and K > 1: param = np.ones((K,)) * param self.param = param if sigma is None: sigma = 1. if np.isscalar(sigma): sigma = np.ones(N) * sigma sigma = np.squeeze(sigma) if sigma.ndim == 1: self.sigma = np.diag(sigma) self.cholsigmainv = np.diag(np.sqrt(sigma)) else: self.sigma = sigma self.cholsigmainv = np.linalg.cholesky(np.linalg.pinv(self.sigma)).T super(GLS, self).__init__(endog, exog) _rwexog = None @property def rwexog(self): """Whitened exogenous variables augmented with restrictions""" if self._rwexog is None: P = self.ncoeffs K = self.nconstraint design = np.zeros((P + K, P + K)) design[:P, :P] = np.dot(self.wexog.T, self.wexog) #top left constr = np.reshape(self.constraint, (K, P)) design[:P, P:] = constr.T #top right partition design[P:, :P] = constr #bottom left partition design[P:, P:] = np.zeros((K, K)) #bottom right partition self._rwexog = design return self._rwexog _inv_rwexog = None @property def inv_rwexog(self): """Inverse of self.rwexog""" if self._inv_rwexog is None: self._inv_rwexog = np.linalg.inv(self.rwexog) return self._inv_rwexog _rwendog = None @property def rwendog(self): """Whitened endogenous variable augmented with restriction parameters""" if self._rwendog is None: P = self.ncoeffs K = self.nconstraint response = np.zeros((P + K,)) response[:P] = np.dot(self.wexog.T, self.wendog) response[P:] = self.param self._rwendog = response return self._rwendog _ncp = None @property def rnorm_cov_params(self): """Parameter covariance under restrictions""" if self._ncp is None: P = self.ncoeffs self._ncp = self.inv_rwexog[:P, :P] return self._ncp _wncp = None @property def wrnorm_cov_params(self): """ Heteroskedasticity-consistent parameter covariance Used to calculate White standard errors. """ if self._wncp is None: df = self.df_resid pred = np.dot(self.wexog, self.coeffs) eps = np.diag((self.wendog - pred) ** 2) sigmaSq = np.sum(eps) pinvX = np.dot(self.rnorm_cov_params, self.wexog.T) self._wncp = np.dot(np.dot(pinvX, eps), pinvX.T) * df / sigmaSq return self._wncp _coeffs = None @property def coeffs(self): """Estimated parameters""" if self._coeffs is None: betaLambda = np.dot(self.inv_rwexog, self.rwendog) self._coeffs = betaLambda[:self.ncoeffs] return self._coeffs def fit(self): rncp = self.wrnorm_cov_params lfit = RegressionResults(self, self.coeffs, normalized_cov_params=rncp) return lfit if __name__=="__main__": import statsmodels.api as sm dta = np.genfromtxt('./rlsdata.txt', names=True) design = np.column_stack((dta['Y'],dta['Y']**2,dta[['NE','NC','W','S']].view(float).reshape(dta.shape[0],-1))) design = sm.add_constant(design, prepend=True) rls_mod = RLS(dta['G'],design, constr=[0,0,0,1,1,1,1]) rls_fit = rls_mod.fit() print(rls_fit.params) statsmodels-0.12.2/statsmodels/sandbox/rlsdata.txt000066400000000000000000000016271400612667500223460ustar00rootroot00000000000000G Y NE NC S W 1.62 1550 1 0 0 0 2.09 3474 1 0 0 0 2.96 4424 1 0 0 0 3.5 5444 1 0 0 0 4.94 6404 1 0 0 0 6.14 7464 1 0 0 0 6.43 8919 1 0 0 0 7 10817 1 0 0 0 8.24 13287 1 0 0 0 9.16 17043 1 0 0 0 10.87 21862 1 0 0 0 12.17 33892 1 0 0 0 1.81 1644 0 1 0 0 2.96 3434 0 1 0 0 3.81 4474 0 1 0 0 4.75 5399 0 1 0 0 5.84 6440 0 1 0 0 6.38 7401 0 1 0 0 7.28 8897 0 1 0 0 8.51 10807 0 1 0 0 8.44 13213 0 1 0 0 10.68 17156 0 1 0 0 10.93 22058 0 1 0 0 12.76 33926 0 1 0 0 2.17 1621 0 0 1 0 3.89 3449 0 0 1 0 5.09 4436 0 0 1 0 5.08 5402 0 0 1 0 6.03 6403 0 0 1 0 6.73 7406 0 0 1 0 7.86 8887 0 0 1 0 9.32 10811 0 0 1 0 9.4 13238 0 0 1 0 10.48 16970 0 0 1 0 11.12 21909 0 0 1 0 11.81 37702 0 0 1 0 2.12 1596 0 0 0 1 3.93 3463 0 0 0 1 5.02 4478 0 0 0 1 6.49 5375 0 0 0 1 5.5 6408 0 0 0 1 6.67 7390 0 0 0 1 7.29 8917 0 0 0 1 8.92 10804 0 0 0 1 9.52 13268 0 0 0 1 10.4 17094 0 0 0 1 11.41 21914 0 0 0 1 11.61 36618 0 0 0 1 statsmodels-0.12.2/statsmodels/sandbox/stats/000077500000000000000000000000001400612667500213035ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/stats/__init__.py000066400000000000000000000012301400612667500234100ustar00rootroot00000000000000'''temporary location for enhancements to scipy.stats includes ^^^^^^^^ * Per Brodtkorb's estimation enhancements to scipy.stats.distributions - distributions_per.py is copy of scipy.stats.distributions.py with changes - distributions_profile.py partially extracted classes and functions to separate code into more managable pieces * josef's extra distribution and helper functions - moment helpers - goodness of fit test - fitting distributions with some fixed parameters - find best distribution that fits data: working script * example and test folders to keep all together status ^^^^^^ mixed status : from not-working to well-tested ''' statsmodels-0.12.2/statsmodels/sandbox/stats/contrast_tools.py000066400000000000000000000701661400612667500247440ustar00rootroot00000000000000'''functions to work with contrasts for multiple tests contrast matrices for comparing all pairs, all levels to reference level, ... extension to 2-way groups in progress TwoWay: class for bringing two-way analysis together and try out various helper functions Idea for second part - get all transformation matrices to move in between different full rank parameterizations - standardize to one parameterization to get all interesting effects. - multivariate normal distribution - exploit or expand what we have in LikelihoodResults, cov_params, f_test, t_test, example: resols_dropf_full.cov_params(C2) - connect to new multiple comparison for contrast matrices, based on multivariate normal or t distribution (Hothorn, Bretz, Westfall) ''' from numpy.testing import assert_equal import numpy as np #next 3 functions copied from multicomp.py def contrast_allpairs(nm): '''contrast or restriction matrix for all pairs of nm variables Parameters ---------- nm : int Returns ------- contr : ndarray, 2d, (nm*(nm-1)/2, nm) contrast matrix for all pairwise comparisons ''' contr = [] for i in range(nm): for j in range(i+1, nm): contr_row = np.zeros(nm) contr_row[i] = 1 contr_row[j] = -1 contr.append(contr_row) return np.array(contr) def contrast_all_one(nm): '''contrast or restriction matrix for all against first comparison Parameters ---------- nm : int Returns ------- contr : ndarray, 2d, (nm-1, nm) contrast matrix for all against first comparisons ''' contr = np.column_stack((np.ones(nm-1), -np.eye(nm-1))) return contr def contrast_diff_mean(nm): '''contrast or restriction matrix for all against mean comparison Parameters ---------- nm : int Returns ------- contr : ndarray, 2d, (nm-1, nm) contrast matrix for all against mean comparisons ''' return np.eye(nm) - np.ones((nm,nm))/nm def signstr(x, noplus=False): if x in [-1,0,1]: if not noplus: return '+' if np.sign(x)>=0 else '-' else: return '' if np.sign(x)>=0 else '-' else: return str(x) def contrast_labels(contrasts, names, reverse=False): if reverse: sl = slice(None, None, -1) else: sl = slice(None) labels = [''.join(['%s%s' % (signstr(c, noplus=True),v) for c,v in zip(row, names)[sl] if c != 0]) for row in contrasts] return labels def contrast_product(names1, names2, intgroup1=None, intgroup2=None, pairs=False): '''build contrast matrices for products of two categorical variables this is an experimental script and should be converted to a class Parameters ---------- names1, names2 : lists of strings contains the list of level labels for each categorical variable intgroup1, intgroup2 : ndarrays TODO: this part not tested, finished yet categorical variable Notes ----- This creates a full rank matrix. It does not do all pairwise comparisons, parameterization is using contrast_all_one to get differences with first level. ? does contrast_all_pairs work as a plugin to get all pairs ? ''' n1 = len(names1) n2 = len(names2) names_prod = ['%s_%s' % (i,j) for i in names1 for j in names2] ee1 = np.zeros((1,n1)) ee1[0,0] = 1 if not pairs: dd = np.r_[ee1, -contrast_all_one(n1)] else: dd = np.r_[ee1, -contrast_allpairs(n1)] contrast_prod = np.kron(dd[1:], np.eye(n2)) names_contrast_prod0 = contrast_labels(contrast_prod, names_prod, reverse=True) names_contrast_prod = [''.join(['%s%s' % (signstr(c, noplus=True),v) for c,v in zip(row, names_prod)[::-1] if c != 0]) for row in contrast_prod] ee2 = np.zeros((1,n2)) ee2[0,0] = 1 #dd2 = np.r_[ee2, -contrast_all_one(n2)] if not pairs: dd2 = np.r_[ee2, -contrast_all_one(n2)] else: dd2 = np.r_[ee2, -contrast_allpairs(n2)] contrast_prod2 = np.kron(np.eye(n1), dd2[1:]) names_contrast_prod2 = [''.join(['%s%s' % (signstr(c, noplus=True),v) for c,v in zip(row, names_prod)[::-1] if c != 0]) for row in contrast_prod2] if (intgroup1 is not None) and (intgroup1 is not None): d1, _ = dummy_1d(intgroup1) d2, _ = dummy_1d(intgroup2) dummy = dummy_product(d1, d2) else: dummy = None return (names_prod, contrast_prod, names_contrast_prod, contrast_prod2, names_contrast_prod2, dummy) def dummy_1d(x, varname=None): '''dummy variable for id integer groups Parameters ---------- x : ndarray, 1d categorical variable, requires integers if varname is None varname : str name of the variable used in labels for category levels Returns ------- dummy : ndarray, 2d array of dummy variables, one column for each level of the category (full set) labels : list[str] labels for the columns, i.e. levels of each category Notes ----- use tools.categorical instead for more more options See Also -------- statsmodels.tools.categorical Examples -------- >>> x = np.array(['F', 'F', 'M', 'M', 'F', 'F', 'M', 'M', 'F', 'F', 'M', 'M'], dtype='|S1') >>> dummy_1d(x, varname='gender') (array([[1, 0], [1, 0], [0, 1], [0, 1], [1, 0], [1, 0], [0, 1], [0, 1], [1, 0], [1, 0], [0, 1], [0, 1]]), ['gender_F', 'gender_M']) ''' if varname is None: #assumes integer labels = ['level_%d' % i for i in range(x.max() + 1)] return (x[:,None]==np.arange(x.max()+1)).astype(int), labels else: grouplabels = np.unique(x) labels = [varname + '_%s' % str(i) for i in grouplabels] return (x[:,None]==grouplabels).astype(int), labels def dummy_product(d1, d2, method='full'): '''dummy variable from product of two dummy variables Parameters ---------- d1, d2 : ndarray two dummy variables, assumes full set for methods 'drop-last' and 'drop-first' method : {'full', 'drop-last', 'drop-first'} 'full' returns the full product, encoding of intersection of categories. The drop methods provide a difference dummy encoding: (constant, main effects, interaction effects). The first or last columns of the dummy variable (i.e. levels) are dropped to get full rank dummy matrix. Returns ------- dummy : ndarray dummy variable for product, see method ''' if method == 'full': dd = (d1[:,:,None]*d2[:,None,:]).reshape(d1.shape[0],-1) elif method == 'drop-last': #same as SAS transreg d12rl = dummy_product(d1[:,:-1], d2[:,:-1]) dd = np.column_stack((np.ones(d1.shape[0], int), d1[:,:-1], d2[:,:-1],d12rl)) #Note: dtype int should preserve dtype of d1 and d2 elif method == 'drop-first': d12r = dummy_product(d1[:,1:], d2[:,1:]) dd = np.column_stack((np.ones(d1.shape[0], int), d1[:,1:], d2[:,1:],d12r)) else: raise ValueError('method not recognized') return dd def dummy_limits(d): '''start and endpoints of groups in a sorted dummy variable array helper function for nested categories Examples -------- >>> d1 = np.array([[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0], [0, 1, 0], [0, 1, 0], [0, 1, 0], [0, 1, 0], [0, 0, 1], [0, 0, 1], [0, 0, 1], [0, 0, 1]]) >>> dummy_limits(d1) (array([0, 4, 8]), array([ 4, 8, 12])) get group slices from an array >>> [np.arange(d1.shape[0])[b:e] for b,e in zip(*dummy_limits(d1))] [array([0, 1, 2, 3]), array([4, 5, 6, 7]), array([ 8, 9, 10, 11])] >>> [np.arange(d1.shape[0])[b:e] for b,e in zip(*dummy_limits(d1))] [array([0, 1, 2, 3]), array([4, 5, 6, 7]), array([ 8, 9, 10, 11])] ''' nobs, nvars = d.shape start1, col1 = np.nonzero(np.diff(d,axis=0)==1) end1, col1_ = np.nonzero(np.diff(d,axis=0)==-1) cc = np.arange(nvars) #print(cc, np.r_[[0], col1], np.r_[col1_, [nvars-1]] if ((not (np.r_[[0], col1] == cc).all()) or (not (np.r_[col1_, [nvars-1]] == cc).all())): raise ValueError('dummy variable is not sorted') start = np.r_[[0], start1+1] end = np.r_[end1+1, [nobs]] return start, end def dummy_nested(d1, d2, method='full'): '''unfinished and incomplete mainly copy past dummy_product dummy variable from product of two dummy variables Parameters ---------- d1, d2 : ndarray two dummy variables, d2 is assumed to be nested in d1 Assumes full set for methods 'drop-last' and 'drop-first'. method : {'full', 'drop-last', 'drop-first'} 'full' returns the full product, which in this case is d2. The drop methods provide an effects encoding: (constant, main effects, subgroup effects). The first or last columns of the dummy variable (i.e. levels) are dropped to get full rank encoding. Returns ------- dummy : ndarray dummy variable for product, see method ''' if method == 'full': return d2 start1, end1 = dummy_limits(d1) start2, end2 = dummy_limits(d2) first = np.in1d(start2, start1) last = np.in1d(end2, end1) equal = (first == last) col_dropf = ~first*~equal col_dropl = ~last*~equal if method == 'drop-last': d12rl = dummy_product(d1[:,:-1], d2[:,:-1]) dd = np.column_stack((np.ones(d1.shape[0], int), d1[:,:-1], d2[:,col_dropl])) #Note: dtype int should preserve dtype of d1 and d2 elif method == 'drop-first': d12r = dummy_product(d1[:,1:], d2[:,1:]) dd = np.column_stack((np.ones(d1.shape[0], int), d1[:,1:], d2[:,col_dropf])) else: raise ValueError('method not recognized') return dd, col_dropf, col_dropl class DummyTransform(object): '''Conversion between full rank dummy encodings y = X b + u b = C a a = C^{-1} b y = X C a + u define Z = X C, then y = Z a + u contrasts: R_b b = r R_a a = R_b C a = r where R_a = R_b C Here C is the transform matrix, with dot_left and dot_right as the main methods, and the same for the inverse transform matrix, C^{-1} Note: - The class was mainly written to keep left and right straight. - No checking is done. - not sure yet if method names make sense ''' def __init__(self, d1, d2): '''C such that d1 C = d2, with d1 = X, d2 = Z should be (x, z) in arguments ? ''' self.transf_matrix = np.linalg.lstsq(d1, d2, rcond=-1)[0] self.invtransf_matrix = np.linalg.lstsq(d2, d1, rcond=-1)[0] def dot_left(self, a): ''' b = C a ''' return np.dot(self.transf_matrix, a) def dot_right(self, x): ''' z = x C ''' return np.dot(x, self.transf_matrix) def inv_dot_left(self, b): ''' a = C^{-1} b ''' return np.dot(self.invtransf_matrix, b) def inv_dot_right(self, z): ''' x = z C^{-1} ''' return np.dot(z, self.invtransf_matrix) def groupmean_d(x, d): '''groupmeans using dummy variables Parameters ---------- x : array_like, ndim data array, tested for 1,2 and 3 dimensions d : ndarray, 1d dummy variable, needs to have the same length as x in axis 0. Returns ------- groupmeans : ndarray, ndim-1 means for each group along axis 0, the levels of the groups are the last axis Notes ----- This will be memory intensive if there are many levels in the categorical variable, i.e. many columns in the dummy variable. In this case it is recommended to use a more efficient version. ''' x = np.asarray(x) ## if x.ndim == 1: ## nvars = 1 ## else: nvars = x.ndim + 1 sli = [slice(None)] + [None]*(nvars-2) + [slice(None)] return (x[...,None] * d[sli]).sum(0)*1./d.sum(0) class TwoWay(object): '''a wrapper class for two way anova type of analysis with OLS currently mainly to bring things together Notes ----- unclear: adding multiple test might assume block design or orthogonality This estimates the full dummy version with OLS. The drop first dummy representation can be recovered through the transform method. TODO: add more methods, tests, pairwise, multiple, marginal effects try out what can be added for userfriendly access. missing: ANOVA table ''' def __init__(self, endog, factor1, factor2, varnames=None): self.nobs = factor1.shape[0] if varnames is None: vname1 = 'a' vname2 = 'b' else: vname1, vname1 = varnames self.d1, self.d1_labels = d1, d1_labels = dummy_1d(factor1, vname1) self.d2, self.d2_labels = d2, d2_labels = dummy_1d(factor2, vname2) self.nlevel1 = nlevel1 = d1.shape[1] self.nlevel2 = nlevel2 = d2.shape[1] #get product dummies res = contrast_product(d1_labels, d2_labels) prodlab, C1, C1lab, C2, C2lab, _ = res self.prod_label, self.C1, self.C1_label, self.C2, self.C2_label, _ = res dp_full = dummy_product(d1, d2, method='full') dp_dropf = dummy_product(d1, d2, method='drop-first') self.transform = DummyTransform(dp_full, dp_dropf) #estimate the model self.nvars = dp_full.shape[1] self.exog = dp_full self.resols = sm.OLS(endog, dp_full).fit() self.params = self.resols.params #get transformed parameters, (constant, main, interaction effect) self.params_dropf = self.transform.inv_dot_left(self.params) self.start_interaction = 1 + (nlevel1 - 1) + (nlevel2 - 1) self.n_interaction = self.nvars - self.start_interaction #convert to cached property def r_nointer(self): '''contrast/restriction matrix for no interaction ''' nia = self.n_interaction R_nointer = np.hstack((np.zeros((nia, self.nvars-nia)), np.eye(nia))) #inter_direct = resols_full_dropf.tval[-nia:] R_nointer_transf = self.transform.inv_dot_right(R_nointer) self.R_nointer_transf = R_nointer_transf return R_nointer_transf def ttest_interaction(self): '''ttests for no-interaction terms are zero ''' #use self.r_nointer instead nia = self.n_interaction R_nointer = np.hstack((np.zeros((nia, self.nvars-nia)), np.eye(nia))) #inter_direct = resols_full_dropf.tval[-nia:] R_nointer_transf = self.transform.inv_dot_right(R_nointer) self.R_nointer_transf = R_nointer_transf t_res = self.resols.t_test(R_nointer_transf) return t_res def ftest_interaction(self): '''ttests for no-interaction terms are zero ''' R_nointer_transf = self.r_nointer() return self.resols.f_test(R_nointer_transf) def ttest_conditional_effect(self, factorind): if factorind == 1: return self.resols.t_test(self.C1), self.C1_label else: return self.resols.t_test(self.C2), self.C2_label def summary_coeff(self): from statsmodels.iolib import SimpleTable params_arr = self.params.reshape(self.nlevel1, self.nlevel2) stubs = self.d1_labels headers = self.d2_labels title = 'Estimated Coefficients by factors' table_fmt = dict( data_fmts = ["%#10.4g"]*self.nlevel2) return SimpleTable(params_arr, headers, stubs, title=title, txt_fmt=table_fmt) # --------------- tests # TODO: several tests still missing, several are in the example with print class TestContrastTools(object): def __init__(self): self.v1name = ['a0', 'a1', 'a2'] self.v2name = ['b0', 'b1'] self.d1 = np.array([[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0], [0, 1, 0], [0, 1, 0], [0, 1, 0], [0, 1, 0], [0, 0, 1], [0, 0, 1], [0, 0, 1], [0, 0, 1]]) def test_dummy_1d(self): x = np.array(['F', 'F', 'M', 'M', 'F', 'F', 'M', 'M', 'F', 'F', 'M', 'M'], dtype='|S1') d, labels = (np.array([[1, 0], [1, 0], [0, 1], [0, 1], [1, 0], [1, 0], [0, 1], [0, 1], [1, 0], [1, 0], [0, 1], [0, 1]]), ['gender_F', 'gender_M']) res_d, res_labels = dummy_1d(x, varname='gender') assert_equal(res_d, d) assert_equal(res_labels, labels) def test_contrast_product(self): res_cp = contrast_product(self.v1name, self.v2name) res_t = [0]*6 res_t[0] = ['a0_b0', 'a0_b1', 'a1_b0', 'a1_b1', 'a2_b0', 'a2_b1'] res_t[1] = np.array([[-1., 0., 1., 0., 0., 0.], [ 0., -1., 0., 1., 0., 0.], [-1., 0., 0., 0., 1., 0.], [ 0., -1., 0., 0., 0., 1.]]) res_t[2] = ['a1_b0-a0_b0', 'a1_b1-a0_b1', 'a2_b0-a0_b0', 'a2_b1-a0_b1'] res_t[3] = np.array([[-1., 1., 0., 0., 0., 0.], [ 0., 0., -1., 1., 0., 0.], [ 0., 0., 0., 0., -1., 1.]]) res_t[4] = ['a0_b1-a0_b0', 'a1_b1-a1_b0', 'a2_b1-a2_b0'] for ii in range(5): np.testing.assert_equal(res_cp[ii], res_t[ii], err_msg=str(ii)) def test_dummy_limits(self): b,e = dummy_limits(self.d1) assert_equal(b, np.array([0, 4, 8])) assert_equal(e, np.array([ 4, 8, 12])) if __name__ == '__main__': tt = TestContrastTools() tt.test_contrast_product() tt.test_dummy_1d() tt.test_dummy_limits() import statsmodels.api as sm examples = ['small', 'large', None][1] v1name = ['a0', 'a1', 'a2'] v2name = ['b0', 'b1'] res_cp = contrast_product(v1name, v2name) print(res_cp) y = np.arange(12) x1 = np.arange(12)//4 x2 = np.arange(12)//2 % 2 if 'small' in examples: d1, d1_labels = dummy_1d(x1) d2, d2_labels = dummy_1d(x2) if 'large' in examples: x1 = np.repeat(x1, 5, axis=0) x2 = np.repeat(x2, 5, axis=0) nobs = x1.shape[0] d1, d1_labels = dummy_1d(x1) d2, d2_labels = dummy_1d(x2) dd_full = dummy_product(d1, d2, method='full') dd_dropl = dummy_product(d1, d2, method='drop-last') dd_dropf = dummy_product(d1, d2, method='drop-first') #Note: full parameterization of dummies is orthogonal #np.eye(6)*10 in "large" example print((np.dot(dd_full.T, dd_full) == np.diag(dd_full.sum(0))).all()) #check that transforms work #generate 3 data sets with the 3 different parameterizations effect_size = [1., 0.01][1] noise_scale = [0.001, 0.1][0] noise = noise_scale * np.random.randn(nobs) beta = effect_size * np.arange(1,7) ydata_full = (dd_full * beta).sum(1) + noise ydata_dropl = (dd_dropl * beta).sum(1) + noise ydata_dropf = (dd_dropf * beta).sum(1) + noise resols_full_full = sm.OLS(ydata_full, dd_full).fit() resols_full_dropf = sm.OLS(ydata_full, dd_dropf).fit() params_f_f = resols_full_full.params params_f_df = resols_full_dropf.params resols_dropf_full = sm.OLS(ydata_dropf, dd_full).fit() resols_dropf_dropf = sm.OLS(ydata_dropf, dd_dropf).fit() params_df_f = resols_dropf_full.params params_df_df = resols_dropf_dropf.params tr_of = np.linalg.lstsq(dd_dropf, dd_full, rcond=-1)[0] tr_fo = np.linalg.lstsq(dd_full, dd_dropf, rcond=-1)[0] print(np.dot(tr_fo, params_df_df) - params_df_f) print(np.dot(tr_of, params_f_f) - params_f_df) transf_f_df = DummyTransform(dd_full, dd_dropf) print(np.max(np.abs((dd_full - transf_f_df.inv_dot_right(dd_dropf))))) print(np.max(np.abs((dd_dropf - transf_f_df.dot_right(dd_full))))) print(np.max(np.abs((params_df_df - transf_f_df.inv_dot_left(params_df_f))))) np.max(np.abs((params_f_df - transf_f_df.inv_dot_left(params_f_f)))) prodlab, C1, C1lab, C2, C2lab,_ = contrast_product(v1name, v2name) print('\ntvalues for no effect of factor 1') print('each test is conditional on a level of factor 2') print(C1lab) print(resols_dropf_full.t_test(C1).tvalue) print('\ntvalues for no effect of factor 2') print('each test is conditional on a level of factor 1') print(C2lab) print(resols_dropf_full.t_test(C2).tvalue) #covariance matrix of restrictions C2, note: orthogonal resols_dropf_full.cov_params(C2) #testing for no interaction effect R_noint = np.hstack((np.zeros((2,4)), np.eye(2))) inter_direct = resols_full_dropf.tvalues[-2:] inter_transf = resols_full_full.t_test(transf_f_df.inv_dot_right(R_noint)).tvalue print(np.max(np.abs((inter_direct - inter_transf)))) #now with class version tw = TwoWay(ydata_dropf, x1, x2) print(tw.ttest_interaction().tvalue) print(tw.ttest_interaction().pvalue) print(tw.ftest_interaction().fvalue) print(tw.ftest_interaction().pvalue) print(tw.ttest_conditional_effect(1)[0].tvalue) print(tw.ttest_conditional_effect(2)[0].tvalue) print(tw.summary_coeff()) ''' documentation for early examples while developing - some have changed already >>> y = np.arange(12) >>> y array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) >>> x1 = np.arange(12)//4 >>> x1 array([0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2]) >>> x2 = np.arange(12)//2%2 >>> x2 array([0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) >>> d1 = dummy_1d(x1) >>> d1 array([[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0], [0, 1, 0], [0, 1, 0], [0, 1, 0], [0, 1, 0], [0, 0, 1], [0, 0, 1], [0, 0, 1], [0, 0, 1]]) >>> d2 = dummy_1d(x2) >>> d2 array([[1, 0], [1, 0], [0, 1], [0, 1], [1, 0], [1, 0], [0, 1], [0, 1], [1, 0], [1, 0], [0, 1], [0, 1]]) >>> d12 = dummy_product(d1, d2) >>> d12 array([[1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1]]) >>> d12rl = dummy_product(d1[:,:-1], d2[:,:-1]) >>> np.column_stack((np.ones(d1.shape[0]), d1[:,:-1], d2[:,:-1],d12rl)) array([[ 1., 1., 0., 1., 1., 0.], [ 1., 1., 0., 1., 1., 0.], [ 1., 1., 0., 0., 0., 0.], [ 1., 1., 0., 0., 0., 0.], [ 1., 0., 1., 1., 0., 1.], [ 1., 0., 1., 1., 0., 1.], [ 1., 0., 1., 0., 0., 0.], [ 1., 0., 1., 0., 0., 0.], [ 1., 0., 0., 1., 0., 0.], [ 1., 0., 0., 1., 0., 0.], [ 1., 0., 0., 0., 0., 0.], [ 1., 0., 0., 0., 0., 0.]]) ''' #nprod = ['%s_%s' % (i,j) for i in ['a0', 'a1', 'a2'] for j in ['b0', 'b1']] #>>> [''.join(['%s%s' % (signstr(c),v) for c,v in zip(row, nprod) if c != 0]) # for row in np.kron(dd[1:], np.eye(2))] ''' >>> nprod = ['%s_%s' % (i,j) for i in ['a0', 'a1', 'a2'] for j in ['b0', 'b1']] >>> nprod ['a0_b0', 'a0_b1', 'a1_b0', 'a1_b1', 'a2_b0', 'a2_b1'] >>> [''.join(['%s%s' % (signstr(c),v) for c,v in zip(row, nprod) if c != 0]) for row in np.kron(dd[1:], np.eye(2))] ['-a0b0+a1b0', '-a0b1+a1b1', '-a0b0+a2b0', '-a0b1+a2b1'] >>> [''.join(['%s%s' % (signstr(c),v) for c,v in zip(row, nprod)[::-1] if c != 0]) for row in np.kron(dd[1:], np.eye(2))] ['+a1_b0-a0_b0', '+a1_b1-a0_b1', '+a2_b0-a0_b0', '+a2_b1-a0_b1'] >>> np.r_[[[1,0,0,0,0]],contrast_all_one(5)] array([[ 1., 0., 0., 0., 0.], [ 1., -1., 0., 0., 0.], [ 1., 0., -1., 0., 0.], [ 1., 0., 0., -1., 0.], [ 1., 0., 0., 0., -1.]]) >>> idxprod = [(i,j) for i in range(3) for j in range(2)] >>> idxprod [(0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (2, 1)] >>> np.array(idxprod).reshape(2,3,2,order='F')[:,:,0] array([[0, 1, 2], [0, 1, 2]]) >>> np.array(idxprod).reshape(2,3,2,order='F')[:,:,1] array([[0, 0, 0], [1, 1, 1]]) >>> dd3_ = np.r_[[[0,0,0]],contrast_all_one(3)] pairwise contrasts and reparameterization dd = np.r_[[[1,0,0,0,0]],-contrast_all_one(5)] >>> dd array([[ 1., 0., 0., 0., 0.], [-1., 1., 0., 0., 0.], [-1., 0., 1., 0., 0.], [-1., 0., 0., 1., 0.], [-1., 0., 0., 0., 1.]]) >>> np.dot(dd.T, np.arange(5)) array([-10., 1., 2., 3., 4.]) >>> np.round(np.linalg.inv(dd.T)).astype(int) array([[1, 1, 1, 1, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]]) >>> np.round(np.linalg.inv(dd)).astype(int) array([[1, 0, 0, 0, 0], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [1, 0, 0, 0, 1]]) >>> dd array([[ 1., 0., 0., 0., 0.], [-1., 1., 0., 0., 0.], [-1., 0., 1., 0., 0.], [-1., 0., 0., 1., 0.], [-1., 0., 0., 0., 1.]]) >>> ddinv=np.round(np.linalg.inv(dd.T)).astype(int) >>> np.dot(ddinv, np.arange(5)) array([10, 1, 2, 3, 4]) >>> np.dot(dd, np.arange(5)) array([ 0., 1., 2., 3., 4.]) >>> np.dot(dd, 5+np.arange(5)) array([ 5., 1., 2., 3., 4.]) >>> ddinv2 = np.round(np.linalg.inv(dd)).astype(int) >>> np.dot(ddinv2, np.arange(5)) array([0, 1, 2, 3, 4]) >>> np.dot(ddinv2, 5+np.arange(5)) array([ 5, 11, 12, 13, 14]) >>> np.dot(ddinv2, [5, 0, 0 , 1, 2]) array([5, 5, 5, 6, 7]) >>> np.dot(ddinv2, dd) array([[ 1., 0., 0., 0., 0.], [ 0., 1., 0., 0., 0.], [ 0., 0., 1., 0., 0.], [ 0., 0., 0., 1., 0.], [ 0., 0., 0., 0., 1.]]) >>> dd3 = -np.r_[[[1,0,0]],contrast_all_one(3)] >>> dd2 = -np.r_[[[1,0]],contrast_all_one(2)] >>> np.kron(np.eye(3), dd2) array([[-1., 0., 0., 0., 0., 0.], [-1., 1., 0., 0., 0., 0.], [ 0., 0., -1., 0., 0., 0.], [ 0., 0., -1., 1., 0., 0.], [ 0., 0., 0., 0., -1., 0.], [ 0., 0., 0., 0., -1., 1.]]) >>> dd2 array([[-1., 0.], [-1., 1.]]) >>> np.kron(np.eye(3), dd2[1:]) array([[-1., 1., 0., 0., 0., 0.], [ 0., 0., -1., 1., 0., 0.], [ 0., 0., 0., 0., -1., 1.]]) >>> np.kron(dd[1:], np.eye(2)) array([[-1., 0., 1., 0., 0., 0.], [ 0., -1., 0., 1., 0., 0.], [-1., 0., 0., 0., 1., 0.], [ 0., -1., 0., 0., 0., 1.]]) d_ = np.r_[[[1,0,0,0,0]],contrast_all_one(5)] >>> d_ array([[ 1., 0., 0., 0., 0.], [ 1., -1., 0., 0., 0.], [ 1., 0., -1., 0., 0.], [ 1., 0., 0., -1., 0.], [ 1., 0., 0., 0., -1.]]) >>> np.round(np.linalg.pinv(d_)).astype(int) array([[ 1, 0, 0, 0, 0], [ 1, -1, 0, 0, 0], [ 1, 0, -1, 0, 0], [ 1, 0, 0, -1, 0], [ 1, 0, 0, 0, -1]]) >>> np.linalg.inv(d_).astype(int) array([[ 1, 0, 0, 0, 0], [ 1, -1, 0, 0, 0], [ 1, 0, -1, 0, 0], [ 1, 0, 0, -1, 0], [ 1, 0, 0, 0, -1]]) group means >>> sli = [slice(None)] + [None]*(3-2) + [slice(None)] >>> (np.column_stack((y, x1, x2))[...,None] * d1[sli]).sum(0)*1./d1.sum(0) array([[ 1.5, 5.5, 9.5], [ 0. , 1. , 2. ], [ 0.5, 0.5, 0.5]]) >>> [(z[:,None] * d1).sum(0)*1./d1.sum(0) for z in np.column_stack((y, x1, x2)).T] [array([ 1.5, 5.5, 9.5]), array([ 0., 1., 2.]), array([ 0.5, 0.5, 0.5])] >>> ''' statsmodels-0.12.2/statsmodels/sandbox/stats/diagnostic.py000066400000000000000000000020531400612667500240010ustar00rootroot00000000000000import warnings from statsmodels.stats.diagnostic import ( CompareCox, CompareJ, HetGoldfeldQuandt, OLS, ResultsStore, acorr_breusch_godfrey, acorr_ljungbox, acorr_lm, breaks_cusumolsresid, breaks_hansen, compare_cox, compare_j, het_arch, het_breuschpagan, het_goldfeldquandt, het_white, linear_harvey_collier, linear_lm, linear_rainbow, recursive_olsresiduals, spec_white ) from statsmodels.tsa.stattools import adfuller __all__ = ["CompareCox", "CompareJ", "HetGoldfeldQuandt", "OLS", "ResultsStore", "acorr_breusch_godfrey", "acorr_ljungbox", "acorr_lm", "adfuller", "breaks_cusumolsresid", "breaks_hansen", "compare_cox", "compare_j", "het_arch", "het_breuschpagan", "het_goldfeldquandt", "het_white", "linear_harvey_collier", "linear_lm", "linear_rainbow", "recursive_olsresiduals", "spec_white"] warnings.warn("The statsmodels.sandbox.stats.diagnostic module is deprecated. " "Use statsmodels.stats.diagnostic.", DeprecationWarning, stacklevel=2) statsmodels-0.12.2/statsmodels/sandbox/stats/ex_newtests.py000066400000000000000000000015031400612667500242240ustar00rootroot00000000000000from statsmodels.tsa.stattools import adfuller import statsmodels.datasets.macrodata.data as macro macrod = macro.load(as_pandas=False).data print(macro.NOTE) print(macrod.dtype.names) datatrendli = [ ('realgdp', 1), ('realcons', 1), ('realinv', 1), ('realgovt', 1), ('realdpi', 1), ('cpi', 1), ('m1', 1), ('tbilrate', 0), ('unemp',0), ('pop', 1), ('infl',0), ('realint', 0) ] print('%-10s %5s %-8s' % ('variable', 'trend', ' adf')) for name, torder in datatrendli: c_order = {0: "nc", 1: "c"} adf_, pval = adfuller(macrod[name], regression=c_order[torder])[:2] print('%-10s %5d %8.4f %8.4f' % (name, torder, adf_, pval)) statsmodels-0.12.2/statsmodels/sandbox/stats/multicomp.py000066400000000000000000002063351400612667500236770ustar00rootroot00000000000000''' from pystatsmodels mailinglist 20100524 Notes: - unfinished, unverified, but most parts seem to work in MonteCarlo - one example taken from lecture notes looks ok - needs cases with non-monotonic inequality for test to see difference between one-step, step-up and step-down procedures - FDR does not look really better then Bonferoni in the MC examples that I tried update: - now tested against R, stats and multtest, I have all of their methods for p-value correction - getting Hommel was impossible until I found reference for pvalue correction - now, since I have p-values correction, some of the original tests (rej/norej) implementation is not really needed anymore. I think I keep it for reference. Test procedure for Hommel in development session log - I have not updated other functions and classes in here. - multtest has some good helper function according to docs - still need to update references, the real papers - fdr with estimated true hypothesis still missing - multiple comparison procedures incomplete or missing - I will get multiple comparison for now only for independent case, which might be conservative in correlated case (?). some References: Gibbons, Jean Dickinson and Chakraborti Subhabrata, 2003, Nonparametric Statistical Inference, Fourth Edition, Marcel Dekker p.363: 10.4 THE KRUSKAL-WALLIS ONE-WAY ANOVA TEST AND MULTIPLE COMPARISONS p.367: multiple comparison for kruskal formula used in multicomp.kruskal Sheskin, David J., 2004, Handbook of Parametric and Nonparametric Statistical Procedures, 3rd ed., Chapman&Hall/CRC Test 21: The Single-Factor Between-Subjects Analysis of Variance Test 22: The Kruskal-Wallis One-Way Analysis of Variance by Ranks Test Zwillinger, Daniel and Stephen Kokoska, 2000, CRC standard probability and statistics tables and formulae, Chapman&Hall/CRC 14.9 WILCOXON RANKSUM (MANN WHITNEY) TEST S. Paul Wright, Adjusted P-Values for Simultaneous Inference, Biometrics Vol. 48, No. 4 (Dec., 1992), pp. 1005-1013, International Biometric Society Stable URL: http://www.jstor.org/stable/2532694 (p-value correction for Hommel in appendix) for multicomparison new book "multiple comparison in R" Hsu is a good reference but I do not have it. Author: Josef Pktd and example from H Raja and rewrite from Vincent Davis TODO ---- * name of function multipletests, rename to something like pvalue_correction? ''' from statsmodels.compat.python import lzip, lrange import copy import math import numpy as np from numpy.testing import assert_almost_equal, assert_equal from scipy import stats, interpolate from statsmodels.iolib.table import SimpleTable #temporary circular import from statsmodels.stats.multitest import multipletests, _ecdf as ecdf, fdrcorrection as fdrcorrection0, fdrcorrection_twostage from statsmodels.graphics import utils from statsmodels.tools.sm_exceptions import ValueWarning qcrit = ''' 2 3 4 5 6 7 8 9 10 5 3.64 5.70 4.60 6.98 5.22 7.80 5.67 8.42 6.03 8.91 6.33 9.32 6.58 9.67 6.80 9.97 6.99 10.24 6 3.46 5.24 4.34 6.33 4.90 7.03 5.30 7.56 5.63 7.97 5.90 8.32 6.12 8.61 6.32 8.87 6.49 9.10 7 3.34 4.95 4.16 5.92 4.68 6.54 5.06 7.01 5.36 7.37 5.61 7.68 5.82 7.94 6.00 8.17 6.16 8.37 8 3.26 4.75 4.04 5.64 4.53 6.20 4.89 6.62 5.17 6.96 5.40 7.24 5.60 7.47 5.77 7.68 5.92 7.86 9 3.20 4.60 3.95 5.43 4.41 5.96 4.76 6.35 5.02 6.66 5.24 6.91 5.43 7.13 5.59 7.33 5.74 7.49 10 3.15 4.48 3.88 5.27 4.33 5.77 4.65 6.14 4.91 6.43 5.12 6.67 5.30 6.87 5.46 7.05 5.60 7.21 11 3.11 4.39 3.82 5.15 4.26 5.62 4.57 5.97 4.82 6.25 5.03 6.48 5.20 6.67 5.35 6.84 5.49 6.99 12 3.08 4.32 3.77 5.05 4.20 5.50 4.51 5.84 4.75 6.10 4.95 6.32 5.12 6.51 5.27 6.67 5.39 6.81 13 3.06 4.26 3.73 4.96 4.15 5.40 4.45 5.73 4.69 5.98 4.88 6.19 5.05 6.37 5.19 6.53 5.32 6.67 14 3.03 4.21 3.70 4.89 4.11 5.32 4.41 5.63 4.64 5.88 4.83 6.08 4.99 6.26 5.13 6.41 5.25 6.54 15 3.01 4.17 3.67 4.84 4.08 5.25 4.37 5.56 4.59 5.80 4.78 5.99 4.94 6.16 5.08 6.31 5.20 6.44 16 3.00 4.13 3.65 4.79 4.05 5.19 4.33 5.49 4.56 5.72 4.74 5.92 4.90 6.08 5.03 6.22 5.15 6.35 17 2.98 4.10 3.63 4.74 4.02 5.14 4.30 5.43 4.52 5.66 4.70 5.85 4.86 6.01 4.99 6.15 5.11 6.27 18 2.97 4.07 3.61 4.70 4.00 5.09 4.28 5.38 4.49 5.60 4.67 5.79 4.82 5.94 4.96 6.08 5.07 6.20 19 2.96 4.05 3.59 4.67 3.98 5.05 4.25 5.33 4.47 5.55 4.65 5.73 4.79 5.89 4.92 6.02 5.04 6.14 20 2.95 4.02 3.58 4.64 3.96 5.02 4.23 5.29 4.45 5.51 4.62 5.69 4.77 5.84 4.90 5.97 5.01 6.09 24 2.92 3.96 3.53 4.55 3.90 4.91 4.17 5.17 4.37 5.37 4.54 5.54 4.68 5.69 4.81 5.81 4.92 5.92 30 2.89 3.89 3.49 4.45 3.85 4.80 4.10 5.05 4.30 5.24 4.46 5.40 4.60 5.54 4.72 5.65 4.82 5.76 40 2.86 3.82 3.44 4.37 3.79 4.70 4.04 4.93 4.23 5.11 4.39 5.26 4.52 5.39 4.63 5.50 4.73 5.60 60 2.83 3.76 3.40 4.28 3.74 4.59 3.98 4.82 4.16 4.99 4.31 5.13 4.44 5.25 4.55 5.36 4.65 5.45 120 2.80 3.70 3.36 4.20 3.68 4.50 3.92 4.71 4.10 4.87 4.24 5.01 4.36 5.12 4.47 5.21 4.56 5.30 infinity 2.77 3.64 3.31 4.12 3.63 4.40 3.86 4.60 4.03 4.76 4.17 4.88 4.29 4.99 4.39 5.08 4.47 5.16 ''' res = [line.split() for line in qcrit.replace('infinity','9999').split('\n')] c=np.array(res[2:-1]).astype(float) #c[c==9999] = np.inf ccols = np.arange(2,11) crows = c[:,0] cv005 = c[:, 1::2] cv001 = c[:, 2::2] def get_tukeyQcrit(k, df, alpha=0.05): ''' return critical values for Tukey's HSD (Q) Parameters ---------- k : int in {2, ..., 10} number of tests df : int degrees of freedom of error term alpha : {0.05, 0.01} type 1 error, 1-confidence level not enough error checking for limitations ''' if alpha == 0.05: intp = interpolate.interp1d(crows, cv005[:,k-2]) elif alpha == 0.01: intp = interpolate.interp1d(crows, cv001[:,k-2]) else: raise ValueError('only implemented for alpha equal to 0.01 and 0.05') return intp(df) def get_tukeyQcrit2(k, df, alpha=0.05): ''' return critical values for Tukey's HSD (Q) Parameters ---------- k : int in {2, ..., 10} number of tests df : int degrees of freedom of error term alpha : {0.05, 0.01} type 1 error, 1-confidence level not enough error checking for limitations ''' from statsmodels.stats.libqsturng import qsturng return qsturng(1-alpha, k, df) def get_tukey_pvalue(k, df, q): ''' return adjusted p-values for Tukey's HSD Parameters ---------- k : int in {2, ..., 10} number of tests df : int degrees of freedom of error term q : scalar, array_like; q >= 0 quantile value of Studentized Range ''' from statsmodels.stats.libqsturng import psturng return psturng(q, k, df) def Tukeythreegene(first, second, third): # Performing the Tukey HSD post-hoc test for three genes # qwb = xlrd.open_workbook('F:/Lab/bioinformatics/qcrittable.xls') # #opening the workbook containing the q crit table # qwb.sheet_names() # qcrittable = qwb.sheet_by_name(u'Sheet1') # means of the three arrays firstmean = np.mean(first) secondmean = np.mean(second) thirdmean = np.mean(third) # standard deviations of the threearrays firststd = np.std(first) secondstd = np.std(second) thirdstd = np.std(third) # standard deviation squared of the three arrays firsts2 = math.pow(firststd, 2) seconds2 = math.pow(secondstd, 2) thirds2 = math.pow(thirdstd, 2) # numerator for mean square error mserrornum = firsts2 * 2 + seconds2 * 2 + thirds2 * 2 # denominator for mean square error mserrorden = (len(first) + len(second) + len(third)) - 3 mserror = mserrornum / mserrorden # mean square error standarderror = math.sqrt(mserror / len(first)) # standard error, which is square root of mserror and # the number of samples in a group # various degrees of freedom dftotal = len(first) + len(second) + len(third) - 1 dfgroups = 2 dferror = dftotal - dfgroups # noqa: F841 qcrit = 0.5 # fix arbitrary#qcrittable.cell(dftotal, 3).value qcrit = get_tukeyQcrit(3, dftotal, alpha=0.05) # getting the q critical value, for degrees of freedom total and 3 groups qtest3to1 = (math.fabs(thirdmean - firstmean)) / standarderror # calculating q test statistic values qtest3to2 = (math.fabs(thirdmean - secondmean)) / standarderror qtest2to1 = (math.fabs(secondmean - firstmean)) / standarderror conclusion = [] # print(qcrit print(qtest3to1) print(qtest3to2) print(qtest2to1) # testing all q test statistic values to q critical values if qtest3to1 > qcrit: conclusion.append('3to1null') else: conclusion.append('3to1alt') if qtest3to2 > qcrit: conclusion.append('3to2null') else: conclusion.append('3to2alt') if qtest2to1 > qcrit: conclusion.append('2to1null') else: conclusion.append('2to1alt') return conclusion #rewrite by Vincent def Tukeythreegene2(genes): #Performing the Tukey HSD post-hoc test for three genes """gend is a list, ie [first, second, third]""" # qwb = xlrd.open_workbook('F:/Lab/bioinformatics/qcrittable.xls') #opening the workbook containing the q crit table # qwb.sheet_names() # qcrittable = qwb.sheet_by_name(u'Sheet1') means = [] stds = [] for gene in genes: means.append(np.mean(gene)) std.append(np.std(gene)) # noqa:F821 See GH#5756 #firstmean = np.mean(first) #means of the three arrays #secondmean = np.mean(second) #thirdmean = np.mean(third) #firststd = np.std(first) #standard deviations of the three arrays #secondstd = np.std(second) #thirdstd = np.std(third) stds2 = [] for std in stds: stds2.append(math.pow(std,2)) #firsts2 = math.pow(firststd,2) #standard deviation squared of the three arrays #seconds2 = math.pow(secondstd,2) #thirds2 = math.pow(thirdstd,2) #mserrornum = firsts2*2+seconds2*2+thirds2*2 #numerator for mean square error mserrornum = sum(stds2)*2 mserrorden = (len(genes[0])+len(genes[1])+len(genes[2]))-3 #denominator for mean square error mserror = mserrornum/mserrorden #mean square error def catstack(args): x = np.hstack(args) labels = np.hstack([k*np.ones(len(arr)) for k,arr in enumerate(args)]) return x, labels def maxzero(x): '''find all up zero crossings and return the index of the highest Not used anymore >>> np.random.seed(12345) >>> x = np.random.randn(8) >>> x array([-0.20470766, 0.47894334, -0.51943872, -0.5557303 , 1.96578057, 1.39340583, 0.09290788, 0.28174615]) >>> maxzero(x) (4, array([1, 4])) no up-zero-crossing at end >>> np.random.seed(0) >>> x = np.random.randn(8) >>> x array([ 1.76405235, 0.40015721, 0.97873798, 2.2408932 , 1.86755799, -0.97727788, 0.95008842, -0.15135721]) >>> maxzero(x) (None, array([6])) ''' x = np.asarray(x) cond1 = x[:-1] < 0 cond2 = x[1:] > 0 #allzeros = np.nonzero(np.sign(x[:-1])*np.sign(x[1:]) <= 0)[0] + 1 allzeros = np.nonzero((cond1 & cond2) | (x[1:]==0))[0] + 1 if x[-1] >=0: maxz = max(allzeros) else: maxz = None return maxz, allzeros def maxzerodown(x): '''find all up zero crossings and return the index of the highest Not used anymore >>> np.random.seed(12345) >>> x = np.random.randn(8) >>> x array([-0.20470766, 0.47894334, -0.51943872, -0.5557303 , 1.96578057, 1.39340583, 0.09290788, 0.28174615]) >>> maxzero(x) (4, array([1, 4])) no up-zero-crossing at end >>> np.random.seed(0) >>> x = np.random.randn(8) >>> x array([ 1.76405235, 0.40015721, 0.97873798, 2.2408932 , 1.86755799, -0.97727788, 0.95008842, -0.15135721]) >>> maxzero(x) (None, array([6])) ''' x = np.asarray(x) cond1 = x[:-1] > 0 cond2 = x[1:] < 0 #allzeros = np.nonzero(np.sign(x[:-1])*np.sign(x[1:]) <= 0)[0] + 1 allzeros = np.nonzero((cond1 & cond2) | (x[1:]==0))[0] + 1 if x[-1] <=0: maxz = max(allzeros) else: maxz = None return maxz, allzeros def rejectionline(n, alpha=0.5): '''reference line for rejection in multiple tests Not used anymore from: section 3.2, page 60 ''' t = np.arange(n)/float(n) frej = t/( t * (1-alpha) + alpha) return frej #I do not remember what I changed or why 2 versions, #this follows german diss ??? with rline #this might be useful if the null hypothesis is not "all effects are zero" #rename to _bak and working again on fdrcorrection0 def fdrcorrection_bak(pvals, alpha=0.05, method='indep'): '''Reject False discovery rate correction for pvalues Old version, to be deleted missing: methods that estimate fraction of true hypotheses ''' pvals = np.asarray(pvals) pvals_sortind = np.argsort(pvals) pvals_sorted = pvals[pvals_sortind] pecdf = ecdf(pvals_sorted) if method in ['i', 'indep', 'p', 'poscorr']: rline = pvals_sorted / alpha elif method in ['n', 'negcorr']: cm = np.sum(1./np.arange(1, len(pvals))) rline = pvals_sorted / alpha * cm elif method in ['g', 'onegcorr']: #what's this ? german diss rline = pvals_sorted / (pvals_sorted*(1-alpha) + alpha) elif method in ['oth', 'o2negcorr']: # other invalid, cut-paste cm = np.sum(np.arange(len(pvals))) rline = pvals_sorted / alpha /cm else: raise ValueError('method not available') reject = pecdf >= rline if reject.any(): rejectmax = max(np.nonzero(reject)[0]) else: rejectmax = 0 reject[:rejectmax] = True return reject[pvals_sortind.argsort()] def mcfdr(nrepl=100, nobs=50, ntests=10, ntrue=6, mu=0.5, alpha=0.05, rho=0.): '''MonteCarlo to test fdrcorrection ''' nfalse = ntests - ntrue locs = np.array([0.]*ntrue + [mu]*(ntests - ntrue)) results = [] for i in range(nrepl): #rvs = locs + stats.norm.rvs(size=(nobs, ntests)) rvs = locs + randmvn(rho, size=(nobs, ntests)) tt, tpval = stats.ttest_1samp(rvs, 0) res = fdrcorrection_bak(np.abs(tpval), alpha=alpha, method='i') res0 = fdrcorrection0(np.abs(tpval), alpha=alpha) #res and res0 give the same results results.append([np.sum(res[:ntrue]), np.sum(res[ntrue:])] + [np.sum(res0[:ntrue]), np.sum(res0[ntrue:])] + res.tolist() + np.sort(tpval).tolist() + [np.sum(tpval[:ntrue] 1] ntot = float(len(xranks)) tiecorrection = 1 - (nties**3 - nties).sum()/(ntot**3 - ntot) return tiecorrection class GroupsStats(object): ''' statistics by groups (another version) groupstats as a class with lazy evaluation (not yet - decorators are still missing) written this time as equivalent of scipy.stats.rankdata gs = GroupsStats(X, useranks=True) assert_almost_equal(gs.groupmeanfilter, stats.rankdata(X[:,0]), 15) TODO: incomplete doc strings ''' def __init__(self, x, useranks=False, uni=None, intlab=None): '''descriptive statistics by groups Parameters ---------- x : ndarray, 2d first column data, second column group labels useranks : bool if true, then use ranks as data corresponding to the scipy.stats.rankdata definition (start at 1, ties get mean) uni, intlab : arrays (optional) to avoid call to unique, these can be given as inputs ''' self.x = np.asarray(x) if intlab is None: uni, intlab = np.unique(x[:,1], return_inverse=True) elif uni is None: uni = np.unique(x[:,1]) self.useranks = useranks self.uni = uni self.intlab = intlab self.groupnobs = groupnobs = np.bincount(intlab) #temporary until separated and made all lazy self.runbasic(useranks=useranks) def runbasic_old(self, useranks=False): """runbasic_old""" #check: refactoring screwed up case useranks=True #groupxsum = np.bincount(intlab, weights=X[:,0]) #groupxmean = groupxsum * 1.0 / groupnobs x = self.x if useranks: self.xx = x[:,1].argsort().argsort() + 1 #rankraw else: self.xx = x[:,0] self.groupsum = groupranksum = np.bincount(self.intlab, weights=self.xx) #print('groupranksum', groupranksum, groupranksum.shape, self.groupnobs.shape # start at 1 for stats.rankdata : self.groupmean = grouprankmean = groupranksum * 1.0 / self.groupnobs # + 1 self.groupmeanfilter = grouprankmean[self.intlab] #return grouprankmean[intlab] def runbasic(self, useranks=False): """runbasic""" #check: refactoring screwed up case useranks=True #groupxsum = np.bincount(intlab, weights=X[:,0]) #groupxmean = groupxsum * 1.0 / groupnobs x = self.x if useranks: xuni, xintlab = np.unique(x[:,0], return_inverse=True) ranksraw = x[:,0].argsort().argsort() + 1 #rankraw self.xx = GroupsStats(np.column_stack([ranksraw, xintlab]), useranks=False).groupmeanfilter else: self.xx = x[:,0] self.groupsum = groupranksum = np.bincount(self.intlab, weights=self.xx) #print('groupranksum', groupranksum, groupranksum.shape, self.groupnobs.shape # start at 1 for stats.rankdata : self.groupmean = grouprankmean = groupranksum * 1.0 / self.groupnobs # + 1 self.groupmeanfilter = grouprankmean[self.intlab] #return grouprankmean[intlab] def groupdemean(self): """groupdemean""" return self.xx - self.groupmeanfilter def groupsswithin(self): """groupsswithin""" xtmp = self.groupdemean() return np.bincount(self.intlab, weights=xtmp**2) def groupvarwithin(self): """groupvarwithin""" return self.groupsswithin()/(self.groupnobs-1) #.sum() class TukeyHSDResults(object): """Results from Tukey HSD test, with additional plot methods Can also compute and plot additional post-hoc evaluations using this results class. Attributes ---------- reject : array of boolean, True if we reject Null for group pair meandiffs : pairwise mean differences confint : confidence interval for pairwise mean differences std_pairs : standard deviation of pairwise mean differences q_crit : critical value of studentized range statistic at given alpha halfwidths : half widths of simultaneous confidence interval pvalues : adjusted p-values from the HSD test Notes ----- halfwidths is only available after call to `plot_simultaneous`. Other attributes contain information about the data from the MultiComparison instance: data, df_total, groups, groupsunique, variance. """ def __init__(self, mc_object, results_table, q_crit, reject=None, meandiffs=None, std_pairs=None, confint=None, df_total=None, reject2=None, variance=None, pvalues=None): self._multicomp = mc_object self._results_table = results_table self.q_crit = q_crit self.reject = reject self.meandiffs = meandiffs self.std_pairs = std_pairs self.confint = confint self.df_total = df_total self.reject2 = reject2 self.variance = variance self.pvalues = pvalues # Taken out of _multicomp for ease of access for unknowledgeable users self.data = self._multicomp.data self.groups = self._multicomp.groups self.groupsunique = self._multicomp.groupsunique def __str__(self): return str(self._results_table) def summary(self): '''Summary table that can be printed ''' return self._results_table def _simultaneous_ci(self): """Compute simultaneous confidence intervals for comparison of means. """ self.halfwidths = simultaneous_ci(self.q_crit, self.variance, self._multicomp.groupstats.groupnobs, self._multicomp.pairindices) def plot_simultaneous(self, comparison_name=None, ax=None, figsize=(10,6), xlabel=None, ylabel=None): """Plot a universal confidence interval of each group mean Visualize significant differences in a plot with one confidence interval per group instead of all pairwise confidence intervals. Parameters ---------- comparison_name : str, optional if provided, plot_intervals will color code all groups that are significantly different from the comparison_name red, and will color code insignificant groups gray. Otherwise, all intervals will just be plotted in black. ax : matplotlib axis, optional An axis handle on which to attach the plot. figsize : tuple, optional tuple for the size of the figure generated xlabel : str, optional Name to be displayed on x axis ylabel : str, optional Name to be displayed on y axis Returns ------- Figure handle to figure object containing interval plots Notes ----- Multiple comparison tests are nice, but lack a good way to be visualized. If you have, say, 6 groups, showing a graph of the means between each group will require 15 confidence intervals. Instead, we can visualize inter-group differences with a single interval for each group mean. Hochberg et al. [1] first proposed this idea and used Tukey's Q critical value to compute the interval widths. Unlike plotting the differences in the means and their respective confidence intervals, any two pairs can be compared for significance by looking for overlap. References ---------- .. [*] Hochberg, Y., and A. C. Tamhane. Multiple Comparison Procedures. Hoboken, NJ: John Wiley & Sons, 1987. Examples -------- >>> from statsmodels.examples.try_tukey_hsd import cylinders, cyl_labels >>> from statsmodels.stats.multicomp import MultiComparison >>> cardata = MultiComparison(cylinders, cyl_labels) >>> results = cardata.tukeyhsd() >>> results.plot_simultaneous() This example shows an example plot comparing significant differences in group means. Significant differences at the alpha=0.05 level can be identified by intervals that do not overlap (i.e. USA vs Japan, USA vs Germany). >>> results.plot_simultaneous(comparison_name="USA") Optionally provide one of the group names to color code the plot to highlight group means different from comparison_name. """ fig, ax1 = utils.create_mpl_ax(ax) if figsize is not None: fig.set_size_inches(figsize) if getattr(self, 'halfwidths', None) is None: self._simultaneous_ci() means = self._multicomp.groupstats.groupmean sigidx = [] nsigidx = [] minrange = [means[i] - self.halfwidths[i] for i in range(len(means))] maxrange = [means[i] + self.halfwidths[i] for i in range(len(means))] if comparison_name is None: ax1.errorbar(means, lrange(len(means)), xerr=self.halfwidths, marker='o', linestyle='None', color='k', ecolor='k') else: if comparison_name not in self.groupsunique: raise ValueError('comparison_name not found in group names.') midx = np.where(self.groupsunique==comparison_name)[0][0] for i in range(len(means)): if self.groupsunique[i] == comparison_name: continue if (min(maxrange[i], maxrange[midx]) - max(minrange[i], minrange[midx]) < 0): sigidx.append(i) else: nsigidx.append(i) #Plot the master comparison ax1.errorbar(means[midx], midx, xerr=self.halfwidths[midx], marker='o', linestyle='None', color='b', ecolor='b') ax1.plot([minrange[midx]]*2, [-1, self._multicomp.ngroups], linestyle='--', color='0.7') ax1.plot([maxrange[midx]]*2, [-1, self._multicomp.ngroups], linestyle='--', color='0.7') #Plot those that are significantly different if len(sigidx) > 0: ax1.errorbar(means[sigidx], sigidx, xerr=self.halfwidths[sigidx], marker='o', linestyle='None', color='r', ecolor='r') #Plot those that are not significantly different if len(nsigidx) > 0: ax1.errorbar(means[nsigidx], nsigidx, xerr=self.halfwidths[nsigidx], marker='o', linestyle='None', color='0.5', ecolor='0.5') ax1.set_title('Multiple Comparisons Between All Pairs (Tukey)') r = np.max(maxrange) - np.min(minrange) ax1.set_ylim([-1, self._multicomp.ngroups]) ax1.set_xlim([np.min(minrange) - r / 10., np.max(maxrange) + r / 10.]) ax1.set_yticklabels(np.insert(self.groupsunique.astype(str), 0, '')) ax1.set_yticks(np.arange(-1, len(means)+1)) ax1.set_xlabel(xlabel if xlabel is not None else '') ax1.set_ylabel(ylabel if ylabel is not None else '') return fig class MultiComparison(object): '''Tests for multiple comparisons Parameters ---------- data : ndarray independent data samples groups : ndarray group labels corresponding to each data point group_order : list[str], optional the desired order for the group mean results to be reported in. If not specified, results are reported in increasing order. If group_order does not contain all labels that are in groups, then only those observations are kept that have a label in group_order. ''' def __init__(self, data, groups, group_order=None): if len(data) != len(groups): raise ValueError('data has %d elements and groups has %d' % (len(data), len(groups))) self.data = np.asarray(data) self.groups = groups = np.asarray(groups) # Allow for user-provided sorting of groups if group_order is None: self.groupsunique, self.groupintlab = np.unique(groups, return_inverse=True) else: #check if group_order has any names not in groups for grp in group_order: if grp not in groups: raise ValueError( "group_order value '%s' not found in groups" % grp) self.groupsunique = np.array(group_order) self.groupintlab = np.empty(len(data), int) self.groupintlab.fill(-999) # instead of a nan count = 0 for name in self.groupsunique: idx = np.where(self.groups == name)[0] count += len(idx) self.groupintlab[idx] = np.where(self.groupsunique == name)[0] if count != self.data.shape[0]: #raise ValueError('group_order does not contain all groups') # warn and keep only observations with label in group_order import warnings warnings.warn('group_order does not contain all groups:' + ' dropping observations', ValueWarning) mask_keep = self.groupintlab != -999 self.groupintlab = self.groupintlab[mask_keep] self.data = self.data[mask_keep] self.groups = self.groups[mask_keep] if len(self.groupsunique) < 2: raise ValueError('2 or more groups required for multiple comparisons') self.datali = [self.data[self.groups == k] for k in self.groupsunique] self.pairindices = np.triu_indices(len(self.groupsunique), 1) #tuple self.nobs = self.data.shape[0] self.ngroups = len(self.groupsunique) def getranks(self): '''convert data to rankdata and attach This creates rankdata as it is used for non-parametric tests, where in the case of ties the average rank is assigned. ''' #bug: the next should use self.groupintlab instead of self.groups #update: looks fixed #self.ranks = GroupsStats(np.column_stack([self.data, self.groups]), self.ranks = GroupsStats(np.column_stack([self.data, self.groupintlab]), useranks=True) self.rankdata = self.ranks.groupmeanfilter def kruskal(self, pairs=None, multimethod='T'): ''' pairwise comparison for kruskal-wallis test This is just a reimplementation of scipy.stats.kruskal and does not yet use a multiple comparison correction. ''' self.getranks() tot = self.nobs meanranks = self.ranks.groupmean groupnobs = self.ranks.groupnobs # simultaneous/separate treatment of multiple tests f=(tot * (tot + 1.) / 12.) / stats.tiecorrect(self.rankdata) #(xranks) print('MultiComparison.kruskal') for i,j in zip(*self.pairindices): #pdiff = np.abs(mrs[i] - mrs[j]) pdiff = np.abs(meanranks[i] - meanranks[j]) se = np.sqrt(f * np.sum(1. / groupnobs[[i,j]] )) #np.array([8,8]))) #Fixme groupnobs[[i,j]] )) Q = pdiff / se # TODO : print(statments, fix print(i,j, pdiff, se, pdiff / se, pdiff / se > 2.6310) print(stats.norm.sf(Q) * 2) return stats.norm.sf(Q) * 2 def allpairtest(self, testfunc, alpha=0.05, method='bonf', pvalidx=1): '''run a pairwise test on all pairs with multiple test correction The statistical test given in testfunc is calculated for all pairs and the p-values are adjusted by methods in multipletests. The p-value correction is generic and based only on the p-values, and does not take any special structure of the hypotheses into account. Parameters ---------- testfunc : function A test function for two (independent) samples. It is assumed that the return value on position pvalidx is the p-value. alpha : float familywise error rate method : str This specifies the method for the p-value correction. Any method of multipletests is possible. pvalidx : int (default: 1) position of the p-value in the return of testfunc Returns ------- sumtab : SimpleTable instance summary table for printing errors: TODO: check if this is still wrong, I think it's fixed. results from multipletests are in different order pval_corrected can be larger than 1 ??? ''' res = [] for i,j in zip(*self.pairindices): res.append(testfunc(self.datali[i], self.datali[j])) res = np.array(res) reject, pvals_corrected, alphacSidak, alphacBonf = \ multipletests(res[:, pvalidx], alpha=alpha, method=method) #print(np.column_stack([res[:,0],res[:,1], reject, pvals_corrected]) i1, i2 = self.pairindices if pvals_corrected is None: resarr = np.array(lzip(self.groupsunique[i1], self.groupsunique[i2], np.round(res[:,0],4), np.round(res[:,1],4), reject), dtype=[('group1', object), ('group2', object), ('stat',float), ('pval',float), ('reject', np.bool8)]) else: resarr = np.array(lzip(self.groupsunique[i1], self.groupsunique[i2], np.round(res[:,0],4), np.round(res[:,1],4), np.round(pvals_corrected,4), reject), dtype=[('group1', object), ('group2', object), ('stat',float), ('pval',float), ('pval_corr',float), ('reject', np.bool8)]) results_table = SimpleTable(resarr, headers=resarr.dtype.names) results_table.title = ( 'Test Multiple Comparison %s \n%s%4.2f method=%s' % (testfunc.__name__, 'FWER=', alpha, method) + '\nalphacSidak=%4.2f, alphacBonf=%5.3f' % (alphacSidak, alphacBonf)) return results_table, (res, reject, pvals_corrected, alphacSidak, alphacBonf), resarr def tukeyhsd(self, alpha=0.05): """ Tukey's range test to compare means of all pairs of groups Parameters ---------- alpha : float, optional Value of FWER at which to calculate HSD. Returns ------- results : TukeyHSDResults instance A results class containing relevant data and some post-hoc calculations """ self.groupstats = GroupsStats( np.column_stack([self.data, self.groupintlab]), useranks=False) gmeans = self.groupstats.groupmean gnobs = self.groupstats.groupnobs # var_ = self.groupstats.groupvarwithin() # #possibly an error in varcorrection in this case var_ = np.var(self.groupstats.groupdemean(), ddof=len(gmeans)) # res contains: 0:(idx1, idx2), 1:reject, 2:meandiffs, 3: std_pairs, # 4:confint, 5:q_crit, 6:df_total, 7:reject2, 8: pvals res = tukeyhsd(gmeans, gnobs, var_, df=None, alpha=alpha, q_crit=None) resarr = np.array(lzip(self.groupsunique[res[0][0]], self.groupsunique[res[0][1]], np.round(res[2], 4), np.round(res[8], 4), np.round(res[4][:, 0], 4), np.round(res[4][:, 1], 4), res[1]), dtype=[('group1', object), ('group2', object), ('meandiff', float), ('p-adj', float), ('lower', float), ('upper', float), ('reject', np.bool8)]) results_table = SimpleTable(resarr, headers=resarr.dtype.names) results_table.title = 'Multiple Comparison of Means - Tukey HSD, ' + \ 'FWER=%4.2f' % alpha return TukeyHSDResults(self, results_table, res[5], res[1], res[2], res[3], res[4], res[6], res[7], var_, res[8]) def rankdata(x): '''rankdata, equivalent to scipy.stats.rankdata just a different implementation, I have not yet compared speed ''' uni, intlab = np.unique(x[:,0], return_inverse=True) groupnobs = np.bincount(intlab) groupxsum = np.bincount(intlab, weights=X[:,0]) groupxmean = groupxsum * 1.0 / groupnobs rankraw = x[:,0].argsort().argsort() groupranksum = np.bincount(intlab, weights=rankraw) # start at 1 for stats.rankdata : grouprankmean = groupranksum * 1.0 / groupnobs + 1 return grouprankmean[intlab] #new def compare_ordered(vals, alpha): '''simple ordered sequential comparison of means vals : array_like means or rankmeans for independent groups incomplete, no return, not used yet ''' vals = np.asarray(vals) alphaf = alpha # Notation ? sortind = np.argsort(vals) pvals = vals[sortind] sortrevind = sortind.argsort() ntests = len(vals) #alphacSidak = 1 - np.power((1. - alphaf), 1./ntests) #alphacBonf = alphaf / float(ntests) v1, v2 = np.triu_indices(ntests, 1) #v1,v2 have wrong sequence for i in range(4): for j in range(4,i, -1): print(i,j) def varcorrection_unbalanced(nobs_all, srange=False): '''correction factor for variance with unequal sample sizes this is just a harmonic mean Parameters ---------- nobs_all : array_like The number of observations for each sample srange : bool if true, then the correction is divided by the number of samples for the variance of the studentized range statistic Returns ------- correction : float Correction factor for variance. Notes ----- variance correction factor is 1/k * sum_i 1/n_i where k is the number of samples and summation is over i=0,...,k-1. If all n_i are the same, then the correction factor is 1. This needs to be multiplied by the joint variance estimate, means square error, MSE. To obtain the correction factor for the standard deviation, square root needs to be taken. ''' nobs_all = np.asarray(nobs_all) if not srange: return (1./nobs_all).sum() else: return (1./nobs_all).sum()/len(nobs_all) def varcorrection_pairs_unbalanced(nobs_all, srange=False): '''correction factor for variance with unequal sample sizes for all pairs this is just a harmonic mean Parameters ---------- nobs_all : array_like The number of observations for each sample srange : bool if true, then the correction is divided by 2 for the variance of the studentized range statistic Returns ------- correction : ndarray Correction factor for variance. Notes ----- variance correction factor is 1/k * sum_i 1/n_i where k is the number of samples and summation is over i=0,...,k-1. If all n_i are the same, then the correction factor is 1. This needs to be multiplies by the joint variance estimate, means square error, MSE. To obtain the correction factor for the standard deviation, square root needs to be taken. For the studentized range statistic, the resulting factor has to be divided by 2. ''' #TODO: test and replace with broadcasting n1, n2 = np.meshgrid(nobs_all, nobs_all) if not srange: return (1./n1 + 1./n2) else: return (1./n1 + 1./n2) / 2. def varcorrection_unequal(var_all, nobs_all, df_all): '''return joint variance from samples with unequal variances and unequal sample sizes something is wrong Parameters ---------- var_all : array_like The variance for each sample nobs_all : array_like The number of observations for each sample df_all : array_like degrees of freedom for each sample Returns ------- varjoint : float joint variance. dfjoint : float joint Satterthwait's degrees of freedom Notes ----- (copy, paste not correct) variance is 1/k * sum_i 1/n_i where k is the number of samples and summation is over i=0,...,k-1. If all n_i are the same, then the correction factor is 1/n. This needs to be multiplies by the joint variance estimate, means square error, MSE. To obtain the correction factor for the standard deviation, square root needs to be taken. This is for variance of mean difference not of studentized range. ''' var_all = np.asarray(var_all) var_over_n = var_all *1./ nobs_all #avoid integer division varjoint = var_over_n.sum() dfjoint = varjoint**2 / (var_over_n**2 * df_all).sum() return varjoint, dfjoint def varcorrection_pairs_unequal(var_all, nobs_all, df_all): '''return joint variance from samples with unequal variances and unequal sample sizes for all pairs something is wrong Parameters ---------- var_all : array_like The variance for each sample nobs_all : array_like The number of observations for each sample df_all : array_like degrees of freedom for each sample Returns ------- varjoint : ndarray joint variance. dfjoint : ndarray joint Satterthwait's degrees of freedom Notes ----- (copy, paste not correct) variance is 1/k * sum_i 1/n_i where k is the number of samples and summation is over i=0,...,k-1. If all n_i are the same, then the correction factor is 1. This needs to be multiplies by the joint variance estimate, means square error, MSE. To obtain the correction factor for the standard deviation, square root needs to be taken. TODO: something looks wrong with dfjoint, is formula from SPSS ''' #TODO: test and replace with broadcasting v1, v2 = np.meshgrid(var_all, var_all) n1, n2 = np.meshgrid(nobs_all, nobs_all) df1, df2 = np.meshgrid(df_all, df_all) varjoint = v1/n1 + v2/n2 dfjoint = varjoint**2 / (df1 * (v1/n1)**2 + df2 * (v2/n2)**2) return varjoint, dfjoint def tukeyhsd(mean_all, nobs_all, var_all, df=None, alpha=0.05, q_crit=None): '''simultaneous Tukey HSD check: instead of sorting, I use absolute value of pairwise differences in means. That's irrelevant for the test, but maybe reporting actual differences would be better. CHANGED: meandiffs are with sign, studentized range uses abs q_crit added for testing TODO: error in variance calculation when nobs_all is scalar, missing 1/n ''' mean_all = np.asarray(mean_all) #check if or when other ones need to be arrays n_means = len(mean_all) if df is None: df = nobs_all - 1 if np.size(df) == 1: # assumes balanced samples with df = n - 1, n_i = n df_total = n_means * df df = np.ones(n_means) * df else: df_total = np.sum(df) if (np.size(nobs_all) == 1) and (np.size(var_all) == 1): #balanced sample sizes and homogenous variance var_pairs = 1. * var_all / nobs_all * np.ones((n_means, n_means)) elif np.size(var_all) == 1: #unequal sample sizes and homogenous variance var_pairs = var_all * varcorrection_pairs_unbalanced(nobs_all, srange=True) elif np.size(var_all) > 1: var_pairs, df_sum = varcorrection_pairs_unequal(nobs_all, var_all, df) var_pairs /= 2. #check division by two for studentized range else: raise ValueError('not supposed to be here') #meandiffs_ = mean_all[:,None] - mean_all meandiffs_ = mean_all - mean_all[:,None] #reverse sign, check with R example std_pairs_ = np.sqrt(var_pairs) #select all pairs from upper triangle of matrix idx1, idx2 = np.triu_indices(n_means, 1) meandiffs = meandiffs_[idx1, idx2] std_pairs = std_pairs_[idx1, idx2] st_range = np.abs(meandiffs) / std_pairs #studentized range statistic df_total_ = max(df_total, 5) #TODO: smallest df in table if q_crit is None: q_crit = get_tukeyQcrit2(n_means, df_total, alpha=alpha) pvalues = get_tukey_pvalue(n_means, df_total, st_range) # we need pvalues to be atleast_1d for iteration. see #6132 pvalues = np.atleast_1d(pvalues) reject = st_range > q_crit crit_int = std_pairs * q_crit reject2 = np.abs(meandiffs) > crit_int confint = np.column_stack((meandiffs - crit_int, meandiffs + crit_int)) return ((idx1, idx2), reject, meandiffs, std_pairs, confint, q_crit, df_total, reject2, pvalues) def simultaneous_ci(q_crit, var, groupnobs, pairindices=None): """Compute simultaneous confidence intervals for comparison of means. q_crit value is generated from tukey hsd test. Variance is considered across all groups. Returned halfwidths can be thought of as uncertainty intervals around each group mean. They allow for simultaneous comparison of pairwise significance among any pairs (by checking for overlap) Parameters ---------- q_crit : float The Q critical value studentized range statistic from Tukey's HSD var : float The group variance groupnobs : array_like object Number of observations contained in each group. pairindices : tuple of lists, optional Indices corresponding to the upper triangle of matrix. Computed here if not supplied Returns ------- halfwidths : ndarray Half the width of each confidence interval for each group given in groupnobs See Also -------- MultiComparison : statistics class providing significance tests tukeyhsd : among other things, computes q_crit value References ---------- .. [*] Hochberg, Y., and A. C. Tamhane. Multiple Comparison Procedures. Hoboken, NJ: John Wiley & Sons, 1987.) """ # Set initial variables ng = len(groupnobs) if pairindices is None: pairindices = np.triu_indices(ng, 1) # Compute dij for all pairwise comparisons ala hochberg p. 95 gvar = var / groupnobs d12 = np.sqrt(gvar[pairindices[0]] + gvar[pairindices[1]]) # Create the full d matrix given all known dij vals d = np.zeros((ng, ng)) d[pairindices] = d12 d = d + d.conj().T # Compute the two global sums from hochberg eq 3.32 sum1 = np.sum(d12) sum2 = np.sum(d, axis=0) if (ng > 2): w = ((ng-1.) * sum2 - sum1) / ((ng - 1.) * (ng - 2.)) else: w = sum1 * np.ones((2, 1)) / 2. return (q_crit / np.sqrt(2))*w def distance_st_range(mean_all, nobs_all, var_all, df=None, triu=False): '''pairwise distance matrix, outsourced from tukeyhsd CHANGED: meandiffs are with sign, studentized range uses abs q_crit added for testing TODO: error in variance calculation when nobs_all is scalar, missing 1/n ''' mean_all = np.asarray(mean_all) #check if or when other ones need to be arrays n_means = len(mean_all) if df is None: df = nobs_all - 1 if np.size(df) == 1: # assumes balanced samples with df = n - 1, n_i = n df_total = n_means * df else: df_total = np.sum(df) if (np.size(nobs_all) == 1) and (np.size(var_all) == 1): #balanced sample sizes and homogenous variance var_pairs = 1. * var_all / nobs_all * np.ones((n_means, n_means)) elif np.size(var_all) == 1: #unequal sample sizes and homogenous variance var_pairs = var_all * varcorrection_pairs_unbalanced(nobs_all, srange=True) elif np.size(var_all) > 1: var_pairs, df_sum = varcorrection_pairs_unequal(nobs_all, var_all, df) var_pairs /= 2. #check division by two for studentized range else: raise ValueError('not supposed to be here') #meandiffs_ = mean_all[:,None] - mean_all meandiffs = mean_all - mean_all[:,None] #reverse sign, check with R example std_pairs = np.sqrt(var_pairs) idx1, idx2 = np.triu_indices(n_means, 1) if triu: #select all pairs from upper triangle of matrix meandiffs = meandiffs_[idx1, idx2] # noqa: F821 See GH#5756 std_pairs = std_pairs_[idx1, idx2] # noqa: F821 See GH#5756 st_range = np.abs(meandiffs) / std_pairs #studentized range statistic return st_range, meandiffs, std_pairs, (idx1,idx2) #return square arrays def contrast_allpairs(nm): '''contrast or restriction matrix for all pairs of nm variables Parameters ---------- nm : int Returns ------- contr : ndarray, 2d, (nm*(nm-1)/2, nm) contrast matrix for all pairwise comparisons ''' contr = [] for i in range(nm): for j in range(i+1, nm): contr_row = np.zeros(nm) contr_row[i] = 1 contr_row[j] = -1 contr.append(contr_row) return np.array(contr) def contrast_all_one(nm): '''contrast or restriction matrix for all against first comparison Parameters ---------- nm : int Returns ------- contr : ndarray, 2d, (nm-1, nm) contrast matrix for all against first comparisons ''' contr = np.column_stack((np.ones(nm-1), -np.eye(nm-1))) return contr def contrast_diff_mean(nm): '''contrast or restriction matrix for all against mean comparison Parameters ---------- nm : int Returns ------- contr : ndarray, 2d, (nm-1, nm) contrast matrix for all against mean comparisons ''' return np.eye(nm) - np.ones((nm,nm))/nm def tukey_pvalues(std_range, nm, df): #corrected but very slow with warnings about integration #nm = len(std_range) contr = contrast_allpairs(nm) corr = np.dot(contr, contr.T)/2. tstat = std_range / np.sqrt(2) * np.ones(corr.shape[0]) #need len of all pairs return multicontrast_pvalues(tstat, corr, df=df) def multicontrast_pvalues(tstat, tcorr, df=None, dist='t', alternative='two-sided'): '''pvalues for simultaneous tests ''' from statsmodels.sandbox.distributions.multivariate import mvstdtprob if (df is None) and (dist == 't'): raise ValueError('df has to be specified for the t-distribution') tstat = np.asarray(tstat) ntests = len(tstat) cc = np.abs(tstat) pval_global = 1 - mvstdtprob(-cc,cc, tcorr, df) pvals = [] for ti in cc: limits = ti*np.ones(ntests) pvals.append(1 - mvstdtprob(-cc,cc, tcorr, df)) return pval_global, np.asarray(pvals) class StepDown(object): '''a class for step down methods This is currently for simple tree subset descend, similar to homogeneous_subsets, but checks all leave-one-out subsets instead of assuming an ordered set. Comment in SAS manual: SAS only uses interval subsets of the sorted list, which is sufficient for range tests (maybe also equal variance and balanced sample sizes are required). For F-test based critical distances, the restriction to intervals is not sufficient. This version uses a single critical value of the studentized range distribution for all comparisons, and is therefore a step-down version of Tukey HSD. The class is written so it can be subclassed, where the get_distance_matrix and get_crit are overwritten to obtain other step-down procedures such as REGW. iter_subsets can be overwritten, to get a recursion as in the many to one comparison with a control such as in Dunnet's test. A one-sided right tail test is not covered because the direction of the inequality is hard coded in check_set. Also Peritz's check of partitions is not possible, but I have not seen it mentioned in any more recent references. I have only partially read the step-down procedure for closed tests by Westfall. One change to make it more flexible, is to separate out the decision on a subset, also because the F-based tests, FREGW in SPSS, take information from all elements of a set and not just pairwise comparisons. I have not looked at the details of the F-based tests such as Sheffe yet. It looks like running an F-test on equality of means in each subset. This would also outsource how pairwise conditions are combined, any larger or max. This would also imply that the distance matrix cannot be calculated in advance for tests like the F-based ones. ''' def __init__(self, vals, nobs_all, var_all, df=None): self.vals = vals self.n_vals = len(vals) self.nobs_all = nobs_all self.var_all = var_all self.df = df # the following has been moved to run #self.cache_result = {} #self.crit = self.getcrit(0.5) #decide where to set alpha, moved to run #self.accepted = [] #store accepted sets, not unique def get_crit(self, alpha): """ get_tukeyQcrit currently tukey Q, add others """ q_crit = get_tukeyQcrit(self.n_vals, self.df, alpha=alpha) return q_crit * np.ones(self.n_vals) def get_distance_matrix(self): '''studentized range statistic''' #make into property, decorate dres = distance_st_range(self.vals, self.nobs_all, self.var_all, df=self.df) self.distance_matrix = dres[0] def iter_subsets(self, indices): """Iterate substeps""" for ii in range(len(indices)): idxsub = copy.copy(indices) idxsub.pop(ii) yield idxsub def check_set(self, indices): '''check whether pairwise distances of indices satisfy condition ''' indtup = tuple(indices) if indtup in self.cache_result: return self.cache_result[indtup] else: set_distance_matrix = self.distance_matrix[np.asarray(indices)[:,None], indices] n_elements = len(indices) if np.any(set_distance_matrix > self.crit[n_elements-1]): res = True else: res = False self.cache_result[indtup] = res return res def stepdown(self, indices): """stepdown""" print(indices) if self.check_set(indices): # larger than critical distance if (len(indices) > 2): # step down into subsets if more than 2 elements for subs in self.iter_subsets(indices): self.stepdown(subs) else: self.rejected.append(tuple(indices)) else: self.accepted.append(tuple(indices)) return indices def run(self, alpha): '''main function to run the test, could be done in __call__ instead this could have all the initialization code ''' self.cache_result = {} self.crit = self.get_crit(alpha) #decide where to set alpha, moved to run self.accepted = [] #store accepted sets, not unique self.rejected = [] self.get_distance_matrix() self.stepdown(lrange(self.n_vals)) return list(set(self.accepted)), list(set(sd.rejected)) def homogeneous_subsets(vals, dcrit): '''recursively check all pairs of vals for minimum distance step down method as in Newman-Keuls and Ryan procedures. This is not a closed procedure since not all partitions are checked. Parameters ---------- vals : array_like values that are pairwise compared dcrit : array_like or float critical distance for rejecting, either float, or 2-dimensional array with distances on the upper triangle. Returns ------- rejs : list of pairs list of pair-indices with (strictly) larger than critical difference nrejs : list of pairs list of pair-indices with smaller than critical difference lli : list of tuples list of subsets with smaller than critical difference res : tree result of all comparisons (for checking) this follows description in SPSS notes on Post-Hoc Tests Because of the recursive structure, some comparisons are made several times, but only unique pairs or sets are returned. Examples -------- >>> m = [0, 2, 2.5, 3, 6, 8, 9, 9.5,10 ] >>> rej, nrej, ssli, res = homogeneous_subsets(m, 2) >>> set_partition(ssli) ([(5, 6, 7, 8), (1, 2, 3), (4,)], [0]) >>> [np.array(m)[list(pp)] for pp in set_partition(ssli)[0]] [array([ 8. , 9. , 9.5, 10. ]), array([ 2. , 2.5, 3. ]), array([ 6.])] ''' nvals = len(vals) indices_ = lrange(nvals) rejected = [] subsetsli = [] if np.size(dcrit) == 1: dcrit = dcrit*np.ones((nvals, nvals)) #example numbers for experimenting def subsets(vals, indices_): '''recursive function for constructing homogeneous subset registers rejected and subsetli in outer scope ''' i, j = (indices_[0], indices_[-1]) if vals[-1] - vals[0] > dcrit[i,j]: rejected.append((indices_[0], indices_[-1])) return [subsets(vals[:-1], indices_[:-1]), subsets(vals[1:], indices_[1:]), (indices_[0], indices_[-1])] else: subsetsli.append(tuple(indices_)) return indices_ res = subsets(vals, indices_) all_pairs = [(i,j) for i in range(nvals) for j in range(nvals-1,i,-1)] rejs = set(rejected) not_rejected = list(set(all_pairs) - rejs) return list(rejs), not_rejected, list(set(subsetsli)), res def set_partition(ssli): '''extract a partition from a list of tuples this should be correctly called select largest disjoint sets. Begun and Gabriel 1981 do not seem to be bothered by sets of accepted hypothesis with joint elements, e.g. maximal_accepted_sets = { {1,2,3}, {2,3,4} } This creates a set partition from a list of sets given as tuples. It tries to find the partition with the largest sets. That is, sets are included after being sorted by length. If the list does not include the singletons, then it will be only a partial partition. Missing items are singletons (I think). Examples -------- >>> li [(5, 6, 7, 8), (1, 2, 3), (4, 5), (0, 1)] >>> set_partition(li) ([(5, 6, 7, 8), (1, 2, 3)], [0, 4]) ''' part = [] for s in sorted(list(set(ssli)), key=len)[::-1]: #print(s, s_ = set(s).copy() if not any(set(s_).intersection(set(t)) for t in part): #print('inside:', s part.append(s) #else: print(part missing = list(set(i for ll in ssli for i in ll) - set(i for ll in part for i in ll)) return part, missing def set_remove_subs(ssli): '''remove sets that are subsets of another set from a list of tuples Parameters ---------- ssli : list of tuples each tuple is considered as a set Returns ------- part : list of tuples new list with subset tuples removed, it is sorted by set-length of tuples. The list contains original tuples, duplicate elements are not removed. Examples -------- >>> set_remove_subs([(0, 1), (1, 2), (1, 2, 3), (0,)]) [(1, 2, 3), (0, 1)] >>> set_remove_subs([(0, 1), (1, 2), (1,1, 1, 2, 3), (0,)]) [(1, 1, 1, 2, 3), (0, 1)] ''' #TODO: maybe convert all tuples to sets immediately, but I do not need the extra efficiency part = [] for s in sorted(list(set(ssli)), key=lambda x: len(set(x)))[::-1]: #print(s, #s_ = set(s).copy() if not any(set(s).issubset(set(t)) for t in part): #print('inside:', s part.append(s) #else: print(part ## missing = list(set(i for ll in ssli for i in ll) ## - set(i for ll in part for i in ll)) return part if __name__ == '__main__': examples = ['tukey', 'tukeycrit', 'fdr', 'fdrmc', 'bonf', 'randmvn', 'multicompdev', 'None']#[-1] if 'tukey' in examples: #Example Tukey x = np.array([[0,0,1]]).T + np.random.randn(3, 20) print(Tukeythreegene(*x)) # Example FDR # ------------ if ('fdr' in examples) or ('bonf' in examples): from .ex_multicomp import example_fdr_bonferroni example_fdr_bonferroni() if 'fdrmc' in examples: mcres = mcfdr(nobs=100, nrepl=1000, ntests=30, ntrue=30, mu=0.1, alpha=0.05, rho=0.3) mcmeans = np.array(mcres).mean(0) print(mcmeans) print(mcmeans[0]/6., 1-mcmeans[1]/4.) print(mcmeans[:4], mcmeans[-4:]) if 'randmvn' in examples: rvsmvn = randmvn(0.8, (5000,5)) print(np.corrcoef(rvsmvn, rowvar=0)) print(rvsmvn.var(0)) if 'tukeycrit' in examples: print(get_tukeyQcrit(8, 8, alpha=0.05), 5.60) print(get_tukeyQcrit(8, 8, alpha=0.01), 7.47) if 'multicompdev' in examples: #development of kruskal-wallis multiple-comparison #example from matlab file exchange X = np.array([[7.68, 1], [7.69, 1], [7.70, 1], [7.70, 1], [7.72, 1], [7.73, 1], [7.73, 1], [7.76, 1], [7.71, 2], [7.73, 2], [7.74, 2], [7.74, 2], [7.78, 2], [7.78, 2], [7.80, 2], [7.81, 2], [7.74, 3], [7.75, 3], [7.77, 3], [7.78, 3], [7.80, 3], [7.81, 3], [7.84, 3], [7.71, 4], [7.71, 4], [7.74, 4], [7.79, 4], [7.81, 4], [7.85, 4], [7.87, 4], [7.91, 4]]) xli = [X[X[:,1]==k,0] for k in range(1,5)] xranks = stats.rankdata(X[:,0]) xranksli = [xranks[X[:,1]==k] for k in range(1,5)] xnobs = np.array([len(xval) for xval in xli]) meanranks = [item.mean() for item in xranksli] sumranks = [item.sum() for item in xranksli] # equivalent function #from scipy import special #-np.sqrt(2.)*special.erfcinv(2-0.5) == stats.norm.isf(0.25) stats.norm.sf(0.67448975019608171) stats.norm.isf(0.25) mrs = np.sort(meanranks) v1, v2 = np.triu_indices(4,1) print('\nsorted rank differences') print(mrs[v2] - mrs[v1]) diffidx = np.argsort(mrs[v2] - mrs[v1])[::-1] mrs[v2[diffidx]] - mrs[v1[diffidx]] print('\nkruskal for all pairs') for i,j in zip(v2[diffidx], v1[diffidx]): print(i,j, stats.kruskal(xli[i], xli[j])) mwu, mwupval = stats.mannwhitneyu(xli[i], xli[j], use_continuity=False) print(mwu, mwupval*2, mwupval*2<0.05/6., mwupval*2<0.1/6.) uni, intlab = np.unique(X[:,0], return_inverse=True) groupnobs = np.bincount(intlab) groupxsum = np.bincount(intlab, weights=X[:,0]) groupxmean = groupxsum * 1.0 / groupnobs rankraw = X[:,0].argsort().argsort() groupranksum = np.bincount(intlab, weights=rankraw) # start at 1 for stats.rankdata : grouprankmean = groupranksum * 1.0 / groupnobs + 1 assert_almost_equal(grouprankmean[intlab], stats.rankdata(X[:,0]), 15) gs = GroupsStats(X, useranks=True) print('\ngroupmeanfilter and grouprankmeans') print(gs.groupmeanfilter) print(grouprankmean[intlab]) #the following has changed #assert_almost_equal(gs.groupmeanfilter, stats.rankdata(X[:,0]), 15) xuni, xintlab = np.unique(X[:,0], return_inverse=True) gs2 = GroupsStats(np.column_stack([X[:,0], xintlab]), useranks=True) #assert_almost_equal(gs2.groupmeanfilter, stats.rankdata(X[:,0]), 15) rankbincount = np.bincount(xranks.astype(int)) nties = rankbincount[rankbincount > 1] ntot = float(len(xranks)) tiecorrection = 1 - (nties**3 - nties).sum()/(ntot**3 - ntot) assert_almost_equal(tiecorrection, stats.tiecorrect(xranks),15) print('\ntiecorrection for data and ranks') print(tiecorrection) print(tiecorrect(xranks)) tot = X.shape[0] t=500 #168 f=(tot*(tot+1.)/12.)-(t/(6.*(tot-1.))) f=(tot*(tot+1.)/12.)/stats.tiecorrect(xranks) print('\npairs of mean rank differences') for i,j in zip(v2[diffidx], v1[diffidx]): #pdiff = np.abs(mrs[i] - mrs[j]) pdiff = np.abs(meanranks[i] - meanranks[j]) se = np.sqrt(f * np.sum(1./xnobs[[i,j]] )) #np.array([8,8]))) #Fixme groupnobs[[i,j]] )) print(i,j, pdiff, se, pdiff/se, pdiff/se>2.6310) multicomp = MultiComparison(*X.T) multicomp.kruskal() gsr = GroupsStats(X, useranks=True) print('\nexamples for kruskal multicomparison') for i in range(10): x1, x2 = (np.random.randn(30,2) + np.array([0, 0.5])).T skw = stats.kruskal(x1, x2) mc2=MultiComparison(np.r_[x1, x2], np.r_[np.zeros(len(x1)), np.ones(len(x2))]) newskw = mc2.kruskal() print(skw, np.sqrt(skw[0]), skw[1]-newskw, (newskw/skw[1]-1)*100) tablett, restt, arrtt = multicomp.allpairtest(stats.ttest_ind) tablemw, resmw, arrmw = multicomp.allpairtest(stats.mannwhitneyu) print('') print(tablett) print('') print(tablemw) tablemwhs, resmw, arrmw = multicomp.allpairtest(stats.mannwhitneyu, method='hs') print('') print(tablemwhs) if 'last' in examples: xli = (np.random.randn(60,4) + np.array([0, 0, 0.5, 0.5])).T #Xrvs = np.array(catstack(xli)) xrvs, xrvsgr = catstack(xli) multicompr = MultiComparison(xrvs, xrvsgr) tablett, restt, arrtt = multicompr.allpairtest(stats.ttest_ind) print(tablett) xli=[[8,10,9,10,9],[7,8,5,8,5],[4,8,7,5,7]] x, labels = catstack(xli) gs4 = GroupsStats(np.column_stack([x, labels])) print(gs4.groupvarwithin()) #test_tukeyhsd() #moved to test_multi.py gmeans = np.array([ 7.71375, 7.76125, 7.78428571, 7.79875]) gnobs = np.array([8, 8, 7, 8]) sd = StepDown(gmeans, gnobs, 0.001, [27]) #example from BKY pvals = [0.0001, 0.0004, 0.0019, 0.0095, 0.0201, 0.0278, 0.0298, 0.0344, 0.0459, 0.3240, 0.4262, 0.5719, 0.6528, 0.7590, 1.000 ] #same number of rejection as in BKY paper: #single step-up:4, two-stage:8, iterated two-step:9 #also alpha_star is the same as theirs for TST print(fdrcorrection0(pvals, alpha=0.05, method='indep')) print(fdrcorrection_twostage(pvals, alpha=0.05, iter=False)) res_tst = fdrcorrection_twostage(pvals, alpha=0.05, iter=False) assert_almost_equal([0.047619, 0.0649], res_tst[-1][:2],3) #alpha_star for stage 2 assert_equal(8, res_tst[0].sum()) print(fdrcorrection_twostage(pvals, alpha=0.05, iter=True)) print('fdr_gbs', multipletests(pvals, alpha=0.05, method='fdr_gbs')) #multicontrast_pvalues(tstat, tcorr, df) tukey_pvalues(3.649, 3, 16) statsmodels-0.12.2/statsmodels/sandbox/stats/notes_fdr.txt000066400000000000000000000104311400612667500240260ustar00rootroot00000000000000 Multiple Tests and Multiple Comparisons ======================================= Introduction ------------ generic multiple testing procedures, p-value corrections and fdr do not use any additional information, only information contained in p-values. I do not know if there are any underlying assumption, except that the raw pvalues are uniformly on [0,1] distributed under the null hypothesis. fdr for microarray or fmri can use special structure A special case in general statistical literature is the comparison of means with specific methods to correct for multiple tests, e.g. Tukey (survey by Shaffer General Methods --------------- pvalue correction ~~~~~~~~~~~~~~~~~ implemented, basic fdr, BH, BY multiple testing procedures ~~~~~~~~~~~~~~~~~~~~~~~~~~~ pvalue correction is not available/implemented, return reject is True/False for a given confidence level. (pvalue correction were initially written this way) fdr bky 2-step procedure with estimation of fraction of false hypothesis. Multiple Comparisons -------------------- Tukey, Dunnet, ... see Hothorn, Bretz, Westfall, University of Munich 2008, working paper, published in ... The general theory in Bretz, Genz and Hothorn, Bretz, Westfall, multcomp, is based on the distribution of the maximum of the statistics when the statistics are distributed according to a joint t or normal distribution distribution. pvalues, whether to reject a hypothesis and joint confidence intervalls can be obtained directly from integration of the joint t or normal distribution. Scipy does not have the cdf of a multivariate t distribution, but according to Bretz and Gentz it can be obtained by a univariate integration from the cdf of the multivariate normal distribution. The distribution for Tukey's range statistic is half (?) of the distribution of the maximum of t-distributed random variables if the underlying means are assumed to be independently distributed. (my interpretation so far, but I have not verified the details yet, see ... ) Bretz and Genz also have a table with the summary of the contrast matrices for different tests, like Tukey and Dunnet. These contrast matrices are implemented in R, but for some of them they are not immediately obvious. As an aside, this seems to be related to getting simultaneous confidence bands for forecasting. But it is not clear to me yet how to define the confidence bands, I have the articles but have not read them yet. The older tests, Tukey, Dunnet and similar assume that the means are independently normally distributed, and critical values are tabulated for this case. Newer methods allow for arbitrary correlation (Bretz, Hothorn,...) or assume a specific structure for simplicity, for example factor structure for the covariance as in Hsu. The latter is the default approach in SAS. The tests based on independence are often categorized as post-hoc tests, a good overview of the formulas is in the SPSS description. It is also mentioned in the literature (?) that these multiple comparison tests loose power if they are only used conditional on the rejection of an overall F-test TODO: * finish Tukey, Dunnet because they will be familiar * add multivariate normal cdf to statsmodels * try Bretz/Gentz cdf of t distribution form the cdf of the multivariate normal special cases ------------- nipy.neurospin follows Schwartzman, A. et al., 2009. Empirical null and false discovery rate analysis in neuroimaging. NeuroImage, 44(1), pp.71-82. test defined for point-wise test on a 2 component mixture distribution. The probability of an observation to be in the null distribution can be estimated from the mixture distribution (not sure) fdr defined on observations not a sample mean alternative literature: use topological properties of the picture to correct fdr. TODO ==== * fdr_bky and check whether prior q can be used with current pvalue-correction * multi-comparison: Tukey, convenience classes/methods expand on current * Monte Carlo * maybe some resampling, bootstrap, permutation, later * for the rest I'm not really interested in doing the work: k-FWER, k-FDR, other estimators for fraction of true or false hypothesis multtest (R) check bootstrap references multcomp (R) contrMat has the contrast matrices for various standard test function parm parm(coef, vcov, df = 0) can work with only the estimates given statsmodels-0.12.2/statsmodels/sandbox/stats/runs.py000066400000000000000000000474211400612667500226540ustar00rootroot00000000000000'''runstest formulas for mean and var of runs taken from SAS manual NPAR tests, also idea for runstest_1samp and runstest_2samp Description in NIST handbook and dataplot does not explain their expected values, or variance Note: There are (at least) two definitions of runs used in literature. The classical definition which is also used here, is that runs are sequences of identical observations separated by observations with different realizations. The second definition allows for overlapping runs, or runs where counting a run is also started after a run of a fixed length of the same kind. TODO * add one-sided tests where possible or where it makes sense ''' import numpy as np from scipy import stats from scipy.special import comb import warnings class Runs(object): '''class for runs in a binary sequence Parameters ---------- x : array_like, 1d data array, Notes ----- This was written as a more general class for runs. This has some redundant calculations when only the runs_test is used. TODO: make it lazy The runs test could be generalized to more than 1d if there is a use case for it. This should be extended once I figure out what the distribution of runs of any length k is. The exact distribution for the runs test is also available but not yet verified. ''' def __init__(self, x): self.x = np.asarray(x) self.runstart = runstart = np.nonzero(np.diff(np.r_[[-np.inf], x, [np.inf]]))[0] self.runs = runs = np.diff(runstart) self.runs_sign = runs_sign = x[runstart[:-1]] self.runs_pos = runs[runs_sign==1] self.runs_neg = runs[runs_sign==0] self.runs_freqs = np.bincount(runs) self.n_runs = len(self.runs) self.n_pos = (x==1).sum() def runs_test(self, correction=True): '''basic version of runs test Parameters ---------- correction : bool Following the SAS manual, for samplesize below 50, the test statistic is corrected by 0.5. This can be turned off with correction=False, and was included to match R, tseries, which does not use any correction. pvalue based on normal distribution, with integer correction ''' self.npo = npo = (self.runs_pos).sum() self.nne = nne = (self.runs_neg).sum() #n_r = self.n_runs n = npo + nne npn = npo * nne rmean = 2. * npn / n + 1 rvar = 2. * npn * (2.*npn - n) / n**2. / (n-1.) rstd = np.sqrt(rvar) rdemean = self.n_runs - rmean if n >= 50 or not correction: z = rdemean else: if rdemean > 0.5: z = rdemean - 0.5 elif rdemean < 0.5: z = rdemean + 0.5 else: z = 0. z /= rstd pval = 2 * stats.norm.sf(np.abs(z)) return z, pval def runstest_1samp(x, cutoff='mean', correction=True): '''use runs test on binary discretized data above/below cutoff Parameters ---------- x : array_like data, numeric cutoff : {'mean', 'median'} or number This specifies the cutoff to split the data into large and small values. correction : bool Following the SAS manual, for samplesize below 50, the test statistic is corrected by 0.5. This can be turned off with correction=False, and was included to match R, tseries, which does not use any correction. Returns ------- z_stat : float test statistic, asymptotically normally distributed p-value : float p-value, reject the null hypothesis if it is below an type 1 error level, alpha . ''' if cutoff == 'mean': cutoff = np.mean(x) elif cutoff == 'median': cutoff = np.median(x) xindicator = (x >= cutoff).astype(int) return Runs(xindicator).runs_test(correction=correction) def runstest_2samp(x, y=None, groups=None, correction=True): '''Wald-Wolfowitz runstest for two samples This tests whether two samples come from the same distribution. Parameters ---------- x : array_like data, numeric, contains either one group, if y is also given, or both groups, if additionally a group indicator is provided y : array_like (optional) data, numeric groups : array_like group labels or indicator the data for both groups is given in a single 1-dimensional array, x. If group labels are not [0,1], then correction : bool Following the SAS manual, for samplesize below 50, the test statistic is corrected by 0.5. This can be turned off with correction=False, and was included to match R, tseries, which does not use any correction. Returns ------- z_stat : float test statistic, asymptotically normally distributed p-value : float p-value, reject the null hypothesis if it is below an type 1 error level, alpha . Notes ----- Wald-Wolfowitz runs test. If there are ties, then then the test statistic and p-value that is reported, is based on the higher p-value between sorting all tied observations of the same group This test is intended for continuous distributions SAS has treatment for ties, but not clear, and sounds more complicated (minimum and maximum possible runs prevent use of argsort) (maybe it's not so difficult, idea: add small positive noise to first one, run test, then to the other, run test, take max(?) p-value - DONE This gives not the minimum and maximum of the number of runs, but should be close. Not true, this is close to minimum but far away from maximum. maximum number of runs would use alternating groups in the ties.) Maybe adding random noise would be the better approach. SAS has exact distribution for sample size <=30, does not look standard but should be easy to add. currently two-sided test only This has not been verified against a reference implementation. In a short Monte Carlo simulation where both samples are normally distribute, the test seems to be correctly sized for larger number of observations (30 or larger), but conservative (i.e. reject less often than nominal) with a sample size of 10 in each group. See Also -------- runs_test_1samp Runs RunsProb ''' x = np.asarray(x) if y is not None: y = np.asarray(y) groups = np.concatenate((np.zeros(len(x)), np.ones(len(y)))) # note reassigning x x = np.concatenate((x, y)) gruni = np.arange(2) elif groups is not None: gruni = np.unique(groups) if gruni.size != 2: # pylint: disable=E1103 raise ValueError('not exactly two groups specified') #require groups to be numeric ??? else: raise ValueError('either y or groups is necessary') xargsort = np.argsort(x) #check for ties x_sorted = x[xargsort] x_diff = np.diff(x_sorted) # used for detecting and handling ties if x_diff.min() == 0: print('ties detected') #replace with warning x_mindiff = x_diff[x_diff > 0].min() eps = x_mindiff/2. xx = x.copy() #do not change original, just in case xx[groups==gruni[0]] += eps xargsort = np.argsort(xx) xindicator = groups[xargsort] z0, p0 = Runs(xindicator).runs_test(correction=correction) xx[groups==gruni[0]] -= eps #restore xx = x xx[groups==gruni[1]] += eps xargsort = np.argsort(xx) xindicator = groups[xargsort] z1, p1 = Runs(xindicator).runs_test(correction=correction) idx = np.argmax([p0,p1]) return [z0, z1][idx], [p0, p1][idx] else: xindicator = groups[xargsort] return Runs(xindicator).runs_test(correction=correction) class TotalRunsProb(object): '''class for the probability distribution of total runs This is the exact probability distribution for the (Wald-Wolfowitz) runs test. The random variable is the total number of runs if the sample has (n0, n1) observations of groups 0 and 1. Notes ----- Written as a class so I can store temporary calculations, but I do not think it matters much. Formulas taken from SAS manual for one-sided significance level. Could be converted to a full univariate distribution, subclassing scipy.stats.distributions. *Status* Not verified yet except for mean. ''' def __init__(self, n0, n1): self.n0 = n0 self.n1 = n1 self.n = n = n0 + n1 self.comball = comb(n, n1) def runs_prob_even(self, r): n0, n1 = self.n0, self.n1 tmp0 = comb(n0-1, r//2-1) tmp1 = comb(n1-1, r//2-1) return tmp0 * tmp1 * 2. / self.comball def runs_prob_odd(self, r): n0, n1 = self.n0, self.n1 k = (r+1)//2 tmp0 = comb(n0-1, k-1) tmp1 = comb(n1-1, k-2) tmp3 = comb(n0-1, k-2) tmp4 = comb(n1-1, k-1) return (tmp0 * tmp1 + tmp3 * tmp4) / self.comball def pdf(self, r): r = np.asarray(r) r_isodd = np.mod(r, 2) > 0 r_odd = r[r_isodd] r_even = r[~r_isodd] runs_pdf = np.zeros(r.shape) runs_pdf[r_isodd] = self.runs_prob_odd(r_odd) runs_pdf[~r_isodd] = self.runs_prob_even(r_even) return runs_pdf def cdf(self, r): r_ = np.arange(2,r+1) cdfval = self.runs_prob_even(r_[::2]).sum() cdfval += self.runs_prob_odd(r_[1::2]).sum() return cdfval class RunsProb(object): '''distribution of success runs of length k or more (classical definition) The underlying process is assumed to be a sequence of Bernoulli trials of a given length n. not sure yet, how to interpret or use the distribution for runs of length k or more. Musseli also has longest success run, and waiting time distribution negative binomial of order k and geometric of order k need to compare with Godpole need a MonteCarlo function to do some quick tests before doing more ''' def pdf(self, x, k, n, p): '''distribution of success runs of length k or more Parameters ---------- x : float count of runs of length n k : int length of runs n : int total number of observations or trials p : float probability of success in each Bernoulli trial Returns ------- pdf : float probability that x runs of length of k are observed Notes ----- not yet vectorized References ---------- Muselli 1996, theorem 3 ''' q = 1-p m = np.arange(x, (n+1)//(k+1)+1)[:,None] terms = (-1)**(m-x) * comb(m, x) * p**(m*k) * q**(m-1) \ * (comb(n - m*k, m - 1) + q * comb(n - m*k, m)) return terms.sum(0) def pdf_nb(self, x, k, n, p): pass #y = np.arange(m-1, n-mk+1 ''' >>> [np.sum([RunsProb().pdf(xi, k, 16, 10/16.) for xi in range(0,16)]) for k in range(16)] [0.99999332193894064, 0.99999999999999367, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0] >>> [(np.arange(0,16) * [RunsProb().pdf(xi, k, 16, 10/16.) for xi in range(0,16)]).sum() for k in range(16)] [6.9998931510341809, 4.1406249999999929, 2.4414062500000075, 1.4343261718749996, 0.83923339843749856, 0.48875808715820324, 0.28312206268310569, 0.1629814505577086, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] >>> np.array([(np.arange(0,16) * [RunsProb().pdf(xi, k, 16, 10/16.) for xi in range(0,16)]).sum() for k in range(16)])/11 array([ 0.63635392, 0.37642045, 0.22194602, 0.13039329, 0.07629395, 0.04443255, 0.02573837, 0.0148165 , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ]) >>> np.diff([(np.arange(0,16) * [RunsProb().pdf(xi, k, 16, 10/16.) for xi in range(0,16)]).sum() for k in range(16)][::-1]) array([ 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.16298145, 0.12014061, 0.20563602, 0.35047531, 0.59509277, 1.00708008, 1.69921875, 2.85926815]) ''' def median_test_ksample(x, groups): '''chisquare test for equality of median/location This tests whether all groups have the same fraction of observations above the median. Parameters ---------- x : array_like data values stacked for all groups groups : array_like group labels or indicator Returns ------- stat : float test statistic pvalue : float pvalue from the chisquare distribution others ???? currently some test output, table and expected ''' x = np.asarray(x) gruni = np.unique(groups) xli = [x[groups==group] for group in gruni] xmedian = np.median(x) counts_larger = np.array([(xg > xmedian).sum() for xg in xli]) counts = np.array([len(xg) for xg in xli]) counts_smaller = counts - counts_larger nobs = counts.sum() n_larger = (x > xmedian).sum() n_smaller = nobs - n_larger table = np.vstack((counts_smaller, counts_larger)) #the following should be replaced by chisquare_contingency table expected = np.vstack((counts * 1. / nobs * n_smaller, counts * 1. / nobs * n_larger)) if (expected < 5).any(): print('Warning: There are cells with less than 5 expected' \ 'observations. The chisquare distribution might not be a good' \ 'approximation for the true distribution.') #check ddof return stats.chisquare(table.ravel(), expected.ravel(), ddof=1), table, expected def cochrans_q(x): '''Cochran's Q test for identical effect of k treatments Cochran's Q is a k-sample extension of the McNemar test. If there are only two treatments, then Cochran's Q test and McNemar test are equivalent. Test that the probability of success is the same for each treatment. The alternative is that at least two treatments have a different probability of success. Parameters ---------- x : array_like, 2d (N,k) data with N cases and k variables Returns ------- q_stat : float test statistic pvalue : float pvalue from the chisquare distribution Notes ----- In Wikipedia terminology, rows are blocks and columns are treatments. The number of rows N, should be large for the chisquare distribution to be a good approximation. The Null hypothesis of the test is that all treatments have the same effect. References ---------- https://en.wikipedia.org/wiki/Cochran_test SAS Manual for NPAR TESTS ''' warnings.warn("Deprecated, use stats.cochrans_q instead", DeprecationWarning) x = np.asarray(x) gruni = np.unique(x) N, k = x.shape count_row_success = (x==gruni[-1]).sum(1, float) count_col_success = (x==gruni[-1]).sum(0, float) count_row_ss = count_row_success.sum() count_col_ss = count_col_success.sum() assert count_row_ss == count_col_ss #just a calculation check #this is SAS manual q_stat = (k-1) * (k * np.sum(count_col_success**2) - count_col_ss**2) \ / (k * count_row_ss - np.sum(count_row_success**2)) #Note: the denominator looks just like k times the variance of the #columns #Wikipedia uses a different, but equivalent expression ## q_stat = (k-1) * (k * np.sum(count_row_success**2) - count_row_ss**2) \ ## / (k * count_col_ss - np.sum(count_col_success**2)) return q_stat, stats.chi2.sf(q_stat, k-1) def mcnemar(x, y=None, exact=True, correction=True): '''McNemar test Parameters ---------- x, y : array_like two paired data samples. If y is None, then x can be a 2 by 2 contingency table. x and y can have more than one dimension, then the results are calculated under the assumption that axis zero contains the observation for the samples. exact : bool If exact is true, then the binomial distribution will be used. If exact is false, then the chisquare distribution will be used, which is the approximation to the distribution of the test statistic for large sample sizes. correction : bool If true, then a continuity correction is used for the chisquare distribution (if exact is false.) Returns ------- stat : float or int, array The test statistic is the chisquare statistic if exact is false. If the exact binomial distribution is used, then this contains the min(n1, n2), where n1, n2 are cases that are zero in one sample but one in the other sample. pvalue : float or array p-value of the null hypothesis of equal effects. Notes ----- This is a special case of Cochran's Q test. The results when the chisquare distribution is used are identical, except for continuity correction. ''' warnings.warn("Deprecated, use stats.TableSymmetry instead", DeprecationWarning) x = np.asarray(x) if y is None and x.shape[0] == x.shape[1]: if x.shape[0] != 2: raise ValueError('table needs to be 2 by 2') n1, n2 = x[1, 0], x[0, 1] else: # I'm not checking here whether x and y are binary, # is not this also paired sign test n1 = np.sum(x < y, 0) n2 = np.sum(x > y, 0) if exact: stat = np.minimum(n1, n2) # binom is symmetric with p=0.5 pval = stats.binom.cdf(stat, n1 + n2, 0.5) * 2 pval = np.minimum(pval, 1) # limit to 1 if n1==n2 else: corr = int(correction) # convert bool to 0 or 1 stat = (np.abs(n1 - n2) - corr)**2 / (1. * (n1 + n2)) df = 1 pval = stats.chi2.sf(stat, df) return stat, pval def symmetry_bowker(table): '''Test for symmetry of a (k, k) square contingency table This is an extension of the McNemar test to test the Null hypothesis that the contingency table is symmetric around the main diagonal, that is n_{i, j} = n_{j, i} for all i, j Parameters ---------- table : array_like, 2d, (k, k) a square contingency table that contains the count for k categories in rows and columns. Returns ------- statistic : float chisquare test statistic p-value : float p-value of the test statistic based on chisquare distribution df : int degrees of freedom of the chisquare distribution Notes ----- Implementation is based on the SAS documentation, R includes it in `mcnemar.test` if the table is not 2 by 2. The pvalue is based on the chisquare distribution which requires that the sample size is not very small to be a good approximation of the true distribution. For 2x2 contingency tables exact distribution can be obtained with `mcnemar` See Also -------- mcnemar ''' warnings.warn("Deprecated, use stats.TableSymmetry instead", DeprecationWarning) table = np.asarray(table) k, k2 = table.shape if k != k2: raise ValueError('table needs to be square') #low_idx = np.tril_indices(k, -1) # this does not have Fortran order upp_idx = np.triu_indices(k, 1) tril = table.T[upp_idx] # lower triangle in column order triu = table[upp_idx] # upper triangle in row order stat = ((tril - triu)**2 / (tril + triu + 1e-20)).sum() df = k * (k-1) / 2. pval = stats.chi2.sf(stat, df) return stat, pval, df if __name__ == '__main__': x1 = np.array([1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1]) print(Runs(x1).runs_test()) print(runstest_1samp(x1, cutoff='mean')) print(runstest_2samp(np.arange(16,0,-1), groups=x1)) print(TotalRunsProb(7,9).cdf(11)) print(median_test_ksample(np.random.randn(100), np.random.randint(0,2,100))) print(cochrans_q(np.random.randint(0,2,(100,8)))) statsmodels-0.12.2/statsmodels/sandbox/stats/stats_dhuard.py000066400000000000000000000235651400612667500243550ustar00rootroot00000000000000''' from David Huard's scipy sandbox, also attached to a ticket and in the matplotlib-user mailinglist (links ???) Notes ===== out of bounds interpolation raises exception and would not be completely defined :: >>> scoreatpercentile(x, [0,25,50,100]) Traceback (most recent call last): ... raise ValueError("A value in x_new is below the interpolation " ValueError: A value in x_new is below the interpolation range. >>> percentileofscore(x, [-50, 50]) Traceback (most recent call last): ... raise ValueError("A value in x_new is below the interpolation " ValueError: A value in x_new is below the interpolation range. idea ==== histogram and empirical interpolated distribution ------------------------------------------------- dual constructor * empirical cdf : cdf on all observations through linear interpolation * binned cdf : based on histogram both should work essentially the same, although pdf of empirical has many spikes, fluctuates a lot - alternative: binning based on interpolated cdf : example in script * ppf: quantileatscore based on interpolated cdf * rvs : generic from ppf * stats, expectation ? how does integration wrt cdf work - theory? Problems * limits, lower and upper bound of support does not work or is undefined with empirical cdf and interpolation * extending bounds ? matlab has pareto tails for empirical distribution, breaks linearity empirical distribution with higher order interpolation ------------------------------------------------------ * should work easily enough with interpolating splines * not piecewise linear * can use pareto (or other) tails * ppf how do I get the inverse function of a higher order spline? Chuck: resample and fit spline to inverse function this will have an approximation error in the inverse function * -> does not work: higher order spline does not preserve monotonicity see mailing list for response to my question * pmf from derivative available in spline -> forget this and use kernel density estimator instead bootstrap/empirical distribution: --------------------------------- discrete distribution on real line given observations what's defined? * cdf : step function * pmf : points with equal weight 1/nobs * rvs : resampling * ppf : quantileatscore on sample? * moments : from data ? * expectation ? sum_{all observations x} [func(x) * pmf(x)] * similar for discrete distribution on real line * References : ? * what's the point? most of it is trivial, just for the record ? Created on Monday, May 03, 2010, 11:47:03 AM Author: josef-pktd, parts based on David Huard License: BSD ''' import scipy.interpolate as interpolate import numpy as np def scoreatpercentile(data, percentile): """Return the score at the given percentile of the data. Example: >>> data = randn(100) >>> scoreatpercentile(data, 50) will return the median of sample `data`. """ per = np.array(percentile) cdf = empiricalcdf(data) interpolator = interpolate.interp1d(np.sort(cdf), np.sort(data)) return interpolator(per/100.) def percentileofscore(data, score): """Return the percentile-position of score relative to data. score: Array of scores at which the percentile is computed. Return percentiles (0-100). Example r = randn(50) x = linspace(-2,2,100) percentileofscore(r,x) Raise an error if the score is outside the range of data. """ cdf = empiricalcdf(data) interpolator = interpolate.interp1d(np.sort(data), np.sort(cdf)) return interpolator(score)*100. def empiricalcdf(data, method='Hazen'): """Return the empirical cdf. Methods available: Hazen: (i-0.5)/N Weibull: i/(N+1) Chegodayev: (i-.3)/(N+.4) Cunnane: (i-.4)/(N+.2) Gringorten: (i-.44)/(N+.12) California: (i-1)/N Where i goes from 1 to N. """ i = np.argsort(np.argsort(data)) + 1. N = len(data) method = method.lower() if method == 'hazen': cdf = (i-0.5)/N elif method == 'weibull': cdf = i/(N+1.) elif method == 'california': cdf = (i-1.)/N elif method == 'chegodayev': cdf = (i-.3)/(N+.4) elif method == 'cunnane': cdf = (i-.4)/(N+.2) elif method == 'gringorten': cdf = (i-.44)/(N+.12) else: raise ValueError('Unknown method. Choose among Weibull, Hazen,' 'Chegodayev, Cunnane, Gringorten and California.') return cdf class HistDist(object): '''Distribution with piecewise linear cdf, pdf is step function can be created from empiricial distribution or from a histogram (not done yet) work in progress, not finished ''' def __init__(self, data): self.data = np.atleast_1d(data) self.binlimit = np.array([self.data.min(), self.data.max()]) sortind = np.argsort(data) self._datasorted = data[sortind] self.ranking = np.argsort(sortind) cdf = self.empiricalcdf() self._empcdfsorted = np.sort(cdf) self.cdfintp = interpolate.interp1d(self._datasorted, self._empcdfsorted) self.ppfintp = interpolate.interp1d(self._empcdfsorted, self._datasorted) def empiricalcdf(self, data=None, method='Hazen'): """Return the empirical cdf. Methods available: Hazen: (i-0.5)/N Weibull: i/(N+1) Chegodayev: (i-.3)/(N+.4) Cunnane: (i-.4)/(N+.2) Gringorten: (i-.44)/(N+.12) California: (i-1)/N Where i goes from 1 to N. """ if data is None: data = self.data i = self.ranking else: i = np.argsort(np.argsort(data)) + 1. N = len(data) method = method.lower() if method == 'hazen': cdf = (i-0.5)/N elif method == 'weibull': cdf = i/(N+1.) elif method == 'california': cdf = (i-1.)/N elif method == 'chegodayev': cdf = (i-.3)/(N+.4) elif method == 'cunnane': cdf = (i-.4)/(N+.2) elif method == 'gringorten': cdf = (i-.44)/(N+.12) else: raise ValueError('Unknown method. Choose among Weibull, Hazen,' 'Chegodayev, Cunnane, Gringorten and California.') return cdf def cdf_emp(self, score): ''' this is score in dh ''' return self.cdfintp(score) #return percentileofscore(self.data, score) def ppf_emp(self, quantile): ''' this is score in dh ''' return self.ppfintp(quantile) #return scoreatpercentile(self.data, quantile*100) #from DHuard http://old.nabble.com/matplotlib-f2903.html def optimize_binning(self, method='Freedman'): """Find the optimal number of bins and update the bin countaccordingly. Available methods : Freedman Scott """ nobs = len(self.data) if method=='Freedman': IQR = self.ppf_emp(0.75) - self.ppf_emp(0.25) # Interquantile range(75% -25%) width = 2* IQR* nobs**(-1./3) elif method=='Scott': width = 3.49 * np.std(self.data) * nobs**(-1./3) self.nbin = (np.ptp(self.binlimit)/width) return self.nbin #changes: josef-pktd if __name__ == '__main__': import matplotlib.pyplot as plt nobs = 100 x = np.random.randn(nobs) examples = [2] if 1 in examples: empiricalcdf(x) print(percentileofscore(x, 0.5)) print(scoreatpercentile(x, 50)) xsupp = np.linspace(x.min(), x.max()) pos = percentileofscore(x, xsupp) plt.plot(xsupp, pos) #perc = np.linspace(2.5, 97.5) #plt.plot(scoreatpercentile(x, perc), perc) plt.plot(scoreatpercentile(x, pos), pos+1) #emp = interpolate.PiecewisePolynomial(np.sort(empiricalcdf(x)), np.sort(x)) emp=interpolate.InterpolatedUnivariateSpline(np.sort(x),np.sort(empiricalcdf(x)),k=1) pdfemp = np.array([emp.derivatives(xi)[1] for xi in xsupp]) plt.figure() plt.plot(xsupp,pdfemp) cdf_ongrid = emp(xsupp) plt.figure() plt.plot(xsupp, cdf_ongrid) #get pdf from interpolated cdf on a regular grid plt.figure() plt.step(xsupp[:-1],np.diff(cdf_ongrid)/np.diff(xsupp)) #reduce number of bins/steps xsupp2 = np.linspace(x.min(), x.max(), 25) plt.figure() plt.step(xsupp2[:-1],np.diff(emp(xsupp2))/np.diff(xsupp2)) #pdf using 25 original observations, every (nobs/25)th xso = np.sort(x) xs = xso[::nobs/25] plt.figure() plt.step(xs[:-1],np.diff(emp(xs))/np.diff(xs)) #lower end looks strange histd = HistDist(x) print(histd.optimize_binning()) print(histd.cdf_emp(histd.binlimit)) print(histd.ppf_emp([0.25, 0.5, 0.75])) print(histd.cdf_emp([-0.5, -0.25, 0, 0.25, 0.5])) xsupp = np.linspace(x.min(), x.max(), 500) emp=interpolate.InterpolatedUnivariateSpline(np.sort(x),np.sort(empiricalcdf(x)),k=1) #pdfemp = np.array([emp.derivatives(xi)[1] for xi in xsupp]) #plt.figure() #plt.plot(xsupp,pdfemp) cdf_ongrid = emp(xsupp) plt.figure() plt.plot(xsupp, cdf_ongrid) ppfintp = interpolate.InterpolatedUnivariateSpline(cdf_ongrid,xsupp,k=3) ppfs = ppfintp(cdf_ongrid) plt.plot(ppfs, cdf_ongrid) #ppfemp=interpolate.InterpolatedUnivariateSpline(np.sort(empiricalcdf(x)),np.sort(x),k=3) #Do not use interpolating splines for function approximation #with s=0.03 the spline is monotonic at the evaluated values ppfemp=interpolate.UnivariateSpline(np.sort(empiricalcdf(x)),np.sort(x),k=3, s=0.03) ppfe = ppfemp(cdf_ongrid) plt.plot(ppfe, cdf_ongrid) print('negative density') print('(np.diff(ppfs)).min()', (np.diff(ppfs)).min()) print('(np.diff(cdf_ongrid)).min()', (np.diff(cdf_ongrid)).min()) #plt.show() statsmodels-0.12.2/statsmodels/sandbox/stats/stats_mstats_short.py000066400000000000000000000350271400612667500256340ustar00rootroot00000000000000'''get versions of mstats percentile functions that also work with non-masked arrays uses dispatch to mstats version for difficult cases: - data is masked array - data requires nan handling (masknan=True) - data should be trimmed (limit is non-empty) handle simple cases directly, which does not require apply_along_axis changes compared to mstats: plotting_positions for n-dim with axis argument addition: plotting_positions_w1d: with weights, 1d ndarray only TODO: consistency with scipy.stats versions not checked docstrings from mstats not updated yet code duplication, better solutions (?) convert examples to tests rename alphap, betap for consistency timing question: one additional argsort versus apply_along_axis weighted plotting_positions - I have not figured out nd version of weighted plotting_positions - add weighted quantiles ''' import numpy as np from numpy import ma from scipy import stats #from numpy.ma import nomask #####-------------------------------------------------------------------------- #---- --- Percentiles --- #####-------------------------------------------------------------------------- def quantiles(a, prob=list([.25,.5,.75]), alphap=.4, betap=.4, axis=None, limit=(), masknan=False): """ Computes empirical quantiles for a data array. Samples quantile are defined by :math:`Q(p) = (1-g).x[i] +g.x[i+1]`, where :math:`x[j]` is the *j*th order statistic, and `i = (floor(n*p+m))`, `m=alpha+p*(1-alpha-beta)` and `g = n*p + m - i`. Typical values of (alpha,beta) are: - (0,1) : *p(k) = k/n* : linear interpolation of cdf (R, type 4) - (.5,.5) : *p(k) = (k+1/2.)/n* : piecewise linear function (R, type 5) - (0,0) : *p(k) = k/(n+1)* : (R type 6) - (1,1) : *p(k) = (k-1)/(n-1)*. In this case, p(k) = mode[F(x[k])]. That's R default (R type 7) - (1/3,1/3): *p(k) = (k-1/3)/(n+1/3)*. Then p(k) ~ median[F(x[k])]. The resulting quantile estimates are approximately median-unbiased regardless of the distribution of x. (R type 8) - (3/8,3/8): *p(k) = (k-3/8)/(n+1/4)*. Blom. The resulting quantile estimates are approximately unbiased if x is normally distributed (R type 9) - (.4,.4) : approximately quantile unbiased (Cunnane) - (.35,.35): APL, used with PWM ?? JP - (0.35, 0.65): PWM ?? JP p(k) = (k-0.35)/n Parameters ---------- a : array_like Input data, as a sequence or array of dimension at most 2. prob : array_like, optional List of quantiles to compute. alpha : float, optional Plotting positions parameter, default is 0.4. beta : float, optional Plotting positions parameter, default is 0.4. axis : int, optional Axis along which to perform the trimming. If None (default), the input array is first flattened. limit : tuple Tuple of (lower, upper) values. Values of `a` outside this closed interval are ignored. Returns ------- quants : MaskedArray An array containing the calculated quantiles. Examples -------- >>> from scipy.stats.mstats import mquantiles >>> a = np.array([6., 47., 49., 15., 42., 41., 7., 39., 43., 40., 36.]) >>> mquantiles(a) array([ 19.2, 40. , 42.8]) Using a 2D array, specifying axis and limit. >>> data = np.array([[ 6., 7., 1.], [ 47., 15., 2.], [ 49., 36., 3.], [ 15., 39., 4.], [ 42., 40., -999.], [ 41., 41., -999.], [ 7., -999., -999.], [ 39., -999., -999.], [ 43., -999., -999.], [ 40., -999., -999.], [ 36., -999., -999.]]) >>> mquantiles(data, axis=0, limit=(0, 50)) array([[ 19.2 , 14.6 , 1.45], [ 40. , 37.5 , 2.5 ], [ 42.8 , 40.05, 3.55]]) >>> data[:, 2] = -999. >>> mquantiles(data, axis=0, limit=(0, 50)) masked_array(data = [[19.2 14.6 --] [40.0 37.5 --] [42.8 40.05 --]], mask = [[False False True] [False False True] [False False True]], fill_value = 1e+20) """ if isinstance(a, np.ma.MaskedArray): return stats.mstats.mquantiles(a, prob=prob, alphap=alphap, betap=alphap, axis=axis, limit=limit) if limit: marr = stats.mstats.mquantiles(a, prob=prob, alphap=alphap, betap=alphap, axis=axis, limit=limit) return ma.filled(marr, fill_value=np.nan) if masknan: nanmask = np.isnan(a) if nanmask.any(): marr = ma.array(a, mask=nanmask) marr = stats.mstats.mquantiles(marr, prob=prob, alphap=alphap, betap=alphap, axis=axis, limit=limit) return ma.filled(marr, fill_value=np.nan) # Initialization & checks --------- data = np.asarray(a) p = np.array(prob, copy=False, ndmin=1) m = alphap + p*(1.-alphap-betap) isrolled = False #from _quantiles1d if (axis is None): data = data.ravel() #reshape(-1,1) axis = 0 else: axis = np.arange(data.ndim)[axis] data = np.rollaxis(data, axis) isrolled = True # keep track, maybe can be removed x = np.sort(data, axis=0) n = x.shape[0] returnshape = list(data.shape) returnshape[axis] = p #TODO: check these if n == 0: return np.empty(len(p), dtype=float) elif n == 1: return np.resize(x, p.shape) aleph = (n*p + m) k = np.floor(aleph.clip(1, n-1)).astype(int) ind = [None]*x.ndim ind[0] = slice(None) gamma = (aleph-k).clip(0,1)[ind] q = (1.-gamma)*x[k-1] + gamma*x[k] if isrolled: return np.rollaxis(q, 0, axis+1) else: return q def scoreatpercentile(data, per, limit=(), alphap=.4, betap=.4, axis=0, masknan=None): """Calculate the score at the given 'per' percentile of the sequence a. For example, the score at per=50 is the median. This function is a shortcut to mquantile """ per = np.asarray(per, float) if (per < 0).any() or (per > 100.).any(): raise ValueError("The percentile should be between 0. and 100. !"\ " (got %s)" % per) return quantiles(data, prob=[per/100.], alphap=alphap, betap=betap, limit=limit, axis=axis, masknan=masknan).squeeze() def plotting_positions(data, alpha=0.4, beta=0.4, axis=0, masknan=False): """Returns the plotting positions (or empirical percentile points) for the data. Plotting positions are defined as (i-alpha)/(n+1-alpha-beta), where: - i is the rank order statistics (starting at 1) - n is the number of unmasked values along the given axis - alpha and beta are two parameters. Typical values for alpha and beta are: - (0,1) : *p(k) = k/n* : linear interpolation of cdf (R, type 4) - (.5,.5) : *p(k) = (k-1/2.)/n* : piecewise linear function (R, type 5) (Bliss 1967: "Rankit") - (0,0) : *p(k) = k/(n+1)* : Weibull (R type 6), (Van der Waerden 1952) - (1,1) : *p(k) = (k-1)/(n-1)*. In this case, p(k) = mode[F(x[k])]. That's R default (R type 7) - (1/3,1/3): *p(k) = (k-1/3)/(n+1/3)*. Then p(k) ~ median[F(x[k])]. The resulting quantile estimates are approximately median-unbiased regardless of the distribution of x. (R type 8), (Tukey 1962) - (3/8,3/8): *p(k) = (k-3/8)/(n+1/4)*. The resulting quantile estimates are approximately unbiased if x is normally distributed (R type 9) (Blom 1958) - (.4,.4) : approximately quantile unbiased (Cunnane) - (.35,.35): APL, used with PWM Parameters ---------- x : sequence Input data, as a sequence or array of dimension at most 2. prob : sequence List of quantiles to compute. alpha : {0.4, float} optional Plotting positions parameter. beta : {0.4, float} optional Plotting positions parameter. Notes ----- I think the adjustments assume that there are no ties in order to be a reasonable approximation to a continuous density function. TODO: check this References ---------- unknown, dates to original papers from Beasley, Erickson, Allison 2009 Behav Genet """ if isinstance(data, np.ma.MaskedArray): if axis is None or data.ndim == 1: return stats.mstats.plotting_positions(data, alpha=alpha, beta=beta) else: return ma.apply_along_axis(stats.mstats.plotting_positions, axis, data, alpha=alpha, beta=beta) if masknan: nanmask = np.isnan(data) if nanmask.any(): marr = ma.array(data, mask=nanmask) #code duplication: if axis is None or data.ndim == 1: marr = stats.mstats.plotting_positions(marr, alpha=alpha, beta=beta) else: marr = ma.apply_along_axis(stats.mstats.plotting_positions, axis, marr, alpha=alpha, beta=beta) return ma.filled(marr, fill_value=np.nan) data = np.asarray(data) if data.size == 1: # use helper function instead data = np.atleast_1d(data) axis = 0 if axis is None: data = data.ravel() axis = 0 n = data.shape[axis] if data.ndim == 1: plpos = np.empty(data.shape, dtype=float) plpos[data.argsort()] = (np.arange(1,n+1) - alpha)/(n+1.-alpha-beta) else: #nd assignment instead of second argsort does not look easy plpos = (data.argsort(axis).argsort(axis) + 1. - alpha)/(n+1.-alpha-beta) return plpos meppf = plotting_positions def plotting_positions_w1d(data, weights=None, alpha=0.4, beta=0.4, method='notnormed'): '''Weighted plotting positions (or empirical percentile points) for the data. observations are weighted and the plotting positions are defined as (ws-alpha)/(n-alpha-beta), where: - ws is the weighted rank order statistics or cumulative weighted sum, normalized to n if method is "normed" - n is the number of values along the given axis if method is "normed" and total weight otherwise - alpha and beta are two parameters. wtd.quantile in R package Hmisc seems to use the "notnormed" version. notnormed coincides with unweighted segment in example, drop "normed" version ? See Also -------- plotting_positions : unweighted version that works also with more than one dimension and has other options ''' x = np.atleast_1d(data) if x.ndim > 1: raise ValueError('currently implemented only for 1d') if weights is None: weights = np.ones(x.shape) else: weights = np.array(weights, float, copy=False, ndmin=1) #atleast_1d(weights) if weights.shape != x.shape: raise ValueError('if weights is given, it needs to be the same' 'shape as data') n = len(x) xargsort = x.argsort() ws = weights[xargsort].cumsum() res = np.empty(x.shape) if method == 'normed': res[xargsort] = (1.*ws/ws[-1]*n-alpha)/(n+1.-alpha-beta) else: res[xargsort] = (1.*ws-alpha)/(ws[-1]+1.-alpha-beta) return res def edf_normal_inverse_transformed(x, alpha=3./8, beta=3./8, axis=0): '''rank based normal inverse transformed cdf ''' from scipy import stats ranks = plotting_positions(x, alpha=alpha, beta=alpha, axis=0, masknan=False) ranks_transf = stats.norm.ppf(ranks) return ranks_transf if __name__ == '__main__': x = np.arange(5) print(plotting_positions(x)) x = np.arange(10).reshape(-1,2) print(plotting_positions(x)) print(quantiles(x, axis=0)) print(quantiles(x, axis=None)) print(quantiles(x, axis=1)) xm = ma.array(x) x2 = x.astype(float) x2[1,0] = np.nan print(plotting_positions(xm, axis=0)) # test 0d, 1d for sl1 in [slice(None), 0]: print((plotting_positions(xm[sl1,0]) == plotting_positions(x[sl1,0])).all()) print((quantiles(xm[sl1,0]) == quantiles(x[sl1,0])).all()) print((stats.mstats.mquantiles(ma.fix_invalid(x2[sl1,0])) == quantiles(x2[sl1,0], masknan=1)).all()) #test 2d for ax in [0, 1, None, -1]: print((plotting_positions(xm, axis=ax) == plotting_positions(x, axis=ax)).all()) print((quantiles(xm, axis=ax) == quantiles(x, axis=ax)).all()) print((stats.mstats.mquantiles(ma.fix_invalid(x2), axis=ax) == quantiles(x2, axis=ax, masknan=1)).all()) #stats version does not have axis print((stats.mstats.plotting_positions(ma.fix_invalid(x2)) == plotting_positions(x2, axis=None, masknan=1)).all()) #test 3d x3 = np.dstack((x,x)).T for ax in [1,2]: print((plotting_positions(x3, axis=ax)[0] == plotting_positions(x.T, axis=ax-1)).all()) np.testing.assert_equal(plotting_positions(np.arange(10), alpha=0.35, beta=1-0.35), (1+np.arange(10)-0.35)/10) np.testing.assert_equal(plotting_positions(np.arange(10), alpha=0.4, beta=0.4), (1+np.arange(10)-0.4)/(10+0.2)) np.testing.assert_equal(plotting_positions(np.arange(10)), (1+np.arange(10)-0.4)/(10+0.2)) print('') print(scoreatpercentile(x, [10,90])) print(plotting_positions_w1d(x[:,0])) print((plotting_positions_w1d(x[:,0]) == plotting_positions(x[:,0])).all()) #weights versus replicating multiple occurencies of same x value w1 = [1, 1, 2, 1, 1] plotexample = 1 if plotexample: import matplotlib.pyplot as plt plt.figure() plt.title('ppf, cdf values on horizontal axis') plt.step(plotting_positions_w1d(x[:,0], weights=w1, method='0'), x[:,0], where='post') plt.step(stats.mstats.plotting_positions(np.repeat(x[:,0],w1,axis=0)),np.repeat(x[:,0],w1,axis=0),where='post') plt.plot(plotting_positions_w1d(x[:,0], weights=w1, method='0'), x[:,0], '-o') plt.plot(stats.mstats.plotting_positions(np.repeat(x[:,0],w1,axis=0)),np.repeat(x[:,0],w1,axis=0), '-o') plt.figure() plt.title('cdf, cdf values on vertical axis') plt.step(x[:,0], plotting_positions_w1d(x[:,0], weights=w1, method='0'),where='post') plt.step(np.repeat(x[:,0],w1,axis=0), stats.mstats.plotting_positions(np.repeat(x[:,0],w1,axis=0)),where='post') plt.plot(x[:,0], plotting_positions_w1d(x[:,0], weights=w1, method='0'), '-o') plt.plot(np.repeat(x[:,0],w1,axis=0), stats.mstats.plotting_positions(np.repeat(x[:,0],w1,axis=0)), '-o') plt.show() statsmodels-0.12.2/statsmodels/sandbox/stats/tests/000077500000000000000000000000001400612667500224455ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/stats/tests/__init__.py000066400000000000000000000000001400612667500245440ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/stats/tests/test_multicomp.py000066400000000000000000000006651400612667500260760ustar00rootroot00000000000000""" Tests corresponding to sandbox.stats.multicomp """ import numpy as np from numpy.testing import assert_almost_equal from statsmodels.sandbox.stats.multicomp import tukey_pvalues def test_tukey_pvalues(): # TODO: testcase with 3 is not good because all pairs # has also 3*(3-1)/2=3 elements res = tukey_pvalues(3.649, 3, 16) assert_almost_equal(0.05, res[0], 3) assert_almost_equal(0.05*np.ones(3), res[1], 3) statsmodels-0.12.2/statsmodels/sandbox/sysreg.py000066400000000000000000000344531400612667500220440ustar00rootroot00000000000000from statsmodels.regression.linear_model import GLS import numpy as np from statsmodels.base.model import LikelihoodModelResults from scipy import sparse # http://www.irisa.fr/aladin/wg-statlin/WORKSHOPS/RENNES02/SLIDES/Foschi.pdf __all__ = ['SUR', 'Sem2SLS'] #probably should have a SystemModel superclass # TODO: does it make sense of SUR equations to have # independent endogenous regressors? If so, then # change docs to LHS = RHS #TODO: make a dictionary that holds equation specific information #rather than these cryptic lists? Slower to get a dict value? #TODO: refine sigma definition class SUR(object): """ Seemingly Unrelated Regression Parameters ---------- sys : list [endog1, exog1, endog2, exog2,...] It will be of length 2 x M, where M is the number of equations endog = exog. sigma : array_like M x M array where sigma[i,j] is the covariance between equation i and j dfk : None, 'dfk1', or 'dfk2' Default is None. Correction for the degrees of freedom should be specified for small samples. See the notes for more information. Attributes ---------- cholsigmainv : ndarray The transpose of the Cholesky decomposition of `pinv_wexog` df_model : ndarray Model degrees of freedom of each equation. p_{m} - 1 where p is the number of regressors for each equation m and one is subtracted for the constant. df_resid : ndarray Residual degrees of freedom of each equation. Number of observations less the number of parameters. endog : ndarray The LHS variables for each equation in the system. It is a M x nobs array where M is the number of equations. exog : ndarray The RHS variable for each equation in the system. It is a nobs x sum(p_{m}) array. Which is just each RHS array stacked next to each other in columns. history : dict Contains the history of fitting the model. Probably not of interest if the model is fit with `igls` = False. iterations : int The number of iterations until convergence if the model is fit iteratively. nobs : float The number of observations of the equations. normalized_cov_params : ndarray sum(p_{m}) x sum(p_{m}) array :math:`\\left[X^{T}\\left(\\Sigma^{-1}\\otimes\\boldsymbol{I}\\right)X\\right]^{-1}` pinv_wexog : ndarray The pseudo-inverse of the `wexog` sigma : ndarray M x M covariance matrix of the cross-equation disturbances. See notes. sp_exog : CSR sparse matrix Contains a block diagonal sparse matrix of the design so that exog1 ... exogM are on the diagonal. wendog : ndarray M * nobs x 1 array of the endogenous variables whitened by `cholsigmainv` and stacked into a single column. wexog : ndarray M*nobs x sum(p_{m}) array of the whitened exogenous variables. Notes ----- All individual equations are assumed to be well-behaved, homoskedastic iid errors. This is basically an extension of GLS, using sparse matrices. .. math:: \\Sigma=\\left[\\begin{array}{cccc} \\sigma_{11} & \\sigma_{12} & \\cdots & \\sigma_{1M}\\\\ \\sigma_{21} & \\sigma_{22} & \\cdots & \\sigma_{2M}\\\\ \\vdots & \\vdots & \\ddots & \\vdots\\\\ \\sigma_{M1} & \\sigma_{M2} & \\cdots & \\sigma_{MM}\\end{array}\\right] References ---------- Zellner (1962), Greene (2003) """ #TODO: Does each equation need nobs to be the same? def __init__(self, sys, sigma=None, dfk=None): if len(sys) % 2 != 0: raise ValueError("sys must be a list of pairs of endogenous and \ exogenous variables. Got length %s" % len(sys)) if dfk: if not dfk.lower() in ['dfk1','dfk2']: raise ValueError("dfk option %s not understood" % (dfk)) self._dfk = dfk M = len(sys[1::2]) self._M = M # exog = np.zeros((M,M), dtype=object) # for i,eq in enumerate(sys[1::2]): # exog[i,i] = np.asarray(eq) # not sure this exog is needed # used to compute resids for now exog = np.column_stack(np.asarray(sys[1::2][i]) for i in range(M)) # exog = np.vstack(np.asarray(sys[1::2][i]) for i in range(M)) self.exog = exog # 2d ndarray exog is better # Endog, might just go ahead and reshape this? endog = np.asarray(sys[::2]) self.endog = endog self.nobs = float(self.endog[0].shape[0]) # assumes all the same length # Degrees of Freedom df_resid = [] df_model = [] [df_resid.append(self.nobs - np.linalg.matrix_rank(_)) for _ in sys[1::2]] [df_model.append(np.linalg.matrix_rank(_) - 1) for _ in sys[1::2]] self.df_resid = np.asarray(df_resid) self.df_model = np.asarray(df_model) # "Block-diagonal" sparse matrix of exog sp_exog = sparse.lil_matrix((int(self.nobs*M), int(np.sum(self.df_model+1)))) # linked lists to build self._cols = np.cumsum(np.hstack((0, self.df_model+1))) for i in range(M): sp_exog[i*self.nobs:(i+1)*self.nobs, self._cols[i]:self._cols[i+1]] = sys[1::2][i] self.sp_exog = sp_exog.tocsr() # cast to compressed for efficiency # Deal with sigma, check shape earlier if given if np.any(sigma): sigma = np.asarray(sigma) # check shape elif sigma is None: resids = [] for i in range(M): resids.append(GLS(endog[i],exog[:, self._cols[i]:self._cols[i+1]]).fit().resid) resids = np.asarray(resids).reshape(M,-1) sigma = self._compute_sigma(resids) self.sigma = sigma self.cholsigmainv = np.linalg.cholesky(np.linalg.pinv(\ self.sigma)).T self.initialize() def initialize(self): self.wendog = self.whiten(self.endog) self.wexog = self.whiten(self.sp_exog) self.pinv_wexog = np.linalg.pinv(self.wexog) self.normalized_cov_params = np.dot(self.pinv_wexog, np.transpose(self.pinv_wexog)) self.history = {'params' : [np.inf]} self.iterations = 0 def _update_history(self, params): self.history['params'].append(params) def _compute_sigma(self, resids): """ Computes the sigma matrix and update the cholesky decomposition. """ M = self._M nobs = self.nobs sig = np.dot(resids, resids.T) # faster way to do this? if not self._dfk: div = nobs elif self._dfk.lower() == 'dfk1': div = np.zeros(M**2) for i in range(M): for j in range(M): div[i+j] = ((self.df_model[i]+1) *\ (self.df_model[j]+1))**(1/2) div.reshape(M,M) else: # 'dfk2' error checking is done earlier div = np.zeros(M**2) for i in range(M): for j in range(M): div[i+j] = nobs - np.max(self.df_model[i]+1, self.df_model[j]+1) div.reshape(M,M) # does not handle (#,) self.cholsigmainv = np.linalg.cholesky(np.linalg.pinv(sig/div)).T return sig/div def whiten(self, X): """ SUR whiten method. Parameters ---------- X : list of arrays Data to be whitened. Returns ------- If X is the exogenous RHS of the system. ``np.dot(np.kron(cholsigmainv,np.eye(M)),np.diag(X))`` If X is the endogenous LHS of the system. """ nobs = self.nobs if X is self.endog: # definitely not a robust check return np.dot(np.kron(self.cholsigmainv,np.eye(nobs)), X.reshape(-1,1)) elif X is self.sp_exog: return (sparse.kron(self.cholsigmainv, sparse.eye(nobs,nobs))*X).toarray()#*=dot until cast to array def fit(self, igls=False, tol=1e-5, maxiter=100): """ igls : bool Iterate until estimates converge if sigma is None instead of two-step GLS, which is the default is sigma is None. tol : float maxiter : int Notes ----- This ia naive implementation that does not exploit the block diagonal structure. It should work for ill-conditioned `sigma` but this is untested. """ if not np.any(self.sigma): self.sigma = self._compute_sigma(self.endog, self.exog) M = self._M beta = np.dot(self.pinv_wexog, self.wendog) self._update_history(beta) self.iterations += 1 if not igls: sur_fit = SysResults(self, beta, self.normalized_cov_params) return sur_fit conv = self.history['params'] while igls and (np.any(np.abs(conv[-2] - conv[-1]) > tol)) and \ (self.iterations < maxiter): fittedvalues = (self.sp_exog*beta).reshape(M,-1) resids = self.endog - fittedvalues # do not attach results yet self.sigma = self._compute_sigma(resids) # need to attach for compute? self.wendog = self.whiten(self.endog) self.wexog = self.whiten(self.sp_exog) self.pinv_wexog = np.linalg.pinv(self.wexog) self.normalized_cov_params = np.dot(self.pinv_wexog, np.transpose(self.pinv_wexog)) beta = np.dot(self.pinv_wexog, self.wendog) self._update_history(beta) self.iterations += 1 sur_fit = SysResults(self, beta, self.normalized_cov_params) return sur_fit def predict(self, design): pass #TODO: Should just have a general 2SLS estimator to subclass # for IV, FGLS, etc. # Also should probably have SEM class and estimators as subclasses class Sem2SLS(object): """ Two-Stage Least Squares for Simultaneous equations Parameters ---------- sys : list [endog1, exog1, endog2, exog2,...] It will be of length 2 x M, where M is the number of equations endog = exog. indep_endog : dict A dictionary mapping the equation to the column numbers of the the independent endogenous regressors in each equation. It is assumed that the system is entered as broken up into LHS and RHS. For now, the values of the dict have to be sequences. Note that the keys for the equations should be zero-indexed. instruments : ndarray Array of the exogenous independent variables. Notes ----- This is unfinished, and the design should be refactored. Estimation is done by brute force and there is no exploitation of the structure of the system. """ def __init__(self, sys, indep_endog=None, instruments=None): if len(sys) % 2 != 0: raise ValueError("sys must be a list of pairs of endogenous and \ exogenous variables. Got length %s" % len(sys)) M = len(sys[1::2]) self._M = M # The lists are probably a bad idea self.endog = sys[::2] # these are just list containers self.exog = sys[1::2] self._K = [np.linalg.matrix_rank(_) for _ in sys[1::2]] # fullexog = np.column_stack((_ for _ in self.exog)) self.instruments = instruments # Keep the Y_j's in a container to get IVs instr_endog = {} [instr_endog.setdefault(_,[]) for _ in indep_endog.keys()] for eq_key in indep_endog: for varcol in indep_endog[eq_key]: instr_endog[eq_key].append(self.exog[eq_key][:,varcol]) # ^ copy needed? # self._instr_endog = instr_endog self._indep_endog = indep_endog _col_map = np.cumsum(np.hstack((0,self._K))) # starting col no.s # move this check to whiten since we're not going to build a full exog? for eq_key in indep_endog: try: iter(indep_endog[eq_key]) except: # eq_key = [eq_key] raise TypeError("The values of the indep_exog dict must be " "iterable. Got type %s for converter %s" % (type(indep_endog[eq_key]), eq_key)) # for del_col in indep_endog[eq_key]: # fullexog = np.delete(fullexog, _col_map[eq_key]+del_col, 1) # _col_map[eq_key+1:] -= 1 # Josef's example for deleting reoccuring "rows" # fullexog = np.unique(fullexog.T.view([('',fullexog.dtype)]*\ # fullexog.shape[0])).view(fullexog.dtype).reshape(\ # fullexog.shape[0],-1) # From http://article.gmane.org/gmane.comp.python.numeric.general/32276/ # Or Jouni' suggetsion of taking a hash: # http://www.mail-archive.com/numpy-discussion@scipy.org/msg04209.html # not clear to me how this would work though, only if they are the *same* # elements? # self.fullexog = fullexog self.wexog = self.whiten(instr_endog) def whiten(self, Y): """ Runs the first stage of the 2SLS. Returns the RHS variables that include the instruments. """ wexog = [] indep_endog = self._indep_endog # this has the col mapping # fullexog = self.fullexog instruments = self.instruments for eq in range(self._M): # need to go through all equations regardless instr_eq = Y.get(eq, None) # Y has the eq to ind endog array map newRHS = self.exog[eq].copy() if instr_eq: for i,LHS in enumerate(instr_eq): yhat = GLS(LHS, self.instruments).fit().fittedvalues newRHS[:,indep_endog[eq][i]] = yhat # this might fail if there is a one variable column (nobs,) # in exog wexog.append(newRHS) return wexog def fit(self): """ """ delta = [] wexog = self.wexog endog = self.endog for j in range(self._M): delta.append(GLS(endog[j], wexog[j]).fit().params) return delta class SysResults(LikelihoodModelResults): """ Not implemented yet. """ def __init__(self, model, params, normalized_cov_params=None, scale=1.): super(SysResults, self).__init__(model, params, normalized_cov_params, scale) self._get_results() def _get_results(self): pass statsmodels-0.12.2/statsmodels/sandbox/tests/000077500000000000000000000000001400612667500213075ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/tests/GreeneEx15_1.s000066400000000000000000000020771400612667500235710ustar00rootroot00000000000000dta <- read.table('/home/skipper/school/MetricsII/Greene\ TableF5-1.txt', header = TRUE) attach(dta) library(systemfit) demand <- realcons + realinvs + realgovt c.1 <- realcons[-204] y.1 <- demand[-204] yd <- demand[-1] - y.1 eqConsump <- realcons[-1] ~ demand[-1] + c.1 eqInvest <- realinvs[-1] ~ tbilrate[-1] + yd system <- list( Consumption = eqConsump, Investment = eqInvest) instruments <- ~ realgovt[-1] + tbilrate[-1] + c.1 + y.1 # 2SLS greene2sls <- systemfit( system, "2SLS", inst = instruments, methodResidCov = "noDfCor" ) print(summary(greene2sls)) greene3sls <- systemfit( system, "3SLS", inst = instruments, methodResidCov = "noDfCor" ) print(summary(greene3sls)) # Python code for finding the dynamics # # Could have done this in R # #gamma = np.array([[1,0,1],[0,1,1],[-.058438620413,-16.5359646223,1]]) #phi = np.array([[-.99200661799,0,0],[0,0,0],[0,-16.5359646223,0]]) #Delta = np.dot(-phi,np.linalg.inv(gamma)) #delta = np.zeros((2,2)) #delta[0,0]=Delta[0,0] #delta[0,1]=Delta[0,-1] #delta[1,0]=Delta[-1,0] #delta[1,1]=Delta[-1,-1] #np.eigvals(delta) #np.max(_) statsmodels-0.12.2/statsmodels/sandbox/tests/__init__.py000066400000000000000000000000001400612667500234060ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/tests/macrodata.s000066400000000000000000000020551400612667500234300ustar00rootroot00000000000000dta <- read.csv('../../datasets/macrodata/macrodata.csv', header = TRUE) attach(dta) library(systemfit) demand <- realcons + realinv + realgovt c.1 <- realcons[-203] y.1 <- demand[-203] yd <- demand[-1] - y.1 eqConsump <- realcons[-1] ~ demand[-1] + c.1 eqInvest <- realinv[-1] ~ tbilrate[-1] + yd system <- list( Consumption = eqConsump, Investment = eqInvest) instruments <- ~ realgovt[-1] + tbilrate[-1] + c.1 + y.1 # 2SLS greene2sls <- systemfit( system, "2SLS", inst = instruments, methodResidCov = "noDfCor" ) print(summary(greene2sls)) greene3sls <- systemfit( system, "3SLS", inst = instruments, methodResidCov = "noDfCor" ) print(summary(greene3sls)) # Python code for finding the dynamics # # Could have done this in R # #gamma = np.array([[1,0,1],[0,1,1],[-.058438620413,-16.5359646223,1]]) #phi = np.array([[-.99200661799,0,0],[0,0,0],[0,-16.5359646223,0]]) #Delta = np.dot(-phi,np.linalg.inv(gamma)) #delta = np.zeros((2,2)) #delta[0,0]=Delta[0,0] #delta[0,1]=Delta[0,-1] #delta[1,0]=Delta[-1,0] #delta[1,1]=Delta[-1,-1] #np.eigvals(delta) #np.max(_) statsmodels-0.12.2/statsmodels/sandbox/tests/maketests_mlabwrap.py000066400000000000000000000214661400612667500255570ustar00rootroot00000000000000'''generate py modules with test cases and results from mlabwrap currently matlab: princomp, garchar, garchma ''' import numpy as np from numpy.testing import assert_array_almost_equal from numpy import array xo = array([[ -419, -731, -1306, -1294], [ 6, 529, -200, -437], [ -27, -833, -6, -564], [ -304, -273, -502, -739], [ 1377, -912, 927, 280], [ -375, -517, -514, 49], [ 247, -504, 123, -259], [ 712, 534, -773, 286], [ 195, -1080, 3256, -178], [ -854, 75, -706, -1084], [-1219, -612, -15, -203], [ 550, -628, -483, -2686], [ -365, 1376, -1266, 317], [ -489, 544, -195, 431], [ -656, 854, 840, -723], [ 16, -1385, -880, -460], [ 258, -2252, 96, 54], [ 2049, -750, -1115, 381], [ -65, 280, -777, 416], [ 755, 82, -806, 1027], [ -39, -170, -2134, 743], [ -859, 780, 746, -133], [ 762, 252, -450, -459], [ -941, -202, 49, -202], [ -54, 115, 455, 388], [-1348, 1246, 1430, -480], [ 229, -535, -1831, 1524], [ -651, -167, 2116, 483], [-1249, -1373, 888, -1092], [ -75, -2162, 486, -496], [ 2436, -1627, -1069, 162], [ -63, 560, -601, 587], [ -60, 1051, -277, 1323], [ 1329, -1294, 68, 5], [ 1532, -633, -923, 696], [ 669, 895, -1762, -375], [ 1129, -548, 2064, 609], [ 1320, 573, 2119, 270], [ -213, -412, -2517, 1685], [ 73, -979, 1312, -1220], [-1360, -2107, -237, 1522], [ -645, 205, -543, -169], [ -212, 1072, 543, -128], [ -352, -129, -605, -904], [ 511, 85, 167, -1914], [ 1515, 1862, 942, 1622], [ -465, 623, -495, -89], [-1396, -979, 1758, 128], [ -255, -47, 980, 501], [-1282, -58, -49, -610], [ -889, -1177, -492, 494], [ 1415, 1146, 696, -722], [ 1237, -224, -1609, -64], [ -528, -1625, 231, 883], [ -327, 1636, -476, -361], [ -781, 793, 1882, 234], [ -506, -561, 1988, -810], [-1233, 1467, -261, 2164], [ 53, 1069, 824, 2123], [-1200, -441, -321, 339], [ 1606, 298, -995, 1292], [-1740, -672, -1628, -129], [-1450, -354, 224, -657], [-2556, 1006, -706, -1453], [ -717, -463, 345, -1821], [ 1056, -38, -420, -455], [ -523, 565, 425, 1138], [-1030, -187, 683, 78], [ -214, -312, -1171, -528], [ 819, 736, -265, 423], [ 1339, 351, 1142, 579], [ -387, -126, -1573, 2346], [ 969, 2, 327, -134], [ 163, 227, 90, 2021], [ 1022, -1076, 174, 304], [ 1042, 1317, 311, 880], [ 2018, -840, 295, 2651], [ -277, 566, 1147, -189], [ 20, 467, 1262, 263], [ -663, 1061, -1552, -1159], [ 1830, 391, 2534, -199], [ -487, 752, -1061, 351], [-2138, -556, -367, -457], [ -868, -411, -559, 726], [ 1770, 819, -892, -363], [ 553, -736, -169, -490], [ 388, -503, 809, -821], [ -516, -1452, -192, 483], [ 493, 2904, 1318, 2591], [ 175, 584, -1001, 1675], [ 1316, -1596, -460, 1500], [ 1212, 214, -644, -696], [ -501, 338, 1197, -841], [ -587, -469, -1101, 24], [-1205, 1910, 659, 1232], [ -150, 398, 594, 394], [ 34, -663, 235, -334], [-1580, 647, 239, -351], [-2177, -345, 1215, -1494], [ 1923, 329, -152, 1128]]) x = xo/1000. class HoldIt(object): def __init__(self, name): self.name = name def save(self, what=None, filename=None, header=True, useinstant=True, comment=None): if what is None: what = (i for i in self.__dict__ if i[0] != '_') if header: txt = ['import numpy as np\nfrom numpy import array\n\n'] if useinstant: txt.append('from statsmodels.tools.testing import Holder\n\n') else: txt = [] if useinstant: txt.append('%s = Holder()' % self.name) prefix = '%s.' % self.name else: prefix = '' if comment is not None: txt.append("%scomment = '%s'" % (prefix, comment)) for x in what: txt.append('%s%s = %s' % (prefix, x, repr(getattr(self,x)))) txt.extend(['','']) #add empty lines at end if filename is not None: with open(filename, 'a+') as fd: fd.write('\n'.join(txt)) return txt def generate_princomp(xo, filen='testsave.py'): # import mlabwrap only when run as script from mlabwrap import mlab np.set_printoptions(precision=14, linewidth=100) data = HoldIt('data') data.xo = xo data.save(filename='testsave.py', comment='generated data, divide by 1000') res_princomp = HoldIt('princomp1') res_princomp.coef, res_princomp.factors, res_princomp.values = \ mlab.princomp(x, nout=3) res_princomp.save(filename=filen, header=False, comment='mlab.princomp(x, nout=3)') res_princomp = HoldIt('princomp2') res_princomp.coef, res_princomp.factors, res_princomp.values = \ mlab.princomp(x[:20,], nout=3) np.set_printoptions(precision=14, linewidth=100) res_princomp.save(filename=filen, header=False, comment='mlab.princomp(x[:20,], nout=3)') res_princomp = HoldIt('princomp3') res_princomp.coef, res_princomp.factors, res_princomp.values = \ mlab.princomp(x[:20,]-x[:20,].mean(0), nout=3) np.set_printoptions(precision=14, linewidth=100) res_princomp.save(filename=filen, header=False, comment='mlab.princomp(x[:20,]-x[:20,].mean(0), nout=3)') def generate_armarep(filen='testsave.py'): # import mlabwrap only when run as script from mlabwrap import mlab res_armarep = HoldIt('armarep') res_armarep.ar = np.array([1., -0.5, +0.8]) res_armarep.ma = np.array([1., -0.6, 0.08]) res_armarep.marep = mlab.garchma(-res_armarep.ar[1:], res_armarep.ma[1:], 20) res_armarep.arrep = mlab.garchar(-res_armarep.ar[1:], res_armarep.ma[1:], 20) res_armarep.save(filename=filen, header=False, comment=("''mlab.garchma(-res_armarep.ar[1:], res_armarep.ma[1:], 20)\n" + "mlab.garchar(-res_armarep.ar[1:], res_armarep.ma[1:], 20)''")) def exampletest(res_armarep): from statsmodels.sandbox import tsa arrep = tsa.arma_impulse_response(res_armarep.ma, res_armarep.ar, nobs=21)[1:] marep = tsa.arma_impulse_response(res_armarep.ar, res_armarep.ma, nobs=21)[1:] assert_array_almost_equal(res_armarep.marep.ravel(), marep, 14) #difference in sign convention to matlab for AR term assert_array_almost_equal(-res_armarep.arrep.ravel(), arrep, 14) if __name__ == '__main__': from mlabwrap import mlab import savedrvs xo = savedrvs.rvsdata.xar2 x100 = xo[-100:]/1000. x1000 = xo/1000. filen = 'testsavetls.py' res_pacf = HoldIt('mlpacf') res_pacf.comment = 'mlab.parcorr(x, [], 2, nout=3)' res_pacf.pacf100, res_pacf.lags100, res_pacf.bounds100 = \ mlab.parcorr(x100, [], 2, nout=3) res_pacf.pacf1000, res_pacf.lags1000, res_pacf.bounds1000 = \ mlab.parcorr(x1000, [], 2, nout=3) res_pacf.save(filename=filen, header=True) res_acf = HoldIt('mlacf') res_acf.comment = 'mlab.autocorr(x, [], 2, nout=3)' res_acf.acf100, res_acf.lags100, res_acf.bounds100 = \ mlab.autocorr(x100, [], 2, nout=3) res_acf.acf1000, res_acf.lags1000, res_acf.bounds1000 = \ mlab.autocorr(x1000, [], 2, nout=3) res_acf.save(filename=filen, header=False) res_ccf = HoldIt('mlccf') res_ccf.comment = 'mlab.crosscorr(x[4:], x[:-4], [], 2, nout=3)' res_ccf.ccf100, res_ccf.lags100, res_ccf.bounds100 = \ mlab.crosscorr(x100[4:], x100[:-4], [], 2, nout=3) res_ccf.ccf1000, res_ccf.lags1000, res_ccf.bounds1000 = \ mlab.crosscorr(x1000[4:], x1000[:-4], [], 2, nout=3) res_ccf.save(filename=filen, header=False) res_ywar = HoldIt('mlywar') res_ywar.comment = "mlab.ar(x100-x100.mean(), 10, 'yw').a.ravel()" mbaryw = mlab.ar(x100-x100.mean(), 10, 'yw') res_ywar.arcoef100 = np.array(mbaryw.a.ravel()) mbaryw = mlab.ar(x1000-x1000.mean(), 20, 'yw') res_ywar.arcoef1000 = np.array(mbaryw.a.ravel()) res_ywar.save(filename=filen, header=False) statsmodels-0.12.2/statsmodels/sandbox/tests/savervs.py000066400000000000000000000022131400612667500233500ustar00rootroot00000000000000'''generates some ARMA random samples and saves to python module file ''' import numpy as np from statsmodels.tsa.arima_process import arma_generate_sample from .maketests_mlabwrap import HoldIt if __name__ == '__main__': filen = 'savedrvs_tmp.py' np.set_printoptions(precision=14, linewidth=100) # check arma to return same as random.normal np.random.seed(10000) xo = arma_generate_sample([1], [1], nsample=100) xo2 = np.round(xo*1000).astype(int) np.random.seed(10000) rvs = np.random.normal(size=100) rvs2 = np.round(xo*1000).astype(int) assert (xo2==rvs2).all() nsample = 1000 data = HoldIt('rvsdata') np.random.seed(10000) xo = arma_generate_sample([1, -0.8, 0.5], [1], nsample=nsample) data.xar2 = np.round(xo*1000).astype(int) np.random.seed(10000) xo = np.random.normal(size=nsample) data.xnormal = np.round(xo*1000).astype(int) np.random.seed(10000) xo = arma_generate_sample([1, -0.8, 0.5, -0.3], [1, 0.3, 0.2], nsample=nsample) data.xarma32 = np.round(xo*1000).astype(int) data.save(filename=filen, comment='generated data, divide by 1000, see savervs') statsmodels-0.12.2/statsmodels/sandbox/tests/sysreg.s000066400000000000000000000032701400612667500230110ustar00rootroot00000000000000# from the systemfit docs and sem docs # depends systemfit and its dependencies # depends sem # depends on plm # depends on R >= 2.9.0 (working on 2.9.2 but not on 2.8.1 at least) library( systemfit ) data( "Kmenta" ) eqDemand <- consump ~ price + income eqSupply <- consump ~ price + farmPrice + trend system <- list( demand = eqDemand, supply = eqSupply ) ## performs OLS on each of the equations in the system fitols <- systemfit( system, data = Kmenta ) # all coefficients coef( fitols ) coef( summary ( fitols ) ) modReg <- matrix(0,7,6) colnames( modReg ) <- c( "demIntercept", "demPrice", "demIncome", "supIntercept", "supPrice2", "supTrend" ) # a lot of typing for a model modReg[ 1, "demIntercept" ] <- 1 modReg[ 2, "demPrice" ] <- 1 modReg[ 3, "demIncome" ] <- 1 modReg[ 4, "supIntercept" ] <- 1 modReg[ 5, "supPrice2" ] <- 1 modReg[ 6, "supPrice2" ] <- 1 modReg[ 7, "supTrend" ] <- 1 fitols3 <- systemfit( system, data = Kmenta, restrict.regMat = modReg ) print(coef( fitols3, modified.regMat = TRUE )) # it seems to me like regMat does the opposite of what it says it does # in python # coef1 = np.array([99.8954229, -0.3162988, 0.3346356, 51.9296460, 0.2361566, 0.2361566, 0.2409308]) # i = np.eye(7,6) # i[-1,-1] = 1 # i[-2,-1] = 0 # i[-2,-2] = 1 # np.dot(coef,i) # regMat = TRUE? print(coef( fitols3 )) ### SUR ### data("GrunfeldGreene") library(plm) GGPanel <- plm.data( GrunfeldGreene, c("firm","year") ) formulaGrunfeld <- invest ~ value + capital greeneSUR <- systemfit( formulaGrunfeld, "SUR", data = GGPanel, methodResidCov = "noDfCor" ) #usinvest <- as.matrix(invest[81:100]) #usvalue <- as.matrix(value col5tbl14_2 <- lm(invest[81:100] ~ value[81:100] + capital[81:100]) statsmodels-0.12.2/statsmodels/sandbox/tests/test_bspline.py.txt000066400000000000000000000036101400612667500251720ustar00rootroot00000000000000import warnings import numpy as np from nipy.testing import * bsp = None def setup(): # Suppress warnings during tests to reduce noise warnings.simplefilter("ignore") # import bspline module after suppressing UserWarnings global bsp import nipy.fixes.scipy.stats.models.bspline as bsp def teardown(): # Clear list of warning filters warnings.resetwarnings() class TestBSpline(TestCase): def test1(self): b = bsp.BSpline(np.linspace(0,10,11), x=np.linspace(0,10,101)) old = b._basisx.shape b.x = np.linspace(0,10,51) new = b._basisx.shape self.assertEqual((old[0], 51), new) # FIXME: Have no idea what this test does. It's here to simply verify the # C extension is working (in a technical sense, not functional). def test_basis(self): b = bsp.BSpline(np.linspace(0,1,11)) x = np.array([0.4, 0.5]) v = b.basis(x, lower=0, upper=13) t = np.array([[ 0. , 0. ], [ 0. , 0. ], [ 0. , 0. ], [ 0. , 0. ], [ 0.16666667, 0. ], [ 0.66666667, 0.16666667], [ 0.16666667, 0.66666667], [ 0. , 0.16666667], [ 0. , 0. ], [ 0. , 0. ], [ 0. , 0. ], [ 0. , 0. ], [ 0. , 0. ]]) assert_array_almost_equal(v, t, decimal=6) # FIXME: Have no idea what this test does. It's here to simply verify the # C extension is working (in a technical sense, not functional). def test_gram(self): b = bsp.BSpline(np.linspace(0,1,11)) grm = b.gram() assert grm.shape == (4, 13) statsmodels-0.12.2/statsmodels/sandbox/tests/test_gam.py000066400000000000000000000256361400612667500235000ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Tests for gam.AdditiveModel and GAM with Polynomials compared to OLS and GLM Created on Sat Nov 05 14:16:07 2011 Author: Josef Perktold License: BSD Notes ----- TODO: TestGAMGamma: has test failure (GLM looks good), adding log-link did not help resolved: gamma does not fail anymore after tightening the convergence criterium (rtol=1e-6) TODO: TestGAMNegativeBinomial: rvs generation does not work, nbinom needs 2 parameters TODO: TestGAMGaussianLogLink: test failure, but maybe precision issue, not completely off but something is wrong, either the testcase or with the link >>> tt3.__class__ >>> tt3.res2.mu_pred.mean() 3.5616368292650766 >>> tt3.res1.mu_pred.mean() 3.6144278964707679 >>> tt3.mu_true.mean() 34.821904835958122 >>> >>> tt3.y_true.mean() 2.685225067611543 >>> tt3.res1.y_pred.mean() 0.52991541684645616 >>> tt3.res2.y_pred.mean() 0.44626406889363229 one possible change ~~~~~~~~~~~~~~~~~~~ add average, integral based tests, instead of or additional to sup * for example mean squared error for mu and eta (predict, fittedvalues) or mean absolute error, what's the scale for this? required precision? * this will also work for real non-parametric tests example: Gamma looks good in average bias and average RMSE (RMISE) >>> tt3 = _estGAMGamma() >>> np.mean((tt3.res2.mu_pred - tt3.mu_true))/tt3.mu_true.mean() -0.0051829977497423706 >>> np.mean((tt3.res2.y_pred - tt3.y_true))/tt3.y_true.mean() 0.00015255264651864049 >>> np.mean((tt3.res1.y_pred - tt3.y_true))/tt3.y_true.mean() 0.00015255538823786711 >>> np.mean((tt3.res1.mu_pred - tt3.mu_true))/tt3.mu_true.mean() -0.0051937668989744494 >>> np.sqrt(np.mean((tt3.res1.mu_pred - tt3.mu_true)**2))/tt3.mu_true.mean() 0.022946118520401692 >>> np.sqrt(np.mean((tt3.res2.mu_pred - tt3.mu_true)**2))/tt3.mu_true.mean() 0.022953913332599746 >>> maxabs = lambda x: np.max(np.abs(x)) >>> maxabs((tt3.res1.mu_pred - tt3.mu_true))/tt3.mu_true.mean() 0.079540546242707733 >>> maxabs((tt3.res2.mu_pred - tt3.mu_true))/tt3.mu_true.mean() 0.079578857986784574 >>> maxabs((tt3.res2.y_pred - tt3.y_true))/tt3.y_true.mean() 0.016282852522951426 >>> maxabs((tt3.res1.y_pred - tt3.y_true))/tt3.y_true.mean() 0.016288391235613865 """ from statsmodels.compat.python import lrange import numpy as np from numpy.testing import assert_almost_equal, assert_equal from scipy import stats import pytest from statsmodels.sandbox.gam import AdditiveModel from statsmodels.sandbox.gam import Model as GAM #? from statsmodels.genmod.families import family, links from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.regression.linear_model import OLS class Dummy(object): pass class CheckAM(object): def test_predict(self): assert_almost_equal(self.res1.y_pred, self.res2.y_pred, decimal=2) assert_almost_equal(self.res1.y_predshort, self.res2.y_pred[:10], decimal=2) @pytest.mark.xfail(reason="Unknown, results do not match expected", raises=AssertionError, strict=True) def test_fitted(self): # check definition of fitted in GLM: eta or mu assert_almost_equal(self.res1.y_pred, self.res2.fittedvalues, decimal=2) assert_almost_equal(self.res1.y_predshort, self.res2.fittedvalues[:10], decimal=2) def test_params(self): #note: only testing slope coefficients #constant is far off in example 4 versus 2 assert_almost_equal(self.res1.params[1:], self.res2.params[1:], decimal=2) #constant assert_almost_equal(self.res1.params[1], self.res2.params[1], decimal=2) @pytest.mark.xfail(reason="res_ps attribute does not exist", strict=True, raises=AttributeError) def test_df(self): # not used yet, copied from PolySmoother tests assert_equal(self.res_ps.df_model(), self.res2.df_model) assert_equal(self.res_ps.df_fit(), self.res2.df_model) #alias assert_equal(self.res_ps.df_resid(), self.res2.df_resid) class CheckGAM(CheckAM): def test_mu(self): # problem with scale for precision assert_almost_equal(self.res1.mu_pred, self.res2.mu_pred, decimal=0) def test_prediction(self): # problem with scale for precision assert_almost_equal(self.res1.y_predshort, self.res2.y_pred[:10], decimal=2) class BaseAM(object): @classmethod def setup_class(cls): #DGP: simple polynomial order = 3 nobs = 200 lb, ub = -3.5, 3 x1 = np.linspace(lb, ub, nobs) x2 = np.sin(2*x1) x = np.column_stack((x1/x1.max()*1, 1.*x2)) exog = (x[:,:,None]**np.arange(order+1)[None, None, :]).reshape(nobs, -1) idx = lrange((order+1)*2) del idx[order+1] exog_reduced = exog[:,idx] #remove duplicate constant y_true = exog.sum(1) #/ 4. #z = y_true #alias check #d = x cls.nobs = nobs cls.y_true, cls.x, cls.exog = y_true, x, exog_reduced class TestAdditiveModel(BaseAM, CheckAM): @classmethod def setup_class(cls): super(TestAdditiveModel, cls).setup_class() #initialize DGP nobs = cls.nobs y_true, x, exog = cls.y_true, cls.x, cls.exog np.random.seed(8765993) sigma_noise = 0.1 y = y_true + sigma_noise * np.random.randn(nobs) m = AdditiveModel(x) m.fit(y) res_gam = m.results #TODO: currently attached to class res_ols = OLS(y, exog).fit() #Note: there still are some naming inconsistencies cls.res1 = res1 = Dummy() #for gam model #res2 = Dummy() #for benchmark cls.res2 = res2 = res_ols #reuse existing ols results, will add additional res1.y_pred = res_gam.predict(x) res2.y_pred = res_ols.model.predict(res_ols.params, exog) res1.y_predshort = res_gam.predict(x[:10]) slopes = [i for ss in m.smoothers for i in ss.params[1:]] const = res_gam.alpha + sum([ss.params[1] for ss in m.smoothers]) #print const, slopes res1.params = np.array([const] + slopes) def test_fitted(self): # We have to override the base class because this case does not fail, # while all others in this module do (as of 2019-05-22) super(TestAdditiveModel, self).test_fitted() class BaseGAM(BaseAM, CheckGAM): @classmethod def init(cls): nobs = cls.nobs y_true, x, exog = cls.y_true, cls.x, cls.exog if not hasattr(cls, 'scale'): scale = 1 else: scale = cls.scale f = cls.family cls.mu_true = mu_true = f.link.inverse(y_true) np.random.seed(8765993) # Discrete distributions do not take `scale`. try: y_obs = cls.rvs(mu_true, scale=scale, size=nobs) except TypeError: y_obs = cls.rvs(mu_true, size=nobs) m = GAM(y_obs, x, family=f) #TODO: y_obs is twice __init__ and fit m.fit(y_obs, maxiter=100) res_gam = m.results cls.res_gam = res_gam #attached for debugging cls.mod_gam = m #attached for debugging res_glm = GLM(y_obs, exog, family=f).fit() #Note: there still are some naming inconsistencies cls.res1 = res1 = Dummy() #for gam model #res2 = Dummy() #for benchmark cls.res2 = res2 = res_glm #reuse existing glm results, will add additional #eta in GLM terminology res2.y_pred = res_glm.model.predict(res_glm.params, exog, linear=True) res1.y_pred = res_gam.predict(x) res1.y_predshort = res_gam.predict(x[:10]) #, linear=True) #mu res2.mu_pred = res_glm.model.predict(res_glm.params, exog, linear=False) res1.mu_pred = res_gam.mu #parameters slopes = [i for ss in m.smoothers for i in ss.params[1:]] const = res_gam.alpha + sum([ss.params[1] for ss in m.smoothers]) res1.params = np.array([const] + slopes) class TestGAMPoisson(BaseGAM): @classmethod def setup_class(cls): super(TestGAMPoisson, cls).setup_class() #initialize DGP cls.family = family.Poisson() cls.rvs = stats.poisson.rvs cls.init() class TestGAMBinomial(BaseGAM): @classmethod def setup_class(cls): super(TestGAMBinomial, cls).setup_class() #initialize DGP cls.family = family.Binomial() cls.rvs = stats.bernoulli.rvs cls.init() @pytest.mark.xfail(reason="Unknown, results do not match expected.", strict=True, raises=AssertionError) class TestGAMGaussianLogLink(BaseGAM): #test failure, but maybe precision issue, not far off #>>> np.mean(np.abs(tt.res2.mu_pred - tt.mu_true)) #0.80409736263199649 #>>> np.mean(np.abs(tt.res2.mu_pred - tt.mu_true))/tt.mu_true.mean() #0.023258245077813208 #>>> np.mean((tt.res2.mu_pred - tt.mu_true)**2)/tt.mu_true.mean() #0.022989403735692578 @classmethod def setup_class(cls): super(TestGAMGaussianLogLink, cls).setup_class() # initialize DGP cls.family = family.Gaussian(links.log()) cls.rvs = stats.norm.rvs cls.scale = 5 cls.init() class TestGAMGamma(BaseGAM): @classmethod def setup_class(cls): super(TestGAMGamma, cls).setup_class() #initialize DGP cls.family = family.Gamma(links.log()) cls.rvs = stats.gamma.rvs cls.init() @pytest.mark.xfail(reason="Passing wrong number of args/kwargs " "to _parse_args_rvs", strict=True, raises=TypeError) class TestGAMNegativeBinomial(BaseGAM): # TODO: rvs generation does not work, nbinom needs 2 parameters @classmethod def setup_class(cls): super(TestGAMNegativeBinomial, cls).setup_class() # initialize DGP cls.family = family.NegativeBinomial() cls.rvs = stats.nbinom.rvs cls.init() @pytest.mark.xfail(reason="Passing wrong number of args/kwargs " "to _parse_args_rvs", strict=True, raises=TypeError) def test_fitted(self): # We have to override the base class method in order to correctly # specify the type of failure we are expecting. super(TestGAMNegativeBinomial, self).test_fitted() @pytest.mark.xfail(reason="Passing wrong number of args/kwargs " "to _parse_args_rvs", strict=True, raises=TypeError) def test_df(self): # We have to override the base class method in order to correctly # specify the type of failure we are expecting. super(TestGAMNegativeBinomial, self).test_df() statsmodels-0.12.2/statsmodels/sandbox/tests/test_pca.py000066400000000000000000000046571400612667500234770ustar00rootroot00000000000000'''tests for pca and arma to ar and ma representation compared with matlab princomp, and garchar, garchma TODO: * convert to generators with yield to have individual tests * incomplete: test relationship of pca-evecs and pinv (adding constant) ''' import numpy as np from numpy.testing import assert_array_almost_equal from statsmodels.sandbox.tools import pca, pcasvd from statsmodels.multivariate.tests.results.datamlw import ( princomp1, princomp2, princomp3, data) def check_pca_princomp(pcares, princomp): factors, evals, evecs = pcares[1:] #res_princomp.coef, res_princomp.factors, res_princomp.values msign = (evecs/princomp.coef)[0] assert_array_almost_equal(msign*evecs, princomp.coef, 13) assert_array_almost_equal(msign*factors, princomp.factors, 13) assert_array_almost_equal(evals, princomp.values.ravel(), 13) def check_pca_svd(pcares, pcasvdres): xreduced, factors, evals, evecs = pcares xred_svd, factors_svd, evals_svd, evecs_svd = pcasvdres assert_array_almost_equal(evals_svd, evals, 14) msign = (evecs/evecs_svd)[0] assert_array_almost_equal(msign*evecs_svd, evecs, 13) assert_array_almost_equal(msign*factors_svd, factors, 13) assert_array_almost_equal(xred_svd, xreduced, 13) xf = data.xo/1000. def test_pca_princomp(): pcares = pca(xf) check_pca_princomp(pcares, princomp1) pcares = pca(xf[:20,:]) check_pca_princomp(pcares, princomp2) pcares = pca(xf[:20,:]-xf[:20,:].mean(0)) check_pca_princomp(pcares, princomp3) pcares = pca(xf[:20,:]-xf[:20,:].mean(0), demean=0) check_pca_princomp(pcares, princomp3) def test_pca_svd(): xreduced, factors, evals, evecs = pca(xf) factors_wconst = np.c_[factors, np.ones((factors.shape[0],1))] beta = np.dot(np.linalg.pinv(factors_wconst), xf) #np.dot(np.linalg.pinv(factors_wconst),x2/1000.).T[:,:4] - evecs assert_array_almost_equal(beta.T[:,:4], evecs, 14) xred_svd, factors_svd, evals_svd, evecs_svd = pcasvd(xf, keepdim=0) assert_array_almost_equal(evals_svd, evals, 14) msign = (evecs/evecs_svd)[0] assert_array_almost_equal(msign*evecs_svd, evecs, 13) assert_array_almost_equal(msign*factors_svd, factors, 12) assert_array_almost_equal(xred_svd, xreduced, 13) pcares = pca(xf, keepdim=2) pcasvdres = pcasvd(xf, keepdim=2) check_pca_svd(pcares, pcasvdres) #print np.dot(factors[:,:3], evecs.T[:3,:])[:5] if __name__ == '__main__': test_pca_svd() statsmodels-0.12.2/statsmodels/sandbox/tests/test_predict_functional.py000066400000000000000000000307521400612667500266030ustar00rootroot00000000000000from statsmodels.sandbox.predict_functional import predict_functional import numpy as np import pandas as pd import pytest import statsmodels.api as sm # If true, the output is written to a multi-page pdf file. pdf_output = False try: import matplotlib.pyplot as plt except ImportError: pass def pctl(q): return lambda x : np.percentile(x, 100 *q) class TestPredFunc(object): @classmethod def setup_class(cls): if pdf_output: from matplotlib.backends.backend_pdf import PdfPages cls.pdf = PdfPages("predict_functional.pdf") @classmethod def teardown_class(cls): if pdf_output: cls.pdf.close() def close_or_save(self, fig): if pdf_output: self.pdf.savefig(fig) @pytest.mark.matplotlib def test_formula(self, close_figures): np.random.seed(542) n = 500 x1 = np.random.normal(size=n) x2 = np.random.normal(size=n) x3 = np.random.normal(size=n) x4 = np.random.randint(0, 5, size=n) x4 = np.asarray(["ABCDE"[i] for i in x4]) x5 = np.random.normal(size=n) y = 0.3*x2**2 + (x4 == "B") + 0.1*(x4 == "B")*x2**2 + x5 + np.random.normal(size=n) df = pd.DataFrame({"y": y, "x1": x1, "x2": x2, "x3": x3, "x4": x4, "x5": x5}) fml = "y ~ x1 + bs(x2, df=4) + x3 + x2*x3 + I(x1**2) + C(x4) + C(x4)*bs(x2, df=4) + x5" model = sm.OLS.from_formula(fml, data=df) result = model.fit() summaries = {"x1": np.mean, "x3": pctl(0.75), "x5": np.mean} values = {"x4": "B"} pr1, ci1, fvals1 = predict_functional(result, "x2", summaries, values) values = {"x4": "C"} pr2, ci2, fvals2 = predict_functional(result, "x2", summaries, values) plt.clf() fig = plt.figure() ax = plt.axes([0.1, 0.1, 0.7, 0.8]) plt.plot(fvals1, pr1, '-', label='x4=B') plt.plot(fvals2, pr2, '-', label='x4=C') ha, lb = ax.get_legend_handles_labels() plt.figlegend(ha, lb, "center right") plt.xlabel("Focus variable", size=15) plt.ylabel("Fitted mean", size=15) plt.title("Linear model prediction") self.close_or_save(fig) plt.clf() fig = plt.figure() ax = plt.axes([0.1, 0.1, 0.7, 0.8]) plt.plot(fvals1, pr1, '-', label='x4=B') plt.fill_between(fvals1, ci1[:, 0], ci1[:, 1], color='grey') plt.plot(fvals2, pr2, '-', label='x4=C') plt.fill_between(fvals2, ci2[:, 0], ci2[:, 1], color='grey') ha, lb = ax.get_legend_handles_labels() plt.figlegend(ha, lb, "center right") plt.xlabel("Focus variable", size=15) plt.ylabel("Fitted mean", size=15) plt.title("Linear model prediction") self.close_or_save(fig) @pytest.mark.matplotlib def test_lm_contrast(self, close_figures): np.random.seed(542) n = 200 x1 = np.random.normal(size=n) x2 = np.random.normal(size=n) x3 = np.random.normal(size=n) y = x1 + 2*x2 + x3 - x1*x2 + x2*x3 + np.random.normal(size=n) df = pd.DataFrame({"y": y, "x1": x1, "x2": x2, "x3": x3}) fml = "y ~ x1 + x2 + x3 + x1*x2 + x2*x3" model = sm.OLS.from_formula(fml, data=df) result = model.fit() values = {"x2": 1, "x3": 1} # y = 4 values2 = {"x2": 0, "x3": 0} # y = x1 pr, cb, fvals = predict_functional(result, "x1", values=values, values2=values2, ci_method='scheffe') plt.clf() fig = plt.figure() ax = plt.axes([0.1, 0.1, 0.67, 0.8]) plt.plot(fvals, pr, '-', label="Estimate", color='orange', lw=4) plt.plot(fvals, 4 - fvals, '-', label="Truth", color='lime', lw=4) plt.fill_between(fvals, cb[:, 0], cb[:, 1], color='grey') ha, lb = ax.get_legend_handles_labels() leg = plt.figlegend(ha, lb, "center right") leg.draw_frame(False) plt.xlabel("Focus variable", size=15) plt.ylabel("Mean contrast", size=15) plt.title("Linear model contrast") self.close_or_save(fig) @pytest.mark.matplotlib def test_glm_formula_contrast(self, close_figures): np.random.seed(542) n = 50 x1 = np.random.normal(size=n) x2 = np.random.normal(size=n) x3 = np.random.normal(size=n) mn = 5 + 0.1*x1 + 0.1*x2 + 0.1*x3 - 0.1*x1*x2 y = np.random.poisson(np.exp(mn), size=len(mn)) df = pd.DataFrame({"y": y, "x1": x1, "x2": x2, "x3": x3}) fml = "y ~ x1 + x2 + x3 + x1*x2" model = sm.GLM.from_formula(fml, data=df, family=sm.families.Poisson()) result = model.fit() values = {"x2": 1, "x3": 1} # y = 5.2 values2 = {"x2": 0, "x3": 0} # y = 5 + 0.1*x1 pr, cb, fvals = predict_functional(result, "x1", values=values, values2=values2, ci_method='simultaneous') plt.clf() fig = plt.figure() ax = plt.axes([0.1, 0.1, 0.67, 0.8]) plt.plot(fvals, pr, '-', label="Estimate", color='orange', lw=4) plt.plot(fvals, 0.2 - 0.1*fvals, '-', label="Truth", color='lime', lw=4) plt.fill_between(fvals, cb[:, 0], cb[:, 1], color='grey') ha, lb = ax.get_legend_handles_labels() leg = plt.figlegend(ha, lb, "center right") leg.draw_frame(False) plt.xlabel("Focus variable", size=15) plt.ylabel("Linear predictor contrast", size=15) plt.title("Poisson regression contrast") self.close_or_save(fig) @pytest.mark.matplotlib def test_scb(self, close_figures): np.random.seed(473) n = 100 x = np.random.normal(size=(n,4)) x[:, 0] = 1 for fam_name in "poisson", "binomial", "gaussian": if fam_name == "poisson": y = np.random.poisson(20, size=n) fam = sm.families.Poisson() true_mean = 20 true_lp = np.log(20) elif fam_name == "binomial": y = 1 * (np.random.uniform(size=n) < 0.5) fam = sm.families.Binomial() true_mean = 0.5 true_lp = 0 elif fam_name == "gaussian": y = np.random.normal(size=n) fam = sm.families.Gaussian() true_mean = 0 true_lp = 0 model = sm.GLM(y, x, family=fam) result = model.fit() # CB is for linear predictor or mean response for linear in False, True: true = true_lp if linear else true_mean values = {'const': 1, "x2": 0} summaries = {"x3": np.mean} pred1, cb1, fvals1 = predict_functional(result, "x1", values=values, summaries=summaries, linear=linear) pred2, cb2, fvals2 = predict_functional(result, "x1", values=values, summaries=summaries, ci_method='simultaneous', linear=linear) plt.clf() fig = plt.figure() ax = plt.axes([0.1, 0.1, 0.58, 0.8]) plt.plot(fvals1, pred1, '-', color='black', label='Estimate') plt.plot(fvals1, true * np.ones(len(pred1)), '-', color='purple', label='Truth') plt.plot(fvals1, cb1[:, 0], color='blue', label='Pointwise CB') plt.plot(fvals1, cb1[:, 1], color='blue') plt.plot(fvals2, cb2[:, 0], color='green', label='Simultaneous CB') plt.plot(fvals2, cb2[:, 1], color='green') ha, lb = ax.get_legend_handles_labels() leg = plt.figlegend(ha, lb, "center right") leg.draw_frame(False) plt.xlabel("Focus variable", size=15) if linear: plt.ylabel("Linear predictor", size=15) else: plt.ylabel("Fitted mean", size=15) plt.title("%s family prediction" % fam_name.capitalize()) self.close_or_save(fig) @pytest.mark.matplotlib def test_glm_formula(self, close_figures): np.random.seed(542) n = 500 x1 = np.random.normal(size=n) x2 = np.random.normal(size=n) x3 = np.random.randint(0, 3, size=n) x3 = np.asarray(["ABC"[i] for i in x3]) lin_pred = -1 + 0.5*x1**2 + (x3 == "B") prob = 1 / (1 + np.exp(-lin_pred)) y = 1 * (np.random.uniform(size=n) < prob) df = pd.DataFrame({"y": y, "x1": x1, "x2": x2, "x3": x3}) fml = "y ~ x1 + I(x1**2) + x2 + C(x3)" model = sm.GLM.from_formula(fml, family=sm.families.Binomial(), data=df) result = model.fit() summaries = {"x2": np.mean} for linear in False, True: values = {"x3": "B"} pr1, ci1, fvals1 = predict_functional(result, "x1", summaries, values, linear=linear) values = {"x3": "C"} pr2, ci2, fvals2 = predict_functional(result, "x1", summaries, values, linear=linear) exact1 = -1 + 0.5*fvals1**2 + 1 exact2 = -1 + 0.5*fvals2**2 if not linear: exact1 = 1 / (1 + np.exp(-exact1)) exact2 = 1 / (1 + np.exp(-exact2)) plt.clf() fig = plt.figure() ax = plt.axes([0.1, 0.1, 0.7, 0.8]) plt.plot(fvals1, pr1, '-', label='x3=B') plt.plot(fvals2, pr2, '-', label='x3=C') plt.plot(fvals1, exact1, '-', label='x3=B (exact)') plt.plot(fvals2, exact2, '-', label='x3=C (exact)') ha, lb = ax.get_legend_handles_labels() plt.figlegend(ha, lb, "center right") plt.xlabel("Focus variable", size=15) if linear: plt.ylabel("Fitted linear predictor", size=15) else: plt.ylabel("Fitted probability", size=15) plt.title("Binomial GLM prediction") self.close_or_save(fig) plt.clf() fig = plt.figure() ax = plt.axes([0.1, 0.1, 0.7, 0.8]) plt.plot(fvals1, pr1, '-', label='x3=B', color='orange') plt.fill_between(fvals1, ci1[:, 0], ci1[:, 1], color='grey') plt.plot(fvals2, pr2, '-', label='x3=C', color='lime') plt.fill_between(fvals2, ci2[:, 0], ci2[:, 1], color='grey') ha, lb = ax.get_legend_handles_labels() plt.figlegend(ha, lb, "center right") plt.xlabel("Focus variable", size=15) if linear: plt.ylabel("Fitted linear predictor", size=15) else: plt.ylabel("Fitted probability", size=15) plt.title("Binomial GLM prediction") self.close_or_save(fig) @pytest.mark.matplotlib def test_noformula_prediction(self, close_figures): np.random.seed(6434) n = 200 x1 = np.random.normal(size=n) x2 = np.random.normal(size=n) x3 = np.random.normal(size=n) y = x1 - x2 + np.random.normal(size=n) exog = np.vstack((x1, x2, x3)).T model = sm.OLS(y, exog) result = model.fit() summaries = {"x3": pctl(0.75)} values = {"x2": 1} pr1, ci1, fvals1 = predict_functional(result, "x1", summaries, values) values = {"x2": -1} pr2, ci2, fvals2 = predict_functional(result, "x1", summaries, values) plt.clf() fig = plt.figure() ax = plt.axes([0.1, 0.1, 0.7, 0.8]) plt.plot(fvals1, pr1, '-', label='x2=1', lw=4, alpha=0.6, color='orange') plt.plot(fvals2, pr2, '-', label='x2=-1', lw=4, alpha=0.6, color='lime') ha, lb = ax.get_legend_handles_labels() leg = plt.figlegend(ha, lb, "center right") leg.draw_frame(False) plt.xlabel("Focus variable", size=15) plt.ylabel("Fitted mean", size=15) plt.title("Linear model prediction") self.close_or_save(fig) plt.clf() fig = plt.figure() ax = plt.axes([0.1, 0.1, 0.7, 0.8]) plt.plot(fvals1, pr1, '-', label='x2=1', lw=4, alpha=0.6, color='orange') plt.fill_between(fvals1, ci1[:, 0], ci1[:, 1], color='grey') plt.plot(fvals1, pr2, '-', label='x2=1', lw=4, alpha=0.6, color='lime') plt.fill_between(fvals2, ci2[:, 0], ci2[:, 1], color='grey') ha, lb = ax.get_legend_handles_labels() plt.figlegend(ha, lb, "center right") plt.xlabel("Focus variable", size=15) plt.ylabel("Fitted mean", size=15) plt.title("Linear model prediction") self.close_or_save(fig) statsmodels-0.12.2/statsmodels/sandbox/tools/000077500000000000000000000000001400612667500213055ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/tools/TODO.txt000066400000000000000000000051711400612667500226170ustar00rootroot00000000000000 * make groupstats into a class with additional functions for easy access use bincount but loop over 2d, or maybe two versions 1d,2d (or nd?) similar to groupbys class GroupStats init with label data attributes/properties on demand: mean, var, callback, devfrommean, meanarr, vararr does var need bias option ? yes? def groupmean(label, data) def groupvar(label, data) def groupnormalize(label, data, reweight = True) * ANOVA wrapper usage example discussed on mailing list and proposed by Skipper create design matrix create restriction matrices for F tests, t tests ? normalization redundant ? reports ANOVA style * maybe: quick helpers for structured arrays and masked arrays formula for selection of variables specification for which variable are factors Anova(y, use='x1;x2;x3', factors='x2', data = dataarray) or Anova(y, use='x1; x2:F; x3', data = dataarray) masked arrays need row compression * meta object for variable names, and .... ? * OLSR, OLS with linear restriction -> design changes ? need to overwrite params_cov calculation - move it back to models * regression: OLS, WLS - add prediction * Granger causality test: which test statistic, F test is easiest, LR, Wald ? -> easy in R: example in Wikipedia * get lag matrix helper function to use lagged dependent and lagged independent regressors * nonlinear hypothesis tests for the estimate parameters, delta method ? -> easy, but derivatives by hand w/o sympy * minimal PCA, PCR, or PLS (NIPALS): interesting also for finance but not urgent -> messy multiplicity of definitions ? * non-linear least squares: use/imitate scipy.interpolate curvefit + full set of results statistics * tests -> needed - GLSAR: check, R's gls - ARMA: check R for arma, e.g. dynamo, also look more closely at GARCH_UCSD (BSD) and offspring (license ?) * other models in draft stage -> requires cleaning - gaussian process -> might fit in - multinomial logit -> requires ML, result statistics do not fit into current classes ? * stochastic processes, time series -> first step is relatively easy more simulators, random process generators, for fun and Monte Carlo and testing estimators to follow first group GARCH, continuous time: not until I need them * other multivariate analysis discriminance, factor analysis, more anova: not my business * MLE, GMM: big open question -> needs to wait until we have more code that uses it difference of approaches - parametric assumptions, distributions fully specified - problem misspecification - efficient estimation with full information MLE -> example panel data, yogurt paper statsmodels-0.12.2/statsmodels/sandbox/tools/__init__.py000066400000000000000000000003271400612667500234200ustar00rootroot00000000000000'''some helper function for principal component and time series analysis Status ------ pca : tested against matlab pcasvd : tested against matlab ''' __all__ = ["pca", "pcasvd"] from .tools_pca import pca, pcasvd statsmodels-0.12.2/statsmodels/sandbox/tools/cross_val.py000066400000000000000000000271031400612667500236550ustar00rootroot00000000000000""" Utilities for cross validation. taken from scikits.learn # Author: Alexandre Gramfort , # Gael Varoquaux # License: BSD Style. # $Id$ changes to code by josef-pktd: - docstring formatting: underlines of headers """ from statsmodels.compat.python import lrange import numpy as np from itertools import combinations ################################################################################ class LeaveOneOut(object): """ Leave-One-Out cross validation iterator: Provides train/test indexes to split data in train test sets """ def __init__(self, n): """ Leave-One-Out cross validation iterator: Provides train/test indexes to split data in train test sets Parameters ---------- n: int Total number of elements Examples -------- >>> from scikits.learn import cross_val >>> X = [[1, 2], [3, 4]] >>> y = [1, 2] >>> loo = cross_val.LeaveOneOut(2) >>> for train_index, test_index in loo: ... print "TRAIN:", train_index, "TEST:", test_index ... X_train, X_test, y_train, y_test = cross_val.split(train_index, test_index, X, y) ... print X_train, X_test, y_train, y_test TRAIN: [False True] TEST: [ True False] [[3 4]] [[1 2]] [2] [1] TRAIN: [ True False] TEST: [False True] [[1 2]] [[3 4]] [1] [2] """ self.n = n def __iter__(self): n = self.n for i in range(n): test_index = np.zeros(n, dtype=bool) test_index[i] = True train_index = np.logical_not(test_index) yield train_index, test_index def __repr__(self): return '%s.%s(n=%i)' % (self.__class__.__module__, self.__class__.__name__, self.n, ) ################################################################################ class LeavePOut(object): """ Leave-P-Out cross validation iterator: Provides train/test indexes to split data in train test sets """ def __init__(self, n, p): """ Leave-P-Out cross validation iterator: Provides train/test indexes to split data in train test sets Parameters ---------- n: int Total number of elements p: int Size test sets Examples -------- >>> from scikits.learn import cross_val >>> X = [[1, 2], [3, 4], [5, 6], [7, 8]] >>> y = [1, 2, 3, 4] >>> lpo = cross_val.LeavePOut(4, 2) >>> for train_index, test_index in lpo: ... print "TRAIN:", train_index, "TEST:", test_index ... X_train, X_test, y_train, y_test = cross_val.split(train_index, test_index, X, y) TRAIN: [False False True True] TEST: [ True True False False] TRAIN: [False True False True] TEST: [ True False True False] TRAIN: [False True True False] TEST: [ True False False True] TRAIN: [ True False False True] TEST: [False True True False] TRAIN: [ True False True False] TEST: [False True False True] TRAIN: [ True True False False] TEST: [False False True True] """ self.n = n self.p = p def __iter__(self): n = self.n p = self.p comb = combinations(lrange(n), p) for idx in comb: test_index = np.zeros(n, dtype=bool) test_index[np.array(idx)] = True train_index = np.logical_not(test_index) yield train_index, test_index def __repr__(self): return '%s.%s(n=%i, p=%i)' % ( self.__class__.__module__, self.__class__.__name__, self.n, self.p, ) ################################################################################ class KFold(object): """ K-Folds cross validation iterator: Provides train/test indexes to split data in train test sets """ def __init__(self, n, k): """ K-Folds cross validation iterator: Provides train/test indexes to split data in train test sets Parameters ---------- n: int Total number of elements k: int number of folds Examples -------- >>> from scikits.learn import cross_val >>> X = [[1, 2], [3, 4], [1, 2], [3, 4]] >>> y = [1, 2, 3, 4] >>> kf = cross_val.KFold(4, k=2) >>> for train_index, test_index in kf: ... print "TRAIN:", train_index, "TEST:", test_index ... X_train, X_test, y_train, y_test = cross_val.split(train_index, test_index, X, y) TRAIN: [False False True True] TEST: [ True True False False] TRAIN: [ True True False False] TEST: [False False True True] Notes ----- All the folds have size trunc(n/k), the last one has the complementary """ assert k>0, ValueError('cannot have k below 1') assert k>> from scikits.learn import cross_val >>> X = [[1, 2], [3, 4], [5, 6], [7, 8]] >>> y = [1, 2, 1, 2] >>> labels = [1, 1, 2, 2] >>> lol = cross_val.LeaveOneLabelOut(labels) >>> for train_index, test_index in lol: ... print "TRAIN:", train_index, "TEST:", test_index ... X_train, X_test, y_train, y_test = cross_val.split(train_index, \ test_index, X, y) ... print X_train, X_test, y_train, y_test TRAIN: [False False True True] TEST: [ True True False False] [[5 6] [7 8]] [[1 2] [3 4]] [1 2] [1 2] TRAIN: [ True True False False] TEST: [False False True True] [[1 2] [3 4]] [[5 6] [7 8]] [1 2] [1 2] """ self.labels = labels def __iter__(self): # We make a copy here to avoid side-effects during iteration labels = np.array(self.labels, copy=True) for i in np.unique(labels): test_index = np.zeros(len(labels), dtype=bool) test_index[labels==i] = True train_index = np.logical_not(test_index) yield train_index, test_index def __repr__(self): return '%s.%s(labels=%s)' % ( self.__class__.__module__, self.__class__.__name__, self.labels, ) def split(train_indexes, test_indexes, *args): """ For each arg return a train and test subsets defined by indexes provided in train_indexes and test_indexes """ ret = [] for arg in args: arg = np.asanyarray(arg) arg_train = arg[train_indexes] arg_test = arg[test_indexes] ret.append(arg_train) ret.append(arg_test) return ret ''' >>> cv = cross_val.LeaveOneLabelOut(X, y) # y making y optional and possible to add other arrays of the same shape[0] too >>> for X_train, y_train, X_test, y_test in cv: ... print np.sqrt((model.fit(X_train, y_train).predict(X_test) - y_test) ** 2).mean()) ''' ################################################################################ #below: Author: josef-pktd class KStepAhead(object): """ KStepAhead cross validation iterator: Provides fit/test indexes to split data in sequential sets """ def __init__(self, n, k=1, start=None, kall=True, return_slice=True): """ KStepAhead cross validation iterator: Provides train/test indexes to split data in train test sets Parameters ---------- n: int Total number of elements k : int number of steps ahead start : int initial size of data for fitting kall : bool if true. all values for up to k-step ahead are included in the test index. If false, then only the k-th step ahead value is returnd Notes ----- I do not think this is really useful, because it can be done with a very simple loop instead. Useful as a plugin, but it could return slices instead for faster array access. Examples -------- >>> from scikits.learn import cross_val >>> X = [[1, 2], [3, 4]] >>> y = [1, 2] >>> loo = cross_val.LeaveOneOut(2) >>> for train_index, test_index in loo: ... print "TRAIN:", train_index, "TEST:", test_index ... X_train, X_test, y_train, y_test = cross_val.split(train_index, test_index, X, y) ... print X_train, X_test, y_train, y_test TRAIN: [False True] TEST: [ True False] [[3 4]] [[1 2]] [2] [1] TRAIN: [ True False] TEST: [False True] [[1 2]] [[3 4]] [1] [2] """ self.n = n self.k = k if start is None: start = int(np.trunc(n*0.25)) # pick something arbitrary self.start = start self.kall = kall self.return_slice = return_slice def __iter__(self): n = self.n k = self.k start = self.start if self.return_slice: for i in range(start, n-k): train_slice = slice(None, i, None) if self.kall: test_slice = slice(i, i+k) else: test_slice = slice(i+k-1, i+k) yield train_slice, test_slice else: #for compatibility with other iterators for i in range(start, n-k): train_index = np.zeros(n, dtype=bool) train_index[:i] = True test_index = np.zeros(n, dtype=bool) if self.kall: test_index[i:i+k] = True # np.logical_not(test_index) else: test_index[i+k-1:i+k] = True #or faster to return np.arange(i,i+k) ? #returning slice should be faster in this case yield train_index, test_index def __repr__(self): return '%s.%s(n=%i)' % (self.__class__.__module__, self.__class__.__name__, self.n, ) statsmodels-0.12.2/statsmodels/sandbox/tools/mctools.py000066400000000000000000000407721400612667500233510ustar00rootroot00000000000000'''Helper class for Monte Carlo Studies for (currently) statistical tests Most of it should also be usable for Bootstrap, and for MC for estimators. Takes the sample generator, dgb, and the statistical results, statistic, as functions in the argument. Author: Josef Perktold (josef-pktd) License: BSD-3 TODOs, Design ------------- If we only care about univariate analysis, i.e. marginal if statistics returns more than one value, the we only need to store the sorted mcres not the original res. Do we want to extend to multivariate analysis? Use distribution function to keep track of MC results, ECDF, non-paramatric? Large parts are similar to a 2d array of independent multivariate random variables. Joint distribution is not used (yet). I guess this is currently only for one sided test statistics, e.g. for two-sided tests basend on t or normal distribution use the absolute value. ''' from statsmodels.compat.python import lrange import numpy as np from statsmodels.iolib.table import SimpleTable #copied from stattools class StatTestMC(object): """class to run Monte Carlo study on a statistical test''' TODO print(summary, for quantiles and for histogram draft in trying out script log Parameters ---------- dgp : callable Function that generates the data to be used in Monte Carlo that should return a new sample with each call statistic : callable Function that calculates the test statistic, which can return either a single statistic or a 1d array_like (tuple, list, ndarray). see also statindices in description of run Attributes ---------- many methods store intermediate results self.mcres : ndarray (nrepl, nreturns) or (nrepl, len(statindices)) Monte Carlo results stored by run Notes ----- .. Warning:: This is (currently) designed for a single call to run. If run is called a second time with different arguments, then some attributes might not be updated, and, therefore, not correspond to the same run. .. Warning:: Under Construction, do not expect stability in Api or implementation Examples -------- Define a function that defines our test statistic: def lb(x): s,p = acorr_ljungbox(x, lags=4) return np.r_[s, p] Note lb returns eight values. Define a random sample generator, for example 500 independently, normal distributed observations in a sample: def normalnoisesim(nobs=500, loc=0.0): return (loc+np.random.randn(nobs)) Create instance and run Monte Carlo. Using statindices=list(range(4)) means that only the first for values of the return of the statistic (lb) are stored in the Monte Carlo results. mc1 = StatTestMC(normalnoisesim, lb) mc1.run(5000, statindices=list(range(4))) Most of the other methods take an idx which indicates for which columns the results should be presented, e.g. print(mc1.cdf(crit, [1,2,3])[1] """ def __init__(self, dgp, statistic): self.dgp = dgp #staticmethod(dgp) #no self self.statistic = statistic # staticmethod(statistic) #no self def run(self, nrepl, statindices=None, dgpargs=[], statsargs=[]): '''run the actual Monte Carlo and save results Parameters ---------- nrepl : int number of Monte Carlo repetitions statindices : None or list of integers determines which values of the return of the statistic functions are stored in the Monte Carlo. Default None means the entire return. If statindices is a list of integers, then it will be used as index into the return. dgpargs : tuple optional parameters for the DGP statsargs : tuple optional parameters for the statistics function Returns ------- None, all results are attached ''' self.nrepl = nrepl self.statindices = statindices self.dgpargs = dgpargs self.statsargs = statsargs dgp = self.dgp statfun = self.statistic # name ? #introspect len of return of statfun, #possible problems with ndim>1, check ValueError mcres0 = statfun(dgp(*dgpargs), *statsargs) self.nreturn = nreturns = len(np.ravel(mcres0)) #single return statistic if statindices is None: #self.nreturn = nreturns = 1 mcres = np.zeros(nrepl) mcres[0] = mcres0 for ii in range(1, nrepl-1, nreturns): x = dgp(*dgpargs) #(1e-4+np.random.randn(nobs)).cumsum() #should I ravel? mcres[ii] = statfun(x, *statsargs) #more than one return statistic else: self.nreturn = nreturns = len(statindices) self.mcres = mcres = np.zeros((nrepl, nreturns)) mcres[0] = [mcres0[i] for i in statindices] for ii in range(1, nrepl-1): x = dgp(*dgpargs) #(1e-4+np.random.randn(nobs)).cumsum() ret = statfun(x, *statsargs) mcres[ii] = [ret[i] for i in statindices] self.mcres = mcres def histogram(self, idx=None, critval=None): '''calculate histogram values does not do any plotting I do not remember what I wanted here, looks similar to the new cdf method, but this also does a binned pdf (self.histo) ''' if self.mcres.ndim == 2: if idx is not None: mcres = self.mcres[:,idx] else: raise ValueError('currently only 1 statistic at a time') else: mcres = self.mcres if critval is None: histo = np.histogram(mcres, bins=10) else: if not critval[0] == -np.inf: bins=np.r_[-np.inf, critval, np.inf] if not critval[0] == -np.inf: bins=np.r_[bins, np.inf] histo = np.histogram(mcres, bins=np.r_[-np.inf, critval, np.inf]) self.histo = histo self.cumhisto = np.cumsum(histo[0])*1./self.nrepl self.cumhistoreversed = np.cumsum(histo[0][::-1])[::-1]*1./self.nrepl return histo, self.cumhisto, self.cumhistoreversed #use cache decorator instead def get_mc_sorted(self): if not hasattr(self, 'mcressort'): self.mcressort = np.sort(self.mcres, axis=0) return self.mcressort def quantiles(self, idx=None, frac=[0.01, 0.025, 0.05, 0.1, 0.975]): '''calculate quantiles of Monte Carlo results similar to ppf Parameters ---------- idx : None or list of integers List of indices into the Monte Carlo results (columns) that should be used in the calculation frac : array_like, float Defines which quantiles should be calculated. For example a frac of 0.1 finds the 10% quantile, x such that cdf(x)=0.1 Returns ------- frac : ndarray same values as input, TODO: I should drop this again ? quantiles : ndarray, (len(frac), len(idx)) the quantiles with frac in rows and idx variables in columns Notes ----- rename to ppf ? make frac required change sequence idx, frac ''' if self.mcres.ndim == 2: if idx is not None: mcres = self.mcres[:,idx] else: raise ValueError('currently only 1 statistic at a time') else: mcres = self.mcres self.frac = frac = np.asarray(frac) mc_sorted = self.get_mc_sorted()[:,idx] return frac, mc_sorted[(self.nrepl*frac).astype(int)] def cdf(self, x, idx=None): '''calculate cumulative probabilities of Monte Carlo results Parameters ---------- idx : None or list of integers List of indices into the Monte Carlo results (columns) that should be used in the calculation frac : array_like, float Defines which quantiles should be calculated. For example a frac of 0.1 finds the 10% quantile, x such that cdf(x)=0.1 Returns ------- x : ndarray same as input, TODO: I should drop this again ? probs : ndarray, (len(x), len(idx)) the quantiles with frac in rows and idx variables in columns ''' idx = np.atleast_1d(idx).tolist() #assure iterable, use list ? # if self.mcres.ndim == 2: # if not idx is None: # mcres = self.mcres[:,idx] # else: # raise ValueError('currently only 1 statistic at a time') # else: # mcres = self.mcres mc_sorted = self.get_mc_sorted() x = np.asarray(x) #TODO:autodetect or explicit option ? if x.ndim > 1 and x.shape[1]==len(idx): use_xi = True else: use_xi = False x_ = x #alias probs = [] for i,ix in enumerate(idx): if use_xi: x_ = x[:,i] probs.append(np.searchsorted(mc_sorted[:,ix], x_)/float(self.nrepl)) probs = np.asarray(probs).T return x, probs def plot_hist(self, idx, distpdf=None, bins=50, ax=None, kwds=None): '''plot the histogram against a reference distribution Parameters ---------- idx : None or list of integers List of indices into the Monte Carlo results (columns) that should be used in the calculation distpdf : callable probability density function of reference distribution bins : {int, array_like} used unchanged for matplotlibs hist call ax : TODO: not implemented yet kwds : None or tuple of dicts extra keyword options to the calls to the matplotlib functions, first dictionary is for his, second dictionary for plot of the reference distribution Returns ------- None ''' if kwds is None: kwds = ({},{}) if self.mcres.ndim == 2: if idx is not None: mcres = self.mcres[:,idx] else: raise ValueError('currently only 1 statistic at a time') else: mcres = self.mcres lsp = np.linspace(mcres.min(), mcres.max(), 100) import matplotlib.pyplot as plt #I do not want to figure this out now # if ax=None: # fig = plt.figure() # ax = fig.addaxis() fig = plt.figure() plt.hist(mcres, bins=bins, normed=True, **kwds[0]) plt.plot(lsp, distpdf(lsp), 'r', **kwds[1]) def summary_quantiles(self, idx, distppf, frac=[0.01, 0.025, 0.05, 0.1, 0.975], varnames=None, title=None): '''summary table for quantiles (critical values) Parameters ---------- idx : None or list of integers List of indices into the Monte Carlo results (columns) that should be used in the calculation distppf : callable probability density function of reference distribution TODO: use `crit` values instead or additional, see summary_cdf frac : array_like, float probabilities for which varnames : None, or list of strings optional list of variable names, same length as idx Returns ------- table : instance of SimpleTable use `print(table` to see results ''' idx = np.atleast_1d(idx) #assure iterable, use list ? quant, mcq = self.quantiles(idx, frac=frac) #not sure whether this will work with single quantile #crit = stats.chi2([2,4]).ppf(np.atleast_2d(quant).T) crit = distppf(np.atleast_2d(quant).T) mml=[] for i, ix in enumerate(idx): #TODO: hardcoded 2 ? mml.extend([mcq[:,i], crit[:,i]]) #mmlar = np.column_stack(mml) mmlar = np.column_stack([quant] + mml) #print(mmlar.shape if title: title = title +' Quantiles (critical values)' else: title='Quantiles (critical values)' #TODO use stub instead if varnames is None: varnames = ['var%d' % i for i in range(mmlar.shape[1]//2)] headers = ['\nprob'] + ['%s\n%s' % (i, t) for i in varnames for t in ['mc', 'dist']] return SimpleTable(mmlar, txt_fmt={'data_fmts': ["%#6.3f"]+["%#10.4f"]*(mmlar.shape[1]-1)}, title=title, headers=headers) def summary_cdf(self, idx, frac, crit, varnames=None, title=None): '''summary table for cumulative density function Parameters ---------- idx : None or list of integers List of indices into the Monte Carlo results (columns) that should be used in the calculation frac : array_like, float probabilities for which crit : array_like values for which cdf is calculated varnames : None, or list of strings optional list of variable names, same length as idx Returns ------- table : instance of SimpleTable use `print(table` to see results ''' idx = np.atleast_1d(idx) #assure iterable, use list ? mml=[] #TODO:need broadcasting in cdf for i in range(len(idx)): #print(i, mc1.cdf(crit[:,i], [idx[i]])[1].ravel() mml.append(self.cdf(crit[:,i], [idx[i]])[1].ravel()) #mml = self.cdf(crit, idx)[1] #mmlar = np.column_stack(mml) #print(mml[0].shape, np.shape(frac) mmlar = np.column_stack([frac] + mml) #print(mmlar.shape if title: title = title +' Probabilites' else: title='Probabilities' #TODO use stub instead #headers = ['\nprob'] + ['var%d\n%s' % (i, t) for i in range(mmlar.shape[1]-1) for t in ['mc']] if varnames is None: varnames = ['var%d' % i for i in range(mmlar.shape[1]-1)] headers = ['prob'] + varnames return SimpleTable(mmlar, txt_fmt={'data_fmts': ["%#6.3f"]+["%#10.4f"]*(np.array(mml).shape[1]-1)}, title=title, headers=headers) if __name__ == '__main__': from scipy import stats from statsmodels.stats.diagnostic import acorr_ljungbox def randwalksim(nobs=100, drift=0.0): return (drift+np.random.randn(nobs)).cumsum() def normalnoisesim(nobs=500, loc=0.0): return (loc+np.random.randn(nobs)) # print('\nResults with MC class' # mc1 = StatTestMC(randwalksim, adf20) # mc1.run(1000) # print(mc1.histogram(critval=[-3.5, -3.17, -2.9 , -2.58, 0.26]) # print(mc1.quantiles() print('\nLjung Box') def lb4(x): s,p = acorr_ljungbox(x, lags=4, return_df=True) return s[-1], p[-1] def lb1(x): s,p = acorr_ljungbox(x, lags=1, return_df=True) return s[0], p[0] def lb(x): s,p = acorr_ljungbox(x, lags=4, return_df=True) return np.r_[s, p] print('Results with MC class') mc1 = StatTestMC(normalnoisesim, lb) mc1.run(10000, statindices=lrange(8)) print(mc1.histogram(1, critval=[0.01, 0.025, 0.05, 0.1, 0.975])) print(mc1.quantiles(1)) print(mc1.quantiles(0)) print(mc1.histogram(0)) #print(mc1.summary_quantiles([1], stats.chi2([2]).ppf, title='acorr_ljungbox') print(mc1.summary_quantiles([1,2,3], stats.chi2([2,3,4]).ppf, varnames=['lag 1', 'lag 2', 'lag 3'], title='acorr_ljungbox')) print(mc1.cdf(0.1026, 1)) print(mc1.cdf(0.7278, 3)) print(mc1.cdf(0.7278, [1,2,3])) frac = [0.01, 0.025, 0.05, 0.1, 0.975] crit = stats.chi2([2,4]).ppf(np.atleast_2d(frac).T) print(mc1.summary_cdf([1,3], frac, crit, title='acorr_ljungbox')) crit = stats.chi2([2,3,4]).ppf(np.atleast_2d(frac).T) print(mc1.summary_cdf([1,2,3], frac, crit, varnames=['lag 1', 'lag 2', 'lag 3'], title='acorr_ljungbox')) print(mc1.cdf(crit, [1,2,3])[1].shape) #fixed broadcasting in cdf Done 2d only ''' >>> mc1.cdf(crit[:,0], [1])[1].shape (5, 1) >>> mc1.cdf(crit[:,0], [1,3])[1].shape (5, 2) >>> mc1.cdf(crit[:,:], [1,3])[1].shape (2, 5, 2) ''' doplot=0 if doplot: import matplotlib.pyplot as plt mc1.plot_hist(0,stats.chi2(2).pdf) #which pdf plt.show() statsmodels-0.12.2/statsmodels/sandbox/tools/tools_pca.py000066400000000000000000000100411400612667500236360ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Principal Component Analysis Created on Tue Sep 29 20:11:23 2009 Author: josef-pktd TODO : add class for better reuse of results """ import numpy as np def pca(data, keepdim=0, normalize=0, demean=True): '''principal components with eigenvector decomposition similar to princomp in matlab Parameters ---------- data : ndarray, 2d data with observations by rows and variables in columns keepdim : int number of eigenvectors to keep if keepdim is zero, then all eigenvectors are included normalize : bool if true, then eigenvectors are normalized by sqrt of eigenvalues demean : bool if true, then the column mean is subtracted from the data Returns ------- xreduced : ndarray, 2d, (nobs, nvars) projection of the data x on the kept eigenvectors factors : ndarray, 2d, (nobs, nfactors) factor matrix, given by np.dot(x, evecs) evals : ndarray, 2d, (nobs, nfactors) eigenvalues evecs : ndarray, 2d, (nobs, nfactors) eigenvectors, normalized if normalize is true Notes ----- See Also -------- pcasvd : principal component analysis using svd ''' x = np.array(data) #make copy so original does not change, maybe not necessary anymore if demean: m = x.mean(0) else: m = np.zeros(x.shape[1]) x -= m # Covariance matrix xcov = np.cov(x, rowvar=0) # Compute eigenvalues and sort into descending order evals, evecs = np.linalg.eig(xcov) indices = np.argsort(evals) indices = indices[::-1] evecs = evecs[:,indices] evals = evals[indices] if keepdim > 0 and keepdim < x.shape[1]: evecs = evecs[:,:keepdim] evals = evals[:keepdim] if normalize: #for i in range(shape(evecs)[1]): # evecs[:,i] / linalg.norm(evecs[:,i]) * sqrt(evals[i]) evecs = evecs/np.sqrt(evals) #np.sqrt(np.dot(evecs.T, evecs) * evals) # get factor matrix #x = np.dot(evecs.T, x.T) factors = np.dot(x, evecs) # get original data from reduced number of components #xreduced = np.dot(evecs.T, factors) + m #print x.shape, factors.shape, evecs.shape, m.shape xreduced = np.dot(factors, evecs.T) + m return xreduced, factors, evals, evecs def pcasvd(data, keepdim=0, demean=True): '''principal components with svd Parameters ---------- data : ndarray, 2d data with observations by rows and variables in columns keepdim : int number of eigenvectors to keep if keepdim is zero, then all eigenvectors are included demean : bool if true, then the column mean is subtracted from the data Returns ------- xreduced : ndarray, 2d, (nobs, nvars) projection of the data x on the kept eigenvectors factors : ndarray, 2d, (nobs, nfactors) factor matrix, given by np.dot(x, evecs) evals : ndarray, 2d, (nobs, nfactors) eigenvalues evecs : ndarray, 2d, (nobs, nfactors) eigenvectors, normalized if normalize is true See Also -------- pca : principal component analysis using eigenvector decomposition Notes ----- This does not have yet the normalize option of pca. ''' nobs, nvars = data.shape #print nobs, nvars, keepdim x = np.array(data) #make copy so original does not change if demean: m = x.mean(0) else: m = 0 ## if keepdim == 0: ## keepdim = nvars ## "print reassigning keepdim to max", keepdim x -= m U, s, v = np.linalg.svd(x.T, full_matrices=1) factors = np.dot(U.T, x.T).T #princomps if keepdim: xreduced = np.dot(factors[:,:keepdim], U[:,:keepdim].T) + m else: xreduced = data keepdim = nvars "print reassigning keepdim to max", keepdim # s = evals, U = evecs # no idea why denominator for s is with minus 1 evals = s**2/(x.shape[0]-1) #print keepdim return xreduced, factors[:,:keepdim], evals[:keepdim], U[:,:keepdim] #, v __all__ = ['pca', 'pcasvd'] statsmodels-0.12.2/statsmodels/sandbox/tools/try_mctools.py000066400000000000000000000036261400612667500242440ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Sep 30 15:20:45 2011 @author: josef """ from statsmodels.compat.python import lrange import numpy as np from scipy import stats from statsmodels.sandbox.tools.mctools import StatTestMC from statsmodels.stats.diagnostic import acorr_ljungbox from statsmodels.tsa.stattools import adfuller def normalnoisesim(nobs=500, loc=0.0): return (loc+np.random.randn(nobs)) def lb(x): s,p = acorr_ljungbox(x, lags=4) return np.r_[s, p] mc1 = StatTestMC(normalnoisesim, lb) mc1.run(5000, statindices=lrange(4)) print(mc1.summary_quantiles([1,2,3], stats.chi2([2,3,4]).ppf, varnames=['lag 1', 'lag 2', 'lag 3'], title='acorr_ljungbox')) print('\n\n') frac = [0.01, 0.025, 0.05, 0.1, 0.975] crit = stats.chi2([2,3,4]).ppf(np.atleast_2d(frac).T) print(mc1.summary_cdf([1,2,3], frac, crit, varnames=['lag 1', 'lag 2', 'lag 3'], title='acorr_ljungbox')) print(mc1.cdf(crit, [1,2,3])[1]) #---------------------- def randwalksim(nobs=500, drift=0.0): return (drift+np.random.randn(nobs)).cumsum() def adf20(x): return adfuller(x, 2, regression="nc", autolag=None) print(adf20(np.random.randn(100))) mc2 = StatTestMC(randwalksim, adf20) mc2.run(10000, statindices=[0,1]) frac = [0.01, 0.05, 0.1] #bug crit = np.array([-3.4996365338407074, -2.8918307730370025, -2.5829283377617176])[:,None] print(mc2.summary_cdf([0], frac, crit, varnames=['adf'], title='adf')) #bug #crit2 = np.column_stack((crit, frac)) #print mc2.summary_cdf([0, 1], frac, crit, # varnames=['adf'], # title='adf') print(mc2.quantiles([0])) print(mc2.cdf(crit, [0])) doplot=1 if doplot: import matplotlib.pyplot as plt mc1.plot_hist([3],stats.chi2([4]).pdf) plt.title('acorr_ljungbox - MC versus chi2') plt.show() statsmodels-0.12.2/statsmodels/sandbox/tsa/000077500000000000000000000000001400612667500207345ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/tsa/__init__.py000066400000000000000000000015101400612667500230420ustar00rootroot00000000000000'''functions and classes time series analysis Status ------ work in progress arima.py ^^^^^^^^ ARIMA : initial class, uses conditional least squares, needs merging with new class arma2ar arma2ma arma_acf arma_acovf arma_generate_sample arma_impulse_response deconvolve index2lpol lpol2index mcarma22 movstat.py ^^^^^^^^^^ I had tested the next group against matlab, but where are the tests ? acf acovf ccf ccovf pacf_ols pacf_yw These hat incorrect array size, were my first implementation, slow compared to cumsum version in la and cython version in pandas. These need checking, and merging/comparing with new class MovStats check_movorder expandarr movmean : movmoment : corrected cutoff movorder movvar ''' #from arima import * from .movstat import movorder, movmean, movvar, movmoment # noqa:F401 #from stattools import * statsmodels-0.12.2/statsmodels/sandbox/tsa/diffusion.py000066400000000000000000000444761400612667500233130ustar00rootroot00000000000000'''getting started with diffusions, continuous time stochastic processes Author: josef-pktd License: BSD References ---------- An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations Author(s): Desmond J. Higham Source: SIAM Review, Vol. 43, No. 3 (Sep., 2001), pp. 525-546 Published by: Society for Industrial and Applied Mathematics Stable URL: http://www.jstor.org/stable/3649798 http://www.sitmo.com/ especially the formula collection Notes ----- OU process: use same trick for ARMA with constant (non-zero mean) and drift some of the processes have easy multivariate extensions *Open Issues* include xzero in returned sample or not? currently not *TODOS* * Milstein from Higham paper, for which processes does it apply * Maximum Likelihood estimation * more statistical properties (useful for tests) * helper functions for display and MonteCarlo summaries (also for testing/checking) * more processes for the menagerie (e.g. from empirical papers) * characteristic functions * transformations, non-linear e.g. log * special estimators, e.g. Ait Sahalia, empirical characteristic functions * fft examples * check naming of methods, "simulate", "sample", "simexact", ... ? stochastic volatility models: estimation unclear finance applications ? option pricing, interest rate models ''' import numpy as np from scipy import stats, signal import matplotlib.pyplot as plt #np.random.seed(987656789) class Diffusion(object): '''Wiener Process, Brownian Motion with mu=0 and sigma=1 ''' def __init__(self): pass def simulateW(self, nobs=100, T=1, dt=None, nrepl=1): '''generate sample of Wiener Process ''' dt = T*1.0/nobs t = np.linspace(dt, 1, nobs) dW = np.sqrt(dt)*np.random.normal(size=(nrepl, nobs)) W = np.cumsum(dW,1) self.dW = dW return W, t def expectedsim(self, func, nobs=100, T=1, dt=None, nrepl=1): '''get expectation of a function of a Wiener Process by simulation initially test example from ''' W, t = self.simulateW(nobs=nobs, T=T, dt=dt, nrepl=nrepl) U = func(t, W) Umean = U.mean(0) return U, Umean, t class AffineDiffusion(Diffusion): r''' differential equation: :math:: dx_t = f(t,x)dt + \sigma(t,x)dW_t integral: :math:: x_T = x_0 + \int_{0}^{T}f(t,S)dt + \int_0^T \sigma(t,S)dW_t TODO: check definition, affine, what about jump diffusion? ''' def __init__(self): pass def sim(self, nobs=100, T=1, dt=None, nrepl=1): # this does not look correct if drift or sig depend on x # see arithmetic BM W, t = self.simulateW(nobs=nobs, T=T, dt=dt, nrepl=nrepl) dx = self._drift() + self._sig() * W x = np.cumsum(dx,1) xmean = x.mean(0) return x, xmean, t def simEM(self, xzero=None, nobs=100, T=1, dt=None, nrepl=1, Tratio=4): ''' from Higham 2001 TODO: reverse parameterization to start with final nobs and DT TODO: check if I can skip the loop using my way from exactprocess problem might be Winc (reshape into 3d and sum) TODO: (later) check memory efficiency for large simulations ''' #TODO: reverse parameterization to start with final nobs and DT nobs = nobs * Tratio # simple way to change parameter # maybe wrong parameterization, # drift too large, variance too small ? which dt/Dt # _drift, _sig independent of dt is wrong if xzero is None: xzero = self.xzero if dt is None: dt = T*1.0/nobs W, t = self.simulateW(nobs=nobs, T=T, dt=dt, nrepl=nrepl) dW = self.dW t = np.linspace(dt, 1, nobs) Dt = Tratio*dt L = nobs/Tratio # L EM steps of size Dt = R*dt Xem = np.zeros((nrepl,L)) # preallocate for efficiency Xtemp = xzero Xem[:,0] = xzero for j in np.arange(1,L): #Winc = np.sum(dW[:,Tratio*(j-1)+1:Tratio*j],1) Winc = np.sum(dW[:,np.arange(Tratio*(j-1)+1,Tratio*j)],1) #Xtemp = Xtemp + Dt*lamda*Xtemp + mu*Xtemp*Winc; Xtemp = Xtemp + self._drift(x=Xtemp) + self._sig(x=Xtemp) * Winc #Dt*lamda*Xtemp + mu*Xtemp*Winc; Xem[:,j] = Xtemp return Xem ''' R = 4; Dt = R*dt; L = N/R; % L EM steps of size Dt = R*dt Xem = zeros(1,L); % preallocate for efficiency Xtemp = Xzero; for j = 1:L Winc = sum(dW(R*(j-1)+1:R*j)); Xtemp = Xtemp + Dt*lambda*Xtemp + mu*Xtemp*Winc; Xem(j) = Xtemp; end ''' class ExactDiffusion(AffineDiffusion): '''Diffusion that has an exact integral representation this is currently mainly for geometric, log processes ''' def __init__(self): pass def exactprocess(self, xzero, nobs, ddt=1., nrepl=2): '''ddt : discrete delta t should be the same as an AR(1) not tested yet ''' t = np.linspace(ddt, nobs*ddt, nobs) #expnt = np.exp(-self.lambd * t) expddt = np.exp(-self.lambd * ddt) normrvs = np.random.normal(size=(nrepl,nobs)) #do I need lfilter here AR(1) ? if mean reverting lag-coeff<1 #lfilter does not handle 2d arrays, it does? inc = self._exactconst(expddt) + self._exactstd(expddt) * normrvs return signal.lfilter([1.], [1.,-expddt], inc) def exactdist(self, xzero, t): expnt = np.exp(-self.lambd * t) meant = xzero * expnt + self._exactconst(expnt) stdt = self._exactstd(expnt) return stats.norm(loc=meant, scale=stdt) class ArithmeticBrownian(AffineDiffusion): ''' :math:: dx_t &= \\mu dt + \\sigma dW_t ''' def __init__(self, xzero, mu, sigma): self.xzero = xzero self.mu = mu self.sigma = sigma def _drift(self, *args, **kwds): return self.mu def _sig(self, *args, **kwds): return self.sigma def exactprocess(self, nobs, xzero=None, ddt=1., nrepl=2): '''ddt : discrete delta t not tested yet ''' if xzero is None: xzero = self.xzero t = np.linspace(ddt, nobs*ddt, nobs) normrvs = np.random.normal(size=(nrepl,nobs)) inc = self._drift + self._sigma * np.sqrt(ddt) * normrvs #return signal.lfilter([1.], [1.,-1], inc) return xzero + np.cumsum(inc,1) def exactdist(self, xzero, t): expnt = np.exp(-self.lambd * t) meant = self._drift * t stdt = self._sigma * np.sqrt(t) return stats.norm(loc=meant, scale=stdt) class GeometricBrownian(AffineDiffusion): '''Geometric Brownian Motion :math:: dx_t &= \\mu x_t dt + \\sigma x_t dW_t $x_t $ stochastic process of Geometric Brownian motion, $\\mu $ is the drift, $\\sigma $ is the Volatility, $W$ is the Wiener process (Brownian motion). ''' def __init__(self, xzero, mu, sigma): self.xzero = xzero self.mu = mu self.sigma = sigma def _drift(self, *args, **kwds): x = kwds['x'] return self.mu * x def _sig(self, *args, **kwds): x = kwds['x'] return self.sigma * x class OUprocess(AffineDiffusion): '''Ornstein-Uhlenbeck :math:: dx_t&=\\lambda(\\mu - x_t)dt+\\sigma dW_t mean reverting process TODO: move exact higher up in class hierarchy ''' def __init__(self, xzero, mu, lambd, sigma): self.xzero = xzero self.lambd = lambd self.mu = mu self.sigma = sigma def _drift(self, *args, **kwds): x = kwds['x'] return self.lambd * (self.mu - x) def _sig(self, *args, **kwds): x = kwds['x'] return self.sigma * x def exact(self, xzero, t, normrvs): #TODO: aggregate over time for process with observations for all t # i.e. exact conditional distribution for discrete time increment # -> exactprocess #TODO: for single t, return stats.norm -> exactdist expnt = np.exp(-self.lambd * t) return (xzero * expnt + self.mu * (1-expnt) + self.sigma * np.sqrt((1-expnt*expnt)/2./self.lambd) * normrvs) def exactprocess(self, xzero, nobs, ddt=1., nrepl=2): '''ddt : discrete delta t should be the same as an AR(1) not tested yet # after writing this I saw the same use of lfilter in sitmo ''' t = np.linspace(ddt, nobs*ddt, nobs) expnt = np.exp(-self.lambd * t) expddt = np.exp(-self.lambd * ddt) normrvs = np.random.normal(size=(nrepl,nobs)) #do I need lfilter here AR(1) ? lfilter does not handle 2d arrays, it does? from scipy import signal #xzero * expnt inc = ( self.mu * (1-expddt) + self.sigma * np.sqrt((1-expddt*expddt)/2./self.lambd) * normrvs ) return signal.lfilter([1.], [1.,-expddt], inc) def exactdist(self, xzero, t): #TODO: aggregate over time for process with observations for all t #TODO: for single t, return stats.norm expnt = np.exp(-self.lambd * t) meant = xzero * expnt + self.mu * (1-expnt) stdt = self.sigma * np.sqrt((1-expnt*expnt)/2./self.lambd) from scipy import stats return stats.norm(loc=meant, scale=stdt) def fitls(self, data, dt): '''assumes data is 1d, univariate time series formula from sitmo ''' # brute force, no parameter estimation errors nobs = len(data)-1 exog = np.column_stack((np.ones(nobs), data[:-1])) parest, res, rank, sing = np.linalg.lstsq(exog, data[1:], rcond=-1) const, slope = parest errvar = res/(nobs-2.) lambd = -np.log(slope)/dt sigma = np.sqrt(-errvar * 2.*np.log(slope)/ (1-slope**2)/dt) mu = const / (1-slope) return mu, lambd, sigma class SchwartzOne(ExactDiffusion): '''the Schwartz type 1 stochastic process :math:: dx_t = \\kappa (\\mu - \\ln x_t) x_t dt + \\sigma x_tdW \\ The Schwartz type 1 process is a log of the Ornstein-Uhlenbeck stochastic process. ''' def __init__(self, xzero, mu, kappa, sigma): self.xzero = xzero self.mu = mu self.kappa = kappa self.lambd = kappa #alias until I fix exact self.sigma = sigma def _exactconst(self, expnt): return (1-expnt) * (self.mu - self.sigma**2 / 2. /self.kappa) def _exactstd(self, expnt): return self.sigma * np.sqrt((1-expnt*expnt)/2./self.kappa) def exactprocess(self, xzero, nobs, ddt=1., nrepl=2): '''uses exact solution for log of process ''' lnxzero = np.log(xzero) lnx = super(self.__class__, self).exactprocess(xzero, nobs, ddt=ddt, nrepl=nrepl) return np.exp(lnx) def exactdist(self, xzero, t): expnt = np.exp(-self.lambd * t) #TODO: check this is still wrong, just guessing meant = np.log(xzero) * expnt + self._exactconst(expnt) stdt = self._exactstd(expnt) return stats.lognorm(loc=meant, scale=stdt) def fitls(self, data, dt): '''assumes data is 1d, univariate time series formula from sitmo ''' # brute force, no parameter estimation errors nobs = len(data)-1 exog = np.column_stack((np.ones(nobs),np.log(data[:-1]))) parest, res, rank, sing = np.linalg.lstsq(exog, np.log(data[1:]), rcond=-1) const, slope = parest errvar = res/(nobs-2.) #check denominator estimate, of sigma too low kappa = -np.log(slope)/dt sigma = np.sqrt(errvar * kappa / (1-np.exp(-2*kappa*dt))) mu = const / (1-np.exp(-kappa*dt)) + sigma**2/2./kappa if np.shape(mu)== (1,): mu = mu[0] # TODO: how to remove scalar array ? if np.shape(sigma)== (1,): sigma = sigma[0] #mu, kappa are good, sigma too small return mu, kappa, sigma class BrownianBridge(object): def __init__(self): pass def simulate(self, x0, x1, nobs, nrepl=1, ddt=1., sigma=1.): nobs=nobs+1 dt = ddt*1./nobs t = np.linspace(dt, ddt-dt, nobs) t = np.linspace(dt, ddt, nobs) wm = [t/ddt, 1-t/ddt] #wmi = wm[1] #wm1 = x1*wm[0] wmi = 1-dt/(ddt-t) wm1 = x1*(dt/(ddt-t)) su = sigma* np.sqrt(t*(1-t)/ddt) s = sigma* np.sqrt(dt*(ddt-t-dt)/(ddt-t)) x = np.zeros((nrepl, nobs)) x[:,0] = x0 rvs = s*np.random.normal(size=(nrepl,nobs)) for i in range(1,nobs): x[:,i] = x[:,i-1]*wmi[i] + wm1[i] + rvs[:,i] return x, t, su class CompoundPoisson(object): '''nobs iid compound poisson distributions, not a process in time ''' def __init__(self, lambd, randfn=np.random.normal): if len(lambd) != len(randfn): raise ValueError('lambd and randfn need to have the same number of elements') self.nobj = len(lambd) self.randfn = randfn self.lambd = np.asarray(lambd) def simulate(self, nobs, nrepl=1): nobj = self.nobj x = np.zeros((nrepl, nobs, nobj)) N = np.random.poisson(self.lambd[None,None,:], size=(nrepl,nobs,nobj)) for io in range(nobj): randfnc = self.randfn[io] nc = N[:,:,io] #print nrepl,nobs,nc #xio = randfnc(size=(nrepl,nobs,np.max(nc))).cumsum(-1)[np.arange(nrepl)[:,None],np.arange(nobs),nc-1] rvs = randfnc(size=(nrepl,nobs,np.max(nc))) print('rvs.sum()', rvs.sum(), rvs.shape) xio = rvs.cumsum(-1)[np.arange(nrepl)[:,None],np.arange(nobs),nc-1] #print xio.shape x[:,:,io] = xio x[N==0] = 0 return x, N ''' randn('state',100) % set the state of randn T = 1; N = 500; dt = T/N; t = [dt:dt:1]; M = 1000; % M paths simultaneously dW = sqrt(dt)*randn(M,N); % increments W = cumsum(dW,2); % cumulative sum U = exp(repmat(t,[M 1]) + 0.5*W); Umean = mean(U); plot([0,t],[1,Umean],'b-'), hold on % plot mean over M paths plot([0,t],[ones(5,1),U(1:5,:)],'r--'), hold off % plot 5 individual paths xlabel('t','FontSize',16) ylabel('U(t)','FontSize',16,'Rotation',0,'HorizontalAlignment','right') legend('mean of 1000 paths','5 individual paths',2) averr = norm((Umean - exp(9*t/8)),'inf') % sample error ''' if __name__ == '__main__': doplot = 1 nrepl = 1000 examples = []#['all'] if 'all' in examples: w = Diffusion() # Wiener Process # ^^^^^^^^^^^^^^ ws = w.simulateW(1000, nrepl=nrepl) if doplot: plt.figure() tmp = plt.plot(ws[0].T) tmp = plt.plot(ws[0].mean(0), linewidth=2) plt.title('Standard Brownian Motion (Wiener Process)') func = lambda t, W: np.exp(t + 0.5*W) us = w.expectedsim(func, nobs=500, nrepl=nrepl) if doplot: plt.figure() tmp = plt.plot(us[0].T) tmp = plt.plot(us[1], linewidth=2) plt.title('Brownian Motion - exp') #plt.show() averr = np.linalg.norm(us[1] - np.exp(9*us[2]/8.), np.inf) print(averr) #print us[1][:10] #print np.exp(9.*us[2][:10]/8.) # Geometric Brownian # ^^^^^^^^^^^^^^^^^^ gb = GeometricBrownian(xzero=1., mu=0.01, sigma=0.5) gbs = gb.simEM(nobs=100, nrepl=100) if doplot: plt.figure() tmp = plt.plot(gbs.T) tmp = plt.plot(gbs.mean(0), linewidth=2) plt.title('Geometric Brownian') plt.figure() tmp = plt.plot(np.log(gbs).T) tmp = plt.plot(np.log(gbs.mean(0)), linewidth=2) plt.title('Geometric Brownian - log-transformed') ab = ArithmeticBrownian(xzero=1, mu=0.05, sigma=1) abs = ab.simEM(nobs=100, nrepl=100) if doplot: plt.figure() tmp = plt.plot(abs.T) tmp = plt.plot(abs.mean(0), linewidth=2) plt.title('Arithmetic Brownian') # Ornstein-Uhlenbeck # ^^^^^^^^^^^^^^^^^^ ou = OUprocess(xzero=2, mu=1, lambd=0.5, sigma=0.1) ous = ou.simEM() oue = ou.exact(1, 1, np.random.normal(size=(5,10))) ou.exact(0, np.linspace(0,10,10/0.1), 0) ou.exactprocess(0,10) print(ou.exactprocess(0,10, ddt=0.1,nrepl=10).mean(0)) #the following looks good, approaches mu oues = ou.exactprocess(0,100, ddt=0.1,nrepl=100) if doplot: plt.figure() tmp = plt.plot(oues.T) tmp = plt.plot(oues.mean(0), linewidth=2) plt.title('Ornstein-Uhlenbeck') # SchwartsOne # ^^^^^^^^^^^ so = SchwartzOne(xzero=0, mu=1, kappa=0.5, sigma=0.1) sos = so.exactprocess(0,50, ddt=0.1,nrepl=100) print(sos.mean(0)) print(np.log(sos.mean(0))) doplot = 1 if doplot: plt.figure() tmp = plt.plot(sos.T) tmp = plt.plot(sos.mean(0), linewidth=2) plt.title('Schwartz One') print(so.fitls(sos[0,:],dt=0.1)) sos2 = so.exactprocess(0,500, ddt=0.1,nrepl=5) print('true: mu=1, kappa=0.5, sigma=0.1') for i in range(5): print(so.fitls(sos2[i],dt=0.1)) # Brownian Bridge # ^^^^^^^^^^^^^^^ bb = BrownianBridge() #bbs = bb.sample(x0, x1, nobs, nrepl=1, ddt=1., sigma=1.) bbs, t, wm = bb.simulate(0, 0.5, 99, nrepl=500, ddt=1., sigma=0.1) if doplot: plt.figure() tmp = plt.plot(bbs.T) tmp = plt.plot(bbs.mean(0), linewidth=2) plt.title('Brownian Bridge') plt.figure() plt.plot(wm,'r', label='theoretical') plt.plot(bbs.std(0), label='simulated') plt.title('Brownian Bridge - Variance') plt.legend() # Compound Poisson # ^^^^^^^^^^^^^^^^ cp = CompoundPoisson([1,1], [np.random.normal,np.random.normal]) cps = cp.simulate(nobs=20000,nrepl=3) print(cps[0].sum(-1).sum(-1)) print(cps[0].sum()) print(cps[0].mean(-1).mean(-1)) print(cps[0].mean()) print(cps[1].size) print(cps[1].sum()) #Note Y = sum^{N} X is compound poisson of iid x, then #E(Y) = E(N)*E(X) eg. eq. (6.37) page 385 in http://ee.stanford.edu/~gray/sp.html #plt.show() statsmodels-0.12.2/statsmodels/sandbox/tsa/diffusion2.py000066400000000000000000000320731400612667500233630ustar00rootroot00000000000000""" Diffusion 2: jump diffusion, stochastic volatility, stochastic time Created on Tue Dec 08 15:03:49 2009 Author: josef-pktd following Meucci License: BSD contains: CIRSubordinatedBrownian Heston IG JumpDiffusionKou JumpDiffusionMerton NIG VG References ---------- Attilio Meucci, Review of Discrete and Continuous Processes in Finance: Theory and Applications Bloomberg Portfolio Research Paper No. 2009-02-CLASSROOM July 1, 2009 http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1373102 this is currently mostly a translation from matlab of http://www.mathworks.com/matlabcentral/fileexchange/23554-review-of-discrete-and-continuous-processes-in-finance license BSD: Copyright (c) 2008, Attilio Meucci All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. TODO: * vectorize where possible * which processes are exactly simulated by finite differences ? * include or exclude (now) the initial observation ? * convert to and merge with diffusion.py (part 1 of diffusions) * which processes can be easily estimated ? loglike or characteristic function ? * tests ? check for possible index errors (random indices), graphs look ok * adjust notation, variable names, more consistent, more pythonic * delete a few unused lines, cleanup * docstrings random bug (showed up only once, need fuzz-testing to replicate) File "../diffusion2.py", line 375, in x = jd.simulate(mu,sigma,lambd,a,D,ts,nrepl) File "../diffusion2.py", line 129, in simulate jumps_ts[n] = CumS[Events] IndexError: index out of bounds CumS is empty array, Events == -1 """ import numpy as np #from scipy import stats # currently only uses np.random import matplotlib.pyplot as plt class JumpDiffusionMerton(object): ''' Example ------- mu=.00 # deterministic drift sig=.20 # Gaussian component l=3.45 # Poisson process arrival rate a=0 # drift of log-jump D=.2 # st.dev of log-jump X = JumpDiffusionMerton().simulate(mu,sig,lambd,a,D,ts,nrepl) plt.figure() plt.plot(X.T) plt.title('Merton jump-diffusion') ''' def __init__(self): pass def simulate(self, m,s,lambd,a,D,ts,nrepl): T = ts[-1] # time points # simulate number of jumps n_jumps = np.random.poisson(lambd*T, size=(nrepl, 1)) jumps=[] nobs=len(ts) jumps=np.zeros((nrepl,nobs)) for j in range(nrepl): # simulate jump arrival time t = T*np.random.rand(n_jumps[j])#,1) #uniform t = np.sort(t,0) # simulate jump size S = a + D*np.random.randn(n_jumps[j],1) # put things together CumS = np.cumsum(S) jumps_ts = np.zeros(nobs) for n in range(nobs): Events = np.sum(t<=ts[n])-1 #print n, Events, CumS.shape, jumps_ts.shape jumps_ts[n]=0 if Events > 0: jumps_ts[n] = CumS[Events] #TODO: out of bounds see top #jumps = np.column_stack((jumps, jumps_ts)) #maybe wrong transl jumps[j,:] = jumps_ts D_Diff = np.zeros((nrepl,nobs)) for k in range(nobs): Dt=ts[k] if k>1: Dt=ts[k]-ts[k-1] D_Diff[:,k]=m*Dt + s*np.sqrt(Dt)*np.random.randn(nrepl) x = np.hstack((np.zeros((nrepl,1)),np.cumsum(D_Diff,1)+jumps)) return x class JumpDiffusionKou(object): def __init__(self): pass def simulate(self, m,s,lambd,p,e1,e2,ts,nrepl): T=ts[-1] # simulate number of jumps N = np.random.poisson(lambd*T,size =(nrepl,1)) jumps=[] nobs=len(ts) jumps=np.zeros((nrepl,nobs)) for j in range(nrepl): # simulate jump arrival time t=T*np.random.rand(N[j]) t=np.sort(t) # simulate jump size ww = np.random.binomial(1, p, size=(N[j])) S = ww * np.random.exponential(e1, size=(N[j])) - \ (1-ww) * np.random.exponential(e2, N[j]) # put things together CumS = np.cumsum(S) jumps_ts = np.zeros(nobs) for n in range(nobs): Events = sum(t<=ts[n])-1 jumps_ts[n]=0 if Events: jumps_ts[n]=CumS[Events] jumps[j,:] = jumps_ts D_Diff = np.zeros((nrepl,nobs)) for k in range(nobs): Dt=ts[k] if k>1: Dt=ts[k]-ts[k-1] D_Diff[:,k]=m*Dt + s*np.sqrt(Dt)*np.random.normal(size=nrepl) x = np.hstack((np.zeros((nrepl,1)),np.cumsum(D_Diff,1)+jumps)) return x class VG(object): '''variance gamma process ''' def __init__(self): pass def simulate(self, m,s,kappa,ts,nrepl): T=len(ts) dXs = np.zeros((nrepl,T)) for t in range(T): dt=ts[1]-0 if t>1: dt = ts[t]-ts[t-1] #print dt/kappa #TODO: check parameterization of gamrnd, checked looks same as np d_tau = kappa * np.random.gamma(dt/kappa,1.,size=(nrepl)) #print s*np.sqrt(d_tau) # this raises exception: #dX = stats.norm.rvs(m*d_tau,(s*np.sqrt(d_tau))) # np.random.normal requires scale >0 dX = np.random.normal(loc=m*d_tau, scale=1e-6+s*np.sqrt(d_tau)) dXs[:,t] = dX x = np.cumsum(dXs,1) return x class IG(object): '''inverse-Gaussian ??? used by NIG ''' def __init__(self): pass def simulate(self, l,m,nrepl): N = np.random.randn(nrepl,1) Y = N**2 X = m + (.5*m*m/l)*Y - (.5*m/l)*np.sqrt(4*m*l*Y+m*m*(Y**2)) U = np.random.rand(nrepl,1) ind = U>m/(X+m) X[ind] = m*m/X[ind] return X.ravel() class NIG(object): '''normal-inverse-Gaussian ''' def __init__(self): pass def simulate(self, th,k,s,ts,nrepl): T = len(ts) DXs = np.zeros((nrepl,T)) for t in range(T): Dt=ts[1]-0 if t>1: Dt=ts[t]-ts[t-1] lfrac = 1/k*(Dt**2) m = Dt DS = IG().simulate(lfrac, m, nrepl) N = np.random.randn(nrepl) DX = s*N*np.sqrt(DS) + th*DS #print DS.shape, DX.shape, DXs.shape DXs[:,t] = DX x = np.cumsum(DXs,1) return x class Heston(object): '''Heston Stochastic Volatility ''' def __init__(self): pass def simulate(self, m, kappa, eta,lambd,r, ts, nrepl,tratio=1.): T = ts[-1] nobs = len(ts) dt = np.zeros(nobs) #/tratio dt[0] = ts[0]-0 dt[1:] = np.diff(ts) DXs = np.zeros((nrepl,nobs)) dB_1 = np.sqrt(dt) * np.random.randn(nrepl,nobs) dB_2u = np.sqrt(dt) * np.random.randn(nrepl,nobs) dB_2 = r*dB_1 + np.sqrt(1-r**2)*dB_2u vt = eta*np.ones(nrepl) v=[] dXs = np.zeros((nrepl,nobs)) vts = np.zeros((nrepl,nobs)) for t in range(nobs): dv = kappa*(eta-vt)*dt[t]+ lambd*np.sqrt(vt)*dB_2[:,t] dX = m*dt[t] + np.sqrt(vt*dt[t]) * dB_1[:,t] vt = vt + dv vts[:,t] = vt dXs[:,t] = dX x = np.cumsum(dXs,1) return x, vts class CIRSubordinatedBrownian(object): '''CIR subordinated Brownian Motion ''' def __init__(self): pass def simulate(self, m, kappa, T_dot,lambd,sigma, ts, nrepl): T = ts[-1] nobs = len(ts) dtarr = np.zeros(nobs) #/tratio dtarr[0] = ts[0]-0 dtarr[1:] = np.diff(ts) DXs = np.zeros((nrepl,nobs)) dB = np.sqrt(dtarr) * np.random.randn(nrepl,nobs) yt = 1. dXs = np.zeros((nrepl,nobs)) dtaus = np.zeros((nrepl,nobs)) y = np.zeros((nrepl,nobs)) for t in range(nobs): dt = dtarr[t] dy = kappa*(T_dot-yt)*dt + lambd*np.sqrt(yt)*dB[:,t] yt = np.maximum(yt+dy,1e-10) # keep away from zero ? dtau = np.maximum(yt*dt, 1e-6) dX = np.random.normal(loc=m*dtau, scale=sigma*np.sqrt(dtau)) y[:,t] = yt dtaus[:,t] = dtau dXs[:,t] = dX tau = np.cumsum(dtaus,1) x = np.cumsum(dXs,1) return x, tau, y def schout2contank(a,b,d): th = d*b/np.sqrt(a**2-b**2) k = 1/(d*np.sqrt(a**2-b**2)) s = np.sqrt(d/np.sqrt(a**2-b**2)) return th,k,s if __name__ == '__main__': #Merton Jump Diffusion #^^^^^^^^^^^^^^^^^^^^^ # grid of time values at which the process is evaluated #("0" will be added, too) nobs = 252.#1000 #252. ts = np.linspace(1./nobs, 1., nobs) nrepl=5 # number of simulations mu=.010 # deterministic drift sigma = .020 # Gaussian component lambd = 3.45 *10 # Poisson process arrival rate a=0 # drift of log-jump D=.2 # st.dev of log-jump jd = JumpDiffusionMerton() x = jd.simulate(mu,sigma,lambd,a,D,ts,nrepl) plt.figure() plt.plot(x.T) #Todo plt.title('Merton jump-diffusion') sigma = 0.2 lambd = 3.45 x = jd.simulate(mu,sigma,lambd,a,D,ts,nrepl) plt.figure() plt.plot(x.T) #Todo plt.title('Merton jump-diffusion') #Kou jump diffusion #^^^^^^^^^^^^^^^^^^ mu=.0 # deterministic drift lambd=4.25 # Poisson process arrival rate p=.5 # prob. of up-jump e1=.2 # parameter of up-jump e2=.3 # parameter of down-jump sig=.2 # Gaussian component x = JumpDiffusionKou().simulate(mu,sig,lambd,p,e1,e2,ts,nrepl) plt.figure() plt.plot(x.T) #Todo plt.title('double exponential (Kou jump diffusion)') #variance-gamma #^^^^^^^^^^^^^^ mu = .1 # deterministic drift in subordinated Brownian motion kappa = 1. #10. #1 # inverse for gamma shape parameter sig = 0.5 #.2 # s.dev in subordinated Brownian motion x = VG().simulate(mu,sig,kappa,ts,nrepl) plt.figure() plt.plot(x.T) #Todo plt.title('variance gamma') #normal-inverse-Gaussian #^^^^^^^^^^^^^^^^^^^^^^^ # (Schoutens notation) al = 2.1 be = 0 de = 1 # convert parameters to Cont-Tankov notation th,k,s = schout2contank(al,be,de) x = NIG().simulate(th,k,s,ts,nrepl) plt.figure() plt.plot(x.T) #Todo x-axis plt.title('normal-inverse-Gaussian') #Heston Stochastic Volatility #^^^^^^^^^^^^^^^^^^^^^^^^^^^^ m=.0 kappa = .6 # 2*Kappa*Eta>Lambda^2 eta = .3**2 lambd =.25 r = -.7 T = 20. nobs = 252.*T#1000 #252. tsh = np.linspace(T/nobs, T, nobs) x, vts = Heston().simulate(m,kappa, eta,lambd,r, tsh, nrepl, tratio=20.) plt.figure() plt.plot(x.T) plt.title('Heston Stochastic Volatility') plt.figure() plt.plot(np.sqrt(vts).T) plt.title('Heston Stochastic Volatility - CIR Vol.') plt.figure() plt.subplot(2,1,1) plt.plot(x[0]) plt.title('Heston Stochastic Volatility process') plt.subplot(2,1,2) plt.plot(np.sqrt(vts[0])) plt.title('CIR Volatility') #CIR subordinated Brownian #^^^^^^^^^^^^^^^^^^^^^^^^^ m=.1 sigma=.4 kappa=.6 # 2*Kappa*T_dot>Lambda^2 T_dot=1 lambd=1 #T=252*10 #dt=1/252 #nrepl=2 T = 10. nobs = 252.*T#1000 #252. tsh = np.linspace(T/nobs, T, nobs) x, tau, y = CIRSubordinatedBrownian().simulate(m, kappa, T_dot,lambd,sigma, tsh, nrepl) plt.figure() plt.plot(tsh, x.T) plt.title('CIRSubordinatedBrownian process') plt.figure() plt.plot(tsh, y.T) plt.title('CIRSubordinatedBrownian - CIR') plt.figure() plt.plot(tsh, tau.T) plt.title('CIRSubordinatedBrownian - stochastic time ') plt.figure() plt.subplot(2,1,1) plt.plot(tsh, x[0]) plt.title('CIRSubordinatedBrownian process') plt.subplot(2,1,2) plt.plot(tsh, y[0], label='CIR') plt.plot(tsh, tau[0], label='stoch. time') plt.legend(loc='upper left') plt.title('CIRSubordinatedBrownian') #plt.show() statsmodels-0.12.2/statsmodels/sandbox/tsa/example_arma.py000066400000000000000000000262571400612667500237550ustar00rootroot00000000000000'''trying to verify theoretical acf of arma explicit functions for autocovariance functions of ARIMA(1,1), MA(1), MA(2) plus 3 functions from nitime.utils ''' import numpy as np from numpy.testing import assert_array_almost_equal import matplotlib.pyplot as plt import statsmodels.api as sm from statsmodels.tsa.arima_process import arma_generate_sample, arma_impulse_response from statsmodels.tsa.arima_process import arma_acovf, arma_acf, ARIMA from statsmodels.tsa.stattools import acf, acovf from statsmodels.graphics.tsaplots import plotacf ar = [1., -0.6] #ar = [1., 0.] ma = [1., 0.4] #ma = [1., 0.4, 0.6] #ma = [1., 0.] mod = ''#'ma2' x = arma_generate_sample(ar, ma, 5000) x_acf = acf(x)[:10] x_ir = arma_impulse_response(ar, ma) #print x_acf[:10] #print x_ir[:10] #irc2 = np.correlate(x_ir,x_ir,'full')[len(x_ir)-1:] #print irc2[:10] #print irc2[:10]/irc2[0] #print irc2[:10-1] / irc2[1:10] #print x_acf[:10-1] / x_acf[1:10] # detrend helper from matplotlib.mlab def detrend(x, key=None): if key is None or key=='constant': return detrend_mean(x) elif key=='linear': return detrend_linear(x) def demean(x, axis=0): "Return x minus its mean along the specified axis" x = np.asarray(x) if axis: ind = [slice(None)] * axis ind.append(np.newaxis) return x - x.mean(axis)[ind] return x - x.mean(axis) def detrend_mean(x): "Return x minus the mean(x)" return x - x.mean() def detrend_none(x): "Return x: no detrending" return x def detrend_linear(y): "Return y minus best fit line; 'linear' detrending " # This is faster than an algorithm based on linalg.lstsq. x = np.arange(len(y), dtype=np.float_) C = np.cov(x, y, bias=1) b = C[0,1]/C[0,0] a = y.mean() - b*x.mean() return y - (b*x + a) def acovf_explicit(ar, ma, nobs): '''add correlation of MA representation explicitely ''' ir = arma_impulse_response(ar, ma) acovfexpl = [np.dot(ir[:nobs-t], ir[t:nobs]) for t in range(10)] return acovfexpl def acovf_arma11(ar, ma): # ARMA(1,1) # Florens et al page 278 # wrong result ? # new calculation bigJudge p 311, now the same a = -ar[1] b = ma[1] #rho = [1.] #rho.append((1-a*b)*(a-b)/(1.+a**2-2*a*b)) rho = [(1.+b**2+2*a*b)/(1.-a**2)] rho.append((1+a*b)*(a+b)/(1.-a**2)) for _ in range(8): last = rho[-1] rho.append(a*last) return np.array(rho) # print acf11[:10] # print acf11[:10] /acf11[0] def acovf_ma2(ma): # MA(2) # from Greene p616 (with typo), Florens p280 b1 = -ma[1] b2 = -ma[2] rho = np.zeros(10) rho[0] = (1 + b1**2 + b2**2) rho[1] = (-b1 + b1*b2) rho[2] = -b2 return rho # rho2 = rho/rho[0] # print rho2 # print irc2[:10]/irc2[0] def acovf_ma1(ma): # MA(1) # from Greene p616 (with typo), Florens p280 b = -ma[1] rho = np.zeros(10) rho[0] = (1 + b**2) rho[1] = -b return rho # rho2 = rho/rho[0] # print rho2 # print irc2[:10]/irc2[0] ar1 = [1., -0.8] ar0 = [1., 0.] ma1 = [1., 0.4] ma2 = [1., 0.4, 0.6] ma0 = [1., 0.] comparefn = dict( [('ma1', acovf_ma1), ('ma2', acovf_ma2), ('arma11', acovf_arma11), ('ar1', acovf_arma11)]) cases = [('ma1', (ar0, ma1)), ('ma2', (ar0, ma2)), ('arma11', (ar1, ma1)), ('ar1', (ar1, ma0))] for c, args in cases: ar, ma = args print('') print(c, ar, ma) myacovf = arma_acovf(ar, ma, nobs=10) myacf = arma_acf(ar, ma, lags=10) if c[:2]=='ma': othacovf = comparefn[c](ma) else: othacovf = comparefn[c](ar, ma) print(myacovf[:5]) print(othacovf[:5]) #something broke again, #for high persistence case eg ar=0.99, nobs of IR has to be large #made changes to arma_acovf assert_array_almost_equal(myacovf, othacovf,10) assert_array_almost_equal(myacf, othacovf/othacovf[0],10) #from nitime.utils def ar_generator(N=512, sigma=1.): # this generates a signal u(n) = a1*u(n-1) + a2*u(n-2) + ... + v(n) # where v(n) is a stationary stochastic process with zero mean # and variance = sigma # this sequence is shown to be estimated well by an order 8 AR system taps = np.array([2.7607, -3.8106, 2.6535, -0.9238]) v = np.random.normal(size=N, scale=sigma**0.5) u = np.zeros(N) P = len(taps) for l in range(P): u[l] = v[l] + np.dot(u[:l][::-1], taps[:l]) for l in range(P,N): u[l] = v[l] + np.dot(u[l-P:l][::-1], taps) return u, v, taps #JP: small differences to using np.correlate, because assumes mean(s)=0 # denominator is N, not N-k, biased estimator # misnomer: (biased) autocovariance not autocorrelation #from nitime.utils def autocorr(s, axis=-1): """Returns the autocorrelation of signal s at all lags. Adheres to the definition r(k) = E{s(n)s*(n-k)} where E{} is the expectation operator. """ N = s.shape[axis] S = np.fft.fft(s, n=2*N-1, axis=axis) sxx = np.fft.ifft(S*S.conjugate(), axis=axis).real[:N] return sxx/N #JP: with valid this returns a single value, if x and y have same length # e.g. norm_corr(x, x) # using std subtracts mean, but correlate does not, requires means are exactly 0 # biased, no n-k correction for laglength #from nitime.utils def norm_corr(x,y,mode = 'valid'): """Returns the correlation between two ndarrays, by calling np.correlate in 'same' mode and normalizing the result by the std of the arrays and by their lengths. This results in a correlation = 1 for an auto-correlation""" return ( np.correlate(x,y,mode) / (np.std(x)*np.std(y)*(x.shape[-1])) ) # from matplotlib axes.py # note: self is axis def pltacorr(self, x, **kwargs): r""" call signature:: acorr(x, normed=True, detrend=detrend_none, usevlines=True, maxlags=10, **kwargs) Plot the autocorrelation of *x*. If *normed* = *True*, normalize the data by the autocorrelation at 0-th lag. *x* is detrended by the *detrend* callable (default no normalization). Data are plotted as ``plot(lags, c, **kwargs)`` Return value is a tuple (*lags*, *c*, *line*) where: - *lags* are a length 2*maxlags+1 lag vector - *c* is the 2*maxlags+1 auto correlation vector - *line* is a :class:`~matplotlib.lines.Line2D` instance returned by :meth:`plot` The default *linestyle* is None and the default *marker* is ``'o'``, though these can be overridden with keyword args. The cross correlation is performed with :func:`numpy.correlate` with *mode* = 2. If *usevlines* is *True*, :meth:`~matplotlib.axes.Axes.vlines` rather than :meth:`~matplotlib.axes.Axes.plot` is used to draw vertical lines from the origin to the acorr. Otherwise, the plot style is determined by the kwargs, which are :class:`~matplotlib.lines.Line2D` properties. *maxlags* is a positive integer detailing the number of lags to show. The default value of *None* will return all :math:`2 \mathrm{len}(x) - 1` lags. The return value is a tuple (*lags*, *c*, *linecol*, *b*) where - *linecol* is the :class:`~matplotlib.collections.LineCollection` - *b* is the *x*-axis. .. seealso:: :meth:`~matplotlib.axes.Axes.plot` or :meth:`~matplotlib.axes.Axes.vlines` For documentation on valid kwargs. **Example:** :func:`~matplotlib.pyplot.xcorr` above, and :func:`~matplotlib.pyplot.acorr` below. **Example:** .. plot:: mpl_examples/pylab_examples/xcorr_demo.py """ return self.xcorr(x, x, **kwargs) def pltxcorr(self, x, y, normed=True, detrend=detrend_none, usevlines=True, maxlags=10, **kwargs): """ call signature:: def xcorr(self, x, y, normed=True, detrend=detrend_none, usevlines=True, maxlags=10, **kwargs): Plot the cross correlation between *x* and *y*. If *normed* = *True*, normalize the data by the cross correlation at 0-th lag. *x* and y are detrended by the *detrend* callable (default no normalization). *x* and *y* must be equal length. Data are plotted as ``plot(lags, c, **kwargs)`` Return value is a tuple (*lags*, *c*, *line*) where: - *lags* are a length ``2*maxlags+1`` lag vector - *c* is the ``2*maxlags+1`` auto correlation vector - *line* is a :class:`~matplotlib.lines.Line2D` instance returned by :func:`~matplotlib.pyplot.plot`. The default *linestyle* is *None* and the default *marker* is 'o', though these can be overridden with keyword args. The cross correlation is performed with :func:`numpy.correlate` with *mode* = 2. If *usevlines* is *True*: :func:`~matplotlib.pyplot.vlines` rather than :func:`~matplotlib.pyplot.plot` is used to draw vertical lines from the origin to the xcorr. Otherwise the plotstyle is determined by the kwargs, which are :class:`~matplotlib.lines.Line2D` properties. The return value is a tuple (*lags*, *c*, *linecol*, *b*) where *linecol* is the :class:`matplotlib.collections.LineCollection` instance and *b* is the *x*-axis. *maxlags* is a positive integer detailing the number of lags to show. The default value of *None* will return all ``(2*len(x)-1)`` lags. **Example:** :func:`~matplotlib.pyplot.xcorr` above, and :func:`~matplotlib.pyplot.acorr` below. **Example:** .. plot:: mpl_examples/pylab_examples/xcorr_demo.py """ Nx = len(x) if Nx!=len(y): raise ValueError('x and y must be equal length') x = detrend(np.asarray(x)) y = detrend(np.asarray(y)) c = np.correlate(x, y, mode=2) if normed: c /= np.sqrt(np.dot(x, x) * np.dot(y, y)) if maxlags is None: maxlags = Nx - 1 if maxlags >= Nx or maxlags < 1: raise ValueError('maxlags must be None or strictly ' 'positive < %d' % Nx) lags = np.arange(-maxlags,maxlags+1) c = c[Nx-1-maxlags:Nx+maxlags] if usevlines: a = self.vlines(lags, [0], c, **kwargs) b = self.axhline(**kwargs) kwargs.setdefault('marker', 'o') kwargs.setdefault('linestyle', 'None') d = self.plot(lags, c, **kwargs) else: kwargs.setdefault('marker', 'o') kwargs.setdefault('linestyle', 'None') a, = self.plot(lags, c, **kwargs) b = None return lags, c, a, b arrvs = ar_generator() ##arma = ARIMA() ##res = arma.fit(arrvs[0], 4, 0) arma = ARIMA(arrvs[0]) res = arma.fit((4,0, 0)) print(res[0]) acf1 = acf(arrvs[0]) acovf1b = acovf(arrvs[0], unbiased=False) acf2 = autocorr(arrvs[0]) acf2m = autocorr(arrvs[0]-arrvs[0].mean()) print(acf1[:10]) print(acovf1b[:10]) print(acf2[:10]) print(acf2m[:10]) x = arma_generate_sample([1.0, -0.8], [1.0], 500) print(acf(x)[:20]) print(sm.regression.yule_walker(x, 10)) #ax = plt.axes() plt.plot(x) #plt.show() plt.figure() pltxcorr(plt,x,x) plt.figure() pltxcorr(plt,x,x, usevlines=False) plt.figure() #FIXME: plotacf was moved to graphics/tsaplots.py, and interface changed plotacf(plt, acf1[:20], np.arange(len(acf1[:20])), usevlines=True) plt.figure() ax = plt.subplot(211) plotacf(ax, acf1[:20], usevlines=True) ax = plt.subplot(212) plotacf(ax, acf1[:20], np.arange(len(acf1[:20])), usevlines=False) #plt.show() statsmodels-0.12.2/statsmodels/sandbox/tsa/examples/000077500000000000000000000000001400612667500225525ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/sandbox/tsa/examples/ex_mle_arma.py000066400000000000000000000105301400612667500253740ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ TODO: broken because of changes to arguments and import paths fixing this needs a closer look Created on Thu Feb 11 23:41:53 2010 Author: josef-pktd copyright: Simplified BSD see license.txt """ import numpy as np import numdifftools as ndt from statsmodels.sandbox import tsa from statsmodels.tsa.arma_mle import Arma # local import from statsmodels.tsa.arima_process import arma_generate_sample examples = ['arma'] if 'arma' in examples: print("\nExample 1") print('----------') ar = [1.0, -0.8] ma = [1.0, 0.5] y1 = arma_generate_sample(ar,ma,1000,0.1) y1 -= y1.mean() #no mean correction/constant in estimation so far arma1 = Arma(y1) arma1.nar = 1 arma1.nma = 1 arma1res = arma1.fit_mle(order=(1,1), method='fmin') print(arma1res.params) #Warning need new instance otherwise results carry over arma2 = Arma(y1) arma2.nar = 1 arma2.nma = 1 res2 = arma2.fit(method='bfgs') print(res2.params) print(res2.model.hessian(res2.params)) print(ndt.Hessian(arma1.loglike, stepMax=1e-2)(res2.params)) arest = tsa.arima.ARIMA(y1) resls = arest.fit((1,0,1)) print(resls[0]) print(resls[1]) print('\nparameter estimate - comparing methods') print('---------------------------------------') print('parameter of DGP ar(1), ma(1), sigma_error') print([-0.8, 0.5, 0.1]) print('mle with fmin') print(arma1res.params) print('mle with bfgs') print(res2.params) print('cond. least squares uses optim.leastsq ?') errls = arest.error_estimate print(resls[0], np.sqrt(np.dot(errls,errls)/errls.shape[0])) err = arma1.geterrors(res2.params) print('cond least squares parameter cov') #print(np.dot(err,err)/err.shape[0] * resls[1]) #errls = arest.error_estimate print(np.dot(errls,errls)/errls.shape[0] * resls[1]) # print('fmin hessian') # print(arma1res.model.optimresults['Hopt'][:2,:2]) print('bfgs hessian') print(res2.model.optimresults['Hopt'][:2,:2]) print('numdifftools inverse hessian') print(-np.linalg.inv(ndt.Hessian(arma1.loglike, stepMax=1e-2)(res2.params))[:2,:2]) print('\nFitting Arma(1,1) to squared data') arma3 = Arma(y1**2) res3 = arma3.fit(method='bfgs') print(res3.params) print('\nFitting Arma(3,3) to data from DGP Arma(1,1)') arma4 = Arma(y1) arma4.nar = 3 arma4.nma = 3 #res4 = arma4.fit(method='bfgs') res4 = arma4.fit(start_params=[-0.5, -0.1,-0.1,0.2,0.1,0.1,0.5]) print(res4.params) print('numdifftools inverse hessian') pcov = -np.linalg.inv(ndt.Hessian(arma4.loglike, stepMax=1e-2)(res4.params)) #print(pcov) print('standard error of parameter estimate from Hessian') pstd = np.sqrt(np.diag(pcov)) print(pstd) print('t-values') print(res4.params/pstd) print('eigenvalues of pcov:') print(np.linalg.eigh(pcov)[0]) print('sometimes they are negative') print("\nExample 2 - DGP is Arma(3,3)") print('-----------------------------') ar = [1.0, -0.6, -0.2, -0.1] ma = [1.0, 0.5, 0.1, 0.1] y2 = arest.generate_sample(ar,ma,1000,0.1) y2 -= y2.mean() #no mean correction/constant in estimation so far print('\nFitting Arma(3,3) to data from DGP Arma(3,3)') arma4 = Arma(y2) arma4.nar = 3 arma4.nma = 3 #res4 = arma4.fit(method='bfgs') print('\ntrue parameters') print('ar', ar[1:]) print('ma', ma[1:]) res4 = arma4.fit(start_params=[-0.5, -0.1,-0.1,0.2,0.1,0.1,0.5]) print(res4.params) print('numdifftools inverse hessian') pcov = -np.linalg.inv(ndt.Hessian(arma4.loglike, stepMax=1e-2)(res4.params)) #print(pcov) print('standard error of parameter estimate from Hessian') pstd = np.sqrt(np.diag(pcov)) print(pstd) print('t-values') print(res4.params/pstd) print('eigenvalues of pcov:') print(np.linalg.eigh(pcov)[0]) print('sometimes they are negative') arma6 = Arma(y2) arma6.nar = 3 arma6.nma = 3 res6 = arma6.fit(start_params=[-0.5, -0.1,-0.1,0.2,0.1,0.1,0.5], method='bfgs') print('\nmle with bfgs') print(res6.params) print('pstd with bfgs hessian') hopt = res6.model.optimresults['Hopt'] print(np.sqrt(np.diag(hopt))) #fmin estimates for coefficients in ARMA(3,3) look good #but not inverse Hessian, sometimes negative values for variance statsmodels-0.12.2/statsmodels/sandbox/tsa/examples/example_var.py000066400000000000000000000022541400612667500254320ustar00rootroot00000000000000""" Look at some macro plots, then do some VARs and IRFs. """ import numpy as np import statsmodels.api as sm import scikits.timeseries as ts import scikits.timeseries.lib.plotlib as tplt data = sm.datasets.macrodata.load(as_pandas=False) data = data.data ### Create Timeseries Representations of a few vars dates = ts.date_array(start_date=ts.Date('Q', year=1959, quarter=1), end_date=ts.Date('Q', year=2009, quarter=3)) ts_data = data[['realgdp','realcons','cpi']].view(float).reshape(-1,3) ts_data = np.column_stack((ts_data, (1 - data['unemp']/100) * data['pop'])) ts_series = ts.time_series(ts_data, dates) fig = tplt.tsfigure() fsp = fig.add_tsplot(221) fsp.tsplot(ts_series[:,0],'-') fsp.set_title("Real GDP") fsp = fig.add_tsplot(222) fsp.tsplot(ts_series[:,1],'r-') fsp.set_title("Real Consumption") fsp = fig.add_tsplot(223) fsp.tsplot(ts_series[:,2],'g-') fsp.set_title("CPI") fsp = fig.add_tsplot(224) fsp.tsplot(ts_series[:,3],'y-') fsp.set_title("Employment") # Plot real GDP #plt.subplot(221) #plt.plot(data['realgdp']) #plt.title("Real GDP") # Plot employment #plt.subplot(222) # Plot cpi #plt.subplot(223) # Plot real consumption #plt.subplot(224) #plt.show() statsmodels-0.12.2/statsmodels/sandbox/tsa/examples/try_ld_nitime.py000066400000000000000000000005461400612667500257730ustar00rootroot00000000000000'''Levinson Durbin recursion adjusted from nitime ''' import numpy as np import nitime.utils as ut import statsmodels.api as sm sxx=None order = 10 npts = 2048*10 sigma = 1 drop_transients = 1024 coefs = np.array([0.9, -0.5]) # Generate AR(2) time series X, v, _ = ut.ar_generator(npts, sigma, coefs, drop_transients) s = X sm.tsa.stattools.pacf(X) statsmodels-0.12.2/statsmodels/sandbox/tsa/fftarma.py000066400000000000000000000376611400612667500227430ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Mon Dec 14 19:53:25 2009 Author: josef-pktd generate arma sample using fft with all the lfilter it looks slow to get the ma representation first apply arma filter (in ar representation) to time series to get white noise but seems slow to be useful for fast estimation for nobs=10000 change/check: instead of using marep, use fft-transform of ar and ma separately, use ratio check theory is correct and example works DONE : feels much faster than lfilter -> use for estimation of ARMA -> use pade (scipy.interpolate) approximation to get starting polynomial from autocorrelation (is autocorrelation of AR(p) related to marep?) check if pade is fast, not for larger arrays ? maybe pade does not do the right thing for this, not tried yet scipy.pade([ 1. , 0.6, 0.25, 0.125, 0.0625, 0.1],2) raises LinAlgError: singular matrix also does not have roots inside unit circle ?? -> even without initialization, it might be fast for estimation -> how do I enforce stationarity and invertibility, need helper function get function drop imag if close to zero from numpy/scipy source, where? """ import numpy as np import numpy.fft as fft #import scipy.fftpack as fft from scipy import signal #from try_var_convolve import maxabs from statsmodels.tsa.arima_process import ArmaProcess #trying to convert old experiments to a class class ArmaFft(ArmaProcess): '''fft tools for arma processes This class contains several methods that are providing the same or similar returns to try out and test different implementations. Notes ----- TODO: check whether we do not want to fix maxlags, and create new instance if maxlag changes. usage for different lengths of timeseries ? or fix frequency and length for fft check default frequencies w, terminology norw n_or_w some ffts are currently done without padding with zeros returns for spectral density methods needs checking, is it always the power spectrum hw*hw.conj() normalization of the power spectrum, spectral density: not checked yet, for example no variance of underlying process is used ''' def __init__(self, ar, ma, n): #duplicates now that are subclassing ArmaProcess super(ArmaFft, self).__init__(ar, ma) self.ar = np.asarray(ar) self.ma = np.asarray(ma) self.nobs = n #could make the polynomials into cached attributes self.arpoly = np.polynomial.Polynomial(ar) self.mapoly = np.polynomial.Polynomial(ma) self.nar = len(ar) #1d only currently self.nma = len(ma) def padarr(self, arr, maxlag, atend=True): '''pad 1d array with zeros at end to have length maxlag function that is a method, no self used Parameters ---------- arr : array_like, 1d array that will be padded with zeros maxlag : int length of array after padding atend : bool If True (default), then the zeros are added to the end, otherwise to the front of the array Returns ------- arrp : ndarray zero-padded array Notes ----- This is mainly written to extend coefficient arrays for the lag-polynomials. It returns a copy. ''' if atend: return np.r_[arr, np.zeros(maxlag-len(arr))] else: return np.r_[np.zeros(maxlag-len(arr)), arr] def pad(self, maxlag): '''construct AR and MA polynomials that are zero-padded to a common length Parameters ---------- maxlag : int new length of lag-polynomials Returns ------- ar : ndarray extended AR polynomial coefficients ma : ndarray extended AR polynomial coefficients ''' arpad = np.r_[self.ar, np.zeros(maxlag-self.nar)] mapad = np.r_[self.ma, np.zeros(maxlag-self.nma)] return arpad, mapad def fftar(self, n=None): '''Fourier transform of AR polynomial, zero-padded at end to n Parameters ---------- n : int length of array after zero-padding Returns ------- fftar : ndarray fft of zero-padded ar polynomial ''' if n is None: n = len(self.ar) return fft.fft(self.padarr(self.ar, n)) def fftma(self, n): '''Fourier transform of MA polynomial, zero-padded at end to n Parameters ---------- n : int length of array after zero-padding Returns ------- fftar : ndarray fft of zero-padded ar polynomial ''' if n is None: n = len(self.ar) return fft.fft(self.padarr(self.ma, n)) def fftarma(self, n=None): '''Fourier transform of ARMA polynomial, zero-padded at end to n The Fourier transform of the ARMA process is calculated as the ratio of the fft of the MA polynomial divided by the fft of the AR polynomial. Parameters ---------- n : int length of array after zero-padding Returns ------- fftarma : ndarray fft of zero-padded arma polynomial ''' if n is None: n = self.nobs return (self.fftma(n) / self.fftar(n)) def spd(self, npos): '''raw spectral density, returns Fourier transform n is number of points in positive spectrum, the actual number of points is twice as large. different from other spd methods with fft ''' n = npos w = fft.fftfreq(2*n) * 2 * np.pi hw = self.fftarma(2*n) #not sure, need to check normalization #return (hw*hw.conj()).real[n//2-1:] * 0.5 / np.pi #does not show in plot return (hw*hw.conj()).real * 0.5 / np.pi, w def spdshift(self, n): '''power spectral density using fftshift currently returns two-sided according to fft frequencies, use first half ''' #size = s1+s2-1 mapadded = self.padarr(self.ma, n) arpadded = self.padarr(self.ar, n) hw = fft.fft(fft.fftshift(mapadded)) / fft.fft(fft.fftshift(arpadded)) #return np.abs(spd)[n//2-1:] w = fft.fftfreq(n) * 2 * np.pi wslice = slice(n//2-1, None, None) #return (hw*hw.conj()).real[wslice], w[wslice] return (hw*hw.conj()).real, w def spddirect(self, n): '''power spectral density using padding to length n done by fft currently returns two-sided according to fft frequencies, use first half ''' #size = s1+s2-1 #abs looks wrong hw = fft.fft(self.ma, n) / fft.fft(self.ar, n) w = fft.fftfreq(n) * 2 * np.pi wslice = slice(None, n//2, None) #return (np.abs(hw)**2)[wslice], w[wslice] return (np.abs(hw)**2) * 0.5/np.pi, w def _spddirect2(self, n): '''this looks bad, maybe with an fftshift ''' #size = s1+s2-1 hw = (fft.fft(np.r_[self.ma[::-1],self.ma], n) / fft.fft(np.r_[self.ar[::-1],self.ar], n)) return (hw*hw.conj()) #.real[n//2-1:] def spdroots(self, w): '''spectral density for frequency using polynomial roots builds two arrays (number of roots, number of frequencies) ''' return self._spdroots(self.arroots, self.maroots, w) def _spdroots(self, arroots, maroots, w): '''spectral density for frequency using polynomial roots builds two arrays (number of roots, number of frequencies) Parameters ---------- arroots : ndarray roots of ar (denominator) lag-polynomial maroots : ndarray roots of ma (numerator) lag-polynomial w : array_like frequencies for which spd is calculated Notes ----- this should go into a function ''' w = np.atleast_2d(w).T cosw = np.cos(w) #Greene 5th edt. p626, section 20.2.7.a. maroots = 1./maroots arroots = 1./arroots num = 1 + maroots**2 - 2* maroots * cosw den = 1 + arroots**2 - 2* arroots * cosw #print 'num.shape, den.shape', num.shape, den.shape hw = 0.5 / np.pi * num.prod(-1) / den.prod(-1) #or use expsumlog return np.squeeze(hw), w.squeeze() def spdpoly(self, w, nma=50): '''spectral density from MA polynomial representation for ARMA process References ---------- Cochrane, section 8.3.3 ''' mpoly = np.polynomial.Polynomial(self.arma2ma(nma)) hw = mpoly(np.exp(1j * w)) spd = np.real_if_close(hw * hw.conj() * 0.5/np.pi) return spd, w def filter(self, x): ''' filter a timeseries with the ARMA filter padding with zero is missing, in example I needed the padding to get initial conditions identical to direct filter Initial filtered observations differ from filter2 and signal.lfilter, but at end they are the same. See Also -------- tsa.filters.fftconvolve ''' n = x.shape[0] if n == self.fftarma: fftarma = self.fftarma else: fftarma = self.fftma(n) / self.fftar(n) tmpfft = fftarma * fft.fft(x) return fft.ifft(tmpfft) def filter2(self, x, pad=0): '''filter a time series using fftconvolve3 with ARMA filter padding of x currently works only if x is 1d in example it produces same observations at beginning as lfilter even without padding. TODO: this returns 1 additional observation at the end ''' from statsmodels.tsa.filters import fftconvolve3 if not pad: pass elif pad == 'auto': #just guessing how much padding x = self.padarr(x, x.shape[0] + 2*(self.nma+self.nar), atend=False) else: x = self.padarr(x, x.shape[0] + int(pad), atend=False) return fftconvolve3(x, self.ma, self.ar) def acf2spdfreq(self, acovf, nfreq=100, w=None): ''' not really a method just for comparison, not efficient for large n or long acf this is also similarly use in tsa.stattools.periodogram with window ''' if w is None: w = np.linspace(0, np.pi, nfreq)[:, None] nac = len(acovf) hw = 0.5 / np.pi * (acovf[0] + 2 * (acovf[1:] * np.cos(w*np.arange(1,nac))).sum(1)) return hw def invpowerspd(self, n): '''autocovariance from spectral density scaling is correct, but n needs to be large for numerical accuracy maybe padding with zero in fft would be faster without slicing it returns 2-sided autocovariance with fftshift >>> ArmaFft([1, -0.5], [1., 0.4], 40).invpowerspd(2**8)[:10] array([ 2.08 , 1.44 , 0.72 , 0.36 , 0.18 , 0.09 , 0.045 , 0.0225 , 0.01125 , 0.005625]) >>> ArmaFft([1, -0.5], [1., 0.4], 40).acovf(10) array([ 2.08 , 1.44 , 0.72 , 0.36 , 0.18 , 0.09 , 0.045 , 0.0225 , 0.01125 , 0.005625]) ''' hw = self.fftarma(n) return np.real_if_close(fft.ifft(hw*hw.conj()), tol=200)[:n] def spdmapoly(self, w, twosided=False): '''ma only, need division for ar, use LagPolynomial ''' if w is None: w = np.linspace(0, np.pi, nfreq) return 0.5 / np.pi * self.mapoly(np.exp(w*1j)) def plot4(self, fig=None, nobs=100, nacf=20, nfreq=100): """Plot results""" rvs = self.generate_sample(nsample=100, burnin=500) acf = self.acf(nacf)[:nacf] #TODO: check return length pacf = self.pacf(nacf) w = np.linspace(0, np.pi, nfreq) spdr, wr = self.spdroots(w) if fig is None: import matplotlib.pyplot as plt fig = plt.figure() ax = fig.add_subplot(2,2,1) ax.plot(rvs) ax.set_title('Random Sample \nar=%s, ma=%s' % (self.ar, self.ma)) ax = fig.add_subplot(2,2,2) ax.plot(acf) ax.set_title('Autocorrelation \nar=%s, ma=%rs' % (self.ar, self.ma)) ax = fig.add_subplot(2,2,3) ax.plot(wr, spdr) ax.set_title('Power Spectrum \nar=%s, ma=%s' % (self.ar, self.ma)) ax = fig.add_subplot(2,2,4) ax.plot(pacf) ax.set_title('Partial Autocorrelation \nar=%s, ma=%s' % (self.ar, self.ma)) return fig def spdar1(ar, w): if np.ndim(ar) == 0: rho = ar else: rho = -ar[1] return 0.5 / np.pi /(1 + rho*rho - 2 * rho * np.cos(w)) if __name__ == '__main__': def maxabs(x,y): return np.max(np.abs(x-y)) nobs = 200 #10000 ar = [1, 0.0] ma = [1, 0.0] ar2 = np.zeros(nobs) ar2[:2] = [1, -0.9] uni = np.zeros(nobs) uni[0]=1. #arrep = signal.lfilter(ma, ar, ar2) #marep = signal.lfilter([1],arrep, uni) # same faster: arcomb = np.convolve(ar, ar2, mode='same') marep = signal.lfilter(ma,arcomb, uni) #[len(ma):] print(marep[:10]) mafr = fft.fft(marep) rvs = np.random.normal(size=nobs) datafr = fft.fft(rvs) y = fft.ifft(mafr*datafr) print(np.corrcoef(np.c_[y[2:], y[1:-1], y[:-2]],rowvar=0)) arrep = signal.lfilter([1],marep, uni) print(arrep[:20]) # roundtrip to ar arfr = fft.fft(arrep) yfr = fft.fft(y) x = fft.ifft(arfr*yfr).real #imag part is e-15 # the next two are equal, roundtrip works print(x[:5]) print(rvs[:5]) print(np.corrcoef(np.c_[x[2:], x[1:-1], x[:-2]],rowvar=0)) # ARMA filter using fft with ratio of fft of ma/ar lag polynomial # seems much faster than using lfilter #padding, note arcomb is already full length arcombp = np.zeros(nobs) arcombp[:len(arcomb)] = arcomb map_ = np.zeros(nobs) #rename: map was shadowing builtin map_[:len(ma)] = ma ar0fr = fft.fft(arcombp) ma0fr = fft.fft(map_) y2 = fft.ifft(ma0fr/ar0fr*datafr) #the next two are (almost) equal in real part, almost zero but different in imag print(y2[:10]) print(y[:10]) print(maxabs(y, y2)) # from chfdiscrete #1.1282071239631782e-014 ar = [1, -0.4] ma = [1, 0.2] arma1 = ArmaFft([1, -0.5,0,0,0,00, -0.7, 0.3], [1, 0.8], nobs) nfreq = nobs w = np.linspace(0, np.pi, nfreq) w2 = np.linspace(0, 2*np.pi, nfreq) import matplotlib.pyplot as plt plt.close('all') plt.figure() spd1, w1 = arma1.spd(2**10) print(spd1.shape) _ = plt.plot(spd1) plt.title('spd fft complex') plt.figure() spd2, w2 = arma1.spdshift(2**10) print(spd2.shape) _ = plt.plot(w2, spd2) plt.title('spd fft shift') plt.figure() spd3, w3 = arma1.spddirect(2**10) print(spd3.shape) _ = plt.plot(w3, spd3) plt.title('spd fft direct') plt.figure() spd3b = arma1._spddirect2(2**10) print(spd3b.shape) _ = plt.plot(spd3b) plt.title('spd fft direct mirrored') plt.figure() spdr, wr = arma1.spdroots(w) print(spdr.shape) plt.plot(w, spdr) plt.title('spd from roots') plt.figure() spdar1_ = spdar1(arma1.ar, w) print(spdar1_.shape) _ = plt.plot(w, spdar1_) plt.title('spd ar1') plt.figure() wper, spdper = arma1.periodogram(nfreq) print(spdper.shape) _ = plt.plot(w, spdper) plt.title('periodogram') startup = 1000 rvs = arma1.generate_sample(startup+10000)[startup:] import matplotlib.mlab as mlb plt.figure() sdm, wm = mlb.psd(x) print('sdm.shape', sdm.shape) sdm = sdm.ravel() plt.plot(wm, sdm) plt.title('matplotlib') from nitime.algorithms import LD_AR_est #yule_AR_est(s, order, Nfreqs) wnt, spdnt = LD_AR_est(rvs, 10, 512) plt.figure() print('spdnt.shape', spdnt.shape) _ = plt.plot(spdnt.ravel()) print(spdnt[:10]) plt.title('nitime') fig = plt.figure() arma1.plot4(fig) #plt.show() statsmodels-0.12.2/statsmodels/sandbox/tsa/movstat.py000066400000000000000000000347321400612667500230140ustar00rootroot00000000000000'''using scipy signal and numpy correlate to calculate some time series statistics original developer notes see also scikits.timeseries (movstat is partially inspired by it) added 2009-08-29 timeseries moving stats are in c, autocorrelation similar to here I thought I saw moving stats somewhere in python, maybe not) TODO moving statistics - filters do not handle boundary conditions nicely (correctly ?) e.g. minimum order filter uses 0 for out of bounds value -> append and prepend with last resp. first value - enhance for nd arrays, with axis = 0 Note: Equivalence for 1D signals >>> np.all(signal.correlate(x,[1,1,1],'valid')==np.correlate(x,[1,1,1])) True >>> np.all(ndimage.filters.correlate(x,[1,1,1], origin = -1)[:-3+1]==np.correlate(x,[1,1,1])) True # multidimensional, but, it looks like it uses common filter across time series, no VAR ndimage.filters.correlate(np.vstack([x,x]),np.array([[1,1,1],[0,0,0]]), origin = 1) ndimage.filters.correlate(x,[1,1,1],origin = 1)) ndimage.filters.correlate(np.vstack([x,x]),np.array([[0.5,0.5,0.5],[0.5,0.5,0.5]]), \ origin = 1) >>> np.all(ndimage.filters.correlate(np.vstack([x,x]),np.array([[1,1,1],[0,0,0]]), origin = 1)[0]==\ ndimage.filters.correlate(x,[1,1,1],origin = 1)) True >>> np.all(ndimage.filters.correlate(np.vstack([x,x]),np.array([[0.5,0.5,0.5],[0.5,0.5,0.5]]), \ origin = 1)[0]==ndimage.filters.correlate(x,[1,1,1],origin = 1)) update 2009-09-06: cosmetic changes, rearrangements ''' import numpy as np from scipy import signal from numpy.testing import assert_array_equal, assert_array_almost_equal def expandarr(x,k): #make it work for 2D or nD with axis kadd = k if np.ndim(x) == 2: kadd = (kadd, np.shape(x)[1]) return np.r_[np.ones(kadd)*x[0],x,np.ones(kadd)*x[-1]] def movorder(x, order = 'med', windsize=3, lag='lagged'): '''moving order statistics Parameters ---------- x : ndarray time series data order : float or 'med', 'min', 'max' which order statistic to calculate windsize : int window size lag : 'lagged', 'centered', or 'leading' location of window relative to current position Returns ------- filtered array ''' #if windsize is even should it raise ValueError if lag == 'lagged': lead = windsize//2 elif lag == 'centered': lead = 0 elif lag == 'leading': lead = -windsize//2 +1 else: raise ValueError if np.isfinite(order): #if np.isnumber(order): ord = order # note: ord is a builtin function elif order == 'med': ord = (windsize - 1)/2 elif order == 'min': ord = 0 elif order == 'max': ord = windsize - 1 else: raise ValueError #return signal.order_filter(x,np.ones(windsize),ord)[:-lead] xext = expandarr(x, windsize) #np.r_[np.ones(windsize)*x[0],x,np.ones(windsize)*x[-1]] return signal.order_filter(xext,np.ones(windsize),ord)[windsize-lead:-(windsize+lead)] def check_movorder(): '''graphical test for movorder''' import matplotlib.pylab as plt x = np.arange(1,10) xo = movorder(x, order='max') assert_array_equal(xo, x) x = np.arange(10,1,-1) xo = movorder(x, order='min') assert_array_equal(xo, x) assert_array_equal(movorder(x, order='min', lag='centered')[:-1], x[1:]) tt = np.linspace(0,2*np.pi,15) x = np.sin(tt) + 1 xo = movorder(x, order='max') plt.figure() plt.plot(tt,x,'.-',tt,xo,'.-') plt.title('moving max lagged') xo = movorder(x, order='max', lag='centered') plt.figure() plt.plot(tt,x,'.-',tt,xo,'.-') plt.title('moving max centered') xo = movorder(x, order='max', lag='leading') plt.figure() plt.plot(tt,x,'.-',tt,xo,'.-') plt.title('moving max leading') # identity filter ##>>> signal.order_filter(x,np.ones(1),0) ##array([ 1., 2., 3., 4., 5., 6., 7., 8., 9.]) # median filter ##signal.medfilt(np.sin(x), kernel_size=3) ##>>> plt.figure() ## ##>>> x=np.linspace(0,3,100);plt.plot(x,np.sin(x),x,signal.medfilt(np.sin(x), kernel_size=3)) # remove old version ##def movmeanvar(x, windowsize=3, valid='same'): ## ''' ## this should also work along axis or at least for columns ## ''' ## n = x.shape[0] ## x = expandarr(x, windowsize - 1) ## takeslice = slice(windowsize-1, n + windowsize-1) ## avgkern = (np.ones(windowsize)/float(windowsize)) ## m = np.correlate(x, avgkern, 'same')#[takeslice] ## print(m.shape) ## print(x.shape) ## xm = x - m ## v = np.correlate(x*x, avgkern, 'same') - m**2 ## v1 = np.correlate(xm*xm, avgkern, valid) #not correct for var of window ###>>> np.correlate(xm*xm,np.array([1,1,1])/3.0,'valid')-np.correlate(xm*xm,np.array([1,1,1])/3.0,'valid')**2 ## return m[takeslice], v[takeslice], v1 def movmean(x, windowsize=3, lag='lagged'): '''moving window mean Parameters ---------- x : ndarray time series data windsize : int window size lag : 'lagged', 'centered', or 'leading' location of window relative to current position Returns ------- mk : ndarray moving mean, with same shape as x Notes ----- for leading and lagging the data array x is extended by the closest value of the array ''' return movmoment(x, 1, windowsize=windowsize, lag=lag) def movvar(x, windowsize=3, lag='lagged'): '''moving window variance Parameters ---------- x : ndarray time series data windsize : int window size lag : 'lagged', 'centered', or 'leading' location of window relative to current position Returns ------- mk : ndarray moving variance, with same shape as x ''' m1 = movmoment(x, 1, windowsize=windowsize, lag=lag) m2 = movmoment(x, 2, windowsize=windowsize, lag=lag) return m2 - m1*m1 def movmoment(x, k, windowsize=3, lag='lagged'): '''non-central moment Parameters ---------- x : ndarray time series data windsize : int window size lag : 'lagged', 'centered', or 'leading' location of window relative to current position Returns ------- mk : ndarray k-th moving non-central moment, with same shape as x Notes ----- If data x is 2d, then moving moment is calculated for each column. ''' windsize = windowsize #if windsize is even should it raise ValueError if lag == 'lagged': #lead = -0 + windsize #windsize//2 lead = -0# + (windsize-1) + windsize//2 sl = slice((windsize-1) or None, -2*(windsize-1) or None) elif lag == 'centered': lead = -windsize//2 #0#-1 #+ #(windsize-1) sl = slice((windsize-1)+windsize//2 or None, -(windsize-1)-windsize//2 or None) elif lag == 'leading': #lead = -windsize +1#+1 #+ (windsize-1)#//2 +1 lead = -windsize +2 #-windsize//2 +1 sl = slice(2*(windsize-1)+1+lead or None, -(2*(windsize-1)+lead)+1 or None) else: raise ValueError avgkern = (np.ones(windowsize)/float(windowsize)) xext = expandarr(x, windsize-1) #Note: expandarr increases the array size by 2*(windsize-1) #sl = slice(2*(windsize-1)+1+lead or None, -(2*(windsize-1)+lead)+1 or None) print(sl) if xext.ndim == 1: return np.correlate(xext**k, avgkern, 'full')[sl] #return np.correlate(xext**k, avgkern, 'same')[windsize-lead:-(windsize+lead)] else: print(xext.shape) print(avgkern[:,None].shape) # try first with 2d along columns, possibly ndim with axis return signal.correlate(xext**k, avgkern[:,None], 'full')[sl,:] #x=0.5**np.arange(10);xm=x-x.mean();a=np.correlate(xm,[1],'full') #x=0.5**np.arange(3);np.correlate(x,x,'same') ##>>> x=0.5**np.arange(10);xm=x-x.mean();a=np.correlate(xm,xo,'full') ## ##>>> xo=np.ones(10);d=np.correlate(xo,xo,'full') ##>>> xo ##xo=np.ones(10);d=np.correlate(xo,xo,'full') ##>>> x=np.ones(10);xo=x-x.mean();a=np.correlate(xo,xo,'full') ##>>> xo=np.ones(10);d=np.correlate(xo,xo,'full') ##>>> d ##array([ 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 9., ## 8., 7., 6., 5., 4., 3., 2., 1.]) ##def ccovf(): ## pass ## #x=0.5**np.arange(10);xm=x-x.mean();a=np.correlate(xm,xo,'full') __all__ = ['movorder', 'movmean', 'movvar', 'movmoment'] if __name__ == '__main__': print('\ncheckin moving mean and variance') nobs = 10 x = np.arange(nobs) ws = 3 ave = np.array([ 0., 1/3., 1., 2., 3., 4., 5., 6., 7., 8., 26/3., 9]) va = np.array([[ 0. , 0. ], [ 0.22222222, 0.88888889], [ 0.66666667, 2.66666667], [ 0.66666667, 2.66666667], [ 0.66666667, 2.66666667], [ 0.66666667, 2.66666667], [ 0.66666667, 2.66666667], [ 0.66666667, 2.66666667], [ 0.66666667, 2.66666667], [ 0.66666667, 2.66666667], [ 0.22222222, 0.88888889], [ 0. , 0. ]]) ave2d = np.c_[ave, 2*ave] print(movmean(x, windowsize=ws, lag='lagged')) print(movvar(x, windowsize=ws, lag='lagged')) print([np.var(x[i-ws:i]) for i in range(ws, nobs)]) m1 = movmoment(x, 1, windowsize=3, lag='lagged') m2 = movmoment(x, 2, windowsize=3, lag='lagged') print(m1) print(m2) print(m2 - m1*m1) # this implicitly also tests moment assert_array_almost_equal(va[ws-1:,0], movvar(x, windowsize=3, lag='leading')) assert_array_almost_equal(va[ws//2:-ws//2+1,0], movvar(x, windowsize=3, lag='centered')) assert_array_almost_equal(va[:-ws+1,0], movvar(x, windowsize=ws, lag='lagged')) print('\nchecking moving moment for 2d (columns only)') x2d = np.c_[x, 2*x] print(movmoment(x2d, 1, windowsize=3, lag='centered')) print(movmean(x2d, windowsize=ws, lag='lagged')) print(movvar(x2d, windowsize=ws, lag='lagged')) assert_array_almost_equal(va[ws-1:,:], movvar(x2d, windowsize=3, lag='leading')) assert_array_almost_equal(va[ws//2:-ws//2+1,:], movvar(x2d, windowsize=3, lag='centered')) assert_array_almost_equal(va[:-ws+1,:], movvar(x2d, windowsize=ws, lag='lagged')) assert_array_almost_equal(ave2d[ws-1:], movmoment(x2d, 1, windowsize=3, lag='leading')) assert_array_almost_equal(ave2d[ws//2:-ws//2+1], movmoment(x2d, 1, windowsize=3, lag='centered')) assert_array_almost_equal(ave2d[:-ws+1], movmean(x2d, windowsize=ws, lag='lagged')) from scipy import ndimage print(ndimage.filters.correlate1d(x2d, np.array([1,1,1])/3., axis=0)) #regression test check xg = np.array([ 0. , 0.1, 0.3, 0.6, 1. , 1.5, 2.1, 2.8, 3.6, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5, 10.5, 11.5, 12.5, 13.5, 14.5, 15.5, 16.5, 17.5, 18.5, 19.5, 20.5, 21.5, 22.5, 23.5, 24.5, 25.5, 26.5, 27.5, 28.5, 29.5, 30.5, 31.5, 32.5, 33.5, 34.5, 35.5, 36.5, 37.5, 38.5, 39.5, 40.5, 41.5, 42.5, 43.5, 44.5, 45.5, 46.5, 47.5, 48.5, 49.5, 50.5, 51.5, 52.5, 53.5, 54.5, 55.5, 56.5, 57.5, 58.5, 59.5, 60.5, 61.5, 62.5, 63.5, 64.5, 65.5, 66.5, 67.5, 68.5, 69.5, 70.5, 71.5, 72.5, 73.5, 74.5, 75.5, 76.5, 77.5, 78.5, 79.5, 80.5, 81.5, 82.5, 83.5, 84.5, 85.5, 86.5, 87.5, 88.5, 89.5, 90.5, 91.5, 92.5, 93.5, 94.5]) assert_array_almost_equal(xg, movmean(np.arange(100), 10,'lagged')) xd = np.array([ 0.3, 0.6, 1. , 1.5, 2.1, 2.8, 3.6, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5, 10.5, 11.5, 12.5, 13.5, 14.5, 15.5, 16.5, 17.5, 18.5, 19.5, 20.5, 21.5, 22.5, 23.5, 24.5, 25.5, 26.5, 27.5, 28.5, 29.5, 30.5, 31.5, 32.5, 33.5, 34.5, 35.5, 36.5, 37.5, 38.5, 39.5, 40.5, 41.5, 42.5, 43.5, 44.5, 45.5, 46.5, 47.5, 48.5, 49.5, 50.5, 51.5, 52.5, 53.5, 54.5, 55.5, 56.5, 57.5, 58.5, 59.5, 60.5, 61.5, 62.5, 63.5, 64.5, 65.5, 66.5, 67.5, 68.5, 69.5, 70.5, 71.5, 72.5, 73.5, 74.5, 75.5, 76.5, 77.5, 78.5, 79.5, 80.5, 81.5, 82.5, 83.5, 84.5, 85.5, 86.5, 87.5, 88.5, 89.5, 90.5, 91.5, 92.5, 93.5, 94.5, 95.4, 96.2, 96.9, 97.5, 98. , 98.4, 98.7, 98.9, 99. ]) assert_array_almost_equal(xd, movmean(np.arange(100), 10,'leading')) xc = np.array([ 1.36363636, 1.90909091, 2.54545455, 3.27272727, 4.09090909, 5. , 6. , 7. , 8. , 9. , 10. , 11. , 12. , 13. , 14. , 15. , 16. , 17. , 18. , 19. , 20. , 21. , 22. , 23. , 24. , 25. , 26. , 27. , 28. , 29. , 30. , 31. , 32. , 33. , 34. , 35. , 36. , 37. , 38. , 39. , 40. , 41. , 42. , 43. , 44. , 45. , 46. , 47. , 48. , 49. , 50. , 51. , 52. , 53. , 54. , 55. , 56. , 57. , 58. , 59. , 60. , 61. , 62. , 63. , 64. , 65. , 66. , 67. , 68. , 69. , 70. , 71. , 72. , 73. , 74. , 75. , 76. , 77. , 78. , 79. , 80. , 81. , 82. , 83. , 84. , 85. , 86. , 87. , 88. , 89. , 90. , 91. , 92. , 93. , 94. , 94.90909091, 95.72727273, 96.45454545, 97.09090909, 97.63636364]) assert_array_almost_equal(xc, movmean(np.arange(100), 11,'centered')) statsmodels-0.12.2/statsmodels/sandbox/tsa/try_arma_more.py000066400000000000000000000053721400612667500241550ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Periodograms for ARMA and time series theoretical periodogram of ARMA process and different version of periodogram estimation uses scikits.talkbox and matplotlib Created on Wed Oct 14 23:02:19 2009 Author: josef-pktd """ import numpy as np from scipy import signal, ndimage import matplotlib.mlab as mlb import matplotlib.pyplot as plt from statsmodels.tsa.arima_process import arma_generate_sample from statsmodels.tsa.stattools import acovf hastalkbox = False try: import scikits.talkbox.spectral.basic as stbs except ImportError: hastalkbox = False ar = [1., -0.7]#[1,0,0,0,0,0,0,-0.7] ma = [1., 0.3] ar = np.convolve([1.]+[0]*50 +[-0.6], ar) ar = np.convolve([1., -0.5]+[0]*49 +[-0.3], ar) n_startup = 1000 nobs = 1000 # throwing away samples at beginning makes sample more "stationary" xo = arma_generate_sample(ar,ma,n_startup+nobs) x = xo[n_startup:] plt.figure() plt.plot(x) rescale = 0 w, h = signal.freqz(ma, ar) sd = np.abs(h)**2/np.sqrt(2*np.pi) if np.sum(np.isnan(h)) > 0: # this happens with unit root or seasonal unit root' print('Warning: nan in frequency response h') h[np.isnan(h)] = 1. rescale = 0 #replace with signal.order_filter ? pm = ndimage.filters.maximum_filter(sd, footprint=np.ones(5)) maxind = np.nonzero(pm == sd) print('local maxima frequencies') wmax = w[maxind] sdmax = sd[maxind] plt.figure() plt.subplot(2,3,1) if rescale: plt.plot(w, sd/sd[0], '-', wmax, sdmax/sd[0], 'o') # plt.plot(w, sd/sd[0], '-') # plt.hold() # plt.plot(wmax, sdmax/sd[0], 'o') else: plt.plot(w, sd, '-', wmax, sdmax, 'o') # plt.hold() # plt.plot(wmax, sdmax, 'o') plt.title('DGP') sdm, wm = mlb.psd(x) sdm = sdm.ravel() pm = ndimage.filters.maximum_filter(sdm, footprint=np.ones(5)) maxind = np.nonzero(pm == sdm) plt.subplot(2,3,2) if rescale: plt.plot(wm,sdm/sdm[0], '-', wm[maxind], sdm[maxind]/sdm[0], 'o') else: plt.plot(wm, sdm, '-', wm[maxind], sdm[maxind], 'o') plt.title('matplotlib') if hastalkbox: sdp, wp = stbs.periodogram(x) plt.subplot(2,3,3) if rescale: plt.plot(wp,sdp/sdp[0]) else: plt.plot(wp, sdp) plt.title('stbs.periodogram') xacov = acovf(x, unbiased=False) plt.subplot(2,3,4) plt.plot(xacov) plt.title('autocovariance') nr = len(x)#*2/3 #xacovfft = np.fft.fft(xacov[:nr], 2*nr-1) xacovfft = np.fft.fft(np.correlate(x,x,'full')) #abs(xacovfft)**2 or equivalently xacovfft = xacovfft * xacovfft.conj() plt.subplot(2,3,5) if rescale: plt.plot(xacovfft[:nr]/xacovfft[0]) else: plt.plot(xacovfft[:nr]) plt.title('fft') if hastalkbox: sdpa, wpa = stbs.arspec(x, 50) plt.subplot(2,3,6) if rescale: plt.plot(wpa,sdpa/sdpa[0]) else: plt.plot(wpa, sdpa) plt.title('stbs.arspec') #plt.show() statsmodels-0.12.2/statsmodels/sandbox/tsa/try_fi.py000066400000000000000000000047641400612667500226150ustar00rootroot00000000000000 ''' using lfilter to get fractional integration polynomial (1-L)^d, d<1 `ri` is (1-L)^(-d), d<1 second part in here is ar2arma only examples left ''' import numpy as np from scipy.special import gamma from scipy import signal from statsmodels.tsa.arima_process import (lpol_fiar, lpol_fima, ar2arma, arma_impulse_response) if __name__ == '__main__': d = 0.4 n = 1000 j = np.arange(n*10) ri0 = gamma(d+j)/(gamma(j+1)*gamma(d)) ri = lpol_fima(d, n=n) # get_ficoefs(d, n=n) old naming? riinv = signal.lfilter([1], ri, [1]+[0]*(n-1))#[[5,10,20,25]] ''' array([-0.029952 , -0.01100641, -0.00410998, -0.00299859]) >>> d=0.4; j=np.arange(1000);ri=gamma(d+j)/(gamma(j+1)*gamma(d)) >>> # (1-L)^d, d<1 is >>> lfilter([1], ri, [1]+[0]*30) array([ 1. , -0.4 , -0.12 , -0.064 , -0.0416 , -0.029952 , -0.0229632 , -0.01837056, -0.01515571, -0.01279816, -0.01100641, -0.0096056 , -0.00848495, -0.00757118, -0.00681406, -0.00617808, -0.0056375 , -0.00517324, -0.00477087, -0.00441934, -0.00410998, -0.00383598, -0.00359188, -0.00337324, -0.00317647, -0.00299859, -0.00283712, -0.00269001, -0.00255551, -0.00243214, -0.00231864]) >>> # verified for points [[5,10,20,25]] at 4 decimals with Bhardwaj, Swanson, Journal of Eonometrics 2006 ''' print(lpol_fiar(0.4, n=20)) print(lpol_fima(-0.4, n=20)) print(np.sum((lpol_fima(-0.4, n=n)[1:] + riinv[1:])**2)) #different signs print(np.sum((lpol_fiar(0.4, n=n)[1:] - riinv[1:])**2)) #corrected signs #test is now in statsmodels.tsa.tests.test_arima_process from statsmodels.tsa.tests.test_arima_process import test_fi test_fi() ar_true = [1, -0.4] ma_true = [1, 0.5] ar_desired = arma_impulse_response(ma_true, ar_true) ar_app, ma_app, res = ar2arma(ar_desired, 2,1, n=100, mse='ar', start=[0.1]) print(ar_app, ma_app) ar_app, ma_app, res = ar2arma(ar_desired, 2,2, n=100, mse='ar', start=[-0.1, 0.1]) print(ar_app, ma_app) ar_app, ma_app, res = ar2arma(ar_desired, 2,3, n=100, mse='ar')#, start = [-0.1, 0.1]) print(ar_app, ma_app) slow = 1 if slow: ar_desired = lpol_fiar(0.4, n=100) ar_app, ma_app, res = ar2arma(ar_desired, 3, 1, n=100, mse='ar')#, start = [-0.1, 0.1]) print(ar_app, ma_app) ar_app, ma_app, res = ar2arma(ar_desired, 10, 10, n=100, mse='ar')#, start = [-0.1, 0.1]) print(ar_app, ma_app) statsmodels-0.12.2/statsmodels/sandbox/tsa/try_var_convolve.py000066400000000000000000000213561400612667500247160ustar00rootroot00000000000000# -*- coding: utf-8 -*- """trying out VAR filtering and multidimensional fft Note: second half is copy and paste and does not run as script incomplete definitions of variables, some I created in shell Created on Thu Jan 07 12:23:40 2010 Author: josef-pktd update 2010-10-22 2 arrays were not defined, copied from fft_filter.log.py but I did not check what the results are. Runs now without raising exception """ import numpy as np from numpy.testing import assert_equal from scipy import signal, stats from scipy.signal.signaltools import _centered as trim_centered from statsmodels.tsa.filters.filtertools import fftconvolveinv as fftconvolve x = np.arange(40).reshape((2,20)).T x = np.arange(60).reshape((3,20)).T a3f = np.array([[[0.5, 1.], [1., 0.5]], [[0.5, 1.], [1., 0.5]]]) a3f = np.ones((2,3,3)) nlags = a3f.shape[0] ntrim = nlags//2 y0 = signal.convolve(x,a3f[:,:,0], mode='valid') y1 = signal.convolve(x,a3f[:,:,1], mode='valid') yf = signal.convolve(x[:,:,None],a3f) y = yf[:,1,:] # yvalid = yf[ntrim:-ntrim,yf.shape[1]//2,:] #same result with fftconvolve #signal.fftconvolve(x[:,:,None],a3f).shape #signal.fftconvolve(x[:,:,None],a3f)[:,1,:] print(trim_centered(y, x.shape)) # this raises an exception: #print(trim_centered(yf, (x.shape).shape) assert_equal(yvalid[:,0], y0.ravel()) assert_equal(yvalid[:,1], y1.ravel()) def arfilter(x, a): '''apply an autoregressive filter to a series x x can be 2d, a can be 1d, 2d, or 3d Parameters ---------- x : array_like data array, 1d or 2d, if 2d then observations in rows a : array_like autoregressive filter coefficients, ar lag polynomial see Notes Returns ------- y : ndarray, 2d filtered array, number of columns determined by x and a Notes ----- In general form this uses the linear filter :: y = a(L)x where x : nobs, nvars a : nlags, nvars, npoly Depending on the shape and dimension of a this uses different Lag polynomial arrays case 1 : a is 1d or (nlags,1) one lag polynomial is applied to all variables (columns of x) case 2 : a is 2d, (nlags, nvars) each series is independently filtered with its own lag polynomial, uses loop over nvar case 3 : a is 3d, (nlags, nvars, npoly) the ith column of the output array is given by the linear filter defined by the 2d array a[:,:,i], i.e. :: y[:,i] = a(.,.,i)(L) * x y[t,i] = sum_p sum_j a(p,j,i)*x(t-p,j) for p = 0,...nlags-1, j = 0,...nvars-1, for all t >= nlags Note: maybe convert to axis=1, Not TODO: initial conditions ''' x = np.asarray(x) a = np.asarray(a) if x.ndim == 1: x = x[:,None] if x.ndim > 2: raise ValueError('x array has to be 1d or 2d') nvar = x.shape[1] nlags = a.shape[0] ntrim = nlags//2 # for x is 2d with ncols >1 if a.ndim == 1: # case: identical ar filter (lag polynomial) return signal.convolve(x, a[:,None], mode='valid') # alternative: #return signal.lfilter(a,[1],x.astype(float),axis=0) elif a.ndim == 2: if min(a.shape) == 1: # case: identical ar filter (lag polynomial) return signal.convolve(x, a, mode='valid') # case: independent ar #(a bit like recserar in gauss, but no x yet) result = np.zeros((x.shape[0]-nlags+1, nvar)) for i in range(nvar): # could also use np.convolve, but easier for swiching to fft result[:,i] = signal.convolve(x[:,i], a[:,i], mode='valid') return result elif a.ndim == 3: # case: vector autoregressive with lag matrices # #not necessary: # if np.any(a.shape[1:] != nvar): # raise ValueError('if 3d shape of a has to be (nobs,nvar,nvar)') yf = signal.convolve(x[:,:,None], a) yvalid = yf[ntrim:-ntrim, yf.shape[1]//2,:] return yvalid a3f = np.ones((2,3,3)) y0ar = arfilter(x,a3f[:,:,0]) print(y0ar, x[1:] + x[:-1]) yres = arfilter(x,a3f[:,:,:2]) print(np.all(yres == (x[1:,:].sum(1) + x[:-1].sum(1))[:,None])) yff = fftconvolve(x.astype(float)[:,:,None],a3f) rvs = np.random.randn(500) ar1fft = fftconvolve(rvs,np.array([1,-0.8])) #ar1fftp = fftconvolve(np.r_[np.zeros(100),rvs,np.zeros(100)],np.array([1,-0.8])) ar1fftp = fftconvolve(np.r_[np.zeros(100),rvs],np.array([1,-0.8])) ar1lf = signal.lfilter([1], [1,-0.8], rvs) ar1 = np.zeros(501) for i in range(1,501): ar1[i] = 0.8*ar1[i-1] + rvs[i-1] #the previous looks wrong, is for generating ar with delayed error, #or maybe for an ma(1) filter, (generating ar and applying ma filter are the same) #maybe not since it replicates lfilter and fftp #still strange explanation for convolution #ok. because this is my fftconvolve, which is an inverse filter (read the namespace!) #This is an AR filter errar1 = np.zeros(501) for i in range(1,500): errar1[i] = rvs[i] - 0.8*rvs[i-1] #print(ar1[-10:]) #print(ar1fft[-11:-1]) #print(ar1lf[-10:]) #print(ar1[:10]) #print(ar1fft[1:11]) #print(ar1lf[:10]) #print(ar1[100:110]) #print(ar1fft[100:110]) #print(ar1lf[100:110]) # #arloop - lfilter - fftp (padded) are the same print('\n compare: \nerrloop - arloop - fft - lfilter - fftp (padded)') #print(np.column_stack((ar1[1:31],ar1fft[:30], ar1lf[:30])) print(np.column_stack((errar1[1:31], ar1[1:31],ar1fft[:30], ar1lf[:30], ar1fftp[100:130]))) def maxabs(x,y): return np.max(np.abs(x-y)) print(maxabs(ar1[1:], ar1lf)) #0 print(maxabs(ar1[1:], ar1fftp[100:-1])) # around 1e-15 rvs3 = np.random.randn(500,3) a3n = np.array([[1,1,1],[-0.8,0.5,0.1]]) a3n = np.array([[1,1,1],[-0.8,0.0,0.0]]) a3n = np.array([[1,-1,-1],[-0.8,0.0,0.0]]) a3n = np.array([[1,0,0],[-0.8,0.0,0.0]]) a3ne = np.r_[np.ones((1,3)),-0.8*np.eye(3)] a3ne = np.r_[np.ones((1,3)),-0.8*np.eye(3)] ar13fft = fftconvolve(rvs3,a3n) ar13 = np.zeros((501,3)) for i in range(1,501): ar13[i] = np.sum(a3n[1,:]*ar13[i-1]) + rvs[i-1] #changes imp was not defined, not sure what it is supposed to be #copied from a .log file imp = np.zeros((10,3)) imp[0]=1 a3n = np.array([[1,0,0],[-0.8,0.0,0.0]]) fftconvolve(np.r_[np.zeros((100,3)),imp],a3n)[100:] a3n = np.array([[1,0,0],[-0.8,-0.50,0.0]]) fftconvolve(np.r_[np.zeros((100,3)),imp],a3n)[100:] a3n3 = np.array([[[ 1. , 0. , 0. ], [ 0. , 1. , 0. ], [ 0. , 0. , 1. ]], [[-0.8, 0. , 0. ], [ 0. , -0.8, 0. ], [ 0. , 0. , -0.8]]]) a3n3 = np.array([[[ 1. , 0.5 , 0. ], [ 0. , 1. , 0. ], [ 0. , 0. , 1. ]], [[-0.8, 0. , 0. ], [ 0. , -0.8, 0. ], [ 0. , 0. , -0.8]]]) ttt = fftconvolve(np.r_[np.zeros((100,3)),imp][:,:,None],a3n3.T)[100:] gftt = ttt/ttt[0,:,:] a3n3 = np.array([[[ 1. , 0 , 0. ], [ 0. , 1. , 0. ], [ 0. , 0. , 1. ]], [[-0.8, 0.2 , 0. ], [ 0 , 0.0, 0. ], [ 0. , 0. , 0.8]]]) ttt = fftconvolve(np.r_[np.zeros((100,3)),imp][:,:,None],a3n3)[100:] gftt = ttt/ttt[0,:,:] signal.fftconvolve(np.dstack((imp,imp,imp)),a3n3)[1,:,:] nobs = 10 imp = np.zeros((nobs,3)) imp[1] = 1. ar13 = np.zeros((nobs+1,3)) for i in range(1,nobs+1): ar13[i] = np.dot(a3n3[1,:,:],ar13[i-1]) + imp[i-1] a3n3inv = np.zeros((nobs+1,3,3)) a3n3inv[0,:,:] = a3n3[0] a3n3inv[1,:,:] = -a3n3[1] for i in range(2,nobs+1): a3n3inv[i,:,:] = np.dot(-a3n3[1],a3n3inv[i-1,:,:]) a3n3sy = np.array([[[ 1. , 0 , 0. ], [ 0. , 1. , 0. ], [ 0. , 0. , 1. ]], [[-0.8, 0.2 , 0. ], [ 0 , 0.0, 0. ], [ 0. , 0. , 0.8]]]) nobs = 10 a = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[-0.8, 0.0 ], [ -0.1 , -0.8]]]) a2n3inv = np.zeros((nobs+1,2,2)) a2n3inv[0,:,:] = a[0] a2n3inv[1,:,:] = -a[1] for i in range(2,nobs+1): a2n3inv[i,:,:] = np.dot(-a[1],a2n3inv[i-1,:,:]) nobs = 10 imp = np.zeros((nobs,2)) imp[0,0] = 1. #a2 was missing, copied from .log file, not sure if correct a2 = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[-0.8, 0. ], [0.1, -0.8]]]) ar12 = np.zeros((nobs+1,2)) for i in range(1,nobs+1): ar12[i] = np.dot(-a2[1,:,:],ar12[i-1]) + imp[i-1] u = np.random.randn(10,2) ar12r = np.zeros((nobs+1,2)) for i in range(1,nobs+1): ar12r[i] = np.dot(-a2[1,:,:],ar12r[i-1]) + u[i-1] a2inv = np.zeros((nobs+1,2,2)) a2inv[0,:,:] = a2[0] a2inv[1,:,:] = -a2[1] for i in range(2,nobs+1): a2inv[i,:,:] = np.dot(-a2[1],a2inv[i-1,:,:]) nbins = 12 binProb = np.zeros(nbins) + 1.0/nbins binSumProb = np.add.accumulate(binProb) print(binSumProb) print(stats.gamma.ppf(binSumProb,0.6379,loc=1.6,scale=39.555)) statsmodels-0.12.2/statsmodels/sandbox/tsa/varma.py000066400000000000000000000114361400612667500224210ustar00rootroot00000000000000'''VAR and VARMA process this does not actually do much, trying out a version for a time loop alternative representation: * textbook, different blocks in matrices * Kalman filter * VAR, VARX and ARX could be calculated with signal.lfilter only tried some examples, not implemented TODO: try minimizing sum of squares of (Y-Yhat) Note: filter has smallest lag at end of array and largest lag at beginning, be careful for asymmetric lags coefficients check this again if it is consistently used changes 2009-09-08 : separated from movstat.py Author : josefpkt License : BSD ''' import numpy as np from scipy import signal #NOTE: this just returns that predicted values given the #B matrix in polynomial form. #TODO: make sure VAR class returns B/params in this form. def VAR(x,B, const=0): ''' multivariate linear filter Parameters ---------- x: (TxK) array columns are variables, rows are observations for time period B: (PxKxK) array b_t-1 is bottom "row", b_t-P is top "row" when printing B(:,:,0) is lag polynomial matrix for variable 1 B(:,:,k) is lag polynomial matrix for variable k B(p,:,k) is pth lag for variable k B[p,:,:].T corresponds to A_p in Wikipedia const : float or array (not tested) constant added to autoregression Returns ------- xhat: (TxK) array filtered, predicted values of x array Notes ----- xhat(t,i) = sum{_p}sum{_k} { x(t-P:t,:) .* B(:,:,i) } for all i = 0,K-1, for all t=p..T xhat does not include the forecasting observation, xhat(T+1), xhat is 1 row shorter than signal.correlate References ---------- https://en.wikipedia.org/wiki/Vector_Autoregression https://en.wikipedia.org/wiki/General_matrix_notation_of_a_VAR(p) ''' p = B.shape[0] T = x.shape[0] xhat = np.zeros(x.shape) for t in range(p,T): #[p+2]:# ## print(p,T) ## print(x[t-p:t,:,np.newaxis].shape) ## print(B.shape) #print(x[t-p:t,:,np.newaxis]) xhat[t,:] = const + (x[t-p:t,:,np.newaxis]*B).sum(axis=1).sum(axis=0) return xhat def VARMA(x,B,C, const=0): ''' multivariate linear filter x (TxK) B (PxKxK) xhat(t,i) = sum{_p}sum{_k} { x(t-P:t,:) .* B(:,:,i) } + sum{_q}sum{_k} { e(t-Q:t,:) .* C(:,:,i) }for all i = 0,K-1 ''' P = B.shape[0] Q = C.shape[0] T = x.shape[0] xhat = np.zeros(x.shape) e = np.zeros(x.shape) start = max(P,Q) for t in range(start,T): #[p+2]:# ## print(p,T ## print(x[t-p:t,:,np.newaxis].shape ## print(B.shape #print(x[t-p:t,:,np.newaxis] xhat[t,:] = const + (x[t-P:t,:,np.newaxis]*B).sum(axis=1).sum(axis=0) + \ (e[t-Q:t,:,np.newaxis]*C).sum(axis=1).sum(axis=0) e[t,:] = x[t,:] - xhat[t,:] return xhat, e if __name__ == '__main__': T = 20 K = 2 P = 3 #x = np.arange(10).reshape(5,2) x = np.column_stack([np.arange(T)]*K) B = np.ones((P,K,K)) #B[:,:,1] = 2 B[:,:,1] = [[0,0],[0,0],[0,1]] xhat = VAR(x,B) print(np.all(xhat[P:,0]==np.correlate(x[:-1,0],np.ones(P))*2)) #print(xhat) T = 20 K = 2 Q = 2 P = 3 const = 1 #x = np.arange(10).reshape(5,2) x = np.column_stack([np.arange(T)]*K) B = np.ones((P,K,K)) #B[:,:,1] = 2 B[:,:,1] = [[0,0],[0,0],[0,1]] C = np.zeros((Q,K,K)) xhat1 = VAR(x,B, const=const) xhat2, err2 = VARMA(x,B,C, const=const) print(np.all(xhat2 == xhat1)) print(np.all(xhat2[P:,0] == np.correlate(x[:-1,0],np.ones(P))*2+const)) C[1,1,1] = 0.5 xhat3, err3 = VARMA(x,B,C) x = np.r_[np.zeros((P,K)),x] #prepend initial conditions xhat4, err4 = VARMA(x,B,C) C[1,1,1] = 1 B[:,:,1] = [[0,0],[0,0],[0,1]] xhat5, err5 = VARMA(x,B,C) #print(err5) #in differences #VARMA(np.diff(x,axis=0),B,C) #Note: # * signal correlate applies same filter to all columns if kernel.shape[1] possible to run signal.correlate K times with different filters, # see the following example, which replicates VAR filter x0 = np.column_stack([np.arange(T), 2*np.arange(T)]) B[:,:,0] = np.ones((P,K)) B[:,:,1] = np.ones((P,K)) B[1,1,1] = 0 xhat0 = VAR(x0,B) xcorr00 = signal.correlate(x0,B[:,:,0])#[:,0] xcorr01 = signal.correlate(x0,B[:,:,1]) print(np.all(signal.correlate(x0,B[:,:,0],'valid')[:-1,0]==xhat0[P:,0])) print(np.all(signal.correlate(x0,B[:,:,1],'valid')[:-1,0]==xhat0[P:,1])) #import error #from movstat import acovf, acf from statsmodels.tsa.stattools import acovf, acf aav = acovf(x[:,0]) print(aav[0] == np.var(x[:,0])) aac = acf(x[:,0]) statsmodels-0.12.2/statsmodels/src/000077500000000000000000000000001400612667500172765ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/src/__init__.py000066400000000000000000000000001400612667500213750ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/src/blas_lapack.pxd000066400000000000000000001227551400612667500222630ustar00rootroot00000000000000cimport numpy as np # # BLAS # ctypedef int sgemm_t( # Compute C := alpha*A*B + beta*C char *transa, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A char *transb, # {'T','C'}: o(B)=B'; {'N'}: o(B)=B int *m, # Rows of o(A) (and of C) int *n, # Columns of o(B) (and of C) int *k, # Columns of o(A) / Rows of o(B) np.float32_t *alpha, # Scalar multiple np.float32_t *a, # Matrix A: mxk int *lda, # The size of the first dimension of A (in memory) np.float32_t *b, # Matrix B: kxn int *ldb, # The size of the first dimension of B (in memory) np.float32_t *beta, # Scalar multiple np.float32_t *c, # Matrix C: mxn int *ldc # The size of the first dimension of C (in memory) ) ctypedef int sgemv_t( # Compute C := alpha*A*x + beta*y char *trans, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A int *m, # Rows of o(A) int *n, # Columns of o(A) / min(len(x)) np.float32_t *alpha, # Scalar multiple np.float32_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) np.float32_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.float32_t *beta, # Scalar multiple np.float32_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef int ssymm_t( # SSYMM - perform one of the matrix-matrix operations C := # alpha*A*B + beta*C, char *side, # {'L', 'R'}: left, right char *uplo, # {'U','L'}, upper, lower int *m, # Rows of C int *n, # Columns of C np.float32_t *alpha, # Scalar multiple np.float32_t *a, # Matrix A int *lda, # The size of the first dimension of A (in memory) np.float32_t *b, # Matrix B int *ldb, # The size of the first dimension of B (in memory) np.float32_t *beta, # Scalar multiple np.float32_t *c, # Matrix C int *ldc, # The size of the first dimension of C (in memory) ) ctypedef int ssymv_t( # SSYMV - perform the matrix-vector operation y := alpha*A*x # + beta*y, char *uplo, # {'U','L'}, upper, lower int *n, # Order of matrix A np.float32_t *alpha, # Scalar multiple np.float32_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) np.float32_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.float32_t *beta, # Scalar multiple np.float32_t *y, # Vector y, min(len(y)) = n int *incy, # The increment between elements of y (usually 1) ) ctypedef int strmm_t( # STRMM - perform one of the matrix-matrix operations B := # alpha*op( A )*B, or B := alpha*B*op( A ), char *side, # {'L', 'R'}: left, right char *uplo, # {'U','L'}, upper, lower char *transa, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A char *diag, # {'U','N'}: unit triangular or not int *m, # Rows of B int *n, # Columns of B np.float32_t *alpha, # Scalar multiple np.float32_t *a, # Matrix A int *lda, # The size of the first dimension of A (in memory) np.float32_t *b, # Matrix B int *ldb, # The size of the first dimension of B (in memory) ) ctypedef int strmv_t( # STRMV - perform one of the matrix-vector operations x := # A*x, or x := A'*x, char *uplo, # {'U','L'}, upper, lower char *trans, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A char *diag, # {'U','N'}: unit triangular or not int *n, # Order of matrix A np.float32_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) np.float32_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) ) ctypedef int scopy_t( int *n, # Number of vector elements to be copied. np.float32_t *x, # Vector from which to copy. int *incx, # Increment between elements of x. np.float32_t *y, # array of dimension (n-1) * |incy| + 1, result vector. int *incy # Increment between elements of y. ) ctypedef int sscal_t( # SSCAL - BLAS level one, scales a double precision vector int *n, # Number of elements in the vector. np.float32_t *alpha, # scalar alpha np.float32_t *x, # Array of dimension (n-1) * |incx| + 1. Vector to be scaled. int *incx # Increment between elements of x. ) ctypedef int saxpy_t( # Compute y := alpha*x + y int *n, # Columns of o(A) / min(len(x)) np.float32_t *alpha, # Scalar multiple np.float32_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.float32_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef int sswap_t( # Swap y and x int *n, # Columns of o(A) / min(len(x)) np.float32_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.float32_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef np.float64_t sdot_t( # Compute DDOT := x.T * y int *n, # Length of vectors np.float32_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.float32_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef int dgemm_t( # Compute C := alpha*A*B + beta*C char *transa, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A char *transb, # {'T','C'}: o(B)=B'; {'N'}: o(B)=B int *m, # Rows of o(A) (and of C) int *n, # Columns of o(B) (and of C) int *k, # Columns of o(A) / Rows of o(B) np.float64_t *alpha, # Scalar multiple np.float64_t *a, # Matrix A: mxk int *lda, # The size of the first dimension of A (in memory) np.float64_t *b, # Matrix B: kxn int *ldb, # The size of the first dimension of B (in memory) np.float64_t *beta, # Scalar multiple np.float64_t *c, # Matrix C: mxn int *ldc # The size of the first dimension of C (in memory) ) ctypedef int dgemv_t( # Compute y := alpha*A*x + beta*y char *trans, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A int *m, # Rows of A (prior to transpose from *trans) int *n, # Columns of A / min(len(x)) np.float64_t *alpha, # Scalar multiple np.float64_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) np.float64_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.float64_t *beta, # Scalar multiple np.float64_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef int dsymm_t( # DSYMM - perform one of the matrix-matrix operations C := # alpha*A*B + beta*C, char *side, # {'L', 'R'}: left, right char *uplo, # {'U','L'}, upper, lower int *m, # Rows of C int *n, # Columns of C np.float64_t *alpha, # Scalar multiple np.float64_t *a, # Matrix A int *lda, # The size of the first dimension of A (in memory) np.float64_t *b, # Matrix B int *ldb, # The size of the first dimension of B (in memory) np.float64_t *beta, # Scalar multiple np.float64_t *c, # Matrix C int *ldc, # The size of the first dimension of C (in memory) ) ctypedef int dsymv_t( # DSYMV - perform the matrix-vector operation y := alpha*A*x # + beta*y, char *uplo, # {'U','L'}, upper, lower int *n, # Order of matrix A np.float64_t *alpha, # Scalar multiple np.float64_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) np.float64_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.float64_t *beta, # Scalar multiple np.float64_t *y, # Vector y, min(len(y)) = n int *incy, # The increment between elements of y (usually 1) ) ctypedef int dtrmm_t( # DTRMM - perform one of the matrix-matrix operations B := # alpha*op( A )*B, or B := alpha*B*op( A ), char *side, # {'L', 'R'}: left, right char *uplo, # {'U','L'}, upper, lower char *transa, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A char *diag, # {'U','N'}: unit triangular or not int *m, # Rows of B int *n, # Columns of B np.float64_t *alpha, # Scalar multiple np.float64_t *a, # Matrix A int *lda, # The size of the first dimension of A (in memory) np.float64_t *b, # Matrix B int *ldb, # The size of the first dimension of B (in memory) ) ctypedef int dtrmv_t( # DTRMV - perform one of the matrix-vector operations x := # A*x, or x := A'*x, char *uplo, # {'U','L'}, upper, lower char *trans, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A char *diag, # {'U','N'}: unit triangular or not int *n, # Order of matrix A np.float64_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) np.float64_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) ) ctypedef int dcopy_t( int *n, # Number of vector elements to be copied. np.float64_t *x, # Vector from which to copy. int *incx, # Increment between elements of x. np.float64_t *y, # array of dimension (n-1) * |incy| + 1, result vector. int *incy # Increment between elements of y. ) ctypedef int dscal_t( # DSCAL - BLAS level one, scales a double precision vector int *n, # Number of elements in the vector. np.float64_t *alpha, # scalar alpha np.float64_t *x, # Array of dimension (n-1) * |incx| + 1. Vector to be scaled. int *incx # Increment between elements of x. ) ctypedef int daxpy_t( # Compute y := alpha*x + y int *n, # Columns of o(A) / min(len(x)) np.float64_t *alpha, # Scalar multiple np.float64_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.float64_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef int dswap_t( # Swap y and x int *n, # Columns of o(A) / min(len(x)) np.float64_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.float64_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef double ddot_t( # Compute DDOT := x.T * y int *n, # Length of vectors np.float64_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.float64_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef int cgemm_t( # Compute C := alpha*A*B + beta*C char *transa, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A char *transb, # {'T','C'}: o(B)=B'; {'N'}: o(B)=B int *m, # Rows of o(A) (and of C) int *n, # Columns of o(B) (and of C) int *k, # Columns of o(A) / Rows of o(B) np.complex64_t *alpha, # Scalar multiple np.complex64_t *a, # Matrix A: mxk int *lda, # The size of the first dimension of A (in memory) np.complex64_t *b, # Matrix B: kxn int *ldb, # The size of the first dimension of B (in memory) np.complex64_t *beta, # Scalar multiple np.complex64_t *c, # Matrix C: mxn int *ldc # The size of the first dimension of C (in memory) ) ctypedef int cgemv_t( # Compute C := alpha*A*x + beta*y char *trans, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A int *m, # Rows of o(A) int *n, # Columns of o(A) / min(len(x)) np.complex64_t *alpha, # Scalar multiple np.complex64_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) np.complex64_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.complex64_t *beta, # Scalar multiple np.complex64_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef int csymm_t( # CSYMM - perform one of the matrix-matrix operations C := # alpha*A*B + beta*C, char *side, # {'L', 'R'}: left, right char *uplo, # {'U','L'}, upper, lower int *m, # Rows of C int *n, # Columns of C np.complex64_t *alpha, # Scalar multiple np.complex64_t *a, # Matrix A int *lda, # The size of the first dimension of A (in memory) np.complex64_t *b, # Matrix B int *ldb, # The size of the first dimension of B (in memory) np.complex64_t *beta, # Scalar multiple np.complex64_t *c, # Matrix C int *ldc, # The size of the first dimension of C (in memory) ) ctypedef int csymv_t( # CSYMV - perform the matrix-vector operation y := alpha*A*x # + beta*y, char *uplo, # {'U','L'}, upper, lower int *n, # Order of matrix A np.complex64_t *alpha, # Scalar multiple np.complex64_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) np.complex64_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.complex64_t *beta, # Scalar multiple np.complex64_t *y, # Vector y, min(len(y)) = n int *incy, # The increment between elements of y (usually 1) ) ctypedef int ctrmm_t( # CTRMM - perform one of the matrix-matrix operations B := # alpha*op( A )*B, or B := alpha*B*op( A ), char *side, # {'L', 'R'}: left, right char *uplo, # {'U','L'}, upper, lower char *transa, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A char *diag, # {'U','N'}: unit triangular or not int *m, # Rows of B int *n, # Columns of B np.complex64_t *alpha, # Scalar multiple np.complex64_t *a, # Matrix A int *lda, # The size of the first dimension of A (in memory) np.complex64_t *b, # Matrix B int *ldb, # The size of the first dimension of B (in memory) ) ctypedef int ctrmv_t( # CTRMV - perform one of the matrix-vector operations x := # A*x, or x := A'*x, char *uplo, # {'U','L'}, upper, lower char *trans, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A char *diag, # {'U','N'}: unit triangular or not int *n, # Order of matrix A np.complex64_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) np.complex64_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) ) ctypedef int ccopy_t( int *n, # Number of vector elements to be copied. np.complex64_t *x, # Vector from which to copy. int *incx, # Increment between elements of x. np.complex64_t *y, # array of dimension (n-1) * |incy| + 1, result vector. int *incy # Increment between elements of y. ) ctypedef int cscal_t( # CSCAL - BLAS level one, scales a double precision vector int *n, # Number of elements in the vector. np.complex64_t *alpha, # scalar alpha np.complex64_t *x, # Array of dimension (n-1) * |incx| + 1. Vector to be scaled. int *incx # Increment between elements of x. ) ctypedef int caxpy_t( # Compute y := alpha*x + y int *n, # Columns of o(A) / min(len(x)) np.complex64_t *alpha, # Scalar multiple np.complex64_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.complex64_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef int cswap_t( # Swap y and x int *n, # Columns of o(A) / min(len(x)) np.complex64_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.complex64_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef np.complex64_t cdotu_t( # Compute CDOTU := x.T * y int *n, # Length of vectors np.complex64_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.complex64_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef int zgemm_t( # Compute C := alpha*A*B + beta*C char *transa, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A char *transb, # {'T','C'}: o(B)=B'; {'N'}: o(B)=B int *m, # Rows of o(A) (and of C) int *n, # Columns of o(B) (and of C) int *k, # Columns of o(A) / Rows of o(B) np.complex128_t *alpha, # Scalar multiple np.complex128_t *a, # Matrix A: mxk int *lda, # The size of the first dimension of A (in memory) np.complex128_t *b, # Matrix B: kxn int *ldb, # The size of the first dimension of B (in memory) np.complex128_t *beta, # Scalar multiple np.complex128_t *c, # Matrix C: mxn int *ldc # The size of the first dimension of C (in memory) ) ctypedef int zgemv_t( # Compute C := alpha*A*x + beta*y char *trans, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A int *m, # Rows of o(A) int *n, # Columns of o(A) / min(len(x)) np.complex128_t *alpha, # Scalar multiple np.complex128_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) np.complex128_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.complex128_t *beta, # Scalar multiple np.complex128_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef int zsymm_t( # ZSYMM - perform one of the matrix-matrix operations C := # alpha*A*B + beta*C, char *side, # {'L', 'R'}: left, right char *uplo, # {'U','L'}, upper, lower int *m, # Rows of C int *n, # Columns of C np.complex128_t *alpha, # Scalar multiple np.complex128_t *a, # Matrix A int *lda, # The size of the first dimension of A (in memory) np.complex128_t *b, # Matrix B int *ldb, # The size of the first dimension of B (in memory) np.complex128_t *beta, # Scalar multiple np.complex128_t *c, # Matrix C int *ldc, # The size of the first dimension of C (in memory) ) ctypedef int zsymv_t( # ZSYMV - perform the matrix-vector operation y := alpha*A*x # + beta*y, char *uplo, # {'U','L'}, upper, lower int *n, # Order of matrix A np.complex128_t *alpha, # Scalar multiple np.complex128_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) np.complex128_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.complex128_t *beta, # Scalar multiple np.complex128_t *y, # Vector y, min(len(y)) = n int *incy, # The increment between elements of y (usually 1) ) ctypedef int ztrmm_t( # ZTRMM - perform one of the matrix-matrix operations B := # alpha*op( A )*B, or B := alpha*B*op( A ), char *side, # {'L', 'R'}: left, right char *uplo, # {'U','L'}, upper, lower char *transa, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A char *diag, # {'U','N'}: unit triangular or not int *m, # Rows of B int *n, # Columns of B np.complex128_t *alpha, # Scalar multiple np.complex128_t *a, # Matrix A int *lda, # The size of the first dimension of A (in memory) np.complex128_t *b, # Matrix B int *ldb, # The size of the first dimension of B (in memory) ) ctypedef int ztrmv_t( # ZTRMV - perform one of the matrix-vector operations x := # A*x, or x := A'*x, char *uplo, # {'U','L'}, upper, lower char *trans, # {'T','C'}: o(A)=A'; {'N'}: o(A)=A char *diag, # {'U','N'}: unit triangular or not int *n, # Order of matrix A np.complex128_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) np.complex128_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) ) ctypedef int zcopy_t( int *n, # Number of vector elements to be copied. np.complex128_t *x, # Vector from which to copy. int *incx, # Increment between elements of x. np.complex128_t *y, # array of dimension (n-1) * |incy| + 1, result vector. int *incy # Increment between elements of y. ) ctypedef int zscal_t( # ZSCAL - BLAS level one, scales a double np.complex128_t precision vector int *n, # Number of elements in the vector. np.complex128_t *alpha, # scalar alpha np.complex128_t *x, # Array of dimension (n-1) * |incx| + 1. Vector to be scaled. int *incx # Increment between elements of x. ) ctypedef int zaxpy_t( # Compute y := alpha*x + y int *n, # Columns of o(A) / min(len(x)) np.complex128_t *alpha, # Scalar multiple np.complex128_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.complex128_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef int zswap_t( # Swap y and x int *n, # Columns of o(A) / min(len(x)) np.complex128_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.complex128_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) ctypedef np.complex128_t zdotu_t( # Compute ZDOTU := x.T * y int *n, # Length of vectors np.complex128_t *x, # Vector x, min(len(x)) = n int *incx, # The increment between elements of x (usually 1) np.complex128_t *y, # Vector y, min(len(y)) = m int *incy # The increment between elements of y (usually 1) ) # # LAPACK # ctypedef int sgetrf_t( # SGETRF - compute an LU factorization of a general M-by-N # matrix A using partial pivoting with row interchanges int *m, # Rows of A int *n, # Columns of A np.float32_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) int *ipiv, # Matrix P: mxn (the pivot indices) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int sgetri_t( # SGETRI - compute the inverse of a matrix using the LU fac- # torization computed by SGETRF int *n, # Order of A np.float32_t *a, # Matrix A: nxn (the LUP decomposed matrix from dgetrf) int *lda, # The size of the first dimension of A (in memory) int *ipiv, # Matrix P: nxn (the pivot indices from the LUP decomposition) np.float32_t *work, # Matrix: nxn (a workspace for the inversion, optimal size=nxn) int *lwork, # Number of elements in the workspace: optimal is n**2 int *info # 0 if success, otherwise an error code (integer) ) ctypedef int sgetrs_t( # SGETRS - solve a system of linear equations A * X = B or A' # * X = B with a general N-by-N matrix A using the LU factori- # zation computed by SGETRF char *trans, # Specifies the form of the system of equations int *n, # Order of A int *nrhs, # The number of right hand sides np.float32_t *a, # Matrix A: nxn (the LUP decomposed matrix from dgetrf) int *lda, # The size of the first dimension of A (in memory) int *ipiv, # Matrix P: nxn (the pivot indices from the LUP decomposition) np.float32_t *b, # Matrix B: nxnrhs int *ldb, # The size of the first dimension of B (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int spotrf_t( # Compute the Cholesky factorization of a # real symmetric positive definite matrix A char *uplo, # 'U': A = U'U and U is stored, 'L': A = LL' and L is stored int *n, # The order of the matrix A. n >= 0. np.float32_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int spotri_t( # SPOTRI - compute the inverse of a real symmetric positive # definite matrix A using the Cholesky factorization A = # U**T*U or A = L*L**T computed by SPOTRF char *uplo, # 'U': A = U'U and U is stored, 'L': A = LL' and L is stored int *n, # The order of the matrix A. n >= 0. np.float32_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int spotrs_t( # SPOTRS - solve a system of linear equations A*X = B with a # symmetric positive definite matrix A using the Cholesky fac- # torization A = U**T*U or A = L*L**T computed by SPOTRF char *uplo, # 'U': A = U'U and U is stored, 'L': A = LL' and L is stored int *n, # The order of the matrix A. n >= 0. int *nrhs, # The number of right hand sides np.float32_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) np.float32_t *b, # Matrix B: nxnrhs int *ldb, # The size of the first dimension of B (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int strtrs_t( # STRTRS solves a triangular system of the form # A * X = B, A**T * X = B, or A**H * X = B, # where A is a triangular matrix of order N, and B is an N-by-NRHS # matrix. A check is made to verify that A is nonsingular. char *uplo, # 'U': A is upper triangular char *trans, # N: A * X = B; T: A**T * X = B; C: A**H * X = B char *diag, # {'U','N'}: unit triangular or not int *n, # The order of the matrix A. n >= 0. int *nrhs, # The number of right hand sides np.float32_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) np.float32_t *b, # Matrix B: nxnrhs int *ldb, # The size of the first dimension of B (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int dgetrf_t( # DGETRF - compute an LU factorization of a general M-by-N # matrix A using partial pivoting with row interchanges int *m, # Rows of A int *n, # Columns of A np.float64_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) int *ipiv, # Matrix P: mxn (the pivot indices) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int dgetri_t( # DGETRI - compute the inverse of a matrix using the LU fac- # torization computed by DGETRF int *n, # Order of A np.float64_t *a, # Matrix A: nxn (the LUP decomposed matrix from dgetrf) int *lda, # The size of the first dimension of A (in memory) int *ipiv, # Matrix P: nxn (the pivot indices from the LUP decomposition) np.float64_t *work, # Matrix: nxn (a workspace for the inversion, optimal size=nxn) int *lwork, # Number of elements in the workspace: optimal is n**2 int *info # 0 if success, otherwise an error code (integer) ) ctypedef int dgetrs_t( # DGETRS - solve a system of linear equations A * X = B or A' # * X = B with a general N-by-N matrix A using the LU factori- # zation computed by DGETRF char *trans, # Specifies the form of the system of equations int *n, # Order of A int *nrhs, # The number of right hand sides np.float64_t *a, # Matrix A: nxn (the LUP decomposed matrix from dgetrf) int *lda, # The size of the first dimension of A (in memory) int *ipiv, # Matrix P: nxn (the pivot indices from the LUP decomposition) np.float64_t *b, # Matrix B: nxnrhs int *ldb, # The size of the first dimension of B (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int dpotrf_t( # Compute the Cholesky factorization of a # real symmetric positive definite matrix A char *uplo, # 'U': A = U'U and U is stored, 'L': A = LL' and L is stored int *n, # The order of the matrix A. n >= 0. np.float64_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int dpotri_t( # DPOTRI - compute the inverse of a real symmetric positive # definite matrix A using the Cholesky factorization A = # U**T*U or A = L*L**T computed by DPOTRF char *uplo, # 'U': A = U'U and U is stored, 'L': A = LL' and L is stored int *n, # The order of the matrix A. n >= 0. np.float64_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int dpotrs_t( # DPOTRS - solve a system of linear equations A*X = B with a # symmetric positive definite matrix A using the Cholesky fac- # torization A = U**T*U or A = L*L**T computed by DPOTRF char *uplo, # 'U': A = U'U and U is stored, 'L': A = LL' and L is stored int *n, # The order of the matrix A. n >= 0. int *nrhs, # The number of right hand sides np.float64_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) np.float64_t *b, # Matrix B: nxnrhs int *ldb, # The size of the first dimension of B (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int dtrtrs_t( # DTRTRS solves a triangular system of the form # A * X = B, A**T * X = B, or A**H * X = B, # where A is a triangular matrix of order N, and B is an N-by-NRHS # matrix. A check is made to verify that A is nonsingular. char *uplo, # 'U': A is upper triangular char *trans, # N: A * X = B; T: A**T * X = B; C: A**H * X = B char *diag, # {'U','N'}: unit triangular or not int *n, # The order of the matrix A. n >= 0. int *nrhs, # The number of right hand sides np.float64_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) np.float64_t *b, # Matrix B: nxnrhs int *ldb, # The size of the first dimension of B (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int cgetrf_t( # CGETRF - compute an LU factorization of a general M-by-N # matrix A using partial pivoting with row interchanges int *m, # Rows of A int *n, # Columns of A np.complex64_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) int *ipiv, # Matrix P: mxn (the pivot indices) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int cgetri_t( # CGETRI - compute the inverse of a matrix using the LU fac- # torization computed by CGETRF int *n, # Order of A np.complex64_t *a, # Matrix A: nxn (the LUP decomposed matrix from dgetrf) int *lda, # The size of the first dimension of A (in memory) int *ipiv, # Matrix P: nxn (the pivot indices from the LUP decomposition) np.complex64_t *work, # Matrix: nxn (a workspace for the inversion, optimal size=nxn) int *lwork, # Number of elements in the workspace: optimal is n**2 int *info # 0 if success, otherwise an error code (integer) ) ctypedef int cgetrs_t( # CGETRS - solve a system of linear equations A * X = B, A**T # * X = B, or A**H * X = B with a general N-by-N matrix A # using the LU factorization computed by CGETRF char *trans, # Specifies the form of the system of equations int *n, # Order of A int *nrhs, # The number of right hand sides np.complex64_t *a, # Matrix A: nxn (the LUP decomposed matrix from dgetrf) int *lda, # The size of the first dimension of A (in memory) int *ipiv, # Matrix P: nxn (the pivot indices from the LUP decomposition) np.complex64_t *b, # Matrix B: nxnrhs int *ldb, # The size of the first dimension of B (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int cpotrf_t( # Compute the Cholesky factorization of a # np.complex128_t Hermitian positive definite matrix A char *uplo, # 'U': A = U'U and U is stored, 'L': A = LL' and L is stored int *n, # The order of the matrix A. n >= 0. np.complex64_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int cpotri_t( # CPOTRI - compute the inverse of a np.complex128_t Hermitian positive # definite matrix A using the Cholesky factorization A = # U**T*U or A = L*L**T computed by CPOTRF char *uplo, # 'U': A = U'U and U is stored, 'L': A = LL' and L is stored int *n, # The order of the matrix A. n >= 0. np.complex64_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int cpotrs_t( # ZPOTRS - solve a system of linear equations A*X = B with a # Hermitian positive definite matrix A using the Cholesky fac- # torization A = U**H*U or A = L*L**H computed by ZPOTRF char *uplo, # 'U': A = U'U and U is stored, 'L': A = LL' and L is stored int *n, # The order of the matrix A. n >= 0. int *nrhs, # The number of right hand sides np.complex64_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) np.complex64_t *b, # Matrix B: nxnrhs int *ldb, # The size of the first dimension of B (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int ctrtrs_t( # CTRTRS solves a triangular system of the form # A * X = B, A**T * X = B, or A**H * X = B, # where A is a triangular matrix of order N, and B is an N-by-NRHS # matrix. A check is made to verify that A is nonsingular. char *uplo, # 'U': A is upper triangular char *trans, # N: A * X = B; T: A**T * X = B; C: A**H * X = B char *diag, # {'U','N'}: unit triangular or not int *n, # The order of the matrix A. n >= 0. int *nrhs, # The number of right hand sides np.complex64_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) np.complex64_t *b, # Matrix B: nxnrhs int *ldb, # The size of the first dimension of B (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int zgetrf_t( # ZGETRF - compute an LU factorization of a general M-by-N # matrix A using partial pivoting with row interchanges int *m, # Rows of A int *n, # Columns of A np.complex128_t *a, # Matrix A: mxn int *lda, # The size of the first dimension of A (in memory) int *ipiv, # Matrix P: mxn (the pivot indices) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int zgetri_t( # ZGETRI - compute the inverse of a matrix using the LU fac- # torization computed by ZGETRF int *n, # Order of A np.complex128_t *a, # Matrix A: nxn (the LUP decomposed matrix from dgetrf) int *lda, # The size of the first dimension of A (in memory) int *ipiv, # Matrix P: nxn (the pivot indices from the LUP decomposition) np.complex128_t *work, # Matrix: nxn (a workspace for the inversion, optimal size=nxn) int *lwork, # Number of elements in the workspace: optimal is n**2 int *info # 0 if success, otherwise an error code (integer) ) ctypedef int zgetrs_t( # ZGETRS - solve a system of linear equations A * X = B, A**T # * X = B, or A**H * X = B with a general N-by-N matrix A # using the LU factorization computed by ZGETRF char *trans, # Specifies the form of the system of equations int *n, # Order of A int *nrhs, # The number of right hand sides np.complex128_t *a, # Matrix A: nxn (the LUP decomposed matrix from dgetrf) int *lda, # The size of the first dimension of A (in memory) int *ipiv, # Matrix P: nxn (the pivot indices from the LUP decomposition) np.complex128_t *b, # Matrix B: nxnrhs int *ldb, # The size of the first dimension of B (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int zpotrf_t( # Compute the Cholesky factorization of a # np.complex128_t Hermitian positive definite matrix A char *uplo, # 'U': A = U'U and U is stored, 'L': A = LL' and L is stored int *n, # The order of the matrix A. n >= 0. np.complex128_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int zpotri_t( # ZPOTRI - compute the inverse of a np.complex128_t Hermitian positive # definite matrix A using the Cholesky factorization A = # U**T*U or A = L*L**T computed by ZPOTRF char *uplo, # 'U': A = U'U and U is stored, 'L': A = LL' and L is stored int *n, # The order of the matrix A. n >= 0. np.complex128_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int zpotrs_t( # ZPOTRS - solve a system of linear equations A*X = B with a # Hermitian positive definite matrix A using the Cholesky fac- # torization A = U**H*U or A = L*L**H computed by ZPOTRF char *uplo, # 'U': A = U'U and U is stored, 'L': A = LL' and L is stored int *n, # The order of the matrix A. n >= 0. int *nrhs, # The number of right hand sides np.complex128_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) np.complex128_t *b, # Matrix B: nxnrhs int *ldb, # The size of the first dimension of B (in memory) int *info # 0 if success, otherwise an error code (integer) ) ctypedef int ztrtrs_t( # ZTRTRS solves a triangular system of the form # A * X = B, A**T * X = B, or A**H * X = B, # where A is a triangular matrix of order N, and B is an N-by-NRHS # matrix. A check is made to verify that A is nonsingular. char *uplo, # 'U': A is upper triangular char *trans, # N: A * X = B; T: A**T * X = B; C: A**H * X = B char *diag, # {'U','N'}: unit triangular or not int *n, # The order of the matrix A. n >= 0. int *nrhs, # The number of right hand sides np.complex128_t *a, # Matrix A: nxn int *lda, # The size of the first dimension of A (in memory) np.complex128_t *b, # Matrix B: nxnrhs int *ldb, # The size of the first dimension of B (in memory) int *info # 0 if success, otherwise an error code (integer) )statsmodels-0.12.2/statsmodels/src/capsule.h000066400000000000000000000005751400612667500211120ustar00rootroot00000000000000/* partially cribbed from numpy/core/include/numpy/npy_3kcompat.h */ #include #if PY_VERSION_HEX >= 0x03000000 void* Capsule_AsVoidPtr(PyObject *obj) { void *ret = PyCapsule_GetPointer(obj, NULL); if (ret == NULL) { PyErr_Clear(); } return ret; } #else void* Capsule_AsVoidPtr(PyObject *ptr) { return PyCObject_AsVoidPtr(ptr); } #endif statsmodels-0.12.2/statsmodels/src/math.pxd000066400000000000000000000014401400612667500207430ustar00rootroot00000000000000# ## Math Functions # Real and complex log and abs functions from libc.math cimport log as dlog, abs as dabs, exp as dexp cimport numpy as np cdef extern from "numpy/npy_math.h": np.float64_t NPY_PI np.float64_t npy_cabs(np.npy_cdouble z) nogil np.npy_cdouble npy_clog(np.npy_cdouble z) nogil np.npy_cdouble npy_cexp(np.npy_cdouble z) nogil cdef inline np.float64_t zabs(np.complex128_t z) nogil: return npy_cabs(( &z)[0]) cdef inline np.complex128_t zlog(np.complex128_t z) nogil: cdef np.npy_cdouble x x = npy_clog(( &z)[0]) return ( &x)[0] cdef inline np.complex128_t zexp(np.complex128_t z) nogil: cdef np.npy_cdouble x x = npy_cexp(( &z)[0]) return ( &x)[0]statsmodels-0.12.2/statsmodels/stats/000077500000000000000000000000001400612667500176455ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/stats/__init__.py000066400000000000000000000001131400612667500217510ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/stats/_adnorm.py000066400000000000000000000103171400612667500216400ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Sep 25 21:23:38 2011 Author: Josef Perktold and Scipy developers License : BSD-3 """ import numpy as np from scipy import stats from statsmodels.tools.validation import array_like, bool_like, int_like def anderson_statistic(x, dist='norm', fit=True, params=(), axis=0): """ Calculate the Anderson-Darling a2 statistic. Parameters ---------- x : array_like The data to test. dist : {'norm', callable} The assumed distribution under the null of test statistic. fit : bool If True, then the distribution parameters are estimated. Currently only for 1d data x, except in case dist='norm'. params : tuple The optional distribution parameters if fit is False. axis : int If dist is 'norm' or fit is False, then data can be an n-dimensional and axis specifies the axis of a variable. Returns ------- {float, ndarray} The Anderson-Darling statistic. """ x = array_like(x, 'x', ndim=None) fit = bool_like(fit, 'fit') axis = int_like(axis, 'axis') y = np.sort(x, axis=axis) nobs = y.shape[axis] if fit: if dist == 'norm': xbar = np.expand_dims(np.mean(x, axis=axis), axis) s = np.expand_dims(np.std(x, ddof=1, axis=axis), axis) w = (y - xbar) / s z = stats.norm.cdf(w) # print z elif callable(dist): params = dist.fit(x) # print params z = dist.cdf(y, *params) print(z) else: raise ValueError("dist must be 'norm' or a Callable") else: if callable(dist): z = dist.cdf(y, *params) else: raise ValueError('if fit is false, then dist must be callable') i = np.arange(1, nobs + 1) sl1 = [None] * x.ndim sl1[axis] = slice(None) sl1 = tuple(sl1) sl2 = [slice(None)] * x.ndim sl2[axis] = slice(None, None, -1) sl2 = tuple(sl2) s = np.sum((2 * i[sl1] - 1.0) / nobs * (np.log(z) + np.log1p(-z[sl2])), axis=axis) a2 = -nobs - s return a2 def normal_ad(x, axis=0): """ Anderson-Darling test for normal distribution unknown mean and variance. Parameters ---------- x : array_like The data array. axis : int The axis to perform the test along. Returns ------- ad2 : float Anderson Darling test statistic. pval : float The pvalue for hypothesis that the data comes from a normal distribution with unknown mean and variance. See Also -------- statsmodels.stats.diagnostic.anderson_statistic The Anderson-Darling a2 statistic. statsmodels.stats.diagnostic.kstest_fit Kolmogorov-Smirnov test with estimated parameters for Normal or Exponential distributions. """ ad2 = anderson_statistic(x, dist='norm', fit=True, axis=axis) n = x.shape[axis] ad2a = ad2 * (1 + 0.75 / n + 2.25 / n ** 2) if np.size(ad2a) == 1: if (ad2a >= 0.00 and ad2a < 0.200): pval = 1 - np.exp(-13.436 + 101.14 * ad2a - 223.73 * ad2a ** 2) elif ad2a < 0.340: pval = 1 - np.exp(-8.318 + 42.796 * ad2a - 59.938 * ad2a ** 2) elif ad2a < 0.600: pval = np.exp(0.9177 - 4.279 * ad2a - 1.38 * ad2a ** 2) elif ad2a <= 13: pval = np.exp(1.2937 - 5.709 * ad2a + 0.0186 * ad2a ** 2) else: pval = 0.0 # is < 4.9542108058458799e-31 else: bounds = np.array([0.0, 0.200, 0.340, 0.600]) pval0 = lambda ad2a: np.nan * np.ones_like(ad2a) pval1 = lambda ad2a: 1 - np.exp( -13.436 + 101.14 * ad2a - 223.73 * ad2a ** 2) pval2 = lambda ad2a: 1 - np.exp( -8.318 + 42.796 * ad2a - 59.938 * ad2a ** 2) pval3 = lambda ad2a: np.exp(0.9177 - 4.279 * ad2a - 1.38 * ad2a ** 2) pval4 = lambda ad2a: np.exp(1.2937 - 5.709 * ad2a + 0.0186 * ad2a ** 2) pvalli = [pval0, pval1, pval2, pval3, pval4] idx = np.searchsorted(bounds, ad2a, side='right') pval = np.nan * np.ones_like(ad2a) for i in range(5): mask = (idx == i) pval[mask] = pvalli[i](ad2a[mask]) return ad2, pval statsmodels-0.12.2/statsmodels/stats/_diagnostic_other.py000066400000000000000000001233451400612667500237130ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Score, lagrange multiplier and conditional moment tests robust to misspecification or without specification of higher moments Created on Thu Oct 30 00:42:38 2014 Author: Josef Perktold License: BSD-3 Notes ----- This module is a mixture of very general and very specific functions for hypothesis testing in general models, targeted mainly to non-normal models. Some of the options or versions of these tests are mainly intented for cross-checking and to replicate different examples in references. We need clean versions with good defaults for those functions that are intended for the user. References ---------- The following references are collected after my intitial implementation and is most likely not exactly what I used. The main articles on which the functions are directly based upon, are Boos 1992, Tauchen 1985 and Whitney 1985a. Wooldrige artificial regression is based on several articles and his text book. Background reading are the textbooks by Cameron and Trivedi, Wooldridge and Davidson and MacKinnon. Newey and MacFadden 1994 provide some of the theoretical background. Poisson dispersion tests are based on Dean 1992 and articles and text books by Cameron and Trivedi. The references currently do not include the literature on LM-test for specification and diagnostic testing, like Pagan, Bera, Bera and Yoon and many others, except those for the Poisson excess dispersion case and Pagan and Vella. Boos, Dennis D. 1992. “On Generalized Score Tests.†The American Statistician 46 (4): 327–33. https://doi.org/10.2307/2685328. Breslow, Norman. 1989. “Score Tests in Overdispersed GLM’s.†In Statistical Modelling, edited by Adriano Decarli, Brian J. Francis, Robert Gilchrist, and Gilg U. H. Seeber, 64–74. Lecture Notes in Statistics 57. Springer New York. http://link.springer.com/chapter/10.1007/978-1-4612-3680-1_8. Breslow, Norman. 1990. “Tests of Hypotheses in Overdispersed Poisson Regression and Other Quasi- Likelihood Models.†Journal of the American Statistical Association 85 (410): 565–71. https://doi.org/10.2307/2289799. Cameron, A. Colin, and Pravin K. Trivedi. 1986. “Econometric Models Based on Count Data. Comparisons and Applications of Some Estimators and Tests.†Journal of Applied Econometrics 1 (1): 29–53. https://doi.org/10.1002/jae.3950010104. Cameron, A. Colin, and Pravin K. Trivedi. 1990a. “Conditional Moment Tests and Orthogonal Polynomials.†Indiana University, Department of Economics, Working Paper, 90–051. Cameron, A. Colin, and Pravin K. Trivedi. 1990b. “Regression-Based Tests for Overdispersion in the Poisson Model.†Journal of Econometrics 46 (3): 347–64. https://doi.org/10.1016/0304-4076(90)90014-K. Cameron, A. Colin, and Pravin K. Trivedi. Microeconometrics: methods and applications. Cambridge university press, 2005. Cameron, A. Colin, and Pravin K. Trivedi. Regression analysis of count data. Vol. 53. Cambridge university press, 2013. Davidson, Russell, and James G. MacKinnon. 1981. “Several Tests for Model Specification in the Presence of Alternative Hypotheses.†Econometrica 49 (3): 781–93. https://doi.org/10.2307/1911522. Davidson, Russell, and James G. MacKinnon. 1990. “Specification Tests Based on Artificial Regressions.†Journal of the American Statistical Association 85 (409): 220–27. https://doi.org/10.2307/2289548. Davidson, Russell, and James G. MacKinnon. 1991. “Artificial Regressions and C (α) Tests.†Economics Letters 35 (2): 149–53. https://doi.org/10.1016/0165-1765(91)90162-E. Davidson, Russell, and James G. MacKinnon. Econometric theory and methods. Vol. 5. New York: Oxford University Press, 2004. Dean, C. B. 1992. “Testing for Overdispersion in Poisson and Binomial Regression Models.†Journal of the American Statistical Association 87 (418): 451–57. https://doi.org/10.2307/2290276. Dean, C., and J. F. Lawless. 1989. “Tests for Detecting Overdispersion in Poisson Regression Models.†Journal of the American Statistical Association 84 (406): 467–72. https://doi.org/10.2307/2289931. Newey, Whitney K. 1985a. “Generalized Method of Moments Specification Testing.†Journal of Econometrics 29 (3): 229–56. https://doi.org/10.1016/0304-4076(85)90154-X. Newey, Whitney K. 1985b. “Maximum Likelihood Specification Testing and Conditional Moment Tests.†Econometrica 53 (5): 1047–70. https://doi.org/10.2307/1911011. Newey, Whitney K. and Kenneth D. West. 1987. “Hypothesis Testing with Efficient Method of Moments Estimation.†International Economic Review 28 (3): 777–87. https://doi.org/10.2307/2526578. Newey, Whitney K. and Daniel McFadden. 1994 "Large sample estimation and hypothesis testing." Handbook of econometrics 4: 2111-2245. Pagan, Adrian, and Frank Vella. 1989. “Diagnostic Tests for Models Based on Individual Data: A Survey.†Journal of Applied Econometrics 4 (S1): S29–59. https://doi.org/10.1002/jae.3950040504. Tauchen, George. 1985. “Diagnostic Testing and Evaluation of Maximum Likelihood Models.†Journal of Econometrics 30 (1–2): 415–43. https://doi.org/10.1016/0304-4076(85)90149-6. White, Halbert. 1981. “Consequences and Detection of Misspecified Nonlinear Regression Models.†Journal of the American Statistical Association 76 (374): 419–33. https://doi.org/10.2307/2287845. White, Halbert. 1983. “Maximum Likelihood Estimation of Misspecified Models.†Econometrica 51 (2): 513. https://doi.org/10.2307/1912004. White, Halbert. 1994. Estimation, Inference and Specification Analysis. Cambridge: Cambridge University Press. https://doi.org/10.1017/CCOL0521252806. Wooldridge, Jeffrey M. 1991. “Specification Testing and Quasi-Maximum- Likelihood Estimation.†Journal of Econometrics 48 (1–2): 29–55. https://doi.org/10.1016/0304-4076(91)90031-8. Wooldridge, Jeffrey M. 1990. “A Unified Approach to Robust, Regression-Based Specification Tests.†Econometric Theory 6 (1): 17–43. Wooldridge, Jeffrey M. 1991a. “On the Application of Robust, Regression- Based Diagnostics to Models of Conditional Means and Conditional Variances.†Journal of Econometrics 47 (1): 5–46. https://doi.org/10.1016/0304-4076(91)90076-P. Wooldridge, Jeffrey M. 1991b. “On the Application of Robust, Regression- Based Diagnostics to Models of Conditional Means and Conditional Variances.†Journal of Econometrics 47 (1): 5–46. https://doi.org/10.1016/0304-4076(91)90076-P. Wooldridge, Jeffrey M. 1991c. “Specification Testing and Quasi-Maximum- Likelihood Estimation.†Journal of Econometrics 48 (1–2): 29–55. https://doi.org/10.1016/0304-4076(91)90031-8. Wooldridge, Jeffrey M. 1994. “On the Limits of GLM for Specification Testing: A Comment on Gurmu and Trivedi.†Econometric Theory 10 (2): 409–18. https://doi.org/10.2307/3532875. Wooldridge, Jeffrey M. 1997. “Quasi-Likelihood Methods for Count Data.†Handbook of Applied Econometrics 2: 352–406. Wooldridge, Jeffrey M. Econometric analysis of cross section and panel data. MIT press, 2010. """ import numpy as np from scipy import stats from statsmodels.tools.decorators import cache_readonly from statsmodels.regression.linear_model import OLS class ResultsGeneric(object): def __init__(self, **kwds): self.__dict__.update(kwds) class TestResults(ResultsGeneric): def summary(self): txt = 'Specification Test (LM, score)\n' stat = [self.c1, self.c2, self.c3] pval = [self.pval1, self.pval2, self.pval3] description = ['nonrobust', 'dispersed', 'HC'] for row in zip(description, stat, pval): txt += '%-12s statistic = %6.4f pvalue = %6.5f\n' % row txt += '\nAssumptions:\n' txt += 'nonrobust: variance is correctly specified\n' txt += 'dispersed: variance correctly specified up to scale factor\n' txt += 'HC : robust to any heteroscedasticity\n' txt += 'test is not robust to correlation across observations' return txt def lm_test_glm(result, exog_extra, mean_deriv=None): '''score/lagrange multiplier test for GLM Wooldridge procedure for test of mean function in GLM Parameters ---------- results : GLMResults instance results instance with the constrained model exog_extra : ndarray or None additional exogenous variables for variable addition test This can be set to None if mean_deriv is provided. mean_deriv : None or ndarray Extra moment condition that correspond to the partial derivative of a mean function with respect to some parameters. Returns ------- test_results : Results instance The results instance has the following attributes which are score statistic and p-value for 3 versions of the score test. c1, pval1 : nonrobust score_test results c2, pval2 : score test results robust to over or under dispersion c3, pval3 : score test results fully robust to any heteroscedasticity The test results instance also has a simple summary method. Notes ----- TODO: add `df` to results and make df detection more robust This implements the auxiliary regression procedure of Wooldridge, implemented based on the presentation in chapter 8 in Handbook of Applied Econometrics 2. References ---------- Wooldridge, Jeffrey M. 1997. “Quasi-Likelihood Methods for Count Data.†Handbook of Applied Econometrics 2: 352–406. and other articles and text book by Wooldridge ''' if hasattr(result, '_result'): res = result._result else: res = result mod = result.model nobs = mod.endog.shape[0] #mean_func = mod.family.link.inverse dlinkinv = mod.family.link.inverse_deriv # derivative of mean function w.r.t. beta (linear params) dm = lambda x, linpred: dlinkinv(linpred)[:,None] * x var_func = mod.family.variance x = result.model.exog x2 = exog_extra # test omitted lin_pred = res.predict(linear=True) dm_incl = dm(x, lin_pred) if x2 is not None: dm_excl = dm(x2, lin_pred) if mean_deriv is not None: # allow both and stack dm_excl = np.column_stack((dm_excl, mean_deriv)) elif mean_deriv is not None: dm_excl = mean_deriv else: raise ValueError('either exog_extra or mean_deriv have to be provided') # TODO check for rank or redundant, note OLS calculates the rank k_constraint = dm_excl.shape[1] fittedvalues = res.predict() # discrete has linpred instead of mean v = var_func(fittedvalues) std = np.sqrt(v) res_ols1 = OLS(res.resid_response / std, np.column_stack((dm_incl, dm_excl)) / std[:, None]).fit() # case: nonrobust assumes variance implied by distribution is correct c1 = res_ols1.ess pval1 = stats.chi2.sf(c1, k_constraint) #print c1, stats.chi2.sf(c1, 2) # case: robust to dispersion c2 = nobs * res_ols1.rsquared pval2 = stats.chi2.sf(c2, k_constraint) #print c2, stats.chi2.sf(c2, 2) # case: robust to heteroscedasticity from statsmodels.stats.multivariate_tools import partial_project pp = partial_project(dm_excl / std[:,None], dm_incl / std[:,None]) resid_p = res.resid_response / std res_ols3 = OLS(np.ones(nobs), pp.resid * resid_p[:,None]).fit() #c3 = nobs * res_ols3.rsquared # this is Wooldridge c3b = res_ols3.ess # simpler if endog is ones pval3 = stats.chi2.sf(c3b, k_constraint) tres = TestResults(c1=c1, pval1=pval1, c2=c2, pval2=pval2, c3=c3b, pval3=pval3) return tres def cm_test_robust(resid, resid_deriv, instruments, weights=1): '''score/lagrange multiplier of Wooldridge generic version of Wooldridge procedure for test of conditional moments Limitation: This version allows only for one unconditional moment restriction, i.e. resid is scalar for each observation. Another limitation is that it assumes independent observations, no correlation in residuals and weights cannot be replaced by cross-observation whitening. Parameters ---------- resid : ndarray, (nobs, ) conditional moment restriction, E(r | x, params) = 0 resid_deriv : ndarray, (nobs, k_params) derivative of conditional moment restriction with respect to parameters instruments : ndarray, (nobs, k_instruments) indicator variables of Wooldridge, multiplies the conditional momen restriction weights : ndarray This is a weights function as used in WLS. The moment restrictions are multiplied by weights. This corresponds to the inverse of the variance in a heteroskedastic model. Returns ------- test_results : Results instance ??? TODO Notes ----- This implements the auxiliary regression procedure of Wooldridge, implemented based on procedure 2.1 in Wooldridge 1990. Wooldridge allows for multivariate conditional moments (`resid`) TODO: check dimensions for multivariate case for extension References ---------- Wooldridge Wooldridge and more Wooldridge ''' # notation: Wooldridge uses too mamny Greek letters # instruments is capital lambda # resid is small phi # resid_deriv is capital phi # weights is C nobs = resid.shape[0] from statsmodels.stats.multivariate_tools import partial_project w_sqrt = np.sqrt(weights) if np.size(weights) > 1: w_sqrt = w_sqrt[:,None] pp = partial_project(instruments * w_sqrt, resid_deriv * w_sqrt) mom_resid = pp.resid moms_test = mom_resid * resid[:, None] * w_sqrt # we get this here in case we extend resid to be more than 1-D k_constraint = moms_test.shape[1] # use OPG variance as in Wooldridge 1990. This might generalize cov = moms_test.T.dot(moms_test) diff = moms_test.sum(0) # see Wooldridge last page in appendix stat = diff.dot(np.linalg.solve(cov, diff)) # for checking, this corresponds to nobs * rsquared of auxiliary regression stat2 = OLS(np.ones(nobs), moms_test).fit().ess pval = stats.chi2.sf(stat, k_constraint) return stat, pval, stat2 def lm_robust(score, constraint_matrix, score_deriv_inv, cov_score, cov_params=None): '''general formula for score/LM test generalized score or lagrange multiplier test for implicit constraints `r(params) = 0`, with gradient `R = d r / d params` linear constraints are given by `R params - q = 0` It is assumed that all arrays are evaluated at the constrained estimates. Parameters ---------- score : ndarray, 1-D derivative of objective function at estimated parameters of constrained model constraint_matrix R : ndarray Linear restriction matrix or Jacobian of nonlinear constraints hessian_inv, Ainv : ndarray, symmetric, square inverse of second derivative of objective function TODO: could be OPG or any other estimator if information matrix equality holds cov_score B : ndarray, symmetric, square covariance matrix of the score. This is the inner part of a sandwich estimator. cov_params V : ndarray, symmetric, square covariance of full parameter vector evaluated at constrained parameter estimate. This can be specified instead of cov_score B. Returns ------- lm_stat : float score/lagrange multiplier statistic Notes ----- ''' # shorthand alias R, Ainv, B, V = constraint_matrix, score_deriv_inv, cov_score, cov_params tmp = R.dot(Ainv) wscore = tmp.dot(score) # C Ainv score if B is None and V is None: # only Ainv is given, so we assume information matrix identity holds # computational short cut, should be same if Ainv == inv(B) lm_stat = score.dot(Ainv.dot(score)) else: # information matrix identity does not hold if V is None: inner = tmp.dot(B).dot(tmp.T) else: inner = R.dot(V).dot(R.T) #lm_stat2 = wscore.dot(np.linalg.pinv(inner).dot(wscore)) # Let's assume inner is invertible, TODO: check if usecase for pinv exists lm_stat = wscore.dot(np.linalg.solve(inner, wscore)) return lm_stat#, lm_stat2 def lm_robust_subset(score, k_constraints, score_deriv_inv, cov_score): '''general formula for score/LM test generalized score or lagrange multiplier test for constraints on a subset of parameters `params_1 = value`, where params_1 is a subset of the unconstrained parameter vector. It is assumed that all arrays are evaluated at the constrained estimates. Parameters ---------- score : ndarray, 1-D derivative of objective function at estimated parameters of constrained model k_constraint : int number of constraints score_deriv_inv : ndarray, symmetric, square inverse of second derivative of objective function TODO: could be OPG or any other estimator if information matrix equality holds cov_score B : ndarray, symmetric, square covariance matrix of the score. This is the inner part of a sandwich estimator. not cov_params V : ndarray, symmetric, square covariance of full parameter vector evaluated at constrained parameter estimate. This can be specified instead of cov_score B. Returns ------- lm_stat : float score/lagrange multiplier statistic p-value : float p-value of the LM test based on chisquare distribution Notes ----- The implementation is based on Boos 1992 section 4.1. The same derivation is also in other articles and in text books. ''' # Notation in Boos # score `S = sum (s_i) # score_obs `s_i` # score_deriv `I` is derivative of score (hessian) # `D` is covariance matrix of score, OPG product given independent observations #k_params = len(score) # Note: I reverse order between constraint and unconstrained compared to Boos # submatrices of score_deriv/hessian # these are I22 and I12 in Boos #h_uu = score_deriv[-k_constraints:, -k_constraints:] h_uu = score_deriv_inv[:-k_constraints, :-k_constraints] h_cu = score_deriv_inv[-k_constraints:, :-k_constraints] # TODO: pinv or solve ? tmp_proj = h_cu.dot(np.linalg.inv(h_uu)) tmp = np.column_stack((-tmp_proj, np.eye(k_constraints))) #, tmp_proj)) cov_score_constraints = tmp.dot(cov_score.dot(tmp.T)) #lm_stat2 = wscore.dot(np.linalg.pinv(inner).dot(wscore)) # Let's assume inner is invertible, TODO: check if usecase for pinv exists lm_stat = score.dot(np.linalg.solve(cov_score_constraints, score)) pval = stats.chi2.sf(lm_stat, k_constraints) # # check second calculation Boos referencing Kent 1982 and Engle 1984 # # we can use this when robust_cov_params of full model is available # #h_inv = np.linalg.inv(score_deriv) # hinv = score_deriv_inv # v = h_inv.dot(cov_score.dot(h_inv)) # this is robust cov_params # v_cc = v[:k_constraints, :k_constraints] # h_cc = score_deriv[:k_constraints, :k_constraints] # # brute force calculation: # h_resid_cu = h_cc - h_cu.dot(np.linalg.solve(h_uu, h_cu)) # cov_s_c = h_resid_cu.dot(v_cc.dot(h_resid_cu)) # diff = np.max(np.abs(cov_s_c - cov_score_constraints)) return lm_stat, pval #, lm_stat2 def lm_robust_subset_parts(score, k_constraints, score_deriv_uu, score_deriv_cu, cov_score_cc, cov_score_cu, cov_score_uu): """robust generalized score tests on subset of parameters This is the same as lm_robust_subset with arguments in parts of partitioned matrices. This can be useful, when we have the parts based on different estimation procedures, i.e. when we do not have the full unconstrained model. Calculates mainly the covariance of the constraint part of the score. Parameters ---------- score : ndarray, 1-D derivative of objective function at estimated parameters of constrained model. These is the score component for the restricted part under hypothesis. The unconstrained part of the score is assumed to be zero. k_constraint : int number of constraints score_deriv_uu : ndarray, symmetric, square first derivative of moment equation or second derivative of objective function for the unconstrained part TODO: could be OPG or any other estimator if information matrix equality holds score_deriv_cu : ndarray first cross derivative of moment equation or second cross derivative of objective function between. cov_score_cc : ndarray covariance matrix of the score for the unconstrained part. This is the inner part of a sandwich estimator. cov_score_cu : ndarray covariance matrix of the score for the off-diagonal block, i.e. covariance between constrained and unconstrained part. cov_score_uu : ndarray covariance matrix of the score for the unconstrained part. Returns ------- lm_stat : float score/lagrange multiplier statistic p-value : float p-value of the LM test based on chisquare distribution Notes ----- TODO: these function should just return the covariance of the score instead of calculating the score/lm test. Implementation similar to lm_robust_subset and is based on Boos 1992, section 4.1 in the form attributed to Breslow (1990). It does not use the computation attributed to Kent (1982) and Engle (1984). """ tmp_proj = np.linalg.solve(score_deriv_uu, score_deriv_cu.T).T tmp = tmp_proj.dot(cov_score_cu.T) # this needs to make a copy of cov_score_cc for further inplace modification cov = cov_score_cc - tmp cov -= tmp.T cov += tmp_proj.dot(cov_score_uu).dot(tmp_proj.T) lm_stat = score.dot(np.linalg.solve(cov, score)) pval = stats.chi2.sf(lm_stat, k_constraints) return lm_stat, pval def lm_robust_reparameterized(score, params_deriv, score_deriv, cov_score): """robust generalized score test for transformed parameters The parameters are given by a nonlinear transformation of the estimated reduced parameters `params = g(params_reduced)` with jacobian `G = d g / d params_reduced` score and other arrays are for full parameter space `params` Parameters ---------- score : ndarray, 1-D derivative of objective function at estimated parameters of constrained model params_deriv : ndarray Jacobian G of the parameter trasnformation score_deriv : ndarray, symmetric, square second derivative of objective function TODO: could be OPG or any other estimator if information matrix equality holds cov_score B : ndarray, symmetric, square covariance matrix of the score. This is the inner part of a sandwich estimator. Returns ------- lm_stat : float score/lagrange multiplier statistic p-value : float p-value of the LM test based on chisquare distribution Notes ----- Boos 1992, section 4.3, expression for T_{GS} just before example 6 """ # Boos notation # params_deriv G k_params, k_reduced = params_deriv.shape k_constraints = k_params - k_reduced G = params_deriv # shortcut alias tmp_c0 = np.linalg.pinv(G.T.dot(score_deriv.dot(G))) tmp_c1 = score_deriv.dot(G.dot(tmp_c0.dot(G.T))) tmp_c = np.eye(k_params) - tmp_c1 cov = tmp_c.dot(cov_score.dot(tmp_c.T)) # warning: reduced rank lm_stat = score.dot(np.linalg.pinv(cov).dot(score)) pval = stats.chi2.sf(lm_stat, k_constraints) return lm_stat, pval def dispersion_poisson(results): """Score/LM type tests for Poisson variance assumptions Null Hypothesis is H0: var(y) = E(y) and assuming E(y) is correctly specified H1: var(y) ~= E(y) The tests are based on the constrained model, i.e. the Poisson model. The tests differ in their assumed alternatives, and in their maintained assumptions. Parameters ---------- results : Poisson results instance This can be a results instance for either a discrete Poisson or a GLM with family Poisson. Returns ------- res : ndarray, shape (7, 2) each row contains the test statistic and p-value for one of the 7 tests computed here. description : 2-D list of strings Each test has two strings a descriptive name and a string for the alternative hypothesis. """ if hasattr(results, '_results'): results = results._results endog = results.model.endog nobs = endog.shape[0] #TODO: use attribute, may need to be added fitted = results.predict() #fitted = results.fittedvalues # discrete has linear prediction #this assumes Poisson resid2 = results.resid_response**2 var_resid_endog = (resid2 - endog) var_resid_fitted = (resid2 - fitted) std1 = np.sqrt(2 * (fitted**2).sum()) var_resid_endog_sum = var_resid_endog.sum() dean_a = var_resid_fitted.sum() / std1 dean_b = var_resid_endog_sum / std1 dean_c = (var_resid_endog / fitted).sum() / np.sqrt(2 * nobs) pval_dean_a = stats.norm.sf(np.abs(dean_a)) pval_dean_b = stats.norm.sf(np.abs(dean_b)) pval_dean_c = stats.norm.sf(np.abs(dean_c)) results_all = [[dean_a, pval_dean_a], [dean_b, pval_dean_b], [dean_c, pval_dean_c]] description = [['Dean A', 'mu (1 + a mu)'], ['Dean B', 'mu (1 + a mu)'], ['Dean C', 'mu (1 + a)']] # Cameron Trived auxiliary regression page 78 count book 1989 endog_v = var_resid_endog / fitted res_ols_nb2 = OLS(endog_v, fitted).fit(use_t=False) stat_ols_nb2 = res_ols_nb2.tvalues[0] pval_ols_nb2 = res_ols_nb2.pvalues[0] results_all.append([stat_ols_nb2, pval_ols_nb2]) description.append(['CT nb2', 'mu (1 + a mu)']) res_ols_nb1 = OLS(endog_v, fitted).fit(use_t=False) stat_ols_nb1 = res_ols_nb1.tvalues[0] pval_ols_nb1 = res_ols_nb1.pvalues[0] results_all.append([stat_ols_nb1, pval_ols_nb1]) description.append(['CT nb1', 'mu (1 + a)']) endog_v = var_resid_endog / fitted res_ols_nb2 = OLS(endog_v, fitted).fit(cov_type='HC1', use_t=False) stat_ols_hc1_nb2 = res_ols_nb2.tvalues[0] pval_ols_hc1_nb2 = res_ols_nb2.pvalues[0] results_all.append([stat_ols_hc1_nb2, pval_ols_hc1_nb2]) description.append(['CT nb2 HC1', 'mu (1 + a mu)']) res_ols_nb1 = OLS(endog_v, np.ones(len(endog_v))).fit(cov_type='HC1', use_t=False) stat_ols_hc1_nb1 = res_ols_nb1.tvalues[0] pval_ols_hc1_nb1 = res_ols_nb1.pvalues[0] results_all.append([stat_ols_hc1_nb1, pval_ols_hc1_nb1]) description.append(['CT nb1 HC1', 'mu (1 + a)']) return np.array(results_all), description def dispersion_poisson_generic(results, exog_new_test, exog_new_control=None, include_score=False, use_endog=True, cov_type='HC1', cov_kwds=None, use_t=False): """A variable addition test for the variance function This uses an artificial regression to calculate a variant of an LM or generalized score test for the specification of the variance assumption in a Poisson model. The performed test is a Wald test on the coefficients of the `exog_new_test`. Warning: insufficiently tested, especially for options """ if hasattr(results, '_results'): results = results._results endog = results.model.endog nobs = endog.shape[0] #TODO: use attribute, may need to be added # fitted = results.fittedvalues # generic has linpred as fittedvalues fitted = results.predict() resid2 = results.resid_response**2 #the following assumes Poisson if use_endog: var_resid = (resid2 - endog) else: var_resid = (resid2 - fitted) endog_v = var_resid / fitted k_constraints = exog_new_test.shape[1] ex_list = [exog_new_test] if include_score: score_obs = results.model.score_obs(results.params) ex_list.append(score_obs) if exog_new_control is not None: ex_list.append(score_obs) if len(ex_list) > 1: ex = np.column_stack(ex_list) use_wald = True else: ex = ex_list[0] # no control variables in exog use_wald = False res_ols = OLS(endog_v, ex).fit(cov_type=cov_type, cov_kwds=cov_kwds, use_t=use_t) if use_wald: # we have controls and need to test coefficients k_vars = ex.shape[1] constraints = np.eye(k_constraints, k_vars) ht = res_ols.wald_test(constraints) stat_ols = ht.statistic pval_ols = ht.pvalue else: # we do not have controls and can use overall fit nobs = endog_v.shape[0] rsquared_noncentered = 1 - res_ols.ssr/res_ols.uncentered_tss stat_ols = nobs * rsquared_noncentered pval_ols = stats.chi2.sf(stat_ols, k_constraints) return stat_ols, pval_ols def conditional_moment_test_generic(mom_test, mom_test_deriv, mom_incl, mom_incl_deriv, var_mom_all=None, cov_type='OPG', cov_kwds=None): """generic conditional moment test This is mainly intended as internal function in support of diagnostic and specification tests. It has no conversion and checking of correct arguments. Parameters ---------- mom_test : ndarray, 2-D (nobs, k_constraints) moment conditions that will be tested to be zero mom_test_deriv : ndarray, 2-D, square (k_constraints, k_constraints) derivative of moment conditions under test with respect to the parameters of the model summed over observations. mom_incl : ndarray, 2-D (nobs, k_params) moment conditions that where use in estimation, assumed to be zero This is score_obs in the case of (Q)MLE mom_incl_deriv : ndarray, 2-D, square (k_params, k_params) derivative of moment conditions of estimator summed over observations This is the information matrix or Hessian in the case of (Q)MLE. var_mom_all : None, or ndarray, 2-D, (k, k) with k = k_constraints + k_params Expected product or variance of the joint (column_stacked) moment conditions. The stacking should have the variance of the moment conditions under test in the first k_constraint rows and columns. If it is not None, then it will be estimated based on cov_type. I think: This is the Hessian of the extended or alternative model under full MLE and score test assuming information matrix identity holds. Returns ------- results Notes ----- TODO: cov_type other than OPG is missing initial implementation based on Cameron Trived countbook 1998 p.48, p.56 also included: mom_incl can be None if expected mom_test_deriv is zero. References ---------- Cameron and Trivedi 1998 count book Wooldridge ??? Pagan and Vella 1989 """ if cov_type != 'OPG': raise NotImplementedError k_constraints = mom_test.shape[1] if mom_incl is None: # assume mom_test_deriv is zero, do not include effect of mom_incl if var_mom_all is None: var_cm = mom_test.T.dot(mom_test) else: var_cm = var_mom_all else: # take into account he effect of parameter estimates on mom_test if var_mom_all is None: mom_all = np.column_stack((mom_test, mom_incl)) # TODO: replace with inner sandwich covariance estimator var_mom_all = mom_all.T.dot(mom_all) tmp = mom_test_deriv.dot(np.linalg.pinv(mom_incl_deriv)) h = np.column_stack((np.eye(k_constraints), -tmp)) var_cm = h.dot(var_mom_all.dot(h.T)) # calculate test results with chisquare var_cm_inv = np.linalg.pinv(var_cm) mom_test_sum = mom_test.sum(0) statistic = mom_test_sum.dot(var_cm_inv.dot(mom_test_sum)) pval = stats.chi2.sf(statistic, k_constraints) # normal test of individual components se = np.sqrt(np.diag(var_cm)) tvalues = mom_test_sum / se pvalues = stats.norm.sf(np.abs(tvalues)) res = ResultsGeneric(var_cm=var_cm, stat_cmt=statistic, pval_cmt=pval, tvalues=tvalues, pvalues=pvalues) return res def conditional_moment_test_regression(mom_test, mom_test_deriv=None, mom_incl=None, mom_incl_deriv=None, var_mom_all=None, demean=False, cov_type='OPG', cov_kwds=None): """generic conditional moment test based artificial regression this is very experimental, no options implemented yet so far OPG regression, or artificial regression with Robust Wald test The latter is (as far as I can see) the same as an overidentifying test in GMM where the test statistic is the value of the GMM objective function and it is assumed that parameters were estimated with optimial GMM, i.e. the weight matrix equal to the expectation of the score variance. """ # so far coded from memory nobs, k_constraints = mom_test.shape endog = np.ones(nobs) if mom_incl is not None: ex = np.column_stack((mom_test, mom_incl)) else: ex = mom_test if demean: ex -= ex.mean(0) if cov_type == 'OPG': res = OLS(endog, ex).fit() statistic = nobs * res.rsquared pval = stats.chi2.sf(statistic, k_constraints) else: res = OLS(endog, ex).fit(cov_type=cov_type, cov_kwds=cov_kwds) tres = res.wald_test(np.eye(ex.shape[1])) statistic = tres.statistic pval = tres.pvalue return statistic, pval class CMTNewey(object): """generic moment test for GMM This is a class to calculate and hold the various results This is based on Newey 1985 on GMM. Lemma 1: Theorem 1 The main method is `chisquare` which returns the result of the conditional moment test. Warning: name of class and methods will likely be changed Parameters ---------- moments : ndarray, 1-D moments that are tested to be zero. They do not need to be derived from a likelihood function. moments_deriv : ndarray derivative of the moment function with respect to the parameters that are estimated cov_moments : ndarray An estimate for the joint (expected) covariance of all moments. This can be a heteroscedasticity or correlation robust covariance estimate, i.e. the inner part of a sandwich covariance. weights : ndarray Weights used in the GMM estimation. transf_mt : ndarray This defines the test moments where `transf_mt` is the matrix that defines a Linear combination of moments that have expected value equal to zero under the Null hypothesis. Notes ----- The one letter names in Newey 1985 are moments, g : cov_moments, V : moments_deriv, H : weights, W : transf_mt, L : linear transformation to get the test condition from the moments not used, add as argument to methods or __init__? K cov for misspecification or mispecification_deriv This follows the GMM version in Newey 1985a, not the MLE version in Newey 1985b. Newey uses the generalized information matrix equality in the MLE version Newey (1985b). Newey 1985b Lemma 1 does not impose correctly specified likelihood, but assumes it in the following. Lemma 1 in both articles are essentially the same assuming D = H' W. References ---------- - Newey 1985a, Generalized Method of Moment specification testing, Journal of Econometrics - Newey 1985b, Maximum Likelihood Specification Testing and Conditional Moment Tests, Econometrica """ def __init__(self, moments, cov_moments, moments_deriv, weights, transf_mt): self.moments = moments self.cov_moments = cov_moments self.moments_deriv = moments_deriv self.weights = weights self.transf_mt = transf_mt # derived quantities self.moments_constraint = transf_mt.dot(moments) self.htw = moments_deriv.T.dot(weights) # H'W # TODO check these self.k_moments = self.moments.shape[-1] # in this case only 1-D # assuming full rank of L' self.k_constraints = self.transf_mt.shape[0] @cache_readonly def asy_transf_params(self): moments_deriv = self.moments_deriv # H #weights = self.weights # W htw = self.htw # moments_deriv.T.dot(weights) # H'W res = np.linalg.solve(htw.dot(moments_deriv), htw) #res = np.linalg.pinv(htw.dot(moments_deriv)).dot(htw) return -res @cache_readonly def project_w(self): # P_w = I - H (H' W H)^{-1} H' W moments_deriv = self.moments_deriv # H res = moments_deriv.dot(self.asy_transf_params) res += np.eye(res.shape[0]) return res @cache_readonly def asy_transform_mom_constraints(self): # L P_w res = self.transf_mt.dot(self.project_w) return res @cache_readonly def asy_cov_moments(self): """ `sqrt(T) * g_T(b_0) asy N(K delta, V)` mean is not implemented, V is the same as cov_moments in __init__ argument """ return self.cov_moments @cache_readonly def cov_mom_constraints(self): # linear transformation transf = self.asy_transform_mom_constraints return transf.dot(self.asy_cov_moments).dot(transf.T) @cache_readonly def rank_cov_mom_constraints(self): return np.linalg.matrix_rank(self.cov_mom_constraints) def ztest(self): """statistic, p-value and degrees of freedom of separate moment test currently two sided test only TODO: This can use generic ztest/ttest features and return ContrastResults """ diff = self.moments_constraint bse = np.sqrt(np.diag(self.cov_mom_constraints)) # Newey uses a generalized inverse stat = diff / bse pval = stats.norm.sf(np.abs(stat))*2 return stat, pval @cache_readonly def chisquare(self): """statistic, p-value and degrees of freedom of joint moment test """ diff = self.moments_constraint cov = self.cov_mom_constraints # Newey uses a generalized inverse stat = diff.T.dot(np.linalg.pinv(cov).dot(diff)) df = self.rank_cov_mom_constraints pval = stats.chi2.sf(stat, df) # Theorem 1 return stat, pval, df class CMTTauchen(object): """generic moment tests or conditional moment tests for Quasi-MLE This is a generic class based on Tauchen 1985 The main method is `chisquare` which returns the result of the conditional moment test. Warning: name of class and of methods will likely be changed Parameters ---------- score : ndarray, 1-D moment condition used in estimation, score of log-likelihood function score_deriv : ndarray derivative of score function with respect to the parameters that are estimated. This is the Hessian in quasi-maximum likelihood moments : ndarray, 1-D moments that are tested to be zero. They do not need to be derived from a likelihood function. moments_deriv : ndarray derivative of the moment function with respect to the parameters that are estimated cov_moments : ndarray An estimate for the joint (expected) covariance of score and test moments. This can be a heteroscedasticity or correlation robust covariance estimate, i.e. the inner part of a sandwich covariance. """ def __init__(self, score, score_deriv, moments, moments_deriv, cov_moments): self.score = score self.score_deriv = score_deriv self.moments = moments self.moments_deriv = moments_deriv self.cov_moments_all = cov_moments self.k_moments_test = moments.shape[-1] self.k_params = score.shape[-1] self.k_moments_all = self.k_params + self.k_moments_test @cache_readonly def cov_params_all(self): m_deriv = np.zeros((self.k_moments_all, self.k_moments_all)) m_deriv[:self.k_params, :self.k_params] = self.score_deriv m_deriv[self.k_params:, :self.k_params] = self.moments_deriv m_deriv[self.k_params:, self.k_params:] = np.eye(self.k_moments_test) m_deriv_inv = np.linalg.inv(m_deriv) cov = m_deriv_inv.dot(self.cov_moments_all.dot(m_deriv_inv.T)) # K_inv J K_inv return cov @cache_readonly def cov_mom_constraints(self): return self.cov_params_all[self.k_params:, self.k_params:] @cache_readonly def rank_cov_mom_constraints(self): return np.linalg.matrix_rank(self.cov_mom_constraints) # TODO: not DRY, just copied from CMTNewey def ztest(self): """statistic, p-value and degrees of freedom of separate moment test currently two sided test only TODO: This can use generic ztest/ttest features and return ContrastResults """ diff = self.moments_constraint bse = np.sqrt(np.diag(self.cov_mom_constraints)) # Newey uses a generalized inverse stat = diff / bse pval = stats.norm.sf(np.abs(stat))*2 return stat, pval @cache_readonly def chisquare(self): """statistic, p-value and degrees of freedom of joint moment test """ diff = self.moments #_constraints cov = self.cov_mom_constraints # Newey uses a generalized inverse, we use it also here stat = diff.T.dot(np.linalg.pinv(cov).dot(diff)) #df = self.k_moments_test # We allow for redundant mom_constraints: df = self.rank_cov_mom_constraints pval = stats.chi2.sf(stat, df) return stat, pval, df statsmodels-0.12.2/statsmodels/stats/_knockoff.py000066400000000000000000000163251400612667500221650ustar00rootroot00000000000000""" The RegressionFDR class implements the 'Knockoff' approach for controlling false discovery rates (FDR) in regression analysis. The knockoff approach does not require standard errors. Thus one application is to provide inference for parameter estimates that are not smooth functions of the data. For example, the knockoff approach can be used to do inference for parameter estimates obtained from the LASSO, of from stepwise variable selection. The knockoff approach controls FDR for parameter estimates that may be dependent, such as coefficient estimates in a multiple regression model. The knockoff approach is applicable whenever the test statistic can be computed entirely from x'y and x'x, where x is the design matrix and y is the vector of responses. Reference --------- Rina Foygel Barber, Emmanuel Candes (2015). Controlling the False Discovery Rate via Knockoffs. Annals of Statistics 43:5. http://statweb.stanford.edu/~candes/papers/FDR_regression.pdf """ import numpy as np import pandas as pd from statsmodels.iolib import summary2 class RegressionFDR(object): """ Control FDR in a regression procedure. Parameters ---------- endog : array_like The dependent variable of the regression exog : array_like The independent variables of the regression regeffects : RegressionEffects instance An instance of a RegressionEffects class that can compute effect sizes for the regression coefficients. method : str The approach used to assess and control FDR, currently must be 'knockoff'. Returns ------- Returns an instance of the RegressionFDR class. The `fdr` attribute holds the estimated false discovery rates. Notes ----- This class Implements the knockoff method of Barber and Candes. This is an approach for controlling the FDR of a variety of regression estimation procedures, including correlation coefficients, OLS regression, OLS with forward selection, and LASSO regression. For other approaches to FDR control in regression, see the statsmodels.stats.multitest module. Methods provided in that module use Z-scores or p-values, and therefore require standard errors for the coefficient estimates to be available. The default method for constructing the augmented design matrix is the 'equivariant' approach, set `design_method='sdp'` to use an alternative approach involving semidefinite programming. See Barber and Candes for more information about both approaches. The sdp approach requires that the cvxopt package be installed. """ def __init__(self, endog, exog, regeffects, method="knockoff", **kwargs): if hasattr(exog, "columns"): self.xnames = exog.columns else: self.xnames = ["x%d" % j for j in range(exog.shape[1])] exog = np.asarray(exog) endog = np.asarray(endog) if "design_method" not in kwargs: kwargs["design_method"] = "equi" nobs, nvar = exog.shape if kwargs["design_method"] == "equi": exog1, exog2, _ = _design_knockoff_equi(exog) elif kwargs["design_method"] == "sdp": exog1, exog2, _ = _design_knockoff_sdp(exog) endog = endog - np.mean(endog) self.endog = endog self.exog = np.concatenate((exog1, exog2), axis=1) self.exog1 = exog1 self.exog2 = exog2 self.stats = regeffects.stats(self) unq, inv, cnt = np.unique(self.stats, return_inverse=True, return_counts=True) # The denominator of the FDR cc = np.cumsum(cnt) denom = len(self.stats) - cc + cnt denom[denom < 1] = 1 # The numerator of the FDR ii = np.searchsorted(unq, -unq, side='right') - 1 numer = cc[ii] numer[ii < 0] = 0 # The knockoff+ estimated FDR fdrp = (1 + numer) / denom # The knockoff estimated FDR fdr = numer / denom self.fdr = fdr[inv] self.fdrp = fdrp[inv] self._ufdr = fdr self._unq = unq df = pd.DataFrame(index=self.xnames) df["Stat"] = self.stats df["FDR+"] = self.fdrp df["FDR"] = self.fdr self.fdr_df = df def threshold(self, tfdr): """ Returns the threshold statistic for a given target FDR. """ if np.min(self._ufdr) <= tfdr: return self._unq[self._ufdr <= tfdr][0] else: return np.inf def summary(self): summ = summary2.Summary() summ.add_title("Regression FDR results") summ.add_df(self.fdr_df) return summ def _design_knockoff_sdp(exog): """ Use semidefinite programming to construct a knockoff design matrix. Requires cvxopt to be installed. """ try: from cvxopt import solvers, matrix except ImportError: raise ValueError("SDP knockoff designs require installation of cvxopt") nobs, nvar = exog.shape # Standardize exog xnm = np.sum(exog**2, 0) xnm = np.sqrt(xnm) exog = exog / xnm Sigma = np.dot(exog.T, exog) c = matrix(-np.ones(nvar)) h0 = np.concatenate((np.zeros(nvar), np.ones(nvar))) h0 = matrix(h0) G0 = np.concatenate((-np.eye(nvar), np.eye(nvar)), axis=0) G0 = matrix(G0) h1 = 2 * Sigma h1 = matrix(h1) i, j = np.diag_indices(nvar) G1 = np.zeros((nvar*nvar, nvar)) G1[i*nvar + j, i] = 1 G1 = matrix(G1) solvers.options['show_progress'] = False sol = solvers.sdp(c, G0, h0, [G1], [h1]) sl = np.asarray(sol['x']).ravel() xcov = np.dot(exog.T, exog) exogn = _get_knmat(exog, xcov, sl) return exog, exogn, sl def _design_knockoff_equi(exog): """ Construct an equivariant design matrix for knockoff analysis. Follows the 'equi-correlated knockoff approach of equation 2.4 in Barber and Candes. Constructs a pair of design matrices exogs, exogn such that exogs is a scaled/centered version of the input matrix exog, exogn is another matrix of the same shape with cov(exogn) = cov(exogs), and the covariances between corresponding columns of exogn and exogs are as small as possible. """ nobs, nvar = exog.shape if nobs < 2*nvar: msg = "The equivariant knockoff can ony be used when n >= 2*p" raise ValueError(msg) # Standardize exog xnm = np.sum(exog**2, 0) xnm = np.sqrt(xnm) exog = exog / xnm xcov = np.dot(exog.T, exog) ev, _ = np.linalg.eig(xcov) evmin = np.min(ev) sl = min(2*evmin, 1) sl = sl * np.ones(nvar) exogn = _get_knmat(exog, xcov, sl) return exog, exogn, sl def _get_knmat(exog, xcov, sl): # Utility function, see equation 2.2 of Barber & Candes. nobs, nvar = exog.shape ash = np.linalg.inv(xcov) ash *= -np.outer(sl, sl) i, j = np.diag_indices(nvar) ash[i, j] += 2 * sl umat = np.random.normal(size=(nobs, nvar)) u, _ = np.linalg.qr(exog) umat -= np.dot(u, np.dot(u.T, umat)) umat, _ = np.linalg.qr(umat) ashr, xc, _ = np.linalg.svd(ash, 0) ashr *= np.sqrt(xc) ashr = ashr.T ex = (sl[:, None] * np.linalg.solve(xcov, exog.T)).T exogn = exog - ex + np.dot(umat, ashr) return exogn statsmodels-0.12.2/statsmodels/stats/_lilliefors.py000066400000000000000000000226441400612667500225320ustar00rootroot00000000000000""" Implements Lilliefors corrected Kolmogorov-Smirnov tests for normal and exponential distributions. `kstest_fit` is provided as a top-level function to access both tests. `kstest_normal` and `kstest_exponential` are provided as convenience functions with the appropriate test as the default. `lilliefors` is provided as an alias for `kstest_fit`. Created on Sat Oct 01 13:16:49 2011 Author: Josef Perktold License: BSD-3 pvalues for Lilliefors test are based on formula and table in An Analytic Approximation to the Distribution of Lilliefors's Test Statistic for Normality Author(s): Gerard E. Dallal and Leland WilkinsonSource: The American Statistician, Vol. 40, No. 4 (Nov., 1986), pp. 294-296 Published by: American Statistical Association Stable URL: http://www.jstor.org/stable/2684607 . On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown Hubert W. Lilliefors Journal of the American Statistical Association, Vol. 62, No. 318. (Jun., 1967), pp. 399-402. --- Updated 2017-07-23 Jacob C. Kimmel Ref: Lilliefors, H.W. On the Kolmogorov-Smirnov test for the exponential distribution with mean unknown. Journal of the American Statistical Association, Vol 64, No. 325. (1969), pp. 387–389. """ from functools import partial import numpy as np from scipy import stats from statsmodels.tools.validation import string_like from ._lilliefors_critical_values import (critical_values, asymp_critical_values, PERCENTILES) from .tabledist import TableDist def _make_asymptotic_function(params): """ Generates an asymptotic distribution callable from a param matrix Polynomial is a[0] * x**(-1/2) + a[1] * x**(-1) + a[2] * x**(-3/2) Parameters ---------- params : ndarray Array with shape (nalpha, 3) where nalpha is the number of significance levels """ def f(n): poly = np.array([1, np.log(n), np.log(n) ** 2]) return np.exp(poly.dot(params.T)) return f def ksstat(x, cdf, alternative='two_sided', args=()): """ Calculate statistic for the Kolmogorov-Smirnov test for goodness of fit This calculates the test statistic for a test of the distribution G(x) of an observed variable against a given distribution F(x). Under the null hypothesis the two distributions are identical, G(x)=F(x). The alternative hypothesis can be either 'two_sided' (default), 'less' or 'greater'. The KS test is only valid for continuous distributions. Parameters ---------- x : array_like, 1d array of observations cdf : str or callable string: name of a distribution in scipy.stats callable: function to evaluate cdf alternative : 'two_sided' (default), 'less' or 'greater' defines the alternative hypothesis (see explanation) args : tuple, sequence distribution parameters for call to cdf Returns ------- D : float KS test statistic, either D, D+ or D- See Also -------- scipy.stats.kstest Notes ----- In the one-sided test, the alternative is that the empirical cumulative distribution function of the random variable is "less" or "greater" than the cumulative distribution function F(x) of the hypothesis, G(x)<=F(x), resp. G(x)>=F(x). In contrast to scipy.stats.kstest, this function only calculates the statistic which can be used either as distance measure or to implement case specific p-values. """ nobs = float(len(x)) if isinstance(cdf, str): cdf = getattr(stats.distributions, cdf).cdf elif hasattr(cdf, 'cdf'): cdf = getattr(cdf, 'cdf') x = np.sort(x) cdfvals = cdf(x, *args) d_plus = (np.arange(1.0, nobs + 1) / nobs - cdfvals).max() d_min = (cdfvals - np.arange(0.0, nobs) / nobs).max() if alternative == 'greater': return d_plus elif alternative == 'less': return d_min return np.max([d_plus, d_min]) def get_lilliefors_table(dist='norm'): """ Generates tables for significance levels of Lilliefors test statistics Tables for available normal and exponential distribution testing, as specified in Lilliefors references above Parameters ---------- dist : str distribution being tested in set {'norm', 'exp'}. Returns ------- lf : TableDist object. table of critical values """ # function just to keep things together # for this test alpha is sf probability, i.e. right tail probability alpha = 1 - np.array(PERCENTILES) / 100.0 alpha = alpha[::-1] dist = 'normal' if dist == 'norm' else dist if dist not in critical_values: raise ValueError("Invalid dist parameter. Must be 'norm' or 'exp'") cv_data = critical_values[dist] acv_data = asymp_critical_values[dist] size = np.array(sorted(cv_data), dtype=float) crit_lf = np.array([cv_data[key] for key in sorted(cv_data)]) crit_lf = crit_lf[:, ::-1] asym_params = np.array([acv_data[key] for key in sorted(acv_data)]) asymp_fn = _make_asymptotic_function((asym_params[::-1])) lf = TableDist(alpha, size, crit_lf, asymptotic=asymp_fn) return lf lilliefors_table_norm = get_lilliefors_table(dist='norm') lilliefors_table_expon = get_lilliefors_table(dist='exp') def pval_lf(d_max, n): """ Approximate pvalues for Lilliefors test This is only valid for pvalues smaller than 0.1 which is not checked in this function. Parameters ---------- d_max : array_like two-sided Kolmogorov-Smirnov test statistic n : int or float sample size Returns ------- p-value : float or ndarray pvalue according to approximation formula of Dallal and Wilkinson. Notes ----- This is mainly a helper function where the calling code should dispatch on bound violations. Therefore it does not check whether the pvalue is in the valid range. Precision for the pvalues is around 2 to 3 decimals. This approximation is also used by other statistical packages (e.g. R:fBasics) but might not be the most precise available. References ---------- DallalWilkinson1986 """ # todo: check boundaries, valid range for n and Dmax if n > 100: d_max *= (n / 100.) ** 0.49 n = 100 pval = np.exp(-7.01256 * d_max ** 2 * (n + 2.78019) + 2.99587 * d_max * np.sqrt(n + 2.78019) - 0.122119 + 0.974598 / np.sqrt(n) + 1.67997 / n) return pval def kstest_fit(x, dist='norm', pvalmethod="table"): """ Test assumed normal or exponential distribution using Lilliefors' test. Lilliefors' test is a Kolmogorov-Smirnov test with estimated parameters. Parameters ---------- x : array_like, 1d Data to test. dist : {'norm', 'exp'}, optional The assumed distribution. pvalmethod : {'approx', 'table'}, optional The method used to compute the p-value of the test statistic. In general, 'table' is preferred and makes use of a very large simulation. 'approx' is only valid for normality. if `dist = 'exp'` `table` is always used. 'approx' uses the approximation formula of Dalal and Wilkinson, valid for pvalues < 0.1. If the pvalue is larger than 0.1, then the result of `table` is returned. Returns ------- ksstat : float Kolmogorov-Smirnov test statistic with estimated mean and variance. pvalue : float If the pvalue is lower than some threshold, e.g. 0.05, then we can reject the Null hypothesis that the sample comes from a normal distribution. Notes ----- 'table' uses an improved table based on 10,000,000 simulations. The critical values are approximated using log(cv_alpha) = b_alpha + c[0] log(n) + c[1] log(n)**2 where cv_alpha is the critical value for a test with size alpha, b_alpha is an alpha-specific intercept term and c[1] and c[2] are coefficients that are shared all alphas. Values in the table are linearly interpolated. Values outside the range are be returned as bounds, 0.990 for large and 0.001 for small pvalues. For implementation details, see lilliefors_critical_value_simulation.py in the test directory. """ pvalmethod = string_like(pvalmethod, "pvalmethod", options=("approx", "table")) x = np.asarray(x) nobs = len(x) if dist == 'norm': z = (x - x.mean()) / x.std(ddof=1) test_d = stats.norm.cdf lilliefors_table = lilliefors_table_norm elif dist == 'exp': z = x / x.mean() test_d = stats.expon.cdf lilliefors_table = lilliefors_table_expon pvalmethod = 'table' else: raise ValueError("Invalid dist parameter, must be 'norm' or 'exp'") min_nobs = 4 if dist == 'norm' else 3 if nobs < min_nobs: raise ValueError('Test for distribution {0} requires at least {1} ' 'observations'.format(dist, min_nobs)) d_ks = ksstat(z, test_d, alternative='two_sided') if pvalmethod == 'approx': pval = pval_lf(d_ks, nobs) # check pval is in desired range if pval > 0.1: pval = lilliefors_table.prob(d_ks, nobs) else: # pvalmethod == 'table' pval = lilliefors_table.prob(d_ks, nobs) return d_ks, pval lilliefors = kstest_fit kstest_normal = kstest_fit kstest_exponential = partial(kstest_fit, dist='exp') statsmodels-0.12.2/statsmodels/stats/_lilliefors_critical_values.py000066400000000000000000000331361400612667500257610ustar00rootroot00000000000000""" This file is automatically generated by littlefors_critical_values.py. Do not directly modifythis file. Value based on 10,000,000 simulations.""" from numpy import array PERCENTILES = [1, 5, 10, 25, 50, 75, 90, 92.5, 95, 97.5, 99, 99.5, 99.7, 99.9] SAMPLE_SIZES = [ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25, 30, 40, 50, 100, 200, 400, 800, 1600 ] normal_crit_vals = { 4: array([ 0.14467854, 0.16876575, 0.18664724, 0.22120362, 0.25828924, 0.29341032, 0.34532673, 0.35917374, 0.37521968, 0.39563998, 0.41307904, 0.42157653, 0.4261507, 0.43265213 ]), 5: array([ 0.13587046, 0.16098893, 0.17638354, 0.20235666, 0.2333944, 0.27766941, 0.31900772, 0.32936832, 0.34309223, 0.36727643, 0.39671728, 0.41322814, 0.42293504, 0.4386304 ]), 6: array([ 0.12919635, 0.15139467, 0.16384021, 0.18597849, 0.2186713, 0.2585473, 0.29713753, 0.30829444, 0.32338252, 0.3456671, 0.37038945, 0.38760943, 0.40001813, 0.42304439 ]), 7: array([ 0.12263812, 0.14163065, 0.15238656, 0.17435948, 0.20617949, 0.24243592, 0.28031415, 0.29068512, 0.3042307, 0.32532967, 0.35070348, 0.3678189, 0.37908881, 0.40078798 ]), 8: array([ 0.11633728, 0.13297288, 0.14353311, 0.16537078, 0.19477376, 0.22936164, 0.2652001, 0.27501697, 0.28804474, 0.30862157, 0.33279908, 0.34911188, 0.3603517, 0.38252055 ]), 9: array([ 0.11029593, 0.126086, 0.1365291, 0.15748048, 0.18510669, 0.21822055, 0.25223085, 0.26161129, 0.27415243, 0.29383667, 0.31708299, 0.33312043, 0.34406772, 0.36524182 ]), 10: array([ 0.10487398, 0.12044377, 0.13065174, 0.15042835, 0.17679904, 0.20848607, 0.24098605, 0.25001629, 0.26202351, 0.2809226, 0.30341763, 0.31888089, 0.32960742, 0.35061378 ]), 11: array([ 0.10036835, 0.11563925, 0.12540948, 0.14421024, 0.1695621, 0.19993088, 0.23119563, 0.23987246, 0.25142048, 0.26961902, 0.29148756, 0.30646087, 0.31678589, 0.33743951 ]), 12: array([ 0.09649147, 0.11137479, 0.12069511, 0.13877133, 0.16313672, 0.19233706, 0.22244871, 0.23082937, 0.24194831, 0.25959488, 0.28077229, 0.29526801, 0.30538827, 0.32558601 ]), 13: array([ 0.09318309, 0.10753337, 0.11647389, 0.13389325, 0.15739248, 0.18555597, 0.21463087, 0.22267463, 0.23346007, 0.25054975, 0.27100552, 0.28519234, 0.29504428, 0.31445229 ]), 14: array([ 0.09024138, 0.1040431, 0.11266368, 0.12948657, 0.15221479, 0.17944478, 0.2075745, 0.21536969, 0.22585144, 0.2423819, 0.26231339, 0.2760657, 0.28555592, 0.30466148 ]), 15: array([ 0.08750578, 0.10085666, 0.1092263, 0.12552356, 0.14751778, 0.17390304, 0.2011939, 0.20879449, 0.21891697, 0.23499116, 0.25427802, 0.26772298, 0.27706522, 0.29551017 ]), 16: array([ 0.08501529, 0.09795236, 0.10607182, 0.1219047, 0.14327014, 0.16885124, 0.19537444, 0.20274039, 0.21257643, 0.22822187, 0.24703504, 0.26003621, 0.26913735, 0.28745211 ]), 17: array([ 0.0827393, 0.09529635, 0.10320903, 0.11859867, 0.13936135, 0.16422592, 0.1900207, 0.19722541, 0.20683438, 0.22204864, 0.2402864, 0.25306469, 0.26200104, 0.2798316 ]), 18: array([ 0.08063198, 0.09285546, 0.10055901, 0.11554003, 0.13575222, 0.15996707, 0.18509495, 0.1921063, 0.20145911, 0.2163409, 0.23420221, 0.24665892, 0.25527246, 0.27285099 ]), 19: array([ 0.0786934, 0.09059543, 0.09810264, 0.11271608, 0.1324079, 0.15602767, 0.18052002, 0.18736281, 0.19652196, 0.21105313, 0.22854301, 0.24068403, 0.24912401, 0.26624557 ]), 20: array([ 0.07686372, 0.08852309, 0.09582876, 0.11008398, 0.12930804, 0.15236687, 0.1762829, 0.18297149, 0.19190794, 0.20610189, 0.22327259, 0.23513834, 0.24349604, 0.2602868 ]), 25: array([ 0.06933943, 0.07985746, 0.08645091, 0.09927555, 0.11656692, 0.1373056, 0.15889286, 0.16493761, 0.17300926, 0.18582499, 0.2013265, 0.21221932, 0.21979198, 0.2350391 ]), 30: array([ 0.06380332, 0.07339662, 0.07942847, 0.09118039, 0.10701841, 0.12603791, 0.14586121, 0.15138566, 0.15878307, 0.17058849, 0.18492078, 0.19492393, 0.20198353, 0.21612086 ]), 40: array([ 0.055784, 0.06414642, 0.06940064, 0.07961554, 0.09339439, 0.10994266, 0.12719016, 0.13202416, 0.13850018, 0.14877502, 0.16131916, 0.17009968, 0.17633078, 0.18870328 ]), 50: array([ 0.05022994, 0.05773701, 0.06243507, 0.07160481, 0.08395875, 0.09882109, 0.11431303, 0.11863768, 0.12444044, 0.1337458, 0.14504504, 0.15299605, 0.15854061, 0.16985345 ]), 100: array([ 0.0361047, 0.04146075, 0.0448043, 0.05131964, 0.06011456, 0.07068396, 0.08173283, 0.08483991, 0.08900091, 0.09564506, 0.10373761, 0.10937278, 0.11338394, 0.12161442 ]), 200: array([ 0.02584151, 0.02963511, 0.03200533, 0.0366259, 0.04286406, 0.05036816, 0.05820564, 0.06041126, 0.06336215, 0.06809025, 0.0738379, 0.07788879, 0.08074047, 0.08663425 ]), 400: array([ 0.01844162, 0.02112065, 0.02280475, 0.02607295, 0.03049198, 0.03580284, 0.04135097, 0.04290933, 0.04500619, 0.04834792, 0.0524239, 0.05530289, 0.05733374, 0.06145404 ]), 800: array([ 0.0131231, 0.01501723, 0.01620598, 0.01852257, 0.02164634, 0.02540595, 0.02933599, 0.03043873, 0.03192094, 0.03429131, 0.03718247, 0.03922491, 0.0406419, 0.04361741 ]), 1600: array([ 0.00932049, 0.01066126, 0.01150366, 0.01314135, 0.0153528, 0.0180115, 0.02079512, 0.02157469, 0.02262168, 0.02429563, 0.02634302, 0.02777611, 0.02879721, 0.03088286 ]) } # Coefficients are model log(cv) = b[0] + b[1] log(n) + b[2] log(n)**2 normal_asymp_crit_vals = { 1.0: array([-1.17114969, -0.45068579, -0.00356741]), 5.0: array([-1.03298277, -0.45068579, -0.00356741]), 10.0: array([-0.95518114, -0.45068579, -0.00356741]), 25.0: array([-0.81912169, -0.45068579, -0.00356741]), 50.0: array([-0.6607348, -0.45068579, -0.00356741]), 75.0: array([-0.49861004, -0.45068579, -0.00356741]), 90.0: array([-0.35446139, -0.45068579, -0.00356741]), 92.5: array([-0.31737193, -0.45068579, -0.00356741]), 95.0: array([-0.26969888, -0.45068579, -0.00356741]), 97.5: array([-0.1979977, -0.45068579, -0.00356741]), 99.0: array([-0.11709649, -0.45068579, -0.00356741]), 99.5: array([-0.06398777, -0.45068579, -0.00356741]), 99.7: array([-0.0281863, -0.45068579, -0.00356741]), 99.9: array([0.04129756, -0.45068579, -0.00356741]) } exp_crit_vals = { 3: array([ 0.2109761, 0.22988438, 0.25444542, 0.30397879, 0.36446945, 0.42814169, 0.51106702, 0.52962262, 0.55088872, 0.57754526, 0.60036174, 0.61179874, 0.61823126, 0.6294291 ]), 4: array([ 0.17384601, 0.20723235, 0.22806298, 0.26607407, 0.31624998, 0.38384024, 0.44420279, 0.46088139, 0.4843941, 0.521064, 0.55751191, 0.57850145, 0.59207384, 0.62098085 ]), 5: array([ 0.15948619, 0.18836122, 0.20519471, 0.2387884, 0.28771415, 0.34487558, 0.40440534, 0.42088543, 0.44200346, 0.47455921, 0.51269224, 0.53654197, 0.55188279, 0.58123527 ]), 6: array([ 0.1480075, 0.17258589, 0.18825927, 0.21978293, 0.2645031, 0.31713484, 0.37308973, 0.38833891, 0.4084249, 0.43908986, 0.47469271, 0.49984099, 0.5170463, 0.54989819 ]), 7: array([ 0.13783797, 0.16039265, 0.17499898, 0.20510973, 0.24578726, 0.29584306, 0.34806914, 0.36231862, 0.38111852, 0.41060597, 0.44579783, 0.46945914, 0.48562857, 0.5179461 ]), 8: array([ 0.12914489, 0.15056654, 0.16462426, 0.19280967, 0.23086956, 0.27829277, 0.3273405, 0.34086546, 0.35894819, 0.3874127, 0.42078514, 0.44361638, 0.45939843, 0.4910784 ]), 9: array([ 0.12209612, 0.1426062, 0.15604163, 0.1823721, 0.21856178, 0.26352862, 0.3101114, 0.32311637, 0.3404356, 0.36744906, 0.39952102, 0.42164587, 0.43719767, 0.46827333 ]), 10: array([ 0.11622346, 0.13594053, 0.14864516, 0.17351161, 0.20820576, 0.25083243, 0.29544984, 0.3078714, 0.32438433, 0.35032272, 0.38135762, 0.40282213, 0.41758788, 0.44762269 ]), 11: array([ 0.11116996, 0.13008811, 0.14214361, 0.16587204, 0.19916, 0.23987837, 0.28264075, 0.29456614, 0.31039145, 0.3353923, 0.36531224, 0.38597334, 0.40039914, 0.42945227 ]), 12: array([ 0.10682852, 0.12494111, 0.13642386, 0.15924117, 0.19119135, 0.23024225, 0.27140493, 0.28285565, 0.29813962, 0.32235591, 0.35118835, 0.37131437, 0.38541362, 0.41355258 ]), 13: array([ 0.10299158, 0.12035679, 0.13139418, 0.15340996, 0.18411715, 0.22174274, 0.26139337, 0.27247472, 0.28721874, 0.31061368, 0.3386004, 0.3579752, 0.37154656, 0.399054 ]), 14: array([ 0.09952544, 0.11620577, 0.12685351, 0.14816724, 0.17777806, 0.21413923, 0.25247245, 0.26312392, 0.27746948, 0.30001199, 0.32724359, 0.34615172, 0.3591787, 0.38578716 ]), 15: array([ 0.09635825, 0.11247223, 0.12279761, 0.1434653, 0.17203838, 0.20728334, 0.2443769, 0.25476058, 0.26865606, 0.29062696, 0.31686937, 0.33520734, 0.34795825, 0.37374779 ]), 16: array([ 0.093446, 0.10911215, 0.11910394, 0.1391716, 0.16686968, 0.20103119, 0.23706762, 0.24716908, 0.26064721, 0.28192033, 0.30753741, 0.32530837, 0.33776015, 0.36287832 ]), 17: array([ 0.09080542, 0.10601186, 0.11575975, 0.13523043, 0.16215573, 0.19534591, 0.2303959, 0.24019386, 0.25330648, 0.27400789, 0.29895143, 0.31623639, 0.32845602, 0.35308388 ]), 18: array([ 0.08844468, 0.10320066, 0.11271261, 0.13163588, 0.15780097, 0.19009349, 0.22420159, 0.2337161, 0.24646825, 0.26673429, 0.29105285, 0.30803457, 0.31984228, 0.34387696 ]), 19: array([ 0.08623885, 0.1006206, 0.10988138, 0.12831526, 0.15380297, 0.18527462, 0.21845938, 0.22776537, 0.2402398, 0.2600306, 0.28378696, 0.30035609, 0.31189906, 0.33544625 ]), 20: array([ 0.08417538, 0.09821659, 0.10727612, 0.12520467, 0.15011026, 0.18077566, 0.21317237, 0.2222683, 0.23446664, 0.25382491, 0.27704397, 0.29319327, 0.30456436, 0.32759304 ]), 25: array([ 0.07575606, 0.08842104, 0.09651937, 0.1126094, 0.13493277, 0.1624784, 0.19169294, 0.19987007, 0.2108557, 0.22828626, 0.24930174, 0.26403731, 0.2743157, 0.29520476 ]), 30: array([ 0.06952264, 0.08110063, 0.08850223, 0.10324683, 0.12365394, 0.14885572, 0.1756019, 0.18308805, 0.19314473, 0.20920585, 0.2285569, 0.24218995, 0.25167821, 0.270999 ]), 40: array([ 0.06066843, 0.07071874, 0.07713823, 0.0899287, 0.10765412, 0.12954118, 0.15278494, 0.15934334, 0.16813288, 0.18214059, 0.19908466, 0.21086902, 0.2192688, 0.23619981 ]), 50: array([ 0.05453287, 0.06354216, 0.06931727, 0.0807706, 0.09664734, 0.11625969, 0.13711892, 0.14300016, 0.15087554, 0.16345379, 0.17865445, 0.18939212, 0.19681564, 0.21177526 ]), 100: array([ 0.03911314, 0.04550435, 0.04958972, 0.05770944, 0.06896805, 0.08288491, 0.09771459, 0.10189766, 0.10752233, 0.1164863, 0.12735376, 0.13497319, 0.14038704, 0.15150129 ]), 200: array([ 0.02793837, 0.03246737, 0.03536757, 0.04111863, 0.04910105, 0.0589757, 0.06949443, 0.0724547, 0.07645096, 0.08280575, 0.09054264, 0.09600477, 0.09980637, 0.10760793 ]), 400: array([ 0.01991454, 0.023116, 0.02516769, 0.0292415, 0.03488679, 0.0418774, 0.04931093, 0.05141711, 0.054236, 0.05874581, 0.06421502, 0.06808278, 0.07079796, 0.07628466 ]), 800: array([ 0.01415514, 0.01642927, 0.0178805, 0.02075938, 0.02475783, 0.02970526, 0.03496731, 0.03645351, 0.03845017, 0.04164885, 0.04552405, 0.0482418, 0.05017098, 0.05406992 ]), 1600: array([ 0.01005851, 0.01165883, 0.0126869, 0.01472426, 0.01754881, 0.02104396, 0.02476615, 0.02581898, 0.02723521, 0.02950141, 0.03224859, 0.03418578, 0.03553487, 0.03829879 ]) } # Coefficients are model log(cv) = b[0] + b[1] log(n) + b[2] log(n)**2 exp_asymp_crit_vals = { 1.0: array([-1.04988875, -0.46444021, -0.00252528]), 5.0: array([-0.89825066, -0.46444021, -0.00252528]), 10.0: array([-0.81197037, -0.46444021, -0.00252528]), 25.0: array([-0.66000008, -0.46444021, -0.00252528]), 50.0: array([-0.4814209, -0.46444021, -0.00252528]), 75.0: array([-0.29737272, -0.46444021, -0.00252528]), 90.0: array([-0.13397474, -0.46444021, -0.00252528]), 92.5: array([-0.09220104, -0.46444021, -0.00252528]), 95.0: array([-0.03868789, -0.46444021, -0.00252528]), 97.5: array([0.0411943, -0.46444021, -0.00252528]), 99.0: array([0.130122, -0.46444021, -0.00252528]), 99.5: array([0.1882404, -0.46444021, -0.00252528]), 99.7: array([0.22712671, -0.46444021, -0.00252528]), 99.9: array([0.30189677, -0.46444021, -0.00252528]) } # Critical Value critical_values = {'normal': normal_crit_vals, 'exp': exp_crit_vals} asymp_critical_values = { 'normal': normal_asymp_crit_vals, 'exp': exp_asymp_crit_vals } statsmodels-0.12.2/statsmodels/stats/anova.py000066400000000000000000000546631400612667500213410ustar00rootroot00000000000000import numpy as np from scipy import stats import pandas as pd from pandas import DataFrame, Index import patsy from statsmodels.regression.linear_model import OLS from statsmodels.compat.python import lrange from statsmodels.formula.formulatools import (_remove_intercept_patsy, _has_intercept, _intercept_idx) from statsmodels.iolib import summary2 def _get_covariance(model, robust): if robust is None: return model.cov_params() elif robust == "hc0": return model.cov_HC0 elif robust == "hc1": return model.cov_HC1 elif robust == "hc2": return model.cov_HC2 elif robust == "hc3": return model.cov_HC3 else: # pragma: no cover raise ValueError("robust options %s not understood" % robust) # NOTE: these need to take into account weights ! def anova_single(model, **kwargs): """ Anova table for one fitted linear model. Parameters ---------- model : fitted linear model results instance A fitted linear model typ : int or str {1,2,3} or {"I","II","III"} Type of sum of squares to use. **kwargs** scale : float Estimate of variance, If None, will be estimated from the largest model. Default is None. test : str {"F", "Chisq", "Cp"} or None Test statistics to provide. Default is "F". Notes ----- Use of this function is discouraged. Use anova_lm instead. """ test = kwargs.get("test", "F") scale = kwargs.get("scale", None) typ = kwargs.get("typ", 1) robust = kwargs.get("robust", None) if robust: robust = robust.lower() endog = model.model.endog exog = model.model.exog nobs = exog.shape[0] response_name = model.model.endog_names design_info = model.model.data.design_info exog_names = model.model.exog_names # +1 for resids n_rows = (len(design_info.terms) - _has_intercept(design_info) + 1) pr_test = "PR(>%s)" % test names = ['df', 'sum_sq', 'mean_sq', test, pr_test] table = DataFrame(np.zeros((n_rows, 5)), columns=names) if typ in [1, "I"]: return anova1_lm_single(model, endog, exog, nobs, design_info, table, n_rows, test, pr_test, robust) elif typ in [2, "II"]: return anova2_lm_single(model, design_info, n_rows, test, pr_test, robust) elif typ in [3, "III"]: return anova3_lm_single(model, design_info, n_rows, test, pr_test, robust) elif typ in [4, "IV"]: raise NotImplementedError("Type IV not yet implemented") else: # pragma: no cover raise ValueError("Type %s not understood" % str(typ)) def anova1_lm_single(model, endog, exog, nobs, design_info, table, n_rows, test, pr_test, robust): """ Anova table for one fitted linear model. Parameters ---------- model : fitted linear model results instance A fitted linear model **kwargs** scale : float Estimate of variance, If None, will be estimated from the largest model. Default is None. test : str {"F", "Chisq", "Cp"} or None Test statistics to provide. Default is "F". Notes ----- Use of this function is discouraged. Use anova_lm instead. """ #maybe we should rethink using pinv > qr in OLS/linear models? effects = getattr(model, 'effects', None) if effects is None: q,r = np.linalg.qr(exog) effects = np.dot(q.T, endog) arr = np.zeros((len(design_info.terms), len(design_info.column_names))) slices = [design_info.slice(name) for name in design_info.term_names] for i,slice_ in enumerate(slices): arr[i, slice_] = 1 sum_sq = np.dot(arr, effects**2) #NOTE: assumes intercept is first column idx = _intercept_idx(design_info) sum_sq = sum_sq[~idx] term_names = np.array(design_info.term_names) # want boolean indexing term_names = term_names[~idx] index = term_names.tolist() table.index = Index(index + ['Residual']) table.loc[index, ['df', 'sum_sq']] = np.c_[arr[~idx].sum(1), sum_sq] # fill in residual table.loc['Residual', ['sum_sq','df']] = model.ssr, model.df_resid if test == 'F': table[test] = ((table['sum_sq'] / table['df']) / (model.ssr / model.df_resid)) table[pr_test] = stats.f.sf(table["F"], table["df"], model.df_resid) table.loc['Residual', [test, pr_test]] = np.nan, np.nan table['mean_sq'] = table['sum_sq'] / table['df'] return table #NOTE: the below is not agnostic about formula... def anova2_lm_single(model, design_info, n_rows, test, pr_test, robust): """ Anova type II table for one fitted linear model. Parameters ---------- model : fitted linear model results instance A fitted linear model **kwargs** scale : float Estimate of variance, If None, will be estimated from the largest model. Default is None. test : str {"F", "Chisq", "Cp"} or None Test statistics to provide. Default is "F". Notes ----- Use of this function is discouraged. Use anova_lm instead. Type II Sum of Squares compares marginal contribution of terms. Thus, it is not particularly useful for models with significant interaction terms. """ terms_info = design_info.terms[:] # copy terms_info = _remove_intercept_patsy(terms_info) names = ['sum_sq', 'df', test, pr_test] table = DataFrame(np.zeros((n_rows, 4)), columns = names) cov = _get_covariance(model, None) robust_cov = _get_covariance(model, robust) col_order = [] index = [] for i, term in enumerate(terms_info): # grab all varaibles except interaction effects that contain term # need two hypotheses matrices L1 is most restrictive, ie., term==0 # L2 is everything except term==0 cols = design_info.slice(term) L1 = lrange(cols.start, cols.stop) L2 = [] term_set = set(term.factors) for t in terms_info: # for the term you have other_set = set(t.factors) if term_set.issubset(other_set) and not term_set == other_set: col = design_info.slice(t) # on a higher order term containing current `term` L1.extend(lrange(col.start, col.stop)) L2.extend(lrange(col.start, col.stop)) L1 = np.eye(model.model.exog.shape[1])[L1] L2 = np.eye(model.model.exog.shape[1])[L2] if L2.size: LVL = np.dot(np.dot(L1,robust_cov),L2.T) from scipy import linalg orth_compl,_ = linalg.qr(LVL) r = L1.shape[0] - L2.shape[0] # L1|2 # use the non-unique orthogonal completion since L12 is rank r L12 = np.dot(orth_compl[:,-r:].T, L1) else: L12 = L1 r = L1.shape[0] #from IPython.core.debugger import Pdb; Pdb().set_trace() if test == 'F': f = model.f_test(L12, cov_p=robust_cov) table.loc[table.index[i], test] = test_value = f.fvalue table.loc[table.index[i], pr_test] = f.pvalue # need to back out SSR from f_test table.loc[table.index[i], 'df'] = r col_order.append(cols.start) index.append(term.name()) table.index = Index(index + ['Residual']) table = table.iloc[np.argsort(col_order + [model.model.exog.shape[1]+1])] # back out sum of squares from f_test ssr = table[test] * table['df'] * model.ssr/model.df_resid table['sum_sq'] = ssr # fill in residual table.loc['Residual', ['sum_sq','df', test, pr_test]] = (model.ssr, model.df_resid, np.nan, np.nan) return table def anova3_lm_single(model, design_info, n_rows, test, pr_test, robust): n_rows += _has_intercept(design_info) terms_info = design_info.terms names = ['sum_sq', 'df', test, pr_test] table = DataFrame(np.zeros((n_rows, 4)), columns = names) cov = _get_covariance(model, robust) col_order = [] index = [] for i, term in enumerate(terms_info): # grab term, hypothesis is that term == 0 cols = design_info.slice(term) L1 = np.eye(model.model.exog.shape[1])[cols] L12 = L1 r = L1.shape[0] if test == 'F': f = model.f_test(L12, cov_p=cov) table.loc[table.index[i], test] = test_value = f.fvalue table.loc[table.index[i], pr_test] = f.pvalue # need to back out SSR from f_test table.loc[table.index[i], 'df'] = r #col_order.append(cols.start) index.append(term.name()) table.index = Index(index + ['Residual']) #NOTE: Do not need to sort because terms are an ordered dict now #table = table.iloc[np.argsort(col_order + [model.model.exog.shape[1]+1])] # back out sum of squares from f_test ssr = table[test] * table['df'] * model.ssr/model.df_resid table['sum_sq'] = ssr # fill in residual table.loc['Residual', ['sum_sq','df', test, pr_test]] = (model.ssr, model.df_resid, np.nan, np.nan) return table def anova_lm(*args, **kwargs): """ Anova table for one or more fitted linear models. Parameters ---------- args : fitted linear model results instance One or more fitted linear models scale : float Estimate of variance, If None, will be estimated from the largest model. Default is None. test : str {"F", "Chisq", "Cp"} or None Test statistics to provide. Default is "F". typ : str or int {"I","II","III"} or {1,2,3} The type of Anova test to perform. See notes. robust : {None, "hc0", "hc1", "hc2", "hc3"} Use heteroscedasticity-corrected coefficient covariance matrix. If robust covariance is desired, it is recommended to use `hc3`. Returns ------- anova : DataFrame When args is a single model, return is DataFrame with columns: sum_sq : float64 Sum of squares for model terms. df : float64 Degrees of freedom for model terms. F : float64 F statistic value for significance of adding model terms. PR(>F) : float64 P-value for significance of adding model terms. When args is multiple models, return is DataFrame with columns: df_resid : float64 Degrees of freedom of residuals in models. ssr : float64 Sum of squares of residuals in models. df_diff : float64 Degrees of freedom difference from previous model in args ss_dff : float64 Difference in ssr from previous model in args F : float64 F statistic comparing to previous model in args PR(>F): float64 P-value for significance comparing to previous model in args Notes ----- Model statistics are given in the order of args. Models must have been fit using the formula api. See Also -------- model_results.compare_f_test, model_results.compare_lm_test Examples -------- >>> import statsmodels.api as sm >>> from statsmodels.formula.api import ols >>> moore = sm.datasets.get_rdataset("Moore", "carData", cache=True) # load >>> data = moore.data >>> data = data.rename(columns={"partner.status" : ... "partner_status"}) # make name pythonic >>> moore_lm = ols('conformity ~ C(fcategory, Sum)*C(partner_status, Sum)', ... data=data).fit() >>> table = sm.stats.anova_lm(moore_lm, typ=2) # Type 2 Anova DataFrame >>> print(table) """ typ = kwargs.get('typ', 1) ### Farm Out Single model Anova Type I, II, III, and IV ### if len(args) == 1: model = args[0] return anova_single(model, **kwargs) if typ not in [1, "I"]: raise ValueError("Multiple models only supported for type I. " "Got type %s" % str(typ)) test = kwargs.get("test", "F") scale = kwargs.get("scale", None) n_models = len(args) pr_test = "Pr(>%s)" % test names = ['df_resid', 'ssr', 'df_diff', 'ss_diff', test, pr_test] table = DataFrame(np.zeros((n_models, 6)), columns=names) if not scale: # assume biggest model is last scale = args[-1].scale table["ssr"] = [mdl.ssr for mdl in args] table["df_resid"] = [mdl.df_resid for mdl in args] table.loc[table.index[1:], "df_diff"] = -np.diff(table["df_resid"].values) table["ss_diff"] = -table["ssr"].diff() if test == "F": table["F"] = table["ss_diff"] / table["df_diff"] / scale table[pr_test] = stats.f.sf(table["F"], table["df_diff"], table["df_resid"]) # for earlier scipy - stats.f.sf(np.nan, 10, 2) -> 0 not nan table[pr_test][table['F'].isnull()] = np.nan return table def _not_slice(slices, slices_to_exclude, n): ind = np.array([True]*n) for term in slices_to_exclude: s = slices[term] ind[s] = False return ind def _ssr_reduced_model(y, x, term_slices, params, keys): """ Residual sum of squares of OLS model excluding factors in `keys` Assumes x matrix is orthogonal Parameters ---------- y : array_like dependent variable x : array_like independent variables term_slices : a dict of slices term_slices[key] is a boolean array specifies the parameters associated with the factor `key` params : ndarray OLS solution of y = x * params keys : keys for term_slices factors to be excluded Returns ------- rss : float residual sum of squares df : int degrees of freedom """ ind = _not_slice(term_slices, keys, x.shape[1]) params1 = params[ind] ssr = np.subtract(y, x[:, ind].dot(params1)) ssr = ssr.T.dot(ssr) df_resid = len(y) - len(params1) return ssr, df_resid class AnovaRM(object): """ Repeated measures Anova using least squares regression The full model regression residual sum of squares is used to compare with the reduced model for calculating the within-subject effect sum of squares [1]. Currently, only fully balanced within-subject designs are supported. Calculation of between-subject effects and corrections for violation of sphericity are not yet implemented. Parameters ---------- data : DataFrame depvar : str The dependent variable in `data` subject : str Specify the subject id within : list[str] The within-subject factors between : list[str] The between-subject factors, this is not yet implemented aggregate_func : {None, 'mean', callable} If the data set contains more than a single observation per subject and cell of the specified model, this function will be used to aggregate the data before running the Anova. `None` (the default) will not perform any aggregation; 'mean' is s shortcut to `numpy.mean`. An exception will be raised if aggregation is required, but no aggregation function was specified. Returns ------- results : AnovaResults instance Raises ------ ValueError If the data need to be aggregated, but `aggregate_func` was not specified. Notes ----- This implementation currently only supports fully balanced designs. If the data contain more than one observation per subject and cell of the design, these observations need to be aggregated into a single observation before the Anova is calculated, either manually or by passing an aggregation function via the `aggregate_func` keyword argument. Note that if the input data set was not balanced before performing the aggregation, the implied heteroscedasticity of the data is ignored. References ---------- .. [*] Rutherford, Andrew. Anova and ANCOVA: a GLM approach. John Wiley & Sons, 2011. """ def __init__(self, data, depvar, subject, within=None, between=None, aggregate_func=None): self.data = data self.depvar = depvar self.within = within if 'C' in within: raise ValueError("Factor name cannot be 'C'! This is in conflict " "with patsy's contrast function name.") self.between = between if between is not None: raise NotImplementedError('Between subject effect not ' 'yet supported!') self.subject = subject if aggregate_func == 'mean': self.aggregate_func = np.mean else: self.aggregate_func = aggregate_func if not data.equals(data.drop_duplicates(subset=[subject] + within)): if self.aggregate_func is not None: self._aggregate() else: msg = ('The data set contains more than one observation per ' 'subject and cell. Either aggregate the data manually, ' 'or pass the `aggregate_func` parameter.') raise ValueError(msg) self._check_data_balanced() def _aggregate(self): self.data = (self.data .groupby([self.subject] + self.within, as_index=False)[self.depvar] .agg(self.aggregate_func)) def _check_data_balanced(self): """raise if data is not balanced This raises a ValueError if the data is not balanced, and returns None if it is balance Return might change """ factor_levels = 1 for wi in self.within: factor_levels *= len(self.data[wi].unique()) cell_count = {} for index in range(self.data.shape[0]): key = [] for col in self.within: key.append(self.data[col].iloc[index]) key = tuple(key) if key in cell_count: cell_count[key] = cell_count[key] + 1 else: cell_count[key] = 1 error_message = "Data is unbalanced." if len(cell_count) != factor_levels: raise ValueError(error_message) count = cell_count[key] for key in cell_count: if count != cell_count[key]: raise ValueError(error_message) if self.data.shape[0] > count * factor_levels: raise ValueError('There are more than 1 element in a cell! Missing' ' factors?') def fit(self): """estimate the model and compute the Anova table Returns ------- AnovaResults instance """ y = self.data[self.depvar].values # Construct OLS endog and exog from string using patsy within = ['C(%s, Sum)' % i for i in self.within] subject = 'C(%s, Sum)' % self.subject factors = within + [subject] x = patsy.dmatrix('*'.join(factors), data=self.data) term_slices = x.design_info.term_name_slices for key in term_slices: ind = np.array([False]*x.shape[1]) ind[term_slices[key]] = True term_slices[key] = np.array(ind) term_exclude = [':'.join(factors)] ind = _not_slice(term_slices, term_exclude, x.shape[1]) x = x[:, ind] # Fit OLS model = OLS(y, x) results = model.fit() if model.rank < x.shape[1]: raise ValueError('Independent variables are collinear.') for i in term_exclude: term_slices.pop(i) for key in term_slices: term_slices[key] = term_slices[key][ind] params = results.params df_resid = results.df_resid ssr = results.ssr columns = ['F Value', 'Num DF', 'Den DF', 'Pr > F'] anova_table = pd.DataFrame(np.zeros((0, 4)), columns=columns) for key in term_slices: if self.subject not in key and key != 'Intercept': # Independen variables are orthogonal ssr1, df_resid1 = _ssr_reduced_model( y, x, term_slices, params, [key]) df1 = df_resid1 - df_resid msm = (ssr1 - ssr) / df1 if (key == ':'.join(factors[:-1]) or (key + ':' + subject not in term_slices)): mse = ssr / df_resid df2 = df_resid else: ssr1, df_resid1 = _ssr_reduced_model( y, x, term_slices, params, [key + ':' + subject]) df2 = df_resid1 - df_resid mse = (ssr1 - ssr) / df2 F = msm / mse p = stats.f.sf(F, df1, df2) term = key.replace('C(', '').replace(', Sum)', '') anova_table.loc[term, 'F Value'] = F anova_table.loc[term, 'Num DF'] = df1 anova_table.loc[term, 'Den DF'] = df2 anova_table.loc[term, 'Pr > F'] = p return AnovaResults(anova_table) class AnovaResults(object): """ Anova results class Attributes ---------- anova_table : DataFrame """ def __init__(self, anova_table): self.anova_table = anova_table def __str__(self): return self.summary().__str__() def summary(self): """create summary results Returns ------- summary : summary2.Summary instance """ summ = summary2.Summary() summ.add_title('Anova') summ.add_df(self.anova_table) return summ if __name__ == "__main__": import pandas from statsmodels.formula.api import ols # in R #library(car) #write.csv(Moore, "moore.csv", row.names=FALSE) moore = pandas.read_csv('moore.csv', skiprows=1, names=['partner_status','conformity', 'fcategory','fscore']) moore_lm = ols('conformity ~ C(fcategory, Sum)*C(partner_status, Sum)', data=moore).fit() mooreB = ols('conformity ~ C(partner_status, Sum)', data=moore).fit() # for each term you just want to test vs the model without its # higher-order terms # using Monette-Fox slides and Marden class notes for linear algebra / # orthogonal complement # https://netfiles.uiuc.edu/jimarden/www/Classes/STAT324/ table = anova_lm(moore_lm, typ=2) statsmodels-0.12.2/statsmodels/stats/api.py000066400000000000000000000111031400612667500207640ustar00rootroot00000000000000# pylint: disable=W0611 # flake8: noqa from . import diagnostic from .diagnostic import ( acorr_ljungbox, acorr_breusch_godfrey, acorr_lm, CompareCox, compare_cox, CompareJ, compare_j, compare_encompassing, HetGoldfeldQuandt, het_goldfeldquandt, het_breuschpagan, het_white, het_arch, linear_harvey_collier, linear_rainbow, linear_lm, linear_reset, breaks_cusumolsresid, breaks_hansen, recursive_olsresiduals, spec_white ) from ._adnorm import normal_ad from ._lilliefors import lilliefors from ._knockoff import RegressionFDR from . import multicomp from .multitest import (multipletests, fdrcorrection, fdrcorrection_twostage, local_fdr, NullDistribution) from .multicomp import tukeyhsd from . import gof from .gof import (powerdiscrepancy, gof_chisquare_discrete, chisquare_effectsize) from . import stattools from .stattools import durbin_watson, omni_normtest, jarque_bera from . import sandwich_covariance from .sandwich_covariance import ( cov_cluster, cov_cluster_2groups, cov_nw_panel, cov_hac, cov_white_simple, cov_hc0, cov_hc1, cov_hc2, cov_hc3, se_cov ) from .weightstats import (DescrStatsW, CompareMeans, ttest_ind, ttost_ind, ttost_paired, ztest, ztost, zconfint) from .proportion import ( binom_test_reject_interval, binom_test, binom_tost, binom_tost_reject_interval, power_binom_tost, power_ztost_prop, proportion_confint, proportion_effectsize, proportions_chisquare, proportions_chisquare_allpairs, proportions_chisquare_pairscontrol, proportions_ztest, proportions_ztost, multinomial_proportions_confint) from .power import (TTestPower, TTestIndPower, GofChisquarePower, NormalIndPower, FTestAnovaPower, FTestPower, tt_solve_power, tt_ind_solve_power, zt_ind_solve_power) from .descriptivestats import Describe from .anova import anova_lm from .oaxaca import OaxacaBlinder from . import moment_helpers from .correlation_tools import ( corr_clipped, corr_nearest, corr_nearest_factor, corr_thresholded, cov_nearest, cov_nearest_factor_homog, FactoredPSDMatrix) from statsmodels.sandbox.stats.runs import Runs, runstest_1samp, runstest_2samp from statsmodels.stats.contingency_tables import (mcnemar, cochrans_q, SquareTable, Table2x2, Table, StratifiedTable) from .mediation import Mediation __all__ = ["acorr_lm", "acorr_breusch_godfrey", "acorr_ljungbox", "anova_lm", "binom_test", "binom_test_reject_interval", "Mediation", "mcnemar", "cochrans_q", "SquareTable", "Table", 'Table2x2', "StratifiedTable", "corr_clipped", "corr_nearest", "corr_nearest_factor", "corr_thresholded", "cov_nearest", "cov_nearest_factor_homog", "FactoredPSDMatrix", "Describe", "OaxacaBlinder", "Runs", "runstest_1samp", "runstest_2samp", "moment_helpers", "binom_tost", "binom_tost_reject_interval", "power_binom_tost", "power_ztost_prop", "proportion_confint", "proportion_effectsize", "proportions_chisquare", "proportions_chisquare_allpairs", "proportions_chisquare_pairscontrol", "proportions_ztest", "proportions_ztost", "multinomial_proportions_confint", "TTestPower", "TTestIndPower", "GofChisquarePower", "NormalIndPower", "FTestAnovaPower", "FTestPower", "tt_solve_power", "tt_ind_solve_power", "zt_ind_solve_power", "cov_cluster", "cov_cluster_2groups", "cov_nw_panel", "cov_hac", "cov_white_simple", "cov_hc0", "cov_hc1", "cov_hc2", "cov_hc3", "se_cov", "CompareCox", "compare_cox", "CompareJ", "compare_j", "compare_encompassing", "HetGoldfeldQuandt", "het_goldfeldquandt", "het_breuschpagan", "het_white", "het_arch", "linear_harvey_collier", "linear_rainbow", "linear_lm", "linear_reset", "breaks_cusumolsresid", "breaks_hansen", "recursive_olsresiduals", "spec_white", "diagnostic", "normal_ad", "lilliefors", "RegressionFDR", "multicomp", "multipletests", "fdrcorrection", "fdrcorrection_twostage", "local_fdr", "NullDistribution", "tukeyhsd", "gof", "powerdiscrepancy", "gof_chisquare_discrete", "chisquare_effectsize", "stattools", "durbin_watson", "omni_normtest", "jarque_bera", "sandwich_covariance", "DescrStatsW", "CompareMeans", "ttest_ind", "ttost_ind", "ttost_paired", "ztest", "ztost", "zconfint"] statsmodels-0.12.2/statsmodels/stats/base.py000066400000000000000000000100441400612667500211300ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Base classes for statistical test results Created on Mon Apr 22 14:03:21 2013 Author: Josef Perktold """ from statsmodels.compat.python import lzip import numpy as np from statsmodels.tools.testing import Holder class HolderTuple(Holder): """Holder class with indexing """ def __init__(self, tuple_=None, **kwds): super(HolderTuple, self).__init__(**kwds) if tuple_ is not None: self.tuple = tuple(getattr(self, att) for att in tuple_) else: self.tuple = (self.statistic, self.pvalue) def __iter__(self): yield from self.tuple def __getitem__(self, idx): return self.tuple[idx] def __len__(self): return len(self.tuple) def __array__(self, dtype=None): return np.asarray(list(self.tuple), dtype=dtype) class AllPairsResults(object): '''Results class for pairwise comparisons, based on p-values Parameters ---------- pvals_raw : array_like, 1-D p-values from a pairwise comparison test all_pairs : list of tuples list of indices, one pair for each comparison multitest_method : str method that is used by default for p-value correction. This is used as default by the methods like if the multiple-testing method is not specified as argument. levels : {list[str], None} optional names of the levels or groups n_levels : None or int If None, then the number of levels or groups is inferred from the other arguments. It can be explicitly specified, if the inferred number is incorrect. Notes ----- This class can also be used for other pairwise comparisons, for example comparing several treatments to a control (as in Dunnet's test). ''' def __init__(self, pvals_raw, all_pairs, multitest_method='hs', levels=None, n_levels=None): self.pvals_raw = pvals_raw self.all_pairs = all_pairs if n_levels is None: # for all_pairs nobs*(nobs-1)/2 self.n_levels = np.max(all_pairs) + 1 else: self.n_levels = n_levels self.multitest_method = multitest_method self.levels = levels if levels is None: self.all_pairs_names = ['%r' % (pairs,) for pairs in all_pairs] else: self.all_pairs_names = ['%s-%s' % (levels[pairs[0]], levels[pairs[1]]) for pairs in all_pairs] def pval_corrected(self, method=None): '''p-values corrected for multiple testing problem This uses the default p-value correction of the instance stored in ``self.multitest_method`` if method is None. ''' import statsmodels.stats.multitest as smt if method is None: method = self.multitest_method # TODO: breaks with method=None return smt.multipletests(self.pvals_raw, method=method)[1] def __str__(self): return self.summary() def pval_table(self): '''create a (n_levels, n_levels) array with corrected p_values this needs to improve, similar to R pairwise output ''' k = self.n_levels pvals_mat = np.zeros((k, k)) # if we do not assume we have all pairs pvals_mat[lzip(*self.all_pairs)] = self.pval_corrected() return pvals_mat def summary(self): '''returns text summarizing the results uses the default pvalue correction of the instance stored in ``self.multitest_method`` ''' import statsmodels.stats.multitest as smt maxlevel = max((len(ss) for ss in self.all_pairs_names)) text = ('Corrected p-values using %s p-value correction\n\n' % smt.multitest_methods_names[self.multitest_method]) text += 'Pairs' + (' ' * (maxlevel - 5 + 1)) + 'p-values\n' text += '\n'.join(('%s %6.4g' % (pairs, pv) for (pairs, pv) in zip(self.all_pairs_names, self.pval_corrected()))) return text statsmodels-0.12.2/statsmodels/stats/contingency_tables.py000066400000000000000000001266551400612667500241100ustar00rootroot00000000000000""" Methods for analyzing two-way contingency tables (i.e. frequency tables for observations that are cross-classified with respect to two categorical variables). The main classes are: * Table : implements methods that can be applied to any two-way contingency table. * SquareTable : implements methods that can be applied to a square two-way contingency table. * Table2x2 : implements methods that can be applied to a 2x2 contingency table. * StratifiedTable : implements methods that can be applied to a collection of 2x2 contingency tables. Also contains functions for conducting McNemar's test and Cochran's q test. Note that the inference procedures may depend on how the data were sampled. In general the observed units are independent and identically distributed. """ from statsmodels.tools.decorators import cache_readonly import numpy as np from scipy import stats import pandas as pd import warnings from statsmodels import iolib from statsmodels.tools import sm_exceptions def _make_df_square(table): """ Reindex a pandas DataFrame so that it becomes square, meaning that the row and column indices contain the same values, in the same order. The row and column index are extended to achieve this. """ if not isinstance(table, pd.DataFrame): return table # If the table is not square, make it square if not table.index.equals(table.columns): ix = list(set(table.index) | set(table.columns)) ix.sort() table = table.reindex(index=ix, columns=ix, fill_value=0) # Ensures that the rows and columns are in the same order. table = table.reindex(table.columns) return table class _Bunch(object): def __repr__(self): return "" def __str__(self): ky = [k for k, _ in self.__dict__.items()] ky.sort() m = max([len(k) for k in ky]) tab = [] f = "{:" + str(m) + "} {}" for k in ky: tab.append(f.format(k, self.__dict__[k])) return "\n".join(tab) class Table(object): """ A two-way contingency table. Parameters ---------- table : array_like A contingency table. shift_zeros : bool If True and any cell count is zero, add 0.5 to all values in the table. Attributes ---------- table_orig : array_like The original table is cached as `table_orig`. See Also -------- statsmodels.graphics.mosaicplot.mosaic scipy.stats.chi2_contingency Notes ----- The inference procedures used here are all based on a sampling model in which the units are independent and identically distributed, with each unit being classified with respect to two categorical variables. References ---------- Definitions of residuals: https://onlinecourses.science.psu.edu/stat504/node/86 """ def __init__(self, table, shift_zeros=True): self.table_orig = table self.table = np.asarray(table, dtype=np.float64) if shift_zeros and (self.table.min() == 0): self.table[self.table == 0] = 0.5 def __str__(self): s = ("A %dx%d contingency table with counts:\n" % tuple(self.table.shape)) s += np.array_str(self.table) return s @classmethod def from_data(cls, data, shift_zeros=True): """ Construct a Table object from data. Parameters ---------- data : array_like The raw data, from which a contingency table is constructed using the first two columns. shift_zeros : bool If True and any cell count is zero, add 0.5 to all values in the table. Returns ------- A Table instance. """ if isinstance(data, pd.DataFrame): table = pd.crosstab(data.iloc[:, 0], data.iloc[:, 1]) else: table = pd.crosstab(data[:, 0], data[:, 1]) return cls(table, shift_zeros) def test_nominal_association(self): """ Assess independence for nominal factors. Assessment of independence between rows and columns using chi^2 testing. The rows and columns are treated as nominal (unordered) categorical variables. Returns ------- A bunch containing the following attributes: statistic : float The chi^2 test statistic. df : int The degrees of freedom of the reference distribution pvalue : float The p-value for the test. """ statistic = np.asarray(self.chi2_contribs).sum() df = np.prod(np.asarray(self.table.shape) - 1) pvalue = 1 - stats.chi2.cdf(statistic, df) b = _Bunch() b.statistic = statistic b.df = df b.pvalue = pvalue return b def test_ordinal_association(self, row_scores=None, col_scores=None): """ Assess independence between two ordinal variables. This is the 'linear by linear' association test, which uses weights or scores to target the test to have more power against ordered alternatives. Parameters ---------- row_scores : array_like An array of numeric row scores col_scores : array_like An array of numeric column scores Returns ------- A bunch with the following attributes: statistic : float The test statistic. null_mean : float The expected value of the test statistic under the null hypothesis. null_sd : float The standard deviation of the test statistic under the null hypothesis. zscore : float The Z-score for the test statistic. pvalue : float The p-value for the test. Notes ----- The scores define the trend to which the test is most sensitive. Using the default row and column scores gives the Cochran-Armitage trend test. """ if row_scores is None: row_scores = np.arange(self.table.shape[0]) if col_scores is None: col_scores = np.arange(self.table.shape[1]) if len(row_scores) != self.table.shape[0]: msg = ("The length of `row_scores` must match the first " + "dimension of `table`.") raise ValueError(msg) if len(col_scores) != self.table.shape[1]: msg = ("The length of `col_scores` must match the second " + "dimension of `table`.") raise ValueError(msg) # The test statistic statistic = np.dot(row_scores, np.dot(self.table, col_scores)) # Some needed quantities n_obs = self.table.sum() rtot = self.table.sum(1) um = np.dot(row_scores, rtot) u2m = np.dot(row_scores**2, rtot) ctot = self.table.sum(0) vn = np.dot(col_scores, ctot) v2n = np.dot(col_scores**2, ctot) # The null mean and variance of the test statistic e_stat = um * vn / n_obs v_stat = (u2m - um**2 / n_obs) * (v2n - vn**2 / n_obs) / (n_obs - 1) sd_stat = np.sqrt(v_stat) zscore = (statistic - e_stat) / sd_stat pvalue = 2 * stats.norm.cdf(-np.abs(zscore)) b = _Bunch() b.statistic = statistic b.null_mean = e_stat b.null_sd = sd_stat b.zscore = zscore b.pvalue = pvalue return b @cache_readonly def marginal_probabilities(self): """ Estimate marginal probability distributions for the rows and columns. Returns ------- row : ndarray Marginal row probabilities col : ndarray Marginal column probabilities """ n = self.table.sum() row = self.table.sum(1) / n col = self.table.sum(0) / n if isinstance(self.table_orig, pd.DataFrame): row = pd.Series(row, self.table_orig.index) col = pd.Series(col, self.table_orig.columns) return row, col @cache_readonly def independence_probabilities(self): """ Returns fitted joint probabilities under independence. The returned table is outer(row, column), where row and column are the estimated marginal distributions of the rows and columns. """ row, col = self.marginal_probabilities itab = np.outer(row, col) if isinstance(self.table_orig, pd.DataFrame): itab = pd.DataFrame(itab, self.table_orig.index, self.table_orig.columns) return itab @cache_readonly def fittedvalues(self): """ Returns fitted cell counts under independence. The returned cell counts are estimates under a model where the rows and columns of the table are independent. """ probs = self.independence_probabilities fit = self.table.sum() * probs return fit @cache_readonly def resid_pearson(self): """ Returns Pearson residuals. The Pearson residuals are calculated under a model where the rows and columns of the table are independent. """ fit = self.fittedvalues resids = (self.table - fit) / np.sqrt(fit) return resids @cache_readonly def standardized_resids(self): """ Returns standardized residuals under independence. """ row, col = self.marginal_probabilities sresids = self.resid_pearson / np.sqrt(np.outer(1 - row, 1 - col)) return sresids @cache_readonly def chi2_contribs(self): """ Returns the contributions to the chi^2 statistic for independence. The returned table contains the contribution of each cell to the chi^2 test statistic for the null hypothesis that the rows and columns are independent. """ return self.resid_pearson**2 @cache_readonly def local_log_oddsratios(self): """ Returns local log odds ratios. The local log odds ratios are the log odds ratios calculated for contiguous 2x2 sub-tables. """ ta = self.table.copy() a = ta[0:-1, 0:-1] b = ta[0:-1, 1:] c = ta[1:, 0:-1] d = ta[1:, 1:] tab = np.log(a) + np.log(d) - np.log(b) - np.log(c) rslt = np.empty(self.table.shape, np.float64) rslt *= np.nan rslt[0:-1, 0:-1] = tab if isinstance(self.table_orig, pd.DataFrame): rslt = pd.DataFrame(rslt, index=self.table_orig.index, columns=self.table_orig.columns) return rslt @cache_readonly def local_oddsratios(self): """ Returns local odds ratios. See documentation for local_log_oddsratios. """ return np.exp(self.local_log_oddsratios) @cache_readonly def cumulative_log_oddsratios(self): """ Returns cumulative log odds ratios. The cumulative log odds ratios for a contingency table with ordered rows and columns are calculated by collapsing all cells to the left/right and above/below a given point, to obtain a 2x2 table from which a log odds ratio can be calculated. """ ta = self.table.cumsum(0).cumsum(1) a = ta[0:-1, 0:-1] b = ta[0:-1, -1:] - a c = ta[-1:, 0:-1] - a d = ta[-1, -1] - (a + b + c) tab = np.log(a) + np.log(d) - np.log(b) - np.log(c) rslt = np.empty(self.table.shape, np.float64) rslt *= np.nan rslt[0:-1, 0:-1] = tab if isinstance(self.table_orig, pd.DataFrame): rslt = pd.DataFrame(rslt, index=self.table_orig.index, columns=self.table_orig.columns) return rslt @cache_readonly def cumulative_oddsratios(self): """ Returns the cumulative odds ratios for a contingency table. See documentation for cumulative_log_oddsratio. """ return np.exp(self.cumulative_log_oddsratios) class SquareTable(Table): """ Methods for analyzing a square contingency table. Parameters ---------- table : array_like A square contingency table, or DataFrame that is converted to a square form. shift_zeros : bool If True and any cell count is zero, add 0.5 to all values in the table. These methods should only be used when the rows and columns of the table have the same categories. If `table` is provided as a Pandas DataFrame, the row and column indices will be extended to create a square table, inserting zeros where a row or column is missing. Otherwise the table should be provided in a square form, with the (implicit) row and column categories appearing in the same order. """ def __init__(self, table, shift_zeros=True): table = _make_df_square(table) # Non-pandas passes through k1, k2 = table.shape if k1 != k2: raise ValueError('table must be square') super(SquareTable, self).__init__(table, shift_zeros) def symmetry(self, method="bowker"): """ Test for symmetry of a joint distribution. This procedure tests the null hypothesis that the joint distribution is symmetric around the main diagonal, that is .. math:: p_{i, j} = p_{j, i} for all i, j Returns ------- A bunch with attributes: statistic : float chisquare test statistic p-value : float p-value of the test statistic based on chisquare distribution df : int degrees of freedom of the chisquare distribution Notes ----- The implementation is based on the SAS documentation. R includes it in `mcnemar.test` if the table is not 2 by 2. However a more direct generalization of the McNemar test to larger tables is provided by the homogeneity test (TableSymmetry.homogeneity). The p-value is based on the chi-square distribution which requires that the sample size is not very small to be a good approximation of the true distribution. For 2x2 contingency tables the exact distribution can be obtained with `mcnemar` See Also -------- mcnemar homogeneity """ if method.lower() != "bowker": raise ValueError("method for symmetry testing must be 'bowker'") k = self.table.shape[0] upp_idx = np.triu_indices(k, 1) tril = self.table.T[upp_idx] # lower triangle in column order triu = self.table[upp_idx] # upper triangle in row order statistic = ((tril - triu)**2 / (tril + triu + 1e-20)).sum() df = k * (k-1) / 2. pvalue = stats.chi2.sf(statistic, df) b = _Bunch() b.statistic = statistic b.pvalue = pvalue b.df = df return b def homogeneity(self, method="stuart_maxwell"): """ Compare row and column marginal distributions. Parameters ---------- method : str Either 'stuart_maxwell' or 'bhapkar', leading to two different estimates of the covariance matrix for the estimated difference between the row margins and the column margins. Returns a bunch with attributes: statistic : float The chi^2 test statistic pvalue : float The p-value of the test statistic df : int The degrees of freedom of the reference distribution Notes ----- For a 2x2 table this is equivalent to McNemar's test. More generally the procedure tests the null hypothesis that the marginal distribution of the row factor is equal to the marginal distribution of the column factor. For this to be meaningful, the two factors must have the same sample space (i.e. the same categories). """ if self.table.shape[0] < 1: raise ValueError('table is empty') elif self.table.shape[0] == 1: b = _Bunch() b.statistic = 0 b.pvalue = 1 b.df = 0 return b method = method.lower() if method not in ["bhapkar", "stuart_maxwell"]: raise ValueError("method '%s' for homogeneity not known" % method) n_obs = self.table.sum() pr = self.table.astype(np.float64) / n_obs # Compute margins, eliminate last row/column so there is no # degeneracy row = pr.sum(1)[0:-1] col = pr.sum(0)[0:-1] pr = pr[0:-1, 0:-1] # The estimated difference between row and column margins. d = col - row # The degrees of freedom of the chi^2 reference distribution. df = pr.shape[0] if method == "bhapkar": vmat = -(pr + pr.T) - np.outer(d, d) dv = col + row - 2*np.diag(pr) - d**2 np.fill_diagonal(vmat, dv) elif method == "stuart_maxwell": vmat = -(pr + pr.T) dv = row + col - 2*np.diag(pr) np.fill_diagonal(vmat, dv) try: statistic = n_obs * np.dot(d, np.linalg.solve(vmat, d)) except np.linalg.LinAlgError: warnings.warn("Unable to invert covariance matrix", sm_exceptions.SingularMatrixWarning) b = _Bunch() b.statistic = np.nan b.pvalue = np.nan b.df = df return b pvalue = 1 - stats.chi2.cdf(statistic, df) b = _Bunch() b.statistic = statistic b.pvalue = pvalue b.df = df return b def summary(self, alpha=0.05, float_format="%.3f"): """ Produce a summary of the analysis. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the interval. float_format : str Used to format numeric values in the table. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. """ fmt = float_format headers = ["Statistic", "P-value", "DF"] stubs = ["Symmetry", "Homogeneity"] sy = self.symmetry() hm = self.homogeneity() data = [[fmt % sy.statistic, fmt % sy.pvalue, '%d' % sy.df], [fmt % hm.statistic, fmt % hm.pvalue, '%d' % hm.df]] tab = iolib.SimpleTable(data, headers, stubs, data_aligns="r", table_dec_above='') return tab class Table2x2(SquareTable): """ Analyses that can be performed on a 2x2 contingency table. Parameters ---------- table : array_like A 2x2 contingency table shift_zeros : bool If true, 0.5 is added to all cells of the table if any cell is equal to zero. Notes ----- The inference procedures used here are all based on a sampling model in which the units are independent and identically distributed, with each unit being classified with respect to two categorical variables. Note that for the risk ratio, the analysis is not symmetric with respect to the rows and columns of the contingency table. The two rows define population subgroups, column 0 is the number of 'events', and column 1 is the number of 'non-events'. """ def __init__(self, table, shift_zeros=True): if type(table) is list: table = np.asarray(table) if (table.ndim != 2) or (table.shape[0] != 2) or (table.shape[1] != 2): raise ValueError("Table2x2 takes a 2x2 table as input.") super(Table2x2, self).__init__(table, shift_zeros) @classmethod def from_data(cls, data, shift_zeros=True): """ Construct a Table object from data. Parameters ---------- data : array_like The raw data, the first column defines the rows and the second column defines the columns. shift_zeros : bool If True, and if there are any zeros in the contingency table, add 0.5 to all four cells of the table. """ if isinstance(data, pd.DataFrame): table = pd.crosstab(data.iloc[:, 0], data.iloc[:, 1]) else: table = pd.crosstab(data[:, 0], data[:, 1]) return cls(table, shift_zeros) @cache_readonly def log_oddsratio(self): """ Returns the log odds ratio for a 2x2 table. """ f = self.table.flatten() return np.dot(np.log(f), np.r_[1, -1, -1, 1]) @cache_readonly def oddsratio(self): """ Returns the odds ratio for a 2x2 table. """ return (self.table[0, 0] * self.table[1, 1] / (self.table[0, 1] * self.table[1, 0])) @cache_readonly def log_oddsratio_se(self): """ Returns the standard error for the log odds ratio. """ return np.sqrt(np.sum(1 / self.table)) def oddsratio_pvalue(self, null=1): """ P-value for a hypothesis test about the odds ratio. Parameters ---------- null : float The null value of the odds ratio. """ return self.log_oddsratio_pvalue(np.log(null)) def log_oddsratio_pvalue(self, null=0): """ P-value for a hypothesis test about the log odds ratio. Parameters ---------- null : float The null value of the log odds ratio. """ zscore = (self.log_oddsratio - null) / self.log_oddsratio_se pvalue = 2 * stats.norm.cdf(-np.abs(zscore)) return pvalue def log_oddsratio_confint(self, alpha=0.05, method="normal"): """ A confidence level for the log odds ratio. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the confidence interval. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. """ f = -stats.norm.ppf(alpha / 2) lor = self.log_oddsratio se = self.log_oddsratio_se lcb = lor - f * se ucb = lor + f * se return lcb, ucb def oddsratio_confint(self, alpha=0.05, method="normal"): """ A confidence interval for the odds ratio. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the confidence interval. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. """ lcb, ucb = self.log_oddsratio_confint(alpha, method=method) return np.exp(lcb), np.exp(ucb) @cache_readonly def riskratio(self): """ Returns the risk ratio for a 2x2 table. The risk ratio is calculated with respect to the rows. """ p = self.table[:, 0] / self.table.sum(1) return p[0] / p[1] @cache_readonly def log_riskratio(self): """ Returns the log of the risk ratio. """ return np.log(self.riskratio) @cache_readonly def log_riskratio_se(self): """ Returns the standard error of the log of the risk ratio. """ n = self.table.sum(1) p = self.table[:, 0] / n va = np.sum((1 - p) / (n*p)) return np.sqrt(va) def riskratio_pvalue(self, null=1): """ p-value for a hypothesis test about the risk ratio. Parameters ---------- null : float The null value of the risk ratio. """ return self.log_riskratio_pvalue(np.log(null)) def log_riskratio_pvalue(self, null=0): """ p-value for a hypothesis test about the log risk ratio. Parameters ---------- null : float The null value of the log risk ratio. """ zscore = (self.log_riskratio - null) / self.log_riskratio_se pvalue = 2 * stats.norm.cdf(-np.abs(zscore)) return pvalue def log_riskratio_confint(self, alpha=0.05, method="normal"): """ A confidence interval for the log risk ratio. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the confidence interval. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. """ f = -stats.norm.ppf(alpha / 2) lrr = self.log_riskratio se = self.log_riskratio_se lcb = lrr - f * se ucb = lrr + f * se return lcb, ucb def riskratio_confint(self, alpha=0.05, method="normal"): """ A confidence interval for the risk ratio. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the confidence interval. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. """ lcb, ucb = self.log_riskratio_confint(alpha, method=method) return np.exp(lcb), np.exp(ucb) def summary(self, alpha=0.05, float_format="%.3f", method="normal"): """ Summarizes results for a 2x2 table analysis. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the confidence intervals. float_format : str Used to format the numeric values in the table. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. """ def fmt(x): if isinstance(x, str): return x return float_format % x headers = ["Estimate", "SE", "LCB", "UCB", "p-value"] stubs = ["Odds ratio", "Log odds ratio", "Risk ratio", "Log risk ratio"] lcb1, ucb1 = self.oddsratio_confint(alpha, method) lcb2, ucb2 = self.log_oddsratio_confint(alpha, method) lcb3, ucb3 = self.riskratio_confint(alpha, method) lcb4, ucb4 = self.log_riskratio_confint(alpha, method) data = [[fmt(x) for x in [self.oddsratio, "", lcb1, ucb1, self.oddsratio_pvalue()]], [fmt(x) for x in [self.log_oddsratio, self.log_oddsratio_se, lcb2, ucb2, self.oddsratio_pvalue()]], [fmt(x) for x in [self.riskratio, "", lcb3, ucb3, self.riskratio_pvalue()]], [fmt(x) for x in [self.log_riskratio, self.log_riskratio_se, lcb4, ucb4, self.riskratio_pvalue()]]] tab = iolib.SimpleTable(data, headers, stubs, data_aligns="r", table_dec_above='') return tab class StratifiedTable(object): """ Analyses for a collection of 2x2 contingency tables. Such a collection may arise by stratifying a single 2x2 table with respect to another factor. This class implements the 'Cochran-Mantel-Haenszel' and 'Breslow-Day' procedures for analyzing collections of 2x2 contingency tables. Parameters ---------- tables : list or ndarray Either a list containing several 2x2 contingency tables, or a 2x2xk ndarray in which each slice along the third axis is a 2x2 contingency table. Notes ----- This results are based on a sampling model in which the units are independent both within and between strata. """ def __init__(self, tables, shift_zeros=False): if isinstance(tables, np.ndarray): sp = tables.shape if (len(sp) != 3) or (sp[0] != 2) or (sp[1] != 2): raise ValueError("If an ndarray, argument must be 2x2xn") table = tables * 1. # use atleast float dtype else: if any([np.asarray(x).shape != (2, 2) for x in tables]): m = "If `tables` is a list, all of its elements should be 2x2" raise ValueError(m) # Create a data cube table = np.dstack(tables).astype(np.float64) if shift_zeros: zx = (table == 0).sum(0).sum(0) ix = np.flatnonzero(zx > 0) if len(ix) > 0: table = table.copy() table[:, :, ix] += 0.5 self.table = table self._cache = {} # Quantities to precompute. Table entries are [[a, b], [c, # d]], 'ad' is 'a * d', 'apb' is 'a + b', 'dma' is 'd - a', # etc. self._apb = table[0, 0, :] + table[0, 1, :] self._apc = table[0, 0, :] + table[1, 0, :] self._bpd = table[0, 1, :] + table[1, 1, :] self._cpd = table[1, 0, :] + table[1, 1, :] self._ad = table[0, 0, :] * table[1, 1, :] self._bc = table[0, 1, :] * table[1, 0, :] self._apd = table[0, 0, :] + table[1, 1, :] self._dma = table[1, 1, :] - table[0, 0, :] self._n = table.sum(0).sum(0) @classmethod def from_data(cls, var1, var2, strata, data): """ Construct a StratifiedTable object from data. Parameters ---------- var1 : int or string The column index or name of `data` specifying the variable defining the rows of the contingency table. The variable must have only two distinct values. var2 : int or string The column index or name of `data` specifying the variable defining the columns of the contingency table. The variable must have only two distinct values. strata : int or string The column index or name of `data` specifying the variable defining the strata. data : array_like The raw data. A cross-table for analysis is constructed from the first two columns. Returns ------- A StratifiedTable instance. """ if not isinstance(data, pd.DataFrame): data1 = pd.DataFrame(index=np.arange(data.shape[0]), columns=[var1, var2, strata]) data1.loc[:, var1] = data[:, var1] data1.loc[:, var2] = data[:, var2] data1.loc[:, strata] = data[:, strata] else: data1 = data[[var1, var2, strata]] gb = data1.groupby(strata).groups tables = [] for g in gb: ii = gb[g] tab = pd.crosstab(data1.loc[ii, var1], data1.loc[ii, var2]) if (tab.shape != np.r_[2, 2]).any(): msg = "Invalid table dimensions" raise ValueError(msg) tables.append(np.asarray(tab)) return cls(tables) def test_null_odds(self, correction=False): """ Test that all tables have odds ratio equal to 1. This is the 'Mantel-Haenszel' test. Parameters ---------- correction : bool If True, use the continuity correction when calculating the test statistic. Returns ------- A bunch containing the chi^2 test statistic and p-value. """ statistic = np.sum(self.table[0, 0, :] - self._apb * self._apc / self._n) statistic = np.abs(statistic) if correction: statistic -= 0.5 statistic = statistic**2 denom = self._apb * self._apc * self._bpd * self._cpd denom /= (self._n**2 * (self._n - 1)) denom = np.sum(denom) statistic /= denom # df is always 1 pvalue = 1 - stats.chi2.cdf(statistic, 1) b = _Bunch() b.statistic = statistic b.pvalue = pvalue return b @cache_readonly def oddsratio_pooled(self): """ The pooled odds ratio. The value is an estimate of a common odds ratio across all of the stratified tables. """ odds_ratio = np.sum(self._ad / self._n) / np.sum(self._bc / self._n) return odds_ratio @cache_readonly def logodds_pooled(self): """ Returns the logarithm of the pooled odds ratio. See oddsratio_pooled for more information. """ return np.log(self.oddsratio_pooled) @cache_readonly def riskratio_pooled(self): """ Estimate of the pooled risk ratio. """ acd = self.table[0, 0, :] * self._cpd cab = self.table[1, 0, :] * self._apb rr = np.sum(acd / self._n) / np.sum(cab / self._n) return rr @cache_readonly def risk_pooled(self): # Deprecated due to name being misleading msg = "'risk_pooled' is deprecated, use 'riskratio_pooled' instead" warnings.warn(msg, DeprecationWarning) return self.riskratio_pooled @cache_readonly def logodds_pooled_se(self): """ Estimated standard error of the pooled log odds ratio References ---------- J. Robins, N. Breslow, S. Greenland. "Estimators of the Mantel-Haenszel Variance Consistent in Both Sparse Data and Large-Strata Limiting Models." Biometrics 42, no. 2 (1986): 311-23. """ adns = np.sum(self._ad / self._n) bcns = np.sum(self._bc / self._n) lor_va = np.sum(self._apd * self._ad / self._n**2) / adns**2 mid = self._apd * self._bc / self._n**2 mid += (1 - self._apd / self._n) * self._ad / self._n mid = np.sum(mid) mid /= (adns * bcns) lor_va += mid lor_va += np.sum((1 - self._apd / self._n) * self._bc / self._n) / bcns**2 lor_va /= 2 lor_se = np.sqrt(lor_va) return lor_se def logodds_pooled_confint(self, alpha=0.05, method="normal"): """ A confidence interval for the pooled log odds ratio. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the interval. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. Returns ------- lcb : float The lower confidence limit. ucb : float The upper confidence limit. """ lor = np.log(self.oddsratio_pooled) lor_se = self.logodds_pooled_se f = -stats.norm.ppf(alpha / 2) lcb = lor - f * lor_se ucb = lor + f * lor_se return lcb, ucb def oddsratio_pooled_confint(self, alpha=0.05, method="normal"): """ A confidence interval for the pooled odds ratio. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the interval. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. Returns ------- lcb : float The lower confidence limit. ucb : float The upper confidence limit. """ lcb, ucb = self.logodds_pooled_confint(alpha, method=method) lcb = np.exp(lcb) ucb = np.exp(ucb) return lcb, ucb def test_equal_odds(self, adjust=False): """ Test that all odds ratios are identical. This is the 'Breslow-Day' testing procedure. Parameters ---------- adjust : bool Use the 'Tarone' adjustment to achieve the chi^2 asymptotic distribution. Returns ------- A bunch containing the following attributes: statistic : float The chi^2 test statistic. p-value : float The p-value for the test. """ table = self.table r = self.oddsratio_pooled a = 1 - r b = r * (self._apb + self._apc) + self._dma c = -r * self._apb * self._apc # Expected value of first cell dr = np.sqrt(b**2 - 4*a*c) e11 = (-b + dr) / (2*a) # Variance of the first cell v11 = (1 / e11 + 1 / (self._apc - e11) + 1 / (self._apb - e11) + 1 / (self._dma + e11)) v11 = 1 / v11 statistic = np.sum((table[0, 0, :] - e11)**2 / v11) if adjust: adj = table[0, 0, :].sum() - e11.sum() adj = adj**2 adj /= np.sum(v11) statistic -= adj pvalue = 1 - stats.chi2.cdf(statistic, table.shape[2] - 1) b = _Bunch() b.statistic = statistic b.pvalue = pvalue return b def summary(self, alpha=0.05, float_format="%.3f", method="normal"): """ A summary of all the main results. Parameters ---------- alpha : float `1 - alpha` is the nominal coverage probability of the confidence intervals. float_format : str Used for formatting numeric values in the summary. method : str The method for producing the confidence interval. Currently must be 'normal' which uses the normal approximation. """ def fmt(x): if isinstance(x, str): return x return float_format % x co_lcb, co_ucb = self.oddsratio_pooled_confint( alpha=alpha, method=method) clo_lcb, clo_ucb = self.logodds_pooled_confint( alpha=alpha, method=method) headers = ["Estimate", "LCB", "UCB"] stubs = ["Pooled odds", "Pooled log odds", "Pooled risk ratio", ""] data = [[fmt(x) for x in [self.oddsratio_pooled, co_lcb, co_ucb]], [fmt(x) for x in [self.logodds_pooled, clo_lcb, clo_ucb]], [fmt(x) for x in [self.riskratio_pooled, "", ""]], ['', '', '']] tab1 = iolib.SimpleTable(data, headers, stubs, data_aligns="r", table_dec_above='') headers = ["Statistic", "P-value", ""] stubs = ["Test of OR=1", "Test constant OR"] rslt1 = self.test_null_odds() rslt2 = self.test_equal_odds() data = [[fmt(x) for x in [rslt1.statistic, rslt1.pvalue, ""]], [fmt(x) for x in [rslt2.statistic, rslt2.pvalue, ""]]] tab2 = iolib.SimpleTable(data, headers, stubs, data_aligns="r") tab1.extend(tab2) headers = ["", "", ""] stubs = ["Number of tables", "Min n", "Max n", "Avg n", "Total n"] ss = self.table.sum(0).sum(0) data = [["%d" % self.table.shape[2], '', ''], ["%d" % min(ss), '', ''], ["%d" % max(ss), '', ''], ["%.0f" % np.mean(ss), '', ''], ["%d" % sum(ss), '', '', '']] tab3 = iolib.SimpleTable(data, headers, stubs, data_aligns="r") tab1.extend(tab3) return tab1 def mcnemar(table, exact=True, correction=True): """ McNemar test of homogeneity. Parameters ---------- table : array_like A square contingency table. exact : bool If exact is true, then the binomial distribution will be used. If exact is false, then the chisquare distribution will be used, which is the approximation to the distribution of the test statistic for large sample sizes. correction : bool If true, then a continuity correction is used for the chisquare distribution (if exact is false.) Returns ------- A bunch with attributes: statistic : float or int, array The test statistic is the chisquare statistic if exact is false. If the exact binomial distribution is used, then this contains the min(n1, n2), where n1, n2 are cases that are zero in one sample but one in the other sample. pvalue : float or array p-value of the null hypothesis of equal marginal distributions. Notes ----- This is a special case of Cochran's Q test, and of the homogeneity test. The results when the chisquare distribution is used are identical, except for continuity correction. """ table = _make_df_square(table) table = np.asarray(table, dtype=np.float64) n1, n2 = table[0, 1], table[1, 0] if exact: statistic = np.minimum(n1, n2) # binom is symmetric with p=0.5 # SciPy 1.7+ requires int arguments int_sum = int(n1 + n2) if int_sum != (n1 + n2): warnings.warn("exact can only be used with tables containing " "integers. This warning will become a ValueError " "after 0.12.", FutureWarning) pvalue = stats.binom.cdf(statistic, int_sum, 0.5) * 2 pvalue = np.minimum(pvalue, 1) # limit to 1 if n1==n2 else: corr = int(correction) # convert bool to 0 or 1 statistic = (np.abs(n1 - n2) - corr)**2 / (1. * (n1 + n2)) df = 1 pvalue = stats.chi2.sf(statistic, df) b = _Bunch() b.statistic = statistic b.pvalue = pvalue return b def cochrans_q(x, return_object=True): """ Cochran's Q test for identical binomial proportions. Parameters ---------- x : array_like, 2d (N, k) data with N cases and k variables return_object : bool Return values as bunch instead of as individual values. Returns ------- Returns a bunch containing the following attributes, or the individual values according to the value of `return_object`. statistic : float test statistic pvalue : float pvalue from the chisquare distribution Notes ----- Cochran's Q is a k-sample extension of the McNemar test. If there are only two groups, then Cochran's Q test and the McNemar test are equivalent. The procedure tests that the probability of success is the same for every group. The alternative hypothesis is that at least two groups have a different probability of success. In Wikipedia terminology, rows are blocks and columns are treatments. The number of rows N, should be large for the chisquare distribution to be a good approximation. The Null hypothesis of the test is that all treatments have the same effect. References ---------- https://en.wikipedia.org/wiki/Cochran_test SAS Manual for NPAR TESTS """ x = np.asarray(x, dtype=np.float64) gruni = np.unique(x) N, k = x.shape count_row_success = (x == gruni[-1]).sum(1, float) count_col_success = (x == gruni[-1]).sum(0, float) count_row_ss = count_row_success.sum() count_col_ss = count_col_success.sum() assert count_row_ss == count_col_ss # just a calculation check # From the SAS manual q_stat = ((k-1) * (k * np.sum(count_col_success**2) - count_col_ss**2) / (k * count_row_ss - np.sum(count_row_success**2))) # Note: the denominator looks just like k times the variance of # the columns # Wikipedia uses a different, but equivalent expression # q_stat = (k-1) * (k * np.sum(count_row_success**2) - count_row_ss**2) # / (k * count_col_ss - np.sum(count_col_success**2)) df = k - 1 pvalue = stats.chi2.sf(q_stat, df) if return_object: b = _Bunch() b.statistic = q_stat b.df = df b.pvalue = pvalue return b return q_stat, pvalue, df statsmodels-0.12.2/statsmodels/stats/contrast.py000066400000000000000000000657361400612667500220750ustar00rootroot00000000000000import numpy as np from scipy.stats import f as fdist from scipy.stats import t as student_t from scipy import stats from statsmodels.tools.tools import clean0, fullrank from statsmodels.stats.multitest import multipletests #TODO: should this be public if it's just a container? class ContrastResults(object): """ Class for results of tests of linear restrictions on coefficients in a model. This class functions mainly as a container for `t_test`, `f_test` and `wald_test` for the parameters of a model. The attributes depend on the statistical test and are either based on the normal, the t, the F or the chisquare distribution. """ def __init__(self, t=None, F=None, sd=None, effect=None, df_denom=None, df_num=None, alpha=0.05, **kwds): self.effect = effect # Let it be None for F if F is not None: self.distribution = 'F' self.fvalue = F self.statistic = self.fvalue self.df_denom = df_denom self.df_num = df_num self.dist = fdist self.dist_args = (df_num, df_denom) self.pvalue = fdist.sf(F, df_num, df_denom) elif t is not None: self.distribution = 't' self.tvalue = t self.statistic = t # generic alias self.sd = sd self.df_denom = df_denom self.dist = student_t self.dist_args = (df_denom,) self.pvalue = self.dist.sf(np.abs(t), df_denom) * 2 elif 'statistic' in kwds: # TODO: currently targeted to normal distribution, and chi2 self.distribution = kwds['distribution'] self.statistic = kwds['statistic'] self.tvalue = value = kwds['statistic'] # keep alias # TODO: for results instance we decided to use tvalues also for normal self.sd = sd self.dist = getattr(stats, self.distribution) self.dist_args = kwds.get('dist_args', ()) if self.distribution == 'chi2': self.pvalue = self.dist.sf(self.statistic, df_denom) self.df_denom = df_denom else: "normal" self.pvalue = np.full_like(value, np.nan) not_nan = ~np.isnan(value) self.pvalue[not_nan] = self.dist.sf(np.abs(value[not_nan])) * 2 # cleanup # should we return python scalar? self.pvalue = np.squeeze(self.pvalue) def conf_int(self, alpha=0.05): """ Returns the confidence interval of the value, `effect` of the constraint. This is currently only available for t and z tests. Parameters ---------- alpha : float, optional The significance level for the confidence interval. ie., The default `alpha` = .05 returns a 95% confidence interval. Returns ------- ci : ndarray, (k_constraints, 2) The array has the lower and the upper limit of the confidence interval in the columns. """ if self.effect is not None: # confidence intervals q = self.dist.ppf(1 - alpha / 2., *self.dist_args) lower = self.effect - q * self.sd upper = self.effect + q * self.sd return np.column_stack((lower, upper)) else: raise NotImplementedError('Confidence Interval not available') def __str__(self): return self.summary().__str__() def __repr__(self): return str(self.__class__) + '\n' + self.__str__() def summary(self, xname=None, alpha=0.05, title=None): """Summarize the Results of the hypothesis test Parameters ---------- xname : list[str], optional Default is `c_##` for ## in the number of regressors alpha : float significance level for the confidence intervals. Default is alpha = 0.05 which implies a confidence level of 95%. title : str, optional Title for the params table. If not None, then this replaces the default title Returns ------- smry : str or Summary instance This contains a parameter results table in the case of t or z test in the same form as the parameter results table in the model results summary. For F or Wald test, the return is a string. """ if self.effect is not None: # TODO: should also add some extra information, e.g. robust cov ? # TODO: can we infer names for constraints, xname in __init__ ? if title is None: title = 'Test for Constraints' elif title == '': # do not add any title, # I think SimpleTable skips on None - check title = None # we have everything for a params table use_t = (self.distribution == 't') yname='constraints' # Not used in params_frame if xname is None: xname = ['c%d' % ii for ii in range(len(self.effect))] from statsmodels.iolib.summary import summary_params pvalues = np.atleast_1d(self.pvalue) summ = summary_params((self, self.effect, self.sd, self.statistic, pvalues, self.conf_int(alpha)), yname=yname, xname=xname, use_t=use_t, title=title, alpha=alpha) return summ elif hasattr(self, 'fvalue'): # TODO: create something nicer for these casee return ('' % (repr(self.fvalue), self.pvalue, self.df_denom, self.df_num)) elif self.distribution == 'chi2': return ('' % (self.distribution, self.statistic, self.pvalue, self.df_denom)) else: # generic return ('' % (self.statistic, self.pvalue)) def summary_frame(self, xname=None, alpha=0.05): """Return the parameter table as a pandas DataFrame This is only available for t and normal tests """ if self.effect is not None: # we have everything for a params table use_t = (self.distribution == 't') yname='constraints' # Not used in params_frame if xname is None: xname = ['c%d' % ii for ii in range(len(self.effect))] from statsmodels.iolib.summary import summary_params_frame summ = summary_params_frame((self, self.effect, self.sd, self.statistic,self.pvalue, self.conf_int(alpha)), yname=yname, xname=xname, use_t=use_t, alpha=alpha) return summ else: # TODO: create something nicer raise NotImplementedError('only available for t and z') class Contrast(object): """ This class is used to construct contrast matrices in regression models. They are specified by a (term, design) pair. The term, T, is a linear combination of columns of the design matrix. The matrix attribute of Contrast is a contrast matrix C so that colspan(dot(D, C)) = colspan(dot(D, dot(pinv(D), T))) where pinv(D) is the generalized inverse of D. Further, the matrix Tnew = dot(C, D) is full rank. The rank attribute is the rank of dot(D, dot(pinv(D), T)) In a regression model, the contrast tests that E(dot(Tnew, Y)) = 0 for each column of Tnew. Parameters ---------- term : array_like design : array_like Attributes ---------- contrast_matrix Examples -------- >>> import statsmodels.api as sm >>> from statsmodels.stats.contrast import Contrast >>> import numpy as np >>> np.random.seed(54321) >>> X = np.random.standard_normal((40,10)) # Get a contrast >>> new_term = np.column_stack((X[:,0], X[:,2])) >>> c = Contrast(new_term, X) >>> test = [[1] + [0]*9, [0]*2 + [1] + [0]*7] >>> np.allclose(c.contrast_matrix, test) True Get another contrast >>> P = np.dot(X, np.linalg.pinv(X)) >>> resid = np.identity(40) - P >>> noise = np.dot(resid,np.random.standard_normal((40,5))) >>> new_term2 = np.column_stack((noise,X[:,2])) >>> c2 = Contrast(new_term2, X) >>> print(c2.contrast_matrix) [ -1.26424750e-16 8.59467391e-17 1.56384718e-01 -2.60875560e-17 -7.77260726e-17 -8.41929574e-18 -7.36359622e-17 -1.39760860e-16 1.82976904e-16 -3.75277947e-18] Get another contrast >>> zero = np.zeros((40,)) >>> new_term3 = np.column_stack((zero,X[:,2])) >>> c3 = Contrast(new_term3, X) >>> test2 = [0]*2 + [1] + [0]*7 >>> np.allclose(c3.contrast_matrix, test2) True """ def _get_matrix(self): """ Gets the contrast_matrix property """ if not hasattr(self, "_contrast_matrix"): self.compute_matrix() return self._contrast_matrix contrast_matrix = property(_get_matrix) def __init__(self, term, design): self.term = np.asarray(term) self.design = np.asarray(design) def compute_matrix(self): """ Construct a contrast matrix C so that colspan(dot(D, C)) = colspan(dot(D, dot(pinv(D), T))) where pinv(D) is the generalized inverse of D=design. """ T = self.term if T.ndim == 1: T = T[:,None] self.T = clean0(T) self.D = self.design self._contrast_matrix = contrastfromcols(self.T, self.D) try: self.rank = self.matrix.shape[1] except: self.rank = 1 #TODO: fix docstring after usage is settled def contrastfromcols(L, D, pseudo=None): """ From an n x p design matrix D and a matrix L, tries to determine a p x q contrast matrix C which determines a contrast of full rank, i.e. the n x q matrix dot(transpose(C), pinv(D)) is full rank. L must satisfy either L.shape[0] == n or L.shape[1] == p. If L.shape[0] == n, then L is thought of as representing columns in the column space of D. If L.shape[1] == p, then L is thought of as what is known as a contrast matrix. In this case, this function returns an estimable contrast corresponding to the dot(D, L.T) Note that this always produces a meaningful contrast, not always with the intended properties because q is always non-zero unless L is identically 0. That is, it produces a contrast that spans the column space of L (after projection onto the column space of D). Parameters ---------- L : array_like D : array_like """ L = np.asarray(L) D = np.asarray(D) n, p = D.shape if L.shape[0] != n and L.shape[1] != p: raise ValueError("shape of L and D mismatched") if pseudo is None: pseudo = np.linalg.pinv(D) # D^+ \approx= ((dot(D.T,D))^(-1),D.T) if L.shape[0] == n: C = np.dot(pseudo, L).T else: C = L C = np.dot(pseudo, np.dot(D, C.T)).T Lp = np.dot(D, C.T) if len(Lp.shape) == 1: Lp.shape = (n, 1) if np.linalg.matrix_rank(Lp) != Lp.shape[1]: Lp = fullrank(Lp) C = np.dot(pseudo, Lp).T return np.squeeze(C) # TODO: this is currently a minimal version, stub class WaldTestResults(object): # for F and chi2 tests of joint hypothesis, mainly for vectorized def __init__(self, statistic, distribution, dist_args, table=None, pvalues=None): self.table = table self.distribution = distribution self.statistic = statistic #self.sd = sd self.dist_args = dist_args # The following is because I do not know which we want if table is not None: self.statistic = table['statistic'].values self.pvalues = table['pvalue'].values self.df_constraints = table['df_constraint'].values if self.distribution == 'F': self.df_denom = table['df_denom'].values else: if self.distribution == 'chi2': self.dist = stats.chi2 self.df_constraints = self.dist_args[0] # assumes tuple # using dist_args[0] is a bit dangerous, elif self.distribution == 'F': self.dist = stats.f self.df_constraints, self.df_denom = self.dist_args else: raise ValueError('only F and chi2 are possible distribution') if pvalues is None: self.pvalues = self.dist.sf(np.abs(statistic), *dist_args) else: self.pvalues = pvalues @property def col_names(self): """column names for summary table """ pr_test = "P>%s" % self.distribution col_names = [self.distribution, pr_test, 'df constraint'] if self.distribution == 'F': col_names.append('df denom') return col_names def summary_frame(self): # needs to be a method for consistency if hasattr(self, '_dframe'): return self._dframe # rename the column nambes, but do not copy data renaming = dict(zip(self.table.columns, self.col_names)) self.dframe = self.table.rename(columns=renaming) return self.dframe def __str__(self): return self.summary_frame().to_string() def __repr__(self): return str(self.__class__) + '\n' + self.__str__() # t_test for pairwise comparison and automatic contrast/restrictions def _get_pairs_labels(k_level, level_names): """helper function for labels for pairwise comparisons """ idx_pairs_all = np.triu_indices(k_level, 1) labels = ['%s-%s' % (level_names[name[1]], level_names[name[0]]) for name in zip(*idx_pairs_all)] return labels def _contrast_pairs(k_params, k_level, idx_start): """create pairwise contrast for reference coding currently not used, using encoding contrast matrix is more general, but requires requires factor information from patsy design_info. Parameters ---------- k_params : int number of parameters k_level : int number of levels or categories (including reference case) idx_start : int Index of the first parameter of this factor. The restrictions on the factor are inserted as a block in the full restriction matrix starting at column with index `idx_start`. Returns ------- contrasts : ndarray restriction matrix with k_params columns and number of rows equal to the number of restrictions. """ k_level_m1 = k_level - 1 idx_pairs = np.triu_indices(k_level_m1, 1) k = len(idx_pairs[0]) c_pairs = np.zeros((k, k_level_m1)) c_pairs[np.arange(k), idx_pairs[0]] = -1 c_pairs[np.arange(k), idx_pairs[1]] = 1 c_reference = np.eye(k_level_m1) c = np.concatenate((c_reference, c_pairs), axis=0) k_all = c.shape[0] contrasts = np.zeros((k_all, k_params)) contrasts[:, idx_start : idx_start + k_level_m1] = c return contrasts def t_test_multi(result, contrasts, method='hs', alpha=0.05, ci_method=None, contrast_names=None): """perform t_test and add multiplicity correction to results dataframe Parameters ---------- result results instance results of an estimated model contrasts : ndarray restriction matrix for t_test method : str or list of strings method for multiple testing p-value correction, default is'hs'. alpha : float significance level for multiple testing reject decision. ci_method : None not used yet, will be for multiplicity corrected confidence intervals contrast_names : {list[str], None} If contrast_names are provided, then they are used in the index of the returned dataframe, otherwise some generic default names are created. Returns ------- res_df : pandas DataFrame The dataframe contains the results of the t_test and additional columns for multiplicity corrected p-values and boolean indicator for whether the Null hypothesis is rejected. """ tt = result.t_test(contrasts) res_df = tt.summary_frame(xname=contrast_names) if type(method) is not list: method = [method] for meth in method: mt = multipletests(tt.pvalue, method=meth, alpha=alpha) res_df['pvalue-%s' % meth] = mt[1] res_df['reject-%s' % meth] = mt[0] return res_df class MultiCompResult(object): """class to hold return of t_test_pairwise currently just a minimal class to hold attributes. """ def __init__(self, **kwargs): self.__dict__.update(kwargs) def _embed_constraints(contrasts, k_params, idx_start, index=None): """helper function to expand constraints to a full restriction matrix Parameters ---------- contrasts : ndarray restriction matrix for t_test k_params : int number of parameters idx_start : int Index of the first parameter of this factor. The restrictions on the factor are inserted as a block in the full restriction matrix starting at column with index `idx_start`. index : slice or ndarray Column index if constraints do not form a block in the full restriction matrix, i.e. if parameters that are subject to restrictions are not consecutive in the list of parameters. If index is not None, then idx_start is ignored. Returns ------- contrasts : ndarray restriction matrix with k_params columns and number of rows equal to the number of restrictions. """ k_c, k_p = contrasts.shape c = np.zeros((k_c, k_params)) if index is None: c[:, idx_start : idx_start + k_p] = contrasts else: c[:, index] = contrasts return c def _constraints_factor(encoding_matrix, comparison='pairwise', k_params=None, idx_start=None): """helper function to create constraints based on encoding matrix Parameters ---------- encoding_matrix : ndarray contrast matrix for the encoding of a factor as defined by patsy. The number of rows should be equal to the number of levels or categories of the factor, the number of columns should be equal to the number of parameters for this factor. comparison : str Currently only 'pairwise' is implemented. The restriction matrix can be used for testing the hypothesis that all pairwise differences are zero. k_params : int number of parameters idx_start : int Index of the first parameter of this factor. The restrictions on the factor are inserted as a block in the full restriction matrix starting at column with index `idx_start`. Returns ------- contrast : ndarray Contrast or restriction matrix that can be used in hypothesis test of model results. The number of columns is k_params. """ cm = encoding_matrix k_level, k_p = cm.shape import statsmodels.sandbox.stats.multicomp as mc if comparison in ['pairwise', 'pw', 'pairs']: c_all = -mc.contrast_allpairs(k_level) else: raise NotImplementedError('currentlyonly pairwise comparison') contrasts = c_all.dot(cm) if k_params is not None: if idx_start is None: raise ValueError("if k_params is not None, then idx_start is " "required") contrasts = _embed_constraints(contrasts, k_params, idx_start) return contrasts def t_test_pairwise(result, term_name, method='hs', alpha=0.05, factor_labels=None, ignore=False): """ Perform pairwise t_test with multiple testing corrected p-values. This uses the formula design_info encoding contrast matrix and should work for all encodings of a main effect. Parameters ---------- result : result instance The results of an estimated model with a categorical main effect. term_name : str name of the term for which pairwise comparisons are computed. Term names for categorical effects are created by patsy and correspond to the main part of the exog names. method : {str, list[str]} multiple testing p-value correction, default is 'hs', see stats.multipletesting alpha : float significance level for multiple testing reject decision. factor_labels : {list[str], None} Labels for the factor levels used for pairwise labels. If not provided, then the labels from the formula design_info are used. ignore : bool Turn off some of the exceptions raised by input checks. Returns ------- MultiCompResult The results are stored as attributes, the main attributes are the following two. Other attributes are added for debugging purposes or as background information. - result_frame : pandas DataFrame with t_test results and multiple testing corrected p-values. - contrasts : matrix of constraints of the null hypothesis in the t_test. Notes ----- Status: experimental. Currently only checked for treatment coding with and without specified reference level. Currently there are no multiple testing corrected confidence intervals available. """ desinfo = result.model.data.design_info term_idx = desinfo.term_names.index(term_name) term = desinfo.terms[term_idx] idx_start = desinfo.term_slices[term].start if not ignore and len(term.factors) > 1: raise ValueError('interaction effects not yet supported') factor = term.factors[0] cat = desinfo.factor_infos[factor].categories if factor_labels is not None: if len(factor_labels) == len(cat): cat = factor_labels else: raise ValueError("factor_labels has the wrong length, should be %d" % len(cat)) k_level = len(cat) cm = desinfo.term_codings[term][0].contrast_matrices[factor].matrix k_params = len(result.params) labels = _get_pairs_labels(k_level, cat) import statsmodels.sandbox.stats.multicomp as mc c_all_pairs = -mc.contrast_allpairs(k_level) contrasts_sub = c_all_pairs.dot(cm) contrasts = _embed_constraints(contrasts_sub, k_params, idx_start) res_df = t_test_multi(result, contrasts, method=method, ci_method=None, alpha=alpha, contrast_names=labels) res = MultiCompResult(result_frame=res_df, contrasts=contrasts, term=term, contrast_labels=labels, term_encoding_matrix=cm) return res def _offset_constraint(r_matrix, params_est, params_alt): """offset to the value of a linear constraint for new params usage: (cm, v) is original constraint vo = offset_constraint(cm, res2.params, params_alt) fs = res2.wald_test((cm, v + vo)) nc = fs.statistic * fs.df_num """ diff_est = r_matrix @ params_est diff_alt = r_matrix @ params_alt return diff_est - diff_alt def wald_test_noncent(params, r_matrix, value, results, diff=None, joint=True): """Moncentrality parameter for a wald test in model results The null hypothesis is ``diff = r_matrix @ params - value = 0`` Parameters ---------- params : ndarray parameters of the model at which to evaluate noncentrality. This can be estimated parameters or parameters under an alternative. r_matrix : ndarray Restriction matrix or contrasts for the Null hypothesis value : None or ndarray Value of the linear combination of parameters under the null hypothesis. If value is None, then it will be replaced by zero. results : Results instance of a model The results instance is used to compute the covariance matrix of the linear constraints using `cov_params. diff : None or ndarray If diff is not None, then it will be used instead of ``diff = r_matrix @ params - value`` joint : bool If joint is True, then the noncentrality parameter for the joint hypothesis will be returned. If joint is True, then an array of noncentrality parameters will be returned, where elements correspond to rows of the restriction matrix. This correspond to the `t_test` in models and is not a quadratic form. Returns ------- nc : float or ndarray Noncentrality parameter for Wald tests, correspondig to `wald_test` or `t_test` depending on whether `joint` is true or not. It needs to be divided by nobs to obtain effect size. Notes ----- Status : experimental, API will likely change """ if diff is None: diff = r_matrix @ params - value # at parameter under alternative cov_c = results.cov_params(r_matrix=r_matrix) if joint: nc = diff @ np.linalg.solve(cov_c, diff) else: nc = diff / np.sqrt(np.diag(cov_c)) return nc def wald_test_noncent_generic(params, r_matrix, value, cov_params, diff=None, joint=True): """noncentrality parameter for a wald test The null hypothesis is ``diff = r_matrix @ params - value = 0`` Parameters ---------- params : ndarray parameters of the model at which to evaluate noncentrality. This can be estimated parameters or parameters under an alternative. r_matrix : ndarray Restriction matrix or contrasts for the Null hypothesis value : None or ndarray Value of the linear combination of parameters under the null hypothesis. If value is None, then it will be replace by zero. cov_params : ndarray covariance matrix of the parameter estimates diff : None or ndarray If diff is not None, then it will be used instead of ``diff = r_matrix @ params - value`` joint : bool If joint is True, then the noncentrality parameter for the joint hypothesis will be returned. If joint is True, then an array of noncentrality parameters will be returned, where elements correspond to rows of the restriction matrix. This correspond to the `t_test` in models and is not a quadratic form. Returns ------- nc : float or ndarray Noncentrality parameter for Wald tests, correspondig to `wald_test` or `t_test` depending on whether `joint` is true or not. It needs to be divided by nobs to obtain effect size. Notes ----- Status : experimental, API will likely change """ if value is None: value = 0 if diff is None: # at parameter under alternative diff = r_matrix @ params - value c = r_matrix cov_c = c.dot(cov_params).dot(c.T) if joint: nc = diff @ np.linalg.solve(cov_c, diff) else: nc = diff / np.sqrt(np.diag(cov_c)) return nc statsmodels-0.12.2/statsmodels/stats/correlation_tools.py000066400000000000000000000770471400612667500237770ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Aug 17 13:10:52 2012 Author: Josef Perktold License: BSD-3 """ import numpy as np import scipy.sparse as sparse from scipy.sparse.linalg import svds from scipy.optimize import fminbound import warnings from statsmodels.tools.tools import Bunch from statsmodels.tools.sm_exceptions import ( IterationLimitWarning, iteration_limit_doc) def clip_evals(x, value=0): # threshold=0, value=0): evals, evecs = np.linalg.eigh(x) clipped = np.any(evals < value) x_new = np.dot(evecs * np.maximum(evals, value), evecs.T) return x_new, clipped def corr_nearest(corr, threshold=1e-15, n_fact=100): ''' Find the nearest correlation matrix that is positive semi-definite. The function iteratively adjust the correlation matrix by clipping the eigenvalues of a difference matrix. The diagonal elements are set to one. Parameters ---------- corr : ndarray, (k, k) initial correlation matrix threshold : float clipping threshold for smallest eigenvalue, see Notes n_fact : int or float factor to determine the maximum number of iterations. The maximum number of iterations is the integer part of the number of columns in the correlation matrix times n_fact. Returns ------- corr_new : ndarray, (optional) corrected correlation matrix Notes ----- The smallest eigenvalue of the corrected correlation matrix is approximately equal to the ``threshold``. If the threshold=0, then the smallest eigenvalue of the correlation matrix might be negative, but zero within a numerical error, for example in the range of -1e-16. Assumes input correlation matrix is symmetric. Stops after the first step if correlation matrix is already positive semi-definite or positive definite, so that smallest eigenvalue is above threshold. In this case, the returned array is not the original, but is equal to it within numerical precision. See Also -------- corr_clipped cov_nearest ''' k_vars = corr.shape[0] if k_vars != corr.shape[1]: raise ValueError("matrix is not square") diff = np.zeros(corr.shape) x_new = corr.copy() diag_idx = np.arange(k_vars) for ii in range(int(len(corr) * n_fact)): x_adj = x_new - diff x_psd, clipped = clip_evals(x_adj, value=threshold) if not clipped: x_new = x_psd break diff = x_psd - x_adj x_new = x_psd.copy() x_new[diag_idx, diag_idx] = 1 else: warnings.warn(iteration_limit_doc, IterationLimitWarning) return x_new def corr_clipped(corr, threshold=1e-15): ''' Find a near correlation matrix that is positive semi-definite This function clips the eigenvalues, replacing eigenvalues smaller than the threshold by the threshold. The new matrix is normalized, so that the diagonal elements are one. Compared to corr_nearest, the distance between the original correlation matrix and the positive definite correlation matrix is larger, however, it is much faster since it only computes eigenvalues once. Parameters ---------- corr : ndarray, (k, k) initial correlation matrix threshold : float clipping threshold for smallest eigenvalue, see Notes Returns ------- corr_new : ndarray, (optional) corrected correlation matrix Notes ----- The smallest eigenvalue of the corrected correlation matrix is approximately equal to the ``threshold``. In examples, the smallest eigenvalue can be by a factor of 10 smaller than the threshold, e.g. threshold 1e-8 can result in smallest eigenvalue in the range between 1e-9 and 1e-8. If the threshold=0, then the smallest eigenvalue of the correlation matrix might be negative, but zero within a numerical error, for example in the range of -1e-16. Assumes input correlation matrix is symmetric. The diagonal elements of returned correlation matrix is set to ones. If the correlation matrix is already positive semi-definite given the threshold, then the original correlation matrix is returned. ``cov_clipped`` is 40 or more times faster than ``cov_nearest`` in simple example, but has a slightly larger approximation error. See Also -------- corr_nearest cov_nearest ''' x_new, clipped = clip_evals(corr, value=threshold) if not clipped: return corr # cov2corr x_std = np.sqrt(np.diag(x_new)) x_new = x_new / x_std / x_std[:, None] return x_new def cov_nearest(cov, method='clipped', threshold=1e-15, n_fact=100, return_all=False): """ Find the nearest covariance matrix that is positive (semi-) definite This leaves the diagonal, i.e. the variance, unchanged Parameters ---------- cov : ndarray, (k,k) initial covariance matrix method : str if "clipped", then the faster but less accurate ``corr_clipped`` is used.if "nearest", then ``corr_nearest`` is used threshold : float clipping threshold for smallest eigen value, see Notes n_fact : int or float factor to determine the maximum number of iterations in ``corr_nearest``. See its doc string return_all : bool if False (default), then only the covariance matrix is returned. If True, then correlation matrix and standard deviation are additionally returned. Returns ------- cov_ : ndarray corrected covariance matrix corr_ : ndarray, (optional) corrected correlation matrix std_ : ndarray, (optional) standard deviation Notes ----- This converts the covariance matrix to a correlation matrix. Then, finds the nearest correlation matrix that is positive semidefinite and converts it back to a covariance matrix using the initial standard deviation. The smallest eigenvalue of the intermediate correlation matrix is approximately equal to the ``threshold``. If the threshold=0, then the smallest eigenvalue of the correlation matrix might be negative, but zero within a numerical error, for example in the range of -1e-16. Assumes input covariance matrix is symmetric. See Also -------- corr_nearest corr_clipped """ from statsmodels.stats.moment_helpers import cov2corr, corr2cov cov_, std_ = cov2corr(cov, return_std=True) if method == 'clipped': corr_ = corr_clipped(cov_, threshold=threshold) else: # method == 'nearest' corr_ = corr_nearest(cov_, threshold=threshold, n_fact=n_fact) cov_ = corr2cov(corr_, std_) if return_all: return cov_, corr_, std_ else: return cov_ def _nmono_linesearch(obj, grad, x, d, obj_hist, M=10, sig1=0.1, sig2=0.9, gam=1e-4, maxiter=100): """ Implements the non-monotone line search of Grippo et al. (1986), as described in Birgin, Martinez and Raydan (2013). Parameters ---------- obj : real-valued function The objective function, to be minimized grad : vector-valued function The gradient of the objective function x : array_like The starting point for the line search d : array_like The search direction obj_hist : array_like Objective function history (must contain at least one value) M : positive int Number of previous function points to consider (see references for details). sig1 : real Tuning parameter, see references for details. sig2 : real Tuning parameter, see references for details. gam : real Tuning parameter, see references for details. maxiter : int The maximum number of iterations; returns Nones if convergence does not occur by this point Returns ------- alpha : real The step value x : Array_like The function argument at the final step obval : Real The function value at the final step g : Array_like The gradient at the final step Notes ----- The basic idea is to take a big step in the direction of the gradient, even if the function value is not decreased (but there is a maximum allowed increase in terms of the recent history of the iterates). References ---------- Grippo L, Lampariello F, Lucidi S (1986). A Nonmonotone Line Search Technique for Newton's Method. SIAM Journal on Numerical Analysis, 23, 707-716. E. Birgin, J.M. Martinez, and M. Raydan. Spectral projected gradient methods: Review and perspectives. Journal of Statistical Software (preprint). """ alpha = 1. last_obval = obj(x) obj_max = max(obj_hist[-M:]) for iter in range(maxiter): obval = obj(x + alpha*d) g = grad(x) gtd = (g * d).sum() if obval <= obj_max + gam*alpha*gtd: return alpha, x + alpha*d, obval, g a1 = -0.5*alpha**2*gtd / (obval - last_obval - alpha*gtd) if (sig1 <= a1) and (a1 <= sig2*alpha): alpha = a1 else: alpha /= 2. last_obval = obval return None, None, None, None def _spg_optim(func, grad, start, project, maxiter=1e4, M=10, ctol=1e-3, maxiter_nmls=200, lam_min=1e-30, lam_max=1e30, sig1=0.1, sig2=0.9, gam=1e-4): """ Implements the spectral projected gradient method for minimizing a differentiable function on a convex domain. Parameters ---------- func : real valued function The objective function to be minimized. grad : real array-valued function The gradient of the objective function start : array_like The starting point project : function In-place projection of the argument to the domain of func. ... See notes regarding additional arguments Returns ------- rslt : Bunch rslt.params is the final iterate, other fields describe convergence status. Notes ----- This can be an effective heuristic algorithm for problems where no guaranteed algorithm for computing a global minimizer is known. There are a number of tuning parameters, but these generally should not be changed except for `maxiter` (positive integer) and `ctol` (small positive real). See the Birgin et al reference for more information about the tuning parameters. Reference --------- E. Birgin, J.M. Martinez, and M. Raydan. Spectral projected gradient methods: Review and perspectives. Journal of Statistical Software (preprint). Available at: http://www.ime.usp.br/~egbirgin/publications/bmr5.pdf """ lam = min(10*lam_min, lam_max) params = start.copy() gval = grad(params) obj_hist = [func(params), ] for itr in range(int(maxiter)): # Check convergence df = params - gval project(df) df -= params if np.max(np.abs(df)) < ctol: return Bunch(**{"Converged": True, "params": params, "objective_values": obj_hist, "Message": "Converged successfully"}) # The line search direction d = params - lam*gval project(d) d -= params # Carry out the nonmonotone line search alpha, params1, fval, gval1 = _nmono_linesearch( func, grad, params, d, obj_hist, M=M, sig1=sig1, sig2=sig2, gam=gam, maxiter=maxiter_nmls) if alpha is None: return Bunch(**{"Converged": False, "params": params, "objective_values": obj_hist, "Message": "Failed in nmono_linesearch"}) obj_hist.append(fval) s = params1 - params y = gval1 - gval sy = (s*y).sum() if sy <= 0: lam = lam_max else: ss = (s*s).sum() lam = max(lam_min, min(ss/sy, lam_max)) params = params1 gval = gval1 return Bunch(**{"Converged": False, "params": params, "objective_values": obj_hist, "Message": "spg_optim did not converge"}) def _project_correlation_factors(X): """ Project a matrix into the domain of matrices whose row-wise sums of squares are less than or equal to 1. The input matrix is modified in-place. """ nm = np.sqrt((X*X).sum(1)) ii = np.flatnonzero(nm > 1) if len(ii) > 0: X[ii, :] /= nm[ii][:, None] class FactoredPSDMatrix: """ Representation of a positive semidefinite matrix in factored form. The representation is constructed based on a vector `diag` and rectangular matrix `root`, such that the PSD matrix represented by the class instance is Diag + root * root', where Diag is the square diagonal matrix with `diag` on its main diagonal. Parameters ---------- diag : 1d array_like See above root : 2d array_like See above Notes ----- The matrix is represented internally in the form Diag^{1/2}(I + factor * scales * factor')Diag^{1/2}, where `Diag` and `scales` are diagonal matrices, and `factor` is an orthogonal matrix. """ def __init__(self, diag, root): self.diag = diag self.root = root root = root / np.sqrt(diag)[:, None] u, s, vt = np.linalg.svd(root, 0) self.factor = u self.scales = s**2 def to_matrix(self): """ Returns the PSD matrix represented by this instance as a full (square) matrix. """ return np.diag(self.diag) + np.dot(self.root, self.root.T) def decorrelate(self, rhs): """ Decorrelate the columns of `rhs`. Parameters ---------- rhs : array_like A 2 dimensional array with the same number of rows as the PSD matrix represented by the class instance. Returns ------- C^{-1/2} * rhs, where C is the covariance matrix represented by this class instance. Notes ----- The returned matrix has the identity matrix as its row-wise population covariance matrix. This function exploits the factor structure for efficiency. """ # I + factor * qval * factor' is the inverse square root of # the covariance matrix in the homogeneous case where diag = # 1. qval = -1 + 1 / np.sqrt(1 + self.scales) # Decorrelate in the general case. rhs = rhs / np.sqrt(self.diag)[:, None] rhs1 = np.dot(self.factor.T, rhs) rhs1 *= qval[:, None] rhs1 = np.dot(self.factor, rhs1) rhs += rhs1 return rhs def solve(self, rhs): """ Solve a linear system of equations with factor-structured coefficients. Parameters ---------- rhs : array_like A 2 dimensional array with the same number of rows as the PSD matrix represented by the class instance. Returns ------- C^{-1} * rhs, where C is the covariance matrix represented by this class instance. Notes ----- This function exploits the factor structure for efficiency. """ qval = -self.scales / (1 + self.scales) dr = np.sqrt(self.diag) rhs = rhs / dr[:, None] mat = qval[:, None] * np.dot(self.factor.T, rhs) rhs = rhs + np.dot(self.factor, mat) return rhs / dr[:, None] def logdet(self): """ Returns the logarithm of the determinant of a factor-structured matrix. """ logdet = np.sum(np.log(self.diag)) logdet += np.sum(np.log(self.scales)) logdet += np.sum(np.log(1 + 1 / self.scales)) return logdet def corr_nearest_factor(corr, rank, ctol=1e-6, lam_min=1e-30, lam_max=1e30, maxiter=1000): """ Find the nearest correlation matrix with factor structure to a given square matrix. Parameters ---------- corr : square array The target matrix (to which the nearest correlation matrix is sought). Must be square, but need not be positive semidefinite. rank : int The rank of the factor structure of the solution, i.e., the number of linearly independent columns of X. ctol : positive real Convergence criterion. lam_min : float Tuning parameter for spectral projected gradient optimization (smallest allowed step in the search direction). lam_max : float Tuning parameter for spectral projected gradient optimization (largest allowed step in the search direction). maxiter : int Maximum number of iterations in spectral projected gradient optimization. Returns ------- rslt : Bunch rslt.corr is a FactoredPSDMatrix defining the estimated correlation structure. Other fields of `rslt` contain returned values from spg_optim. Notes ----- A correlation matrix has factor structure if it can be written in the form I + XX' - diag(XX'), where X is n x k with linearly independent columns, and with each row having sum of squares at most equal to 1. The approximation is made in terms of the Frobenius norm. This routine is useful when one has an approximate correlation matrix that is not positive semidefinite, and there is need to estimate the inverse, square root, or inverse square root of the population correlation matrix. The factor structure allows these tasks to be done without constructing any n x n matrices. This is a non-convex problem with no known guaranteed globally convergent algorithm for computing the solution. Borsdof, Higham and Raydan (2010) compared several methods for this problem and found the spectral projected gradient (SPG) method (used here) to perform best. The input matrix `corr` can be a dense numpy array or any scipy sparse matrix. The latter is useful if the input matrix is obtained by thresholding a very large sample correlation matrix. If `corr` is sparse, the calculations are optimized to save memory, so no working matrix with more than 10^6 elements is constructed. References ---------- .. [*] R Borsdof, N Higham, M Raydan (2010). Computing a nearest correlation matrix with factor structure. SIAM J Matrix Anal Appl, 31:5, 2603-2622. http://eprints.ma.man.ac.uk/1523/01/covered/MIMS_ep2009_87.pdf Examples -------- Hard thresholding a correlation matrix may result in a matrix that is not positive semidefinite. We can approximate a hard thresholded correlation matrix with a PSD matrix as follows, where `corr` is the input correlation matrix. >>> import numpy as np >>> from statsmodels.stats.correlation_tools import corr_nearest_factor >>> np.random.seed(1234) >>> b = 1.5 - np.random.rand(10, 1) >>> x = np.random.randn(100,1).dot(b.T) + np.random.randn(100,10) >>> corr = np.corrcoef(x.T) >>> corr = corr * (np.abs(corr) >= 0.3) >>> rslt = corr_nearest_factor(corr, 3) """ p, _ = corr.shape # Starting values (following the PCA method in BHR). u, s, vt = svds(corr, rank) X = u * np.sqrt(s) nm = np.sqrt((X**2).sum(1)) ii = np.flatnonzero(nm > 1e-5) X[ii, :] /= nm[ii][:, None] # Zero the diagonal corr1 = corr.copy() if type(corr1) == np.ndarray: np.fill_diagonal(corr1, 0) elif sparse.issparse(corr1): corr1.setdiag(np.zeros(corr1.shape[0])) corr1.eliminate_zeros() corr1.sort_indices() else: raise ValueError("Matrix type not supported") # The gradient, from lemma 4.1 of BHR. def grad(X): gr = np.dot(X, np.dot(X.T, X)) if type(corr1) == np.ndarray: gr -= np.dot(corr1, X) else: gr -= corr1.dot(X) gr -= (X*X).sum(1)[:, None] * X return 4*gr # The objective function (sum of squared deviations between fitted # and observed arrays). def func(X): if type(corr1) == np.ndarray: M = np.dot(X, X.T) np.fill_diagonal(M, 0) M -= corr1 fval = (M*M).sum() return fval else: fval = 0. # Control the size of intermediates max_ws = 1e6 bs = int(max_ws / X.shape[0]) ir = 0 while ir < X.shape[0]: ir2 = min(ir+bs, X.shape[0]) u = np.dot(X[ir:ir2, :], X.T) ii = np.arange(u.shape[0]) u[ii, ir+ii] = 0 u -= np.asarray(corr1[ir:ir2, :].todense()) fval += (u*u).sum() ir += bs return fval rslt = _spg_optim(func, grad, X, _project_correlation_factors, ctol=ctol, lam_min=lam_min, lam_max=lam_max, maxiter=maxiter) root = rslt.params diag = 1 - (root**2).sum(1) soln = FactoredPSDMatrix(diag, root) rslt.corr = soln del rslt.params return rslt def cov_nearest_factor_homog(cov, rank): """ Approximate an arbitrary square matrix with a factor-structured matrix of the form k*I + XX'. Parameters ---------- cov : array_like The input array, must be square but need not be positive semidefinite rank : int The rank of the fitted factor structure Returns ------- A FactoredPSDMatrix instance containing the fitted matrix Notes ----- This routine is useful if one has an estimated covariance matrix that is not SPD, and the ultimate goal is to estimate the inverse, square root, or inverse square root of the true covariance matrix. The factor structure allows these tasks to be performed without constructing any n x n matrices. The calculations use the fact that if k is known, then X can be determined from the eigen-decomposition of cov - k*I, which can in turn be easily obtained form the eigen-decomposition of `cov`. Thus the problem can be reduced to a 1-dimensional search for k that does not require repeated eigen-decompositions. If the input matrix is sparse, then cov - k*I is also sparse, so the eigen-decomposition can be done efficiently using sparse routines. The one-dimensional search for the optimal value of k is not convex, so a local minimum could be obtained. Examples -------- Hard thresholding a covariance matrix may result in a matrix that is not positive semidefinite. We can approximate a hard thresholded covariance matrix with a PSD matrix as follows: >>> import numpy as np >>> np.random.seed(1234) >>> b = 1.5 - np.random.rand(10, 1) >>> x = np.random.randn(100,1).dot(b.T) + np.random.randn(100,10) >>> cov = np.cov(x) >>> cov = cov * (np.abs(cov) >= 0.3) >>> rslt = cov_nearest_factor_homog(cov, 3) """ m, n = cov.shape Q, Lambda, _ = svds(cov, rank) if sparse.issparse(cov): QSQ = np.dot(Q.T, cov.dot(Q)) ts = cov.diagonal().sum() tss = cov.dot(cov).diagonal().sum() else: QSQ = np.dot(Q.T, np.dot(cov, Q)) ts = np.trace(cov) tss = np.trace(np.dot(cov, cov)) def fun(k): Lambda_t = Lambda - k v = tss + m*(k**2) + np.sum(Lambda_t**2) - 2*k*ts v += 2*k*np.sum(Lambda_t) - 2*np.sum(np.diag(QSQ) * Lambda_t) return v # Get the optimal decomposition k_opt = fminbound(fun, 0, 1e5) Lambda_opt = Lambda - k_opt fac_opt = Q * np.sqrt(Lambda_opt) diag = k_opt * np.ones(m, dtype=np.float64) # - (fac_opt**2).sum(1) return FactoredPSDMatrix(diag, fac_opt) def corr_thresholded(data, minabs=None, max_elt=1e7): r""" Construct a sparse matrix containing the thresholded row-wise correlation matrix from a data array. Parameters ---------- data : array_like The data from which the row-wise thresholded correlation matrix is to be computed. minabs : non-negative real The threshold value; correlation coefficients smaller in magnitude than minabs are set to zero. If None, defaults to 1 / sqrt(n), see Notes for more information. Returns ------- cormat : sparse.coo_matrix The thresholded correlation matrix, in COO format. Notes ----- This is an alternative to C = np.corrcoef(data); C \*= (np.abs(C) >= absmin), suitable for very tall data matrices. If the data are jointly Gaussian, the marginal sampling distributions of the elements of the sample correlation matrix are approximately Gaussian with standard deviation 1 / sqrt(n). The default value of ``minabs`` is thus equal to 1 standard error, which will set to zero approximately 68% of the estimated correlation coefficients for which the population value is zero. No intermediate matrix with more than ``max_elt`` values will be constructed. However memory use could still be high if a large number of correlation values exceed `minabs` in magnitude. The thresholded matrix is returned in COO format, which can easily be converted to other sparse formats. Examples -------- Here X is a tall data matrix (e.g. with 100,000 rows and 50 columns). The row-wise correlation matrix of X is calculated and stored in sparse form, with all entries smaller than 0.3 treated as 0. >>> import numpy as np >>> np.random.seed(1234) >>> b = 1.5 - np.random.rand(10, 1) >>> x = np.random.randn(100,1).dot(b.T) + np.random.randn(100,10) >>> cmat = corr_thresholded(x, 0.3) """ nrow, ncol = data.shape if minabs is None: minabs = 1. / float(ncol) # Row-standardize the data data = data.copy() data -= data.mean(1)[:, None] sd = data.std(1, ddof=1) ii = np.flatnonzero(sd > 1e-5) data[ii, :] /= sd[ii][:, None] ii = np.flatnonzero(sd <= 1e-5) data[ii, :] = 0 # Number of rows to process in one pass bs = int(np.floor(max_elt / nrow)) ipos_all, jpos_all, cor_values = [], [], [] ir = 0 while ir < nrow: ir2 = min(data.shape[0], ir + bs) cm = np.dot(data[ir:ir2, :], data.T) / (ncol - 1) cma = np.abs(cm) ipos, jpos = np.nonzero(cma >= minabs) ipos_all.append(ipos + ir) jpos_all.append(jpos) cor_values.append(cm[ipos, jpos]) ir += bs ipos = np.concatenate(ipos_all) jpos = np.concatenate(jpos_all) cor_values = np.concatenate(cor_values) cmat = sparse.coo_matrix((cor_values, (ipos, jpos)), (nrow, nrow)) return cmat class MultivariateKernel(object): """ Base class for multivariate kernels. An instance of MultivariateKernel implements a `call` method having signature `call(x, loc)`, returning the kernel weights comparing `x` (a 1d ndarray) to each row of `loc` (a 2d ndarray). """ def call(self, x, loc): raise NotImplementedError def set_bandwidth(self, bw): """ Set the bandwidth to the given vector. Parameters ---------- bw : array_like A vector of non-negative bandwidth values. """ self.bw = bw self._setup() def _setup(self): # Precompute the squared bandwidth values. self.bwk = np.prod(self.bw) self.bw2 = self.bw * self.bw def set_default_bw(self, loc, bwm=None): """ Set default bandwiths based on domain values. Parameters ---------- loc : array_like Values from the domain to which the kernel will be applied. bwm : scalar, optional A non-negative scalar that is used to multiply the default bandwidth. """ sd = loc.std(0) q25, q75 = np.percentile(loc, [25, 75], axis=0) iqr = (q75 - q25) / 1.349 bw = np.where(iqr < sd, iqr, sd) bw *= 0.9 / loc.shape[0] ** 0.2 if bwm is not None: bw *= bwm # The final bandwidths self.bw = np.asarray(bw, dtype=np.float64) self._setup() class GaussianMultivariateKernel(MultivariateKernel): """ The Gaussian (squared exponential) multivariate kernel. """ def call(self, x, loc): return np.exp(-(x - loc)**2 / (2 * self.bw2)).sum(1) / self.bwk def kernel_covariance(exog, loc, groups, kernel=None, bw=None): """ Use kernel averaging to estimate a multivariate covariance function. The goal is to estimate a covariance function C(x, y) = cov(Z(x), Z(y)) where x, y are vectors in R^p (e.g. representing locations in time or space), and Z(.) represents a multivariate process on R^p. The data used for estimation can be observed at arbitrary values of the position vector, and there can be multiple independent observations from the process. Parameters ---------- exog : array_like The rows of exog are realizations of the process obtained at specified points. loc : array_like The rows of loc are the locations (e.g. in space or time) at which the rows of exog are observed. groups : array_like The values of groups are labels for distinct independent copies of the process. kernel : MultivariateKernel instance, optional An instance of MultivariateKernel, defaults to GaussianMultivariateKernel. bw : array_like or scalar A bandwidth vector, or bandwidth multiplier. If a 1d array, it contains kernel bandwidths for each component of the process, and must have length equal to the number of columns of exog. If a scalar, bw is a bandwidth multiplier used to adjust the default bandwidth; if None, a default bandwidth is used. Returns ------- A real-valued function C(x, y) that returns an estimate of the covariance between values of the process located at x and y. References ---------- .. [1] Genton M, W Kleiber (2015). Cross covariance functions for multivariate geostatics. Statistical Science 30(2). https://arxiv.org/pdf/1507.08017.pdf """ exog = np.asarray(exog) loc = np.asarray(loc) groups = np.asarray(groups) if loc.ndim == 1: loc = loc[:, None] v = [exog.shape[0], loc.shape[0], len(groups)] if min(v) != max(v): msg = "exog, loc, and groups must have the same number of rows" raise ValueError(msg) # Map from group labels to the row indices in each group. ix = {} for i, g in enumerate(groups): if g not in ix: ix[g] = [] ix[g].append(i) for g in ix.keys(): ix[g] = np.sort(ix[g]) if kernel is None: kernel = GaussianMultivariateKernel() if bw is None: kernel.set_default_bw(loc) elif np.isscalar(bw): kernel.set_default_bw(loc, bwm=bw) else: kernel.set_bandwidth(bw) def cov(x, y): kx = kernel.call(x, loc) ky = kernel.call(y, loc) cm, cw = 0., 0. for g, ii in ix.items(): m = len(ii) j1, j2 = np.indices((m, m)) j1 = ii[j1.flat] j2 = ii[j2.flat] w = kx[j1] * ky[j2] # TODO: some other form of broadcasting may be faster than # einsum here cm += np.einsum("ij,ik,i->jk", exog[j1, :], exog[j2, :], w) cw += w.sum() if cw < 1e-10: msg = ("Effective sample size is 0. The bandwidth may be too " + "small, or you are outside the range of your data.") warnings.warn(msg) return np.nan * np.ones_like(cm) return cm / cw return cov statsmodels-0.12.2/statsmodels/stats/descriptivestats.py000066400000000000000000000731621400612667500236300ustar00rootroot00000000000000from statsmodels.compat.pandas import Appender, is_numeric_dtype from statsmodels.compat.python import lmap, lrange from typing import Sequence, Union import warnings import numpy as np import pandas as pd from pandas.core.dtypes.common import is_categorical_dtype from scipy import stats from statsmodels.iolib.table import SimpleTable from statsmodels.stats.stattools import jarque_bera from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.docstring import Docstring, Parameter from statsmodels.tools.validation import ( array_like, bool_like, float_like, int_like, ) DEPRECATION_MSG = """/ ``Describe`` has been deprecated in favor of ``Description`` and it's simplified functional version, ``describe``. ``Describe`` will be removed after 0.13. """ PERCENTILES = (1, 5, 10, 25, 50, 75, 90, 95, 99) QUANTILES = np.array(PERCENTILES) / 100.0 def pd_ptp(df): return df.max() - df.min() def pd_percentiles(df): return df.quantiles(QUANTILES) PANDAS = { "obs": lambda df: df.count(), "mean": lambda df: df.mean(), "std": lambda df: df.std(), "max": lambda df: df.max(), "min": lambda df: df.min(), "mode": lambda df: df.mode(), "ptp": pd_ptp, "var": lambda df: df.var(), "skew": lambda df: df.skewness(), "uss": lambda df: (df ** 2).sum(), "kurtosis": lambda df: df.kurtosis(), "percentiles": pd_percentiles, } def nancount(x, axis=0): return (1 - np.isnan(x)).sum(axis=axis) def nanptp(arr, axis=0): return np.nanmax(arr, axis=axis) - np.nanmin(arr, axis=axis) def nanuss(arr, axis=0): return np.nansum(arr ** 2, axis=axis) def nanpercentile(arr, axis=0): return np.nanpercentile(arr, PERCENTILES, axis=axis) def nankurtosis(arr, axis=0): return stats.kurtosis(arr, axis=axis, nan_policy="omit") def nanskewness(arr, axis=0): return stats.skew(arr, axis=axis, nan_policy="omit") MISSING = { "obs": nancount, "mean": np.nanmean, "std": np.nanstd, "max": np.nanmax, "min": np.nanmin, "ptp": nanptp, "var": np.nanvar, "skew": nanskewness, "uss": nanuss, "kurtosis": nankurtosis, "percentiles": nanpercentile, } def _kurtosis(a): """ wrapper for scipy.stats.kurtosis that returns nan instead of raising Error missing options """ try: res = stats.kurtosis(a) except ValueError: res = np.nan return res def _skew(a): """ wrapper for scipy.stats.skew that returns nan instead of raising Error missing options """ try: res = stats.skew(a) except ValueError: res = np.nan return res def sign_test(samp, mu0=0): """ Signs test Parameters ---------- samp : array_like 1d array. The sample for which you want to perform the sign test. mu0 : float See Notes for the definition of the sign test. mu0 is 0 by default, but it is common to set it to the median. Returns ------- M p-value Notes ----- The signs test returns M = (N(+) - N(-))/2 where N(+) is the number of values above `mu0`, N(-) is the number of values below. Values equal to `mu0` are discarded. The p-value for M is calculated using the binomial distribution and can be interpreted the same as for a t-test. The test-statistic is distributed Binom(min(N(+), N(-)), n_trials, .5) where n_trials equals N(+) + N(-). See Also -------- scipy.stats.wilcoxon """ samp = np.asarray(samp) pos = np.sum(samp > mu0) neg = np.sum(samp < mu0) M = (pos - neg) / 2.0 p = stats.binom_test(min(pos, neg), pos + neg, 0.5) return M, p NUMERIC_STATISTICS = ( "nobs", "missing", "mean", "std_err", "ci", "std", "iqr", "iqr_normal", "mad", "mad_normal", "coef_var", "range", "max", "min", "skew", "kurtosis", "jarque_bera", "mode", "median", "percentiles", ) CATEGORICAL_STATISTICS = ("nobs", "missing", "distinct", "top", "freq") _additional = [ stat for stat in CATEGORICAL_STATISTICS if stat not in NUMERIC_STATISTICS ] DEFAULT_STATISTICS = NUMERIC_STATISTICS + tuple(_additional) class Description: """ Extended descriptive statistics for data Parameters ---------- data : array_like Data to describe. Must be convertible to a pandas DataFrame. stats : Sequence[str], optional Statistics to include. If not provided the full set of statistics is computed. This list may evolve across versions to reflect best practices. Supported options are: "nobs", "missing", "mean", "std_err", "ci", "ci", "std", "iqr", "iqr_normal", "mad", "mad_normal", "coef_var", "range", "max", "min", "skew", "kurtosis", "jarque_bera", "mode", "freq", "median", "percentiles", "distinct", "top", and "freq". See Notes for details. numeric : bool, default True Whether to include numeric columns in the descriptive statistics. categorical : bool, default True Whether to include categorical columns in the descriptive statistics. alpha : float, default 0.05 A number between 0 and 1 representing the size used to compute the confidence interval, which has coverage 1 - alpha. use_t : bool, default False Use the Student's t distribution to construct confidence intervals. percentiles : sequence[float] A distinct sequence of floating point values all between 0 and 100. The default percentiles are 1, 5, 10, 25, 50, 75, 90, 95, 99. ntop : int, default 5 The number of top categorical labels to report. Default is Attributes ---------- numeric_statistics The list of supported statistics for numeric data categorical_statistics The list of supported statistics for categorical data default_statistics The default list of statistics See Also -------- pandas.DataFrame.describe Basic descriptive statistics describe A simplified version that returns a DataFrame Notes ----- The selectable statistics include: * "nobs" - Number of observations * "missing" - Number of missing observations * "mean" - Mean * "std_err" - Standard Error of the mean assuming no correlation * "ci" - Confidence interval with coverage (1 - alpha) using the normal or t. This option creates two entries in any tables: lower_ci and upper_ci. * "std" - Standard Deviation * "iqr" - Interquartile range * "iqr_normal" - Interquartile range relative to a Normal * "mad" - Mean absolute deviation * "mad_normal" - Mean absolute deviation relative to a Normal * "coef_var" - Coefficient of variation * "range" - Range between the maximum and the minimum * "max" - The maximum * "min" - The minimum * "skew" - The skewness defined as the standardized 3rd central moment * "kurtosis" - The kurtosis defined as the standardized 4th central moment * "jarque_bera" - The Jarque-Bera test statistic for normality based on the skewness and kurtosis. This option creates two entries, jarque_bera and jarque_beta_pval. * "mode" - The mode of the data. This option creates two entries in all tables, mode and mode_freq which is the empirical frequency of the modal value. * "median" - The median of the data. * "percentiles" - The percentiles. Values included depend on the input value of ``percentiles``. * "distinct" - The number of distinct categories in a categorical. * "top" - The mode common categories. Labeled top_n for n in 1, 2, ..., ``ntop``. * "freq" - The frequency of the common categories. Labeled freq_n for n in 1, 2, ..., ``ntop``. """ _int_fmt = ["nobs", "missing", "distinct"] numeric_statistics = NUMERIC_STATISTICS categorical_statistics = CATEGORICAL_STATISTICS default_statistics = DEFAULT_STATISTICS def __init__( self, data: Union[np.ndarray, pd.Series, pd.DataFrame], stats: Sequence[str] = None, *, numeric: bool = True, categorical: bool = True, alpha: float = 0.05, use_t: bool = False, percentiles: Sequence[Union[int, float]] = PERCENTILES, ntop: bool = 5, ): data_arr = data if not isinstance(data, (pd.Series, pd.DataFrame)): data_arr = array_like(data, "data", maxdim=2) if data_arr.ndim == 1: data = pd.Series(data) numeric = bool_like(numeric, "numeric") categorical = bool_like(categorical, "categorical") include = [] col_types = "" if numeric: include.append(np.number) col_types = "numeric" if categorical: include.append("category") col_types += "and " if col_types != "" else "" col_types += "categorical" if not numeric and not categorical: raise ValueError( "At least one of numeric and categorical must be True" ) self._data = pd.DataFrame(data).select_dtypes(include) if self._data.shape[1] == 0: raise ValueError( "Selecting {col_types} results in an empty DataFrame" ) self._is_numeric = [is_numeric_dtype(dt) for dt in self._data.dtypes] self._is_cat_like = [ is_categorical_dtype(dt) for dt in self._data.dtypes ] if stats is not None: undef = [stat for stat in stats if stat not in DEFAULT_STATISTICS] if undef: raise ValueError( f"{', '.join(undef)} are not known statistics" ) self._stats = ( list(DEFAULT_STATISTICS) if stats is None else list(stats) ) self._ntop = int_like(ntop, "ntop") self._compute_top = "top" in self._stats self._compute_freq = "freq" in self._stats if self._compute_top and self._ntop <= 0 < sum(self._is_cat_like): raise ValueError("top must be a non-negative integer") # Expand special stats replacements = { "mode": ["mode", "mode_freq"], "ci": ["upper_ci", "lower_ci"], "jarque_bera": ["jarque_bera", "jarque_bera_pval"], "top": [f"top_{i}" for i in range(1, self._ntop + 1)], "freq": [f"freq_{i}" for i in range(1, self._ntop + 1)], } for key in replacements: if key in self._stats: idx = self._stats.index(key) self._stats = ( self._stats[:idx] + replacements[key] + self._stats[idx + 1 :] ) self._percentiles = array_like( percentiles, "percentiles", maxdim=1, dtype="d" ) self._percentiles = np.sort(self._percentiles) if np.unique(self._percentiles).shape[0] != self._percentiles.shape[0]: raise ValueError("percentiles must be distinct") if np.any(self._percentiles >= 100) or np.any(self._percentiles <= 0): raise ValueError("percentiles must be strictly between 0 and 100") self._alpha = float_like(alpha, "alpha") if not 0 < alpha < 1: raise ValueError("alpha must be strictly between 0 and 1") self._use_t = bool_like(use_t, "use_t") def _reorder(self, df: pd.DataFrame) -> pd.DataFrame: return df.loc[[s for s in self._stats if s in df.index]] @cache_readonly def frame(self) -> pd.DataFrame: """ Descriptive statistics for both numeric and categorical data Returns ------- DataFrame The statistics """ numeric = self.numeric categorical = self.categorical if categorical.shape[1] == 0: return numeric elif numeric.shape[1] == 0: return categorical df = pd.concat([numeric, categorical], axis=1) return self._reorder(df[self._data.columns]) @cache_readonly def numeric(self) -> pd.DataFrame: """ Descriptive statistics for numeric data Returns ------- DataFrame The statistics of the numeric columns """ df: pd.DataFrame = self._data.loc[:, self._is_numeric] cols = df.columns _, k = df.shape std = df.std() count = df.count() mean = df.mean() mad = (df - mean).abs().mean() std_err = std.copy() std_err.loc[count > 0] /= count.loc[count > 0] if self._use_t: q = stats.t(count - 1).ppf(1.0 - self._alpha / 2) else: q = stats.norm.ppf(1.0 - self._alpha / 2) def _mode(ser): mode_res = stats.mode(ser.dropna()) if mode_res[0].shape[0] > 0: return [float(val) for val in mode_res] return np.nan, np.nan mode_values = df.apply(_mode).T if mode_values.size > 0: if isinstance(mode_values, pd.DataFrame): # pandas 1.0 or later mode = np.asarray(mode_values[0], dtype=float) mode_counts = np.asarray(mode_values[1], dtype=np.int64) else: # pandas before 1.0 returns a Series of 2-elem list mode = [] mode_counts = [] for idx in mode_values.index: val = mode_values.loc[idx] mode.append(val[0]) mode_counts.append(val[1]) mode = np.atleast_1d(mode) mode_counts = np.atleast_1d(mode_counts) else: mode = mode_counts = np.empty(0) loc = count > 0 mode_freq = np.full(mode.shape[0], np.nan) mode_freq[loc] = mode_counts[loc] / count.loc[loc] if df.shape[1] > 0: iqr = df.quantile(0.75) - df.quantile(0.25) else: iqr = mean jb = df.apply( lambda x: list(jarque_bera(x.dropna())), result_type="expand" ).T nan_mean = mean.copy() nan_mean.loc[nan_mean == 0] = np.nan coef_var = std / nan_mean results = { "nobs": pd.Series( np.ones(k, dtype=np.int64) * df.shape[0], index=cols ), "missing": df.shape[0] - count, "mean": mean, "std_err": std_err, "upper_ci": mean + q * std_err, "lower_ci": mean - q * std_err, "std": std, "iqr": iqr, "mad": mad, "coef_var": coef_var, "range": pd_ptp(df), "max": df.max(), "min": df.min(), "skew": jb[2], "kurtosis": jb[3], "iqr_normal": iqr / np.diff(stats.norm.ppf([0.25, 0.75])), "mad_normal": mad / np.sqrt(2 / np.pi), "jarque_bera": jb[0], "jarque_bera_pval": jb[1], "mode": pd.Series(mode, index=cols), "mode_freq": pd.Series(mode_freq, index=cols), "median": df.median(), } final = {k: v for k, v in results.items() if k in self._stats} results_df = pd.DataFrame( list(final.values()), columns=cols, index=list(final.keys()) ) if "percentiles" not in self._stats: return results_df # Pandas before 1.0 cannot handle empty DF if df.shape[1] > 0: perc = df.quantile(self._percentiles / 100).astype(float) else: perc = pd.DataFrame(index=self._percentiles / 100, dtype=float) if np.all(np.floor(100 * perc.index) == (100 * perc.index)): perc.index = [f"{int(100 * idx)}%" for idx in perc.index] else: dupe = True scale = 100 index = perc.index while dupe: scale *= 10 idx = np.floor(scale * perc.index) if np.all(np.diff(idx) > 0): dupe = False index = np.floor(scale * index) / (scale / 100) fmt = f"0.{len(str(scale//100))-1}f" output = f"{{0:{fmt}}}%" perc.index = [output.format(val) for val in index] return self._reorder(pd.concat([results_df, perc], 0)) @cache_readonly def categorical(self) -> pd.DataFrame: """ Descriptive statistics for categorical data Returns ------- DataFrame The statistics of the categorical columns """ df = self._data.loc[:, [col for col in self._is_cat_like]] k = df.shape[1] cols = df.columns vc = {col: df[col].value_counts(normalize=True) for col in df} distinct = pd.Series( {col: vc[col].shape[0] for col in vc}, dtype=np.int64 ) top = {} freq = {} for col in vc: single = vc[col] if single.shape[0] >= self._ntop: top[col] = single.index[: self._ntop] freq[col] = np.asarray(single.iloc[:5]) else: val = list(single.index) val += [None] * (self._ntop - len(val)) top[col] = val freq_val = list(single) freq_val += [np.nan] * (self._ntop - len(freq_val)) freq[col] = np.asarray(freq_val) index = [f"top_{i}" for i in range(1, self._ntop + 1)] top_df = pd.DataFrame(top, dtype="object", index=index, columns=cols) index = [f"freq_{i}" for i in range(1, self._ntop + 1)] freq_df = pd.DataFrame(freq, dtype="object", index=index, columns=cols) results = { "nobs": pd.Series( np.ones(k, dtype=np.int64) * df.shape[0], index=cols ), "missing": df.shape[0] - df.count(), "distinct": distinct, } final = {k: v for k, v in results.items() if k in self._stats} results_df = pd.DataFrame( list(final.values()), columns=cols, index=list(final.keys()), dtype="object", ) if self._compute_top: results_df = pd.concat([results_df, top_df], axis=0) if self._compute_freq: results_df = pd.concat([results_df, freq_df], axis=0) return self._reorder(results_df) def summary(self) -> SimpleTable: """ Summary table of the descriptive statistics Returns ------- SimpleTable A table instance supporting export to text, csv and LaTeX """ df = self.frame.astype(object) df = df.fillna("") cols = [str(col) for col in df.columns] stubs = [str(idx) for idx in df.index] data = [] for _, row in df.iterrows(): data.append([v for v in row]) def _formatter(v): if isinstance(v, str): return v elif v // 1 == v: return str(int(v)) return f"{v:0.4g}" return SimpleTable( data, header=cols, stubs=stubs, title="Descriptive Statistics", txt_fmt={"data_fmts": {0: "%s", 1: _formatter}}, datatypes=[1] * len(data), ) def __str__(self) -> str: return str(self.summary().as_text()) ds = Docstring(Description.__doc__) ds.replace_block( "Returns", Parameter(None, "DataFrame", ["Descriptive statistics"]) ) ds.replace_block("Attributes", []) ds.replace_block( "See Also", [ ( [("pandas.DataFrame.describe", None)], ["Basic descriptive statistics"], ), ( [("Description", None)], ["Descriptive statistics class with additional output options"], ), ], ) @Appender(str(ds)) def describe( data: Union[np.ndarray, pd.Series, pd.DataFrame], stats: Sequence[str] = None, *, numeric: bool = True, categorical: bool = True, alpha: float = 0.05, use_t: bool = False, percentiles: Sequence[Union[int, float]] = PERCENTILES, ntop: bool = 5, ) -> pd.DataFrame: return Description( data, stats, numeric=numeric, categorical=categorical, alpha=alpha, use_t=use_t, percentiles=percentiles, ntop=ntop, ).frame class Describe(object): """ Calculates descriptive statistics for data. .. deprecated:: 0.12 Use ``Description`` or ``describe`` instead Defaults to a basic set of statistics, "all" can be specified, or a list can be given. Parameters ---------- dataset : array_like 2D dataset for descriptive statistics. """ def __init__(self, dataset): warnings.warn(DEPRECATION_MSG, DeprecationWarning) self.dataset = dataset # better if this is initially a list to define order, or use an # ordered dict. First position is the function # Second position is the tuple/list of column names/numbers # third is are the results in order of the columns self.univariate = dict( obs=[len, None, None], mean=[np.mean, None, None], std=[np.std, None, None], min=[np.min, None, None], max=[np.max, None, None], ptp=[np.ptp, None, None], var=[np.var, None, None], mode_val=[self._mode_val, None, None], mode_bin=[self._mode_bin, None, None], median=[np.median, None, None], skew=[stats.skew, None, None], uss=[lambda x: np.sum(np.asarray(x) ** 2, axis=0), None, None], kurtosis=[stats.kurtosis, None, None], percentiles=[self._percentiles, None, None], # BUG: not single value # sign_test_M = [self.sign_test_m, None, None], # sign_test_P = [self.sign_test_p, None, None] ) # TODO: Basic stats for strings # self.strings = dict( # unique = [np.unique, None, None], # number_uniq = [len( # most = [ # least = [ # TODO: Multivariate # self.multivariate = dict( # corrcoef(x[, y, rowvar, bias]), # cov(m[, y, rowvar, bias]), # histogram2d(x, y[, bins, range, normed, weights]) # ) self._arraytype = None self._columns_list = None def _percentiles(self, x): p = [ stats.scoreatpercentile(x, per) for per in (1, 5, 10, 25, 50, 75, 90, 95, 99) ] return p def _mode_val(self, x): return stats.mode(x)[0][0] def _mode_bin(self, x): return stats.mode(x)[1][0] def _array_typer(self): """if not a sctructured array""" if not (self.dataset.dtype.names): """homogeneous dtype array""" self._arraytype = "homog" elif self.dataset.dtype.names: """structured or rec array""" self._arraytype = "sctruct" else: assert self._arraytype == "sctruct" or self._arraytype == "homog" def _is_dtype_like(self, col): """ Check whether self.dataset.[col][0] behaves like a string, numbern unknown. `numpy.lib._iotools._is_string_like` """ def string_like(): # TODO: not sure what the result is if the first item is some # type of missing value try: self.dataset[col][0] + "" except (TypeError, ValueError): return False return True def number_like(): try: self.dataset[col][0] + 1.0 except (TypeError, ValueError): return False return True if number_like() and not string_like(): return "number" elif not number_like() and string_like(): return "string" else: assert number_like() or string_like(), ( "\ Not sure of dtype" + str(self.dataset[col][0]) ) # @property def summary(self, stats="basic", columns="all", orientation="auto"): """ Return a summary of descriptive statistics. Parameters ---------- stats: list or str The desired statistics, Accepts 'basic' or 'all' or a list. 'basic' = ('obs', 'mean', 'std', 'min', 'max') 'all' = ('obs', 'mean', 'std', 'min', 'max', 'ptp', 'var', 'mode', 'meadian', 'skew', 'uss', 'kurtosis', 'percentiles') columns : list or str The columns/variables to report the statistics, default is 'all' If an object with named columns is given, you may specify the column names. For example """ # NOTE # standard array: Specifiy column numbers (NEED TO TEST) # percentiles currently broken # mode requires mode_val and mode_bin separately if self._arraytype is None: self._array_typer() if stats == "basic": stats = ("obs", "mean", "std", "min", "max") elif stats == "all": # stats = self.univariate.keys() # dict does not keep an order, use full list instead stats = [ "obs", "mean", "std", "min", "max", "ptp", "var", "mode_val", "mode_bin", "median", "uss", "skew", "kurtosis", "percentiles", ] else: for astat in stats: pass # assert astat in self.univariate # hack around percentiles multiple output # bad naming import scipy.stats # BUG: the following has all per the same per=99 ##perdict = dict(('perc_%2d'%per, [lambda x: # scipy.stats.scoreatpercentile(x, per), None, None]) ## for per in (1,5,10,25,50,75,90,95,99)) def _fun(per): return lambda x: scipy.stats.scoreatpercentile(x, per) perdict = dict( ("perc_%02d" % per, [_fun(per), None, None]) for per in (1, 5, 10, 25, 50, 75, 90, 95, 99) ) if "percentiles" in stats: self.univariate.update(perdict) idx = stats.index("percentiles") stats[idx : idx + 1] = sorted(perdict.keys()) # JP: this does not allow a change in sequence, sequence in stats is # ignored # this is just an if condition if any( [ aitem[1] for aitem in self.univariate.items() if aitem[0] in stats ] ): if columns == "all": self._columns_list = [] if self._arraytype == "sctruct": self._columns_list = self.dataset.dtype.names # self._columns_list = [col for col in # self.dataset.dtype.names if # (self._is_dtype_like(col)=='number')] else: self._columns_list = lrange(self.dataset.shape[1]) else: self._columns_list = columns if self._arraytype == "sctruct": for col in self._columns_list: assert col in self.dataset.dtype.names else: assert self._is_dtype_like(self.dataset) == "number" columstypes = self.dataset.dtype # TODO: do we need to make sure they dtype is float64 ? for astat in stats: calc = self.univariate[astat] if self._arraytype == "sctruct": calc[1] = self._columns_list calc[2] = [ calc[0](self.dataset[col]) for col in self._columns_list if (self._is_dtype_like(col) == "number") ] # calc[2].append([len(np.unique(self.dataset[col])) for col # in self._columns_list if # self._is_dtype_like(col)=='string'] else: calc[1] = ["Col " + str(col) for col in self._columns_list] calc[2] = [ calc[0](self.dataset[:, col]) for col in self._columns_list ] return self.print_summary(stats, orientation=orientation) else: return self.print_summary(stats, orientation=orientation) def print_summary(self, stats, orientation="auto"): # TODO: need to specify a table formating for the numbers, using defualt title = "Summary Statistics" header = stats stubs = self.univariate["obs"][1] data = [ [self.univariate[astat][2][col] for astat in stats] for col in range(len(self.univariate["obs"][2])) ] if (orientation == "varcols") or ( orientation == "auto" and len(stubs) < len(header) ): # swap rows and columns data = lmap(lambda *row: list(row), *data) header, stubs = stubs, header part_fmt = dict(data_fmts=["%#8.4g"] * (len(header) - 1)) table = SimpleTable(data, header, stubs, title=title, txt_fmt=part_fmt) return table @Appender(sign_test.__doc__) # i.e. module-level sign_test def sign_test(self, samp, mu0=0): return sign_test(samp, mu0) # TODO: There must be a better way but formating the stats of a fuction that # returns 2 values is a problem. # def sign_test_m(samp,mu0=0): # return self.sign_test(samp,mu0)[0] # def sign_test_p(samp,mu0=0): # return self.sign_test(samp,mu0)[1] statsmodels-0.12.2/statsmodels/stats/diagnostic.py000066400000000000000000002040541400612667500223500ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Various Statistical Tests Author: josef-pktd License: BSD-3 Notes ----- Almost fully verified against R or Gretl, not all options are the same. In many cases of Lagrange multiplier tests both the LM test and the F test is returned. In some but not all cases, R has the option to choose the test statistic. Some alternative test statistic results have not been verified. TODO * refactor to store intermediate results * how easy is it to attach a test that is a class to a result instance, for example CompareCox as a method compare_cox(self, other) ? missing: * pvalues for breaks_hansen * additional options, compare with R, check where ddof is appropriate * new tests: - breaks_ap, more recent breaks tests - specification tests against nonparametric alternatives """ from statsmodels.compat.pandas import deprecate_kwarg from collections.abc import Iterable import numpy as np import pandas as pd from scipy import stats from statsmodels.regression.linear_model import OLS, RegressionResultsWrapper from statsmodels.tsa.tsatools import lagmat from statsmodels.tools.validation import (array_like, int_like, bool_like, string_like, dict_like, float_like) from statsmodels.stats._lilliefors import (kstest_fit, lilliefors, kstest_normal, kstest_exponential) from statsmodels.stats._adnorm import normal_ad, anderson_statistic __all__ = ["kstest_fit", "lilliefors", "kstest_normal", "kstest_exponential", "normal_ad", "compare_cox", "compare_j", "acorr_breusch_godfrey", "acorr_ljungbox", "acorr_lm", "het_arch", "het_breuschpagan", "het_goldfeldquandt", "het_white", "spec_white", "linear_lm", "linear_rainbow", "linear_harvey_collier", "anderson_statistic"] NESTED_ERROR = """\ The exog in results_x and in results_z are nested. {test} requires \ that models are non-nested. """ def _check_nested_exog(small, large): """ Check if a larger exog nests a smaller exog Parameters ---------- small : ndarray exog from smaller model large : ndarray exog from larger model Returns ------- bool True if small is nested by large """ if small.shape[1] > large.shape[1]: return False coef = np.linalg.lstsq(large, small, rcond=None)[0] err = small - large @ coef return np.linalg.matrix_rank(np.c_[large, err]) == large.shape[1] def _check_nested_results(results_x, results_z): if not isinstance(results_x, RegressionResultsWrapper): raise TypeError("results_x must come from a linear regression model") if not isinstance(results_z, RegressionResultsWrapper): raise TypeError("results_z must come from a linear regression model") if not np.allclose(results_x.model.endog, results_z.model.endog): raise ValueError("endogenous variables in models are not the same") x = results_x.model.exog z = results_z.model.exog nested = False if x.shape[1] <= z.shape[1]: nested = nested or _check_nested_exog(x, z) else: nested = nested or _check_nested_exog(z, x) return nested class ResultsStore(object): def __str__(self): return getattr(self, '_str', self.__class__.__name__) def compare_cox(results_x, results_z, store=False): """ Compute the Cox test for non-nested models Parameters ---------- results_x : Result instance result instance of first model results_z : Result instance result instance of second model store : bool, default False If true, then the intermediate results are returned. Returns ------- tstat : float t statistic for the test that including the fitted values of the first model in the second model has no effect. pvalue : float two-sided pvalue for the t statistic res_store : ResultsStore, optional Intermediate results. Returned if store is True. Notes ----- Tests of non-nested hypothesis might not provide unambiguous answers. The test should be performed in both directions and it is possible that both or neither test rejects. see [1]_ for more information. Formulas from [1]_, section 8.3.4 translated to code Matches results for Example 8.3 in Greene References ---------- .. [1] Greene, W. H. Econometric Analysis. New Jersey. Prentice Hall; 5th edition. (2002). """ if _check_nested_results(results_x, results_z): raise ValueError(NESTED_ERROR.format(test="Cox comparison")) x = results_x.model.exog z = results_z.model.exog nobs = results_x.model.endog.shape[0] sigma2_x = results_x.ssr / nobs sigma2_z = results_z.ssr / nobs yhat_x = results_x.fittedvalues res_dx = OLS(yhat_x, z).fit() err_zx = res_dx.resid res_xzx = OLS(err_zx, x).fit() err_xzx = res_xzx.resid sigma2_zx = sigma2_x + np.dot(err_zx.T, err_zx) / nobs c01 = nobs / 2. * (np.log(sigma2_z) - np.log(sigma2_zx)) v01 = sigma2_x * np.dot(err_xzx.T, err_xzx) / sigma2_zx ** 2 q = c01 / np.sqrt(v01) pval = 2 * stats.norm.sf(np.abs(q)) if store: res = ResultsStore() res.res_dx = res_dx res.res_xzx = res_xzx res.c01 = c01 res.v01 = v01 res.q = q res.pvalue = pval res.dist = stats.norm return q, pval, res return q, pval class CompareCox(object): """ Cox Test for non-nested models .. deprecated:: 0.11 CompareCox is deprecated in favor of compare_cox. CompareCox will be removed after 0.12. """ def __init__(self): import warnings warnings.warn("CompareCox is deprecated in favor of compare_cox and " "will be removed after 0.12.", FutureWarning) self.res_dx = self.res_xzx = self.c01 = None self.v01 = self.q = self.pvalue = self.dist = None def run(self, results_x, results_z, attach=False): results = compare_cox(results_x, results_z, store=attach) if attach: res = results[-1] self.res_dx = res.res_dx self.res_xzx = res.res_xzx self.c01 = res.c01 self.v01 = res.v01 self.q = res.q self.pvalue = res.pvalue self.dist = res.dist return results def __call__(self, results_x, results_z): return self.run(results_x, results_z, attach=False) def compare_j(results_x, results_z, store=False): """ Compute the J-test for non-nested models Parameters ---------- results_x : RegressionResults The result instance of first model. results_z : RegressionResults The result instance of second model. store : bool, default False If true, then the intermediate results are returned. Returns ------- tstat : float t statistic for the test that including the fitted values of the first model in the second model has no effect. pvalue : float two-sided pvalue for the t statistic res_store : ResultsStore, optional Intermediate results. Returned if store is True. Notes ----- From description in Greene, section 8.3.3. Matches results for Example 8.3, Greene. Tests of non-nested hypothesis might not provide unambiguous answers. The test should be performed in both directions and it is possible that both or neither test rejects. see Greene for more information. References ---------- .. [1] Greene, W. H. Econometric Analysis. New Jersey. Prentice Hall; 5th edition. (2002). """ # TODO: Allow cov to be specified if _check_nested_results(results_x, results_z): raise ValueError(NESTED_ERROR.format(test="J comparison")) y = results_x.model.endog z = results_z.model.exog yhat_x = results_x.fittedvalues res_zx = OLS(y, np.column_stack((yhat_x, z))).fit() tstat = res_zx.tvalues[0] pval = res_zx.pvalues[0] if store: res = ResultsStore() res.res_zx = res_zx res.dist = stats.t(res_zx.df_resid) res.teststat = tstat res.pvalue = pval return tstat, pval, res return tstat, pval class CompareJ(object): """ J-Test for comparing non-nested models .. deprecated:: 0.11 CompareJ is deprecated in favor of compare_j. CompareJ will be removed after 0.12. """ def __init__(self): import warnings warnings.warn("CompareJ is deprecated in favor of compare_j and will " "be removed after 0.12.", FutureWarning) self.res_zx = self.dist = self.teststat = self.pvalue = None def run(self, results_x, results_z, attach=True): res = compare_j(results_x, results_z, store=attach) tstat, pval = res[:2] if attach: self.res_zx = res[-1].res_zx self.dist = res[-1].dist self.teststat = res[-1].teststat self.pvalue = res[-1].pvalue return tstat, pval def __call__(self, results_x, results_z): return self.run(results_x, results_z, attach=False) def compare_encompassing(results_x, results_z, cov_type="nonrobust", cov_kwargs=None): r""" Davidson-MacKinnon encompassing test for comparing non-nested models Parameters ---------- results_x : Result instance result instance of first model results_z : Result instance result instance of second model cov_type : str, default "nonrobust Covariance type. The default is "nonrobust` which uses the classic OLS covariance estimator. Specify one of "HC0", "HC1", "HC2", "HC3" to use White's covariance estimator. All covariance types supported by ``OLS.fit`` are accepted. cov_kwargs : dict, default None Dictionary of covariance options passed to ``OLS.fit``. See OLS.fit for more details. Returns ------- DataFrame A DataFrame with two rows and four columns. The row labeled x contains results for the null that the model contained in results_x is equivalent to the encompassing model. The results in the row labeled z correspond to the test that the model contained in results_z are equivalent to the encompassing model. The columns are the test statistic, its p-value, and the numerator and denominator degrees of freedom. The test statistic has an F distribution. The numerator degree of freedom is the number of variables in the encompassing model that are not in the x or z model. The denominator degree of freedom is the number of observations minus the number of variables in the nesting model. Notes ----- The null is that the fit produced using x is the same as the fit produced using both x and z. When testing whether x is encompassed, the model estimated is .. math:: Y = X\beta + Z_1\gamma + \epsilon where :math:`Z_1` are the columns of :math:`Z` that are not spanned by :math:`X`. The null is :math:`H_0:\gamma=0`. When testing whether z is encompassed, the roles of :math:`X` and :math:`Z` are reversed. Implementation of Davidson and MacKinnon (1993)'s encompassing test. Performs two Wald tests where models x and z are compared to a model that nests the two. The Wald tests are performed by using an OLS regression. """ if _check_nested_results(results_x, results_z): raise ValueError(NESTED_ERROR.format(test="Testing encompassing")) y = results_x.model.endog x = results_x.model.exog z = results_z.model.exog def _test_nested(endog, a, b, cov_est, cov_kwds): err = b - a @ np.linalg.lstsq(a, b, rcond=None)[0] u, s, v = np.linalg.svd(err) eps = np.finfo(np.double).eps tol = s.max(axis=-1, keepdims=True) * max(err.shape) * eps non_zero = np.abs(s) > tol aug = err @ v[:, non_zero] aug_reg = np.hstack([a, aug]) k_a = aug.shape[1] k = aug_reg.shape[1] res = OLS(endog, aug_reg).fit(cov_type=cov_est, cov_kwds=cov_kwds) r_matrix = np.zeros((k_a, k)) r_matrix[:, -k_a:] = np.eye(k_a) test = res.wald_test(r_matrix, use_f=True) stat, pvalue = float(np.squeeze(test.statistic)), float(test.pvalue) df_num, df_denom = int(test.df_num), int(test.df_denom) return stat, pvalue, df_num, df_denom x_nested = _test_nested(y, x, z, cov_type, cov_kwargs) z_nested = _test_nested(y, z, x, cov_type, cov_kwargs) return pd.DataFrame([x_nested, z_nested], index=["x", "z"], columns=["stat", "pvalue", "df_num", "df_denom"]) def acorr_ljungbox(x, lags=None, boxpierce=False, model_df=0, period=None, return_df=None, auto_lag=False): """ Ljung-Box test of autocorrelation in residuals. Parameters ---------- x : array_like The data series. The data is demeaned before the test statistic is computed. lags : {int, array_like}, default None If lags is an integer then this is taken to be the largest lag that is included, the test result is reported for all smaller lag length. If lags is a list or array, then all lags are included up to the largest lag in the list, however only the tests for the lags in the list are reported. If lags is None, then the default maxlag is currently min((nobs // 2 - 2), 40). After 0.12 this will change to min(10, nobs // 5). The default number of lags changes if period is set. boxpierce : bool, default False If true, then additional to the results of the Ljung-Box test also the Box-Pierce test results are returned. model_df : int, default 0 Number of degrees of freedom consumed by the model. In an ARMA model, this value is usually p+q where p is the AR order and q is the MA order. This value is subtracted from the degrees-of-freedom used in the test so that the adjusted dof for the statistics are lags - model_df. If lags - model_df <= 0, then NaN is returned. period : int, default None The period of a Seasonal time series. Used to compute the max lag for seasonal data which uses min(2*period, nobs // 5) if set. If None, then the default rule is used to set the number of lags. When set, must be >= 2. return_df : bool, default None Flag indicating whether to return the result as a single DataFrame with columns lb_stat, lb_pvalue, and optionally bp_stat and bp_pvalue. After 0.12, this will become the only return method. Set to True to return the DataFrame or False to continue returning the 2 - 4 output. If None (the default), a warning is raised. auto_lag : bool, default False Flag indicating whether to automatically determine the optimal lag length based on threshold of maximum correlation value. Returns ------- lbvalue : float or array The Ljung-Box test statistic. pvalue : float or array The p-value based on chi-square distribution. The p-value is computed as 1.0 - chi2.cdf(lbvalue, dof) where dof is lag - model_df. If lag - model_df <= 0, then NaN is returned for the pvalue. bpvalue : (optional), float or array The test statistic for Box-Pierce test. bppvalue : (optional), float or array The p-value based for Box-Pierce test on chi-square distribution. The p-value is computed as 1.0 - chi2.cdf(bpvalue, dof) where dof is lag - model_df. If lag - model_df <= 0, then NaN is returned for the pvalue. See Also -------- statsmodels.regression.linear_model.OLS.fit Regression model fitting. statsmodels.regression.linear_model.RegressionResults Results from linear regression models. Notes ----- Ljung-Box and Box-Pierce statistic differ in their scaling of the autocorrelation function. Ljung-Box test is has better finite-sample properties. References ---------- .. [*] Green, W. "Econometric Analysis," 5th ed., Pearson, 2003. .. [*] J. Carlos Escanciano, Ignacio N. Lobato "An automatic Portmanteau test for serial correlation"., Volume 151, 2009. Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.sunspots.load_pandas().data >>> res = sm.tsa.ARMA(data["SUNACTIVITY"], (1,1)).fit(disp=-1) >>> sm.stats.acorr_ljungbox(res.resid, lags=[10], return_df=True) lb_stat lb_pvalue 10 214.106992 1.827374e-40 """ def get_optimal_length(threshold_metric, threshold, maxlag, func): optimal_lag = 0 least_penalised = 0 for lags in range(1, maxlag + 1): if (threshold_metric <= threshold): penalty = lags * np.log(nobs) else: penalty = 2 * lags test_statistic = func(lags) penalised = test_statistic - penalty if (penalised > least_penalised): optimal_lag = lags least_penalised = penalised return optimal_lag # Avoid cyclic import from statsmodels.tsa.stattools import acf x = array_like(x, "x") period = int_like(period, "period", optional=True) return_df = bool_like(return_df, "return_df", optional=True) model_df = int_like(model_df, "model_df", optional=False) if period is not None and period <= 1: raise ValueError("period must be >= 2") if model_df < 0: raise ValueError("model_df must be >= 0") nobs = x.shape[0] if auto_lag: maxlag = nobs - 1 # Compute threshold metrics sacf = acf(x, nlags=maxlag, fft=False) sacf2 = sacf[1:maxlag + 1] ** 2 / (nobs - np.arange(1, maxlag + 1)) q = 2.4 threshold = np.sqrt(q * np.log(nobs)) threshold_metric = max(np.abs(sacf)) * np.sqrt(nobs) if not boxpierce: lags = get_optimal_length( threshold_metric, threshold, maxlag, lambda p: nobs * (nobs + 2) * np.cumsum(sacf2)[p - 1]) else: lags = get_optimal_length( threshold_metric, threshold, maxlag, lambda p: nobs * np.cumsum(sacf[1:maxlag + 1] ** 2)[p - 1]) lags = int_like(lags, "lags") lags = np.arange(1, lags + 1) elif period is not None: lags = np.arange(1, min(nobs // 5, 2 * period) + 1, dtype=int) elif lags is None: # TODO: Switch to min(10, nobs//5) after 0.12 import warnings warnings.warn("The default value of lags is changing. After 0.12, " "this value will become min(10, nobs//5). Directly set" "lags to silence this warning.", FutureWarning) # Future # lags = np.arange(1, min(nobs // 5, 10) + 1, dtype=int) lags = np.arange(1, min((nobs // 2 - 2), 40) + 1, dtype=int) elif not isinstance(lags, Iterable): lags = int_like(lags, "lags") lags = np.arange(1, lags + 1) lags = array_like(lags, "lags", dtype="int") maxlag = lags.max() # normalize by nobs not (nobs-nlags) # SS: unbiased=False is default now sacf = acf(x, nlags=maxlag, fft=False) sacf2 = sacf[1:maxlag + 1] ** 2 / (nobs - np.arange(1, maxlag + 1)) qljungbox = nobs * (nobs + 2) * np.cumsum(sacf2)[lags - 1] adj_lags = lags - model_df pval = np.full_like(qljungbox, np.nan) loc = adj_lags > 0 pval[loc] = stats.chi2.sf(qljungbox[loc], adj_lags[loc]) if return_df is None: msg = ("The value returned will change to a single DataFrame after " "0.12 is released. Set return_df to True to use to return a " "DataFrame now. Set return_df to False to silence this " "warning.") import warnings warnings.warn(msg, FutureWarning) if not boxpierce: if return_df: return pd.DataFrame({"lb_stat": qljungbox, "lb_pvalue": pval}, index=lags) return qljungbox, pval qboxpierce = nobs * np.cumsum(sacf[1:maxlag + 1] ** 2)[lags - 1] pvalbp = np.full_like(qljungbox, np.nan) pvalbp[loc] = stats.chi2.sf(qboxpierce[loc], adj_lags[loc]) if return_df: return pd.DataFrame({"lb_stat": qljungbox, "lb_pvalue": pval, "bp_stat": qboxpierce, "bp_pvalue": pvalbp}, index=lags) return qljungbox, pval, qboxpierce, pvalbp @deprecate_kwarg("maxlag", "nlags") def acorr_lm(resid, nlags=None, autolag="AIC", store=False, *, period=None, ddof=0, cov_type="nonrobust", cov_kwargs=None): """ Lagrange Multiplier tests for autocorrelation. This is a generic Lagrange Multiplier test for autocorrelation. Returns Engle's ARCH test if resid is the squared residual array. Breusch-Godfrey is a variation on this test with additional exogenous variables. Parameters ---------- resid : array_like Time series to test. nlags : int, default None Highest lag to use. The behavior of this parameter will change after 0.12. autolag : {str, None}, default "AIC" If None, then a fixed number of lags given by maxlag is used. This parameter is deprecated and will be removed after 0.12. Searching for model specification cannot control test size. store : bool, default False If true then the intermediate results are also returned. period : int, default none The period of a Seasonal time series. Used to compute the max lag for seasonal data which uses min(2*period, nobs // 5) if set. If None, then the default rule is used to set the number of lags. When set, must be >= 2. ddof : int, default 0 The number of degrees of freedom consumed by the model used to produce resid. The default value is 0. cov_type : str, default "nonrobust" Covariance type. The default is "nonrobust` which uses the classic OLS covariance estimator. Specify one of "HC0", "HC1", "HC2", "HC3" to use White's covariance estimator. All covariance types supported by ``OLS.fit`` are accepted. cov_kwargs : dict, default None Dictionary of covariance options passed to ``OLS.fit``. See OLS.fit for more details. Returns ------- lm : float Lagrange multiplier test statistic. lmpval : float The p-value for Lagrange multiplier test. fval : float The f statistic of the F test, alternative version of the same test based on F test for the parameter restriction. fpval : float The pvalue of the F test. res_store : ResultsStore, optional Intermediate results. Only returned if store=True. See Also -------- het_arch Conditional heteroskedasticity testing. acorr_breusch_godfrey Breusch-Godfrey test for serial correlation. acorr_ljung_box Ljung-Box test for serial correlation. Notes ----- The test statistic is computed as (nobs - ddof) * r2 where r2 is the R-squared from a regression on the residual on nlags lags of the residual. """ resid = array_like(resid, "resid", ndim=1) cov_type = string_like(cov_type, "cov_type") cov_kwargs = {} if cov_kwargs is None else cov_kwargs cov_kwargs = dict_like(cov_kwargs, "cov_kwargs") nobs = resid.shape[0] if period is not None and nlags is None: maxlag = min(nobs // 5, 2 * period) elif nlags is None: # TODO: Switch to min(10, nobs//5) after 0.12 import warnings warnings.warn("The default value of nlags is changing. After 0.12, " "this value will become min(10, nobs//5). Directly set" "maxlags or period to silence this warning.", FutureWarning) # Future # maxlag = min(nobs // 5, 10) # Old: for adf from Greene referencing Schwert 1989 maxlag = int(np.ceil(12. * np.power(nobs / 100., 1 / 4.))) else: maxlag = nlags xdall = lagmat(resid[:, None], maxlag, trim="both") nobs = xdall.shape[0] xdall = np.c_[np.ones((nobs, 1)), xdall] xshort = resid[-nobs:] res_store = ResultsStore() if autolag: # TODO: Deprecate this # Use same rules as autocorr # search for lag length with highest information criteria # Note: I use the same number of observations to have comparable IC import warnings warnings.warn("autolag is deprecated and will be removed after 0.12. " "Model selection before testing fails to control test " "size. Set autolag to False to silence this warning.", FutureWarning) results = {} for mlag in range(1, maxlag + 1): results[mlag] = OLS(xshort, xdall[:, :mlag + 1]).fit() if autolag.lower() == "aic": bestic, icbestlag = min((v.aic, k) for k, v in results.items()) elif autolag.lower() == "bic": icbest, icbestlag = min((v.bic, k) for k, v in results.items()) else: raise ValueError("autolag can only be None, \"AIC\" or \"BIC\"") # rerun ols with best ic xdall = lagmat(resid[:, None], icbestlag, trim="both") nobs = xdall.shape[0] xdall = np.c_[np.ones((nobs, 1)), xdall] xshort = resid[-nobs:] usedlag = icbestlag if store: res_store.results = results else: usedlag = maxlag resols = OLS(xshort, xdall[:, :usedlag + 1]).fit(cov_type=cov_type, cov_kwargs=cov_kwargs) fval = float(resols.fvalue) fpval = float(resols.f_pvalue) if cov_type == "nonrobust": lm = (nobs - ddof) * resols.rsquared lmpval = stats.chi2.sf(lm, usedlag) # Note: deg of freedom for LM test: nvars - constant = lags used else: r_matrix = np.hstack((np.zeros((usedlag, 1)), np.eye(usedlag))) test_stat = resols.wald_test(r_matrix, use_f=False) lm = float(test_stat.statistic) lmpval = float(test_stat.pvalue) if store: res_store.resols = resols res_store.usedlag = usedlag return lm, lmpval, fval, fpval, res_store else: return lm, lmpval, fval, fpval @deprecate_kwarg("maxlag", "nlags") def het_arch(resid, nlags=None, autolag=None, store=False, ddof=0): """ Engle's Test for Autoregressive Conditional Heteroscedasticity (ARCH). Parameters ---------- resid : ndarray residuals from an estimation, or time series nlags : int, default None Highest lag to use. The behavior of this parameter will change after 0.12. autolag : {str, None}, default None If None, then a fixed number of lags given by maxlag is used. This parameter is deprecated and will be removed after 0.12. Searching for model specification cannot control test size. store : bool, default False If true then the intermediate results are also returned ddof : int, default 0 If the residuals are from a regression, or ARMA estimation, then there are recommendations to correct the degrees of freedom by the number of parameters that have been estimated, for example ddof=p+q for an ARMA(p,q). Returns ------- lm : float Lagrange multiplier test statistic lmpval : float p-value for Lagrange multiplier test fval : float fstatistic for F test, alternative version of the same test based on F test for the parameter restriction fpval : float pvalue for F test res_store : ResultsStore, optional Intermediate results. Returned if store is True. Notes ----- verified against R:FinTS::ArchTest """ return acorr_lm(resid ** 2, nlags=nlags, autolag=autolag, store=store, ddof=ddof) @deprecate_kwarg("results", "res") def acorr_breusch_godfrey(res, nlags=None, store=False): """ Breusch-Godfrey Lagrange Multiplier tests for residual autocorrelation. Parameters ---------- res : RegressionResults Estimation results for which the residuals are tested for serial correlation. nlags : int, default None Number of lags to include in the auxiliary regression. (nlags is highest lag). store : bool, default False If store is true, then an additional class instance that contains intermediate results is returned. Returns ------- lm : float Lagrange multiplier test statistic. lmpval : float The p-value for Lagrange multiplier test. fval : float The value of the f statistic for F test, alternative version of the same test based on F test for the parameter restriction. fpval : float The pvalue for F test. res_store : ResultsStore A class instance that holds intermediate results. Only returned if store=True. Notes ----- BG adds lags of residual to exog in the design matrix for the auxiliary regression with residuals as endog. See [1]_, section 12.7.1. References ---------- .. [1] Greene, W. H. Econometric Analysis. New Jersey. Prentice Hall; 5th edition. (2002). """ x = np.asarray(res.resid).squeeze() if x.ndim != 1: raise ValueError("Model resid must be a 1d array. Cannot be used on" " multivariate models.") exog_old = res.model.exog nobs = x.shape[0] if nlags is None: # TODO: Switch to min(10, nobs//5) after 0.12 import warnings warnings.warn("The default value of nlags is changing. After 0.12, " "this value will become min(10, nobs//5). Directly set" "nlags or period to silence this warning.", FutureWarning) nlags = np.trunc(12. * np.power(nobs / 100., 1 / 4.)) nlags = int(nlags) x = np.concatenate((np.zeros(nlags), x)) xdall = lagmat(x[:, None], nlags, trim="both") nobs = xdall.shape[0] xdall = np.c_[np.ones((nobs, 1)), xdall] xshort = x[-nobs:] exog = np.column_stack((exog_old, xdall)) k_vars = exog.shape[1] resols = OLS(xshort, exog).fit() ft = resols.f_test(np.eye(nlags, k_vars, k_vars - nlags)) fval = ft.fvalue fpval = ft.pvalue fval = float(np.squeeze(fval)) fpval = float(np.squeeze(fpval)) lm = nobs * resols.rsquared lmpval = stats.chi2.sf(lm, nlags) # Note: degrees of freedom for LM test is nvars minus constant = usedlags if store: res_store = ResultsStore() res_store.resols = resols res_store.usedlag = nlags return lm, lmpval, fval, fpval, res_store else: return lm, lmpval, fval, fpval def het_breuschpagan(resid, exog_het, robust=True): r""" Breusch-Pagan Lagrange Multiplier test for heteroscedasticity The tests the hypothesis that the residual variance does not depend on the variables in x in the form .. :math: \sigma_i = \sigma * f(\alpha_0 + \alpha z_i) Homoscedasticity implies that :math:`\alpha=0`. Parameters ---------- resid : array_like For the Breusch-Pagan test, this should be the residual of a regression. If an array is given in exog, then the residuals are calculated by the an OLS regression or resid on exog. In this case resid should contain the dependent variable. Exog can be the same as x. exog_het : array_like This contains variables suspected of being related to heteroscedasticity in resid. robust : bool, default True Flag indicating whether to use the Koenker version of the test (default) which assumes independent and identically distributed error terms, or the original Breusch-Pagan version which assumes residuals are normally distributed. Returns ------- lm : float lagrange multiplier statistic lm_pvalue : float p-value of lagrange multiplier test fvalue : float f-statistic of the hypothesis that the error variance does not depend on x f_pvalue : float p-value for the f-statistic Notes ----- Assumes x contains constant (for counting dof and calculation of R^2). In the general description of LM test, Greene mentions that this test exaggerates the significance of results in small or moderately large samples. In this case the F-statistic is preferable. **Verification** Chisquare test statistic is exactly (<1e-13) the same result as bptest in R-stats with defaults (studentize=True). **Implementation** This is calculated using the generic formula for LM test using $R^2$ (Greene, section 17.6) and not with the explicit formula (Greene, section 11.4.3), unless `robust` is set to False. The degrees of freedom for the p-value assume x is full rank. References ---------- .. [1] Greene, W. H. Econometric Analysis. New Jersey. Prentice Hall; 5th edition. (2002). .. [2] Breusch, T. S.; Pagan, A. R. (1979). "A Simple Test for Heteroskedasticity and Random Coefficient Variation". Econometrica. 47 (5): 1287–1294. .. [3] Koenker, R. (1981). "A note on studentizing a test for heteroskedasticity". Journal of Econometrics 17 (1): 107–112. """ x = np.asarray(exog_het) y = np.asarray(resid) ** 2 if not robust: y = y / np.mean(y) nobs, nvars = x.shape resols = OLS(y, x).fit() fval = resols.fvalue fpval = resols.f_pvalue lm = nobs * resols.rsquared if robust else resols.ess / 2 # Note: degrees of freedom for LM test is nvars minus constant return lm, stats.chi2.sf(lm, nvars - 1), fval, fpval def het_white(resid, exog): """ White's Lagrange Multiplier Test for Heteroscedasticity. Parameters ---------- resid : array_like The residuals. The squared residuals are used as the endogenous variable. exog : array_like The explanatory variables for the variance. Squares and interaction terms are automatically included in the auxiliary regression. Returns ------- lm : float The lagrange multiplier statistic. lm_pvalue :float The p-value of lagrange multiplier test. fvalue : float The f-statistic of the hypothesis that the error variance does not depend on x. This is an alternative test variant not the original LM test. f_pvalue : float The p-value for the f-statistic. Notes ----- Assumes x contains constant (for counting dof). question: does f-statistic make sense? constant ? References ---------- Greene section 11.4.1 5th edition p. 222. Test statistic reproduces Greene 5th, example 11.3. """ x = array_like(exog, "exog", ndim=2) y = array_like(resid, "resid", ndim=2, shape=(x.shape[0], 1)) if x.shape[1] < 2: raise ValueError("White's heteroskedasticity test requires exog to" "have at least two columns where one is a constant.") nobs, nvars0 = x.shape i0, i1 = np.triu_indices(nvars0) exog = x[:, i0] * x[:, i1] nobs, nvars = exog.shape assert nvars == nvars0 * (nvars0 - 1) / 2. + nvars0 resols = OLS(y ** 2, exog).fit() fval = resols.fvalue fpval = resols.f_pvalue lm = nobs * resols.rsquared # Note: degrees of freedom for LM test is nvars minus constant # degrees of freedom take possible reduced rank in exog into account # df_model checks the rank to determine df # extra calculation that can be removed: assert resols.df_model == np.linalg.matrix_rank(exog) - 1 lmpval = stats.chi2.sf(lm, resols.df_model) return lm, lmpval, fval, fpval def het_goldfeldquandt(y, x, idx=None, split=None, drop=None, alternative="increasing", store=False): """ Goldfeld-Quandt homoskedasticity test. This test examines whether the residual variance is the same in 2 subsamples. Parameters ---------- y : array_like endogenous variable x : array_like exogenous variable, regressors idx : int, default None column index of variable according to which observations are sorted for the split split : {int, float}, default None If an integer, this is the index at which sample is split. If a float in 01: if alternative.lower() in ["i", "inc", "increasing"]: fpval = stats.f.sf(fval, resols1.df_resid, resols2.df_resid) ordering = "increasing" elif alternative.lower() in ["d", "dec", "decreasing"]: fpval = stats.f.sf(1. / fval, resols2.df_resid, resols1.df_resid) ordering = "decreasing" elif alternative.lower() in ["2", "2-sided", "two-sided"]: fpval_sm = stats.f.cdf(fval, resols2.df_resid, resols1.df_resid) fpval_la = stats.f.sf(fval, resols2.df_resid, resols1.df_resid) fpval = 2 * min(fpval_sm, fpval_la) ordering = "two-sided" else: raise ValueError("invalid alternative") if store: res = ResultsStore() res.__doc__ = "Test Results for Goldfeld-Quandt test of" \ "heterogeneity" res.fval = fval res.fpval = fpval res.df_fval = (resols2.df_resid, resols1.df_resid) res.resols1 = resols1 res.resols2 = resols2 res.ordering = ordering res.split = split res._str = """\ The Goldfeld-Quandt test for null hypothesis that the variance in the second subsample is %s than in the first subsample: F-statistic =%8.4f and p-value =%8.4f""" % (ordering, fval, fpval) return fval, fpval, ordering, res return fval, fpval, ordering class HetGoldfeldQuandt(object): """ Test whether variance is the same in 2 subsamples .. deprecated:: 0.11 HetGoldfeldQuandt is deprecated in favor of het_goldfeldquandt. HetGoldfeldQuandt will be removed after 0.12. See Also -------- het_goldfeldquant Goldfeld-Quant heteroskedasticity test. """ def __init__(self): import warnings warnings.warn("HetGoldfeldQuandt is deprecated in favor of" "het_goldfeldquandt. HetGoldfeldQuandt will be removed" "after 0.12.", FutureWarning) self.fval = self.fpval = self.df_fval = self.resols1 = None self.resols2 = self.ordering = self.split = self._str = None def run(self, y, x, idx=None, split=None, drop=None, alternative="increasing", attach=True): """ .. deprecated:: 0.11 Use het_goldfeldquant instead. See Also -------- het_goldfeldquant Goldfeld-Quant heteroskedasticity test. """ res = het_goldfeldquandt(y, x, idx=idx, split=split, drop=drop, alternative=alternative, store=attach) if attach: store = res[-1] self.__doc__ = store.__doc__ self.fval = store.fval self.fpval = store.fpval self.df_fval = store.df_fval self.resols1 = store.resols1 self.resols2 = store.resols2 self.ordering = store.ordering self.split = store.split return res[:3] def __call__(self, y, x, idx=None, split=None, drop=None, alternative="increasing"): return self.run(y, x, idx=idx, split=split, drop=drop, attach=False, alternative=alternative) @deprecate_kwarg("result", "res") def linear_reset(res, power=3, test_type="fitted", use_f=False, cov_type="nonrobust", cov_kwargs=None): r""" Ramsey's RESET test for neglected nonlinearity Parameters ---------- res : RegressionResults A results instance from a linear regression. power : {int, List[int]}, default 3 The maximum power to include in the model, if an integer. Includes powers 2, 3, ..., power. If an list of integers, includes all powers in the list. test_type : str, default "fitted" The type of augmentation to use: * "fitted" : (default) Augment regressors with powers of fitted values. * "exog" : Augment exog with powers of exog. Excludes binary regressors. * "princomp": Augment exog with powers of first principal component of exog. use_f : bool, default False Flag indicating whether an F-test should be used (True) or a chi-square test (False). cov_type : str, default "nonrobust Covariance type. The default is "nonrobust` which uses the classic OLS covariance estimator. Specify one of "HC0", "HC1", "HC2", "HC3" to use White's covariance estimator. All covariance types supported by ``OLS.fit`` are accepted. cov_kwargs : dict, default None Dictionary of covariance options passed to ``OLS.fit``. See OLS.fit for more details. Returns ------- ContrastResults Test results for Ramsey's Reset test. See notes for implementation details. Notes ----- The RESET test uses an augmented regression of the form .. math:: Y = X\beta + Z\gamma + \epsilon where :math:`Z` are a set of regressors that are one of: * Powers of :math:`X\hat{\beta}` from the original regression. * Powers of :math:`X`, excluding the constant and binary regressors. * Powers of the first principal component of :math:`X`. If the model includes a constant, this column is dropped before computing the principal component. In either case, the principal component is extracted from the correlation matrix of remaining columns. The test is a Wald test of the null :math:`H_0:\gamma=0`. If use_f is True, then the quadratic-form test statistic is divided by the number of restrictions and the F distribution is used to compute the critical value. """ if not isinstance(res, RegressionResultsWrapper): raise TypeError("result must come from a linear regression model") if bool(res.model.k_constant) and res.model.exog.shape[1] == 1: raise ValueError("exog contains only a constant column. The RESET " "test requires exog to have at least 1 " "non-constant column.") test_type = string_like(test_type, "test_type", options=("fitted", "exog", "princomp")) cov_kwargs = dict_like(cov_kwargs, "cov_kwargs", optional=True) use_f = bool_like(use_f, "use_f") if isinstance(power, int): if power < 2: raise ValueError("power must be >= 2") power = np.arange(2, power + 1, dtype=int) else: try: power = np.array(power, dtype=int) except Exception: raise ValueError("power must be an integer or list of integers") if power.ndim != 1 or len(set(power)) != power.shape[0] or \ (power < 2).any(): raise ValueError("power must contains distinct integers all >= 2") exog = res.model.exog if test_type == "fitted": aug = res.fittedvalues[:, None] elif test_type == "exog": # Remove constant and binary aug = res.model.exog binary = ((exog == exog.max(axis=0)) | (exog == exog.min(axis=0))) binary = binary.all(axis=0) if binary.all(): raise ValueError("Model contains only constant or binary data") aug = aug[:, ~binary] else: from statsmodels.multivariate.pca import PCA aug = exog if res.k_constant: retain = np.arange(aug.shape[1]).tolist() retain.pop(int(res.model.data.const_idx)) aug = aug[:, retain] pca = PCA(aug, ncomp=1, standardize=bool(res.k_constant), demean=bool(res.k_constant), method="nipals") aug = pca.factors[:, :1] aug_exog = np.hstack([exog] + [aug ** p for p in power]) mod_class = res.model.__class__ mod = mod_class(res.model.data.endog, aug_exog) cov_kwargs = {} if cov_kwargs is None else cov_kwargs res = mod.fit(cov_type=cov_type, cov_kwargs=cov_kwargs) nrestr = aug_exog.shape[1] - exog.shape[1] nparams = aug_exog.shape[1] r_mat = np.eye(nrestr, nparams, k=nparams-nrestr) return res.wald_test(r_mat, use_f=use_f) def linear_harvey_collier(res, order_by=None, skip=None): """ Harvey Collier test for linearity The Null hypothesis is that the regression is correctly modeled as linear. Parameters ---------- res : RegressionResults A results instance from a linear regression. order_by : array_like, default None Integer array specifying the order of the residuals. If not provided, the order of the residuals is not changed. If provided, must have the same number of observations as the endogenous variable. skip : int, default None The number of observations to use for initial OLS, if None then skip is set equal to the number of regressors (columns in exog). Returns ------- tvalue : float The test statistic, based on ttest_1sample. pvalue : float The pvalue of the test. See Also -------- statsmodels.stats.diadnostic.recursive_olsresiduals Recursive OLS residual calculation used in the test. Notes ----- This test is a t-test that the mean of the recursive ols residuals is zero. Calculating the recursive residuals might take some time for large samples. """ # I think this has different ddof than # B.H. Baltagi, Econometrics, 2011, chapter 8 # but it matches Gretl and R:lmtest, pvalue at decimal=13 rr = recursive_olsresiduals(res, skip=skip, alpha=0.95, order_by=order_by) return stats.ttest_1samp(rr[3][3:], 0) def linear_rainbow(res, frac=0.5, order_by=None, use_distance=False, center=None): """ Rainbow test for linearity The null hypothesis is the fit of the model using full sample is the same as using a central subset. The alternative is that the fits are difference. The rainbow test has power against many different forms of nonlinearity. Parameters ---------- res : RegressionResults A results instance from a linear regression. frac : float, default 0.5 The fraction of the data to include in the center model. order_by : {ndarray, str, List[str]}, default None If an ndarray, the values in the array are used to sort the observations. If a string or a list of strings, these are interpreted as column name(s) which are then used to lexicographically sort the data. use_distance : bool, default False Flag indicating whether data should be ordered by the Mahalanobis distance to the center. center : {float, int}, default None If a float, the value must be in [0, 1] and the center is center * nobs of the ordered data. If an integer, must be in [0, nobs) and is interpreted as the observation of the ordered data to use. Returns ------- fstat : float The test statistic based on the F test. pvalue : float The pvalue of the test. Notes ----- This test assumes residuals are homoskedastic and may reject a correct linear specification if the residuals are heteroskedastic. """ if not isinstance(res, RegressionResultsWrapper): raise TypeError("res must be a results instance from a linear model.") frac = float_like(frac, "frac") use_distance = bool_like(use_distance, "use_distance") nobs = res.nobs endog = res.model.endog exog = res.model.exog if order_by is not None and use_distance: raise ValueError("order_by and use_distance cannot be simultaneously" "used.") if order_by is not None: if isinstance(order_by, np.ndarray): order_by = array_like(order_by, "order_by", ndim=1, dtype="int") else: if isinstance(order_by, str): order_by = [order_by] try: cols = res.model.data.orig_exog[order_by].copy() except (IndexError, KeyError): raise TypeError("order_by must contain valid column names " "from the exog data used to construct res," "and exog must be a pandas DataFrame.") name = "__index__" while name in cols: name += '_' cols[name] = np.arange(cols.shape[0]) cols = cols.sort_values(order_by) order_by = np.asarray(cols[name]) endog = endog[order_by] exog = exog[order_by] if use_distance: center = int(nobs) // 2 if center is None else center if isinstance(center, float): if not 0.0 <= center <= 1.0: raise ValueError("center must be in (0, 1) when a float.") center = int(center * (nobs-1)) else: center = int_like(center, "center") if not 0 < center < nobs - 1: raise ValueError("center must be in [0, nobs) when an int.") center_obs = exog[center:center+1] from scipy.spatial.distance import cdist try: err = exog - center_obs vi = np.linalg.inv(err.T @ err / nobs) except np.linalg.LinAlgError: err = exog - exog.mean(0) vi = np.linalg.inv(err.T @ err / nobs) dist = cdist(exog, center_obs, metric='mahalanobis', VI=vi) idx = np.argsort(dist.ravel()) endog = endog[idx] exog = exog[idx] lowidx = np.ceil(0.5 * (1 - frac) * nobs).astype(int) uppidx = np.floor(lowidx + frac * nobs).astype(int) if uppidx - lowidx < exog.shape[1]: raise ValueError("frac is too small to perform test. frac * nobs" "must be greater than the number of exogenous" "variables in the model.") mi_sl = slice(lowidx, uppidx) res_mi = OLS(endog[mi_sl], exog[mi_sl]).fit() nobs_mi = res_mi.model.endog.shape[0] ss_mi = res_mi.ssr ss = res.ssr fstat = (ss - ss_mi) / (nobs - nobs_mi) / ss_mi * res_mi.df_resid pval = stats.f.sf(fstat, nobs - nobs_mi, res_mi.df_resid) return fstat, pval def linear_lm(resid, exog, func=None): """ Lagrange multiplier test for linearity against functional alternative # TODO: Remove the restriction limitations: Assumes currently that the first column is integer. Currently it does not check whether the transformed variables contain NaNs, for example log of negative number. Parameters ---------- resid : ndarray residuals of a regression exog : ndarray exogenous variables for which linearity is tested func : callable, default None If func is None, then squares are used. func needs to take an array of exog and return an array of transformed variables. Returns ------- lm : float Lagrange multiplier test statistic lm_pval : float p-value of Lagrange multiplier tes ftest : ContrastResult instance the results from the F test variant of this test Notes ----- Written to match Gretl's linearity test. The test runs an auxiliary regression of the residuals on the combined original and transformed regressors. The Null hypothesis is that the linear specification is correct. """ if func is None: def func(x): return np.power(x, 2) exog_aux = np.column_stack((exog, func(exog[:, 1:]))) nobs, k_vars = exog.shape ls = OLS(resid, exog_aux).fit() ftest = ls.f_test(np.eye(k_vars - 1, k_vars * 2 - 1, k_vars)) lm = nobs * ls.rsquared lm_pval = stats.chi2.sf(lm, k_vars - 1) return lm, lm_pval, ftest def spec_white(resid, exog): """ White's Two-Moment Specification Test Parameters ---------- resid : array_like OLS residuals. exog : array_like OLS design matrix. Returns ------- stat : float The test statistic. pval : float A chi-square p-value for test statistic. dof : int The degrees of freedom. See Also -------- het_white White's test for heteroskedasticity. Notes ----- Implements the two-moment specification test described by White's Theorem 2 (1980, p. 823) which compares the standard OLS covariance estimator with White's heteroscedasticity-consistent estimator. The test statistic is shown to be chi-square distributed. Null hypothesis is homoscedastic and correctly specified. Assumes the OLS design matrix contains an intercept term and at least one variable. The intercept is removed to calculate the test statistic. Interaction terms (squares and crosses of OLS regressors) are added to the design matrix to calculate the test statistic. Degrees-of-freedom (full rank) = nvar + nvar * (nvar + 1) / 2 Linearly dependent columns are removed to avoid singular matrix error. References ---------- .. [*] White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroscedasticity. Econometrica, 48: 817-838. """ x = array_like(exog, "exog", ndim=2) e = array_like(resid, "resid", ndim=1) if x.shape[1] < 2 or not np.any(np.ptp(x, 0) == 0.0): raise ValueError("White's specification test requires at least two" "columns where one is a constant.") # add interaction terms i0, i1 = np.triu_indices(x.shape[1]) exog = np.delete(x[:, i0] * x[:, i1], 0, 1) # collinearity check - see _fit_collinear atol = 1e-14 rtol = 1e-13 tol = atol + rtol * exog.var(0) r = np.linalg.qr(exog, mode="r") mask = np.abs(r.diagonal()) < np.sqrt(tol) exog = exog[:, np.where(~mask)[0]] # calculate test statistic sqe = e * e sqmndevs = sqe - np.mean(sqe) d = np.dot(exog.T, sqmndevs) devx = exog - np.mean(exog, axis=0) devx *= sqmndevs[:, None] b = devx.T.dot(devx) stat = d.dot(np.linalg.solve(b, d)) # chi-square test dof = devx.shape[1] pval = stats.chi2.sf(stat, dof) return stat, pval, dof @deprecate_kwarg("olsresults", "res") def recursive_olsresiduals(res, skip=None, lamda=0.0, alpha=0.95, order_by=None): """ Calculate recursive ols with residuals and Cusum test statistic Parameters ---------- res : RegressionResults Results from estimation of a regression model. skip : int, default None The number of observations to use for initial OLS, if None then skip is set equal to the number of regressors (columns in exog). lamda : float, default 0.0 The weight for Ridge correction to initial (X'X)^{-1}. alpha : {0.90, 0.95, 0.99}, default 0.95 Confidence level of test, currently only two values supported, used for confidence interval in cusum graph. order_by : array_like, default None Integer array specifying the order of the residuals. If not provided, the order of the residuals is not changed. If provided, must have the same number of observations as the endogenous variable. Returns ------- rresid : ndarray The recursive ols residuals. rparams : ndarray The recursive ols parameter estimates. rypred : ndarray The recursive prediction of endogenous variable. rresid_standardized : ndarray The recursive residuals standardized so that N(0,sigma2) distributed, where sigma2 is the error variance. rresid_scaled : ndarray The recursive residuals normalize so that N(0,1) distributed. rcusum : ndarray The cumulative residuals for cusum test. rcusumci : ndarray The confidence interval for cusum test using a size of alpha. Notes ----- It produces same recursive residuals as other version. This version updates the inverse of the X'X matrix and does not require matrix inversion during updating. looks efficient but no timing Confidence interval in Greene and Brown, Durbin and Evans is the same as in Ploberger after a little bit of algebra. References ---------- jplv to check formulas, follows Harvey BigJudge 5.5.2b for formula for inverse(X'X) updating Greene section 7.5.2 Brown, R. L., J. Durbin, and J. M. Evans. “Techniques for Testing the Constancy of Regression Relationships over Time.†Journal of the Royal Statistical Society. Series B (Methodological) 37, no. 2 (1975): 149-192. """ y = res.model.endog x = res.model.exog order_by = array_like(order_by, "order_by", dtype="int", optional=True, ndim=1, shape=(y.shape[0],)) # intialize with skip observations if order_by is not None: x = x[order_by] y = y[order_by] nobs, nvars = x.shape if skip is None: skip = nvars rparams = np.nan * np.zeros((nobs, nvars)) rresid = np.nan * np.zeros(nobs) rypred = np.nan * np.zeros(nobs) rvarraw = np.nan * np.zeros(nobs) x0 = x[:skip] if np.linalg.matrix_rank(x0) < x0.shape[1]: err_msg = """\ "The initial regressor matrix, x[:skip], issingular. You must use a value of skip large enough to ensure that the first OLS estimator is well-defined. """ raise ValueError(err_msg) y0 = y[:skip] # add Ridge to start (not in jplv) xtxi = np.linalg.inv(np.dot(x0.T, x0) + lamda * np.eye(nvars)) xty = np.dot(x0.T, y0) # xi * y #np.dot(xi, y) beta = np.dot(xtxi, xty) rparams[skip - 1] = beta yipred = np.dot(x[skip - 1], beta) rypred[skip - 1] = yipred rresid[skip - 1] = y[skip - 1] - yipred rvarraw[skip - 1] = 1 + np.dot(x[skip - 1], np.dot(xtxi, x[skip - 1])) for i in range(skip, nobs): xi = x[i:i + 1, :] yi = y[i] # get prediction error with previous beta yipred = np.dot(xi, beta) rypred[i] = yipred residi = yi - yipred rresid[i] = residi # update beta and inverse(X'X) tmp = np.dot(xtxi, xi.T) ft = 1 + np.dot(xi, tmp) xtxi = xtxi - np.dot(tmp, tmp.T) / ft # BigJudge equ 5.5.15 beta = beta + (tmp * residi / ft).ravel() # BigJudge equ 5.5.14 rparams[i] = beta rvarraw[i] = ft rresid_scaled = rresid / np.sqrt(rvarraw) # N(0,sigma2) distributed nrr = nobs - skip # sigma2 = rresid_scaled[skip-1:].var(ddof=1) #var or sum of squares ? # Greene has var, jplv and Ploberger have sum of squares (Ass.:mean=0) # Gretl uses: by reverse engineering matching their numbers sigma2 = rresid_scaled[skip:].var(ddof=1) rresid_standardized = rresid_scaled / np.sqrt(sigma2) # N(0,1) distributed rcusum = rresid_standardized[skip - 1:].cumsum() # confidence interval points in Greene p136 looks strange. Cleared up # this assumes sum of independent standard normal, which does not take into # account that we make many tests at the same time if alpha == 0.90: a = 0.850 elif alpha == 0.95: a = 0.948 elif alpha == 0.99: a = 1.143 else: raise ValueError("alpha can only be 0.9, 0.95 or 0.99") # following taken from Ploberger, # crit = a * np.sqrt(nrr) rcusumci = (a * np.sqrt(nrr) + 2 * a * np.arange(0, nobs - skip) / np.sqrt( nrr)) * np.array([[-1.], [+1.]]) return (rresid, rparams, rypred, rresid_standardized, rresid_scaled, rcusum, rcusumci) def breaks_hansen(olsresults): """ Test for model stability, breaks in parameters for ols, Hansen 1992 Parameters ---------- olsresults : RegressionResults Results from estimation of a regression model. Returns ------- teststat : float Hansen's test statistic. crit : ndarray The critical values at alpha=0.95 for different nvars. Notes ----- looks good in example, maybe not very powerful for small changes in parameters According to Greene, distribution of test statistics depends on nvar but not on nobs. Test statistic is verified against R:strucchange References ---------- Greene section 7.5.1, notation follows Greene """ x = olsresults.model.exog resid = array_like(olsresults.resid, "resid", shape=(x.shape[0], 1)) nobs, nvars = x.shape resid2 = resid ** 2 ft = np.c_[x * resid[:, None], (resid2 - resid2.mean())] score = ft.cumsum(0) f = nobs * (ft[:, :, None] * ft[:, None, :]).sum(0) s = (score[:, :, None] * score[:, None, :]).sum(0) h = np.trace(np.dot(np.linalg.inv(f), s)) crit95 = np.array([(2, 1.9), (6, 3.75), (15, 3.75), (19, 4.52)], dtype=[("nobs", int), ("crit", float)]) # TODO: get critical values from Bruce Hansen's 1992 paper return h, crit95 def breaks_cusumolsresid(resid, ddof=0): """ Cusum test for parameter stability based on ols residuals. Parameters ---------- resid : ndarray An array of residuals from an OLS estimation. ddof : int The number of parameters in the OLS estimation, used as degrees of freedom correction for error variance. Returns ------- sup_b : float The test statistic, maximum of absolute value of scaled cumulative OLS residuals. pval : float Probability of observing the data under the null hypothesis of no structural change, based on asymptotic distribution which is a Brownian Bridge crit: list The tabulated critical values, for alpha = 1%, 5% and 10%. Notes ----- Tested against R:structchange. Not clear: Assumption 2 in Ploberger, Kramer assumes that exog x have asymptotically zero mean, x.mean(0) = [1, 0, 0, ..., 0] Is this really necessary? I do not see how it can affect the test statistic under the null. It does make a difference under the alternative. Also, the asymptotic distribution of test statistic depends on this. From examples it looks like there is little power for standard cusum if exog (other than constant) have mean zero. References ---------- Ploberger, Werner, and Walter Kramer. “The Cusum Test with OLS Residuals.†Econometrica 60, no. 2 (March 1992): 271-285. """ resid = resid.ravel() nobs = len(resid) nobssigma2 = (resid ** 2).sum() if ddof > 0: nobssigma2 = nobssigma2 / (nobs - ddof) * nobs # b is asymptotically a Brownian Bridge b = resid.cumsum() / np.sqrt(nobssigma2) # use T*sigma directly # asymptotically distributed as standard Brownian Bridge sup_b = np.abs(b).max() crit = [(1, 1.63), (5, 1.36), (10, 1.22)] # Note stats.kstwobign.isf(0.1) is distribution of sup.abs of Brownian # Bridge # >>> stats.kstwobign.isf([0.01,0.05,0.1]) # array([ 1.62762361, 1.35809864, 1.22384787]) pval = stats.kstwobign.sf(sup_b) return sup_b, pval, crit # def breaks_cusum(recolsresid): # """renormalized cusum test for parameter stability based on recursive # residuals # # # still incorrect: in PK, the normalization for sigma is by T not T-K # also the test statistic is asymptotically a Wiener Process, Brownian # motion # not Brownian Bridge # for testing: result reject should be identical as in standard cusum # version # # References # ---------- # Ploberger, Werner, and Walter Kramer. “The Cusum Test with OLS Residuals.†# Econometrica 60, no. 2 (March 1992): 271-285. # # """ # resid = recolsresid.ravel() # nobssigma2 = (resid**2).sum() # #B is asymptotically a Brownian Bridge # B = resid.cumsum()/np.sqrt(nobssigma2) # use T*sigma directly # nobs = len(resid) # denom = 1. + 2. * np.arange(nobs)/(nobs-1.) #not sure about limits # sup_b = np.abs(B/denom).max() # #asymptotically distributed as standard Brownian Bridge # crit = [(1,1.63), (5, 1.36), (10, 1.22)] # #Note stats.kstwobign.isf(0.1) is distribution of sup.abs of Brownian # Bridge # #>>> stats.kstwobign.isf([0.01,0.05,0.1]) # #array([ 1.62762361, 1.35809864, 1.22384787]) # pval = stats.kstwobign.sf(sup_b) # return sup_b, pval, crit statsmodels-0.12.2/statsmodels/stats/dist_dependence_measures.py000066400000000000000000000424241400612667500252460ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Distance dependence measure and the dCov test. Implementation of Székely et al. (2007) calculation of distance dependence statistics, including the Distance covariance (dCov) test for independence of random vectors of arbitrary length. Author: Ron Itzikovitch References ---------- .. Szekely, G.J., Rizzo, M.L., and Bakirov, N.K. (2007) "Measuring and testing dependence by correlation of distances". Annals of Statistics, Vol. 35 No. 6, pp. 2769-2794. """ from collections import namedtuple import warnings import numpy as np from scipy.spatial.distance import pdist, squareform from scipy.stats import norm from statsmodels.tools.sm_exceptions import HypothesisTestWarning DistDependStat = namedtuple( "DistDependStat", ["test_statistic", "distance_correlation", "distance_covariance", "dvar_x", "dvar_y", "S"], ) def distance_covariance_test(x, y, B=None, method="auto"): r"""The Distance Covariance (dCov) test Apply the Distance Covariance (dCov) test of independence to `x` and `y`. This test was introduced in [1]_, and is based on the distance covariance statistic. The test is applicable to random vectors of arbitrary length (see the notes section for more details). Parameters ---------- x : array_like, 1-D or 2-D If `x` is 1-D than it is assumed to be a vector of observations of a single random variable. If `x` is 2-D than the rows should be observations and the columns are treated as the components of a random vector, i.e., each column represents a different component of the random vector `x`. y : array_like, 1-D or 2-D Same as `x`, but only the number of observation has to match that of `x`. If `y` is 2-D note that the number of columns of `y` (i.e., the number of components in the random vector) does not need to match the number of columns in `x`. B : int, optional, default=`None` The number of iterations to perform when evaluating the null distribution of the test statistic when the `emp` method is applied (see below). if `B` is `None` than as in [1]_ we set `B` to be ``B = 200 + 5000/n``, where `n` is the number of observations. method : {'auto', 'emp', 'asym'}, optional, default=auto The method by which to obtain the p-value for the test. - `auto` : Default method. The number of observations will be used to determine the method. - `emp` : Empirical evaluation of the p-value using permutations of the rows of `y` to obtain the null distribution. - `asym` : An asymptotic approximation of the distribution of the test statistic is used to find the p-value. Returns ------- test_statistic : float The value of the test statistic used in the test. pval : float The p-value. chosen_method : str The method that was used to obtain the p-value. Mostly relevant when the function is called with `method='auto'`. Notes ----- The test applies to random vectors of arbitrary dimensions, i.e., `x` can be a 1-D vector of observations for a single random variable while `y` can be a `k` by `n` 2-D array (where `k > 1`). In other words, it is also possible for `x` and `y` to both be 2-D arrays and have the same number of rows (observations) while differing in the number of columns. As noted in [1]_ the statistics are sensitive to all types of departures from independence, including nonlinear or nonmonotone dependence structure. References ---------- .. [1] Szekely, G.J., Rizzo, M.L., and Bakirov, N.K. (2007) "Measuring and testing by correlation of distances". Annals of Statistics, Vol. 35 No. 6, pp. 2769-2794. Examples -------- >>> from statsmodels.stats.dist_dependence_measures import ... distance_covariance_test >>> data = np.random.rand(1000, 10) >>> x, y = data[:, :3], data[:, 3:] >>> x.shape (1000, 3) >>> y.shape (1000, 7) >>> distance_covariance_test(x, y) (1.0426404792714983, 0.2971148340813543, 'asym') # (test_statistic, pval, chosen_method) """ x, y = _validate_and_tranform_x_and_y(x, y) n = x.shape[0] stats = distance_statistics(x, y) if method == "auto" and n <= 500 or method == "emp": chosen_method = "emp" test_statistic, pval = _empirical_pvalue(x, y, B, n, stats) elif method == "auto" and n > 500 or method == "asym": chosen_method = "asym" test_statistic, pval = _asymptotic_pvalue(stats) else: raise ValueError("Unknown 'method' parameter: {}".format(method)) # In case we got an extreme p-value (0 or 1) when using the empirical # distribution of the test statistic under the null, we fall back # to the asymptotic approximation. if chosen_method == "emp" and pval in [0, 1]: msg = ( f"p-value was {pval} when using the empirical method. " "The asymptotic approximation will be used instead" ) warnings.warn(msg, HypothesisTestWarning) _, pval = _asymptotic_pvalue(stats) return test_statistic, pval, chosen_method def _validate_and_tranform_x_and_y(x, y): r"""Ensure `x` and `y` have proper shape and transform/reshape them if required. Parameters ---------- x : array_like, 1-D or 2-D If `x` is 1-D than it is assumed to be a vector of observations of a single random variable. If `x` is 2-D than the rows should be observations and the columns are treated as the components of a random vector, i.e., each column represents a different component of the random vector `x`. y : array_like, 1-D or 2-D Same as `x`, but only the number of observation has to match that of `x`. If `y` is 2-D note that the number of columns of `y` (i.e., the number of components in the random vector) does not need to match the number of columns in `x`. Returns ------- x : array_like, 1-D or 2-D y : array_like, 1-D or 2-D Raises ------ ValueError If `x` and `y` have a different number of observations. """ x = np.asanyarray(x) y = np.asanyarray(y) if x.shape[0] != y.shape[0]: raise ValueError( "x and y must have the same number of observations (rows)." ) if len(x.shape) == 1: x = x.reshape((x.shape[0], 1)) if len(y.shape) == 1: y = y.reshape((y.shape[0], 1)) return x, y def _empirical_pvalue(x, y, B, n, stats): r"""Calculate the empirical p-value based on permutations of `y`'s rows Parameters ---------- x : array_like, 1-D or 2-D If `x` is 1-D than it is assumed to be a vector of observations of a single random variable. If `x` is 2-D than the rows should be observations and the columns are treated as the components of a random vector, i.e., each column represents a different component of the random vector `x`. y : array_like, 1-D or 2-D Same as `x`, but only the number of observation has to match that of `x`. If `y` is 2-D note that the number of columns of `y` (i.e., the number of components in the random vector) does not need to match the number of columns in `x`. B : int The number of iterations when evaluating the null distribution. n : Number of observations found in each of `x` and `y`. stats: namedtuple The result obtained from calling ``distance_statistics(x, y)``. Returns ------- test_statistic : float The empirical test statistic. pval : float The empirical p-value. """ B = int(B) if B else int(np.floor(200 + 5000 / n)) empirical_dist = _get_test_statistic_distribution(x, y, B) pval = 1 - np.searchsorted( sorted(empirical_dist), stats.test_statistic ) / len(empirical_dist) test_statistic = stats.test_statistic return test_statistic, pval def _asymptotic_pvalue(stats): r"""Calculate the p-value based on an approximation of the distribution of the test statistic under the null. Parameters ---------- stats: namedtuple The result obtained from calling ``distance_statistics(x, y)``. Returns ------- test_statistic : float The test statistic. pval : float The asymptotic p-value. """ test_statistic = np.sqrt(stats.test_statistic / stats.S) pval = (1 - norm.cdf(test_statistic)) * 2 return test_statistic, pval def _get_test_statistic_distribution(x, y, B): r""" Parameters ---------- x : array_like, 1-D or 2-D If `x` is 1-D than it is assumed to be a vector of observations of a single random variable. If `x` is 2-D than the rows should be observations and the columns are treated as the components of a random vector, i.e., each column represents a different component of the random vector `x`. y : array_like, 1-D or 2-D Same as `x`, but only the number of observation has to match that of `x`. If `y` is 2-D note that the number of columns of `y` (i.e., the number of components in the random vector) does not need to match the number of columns in `x`. B : int The number of iterations to perform when evaluating the null distribution. Returns ------- emp_dist : array_like The empirical distribution of the test statistic. """ y = y.copy() emp_dist = np.zeros(B) x_dist = squareform(pdist(x, "euclidean")) for i in range(B): np.random.shuffle(y) emp_dist[i] = distance_statistics(x, y, x_dist=x_dist).test_statistic return emp_dist def distance_statistics(x, y, x_dist=None, y_dist=None): r"""Calculate various distance dependence statistics. Calculate several distance dependence statistics as described in [1]_. Parameters ---------- x : array_like, 1-D or 2-D If `x` is 1-D than it is assumed to be a vector of observations of a single random variable. If `x` is 2-D than the rows should be observations and the columns are treated as the components of a random vector, i.e., each column represents a different component of the random vector `x`. y : array_like, 1-D or 2-D Same as `x`, but only the number of observation has to match that of `x`. If `y` is 2-D note that the number of columns of `y` (i.e., the number of components in the random vector) does not need to match the number of columns in `x`. x_dist : array_like, 2-D, optional A square 2-D array_like object whose values are the euclidean distances between `x`'s rows. y_dist : array_like, 2-D, optional A square 2-D array_like object whose values are the euclidean distances between `y`'s rows. Returns ------- namedtuple A named tuple of distance dependence statistics (DistDependStat) with the following values: - test_statistic : float - The "basic" test statistic (i.e., the one used when the `emp` method is chosen when calling ``distance_covariance_test()`` - distance_correlation : float - The distance correlation between `x` and `y`. - distance_covariance : float - The distance covariance of `x` and `y`. - dvar_x : float - The distance variance of `x`. - dvar_y : float - The distance variance of `y`. - S : float - The mean of the euclidean distances in `x` multiplied by those of `y`. Mostly used internally. References ---------- .. [1] Szekely, G.J., Rizzo, M.L., and Bakirov, N.K. (2007) "Measuring and testing dependence by correlation of distances". Annals of Statistics, Vol. 35 No. 6, pp. 2769-2794. Examples -------- >>> from statsmodels.stats.dist_dependence_measures import ... distance_statistics >>> distance_statistics(np.random.random(1000), np.random.random(1000)) DistDependStat(test_statistic=0.07948284320205831, distance_correlation=0.04269511890990793, distance_covariance=0.008915315092696293, dvar_x=0.20719027438266704, dvar_y=0.21044934264957588, S=0.10892061635588891) """ x, y = _validate_and_tranform_x_and_y(x, y) n = x.shape[0] a = x_dist if x_dist is not None else squareform(pdist(x, "euclidean")) b = y_dist if y_dist is not None else squareform(pdist(y, "euclidean")) a_row_means = a.mean(axis=0, keepdims=True) b_row_means = b.mean(axis=0, keepdims=True) a_col_means = a.mean(axis=1, keepdims=True) b_col_means = b.mean(axis=1, keepdims=True) a_mean = a.mean() b_mean = b.mean() A = a - a_row_means - a_col_means + a_mean B = b - b_row_means - b_col_means + b_mean S = a_mean * b_mean dcov = np.sqrt(np.multiply(A, B).mean()) dvar_x = np.sqrt(np.multiply(A, A).mean()) dvar_y = np.sqrt(np.multiply(B, B).mean()) dcor = dcov / np.sqrt(dvar_x * dvar_y) test_statistic = n * dcov ** 2 return DistDependStat( test_statistic=test_statistic, distance_correlation=dcor, distance_covariance=dcov, dvar_x=dvar_x, dvar_y=dvar_y, S=S, ) def distance_covariance(x, y): r"""Distance covariance. Calculate the empirical distance covariance as described in [1]_. Parameters ---------- x : array_like, 1-D or 2-D If `x` is 1-D than it is assumed to be a vector of observations of a single random variable. If `x` is 2-D than the rows should be observations and the columns are treated as the components of a random vector, i.e., each column represents a different component of the random vector `x`. y : array_like, 1-D or 2-D Same as `x`, but only the number of observation has to match that of `x`. If `y` is 2-D note that the number of columns of `y` (i.e., the number of components in the random vector) does not need to match the number of columns in `x`. Returns ------- float The empirical distance covariance between `x` and `y`. References ---------- .. [1] Szekely, G.J., Rizzo, M.L., and Bakirov, N.K. (2007) "Measuring and testing dependence by correlation of distances". Annals of Statistics, Vol. 35 No. 6, pp. 2769-2794. Examples -------- >>> from statsmodels.stats.dist_dependence_measures import ... distance_covariance >>> distance_covariance(np.random.random(1000), np.random.random(1000)) 0.007575063951951362 """ return distance_statistics(x, y).distance_covariance def distance_variance(x): r"""Distance variance. Calculate the empirical distance variance as described in [1]_. Parameters ---------- x : array_like, 1-D or 2-D If `x` is 1-D than it is assumed to be a vector of observations of a single random variable. If `x` is 2-D than the rows should be observations and the columns are treated as the components of a random vector, i.e., each column represents a different component of the random vector `x`. Returns ------- float The empirical distance variance of `x`. References ---------- .. [1] Szekely, G.J., Rizzo, M.L., and Bakirov, N.K. (2007) "Measuring and testing dependence by correlation of distances". Annals of Statistics, Vol. 35 No. 6, pp. 2769-2794. Examples -------- >>> from statsmodels.stats.dist_dependence_measures import ... distance_variance >>> distance_variance(np.random.random(1000)) 0.21732609190659702 """ return distance_covariance(x, x) def distance_correlation(x, y): r"""Distance correlation. Calculate the empirical distance correlation as described in [1]_. This statistic is analogous to product-moment correlation and describes the dependence between `x` and `y`, which are random vectors of arbitrary length. The statistics' values range between 0 (implies independence) and 1 (implies complete dependence). Parameters ---------- x : array_like, 1-D or 2-D If `x` is 1-D than it is assumed to be a vector of observations of a single random variable. If `x` is 2-D than the rows should be observations and the columns are treated as the components of a random vector, i.e., each column represents a different component of the random vector `x`. y : array_like, 1-D or 2-D Same as `x`, but only the number of observation has to match that of `x`. If `y` is 2-D note that the number of columns of `y` (i.e., the number of components in the random vector) does not need to match the number of columns in `x`. Returns ------- float The empirical distance correlation between `x` and `y`. References ---------- .. [1] Szekely, G.J., Rizzo, M.L., and Bakirov, N.K. (2007) "Measuring and testing dependence by correlation of distances". Annals of Statistics, Vol. 35 No. 6, pp. 2769-2794. Examples -------- >>> from statsmodels.stats.dist_dependence_measures import ... distance_correlation >>> distance_correlation(np.random.random(1000), np.random.random(1000)) 0.04060497840149489 """ return distance_statistics(x, y).distance_correlation statsmodels-0.12.2/statsmodels/stats/gof.py000066400000000000000000000403341400612667500207760ustar00rootroot00000000000000'''extra statistical function and helper functions contains: * goodness-of-fit tests - powerdiscrepancy - gof_chisquare_discrete - gof_binning_discrete Author: Josef Perktold License : BSD-3 changes ------- 2013-02-25 : add chisquare_power, effectsize and "value" ''' from statsmodels.compat.python import lrange import numpy as np from scipy import stats # copied from regression/stats.utils def powerdiscrepancy(observed, expected, lambd=0.0, axis=0, ddof=0): r"""Calculates power discrepancy, a class of goodness-of-fit tests as a measure of discrepancy between observed and expected data. This contains several goodness-of-fit tests as special cases, see the description of lambd, the exponent of the power discrepancy. The pvalue is based on the asymptotic chi-square distribution of the test statistic. freeman_tukey: D(x|\theta) = \sum_j (\sqrt{x_j} - \sqrt{e_j})^2 Parameters ---------- o : Iterable Observed values e : Iterable Expected values lambd : {float, str} * float : exponent `a` for power discrepancy * 'loglikeratio': a = 0 * 'freeman_tukey': a = -0.5 * 'pearson': a = 1 (standard chisquare test statistic) * 'modified_loglikeratio': a = -1 * 'cressie_read': a = 2/3 * 'neyman' : a = -2 (Neyman-modified chisquare, reference from a book?) axis : int axis for observations of one series ddof : int degrees of freedom correction, Returns ------- D_obs : Discrepancy of observed values pvalue : pvalue References ---------- Cressie, Noel and Timothy R. C. Read, Multinomial Goodness-of-Fit Tests, Journal of the Royal Statistical Society. Series B (Methodological), Vol. 46, No. 3 (1984), pp. 440-464 Campbell B. Read: Freeman-Tukey chi-squared goodness-of-fit statistics, Statistics & Probability Letters 18 (1993) 271-278 Nobuhiro Taneichi, Yuri Sekiya, Akio Suzukawa, Asymptotic Approximations for the Distributions of the Multinomial Goodness-of-Fit Statistics under Local Alternatives, Journal of Multivariate Analysis 81, 335?359 (2002) Steele, M. 1,2, C. Hurst 3 and J. Chaseling, Simulated Power of Discrete Goodness-of-Fit Tests for Likert Type Data Examples -------- >>> observed = np.array([ 2., 4., 2., 1., 1.]) >>> expected = np.array([ 0.2, 0.2, 0.2, 0.2, 0.2]) for checking correct dimension with multiple series >>> powerdiscrepancy(np.column_stack((observed,observed)).T, 10*expected, lambd='freeman_tukey',axis=1) (array([[ 2.745166, 2.745166]]), array([[ 0.6013346, 0.6013346]])) >>> powerdiscrepancy(np.column_stack((observed,observed)).T, 10*expected,axis=1) (array([[ 2.77258872, 2.77258872]]), array([[ 0.59657359, 0.59657359]])) >>> powerdiscrepancy(np.column_stack((observed,observed)).T, 10*expected, lambd=0,axis=1) (array([[ 2.77258872, 2.77258872]]), array([[ 0.59657359, 0.59657359]])) >>> powerdiscrepancy(np.column_stack((observed,observed)).T, 10*expected, lambd=1,axis=1) (array([[ 3., 3.]]), array([[ 0.5578254, 0.5578254]])) >>> powerdiscrepancy(np.column_stack((observed,observed)).T, 10*expected, lambd=2/3.0,axis=1) (array([[ 2.89714546, 2.89714546]]), array([[ 0.57518277, 0.57518277]])) >>> powerdiscrepancy(np.column_stack((observed,observed)).T, expected, lambd=2/3.0,axis=1) (array([[ 2.89714546, 2.89714546]]), array([[ 0.57518277, 0.57518277]])) >>> powerdiscrepancy(np.column_stack((observed,observed)), expected, lambd=2/3.0, axis=0) (array([[ 2.89714546, 2.89714546]]), array([[ 0.57518277, 0.57518277]])) each random variable can have different total count/sum >>> powerdiscrepancy(np.column_stack((observed,2*observed)), expected, lambd=2/3.0, axis=0) (array([[ 2.89714546, 5.79429093]]), array([[ 0.57518277, 0.21504648]])) >>> powerdiscrepancy(np.column_stack((observed,2*observed)), expected, lambd=2/3.0, axis=0) (array([[ 2.89714546, 5.79429093]]), array([[ 0.57518277, 0.21504648]])) >>> powerdiscrepancy(np.column_stack((2*observed,2*observed)), expected, lambd=2/3.0, axis=0) (array([[ 5.79429093, 5.79429093]]), array([[ 0.21504648, 0.21504648]])) >>> powerdiscrepancy(np.column_stack((2*observed,2*observed)), 20*expected, lambd=2/3.0, axis=0) (array([[ 5.79429093, 5.79429093]]), array([[ 0.21504648, 0.21504648]])) >>> powerdiscrepancy(np.column_stack((observed,2*observed)), np.column_stack((10*expected,20*expected)), lambd=2/3.0, axis=0) (array([[ 2.89714546, 5.79429093]]), array([[ 0.57518277, 0.21504648]])) >>> powerdiscrepancy(np.column_stack((observed,2*observed)), np.column_stack((10*expected,20*expected)), lambd=-1, axis=0) (array([[ 2.77258872, 5.54517744]]), array([[ 0.59657359, 0.2357868 ]])) """ o = np.array(observed) e = np.array(expected) if not isinstance(lambd, str): a = lambd else: if lambd == 'loglikeratio': a = 0 elif lambd == 'freeman_tukey': a = -0.5 elif lambd == 'pearson': a = 1 elif lambd == 'modified_loglikeratio': a = -1 elif lambd == 'cressie_read': a = 2/3.0 else: raise ValueError('lambd has to be a number or one of ' 'loglikeratio, freeman_tukey, pearson, ' 'modified_loglikeratio or cressie_read') n = np.sum(o, axis=axis) nt = n if n.size>1: n = np.atleast_2d(n) if axis == 1: nt = n.T # need both for 2d, n and nt for broadcasting if e.ndim == 1: e = np.atleast_2d(e) if axis == 0: e = e.T if np.all(np.sum(e, axis=axis) == n): p = e/(1.0*nt) elif np.all(np.sum(e, axis=axis) == 1): p = e e = nt * e else: raise ValueError('observed and expected need to have the same ' 'number of observations, or e needs to add to 1') k = o.shape[axis] if e.shape[axis] != k: raise ValueError('observed and expected need to have the same ' 'number of bins') # Note: taken from formulas, to simplify cancel n if a == 0: # log likelihood ratio D_obs = 2*n * np.sum(o/(1.0*nt) * np.log(o/e), axis=axis) elif a == -1: # modified log likelihood ratio D_obs = 2*n * np.sum(e/(1.0*nt) * np.log(e/o), axis=axis) else: D_obs = 2*n/a/(a+1) * np.sum(o/(1.0*nt) * ((o/e)**a - 1), axis=axis) return D_obs, stats.chi2.sf(D_obs,k-1-ddof) #todo: need also binning for continuous distribution # and separated binning function to be used for powerdiscrepancy def gof_chisquare_discrete(distfn, arg, rvs, alpha, msg): '''perform chisquare test for random sample of a discrete distribution Parameters ---------- distname : str name of distribution function arg : sequence parameters of distribution alpha : float significance level, threshold for p-value Returns ------- result : bool 0 if test passes, 1 if test fails Notes ----- originally written for scipy.stats test suite, still needs to be checked for standalone usage, insufficient input checking may not run yet (after copy/paste) refactor: maybe a class, check returns, or separate binning from test results ''' # define parameters for test ## n=2000 n = len(rvs) nsupp = 20 wsupp = 1.0/nsupp ## distfn = getattr(stats, distname) ## np.random.seed(9765456) ## rvs = distfn.rvs(size=n,*arg) # construct intervals with minimum mass 1/nsupp # intervalls are left-half-open as in a cdf difference distsupport = lrange(max(distfn.a, -1000), min(distfn.b, 1000) + 1) last = 0 distsupp = [max(distfn.a, -1000)] distmass = [] for ii in distsupport: current = distfn.cdf(ii,*arg) if current - last >= wsupp-1e-14: distsupp.append(ii) distmass.append(current - last) last = current if current > (1-wsupp): break if distsupp[-1] < distfn.b: distsupp.append(distfn.b) distmass.append(1-last) distsupp = np.array(distsupp) distmass = np.array(distmass) # convert intervals to right-half-open as required by histogram histsupp = distsupp+1e-8 histsupp[0] = distfn.a # find sample frequencies and perform chisquare test #TODO: move to compatibility.py freq, hsupp = np.histogram(rvs,histsupp) cdfs = distfn.cdf(distsupp,*arg) (chis,pval) = stats.chisquare(np.array(freq),n*distmass) return chis, pval, (pval > alpha), 'chisquare - test for %s' \ 'at arg = %s with pval = %s' % (msg,str(arg),str(pval)) # copy/paste, remove code duplication when it works def gof_binning_discrete(rvs, distfn, arg, nsupp=20): '''get bins for chisquare type gof tests for a discrete distribution Parameters ---------- rvs : ndarray sample data distname : str name of distribution function arg : sequence parameters of distribution nsupp : int number of bins. The algorithm tries to find bins with equal weights. depending on the distribution, the actual number of bins can be smaller. Returns ------- freq : ndarray empirical frequencies for sample; not normalized, adds up to sample size expfreq : ndarray theoretical frequencies according to distribution histsupp : ndarray bin boundaries for histogram, (added 1e-8 for numerical robustness) Notes ----- The results can be used for a chisquare test :: (chis,pval) = stats.chisquare(freq, expfreq) originally written for scipy.stats test suite, still needs to be checked for standalone usage, insufficient input checking may not run yet (after copy/paste) refactor: maybe a class, check returns, or separate binning from test results todo : optimal number of bins ? (check easyfit), recommendation in literature at least 5 expected observations in each bin ''' # define parameters for test ## n=2000 n = len(rvs) wsupp = 1.0/nsupp ## distfn = getattr(stats, distname) ## np.random.seed(9765456) ## rvs = distfn.rvs(size=n,*arg) # construct intervals with minimum mass 1/nsupp # intervalls are left-half-open as in a cdf difference distsupport = lrange(max(distfn.a, -1000), min(distfn.b, 1000) + 1) last = 0 distsupp = [max(distfn.a, -1000)] distmass = [] for ii in distsupport: current = distfn.cdf(ii,*arg) if current - last >= wsupp-1e-14: distsupp.append(ii) distmass.append(current - last) last = current if current > (1-wsupp): break if distsupp[-1] < distfn.b: distsupp.append(distfn.b) distmass.append(1-last) distsupp = np.array(distsupp) distmass = np.array(distmass) # convert intervals to right-half-open as required by histogram histsupp = distsupp+1e-8 histsupp[0] = distfn.a # find sample frequencies and perform chisquare test freq,hsupp = np.histogram(rvs,histsupp) #freq,hsupp = np.histogram(rvs,histsupp,new=True) cdfs = distfn.cdf(distsupp,*arg) return np.array(freq), n*distmass, histsupp # -*- coding: utf-8 -*- """Extension to chisquare goodness-of-fit test Created on Mon Feb 25 13:46:53 2013 Author: Josef Perktold License: BSD-3 """ def chisquare(f_obs, f_exp=None, value=0, ddof=0, return_basic=True): '''chisquare goodness-of-fit test The null hypothesis is that the distance between the expected distribution and the observed frequencies is ``value``. The alternative hypothesis is that the distance is larger than ``value``. ``value`` is normalized in terms of effect size. The standard chisquare test has the null hypothesis that ``value=0``, that is the distributions are the same. Notes ----- The case with value greater than zero is similar to an equivalence test, that the exact null hypothesis is replaced by an approximate hypothesis. However, TOST "reverses" null and alternative hypothesis, while here the alternative hypothesis is that the distance (divergence) is larger than a threshold. References ---------- McLaren, ... Drost,... See Also -------- powerdiscrepancy scipy.stats.chisquare ''' f_obs = np.asarray(f_obs) n_bins = len(f_obs) nobs = f_obs.sum(0) if f_exp is None: # uniform distribution f_exp = np.empty(n_bins, float) f_exp.fill(nobs / float(n_bins)) f_exp = np.asarray(f_exp, float) chisq = ((f_obs - f_exp)**2 / f_exp).sum(0) if value == 0: pvalue = stats.chi2.sf(chisq, n_bins - 1 - ddof) else: pvalue = stats.ncx2.sf(chisq, n_bins - 1 - ddof, value**2 * nobs) if return_basic: return chisq, pvalue else: return chisq, pvalue #TODO: replace with TestResults def chisquare_power(effect_size, nobs, n_bins, alpha=0.05, ddof=0): '''power of chisquare goodness of fit test effect size is sqrt of chisquare statistic divided by nobs Parameters ---------- effect_size : float This is the deviation from the Null of the normalized chi_square statistic. This follows Cohen's definition (sqrt). nobs : int or float number of observations n_bins : int (or float) number of bins, or points in the discrete distribution alpha : float in (0,1) significance level of the test, default alpha=0.05 Returns ------- power : float power of the test at given significance level at effect size Notes ----- This function also works vectorized if all arguments broadcast. This can also be used to calculate the power for power divergence test. However, for the range of more extreme values of the power divergence parameter, this power is not a very good approximation for samples of small to medium size (Drost et al. 1989) References ---------- Drost, ... See Also -------- chisquare_effectsize statsmodels.stats.GofChisquarePower ''' crit = stats.chi2.isf(alpha, n_bins - 1 - ddof) power = stats.ncx2.sf(crit, n_bins - 1 - ddof, effect_size**2 * nobs) return power def chisquare_effectsize(probs0, probs1, correction=None, cohen=True, axis=0): '''effect size for a chisquare goodness-of-fit test Parameters ---------- probs0 : array_like probabilities or cell frequencies under the Null hypothesis probs1 : array_like probabilities or cell frequencies under the Alternative hypothesis probs0 and probs1 need to have the same length in the ``axis`` dimension. and broadcast in the other dimensions Both probs0 and probs1 are normalized to add to one (in the ``axis`` dimension). correction : None or tuple If None, then the effect size is the chisquare statistic divide by the number of observations. If the correction is a tuple (nobs, df), then the effectsize is corrected to have less bias and a smaller variance. However, the correction can make the effectsize negative. In that case, the effectsize is set to zero. Pederson and Johnson (1990) as referenced in McLaren et all. (1994) cohen : bool If True, then the square root is returned as in the definition of the effect size by Cohen (1977), If False, then the original effect size is returned. axis : int If the probability arrays broadcast to more than 1 dimension, then this is the axis over which the sums are taken. Returns ------- effectsize : float effect size of chisquare test ''' probs0 = np.asarray(probs0, float) probs1 = np.asarray(probs1, float) probs0 = probs0 / probs0.sum(axis) probs1 = probs1 / probs1.sum(axis) d2 = ((probs1 - probs0)**2 / probs0).sum(axis) if correction is not None: nobs, df = correction diff = ((probs1 - probs0) / probs0).sum(axis) d2 = np.maximum((d2 * nobs - diff - df) / (nobs - 1.), 0) if cohen: return np.sqrt(d2) else: return d2 statsmodels-0.12.2/statsmodels/stats/inter_rater.py000066400000000000000000000445201400612667500225420ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Inter Rater Agreement contains -------- fleiss_kappa cohens_kappa aggregate_raters: helper function to get data into fleiss_kappa format to_table: helper function to create contingency table, can be used for cohens_kappa Created on Thu Dec 06 22:57:56 2012 Author: Josef Perktold License: BSD-3 References ---------- Wikipedia: kappa's initially based on these two pages https://en.wikipedia.org/wiki/Fleiss%27_kappa https://en.wikipedia.org/wiki/Cohen's_kappa SAS-Manual : formulas for cohens_kappa, especially variances see also R package irr TODO ---- standard errors and hypothesis tests for fleiss_kappa other statistics and tests, in R package irr, SAS has more inconsistent internal naming, changed variable names as I added more functionality convenience functions to create required data format from raw data DONE """ import numpy as np from scipy import stats #get rid of this? need only norm.sf class ResultsBunch(dict): template = '%r' def __init__(self, **kwds): dict.__init__(self, kwds) self.__dict__ = self self._initialize() def _initialize(self): pass def __str__(self): return self.template % self def _int_ifclose(x, dec=1, width=4): '''helper function for creating result string for int or float only dec=1 and width=4 is implemented Parameters ---------- x : int or float value to format dec : 1 number of decimals to print if x is not an integer width : 4 width of string Returns ------- xint : int or float x is converted to int if it is within 1e-14 of an integer x_string : str x formatted as string, either '%4d' or '%4.1f' ''' xint = int(round(x)) if np.max(np.abs(xint - x)) < 1e-14: return xint, '%4d' % xint else: return x, '%4.1f' % x def aggregate_raters(data, n_cat=None): '''convert raw data with shape (subject, rater) to (subject, cat_counts) brings data into correct format for fleiss_kappa bincount will raise exception if data cannot be converted to integer. Parameters ---------- data : array_like, 2-Dim data containing category assignment with subjects in rows and raters in columns. n_cat : None or int If None, then the data is converted to integer categories, 0,1,2,...,n_cat-1. Because of the relabeling only category levels with non-zero counts are included. If this is an integer, then the category levels in the data are already assumed to be in integers, 0,1,2,...,n_cat-1. In this case, the returned array may contain columns with zero count, if no subject has been categorized with this level. Returns ------- arr : nd_array, (n_rows, n_cat) Contains counts of raters that assigned a category level to individuals. Subjects are in rows, category levels in columns. ''' data = np.asarray(data) n_rows = data.shape[0] if n_cat is None: #I could add int conversion (reverse_index) to np.unique cat_uni, cat_int = np.unique(data.ravel(), return_inverse=True) n_cat = len(cat_uni) data_ = cat_int.reshape(data.shape) else: cat_uni = np.arange(n_cat) #for return only, assumed cat levels data_ = data tt = np.zeros((n_rows, n_cat), int) for idx, row in enumerate(data_): ro = np.bincount(row) tt[idx, :len(ro)] = ro return tt, cat_uni def to_table(data, bins=None): '''convert raw data with shape (subject, rater) to (rater1, rater2) brings data into correct format for cohens_kappa Parameters ---------- data : array_like, 2-Dim data containing category assignment with subjects in rows and raters in columns. bins : None, int or tuple of array_like If None, then the data is converted to integer categories, 0,1,2,...,n_cat-1. Because of the relabeling only category levels with non-zero counts are included. If this is an integer, then the category levels in the data are already assumed to be in integers, 0,1,2,...,n_cat-1. In this case, the returned array may contain columns with zero count, if no subject has been categorized with this level. If bins are a tuple of two array_like, then the bins are directly used by ``numpy.histogramdd``. This is useful if we want to merge categories. Returns ------- arr : nd_array, (n_cat, n_cat) Contingency table that contains counts of category level with rater1 in rows and rater2 in columns. Notes ----- no NaN handling, delete rows with missing values This works also for more than two raters. In that case the dimension of the resulting contingency table is the same as the number of raters instead of 2-dimensional. ''' data = np.asarray(data) n_rows, n_cols = data.shape if bins is None: #I could add int conversion (reverse_index) to np.unique cat_uni, cat_int = np.unique(data.ravel(), return_inverse=True) n_cat = len(cat_uni) data_ = cat_int.reshape(data.shape) bins_ = np.arange(n_cat+1) - 0.5 #alternative implementation with double loop #tt = np.asarray([[(x == [i,j]).all(1).sum() for j in cat_uni] # for i in cat_uni] ) #other altervative: unique rows and bincount elif np.isscalar(bins): bins_ = np.arange(bins+1) - 0.5 data_ = data else: bins_ = bins data_ = data tt = np.histogramdd(data_, (bins_,)*n_cols) return tt[0], bins_ def fleiss_kappa(table, method='fleiss'): """Fleiss' and Randolph's kappa multi-rater agreement measure Parameters ---------- table : array_like, 2-D assumes subjects in rows, and categories in columns method : str Method 'fleiss' returns Fleiss' kappa which uses the sample margin to define the chance outcome. Method 'randolph' or 'uniform' (only first 4 letters are needed) returns Randolph's (2005) multirater kappa which assumes a uniform distribution of the categories to define the chance outcome. Returns ------- kappa : float Fleiss's or Randolph's kappa statistic for inter rater agreement Notes ----- no variance or hypothesis tests yet Interrater agreement measures like Fleiss's kappa measure agreement relative to chance agreement. Different authors have proposed ways of defining these chance agreements. Fleiss' is based on the marginal sample distribution of categories, while Randolph uses a uniform distribution of categories as benchmark. Warrens (2010) showed that Randolph's kappa is always larger or equal to Fleiss' kappa. Under some commonly observed condition, Fleiss' and Randolph's kappa provide lower and upper bounds for two similar kappa_like measures by Light (1971) and Hubert (1977). References ---------- Wikipedia https://en.wikipedia.org/wiki/Fleiss%27_kappa Fleiss, Joseph L. 1971. "Measuring Nominal Scale Agreement among Many Raters." Psychological Bulletin 76 (5): 378-82. https://doi.org/10.1037/h0031619. Randolph, Justus J. 2005 "Free-Marginal Multirater Kappa (multirater K [free]): An Alternative to Fleiss' Fixed-Marginal Multirater Kappa." Presented at the Joensuu Learning and Instruction Symposium, vol. 2005 https://eric.ed.gov/?id=ED490661 Warrens, Matthijs J. 2010. "Inequalities between Multi-Rater Kappas." Advances in Data Analysis and Classification 4 (4): 271-86. https://doi.org/10.1007/s11634-010-0073-4. """ table = 1.0 * np.asarray(table) #avoid integer division n_sub, n_cat = table.shape n_total = table.sum() n_rater = table.sum(1) n_rat = n_rater.max() #assume fully ranked assert n_total == n_sub * n_rat #marginal frequency of categories p_cat = table.sum(0) / n_total table2 = table * table p_rat = (table2.sum(1) - n_rat) / (n_rat * (n_rat - 1.)) p_mean = p_rat.mean() if method == 'fleiss': p_mean_exp = (p_cat*p_cat).sum() elif method.startswith('rand') or method.startswith('unif'): p_mean_exp = 1 / n_cat kappa = (p_mean - p_mean_exp) / (1- p_mean_exp) return kappa def cohens_kappa(table, weights=None, return_results=True, wt=None): '''Compute Cohen's kappa with variance and equal-zero test Parameters ---------- table : array_like, 2-Dim square array with results of two raters, one rater in rows, second rater in columns weights : array_like The interpretation of weights depends on the wt argument. If both are None, then the simple kappa is computed. see wt for the case when wt is not None If weights is two dimensional, then it is directly used as a weight matrix. For computing the variance of kappa, the maximum of the weights is assumed to be smaller or equal to one. TODO: fix conflicting definitions in the 2-Dim case for wt : {None, str} If wt and weights are None, then the simple kappa is computed. If wt is given, but weights is None, then the weights are set to be [0, 1, 2, ..., k]. If weights is a one-dimensional array, then it is used to construct the weight matrix given the following options. wt in ['linear', 'ca' or None] : use linear weights, Cicchetti-Allison actual weights are linear in the score "weights" difference wt in ['quadratic', 'fc'] : use linear weights, Fleiss-Cohen actual weights are squared in the score "weights" difference wt = 'toeplitz' : weight matrix is constructed as a toeplitz matrix from the one dimensional weights. return_results : bool If True (default), then an instance of KappaResults is returned. If False, then only kappa is computed and returned. Returns ------- results or kappa If return_results is True (default), then a results instance with all statistics is returned If return_results is False, then only kappa is calculated and returned. Notes ----- There are two conflicting definitions of the weight matrix, Wikipedia versus SAS manual. However, the computation are invariant to rescaling of the weights matrix, so there is no difference in the results. Weights for 'linear' and 'quadratic' are interpreted as scores for the categories, the weights in the computation are based on the pairwise difference between the scores. Weights for 'toeplitz' are a interpreted as weighted distance. The distance only depends on how many levels apart two entries in the table are but not on the levels themselves. example: weights = '0, 1, 2, 3' and wt is either linear or toeplitz means that the weighting only depends on the simple distance of levels. weights = '0, 0, 1, 1' and wt = 'linear' means that the first two levels are zero distance apart and the same for the last two levels. This is the sample as forming two aggregated levels by merging the first two and the last two levels, respectively. weights = [0, 1, 2, 3] and wt = 'quadratic' is the same as squaring these weights and using wt = 'toeplitz'. References ---------- Wikipedia SAS Manual ''' table = np.asarray(table, float) #avoid integer division agree = np.diag(table).sum() nobs = table.sum() probs = table / nobs freqs = probs #TODO: rename to use freqs instead of probs for observed probs_diag = np.diag(probs) freq_row = table.sum(1) / nobs freq_col = table.sum(0) / nobs prob_exp = freq_col * freq_row[:, None] assert np.allclose(prob_exp.sum(), 1) #print prob_exp.sum() agree_exp = np.diag(prob_exp).sum() #need for kappa_max if weights is None and wt is None: kind = 'Simple' kappa = (agree / nobs - agree_exp) / (1 - agree_exp) if return_results: #variance term_a = probs_diag * (1 - (freq_row + freq_col) * (1 - kappa))**2 term_a = term_a.sum() term_b = probs * (freq_col[:, None] + freq_row)**2 d_idx = np.arange(table.shape[0]) term_b[d_idx, d_idx] = 0 #set diagonal to zero term_b = (1 - kappa)**2 * term_b.sum() term_c = (kappa - agree_exp * (1-kappa))**2 var_kappa = (term_a + term_b - term_c) / (1 - agree_exp)**2 / nobs #term_c = freq_col * freq_row[:, None] * (freq_col + freq_row[:,None]) term_c = freq_col * freq_row * (freq_col + freq_row) var_kappa0 = (agree_exp + agree_exp**2 - term_c.sum()) var_kappa0 /= (1 - agree_exp)**2 * nobs else: if weights is None: weights = np.arange(table.shape[0]) #weights follows the Wikipedia definition, not the SAS, which is 1 - kind = 'Weighted' weights = np.asarray(weights, float) if weights.ndim == 1: if wt in ['ca', 'linear', None]: weights = np.abs(weights[:, None] - weights) / \ (weights[-1] - weights[0]) elif wt in ['fc', 'quadratic']: weights = (weights[:, None] - weights)**2 / \ (weights[-1] - weights[0])**2 elif wt == 'toeplitz': #assume toeplitz structure from scipy.linalg import toeplitz #weights = toeplitz(np.arange(table.shape[0])) weights = toeplitz(weights) else: raise ValueError('wt option is not known') else: rows, cols = table.shape if (table.shape != weights.shape): raise ValueError('weights are not square') #this is formula from Wikipedia kappa = 1 - (weights * table).sum() / nobs / (weights * prob_exp).sum() #TODO: add var_kappa for weighted version if return_results: var_kappa = np.nan var_kappa0 = np.nan #switch to SAS manual weights, problem if user specifies weights #w is negative in some examples, #but weights is scale invariant in examples and rough check of source w = 1. - weights w_row = (freq_col * w).sum(1) w_col = (freq_row[:, None] * w).sum(0) agree_wexp = (w * freq_col * freq_row[:, None]).sum() term_a = freqs * (w - (w_col + w_row[:, None]) * (1 - kappa))**2 fac = 1. / ((1 - agree_wexp)**2 * nobs) var_kappa = term_a.sum() - (kappa - agree_wexp * (1 - kappa))**2 var_kappa *= fac freqse = freq_col * freq_row[:, None] var_kappa0 = (freqse * (w - (w_col + w_row[:, None]))**2).sum() var_kappa0 -= agree_wexp**2 var_kappa0 *= fac kappa_max = (np.minimum(freq_row, freq_col).sum() - agree_exp) / \ (1 - agree_exp) if return_results: res = KappaResults( kind=kind, kappa=kappa, kappa_max=kappa_max, weights=weights, var_kappa=var_kappa, var_kappa0=var_kappa0) return res else: return kappa _kappa_template = '''\ %(kind)s Kappa Coefficient -------------------------------- Kappa %(kappa)6.4f ASE %(std_kappa)6.4f %(alpha_ci)s%% Lower Conf Limit %(kappa_low)6.4f %(alpha_ci)s%% Upper Conf Limit %(kappa_upp)6.4f Test of H0: %(kind)s Kappa = 0 ASE under H0 %(std_kappa0)6.4f Z %(z_value)6.4f One-sided Pr > Z %(pvalue_one_sided)6.4f Two-sided Pr > |Z| %(pvalue_two_sided)6.4f ''' ''' Weighted Kappa Coefficient -------------------------------- Weighted Kappa 0.4701 ASE 0.1457 95% Lower Conf Limit 0.1845 95% Upper Conf Limit 0.7558 Test of H0: Weighted Kappa = 0 ASE under H0 0.1426 Z 3.2971 One-sided Pr > Z 0.0005 Two-sided Pr > |Z| 0.0010 ''' class KappaResults(ResultsBunch): '''Results for Cohen's kappa Attributes ---------- kappa : cohen's kappa var_kappa : variance of kappa std_kappa : standard deviation of kappa alpha : one-sided probability for confidence interval kappa_low : lower (1-alpha) confidence limit kappa_upp : upper (1-alpha) confidence limit var_kappa0 : variance of kappa under H0: kappa=0 std_kappa0 : standard deviation of kappa under H0: kappa=0 z_value : test statistic for H0: kappa=0, is standard normal distributed pvalue_one_sided : one sided p-value for H0: kappa=0 and H1: kappa>0 pvalue_two_sided : two sided p-value for H0: kappa=0 and H1: kappa!=0 distribution_kappa : asymptotic normal distribution of kappa distribution_zero_null : asymptotic normal distribution of kappa under H0: kappa=0 The confidence interval for kappa and the statistics for the test of H0: kappa=0 are based on the asymptotic normal distribution of kappa. ''' template = _kappa_template def _initialize(self): if 'alpha' not in self: self['alpha'] = 0.025 self['alpha_ci'] = _int_ifclose(100 - 0.025 * 200)[1] self['std_kappa'] = np.sqrt(self['var_kappa']) self['std_kappa0'] = np.sqrt(self['var_kappa0']) self['z_value'] = self['kappa'] / self['std_kappa0'] self['pvalue_one_sided'] = stats.norm.sf(self['z_value']) self['pvalue_two_sided'] = stats.norm.sf(np.abs(self['z_value'])) * 2 delta = stats.norm.isf(self['alpha']) * self['std_kappa'] self['kappa_low'] = self['kappa'] - delta self['kappa_upp'] = self['kappa'] + delta self['distribution_kappa'] = stats.norm(loc=self['kappa'], scale=self['std_kappa']) self['distribution_zero_null'] = stats.norm(loc=0, scale=self['std_kappa0']) def __str__(self): return self.template % self statsmodels-0.12.2/statsmodels/stats/knockoff_regeffects.py000066400000000000000000000123051400612667500242150ustar00rootroot00000000000000import numpy as np import statsmodels.api as sm class RegressionEffects(object): """ Base class for regression effects used in RegressionFDR. Any implementation of the class must provide a method called 'stats' that takes a RegressionFDR object and returns effect sizes for the model coefficients. Greater values for these statistics imply greater evidence that the effect is real. Knockoff effect sizes are based on fitting the regression model to an extended design matrix [X X'], where X' is a design matrix with the same shape as the actual design matrix X. The construction of X' guarantees that there are no true associations between the columns of X' and the dependent variable of the regression. If X has p columns, then the effect size of covariate j is based on the strength of the estimated association for coefficient j compared to the strength of the estimated association for coefficient p+j. """ def stats(self, parent): raise NotImplementedError class CorrelationEffects(RegressionEffects): """ Marginal correlation effect sizes for FDR control. Parameters ---------- parent : RegressionFDR The RegressionFDR instance to which this effect size is applied. Notes ----- This class implements the marginal correlation approach to constructing test statistics for a knockoff analysis, as described under (1) in section 2.2 of the Barber and Candes paper. """ def stats(self, parent): s1 = np.dot(parent.exog1.T, parent.endog) s2 = np.dot(parent.exog2.T, parent.endog) return np.abs(s1) - np.abs(s2) class ForwardEffects(RegressionEffects): """ Forward selection effect sizes for FDR control. Parameters ---------- parent : RegressionFDR The RegressionFDR instance to which this effect size is applied. pursuit : bool If True, 'basis pursuit' is used, which amounts to performing a full regression at each selection step to adjust the working residual vector. If False (the default), the residual is adjusted by regressing out each selected variable marginally. Setting pursuit=True will be considerably slower, but may give better results when exog is not orthogonal. Notes ----- This class implements the forward selection approach to constructing test statistics for a knockoff analysis, as described under (5) in section 2.2 of the Barber and Candes paper. """ def __init__(self, pursuit): self.pursuit = pursuit def stats(self, parent): nvar = parent.exog.shape[1] rv = parent.endog.copy() vl = [(i, parent.exog[:, i]) for i in range(nvar)] z = np.empty(nvar) past = [] for i in range(nvar): dp = np.r_[[np.abs(np.dot(rv, x[1])) for x in vl]] j = np.argmax(dp) z[vl[j][0]] = nvar - i - 1 x = vl[j][1] del vl[j] if self.pursuit: for v in past: x -= np.dot(x, v)*v past.append(x) rv -= np.dot(rv, x) * x z1 = z[0:nvar//2] z2 = z[nvar//2:] st = np.where(z1 > z2, z1, z2) * np.sign(z1 - z2) return st class OLSEffects(RegressionEffects): """ OLS regression for knockoff analysis. Parameters ---------- parent : RegressionFDR The RegressionFDR instance to which this effect size is applied. Notes ----- This class implements the ordinary least squares regression approach to constructing test statistics for a knockoff analysis, as described under (2) in section 2.2 of the Barber and Candes paper. """ def stats(self, parent): model = sm.OLS(parent.endog, parent.exog) result = model.fit() q = len(result.params) // 2 stats = np.abs(result.params[0:q]) - np.abs(result.params[q:]) return stats class RegModelEffects(RegressionEffects): """ Use any regression model for Regression FDR analysis. Parameters ---------- parent : RegressionFDR The RegressionFDR instance to which this effect size is applied. model_cls : class Any model with appropriate fit or fit_regularized functions regularized : bool If True, use fit_regularized to fit the model model_kws : dict Keywords passed to model initializer fit_kws : dict Dictionary of keyword arguments for fit or fit_regularized """ def __init__(self, model_cls, regularized=False, model_kws=None, fit_kws=None): self.model_cls = model_cls self.regularized = regularized self.model_kws = model_kws if model_kws is not None else {} self.fit_kws = fit_kws if fit_kws is not None else {} def stats(self, parent): model = self.model_cls(parent.endog, parent.exog, **self.model_kws) if self.regularized: params = model.fit_regularized(**self.fit_kws).params else: params = model.fit(**self.fit_kws).params q = len(params) // 2 stats = np.abs(params[0:q]) - np.abs(params[q:]) return stats statsmodels-0.12.2/statsmodels/stats/libqsturng/000077500000000000000000000000001400612667500220375ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/stats/libqsturng/CH.r000066400000000000000000000046071400612667500225230ustar00rootroot00000000000000% Copyright (c) 2011, Roger Lew BSD [see LICENSE.txt] % This software is funded in part by NIH Grant P20 RR016454. % This is a collection of scripts used to generate C-H comparisons % for qsturng. As you can probably guess, my R's skills are not all that good. setwd('D:\\USERS\\roger\\programming\\python\\development\\qsturng') ps = seq(length=100, from=.5, to=.999) for (r in c(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21, 22,23,24,25,26,27,28,29,30,35,40,50,60,70,80,90,100,200)) { for (v in c(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20, 22,24,26,30,35,40,50,60,90,120,240,480,1e38)) { m = qtukey(ps, r, v) fname = sprintf('CH_r=%i,v=%.0f.dat',r,v) print(fname) write(rbind(ps, m), file=fname, ncolumns=2, append=FALSE, sep=',') } } rs = c(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,30,40,60,80,100) for (v in c(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16, 17,18,19,20,24,30,40,60,120,1e38)) { m = qtukey(0.30, rs, v) fname = sprintf('CH_p30.dat') print(fname) write(rbind(m), file=fname, ncolumns=26, append=TRUE, sep=' ') } for i in for (v in c(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16, 17,18,19,20,24,30,40,60,120,1e38)) { m = qtukey(0.675, rs, v) fname = sprintf('CH_p675.dat',r,v) print(fname) write(rbind(m), file=fname, ncolumns=26, append=TRUE, sep=' ') } for (v in c(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16, 17,18,19,20,24,30,40,60,120,1e38)) { m = qtukey(0.75, rs, v) fname = sprintf('CH_p75.dat',r,v) print(fname) write(rbind(m), file=fname, ncolumns=26, append=TRUE, sep=' ') } for (v in c(2,3,4,5,6,7,8,9,10,11,12,13,14,15,16, 17,18,19,20,24,30,40,60,120,1e38)) { m = qtukey(0.975, rs, v) fname = sprintf('CH_p975.dat') print(fname) write(rbind(m), file=fname, ncolumns=26, append=TRUE, sep=' ') } i = 0; for (i in 0:9999) { p = runif(1, .5, .95); r = sample(2:100, 1); v = runif(1, 2, 1000); q = qtukey(p,r,v); if (!is.nan(q)) { write(c(p,r,v,q), file='bootleg.dat', ncolumns=4, append=TRUE, sep=','); i = i + 1; } }statsmodels-0.12.2/statsmodels/stats/libqsturng/LICENSE.txt000066400000000000000000000030361400612667500236640ustar00rootroot00000000000000Copyright (c) 2011, Roger Lew [see LICENSE.txt] All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the organizations affiliated with the contributors or the names of its contributors themselves may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. statsmodels-0.12.2/statsmodels/stats/libqsturng/__init__.py000066400000000000000000000003011400612667500241420ustar00rootroot00000000000000from .qsturng_ import psturng, qsturng, p_keys, v_keys from statsmodels.tools._testing import PytestTester __all__ = ['p_keys', 'psturng', 'qsturng', 'v_keys', 'test'] test = PytestTester() statsmodels-0.12.2/statsmodels/stats/libqsturng/make_tbls.py000066400000000000000000001742031400612667500243610ustar00rootroot00000000000000"""this script builds the T table and A table for the upper quantile stundentized range algorithm""" from statsmodels.compat.python import lrange, lmap import math import scipy.stats from scipy.optimize import leastsq import numpy as np from numpy.random import random # The values for p in [.5, .75, .9, .95, .975, .99, .995, .999] # were pulled from: # http://www.stata.com/stb/stb46/dm64/sturng.pdf # # Values for p in [.1, .675, .8, .85] were calculated using R's qtukey function # # the table was programmed by Gleason and extends Harter's (1960) table # using the Copenhaver & Holland (1988) algorithm (C&H). Gleason found # that the 4th significant digit of the C&H differed from Harter's # tables on about 20% of the values. Gleason states this was do to # consevative rounding by Harter. In those event the table reflects # Harter's orginal approximations. q0100 = """\ 2 0.2010022 0.6351172 0.9504689 1.179321 1.354691 1.495126 1.611354 1.709984 1.795325 1.87032 1.937057 1.997068 2.051505 2.101256 2.147016 2.189342 2.228683 2.265408 2.299823 2.558612 2.729718 2.95625 3.184742938 3.398609188 3 0.193179 0.6294481 0.9564746 1.19723 1.383028 1.532369 1.656225 1.761451 1.852559 1.93265 2.003933 2.068034 2.126178 2.179312 2.228177 2.273367 2.315364 2.354561 2.391287 2.667213 2.849389 3.009265469 3.237758406 3.451624656 4 0.1892648 0.6266441 0.9606115 1.2089 1.401557 1.55691 1.686009 1.795829 1.890994 1.974697 2.049222 2.116253 2.177065 2.232641 2.283754 2.331023 2.37495 2.415949 2.454361 2.742846 2.933173 3.062280938 3.290773875 3.504640125 5 0.1869239 0.6249713 0.963532 1.217021 1.414548 1.574255 1.707205 1.820437 1.91864 2.005066 2.082048 2.151312 2.214162 2.271609 2.324449 2.37332 2.418737 2.461128 2.500844 2.7991 2.9958 3.115296406 3.343789344 3.557655594 6 0.185369 0.6238602 0.9656833 1.22298 1.424151 1.587166 1.723076 1.838955 1.939532 2.028098 2.107021 2.178053 2.242524 2.301465 2.355686 2.40584 2.452454 2.495964 2.536731 2.842892 3.027993254 3.168311875 3.396804813 3.610671063 7 0.1842618 0.6230685 0.9673274 1.227534 1.431536 1.597154 1.735417 1.853415 1.955904 2.046203 2.126704 2.19918 2.264979 2.325144 2.380502 2.431713 2.479315 2.52375 2.565387 2.878126 3.060186557 3.221327344 3.449820281 3.663686531 8 0.1834338 0.6224757 0.9686225 1.231126 1.437392 1.605113 1.745294 1.86503 1.969097 2.060832 2.142645 2.216325 2.283234 2.344427 2.400739 2.45284 2.501275 2.546491 2.588864 2.861237 3.092379859 3.274342813 3.50283575 3.716702 9 0.1827912 0.6220153 0.969668 1.23403 1.442149 1.611608 1.753382 1.874572 1.979964 2.07291 2.155833 2.230535 2.298388 2.360458 2.417585 2.470448 2.519597 2.565484 2.608488 2.871492 3.1631665 3.362394 3.613696 3.7452106 10 0.1822783 0.6216474 0.9705293 1.236426 1.446091 1.617009 1.76013 1.882554 1.989077 2.083059 2.166935 2.242517 2.311185 2.374011 2.431845 2.485368 2.535137 2.581607 2.625162 2.898717 3.1760535 3.45339 3.6807265 3.7737192 11 0.1818593 0.6213467 0.9712507 1.238437 1.449411 1.621571 1.765847 1.889333 1.996831 2.091711 2.176415 2.252763 2.322141 2.38563 2.444082 2.498185 2.548497 2.59548 2.639519 2.923558 3.19971275 3.4758675 3.70202225 3.8022278 12 0.1815106 0.6210962 0.9718637 1.240149 1.452244 1.625478 1.770753 1.895163 2.003512 2.099178 2.184609 2.26163 2.331635 2.395707 2.454706 2.509321 2.560115 2.607554 2.652022 2.94649 3.2224175 3.498345 3.7242725 3.8307364 13 0.181216 0.6208845 0.9723908 1.241623 1.454692 1.62886 1.77501 1.900231 2.009331 2.10569 2.191763 2.269382 2.339943 2.404535 2.46402 2.519093 2.570318 2.618162 2.663015 2.967868 3.242456 3.517044 3.741632 3.859245 14 0.1809637 0.620703 0.972849 1.242906 1.456827 1.631817 1.778739 1.904678 2.014444 2.11142 2.198067 2.276219 2.347278 2.412335 2.472257 2.52774 2.579352 2.627563 2.672763 2.987963 3.245505708 3.503048417 3.748851667 3.878849 15 0.1807453 0.6205458 0.9732508 1.244033 1.458706 1.634424 1.782034 1.908613 2.018974 2.116503 2.203664 2.282296 2.353802 2.41928 2.479596 2.53545 2.587413 2.635954 2.681468 3.006982 3.275778125 3.489052833 3.758247778 3.896564 16 0.1805544 0.6204084 0.973606 1.24503 1.460373 1.636741 1.784965 1.912119 2.023015 2.121043 2.208668 2.287733 2.359646 2.425503 2.486177 2.542369 2.59465 2.643493 2.689292 3.025091 3.281966688 3.49479125 3.763291 3.9179256 17 0.1803861 0.6202871 0.9739223 1.245919 1.461861 1.638813 1.78759 1.915263 2.026643 2.125123 2.21317 2.292628 2.36491 2.431114 2.492114 2.548614 2.601186 2.650304 2.696365 3.032426 3.272395 3.50687125 3.77704 3.9392872 18 0.1802366 0.6201793 0.9742057 1.246717 1.463198 1.640677 1.789955 1.918099 2.029919 2.128809 2.21724 2.297059 2.369678 2.436199 2.497498 2.55428 2.607118 2.656491 2.702792 3.039093 3.282026 3.586406 3.789645 3.9606488 19 0.1801029 0.620083 0.9744612 1.247436 1.464405 1.642363 1.792096 1.920669 2.032891 2.132158 2.22094 2.301089 2.374017 2.44083 2.502404 2.559444 2.612529 2.662134 2.708658 3.045182 3.296680985 3.603883649 3.801248 3.974888443 20 0.1799827 0.6199962 0.9746925 1.248088 1.465502 1.643895 1.794045 1.923011 2.035601 2.135212 2.224318 2.30477 2.377983 2.445065 2.506892 2.564173 2.617485 2.667306 2.714034 3.050762 3.311335993 3.621361325 3.788047375 3.989130221 24 0.1796023 0.6197217 0.9754345 1.250184 1.469033 1.648844 1.800353 1.930604 2.044404 2.145153 2.235327 2.316784 2.390945 2.45892 2.521592 2.579673 2.633745 2.684289 2.731705 3.089271 3.325991 3.638839 3.77484675 4.003372 30 0.1792227 0.6194474 0.9761909 1.252326 1.47266 1.653946 1.806877 1.938484 2.053567 2.155527 2.246844 2.329381 2.404562 2.473504 2.537093 2.596046 2.650947 2.702281 2.750452 3.088623 3.365526818 3.632653344 3.810852875 4.0480485 40 0.1788439 0.6191733 0.976962 1.254517 1.476384 1.659208 1.813634 1.946672 2.063118 2.166372 2.258917 2.342618 2.418905 2.488898 2.553488 2.613394 2.669206 2.731569 2.770415 3.109261 3.405062637 3.629560516 3.846859 4.092725 60 0.1784658 0.6188994 0.9777482 1.256759 1.480212 1.664639 1.820636 1.955191 2.07309 2.177731 2.271599 2.356562 2.434053 2.505196 2.570884 2.631843 2.688663 2.745483 2.802303 3.159123 3.406221516 3.626467688 3.90118925 4.1497775 120 0.1780885 0.6186256 0.9785495 1.259052 1.484147 1.67025 1.827902 1.964066 2.083518 2.189653 2.284954 2.371292 2.450102 2.522511 2.589417 2.651546 2.71243375 2.763748 2.8156585 3.201588 3.459897 3.67055425 3.9555195 4.20683 1e38 0.177712 0.6183521 0.9793662 1.261398 1.488195 1.676051 1.835449 1.973327 2.094446 2.202195 2.299057 2.386902 2.467168 2.540983 2.609248 2.677513 2.745778 2.787396 2.829014 3.236691 3.487830797 3.721309063 4.01874075 4.279424""" q0300 = """\ 2 0.6289521 1.248281 1.638496 1.916298 2.129504 2.301246 2.444313 2.566465 2.672747 2.766604 2.850494 2.926224 2.995161 3.05836 3.116655 3.170712 3.221076 3.268192 3.312433 3.647666 3.871606 4.170521 4.372227 4.52341 3 0.5999117 1.209786 1.598235 1.875707 2.088948 2.260822 2.404037 2.52633 2.632732 2.726691 2.810665 2.886463 2.955453 3.018695 3.077022 3.131103 3.181483 3.228609 3.272854 3.607961 3.831649 4.130021 4.331231 4.48198 4 0.5857155 1.19124 1.579749 1.858059 2.072245 2.245015 2.389043 2.512062 2.619115 2.713659 2.798159 2.874434 2.943859 3.007497 3.066189 3.120607 3.171298 3.218713 3.263228 3.600301 3.825208 4.125075 4.327208 4.478602 5 0.5773226 1.18033 1.569213 1.84843 2.063579 2.237255 2.382108 2.505872 2.613597 2.708749 2.793803 2.870583 2.94047 3.004536 3.063622 3.118406 3.169439 3.217173 3.261987 3.601296 3.827646 4.129353 4.332665 4.48491 6 0.5717854 1.173145 1.562427 1.842442 2.058433 2.232905 2.378487 2.502915 2.611243 2.706943 2.792499 2.869739 2.940051 3.004509 3.06396 3.119085 3.170435 3.218468 3.263562 3.604991 3.832733 4.136241 4.340726 4.493824 7 0.5678608 1.168056 1.5577 1.838389 2.055092 2.230242 2.376451 2.501451 2.610302 2.706482 2.792477 2.870123 2.94081 3.005616 3.065391 3.120818 3.172464 3.220752 3.266098 3.609448 3.838467 4.143645 4.349225 4.503125 8 0.5649349 1.164263 1.55422 1.835477 2.052781 2.228508 2.375251 2.500743 2.610046 2.706641 2.793019 2.871019 2.942034 3.007146 3.067207 3.122901 3.174787 3.223323 3.268893 3.61396 3.844133 4.150832 4.357416 4.512054 9 0.56267 1.161326 1.551554 1.833289 2.051105 2.227323 2.374526 2.500442 2.610136 2.707092 2.793803 2.872112 2.943416 3.008796 3.069108 3.125039 3.177147 3.225893 3.27166 3.618262 3.849473 4.157551 4.365051 4.520364 10 0.5608651 1.158985 1.549445 1.831589 2.049842 2.226484 2.374084 2.500369 2.610403 2.707674 2.794677 2.873258 2.944815 3.010432 3.070966 3.127106 3.179411 3.228343 3.274287 3.62226 3.854408 4.16298725 4.372072 4.51335807 11 0.5593931 1.157076 1.547737 1.830233 2.048863 2.225872 2.373818 2.500424 2.610757 2.708305 2.795566 2.874386 2.946167 3.011994 3.072726 3.129052 3.181532 3.23063 3.276732 3.625936 3.8583805 4.1684235 4.378495 4.527370035 12 0.5581697 1.155489 1.546325 1.829125 2.048085 2.225415 2.373664 2.500554 2.61115 2.708943 2.796432 2.875466 2.947446 3.01346 3.074368 3.13086 3.183497 3.232744 3.278987 3.629302 3.862353 4.17385975 4.384365 4.541382 13 0.557137 1.154148 1.545138 1.828206 2.047454 2.225068 2.373584 2.500725 2.611555 2.709566 2.797258 2.876482 2.948641 3.014823 3.075889 3.13253 3.185309 3.23469 3.28106 3.63238 3.8663255 4.179296 4.3895105 4.547231 14 0.5562535 1.153001 1.544127 1.82743 2.046934 2.224798 2.373553 2.500918 2.611956 2.710162 2.798038 2.877433 2.949752 3.016085 3.077294 3.134069 3.186976 3.236478 3.282963 3.635197 3.870298 4.183625 4.394656 4.552594 15 0.5554892 1.152009 1.543255 1.826767 2.046499 2.224587 2.373555 2.50112 2.612347 2.710728 2.798768 2.878317 2.950781 3.017251 3.078589 3.135487 3.188509 3.238121 3.284712 3.637674 3.8733385 4.187597 4.399177 4.557525 16 0.5548214 1.151142 1.542495 1.826194 2.04613 2.224419 2.373579 2.501325 2.612721 2.711261 2.799449 2.879139 2.951735 3.018329 3.079784 3.136793 3.189921 3.239634 3.28632 3.640151 3.876379 4.191252 4.40334 4.56207 17 0.554233 1.150377 1.541828 1.825694 2.045813 2.224284 2.373618 2.501527 2.613077 2.711761 2.800085 2.879902 2.952618 3.019325 3.080888 3.137998 3.191223 3.241028 3.287802 3.642251 3.878959 4.1944965 4.407184 4.56627 18 0.5537107 1.149699 1.541236 1.825254 2.04554 2.224175 2.373667 2.501725 2.613414 2.71223 2.800678 2.880611 2.953437 3.020248 3.081909 3.139113 3.192426 3.242315 3.28917 3.644351 3.881539 4.197741 4.410743 4.570162 19 0.5532438 1.149092 1.540709 1.824864 2.045301 2.224086 2.373722 2.501915 2.613733 2.71267 2.801231 2.881271 2.954198 3.021104 3.082855 3.140145 3.19354 3.243507 3.290436 3.641213698 3.877674372 4.200632 4.414046 4.573776 20 0.552824 1.148546 1.540235 1.824516 2.045091 2.224013 2.37378 2.502099 2.614034 2.713082 2.801747 2.881885 2.954905 3.0219 3.083734 3.141103 3.194574 3.244613 3.291611 3.647488349 3.885403686 4.203319 4.4207865 4.577142 24 0.5514973 1.146821 1.538745 1.823433 2.044456 2.223827 2.374026 2.502754 2.615077 2.71449 2.8035 2.883965 2.957293 3.02458 3.086693 3.144327 3.198049 3.248329 3.295558 3.653763 3.893133 4.212396 4.427527 4.588561 30 0.5501747 1.1451 1.537267 1.822378 2.04387 2.223711 2.374365 2.503527 2.616262 2.716064 2.805443 2.886257 2.959917 3.027519 3.089932 3.147852 3.201849 3.252391 3.29987 3.646771403 3.901009 4.201241112 4.423813037 4.57425581 40 0.5488561 1.143384 1.535803 1.821351 2.043333 2.223667 2.3748 2.504422 2.617594 2.717812 2.807585 2.888774 2.962791 3.030734 3.093472 3.151703 3.205997 3.256824 3.304577 3.660754702 3.910106 4.223551056 4.431241019 4.602866405 60 0.5475416 1.141671 1.53435 1.820353 2.042846 2.223698 2.375337 2.505445 2.619082 2.719743 2.809939 2.891531 2.965932 3.034243 3.097332 3.1559 3.210518 3.261657 3.30971 3.674738 3.919203 4.245861 4.438669 4.631477 120 0.5462314 1.139963 1.532911 1.819385 2.04241 2.223806 2.375978 2.506602 2.620733 2.721868 2.812516 2.894541 2.969356 3.038064 3.101534 3.160468 3.215439 3.39400025 3.5725615 3.75112275 3.929684 4.256342 4.44915 4.641958 1e38 0.5449254 1.138259 1.531485 1.818447 2.042028 2.223993 2.376728 2.507898 2.622556 2.724195 2.815328 2.897817 2.973079 3.042215 3.106097 3.165428 3.220399 3.39896025 3.5775215 3.75608275 3.934644 4.261302 4.45411 4.646918""" q0500 = """\ 2 1.155 1.908 2.377 2.713 2.973 3.184 3.361 3.513 3.645 3.762 3.867 3.963 4.049 4.129 4.203 4.271 4.335 4.394 4.451 4.878 5.165 5.549 5.810 6.006 3 1.082 1.791 2.230 2.545 2.789 2.986 3.152 3.294 3.418 3.528 3.626 3.715 3.796 3.871 3.940 4.004 4.064 4.120 4.172 4.573 4.842 5.202 5.447 5.630 4 1.048 1.736 2.163 2.468 2.704 2.895 3.055 3.193 3.313 3.419 3.515 3.601 3.680 3.752 3.819 3.881 3.939 3.993 4.044 4.432 4.693 5.043 5.279 5.457 5 1.028 1.705 2.124 2.423 2.655 2.843 3.000 3.135 3.253 3.357 3.451 3.535 3.613 3.684 3.749 3.810 3.867 3.920 3.970 4.351 4.608 4.951 5.184 5.358 6 1.015 1.684 2.098 2.394 2.623 2.808 2.964 3.097 3.213 3.317 3.409 3.493 3.569 3.639 3.704 3.764 3.820 3.873 3.922 4.299 4.552 4.891 5.121 5.294 7 1.006 1.670 2.080 2.374 2.601 2.784 2.938 3.070 3.186 3.288 3.380 3.463 3.538 3.608 3.672 3.732 3.787 3.840 3.889 4.262 4.513 4.849 5.077 5.249 8 .9990 1.659 2.067 2.359 2.584 2.767 2.919 3.051 3.165 3.267 3.358 3.440 3.515 3.584 3.648 3.708 3.763 3.815 3.863 4.234 4.484 4.818 5.045 5.215 9 .9938 1.651 2.057 2.347 2.571 2.753 2.905 3.035 3.149 3.250 3.341 3.423 3.498 3.566 3.630 3.689 3.744 3.796 3.844 4.213 4.461 4.794 5.020 5.189 10 .9897 1.645 2.049 2.338 2.561 2.742 2.893 3.023 3.137 3.237 3.328 3.409 3.484 3.552 3.615 3.674 3.729 3.780 3.829 4.196 4.443 4.775 5.000 5.168 11 .9863 1.639 2.042 2.330 2.553 2.733 2.884 3.013 3.127 3.227 3.317 3.398 3.472 3.540 3.603 3.662 3.717 3.768 3.816 4.182 4.429 4.759 4.983 5.152 12 .9836 1.635 2.037 2.324 2.546 2.726 2.876 3.005 3.118 3.218 3.308 3.389 3.463 3.531 3.594 3.652 3.706 3.757 3.805 4.171 4.417 4.746 4.970 5.138 13 .9812 1.631 2.032 2.319 2.540 2.719 2.869 2.998 3.111 3.210 3.300 3.381 3.455 3.522 3.585 3.643 3.698 3.749 3.796 4.161 4.406 4.735 4.958 5.126 14 .9792 1.628 2.028 2.314 2.535 2.714 2.864 2.992 3.105 3.204 3.293 3.374 3.448 3.515 3.578 3.636 3.690 3.741 3.789 4.153 4.397 4.726 4.948 5.115 15 .9775 1.625 2.025 2.310 2.531 2.709 2.859 2.987 3.099 3.199 3.288 3.368 3.442 3.509 3.572 3.630 3.684 3.735 3.782 4.145 4.390 4.718 4.940 5.107 16 .9760 1.623 2.022 2.307 2.527 2.705 2.855 2.983 3.095 3.194 3.283 3.363 3.436 3.504 3.566 3.624 3.678 3.729 3.776 4.139 4.383 4.710 4.932 5.099 17 .9747 1.621 2.019 2.304 2.524 2.702 2.851 2.979 3.090 3.189 3.278 3.359 3.432 3.499 3.561 3.619 3.673 3.724 3.771 4.133 4.377 4.704 4.926 5.092 18 .9735 1.619 2.017 2.301 2.521 2.699 2.848 2.975 3.087 3.186 3.274 3.354 3.428 3.495 3.557 3.615 3.669 3.719 3.767 4.128 4.372 4.698 4.920 5.086 19 .9724 1.617 2.015 2.299 2.518 2.696 2.845 2.972 3.084 3.182 3.271 3.351 3.424 3.491 3.553 3.611 3.665 3.715 3.763 4.124 4.367 4.693 4.914 5.080 20 .9715 1.616 2.013 2.297 2.516 2.693 2.842 2.969 3.081 3.179 3.268 3.348 3.421 3.488 3.550 3.607 3.661 3.712 3.759 4.120 4.363 4.688 4.909 5.075 24 .9685 1.611 2.007 2.290 2.508 2.685 2.833 2.960 3.071 3.170 3.258 3.337 3.410 3.477 3.539 3.596 3.650 3.700 3.747 4.107 4.349 4.674 4.894 5.060 30 .9656 1.606 2.001 2.283 2.501 2.677 2.825 2.951 3.062 3.160 3.248 3.327 3.400 3.466 3.528 3.585 3.638 3.688 3.735 4.094 4.335 4.659 4.878 5.043 40 .9626 1.602 1.996 2.277 2.494 2.669 2.816 2.942 3.053 3.150 3.238 3.317 3.389 3.455 3.517 3.574 3.627 3.677 3.723 4.080 4.321 4.643 4.862 5.027 60 .9597 1.597 1.990 2.270 2.486 2.661 2.808 2.933 3.043 3.140 3.227 3.306 3.378 3.444 3.505 3.562 3.615 3.665 3.711 4.067 4.306 4.627 4.845 5.009 120 .9568 1.592 1.984 2.263 2.479 2.653 2.799 2.924 3.034 3.130 3.217 3.296 3.367 3.433 3.494 3.550 3.603 3.652 3.699 4.052 4.290 4.610 4.827 4.990 1e38 .9539 1.588 1.978 2.257 2.472 2.645 2.791 2.915 3.024 3.121 3.207 3.285 3.356 3.422 3.482 3.538 3.591 3.640 3.686 4.037 4.274 4.591 4.806 4.968""" q0675 = """\ 2 1.829602 2.751705 3.332700 3.754119 4.082579 4.350351 4.575528 4.769258 4.938876 5.089456 5.22465 5.347168 5.459072 5.56197 5.657136 5.745596 5.828188 5.905606 5.978428 6.534036 6.908522 7.411898 7.753537 8.010516 3 1.660743 2.469725 2.973973 3.338757 3.622958 3.854718 4.049715 4.217574 4.364624 4.495236 4.612559 4.718926 4.816117 4.905518 4.988228 5.065133 5.136955 5.204295 5.267653 5.751485 6.07799 6.517299 6.815682 7.040219 4 1.585479 2.344680 2.814410 3.153343 3.417165 3.632254 3.813232 3.96905 4.105579 4.226877 4.335857 4.434684 4.525004 4.608102 4.684995 4.756504 4.823298 4.885932 4.944872 5.395226 5.699385 6.108899 6.387203 6.596702 5 1.543029 2.27426 2.72431 3.048331 3.300303 3.505645 3.678397 3.827131 3.957462 4.073264 4.177319 4.27169 4.35795 4.437321 4.510774 4.579091 4.642911 4.702763 4.759089 5.189651 5.480611 5.872552 6.139026 6.339673 6 1.515809 2.229127 2.666435 2.980707 3.224876 3.423769 3.591058 3.735076 3.861273 3.973403 4.074164 4.165554 4.249094 4.325968 4.397115 4.463293 4.525119 4.583105 4.637678 5.054965 5.337079 5.717251 5.975813 6.170546 7 1.496881 2.197746 2.626119 2.933501 3.17212 3.366405 3.529778 3.670406 3.793624 3.903106 4.001488 4.090723 4.172295 4.247362 4.31684 4.381468 4.441849 4.498482 4.551786 4.959448 5.235148 5.606794 5.859629 6.050083 8 1.482962 2.174667 2.596423 2.898666 3.133126 3.323942 3.484357 3.622418 3.743376 3.850846 3.947419 4.035012 4.115085 4.188774 4.256978 4.320423 4.379701 4.435301 4.487633 4.887938 5.158734 5.523864 5.772325 5.959514 9 1.472298 2.156982 2.573637 2.871897 3.103116 3.29122 3.449316 3.585359 3.704538 3.810421 3.905564 3.991859 4.070746 4.143343 4.210539 4.273046 4.331448 4.386229 4.437792 4.832253 5.099153 5.459107 5.704096 5.888693 10 1.463868 2.142999 2.555601 2.85068 3.079300 3.265222 3.421445 3.555857 3.673594 3.778189 3.872171 3.957411 4.035332 4.107041 4.173413 4.235156 4.292845 4.346957 4.39789 4.787576 5.05129 5.407011 5.649161 5.831642 11 1.457037 2.131666 2.540969 2.833447 3.059936 3.244061 3.398740 3.531802 3.648345 3.751871 3.844888 3.929251 4.006369 4.077337 4.143024 4.204129 4.261223 4.314777 4.365186 4.750882 5.01193 5.36411 5.603886 5.784574 12 1.451389 2.122295 2.528860 2.819172 3.043878 3.226497 3.379879 3.511805 3.627341 3.729965 3.822167 3.905787 3.982224 4.052565 4.117671 4.178235 4.234823 4.287903 4.337867 4.720168 4.978946 5.32811 5.565864 5.745066 13 1.446642 2.114418 2.518673 2.807152 3.030346 3.211683 3.363958 3.494914 3.609588 3.71144 3.802942 3.885925 3.961777 4.031579 4.096185 4.156283 4.212436 4.265108 4.314686 4.694058 4.950875 5.297431 5.533435 5.711335 14 1.442597 2.107703 2.509984 2.796892 3.018785 3.199019 3.350338 3.480454 3.594382 3.695564 3.786459 3.868888 3.944232 4.013564 4.077734 4.137427 4.1932 4.245515 4.294759 4.671571 4.926672 5.270944 5.505418 5.682176 15 1.439108 2.101911 2.502485 2.788030 3.008793 3.188066 3.338551 3.467934 3.581209 3.681803 3.772166 3.854108 3.929005 3.997925 4.061712 4.121047 4.176486 4.228488 4.277436 4.651989 4.905573 5.247825 5.480945 5.656694 16 1.436068 2.096865 2.495948 2.7803 3.000071 3.178498 3.328250 3.456985 3.569684 3.669759 3.75965 3.841162 3.915663 3.984216 4.047663 4.106681 4.161824 4.213546 4.262231 4.634774 4.887015 5.227455 5.459365 5.634213 17 1.433397 2.092428 2.490198 2.773497 2.992391 3.170069 3.319169 3.447329 3.559514 3.659127 3.748598 3.829725 3.903873 3.972099 4.035242 4.093976 4.148852 4.200325 4.248775 4.619514 4.870529 5.209359 5.440181 5.614218 18 1.431030 2.088497 2.485101 2.767464 2.985576 3.162585 3.311102 3.438749 3.550474 3.649671 3.738765 3.819547 3.893377 3.961308 4.024178 4.082656 4.137293 4.188541 4.236778 4.605888 4.855804 5.193166 5.423003 5.596306 19 1.428918 2.08499 2.480552 2.762076 2.979488 3.155896 3.30389 3.431072 3.542383 3.641206 3.729960 3.810429 3.883971 3.951636 4.014258 4.072505 4.126925 4.177969 4.226014 4.593643 4.84256 5.178585 5.407524 5.580158 20 1.427023 2.081842 2.476467 2.757236 2.974016 3.149882 3.297401 3.424164 3.535099 3.633583 3.722027 3.802213 3.875493 3.942916 4.005312 4.063349 4.117571 4.168429 4.216298 4.582577 4.830579 5.16538 5.393498 5.565519 24 1.421053 2.071924 2.463589 2.741964 2.956732 3.130867 3.276871 3.402288 3.512015 3.609405 3.696852 3.776122 3.848556 3.915194 3.976858 4.03421 4.087789 4.138042 4.185340 4.547205 4.792208 5.122986 5.348394 5.518394 30 1.415131 2.062082 2.450796 2.726770 2.939512 3.111895 3.256356 3.380399 3.488888 3.585153 3.67157 3.749892 3.821449 3.887270 3.948172 4.00481 4.057717 4.107336 4.154034 4.511241 4.753052 5.079524 5.302021 5.469846 40 1.409257 2.052316 2.438086 2.711654 2.922351 3.092956 3.235846 3.358481 3.465697 3.5608 3.646150 3.723487 3.794128 3.859096 3.919198 3.975085 4.027284 4.076232 4.122296 4.474532 4.712898 5.034679 5.253982 5.419412 60 1.40343 2.042626 2.425459 2.696611 2.905244 3.074043 3.215327 3.336516 3.442417 3.536316 3.620555 3.696861 3.766541 3.830609 3.889866 3.944956 3.996401 4.044636 4.09002 4.436878 4.671454 4.987998 5.203693 5.366394 120 1.397651 2.033010 2.412913 2.681639 2.888185 3.055146 3.194785 3.314484 3.419022 3.511665 3.59474 3.66996 3.738623 3.801735 3.86009 3.914325 3.96496 4.012423 4.057072 4.398008 4.628308 4.938805 5.150236 5.309666 1e38 1.391918 2.023469 2.400447 2.666735 2.871167 3.036254 3.174203 3.292360 3.395479 3.486805 3.568651 3.642718 3.710296 3.772381 3.829761 3.883069 3.93282 3.979437 4.023276 4.357546 4.582861 4.886029 5.092081 5.247256""" q0750 = """\ 2 2.267583 3.308014 3.969236 4.451126 4.82785 5.13561 5.394819 5.618097 5.813776 5.987632 6.143829 6.285461 6.41489 6.533954 6.644113 6.746546 6.842214 6.931913 7.01631 7.660853 8.09584 8.68119 9.0788 9.377929 3 2.011896 2.883775 3.431223 3.829258 4.140443 4.394852 4.609323 4.794233 4.956425 5.10064 5.230299 5.347941 5.455509 5.554514 5.646158 5.73141 5.811064 5.885775 5.956093 6.493827 6.857365 7.3472 7.680302 7.931152 4 1.901267 2.701018 3.198596 3.559322 3.841087 4.071417 4.265624 4.433118 4.580085 4.710812 4.828384 4.935098 5.032703 5.122566 5.205771 5.283192 5.355547 5.423427 5.48733 5.976418 6.307462 6.753955 7.057827 7.286775 5 1.839820 2.599651 3.069171 3.40865 3.673526 3.889955 4.072422 4.229795 4.367901 4.490764 4.601285 4.701617 4.793402 4.877922 4.956192 5.029034 5.09712 5.161005 5.221154 5.681792 5.993844 6.415033 6.70187 6.918073 6 1.800788 2.535293 2.986795 3.312495 3.566338 3.773641 3.948369 4.099056 4.231292 4.348941 4.45478 4.550869 4.638783 4.719746 4.794731 4.864523 4.929764 4.990987 5.048635 5.490302 5.789693 6.194025 6.469523 6.677248 7 1.773818 2.490830 2.929770 3.245783 3.491823 3.692639 3.86185 4.007755 4.135786 4.249692 4.352165 4.445203 4.530329 4.608729 4.681345 4.748937 4.812126 4.871427 4.927269 5.35523 5.64547 6.037624 6.304935 6.506543 8 1.754075 2.458283 2.887956 3.196776 3.436989 3.632943 3.798002 3.940301 4.065154 4.176226 4.276148 4.366871 4.44988 4.526332 4.597147 4.663065 4.724692 4.782528 4.836995 5.254505 5.537762 5.920623 6.18169 6.378634 9 1.739001 2.433431 2.855984 3.159245 3.394934 3.587097 3.748912 3.888384 4.010742 4.119586 4.2175 4.306396 4.387735 4.462649 4.532041 4.596635 4.657026 4.713704 4.767081 5.176307 5.454025 5.829512 6.085625 6.27887 10 1.727116 2.413835 2.830746 3.129578 3.361648 3.550769 3.709972 3.847165 3.967506 4.074547 4.170832 4.258248 4.33823 4.411895 4.480128 4.543645 4.60303 4.658765 4.711254 5.113722 5.386914 5.756374 6.008439 6.198662 11 1.717506 2.397989 2.810315 3.105535 3.334641 3.521265 3.678317 3.813629 3.932304 4.037852 4.132788 4.218976 4.297831 4.370457 4.437728 4.500349 4.558895 4.613844 4.665594 5.062423 5.331834 5.696254 5.944934 6.13263 12 1.709576 2.384911 2.793439 3.085654 3.312288 3.496821 3.65207 3.785802 3.903075 4.007365 4.101163 4.186312 4.264215 4.335963 4.402419 4.46428 4.522117 4.5764 4.627523 5.019561 5.285754 5.645883 5.891679 6.077222 13 1.70292 2.373934 2.779263 3.068939 3.293478 3.476235 3.62995 3.762334 3.878409 3.981623 4.074447 4.158707 4.235793 4.306786 4.372542 4.433751 4.490977 4.544687 4.595269 4.983178 5.246593 5.603014 5.846316 6.029999 14 1.697255 2.364590 2.767188 3.05469 3.27743 3.458659 3.611050 3.742271 3.85731 3.959593 4.051572 4.13506 4.211437 4.281774 4.346922 4.407563 4.464258 4.517468 4.567581 4.951886 5.212872 5.566049 5.807169 5.989222 15 1.692374 2.356539 2.756778 3.042397 3.263576 3.443476 3.594714 3.724919 3.839053 3.940521 4.031759 4.114571 4.190326 4.260088 4.324701 4.384844 4.441071 4.493842 4.54354 4.92467 5.183511 5.533819 5.773008 5.95362 16 1.688126 2.349531 2.747712 3.031684 3.251494 3.430227 3.580451 3.709761 3.823097 3.923845 4.01443 4.096644 4.171848 4.2411 4.305239 4.364939 4.420752 4.473133 4.522464 4.900769 5.1577 5.505449 5.742915 5.92224 17 1.684395 2.343375 2.739744 3.022264 3.240865 3.418565 3.567889 3.696405 3.809031 3.909139 3.999142 4.080823 4.155535 4.224333 4.288048 4.347353 4.402795 4.454828 4.50383 4.879604 5.134819 5.48027 5.716186 5.894353 18 1.681092 2.337926 2.732687 3.013916 3.23144 3.408218 3.55674 3.684546 3.796536 3.896071 3.985552 4.066754 4.141026 4.209415 4.27275 4.331699 4.386808 4.438527 4.487232 4.860723 5.114389 5.457759 5.692272 5.86939 19 1.678147 2.333067 2.726393 3.006467 3.223026 3.398978 3.546777 3.673945 3.785363 3.884381 3.973391 4.054162 4.128035 4.196054 4.259045 4.317673 4.37248 4.423914 4.472351 4.843772 5.096029 5.437505 5.67074 5.846902 20 1.675506 2.328708 2.720745 2.999780 3.215469 3.390674 3.537821 3.664411 3.775312 3.873861 3.962444 4.042823 4.116334 4.184018 4.246696 4.305031 4.359563 4.410739 4.458932 4.828464 5.079434 5.419178 5.651242 5.82653 24 1.667194 2.314991 2.702957 2.978701 3.191627 3.364455 3.50952 3.63426 3.7435 3.840544 3.927753 4.006868 4.079211 4.14581 4.207477 4.264864 4.318505 4.368841 4.416241 4.779619 5.026378 5.360437 5.58865 5.761054 30 1.658964 2.301406 2.68532 2.957771 3.167919 3.338345 3.481298 3.604155 3.711699 3.8072 3.892996 3.970809 4.041947 4.107423 4.168039 4.224442 4.277156 4.326617 4.373187 4.730101 4.9724 5.300398 5.524486 5.693793 40 1.650814 2.28795 2.667830 2.936984 3.144337 3.312335 3.453142 3.574077 3.679882 3.773798 3.858136 3.934602 4.004488 4.068796 4.128318 4.183691 4.235434 4.283976 4.329675 4.679735 4.917252 5.238689 5.458277 5.62419 60 1.642744 2.274622 2.650486 2.916339 3.120874 3.286413 3.425034 3.544004 3.648023 3.740302 3.823131 3.898196 3.966776 4.029861 4.088234 4.142523 4.19324 4.24081 4.285584 4.628295 4.860604 5.174794 5.389348 5.551435 120 1.634753 2.261421 2.633285 2.895829 3.097525 3.260567 3.396959 3.513912 3.616089 3.706672 3.787929 3.861531 3.92874 3.990536 4.047692 4.10083 4.150455 4.196985 4.240768 4.575490 4.802013 5.107977 5.316696 5.474283 1e38 1.626840 2.248346 2.616224 2.875451 3.074279 3.234786 3.368898 3.483775 3.584045 3.672862 3.752475 3.824535 3.890294 3.950721 4.006580 4.058483 4.106932 4.152338 4.195044 4.520933 4.740866 5.037152 5.238766 5.390726""" q0800 = """\ 2 2.666345 3.820436 4.558532 5.098158 5.520848 5.866626 6.158145 6.409446 6.62982 6.825717 7.001791 7.161505 7.307502 7.441845 7.566171 7.681802 7.789818 7.891113 7.986436 8.714887 9.206808 9.868718 10.31830 10.65683 3 2.316120 3.245426 3.832597 4.261107 4.596942 4.871989 5.104169 5.304561 5.480484 5.637021 5.777843 5.905682 6.022626 6.130305 6.230013 6.322797 6.409513 6.49087 6.567462 7.153711 7.55053 8.085698 8.449862 8.724212 4 2.168283 3.003795 3.52645 3.90676 4.204595 4.44853 4.654519 4.832388 4.988615 5.127694 5.25287 5.366554 5.470593 5.566425 5.655195 5.737827 5.815079 5.887577 5.955847 6.47896 6.833568 7.31242 7.638648 7.884592 5 2.087215 2.871505 3.358337 3.711564 3.987876 4.214094 4.405111 4.57007 4.714986 4.844026 4.960193 5.065723 5.162321 5.25132 5.333779 5.410553 5.482342 5.549725 5.613191 6.099852 6.430105 6.876484 7.180827 7.410389 6 2.036122 2.788188 3.252203 3.588013 3.850385 4.06507 4.246305 4.402806 4.540296 4.662734 4.772969 4.873124 4.964814 5.049304 5.127595 5.200498 5.268677 5.33268 5.392969 5.855517 6.169658 6.594568 6.884463 7.103222 7 2.001005 2.730943 3.179141 3.502777 3.755348 3.961886 4.136188 4.286677 4.418877 4.536604 4.642603 4.738913 4.82709 4.908349 4.983652 5.05378 5.119368 5.180945 5.238953 5.684175 5.986732 6.39621 6.675724 6.886723 8 1.975395 2.689205 3.125785 3.440421 3.685706 3.886163 4.055272 4.201248 4.329470 4.443647 4.546448 4.639854 4.725375 4.804189 4.87723 4.945254 5.008879 5.068616 5.124894 5.556957 5.850708 6.248453 6.520077 6.725179 9 1.955898 2.657432 3.085114 3.392817 3.632464 3.828199 3.993263 4.135716 4.260824 4.37222 4.472512 4.563637 4.64707 4.723960 4.79522 4.861587 4.923664 4.981949 5.036862 5.458529 5.745314 6.133773 6.399153 6.59959 10 1.940561 2.632439 3.053086 3.355281 3.590431 3.782386 3.944205 4.083824 4.206424 4.315576 4.413841 4.503121 4.584862 4.660193 4.730009 4.795032 4.855852 4.912959 4.966762 5.37997 5.661078 6.041965 6.302252 6.498885 11 1.928182 2.612267 3.027211 3.324922 3.556399 3.745257 3.904411 4.041698 4.16223 4.269529 4.366119 4.453871 4.534212 4.608251 4.676869 4.740775 4.800552 4.85668 4.909561 5.315725 5.5921 5.966667 6.222702 6.41616 12 1.917981 2.595645 3.005872 3.299861 3.528278 3.714552 3.871475 4.006806 4.125603 4.231343 4.326522 4.412988 4.492148 4.565096 4.632701 4.695665 4.754559 4.809858 4.861959 5.262152 5.534506 5.9037 6.156119 6.346875 13 1.909431 2.581711 2.987972 3.278821 3.504650 3.688731 3.843759 3.977426 4.094742 4.199153 4.293127 4.378492 4.45664 4.528654 4.595391 4.657546 4.715682 4.770269 4.8217 5.216755 5.485643 5.850201 6.099497 6.287919 14 1.90216 2.569864 2.972742 3.260906 3.484516 3.666713 3.82011 3.952342 4.068380 4.171642 4.264573 4.348985 4.426256 4.497459 4.563444 4.624895 4.682373 4.736342 4.787189 5.177769 5.443632 5.804138 6.050703 6.237084 15 1.895903 2.559666 2.959626 3.245467 3.467154 3.647714 3.799691 3.930673 4.045596 4.147854 4.239872 4.32345 4.399954 4.470446 4.53577 4.596605 4.653505 4.706931 4.757265 5.143906 5.4071 5.764029 6.00818 6.192757 16 1.89046 2.550797 2.948212 3.232024 3.452027 3.631152 3.781882 3.911763 4.025705 4.127077 4.218291 4.301132 4.376957 4.446821 4.511561 4.571849 4.628237 4.681181 4.731062 5.114203 5.375025 5.728765 5.970765 6.153733 17 1.885683 2.543012 2.93819 3.220213 3.438729 3.616585 3.766210 3.895117 4.008187 4.108772 4.19927 4.281455 4.356676 4.42598 4.490198 4.549999 4.605930 4.658444 4.707919 5.08793 5.346623 5.697501 5.937567 6.119088 18 1.881457 2.536125 2.929319 3.209754 3.426947 3.603672 3.752313 3.880348 3.992639 4.09252 4.182377 4.263975 4.338653 4.407454 4.471204 4.530568 4.586089 4.638215 4.687324 5.064516 5.321288 5.66958 5.907896 6.088107 19 1.877691 2.529988 2.921412 3.200427 3.416435 3.592147 3.739903 3.867156 3.978745 4.077993 4.167272 4.24834 4.322529 4.390877 4.454204 4.513172 4.568321 4.620098 4.668877 5.043513 5.298541 5.644481 5.881205 6.060224 20 1.874315 2.524485 2.914320 3.192058 3.407000 3.581797 3.728755 3.855300 3.966255 4.064929 4.153685 4.234272 4.308018 4.375954 4.438897 4.497506 4.552317 4.603776 4.652254 5.024562 5.277998 5.621789 5.857057 6.034984 24 1.863701 2.507187 2.89201 3.165709 3.377268 3.549158 3.69357 3.817854 3.92678 4.023614 4.110690 4.189731 4.262048 4.328656 4.390359 4.447807 4.501527 4.551956 4.599461 4.964202 5.212441 5.549191 5.779675 5.954012 30 1.853207 2.490080 2.869925 3.139592 3.347756 3.516716 3.658554 3.780544 3.887403 3.982357 4.067712 4.145167 4.216014 4.281252 4.341675 4.397921 4.450509 4.49987 4.546362 4.903188 5.145946 5.47522 5.700597 5.871091 40 1.842829 2.473164 2.848060 3.113699 3.318456 3.484461 3.62369 3.743347 3.848096 3.941126 4.024712 4.100533 4.16986 4.233681 4.292775 4.34777 4.399178 4.447421 4.492854 4.841333 5.078248 5.399473 5.619306 5.785608 60 1.832568 2.456435 2.826413 3.088026 3.289358 3.452379 3.588962 3.70624 3.808829 3.899882 3.981645 4.055774 4.123524 4.185868 4.243575 4.297261 4.34743 4.394499 4.438814 4.778404 5.009002 5.321406 5.535087 5.696698 120 1.822478 2.439890 2.804980 3.062567 3.260456 3.420458 3.55435 3.669198 3.769570 3.858583 3.938458 4.010829 4.076934 4.137731 4.193979 4.246285 4.295145 4.340968 4.384094 4.714106 4.937761 5.24027 5.446912 5.603078 1e38 1.812388 2.423529 2.783758 3.037317 3.231739 3.388684 3.519834 3.632192 3.73028 3.817183 3.895093 3.965627 4.030005 4.089173 4.143877 4.194716 4.242179 4.286668 4.328517 4.648069 4.863937 5.155024 5.353283 5.50281""" q0850 = """\ 2 3.226562 4.548022 5.398759 6.022701 6.512387 6.913502 7.251997 7.54401 7.800236 8.028116 8.233021 8.418953 8.588968 8.74545 8.890294 9.02503 9.150913 9.268977 9.380094 10.22972 10.80450 11.58094 12.11086 12.51097 3 2.721399 3.731515 4.374509 4.845675 5.215912 5.5197 5.776502 5.998388 6.193356 6.366968 6.523249 6.665198 6.795111 6.914781 7.025634 7.128823 7.225292 7.315823 7.401073 8.054202 8.496827 9.094477 9.501702 9.808753 4 2.514747 3.399285 3.956491 4.363675 4.68348 4.945965 5.16798 5.359938 5.52872 5.679113 5.814574 5.937683 6.050411 6.154302 6.25058 6.34024 6.424092 6.502812 6.576963 7.145835 7.532079 8.054293 8.410406 8.679063 5 2.403262 3.220436 3.730867 4.102766 4.394545 4.633955 4.836465 5.011596 5.165628 5.302922 5.426626 5.539086 5.642096 5.737057 5.825086 5.907085 5.983793 6.055822 6.123687 6.644817 6.999123 7.478735 7.806159 8.05333 6 2.333697 3.108965 3.589945 3.939419 4.213263 4.437836 4.627757 4.791998 4.936465 5.06525 5.181307 5.286833 5.38351 5.47265 5.555297 5.632296 5.704339 5.771998 5.835756 6.325681 6.659107 7.110867 7.419518 7.652631 7 2.286206 3.032919 3.493643 3.827573 4.088914 4.303095 4.484169 4.640738 4.77845 4.901217 5.011858 5.112468 5.20465 5.289655 5.368478 5.441922 5.510646 5.575196 5.63603 6.103717 6.422253 6.85415 7.149428 7.372543 8 2.251741 2.977758 3.423692 3.746199 3.998303 4.204778 4.379271 4.530117 4.662781 4.781044 4.887624 4.984545 5.073351 5.155248 5.231193 5.30196 5.368185 5.430392 5.489022 5.939926 6.24721 6.664096 6.949269 7.16483 9 2.225598 2.935932 3.370588 3.684337 3.92933 4.12985 4.299243 4.445643 4.57438 4.68913 4.792542 4.88658 4.972745 5.052208 5.125899 5.194568 5.258832 5.319201 5.376101 5.81381 6.112237 6.517297 6.794508 7.004117 10 2.205093 2.903132 3.328904 3.635722 3.875064 4.070838 4.236155 4.378996 4.504581 4.61651 4.717372 4.809088 4.893124 4.970624 5.042494 5.109469 5.172148 5.231029 5.28653 5.713546 6.004781 6.400234 6.670974 6.875744 11 2.18858 2.876725 3.295316 3.596509 3.831250 4.023149 4.18513 4.325052 4.448048 4.557656 4.656418 4.74622 4.828499 4.904377 4.974743 5.040315 5.101683 5.159333 5.213674 5.631818 5.917077 6.304535 6.569888 6.770631 12 2.174999 2.855009 3.267675 3.564211 3.795132 3.983803 4.143002 4.280484 4.401312 4.508975 4.605974 4.694168 4.77497 4.849483 4.918582 4.982973 5.043235 5.099847 5.153209 5.563854 5.84405 6.22473 6.485512 6.682838 13 2.163633 2.836837 3.244531 3.537147 3.764842 3.950784 4.107624 4.243034 4.36202 4.468027 4.563524 4.650346 4.729887 4.803233 4.871249 4.93463 4.993946 5.049668 5.102191 5.5064 5.782244 6.157087 6.413931 6.608311 14 2.153982 2.821408 3.224869 3.514139 3.739075 3.922677 4.077491 4.21112 4.328519 4.433097 4.527298 4.612934 4.691385 4.763723 4.830801 4.893306 4.951801 5.006752 5.058548 5.457164 5.729217 6.09897 6.352377 6.544185 15 2.145684 2.808145 3.207959 3.494339 3.716887 3.898461 4.051515 4.183594 4.299611 4.402944 4.496014 4.580615 4.658112 4.729568 4.795825 4.857564 4.91534 4.969615 5.020773 5.414476 5.683193 6.048461 6.298836 6.488374 16 2.138475 2.796621 3.193261 3.47712 3.697581 3.877377 4.028889 4.159607 4.274409 4.376647 4.468721 4.55241 4.629066 4.699743 4.765275 4.826337 4.883478 4.937154 4.987748 5.377097 5.642851 6.004129 6.251805 6.439321 17 2.132153 2.786517 3.180367 3.462007 3.680628 3.858856 4.009003 4.138517 4.252242 4.353508 4.444698 4.527576 4.603485 4.673469 4.738356 4.798814 4.855389 4.908532 4.958622 5.344083 5.607184 5.964886 6.21014 6.395841 18 2.126564 2.777584 3.168965 3.448637 3.665623 3.842455 3.991387 4.119827 4.232591 4.332989 4.423388 4.505541 4.58078 4.650143 4.714452 4.774369 4.830436 4.883101 4.932739 5.314701 5.575413 5.929888 6.172953 6.357013 19 2.121587 2.769631 3.158810 3.436724 3.652248 3.82783 3.975673 4.103149 4.21505 4.314667 4.404354 4.485854 4.560491 4.629294 4.693081 4.752509 4.808118 4.860351 4.909581 5.288379 5.546924 5.898469 6.139544 6.322112 20 2.117128 2.762505 3.149708 3.426043 3.640251 3.814707 3.961568 4.088173 4.199295 4.298206 4.387249 4.468158 4.542248 4.610545 4.673858 4.732844 4.788036 4.839877 4.888736 5.264656 5.521227 5.870097 6.109355 6.290558 24 2.103128 2.740133 3.121118 3.392466 3.60251 3.773393 3.917129 4.040961 4.149593 4.246248 4.33323 4.412242 4.484578 4.551244 4.613036 4.670595 4.724445 4.775019 4.822681 5.189274 5.439419 5.779554 6.012859 6.189586 30 2.089309 2.718054 3.092876 3.359261 3.56514 3.732436 3.873024 3.994053 4.10016 4.19452 4.2794 4.356475 4.427015 4.492009 4.552236 4.608325 4.660792 4.710058 4.756481 5.113372 5.356776 5.687685 5.914664 6.08662 40 2.07567 2.696264 3.064978 3.326418 3.52813 3.691822 3.829233 3.947423 4.050965 4.142986 4.225718 4.300807 4.369502 4.432773 4.491385 4.545955 4.596987 4.644896 4.69003 5.036754 5.27302 5.594062 5.814221 5.981005 60 2.062208 2.674759 3.037417 3.293931 3.491470 3.651535 3.785736 3.901046 4.001976 4.091607 4.172136 4.245183 4.311975 4.373463 4.430401 4.483391 4.532928 4.579419 4.623205 4.95919 5.187807 5.498134 5.710792 5.871841 120 2.048920 2.653534 3.010189 3.261791 3.455148 3.611561 3.742514 3.854896 3.953159 4.040341 4.118605 4.189543 4.254363 4.314 4.369191 4.42053 4.4685 4.513501 4.555864 4.880396 5.100706 5.399172 5.60337 5.757859 1e38 2.035805 2.632586 2.983286 3.229990 3.419154 3.571884 3.699544 3.808945 3.904479 3.989143 4.065068 4.133821 4.19659 4.254292 4.307653 4.357255 4.403572 4.446994 4.487848 4.800043 5.011193 5.296241 5.4906 5.637297""" q0900 = """\ 1 8.929 13.44 16.36 18.49 20.15 21.51 22.64 23.62 24.48 25.24 25.92 26.54 27.10 27.62 28.10 28.54 28.96 29.35 29.71 32.50 34.38 36.91 38.62 39.91 2 4.129 5.733 6.773 7.538 8.139 8.633 9.049 9.409 9.725 10.01 10.26 10.49 10.70 10.89 11.07 11.24 11.39 11.54 11.68 12.73 13.44 14.40 15.04 15.54 3 3.328 4.467 5.199 5.738 6.162 6.511 6.806 7.062 7.287 7.487 7.667 7.831 7.982 8.120 8.248 8.368 8.479 8.584 8.683 9.440 9.954 10.65 11.12 11.48 4 3.015 3.976 4.586 5.035 5.388 5.679 5.926 6.139 6.327 6.494 6.645 6.783 6.909 7.025 7.132 7.233 7.326 7.414 7.497 8.135 8.569 9.156 9.558 9.861 5 2.850 3.717 4.264 4.664 4.979 5.238 5.458 5.648 5.816 5.965 6.100 6.223 6.336 6.439 6.536 6.626 6.710 6.788 6.863 7.435 7.824 8.353 8.714 8.987 6 2.748 3.558 4.065 4.435 4.726 4.966 5.168 5.344 5.499 5.637 5.762 5.875 5.979 6.075 6.164 6.247 6.325 6.398 6.466 6.996 7.358 7.848 8.184 8.438 7 2.679 3.451 3.931 4.280 4.555 4.780 4.971 5.137 5.283 5.413 5.530 5.637 5.735 5.826 5.910 5.988 6.061 6.130 6.195 6.695 7.036 7.500 7.818 8.059 8 2.630 3.374 3.834 4.169 4.431 4.646 4.829 4.987 5.126 5.250 5.362 5.464 5.558 5.644 5.724 5.799 5.869 5.935 5.997 6.475 6.801 7.245 7.550 7.780 9 2.592 3.316 3.761 4.084 4.337 4.545 4.721 4.873 5.007 5.126 5.234 5.333 5.423 5.506 5.583 5.655 5.722 5.786 5.845 6.306 6.621 7.049 7.343 7.566 10 2.563 3.270 3.704 4.018 4.264 4.465 4.636 4.783 4.913 5.029 5.134 5.229 5.316 5.397 5.472 5.542 5.607 5.668 5.726 6.173 6.478 6.894 7.180 7.396 11 2.540 3.234 3.658 3.965 4.205 4.401 4.567 4.711 4.838 4.951 5.053 5.145 5.231 5.309 5.382 5.450 5.514 5.573 5.630 6.065 6.363 6.768 7.046 7.257 12 2.521 3.204 3.621 3.921 4.156 4.349 4.511 4.652 4.776 4.886 4.986 5.076 5.160 5.236 5.308 5.374 5.436 5.495 5.550 5.975 6.267 6.663 6.936 7.142 13 2.504 3.179 3.589 3.885 4.116 4.304 4.464 4.602 4.724 4.832 4.930 5.019 5.100 5.175 5.245 5.310 5.371 5.429 5.483 5.900 6.186 6.575 6.842 7.045 14 2.491 3.158 3.563 3.854 4.081 4.267 4.424 4.560 4.679 4.786 4.882 4.969 5.050 5.124 5.192 5.256 5.316 5.372 5.426 5.836 6.116 6.499 6.762 6.961 15 2.479 3.140 3.540 3.828 4.052 4.235 4.390 4.524 4.641 4.746 4.841 4.927 5.006 5.079 5.146 5.209 5.268 5.324 5.376 5.780 6.056 6.433 6.692 6.888 16 2.469 3.124 3.520 3.804 4.026 4.207 4.360 4.492 4.608 4.712 4.805 4.890 4.968 5.040 5.106 5.169 5.227 5.282 5.333 5.731 6.004 6.376 6.631 6.825 17 2.460 3.110 3.503 3.784 4.003 4.182 4.334 4.464 4.579 4.681 4.774 4.857 4.934 5.005 5.071 5.133 5.190 5.244 5.295 5.688 5.958 6.325 6.577 6.769 18 2.452 3.098 3.487 3.766 3.984 4.161 4.310 4.440 4.553 4.654 4.746 4.829 4.905 4.975 5.040 5.101 5.158 5.211 5.262 5.650 5.917 6.280 6.529 6.718 19 2.445 3.087 3.474 3.751 3.966 4.142 4.290 4.418 4.530 4.630 4.721 4.803 4.878 4.948 5.012 5.072 5.129 5.182 5.232 5.616 5.880 6.239 6.486 6.673 20 2.439 3.077 3.462 3.736 3.950 4.124 4.271 4.398 4.510 4.609 4.699 4.780 4.855 4.923 4.987 5.047 5.103 5.155 5.205 5.586 5.847 6.202 6.447 6.633 24 2.420 3.047 3.423 3.692 3.900 4.070 4.213 4.336 4.445 4.541 4.628 4.707 4.780 4.847 4.909 4.966 5.020 5.071 5.119 5.489 5.741 6.086 6.323 6.503 30 2.400 3.017 3.386 3.648 3.851 4.016 4.155 4.275 4.381 4.474 4.559 4.635 4.706 4.770 4.830 4.886 4.939 4.988 5.034 5.391 5.636 5.969 6.198 6.372 40 2.381 2.988 3.348 3.605 3.802 3.963 4.099 4.215 4.317 4.408 4.490 4.564 4.632 4.694 4.752 4.806 4.857 4.904 4.949 5.294 5.529 5.850 6.071 6.238 60 2.363 2.959 3.312 3.562 3.755 3.911 4.042 4.155 4.254 4.342 4.421 4.493 4.558 4.619 4.675 4.727 4.775 4.821 4.864 5.196 5.422 5.730 5.941 6.101 120 2.344 2.930 3.276 3.520 3.707 3.859 3.986 4.096 4.191 4.276 4.353 4.422 4.485 4.543 4.597 4.647 4.694 4.738 4.779 5.097 5.313 5.606 5.808 5.960 1e38 2.326 2.902 3.240 3.478 3.661 3.808 3.931 4.037 4.129 4.211 4.285 4.351 4.412 4.468 4.519 4.568 4.612 4.654 4.694 4.997 5.202 5.480 5.669 5.812""" q0950 = """\ 1 17.97 26.98 32.82 37.08 40.41 43.12 45.40 47.36 49.07 50.59 51.96 53.20 54.33 55.36 56.32 57.22 58.04 58.83 59.56 65.15 68.92 73.97 77.40 79.98 2 6.085 8.331 9.799 10.88 11.73 12.43 13.03 13.54 13.99 14.40 14.76 15.09 15.39 15.65 15.92 16.14 16.38 16.57 16.78 18.27 19.28 20.66 21.59 22.29 3 4.501 5.910 6.825 7.502 8.037 8.478 8.852 9.177 9.462 9.717 9.946 10.15 10.35 10.52 10.69 10.84 10.98 11.11 11.24 12.21 12.86 13.76 14.36 14.82 4 3.926 5.040 5.757 6.287 6.706 7.053 7.347 7.602 7.826 8.027 8.208 8.373 8.524 8.664 8.793 8.914 9.027 9.133 9.233 10.00 10.53 11.24 11.73 12.10 5 3.635 4.602 5.218 5.673 6.033 6.330 6.582 6.801 6.995 7.167 7.323 7.466 7.596 7.716 7.828 7.932 8.030 8.122 8.208 8.875 9.330 9.949 10.37 10.69 6 3.460 4.339 4.896 5.305 5.628 5.895 6.122 6.319 6.493 6.649 6.789 6.917 7.034 7.143 7.244 7.338 7.426 7.508 7.586 8.189 8.601 9.162 9.547 9.839 7 3.344 4.165 4.681 5.060 5.359 5.606 5.815 5.997 6.158 6.302 6.431 6.550 6.658 6.759 6.852 6.939 7.020 7.097 7.169 7.727 8.110 8.631 8.989 9.260 8 3.261 4.041 4.529 4.886 5.167 5.399 5.596 5.767 5.918 6.053 6.175 6.287 6.389 6.483 6.571 6.653 6.729 6.801 6.869 7.395 7.756 8.248 8.586 8.843 9 3.199 3.948 4.415 4.755 5.024 5.244 5.432 5.595 5.738 5.867 5.983 6.089 6.186 6.276 6.359 6.437 6.510 6.579 6.643 7.144 7.488 7.958 8.281 8.526 10 3.151 3.877 4.327 4.654 4.912 5.124 5.304 5.460 5.598 5.722 5.833 5.935 6.028 6.114 6.194 6.269 6.339 6.405 6.467 6.948 7.278 7.730 8.041 8.276 11 3.113 3.820 4.256 4.574 4.823 5.028 5.202 5.353 5.486 5.605 5.713 5.811 5.901 5.984 6.062 6.134 6.202 6.265 6.325 6.790 7.109 7.546 7.847 8.075 12 3.081 3.773 4.199 4.508 4.750 4.950 5.119 5.265 5.395 5.510 5.615 5.710 5.797 5.878 5.953 6.023 6.089 6.151 6.209 6.660 6.970 7.394 7.687 7.908 13 3.055 3.734 4.151 4.453 4.690 4.884 5.049 5.192 5.318 5.431 5.533 5.625 5.711 5.789 5.862 5.931 5.995 6.055 6.112 6.551 6.853 7.267 7.552 7.769 14 3.033 3.701 4.111 4.407 4.639 4.829 4.990 5.130 5.253 5.364 5.463 5.554 5.637 5.714 5.785 5.852 5.915 5.973 6.029 6.459 6.754 7.159 7.437 7.649 15 3.014 3.673 4.076 4.367 4.595 4.782 4.940 5.077 5.198 5.306 5.403 5.492 5.574 5.649 5.719 5.785 5.846 5.904 5.958 6.379 6.669 7.065 7.338 7.546 16 2.998 3.649 4.046 4.333 4.557 4.741 4.896 5.031 5.150 5.256 5.352 5.439 5.519 5.593 5.662 5.726 5.786 5.843 5.896 6.310 6.594 6.983 7.252 7.456 17 2.984 3.628 4.020 4.303 4.524 4.705 4.858 4.991 5.108 5.212 5.306 5.392 5.471 5.544 5.612 5.675 5.734 5.790 5.842 6.249 6.529 6.912 7.176 7.377 18 2.971 3.609 3.997 4.276 4.494 4.673 4.824 4.955 5.071 5.173 5.266 5.351 5.429 5.501 5.567 5.629 5.688 5.743 5.794 6.195 6.471 6.848 7.108 7.307 19 2.960 3.593 3.977 4.253 4.468 4.645 4.794 4.924 5.037 5.139 5.231 5.314 5.391 5.462 5.528 5.589 5.647 5.701 5.752 6.147 6.419 6.791 7.048 7.244 20 2.950 3.578 3.958 4.232 4.445 4.620 4.768 4.895 5.008 5.108 5.199 5.282 5.357 5.427 5.492 5.553 5.610 5.663 5.714 6.104 6.372 6.740 6.994 7.187 24 2.919 3.532 3.901 4.166 4.373 4.541 4.684 4.807 4.915 5.012 5.099 5.179 5.251 5.319 5.381 5.439 5.494 5.545 5.594 5.968 6.226 6.578 6.822 7.007 30 2.888 3.486 3.845 4.102 4.301 4.464 4.601 4.720 4.824 4.917 5.001 5.077 5.147 5.211 5.271 5.327 5.379 5.429 5.475 5.833 6.080 6.417 6.650 6.827 40 2.858 3.442 3.791 4.039 4.232 4.388 4.521 4.634 4.735 4.824 4.904 4.977 5.044 5.106 5.163 5.216 5.266 5.313 5.358 5.700 5.934 6.255 6.477 6.645 60 2.829 3.399 3.737 3.977 4.163 4.314 4.441 4.550 4.646 4.732 4.808 4.878 4.942 5.001 5.056 5.107 5.154 5.199 5.241 5.566 5.789 6.093 6.302 6.462 120 2.800 3.356 3.685 3.917 4.096 4.241 4.363 4.468 4.560 4.641 4.714 4.781 4.842 4.898 4.950 4.998 5.043 5.086 5.126 5.434 5.644 5.929 6.126 6.275 1e38 2.772 3.314 3.633 3.858 4.030 4.170 4.286 4.387 4.474 4.552 4.622 4.685 4.743 4.796 4.845 4.891 4.934 4.974 5.012 5.301 5.498 5.764 5.947 6.085""" q0975 = """\ 1 35.99 54.00 65.69 74.22 80.87 86.29 90.85 94.77 98.20 101.3 104.0 106.5 108.8 110.8 112.7 114.5 116.2 117.7 119.2 130.4 137.9 148.1 154.9 160.0 2 8.776 11.94 14.02 15.54 16.75 17.74 18.58 19.31 19.95 20.52 21.03 21.49 21.91 22.30 22.67 23.01 23.32 23.62 23.89 26.03 27.47 29.42 30.74 31.74 3 5.907 7.661 8.808 9.659 10.33 10.89 11.36 11.77 12.14 12.46 12.75 13.01 13.25 13.47 13.68 13.87 14.05 14.22 14.38 15.62 16.46 17.58 18.37 18.95 4 4.943 6.244 7.088 7.715 8.213 8.625 8.975 9.279 9.548 9.788 10.00 10.20 10.38 10.55 10.71 10.85 10.99 11.11 11.23 12.16 12.78 13.65 14.23 14.68 5 4.474 5.558 6.257 6.775 7.186 7.526 7.816 8.068 8.291 8.490 8.670 8.834 8.984 9.124 9.253 9.373 9.486 9.592 9.693 10.47 11.00 11.72 12.21 12.59 6 4.198 5.158 5.772 6.226 6.586 6.884 7.138 7.359 7.554 7.729 7.887 8.031 8.163 8.285 8.399 8.505 8.605 8.698 8.787 9.469 9.937 10.57 11.01 11.34 7 4.018 4.897 5.455 5.867 6.194 6.464 6.694 6.894 7.071 7.230 7.373 7.504 7.624 7.735 7.838 7.935 8.025 8.110 8.191 8.812 9.239 9.822 10.22 10.53 8 3.891 4.714 5.233 5.616 5.919 6.169 6.382 6.567 6.731 6.878 7.011 7.132 7.244 7.347 7.442 7.532 7.616 7.694 7.769 8.346 8.743 9.286 9.660 9.944 9 3.797 4.578 5.069 5.430 5.715 5.950 6.151 6.325 6.479 6.617 6.742 6.856 6.961 7.057 7.148 7.232 7.311 7.385 7.455 7.999 8.373 8.885 9.238 9.506 10 3.725 4.474 4.943 5.286 5.558 5.782 5.972 6.138 6.284 6.415 6.534 6.642 6.742 6.834 6.920 7.000 7.075 7.145 7.212 7.729 8.085 8.574 8.910 9.166 11 3.667 4.391 4.843 5.173 5.433 5.648 5.830 5.989 6.130 6.255 6.369 6.473 6.568 6.656 6.738 6.815 6.887 6.955 7.018 7.514 7.856 8.324 8.648 8.894 12 3.620 4.324 4.761 5.080 5.332 5.539 5.715 5.868 6.004 6.125 6.235 6.335 6.426 6.511 6.591 6.664 6.734 6.799 6.860 7.338 7.668 8.120 8.433 8.670 13 3.582 4.269 4.694 5.004 5.248 5.449 5.620 5.768 5.899 6.017 6.123 6.220 6.309 6.391 6.468 6.539 6.606 6.670 6.729 7.192 7.511 7.950 8.253 8.484 14 3.549 4.222 4.638 4.940 5.178 5.373 5.540 5.684 5.812 5.926 6.029 6.123 6.210 6.290 6.364 6.434 6.499 6.560 6.618 7.068 7.379 7.806 8.100 8.325 15 3.521 4.182 4.589 4.885 5.117 5.309 5.471 5.612 5.736 5.848 5.948 6.040 6.125 6.205 6.275 6.343 6.407 6.467 6.523 6.962 7.265 7.682 7.969 8.189 16 3.497 4.148 4.548 4.838 5.065 5.253 5.412 5.550 5.671 5.780 5.879 5.969 6.051 6.128 6.199 6.265 6.327 6.386 6.441 6.870 7.167 7.574 7.856 8.070 17 3.476 4.118 4.511 4.797 5.020 5.204 5.360 5.495 5.615 5.722 5.818 5.906 5.987 6.062 6.132 6.197 6.258 6.315 6.369 6.790 7.080 7.479 7.756 7.966 18 3.458 4.091 4.479 4.760 4.980 5.161 5.315 5.448 5.565 5.670 5.765 5.851 5.931 6.004 6.073 6.137 6.196 6.253 6.306 6.719 7.004 7.396 7.667 7.874 19 3.441 4.068 4.451 4.728 4.945 5.123 5.274 5.405 5.521 5.624 5.717 5.803 5.881 5.953 6.020 6.083 6.142 6.197 6.250 6.656 6.936 7.322 7.589 7.792 20 3.427 4.047 4.426 4.699 4.914 5.089 5.238 5.367 5.481 5.583 5.675 5.759 5.836 5.907 5.974 6.035 6.093 6.148 6.199 6.599 6.876 7.255 7.518 7.718 24 3.381 3.982 4.347 4.610 4.816 4.984 5.126 5.250 5.358 5.455 5.543 5.623 5.696 5.764 5.827 5.886 5.941 5.993 6.042 6.422 6.685 7.046 7.295 7.486 30 3.337 3.919 4.271 4.523 4.720 4.881 5.017 5.134 5.238 5.330 5.414 5.490 5.560 5.624 5.684 5.740 5.792 5.841 5.888 6.248 6.497 6.838 7.075 7.255 40 3.294 3.858 4.196 4.439 4.627 4.780 4.910 5.022 5.120 5.208 5.287 5.360 5.426 5.487 5.543 5.596 5.646 5.692 5.736 6.077 6.311 6.633 6.855 7.025 60 3.251 3.798 4.124 4.356 4.536 4.682 4.806 4.912 5.006 5.089 5.164 5.232 5.295 5.352 5.406 5.456 5.502 5.546 5.588 5.908 6.127 6.428 6.636 6.795 120 3.210 3.739 4.053 4.275 4.447 4.587 4.704 4.805 4.894 4.972 5.043 5.107 5.166 5.221 5.271 5.318 5.362 5.403 5.442 5.741 5.946 6.225 6.418 6.564 1e38 3.170 3.682 3.984 4.197 4.361 4.494 4.605 4.700 4.784 4.858 4.925 4.985 5.041 5.092 5.139 5.183 5.224 5.262 5.299 5.577 5.766 6.023 6.199 6.333""" q0990 = """\ 1 90.02 135.0 164.3 185.6 202.2 215.8 227.2 237.0 245.6 253.2 260.0 266.2 271.8 277.0 281.8 286.3 290.4 294.3 298.0 326.0 344.8 370.1 387.3 400.1 2 14.04 19.02 22.29 24.72 26.63 28.20 29.53 30.68 31.69 32.59 33.40 34.13 34.81 35.43 36.00 36.53 37.03 37.50 37.95 41.32 43.61 46.70 48.80 50.38 3 8.260 10.62 12.17 13.32 14.24 15.00 15.65 16.21 16.69 17.13 17.53 17.89 18.22 18.52 18.81 19.07 19.32 19.55 19.77 21.44 22.59 24.13 25.19 25.99 4 6.511 8.120 9.173 9.958 10.58 11.10 11.54 11.92 12.26 12.57 12.84 13.09 13.32 13.53 13.72 13.91 14.08 14.24 14.39 15.57 16.38 17.46 18.20 18.77 5 5.702 6.976 7.804 8.421 8.913 9.321 9.669 9.971 10.24 10.48 10.70 10.89 11.08 11.24 11.40 11.55 11.68 11.81 11.93 12.87 13.51 14.39 14.99 15.45 6 5.243 6.331 7.033 7.556 7.972 8.318 8.612 8.869 9.097 9.300 9.485 9.653 9.808 9.951 10.08 10.21 10.32 10.43 10.54 11.34 11.89 12.65 13.17 13.55 7 4.949 5.919 6.542 7.005 7.373 7.678 7.939 8.166 8.367 8.548 8.711 8.860 8.997 9.124 9.242 9.353 9.456 9.553 9.645 10.36 10.85 11.52 11.98 12.34 8 4.745 5.635 6.204 6.625 6.959 7.237 7.474 7.680 7.863 8.027 8.176 8.311 8.436 8.552 8.659 8.760 8.854 8.943 9.027 9.677 10.13 10.74 11.17 11.49 9 4.596 5.428 5.957 6.347 6.657 6.915 7.134 7.325 7.494 7.646 7.784 7.910 8.025 8.132 8.232 8.325 8.412 8.495 8.573 9.177 9.594 10.17 10.56 10.86 10 4.482 5.270 5.769 6.136 6.428 6.669 6.875 7.054 7.213 7.356 7.485 7.603 7.712 7.812 7.906 7.993 8.075 8.153 8.226 8.794 9.186 9.726 10.10 10.38 11 4.392 5.146 5.621 5.970 6.247 6.476 6.671 6.841 6.992 7.127 7.250 7.362 7.464 7.560 7.648 7.731 7.809 7.883 7.952 8.491 8.864 9.377 9.732 10.00 12 4.320 5.046 5.502 5.836 6.101 6.320 6.507 6.670 6.814 6.943 7.060 7.166 7.265 7.356 7.441 7.520 7.594 7.664 7.730 8.246 8.602 9.093 9.433 9.693 13 4.260 4.964 5.404 5.726 5.981 6.192 6.372 6.528 6.666 6.791 6.903 7.006 7.100 7.188 7.269 7.345 7.417 7.484 7.548 8.043 8.386 8.859 9.186 9.436 14 4.210 4.895 5.322 5.634 5.881 6.085 6.258 6.409 6.543 6.663 6.772 6.871 6.962 7.047 7.125 7.199 7.268 7.333 7.394 7.873 8.204 8.661 8.978 9.219 15 4.167 4.836 5.252 5.556 5.796 5.994 6.162 6.309 6.438 6.555 6.660 6.756 6.845 6.927 7.003 7.074 7.141 7.204 7.264 7.727 8.049 8.492 8.800 9.034 16 4.131 4.786 5.192 5.489 5.722 5.915 6.079 6.222 6.348 6.461 6.564 6.658 6.744 6.823 6.897 6.967 7.032 7.093 7.151 7.602 7.915 8.346 8.646 8.874 17 4.099 4.742 5.140 5.430 5.659 5.847 6.007 6.147 6.270 6.380 6.480 6.572 6.656 6.733 6.806 6.873 6.937 6.997 7.053 7.493 7.798 8.219 8.511 8.734 18 4.071 4.703 5.094 5.379 5.603 5.787 5.944 6.081 6.201 6.309 6.407 6.496 6.579 6.655 6.725 6.791 6.854 6.912 6.967 7.397 7.696 8.107 8.393 8.611 19 4.046 4.669 5.054 5.334 5.553 5.735 5.889 6.022 6.141 6.246 6.342 6.430 6.510 6.585 6.654 6.719 6.780 6.837 6.891 7.312 7.605 8.008 8.288 8.501 20 4.024 4.639 5.018 5.293 5.510 5.688 5.839 5.970 6.086 6.190 6.285 6.370 6.449 6.523 6.591 6.654 6.714 6.770 6.823 7.237 7.523 7.919 8.194 8.404 24 3.955 4.546 4.907 5.168 5.373 5.542 5.685 5.809 5.919 6.017 6.105 6.186 6.261 6.330 6.394 6.453 6.510 6.562 6.612 7.001 7.270 7.641 7.900 8.097 30 3.889 4.455 4.799 5.048 5.242 5.401 5.536 5.653 5.756 5.848 5.932 6.008 6.078 6.142 6.202 6.258 6.311 6.361 6.407 6.771 7.023 7.370 7.611 7.796 40 3.825 4.367 4.695 4.931 5.114 5.265 5.392 5.502 5.599 5.685 5.764 5.835 5.900 5.961 6.017 6.069 6.118 6.165 6.208 6.547 6.781 7.104 7.328 7.499 60 3.762 4.282 4.594 4.818 4.991 5.133 5.253 5.356 5.447 5.528 5.601 5.667 5.728 5.784 5.837 5.886 5.931 5.974 6.015 6.329 6.546 6.843 7.049 7.207 120 3.702 4.200 4.497 4.708 4.872 5.005 5.118 5.214 5.299 5.375 5.443 5.505 5.561 5.614 5.662 5.708 5.750 5.790 5.827 6.117 6.316 6.588 6.776 6.919 1e38 3.643 4.120 4.403 4.603 4.757 4.882 4.987 5.078 5.157 5.227 5.290 5.348 5.400 5.448 5.493 5.535 5.574 5.611 5.645 5.911 6.092 6.338 6.507 6.636""" q0995 = """\ 1 180.1 270.1 328.5 371.2 404.4 431.6 454.4 474.0 491.1 506.3 520.0 532.4 543.6 554.0 563.6 572.5 580.9 588.7 596.0 652.0 689.6 740.2 774.5 800.3 2 19.92 26.97 31.60 35.02 37.73 39.95 41.83 43.46 44.89 46.16 47.31 48.35 49.30 50.17 50.99 51.74 52.45 53.12 53.74 58.52 61.76 66.13 69.10 71.35 3 10.54 13.51 15.45 16.91 18.06 19.01 19.83 20.53 21.15 21.70 22.20 22.66 23.08 23.46 23.82 24.15 24.46 24.76 25.03 27.15 28.60 30.55 31.88 32.90 4 7.916 9.813 11.06 11.99 12.74 13.35 13.88 14.33 14.74 15.10 15.42 15.72 15.99 16.24 16.47 16.70 16.90 17.09 17.28 18.68 19.63 20.93 21.83 22.50 5 6.751 8.195 9.140 9.846 10.41 10.88 11.28 11.62 11.93 12.21 12.46 12.69 12.90 13.09 13.27 13.44 13.60 13.74 13.89 14.96 15.71 16.72 17.41 17.94 6 6.105 7.306 8.087 8.670 9.135 9.522 9.852 10.14 10.39 10.62 10.83 11.02 11.19 11.35 11.50 11.64 11.78 11.90 12.02 12.92 13.54 14.40 14.98 15.43 7 5.698 6.750 7.429 7.935 8.339 8.674 8.961 9.211 9.433 9.632 9.812 9.976 10.13 10.27 10.40 10.52 10.64 10.74 10.84 11.64 12.18 12.93 13.45 13.85 8 5.420 6.370 6.981 7.435 7.796 8.097 8.354 8.578 8.777 8.955 9.117 9.265 9.401 9.527 9.644 9.754 9.856 9.953 10.04 10.76 11.25 11.92 12.39 12.75 9 5.218 6.096 6.657 7.073 7.405 7.680 7.915 8.120 8.302 8.466 8.614 8.749 8.874 8.989 9.097 9.197 9.292 9.381 9.465 10.12 10.57 11.19 11.62 11.95 10 5.065 5.888 6.412 6.800 7.109 7.365 7.584 7.775 7.944 8.096 8.233 8.359 8.475 8.583 8.683 8.777 8.864 8.947 9.025 9.635 10.06 10.64 11.04 11.35 11 4.945 5.726 6.221 6.587 6.878 7.119 7.325 7.504 7.664 7.807 7.936 8.055 8.164 8.265 8.359 8.447 8.530 8.608 8.681 9.255 9.653 10.20 10.58 10.87 12 4.849 5.596 6.068 6.416 6.693 6.922 7.117 7.288 7.439 7.574 7.697 7.810 7.913 8.009 8.099 8.182 8.261 8.335 8.405 8.950 9.328 9.850 10.21 10.49 13 4.769 5.489 5.943 6.276 6.541 6.760 6.947 7.110 7.254 7.384 7.502 7.609 7.708 7.800 7.885 7.965 8.040 8.111 8.178 8.699 9.061 9.560 9.907 10.17 14 4.703 5.401 5.838 6.160 6.414 6.625 6.805 6.962 7.101 7.225 7.338 7.442 7.537 7.625 7.707 7.784 7.856 7.924 7.988 8.489 8.837 9.317 9.651 9.906 15 4.647 5.325 5.750 6.061 6.307 6.511 6.685 6.836 6.970 7.091 7.200 7.300 7.391 7.476 7.556 7.630 7.699 7.765 7.827 8.310 8.647 9.111 9.434 9.680 16 4.599 5.261 5.674 5.976 6.216 6.413 6.582 6.729 6.859 6.975 7.081 7.178 7.267 7.349 7.426 7.498 7.565 7.629 7.689 8.157 8.483 8.933 9.246 9.486 17 4.557 5.205 5.608 5.903 6.136 6.329 6.493 6.636 6.762 6.876 6.978 7.072 7.159 7.239 7.313 7.383 7.449 7.510 7.569 8.024 8.341 8.779 9.083 9.316 18 4.521 5.156 5.550 5.839 6.067 6.255 6.415 6.554 6.677 6.788 6.888 6.980 7.064 7.142 7.215 7.283 7.347 7.407 7.464 7.908 8.216 8.643 8.940 9.167 19 4.488 5.112 5.500 5.782 6.005 6.189 6.346 6.482 6.603 6.711 6.809 6.898 6.981 7.057 7.128 7.194 7.257 7.316 7.371 7.805 8.106 8.523 8.813 9.035 20 4.460 5.074 5.455 5.732 5.951 6.131 6.285 6.418 6.536 6.642 6.738 6.826 6.906 6.981 7.051 7.116 7.177 7.234 7.289 7.713 8.008 8.416 8.700 8.917 24 4.371 4.955 5.315 5.577 5.783 5.952 6.096 6.221 6.331 6.430 6.520 6.602 6.677 6.747 6.812 6.872 6.929 6.983 7.034 7.429 7.703 8.083 8.348 8.551 30 4.285 4.841 5.181 5.428 5.621 5.779 5.914 6.031 6.134 6.226 6.310 6.386 6.456 6.521 6.581 6.638 6.691 6.740 6.787 7.154 7.409 7.760 8.005 8.193 40 4.202 4.731 5.052 5.284 5.465 5.614 5.739 5.848 5.944 6.030 6.108 6.178 6.243 6.303 6.359 6.411 6.460 6.507 6.550 6.888 7.123 7.447 7.672 7.844 60 4.122 4.625 4.928 5.146 5.316 5.454 5.571 5.673 5.762 5.841 5.913 5.979 6.039 6.094 6.146 6.194 6.239 6.281 6.321 6.632 6.846 7.142 7.347 7.504 120 4.044 4.523 4.809 5.013 5.172 5.301 5.410 5.504 5.586 5.660 5.726 5.786 5.842 5.893 5.940 5.984 6.025 6.064 6.101 6.384 6.579 6.846 7.031 7.172 1e38 3.970 4.424 4.694 4.886 5.033 5.154 5.255 5.341 5.418 5.485 5.546 5.602 5.652 5.699 5.742 5.783 5.820 5.856 5.889 6.146 6.322 6.561 6.725 6.850""" q0999 = """\ 1 900.3 1351. 1643. 1856. 2022. 2158. 2272. 2370. 2455. 2532. 2600. 2662. 2718. 2770. 2818. 2863. 2904. 2943. 2980. 3260. 3448. 3701. 3873. 4002. 2 44.69 60.42 70.77 78.43 84.49 89.46 93.67 97.30 100.5 103.3 105.9 108.2 110.4 112.3 114.2 115.9 117.4 118.9 120.3 131.0 138.3 148.0 154.7 159.7 3 18.28 23.32 26.65 29.13 31.11 32.74 34.12 35.33 36.39 37.34 38.20 38.98 39.69 40.35 40.97 41.54 42.07 42.58 43.05 46.68 49.16 52.51 54.81 56.53 4 12.18 14.98 16.84 18.23 19.34 20.26 21.04 21.73 22.33 22.87 23.36 23.81 24.21 24.59 24.94 25.27 25.58 25.87 26.14 28.24 29.68 31.65 32.98 34.00 5 9.714 11.67 12.96 13.93 14.71 15.35 15.91 16.39 16.82 17.18 17.53 17.85 18.13 18.41 18.66 18.89 19.10 19.31 19.51 21.01 22.03 23.45 24.41 25.15 6 8.427 9.960 10.97 11.72 12.32 12.82 13.25 13.63 13.96 14.26 14.53 14.78 15.00 15.21 15.41 15.59 15.78 15.94 16.09 17.28 18.10 19.22 20.00 20.58 7 7.648 8.930 9.768 10.40 10.90 11.32 11.67 11.99 12.27 12.52 12.74 12.95 13.14 13.32 13.48 13.64 13.78 13.92 14.05 15.06 15.74 16.69 17.35 17.85 8 7.129 8.250 8.977 9.522 9.958 10.32 10.63 10.90 11.15 11.36 11.56 11.74 11.91 12.06 12.20 12.34 12.46 12.58 12.69 13.57 14.17 15.01 15.59 16.02 9 6.761 7.768 8.419 8.906 9.295 9.619 9.896 10.14 10.35 10.55 10.72 10.89 11.03 11.17 11.30 11.42 11.53 11.64 11.74 12.52 13.07 13.82 14.34 14.74 10 6.487 7.411 8.006 8.449 8.804 9.099 9.352 9.573 9.769 9.946 10.11 10.25 10.39 10.51 10.63 10.74 10.84 10.94 11.03 11.75 12.25 12.94 13.42 13.79 11 6.275 7.135 7.687 8.098 8.426 8.699 8.933 9.137 9.319 9.482 9.630 9.766 9.891 10.01 10.12 10.22 10.31 10.40 10.49 11.15 11.61 12.25 12.70 13.03 12 6.106 6.917 7.435 7.820 8.127 8.382 8.601 8.792 8.962 9.115 9.253 9.380 9.497 9.606 9.707 9.802 9.891 9.975 10.05 10.68 11.11 11.71 12.12 12.44 13 5.969 6.740 7.231 7.595 7.885 8.126 8.332 8.513 8.673 8.817 8.948 9.068 9.178 9.280 9.376 9.465 9.549 9.629 9.704 10.29 10.70 11.27 11.66 11.96 14 5.855 6.593 7.062 7.409 7.685 7.914 8.110 8.282 8.434 8.571 8.695 8.809 8.914 9.011 9.102 9.187 9.267 9.342 9.414 9.972 10.36 10.90 11.28 11.57 15 5.760 6.470 6.920 7.252 7.517 7.736 7.924 8.088 8.234 8.364 8.483 8.592 8.692 8.785 8.872 8.953 9.030 9.102 9.170 9.703 10.08 10.59 10.95 11.23 16 5.678 6.365 6.799 7.119 7.374 7.585 7.765 7.923 8.063 8.189 8.303 8.407 8.504 8.593 8.676 8.754 8.828 8.897 8.962 9.475 9.832 10.33 10.68 10.94 17 5.608 6.274 6.695 7.004 7.250 7.454 7.629 7.781 7.916 8.037 8.147 8.248 8.341 8.427 8.507 8.583 8.653 8.720 8.783 9.277 9.623 10.10 10.44 10.69 18 5.546 6.195 6.604 6.905 7.143 7.341 7.510 7.657 7.788 7.905 8.012 8.109 8.199 8.283 8.361 8.433 8.502 8.566 8.627 9.106 9.440 9.904 10.23 10.48 19 5.492 6.126 6.524 6.817 7.049 7.241 7.405 7.549 7.676 7.790 7.893 7.988 8.075 8.156 8.232 8.302 8.369 8.431 8.491 8.955 9.279 9.729 10.04 10.29 20 5.444 6.065 6.454 6.740 6.966 7.153 7.313 7.453 7.576 7.687 7.788 7.880 7.965 8.044 8.118 8.186 8.251 8.312 8.370 8.821 9.136 9.575 9.881 10.12 24 5.297 5.877 6.238 6.502 6.711 6.884 7.031 7.159 7.272 7.374 7.467 7.551 7.629 7.701 7.768 7.831 7.890 7.946 7.999 8.411 8.699 9.100 9.380 9.595 30 5.156 5.698 6.033 6.277 6.469 6.628 6.763 6.880 6.984 7.077 7.161 7.239 7.310 7.375 7.437 7.494 7.548 7.598 7.646 8.021 8.283 8.646 8.901 9.096 40 5.022 5.527 5.838 6.063 6.240 6.385 6.509 6.616 6.710 6.795 6.872 6.942 7.007 7.066 7.122 7.174 7.223 7.268 7.312 7.651 7.887 8.214 8.442 8.618 60 4.893 5.365 5.653 5.860 6.022 6.155 6.268 6.365 6.451 6.528 6.598 6.661 6.720 6.773 6.824 6.870 6.914 6.956 6.995 7.299 7.510 7.802 8.005 8.161 120 4.771 5.211 5.476 5.667 5.815 5.937 6.039 6.128 6.206 6.275 6.338 6.395 6.448 6.496 6.541 6.583 6.623 6.660 6.695 6.966 7.153 7.410 7.589 7.726 1e38 4.654 5.063 5.309 5.484 5.619 5.730 5.823 5.903 5.973 6.036 6.092 6.144 6.191 6.234 6.274 6.312 6.347 6.380 6.411 6.651 6.816 7.041 7.196 7.314""" # Build the T+ 'matrix' # T is a dict of dicts of lists # [alpha keys] [v keys] # [table values as lists of floats] T = dict([(0.100, dict([(float(L.split()[0]), lmap(float, L.split()[1:])) for L in q0100.split('\n')])), (0.500, dict([(float(L.split()[0]), lmap(float, L.split()[1:])) for L in q0500.split('\n')])), (0.675, dict([(float(L.split()[0]), lmap(float, L.split()[1:])) for L in q0675.split('\n')])), (0.750, dict([(float(L.split()[0]), lmap(float, L.split()[1:])) for L in q0750.split('\n')])), (0.800, dict([(float(L.split()[0]), lmap(float, L.split()[1:])) for L in q0800.split('\n')])), (0.850, dict([(float(L.split()[0]), lmap(float, L.split()[1:])) for L in q0850.split('\n')])), (0.900, dict([(float(L.split()[0]), lmap(float, L.split()[1:])) for L in q0900.split('\n')])), (0.950, dict([(float(L.split()[0]), lmap(float, L.split()[1:])) for L in q0950.split('\n')])), (0.975, dict([(float(L.split()[0]), lmap(float, L.split()[1:])) for L in q0975.split('\n')])), (0.990, dict([(float(L.split()[0]), lmap(float, L.split()[1:])) for L in q0990.split('\n')])), (0.995, dict([(float(L.split()[0]), lmap(float, L.split()[1:])) for L in q0995.split('\n')])), (0.999, dict([(float(L.split()[0]), lmap(float, L.split()[1:])) for L in q0999.split('\n')]))]) # This dict maps r values to the correct list index R = dict(zip([2,3,4,5,6,7,8,9,10,11,12,13,14,15,16, 17,18,19,20,30,40,60,80,100], lrange(24))) inf = np.inf # we will need a tinv function _tinv = lambda p, df : scipy.stats.t.isf(p, df) _phi = lambda p : scipy.stats.norm.isf(p) # Now we can build the A 'matrix' # these are for the least squares fitting def qhat(a, p, r, v): # eq. 2.3 p_ = (1. + p) /2. f = a[0]*np.log(r-1.) + \ a[1]*np.log(r-1.)**2 + \ a[2]*np.log(r-1.)**3 + \ a[3]*np.log(r-1.)**4 # eq. 2.7 and 2.8 corrections for i, r_ in enumerate(r): if r_ == 3: f[i] += -0.002 / (1. + 12. * _phi(p)**2) if v <= 4.364: f[i] += 1./517. - 1./(312.*v) else: f[i] += 1./(191.*v) return math.sqrt(2) * (f - 1.) * _tinv(p_, v) errfunc = lambda a, p, r, v, q: qhat(a, p, r, v) - q A = {} # this is the error matrix for p in T: for v in T[p]: #eq. 2.4 a0 = random(4) a1, success = leastsq(errfunc, a0, args=(p, np.array(list(R.keys())), v, np.array(T[p][v]))) if v == 1e38: A[(p,inf)] = list(a1) else: A[(p,v)] = list(a1) raise ImportError("we do not want to import this") # uncomment the lines below to repr-ize A ##import pprint ##pprint.pprint(A, width=160) statsmodels-0.12.2/statsmodels/stats/libqsturng/qsturng_.py000066400000000000000000001500121400612667500242520ustar00rootroot00000000000000# Copyright (c) 2011, Roger Lew [see LICENSE.txt] # This software is funded in part by NIH Grant P20 RR016454. """ Implementation of Gleason's (1999) non-iterative upper quantile studentized range approximation. According to Gleason this method should be more accurate than the AS190 FORTRAN algorithm of Lund and Lund (1983) and works from .5 <= p <= .999 (The AS190 only works from .9 <= p <= .99). It is more efficient then the Copenhaver & Holland (1988) algorithm (used by the _qtukey_ R function) although it requires storing the A table in memory. (q distribution) approximations in Python. see: Gleason, J. R. (1999). An accurate, non-iterative approximation for studentized range quantiles. Computational Statistics & Data Analysis, (31), 147-158. Gleason, J. R. (1998). A table of quantile points of the Studentized range distribution. http://www.stata.com/stb/stb46/dm64/sturng.pdf """ from statsmodels.compat.python import lrange import math import scipy.stats import numpy as np from scipy.optimize import fminbound inf = np.inf __version__ = '0.2.3' # changelog # 0.1 - initial release # 0.1.1 - vectorized # 0.2 - psturng added # 0.2.1 - T, R generation script relegated to make_tbls.py # 0.2.2 # - select_points refactored for performance to select_ps and # select_vs # - pysturng tester added. # 0.2.3 - uses np.inf and np.isinf # Gleason's table was derived using least square estimation on the tabled # r values for combinations of p and v. In total there are 206 # estimates over p-values of .5, .75, .9, .95, .975, .99, .995, # and .999, and over v (degrees of freedom) of (1) - 20, 24, 30, 40, # 60, 120, and inf. combinations with p < .95 do not have coefficients # for v = 1. Hence the parentheses. These coefficients allow us to # form f-hat. f-hat with the inverse t transform of tinv(p,v) yields # a fairly accurate estimate of the studentized range distribution # across a wide range of values. According to Gleason this method # should be more accurate than algorithm AS190 of Lund and Lund (1983) # and work across a wider range of values (The AS190 only works # from .9 <= p <= .99). R's qtukey algorithm was used to add tables # at .675, .8, and .85. These aid approximations when p < .9. # # The code that generated this table is called make_tbls.py and is # located in version control. A = {(0.1, 2.0): [-2.2485085243379075, -1.5641014278923464, 0.55942294426816752, -0.060006608853883377], (0.1, 3.0): [-2.2061105943901564, -1.8415406600571855, 0.61880788039834955, -0.062217093661209831], (0.1, 4.0): [-2.1686691786678178, -2.008196172372553, 0.65010084431947401, -0.06289005500114471], (0.1, 5.0): [-2.145077200277393, -2.112454843879346, 0.66701240582821342, -0.062993502233654797], (0.1, 6.0): [-2.0896098049743155, -2.2400004934286497, 0.70088523391700142, -0.065907568563272748], (0.1, 7.0): [-2.0689296655661584, -2.3078445479584873, 0.71577374609418909, -0.067081034249350552], (0.1, 8.0): [-2.0064956480711262, -2.437400413087452, 0.76297532367415266, -0.072805518121505458], (0.1, 9.0): [-2.3269477513436061, -2.0469494712773089, 0.60662518717720593, -0.054887108437009016], (0.1, 10.0): [-2.514024350177229, -1.8261187841127482, 0.51674358077906746, -0.044590425150963633], (0.1, 11.0): [-2.5130181309130828, -1.8371718595995694, 0.51336701694862252, -0.043761825829092445], (0.1, 12.0): [-2.5203508109278823, -1.8355687130611862, 0.5063486549107169, -0.042646205063108261], (0.1, 13.0): [-2.5142536438310477, -1.8496969402776282, 0.50616991367764153, -0.042378379905665363], (0.1, 14.0): [-2.3924634153781352, -2.013859173066078, 0.56421893251638688, -0.048716888109540266], (0.1, 15.0): [-2.3573552940582574, -2.0576676976224362, 0.57424068771143233, -0.049367487649225841], (0.1, 16.0): [-2.3046427483044871, -2.1295959138627993, 0.59778272657680553, -0.051864829216301617], (0.1, 17.0): [-2.2230551072316125, -2.2472837435427127, 0.64255758243215211, -0.057186665209197643], (0.1, 18.0): [-2.3912859179716897, -2.0350604070641269, 0.55924788749333332, -0.047729331835226464], (0.1, 19.0): [-2.4169773092220623, -2.0048217969339146, 0.54493039319748915, -0.045991241346224065], (0.1, 20.0): [-2.4264087194660751, -1.9916614057049267, 0.53583555139648154, -0.04463049934517662], (0.1, 24.0): [-2.3969903132061869, -2.0252941869225345, 0.53428382141200137, -0.043116495567779786], (0.1, 30.0): [-2.2509922780354623, -2.2309248956124894, 0.60748041324937263, -0.051427415888817322], (0.1, 40.0): [-2.1310090183854946, -2.3908466074610564, 0.65844375382323217, -0.05676653804036895], (0.1, 60.0): [-1.9240060179027036, -2.6685751031012233, 0.75678826647453024, -0.067938584352398995], (0.1, 120.0): [-1.9814895487030182, -2.5962051736978373, 0.71793969041292693, -0.063126863201511618], (0.1, inf): [-1.913410267066703, -2.6947367328724732, 0.74742335122750592, -0.06660897234304515], (0.5, 2.0): [-0.88295935738770648, -0.1083576698911433, 0.035214966839394388, -0.0028576288978276461], (0.5, 3.0): [-0.89085829205846834, -0.10255696422201063, 0.033613638666631696, -0.0027101699918520737], (0.5, 4.0): [-0.89627345339338116, -0.099072524607668286, 0.032657774808907684, -0.0026219007698204916], (0.5, 5.0): [-0.89959145511941052, -0.097272836582026817, 0.032236187675182958, -0.0025911555217019663], (0.5, 6.0): [-0.89959428735702474, -0.098176292411106647, 0.032590766960226995, -0.0026319890073613164], (0.5, 7.0): [-0.90131491102863937, -0.097135907620296544, 0.032304124993269533, -0.0026057965808244125], (0.5, 8.0): [-0.90292500599432901, -0.096047500971337962, 0.032030946615574568, -0.0025848748659053891], (0.5, 9.0): [-0.90385598607803697, -0.095390771554571888, 0.031832651111105899, -0.0025656060219315991], (0.5, 10.0): [-0.90562524936125388, -0.093954488089771915, 0.031414451048323286, -0.0025257834705432031], (0.5, 11.0): [-0.90420347371173826, -0.095851656370277288, 0.0321150356209743, -0.0026055056400093451], (0.5, 12.0): [-0.90585973471757664, -0.094449306296728028, 0.031705945923210958, -0.0025673330195780191], (0.5, 13.0): [-0.90555437067293054, -0.094792991050780248, 0.031826594964571089, -0.0025807109129488545], (0.5, 14.0): [-0.90652756604388762, -0.093792156994564738, 0.031468966328889042, -0.0025395175361083741], (0.5, 15.0): [-0.90642323700400085, -0.094173017520487984, 0.031657517378893905, -0.0025659271829033877], (0.5, 16.0): [-0.90716338636685234, -0.093785178083820434, 0.031630091949657997, -0.0025701459247416637], (0.5, 17.0): [-0.90790133816769714, -0.093001147638638884, 0.031376863944487084, -0.002545143621663892], (0.5, 18.0): [-0.9077432927051563, -0.093343516378180599, 0.031518139662395313, -0.0025613906133277178], (0.5, 19.0): [-0.90789499456490286, -0.09316964789456067, 0.031440782366342901, -0.0025498353345867453], (0.5, 20.0): [-0.90842707861030725, -0.092696016476608592, 0.031296040311388329, -0.0025346963982742186], (0.5, 24.0): [-0.9083281347135469, -0.092959308144970776, 0.031464063190077093, -0.0025611384271086285], (0.5, 30.0): [-0.90857624050016828, -0.093043139391980514, 0.031578791729341332, -0.0025766595412777147], (0.5, 40.0): [-0.91034085045438684, -0.091978035738914568, 0.031451631000052639, -0.0025791418103733297], (0.5, 60.0): [-0.91084356681030032, -0.091452675572423425, 0.031333147984820044, -0.0025669786958144843], (0.5, 120.0): [-0.90963649561463833, -0.093414563261352349, 0.032215602703677425, -0.0026704024780441257], (0.5, inf): [-0.91077157500981665, -0.092899220350334571, 0.032230422399363315, -0.0026696941964372916], (0.675, 2.0): [-0.67231521026565144, -0.097083624030663451, 0.027991378901661649, -0.0021425184069845558], (0.675, 3.0): [-0.65661724764645824, -0.08147195494632696, 0.02345732427073333, -0.0017448570400999351], (0.675, 4.0): [-0.65045677697461124, -0.071419073399450431, 0.020741962576852499, -0.0015171262565892491], (0.675, 5.0): [-0.64718875357808325, -0.064720611425218344, 0.019053450246546449, -0.0013836232986228711], (0.675, 6.0): [-0.64523003702018655, -0.059926313672731824, 0.017918997181483924, -0.0012992250285556828], (0.675, 7.0): [-0.64403313148478836, -0.056248191513784476, 0.017091446791293721, -0.0012406558789511822], (0.675, 8.0): [-0.64325095865764359, -0.053352543126426684, 0.016471879286491072, -0.0011991839050964099], (0.675, 9.0): [-0.64271152754911653, -0.051023769620449078, 0.01599799600547195, -0.0011693637984597086], (0.675, 10.0): [-0.64232244408502626, -0.049118327462884373, 0.015629704966568955, -0.0011477775513952285], (0.675, 11.0): [-0.64203897854353564, -0.047524627960277892, 0.015334801262767227, -0.0011315057284007177], (0.675, 12.0): [-0.64180344973512771, -0.046205907576003291, 0.015108290595438166, -0.0011207364514518488], (0.675, 13.0): [-0.64162086456823342, -0.045076099336874231, 0.0149226565346125, -0.0011126140690497352], (0.675, 14.0): [-0.64146906480198984, -0.044108523550512715, 0.014772954218646743, -0.0011069708562369386], (0.675, 15.0): [-0.64133915151966603, -0.043273370927039825, 0.014651691599222836, -0.0011032216539514398], (0.675, 16.0): [-0.64123237842752079, -0.042538925012463868, 0.014549992487506169, -0.0011005633864334021], (0.675, 17.0): [-0.64113034037536609, -0.041905699463005854, 0.014470805560767184, -0.0010995286436738471], (0.675, 18.0): [-0.64104137391561256, -0.041343885546229336, 0.014404563657113593, -0.0010991304223377683], (0.675, 19.0): [-0.64096064882827297, -0.04084569291139839, 0.014350159655133801, -0.0010993656711121901], (0.675, 20.0): [-0.64088647405089572, -0.040402175957178085, 0.014305769823654429, -0.0011001304776712105], (0.675, 24.0): [-0.64063763965937837, -0.039034716348048545, 0.014196703837251648, -0.0011061961945598175], (0.675, 30.0): [-0.64034987716294889, -0.037749651156941719, 0.014147040999127263, -0.0011188251352919833], (0.675, 40.0): [-0.6399990514713938, -0.036583307574857803, 0.014172070700846548, -0.0011391004138624943], (0.675, 60.0): [-0.63955586202430248, -0.035576938958184395, 0.014287299153378865, -0.0011675811805794236], (0.675, 120.0): [-0.63899242674778622, -0.034763757512388853, 0.014500726912982405, -0.0012028491454427466], (0.675, inf): [-0.63832682579247613, -0.034101476695520404, 0.014780921043580184, -0.0012366204114216408], (0.75, 2.0): [-0.60684073638504454, -0.096375192078057031, 0.026567529471304554, -0.0019963228971914488], (0.75, 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[-0.24420834707522676, -0.012911171716272752, 0.0031977676700968051, -0.00020114907914487053], (0.975, 40.0): [-0.24105725356215926, -0.010836526056169627, 0.0030231303550754159, -0.00020128696343148667], (0.975, 60.0): [-0.23732082703955223, -0.0095442727157385391, 0.0031432904473555259, -0.00023062224109383941], (0.975, 120.0): [-0.23358581879594578, -0.0081281259918709343, 0.0031877298679120094, -0.00024496230446851501], (0.975, inf): [-0.23004105093119268, -0.0067112585174133573, 0.0032760251638919435, -0.00026244001319462992], (0.99, 1.0): [-0.65154119422706203, -0.1266603927572312, 0.03607480609672048, -0.0028668112687608113], (0.99, 2.0): [-0.45463403324378804, -0.098701236234527367, 0.024412715761684689, -0.0017613772919362193], (0.99, 3.0): [-0.36402060051035778, -0.079244959193729148, 0.017838124021360584, -0.00119080116484847], (0.99, 4.0): [-0.31903506063953818, -0.061060740682445241, 0.012093154962939612, -0.00067268347188443093], (0.99, 5.0): [-0.28917014580689182, -0.052940780099313689, 0.010231009146279354, -0.00057178339184615239], (0.99, 6.0): [-0.27283240161179012, -0.042505435573209085, 0.0072753401118264534, -0.00031314034710725922], (0.99, 7.0): [-0.25773968720546719, -0.039384214480463406, 0.0069120882597286867, -0.00032994068754356204], (0.99, 8.0): [-0.24913629282433833, -0.033831567178432859, 0.0055516244725724185, -0.00022570786249671376], (0.99, 9.0): [-0.24252380896373404, -0.029488280751457097, 0.0045215453527922998, -0.00014424552929022646], (0.99, 10.0): [-0.23654349556639986, -0.02705600214566789, 0.0041627255469343632, -0.00013804427029504753], (0.99, 11.0): [-0.23187404969432468, -0.024803662094970855, 0.0037885852786822475, -0.00012334999287725012], (0.99, 12.0): [-0.22749929386320905, -0.023655085290534145, 0.0037845051889055896, -0.00014785715789924055], (0.99, 13.0): [-0.22458989143485605, -0.021688394892771506, 0.0034075294601425251, -0.00012436961982044268], (0.99, 14.0): [-0.22197623872225777, -0.020188830700102918, 0.0031648685865587473, -0.00011320740119998819], (0.99, 15.0): [-0.2193924323730066, -0.019327469111698265, 0.0031295453754886576, -0.00012373072900083014], (0.99, 16.0): [-0.21739436875855705, -0.018215854969324128, 0.0029638341057222645, -0.00011714667871412003], (0.99, 17.0): [-0.21548926805467686, -0.017447822179412719, 0.0028994805120482812, -0.00012001887015183794], (0.99, 18.0): [-0.21365014687077843, -0.01688869353338961, 0.0028778031289216546, -0.00012591199104792711], (0.99, 19.0): [-0.21236653761262406, -0.016057151563612645, 0.0027571468998022017, -0.00012049196593780046], (0.99, 20.0): [-0.21092693178421842, -0.015641706950956638, 0.0027765989877361293, -0.00013084915163086915], (0.99, 24.0): [-0.20681960327410207, -0.013804298040271909, 0.0026308276736585674, -0.0001355061502101814], (0.99, 30.0): [-0.20271691131071576, -0.01206095288359876, 0.0025426138004198909, -0.00014589047959047533], (0.99, 40.0): [-0.19833098054449289, -0.010714533963740719, 0.0025985992420317597, -0.0001688279944262007], (0.99, 60.0): [-0.19406768821236584, -0.0093297106482013985, 0.0026521518387539584, -0.00018884874193665104], (0.99, 120.0): [-0.19010213174677365, -0.0075958207221300924, 0.0025660823297025633, -0.00018906475172834352], (0.99, inf): [-0.18602070255787137, -0.0062121155165363188, 0.0026328293420766593, -0.00020453366529867131], (0.995, 1.0): [-0.65135583544951825, -0.1266868999507193, 0.036067522182457165, -0.0028654516958844922], (0.995, 2.0): [-0.45229774013072793, -0.09869462954369547, 0.024381858599368908, -0.0017594734553033394], (0.995, 3.0): [-0.35935765236429706, -0.076650408326671915, 0.016823026893528978, -0.0010835134496404637], (0.995, 4.0): [-0.30704474720931169, -0.063093047731613019, 0.012771683306774929, -0.00075852491621809955], (0.995, 5.0): [-0.27582551740863454, -0.052533353137885791, 0.0097776009845174372, -0.00051338031756399129], (0.995, 6.0): [-0.25657971464398704, -0.043424914996692286, 0.0074324147435969991, -0.00034105188850494067], (0.995, 7.0): [-0.24090407819707738, -0.039591604712200287, 0.0068848429451020387, -0.00034737131709273414], (0.995, 8.0): [-0.23089540800827862, -0.034353305816361958, 0.0056009527629820111, -0.00024389336976992433], (0.995, 9.0): [-0.22322694848310584, -0.030294770709722547, 0.0046751239747245543, -0.00017437479314218922], (0.995, 10.0): [-0.21722684126671632, -0.026993563560163809, 0.0039811592710905491, -0.00013135281785826703], (0.995, 11.0): [-0.21171635822852911, -0.025156193618212551, 0.0037507759652964205, -0.00012959836685175671], (0.995, 12.0): [-0.20745332165849167, -0.023318819535607219, 0.0034935020002058903, -0.00012642826898405916], (0.995, 13.0): [-0.20426054591612508, -0.021189796175249527, 0.003031472176128759, -9.0497733877531618e-05], (0.995, 14.0): [-0.20113536905578902, -0.020011536696623061, 0.0029215880889956729, -9.571527213951222e-05], (0.995, 15.0): [-0.19855601561006403, -0.018808533734002542, 0.0027608859956002344, -9.2472995256929217e-05], (0.995, 16.0): [-0.19619157579534008, -0.017970461530551096, 0.0027113719105000371, -9.9864874982890861e-05], (0.995, 17.0): [-0.19428015140726104, -0.017009762497670704, 0.0025833389598201345, -9.6137545738061124e-05], (0.995, 18.0): [-0.19243180236773033, -0.01631617252107519, 0.0025227443561618621, -9.8067580523432881e-05], (0.995, 19.0): [-0.19061294393069844, -0.01586226613672222, 0.0025207005902641781, -0.00010466151274918466], (0.995, 20.0): [-0.18946302696580328, -0.014975796567260896, 0.0023700506576419867, -9.5507779057884629e-05], (0.995, 24.0): [-0.18444251428695257, -0.013770955893918012, 0.0024579445553339903, -0.00012688402863358003], (0.995, 30.0): [-0.18009742499570078, -0.011831341846559026, 0.0022801125189390046, -0.00012536249967254906], (0.995, 40.0): [-0.17562721880943261, -0.010157142650455463, 0.0022121943861923474, -0.000134542652873434], (0.995, 60.0): [-0.17084630673594547, -0.0090224965852754805, 0.0023435529965815565, -0.00016240306777440115], (0.995, 120.0): [-0.16648414081054147, -0.0074792163241677225, 0.0023284585524533607, -0.00017116464012147041], (0.995, inf): [-0.16213921875452461, -0.0058985998630496144, 0.0022605819363689093, -0.00016896211491119114], (0.999, 1.0): [-0.65233994072089363, -0.12579427445444219, 0.035830577995679271, -0.0028470555202945564], (0.999, 2.0): [-0.45050164311326341, -0.098294804380698292, 0.024134463919493736, -0.0017269603956852841], (0.999, 3.0): [-0.35161741499307819, -0.076801152272374273, 0.016695693063138672, -0.0010661121974071864], (0.999, 4.0): [-0.29398448788574133, -0.06277319725219685, 0.012454220010543127, -0.00072644165723402445], (0.999, 5.0): [-0.25725364564365477, -0.053463787584337355, 0.0099664236557431545, -0.00054866039388980659], (0.999, 6.0): [-0.23674225795168574, -0.040973155890031254, 0.0062599481191736696, -0.00021565734226586692], (0.999, 7.0): [-0.21840108878983297, -0.037037020271877719, 0.0055908063671900703, -0.00020238790479809623], (0.999, 8.0): [-0.2057964743918449, -0.032500885103194356, 0.0046441644585661756, -0.00014769592268680274], (0.999, 9.0): [-0.19604592954882674, -0.029166922919677936, 0.0040644333111949814, -0.00012854052861297006], (0.999, 10.0): [-0.18857328935948367, -0.026316705703161091, 0.0035897350868809275, -0.00011572282691335702], (0.999, 11.0): [-0.18207431428535406, -0.024201081944369412, 0.0031647372098056077, -8.1145935982296439e-05], (0.999, 12.0): [-0.17796358148991101, -0.021054306118620879, 0.0023968085939602055, -1.5907156771296993e-05], (0.999, 13.0): [-0.17371965962745489, -0.019577162950177709, 0.0022391783473999739, -2.0613023472812558e-05], (0.999, 14.0): [-0.16905298116759873, -0.01967115985443986, 0.0026495208325889269, -9.1074275220634073e-05], (0.999, 15.0): [-0.16635662558214312, -0.017903767183469876, 0.0022301322677100496, -5.1956773935885426e-05], (0.999, 16.0): [-0.16388776549525449, -0.016671918839902419, 0.0020365289602744382, -4.3592447599724942e-05], (0.999, 17.0): [-0.16131934177990759, -0.015998918405126326, 0.0019990454743285904, -4.8176277491327653e-05], (0.999, 18.0): [-0.15880633110376571, -0.015830715141055916, 0.0021688405343832091, -8.061825248932771e-05], (0.999, 19.0): [-0.15644841913314136, -0.015729364721105681, 0.0022981443610378136, -0.00010093672643417343], (0.999, 20.0): [-0.15516596606222705, -0.014725095968258637, 0.0021117117014292155, -8.8806880297328484e-05], (0.999, 24.0): [-0.14997437768645827, -0.012755323295476786, 0.0018871651510496939, -8.0896370662414938e-05], (0.999, 30.0): [-0.14459974882323703, -0.011247323832877647, 0.0018637400643826279, -9.6415323191606741e-05], (0.999, 40.0): [-0.13933285919392555, -0.0097151769692496587, 0.0018131251876208683, -0.00010452598991994023], (0.999, 60.0): [-0.13424555343804143, -0.0082163027951669444, 0.0017883427892173382, -0.00011415865110808405], (0.999, 120.0): [-0.12896119523040372, -0.0070426701112581112, 0.0018472364154226955, -0.00012862202979478294], (0.999, inf): [-0.12397213562666673, -0.0056901201604149998, 0.0018260689406957129, -0.00013263452567995485]} # p values that are defined in the A table p_keys = [.1,.5,.675,.75,.8,.85,.9,.95,.975,.99,.995,.999] # v values that are defined in the A table v_keys = lrange(2, 21) + [24, 30, 40, 60, 120, inf] def _isfloat(x): """ returns True if x is a float, returns False otherwise """ try: float(x) except: return False return True ##def _phi(p): ## """returns the pth quantile inverse norm""" ## return scipy.stats.norm.isf(p) def _phi( p ): # this function is faster than using scipy.stats.norm.isf(p) # but the permissity of the license is not explicitly listed. # using scipy.stats.norm.isf(p) is an acceptable alternative """ Modified from the author's original perl code (original comments follow below) by dfield@yahoo-inc.com. May 3, 2004. Lower tail quantile for standard normal distribution function. This function returns an approximation of the inverse cumulative standard normal distribution function. I.e., given P, it returns an approximation to the X satisfying P = Pr{Z <= X} where Z is a random variable from the standard normal distribution. The algorithm uses a minimax approximation by rational functions and the result has a relative error whose absolute value is less than 1.15e-9. Author: Peter John Acklam Time-stamp: 2000-07-19 18:26:14 E-mail: pjacklam@online.no WWW URL: http://home.online.no/~pjacklam """ if p <= 0 or p >= 1: # The original perl code exits here, we'll throw an exception instead raise ValueError( "Argument to ltqnorm %f must be in open interval (0,1)" % p ) # Coefficients in rational approximations. a = (-3.969683028665376e+01, 2.209460984245205e+02, \ -2.759285104469687e+02, 1.383577518672690e+02, \ -3.066479806614716e+01, 2.506628277459239e+00) b = (-5.447609879822406e+01, 1.615858368580409e+02, \ -1.556989798598866e+02, 6.680131188771972e+01, \ -1.328068155288572e+01 ) c = (-7.784894002430293e-03, -3.223964580411365e-01, \ -2.400758277161838e+00, -2.549732539343734e+00, \ 4.374664141464968e+00, 2.938163982698783e+00) d = ( 7.784695709041462e-03, 3.224671290700398e-01, \ 2.445134137142996e+00, 3.754408661907416e+00) # Define break-points. plow = 0.02425 phigh = 1 - plow # Rational approximation for lower region: if p < plow: q = math.sqrt(-2*math.log(p)) return -(((((c[0]*q+c[1])*q+c[2])*q+c[3])*q+c[4])*q+c[5]) / \ ((((d[0]*q+d[1])*q+d[2])*q+d[3])*q+1) # Rational approximation for upper region: if phigh < p: q = math.sqrt(-2*math.log(1-p)) return (((((c[0]*q+c[1])*q+c[2])*q+c[3])*q+c[4])*q+c[5]) / \ ((((d[0]*q+d[1])*q+d[2])*q+d[3])*q+1) # Rational approximation for central region: q = p - 0.5 r = q*q return -(((((a[0]*r+a[1])*r+a[2])*r+a[3])*r+a[4])*r+a[5])*q / \ (((((b[0]*r+b[1])*r+b[2])*r+b[3])*r+b[4])*r+1) def _ptransform(p): """function for p-value abcissa transformation""" return -1. / (1. + 1.5 * _phi((1. + p)/2.)) def _func(a, p, r, v): """ calculates f-hat for the coefficients in a, probability p, sample mean difference r, and degrees of freedom v. """ # eq. 2.3 f = a[0]*math.log(r-1.) + \ a[1]*math.log(r-1.)**2 + \ a[2]*math.log(r-1.)**3 + \ a[3]*math.log(r-1.)**4 # eq. 2.7 and 2.8 corrections if r == 3: f += -0.002 / (1. + 12. * _phi(p)**2) if v <= 4.364: v = v if not np.isinf(v) else 1e38 f += 1. / 517. - 1. / (312. * v) else: v = v if not np.isinf(v) else 1e38 f += 1. / (191. * v) return -f def _select_ps(p): # There are more generic ways of doing this but profiling # revealed that selecting these points is one of the slow # things that is easy to change. This is about 11 times # faster than the generic algorithm it is replacing. # # it is possible that different break points could yield # better estimates, but the function this is refactoring # just used linear distance. """returns the points to use for interpolating p""" if p >= .99: return .990, .995, .999 elif p >= .975: return .975, .990, .995 elif p >= .95: return .950, .975, .990 elif p >= .9125: return .900, .950, .975 elif p >= .875: return .850, .900, .950 elif p >= .825: return .800, .850, .900 elif p >= .7625: return .750, .800, .850 elif p >= .675: return .675, .750, .800 elif p >= .500: return .500, .675, .750 else: return .100, .500, .675 def _interpolate_p(p, r, v): """ interpolates p based on the values in the A table for the scalar value of r and the scalar value of v """ # interpolate p (v should be in table) # if .5 < p < .75 use linear interpolation in q # if p > .75 use quadratic interpolation in log(y + r/v) # by -1. / (1. + 1.5 * _phi((1. + p)/2.)) # find the 3 closest v values p0, p1, p2 = _select_ps(p) try: y0 = _func(A[(p0, v)], p0, r, v) + 1. except: print(p,r,v) raise y1 = _func(A[(p1, v)], p1, r, v) + 1. y2 = _func(A[(p2, v)], p2, r, v) + 1. y_log0 = math.log(y0 + float(r)/float(v)) y_log1 = math.log(y1 + float(r)/float(v)) y_log2 = math.log(y2 + float(r)/float(v)) # If p < .85 apply only the ordinate transformation # if p > .85 apply the ordinate and the abcissa transformation # In both cases apply quadratic interpolation if p > .85: p_t = _ptransform(p) p0_t = _ptransform(p0) p1_t = _ptransform(p1) p2_t = _ptransform(p2) # calculate derivatives for quadratic interpolation d2 = 2*((y_log2-y_log1)/(p2_t-p1_t) - \ (y_log1-y_log0)/(p1_t-p0_t))/(p2_t-p0_t) if (p2+p0)>=(p1+p1): d1 = (y_log2-y_log1)/(p2_t-p1_t) - 0.5*d2*(p2_t-p1_t) else: d1 = (y_log1-y_log0)/(p1_t-p0_t) + 0.5*d2*(p1_t-p0_t) d0 = y_log1 # interpolate value y_log = (d2/2.) * (p_t-p1_t)**2. + d1 * (p_t-p1_t) + d0 # transform back to y y = math.exp(y_log) - float(r)/float(v) elif p > .5: # calculate derivatives for quadratic interpolation d2 = 2*((y_log2-y_log1)/(p2-p1) - \ (y_log1-y_log0)/(p1-p0))/(p2-p0) if (p2+p0)>=(p1+p1): d1 = (y_log2-y_log1)/(p2-p1) - 0.5*d2*(p2-p1) else: d1 = (y_log1-y_log0)/(p1-p0) + 0.5*d2*(p1-p0) d0 = y_log1 # interpolate values y_log = (d2/2.) * (p-p1)**2. + d1 * (p-p1) + d0 # transform back to y y = math.exp(y_log) - float(r)/float(v) else: # linear interpolation in q and p v = min(v, 1e38) q0 = math.sqrt(2) * -y0 * \ scipy.stats.t.isf((1.+p0)/2., v) q1 = math.sqrt(2) * -y1 * \ scipy.stats.t.isf((1.+p1)/2., v) d1 = (q1-q0)/(p1-p0) d0 = q0 # interpolate values q = d1 * (p-p0) + d0 # transform back to y y = -q / (math.sqrt(2) * scipy.stats.t.isf((1.+p)/2., v)) return y def _select_vs(v, p): # This one is is about 30 times faster than # the generic algorithm it is replacing. """returns the points to use for interpolating v""" if v >= 120.: return 60, 120, inf elif v >= 60.: return 40, 60, 120 elif v >= 40.: return 30, 40, 60 elif v >= 30.: return 24, 30, 40 elif v >= 24.: return 20, 24, 30 elif v >= 19.5: return 19, 20, 24 if p >= .9: if v < 2.5: return 1, 2, 3 else: if v < 3.5: return 2, 3, 4 vi = int(round(v)) return vi - 1, vi, vi + 1 def _interpolate_v(p, r, v): """ interpolates v based on the values in the A table for the scalar value of r and th """ # interpolate v (p should be in table) # ordinate: y**2 # abcissa: 1./v # find the 3 closest v values # only p >= .9 have table values for 1 degree of freedom. # The boolean is used to index the tuple and append 1 when # p >= .9 v0, v1, v2 = _select_vs(v, p) # y = f - 1. y0_sq = (_func(A[(p,v0)], p, r, v0) + 1.)**2. y1_sq = (_func(A[(p,v1)], p, r, v1) + 1.)**2. y2_sq = (_func(A[(p,v2)], p, r, v2) + 1.)**2. # if v2 is inf set to a big number so interpolation # calculations will work if v2 > 1e38: v2 = 1e38 # transform v v_, v0_, v1_, v2_ = 1./v, 1./v0, 1./v1, 1./v2 # calculate derivatives for quadratic interpolation d2 = 2.*((y2_sq-y1_sq)/(v2_-v1_) - \ (y0_sq-y1_sq)/(v0_-v1_)) / (v2_-v0_) if (v2_ + v0_) >= (v1_ + v1_): d1 = (y2_sq-y1_sq) / (v2_-v1_) - 0.5*d2*(v2_-v1_) else: d1 = (y1_sq-y0_sq) / (v1_-v0_) + 0.5*d2*(v1_-v0_) d0 = y1_sq # calculate y y = math.sqrt((d2/2.)*(v_-v1_)**2. + d1*(v_-v1_)+ d0) return y def _qsturng(p, r, v): """scalar version of qsturng""" ## print 'q',p # r is interpolated through the q to y here we only need to # account for when p and/or v are not found in the table. global A, p_keys, v_keys if p < .1 or p > .999: raise ValueError('p must be between .1 and .999') if p < .9: if v < 2: raise ValueError('v must be > 2 when p < .9') else: if v < 1: raise ValueError('v must be > 1 when p >= .9') # The easy case. A tabled value is requested. #numpy 1.4.1: TypeError: unhashable type: 'numpy.ndarray' : p = float(p) if isinstance(v, np.ndarray): v = v.item() if (p,v) in A: y = _func(A[(p,v)], p, r, v) + 1. elif p not in p_keys and v not in v_keys+([],[1])[p>=.90]: # apply bilinear (quadratic) interpolation # # p0,v2 + o + p1,v2 + p2,v2 # r2 # # 1 # - (p,v) # v x # # r1 # p0,v1 + o + p1,v1 + p2,v1 # # # p0,v0 + o r0 + p1,v0 + p2,v0 # # _ptransform(p) # # (p1 and v1 may be below or above (p,v). The algorithm # works in both cases. For diagramatic simplicity it is # shown as above) # # 1. at v0, v1, and v2 use quadratic interpolation # to find r0, r1, r2 # # 2. use r0, r1, r2 and quadratic interpolaiton # to find y and (p,v) # find the 3 closest v values v0, v1, v2 = _select_vs(v, p) # find the 3 closest p values p0, p1, p2 = _select_ps(p) # calculate r0, r1, and r2 r0_sq = _interpolate_p(p, r, v0)**2 r1_sq = _interpolate_p(p, r, v1)**2 r2_sq = _interpolate_p(p, r, v2)**2 # transform v v_, v0_, v1_, v2_ = 1./v, 1./v0, 1./v1, 1./v2 # calculate derivatives for quadratic interpolation d2 = 2.*((r2_sq-r1_sq)/(v2_-v1_) - \ (r0_sq-r1_sq)/(v0_-v1_)) / (v2_-v0_) if (v2_ + v0_) >= (v1_ + v1_): d1 = (r2_sq-r1_sq) / (v2_-v1_) - 0.5*d2*(v2_-v1_) else: d1 = (r1_sq-r0_sq) / (v1_-v0_) + 0.5*d2*(v1_-v0_) d0 = r1_sq # calculate y y = math.sqrt((d2/2.)*(v_-v1_)**2. + d1*(v_-v1_)+ d0) elif v not in v_keys+([],[1])[p>=.90]: y = _interpolate_v(p, r, v) elif p not in p_keys: y = _interpolate_p(p, r, v) v = min(v, 1e38) return math.sqrt(2) * -y * scipy.stats.t.isf((1. + p) / 2., v) # make a qsturng functinon that will accept list-like objects _vqsturng = np.vectorize(_qsturng) _vqsturng.__doc__ = """vector version of qsturng""" def qsturng(p, r, v): """Approximates the quantile p for a studentized range distribution having v degrees of freedom and r samples for probability p. Parameters ---------- p : (scalar, array_like) The cumulative probability value p >= .1 and p <=.999 (values under .5 are not recommended) r : (scalar, array_like) The number of samples r >= 2 and r <= 200 (values over 200 are permitted but not recommended) v : (scalar, array_like) The sample degrees of freedom if p >= .9: v >=1 and v >= inf else: v >=2 and v >= inf Returns ------- q : (scalar, array_like) approximation of the Studentized Range """ if all(map(_isfloat, [p, r, v])): return _qsturng(p, r, v) return _vqsturng(p, r, v) ##def _qsturng0(p, r, v): #### print 'q0',p ## """ ## returns a first order approximation of q studentized range ## value. Based on Lund and Lund's 1983 based on the FORTRAN77 ## algorithm AS 190.2 Appl. Statist. (1983). ## """ ## vmax = 120. ## c = [0.8843, 0.2368, 1.214, 1.208, 1.4142] ## ## t = -_phi(.5+.5*p) ## if (v < vmax): ## t += (t**3. + t) / float(v) / 4. ## ## q = c[0] - c[1] * t ## if (v < vmax): ## q = q - c[2] / float(v) + c[3] * t / float(v) ## q = t * (q * math.log(r - 1.) + c[4]) ## ## # apply "bar napkin" correction for when p < .85 ## # this is good enough for our intended purpose ## if p < .85: ## q += math.log10(r) * 2.25 * (.85-p) ## return q def _psturng(q, r, v): """scalar version of psturng""" if q < 0.: raise ValueError('q should be >= 0') def opt_func(p, r, v): return np.squeeze(abs(_qsturng(p, r, v) - q)) if v == 1: if q < _qsturng(.9, r, 1): return .1 elif q > _qsturng(.999, r, 1): return .001 soln = 1. - fminbound(opt_func, .9, .999, args=(r,v)) return np.atleast_1d(soln) else: if q < _qsturng(.1, r, v): return .9 elif q > _qsturng(.999, r, v): return .001 soln = 1. - fminbound(opt_func, .1, .999, args=(r,v)) return np.atleast_1d(soln) _vpsturng = np.vectorize(_psturng) _vpsturng.__doc__ = """vector version of psturng""" def psturng(q, r, v): """Evaluates the probability from 0 to q for a studentized range having v degrees of freedom and r samples. Parameters ---------- q : (scalar, array_like) quantile value of Studentized Range q >= 0. r : (scalar, array_like) The number of samples r >= 2 and r <= 200 (values over 200 are permitted but not recommended) v : (scalar, array_like) The sample degrees of freedom if p >= .9: v >=1 and v >= inf else: v >=2 and v >= inf Returns ------- p : (scalar, array_like) 1. - area from zero to q under the Studentized Range distribution. When v == 1, p is bound between .001 and .1, when v > 1, p is bound between .001 and .9. Values between .5 and .9 are 1st order appoximations. """ if all(map(_isfloat, [q, r, v])): return _psturng(q, r, v) return _vpsturng(q, r, v) ##p, r, v = .9, 10, 20 ##print ##print 'p and v interpolation' ##print '\t20\t22\t24' ##print '.75',qsturng(.75, r, 20),qsturng(.75, r, 22),qsturng(.75, r, 24) ##print '.85',qsturng(.85, r, 20),qsturng(.85, r, 22),qsturng(.85, r, 24) ##print '.90',qsturng(.90, r, 20),qsturng(.90, r, 22),qsturng(.90, r, 24) ##print ##print 'p and v interpolation' ##print '\t120\t500\tinf' ##print '.950',qsturng(.95, r, 120),qsturng(.95, r, 500),qsturng(.95, r, inf) ##print '.960',qsturng(.96, r, 120),qsturng(.96, r, 500),qsturng(.96, r, inf) ##print '.975',qsturng(.975, r, 120),qsturng(.975, r, 500),qsturng(.975, r, inf) ##print ##print 'p and v interpolation' ##print '\t40\t50\t60' ##print '.950',qsturng(.95, r, 40),qsturng(.95, r, 50),qsturng(.95, r, 60) ##print '.960',qsturng(.96, r, 40),qsturng(.96, r, 50),qsturng(.96, r, 60) ##print '.975',qsturng(.975, r, 40),qsturng(.975, r, 50),qsturng(.975, r, 60) ##print ##print 'p and v interpolation' ##print '\t20\t22\t24' ##print '.50',qsturng(.5, r, 20),qsturng(.5, r, 22),qsturng(.5, r, 24) ##print '.60',qsturng(.6, r, 20),qsturng(.6, r, 22),qsturng(.6, r, 24) ##print '.75',qsturng(.75, r, 20),qsturng(.75, r, 22),qsturng(.75, r, 24) statsmodels-0.12.2/statsmodels/stats/libqsturng/tests/000077500000000000000000000000001400612667500232015ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/stats/libqsturng/tests/__init__.py000066400000000000000000000000001400612667500253000ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/stats/libqsturng/tests/bootleg.dat000066400000000000000000010505601400612667500253350ustar00rootroot000000000000000.950300,2,4.43400,3.787121 0.613586,75,149.1170,4.974391 0.8372366,53,501.2317,5.193843 0.9023396,58,546.2543,5.495572 0.9061918,96,424.4232,5.856011 0.7911643,8,200.5667,3.511362 0.5360133,7,806.1763,2.722873 0.6327574,56,56.17163,4.84627 0.7634097,28,996.1946,4.506239 0.5940891,78,56.14756,5.015406 0.7991432,12,157.4574,3.92541 0.6599134,72,944.1173,4.99709 0.6845088,98,268.675,5.280095 0.6883003,80,632.1445,5.128627 0.787793,90,178.9085,5.466432 0.5937039,11,637.886,3.312434 0.6812908,31,477.9169,4.407207 0.6260902,30,145.0597,4.289132 0.5198778,20,172.1525,3.732414 0.551296,21,539.7639,3.826797 0.9473277,43,364.0211,5.573688 0.6470059,32,446.2837,4.363963 0.7304492,69,854.5265,5.104756 0.8461879,49,341.8976,5.17709 0.6998816,32,420.9467,4.473319 0.7708307,73,782.7106,5.234264 0.8517651,65,50.74249,5.601281 0.7680614,23,782.7298,4.362934 0.6772532,10,62.75346,3.446085 0.8061568,53,941.9258,5.094457 0.535348,87,579.7095,4.927541 0.7317784,8,760.4088,3.322854 0.647424,35,973.2097,4.430608 0.7205917,62,451.4614,5.016029 0.8310729,46,867.2378,5.064711 0.7092925,93,252.9435,5.294547 0.7614025,42,18.29759,5.194786 0.768294,92,443.8754,5.398033 0.611393,96,660.7554,5.120007 0.5584655,9,544.9949,3.037984 0.5757473,27,207.4046,4.096346 0.7165018,66,868.694,5.044124 0.8916566,90,891.3335,5.730434 0.930496,81,680.2784,5.855139 0.9493338,21,814.3338,5.058685 0.8789807,96,958.6534,5.722715 0.6453387,99,32.75148,5.368509 0.9432753,88,44.19807,6.429427 0.7734237,11,481.0691,3.747131 0.9275644,15,31.61525,4.961554 0.8814721,68,452.8735,5.521471 0.5684593,38,359.6916,4.35714 0.7915564,34,395.8539,4.741082 0.6212993,97,578.4411,5.14523 0.786856,89,643.049,5.411403 0.5872209,30,947.6958,4.193762 0.863228,58,644.4567,5.336585 0.6852954,2,650.4337,1.422949 0.8156778,80,626.9999,5.412793 0.7758632,40,146.7813,4.857534 0.6193542,63,757.0062,4.82912 0.698619,62,144.0496,5.004096 0.924634,5,682.612,3.647421 0.6921237,49,433.7529,4.784743 0.6682577,12,709.6476,3.557659 0.7406304,98,958.277,5.368286 0.5085852,22,433.0734,3.789960 0.8567905,78,869.9651,5.511207 0.6796293,27,770.1198,4.288455 0.8970843,7,914.6475,3.798629 0.8490929,46,340.834,5.141464 0.609374,71,516.113,4.902681 0.8709478,20,759.5428,4.57836 0.720285,94,205.1919,5.332692 0.7809733,3,290.1928,2.359907 0.6695694,62,545.2842,4.911675 0.6835529,2,482.5781,1.418211 0.8061166,2,952.5813,1.83861 0.5194726,41,996.1952,4.328192 0.8214913,51,699.2729,5.113396 0.7761068,36,304.3256,4.749856 0.7338799,63,84.29842,5.132537 0.5905524,53,981.4905,4.648476 0.9062086,43,145.8958,5.377721 0.6504464,84,494.4505,5.096346 0.8689327,93,276.0934,5.706336 0.5645257,7,580.0792,2.785004 0.650522,63,428.5393,4.890803 0.839554,48,209.0835,5.161268 0.6790368,57,874.8717,4.863635 0.8461706,95,497.4795,5.621337 0.9483254,95,113.4526,6.237262 0.6620466,71,782.7844,4.992363 0.6950035,72,745.4756,5.064967 0.6869721,9,119.0430,3.344547 0.6628797,22,627.2988,4.08501 0.658888,51,74.652,4.809383 0.830574,75,794.5755,5.406187 0.6937293,17,435.4039,3.933864 0.7577239,24,225.9839,4.390343 0.7776778,92,830.089,5.408262 0.764957,95,124.2182,5.472132 0.9206389,17,727.5881,4.694345 0.898351,70,950.8781,5.591991 0.7973998,11,220.2692,3.831447 0.7214944,95,380.3205,5.322659 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0.7299095,48,298.656,4.85679 0.6956586,32,739.8781,4.458631 0.6287844,35,862.2396,4.395717 0.8391402,38,300.8604,4.973045 0.510979,99,235.7683,4.990011 0.508311,83,427.9368,4.852489 0.6374083,53,722.2017,4.733101 0.8431894,21,933.971,4.51148 0.6286747,89,648.9947,5.096027 0.9137417,88,684.3439,5.819049 0.7000148,65,253.8147,5.020509 0.9283806,36,485.4688,5.30663 0.5502186,97,901.5118,5.026643 0.6794158,92,491.8415,5.2134 0.5004906,9,369.889,2.919374 0.8813509,4,156.3115,3.159320 0.5316867,79,888.0104,4.849485 0.7776448,23,552.1755,4.391651 0.6669258,42,541.5799,4.614754 statsmodels-0.12.2/statsmodels/stats/libqsturng/tests/test_qsturng.py000066400000000000000000000213611400612667500263200ustar00rootroot00000000000000# Copyright (c) 2011 BSD, Roger Lew [see LICENSE.txt] # This software is funded in part by NIH Grant P20 RR016454. """The 'handful' tests are intended to aid refactoring. The tests with the @pytest.mark..slow are empirical (test within error limits) and intended to more extensively ensure the stability and accuracy of the functions""" from statsmodels.compat.python import lzip, lmap from numpy.testing import ( assert_equal, assert_almost_equal, assert_array_almost_equal, assert_raises) import numpy as np import pytest from statsmodels.stats.libqsturng import qsturng, psturng def read_ch(fname): with open(fname) as f: lines = f.readlines() ps,rs,vs,qs = lzip(*[L.split(',') for L in lines]) return lmap(float, ps), lmap(float, rs),lmap(float, vs), lmap(float, qs) class TestQsturng(object): def test_scalar(self): # scalar input -> scalar output assert_almost_equal(4.43645545899562, qsturng(.9,5,6), 5) def test_vector(self): # vector input -> vector output assert_array_almost_equal(np.array([3.98832389, 4.56835318, 6.26400894]), qsturng([.8932, .9345,.9827], [4, 4, 4], [6, 6, 6]), 5) def test_invalid_parameters(self): # p < .1 assert_raises(ValueError, qsturng, -.1,5,6) # p > .999 assert_raises(ValueError, qsturng, .9991,5,6) # p < .9, v = 1 assert_raises(ValueError, qsturng, .89,5,1) # p >= .9, v = 0 assert_raises(ValueError, qsturng, .9,5,0) # r < 2 assert_raises((ValueError, OverflowError), qsturng, .9,1,2) def test_handful_to_tbl(self): cases = [(0.75, 30.0, 12.0, 5.01973488482), (0.975, 15.0, 18.0, 6.00428263999), (0.1, 8.0, 11.0, 1.76248712658), (0.995, 6.0, 17.0, 6.13684839819), (0.85, 15.0, 18.0, 4.65007986215), (0.75, 17.0, 18.0, 4.33179650607), (0.75, 60.0, 16.0, 5.50520795792), (0.99, 100.0, 2.0, 50.3860723433), (0.9, 2.0, 40.0, 2.38132493732), (0.8, 12.0, 20.0, 4.15361239056), (0.675, 8.0, 14.0, 3.35011529943), (0.75, 30.0, 24.0, 4.77976803574), (0.75, 2.0, 18.0, 1.68109190167), (0.99, 7.0, 120.0, 5.00525918406), (0.8, 19.0, 15.0, 4.70694373713), (0.8, 15.0, 8.0, 4.80392205906), (0.5, 12.0, 11.0, 3.31672775449), (0.85, 30.0, 2.0, 10.2308503607), (0.675, 20.0, 18.0, 4.23706426096), (0.1, 60.0, 60.0, 3.69215469278)] for p,r,v,q in cases: assert_almost_equal(q, qsturng(p,r,v), 5) # TODO: do something with this? #remove from testsuite, used only for table generation and fails on #Debian S390, no idea why @pytest.mark.skip def test_all_to_tbl(self): from statsmodels.stats.libqsturng.make_tbls import T,R ps, rs, vs, qs = [], [], [], [] for p in T: for v in T[p]: for r in R.keys(): ps.append(p) vs.append(v) rs.append(r) qs.append(T[p][v][R[r]]) qs = np.array(qs) errors = np.abs(qs-qsturng(ps,rs,vs))/qs assert_equal(np.array([]), np.where(errors > .03)[0]) def test_handful_to_ch(self): cases = [(0.8699908, 10.0, 465.4956, 3.997799075635331), (0.8559087, 43.0, 211.7474, 5.1348419692951675), (0.6019187, 11.0, 386.5556, 3.3383101487698821), (0.658888, 51.0, 74.652, 4.8108880483153733), (0.6183604, 77.0, 479.8493, 4.9864059321732874), (0.9238978, 77.0, 787.5278, 5.7871053003022936), (0.8408322, 7.0, 227.3483, 3.5555798311413578), (0.5930279, 60.0, 325.3461, 4.7658023123882396), (0.6236158, 61.0, 657.5285, 4.8207812755987867), (0.9344575, 72.0, 846.4138, 5.8014341329259107), (0.8761198, 56.0, 677.8171, 5.362460718311719), (0.7901517, 41.0, 131.525, 4.9222831341950544), (0.6396423, 44.0, 624.3828, 4.6015127250083152), (0.8085966, 14.0, 251.4224, 4.0793058424719746), (0.716179, 45.0, 136.7055, 4.8055498089340087), (0.8204, 6.0, 290.9876, 3.3158771384085597), (0.8705345, 83.0, 759.6216, 5.5969334564485376), (0.8249085, 18.0, 661.9321, 4.3283725986180395), (0.9503, 2.0, 4.434, 3.7871158594867262), (0.7276132, 95.0, 91.43983, 5.4100384868499889)] for p,r,v,q in cases: assert_almost_equal(q, qsturng(p,r,v), 5) @pytest.mark.slow def test_10000_to_ch(self): import os curdir = os.path.dirname(os.path.abspath(__file__)) #ps, rs, vs, qs = read_ch(curdir + '/bootleg.dat') # <- generated by qtukey in R # work around problem getting libqsturng.tests.bootleg.dat installed ps, rs, vs, qs = read_ch(os.path.split(os.path.split(curdir)[0])[0] + '/tests/results/bootleg.csv') qs = np.array(qs) errors = np.abs(qs-qsturng(ps,rs,vs))/qs assert_equal(np.array([]), np.where(errors > .03)[0]) class TestPsturng(object): def test_scalar(self): "scalar input -> scalar output" assert_almost_equal(.1, psturng(4.43645545899562,5,6), 5) def test_vector(self): "vector input -> vector output" assert_array_almost_equal(np.array([0.10679889, 0.06550009, 0.01730145]), psturng([3.98832389, 4.56835318, 6.26400894], [4, 4, 4], [6, 6, 6]), 5) def test_v_equal_one(self): assert_almost_equal(.1, psturng(.2,5,1), 5) def test_invalid_parameters(self): # q < .1 assert_raises(ValueError, psturng, -.1,5,6) # r < 2 assert_raises((ValueError, OverflowError), psturng, .9,1,2) def test_handful_to_known_values(self): cases = [(0.71499578726111435, 67, 956.70742488392386, 5.0517658443070692), (0.42974234855067672, 16, 723.50261736502318, 3.3303582093701354), (0.94936429359548424, 2, 916.1867328010926, 2.7677975546417244), (0.85357381770725038, 66, 65.67055060832368, 5.5647438108270109), (0.87372108021900929, 74, 626.42369474993632, 5.5355540570701107), (0.53891960564713726, 49, 862.63799438485785, 4.5108645923377146), (0.98818659555664567, 18, 36.269686711464274, 6.0906643750886156), (0.53031994896037626, 50, 265.29558652727917, 4.5179640079726795), (0.7318857887397332, 59, 701.41497552251201, 4.9980139875409915), (0.65332019368982697, 61, 591.01183664195912, 4.8706581766706893), (0.55403221657248558, 77, 907.34156725405194, 4.8786135917984632), (0.30783916857266003, 83, 82.446923487980882, 4.4396401242858294), (0.29321720242415661, 16, 709.64382575553009, 3.0304277540702729), (0.27146478168880306, 31, 590.00594683574172, 3.5870031664477215), (0.67348796958433776, 81, 608.02706111127657, 5.1096199974432936), (0.32774393945968938, 18, 17.706224399250839, 3.2119038163765432), (0.7081637474795982, 72, 443.10678914889695, 5.0990030889410649), (0.33354939276757861, 47, 544.0772192199048, 4.0613352964193279), (0.60412143947363051, 36, 895.83526933271548, 4.381717596850172), (0.88739052300665977, 77, 426.03665511558262, 5.6333929480341309)] for p,r,v,q in cases: assert_almost_equal(1.-p, psturng(q,r,v), 5) @pytest.mark.slow def test_100_random_values(self, reset_randomstate): n = 100 random_state = np.random.RandomState(12345) ps = random_state.random_sample(n)*(.999 - .1) + .1 rs = random_state.randint(2, 101, n) vs = random_state.random_sample(n)*998. + 2. qs = qsturng(ps, rs, vs) estimates = psturng(qs, rs, vs) actuals = 1. - ps errors = estimates - actuals assert_equal(np.array([]), np.where(errors > 1e-5)[0]) statsmodels-0.12.2/statsmodels/stats/mediation.py000066400000000000000000000400211400612667500221650ustar00rootroot00000000000000""" Mediation analysis Implements algorithm 1 ('parametric inference') and algorithm 2 ('nonparametric inference') from: Imai, Keele, Tingley (2010). A general approach to causal mediation analysis. Psychological Methods 15:4, 309-334. http://imai.princeton.edu/research/files/BaronKenny.pdf The algorithms are described on page 317 of the paper. In the case of linear models with no interactions involving the mediator, the results should be similar or identical to the earlier Barron-Kenny approach. """ import numpy as np import pandas as pd from statsmodels.graphics.utils import maybe_name_or_idx class Mediation(object): """ Conduct a mediation analysis. Parameters ---------- outcome_model : statsmodels model Regression model for the outcome. Predictor variables include the treatment/exposure, the mediator, and any other variables of interest. mediator_model : statsmodels model Regression model for the mediator variable. Predictor variables include the treatment/exposure and any other variables of interest. exposure : str or (int, int) tuple The name or column position of the treatment/exposure variable. If positions are given, the first integer is the column position of the exposure variable in the outcome model and the second integer is the position of the exposure variable in the mediator model. If a string is given, it must be the name of the exposure variable in both regression models. mediator : {str, int} The name or column position of the mediator variable in the outcome regression model. If None, infer the name from the mediator model formula (if present). moderators : dict Map from variable names or index positions to values of moderator variables that are held fixed when calculating mediation effects. If the keys are index position they must be tuples `(i, j)` where `i` is the index in the outcome model and `j` is the index in the mediator model. Otherwise the keys must be variable names. outcome_fit_kwargs : dict-like Keyword arguments to use when fitting the outcome model. mediator_fit_kwargs : dict-like Keyword arguments to use when fitting the mediator model. outcome_predict_kwargs : dict-like Keyword arguments to use when calling predict on the outcome model. Returns a ``MediationResults`` object. Notes ----- The mediator model class must implement ``get_distribution``. Examples -------- A basic mediation analysis using formulas: >>> import statsmodels.api as sm >>> import statsmodels.genmod.families.links as links >>> probit = links.probit >>> outcome_model = sm.GLM.from_formula("cong_mesg ~ emo + treat + age + educ + gender + income", ... data, family=sm.families.Binomial(link=probit())) >>> mediator_model = sm.OLS.from_formula("emo ~ treat + age + educ + gender + income", data) >>> med = Mediation(outcome_model, mediator_model, "treat", "emo").fit() >>> med.summary() A basic mediation analysis without formulas. This may be slightly faster than the approach using formulas. If there are any interactions involving the treatment or mediator variables this approach will not work, you must use formulas. >>> import patsy >>> outcome = np.asarray(data["cong_mesg"]) >>> outcome_exog = patsy.dmatrix("emo + treat + age + educ + gender + income", data, ... return_type='dataframe') >>> probit = sm.families.links.probit >>> outcome_model = sm.GLM(outcome, outcome_exog, family=sm.families.Binomial(link=probit())) >>> mediator = np.asarray(data["emo"]) >>> mediator_exog = patsy.dmatrix("treat + age + educ + gender + income", data, ... return_type='dataframe') >>> mediator_model = sm.OLS(mediator, mediator_exog) >>> tx_pos = [outcome_exog.columns.tolist().index("treat"), ... mediator_exog.columns.tolist().index("treat")] >>> med_pos = outcome_exog.columns.tolist().index("emo") >>> med = Mediation(outcome_model, mediator_model, tx_pos, med_pos).fit() >>> med.summary() A moderated mediation analysis. The mediation effect is computed for people of age 20. >>> fml = "cong_mesg ~ emo + treat*age + emo*age + educ + gender + income", >>> outcome_model = sm.GLM.from_formula(fml, data, ... family=sm.families.Binomial()) >>> mediator_model = sm.OLS.from_formula("emo ~ treat*age + educ + gender + income", data) >>> moderators = {"age" : 20} >>> med = Mediation(outcome_model, mediator_model, "treat", "emo", ... moderators=moderators).fit() References ---------- Imai, Keele, Tingley (2010). A general approach to causal mediation analysis. Psychological Methods 15:4, 309-334. http://imai.princeton.edu/research/files/BaronKenny.pdf Tingley, Yamamoto, Hirose, Keele, Imai (2014). mediation : R package for causal mediation analysis. Journal of Statistical Software 59:5. http://www.jstatsoft.org/v59/i05/paper """ def __init__(self, outcome_model, mediator_model, exposure, mediator=None, moderators=None, outcome_fit_kwargs=None, mediator_fit_kwargs=None, outcome_predict_kwargs=None): self.outcome_model = outcome_model self.mediator_model = mediator_model self.exposure = exposure self.moderators = moderators if moderators is not None else {} if mediator is None: self.mediator = self._guess_endog_name(mediator_model, 'mediator') else: self.mediator = mediator self._outcome_fit_kwargs = (outcome_fit_kwargs if outcome_fit_kwargs is not None else {}) self._mediator_fit_kwargs = (mediator_fit_kwargs if mediator_fit_kwargs is not None else {}) self._outcome_predict_kwargs = (outcome_predict_kwargs if outcome_predict_kwargs is not None else {}) # We will be changing these so need to copy. self._outcome_exog = outcome_model.exog.copy() self._mediator_exog = mediator_model.exog.copy() # Position of the exposure variable in the mediator model. self._exp_pos_mediator = self._variable_pos('exposure', 'mediator') # Position of the exposure variable in the outcome model. self._exp_pos_outcome = self._variable_pos('exposure', 'outcome') # Position of the mediator variable in the outcome model. self._med_pos_outcome = self._variable_pos('mediator', 'outcome') def _variable_pos(self, var, model): if model == 'mediator': mod = self.mediator_model else: mod = self.outcome_model if var == 'mediator': return maybe_name_or_idx(self.mediator, mod)[1] exp = self.exposure exp_is_2 = ((len(exp) == 2) and not isinstance(exp, str)) if exp_is_2: if model == 'outcome': return exp[0] elif model == 'mediator': return exp[1] else: return maybe_name_or_idx(exp, mod)[1] def _guess_endog_name(self, model, typ): if hasattr(model, 'formula'): return model.formula.split("~")[0].strip() else: raise ValueError('cannot infer %s name without formula' % typ) def _simulate_params(self, result): """ Simulate model parameters from fitted sampling distribution. """ mn = result.params cov = result.cov_params() return np.random.multivariate_normal(mn, cov) def _get_mediator_exog(self, exposure): """ Return the mediator exog matrix with exposure set to the given value. Set values of moderated variables as needed. """ mediator_exog = self._mediator_exog if not hasattr(self.mediator_model, 'formula'): mediator_exog[:, self._exp_pos_mediator] = exposure for ix in self.moderators: v = self.moderators[ix] mediator_exog[:, ix[1]] = v else: # Need to regenerate the model exog df = self.mediator_model.data.frame.copy() df.loc[:, self.exposure] = exposure for vname in self.moderators: v = self.moderators[vname] df.loc[:, vname] = v klass = self.mediator_model.__class__ init_kwargs = self.mediator_model._get_init_kwds() model = klass.from_formula(data=df, **init_kwargs) mediator_exog = model.exog return mediator_exog def _get_outcome_exog(self, exposure, mediator): """ Retun the exog design matrix with mediator and exposure set to the given values. Set values of moderated variables as needed. """ outcome_exog = self._outcome_exog if not hasattr(self.outcome_model, 'formula'): outcome_exog[:, self._med_pos_outcome] = mediator outcome_exog[:, self._exp_pos_outcome] = exposure for ix in self.moderators: v = self.moderators[ix] outcome_exog[:, ix[0]] = v else: # Need to regenerate the model exog df = self.outcome_model.data.frame.copy() df.loc[:, self.exposure] = exposure df.loc[:, self.mediator] = mediator for vname in self.moderators: v = self.moderators[vname] df.loc[:, vname] = v klass = self.outcome_model.__class__ init_kwargs = self.outcome_model._get_init_kwds() model = klass.from_formula(data=df, **init_kwargs) outcome_exog = model.exog return outcome_exog def _fit_model(self, model, fit_kwargs, boot=False): klass = model.__class__ init_kwargs = model._get_init_kwds() endog = model.endog exog = model.exog if boot: ii = np.random.randint(0, len(endog), len(endog)) endog = endog[ii] exog = exog[ii, :] outcome_model = klass(endog, exog, **init_kwargs) return outcome_model.fit(**fit_kwargs) def fit(self, method="parametric", n_rep=1000): """ Fit a regression model to assess mediation. Parameters ---------- method : str Either 'parametric' or 'bootstrap'. n_rep : int The number of simulation replications. Returns a MediationResults object. """ if method.startswith("para"): # Initial fit to unperturbed data. outcome_result = self._fit_model(self.outcome_model, self._outcome_fit_kwargs) mediator_result = self._fit_model(self.mediator_model, self._mediator_fit_kwargs) elif not method.startswith("boot"): raise("method must be either 'parametric' or 'bootstrap'") indirect_effects = [[], []] direct_effects = [[], []] for iter in range(n_rep): if method == "parametric": # Realization of outcome model parameters from sampling distribution outcome_params = self._simulate_params(outcome_result) # Realization of mediation model parameters from sampling distribution mediation_params = self._simulate_params(mediator_result) else: outcome_result = self._fit_model(self.outcome_model, self._outcome_fit_kwargs, boot=True) outcome_params = outcome_result.params mediator_result = self._fit_model(self.mediator_model, self._mediator_fit_kwargs, boot=True) mediation_params = mediator_result.params # predicted outcomes[tm][te] is the outcome when the # mediator is set to tm and the outcome/exposure is set to # te. predicted_outcomes = [[None, None], [None, None]] for tm in 0, 1: mex = self._get_mediator_exog(tm) kwargs = {"exog": mex} if hasattr(mediator_result, "scale"): kwargs["scale"] = mediator_result.scale gen = self.mediator_model.get_distribution(mediation_params, **kwargs) potential_mediator = gen.rvs(mex.shape[0]) for te in 0, 1: oex = self._get_outcome_exog(te, potential_mediator) po = self.outcome_model.predict(outcome_params, oex, **self._outcome_predict_kwargs) predicted_outcomes[tm][te] = po for t in 0, 1: indirect_effects[t].append(predicted_outcomes[1][t] - predicted_outcomes[0][t]) direct_effects[t].append(predicted_outcomes[t][1] - predicted_outcomes[t][0]) for t in 0, 1: indirect_effects[t] = np.asarray(indirect_effects[t]).T direct_effects[t] = np.asarray(direct_effects[t]).T self.indirect_effects = indirect_effects self.direct_effects = direct_effects rslt = MediationResults(self.indirect_effects, self.direct_effects) rslt.method = method return rslt def _pvalue(vec): return 2 * min(sum(vec > 0), sum(vec < 0)) / float(len(vec)) class MediationResults(object): """ A class for holding the results of a mediation analysis. The following terms are used in the summary output: ACME : average causal mediated effect ADE : average direct effect """ def __init__(self, indirect_effects, direct_effects): self.indirect_effects = indirect_effects self.direct_effects = direct_effects indirect_effects_avg = [None, None] direct_effects_avg = [None, None] for t in 0, 1: indirect_effects_avg[t] = indirect_effects[t].mean(0) direct_effects_avg[t] = direct_effects[t].mean(0) self.ACME_ctrl = indirect_effects_avg[0] self.ACME_tx = indirect_effects_avg[1] self.ADE_ctrl = direct_effects_avg[0] self.ADE_tx = direct_effects_avg[1] self.total_effect = (self.ACME_ctrl + self.ACME_tx + self.ADE_ctrl + self.ADE_tx) / 2 self.prop_med_ctrl = self.ACME_ctrl / self.total_effect self.prop_med_tx = self.ACME_tx / self.total_effect self.prop_med_avg = (self.prop_med_ctrl + self.prop_med_tx) / 2 self.ACME_avg = (self.ACME_ctrl + self.ACME_tx) / 2 self.ADE_avg = (self.ADE_ctrl + self.ADE_tx) / 2 def summary(self, alpha=0.05): """ Provide a summary of a mediation analysis. """ columns = ["Estimate", "Lower CI bound", "Upper CI bound", "P-value"] index = ["ACME (control)", "ACME (treated)", "ADE (control)", "ADE (treated)", "Total effect", "Prop. mediated (control)", "Prop. mediated (treated)", "ACME (average)", "ADE (average)", "Prop. mediated (average)"] smry = pd.DataFrame(columns=columns, index=index) for i, vec in enumerate([self.ACME_ctrl, self.ACME_tx, self.ADE_ctrl, self.ADE_tx, self.total_effect, self.prop_med_ctrl, self.prop_med_tx, self.ACME_avg, self.ADE_avg, self.prop_med_avg]): if ((vec is self.prop_med_ctrl) or (vec is self.prop_med_tx) or (vec is self.prop_med_avg)): smry.iloc[i, 0] = np.median(vec) else: smry.iloc[i, 0] = vec.mean() smry.iloc[i, 1] = np.percentile(vec, 100 * alpha / 2) smry.iloc[i, 2] = np.percentile(vec, 100 * (1 - alpha / 2)) smry.iloc[i, 3] = _pvalue(vec) smry = smry.apply(pd.to_numeric, errors='coerce') return smry statsmodels-0.12.2/statsmodels/stats/meta_analysis.py000066400000000000000000000616661400612667500230670ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Thu Apr 2 14:34:25 2020 Author: Josef Perktold License: BSD-3 """ import numpy as np import pandas as pd from scipy import stats from statsmodels.stats.base import HolderTuple class CombineResults(object): """Results from combined estimate of means or effect sizes This currently includes intermediate results that might be removed """ def __init__(self, **kwds): self.__dict__.update(kwds) self._ini_keys = list(kwds.keys()) self.df_resid = self.k - 1 # TODO: move to property ? self.sd_eff_w_fe_hksj = np.sqrt(self.var_hksj_fe) self.sd_eff_w_re_hksj = np.sqrt(self.var_hksj_re) # explained variance measures self.h2 = self.q / (self.k - 1) self.i2 = 1 - 1 / self.h2 # memoize ci_samples self.cache_ci = {} def conf_int_samples(self, alpha=0.05, use_t=None, nobs=None, ci_func=None): """confidence intervals for the effect size estimate of samples Additional information needs to be provided for confidence intervals that are not based on normal distribution using available variance. This is likely to change in future. Parameters ---------- alpha : float in (0, 1) Significance level for confidence interval. Nominal coverage is ``1 - alpha``. use_t : None or bool If use_t is None, then the attribute `use_t` determines whether normal or t-distribution is used for confidence intervals. Specifying use_t overrides the attribute. If use_t is false, then confidence intervals are based on the normal distribution. If it is true, then the t-distribution is used. nobs : None or float Number of observations used for degrees of freedom computation. Only used if use_t is true. ci_func : None or callable User provided function to compute confidence intervals. This is not used yet and will allow using non-standard confidence intervals. Returns ------- ci_eff : tuple of ndarrays Tuple (ci_low, ci_upp) with confidence interval computed for each sample. Notes ----- CombineResults currently only has information from the combine_effects function, which does not provide details about individual samples. """ # this is a bit messy, we don't have enough information about # computing conf_int already in results for other than normal # TODO: maybe there is a better if (alpha, use_t) in self.cache_ci: return self.cache_ci[(alpha, use_t)] if use_t is None: use_t = self.use_t if ci_func is not None: kwds = {"use_t": use_t} if use_t is not None else {} ci_eff = ci_func(alpha=alpha, **kwds) self.ci_sample_distr = "ci_func" else: if use_t is False: crit = stats.norm.isf(alpha / 2) self.ci_sample_distr = "normal" else: if nobs is not None: df_resid = nobs - 1 crit = stats.t.isf(alpha / 2, df_resid) self.ci_sample_distr = "t" else: msg = ("`use_t=True` requires `nobs` for each sample " "or `ci_func`. Using normal distribution for " "confidence interval of individual samples.") import warnings warnings.warn(msg) crit = stats.norm.isf(alpha / 2) self.ci_sample_distr = "normal" # sgn = np.asarray([-1, 1]) # ci_eff = self.eff + sgn * crit * self.sd_eff ci_low = self.eff - crit * self.sd_eff ci_upp = self.eff + crit * self.sd_eff ci_eff = (ci_low, ci_upp) # if (alpha, use_t) not in self.cache_ci: # not needed self.cache_ci[(alpha, use_t)] = ci_eff return ci_eff def conf_int(self, alpha=0.05, use_t=None): """confidence interval for the overall mean estimate Parameters ---------- alpha : float in (0, 1) Significance level for confidence interval. Nominal coverage is ``1 - alpha``. use_t : None or bool If use_t is None, then the attribute `use_t` determines whether normal or t-distribution is used for confidence intervals. Specifying use_t overrides the attribute. If use_t is false, then confidence intervals are based on the normal distribution. If it is true, then the t-distribution is used. Returns ------- ci_eff_fe : tuple of floats Confidence interval for mean effects size based on fixed effects model with scale=1. ci_eff_re : tuple of floats Confidence interval for mean effects size based on random effects model with scale=1 ci_eff_fe_wls : tuple of floats Confidence interval for mean effects size based on fixed effects model with estimated scale corresponding to WLS, ie. HKSJ. ci_eff_re_wls : tuple of floats Confidence interval for mean effects size based on random effects model with estimated scale corresponding to WLS, ie. HKSJ. If random effects method is fully iterated, i.e. Paule-Mandel, then the estimated scale is 1. """ if use_t is None: use_t = self.use_t if use_t is False: crit = stats.norm.isf(alpha / 2) else: crit = stats.t.isf(alpha / 2, self.df_resid) sgn = np.asarray([-1, 1]) m_fe = self.mean_effect_fe m_re = self.mean_effect_re ci_eff_fe = m_fe + sgn * crit * self.sd_eff_w_fe ci_eff_re = m_re + sgn * crit * self.sd_eff_w_re ci_eff_fe_wls = m_fe + sgn * crit * np.sqrt(self.var_hksj_fe) ci_eff_re_wls = m_re + sgn * crit * np.sqrt(self.var_hksj_re) return ci_eff_fe, ci_eff_re, ci_eff_fe_wls, ci_eff_re_wls def test_homogeneity(self): """Test whether the means of all samples are the same currently no options, test uses chisquare distribution default might change depending on `use_t` Returns ------- res : HolderTuple instance The results include the following attributes: - statistic : float Test statistic, ``q`` in meta-analysis, this is the pearson_chi2 statistic for the fixed effects model. - pvalue : float P-value based on chisquare distribution. - df : float Degrees of freedom, equal to number of studies or samples minus 1. """ pvalue = stats.chi2.sf(self.q, self.k - 1) res = HolderTuple(statistic=self.q, pvalue=pvalue, df=self.k - 1, distr="chi2") return res def summary_array(self, alpha=0.05, use_t=None): """Create array with sample statistics and mean estimates Parameters ---------- alpha : float in (0, 1) Significance level for confidence interval. Nominal coverage is ``1 - alpha``. use_t : None or bool If use_t is None, then the attribute `use_t` determines whether normal or t-distribution is used for confidence intervals. Specifying use_t overrides the attribute. If use_t is false, then confidence intervals are based on the normal distribution. If it is true, then the t-distribution is used. Returns ------- res : ndarray Array with columns ['eff', "sd_eff", "ci_low", "ci_upp", "w_fe","w_re"]. Rows include statistics for samples and estimates of overall mean. column_names : list of str The names for the columns, used when creating summary DataFrame. """ ci_low, ci_upp = self.conf_int_samples(alpha=alpha, use_t=use_t) res = np.column_stack([self.eff, self.sd_eff, ci_low, ci_upp, self.weights_rel_fe, self.weights_rel_re]) ci = self.conf_int(alpha=alpha, use_t=use_t) res_fe = [[self.mean_effect_fe, self.sd_eff_w_fe, ci[0][0], ci[0][1], 1, np.nan]] res_re = [[self.mean_effect_re, self.sd_eff_w_re, ci[1][0], ci[1][1], np.nan, 1]] res_fe_wls = [[self.mean_effect_fe, self.sd_eff_w_fe_hksj, ci[2][0], ci[2][1], 1, np.nan]] res_re_wls = [[self.mean_effect_re, self.sd_eff_w_re_hksj, ci[3][0], ci[3][1], np.nan, 1]] res = np.concatenate([res, res_fe, res_re, res_fe_wls, res_re_wls], axis=0) column_names = ['eff', "sd_eff", "ci_low", "ci_upp", "w_fe", "w_re"] return res, column_names def summary_frame(self, alpha=0.05, use_t=None): """Create DataFrame with sample statistics and mean estimates Parameters ---------- alpha : float in (0, 1) Significance level for confidence interval. Nominal coverage is ``1 - alpha``. use_t : None or bool If use_t is None, then the attribute `use_t` determines whether normal or t-distribution is used for confidence intervals. Specifying use_t overrides the attribute. If use_t is false, then confidence intervals are based on the normal distribution. If it is true, then the t-distribution is used. Returns ------- res : DataFrame pandas DataFrame instance with columns ['eff', "sd_eff", "ci_low", "ci_upp", "w_fe","w_re"]. Rows include statistics for samples and estimates of overall mean. """ if use_t is None: use_t = self.use_t labels = (list(self.row_names) + ["fixed effect", "random effect", "fixed effect wls", "random effect wls"]) res, col_names = self.summary_array(alpha=alpha, use_t=use_t) results = pd.DataFrame(res, index=labels, columns=col_names) return results def plot_forest(self, ax=None, **kwds): """Forest plot with means and confidence intervals Parameters ---------- ax : None or matplotlib axis instance If ax is provided, then the plot will be added to it. kwds : optional keyword arguments Keywords are forwarded to the dot_plot function that creates the plot. Returns ------- fig : Matplotlib figure instance See Also -------- dot_plot """ from statsmodels.graphics.dotplots import dot_plot res_df = self.summary_frame() hw = np.abs(res_df[["ci_low", "ci_upp"]] - res_df[["eff"]].values) fig = dot_plot(points=res_df["eff"], intervals=hw, lines=res_df.index, line_order=res_df.index, **kwds) return fig def effectsize_smd(mean1, sd1, nobs1, mean2, sd2, nobs2): """effect sizes for mean difference for use in meta-analysis mean1, sd1, nobs1 are for treatment mean2, sd2, nobs2 are for control Effect sizes are computed for the mean difference ``mean1 - mean2`` standardized by an estimate of the within variance. This does not have option yet. It uses standardized mean difference with bias correction as effect size. This currently does not use np.asarray, all computations are possible in pandas. Parameters ---------- mean1 : array mean of second sample, treatment groups sd1 : array standard deviation of residuals in treatment groups, within nobs1 : array number of observations in treatment groups mean2, sd2, nobs2 : arrays mean, standard deviation and number of observations of control groups Returns ------- smd_bc : array bias corrected estimate of standardized mean difference var_smdbc : array estimate of variance of smd_bc Notes ----- Status: API will still change. This is currently intended for support of meta-analysis. References ---------- Borenstein, Michael. 2009. Introduction to Meta-Analysis. Chichester: Wiley. Chen, Ding-Geng, and Karl E. Peace. 2013. Applied Meta-Analysis with R. Chapman & Hall/CRC Biostatistics Series. Boca Raton: CRC Press/Taylor & Francis Group. """ # TODO: not used yet, design and options ? # k = len(mean1) # if row_names is None: # row_names = list(range(k)) # crit = stats.norm.isf(alpha / 2) # var_diff_uneq = sd1**2 / nobs1 + sd2**2 / nobs2 var_diff = (sd1**2 * (nobs1 - 1) + sd2**2 * (nobs2 - 1)) / (nobs1 + nobs2 - 2) sd_diff = np.sqrt(var_diff) nobs = nobs1 + nobs2 bias_correction = 1 - 3 / (4 * nobs - 9) smd = (mean1 - mean2) / sd_diff smd_bc = bias_correction * smd var_smdbc = nobs / nobs1 / nobs2 + smd_bc**2 / 2 / (nobs - 3.94) return smd_bc, var_smdbc def effectsize_2proportions(count1, nobs1, count2, nobs2, statistic="diff", zero_correction=None, zero_kwds=None): """Effects sizes for two sample binomial proportions Parameters ---------- count1, nobs1, count2, nobs2 : array_like data for two samples statistic : {"diff", "odds-ratio", "risk-ratio", "arcsine"} statistic for the comparison of two proportions Effect sizes for "odds-ratio" and "risk-ratio" are in logarithm. zero_correction : {None, float, "tac", "clip"} Some statistics are not finite when zero counts are in the data. The options to remove zeros are: * float : if zero_correction is a single float, then it will be added to all count (cells) if the sample has any zeros. * "tac" : treatment arm continuity correction see Ruecker et al 2009, section 3.2 * "clip" : clip proportions without adding a value to all cells The clip bounds can be set with zero_kwds["clip_bounds"] zero_kwds : dict additional options to handle zero counts "clip_bounds" tuple, default (1e-6, 1 - 1e-6) if zero_correction="clip" other options not yet implemented Returns ------- effect size : array Effect size for each sample. var_es : array Estimate of variance of the effect size Notes ----- Status: API is experimental, Options for zero handling is incomplete. The names for ``statistics`` keyword can be shortened to "rd", "rr", "or" and "as". The statistics are defined as: - risk difference = p1 - p2 - log risk ratio = log(p1 / p2) - log odds_ratio = log(p1 / (1 - p1) * (1 - p2) / p2) - arcsine-sqrt = arcsin(sqrt(p1)) - arcsin(sqrt(p2)) where p1 and p2 are the estimated proportions in sample 1 (treatment) and sample 2 (control). log-odds-ratio and log-risk-ratio can be transformed back to ``or`` and `rr` using `exp` function. See Also -------- statsmodels.stats.contingency_tables """ if zero_correction is None: cc1 = cc2 = 0 elif zero_correction == "tac": # treatment arm continuity correction Ruecker et al 2009, section 3.2 nobs_t = nobs1 + nobs2 cc1 = nobs2 / nobs_t cc2 = nobs1 / nobs_t elif zero_correction == "clip": clip_bounds = zero_kwds.get("clip_bounds", (1e-6, 1 - 1e-6)) cc1 = cc2 = 0 elif zero_correction: # TODO: check is float_like cc1 = cc2 = zero_correction else: msg = "zero_correction not recognized or supported" raise NotImplementedError(msg) zero_mask1 = (count1 == 0) | (count1 == nobs1) zero_mask2 = (count2 == 0) | (count2 == nobs2) zmask = np.logical_or(zero_mask1, zero_mask2) n1 = nobs1 + (cc1 + cc2) * zmask n2 = nobs2 + (cc1 + cc2) * zmask p1 = (count1 + cc1) / (n1) p2 = (count2 + cc2) / (n2) if zero_correction == "clip": p1 = np.clip(p1, *clip_bounds) p2 = np.clip(p2, *clip_bounds) if statistic in ["diff", "rd"]: rd = p1 - p2 rd_var = p1 * (1 - p1) / n1 + p2 * (1 - p2) / n2 eff = rd var_eff = rd_var elif statistic in ["risk-ratio", "rr"]: # rr = p1 / p2 log_rr = np.log(p1) - np.log(p2) log_rr_var = (1 - p1) / p1 / n1 + (1 - p2) / p2 / n2 eff = log_rr var_eff = log_rr_var elif statistic in ["odds-ratio", "or"]: # or_ = p1 / (1 - p1) * (1 - p2) / p2 log_or = np.log(p1) - np.log(1 - p1) - np.log(p2) + np.log(1 - p2) log_or_var = 1 / (p1 * (1 - p1) * n1) + 1 / (p2 * (1 - p2) * n2) eff = log_or var_eff = log_or_var elif statistic in ["arcsine", "arcsin", "as"]: as_ = np.arcsin(np.sqrt(p1)) - np.arcsin(np.sqrt(p2)) as_var = (1 / n1 + 1 / n2) / 4 eff = as_ var_eff = as_var else: msg = 'statistic not recognized, use one of "rd", "rr", "or", "as"' raise NotImplementedError(msg) return eff, var_eff def combine_effects(effect, variance, method_re="iterated", row_names=None, use_t=False, alpha=0.05, **kwds): """combining effect sizes for effect sizes using meta-analysis This currently does not use np.asarray, all computations are possible in pandas. Parameters ---------- effect : array mean of effect size measure for all samples variance : array variance of mean or effect size measure for all samples method_re : {"iterated", "chi2"} method that is use to compute the between random effects variance "iterated" or "pm" uses Paule and Mandel method to iteratively estimate the random effects variance. Options for the iteration can be provided in the ``kwds`` "chi2" or "dl" uses DerSimonian and Laird one-step estimator. row_names : list of strings (optional) names for samples or studies, will be included in results summary and table. alpha : float in (0, 1) significance level, default is 0.05, for the confidence intervals Returns ------- results : CombineResults Contains estimation results and intermediate statistics, and includes a method to return a summary table. Statistics from intermediate calculations might be removed at a later time. Notes ----- Status: Basic functionality is verified, mainly compared to R metafor package. However, API might still change. This computes both fixed effects and random effects estimates. The random effects results depend on the method to estimate the RE variance. Scale estimate In fixed effects models and in random effects models without fully iterated random effects variance, the model will in general not account for all residual variance. Traditional meta-analysis uses a fixed scale equal to 1, that might not produce test statistics and confidence intervals with the correct size. Estimating the scale to account for residual variance often improves the small sample properties of inference and confidence intervals. This adjustment to the standard errors is often referred to as HKSJ method based attributed to Hartung and Knapp and Sidik and Jonkman. However, this is equivalent to estimating the scale in WLS. The results instance includes both, fixed scale and estimated scale versions of standard errors and confidence intervals. References ---------- Borenstein, Michael. 2009. Introduction to Meta-Analysis. Chichester: Wiley. Chen, Ding-Geng, and Karl E. Peace. 2013. Applied Meta-Analysis with R. Chapman & Hall/CRC Biostatistics Series. Boca Raton: CRC Press/Taylor & Francis Group. """ k = len(effect) if row_names is None: row_names = list(range(k)) crit = stats.norm.isf(alpha / 2) # alias for initial version eff = effect var_eff = variance sd_eff = np.sqrt(var_eff) # fixed effects computation weights_fe = 1 / var_eff # no bias correction ? w_total_fe = weights_fe.sum(0) weights_rel_fe = weights_fe / w_total_fe eff_w_fe = weights_rel_fe * eff mean_effect_fe = eff_w_fe.sum() var_eff_w_fe = 1 / w_total_fe sd_eff_w_fe = np.sqrt(var_eff_w_fe) # random effects computation q = (weights_fe * eff**2).sum(0) q -= (weights_fe * eff).sum()**2 / w_total_fe df = k - 1 if method_re.lower() in ["iterated", "pm"]: tau2, _ = _fit_tau_iterative(eff, var_eff, **kwds) elif method_re.lower() in ["chi2", "dl"]: c = w_total_fe - (weights_fe**2).sum() / w_total_fe tau2 = (q - df) / c else: raise ValueError('method_re should be "iterated" or "chi2"') weights_re = 1 / (var_eff + tau2) # no bias_correction ? w_total_re = weights_re.sum(0) weights_rel_re = weights_re / weights_re.sum(0) eff_w_re = weights_rel_re * eff mean_effect_re = eff_w_re.sum() var_eff_w_re = 1 / w_total_re sd_eff_w_re = np.sqrt(var_eff_w_re) # ci_low_eff_re = mean_effect_re - crit * sd_eff_w_re # ci_upp_eff_re = mean_effect_re + crit * sd_eff_w_re scale_hksj_re = (weights_re * (eff - mean_effect_re)**2).sum() / df scale_hksj_fe = (weights_fe * (eff - mean_effect_fe)**2).sum() / df var_hksj_re = (weights_rel_re * (eff - mean_effect_re)**2).sum() / df var_hksj_fe = (weights_rel_fe * (eff - mean_effect_fe)**2).sum() / df res = CombineResults(**locals()) return res def _fit_tau_iterative(eff, var_eff, tau2_start=0, atol=1e-5, maxiter=50): """Paule-Mandel iterative estimate of between random effect variance implementation follows DerSimonian and Kacker 2007 Appendix 8 see also Kacker 2004 Parameters ---------- eff : ndarray effect sizes var_eff : ndarray variance of effect sizes tau2_start : float starting value for iteration atol : float, default: 1e-5 convergence tolerance for absolute value of estimating equation maxiter : int maximum number of iterations Returns ------- tau2 : float estimate of random effects variance tau squared converged : bool True if iteration has converged. """ tau2 = tau2_start k = eff.shape[0] converged = False for i in range(maxiter): w = 1 / (var_eff + tau2) m = w.dot(eff) / w.sum(0) resid_sq = (eff - m)**2 q_w = w.dot(resid_sq) # estimating equation ee = q_w - (k - 1) if ee < 0: tau2 = 0 converged = 0 break if np.allclose(ee, 0, atol=atol): converged = True break # update tau2 delta = ee / (w**2).dot(resid_sq) tau2 += delta return tau2, converged def _fit_tau_mm(eff, var_eff, weights): """one-step method of moment estimate of between random effect variance implementation follows Kacker 2004 and DerSimonian and Kacker 2007 eq. 6 Parameters ---------- eff : ndarray effect sizes var_eff : ndarray variance of effect sizes weights : ndarray weights for estimating overall weighted mean Returns ------- tau2 : float estimate of random effects variance tau squared """ w = weights m = w.dot(eff) / w.sum(0) resid_sq = (eff - m)**2 q_w = w.dot(resid_sq) w_t = w.sum() expect = w.dot(var_eff) - (w**2).dot(var_eff) / w_t denom = w_t - (w**2).sum() / w_t # moment estimate from estimating equation tau2 = (q_w - expect) / denom return tau2 def _fit_tau_iter_mm(eff, var_eff, tau2_start=0, atol=1e-5, maxiter=50): """iterated method of moment estimate of between random effect variance This repeatedly estimates tau, updating weights in each iteration see two-step estimators in DerSimonian and Kacker 2007 Parameters ---------- eff : ndarray effect sizes var_eff : ndarray variance of effect sizes tau2_start : float starting value for iteration atol : float, default: 1e-5 convergence tolerance for change in tau2 estimate between iterations maxiter : int maximum number of iterations Returns ------- tau2 : float estimate of random effects variance tau squared converged : bool True if iteration has converged. """ tau2 = tau2_start converged = False for _ in range(maxiter): w = 1 / (var_eff + tau2) tau2_new = _fit_tau_mm(eff, var_eff, w) tau2_new = max(0, tau2_new) delta = tau2_new - tau2 if np.allclose(delta, 0, atol=atol): converged = True break tau2 = tau2_new return tau2, converged statsmodels-0.12.2/statsmodels/stats/moment_helpers.py000066400000000000000000000207061400612667500232450ustar00rootroot00000000000000"""helper functions conversion between moments contains: * conversion between central and non-central moments, skew, kurtosis and cummulants * cov2corr : convert covariance matrix to correlation matrix Author: Josef Perktold License: BSD-3 """ import numpy as np from scipy.special import comb def _convert_to_multidim(x): if any([isinstance(x, list), isinstance(x, tuple)]): return np.array(x) elif isinstance(x, np.ndarray): return x else: # something strange was passed and the function probably # will fall, maybe insert an exception? return x def _convert_from_multidim(x, totype=list): if len(x.shape) < 2: return totype(x) return x.T def mc2mnc(mc): """convert central to non-central moments, uses recursive formula optionally adjusts first moment to return mean """ x = _convert_to_multidim(mc) def _local_counts(mc): mean = mc[0] mc = [1] + list(mc) # add zero moment = 1 mc[1] = 0 # define central mean as zero for formula mnc = [1, mean] # zero and first raw moments for nn, m in enumerate(mc[2:]): n = nn + 2 mnc.append(0) for k in range(n + 1): mnc[n] += comb(n, k, exact=True) * mc[k] * mean ** (n - k) return mnc[1:] res = np.apply_along_axis(_local_counts, 0, x) # for backward compatibility convert 1-dim output to list/tuple return _convert_from_multidim(res) def mnc2mc(mnc, wmean=True): """convert non-central to central moments, uses recursive formula optionally adjusts first moment to return mean """ X = _convert_to_multidim(mnc) def _local_counts(mnc): mean = mnc[0] mnc = [1] + list(mnc) # add zero moment = 1 mu = [] for n, m in enumerate(mnc): mu.append(0) for k in range(n + 1): sgn_comb = (-1) ** (n - k) * comb(n, k, exact=True) mu[n] += sgn_comb * mnc[k] * mean ** (n - k) if wmean: mu[1] = mean return mu[1:] res = np.apply_along_axis(_local_counts, 0, X) # for backward compatibility convert 1-dim output to list/tuple return _convert_from_multidim(res) def cum2mc(kappa): """convert non-central moments to cumulants recursive formula produces as many cumulants as moments References ---------- Kenneth Lange: Numerical Analysis for Statisticians, page 40 """ X = _convert_to_multidim(kappa) def _local_counts(kappa): mc = [1, 0.0] # _kappa[0]] #insert 0-moment and mean kappa0 = kappa[0] kappa = [1] + list(kappa) for nn, m in enumerate(kappa[2:]): n = nn + 2 mc.append(0) for k in range(n - 1): mc[n] += comb(n - 1, k, exact=True) * kappa[n - k] * mc[k] mc[1] = kappa0 # insert mean as first moments by convention return mc[1:] res = np.apply_along_axis(_local_counts, 0, X) # for backward compatibility convert 1-dim output to list/tuple return _convert_from_multidim(res) def mnc2cum(mnc): """convert non-central moments to cumulants recursive formula produces as many cumulants as moments https://en.wikipedia.org/wiki/Cumulant#Cumulants_and_moments """ X = _convert_to_multidim(mnc) def _local_counts(mnc): mnc = [1] + list(mnc) kappa = [1] for nn, m in enumerate(mnc[1:]): n = nn + 1 kappa.append(m) for k in range(1, n): num_ways = comb(n - 1, k - 1, exact=True) kappa[n] -= num_ways * kappa[k] * mnc[n - k] return kappa[1:] res = np.apply_along_axis(_local_counts, 0, X) # for backward compatibility convert 1-dim output to list/tuple return _convert_from_multidim(res) def mc2cum(mc): """ just chained because I have still the test case """ first_step = mc2mnc(mc) if isinstance(first_step, np.ndarray): first_step = first_step.T return mnc2cum(first_step) # return np.apply_along_axis(lambda x: mnc2cum(mc2mnc(x)), 0, mc) def mvsk2mc(args): """convert mean, variance, skew, kurtosis to central moments""" X = _convert_to_multidim(args) def _local_counts(args): mu, sig2, sk, kur = args cnt = [None] * 4 cnt[0] = mu cnt[1] = sig2 cnt[2] = sk * sig2 ** 1.5 cnt[3] = (kur + 3.0) * sig2 ** 2.0 return tuple(cnt) res = np.apply_along_axis(_local_counts, 0, X) # for backward compatibility convert 1-dim output to list/tuple return _convert_from_multidim(res, tuple) def mvsk2mnc(args): """convert mean, variance, skew, kurtosis to non-central moments""" X = _convert_to_multidim(args) def _local_counts(args): mc, mc2, skew, kurt = args mnc = mc mnc2 = mc2 + mc * mc mc3 = skew * (mc2 ** 1.5) # 3rd central moment mnc3 = mc3 + 3 * mc * mc2 + mc ** 3 # 3rd non-central moment mc4 = (kurt + 3.0) * (mc2 ** 2.0) # 4th central moment mnc4 = mc4 + 4 * mc * mc3 + 6 * mc * mc * mc2 + mc ** 4 return (mnc, mnc2, mnc3, mnc4) res = np.apply_along_axis(_local_counts, 0, X) # for backward compatibility convert 1-dim output to list/tuple return _convert_from_multidim(res, tuple) def mc2mvsk(args): """convert central moments to mean, variance, skew, kurtosis""" X = _convert_to_multidim(args) def _local_counts(args): mc, mc2, mc3, mc4 = args skew = np.divide(mc3, mc2 ** 1.5) kurt = np.divide(mc4, mc2 ** 2.0) - 3.0 return (mc, mc2, skew, kurt) res = np.apply_along_axis(_local_counts, 0, X) # for backward compatibility convert 1-dim output to list/tuple return _convert_from_multidim(res, tuple) def mnc2mvsk(args): """convert central moments to mean, variance, skew, kurtosis """ X = _convert_to_multidim(args) def _local_counts(args): # convert four non-central moments to central moments mnc, mnc2, mnc3, mnc4 = args mc = mnc mc2 = mnc2 - mnc * mnc mc3 = mnc3 - (3 * mc * mc2 + mc ** 3) # 3rd central moment mc4 = mnc4 - (4 * mc * mc3 + 6 * mc * mc * mc2 + mc ** 4) return mc2mvsk((mc, mc2, mc3, mc4)) res = np.apply_along_axis(_local_counts, 0, X) # for backward compatibility convert 1-dim output to list/tuple return _convert_from_multidim(res, tuple) # def mnc2mc(args): # """convert four non-central moments to central moments # """ # mnc, mnc2, mnc3, mnc4 = args # mc = mnc # mc2 = mnc2 - mnc*mnc # mc3 = mnc3 - (3*mc*mc2+mc**3) # 3rd central moment # mc4 = mnc4 - (4*mc*mc3+6*mc*mc*mc2+mc**4) # return mc, mc2, mc # TODO: no return, did it get lost in cut-paste? def cov2corr(cov, return_std=False): """ convert covariance matrix to correlation matrix Parameters ---------- cov : array_like, 2d covariance matrix, see Notes Returns ------- corr : ndarray (subclass) correlation matrix return_std : bool If this is true then the standard deviation is also returned. By default only the correlation matrix is returned. Notes ----- This function does not convert subclasses of ndarrays. This requires that division is defined elementwise. np.ma.array and np.matrix are allowed. """ cov = np.asanyarray(cov) std_ = np.sqrt(np.diag(cov)) corr = cov / np.outer(std_, std_) if return_std: return corr, std_ else: return corr def corr2cov(corr, std): """ convert correlation matrix to covariance matrix given standard deviation Parameters ---------- corr : array_like, 2d correlation matrix, see Notes std : array_like, 1d standard deviation Returns ------- cov : ndarray (subclass) covariance matrix Notes ----- This function does not convert subclasses of ndarrays. This requires that multiplication is defined elementwise. np.ma.array are allowed, but not matrices. """ corr = np.asanyarray(corr) std_ = np.asanyarray(std) cov = corr * np.outer(std_, std_) return cov def se_cov(cov): """ get standard deviation from covariance matrix just a shorthand function np.sqrt(np.diag(cov)) Parameters ---------- cov : array_like, square covariance matrix Returns ------- std : ndarray standard deviation from diagonal of cov """ return np.sqrt(np.diag(cov)) statsmodels-0.12.2/statsmodels/stats/multicomp.py000066400000000000000000000020271400612667500222310ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Mar 30 18:27:25 2012 Author: Josef Perktold """ from statsmodels.sandbox.stats.multicomp import ( # noqa:F401 tukeyhsd, MultiComparison) __all__ = ['tukeyhsd', 'MultiComparison'] def pairwise_tukeyhsd(endog, groups, alpha=0.05): """ Calculate all pairwise comparisons with TukeyHSD confidence intervals Parameters ---------- endog : ndarray, float, 1d response variable groups : ndarray, 1d array with groups, can be string or integers alpha : float significance level for the test Returns ------- results : TukeyHSDResults instance A results class containing relevant data and some post-hoc calculations, including adjusted p-value Notes ----- This is just a wrapper around tukeyhsd method of MultiComparison See Also -------- MultiComparison tukeyhsd statsmodels.sandbox.stats.multicomp.TukeyHSDResults """ return MultiComparison(endog, groups).tukeyhsd(alpha=alpha) statsmodels-0.12.2/statsmodels/stats/multitest.py000066400000000000000000000574661400612667500222730ustar00rootroot00000000000000'''Multiple Testing and P-Value Correction Author: Josef Perktold License: BSD-3 ''' import numpy as np from statsmodels.stats._knockoff import RegressionFDR __all__ = ['fdrcorrection', 'fdrcorrection_twostage', 'local_fdr', 'multipletests', 'NullDistribution', 'RegressionFDR'] # ============================================== # # Part 1: Multiple Tests and P-Value Correction # # ============================================== def _ecdf(x): '''no frills empirical cdf used in fdrcorrection ''' nobs = len(x) return np.arange(1,nobs+1)/float(nobs) multitest_methods_names = {'b': 'Bonferroni', 's': 'Sidak', 'h': 'Holm', 'hs': 'Holm-Sidak', 'sh': 'Simes-Hochberg', 'ho': 'Hommel', 'fdr_bh': 'FDR Benjamini-Hochberg', 'fdr_by': 'FDR Benjamini-Yekutieli', 'fdr_tsbh': 'FDR 2-stage Benjamini-Hochberg', 'fdr_tsbky': 'FDR 2-stage Benjamini-Krieger-Yekutieli', 'fdr_gbs': 'FDR adaptive Gavrilov-Benjamini-Sarkar' } _alias_list = [['b', 'bonf', 'bonferroni'], ['s', 'sidak'], ['h', 'holm'], ['hs', 'holm-sidak'], ['sh', 'simes-hochberg'], ['ho', 'hommel'], ['fdr_bh', 'fdr_i', 'fdr_p', 'fdri', 'fdrp'], ['fdr_by', 'fdr_n', 'fdr_c', 'fdrn', 'fdrcorr'], ['fdr_tsbh', 'fdr_2sbh'], ['fdr_tsbky', 'fdr_2sbky', 'fdr_twostage'], ['fdr_gbs'] ] multitest_alias = {} for m in _alias_list: multitest_alias[m[0]] = m[0] for a in m[1:]: multitest_alias[a] = m[0] def multipletests(pvals, alpha=0.05, method='hs', is_sorted=False, returnsorted=False): """ Test results and p-value correction for multiple tests Parameters ---------- pvals : array_like, 1-d uncorrected p-values. Must be 1-dimensional. alpha : float FWER, family-wise error rate, e.g. 0.1 method : str Method used for testing and adjustment of pvalues. Can be either the full name or initial letters. Available methods are: - `bonferroni` : one-step correction - `sidak` : one-step correction - `holm-sidak` : step down method using Sidak adjustments - `holm` : step-down method using Bonferroni adjustments - `simes-hochberg` : step-up method (independent) - `hommel` : closed method based on Simes tests (non-negative) - `fdr_bh` : Benjamini/Hochberg (non-negative) - `fdr_by` : Benjamini/Yekutieli (negative) - `fdr_tsbh` : two stage fdr correction (non-negative) - `fdr_tsbky` : two stage fdr correction (non-negative) is_sorted : bool If False (default), the p_values will be sorted, but the corrected pvalues are in the original order. If True, then it assumed that the pvalues are already sorted in ascending order. returnsorted : bool not tested, return sorted p-values instead of original sequence Returns ------- reject : ndarray, boolean true for hypothesis that can be rejected for given alpha pvals_corrected : ndarray p-values corrected for multiple tests alphacSidak : float corrected alpha for Sidak method alphacBonf : float corrected alpha for Bonferroni method Notes ----- There may be API changes for this function in the future. Except for 'fdr_twostage', the p-value correction is independent of the alpha specified as argument. In these cases the corrected p-values can also be compared with a different alpha. In the case of 'fdr_twostage', the corrected p-values are specific to the given alpha, see ``fdrcorrection_twostage``. The 'fdr_gbs' procedure is not verified against another package, p-values are derived from scratch and are not derived in the reference. In Monte Carlo experiments the method worked correctly and maintained the false discovery rate. All procedures that are included, control FWER or FDR in the independent case, and most are robust in the positively correlated case. `fdr_gbs`: high power, fdr control for independent case and only small violation in positively correlated case **Timing**: Most of the time with large arrays is spent in `argsort`. When we want to calculate the p-value for several methods, then it is more efficient to presort the pvalues, and put the results back into the original order outside of the function. Method='hommel' is very slow for large arrays, since it requires the evaluation of n partitions, where n is the number of p-values. """ import gc pvals = np.asarray(pvals) alphaf = alpha # Notation ? if not is_sorted: sortind = np.argsort(pvals) pvals = np.take(pvals, sortind) ntests = len(pvals) alphacSidak = 1 - np.power((1. - alphaf), 1./ntests) alphacBonf = alphaf / float(ntests) if method.lower() in ['b', 'bonf', 'bonferroni']: reject = pvals <= alphacBonf pvals_corrected = pvals * float(ntests) elif method.lower() in ['s', 'sidak']: reject = pvals <= alphacSidak pvals_corrected = 1 - np.power((1. - pvals), ntests) elif method.lower() in ['hs', 'holm-sidak']: alphacSidak_all = 1 - np.power((1. - alphaf), 1./np.arange(ntests, 0, -1)) notreject = pvals > alphacSidak_all del alphacSidak_all nr_index = np.nonzero(notreject)[0] if nr_index.size == 0: # nonreject is empty, all rejected notrejectmin = len(pvals) else: notrejectmin = np.min(nr_index) notreject[notrejectmin:] = True reject = ~notreject del notreject pvals_corrected_raw = 1 - np.power((1. - pvals), np.arange(ntests, 0, -1)) pvals_corrected = np.maximum.accumulate(pvals_corrected_raw) del pvals_corrected_raw elif method.lower() in ['h', 'holm']: notreject = pvals > alphaf / np.arange(ntests, 0, -1) nr_index = np.nonzero(notreject)[0] if nr_index.size == 0: # nonreject is empty, all rejected notrejectmin = len(pvals) else: notrejectmin = np.min(nr_index) notreject[notrejectmin:] = True reject = ~notreject pvals_corrected_raw = pvals * np.arange(ntests, 0, -1) pvals_corrected = np.maximum.accumulate(pvals_corrected_raw) del pvals_corrected_raw gc.collect() elif method.lower() in ['sh', 'simes-hochberg']: alphash = alphaf / np.arange(ntests, 0, -1) reject = pvals <= alphash rejind = np.nonzero(reject) if rejind[0].size > 0: rejectmax = np.max(np.nonzero(reject)) reject[:rejectmax] = True pvals_corrected_raw = np.arange(ntests, 0, -1) * pvals pvals_corrected = np.minimum.accumulate(pvals_corrected_raw[::-1])[::-1] del pvals_corrected_raw elif method.lower() in ['ho', 'hommel']: # we need a copy because we overwrite it in a loop a = pvals.copy() for m in range(ntests, 1, -1): cim = np.min(m * pvals[-m:] / np.arange(1,m+1.)) a[-m:] = np.maximum(a[-m:], cim) a[:-m] = np.maximum(a[:-m], np.minimum(m * pvals[:-m], cim)) pvals_corrected = a reject = a <= alphaf elif method.lower() in ['fdr_bh', 'fdr_i', 'fdr_p', 'fdri', 'fdrp']: # delegate, call with sorted pvals reject, pvals_corrected = fdrcorrection(pvals, alpha=alpha, method='indep', is_sorted=True) elif method.lower() in ['fdr_by', 'fdr_n', 'fdr_c', 'fdrn', 'fdrcorr']: # delegate, call with sorted pvals reject, pvals_corrected = fdrcorrection(pvals, alpha=alpha, method='n', is_sorted=True) elif method.lower() in ['fdr_tsbky', 'fdr_2sbky', 'fdr_twostage']: # delegate, call with sorted pvals reject, pvals_corrected = fdrcorrection_twostage(pvals, alpha=alpha, method='bky', is_sorted=True)[:2] elif method.lower() in ['fdr_tsbh', 'fdr_2sbh']: # delegate, call with sorted pvals reject, pvals_corrected = fdrcorrection_twostage(pvals, alpha=alpha, method='bh', is_sorted=True)[:2] elif method.lower() in ['fdr_gbs']: #adaptive stepdown in Gavrilov, Benjamini, Sarkar, Annals of Statistics 2009 ## notreject = pvals > alphaf / np.arange(ntests, 0, -1) #alphacSidak ## notrejectmin = np.min(np.nonzero(notreject)) ## notreject[notrejectmin:] = True ## reject = ~notreject ii = np.arange(1, ntests + 1) q = (ntests + 1. - ii)/ii * pvals / (1. - pvals) pvals_corrected_raw = np.maximum.accumulate(q) #up requirementd pvals_corrected = np.minimum.accumulate(pvals_corrected_raw[::-1])[::-1] del pvals_corrected_raw reject = pvals_corrected <= alpha else: raise ValueError('method not recognized') if pvals_corrected is not None: #not necessary anymore pvals_corrected[pvals_corrected>1] = 1 if is_sorted or returnsorted: return reject, pvals_corrected, alphacSidak, alphacBonf else: pvals_corrected_ = np.empty_like(pvals_corrected) pvals_corrected_[sortind] = pvals_corrected del pvals_corrected reject_ = np.empty_like(reject) reject_[sortind] = reject return reject_, pvals_corrected_, alphacSidak, alphacBonf def fdrcorrection(pvals, alpha=0.05, method='indep', is_sorted=False): '''pvalue correction for false discovery rate This covers Benjamini/Hochberg for independent or positively correlated and Benjamini/Yekutieli for general or negatively correlated tests. Both are available in the function multipletests, as method=`fdr_bh`, resp. `fdr_by`. Parameters ---------- pvals : array_like set of p-values of the individual tests. alpha : float error rate method : {'indep', 'negcorr'} is_sorted : bool If False (default), the p_values will be sorted, but the corrected pvalues are in the original order. If True, then it assumed that the pvalues are already sorted in ascending order. Returns ------- rejected : ndarray, bool True if a hypothesis is rejected, False if not pvalue-corrected : ndarray pvalues adjusted for multiple hypothesis testing to limit FDR Notes ----- If there is prior information on the fraction of true hypothesis, then alpha should be set to alpha * m/m_0 where m is the number of tests, given by the p-values, and m_0 is an estimate of the true hypothesis. (see Benjamini, Krieger and Yekuteli) The two-step method of Benjamini, Krieger and Yekutiel that estimates the number of false hypotheses will be available (soon). Method names can be abbreviated to first letter, 'i' or 'p' for fdr_bh and 'n' for fdr_by. ''' pvals = np.asarray(pvals) if not is_sorted: pvals_sortind = np.argsort(pvals) pvals_sorted = np.take(pvals, pvals_sortind) else: pvals_sorted = pvals # alias if method in ['i', 'indep', 'p', 'poscorr']: ecdffactor = _ecdf(pvals_sorted) elif method in ['n', 'negcorr']: cm = np.sum(1./np.arange(1, len(pvals_sorted)+1)) #corrected this ecdffactor = _ecdf(pvals_sorted) / cm ## elif method in ['n', 'negcorr']: ## cm = np.sum(np.arange(len(pvals))) ## ecdffactor = ecdf(pvals_sorted)/cm else: raise ValueError('only indep and negcorr implemented') reject = pvals_sorted <= ecdffactor*alpha if reject.any(): rejectmax = max(np.nonzero(reject)[0]) reject[:rejectmax] = True pvals_corrected_raw = pvals_sorted / ecdffactor pvals_corrected = np.minimum.accumulate(pvals_corrected_raw[::-1])[::-1] del pvals_corrected_raw pvals_corrected[pvals_corrected>1] = 1 if not is_sorted: pvals_corrected_ = np.empty_like(pvals_corrected) pvals_corrected_[pvals_sortind] = pvals_corrected del pvals_corrected reject_ = np.empty_like(reject) reject_[pvals_sortind] = reject return reject_, pvals_corrected_ else: return reject, pvals_corrected def fdrcorrection_twostage(pvals, alpha=0.05, method='bky', iter=False, is_sorted=False): '''(iterated) two stage linear step-up procedure with estimation of number of true hypotheses Benjamini, Krieger and Yekuteli, procedure in Definition 6 Parameters ---------- pvals : array_like set of p-values of the individual tests. alpha : float error rate method : {'bky', 'bh') see Notes for details * 'bky' - implements the procedure in Definition 6 of Benjamini, Krieger and Yekuteli 2006 * 'bh' - the two stage method of Benjamini and Hochberg iter : bool Returns ------- rejected : ndarray, bool True if a hypothesis is rejected, False if not pvalue-corrected : ndarray pvalues adjusted for multiple hypotheses testing to limit FDR m0 : int ntest - rej, estimated number of true hypotheses alpha_stages : list of floats A list of alphas that have been used at each stage Notes ----- The returned corrected p-values are specific to the given alpha, they cannot be used for a different alpha. The returned corrected p-values are from the last stage of the fdr_bh linear step-up procedure (fdrcorrection0 with method='indep') corrected for the estimated fraction of true hypotheses. This means that the rejection decision can be obtained with ``pval_corrected <= alpha``, where ``alpha`` is the original significance level. (Note: This has changed from earlier versions (<0.5.0) of statsmodels.) BKY described several other multi-stage methods, which would be easy to implement. However, in their simulation the simple two-stage method (with iter=False) was the most robust to the presence of positive correlation TODO: What should be returned? ''' pvals = np.asarray(pvals) if not is_sorted: pvals_sortind = np.argsort(pvals) pvals = np.take(pvals, pvals_sortind) ntests = len(pvals) if method == 'bky': fact = (1.+alpha) alpha_prime = alpha / fact elif method == 'bh': fact = 1. alpha_prime = alpha else: raise ValueError("only 'bky' and 'bh' are available as method") alpha_stages = [alpha_prime] rej, pvalscorr = fdrcorrection(pvals, alpha=alpha_prime, method='indep', is_sorted=True) r1 = rej.sum() if (r1 == 0) or (r1 == ntests): return rej, pvalscorr * fact, ntests - r1, alpha_stages ri_old = r1 while True: ntests0 = 1.0 * ntests - ri_old alpha_star = alpha_prime * ntests / ntests0 alpha_stages.append(alpha_star) #print ntests0, alpha_star rej, pvalscorr = fdrcorrection(pvals, alpha=alpha_star, method='indep', is_sorted=True) ri = rej.sum() if (not iter) or ri == ri_old: break elif ri < ri_old: # prevent cycles and endless loops raise RuntimeError(" oops - should not be here") ri_old = ri # make adjustment to pvalscorr to reflect estimated number of Non-Null cases # decision is then pvalscorr < alpha (or <=) pvalscorr *= ntests0 * 1.0 / ntests if method == 'bky': pvalscorr *= (1. + alpha) if not is_sorted: pvalscorr_ = np.empty_like(pvalscorr) pvalscorr_[pvals_sortind] = pvalscorr del pvalscorr reject = np.empty_like(rej) reject[pvals_sortind] = rej return reject, pvalscorr_, ntests - ri, alpha_stages else: return rej, pvalscorr, ntests - ri, alpha_stages def local_fdr(zscores, null_proportion=1.0, null_pdf=None, deg=7, nbins=30, alpha=0): """ Calculate local FDR values for a list of Z-scores. Parameters ---------- zscores : array_like A vector of Z-scores null_proportion : float The assumed proportion of true null hypotheses null_pdf : function mapping reals to positive reals The density of null Z-scores; if None, use standard normal deg : int The maximum exponent in the polynomial expansion of the density of non-null Z-scores nbins : int The number of bins for estimating the marginal density of Z-scores. alpha : float Use Poisson ridge regression with parameter alpha to estimate the density of non-null Z-scores. Returns ------- fdr : array_like A vector of FDR values References ---------- B Efron (2008). Microarrays, Empirical Bayes, and the Two-Groups Model. Statistical Science 23:1, 1-22. Examples -------- Basic use (the null Z-scores are taken to be standard normal): >>> from statsmodels.stats.multitest import local_fdr >>> import numpy as np >>> zscores = np.random.randn(30) >>> fdr = local_fdr(zscores) Use a Gaussian null distribution estimated from the data: >>> null = EmpiricalNull(zscores) >>> fdr = local_fdr(zscores, null_pdf=null.pdf) """ from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod.generalized_linear_model import families from statsmodels.regression.linear_model import OLS # Bins for Poisson modeling of the marginal Z-score density minz = min(zscores) maxz = max(zscores) bins = np.linspace(minz, maxz, nbins) # Bin counts zhist = np.histogram(zscores, bins)[0] # Bin centers zbins = (bins[:-1] + bins[1:]) / 2 # The design matrix at bin centers dmat = np.vander(zbins, deg + 1) # Rescale the design matrix sd = dmat.std(0) ii = sd >1e-8 dmat[:, ii] /= sd[ii] start = OLS(np.log(1 + zhist), dmat).fit().params # Poisson regression if alpha > 0: md = GLM(zhist, dmat, family=families.Poisson()).fit_regularized(L1_wt=0, alpha=alpha, start_params=start) else: md = GLM(zhist, dmat, family=families.Poisson()).fit(start_params=start) # The design matrix for all Z-scores dmat_full = np.vander(zscores, deg + 1) dmat_full[:, ii] /= sd[ii] # The height of the estimated marginal density of Z-scores, # evaluated at every observed Z-score. fz = md.predict(dmat_full) / (len(zscores) * (bins[1] - bins[0])) # The null density. if null_pdf is None: f0 = np.exp(-0.5 * zscores**2) / np.sqrt(2 * np.pi) else: f0 = null_pdf(zscores) # The local FDR values fdr = null_proportion * f0 / fz fdr = np.clip(fdr, 0, 1) return fdr class NullDistribution(object): """ Estimate a Gaussian distribution for the null Z-scores. The observed Z-scores consist of both null and non-null values. The fitted distribution of null Z-scores is Gaussian, but may have non-zero mean and/or non-unit scale. Parameters ---------- zscores : array_like The observed Z-scores. null_lb : float Z-scores between `null_lb` and `null_ub` are all considered to be true null hypotheses. null_ub : float See `null_lb`. estimate_mean : bool If True, estimate the mean of the distribution. If False, the mean is fixed at zero. estimate_scale : bool If True, estimate the scale of the distribution. If False, the scale parameter is fixed at 1. estimate_null_proportion : bool If True, estimate the proportion of true null hypotheses (i.e. the proportion of z-scores with expected value zero). If False, this parameter is fixed at 1. Attributes ---------- mean : float The estimated mean of the empirical null distribution sd : float The estimated standard deviation of the empirical null distribution null_proportion : float The estimated proportion of true null hypotheses among all hypotheses References ---------- B Efron (2008). Microarrays, Empirical Bayes, and the Two-Groups Model. Statistical Science 23:1, 1-22. Notes ----- See also: http://nipy.org/nipy/labs/enn.html#nipy.algorithms.statistics.empirical_pvalue.NormalEmpiricalNull.fdr """ def __init__(self, zscores, null_lb=-1, null_ub=1, estimate_mean=True, estimate_scale=True, estimate_null_proportion=False): # Extract the null z-scores ii = np.flatnonzero((zscores >= null_lb) & (zscores <= null_ub)) if len(ii) == 0: raise RuntimeError("No Z-scores fall between null_lb and null_ub") zscores0 = zscores[ii] # Number of Z-scores, and null Z-scores n_zs, n_zs0 = len(zscores), len(zscores0) # Unpack and transform the parameters to the natural scale, hold # parameters fixed as specified. def xform(params): mean = 0. sd = 1. prob = 1. ii = 0 if estimate_mean: mean = params[ii] ii += 1 if estimate_scale: sd = np.exp(params[ii]) ii += 1 if estimate_null_proportion: prob = 1 / (1 + np.exp(-params[ii])) return mean, sd, prob from scipy.stats.distributions import norm def fun(params): """ Negative log-likelihood of z-scores. The function has three arguments, packed into a vector: mean : location parameter logscale : log of the scale parameter logitprop : logit of the proportion of true nulls The implementation follows section 4 from Efron 2008. """ d, s, p = xform(params) # Mass within the central region central_mass = (norm.cdf((null_ub - d) / s) - norm.cdf((null_lb - d) / s)) # Probability that a Z-score is null and is in the central region cp = p * central_mass # Binomial term rval = n_zs0 * np.log(cp) + (n_zs - n_zs0) * np.log(1 - cp) # Truncated Gaussian term for null Z-scores zv = (zscores0 - d) / s rval += np.sum(-zv**2 / 2) - n_zs0 * np.log(s) rval -= n_zs0 * np.log(central_mass) return -rval # Estimate the parameters from scipy.optimize import minimize # starting values are mean = 0, scale = 1, p0 ~ 1 mz = minimize(fun, np.r_[0., 0, 3], method="Nelder-Mead") mean, sd, prob = xform(mz['x']) self.mean = mean self.sd = sd self.null_proportion = prob # The fitted null density function def pdf(self, zscores): """ Evaluates the fitted empirical null Z-score density. Parameters ---------- zscores : scalar or array_like The point or points at which the density is to be evaluated. Returns ------- The empirical null Z-score density evaluated at the given points. """ zval = (zscores - self.mean) / self.sd return np.exp(-0.5*zval**2 - np.log(self.sd) - 0.5*np.log(2*np.pi)) statsmodels-0.12.2/statsmodels/stats/multivariate.py000066400000000000000000000454631400612667500227410ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Nov 5 14:48:19 2017 Author: Josef Perktold License: BSD-3 """ import numpy as np from scipy import stats from statsmodels.stats.moment_helpers import cov2corr from statsmodels.stats.base import HolderTuple from statsmodels.tools.validation import array_like # shortcut function def _logdet(x): return np.linalg.slogdet(x)[1] def test_mvmean(data, mean_null=0, return_results=True): """Hotellings test for multivariate mean in one sample Parameters ---------- data : array_like data with observations in rows and variables in columns mean_null : array_like mean of the multivariate data under the null hypothesis return_results : bool If true, then a results instance is returned. If False, then only the test statistic and pvalue are returned. Returns ------- results : instance of a results class with attributes statistic, pvalue, t2 and df (statistic, pvalue) : tuple If return_results is false, then only the test statistic and the pvalue are returned. """ x = np.asarray(data) nobs, k_vars = x.shape mean = x.mean(0) cov = np.cov(x, rowvar=False, ddof=1) diff = mean - mean_null t2 = nobs * diff.dot(np.linalg.solve(cov, diff)) factor = (nobs - 1) * k_vars / (nobs - k_vars) statistic = t2 / factor df = (k_vars, nobs - k_vars) pvalue = stats.f.sf(statistic, df[0], df[1]) if return_results: res = HolderTuple(statistic=statistic, pvalue=pvalue, df=df, t2=t2, distr="F") return res else: return statistic, pvalue def test_mvmean_2indep(data1, data2): """Hotellings test for multivariate mean in two independent samples The null hypothesis is that both samples have the same mean. The alternative hypothesis is that means differ. Parameters ---------- data1 : array_like first sample data with observations in rows and variables in columns data2 : array_like second sample data with observations in rows and variables in columns Returns ------- results : instance of a results class with attributes statistic, pvalue, t2 and df """ x1 = array_like(data1, "x1", ndim=2) x2 = array_like(data2, "x2", ndim=2) nobs1, k_vars = x1.shape nobs2, k_vars2 = x2.shape if k_vars2 != k_vars: msg = "both samples need to have the same number of columns" raise ValueError(msg) mean1 = x1.mean(0) mean2 = x2.mean(0) cov1 = np.cov(x1, rowvar=False, ddof=1) cov2 = np.cov(x2, rowvar=False, ddof=1) nobs_t = nobs1 + nobs2 combined_cov = ((nobs1 - 1) * cov1 + (nobs2 - 1) * cov2) / (nobs_t - 2) diff = mean1 - mean2 t2 = (nobs1 * nobs2) / nobs_t * diff @ np.linalg.solve(combined_cov, diff) factor = ((nobs_t - 2) * k_vars) / (nobs_t - k_vars - 1) statistic = t2 / factor df = (k_vars, nobs_t - 1 - k_vars) pvalue = stats.f.sf(statistic, df[0], df[1]) return HolderTuple(statistic=statistic, pvalue=pvalue, df=df, t2=t2, distr="F") def confint_mvmean(data, lin_transf=None, alpha=0.5, simult=False): """Confidence interval for linear transformation of a multivariate mean Either pointwise or simultaneous confidence intervals are returned. Parameters ---------- data : array_like data with observations in rows and variables in columns lin_transf : array_like or None The linear transformation or contrast matrix for transforming the vector of means. If this is None, then the identity matrix is used which specifies the means themselves. alpha : float in (0, 1) confidence level for the confidence interval, commonly used is alpha=0.05. simult : bool If ``simult`` is False (default), then the pointwise confidence interval is returned. Otherwise, a simultaneous confidence interval is returned. Warning: additional simultaneous confidence intervals might be added and the default for those might change. Returns ------- low : ndarray lower confidence bound on the linear transformed upp : ndarray upper confidence bound on the linear transformed values : ndarray mean or their linear transformation, center of the confidence region Notes ----- Pointwise confidence interval is based on Johnson and Wichern equation (5-21) page 224. Simultaneous confidence interval is based on Johnson and Wichern Result 5.3 page 225. This looks like Sheffe simultaneous confidence intervals. Bonferroni corrected simultaneous confidence interval might be added in future References ---------- Johnson, Richard A., and Dean W. Wichern. 2007. Applied Multivariate Statistical Analysis. 6th ed. Upper Saddle River, N.J: Pearson Prentice Hall. """ x = np.asarray(data) nobs, k_vars = x.shape if lin_transf is None: lin_transf = np.eye(k_vars) mean = x.mean(0) cov = np.cov(x, rowvar=False, ddof=0) ci = confint_mvmean_fromstats(mean, cov, nobs, lin_transf=lin_transf, alpha=alpha, simult=simult) return ci def confint_mvmean_fromstats(mean, cov, nobs, lin_transf=None, alpha=0.05, simult=False): """Confidence interval for linear transformation of a multivariate mean Either pointwise or simultaneous confidence intervals are returned. Data is provided in the form of summary statistics, mean, cov, nobs. Parameters ---------- mean : ndarray cov : ndarray nobs : int lin_transf : array_like or None The linear transformation or contrast matrix for transforming the vector of means. If this is None, then the identity matrix is used which specifies the means themselves. alpha : float in (0, 1) confidence level for the confidence interval, commonly used is alpha=0.05. simult : bool If simult is False (default), then pointwise confidence interval is returned. Otherwise, a simultaneous confidence interval is returned. Warning: additional simultaneous confidence intervals might be added and the default for those might change. Notes ----- Pointwise confidence interval is based on Johnson and Wichern equation (5-21) page 224. Simultaneous confidence interval is based on Johnson and Wichern Result 5.3 page 225. This looks like Sheffe simultaneous confidence intervals. Bonferroni corrected simultaneous confidence interval might be added in future References ---------- Johnson, Richard A., and Dean W. Wichern. 2007. Applied Multivariate Statistical Analysis. 6th ed. Upper Saddle River, N.J: Pearson Prentice Hall. """ mean = np.asarray(mean) cov = np.asarray(cov) c = np.atleast_2d(lin_transf) k_vars = len(mean) if simult is False: values = c.dot(mean) quad_form = (c * cov.dot(c.T).T).sum(1) df = nobs - 1 t_critval = stats.t.isf(alpha / 2, df) ci_diff = np.sqrt(quad_form / df) * t_critval low = values - ci_diff upp = values + ci_diff else: values = c.dot(mean) quad_form = (c * cov.dot(c.T).T).sum(1) factor = (nobs - 1) * k_vars / (nobs - k_vars) / nobs df = (k_vars, nobs - k_vars) f_critval = stats.f.isf(alpha, df[0], df[1]) ci_diff = np.sqrt(factor * quad_form * f_critval) low = values - ci_diff upp = values + ci_diff return low, upp, values # , (f_critval, factor, quad_form, df) """ Created on Tue Nov 7 13:22:44 2017 Author: Josef Perktold References ---------- Stata manual for mvtest covariances Rencher and Christensen 2012 Bartlett 1954 Stata refers to Rencher and Christensen for the formulas. Those correspond to the formula collection in Bartlett 1954 for several of them. """ # pylint: disable=W0105 def test_cov(cov, nobs, cov_null): """One sample hypothesis test for covariance equal to null covariance The Null hypothesis is that cov = cov_null, against the alternative that it is not equal to cov_null Parameters ---------- cov : array_like Covariance matrix of the data, estimated with denominator ``(N - 1)``, i.e. `ddof=1`. nobs : int number of observations used in the estimation of the covariance cov_null : nd_array covariance under the null hypothesis Returns ------- res : instance of HolderTuple results with ``statistic, pvalue`` and other attributes like ``df`` References ---------- Bartlett, M. S. 1954. “A Note on the Multiplying Factors for Various Χ2 Approximations.†Journal of the Royal Statistical Society. Series B (Methodological) 16 (2): 296–98. Rencher, Alvin C., and William F. Christensen. 2012. Methods of Multivariate Analysis: Rencher/Methods. Wiley Series in Probability and Statistics. Hoboken, NJ, USA: John Wiley & Sons, Inc. https://doi.org/10.1002/9781118391686. StataCorp, L. P. Stata Multivariate Statistics: Reference Manual. Stata Press Publication. """ # using Stata formulas where cov_sample use nobs in denominator # Bartlett 1954 has fewer terms S = np.asarray(cov) * (nobs - 1) / nobs S0 = np.asarray(cov_null) k = cov.shape[0] n = nobs fact = nobs - 1. fact *= 1 - (2 * k + 1 - 2 / (k + 1)) / (6 * (n - 1) - 1) fact2 = _logdet(S0) - _logdet(n / (n - 1) * S) fact2 += np.trace(n / (n - 1) * np.linalg.solve(S0, S)) - k statistic = fact * fact2 df = k * (k + 1) / 2 pvalue = stats.chi2.sf(statistic, df) return HolderTuple(statistic=statistic, pvalue=pvalue, df=df, distr="chi2", null="equal value", cov_null=cov_null ) def test_cov_spherical(cov, nobs): r"""One sample hypothesis test that covariance matrix is spherical The Null and alternative hypotheses are .. math:: H0 &: \Sigma = \sigma I \\ H1 &: \Sigma \neq \sigma I where :math:`\sigma_i` is the common variance with unspecified value. Parameters ---------- cov : array_like Covariance matrix of the data, estimated with denominator ``(N - 1)``, i.e. `ddof=1`. nobs : int number of observations used in the estimation of the covariance Returns ------- res : instance of HolderTuple results with ``statistic, pvalue`` and other attributes like ``df`` References ---------- Bartlett, M. S. 1954. “A Note on the Multiplying Factors for Various Χ2 Approximations.†Journal of the Royal Statistical Society. Series B (Methodological) 16 (2): 296–98. Rencher, Alvin C., and William F. Christensen. 2012. Methods of Multivariate Analysis: Rencher/Methods. Wiley Series in Probability and Statistics. Hoboken, NJ, USA: John Wiley & Sons, Inc. https://doi.org/10.1002/9781118391686. StataCorp, L. P. Stata Multivariate Statistics: Reference Manual. Stata Press Publication. """ # unchanged Stata formula, but denom is cov cancels, AFAICS # Bartlett 1954 correction factor in IIIc cov = np.asarray(cov) k = cov.shape[0] statistic = nobs - 1 - (2 * k**2 + k + 2) / (6 * k) statistic *= k * np.log(np.trace(cov)) - _logdet(cov) - k * np.log(k) df = k * (k + 1) / 2 - 1 pvalue = stats.chi2.sf(statistic, df) return HolderTuple(statistic=statistic, pvalue=pvalue, df=df, distr="chi2", null="spherical" ) def test_cov_diagonal(cov, nobs): r"""One sample hypothesis test that covariance matrix is diagonal matrix. The Null and alternative hypotheses are .. math:: H0 &: \Sigma = diag(\sigma_i) \\ H1 &: \Sigma \neq diag(\sigma_i) where :math:`\sigma_i` are the variances with unspecified values. Parameters ---------- cov : array_like Covariance matrix of the data, estimated with denominator ``(N - 1)``, i.e. `ddof=1`. nobs : int number of observations used in the estimation of the covariance Returns ------- res : instance of HolderTuple results with ``statistic, pvalue`` and other attributes like ``df`` References ---------- Rencher, Alvin C., and William F. Christensen. 2012. Methods of Multivariate Analysis: Rencher/Methods. Wiley Series in Probability and Statistics. Hoboken, NJ, USA: John Wiley & Sons, Inc. https://doi.org/10.1002/9781118391686. StataCorp, L. P. Stata Multivariate Statistics: Reference Manual. Stata Press Publication. """ cov = np.asarray(cov) k = cov.shape[0] R = cov2corr(cov) statistic = -(nobs - 1 - (2 * k + 5) / 6) * _logdet(R) df = k * (k - 1) / 2 pvalue = stats.chi2.sf(statistic, df) return HolderTuple(statistic=statistic, pvalue=pvalue, df=df, distr="chi2", null="diagonal" ) def _get_blocks(mat, block_len): """get diagonal blocks from matrix """ k = len(mat) idx = np.cumsum(block_len) if idx[-1] == k: idx = idx[:-1] elif idx[-1] > k: raise ValueError("sum of block_len larger than shape of mat") else: # allow one missing block that is the remainder pass idx_blocks = np.split(np.arange(k), idx) blocks = [] for ii in idx_blocks: blocks.append(mat[ii[:, None], ii]) return blocks, idx_blocks def test_cov_blockdiagonal(cov, nobs, block_len): r"""One sample hypothesis test that covariance is block diagonal. The Null and alternative hypotheses are .. math:: H0 &: \Sigma = diag(\Sigma_i) \\ H1 &: \Sigma \neq diag(\Sigma_i) where :math:`\Sigma_i` are covariance blocks with unspecified values. Parameters ---------- cov : array_like Covariance matrix of the data, estimated with denominator ``(N - 1)``, i.e. `ddof=1`. nobs : int number of observations used in the estimation of the covariance block_len : list list of length of each square block Returns ------- res : instance of HolderTuple results with ``statistic, pvalue`` and other attributes like ``df`` References ---------- Rencher, Alvin C., and William F. Christensen. 2012. Methods of Multivariate Analysis: Rencher/Methods. Wiley Series in Probability and Statistics. Hoboken, NJ, USA: John Wiley & Sons, Inc. https://doi.org/10.1002/9781118391686. StataCorp, L. P. Stata Multivariate Statistics: Reference Manual. Stata Press Publication. """ cov = np.asarray(cov) cov_blocks = _get_blocks(cov, block_len)[0] k = cov.shape[0] k_blocks = [c.shape[0] for c in cov_blocks] if k != sum(k_blocks): msg = "sample covariances and blocks do not have matching shape" raise ValueError(msg) logdet_blocks = sum(_logdet(c) for c in cov_blocks) a2 = k**2 - sum(ki**2 for ki in k_blocks) a3 = k**3 - sum(ki**3 for ki in k_blocks) statistic = (nobs - 1 - (2 * a3 + 3 * a2) / (6. * a2)) statistic *= logdet_blocks - _logdet(cov) df = a2 / 2 pvalue = stats.chi2.sf(statistic, df) return HolderTuple(statistic=statistic, pvalue=pvalue, df=df, distr="chi2", null="block-diagonal" ) def test_cov_oneway(cov_list, nobs_list): r"""Multiple sample hypothesis test that covariance matrices are equal. This is commonly known as Box-M test. The Null and alternative hypotheses are .. math:: H0 &: \Sigma_i = \Sigma_j \text{ for all i and j} \\ H1 &: \Sigma_i \neq \Sigma_j \text{ for at least one i and j} where :math:`\Sigma_i` is the covariance of sample `i`. Parameters ---------- cov_list : list of array_like Covariance matrices of the sample, estimated with denominator ``(N - 1)``, i.e. `ddof=1`. nobs_list : list List of the number of observations used in the estimation of the covariance for each sample. Returns ------- res : instance of HolderTuple Results contains test statistic and pvalues for both chisquare and F distribution based tests, identified by the name ending "_chi2" and "_f". Attributes ``statistic, pvalue`` refer to the F-test version. Notes ----- approximations to distribution of test statistic is by Box References ---------- Rencher, Alvin C., and William F. Christensen. 2012. Methods of Multivariate Analysis: Rencher/Methods. Wiley Series in Probability and Statistics. Hoboken, NJ, USA: John Wiley & Sons, Inc. https://doi.org/10.1002/9781118391686. StataCorp, L. P. Stata Multivariate Statistics: Reference Manual. Stata Press Publication. """ # Note stata uses nobs in cov, this uses nobs - 1 cov_list = list(map(np.asarray, cov_list)) m = len(cov_list) nobs = sum(nobs_list) # total number of observations k = cov_list[0].shape[0] cov_pooled = sum((n - 1) * c for (n, c) in zip(nobs_list, cov_list)) cov_pooled /= (nobs - m) stat0 = (nobs - m) * _logdet(cov_pooled) stat0 -= sum((n - 1) * _logdet(c) for (n, c) in zip(nobs_list, cov_list)) # Box's chi2 c1 = sum(1 / (n - 1) for n in nobs_list) - 1 / (nobs - m) c1 *= (2 * k*k + 3 * k - 1) / (6 * (k + 1) * (m - 1)) df_chi2 = (m - 1) * k * (k + 1) / 2 statistic_chi2 = (1 - c1) * stat0 pvalue_chi2 = stats.chi2.sf(statistic_chi2, df_chi2) c2 = sum(1 / (n - 1)**2 for n in nobs_list) - 1 / (nobs - m)**2 c2 *= (k - 1) * (k + 2) / (6 * (m - 1)) a1 = df_chi2 a2 = (a1 + 2) / abs(c2 - c1**2) b1 = (1 - c1 - a1 / a2) / a1 b2 = (1 - c1 + 2 / a2) / a2 if c2 > c1**2: statistic_f = b1 * stat0 else: tmp = b2 * stat0 statistic_f = a2 / a1 * tmp / (1 + tmp) df_f = (a1, a2) pvalue_f = stats.f.sf(statistic_f, *df_f) return HolderTuple(statistic=statistic_f, # name convention, using F here pvalue=pvalue_f, # name convention, using F here statistic_base=stat0, statistic_chi2=statistic_chi2, pvalue_chi2=pvalue_chi2, df_chi2=df_chi2, distr_chi2='chi2', statistic_f=statistic_f, pvalue_f=pvalue_f, df_f=df_f, distr_f='F') statsmodels-0.12.2/statsmodels/stats/multivariate_tools.py000066400000000000000000000160061400612667500241500ustar00rootroot00000000000000'''Tools for multivariate analysis Author : Josef Perktold License : BSD-3 TODO: - names of functions, currently just "working titles" ''' import numpy as np from statsmodels.tools.tools import Bunch def partial_project(endog, exog): '''helper function to get linear projection or partialling out of variables endog variables are projected on exog variables Parameters ---------- endog : ndarray array of variables where the effect of exog is partialled out. exog : ndarray array of variables on which the endog variables are projected. Returns ------- res : instance of Bunch with - params : OLS parameter estimates from projection of endog on exog - fittedvalues : predicted values of endog given exog - resid : residual of the regression, values of endog with effect of exog partialled out Notes ----- This is no-frills mainly for internal calculations, no error checking or array conversion is performed, at least for now. ''' x1, x2 = endog, exog params = np.linalg.pinv(x2).dot(x1) predicted = x2.dot(params) residual = x1 - predicted res = Bunch(params=params, fittedvalues=predicted, resid=residual) return res def cancorr(x1, x2, demean=True, standardize=False): '''canonical correlation coefficient beween 2 arrays Parameters ---------- x1, x2 : ndarrays, 2_D two 2-dimensional data arrays, observations in rows, variables in columns demean : bool If demean is true, then the mean is subtracted from each variable standardize : bool If standardize is true, then each variable is demeaned and divided by its standard deviation. Rescaling does not change the canonical correlation coefficients. Returns ------- ccorr : ndarray, 1d canonical correlation coefficients, sorted from largest to smallest. Note, that these are the square root of the eigenvalues. Notes ----- This is a helper function for other statistical functions. It only calculates the canonical correlation coefficients and does not do a full canoncial correlation analysis The canonical correlation coefficient is calculated with the generalized matrix inverse and does not raise an exception if one of the data arrays have less than full column rank. See Also -------- cc_ranktest cc_stats CCA not yet ''' #x, y = x1, x2 if demean or standardize: x1 = (x1 - x1.mean(0)) x2 = (x2 - x2.mean(0)) if standardize: #std does not make a difference to canonical correlation coefficients x1 /= x1.std(0) x2 /= x2.std(0) t1 = np.linalg.pinv(x1).dot(x2) t2 = np.linalg.pinv(x2).dot(x1) m = t1.dot(t2) cc = np.sqrt(np.linalg.eigvals(m)) cc.sort() return cc[::-1] def cc_ranktest(x1, x2, demean=True, fullrank=False): '''rank tests based on smallest canonical correlation coefficients Anderson canonical correlations test (LM test) and Cragg-Donald test (Wald test) Assumes homoskedasticity and independent observations, overrejects if there is heteroscedasticity or autocorrelation. The Null Hypothesis is that the rank is k - 1, the alternative hypothesis is that the rank is at least k. Parameters ---------- x1, x2 : ndarrays, 2_D two 2-dimensional data arrays, observations in rows, variables in columns demean : bool If demean is true, then the mean is subtracted from each variable. fullrank : bool If true, then only the test that the matrix has full rank is returned. If false, the test for all possible ranks are returned. However, no the p-values are not corrected for the multiplicity of tests. Returns ------- value : float value of the test statistic p-value : float p-value for the test Null Hypothesis tha the smallest canonical correlation coefficient is zero. based on chi-square distribution df : int degrees of freedom for thechi-square distribution in the hypothesis test ccorr : ndarray, 1d All canonical correlation coefficients sorted from largest to smallest. Notes ----- Degrees of freedom for the distribution of the test statistic are based on number of columns of x1 and x2 and not on their matrix rank. (I'm not sure yet what the interpretation of the test is if x1 or x2 are of reduced rank.) See Also -------- cancorr cc_stats ''' from scipy import stats nobs1, k1 = x1.shape nobs2, k2 = x2.shape cc = cancorr(x1, x2, demean=demean) cc2 = cc * cc if fullrank: df = np.abs(k1 - k2) + 1 value = nobs1 * cc2[-1] w_value = nobs1 * (cc2[-1] / (1. - cc2[-1])) return value, stats.chi2.sf(value, df), df, cc, w_value, stats.chi2.sf(w_value, df) else: r = np.arange(min(k1, k2))[::-1] df = (k1 - r) * (k2 - r) values = nobs1 * cc2[::-1].cumsum() w_values = nobs1 * (cc2 / (1. - cc2))[::-1].cumsum() return values, stats.chi2.sf(values, df), df, cc, w_values, stats.chi2.sf(w_values, df) def cc_stats(x1, x2, demean=True): '''MANOVA statistics based on canonical correlation coefficient Calculates Pillai's Trace, Wilk's Lambda, Hotelling's Trace and Roy's Largest Root. Parameters ---------- x1, x2 : ndarrays, 2_D two 2-dimensional data arrays, observations in rows, variables in columns demean : bool If demean is true, then the mean is subtracted from each variable. Returns ------- res : dict Dictionary containing the test statistics. Notes ----- same as `canon` in Stata missing: F-statistics and p-values TODO: should return a results class instead produces nans sometimes, singular, perfect correlation of x1, x2 ? ''' nobs1, k1 = x1.shape # endogenous ? nobs2, k2 = x2.shape cc = cancorr(x1, x2, demean=demean) cc2 = cc**2 lam = (cc2 / (1 - cc2)) # what if max cc2 is 1 ? # Problem: ccr might not care if x1 or x2 are reduced rank, # but df will depend on rank df_model = k1 * k2 # df_hypothesis (we do not include mean in x1, x2) df_resid = k1 * (nobs1 - k2 - demean) s = min(df_model, k1) m = 0.5 * (df_model - k1) n = 0.5 * (df_resid - k1 - 1) df1 = k1 * df_model df2 = k2 pt_value = cc2.sum() # Pillai's trace wl_value = np.product(1 / (1 + lam)) # Wilk's Lambda ht_value = lam.sum() # Hotelling's Trace rm_value = lam.max() # Roy's largest root #from scipy import stats # what's the distribution, the test statistic ? res = {} res['canonical correlation coefficient'] = cc res['eigenvalues'] = lam res["Pillai's Trace"] = pt_value res["Wilk's Lambda"] = wl_value res["Hotelling's Trace"] = ht_value res["Roy's Largest Root"] = rm_value res['df_resid'] = df_resid res['df_m'] = m return res statsmodels-0.12.2/statsmodels/stats/oaxaca.py000066400000000000000000000235521400612667500214620ustar00rootroot00000000000000# TODO Variance can be calculated for the three_fold # TODO Group Size Effects can be accounted for # TODO Non-Linear Oaxaca-Blinder can be used """ Author: Austin Adams This class implements Oaxaca-Blinder Decomposition. It returns a OaxacaResults Class: OaxacaBlinder: Two-Fold/Pooled (two_fold) Three-Fold (three_fold) OaxacaResults: Table Summary (summary) Oaxaca-Blinder is a statistical method that is used to explain the differences between two mean values. The idea is to show from two mean values what can be explained by the data and what cannot by using OLS regression frameworks. "The original use by Oaxaca's was to explain the wage differential between two different groups of workers, but the method has since been applied to numerous other topics." (Wikipedia) The model is designed to accept two endogenous response variables and two exogenous explanitory variables. They are then fit using the specific type of decomposition that you want. The method was famously used in Card and Krueger's paper "School Quality and Black-White Relative Earnings: A Direct Assessment" (1992) General reference for Oaxaca-Blinder: B. Jann "The Blinder-Oaxaca decomposition for linear regression models," The Stata Journal, 2008. Econometrics references for regression models: E. M. Kitagawa "Components of a Difference Between Two Rates" Journal of the American Statistical Association, 1955. A. S. Blinder "Wage Discrimination: Reduced Form and Structural Estimates," The Journal of Human Resources, 1973. """ from statsmodels.regression.linear_model import OLS from statsmodels.tools.tools import add_constant import numpy as np from textwrap import dedent class OaxacaBlinder(object): """ Class to perform Oaxaca-Blinder Decomposition. Parameters ---------- endog : array_like The endogenous variable or the dependent variable that you are trying to explain. exog : array_like The exogenous variable(s) or the independent variable(s) that you are using to explain the endogenous variable. bifurcate : {int, str} The column of the exogenous variable(s) on which to split. This would generally be the group that you wish to explain the two means for. Int of the column for a NumPy array or int/string for the name of the column in Pandas. hasconst : bool, optional Indicates whether the two exogenous variables include a user-supplied constant. If True, a constant is assumed. If False, a constant is added at the start. If nothing is supplied, then True is assumed. swap : bool, optional Imitates the STATA Oaxaca command by allowing users to choose to swap groups. Unlike STATA, this is assumed to be True instead of False cov_type : str, optional See regression.linear_model.RegressionResults for a description of the available covariance estimators cov_kwds : dict, optional See linear_model.RegressionResults.get_robustcov_results for a description required keywords for alternative covariance estimators Notes ----- Please check if your data includes at constant. This will still run, but will return incorrect values if set incorrectly. You can access the models by using their code as an attribute, e.g., _t_model for the total model, _f_model for the first model, _s_model for the second model. Examples -------- >>> import numpy as np >>> import statsmodels.api as sm >>> data = sm.datasets.ccards.load() '3' is the column of which we want to explain or which indicates the two groups. In this case, it is if you rent. >>> model = sm.OaxacaBlinder(df.endog, df.exog, 3, hasconst = False) >>> model.two_fold().summary() Oaxaca-Blinder Two-fold Effects Unexplained Effect: 27.94091 Explained Effect: 130.80954 Gap: 158.75044 >>> model.three_fold().summary() Oaxaca-Blinder Three-fold Effects Characteristic Effect: 321.74824 Coefficient Effect: 75.45371 Interaction Effect: -238.45151 Gap: 158.75044 """ def __init__(self, endog, exog, bifurcate, hasconst=True, swap=True, cov_type='nonrobust', cov_kwds=None): if str(type(exog)).find('pandas') != -1: bifurcate = exog.columns.get_loc(bifurcate) endog, exog = np.array(endog), np.array(exog) bi_col = exog[:, bifurcate] endog = np.column_stack((bi_col, endog)) bi = np.unique(bi_col) # split the data along the bifurcate axis, the issue is you need to # delete it after you fit the model for the total model. exog_f = exog[np.where(exog[:, bifurcate] == bi[0])] exog_s = exog[np.where(exog[:, bifurcate] == bi[1])] endog_f = endog[np.where(endog[:, 0] == bi[0])] endog_s = endog[np.where(endog[:, 0] == bi[1])] exog_f = np.delete(exog_f, bifurcate, axis=1) exog_s = np.delete(exog_s, bifurcate, axis=1) endog_f = endog_f[:, 1] endog_s = endog_s[:, 1] endog = endog[:, 1] self.gap = endog_f.mean() - endog_s.mean() if swap and self.gap < 0: endog_f, endog_s = endog_s, endog_f exog_f, exog_s = exog_s, exog_f self.gap = endog_f.mean() - endog_s.mean() if hasconst is False: exog_f = add_constant(exog_f, prepend=False) exog_s = add_constant(exog_s, prepend=False) exog = add_constant(exog, prepend=False) self._t_model = OLS(endog, exog).fit( cov_type=cov_type, cov_kwds=cov_kwds) self._f_model = OLS(endog_f, exog_f).fit( cov_type=cov_type, cov_kwds=cov_kwds) self._s_model = OLS(endog_s, exog_s).fit( cov_type=cov_type, cov_kwds=cov_kwds) self.exog_f_mean = np.mean(exog_f, axis=0) self.exog_s_mean = np.mean(exog_s, axis=0) self.t_params = np.delete(self._t_model.params, bifurcate) def three_fold(self): """ Calculates the three-fold Oaxaca Blinder Decompositions Returns ------- OaxacaResults A results container for the three-fold decomposition. """ self.char_eff = ( (self.exog_f_mean - self.exog_s_mean) @ self._s_model.params) self.coef_eff = self.exog_s_mean @ (self._f_model.params - self._s_model.params) self.int_eff = ((self.exog_f_mean - self.exog_s_mean) @ (self._f_model.params - self._s_model.params)) return OaxacaResults( (self.char_eff, self.coef_eff, self.int_eff, self.gap), 3) def two_fold(self): """ Calculates the two-fold or pooled Oaxaca Blinder Decompositions Returns ------- OaxacaResults A results container for the two-fold decomposition. """ self.unexplained = ((self.exog_f_mean @ (self._f_model.params - self.t_params)) + (self.exog_s_mean @ (self.t_params - self._s_model.params))) self.explained = (self.exog_f_mean - self.exog_s_mean) @ self.t_params return OaxacaResults((self.unexplained, self.explained, self.gap), 2) class OaxacaResults: """ This class summarizes the fit of the OaxacaBlinder model. Use .summary() to get a table of the fitted values or use .params to receive a list of the values If a two-fold model was fitted, this will return unexplained effect, explained effect, and the mean gap. The list will be of the following order and type. unexplained : float This is the effect that cannot be explained by the data at hand. This does not mean it cannot be explained with more. explained : float This is the effect that can be explained using the data. gap : float This is the gap in the mean differences of the two groups. If a three-fold model was fitted, this will return characteristic effect, coefficient effect interaction effect, and the mean gap. The list will be of the following order and type. characteristic effect : float This is the effect due to the group differences in predictors coefficient effect : float This is the effect due to differences of the coefficients of the two groups interaction effect : float This is the effect due to differences in both effects existing at the same time between the two groups. gap : float This is the gap in the mean differences of the two groups. Attributes ---------- params A list of all values for the fitted models. """ def __init__(self, results, model_type): self.params = results self.model_type = model_type def summary(self): """ Print a summary table with the Oaxaca-Blinder effects """ if self.model_type == 2: print(dedent("""\ Oaxaca-Blinder Two-fold Effects Unexplained Effect: {:.5f} Explained Effect: {:.5f} Gap: {:.5f}""".format( self.params[0], self.params[1], self.params[2]))) if self.model_type == 3: print(dedent("""\ Oaxaca-Blinder Three-fold Effects Characteristic Effect: {:.5f} Coefficient Effect: {:.5f} Interaction Effect: {:.5f} Gap: {:.5f}""".format( self.params[0], self.params[1], self.params[2], self.params[3]))) statsmodels-0.12.2/statsmodels/stats/oneway.py000066400000000000000000001312231400612667500215230ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Mar 18 10:33:38 2020 Author: Josef Perktold License: BSD-3 """ import numpy as np from scipy import stats from scipy.special import ncfdtrinc from statsmodels.stats.robust_compare import TrimmedMean, scale_transform from statsmodels.tools.testing import Holder from statsmodels.stats.base import HolderTuple def effectsize_oneway(means, vars_, nobs, use_var="unequal", ddof_between=0): """ Effect size corresponding to Cohen's f = nc / nobs for oneway anova This contains adjustment for Welch and Brown-Forsythe Anova so that effect size can be used with FTestAnovaPower. Parameters ---------- means : array_like Mean of samples to be compared vars_ : float or array_like Residual (within) variance of each sample or pooled If ``vars_`` is scalar, then it is interpreted as pooled variance that is the same for all samples, ``use_var`` will be ignored. Otherwise, the variances are used depending on the ``use_var`` keyword. nobs : int or array_like Number of observations for the samples. If nobs is scalar, then it is assumed that all samples have the same number ``nobs`` of observation, i.e. a balanced sample case. Otherwise, statistics will be weighted corresponding to nobs. Only relative sizes are relevant, any proportional change to nobs does not change the effect size. use_var : {"unequal", "equal", "bf"} If ``use_var`` is "unequal", then the variances can differ across samples and the effect size for Welch anova will be computed. ddof_between : int Degrees of freedom correction for the weighted between sum of squares. The denominator is ``nobs_total - ddof_between`` This can be used to match differences across reference literature. Returns ------- f2 : float Effect size corresponding to squared Cohen's f, which is also equal to the noncentrality divided by total number of observations. Notes ----- This currently handles the following cases for oneway anova - balanced sample with homoscedastic variances - samples with different number of observations and with homoscedastic variances - samples with different number of observations and with heteroskedastic variances. This corresponds to Welch anova In the case of "unequal" and "bf" methods for unequal variances, the effect sizes do not directly correspond to the test statistic in Anova. Both have correction terms dropped or added, so the effect sizes match up with using FTestAnovaPower. If all variances are equal, then all three methods result in the same effect size. If variances are unequal, then the three methods produce small differences in effect size. Note, the effect size and power computation for BF Anova was not found in the literature. The correction terms were added so that FTestAnovaPower provides a good approximation to the power. Status: experimental We might add additional returns, if those are needed to support power and sample size applications. Examples -------- The following shows how to compute effect size and power for each of the three anova methods. The null hypothesis is that the means are equal which corresponds to a zero effect size. Under the alternative, means differ with two sample means at a distance delta from the mean. We assume the variance is the same under the null and alternative hypothesis. ``nobs`` for the samples defines the fraction of observations in the samples. ``nobs`` in the power method defines the total sample size. In simulations, the computed power for standard anova, i.e.``use_var="equal"`` overestimates the simulated power by a few percent. The equal variance assumption does not hold in this example. >>> from statsmodels.stats.oneway import effectsize_oneway >>> from statsmodels.stats.power import FTestAnovaPower >>> >>> nobs = np.array([10, 12, 13, 15]) >>> delta = 0.5 >>> means_alt = np.array([-1, 0, 0, 1]) * delta >>> vars_ = np.arange(1, len(means_alt) + 1) >>> >>> f2_alt = effectsize_oneway(means_alt, vars_, nobs, use_var="equal") >>> f2_alt 0.04581300813008131 >>> >>> kwds = {'effect_size': np.sqrt(f2_alt), 'nobs': 100, 'alpha': 0.05, ... 'k_groups': 4} >>> power = FTestAnovaPower().power(**kwds) >>> power 0.39165892158983273 >>> >>> f2_alt = effectsize_oneway(means_alt, vars_, nobs, use_var="unequal") >>> f2_alt 0.060640138408304504 >>> >>> kwds['effect_size'] = np.sqrt(f2_alt) >>> power = FTestAnovaPower().power(**kwds) >>> power 0.5047366512800622 >>> >>> f2_alt = effectsize_oneway(means_alt, vars_, nobs, use_var="bf") >>> f2_alt 0.04391324307956788 >>> >>> kwds['effect_size'] = np.sqrt(f2_alt) >>> power = FTestAnovaPower().power(**kwds) >>> power 0.3765792117047725 """ # the code here is largely a copy of onway_generic with adjustments means = np.asarray(means) n_groups = means.shape[0] if np.size(nobs) == 1: nobs = np.ones(n_groups) * nobs nobs_t = nobs.sum() if use_var == "equal": if np.size(vars_) == 1: var_resid = vars_ else: vars_ = np.asarray(vars_) var_resid = ((nobs - 1) * vars_).sum() / (nobs_t - n_groups) vars_ = var_resid # scalar, if broadcasting works weights = nobs / vars_ w_total = weights.sum() w_rel = weights / w_total # meanw_t = (weights * means).sum() / w_total meanw_t = w_rel @ means f2 = np.dot(weights, (means - meanw_t)**2) / (nobs_t - ddof_between) if use_var.lower() == "bf": weights = nobs w_total = weights.sum() w_rel = weights / w_total meanw_t = w_rel @ means # TODO: reuse general case with weights tmp = ((1. - nobs / nobs_t) * vars_).sum() statistic = 1. * (nobs * (means - meanw_t)**2).sum() statistic /= tmp f2 = statistic * (1. - nobs / nobs_t).sum() / nobs_t # correction factor for df_num in BFM df_num2 = n_groups - 1 df_num = tmp**2 / ((vars_**2).sum() + (nobs / nobs_t * vars_).sum()**2 - 2 * (nobs / nobs_t * vars_**2).sum()) f2 *= df_num / df_num2 return f2 def convert_effectsize_fsqu(f2=None, eta2=None): """Convert squared effect sizes in f family f2 is signal to noise ratio, var_explained / var_residual eta2 is proportion of explained variance, var_explained / var_total uses the relationship: f2 = eta2 / (1 - eta2) Parameters ---------- f2 : None or float Squared Cohen's F effect size. If f2 is not None, then eta2 will be computed. eta2 : None or float Squared eta effect size. If f2 is None and eta2 is not None, then f2 is computed. Returns ------- res : Holder instance An instance of the Holder class with f2 and eta2 as attributes. """ if f2 is not None: eta2 = 1 / (1 + 1 / f2) elif eta2 is not None: f2 = eta2 / (1 - eta2) res = Holder(f2=f2, eta2=eta2) return res def _fstat2effectsize(f_stat, df): """Compute anova effect size from F-statistic This might be combined with convert_effectsize_fsqu Parameters ---------- f_stat : array_like Test statistic of an F-test df : tuple degrees of freedom ``df = (df1, df2)`` where - df1 : numerator degrees of freedom, number of constraints - df2 : denominator degrees of freedom, df_resid Returns ------- res : Holder instance This instance contains effect size measures f2, eta2, omega2 and eps2 as attributes. Notes ----- This uses the following definitions: - f2 = f_stat * df1 / df2 - eta2 = f2 / (f2 + 1) - omega2 = (f2 - df1 / df2) / (f2 + 2) - eps2 = (f2 - df1 / df2) / (f2 + 1) This differs from effect size measures in other function which define ``f2 = f_stat * df1 / nobs`` or an equivalent expression for power computation. The noncentrality index for the hypothesis test is in those cases given by ``nc = f_stat * df1``. Currently omega2 and eps2 are computed in two different ways. Those values agree for regular cases but can show different behavior in corner cases (e.g. zero division). """ df1, df2 = df f2 = f_stat * df1 / df2 eta2 = f2 / (f2 + 1) omega2_ = (f_stat - 1) / (f_stat + (df2 + 1) / df1) omega2 = (f2 - df1 / df2) / (f2 + 1 + 1 / df2) # rewrite eps2_ = (f_stat - 1) / (f_stat + df2 / df1) eps2 = (f2 - df1 / df2) / (f2 + 1) # rewrite return Holder(f2=f2, eta2=eta2, omega2=omega2, eps2=eps2, eps2_=eps2_, omega2_=omega2_) # conversion functions for Wellek's equivalence effect size # these are mainly to compare with literature def wellek_to_f2(eps, n_groups): """Convert Wellek's effect size (sqrt) to Cohen's f-squared This computes the following effect size : f2 = 1 / n_groups * eps**2 Parameters ---------- eps : float or ndarray Wellek's effect size used in anova equivalence test n_groups : int Number of groups in oneway comparison Returns ------- f2 : effect size Cohen's f-squared """ f2 = 1 / n_groups * eps**2 return f2 def f2_to_wellek(f2, n_groups): """Convert Cohen's f-squared to Wellek's effect size (sqrt) This computes the following effect size : eps = sqrt(n_groups * f2) Parameters ---------- f2 : float or ndarray Effect size Cohen's f-squared n_groups : int Number of groups in oneway comparison Returns ------- eps : float or ndarray Wellek's effect size used in anova equivalence test """ eps = np.sqrt(n_groups * f2) return eps def fstat_to_wellek(f_stat, n_groups, nobs_mean): """Convert F statistic to wellek's effect size eps squared This computes the following effect size : es = f_stat * (n_groups - 1) / nobs_mean Parameters ---------- f_stat : float or ndarray Test statistic of an F-test. n_groups : int Number of groups in oneway comparison nobs_mean : float or ndarray Average number of observations across groups. Returns ------- eps : float or ndarray Wellek's effect size used in anova equivalence test """ es = f_stat * (n_groups - 1) / nobs_mean return es def confint_noncentrality(f_stat, df, alpha=0.05, alternative="two-sided"): """ Confidence interval for noncentrality parameter in F-test This does not yet handle non-negativity constraint on nc. Currently only two-sided alternative is supported. Parameters ---------- f_stat : float df : tuple degrees of freedom ``df = (df1, df2)`` where - df1 : numerator degrees of freedom, number of constraints - df2 : denominator degrees of freedom, df_resid alpha : float, default 0.05 alternative : {"two-sided"} Other alternatives have not been implements. Returns ------- float The end point of the confidence interval. Notes ----- The algorithm inverts the cdf of the noncentral F distribution with respect to the noncentrality parameters. See Steiger 2004 and references cited in it. References ---------- .. [1] Steiger, James H. 2004. “Beyond the F Test: Effect Size Confidence Intervals and Tests of Close Fit in the Analysis of Variance and Contrast Analysis.†Psychological Methods 9 (2): 164–82. https://doi.org/10.1037/1082-989X.9.2.164. See Also -------- confint_effectsize_oneway """ df1, df2 = df if alternative in ["two-sided", "2s", "ts"]: alpha1s = alpha / 2 ci = ncfdtrinc(df1, df2, [1 - alpha1s, alpha1s], f_stat) else: raise NotImplementedError return ci def confint_effectsize_oneway(f_stat, df, alpha=0.05, nobs=None): """ Confidence interval for effect size in oneway anova for F distribution This does not yet handle non-negativity constraint on nc. Currently only two-sided alternative is supported. Parameters ---------- f_stat : float df : tuple degrees of freedom ``df = (df1, df2)`` where - df1 : numerator degrees of freedom, number of constraints - df2 : denominator degrees of freedom, df_resid alpha : float, default 0.05 nobs : int, default None Returns ------- Holder Class with effect size and confidence attributes Notes ----- The confidence interval for the noncentrality parameter is obtained by inverting the cdf of the noncentral F distribution. Confidence intervals for other effect sizes are computed by endpoint transformation. R package ``effectsize`` does not compute the confidence intervals in the same way. Their confidence intervals can be replicated with >>> ci_nc = confint_noncentrality(f_stat, df1, df2, alpha=0.1) >>> ci_es = smo._fstat2effectsize(ci_nc / df1, df1, df2) See Also -------- confint_noncentrality """ df1, df2 = df if nobs is None: nobs = df1 + df2 + 1 ci_nc = confint_noncentrality(f_stat, df, alpha=alpha) ci_f2 = ci_nc / nobs ci_res = convert_effectsize_fsqu(f2=ci_f2) ci_res.ci_omega2 = (ci_f2 - df1 / df2) / (ci_f2 + 1 + 1 / df2) ci_res.ci_nc = ci_nc ci_res.ci_f = np.sqrt(ci_res.f2) ci_res.ci_eta = np.sqrt(ci_res.eta2) ci_res.ci_f_corrected = np.sqrt(ci_res.f2 * (df1 + 1) / df1) return ci_res def anova_generic(means, variances, nobs, use_var="unequal", welch_correction=True, info=None): """ Oneway Anova based on summary statistics Parameters ---------- means : array_like Mean of samples to be compared variances : float or array_like Residual (within) variance of each sample or pooled. If ``variances`` is scalar, then it is interpreted as pooled variance that is the same for all samples, ``use_var`` will be ignored. Otherwise, the variances are used depending on the ``use_var`` keyword. nobs : int or array_like Number of observations for the samples. If nobs is scalar, then it is assumed that all samples have the same number ``nobs`` of observation, i.e. a balanced sample case. Otherwise, statistics will be weighted corresponding to nobs. Only relative sizes are relevant, any proportional change to nobs does not change the effect size. use_var : {"unequal", "equal", "bf"} If ``use_var`` is "unequal", then the variances can differ across samples and the effect size for Welch anova will be computed. welch_correction : bool If this is false, then the Welch correction to the test statistic is not included. This allows the computation of an effect size measure that corresponds more closely to Cohen's f. info : not used yet Returns ------- res : results instance This includes `statistic` and `pvalue`. """ options = {"use_var": use_var, "welch_correction": welch_correction } if means.ndim != 1: raise ValueError('data (means, ...) has to be one-dimensional') nobs_t = nobs.sum() n_groups = len(means) # mean_t = (nobs * means).sum() / nobs_t if use_var == "unequal": weights = nobs / variances else: weights = nobs w_total = weights.sum() w_rel = weights / w_total # meanw_t = (weights * means).sum() / w_total meanw_t = w_rel @ means statistic = np.dot(weights, (means - meanw_t)**2) / (n_groups - 1.) df_num = n_groups - 1. if use_var == "unequal": tmp = ((1 - w_rel)**2 / (nobs - 1)).sum() / (n_groups**2 - 1) if welch_correction: statistic /= 1 + 2 * (n_groups - 2) * tmp df_denom = 1. / (3. * tmp) elif use_var == "equal": # variance of group demeaned total sample, pooled var_resid tmp = ((nobs - 1) * variances).sum() / (nobs_t - n_groups) statistic /= tmp df_denom = nobs_t - n_groups elif use_var == "bf": tmp = ((1. - nobs / nobs_t) * variances).sum() statistic = 1. * (nobs * (means - meanw_t)**2).sum() statistic /= tmp df_num2 = n_groups - 1 df_denom = tmp**2 / ((1. - nobs / nobs_t) ** 2 * variances ** 2 / (nobs - 1)).sum() df_num = tmp**2 / ((variances ** 2).sum() + (nobs / nobs_t * variances).sum() ** 2 - 2 * (nobs / nobs_t * variances ** 2).sum()) pval2 = stats.f.sf(statistic, df_num2, df_denom) options["df2"] = (df_num2, df_denom) options["df_num2"] = df_num2 options["pvalue2"] = pval2 else: raise ValueError('use_var is to be one of "unequal", "equal" or "bf"') pval = stats.f.sf(statistic, df_num, df_denom) res = HolderTuple(statistic=statistic, pvalue=pval, df=(df_num, df_denom), df_num=df_num, df_denom=df_denom, nobs_t=nobs_t, n_groups=n_groups, means=means, nobs=nobs, vars_=variances, **options ) return res def anova_oneway(data, groups=None, use_var="unequal", welch_correction=True, trim_frac=0): """Oneway Anova This implements standard anova, Welch and Brown-Forsythe, and trimmed (Yuen) variants of those. Parameters ---------- data : tuple of array_like or DataFrame or Series Data for k independent samples, with k >= 2. The data can be provided as a tuple or list of arrays or in long format with outcome observations in ``data`` and group membership in ``groups``. groups : ndarray or Series If data is in long format, then groups is needed as indicator to which group or sample and observations belongs. use_var : {"unequal", "equal" or "bf"} `use_var` specified how to treat heteroscedasticity, unequal variance, across samples. Three approaches are available "unequal" : Variances are not assumed to be equal across samples. Heteroscedasticity is taken into account with Welch Anova and Satterthwaite-Welch degrees of freedom. This is the default. "equal" : Variances are assumed to be equal across samples. This is the standard Anova. "bf: Variances are not assumed to be equal across samples. The method is Browne-Forsythe (1971) for testing equality of means with the corrected degrees of freedom by Merothra. The original BF degrees of freedom are available as additional attributes in the results instance, ``df_denom2`` and ``p_value2``. welch_correction : bool If this is false, then the Welch correction to the test statistic is not included. This allows the computation of an effect size measure that corresponds more closely to Cohen's f. trim_frac : float in [0, 0.5) Optional trimming for Anova with trimmed mean and winsorized variances. With the default trim_frac equal to zero, the oneway Anova statistics are computed without trimming. If `trim_frac` is larger than zero, then the largest and smallest observations in each sample are trimmed. The number of trimmed observations is the fraction of number of observations in the sample truncated to the next lower integer. `trim_frac` has to be smaller than 0.5, however, if the fraction is so large that there are not enough observations left over, then `nan` will be returned. Returns ------- res : results instance The returned HolderTuple instance has the following main attributes and some additional information in other attributes. statistic : float Test statistic for k-sample mean comparison which is approximately F-distributed. pvalue : float If ``use_var="bf"``, then the p-value is based on corrected degrees of freedom following Mehrotra 1997. pvalue2 : float This is the p-value based on degrees of freedom as in Brown-Forsythe 1974 and is only available if ``use_var="bf"``. df = (df_denom, df_num) : tuple of floats Degreeds of freedom for the F-distribution depend on ``use_var``. If ``use_var="bf"``, then `df_denom` is for Mehrotra p-values `df_denom2` is available for Brown-Forsythe 1974 p-values. `df_num` is the same numerator degrees of freedom for both p-values. Notes ----- Welch's anova is correctly sized (not liberal or conservative) in smaller samples if the distribution of the samples is not very far away from the normal distribution. The test can become liberal if the data is strongly skewed. Welch's Anova can also be correctly sized for discrete distributions with finite support, like Lickert scale data. The trimmed version is robust to many non-normal distributions, it stays correctly sized in many cases, and is more powerful in some cases with skewness or heavy tails. Trimming is currently based on the integer part of ``nobs * trim_frac``. The default might change to including fractional observations as in the original articles by Yuen. See Also -------- anova_generic References ---------- Brown, Morton B., and Alan B. Forsythe. 1974. “The Small Sample Behavior of Some Statistics Which Test the Equality of Several Means.†Technometrics 16 (1) (February 1): 129–132. doi:10.2307/1267501. Mehrotra, Devan V. 1997. “Improving the Brown-Forsythe Solution to the Generalized Behrens-Fisher Problem.†Communications in Statistics - Simulation and Computation 26 (3): 1139–1145. doi:10.1080/03610919708813431. """ if groups is not None: uniques = np.unique(groups) data = [data[groups == uni] for uni in uniques] else: # uniques = None # not used yet, add to info? pass args = list(map(np.asarray, data)) if any([x.ndim != 1 for x in args]): raise ValueError('data arrays have to be one-dimensional') nobs = np.array([len(x) for x in args], float) # n_groups = len(args) # not used # means = np.array([np.mean(x, axis=0) for x in args], float) # vars_ = np.array([np.var(x, ddof=1, axis=0) for x in args], float) if trim_frac == 0: means = np.array([x.mean() for x in args]) vars_ = np.array([x.var(ddof=1) for x in args]) else: tms = [TrimmedMean(x, trim_frac) for x in args] means = np.array([tm.mean_trimmed for tm in tms]) # R doesn't use uncorrected var_winsorized # vars_ = np.array([tm.var_winsorized for tm in tms]) vars_ = np.array([tm.var_winsorized * (tm.nobs - 1) / (tm.nobs_reduced - 1) for tm in tms]) # nobs_original = nobs # store just in case nobs = np.array([tm.nobs_reduced for tm in tms]) res = anova_generic(means, vars_, nobs, use_var=use_var, welch_correction=welch_correction) return res def equivalence_oneway_generic(f_stat, n_groups, nobs, equiv_margin, df, alpha=0.05, margin_type="f2"): """Equivalence test for oneway anova (Wellek and extensions) This is an helper function when summary statistics are available. Use `equivalence_oneway` instead. The null hypothesis is that the means differ by more than `equiv_margin` in the anova distance measure. If the Null is rejected, then the data supports that means are equivalent, i.e. within a given distance. Parameters ---------- f_stat : float F-statistic n_groups : int Number of groups in oneway comparison. nobs : ndarray Array of number of observations in groups. equiv_margin : float Equivalence margin in terms of effect size. Effect size can be chosen with `margin_type`. default is squared Cohen's f. df : tuple degrees of freedom ``df = (df1, df2)`` where - df1 : numerator degrees of freedom, number of constraints - df2 : denominator degrees of freedom, df_resid alpha : float in (0, 1) Significance level for the hypothesis test. margin_type : "f2" or "wellek" Type of effect size used for equivalence margin. Returns ------- results : instance of HolderTuple class The two main attributes are test statistic `statistic` and p-value `pvalue`. Notes ----- Equivalence in this function is defined in terms of a squared distance measure similar to Mahalanobis distance. Alternative definitions for the oneway case are based on maximum difference between pairs of means or similar pairwise distances. The equivalence margin is used for the noncentrality parameter in the noncentral F distribution for the test statistic. In samples with unequal variances estimated using Welch or Brown-Forsythe Anova, the f-statistic depends on the unequal variances and corrections to the test statistic. This means that the equivalence margins are not fully comparable across methods for treating unequal variances. References ---------- Wellek, Stefan. 2010. Testing Statistical Hypotheses of Equivalence and Noninferiority. 2nd ed. Boca Raton: CRC Press. Cribbie, Robert A., Chantal A. Arpin-Cribbie, and Jamie A. Gruman. 2009. “Tests of Equivalence for One-Way Independent Groups Designs.†The Journal of Experimental Education 78 (1): 1–13. https://doi.org/10.1080/00220970903224552. Jan, Show-Li, and Gwowen Shieh. 2019. “On the Extended Welch Test for Assessing Equivalence of Standardized Means.†Statistics in Biopharmaceutical Research 0 (0): 1–8. https://doi.org/10.1080/19466315.2019.1654915. """ nobs_t = nobs.sum() nobs_mean = nobs_t / n_groups if margin_type == "wellek": nc_null = nobs_mean * equiv_margin**2 es = f_stat * (n_groups - 1) / nobs_mean type_effectsize = "Wellek's psi_squared" elif margin_type in ["f2", "fsqu", "fsquared"]: nc_null = nobs_t * equiv_margin es = f_stat / nobs_t type_effectsize = "Cohen's f_squared" else: raise ValueError('`margin_type` should be "f2" or "wellek"') crit_f = stats.ncf.ppf(alpha, df[0], df[1], nc_null) if margin_type == "wellek": # TODO: do we need a sqrt crit_es = crit_f * (n_groups - 1) / nobs_mean elif margin_type in ["f2", "fsqu", "fsquared"]: crit_es = crit_f / nobs_t reject = (es < crit_es) pv = stats.ncf.cdf(f_stat, df[0], df[1], nc_null) pwr = stats.ncf.cdf(crit_f, df[0], df[1], 1e-13) # scipy, cannot be 0 res = HolderTuple(statistic=f_stat, pvalue=pv, effectsize=es, # match es type to margin_type crit_f=crit_f, crit_es=crit_es, reject=reject, power_zero=pwr, df=df, f_stat=f_stat, type_effectsize=type_effectsize ) return res def equivalence_oneway(data, equiv_margin, groups=None, use_var="unequal", welch_correction=True, trim_frac=0, margin_type="f2"): """equivalence test for oneway anova (Wellek's Anova) The null hypothesis is that the means differ by more than `equiv_margin` in the anova distance measure. If the Null is rejected, then the data supports that means are equivalent, i.e. within a given distance. Parameters ---------- data : tuple of array_like or DataFrame or Series Data for k independent samples, with k >= 2. The data can be provided as a tuple or list of arrays or in long format with outcome observations in ``data`` and group membership in ``groups``. equiv_margin : float Equivalence margin in terms of effect size. Effect size can be chosen with `margin_type`. default is squared Cohen's f. groups : ndarray or Series If data is in long format, then groups is needed as indicator to which group or sample and observations belongs. use_var : {"unequal", "equal" or "bf"} `use_var` specified how to treat heteroscedasticity, unequal variance, across samples. Three approaches are available "unequal" : Variances are not assumed to be equal across samples. Heteroscedasticity is taken into account with Welch Anova and Satterthwaite-Welch degrees of freedom. This is the default. "equal" : Variances are assumed to be equal across samples. This is the standard Anova. "bf: Variances are not assumed to be equal across samples. The method is Browne-Forsythe (1971) for testing equality of means with the corrected degrees of freedom by Merothra. The original BF degrees of freedom are available as additional attributes in the results instance, ``df_denom2`` and ``p_value2``. welch_correction : bool If this is false, then the Welch correction to the test statistic is not included. This allows the computation of an effect size measure that corresponds more closely to Cohen's f. trim_frac : float in [0, 0.5) Optional trimming for Anova with trimmed mean and winsorized variances. With the default trim_frac equal to zero, the oneway Anova statistics are computed without trimming. If `trim_frac` is larger than zero, then the largest and smallest observations in each sample are trimmed. The number of trimmed observations is the fraction of number of observations in the sample truncated to the next lower integer. `trim_frac` has to be smaller than 0.5, however, if the fraction is so large that there are not enough observations left over, then `nan` will be returned. margin_type : "f2" or "wellek" Type of effect size used for equivalence margin, either squared Cohen's f or Wellek's psi. Default is "f2". Returns ------- results : instance of HolderTuple class The two main attributes are test statistic `statistic` and p-value `pvalue`. See Also -------- anova_oneway equivalence_scale_oneway """ # use anova to compute summary statistics and f-statistic res0 = anova_oneway(data, groups=groups, use_var=use_var, welch_correction=welch_correction, trim_frac=trim_frac) f_stat = res0.statistic res = equivalence_oneway_generic(f_stat, res0.n_groups, res0.nobs_t, equiv_margin, res0.df, alpha=0.05, margin_type=margin_type) return res def _power_equivalence_oneway_emp(f_stat, n_groups, nobs, eps, df, alpha=0.05): """Empirical power of oneway equivalence test This only returns post-hoc, empirical power. Warning: eps is currently effect size margin as defined as in Wellek, and not the signal to noise ratio (Cohen's f family). Parameters ---------- f_stat : float F-statistic from oneway anova, used to compute empirical effect size n_groups : int Number of groups in oneway comparison. nobs : ndarray Array of number of observations in groups. eps : float Equivalence margin in terms of effect size given by Wellek's psi. df : tuple Degrees of freedom for F distribution. alpha : float in (0, 1) Significance level for the hypothesis test. Returns ------- pow : float Ex-post, post-hoc or empirical power at f-statistic of the equivalence test. """ res = equivalence_oneway_generic(f_stat, n_groups, nobs, eps, df, alpha=alpha, margin_type="wellek") nobs_mean = nobs.sum() / n_groups fn = f_stat # post-hoc power, empirical power at estimate esn = fn * (n_groups - 1) / nobs_mean # Wellek psi pow_ = stats.ncf.cdf(res.crit_f, df[0], df[1], nobs_mean * esn) return pow_ def power_equivalence_oneway(f2_alt, equiv_margin, nobs_t, n_groups=None, df=None, alpha=0.05, margin_type="f2"): """ Power of oneway equivalence test Parameters ---------- f2_alt : float Effect size, squared Cohen's f, under the alternative. equiv_margin : float Equivalence margin in terms of effect size. Effect size can be chosen with `margin_type`. default is squared Cohen's f. nobs_t : ndarray Total number of observations summed over all groups. n_groups : int Number of groups in oneway comparison. If margin_type is "wellek", then either ``n_groups`` or ``df`` has to be given. df : tuple Degrees of freedom for F distribution, ``df = (n_groups - 1, nobs_t - n_groups)`` alpha : float in (0, 1) Significance level for the hypothesis test. margin_type : "f2" or "wellek" Type of effect size used for equivalence margin, either squared Cohen's f or Wellek's psi. Default is "f2". Returns ------- pow_alt : float Power of the equivalence test at given equivalence effect size under the alternative. """ # one of n_groups or df has to be specified if df is None: if n_groups is None: raise ValueError("either df or n_groups has to be provided") df = (n_groups - 1, nobs_t - n_groups) # esn = fn * (n_groups - 1) / nobs_mean # Wellek psi # fix for scipy, ncf does not allow nc == 0, fixed in scipy master if f2_alt == 0: f2_alt = 1e-13 # effect size, critical value at margin # f2_null = equiv_margin if margin_type in ["f2", "fsqu", "fsquared"]: f2_null = equiv_margin elif margin_type == "wellek": if n_groups is None: raise ValueError("If margin_type is wellek, then n_groups has " "to be provided") # f2_null = (n_groups - 1) * n_groups / nobs_t * equiv_margin**2 nobs_mean = nobs_t / n_groups f2_null = nobs_mean * equiv_margin**2 / nobs_t f2_alt = nobs_mean * f2_alt**2 / nobs_t else: raise ValueError('`margin_type` should be "f2" or "wellek"') crit_f_margin = stats.ncf.ppf(alpha, df[0], df[1], nobs_t * f2_null) pwr_alt = stats.ncf.cdf(crit_f_margin, df[0], df[1], nobs_t * f2_alt) return pwr_alt def simulate_power_equivalence_oneway(means, nobs, equiv_margin, vars_=None, k_mc=1000, trim_frac=0, options_var=None, margin_type="f2" ): # , anova_options=None): #TODO """Simulate Power for oneway equivalence test (Wellek's Anova) This function is experimental and written to evaluate asymptotic power function. This function will change without backwards compatibility constraints. The only part that is stable is `pvalue` attribute in results. Effect size for equivalence margin """ if options_var is None: options_var = ["unequal", "equal", "bf"] if vars_ is not None: stds = np.sqrt(vars_) else: stds = np.ones(len(means)) nobs_mean = nobs.mean() n_groups = len(nobs) res_mc = [] f_mc = [] reject_mc = [] other_mc = [] for _ in range(k_mc): y0, y1, y2, y3 = [m + std * np.random.randn(n) for (n, m, std) in zip(nobs, means, stds)] res_i = [] f_i = [] reject_i = [] other_i = [] for uv in options_var: # for welch in options_welch: # res1 = sma.anova_generic(means, vars_, nobs, use_var=uv, # welch_correction=welch) res0 = anova_oneway([y0, y1, y2, y3], use_var=uv, trim_frac=trim_frac) f_stat = res0.statistic res1 = equivalence_oneway_generic(f_stat, n_groups, nobs.sum(), equiv_margin, res0.df, alpha=0.05, margin_type=margin_type) res_i.append(res1.pvalue) es_wellek = f_stat * (n_groups - 1) / nobs_mean f_i.append(es_wellek) reject_i.append(res1.reject) other_i.extend([res1.crit_f, res1.crit_es, res1.power_zero]) res_mc.append(res_i) f_mc.append(f_i) reject_mc.append(reject_i) other_mc.append(other_i) f_mc = np.asarray(f_mc) other_mc = np.asarray(other_mc) res_mc = np.asarray(res_mc) reject_mc = np.asarray(reject_mc) res = Holder(f_stat=f_mc, other=other_mc, pvalue=res_mc, reject=reject_mc ) return res def test_scale_oneway(data, method="bf", center="median", transform="abs", trim_frac_mean=0.1, trim_frac_anova=0.0): """Oneway Anova test for equal scale, variance or dispersion This hypothesis test performs a oneway anova test on transformed data and includes Levene and Brown-Forsythe tests for equal variances as special cases. Parameters ---------- data : tuple of array_like or DataFrame or Series Data for k independent samples, with k >= 2. The data can be provided as a tuple or list of arrays or in long format with outcome observations in ``data`` and group membership in ``groups``. method : {"unequal", "equal" or "bf"} How to treat heteroscedasticity across samples. This is used as `use_var` option in `anova_oneway` and refers to the variance of the transformed data, i.e. assumption is on 4th moment if squares are used as transform. Three approaches are available: "unequal" : Variances are not assumed to be equal across samples. Heteroscedasticity is taken into account with Welch Anova and Satterthwaite-Welch degrees of freedom. This is the default. "equal" : Variances are assumed to be equal across samples. This is the standard Anova. "bf" : Variances are not assumed to be equal across samples. The method is Browne-Forsythe (1971) for testing equality of means with the corrected degrees of freedom by Merothra. The original BF degrees of freedom are available as additional attributes in the results instance, ``df_denom2`` and ``p_value2``. center : "median", "mean", "trimmed" or float Statistic used for centering observations. If a float, then this value is used to center. Default is median. transform : "abs", "square" or callable Transformation for the centered observations. If a callable, then this function is called on the centered data. Default is absolute value. trim_frac_mean=0.1 : float in [0, 0.5) Trim fraction for the trimmed mean when `center` is "trimmed" trim_frac_anova : float in [0, 0.5) Optional trimming for Anova with trimmed mean and Winsorized variances. With the default trim_frac equal to zero, the oneway Anova statistics are computed without trimming. If `trim_frac` is larger than zero, then the largest and smallest observations in each sample are trimmed. see ``trim_frac`` option in `anova_oneway` Returns ------- res : results instance The returned HolderTuple instance has the following main attributes and some additional information in other attributes. statistic : float Test statistic for k-sample mean comparison which is approximately F-distributed. pvalue : float If ``method="bf"``, then the p-value is based on corrected degrees of freedom following Mehrotra 1997. pvalue2 : float This is the p-value based on degrees of freedom as in Brown-Forsythe 1974 and is only available if ``method="bf"``. df : (df_denom, df_num) Tuple containing degrees of freedom for the F-distribution depend on ``method``. If ``method="bf"``, then `df_denom` is for Mehrotra p-values `df_denom2` is available for Brown-Forsythe 1974 p-values. `df_num` is the same numerator degrees of freedom for both p-values. See Also -------- anova_oneway scale_transform """ data = map(np.asarray, data) xxd = [scale_transform(x, center=center, transform=transform, trim_frac=trim_frac_mean) for x in data] res = anova_oneway(xxd, groups=None, use_var=method, welch_correction=True, trim_frac=trim_frac_anova) res.data_transformed = xxd return res def equivalence_scale_oneway(data, equiv_margin, method='bf', center='median', transform='abs', trim_frac_mean=0., trim_frac_anova=0.): """Oneway Anova test for equivalence of scale, variance or dispersion This hypothesis test performs a oneway equivalence anova test on transformed data. Note, the interpretation of the equivalence margin `equiv_margin` will depend on the transformation of the data. Transformations like absolute deviation are not scaled to correspond to the variance under normal distribution. Parameters ---------- data : tuple of array_like or DataFrame or Series Data for k independent samples, with k >= 2. The data can be provided as a tuple or list of arrays or in long format with outcome observations in ``data`` and group membership in ``groups``. equiv_margin : float Equivalence margin in terms of effect size. Effect size can be chosen with `margin_type`. default is squared Cohen's f. method : {"unequal", "equal" or "bf"} How to treat heteroscedasticity across samples. This is used as `use_var` option in `anova_oneway` and refers to the variance of the transformed data, i.e. assumption is on 4th moment if squares are used as transform. Three approaches are available: "unequal" : Variances are not assumed to be equal across samples. Heteroscedasticity is taken into account with Welch Anova and Satterthwaite-Welch degrees of freedom. This is the default. "equal" : Variances are assumed to be equal across samples. This is the standard Anova. "bf" : Variances are not assumed to be equal across samples. The method is Browne-Forsythe (1971) for testing equality of means with the corrected degrees of freedom by Merothra. The original BF degrees of freedom are available as additional attributes in the results instance, ``df_denom2`` and ``p_value2``. center : "median", "mean", "trimmed" or float Statistic used for centering observations. If a float, then this value is used to center. Default is median. transform : "abs", "square" or callable Transformation for the centered observations. If a callable, then this function is called on the centered data. Default is absolute value. trim_frac_mean : float in [0, 0.5) Trim fraction for the trimmed mean when `center` is "trimmed" trim_frac_anova : float in [0, 0.5) Optional trimming for Anova with trimmed mean and Winsorized variances. With the default trim_frac equal to zero, the oneway Anova statistics are computed without trimming. If `trim_frac` is larger than zero, then the largest and smallest observations in each sample are trimmed. see ``trim_frac`` option in `anova_oneway` Returns ------- results : instance of HolderTuple class The two main attributes are test statistic `statistic` and p-value `pvalue`. See Also -------- anova_oneway scale_transform equivalence_oneway """ data = map(np.asarray, data) xxd = [scale_transform(x, center=center, transform=transform, trim_frac=trim_frac_mean) for x in data] res = equivalence_oneway(xxd, equiv_margin, use_var=method, welch_correction=True, trim_frac=trim_frac_anova) res.x_transformed = xxd return res statsmodels-0.12.2/statsmodels/stats/outliers_influence.py000066400000000000000000001406461400612667500241300ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Influence and Outlier Measures Created on Sun Jan 29 11:16:09 2012 Author: Josef Perktold License: BSD-3 """ from collections import defaultdict import numpy as np from statsmodels.compat.python import lzip from statsmodels.compat.pandas import Appender from statsmodels.graphics._regressionplots_doc import _plot_influence_doc from statsmodels.regression.linear_model import OLS from statsmodels.stats.multitest import multipletests from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.tools import maybe_unwrap_results # outliers test convenience wrapper def outlier_test(model_results, method='bonf', alpha=.05, labels=None, order=False, cutoff=None): """ Outlier Tests for RegressionResults instances. Parameters ---------- model_results : RegressionResults Linear model results method : str - `bonferroni` : one-step correction - `sidak` : one-step correction - `holm-sidak` : - `holm` : - `simes-hochberg` : - `hommel` : - `fdr_bh` : Benjamini/Hochberg - `fdr_by` : Benjamini/Yekutieli See `statsmodels.stats.multitest.multipletests` for details. alpha : float familywise error rate labels : None or array_like If `labels` is not None, then it will be used as index to the returned pandas DataFrame. See also Returns below order : bool Whether or not to order the results by the absolute value of the studentized residuals. If labels are provided they will also be sorted. cutoff : None or float in [0, 1] If cutoff is not None, then the return only includes observations with multiple testing corrected p-values strictly below the cutoff. The returned array or dataframe can be empty if there are no outlier candidates at the specified cutoff. Returns ------- table : ndarray or DataFrame Returns either an ndarray or a DataFrame if labels is not None. Will attempt to get labels from model_results if available. The columns are the Studentized residuals, the unadjusted p-value, and the corrected p-value according to method. Notes ----- The unadjusted p-value is stats.t.sf(abs(resid), df) where df = df_resid - 1. """ from scipy import stats # lazy import if labels is None: labels = getattr(model_results.model.data, 'row_labels', None) infl = getattr(model_results, 'get_influence', None) if infl is None: results = maybe_unwrap_results(model_results) raise AttributeError("model_results object %s does not have a " "get_influence " "method." % results.__class__.__name__) resid = infl().resid_studentized_external if order: idx = np.abs(resid).argsort()[::-1] resid = resid[idx] if labels is not None: labels = np.asarray(labels)[idx] df = model_results.df_resid - 1 unadj_p = stats.t.sf(np.abs(resid), df) * 2 adj_p = multipletests(unadj_p, alpha=alpha, method=method) data = np.c_[resid, unadj_p, adj_p[1]] if cutoff is not None: mask = data[:, -1] < cutoff data = data[mask] else: mask = slice(None) if labels is not None: from pandas import DataFrame return DataFrame(data, columns=['student_resid', 'unadj_p', method + "(p)"], index=np.asarray(labels)[mask]) return data # influence measures def reset_ramsey(res, degree=5): """Ramsey's RESET specification test for linear models This is a general specification test, for additional non-linear effects in a model. Parameters ---------- degree : int Maximum power to include in the RESET test. Powers 0 and 1 are excluded, so that degree tests powers 2, ..., degree of the fitted values. Notes ----- The test fits an auxiliary OLS regression where the design matrix, exog, is augmented by powers 2 to degree of the fitted values. Then it performs an F-test whether these additional terms are significant. If the p-value of the f-test is below a threshold, e.g. 0.1, then this indicates that there might be additional non-linear effects in the model and that the linear model is mis-specified. References ---------- https://en.wikipedia.org/wiki/Ramsey_RESET_test """ order = degree + 1 k_vars = res.model.exog.shape[1] # vander without constant and x, and drop constant norm_values = np.asarray(res.fittedvalues) norm_values = norm_values / np.sqrt((norm_values ** 2).mean()) y_fitted_vander = np.vander(norm_values, order)[:, :-2] exog = np.column_stack((res.model.exog, y_fitted_vander)) exog /= np.sqrt((exog ** 2).mean(0)) endog = res.model.endog / (res.model.endog ** 2).mean() res_aux = OLS(endog, exog).fit() # r_matrix = np.eye(degree, exog.shape[1], k_vars) r_matrix = np.eye(degree - 1, exog.shape[1], k_vars) # df1 = degree - 1 # df2 = exog.shape[0] - degree - res.df_model (without constant) return res_aux.f_test(r_matrix) # , r_matrix, res_aux def variance_inflation_factor(exog, exog_idx): """variance inflation factor, VIF, for one exogenous variable The variance inflation factor is a measure for the increase of the variance of the parameter estimates if an additional variable, given by exog_idx is added to the linear regression. It is a measure for multicollinearity of the design matrix, exog. One recommendation is that if VIF is greater than 5, then the explanatory variable given by exog_idx is highly collinear with the other explanatory variables, and the parameter estimates will have large standard errors because of this. Parameters ---------- exog : ndarray design matrix with all explanatory variables, as for example used in regression exog_idx : int index of the exogenous variable in the columns of exog Returns ------- vif : float variance inflation factor Notes ----- This function does not save the auxiliary regression. See Also -------- xxx : class for regression diagnostics TODO: does not exist yet References ---------- https://en.wikipedia.org/wiki/Variance_inflation_factor """ k_vars = exog.shape[1] x_i = exog[:, exog_idx] mask = np.arange(k_vars) != exog_idx x_noti = exog[:, mask] r_squared_i = OLS(x_i, x_noti).fit().rsquared vif = 1. / (1. - r_squared_i) return vif class _BaseInfluenceMixin(object): """common methods between OLSInfluence and MLE/GLMInfluence """ @Appender(_plot_influence_doc.format(**{'extra_params_doc': ""})) def plot_influence(self, external=None, alpha=.05, criterion="cooks", size=48, plot_alpha=.75, ax=None, **kwargs): if external is None: external = hasattr(self, '_cache') and 'res_looo' in self._cache from statsmodels.graphics.regressionplots import _influence_plot res = _influence_plot(self.results, self, external=external, alpha=alpha, criterion=criterion, size=size, plot_alpha=plot_alpha, ax=ax, **kwargs) return res def _plot_index(self, y, ylabel, threshold=None, title=None, ax=None, **kwds): from statsmodels.graphics import utils fig, ax = utils.create_mpl_ax(ax) if title is None: title = "Index Plot" nobs = len(self.endog) index = np.arange(nobs) ax.scatter(index, y, **kwds) if threshold == 'all': large_points = np.ones(nobs, np.bool_) else: large_points = np.abs(y) > threshold psize = 3 * np.ones(nobs) # add point labels labels = self.results.model.data.row_labels if labels is None: labels = np.arange(nobs) ax = utils.annotate_axes(np.where(large_points)[0], labels, lzip(index, y), lzip(-psize, psize), "large", ax) font = {"fontsize": 16, "color": "black"} ax.set_ylabel(ylabel, **font) ax.set_xlabel("Observation", **font) ax.set_title(title, **font) return fig def plot_index(self, y_var='cooks', threshold=None, title=None, ax=None, idx=None, **kwds): """index plot for influence attributes Parameters ---------- y_var : str Name of attribute or shortcut for predefined attributes that will be plotted on the y-axis. threshold : None or float Threshold for adding annotation with observation labels. Observations for which the absolute value of the y_var is larger than the threshold will be annotated. Set to a negative number to label all observations or to a large number to have no annotation. title : str If provided, the title will replace the default "Index Plot" title. ax : matplolib axis instance The plot will be added to the `ax` if provided, otherwise a new figure is created. idx : {None, int} Some attributes require an additional index to select the y-var. In dfbetas this refers to the column indes. kwds : optional keywords Keywords will be used in the call to matplotlib scatter function. """ criterion = y_var # alias if threshold is None: # TODO: criterion specific defaults threshold = 'all' if criterion == 'dfbeta': y = self.dfbetas[:, idx] ylabel = 'DFBETA for ' + self.results.model.exog_names[idx] elif criterion.startswith('cook'): y = self.cooks_distance[0] ylabel = "Cook's distance" elif criterion.startswith('hat') or criterion.startswith('lever'): y = self.hat_matrix_diag ylabel = "Leverage (diagonal of hat matrix)" elif criterion.startswith('cook'): y = self.cooks_distance[0] ylabel = "Cook's distance" elif criterion.startswith('resid'): y = self.resid_studentized ylabel = "Internally Studentized Residuals" else: # assume we have the name of an attribute y = getattr(self, y_var) if idx is not None: y = y[idx] ylabel = y_var fig = self._plot_index(y, ylabel, threshold=threshold, title=title, ax=ax, **kwds) return fig class MLEInfluence(_BaseInfluenceMixin): """Local Influence and outlier measures (experimental) This currently subclasses GLMInfluence instead of the other way. No common superclass yet. This is another version before checking what is common Parameters ---------- results : instance of results class This only works for model and results classes that have the necessary helper methods. other arguments are only to override default behavior and are used instead of the corresponding attribute of the results class. By default resid_pearson is used as resid. Attributes ---------- hat_matrix_diag (hii) : This is the generalized leverage computed as the local derivative of fittedvalues (predicted mean) with respect to the observed response for each observation. d_params : Change in parameters computed with one Newton step using the full Hessian corrected by division by (1 - hii). dbetas : change in parameters divided by the standard error of parameters from the full model results, ``bse``. cooks_distance : quadratic form for change in parameters weighted by ``cov_params`` from the full model divided by the number of variables. It includes p-values based on the F-distribution which are only approximate outside of linear Gaussian models. resid_studentized : In the general MLE case resid_studentized are computed from the score residuals scaled by hessian factor and leverage. This does not use ``cov_params``. d_fittedvalues : local change of expected mean given the change in the parameters as computed in ``d_params``. d_fittedvalues_scaled : same as d_fittedvalues but scaled by the standard errors of a predicted mean of the response. params_one : is the one step parameter estimate computed as ``params`` from the full sample minus ``d_params``. Notes ----- MLEInfluence produces the same results as GLMInfluence (verified for GLM Binomial and Gaussian). There will be some differences for non-canonical links or if a robust cov_type is used. Warning: This does currently not work for constrained or penalized models, e.g. models estimated with fit_constrained or fit_regularized. This has not yet been tested for correctness when offset or exposure are used, although they should be supported by the code. status: experimental, This class will need changes to support different kinds of models, e.g. extra parameters in discrete.NegativeBinomial or two-part models like ZeroInflatedPoisson. """ def __init__(self, results, resid=None, endog=None, exog=None, hat_matrix_diag=None, cov_params=None, scale=None): # I'm not calling super for now, OLS attributes might not be available # check which model is allowed self.results = results = maybe_unwrap_results(results) # TODO: check for extra params in e.g. NegBin self.nobs, self.k_vars = results.model.exog.shape self.endog = endog if endog is not None else results.model.endog self.exog = exog if exog is not None else results.model.exog self.resid = resid if resid is not None else results.resid_pearson self.scale = scale if scale is not None else results.scale self.cov_params = (cov_params if cov_params is not None else results.cov_params()) self.model_class = results.model.__class__ self.hessian = self.results.model.hessian(self.results.params) self.score_obs = self.results.model.score_obs(self.results.params) if hat_matrix_diag is not None: self._hat_matrix_diag = hat_matrix_diag @cache_readonly def hat_matrix_diag(self): """Diagonal of the generalized leverage This is the analogue of the hat matrix diagonal for general MLE. """ if hasattr(self, '_hat_matrix_diag'): return self._hat_matrix_diag dmu_dp = self.results.model._deriv_mean_dparams(self.results.params) dsdy = self.results.model._deriv_score_obs_dendog(self.results.params) # dmu_dp = 1 / # self.results.model.family.link.deriv(self.results.fittedvalues) h = (dmu_dp * np.linalg.solve(-self.hessian, dsdy.T).T).sum(1) return h @cache_readonly def d_params(self): """Change in parameter estimates This uses one-step approximation of the parameter change to deleting one observation. """ so_noti = self.score_obs.sum(0) - self.score_obs beta_i = np.linalg.solve(self.hessian, so_noti.T).T return beta_i / (1 - self.hat_matrix_diag)[:, None] @cache_readonly def dfbetas(self): """Scaled change in parameter estimates The one-step change of parameters in d_params is rescaled by dividing by the standard error of the parameter estimate given by results.bse. """ beta_i = self.d_params / self.results.bse return beta_i @cache_readonly def params_one(self): """Parameter estimate based on one-step approximation This the one step parameter estimate computed as ``params`` from the full sample minus ``d_params``. """ return self.results.params - self.d_params @cache_readonly def cooks_distance(self): """Cook's distance and p-values Based on one step approximation d_params and on results.cov_params Cook's distance divides by the number of explanatory variables. p-values are based on the F-distribution which are only approximate outside of linear Gaussian models. Warning: The definition of p-values might change if we switch to using chi-square distribution instead of F-distribution, or if we make it dependent on the fit keyword use_t. """ cooks_d2 = (self.d_params * np.linalg.solve(self.cov_params, self.d_params.T).T).sum(1) cooks_d2 /= self.k_vars from scipy import stats # alpha = 0.1 # print stats.f.isf(1-alpha, n_params, res.df_modelwc) # TODO use chi2 # use_f option pvals = stats.f.sf(cooks_d2, self.k_vars, self.results.df_resid) return cooks_d2, pvals @cache_readonly def resid_studentized(self): """Score residual divided by sqrt of hessian factor experimental, agrees with GLMInfluence for Binomial and Gaussian. no reference for this """ sf = self.results.model.score_factor(self.results.params) hf = self.results.model.hessian_factor(self.results.params) return sf / np.sqrt(hf) / np.sqrt(1 - self.hat_matrix_diag) @cache_readonly def _get_prediction(self): # TODO: do we cache this or does it need to be a method # we only need unchanging parts, alpha for confint could change return self.results.get_prediction() @cache_readonly def d_fittedvalues(self): """Change in expected response, fittedvalues Local change of expected mean given the change in the parameters as computed in d_params. Notes ----- This uses one-step approximation of the parameter change to deleting one observation ``d_params``. """ # results.params might be a pandas.Series params = np.asarray(self.results.params) deriv = self.results.model._deriv_mean_dparams(params) return (deriv * self.d_params).sum(1) @property def d_fittedvalues_scaled(self): """ Change in fittedvalues scaled by standard errors This uses one-step approximation of the parameter change to deleting one observation ``d_params``, and divides by the standard errors for the predicted mean provided by results.get_prediction. """ # Note: this and the previous methods are for the response # and not for a weighted response, i.e. not the self.exog, self.endog # this will be relevant for WLS comparing fitted endog versus wendog return self.d_fittedvalues / self._get_prediction.se_mean def summary_frame(self): """ Creates a DataFrame with influence results. Returns ------- frame : pandas DataFrame A DataFrame with selected results for each observation. The index will be the same as provided to the model. Notes ----- The resultant DataFrame contains six variables in addition to the ``dfbetas``. These are: * cooks_d : Cook's Distance defined in ``cooks_distance`` * standard_resid : Standardized residuals defined in `resid_studentizedl` * hat_diag : The diagonal of the projection, or hat, matrix defined in `hat_matrix_diag` * dffits_internal : DFFITS statistics using internally Studentized residuals defined in `d_fittedvalues_scaled` """ from pandas import DataFrame # row and column labels data = self.results.model.data row_labels = data.row_labels beta_labels = ['dfb_' + i for i in data.xnames] # grab the results summary_data = DataFrame(dict( cooks_d=self.cooks_distance[0], standard_resid=self.resid_studentized, hat_diag=self.hat_matrix_diag, dffits_internal=self.d_fittedvalues_scaled), index=row_labels) # NOTE: if we do not give columns, order of above will be arbitrary dfbeta = DataFrame(self.dfbetas, columns=beta_labels, index=row_labels) return dfbeta.join(summary_data) class OLSInfluence(_BaseInfluenceMixin): """class to calculate outlier and influence measures for OLS result Parameters ---------- results : RegressionResults currently assumes the results are from an OLS regression Notes ----- One part of the results can be calculated without any auxiliary regression (some of which have the `_internal` postfix in the name. Other statistics require leave-one-observation-out (LOOO) auxiliary regression, and will be slower (mainly results with `_external` postfix in the name). The auxiliary LOOO regression only the required results are stored. Using the LOO measures is currently only recommended if the data set is not too large. One possible approach for LOOO measures would be to identify possible problem observations with the _internal measures, and then run the leave-one-observation-out only with observations that are possible outliers. (However, this is not yet available in an automated way.) This should be extended to general least squares. The leave-one-variable-out (LOVO) auxiliary regression are currently not used. """ def __init__(self, results): # check which model is allowed self.results = maybe_unwrap_results(results) self.nobs, self.k_vars = results.model.exog.shape self.endog = results.model.endog self.exog = results.model.exog self.resid = results.resid self.model_class = results.model.__class__ # self.sigma_est = np.sqrt(results.mse_resid) self.scale = results.mse_resid self.aux_regression_exog = {} self.aux_regression_endog = {} @cache_readonly def hat_matrix_diag(self): """Diagonal of the hat_matrix for OLS Notes ----- temporarily calculated here, this should go to model class """ return (self.exog * self.results.model.pinv_wexog.T).sum(1) @cache_readonly def resid_press(self): """PRESS residuals """ hii = self.hat_matrix_diag return self.resid / (1 - hii) @cache_readonly def influence(self): """Influence measure matches the influence measure that gretl reports u * h / (1 - h) where u are the residuals and h is the diagonal of the hat_matrix """ hii = self.hat_matrix_diag return self.resid * hii / (1 - hii) @cache_readonly def hat_diag_factor(self): """Factor of diagonal of hat_matrix used in influence this might be useful for internal reuse h / (1 - h) """ hii = self.hat_matrix_diag return hii / (1 - hii) @cache_readonly def ess_press(self): """Error sum of squares of PRESS residuals """ return np.dot(self.resid_press, self.resid_press) @cache_readonly def resid_studentized(self): """Studentized residuals using variance from OLS alias for resid_studentized_internal for compatibility with MLEInfluence this uses sigma from original estimate and does not require leave one out loop """ return self.resid_studentized_internal @cache_readonly def resid_studentized_internal(self): """Studentized residuals using variance from OLS this uses sigma from original estimate does not require leave one out loop """ return self.get_resid_studentized_external(sigma=None) # return self.results.resid / self.sigma_est @cache_readonly def resid_studentized_external(self): """Studentized residuals using LOOO variance this uses sigma from leave-one-out estimates requires leave one out loop for observations """ sigma_looo = np.sqrt(self.sigma2_not_obsi) return self.get_resid_studentized_external(sigma=sigma_looo) def get_resid_studentized_external(self, sigma=None): """calculate studentized residuals Parameters ---------- sigma : None or float estimate of the standard deviation of the residuals. If None, then the estimate from the regression results is used. Returns ------- stzd_resid : ndarray studentized residuals Notes ----- studentized residuals are defined as :: resid / sigma / np.sqrt(1 - hii) where resid are the residuals from the regression, sigma is an estimate of the standard deviation of the residuals, and hii is the diagonal of the hat_matrix. """ hii = self.hat_matrix_diag if sigma is None: sigma2_est = self.scale # can be replace by different estimators of sigma sigma = np.sqrt(sigma2_est) return self.resid / sigma / np.sqrt(1 - hii) # same computation as GLMInfluence @cache_readonly def cooks_distance(self): """ Cooks distance Uses original results, no nobs loop References ---------- .. [*] Eubank, R. L. (1999). Nonparametric regression and spline smoothing. CRC press. .. [*] Cook's distance. (n.d.). In Wikipedia. July 2019, from https://en.wikipedia.org/wiki/Cook%27s_distance """ hii = self.hat_matrix_diag # Eubank p.93, 94 cooks_d2 = self.resid_studentized ** 2 / self.k_vars cooks_d2 *= hii / (1 - hii) from scipy import stats # alpha = 0.1 # print stats.f.isf(1-alpha, n_params, res.df_modelwc) pvals = stats.f.sf(cooks_d2, self.k_vars, self.results.df_resid) return cooks_d2, pvals @cache_readonly def dffits_internal(self): """dffits measure for influence of an observation based on resid_studentized_internal uses original results, no nobs loop """ # TODO: do I want to use different sigma estimate in # resid_studentized_external # -> move definition of sigma_error to the __init__ hii = self.hat_matrix_diag dffits_ = self.resid_studentized_internal * np.sqrt(hii / (1 - hii)) dffits_threshold = 2 * np.sqrt(self.k_vars * 1. / self.nobs) return dffits_, dffits_threshold @cache_readonly def dffits(self): """ dffits measure for influence of an observation based on resid_studentized_external, uses results from leave-one-observation-out loop It is recommended that observations with dffits large than a threshold of 2 sqrt{k / n} where k is the number of parameters, should be investigated. Returns ------- dffits : float dffits_threshold : float References ---------- `Wikipedia `_ """ # TODO: do I want to use different sigma estimate in # resid_studentized_external # -> move definition of sigma_error to the __init__ hii = self.hat_matrix_diag dffits_ = self.resid_studentized_external * np.sqrt(hii / (1 - hii)) dffits_threshold = 2 * np.sqrt(self.k_vars * 1. / self.nobs) return dffits_, dffits_threshold @cache_readonly def dfbetas(self): """dfbetas uses results from leave-one-observation-out loop """ dfbetas = self.results.params - self.params_not_obsi # [None,:] dfbetas /= np.sqrt(self.sigma2_not_obsi[:, None]) dfbetas /= np.sqrt(np.diag(self.results.normalized_cov_params)) return dfbetas @cache_readonly def dfbeta(self): """dfbetas uses results from leave-one-observation-out loop """ dfbeta = self.results.params - self.params_not_obsi return dfbeta @cache_readonly def sigma2_not_obsi(self): """error variance for all LOOO regressions This is 'mse_resid' from each auxiliary regression. uses results from leave-one-observation-out loop """ return np.asarray(self._res_looo['mse_resid']) @property def params_not_obsi(self): """parameter estimates for all LOOO regressions uses results from leave-one-observation-out loop """ return np.asarray(self._res_looo['params']) @property def det_cov_params_not_obsi(self): """determinant of cov_params of all LOOO regressions uses results from leave-one-observation-out loop """ return np.asarray(self._res_looo['det_cov_params']) @cache_readonly def cov_ratio(self): """covariance ratio between LOOO and original This uses determinant of the estimate of the parameter covariance from leave-one-out estimates. requires leave one out loop for observations """ # do not use inplace division / because then we change original cov_ratio = (self.det_cov_params_not_obsi / np.linalg.det(self.results.cov_params())) return cov_ratio @cache_readonly def resid_var(self): """estimate of variance of the residuals :: sigma2 = sigma2_OLS * (1 - hii) where hii is the diagonal of the hat matrix """ # TODO:check if correct outside of ols return self.scale * (1 - self.hat_matrix_diag) @cache_readonly def resid_std(self): """estimate of standard deviation of the residuals See Also -------- resid_var """ return np.sqrt(self.resid_var) def _ols_xnoti(self, drop_idx, endog_idx='endog', store=True): """regression results from LOVO auxiliary regression with cache The result instances are stored, which could use a large amount of memory if the datasets are large. There are too many combinations to store them all, except for small problems. Parameters ---------- drop_idx : int index of exog that is dropped from the regression endog_idx : 'endog' or int If 'endog', then the endogenous variable of the result instance is regressed on the exogenous variables, excluding the one at drop_idx. If endog_idx is an integer, then the exog with that index is regressed with OLS on all other exogenous variables. (The latter is the auxiliary regression for the variance inflation factor.) this needs more thought, memory versus speed not yet used in any other parts, not sufficiently tested """ # reverse the structure, access store, if fail calculate ? # this creates keys in store even if store = false ! bug if endog_idx == 'endog': stored = self.aux_regression_endog if hasattr(stored, drop_idx): return stored[drop_idx] x_i = self.results.model.endog else: # nested dictionary try: self.aux_regression_exog[endog_idx][drop_idx] except KeyError: pass stored = self.aux_regression_exog[endog_idx] stored = {} x_i = self.exog[:, endog_idx] k_vars = self.exog.shape[1] mask = np.arange(k_vars) != drop_idx x_noti = self.exog[:, mask] res = OLS(x_i, x_noti).fit() if store: stored[drop_idx] = res return res def _get_drop_vari(self, attributes): """ regress endog on exog without one of the variables This uses a k_vars loop, only attributes of the OLS instance are stored. Parameters ---------- attributes : list[str] These are the names of the attributes of the auxiliary OLS results instance that are stored and returned. not yet used """ from statsmodels.sandbox.tools.cross_val import LeaveOneOut endog = self.results.model.endog exog = self.exog cv_iter = LeaveOneOut(self.k_vars) res_loo = defaultdict(list) for inidx, outidx in cv_iter: for att in attributes: res_i = self.model_class(endog, exog[:, inidx]).fit() res_loo[att].append(getattr(res_i, att)) return res_loo @cache_readonly def _res_looo(self): """collect required results from the LOOO loop all results will be attached. currently only 'params', 'mse_resid', 'det_cov_params' are stored regresses endog on exog dropping one observation at a time this uses a nobs loop, only attributes of the OLS instance are stored. """ from statsmodels.sandbox.tools.cross_val import LeaveOneOut def get_det_cov_params(res): return np.linalg.det(res.cov_params()) endog = self.results.model.endog exog = self.results.model.exog params = np.zeros(exog.shape, dtype=float) mse_resid = np.zeros(endog.shape, dtype=float) det_cov_params = np.zeros(endog.shape, dtype=float) cv_iter = LeaveOneOut(self.nobs) for inidx, outidx in cv_iter: res_i = self.model_class(endog[inidx], exog[inidx]).fit() params[outidx] = res_i.params mse_resid[outidx] = res_i.mse_resid det_cov_params[outidx] = get_det_cov_params(res_i) return dict(params=params, mse_resid=mse_resid, det_cov_params=det_cov_params) def summary_frame(self): """ Creates a DataFrame with all available influence results. Returns ------- frame : DataFrame A DataFrame with all results. Notes ----- The resultant DataFrame contains six variables in addition to the DFBETAS. These are: * cooks_d : Cook's Distance defined in `Influence.cooks_distance` * standard_resid : Standardized residuals defined in `Influence.resid_studentized_internal` * hat_diag : The diagonal of the projection, or hat, matrix defined in `Influence.hat_matrix_diag` * dffits_internal : DFFITS statistics using internally Studentized residuals defined in `Influence.dffits_internal` * dffits : DFFITS statistics using externally Studentized residuals defined in `Influence.dffits` * student_resid : Externally Studentized residuals defined in `Influence.resid_studentized_external` """ from pandas import DataFrame # row and column labels data = self.results.model.data row_labels = data.row_labels beta_labels = ['dfb_' + i for i in data.xnames] # grab the results summary_data = DataFrame(dict( cooks_d=self.cooks_distance[0], standard_resid=self.resid_studentized_internal, hat_diag=self.hat_matrix_diag, dffits_internal=self.dffits_internal[0], student_resid=self.resid_studentized_external, dffits=self.dffits[0], ), index=row_labels) # NOTE: if we do not give columns, order of above will be arbitrary dfbeta = DataFrame(self.dfbetas, columns=beta_labels, index=row_labels) return dfbeta.join(summary_data) def summary_table(self, float_fmt="%6.3f"): """create a summary table with all influence and outlier measures This does currently not distinguish between statistics that can be calculated from the original regression results and for which a leave-one-observation-out loop is needed Returns ------- res : SimpleTable SimpleTable instance with the results, can be printed Notes ----- This also attaches table_data to the instance. """ # print self.dfbetas # table_raw = [ np.arange(self.nobs), # self.endog, # self.fittedvalues, # self.cooks_distance(), # self.resid_studentized_internal, # self.hat_matrix_diag, # self.dffits_internal, # self.resid_studentized_external, # self.dffits, # self.dfbetas # ] table_raw = [('obs', np.arange(self.nobs)), ('endog', self.endog), ('fitted\nvalue', self.results.fittedvalues), ("Cook's\nd", self.cooks_distance[0]), ("student.\nresidual", self.resid_studentized_internal), ('hat diag', self.hat_matrix_diag), ('dffits \ninternal', self.dffits_internal[0]), ("ext.stud.\nresidual", self.resid_studentized_external), ('dffits', self.dffits[0]) ] colnames, data = lzip(*table_raw) # unzip data = np.column_stack(data) self.table_data = data from statsmodels.iolib.table import SimpleTable, default_html_fmt from statsmodels.iolib.tableformatting import fmt_base from copy import deepcopy fmt = deepcopy(fmt_base) fmt_html = deepcopy(default_html_fmt) fmt['data_fmts'] = ["%4d"] + [float_fmt] * (data.shape[1] - 1) # fmt_html['data_fmts'] = fmt['data_fmts'] return SimpleTable(data, headers=colnames, txt_fmt=fmt, html_fmt=fmt_html) def summary_table(res, alpha=0.05): """ Generate summary table of outlier and influence similar to SAS Parameters ---------- alpha : float significance level for confidence interval Returns ------- st : SimpleTable table with results that can be printed data : ndarray calculated measures and statistics for the table ss2 : list[str] column_names for table (Note: rows of table are observations) """ from scipy import stats from statsmodels.sandbox.regression.predstd import wls_prediction_std infl = OLSInfluence(res) # standard error for predicted mean # Note: using hat_matrix only works for fitted values predict_mean_se = np.sqrt(infl.hat_matrix_diag * res.mse_resid) tppf = stats.t.isf(alpha / 2., res.df_resid) predict_mean_ci = np.column_stack([ res.fittedvalues - tppf * predict_mean_se, res.fittedvalues + tppf * predict_mean_se]) # standard error for predicted observation tmp = wls_prediction_std(res, alpha=alpha) predict_se, predict_ci_low, predict_ci_upp = tmp predict_ci = np.column_stack((predict_ci_low, predict_ci_upp)) # standard deviation of residual resid_se = np.sqrt(res.mse_resid * (1 - infl.hat_matrix_diag)) table_sm = np.column_stack([ np.arange(res.nobs) + 1, res.model.endog, res.fittedvalues, predict_mean_se, predict_mean_ci[:, 0], predict_mean_ci[:, 1], predict_ci[:, 0], predict_ci[:, 1], res.resid, resid_se, infl.resid_studentized_internal, infl.cooks_distance[0] ]) # colnames, data = lzip(*table_raw) #unzip data = table_sm ss2 = ['Obs', 'Dep Var\nPopulation', 'Predicted\nValue', 'Std Error\nMean Predict', 'Mean ci\n95% low', 'Mean ci\n95% upp', 'Predict ci\n95% low', 'Predict ci\n95% upp', 'Residual', 'Std Error\nResidual', 'Student\nResidual', "Cook's\nD"] colnames = ss2 # self.table_data = data # data = np.column_stack(data) from statsmodels.iolib.table import SimpleTable, default_html_fmt from statsmodels.iolib.tableformatting import fmt_base from copy import deepcopy fmt = deepcopy(fmt_base) fmt_html = deepcopy(default_html_fmt) fmt['data_fmts'] = ["%4d"] + ["%6.3f"] * (data.shape[1] - 1) # fmt_html['data_fmts'] = fmt['data_fmts'] st = SimpleTable(data, headers=colnames, txt_fmt=fmt, html_fmt=fmt_html) return st, data, ss2 class GLMInfluence(MLEInfluence): """Influence and outlier measures (experimental) This uses partly formulas specific to GLM, specifically cooks_distance is based on the hessian, i.e. observed or expected information matrix and not on cov_params, in contrast to MLEInfluence. Standardization for changes in parameters, in fittedvalues and in the linear predictor are based on cov_params. Parameters ---------- results : instance of results class This only works for model and results classes that have the necessary helper methods. other arguments are only to override default behavior and are used instead of the corresponding attribute of the results class. By default resid_pearson is used as resid. Attributes ---------- dbetas change in parameters divided by the standard error of parameters from the full model results, ``bse``. d_fittedvalues_scaled same as d_fittedvalues but scaled by the standard errors of a predicted mean of the response. d_linpred local change in linear prediction. d_linpred_scale local change in linear prediction scaled by the standard errors for the prediction based on cov_params. Notes ----- This has not yet been tested for correctness when offset or exposure are used, although they should be supported by the code. Some GLM specific measures like d_deviance are still missing. Computing an explicit leave-one-observation-out (LOOO) loop is included but no influence measures are currently computed from it. """ @cache_readonly def hat_matrix_diag(self): """ Diagonal of the hat_matrix for GLM Notes ----- This returns the diagonal of the hat matrix that was provided as argument to GLMInfluence or computes it using the results method `get_hat_matrix`. """ if hasattr(self, '_hat_matrix_diag'): return self._hat_matrix_diag else: return self.results.get_hat_matrix() @cache_readonly def d_params(self): """Change in parameter estimates Notes ----- This uses one-step approximation of the parameter change to deleting one observation. """ beta_i = np.linalg.pinv(self.exog) * self.resid_studentized beta_i /= np.sqrt(1 - self.hat_matrix_diag) return beta_i.T # same computation as OLS @cache_readonly def resid_studentized(self): """ Internally studentized pearson residuals Notes ----- residuals / sqrt( scale * (1 - hii)) where residuals are those provided to GLMInfluence which are pearson residuals by default, and hii is the diagonal of the hat matrix. """ hii = self.hat_matrix_diag return self.resid / np.sqrt(self.scale * (1 - hii)) # same computation as OLS @cache_readonly def cooks_distance(self): """Cook's distance Notes ----- Based on one step approximation using resid_studentized and hat_matrix_diag for the computation. Cook's distance divides by the number of explanatory variables. Computed using formulas for GLM and does not use results.cov_params. It includes p-values based on the F-distribution which are only approximate outside of linear Gaussian models. """ hii = self.hat_matrix_diag # Eubank p.93, 94 cooks_d2 = self.resid_studentized ** 2 / self.k_vars cooks_d2 *= hii / (1 - hii) from scipy import stats # alpha = 0.1 # print stats.f.isf(1-alpha, n_params, res.df_modelwc) pvals = stats.f.sf(cooks_d2, self.k_vars, self.results.df_resid) return cooks_d2, pvals @property def d_linpred(self): """ Change in linear prediction This uses one-step approximation of the parameter change to deleting one observation ``d_params``. """ # TODO: This will need adjustment for extra params in Poisson # use original model exog not transformed influence exog exog = self.results.model.exog return (exog * self.d_params).sum(1) @property def d_linpred_scaled(self): """ Change in linpred scaled by standard errors This uses one-step approximation of the parameter change to deleting one observation ``d_params``, and divides by the standard errors for linpred provided by results.get_prediction. """ # Note: this and the previous methods are for the response # and not for a weighted response, i.e. not the self.exog, self.endog # this will be relevant for WLS comparing fitted endog versus wendog return self.d_linpred / self._get_prediction.linpred.se_mean @property def _fittedvalues_one(self): """experimental code """ import warnings warnings.warn('this ignores offset and exposure', UserWarning) # TODO: we need to handle offset, exposure and weights # use original model exog not transformed influence exog exog = self.results.model.exog fitted = np.array([self.results.model.predict(pi, exog[i]) for i, pi in enumerate(self.params_one)]) return fitted.squeeze() @property def _diff_fittedvalues_one(self): """experimental code """ # in discrete we cannot reuse results.fittedvalues return self.results.predict() - self._fittedvalues_one @cache_readonly def _res_looo(self): """collect required results from the LOOO loop all results will be attached. currently only 'params', 'mse_resid', 'det_cov_params' are stored Reestimates the model with endog and exog dropping one observation at a time This uses a nobs loop, only attributes of the results instance are stored. Warning: This will need refactoring and API changes to be able to add options. """ from statsmodels.sandbox.tools.cross_val import LeaveOneOut get_det_cov_params = lambda res: np.linalg.det(res.cov_params()) endog = self.results.model.endog exog = self.results.model.exog init_kwds = self.results.model._get_init_kwds() # We need to drop obs also from extra arrays freq_weights = init_kwds.pop('freq_weights') var_weights = init_kwds.pop('var_weights') offset = offset_ = init_kwds.pop('offset') exposure = exposure_ = init_kwds.pop('exposure') n_trials = init_kwds.pop('n_trials', None) # family Binomial creates `n` i.e. `n_trials` # we need to reset it # TODO: figure out how to do this properly if hasattr(init_kwds['family'], 'initialize'): # assume we have Binomial is_binomial = True else: is_binomial = False params = np.zeros(exog.shape, dtype=float) scale = np.zeros(endog.shape, dtype=float) det_cov_params = np.zeros(endog.shape, dtype=float) cv_iter = LeaveOneOut(self.nobs) for inidx, outidx in cv_iter: if offset is not None: offset_ = offset[inidx] if exposure is not None: exposure_ = exposure[inidx] if n_trials is not None: init_kwds['n_trials'] = n_trials[inidx] mod_i = self.model_class(endog[inidx], exog[inidx], offset=offset_, exposure=exposure_, freq_weights=freq_weights[inidx], var_weights=var_weights[inidx], **init_kwds) if is_binomial: mod_i.family.n = init_kwds['n_trials'] res_i = mod_i.fit(start_params=self.results.params, method='newton') params[outidx] = res_i.params.copy() scale[outidx] = res_i.scale det_cov_params[outidx] = get_det_cov_params(res_i) return dict(params=params, scale=scale, mse_resid=scale, # alias for now det_cov_params=det_cov_params) statsmodels-0.12.2/statsmodels/stats/power.py000066400000000000000000001460671400612667500213710ustar00rootroot00000000000000# -*- coding: utf-8 -*- #pylint: disable-msg=W0142 """Statistical power, solving for nobs, ... - trial version Created on Sat Jan 12 21:48:06 2013 Author: Josef Perktold Example roundtrip - root with respect to all variables calculated, desired nobs 33.367204205 33.367204205 effect 0.5 0.5 alpha 0.05 0.05 power 0.8 0.8 TODO: refactoring - rename beta -> power, beta (type 2 error is beta = 1-power) DONE - I think the current implementation can handle any kinds of extra keywords (except for maybe raising meaningful exceptions - streamline code, I think internally classes can be merged how to extend to k-sample tests? user interface for different tests that map to the same (internal) test class - sequence of arguments might be inconsistent, arg and/or kwds so python checks what's required and what can be None. - templating for docstrings ? """ import numpy as np from scipy import stats, optimize from statsmodels.tools.rootfinding import brentq_expanding def ttest_power(effect_size, nobs, alpha, df=None, alternative='two-sided'): '''Calculate power of a ttest ''' d = effect_size if df is None: df = nobs - 1 if alternative in ['two-sided', '2s']: alpha_ = alpha / 2. #no inplace changes, does not work elif alternative in ['smaller', 'larger']: alpha_ = alpha else: raise ValueError("alternative has to be 'two-sided', 'larger' " + "or 'smaller'") pow_ = 0 if alternative in ['two-sided', '2s', 'larger']: crit_upp = stats.t.isf(alpha_, df) #print crit_upp, df, d*np.sqrt(nobs) # use private methods, generic methods return nan with negative d if np.any(np.isnan(crit_upp)): # avoid endless loop, https://github.com/scipy/scipy/issues/2667 pow_ = np.nan else: pow_ = stats.nct._sf(crit_upp, df, d*np.sqrt(nobs)) if alternative in ['two-sided', '2s', 'smaller']: crit_low = stats.t.ppf(alpha_, df) #print crit_low, df, d*np.sqrt(nobs) if np.any(np.isnan(crit_low)): pow_ = np.nan else: pow_ += stats.nct._cdf(crit_low, df, d*np.sqrt(nobs)) return pow_ def normal_power(effect_size, nobs, alpha, alternative='two-sided', sigma=1.): """Calculate power of a normal distributed test statistic This is an generalization of `normal_power` when variance under Null and Alternative differ. Parameters ---------- effect size : float difference in the estimated means or statistics under the alternative normalized by the standard deviation (without division by sqrt(nobs). nobs : float or int number of observations alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. alternative : string, 'two-sided' (default), 'larger', 'smaller' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either 'larger', 'smaller'. """ d = effect_size if alternative in ['two-sided', '2s']: alpha_ = alpha / 2. #no inplace changes, does not work elif alternative in ['smaller', 'larger']: alpha_ = alpha else: raise ValueError("alternative has to be 'two-sided', 'larger' " + "or 'smaller'") pow_ = 0 if alternative in ['two-sided', '2s', 'larger']: crit = stats.norm.isf(alpha_) pow_ = stats.norm.sf(crit - d*np.sqrt(nobs)/sigma) if alternative in ['two-sided', '2s', 'smaller']: crit = stats.norm.ppf(alpha_) pow_ += stats.norm.cdf(crit - d*np.sqrt(nobs)/sigma) return pow_ def normal_power_het(diff, nobs, alpha, std_null=1., std_alternative=None, alternative='two-sided'): """Calculate power of a normal distributed test statistic This is an generalization of `normal_power` when variance under Null and Alternative differ. Parameters ---------- diff : float difference in the estimated means or statistics under the alternative. nobs : float or int number of observations alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. std_null : float standard deviation under the Null hypothesis without division by sqrt(nobs) std_null : float standard deviation under the Alternative hypothesis without division by sqrt(nobs) alternative : string, 'two-sided' (default), 'larger', 'smaller' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either 'larger', 'smaller'. Returns ------- power : float """ d = diff if std_alternative is None: std_alternative = std_null if alternative in ['two-sided', '2s']: alpha_ = alpha / 2. #no inplace changes, does not work elif alternative in ['smaller', 'larger']: alpha_ = alpha else: raise ValueError("alternative has to be 'two-sided', 'larger' " + "or 'smaller'") std_ratio = std_null / std_alternative pow_ = 0 if alternative in ['two-sided', '2s', 'larger']: crit = stats.norm.isf(alpha_) pow_ = stats.norm.sf(crit * std_ratio - d*np.sqrt(nobs) / std_alternative) if alternative in ['two-sided', '2s', 'smaller']: crit = stats.norm.ppf(alpha_) pow_ += stats.norm.cdf(crit * std_ratio - d*np.sqrt(nobs) / std_alternative) return pow_ def normal_sample_size_one_tail(diff, power, alpha, std_null=1., std_alternative=None): """explicit sample size computation if only one tail is relevant The sample size is based on the power in one tail assuming that the alternative is in the tail where the test has power that increases with sample size. Use alpha/2 to compute the one tail approximation to the two-sided test, i.e. consider only one tail of two-sided test. Parameters ---------- diff : float difference in the estimated means or statistics under the alternative. power : float in interval (alpha, 1) number of observations alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. std_null : float standard deviation under the Null hypothesis without division by sqrt(nobs) std_null : float standard deviation under the Alternative hypothesis without division by sqrt(nobs) Returns ------- nobs : float sample size to achieve the desired power """ crit_power = stats.norm.isf(power) crit = stats.norm.isf(alpha) n1 = ((crit * std_null - crit_power * std_alternative) / diff)**2 return n1 def ftest_anova_power(effect_size, nobs, alpha, k_groups=2, df=None): '''power for ftest for one way anova with k equal sized groups nobs total sample size, sum over all groups should be general nobs observations, k_groups restrictions ??? ''' df_num = nobs - k_groups df_denom = k_groups - 1 crit = stats.f.isf(alpha, df_denom, df_num) pow_ = stats.ncf.sf(crit, df_denom, df_num, effect_size**2 * nobs) return pow_#, crit def ftest_power(effect_size, df_num, df_denom, alpha, ncc=1): '''Calculate the power of a F-test. Parameters ---------- effect_size : float standardized effect size, mean divided by the standard deviation. effect size has to be positive. df_num : int or float numerator degrees of freedom. df_denom : int or float denominator degrees of freedom. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. ncc : int degrees of freedom correction for non-centrality parameter. see Notes Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. Notes ----- sample size is given implicitly by df_num set ncc=0 to match t-test, or f-test in LikelihoodModelResults. ncc=1 matches the non-centrality parameter in R::pwr::pwr.f2.test ftest_power with ncc=0 should also be correct for f_test in regression models, with df_num and d_denom as defined there. (not verified yet) ''' nc = effect_size**2 * (df_denom + df_num + ncc) crit = stats.f.isf(alpha, df_denom, df_num) pow_ = stats.ncf.sf(crit, df_denom, df_num, nc) return pow_ #, crit, nc #class based implementation #-------------------------- class Power(object): '''Statistical Power calculations, Base Class so far this could all be class methods ''' def __init__(self, **kwds): self.__dict__.update(kwds) # used only for instance level start values self.start_ttp = dict(effect_size=0.01, nobs=10., alpha=0.15, power=0.6, nobs1=10., ratio=1, df_num=10, df_denom=3 # for FTestPower ) # TODO: nobs1 and ratio are for ttest_ind, # need start_ttp for each test/class separately, # possible rootfinding problem for effect_size, starting small seems to # work from collections import defaultdict self.start_bqexp = defaultdict(dict) for key in ['nobs', 'nobs1', 'df_num', 'df_denom']: self.start_bqexp[key] = dict(low=2., start_upp=50.) for key in ['df_denom']: self.start_bqexp[key] = dict(low=1., start_upp=50.) for key in ['ratio']: self.start_bqexp[key] = dict(low=1e-8, start_upp=2) for key in ['alpha']: self.start_bqexp[key] = dict(low=1e-12, upp=1 - 1e-12) def power(self, *args, **kwds): raise NotImplementedError def _power_identity(self, *args, **kwds): power_ = kwds.pop('power') return self.power(*args, **kwds) - power_ def solve_power(self, **kwds): '''solve for any one of the parameters of a t-test for t-test the keywords are: effect_size, nobs, alpha, power exactly one needs to be ``None``, all others need numeric values *attaches* cache_fit_res : list Cache of the result of the root finding procedure for the latest call to ``solve_power``, mainly for debugging purposes. The first element is the success indicator, one if successful. The remaining elements contain the return information of the up to three solvers that have been tried. ''' #TODO: maybe use explicit kwds, # nicer but requires inspect? and not generic across tests # I'm duplicating this in the subclass to get informative docstring key = [k for k,v in kwds.items() if v is None] #print kwds, key if len(key) != 1: raise ValueError('need exactly one keyword that is None') key = key[0] if key == 'power': del kwds['power'] return self.power(**kwds) if kwds['effect_size'] == 0: import warnings from statsmodels.tools.sm_exceptions import HypothesisTestWarning warnings.warn('Warning: Effect size of 0 detected', HypothesisTestWarning) if key == 'power': return kwds['alpha'] if key == 'alpha': return kwds['power'] else: raise ValueError('Cannot detect an effect-size of 0. Try changing your effect-size.') self._counter = 0 def func(x): kwds[key] = x fval = self._power_identity(**kwds) self._counter += 1 #print self._counter, if self._counter > 500: raise RuntimeError('possible endless loop (500 NaNs)') if np.isnan(fval): return np.inf else: return fval #TODO: I'm using the following so I get a warning when start_ttp is not defined try: start_value = self.start_ttp[key] except KeyError: start_value = 0.9 import warnings from statsmodels.tools.sm_exceptions import ValueWarning warnings.warn('Warning: using default start_value for {0}'.format(key), ValueWarning) fit_kwds = self.start_bqexp[key] fit_res = [] #print vars() try: val, res = brentq_expanding(func, full_output=True, **fit_kwds) failed = False fit_res.append(res) except ValueError: failed = True fit_res.append(None) success = None if (not failed) and res.converged: success = 1 else: # try backup # TODO: check more cases to make this robust if not np.isnan(start_value): val, infodict, ier, msg = optimize.fsolve(func, start_value, full_output=True) #scalar #val = optimize.newton(func, start_value) #scalar fval = infodict['fvec'] fit_res.append(infodict) else: ier = -1 fval = 1 fit_res.append([None]) if ier == 1 and np.abs(fval) < 1e-4 : success = 1 else: #print infodict if key in ['alpha', 'power', 'effect_size']: val, r = optimize.brentq(func, 1e-8, 1-1e-8, full_output=True) #scalar success = 1 if r.converged else 0 fit_res.append(r) else: success = 0 if not success == 1: import warnings from statsmodels.tools.sm_exceptions import (ConvergenceWarning, convergence_doc) warnings.warn(convergence_doc, ConvergenceWarning) #attach fit_res, for reading only, should be needed only for debugging fit_res.insert(0, success) self.cache_fit_res = fit_res return val def plot_power(self, dep_var='nobs', nobs=None, effect_size=None, alpha=0.05, ax=None, title=None, plt_kwds=None, **kwds): """ Plot power with number of observations or effect size on x-axis Parameters ---------- dep_var : {'nobs', 'effect_size', 'alpha'} This specifies which variable is used for the horizontal axis. If dep_var='nobs' (default), then one curve is created for each value of ``effect_size``. If dep_var='effect_size' or alpha, then one curve is created for each value of ``nobs``. nobs : {scalar, array_like} specifies the values of the number of observations in the plot effect_size : {scalar, array_like} specifies the values of the effect_size in the plot alpha : {float, array_like} The significance level (type I error) used in the power calculation. Can only be more than a scalar, if ``dep_var='alpha'`` ax : None or axis instance If ax is None, than a matplotlib figure is created. If ax is a matplotlib axis instance, then it is reused, and the plot elements are created with it. title : str title for the axis. Use an empty string, ``''``, to avoid a title. plt_kwds : {None, dict} not used yet kwds : dict These remaining keyword arguments are used as arguments to the power function. Many power function support ``alternative`` as a keyword argument, two-sample test support ``ratio``. Returns ------- Figure If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. Notes ----- This works only for classes where the ``power`` method has ``effect_size``, ``nobs`` and ``alpha`` as the first three arguments. If the second argument is ``nobs1``, then the number of observations in the plot are those for the first sample. TODO: fix this for FTestPower and GofChisquarePower TODO: maybe add line variable, if we want more than nobs and effectsize """ #if pwr_kwds is None: # pwr_kwds = {} from statsmodels.graphics import utils from statsmodels.graphics.plottools import rainbow fig, ax = utils.create_mpl_ax(ax) import matplotlib.pyplot as plt colormap = plt.cm.Dark2 #pylint: disable-msg=E1101 plt_alpha = 1 #0.75 lw = 2 if dep_var == 'nobs': colors = rainbow(len(effect_size)) colors = [colormap(i) for i in np.linspace(0, 0.9, len(effect_size))] for ii, es in enumerate(effect_size): power = self.power(es, nobs, alpha, **kwds) ax.plot(nobs, power, lw=lw, alpha=plt_alpha, color=colors[ii], label='es=%4.2F' % es) xlabel = 'Number of Observations' elif dep_var in ['effect size', 'effect_size', 'es']: colors = rainbow(len(nobs)) colors = [colormap(i) for i in np.linspace(0, 0.9, len(nobs))] for ii, n in enumerate(nobs): power = self.power(effect_size, n, alpha, **kwds) ax.plot(effect_size, power, lw=lw, alpha=plt_alpha, color=colors[ii], label='N=%4.2F' % n) xlabel = 'Effect Size' elif dep_var in ['alpha']: # experimental nobs as defining separate lines colors = rainbow(len(nobs)) for ii, n in enumerate(nobs): power = self.power(effect_size, n, alpha, **kwds) ax.plot(alpha, power, lw=lw, alpha=plt_alpha, color=colors[ii], label='N=%4.2F' % n) xlabel = 'alpha' else: raise ValueError('depvar not implemented') if title is None: title = 'Power of Test' ax.set_xlabel(xlabel) ax.set_title(title) ax.legend(loc='lower right') return fig class TTestPower(Power): '''Statistical Power calculations for one sample or paired sample t-test ''' def power(self, effect_size, nobs, alpha, df=None, alternative='two-sided'): '''Calculate the power of a t-test for one sample or paired samples. Parameters ---------- effect_size : float standardized effect size, mean divided by the standard deviation. effect size has to be positive. nobs : int or float sample size, number of observations. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. df : int or float degrees of freedom. By default this is None, and the df from the one sample or paired ttest is used, ``df = nobs1 - 1`` alternative : str, 'two-sided' (default), 'larger', 'smaller' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either 'larger', 'smaller'. . Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. ''' # for debugging #print 'calling ttest power with', (effect_size, nobs, alpha, df, alternative) return ttest_power(effect_size, nobs, alpha, df=df, alternative=alternative) #method is only added to have explicit keywords and docstring def solve_power(self, effect_size=None, nobs=None, alpha=None, power=None, alternative='two-sided'): '''solve for any one parameter of the power of a one sample t-test for the one sample t-test the keywords are: effect_size, nobs, alpha, power Exactly one needs to be ``None``, all others need numeric values. This test can also be used for a paired t-test, where effect size is defined in terms of the mean difference, and nobs is the number of pairs. Parameters ---------- effect_size : float standardized effect size, mean divided by the standard deviation. effect size has to be positive. nobs : int or float sample size, number of observations. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. power : float in interval (0,1) power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. alternative : str, 'two-sided' (default) or 'one-sided' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. 'one-sided' assumes we are in the relevant tail. Returns ------- value : float The value of the parameter that was set to None in the call. The value solves the power equation given the remaining parameters. *attaches* cache_fit_res : list Cache of the result of the root finding procedure for the latest call to ``solve_power``, mainly for debugging purposes. The first element is the success indicator, one if successful. The remaining elements contain the return information of the up to three solvers that have been tried. Notes ----- The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses ``brentq`` with a prior search for bounds. If this fails to find a root, ``fsolve`` is used. If ``fsolve`` also fails, then, for ``alpha``, ``power`` and ``effect_size``, ``brentq`` with fixed bounds is used. However, there can still be cases where this fails. ''' # for debugging #print 'calling ttest solve with', (effect_size, nobs, alpha, power, alternative) return super(TTestPower, self).solve_power(effect_size=effect_size, nobs=nobs, alpha=alpha, power=power, alternative=alternative) class TTestIndPower(Power): '''Statistical Power calculations for t-test for two independent sample currently only uses pooled variance ''' def power(self, effect_size, nobs1, alpha, ratio=1, df=None, alternative='two-sided'): '''Calculate the power of a t-test for two independent sample Parameters ---------- effect_size : float standardized effect size, difference between the two means divided by the standard deviation. `effect_size` has to be positive. nobs1 : int or float number of observations of sample 1. The number of observations of sample two is ratio times the size of sample 1, i.e. ``nobs2 = nobs1 * ratio`` alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. ratio : float ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1 The default for ratio is 1; to solve for ratio given the other arguments, it has to be explicitly set to None. df : int or float degrees of freedom. By default this is None, and the df from the ttest with pooled variance is used, ``df = (nobs1 - 1 + nobs2 - 1)`` alternative : str, 'two-sided' (default), 'larger', 'smaller' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either 'larger', 'smaller'. Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. ''' nobs2 = nobs1*ratio #pooled variance if df is None: df = (nobs1 - 1 + nobs2 - 1) nobs = 1./ (1. / nobs1 + 1. / nobs2) #print 'calling ttest power with', (effect_size, nobs, alpha, df, alternative) return ttest_power(effect_size, nobs, alpha, df=df, alternative=alternative) #method is only added to have explicit keywords and docstring def solve_power(self, effect_size=None, nobs1=None, alpha=None, power=None, ratio=1., alternative='two-sided'): '''solve for any one parameter of the power of a two sample t-test for t-test the keywords are: effect_size, nobs1, alpha, power, ratio exactly one needs to be ``None``, all others need numeric values Parameters ---------- effect_size : float standardized effect size, difference between the two means divided by the standard deviation. `effect_size` has to be positive. nobs1 : int or float number of observations of sample 1. The number of observations of sample two is ratio times the size of sample 1, i.e. ``nobs2 = nobs1 * ratio`` alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. power : float in interval (0,1) power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. ratio : float ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1 The default for ratio is 1; to solve for ratio given the other arguments it has to be explicitly set to None. alternative : str, 'two-sided' (default), 'larger', 'smaller' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either 'larger', 'smaller'. Returns ------- value : float The value of the parameter that was set to None in the call. The value solves the power equation given the remaining parameters. Notes ----- The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses ``brentq`` with a prior search for bounds. If this fails to find a root, ``fsolve`` is used. If ``fsolve`` also fails, then, for ``alpha``, ``power`` and ``effect_size``, ``brentq`` with fixed bounds is used. However, there can still be cases where this fails. ''' return super(TTestIndPower, self).solve_power(effect_size=effect_size, nobs1=nobs1, alpha=alpha, power=power, ratio=ratio, alternative=alternative) class NormalIndPower(Power): '''Statistical Power calculations for z-test for two independent samples. currently only uses pooled variance ''' def __init__(self, ddof=0, **kwds): self.ddof = ddof super(NormalIndPower, self).__init__(**kwds) def power(self, effect_size, nobs1, alpha, ratio=1, alternative='two-sided'): '''Calculate the power of a z-test for two independent sample Parameters ---------- effect_size : float standardized effect size, difference between the two means divided by the standard deviation. effect size has to be positive. nobs1 : int or float number of observations of sample 1. The number of observations of sample two is ratio times the size of sample 1, i.e. ``nobs2 = nobs1 * ratio`` ``ratio`` can be set to zero in order to get the power for a one sample test. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. ratio : float ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1 alternative : str, 'two-sided' (default), 'larger', 'smaller' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either 'larger', 'smaller'. Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. ''' ddof = self.ddof # for correlation, ddof=3 # get effective nobs, factor for std of test statistic if ratio > 0: nobs2 = nobs1*ratio #equivalent to nobs = n1*n2/(n1+n2)=n1*ratio/(1+ratio) nobs = 1./ (1. / (nobs1 - ddof) + 1. / (nobs2 - ddof)) else: nobs = nobs1 - ddof return normal_power(effect_size, nobs, alpha, alternative=alternative) #method is only added to have explicit keywords and docstring def solve_power(self, effect_size=None, nobs1=None, alpha=None, power=None, ratio=1., alternative='two-sided'): '''solve for any one parameter of the power of a two sample z-test for z-test the keywords are: effect_size, nobs1, alpha, power, ratio exactly one needs to be ``None``, all others need numeric values Parameters ---------- effect_size : float standardized effect size, difference between the two means divided by the standard deviation. If ratio=0, then this is the standardized mean in the one sample test. nobs1 : int or float number of observations of sample 1. The number of observations of sample two is ratio times the size of sample 1, i.e. ``nobs2 = nobs1 * ratio`` ``ratio`` can be set to zero in order to get the power for a one sample test. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. power : float in interval (0,1) power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. ratio : float ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1 The default for ratio is 1; to solve for ration given the other arguments it has to be explicitly set to None. alternative : str, 'two-sided' (default), 'larger', 'smaller' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either 'larger', 'smaller'. Returns ------- value : float The value of the parameter that was set to None in the call. The value solves the power equation given the remaining parameters. Notes ----- The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses ``brentq`` with a prior search for bounds. If this fails to find a root, ``fsolve`` is used. If ``fsolve`` also fails, then, for ``alpha``, ``power`` and ``effect_size``, ``brentq`` with fixed bounds is used. However, there can still be cases where this fails. ''' return super(NormalIndPower, self).solve_power(effect_size=effect_size, nobs1=nobs1, alpha=alpha, power=power, ratio=ratio, alternative=alternative) class FTestPower(Power): '''Statistical Power calculations for generic F-test ''' def power(self, effect_size, df_num, df_denom, alpha, ncc=1): '''Calculate the power of a F-test. Parameters ---------- effect_size : float standardized effect size, mean divided by the standard deviation. effect size has to be positive. df_num : int or float numerator degrees of freedom. df_denom : int or float denominator degrees of freedom. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. ncc : int degrees of freedom correction for non-centrality parameter. see Notes Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. Notes ----- sample size is given implicitly by df_num set ncc=0 to match t-test, or f-test in LikelihoodModelResults. ncc=1 matches the non-centrality parameter in R::pwr::pwr.f2.test ftest_power with ncc=0 should also be correct for f_test in regression models, with df_num and d_denom as defined there. (not verified yet) ''' pow_ = ftest_power(effect_size, df_num, df_denom, alpha, ncc=ncc) #print effect_size, df_num, df_denom, alpha, pow_ return pow_ #method is only added to have explicit keywords and docstring def solve_power(self, effect_size=None, df_num=None, df_denom=None, nobs=None, alpha=None, power=None, ncc=1): '''solve for any one parameter of the power of a F-test for the one sample F-test the keywords are: effect_size, df_num, df_denom, alpha, power Exactly one needs to be ``None``, all others need numeric values. Parameters ---------- effect_size : float standardized effect size, mean divided by the standard deviation. effect size has to be positive. nobs : int or float sample size, number of observations. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. power : float in interval (0,1) power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. alternative : str, 'two-sided' (default) or 'one-sided' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. 'one-sided' assumes we are in the relevant tail. Returns ------- value : float The value of the parameter that was set to None in the call. The value solves the power equation given the remaining parameters. Notes ----- The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses ``brentq`` with a prior search for bounds. If this fails to find a root, ``fsolve`` is used. If ``fsolve`` also fails, then, for ``alpha``, ``power`` and ``effect_size``, ``brentq`` with fixed bounds is used. However, there can still be cases where this fails. ''' return super(FTestPower, self).solve_power(effect_size=effect_size, df_num=df_num, df_denom=df_denom, alpha=alpha, power=power, ncc=ncc) class FTestAnovaPower(Power): '''Statistical Power calculations F-test for one factor balanced ANOVA ''' def power(self, effect_size, nobs, alpha, k_groups=2): '''Calculate the power of a F-test for one factor ANOVA. Parameters ---------- effect_size : float standardized effect size, mean divided by the standard deviation. effect size has to be positive. nobs : int or float sample size, number of observations. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. k_groups : int or float number of groups in the ANOVA or k-sample comparison. Default is 2. Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. ''' return ftest_anova_power(effect_size, nobs, alpha, k_groups=k_groups) #method is only added to have explicit keywords and docstring def solve_power(self, effect_size=None, nobs=None, alpha=None, power=None, k_groups=2): '''solve for any one parameter of the power of a F-test for the one sample F-test the keywords are: effect_size, nobs, alpha, power Exactly one needs to be ``None``, all others need numeric values. Parameters ---------- effect_size : float standardized effect size, mean divided by the standard deviation. effect size has to be positive. nobs : int or float sample size, number of observations. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. power : float in interval (0,1) power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. Returns ------- value : float The value of the parameter that was set to None in the call. The value solves the power equation given the remaining parameters. Notes ----- The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses ``brentq`` with a prior search for bounds. If this fails to find a root, ``fsolve`` is used. If ``fsolve`` also fails, then, for ``alpha``, ``power`` and ``effect_size``, ``brentq`` with fixed bounds is used. However, there can still be cases where this fails. ''' # update start values for root finding if k_groups is not None: self.start_ttp['nobs'] = k_groups * 10 self.start_bqexp['nobs'] = dict(low=k_groups * 2, start_upp=k_groups * 10) # first attempt at special casing if effect_size is None: return self._solve_effect_size(effect_size=effect_size, nobs=nobs, alpha=alpha, k_groups=k_groups, power=power) return super(FTestAnovaPower, self).solve_power(effect_size=effect_size, nobs=nobs, alpha=alpha, k_groups=k_groups, power=power) def _solve_effect_size(self, effect_size=None, nobs=None, alpha=None, power=None, k_groups=2): '''experimental, test failure in solve_power for effect_size ''' def func(x): effect_size = x return self._power_identity(effect_size=effect_size, nobs=nobs, alpha=alpha, k_groups=k_groups, power=power) val, r = optimize.brentq(func, 1e-8, 1-1e-8, full_output=True) if not r.converged: print(r) return val class GofChisquarePower(Power): '''Statistical Power calculations for one sample chisquare test ''' def power(self, effect_size, nobs, alpha, n_bins, ddof=0):#alternative='two-sided'): '''Calculate the power of a chisquare test for one sample Only two-sided alternative is implemented Parameters ---------- effect_size : float standardized effect size, according to Cohen's definition. see :func:`statsmodels.stats.gof.chisquare_effectsize` nobs : int or float sample size, number of observations. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. n_bins : int number of bins or cells in the distribution. Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. ''' from statsmodels.stats.gof import chisquare_power return chisquare_power(effect_size, nobs, n_bins, alpha, ddof=0) #method is only added to have explicit keywords and docstring def solve_power(self, effect_size=None, nobs=None, alpha=None, power=None, n_bins=2): '''solve for any one parameter of the power of a one sample chisquare-test for the one sample chisquare-test the keywords are: effect_size, nobs, alpha, power Exactly one needs to be ``None``, all others need numeric values. n_bins needs to be defined, a default=2 is used. Parameters ---------- effect_size : float standardized effect size, according to Cohen's definition. see :func:`statsmodels.stats.gof.chisquare_effectsize` nobs : int or float sample size, number of observations. alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. power : float in interval (0,1) power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. n_bins : int number of bins or cells in the distribution Returns ------- value : float The value of the parameter that was set to None in the call. The value solves the power equation given the remaining parameters. Notes ----- The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses ``brentq`` with a prior search for bounds. If this fails to find a root, ``fsolve`` is used. If ``fsolve`` also fails, then, for ``alpha``, ``power`` and ``effect_size``, ``brentq`` with fixed bounds is used. However, there can still be cases where this fails. ''' return super(GofChisquarePower, self).solve_power(effect_size=effect_size, nobs=nobs, n_bins=n_bins, alpha=alpha, power=power) class _GofChisquareIndPower(Power): '''Statistical Power calculations for chisquare goodness-of-fit test TODO: this is not working yet for 2sample case need two nobs in function no one-sided chisquare test, is there one? use normal distribution? -> drop one-sided options? ''' def power(self, effect_size, nobs1, alpha, ratio=1, alternative='two-sided'): '''Calculate the power of a chisquare for two independent sample Parameters ---------- effect_size : float standardize effect size, difference between the two means divided by the standard deviation. effect size has to be positive. nobs1 : int or float number of observations of sample 1. The number of observations of sample two is ratio times the size of sample 1, i.e. ``nobs2 = nobs1 * ratio`` alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. ratio : float ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1 The default for ratio is 1; to solve for ration given the other arguments it has to be explicitely set to None. alternative : str, 'two-sided' (default) or 'one-sided' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. 'one-sided' assumes we are in the relevant tail. Returns ------- power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. ''' from statsmodels.stats.gof import chisquare_power nobs2 = nobs1*ratio #equivalent to nobs = n1*n2/(n1+n2)=n1*ratio/(1+ratio) nobs = 1./ (1. / nobs1 + 1. / nobs2) return chisquare_power(effect_size, nobs, alpha) #method is only added to have explicit keywords and docstring def solve_power(self, effect_size=None, nobs1=None, alpha=None, power=None, ratio=1., alternative='two-sided'): '''solve for any one parameter of the power of a two sample z-test for z-test the keywords are: effect_size, nobs1, alpha, power, ratio exactly one needs to be ``None``, all others need numeric values Parameters ---------- effect_size : float standardize effect size, difference between the two means divided by the standard deviation. nobs1 : int or float number of observations of sample 1. The number of observations of sample two is ratio times the size of sample 1, i.e. ``nobs2 = nobs1 * ratio`` alpha : float in interval (0,1) significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. power : float in interval (0,1) power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. ratio : float ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1 The default for ratio is 1; to solve for ration given the other arguments it has to be explicitely set to None. alternative : str, 'two-sided' (default) or 'one-sided' extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. 'one-sided' assumes we are in the relevant tail. Returns ------- value : float The value of the parameter that was set to None in the call. The value solves the power equation given the remaining parameters. Notes ----- The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses ``brentq`` with a prior search for bounds. If this fails to find a root, ``fsolve`` is used. If ``fsolve`` also fails, then, for ``alpha``, ``power`` and ``effect_size``, ``brentq`` with fixed bounds is used. However, there can still be cases where this fails. ''' return super(_GofChisquareIndPower, self).solve_power(effect_size=effect_size, nobs1=nobs1, alpha=alpha, power=power, ratio=ratio, alternative=alternative) #shortcut functions tt_solve_power = TTestPower().solve_power tt_ind_solve_power = TTestIndPower().solve_power zt_ind_solve_power = NormalIndPower().solve_power statsmodels-0.12.2/statsmodels/stats/proportion.py000066400000000000000000002307431400612667500224430ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Tests and Confidence Intervals for Binomial Proportions Created on Fri Mar 01 00:23:07 2013 Author: Josef Perktold License: BSD-3 """ from statsmodels.compat.python import lzip import numpy as np from scipy import stats, optimize from sys import float_info from statsmodels.stats.base import AllPairsResults from statsmodels.tools.sm_exceptions import HypothesisTestWarning from statsmodels.stats.weightstats import _zstat_generic2 from statsmodels.stats.base import HolderTuple from statsmodels.tools.testing import Holder def proportion_confint(count, nobs, alpha=0.05, method='normal'): '''confidence interval for a binomial proportion Parameters ---------- count : int or array_array_like number of successes, can be pandas Series or DataFrame nobs : int total number of trials alpha : float in (0, 1) significance level, default 0.05 method : {'normal', 'agresti_coull', 'beta', 'wilson', 'binom_test'} default: 'normal' method to use for confidence interval, currently available methods : - `normal` : asymptotic normal approximation - `agresti_coull` : Agresti-Coull interval - `beta` : Clopper-Pearson interval based on Beta distribution - `wilson` : Wilson Score interval - `jeffreys` : Jeffreys Bayesian Interval - `binom_test` : experimental, inversion of binom_test Returns ------- ci_low, ci_upp : float, ndarray, or pandas Series or DataFrame lower and upper confidence level with coverage (approximately) 1-alpha. When a pandas object is returned, then the index is taken from the `count`. Notes ----- Beta, the Clopper-Pearson exact interval has coverage at least 1-alpha, but is in general conservative. Most of the other methods have average coverage equal to 1-alpha, but will have smaller coverage in some cases. The 'beta' and 'jeffreys' interval are central, they use alpha/2 in each tail, and alpha is not adjusted at the boundaries. In the extreme case when `count` is zero or equal to `nobs`, then the coverage will be only 1 - alpha/2 in the case of 'beta'. The confidence intervals are clipped to be in the [0, 1] interval in the case of 'normal' and 'agresti_coull'. Method "binom_test" directly inverts the binomial test in scipy.stats. which has discrete steps. TODO: binom_test intervals raise an exception in small samples if one interval bound is close to zero or one. References ---------- https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval Brown, Lawrence D.; Cai, T. Tony; DasGupta, Anirban (2001). "Interval Estimation for a Binomial Proportion", Statistical Science 16 (2): 101–133. doi:10.1214/ss/1009213286. TODO: Is this the correct one ? ''' pd_index = getattr(count, 'index', None) if pd_index is not None and callable(pd_index): # this rules out lists, lists have an index method pd_index = None count = np.asarray(count) nobs = np.asarray(nobs) q_ = count * 1. / nobs alpha_2 = 0.5 * alpha if method == 'normal': std_ = np.sqrt(q_ * (1 - q_) / nobs) dist = stats.norm.isf(alpha / 2.) * std_ ci_low = q_ - dist ci_upp = q_ + dist elif method == 'binom_test': # inverting the binomial test def func(qi): return stats.binom_test(q_ * nobs, nobs, p=qi) - alpha if count == 0: ci_low = 0 else: ci_low = optimize.brentq(func, float_info.min, q_) if count == nobs: ci_upp = 1 else: ci_upp = optimize.brentq(func, q_, 1. - float_info.epsilon) elif method == 'beta': ci_low = stats.beta.ppf(alpha_2, count, nobs - count + 1) ci_upp = stats.beta.isf(alpha_2, count + 1, nobs - count) if np.ndim(ci_low) > 0: ci_low[q_ == 0] = 0 ci_upp[q_ == 1] = 1 else: ci_low = ci_low if (q_ != 0) else 0 ci_upp = ci_upp if (q_ != 1) else 1 elif method == 'agresti_coull': crit = stats.norm.isf(alpha / 2.) nobs_c = nobs + crit**2 q_c = (count + crit**2 / 2.) / nobs_c std_c = np.sqrt(q_c * (1. - q_c) / nobs_c) dist = crit * std_c ci_low = q_c - dist ci_upp = q_c + dist elif method == 'wilson': crit = stats.norm.isf(alpha / 2.) crit2 = crit**2 denom = 1 + crit2 / nobs center = (q_ + crit2 / (2 * nobs)) / denom dist = crit * np.sqrt(q_ * (1. - q_) / nobs + crit2 / (4. * nobs**2)) dist /= denom ci_low = center - dist ci_upp = center + dist # method adjusted to be more forgiving of misspellings or incorrect option name elif method[:4] == 'jeff': ci_low, ci_upp = stats.beta.interval(1 - alpha, count + 0.5, nobs - count + 0.5) else: raise NotImplementedError('method "%s" is not available' % method) if method in ['normal', 'agresti_coull']: ci_low = np.clip(ci_low, 0, 1) ci_upp = np.clip(ci_upp, 0, 1) if pd_index is not None and np.ndim(ci_low) > 0: import pandas as pd if np.ndim(ci_low) == 1: ci_low = pd.Series(ci_low, index=pd_index) ci_upp = pd.Series(ci_upp, index=pd_index) if np.ndim(ci_low) == 2: ci_low = pd.DataFrame(ci_low, index=pd_index) ci_upp = pd.DataFrame(ci_upp, index=pd_index) return ci_low, ci_upp def multinomial_proportions_confint(counts, alpha=0.05, method='goodman'): '''Confidence intervals for multinomial proportions. Parameters ---------- counts : array_like of int, 1-D Number of observations in each category. alpha : float in (0, 1), optional Significance level, defaults to 0.05. method : {'goodman', 'sison-glaz'}, optional Method to use to compute the confidence intervals; available methods are: - `goodman`: based on a chi-squared approximation, valid if all values in `counts` are greater or equal to 5 [2]_ - `sison-glaz`: less conservative than `goodman`, but only valid if `counts` has 7 or more categories (``len(counts) >= 7``) [3]_ Returns ------- confint : ndarray, 2-D Array of [lower, upper] confidence levels for each category, such that overall coverage is (approximately) `1-alpha`. Raises ------ ValueError If `alpha` is not in `(0, 1)` (bounds excluded), or if the values in `counts` are not all positive or null. NotImplementedError If `method` is not kown. Exception When ``method == 'sison-glaz'``, if for some reason `c` cannot be computed; this signals a bug and should be reported. Notes ----- The `goodman` method [2]_ is based on approximating a statistic based on the multinomial as a chi-squared random variable. The usual recommendation is that this is valid if all the values in `counts` are greater than or equal to 5. There is no condition on the number of categories for this method. The `sison-glaz` method [3]_ approximates the multinomial probabilities, and evaluates that with a maximum-likelihood estimator. The first approximation is an Edgeworth expansion that converges when the number of categories goes to infinity, and the maximum-likelihood estimator converges when the number of observations (``sum(counts)``) goes to infinity. In their paper, Sison & Glaz demo their method with at least 7 categories, so ``len(counts) >= 7`` with all values in `counts` at or above 5 can be used as a rule of thumb for the validity of this method. This method is less conservative than the `goodman` method (i.e. it will yield confidence intervals closer to the desired significance level), but produces confidence intervals of uniform width over all categories (except when the intervals reach 0 or 1, in which case they are truncated), which makes it most useful when proportions are of similar magnitude. Aside from the original sources ([1]_, [2]_, and [3]_), the implementation uses the formulas (though not the code) presented in [4]_ and [5]_. References ---------- .. [1] Levin, Bruce, "A representation for multinomial cumulative distribution functions," The Annals of Statistics, Vol. 9, No. 5, 1981, pp. 1123-1126. .. [2] Goodman, L.A., "On simultaneous confidence intervals for multinomial proportions," Technometrics, Vol. 7, No. 2, 1965, pp. 247-254. .. [3] Sison, Cristina P., and Joseph Glaz, "Simultaneous Confidence Intervals and Sample Size Determination for Multinomial Proportions," Journal of the American Statistical Association, Vol. 90, No. 429, 1995, pp. 366-369. .. [4] May, Warren L., and William D. Johnson, "A SAS® macro for constructing simultaneous confidence intervals for multinomial proportions," Computer methods and programs in Biomedicine, Vol. 53, No. 3, 1997, pp. 153-162. .. [5] May, Warren L., and William D. Johnson, "Constructing two-sided simultaneous confidence intervals for multinomial proportions for small counts in a large number of cells," Journal of Statistical Software, Vol. 5, No. 6, 2000, pp. 1-24. ''' if alpha <= 0 or alpha >= 1: raise ValueError('alpha must be in (0, 1), bounds excluded') counts = np.array(counts, dtype=float) if (counts < 0).any(): raise ValueError('counts must be >= 0') n = counts.sum() k = len(counts) proportions = counts / n if method == 'goodman': chi2 = stats.chi2.ppf(1 - alpha / k, 1) delta = chi2 ** 2 + (4 * n * proportions * chi2 * (1 - proportions)) region = ((2 * n * proportions + chi2 + np.array([- np.sqrt(delta), np.sqrt(delta)])) / (2 * (chi2 + n))).T elif method[:5] == 'sison': # We accept any name starting with 'sison' # Define a few functions we'll use a lot. def poisson_interval(interval, p): """Compute P(b <= Z <= a) where Z ~ Poisson(p) and `interval = (b, a)`.""" b, a = interval prob = stats.poisson.cdf(a, p) - stats.poisson.cdf(b - 1, p) if p == 0 and np.isnan(prob): # hack for older scipy <=0.16.1 return int(b - 1 < 0) return prob def truncated_poisson_factorial_moment(interval, r, p): """Compute mu_r, the r-th factorial moment of a poisson random variable of parameter `p` truncated to `interval = (b, a)`.""" b, a = interval return p ** r * (1 - ((poisson_interval((a - r + 1, a), p) - poisson_interval((b - r, b - 1), p)) / poisson_interval((b, a), p))) def edgeworth(intervals): """Compute the Edgeworth expansion term of Sison & Glaz's formula (1) (approximated probability for multinomial proportions in a given box).""" # Compute means and central moments of the truncated poisson # variables. mu_r1, mu_r2, mu_r3, mu_r4 = [ np.array([truncated_poisson_factorial_moment(interval, r, p) for (interval, p) in zip(intervals, counts)]) for r in range(1, 5) ] mu = mu_r1 mu2 = mu_r2 + mu - mu ** 2 mu3 = mu_r3 + mu_r2 * (3 - 3 * mu) + mu - 3 * mu ** 2 + 2 * mu ** 3 mu4 = (mu_r4 + mu_r3 * (6 - 4 * mu) + mu_r2 * (7 - 12 * mu + 6 * mu ** 2) + mu - 4 * mu ** 2 + 6 * mu ** 3 - 3 * mu ** 4) # Compute expansion factors, gamma_1 and gamma_2. g1 = mu3.sum() / mu2.sum() ** 1.5 g2 = (mu4.sum() - 3 * (mu2 ** 2).sum()) / mu2.sum() ** 2 # Compute the expansion itself. x = (n - mu.sum()) / np.sqrt(mu2.sum()) phi = np.exp(- x ** 2 / 2) / np.sqrt(2 * np.pi) H3 = x ** 3 - 3 * x H4 = x ** 4 - 6 * x ** 2 + 3 H6 = x ** 6 - 15 * x ** 4 + 45 * x ** 2 - 15 f = phi * (1 + g1 * H3 / 6 + g2 * H4 / 24 + g1 ** 2 * H6 / 72) return f / np.sqrt(mu2.sum()) def approximated_multinomial_interval(intervals): """Compute approximated probability for Multinomial(n, proportions) to be in `intervals` (Sison & Glaz's formula (1)).""" return np.exp( np.sum(np.log([poisson_interval(interval, p) for (interval, p) in zip(intervals, counts)])) + np.log(edgeworth(intervals)) - np.log(stats.poisson._pmf(n, n)) ) def nu(c): """Compute interval coverage for a given `c` (Sison & Glaz's formula (7)).""" return approximated_multinomial_interval( [(np.maximum(count - c, 0), np.minimum(count + c, n)) for count in counts]) # Find the value of `c` that will give us the confidence intervals # (solving nu(c) <= 1 - alpha < nu(c + 1). c = 1.0 nuc = nu(c) nucp1 = nu(c + 1) while not (nuc <= (1 - alpha) < nucp1): if c > n: raise Exception("Couldn't find a value for `c` that " "solves nu(c) <= 1 - alpha < nu(c + 1)") c += 1 nuc = nucp1 nucp1 = nu(c + 1) # Compute gamma and the corresponding confidence intervals. g = (1 - alpha - nuc) / (nucp1 - nuc) ci_lower = np.maximum(proportions - c / n, 0) ci_upper = np.minimum(proportions + (c + 2 * g) / n, 1) region = np.array([ci_lower, ci_upper]).T else: raise NotImplementedError('method "%s" is not available' % method) return region def samplesize_confint_proportion(proportion, half_length, alpha=0.05, method='normal'): '''find sample size to get desired confidence interval length Parameters ---------- proportion : float in (0, 1) proportion or quantile half_length : float in (0, 1) desired half length of the confidence interval alpha : float in (0, 1) significance level, default 0.05, coverage of the two-sided interval is (approximately) ``1 - alpha`` method : str in ['normal'] method to use for confidence interval, currently only normal approximation Returns ------- n : float sample size to get the desired half length of the confidence interval Notes ----- this is mainly to store the formula. possible application: number of replications in bootstrap samples ''' q_ = proportion if method == 'normal': n = q_ * (1 - q_) / (half_length / stats.norm.isf(alpha / 2.))**2 else: raise NotImplementedError('only "normal" is available') return n def proportion_effectsize(prop1, prop2, method='normal'): ''' Effect size for a test comparing two proportions for use in power function Parameters ---------- prop1, prop2 : float or array_like The proportion value(s). Returns ------- es : float or ndarray effect size for (transformed) prop1 - prop2 Notes ----- only method='normal' is implemented to match pwr.p2.test see http://www.statmethods.net/stats/power.html Effect size for `normal` is defined as :: 2 * (arcsin(sqrt(prop1)) - arcsin(sqrt(prop2))) I think other conversions to normality can be used, but I need to check. Examples -------- >>> import statsmodels.api as sm >>> sm.stats.proportion_effectsize(0.5, 0.4) 0.20135792079033088 >>> sm.stats.proportion_effectsize([0.3, 0.4, 0.5], 0.4) array([-0.21015893, 0. , 0.20135792]) ''' if method != 'normal': raise ValueError('only "normal" is implemented') es = 2 * (np.arcsin(np.sqrt(prop1)) - np.arcsin(np.sqrt(prop2))) return es def std_prop(prop, nobs): '''standard error for the estimate of a proportion This is just ``np.sqrt(p * (1. - p) / nobs)`` Parameters ---------- prop : array_like proportion nobs : int, array_like number of observations Returns ------- std : array_like standard error for a proportion of nobs independent observations ''' return np.sqrt(prop * (1. - prop) / nobs) def _std_diff_prop(p1, p2, ratio=1): return np.sqrt(p1 * (1 - p1) + p2 * (1 - p2) / ratio) def _power_ztost(mean_low, var_low, mean_upp, var_upp, mean_alt, var_alt, alpha=0.05, discrete=True, dist='norm', nobs=None, continuity=0, critval_continuity=0): '''Generic statistical power function for normal based equivalence test This includes options to adjust the normal approximation and can use the binomial to evaluate the probability of the rejection region see power_ztost_prob for a description of the options ''' # TODO: refactor structure, separate norm and binom better if not isinstance(continuity, tuple): continuity = (continuity, continuity) crit = stats.norm.isf(alpha) k_low = mean_low + np.sqrt(var_low) * crit k_upp = mean_upp - np.sqrt(var_upp) * crit if discrete or dist == 'binom': k_low = np.ceil(k_low * nobs + 0.5 * critval_continuity) k_upp = np.trunc(k_upp * nobs - 0.5 * critval_continuity) if dist == 'norm': #need proportion k_low = (k_low) * 1. / nobs #-1 to match PASS k_upp = k_upp * 1. / nobs # else: # if dist == 'binom': # #need counts # k_low *= nobs # k_upp *= nobs #print mean_low, np.sqrt(var_low), crit, var_low #print mean_upp, np.sqrt(var_upp), crit, var_upp if np.any(k_low > k_upp): #vectorize import warnings warnings.warn("no overlap, power is zero", HypothesisTestWarning) std_alt = np.sqrt(var_alt) z_low = (k_low - mean_alt - continuity[0] * 0.5 / nobs) / std_alt z_upp = (k_upp - mean_alt + continuity[1] * 0.5 / nobs) / std_alt if dist == 'norm': power = stats.norm.cdf(z_upp) - stats.norm.cdf(z_low) elif dist == 'binom': power = (stats.binom.cdf(k_upp, nobs, mean_alt) - stats.binom.cdf(k_low-1, nobs, mean_alt)) return power, (k_low, k_upp, z_low, z_upp) def binom_tost(count, nobs, low, upp): '''exact TOST test for one proportion using binomial distribution Parameters ---------- count : {int, array_like} the number of successes in nobs trials. nobs : int the number of trials or observations. low, upp : floats lower and upper limit of equivalence region Returns ------- pvalue : float p-value of equivalence test pval_low, pval_upp : floats p-values of lower and upper one-sided tests ''' # binom_test_stat only returns pval tt1 = binom_test(count, nobs, alternative='larger', prop=low) tt2 = binom_test(count, nobs, alternative='smaller', prop=upp) return np.maximum(tt1, tt2), tt1, tt2, def binom_tost_reject_interval(low, upp, nobs, alpha=0.05): '''rejection region for binomial TOST The interval includes the end points, `reject` if and only if `r_low <= x <= r_upp`. The interval might be empty with `r_upp < r_low`. Parameters ---------- low, upp : floats lower and upper limit of equivalence region nobs : int the number of trials or observations. Returns ------- x_low, x_upp : float lower and upper bound of rejection region ''' x_low = stats.binom.isf(alpha, nobs, low) + 1 x_upp = stats.binom.ppf(alpha, nobs, upp) - 1 return x_low, x_upp def binom_test_reject_interval(value, nobs, alpha=0.05, alternative='two-sided'): '''rejection region for binomial test for one sample proportion The interval includes the end points of the rejection region. Parameters ---------- value : float proportion under the Null hypothesis nobs : int the number of trials or observations. Returns ------- x_low, x_upp : float lower and upper bound of rejection region ''' if alternative in ['2s', 'two-sided']: alternative = '2s' # normalize alternative name alpha = alpha / 2 if alternative in ['2s', 'smaller']: x_low = stats.binom.ppf(alpha, nobs, value) - 1 else: x_low = 0 if alternative in ['2s', 'larger']: x_upp = stats.binom.isf(alpha, nobs, value) + 1 else : x_upp = nobs return x_low, x_upp def binom_test(count, nobs, prop=0.5, alternative='two-sided'): '''Perform a test that the probability of success is p. This is an exact, two-sided test of the null hypothesis that the probability of success in a Bernoulli experiment is `p`. Parameters ---------- count : {int, array_like} the number of successes in nobs trials. nobs : int the number of trials or observations. prop : float, optional The probability of success under the null hypothesis, `0 <= prop <= 1`. The default value is `prop = 0.5` alternative : str in ['two-sided', 'smaller', 'larger'] alternative hypothesis, which can be two-sided or either one of the one-sided tests. Returns ------- p-value : float The p-value of the hypothesis test Notes ----- This uses scipy.stats.binom_test for the two-sided alternative. ''' if np.any(prop > 1.0) or np.any(prop < 0.0): raise ValueError("p must be in range [0,1]") if alternative in ['2s', 'two-sided']: pval = stats.binom_test(count, n=nobs, p=prop) elif alternative in ['l', 'larger']: pval = stats.binom.sf(count-1, nobs, prop) elif alternative in ['s', 'smaller']: pval = stats.binom.cdf(count, nobs, prop) else: raise ValueError('alternative not recognized\n' 'should be two-sided, larger or smaller') return pval def power_binom_tost(low, upp, nobs, p_alt=None, alpha=0.05): if p_alt is None: p_alt = 0.5 * (low + upp) x_low, x_upp = binom_tost_reject_interval(low, upp, nobs, alpha=alpha) power = (stats.binom.cdf(x_upp, nobs, p_alt) - stats.binom.cdf(x_low-1, nobs, p_alt)) return power def power_ztost_prop(low, upp, nobs, p_alt, alpha=0.05, dist='norm', variance_prop=None, discrete=True, continuity=0, critval_continuity=0): '''Power of proportions equivalence test based on normal distribution Parameters ---------- low, upp : floats lower and upper limit of equivalence region nobs : int number of observations p_alt : float in (0,1) proportion under the alternative alpha : float in (0,1) significance level of the test dist : str in ['norm', 'binom'] This defines the distribution to evaluate the power of the test. The critical values of the TOST test are always based on the normal approximation, but the distribution for the power can be either the normal (default) or the binomial (exact) distribution. variance_prop : None or float in (0,1) If this is None, then the variances for the two one sided tests are based on the proportions equal to the equivalence limits. If variance_prop is given, then it is used to calculate the variance for the TOST statistics. If this is based on an sample, then the estimated proportion can be used. discrete : bool If true, then the critical values of the rejection region are converted to integers. If dist is "binom", this is automatically assumed. If discrete is false, then the TOST critical values are used as floating point numbers, and the power is calculated based on the rejection region that is not discretized. continuity : bool or float adjust the rejection region for the normal power probability. This has and effect only if ``dist='norm'`` critval_continuity : bool or float If this is non-zero, then the critical values of the tost rejection region are adjusted before converting to integers. This affects both distributions, ``dist='norm'`` and ``dist='binom'``. Returns ------- power : float statistical power of the equivalence test. (k_low, k_upp, z_low, z_upp) : tuple of floats critical limits in intermediate steps temporary return, will be changed Notes ----- In small samples the power for the ``discrete`` version, has a sawtooth pattern as a function of the number of observations. As a consequence, small changes in the number of observations or in the normal approximation can have a large effect on the power. ``continuity`` and ``critval_continuity`` are added to match some results of PASS, and are mainly to investigate the sensitivity of the ztost power to small changes in the rejection region. From my interpretation of the equations in the SAS manual, both are zero in SAS. works vectorized **verification:** The ``dist='binom'`` results match PASS, The ``dist='norm'`` results look reasonable, but no benchmark is available. References ---------- SAS Manual: Chapter 68: The Power Procedure, Computational Resources PASS Chapter 110: Equivalence Tests for One Proportion. ''' mean_low = low var_low = std_prop(low, nobs)**2 mean_upp = upp var_upp = std_prop(upp, nobs)**2 mean_alt = p_alt var_alt = std_prop(p_alt, nobs)**2 if variance_prop is not None: var_low = var_upp = std_prop(variance_prop, nobs)**2 power = _power_ztost(mean_low, var_low, mean_upp, var_upp, mean_alt, var_alt, alpha=alpha, discrete=discrete, dist=dist, nobs=nobs, continuity=continuity, critval_continuity=critval_continuity) return np.maximum(power[0], 0), power[1:] def _table_proportion(count, nobs): '''create a k by 2 contingency table for proportion helper function for proportions_chisquare Parameters ---------- count : {int, array_like} the number of successes in nobs trials. nobs : int the number of trials or observations. Returns ------- table : ndarray (k, 2) contingency table Notes ----- recent scipy has more elaborate contingency table functions ''' table = np.column_stack((count, nobs - count)) expected = table.sum(0) * table.sum(1)[:,None] * 1. / table.sum() n_rows = table.shape[0] return table, expected, n_rows def proportions_ztest(count, nobs, value=None, alternative='two-sided', prop_var=False): """ Test for proportions based on normal (z) test Parameters ---------- count : {int, array_like} the number of successes in nobs trials. If this is array_like, then the assumption is that this represents the number of successes for each independent sample nobs : {int, array_like} the number of trials or observations, with the same length as count. value : float, array_like or None, optional This is the value of the null hypothesis equal to the proportion in the case of a one sample test. In the case of a two-sample test, the null hypothesis is that prop[0] - prop[1] = value, where prop is the proportion in the two samples. If not provided value = 0 and the null is prop[0] = prop[1] alternative : str in ['two-sided', 'smaller', 'larger'] The alternative hypothesis can be either two-sided or one of the one- sided tests, smaller means that the alternative hypothesis is ``prop < value`` and larger means ``prop > value``. In the two sample test, smaller means that the alternative hypothesis is ``p1 < p2`` and larger means ``p1 > p2`` where ``p1`` is the proportion of the first sample and ``p2`` of the second one. prop_var : False or float in (0, 1) If prop_var is false, then the variance of the proportion estimate is calculated based on the sample proportion. Alternatively, a proportion can be specified to calculate this variance. Common use case is to use the proportion under the Null hypothesis to specify the variance of the proportion estimate. Returns ------- zstat : float test statistic for the z-test p-value : float p-value for the z-test Examples -------- >>> count = 5 >>> nobs = 83 >>> value = .05 >>> stat, pval = proportions_ztest(count, nobs, value) >>> print('{0:0.3f}'.format(pval)) 0.695 >>> import numpy as np >>> from statsmodels.stats.proportion import proportions_ztest >>> count = np.array([5, 12]) >>> nobs = np.array([83, 99]) >>> stat, pval = proportions_ztest(count, nobs) >>> print('{0:0.3f}'.format(pval)) 0.159 Notes ----- This uses a simple normal test for proportions. It should be the same as running the mean z-test on the data encoded 1 for event and 0 for no event so that the sum corresponds to the count. In the one and two sample cases with two-sided alternative, this test produces the same p-value as ``proportions_chisquare``, since the chisquare is the distribution of the square of a standard normal distribution. """ # TODO: verify that this really holds # TODO: add continuity correction or other improvements for small samples # TODO: change options similar to propotion_ztost ? count = np.asarray(count) nobs = np.asarray(nobs) if nobs.size == 1: nobs = nobs * np.ones_like(count) prop = count * 1. / nobs k_sample = np.size(prop) if value is None: if k_sample == 1: raise ValueError('value must be provided for a 1-sample test') value = 0 if k_sample == 1: diff = prop - value elif k_sample == 2: diff = prop[0] - prop[1] - value else: msg = 'more than two samples are not implemented yet' raise NotImplementedError(msg) p_pooled = np.sum(count) * 1. / np.sum(nobs) nobs_fact = np.sum(1. / nobs) if prop_var: p_pooled = prop_var var_ = p_pooled * (1 - p_pooled) * nobs_fact std_diff = np.sqrt(var_) from statsmodels.stats.weightstats import _zstat_generic2 return _zstat_generic2(diff, std_diff, alternative) def proportions_ztost(count, nobs, low, upp, prop_var='sample'): '''Equivalence test based on normal distribution Parameters ---------- count : {int, array_like} the number of successes in nobs trials. If this is array_like, then the assumption is that this represents the number of successes for each independent sample nobs : int the number of trials or observations, with the same length as count. low, upp : float equivalence interval low < prop1 - prop2 < upp prop_var : str or float in (0, 1) prop_var determines which proportion is used for the calculation of the standard deviation of the proportion estimate The available options for string are 'sample' (default), 'null' and 'limits'. If prop_var is a float, then it is used directly. Returns ------- pvalue : float pvalue of the non-equivalence test t1, pv1 : tuple of floats test statistic and pvalue for lower threshold test t2, pv2 : tuple of floats test statistic and pvalue for upper threshold test Notes ----- checked only for 1 sample case ''' if prop_var == 'limits': prop_var_low = low prop_var_upp = upp elif prop_var == 'sample': prop_var_low = prop_var_upp = False #ztest uses sample elif prop_var == 'null': prop_var_low = prop_var_upp = 0.5 * (low + upp) elif np.isreal(prop_var): prop_var_low = prop_var_upp = prop_var tt1 = proportions_ztest(count, nobs, alternative='larger', prop_var=prop_var_low, value=low) tt2 = proportions_ztest(count, nobs, alternative='smaller', prop_var=prop_var_upp, value=upp) return np.maximum(tt1[1], tt2[1]), tt1, tt2, def proportions_chisquare(count, nobs, value=None): '''test for proportions based on chisquare test Parameters ---------- count : {int, array_like} the number of successes in nobs trials. If this is array_like, then the assumption is that this represents the number of successes for each independent sample nobs : int the number of trials or observations, with the same length as count. value : None or float or array_like Returns ------- chi2stat : float test statistic for the chisquare test p-value : float p-value for the chisquare test (table, expected) table is a (k, 2) contingency table, ``expected`` is the corresponding table of counts that are expected under independence with given margins Notes ----- Recent version of scipy.stats have a chisquare test for independence in contingency tables. This function provides a similar interface to chisquare tests as ``prop.test`` in R, however without the option for Yates continuity correction. count can be the count for the number of events for a single proportion, or the counts for several independent proportions. If value is given, then all proportions are jointly tested against this value. If value is not given and count and nobs are not scalar, then the null hypothesis is that all samples have the same proportion. ''' nobs = np.atleast_1d(nobs) table, expected, n_rows = _table_proportion(count, nobs) if value is not None: expected = np.column_stack((nobs * value, nobs * (1 - value))) ddof = n_rows - 1 else: ddof = n_rows #print table, expected chi2stat, pval = stats.chisquare(table.ravel(), expected.ravel(), ddof=ddof) return chi2stat, pval, (table, expected) def proportions_chisquare_allpairs(count, nobs, multitest_method='hs'): '''chisquare test of proportions for all pairs of k samples Performs a chisquare test for proportions for all pairwise comparisons. The alternative is two-sided Parameters ---------- count : {int, array_like} the number of successes in nobs trials. nobs : int the number of trials or observations. prop : float, optional The probability of success under the null hypothesis, `0 <= prop <= 1`. The default value is `prop = 0.5` multitest_method : str This chooses the method for the multiple testing p-value correction, that is used as default in the results. It can be any method that is available in ``multipletesting``. The default is Holm-Sidak 'hs'. Returns ------- result : AllPairsResults instance The returned results instance has several statistics, such as p-values, attached, and additional methods for using a non-default ``multitest_method``. Notes ----- Yates continuity correction is not available. ''' #all_pairs = lmap(list, lzip(*np.triu_indices(4, 1))) all_pairs = lzip(*np.triu_indices(len(count), 1)) pvals = [proportions_chisquare(count[list(pair)], nobs[list(pair)])[1] for pair in all_pairs] return AllPairsResults(pvals, all_pairs, multitest_method=multitest_method) def proportions_chisquare_pairscontrol(count, nobs, value=None, multitest_method='hs', alternative='two-sided'): '''chisquare test of proportions for pairs of k samples compared to control Performs a chisquare test for proportions for pairwise comparisons with a control (Dunnet's test). The control is assumed to be the first element of ``count`` and ``nobs``. The alternative is two-sided, larger or smaller. Parameters ---------- count : {int, array_like} the number of successes in nobs trials. nobs : int the number of trials or observations. prop : float, optional The probability of success under the null hypothesis, `0 <= prop <= 1`. The default value is `prop = 0.5` multitest_method : str This chooses the method for the multiple testing p-value correction, that is used as default in the results. It can be any method that is available in ``multipletesting``. The default is Holm-Sidak 'hs'. alternative : str in ['two-sided', 'smaller', 'larger'] alternative hypothesis, which can be two-sided or either one of the one-sided tests. Returns ------- result : AllPairsResults instance The returned results instance has several statistics, such as p-values, attached, and additional methods for using a non-default ``multitest_method``. Notes ----- Yates continuity correction is not available. ``value`` and ``alternative`` options are not yet implemented. ''' if (value is not None) or (alternative not in ['two-sided', '2s']): raise NotImplementedError #all_pairs = lmap(list, lzip(*np.triu_indices(4, 1))) all_pairs = [(0, k) for k in range(1, len(count))] pvals = [proportions_chisquare(count[list(pair)], nobs[list(pair)], #alternative=alternative)[1] )[1] for pair in all_pairs] return AllPairsResults(pvals, all_pairs, multitest_method=multitest_method) def confint_proportions_2indep(count1, nobs1, count2, nobs2, method=None, compare='diff', alpha=0.05, correction=True): """Confidence intervals for comparing two independent proportions This assumes that we have two independent binomial samples. Parameters ---------- count1, nobs1 : float Count and sample size for first sample. count2, nobs2 : float Count and sample size for the second sample. method : str Method for computing confidence interval. If method is None, then a default method is used. The default might change as more methods are added. diff: - 'wald', - 'agresti-caffo' - 'newcomb' (default) - 'score' ratio: - 'log' - 'log-adjusted' (default) - 'score' odds-ratio: - 'logit' - 'logit-adjusted' (default) - 'score' compare : string in ['diff', 'ratio' 'odds-ratio'] If compare is diff, then the confidence interval is for diff = p1 - p2. If compare is ratio, then the confidence interval is for the risk ratio defined by ratio = p1 / p2. If compare is odds-ratio, then the confidence interval is for the odds-ratio defined by or = p1 / (1 - p1) / (p2 / (1 - p2). alpha : float Significance level for the confidence interval, default is 0.05. The nominal coverage probability is 1 - alpha. Returns ------- low, upp Notes ----- Status: experimental, API and defaults might still change. more ``methods`` will be added. """ method_default = {'diff': 'newcomb', 'ratio': 'log-adjusted', 'odds-ratio': 'logit-adjusted'} # normalize compare name if compare.lower() == 'or': compare = 'odds-ratio' if method is None: method = method_default[compare] method = method.lower() if method.startswith('agr'): method = 'agresti-caffo' p1 = count1 / nobs1 p2 = count2 / nobs2 diff = p1 - p2 addone = 1 if method == 'agresti-caffo' else 0 if compare == 'diff': if method in ['wald', 'agresti-caffo']: count1_, nobs1_ = count1 + addone, nobs1 + 2 * addone count2_, nobs2_ = count2 + addone, nobs2 + 2 * addone p1_ = count1_ / nobs1_ p2_ = count2_ / nobs2_ diff_ = p1_ - p2_ var = p1_ * (1 - p1_) / nobs1_ + p2_ * (1 - p2_) / nobs2_ z = stats.norm.isf(alpha / 2) d_wald = z * np.sqrt(var) low = diff_ - d_wald upp = diff_ + d_wald elif method.startswith('newcomb'): low1, upp1 = proportion_confint(count1, nobs1, method='wilson', alpha=alpha) low2, upp2 = proportion_confint(count2, nobs2, method='wilson', alpha=alpha) d_low = np.sqrt((p1 - low1)**2 + (upp2 - p2)**2) d_upp = np.sqrt((p2 - low2)**2 + (upp1 - p1)**2) low = diff - d_low upp = diff + d_upp elif method == "score": low, upp = _score_confint_inversion(count1, nobs1, count2, nobs2, compare=compare, alpha=alpha, correction=correction) else: raise ValueError('method not recognized') elif compare == 'ratio': # ratio = p1 / p2 if method in ['log', 'log-adjusted']: addhalf = 0.5 if method == 'log-adjusted' else 0 count1_, nobs1_ = count1 + addhalf, nobs1 + addhalf count2_, nobs2_ = count2 + addhalf, nobs2 + addhalf p1_ = count1_ / nobs1_ p2_ = count2_ / nobs2_ ratio_ = p1_ / p2_ var = (1 / count1_) - 1 / nobs1_ + 1 / count2_ - 1 / nobs2_ z = stats.norm.isf(alpha / 2) d_log = z * np.sqrt(var) low = np.exp(np.log(ratio_) - d_log) upp = np.exp(np.log(ratio_) + d_log) elif method == 'score': res = _confint_riskratio_koopman(count1, nobs1, count2, nobs2, alpha=alpha, correction=correction) low, upp = res.confint else: raise ValueError('method not recognized') elif compare == 'odds-ratio': # odds_ratio = p1 / (1 - p1) / p2 * (1 - p2) if method in ['logit', 'logit-adjusted', 'logit-smoothed']: if method in ['logit-smoothed']: adjusted = _shrink_prob(count1, nobs1, count2, nobs2, shrink_factor=2, return_corr=False)[0] count1_, nobs1_, count2_, nobs2_ = adjusted else: addhalf = 0.5 if method == 'logit-adjusted' else 0 count1_, nobs1_ = count1 + addhalf, nobs1 + 2 * addhalf count2_, nobs2_ = count2 + addhalf, nobs2 + 2 * addhalf p1_ = count1_ / nobs1_ p2_ = count2_ / nobs2_ odds_ratio_ = p1_ / (1 - p1_) / p2_ * (1 - p2_) var = (1 / count1_ + 1 / (nobs1_ - count1_) + 1 / count2_ + 1 / (nobs2_ - count2_)) z = stats.norm.isf(alpha / 2) d_log = z * np.sqrt(var) low = np.exp(np.log(odds_ratio_) - d_log) upp = np.exp(np.log(odds_ratio_) + d_log) elif method == "score": low, upp = _score_confint_inversion(count1, nobs1, count2, nobs2, compare=compare, alpha=alpha, correction=correction) else: raise ValueError('method not recognized') else: raise ValueError('compare not recognized') return low, upp def _shrink_prob(count1, nobs1, count2, nobs2, shrink_factor=2, return_corr=True): """shrink observed counts towards independence Helper function for 'logit-smoothed' inference for the odds-ratio of two independent proportions. Parameters ---------- count1, nobs1 : float or int count and sample size for first sample count2, nobs2 : float or int count and sample size for the second sample shrink_factor : float This corresponds to the number of observations that are added in total proportional to the probabilities under independence. return_corr : bool If true, then only the correction term is returned If false, then the corrected counts, i.e. original counts plus correction term, are returned. Returns ------- count1_corr, nobs1_corr, count2_corr, nobs2_corr : float correction or corrected counts prob_indep : TODO/Warning : this will change most likely probabilities under independence, only returned if return_corr is false. """ nobs_col = np.array([count1 + count2, nobs1 - count1 + nobs2 - count2]) nobs_row = np.array([nobs1, nobs2]) nobs = nobs1 + nobs2 prob_indep = (nobs_col * nobs_row[:, None]) / nobs**2 corr = shrink_factor * prob_indep if return_corr: return (corr[0, 0], corr[0].sum(), corr[1, 0], corr[1].sum()) else: return (count1 + corr[0, 0], nobs1 + corr[0].sum(), count2 + corr[1, 0], nobs2 + corr[1].sum()), prob_indep def score_test_proportions_2indep(count1, nobs1, count2, nobs2, value=None, compare='diff', alternative='two-sided', correction=True, return_results=True): """score_test for two independent proportions This uses the constrained estimate of the proportions to compute the variance under the Null hypothesis. Parameters ---------- count1, nobs1 : count and sample size for first sample count2, nobs2 : count and sample size for the second sample value : float diff, ratio or odds-ratio under the null hypothesis. If value is None, then equality of proportions under the Null is assumed, i.e. value=0 for 'diff' or value=1 for either rate or odds-ratio. compare : string in ['diff', 'ratio' 'odds-ratio'] If compare is diff, then the confidence interval is for diff = p1 - p2. If compare is ratio, then the confidence interval is for the risk ratio defined by ratio = p1 / p2. If compare is odds-ratio, then the confidence interval is for the odds-ratio defined by or = p1 / (1 - p1) / (p2 / (1 - p2) return_results : bool If true, then a results instance with extra information is returned, otherwise a tuple with statistic and pvalue is returned. Returns ------- results : results instance or tuple If return_results is True, then a results instance with the information in attributes is returned. If return_results is False, then only ``statistic`` and ``pvalue`` are returned. statistic : float test statistic asymptotically normal distributed N(0, 1) pvalue : float p-value based on normal distribution other attributes : additional information about the hypothesis test Notes ----- Status: experimental, the type or extra information in the return might change. """ value_default = 0 if compare == 'diff' else 1 if value is None: # TODO: odds ratio does not work if value=1 value = value_default nobs = nobs1 + nobs2 count = count1 + count2 p1 = count1 / nobs1 p2 = count2 / nobs2 if value == value_default: # use pooled estimator if equality test # shortcut, but required for odds ratio prop0 = prop1 = count / nobs # this uses index 0 from Miettinen Nurminned 1985 count0, nobs0 = count2, nobs2 p0 = p2 if compare == 'diff': diff = value # hypothesis value if diff != 0: tmp3 = nobs tmp2 = (nobs1 + 2 * nobs0) * diff - nobs - count tmp1 = (count0 * diff - nobs - 2 * count0) * diff + count tmp0 = count0 * diff * (1 - diff) q = ((tmp2 / (3 * tmp3))**3 - tmp1 * tmp2 / (6 * tmp3**2) + tmp0 / (2 * tmp3)) p = np.sign(q) * np.sqrt((tmp2 / (3 * tmp3))**2 - tmp1 / (3 * tmp3)) a = (np.pi + np.arccos(q / p**3)) / 3 prop0 = 2 * p * np.cos(a) - tmp2 / (3 * tmp3) prop1 = prop0 + diff correction = True var = prop1 * (1 - prop1) / nobs1 + prop0 * (1 - prop0) / nobs0 if correction: var *= nobs / (nobs - 1) diff_stat = (p1 - p0 - diff) elif compare == 'ratio': # risk ratio ratio = value if ratio != 1: a = nobs * ratio b = -(nobs1 * ratio + count1 + nobs2 + count0 * ratio) c = count prop0 = (-b - np.sqrt(b**2 - 4 * a * c)) / (2 * a) prop1 = prop0 * ratio var = (prop1 * (1 - prop1) / nobs1 + ratio**2 * prop0 * (1 - prop0) / nobs0) if correction: var *= nobs / (nobs - 1) # NCSS looks incorrect for var, but it is what should be reported # diff_stat = (p1 / p0 - ratio) # NCSS/PASS diff_stat = (p1 - ratio * p0) # Miettinen Nurminen elif compare in ['or', 'odds-ratio']: # odds ratio oratio = value if oratio != 1: # Note the constraint estimator does not handle odds-ratio = 1 a = nobs0 * (oratio - 1) b = nobs1 * oratio + nobs0 - count * (oratio - 1) c = -count prop0 = (-b + np.sqrt(b**2 - 4 * a * c)) / (2 * a) prop1 = prop0 * oratio / (1 + prop0 * (oratio - 1)) # try to avoid 0 and 1 proportions, # those raise Zero Division Runtime Warnings eps = 1e-10 prop0 = np.clip(prop0, eps, 1 - eps) prop1 = np.clip(prop1, eps, 1 - eps) var = (1 / (prop1 * (1 - prop1) * nobs1) + 1 / (prop0 * (1 - prop0) * nobs0)) if correction: var *= nobs / (nobs - 1) diff_stat = ((p1 - prop1) / (prop1 * (1 - prop1)) - (p0 - prop0) / (prop0 * (1 - prop0))) statistic, pvalue = _zstat_generic2(diff_stat, np.sqrt(var), alternative=alternative) if return_results: res = HolderTuple(statistic=statistic, pvalue=pvalue, compare=compare, method='score', variance=var, alternative=alternative, prop1_null=prop1, prop2_null=prop0, ) return res else: return statistic, pvalue def test_proportions_2indep(count1, nobs1, count2, nobs2, value=None, method=None, compare='diff', alternative='two-sided', correction=True, return_results=True): """Hypothesis test for comparing two independent proportions This assumes that we have two independent binomial samples. The Null and alternative hypothesis are for compare = 'diff' - H0: prop1 - prop2 - value = 0 - H1: prop1 - prop2 - value != 0 if alternative = 'two-sided' - H1: prop1 - prop2 - value > 0 if alternative = 'larger' - H1: prop1 - prop2 - value < 0 if alternative = 'smaller' for compare = 'ratio' - H0: prop1 / prop2 - value = 0 - H1: prop1 / prop2 - value != 0 if alternative = 'two-sided' - H1: prop1 / prop2 - value > 0 if alternative = 'larger' - H1: prop1 / prop2 - value < 0 if alternative = 'smaller' for compare = 'odds-ratio' - H0: or - value = 0 - H1: or - value != 0 if alternative = 'two-sided' - H1: or - value > 0 if alternative = 'larger' - H1: or - value < 0 if alternative = 'smaller' where odds-ratio or = prop1 / (1 - prop1) / (prop2 / (1 - prop2)) Parameters ---------- count1 : int Count for first sample. nobs1 : int Sample size for first sample. count2 : int Count for the second sample. nobs2 : int Sample size for the second sample. method : string Method for computing confidence interval. If method is None, then a default method is used. The default might change as more methods are added. diff: - 'wald', - 'agresti-caffo' - 'score' if correction is True, then this uses the degrees of freedom correction ``nobs / (nobs - 1)`` as in Miettinen Nurminen 1985 ratio: - 'log': wald test using log transformation - 'log-adjusted': wald test using log transformation, adds 0.5 to counts - 'score' if correction is True, then this uses the degrees of freedom correction ``nobs / (nobs - 1)`` as in Miettinen Nurminen 1985 odds-ratio: - 'logit': wald test using logit transformation - 'logit-adjusted': : wald test using logit transformation, adds 0.5 to counts - 'logit-smoothed': : wald test using logit transformation, biases cell counts towards independence by adding two observations in total. - 'score' if correction is True, then this uses the degrees of freedom correction ``nobs / (nobs - 1)`` as in Miettinen Nurminen 1985 compare : {'diff', 'ratio' 'odds-ratio'} If compare is `diff`, then the confidence interval is for diff = p1 - p2. If compare is `ratio`, then the confidence interval is for the risk ratio defined by ratio = p1 / p2. If compare is `odds-ratio`, then the confidence interval is for the odds-ratio defined by or = p1 / (1 - p1) / (p2 / (1 - p2) alternative : {'two-sided', 'smaller', 'larger'} alternative hypothesis, which can be two-sided or either one of the one-sided tests. correction : bool If correction is True (default), then the Miettinen and Nurminen small sample correction to the variance nobs / (nobs - 1) is used. Applies only if method='score'. return_results : bool If true, then a results instance with extra information is returned, otherwise a tuple with statistic and pvalue is returned. Returns ------- results : results instance or tuple If return_results is True, then a results instance with the information in attributes is returned. If return_results is False, then only ``statistic`` and ``pvalue`` are returned. statistic : float test statistic asymptotically normal distributed N(0, 1) pvalue : float p-value based on normal distribution other attributes : additional information about the hypothesis test Notes ----- Status: experimental, API and defaults might still change. More ``methods`` will be added. """ method_default = {'diff': 'agresti-caffo', 'ratio': 'log-adjusted', 'odds-ratio': 'logit-adjusted'} # normalize compare name if compare.lower() == 'or': compare = 'odds-ratio' if method is None: method = method_default[compare] method = method.lower() if method.startswith('agr'): method = 'agresti-caffo' if value is None: # TODO: odds ratio does not work if value=1 for score test value = 0 if compare == 'diff' else 1 p1 = count1 / nobs1 p2 = count2 / nobs2 diff = p1 - p2 ratio = p1 / p2 odds_ratio = p1 / (1 - p1) / p2 * (1 - p2) res = None if compare == 'diff': if method in ['wald', 'agresti-caffo']: addone = 1 if method == 'agresti-caffo' else 0 count1_, nobs1_ = count1 + addone, nobs1 + 2 * addone count2_, nobs2_ = count2 + addone, nobs2 + 2 * addone p1_ = count1_ / nobs1_ p2_ = count2_ / nobs2_ diff_stat = p1_ - p2_ - value var = p1_ * (1 - p1_) / nobs1_ + p2_ * (1 - p2_) / nobs2_ statistic = diff_stat / np.sqrt(var) distr = 'normal' elif method.startswith('newcomb'): msg = 'newcomb not available for hypothesis test' raise NotImplementedError(msg) elif method == 'score': # Note score part is the same call for all compare res = score_test_proportions_2indep(count1, nobs1, count2, nobs2, value=value, compare=compare, alternative=alternative, correction=correction, return_results=return_results) if return_results is False: statistic, pvalue = res[:2] distr = 'normal' # TODO/Note score_test_proportion_2samp returns statistic and # not diff_stat diff_stat = None else: raise ValueError('method not recognized') elif compare == 'ratio': if method in ['log', 'log-adjusted']: addhalf = 0.5 if method == 'log-adjusted' else 0 count1_, nobs1_ = count1 + addhalf, nobs1 + addhalf count2_, nobs2_ = count2 + addhalf, nobs2 + addhalf p1_ = count1_ / nobs1_ p2_ = count2_ / nobs2_ ratio_ = p1_ / p2_ var = (1 / count1_) - 1 / nobs1_ + 1 / count2_ - 1 / nobs2_ diff_stat = np.log(ratio_) - np.log(value) statistic = diff_stat / np.sqrt(var) distr = 'normal' elif method == 'score': res = score_test_proportions_2indep(count1, nobs1, count2, nobs2, value=value, compare=compare, alternative=alternative, correction=correction, return_results=return_results) if return_results is False: statistic, pvalue = res[:2] distr = 'normal' diff_stat = None else: raise ValueError('method not recognized') elif compare == "odds-ratio": if method in ['logit', 'logit-adjusted', 'logit-smoothed']: if method in ['logit-smoothed']: adjusted = _shrink_prob(count1, nobs1, count2, nobs2, shrink_factor=2, return_corr=False)[0] count1_, nobs1_, count2_, nobs2_ = adjusted else: addhalf = 0.5 if method == 'logit-adjusted' else 0 count1_, nobs1_ = count1 + addhalf, nobs1 + 2 * addhalf count2_, nobs2_ = count2 + addhalf, nobs2 + 2 * addhalf p1_ = count1_ / nobs1_ p2_ = count2_ / nobs2_ odds_ratio_ = p1_ / (1 - p1_) / p2_ * (1 - p2_) var = (1 / count1_ + 1 / (nobs1_ - count1_) + 1 / count2_ + 1 / (nobs2_ - count2_)) diff_stat = np.log(odds_ratio_) - np.log(value) statistic = diff_stat / np.sqrt(var) distr = 'normal' elif method == 'score': res = score_test_proportions_2indep(count1, nobs1, count2, nobs2, value=value, compare=compare, alternative=alternative, correction=correction, return_results=return_results) if return_results is False: statistic, pvalue = res[:2] distr = 'normal' diff_stat = None else: raise ValueError('method "%s" not recognized' % method) else: raise ValueError('compare "%s" not recognized' % compare) if distr == 'normal' and diff_stat is not None: statistic, pvalue = _zstat_generic2(diff_stat, np.sqrt(var), alternative=alternative) if return_results: if res is None: res = HolderTuple(statistic=statistic, pvalue=pvalue, compare=compare, method=method, diff=diff, ratio=ratio, odds_ratio=odds_ratio, variance=var, alternative=alternative, value=value, ) else: # we already have a return result from score test # add missing attributes res.diff = diff res.ratio = ratio res.odds_ratio = odds_ratio res.value = value return res else: return statistic, pvalue def tost_proportions_2indep(count1, nobs1, count2, nobs2, low, upp, method=None, compare='diff', correction=True): """ Equivalence test based on two one-sided `test_proportions_2indep` This assumes that we have two independent binomial samples. The Null and alternative hypothesis for equivalence testing are for compare = 'diff' - H0: prop1 - prop2 <= low or upp <= prop1 - prop2 - H1: low < prop1 - prop2 < upp for compare = 'ratio' - H0: prop1 / prop2 <= low or upp <= prop1 / prop2 - H1: low < prop1 / prop2 < upp for compare = 'odds-ratio' - H0: or <= low or upp <= or - H1: low < or < upp where odds-ratio or = prop1 / (1 - prop1) / (prop2 / (1 - prop2)) Parameters ---------- count1, nobs1 : count and sample size for first sample count2, nobs2 : count and sample size for the second sample low, upp : equivalence margin for diff, risk ratio or odds ratio method : string method for computing confidence interval. If method is None, then a default method is used. The default might change as more methods are added. diff: - 'wald', - 'agresti-caffo' - 'score' if correction is True, then this uses the degrees of freedom correction ``nobs / (nobs - 1)`` as in Miettinen Nurminen 1985. ratio: - 'log': wald test using log transformation - 'log-adjusted': wald test using log transformation, adds 0.5 to counts - 'score' if correction is True, then this uses the degrees of freedom correction ``nobs / (nobs - 1)`` as in Miettinen Nurminen 1985. odds-ratio: - 'logit': wald test using logit transformation - 'logit-adjusted': : wald test using logit transformation, adds 0.5 to counts - 'logit-smoothed': : wald test using logit transformation, biases cell counts towards independence by adding two observations in total. - 'score' if correction is True, then this uses the degrees of freedom correction ``nobs / (nobs - 1)`` as in Miettinen Nurminen 1985 compare : string in ['diff', 'ratio' 'odds-ratio'] If compare is `diff`, then the confidence interval is for diff = p1 - p2. If compare is `ratio`, then the confidence interval is for the risk ratio defined by ratio = p1 / p2. If compare is `odds-ratio`, then the confidence interval is for the odds-ratio defined by or = p1 / (1 - p1) / (p2 / (1 - p2). correction : bool If correction is True (default), then the Miettinen and Nurminen small sample correction to the variance nobs / (nobs - 1) is used. Applies only if method='score'. Returns ------- pvalue : float p-value is the max of the pvalues of the two one-sided tests t1 : test results results instance for one-sided hypothesis at the lower margin t1 : test results results instance for one-sided hypothesis at the upper margin Notes ----- Status: experimental, API and defaults might still change. """ tt1 = test_proportions_2indep(count1, nobs1, count2, nobs2, value=low, method=method, compare=compare, alternative='larger', correction=correction, return_results=True) tt2 = test_proportions_2indep(count1, nobs1, count2, nobs2, value=upp, method=method, compare=compare, alternative='smaller', correction=correction, return_results=True) idx_max = 0 if tt1.pvalue < tt2.pvalue else 1 res = HolderTuple(statistic=[tt1.statistic, tt2.statistic][idx_max], pvalue=[tt1.pvalue, tt2.pvalue][idx_max], compare=compare, method=method, results_larger=tt1, results_smaller=tt2, title="Equivalence test for 2 independent proportions" ) return res def _std_2prop_power(diff, p2, ratio=1, alpha=0.05, value=0): """compute standard error under null and alternative for 2 proportions helper function for power and sample size computation """ if value != 0: msg = 'non-zero diff under null, value, is not yet implemented' raise NotImplementedError(msg) nobs_ratio = ratio p1 = p2 + diff # The following contains currently redundant variables that will # be useful for different options for the null variance p_pooled = (p1 + p2 * ratio) / (1 + ratio) # probabilities for the variance for the null statistic p1_vnull, p2_vnull = p_pooled, p_pooled p2_alt = p2 p1_alt = p2_alt + diff std_null = _std_diff_prop(p1_vnull, p2_vnull) std_alt = _std_diff_prop(p1_alt, p2_alt, ratio=nobs_ratio) return p_pooled, std_null, std_alt def power_proportions_2indep(diff, prop2, nobs1, ratio=1, alpha=0.05, value=0, alternative='two-sided', return_results=True): """power for ztest that two independent proportions are equal This assumes that the variance is based on the pooled proportion under the null and the non-pooled variance under the alternative Parameters ---------- diff : float difference between proportion 1 and 2 under the alternative prop2 : float proportion for the reference case, prop2, proportions for the first case will be computing using p2 and diff p1 = p2 + diff nobs1 : float or int number of observations in sample 1 ratio : float sample size ratio, nobs2 = ratio * nobs1 alpha : float in interval (0,1) Significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. value : float currently only `value=0`, i.e. equality testing, is supported alternative : string, 'two-sided' (default), 'larger', 'smaller' Alternative hypothesis whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either 'larger', 'smaller'. return_results : bool If true, then a results instance with extra information is returned, otherwise only the computed power is returned. Returns ------- results : results instance or float If return_results is True, then a results instance with the information in attributes is returned. If return_results is False, then only the power is returned. power : float Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true. Other attributes in results instance include : p_pooled pooled proportion, used for std_null std_null standard error of difference under the null hypothesis (without sqrt(nobs)) std_alt standard error of difference under the alternative hypothesis (without sqrt(nobs)) """ # TODO: avoid possible circular import, check if needed from statsmodels.stats.power import normal_power_het p_pooled, std_null, std_alt = _std_2prop_power(diff, prop2, ratio=1, alpha=0.05, value=0) pow_ = normal_power_het(diff, nobs1, alpha, std_null=std_null, std_alternative=std_alt, alternative=alternative) if return_results: res = Holder(power=pow_, p_pooled=p_pooled, std_null=std_null, std_alt=std_alt, nobs1=nobs1, nobs2=ratio * nobs1, nobs_ratio=ratio, alpha=alpha, ) return res else: return pow_ def samplesize_proportions_2indep_onetail(diff, prop2, power, ratio=1, alpha=0.05, value=0, alternative='two-sided'): """required sample size assuming normal distribution based on one tail This uses an explicit computation for the sample size that is required to achieve a given power corresponding to the appropriate tails of the normal distribution. This ignores the far tail in a two-sided test which is negligible in the common case when alternative and null are far apart. Parameters ---------- diff : float Difference between proportion 1 and 2 under the alternative prop2 : float proportion for the reference case, prop2, proportions for the first case will be computing using p2 and diff p1 = p2 + diff power : float Power for which sample size is computed. ratio : float Sample size ratio, nobs2 = ratio * nobs1 alpha : float in interval (0,1) Significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. value : float Currently only `value=0`, i.e. equality testing, is supported alternative : string, 'two-sided' (default), 'larger', 'smaller' Alternative hypothesis whether the power is calculated for a two-sided (default) or one sided test. In the case of a one-sided alternative, it is assumed that the test is in the appropriate tail. Returns ------- nobs1 : float Number of observations in sample 1. """ # TODO: avoid possible circular import, check if needed from statsmodels.stats.power import normal_sample_size_one_tail if alternative in ['two-sided', '2s']: alpha = alpha / 2 _, std_null, std_alt = _std_2prop_power(diff, prop2, ratio=ratio, alpha=alpha, value=value) nobs = normal_sample_size_one_tail(diff, power, alpha, std_null=std_null, std_alternative=std_alt) return nobs def _score_confint_inversion(count1, nobs1, count2, nobs2, compare='diff', alpha=0.05, correction=True): """Compute score confidence interval by inverting score test Parameters ---------- count1, nobs1 : Count and sample size for first sample. count2, nobs2 : Count and sample size for the second sample. compare : string in ['diff', 'ratio' 'odds-ratio'] If compare is `diff`, then the confidence interval is for diff = p1 - p2. If compare is `ratio`, then the confidence interval is for the risk ratio defined by ratio = p1 / p2. If compare is `odds-ratio`, then the confidence interval is for the odds-ratio defined by or = p1 / (1 - p1) / (p2 / (1 - p2). alpha : float in interval (0,1) Significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true. correction : bool If correction is True (default), then the Miettinen and Nurminen small sample correction to the variance nobs / (nobs - 1) is used. Applies only if method='score'. Returns ------- low : float Lower confidence bound. upp : float Upper confidence bound. """ def func(v): r = test_proportions_2indep(count1, nobs1, count2, nobs2, value=v, compare=compare, method='score', correction=correction, alternative="two-sided") return r.pvalue - alpha rt0 = test_proportions_2indep(count1, nobs1, count2, nobs2, value=0, compare=compare, method='score', correction=correction, alternative="two-sided") # use default method to get starting values # this will not work if score confint becomes default # maybe use "wald" as alias that works for all compare statistics use_method = {"diff": "wald", "ratio": "log", "odds-ratio": "logit"} rci0 = confint_proportions_2indep(count1, nobs1, count2, nobs2, method=use_method[compare], compare=compare, alpha=alpha) # Note diff might be negative ub = rci0[1] + np.abs(rci0[1]) * 0.5 lb = rci0[0] - np.abs(rci0[0]) * 0.25 if compare == 'diff': param = rt0.diff # 1 might not be the correct upper bound because # rootfinding is for the `diff` and not for a probability. ub = min(ub, 0.99999) elif compare == 'ratio': param = rt0.ratio ub *= 2 # add more buffer if compare == 'odds-ratio': param = rt0.odds_ratio # root finding for confint bounds upp = optimize.brentq(func, param, ub) low = optimize.brentq(func, lb, param) return low, upp def _confint_riskratio_koopman(count1, nobs1, count2, nobs2, alpha=0.05, correction=True): """score confidence interval for ratio or proportions, Koopman/Nam signature not consistent with other functions When correction is True, then the small sample correction nobs / (nobs - 1) by Miettinen/Nurminen is used. """ # The names below follow Nam x0, x1, n0, n1 = count2, count1, nobs2, nobs1 x = x0 + x1 n = n0 + n1 z = stats.norm.isf(alpha / 2)**2 if correction: # Mietinnen/Nurminen small sample correction z *= n / (n - 1) # z = stats.chi2.isf(alpha, 1) # equ 6 in Nam 1995 a1 = n0 * (n0 * n * x1 + n1 * (n0 + x1) * z) a2 = - n0 * (n0 * n1 * x + 2 * n * x0 * x1 + n1 * (n0 + x0 + 2 * x1) * z) a3 = 2 * n0 * n1 * x0 * x + n * x0 * x0 * x1 + n0 * n1 * x * z a4 = - n1 * x0 * x0 * x p_roots_ = np.sort(np.roots([a1, a2, a3, a4])) p_roots = p_roots_[:2][::-1] # equ 5 ci = (1 - (n1 - x1) * (1 - p_roots) / (x0 + n1 - n * p_roots)) / p_roots res = Holder() res.confint = ci res._p_roots = p_roots_ # for unit tests, can be dropped return res def _confint_riskratio_paired_nam(table, alpha=0.05): """confidence interval for marginal risk ratio for matched pairs need full table success fail marginal success x11 x10 x1. fail x01 x00 x0. marginal x.1 x.0 n The confidence interval is for the ratio p1 / p0 where p1 = x1. / n and p0 - x.1 / n Todo: rename p1 to pa and p2 to pb, so we have a, b for treatment and 0, 1 for success/failure current namings follow Nam 2009 status testing: compared to example in Nam 2009 internal polynomial coefficients in calculation correspond at around 4 decimals confidence interval agrees only at 2 decimals """ x11, x10, x01, x00 = np.ravel(table) n = np.sum(table) # nobs p10, p01 = x10 / n, x01 / n p1 = (x11 + x10) / n p0 = (x11 + x01) / n q00 = 1 - x00 / n z2 = stats.norm.isf(alpha / 2)**2 # z = stats.chi2.isf(alpha, 1) # before equ 3 in Nam 2009 g1 = (n * p0 + z2 / 2) * p0 g2 = - (2 * n * p1 * p0 + z2 * q00) g3 = (n * p1 + z2 / 2) * p1 a0 = g1**2 - (z2 * p0 / 2)**2 a1 = 2 * g1 * g2 a2 = g2**2 + 2 * g1 * g3 + z2**2 * (p1 * p0 - 2 * p10 * p01) / 2 a3 = 2 * g2 * g3 a4 = g3**2 - (z2 * p1 / 2)**2 p_roots = np.sort(np.roots([a0, a1, a2, a3, a4])) # p_roots = np.sort(np.roots([1, a1 / a0, a2 / a0, a3 / a0, a4 / a0])) ci = [p_roots.min(), p_roots.max()] res = Holder() res.confint = ci res.p = p1, p0 res._p_roots = p_roots # for unit tests, can be dropped return res statsmodels-0.12.2/statsmodels/stats/rates.py000066400000000000000000000273451400612667500213500ustar00rootroot00000000000000'''Test for ratio of Poisson intensities in two independent samples Author: Josef Perktold License: BSD-3 ''' import numpy as np from scipy import stats from statsmodels.stats.weightstats import _zstat_generic2 from statsmodels.stats.base import HolderTuple def test_poisson_2indep(count1, exposure1, count2, exposure2, ratio_null=1, method='score', alternative='two-sided', etest_kwds=None): '''test for ratio of two sample Poisson intensities If the two Poisson rates are g1 and g2, then the Null hypothesis is - H0: g1 / g2 = ratio_null against one of the following alternatives - H1_2-sided: g1 / g2 != ratio_null - H1_larger: g1 / g2 > ratio_null - H1_smaller: g1 / g2 < ratio_null Parameters ---------- count1 : int Number of events in first sample. exposure1 : float Total exposure (time * subjects) in first sample. count2 : int Number of events in second sample. exposure2 : float Total exposure (time * subjects) in second sample. ratio: float ratio of the two Poisson rates under the Null hypothesis. Default is 1. method : string Method for the test statistic and the p-value. Defaults to `'score'`. Current Methods are based on Gu et. al 2008. Implemented are 'wald', 'score' and 'sqrt' based asymptotic normal distribution, and the exact conditional test 'exact-cond', and its mid-point version 'cond-midp'. method='etest' and method='etest-wald' provide pvalues from `etest_poisson_2indep` using score or wald statistic respectively. see Notes. alternative : string The alternative hypothesis, H1, has to be one of the following - 'two-sided': H1: ratio of rates is not equal to ratio_null (default) - 'larger' : H1: ratio of rates is larger than ratio_null - 'smaller' : H1: ratio of rates is smaller than ratio_null etest_kwds: dictionary Additional parameters to be passed to the etest_poisson_2indep funtcion, namely ygrid. Returns ------- results : instance of HolderTuple class The two main attributes are test statistic `statistic` and p-value `pvalue`. Notes ----- - 'wald': method W1A, wald test, variance based on separate estimates - 'score': method W2A, score test, variance based on estimate under Null - 'wald-log': W3A - 'score-log' W4A - 'sqrt': W5A, based on variance stabilizing square root transformation - 'exact-cond': exact conditional test based on binomial distribution - 'cond-midp': midpoint-pvalue of exact conditional test - 'etest': etest with score test statistic - 'etest-wald': etest with wald test statistic References ---------- Gu, Ng, Tang, Schucany 2008: Testing the Ratio of Two Poisson Rates, Biometrical Journal 50 (2008) 2, 2008 See Also -------- tost_poisson_2indep etest_poisson_2indep ''' # shortcut names y1, n1, y2, n2 = count1, exposure1, count2, exposure2 d = n2 / n1 r = ratio_null r_d = r / d if method in ['score']: stat = (y1 - y2 * r_d) / np.sqrt((y1 + y2) * r_d) dist = 'normal' elif method in ['wald']: stat = (y1 - y2 * r_d) / np.sqrt(y1 + y2 * r_d**2) dist = 'normal' elif method in ['sqrt']: stat = 2 * (np.sqrt(y1 + 3 / 8.) - np.sqrt((y2 + 3 / 8.) * r_d)) stat /= np.sqrt(1 + r_d) dist = 'normal' elif method in ['exact-cond', 'cond-midp']: from statsmodels.stats import proportion bp = r_d / (1 + r_d) y_total = y1 + y2 stat = None # TODO: why y2 in here and not y1, check definition of H1 "larger" pvalue = proportion.binom_test(y1, y_total, prop=bp, alternative=alternative) if method in ['cond-midp']: # not inplace in case we still want binom pvalue pvalue = pvalue - 0.5 * stats.binom.pmf(y1, y_total, bp) dist = 'binomial' elif method.startswith('etest'): if method.endswith('wald'): method_etest = 'wald' else: method_etest = 'score' if etest_kwds is None: etest_kwds = {} stat, pvalue = etest_poisson_2indep( count1, exposure1, count2, exposure2, ratio_null=ratio_null, method=method_etest, alternative=alternative, **etest_kwds) dist = 'poisson' else: raise ValueError('method not recognized') if dist == 'normal': stat, pvalue = _zstat_generic2(stat, 1, alternative) rates = (y1 / n1, y2 / n2) ratio = rates[0] / rates[1] res = HolderTuple(statistic=stat, pvalue=pvalue, distribution=dist, method=method, alternative=alternative, rates=rates, ratio=ratio, ratio_null=ratio_null) return res def etest_poisson_2indep(count1, exposure1, count2, exposure2, ratio_null=1, method='score', alternative='2-sided', ygrid=None): """E-test for ratio of two sample Poisson rates If the two Poisson rates are g1 and g2, then the Null hypothesis is - H0: g1 / g2 = ratio_null against one of the following alternatives - H1_2-sided: g1 / g2 != ratio_null - H1_larger: g1 / g2 > ratio_null - H1_smaller: g1 / g2 < ratio_null Parameters ---------- count1 : int Number of events in first sample exposure1 : float Total exposure (time * subjects) in first sample count2 : int Number of events in first sample exposure2 : float Total exposure (time * subjects) in first sample ratio : float ratio of the two Poisson rates under the Null hypothesis. Default is 1. method : {"score", "wald"} Method for the test statistic that defines the rejection region. alternative : string The alternative hypothesis, H1, has to be one of the following 'two-sided': H1: ratio of rates is not equal to ratio_null (default) 'larger' : H1: ratio of rates is larger than ratio_null 'smaller' : H1: ratio of rates is smaller than ratio_null ygrid : None or 1-D ndarray Grid values for counts of the Poisson distribution used for computing the pvalue. By default truncation is based on an upper tail Poisson quantiles. Returns ------- stat_sample : float test statistic for the sample pvalue : float References ---------- Gu, Ng, Tang, Schucany 2008: Testing the Ratio of Two Poisson Rates, Biometrical Journal 50 (2008) 2, 2008 """ y1, n1, y2, n2 = count1, exposure1, count2, exposure2 d = n2 / n1 r = ratio_null r_d = r / d eps = 1e-20 # avoid zero division in stat_func if method in ['score']: def stat_func(x1, x2): return (x1 - x2 * r_d) / np.sqrt((x1 + x2) * r_d + eps) # TODO: do I need these? return_results ? # rate2_cmle = (y1 + y2) / n2 / (1 + r_d) # rate1_cmle = rate2_cmle * r # rate1 = rate1_cmle # rate2 = rate2_cmle elif method in ['wald']: def stat_func(x1, x2): return (x1 - x2 * r_d) / np.sqrt(x1 + x2 * r_d**2 + eps) # rate2_mle = y2 / n2 # rate1_mle = y1 / n1 # rate1 = rate1_mle # rate2 = rate2_mle else: raise ValueError('method not recognized') # The sampling distribution needs to be based on the null hypotheis # use constrained MLE from 'score' calculation rate2_cmle = (y1 + y2) / n2 / (1 + r_d) rate1_cmle = rate2_cmle * r rate1 = rate1_cmle rate2 = rate2_cmle mean1 = n1 * rate1 mean2 = n2 * rate2 stat_sample = stat_func(y1, y2) # The following uses a fixed truncation for evaluating the probabilities # It will currently only work for small counts, so that sf at truncation # point is small # We can make it depend on the amount of truncated sf. # Some numerical optimization or checks for large means need to be added. if ygrid is None: threshold = stats.poisson.isf(1e-13, max(mean1, mean2)) threshold = max(threshold, 100) # keep at least 100 y_grid = np.arange(threshold + 1) pdf1 = stats.poisson.pmf(y_grid, mean1) pdf2 = stats.poisson.pmf(y_grid, mean2) stat_space = stat_func(y_grid[:, None], y_grid[None, :]) # broadcasting eps = 1e-15 # correction for strict inequality check if alternative in ['two-sided', '2-sided', '2s']: mask = np.abs(stat_space) >= np.abs(stat_sample) - eps elif alternative in ['larger', 'l']: mask = stat_space >= stat_sample - eps elif alternative in ['smaller', 's']: mask = stat_space <= stat_sample + eps else: raise ValueError('invalid alternative') pvalue = ((pdf1[:, None] * pdf2[None, :])[mask]).sum() return stat_sample, pvalue def tost_poisson_2indep(count1, exposure1, count2, exposure2, low, upp, method='score'): '''Equivalence test based on two one-sided `test_proportions_2indep` This assumes that we have two independent binomial samples. The Null and alternative hypothesis for equivalence testing are - H0: g1 / g2 <= low or upp <= g1 / g2 - H1: low < g1 / g2 < upp where g1 and g2 are the Poisson rates. Parameters ---------- count1 : int Number of events in first sample exposure1 : float Total exposure (time * subjects) in first sample count2 : int Number of events in second sample exposure2 : float Total exposure (time * subjects) in second sample low, upp : equivalence margin for the ratio of Poisson rates method: string Method for the test statistic and the p-value. Defaults to `'score'`. Current Methods are based on Gu et. al 2008 Implemented are 'wald', 'score' and 'sqrt' based asymptotic normal distribution, and the exact conditional test 'exact-cond', and its mid-point version 'cond-midp', see Notes Returns ------- results : instance of HolderTuple class The two main attributes are test statistic `statistic` and p-value `pvalue`. Notes ----- - 'wald': method W1A, wald test, variance based on separate estimates - 'score': method W2A, score test, variance based on estimate under Null - 'wald-log': W3A not implemented - 'score-log' W4A not implemented - 'sqrt': W5A, based on variance stabilizing square root transformation - 'exact-cond': exact conditional test based on binomial distribution - 'cond-midp': midpoint-pvalue of exact conditional test The latter two are only verified for one-sided example. References ---------- Gu, Ng, Tang, Schucany 2008: Testing the Ratio of Two Poisson Rates, Biometrical Journal 50 (2008) 2, 2008 See Also -------- test_poisson_2indep ''' tt1 = test_poisson_2indep(count1, exposure1, count2, exposure2, ratio_null=low, method=method, alternative='larger') tt2 = test_poisson_2indep(count1, exposure1, count2, exposure2, ratio_null=upp, method=method, alternative='smaller') idx_max = 0 if tt1.pvalue < tt2.pvalue else 1 res = HolderTuple(statistic=[tt1.statistic, tt2.statistic][idx_max], pvalue=[tt1.pvalue, tt2.pvalue][idx_max], method=method, results_larger=tt1, results_smaller=tt2, title="Equivalence test for 2 independent Poisson rates" ) return res statsmodels-0.12.2/statsmodels/stats/regularized_covariance.py000066400000000000000000000113011400612667500247220ustar00rootroot00000000000000from statsmodels.regression.linear_model import OLS import numpy as np def _calc_nodewise_row(exog, idx, alpha): """calculates the nodewise_row values for the idxth variable, used to estimate approx_inv_cov. Parameters ---------- exog : array_like The weighted design matrix for the current partition. idx : scalar Index of the current variable. alpha : scalar or array_like The penalty weight. If a scalar, the same penalty weight applies to all variables in the model. If a vector, it must have the same length as `params`, and contains a penalty weight for each coefficient. Returns ------- An array-like object of length p-1 Notes ----- nodewise_row_i = arg min 1/(2n) ||exog_i - exog_-i gamma||_2^2 + alpha ||gamma||_1 """ p = exog.shape[1] ind = list(range(p)) ind.pop(idx) # handle array alphas if not np.isscalar(alpha): alpha = alpha[ind] tmod = OLS(exog[:, idx], exog[:, ind]) nodewise_row = tmod.fit_regularized(alpha=alpha).params return nodewise_row def _calc_nodewise_weight(exog, nodewise_row, idx, alpha): """calculates the nodewise_weightvalue for the idxth variable, used to estimate approx_inv_cov. Parameters ---------- exog : array_like The weighted design matrix for the current partition. nodewise_row : array_like The nodewise_row values for the current variable. idx : scalar Index of the current variable alpha : scalar or array_like The penalty weight. If a scalar, the same penalty weight applies to all variables in the model. If a vector, it must have the same length as `params`, and contains a penalty weight for each coefficient. Returns ------- A scalar Notes ----- nodewise_weight_i = sqrt(1/n ||exog,i - exog_-i nodewise_row||_2^2 + alpha ||nodewise_row||_1) """ n, p = exog.shape ind = list(range(p)) ind.pop(idx) # handle array alphas if not np.isscalar(alpha): alpha = alpha[ind] d = np.linalg.norm(exog[:, idx] - exog[:, ind].dot(nodewise_row))**2 d = np.sqrt(d / n + alpha * np.linalg.norm(nodewise_row, 1)) return d def _calc_approx_inv_cov(nodewise_row_l, nodewise_weight_l): """calculates the approximate inverse covariance matrix Parameters ---------- nodewise_row_l : list A list of array-like object where each object corresponds to the nodewise_row values for the corresponding variable, should be length p. nodewise_weight_l : list A list of scalars where each scalar corresponds to the nodewise_weight value for the corresponding variable, should be length p. Returns ------ An array-like object, p x p matrix Notes ----- nwr = nodewise_row nww = nodewise_weight approx_inv_cov_j = - 1 / nww_j [nwr_j,1,...,1,...nwr_j,p] """ p = len(nodewise_weight_l) approx_inv_cov = -np.eye(p) for idx in range(p): ind = list(range(p)) ind.pop(idx) approx_inv_cov[idx, ind] = nodewise_row_l[idx] approx_inv_cov *= -1 / nodewise_weight_l[:, None]**2 return approx_inv_cov class RegularizedInvCovariance(object): """ Class for estimating regularized inverse covariance with nodewise regression Parameters ---------- exog : array_like A weighted design matrix for covariance Attributes ---------- exog : array_like A weighted design matrix for covariance alpha : scalar Regularizing constant """ def __init__(self, exog): self.exog = exog def fit(self, alpha=0): """estimates the regularized inverse covariance using nodewise regression Parameters ---------- alpha : scalar Regularizing constant """ n, p = self.exog.shape nodewise_row_l = [] nodewise_weight_l = [] for idx in range(p): nodewise_row = _calc_nodewise_row(self.exog, idx, alpha) nodewise_row_l.append(nodewise_row) nodewise_weight = _calc_nodewise_weight(self.exog, nodewise_row, idx, alpha) nodewise_weight_l.append(nodewise_weight) nodewise_row_l = np.array(nodewise_row_l) nodewise_weight_l = np.array(nodewise_weight_l) approx_inv_cov = _calc_approx_inv_cov(nodewise_row_l, nodewise_weight_l) self._approx_inv_cov = approx_inv_cov def approx_inv_cov(self): return self._approx_inv_cov statsmodels-0.12.2/statsmodels/stats/robust_compare.py000066400000000000000000000221071400612667500232450ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Anova k-sample comparison without and with trimming Created on Sun Jun 09 23:51:34 2013 Author: Josef Perktold """ import numbers import numpy as np # the trimboth and trim_mean are taken from scipy.stats.stats # and enhanced by axis def trimboth(a, proportiontocut, axis=0): """ Slices off a proportion of items from both ends of an array. Slices off the passed proportion of items from both ends of the passed array (i.e., with `proportiontocut` = 0.1, slices leftmost 10% **and** rightmost 10% of scores). You must pre-sort the array if you want 'proper' trimming. Slices off less if proportion results in a non-integer slice index (i.e., conservatively slices off `proportiontocut`). Parameters ---------- a : array_like Data to trim. proportiontocut : float or int Proportion of total data set to trim of each end. axis : int or None Axis along which the observations are trimmed. The default is to trim along axis=0. If axis is None then the array will be flattened before trimming. Returns ------- out : ndarray Trimmed version of array `a`. Examples -------- >>> from scipy import stats >>> a = np.arange(20) >>> b = stats.trimboth(a, 0.1) >>> b.shape (16,) """ a = np.asarray(a) if axis is None: a = a.ravel() axis = 0 nobs = a.shape[axis] lowercut = int(proportiontocut * nobs) uppercut = nobs - lowercut if (lowercut >= uppercut): raise ValueError("Proportion too big.") sl = [slice(None)] * a.ndim sl[axis] = slice(lowercut, uppercut) return a[tuple(sl)] def trim_mean(a, proportiontocut, axis=0): """ Return mean of array after trimming observations from both lower and upper tails. If `proportiontocut` = 0.1, slices off 'leftmost' and 'rightmost' 10% of scores. Slices off LESS if proportion results in a non-integer slice index (i.e., conservatively slices off `proportiontocut` ). Parameters ---------- a : array_like Input array proportiontocut : float Fraction to cut off of both tails of the observations axis : int or None Axis along which the trimmed means are computed. The default is axis=0. If axis is None then the trimmed mean will be computed for the flattened array. Returns ------- trim_mean : ndarray Mean of trimmed array. """ newa = trimboth(np.sort(a, axis), proportiontocut, axis=axis) return np.mean(newa, axis=axis) class TrimmedMean(object): """ class for trimmed and winsorized one sample statistics axis is None, i.e. ravelling, is not supported """ def __init__(self, data, fraction, is_sorted=False, axis=0): self.data = np.asarray(data) # TODO: add pandas handling, maybe not if this stays internal self.axis = axis self.fraction = fraction self.nobs = nobs = self.data.shape[axis] self.lowercut = lowercut = int(fraction * nobs) self.uppercut = uppercut = nobs - lowercut if (lowercut >= uppercut): raise ValueError("Proportion too big.") self.nobs_reduced = nobs - 2 * lowercut self.sl = [slice(None)] * self.data.ndim self.sl[axis] = slice(self.lowercut, self.uppercut) # numpy requires now tuple for indexing, not list self.sl = tuple(self.sl) if not is_sorted: self.data_sorted = np.sort(self.data, axis=axis) else: self.data_sorted = self.data # this only works for axis=0 self.lowerbound = np.take(self.data_sorted, lowercut, axis=axis) self.upperbound = np.take(self.data_sorted, uppercut - 1, axis=axis) # self.lowerbound = self.data_sorted[lowercut] # self.upperbound = self.data_sorted[uppercut - 1] @property def data_trimmed(self): # returns a view return self.data_sorted[self.sl] @property # cache def data_winsorized(self): """winsorized data """ lb = np.expand_dims(self.lowerbound, self.axis) ub = np.expand_dims(self.upperbound, self.axis) return np.clip(self.data_sorted, lb, ub) @property def mean_trimmed(self): """mean of trimmed data """ return np.mean(self.data_sorted[tuple(self.sl)], self.axis) @property def mean_winsorized(self): """mean of winsorized data """ return np.mean(self.data_winsorized, self.axis) @property def var_winsorized(self): """variance of winsorized data """ # hardcoded ddof = 1 return np.var(self.data_winsorized, ddof=1, axis=self.axis) @property def std_mean_trimmed(self): """standard error of trimmed mean """ se = np.sqrt(self.var_winsorized / self.nobs_reduced) # trimming creates correlation across trimmed observations # trimming is based on order statistics of the data # wilcox 2012, p.61 se *= np.sqrt(self.nobs / self.nobs_reduced) return se @property def std_mean_winsorized(self): """standard error of winsorized mean """ # the following matches Wilcox, WRS2 std_ = np.sqrt(self.var_winsorized / self.nobs) std_ *= (self.nobs - 1) / (self.nobs_reduced - 1) # old version # tm = self # formula from an old SAS manual page, simplified # std_ = np.sqrt(tm.var_winsorized / (tm.nobs_reduced - 1) * # (tm.nobs - 1.) / tm.nobs) return std_ def ttest_mean(self, value=0, transform='trimmed', alternative='two-sided'): """ One sample ttest for trimmed or Winsorized mean Parameters ---------- value : float Value of the mean under the Null hypothesis transform : {'trimmed', 'winsorized'} Specified whether the mean test is based on trimmed or winsorized data. alternative : {'two-sided', 'larger', 'smaller'} Notes ----- p-value is based on the approximate t-distribution of the test statistic. The approximation is valid if the underlying distribution is symmetric. """ import statsmodels.stats.weightstats as smws df = self.nobs_reduced - 1 if transform == 'trimmed': mean_ = self.mean_trimmed std_ = self.std_mean_trimmed elif transform == 'winsorized': mean_ = self.mean_winsorized std_ = self.std_mean_winsorized else: raise ValueError("transform can only be 'trimmed' or 'winsorized'") res = smws._tstat_generic(mean_, 0, std_, df, alternative=alternative, diff=value) return res + (df,) def reset_fraction(self, frac): """create a TrimmedMean instance with a new trimming fraction This reuses the sorted array from the current instance. """ tm = TrimmedMean(self.data_sorted, frac, is_sorted=True, axis=self.axis) tm.data = self.data # TODO: this will not work if there is processing of meta-information # in __init__, # for example storing a pandas DataFrame or Series index return tm def scale_transform(data, center='median', transform='abs', trim_frac=0.2, axis=0): """Transform data for variance comparison for Levene type tests Parameters ---------- data : array_like Observations for the data. center : "median", "mean", "trimmed" or float Statistic used for centering observations. If a float, then this value is used to center. Default is median. transform : 'abs', 'square', 'identity' or a callable The transform for the centered data. trim_frac : float in [0, 0.5) Fraction of observations that are trimmed on each side of the sorted observations. This is only used if center is `trimmed`. axis : int Axis along which the data are transformed when centering. Returns ------- res : ndarray transformed data in the same shape as the original data. """ x = np.asarray(data) # x is shorthand from earlier code if transform == 'abs': tfunc = np.abs elif transform == 'square': tfunc = lambda x: x * x # noqa elif transform == 'identity': tfunc = lambda x: x # noqa elif callable(transform): tfunc = transform else: raise ValueError('transform should be abs, square or exp') if center == 'median': res = tfunc(x - np.expand_dims(np.median(x, axis=axis), axis)) elif center == 'mean': res = tfunc(x - np.expand_dims(np.mean(x, axis=axis), axis)) elif center == 'trimmed': center = trim_mean(x, trim_frac, axis=axis) res = tfunc(x - np.expand_dims(center, axis)) elif isinstance(center, numbers.Number): res = tfunc(x - center) else: raise ValueError('center should be median, mean or trimmed') return res statsmodels-0.12.2/statsmodels/stats/sandwich_covariance.py000066400000000000000000000664221400612667500242230ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Sandwich covariance estimators Created on Sun Nov 27 14:10:57 2011 Author: Josef Perktold Author: Skipper Seabold for HCxxx in linear_model.RegressionResults License: BSD-3 Notes ----- for calculating it, we have two versions version 1: use pinv pinv(x) scale pinv(x) used currently in linear_model, with scale is 1d (or diagonal matrix) (x'x)^(-1) x' scale x (x'x)^(-1), scale in general is (nobs, nobs) so pretty large general formulas for scale in cluster case are in [4], which can be found (as of 2017-05-20) at http://www.tandfonline.com/doi/abs/10.1198/jbes.2010.07136 This paper also has the second version. version 2: (x'x)^(-1) S (x'x)^(-1) with S = x' scale x, S is (kvar,kvars), (x'x)^(-1) is available as normalized_covparams. S = sum (x*u) dot (x*u)' = sum x*u*u'*x' where sum here can aggregate over observations or groups. u is regression residual. x is (nobs, k_var) u is (nobs, 1) x*u is (nobs, k_var) For cluster robust standard errors, we first sum (x*w) over other groups (including time) and then take the dot product (sum of outer products) S = sum_g(x*u)' dot sum_g(x*u) For HAC by clusters, we first sum over groups for each time period, and then use HAC on the group sums of (x*w). If we have several groups, we have to sum first over all relevant groups, and then take the outer product sum. This can be done by summing using indicator functions or matrices or with explicit loops. Alternatively we calculate separate covariance matrices for each group, sum them and subtract the duplicate counted intersection. Not checked in details yet: degrees of freedom or small sample correction factors, see (two) references (?) This is the general case for MLE and GMM also in MLE hessian H, outerproduct of jacobian S, cov_hjjh = HJJH, which reduces to the above in the linear case, but can be used generally, e.g. in discrete, and is misnomed in GenericLikelihoodModel in GMM it's similar but I would have to look up the details, (it comes out in sandwich form by default, it's in the sandbox), standard Newey West or similar are on the covariance matrix of the moment conditions quasi-MLE: MLE with mis-specified model where parameter estimates are fine (consistent ?) but cov_params needs to be adjusted similar or same as in sandwiches. (I did not go through any details yet.) TODO ---- * small sample correction factors, Done for cluster, not yet for HAC * automatic lag-length selection for Newey-West HAC, -> added: nlag = floor[4(T/100)^(2/9)] Reference: xtscc paper, Newey-West note this will not be optimal in the panel context, see Peterson * HAC should maybe return the chosen nlags * get consistent notation, varies by paper, S, scale, sigma? * replace diag(hat_matrix) calculations in cov_hc2, cov_hc3 References ---------- [1] John C. Driscoll and Aart C. Kraay, “Consistent Covariance Matrix Estimation with Spatially Dependent Panel Data,†Review of Economics and Statistics 80, no. 4 (1998): 549-560. [2] Daniel Hoechle, "Robust Standard Errors for Panel Regressions with Cross-Sectional Dependence", The Stata Journal [3] Mitchell A. Petersen, “Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches,†Review of Financial Studies 22, no. 1 (January 1, 2009): 435 -480. [4] A. Colin Cameron, Jonah B. Gelbach, and Douglas L. Miller, “Robust Inference With Multiway Clustering,†Journal of Business and Economic Statistics 29 (April 2011): 238-249. not used yet: A.C. Cameron, J.B. Gelbach, and D.L. Miller, “Bootstrap-based improvements for inference with clustered errors,†The Review of Economics and Statistics 90, no. 3 (2008): 414–427. """ import numpy as np from statsmodels.tools.grouputils import combine_indices, group_sums from statsmodels.stats.moment_helpers import se_cov __all__ = ['cov_cluster', 'cov_cluster_2groups', 'cov_hac', 'cov_nw_panel', 'cov_white_simple', 'cov_hc0', 'cov_hc1', 'cov_hc2', 'cov_hc3', 'se_cov', 'weights_bartlett', 'weights_uniform'] #----------- from linear_model.RegressionResults ''' HC0_se White's (1980) heteroskedasticity robust standard errors. Defined as sqrt(diag(X.T X)^(-1)X.T diag(e_i^(2)) X(X.T X)^(-1) where e_i = resid[i] HC0_se is a property. It is not evaluated until it is called. When it is called the RegressionResults instance will then have another attribute cov_HC0, which is the full heteroskedasticity consistent covariance matrix and also `het_scale`, which is in this case just resid**2. HCCM matrices are only appropriate for OLS. HC1_se MacKinnon and White's (1985) alternative heteroskedasticity robust standard errors. Defined as sqrt(diag(n/(n-p)*HC_0) HC1_se is a property. It is not evaluated until it is called. When it is called the RegressionResults instance will then have another attribute cov_HC1, which is the full HCCM and also `het_scale`, which is in this case n/(n-p)*resid**2. HCCM matrices are only appropriate for OLS. HC2_se MacKinnon and White's (1985) alternative heteroskedasticity robust standard errors. Defined as (X.T X)^(-1)X.T diag(e_i^(2)/(1-h_ii)) X(X.T X)^(-1) where h_ii = x_i(X.T X)^(-1)x_i.T HC2_se is a property. It is not evaluated until it is called. When it is called the RegressionResults instance will then have another attribute cov_HC2, which is the full HCCM and also `het_scale`, which is in this case is resid^(2)/(1-h_ii). HCCM matrices are only appropriate for OLS. HC3_se MacKinnon and White's (1985) alternative heteroskedasticity robust standard errors. Defined as (X.T X)^(-1)X.T diag(e_i^(2)/(1-h_ii)^(2)) X(X.T X)^(-1) where h_ii = x_i(X.T X)^(-1)x_i.T HC3_se is a property. It is not evaluated until it is called. When it is called the RegressionResults instance will then have another attribute cov_HC3, which is the full HCCM and also `het_scale`, which is in this case is resid^(2)/(1-h_ii)^(2). HCCM matrices are only appropriate for OLS. ''' # Note: HCCM stands for Heteroskedasticity Consistent Covariance Matrix def _HCCM(results, scale): ''' sandwich with pinv(x) * diag(scale) * pinv(x).T where pinv(x) = (X'X)^(-1) X and scale is (nobs,) ''' H = np.dot(results.model.pinv_wexog, scale[:,None]*results.model.pinv_wexog.T) return H def cov_hc0(results): """ See statsmodels.RegressionResults """ het_scale = results.resid**2 # or whitened residuals? only OLS? cov_hc0 = _HCCM(results, het_scale) return cov_hc0 def cov_hc1(results): """ See statsmodels.RegressionResults """ het_scale = results.nobs/(results.df_resid)*(results.resid**2) cov_hc1 = _HCCM(results, het_scale) return cov_hc1 def cov_hc2(results): """ See statsmodels.RegressionResults """ # probably could be optimized h = np.diag(np.dot(results.model.exog, np.dot(results.normalized_cov_params, results.model.exog.T))) het_scale = results.resid**2/(1-h) cov_hc2_ = _HCCM(results, het_scale) return cov_hc2_ def cov_hc3(results): """ See statsmodels.RegressionResults """ # above probably could be optimized to only calc the diag h = np.diag(np.dot(results.model.exog, np.dot(results.normalized_cov_params, results.model.exog.T))) het_scale=(results.resid/(1-h))**2 cov_hc3_ = _HCCM(results, het_scale) return cov_hc3_ #--------------------------------------- def _get_sandwich_arrays(results, cov_type=''): """Helper function to get scores from results Parameters """ if isinstance(results, tuple): # assume we have jac and hessian_inv jac, hessian_inv = results xu = jac = np.asarray(jac) hessian_inv = np.asarray(hessian_inv) elif hasattr(results, 'model'): if hasattr(results, '_results'): # remove wrapper results = results._results # assume we have a results instance if hasattr(results.model, 'jac'): xu = results.model.jac(results.params) hessian_inv = np.linalg.inv(results.model.hessian(results.params)) elif hasattr(results.model, 'score_obs'): xu = results.model.score_obs(results.params) hessian_inv = np.linalg.inv(results.model.hessian(results.params)) else: xu = results.model.wexog * results.wresid[:, None] hessian_inv = np.asarray(results.normalized_cov_params) # experimental support for freq_weights if hasattr(results.model, 'freq_weights') and not cov_type == 'clu': # we do not want to square the weights in the covariance calculations # assumes that freq_weights are incorporated in score_obs or equivalent # assumes xu/score_obs is 2D # temporary asarray xu /= np.sqrt(np.asarray(results.model.freq_weights)[:, None]) else: raise ValueError('need either tuple of (jac, hessian_inv) or results' + 'instance') return xu, hessian_inv def _HCCM1(results, scale): ''' sandwich with pinv(x) * scale * pinv(x).T where pinv(x) = (X'X)^(-1) X and scale is (nobs, nobs), or (nobs,) with diagonal matrix diag(scale) Parameters ---------- results : result instance need to contain regression results, uses results.model.pinv_wexog scale : ndarray (nobs,) or (nobs, nobs) scale matrix, treated as diagonal matrix if scale is one-dimensional Returns ------- H : ndarray (k_vars, k_vars) robust covariance matrix for the parameter estimates ''' if scale.ndim == 1: H = np.dot(results.model.pinv_wexog, scale[:,None]*results.model.pinv_wexog.T) else: H = np.dot(results.model.pinv_wexog, np.dot(scale, results.model.pinv_wexog.T)) return H def _HCCM2(hessian_inv, scale): ''' sandwich with (X'X)^(-1) * scale * (X'X)^(-1) scale is (kvars, kvars) this uses results.normalized_cov_params for (X'X)^(-1) Parameters ---------- results : result instance need to contain regression results, uses results.normalized_cov_params scale : ndarray (k_vars, k_vars) scale matrix Returns ------- H : ndarray (k_vars, k_vars) robust covariance matrix for the parameter estimates ''' if scale.ndim == 1: scale = scale[:,None] xxi = hessian_inv H = np.dot(np.dot(xxi, scale), xxi.T) return H #TODO: other kernels, move ? def weights_bartlett(nlags): '''Bartlett weights for HAC this will be moved to another module Parameters ---------- nlags : int highest lag in the kernel window, this does not include the zero lag Returns ------- kernel : ndarray, (nlags+1,) weights for Bartlett kernel ''' #with lag zero return 1 - np.arange(nlags+1)/(nlags+1.) def weights_uniform(nlags): '''uniform weights for HAC this will be moved to another module Parameters ---------- nlags : int highest lag in the kernel window, this does not include the zero lag Returns ------- kernel : ndarray, (nlags+1,) weights for uniform kernel ''' #with lag zero return np.ones(nlags+1) kernel_dict = {'bartlett': weights_bartlett, 'uniform': weights_uniform} def S_hac_simple(x, nlags=None, weights_func=weights_bartlett): '''inner covariance matrix for HAC (Newey, West) sandwich assumes we have a single time series with zero axis consecutive, equal spaced time periods Parameters ---------- x : ndarray (nobs,) or (nobs, k_var) data, for HAC this is array of x_i * u_i nlags : int or None highest lag to include in kernel window. If None, then nlags = floor(4(T/100)^(2/9)) is used. weights_func : callable weights_func is called with nlags as argument to get the kernel weights. default are Bartlett weights Returns ------- S : ndarray, (k_vars, k_vars) inner covariance matrix for sandwich Notes ----- used by cov_hac_simple options might change when other kernels besides Bartlett are available. ''' if x.ndim == 1: x = x[:,None] n_periods = x.shape[0] if nlags is None: nlags = int(np.floor(4 * (n_periods / 100.)**(2./9.))) weights = weights_func(nlags) S = weights[0] * np.dot(x.T, x) #weights[0] just for completeness, is 1 for lag in range(1, nlags+1): s = np.dot(x[lag:].T, x[:-lag]) S += weights[lag] * (s + s.T) return S def S_white_simple(x): '''inner covariance matrix for White heteroscedastistity sandwich Parameters ---------- x : ndarray (nobs,) or (nobs, k_var) data, for HAC this is array of x_i * u_i Returns ------- S : ndarray, (k_vars, k_vars) inner covariance matrix for sandwich Notes ----- this is just dot(X.T, X) ''' if x.ndim == 1: x = x[:,None] return np.dot(x.T, x) def S_hac_groupsum(x, time, nlags=None, weights_func=weights_bartlett): '''inner covariance matrix for HAC over group sums sandwich This assumes we have complete equal spaced time periods. The number of time periods per group need not be the same, but we need at least one observation for each time period For a single categorical group only, or a everything else but time dimension. This first aggregates x over groups for each time period, then applies HAC on the sum per period. Parameters ---------- x : ndarray (nobs,) or (nobs, k_var) data, for HAC this is array of x_i * u_i time : ndarray, (nobs,) timeindes, assumed to be integers range(n_periods) nlags : int or None highest lag to include in kernel window. If None, then nlags = floor[4(T/100)^(2/9)] is used. weights_func : callable weights_func is called with nlags as argument to get the kernel weights. default are Bartlett weights Returns ------- S : ndarray, (k_vars, k_vars) inner covariance matrix for sandwich References ---------- Daniel Hoechle, xtscc paper Driscoll and Kraay ''' #needs groupsums x_group_sums = group_sums(x, time).T #TODO: transpose return in grou_sum return S_hac_simple(x_group_sums, nlags=nlags, weights_func=weights_func) def S_crosssection(x, group): '''inner covariance matrix for White on group sums sandwich I guess for a single categorical group only, categorical group, can also be the product/intersection of groups This is used by cov_cluster and indirectly verified ''' x_group_sums = group_sums(x, group).T #TODO: why transposed return S_white_simple(x_group_sums) def cov_crosssection_0(results, group): '''this one is still wrong, use cov_cluster instead''' #TODO: currently used version of groupsums requires 2d resid scale = S_crosssection(results.resid[:,None], group) scale = np.squeeze(scale) cov = _HCCM1(results, scale) return cov def cov_cluster(results, group, use_correction=True): '''cluster robust covariance matrix Calculates sandwich covariance matrix for a single cluster, i.e. grouped variables. Parameters ---------- results : result instance result of a regression, uses results.model.exog and results.resid TODO: this should use wexog instead use_correction : bool If true (default), then the small sample correction factor is used. Returns ------- cov : ndarray, (k_vars, k_vars) cluster robust covariance matrix for parameter estimates Notes ----- same result as Stata in UCLA example and same as Peterson ''' #TODO: currently used version of groupsums requires 2d resid xu, hessian_inv = _get_sandwich_arrays(results, cov_type='clu') if not hasattr(group, 'dtype') or group.dtype != np.dtype('int'): clusters, group = np.unique(group, return_inverse=True) else: clusters = np.unique(group) scale = S_crosssection(xu, group) nobs, k_params = xu.shape n_groups = len(clusters) #replace with stored group attributes if available cov_c = _HCCM2(hessian_inv, scale) if use_correction: cov_c *= (n_groups / (n_groups - 1.) * ((nobs-1.) / float(nobs - k_params))) return cov_c def cov_cluster_2groups(results, group, group2=None, use_correction=True): '''cluster robust covariance matrix for two groups/clusters Parameters ---------- results : result instance result of a regression, uses results.model.exog and results.resid TODO: this should use wexog instead use_correction : bool If true (default), then the small sample correction factor is used. Returns ------- cov_both : ndarray, (k_vars, k_vars) cluster robust covariance matrix for parameter estimates, for both clusters cov_0 : ndarray, (k_vars, k_vars) cluster robust covariance matrix for parameter estimates for first cluster cov_1 : ndarray, (k_vars, k_vars) cluster robust covariance matrix for parameter estimates for second cluster Notes ----- verified against Peterson's table, (4 decimal print precision) ''' if group2 is None: if group.ndim !=2 or group.shape[1] != 2: raise ValueError('if group2 is not given, then groups needs to be ' + 'an array with two columns') group0 = group[:, 0] group1 = group[:, 1] else: group0 = group group1 = group2 group = (group0, group1) cov0 = cov_cluster(results, group0, use_correction=use_correction) #[0] because we get still also returns bse cov1 = cov_cluster(results, group1, use_correction=use_correction) # cov of cluster formed by intersection of two groups cov01 = cov_cluster(results, combine_indices(group)[0], use_correction=use_correction) #robust cov matrix for union of groups cov_both = cov0 + cov1 - cov01 #return all three (for now?) return cov_both, cov0, cov1 def cov_white_simple(results, use_correction=True): ''' heteroscedasticity robust covariance matrix (White) Parameters ---------- results : result instance result of a regression, uses results.model.exog and results.resid TODO: this should use wexog instead Returns ------- cov : ndarray, (k_vars, k_vars) heteroscedasticity robust covariance matrix for parameter estimates Notes ----- This produces the same result as cov_hc0, and does not include any small sample correction. verified (against LinearRegressionResults and Peterson) See Also -------- cov_hc1, cov_hc2, cov_hc3 : heteroscedasticity robust covariance matrices with small sample corrections ''' xu, hessian_inv = _get_sandwich_arrays(results) sigma = S_white_simple(xu) cov_w = _HCCM2(hessian_inv, sigma) #add bread to sandwich if use_correction: nobs, k_params = xu.shape cov_w *= nobs / float(nobs - k_params) return cov_w def cov_hac_simple(results, nlags=None, weights_func=weights_bartlett, use_correction=True): ''' heteroscedasticity and autocorrelation robust covariance matrix (Newey-West) Assumes we have a single time series with zero axis consecutive, equal spaced time periods Parameters ---------- results : result instance result of a regression, uses results.model.exog and results.resid TODO: this should use wexog instead nlags : int or None highest lag to include in kernel window. If None, then nlags = floor[4(T/100)^(2/9)] is used. weights_func : callable weights_func is called with nlags as argument to get the kernel weights. default are Bartlett weights Returns ------- cov : ndarray, (k_vars, k_vars) HAC robust covariance matrix for parameter estimates Notes ----- verified only for nlags=0, which is just White just guessing on correction factor, need reference options might change when other kernels besides Bartlett are available. ''' xu, hessian_inv = _get_sandwich_arrays(results) sigma = S_hac_simple(xu, nlags=nlags, weights_func=weights_func) cov_hac = _HCCM2(hessian_inv, sigma) if use_correction: nobs, k_params = xu.shape cov_hac *= nobs / float(nobs - k_params) return cov_hac cov_hac = cov_hac_simple #alias for users #---------------------- use time lags corrected for groups #the following were copied from a different experimental script, #groupidx is tuple, observations assumed to be stacked by group member and #sorted by time, equal number of periods is not required, but equal spacing is. #I think this is pure within group HAC: apply HAC to each group member #separately def lagged_groups(x, lag, groupidx): ''' assumes sorted by time, groupidx is tuple of start and end values not optimized, just to get a working version, loop over groups ''' out0 = [] out_lagged = [] for l,u in groupidx: if l+lag < u: #group is longer than lag out0.append(x[l+lag:u]) out_lagged.append(x[l:u-lag]) if out0 == []: raise ValueError('all groups are empty taking lags') #return out0, out_lagged return np.vstack(out0), np.vstack(out_lagged) def S_nw_panel(xw, weights, groupidx): '''inner covariance matrix for HAC for panel data no denominator nobs used no reference for this, just accounting for time indices ''' nlags = len(weights)-1 S = weights[0] * np.dot(xw.T, xw) #weights just for completeness for lag in range(1, nlags+1): xw0, xwlag = lagged_groups(xw, lag, groupidx) s = np.dot(xw0.T, xwlag) S += weights[lag] * (s + s.T) return S def cov_nw_panel(results, nlags, groupidx, weights_func=weights_bartlett, use_correction='hac'): '''Panel HAC robust covariance matrix Assumes we have a panel of time series with consecutive, equal spaced time periods. Data is assumed to be in long format with time series of each individual stacked into one array. Panel can be unbalanced. Parameters ---------- results : result instance result of a regression, uses results.model.exog and results.resid TODO: this should use wexog instead nlags : int or None Highest lag to include in kernel window. Currently, no default because the optimal length will depend on the number of observations per cross-sectional unit. groupidx : list of tuple each tuple should contain the start and end index for an individual. (groupidx might change in future). weights_func : callable weights_func is called with nlags as argument to get the kernel weights. default are Bartlett weights use_correction : 'cluster' or 'hac' or False If False, then no small sample correction is used. If 'cluster' (default), then the same correction as in cov_cluster is used. If 'hac', then the same correction as in single time series, cov_hac is used. Returns ------- cov : ndarray, (k_vars, k_vars) HAC robust covariance matrix for parameter estimates Notes ----- For nlags=0, this is just White covariance, cov_white. If kernel is uniform, `weights_uniform`, with nlags equal to the number of observations per unit in a balance panel, then cov_cluster and cov_hac_panel are identical. Tested against STATA `newey` command with same defaults. Options might change when other kernels besides Bartlett and uniform are available. ''' if nlags == 0: #so we can reproduce HC0 White weights = [1, 0] #to avoid the scalar check in hac_nw else: weights = weights_func(nlags) xu, hessian_inv = _get_sandwich_arrays(results) S_hac = S_nw_panel(xu, weights, groupidx) cov_hac = _HCCM2(hessian_inv, S_hac) if use_correction: nobs, k_params = xu.shape if use_correction == 'hac': cov_hac *= nobs / float(nobs - k_params) elif use_correction in ['c', 'clu', 'cluster']: n_groups = len(groupidx) cov_hac *= n_groups / (n_groups - 1.) cov_hac *= ((nobs-1.) / float(nobs - k_params)) return cov_hac def cov_nw_groupsum(results, nlags, time, weights_func=weights_bartlett, use_correction=0): '''Driscoll and Kraay Panel robust covariance matrix Robust covariance matrix for panel data of Driscoll and Kraay. Assumes we have a panel of time series where the time index is available. The time index is assumed to represent equal spaced periods. At least one observation per period is required. Parameters ---------- results : result instance result of a regression, uses results.model.exog and results.resid TODO: this should use wexog instead nlags : int or None Highest lag to include in kernel window. Currently, no default because the optimal length will depend on the number of observations per cross-sectional unit. time : ndarray of int this should contain the coding for the time period of each observation. time periods should be integers in range(maxT) where maxT is obs of i weights_func : callable weights_func is called with nlags as argument to get the kernel weights. default are Bartlett weights use_correction : 'cluster' or 'hac' or False If False, then no small sample correction is used. If 'hac' (default), then the same correction as in single time series, cov_hac is used. If 'cluster', then the same correction as in cov_cluster is used. Returns ------- cov : ndarray, (k_vars, k_vars) HAC robust covariance matrix for parameter estimates Notes ----- Tested against STATA xtscc package, which uses no small sample correction This first averages relevant variables for each time period over all individuals/groups, and then applies the same kernel weighted averaging over time as in HAC. Warning: In the example with a short panel (few time periods and many individuals) with mainly across individual variation this estimator did not produce reasonable results. Options might change when other kernels besides Bartlett and uniform are available. References ---------- Daniel Hoechle, xtscc paper Driscoll and Kraay ''' xu, hessian_inv = _get_sandwich_arrays(results) #S_hac = S_nw_panel(xw, weights, groupidx) S_hac = S_hac_groupsum(xu, time, nlags=nlags, weights_func=weights_func) cov_hac = _HCCM2(hessian_inv, S_hac) if use_correction: nobs, k_params = xu.shape if use_correction == 'hac': cov_hac *= nobs / float(nobs - k_params) elif use_correction in ['c', 'cluster']: n_groups = len(np.unique(time)) cov_hac *= n_groups / (n_groups - 1.) cov_hac *= ((nobs-1.) / float(nobs - k_params)) return cov_hac statsmodels-0.12.2/statsmodels/stats/stattools.py000066400000000000000000000334131400612667500222570ustar00rootroot00000000000000""" Statistical tests to be used in conjunction with the models Notes ----- These functions have not been formally tested. """ from scipy import stats import numpy as np from statsmodels.tools.sm_exceptions import ValueWarning def durbin_watson(resids, axis=0): r""" Calculates the Durbin-Watson statistic. Parameters ---------- resids : array_like Data for which to compute the Durbin-Watson statistic. Usually regression model residuals. axis : int, optional Axis to use if data has more than 1 dimension. Default is 0. Returns ------- dw : float, array_like The Durbin-Watson statistic. Notes ----- The null hypothesis of the test is that there is no serial correlation in the residuals. The Durbin-Watson test statistic is defined as: .. math:: \sum_{t=2}^T((e_t - e_{t-1})^2)/\sum_{t=1}^Te_t^2 The test statistic is approximately equal to 2*(1-r) where ``r`` is the sample autocorrelation of the residuals. Thus, for r == 0, indicating no serial correlation, the test statistic equals 2. This statistic will always be between 0 and 4. The closer to 0 the statistic, the more evidence for positive serial correlation. The closer to 4, the more evidence for negative serial correlation. """ resids = np.asarray(resids) diff_resids = np.diff(resids, 1, axis=axis) dw = np.sum(diff_resids**2, axis=axis) / np.sum(resids**2, axis=axis) return dw def omni_normtest(resids, axis=0): """ Omnibus test for normality Parameters ---------- resid : array_like axis : int, optional Default is 0 Returns ------- Chi^2 score, two-tail probability """ # TODO: change to exception in summary branch and catch in summary() # behavior changed between scipy 0.9 and 0.10 resids = np.asarray(resids) n = resids.shape[axis] if n < 8: from warnings import warn warn("omni_normtest is not valid with less than 8 observations; %i " "samples were given." % int(n), ValueWarning) return np.nan, np.nan return stats.normaltest(resids, axis=axis) def jarque_bera(resids, axis=0): r""" The Jarque-Bera test of normality. Parameters ---------- resids : array_like Data to test for normality. Usually regression model residuals that are mean 0. axis : int, optional Axis to use if data has more than 1 dimension. Default is 0. Returns ------- JB : {float, ndarray} The Jarque-Bera test statistic. JBpv : {float, ndarray} The pvalue of the test statistic. skew : {float, ndarray} Estimated skewness of the data. kurtosis : {float, ndarray} Estimated kurtosis of the data. Notes ----- Each output returned has 1 dimension fewer than data The Jarque-Bera test statistic tests the null that the data is normally distributed against an alternative that the data follow some other distribution. The test statistic is based on two moments of the data, the skewness, and the kurtosis, and has an asymptotic :math:`\chi^2_2` distribution. The test statistic is defined .. math:: JB = n(S^2/6+(K-3)^2/24) where n is the number of data points, S is the sample skewness, and K is the sample kurtosis of the data. """ resids = np.asarray(resids) # Calculate residual skewness and kurtosis skew = stats.skew(resids, axis=axis) kurtosis = 3 + stats.kurtosis(resids, axis=axis) # Calculate the Jarque-Bera test for normality n = resids.shape[axis] jb = (n / 6.) * (skew ** 2 + (1 / 4.) * (kurtosis - 3) ** 2) jb_pv = stats.chi2.sf(jb, 2) return jb, jb_pv, skew, kurtosis def robust_skewness(y, axis=0): """ Calculates the four skewness measures in Kim & White Parameters ---------- y : array_like Data to compute use in the estimator. axis : int or None, optional Axis along which the skewness measures are computed. If `None`, the entire array is used. Returns ------- sk1 : ndarray The standard skewness estimator. sk2 : ndarray Skewness estimator based on quartiles. sk3 : ndarray Skewness estimator based on mean-median difference, standardized by absolute deviation. sk4 : ndarray Skewness estimator based on mean-median difference, standardized by standard deviation. Notes ----- The robust skewness measures are defined .. math:: SK_{2}=\\frac{\\left(q_{.75}-q_{.5}\\right) -\\left(q_{.5}-q_{.25}\\right)}{q_{.75}-q_{.25}} .. math:: SK_{3}=\\frac{\\mu-\\hat{q}_{0.5}} {\\hat{E}\\left[\\left|y-\\hat{\\mu}\\right|\\right]} .. math:: SK_{4}=\\frac{\\mu-\\hat{q}_{0.5}}{\\hat{\\sigma}} .. [*] Tae-Hwan Kim and Halbert White, "On more robust estimation of skewness and kurtosis," Finance Research Letters, vol. 1, pp. 56-73, March 2004. """ if axis is None: y = y.ravel() axis = 0 y = np.sort(y, axis) q1, q2, q3 = np.percentile(y, [25.0, 50.0, 75.0], axis=axis) mu = y.mean(axis) shape = (y.size,) if axis is not None: shape = list(mu.shape) shape.insert(axis, 1) shape = tuple(shape) mu_b = np.reshape(mu, shape) q2_b = np.reshape(q2, shape) sigma = np.sqrt(np.mean(((y - mu_b)**2), axis)) sk1 = stats.skew(y, axis=axis) sk2 = (q1 + q3 - 2.0 * q2) / (q3 - q1) sk3 = (mu - q2) / np.mean(abs(y - q2_b), axis=axis) sk4 = (mu - q2) / sigma return sk1, sk2, sk3, sk4 def _kr3(y, alpha=5.0, beta=50.0): """ KR3 estimator from Kim & White Parameters ---------- y : array_like, 1-d Data to compute use in the estimator. alpha : float, optional Lower cut-off for measuring expectation in tail. beta : float, optional Lower cut-off for measuring expectation in center. Returns ------- kr3 : float Robust kurtosis estimator based on standardized lower- and upper-tail expected values Notes ----- .. [*] Tae-Hwan Kim and Halbert White, "On more robust estimation of skewness and kurtosis," Finance Research Letters, vol. 1, pp. 56-73, March 2004. """ perc = (alpha, 100.0 - alpha, beta, 100.0 - beta) lower_alpha, upper_alpha, lower_beta, upper_beta = np.percentile(y, perc) l_alpha = np.mean(y[y < lower_alpha]) u_alpha = np.mean(y[y > upper_alpha]) l_beta = np.mean(y[y < lower_beta]) u_beta = np.mean(y[y > upper_beta]) return (u_alpha - l_alpha) / (u_beta - l_beta) def expected_robust_kurtosis(ab=(5.0, 50.0), dg=(2.5, 25.0)): """ Calculates the expected value of the robust kurtosis measures in Kim and White assuming the data are normally distributed. Parameters ---------- ab : iterable, optional Contains 100*(alpha, beta) in the kr3 measure where alpha is the tail quantile cut-off for measuring the extreme tail and beta is the central quantile cutoff for the standardization of the measure db : iterable, optional Contains 100*(delta, gamma) in the kr4 measure where delta is the tail quantile for measuring extreme values and gamma is the central quantile used in the the standardization of the measure Returns ------- ekr : ndarray, 4-element Contains the expected values of the 4 robust kurtosis measures Notes ----- See `robust_kurtosis` for definitions of the robust kurtosis measures """ alpha, beta = ab delta, gamma = dg expected_value = np.zeros(4) ppf = stats.norm.ppf pdf = stats.norm.pdf q1, q2, q3, q5, q6, q7 = ppf(np.array((1.0, 2.0, 3.0, 5.0, 6.0, 7.0)) / 8) expected_value[0] = 3 expected_value[1] = ((q7 - q5) + (q3 - q1)) / (q6 - q2) q_alpha, q_beta = ppf(np.array((alpha / 100.0, beta / 100.0))) expected_value[2] = (2 * pdf(q_alpha) / alpha) / (2 * pdf(q_beta) / beta) q_delta, q_gamma = ppf(np.array((delta / 100.0, gamma / 100.0))) expected_value[3] = (-2.0 * q_delta) / (-2.0 * q_gamma) return expected_value def robust_kurtosis(y, axis=0, ab=(5.0, 50.0), dg=(2.5, 25.0), excess=True): """ Calculates the four kurtosis measures in Kim & White Parameters ---------- y : array_like Data to compute use in the estimator. axis : int or None, optional Axis along which the kurtosis are computed. If `None`, the entire array is used. a iterable, optional Contains 100*(alpha, beta) in the kr3 measure where alpha is the tail quantile cut-off for measuring the extreme tail and beta is the central quantile cutoff for the standardization of the measure db : iterable, optional Contains 100*(delta, gamma) in the kr4 measure where delta is the tail quantile for measuring extreme values and gamma is the central quantile used in the the standardization of the measure excess : bool, optional If true (default), computed values are excess of those for a standard normal distribution. Returns ------- kr1 : ndarray The standard kurtosis estimator. kr2 : ndarray Kurtosis estimator based on octiles. kr3 : ndarray Kurtosis estimators based on exceedance expectations. kr4 : ndarray Kurtosis measure based on the spread between high and low quantiles. Notes ----- The robust kurtosis measures are defined .. math:: KR_{2}=\\frac{\\left(\\hat{q}_{.875}-\\hat{q}_{.625}\\right) +\\left(\\hat{q}_{.375}-\\hat{q}_{.125}\\right)} {\\hat{q}_{.75}-\\hat{q}_{.25}} .. math:: KR_{3}=\\frac{\\hat{E}\\left(y|y>\\hat{q}_{1-\\alpha}\\right) -\\hat{E}\\left(y|y<\\hat{q}_{\\alpha}\\right)} {\\hat{E}\\left(y|y>\\hat{q}_{1-\\beta}\\right) -\\hat{E}\\left(y|y<\\hat{q}_{\\beta}\\right)} .. math:: KR_{4}=\\frac{\\hat{q}_{1-\\delta}-\\hat{q}_{\\delta}} {\\hat{q}_{1-\\gamma}-\\hat{q}_{\\gamma}} where :math:`\\hat{q}_{p}` is the estimated quantile at :math:`p`. .. [*] Tae-Hwan Kim and Halbert White, "On more robust estimation of skewness and kurtosis," Finance Research Letters, vol. 1, pp. 56-73, March 2004. """ if (axis is None or (y.squeeze().ndim == 1 and y.ndim != 1)): y = y.ravel() axis = 0 alpha, beta = ab delta, gamma = dg perc = (12.5, 25.0, 37.5, 62.5, 75.0, 87.5, delta, 100.0 - delta, gamma, 100.0 - gamma) e1, e2, e3, e5, e6, e7, fd, f1md, fg, f1mg = np.percentile(y, perc, axis=axis) expected_value = (expected_robust_kurtosis(ab, dg) if excess else np.zeros(4)) kr1 = stats.kurtosis(y, axis, False) - expected_value[0] kr2 = ((e7 - e5) + (e3 - e1)) / (e6 - e2) - expected_value[1] if y.ndim == 1: kr3 = _kr3(y, alpha, beta) else: kr3 = np.apply_along_axis(_kr3, axis, y, alpha, beta) kr3 -= expected_value[2] kr4 = (f1md - fd) / (f1mg - fg) - expected_value[3] return kr1, kr2, kr3, kr4 def _medcouple_1d(y): """ Calculates the medcouple robust measure of skew. Parameters ---------- y : array_like, 1-d Data to compute use in the estimator. Returns ------- mc : float The medcouple statistic Notes ----- The current algorithm requires a O(N**2) memory allocations, and so may not work for very large arrays (N>10000). .. [*] M. Huberta and E. Vandervierenb, "An adjusted boxplot for skewed distributions" Computational Statistics & Data Analysis, vol. 52, pp. 5186-5201, August 2008. """ # Parameter changes the algorithm to the slower for large n y = np.squeeze(np.asarray(y)) if y.ndim != 1: raise ValueError("y must be squeezable to a 1-d array") y = np.sort(y) n = y.shape[0] if n % 2 == 0: mf = (y[n // 2 - 1] + y[n // 2]) / 2 else: mf = y[(n - 1) // 2] z = y - mf lower = z[z <= 0.0] upper = z[z >= 0.0] upper = upper[:, None] standardization = upper - lower is_zero = np.logical_and(lower == 0.0, upper == 0.0) standardization[is_zero] = np.inf spread = upper + lower h = spread / standardization # GH5395 num_ties = np.sum(lower == 0.0) if num_ties: # Replacements has -1 above the anti-diagonal, 0 on the anti-diagonal, # and 1 below the anti-diagonal replacements = np.ones((num_ties, num_ties)) - np.eye(num_ties) replacements -= 2 * np.triu(replacements) # Convert diagonal to anti-diagonal replacements = np.fliplr(replacements) # Always replace upper right block h[:num_ties, -num_ties:] = replacements return np.median(h) def medcouple(y, axis=0): """ Calculate the medcouple robust measure of skew. Parameters ---------- y : array_like Data to compute use in the estimator. axis : {int, None} Axis along which the medcouple statistic is computed. If `None`, the entire array is used. Returns ------- mc : ndarray The medcouple statistic with the same shape as `y`, with the specified axis removed. Notes ----- The current algorithm requires a O(N**2) memory allocations, and so may not work for very large arrays (N>10000). .. [*] M. Huberta and E. Vandervierenb, "An adjusted boxplot for skewed distributions" Computational Statistics & Data Analysis, vol. 52, pp. 5186-5201, August 2008. """ y = np.asarray(y, dtype=np.double) # GH 4243 if axis is None: return _medcouple_1d(y.ravel()) return np.apply_along_axis(_medcouple_1d, axis, y) statsmodels-0.12.2/statsmodels/stats/tabledist.py000066400000000000000000000230231400612667500221720ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sat Oct 01 20:20:16 2011 Author: Josef Perktold License: BSD-3 TODO: check orientation, size and alpha should be increasing for interp1d, but what is alpha? can be either sf or cdf probability change it to use one consistent notation check: instead of bound checking I could use the fill-value of the interpolators """ import numpy as np from scipy.interpolate import interp1d, interp2d, Rbf from statsmodels.tools.decorators import cache_readonly class TableDist(object): """ Distribution, critical values and p-values from tables currently only 1 extra parameter, e.g. sample size Parameters ---------- alpha : array_like, 1d probabiliy in the table, could be either sf (right tail) or cdf (left tail) size : array_like, 1d The sample sizes for the table crit_table : array_like, 2d The sample sizes in the table array with critical values for sample size in rows and probability in columns asymptotic : callable, optional Callable function with the form fn(nobs) that returns len(alpha) critical values where the critical value in position i corresponds to alpha[i] min_nobs : int, optional Minimum number of observations to use the asymptotic distribution. If not provided, uses max(size). max_nobs : int, optional Maximum number of observations to use the tabular distribution. If not provided, uses max(size) Notes ----- size and alpha must be sorted and increasing. If both min_nobs and max_nobs are provided, then the critical values from the tabular distribution and the asymptotic distribution are linearly blended using the formula :math:`w cv_a + (1-w) cv_t` where the weight is :math:`w = (n - a_{min}) / (a_{max} - a_{min})`. This ensures the transition between the tabular and the asymptotic critical values is continuous. If these are not provided, then the asymptotic critical value is used for nobs > max(size). """ def __init__(self, alpha, size, crit_table, asymptotic=None, min_nobs=None, max_nobs=None): self.alpha = np.asarray(alpha) if self.alpha.ndim != 1: raise ValueError('alpha is not 1d') elif (np.diff(self.alpha) <= 0).any(): raise ValueError('alpha is not sorted') self.size = np.asarray(size) if self.size.ndim != 1: raise ValueError('size is not 1d') elif (np.diff(self.size) <= 0).any(): raise ValueError('size is not sorted') if self.size.ndim == 1: if (np.diff(alpha) <= 0).any(): raise ValueError('alpha is not sorted') self.crit_table = np.asarray(crit_table) if self.crit_table.shape != (self.size.shape[0], self.alpha.shape[0]): raise ValueError('crit_table must have shape' '(len(size), len(alpha))') self.n_alpha = len(alpha) self.signcrit = np.sign(np.diff(self.crit_table, 1).mean()) if self.signcrit > 0: # increasing self.critv_bounds = self.crit_table[:, [0, 1]] else: self.critv_bounds = self.crit_table[:, [1, 0]] self.asymptotic = None max_size = self.max_size = max(size) if asymptotic is not None: try: cv = asymptotic(self.max_size + 1) except Exception as exc: raise type(exc)('Calling asymptotic(self.size+1) failed. The ' 'error message was:' '\n\n{err_msg}'.format(err_msg=exc.args[0])) if len(cv) != len(alpha): raise ValueError('asymptotic does not return len(alpha) ' 'values') self.asymptotic = asymptotic self.min_nobs = max_size if min_nobs is None else min_nobs self.max_nobs = max_size if max_nobs is None else max_nobs if self.min_nobs > max_size: raise ValueError('min_nobs > max(size)') if self.max_nobs > max_size: raise ValueError('max_nobs > max(size)') @cache_readonly def polyn(self): polyn = [interp1d(self.size, self.crit_table[:, i]) for i in range(self.n_alpha)] return polyn @cache_readonly def poly2d(self): # check for monotonicity ? # fix this, interp needs increasing poly2d = interp2d(self.size, self.alpha, self.crit_table) return poly2d @cache_readonly def polyrbf(self): xs, xa = np.meshgrid(self.size.astype(float), self.alpha) polyrbf = Rbf(xs.ravel(), xa.ravel(), self.crit_table.T.ravel(), function='linear') return polyrbf def _critvals(self, n): """ Rows of the table, linearly interpolated for given sample size Parameters ---------- n : float sample size, second parameter of the table Returns ------- critv : ndarray, 1d critical values (ppf) corresponding to a row of the table Notes ----- This is used in two step interpolation, or if we want to know the critical values for all alphas for any sample size that we can obtain through interpolation """ if n > self.max_size: if self.asymptotic is not None: cv = self.asymptotic(n) else: raise ValueError('n is above max(size) and no asymptotic ' 'distribtuion is provided') else: cv = ([p(n) for p in self.polyn]) if n > self.min_nobs: w = (n - self.min_nobs) / (self.max_nobs - self.min_nobs) w = min(1.0, w) a_cv = self.asymptotic(n) cv = w * a_cv + (1 - w) * cv return cv def prob(self, x, n): """ Find pvalues by interpolation, either cdf(x) Returns extreme probabilities, 0.001 and 0.2, for out of range Parameters ---------- x : array_like observed value, assumed to follow the distribution in the table n : float sample size, second parameter of the table Returns ------- prob : array_like This is the probability for each value of x, the p-value in underlying distribution is for a statistical test. """ critv = self._critvals(n) alpha = self.alpha if self.signcrit < 1: # reverse if critv is decreasing critv, alpha = critv[::-1], alpha[::-1] # now critv is increasing if np.size(x) == 1: if x < critv[0]: return alpha[0] elif x > critv[-1]: return alpha[-1] return interp1d(critv, alpha)(x)[()] else: # vectorized cond_low = (x < critv[0]) cond_high = (x > critv[-1]) cond_interior = ~np.logical_or(cond_low, cond_high) probs = np.nan * np.ones(x.shape) # mistake if nan left probs[cond_low] = alpha[0] probs[cond_low] = alpha[-1] probs[cond_interior] = interp1d(critv, alpha)(x[cond_interior]) return probs def crit(self, prob, n): """ Returns interpolated quantiles, similar to ppf or isf use two sequential 1d interpolation, first by n then by prob Parameters ---------- prob : array_like probabilities corresponding to the definition of table columns n : int or float sample size, second parameter of the table Returns ------- ppf : array_like critical values with same shape as prob """ prob = np.asarray(prob) alpha = self.alpha critv = self._critvals(n) # vectorized cond_ilow = (prob > alpha[0]) cond_ihigh = (prob < alpha[-1]) cond_interior = np.logical_or(cond_ilow, cond_ihigh) # scalar if prob.size == 1: if cond_interior: return interp1d(alpha, critv)(prob) else: return np.nan # vectorized quantile = np.nan * np.ones(prob.shape) # nans for outside quantile[cond_interior] = interp1d(alpha, critv)(prob[cond_interior]) return quantile def crit3(self, prob, n): """ Returns interpolated quantiles, similar to ppf or isf uses Rbf to interpolate critical values as function of `prob` and `n` Parameters ---------- prob : array_like probabilities corresponding to the definition of table columns n : int or float sample size, second parameter of the table Returns ------- ppf : array_like critical values with same shape as prob, returns nan for arguments that are outside of the table bounds """ prob = np.asarray(prob) alpha = self.alpha # vectorized cond_ilow = (prob > alpha[0]) cond_ihigh = (prob < alpha[-1]) cond_interior = np.logical_or(cond_ilow, cond_ihigh) # scalar if prob.size == 1: if cond_interior: return self.polyrbf(n, prob) else: return np.nan # vectorized quantile = np.nan * np.ones(prob.shape) # nans for outside quantile[cond_interior] = self.polyrbf(n, prob[cond_interior]) return quantile statsmodels-0.12.2/statsmodels/stats/tests/000077500000000000000000000000001400612667500210075ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/stats/tests/__init__.py000066400000000000000000000000001400612667500231060ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/stats/tests/gen_contingency_table_tests.R000066400000000000000000000050131400612667500266730ustar00rootroot00000000000000library(coin) library(exact2x2) tables = list() tables[[1]] = matrix(c(23, 15, 19, 31), ncol=2, byrow=TRUE) tables[[2]] = matrix(c(144, 33, 84, 126, 2, 4, 14, 29, 0, 2, 6, 25, 0, 0, 1, 5), ncol=4, byrow=TRUE) tables[[3]] = matrix(c(20, 10, 5, 3, 30, 15, 0, 5, 40), ncol=3, byrow=TRUE) results = array(0, c(length(tables), 17)) for (k in 1:3) { table = as.table(tables[[k]]) names(attributes(table)$dimnames) = c("x", "y") # Nominal homogeneity test with chi^2 reference rslt = mh_test(table) results[k, 1] = rslt@statistic@teststatistic results[k, 2] = rslt@statistic@df # Nominal homogeneity test with binomial reference if (prod(dim(table)) == 4) { rslt = mcnemar.exact(table) results[k, 3] = rslt$p.value } # Nominal homogeneity test with continuity correction if (prod(dim(table)) == 4) { rslt = mcnemar.test(table) results[k, 4] = rslt$p.value } # Linear-by-linear homogeneity test with linear weights scores = list(x=seq(dim(table)[1]), y=seq(dim(table)[2])) rslt = lbl_test(table, scores=scores) results[k, 5] = rslt@statistic@linearstatistic results[k, 6] = rslt@statistic@expectation results[k, 7] = rslt@statistic@covariance@variance results[k, 8] = rslt@statistic@teststatistic results[k, 9] = rslt@distribution@pvalue(rslt@statistic@teststatistic) # Linear-by-linear homogeneity test with quadratic column weights scores = list(x=seq(dim(table)[1]), y=seq(dim(table)[2])^2) rslt = lbl_test(table, scores=scores) results[k, 10] = rslt@statistic@linearstatistic results[k, 11] = rslt@statistic@expectation results[k, 12] = rslt@statistic@covariance@variance results[k, 13] = rslt@statistic@teststatistic results[k, 14] = rslt@distribution@pvalue(rslt@statistic@teststatistic) # Bowker symmetry test (apparently mcnemar.test performs a # symmetry test when dim>2 although this is not documented). rslt = mcnemar.test(table, correct=FALSE) results[k, 15] = rslt$statistic results[k, 16] = rslt$parameter[1] results[k, 17] = rslt$p.value } colnames(results) = c("homog_stat", "homog_df", "homog_binom_p", "homog_cont_p", "lbl_stat", "lbl_expval", "lbl_var", "lbl_chi2", "lbl_pvalue", "lbl2_stat", "lbl2_expval", "lbl2_var", "lbl2_chi2", "lbl2_pvalue", "bowker_stat", "bowker_df", "bowker_pvalue") write.csv(results, file="contingency_table_r_results.csv", row.names=FALSE) statsmodels-0.12.2/statsmodels/stats/tests/results/000077500000000000000000000000001400612667500225105ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/stats/tests/results/__init__.py000066400000000000000000000000001400612667500246070ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/stats/tests/results/anova.R000066400000000000000000000062501400612667500237420ustar00rootroot00000000000000dta <- read.table('data.dat', header=TRUE) dta$Duration <- factor(dta$Duration) dta$Weight <- factor(dta$Weight) dta$logDays <- log(dta$Days + 1) # Use log days to "stabilize" variance attach(dta) library(car) source('/home/skipper/statsmodels/statsmodels/tools/topy.R') sum.lm = lm(logDays ~ Duration * Weight, contrasts=list(Duration=contr.sum, Weight=contr.sum)) anova.lm.sum <- anova(sum.lm) for(name in names(anova.lm.sum)) { mkarray2(anova.lm.sum[[name]], name, TRUE) }; cat("\n") anova.lm.interaction <- anova(lm(logDays ~ Duration + Weight), sum.lm) for(name in names(anova.lm.interaction)) { mkarray2(anova.lm.interaction[[name]], name, TRUE) }; cat("\n") anova.lm.variable <- anova(lm(logDays ~ Duration), lm(logDays ~ Duration + Weight)) anova.lm.variable2 <- anova(lm(logDays ~ Weight), lm(logDays ~ Duration + Weight)) anova.i <- anova(sum.lm) anova.ii <- Anova(sum.lm, type='II') anova.iii <- Anova(sum.lm, type='III') nosum.lm = lm(logDays ~ Duration * Weight, contrasts=list(Duration=contr.treatment, Weight=contr.treatment)) anova.i.nosum <- anova(nosum.lm) anova.ii.nosum <- Anova(nosum.lm, type='II') anova.iii.nosum <- Anova(nosum.lm, type='III') dta.dropped <- dta[4:60, ] sum.lm.dropped <- lm(logDays ~ Duration * Weight, dta.dropped, contrasts=list(Duration=contr.sum, Weight=contr.sum)) anova.i.dropped <- anova(sum.lm.dropped) anova.ii.dropped <- Anova(sum.lm.dropped, type='II') anova.iii.dropped <- Anova(sum.lm.dropped, type='III') for(name in names(anova.ii.dropped)) { mkarray2(anova.ii.dropped[[name]], name, TRUE) }; cat("\n") for(name in names(anova.iii.dropped)) { mkarray2(anova.iii.dropped[[name]], name, TRUE) }; cat("\n") anova.iii.dropped <- Anova(sum.lm.dropped, white="hc0", type='III') for(name in names(anova.iii.dropped)) { mkarray2(anova.iii.dropped[[name]], name, TRUE) }; cat("\n") anova.iii.dropped <- Anova(sum.lm.dropped, white="hc1", type='III') for(name in names(anova.iii.dropped)) { mkarray2(anova.iii.dropped[[name]], name, TRUE) }; cat("\n") anova.iii.dropped <- Anova(sum.lm.dropped, white="hc2", type='III') for(name in names(anova.iii.dropped)) { mkarray2(anova.iii.dropped[[name]], name, TRUE) }; cat("\n") anova.iii.dropped <- Anova(sum.lm.dropped, white="hc3", type='III') for(name in names(anova.iii.dropped)) { mkarray2(anova.iii.dropped[[name]], name, TRUE) }; cat("\n") anova.ii.dropped <- Anova(sum.lm.dropped, type='II', white="hc0") for(name in names(anova.ii.dropped)) { mkarray2(anova.ii.dropped[[name]], name, TRUE) }; cat("\n") anova.ii.dropped <- Anova(sum.lm.dropped, type='II', white="hc1") for(name in names(anova.ii.dropped)) { mkarray2(anova.ii.dropped[[name]], name, TRUE) }; cat("\n") anova.ii.dropped <- Anova(sum.lm.dropped, type='II', white="hc2") for(name in names(anova.ii.dropped)) { mkarray2(anova.ii.dropped[[name]], name, TRUE) }; cat("\n") anova.ii.dropped <- Anova(sum.lm.dropped, type='II', white="hc3") for(name in names(anova.ii.dropped)) { mkarray2(anova.ii.dropped[[name]], name, TRUE) }; cat("\n") statsmodels-0.12.2/statsmodels/stats/tests/results/binary_constrict.csv000066400000000000000000000052471400612667500266110ustar00rootroot00000000000000Case,diagnosis,rate,volumne,constrict,const,log_rate,log_volumne 1,constrict,0.825,3.7,1,1.0,-0.19237189264745613,1.308332819650179 2,constrict,1.09,3.5,1,1.0,0.08617769624105241,1.252762968495368 3,constrict,2.5,1.25,1,1.0,0.9162907318741551,0.22314355131420976 4,constrict,1.5,0.75,1,1.0,0.4054651081081644,-0.2876820724517809 5,constrict,3.2,0.8,1,1.0,1.1631508098056809,-0.2231435513142097 6,constrict,3.5,0.7,1,1.0,1.252762968495368,-0.35667494393873245 7,no_constrict,0.75,0.6,0,1.0,-0.2876820724517809,-0.5108256237659907 8,no_constrict,1.7,1.1,0,1.0,0.5306282510621704,0.09531017980432493 9,no_constrict,0.75,0.9,0,1.0,-0.2876820724517809,-0.10536051565782628 10,no_constrict,0.45,0.9,0,1.0,-0.7985076962177716,-0.10536051565782628 11,no_constrict,0.57,0.8,0,1.0,-0.5621189181535413,-0.2231435513142097 12,no_constrict,2.75,0.55,0,1.0,1.0116009116784799,-0.5978370007556204 13,no_constrict,3.0,0.6,0,1.0,1.0986122886681098,-0.5108256237659907 14,constrict,2.33,1.4,1,1.0,0.8458682675776092,0.3364722366212129 15,constrict,3.75,0.75,1,1.0,1.3217558399823195,-0.2876820724517809 16,constrict,1.64,2.3,1,1.0,0.494696241836107,0.8329091229351039 17,constrict,1.6,3.2,1,1.0,0.47000362924573563,1.1631508098056809 18,constrict,1.415,0.85,1,1.0,0.34712953109520095,-0.16251892949777494 19,no_constrict,1.06,1.7,0,1.0,0.058268908123975824,0.5306282510621704 20,constrict,1.8,1.8,1,1.0,0.5877866649021191,0.5877866649021191 21,no_constrict,2.0,0.4,0,1.0,0.6931471805599453,-0.916290731874155 22,no_constrict,1.36,0.95,0,1.0,0.3074846997479607,-0.05129329438755058 23,no_constrict,1.35,1.35,0,1.0,0.30010459245033816,0.30010459245033816 24,no_constrict,1.36,1.5,0,1.0,0.3074846997479607,0.4054651081081644 25,constrict,1.78,1.6,1,1.0,0.5766133643039938,0.47000362924573563 26,no_constrict,1.5,0.6,0,1.0,0.4054651081081644,-0.5108256237659907 27,constrict,1.5,1.8,1,1.0,0.4054651081081644,0.5877866649021191 28,no_constrict,1.9,0.95,0,1.0,0.6418538861723947,-0.05129329438755058 29,constrict,0.95,1.9,1,1.0,-0.05129329438755058,0.6418538861723947 30,no_constrict,0.4,1.6,0,1.0,-0.916290731874155,0.47000362924573563 31,constrict,0.75,2.7,1,1.0,-0.2876820724517809,0.9932517730102834 32,no_constrict,0.03,2.35,0,1.0,-3.506557897319982,0.8544153281560676 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Oppose",4,0,0 "48","2","a little anxious",42,"less than high school","male",8,9,8,1,0,0,"Oppose",4,0,1 "49","1","a little anxious",71,"some college","female",12,8,8,1,1,1,"Strongly Oppose",4,0,0 "50","1","a little anxious",56,"high school","male",11,11,8,1,1,1,"Strongly Oppose",4,0,1 "51","1","a little anxious",67,"less than high school","female",8,10,5,1,1,1,"Oppose",4,0,1 "52","4","a little anxious",77,"some college","female",6,7,6,0,0,0,"Strongly Oppose",2,1,0 "53","1","not anxious at all",24,"some college","female",15,11,7,1,1,1,"Strongly Oppose",4,1,1 "54","4","a little anxious",42,"high school","male",3,7,5,0,0,0,"Oppose",2,0,0 "55","3","very anxious",25,"bachelor's degree or higher","female",11,3,4,0,1,0,"Oppose",2,0,0 "56","1","a little anxious",60,"high school","female",12,8,6,1,1,1,"Oppose",4,0,0 "57","1","somewhat anxious",43,"some college","male",14,10,8,1,1,1,"Strongly Oppose",1,0,1 "58","1","a little anxious",60,"some college","male",6,9,6,1,1,1,"Strongly Oppose",3,0,0 "59","4","not anxious at all",31,"high school","male",11,11,7,0,0,0,"Strongly Oppose",4,1,0 "60","2","somewhat anxious",47,"some college","female",13,7,6,1,0,0,"Favor",3,0,0 "61","1","very anxious",32,"bachelor's degree or higher","female",10,3,2,1,1,1,"Favor",2,0,0 "62","2","somewhat anxious",66,"some college","male",8,8,7,1,0,0,"Strongly Oppose",3,0,0 "63","2","very anxious",44,"high school","female",15,6,8,1,0,0,"Strongly Oppose",4,0,0 "64","2","somewhat anxious",46,"high school","male",17,6,4,1,0,0,"Strongly Oppose",3,0,0 "65","4","very anxious",41,"high school","female",10,3,3,0,0,0,"Strongly Oppose",2,0,0 "66","2","a little anxious",75,"high school","female",9,7,4,1,0,0,"Strongly Oppose",3,0,0 "67","1","not anxious at all",53,"bachelor's degree or higher","male",10,12,8,1,1,1,"Strongly Oppose",4,0,1 "68","3","very anxious",60,"bachelor's degree or higher","male",12,3,4,0,1,0,"Favor",2,0,0 "69","3","very anxious",75,"high school","female",2,4,6,0,1,0,"Favor",2,0,0 "70","2","not anxious at all",45,"high school","male",9,12,8,1,0,0,"Strongly Oppose",4,0,0 "71","2","not anxious at all",69,"less than high school","female",5,12,8,1,0,0,"Strongly Oppose",4,0,1 "72","4","somewhat anxious",67,"high school","female",15,6,4,0,0,0,"Strongly Oppose",3,0,0 "73","4","somewhat anxious",20,"high school","male",9,5,5,0,0,0,"Oppose",2,0,0 "74","1","somewhat anxious",43,"bachelor's degree or higher","male",16,6,4,1,1,1,"Strongly Oppose",2,0,0 "75","4","a little anxious",32,"some college","male",10,9,8,0,0,0,"Strongly Oppose",4,0,0 "76","3","somewhat anxious",39,"high school","male",12,5,4,0,1,0,"Favor",3,0,0 "77","3","very anxious",53,"bachelor's degree or higher","female",13,4,3,0,1,0,"Favor",2,0,0 "78","2","not anxious at all",57,"some college","female",2,12,8,1,0,0,"Strongly Oppose",4,1,0 "79","4","a little anxious",62,"high school","female",7,8,7,0,0,0,"Strongly Oppose",3,1,1 "80","2","a little anxious",69,"high school","female",7,9,8,1,0,0,"Strongly Oppose",4,0,0 "81","2","somewhat anxious",44,"high school","female",13,7,6,1,0,0,"Oppose",4,0,0 "82","1","not anxious at all",57,"high school","male",11,12,8,1,1,1,"Strongly Oppose",4,0,0 "83","4","a little anxious",27,"some college","female",15,7,4,0,0,0,"Strongly Oppose",2,0,0 "84","3","somewhat anxious",82,"bachelor's degree or higher","female",17,7,5,0,1,0,"Oppose",2,0,0 "85","4","somewhat anxious",84,"high school","male",12,6,6,0,0,0,"Strongly Oppose",3,1,1 "86","3","somewhat anxious",54,"some college","female",13,5,6,0,1,0,"Oppose",2,0,0 "87","2","very anxious",36,"less than high school","male",11,4,6,1,0,0,"Oppose",4,0,0 "88","1","not anxious at all",47,"some college","male",13,12,8,1,1,1,"Strongly Oppose",4,1,1 "89","1","very anxious",28,"bachelor's degree or higher","female",12,3,6,1,1,1,"Strongly Oppose",4,0,0 "90","2","very anxious",42,"high school","female",14,4,8,1,0,0,"Strongly Oppose",4,0,1 "91","3","very anxious",60,"high school","male",6,7,8,0,1,0,"Strongly Oppose",4,0,0 "92","1","very anxious",55,"bachelor's degree or higher","male",15,3,4,1,1,1,"Strongly Oppose",3,0,0 "93","2","a little anxious",55,"high school","female",6,9,7,1,0,0,"Strongly Oppose",4,0,0 "94","4","not anxious at all",61,"some college","male",12,12,8,0,0,0,"Strongly Oppose",4,1,1 "95","3","somewhat anxious",84,"high school","female",11,5,2,0,1,0,"Favor",2,0,0 "96","4","not anxious at all",45,"high school","female",3,10,8,0,0,0,"Oppose",1,0,1 "97","1","a little anxious",67,"some college","male",7,8,8,1,1,1,"Oppose",3,0,0 "98","2","not anxious at all",24,"some college","male",12,11,8,1,0,0,"Strongly Oppose",4,0,0 "99","2","not anxious at all",64,"less than high school","male",11,10,7,1,0,0,"Strongly Oppose",4,1,1 "100","1","a little anxious",72,"high school","female",7,10,3,1,1,1,"Strongly Oppose",4,0,0 "101","2","not anxious at all",40,"high school","female",4,12,8,1,0,0,"Strongly Favor",1,0,1 "102","4","not anxious at all",35,"bachelor's degree or higher","female",11,9,8,0,0,0,"Strongly Oppose",4,1,1 "103","1","not anxious at all",69,"high school","female",8,12,8,1,1,1,"Oppose",4,0,1 "104","1","a little anxious",30,"less than high school","female",6,11,7,1,1,1,"Oppose",4,0,0 "105","2","a little anxious",45,"high school","female",7,8,8,1,0,0,"Strongly Oppose",3,0,0 "106","4","very anxious",35,"some college","male",9,3,4,0,0,0,"Oppose",2,0,0 "107","4","not anxious at all",47,"high school","male",11,10,8,0,0,0,"Oppose",3,1,1 "108","4","a little anxious",53,"some college","male",11,5,4,0,0,0,"Strongly Oppose",2,0,0 "109","3","a little anxious",75,"high school","male",4,9,6,0,1,0,"Oppose",2,0,0 "110","1","somewhat anxious",70,"high school","female",13,8,6,1,1,1,"Favor",3,0,0 "111","1","somewhat anxious",56,"high school","female",8,7,8,1,1,1,"Strongly Oppose",4,0,1 "112","3","a little anxious",70,"less than high school","female",7,8,8,0,1,0,"Strongly Oppose",3,0,0 "113","4","somewhat anxious",35,"bachelor's degree or higher","male",11,4,3,0,0,0,"Strongly Oppose",2,0,0 "114","1","not anxious at all",54,"bachelor's degree or higher","female",11,12,6,1,1,1,"Strongly Oppose",4,0,0 "115","2","somewhat anxious",76,"bachelor's degree or higher","male",12,5,6,1,0,0,"Strongly Oppose",2,0,0 "116","1","a little anxious",65,"high school","female",13,9,6,1,1,1,"Strongly Oppose",4,1,1 "117","2","somewhat anxious",22,"high school","male",12,5,4,1,0,0,"Oppose",2,0,0 "118","3","somewhat anxious",28,"high school","male",13,8,8,0,1,0,"Strongly Oppose",4,0,1 "119","4","very anxious",26,"bachelor's degree or higher","male",11,3,5,0,0,0,"Favor",3,0,0 "120","1","somewhat anxious",67,"high school","male",13,5,6,1,1,1,"Strongly Oppose",4,0,0 "121","4","very anxious",58,"high school","male",13,5,4,0,0,0,"Strongly Oppose",3,0,1 "122","3","somewhat anxious",34,"some college","female",16,6,3,0,1,0,"Strongly Oppose",3,0,0 "123","2","very anxious",29,"bachelor's degree or higher","female",1,5,6,1,0,0,"Oppose",2,0,0 "124","3","a little anxious",61,"less than high school","male",13,10,6,0,1,0,"Oppose",4,0,1 "125","4","not anxious at all",58,"some college","female",6,11,8,0,0,0,"Strongly Oppose",4,0,0 "126","1","very anxious",46,"some college","female",10,5,4,1,1,1,"Oppose",2,0,0 "127","3","not anxious at all",73,"less than high school","female",6,8,6,0,1,0,"Strongly Oppose",4,0,1 "128","4","very anxious",23,"bachelor's degree or higher","male",1,3,3,0,0,0,"Strongly Oppose",1,0,0 "129","3","very anxious",19,"high school","male",15,4,6,0,1,0,"Strongly Oppose",3,0,0 "130","2","somewhat anxious",35,"some college","male",8,4,4,1,0,0,"Strongly Oppose",2,0,0 "131","2","very anxious",29,"bachelor's degree or higher","male",19,4,5,1,0,0,"Strongly Oppose",3,0,0 "132","2","very anxious",53,"bachelor's degree or higher","male",8,3,3,1,0,0,"Strongly Oppose",3,0,0 "133","3","a little anxious",72,"bachelor's degree or higher","male",12,7,6,0,1,0,"Oppose",3,0,1 "134","3","somewhat anxious",36,"bachelor's degree or higher","male",14,5,4,0,1,0,"Favor",1,0,0 "135","1","not anxious at all",26,"less than high school","male",5,11,8,1,1,1,"Strongly Oppose",3,0,0 "136","2","a little anxious",46,"bachelor's degree or higher","female",13,7,8,1,0,0,"Strongly Oppose",4,0,1 "137","3","a little anxious",31,"high school","male",6,9,8,0,1,0,"Strongly Oppose",4,0,0 "138","2","a little anxious",70,"high school","female",1,8,7,1,0,0,"Strongly Oppose",4,0,0 "139","4","a little anxious",65,"bachelor's degree or higher","male",13,7,6,0,0,0,"Strongly Oppose",3,0,1 "140","4","very anxious",69,"less than high school","female",1,4,4,0,0,0,"Oppose",2,0,0 "141","4","very anxious",72,"bachelor's degree or higher","male",11,4,4,0,0,0,"Oppose",2,0,0 "142","1","not anxious at all",71,"less than high school","female",13,12,8,1,1,1,"Strongly Oppose",4,1,1 "143","2","very anxious",62,"some college","male",12,4,6,1,0,0,"Oppose",3,0,0 "144","3","a little anxious",37,"bachelor's degree or higher","male",13,7,5,0,1,0,"Oppose",3,0,0 "145","2","very anxious",36,"high school","female",5,3,6,1,0,0,"Oppose",3,0,0 "146","4","somewhat anxious",47,"some college","female",9,4,4,0,0,0,"Favor",3,0,0 "147","3","somewhat anxious",47,"bachelor's degree or higher","male",16,5,4,0,1,0,"Oppose",3,0,0 "148","1","very anxious",28,"bachelor's degree or higher","male",4,3,3,1,1,1,"Oppose",3,0,0 "149","2","somewhat anxious",34,"bachelor's degree or higher","female",11,5,6,1,0,0,"Oppose",2,0,0 "150","2","very anxious",69,"bachelor's degree or higher","male",10,3,4,1,0,0,"Favor",2,0,0 "151","3","a little anxious",47,"high school","male",12,10,8,0,1,0,"Oppose",3,0,1 "152","1","not anxious at all",73,"high school","male",11,11,8,1,1,1,"Strongly Oppose",4,0,1 "153","3","very anxious",63,"high school","female",10,3,3,0,1,0,"Strongly Oppose",2,0,0 "154","2","somewhat anxious",33,"less than high school","male",1,7,4,1,0,0,"Strongly Oppose",2,0,0 "155","1","somewhat anxious",42,"high school","female",6,7,4,1,1,1,"Oppose",2,0,0 "156","3","somewhat anxious",43,"high school","female",7,5,6,0,1,0,"Strongly Oppose",4,1,1 "157","4","very anxious",50,"bachelor's degree or higher","female",16,3,4,0,0,0,"Oppose",2,0,0 "158","2","somewhat anxious",56,"bachelor's degree or higher","male",10,6,7,1,0,0,"Strongly Oppose",3,0,1 "159","3","somewhat anxious",28,"some college","female",11,6,6,0,1,0,"Strongly Oppose",2,0,0 "160","1","somewhat anxious",44,"some college","female",13,8,8,1,1,1,"Oppose",4,0,0 "161","3","somewhat anxious",38,"bachelor's degree or higher","female",9,5,6,0,1,0,"Oppose",1,0,0 "162","1","not anxious at all",34,"bachelor's degree or higher","female",14,11,7,1,1,1,"Strongly Oppose",2,0,0 "163","2","very anxious",56,"some college","male",16,3,3,1,0,0,"Strongly Oppose",2,0,0 "164","3","somewhat anxious",47,"bachelor's degree or higher","male",11,4,6,0,1,0,"Oppose",2,0,0 "165","4","somewhat anxious",42,"bachelor's degree or higher","male",7,7,6,0,0,0,"Strongly Oppose",4,0,1 "166","3","somewhat anxious",53,"some college","female",16,4,5,0,1,0,"Strongly Oppose",2,0,0 "167","3","very anxious",38,"bachelor's degree or higher","female",11,4,4,0,1,0,"Strongly Favor",1,0,0 "168","2","somewhat anxious",50,"bachelor's degree or higher","female",11,6,4,1,0,0,"Favor",3,0,0 "169","3","a little anxious",21,"high school","male",15,8,7,0,1,0,"Strongly Oppose",3,0,1 "170","4","somewhat anxious",25,"some college","male",18,5,6,0,0,0,"Strongly Oppose",3,0,0 "171","3","very anxious",58,"high school","female",16,5,8,0,1,0,"Oppose",4,0,1 "172","4","somewhat anxious",39,"some college","male",10,5,7,0,0,0,"Strongly Oppose",3,1,0 "173","4","not anxious at all",26,"some college","female",7,12,8,0,0,0,"Strongly Oppose",4,0,0 "174","4","somewhat anxious",61,"some college","female",8,8,6,0,0,0,"Strongly Oppose",4,0,1 "175","1","somewhat anxious",29,"some college","female",11,5,4,1,1,1,"Oppose",1,0,0 "176","3","not anxious at all",39,"some college","female",12,12,7,0,1,0,"Strongly Oppose",4,0,1 "177","2","somewhat anxious",40,"bachelor's degree or higher","male",11,7,6,1,0,0,"Strongly Oppose",4,0,1 "178","1","somewhat anxious",30,"bachelor's degree or higher","female",11,4,4,1,1,1,"Strongly Favor",2,0,0 "179","2","very anxious",64,"bachelor's degree or higher","female",10,3,5,1,0,0,"Oppose",1,0,0 "180","2","a little anxious",50,"less than high school","male",5,10,7,1,0,0,"Strongly Oppose",3,0,1 "181","2","somewhat anxious",33,"bachelor's degree or higher","female",12,9,8,1,0,0,"Strongly Oppose",4,0,0 "182","3","somewhat anxious",35,"high school","male",9,6,6,0,1,0,"Oppose",4,0,1 "183","1","somewhat anxious",26,"bachelor's degree or higher","female",16,6,5,1,1,1,"Oppose",3,0,0 "184","1","not anxious at all",44,"some college","male",16,10,8,1,1,1,"Strongly Oppose",4,0,0 "185","1","somewhat anxious",44,"some college","male",13,6,6,1,1,1,"Oppose",4,0,1 "186","1","not anxious at all",25,"some college","male",11,12,8,1,1,1,"Strongly Oppose",4,1,1 "187","3","very anxious",44,"bachelor's degree or higher","male",17,3,4,0,1,0,"Oppose",1,0,0 "188","2","a little anxious",51,"bachelor's degree or higher","female",17,9,8,1,0,0,"Strongly Oppose",4,1,1 "189","2","very anxious",62,"bachelor's degree or higher","female",14,5,6,1,0,0,"Strongly Oppose",3,0,0 "190","4","very anxious",55,"bachelor's degree or higher","female",18,3,8,0,0,0,"Strongly Oppose",4,0,1 "191","3","somewhat anxious",43,"bachelor's degree or higher","male",13,5,6,0,1,0,"Strongly Oppose",3,0,1 "192","4","very anxious",53,"bachelor's degree or higher","male",12,3,3,0,0,0,"Strongly Oppose",3,1,1 "193","3","a little anxious",49,"some college","female",10,6,4,0,1,0,"Oppose",3,0,1 "194","3","somewhat anxious",34,"some college","male",11,5,4,0,1,0,"Favor",2,0,0 "195","4","not anxious at all",36,"high school","male",11,9,7,0,0,0,"Strongly Oppose",4,0,0 "196","2","very anxious",31,"bachelor's degree or higher","male",11,3,3,1,0,0,"Strongly Oppose",3,0,1 "197","4","somewhat anxious",57,"bachelor's degree or higher","female",15,5,5,0,0,0,"Strongly Oppose",2,0,0 "198","2","somewhat anxious",18,"less than high school","female",16,6,6,1,0,0,"Oppose",1,0,0 "199","3","somewhat anxious",37,"bachelor's degree or higher","female",12,5,6,0,1,0,"Strongly Oppose",3,0,0 "200","3","very anxious",63,"bachelor's degree or higher","male",16,3,4,0,1,0,"Strongly Oppose",1,0,0 "201","2","a little anxious",48,"bachelor's degree or higher","female",16,8,8,1,0,0,"Oppose",3,0,0 "202","4","not anxious at all",32,"high school","male",13,12,8,0,0,0,"Strongly Oppose",4,0,1 "203","2","a little anxious",28,"some college","female",9,7,5,1,0,0,"Oppose",2,0,0 "204","4","somewhat anxious",45,"high school","female",13,6,5,0,0,0,"Favor",3,0,0 "205","1","a little anxious",59,"some college","male",13,7,8,1,1,1,"Oppose",4,1,1 "206","4","not anxious at all",82,"high school","female",10,11,8,0,0,0,"Strongly Oppose",3,1,0 "207","2","very anxious",62,"bachelor's degree or higher","female",2,4,4,1,0,0,"Favor",2,0,0 "208","1","very anxious",35,"bachelor's degree or higher","female",19,4,5,1,1,1,"Oppose",3,0,0 "209","4","very anxious",47,"some college","female",15,4,5,0,0,0,"Oppose",1,0,1 "210","3","not anxious at all",65,"some college","male",15,11,8,0,1,0,"Strongly Oppose",2,0,0 "211","1","a little anxious",62,"high school","male",13,8,8,1,1,1,"Strongly Oppose",4,0,0 "212","4","a little anxious",59,"bachelor's degree or higher","female",18,7,7,0,0,0,"Strongly Oppose",4,0,1 "213","4","somewhat anxious",51,"bachelor's degree or higher","female",9,6,6,0,0,0,"Oppose",2,0,0 "214","1","somewhat anxious",33,"high school","female",12,8,6,1,1,1,"Strongly Oppose",4,0,0 "215","1","a little anxious",27,"some college","female",8,9,6,1,1,1,"Oppose",3,0,0 "216","2","somewhat anxious",54,"bachelor's degree or higher","female",10,5,3,1,0,0,"Strongly Oppose",2,1,0 "217","3","very anxious",58,"bachelor's degree or higher","male",5,3,2,0,1,0,"Favor",1,0,0 "218","2","very anxious",20,"some college","male",3,3,3,1,0,0,"Strongly Favor",2,0,0 "219","3","very anxious",47,"bachelor's degree or higher","male",5,3,3,0,1,0,"Oppose",3,0,0 "220","2","a little anxious",29,"high school","male",12,10,7,1,0,0,"Oppose",4,1,1 "221","3","not anxious at all",54,"high school","female",4,12,8,0,1,0,"Strongly Oppose",4,0,0 "222","1","a little anxious",24,"bachelor's degree or higher","female",7,7,6,1,1,1,"Oppose",3,0,0 "223","2","not anxious at all",47,"high school","female",10,12,8,1,0,0,"Strongly Oppose",4,1,1 "224","3","a little anxious",25,"some college","female",11,7,3,0,1,0,"Oppose",2,0,0 "225","4","somewhat anxious",28,"high school","male",10,5,6,0,0,0,"Oppose",3,0,0 "226","2","somewhat anxious",57,"bachelor's degree or higher","male",16,7,6,1,0,0,"Strongly Favor",3,0,1 "227","4","a little anxious",26,"high school","male",8,10,6,0,0,0,"Strongly Oppose",4,0,0 "228","1","a little anxious",43,"high school","male",7,7,7,1,1,1,"Strongly Favor",3,0,1 "229","4","somewhat 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20, 25, 30, 40, 50, 100, 200, 400, 800, 1600] MIN_SAMPLE_SIZE = {'normal': 4, 'exp': 3} MAX_SIZE = max(SAMPLE_SIZES) MAX_SIM_SIZE = MAX_MEMORY // (MAX_SIZE * 8) PERCENTILES = [1, 5, 10, 25, 50, 75, 90, 92.5, 95, 97.5, 99, 99.5, 99.7, 99.9] seed = 113682199084250344115761738871133961874 seed = np.array([(seed >> (32 * i)) % 2 ** 32 for i in range(4)], dtype=np.uint32) def simulations(sim_type, save=False): rs = np.random.RandomState(seed) remaining = NUM_SIM results = defaultdict(list) start = dt.datetime.now() while remaining > 0: this_iter = min(remaining, MAX_SIM_SIZE) remaining -= this_iter if sim_type == 'normal': dist = rs.standard_normal else: dist = rs.standard_exponential rvs = dist((MAX_SIZE, this_iter)) sample_sizes = [ss for ss in SAMPLE_SIZES if ss >= MIN_SAMPLE_SIZE[sim_type]] for ss in sample_sizes: sample = rvs[:ss] mu = sample.mean(0) if sim_type == 'normal': std = sample.std(0, ddof=1) z = (sample - mu) / std cdf_fn = stats.norm.cdf else: z = sample / mu cdf_fn = stats.expon.cdf z = np.sort(z, axis=0) nobs = ss cdf = cdf_fn(z) plus = np.arange(1.0, nobs + 1) / nobs d_plus = (plus[:, None] - cdf).max(0) minus = np.arange(0.0, nobs) / nobs d_minus = (cdf - minus[:, None]).max(0) d = np.max(np.abs(np.c_[d_plus, d_minus]), 1) results[ss].append(d) logging.log(logging.INFO, 'Completed {0}, remaining {1}'.format(NUM_SIM - remaining, remaining)) elapsed = dt.datetime.now() - start rem = elapsed.total_seconds() / (NUM_SIM - remaining) * remaining logging.log(logging.INFO, '({0}) Time remaining {1:0.1f}s'.format(sim_type, rem)) for key in results: results[key] = np.concatenate(results[key]) if save: file_name = 'lilliefors-sim-{0}-results.pkl.gz'.format(sim_type) with gzip.open(file_name, 'wb', 5) as pkl: pickle.dump(results, pkl) crit_vals = {} for key in results: crit_vals[key] = np.percentile(results[key], PERCENTILES) start = 20 num = len([k for k in crit_vals if k >= start]) all_x = np.zeros((num * len(PERCENTILES), len(PERCENTILES) + 2)) all_y = np.zeros(num * len(PERCENTILES)) loc = 0 for i, perc in enumerate(PERCENTILES): y = pd.DataFrame(results).quantile(perc / 100.) y = y.loc[start:] all_y[loc:loc + len(y)] = np.log(y) x = y.index.values.astype(float) all_x[loc:loc + len(y), -2:] = np.c_[np.log(x), np.log(x) ** 2] all_x[loc:loc + len(y), i:(i + 1)] = 1 loc += len(y) w = np.ones_like(all_y).reshape(len(PERCENTILES), -1) w[6:, -5:] = 3 w = w.ravel() res = sm.WLS(all_y, all_x, weights=w).fit() params = [] for i in range(len(PERCENTILES)): params.append(np.r_[res.params[i], res.params[-2:]]) params = np.array(params) df = pd.DataFrame(params).T df.columns = PERCENTILES asymp_crit_vals = {} for col in df: asymp_crit_vals[col] = df[col].values code = '{0}_crit_vals = '.format(sim_type) code += str(crit_vals).strip() + '\n\n' code += '\n# Coefficients are model ' code += 'log(cv) = b[0] + b[1] log(n) + b[2] log(n)**2\n' code += '{0}_asymp_crit_vals = '.format(sim_type) code += str(asymp_crit_vals) + '\n\n' return code if __name__ == '__main__': logging.getLogger().setLevel(logging.INFO) header = '"""\nThis file is automatically generated by ' \ 'littlefors_critical_values.py.\nDo not directly modify' \ 'this file.\n\nValue based on 10,000,000 simulations."""\n\n' header += 'from numpy import array\n\n' header += 'PERCENTILES = ' + str(PERCENTILES).strip() + '\n\n' header += 'SAMPLE_SIZES = ' + str(SAMPLE_SIZES).strip() + '\n\n' normal = simulations('normal', True) exp = simulations('exp', True) footer = """ # Critical Value critical_values = {'normal': normal_crit_vals, 'exp': exp_crit_vals} asymp_critical_values = {'normal': normal_asymp_crit_vals, 'exp': exp_asymp_crit_vals} """ cv_filename = '../../_lilliefors_critical_values.py' with io.open(cv_filename, 'w', newline='\n') as cv: cv.write(FormatCode(header)[0]) cv.write(FormatCode(normal)[0]) cv.write('\n\n') cv.write(FormatCode(exp)[0]) cv.write('\n\n') cv.write(FormatCode(footer)[0]) 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statsmodels-0.12.2/statsmodels/stats/tests/results/results_meta.py000066400000000000000000000441171400612667500256000ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Tue Apr 7 11:31:21 2020 Author: Josef Perktold License: BSD-3 """ import numpy as np from statsmodels.tools.testing import Holder """ example from Kacker 2004, computed with R metafor > y = c(61.0, 61.4 , 62.21, 62.3 , 62.34, 62.6 , 62.7 , 62.84, 65.9) > v = c(0.2025, 1.2100, 0.0900, 0.2025, 0.3844, 0.5625, 0.0676, 0.0225, 1.8225) > res = rma(y, v, data=dat, method="PM", control=list(tol=1e-9)) > convert_items(res, prefix="exk1_metafor.") """ exk1_metafor = Holder() exk1_metafor.b = 62.4076199113286 exk1_metafor.beta = 62.4076199113286 exk1_metafor.se = 0.338030602684471 exk1_metafor.zval = 184.621213037276 exk1_metafor.pval = 0 exk1_metafor.ci_lb = 61.7450921043947 exk1_metafor.ci_ub = 63.0701477182625 exk1_metafor.vb = 0.114264688351227 exk1_metafor.tau2 = 0.705395309224248 exk1_metafor.se_tau2 = 0.51419109758052 exk1_metafor.tau2_f = 0.705395309224248 exk1_metafor.k = 9 exk1_metafor.k_f = 9 exk1_metafor.k_eff = 9 exk1_metafor.k_all = 9 exk1_metafor.p = 1 exk1_metafor.p_eff = 1 exk1_metafor.parms = 2 exk1_metafor.m = 1 exk1_metafor.QE = 24.801897741835 exk1_metafor.QEp = 0.00167935146372742 exk1_metafor.QM = 34084.9923033553 exk1_metafor.QMp = 0 exk1_metafor.I2 = 83.7218626490482 exk1_metafor.H2 = 6.14320900751909 exk1_metafor.yi = np.array([ 61, 61.4, 62.21, 62.3, 62.34, 62.6, 62.7, 62.84, 65.9 ]) exk1_metafor.vi = np.array([ 0.2025, 1.21, 0.09, 0.2025, 0.3844, 0.5625, 0.0676, 0.0225, 1.8225 ]) exk1_metafor.X = np.array([ 1, 1, 1, 1, 1, 1, 1, 1, 1 ]).reshape(9, 1, order='F') exk1_metafor.yi_f = np.array([ 61, 61.4, 62.21, 62.3, 62.34, 62.6, 62.7, 62.84, 65.9 ]) exk1_metafor.vi_f = np.array([ 0.2025, 1.21, 0.09, 0.2025, 0.3844, 0.5625, 0.0676, 0.0225, 1.8225 ]) exk1_metafor.X_f = np.array([ 1, 1, 1, 1, 1, 1, 1, 1, 1 ]).reshape(9, 1, order='F') exk1_metafor.M = np.array([ 0.907895309224248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.91539530922425, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.795395309224248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.907895309224248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.08979530922425, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.26789530922425, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.772995309224248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.727895309224248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2.52789530922425 ]).reshape(9, 9, order='F') exk1_metafor.ids = np.array([ 1, 2, 3, 4, 5, 6, 7, 8, 9 ]) exk1_metafor.slab = np.array([ 1, 2, 3, 4, 5, 6, 7, 8, 9 ]) exk1_metafor.measure = 'GEN' exk1_metafor.method = 'PM' exk1_metafor.test = 'z' exk1_metafor.s2w = 1 exk1_metafor.btt = 1 exk1_metafor.digits = np.array([ 4, 4, 4, 4, 4, 4, 4, 4, 4 ]) exk1_metafor.level = 0.05 exk1_metafor.add = 0.5 exk1_metafor.to = 'only0' exk1_metafor.fit_stats = np.array([ -12.722152033808, 21.73438033144, 29.4443040676159, 29.8387532222884, 31.4443040676159, -11.7892200590463, 23.5784401180925, 27.5784401180925, 27.7373232014522, 29.9784401180925 ]).reshape(5, 2, order='F') exk1_metafor.model = 'rma.uni' # > res = rma(y, v, data=dat, method="DL", control=list(tol=1e-9)) # > convert_items(res, prefix="exk1_dl.") exk1_dl = Holder() exk1_dl.b = 62.3901386044504 exk1_dl.beta = 62.3901386044504 exk1_dl.se = 0.245749668040304 exk1_dl.zval = 253.876797075543 exk1_dl.pval = 0 exk1_dl.ci_lb = 61.9084781058787 exk1_dl.ci_ub = 62.8717991030221 exk1_dl.vb = 0.0603928993419195 exk1_dl.tau2 = 0.288049246973751 exk1_dl.se_tau2 = 0.269366223207558 exk1_dl.tau2_f = 0.288049246973751 exk1_dl.k = 9 exk1_dl.k_f = 9 exk1_dl.k_eff = 9 exk1_dl.k_all = 9 exk1_dl.p = 1 exk1_dl.p_eff = 1 exk1_dl.parms = 2 exk1_dl.m = 1 exk1_dl.QE = 24.801897741835 exk1_dl.QEp = 0.00167935146372742 exk1_dl.QM = 64453.4280933367 exk1_dl.QMp = 0 exk1_dl.I2 = 67.744403741711 exk1_dl.H2 = 3.10023721772938 # > res = rma(y, v, data=dat, method="DL", test="knha", control=list(tol=1e-9)) # > convert_items(res, prefix="exk1_dl_hksj.") exk1_dl_hksj = Holder() exk1_dl_hksj.b = 62.3901386044504 exk1_dl_hksj.beta = 62.3901386044504 exk1_dl_hksj.se = 0.29477605699879 exk1_dl_hksj.zval = 211.652666908108 exk1_dl_hksj.pval = 2.77938607433693e-16 exk1_dl_hksj.ci_lb = 61.710383798052 exk1_dl_hksj.ci_ub = 63.0698934108488 exk1_dl_hksj.vb = 0.0868929237797541 exk1_dl_hksj.tau2 = 0.288049246973751 exk1_dl_hksj.se_tau2 = 0.269366223207558 exk1_dl_hksj.tau2_f = 0.288049246973751 exk1_dl_hksj.k = 9 exk1_dl_hksj.k_f = 9 exk1_dl_hksj.k_eff = 9 exk1_dl_hksj.k_all = 9 exk1_dl_hksj.p = 1 exk1_dl_hksj.p_eff = 1 exk1_dl_hksj.parms = 2 exk1_dl_hksj.m = 1 exk1_dl_hksj.QE = 24.801897741835 exk1_dl_hksj.QEp = 0.00167935146372742 exk1_dl_hksj.QM = 44796.8514093144 exk1_dl_hksj.QMp = 2.77938607433693e-16 exk1_dl_hksj.I2 = 67.744403741711 exk1_dl_hksj.H2 = 3.10023721772938 # > res = rma(y, v, data=dat, method="FE", control=list(tol=1e-9)) # > convert_items(res, prefix="exk1_fe.") exk1_fe = Holder() exk1_fe.b = 62.5833970939982 exk1_fe.beta = 62.5833970939982 exk1_fe.se = 0.107845705498231 exk1_fe.zval = 580.304953311515 exk1_fe.pval = 0 exk1_fe.ci_lb = 62.3720233953344 exk1_fe.ci_ub = 62.7947707926621 exk1_fe.vb = 0.0116306961944112 exk1_fe.tau2 = 0 exk1_fe.tau2_f = 0 exk1_fe.k = 9 exk1_fe.k_f = 9 exk1_fe.k_eff = 9 exk1_fe.k_all = 9 exk1_fe.p = 1 exk1_fe.p_eff = 1 exk1_fe.parms = 1 exk1_fe.m = 1 exk1_fe.QE = 24.801897741835 exk1_fe.QEp = 0.00167935146372742 exk1_fe.QM = 336753.838837879 exk1_fe.QMp = 0 exk1_fe.I2 = 67.744403741711 exk1_fe.H2 = 3.10023721772938 # > res = rma(y, v, data=dat, method="FE", test="knha", control=list(tol=1e-9)) # Warning message: # In rma(y, v, data = dat, method = "FE", test = "knha", # control = list(tol = 1e-09)) : # Knapp & Hartung method is not meant to be used in the context of FE models. # > convert_items(res, prefix="exk1_fe_hksj.") exk1_fe_hksj = Holder() exk1_fe_hksj.b = 62.5833970939982 exk1_fe_hksj.beta = 62.5833970939982 exk1_fe_hksj.se = 0.189889223522271 exk1_fe_hksj.zval = 329.57845597098 exk1_fe_hksj.pval = 8.04326466920145e-18 exk1_fe_hksj.ci_lb = 62.1455117593252 exk1_fe_hksj.ci_ub = 63.0212824286713 exk1_fe_hksj.vb = 0.0360579172098909 exk1_fe_hksj.tau2 = 0 exk1_fe_hksj.tau2_f = 0 exk1_fe_hksj.k = 9 exk1_fe_hksj.k_f = 9 exk1_fe_hksj.k_eff = 9 exk1_fe_hksj.k_all = 9 exk1_fe_hksj.p = 1 exk1_fe_hksj.p_eff = 1 exk1_fe_hksj.parms = 1 exk1_fe_hksj.m = 1 exk1_fe_hksj.QE = 24.801897741835 exk1_fe_hksj.QEp = 0.00167935146372742 exk1_fe_hksj.QM = 108621.958640215 exk1_fe_hksj.QMp = 8.04326466920145e-18 exk1_fe_hksj.I2 = 67.744403741711 exk1_fe_hksj.H2 = 3.10023721772938 # effect size for proportions, metafor `escalc` function # > library(metafor) # > dat <- dat.fine1993 # > dat_or <- escalc(measure="OR", ai=e2i, n1i=nei, ci=c2i, n2i=nci, data=dat, # var.names=c("y2i","v2i")) # > r = dat_or[c("y2i", "v2i")] # > cat_items(r) y_or = np.array([ 0.13613217432458, 0.768370601797533, 0.374938517449009, 1.65822807660353, 0.784954729813068, 0.361663949151077, 0.575364144903562, 0.250542525502324, 0.650587566141149, 0.0918075492531228, 0.273865253802803, 0.485755524477543, 0.182321556793955, 0.980829253011726, 1.31218638896617, -0.259511195485084, 0.138402322859119 ]) v_or = np.array([ 0.399242424242424, 0.244867149758454, 0.152761481951271, 0.463095238095238, 0.189078465394255, 0.0689052107900588, 0.240651709401709, 0.142027027027027, 0.280657748049052, 0.210140736456526, 0.0373104717196078, 0.0427774287950624, 0.194901960784314, 0.509259259259259, 1.39835164835165, 0.365873015873016, 0.108630952380952 ]) # > dat_rr <- escalc(measure="RR", ai=e2i, n1i=nei, ci=c2i, n2i=nci, data=dat, # var.names=c("y2i","v2i")) # > r = dat_rr[c("y2i", "v2i")] # > cat_items(r) y_rr = np.array([ 0.0595920972022457, 0.434452644981417, 0.279313822781264, 0.934309237376833, 0.389960921572199, 0.219327702635984, 0.328504066972036, 0.106179852041229, 0.28594445255324, 0.0540672212702757, 0.164912297594691, 0.300079561474504, 0.0813456394539525, 0.693147180559945, 0.177206456127184, -0.131336002061087, 0.0622131845015728 ]) v_rr = np.array([ 0.0761562998405104, 0.080905695611578, 0.0856909430438842, 0.175974025974026, 0.0551968864468864, 0.0267002515563729, 0.074017094017094, 0.0257850995555914, 0.0590338164251208, 0.073266499582289, 0.0137191240428942, 0.0179386112192693, 0.0400361415752742, 0.3, 0.0213675213675214, 0.0922402159244264, 0.021962676962677 ]) # > dat_rd <- escalc(measure="RD", ai=e2i, n1i=nei, ci=c2i, n2i=nci, data=dat, # var.names=c("y2i","v2i")) # > r = dat_rd[c("y2i", "v2i")] # > cat_items(r) y_rd = np.array([ 0.0334928229665072, 0.186554621848739, 0.071078431372549, 0.386363636363636, 0.19375, 0.0860946401581211, 0.14, 0.0611028315946349, 0.158888888888889, 0.0222222222222222, 0.0655096935584741, 0.114173373020248, 0.045021186440678, 0.2, 0.150793650793651, -0.0647773279352226, 0.0342342342342342 ]) v_rd = np.array([ 0.0240995805934916, 0.0137648162576944, 0.00539777447807907, 0.0198934072126221, 0.0109664132254464, 0.00376813659489987, 0.0142233846153846, 0.00842011053321928, 0.0163926076817558, 0.0122782676856751, 0.00211164860232433, 0.00219739135615223, 0.0119206723560942, 0.016, 0.014339804116826, 0.0226799351233969, 0.00663520262409963 ]) # > dat_as <- escalc(measure="AS", ai=e2i, n1i=nei, ci=c2i, n2i=nci, data=dat, # var.names=c("y2i","v2i")) # > r = dat_as[c("y2i", "v2i")] # > cat_items(r) y_as = np.array([ 0.0337617513001424, 0.189280827304914, 0.0815955178338458, 0.399912703180945, 0.194987153482868, 0.0882233598093272, 0.141897054604164, 0.0618635353537276, 0.160745373792417, 0.0225840453649413, 0.0669694915300637, 0.117733830714136, 0.0452997410410423, 0.221071594001477, 0.220332915310739, -0.0648275244591966, 0.0344168494848509 ]) v_as = np.array([ 0.0245215311004785, 0.0144957983193277, 0.00714869281045752, 0.0238636363636364, 0.0113839285714286, 0.00402569468666434, 0.0146153846153846, 0.00864381520119225, 0.0169444444444444, 0.0126984126984127, 0.0022181832395247, 0.00242071803917245, 0.0120497881355932, 0.0222222222222222, 0.0317460317460317, 0.0227732793522267, 0.00671171171171171 ]) eff_prop1 = Holder(y_rd=y_rd, v_rd=v_rd, y_rr=y_rr, v_rr=v_rr, y_or=y_or, v_or=v_or, y_as=y_as, v_as=v_as) # package meta metabin OR NA = np.nan # for R output results_or_dl_hk = Holder() # > res_mb_hk = metabin(e2i, nei, c2i, nci, data=dat2, sm="OR", # Q.Cochrane=FALSE, method="Inverse", method.tau="DL", hakn=TRUE, # backtransf=FALSE) # > cat_items(res_mb_hk, prefix="results_or_dl_hk.") results_or_dl_hk.event_e = np.array([ 18, 22, 21, 14, 42, 80, 13, 37, 23, 19, 106, 170, 34, 18, 13, 12, 42 ]) results_or_dl_hk.n_e = np.array([ 19, 34, 72, 22, 70, 183, 26, 61, 36, 45, 246, 386, 59, 45, 14, 26, 74 ]) results_or_dl_hk.event_c = np.array([ 12, 12, 15, 5, 13, 33, 18, 30, 12, 14, 76, 46, 17, 3, 14, 10, 40 ]) results_or_dl_hk.n_c = np.array([ 22, 35, 68, 20, 32, 94, 50, 55, 25, 35, 208, 141, 32, 15, 18, 19, 75 ]) results_or_dl_hk.method = 'Inverse' results_or_dl_hk.incr = 0.5 results_or_dl_hk.Q_CMH = 24.9044036917599 results_or_dl_hk.df_Q_CMH = 1 results_or_dl_hk.pval_Q_CMH = 6.02446516918864e-07 results_or_dl_hk.incr_e = np.array([ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]) results_or_dl_hk.incr_c = np.array([ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]) results_or_dl_hk.studlab = np.array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 ]) results_or_dl_hk.TE = np.array([ 2.70805020110221, 1.25672336971146, 0.374938517449009, 1.65822807660353, 0.784954729813068, 0.361663949151077, 0.575364144903562, 0.250542525502324, 0.650587566141149, 0.0918075492531229, 0.273865253802803, 0.485755524477543, 0.182321556793955, 0.980829253011726, 1.31218638896617, -0.259511195485085, 0.138402322859119 ]) results_or_dl_hk.seTE = np.array([ 1.1130538571376, 0.505568465186247, 0.390847133738078, 0.680511012471685, 0.434831536798166, 0.26249802054503, 0.490562645746402, 0.376864733063505, 0.529771411128472, 0.458411099840008, 0.193159187510219, 0.206827050443269, 0.441477021807833, 0.713624032148063, 1.18251919576455, 0.604874380241894, 0.329592099997789 ]) results_or_dl_hk.lower = np.array([ 0.526504728259124, 0.265827386227229, -0.391107788138334, 0.324451001076142, -0.0672994216535403, -0.152822717130236, -0.386120972920066, -0.488098778345447, -0.387745319709617, -0.806661696546688, -0.104719797000245, 0.0803819545800872, -0.682957505951402, -0.41784814850073, -1.00550864575963, -1.44504319593018, -0.507586322725471 ]) results_or_dl_hk.upper = np.array([ 4.8895956739453, 2.2476193531957, 1.14098482303635, 2.99200515213092, 1.63720888127968, 0.87615061543239, 1.53684926272719, 0.989183829350096, 1.68892045199192, 0.990276795052934, 0.65245030460585, 0.891129094374998, 1.04760061953931, 2.37950665452418, 3.62988142369196, 0.926020804960014, 0.784390968443709 ]) results_or_dl_hk.zval = np.array([ 2.43299116546472, 2.48576297030017, 0.959297088514073, 2.43673951811695, 1.80519273186346, 1.37777781485798, 1.17286578970589, 0.664807564946931, 1.22805336882057, 0.200273399324678, 1.41782152499639, 2.34860731919001, 0.412980852428863, 1.37443416817026, 1.10965335164625, -0.429033207492279, 0.419920024964335 ]) results_or_dl_hk.pval = np.array([ 0.0149746662574385, 0.012927403688425, 0.337409101687073, 0.0148203508441569, 0.0710445278963136, 0.168271897623853, 0.240849630303111, 0.50617358344946, 0.21942693438385, 0.841266765353313, 0.15624287815226, 0.0188437679780689, 0.67962064241999, 0.169306934699306, 0.267148431658854, 0.667899058451397, 0.674543878468201 ]) results_or_dl_hk.w_fixed = np.array([ 0.807174887892376, 3.91237113402062, 6.54615278162192, 2.15938303341902, 5.28880958450166, 14.5126905285409, 4.15538290788013, 7.04091341579448, 3.5630585898709, 4.75871559633028, 26.8021269609001, 23.3768140855494, 5.1307847082495, 1.96363636363636, 0.715127701375246, 2.73318872017354, 9.2054794520548 ]) results_or_dl_hk.w_random = np.array([ 0.806082838403413, 3.8868480814364, 6.47501150011912, 2.15158503393154, 5.24227532998639, 14.1675952027965, 4.12660238520421, 6.95867952431796, 3.54187734484692, 4.72100880622866, 25.6483453428049, 22.4942390635843, 5.0869781966579, 1.95718594121596, 0.714270384745876, 2.72070780232418, 9.06541462543771 ]) results_or_dl_hk.TE_fixed = 0.428036725396544 results_or_dl_hk.seTE_fixed = 0.0902874968199668 results_or_dl_hk.lower_fixed = 0.251076483375135 results_or_dl_hk.upper_fixed = 0.604996967417954 results_or_dl_hk.zval_fixed = 4.74081949851871 results_or_dl_hk.pval_fixed = 2.12855503378502e-06 results_or_dl_hk.TE_random = 0.429520368698268 results_or_dl_hk.seTE_random = 0.0915952752397692 results_or_dl_hk.lower_random = 0.235347059333852 results_or_dl_hk.upper_random = 0.623693678062684 results_or_dl_hk.zval_random = 4.68932887175579 results_or_dl_hk.pval_random = 0.000246175101510513 results_or_dl_hk.null_effect = 0 results_or_dl_hk.seTE_predict = 0.100339885576592 results_or_dl_hk.lower_predict = 0.215650965184522 results_or_dl_hk.upper_predict = 0.643389772212014 results_or_dl_hk.level_predict = 0.95 results_or_dl_hk.k = 17 results_or_dl_hk.Q = 16.181374262823 results_or_dl_hk.df_Q = 16 results_or_dl_hk.pval_Q = 0.440375456698129 results_or_dl_hk.tau2 = 0.0016783981912744 results_or_dl_hk.se_tau2 = 0.0529437644950009 results_or_dl_hk.lower_tau2 = 0 results_or_dl_hk.upper_tau2 = 0.45893520964914 results_or_dl_hk.tau = 0.0409682583383086 results_or_dl_hk.lower_tau = 0 results_or_dl_hk.upper_tau = 0.677447569668045 results_or_dl_hk.method_tau_ci = 'J' results_or_dl_hk.sign_lower_tau = '' results_or_dl_hk.sign_upper_tau = '' results_or_dl_hk.H = 1.00565197331206 results_or_dl_hk.lower_H = 1 results_or_dl_hk.upper_H = 1.43793739981697 results_or_dl_hk.I2 = 0.0112088293538659 results_or_dl_hk.lower_I2 = 0 results_or_dl_hk.upper_I2 = 0.516362418389019 results_or_dl_hk.Rb = 0.0117679262339789 results_or_dl_hk.lower_Rb = 0 results_or_dl_hk.upper_Rb = 0.725656377301252 results_or_dl_hk.approx_TE = np.array([ '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '' ]) results_or_dl_hk.approx_seTE = np.array([ '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '', '' ]) results_or_dl_hk.sm = 'OR' results_or_dl_hk.level = 0.95 results_or_dl_hk.level_comb = 0.95 results_or_dl_hk.df_hakn = 16 results_or_dl_hk.method_tau = 'DL' results_or_dl_hk.method_bias = 'score' results_or_dl_hk.title = '' results_or_dl_hk.complab = '' results_or_dl_hk.outclab = '' results_or_dl_hk.label_e = 'Experimental' results_or_dl_hk.label_c = 'Control' results_or_dl_hk.label_left = '' results_or_dl_hk.label_right = '' results_or_dl_hk.data = np.array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 34, 72, 22, 70, 183, 26, 61, 36, 45, 246, 386, 59, 45, 14, 26, 74, 22, 35, 68, 20, 32, 94, 50, 55, 25, 35, 208, 141, 32, 15, 18, 19, 75, 16, 22, 44, 19, 62, 130, 24, 51, 30, 43, 169, 279, 56, 42, 14, 21, NA, 20, 22, 40, 12, 27, 65, 30, 44, 17, 35, 139, 97, 30, 10, 18, 15, NA, 18, 22, 21, 14, 42, 80, 13, 37, 23, 19, 106, 170, 34, 18, 13, 12, 42, 12, 12, 15, 5, 13, 33, 18, 30, 12, 14, 76, 46, 17, 3, 14, 10, 40, 4, 15, 10, 5, 26, 47, 5, 19, 13, 8, 67, 97, 21, 9, 12, 6, NA, 8, 8, 3, 4, 6, 14, 10, 19, 4, 4, 42, 21, 9, 1, 13, 4, NA, 4, 15, 3, 2, 15, 30, 3, 11, 10, 6, 51, 73, 20, 9, 9, 5, 23, 3, 6, 0, 3, 5, 11, 9, 15, 4, 0, 35, 8, 7, 1, 12, 1, 30, 18, 22, 21, 14, 42, 80, 13, 37, 23, 19, 106, 170, 34, 18, 13, 12, 42, 19, 34, 72, 22, 70, 183, 26, 61, 36, 45, 246, 386, 59, 45, 14, 26, 74, 12, 12, 15, 5, 13, 33, 18, 30, 12, 14, 76, 46, 17, 3, 14, 10, 40, 22, 35, 68, 20, 32, 94, 50, 55, 25, 35, 208, 141, 32, 15, 18, 19, 75, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5 ]).reshape(17, 17, order='F') results_or_dl_hk.byseparator = ' = ' results_or_dl_hk.pscale = 1 results_or_dl_hk.irscale = 1 results_or_dl_hk.irunit = 'person-years' results_or_dl_hk.version = '4.11-0' statsmodels-0.12.2/statsmodels/stats/tests/results/results_multinomial_proportions.py000066400000000000000000000051721400612667500316600ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Test values for multinomial_proportion_confint. Author: Sébastien Lerique """ import collections import numpy as np from statsmodels.tools.testing import Holder res_multinomial = collections.defaultdict(Holder) # The following examples come from the Sison & Glaz paper, and the values were # computed using the R MultinomialCI package. # Floating-point arithmetic errors get blown up in the Edgeworth expansion # (starting in g1 and g2, but mostly when computing f, because of the # polynomials), which explains why we only obtain a precision of 4 decimals # when comparing to values computed in R. # We test with any method name that starts with 'sison', as that is the # criterion. key1 = ('sison', 'Sison-Glaz example 1') res_multinomial[key1].proportions = [56, 72, 73, 59, 62, 87, 58] res_multinomial[key1].cis = np.array([ [.07922912, .1643361], [.11349036, .1985973], [.11563169, .2007386], [.08565310, .1707601], [.09207709, .1771840], [.14561028, .2307172], [.08351178, .1686187]]) res_multinomial[key1].precision = 4 key2 = ('sisonandglaz', 'Sison-Glaz example 2') res_multinomial[key2].proportions = [5] * 50 res_multinomial[key2].cis = [0, .05304026] * np.ones((50, 2)) res_multinomial[key2].precision = 4 key3 = ('sison-whatever', 'Sison-Glaz example 3') res_multinomial[key3].proportions = ( [1] * 10 + [12] * 10 + [5] * 10 + [3] * 10 + [4] * 10) res_multinomial[key3].cis = np.concatenate([ [0, .04120118] * np.ones((10, 2)), [.012, .08520118] * np.ones((10, 2)), [0, .05720118] * np.ones((10, 2)), [0, .04920118] * np.ones((10, 2)), [0, .05320118] * np.ones((10, 2)) ]) res_multinomial[key3].precision = 4 # The examples from the Sison & Glaz paper only include 3 decimals. gkey1 = ('goodman', 'Sison-Glaz example 1') res_multinomial[gkey1].proportions = [56, 72, 73, 59, 62, 87, 58] res_multinomial[gkey1].cis = np.array([ [.085, .166], [.115, .204], [.116, .207], [.091, .173], [.096, .181], [.143, .239], [.089, .171]]) res_multinomial[gkey1].precision = 3 gkey2 = ('goodman', 'Sison-Glaz example 2') res_multinomial[gkey2].proportions = [5] * 50 res_multinomial[gkey2].cis = [.005, .075] * np.ones((50, 2)) res_multinomial[gkey2].precision = 3 gkey3 = ('goodman', 'Sison-Glaz example 3') res_multinomial[gkey3].proportions = ( [1] * 10 + [12] * 10 + [5] * 10 + [3] * 10 + [4] * 10) res_multinomial[gkey3].cis = np.concatenate([ [0, .049] * np.ones((10, 2)), [.019, .114] * np.ones((10, 2)), [.005, .075] * np.ones((10, 2)), [.002, .062] * np.ones((10, 2)), [.004, .069] * np.ones((10, 2)) ]) res_multinomial[gkey3].precision = 3 statsmodels-0.12.2/statsmodels/stats/tests/results/results_panelrobust.py000066400000000000000000000036741400612667500272130ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch cov_clu_stata = np.array([ .00025262993207, -.00065043385106, .20961897960949, -.00065043385106, .00721940994738, -1.2171040967615, .20961897960949, -1.2171040967615, 417.18890043724]).reshape(3, 3) cov_pnw0_stata = np.array([ .00004638910396, -.00006781406833, -.00501232990882, -.00006781406833, .00238784043122, -.49683062350622, -.00501232990882, -.49683062350622, 133.97367476797]).reshape(3, 3) cov_pnw1_stata = np.array([ .00007381482253, -.00009936717692, -.00613513582975, -.00009936717692, .00341979122583, -.70768252183061, -.00613513582975, -.70768252183061, 197.31345000598]).reshape(3, 3) cov_pnw4_stata = np.array([ .0001305958131, -.00022910455176, .00889686530849, -.00022910455176, .00468152667913, -.88403667445531, .00889686530849, -.88403667445531, 261.76140136858]).reshape(3, 3) cov_dk0_stata = np.array([ .00005883478135, -.00011241470772, -.01670183921469, -.00011241470772, .00140649264687, -.29263014921586, -.01670183921469, -.29263014921586, 99.248049966902]).reshape(3, 3) cov_dk1_stata = np.array([ .00009855800275, -.00018443722054, -.03257408922788, -.00018443722054, .00205106413403, -.3943459697384, -.03257408922788, -.3943459697384, 140.50692606398]).reshape(3, 3) cov_dk4_stata = np.array([ .00018052657317, -.00035661054613, -.06728261073866, -.00035661054613, .0024312795189, -.32394785247278, -.06728261073866, -.32394785247278, 148.60456447156]).reshape(3, 3) results = Bunch( cov_clu_stata=cov_clu_stata, cov_pnw0_stata=cov_pnw0_stata, cov_pnw1_stata=cov_pnw1_stata, cov_pnw4_stata=cov_pnw4_stata, cov_dk0_stata=cov_dk0_stata, cov_dk1_stata=cov_dk1_stata, cov_dk4_stata=cov_dk4_stata ) statsmodels-0.12.2/statsmodels/stats/tests/results/results_power.py000066400000000000000000000107051400612667500260020ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Thu Feb 28 13:23:09 2013 Author: Josef Perktold """ import collections from statsmodels.tools.testing import Holder # numbers from R package `pwr` pwr.chisq.test pwr_chisquare = collections.defaultdict(Holder) pwr_chisquare[0].w = 1e-04 pwr_chisquare[0].N = 5 pwr_chisquare[0].df = 4 pwr_chisquare[0].sig_level = 0.05 pwr_chisquare[0].power = 0.05000000244872708 pwr_chisquare[0].method = 'Chi squared power calculation' pwr_chisquare[0].note = 'N is the number of observations' pwr_chisquare[1].w = 0.005 pwr_chisquare[1].N = 5 pwr_chisquare[1].df = 4 pwr_chisquare[1].sig_level = 0.05 pwr_chisquare[1].power = 0.05000612192891004 pwr_chisquare[1].method = 'Chi squared power calculation' pwr_chisquare[1].note = 'N is the number of observations' pwr_chisquare[2].w = 0.1 pwr_chisquare[2].N = 5 pwr_chisquare[2].df = 4 pwr_chisquare[2].sig_level = 0.05 pwr_chisquare[2].power = 0.05246644635810126 pwr_chisquare[2].method = 'Chi squared power calculation' pwr_chisquare[2].note = 'N is the number of observations' pwr_chisquare[3].w = 1 pwr_chisquare[3].N = 5 pwr_chisquare[3].df = 4 pwr_chisquare[3].sig_level = 0.05 pwr_chisquare[3].power = 0.396188517504065 pwr_chisquare[3].method = 'Chi squared power calculation' pwr_chisquare[3].note = 'N is the number of observations' pwr_chisquare[4].w = 1e-04 pwr_chisquare[4].N = 100 pwr_chisquare[4].df = 4 pwr_chisquare[4].sig_level = 0.05 pwr_chisquare[4].power = 0.05000004897454883 pwr_chisquare[4].method = 'Chi squared power calculation' pwr_chisquare[4].note = 'N is the number of observations' pwr_chisquare[5].w = 0.005 pwr_chisquare[5].N = 100 pwr_chisquare[5].df = 4 pwr_chisquare[5].sig_level = 0.05 pwr_chisquare[5].power = 0.05012248082672883 pwr_chisquare[5].method = 'Chi squared power calculation' pwr_chisquare[5].note = 'N is the number of observations' pwr_chisquare[6].w = 0.1 pwr_chisquare[6].N = 100 pwr_chisquare[6].df = 4 pwr_chisquare[6].sig_level = 0.05 pwr_chisquare[6].power = 0.1054845044462312 pwr_chisquare[6].method = 'Chi squared power calculation' pwr_chisquare[6].note = 'N is the number of observations' pwr_chisquare[7].w = 1 pwr_chisquare[7].N = 100 pwr_chisquare[7].df = 4 pwr_chisquare[7].sig_level = 0.05 pwr_chisquare[7].power = 0.999999999999644 pwr_chisquare[7].method = 'Chi squared power calculation' pwr_chisquare[7].note = 'N is the number of observations' pwr_chisquare[8].w = 1e-04 pwr_chisquare[8].N = 1000 pwr_chisquare[8].df = 4 pwr_chisquare[8].sig_level = 0.05 pwr_chisquare[8].power = 0.0500004897461283 pwr_chisquare[8].method = 'Chi squared power calculation' pwr_chisquare[8].note = 'N is the number of observations' pwr_chisquare[9].w = 0.005 pwr_chisquare[9].N = 1000 pwr_chisquare[9].df = 4 pwr_chisquare[9].sig_level = 0.05 pwr_chisquare[9].power = 0.0512288025485101 pwr_chisquare[9].method = 'Chi squared power calculation' pwr_chisquare[9].note = 'N is the number of observations' pwr_chisquare[10].w = 0.1 pwr_chisquare[10].N = 1000 pwr_chisquare[10].df = 4 pwr_chisquare[10].sig_level = 0.05 pwr_chisquare[10].power = 0.715986350467412 pwr_chisquare[10].method = 'Chi squared power calculation' pwr_chisquare[10].note = 'N is the number of observations' pwr_chisquare[11].w = 1 pwr_chisquare[11].N = 1000 pwr_chisquare[11].df = 4 pwr_chisquare[11].sig_level = 0.05 pwr_chisquare[11].power = 1 pwr_chisquare[11].method = 'Chi squared power calculation' pwr_chisquare[11].note = 'N is the number of observations' pwr_chisquare[12].w = 1e-04 pwr_chisquare[12].N = 30000 pwr_chisquare[12].df = 4 pwr_chisquare[12].sig_level = 0.05 pwr_chisquare[12].power = 0.05001469300301765 pwr_chisquare[12].method = 'Chi squared power calculation' pwr_chisquare[12].note = 'N is the number of observations' pwr_chisquare[13].w = 0.005 pwr_chisquare[13].N = 30000 pwr_chisquare[13].df = 4 pwr_chisquare[13].sig_level = 0.05 pwr_chisquare[13].power = 0.0904799545200348 pwr_chisquare[13].method = 'Chi squared power calculation' pwr_chisquare[13].note = 'N is the number of observations' pwr_chisquare[14].w = 0.1 pwr_chisquare[14].N = 30000 pwr_chisquare[14].df = 4 pwr_chisquare[14].sig_level = 0.05 pwr_chisquare[14].power = 1 pwr_chisquare[14].method = 'Chi squared power calculation' pwr_chisquare[14].note = 'N is the number of observations' pwr_chisquare[15].w = 1 pwr_chisquare[15].N = 30000 pwr_chisquare[15].df = 4 pwr_chisquare[15].sig_level = 0.05 pwr_chisquare[15].power = 1 pwr_chisquare[15].method = 'Chi squared power calculation' pwr_chisquare[15].note = 'N is the number of observations' statsmodels-0.12.2/statsmodels/stats/tests/results/results_proportion.py000066400000000000000000000117101400612667500270560ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Mar 01 14:48:59 2013 Author: Josef Perktold """ import collections import numpy as np from statsmodels.tools.testing import Holder # numbers from R package `pwr` pwr.chisq.test res_binom = collections.defaultdict(Holder) res_binom_methods = ["agresti-coull", "asymptotic", "bayes", "cloglog", "exact", "logit", "probit", "profile", "lrt", "prop.test", "wilson"] # > bci = binom.confint(x = c(18), n = 20, tol = 1e-8) # > mkarray2(bci$lower, "res_binom[(18, 20)].ci_low") res_binom[(18, 20)].ci_low = np.array([ 0.6867561125596077, 0.768521618913513, 0.716146742695748, 0.656030707261567, 0.6830172859809176, 0.676197991611287, 0.7027685414174645, 0.722052946372325, 0.7220576251734515, 0.668722403162941, 0.6989663547715128 ]) # > mkarray2(bci$upper, "res_binom[(18, 20)].ci_upp") res_binom[(18, 20)].ci_upp = np.array([ 0.984343760998137, 1.031478381086487, 0.97862751197755, 0.974010174395775, 0.9876514728297052, 0.974866415649319, 0.978858461808406, 0.982318186566456, 0.982639913376776, 0.982487361226571, 0.972133518786232 ]) # > # > bci = binom.confint(x = c(4), n = 20, tol = 1e-8) # > mkarray2(bci$lower, "res_binom[(4, 20)].ci_low") res_binom[(4, 20)].ci_low = np.array([ 0.0749115102767071, 0.0246954918846837, 0.07152005247873425, 0.0623757232566298, 0.05733399705003284, 0.0771334546771001, 0.0710801045992076, 0.0668624655835687, 0.0668375191189685, 0.0661062308910436, 0.0806576625797981 ]) # > mkarray2(bci$upper, "res_binom[(4, 20)].ci_upp") res_binom[(4, 20)].ci_upp = np.array([ 0.4217635845549845, 0.3753045081153163, 0.4082257625169254, 0.393143902056907, 0.436614002996668, 0.427846901518118, 0.4147088121599544, 0.405367872119342, 0.405364309586823, 0.442686245059445, 0.4160174322518935 ]) # > # > bci = binom.confint(x = c(4), n = 200, tol = 1e-8) # > mkarray2(bci$lower, "res_binom[(4, 200)].ci_low") res_binom[(4, 200)].ci_low = np.array([ 0.005991954548218395, 0.000597346459104517, 0.00678759879519299, 0.006650668467968445, 0.005475565879556443, 0.00752663882411158, 0.00705442514086136, 0.00625387073493174, 0.00625223049303646, 0.00642601313670221, 0.00780442641634947 ]) # > mkarray2(bci$upper, "res_binom[(4, 200)].ci_upp") res_binom[(4, 200)].ci_upp = np.array([ 0.0520995587739575, 0.0394026535408955, 0.0468465669668423, 0.04722535678688564, 0.05041360908989634, 0.05206026227201098, 0.04916362085874019, 0.04585048214247203, 0.0458490848884339, 0.0537574613520185, 0.05028708690582643 ]) # > bci = binom.confint(x = c(190), n = 200, tol = 1e-8) # Warning message: # In binom.bayes(x, n, conf.level = conf.level, ...) : # 1 confidence interval failed to converge (marked by '*'). # Try changing 'tol' to a different value. # JP: I replace 0.02094150654714356 by np.nan in Bayes # > mkarray2(bci$lower, "res_binom[(190, 200)].ci_low") res_binom[(190, 200)].ci_low = np.array([ 0.909307307911624, 0.919794926420966, np.nan, 0.909066091776046, 0.9099724622986486, 0.9095820742314172, 0.9118101288857796, 0.913954651984184, 0.913956305842353, 0.9073089225133698, 0.910421851861224 ]) # > mkarray2(bci$upper, "res_binom[(190, 200)].ci_upp") res_binom[(190, 200)].ci_upp = np.array([ 0.973731898348837, 0.980205073579034, 1, 0.972780587302479, 0.975765834527891, 0.9728891271086528, 0.973671370402242, 0.974623779100809, 0.974626983311416, 0.974392083257476, 0.972617354399236 ]) # > bci = binom.confint(x = c(1), n = 30, tol = 1e-8) res_binom[(1, 30)].ci_low = np.array([ -8.305484e-03, -3.090070e-02, 6.903016e-05, 2.494567e-03, 8.435709e-04, 4.675346e-03, 3.475014e-03, 3.012987e-03, 1.932430e-03, 1.742467e-03, 5.908590e-03]) res_binom[(1, 30)].ci_upp = np.array([ 0.18091798, 0.09756737, 0.12314380, 0.14513807, 0.17216946, 0.20200244, 0.16637241, 0.13868254, 0.13868375, 0.19053022, 0.16670391]) # > bci = binom.confint(x = c(29), n = 30, tol = 1e-8) res_binom[(29, 30)].ci_low = np.array([ 0.8190820, 0.9024326, 0.8768562, 0.7860836, 0.8278305, 0.7979976, 0.8336276, 0.8613175, 0.8613162, 0.8094698, 0.8332961]) res_binom[(29, 30)].ci_upp = np.array([ 1.0083055, 1.0309007, 0.9999310, 0.9952363, 0.9991564, 0.9953247, 0.9965250, 0.9969870, 0.9980676, 0.9982575, 0.9940914]) # > bci = binom.confint(x = c(0), n = 30, tol = 1e-8) # Note: this ci_low clips one negative value to 0 res_binom[(0, 30)].ci_low = np.zeros(11) res_binom[(0, 30)].ci_upp = np.array([ 0.13471170, 0.00000000, 0.06151672, 0.11570331, 0.11570331, 0.11570331, 0.11570331, 0.10402893, 0.06201781, 0.14132048, 0.11351339]) # > bci = binom.confint(x = c(30), n = 30, tol = 1e-8) res_binom[(30, 30)].ci_low = np.array([ 0.8652883, 1.0000000, 0.9384833, 0.8842967, 0.8842967, 0.8842967, 0.8842967, 0.8959711, 0.9379822, 0.8586795, 0.8864866]) # Note: this ci_upp clips one value > 1 res_binom[(30, 30)].ci_upp = np.ones(11) statsmodels-0.12.2/statsmodels/stats/tests/results/results_rates.py000066400000000000000000000024561400612667500257700ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Mon May 4 21:21:09 2020 Author: Josef Perktold License: BSD-3 """ import numpy as np from statsmodels.tools.testing import Holder NA = np.nan # > pe = poisson.exact(c(60, 30), c(51477.5, 54308.7), tsmethod="minlike", # midp=FALSE) # > cat_items(pe, prefix="res.") res_pexact_cond = res = Holder() res.statistic = 60 res.parameter = 43.7956463130352 res.p_value = 0.000675182658686321 res.conf_int = np.array([ 1.34983090611567, 3.27764509862914 ]) res.estimate = 2.10999757175465 res.null_value = 1 res.alternative = 'two.sided' res.method = ('Exact two-sided Poisson test (sum of minimum likelihood' ' method)') res.data_name = 'c(60, 30) time base: c(51477.5, 54308.7)' # > pe = poisson.exact(c(60, 30), c(51477.5, 54308.7), tsmethod="minlike", # midp=TRUE) # > cat_items(pe, prefix="res.") res_pexact_cond_midp = res = Holder() res.statistic = 60 res.parameter = 43.7956463130352 res.p_value = 0.000557262406619052 res.conf_int = np.array([ NA, NA ]) res.estimate = 2.10999757175465 res.null_value = 1 res.alternative = 'two.sided' res.method = ('Exact two-sided Poisson test (sum of minimum' ' likelihood method), mid-p version') res.data_name = 'c(60, 30) time base: c(51477.5, 54308.7)' statsmodels-0.12.2/statsmodels/stats/tests/results/wspec1.csv000066400000000000000000000014371400612667500244340ustar00rootroot00000000000000IV1,IV2,DV -0.02015,-8.12,-0.00262 -0.09145,22.6,0.06002 -0.23417,34.14,0.28942 -0.11179,-24.21,-0.01991 0.16144,-14.37,-0.11282 0.15733,-10.98,-0.15465 0.05293,-0.61,-0.09055 0.05686,-3.38,-0.01311 -0.11524,18.48,0.01793 0.10973,-12.93,-0.02117 0.11152,-9.32,-0.08318 0.05917,5.86,-0.01982 -0.00468,-6.67,0.03378 -0.15653,25.27,0.10565 0.115,-2.55,0.0483 0.12352,-22.48,-0.07733 -0.03604,3.69,0.07183 0.05634,-6.19,-0.05512 -0.00401,2.25,0.01318 0.10524,-3.73,-0.00379 0.02288,1.5,0.00922 0.05646,-3.48,-0.02355 0.09566,3.33,-0.06103 0.01535,1.1,-0.0343 0.0435,-4.41,-0.02346 -0.00534,0,-0.05993 0.04721,9.22,-0.00264 0.01321,-3.86,-0.02038 -0.00353,-3.54,-0.00693 -0.07728,21.89,0.04091 0.0572,-16.35,0.00791 0.00372,3.75,0.10267 0.02087,-2.38,-0.04426 0.03918,-7.62,-0.05083 0.03597,4.37,0.01428 statsmodels-0.12.2/statsmodels/stats/tests/results/wspec2.csv000066400000000000000000000017571400612667500244420ustar00rootroot00000000000000IV1,IV2,IV3,DV 144.6,0.02846,2.28,-0.00262 30,0.15082,2.768,0.06002 -293.1,0.58902,3.323,0.28942 -166,0.01642,-5.012,-0.01991 -43.5,-0.23772,-1.471,-0.11282 43.7,-0.42052,1.129,-0.15465 182.4,-0.2129,1.837,-0.09055 114.6,-0.22211,1.686,-0.01311 207.5,0.02502,0.344,0.01793 169.1,0.10521,-0.077,-0.02117 172.5,-0.07982,0.637,-0.08318 8.2,-0.08353,1.765,-0.01982 222.5,-0.02544,2.345,0.03378 126.2,0.28108,2.524,0.10565 198.2,0.18466,1.465,0.0483 188.6,-0.09714,1.014,-0.07733 148,0.01393,1.279,0.07183 106,-0.04318,0.482,-0.05512 69.4,-0.14695,1.033,0.01318 178.1,-0.07366,1.528,-0.00379 66,0.02879,0.93,0.00922 207.9,0.01782,-0.271,-0.02355 250.6,-0.06627,1.253,-0.06103 31.4,-0.114,0.906,-0.0343 289.6,-0.08656,1.491,-0.02346 301.4,0.01026,1.099,-0.05993 113.6,0.12251,0.612,-0.00264 138.8,0.05026,-0.418,-0.02038 218.5,0,-1.507,-0.00693 134.5,0.12344,1.373,0.04091 59.5,0.05136,0.881,0.00791 38,0.10883,0.212,0.10267 212.8,-0.12725,0.067,-0.04426 191.1,-0.09324,1.374,-0.05083 176.4,-0.09707,1.06,0.01428 statsmodels-0.12.2/statsmodels/stats/tests/results/wspec3.csv000066400000000000000000000016111400612667500244300ustar00rootroot00000000000000IV1,IV2,DUM1,DUM2,DV -0.02015,7.6,0,0,0.01291 -0.09145,44.1,0,0,-0.04267 -0.23417,252.7,0,0,-0.25406 -0.11179,9.4,1,0,0.34175 0.16144,-122.1,0,0,0.10051 0.15733,-156.2,0,0,0.13155 0.05293,-57.3,0,0,0.09492 0.05686,-48.1,0,0,0.03839 -0.11524,4.9,0,0,0.0188 0.10973,22,0,0,0.01934 0.11152,-16.9,0,0,0.10318 0.05917,-16.3,0,0,0.06143 -0.00468,-4.7,0,0,0.00608 -0.15653,59.2,0,0,-0.00281 0.115,49,0,0,0.01905 0.12352,-26.9,0,0,0.06962 -0.03604,3.7,0,1,0.21069 0.05634,-11.3,0,0,0.06319 -0.00401,-35,0,0,0.03645 0.10524,-15.7,0,0,0.0444 0.02288,6,0,0,0.02033 0.05646,3.8,0,0,0.06044 0.09566,-13.8,0,0,0.06762 0.01535,-21.7,0,0,0.03301 0.0435,-14.9,0,0,0.01857 -0.00534,1.7,0,0,0.06799 0.04721,21.7,0,0,0.01813 0.01321,9.7,0,0,0.02022 -0.00353,0,0,0,0.01317 -0.07728,26,0,0,-0.00628 0.0572,11.8,0,0,0.02035 0.00372,27.1,0,0,-0.04564 0.02087,-31.4,0,0,0.04537 0.03918,-20.6,0,0,0.07685 0.03597,-19.5,0,0,0.03299 statsmodels-0.12.2/statsmodels/stats/tests/results/wspec4.csv000066400000000000000000000023051400612667500244320ustar00rootroot00000000000000IV1,IV2,IV3,DUM1,DUM2,DV 144.6,-0.02036,0.03699,0,0,0.01291 30,-0.09591,-0.25186,0,0,-0.04267 -293.1,-0.2668,0.93698,0,0,-0.25406 -166,-0.11855,0.73074,1,0,0.34175 -43.5,0.14966,-0.29941,0,0,0.10051 43.7,0.14612,-0.25366,0,0,0.13155 182.4,0.05158,-0.2597,0,0,0.09492 114.6,0.0553,-0.01949,0,0,0.03839 207.5,-0.12244,-0.11013,0,0,0.0188 169.1,0.10412,0.67668,0,0,0.01934 172.5,0.10573,-0.28238,0,0,0.10318 8.2,0.05749,-0.28363,0,0,0.06143 222.5,-0.00469,0.24894,0,0,0.00608 126.2,-0.17023,-0.22687,0,0,-0.00281 198.2,0.10886,1.11175,0,0,0.01905 188.6,0.11647,-0.05312,0,0,0.06962 148,-0.03671,-0.49461,0,1,0.21069 106,0.05481,0.16064,0,0,0.06319 69.4,-0.00402,-0.23218,0,0,0.03645 178.1,0.10007,0.10992,0,0,0.0444 66,0.02262,-0.16417,0,0,0.02033 207.9,0.05493,0.07899,0,0,0.06044 250.6,0.09136,-0.16984,0,0,0.06762 31.4,0.01524,0.19577,0,0,0.03301 289.6,0.04258,0.05408,0,0,0.01857 301.4,-0.00535,-0.20569,0,0,0.06799 113.6,0.04613,0,0,0,0.01813 138.8,0.01312,0.5414,0,0,0.02022 218.5,-0.00354,-0.14705,0,0,0.01317 134.5,-0.08043,-0.15811,0,0,-0.00628 59.5,0.05562,1.16127,0,0,0.02035 38,0.00371,-0.40133,0,0,-0.04564 212.8,0.02066,0.15375,0,0,0.04537 191.1,0.03843,-0.08458,0,0,0.07685 176.4,0.03534,-0.29581,0,0,0.03299 statsmodels-0.12.2/statsmodels/stats/tests/test_anova.py000066400000000000000000000447571400612667500235450ustar00rootroot00000000000000# -*- coding: utf-8 -*- from io import StringIO import numpy as np from statsmodels.stats.anova import anova_lm from statsmodels.formula.api import ols from pandas import read_csv kidney_table = StringIO("""Days Duration Weight ID 0.0 1 1 1 2.0 1 1 2 1.0 1 1 3 3.0 1 1 4 0.0 1 1 5 2.0 1 1 6 0.0 1 1 7 5.0 1 1 8 6.0 1 1 9 8.0 1 1 10 2.0 1 2 1 4.0 1 2 2 7.0 1 2 3 12.0 1 2 4 15.0 1 2 5 4.0 1 2 6 3.0 1 2 7 1.0 1 2 8 5.0 1 2 9 20.0 1 2 10 15.0 1 3 1 10.0 1 3 2 8.0 1 3 3 5.0 1 3 4 25.0 1 3 5 16.0 1 3 6 7.0 1 3 7 30.0 1 3 8 3.0 1 3 9 27.0 1 3 10 0.0 2 1 1 1.0 2 1 2 1.0 2 1 3 0.0 2 1 4 4.0 2 1 5 2.0 2 1 6 7.0 2 1 7 4.0 2 1 8 0.0 2 1 9 3.0 2 1 10 5.0 2 2 1 3.0 2 2 2 2.0 2 2 3 0.0 2 2 4 1.0 2 2 5 1.0 2 2 6 3.0 2 2 7 6.0 2 2 8 7.0 2 2 9 9.0 2 2 10 10.0 2 3 1 8.0 2 3 2 12.0 2 3 3 3.0 2 3 4 7.0 2 3 5 15.0 2 3 6 4.0 2 3 7 9.0 2 3 8 6.0 2 3 9 1.0 2 3 10 """) kidney_table.seek(0) kidney_table = read_csv(kidney_table, sep=r"\s+", engine='python').astype(int) class TestAnovaLM(object): @classmethod def setup_class(cls): # kidney data taken from JT's course # do not know the license cls.data = kidney_table cls.kidney_lm = ols('np.log(Days+1) ~ C(Duration) * C(Weight)', data=cls.data).fit() def test_results(self): Df = np.array([1, 2, 2, 54]) sum_sq = np.array([2.339693, 16.97129, 0.6356584, 28.9892]) mean_sq = np.array([2.339693, 8.485645, 0.3178292, 0.536837]) f_value = np.array([4.358293, 15.80674, 0.5920404, np.nan]) pr_f = np.array([0.0415617, 3.944502e-06, 0.5567479, np.nan]) results = anova_lm(self.kidney_lm) np.testing.assert_equal(results['df'].values, Df) np.testing.assert_almost_equal(results['sum_sq'].values, sum_sq, 4) np.testing.assert_almost_equal(results['F'].values, f_value, 4) np.testing.assert_almost_equal(results['PR(>F)'].values, pr_f) class TestAnovaLMNoconstant(object): @classmethod def setup_class(cls): # kidney data taken from JT's course # do not know the license cls.data = kidney_table cls.kidney_lm = ols('np.log(Days+1) ~ C(Duration) * C(Weight) - 1', data=cls.data).fit() def test_results(self): Df = np.array([2, 2, 2, 54]) sum_sq = np.array([158.6415227, 16.97129, 0.6356584, 28.9892]) mean_sq = np.array([79.3207613, 8.485645, 0.3178292, 0.536837]) f_value = np.array([147.7557648, 15.80674, 0.5920404, np.nan]) pr_f = np.array([1.262324e-22, 3.944502e-06, 0.5567479, np.nan]) results = anova_lm(self.kidney_lm) np.testing.assert_equal(results['df'].values, Df) np.testing.assert_almost_equal(results['sum_sq'].values, sum_sq, 4) np.testing.assert_almost_equal(results['F'].values, f_value, 4) np.testing.assert_almost_equal(results['PR(>F)'].values, pr_f) # > sum2.lm = lm(logDays ~ Duration * Weight - 1, contrasts=list(Duration=contr.sum, Weight=contr.sum)) # > anova.lm.sum2 <- anova(sum2.lm) # > anova.lm.sum2 # Analysis of Variance Table # # Response: logDays # Df Sum Sq Mean Sq F value Pr(>F) # Duration 2 158.642 79.321 147.756 < 2.2e-16 *** # Weight 2 16.971 8.486 15.807 3.945e-06 *** # Duration:Weight 2 0.636 0.318 0.592 0.5567 # Residuals 54 28.989 0.537 # --- # Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 class TestAnovaLMCompare(TestAnovaLM): def test_results(self): new_model = ols("np.log(Days+1) ~ C(Duration) + C(Weight)", self.data).fit() results = anova_lm(new_model, self.kidney_lm) Res_Df = np.array([ 56, 54 ]) RSS = np.array([ 29.62486, 28.9892 ]) Df = np.array([ 0, 2 ]) Sum_of_Sq = np.array([ np.nan, 0.6356584 ]) F = np.array([ np.nan, 0.5920404 ]) PrF = np.array([ np.nan, 0.5567479 ]) np.testing.assert_equal(results["df_resid"].values, Res_Df) np.testing.assert_almost_equal(results["ssr"].values, RSS, 4) np.testing.assert_almost_equal(results["df_diff"].values, Df) np.testing.assert_almost_equal(results["ss_diff"].values, Sum_of_Sq) np.testing.assert_almost_equal(results["F"].values, F) np.testing.assert_almost_equal(results["Pr(>F)"].values, PrF) class TestAnovaLMCompareNoconstant(TestAnovaLM): def test_results(self): new_model = ols("np.log(Days+1) ~ C(Duration) + C(Weight) - 1", self.data).fit() results = anova_lm(new_model, self.kidney_lm) Res_Df = np.array([ 56, 54 ]) RSS = np.array([ 29.62486, 28.9892 ]) Df = np.array([ 0, 2 ]) Sum_of_Sq = np.array([ np.nan, 0.6356584 ]) F = np.array([ np.nan, 0.5920404 ]) PrF = np.array([ np.nan, 0.5567479 ]) np.testing.assert_equal(results["df_resid"].values, Res_Df) np.testing.assert_almost_equal(results["ssr"].values, RSS, 4) np.testing.assert_almost_equal(results["df_diff"].values, Df) np.testing.assert_almost_equal(results["ss_diff"].values, Sum_of_Sq) np.testing.assert_almost_equal(results["F"].values, F) np.testing.assert_almost_equal(results["Pr(>F)"].values, PrF) class TestAnova2(TestAnovaLM): # drop some observations to make an unbalanced, disproportionate panel # to make sure things are okay def test_results(self): data = self.data.drop([0,1,2]) anova_ii = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit() Sum_Sq = np.array([ 3.067066, 13.27205, 0.1905093, 27.60181 ]) Df = np.array([ 1, 2, 2, 51 ]) F_value = np.array([ 5.667033, 12.26141, 0.1760025, np.nan ]) PrF = np.array([ 0.02106078, 4.487909e-05, 0.8391231, np.nan ]) results = anova_lm(anova_ii, typ="II") np.testing.assert_equal(results['df'].values, Df) np.testing.assert_almost_equal(results['sum_sq'].values, Sum_Sq, 4) np.testing.assert_almost_equal(results['F'].values, F_value, 4) np.testing.assert_almost_equal(results['PR(>F)'].values, PrF) class TestAnova2Noconstant(TestAnovaLM): # drop some observations to make an unbalanced, disproportionate panel # to make sure things are okay def test_results(self): data = self.data.drop([0,1,2]) anova_ii = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum) - 1", data).fit() Sum_Sq = np.array([ 154.7131692, 13.27205, 0.1905093, 27.60181 ]) Df = np.array([ 2, 2, 2, 51 ]) F_value = np.array([ 142.9321191, 12.26141, 0.1760025, np.nan ]) PrF = np.array([ 1.238624e-21, 4.487909e-05, 0.8391231, np.nan ]) results = anova_lm(anova_ii, typ="II") np.testing.assert_equal(results['df'].values, Df) np.testing.assert_almost_equal(results['sum_sq'].values, Sum_Sq, 4) np.testing.assert_almost_equal(results['F'].values, F_value, 4) np.testing.assert_almost_equal(results['PR(>F)'].values, PrF) # > sum2.lm.dropped <- lm(logDays ~ Duration * Weight - 1, dta.dropped, # contrasts=list(Duration=contr.sum, Weight=contr.sum)) # > anova.ii.dropped2 <- Anova(sum2.lm.dropped, type='II') # > anova.ii.dropped2 # Anova Table (Type II tests) # # Response: logDays # Sum Sq Df F value Pr(>F) # Duration 154.713 2 142.932 < 2.2e-16 *** # Weight 13.272 2 12.261 4.488e-05 *** # Duration:Weight 0.191 2 0.176 0.8391 # Residuals 27.602 51 class TestAnova2HC0(TestAnovaLM): #NOTE: R does not return SSq with robust covariance. Why? # drop some observations to make an unbalanced, disproportionate panel # to make sure things are okay def test_results(self): data = self.data.drop([0,1,2]) anova_ii = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit() Sum_Sq = np.array([ 151.4065, 2.904723, 13.45718, 0.1905093, 27.60181 ]) Df = np.array([ 1, 2, 2, 51 ]) F = np.array([ 6.972744, 13.7804, 0.1709936, np.nan ]) PrF = np.array([ 0.01095599, 1.641682e-05, 0.8433081, np.nan ]) results = anova_lm(anova_ii, typ="II", robust="hc0") np.testing.assert_equal(results['df'].values, Df) #np.testing.assert_almost_equal(results['sum_sq'].values, Sum_Sq, 4) np.testing.assert_almost_equal(results['F'].values, F, 4) np.testing.assert_almost_equal(results['PR(>F)'].values, PrF) class TestAnova2HC1(TestAnovaLM): # drop some observations to make an unbalanced, disproportionate panel # to make sure things are okay def test_results(self): data = self.data.drop([0,1,2]) anova_ii = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit() Sum_Sq = np.array([ 151.4065, 2.904723, 13.45718, 0.1905093, 27.60181 ]) Df = np.array([ 1, 2, 2, 51 ]) F = np.array([ 6.238771, 12.32983, 0.1529943, np.nan ]) PrF = np.array([ 0.01576555, 4.285456e-05, 0.858527, np.nan ]) results = anova_lm(anova_ii, typ="II", robust="hc1") np.testing.assert_equal(results['df'].values, Df) #np.testing.assert_almost_equal(results['sum_sq'].values, Sum_Sq, 4) np.testing.assert_almost_equal(results['F'].values, F, 4) np.testing.assert_almost_equal(results['PR(>F)'].values, PrF) class TestAnova2HC2(TestAnovaLM): # drop some observations to make an unbalanced, disproportionate panel # to make sure things are okay def test_results(self): data = self.data.drop([0,1,2]) anova_ii = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit() Sum_Sq = np.array([ 151.4065, 2.904723, 13.45718, 0.1905093, 27.60181 ]) Df = np.array([ 1, 2, 2, 51 ]) F = np.array([ 6.267499, 12.25354, 0.1501224, np.nan ]) PrF = np.array([ 0.01554009, 4.511826e-05, 0.8609815, np.nan ]) results = anova_lm(anova_ii, typ="II", robust="hc2") np.testing.assert_equal(results['df'].values, Df) #np.testing.assert_almost_equal(results['sum_sq'].values, Sum_Sq, 4) np.testing.assert_almost_equal(results['F'].values, F, 4) np.testing.assert_almost_equal(results['PR(>F)'].values, PrF) class TestAnova2HC3(TestAnovaLM): # drop some observations to make an unbalanced, disproportionate panel # to make sure things are okay def test_results(self): data = self.data.drop([0,1,2]) anova_ii = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit() Sum_Sq = np.array([ 151.4065, 2.904723, 13.45718, 0.1905093, 27.60181 ]) Df = np.array([ 1, 2, 2, 51 ]) F = np.array([ 5.633786, 10.89842, 0.1317223, np.nan ]) PrF = np.array([ 0.02142223, 0.0001145965, 0.8768817, np.nan ]) results = anova_lm(anova_ii, typ="II", robust="hc3") np.testing.assert_equal(results['df'].values, Df) #np.testing.assert_almost_equal(results['sum_sq'].values, Sum_Sq, 4) np.testing.assert_almost_equal(results['F'].values, F, 4) np.testing.assert_almost_equal(results['PR(>F)'].values, PrF) class TestAnova3(TestAnovaLM): # drop some observations to make an unbalanced, disproportionate panel # to make sure things are okay def test_results(self): data = self.data.drop([0,1,2]) anova_iii = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit() Sum_Sq = np.array([ 151.4065, 2.904723, 13.45718, 0.1905093, 27.60181 ]) Df = np.array([ 1, 1, 2, 2, 51 ]) F_value = np.array([ 279.7545, 5.367071, 12.43245, 0.1760025, np.nan ]) PrF = np.array([ 2.379855e-22, 0.02457384, 3.999431e-05, 0.8391231, np.nan ]) results = anova_lm(anova_iii, typ="III") np.testing.assert_equal(results['df'].values, Df) np.testing.assert_almost_equal(results['sum_sq'].values, Sum_Sq, 4) np.testing.assert_almost_equal(results['F'].values, F_value, 4) np.testing.assert_almost_equal(results['PR(>F)'].values, PrF) class TestAnova3HC0(TestAnovaLM): #NOTE: R does not return SSq with robust covariance. Why? # drop some observations to make an unbalanced, disproportionate panel # to make sure things are okay def test_results(self): data = self.data.drop([0,1,2]) anova_iii = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit() Sum_Sq = np.array([ 151.4065, 2.904723, 13.45718, 0.1905093, 27.60181 ]) Df = np.array([ 1, 1, 2, 2, 51 ]) F = np.array([ 298.3404, 5.723638, 13.76069, 0.1709936, np.nan ]) PrF = np.array([ 5.876255e-23, 0.02046031, 1.662826e-05, 0.8433081, np.nan ]) results = anova_lm(anova_iii, typ="III", robust="hc0") np.testing.assert_equal(results['df'].values, Df) #np.testing.assert_almost_equal(results['sum_sq'].values, Sum_Sq, 4) np.testing.assert_almost_equal(results['F'].values, F, 4) np.testing.assert_almost_equal(results['PR(>F)'].values, PrF) class TestAnova3HC1(TestAnovaLM): # drop some observations to make an unbalanced, disproportionate panel # to make sure things are okay def test_results(self): data = self.data.drop([0,1,2]) anova_iii = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit() Sum_Sq = np.array([ 151.4065, 2.904723, 13.45718, 0.1905093, 27.60181 ]) Df = np.array([ 1, 1, 2, 2, 51 ]) F = np.array([ 266.9361, 5.12115, 12.3122, 0.1529943, np.nan ]) PrF = np.array([ 6.54355e-22, 0.02792296, 4.336712e-05, 0.858527, np.nan ]) results = anova_lm(anova_iii, typ="III", robust="hc1") np.testing.assert_equal(results['df'].values, Df) #np.testing.assert_almost_equal(results['sum_sq'].values, Sum_Sq, 4) np.testing.assert_almost_equal(results['F'].values, F, 4) np.testing.assert_almost_equal(results['PR(>F)'].values, PrF) class TestAnova3HC2(TestAnovaLM): # drop some observations to make an unbalanced, disproportionate panel # to make sure things are okay def test_results(self): data = self.data.drop([0,1,2]) anova_iii = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit() Sum_Sq = np.array([ 151.4065, 2.904723, 13.45718, 0.1905093, 27.60181 ]) Df = np.array([ 1, 1, 2, 2, 51 ]) F = np.array([ 264.5137, 5.074677, 12.19158, 0.1501224, np.nan ]) PrF = np.array([ 7.958286e-22, 0.02860926, 4.704831e-05, 0.8609815, np.nan ]) results = anova_lm(anova_iii, typ="III", robust="hc2") np.testing.assert_equal(results['df'].values, Df) #np.testing.assert_almost_equal(results['sum_sq'].values, Sum_Sq, 4) np.testing.assert_almost_equal(results['F'].values, F, 4) np.testing.assert_almost_equal(results['PR(>F)'].values, PrF) class TestAnova3HC3(TestAnovaLM): # drop some observations to make an unbalanced, disproportionate panel # to make sure things are okay def test_results(self): data = self.data.drop([0,1,2]) anova_iii = ols("np.log(Days+1) ~ C(Duration, Sum)*C(Weight, Sum)", data).fit() Sum_Sq = np.array([ 151.4065, 2.904723, 13.45718, 0.1905093, 27.60181 ]) Df = np.array([ 1, 1, 2, 2, 51 ]) F = np.array([ 234.4026, 4.496996, 10.79903, 0.1317223, np.nan ]) PrF = np.array([ 1.037224e-20, 0.03883841, 0.0001228716, 0.8768817, np.nan ]) results = anova_lm(anova_iii, typ="III", robust="hc3") np.testing.assert_equal(results['df'].values, Df) #np.testing.assert_almost_equal(results['sum_sq'].values, Sum_Sq, 4) np.testing.assert_almost_equal(results['F'].values, F, 4) np.testing.assert_almost_equal(results['PR(>F)'].values, PrF) statsmodels-0.12.2/statsmodels/stats/tests/test_anova_rm.py000066400000000000000000000162161400612667500242300ustar00rootroot00000000000000from statsmodels.compat.pandas import assert_frame_equal import pandas as pd import numpy as np from statsmodels.stats.anova import AnovaRM from numpy.testing import (assert_array_almost_equal, assert_raises, assert_equal) DV = [7, 3, 6, 6, 5, 8, 6, 7, 7, 11, 9, 11, 10, 10, 11, 11, 8, 14, 10, 11, 12, 10, 11, 12, 16, 7, 11, 9, 10, 11, 8, 8, 16, 10, 13, 10, 10, 14, 11, 12, 24, 29, 10, 22, 25, 28, 22, 24, 1, 3, 5, 8, 3, 5, 6, 8, 9, 18, 19, 1, 12, 15, 2, 3, 3, 4, 13, 21, 2, 11, 18, 2, 12, 7, 12, 3, 19, 1, 4, 13, 13, 14, 3, 4, 8, 19, 21, 2, 4, 9, 12, 2, 5, 8, 2, 4] id = [1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8] id = ['%d' % i for i in id] A = ['a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b'] B = ['a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c'] D = ['a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b'] data = pd.DataFrame([id, A, B, D, DV], index=['id', 'A', 'B', 'D', 'DV']).T data['DV'] = data['DV'].astype('int') def test_single_factor_repeated_measures_anova(): """ Testing single factor repeated measures anova Results reproduces R `ezANOVA` function from library ez """ df = AnovaRM(data.iloc[:16, :], 'DV', 'id', within=['B']).fit() a = [[1, 7, 22.4, 0.002125452]] assert_array_almost_equal(df.anova_table.iloc[:, [1, 2, 0, 3]].values, a, decimal=5) def test_two_factors_repeated_measures_anova(): """ Testing two factors repeated measures anova Results reproduces R `ezANOVA` function from library ez """ df = AnovaRM(data.iloc[:48, :], 'DV', 'id', within=['A', 'B']).fit() a = [[1, 7, 40.14159, 3.905263e-04], [2, 14, 29.21739, 1.007549e-05], [2, 14, 17.10545, 1.741322e-04]] assert_array_almost_equal(df.anova_table.iloc[:, [1, 2, 0, 3]].values, a, decimal=5) def test_three_factors_repeated_measures_anova(): """ Testing three factors repeated measures anova Results reproduces R `ezANOVA` function from library ez """ df = AnovaRM(data, 'DV', 'id', within=['A', 'B', 'D']).fit() a = [[1, 7, 8.7650709, 0.021087505], [2, 14, 8.4985785, 0.003833921], [1, 7, 20.5076546, 0.002704428], [2, 14, 0.8457797, 0.450021759], [1, 7, 21.7593382, 0.002301792], [2, 14, 6.2416695, 0.011536846], [2, 14, 5.4253359, 0.018010647]] assert_array_almost_equal(df.anova_table.iloc[:, [1, 2, 0, 3]].values, a, decimal=5) def test_repeated_measures_invalid_factor_name(): """ Test with a factor name of 'C', which conflicts with patsy. """ assert_raises(ValueError, AnovaRM, data.iloc[:16, :], 'DV', 'id', within=['C']) def test_repeated_measures_collinearity(): data1 = data.iloc[:48, :].copy() data1['E'] = data1['A'] assert_raises(ValueError, AnovaRM, data1, 'DV', 'id', within=['A', 'E']) def test_repeated_measures_unbalanced_data(): assert_raises(ValueError, AnovaRM, data.iloc[1:48, :], 'DV', 'id', within=['A', 'B']) def test_repeated_measures_aggregation(): df1 = AnovaRM(data, 'DV', 'id', within=['A', 'B', 'D']).fit() df2 = AnovaRM(data.append(data), 'DV', 'id', within=['A', 'B', 'D'], aggregate_func=np.mean).fit() assert_frame_equal(df1.anova_table, df2.anova_table) def test_repeated_measures_aggregation_one_subject_duplicated(): df1 = AnovaRM(data, 'DV', 'id', within=['A', 'B', 'D']).fit() df2 = AnovaRM(data.append(data.loc[data['id'] == '1', :]).reset_index(), 'DV', 'id', within=['A', 'B', 'D'], aggregate_func=np.mean).fit() assert_frame_equal(df1.anova_table, df2.anova_table) def test_repeated_measures_aggregate_func(): assert_raises(ValueError, AnovaRM, data.append(data), 'DV', 'id', within=['A', 'B', 'D']) m1 = AnovaRM(data.append(data), 'DV', 'id', within=['A', 'B', 'D'], aggregate_func=np.mean) m2 = AnovaRM(data.append(data), 'DV', 'id', within=['A', 'B', 'D'], aggregate_func=np.median) assert_raises(AssertionError, assert_equal, m1.aggregate_func, m2.aggregate_func) assert_frame_equal(m1.fit().anova_table, m2.fit().anova_table) def test_repeated_measures_aggregate_func_mean(): m1 = AnovaRM(data.append(data), 'DV', 'id', within=['A', 'B', 'D'], aggregate_func=np.mean) m2 = AnovaRM(data.append(data), 'DV', 'id', within=['A', 'B', 'D'], aggregate_func='mean') assert_equal(m1.aggregate_func, m2.aggregate_func) def test_repeated_measures_aggregate_compare_with_ezANOVA(): # Results should reproduces those from R's `ezANOVA` (library ez). ez = pd.DataFrame( {'F Value': [8.7650709, 8.4985785, 20.5076546, 0.8457797, 21.7593382, 6.2416695, 5.4253359], 'Num DF': [1, 2, 1, 2, 1, 2, 2], 'Den DF': [7, 14, 7, 14, 7, 14, 14], 'Pr > F': [0.021087505, 0.003833921, 0.002704428, 0.450021759, 0.002301792, 0.011536846, 0.018010647]}, index=pd.Index(['A', 'B', 'D', 'A:B', 'A:D', 'B:D', 'A:B:D'])) ez = ez[['F Value', 'Num DF', 'Den DF', 'Pr > F']] df = (AnovaRM(data.append(data), 'DV', 'id', within=['A', 'B', 'D'], aggregate_func=np.mean) .fit() .anova_table) assert_frame_equal(ez, df, check_dtype=False) statsmodels-0.12.2/statsmodels/stats/tests/test_base.py000066400000000000000000000032561400612667500233400ustar00rootroot00000000000000 import numpy as np from numpy.testing import assert_equal import pandas as pd from statsmodels.stats.base import HolderTuple def test_holdertuple(): ht = HolderTuple(statistic=5, pvalue=0.1, text="just something", extra=[1, 2, 4]) assert_equal(len(ht), 2) assert_equal(ht[:], [5, 0.1]) p, v = ht assert_equal([p, v], [5, 0.1]) p, v = ht[0], ht[1] assert_equal([p, v], [5, 0.1]) assert_equal(list(ht), [5, 0.1]) assert_equal(np.asarray(ht), [5, 0.1]) assert_equal(np.asarray(ht).dtype, np.float64) x = np.zeros((2, 2)) x[0] = ht assert_equal(x, [[5, 0.1], [0, 0]]) assert_equal(pd.Series(ht).values, [5, 0.1]) assert_equal(pd.DataFrame([ht, ht]).values, [[5, 0.1], [5, 0.1]]) assert_equal(ht.statistic, 5) assert_equal(ht.pvalue, 0.1) assert_equal(ht.extra, [1, 2, 4]) assert_equal(ht.text, "just something") def test_holdertuple2(): ht = HolderTuple(tuple_=("statistic", "extra"), statistic=5, pvalue=0.1, text="just something", extra=[1, 2, 4]) assert_equal(len(ht), 2) assert_equal(ht[:], [5, [1, 2, 4]]) p, v = ht assert_equal([p, v], [5, [1, 2, 4]]) p, v = ht[0], ht[1] assert_equal([p, v], [5, [1, 2, 4]]) assert_equal(list(ht), [5, [1, 2, 4]]) x = np.asarray(ht, dtype=object) assert_equal(x, np.asarray([5, [1, 2, 4]], dtype=object)) assert_equal(x.dtype, np.dtype('O')) # assert_equal(pd.Series(ht).values, [5, [1, 2, 4]]) # assert_equal(pd.Series(ht).dtype, np.dtype('O')) assert_equal(ht.statistic, 5) assert_equal(ht.pvalue, 0.1) assert_equal(ht.extra, [1, 2, 4]) assert_equal(ht.text, "just something") statsmodels-0.12.2/statsmodels/stats/tests/test_contingency_tables.py000066400000000000000000000475361400612667500263110ustar00rootroot00000000000000""" Tests for contingency table analyses. """ import os import warnings import numpy as np import statsmodels.stats.contingency_tables as ctab import pandas as pd from numpy.testing import assert_allclose, assert_equal import statsmodels.api as sm cur_dir = os.path.dirname(os.path.abspath(__file__)) fname = "contingency_table_r_results.csv" fpath = os.path.join(cur_dir, 'results', fname) r_results = pd.read_csv(fpath) tables = [None, None, None] tables[0] = np.asarray([[23, 15], [19, 31]]) tables[1] = np.asarray([[144, 33, 84, 126], [2, 4, 14, 29], [0, 2, 6, 25], [0, 0, 1, 5]]) tables[2] = np.asarray([[20, 10, 5], [3, 30, 15], [0, 5, 40]]) def test_homogeneity(): for k,table in enumerate(tables): st = sm.stats.SquareTable(table, shift_zeros=False) hm = st.homogeneity() assert_allclose(hm.statistic, r_results.loc[k, "homog_stat"]) assert_allclose(hm.df, r_results.loc[k, "homog_df"]) # Test Bhapkar via its relationship to Stuart_Maxwell. hmb = st.homogeneity(method="bhapkar") assert_allclose(hmb.statistic, hm.statistic / (1 - hm.statistic / table.sum())) def test_SquareTable_from_data(): np.random.seed(434) df = pd.DataFrame(index=range(100), columns=["v1", "v2"]) df["v1"] = np.random.randint(0, 5, 100) df["v2"] = np.random.randint(0, 5, 100) table = pd.crosstab(df["v1"], df["v2"]) rslt1 = ctab.SquareTable(table) rslt2 = ctab.SquareTable.from_data(df) rslt3 = ctab.SquareTable(np.asarray(table)) assert_equal(rslt1.summary().as_text(), rslt2.summary().as_text()) assert_equal(rslt2.summary().as_text(), rslt3.summary().as_text()) s = str(rslt1) assert_equal(s.startswith('A 5x5 contingency table with counts:'), True) assert_equal(rslt1.table[0, 0], 8.) def test_SquareTable_nonsquare(): tab = [[1, 0, 3], [2, 1, 4], [3, 0, 5]] df = pd.DataFrame(tab, index=[0, 1, 3], columns=[0, 2, 3]) df2 = ctab.SquareTable(df, shift_zeros=False) e = np.asarray([[1, 0, 0, 3], [2, 0, 1, 4], [0, 0, 0, 0], [3, 0, 0, 5]], dtype=np.float64) assert_equal(e, df2.table) def test_cumulative_odds(): table = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] table = np.asarray(table) tbl_obj = ctab.Table(table) cum_odds = tbl_obj.cumulative_oddsratios assert_allclose(cum_odds[0, 0], 28 / float(5 * 11)) assert_allclose(cum_odds[0, 1], (3 * 15) / float(3 * 24), atol=1e-5, rtol=1e-5) assert_allclose(np.log(cum_odds), tbl_obj.cumulative_log_oddsratios, atol=1e-5, rtol=1e-5) def test_local_odds(): table = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] table = np.asarray(table) tbl_obj = ctab.Table(table) loc_odds = tbl_obj.local_oddsratios assert_allclose(loc_odds[0, 0], 5 / 8.) assert_allclose(loc_odds[0, 1], 12 / float(15), atol=1e-5, rtol=1e-5) assert_allclose(np.log(loc_odds), tbl_obj.local_log_oddsratios, atol=1e-5, rtol=1e-5) def test_shifting(): t = np.zeros((3, 4), dtype=np.float64) result = np.full((3, 4), 0.5) assert_equal(ctab.Table(t, shift_zeros=False).table, t) assert_equal(ctab.Table(t, shift_zeros=True).table, result) t = np.asarray([[0, 1, 2], [3, 0, 4], [5, 6, 0]], dtype=np.float64) r = np.asarray([[0.5, 1, 2], [3, 0.5, 4], [5, 6, 0.5]], dtype=np.float64) assert_equal(ctab.Table(t).table, r) assert_equal(ctab.Table(t, shift_zeros=True).table, r) def test_stratified_table_cube(): # Test that we can pass a rank 3 ndarray or a list of rank 2 # ndarrays to StratifiedTable and get the same results. tab1 = [[[8, 9], [6, 7]], [[4, 9], [5, 5]], [[8, 8], [9, 11]]] tab2 = np.asarray(tab1).T ct1 = ctab.StratifiedTable(tab1) ct2 = ctab.StratifiedTable(tab2) assert_allclose(ct1.oddsratio_pooled, ct2.oddsratio_pooled) assert_allclose(ct1.logodds_pooled, ct2.logodds_pooled) def test_resids(): # CHD x serum data table = [[12, 8, 31, 41], [307, 246, 439, 245]] # These results come from SAS fit = [[22.083, 17.583, 32.536, 19.798], [296.92, 236.42, 437.46, 266.2]] c2 = [[4.6037, 5.223, 0.0725, 22.704], [0.3424, 0.3885, 0.0054, 1.6886]] # These are regression tests pr = np.array([[-2.14562121, -2.28538719, -0.26923882, 4.7649169 ], [ 0.58514314, 0.62325942, 0.07342547, -1.29946443]]) sr = np.array([[-2.55112945, -2.6338782 , -0.34712127, 5.5751083 ], [ 2.55112945, 2.6338782 , 0.34712127, -5.5751083 ]]) tab = ctab.Table(table) assert_allclose(tab.fittedvalues, fit, atol=1e-4, rtol=1e-4) assert_allclose(tab.chi2_contribs, c2, atol=1e-4, rtol=1e-4) assert_allclose(tab.resid_pearson, pr, atol=1e-4, rtol=1e-4) assert_allclose(tab.standardized_resids, sr, atol=1e-4, rtol=1e-4) def test_ordinal_association(): for k,table in enumerate(tables): row_scores = 1 + np.arange(table.shape[0]) col_scores = 1 + np.arange(table.shape[1]) # First set of scores rslt = ctab.Table(table, shift_zeros=False).test_ordinal_association(row_scores, col_scores) assert_allclose(rslt.statistic, r_results.loc[k, "lbl_stat"]) assert_allclose(rslt.null_mean, r_results.loc[k, "lbl_expval"]) assert_allclose(rslt.null_sd**2, r_results.loc[k, "lbl_var"]) assert_allclose(rslt.zscore**2, r_results.loc[k, "lbl_chi2"], rtol=1e-5, atol=1e-5) assert_allclose(rslt.pvalue, r_results.loc[k, "lbl_pvalue"], rtol=1e-5, atol=1e-5) # Second set of scores rslt = ctab.Table(table, shift_zeros=False).test_ordinal_association(row_scores, col_scores**2) assert_allclose(rslt.statistic, r_results.loc[k, "lbl2_stat"]) assert_allclose(rslt.null_mean, r_results.loc[k, "lbl2_expval"]) assert_allclose(rslt.null_sd**2, r_results.loc[k, "lbl2_var"]) assert_allclose(rslt.zscore**2, r_results.loc[k, "lbl2_chi2"]) assert_allclose(rslt.pvalue, r_results.loc[k, "lbl2_pvalue"], rtol=1e-5, atol=1e-5) def test_chi2_association(): np.random.seed(8743) table = np.random.randint(10, 30, size=(4, 4)) from scipy.stats import chi2_contingency rslt_scipy = chi2_contingency(table) b = ctab.Table(table).test_nominal_association() assert_allclose(b.statistic, rslt_scipy[0]) assert_allclose(b.pvalue, rslt_scipy[1]) def test_symmetry(): for k,table in enumerate(tables): st = sm.stats.SquareTable(table, shift_zeros=False) b = st.symmetry() assert_allclose(b.statistic, r_results.loc[k, "bowker_stat"]) assert_equal(b.df, r_results.loc[k, "bowker_df"]) assert_allclose(b.pvalue, r_results.loc[k, "bowker_pvalue"]) def test_mcnemar(): # Use chi^2 without continuity correction b1 = ctab.mcnemar(tables[0], exact=False, correction=False) st = sm.stats.SquareTable(tables[0]) b2 = st.homogeneity() assert_allclose(b1.statistic, b2.statistic) assert_equal(b2.df, 1) # Use chi^2 with continuity correction b3 = ctab.mcnemar(tables[0], exact=False, correction=True) assert_allclose(b3.pvalue, r_results.loc[0, "homog_cont_p"]) # Use binomial reference distribution b4 = ctab.mcnemar(tables[0], exact=True) assert_allclose(b4.pvalue, r_results.loc[0, "homog_binom_p"]) def test_from_data_stratified(): df = pd.DataFrame([[1, 1, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 1, 1, 1, 1]]).T e = np.asarray([[[0, 1], [1, 1]], [[2, 2], [1, 0]]]) # Test pandas tab1 = ctab.StratifiedTable.from_data(0, 1, 2, df) assert_equal(tab1.table, e) # Test ndarray tab1 = ctab.StratifiedTable.from_data(0, 1, 2, np.asarray(df)) assert_equal(tab1.table, e) def test_from_data_2x2(): df = pd.DataFrame([[1, 1, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0, 0]]).T e = np.asarray([[1, 2], [4, 1]]) # Test pandas tab1 = ctab.Table2x2.from_data(df, shift_zeros=False) assert_equal(tab1.table, e) # Test ndarray tab1 = ctab.Table2x2.from_data(np.asarray(df), shift_zeros=False) assert_equal(tab1.table, e) def test_cochranq(): # library(CVST) # table1 = matrix(c(1, 0, 1, 1, # 0, 1, 1, 1, # 1, 1, 1, 0, # 0, 1, 0, 0, # 0, 1, 0, 0, # 1, 0, 1, 0, # 0, 1, 0, 0, # 1, 1, 1, 1, # 0, 1, 0, 0), ncol=4, byrow=TRUE) # rslt1 = cochranq.test(table1) # table2 = matrix(c(0, 0, 1, 1, 0, # 0, 1, 0, 1, 0, # 0, 1, 1, 0, 1, # 1, 0, 0, 0, 1, # 1, 1, 0, 0, 0, # 1, 0, 1, 0, 0, # 0, 1, 0, 0, 0, # 0, 0, 1, 1, 0, # 0, 0, 0, 0, 0), ncol=5, byrow=TRUE) # rslt2 = cochranq.test(table2) table = [[1, 0, 1, 1], [0, 1, 1, 1], [1, 1, 1, 0], [0, 1, 0, 0], [0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 0], [1, 1, 1, 1], [0, 1, 0, 0]] table = np.asarray(table) stat, pvalue, df = ctab.cochrans_q(table, return_object=False) assert_allclose(stat, 4.2) assert_allclose(df, 3) table = [[0, 0, 1, 1, 0], [0, 1, 0, 1, 0], [0, 1, 1, 0, 1], [1, 0, 0, 0, 1], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 0, 0]] table = np.asarray(table) stat, pvalue, df = ctab.cochrans_q(table, return_object=False) assert_allclose(stat, 1.2174, rtol=1e-4) assert_allclose(df, 4) # Cochran's q and Mcnemar are equivalent for 2x2 tables data = table[:, 0:2] xtab = np.asarray(pd.crosstab(data[:, 0], data[:, 1])) b1 = ctab.cochrans_q(data, return_object=True) b2 = ctab.mcnemar(xtab, exact=False, correction=False) assert_allclose(b1.statistic, b2.statistic) assert_allclose(b1.pvalue, b2.pvalue) # Test for printing bunch assert_equal(str(b1).startswith("df 1\npvalue 0.65"), True) class CheckStratifiedMixin(object): @classmethod def initialize(cls, tables, use_arr=False): tables1 = tables if not use_arr else np.dstack(tables) cls.rslt = ctab.StratifiedTable(tables1) cls.rslt_0 = ctab.StratifiedTable(tables, shift_zeros=True) tables_pandas = [pd.DataFrame(x) for x in tables] cls.rslt_pandas = ctab.StratifiedTable(tables_pandas) def test_oddsratio_pooled(self): assert_allclose(self.rslt.oddsratio_pooled, self.oddsratio_pooled, rtol=1e-4, atol=1e-4) def test_logodds_pooled(self): assert_allclose(self.rslt.logodds_pooled, self.logodds_pooled, rtol=1e-4, atol=1e-4) def test_null_odds(self): rslt = self.rslt.test_null_odds(correction=True) assert_allclose(rslt.statistic, self.mh_stat, rtol=1e-4, atol=1e-5) assert_allclose(rslt.pvalue, self.mh_pvalue, rtol=1e-4, atol=1e-4) def test_oddsratio_pooled_confint(self): lcb, ucb = self.rslt.oddsratio_pooled_confint() assert_allclose(lcb, self.or_lcb, rtol=1e-4, atol=1e-4) assert_allclose(ucb, self.or_ucb, rtol=1e-4, atol=1e-4) def test_logodds_pooled_confint(self): lcb, ucb = self.rslt.logodds_pooled_confint() assert_allclose(lcb, np.log(self.or_lcb), rtol=1e-4, atol=1e-4) assert_allclose(ucb, np.log(self.or_ucb), rtol=1e-4, atol=1e-4) def test_equal_odds(self): if not hasattr(self, "or_homog"): return rslt = self.rslt.test_equal_odds(adjust=False) assert_allclose(rslt.statistic, self.or_homog, rtol=1e-4, atol=1e-4) assert_allclose(rslt.pvalue, self.or_homog_p, rtol=1e-4, atol=1e-4) rslt = self.rslt.test_equal_odds(adjust=True) assert_allclose(rslt.statistic, self.or_homog_adj, rtol=1e-4, atol=1e-4) assert_allclose(rslt.pvalue, self.or_homog_adj_p, rtol=1e-4, atol=1e-4) def test_pandas(self): with warnings.catch_warnings(): warnings.simplefilter("ignore", RuntimeWarning) assert_equal(self.rslt.summary().as_text(), self.rslt_pandas.summary().as_text()) def test_from_data(self): np.random.seed(241) df = pd.DataFrame(index=range(100), columns=("v1", "v2", "strat")) df["v1"] = np.random.randint(0, 2, 100) df["v2"] = np.random.randint(0, 2, 100) df["strat"] = np.kron(np.arange(10), np.ones(10)) tables = [] for k in range(10): ii = np.arange(10*k, 10*(k+1)) tables.append(pd.crosstab(df.loc[ii, "v1"], df.loc[ii, "v2"])) rslt1 = ctab.StratifiedTable(tables) rslt2 = ctab.StratifiedTable.from_data("v1", "v2", "strat", df) assert_equal(rslt1.summary().as_text(), rslt2.summary().as_text()) class TestStratified1(CheckStratifiedMixin): """ data = array(c(0, 0, 6, 5, 3, 0, 3, 6, 6, 2, 0, 4, 5, 6, 1, 0, 2, 5, 0, 0), dim=c(2, 2, 5)) rslt = mantelhaen.test(data) """ @classmethod def setup_class(cls): tables = [None] * 5 tables[0] = np.array([[0, 0], [6, 5]]) tables[1] = np.array([[3, 0], [3, 6]]) tables[2] = np.array([[6, 2], [0, 4]]) tables[3] = np.array([[5, 6], [1, 0]]) tables[4] = np.array([[2, 5], [0, 0]]) cls.initialize(tables) cls.oddsratio_pooled = 7 cls.logodds_pooled = np.log(7) cls.mh_stat = 3.9286 cls.mh_pvalue = 0.04747 cls.or_lcb = 1.026713 cls.or_ucb = 47.725133 class TestStratified2(CheckStratifiedMixin): """ library(DescTools) data = array(c(20, 14, 10, 24, 15, 12, 3, 15, 3, 2, 3, 2, 12, 3, 7, 5, 1, 0, 3, 2), dim=c(2, 2, 5)) rslt = mantelhaen.test(data) bd1 = BreslowDayTest(data, correct=FALSE) bd2 = BreslowDayTest(data, correct=TRUE) """ @classmethod def setup_class(cls): tables = [None] * 5 tables[0] = np.array([[20, 14], [10, 24]]) tables[1] = np.array([[15, 12], [3, 15]]) tables[2] = np.array([[3, 2], [3, 2]]) tables[3] = np.array([[12, 3], [7, 5]]) tables[4] = np.array([[1, 0], [3, 2]]) # check array of int cls.initialize(tables, use_arr=True) cls.oddsratio_pooled = 3.5912 cls.logodds_pooled = np.log(3.5912) cls.mh_stat = 11.8852 cls.mh_pvalue = 0.0005658 cls.or_lcb = 1.781135 cls.or_ucb = 7.240633 # Breslow Day test without Tarone adjustment cls.or_homog = 1.8438 cls.or_homog_p = 0.7645 # Breslow Day test with Tarone adjustment cls.or_homog_adj = 1.8436 cls.or_homog_adj_p = 0.7645 class TestStratified3(CheckStratifiedMixin): """ library(DescTools) data = array(c(313, 512, 19, 89, 207, 353, 8, 17, 205, 120, 391, 202, 278, 139, 244, 131, 138, 53, 299, 94, 351, 22, 317, 24), dim=c(2, 2, 6)) rslt = mantelhaen.test(data) bd1 = BreslowDayTest(data, correct=FALSE) bd2 = BreslowDayTest(data, correct=TRUE) """ @classmethod def setup_class(cls): tables = [None] * 6 tables[0] = np.array([[313, 512], [19, 89]]) tables[1] = np.array([[207, 353], [8, 17]]) tables[2] = np.array([[205, 120], [391, 202]]) tables[3] = np.array([[278, 139], [244, 131]]) tables[4] = np.array([[138, 53], [299, 94]]) tables[5] = np.array([[351, 22], [317, 24]]) cls.initialize(tables) cls.oddsratio_pooled = 1.101879 cls.logodds_pooled = np.log(1.101879) cls.mh_stat = 1.3368 cls.mh_pvalue = 0.2476 cls.or_lcb = 0.9402012 cls.or_ucb = 1.2913602 # Breslow Day test without Tarone adjustment cls.or_homog = 18.83297 cls.or_homog_p = 0.002064786 # Breslow Day test with Tarone adjustment cls.or_homog_adj = 18.83297 cls.or_homog_adj_p = 0.002064786 class Check2x2Mixin(object): @classmethod def initialize(cls): cls.tbl_obj = ctab.Table2x2(cls.table) cls.tbl_data_obj = ctab.Table2x2.from_data(cls.data) def test_oddsratio(self): assert_allclose(self.tbl_obj.oddsratio, self.oddsratio) def test_log_oddsratio(self): assert_allclose(self.tbl_obj.log_oddsratio, self.log_oddsratio) def test_log_oddsratio_se(self): assert_allclose(self.tbl_obj.log_oddsratio_se, self.log_oddsratio_se) def test_oddsratio_pvalue(self): assert_allclose(self.tbl_obj.oddsratio_pvalue(), self.oddsratio_pvalue) def test_oddsratio_confint(self): lcb1, ucb1 = self.tbl_obj.oddsratio_confint(0.05) lcb2, ucb2 = self.oddsratio_confint assert_allclose(lcb1, lcb2) assert_allclose(ucb1, ucb2) def test_riskratio(self): assert_allclose(self.tbl_obj.riskratio, self.riskratio) def test_log_riskratio(self): assert_allclose(self.tbl_obj.log_riskratio, self.log_riskratio) def test_log_riskratio_se(self): assert_allclose(self.tbl_obj.log_riskratio_se, self.log_riskratio_se) def test_riskratio_pvalue(self): assert_allclose(self.tbl_obj.riskratio_pvalue(), self.riskratio_pvalue) def test_riskratio_confint(self): lcb1, ucb1 = self.tbl_obj.riskratio_confint(0.05) lcb2, ucb2 = self.riskratio_confint assert_allclose(lcb1, lcb2) assert_allclose(ucb1, ucb2) def test_log_riskratio_confint(self): lcb1, ucb1 = self.tbl_obj.log_riskratio_confint(0.05) lcb2, ucb2 = self.log_riskratio_confint assert_allclose(lcb1, lcb2) assert_allclose(ucb1, ucb2) def test_from_data(self): assert_equal(self.tbl_obj.summary().as_text(), self.tbl_data_obj.summary().as_text()) def test_summary(self): assert_equal(self.tbl_obj.summary().as_text(), self.summary_string) class Test2x2_1(Check2x2Mixin): @classmethod def setup_class(cls): data = np.zeros((8, 2)) data[:, 0] = [0, 0, 1, 1, 0, 0, 1, 1] data[:, 1] = [0, 1, 0, 1, 0, 1, 0, 1] cls.data = np.asarray(data) cls.table = np.asarray([[2, 2], [2, 2]]) cls.oddsratio = 1. cls.log_oddsratio = 0. cls.log_oddsratio_se = np.sqrt(2) cls.oddsratio_confint = [0.062548836166112329, 15.987507702689751] cls.oddsratio_pvalue = 1. cls.riskratio = 1. cls.log_riskratio = 0. cls.log_riskratio_se = 1 / np.sqrt(2) cls.riskratio_pvalue = 1. cls.riskratio_confint = [0.25009765325990629, 3.9984381579173824] cls.log_riskratio_confint = [-1.3859038243496782, 1.3859038243496782] ss = [ ' Estimate SE LCB UCB p-value', '---------------------------------------------------', 'Odds ratio 1.000 0.063 15.988 1.000', 'Log odds ratio 0.000 1.414 -2.772 2.772 1.000', 'Risk ratio 1.000 0.250 3.998 1.000', 'Log risk ratio 0.000 0.707 -1.386 1.386 1.000', '---------------------------------------------------'] cls.summary_string = '\n'.join(ss) cls.initialize() statsmodels-0.12.2/statsmodels/stats/tests/test_contrast.py000066400000000000000000000046051400612667500242620ustar00rootroot00000000000000import numpy as np import numpy.random from numpy.testing import assert_almost_equal, assert_equal from statsmodels.stats.contrast import Contrast import statsmodels.stats.contrast as smc class TestContrast(object): @classmethod def setup_class(cls): numpy.random.seed(54321) cls.X = numpy.random.standard_normal((40,10)) def test_contrast1(self): term = np.column_stack((self.X[:,0], self.X[:,2])) c = Contrast(term, self.X) test_contrast = [[1] + [0]*9, [0]*2 + [1] + [0]*7] assert_almost_equal(test_contrast, c.contrast_matrix) def test_contrast2(self): zero = np.zeros((40,)) term = np.column_stack((zero, self.X[:,2])) c = Contrast(term, self.X) test_contrast = [0]*2 + [1] + [0]*7 assert_almost_equal(test_contrast, c.contrast_matrix) def test_contrast3(self): P = np.dot(self.X, np.linalg.pinv(self.X)) resid = np.identity(40) - P noise = np.dot(resid, numpy.random.standard_normal((40, 5))) term = np.column_stack((noise, self.X[:,2])) c = Contrast(term, self.X) assert_equal(c.contrast_matrix.shape, (10,)) #TODO: this should actually test the value of the contrast, not only its dimension def test_estimable(self): X2 = np.column_stack((self.X, self.X[:,5])) c = Contrast(self.X[:,5],X2) #TODO: I do not think this should be estimable? isestimable correct? def test_constraints(): cm_ = np.eye(4, 3, k=-1) cpairs = np.array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.], [-1., 1., 0.], [-1., 0., 1.], [ 0., -1., 1.]]) c0 = smc._constraints_factor(cm_) assert_equal(c0, cpairs) c1 = smc._contrast_pairs(3, 4, 0) assert_equal(c1, cpairs) # embedded cpairs2 = np.array([[ 0., 1., 0., 0., 0., 0.], [ 0., 0., 1., 0., 0., 0.], [ 0., 0., 0., 1., 0., 0.], [ 0., -1., 1., 0., 0., 0.], [ 0., -1., 0., 1., 0., 0.], [ 0., 0., -1., 1., 0., 0.]]) c0 = smc._constraints_factor(cm_, k_params=6, idx_start=1) assert_equal(c0, cpairs2) c1 = smc._contrast_pairs(6, 4, 1) # k_params, k_level, idx_start assert_equal(c1, cpairs2) statsmodels-0.12.2/statsmodels/stats/tests/test_correlation.py000066400000000000000000000032721400612667500247450ustar00rootroot00000000000000import numpy as np from statsmodels.stats.correlation_tools import ( kernel_covariance, GaussianMultivariateKernel) from numpy.testing import assert_allclose def test_kernel_covariance(): np.random.seed(342) # Number of independent observations ng = 1000 # Dimension of the process p = 3 # Each component of the process in an AR(r) with 10 values # observed on a grid r = 0.5 ii = np.arange(10) qm = r**np.abs(np.subtract.outer(ii, ii)) qm = np.linalg.cholesky(qm) exog, groups, pos = [], [], [] for j in range(ng): pos1 = np.arange(10)[:, None] groups1 = j * np.ones(10) # The components are independent AR processes ex1 = np.random.normal(size=(10, 3)) ex1 = np.dot(qm, ex1) pos.append(pos1) groups.append(groups1) exog.append(ex1) groups = np.concatenate(groups) pos = np.concatenate(pos, axis=0) exog = np.concatenate(exog, axis=0) for j in range(4): if j == 0: kernel = None bw = None elif j == 1: kernel = GaussianMultivariateKernel() bw = None elif j == 2: kernel = GaussianMultivariateKernel() bw = 1 elif j == 3: kernel = GaussianMultivariateKernel() bw = kernel.set_default_bw(pos) cv = kernel_covariance(exog, pos, groups, kernel=kernel, bw=bw) assert_allclose(cv(0, 0), np.eye(p), atol=0.1, rtol=0.01) assert_allclose(cv(0, 1), 0.5*np.eye(p), atol=0.1, rtol=0.01) assert_allclose(cv(0, 2), 0.25*np.eye(p), atol=0.1, rtol=0.01) assert_allclose(cv(1, 2), 0.5*np.eye(p), atol=0.1, rtol=0.01) statsmodels-0.12.2/statsmodels/stats/tests/test_corrpsd.py000066400000000000000000000401031400612667500240720ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Tests for finding a positive semi-definite correlation or covariance matrix Created on Mon May 27 12:07:02 2013 Author: Josef Perktold """ import warnings import numpy as np from numpy.testing import assert_almost_equal, assert_allclose import scipy.sparse as sparse import pytest from statsmodels.stats.correlation_tools import ( corr_nearest, corr_clipped, cov_nearest, _project_correlation_factors, corr_nearest_factor, _spg_optim, corr_thresholded, cov_nearest_factor_homog, FactoredPSDMatrix) from statsmodels.tools.testing import Holder def norm_f(x, y): '''Frobenious norm (squared sum) of difference between two arrays ''' d = ((x - y)**2).sum() return np.sqrt(d) # R library Matrix results cov1_r = Holder() #> nc <- nearPD(pr, conv.tol = 1e-7, keepDiag = TRUE, doDykstra =FALSE, corr=TRUE) #> cat_items(nc, prefix="cov1_r.") cov1_r.mat = '''''' cov1_r.eigenvalues = np.array([ 4.197315628646795, 0.7540460243978023, 0.5077608149667492, 0.3801267599652769, 0.1607508970775889, 4.197315628646795e-08 ]) cov1_r.corr = '''TRUE''' cov1_r.normF = 0.0743805226512533 cov1_r.iterations = 11 cov1_r.rel_tol = 8.288594638441735e-08 cov1_r.converged = '''TRUE''' #> mkarray2(as.matrix(nc$mat), name="cov1_r.mat") cov1_r.mat = np.array([ 1, 0.487968018215892, 0.642651880010906, 0.4906386709070835, 0.6440990530811909, 0.8087111845493985, 0.487968018215892, 1, 0.5141147294352735, 0.2506688108312097, 0.672351311297074, 0.725832055882795, 0.642651880010906, 0.5141147294352735, 1, 0.596827778712154, 0.5821917790519067, 0.7449631633814129, 0.4906386709070835, 0.2506688108312097, 0.596827778712154, 1, 0.729882058012399, 0.772150225146826, 0.6440990530811909, 0.672351311297074, 0.5821917790519067, 0.729882058012399, 1, 0.813191720191944, 0.8087111845493985, 0.725832055882795, 0.7449631633814129, 0.772150225146826, 0.813191720191944, 1 ]).reshape(6,6, order='F') cov_r = Holder() #nc <- nearPD(pr+0.01*diag(6), conv.tol = 1e-7, keepDiag = TRUE, doDykstra =FALSE, corr=FALSE) #> cat_items(nc, prefix="cov_r.") #cov_r.mat = '''''' cov_r.eigenvalues = np.array([ 4.209897516692652, 0.7668341923072066, 0.518956980021938, 0.390838551407132, 0.1734728460460068, 4.209897516692652e-08 ]) cov_r.corr = '''FALSE''' cov_r.normF = 0.0623948693159157 cov_r.iterations = 11 cov_r.rel_tol = 5.83987595937896e-08 cov_r.converged = '''TRUE''' #> mkarray2(as.matrix(nc$mat), name="cov_r.mat") cov_r.mat = np.array([ 1.01, 0.486207476951913, 0.6428524769306785, 0.4886092840296514, 0.645175579158233, 0.811533860074678, 0.486207476951913, 1.01, 0.514394615153752, 0.2478398278204047, 0.673852495852274, 0.7297661648968664, 0.6428524769306785, 0.514394615153752, 1.01, 0.5971503271420517, 0.582018469844712, 0.7445177382760834, 0.4886092840296514, 0.2478398278204047, 0.5971503271420517, 1.01, 0.73161232298669, 0.7766852947049376, 0.645175579158233, 0.673852495852274, 0.582018469844712, 0.73161232298669, 1.01, 0.8107916469252828, 0.811533860074678, 0.7297661648968664, 0.7445177382760834, 0.7766852947049376, 0.8107916469252828, 1.01 ]).reshape(6,6, order='F') def test_corr_psd(): # test positive definite matrix is unchanged x = np.array([[1, -0.2, -0.9], [-0.2, 1, -0.2], [-0.9, -0.2, 1]]) y = corr_nearest(x, n_fact=100) #print np.max(np.abs(x - y)) assert_almost_equal(x, y, decimal=14) y = corr_clipped(x) assert_almost_equal(x, y, decimal=14) y = cov_nearest(x, n_fact=100) assert_almost_equal(x, y, decimal=14) x2 = x + 0.001 * np.eye(3) y = cov_nearest(x2, n_fact=100) assert_almost_equal(x2, y, decimal=14) class CheckCorrPSDMixin(object): def test_nearest(self): x = self.x res_r = self.res y = corr_nearest(x, threshold=1e-7, n_fact=100) #print np.max(np.abs(x - y)) assert_almost_equal(y, res_r.mat, decimal=3) d = norm_f(x, y) assert_allclose(d, res_r.normF, rtol=0.0015) evals = np.linalg.eigvalsh(y) #print 'evals', evals / res_r.eigenvalues[::-1] - 1 assert_allclose(evals, res_r.eigenvalues[::-1], rtol=0.003, atol=1e-7) #print evals[0] / 1e-7 - 1 assert_allclose(evals[0], 1e-7, rtol=1e-6) def test_clipped(self): x = self.x res_r = self.res y = corr_clipped(x, threshold=1e-7) #print np.max(np.abs(x - y)), np.max(np.abs((x - y) / y)) assert_almost_equal(y, res_r.mat, decimal=1) d = norm_f(x, y) assert_allclose(d, res_r.normF, rtol=0.15) evals = np.linalg.eigvalsh(y) assert_allclose(evals, res_r.eigenvalues[::-1], rtol=0.1, atol=1e-7) assert_allclose(evals[0], 1e-7, rtol=0.02) def test_cov_nearest(self): x = self.x res_r = self.res with warnings.catch_warnings(): warnings.simplefilter("ignore") y = cov_nearest(x, method='nearest', threshold=1e-7) #print np.max(np.abs(x - y)) assert_almost_equal(y, res_r.mat, decimal=2) d = norm_f(x, y) assert_allclose(d, res_r.normF, rtol=0.0015) class TestCovPSD(object): @classmethod def setup_class(cls): x = np.array([ 1, 0.477, 0.644, 0.478, 0.651, 0.826, 0.477, 1, 0.516, 0.233, 0.682, 0.75, 0.644, 0.516, 1, 0.599, 0.581, 0.742, 0.478, 0.233, 0.599, 1, 0.741, 0.8, 0.651, 0.682, 0.581, 0.741, 1, 0.798, 0.826, 0.75, 0.742, 0.8, 0.798, 1]).reshape(6,6) cls.x = x + 0.01 * np.eye(6) cls.res = cov_r def test_cov_nearest(self): x = self.x res_r = self.res y = cov_nearest(x, method='nearest') #print np.max(np.abs(x - y)) assert_almost_equal(y, res_r.mat, decimal=3) d = norm_f(x, y) assert_allclose(d, res_r.normF, rtol=0.001) y = cov_nearest(x, method='clipped') #print np.max(np.abs(x - y)) assert_almost_equal(y, res_r.mat, decimal=2) d = norm_f(x, y) assert_allclose(d, res_r.normF, rtol=0.15) class TestCorrPSD1(CheckCorrPSDMixin): @classmethod def setup_class(cls): x = np.array([ 1, 0.477, 0.644, 0.478, 0.651, 0.826, 0.477, 1, 0.516, 0.233, 0.682, 0.75, 0.644, 0.516, 1, 0.599, 0.581, 0.742, 0.478, 0.233, 0.599, 1, 0.741, 0.8, 0.651, 0.682, 0.581, 0.741, 1, 0.798, 0.826, 0.75, 0.742, 0.8, 0.798, 1]).reshape(6,6) cls.x = x cls.res = cov1_r @pytest.mark.parametrize('threshold', [0, 1e-15, 1e-10, 1e-6]) def test_corrpsd_threshold(threshold): x = np.array([[1, -0.9, -0.9], [-0.9, 1, -0.9], [-0.9, -0.9, 1]]) y = corr_nearest(x, n_fact=100, threshold=threshold) evals = np.linalg.eigvalsh(y) assert_allclose(evals[0], threshold, rtol=1e-6, atol=1e-15) y = corr_clipped(x, threshold=threshold) evals = np.linalg.eigvalsh(y) assert_allclose(evals[0], threshold, rtol=0.25, atol=1e-15) y = cov_nearest(x, method='nearest', n_fact=100, threshold=threshold) evals = np.linalg.eigvalsh(y) assert_allclose(evals[0], threshold, rtol=1e-6, atol=1e-15) y = cov_nearest(x, n_fact=100, threshold=threshold) evals = np.linalg.eigvalsh(y) assert_allclose(evals[0], threshold, rtol=0.25, atol=1e-15) class Test_Factor(object): def test_corr_nearest_factor_arrpack(self): # regression results for svds call u2 = np.array([[ 6.39407581e-19, 9.15225947e-03, 1.82631698e-02, 2.72917181e-02, 3.61975557e-02, 4.49413101e-02, 5.34848732e-02, 6.17916613e-02, 6.98268388e-02, 7.75575058e-02, 8.49528448e-02, 9.19842264e-02, 9.86252769e-02, 1.04851906e-01, 1.10642305e-01, 1.15976906e-01, 1.20838331e-01, 1.25211306e-01, 1.29082570e-01, 1.32440778e-01, 1.35276397e-01, 1.37581605e-01, 1.39350201e-01, 1.40577526e-01, 1.41260396e-01, 1.41397057e-01, 1.40987160e-01, 1.40031756e-01, 1.38533306e-01, 1.36495727e-01, 1.33924439e-01, 1.30826443e-01, 1.27210404e-01, 1.23086750e-01, 1.18467769e-01, 1.13367717e-01, 1.07802909e-01, 1.01791811e-01, 9.53551023e-02, 8.85157320e-02, 8.12989329e-02, 7.37322125e-02, 6.58453049e-02, 5.76700847e-02, 4.92404406e-02, 4.05921079e-02, 3.17624629e-02, 2.27902803e-02, 1.37154584e-02, 4.57871801e-03, -4.57871801e-03, -1.37154584e-02, -2.27902803e-02, -3.17624629e-02, -4.05921079e-02, -4.92404406e-02, -5.76700847e-02, -6.58453049e-02, -7.37322125e-02, -8.12989329e-02, -8.85157320e-02, -9.53551023e-02, -1.01791811e-01, -1.07802909e-01, -1.13367717e-01, -1.18467769e-01, -1.23086750e-01, -1.27210404e-01, -1.30826443e-01, -1.33924439e-01, -1.36495727e-01, -1.38533306e-01, -1.40031756e-01, -1.40987160e-01, -1.41397057e-01, -1.41260396e-01, -1.40577526e-01, -1.39350201e-01, -1.37581605e-01, -1.35276397e-01, -1.32440778e-01, -1.29082570e-01, -1.25211306e-01, -1.20838331e-01, -1.15976906e-01, -1.10642305e-01, -1.04851906e-01, -9.86252769e-02, -9.19842264e-02, -8.49528448e-02, -7.75575058e-02, -6.98268388e-02, -6.17916613e-02, -5.34848732e-02, -4.49413101e-02, -3.61975557e-02, -2.72917181e-02, -1.82631698e-02, -9.15225947e-03, -3.51829569e-17]]).T s2 = np.array([ 24.88812183]) d = 100 dm = 1 # Construct a test matrix with exact factor structure X = np.zeros((d,dm), dtype=np.float64) x = np.linspace(0, 2*np.pi, d) for j in range(dm): X[:,j] = np.sin(x*(j+1)) _project_correlation_factors(X) X *= 0.7 mat = np.dot(X, X.T) np.fill_diagonal(mat, 1.) from scipy.sparse.linalg import svds u, s, vt = svds(mat, dm) #difference in sign dsign = np.sign(u[1]) * np.sign(u2[1]) assert_allclose(u, dsign * u2, rtol=1e-6, atol=1e-14) assert_allclose(s, s2, rtol=1e-6) @pytest.mark.parametrize('dm', [1, 2]) def test_corr_nearest_factor(self, dm): objvals = [np.array([6241.8, 6241.8, 579.4, 264.6, 264.3]), np.array([2104.9, 2104.9, 710.5, 266.3, 286.1])] d = 100 # Construct a test matrix with exact factor structure X = np.zeros((d, dm), dtype=np.float64) x = np.linspace(0, 2 * np.pi, d) np.random.seed(10) for j in range(dm): X[:, j] = np.sin(x * (j + 1)) + 1e-10 * np.random.randn(d) _project_correlation_factors(X) assert np.isfinite(X).all() X *= 0.7 mat = np.dot(X, X.T) np.fill_diagonal(mat, 1.) # Try to recover the structure rslt = corr_nearest_factor(mat, dm, maxiter=10000) err_msg = 'rank=%d, niter=%d' % (dm, len(rslt.objective_values)) assert_allclose(rslt.objective_values[:5], objvals[dm - 1], rtol=0.5, err_msg=err_msg) assert rslt.Converged mat1 = rslt.corr.to_matrix() assert_allclose(mat, mat1, rtol=0.25, atol=1e-3, err_msg=err_msg) @pytest.mark.slow @pytest.mark.parametrize('dm', [1, 2]) def test_corr_nearest_factor_sparse(self, dm): # Test that result is the same if the input is dense or sparse d = 200 # Generate a test matrix of factors X = np.zeros((d, dm), dtype=np.float64) x = np.linspace(0, 2 * np.pi, d) rs = np.random.RandomState(10) for j in range(dm): X[:, j] = np.sin(x * (j + 1)) + rs.randn(d) # Get the correlation matrix _project_correlation_factors(X) X *= 0.7 mat = np.dot(X, X.T) np.fill_diagonal(mat, 1) # Threshold it mat.flat[np.abs(mat.flat) < 0.35] = 0.0 smat = sparse.csr_matrix(mat) dense_rslt = corr_nearest_factor(mat, dm, maxiter=10000) sparse_rslt = corr_nearest_factor(smat, dm, maxiter=10000) mat_dense = dense_rslt.corr.to_matrix() mat_sparse = sparse_rslt.corr.to_matrix() assert dense_rslt.Converged is sparse_rslt.Converged assert dense_rslt.Converged is True assert_allclose(mat_dense, mat_sparse, rtol=.25, atol=1e-3) # Test on a quadratic function. def test_spg_optim(self, reset_randomstate): dm = 100 ind = np.arange(dm) indmat = np.abs(ind[:,None] - ind[None,:]) M = 0.8**indmat def obj(x): return np.dot(x, np.dot(M, x)) def grad(x): return 2*np.dot(M, x) def project(x): return x x = np.random.normal(size=dm) rslt = _spg_optim(obj, grad, x, project) xnew = rslt.params assert rslt.Converged is True assert_almost_equal(obj(xnew), 0, decimal=3) def test_decorrelate(self, reset_randomstate): d = 30 dg = np.linspace(1, 2, d) root = np.random.normal(size=(d, 4)) fac = FactoredPSDMatrix(dg, root) mat = fac.to_matrix() rmat = np.linalg.cholesky(mat) dcr = fac.decorrelate(rmat) idm = np.dot(dcr, dcr.T) assert_almost_equal(idm, np.eye(d)) rhs = np.random.normal(size=(d, 5)) mat2 = np.dot(rhs.T, np.linalg.solve(mat, rhs)) mat3 = fac.decorrelate(rhs) mat3 = np.dot(mat3.T, mat3) assert_almost_equal(mat2, mat3) def test_logdet(self, reset_randomstate): d = 30 dg = np.linspace(1, 2, d) root = np.random.normal(size=(d, 4)) fac = FactoredPSDMatrix(dg, root) mat = fac.to_matrix() _, ld = np.linalg.slogdet(mat) ld2 = fac.logdet() assert_almost_equal(ld, ld2) def test_solve(self, reset_randomstate): d = 30 dg = np.linspace(1, 2, d) root = np.random.normal(size=(d, 2)) fac = FactoredPSDMatrix(dg, root) rhs = np.random.normal(size=(d, 5)) sr1 = fac.solve(rhs) mat = fac.to_matrix() sr2 = np.linalg.solve(mat, rhs) assert_almost_equal(sr1, sr2) @pytest.mark.parametrize('dm', [1, 2]) def test_cov_nearest_factor_homog(self, dm): d = 100 # Construct a test matrix with exact factor structure X = np.zeros((d, dm), dtype=np.float64) x = np.linspace(0, 2*np.pi, d) for j in range(dm): X[:, j] = np.sin(x*(j+1)) mat = np.dot(X, X.T) np.fill_diagonal(mat, np.diag(mat) + 3.1) # Try to recover the structure rslt = cov_nearest_factor_homog(mat, dm) mat1 = rslt.to_matrix() assert_allclose(mat, mat1, rtol=0.25, atol=1e-3) @pytest.mark.parametrize('dm', [1, 2]) def test_cov_nearest_factor_homog_sparse(self, dm): # Check that dense and sparse inputs give the same result d = 100 # Construct a test matrix with exact factor structure X = np.zeros((d, dm), dtype=np.float64) x = np.linspace(0, 2*np.pi, d) for j in range(dm): X[:, j] = np.sin(x*(j+1)) mat = np.dot(X, X.T) np.fill_diagonal(mat, np.diag(mat) + 3.1) # Fit to dense rslt = cov_nearest_factor_homog(mat, dm) mat1 = rslt.to_matrix() # Fit to sparse smat = sparse.csr_matrix(mat) rslt = cov_nearest_factor_homog(smat, dm) mat2 = rslt.to_matrix() assert_allclose(mat1, mat2, rtol=0.25, atol=1e-3) def test_corr_thresholded(self, reset_randomstate): import datetime t1 = datetime.datetime.now() X = np.random.normal(size=(2000,10)) tcor = corr_thresholded(X, 0.2, max_elt=4e6) t2 = datetime.datetime.now() ss = (t2-t1).seconds fcor = np.corrcoef(X) fcor *= (np.abs(fcor) >= 0.2) assert_allclose(tcor.todense(), fcor, rtol=0.25, atol=1e-3) statsmodels-0.12.2/statsmodels/stats/tests/test_data.txt000066400000000000000000006437301400612667500235350ustar00rootroot00000000000000 1 1 -1.113973 2.251535 1 2 -.0808538 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-.0823599 .4922651 499 3 .4505591 -1.388515 499 4 .3475047 .7941831 499 5 -.7609926 -1.08425 499 6 -.8916075 -3.299844 499 7 -.6039193 -2.204624 499 8 .7171692 1.272819 499 9 .4266107 -2.184453 499 10 .6624547 -1.470384 500 1 .0283524 1.502491 500 2 -.5271088 -.5950647 500 3 -.4184161 2.122376 500 4 1.557888 .6030506 500 5 -.1874991 -.8182437 500 6 -.077057 3.720502 500 7 .2188469 .5591205 500 8 -.15553 -3.766785 500 9 -.0401722 .9033538 500 10 -.0011715 -.5297611 statsmodels-0.12.2/statsmodels/stats/tests/test_descriptivestats.py000066400000000000000000000141101400612667500260150ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_almost_equal, assert_equal import pandas as pd import pytest from statsmodels.iolib.table import SimpleTable from statsmodels.stats.descriptivestats import ( Describe, Description, describe, sign_test, ) pytestmark = pytest.mark.filterwarnings( "ignore::DeprecationWarning:statsmodels.stats.descriptivestats" ) @pytest.fixture(scope="function") def df(): a = np.random.RandomState(0).standard_normal(100) b = pd.Series(np.arange(100) % 10, dtype="category") return pd.DataFrame({"a": a, "b": b}) def test_sign_test(): x = [7.8, 6.6, 6.5, 7.4, 7.3, 7.0, 6.4, 7.1, 6.7, 7.6, 6.8] M, p = sign_test(x, mu0=6.5) # from R SIGN.test(x, md=6.5) # from R assert_almost_equal(p, 0.02148, 5) # not from R, we use a different convention assert_equal(M, 4) data5 = [ [25, "Bob", True, 1.2], [41, "John", False, 0.5], [30, "Alice", True, 0.3], ] data1 = np.array( [(1, 2, "a", "aa"), (2, 3, "b", "bb"), (2, 4, "b", "cc")], dtype=[ ("alpha", float), ("beta", int), ("gamma", "|S1"), ("delta", "|S2"), ], ) data2 = np.array( [(1, 2), (2, 3), (2, 4)], dtype=[("alpha", float), ("beta", float)] ) data3 = np.array([[1, 2, 4, 4], [2, 3, 3, 3], [2, 4, 4, 3]], dtype=float) data4 = np.array([[1, 2, 3, 4, 5, 6], [6, 5, 4, 3, 2, 1], [9, 9, 9, 9, 9, 9]]) class TestSimpleTable(object): # from statsmodels.iolib.table import SimpleTable, default_txt_fmt @pytest.mark.xfail(reason="Bad test") def test_basic_1(self): print("test_basic_1") t1 = Describe(data1) print(t1.summary()) def test_basic_2(self): print("test_basic_2") t2 = Describe(data2) print(t2.summary()) def test_describe_summary_float_ndarray(self): print("test_describe_summary_float_ndarray") t1 = Describe(data3) print(t1.summary()) def test_basic_4(self): print("test_basic_4") t1 = Describe(data4) print(t1.summary()) @pytest.mark.xfail(reason="Bad test") def test_basic_1a(self): print("test_basic_1a") t1 = Describe(data1) print(t1.summary(stats="basic", columns=["alpha"])) @pytest.mark.xfail(reason="Bad test") def test_basic_1b(self): print("test_basic_1b") t1 = Describe(data1) print(t1.summary(stats="basic", columns="all")) def test_basic_2a(self): print("test_basic_2a") t2 = Describe(data2) print(t2.summary(stats="all")) def test_basic_3(aself): t1 = Describe(data3) print(t1.summary(stats="all")) def test_basic_4a(self): t1 = Describe(data4) print(t1.summary(stats="all")) def test_description_exceptions(): df = pd.DataFrame( {"a": np.empty(100), "b": pd.Series(np.arange(100) % 10)}, dtype="category", ) with pytest.raises(ValueError): Description(df, stats=["unknown"]) with pytest.raises(ValueError): Description(df, alpha=-0.3) with pytest.raises(ValueError): Description(df, percentiles=[0, 100]) with pytest.raises(ValueError): Description(df, percentiles=[10, 20, 30, 10]) with pytest.raises(ValueError): Description(df, ntop=-3) with pytest.raises(ValueError): Description(df, numeric=False, categorical=False) def test_description_basic(df): res = Description(df) assert isinstance(res.frame, pd.DataFrame) assert isinstance(res.numeric, pd.DataFrame) assert isinstance(res.categorical, pd.DataFrame) assert isinstance(res.summary(), SimpleTable) assert isinstance(res.summary().as_text(), str) assert "Descriptive" in str(res) res = Description(df.a) assert isinstance(res.frame, pd.DataFrame) assert isinstance(res.numeric, pd.DataFrame) assert isinstance(res.categorical, pd.DataFrame) assert isinstance(res.summary(), SimpleTable) assert isinstance(res.summary().as_text(), str) assert "Descriptive" in str(res) res = Description(df.b) assert isinstance(res.frame, pd.DataFrame) assert isinstance(res.numeric, pd.DataFrame) assert isinstance(res.categorical, pd.DataFrame) assert isinstance(res.summary(), SimpleTable) assert isinstance(res.summary().as_text(), str) assert "Descriptive" in str(res) def test_odd_percentiles(df): percentiles = np.linspace(7.0, 93.0, 13) res = Description(df, percentiles=percentiles) print(res.frame.index) def test_large_ntop(df): res = Description(df, ntop=15) assert "top_15" in res.frame.index def test_use_t(df): res = Description(df) res_t = Description(df, use_t=True) assert res_t.frame.a.lower_ci < res.frame.a.lower_ci assert res_t.frame.a.upper_ci > res.frame.a.upper_ci SPECIAL = ( ("ci", ("lower_ci", "upper_ci")), ("jarque_bera", ("jarque_bera", "jarque_bera_pval")), ("mode", ("mode", "mode_freq")), ("top", tuple([f"top_{i}" for i in range(1, 6)])), ("freq", tuple([f"freq_{i}" for i in range(1, 6)])), ) @pytest.mark.parametrize("stat", SPECIAL, ids=[s[0] for s in SPECIAL]) def test_special_stats(df, stat): all_stats = [st for st in Description.default_statistics] all_stats.remove(stat[0]) res = Description(df, stats=all_stats) for val in stat[1]: assert val not in res.frame.index def test_empty_columns(df): df["c"] = np.nan res = Description(df) dropped = res.frame.c.dropna() assert dropped.shape[0] == 2 assert "missing" in dropped assert "nobs" in dropped df["c"] = np.nan res = Description(df.c) dropped = res.frame.dropna() assert dropped.shape[0] == 2 @pytest.mark.skipif(not hasattr(pd, "NA"), reason="Must support NA") def test_extension_types(df): df["c"] = pd.Series(np.arange(100.0)) df["d"] = pd.Series(np.arange(100), dtype=pd.Int64Dtype()) df.loc[df.index[::2], "c"] = np.nan df.loc[df.index[::2], "d"] = pd.NA res = Description(df) np.testing.assert_allclose(res.frame.c, res.frame.d) def test_describe(df): pd.testing.assert_frame_equal(describe(df), Description(df).frame) statsmodels-0.12.2/statsmodels/stats/tests/test_diagnostic.py000066400000000000000000001606031400612667500245520ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Tests for Regression Diagnostics and Specification Tests Created on Thu Feb 09 13:19:47 2012 Author: Josef Perktold License: BSD-3 currently all tests are against R """ import json import os import numpy as np import pandas as pd import pytest from numpy.testing import (assert_, assert_almost_equal, assert_equal, assert_allclose, assert_array_equal) from pandas.testing import assert_frame_equal import statsmodels.stats.diagnostic as smsdia import statsmodels.stats.outliers_influence as oi import statsmodels.stats.sandwich_covariance as sw from statsmodels.datasets import macrodata from statsmodels.datasets import sunspots from statsmodels.regression.linear_model import OLS from statsmodels.tools.tools import Bunch from statsmodels.tools.tools import add_constant from statsmodels.tsa.ar_model import AutoReg cur_dir = os.path.abspath(os.path.dirname(__file__)) @pytest.fixture(scope="module") def diagnostic_data(): rs = np.random.RandomState(93674328) e = rs.standard_normal(500) x = rs.standard_normal((500, 3)) y = x.sum(1) + e c = np.ones_like(y) data = pd.DataFrame(np.c_[y, c, x], columns=["y", "c", "x1", "x2", "x3"]) return data def compare_to_reference(sp, sp_dict, decimal=(12, 12)): assert_allclose(sp[0], sp_dict['statistic'], atol=10 ** -decimal[0], rtol=10 ** -decimal[0]) assert_allclose(sp[1], sp_dict['pvalue'], atol=10 ** -decimal[1], rtol=10 ** -decimal[0]) def test_gq(): d = macrodata.load(as_pandas=False).data realinv = d['realinv'] realgdp = d['realgdp'] realint = d['realint'] endog = realinv exog = add_constant(np.c_[realgdp, realint]) # goldfeld-quandt het_gq_greater = dict(statistic=13.20512768685082, df1=99, df2=98, pvalue=1.246141976112324e-30, distr='f') gq = smsdia.het_goldfeldquandt(endog, exog, split=0.5) compare_to_reference(gq, het_gq_greater, decimal=(12, 12)) assert_equal(gq[-1], 'increasing') class TestDiagnosticG(object): @classmethod def setup_class(cls): d = macrodata.load_pandas().data # growth rates gs_l_realinv = 400 * np.diff(np.log(d['realinv'].values)) gs_l_realgdp = 400 * np.diff(np.log(d['realgdp'].values)) lint = d['realint'][:-1].values tbilrate = d['tbilrate'][:-1].values endogg = gs_l_realinv exogg = add_constant(np.c_[gs_l_realgdp, lint]) exogg2 = add_constant(np.c_[gs_l_realgdp, tbilrate]) exogg3 = add_constant(np.c_[gs_l_realgdp]) res_ols = OLS(endogg, exogg).fit() res_ols2 = OLS(endogg, exogg2).fit() res_ols3 = OLS(endogg, exogg3).fit() cls.res = res_ols cls.res2 = res_ols2 cls.res3 = res_ols3 cls.endog = cls.res.model.endog cls.exog = cls.res.model.exog def test_basic(self): # mainly to check I got the right regression # > mkarray(fm$coefficients, "params") params = np.array([-9.48167277465485, 4.3742216647032, -0.613996969478989]) assert_almost_equal(self.res.params, params, decimal=12) def test_hac(self): res = self.res # > nw = NeweyWest(fm, lag = 4, prewhite = FALSE, verbose=TRUE) # > nw2 = NeweyWest(fm, lag=10, prewhite = FALSE, verbose=TRUE) # > mkarray(nw, "cov_hac_4") cov_hac_4 = np.array([1.385551290884014, -0.3133096102522685, -0.0597207976835705, -0.3133096102522685, 0.1081011690351306, 0.000389440793564336, -0.0597207976835705, 0.000389440793564339, 0.0862118527405036]).reshape((3, 3), order='F') # > mkarray(nw2, "cov_hac_10") cov_hac_10 = np.array([1.257386180080192, -0.2871560199899846, -0.03958300024627573, -0.2871560199899845, 0.1049107028987101, 0.0003896205316866944, -0.03958300024627578, 0.0003896205316866961, 0.0985539340694839]).reshape((3, 3), order='F') cov = sw.cov_hac_simple(res, nlags=4, use_correction=False) bse_hac = sw.se_cov(cov) assert_almost_equal(cov, cov_hac_4, decimal=12) assert_almost_equal(bse_hac, np.sqrt(np.diag(cov)), decimal=12) cov = sw.cov_hac_simple(res, nlags=10, use_correction=False) bse_hac = sw.se_cov(cov) assert_almost_equal(cov, cov_hac_10, decimal=12) assert_almost_equal(bse_hac, np.sqrt(np.diag(cov)), decimal=12) def test_het_goldfeldquandt(self): # TODO: test options missing # > gq = gqtest(fm, alternative='greater') # > mkhtest_f(gq, 'het_gq_greater', 'f') het_gq_greater = dict(statistic=0.5313259064778423, pvalue=0.9990217851193723, parameters=(98, 98), distr='f') # > gq = gqtest(fm, alternative='less') # > mkhtest_f(gq, 'het_gq_less', 'f') het_gq_less = dict(statistic=0.5313259064778423, pvalue=0.000978214880627621, parameters=(98, 98), distr='f') # > gq = gqtest(fm, alternative='two.sided') # > mkhtest_f(gq, 'het_gq_two_sided', 'f') het_gq_two_sided = dict(statistic=0.5313259064778423, pvalue=0.001956429761255241, parameters=(98, 98), distr='f') # > gq = gqtest(fm, fraction=0.1, alternative='two.sided') # > mkhtest_f(gq, 'het_gq_two_sided_01', 'f') het_gq_two_sided_01 = dict(statistic=0.5006976835928314, pvalue=0.001387126702579789, parameters=(88, 87), distr='f') endogg, exogg = self.endog, self.exog # tests gq = smsdia.het_goldfeldquandt(endogg, exogg, split=0.5) compare_to_reference(gq, het_gq_greater, decimal=(12, 12)) assert_equal(gq[-1], 'increasing') gq = smsdia.het_goldfeldquandt(endogg, exogg, split=0.5, alternative='decreasing') compare_to_reference(gq, het_gq_less, decimal=(12, 12)) assert_equal(gq[-1], 'decreasing') gq = smsdia.het_goldfeldquandt(endogg, exogg, split=0.5, alternative='two-sided') compare_to_reference(gq, het_gq_two_sided, decimal=(12, 12)) assert_equal(gq[-1], 'two-sided') # TODO: forcing the same split as R 202-90-90-1=21 gq = smsdia.het_goldfeldquandt(endogg, exogg, split=90, drop=21, alternative='two-sided') compare_to_reference(gq, het_gq_two_sided_01, decimal=(12, 12)) assert_equal(gq[-1], 'two-sided') # TODO other options ??? def test_het_breusch_pagan(self): res = self.res bptest = dict(statistic=0.709924388395087, pvalue=0.701199952134347, parameters=(2,), distr='f') bp = smsdia.het_breuschpagan(res.resid, res.model.exog) compare_to_reference(bp, bptest, decimal=(12, 12)) def test_het_breusch_pagan_nonrobust(self): res = self.res bptest = dict(statistic=1.302014063483341, pvalue=0.5215203247110649, parameters=(2,), distr='f') bp = smsdia.het_breuschpagan(res.resid, res.model.exog, robust=False) compare_to_reference(bp, bptest, decimal=(12, 12)) def test_het_white(self): res = self.res # TODO: regressiontest, compare with Greene or Gretl or Stata hw = smsdia.het_white(res.resid, res.model.exog) hw_values = (33.503722896538441, 2.9887960597830259e-06, 7.7945101228430946, 1.0354575277704231e-06) assert_almost_equal(hw, hw_values) def test_het_white_error(self): res = self.res with pytest.raises(ValueError, match="White's heteroskedasticity"): smsdia.het_white(res.resid, res.model.exog[:, :1]) def test_het_arch(self): # test het_arch and indirectly het_lm against R # > library(FinTS) # > at = ArchTest(residuals(fm), lags=4) # > mkhtest(at, 'archtest_4', 'chi2') archtest_4 = dict(statistic=3.43473400836259, pvalue=0.487871315392619, parameters=(4,), distr='chi2') # > at = ArchTest(residuals(fm), lags=12) # > mkhtest(at, 'archtest_12', 'chi2') archtest_12 = dict(statistic=8.648320999014171, pvalue=0.732638635007718, parameters=(12,), distr='chi2') at4 = smsdia.het_arch(self.res.resid, nlags=4) at12 = smsdia.het_arch(self.res.resid, nlags=12) compare_to_reference(at4[:2], archtest_4, decimal=(12, 13)) compare_to_reference(at12[:2], archtest_12, decimal=(12, 13)) def test_het_arch2(self): # test autolag options, this also test het_lm # unfortunately optimal lag=1 for this data resid = self.res.resid res1 = smsdia.het_arch(resid, nlags=1, autolag=None, store=True) rs1 = res1[-1] with pytest.warns(FutureWarning, match="autolag is deprecated and"): res2 = smsdia.het_arch(resid, nlags=5, autolag='aic', store=True) rs2 = res2[-1] assert_almost_equal(rs2.resols.params, rs1.resols.params, decimal=12) assert_almost_equal(res2[:4], res1[:4], decimal=12) # test that smallest lag, nlags=1 works with pytest.warns(FutureWarning, match="autolag is deprecated and"): res3 = smsdia.het_arch(resid, nlags=1, autolag='aic') assert_almost_equal(res3[:4], res1[:4], decimal=12) def test_acorr_breusch_godfrey(self): res = self.res # bgf = bgtest(fm, order = 4, type="F") breuschgodfrey_f = dict(statistic=1.179280833676792, pvalue=0.321197487261203, parameters=(4, 195,), distr='f') # > bgc = bgtest(fm, order = 4, type="Chisq") # > mkhtest(bgc, "breuschpagan_c", "chi2") breuschgodfrey_c = dict(statistic=4.771042651230007, pvalue=0.3116067133066697, parameters=(4,), distr='chi2') bg = smsdia.acorr_breusch_godfrey(res, nlags=4) bg_r = [breuschgodfrey_c['statistic'], breuschgodfrey_c['pvalue'], breuschgodfrey_f['statistic'], breuschgodfrey_f['pvalue']] assert_almost_equal(bg, bg_r, decimal=11) # check that lag choice works with pytest.warns(FutureWarning, match="The default value of nlags"): bg2 = smsdia.acorr_breusch_godfrey(res, nlags=None) bg3 = smsdia.acorr_breusch_godfrey(res, nlags=14) assert_almost_equal(bg2, bg3, decimal=12) def test_acorr_breusch_godfrey_multidim(self): res = Bunch(resid=np.empty((100, 2))) with pytest.raises(ValueError, match='Model resid must be a 1d array'): smsdia.acorr_breusch_godfrey(res) def test_acorr_ljung_box(self): # unit-test which may be useful later # ddof correction for fitted parameters in ARMA(p,q) fitdf=p+q # bt = Box.test(residuals(fm), lag=4, type = "Ljung-Box", fitdf=2) # mkhtest(bt, "ljung_box_4df2", "chi2") # ljung_box_4df2 = dict(statistic=5.23587172795227, # pvalue=0.0729532930400377, # parameters=(2,), distr='chi2') # bt = Box.test(residuals(fm), lag=4, type = "Box-Pierce", fitdf=2) # mkhtest(bt, "ljung_box_bp_4df2", "chi2") # ljung_box_bp_4df2 = dict(statistic=5.12462932741681, # pvalue=0.0771260128929921, # parameters=(2,), distr='chi2') res = self.res # general test # bt = Box.test(residuals(fm), lag=4, type = "Ljung-Box") # mkhtest(bt, "ljung_box_4", "chi2") ljung_box_4 = dict(statistic=5.23587172795227, pvalue=0.263940335284713, parameters=(4,), distr='chi2') # bt = Box.test(residuals(fm), lag=4, type = "Box-Pierce") # mkhtest(bt, "ljung_box_bp_4", "chi2") ljung_box_bp_4 = dict(statistic=5.12462932741681, pvalue=0.2747471266820692, parameters=(4,), distr='chi2') lb, lbpval, bp, bppval = smsdia.acorr_ljungbox(res.resid, 4, boxpierce=True, return_df=False) compare_to_reference([lb[-1], lbpval[-1]], ljung_box_4, decimal=(12, 12)) compare_to_reference([bp[-1], bppval[-1]], ljung_box_bp_4, decimal=(12, 12)) def test_acorr_ljung_box_big_default(self): res = self.res # R test with big dataset and default lag # bt = Box.test(residuals(fm), type = "Ljung-Box") # mkhtest(bt, "ljung_box_none", "chi2") ljung_box_none = dict(statistic=51.03724531797195, pvalue=0.11334744923390, distr='chi2') # bt = Box.test(residuals(fm), type = "Box-Pierce") # mkhtest(bt, "ljung_box_bp_none", "chi2") ljung_box_bp_none = dict(statistic=45.12238537034000, pvalue=0.26638168491464, distr='chi2') lags = min(40, res.resid.shape[0] // 2 - 2) lb, lbpval, bp, bppval = smsdia.acorr_ljungbox(res.resid, boxpierce=True, lags=lags, return_df=False) compare_to_reference([lb[-1], lbpval[-1]], ljung_box_none, decimal=(12, 12)) compare_to_reference([bp[-1], bppval[-1]], ljung_box_bp_none, decimal=(12, 12)) def test_acorr_ljung_box_small_default(self): res = self.res # R test with small dataset and default lag # bt = Box.test(residuals(fm), type = "Ljung-Box") # mkhtest(bt, "ljung_box_small", "chi2") ljung_box_small = dict(statistic=9.61503968281915, pvalue=0.72507000996945, parameters=(0,), distr='chi2') # bt = Box.test(residuals(fm), type = "Box-Pierce") # mkhtest(bt, "ljung_box_bp_small", "chi2") ljung_box_bp_small = dict(statistic=7.41692150864936, pvalue=0.87940785887006, parameters=(0,), distr='chi2') lb, lbpval, bp, bppval = smsdia.acorr_ljungbox(res.resid[:30], boxpierce=True, lags=13, return_df=False) compare_to_reference([lb[-1], lbpval[-1]], ljung_box_small, decimal=(12, 12)) compare_to_reference([bp[-1], bppval[-1]], ljung_box_bp_small, decimal=(12, 12)) def test_acorr_ljung_box_against_r(self, reset_randomstate): rs = np.random.RandomState(9876543) y1 = rs.standard_normal(100) e = rs.standard_normal(201) y2 = np.zeros_like(e) y2[0] = e[0] for i in range(1, 201): y2[i] = 0.5 * y2[i - 1] - 0.4 * e[i - 1] + e[i] y2 = y2[-100:] r_results_y1_lb = [[0.15685, 1, 0.6921], [5.4737, 5, 0.3608], [10.508, 10, 0.3971]] r_results_y2_lb = [[2.8764, 1, 0.08989], [3.8104, 5, 0.577], [8.4779, 10, 0.5823]] res_y1 = smsdia.acorr_ljungbox(y1, 10, return_df=True) res_y2 = smsdia.acorr_ljungbox(y2, 10, return_df=True) for i, loc in enumerate((1, 5, 10)): row = res_y1.loc[loc] assert_allclose(r_results_y1_lb[i][0], row.loc["lb_stat"], rtol=1e-3) assert_allclose(r_results_y1_lb[i][2], row.loc["lb_pvalue"], rtol=1e-3) row = res_y2.loc[loc] assert_allclose(r_results_y2_lb[i][0], row.loc["lb_stat"], rtol=1e-3) assert_allclose(r_results_y2_lb[i][2], row.loc["lb_pvalue"], rtol=1e-3) res = smsdia.acorr_ljungbox(y2, 10, boxpierce=True, return_df=True) assert_allclose(res.loc[10, "bp_stat"], 7.8935, rtol=1e-3) assert_allclose(res.loc[10, "bp_pvalue"], 0.639, rtol=1e-3) res = smsdia.acorr_ljungbox(y2, 10, boxpierce=True, return_df=True, model_df=1) assert_allclose(res.loc[10, "bp_pvalue"], 0.5449, rtol=1e-3) def test_harvey_collier(self): # > hc = harvtest(fm, order.by = NULL, data = list()) # > mkhtest_f(hc, 'harvey_collier', 't') harvey_collier = dict(statistic=0.494432160939874, pvalue=0.6215491310408242, parameters=198, distr='t') hc = smsdia.linear_harvey_collier(self.res) compare_to_reference(hc, harvey_collier, decimal=(12, 12)) hc_skip = smsdia.linear_harvey_collier(self.res, skip=20) assert not np.allclose(hc[0], hc_skip[0]) def test_rainbow(self): # rainbow test # > rt = raintest(fm) # > mkhtest_f(rt, 'raintest', 'f') raintest = dict(statistic=0.6809600116739604, pvalue=0.971832843583418, parameters=(101, 98), distr='f') # > rt = raintest(fm, fraction=0.4) # > mkhtest_f(rt, 'raintest_fraction_04', 'f') raintest_fraction_04 = dict(statistic=0.565551237772662, pvalue=0.997592305968473, parameters=(122, 77), distr='f') rb = smsdia.linear_rainbow(self.res) compare_to_reference(rb, raintest, decimal=(12, 12)) rb = smsdia.linear_rainbow(self.res, frac=0.4) compare_to_reference(rb, raintest_fraction_04, decimal=(12, 12)) def test_compare_lr(self): res = self.res res3 = self.res3 # nested within res # lrtest # lrt = lrtest(fm, fm2) # Model 1: ginv ~ ggdp + lint # Model 2: ginv ~ ggdp lrtest = dict(loglike1=-763.9752181602237, loglike2=-766.3091902020184, chi2value=4.66794408358942, pvalue=0.03073069384028677, df=(4, 3, 1)) lrt = res.compare_lr_test(res3) assert_almost_equal(lrt[0], lrtest['chi2value'], decimal=11) assert_almost_equal(lrt[1], lrtest['pvalue'], decimal=11) waldtest = dict(fvalue=4.65216373312492, pvalue=0.03221346195239025, df=(199, 200, 1)) wt = res.compare_f_test(res3) assert_almost_equal(wt[0], waldtest['fvalue'], decimal=11) assert_almost_equal(wt[1], waldtest['pvalue'], decimal=11) def test_compare_j(self): res = self.res res2 = self.res2 # jt = jtest(fm, lm(ginv ~ ggdp + tbilrate)) # Estimate Std. Error t value Pr(>|t|) jtest = [('M1 + fitted(M2)', 1.591505670785873, 0.7384552861695823, 2.155182176352370, 0.032354572525314450, '*'), ('M2 + fitted(M1)', 1.305687653016899, 0.4808385176653064, 2.715438978051544, 0.007203854534057954, '**')] jt1 = smsdia.compare_j(res2, res) assert_almost_equal(jt1, jtest[0][3:5], decimal=12) jt2 = smsdia.compare_j(res, res2) assert_almost_equal(jt2, jtest[1][3:5], decimal=12) def test_compare_j_class(self, diagnostic_data): # Only to verify not broken, deprecated with pytest.warns(FutureWarning, match="CompareJ is deprecated"): cj = smsdia.CompareJ() data = diagnostic_data res1 = OLS(data.y, data[["c", "x1"]]).fit() res2 = OLS(data.y, data[["c", "x2"]]).fit() cj(res1, res2) cj.run(res1, res2, attach=True) assert cj.res_zx is not None @pytest.mark.parametrize("comp", [smsdia.compare_cox, smsdia.compare_j]) def test_compare_error(self, comp, diagnostic_data): data = diagnostic_data res1 = OLS(data.y, data[["c", "x1"]]).fit() res2 = OLS(data.x3, data[["c", "x2"]]).fit() with pytest.raises(ValueError, match="endogenous variables"): comp(res1, res2) @pytest.mark.parametrize("comp", [smsdia.compare_cox, smsdia.compare_j]) def test_compare_nested(self, comp, diagnostic_data): data = diagnostic_data res1 = OLS(data.y, data[["c", "x1"]]).fit() res2 = OLS(data.y, data[["c", "x1", "x2"]]).fit() with pytest.raises(ValueError, match="The exog in results_x"): comp(res1, res2) with pytest.raises(ValueError, match="The exog in results_x"): comp(res2, res1) def test_compare_cox(self): res = self.res res2 = self.res2 # Estimate Std. Error z value Pr(>|z|) coxtest = [('fitted(M1) ~ M2', -0.782030488930356, 0.599696502782265, -1.304043770977755, 1.922186587840554e-01, ' '), ('fitted(M2) ~ M1', -2.248817107408537, 0.392656854330139, -5.727181590258883, 1.021128495098556e-08, '***')] ct1 = smsdia.compare_cox(res, res2) assert_almost_equal(ct1, coxtest[0][3:5], decimal=12) ct2 = smsdia.compare_cox(res2, res) assert_almost_equal(ct2, coxtest[1][3:5], decimal=12) _, _, store = smsdia.compare_cox(res, res2, store=True) assert isinstance(store, smsdia.ResultsStore) def test_compare_cox_class(self, diagnostic_data): # Only to verify not broken, deprecated with pytest.warns(FutureWarning, match="CompareCox is deprecated"): cc = smsdia.CompareCox() data = diagnostic_data res1 = OLS(data.y, data[["c", "x1"]]).fit() res2 = OLS(data.y, data[["c", "x2"]]).fit() cc(res1, res2) cc.run(res1, res2, attach=True) assert cc.res_dx is not None def test_cusum_ols(self): # R library(strucchange) # > sc = sctest(ginv ~ ggdp + lint, type="OLS-CUSUM") # > mkhtest(sc, 'cusum_ols', 'BB') cusum_ols = dict(statistic=1.055750610401214, pvalue=0.2149567397376543, parameters=(), distr='BB') # Brownian Bridge k_vars = 3 cs_ols = smsdia.breaks_cusumolsresid(self.res.resid, ddof=k_vars) # compare_to_reference(cs_ols, cusum_ols, decimal=(12, 12)) def test_breaks_hansen(self): # > sc = sctest(ginv ~ ggdp + lint, type="Nyblom-Hansen") # > mkhtest(sc, 'breaks_nyblom_hansen', 'BB') breaks_nyblom_hansen = dict(statistic=1.0300792740544484, pvalue=0.1136087530212015, parameters=(), distr='BB') bh = smsdia.breaks_hansen(self.res) assert_almost_equal(bh[0], breaks_nyblom_hansen['statistic'], decimal=12) # TODO: breaks_hansen does not return pvalues def test_recursive_residuals(self): reccumres_standardize = np.array([-2.151, -3.748, -3.114, -3.096, -1.865, -2.230, -1.194, -3.500, -3.638, -4.447, -4.602, -4.631, -3.999, -4.830, -5.429, -5.435, -6.554, -8.093, -8.567, -7.532, -7.079, -8.468, -9.320, -12.256, -11.932, -11.454, -11.690, -11.318, -12.665, -12.842, -11.693, -10.803, -12.113, -12.109, -13.002, -11.897, -10.787, -10.159, -9.038, -9.007, -8.634, -7.552, -7.153, -6.447, -5.183, -3.794, -3.511, -3.979, -3.236, -3.793, -3.699, -5.056, -5.724, -4.888, -4.309, -3.688, -3.918, -3.735, -3.452, -2.086, -6.520, -7.959, -6.760, -6.855, -6.032, -4.405, -4.123, -4.075, -3.235, -3.115, -3.131, -2.986, -1.813, -4.824, -4.424, -4.796, -4.000, -3.390, -4.485, -4.669, -4.560, -3.834, -5.507, -3.792, -2.427, -1.756, -0.354, 1.150, 0.586, 0.643, 1.773, -0.830, -0.388, 0.517, 0.819, 2.240, 3.791, 3.187, 3.409, 2.431, 0.668, 0.957, -0.928, 0.327, -0.285, -0.625, -2.316, -1.986, -0.744, -1.396, -1.728, -0.646, -2.602, -2.741, -2.289, -2.897, -1.934, -2.532, -3.175, -2.806, -3.099, -2.658, -2.487, -2.515, -2.224, -2.416, -1.141, 0.650, -0.947, 0.725, 0.439, 0.885, 2.419, 2.642, 2.745, 3.506, 4.491, 5.377, 4.624, 5.523, 6.488, 6.097, 5.390, 6.299, 6.656, 6.735, 8.151, 7.260, 7.846, 8.771, 8.400, 8.717, 9.916, 9.008, 8.910, 8.294, 8.982, 8.540, 8.395, 7.782, 7.794, 8.142, 8.362, 8.400, 7.850, 7.643, 8.228, 6.408, 7.218, 7.699, 7.895, 8.725, 8.938, 8.781, 8.350, 9.136, 9.056, 10.365, 10.495, 10.704, 10.784, 10.275, 10.389, 11.586, 11.033, 11.335, 11.661, 10.522, 10.392, 10.521, 10.126, 9.428, 9.734, 8.954, 9.949, 10.595, 8.016, 6.636, 6.975]) rr = smsdia.recursive_olsresiduals(self.res, skip=3, alpha=0.95) assert_equal(np.round(rr[5][1:], 3), reccumres_standardize) # extra zero in front # assert_equal(np.round(rr[3][4:], 3), np.diff(reccumres_standardize)) assert_almost_equal(rr[3][4:], np.diff(reccumres_standardize), 3) assert_almost_equal(rr[4][3:].std(ddof=1), 10.7242, decimal=4) order = np.arange(self.res.model.endog.shape[0]) rr_order = smsdia.recursive_olsresiduals(self.res, skip=3, alpha=0.95, order_by=order) assert_allclose(rr[0], rr_order[0], atol=1e-6) # regression number, visually checked with graph from gretl ub0 = np.array([13.37318571, 13.50758959, 13.64199346, 13.77639734, 13.91080121]) ub1 = np.array([39.44753774, 39.58194162, 39.7163455, 39.85074937, 39.98515325]) lb, ub = rr[6] assert_almost_equal(ub[:5], ub0, decimal=7) assert_almost_equal(lb[:5], -ub0, decimal=7) assert_almost_equal(ub[-5:], ub1, decimal=7) assert_almost_equal(lb[-5:], -ub1, decimal=7) # test a few values with explicit OLS endog = self.res.model.endog exog = self.res.model.exog params = [] ypred = [] for i in range(3, 10): resi = OLS(endog[:i], exog[:i]).fit() ypred.append(resi.model.predict(resi.params, exog[i])) params.append(resi.params) assert_almost_equal(rr[2][3:10], ypred, decimal=12) assert_almost_equal(rr[0][3:10], endog[3:10] - ypred, decimal=12) assert_almost_equal(rr[1][2:9], params, decimal=12) def test_normality(self): res = self.res # > library(nortest) #Lilliefors (Kolmogorov-Smirnov) normality test # > lt = lillie.test(residuals(fm)) # > mkhtest(lt, "lilliefors", "-") lilliefors1 = dict(statistic=0.0723390908786589, pvalue=0.01204113540102896, parameters=(), distr='-') # > lt = lillie.test(residuals(fm)**2) # > mkhtest(lt, "lilliefors", "-") lilliefors2 = dict(statistic=0.301311621898024, pvalue=1.004305736618051e-51, parameters=(), distr='-') # > lt = lillie.test(residuals(fm)[1:20]) # > mkhtest(lt, "lilliefors", "-") lilliefors3 = dict(statistic=0.1333956004203103, pvalue=0.455683, parameters=(), distr='-') lf1 = smsdia.lilliefors(res.resid, pvalmethod='approx') lf2 = smsdia.lilliefors(res.resid ** 2, pvalmethod='approx') lf3 = smsdia.lilliefors(res.resid[:20], pvalmethod='approx') compare_to_reference(lf1, lilliefors1, decimal=(12, 12)) compare_to_reference(lf2, lilliefors2, decimal=(12, 12)) # pvalue very small assert_allclose(lf2[1], lilliefors2['pvalue'], rtol=1e-10) compare_to_reference(lf3, lilliefors3, decimal=(12, 1)) # R uses different approximation for pvalue in last case # > ad = ad.test(residuals(fm)) # > mkhtest(ad, "ad3", "-") adr1 = dict(statistic=1.602209621518313, pvalue=0.0003937979149362316, parameters=(), distr='-') # > ad = ad.test(residuals(fm)**2) # > mkhtest(ad, "ad3", "-") # > ad = ad.test(residuals(fm)[1:20]) # > mkhtest(ad, "ad3", "-") adr3 = dict(statistic=0.3017073732210775, pvalue=0.5443499281265933, parameters=(), distr='-') ad1 = smsdia.normal_ad(res.resid) compare_to_reference(ad1, adr1, decimal=(11, 13)) ad2 = smsdia.normal_ad(res.resid ** 2) assert_(np.isinf(ad2[0])) ad3 = smsdia.normal_ad(res.resid[:20]) compare_to_reference(ad3, adr3, decimal=(11, 12)) def test_influence(self): res = self.res # this test is slow infl = oi.OLSInfluence(res) path = os.path.join(cur_dir, "results", "influence_lsdiag_R.json") with open(path, 'r') as fp: lsdiag = json.load(fp) # basic assert_almost_equal(np.array(lsdiag['cov.scaled']).reshape(3, 3), res.cov_params(), decimal=12) assert_almost_equal(np.array(lsdiag['cov.unscaled']).reshape(3, 3), res.normalized_cov_params, decimal=12) c0, c1 = infl.cooks_distance # TODO: what's c1 assert_almost_equal(c0, lsdiag['cooks'], decimal=12) assert_almost_equal(infl.hat_matrix_diag, lsdiag['hat'], decimal=12) assert_almost_equal(infl.resid_studentized_internal, lsdiag['std.res'], decimal=12) # slow: # infl._get_all_obs() #slow, nobs estimation loop, called implicitly dffits, dffth = infl.dffits assert_almost_equal(dffits, lsdiag['dfits'], decimal=12) assert_almost_equal(infl.resid_studentized_external, lsdiag['stud.res'], decimal=12) fn = os.path.join(cur_dir, "results/influence_measures_R.csv") infl_r = pd.read_csv(fn, index_col=0) # not used yet: # infl_bool_r = pandas.read_csv(fn, index_col=0, # converters=dict(zip(lrange(7),[conv]*7))) infl_r2 = np.asarray(infl_r) assert_almost_equal(infl.dfbetas, infl_r2[:, :3], decimal=12) assert_almost_equal(infl.cov_ratio, infl_r2[:, 4], decimal=12) # duplicates assert_almost_equal(dffits, infl_r2[:, 3], decimal=12) assert_almost_equal(c0, infl_r2[:, 5], decimal=12) assert_almost_equal(infl.hat_matrix_diag, infl_r2[:, 6], decimal=12) # TODO: finish and check thresholds and pvalues # Note: for dffits, R uses a threshold around 0.36, # mine: dffits[1]=0.24373 # R has # >>> np.nonzero(np.asarray(infl_bool_r["dffit"]))[0] # array([ 6, 26, 63, 76, 90, 199]) # >>> np.nonzero(np.asarray(infl_bool_r["cov.r"]))[0] # array([ 4, 26, 59, 61, 63, 72, 76, 84, 91, 92, 94, 95, # 108, 197, 198]) # >>> np.nonzero(np.asarray(infl_bool_r["hat"]))[0] # array([ 62, 76, 84, 90, 91, 92, 95, 108, 197, 199]) class TestDiagnosticGPandas(TestDiagnosticG): @classmethod def setup_class(cls): d = macrodata.load_pandas().data # growth rates d['gs_l_realinv'] = 400 * np.log(d['realinv']).diff() d['gs_l_realgdp'] = 400 * np.log(d['realgdp']).diff() d['lint'] = d['realint'].shift(1) d['tbilrate'] = d['tbilrate'].shift(1) d = d.dropna() cls.d = d endogg = d['gs_l_realinv'] exogg = add_constant(d[['gs_l_realgdp', 'lint']]) exogg2 = add_constant(d[['gs_l_realgdp', 'tbilrate']]) exogg3 = add_constant(d[['gs_l_realgdp']]) res_ols = OLS(endogg, exogg).fit() res_ols2 = OLS(endogg, exogg2).fit() res_ols3 = OLS(endogg, exogg3).fit() cls.res = res_ols cls.res2 = res_ols2 cls.res3 = res_ols3 cls.endog = cls.res.model.endog cls.exog = cls.res.model.exog def test_spec_white(): resdir = os.path.join(cur_dir, "results") wsfiles = ['wspec1.csv', 'wspec2.csv', 'wspec3.csv', 'wspec4.csv'] for file in wsfiles: mdlfile = os.path.join(resdir, file) mdl = np.asarray(pd.read_csv(mdlfile)) # DV is in last column lastcol = mdl.shape[1] - 1 dv = mdl[:, lastcol] # create design matrix design = np.concatenate((np.ones((mdl.shape[0], 1)), np.delete(mdl, lastcol, 1)), axis=1) # perform OLS and generate residuals resids = dv - np.dot(design, np.linalg.lstsq(design, dv, rcond=-1)[0]) # perform White spec test. wspec3/wspec4 contain dummies. wsres = smsdia.spec_white(resids, design) # compare results to SAS 9.3 output if file == 'wspec1.csv': assert_almost_equal(wsres, [3.251, 0.661, 5], decimal=3) elif file == 'wspec2.csv': assert_almost_equal(wsres, [6.070, 0.733, 9], decimal=3) elif file == 'wspec3.csv': assert_almost_equal(wsres, [6.767, 0.454, 7], decimal=3) else: assert_almost_equal(wsres, [8.462, 0.671, 11], decimal=3) def test_spec_white_error(reset_randomstate): with pytest.raises(ValueError, match="White's specification test "): smsdia.spec_white(np.random.standard_normal(100), np.random.standard_normal((100, 1))) with pytest.raises(ValueError, match="White's specification test "): smsdia.spec_white(np.random.standard_normal(100), np.random.standard_normal((100, 2))) def test_linear_lm_direct(reset_randomstate): endog = np.random.standard_normal(500) exog = add_constant(np.random.standard_normal((500, 3))) res = OLS(endog, exog).fit() lm_res = smsdia.linear_lm(res.resid, exog) aug = np.hstack([exog, exog[:, 1:]**2]) res_aug = OLS(res.resid, aug).fit() stat = res_aug.rsquared * aug.shape[0] assert_allclose(lm_res[0], stat) # TODO: make this a test or move/remove def grangertest(): # > gt = grangertest(ginv, ggdp, order=4) # > gt # Granger causality test # # Model 1: ggdp ~ Lags(ggdp, 1:4) + Lags(ginv, 1:4) # Model 2: ggdp ~ Lags(ggdp, 1:4) dict(fvalue=1.589672703015157, pvalue=0.178717196987075, df=(198, 193)) @pytest.mark.smoke def test_outlier_influence_funcs(reset_randomstate): x = add_constant(np.random.randn(10, 2)) y = x.sum(1) + np.random.randn(10) res = OLS(y, x).fit() out_05 = oi.summary_table(res) # GH3344 : Check alpha has an effect out_01 = oi.summary_table(res, alpha=0.01) assert_(np.all(out_01[1][:, 6] <= out_05[1][:, 6])) assert_(np.all(out_01[1][:, 7] >= out_05[1][:, 7])) res2 = OLS(y, x[:, 0]).fit() oi.summary_table(res2, alpha=0.05) infl = res2.get_influence() infl.summary_table() def test_influence_wrapped(): from pandas import DataFrame d = macrodata.load_pandas().data # growth rates gs_l_realinv = 400 * np.log(d['realinv']).diff().dropna() gs_l_realgdp = 400 * np.log(d['realgdp']).diff().dropna() lint = d['realint'][:-1] # re-index these because they will not conform to lint gs_l_realgdp.index = lint.index gs_l_realinv.index = lint.index data = dict(const=np.ones_like(lint), lint=lint, lrealgdp=gs_l_realgdp) # order is important exog = DataFrame(data, columns=['const', 'lrealgdp', 'lint']) res = OLS(gs_l_realinv, exog).fit() # basic # already tested # assert_almost_equal(lsdiag['cov.scaled'], # res.cov_params().values.ravel(), decimal=12) # assert_almost_equal(lsdiag['cov.unscaled'], # res.normalized_cov_params.values.ravel(), decimal=12) infl = oi.OLSInfluence(res) # smoke test just to make sure it works, results separately tested df = infl.summary_frame() assert_(isinstance(df, DataFrame)) # this test is slow path = os.path.join(cur_dir, "results", "influence_lsdiag_R.json") with open(path, "r") as fp: lsdiag = json.load(fp) c0, c1 = infl.cooks_distance # TODO: what's c1, it's pvalues? -ss # NOTE: we get a hard-cored 5 decimals with pandas testing assert_almost_equal(c0, lsdiag['cooks'], 12) assert_almost_equal(infl.hat_matrix_diag, (lsdiag['hat']), 12) assert_almost_equal(infl.resid_studentized_internal, lsdiag['std.res'], 12) # slow: dffits, dffth = infl.dffits assert_almost_equal(dffits, lsdiag['dfits'], 12) assert_almost_equal(infl.resid_studentized_external, lsdiag['stud.res'], 12) fn = os.path.join(cur_dir, "results/influence_measures_R.csv") infl_r = pd.read_csv(fn, index_col=0) # not used yet: # infl_bool_r = pandas.read_csv(fn, index_col=0, # converters=dict(zip(lrange(7),[conv]*7))) infl_r2 = np.asarray(infl_r) # TODO: finish wrapping this stuff assert_almost_equal(infl.dfbetas, infl_r2[:, :3], decimal=12) assert_almost_equal(infl.cov_ratio, infl_r2[:, 4], decimal=12) def test_influence_dtype(): # see #2148 bug when endog is integer y = np.ones(20) np.random.seed(123) x = np.random.randn(20, 3) res1 = OLS(y, x).fit() res2 = OLS(y * 1., x).fit() cr1 = res1.get_influence().cov_ratio cr2 = res2.get_influence().cov_ratio assert_allclose(cr1, cr2, rtol=1e-14) # regression test for values cr3 = np.array( [1.22239215, 1.31551021, 1.52671069, 1.05003921, 0.89099323, 1.57405066, 1.03230092, 0.95844196, 1.15531836, 1.21963623, 0.87699564, 1.16707748, 1.10481391, 0.98839447, 1.08999334, 1.35680102, 1.46227715, 1.45966708, 1.13659521, 1.22799038]) assert_almost_equal(cr1, cr3, decimal=8) def get_duncan_data(): # results from R with NA -> 1. Just testing interface here because # outlier_test is just a wrapper labels = ['accountant', 'pilot', 'architect', 'author', 'chemist', 'minister', 'professor', 'dentist', 'reporter', 'engineer', 'undertaker', 'lawyer', 'physician', 'welfare.worker', 'teacher', 'conductor', 'contractor', 'factory.owner', 'store.manager', 'banker', 'bookkeeper', 'mail.carrier', 'insurance.agent', 'store.clerk', 'carpenter', 'electrician', 'RR.engineer', 'machinist', 'auto.repairman', 'plumber', 'gas.stn.attendant', 'coal.miner', 'streetcar.motorman', 'taxi.driver', 'truck.driver', 'machine.operator', 'barber', 'bartender', 'shoe.shiner', 'cook', 'soda.clerk', 'watchman', 'janitor', 'policeman', 'waiter'] # Duncan's prestige data from car exog = [[1.0, 62.0, 86.0], [1.0, 72.0, 76.0], [1.0, 75.0, 92.0], [1.0, 55.0, 90.0], [1.0, 64.0, 86.0], [1.0, 21.0, 84.0], [1.0, 64.0, 93.0], [1.0, 80.0, 100.0], [1.0, 67.0, 87.0], [1.0, 72.0, 86.0], [1.0, 42.0, 74.0], [1.0, 76.0, 98.0], [1.0, 76.0, 97.0], [1.0, 41.0, 84.0], [1.0, 48.0, 91.0], [1.0, 76.0, 34.0], [1.0, 53.0, 45.0], [1.0, 60.0, 56.0], [1.0, 42.0, 44.0], [1.0, 78.0, 82.0], [1.0, 29.0, 72.0], [1.0, 48.0, 55.0], [1.0, 55.0, 71.0], [1.0, 29.0, 50.0], [1.0, 21.0, 23.0], [1.0, 47.0, 39.0], [1.0, 81.0, 28.0], [1.0, 36.0, 32.0], [1.0, 22.0, 22.0], [1.0, 44.0, 25.0], [1.0, 15.0, 29.0], [1.0, 7.0, 7.0], [1.0, 42.0, 26.0], [1.0, 9.0, 19.0], [1.0, 21.0, 15.0], [1.0, 21.0, 20.0], [1.0, 16.0, 26.0], [1.0, 16.0, 28.0], [1.0, 9.0, 17.0], [1.0, 14.0, 22.0], [1.0, 12.0, 30.0], [1.0, 17.0, 25.0], [1.0, 7.0, 20.0], [1.0, 34.0, 47.0], [1.0, 8.0, 32.0]] endog = [82., 83., 90., 76., 90., 87., 93., 90., 52., 88., 57., 89., 97., 59., 73., 38., 76., 81., 45., 92., 39., 34., 41., 16., 33., 53., 67., 57., 26., 29., 10., 15., 19., 10., 13., 24., 20., 7., 3., 16., 6., 11., 8., 41., 10.] return endog, exog, labels def test_outlier_test(): endog, exog, labels = get_duncan_data() ndarray_mod = OLS(endog, exog).fit() rstudent = [3.1345185839, -2.3970223990, 2.0438046359, -1.9309187757, 1.8870465798, -1.7604905300, -1.7040324156, 1.6024285876, -1.4332485037, -1.1044851583, 1.0688582315, 1.0185271840, -0.9024219332, -0.9023876471, -0.8830953936, 0.8265782334, 0.8089220547, 0.7682770197, 0.7319491074, -0.6665962829, 0.5227352794, -0.5135016547, 0.5083881518, 0.4999224372, -0.4980818221, -0.4759717075, -0.4293565820, -0.4114056499, -0.3779540862, 0.3556874030, 0.3409200462, 0.3062248646, 0.3038999429, -0.3030815773, -0.1873387893, 0.1738050251, 0.1424246593, -0.1292266025, 0.1272066463, -0.0798902878, 0.0788467222, 0.0722556991, 0.0505098280, 0.0233215136, 0.0007112055] unadj_p = [0.003177202, 0.021170298, 0.047432955, 0.060427645, 0.066248120, 0.085783008, 0.095943909, 0.116738318, 0.159368890, 0.275822623, 0.291386358, 0.314400295, 0.372104049, 0.372122040, 0.382333561, 0.413260793, 0.423229432, 0.446725370, 0.468363101, 0.508764039, 0.603971990, 0.610356737, 0.613905871, 0.619802317, 0.621087703, 0.636621083, 0.669911674, 0.682917818, 0.707414459, 0.723898263, 0.734904667, 0.760983108, 0.762741124, 0.763360242, 0.852319039, 0.862874018, 0.887442197, 0.897810225, 0.899398691, 0.936713197, 0.937538115, 0.942749758, 0.959961394, 0.981506948, 0.999435989] bonf_p = [0.1429741, 0.9526634, 2.1344830, 2.7192440, 2.9811654, 3.8602354, 4.3174759, 5.2532243, 7.1716001, 12.4120180, 13.1123861, 14.1480133, 16.7446822, 16.7454918, 17.2050103, 18.5967357, 19.0453245, 20.1026416, 21.0763395, 22.8943818, 27.1787396, 27.4660532, 27.6257642, 27.8911043, 27.9489466, 28.6479487, 30.1460253, 30.7313018, 31.8336506, 32.5754218, 33.0707100, 34.2442399, 34.3233506, 34.3512109, 38.3543568, 38.8293308, 39.9348989, 40.4014601, 40.4729411, 42.1520939, 42.1892152, 42.4237391, 43.1982627, 44.1678127, 44.9746195] bonf_p = np.array(bonf_p) bonf_p[bonf_p > 1] = 1 sorted_labels = ["minister", "reporter", "contractor", "insurance.agent", "machinist", "store.clerk", "conductor", "factory.owner", "mail.carrier", "streetcar.motorman", "carpenter", "coal.miner", "bartender", "bookkeeper", "soda.clerk", "chemist", "RR.engineer", "professor", "electrician", "gas.stn.attendant", "auto.repairman", "watchman", "banker", "machine.operator", "dentist", "waiter", "shoe.shiner", "welfare.worker", "plumber", "physician", "pilot", "engineer", "accountant", "lawyer", "undertaker", "barber", "store.manager", "truck.driver", "cook", "janitor", "policeman", "architect", "teacher", "taxi.driver", "author"] res2 = np.c_[rstudent, unadj_p, bonf_p] res = oi.outlier_test(ndarray_mod, method='b', labels=labels, order=True) np.testing.assert_almost_equal(res.values, res2, 7) np.testing.assert_equal(res.index.tolist(), sorted_labels) # pylint: disable-msg=E1103 data = pd.DataFrame(np.column_stack((endog, exog)), columns='y const var1 var2'.split(), index=labels) # check `order` with pandas bug in #3971 res_pd = OLS.from_formula('y ~ const + var1 + var2 - 0', data).fit() res_outl2 = oi.outlier_test(res_pd, method='b', order=True) assert_almost_equal(res_outl2.values, res2, 7) assert_equal(res_outl2.index.tolist(), sorted_labels) res_outl1 = res_pd.outlier_test(method='b') res_outl1 = res_outl1.sort_values(['unadj_p'], ascending=True) assert_almost_equal(res_outl1.values, res2, 7) assert_equal(res_outl1.index.tolist(), sorted_labels) assert_array_equal(res_outl2.index, res_outl1.index) # additional keywords in method res_outl3 = res_pd.outlier_test(method='b', order=True) assert_equal(res_outl3.index.tolist(), sorted_labels) res_outl4 = res_pd.outlier_test(method='b', order=True, cutoff=0.15) assert_equal(res_outl4.index.tolist(), sorted_labels[:1]) def test_ljungbox_dof_adj(): data = sunspots.load_pandas().data['SUNACTIVITY'] res = AutoReg(data, 4, old_names=False).fit() resid = res.resid res1 = smsdia.acorr_ljungbox(resid, lags=10, return_df=False) res2 = smsdia.acorr_ljungbox(resid, lags=10, model_df=4, return_df=False) assert_allclose(res1[0], res2[0]) assert np.all(np.isnan(res2[1][:4])) assert np.all(res2[1][4:] <= res1[1][4:]) def test_ljungbox_auto_lag_selection(): data = sunspots.load_pandas().data['SUNACTIVITY'] res = AutoReg(data, 4, old_names=False).fit() resid = res.resid res1 = smsdia.acorr_ljungbox(resid, return_df=False, auto_lag=True) res2 = smsdia.acorr_ljungbox(resid, model_df=4, return_df=False, auto_lag=True) assert_allclose(res1[0], res2[0]) assert np.all(np.isnan(res2[1][:4])) assert np.all(res2[1][4:] <= res1[1][4:]) def test_ljungbox_errors_warnings(): data = sunspots.load_pandas().data['SUNACTIVITY'] with pytest.raises(ValueError, match="model_df must"): smsdia.acorr_ljungbox(data, model_df=-1) with pytest.raises(ValueError, match="period must"): smsdia.acorr_ljungbox(data, model_df=-1, period=1) with pytest.raises(ValueError, match="period must"): smsdia.acorr_ljungbox(data, model_df=-1, period=-2) with pytest.warns(FutureWarning, match="The default value of lags"): smsdia.acorr_ljungbox(data, return_df=False) with pytest.warns(FutureWarning, match="The value returned"): smsdia.acorr_ljungbox(data, lags=10) def test_ljungbox_period(): data = sunspots.load_pandas().data['SUNACTIVITY'] ar_res = AutoReg(data, 4, old_names=False).fit() res = smsdia.acorr_ljungbox(ar_res.resid, period=13, return_df=True) res2 = smsdia.acorr_ljungbox(ar_res.resid, lags=26, return_df=True) assert_frame_equal(res, res2) @pytest.mark.parametrize('cov_type', ['nonrobust', 'HC0']) def test_encompasing_direct(cov_type, reset_randomstate): x = np.random.standard_normal((500, 2)) e = np.random.standard_normal((500, 1)) x_extra = np.random.standard_normal((500, 2)) z_extra = np.random.standard_normal((500, 3)) y = x @ np.ones((2, 1)) + e x1 = np.hstack([x[:, :1], x_extra]) z1 = np.hstack([x, z_extra]) res1 = OLS(y, x1).fit() res2 = OLS(y, z1).fit() df = smsdia.compare_encompassing(res1, res2, cov_type=cov_type) direct1 = OLS(y, np.hstack([x1, x[:, 1:], z_extra])).fit(cov_type=cov_type) r1 = np.zeros((4, 3 + 1 + 3)) r1[:, -4:] = np.eye(4) direct_test_1 = direct1.wald_test(r1, use_f=True) expected = (float(np.squeeze(direct_test_1.statistic)), float(np.squeeze(direct_test_1.pvalue)), int(direct_test_1.df_num), int(direct_test_1.df_denom)) assert_allclose(np.asarray(df.loc['x']), expected, atol=1e-8) direct2 = OLS(y, np.hstack([z1, x_extra])).fit(cov_type=cov_type) r2 = np.zeros((2, 2 + 3 + 2)) r2[:, -2:] = np.eye(2) direct_test_2 = direct2.wald_test(r2, use_f=True) expected = (float(np.squeeze(direct_test_2.statistic)), float(np.squeeze(direct_test_2.pvalue)), int(direct_test_2.df_num), int(direct_test_2.df_denom)) assert_allclose(np.asarray(df.loc['z']), expected, atol=1e-8) def test_encompasing_error(reset_randomstate): x = np.random.standard_normal((500, 2)) e = np.random.standard_normal((500, 1)) z_extra = np.random.standard_normal((500, 3)) y = x @ np.ones((2, 1)) + e z = np.hstack([x, z_extra]) res1 = OLS(y, x).fit() res2 = OLS(y, z).fit() with pytest.raises(ValueError, match="The exog in results_x"): smsdia.compare_encompassing(res1, res2) with pytest.raises(TypeError, match="results_z must come from a linear"): smsdia.compare_encompassing(res1, 2) with pytest.raises(TypeError, match="results_x must come from a linear"): smsdia.compare_encompassing(4, 2) @pytest.mark.smoke @pytest.mark.parametrize('power', [2, 3]) @pytest.mark.parametrize('test_type', ["fitted", "exog", "princomp"]) @pytest.mark.parametrize('use_f', [True, False]) @pytest.mark.parametrize('cov', [dict(cov_type="nonrobust", cov_kwargs={}), dict(cov_type="HC0", cov_kwargs={})]) def test_reset_smoke(power, test_type, use_f, cov, reset_randomstate): x = add_constant(np.random.standard_normal((1000, 3))) e = np.random.standard_normal((1000, 1)) x = np.hstack([x, x[:, 1:] ** 2]) y = x @ np.ones((7, 1)) + e res = OLS(y, x[:, :4]).fit() smsdia.linear_reset(res, power=power, test_type=test_type, use_f=use_f, **cov) @pytest.mark.smoke @pytest.mark.parametrize("autolag", ["AIC", "BIC"]) @pytest.mark.parametrize("store", [True, False]) @pytest.mark.parametrize("ddof", [0, 2]) @pytest.mark.parametrize('cov', [dict(cov_type="nonrobust", cov_kwargs={}), dict(cov_type="HC0", cov_kwargs={})]) def test_acorr_lm_smoke(autolag, store, ddof, cov, reset_randomstate): e = np.random.standard_normal(250) with pytest.warns(FutureWarning): smsdia.acorr_lm(e, nlags=6, autolag=autolag, store=store, ddof=ddof, **cov) with pytest.warns(FutureWarning): smsdia.acorr_lm(e, nlags=None, autolag=autolag, store=store, period=12, ddof=ddof, **cov) def test_acorr_lm_smoke_no_autolag(reset_randomstate): e = np.random.standard_normal(250) smsdia.acorr_lm(e, nlags=6, autolag=None, store=False, ddof=0) @pytest.mark.parametrize("frac", [0.25, 0.5, 0.75]) @pytest.mark.parametrize("order_by", [None, np.arange(500), np.random.choice(500, size=500, replace=False), "x0", ["x0", "x2"]]) def test_rainbow_smoke_order_by(frac, order_by, reset_randomstate): e = pd.DataFrame(np.random.standard_normal((500, 1))) x = pd.DataFrame(np.random.standard_normal((500, 3)), columns=["x{0}".format(i) for i in range(3)]) y = x @ np.ones((3, 1)) + e res = OLS(y, x).fit() smsdia.linear_rainbow(res, frac=frac, order_by=order_by) @pytest.mark.parametrize("center", [None, 0.33, 300]) def test_rainbow_smoke_centered(center, reset_randomstate): e = pd.DataFrame(np.random.standard_normal((500, 1))) x = pd.DataFrame(np.random.standard_normal((500, 3)), columns=["x{0}".format(i) for i in range(3)]) y = x @ np.ones((3, 1)) + e res = OLS(y, x).fit() smsdia.linear_rainbow(res, use_distance=True, center=center) def test_rainbow_exception(reset_randomstate): e = pd.DataFrame(np.random.standard_normal((500, 1))) x = pd.DataFrame(np.random.standard_normal((500, 3)), columns=["x{0}".format(i) for i in range(3)]) y = x @ np.ones((3, 1)) + e res = OLS(y, x).fit() with pytest.raises(TypeError, match="order_by must contain"): smsdia.linear_rainbow(res, order_by="x5") res = OLS(np.asarray(y), np.asarray(x)).fit() with pytest.raises(TypeError, match="order_by must contain"): smsdia.linear_rainbow(res, order_by=("x0",)) def test_small_skip(reset_randomstate): y = np.random.standard_normal(10) x = np.random.standard_normal((10, 3)) x[:3] = x[:1] with pytest.raises(ValueError, match="The initial regressor matrix,"): smsdia.recursive_olsresiduals(OLS(y, x).fit()) # R code used in testing # J test # # Model 1: ginv ~ ggdp + lint # Model 2: ginv ~ ggdp + tbilrate # Estimate Std. Error t value Pr(>|t|) # M1 + fitted(M2) 1.591505670785873 0.7384552861695823 2.15518 0.0323546 * # M2 + fitted(M1) 1.305687653016899 0.4808385176653064 2.71544 0.0072039 ** # --- # Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 # # # = lm(ginv ~ ggdp + tbilrate) # > ct = coxtest(fm, fm3) # > ct # Cox test # # Model 1: ginv ~ ggdp + lint # Model 2: ginv ~ ggdp + tbilrate # Estimate Std. Error z value Pr(>|z|) # fitted(M1) ~ M2 -0.782030488930356 0.599696502782265 -1.30404 0.19222 # fitted(M2) ~ M1 -2.248817107408537 0.392656854330139 -5.72718 1.0211e-08 *** # --- # Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 # # # # > et = encomptest(fm, fm3) # > et # Encompassing test # # Model 1: ginv ~ ggdp + lint # Model 2: ginv ~ ggdp + tbilrate # Model E: ginv ~ ggdp + lint + tbilrate # Res.Df Df F Pr(>F) # M1 vs. ME 198 -1 4.64481 0.0323546 * # M2 vs. ME 198 -1 7.37361 0.0072039 ** # --- # Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 # # # > fm4 = lm(realinv ~ realgdp + realint, data=d) # > fm5 = lm(log(realinv) ~ realgdp + realint, data=d) # > pet = petest(fm4, fm5) # > pet # PE test # # Model 1: realinv ~ realgdp + realint # Model 2: log(realinv) ~ realgdp + realint # Estimate Std. Error t value # M1 + log(fit(M1))-fit(M2) -229.281878354594596 44.5087822087058598 -5.15139 # M2 + fit(M1)-exp(fit(M2)) 0.000634664704814 0.0000462387010349 13.72583 # Pr(>|t|) # M1 + log(fit(M1))-fit(M2) 6.2013e-07 *** # M2 + fit(M1)-exp(fit(M2)) < 2.22e-16 *** # --- # Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 statsmodels-0.12.2/statsmodels/stats/tests/test_diagnostic_other.py000066400000000000000000000215761400612667500257600ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Unit tests for generic score/LM tests and conditional moment tests Created on Mon Nov 17 08:44:06 2014 Author: Josef Perktold License: BSD-3 """ import numpy as np from numpy.testing import assert_allclose from statsmodels.regression.linear_model import OLS from statsmodels.stats._diagnostic_other import CMTNewey, CMTTauchen import statsmodels.stats._diagnostic_other as diao class CheckCMT(object): def test_score(self): expected = self.results_score for msg, actual in self.res_score(): # not all cases provide all 3 elements, # TODO: fix API, returns of functions assert_allclose(actual, expected[:np.size(actual)], rtol=1e-13, err_msg=msg) def test_scorehc0(self): expected = self.results_hc0 for msg, actual in self.res_hc0(): assert_allclose(actual, expected[:np.size(actual)], rtol=1e-13, err_msg=msg) def test_scoreopg(self): expected = self.results_opg for msg, actual in self.res_opg(): assert_allclose(actual, expected[:np.size(actual)], rtol=1e-13, err_msg=msg) class TestCMTOLS(CheckCMT): @classmethod def setup_class(cls): np.random.seed(864259) nobs, k_vars = 100, 4 sig_e = 1 x0 = np.random.randn(nobs, k_vars) x0[:,0] = 1 y_true = x0.sum(1) y = y_true + sig_e * np.random.randn(nobs) x1 = np.random.randn(nobs, 2) x = np.column_stack((x0, x1)) cls.exog_full = x cls.exog_add = x1 cls.res_ols = OLS(y, x0).fit() cls.attach_moment_conditions() # results from initial run, not reference package (drooped 2 digits) cls.results_score = (1.6857659627548, 0.43046770240535, 2) cls.results_hc0 = (1.6385932313952, 0.4407415561953, 2) cls.results_opg = (1.72226002418488, 0.422684174119544, 2.0) @classmethod # TODO: a better structure ? def attach_moment_conditions(self): res_ols = self.res_ols # assumes x = column_stack([x0, x1]) x = self.exog_full #x0 = self.res_ols.model.exog # not used here x1 = self.exog_add nobs, k_constraints = x1.shape # TODO: cleanup after initial copy past moms_obs = res_ols.resid[:, None] * x moms = moms_obs.sum(0) cov_moms = res_ols.mse_resid * x.T.dot(x) #np.linalg.inv(x.T.dot(x)) cov_moms *= res_ols.df_resid / nobs # weights used for GMM to replicate OLS weights = np.linalg.inv(cov_moms) # we do not use last two variables weights[:, -k_constraints:] = 0 weights[-k_constraints:, :] = 0 k_moms = moms.shape[0] # TODO: Newey has different versions that all produce the same result # in example L = np.eye(k_moms)[-k_constraints:] #.dot(np.linalg.inv(cov_moms)) moms_deriv = cov_moms[:, :-k_constraints] covm = moms_obs.T.dot(moms_obs) #attach self.nobs = nobs self.moms = moms self.moms_obs = moms_obs self.cov_moms = cov_moms self.covm = covm self.moms_deriv = moms_deriv self.weights = weights self.L = L def res_score(self): res_ols = self.res_ols nobs = self.nobs moms = self.moms moms_obs = self.moms_obs cov_moms = self.cov_moms covm = self.covm moms_deriv = self.moms_deriv weights = self.weights L = self.L x = self.exog_full # for auxiliary regression only res_all = [] # auxiliary regression stat = nobs * OLS(res_ols.resid, x).fit().rsquared res_all.append(('ols R2', stat)) stat = moms.dot(np.linalg.solve(cov_moms, moms)) res_all.append(('score simple', stat)) tres = diao.lm_robust(moms, np.eye(moms.shape[0])[-2:], np.linalg.inv(cov_moms), cov_moms) res_all.append(('score mle', tres)) tres = CMTNewey(moms, cov_moms, cov_moms[:,:-2], weights, L).chisquare res_all.append(('Newey', tres)) tres = CMTTauchen(moms[:-2], cov_moms[:-2, :-2], moms[-2:], cov_moms[-2:, :-2], cov_moms).chisquare res_all.append(('Tauchen', tres)) return res_all def res_opg(self): res_ols = self.res_ols nobs = self.nobs moms = self.moms moms_obs = self.moms_obs covm = self.covm moms_deriv = self.moms_deriv weights = self.weights L = self.L x = self.exog_full res_ols2_hc0 = OLS(res_ols.model.endog, x).fit(cov_type='HC0') res_all = [] # auxiliary regression ones = np.ones(nobs) stat = nobs * OLS(ones, moms_obs).fit().rsquared res_all.append(('ols R2', stat)) tres = res_ols2_hc0.compare_lm_test(res_ols, demean=False) res_all.append(('comp_lm uc', tres)) tres = CMTNewey(moms, covm, covm[:,:-2], weights, L).chisquare res_all.append(('Newey', tres)) tres = CMTTauchen(moms[:-2], covm[:-2, :-2], moms[-2:], covm[-2:, :-2], covm).chisquare res_all.append(('Tauchen', tres)) tres = diao.lm_robust_subset(moms[-2:], 2, covm, covm) res_all.append(('score subset QMLE', tres)) tres = diao.lm_robust(moms, np.eye(moms.shape[0])[-2:], np.linalg.inv(covm), covm, cov_params=None) res_all.append(('scoreB QMLE', tres)) tres = diao.lm_robust(moms, np.eye(moms.shape[0])[-2:], np.linalg.inv(covm), None, cov_params=np.linalg.inv(covm)) res_all.append(('scoreV QMLE', tres)) return res_all def res_hc0(self): res_ols = self.res_ols nobs = self.nobs moms = self.moms moms_obs = self.moms_obs cov_moms = self.cov_moms # Hessian with scale covm = self.covm moms_deriv = self.moms_deriv weights = self.weights L = self.L x0 = res_ols.model.exog x1 = self.exog_add res_all = [] tres = diao.cm_test_robust(resid=res_ols.resid, resid_deriv=x0, instruments=x1, weights=1) # TODO: extra return and no df in cm_test_robust Wooldridge res_all.append(('Wooldridge', tres[:2])) tres = CMTNewey(moms, covm, moms_deriv, weights, L).chisquare res_all.append(('Newey', tres)) tres = CMTTauchen(moms[:-2], cov_moms[:-2, :-2], moms[-2:], cov_moms[-2:, :-2], covm).chisquare res_all.append(('Tauchen', tres)) tres = diao.lm_robust_subset(moms[-2:], 2, cov_moms, covm) res_all.append(('score subset QMLE', tres)) tres = diao.lm_robust(moms, np.eye(moms.shape[0])[-2:], np.linalg.inv(cov_moms), covm) res_all.append(('scoreB QMLE', tres)) # need sandwich cov_params V Ainv = np.linalg.inv(cov_moms) vv = Ainv.dot(covm).dot(Ainv) tres = diao.lm_robust(moms, np.eye(moms.shape[0])[-2:], np.linalg.inv(cov_moms), None, cov_params=vv) res_all.append(('scoreV QMLE', tres)) tres = diao.conditional_moment_test_generic(moms_obs[:, -2:], cov_moms[-2:, :-2], moms_obs[:,:-2], cov_moms[:-2, :-2]) tres_ = (tres.stat_cmt, tres.pval_cmt) res_all.append(('cmt', tres_)) # using unscaled hessian instead of scaled x = self.exog_full hess_unscaled = x.T.dot(x) tres = diao.conditional_moment_test_generic(moms_obs[:, -2:], hess_unscaled[-2:, :-2], moms_obs[:,:-2], hess_unscaled[:-2, :-2])#, covm) tres_ = (tres.stat_cmt, tres.pval_cmt) res_all.append(('cmt', tres_)) score_deriv_uu = cov_moms[:-2, :-2] score_deriv_cu = cov_moms[-2:, :-2] cov_score_cc = covm[-2:, -2:] cov_score_cu = covm[-2:, :-2] cov_score_uu = covm[:-2, :-2] moms[-2:], 2, cov_moms, covm tres = diao.lm_robust_subset_parts(moms[-2:], 2, score_deriv_uu, score_deriv_cu, cov_score_cc, cov_score_cu, cov_score_uu) res_all.append(('score subset_parts QMLE', tres)) params_deriv = np.eye(x.shape[1], x.shape[1] - 2) #params_deriv[[-2, -1], [-2, -1]] = 0 score = moms score_deriv = cov_moms cov_score = covm tres = diao.lm_robust_reparameterized(score, params_deriv, score_deriv, cov_score) res_all.append(('score reparam QMLE', tres)) return res_all statsmodels-0.12.2/statsmodels/stats/tests/test_dist_dependant_measures.py000066400000000000000000000157601400612667500273220ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_almost_equal import pytest from statsmodels.datasets import get_rdataset from statsmodels.datasets.tests.test_utils import IGNORED_EXCEPTIONS import statsmodels.stats.dist_dependence_measures as ddm from statsmodels.tools.sm_exceptions import HypothesisTestWarning class TestDistDependenceMeasures(object): @classmethod def setup_class(cls): """ Values were obtained via the R `energy` package. R code: ------ > dcov.test(x, y, R=200) dCov independence test (permutation test) data: index 1, replicates 200 nV^2 = 45829, p-value = 0.004975 sample estimates: dCov 47.86925 > DCOR(x, y) $dCov [1] 47.86925 $dCor [1] 0.9999704 $dVarX [1] 47.28702 $dVarY [1] 48.46151 """ np.random.seed(3) cls.x = np.array(range(1, 101)).reshape((20, 5)) cls.y = cls.x + np.log(cls.x) cls.dcor_exp = 0.9999704 cls.dcov_exp = 47.86925 cls.dvar_x_exp = 47.28702 cls.dvar_y_exp = 48.46151 cls.pval_emp_exp = 0.004975 cls.test_stat_emp_exp = 45829 # The values above are functions of the following values, and # therefore when the above group of variables is computed correctly # it means this group of variables was also correctly calculated. cls.S_exp = 5686.03162 cls.test_stat_asym_exp = 2.8390102 cls.pval_asym_exp = 0.00452 def test_input_validation_nobs(self): with pytest.raises(ValueError, match="same number of observations"): ddm.distance_covariance_test(self.x[:2, :], self.y) def test_input_validation_unknown_method(self): with pytest.raises(ValueError, match="Unknown 'method' parameter"): ddm.distance_covariance_test(self.x, self.y, method="wrong_name") def test_statistic_value_asym_method(self): statistic, pval, method = ddm.distance_covariance_test( self.x, self.y, method="asym") assert method == "asym" assert_almost_equal(statistic, self.test_stat_asym_exp, 4) assert_almost_equal(pval, self.pval_asym_exp, 3) def test_statistic_value_emp_method(self): with pytest.warns(HypothesisTestWarning): statistic, pval, method = ddm.distance_covariance_test( self.x, self.y, method="emp" ) assert method == "emp" assert_almost_equal(statistic, self.test_stat_emp_exp, 0) assert_almost_equal(pval, self.pval_emp_exp, 3) def test_fallback_to_asym_method(self): match_text = "The asymptotic approximation will be used" with pytest.warns(UserWarning, match=match_text): statistic, pval, _ = ddm.distance_covariance_test( self.x, self.y, method="emp", B=200 ) assert_almost_equal(statistic, self.test_stat_emp_exp, 0) assert_almost_equal(pval, self.pval_asym_exp, 3) def test_statistics_for_2d_input(self): stats = ddm.distance_statistics(self.x, self.y) assert_almost_equal(stats.test_statistic, self.test_stat_emp_exp, 0) assert_almost_equal(stats.distance_correlation, self.dcor_exp, 4) assert_almost_equal(stats.distance_covariance, self.dcov_exp, 4) assert_almost_equal(stats.dvar_x, self.dvar_x_exp, 4) assert_almost_equal(stats.dvar_y, self.dvar_y_exp, 4) assert_almost_equal(stats.S, self.S_exp, 4) def test_statistics_for_1d_input(self): x = np.array(range(1, 21)) y = x + np.log(x) stats = ddm.distance_statistics(x, y) # Values were obtained using the R `energy` package assert_almost_equal(stats.test_statistic, 398.94623, 5) assert_almost_equal(stats.distance_correlation, 0.9996107, 4) assert_almost_equal(stats.distance_covariance, 4.4662414, 4) assert_almost_equal(stats.dvar_x, 4.2294799, 4) assert_almost_equal(stats.dvar_y, 4.7199304, 4) assert_almost_equal(stats.S, 49.880200, 4) def test_results_on_the_iris_dataset(self): """ R code example from the `energy` package documentation for `energy::distance_covariance.test`: > x <- iris[1:50, 1:4] > y <- iris[51:100, 1:4] > set.seed(1) > dcov.test(x, y, R=200) dCov independence test (permutation test) data: index 1, replicates 200 nV^2 = 0.5254, p-value = 0.9552 sample estimates: dCov 0.1025087 """ try: iris = get_rdataset("iris").data.values[:, :4] except IGNORED_EXCEPTIONS: pytest.skip('Failed with HTTPError or URLError, these are random') x = iris[:50] y = iris[50:100] stats = ddm.distance_statistics(x, y) assert_almost_equal(stats.test_statistic, 0.5254, 4) assert_almost_equal(stats.distance_correlation, 0.3060479, 4) assert_almost_equal(stats.distance_covariance, 0.1025087, 4) assert_almost_equal(stats.dvar_x, 0.2712927, 4) assert_almost_equal(stats.dvar_y, 0.4135274, 4) assert_almost_equal(stats.S, 0.667456, 4) test_statistic, _, method = ddm.distance_covariance_test(x, y, B=199) assert_almost_equal(test_statistic, 0.5254, 4) assert method == "emp" def test_results_on_the_quakes_dataset(self): """ R code: ------ > data("quakes") > x = quakes[1:50, 1:3] > y = quakes[51:100, 1:3] > dcov.test(x, y, R=200) dCov independence test (permutation test) data: index 1, replicates 200 nV^2 = 45046, p-value = 0.4577 sample estimates: dCov 30.01526 """ try: quakes = get_rdataset("quakes").data.values[:, :3] except IGNORED_EXCEPTIONS: pytest.skip('Failed with HTTPError or URLError, these are random') x = quakes[:50] y = quakes[50:100] stats = ddm.distance_statistics(x, y) assert_almost_equal(np.round(stats.test_statistic), 45046, 0) assert_almost_equal(stats.distance_correlation, 0.1894193, 4) assert_almost_equal(stats.distance_covariance, 30.01526, 4) assert_almost_equal(stats.dvar_x, 170.1702, 4) assert_almost_equal(stats.dvar_y, 147.5545, 4) assert_almost_equal(stats.S, 52265, 0) test_statistic, _, method = ddm.distance_covariance_test(x, y, B=199) assert_almost_equal(np.round(test_statistic), 45046, 0) assert method == "emp" def test_dcor(self): assert_almost_equal(ddm.distance_correlation(self.x, self.y), self.dcor_exp, 4) def test_dcov(self): assert_almost_equal(ddm.distance_covariance(self.x, self.y), self.dcov_exp, 4) def test_dvar(self): assert_almost_equal(ddm.distance_variance(self.x), self.dvar_x_exp, 4) statsmodels-0.12.2/statsmodels/stats/tests/test_gof.py000066400000000000000000000065421400612667500232020ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Thu Feb 28 13:24:59 2013 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_almost_equal, assert_equal from statsmodels.stats.gof import (chisquare, chisquare_power, chisquare_effectsize) from statsmodels.tools.testing import Holder def test_chisquare_power(): from .results.results_power import pwr_chisquare for case in pwr_chisquare.values(): power = chisquare_power(case.w, case.N, case.df + 1, alpha=case.sig_level) assert_almost_equal(power, case.power, decimal=6, err_msg=repr(vars(case))) def test_chisquare(): # TODO: no tests for ``value`` yet res1 = Holder() res2 = Holder() #> freq = c(1048, 660, 510, 420, 362) #> pr1 = c(1020, 690, 510, 420, 360) #> pr2 = c(1050, 660, 510, 420, 360) #> c = chisq.test(freq, p=pr1, rescale.p = TRUE) #> cat_items(c, "res1.") res1.statistic = 2.084086388178453 res1.parameter = 4 res1.p_value = 0.72029651761105 res1.method = 'Chi-squared test for given probabilities' res1.data_name = 'freq' res1.observed = np.array([ 1048, 660, 510, 420, 362 ]) res1.expected = np.array([ 1020, 690, 510, 420, 360 ]) res1.residuals = np.array([ 0.876714007519206, -1.142080481440321, -2.517068894406109e-15, -2.773674830645328e-15, 0.105409255338946 ]) #> c = chisq.test(freq, p=pr2, rescale.p = TRUE) #> cat_items(c, "res2.") res2.statistic = 0.01492063492063492 res2.parameter = 4 res2.p_value = 0.999972309849908 res2.method = 'Chi-squared test for given probabilities' res2.data_name = 'freq' res2.observed = np.array([ 1048, 660, 510, 420, 362 ]) res2.expected = np.array([ 1050, 660, 510, 420, 360 ]) res2.residuals = np.array([ -0.06172133998483677, 0, -2.517068894406109e-15, -2.773674830645328e-15, 0.105409255338946 ]) freq = np.array([1048, 660, 510, 420, 362]) pr1 = np.array([1020, 690, 510, 420, 360]) pr2 = np.array([1050, 660, 510, 420, 360]) for pr, res in zip([pr1, pr2], [res1, res2]): stat, pval = chisquare(freq, pr) assert_almost_equal(stat, res.statistic, decimal=12) assert_almost_equal(pval, res.p_value, decimal=13) def test_chisquare_effectsize(): pr1 = np.array([1020, 690, 510, 420, 360]) pr2 = np.array([1050, 660, 510, 420, 360]) #> library(pwr) #> ES.w1(pr1/3000, pr2/3000) es_r = 0.02699815282115563 es1 = chisquare_effectsize(pr1, pr2) es2 = chisquare_effectsize(pr1, pr2, cohen=False) assert_almost_equal(es1, es_r, decimal=14) assert_almost_equal(es2, es_r**2, decimal=14) # regression tests for correction res1 = chisquare_effectsize(pr1, pr2, cohen=False, correction=(3000, len(pr1)-1)) res0 = 0 #-0.00059994422693327625 assert_equal(res1, res0) pr3 = pr2 + [0,0,0,50,50] res1 = chisquare_effectsize(pr1, pr3, cohen=False, correction=(3000, len(pr1)-1)) res0 = 0.0023106468846296755 assert_almost_equal(res1, res0, decimal=14) # compare # res_nc = chisquare_effectsize(pr1, pr3, cohen=False) # 0.0036681143072077533 statsmodels-0.12.2/statsmodels/stats/tests/test_groups_sw.py000066400000000000000000000051431400612667500244530ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Test for a helper function for PanelHAC robust covariance the functions should be rewritten to make it more efficient Created on Thu May 17 21:09:41 2012 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_equal, assert_raises import statsmodels.stats.sandwich_covariance as sw from statsmodels.tools.grouputils import GroupSorted class CheckPanelLagMixin(object): @classmethod def calculate(cls): cls.g = g = GroupSorted(cls.gind) # pylint: disable-msg=W0201 cls.alla = [(lag, sw.lagged_groups(cls.x, lag, g.groupidx)) # pylint: disable-msg=W0201 for lag in range(5)] def test_values(self): for lag, (y0, ylag) in self.alla: assert_equal(y0, self.alle[lag].T) assert_equal(y0, ylag + lag) def test_raises(self): mlag = self.mlag assert_raises(ValueError, sw.lagged_groups, self.x, mlag, self.g.groupidx) class TestBalanced(CheckPanelLagMixin): @classmethod def setup_class(cls): cls.gind = np.repeat([0,1,2], 5) cls.mlag = 5 x = np.arange(15) x += 10**cls.gind cls.x = x[:,None] #expected result cls.alle = { 0 : np.array([[ 1, 2, 3, 4, 5, 15, 16, 17, 18, 19, 110, 111, 112, 113, 114]]), 1 : np.array([[ 2, 3, 4, 5, 16, 17, 18, 19, 111, 112, 113, 114]]), 2 : np.array([[ 3, 4, 5, 17, 18, 19, 112, 113, 114]]), 3 : np.array([[ 4, 5, 18, 19, 113, 114]]), 4 : np.array([[ 5, 19, 114]]) } cls.calculate() class TestUnBalanced(CheckPanelLagMixin): @classmethod def setup_class(cls): cls.gind = gind = np.repeat([0,1,2], [3, 5, 10]) cls.mlag = 10 #maxlag x = np.arange(18) x += 10**gind cls.x = x[:,None] #expected result cls.alle = { 0 : np.array([[ 1, 2, 3, 13, 14, 15, 16, 17, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117]]), 1 : np.array([[ 2, 3, 14, 15, 16, 17, 109, 110, 111, 112, 113, 114, 115, 116, 117]]), 2 : np.array([[ 3, 15, 16, 17, 110, 111, 112, 113, 114, 115, 116, 117]]), 3 : np.array([[ 16, 17, 111, 112, 113, 114, 115, 116, 117]]), 4 : np.array([[ 17, 112, 113, 114, 115, 116, 117]]), 5 : np.array([[113, 114, 115, 116, 117]]), } cls.calculate() statsmodels-0.12.2/statsmodels/stats/tests/test_influence.py000066400000000000000000000214301400612667500243700ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Tue Jun 12 13:18:12 2018 Author: Josef Perktold """ from statsmodels.compat.pandas import testing as pdt import os.path import numpy as np from numpy.testing import assert_allclose import pandas as pd import pytest from statsmodels.regression.linear_model import OLS from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.genmod import families from statsmodels.stats.outliers_influence import MLEInfluence cur_dir = os.path.abspath(os.path.dirname(__file__)) file_name = 'binary_constrict.csv' file_path = os.path.join(cur_dir, 'results', file_name) data_bin = pd.read_csv(file_path, index_col=0) file_name = 'results_influence_logit.csv' file_path = os.path.join(cur_dir, 'results', file_name) results_sas_df = pd.read_csv(file_path, index_col=0) def test_influence_glm_bernoulli(): # example uses Finney's data and is used in Pregibon 1981 df = data_bin results_sas = np.asarray(results_sas_df) res = GLM(df['constrict'], df[['const', 'log_rate', 'log_volumne']], family=families.Binomial()).fit(attach_wls=True, atol=1e-10) infl = res.get_influence(observed=False) k_vars = 3 assert_allclose(infl.dfbetas, results_sas[:, 5:8], atol=1e-4) assert_allclose(infl.d_params, results_sas[:, 5:8] * res.bse.values, atol=1e-4) assert_allclose(infl.cooks_distance[0] * k_vars, results_sas[:, 8], atol=6e-5) assert_allclose(infl.hat_matrix_diag, results_sas[:, 4], atol=6e-5) c_bar = infl.cooks_distance[0] * 3 * (1 - infl.hat_matrix_diag) assert_allclose(c_bar, results_sas[:, 9], atol=6e-5) class InfluenceCompareExact(object): # Mixin to compare and test two Influence instances def test_basics(self): infl1 = self.infl1 infl0 = self.infl0 assert_allclose(infl0.hat_matrix_diag, infl1.hat_matrix_diag, rtol=1e-12) assert_allclose(infl0.resid_studentized, infl1.resid_studentized, rtol=1e-12, atol=1e-7) cd_rtol = getattr(self, 'cd_rtol', 1e-7) assert_allclose(infl0.cooks_distance[0], infl1.cooks_distance[0], rtol=cd_rtol) assert_allclose(infl0.dfbetas, infl1.dfbetas, rtol=1e-9, atol=5e-9) assert_allclose(infl0.d_params, infl1.d_params, rtol=1e-9, atol=5e-9) assert_allclose(infl0.d_fittedvalues, infl1.d_fittedvalues, rtol=5e-9) assert_allclose(infl0.d_fittedvalues_scaled, infl1.d_fittedvalues_scaled, rtol=5e-9) @pytest.mark.smoke @pytest.mark.matplotlib def test_plots(self, close_figures): infl1 = self.infl1 infl0 = self.infl0 fig = infl0.plot_influence(external=False) fig = infl1.plot_influence(external=False) fig = infl0.plot_index('resid', threshold=0.2, title='') fig = infl1.plot_index('resid', threshold=0.2, title='') fig = infl0.plot_index('dfbeta', idx=1, threshold=0.2, title='') fig = infl1.plot_index('dfbeta', idx=1, threshold=0.2, title='') fig = infl0.plot_index('cook', idx=1, threshold=0.2, title='') fig = infl1.plot_index('cook', idx=1, threshold=0.2, title='') fig = infl0.plot_index('hat', idx=1, threshold=0.2, title='') fig = infl1.plot_index('hat', idx=1, threshold=0.2, title='') def test_summary(self): infl1 = self.infl1 infl0 = self.infl0 df0 = infl0.summary_frame() df1 = infl1.summary_frame() assert_allclose(df0.values, df1.values, rtol=5e-5) pdt.assert_index_equal(df0.index, df1.index) def _check_looo(self): infl = self.infl1 # unwrap if needed results = getattr(infl.results, '_results', infl.results) res_looo = infl._res_looo mask_infl = infl.cooks_distance[0] > 2 * infl.cooks_distance[0].std() mask_low = ~mask_infl diff_params = results.params - res_looo['params'] assert_allclose(infl.d_params[mask_low], diff_params[mask_low], atol=0.05) assert_allclose(infl.params_one[mask_low], res_looo['params'][mask_low], rtol=0.01) class TestInfluenceLogitGLMMLE(InfluenceCompareExact): @classmethod def setup_class(cls): df = data_bin res = GLM(df['constrict'], df[['const', 'log_rate', 'log_volumne']], family=families.Binomial()).fit(attach_wls=True, atol=1e-10) cls.infl1 = res.get_influence() cls.infl0 = MLEInfluence(res) def test_looo(self): _check_looo(self) class TestInfluenceBinomialGLMMLE(InfluenceCompareExact): # example based on Williams and R docs @classmethod def setup_class(cls): yi = np.array([0, 2, 14, 19, 30]) ni = 40 * np.ones(len(yi)) xi = np.arange(1, len(yi) + 1) exog = np.column_stack((np.ones(len(yi)), xi)) endog = np.column_stack((yi, ni - yi)) res = GLM(endog, exog, family=families.Binomial()).fit() cls.infl1 = res.get_influence() cls.infl0 = MLEInfluence(res) cls.cd_rtol = 5e-5 def test_looo(self): _check_looo(self) def test_r(self): # values from R, # > xi <- 1:5 # > yi <- c(0,2,14,19,30) # number of mice responding to dose xi # > mi <- rep(40, 5) # number of mice exposed # > glmI <- glm(cbind(yi, mi -yi) ~ xi, family = binomial) # > imI <- influence.measures(glmI) # > t(imI$infmat) # dfbeta/dfbetas and dffits do not make sense to me and are furthe away from # looo than mine # resid seem to be resid_deviance based and not resid_pearson # I did not compare cov.r infl1 = self.infl1 cooks_d = [0.25220202795934726, 0.26107981497746285, 1.28985614424132389, 0.08449722285516942, 0.36362110845918005] hat = [0.2594393406119333, 0.3696442663244837, 0.3535768402250521, 0.389209198535791057, 0.6281303543027403] assert_allclose(infl1.hat_matrix_diag, hat, rtol=5e-6) assert_allclose(infl1.cooks_distance[0], cooks_d, rtol=1e-5) class TestInfluenceGaussianGLMMLE(InfluenceCompareExact): @classmethod def setup_class(cls): from .test_diagnostic import get_duncan_data endog, exog, labels = get_duncan_data() data = pd.DataFrame(np.column_stack((endog, exog)), columns='y const var1 var2'.split(), index=labels) res = GLM.from_formula('y ~ const + var1 + var2 - 1', data).fit() #res = GLM(endog, exog).fit() cls.infl1 = res.get_influence() cls.infl0 = MLEInfluence(res) def test_looo(self): _check_looo(self) class TestInfluenceGaussianGLMOLS(InfluenceCompareExact): @classmethod def setup_class(cls): from .test_diagnostic import get_duncan_data endog, exog, labels = get_duncan_data() data = pd.DataFrame(np.column_stack((endog, exog)), columns='y const var1 var2'.split(), index=labels) res0 = GLM.from_formula('y ~ const + var1 + var2 - 1', data).fit() res1 = OLS.from_formula('y ~ const + var1 + var2 - 1', data).fit() cls.infl1 = res1.get_influence() cls.infl0 = res0.get_influence() def test_basics(self): # needs to override attributes that are not equivalent, # i.e. not available or different definition like external vs internal infl1 = self.infl1 infl0 = self.infl0 assert_allclose(infl0.hat_matrix_diag, infl1.hat_matrix_diag, rtol=1e-12) assert_allclose(infl0.resid_studentized, infl1.resid_studentized, rtol=1e-12, atol=1e-7) assert_allclose(infl0.cooks_distance, infl1.cooks_distance, rtol=1e-7) assert_allclose(infl0.dfbetas, infl1.dfbetas, rtol=0.1) # changed # OLSInfluence only has looo dfbeta/d_params assert_allclose(infl0.d_params, infl1.dfbeta, rtol=1e-9, atol=1e-14) # d_fittedvalues is not available in OLSInfluence, i.e. only scaled dffits # assert_allclose(infl0.d_fittedvalues, infl1.d_fittedvalues, rtol=1e-9) assert_allclose(infl0.d_fittedvalues_scaled, infl1.dffits_internal[0], rtol=1e-9) # specific to linear link assert_allclose(infl0.d_linpred, infl0.d_fittedvalues, rtol=1e-12) assert_allclose(infl0.d_linpred_scaled, infl0.d_fittedvalues_scaled, rtol=1e-12) def test_summary(self): infl1 = self.infl1 infl0 = self.infl0 df0 = infl0.summary_frame() df1 = infl1.summary_frame() # just some basic check on overlap except for dfbetas cols = ['cooks_d', 'standard_resid', 'hat_diag', 'dffits_internal'] assert_allclose(df0[cols].values, df1[cols].values, rtol=1e-5) pdt.assert_index_equal(df0.index, df1.index) statsmodels-0.12.2/statsmodels/stats/tests/test_inter_rater.py000066400000000000000000000307171400612667500247460ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Mon Dec 10 09:18:14 2012 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_almost_equal, assert_equal, assert_allclose from statsmodels.stats.inter_rater import (fleiss_kappa, cohens_kappa, to_table, aggregate_raters) from statsmodels.tools.testing import Holder table0 = np.asarray('''\ 1 0 0 0 0 14 1.000 2 0 2 6 4 2 0.253 3 0 0 3 5 6 0.308 4 0 3 9 2 0 0.440 5 2 2 8 1 1 0.330 6 7 7 0 0 0 0.462 7 3 2 6 3 0 0.242 8 2 5 3 2 2 0.176 9 6 5 2 1 0 0.286 10 0 2 2 3 7 0.286'''.split(), float).reshape(10,-1) table1 = table0[:, 1:-1] table10 = [[0, 4, 1], [0, 8, 0], [0, 1, 5]] #Fleiss 1971, Fleiss has only the transformed table diagnoses = np.array( [[4, 4, 4, 4, 4, 4], [2, 2, 2, 5, 5, 5], [2, 3, 3, 3, 3, 5], [5, 5, 5, 5, 5, 5], [2, 2, 2, 4, 4, 4], [1, 1, 3, 3, 3, 3], [3, 3, 3, 3, 5, 5], [1, 1, 3, 3, 3, 4], [1, 1, 4, 4, 4, 4], [5, 5, 5, 5, 5, 5], [1, 4, 4, 4, 4, 4], [1, 2, 4, 4, 4, 4], [2, 2, 2, 3, 3, 3], [1, 4, 4, 4, 4, 4], [2, 2, 4, 4, 4, 5], [3, 3, 3, 3, 3, 5], [1, 1, 1, 4, 5, 5], [1, 1, 1, 1, 1, 2], [2, 2, 4, 4, 4, 4], [1, 3, 3, 5, 5, 5], [5, 5, 5, 5, 5, 5], [2, 4, 4, 4, 4, 4], [2, 2, 4, 5, 5, 5], [1, 1, 4, 4, 4, 4], [1, 4, 4, 4, 4, 5], [2, 2, 2, 2, 2, 4], [1, 1, 1, 1, 5, 5], [2, 2, 4, 4, 4, 4], [1, 3, 3, 3, 3, 3], [5, 5, 5, 5, 5, 5]]) diagnoses_rownames = ['1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12', '13', '14', '15', '16', '17', '18', '19', '20', '21', '22', '23', '24', '25', '26', '27', '28', '29', '30', ] diagnoses_colnames = ['rater1', 'rater2', 'rater3', 'rater4', 'rater5', 'rater6', ] def test_fleiss_kappa(): #currently only example from Wikipedia page kappa_wp = 0.210 assert_almost_equal(fleiss_kappa(table1), kappa_wp, decimal=3) def test_fleis_randolph(): # reference numbers from online calculator # http://justusrandolph.net/kappa/#dInfo table = [[7, 0], [7, 0]] assert_equal(fleiss_kappa(table, method='unif'), 1) table = [[6.99, 0.01], [6.99, 0.01]] # % Overall Agreement 0.996671 # Fixed Marginal Kappa: -0.166667 # Free Marginal Kappa: 0.993343 assert_allclose(fleiss_kappa(table), -0.166667, atol=6e-6) assert_allclose(fleiss_kappa(table, method='unif'), 0.993343, atol=6e-6) table = [[7, 1], [3, 5]] # % Overall Agreement 0.607143 # Fixed Marginal Kappa: 0.161905 # Free Marginal Kappa: 0.214286 assert_allclose(fleiss_kappa(table, method='fleiss'), 0.161905, atol=6e-6) assert_allclose(fleiss_kappa(table, method='randolph'), 0.214286, atol=6e-6) table = [[7, 0], [0, 7]] # % Overall Agreement 1.000000 # Fixed Marginal Kappa: 1.000000 # Free Marginal Kappa: 1.000000 assert_allclose(fleiss_kappa(table), 1) assert_allclose(fleiss_kappa(table, method='uniform'), 1) table = [[6, 1, 0], [0, 7, 0]] # % Overall Agreement 0.857143 # Fixed Marginal Kappa: 0.708333 # Free Marginal Kappa: 0.785714 assert_allclose(fleiss_kappa(table), 0.708333, atol=6e-6) assert_allclose(fleiss_kappa(table, method='rand'), 0.785714, atol=6e-6) class CheckCohens(object): def test_results(self): res = self.res res2 = self.res2 res_ = [res.kappa, res.std_kappa, res.kappa_low, res.kappa_upp, res.std_kappa0, res.z_value, res.pvalue_one_sided, res.pvalue_two_sided] assert_almost_equal(res_, res2, decimal=4) assert_equal(str(res), self.res_string) class TestUnweightedCohens(CheckCohens): # comparison to printout of a SAS example @classmethod def setup_class(cls): #temporary: res instance is at last position cls.res = cohens_kappa(table10) res10_sas = [0.4842, 0.1380, 0.2137, 0.7547] res10_sash0 = [0.1484, 3.2626, 0.0006, 0.0011] #for test H0:kappa=0 cls.res2 = res10_sas + res10_sash0 #concatenate cls.res_string = '''\ Simple Kappa Coefficient -------------------------------- Kappa 0.4842 ASE 0.1380 95% Lower Conf Limit 0.2137 95% Upper Conf Limit 0.7547 Test of H0: Simple Kappa = 0 ASE under H0 0.1484 Z 3.2626 One-sided Pr > Z 0.0006 Two-sided Pr > |Z| 0.0011''' + '\n' def test_option(self): kappa = cohens_kappa(table10, return_results=False) assert_almost_equal(kappa, self.res2[0], decimal=4) class TestWeightedCohens(CheckCohens): #comparison to printout of a SAS example @classmethod def setup_class(cls): #temporary: res instance is at last position cls.res = cohens_kappa(table10, weights=[0, 1, 2]) res10w_sas = [0.4701, 0.1457, 0.1845, 0.7558] res10w_sash0 = [0.1426, 3.2971, 0.0005, 0.0010] #for test H0:kappa=0 cls.res2 = res10w_sas + res10w_sash0 #concatenate cls.res_string = '''\ Weighted Kappa Coefficient -------------------------------- Kappa 0.4701 ASE 0.1457 95% Lower Conf Limit 0.1845 95% Upper Conf Limit 0.7558 Test of H0: Weighted Kappa = 0 ASE under H0 0.1426 Z 3.2971 One-sided Pr > Z 0.0005 Two-sided Pr > |Z| 0.0010''' + '\n' def test_option(self): kappa = cohens_kappa(table10, weights=[0, 1, 2], return_results=False) assert_almost_equal(kappa, self.res2[0], decimal=4) def test_cohenskappa_weights(): #some tests for equivalent results with different options np.random.seed(9743678) table = np.random.randint(0, 10, size=(5,5)) + 5*np.eye(5) #example aggregation, 2 groups of levels mat = np.array([[1,1,1, 0,0],[0,0,0,1,1]]) table_agg = np.dot(np.dot(mat, table), mat.T) res1 = cohens_kappa(table, weights=np.arange(5) > 2, wt='linear') res2 = cohens_kappa(table_agg, weights=np.arange(2), wt='linear') assert_almost_equal(res1.kappa, res2.kappa, decimal=14) assert_almost_equal(res1.var_kappa, res2.var_kappa, decimal=14) #equivalence toeplitz with linear for special cases res1 = cohens_kappa(table, weights=2*np.arange(5), wt='linear') res2 = cohens_kappa(table, weights=2*np.arange(5), wt='toeplitz') res3 = cohens_kappa(table, weights=res1.weights[0], wt='toeplitz') #2-Dim weights res4 = cohens_kappa(table, weights=res1.weights) assert_almost_equal(res1.kappa, res2.kappa, decimal=14) assert_almost_equal(res1.var_kappa, res2.var_kappa, decimal=14) assert_almost_equal(res1.kappa, res3.kappa, decimal=14) assert_almost_equal(res1.var_kappa, res3.var_kappa, decimal=14) assert_almost_equal(res1.kappa, res4.kappa, decimal=14) assert_almost_equal(res1.var_kappa, res4.var_kappa, decimal=14) #equivalence toeplitz with quadratic for special cases res1 = cohens_kappa(table, weights=5*np.arange(5)**2, wt='toeplitz') res2 = cohens_kappa(table, weights=5*np.arange(5), wt='quadratic') assert_almost_equal(res1.kappa, res2.kappa, decimal=14) assert_almost_equal(res1.var_kappa, res2.var_kappa, decimal=14) anxiety = np.array([ 3, 3, 3, 4, 5, 5, 2, 3, 5, 2, 2, 6, 1, 5, 2, 2, 1, 2, 4, 3, 3, 6, 4, 6, 2, 4, 2, 4, 3, 3, 2, 3, 3, 3, 2, 2, 1, 3, 3, 4, 2, 1, 4, 4, 3, 2, 1, 6, 1, 1, 1, 2, 3, 3, 1, 1, 3, 3, 2, 2 ]).reshape(20,3, order='F') anxiety_rownames = ['1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11', '12', '13', '14', '15', '16', '17', '18', '19', '20', ] anxiety_colnames = ['rater1', 'rater2', 'rater3', ] def test_cohens_kappa_irr(): ck_w3 = Holder() ck_w4 = Holder() #>r = kappa2(anxiety[,1:2], c(0,0,0,1,1,1)) #> cat_items(r, pref="ck_w3.") ck_w3.method = "Cohen's Kappa for 2 Raters (Weights: 0,0,0,1,1,1)" ck_w3.irr_name = 'Kappa' ck_w3.value = 0.1891892 ck_w3.stat_name = 'z' ck_w3.statistic = 0.5079002 ck_w3.p_value = 0.6115233 #> r = kappa2(anxiety[,1:2], c(0,0,1,1,2,2)) #> cat_items(r, pref="ck_w4.") ck_w4.method = "Cohen's Kappa for 2 Raters (Weights: 0,0,1,1,2,2)" ck_w4.irr_name = 'Kappa' ck_w4.value = 0.2820513 ck_w4.stat_name = 'z' ck_w4.statistic = 1.257410 ck_w4.p_value = 0.2086053 ck_w1 = Holder() ck_w2 = Holder() ck_w3 = Holder() ck_w4 = Holder() #> r = kappa2(anxiety[,2:3]) #> cat_items(r, pref="ck_w1.") ck_w1.method = "Cohen's Kappa for 2 Raters (Weights: unweighted)" ck_w1.irr_name = 'Kappa' ck_w1.value = -0.006289308 ck_w1.stat_name = 'z' ck_w1.statistic = -0.0604067 ck_w1.p_value = 0.9518317 #> r = kappa2(anxiety[,2:3], "equal") #> cat_items(r, pref="ck_w2.") ck_w2.method = "Cohen's Kappa for 2 Raters (Weights: equal)" ck_w2.irr_name = 'Kappa' ck_w2.value = 0.1459075 ck_w2.stat_name = 'z' ck_w2.statistic = 1.282472 ck_w2.p_value = 0.1996772 #> r = kappa2(anxiety[,2:3], "squared") #> cat_items(r, pref="ck_w3.") ck_w3.method = "Cohen's Kappa for 2 Raters (Weights: squared)" ck_w3.irr_name = 'Kappa' ck_w3.value = 0.2520325 ck_w3.stat_name = 'z' ck_w3.statistic = 1.437451 ck_w3.p_value = 0.1505898 #> r = kappa2(anxiety[,2:3], c(0,0,1,1,2)) #> cat_items(r, pref="ck_w4.") ck_w4.method = "Cohen's Kappa for 2 Raters (Weights: 0,0,1,1,2)" ck_w4.irr_name = 'Kappa' ck_w4.value = 0.2391304 ck_w4.stat_name = 'z' ck_w4.statistic = 1.223734 ck_w4.p_value = 0.2210526 all_cases = [(ck_w1, None, None), (ck_w2, None, 'linear'), (ck_w2, np.arange(5), None), (ck_w2, np.arange(5), 'toeplitz'), (ck_w3, None, 'quadratic'), (ck_w3, np.arange(5)**2, 'toeplitz'), (ck_w3, 4*np.arange(5)**2, 'toeplitz'), (ck_w4, [0,0,1,1,2], 'toeplitz')] #Note R:irr drops the missing category level 4 and uses the reduced matrix r = np.histogramdd(anxiety[:,1:], ([1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 7])) for res2, w, wt in all_cases: msg = repr(w) + repr(wt) res1 = cohens_kappa(r[0], weights=w, wt=wt) assert_almost_equal(res1.kappa, res2.value, decimal=6, err_msg=msg) assert_almost_equal(res1.z_value, res2.statistic, decimal=5, err_msg=msg) assert_almost_equal(res1.pvalue_two_sided, res2.p_value, decimal=6, err_msg=msg) def test_fleiss_kappa_irr(): fleiss = Holder() #> r = kappam.fleiss(diagnoses) #> cat_items(r, pref="fleiss.") fleiss.method = "Fleiss' Kappa for m Raters" fleiss.irr_name = 'Kappa' fleiss.value = 0.4302445 fleiss.stat_name = 'z' fleiss.statistic = 17.65183 fleiss.p_value = 0 data_ = aggregate_raters(diagnoses)[0] res1_kappa = fleiss_kappa(data_) assert_almost_equal(res1_kappa, fleiss.value, decimal=7) def test_to_table(): data = diagnoses res1 = to_table(data[:,:2]-1, 5) res0 = np.asarray([[(data[:,:2]-1 == [i,j]).all(1).sum() for j in range(5)] for i in range(5)] ) assert_equal(res1[0], res0) res2 = to_table(data[:,:2]) assert_equal(res2[0], res0) bins = [0.5, 1.5, 2.5, 3.5, 4.5, 5.5] res3 = to_table(data[:,:2], bins) assert_equal(res3[0], res0) #more than 2 columns res4 = to_table(data[:,:3]-1, bins=[-0.5, 0.5, 1.5, 2.5, 3.5, 4.5]) res5 = to_table(data[:,:3]-1, bins=5) assert_equal(res4[0].sum(-1), res0) assert_equal(res5[0].sum(-1), res0) def test_aggregate_raters(): data = diagnoses resf = aggregate_raters(data) colsum = np.array([26, 26, 30, 55, 43]) assert_equal(resf[0].sum(0), colsum) statsmodels-0.12.2/statsmodels/stats/tests/test_knockoff.py000066400000000000000000000104211400612667500242160ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_allclose, assert_array_equal, assert_equal import pytest import statsmodels.api as sm from statsmodels.stats import knockoff_regeffects as kr from statsmodels.stats._knockoff import (RegressionFDR, _design_knockoff_equi, _design_knockoff_sdp) try: import cvxopt # noqa:F401 has_cvxopt = True except ImportError: has_cvxopt = False def test_equi(): # Test the structure of the equivariant knockoff construction. np.random.seed(2342) exog = np.random.normal(size=(10, 4)) exog1, exog2, sl = _design_knockoff_equi(exog) exoga = np.concatenate((exog1, exog2), axis=1) gmat = np.dot(exoga.T, exoga) cm1 = gmat[0:4, 0:4] cm2 = gmat[4:, 4:] cm3 = gmat[0:4, 4:] assert_allclose(cm1, cm2, rtol=1e-4, atol=1e-4) assert_allclose(cm1 - cm3, np.diag(sl * np.ones(4)), rtol=1e-4, atol=1e-4) def test_sdp(): # Test the structure of the SDP knockoff construction. if not has_cvxopt: return np.random.seed(2342) exog = np.random.normal(size=(10, 4)) exog1, exog2, sl = _design_knockoff_sdp(exog) exoga = np.concatenate((exog1, exog2), axis=1) gmat = np.dot(exoga.T, exoga) cm1 = gmat[0:4, 0:4] cm2 = gmat[4:, 4:] cm3 = gmat[0:4, 4:] assert_allclose(cm1, cm2, rtol=1e-4, atol=1e-4) assert_allclose(cm1 - cm3, np.diag(sl * np.ones(4)), rtol=1e-5, atol=1e-5) @pytest.mark.parametrize("p", [49, 50]) @pytest.mark.parametrize("tester", [ kr.CorrelationEffects(), kr.ForwardEffects(pursuit=False), kr.ForwardEffects(pursuit=True), kr.OLSEffects(), kr.RegModelEffects(sm.OLS), kr.RegModelEffects(sm.OLS, True, fit_kws={"L1_wt": 0, "alpha": 1}), ]) @pytest.mark.parametrize("method", ["equi", "sdp"]) def test_testers(p, tester, method): if method == "sdp" and not has_cvxopt: return np.random.seed(2432) n = 200 y = np.random.normal(size=n) x = np.random.normal(size=(n, p)) kn = RegressionFDR(y, x, tester, design_method=method) assert_equal(len(kn.stats), p) assert_equal(len(kn.fdr), p) kn.summary() # smoke test @pytest.mark.slow @pytest.mark.parametrize("method", ["equi", "sdp"]) @pytest.mark.parametrize("tester,n,p,es", [ [kr.CorrelationEffects(), 300, 100, 6], [kr.ForwardEffects(pursuit=False), 300, 100, 3.5], [kr.ForwardEffects(pursuit=True), 300, 100, 3.5], [kr.OLSEffects(), 3000, 200, 3.5], ]) def test_sim(method, tester, n, p, es): # This function assesses the performance of the knockoff approach # relative to its theoretical claims. if method == "sdp" and not has_cvxopt: return np.random.seed(43234) # Number of variables with a non-zero coefficient npos = 30 # Aim to control FDR to this level target_fdr = 0.2 # Number of siumulation replications nrep = 10 if method == "sdp" and not has_cvxopt: return fdr, power = 0, 0 for k in range(nrep): # Generate the predictors x = np.random.normal(size=(n, p)) x /= np.sqrt(np.sum(x*x, 0)) # Generate the response variable coeff = es * (-1)**np.arange(npos) y = np.dot(x[:, 0:npos], coeff) + np.random.normal(size=n) kn = RegressionFDR(y, x, tester) # Threshold to achieve the target FDR tr = kn.threshold(target_fdr) # Number of selected coefficients cp = np.sum(kn.stats >= tr) # Number of false positives fp = np.sum(kn.stats[npos:] >= tr) # Observed FDR fdr += fp / max(cp, 1) # Proportion of true positives that are detected power += np.mean(kn.stats[0:npos] >= tr) # The estimated FDR may never exceed the target FDR estimated_fdr = (np.sum(kn.stats <= -tr) / (1 + np.sum(kn.stats >= tr))) assert_equal(estimated_fdr < target_fdr, True) power /= nrep fdr /= nrep # Check for reasonable power assert_array_equal(power > 0.6, True) # Check that we are close to the target FDR assert_array_equal(fdr < target_fdr + 0.05, True) statsmodels-0.12.2/statsmodels/stats/tests/test_lilliefors.py000066400000000000000000000071011400612667500245630ustar00rootroot00000000000000import numpy as np import pytest from numpy.testing import assert_almost_equal from scipy import stats from statsmodels.stats._lilliefors import lilliefors, get_lilliefors_table, \ kstest_fit, ksstat class TestLilliefors(object): def test_normal(self): np.random.seed(3975) x_n = stats.norm.rvs(size=500) # R function call: # require(nortest) # lillie.test(x_n) d_ks_norm, p_norm = lilliefors(x_n, dist='norm', pvalmethod='approx') # shift normal distribution > 0 to exactly mirror R `KScorrect` test # R `KScorrect` requires all values tested for exponential # distribution to be > 0 # R function call: # require(KScorrect) # LcKS(x_n+abs(min(x_n))+0.001, 'pexp') d_ks_exp, p_exp = lilliefors(x_n + np.abs(x_n.min()) + 0.001, dist='exp', pvalmethod='approx') # assert normal assert_almost_equal(d_ks_norm, 0.025957, decimal=3) assert_almost_equal(p_norm, 0.64175, decimal=3) # assert exp assert_almost_equal(d_ks_exp, 0.3436007, decimal=3) assert_almost_equal(p_exp, 0.001, decimal=3) def test_normal_table(self): np.random.seed(3975) x_n = stats.norm.rvs(size=500) d_ks_norm, p_norm = lilliefors(x_n, dist='norm', pvalmethod='table') # assert normal assert_almost_equal(d_ks_norm, 0.025957, decimal=3) assert_almost_equal(p_norm, 0.64175, decimal=3) def test_expon(self): np.random.seed(3975) x_e = stats.expon.rvs(size=500) # R function call: # require(nortest) # lillie.test(x_n) d_ks_norm, p_norm = lilliefors(x_e, dist='norm', pvalmethod='approx') # R function call: # require(KScorrect) # LcKS(x_e, 'pexp') d_ks_exp, p_exp = lilliefors(x_e, dist='exp', pvalmethod='approx') # assert normal assert_almost_equal(d_ks_norm, 0.15581, decimal=3) assert_almost_equal(p_norm, 2.2e-16, decimal=3) # assert exp assert_almost_equal(d_ks_exp, 0.02763748, decimal=3) assert_almost_equal(p_exp, 0.72540, decimal=3) def test_pval_bounds(self): x = stats.norm.ppf((np.arange(10.) + 0.5) / 10) d_ks_n, p_n = lilliefors(x, dist='norm', pvalmethod='approx') x = stats.expon.ppf((np.arange(10.) + 0.5) / 10) d_ks_e, p_e = lilliefors(x, dist='exp', pvalmethod='approx') assert_almost_equal(p_n, 0.99, decimal=7) assert_almost_equal(p_e, 0.99, decimal=7) def test_min_nobs(self): x = np.arange(3.) with pytest.raises(ValueError): lilliefors(x, dist='norm', pvalmethod='approx') x = np.arange(2.) with pytest.raises(ValueError): lilliefors(x, dist='exp', pvalmethod='approx') @pytest.mark.smoke def test_large_sample(self, reset_randomstate): x = np.random.randn(10000) lilliefors(x, pvalmethod='approx') def test_get_lilliefors_errors(reset_randomstate): with pytest.raises(ValueError): get_lilliefors_table(dist='unknown') with pytest.raises(ValueError): kstest_fit(np.random.standard_normal(100), dist='unknown', pvalmethod='table') def test_ksstat(reset_randomstate): x = np.random.uniform(0, 1, 100) two_sided = ksstat(x, 'uniform', alternative='two_sided') greater = ksstat(x, 'uniform', alternative='greater') lower = ksstat(x, stats.uniform, alternative='lower') print(two_sided, greater, lower) assert lower <= two_sided assert greater <= two_sided statsmodels-0.12.2/statsmodels/stats/tests/test_mediation.py000066400000000000000000000246631400612667500244040ustar00rootroot00000000000000import numpy as np import statsmodels.api as sm import os from statsmodels.stats.mediation import Mediation import pandas as pd from numpy.testing import assert_allclose import patsy import pytest # Compare to mediation R package vignette df = [['index', 'Estimate', 'Lower CI bound', 'Upper CI bound', 'P-value'], ['ACME (control)', 0.085106, 0.029938, 0.141525, 0.00], ['ACME (treated)', 0.085674, 0.031089, 0.147762, 0.00], ['ADE (control)', 0.016938, -0.129157, 0.121945, 0.66], ['ADE (treated)', 0.017506, -0.139649, 0.130030, 0.66], ['Total effect', 0.102612, -0.036749, 0.227213, 0.20], ['Prop. mediated (control)', 0.698070, -6.901715, 2.725978, 0.20], ['Prop. mediated (treated)', 0.718648, -6.145419, 2.510750, 0.20], ['ACME (average)', 0.085390, 0.030272, 0.144768, 0.00], ['ADE (average)', 0.017222, -0.134465, 0.125987, 0.66], ['Prop. mediated (average)', 0.710900, -6.523567, 2.618364, 0.20]] framing_boot_4231 = pd.DataFrame(df[1:], columns=df[0]).set_index('index') # Compare to mediation R package vignette df = [['index', 'Estimate', 'Lower CI bound', 'Upper CI bound', 'P-value'], ['ACME (control)', 0.075529, 0.024995, 0.132408, 0.00], ['ACME (treated)', 0.076348, 0.027475, 0.130138, 0.00], ['ADE (control)', 0.021389, -0.094323, 0.139148, 0.68], ['ADE (treated)', 0.022207, -0.101239, 0.145740, 0.68], ['Total effect', 0.097736, -0.025384, 0.225386, 0.16], ['Prop. mediated (control)', 0.656820, -3.664956, 4.845269, 0.16], ['Prop. mediated (treated)', 0.687690, -3.449415, 4.469289, 0.16], ['ACME (average)', 0.075938, 0.026109, 0.129450, 0.00], ['ADE (average)', 0.021798, -0.097781, 0.142444, 0.68], ['Prop. mediated (average)', 0.669659, -3.557185, 4.657279, 0.16]] framing_para_4231 = pd.DataFrame(df[1:], columns=df[0]).set_index('index') df = [['index', 'Estimate', 'Lower CI bound', 'Upper CI bound', 'P-value'], ['ACME (control)', 0.065989, 0.003366, 0.152261, 0.04], ['ACME (treated)', 0.081424, 0.008888, 0.199853, 0.04], ['ADE (control)', 0.240392, -0.026286, 0.470918, 0.08], ['ADE (treated)', 0.255827, -0.030681, 0.491535, 0.08], ['Total effect', 0.321816, 0.037238, 0.549530, 0.00], ['Prop. mediated (control)', 0.196935, 0.015232, 1.864804, 0.04], ['Prop. mediated (treated)', 0.248896, 0.032229, 1.738846, 0.04], ['ACME (average)', 0.073707, 0.006883, 0.169923, 0.04], ['ADE (average)', 0.248109, -0.028483, 0.478978, 0.08], ['Prop. mediated (average)', 0.226799, 0.028865, 1.801825, 0.04]] framing_moderated_4231 = pd.DataFrame(df[1:], columns=df[0]).set_index('index') @pytest.mark.slow def test_framing_example(): cur_dir = os.path.dirname(os.path.abspath(__file__)) data = pd.read_csv(os.path.join(cur_dir, 'results', "framing.csv")) outcome = np.asarray(data["cong_mesg"]) outcome_exog = patsy.dmatrix("emo + treat + age + educ + gender + income", data, return_type='dataframe') probit = sm.families.links.probit outcome_model = sm.GLM(outcome, outcome_exog, family=sm.families.Binomial(link=probit())) mediator = np.asarray(data["emo"]) mediator_exog = patsy.dmatrix("treat + age + educ + gender + income", data, return_type='dataframe') mediator_model = sm.OLS(mediator, mediator_exog) tx_pos = [outcome_exog.columns.tolist().index("treat"), mediator_exog.columns.tolist().index("treat")] med_pos = outcome_exog.columns.tolist().index("emo") med = Mediation(outcome_model, mediator_model, tx_pos, med_pos, outcome_fit_kwargs={'atol':1e-11}) np.random.seed(4231) para_rslt = med.fit(method='parametric', n_rep=100) diff = np.asarray(para_rslt.summary() - framing_para_4231) assert_allclose(diff, 0, atol=1e-6) np.random.seed(4231) boot_rslt = med.fit(method='boot', n_rep=100) diff = np.asarray(boot_rslt.summary() - framing_boot_4231) assert_allclose(diff, 0, atol=1e-6) def test_framing_example_moderator(): # moderation without formulas, generally not useful but test anyway cur_dir = os.path.dirname(os.path.abspath(__file__)) data = pd.read_csv(os.path.join(cur_dir, 'results', "framing.csv")) outcome = np.asarray(data["cong_mesg"]) outcome_exog = patsy.dmatrix("emo + treat + age + educ + gender + income", data, return_type='dataframe') probit = sm.families.links.probit outcome_model = sm.GLM(outcome, outcome_exog, family=sm.families.Binomial(link=probit())) mediator = np.asarray(data["emo"]) mediator_exog = patsy.dmatrix("treat + age + educ + gender + income", data, return_type='dataframe') mediator_model = sm.OLS(mediator, mediator_exog) tx_pos = [outcome_exog.columns.tolist().index("treat"), mediator_exog.columns.tolist().index("treat")] med_pos = outcome_exog.columns.tolist().index("emo") ix = (outcome_exog.columns.tolist().index("age"), mediator_exog.columns.tolist().index("age")) moderators = {ix : 20} med = Mediation(outcome_model, mediator_model, tx_pos, med_pos, moderators=moderators) # Just a smoke test np.random.seed(4231) med_rslt = med.fit(method='parametric', n_rep=100) @pytest.mark.slow def test_framing_example_formula(): cur_dir = os.path.dirname(os.path.abspath(__file__)) data = pd.read_csv(os.path.join(cur_dir, 'results', "framing.csv")) probit = sm.families.links.probit outcome_model = sm.GLM.from_formula("cong_mesg ~ emo + treat + age + educ + gender + income", data, family=sm.families.Binomial(link=probit())) mediator_model = sm.OLS.from_formula("emo ~ treat + age + educ + gender + income", data) med = Mediation(outcome_model, mediator_model, "treat", "emo", outcome_fit_kwargs={'atol': 1e-11}) np.random.seed(4231) med_rslt = med.fit(method='boot', n_rep=100) diff = np.asarray(med_rslt.summary() - framing_boot_4231) assert_allclose(diff, 0, atol=1e-6) np.random.seed(4231) med_rslt = med.fit(method='parametric', n_rep=100) diff = np.asarray(med_rslt.summary() - framing_para_4231) assert_allclose(diff, 0, atol=1e-6) @pytest.mark.slow def test_framing_example_moderator_formula(): cur_dir = os.path.dirname(os.path.abspath(__file__)) data = pd.read_csv(os.path.join(cur_dir, 'results', "framing.csv")) probit = sm.families.links.probit outcome_model = sm.GLM.from_formula("cong_mesg ~ emo + treat*age + emo*age + educ + gender + income", data, family=sm.families.Binomial(link=probit())) mediator_model = sm.OLS.from_formula("emo ~ treat*age + educ + gender + income", data) moderators = {"age" : 20} med = Mediation(outcome_model, mediator_model, "treat", "emo", moderators=moderators) np.random.seed(4231) med_rslt = med.fit(method='parametric', n_rep=100) diff = np.asarray(med_rslt.summary() - framing_moderated_4231) assert_allclose(diff, 0, atol=1e-6) def test_mixedlm(): np.random.seed(3424) n = 200 # The exposure (not time varying) x = np.random.normal(size=n) xv = np.outer(x, np.ones(3)) # The mediator (with random intercept) mx = np.asarray([4., 4, 1]) mx /= np.sqrt(np.sum(mx**2)) med = mx[0] * np.outer(x, np.ones(3)) med += mx[1] * np.outer(np.random.normal(size=n), np.ones(3)) med += mx[2] * np.random.normal(size=(n, 3)) # The outcome (exposure and mediator effects) ey = np.outer(x, np.r_[0, 0.5, 1]) + med # Random structure of the outcome (random intercept and slope) ex = np.asarray([5., 2, 2]) ex /= np.sqrt(np.sum(ex**2)) e = ex[0] * np.outer(np.random.normal(size=n), np.ones(3)) e += ex[1] * np.outer(np.random.normal(size=n), np.r_[-1, 0, 1]) e += ex[2] * np.random.normal(size=(n, 3)) y = ey + e # Group membership idx = np.outer(np.arange(n), np.ones(3)) # Time tim = np.outer(np.ones(n), np.r_[-1, 0, 1]) df = pd.DataFrame({"y": y.flatten(), "x": xv.flatten(), "id": idx.flatten(), "time": tim.flatten(), "med": med.flatten()}) mediator_model = sm.MixedLM.from_formula("med ~ x", groups="id", data=df) outcome_model = sm.MixedLM.from_formula("y ~ med + x", groups="id", data=df) me = Mediation(outcome_model, mediator_model, "x", "med") mr = me.fit(n_rep=2) st = mr.summary() pm = st.loc["Prop. mediated (average)", "Estimate"] assert_allclose(pm, 0.52, rtol=1e-2, atol=1e-2) def test_surv(): np.random.seed(2341) n = 1000 # Generate exposures exp = np.random.normal(size=n) # Generate mediators mn = np.exp(exp) mtime0 = -mn * np.log(np.random.uniform(size=n)) ctime = -2 * mn * np.log(np.random.uniform(size=n)) mstatus = (ctime >= mtime0).astype(int) mtime = np.where(mtime0 <= ctime, mtime0, ctime) for mt in "full", "partial", "no": # Outcome if mt == "full": lp = 0.5*mtime0 elif mt == "partial": lp = exp + mtime0 else: lp = exp # Generate outcomes mn = np.exp(-lp) ytime0 = -mn * np.log(np.random.uniform(size=n)) ctime = -2 * mn * np.log(np.random.uniform(size=n)) ystatus = (ctime >= ytime0).astype(int) ytime = np.where(ytime0 <= ctime, ytime0, ctime) df = pd.DataFrame({"ytime": ytime, "ystatus": ystatus, "mtime": mtime, "mstatus": mstatus, "exp": exp}) fml = "ytime ~ exp + mtime" outcome_model = sm.PHReg.from_formula(fml, status="ystatus", data=df) fml = "mtime ~ exp" mediator_model = sm.PHReg.from_formula(fml, status="mstatus", data=df) med = Mediation(outcome_model, mediator_model, "exp", "mtime", outcome_predict_kwargs={"pred_only": True}, outcome_fit_kwargs={"method": "lbfgs"}, mediator_fit_kwargs={"method": "lbfgs"}) med_result = med.fit(n_rep=2) dr = med_result.summary() pm = dr.loc["Prop. mediated (average)", "Estimate"] if mt == "no": assert_allclose(pm, 0, atol=0.1, rtol=0.1) elif mt == "full": assert_allclose(pm, 1, atol=0.1, rtol=0.1) else: assert_allclose(pm, 0.5, atol=0.1, rtol=0.1) statsmodels-0.12.2/statsmodels/stats/tests/test_meta.py000066400000000000000000000341371400612667500233560ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Tue Apr 7 13:08:37 2020 Author: Josef Perktold License: BSD-3 """ import io import numpy as np import pandas as pd from numpy.testing import assert_equal, assert_allclose from statsmodels.regression.linear_model import WLS from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.stats.meta_analysis import ( effectsize_smd, effectsize_2proportions, combine_effects, _fit_tau_iterative, _fit_tau_mm, _fit_tau_iter_mm) from .results import results_meta class TestEffectsizeBinom(object): @classmethod def setup_class(cls): cls.results = results_meta.eff_prop1 ss = """\ study,nei,nci,e1i,c1i,e2i,c2i,e3i,c3i,e4i,c4i 1,19,22,16.0,20.0,11,12,4.0,8.0,4,3 2,34,35,22.0,22.0,18,12,15.0,8.0,15,6 3,72,68,44.0,40.0,21,15,10.0,3.0,3,0 4,22,20,19.0,12.0,14,5,5.0,4.0,2,3 5,70,32,62.0,27.0,42,13,26.0,6.0,15,5 6,183,94,130.0,65.0,80,33,47.0,14.0,30,11 7,26,50,24.0,30.0,13,18,5.0,10.0,3,9 8,61,55,51.0,44.0,37,30,19.0,19.0,11,15 9,36,25,30.0,17.0,23,12,13.0,4.0,10,4 10,45,35,43.0,35.0,19,14,8.0,4.0,6,0 11,246,208,169.0,139.0,106,76,67.0,42.0,51,35 12,386,141,279.0,97.0,170,46,97.0,21.0,73,8 13,59,32,56.0,30.0,34,17,21.0,9.0,20,7 14,45,15,42.0,10.0,18,3,9.0,1.0,9,1 15,14,18,14.0,18.0,13,14,12.0,13.0,9,12 16,26,19,21.0,15.0,12,10,6.0,4.0,5,1 17,74,75,,,42,40,,,23,30""" df3 = pd.read_csv(io.StringIO(ss)) df_12y = df3[["e2i", "nei", "c2i", "nci"]] # TODO: currently 1 is reference, switch labels # cls.count2, cls.nobs2, cls.count1, cls.nobs1 = df_12y.values.T cls.count1, cls.nobs1, cls.count2, cls.nobs2 = df_12y.values.T def test_effectsize(self): res2 = self.results dta = (self.count1, self.nobs1, self.count2, self.nobs2) # count1, nobs1, count2, nobs2 = dta eff, var_eff = effectsize_2proportions(*dta) assert_allclose(eff, res2.y_rd, rtol=1e-13) assert_allclose(var_eff, res2.v_rd, rtol=1e-13) eff, var_eff = effectsize_2proportions(*dta, statistic="rr") assert_allclose(eff, res2.y_rr, rtol=1e-13) assert_allclose(var_eff, res2.v_rr, rtol=1e-13) eff, var_eff = effectsize_2proportions(*dta, statistic="or") assert_allclose(eff, res2.y_or, rtol=1e-13) assert_allclose(var_eff, res2.v_or, rtol=1e-13) eff, var_eff = effectsize_2proportions(*dta, statistic="as") assert_allclose(eff, res2.y_as, rtol=1e-13) assert_allclose(var_eff, res2.v_as, rtol=1e-13) class TestEffSmdMeta(object): @classmethod def setup_class(cls): # example from book Applied Meta-Analysis with R data = [ ["Carroll", 94, 22, 60, 92, 20, 60], ["Grant", 98, 21, 65, 92, 22, 65], ["Peck", 98, 28, 40, 88, 26, 40], ["Donat", 94, 19, 200, 82, 17, 200], ["Stewart", 98, 21, 50, 88, 22, 45], ["Young", 96, 21, 85, 92, 22, 85]] colnames = ["study", "mean_t", "sd_t", "n_t", "mean_c", "sd_c", "n_c"] dframe = pd.DataFrame(data, columns=colnames) cls.dta = np.asarray(dframe[["mean_t", "sd_t", "n_t", "mean_c", "sd_c", "n_c"]]).T cls.row_names = dframe["study"] def test_smd(self): # compare with metafor yi = np.array([ 0.09452415852032972, 0.27735586626551018, 0.36654442951591998, 0.66438496832691396, 0.46180628128769841, 0.18516443739910043]) vi_asy = np.array([ 0.03337056173559990, 0.03106510106366112, 0.05083971761755720, 0.01055175923267344, 0.04334466980873156, 0.02363025255552155]) vi_ub = np.array([ 0.03337176211751222, 0.03107388569950075, 0.05088098670518214, 0.01055698026322296, 0.04339077140867459, 0.02363252645927709]) eff, var_eff = effectsize_smd(*self.dta) # agreement with metafor is lower, atol for var 2.5e-06 # It's likely a small difference in bias correction assert_allclose(eff, yi, rtol=1e-5) assert_allclose(var_eff, vi_ub, rtol=1e-4) assert_allclose(var_eff, vi_asy, rtol=2e-3) # not the same definition # with unequal variance, not available yet # > r = escalc(measure="SMDH", m1i=m.t, sd1i=sd.t, n1i=n.t, m2i=m.c, # sd2i=sd.c, n2i=n.c, data=dat, vtype="UB") yi = np.array([ 0.09452415852032972, 0.27735586626551023, 0.36654442951591998, 0.66438496832691396, 0.46122883016705268, 0.18516443739910043]) vi_ub = np.array([ 0.03350541862210323, 0.03118164624093491, 0.05114625874744853, 0.01057160214284120, 0.04368303906568672, 0.02369839436451885]) # compare with package `meta` # high agreement, using smd function was written based on meta example # > rm = metacont(n.t,m.t,sd.t,n.c,m.c,sd.c, # + data=dat,studlab=rownames(dat),sm="SMD") # > rm$TE yi_m = np.array([ 0.09452437336063831, 0.27735640148036095, 0.36654634845797818, 0.66438509989113559, 0.46180797677414176, 0.18516464424648887]) # > rm$seTE**2 vi_m = np.array([ 0.03337182573880991, 0.03107434965484927, 0.05088322525353587, 0.01055724834741877, 0.04339324466573324, 0.02363264537147130]) assert_allclose(eff, yi_m, rtol=1e-13) assert_allclose(var_eff, vi_m, rtol=1e-13) class TestMetaK1(object): @classmethod def setup_class(cls): cls.eff = np.array([61.00, 61.40, 62.21, 62.30, 62.34, 62.60, 62.70, 62.84, 65.90]) cls.var_eff = np.array([0.2025, 1.2100, 0.0900, 0.2025, 0.3844, 0.5625, 0.0676, 0.0225, 1.8225]) def test_tau_kacker(self): # test iterative and two-step methods, Kacker 2004 # PM CA DL C2 from table 1 first row p. 135 # test for PM and DL are also against R metafor in other tests eff, var_eff = self.eff, self.var_eff t_PM, t_CA, t_DL, t_C2 = [0.8399, 1.1837, 0.5359, 0.9352] tau2, converged = _fit_tau_iterative(eff, var_eff, tau2_start=0.1, atol=1e-8) assert_equal(converged, True) assert_allclose(np.sqrt(tau2), t_PM, atol=6e-5) k = len(eff) # cochrane uniform weights tau2_ca = _fit_tau_mm(eff, var_eff, np.ones(k) / k) assert_allclose(np.sqrt(tau2_ca), t_CA, atol=6e-5) # DL one step, and 1 iteration, reduced agreement with Kacker tau2_dl = _fit_tau_mm(eff, var_eff, 1 / var_eff) assert_allclose(np.sqrt(tau2_dl), t_DL, atol=1e-3) tau2_dl_, converged = _fit_tau_iter_mm(eff, var_eff, tau2_start=0, maxiter=1) assert_equal(converged, False) assert_allclose(tau2_dl_, tau2_dl, atol=1e-10) # C2 two step, start with CA tau2_c2, converged = _fit_tau_iter_mm(eff, var_eff, tau2_start=tau2_ca, maxiter=1) assert_equal(converged, False) assert_allclose(np.sqrt(tau2_c2), t_C2, atol=6e-5) def test_pm(self): res = results_meta.exk1_metafor eff, var_eff = self.eff, self.var_eff tau2, converged = _fit_tau_iterative(eff, var_eff, tau2_start=0.1, atol=1e-8) assert_equal(converged, True) assert_allclose(tau2, res.tau2, atol=1e-10) # compare with WLS, PM weights mod_wls = WLS(eff, np.ones(len(eff)), weights=1 / (var_eff + tau2)) res_wls = mod_wls.fit(cov_type="fixed_scale") assert_allclose(res_wls.params, res.b, atol=1e-13) assert_allclose(res_wls.bse, res.se, atol=1e-10) ci_low, ci_upp = res_wls.conf_int()[0] assert_allclose(ci_low, res.ci_lb, atol=1e-10) assert_allclose(ci_upp, res.ci_ub, atol=1e-10) # need stricter atol to match metafor, # I also used higher precision in metafor res3 = combine_effects(eff, var_eff, method_re="pm", atol=1e-7) # TODO: asserts below are copy paste, DRY? assert_allclose(res3.tau2, res.tau2, atol=1e-10) assert_allclose(res3.mean_effect_re, res.b, atol=1e-13) assert_allclose(res3.sd_eff_w_re, res.se, atol=1e-10) ci = res3.conf_int(use_t=False)[1] assert_allclose(ci[0], res.ci_lb, atol=1e-10) assert_allclose(ci[1], res.ci_ub, atol=1e-10) assert_allclose(res3.q, res.QE, atol=1e-10) # the following does not pass yet # assert_allclose(res3.i2, res.I2 / 100, atol=1e-10) # percent in R # assert_allclose(res3.h2, res.H2, atol=1e-10) th = res3.test_homogeneity() q, pv = th df = th.df assert_allclose(pv, res.QEp, atol=1e-10) assert_allclose(q, res.QE, atol=1e-10) assert_allclose(df, 9 - 1, atol=1e-10) def test_dl(self): res = results_meta.exk1_dl eff, var_eff = self.eff, self.var_eff tau2 = _fit_tau_mm(eff, var_eff, 1 / var_eff) assert_allclose(tau2, res.tau2, atol=1e-10) res3 = combine_effects(eff, var_eff, method_re="dl") assert_allclose(res3.tau2, res.tau2, atol=1e-10) assert_allclose(res3.mean_effect_re, res.b, atol=1e-13) assert_allclose(res3.sd_eff_w_re, res.se, atol=1e-10) ci = res3.conf_int(use_t=False) # fe, re, fe_wls, re_wls assert_allclose(ci[1][0], res.ci_lb, atol=1e-10) assert_allclose(ci[1][1], res.ci_ub, atol=1e-10) assert_allclose(res3.q, res.QE, atol=1e-10) # I2 is in percent in metafor assert_allclose(res3.i2, res.I2 / 100, atol=1e-10) assert_allclose(res3.h2, res.H2, atol=1e-10) th = res3.test_homogeneity() q, pv = th df = th.df assert_allclose(pv, res.QEp, atol=1e-10) assert_allclose(q, res.QE, atol=1e-10) assert_allclose(df, 9 - 1, atol=1e-10) # compare FE estimate res_fe = results_meta.exk1_fe assert_allclose(res3.mean_effect_fe, res_fe.b, atol=1e-13) assert_allclose(res3.sd_eff_w_fe, res_fe.se, atol=1e-10) assert_allclose(ci[0][0], res_fe.ci_lb, atol=1e-10) assert_allclose(ci[0][1], res_fe.ci_ub, atol=1e-10) # compare FE, RE with HKSJ adjustment res_dls = results_meta.exk1_dl_hksj res_fes = results_meta.exk1_fe_hksj assert_allclose(res3.mean_effect_re, res_dls.b, atol=1e-13) assert_allclose(res3.mean_effect_fe, res_fes.b, atol=1e-13) assert_allclose(res3.sd_eff_w_fe * np.sqrt(res3.scale_hksj_fe), res_fes.se, atol=1e-10) assert_allclose(res3.sd_eff_w_re * np.sqrt(res3.scale_hksj_re), res_dls.se, atol=1e-10) assert_allclose(np.sqrt(res3.var_hksj_fe), res_fes.se, atol=1e-10) assert_allclose(np.sqrt(res3.var_hksj_re), res_dls.se, atol=1e-10) # metafor uses t distribution for hksj ci = res3.conf_int(use_t=True) # fe, re, fe_wls, re_wls assert_allclose(ci[3][0], res_dls.ci_lb, atol=1e-10) assert_allclose(ci[3][1], res_dls.ci_ub, atol=1e-10) assert_allclose(ci[2][0], res_fes.ci_lb, atol=1e-10) assert_allclose(ci[2][1], res_fes.ci_ub, atol=1e-10) th = res3.test_homogeneity() q, pv = th df = th.df assert_allclose(pv, res_dls.QEp, atol=1e-10) assert_allclose(q, res_dls.QE, atol=1e-10) assert_allclose(df, 9 - 1, atol=1e-10) class TestMetaBinOR(object): # testing against results from R package `meta` @classmethod def setup_class(cls): cls.res2 = res2 = results_meta.results_or_dl_hk cls.dta = (res2.event_e, res2.n_e, res2.event_c, res2.n_c) eff, var_eff = effectsize_2proportions(*cls.dta, statistic="or") res1 = combine_effects(eff, var_eff, method_re="chi2", use_t=True) cls.eff = eff cls.var_eff = var_eff cls.res1 = res1 def test_basic(self): res1 = self.res1 res2 = self.res2 assert_allclose(self.eff, res2.TE, rtol=1e-13) assert_allclose(self.var_eff, res2.seTE**2, rtol=1e-13) assert_allclose(res1.mean_effect_fe, res2.TE_fixed, rtol=1e-13) # R meta does not adjust sd FE for HKSJ assert_allclose(res1.sd_eff_w_fe, res2.seTE_fixed, rtol=1e-13) assert_allclose(res1.q, res2.Q, rtol=1e-13) assert_allclose(res1.tau2, res2.tau2, rtol=1e-10) assert_allclose(res1.mean_effect_re, res2.TE_random, rtol=1e-13) assert_allclose(res1.sd_eff_w_re_hksj, res2.seTE_random, rtol=1e-13) th = res1.test_homogeneity() q, pv = th df = th.df assert_allclose(q, res2.Q, rtol=1e-13) assert_allclose(pv, res2.pval_Q, rtol=1e-13) assert_allclose(df, res2.df_Q, rtol=1e-13) assert_allclose(res1.i2, res2.I2, rtol=1e-13) assert_allclose(res1.h2, res2.H**2, rtol=1e-13) ci = res1.conf_int(use_t=True) # fe, re, fe_wls, re_wls # R meta does not adjust FE for HKSJ, still uses normal dist # assert_allclose(ci[0][0], res2.lower_fixed, atol=1e-10) # assert_allclose(ci[0][1], res2.upper_fixed, atol=1e-10) assert_allclose(ci[3][0], res2.lower_random, rtol=1e-13) assert_allclose(ci[3][1], res2.upper_random, rtol=1e-10) ci = res1.conf_int(use_t=False) # fe, re, fe_wls, re_wls assert_allclose(ci[0][0], res2.lower_fixed, rtol=1e-13) assert_allclose(ci[0][1], res2.upper_fixed, rtol=1e-13) weights = 1 / self.var_eff mod_glm = GLM(self.eff, np.ones(len(self.eff)), var_weights=weights) res_glm = mod_glm.fit() assert_allclose(res_glm.params, res2.TE_fixed, rtol=1e-13) weights = 1 / (self.var_eff + res1.tau2) mod_glm = GLM(self.eff, np.ones(len(self.eff)), var_weights=weights) res_glm = mod_glm.fit() assert_allclose(res_glm.params, res2.TE_random, rtol=1e-13) statsmodels-0.12.2/statsmodels/stats/tests/test_moment_helpers.py000066400000000000000000000114341400612667500254440ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Oct 16 17:33:56 2011 Author: Josef Perktold """ import numpy as np import pytest from numpy.testing import assert_almost_equal, assert_, assert_equal from statsmodels.stats import moment_helpers from statsmodels.stats.moment_helpers import (cov2corr, mvsk2mc, mc2mvsk, mnc2mc, mc2mnc, cum2mc, mc2cum, mnc2cum) def test_cov2corr(): cov_a = np.ones((3, 3)) + np.diag(np.arange(1, 4) ** 2 - 1) corr_a = np.array([[1, 1 / 2., 1 / 3.], [1 / 2., 1, 1 / 2. / 3.], [1 / 3., 1 / 2. / 3., 1]]) corr = cov2corr(cov_a) assert_almost_equal(corr, corr_a, decimal=15) cov_mat = cov_a corr_mat = cov2corr(cov_mat) assert_(isinstance(corr_mat, np.ndarray)) assert_equal(corr_mat, corr) cov_ma = np.ma.array(cov_a) corr_ma = cov2corr(cov_ma) assert_equal(corr_mat, corr) assert_(isinstance(corr_ma, np.ma.core.MaskedArray)) cov_ma2 = np.ma.array(cov_a, mask=[[False, True, False], [True, False, False], [False, False, False]]) corr_ma2 = cov2corr(cov_ma2) assert_(np.ma.allclose(corr_ma, corr, atol=1e-15)) assert_equal(corr_ma2.mask, cov_ma2.mask) ms = [([0.0, 1, 0, 3], [0.0, 1.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0]), ([1.0, 1, 0, 3], [1.0, 1.0, 0.0, 0.0], [1.0, 0.0, -1.0, 6.0]), ([0.0, 1, 1, 3], [0.0, 1.0, 1.0, 0.0], [0.0, 1.0, 1.0, 0.0]), ([1.0, 1, 1, 3], [1.0, 1.0, 1.0, 0.0], [1.0, 0.0, 0.0, 2.0]), ([1.0, 1, 1, 4], [1.0, 1.0, 1.0, 1.0], [1.0, 0.0, 0.0, 3.0]), ([1.0, 2, 0, 3], [1.0, 2.0, 0.0, -9.0], [1.0, 1.0, -4.0, 9.0]), ([0.0, 2, 1, 3], [0.0, 2.0, 1.0, -9.0], [0.0, 2.0, 1.0, -9.0]), # neg.variance if mnc2 cumulant assert_equal(mnc2cum(mc2mnc(mom[0])), mom[1]) assert_equal(mnc2cum(mom[0]), mom[2]) if len(mom) <= 4: assert_equal(mc2cum(mom[0]), mom[1]) # test cumulant -> moment assert_equal(cum2mc(mom[1]), mom[0]) assert_equal(mc2mnc(cum2mc(mom[2])), mom[0]) if len(mom) <= 4: assert_equal(cum2mc(mom[1]), mom[0]) # round trip: mnc -> cum -> mc == mnc -> mc, assert_equal(cum2mc(mnc2cum(mom[0])), mnc2mc(mom[0])) # round trip: mc -> mnc -> mc == mc, assert_equal(mc2mnc(mnc2mc(mom[0])), mom[0]) if len(mom[0]) == 4: # round trip: mc -> mvsk -> mc == mc assert_equal(mvsk2mc(mc2mvsk(mom[0])), mom[0]) # round trip: mc -> mvsk -> mnc == mc -> mnc # TODO: mvsk2mnc not defined # assert_equal(mvsk2mnc(mc2mvsk(mom[0])), mc2mnc(mom[0])) rs = np.random.RandomState(12345) random_vals = rs.randint(0, 100, 12).reshape(4, 3) multidimension_test_vals = [np.array([[5., 10., 1.], [5., 10., 1.], [5., 10., 1.], [80., 310., 4.]]), random_vals] @pytest.mark.parametrize('test_vals', multidimension_test_vals) def test_multidimensional(test_vals): assert_almost_equal(cum2mc(mnc2cum(mc2mnc(test_vals).T).T).T, test_vals) assert_almost_equal(cum2mc(mc2cum(test_vals).T).T, test_vals) assert_almost_equal(mvsk2mc(mc2mvsk(test_vals).T).T, test_vals) @pytest.mark.parametrize('func_name', ['cum2mc', 'cum2mc', 'mc2cum', 'mc2mnc', 'mc2mvsk', 'mnc2cum', 'mnc2mc', 'mnc2mc', 'mvsk2mc', 'mvsk2mnc']) def test_moment_conversion_types(func_name): # written in 2009 # TODO: why did I use list as return type? func = getattr(moment_helpers, func_name) assert (isinstance(func([1.0, 1, 0, 3]), list) or isinstance(func(np.array([1.0, 1, 0, 3])), tuple) or isinstance(func(np.array([1.0, 1, 0, 3])), np.ndarray)) assert (isinstance(func(np.array([1.0, 1, 0, 3])), list) or isinstance(func(np.array([1.0, 1, 0, 3])), tuple) or isinstance(func(np.array([1.0, 1, 0, 3])), np.ndarray)) assert (isinstance(func(tuple([1.0, 1, 0, 3])), list) or isinstance(func(np.array([1.0, 1, 0, 3])), tuple) or isinstance(func(np.array([1.0, 1, 0, 3])), np.ndarray)) statsmodels-0.12.2/statsmodels/stats/tests/test_multi.py000066400000000000000000000502721400612667500235600ustar00rootroot00000000000000'''Tests for multipletests and fdr pvalue corrections Author : Josef Perktold ['b', 's', 'sh', 'hs', 'h', 'fdr_i', 'fdr_n', 'fdr_tsbh'] are tested against R:multtest 'hommel' is tested against R stats p_adjust (not available in multtest 'fdr_gbs', 'fdr_2sbky' I did not find them in R, currently tested for consistency only ''' import pytest import numpy as np from numpy.testing import (assert_almost_equal, assert_equal, assert_allclose) from statsmodels.stats.multitest import (multipletests, fdrcorrection, fdrcorrection_twostage, NullDistribution, local_fdr, multitest_methods_names) from statsmodels.stats.multicomp import tukeyhsd from scipy.stats.distributions import norm pval0 = np.array([ 0.838541367553, 0.642193923795, 0.680845947633, 0.967833824309, 0.71626938238, 0.177096952723, 5.23656777208e-005, 0.0202732688798, 0.00028140506198, 0.0149877310796]) res_multtest1 = np.array([ [5.2365677720800003e-05, 5.2365677720800005e-04, 5.2365677720800005e-04, 5.2365677720800005e-04, 5.2353339704891422e-04, 5.2353339704891422e-04, 5.2365677720800005e-04, 1.5337740764175588e-03], [2.8140506198000000e-04, 2.8140506197999998e-03, 2.5326455578199999e-03, 2.5326455578199999e-03, 2.8104897961789277e-03, 2.5297966317768816e-03, 1.4070253098999999e-03, 4.1211324652269442e-03], [1.4987731079600001e-02, 1.4987731079600000e-01, 1.1990184863680001e-01, 1.1990184863680001e-01, 1.4016246580579017e-01, 1.1379719679449507e-01, 4.9959103598666670e-02, 1.4632862843720582e-01], [2.0273268879800001e-02, 2.0273268879799999e-01, 1.4191288215860001e-01, 1.4191288215860001e-01, 1.8520270949069695e-01, 1.3356756197485375e-01, 5.0683172199499998e-02, 1.4844940238274187e-01], [1.7709695272300000e-01, 1.0000000000000000e+00, 1.0000000000000000e+00, 9.6783382430900000e-01, 8.5760763426056130e-01, 6.8947825122356643e-01, 3.5419390544599999e-01, 1.0000000000000000e+00], [6.4219392379499995e-01, 1.0000000000000000e+00, 1.0000000000000000e+00, 9.6783382430900000e-01, 9.9996560644133570e-01, 9.9413539782557070e-01, 8.9533672797500008e-01, 1.0000000000000000e+00], [6.8084594763299999e-01, 1.0000000000000000e+00, 1.0000000000000000e+00, 9.6783382430900000e-01, 9.9998903512635740e-01, 9.9413539782557070e-01, 8.9533672797500008e-01, 1.0000000000000000e+00], [7.1626938238000004e-01, 1.0000000000000000e+00, 1.0000000000000000e+00, 9.6783382430900000e-01, 9.9999661886871472e-01, 9.9413539782557070e-01, 8.9533672797500008e-01, 1.0000000000000000e+00], [8.3854136755300002e-01, 1.0000000000000000e+00, 1.0000000000000000e+00, 9.6783382430900000e-01, 9.9999998796038225e-01, 9.9413539782557070e-01, 9.3171263061444454e-01, 1.0000000000000000e+00], [9.6783382430900000e-01, 1.0000000000000000e+00, 1.0000000000000000e+00, 9.6783382430900000e-01, 9.9999999999999878e-01, 9.9413539782557070e-01, 9.6783382430900000e-01, 1.0000000000000000e+00]]) res_multtest2_columns = [ 'rawp', 'Bonferroni', 'Holm', 'Hochberg', 'SidakSS', 'SidakSD', 'BH', 'BY', 'ABH', 'TSBH_0.05'] rmethods = { 'rawp': (0, 'pval'), 'Bonferroni': (1, 'b'), 'Holm': (2, 'h'), 'Hochberg': (3, 'sh'), 'SidakSS': (4, 's'), 'SidakSD': (5, 'hs'), 'BH': (6, 'fdr_i'), 'BY': (7, 'fdr_n'), 'TSBH_0.05': (9, 'fdr_tsbh') } NA = np.nan # all rejections, except for Bonferroni and Sidak res_multtest2 = np.array([ 0.002, 0.004, 0.006, 0.008, 0.01, 0.012, 0.012, 0.024, 0.036, 0.048, 0.06, 0.072, 0.012, 0.02, 0.024, 0.024, 0.024, 0.024, 0.012, 0.012, 0.012, 0.012, 0.012, 0.012, 0.01194015976019192, 0.02376127616613988, 0.03546430060660932, 0.04705017875634587, 0.058519850599, 0.06987425045000606, 0.01194015976019192, 0.01984063872102404, 0.02378486270400004, 0.023808512, 0.023808512, 0.023808512, 0.012, 0.012, 0.012, 0.012, 0.012, 0.012, 0.0294, 0.0294, 0.0294, 0.0294, 0.0294, 0.0294, NA, NA, NA, NA, NA, NA, 0, 0, 0, 0, 0, 0 ]).reshape(6, 10, order='F') res_multtest3 = np.array([ 0.001, 0.002, 0.003, 0.004, 0.005, 0.05, 0.06, 0.07, 0.08, 0.09, 0.01, 0.02, 0.03, 0.04, 0.05, 0.5, 0.6, 0.7, 0.8, 0.9, 0.01, 0.018, 0.024, 0.028, 0.03, 0.25, 0.25, 0.25, 0.25, 0.25, 0.01, 0.018, 0.024, 0.028, 0.03, 0.09, 0.09, 0.09, 0.09, 0.09, 0.00995511979025177, 0.01982095664805061, 0.02959822305108317, 0.03928762649718986, 0.04888986953422814, 0.4012630607616213, 0.4613848859051006, 0.5160176928207072, 0.5656115457763677, 0.6105838818818925, 0.00995511979025177, 0.0178566699880266, 0.02374950634358763, 0.02766623106147537, 0.02962749064373438, 0.2262190625000001, 0.2262190625000001, 0.2262190625000001, 0.2262190625000001, 0.2262190625000001, 0.01, 0.01, 0.01, 0.01, 0.01, 0.08333333333333334, 0.0857142857142857, 0.0875, 0.0888888888888889, 0.09, 0.02928968253968254, 0.02928968253968254, 0.02928968253968254, 0.02928968253968254, 0.02928968253968254, 0.2440806878306878, 0.2510544217687075, 0.2562847222222222, 0.2603527336860670, 0.2636071428571428, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.005, 0.005, 0.005, 0.005, 0.005, 0.04166666666666667, 0.04285714285714286, 0.04375, 0.04444444444444445, 0.045 ]).reshape(10, 10, order='F') res0_large = np.array([ 0.00031612, 0.0003965, 0.00048442, 0.00051932, 0.00101436, 0.00121506, 0.0014516, 0.00265684, 0.00430043, 0.01743686, 0.02080285, 0.02785414, 0.0327198, 0.03494679, 0.04206808, 0.08067095, 0.23882767, 0.28352304, 0.36140401, 0.43565145, 0.44866768, 0.45368782, 0.48282088, 0.49223781, 0.55451638, 0.6207473, 0.71847853, 0.72424145, 0.85950263, 0.89032747, 0.0094836, 0.011895, 0.0145326, 0.0155796, 0.0304308, 0.0364518, 0.043548, 0.0797052, 0.1290129, 0.5231058, 0.6240855, 0.8356242, 0.981594, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.0094836, 0.0114985, 0.01356376, 0.01402164, 0.02637336, 0.0303765, 0.0348384, 0.06110732, 0.09460946, 0.36617406, 0.416057, 0.52922866, 0.5889564, 0.59409543, 0.67308928, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.0094836, 0.0114985, 0.01356376, 0.01402164, 0.02637336, 0.0303765, 0.0348384, 0.06110732, 0.09460946, 0.36617406, 0.416057, 0.52922866, 0.5889564, 0.59409543, 0.67308928, 0.89032747, 0.89032747, 0.89032747, 0.89032747, 0.89032747, 0.89032747, 0.89032747, 0.89032747, 0.89032747, 0.89032747, 0.89032747, 0.89032747, 0.89032747, 0.89032747, 0.89032747, 0.009440257627368331, 0.01182686507401931, 0.01443098172617119, 0.01546285007478554, 0.02998742566629453, 0.03581680249125385, 0.04264369065603335, 0.0767094173291795, 0.1212818694859857, 0.410051586220387, 0.4677640287633493, 0.5715077903157826, 0.631388450393325, 0.656016359012282, 0.724552174001554, 0.919808283456286, 0.999721715014484, 0.9999547032674126, 0.9999985652190126, 0.999999964809746, 0.999999982525548, 0.999999986719131, 0.999999997434160, 0.999999998521536, 0.999999999970829, 0.999999999999767, 1, 1, 1, 1, 0.009440257627368331, 0.01143489901147732, 0.0134754287611275, 0.01392738605848343, 0.0260416568490015, 0.02993768724817902, 0.0342629726119179, 0.0593542206208364, 0.09045742964699988, 0.308853956167216, 0.343245865702423, 0.4153483370083637, 0.4505333180190900, 0.453775200643535, 0.497247406680671, 0.71681858015803, 0.978083969553718, 0.986889206426321, 0.995400461639735, 0.9981506396214986, 0.9981506396214986, 0.9981506396214986, 0.9981506396214986, 0.9981506396214986, 0.9981506396214986, 0.9981506396214986, 0.9981506396214986, 0.9981506396214986, 0.9981506396214986, 0.9981506396214986, 0.0038949, 0.0038949, 0.0038949, 0.0038949, 0.0060753, 0.0060753, 0.006221142857142857, 0.00996315, 0.01433476666666667, 0.05231058, 0.05673504545454545, 0.06963535, 0.07488597857142856, 0.07488597857142856, 0.08413616, 0.15125803125, 0.421460594117647, 0.4725384, 0.570637910526316, 0.6152972625, 0.6152972625, 0.6152972625, 0.6152972625, 0.6152972625, 0.665419656, 0.7162468846153845, 0.775972982142857, 0.775972982142857, 0.889140651724138, 0.89032747, 0.01556007537622183, 0.01556007537622183, 0.01556007537622183, 0.01556007537622183, 0.02427074531648065, 0.02427074531648065, 0.02485338565390302, 0.0398026560334295, 0.0572672083580799, 0.2089800939109816, 0.2266557764630925, 0.2781923271071372, 0.2991685206792373, 0.2991685206792373, 0.336122876445059, 0.6042738882921044, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.00220711, 0.00220711, 0.00220711, 0.00220711, 0.00344267, 0.00344267, 0.003525314285714285, 0.005645785, 0.00812303444444444, 0.029642662, 0.0321498590909091, 0.03946003166666667, 0.04243538785714285, 0.04243538785714285, 0.0476771573333333, 0.085712884375, 0.23882767, 0.26777176, 0.323361482631579, 0.34866844875, 0.34866844875, 0.34866844875, 0.34866844875, 0.34866844875, 0.3770711384, 0.4058732346153846, 0.4397180232142857, 0.4397180232142857, 0.503846369310345, 0.504518899666667, 0.00272643, 0.00272643, 0.00272643, 0.00272643, 0.00425271, 0.00425271, 0.0043548, 0.006974205, 0.01003433666666667, 0.036617406, 0.03971453181818182, 0.048744745, 0.052420185, 0.052420185, 0.058895312, 0.105880621875, 0.295022415882353, 0.33077688, 0.399446537368421, 0.43070808375, 0.43070808375, 0.43070808375, 0.43070808375, 0.43070808375, 0.4657937592, 0.5013728192307692, 0.5431810875, 0.5431810875, 0.622398456206897, 0.623229229 ]).reshape(30, 10, order='F') class CheckMultiTestsMixin(object): @pytest.mark.parametrize('key,val', sorted(rmethods.items())) def test_multi_pvalcorrection_rmethods(self, key, val): # test against R package multtest mt.rawp2adjp res_multtest = self.res2 pval0 = res_multtest[:, 0] if val[1] in self.methods: reject, pvalscorr = multipletests(pval0, alpha=self.alpha, method=val[1])[:2] assert_almost_equal(pvalscorr, res_multtest[:, val[0]], 15) assert_equal(reject, pvalscorr <= self.alpha) def test_multi_pvalcorrection(self): # test against R package multtest mt.rawp2adjp res_multtest = self.res2 pval0 = res_multtest[:, 0] pvalscorr = np.sort(fdrcorrection(pval0, method='n')[1]) assert_almost_equal(pvalscorr, res_multtest[:, 7], 15) pvalscorr = np.sort(fdrcorrection(pval0, method='i')[1]) assert_almost_equal(pvalscorr, res_multtest[:, 6], 15) class TestMultiTests1(CheckMultiTestsMixin): @classmethod def setup_class(cls): cls.methods = ['b', 's', 'sh', 'hs', 'h', 'fdr_i', 'fdr_n'] cls.alpha = 0.1 cls.res2 = res_multtest1 class TestMultiTests2(CheckMultiTestsMixin): # case: all hypothesis rejected (except 'b' and 's' @classmethod def setup_class(cls): cls.methods = ['b', 's', 'sh', 'hs', 'h', 'fdr_i', 'fdr_n'] cls.alpha = 0.05 cls.res2 = res_multtest2 class TestMultiTests3(CheckMultiTestsMixin): @classmethod def setup_class(cls): cls.methods = ['b', 's', 'sh', 'hs', 'h', 'fdr_i', 'fdr_n', 'fdr_tsbh'] cls.alpha = 0.05 cls.res2 = res0_large class TestMultiTests4(CheckMultiTestsMixin): # in simulations, all two stage fdr, fdr_tsbky, fdr_tsbh, fdr_gbs, have in # some cases (cases with large Alternative) an FDR that looks too large # this is the first case #rejected = 12, DGP : has 10 false @classmethod def setup_class(cls): cls.methods = ['b', 's', 'sh', 'hs', 'h', 'fdr_i', 'fdr_n', 'fdr_tsbh'] cls.alpha = 0.05 cls.res2 = res_multtest3 @pytest.mark.parametrize('alpha', [0.01, 0.05, 0.1]) @pytest.mark.parametrize('method', ['b', 's', 'sh', 'hs', 'h', 'hommel', 'fdr_i', 'fdr_n', 'fdr_tsbky', 'fdr_tsbh', 'fdr_gbs']) @pytest.mark.parametrize('ii', list(range(11))) def test_pvalcorrection_reject(alpha, method, ii): # consistency test for reject boolean and pvalscorr pval1 = np.hstack((np.linspace(0.0001, 0.0100, ii), np.linspace(0.05001, 0.11, 10 - ii))) # using .05001 instead of 0.05 to avoid edge case issue #768 reject, pvalscorr = multipletests(pval1, alpha=alpha, method=method)[:2] msg = 'case %s %3.2f rejected:%d\npval_raw=%r\npvalscorr=%r' % ( method, alpha, reject.sum(), pval1, pvalscorr) assert_equal(reject, pvalscorr <= alpha, err_msg=msg) def test_hommel(): # tested against R stats p_adjust(pval0, method='hommel') pval0 = np.array([ 0.00116, 0.00924, 0.01075, 0.01437, 0.01784, 0.01918, 0.02751, 0.02871, 0.03054, 0.03246, 0.04259, 0.06879, 0.0691, 0.08081, 0.08593, 0.08993, 0.09386, 0.09412, 0.09718, 0.09758, 0.09781, 0.09788, 0.13282, 0.20191, 0.21757, 0.24031, 0.26061, 0.26762, 0.29474, 0.32901, 0.41386, 0.51479, 0.52461, 0.53389, 0.56276, 0.62967, 0.72178, 0.73403, 0.87182, 0.95384]) result_ho = np.array([ 0.0464, 0.25872, 0.29025, 0.3495714285714286, 0.41032, 0.44114, 0.57771, 0.60291, 0.618954, 0.6492, 0.7402725000000001, 0.86749, 0.86749, 0.8889100000000001, 0.8971477777777778, 0.8993, 0.9175374999999999, 0.9175374999999999, 0.9175374999999999, 0.9175374999999999, 0.9175374999999999, 0.9175374999999999, 0.95384, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001, 0.9538400000000001]) rej, pvalscorr, _, _ = multipletests(pval0, alpha=0.1, method='ho') assert_almost_equal(pvalscorr, result_ho, 15) assert_equal(rej, result_ho < 0.1) def test_fdr_bky(): # test for fdrcorrection_twostage # example from BKY pvals = [ 0.0001, 0.0004, 0.0019, 0.0095, 0.0201, 0.0278, 0.0298, 0.0344, 0.0459, 0.3240, 0.4262, 0.5719, 0.6528, 0.7590, 1.000] # no test for corrected p-values, but they are inherited # same number of rejection as in BKY paper: # single step-up:4, two-stage:8, iterated two-step:9 # also alpha_star is the same as theirs for TST # alpha_star for stage 2 res_tst = fdrcorrection_twostage(pvals, alpha=0.05, iter=False) assert_almost_equal([0.047619, 0.0649], res_tst[-1][:2], 3) assert_equal(8, res_tst[0].sum()) @pytest.mark.parametrize('method', sorted(multitest_methods_names)) def test_issorted(method): # test that is_sorted keyword works correctly # the fdrcorrection functions are tested indirectly # data generated as random numbers np.random.beta(0.2, 0.5, size=10) pvals = np.array([31, 9958111, 7430818, 8653643, 9892855, 876, 2651691, 145836, 9931, 6174747]) * 1e-7 sortind = np.argsort(pvals) sortrevind = sortind.argsort() pvals_sorted = pvals[sortind] res1 = multipletests(pvals, method=method, is_sorted=False) res2 = multipletests(pvals_sorted, method=method, is_sorted=True) assert_equal(res2[0][sortrevind], res1[0]) assert_allclose(res2[0][sortrevind], res1[0], rtol=1e-10) def test_tukeyhsd(): # example multicomp in R p 83 res = '''\ pair diff lwr upr p adj P-M 8.150000 -10.037586 26.3375861 0.670063958 S-M -3.258333 -21.445919 14.9292527 0.982419709 T-M 23.808333 5.620747 41.9959194 0.006783701 V-M 4.791667 -13.395919 22.9792527 0.931020848 S-P -11.408333 -29.595919 6.7792527 0.360680099 T-P 15.658333 -2.529253 33.8459194 0.113221634 V-P -3.358333 -21.545919 14.8292527 0.980350080 T-S 27.066667 8.879081 45.2542527 0.002027122 V-S 8.050000 -10.137586 26.2375861 0.679824487 V-T -19.016667 -37.204253 -0.8290806 0.037710044 ''' res = np.array([ [8.150000, -10.037586, 26.3375861, 0.670063958], [-3.258333, -21.445919, 14.9292527, 0.982419709], [23.808333, 5.620747, 41.9959194, 0.006783701], [4.791667, -13.395919, 22.9792527, 0.931020848], [-11.408333, -29.595919, 6.7792527, 0.360680099], [15.658333, -2.529253, 33.8459194, 0.113221634], [-3.358333, -21.545919, 14.8292527, 0.980350080], [27.066667, 8.879081, 45.2542527, 0.002027122], [8.050000, -10.137586, 26.2375861, 0.679824487], [-19.016667, -37.204253, -0.8290806, 0.037710044]]) m_r = [94.39167, 102.54167, 91.13333, 118.20000, 99.18333] myres = tukeyhsd(m_r, 6, 110.8, alpha=0.05, df=4) pairs, reject, meandiffs, std_pairs, confint, q_crit = myres[:6] assert_almost_equal(meandiffs, res[:, 0], decimal=5) assert_almost_equal(confint, res[:, 1:3], decimal=2) assert_equal(reject, res[:, 3] < 0.05) # check p-values (divergence of high values is expected) small_pvals_idx = [2, 5, 7, 9] assert_allclose(myres[8][small_pvals_idx], res[small_pvals_idx, 3], rtol=1e-3) def test_local_fdr(): # Create a mixed population of Z-scores: 1000 standard normal and # 20 uniformly distributed between 3 and 4. grid = np.linspace(0.001, 0.999, 1000) z0 = norm.ppf(grid) z1 = np.linspace(3, 4, 20) zs = np.concatenate((z0, z1)) # Exact local FDR for U(3, 4) component. f1 = np.exp(-z1**2 / 2) / np.sqrt(2*np.pi) r = len(z1) / float(len(z0) + len(z1)) f1 /= (1 - r) * f1 + r for alpha in None, 0, 1e-8: if alpha is None: fdr = local_fdr(zs) else: fdr = local_fdr(zs, alpha=alpha) fdr1 = fdr[len(z0):] assert_allclose(f1, fdr1, rtol=0.05, atol=0.1) def test_null_distribution(): # Create a mixed population of Z-scores: 1000 standard normal and # 20 uniformly distributed between 3 and 4. grid = np.linspace(0.001, 0.999, 1000) z0 = norm.ppf(grid) z1 = np.linspace(3, 4, 20) zs = np.concatenate((z0, z1)) emp_null = NullDistribution(zs, estimate_null_proportion=True) assert_allclose(emp_null.mean, 0, atol=1e-5, rtol=1e-5) assert_allclose(emp_null.sd, 1, atol=1e-5, rtol=1e-2) assert_allclose(emp_null.null_proportion, 0.98, atol=1e-5, rtol=1e-2) # consistency check assert_allclose(emp_null.pdf(np.r_[-1, 0, 1]), norm.pdf(np.r_[-1, 0, 1], loc=emp_null.mean, scale=emp_null.sd), rtol=1e-13) @pytest.mark.parametrize('estimate_prob', [True, False]) @pytest.mark.parametrize('estimate_scale', [True, False]) @pytest.mark.parametrize('estimate_mean', [True, False]) def test_null_constrained(estimate_mean, estimate_scale, estimate_prob): # Create a mixed population of Z-scores: 1000 standard normal and # 20 uniformly distributed between 3 and 4. grid = np.linspace(0.001, 0.999, 1000) z0 = norm.ppf(grid) z1 = np.linspace(3, 4, 20) zs = np.concatenate((z0, z1)) emp_null = NullDistribution(zs, estimate_mean=estimate_mean, estimate_scale=estimate_scale, estimate_null_proportion=estimate_prob) if not estimate_mean: assert_allclose(emp_null.mean, 0, atol=1e-5, rtol=1e-5) if not estimate_scale: assert_allclose(emp_null.sd, 1, atol=1e-5, rtol=1e-2) if not estimate_prob: assert_allclose(emp_null.null_proportion, 1, atol=1e-5, rtol=1e-2) # consistency check assert_allclose(emp_null.pdf(np.r_[-1, 0, 1]), norm.pdf(np.r_[-1, 0, 1], loc=emp_null.mean, scale=emp_null.sd), rtol=1e-13) statsmodels-0.12.2/statsmodels/stats/tests/test_multivariate.py000066400000000000000000000267571400612667500251470ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sun Nov 5 14:48:19 2017 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_allclose, assert_equal #noqa from statsmodels.stats import weightstats import statsmodels.stats.multivariate as smmv # pytest cannot import test_xxx from statsmodels.stats.multivariate import confint_mvmean_fromstats from statsmodels.tools.testing import Holder def test_mv_mean(): # names = ['id', 'mpg1', 'mpg2', 'add'] x = np.asarray([[1.0, 24.0, 23.5, 1.0], [2.0, 25.0, 24.5, 1.0], [3.0, 21.0, 20.5, 1.0], [4.0, 22.0, 20.5, 1.0], [5.0, 23.0, 22.5, 1.0], [6.0, 18.0, 16.5, 1.0], [7.0, 17.0, 16.5, 1.0], [8.0, 28.0, 27.5, 1.0], [9.0, 24.0, 23.5, 1.0], [10.0, 27.0, 25.5, 1.0], [11.0, 21.0, 20.5, 1.0], [12.0, 23.0, 22.5, 1.0], [1.0, 20.0, 19.0, 0.0], [2.0, 23.0, 22.0, 0.0], [3.0, 21.0, 20.0, 0.0], [4.0, 25.0, 24.0, 0.0], [5.0, 18.0, 17.0, 0.0], [6.0, 17.0, 16.0, 0.0], [7.0, 18.0, 17.0, 0.0], [8.0, 24.0, 23.0, 0.0], [9.0, 20.0, 19.0, 0.0], [10.0, 24.0, 22.0, 0.0], [11.0, 23.0, 22.0, 0.0], [12.0, 19.0, 18.0, 0.0]]) res = smmv.test_mvmean(x[:, 1:3], [21, 21]) res_stata = Holder(p_F=1.25062334808e-09, df_r=22, df_m=2, F=59.91609589041116, T2=125.2791095890415) assert_allclose(res.statistic, res_stata.F, rtol=1e-10) assert_allclose(res.pvalue, res_stata.p_F, rtol=1e-10) assert_allclose(res.t2, res_stata.T2, rtol=1e-10) assert_equal(res.df, [res_stata.df_m, res_stata.df_r]) # diff of paired sample mask = x[:, -1] == 1 x1 = x[mask, 1:3] x0 = x[~mask, 1:3] res_p = smmv.test_mvmean(x1 - x0, [0, 0]) # result Stata hotelling res_stata = Holder(T2=9.698067632850247, df=10, k=2, N=12, F=4.4082126, # not in return List p_F=0.0424) # not in return List res = res_p assert_allclose(res.statistic, res_stata.F, atol=5e-7) assert_allclose(res.pvalue, res_stata.p_F, atol=5e-4) assert_allclose(res.t2, res_stata.T2, rtol=1e-10) assert_equal(res.df, [res_stata.k, res_stata.df]) # mvtest means diff1 diff2, zero res_stata = Holder(p_F=.0423949782937231, df_r=10, df_m=2, F=4.408212560386478, T2=9.69806763285025) assert_allclose(res.statistic, res_stata.F, rtol=1e-12) assert_allclose(res.pvalue, res_stata.p_F, rtol=1e-12) assert_allclose(res.t2, res_stata.T2, rtol=1e-12) assert_equal(res.df, [res_stata.df_m, res_stata.df_r]) dw = weightstats.DescrStatsW(x) ci0 = dw.tconfint_mean(alpha=0.05) nobs = len(x[:, 1:]) ci1 = confint_mvmean_fromstats(dw.mean, np.diag(dw.var), nobs, lin_transf=np.eye(4), alpha=0.05) ci2 = confint_mvmean_fromstats(dw.mean, dw.cov, nobs, lin_transf=np.eye(4), alpha=0.05) assert_allclose(ci1[:2], ci0, rtol=1e-13) assert_allclose(ci2[:2], ci0, rtol=1e-13) # test from data res = smmv.confint_mvmean(x, lin_transf=np.eye(4), alpha=0.05) assert_allclose(res, ci2, rtol=1e-13) def test_mvmean_2indep(): x = np.asarray([[1.0, 24.0, 23.5, 1.0], [2.0, 25.0, 24.5, 1.0], [3.0, 21.0, 20.5, 1.0], [4.0, 22.0, 20.5, 1.0], [5.0, 23.0, 22.5, 1.0], [6.0, 18.0, 16.5, 1.0], [7.0, 17.0, 16.5, 1.0], [8.0, 28.0, 27.5, 1.0], [9.0, 24.0, 23.5, 1.0], [10.0, 27.0, 25.5, 1.0], [11.0, 21.0, 20.5, 1.0], [12.0, 23.0, 22.5, 1.0], [1.0, 20.0, 19.0, 0.0], [2.0, 23.0, 22.0, 0.0], [3.0, 21.0, 20.0, 0.0], [4.0, 25.0, 24.0, 0.0], [5.0, 18.0, 17.0, 0.0], [6.0, 17.0, 16.0, 0.0], [7.0, 18.0, 17.0, 0.0], [8.0, 24.0, 23.0, 0.0], [9.0, 20.0, 19.0, 0.0], [10.0, 24.0, 22.0, 0.0], [11.0, 23.0, 22.0, 0.0], [12.0, 19.0, 18.0, 0.0]]) y = np.asarray([[1.1, 24.1, 23.4, 1.1], [1.9, 25.2, 24.3, 1.2], [3.2, 20.9, 20.2, 1.3], [4.1, 21.8, 20.6, 0.9], [5.2, 23.0, 22.7, 0.8], [6.3, 18.1, 16.8, 0.7], [7.1, 17.2, 16.5, 1.0], [7.8, 28.3, 27.4, 1.1], [9.5, 23.9, 23.3, 1.2], [10.1, 26.8, 25.2, 1.3], [10.5, 26.7, 20.6, 0.9], [12.1, 23.0, 22.7, 0.8], [1.1, 20.1, 19.0, 0.7], [1.8, 23.2, 22.0, 0.1], [3.2, 21.3, 20.3, 0.2], [4.3, 24.9, 24.2, 0.3], [5.5, 17.9, 17.1, 0.0], [5.5, 17.8, 16.0, 0.6], [7.1, 17.7, 16.7, 0.0], [7.7, 24.0, 22.8, 0.5], [9.1, 20.1, 18.9, 0.0], [10.2, 24.2, 22.3, 0.3], [11.3, 23.3, 22.2, 0.0], [11.7, 18.8, 18.1, 0.1]]) res = smmv.test_mvmean_2indep(x, y) res_stata = Holder(p_F=0.6686659171701677, df_r=43, df_m=4, F=0.594263378678938, T2=2.5428944576028973) assert_allclose(res.statistic, res_stata.F, rtol=1e-10) assert_allclose(res.pvalue, res_stata.p_F, rtol=1e-10) assert_allclose(res.t2, res_stata.T2, rtol=1e-10) assert_equal(res.df, [res_stata.df_m, res_stata.df_r]) def test_confint_simult(): # example from book for simultaneous confint m = [526.29, 54.69, 25.13] cov = [[5808.06, 597.84, 222.03], [597.84, 126.05, 23.39], [222.03, 23.39, 23.11]] nobs = 87 res_ci = confint_mvmean_fromstats(m, cov, nobs, lin_transf=np.eye(3), simult=True) cii = [confint_mvmean_fromstats( m, cov, nobs, lin_transf=np.eye(3)[i], simult=True)[:2] for i in range(3)] cii = np.array(cii).squeeze() # these might use rounded numbers in intermediate computation res_ci_book = np.array([[503.06, 550.12], [51.22, 58.16], [23.65, 26.61]]) assert_allclose(res_ci[0], res_ci_book[:, 0], rtol=1e-3) # low assert_allclose(res_ci[0], res_ci_book[:, 0], rtol=1e-3) # upp assert_allclose(res_ci[0], cii[:, 0], rtol=1e-13) assert_allclose(res_ci[1], cii[:, 1], rtol=1e-13) res_constr = confint_mvmean_fromstats(m, cov, nobs, lin_transf=[0, 1, -1], simult=True) assert_allclose(res_constr[0], 29.56 - 3.12, rtol=1e-3) assert_allclose(res_constr[1], 29.56 + 3.12, rtol=1e-3) # TODO: this assumes separate constraints, # but we want multiplicity correction # test if several constraints or transformations work # original, flipping sign, multiply by 2 lt = [[0, 1, -1], [0, -1, 1], [0, 2, -2]] res_constr2 = confint_mvmean_fromstats(m, cov, nobs, lin_transf=lt, simult=True) lows = res_constr[0], - res_constr[1], 2 * res_constr[0] upps = res_constr[1], - res_constr[0], 2 * res_constr[1] # TODO: check return dimensions lows = np.asarray(lows).squeeze() upps = np.asarray(upps).squeeze() assert_allclose(res_constr2[0], lows, rtol=1e-13) assert_allclose(res_constr2[1], upps, rtol=1e-13) class TestCovStructure(object): @classmethod def setup_class(cls): # computed from data with ``cov = np.cov(dta1, rowvar=0, ddof=1)`` cls.cov = np.array( [[28.965925000000002, 17.215358333333327, 2.6945666666666654], [17.215358333333327, 21.452852666666672, 6.044527833333332], [2.6945666666666654, 6.044527833333332, 13.599042333333331]]) cls.nobs = 25 def test_spherical(self): cov, nobs = self.cov, self.nobs # from Stata 14 p_chi2 = 0.0006422366870356 # df = 5 chi2 = 21.53275509455011 stat, pv = smmv.test_cov_spherical(cov, nobs) assert_allclose(stat, chi2, rtol=1e-7) assert_allclose(pv, p_chi2, rtol=1e-6) def test_diagonal(self): cov, nobs = self.cov, self.nobs # from Stata 14 p_chi2 = 0.0004589987613319 # df = 3 chi2 = 17.91025335733012 stat, pv = smmv.test_cov_diagonal(cov, nobs) assert_allclose(stat, chi2, rtol=1e-8) assert_allclose(pv, p_chi2, rtol=1e-7) def test_blockdiagonal(self): cov, nobs = self.cov, self.nobs # from Stata 14 p_chi2 = 0.1721758850671037 # df = 2 chi2 = 3.518477474111563 # cov_blocks = cov[:2, :2], cov[-1:, -1:] # stat, pv = smmv.test_cov_blockdiagonal(cov, nobs, cov_blocks) block_len = [2, 1] stat, pv = smmv.test_cov_blockdiagonal(cov, nobs, block_len) assert_allclose(stat, chi2, rtol=1e-7) assert_allclose(pv, p_chi2, rtol=1e-6) def test_covmat(self): cov, nobs = self.cov, self.nobs # from Stata 14 p_chi2 = 0.4837049015162541 # df = 6 chi2 = 5.481422374989864 cov_null = np.array([[30, 15, 0], [15, 20, 0], [0, 0, 10]]) stat, pv = smmv.test_cov(cov, nobs, cov_null) assert_allclose(stat, chi2, rtol=1e-7) assert_allclose(pv, p_chi2, rtol=1e-6) def test_cov_oneway(): # from Stata 14 p_chi2 = .1944866419800838 chi2 = 13.55075120374669 df = 10 p_F_Box = .1949865290585139 df_r_Box = 18377.68924302788 df_m_Box = 10 F_Box = 1.354282822767436 nobs = [32, 32] cov_m = np.array( [[5.192540322580645, 4.545362903225806, 6.522177419354839, 5.25], [4.545362903225806, 13.184475806451612, 6.76008064516129, 6.266129032258064], [6.522177419354839, 6.76008064516129, 28.673387096774192, 14.46774193548387], [5.25, 6.266129032258064, 14.46774193548387, 16.64516129032258]]) cov_f = np.array( [[9.13608870967742, 7.549395161290322, 4.86391129032258, 4.151209677419355], [7.549395161290322, 18.60383064516129, 10.224798387096774, 5.445564516129032], [4.86391129032258, 10.224798387096774, 30.039314516129032, 13.493951612903226], [4.151209677419355, 5.445564516129032, 13.493951612903226, 27.995967741935484]]) res = smmv.test_cov_oneway([cov_m, cov_f], nobs) stat, pv = res assert_allclose(stat, F_Box, rtol=1e-10) assert_allclose(pv, p_F_Box, rtol=1e-6) assert_allclose(res.statistic_f, F_Box, rtol=1e-10) assert_allclose(res.pvalue_f, p_F_Box, rtol=1e-6) assert_allclose(res.df_f, (df_m_Box, df_r_Box), rtol=1e-13) assert_allclose(res.statistic_chi2, chi2, rtol=1e-10) assert_allclose(res.pvalue_chi2, p_chi2, rtol=1e-6) assert_equal(res.df_chi2, df) statsmodels-0.12.2/statsmodels/stats/tests/test_nonparametric.py000066400000000000000000000234531400612667500252710ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Jul 05 14:05:24 2013 Author: Josef Perktold """ from statsmodels.compat.python import lzip import numpy as np from numpy.testing import assert_allclose, assert_almost_equal import pytest from statsmodels.stats.contingency_tables import mcnemar, cochrans_q, SquareTable from statsmodels.sandbox.stats.runs import (Runs, runstest_1samp, runstest_2samp) from statsmodels.sandbox.stats.runs import mcnemar as sbmcnemar def _expand_table(table): '''expand a 2 by 2 contingency table to observations ''' return np.repeat([[1, 1], [1, 0], [0, 1], [0, 0]], table.ravel(), axis=0) def test_mcnemar_exact(): f_obs1 = np.array([[101, 121], [59, 33]]) f_obs2 = np.array([[101, 70], [59, 33]]) f_obs3 = np.array([[101, 80], [59, 33]]) f_obs4 = np.array([[101, 30], [60, 33]]) f_obs5 = np.array([[101, 10], [30, 33]]) f_obs6 = np.array([[101, 10], [10, 33]]) #vassar college online computation res1 = 0.000004 res2 = 0.378688 res3 = 0.089452 res4 = 0.00206 res5 = 0.002221 res6 = 1. stat = mcnemar(f_obs1, exact=True) assert_almost_equal([stat.statistic, stat.pvalue], [59, res1], decimal=6) stat = mcnemar(f_obs2, exact=True) assert_almost_equal([stat.statistic, stat.pvalue], [59, res2], decimal=6) stat = mcnemar(f_obs3, exact=True) assert_almost_equal([stat.statistic, stat.pvalue], [59, res3], decimal=6) stat = mcnemar(f_obs4, exact=True) assert_almost_equal([stat.statistic, stat.pvalue], [30, res4], decimal=6) stat = mcnemar(f_obs5, exact=True) assert_almost_equal([stat.statistic, stat.pvalue], [10, res5], decimal=6) stat = mcnemar(f_obs6, exact=True) assert_almost_equal([stat.statistic, stat.pvalue], [10, res6], decimal=6) def test_mcnemar_chisquare(): f_obs1 = np.array([[101, 121], [59, 33]]) f_obs2 = np.array([[101, 70], [59, 33]]) f_obs3 = np.array([[101, 80], [59, 33]]) #> mcn = mcnemar.test(matrix(c(101, 121, 59, 33),nrow=2)) res1 = [2.067222e01, 5.450095e-06] res2 = [0.7751938, 0.3786151] res3 = [2.87769784, 0.08981434] stat = mcnemar(f_obs1, exact=False) assert_allclose([stat.statistic, stat.pvalue], res1, rtol=1e-6) stat = mcnemar(f_obs2, exact=False) assert_allclose([stat.statistic, stat.pvalue], res2, rtol=1e-6) stat = mcnemar(f_obs3, exact=False) assert_allclose([stat.statistic, stat.pvalue], res3, rtol=1e-6) # test correction = False res1 = [2.135556e01, 3.815136e-06] res2 = [0.9379845, 0.3327967] res3 = [3.17266187, 0.07488031] res = mcnemar(f_obs1, exact=False, correction=False) assert_allclose([res.statistic, res.pvalue], res1, rtol=1e-6) res = mcnemar(f_obs2, exact=False, correction=False) assert_allclose([res.statistic, res.pvalue], res2, rtol=1e-6) res = mcnemar(f_obs3, exact=False, correction=False) assert_allclose([res.statistic, res.pvalue], res3, rtol=1e-6) def test_mcnemar_vectorized(reset_randomstate): ttk = np.random.randint(5,15, size=(2,2,3)) with pytest.deprecated_call(): res = sbmcnemar(ttk, exact=False) with pytest.deprecated_call(): res1 = lzip(*[sbmcnemar(ttk[:, :, i], exact=False) for i in range(3)]) assert_allclose(res, res1, rtol=1e-13) with pytest.deprecated_call(): res = sbmcnemar(ttk, exact=False, correction=False) with pytest.deprecated_call(): res1 = lzip(*[sbmcnemar(ttk[:, :, i], exact=False, correction=False) for i in range(3)]) assert_allclose(res, res1, rtol=1e-13) with pytest.deprecated_call(): res = sbmcnemar(ttk, exact=True) with pytest.deprecated_call(): res1 = lzip(*[sbmcnemar(ttk[:, :, i], exact=True) for i in range(3)]) assert_allclose(res, res1, rtol=1e-13) def test_symmetry_bowker(): table = np.array([0, 3, 4, 4, 2, 4, 1, 2, 4, 3, 5, 3, 0, 0, 2, 2, 3, 0, 0, 1, 5, 5, 5, 5, 5]).reshape(5, 5) res = SquareTable(table, shift_zeros=False).symmetry() mcnemar5_1 = dict(statistic=7.001587, pvalue=0.7252951, parameters=(10,), distr='chi2') assert_allclose([res.statistic, res.pvalue], [mcnemar5_1['statistic'], mcnemar5_1['pvalue']], rtol=1e-7) res = SquareTable(1 + table, shift_zeros=False).symmetry() mcnemar5_1b = dict(statistic=5.355988, pvalue=0.8661652, parameters=(10,), distr='chi2') assert_allclose([res.statistic, res.pvalue], [mcnemar5_1b['statistic'], mcnemar5_1b['pvalue']], rtol=1e-7) table = np.array([2, 2, 3, 6, 2, 3, 4, 3, 6, 6, 6, 7, 1, 9, 6, 7, 1, 1, 9, 8, 0, 1, 8, 9, 4]).reshape(5, 5) res = SquareTable(table, shift_zeros=False).symmetry() mcnemar5_2 = dict(statistic=18.76432, pvalue=0.04336035, parameters=(10,), distr='chi2') assert_allclose([res.statistic, res.pvalue], [mcnemar5_2['statistic'], mcnemar5_2['pvalue']], rtol=1.5e-7) res = SquareTable(1 + table, shift_zeros=False).symmetry() mcnemar5_2b = dict(statistic=14.55256, pvalue=0.1492461, parameters=(10,), distr='chi2') assert_allclose([res.statistic, res.pvalue], [mcnemar5_2b['statistic'], mcnemar5_2b['pvalue']], rtol=1e-7) def test_cochransq(): #example from dataplot docs, Conovover p. 253 #http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/cochran.htm x = np.array([[1, 1, 1], [1, 1, 1], [0, 1, 0], [1, 1, 0], [0, 0, 0], [1, 1, 1], [1, 1, 1], [1, 1, 0], [0, 0, 1], [0, 1, 0], [1, 1, 1], [1, 1, 1]]) res_qstat = 2.8 res_pvalue = 0.246597 res = cochrans_q(x) assert_almost_equal([res.statistic, res.pvalue], [res_qstat, res_pvalue]) #equivalence of mcnemar and cochranq for 2 samples a,b = x[:,:2].T res = cochrans_q(x[:, :2]) with pytest.deprecated_call(): assert_almost_equal(sbmcnemar(a, b, exact=False, correction=False), [res.statistic, res.pvalue]) def test_cochransq2(): # from an example found on web, verifies 13.286 data = np.array(''' 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1'''.split(), int).reshape(-1, 4) res = cochrans_q(data) assert_allclose([res.statistic, res.pvalue], [13.2857143, 0.00405776], rtol=1e-6) def test_cochransq3(): # another example compared to SAS # in frequency weight format dt = [('A', 'S1'), ('B', 'S1'), ('C', 'S1'), ('count', int)] dta = np.array([('F', 'F', 'F', 6), ('U', 'F', 'F', 2), ('F', 'F', 'U', 16), ('U', 'F', 'U', 4), ('F', 'U', 'F', 2), ('U', 'U', 'F', 6), ('F', 'U', 'U', 4), ('U', 'U', 'U', 6)], dt) cases = np.array([[0, 0, 0], [1, 0, 0], [0, 0, 1], [1, 0, 1], [0, 1, 0], [1, 1, 0], [0, 1, 1], [1, 1, 1]]) count = np.array([ 6, 2, 16, 4, 2, 6, 4, 6]) data = np.repeat(cases, count, 0) res = cochrans_q(data) assert_allclose([res.statistic, res.pvalue], [8.4706, 0.0145], atol=5e-5) def test_runstest(reset_randomstate): #comparison numbers from R, tseries, runs.test #currently only 2-sided used x = np.array([1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1]) z_twosided = 1.386750 pvalue_twosided = 0.1655179 z_greater = 1.386750 pvalue_greater = 0.08275893 z_less = 1.386750 pvalue_less = 0.917241 #print Runs(x).runs_test(correction=False) assert_almost_equal(np.array(Runs(x).runs_test(correction=False)), [z_twosided, pvalue_twosided], decimal=6) # compare with runstest_1samp which should have same indicator assert_almost_equal(runstest_1samp(x, correction=False), [z_twosided, pvalue_twosided], decimal=6) x2 = x - 0.5 + np.random.uniform(-0.1, 0.1, size=len(x)) assert_almost_equal(runstest_1samp(x2, cutoff=0, correction=False), [z_twosided, pvalue_twosided], decimal=6) assert_almost_equal(runstest_1samp(x2, cutoff='mean', correction=False), [z_twosided, pvalue_twosided], decimal=6) assert_almost_equal(runstest_1samp(x2, cutoff=x2.mean(), correction=False), [z_twosided, pvalue_twosided], decimal=6) # check median assert_almost_equal(runstest_1samp(x2, cutoff='median', correction=False), runstest_1samp(x2, cutoff=np.median(x2), correction=False), decimal=6) def test_runstest_2sample(): # regression test, checked with MonteCarlo and looks reasonable x = [31.8, 32.8, 39.2, 36, 30, 34.5, 37.4] y = [35.5, 27.6, 21.3, 24.8, 36.7, 30] y[-1] += 1e-6 #avoid tie that creates warning groups = np.concatenate((np.zeros(len(x)), np.ones(len(y)))) res = runstest_2samp(x, y) res1 = (0.022428065200812752, 0.98210649318649212) assert_allclose(res, res1, rtol=1e-6) # check as stacked array res2 = runstest_2samp(x, y) assert_allclose(res2, res, rtol=1e-6) xy = np.concatenate((x, y)) res_1s = runstest_1samp(xy) assert_allclose(res_1s, res1, rtol=1e-6) # check cutoff res2_1s = runstest_1samp(xy, xy.mean()) assert_allclose(res2_1s, res_1s, rtol=1e-6) statsmodels-0.12.2/statsmodels/stats/tests/test_oaxaca.py000066400000000000000000000203731400612667500236610ustar00rootroot00000000000000# -*- coding: utf-8 -*- # STATA adds a constant no matter if you want to or not, # so I cannot test for having no intercept. This also would make # no sense for Oaxaca. All of these stata_results # are from using the oaxaca command in STATA. import numpy as np from statsmodels.datasets.ccard.data import load_pandas from statsmodels.stats.oaxaca import OaxacaBlinder from statsmodels.tools.tools import add_constant pandas_df = load_pandas() endog = pandas_df.endog.values exog = add_constant(pandas_df.exog.values, prepend=False) pd_endog, pd_exog = pandas_df.endog, add_constant( pandas_df.exog, prepend=False) class TestOaxaca(object): @classmethod def setup_class(cls): cls.model = OaxacaBlinder(endog, exog, 3) def test_results(self): stata_results = np.array([158.7504, 321.7482, 75.45371, -238.4515]) stata_results_pooled = np.array([158.7504, 130.8095, 27.94091]) char, coef, inter, gap = self.model.three_fold().params unexp, exp, gap = self.model.two_fold().params np.testing.assert_almost_equal(gap, stata_results[0], 3) np.testing.assert_almost_equal(char, stata_results[1], 3) np.testing.assert_almost_equal(coef, stata_results[2], 3) np.testing.assert_almost_equal(inter, stata_results[3], 3) np.testing.assert_almost_equal(gap, stata_results_pooled[0], 3) np.testing.assert_almost_equal(exp, stata_results_pooled[1], 3) np.testing.assert_almost_equal(unexp, stata_results_pooled[2], 3) class TestOaxacaNoSwap(object): @classmethod def setup_class(cls): cls.model = OaxacaBlinder(endog, exog, 3, swap=False) def test_results(self): stata_results = np.array([-158.7504, -83.29674, 162.9978, -238.4515]) stata_results_pooled = np.array([-158.7504, -130.8095, -27.94091]) char, coef, inter, gap = self.model.three_fold().params unexp, exp, gap = self.model.two_fold().params np.testing.assert_almost_equal(gap, stata_results[0], 3) np.testing.assert_almost_equal(char, stata_results[1], 3) np.testing.assert_almost_equal(coef, stata_results[2], 3) np.testing.assert_almost_equal(inter, stata_results[3], 3) np.testing.assert_almost_equal(gap, stata_results_pooled[0], 3) np.testing.assert_almost_equal(exp, stata_results_pooled[1], 3) np.testing.assert_almost_equal(unexp, stata_results_pooled[2], 3) class TestOaxacaPandas(object): @classmethod def setup_class(cls): cls.model = OaxacaBlinder(pd_endog, pd_exog, 'OWNRENT') def test_results(self): stata_results = np.array([158.7504, 321.7482, 75.45371, -238.4515]) stata_results_pooled = np.array([158.7504, 130.8095, 27.94091]) char, coef, inter, gap = self.model.three_fold().params unexp, exp, gap = self.model.two_fold().params np.testing.assert_almost_equal(gap, stata_results[0], 3) np.testing.assert_almost_equal(char, stata_results[1], 3) np.testing.assert_almost_equal(coef, stata_results[2], 3) np.testing.assert_almost_equal(inter, stata_results[3], 3) np.testing.assert_almost_equal(gap, stata_results_pooled[0], 3) np.testing.assert_almost_equal(exp, stata_results_pooled[1], 3) np.testing.assert_almost_equal(unexp, stata_results_pooled[2], 3) class TestOaxacaPandasNoSwap(object): @classmethod def setup_class(cls): cls.model = OaxacaBlinder(pd_endog, pd_exog, 'OWNRENT', swap=False) def test_results(self): stata_results = np.array([-158.7504, -83.29674, 162.9978, -238.4515]) stata_results_pooled = np.array([-158.7504, -130.8095, -27.94091]) char, coef, inter, gap = self.model.three_fold().params unexp, exp, gap = self.model.two_fold().params np.testing.assert_almost_equal(gap, stata_results[0], 3) np.testing.assert_almost_equal(char, stata_results[1], 3) np.testing.assert_almost_equal(coef, stata_results[2], 3) np.testing.assert_almost_equal(inter, stata_results[3], 3) np.testing.assert_almost_equal(gap, stata_results_pooled[0], 3) np.testing.assert_almost_equal(exp, stata_results_pooled[1], 3) np.testing.assert_almost_equal(unexp, stata_results_pooled[2], 3) class TestOaxacaNoConstPassed(object): @classmethod def setup_class(cls): cls.model = OaxacaBlinder(pandas_df.endog.values, pandas_df.exog.values, 3, hasconst=False) def test_results(self): stata_results = np.array([158.7504, 321.7482, 75.45371, -238.4515]) stata_results_pooled = np.array([158.7504, 130.8095, 27.94091]) char, coef, inter, gap = self.model.three_fold().params unexp, exp, gap = self.model.two_fold().params np.testing.assert_almost_equal(gap, stata_results[0], 3) np.testing.assert_almost_equal(char, stata_results[1], 3) np.testing.assert_almost_equal(coef, stata_results[2], 3) np.testing.assert_almost_equal(inter, stata_results[3], 3) np.testing.assert_almost_equal(gap, stata_results_pooled[0], 3) np.testing.assert_almost_equal(exp, stata_results_pooled[1], 3) np.testing.assert_almost_equal(unexp, stata_results_pooled[2], 3) class TestOaxacaNoSwapNoConstPassed(object): @classmethod def setup_class(cls): cls.model = OaxacaBlinder(pandas_df.endog.values, pandas_df.exog.values, 3, hasconst=False, swap=False) def test_results(self): stata_results = np.array([-158.7504, -83.29674, 162.9978, -238.4515]) stata_results_pooled = np.array([-158.7504, -130.8095, -27.94091]) char, coef, inter, gap = self.model.three_fold().params unexp, exp, gap = self.model.two_fold().params np.testing.assert_almost_equal(gap, stata_results[0], 3) np.testing.assert_almost_equal(char, stata_results[1], 3) np.testing.assert_almost_equal(coef, stata_results[2], 3) np.testing.assert_almost_equal(inter, stata_results[3], 3) np.testing.assert_almost_equal(gap, stata_results_pooled[0], 3) np.testing.assert_almost_equal(exp, stata_results_pooled[1], 3) np.testing.assert_almost_equal(unexp, stata_results_pooled[2], 3) class TestOaxacaPandasNoConstPassed(object): @classmethod def setup_class(cls): cls.model = OaxacaBlinder(pandas_df.endog, pandas_df.exog, 'OWNRENT', hasconst=False) def test_results(self): stata_results = np.array([158.7504, 321.7482, 75.45371, -238.4515]) stata_results_pooled = np.array([158.7504, 130.8095, 27.94091]) char, coef, inter, gap = self.model.three_fold().params unexp, exp, gap = self.model.two_fold().params np.testing.assert_almost_equal(gap, stata_results[0], 3) np.testing.assert_almost_equal(char, stata_results[1], 3) np.testing.assert_almost_equal(coef, stata_results[2], 3) np.testing.assert_almost_equal(inter, stata_results[3], 3) np.testing.assert_almost_equal(gap, stata_results_pooled[0], 3) np.testing.assert_almost_equal(exp, stata_results_pooled[1], 3) np.testing.assert_almost_equal(unexp, stata_results_pooled[2], 3) class TestOaxacaPandasNoSwapNoConstPassed(object): @classmethod def setup_class(cls): cls.model = OaxacaBlinder(pandas_df.endog, pandas_df.exog, 'OWNRENT', hasconst=False, swap=False) def test_results(self): stata_results = np.array([-158.7504, -83.29674, 162.9978, -238.4515]) stata_results_pooled = np.array([-158.7504, -130.8095, -27.94091]) char, coef, inter, gap = self.model.three_fold().params unexp, exp, gap = self.model.two_fold().params np.testing.assert_almost_equal(gap, stata_results[0], 3) np.testing.assert_almost_equal(char, stata_results[1], 3) np.testing.assert_almost_equal(coef, stata_results[2], 3) np.testing.assert_almost_equal(inter, stata_results[3], 3) np.testing.assert_almost_equal(gap, stata_results_pooled[0], 3) np.testing.assert_almost_equal(exp, stata_results_pooled[1], 3) np.testing.assert_almost_equal(unexp, stata_results_pooled[2], 3) statsmodels-0.12.2/statsmodels/stats/tests/test_oneway.py000066400000000000000000000531501400612667500237260ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Mar 18 17:45:51 2020 Author: Josef Perktold License: BSD-3 """ import numpy as np from numpy.testing import assert_allclose, assert_equal import pytest from statsmodels.regression.linear_model import OLS import statsmodels.stats.power as smpwr import statsmodels.stats.oneway as smo # needed for function with `test` from statsmodels.stats.oneway import ( confint_effectsize_oneway, confint_noncentrality, effectsize_oneway, anova_oneway, anova_generic, equivalence_oneway, equivalence_oneway_generic, power_equivalence_oneway, _power_equivalence_oneway_emp, f2_to_wellek, fstat_to_wellek, wellek_to_f2) from statsmodels.stats.robust_compare import scale_transform from statsmodels.stats.contrast import ( wald_test_noncent_generic, wald_test_noncent, _offset_constraint) def test_oneway_effectsize(): # examole 3 in Steiger 2004 Beyond the F-test, p. 169 F = 5 df1 = 3 df2 = 76 nobs = 80 ci = confint_noncentrality(F, (df1, df2), alpha=0.05, alternative="two-sided") ci_es = confint_effectsize_oneway(F, (df1, df2), alpha=0.05) ci_steiger = ci_es.ci_f * np.sqrt(4 / 3) res_ci_steiger = [0.1764, 0.7367] res_ci_nc = np.asarray([1.8666, 32.563]) assert_allclose(ci, res_ci_nc, atol=0.0001) assert_allclose(ci_es.ci_f_corrected, res_ci_steiger, atol=0.00006) assert_allclose(ci_steiger, res_ci_steiger, atol=0.00006) assert_allclose(ci_es.ci_f**2, res_ci_nc / nobs, atol=0.00006) assert_allclose(ci_es.ci_nc, res_ci_nc, atol=0.0001) def test_effectsize_power(): # example and results from PASS documentation n_groups = 3 means = [527.86, 660.43, 649.14] vars_ = 107.4304**2 nobs = 12 es = effectsize_oneway(means, vars_, nobs, use_var="equal", ddof_between=0) es = np.sqrt(es) alpha = 0.05 power = 0.8 nobs_t = nobs * n_groups kwds = {'effect_size': es, 'nobs': nobs_t, 'alpha': alpha, 'power': power, 'k_groups': n_groups} from statsmodels.stats.power import FTestAnovaPower res_pow = 0.8251 res_es = 0.559 kwds_ = kwds.copy() del kwds_['power'] p = FTestAnovaPower().power(**kwds_) assert_allclose(p, res_pow, atol=0.0001) assert_allclose(es, res_es, atol=0.0006) # example unequal sample sizes nobs = np.array([15, 9, 9]) kwds['nobs'] = nobs es = effectsize_oneway(means, vars_, nobs, use_var="equal", ddof_between=0) es = np.sqrt(es) kwds['effect_size'] = es p = FTestAnovaPower().power(**kwds_) res_pow = 0.8297 res_es = 0.590 assert_allclose(p, res_pow, atol=0.005) # lower than print precision assert_allclose(es, res_es, atol=0.0006) def test_effectsize_fstat(): # results from R package `effectsize`, confint is 0.9 confidence # > es = F_to_eta2(45.8, 3, 35) Eta_Sq_partial = 0.796983758700696 CI_eta2 = 0.685670133284926, 0.855981325777856 # reformated from output # > es = F_to_epsilon2(45.8, 3, 35) Epsilon_Sq_partial = 0.779582366589327 CI_eps2 = 0.658727573280777, 0.843636867987386 # > es = F_to_omega2(45.8, 3, 35) Omega_Sq_partial = 0.775086505190311 CI_omega2 = 0.65286429480169, 0.840179680453464 # > es = F_to_f(45.8, 3, 35) Cohens_f_partial = 1.98134153686695 CI_f = 1.47694659580859, 2.43793847155554 f_stat, df1, df2 = 45.8, 3, 35 # nobs = df1 + df2 + 1 # not directly used in the following, only df fes = smo._fstat2effectsize(f_stat, (df1, df2)) assert_allclose(np.sqrt(fes.f2), Cohens_f_partial, rtol=1e-13) assert_allclose(fes.eta2, Eta_Sq_partial, rtol=1e-13) assert_allclose(fes.eps2, Epsilon_Sq_partial, rtol=1e-13) assert_allclose(fes.omega2, Omega_Sq_partial, rtol=1e-13) ci_nc = confint_noncentrality(f_stat, (df1, df2), alpha=0.1) # the following replicates R package effectsize ci_es = smo._fstat2effectsize(ci_nc / df1, (df1, df2)) assert_allclose(ci_es.eta2, CI_eta2, rtol=2e-4) assert_allclose(ci_es.eps2, CI_eps2, rtol=2e-4) assert_allclose(ci_es.omega2, CI_omega2, rtol=2e-4) assert_allclose(np.sqrt(ci_es.f2), CI_f, rtol=2e-4) def test_effectsize_fstat_stata(): # reference numbers computed with Stata 14 # Stata 16 does not seem to have confint for omega2 # esizei 2 40 7.47403193349075, level(90) eta2 = 0.2720398648288652 lb_eta2 = 0.0742092468714613 ub_eta2 = 0.4156116886974804 omega2 = 0.2356418580703085 lb_omega2 = 0.0279197092150344 ub_omega2 = 0.3863922731323545 # level = 90 f_stat, df1, df2 = 7.47403193349075, 2, 40 fes = smo._fstat2effectsize(f_stat, (df1, df2)) assert_allclose(fes.eta2, eta2, rtol=1e-13) assert_allclose(fes.omega2, omega2, rtol=0.02) # low agreement ci_es = smo.confint_effectsize_oneway(f_stat, (df1, df2), alpha=0.1) assert_allclose(ci_es.eta2, (lb_eta2, ub_eta2), rtol=1e-4) assert_allclose(ci_es.ci_omega2, (lb_omega2, ub_omega2), rtol=0.025) @pytest.mark.parametrize("center", ['median', 'mean', 'trimmed']) def test_scale_transform(center): x = np.random.randn(5, 3) xt = scale_transform(x, center=center, transform='abs', trim_frac=0.2, axis=0) xtt = scale_transform(x.T, center=center, transform='abs', trim_frac=0.2, axis=1) assert_allclose(xt.T, xtt, rtol=1e-13) xt0 = scale_transform(x[:, 0], center=center, transform='abs', trim_frac=0.2) assert_allclose(xt0, xt[:, 0], rtol=1e-13) assert_allclose(xt0, xtt[0, :], rtol=1e-13) class TestOnewayEquivalenc(object): @classmethod def setup_class(cls): y0 = [112.488, 103.738, 86.344, 101.708, 95.108, 105.931, 95.815, 91.864, 102.479, 102.644] y1 = [100.421, 101.966, 99.636, 105.983, 88.377, 102.618, 105.486, 98.662, 94.137, 98.626, 89.367, 106.204] y2 = [84.846, 100.488, 119.763, 103.736, 93.141, 108.254, 99.510, 89.005, 108.200, 82.209, 100.104, 103.706, 107.067] y3 = [100.825, 100.255, 103.363, 93.230, 95.325, 100.288, 94.750, 107.129, 98.246, 96.365, 99.740, 106.049, 92.691, 93.111, 98.243] n_groups = 4 arrs_w = [np.asarray(yi) for yi in [y0, y1, y2, y3]] nobs = np.asarray([len(yi) for yi in arrs_w]) nobs_mean = np.mean(nobs) means = np.asarray([yi.mean() for yi in arrs_w]) stds = np.asarray([yi.std(ddof=1) for yi in arrs_w]) cls.data = arrs_w # TODO use `data` cls.means = means cls.nobs = nobs cls.stds = stds cls.n_groups = n_groups cls.nobs_mean = nobs_mean def test_equivalence_equal(self): # reference numbers from Jan and Shieh 2019, p. 5 means = self.means nobs = self.nobs stds = self.stds n_groups = self.n_groups eps = 0.5 res0 = anova_generic(means, stds**2, nobs, use_var="equal") f = res0.statistic res = equivalence_oneway_generic(f, n_groups, nobs.sum(), eps, res0.df, alpha=0.05, margin_type="wellek") assert_allclose(res.pvalue, 0.0083, atol=0.001) assert_equal(res.df, [3, 46]) # the agreement for f-stat looks too low assert_allclose(f, 0.0926, atol=0.0006) res = equivalence_oneway(self.data, eps, use_var="equal", margin_type="wellek") assert_allclose(res.pvalue, 0.0083, atol=0.001) assert_equal(res.df, [3, 46]) def test_equivalence_welch(self): # reference numbers from Jan and Shieh 2019, p. 6 means = self.means nobs = self.nobs stds = self.stds n_groups = self.n_groups vars_ = stds**2 eps = 0.5 res0 = anova_generic(means, vars_, nobs, use_var="unequal", welch_correction=False) f_stat = res0.statistic res = equivalence_oneway_generic(f_stat, n_groups, nobs.sum(), eps, res0.df, alpha=0.05, margin_type="wellek") assert_allclose(res.pvalue, 0.0110, atol=0.001) assert_allclose(res.df, [3.0, 22.6536], atol=0.0006) # agreement for Welch f-stat looks too low b/c welch_correction=False assert_allclose(f_stat, 0.1102, atol=0.007) res = equivalence_oneway(self.data, eps, use_var="unequal", margin_type="wellek") assert_allclose(res.pvalue, 0.0110, atol=1e-4) assert_allclose(res.df, [3.0, 22.6536], atol=0.0006) assert_allclose(res.f_stat, 0.1102, atol=1e-4) # 0.007) # check post-hoc power, JS p. 6 pow_ = _power_equivalence_oneway_emp(f_stat, n_groups, nobs, eps, res0.df) assert_allclose(pow_, 0.1552, atol=0.007) pow_ = power_equivalence_oneway(eps, eps, nobs.sum(), n_groups=n_groups, df=None, alpha=0.05, margin_type="wellek") assert_allclose(pow_, 0.05, atol=1e-13) nobs_t = nobs.sum() es = effectsize_oneway(means, vars_, nobs, use_var="unequal") es = np.sqrt(es) es_w0 = f2_to_wellek(es**2, n_groups) es_w = np.sqrt(fstat_to_wellek(f_stat, n_groups, nobs_t / n_groups)) pow_ = power_equivalence_oneway(es_w, eps, nobs_t, n_groups=n_groups, df=None, alpha=0.05, margin_type="wellek") assert_allclose(pow_, 0.1552, atol=0.007) assert_allclose(es_w0, es_w, atol=0.007) margin = wellek_to_f2(eps, n_groups) pow_ = power_equivalence_oneway(es**2, margin, nobs_t, n_groups=n_groups, df=None, alpha=0.05, margin_type="f2") assert_allclose(pow_, 0.1552, atol=0.007) class TestOnewayScale(object): @classmethod def setup_class(cls): yt0 = np.array([102., 320., 0., 107., 198., 200., 4., 20., 110., 128., 7., 119., 309.]) yt1 = np.array([0., 1., 228., 81., 87., 119., 79., 181., 43., 12., 90., 105., 108., 119., 0., 9.]) yt2 = np.array([33., 294., 134., 216., 83., 105., 69., 20., 20., 63., 98., 155., 78., 75.]) y0 = np.array([452., 874., 554., 447., 356., 754., 558., 574., 664., 682., 547., 435., 245.]) y1 = np.array([546., 547., 774., 465., 459., 665., 467., 365., 589., 534., 456., 651., 654., 665., 546., 537.]) y2 = np.array([785., 458., 886., 536., 669., 857., 821., 772., 732., 689., 654., 597., 830., 827.]) n_groups = 3 data = [y0, y1, y2] nobs = np.asarray([len(yi) for yi in data]) nobs_mean = np.mean(nobs) means = np.asarray([yi.mean() for yi in data]) stds = np.asarray([yi.std(ddof=1) for yi in data]) cls.data = data cls.data_transformed = [yt0, yt1, yt2] cls.means = means cls.nobs = nobs cls.stds = stds cls.n_groups = n_groups cls.nobs_mean = nobs_mean def test_means(self): # library onewaystats, BF test for equality of means # st = bf.test(y ~ g, df3) statistic = 7.10900606421182 parameter = [2, 31.4207256105052] p_value = 0.00283841965791224 # method = 'Brown-Forsythe Test' res = anova_oneway(self.data, use_var="bf") # R bf.test uses original BF df_num assert_allclose(res.pvalue2, p_value, rtol=1e-13) assert_allclose(res.statistic, statistic, rtol=1e-13) assert_allclose([res.df_num2, res.df_denom], parameter) def test_levene(self): data = self.data # lawstat: Test Statistic = 1.0866123063642, p-value = 0.3471072204516 statistic = 1.0866123063642 p_value = 0.3471072204516 res0 = smo.test_scale_oneway(data, method='equal', center='median', transform='abs', trim_frac_mean=0.2) assert_allclose(res0.pvalue, p_value, rtol=1e-13) assert_allclose(res0.statistic, statistic, rtol=1e-13) # library car # > lt = leveneTest(y ~ g, df3, center=mean, trim=0.2) statistic = 1.10732113109744 p_value = 0.340359251994645 df = [2, 40] res0 = smo.test_scale_oneway(data, method='equal', center='trimmed', transform='abs', trim_frac_mean=0.2) assert_allclose(res0.pvalue, p_value, rtol=1e-13) assert_allclose(res0.statistic, statistic, rtol=1e-13) assert_allclose(res0.df, df) # library(onewaytests) # test uses mean as center # > st = homog.test(y ~ g, df3) statistic = 1.07894485177512 parameter = [2, 40] # df p_value = 0.349641166869223 # method = "Levene's Homogeneity Test" res0 = smo.test_scale_oneway(data, method='equal', center='mean', transform='abs', trim_frac_mean=0.2) assert_allclose(res0.pvalue, p_value, rtol=1e-13) assert_allclose(res0.statistic, statistic, rtol=1e-13) assert_allclose(res0.df, parameter) # > st = homog.test(y ~ g, df3, method = "Bartlett") statistic = 3.01982414477323 # parameter = 2 # scipy bartlett does not return df p_value = 0.220929402900495 # method = "Bartlett's Homogeneity Test" # Bartlett is in scipy.stats from scipy import stats stat, pv = stats.bartlett(*data) assert_allclose(pv, p_value, rtol=1e-13) assert_allclose(stat, statistic, rtol=1e-13) def test_options(self): # regression tests for options, # many might not be implemented in other packages data = self.data # regression numbers from initial run statistic, p_value = 1.0173464626246675, 0.3763806150460239 df = (2.0, 24.40374758005409) res = smo.test_scale_oneway(data, method='unequal', center='median', transform='abs', trim_frac_mean=0.2) assert_allclose(res.pvalue, p_value, rtol=1e-13) assert_allclose(res.statistic, statistic, rtol=1e-13) assert_allclose(res.df, df) statistic, p_value = 1.0329722145270606, 0.3622778213868562 df = (1.83153791573948, 30.6733640949525) p_value2 = 0.3679999679787619 df2 = (2, 30.6733640949525) res = smo.test_scale_oneway(data, method='bf', center='median', transform='abs', trim_frac_mean=0.2) assert_allclose(res.pvalue, p_value, rtol=1e-13) assert_allclose(res.statistic, statistic, rtol=1e-13) assert_allclose(res.df, df) assert_allclose(res.pvalue2, p_value2, rtol=1e-13) assert_allclose(res.df2, df2) statistic, p_value = 1.7252431333701745, 0.19112038168209514 df = (2.0, 40.0) res = smo.test_scale_oneway(data, method='equal', center='mean', transform='square', trim_frac_mean=0.2) assert_allclose(res.pvalue, p_value, rtol=1e-13) assert_allclose(res.statistic, statistic, rtol=1e-13) assert_equal(res.df, df) statistic, p_value = 0.4129696057329463, 0.6644711582864451 df = (2.0, 40.0) res = smo.test_scale_oneway(data, method='equal', center='mean', transform=lambda x: np.log(x * x), # noqa trim_frac_mean=0.2) assert_allclose(res.pvalue, p_value, rtol=1e-13) assert_allclose(res.statistic, statistic, rtol=1e-13) assert_allclose(res.df, df) # compare no transform with standard anova res = smo.test_scale_oneway(data, method='unequal', center=0, transform='identity', trim_frac_mean=0.2) res2 = anova_oneway(self.data, use_var="unequal") assert_allclose(res.pvalue, res2.pvalue, rtol=1e-13) assert_allclose(res.statistic, res2.statistic, rtol=1e-13) assert_allclose(res.df, res2.df) def test_equivalence(self): data = self.data # compare no transform with standard anova res = smo.equivalence_scale_oneway(data, 0.5, method='unequal', center=0, transform='identity') res2 = equivalence_oneway(self.data, 0.5, use_var="unequal") assert_allclose(res.pvalue, res2.pvalue, rtol=1e-13) assert_allclose(res.statistic, res2.statistic, rtol=1e-13) assert_allclose(res.df, res2.df) res = smo.equivalence_scale_oneway(data, 0.5, method='bf', center=0, transform='identity') res2 = equivalence_oneway(self.data, 0.5, use_var="bf") assert_allclose(res.pvalue, res2.pvalue, rtol=1e-13) assert_allclose(res.statistic, res2.statistic, rtol=1e-13) assert_allclose(res.df, res2.df) class TestOnewayOLS(object): @classmethod def setup_class(cls): y0 = [112.488, 103.738, 86.344, 101.708, 95.108, 105.931, 95.815, 91.864, 102.479, 102.644] y1 = [100.421, 101.966, 99.636, 105.983, 88.377, 102.618, 105.486, 98.662, 94.137, 98.626, 89.367, 106.204] y2 = [84.846, 100.488, 119.763, 103.736, 93.141, 108.254, 99.510, 89.005, 108.200, 82.209, 100.104, 103.706, 107.067] y3 = [100.825, 100.255, 103.363, 93.230, 95.325, 100.288, 94.750, 107.129, 98.246, 96.365, 99.740, 106.049, 92.691, 93.111, 98.243] cls.k_groups = k = 4 cls.data = data = [y0, y1, y2, y3] cls.nobs = nobs = np.asarray([len(yi) for yi in data]) groups = np.repeat(np.arange(k), nobs) cls.ex = (groups[:, None] == np.arange(k)).astype(np.int64) cls.y = np.concatenate(data) def test_ols_noncentrality(self): k = self.k_groups res_ols = OLS(self.y, self.ex).fit() nobs_t = res_ols.model.nobs # constraint c_equal = -np.eye(k)[1:] c_equal[:, 0] = 1 v = np.zeros(c_equal.shape[0]) # noncentrality at estimated parameters wt = res_ols.wald_test(c_equal) df_num, df_denom = wt.df_num, wt.df_denom cov_p = res_ols.cov_params() nc_wt = wald_test_noncent_generic(res_ols.params, c_equal, v, cov_p, diff=None, joint=True) assert_allclose(nc_wt, wt.statistic * wt.df_num, rtol=1e-13) nc_wt2 = wald_test_noncent(res_ols.params, c_equal, v, res_ols, diff=None, joint=True) assert_allclose(nc_wt2, nc_wt, rtol=1e-13) es_ols = nc_wt / nobs_t es_oneway = smo.effectsize_oneway(res_ols.params, res_ols.scale, self.nobs, use_var="equal") assert_allclose(es_ols, es_oneway, rtol=1e-13) alpha = 0.05 pow_ols = smpwr.ftest_power(np.sqrt(es_ols), df_denom, df_num, alpha, ncc=1) pow_oneway = smpwr.ftest_anova_power(np.sqrt(es_oneway), nobs_t, alpha, k_groups=k, df=None) assert_allclose(pow_ols, pow_oneway, rtol=1e-13) # noncentrality at other params params_alt = res_ols.params * 0.75 # compute constraint value so we can get noncentrality from wald_test v_off = _offset_constraint(c_equal, res_ols.params, params_alt) wt_off = res_ols.wald_test((c_equal, v + v_off)) nc_wt_off = wald_test_noncent_generic(params_alt, c_equal, v, cov_p, diff=None, joint=True) assert_allclose(nc_wt_off, wt_off.statistic * wt_off.df_num, rtol=1e-13) # check vectorized version, joint=False nc_wt_vec = wald_test_noncent_generic(params_alt, c_equal, v, cov_p, diff=None, joint=False) for i in range(c_equal.shape[0]): nc_wt_i = wald_test_noncent_generic(params_alt, c_equal[i : i + 1], # noqa v[i : i + 1], cov_p, diff=None, # noqa joint=False) assert_allclose(nc_wt_vec[i], nc_wt_i, rtol=1e-13) def test_simulate_equivalence(): # regression test, needs large k_mc to be reliable k_groups = 4 k_repl = 10 nobs = np.array([10, 12, 13, 15]) * k_repl means = np.array([-1, 0, 0, 1]) * 0.12 vars_ = np.array([1, 2, 3, 4]) nobs_t = nobs.sum() eps = 0.0191 * 10 opt_var = ["unequal", "equal", "bf"] k_mc = 100 np.random.seed(987126) res_mc = smo.simulate_power_equivalence_oneway( means, nobs, eps, vars_=vars_, k_mc=k_mc, trim_frac=0.1, options_var=opt_var, margin_type="wellek") frac_reject = (res_mc.pvalue <= 0.05).sum(0) / k_mc assert_allclose(frac_reject, [0.17, 0.18, 0.14], atol=0.001) # result with k_mc = 10000 is [0.1466, 0.1871, 0.1606] # similar to asy below, but not very close for all es_alt_li = [] for uv in opt_var: es = effectsize_oneway(means, vars_, nobs, use_var=uv) es_alt_li.append(es) # compute asy power as comparison margin = wellek_to_f2(eps, k_groups) pow_ = [power_equivalence_oneway( es_, margin, nobs_t, n_groups=k_groups, df=None, alpha=0.05, margin_type="f2") for es_ in es_alt_li] # regression test numbers assert_allclose(pow_, [0.147749, 0.173358, 0.177412], atol=0.007) statsmodels-0.12.2/statsmodels/stats/tests/test_outliers_influence.py000066400000000000000000000010561400612667500263200ustar00rootroot00000000000000from numpy.testing import assert_almost_equal from statsmodels.datasets import statecrime from statsmodels.regression.linear_model import OLS from statsmodels.stats.outliers_influence import reset_ramsey from statsmodels.tools import add_constant data = statecrime.load_pandas().data def test_reset_stata(): mod = OLS(data.violent, add_constant(data[['murder', 'hs_grad']])) res = mod.fit() stat = reset_ramsey(res, degree=4) assert_almost_equal(stat.fvalue[0, 0], 1.52, decimal=2) assert_almost_equal(stat.pvalue, 0.2221, decimal=4) statsmodels-0.12.2/statsmodels/stats/tests/test_pairwise.py000066400000000000000000000312231400612667500242440ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Mar 28 15:34:18 2012 Author: Josef Perktold """ from statsmodels.compat.python import asbytes from io import BytesIO import warnings import numpy as np import pandas as pd import pytest from numpy.testing import assert_, assert_allclose, assert_almost_equal, assert_equal, \ assert_raises from statsmodels.stats.libqsturng import qsturng from statsmodels.stats.multicomp import (tukeyhsd, pairwise_tukeyhsd, MultiComparison) ss = '''\ 43.9 1 1 39.0 1 2 46.7 1 3 43.8 1 4 44.2 1 5 47.7 1 6 43.6 1 7 38.9 1 8 43.6 1 9 40.0 1 10 89.8 2 1 87.1 2 2 92.7 2 3 90.6 2 4 87.7 2 5 92.4 2 6 86.1 2 7 88.1 2 8 90.8 2 9 89.1 2 10 68.4 3 1 69.3 3 2 68.5 3 3 66.4 3 4 70.0 3 5 68.1 3 6 70.6 3 7 65.2 3 8 63.8 3 9 69.2 3 10 36.2 4 1 45.2 4 2 40.7 4 3 40.5 4 4 39.3 4 5 40.3 4 6 43.2 4 7 38.7 4 8 40.9 4 9 39.7 4 10''' #idx Treatment StressReduction ss2 = '''\ 1 mental 2 2 mental 2 3 mental 3 4 mental 4 5 mental 4 6 mental 5 7 mental 3 8 mental 4 9 mental 4 10 mental 4 11 physical 4 12 physical 4 13 physical 3 14 physical 5 15 physical 4 16 physical 1 17 physical 1 18 physical 2 19 physical 3 20 physical 3 21 medical 1 22 medical 2 23 medical 2 24 medical 2 25 medical 3 26 medical 2 27 medical 3 28 medical 1 29 medical 3 30 medical 1''' ss3 = '''\ 1 24.5 1 23.5 1 26.4 1 27.1 1 29.9 2 28.4 2 34.2 2 29.5 2 32.2 2 30.1 3 26.1 3 28.3 3 24.3 3 26.2 3 27.8''' ss5 = '''\ 2 - 3\t4.340\t0.691\t7.989\t*** 2 - 1\t4.600\t0.951\t8.249\t*** 3 - 2\t-4.340\t-7.989\t-0.691\t*** 3 - 1\t0.260\t-3.389\t3.909\t- 1 - 2\t-4.600\t-8.249\t-0.951\t*** 1 - 3\t-0.260\t-3.909\t3.389\t- ''' cylinders = np.array([8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 6, 6, 6, 4, 4, 4, 4, 4, 4, 6, 8, 8, 8, 8, 4, 4, 4, 4, 8, 8, 8, 8, 6, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 4, 4, 8, 4, 6, 6, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4]) cyl_labels = np.array(['USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'France', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'Japan', 'USA', 'USA', 'USA', 'Japan', 'Germany', 'France', 'Germany', 'Sweden', 'Germany', 'USA', 'USA', 'USA', 'USA', 'USA', 'Germany', 'USA', 'USA', 'France', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'Germany', 'Japan', 'USA', 'USA', 'USA', 'USA', 'Germany', 'Japan', 'Japan', 'USA', 'Sweden', 'USA', 'France', 'Japan', 'Germany', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'USA', 'Germany', 'Japan', 'Japan', 'USA', 'USA', 'Japan', 'Japan', 'Japan', 'Japan', 'Japan', 'Japan', 'USA', 'USA', 'USA', 'USA', 'Japan', 'USA', 'USA', 'USA', 'Germany', 'USA', 'USA', 'USA']) #accommodate recfromtxt for python 3.2, requires bytes ss = asbytes(ss) ss2 = asbytes(ss2) ss3 = asbytes(ss3) ss5 = asbytes(ss5) dta = pd.read_csv(BytesIO(ss), sep=r'\s+', header=None, engine='python') dta.columns = "Rust", "Brand", "Replication" dta2 = pd.read_csv(BytesIO(ss2), sep=r'\s+', header=None, engine='python') dta2.columns = "idx", "Treatment", "StressReduction" dta2["Treatment"] = dta2["Treatment"].map(lambda v: v.encode('utf-8')) dta3 = pd.read_csv(BytesIO(ss3), sep=r'\s+', header=None, engine='python') dta3.columns = ["Brand", "Relief"] dta5 = pd.read_csv(BytesIO(ss5), sep=r'\t', header=None, engine='python') dta5.columns = ['pair', 'mean', 'lower', 'upper', 'sig'] for col in ('pair', 'sig'): dta5[col] = dta5[col].map(lambda v: v.encode('utf-8')) sas_ = dta5.iloc[[1, 3, 2]] def get_thsd(mci, alpha=0.05): var_ = np.var(mci.groupstats.groupdemean(), ddof=len(mci.groupsunique)) means = mci.groupstats.groupmean nobs = mci.groupstats.groupnobs resi = tukeyhsd(means, nobs, var_, df=None, alpha=alpha, q_crit=qsturng(1-alpha, len(means), (nobs-1).sum())) #print resi[4] var2 = (mci.groupstats.groupvarwithin() * (nobs - 1.)).sum() \ / (nobs - 1.).sum() #print nobs, (nobs - 1).sum() #print mci.groupstats.groupvarwithin() assert_almost_equal(var_, var2, decimal=14) return resi class CheckTuckeyHSDMixin(object): @classmethod def setup_class_(cls): cls.mc = MultiComparison(cls.endog, cls.groups) cls.res = cls.mc.tukeyhsd(alpha=cls.alpha) def test_multicomptukey(self): assert_almost_equal(self.res.meandiffs, self.meandiff2, decimal=14) assert_almost_equal(self.res.confint, self.confint2, decimal=2) assert_equal(self.res.reject, self.reject2) def test_group_tukey(self): res_t = get_thsd(self.mc, alpha=self.alpha) assert_almost_equal(res_t[4], self.confint2, decimal=2) def test_shortcut_function(self): #check wrapper function res = pairwise_tukeyhsd(self.endog, self.groups, alpha=self.alpha) assert_almost_equal(res.confint, self.res.confint, decimal=14) @pytest.mark.smoke @pytest.mark.matplotlib def test_plot_simultaneous_ci(self, close_figures): self.res._simultaneous_ci() reference = self.res.groupsunique[1] self.res.plot_simultaneous(comparison_name=reference) class TestTuckeyHSD2(CheckTuckeyHSDMixin): @classmethod def setup_class(cls): #balanced case cls.endog = dta2['StressReduction'] cls.groups = dta2['Treatment'] cls.alpha = 0.05 cls.setup_class_() #in super #from R tukeyhsd2s = np.array([ 1.5,1,-0.5,0.3214915, -0.1785085,-1.678509,2.678509,2.178509, 0.6785085,0.01056279,0.1079035,0.5513904] ).reshape(3,4, order='F') cls.meandiff2 = tukeyhsd2s[:, 0] cls.confint2 = tukeyhsd2s[:, 1:3] pvals = tukeyhsd2s[:, 3] cls.reject2 = pvals < 0.05 def test_table_names_default_group_order(self): t = self.res._results_table # if the group_order parameter is not used, the groups should # be reported in alphabetical order expected_order = [(b'medical', b'mental'), (b'medical', b'physical'), (b'mental', b'physical')] for i in range(1, 4): first_group = t[i][0].data second_group = t[i][1].data assert_((first_group, second_group) == expected_order[i - 1]) def test_table_names_custom_group_order(self): # if the group_order parameter is used, the groups should # be reported in the specified order mc = MultiComparison(self.endog, self.groups, group_order=[b'physical', b'medical', b'mental']) res = mc.tukeyhsd(alpha=self.alpha) #print(res) t = res._results_table expected_order = [(b'physical',b'medical'), (b'physical',b'mental'), (b'medical', b'mental')] for i in range(1, 4): first_group = t[i][0].data second_group = t[i][1].data assert_((first_group, second_group) == expected_order[i - 1]) class TestTuckeyHSD2Pandas(TestTuckeyHSD2): @classmethod def setup_class(cls): super(TestTuckeyHSD2Pandas, cls).setup_class() cls.endog = pd.Series(cls.endog) # we are working with bytes on python 3, not with strings in this case cls.groups = pd.Series(cls.groups, dtype=object) def test_incorrect_output(self): # too few groups with pytest.raises(ValueError): MultiComparison(np.array([1] * 10), [1, 2] * 4) # too many groups with pytest.raises(ValueError): MultiComparison(np.array([1] * 10), [1, 2] * 6) # just one group with pytest.raises(ValueError): MultiComparison(np.array([1] * 10), [1] * 10) # group_order does not select all observations, only one group left with warnings.catch_warnings(record=True) as w: warnings.simplefilter('always') assert_raises(ValueError, MultiComparison, np.array([1] * 10), [1, 2] * 5, group_order=[1]) # group_order does not select all observations, # we do tukey_hsd with reduced set of observations data = np.arange(15) groups = np.repeat([1, 2, 3], 5) with warnings.catch_warnings(record=True) as w: warnings.simplefilter('always') mod1 = MultiComparison(np.array(data), groups, group_order=[1, 2]) assert_equal(len(w), 1) assert issubclass(w[0].category, UserWarning) res1 = mod1.tukeyhsd(alpha=0.01) mod2 = MultiComparison(np.array(data[:10]), groups[:10]) res2 = mod2.tukeyhsd(alpha=0.01) attributes = ['confint', 'data', 'df_total', 'groups', 'groupsunique', 'meandiffs', 'q_crit', 'reject', 'reject2', 'std_pairs', 'variance'] for att in attributes: err_msg = att + 'failed' assert_allclose(getattr(res1, att), getattr(res2, att), rtol=1e-14, err_msg=err_msg) attributes = ['data', 'datali', 'groupintlab', 'groups', 'groupsunique', 'ngroups', 'nobs', 'pairindices'] for att in attributes: err_msg = att + 'failed' assert_allclose(getattr(mod1, att), getattr(mod2, att), rtol=1e-14, err_msg=err_msg) class TestTuckeyHSD2s(CheckTuckeyHSDMixin): @classmethod def setup_class(cls): #unbalanced case cls.endog = dta2['StressReduction'][3:29] cls.groups = dta2['Treatment'][3:29] cls.alpha = 0.01 cls.setup_class_() #from R tukeyhsd2s = np.array( [1.8888888888888889, 0.888888888888889, -1, 0.2658549, -0.5908785, -2.587133, 3.511923, 2.368656, 0.5871331, 0.002837638, 0.150456, 0.1266072] ).reshape(3,4, order='F') cls.meandiff2 = tukeyhsd2s[:, 0] cls.confint2 = tukeyhsd2s[:, 1:3] pvals = tukeyhsd2s[:, 3] cls.reject2 = pvals < 0.01 class TestTuckeyHSD3(CheckTuckeyHSDMixin): @classmethod def setup_class(cls): #SAS case cls.endog = dta3['Relief'] cls.groups = dta3['Brand'] cls.alpha = 0.05 cls.setup_class_() #super(cls, cls).setup_class_() #CheckTuckeyHSD.setup_class_() cls.meandiff2 = sas_['mean'] cls.confint2 = sas_[['lower','upper']].astype(float).values.reshape((3, 2)) cls.reject2 = sas_['sig'] == asbytes('***') class TestTuckeyHSD4(CheckTuckeyHSDMixin): @classmethod def setup_class(cls): #unbalanced case verified in Matlab cls.endog = cylinders cls.groups = cyl_labels cls.alpha = 0.05 cls.setup_class_() cls.res._simultaneous_ci() #from Matlab cls.halfwidth2 = np.array([1.5228335685980883, 0.9794949704444682, 0.78673802805533644, 2.3321237694566364, 0.57355135882752939]) cls.meandiff2 = np.array([0.22222222222222232, 0.13333333333333375, 0.0, 2.2898550724637685, -0.088888888888888573, -0.22222222222222232, 2.0676328502415462, -0.13333333333333375, 2.1565217391304348, 2.2898550724637685]) cls.confint2 = np.array([-2.32022210717, 2.76466655161, -2.247517583, 2.51418424967, -3.66405224956, 3.66405224956, 0.113960166573, 4.46574997835, -1.87278583908, 1.6950080613, -3.529655688, 3.08521124356, 0.568180988881, 3.5670847116, -3.31822643175, 3.05155976508, 0.951206924521, 3.36183655374, -0.74487911754, 5.32458926247]).reshape(10,2) cls.reject2 = np.array([False, False, False, True, False, False, True, False, True, False]) def test_hochberg_intervals(self): assert_almost_equal(self.res.halfwidths, self.halfwidth2, 14) statsmodels-0.12.2/statsmodels/stats/tests/test_panel_robustcov.py000066400000000000000000000052371400612667500256340ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Test for panel robust covariance estimators after pooled ols this follows the example from xtscc paper/help Created on Tue May 22 20:27:57 2012 Author: Josef Perktold """ from statsmodels.compat.python import lmap import numpy as np from numpy.testing import assert_almost_equal from statsmodels.regression.linear_model import OLS from statsmodels.tools.tools import add_constant import statsmodels.stats.sandwich_covariance as sw def test_panel_robust_cov(): import statsmodels.datasets.grunfeld as gr from .results.results_panelrobust import results as res_stata dtapa = gr.data.load_pandas() #Stata example/data seems to miss last firm dtapa_endog = dtapa.endog[:200] dtapa_exog = dtapa.exog[:200] res = OLS(dtapa_endog, add_constant(dtapa_exog[['value', 'capital']], prepend=False)).fit() #time indicator in range(max Ti) time = np.asarray(dtapa_exog[['year']]) time -= time.min() time = np.squeeze(time).astype(int) #sw.cov_nw_panel requires bounds instead of index tidx = [(i*20, 20*(i+1)) for i in range(10)] #firm index in range(n_firms) firm_names, firm_id = np.unique(np.asarray(dtapa_exog[['firm']], 'S20'), return_inverse=True) #panel newey west standard errors cov = sw.cov_nw_panel(res, 0, tidx, use_correction='hac') #dropping numpy 1.4 soon #np.testing.assert_allclose(cov, res_stata.cov_pnw0_stata, rtol=1e-6) assert_almost_equal(cov, res_stata.cov_pnw0_stata, decimal=4) cov = sw.cov_nw_panel(res, 1, tidx, use_correction='hac') #np.testing.assert_allclose(cov, res_stata.cov_pnw1_stata, rtol=1e-6) assert_almost_equal(cov, res_stata.cov_pnw1_stata, decimal=4) cov = sw.cov_nw_panel(res, 4, tidx) #check default #np.testing.assert_allclose(cov, res_stata.cov_pnw4_stata, rtol=1e-6) assert_almost_equal(cov, res_stata.cov_pnw4_stata, decimal=4) #cluster robust standard errors cov_clu = sw.cov_cluster(res, firm_id) assert_almost_equal(cov_clu, res_stata.cov_clu_stata, decimal=4) #cluster robust standard errors, non-int groups cov_clu = sw.cov_cluster(res, lmap(str, firm_id)) assert_almost_equal(cov_clu, res_stata.cov_clu_stata, decimal=4) #Driscoll and Kraay panel robust standard errors rcov = sw.cov_nw_groupsum(res, 0, time, use_correction=0) assert_almost_equal(rcov, res_stata.cov_dk0_stata, decimal=4) rcov = sw.cov_nw_groupsum(res, 1, time, use_correction=0) assert_almost_equal(rcov, res_stata.cov_dk1_stata, decimal=4) rcov = sw.cov_nw_groupsum(res, 4, time) #check default assert_almost_equal(rcov, res_stata.cov_dk4_stata, decimal=4) statsmodels-0.12.2/statsmodels/stats/tests/test_power.py000066400000000000000000000631661400612667500235700ustar00rootroot00000000000000# -*- coding: utf-8 -*- # pylint: disable=W0231, W0142 """Tests for statistical power calculations Note: tests for chisquare power are in test_gof.py Created on Sat Mar 09 08:44:49 2013 Author: Josef Perktold """ import copy import warnings import numpy as np from numpy.testing import (assert_almost_equal, assert_allclose, assert_raises, assert_equal, assert_warns) import pytest import statsmodels.stats.power as smp from statsmodels.stats.tests.test_weightstats import Holder from statsmodels.tools.sm_exceptions import HypothesisTestWarning try: import matplotlib.pyplot as plt # noqa:F401 except ImportError: pass class CheckPowerMixin(object): def test_power(self): #test against R results kwds = copy.copy(self.kwds) del kwds['power'] kwds.update(self.kwds_extra) if hasattr(self, 'decimal'): decimal = self.decimal else: decimal = 6 res1 = self.cls() assert_almost_equal(res1.power(**kwds), self.res2.power, decimal=decimal) #@pytest.mark.xfail(strict=True) def test_positional(self): res1 = self.cls() kwds = copy.copy(self.kwds) del kwds['power'] kwds.update(self.kwds_extra) # positional args if hasattr(self, 'args_names'): args_names = self.args_names else: nobs_ = 'nobs' if 'nobs' in kwds else 'nobs1' args_names = ['effect_size', nobs_, 'alpha'] # pop positional args args = [kwds.pop(arg) for arg in args_names] if hasattr(self, 'decimal'): decimal = self.decimal else: decimal = 6 res = res1.power(*args, **kwds) assert_almost_equal(res, self.res2.power, decimal=decimal) def test_roots(self): kwds = copy.copy(self.kwds) kwds.update(self.kwds_extra) # kwds_extra are used as argument, but not as target for root for key in self.kwds: # keep print to check whether tests are really executed #print 'testing roots', key value = kwds[key] kwds[key] = None result = self.cls().solve_power(**kwds) assert_allclose(result, value, rtol=0.001, err_msg=key+' failed') # yield can be used to investigate specific errors #yield assert_allclose, result, value, 0.001, 0, key+' failed' kwds[key] = value # reset dict @pytest.mark.matplotlib def test_power_plot(self, close_figures): if self.cls == smp.FTestPower: pytest.skip('skip FTestPower plot_power') fig = plt.figure() ax = fig.add_subplot(2,1,1) fig = self.cls().plot_power(dep_var='nobs', nobs= np.arange(2, 100), effect_size=np.array([0.1, 0.2, 0.3, 0.5, 1]), #alternative='larger', ax=ax, title='Power of t-Test', **self.kwds_extra) ax = fig.add_subplot(2,1,2) self.cls().plot_power(dep_var='es', nobs=np.array([10, 20, 30, 50, 70, 100]), effect_size=np.linspace(0.01, 2, 51), #alternative='larger', ax=ax, title='', **self.kwds_extra) #''' test cases #one sample # two-sided one-sided #large power OneS1 OneS3 #small power OneS2 OneS4 # #two sample # two-sided one-sided #large power TwoS1 TwoS3 #small power TwoS2 TwoS4 #small p, ratio TwoS4 TwoS5 #''' class TestTTPowerOneS1(CheckPowerMixin): @classmethod def setup_class(cls): #> p = pwr.t.test(d=1,n=30,sig.level=0.05,type="two.sample",alternative="two.sided") #> cat_items(p, prefix='tt_power2_1.') res2 = Holder() res2.n = 30 res2.d = 1 res2.sig_level = 0.05 res2.power = 0.9995636009612725 res2.alternative = 'two.sided' res2.note = 'NULL' res2.method = 'One-sample t test power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs': res2.n, 'alpha': res2.sig_level, 'power':res2.power} cls.kwds_extra = {} cls.cls = smp.TTestPower class TestTTPowerOneS2(CheckPowerMixin): # case with small power @classmethod def setup_class(cls): res2 = Holder() #> p = pwr.t.test(d=0.2,n=20,sig.level=0.05,type="one.sample",alternative="two.sided") #> cat_items(p, "res2.") res2.n = 20 res2.d = 0.2 res2.sig_level = 0.05 res2.power = 0.1359562887679666 res2.alternative = 'two.sided' res2.note = '''NULL''' res2.method = 'One-sample t test power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs': res2.n, 'alpha': res2.sig_level, 'power':res2.power} cls.kwds_extra = {} cls.cls = smp.TTestPower class TestTTPowerOneS3(CheckPowerMixin): @classmethod def setup_class(cls): res2 = Holder() #> p = pwr.t.test(d=1,n=30,sig.level=0.05,type="one.sample",alternative="greater") #> cat_items(p, prefix='tt_power1_1g.') res2.n = 30 res2.d = 1 res2.sig_level = 0.05 res2.power = 0.999892010204909 res2.alternative = 'greater' res2.note = 'NULL' res2.method = 'One-sample t test power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs': res2.n, 'alpha': res2.sig_level, 'power': res2.power} cls.kwds_extra = {'alternative': 'larger'} cls.cls = smp.TTestPower class TestTTPowerOneS4(CheckPowerMixin): @classmethod def setup_class(cls): res2 = Holder() #> p = pwr.t.test(d=0.05,n=20,sig.level=0.05,type="one.sample",alternative="greater") #> cat_items(p, "res2.") res2.n = 20 res2.d = 0.05 res2.sig_level = 0.05 res2.power = 0.0764888785042198 res2.alternative = 'greater' res2.note = '''NULL''' res2.method = 'One-sample t test power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs': res2.n, 'alpha': res2.sig_level, 'power': res2.power} cls.kwds_extra = {'alternative': 'larger'} cls.cls = smp.TTestPower class TestTTPowerOneS5(CheckPowerMixin): # case one-sided less, not implemented yet @classmethod def setup_class(cls): res2 = Holder() #> p = pwr.t.test(d=0.2,n=20,sig.level=0.05,type="one.sample",alternative="less") #> cat_items(p, "res2.") res2.n = 20 res2.d = 0.2 res2.sig_level = 0.05 res2.power = 0.006063932667926375 res2.alternative = 'less' res2.note = '''NULL''' res2.method = 'One-sample t test power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs': res2.n, 'alpha': res2.sig_level, 'power': res2.power} cls.kwds_extra = {'alternative': 'smaller'} cls.cls = smp.TTestPower class TestTTPowerOneS6(CheckPowerMixin): # case one-sided less, negative effect size, not implemented yet @classmethod def setup_class(cls): res2 = Holder() #> p = pwr.t.test(d=-0.2,n=20,sig.level=0.05,type="one.sample",alternative="less") #> cat_items(p, "res2.") res2.n = 20 res2.d = -0.2 res2.sig_level = 0.05 res2.power = 0.21707518167191 res2.alternative = 'less' res2.note = '''NULL''' res2.method = 'One-sample t test power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs': res2.n, 'alpha': res2.sig_level, 'power': res2.power} cls.kwds_extra = {'alternative': 'smaller'} cls.cls = smp.TTestPower class TestTTPowerTwoS1(CheckPowerMixin): @classmethod def setup_class(cls): #> p = pwr.t.test(d=1,n=30,sig.level=0.05,type="two.sample",alternative="two.sided") #> cat_items(p, prefix='tt_power2_1.') res2 = Holder() res2.n = 30 res2.d = 1 res2.sig_level = 0.05 res2.power = 0.967708258242517 res2.alternative = 'two.sided' res2.note = 'n is number in *each* group' res2.method = 'Two-sample t test power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs1': res2.n, 'alpha': res2.sig_level, 'power': res2.power, 'ratio': 1} cls.kwds_extra = {} cls.cls = smp.TTestIndPower class TestTTPowerTwoS2(CheckPowerMixin): @classmethod def setup_class(cls): res2 = Holder() #> p = pwr.t.test(d=0.1,n=20,sig.level=0.05,type="two.sample",alternative="two.sided") #> cat_items(p, "res2.") res2.n = 20 res2.d = 0.1 res2.sig_level = 0.05 res2.power = 0.06095912465411235 res2.alternative = 'two.sided' res2.note = 'n is number in *each* group' res2.method = 'Two-sample t test power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs1': res2.n, 'alpha': res2.sig_level, 'power': res2.power, 'ratio': 1} cls.kwds_extra = {} cls.cls = smp.TTestIndPower class TestTTPowerTwoS3(CheckPowerMixin): @classmethod def setup_class(cls): res2 = Holder() #> p = pwr.t.test(d=1,n=30,sig.level=0.05,type="two.sample",alternative="greater") #> cat_items(p, prefix='tt_power2_1g.') res2.n = 30 res2.d = 1 res2.sig_level = 0.05 res2.power = 0.985459690251624 res2.alternative = 'greater' res2.note = 'n is number in *each* group' res2.method = 'Two-sample t test power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs1': res2.n, 'alpha': res2.sig_level, 'power':res2.power, 'ratio': 1} cls.kwds_extra = {'alternative': 'larger'} cls.cls = smp.TTestIndPower class TestTTPowerTwoS4(CheckPowerMixin): # case with small power @classmethod def setup_class(cls): res2 = Holder() #> p = pwr.t.test(d=0.01,n=30,sig.level=0.05,type="two.sample",alternative="greater") #> cat_items(p, "res2.") res2.n = 30 res2.d = 0.01 res2.sig_level = 0.05 res2.power = 0.0540740302835667 res2.alternative = 'greater' res2.note = 'n is number in *each* group' res2.method = 'Two-sample t test power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs1': res2.n, 'alpha': res2.sig_level, 'power':res2.power} cls.kwds_extra = {'alternative': 'larger'} cls.cls = smp.TTestIndPower class TestTTPowerTwoS5(CheckPowerMixin): # case with unequal n, ratio>1 @classmethod def setup_class(cls): res2 = Holder() #> p = pwr.t2n.test(d=0.1,n1=20, n2=30,sig.level=0.05,alternative="two.sided") #> cat_items(p, "res2.") res2.n1 = 20 res2.n2 = 30 res2.d = 0.1 res2.sig_level = 0.05 res2.power = 0.0633081832564667 res2.alternative = 'two.sided' res2.method = 't test power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs1': res2.n1, 'alpha': res2.sig_level, 'power':res2.power, 'ratio': 1.5} cls.kwds_extra = {'alternative': 'two-sided'} cls.cls = smp.TTestIndPower class TestTTPowerTwoS6(CheckPowerMixin): # case with unequal n, ratio>1 @classmethod def setup_class(cls): res2 = Holder() #> p = pwr.t2n.test(d=0.1,n1=20, n2=30,sig.level=0.05,alternative="greater") #> cat_items(p, "res2.") res2.n1 = 20 res2.n2 = 30 res2.d = 0.1 res2.sig_level = 0.05 res2.power = 0.09623589080917805 res2.alternative = 'greater' res2.method = 't test power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs1': res2.n1, 'alpha': res2.sig_level, 'power':res2.power, 'ratio': 1.5} cls.kwds_extra = {'alternative': 'larger'} cls.cls = smp.TTestIndPower def test_normal_power_explicit(): # a few initial test cases for NormalIndPower sigma = 1 d = 0.3 nobs = 80 alpha = 0.05 res1 = smp.normal_power(d, nobs/2., 0.05) res2 = smp.NormalIndPower().power(d, nobs, 0.05) res3 = smp.NormalIndPower().solve_power(effect_size=0.3, nobs1=80, alpha=0.05, power=None) res_R = 0.475100870572638 assert_almost_equal(res1, res_R, decimal=13) assert_almost_equal(res2, res_R, decimal=13) assert_almost_equal(res3, res_R, decimal=13) norm_pow = smp.normal_power(-0.01, nobs/2., 0.05) norm_pow_R = 0.05045832927039234 #value from R: >pwr.2p.test(h=0.01,n=80,sig.level=0.05,alternative="two.sided") assert_almost_equal(norm_pow, norm_pow_R, decimal=11) norm_pow = smp.NormalIndPower().power(0.01, nobs, 0.05, alternative="larger") norm_pow_R = 0.056869534873146124 #value from R: >pwr.2p.test(h=0.01,n=80,sig.level=0.05,alternative="greater") assert_almost_equal(norm_pow, norm_pow_R, decimal=11) # Note: negative effect size is same as switching one-sided alternative # TODO: should I switch to larger/smaller instead of "one-sided" options norm_pow = smp.NormalIndPower().power(-0.01, nobs, 0.05, alternative="larger") norm_pow_R = 0.0438089705093578 #value from R: >pwr.2p.test(h=0.01,n=80,sig.level=0.05,alternative="less") assert_almost_equal(norm_pow, norm_pow_R, decimal=11) class TestNormalIndPower1(CheckPowerMixin): @classmethod def setup_class(cls): #> example from above # results copied not directly from R res2 = Holder() res2.n = 80 res2.d = 0.3 res2.sig_level = 0.05 res2.power = 0.475100870572638 res2.alternative = 'two.sided' res2.note = 'NULL' res2.method = 'two sample power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs1': res2.n, 'alpha': res2.sig_level, 'power':res2.power, 'ratio': 1} cls.kwds_extra = {} cls.cls = smp.NormalIndPower class TestNormalIndPower2(CheckPowerMixin): @classmethod def setup_class(cls): res2 = Holder() #> np = pwr.2p.test(h=0.01,n=80,sig.level=0.05,alternative="less") #> cat_items(np, "res2.") res2.h = 0.01 res2.n = 80 res2.sig_level = 0.05 res2.power = 0.0438089705093578 res2.alternative = 'less' res2.method = ('Difference of proportion power calculation for' + ' binomial distribution (arcsine transformation)') res2.note = 'same sample sizes' cls.res2 = res2 cls.kwds = {'effect_size': res2.h, 'nobs1': res2.n, 'alpha': res2.sig_level, 'power':res2.power, 'ratio': 1} cls.kwds_extra = {'alternative':'smaller'} cls.cls = smp.NormalIndPower class TestNormalIndPower_onesamp1(CheckPowerMixin): @classmethod def setup_class(cls): # forcing one-sample by using ratio=0 #> example from above # results copied not directly from R res2 = Holder() res2.n = 40 res2.d = 0.3 res2.sig_level = 0.05 res2.power = 0.475100870572638 res2.alternative = 'two.sided' res2.note = 'NULL' res2.method = 'two sample power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs1': res2.n, 'alpha': res2.sig_level, 'power':res2.power} # keyword for which we do not look for root: cls.kwds_extra = {'ratio': 0} cls.cls = smp.NormalIndPower class TestNormalIndPower_onesamp2(CheckPowerMixin): # Note: same power as two sample case with twice as many observations @classmethod def setup_class(cls): # forcing one-sample by using ratio=0 res2 = Holder() #> np = pwr.norm.test(d=0.01,n=40,sig.level=0.05,alternative="less") #> cat_items(np, "res2.") res2.d = 0.01 res2.n = 40 res2.sig_level = 0.05 res2.power = 0.0438089705093578 res2.alternative = 'less' res2.method = 'Mean power calculation for normal distribution with known variance' cls.res2 = res2 cls.kwds = {'effect_size': res2.d, 'nobs1': res2.n, 'alpha': res2.sig_level, 'power':res2.power} # keyword for which we do not look for root: cls.kwds_extra = {'ratio': 0, 'alternative':'smaller'} cls.cls = smp.NormalIndPower class TestChisquarePower(CheckPowerMixin): @classmethod def setup_class(cls): # one example from test_gof, results_power res2 = Holder() res2.w = 0.1 res2.N = 5 res2.df = 4 res2.sig_level = 0.05 res2.power = 0.05246644635810126 res2.method = 'Chi squared power calculation' res2.note = 'N is the number of observations' cls.res2 = res2 cls.kwds = {'effect_size': res2.w, 'nobs': res2.N, 'alpha': res2.sig_level, 'power':res2.power} # keyword for which we do not look for root: # solving for n_bins does not work, will not be used in regular usage cls.kwds_extra = {'n_bins': res2.df + 1} cls.cls = smp.GofChisquarePower def test_positional(self): res1 = self.cls() args_names = ['effect_size','nobs', 'alpha', 'n_bins'] kwds = copy.copy(self.kwds) del kwds['power'] kwds.update(self.kwds_extra) args = [kwds[arg] for arg in args_names] if hasattr(self, 'decimal'): decimal = self.decimal #pylint: disable-msg=E1101 else: decimal = 6 assert_almost_equal(res1.power(*args), self.res2.power, decimal=decimal) def test_ftest_power(): #equivalence ftest, ttest for alpha in [0.01, 0.05, 0.1, 0.20, 0.50]: res0 = smp.ttest_power(0.01, 200, alpha) res1 = smp.ftest_power(0.01, 199, 1, alpha=alpha, ncc=0) assert_almost_equal(res1, res0, decimal=6) #example from Gplus documentation F-test ANOVA #Total sample size:200 #Effect size "f":0.25 #Beta/alpha ratio:1 #Result: #Alpha:0.1592 #Power (1-beta):0.8408 #Critical F:1.4762 #Lambda: 12.50000 res1 = smp.ftest_anova_power(0.25, 200, 0.1592, k_groups=10) res0 = 0.8408 assert_almost_equal(res1, res0, decimal=4) # TODO: no class yet # examples against R::pwr res2 = Holder() #> rf = pwr.f2.test(u=5, v=199, f2=0.1**2, sig.level=0.01) #> cat_items(rf, "res2.") res2.u = 5 res2.v = 199 res2.f2 = 0.01 res2.sig_level = 0.01 res2.power = 0.0494137732920332 res2.method = 'Multiple regression power calculation' res1 = smp.ftest_power(np.sqrt(res2.f2), res2.v, res2.u, alpha=res2.sig_level, ncc=1) assert_almost_equal(res1, res2.power, decimal=5) res2 = Holder() #> rf = pwr.f2.test(u=5, v=199, f2=0.3**2, sig.level=0.01) #> cat_items(rf, "res2.") res2.u = 5 res2.v = 199 res2.f2 = 0.09 res2.sig_level = 0.01 res2.power = 0.7967191006290872 res2.method = 'Multiple regression power calculation' res1 = smp.ftest_power(np.sqrt(res2.f2), res2.v, res2.u, alpha=res2.sig_level, ncc=1) assert_almost_equal(res1, res2.power, decimal=5) res2 = Holder() #> rf = pwr.f2.test(u=5, v=19, f2=0.3**2, sig.level=0.1) #> cat_items(rf, "res2.") res2.u = 5 res2.v = 19 res2.f2 = 0.09 res2.sig_level = 0.1 res2.power = 0.235454222377575 res2.method = 'Multiple regression power calculation' res1 = smp.ftest_power(np.sqrt(res2.f2), res2.v, res2.u, alpha=res2.sig_level, ncc=1) assert_almost_equal(res1, res2.power, decimal=5) # class based version of two above test for Ftest class TestFtestAnovaPower(CheckPowerMixin): @classmethod def setup_class(cls): res2 = Holder() #example from Gplus documentation F-test ANOVA #Total sample size:200 #Effect size "f":0.25 #Beta/alpha ratio:1 #Result: #Alpha:0.1592 #Power (1-beta):0.8408 #Critical F:1.4762 #Lambda: 12.50000 #converted to res2 by hand res2.f = 0.25 res2.n = 200 res2.k = 10 res2.alpha = 0.1592 res2.power = 0.8408 res2.method = 'Multiple regression power calculation' cls.res2 = res2 cls.kwds = {'effect_size': res2.f, 'nobs': res2.n, 'alpha': res2.alpha, 'power': res2.power} # keyword for which we do not look for root: # solving for n_bins does not work, will not be used in regular usage cls.kwds_extra = {'k_groups': res2.k} # rootfinding does not work #cls.args_names = ['effect_size','nobs', 'alpha']#, 'k_groups'] cls.cls = smp.FTestAnovaPower # precision for test_power cls.decimal = 4 class TestFtestPower(CheckPowerMixin): @classmethod def setup_class(cls): res2 = Holder() #> rf = pwr.f2.test(u=5, v=19, f2=0.3**2, sig.level=0.1) #> cat_items(rf, "res2.") res2.u = 5 res2.v = 19 res2.f2 = 0.09 res2.sig_level = 0.1 res2.power = 0.235454222377575 res2.method = 'Multiple regression power calculation' cls.res2 = res2 cls.kwds = {'effect_size': np.sqrt(res2.f2), 'df_num': res2.v, 'df_denom': res2.u, 'alpha': res2.sig_level, 'power': res2.power} # keyword for which we do not look for root: # solving for n_bins does not work, will not be used in regular usage cls.kwds_extra = {} cls.args_names = ['effect_size', 'df_num', 'df_denom', 'alpha'] cls.cls = smp.FTestPower # precision for test_power cls.decimal = 5 def test_power_solver(): # messing up the solver to trigger backup nip = smp.NormalIndPower() # check result es0 = 0.1 pow_ = nip.solve_power(es0, nobs1=1600, alpha=0.01, power=None, ratio=1, alternative='larger') # value is regression test assert_almost_equal(pow_, 0.69219411243824214, decimal=5) es = nip.solve_power(None, nobs1=1600, alpha=0.01, power=pow_, ratio=1, alternative='larger') assert_almost_equal(es, es0, decimal=4) assert_equal(nip.cache_fit_res[0], 1) assert_equal(len(nip.cache_fit_res), 2) # cause first optimizer to fail nip.start_bqexp['effect_size'] = {'upp': -10, 'low': -20} nip.start_ttp['effect_size'] = 0.14 es = nip.solve_power(None, nobs1=1600, alpha=0.01, power=pow_, ratio=1, alternative='larger') assert_almost_equal(es, es0, decimal=4) assert_equal(nip.cache_fit_res[0], 1) assert_equal(len(nip.cache_fit_res), 3, err_msg=repr(nip.cache_fit_res)) nip.start_ttp['effect_size'] = np.nan es = nip.solve_power(None, nobs1=1600, alpha=0.01, power=pow_, ratio=1, alternative='larger') assert_almost_equal(es, es0, decimal=4) assert_equal(nip.cache_fit_res[0], 1) assert_equal(len(nip.cache_fit_res), 4) # Test our edge-case where effect_size = 0 es = nip.solve_power(nobs1=1600, alpha=0.01, effect_size=0, power=None) assert_almost_equal(es, 0.01) # I let this case fail, could be fixed for some statistical tests # (we should not get here in the first place) # effect size is negative, but last stage brentq uses [1e-8, 1-1e-8] assert_raises(ValueError, nip.solve_power, None, nobs1=1600, alpha=0.01, power=0.005, ratio=1, alternative='larger') with pytest.warns(HypothesisTestWarning): with pytest.raises(ValueError): nip.solve_power(nobs1=None, effect_size=0, alpha=0.01, power=0.005, ratio=1, alternative='larger') # TODO: can something useful be made from this? @pytest.mark.xfail(reason='Known failure on modern SciPy >= 0.10', strict=True) def test_power_solver_warn(): # messing up the solver to trigger warning # I wrote this with scipy 0.9, # convergence behavior of scipy 0.11 is different, # fails at a different case, but is successful where it failed before pow_ = 0.69219411243824214 # from previous function nip = smp.NormalIndPower() # using nobs, has one backup (fsolve) nip.start_bqexp['nobs1'] = {'upp': 50, 'low': -20} val = nip.solve_power(0.1, nobs1=None, alpha=0.01, power=pow_, ratio=1, alternative='larger') assert_almost_equal(val, 1600, decimal=4) assert_equal(nip.cache_fit_res[0], 1) assert_equal(len(nip.cache_fit_res), 3) # case that has convergence failure, and should warn nip.start_ttp['nobs1'] = np.nan from statsmodels.tools.sm_exceptions import ConvergenceWarning assert_warns(ConvergenceWarning, nip.solve_power, 0.1, nobs1=None, alpha=0.01, power=pow_, ratio=1, alternative='larger') # this converges with scipy 0.11 ??? # nip.solve_power(0.1, nobs1=None, alpha=0.01, power=pow_, ratio=1, alternative='larger') with warnings.catch_warnings(): # python >= 2.6 warnings.simplefilter("ignore") val = nip.solve_power(0.1, nobs1=None, alpha=0.01, power=pow_, ratio=1, alternative='larger') assert_equal(nip.cache_fit_res[0], 0) assert_equal(len(nip.cache_fit_res), 3) statsmodels-0.12.2/statsmodels/stats/tests/test_proportion.py000066400000000000000000001147761400612667500246530ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Mar 01 14:56:56 2013 Author: Josef Perktold """ import warnings import pytest import numpy as np import pandas as pd from numpy.testing import (assert_almost_equal, assert_equal, assert_array_less, assert_raises, assert_allclose) from statsmodels.stats.proportion import (proportion_confint, confint_proportions_2indep, multinomial_proportions_confint, score_test_proportions_2indep, power_proportions_2indep, samplesize_proportions_2indep_onetail, ) import statsmodels.stats.proportion as smprop from statsmodels.tools.sm_exceptions import HypothesisTestWarning from statsmodels.tools.testing import Holder probci_methods = {'agresti_coull': 'agresti-coull', 'normal': 'asymptotic', 'beta': 'exact', 'wilson': 'wilson', 'jeffreys': 'bayes' } def test_confint_proportion(): from .results.results_proportion import res_binom, res_binom_methods for case in res_binom: count, nobs = case for method in probci_methods: idx = res_binom_methods.index(probci_methods[method]) res_low = res_binom[case].ci_low[idx] res_upp = res_binom[case].ci_upp[idx] if np.isnan(res_low) or np.isnan(res_upp): continue if (count == 0 or count == nobs) and method == 'jeffreys': # maybe a bug or different corner case definition continue if method == 'jeffreys' and nobs == 30: # something is strange in extreme case e.g 0/30 or 1/30 continue ci = proportion_confint(count, nobs, alpha=0.05, method=method) # we impose that confint is in [0, 1] res_low = max(res_low, 0) res_upp = min(res_upp, 1) assert_almost_equal(ci, [res_low, res_upp], decimal=6, err_msg=repr(case) + method) @pytest.mark.parametrize('method', probci_methods) def test_confint_proportion_ndim(method): # check that it works with 1-D, 2-D and pandas count = np.arange(6).reshape(2, 3) nobs = 10 * np.ones((2, 3)) count_pd = pd.DataFrame(count) nobs_pd = pd.DataFrame(nobs) ci_arr = proportion_confint(count, nobs, alpha=0.05, method=method) ci_pd = proportion_confint(count_pd, nobs_pd, alpha=0.05, method=method) assert_allclose(ci_arr, (ci_pd[0].values, ci_pd[1].values), rtol=1e-13) # spot checking one value ci12 = proportion_confint(count[1, 2], nobs[1, 2], alpha=0.05, method=method) assert_allclose((ci_pd[0].values[1, 2], ci_pd[1].values[1, 2]), ci12, rtol=1e-13) assert_allclose((ci_arr[0][1, 2], ci_arr[1][1, 2]), ci12, rtol=1e-13) # check that lists work as input ci_li = proportion_confint(count.tolist(), nobs.tolist(), alpha=0.05, method=method) assert_allclose(ci_arr, (ci_li[0], ci_li[1]), rtol=1e-13) # check pandas Series, 1-D ci_pds = proportion_confint(count_pd.iloc[0], nobs_pd.iloc[0], alpha=0.05, method=method) assert_allclose((ci_pds[0].values, ci_pds[1].values), (ci_pd[0].values[0], ci_pd[1].values[0]), rtol=1e-13) # check scalar nobs, verifying one value ci_arr2 = proportion_confint(count, nobs[1, 2], alpha=0.05, method=method) assert_allclose((ci_arr2[0][1, 2], ci_arr[1][1, 2]), ci12, rtol=1e-13) def test_samplesize_confidenceinterval_prop(): #consistency test for samplesize to achieve confidence_interval nobs = 20 ci = smprop.proportion_confint(12, nobs, alpha=0.05, method='normal') res = smprop.samplesize_confint_proportion(12./nobs, (ci[1] - ci[0]) / 2) assert_almost_equal(res, nobs, decimal=13) def test_proportion_effect_size(): # example from blog es = smprop.proportion_effectsize(0.5, 0.4) assert_almost_equal(es, 0.2013579207903309, decimal=13) def test_confint_multinomial_proportions(): from .results.results_multinomial_proportions import res_multinomial for ((method, description), values) in res_multinomial.items(): cis = multinomial_proportions_confint(values.proportions, 0.05, method=method) assert_almost_equal( values.cis, cis, decimal=values.precision, err_msg='"%s" method, %s' % (method, description)) def test_multinomial_proportions_errors(): # Out-of-bounds values for alpha raise a ValueError for alpha in [-.1, 0, 1, 1.1]: assert_raises(ValueError, multinomial_proportions_confint, [5] * 50, alpha=alpha) assert_raises(ValueError, multinomial_proportions_confint, np.arange(50) - 1) # Any unknown method is reported. for method in ['unknown_method', 'sisok_method', 'unknown-glaz']: assert_raises(NotImplementedError, multinomial_proportions_confint, [5] * 50, method=method) def test_confint_multinomial_proportions_zeros(): # test when a count is zero or close to zero # values from R MultinomialCI ci01 = np.array([ 0.09364718, 0.1898413, 0.00000000, 0.0483581, 0.13667426, 0.2328684, 0.10124019, 0.1974343, 0.10883321, 0.2050273, 0.17210833, 0.2683024, 0.09870919, 0.1949033]).reshape(-1,2) ci0 = np.array([ 0.09620253, 0.19238867, 0.00000000, 0.05061652, 0.13924051, 0.23542664, 0.10379747, 0.19998360, 0.11139241, 0.20757854, 0.17468354, 0.27086968, 0.10126582, 0.19745196]).reshape(-1,2) # the shifts are the differences between "LOWER(SG)" "UPPER(SG)" and # "LOWER(C+1)" "UPPER(C+1)" in verbose printout # ci01_shift = np.array([0.002531008, -0.002515122]) # not needed ci0_shift = np.array([0.002531642, 0.002515247]) p = [56, 0.1, 73, 59, 62, 87, 58] ci_01 = smprop.multinomial_proportions_confint(p, 0.05, method='sison_glaz') p = [56, 0, 73, 59, 62, 87, 58] ci_0 = smprop.multinomial_proportions_confint(p, 0.05, method='sison_glaz') assert_allclose(ci_01, ci01, atol=1e-5) assert_allclose(ci_0, np.maximum(ci0 - ci0_shift, 0), atol=1e-5) assert_allclose(ci_01, ci_0, atol=5e-4) class CheckProportionMixin(object): def test_proptest(self): # equality of k-samples pt = smprop.proportions_chisquare(self.n_success, self.nobs, value=None) assert_almost_equal(pt[0], self.res_prop_test.statistic, decimal=13) assert_almost_equal(pt[1], self.res_prop_test.p_value, decimal=13) # several against value pt = smprop.proportions_chisquare(self.n_success, self.nobs, value=self.res_prop_test_val.null_value[0]) assert_almost_equal(pt[0], self.res_prop_test_val.statistic, decimal=13) assert_almost_equal(pt[1], self.res_prop_test_val.p_value, decimal=13) # one proportion against value pt = smprop.proportions_chisquare(self.n_success[0], self.nobs[0], value=self.res_prop_test_1.null_value) assert_almost_equal(pt[0], self.res_prop_test_1.statistic, decimal=13) assert_almost_equal(pt[1], self.res_prop_test_1.p_value, decimal=13) def test_pairwiseproptest(self): ppt = smprop.proportions_chisquare_allpairs(self.n_success, self.nobs, multitest_method=None) assert_almost_equal(ppt.pvals_raw, self.res_ppt_pvals_raw) ppt = smprop.proportions_chisquare_allpairs(self.n_success, self.nobs, multitest_method='h') assert_almost_equal(ppt.pval_corrected(), self.res_ppt_pvals_holm) pptd = smprop.proportions_chisquare_pairscontrol(self.n_success, self.nobs, multitest_method='hommel') assert_almost_equal(pptd.pvals_raw, ppt.pvals_raw[:len(self.nobs) - 1], decimal=13) def test_number_pairs_1493(self): ppt = smprop.proportions_chisquare_allpairs(self.n_success[:3], self.nobs[:3], multitest_method=None) assert_equal(len(ppt.pvals_raw), 3) idx = [0, 1, 3] assert_almost_equal(ppt.pvals_raw, self.res_ppt_pvals_raw[idx]) class TestProportion(CheckProportionMixin): def setup(self): self.n_success = np.array([ 73, 90, 114, 75]) self.nobs = np.array([ 86, 93, 136, 82]) self.res_ppt_pvals_raw = np.array([ 0.00533824886503131, 0.8327574849753566, 0.1880573726722516, 0.002026764254350234, 0.1309487516334318, 0.1076118730631731 ]) self.res_ppt_pvals_holm = np.array([ 0.02669124432515654, 0.8327574849753566, 0.4304474922526926, 0.0121605855261014, 0.4304474922526926, 0.4304474922526926 ]) res_prop_test = Holder() res_prop_test.statistic = 11.11938768628861 res_prop_test.parameter = 3 res_prop_test.p_value = 0.011097511366581344 res_prop_test.estimate = np.array([ 0.848837209302326, 0.967741935483871, 0.838235294117647, 0.9146341463414634 ]).reshape(4,1, order='F') res_prop_test.null_value = '''NULL''' res_prop_test.conf_int = '''NULL''' res_prop_test.alternative = 'two.sided' res_prop_test.method = '4-sample test for equality of proportions ' + \ 'without continuity correction' res_prop_test.data_name = 'smokers2 out of patients' self.res_prop_test = res_prop_test #> pt = prop.test(smokers2, patients, p=rep(c(0.9), 4), correct=FALSE) #> cat_items(pt, "res_prop_test_val.") res_prop_test_val = Holder() res_prop_test_val.statistic = np.array([ 13.20305530710751 ]).reshape(1,1, order='F') res_prop_test_val.parameter = np.array([ 4 ]).reshape(1,1, order='F') res_prop_test_val.p_value = 0.010325090041836 res_prop_test_val.estimate = np.array([ 0.848837209302326, 0.967741935483871, 0.838235294117647, 0.9146341463414634 ]).reshape(4,1, order='F') res_prop_test_val.null_value = np.array([ 0.9, 0.9, 0.9, 0.9 ]).reshape(4,1, order='F') res_prop_test_val.conf_int = '''NULL''' res_prop_test_val.alternative = 'two.sided' res_prop_test_val.method = '4-sample test for given proportions without continuity correction' res_prop_test_val.data_name = 'smokers2 out of patients, null probabilities rep(c(0.9), 4)' self.res_prop_test_val = res_prop_test_val #> pt = prop.test(smokers2[1], patients[1], p=0.9, correct=FALSE) #> cat_items(pt, "res_prop_test_1.") res_prop_test_1 = Holder() res_prop_test_1.statistic = 2.501291989664086 res_prop_test_1.parameter = 1 res_prop_test_1.p_value = 0.113752943640092 res_prop_test_1.estimate = 0.848837209302326 res_prop_test_1.null_value = 0.9 res_prop_test_1.conf_int = np.array([0.758364348004061, 0.9094787701686766]) res_prop_test_1.alternative = 'two.sided' res_prop_test_1.method = '1-sample proportions test without continuity correction' res_prop_test_1.data_name = 'smokers2[1] out of patients[1], null probability 0.9' self.res_prop_test_1 = res_prop_test_1 # GH 2969 def test_default_values(self): count = np.array([5, 12]) nobs = np.array([83, 99]) stat, pval = smprop.proportions_ztest(count, nobs, value=None) assert_almost_equal(stat, -1.4078304151258787) assert_almost_equal(pval, 0.15918129181156992) # GH 2779 def test_scalar(self): count = 5 nobs = 83 value = 0.05 stat, pval = smprop.proportions_ztest(count, nobs, value=value) assert_almost_equal(stat, 0.392126026314) assert_almost_equal(pval, 0.694965098115) assert_raises(ValueError, smprop.proportions_ztest, count, nobs, value=None) def test_binom_test(): #> bt = binom.test(51,235,(1/6),alternative="less") #> cat_items(bt, "binom_test_less.") binom_test_less = Holder() binom_test_less.statistic = 51 binom_test_less.parameter = 235 binom_test_less.p_value = 0.982022657605858 binom_test_less.conf_int = [0, 0.2659460862574313] binom_test_less.estimate = 0.2170212765957447 binom_test_less.null_value = 1. / 6 binom_test_less.alternative = 'less' binom_test_less.method = 'Exact binomial test' binom_test_less.data_name = '51 and 235' #> bt = binom.test(51,235,(1/6),alternative="greater") #> cat_items(bt, "binom_test_greater.") binom_test_greater = Holder() binom_test_greater.statistic = 51 binom_test_greater.parameter = 235 binom_test_greater.p_value = 0.02654424571169085 binom_test_greater.conf_int = [0.1735252778065201, 1] binom_test_greater.estimate = 0.2170212765957447 binom_test_greater.null_value = 1. / 6 binom_test_greater.alternative = 'greater' binom_test_greater.method = 'Exact binomial test' binom_test_greater.data_name = '51 and 235' #> bt = binom.test(51,235,(1/6),alternative="t") #> cat_items(bt, "binom_test_2sided.") binom_test_2sided = Holder() binom_test_2sided.statistic = 51 binom_test_2sided.parameter = 235 binom_test_2sided.p_value = 0.0437479701823997 binom_test_2sided.conf_int = [0.1660633298083073, 0.2752683640289254] binom_test_2sided.estimate = 0.2170212765957447 binom_test_2sided.null_value = 1. / 6 binom_test_2sided.alternative = 'two.sided' binom_test_2sided.method = 'Exact binomial test' binom_test_2sided.data_name = '51 and 235' alltests = [('larger', binom_test_greater), ('smaller', binom_test_less), ('two-sided', binom_test_2sided)] for alt, res0 in alltests: # only p-value is returned res = smprop.binom_test(51, 235, prop=1. / 6, alternative=alt) #assert_almost_equal(res[0], res0.statistic) assert_almost_equal(res, res0.p_value, decimal=13) # R binom_test returns Copper-Pearson confint ci_2s = smprop.proportion_confint(51, 235, alpha=0.05, method='beta') ci_low, ci_upp = smprop.proportion_confint(51, 235, alpha=0.1, method='beta') assert_almost_equal(ci_2s, binom_test_2sided.conf_int, decimal=13) assert_almost_equal(ci_upp, binom_test_less.conf_int[1], decimal=13) assert_almost_equal(ci_low, binom_test_greater.conf_int[0], decimal=13) def test_binom_rejection_interval(): # consistency check with binom_test # some code duplication but limit checks are different alpha = 0.05 nobs = 200 prop = 12./20 alternative='smaller' ci_low, ci_upp = smprop.binom_test_reject_interval(prop, nobs, alpha=alpha, alternative=alternative) assert_equal(ci_upp, nobs) pval = smprop.binom_test(ci_low, nobs, prop=prop, alternative=alternative) assert_array_less(pval, alpha) pval = smprop.binom_test(ci_low + 1, nobs, prop=prop, alternative=alternative) assert_array_less(alpha, pval) alternative='larger' ci_low, ci_upp = smprop.binom_test_reject_interval(prop, nobs, alpha=alpha, alternative=alternative) assert_equal(ci_low, 0) pval = smprop.binom_test(ci_upp, nobs, prop=prop, alternative=alternative) assert_array_less(pval, alpha) pval = smprop.binom_test(ci_upp - 1, nobs, prop=prop, alternative=alternative) assert_array_less(alpha, pval) alternative='two-sided' ci_low, ci_upp = smprop.binom_test_reject_interval(prop, nobs, alpha=alpha, alternative=alternative) pval = smprop.binom_test(ci_upp, nobs, prop=prop, alternative=alternative) assert_array_less(pval, alpha) pval = smprop.binom_test(ci_upp - 1, nobs, prop=prop, alternative=alternative) assert_array_less(alpha, pval) pval = smprop.binom_test(ci_upp, nobs, prop=prop, alternative=alternative) assert_array_less(pval, alpha) pval = smprop.binom_test(ci_upp - 1, nobs, prop=prop, alternative=alternative) assert_array_less(alpha, pval) def test_binom_tost(): # consistency check with two different implementation, # proportion_confint is tested against R # no reference case from other package available ci = smprop.proportion_confint(10, 20, method='beta', alpha=0.1) bt = smprop.binom_tost(10, 20, *ci) assert_almost_equal(bt, [0.05] * 3, decimal=12) ci = smprop.proportion_confint(5, 20, method='beta', alpha=0.1) bt = smprop.binom_tost(5, 20, *ci) assert_almost_equal(bt, [0.05] * 3, decimal=12) # vectorized, TODO: observed proportion = 0 returns nan ci = smprop.proportion_confint(np.arange(1, 20), 20, method='beta', alpha=0.05) bt = smprop.binom_tost(np.arange(1, 20), 20, *ci) bt = np.asarray(bt) assert_almost_equal(bt, 0.025 * np.ones(bt.shape), decimal=12) def test_power_binom_tost(): # comparison numbers from PASS manual p_alt = 0.6 + np.linspace(0, 0.09, 10) power = smprop.power_binom_tost(0.5, 0.7, 500, p_alt=p_alt, alpha=0.05) res_power = np.array([0.9965, 0.9940, 0.9815, 0.9482, 0.8783, 0.7583, 0.5914, 0.4041, 0.2352, 0.1139]) assert_almost_equal(power, res_power, decimal=4) rej_int = smprop.binom_tost_reject_interval(0.5, 0.7, 500) res_rej_int = (269, 332) assert_equal(rej_int, res_rej_int) # TODO: actual alpha=0.0489 for all p_alt above # another case nobs = np.arange(20, 210, 20) power = smprop.power_binom_tost(0.4, 0.6, nobs, p_alt=0.5, alpha=0.05) res_power = np.array([ 0., 0., 0., 0.0889, 0.2356, 0.3517, 0.4457, 0.6154, 0.6674, 0.7708]) # TODO: I currently do not impose power>=0, i.e np.maximum(power, 0) assert_almost_equal(np.maximum(power, 0), res_power, decimal=4) def test_power_ztost_prop(): power = smprop.power_ztost_prop(0.1, 0.9, 10, p_alt=0.6, alpha=0.05, discrete=True, dist='binom')[0] assert_almost_equal(power, 0.8204, decimal=4) # PASS example with warnings.catch_warnings(): # python >= 2.6 warnings.simplefilter("ignore", HypothesisTestWarning) power = smprop.power_ztost_prop(0.4, 0.6, np.arange(20, 210, 20), p_alt=0.5, alpha=0.05, discrete=False, dist='binom')[0] res_power = np.array([ 0., 0., 0., 0.0889, 0.2356, 0.4770, 0.5530, 0.6154, 0.7365, 0.7708]) # TODO: I currently do not impose power>=0, i.e np.maximum(power, 0) assert_almost_equal(np.maximum(power, 0), res_power, decimal=4) # with critval_continuity correction power = smprop.power_ztost_prop(0.4, 0.6, np.arange(20, 210, 20), p_alt=0.5, alpha=0.05, discrete=False, dist='binom', variance_prop=None, continuity=2, critval_continuity=1)[0] res_power = np.array([0., 0., 0., 0.0889, 0.2356, 0.3517, 0.4457, 0.6154, 0.6674, 0.7708]) # TODO: I currently do not impose power>=0, i.e np.maximum(power, 0) assert_almost_equal(np.maximum(power, 0), res_power, decimal=4) power = smprop.power_ztost_prop(0.4, 0.6, np.arange(20, 210, 20), p_alt=0.5, alpha=0.05, discrete=False, dist='binom', variance_prop=0.5, critval_continuity=1)[0] res_power = np.array([0., 0., 0., 0.0889, 0.2356, 0.3517, 0.4457, 0.6154, 0.6674, 0.7112]) # TODO: I currently do not impose power>=0, i.e np.maximum(power, 0) assert_almost_equal(np.maximum(power, 0), res_power, decimal=4) def test_ztost(): xfair = np.repeat([1, 0], [228, 762-228]) # comparing to SAS last output at # http://support.sas.com/documentation/cdl/en/procstat/63104/HTML/default/viewer.htm#procstat_freq_sect028.htm # confidence interval for tost # generic ztost is moved to weightstats from statsmodels.stats.weightstats import zconfint, ztost ci01 = zconfint(xfair, alpha=0.1, ddof=0) assert_almost_equal(ci01, [0.2719, 0.3265], 4) res = ztost(xfair, 0.18, 0.38, ddof=0) assert_almost_equal(res[1][0], 7.1865, 4) assert_almost_equal(res[2][0], -4.8701, 4) assert_array_less(res[0], 0.0001) def test_power_ztost_prop_norm(): # regression test for normal distribution # from a rough comparison, the results and variations look reasonable with pytest.warns(HypothesisTestWarning): power = smprop.power_ztost_prop(0.4, 0.6, np.arange(20, 210, 20), p_alt=0.5, alpha=0.05, discrete=False, dist='norm', variance_prop=0.5, continuity=0, critval_continuity=0)[0] res_power = np.array([0., 0., 0., 0.11450013, 0.27752006, 0.41495922, 0.52944621, 0.62382638, 0.70092914, 0.76341806]) # TODO: I currently do not impose power>=0, i.e np.maximum(power, 0) assert_almost_equal(np.maximum(power, 0), res_power, decimal=4) # regression test for normal distribution with pytest.warns(HypothesisTestWarning): power = smprop.power_ztost_prop(0.4, 0.6, np.arange(20, 210, 20), p_alt=0.5, alpha=0.05, discrete=False, dist='norm', variance_prop=0.5, continuity=1, critval_continuity=0)[0] res_power = np.array([0., 0., 0.02667562, 0.20189793, 0.35099606, 0.47608598, 0.57981118, 0.66496683, 0.73427591, 0.79026127]) # TODO: I currently do not impose power>=0, i.e np.maximum(power, 0) assert_almost_equal(np.maximum(power, 0), res_power, decimal=4) # regression test for normal distribution with pytest.warns(HypothesisTestWarning): power = smprop.power_ztost_prop(0.4, 0.6, np.arange(20, 210, 20), p_alt=0.5, alpha=0.05, discrete=True, dist='norm', variance_prop=0.5, continuity=1, critval_continuity=0)[0] res_power = np.array([0., 0., 0., 0.08902071, 0.23582284, 0.35192313, 0.55312718, 0.61549537, 0.66743625, 0.77066806]) # TODO: I currently do not impose power>=0, i.e np.maximum(power, 0) assert_almost_equal(np.maximum(power, 0), res_power, decimal=4) # regression test for normal distribution with pytest.warns(HypothesisTestWarning): power = smprop.power_ztost_prop(0.4, 0.6, np.arange(20, 210, 20), p_alt=0.5, alpha=0.05, discrete=True, dist='norm', variance_prop=0.5, continuity=1, critval_continuity=1)[0] res_power = np.array([0., 0., 0., 0.08902071, 0.23582284, 0.35192313, 0.44588687, 0.61549537, 0.66743625, 0.71115563]) # TODO: I currently do not impose power>=0, i.e np.maximum(power, 0) assert_almost_equal(np.maximum(power, 0), res_power, decimal=4) # regression test for normal distribution with pytest.warns(HypothesisTestWarning): power = smprop.power_ztost_prop(0.4, 0.6, np.arange(20, 210, 20), p_alt=0.5, alpha=0.05, discrete=True, dist='norm', variance_prop=None, continuity=0, critval_continuity=0)[0] res_power = np.array([0., 0., 0., 0., 0.15851942, 0.41611758, 0.5010377, 0.5708047, 0.70328247, 0.74210096]) # TODO: I currently do not impose power>=0, i.e np.maximum(power, 0) assert_almost_equal(np.maximum(power, 0), res_power, decimal=4) def test_proportion_ztests(): # currently only consistency test with proportions chisquare # Note: alternative handling is generic res1 = smprop.proportions_ztest(15, 20., value=0.5, prop_var=0.5) res2 = smprop.proportions_chisquare(15, 20., value=0.5) assert_almost_equal(res1[1], res2[1], decimal=13) res1 = smprop.proportions_ztest(np.asarray([15, 10]), np.asarray([20., 20]), value=0, prop_var=None) res2 = smprop.proportions_chisquare(np.asarray([15, 10]), np.asarray([20., 20])) # test only p-value assert_almost_equal(res1[1], res2[1], decimal=13) def test_confint_2indep(): # alpha = 0.05 count1, nobs1 = 7, 34 count2, nobs2 = 1, 34 # result tables from Fagerland et al 2015 ''' diff: Wald 0.029 0.32 0.29 Agresti–Caffo 0.012 0.32 0.31 Newcombe hybrid score 0.019 0.34 0.32 Miettinen–Nurminen asymptotic score 0.028 0.34 0.31 Santner–Snell exact unconditional -0.069 0.41 0.48 Chan–Zhang exact unconditional 0.019 0.36 0.34 Agresti–Min exact unconditional 0.024 0.35 0.33 ratio: Katz log 0.91 54 4.08 Adjusted log 0.92 27 3.38 Inverse sinh 1.17 42 3.58 Koopman asymptotic score 1.21 43 3.57 Chan–Zhang 1.22 181 5.00 Agresti–Min 1.15 89 4.35 odds-ratio Woolf logit 0.99 74 4.31 Gart adjusted logit 0.98 38 3.65 Independence-smoothed logit 0.99 60 4.11 Cornfield exact conditional 0.97 397 6.01 Cornfield mid-p 1.19 200 5.12 Baptista–Pike exact conditional 1.00 195 5.28 Baptista–Pike mid-p 1.33 99 4.31 Agresti–Min exact unconditional 1.19 72 4.10 ''' # pylint: disable=W0105 ci = confint_proportions_2indep(count1, nobs1, count2, nobs2, method='newcomb', compare='diff', alpha=0.05) # one decimal to upp added from regression result assert_allclose(ci, [0.019, 0.340], atol=0.005) ci = confint_proportions_2indep(count1, nobs1, count2, nobs2, method='wald', compare='diff', alpha=0.05) assert_allclose(ci, [0.029, 0.324], atol=0.005) ci = confint_proportions_2indep(count1, nobs1, count2, nobs2, method='agresti-caffo', compare='diff', alpha=0.05) assert_allclose(ci, [0.012, 0.322], atol=0.005) ci = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare='diff', method='score', correction=True) assert_allclose(ci, [0.028, 0.343], rtol=0.03) # ratio ci = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare='ratio', method='log') assert_allclose(ci, [0.91, 54], rtol=0.01) ci = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare='ratio', method='log-adjusted') assert_allclose(ci, [0.92, 27], rtol=0.01) ci = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare='ratio', method='score', correction=False) assert_allclose(ci, [1.21, 43], rtol=0.01) # odds-ratio ci = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare='or', method='logit') assert_allclose(ci, [0.99, 74], rtol=0.01) ci = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare='or', method='logit-adjusted') assert_allclose(ci, [0.98, 38], rtol=0.01) ci = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare='or', method='logit-smoothed') assert_allclose(ci, [0.99, 60], rtol=0.01) ci = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare='odds-ratio', method='score', correction=True) # regression test assert_allclose(ci, [1.246622, 56.461576], rtol=0.01) def test_confint_2indep_propcis(): # unit tests compared to R package PropCis # alpha = 0.05 count1, nobs1 = 7, 34 count2, nobs2 = 1, 34 # > library(PropCIs) # > diffscoreci(7, 34, 1, 34, 0.95) ci = 0.0270416, 0.3452912 ci1 = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare="diff", method="score", correction=False) assert_allclose(ci1, ci, atol=0.002) # lower agreement (iterative) # > wald2ci(7, 34, 1, 34, 0.95, adjust="AC") ci = 0.01161167, 0.32172166 ci1 = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare="diff", method="agresti-caffo") assert_allclose(ci1, ci, atol=6e-7) # > wald2ci(7, 34, 1, 34, 0.95, adjust="Wald") ci = 0.02916942, 0.32377176 ci1 = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare="diff", method="wald", correction=False) assert_allclose(ci1, ci, atol=6e-7) # > orscoreci(7, 34, 1, 34, 0.95) ci = 1.246309, 56.486130 ci1 = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare="odds-ratio", method="score", correction=True) assert_allclose(ci1, ci, rtol=5e-4) # lower agreement (iterative) # > riskscoreci(7, 34, 1, 34, 0.95) ci = 1.220853, 42.575718 ci1 = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare="ratio", method="score", correction=False) assert_allclose(ci1, ci, atol=6e-7) def test_score_test_2indep(): # this does not verify the statistic and pvalue yet count1, nobs1 = 7, 34 count2, nobs2 = 1, 34 for co in ['diff', 'ratio', 'or']: res = score_test_proportions_2indep(count1, nobs1, count2, nobs2, compare=co) assert_allclose(res.prop1_null, res.prop2_null, rtol=1e-10) # check that equality case is handled val = 0 if co == 'diff' else 1. s0, pv0 = score_test_proportions_2indep(count1, nobs1, count2, nobs2, compare=co, value=val, return_results=False)[:2] s1, pv1 = score_test_proportions_2indep(count1, nobs1, count2, nobs2, compare=co, value=val + 1e-10, return_results=False)[:2] assert_allclose(s0, s1, rtol=1e-8) assert_allclose(pv0, pv1, rtol=1e-8) s1, pv1 = score_test_proportions_2indep(count1, nobs1, count2, nobs2, compare=co, value=val - 1e-10, return_results=False)[:2] assert_allclose(s0, s1, rtol=1e-8) assert_allclose(pv0, pv1, rtol=1e-8) def test_test_2indep(): # this checks the pvalue of the hypothesis test at value equal to the # confidence limit alpha = 0.05 count1, nobs1 = 7, 34 count2, nobs2 = 1, 34 methods_both = [ ('diff', 'agresti-caffo'), # ('diff', 'newcomb'), # only confint ('diff', 'score'), ('diff', 'wald'), ('ratio', 'log'), ('ratio', 'log-adjusted'), ('ratio', 'score'), ('odds-ratio', 'logit'), ('odds-ratio', 'logit-adjusted'), ('odds-ratio', 'logit-smoothed'), ('odds-ratio', 'score'), ] for co, method in methods_both: low, upp = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare=co, method=method, alpha=alpha, correction=False) res = smprop.test_proportions_2indep( count1, nobs1, count2, nobs2, value=low, compare=co, method=method, correction=False) assert_allclose(res.pvalue, alpha, atol=1e-10) res = smprop.test_proportions_2indep( count1, nobs1, count2, nobs2, value=upp, compare=co, method=method, correction=False) assert_allclose(res.pvalue, alpha, atol=1e-10) _, pv = smprop.test_proportions_2indep( count1, nobs1, count2, nobs2, value=upp, compare=co, method=method, alternative='smaller', correction=False, return_results=False) assert_allclose(pv, alpha / 2, atol=1e-10) _, pv = smprop.test_proportions_2indep( count1, nobs1, count2, nobs2, value=low, compare=co, method=method, alternative='larger', correction=False, return_results=False) assert_allclose(pv, alpha / 2, atol=1e-10) # test Miettinen/Nurminen small sample correction co, method = 'ratio', 'score' low, upp = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare=co, method=method, alpha=alpha, correction=True) res = smprop.test_proportions_2indep( count1, nobs1, count2, nobs2, value=low, compare=co, method=method, correction=True) assert_allclose(res.pvalue, alpha, atol=1e-10) def test_equivalence_2indep(): # this checks the pvalue of the equivalence test at value equal to the # confidence limit alpha = 0.05 count1, nobs1 = 7, 34 count2, nobs2 = 1, 34 methods_both = [ ('diff', 'agresti-caffo'), # ('diff', 'newcomb'), # only confint ('diff', 'score'), ('diff', 'wald'), ('ratio', 'log'), ('ratio', 'log-adjusted'), ('ratio', 'score'), ('odds-ratio', 'logit'), ('odds-ratio', 'logit-adjusted'), ('odds-ratio', 'logit-smoothed'), ('odds-ratio', 'score'), ] for co, method in methods_both: low, upp = confint_proportions_2indep(count1, nobs1, count2, nobs2, compare=co, method=method, alpha=2 * alpha, correction=False) res = smprop.tost_proportions_2indep( count1, nobs1, count2, nobs2, low, upp, compare=co, method=method, correction=False) assert_allclose(res.pvalue, alpha, atol=1e-10) def test_score_confint_koopman_nam(): # example Koopman, based on Nam 1995 x0, n0 = 16, 80 x1, n1 = 36, 40 # x = x0 + x1 # n = n0 + n1 # p0 = x0 / n0 # p1 = x1 / n1 results_nam = Holder() results_nam.p0_roots = [0.1278, 0.2939, 0.4876] results_nam.conf_int = [2.940, 7.152] res = smprop._confint_riskratio_koopman(x1, n1, x0, n0, alpha=0.05) assert_allclose(res._p_roots, results_nam.p0_roots, atol=4) assert_allclose(res.confint, results_nam.conf_int, atol=3) table = [67, 9, 7, 16] # [67, 7, 9, 16] resp = smprop._confint_riskratio_paired_nam(table, alpha=0.05) # TODO: currently regression test, need verified results ci_old = [0.917832, 1.154177] assert_allclose(resp.confint, ci_old, atol=3) def test_power_2indep(): # test against R pow_ = power_proportions_2indep(-0.25, 0.75, 76.70692) assert_allclose(pow_.power, 0.9, atol=1e-8) n = samplesize_proportions_2indep_onetail(-0.25, 0.75, 0.9, ratio=1, alpha=0.05, value=0, alternative='two-sided') assert_allclose(n, 76.70692, atol=1e-5) power_proportions_2indep(-0.25, 0.75, 62.33551, alternative="smaller") assert_allclose(pow_.power, 0.9, atol=1e-8) pow_ = power_proportions_2indep(0.25, 0.5, 62.33551, alternative="smaller") assert_array_less(pow_.power, 0.05) pow_ = power_proportions_2indep(0.25, 0.5, 62.33551, alternative="larger", return_results=False) assert_allclose(pow_, 0.9, atol=1e-8) pow_ = power_proportions_2indep(-0.15, 0.65, 83.4373, return_results=False) assert_allclose(pow_, 0.5, atol=1e-8) n = samplesize_proportions_2indep_onetail(-0.15, 0.65, 0.5, ratio=1, alpha=0.05, value=0, alternative='two-sided') assert_allclose(n, 83.4373, atol=0.05) # Stata example from statsmodels.stats.power import normal_sample_size_one_tail res = power_proportions_2indep(-0.014, 0.015, 550, ratio=1.) assert_allclose(res.power, 0.7415600, atol=1e-7) n = normal_sample_size_one_tail(-0.014, 0.7415600, 0.05 / 2, std_null=res.std_null, std_alternative=res.std_alt) assert_allclose(n, 550, atol=0.05) n2 = samplesize_proportions_2indep_onetail(-0.014, 0.015, 0.7415600, ratio=1, alpha=0.05, value=0, alternative='two-sided') assert_allclose(n2, n, rtol=1e-13) statsmodels-0.12.2/statsmodels/stats/tests/test_qsturng.py000066400000000000000000000015141400612667500241240ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Mar 28 13:49:11 2012 Author: Josef Perktold """ import pytest import numpy as np from numpy.testing import assert_almost_equal from statsmodels.stats.libqsturng import qsturng, psturng from statsmodels.sandbox.stats.multicomp import get_tukeyQcrit @pytest.mark.parametrize('alpha', [0.01, 0.05]) @pytest.mark.parametrize('k', np.arange(2, 11)) def test_qstrung(alpha, k): rows = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 24, 30, 40, 60, 120, 9999] c1 = get_tukeyQcrit(k, rows, alpha=alpha) c2 = qsturng(1 - alpha, k, rows) assert_almost_equal(c1, c2, decimal=2) # roundtrip assert_almost_equal(psturng(qsturng(1 - alpha, k, rows), k, rows), alpha, 5) statsmodels-0.12.2/statsmodels/stats/tests/test_rates_poisson.py000066400000000000000000000240511400612667500253120ustar00rootroot00000000000000 import pytest from numpy.testing import assert_allclose, assert_equal # we cannot import test_poisson_2indep directly, pytest treats that as test import statsmodels.stats.rates as smr from statsmodels.stats.rates import etest_poisson_2indep def test_twosample_poisson(): # testing against two examples in Gu et al # example 1 count1, n1, count2, n2 = 60, 51477.5, 30, 54308.7 s1, pv1 = smr.test_poisson_2indep(count1, n1, count2, n2, method='wald') pv1r = 0.000356 assert_allclose(pv1, pv1r*2, rtol=0, atol=5e-6) assert_allclose(s1, 3.384913, atol=0, rtol=5e-6) # regression test s2, pv2 = smr.test_poisson_2indep(count1, n1, count2, n2, method='score') pv2r = 0.000316 assert_allclose(pv2, pv2r*2, rtol=0, atol=5e-6) assert_allclose(s2, 3.417402, atol=0, rtol=5e-6) # regression test s2, pv2 = smr.test_poisson_2indep(count1, n1, count2, n2, method='sqrt') pv2r = 0.000285 assert_allclose(pv2, pv2r*2, rtol=0, atol=5e-6) assert_allclose(s2, 3.445485, atol=0, rtol=5e-6) # regression test # two-sided # example2 # I don't know why it's only 2.5 decimal agreement, rounding? count1, n1, count2, n2 = 41, 28010, 15, 19017 s1, pv1 = smr.test_poisson_2indep(count1, n1, count2, n2, method='wald', ratio_null=1.5) pv1r = 0.2309 assert_allclose(pv1, pv1r*2, rtol=0, atol=5e-3) assert_allclose(s1, 0.735447, atol=0, rtol=5e-6) # regression test s2, pv2 = smr.test_poisson_2indep(count1, n1, count2, n2, method='score', ratio_null=1.5) pv2r = 0.2398 assert_allclose(pv2, pv2r*2, rtol=0, atol=5e-3) assert_allclose(s2, 0.706631, atol=0, rtol=5e-6) # regression test s2, pv2 = smr.test_poisson_2indep(count1, n1, count2, n2, method='sqrt', ratio_null=1.5) pv2r = 0.2499 assert_allclose(pv2, pv2r*2, rtol=0, atol=5e-3) assert_allclose(s2, 0.674401, atol=0, rtol=5e-6) # regression test # one-sided # example 1 onesided count1, n1, count2, n2 = 60, 51477.5, 30, 54308.7 s1, pv1 = smr.test_poisson_2indep(count1, n1, count2, n2, method='wald', alternative='larger') pv1r = 0.000356 assert_allclose(pv1, pv1r, rtol=0, atol=5e-6) s2, pv2 = smr.test_poisson_2indep(count1, n1, count2, n2, method='score', alternative='larger') pv2r = 0.000316 assert_allclose(pv2, pv2r, rtol=0, atol=5e-6) s2, pv2 = smr.test_poisson_2indep(count1, n1, count2, n2, method='sqrt', alternative='larger') pv2r = 0.000285 assert_allclose(pv2, pv2r, rtol=0, atol=5e-6) # 'exact-cond', 'cond-midp' s2, pv2 = smr.test_poisson_2indep(count1, n1, count2, n2, method='exact-cond', ratio_null=1, alternative='larger') pv2r = 0.000428 # typo in Gu et al, switched pvalues between C and M assert_allclose(pv2, pv2r, rtol=0, atol=5e-4) s2, pv2 = smr.test_poisson_2indep(count1, n1, count2, n2, method='cond-midp', ratio_null=1, alternative='larger') pv2r = 0.000310 assert_allclose(pv2, pv2r, rtol=0, atol=5e-4) _, pve1 = etest_poisson_2indep(count1, n1, count2, n2, method='score', ratio_null=1, alternative='larger') pve1r = 0.000298 assert_allclose(pve1, pve1r, rtol=0, atol=5e-4) _, pve1 = etest_poisson_2indep(count1, n1, count2, n2, method='wald', ratio_null=1, alternative='larger') pve1r = 0.000298 assert_allclose(pve1, pve1r, rtol=0, atol=5e-4) # example2 onesided # I don't know why it's only 2.5 decimal agreement, rounding? count1, n1, count2, n2 = 41, 28010, 15, 19017 s1, pv1 = smr.test_poisson_2indep(count1, n1, count2, n2, method='wald', ratio_null=1.5, alternative='larger') pv1r = 0.2309 assert_allclose(pv1, pv1r, rtol=0, atol=5e-4) s2, pv2 = smr.test_poisson_2indep(count1, n1, count2, n2, method='score', ratio_null=1.5, alternative='larger') pv2r = 0.2398 assert_allclose(pv2, pv2r, rtol=0, atol=5e-4) s2, pv2 = smr.test_poisson_2indep(count1, n1, count2, n2, method='sqrt', ratio_null=1.5, alternative='larger') pv2r = 0.2499 assert_allclose(pv2, pv2r, rtol=0, atol=5e-4) # 'exact-cond', 'cond-midp' s2, pv2 = smr.test_poisson_2indep(count1, n1, count2, n2, method='exact-cond', ratio_null=1.5, alternative='larger') pv2r = 0.2913 assert_allclose(pv2, pv2r, rtol=0, atol=5e-4) s2, pv2 = smr.test_poisson_2indep(count1, n1, count2, n2, method='cond-midp', ratio_null=1.5, alternative='larger') pv2r = 0.2450 assert_allclose(pv2, pv2r, rtol=0, atol=5e-4) _, pve2 = etest_poisson_2indep(count1, n1, count2, n2, method='score', ratio_null=1.5, alternative='larger') pve2r = 0.2453 assert_allclose(pve2, pve2r, rtol=0, atol=5e-4) _, pve2 = etest_poisson_2indep(count1, n1, count2, n2, method='wald', ratio_null=1.5, alternative='larger') pve2r = 0.2453 assert_allclose(pve2, pve2r, rtol=0, atol=5e-4) def test_twosample_poisson_r(): # testing against R package `exactci from .results.results_rates import res_pexact_cond, res_pexact_cond_midp # example 1 from Gu count1, n1, count2, n2 = 60, 51477.5, 30, 54308.7 res2 = res_pexact_cond res1 = smr.test_poisson_2indep(count1, n1, count2, n2, method='exact-cond') assert_allclose(res1.pvalue, res2.p_value, rtol=1e-13) assert_allclose(res1.ratio, res2.estimate, rtol=1e-13) assert_equal(res1.ratio_null, res2.null_value) res2 = res_pexact_cond_midp res1 = smr.test_poisson_2indep(count1, n1, count2, n2, method='cond-midp') assert_allclose(res1.pvalue, res2.p_value, rtol=0, atol=5e-6) assert_allclose(res1.ratio, res2.estimate, rtol=1e-13) assert_equal(res1.ratio_null, res2.null_value) # one-sided # > pe = poisson.exact(c(60, 30), c(51477.5, 54308.7), r=1.2, # alternative="less", tsmethod="minlike", midp=TRUE) # > pe$p.value pv2 = 0.9949053964701466 rest = smr.test_poisson_2indep(count1, n1, count2, n2, method='cond-midp', ratio_null=1.2, alternative='smaller') assert_allclose(rest.pvalue, pv2, rtol=1e-12) # > pe = poisson.exact(c(60, 30), c(51477.5, 54308.7), r=1.2, # alternative="greater", tsmethod="minlike", midp=TRUE) # > pe$p.value pv2 = 0.005094603529853279 rest = smr.test_poisson_2indep(count1, n1, count2, n2, method='cond-midp', ratio_null=1.2, alternative='larger') assert_allclose(rest.pvalue, pv2, rtol=1e-12) # > pe = poisson.exact(c(60, 30), c(51477.5, 54308.7), r=1.2, # alternative="greater", tsmethod="minlike", midp=FALSE) # > pe$p.value pv2 = 0.006651774552714537 rest = smr.test_poisson_2indep(count1, n1, count2, n2, method='exact-cond', ratio_null=1.2, alternative='larger') assert_allclose(rest.pvalue, pv2, rtol=1e-12) # > pe = poisson.exact(c(60, 30), c(51477.5, 54308.7), r=1.2, # alternative="less", tsmethod="minlike", midp=FALSE) # > pe$p.value pv2 = 0.9964625674930079 rest = smr.test_poisson_2indep(count1, n1, count2, n2, method='exact-cond', ratio_null=1.2, alternative='smaller') assert_allclose(rest.pvalue, pv2, rtol=1e-12) def test_tost_poisson(): count1, n1, count2, n2 = 60, 51477.5, 30, 54308.7 # # central conf_int from R exactci low, upp = 1.339735721772650, 3.388365573616252 res = smr.tost_poisson_2indep(count1, n1, count2, n2, low, upp, method="exact-cond") assert_allclose(res.pvalue, 0.025, rtol=1e-12) methods = ['wald', 'score', 'sqrt', 'exact-cond', 'cond-midp'] # test that we are in the correct range for other methods for meth in methods: res = smr.tost_poisson_2indep(count1, n1, count2, n2, low, upp, method=meth) assert_allclose(res.pvalue, 0.025, atol=0.01) cases_alt = { ("two-sided", "wald"): 0.07136366497984171, ("two-sided", "score"): 0.0840167525117227, ("two-sided", "sqrt"): 0.0804675114297235, ("two-sided", "exact-cond"): 0.1301269270479679, ("two-sided", "cond-midp"): 0.09324590196774807, ("two-sided", "etest"): 0.09054824785458056, ("two-sided", "etest-wald"): 0.06895289560607239, ("larger", "wald"): 0.03568183248992086, ("larger", "score"): 0.04200837625586135, ("larger", "sqrt"): 0.04023375571486175, ("larger", "exact-cond"): 0.08570447732927276, ("larger", "cond-midp"): 0.04882345224905293, ("larger", "etest"): 0.043751060642682936, ("larger", "etest-wald"): 0.043751050280207024, ("smaller", "wald"): 0.9643181675100791, ("smaller", "score"): 0.9579916237441386, ("smaller", "sqrt"): 0.9597662442851382, ("smaller", "exact-cond"): 0.9880575728311669, ("smaller", "cond-midp"): 0.9511765477509471, ("smaller", "etest"): 0.9672396898656999, ("smaller", "etest-wald"): 0.9672397002281757 } @pytest.mark.parametrize('case', list(cases_alt.keys())) def test_alternative(case): # regression test numbers, but those are close to each other alt, meth = case count1, n1, count2, n2 = 6, 51., 1, 54. _, pv = smr.test_poisson_2indep(count1, n1, count2, n2, method=meth, ratio_null=1.2, alternative=alt) assert_allclose(pv, cases_alt[case], rtol=1e-13) statsmodels-0.12.2/statsmodels/stats/tests/test_regularized_covariance.py000066400000000000000000000027541400612667500271370ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_equal, assert_ from statsmodels.stats.regularized_covariance import ( _calc_nodewise_row, _calc_nodewise_weight, _calc_approx_inv_cov, RegularizedInvCovariance) def test_calc_nodewise_row(): np.random.seed(435265) X = np.random.normal(size=(50, 3)) ghat = _calc_nodewise_row(X, 0, 0.01) assert_equal(ghat.shape, (2,)) def test_calc_nodewise_weight(): np.random.seed(435265) X = np.random.normal(size=(50, 3)) ghat = np.random.normal(size=2) that = _calc_nodewise_weight(X, ghat, 0, 0.01) assert_(isinstance(that, float)) def test_calc_approx_inv_cov(): np.random.seed(435265) X = np.random.normal(size=(50, 3)) ghat_l = [] that_l = [] for i in range(3): ghat = _calc_nodewise_row(X, i, 0.01) that = _calc_nodewise_weight(X, ghat, i, 0.01) ghat_l.append(ghat) that_l.append(that) theta_hat = _calc_approx_inv_cov(np.array(ghat_l), np.array(that_l)) assert_equal(theta_hat.shape, (3, 3)) def test_fit(): np.random.seed(435265) X = np.random.normal(size=(50, 3)) inv = np.linalg.inv(np.cov(X.T)) regcov = RegularizedInvCovariance(exog=X) regcov.fit() # check that unregularized is what we expect diff = np.linalg.norm(regcov.approx_inv_cov() - inv) assert_(diff < 0.1) # check that regularizing actually does something regcov.fit(alpha=0.5) assert_(np.sum(regcov.approx_inv_cov() == 0) > np.sum(inv == 0)) statsmodels-0.12.2/statsmodels/stats/tests/test_robust_compare.py000066400000000000000000000254751400612667500254610ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Fri Aug 16 13:41:12 2013 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_equal, assert_allclose, assert_raises import pytest from statsmodels.stats.robust_compare import ( TrimmedMean, trim_mean, trimboth) import statsmodels.stats.oneway as smo from statsmodels.tools.testing import Holder # TODO: scipy trim1 is not compatible anymore with my old unit tests from scipy.stats import trim1 class Test_Trim(object): # test trim functions # taken from scipy and adjusted def t_est_trim1(self): a = np.arange(11) assert_equal(trim1(a, 0.1), np.arange(10)) assert_equal(trim1(a, 0.2), np.arange(9)) assert_equal(trim1(a, 0.2, tail='left'), np.arange(2, 11)) assert_equal(trim1(a, 3 / 11., tail='left'), np.arange(3, 11)) def test_trimboth(self): a = np.arange(11) a2 = np.arange(24).reshape(6, 4) a3 = np.arange(24).reshape(6, 4, order='F') assert_equal(trimboth(a, 3 / 11.), np.arange(3, 8)) assert_equal(trimboth(a, 0.2), np.array([2, 3, 4, 5, 6, 7, 8])) assert_equal(trimboth(a2, 0.2), np.arange(4, 20).reshape(4, 4)) assert_equal(trimboth(a3, 2 / 6.), np.array([[2, 8, 14, 20], [3, 9, 15, 21]])) assert_raises(ValueError, trimboth, np.arange(24).reshape(4, 6).T, 4 / 6.) def test_trim_mean(self): # a = np.array([4, 8, 2, 0, 9, 5, 10, 1, 7, 3, 6]) idx = np.array([3, 5, 0, 1, 2, 4]) a2 = np.arange(24).reshape(6, 4)[idx, :] a3 = np.arange(24).reshape(6, 4, order='F')[idx, :] assert_equal(trim_mean(a3, 2 / 6.), np.array([2.5, 8.5, 14.5, 20.5])) assert_equal(trim_mean(a2, 2 / 6.), np.array([10., 11., 12., 13.])) idx4 = np.array([1, 0, 3, 2]) a4 = np.arange(24).reshape(4, 6)[idx4, :] assert_equal(trim_mean(a4, 2 / 6.), np.array([9., 10., 11., 12., 13., 14.])) # shuffled arange(24) a = np.array([7, 11, 12, 21, 16, 6, 22, 1, 5, 0, 18, 10, 17, 9, 19, 15, 23, 20, 2, 14, 4, 13, 8, 3]) assert_equal(trim_mean(a, 2 / 6.), 11.5) assert_equal(trim_mean([5, 4, 3, 1, 2, 0], 2 / 6.), 2.5) # check axis argument np.random.seed(1234) a = np.random.randint(20, size=(5, 6, 4, 7)) for axis in [0, 1, 2, 3, -1]: res1 = trim_mean(a, 2 / 6., axis=axis) res2 = trim_mean(np.rollaxis(a, axis), 2 / 6.) assert_equal(res1, res2) res1 = trim_mean(a, 2 / 6., axis=None) res2 = trim_mean(a.ravel(), 2 / 6.) assert_equal(res1, res2) class TestTrimmedR1(object): @classmethod def setup_class(cls): x = np.array([77, 87, 88, 114, 151, 210, 219, 246, 253, 262, 296, 299, 306, 376, 428, 515, 666, 1310, 2611]) cls.get_results() # attach k and results cls.tm = TrimmedMean(x, cls.k / 19) @classmethod def get_results(cls): cls.k = 1 # results from R WRS2 cls.res_basic = np.array([ 342.705882352941, 92.3342348150314, 380.157894736842, 92.9416968861829, 129679.029239766]) # results from R PairedData ytt1 = Holder() ytt1.statistic = 3.71157981694944 ytt1.parameter = 16 ytt1.p_value = 0.00189544440273015 ytt1.conf_int = np.array([146.966048669017, 538.445716036866]) ytt1.estimate = 342.705882352941 ytt1.null_value = 0 ytt1.alternative = 'two.sided' ytt1.method = 'One sample Yuen test, trim=0.0526315789473684' ytt1.data_name = 'x' cls.ytt1 = ytt1 def test_basic(self): tm = self.tm assert_equal(tm.nobs, 19) assert_equal(tm.nobs_reduced, 17) assert_equal(tm.fraction, self.k / 19) assert_equal(tm.data_trimmed.shape[0], tm.nobs_reduced) res = [tm.mean_trimmed, tm.std_mean_trimmed, tm.mean_winsorized, tm.std_mean_winsorized, tm.var_winsorized] assert_allclose(res, self.res_basic, rtol=1e-15) def test_inference(self): ytt1 = self.ytt1 tm = self.tm ttt = tm.ttest_mean() assert_allclose(ttt[0], ytt1.statistic, rtol=1e-13) assert_allclose(ttt[1], ytt1.p_value, rtol=1e-13) assert_equal(ttt[2], ytt1.parameter) assert_allclose(tm.mean_trimmed, ytt1.estimate, rtol=1e-13) # regression test for Winsorized t-test, # mean, std for it are separately unit tested, # df is nobs_reduced-1 in references ttw_statistic, ttw_pvalue, tt_w_df = (4.090283559190728, 0.0008537789444194812, 16) ttw = tm.ttest_mean(transform='winsorized') assert_allclose(ttw[0], ttw_statistic, rtol=1e-13) assert_allclose(ttw[1], ttw_pvalue, rtol=1e-13) assert_equal(ttw[2], tt_w_df) def test_other(self): tm = self.tm tm2 = tm.reset_fraction(0.) assert_equal(tm2.nobs_reduced, tm2.nobs) @pytest.mark.parametrize('axis', [0, 1]) def test_vectorized(self, axis): tm = self.tm x = tm.data x2 = np.column_stack((x, 2 * x)) if axis == 0: tm2d = TrimmedMean(x2, self.k / 19, axis=0) else: tm2d = TrimmedMean(x2.T, self.k / 19, axis=1) t1 = [tm.mean_trimmed, 2 * tm.mean_trimmed] assert_allclose(tm2d.mean_trimmed, t1, rtol=1e-13) t1 = [tm.var_winsorized, 4 * tm.var_winsorized] assert_allclose(tm2d.var_winsorized, t1, rtol=1e-13) t1 = [tm.std_mean_trimmed, 2 * tm.std_mean_trimmed] assert_allclose(tm2d.std_mean_trimmed, t1, rtol=1e-13) t1 = [tm.mean_winsorized, 2 * tm.mean_winsorized] assert_allclose(tm2d.mean_winsorized, t1, rtol=1e-13) t1 = [tm.std_mean_winsorized, 2 * tm.std_mean_winsorized] assert_allclose(tm2d.std_mean_winsorized, t1, rtol=1e-13) s2, pv2, df2 = tm2d.ttest_mean() s, pv, df = tm.ttest_mean() assert_allclose(s2, [s, s], rtol=1e-13) assert_allclose(pv2, [pv, pv], rtol=1e-13) assert_allclose(df2, df, rtol=1e-13) s2, pv2, df2 = tm2d.ttest_mean(transform='winsorized') s, pv, df = tm.ttest_mean(transform='winsorized') assert_allclose(s2, [s, s], rtol=1e-13) assert_allclose(pv2, [pv, pv], rtol=1e-13) assert_allclose(df2, df, rtol=1e-13) class TestTrimmedRAnova(object): @classmethod def setup_class(cls): x = [np.array([452., 874., 554., 447., 356., 754., 558., 574., 664., 682., 547., 435., 245.]), np.array([546., 547., 774., 465., 459., 665., 467., 365., 589., 534., 456., 651., 654., 665., 546., 537.]), np.array([785., 458., 886., 536., 669., 857., 821., 772., 732., 689., 654., 597., 830., 827.])] cls.x = x cls.get_results() # attach k and results @classmethod def get_results(cls): cls.res_m = [549.3846153846154, 557.5, 722.3571428571429] # results from R WRS2 # > t1w = t1way(y ~ g, df3, tr=1/13) cls.res_oneway = Holder(test=8.81531710400927, df1=2, df2=19.8903710685394, p_value=0.00181464966984701, effsize=0.647137153056774, ) # > yt = yuen(y ~ g, df3[1:29, ], tr=1/13) # WRS2 cls.res_2s = Holder(test=0.161970203096559, conf_int=np.array([-116.437383793431, 99.9568643129114]), p_value=0.873436269777141, df=15.3931262881751, diff=-8.24025974025983, effsize=0.0573842557922749, ) # from library onewaytests # > bft = bf.test(y ~ g, df3) cls.res_bfm = Holder(statistic=7.10900606421182, parameter=np.array([2, 31.4207256105052]), p_value=0.00283841965791224, alpha=0.05, method='Brown-Forsythe Test' ) # > oww = oneway.test(y ~ g, df3, var.equal = FALSE) cls.res_wa = Holder(statistic=8.02355212103924, parameter=np.array([2, 24.272320628139]), p_value=0.00211423625518082, method=('One-way analysis of means ' '(not assuming equal variances)') ) # > ow = oneway.test(y ~ g, df3, var.equal = TRUE) cls.res_fa = Holder(statistic=7.47403193349076, parameter=np.array([2, 40]), p_value=0.00174643304119871, method='One-way analysis of means' ) def test_oneway(self): r1 = self.res_oneway r2s = self.res_2s res_bfm = self.res_bfm res_wa = self.res_wa res_fa = self.res_fa # check we got the correct data m = [x_i.mean() for x_i in self.x] assert_allclose(m, self.res_m, rtol=1e-13) # 3 sample case resg = smo.anova_oneway(self.x, use_var="unequal", trim_frac=1 / 13) # assert_allclose(res.statistic, res_bfm.statistic, rtol=1e-13) assert_allclose(resg.pvalue, r1.p_value, rtol=1e-13) assert_allclose(resg.df, [r1.df1, r1.df2], rtol=1e-13) # df # 2-sample against yuen t-test resg = smo.anova_oneway(self.x[:2], use_var="unequal", trim_frac=1 / 13) # assert_allclose(res.statistic, res_bfm.statistic, rtol=1e-13) assert_allclose(resg.pvalue, r2s.p_value, rtol=1e-13) assert_allclose(resg.df, [1, r2s.df], rtol=1e-13) # df # no trimming bfm res = smo.anova_oneway(self.x, use_var="bf") assert_allclose(res[0], res_bfm.statistic, rtol=1e-13) assert_allclose(res.pvalue2, res_bfm.p_value, rtol=1e-13) assert_allclose(res.df2, res_bfm.parameter, rtol=1e-13) # df # no trimming welch res = smo.anova_oneway(self.x, use_var="unequal") assert_allclose(res.statistic, res_wa.statistic, rtol=1e-13) assert_allclose(res.pvalue, res_wa.p_value, rtol=1e-13) assert_allclose(res.df, res_wa.parameter, rtol=1e-13) # df # no trimming standard anova res = smo.anova_oneway(self.x, use_var="equal") assert_allclose(res.statistic, res_fa.statistic, rtol=1e-13) assert_allclose(res.pvalue, res_fa.p_value, rtol=1e-13) assert_allclose(res.df, res_fa.parameter, rtol=1e-13) # df statsmodels-0.12.2/statsmodels/stats/tests/test_sandwich.py000066400000000000000000000070101400612667500242160ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Tests for sandwich robust covariance estimation see also in regression for cov_hac compared to Gretl and sandbox.panel test_random_panel for comparing cov_cluster, cov_hac_panel and cov_white Created on Sat Dec 17 08:39:16 2011 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_almost_equal from statsmodels.regression.linear_model import OLS from statsmodels.tools.tools import add_constant import statsmodels.stats.sandwich_covariance as sw def test_cov_cluster_2groups(): #comparing cluster robust standard errors to Peterson #requires Petersen's test_data #http://www.kellogg.northwestern.edu/faculty/petersen/htm/papers/se/test_data.txt import os cur_dir = os.path.abspath(os.path.dirname(__file__)) fpath = os.path.join(cur_dir,"test_data.txt") pet = np.genfromtxt(fpath) endog = pet[:,-1] group = pet[:,0].astype(int) time = pet[:,1].astype(int) exog = add_constant(pet[:,2]) res = OLS(endog, exog).fit() cov01, covg, covt = sw.cov_cluster_2groups(res, group, group2=time) #Reference number from Petersen #http://www.kellogg.northwestern.edu/faculty/petersen/htm/papers/se/test_data.htm bse_petw = [0.0284, 0.0284] bse_pet0 = [0.0670, 0.0506] bse_pet1 = [0.0234, 0.0334] #year bse_pet01 = [0.0651, 0.0536] #firm and year bse_0 = sw.se_cov(covg) bse_1 = sw.se_cov(covt) bse_01 = sw.se_cov(cov01) #print res.HC0_se, bse_petw - res.HC0_se #print bse_0, bse_0 - bse_pet0 #print bse_1, bse_1 - bse_pet1 #print bse_01, bse_01 - bse_pet01 assert_almost_equal(bse_petw, res.HC0_se, decimal=4) assert_almost_equal(bse_0, bse_pet0, decimal=4) assert_almost_equal(bse_1, bse_pet1, decimal=4) assert_almost_equal(bse_01, bse_pet01, decimal=4) def test_hac_simple(): from statsmodels.datasets import macrodata d2 = macrodata.load_pandas().data g_gdp = 400*np.diff(np.log(d2['realgdp'].values)) g_inv = 400*np.diff(np.log(d2['realinv'].values)) exogg = add_constant(np.c_[g_gdp, d2['realint'][:-1].values]) res_olsg = OLS(g_inv, exogg).fit() #> NeweyWest(fm, lag = 4, prewhite = FALSE, sandwich = TRUE, verbose=TRUE, adjust=TRUE) #Lag truncation parameter chosen: 4 # (Intercept) ggdp lint cov1_r = [[ 1.40643899878678802, -0.3180328707083329709, -0.060621111216488610], [ -0.31803287070833292, 0.1097308348999818661, 0.000395311760301478], [ -0.06062111121648865, 0.0003953117603014895, 0.087511528912470993]] #> NeweyWest(fm, lag = 4, prewhite = FALSE, sandwich = TRUE, verbose=TRUE, adjust=FALSE) #Lag truncation parameter chosen: 4 # (Intercept) ggdp lint cov2_r = [[ 1.3855512908840137, -0.313309610252268500, -0.059720797683570477], [ -0.3133096102522685, 0.108101169035130618, 0.000389440793564339], [ -0.0597207976835705, 0.000389440793564336, 0.086211852740503622]] cov1 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=True) se1 = sw.se_cov(cov1) cov2 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=False) se2 = sw.se_cov(cov2) assert_almost_equal(cov1, cov1_r, decimal=14) assert_almost_equal(cov2, cov2_r, decimal=14) # compare default for nlags cov3 = sw.cov_hac_simple(res_olsg, use_correction=False) cov4 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=False) assert_almost_equal(cov3, cov4, decimal=14) statsmodels-0.12.2/statsmodels/stats/tests/test_statstools.py000066400000000000000000000262671400612667500246540ustar00rootroot00000000000000# TODO: Test robust skewness # TODO: Test robust kurtosis import numpy as np import pandas as pd from numpy.testing import (assert_almost_equal, assert_raises, assert_equal, assert_allclose) from statsmodels.stats._adnorm import normal_ad from statsmodels.stats.stattools import (omni_normtest, jarque_bera, durbin_watson, _medcouple_1d, medcouple, robust_kurtosis, robust_skewness) # a random array, rounded to 4 decimals x = np.array([-0.1184, -1.3403, 0.0063, -0.612, -0.3869, -0.2313, -2.8485, -0.2167, 0.4153, 1.8492, -0.3706, 0.9726, -0.1501, -0.0337, -1.4423, 1.2489, 0.9182, -0.2331, -0.6182, 0.183]) def test_durbin_watson(): #benchmark values from R car::durbinWatsonTest(x) #library("car") #> durbinWatsonTest(x) #[1] 1.95298958377419 #> durbinWatsonTest(x**2) #[1] 1.848802400319998 #> durbinWatsonTest(x[2:20]+0.5*x[1:19]) #[1] 1.09897993228779 #> durbinWatsonTest(x[2:20]+0.8*x[1:19]) #[1] 0.937241876707273 #> durbinWatsonTest(x[2:20]+0.9*x[1:19]) #[1] 0.921488912587806 st_R = 1.95298958377419 assert_almost_equal(durbin_watson(x), st_R, 14) st_R = 1.848802400319998 assert_almost_equal(durbin_watson(x**2), st_R, 14) st_R = 1.09897993228779 assert_almost_equal(durbin_watson(x[1:] + 0.5 * x[:-1]), st_R, 14) st_R = 0.937241876707273 assert_almost_equal(durbin_watson(x[1:] + 0.8 * x[:-1]), st_R, 14) st_R = 0.921488912587806 assert_almost_equal(durbin_watson(x[1:] + 0.9 * x[:-1]), st_R, 14) X = np.array([x, x]) st_R = 1.95298958377419 assert_almost_equal(durbin_watson(X, axis=1), np.array([st_R, st_R]), 14) assert_almost_equal(durbin_watson(X.T, axis=0), np.array([st_R, st_R]), 14) def test_omni_normtest(): #tests against R fBasics from scipy import stats st_pv_R = np.array( [[3.994138321207883, -1.129304302161460, 1.648881473704978], [0.1357325110375005, 0.2587694866795507, 0.0991719192710234]]) nt = omni_normtest(x) assert_almost_equal(nt, st_pv_R[:, 0], 14) st = stats.skewtest(x) assert_almost_equal(st, st_pv_R[:, 1], 14) kt = stats.kurtosistest(x) assert_almost_equal(kt, st_pv_R[:, 2], 11) st_pv_R = np.array( [[34.523210399523926, 4.429509162503833, 3.860396220444025], [3.186985686465249e-08, 9.444780064482572e-06, 1.132033129378485e-04]]) x2 = x**2 #TODO: fix precision in these test with relative tolerance nt = omni_normtest(x2) assert_almost_equal(nt, st_pv_R[:, 0], 12) st = stats.skewtest(x2) assert_almost_equal(st, st_pv_R[:, 1], 12) kt = stats.kurtosistest(x2) assert_almost_equal(kt, st_pv_R[:, 2], 12) def test_omni_normtest_axis(reset_randomstate): #test axis of omni_normtest x = np.random.randn(25, 3) nt1 = omni_normtest(x) nt2 = omni_normtest(x, axis=0) nt3 = omni_normtest(x.T, axis=1) assert_almost_equal(nt2, nt1, decimal=13) assert_almost_equal(nt3, nt1, decimal=13) def test_jarque_bera(): #tests against R fBasics st_pv_R = np.array([1.9662677226861689, 0.3741367669648314]) jb = jarque_bera(x)[:2] assert_almost_equal(jb, st_pv_R, 14) st_pv_R = np.array([78.329987305556, 0.000000000000]) jb = jarque_bera(x**2)[:2] assert_almost_equal(jb, st_pv_R, 13) st_pv_R = np.array([5.7135750796706670, 0.0574530296971343]) jb = jarque_bera(np.log(x**2))[:2] assert_almost_equal(jb, st_pv_R, 14) st_pv_R = np.array([2.6489315748495761, 0.2659449923067881]) jb = jarque_bera(np.exp(-x**2))[:2] assert_almost_equal(jb, st_pv_R, 14) def test_shapiro(): #tests against R fBasics #testing scipy.stats from scipy.stats import shapiro st_pv_R = np.array([0.939984787255526, 0.239621898000460]) sh = shapiro(x) assert_almost_equal(sh, st_pv_R, 4) #st is ok -7.15e-06, pval agrees at -3.05e-10 st_pv_R = np.array([5.799574255943298e-01, 1.838456834681376e-06 * 1e4]) sh = shapiro(x**2) * np.array([1, 1e4]) assert_almost_equal(sh, st_pv_R, 5) st_pv_R = np.array([0.91730442643165588, 0.08793704167882448]) sh = shapiro(np.log(x**2)) assert_almost_equal(sh, st_pv_R, 5) #diff is [ 9.38773155e-07, 5.48221246e-08] st_pv_R = np.array([0.818361863493919373, 0.001644620895206969]) sh = shapiro(np.exp(-x**2)) assert_almost_equal(sh, st_pv_R, 5) def test_adnorm(): #tests against R fBasics st_pv = [] st_pv_R = np.array([0.5867235358882148, 0.1115380760041617]) ad = normal_ad(x) assert_almost_equal(ad, st_pv_R, 12) st_pv.append(st_pv_R) st_pv_R = np.array([2.976266267594575e+00, 8.753003709960645e-08]) ad = normal_ad(x**2) assert_almost_equal(ad, st_pv_R, 11) st_pv.append(st_pv_R) st_pv_R = np.array([0.4892557856308528, 0.1968040759316307]) ad = normal_ad(np.log(x**2)) assert_almost_equal(ad, st_pv_R, 12) st_pv.append(st_pv_R) st_pv_R = np.array([1.4599014654282669312, 0.0006380009232897535]) ad = normal_ad(np.exp(-x**2)) assert_almost_equal(ad, st_pv_R, 12) st_pv.append(st_pv_R) ad = normal_ad(np.column_stack((x, x**2, np.log(x**2), np.exp(-x**2))).T, axis=1) assert_almost_equal(ad, np.column_stack(st_pv), 11) def test_durbin_watson_pandas(reset_randomstate): x = np.random.randn(50) x_series = pd.Series(x) assert_almost_equal(durbin_watson(x), durbin_watson(x_series), decimal=13) class TestStattools(object): @classmethod def setup_class(cls): x = np.random.standard_normal(1000) e1, e2, e3, e4, e5, e6, e7 = np.percentile(x, (12.5, 25.0, 37.5, 50.0, 62.5, 75.0, 87.5)) c05, c50, c95 = np.percentile(x, (5.0, 50.0, 95.0)) f025, f25, f75, f975 = np.percentile(x, (2.5, 25.0, 75.0, 97.5)) mean = np.mean kr1 = mean(((x - mean(x)) / np.std(x))**4.0) - 3.0 kr2 = ((e7 - e5) + (e3 - e1)) / (e6 - e2) - 1.2330951154852172 kr3 = (mean(x[x > c95]) - mean(x[x < c05])) / (mean(x[x > c50]) - mean(x[x < c50])) - 2.5852271228708048 kr4 = (f975 - f025) / (f75 - f25) - 2.9058469516701639 cls.kurtosis_x = x cls.expected_kurtosis = np.array([kr1, kr2, kr3, kr4]) cls.kurtosis_constants = np.array([3.0,1.2330951154852172,2.5852271228708048,2.9058469516701639]) def test_medcouple_no_axis(self): x = np.reshape(np.arange(100.0), (50, 2)) mc = medcouple(x, axis=None) assert_almost_equal(mc, medcouple(x.ravel())) def test_medcouple_1d(self): x = np.reshape(np.arange(100.0),(50,2)) assert_raises(ValueError, _medcouple_1d, x) def test_medcouple_symmetric(self): mc = medcouple(np.arange(5.0)) assert_almost_equal(mc, 0) def test_medcouple_nonzero(self): mc = medcouple(np.array([1, 2, 7, 9, 10.0])) assert_almost_equal(mc, -0.3333333) def test_medcouple_int(self): # GH 4243 mc1 = medcouple(np.array([1, 2, 7, 9, 10])) mc2 = medcouple(np.array([1, 2, 7, 9, 10.0])) assert_equal(mc1, mc2) def test_medcouple_symmetry(self, reset_randomstate): x = np.random.standard_normal(100) mcp = medcouple(x) mcn = medcouple(-x) assert_almost_equal(mcp + mcn, 0) def test_medcouple_ties(self, reset_randomstate): x = np.array([1, 2, 2, 3, 4]) mc = medcouple(x) assert_almost_equal(mc, 1.0 / 6.0) def test_durbin_watson(self, reset_randomstate): x = np.random.standard_normal(100) dw = sum(np.diff(x)**2.0) / np.dot(x, x) assert_almost_equal(dw, durbin_watson(x)) def test_durbin_watson_2d(self, reset_randomstate): shape = (1, 10) x = np.random.standard_normal(100) dw = sum(np.diff(x)**2.0) / np.dot(x, x) x = np.tile(x[:, None], shape) assert_almost_equal(np.squeeze(dw * np.ones(shape)), durbin_watson(x)) def test_durbin_watson_3d(self, reset_randomstate): shape = (10, 1, 10) x = np.random.standard_normal(100) dw = sum(np.diff(x)**2.0) / np.dot(x, x) x = np.tile(x[None, :, None], shape) assert_almost_equal(np.squeeze(dw * np.ones(shape)), durbin_watson(x, axis=1)) def test_robust_skewness_1d(self): x = np.arange(21.0) sk = robust_skewness(x) assert_almost_equal(np.array(sk), np.zeros(4)) def test_robust_skewness_1d_2d(self, reset_randomstate): x = np.random.randn(21) y = x[:, None] sk_x = robust_skewness(x) sk_y = robust_skewness(y, axis=None) assert_almost_equal(np.array(sk_x), np.array(sk_y)) def test_robust_skewness_symmetric(self, reset_randomstate): x = np.random.standard_normal(100) x = np.hstack([x, np.zeros(1), -x]) sk = robust_skewness(x) assert_almost_equal(np.array(sk), np.zeros(4)) def test_robust_skewness_3d(self, reset_randomstate): x = np.random.standard_normal(100) x = np.hstack([x, np.zeros(1), -x]) x = np.tile(x, (10, 10, 1)) sk_3d = robust_skewness(x, axis=2) result = np.zeros((10, 10)) for sk in sk_3d: assert_almost_equal(sk, result) def test_robust_skewness_4(self, reset_randomstate): x = np.random.standard_normal(1000) x[x > 0] *= 3 m = np.median(x) s = x.std(ddof=0) expected = (x.mean() - m) / s _, _, _, sk4 = robust_skewness(x) assert_allclose(expected, sk4) def test_robust_kurtosis_1d_2d(self, reset_randomstate): x = np.random.randn(100) y = x[:, None] kr_x = np.array(robust_kurtosis(x)) kr_y = np.array(robust_kurtosis(y, axis=None)) assert_almost_equal(kr_x, kr_y) def test_robust_kurtosis(self): x = self.kurtosis_x assert_almost_equal(np.array(robust_kurtosis(x)), self.expected_kurtosis) def test_robust_kurtosis_3d(self): x = np.tile(self.kurtosis_x, (10, 10, 1)) kurtosis = np.array(robust_kurtosis(x, axis=2)) for i, r in enumerate(self.expected_kurtosis): assert_almost_equal(r * np.ones((10, 10)), kurtosis[i]) def test_robust_kurtosis_excess_false(self): x = self.kurtosis_x expected = self.expected_kurtosis + self.kurtosis_constants kurtosis = np.array(robust_kurtosis(x, excess=False)) assert_almost_equal(expected, kurtosis) def test_robust_kurtosis_ab(self): # Test custom alpha, beta in kr3 x = self.kurtosis_x alpha, beta = (10.0, 45.0) kurtosis = robust_kurtosis(self.kurtosis_x, ab=(alpha,beta), excess=False) num = np.mean(x[x>np.percentile(x,100.0 - alpha)]) - np.mean(x[xnp.percentile(x,100.0 - beta)]) - np.mean(x[x crit_lf[:, 1:]).all() vals = [lf.prob(c * 0.9, size[i]) for i in range(len(size)) for c in crit_lf[i, :-1]] vals = np.array(vals).reshape(-1, lf.n_alpha - 1) assert (vals > lf.alpha[:-1]).all() vals = [lf.prob(c * 1.1, size[i]) for i in range(len(size)) for c in crit_lf[i, 1:]] vals = np.array(vals).reshape(-1, lf.n_alpha - 1) assert (vals < lf.alpha[1:]).all() # start at size_idx=2 because of non-monotonicity of lf_crit vals = [lf.prob(c, size[i] * 0.9) for i in range(2, len(size)) for c in crit_lf[i, :-1]] vals = np.array(vals).reshape(-1, lf.n_alpha - 1) assert (vals > lf.alpha[:-1]).all() statsmodels-0.12.2/statsmodels/stats/tests/test_tost.py000066400000000000000000000572461400612667500234270ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Wed Oct 17 09:48:34 2012 Author: Josef Perktold """ import numpy as np from numpy.testing import assert_almost_equal, assert_equal, assert_ import pytest import statsmodels.stats.weightstats as smws from statsmodels.tools.testing import Holder def assert_almost_equal_inf(x, y, decimal=6, msg=None): x = np.atleast_1d(x) y = np.atleast_1d(y) assert_equal(np.isposinf(x), np.isposinf(y)) assert_equal(np.isneginf(x), np.isneginf(y)) assert_equal(np.isnan(x), np.isnan(y)) assert_almost_equal(x[np.isfinite(x)], y[np.isfinite(y)]) raw_clinic = '''\ 1 1 2.84 4.00 3.45 2.55 2.46 2 1 2.51 3.26 3.10 2.82 2.48 3 1 2.41 4.14 3.37 2.99 3.04 4 1 2.95 3.42 2.82 3.37 3.35 5 1 3.14 3.25 3.31 2.87 3.41 6 1 3.79 4.34 3.88 3.40 3.16 7 1 4.14 4.97 4.25 3.43 3.06 8 1 3.85 4.31 3.92 3.58 3.91 9 1 3.02 3.11 2.20 2.24 2.28 10 1 3.45 3.41 3.80 3.86 3.91 11 1 5.37 5.02 4.59 3.99 4.27 12 1 3.81 4.21 4.08 3.18 1.86 13 1 4.19 4.59 4.79 4.17 2.60 14 1 3.16 5.30 4.69 4.83 4.51 15 1 3.84 4.32 4.25 3.87 2.93 16 2 2.60 3.76 2.86 2.41 2.71 17 2 2.82 3.66 3.20 2.49 2.49 18 2 2.18 3.65 3.87 3.00 2.65 19 2 3.46 3.60 2.97 1.80 1.74 20 2 4.01 3.48 4.42 3.06 2.76 21 2 3.04 2.87 2.87 2.71 2.87 22 2 3.47 3.24 3.47 3.26 3.14 23 2 4.06 3.92 3.18 3.06 1.74 24 2 2.91 3.99 3.06 2.02 3.18 25 2 3.59 4.21 4.02 3.26 2.85 26 2 4.51 4.21 3.78 2.63 1.92 27 2 3.16 3.31 3.28 3.25 3.52 28 2 3.86 3.61 3.28 3.19 3.09 29 2 3.31 2.97 3.76 3.18 2.60 30 2 3.02 2.73 3.87 3.50 2.93'''.split() clinic = np.array(raw_clinic, float).reshape(-1,7) #t = tost(-clinic$var2[16:30] + clinic$var2[1:15], eps=0.6) tost_clinic_paired = Holder() tost_clinic_paired.sample = 'paired' tost_clinic_paired.mean_diff = 0.5626666666666665 tost_clinic_paired.se_diff = 0.2478276410785118 tost_clinic_paired.alpha = 0.05 tost_clinic_paired.ci_diff = (0.1261653305099018, 0.999168002823431) tost_clinic_paired.df = 14 tost_clinic_paired.epsilon = 0.6 tost_clinic_paired.result = 'not rejected' tost_clinic_paired.p_value = 0.4412034046017588 tost_clinic_paired.check_me = (0.525333333333333, 0.6) #> t = tost(-clinic$var1[16:30] + clinic$var1[1:15], eps=0.6) #> cat_items(t, prefix="tost_clinic_paired_1.") tost_clinic_paired_1 = Holder() tost_clinic_paired_1.mean_diff = 0.1646666666666667 tost_clinic_paired_1.se_diff = 0.1357514067862445 tost_clinic_paired_1.alpha = 0.05 tost_clinic_paired_1.ci_diff = (-0.0744336620516462, 0.4037669953849797) tost_clinic_paired_1.df = 14 tost_clinic_paired_1.epsilon = 0.6 tost_clinic_paired_1.result = 'rejected' tost_clinic_paired_1.p_value = 0.003166881489265175 tost_clinic_paired_1.check_me = (-0.2706666666666674, 0.600000000000001) #> t = tost(clinic$var2[1:15], clinic$var2[16:30], eps=0.6) #> cat_items(t, prefix="tost_clinic_indep.") tost_clinic_indep = Holder() tost_clinic_indep.sample = 'independent' tost_clinic_indep.mean_diff = 0.562666666666666 tost_clinic_indep.se_diff = 0.2149871904637392 tost_clinic_indep.alpha = 0.05 tost_clinic_indep.ci_diff = (0.194916250699966, 0.930417082633366) tost_clinic_indep.df = 24.11000151062728 tost_clinic_indep.epsilon = 0.6 tost_clinic_indep.result = 'not rejected' tost_clinic_indep.p_value = 0.4317936812594803 tost_clinic_indep.check_me = (0.525333333333332, 0.6) #> t = tost(clinic$var1[1:15], clinic$var1[16:30], eps=0.6) #> cat_items(t, prefix="tost_clinic_indep_1.") tost_clinic_indep_1 = Holder() tost_clinic_indep_1.sample = 'independent' tost_clinic_indep_1.mean_diff = 0.1646666666666667 tost_clinic_indep_1.se_diff = 0.2531625991083627 tost_clinic_indep_1.alpha = 0.05 tost_clinic_indep_1.ci_diff = (-0.2666862980722534, 0.596019631405587) tost_clinic_indep_1.df = 26.7484787582315 tost_clinic_indep_1.epsilon = 0.6 tost_clinic_indep_1.result = 'rejected' tost_clinic_indep_1.p_value = 0.04853083976236974 tost_clinic_indep_1.check_me = (-0.2706666666666666, 0.6) #pooled variance #> t = tost(clinic$var1[1:15], clinic$var1[16:30], eps=0.6, var.equal = TRUE) #> cat_items(t, prefix="tost_clinic_indep_1_pooled.") tost_clinic_indep_1_pooled = Holder() tost_clinic_indep_1_pooled.mean_diff = 0.1646666666666667 tost_clinic_indep_1_pooled.se_diff = 0.2531625991083628 tost_clinic_indep_1_pooled.alpha = 0.05 tost_clinic_indep_1_pooled.ci_diff = (-0.2659960620757337, 0.595329395409067) tost_clinic_indep_1_pooled.df = 28 tost_clinic_indep_1_pooled.epsilon = 0.6 tost_clinic_indep_1_pooled.result = 'rejected' tost_clinic_indep_1_pooled.p_value = 0.04827315100761467 tost_clinic_indep_1_pooled.check_me = (-0.2706666666666666, 0.6) #> t = tost(clinic$var2[1:15], clinic$var2[16:30], eps=0.6, var.equal = TRUE) #> cat_items(t, prefix="tost_clinic_indep_2_pooled.") tost_clinic_indep_2_pooled = Holder() tost_clinic_indep_2_pooled.mean_diff = 0.562666666666666 tost_clinic_indep_2_pooled.se_diff = 0.2149871904637392 tost_clinic_indep_2_pooled.alpha = 0.05 tost_clinic_indep_2_pooled.ci_diff = (0.1969453064978777, 0.928388026835454) tost_clinic_indep_2_pooled.df = 28 tost_clinic_indep_2_pooled.epsilon = 0.6 tost_clinic_indep_2_pooled.result = 'not rejected' tost_clinic_indep_2_pooled.p_value = 0.43169347692374 tost_clinic_indep_2_pooled.check_me = (0.525333333333332, 0.6) #tost ratio, log transformed #> t = tost(log(clinic$var1[1:15]), log(clinic$var1[16:30]), eps=log(1.25), paired=TRUE) #> cat_items(t, prefix="tost_clinic_1_paired.") tost_clinic_1_paired = Holder() tost_clinic_1_paired.mean_diff = 0.0431223318225235 tost_clinic_1_paired.se_diff = 0.03819576328421437 tost_clinic_1_paired.alpha = 0.05 tost_clinic_1_paired.ci_diff = (-0.02415225319362176, 0.1103969168386687) tost_clinic_1_paired.df = 14 tost_clinic_1_paired.epsilon = 0.2231435513142098 tost_clinic_1_paired.result = 'rejected' tost_clinic_1_paired.p_value = 0.0001664157928976468 tost_clinic_1_paired.check_me = (-0.1368988876691603, 0.2231435513142073) #> t = tost(log(clinic$var1[1:15]), log(clinic$var1[16:30]), eps=log(1.25), paired=FALSE) #> cat_items(t, prefix="tost_clinic_1_indep.") tost_clinic_1_indep = Holder() tost_clinic_1_indep.mean_diff = 0.04312233182252334 tost_clinic_1_indep.se_diff = 0.073508371131806 tost_clinic_1_indep.alpha = 0.05 tost_clinic_1_indep.ci_diff = (-0.0819851930203655, 0.1682298566654122) tost_clinic_1_indep.df = 27.61177037646526 tost_clinic_1_indep.epsilon = 0.2231435513142098 tost_clinic_1_indep.result = 'rejected' tost_clinic_1_indep.p_value = 0.01047085593138891 tost_clinic_1_indep.check_me = (-0.1368988876691633, 0.22314355131421) #> t = tost(log(y), log(x), eps=log(1.25), paired=TRUE) #> cat_items(t, prefix="tost_s_paired.") tost_s_paired = Holder() tost_s_paired.mean_diff = 0.06060076667771316 tost_s_paired.se_diff = 0.04805826005366752 tost_s_paired.alpha = 0.05 tost_s_paired.ci_diff = (-0.0257063329659993, 0.1469078663214256) tost_s_paired.df = 11 tost_s_paired.epsilon = 0.2231435513142098 tost_s_paired.result = 'rejected' tost_s_paired.p_value = 0.003059338540563293 tost_s_paired.check_me = (-0.1019420179587835, 0.2231435513142098) #multiple endpoints #> compvall <- multeq.diff(data=clinic,grp="fact",method="step.up",margin.up=rep(0.6,5), margin.lo=c(-1.0, -1.0, -1.5, -1.5, -1.5)) #> cat_items(compvall, prefix="tost_clinic_all_no_multi.") tost_clinic_all_no_multi = Holder() tost_clinic_all_no_multi.comp_name = '2-1' tost_clinic_all_no_multi.estimate = np.array([ -0.1646666666666667, -0.562666666666666, -0.3073333333333332, -0.5553333333333335, -0.469333333333333]) tost_clinic_all_no_multi.degr_fr = np.array([ 26.74847875823152, 24.1100015106273, 23.90046331918926, 25.71678948210178, 24.88436709341423]) tost_clinic_all_no_multi.test_stat = np.array([ 3.020456692101513, 2.034229724989578, 4.052967897750272, 4.37537447933403, 4.321997343344]) tost_clinic_all_no_multi.p_value = np.array([ 0.00274867705173331, 0.02653543052872217, 0.0002319468040526358, 8.916466517494902e-05, 0.00010890038649094043]) tost_clinic_all_no_multi.lower = np.array([ -0.596019631405587, -0.930417082633366, -0.690410573009442, -0.92373513818557, -0.876746448909633]) tost_clinic_all_no_multi.upper = np.array([ 0.2666862980722534, -0.194916250699966, 0.07574390634277595, -0.186931528481097, -0.06192021775703377]) tost_clinic_all_no_multi.margin_lo = np.array([ -1, -1, -1.5, -1.5, -1.5]) tost_clinic_all_no_multi.margin_up = np.array([ 0.6, 0.6, 0.6, 0.6, 0.6]) tost_clinic_all_no_multi.base = 1 tost_clinic_all_no_multi.method = 'step.up' tost_clinic_all_no_multi.var_equal = '''FALSE''' tost_clinic_all_no_multi.FWER = 0.05 #> comp <- multeq.diff(data=clinic,grp="fact", resp=c("var1"),method="step.up",margin.up=rep(0.6), margin.lo=rep(-1.5)) #> cat_items(comp, prefix="tost_clinic_1_asym.") tost_clinic_1_asym = Holder tost_clinic_1_asym.comp_name = '2-1' tost_clinic_1_asym.estimate = -0.1646666666666667 tost_clinic_1_asym.degr_fr = 26.74847875823152 tost_clinic_1_asym.test_stat = 3.020456692101513 tost_clinic_1_asym.p_value = 0.00274867705173331 tost_clinic_1_asym.lower = -0.596019631405587 tost_clinic_1_asym.upper = 0.2666862980722534 tost_clinic_1_asym.margin_lo = -1.5 tost_clinic_1_asym.margin_up = 0.6 tost_clinic_1_asym.base = 1 tost_clinic_1_asym.method = 'step.up' tost_clinic_1_asym.var_equal = '''FALSE''' tost_clinic_1_asym.FWER = 0.05 #TODO: not used yet, some p-values are multi-testing adjusted # not implemented #> compvall <- multeq.diff(data=clinic,grp="fact",method="step.up",margin.up=rep(0.6,5), margin.lo=c(-0.5, -0.5, -1.5, -1.5, -1.5)) #> cat_items(compvall, prefix="tost_clinic_all_multi.") tost_clinic_all_multi = Holder() tost_clinic_all_multi.comp_name = '2-1' tost_clinic_all_multi.estimate = np.array([ -0.1646666666666667, -0.562666666666666, -0.3073333333333332, -0.5553333333333335, -0.469333333333333]) tost_clinic_all_multi.degr_fr = np.array([ 26.74847875823152, 24.1100015106273, 23.90046331918926, 25.71678948210178, 24.88436709341423]) tost_clinic_all_multi.test_stat = np.array([ 1.324576910311299, -0.2914902349832590, 4.052967897750272, 4.37537447933403, 4.321997343344]) tost_clinic_all_multi.p_value = np.array([ 0.0982588867413542, 0.6134151998456164, 0.0006958404121579073, 0.0002674939955248471, 0.0003267011594728213]) tost_clinic_all_multi.lower = np.array([ -0.596019631405587, -0.930417082633366, -0.812901144055456, -1.040823983574101, -1.006578759345919]) tost_clinic_all_multi.upper = np.array([ 0.2666862980722534, -0.194916250699966, 0.1982344773887895, -0.0698426830925655, 0.0679120926792529]) tost_clinic_all_multi.margin_lo = np.array([ -0.5, -0.5, -1.5, -1.5, -1.5]) tost_clinic_all_multi.margin_up = np.array([ 0.6, 0.6, 0.6, 0.6, 0.6]) tost_clinic_all_multi.base = 1 tost_clinic_all_multi.method = 'step.up' tost_clinic_all_multi.var_equal = '''FALSE''' tost_clinic_all_multi.FWER = 0.05 #t-tests #> tt = t.test(clinic$var1[16:30], clinic$var1[1:15], data=clinic, mu=-0., alternative="two.sided", paired=TRUE) #> cat_items(tt, prefix="ttest_clinic_paired_1.") ttest_clinic_paired_1 = Holder() ttest_clinic_paired_1.statistic = 1.213001548676048 ttest_clinic_paired_1.parameter = 14 ttest_clinic_paired_1.p_value = 0.245199929713149 ttest_clinic_paired_1.conf_int = (-0.1264911434745851, 0.4558244768079186) ttest_clinic_paired_1.estimate = 0.1646666666666667 ttest_clinic_paired_1.null_value = 0 ttest_clinic_paired_1.alternative = 'two.sided' ttest_clinic_paired_1.method = 'Paired t-test' ttest_clinic_paired_1.data_name = 'clinic$var1[1:15] and clinic$var1[16:30]' #> ttless = t.test(clinic$var1[1:15], clinic$var1[16:30],, data=clinic, mu=-0., alternative="less", paired=FALSE) #> cat_items(ttless, prefix="ttest_clinic_paired_1_l.") ttest_clinic_paired_1_l = Holder() ttest_clinic_paired_1_l.statistic = 0.650438363512706 ttest_clinic_paired_1_l.parameter = 26.7484787582315 ttest_clinic_paired_1_l.p_value = 0.739521349864458 ttest_clinic_paired_1_l.conf_int = (-np.inf, 0.596019631405587) ttest_clinic_paired_1_l.estimate = (3.498, 3.333333333333333) ttest_clinic_paired_1_l.null_value = 0 ttest_clinic_paired_1_l.alternative = 'less' ttest_clinic_paired_1_l.method = 'Welch Two Sample t-test' ttest_clinic_paired_1_l.data_name = 'clinic$var1[1:15] and clinic$var1[16:30]' #> cat_items(tt, prefix="ttest_clinic_indep_1_g.") ttest_clinic_indep_1_g = Holder() ttest_clinic_indep_1_g.statistic = 0.650438363512706 ttest_clinic_indep_1_g.parameter = 26.7484787582315 ttest_clinic_indep_1_g.p_value = 0.2604786501355416 ttest_clinic_indep_1_g.conf_int = (-0.2666862980722534, np.inf) ttest_clinic_indep_1_g.estimate = (3.498, 3.333333333333333) ttest_clinic_indep_1_g.null_value = 0 ttest_clinic_indep_1_g.alternative = 'greater' ttest_clinic_indep_1_g.method = 'Welch Two Sample t-test' ttest_clinic_indep_1_g.data_name = 'clinic$var1[1:15] and clinic$var1[16:30]' #> cat_items(ttless, prefix="ttest_clinic_indep_1_l.") ttest_clinic_indep_1_l = Holder() ttest_clinic_indep_1_l.statistic = 0.650438363512706 ttest_clinic_indep_1_l.parameter = 26.7484787582315 ttest_clinic_indep_1_l.p_value = 0.739521349864458 ttest_clinic_indep_1_l.conf_int = (-np.inf, 0.596019631405587) ttest_clinic_indep_1_l.estimate = (3.498, 3.333333333333333) ttest_clinic_indep_1_l.null_value = 0 ttest_clinic_indep_1_l.alternative = 'less' ttest_clinic_indep_1_l.method = 'Welch Two Sample t-test' ttest_clinic_indep_1_l.data_name = 'clinic$var1[1:15] and clinic$var1[16:30]' #> ttless = t.test(clinic$var1[1:15], clinic$var1[16:30],, data=clinic, mu=1., alternative="less", paired=FALSE) #> cat_items(ttless, prefix="ttest_clinic_indep_1_l_mu.") ttest_clinic_indep_1_l_mu = Holder() ttest_clinic_indep_1_l_mu.statistic = -3.299592184135306 ttest_clinic_indep_1_l_mu.parameter = 26.7484787582315 ttest_clinic_indep_1_l_mu.p_value = 0.001372434925571605 ttest_clinic_indep_1_l_mu.conf_int = (-np.inf, 0.596019631405587) ttest_clinic_indep_1_l_mu.estimate = (3.498, 3.333333333333333) ttest_clinic_indep_1_l_mu.null_value = 1 ttest_clinic_indep_1_l_mu.alternative = 'less' ttest_clinic_indep_1_l_mu.method = 'Welch Two Sample t-test' ttest_clinic_indep_1_l_mu.data_name = 'clinic$var1[1:15] and clinic$var1[16:30]' #> tt2 = t.test(clinic$var1[1:15], clinic$var1[16:30],, data=clinic, mu=1, alternative="two.sided", paired=FALSE) #> cat_items(tt2, prefix="ttest_clinic_indep_1_two_mu.") ttest_clinic_indep_1_two_mu = Holder() ttest_clinic_indep_1_two_mu.statistic = -3.299592184135306 ttest_clinic_indep_1_two_mu.parameter = 26.7484787582315 ttest_clinic_indep_1_two_mu.p_value = 0.00274486985114321 ttest_clinic_indep_1_two_mu.conf_int = (-0.3550087243406, 0.6843420576739336) ttest_clinic_indep_1_two_mu.estimate = (3.498, 3.333333333333333) ttest_clinic_indep_1_two_mu.null_value = 1 ttest_clinic_indep_1_two_mu.alternative = 'two.sided' ttest_clinic_indep_1_two_mu.method = 'Welch Two Sample t-test' ttest_clinic_indep_1_two_mu.data_name = 'clinic$var1[1:15] and clinic$var1[16:30]' #> tt2 = t.test(clinic$var1[1:15], clinic$var1[16:30],, data=clinic, mu=1, alternative="two.sided", paired=FALSE, var.equal=TRUE) #> cat_items(tt2, prefix="ttest_clinic_indep_1_two_mu_pooled.") ttest_clinic_indep_1_two_mu_pooled = Holder() ttest_clinic_indep_1_two_mu_pooled.statistic = -3.299592184135305 ttest_clinic_indep_1_two_mu_pooled.parameter = 28 ttest_clinic_indep_1_two_mu_pooled.p_value = 0.002643203760742494 ttest_clinic_indep_1_two_mu_pooled.conf_int = (-0.35391340938235, 0.6832467427156834) ttest_clinic_indep_1_two_mu_pooled.estimate = (3.498, 3.333333333333333) ttest_clinic_indep_1_two_mu_pooled.null_value = 1 ttest_clinic_indep_1_two_mu_pooled.alternative = 'two.sided' ttest_clinic_indep_1_two_mu_pooled.method = ' Two Sample t-test' ttest_clinic_indep_1_two_mu_pooled.data_name = 'clinic$var1[1:15] and clinic$var1[16:30]' res1 = smws.ttost_paired(clinic[:15, 2], clinic[15:, 2], -0.6, 0.6, transform=None) res2 = smws.ttost_paired(clinic[:15, 3], clinic[15:, 3], -0.6, 0.6, transform=None) res = smws.ttost_ind(clinic[:15, 3], clinic[15:, 3], -0.6, 0.6, usevar='unequal') class CheckTostMixin(object): def test_pval(self): assert_almost_equal(self.res1.pvalue, self.res2.p_value, decimal=13) #assert_almost_equal(self.res1.df, self.res2.df, decimal=13) class TestTostp1(CheckTostMixin): #paired var1 @classmethod def setup_class(cls): cls.res2 = tost_clinic_paired_1 x1, x2 = clinic[:15, 2], clinic[15:, 2] cls.res1 = Holder() res = smws.ttost_paired(x1, x2, -0.6, 0.6, transform=None) cls.res1.pvalue = res[0] #cls.res1.df = res[1][-1] not yet res_ds = smws.DescrStatsW(x1 - x2, weights=None, ddof=0) #tost confint 2*alpha TODO: check again cls.res1.tconfint_diff = res_ds.tconfint_mean(0.1) cls.res1.confint_05 = res_ds.tconfint_mean(0.05) cls.res1.mean_diff = res_ds.mean cls.res1.std_mean_diff = res_ds.std_mean cls.res2b = ttest_clinic_paired_1 def test_special(self): #TODO: add attributes to other cases and move to superclass assert_almost_equal(self.res1.tconfint_diff, self.res2.ci_diff, decimal=13) assert_almost_equal(self.res1.mean_diff, self.res2.mean_diff, decimal=13) assert_almost_equal(self.res1.std_mean_diff, self.res2.se_diff, decimal=13) #compare with ttest assert_almost_equal(self.res1.confint_05, self.res2b.conf_int, decimal=13) class TestTostp2(CheckTostMixin): #paired var2 @classmethod def setup_class(cls): cls.res2 = tost_clinic_paired x, y = clinic[:15, 3], clinic[15:, 3] cls.res1 = Holder() res = smws.ttost_paired(x, y, -0.6, 0.6, transform=None) cls.res1.pvalue = res[0] class TestTosti1(CheckTostMixin): @classmethod def setup_class(cls): cls.res2 = tost_clinic_indep_1 x, y = clinic[:15, 2], clinic[15:, 2] cls.res1 = Holder() res = smws.ttost_ind(x, y, -0.6, 0.6, usevar='unequal') cls.res1.pvalue = res[0] class TestTosti2(CheckTostMixin): @classmethod def setup_class(cls): cls.res2 = tost_clinic_indep x, y = clinic[:15, 3], clinic[15:, 3] cls.res1 = Holder() res = smws.ttost_ind(x, y, -0.6, 0.6, usevar='unequal') cls.res1.pvalue = res[0] class TestTostip1(CheckTostMixin): @classmethod def setup_class(cls): cls.res2 = tost_clinic_indep_1_pooled x, y = clinic[:15, 2], clinic[15:, 2] cls.res1 = Holder() res = smws.ttost_ind(x, y, -0.6, 0.6, usevar='pooled') cls.res1.pvalue = res[0] class TestTostip2(CheckTostMixin): @classmethod def setup_class(cls): cls.res2 = tost_clinic_indep_2_pooled x, y = clinic[:15, 3], clinic[15:, 3] cls.res1 = Holder() res = smws.ttost_ind(x, y, -0.6, 0.6, usevar='pooled') cls.res1.pvalue = res[0] #transform=np.log #class TestTostp1_log(CheckTost): def test_tost_log(): x1, x2 = clinic[:15, 2], clinic[15:, 2] resp = smws.ttost_paired(x1, x2, 0.8, 1.25, transform=np.log) assert_almost_equal(resp[0], tost_clinic_1_paired.p_value, 13) resi = smws.ttost_ind(x1, x2, 0.8, 1.25, transform=np.log, usevar='unequal') assert_almost_equal(resi[0], tost_clinic_1_indep.p_value, 13) def test_tost_asym(): x1, x2 = clinic[:15, 2], clinic[15:, 2] #Note: x1, x2 reversed by definition in multeq.dif assert_almost_equal(x2.mean() - x1.mean(), tost_clinic_1_asym.estimate, 13) resa = smws.ttost_ind(x2, x1, -1.5, 0.6, usevar='unequal') assert_almost_equal(resa[0], tost_clinic_1_asym.p_value, 13) #multi-endpoints, asymmetric bounds, vectorized resall = smws.ttost_ind(clinic[15:, 2:7], clinic[:15, 2:7], [-1.0, -1.0, -1.5, -1.5, -1.5], 0.6, usevar='unequal') assert_almost_equal(resall[0], tost_clinic_all_no_multi.p_value, 13) #SMOKE tests: foe multi-endpoint vectorized, k on k resall = smws.ttost_ind(clinic[15:, 2:7], clinic[:15, 2:7], np.exp([-1.0, -1.0, -1.5, -1.5, -1.5]), 0.6, usevar='unequal', transform=np.log) resall = smws.ttost_ind(clinic[15:, 2:7], clinic[:15, 2:7], [-1.0, -1.0, -1.5, -1.5, -1.5], 0.6, usevar='unequal', transform=np.exp) resall = smws.ttost_paired(clinic[15:, 2:7], clinic[:15, 2:7], [-1.0, -1.0, -1.5, -1.5, -1.5], 0.6, transform=np.log) resall = smws.ttost_paired(clinic[15:, 2:7], clinic[:15, 2:7], [-1.0, -1.0, -1.5, -1.5, -1.5], 0.6, transform=np.exp) resall = smws.ttest_ind(clinic[15:, 2:7], clinic[:15, 2:7], value=[-1.0, -1.0, -1.5, -1.5, -1.5]) #k on 1: compare all with reference resall = smws.ttost_ind(clinic[15:, 2:7], clinic[:15, 2:3], [-1.0, -1.0, -1.5, -1.5, -1.5], 0.6, usevar='unequal') resa3_2 = smws.ttost_ind(clinic[15:, 3:4], clinic[:15, 2:3], [-1.0, -1.0, -1.5, -1.5, -1.5], 0.6, usevar='unequal') assert_almost_equal(resall[0][1], resa3_2[0][1], decimal=13) resall = smws.ttost_ind(clinic[15:, 2], clinic[:15, 2], [-1.0, -0.5, -0.7, -1.5, -1.5], 0.6, usevar='unequal') resall = smws.ttost_ind(clinic[15:, 2], clinic[:15, 2], [-1.0, -0.5, -0.7, -1.5, -1.5], np.repeat(0.6,5), usevar='unequal') def test_ttest(): x1, x2 = clinic[:15, 2], clinic[15:, 2] all_tests = [] t1 = smws.ttest_ind(x1, x2, alternative='larger', usevar='unequal') all_tests.append((t1, ttest_clinic_indep_1_g)) t2 = smws.ttest_ind(x1, x2, alternative='smaller', usevar='unequal') all_tests.append((t2, ttest_clinic_indep_1_l)) t3 = smws.ttest_ind(x1, x2, alternative='smaller', usevar='unequal', value=1) all_tests.append((t3, ttest_clinic_indep_1_l_mu)) for res1, res2 in all_tests: assert_almost_equal(res1[0], res2.statistic, decimal=13) assert_almost_equal(res1[1], res2.p_value, decimal=13) #assert_almost_equal(res1[2], res2.df, decimal=13) cm = smws.CompareMeans(smws.DescrStatsW(x1), smws.DescrStatsW(x2)) ci = cm.tconfint_diff(alternative='two-sided', usevar='unequal') assert_almost_equal(ci, ttest_clinic_indep_1_two_mu.conf_int, decimal=13) ci = cm.tconfint_diff(alternative='two-sided', usevar='pooled') assert_almost_equal(ci, ttest_clinic_indep_1_two_mu_pooled.conf_int, decimal=13) ci = cm.tconfint_diff(alternative='smaller', usevar='unequal') assert_almost_equal_inf(ci, ttest_clinic_indep_1_l.conf_int, decimal=13) ci = cm.tconfint_diff(alternative='larger', usevar='unequal') assert_almost_equal_inf(ci, ttest_clinic_indep_1_g.conf_int, decimal=13) #test get_compare cm = smws.CompareMeans(smws.DescrStatsW(x1), smws.DescrStatsW(x2)) cm1 = cm.d1.get_compare(cm.d2) cm2 = cm.d1.get_compare(x2) cm3 = cm.d1.get_compare(np.hstack((x2,x2))) #all use the same d1, no copying assert_(cm.d1 is cm1.d1) assert_(cm.d1 is cm2.d1) assert_(cm.d1 is cm3.d1) @pytest.mark.xfail(reason="shape mismatch between res1[1:] and res_sas[1:]", raises=AssertionError, strict=True) def test_tost_transform_paired(): raw = np.array('''\ 103.4 90.11 59.92 77.71 68.17 77.71 94.54 97.51 69.48 58.21 72.17 101.3 74.37 79.84 84.44 96.06 96.74 89.30 94.26 97.22 48.52 61.62 95.68 85.80'''.split(), float) x, y = raw.reshape(-1,2).T res1 = smws.ttost_paired(x, y, 0.8, 1.25, transform=np.log) res_sas = (0.0031, (3.38, 0.0031), (-5.90, 0.00005)) assert_almost_equal(res1[0], res_sas[0], 3) assert_almost_equal(res1[1:], res_sas[1:], 2) #result R tost assert_almost_equal(res1[0], tost_s_paired.p_value, 13) statsmodels-0.12.2/statsmodels/stats/tests/test_weightstats.py000066400000000000000000000665471400612667500250100ustar00rootroot00000000000000'''tests for weightstats, compares with replication no failures but needs cleanup update 2012-09-09: added test after fixing bug in covariance TODOs: - I do not remember what all the commented out code is doing - should be refactored to use generator or inherited tests - still gaps in test coverage - value/diff in ttest_ind is tested in test_tost.py - what about pandas data structures? Author: Josef Perktold License: BSD (3-clause) ''' import numpy as np from scipy import stats import pandas as pd from numpy.testing import assert_, assert_almost_equal, assert_allclose from statsmodels.stats.weightstats import (DescrStatsW, CompareMeans, ttest_ind, ztest, zconfint) from statsmodels.tools.testing import Holder # Mixin for tests against other packages. class CheckExternalMixin(object): @classmethod def get_descriptives(cls, ddof=0): cls.descriptive = DescrStatsW(cls.data, cls.weights, ddof) # TODO: not a test, belongs elsewhere? @classmethod def save_data(cls, fname="data.csv"): # Utility to get data into another package. df = pd.DataFrame(index=np.arange(len(cls.weights))) df["weights"] = cls.weights if cls.data.ndim == 1: df["data1"] = cls.data else: for k in range(cls.data.shape[1]): df["data%d" % (k + 1)] = cls.data[:, k] df.to_csv(fname) def test_mean(self): mn = self.descriptive.mean assert_allclose(mn, self.mean, rtol=1e-4) def test_sum(self): sm = self.descriptive.sum assert_allclose(sm, self.sum, rtol=1e-4) def test_var(self): # Use vardef=wgt option in SAS to match var = self.descriptive.var assert_allclose(var, self.var, rtol=1e-4) def test_std(self): # Use vardef=wgt option in SAS to match std = self.descriptive.std assert_allclose(std, self.std, rtol=1e-4) def test_sem(self): # Use default vardef in SAS to match; only makes sense if # weights sum to n. if not hasattr(self, "sem"): return sem = self.descriptive.std_mean assert_allclose(sem, self.sem, rtol=1e-4) def test_quantiles(self): quant = np.asarray(self.quantiles, dtype=np.float64) for return_pandas in False, True: qtl = self.descriptive.quantile(self.quantile_probs, return_pandas=return_pandas) qtl = np.asarray(qtl, dtype=np.float64) assert_allclose(qtl, quant, rtol=1e-4) class TestSim1(CheckExternalMixin): # 1d data # Taken from SAS mean = 0.401499 sum = 12.9553441 var = 1.08022 std = 1.03933 quantiles = np.r_[-1.81098, -0.84052, 0.32859, 0.77808, 2.93431] @classmethod def setup_class(cls): np.random.seed(9876789) cls.data = np.random.normal(size=20) cls.weights = np.random.uniform(0, 3, size=20) cls.quantile_probs = np.r_[0, 0.1, 0.5, 0.75, 1] cls.get_descriptives() class TestSim1t(CheckExternalMixin): # 1d data with ties # Taken from SAS mean = 5.05103296 sum = 156.573464 var = 9.9711934 std = 3.15771965 quantiles = np.r_[0, 1, 5, 8, 9] @classmethod def setup_class(cls): np.random.seed(9876789) cls.data = np.random.randint(0, 10, size=20) cls.data[15:20] = cls.data[0:5] cls.data[18:20] = cls.data[15:17] cls.weights = np.random.uniform(0, 3, size=20) cls.quantile_probs = np.r_[0, 0.1, 0.5, 0.75, 1] cls.get_descriptives() class TestSim1n(CheckExternalMixin): # 1d data with weights summing to n so we can check the standard # error of the mean # Taken from SAS mean = -0.3131058 sum = -6.2621168 var = 0.49722696 std = 0.70514322 sem = 0.15767482 quantiles = np.r_[-1.61593, -1.45576, -0.24356, 0.16770, 1.18791] @classmethod def setup_class(cls): np.random.seed(4342) cls.data = np.random.normal(size=20) cls.weights = np.random.uniform(0, 3, size=20) cls.weights *= 20 / cls.weights.sum() cls.quantile_probs = np.r_[0, 0.1, 0.5, 0.75, 1] cls.get_descriptives(1) class TestSim2(CheckExternalMixin): # 2d data # Taken from SAS mean = [-0.2170406, -0.2387543] sum = [-6.8383999, -7.5225444] var = [1.77426344, 0.61933542] std = [1.3320148, 0.78697867] quantiles = np.column_stack( (np.r_[-2.55277, -1.40479, -0.61040, 0.52740, 2.66246], np.r_[-1.49263, -1.15403, -0.16231, 0.16464, 1.83062])) @classmethod def setup_class(cls): np.random.seed(2249) cls.data = np.random.normal(size=(20, 2)) cls.weights = np.random.uniform(0, 3, size=20) cls.quantile_probs = np.r_[0, 0.1, 0.5, 0.75, 1] cls.get_descriptives() class TestWeightstats(object): @classmethod def setup_class(cls): np.random.seed(9876789) n1, n2 = 20, 20 m1, m2 = 1, 1.2 x1 = m1 + np.random.randn(n1) x2 = m2 + np.random.randn(n2) x1_2d = m1 + np.random.randn(n1, 3) x2_2d = m2 + np.random.randn(n2, 3) w1 = np.random.randint(1,4, n1) w2 = np.random.randint(1,4, n2) cls.x1, cls.x2 = x1, x2 cls.w1, cls.w2 = w1, w2 cls.x1_2d, cls.x2_2d = x1_2d, x2_2d def test_weightstats_1(self): x1, x2 = self.x1, self.x2 w1, w2 = self.w1, self.w2 w1_ = 2. * np.ones(len(x1)) w2_ = 2. * np.ones(len(x2)) d1 = DescrStatsW(x1) # print ttest_ind(x1, x2) # print ttest_ind(x1, x2, usevar='unequal') # #print ttest_ind(x1, x2, usevar='unequal') # print stats.ttest_ind(x1, x2) # print ttest_ind(x1, x2, usevar='unequal', alternative='larger') # print ttest_ind(x1, x2, usevar='unequal', alternative='smaller') # print ttest_ind(x1, x2, usevar='unequal', weights=(w1_, w2_)) # print stats.ttest_ind(np.r_[x1, x1], np.r_[x2,x2]) assert_almost_equal(ttest_ind(x1, x2, weights=(w1_, w2_))[:2], stats.ttest_ind(np.r_[x1, x1], np.r_[x2, x2])) def test_weightstats_2(self): x1, x2 = self.x1, self.x2 w1, w2 = self.w1, self.w2 d1 = DescrStatsW(x1) d1w = DescrStatsW(x1, weights=w1) d2w = DescrStatsW(x2, weights=w2) x1r = d1w.asrepeats() x2r = d2w.asrepeats() # print 'random weights' # print ttest_ind(x1, x2, weights=(w1, w2)) # print stats.ttest_ind(x1r, x2r) assert_almost_equal(ttest_ind(x1, x2, weights=(w1, w2))[:2], stats.ttest_ind(x1r, x2r), 14) # not the same as new version with random weights/replication # assert x1r.shape[0] == d1w.sum_weights # assert x2r.shape[0] == d2w.sum_weights assert_almost_equal(x2r.mean(0), d2w.mean, 14) assert_almost_equal(x2r.var(), d2w.var, 14) assert_almost_equal(x2r.std(), d2w.std, 14) # note: the following is for 1d assert_almost_equal(np.cov(x2r, bias=1), d2w.cov, 14) # assert_almost_equal(np.corrcoef(np.x2r), d2w.corrcoef, 19) # TODO: exception in corrcoef (scalar case) # one-sample tests # print d1.ttest_mean(3) # print stats.ttest_1samp(x1, 3) # print d1w.ttest_mean(3) # print stats.ttest_1samp(x1r, 3) assert_almost_equal(d1.ttest_mean(3)[:2], stats.ttest_1samp(x1, 3), 11) assert_almost_equal(d1w.ttest_mean(3)[:2], stats.ttest_1samp(x1r, 3), 11) def test_weightstats_3(self): x1_2d, x2_2d = self.x1_2d, self.x2_2d w1, w2 = self.w1, self.w2 d1w_2d = DescrStatsW(x1_2d, weights=w1) d2w_2d = DescrStatsW(x2_2d, weights=w2) x1r_2d = d1w_2d.asrepeats() x2r_2d = d2w_2d.asrepeats() assert_almost_equal(x2r_2d.mean(0), d2w_2d.mean, 14) assert_almost_equal(x2r_2d.var(0), d2w_2d.var, 14) assert_almost_equal(x2r_2d.std(0), d2w_2d.std, 14) assert_almost_equal(np.cov(x2r_2d.T, bias=1), d2w_2d.cov, 14) assert_almost_equal(np.corrcoef(x2r_2d.T), d2w_2d.corrcoef, 14) # print d1w_2d.ttest_mean(3) # #scipy.stats.ttest is also vectorized # print stats.ttest_1samp(x1r_2d, 3) t, p, d = d1w_2d.ttest_mean(3) assert_almost_equal([t, p], stats.ttest_1samp(x1r_2d, 3), 11) # print [stats.ttest_1samp(xi, 3) for xi in x1r_2d.T] cm = CompareMeans(d1w_2d, d2w_2d) ressm = cm.ttest_ind() resss = stats.ttest_ind(x1r_2d, x2r_2d) assert_almost_equal(ressm[:2], resss, 14) # does not work for 2d, levene does not use weights # cm = CompareMeans(d1w_2d, d2w_2d) # ressm = cm.test_equal_var() # resss = stats.levene(x1r_2d, x2r_2d) # assert_almost_equal(ressm[:2], resss, 14) def test_weightstats_ddof_tests(self): # explicit test that ttest and confint are independent of ddof # one sample case x1_2d = self.x1_2d w1 = self.w1 d1w_d0 = DescrStatsW(x1_2d, weights=w1, ddof=0) d1w_d1 = DescrStatsW(x1_2d, weights=w1, ddof=1) d1w_d2 = DescrStatsW(x1_2d, weights=w1, ddof=2) # check confint independent of user ddof res0 = d1w_d0.ttest_mean() res1 = d1w_d1.ttest_mean() res2 = d1w_d2.ttest_mean() # concatenate into one array with np.r_ assert_almost_equal(np.r_[res1], np.r_[res0], 14) assert_almost_equal(np.r_[res2], np.r_[res0], 14) res0 = d1w_d0.ttest_mean(0.5) res1 = d1w_d1.ttest_mean(0.5) res2 = d1w_d2.ttest_mean(0.5) assert_almost_equal(np.r_[res1], np.r_[res0], 14) assert_almost_equal(np.r_[res2], np.r_[res0], 14) # check confint independent of user ddof res0 = d1w_d0.tconfint_mean() res1 = d1w_d1.tconfint_mean() res2 = d1w_d2.tconfint_mean() assert_almost_equal(res1, res0, 14) assert_almost_equal(res2, res0, 14) def test_comparemeans_convenient_interface(self): x1_2d, x2_2d = self.x1_2d, self.x2_2d d1 = DescrStatsW(x1_2d) d2 = DescrStatsW(x2_2d) cm1 = CompareMeans(d1, d2) # smoke test for summary from statsmodels.iolib.table import SimpleTable for use_t in [True, False]: for usevar in ['pooled', 'unequal']: smry = cm1.summary(use_t=use_t, usevar=usevar) assert_(isinstance(smry, SimpleTable)) # test for from_data method cm2 = CompareMeans.from_data(x1_2d, x2_2d) assert_(str(cm1.summary()) == str(cm2.summary())) def test_comparemeans_convenient_interface_1d(self): # same as above for 2d, just use 1d data instead x1_2d, x2_2d = self.x1, self.x2 d1 = DescrStatsW(x1_2d) d2 = DescrStatsW(x2_2d) cm1 = CompareMeans(d1, d2) # smoke test for summary from statsmodels.iolib.table import SimpleTable for use_t in [True, False]: for usevar in ['pooled', 'unequal']: smry = cm1.summary(use_t=use_t, usevar=usevar) assert_(isinstance(smry, SimpleTable)) # test for from_data method cm2 = CompareMeans.from_data(x1_2d, x2_2d) assert_(str(cm1.summary()) == str(cm2.summary())) class CheckWeightstats1dMixin(object): def test_basic(self): x1r = self.x1r d1w = self.d1w assert_almost_equal(x1r.mean(0), d1w.mean, 14) assert_almost_equal(x1r.var(0, ddof=d1w.ddof), d1w.var, 14) assert_almost_equal(x1r.std(0, ddof=d1w.ddof), d1w.std, 14) var1 = d1w.var_ddof(ddof=1) assert_almost_equal(x1r.var(0, ddof=1), var1, 14) std1 = d1w.std_ddof(ddof=1) assert_almost_equal(x1r.std(0, ddof=1), std1, 14) assert_almost_equal(np.cov(x1r.T, bias=1-d1w.ddof), d1w.cov, 14) # assert_almost_equal(np.corrcoef(x1r.T), d1w.corrcoef, 14) def test_ttest(self): x1r = self.x1r d1w = self.d1w assert_almost_equal(d1w.ttest_mean(3)[:2], stats.ttest_1samp(x1r, 3), 11) # def # assert_almost_equal(ttest_ind(x1, x2, weights=(w1, w2))[:2], # stats.ttest_ind(x1r, x2r), 14) def test_ttest_2sample(self): x1, x2 = self.x1, self.x2 x1r, x2r = self.x1r, self.x2r w1, w2 = self.w1, self.w2 # Note: stats.ttest_ind handles 2d/nd arguments res_sp = stats.ttest_ind(x1r, x2r) assert_almost_equal(ttest_ind(x1, x2, weights=(w1, w2))[:2], res_sp, 14) # check correct ttest independent of user ddof cm = CompareMeans(DescrStatsW(x1, weights=w1, ddof=0), DescrStatsW(x2, weights=w2, ddof=1)) assert_almost_equal(cm.ttest_ind()[:2], res_sp, 14) cm = CompareMeans(DescrStatsW(x1, weights=w1, ddof=1), DescrStatsW(x2, weights=w2, ddof=2)) assert_almost_equal(cm.ttest_ind()[:2], res_sp, 14) cm0 = CompareMeans(DescrStatsW(x1, weights=w1, ddof=0), DescrStatsW(x2, weights=w2, ddof=0)) cm1 = CompareMeans(DescrStatsW(x1, weights=w1, ddof=0), DescrStatsW(x2, weights=w2, ddof=1)) cm2 = CompareMeans(DescrStatsW(x1, weights=w1, ddof=1), DescrStatsW(x2, weights=w2, ddof=2)) res0 = cm0.ttest_ind(usevar='unequal') res1 = cm1.ttest_ind(usevar='unequal') res2 = cm2.ttest_ind(usevar='unequal') assert_almost_equal(res1, res0, 14) assert_almost_equal(res2, res0, 14) # check confint independent of user ddof res0 = cm0.tconfint_diff(usevar='pooled') res1 = cm1.tconfint_diff(usevar='pooled') res2 = cm2.tconfint_diff(usevar='pooled') assert_almost_equal(res1, res0, 14) assert_almost_equal(res2, res0, 14) res0 = cm0.tconfint_diff(usevar='unequal') res1 = cm1.tconfint_diff(usevar='unequal') res2 = cm2.tconfint_diff(usevar='unequal') assert_almost_equal(res1, res0, 14) assert_almost_equal(res2, res0, 14) def test_confint_mean(self): # compare confint_mean with ttest d1w = self.d1w alpha = 0.05 low, upp = d1w.tconfint_mean() t, p, d = d1w.ttest_mean(low) assert_almost_equal(p, alpha * np.ones(p.shape), 8) t, p, d = d1w.ttest_mean(upp) assert_almost_equal(p, alpha * np.ones(p.shape), 8) t, p, d = d1w.ttest_mean(np.vstack((low, upp))) assert_almost_equal(p, alpha * np.ones(p.shape), 8) class CheckWeightstats2dMixin(CheckWeightstats1dMixin): def test_corr(self): x1r = self.x1r d1w = self.d1w assert_almost_equal(np.corrcoef(x1r.T), d1w.corrcoef, 14) class TestWeightstats1d_ddof(CheckWeightstats1dMixin): @classmethod def setup_class(cls): np.random.seed(9876789) n1, n2 = 20, 20 m1, m2 = 1, 1.2 x1 = m1 + np.random.randn(n1, 1) x2 = m2 + np.random.randn(n2, 1) w1 = np.random.randint(1, 4, n1) w2 = np.random.randint(1, 4, n2) cls.x1, cls.x2 = x1, x2 cls.w1, cls.w2 = w1, w2 cls.d1w = DescrStatsW(x1, weights=w1, ddof=1) cls.d2w = DescrStatsW(x2, weights=w2, ddof=1) cls.x1r = cls.d1w.asrepeats() cls.x2r = cls.d2w.asrepeats() class TestWeightstats2d(CheckWeightstats2dMixin): @classmethod def setup_class(cls): np.random.seed(9876789) n1, n2 = 20, 20 m1, m2 = 1, 1.2 x1 = m1 + np.random.randn(n1, 3) x2 = m2 + np.random.randn(n2, 3) w1 = np.random.randint(1, 4, n1) w2 = np.random.randint(1, 4, n2) cls.x1, cls.x2 = x1, x2 cls.w1, cls.w2 = w1, w2 cls.d1w = DescrStatsW(x1, weights=w1) cls.d2w = DescrStatsW(x2, weights=w2) cls.x1r = cls.d1w.asrepeats() cls.x2r = cls.d2w.asrepeats() class TestWeightstats2d_ddof(CheckWeightstats2dMixin): @classmethod def setup_class(cls): np.random.seed(9876789) n1, n2 = 20, 20 m1, m2 = 1, 1.2 x1 = m1 + np.random.randn(n1, 3) x2 = m2 + np.random.randn(n2, 3) w1 = np.random.randint(1, 4, n1) w2 = np.random.randint(1, 4, n2) cls.x1, cls.x2 = x1, x2 cls.w1, cls.w2 = w1, w2 cls.d1w = DescrStatsW(x1, weights=w1, ddof=1) cls.d2w = DescrStatsW(x2, weights=w2, ddof=1) cls.x1r = cls.d1w.asrepeats() cls.x2r = cls.d2w.asrepeats() class TestWeightstats2d_nobs(CheckWeightstats2dMixin): @classmethod def setup_class(cls): np.random.seed(9876789) n1, n2 = 20, 30 m1, m2 = 1, 1.2 x1 = m1 + np.random.randn(n1, 3) x2 = m2 + np.random.randn(n2, 3) w1 = np.random.randint(1, 4, n1) w2 = np.random.randint(1, 4, n2) cls.x1, cls.x2 = x1, x2 cls.w1, cls.w2 = w1, w2 cls.d1w = DescrStatsW(x1, weights=w1, ddof=0) cls.d2w = DescrStatsW(x2, weights=w2, ddof=1) cls.x1r = cls.d1w.asrepeats() cls.x2r = cls.d2w.asrepeats() def test_ttest_ind_with_uneq_var(): # from scipy # check vs. R a = (1, 2, 3) b = (1.1, 2.9, 4.2) pr = 0.53619490753126731 tr = -0.68649512735572582 t, p, df = ttest_ind(a, b, usevar='unequal') assert_almost_equal([t, p], [tr, pr], 13) a = (1, 2, 3, 4) pr = 0.84354139131608286 tr = -0.2108663315950719 t, p, df = ttest_ind(a, b, usevar='unequal') assert_almost_equal([t, p], [tr, pr], 13) def test_ztest_ztost(): # compare weightstats with separately tested proportion ztest ztost import statsmodels.stats.proportion as smprop x1 = [0, 1] w1 = [5, 15] res2 = smprop.proportions_ztest(15, 20., value=0.5) d1 = DescrStatsW(x1, w1) res1 = d1.ztest_mean(0.5) assert_allclose(res1, res2, rtol=0.03, atol=0.003) d2 = DescrStatsW(x1, np.array(w1)*21./20) res1 = d2.ztest_mean(0.5) assert_almost_equal(res1, res2, decimal=12) res1 = d2.ztost_mean(0.4, 0.6) res2 = smprop.proportions_ztost(15, 20., 0.4, 0.6) assert_almost_equal(res1[0], res2[0], decimal=12) x2 = [0, 1] w2 = [10, 10] # d2 = DescrStatsW(x1, np.array(w1)*21./20) d2 = DescrStatsW(x2, w2) res1 = ztest(d1.asrepeats(), d2.asrepeats()) res2 = smprop.proportions_chisquare(np.asarray([15, 10]), np.asarray([20., 20])) # TODO: check this is this difference expected?, see test_proportion assert_allclose(res1[1], res2[1], rtol=0.03) res1a = CompareMeans(d1, d2).ztest_ind() assert_allclose(res1a[1], res2[1], rtol=0.03) assert_almost_equal(res1a, res1, decimal=12) # test for ztest and z confidence interval against R BSDA z.test # Note: I needed to calculate the pooled standard deviation for R # std = np.std(np.concatenate((x-x.mean(),y-y.mean())), ddof=2) # > zt = z.test(x, sigma.x=0.57676142668828667, y, sigma.y=0.57676142668828667) # > cat_items(zt, "ztest.") ztest_ = Holder() ztest_.statistic = 6.55109865675183 ztest_.p_value = 5.711530850508982e-11 ztest_.conf_int = np.array([1.230415246535603, 2.280948389828034]) ztest_.estimate = np.array([7.01818181818182, 5.2625]) ztest_.null_value = 0 ztest_.alternative = 'two.sided' ztest_.method = 'Two-sample z-Test' ztest_.data_name = 'x and y' # > zt = z.test(x, sigma.x=0.57676142668828667, y, # sigma.y=0.57676142668828667, alternative="less") # > cat_items(zt, "ztest_smaller.") ztest_smaller = Holder() ztest_smaller.statistic = 6.55109865675183 ztest_smaller.p_value = 0.999999999971442 ztest_smaller.conf_int = np.array([np.nan, 2.196499421109045]) ztest_smaller.estimate = np.array([7.01818181818182, 5.2625]) ztest_smaller.null_value = 0 ztest_smaller.alternative = 'less' ztest_smaller.method = 'Two-sample z-Test' ztest_smaller.data_name = 'x and y' # > zt = z.test(x, sigma.x=0.57676142668828667, y, # sigma.y=0.57676142668828667, alternative="greater") # > cat_items(zt, "ztest_larger.") ztest_larger = Holder() ztest_larger.statistic = 6.55109865675183 ztest_larger.p_value = 2.855760072861813e-11 ztest_larger.conf_int = np.array([1.314864215254592, np.nan]) ztest_larger.estimate = np.array([7.01818181818182, 5.2625]) ztest_larger.null_value = 0 ztest_larger.alternative = 'greater' ztest_larger.method = 'Two-sample z-Test' ztest_larger.data_name = 'x and y' # > zt = z.test(x, sigma.x=0.57676142668828667, y, # sigma.y=0.57676142668828667, mu=1, alternative="two.sided") # > cat_items(zt, "ztest_mu.") ztest_mu = Holder() ztest_mu.statistic = 2.81972854805176 ztest_mu.p_value = 0.00480642898427981 ztest_mu.conf_int = np.array([1.230415246535603, 2.280948389828034]) ztest_mu.estimate = np.array([7.01818181818182, 5.2625]) ztest_mu.null_value = 1 ztest_mu.alternative = 'two.sided' ztest_mu.method = 'Two-sample z-Test' ztest_mu.data_name = 'x and y' # > zt = z.test(x, sigma.x=0.57676142668828667, y, # sigma.y=0.57676142668828667, mu=1, alternative="greater") # > cat_items(zt, "ztest_larger_mu.") ztest_larger_mu = Holder() ztest_larger_mu.statistic = 2.81972854805176 ztest_larger_mu.p_value = 0.002403214492139871 ztest_larger_mu.conf_int = np.array([1.314864215254592, np.nan]) ztest_larger_mu.estimate = np.array([7.01818181818182, 5.2625]) ztest_larger_mu.null_value = 1 ztest_larger_mu.alternative = 'greater' ztest_larger_mu.method = 'Two-sample z-Test' ztest_larger_mu.data_name = 'x and y' # > zt = z.test(x, sigma.x=0.57676142668828667, y, # sigma.y=0.57676142668828667, mu=2, alternative="less") # > cat_items(zt, "ztest_smaller_mu.") ztest_smaller_mu = Holder() ztest_smaller_mu.statistic = -0.911641560648313 ztest_smaller_mu.p_value = 0.1809787183191324 ztest_smaller_mu.conf_int = np.array([np.nan, 2.196499421109045]) ztest_smaller_mu.estimate = np.array([7.01818181818182, 5.2625]) ztest_smaller_mu.null_value = 2 ztest_smaller_mu.alternative = 'less' ztest_smaller_mu.method = 'Two-sample z-Test' ztest_smaller_mu.data_name = 'x and y' # > zt = z.test(x, sigma.x=0.46436662631627995, mu=6.4, # alternative="two.sided") # > cat_items(zt, "ztest_mu_1s.") ztest_mu_1s = Holder() ztest_mu_1s.statistic = 4.415212090914452 ztest_mu_1s.p_value = 1.009110038015147e-05 ztest_mu_1s.conf_int = np.array([6.74376372125119, 7.29259991511245]) ztest_mu_1s.estimate = 7.01818181818182 ztest_mu_1s.null_value = 6.4 ztest_mu_1s.alternative = 'two.sided' ztest_mu_1s.method = 'One-sample z-Test' ztest_mu_1s.data_name = 'x' # > zt = z.test(x, sigma.x=0.46436662631627995, mu=7.4, alternative="less") # > cat_items(zt, "ztest_smaller_mu_1s.") ztest_smaller_mu_1s = Holder() ztest_smaller_mu_1s.statistic = -2.727042762035397 ztest_smaller_mu_1s.p_value = 0.00319523783881176 ztest_smaller_mu_1s.conf_int = np.array([np.nan, 7.248480744895716]) ztest_smaller_mu_1s.estimate = 7.01818181818182 ztest_smaller_mu_1s.null_value = 7.4 ztest_smaller_mu_1s.alternative = 'less' ztest_smaller_mu_1s.method = 'One-sample z-Test' ztest_smaller_mu_1s.data_name = 'x' # > zt = z.test(x, sigma.x=0.46436662631627995, mu=6.4, alternative="greater") # > cat_items(zt, "ztest_greater_mu_1s.") ztest_larger_mu_1s = Holder() ztest_larger_mu_1s.statistic = 4.415212090914452 ztest_larger_mu_1s.p_value = 5.045550190097003e-06 ztest_larger_mu_1s.conf_int = np.array([6.78788289146792, np.nan]) ztest_larger_mu_1s.estimate = 7.01818181818182 ztest_larger_mu_1s.null_value = 6.4 ztest_larger_mu_1s.alternative = 'greater' ztest_larger_mu_1s.method = 'One-sample z-Test' ztest_larger_mu_1s.data_name = 'x' alternatives = {'less': 'smaller', 'greater': 'larger', 'two.sided': 'two-sided'} class TestZTest(object): # all examples use the same data # no weights used in tests @classmethod def setup_class(cls): cls.x1 = np.array([7.8, 6.6, 6.5, 7.4, 7.3, 7., 6.4, 7.1, 6.7, 7.6, 6.8]) cls.x2 = np.array([4.5, 5.4, 6.1, 6.1, 5.4, 5., 4.1, 5.5]) cls.d1 = DescrStatsW(cls.x1) cls.d2 = DescrStatsW(cls.x2) cls.cm = CompareMeans(cls.d1, cls.d2) def test(self): x1, x2 = self.x1, self.x2 cm = self.cm # tc : test cases for tc in [ztest_, ztest_smaller, ztest_larger, ztest_mu, ztest_smaller_mu, ztest_larger_mu]: zstat, pval = ztest(x1, x2, value=tc.null_value, alternative=alternatives[tc.alternative]) assert_allclose(zstat, tc.statistic, rtol=1e-10) assert_allclose(pval, tc.p_value, rtol=1e-10, atol=1e-16) zstat, pval = cm.ztest_ind(value=tc.null_value, alternative=alternatives[tc.alternative]) assert_allclose(zstat, tc.statistic, rtol=1e-10) assert_allclose(pval, tc.p_value, rtol=1e-10, atol=1e-16) # overwrite nan in R's confint tc_conf_int = tc.conf_int.copy() if np.isnan(tc_conf_int[0]): tc_conf_int[0] = - np.inf if np.isnan(tc_conf_int[1]): tc_conf_int[1] = np.inf # Note: value is shifting our confidence interval in zconfint ci = zconfint(x1, x2, value=0, alternative=alternatives[tc.alternative]) assert_allclose(ci, tc_conf_int, rtol=1e-10) ci = cm.zconfint_diff(alternative=alternatives[tc.alternative]) assert_allclose(ci, tc_conf_int, rtol=1e-10) ci = zconfint(x1, x2, value=tc.null_value, alternative=alternatives[tc.alternative]) assert_allclose(ci, tc_conf_int - tc.null_value, rtol=1e-10) # 1 sample test copy-paste d1 = self.d1 for tc in [ztest_mu_1s, ztest_smaller_mu_1s, ztest_larger_mu_1s]: zstat, pval = ztest(x1, value=tc.null_value, alternative=alternatives[tc.alternative]) assert_allclose(zstat, tc.statistic, rtol=1e-10) assert_allclose(pval, tc.p_value, rtol=1e-10, atol=1e-16) zstat, pval = d1.ztest_mean(value=tc.null_value, alternative=alternatives[tc.alternative]) assert_allclose(zstat, tc.statistic, rtol=1e-10) assert_allclose(pval, tc.p_value, rtol=1e-10, atol=1e-16) # overwrite nan in R's confint tc_conf_int = tc.conf_int.copy() if np.isnan(tc_conf_int[0]): tc_conf_int[0] = - np.inf if np.isnan(tc_conf_int[1]): tc_conf_int[1] = np.inf # Note: value is shifting our confidence interval in zconfint ci = zconfint(x1, value=0, alternative=alternatives[tc.alternative]) assert_allclose(ci, tc_conf_int, rtol=1e-10) ci = d1.zconfint_mean(alternative=alternatives[tc.alternative]) assert_allclose(ci, tc_conf_int, rtol=1e-10) def test_weightstats_len_1(): x1 = [1] w1 = [1] d1 = DescrStatsW(x1, w1) assert (d1.quantile([0.0, 0.5, 1.0]) == 1).all() def test_weightstats_2d_w1(): x1 = [[1], [2]] w1 = [[1], [2]] d1 = DescrStatsW(x1, w1) print(len(np.array(w1).shape)) assert (d1.quantile([0.5, 1.0]) == 2).all().all() def test_weightstats_2d_w2(): x1 = [[1]] w1 = [[1]] d1 = DescrStatsW(x1, w1) assert (d1.quantile([0, 0.5, 1.0]) == 1).all().all() statsmodels-0.12.2/statsmodels/stats/weightstats.py000066400000000000000000001536741400612667500226050ustar00rootroot00000000000000"""Tests and descriptive statistics with weights Created on 2010-09-18 Author: josef-pktd License: BSD (3-clause) References ---------- SPSS manual SAS manual This follows in large parts the SPSS manual, which is largely the same as the SAS manual with different, simpler notation. Freq, Weight in SAS seems redundant since they always show up as product, SPSS has only weights. Notes ----- This has potential problems with ddof, I started to follow numpy with ddof=0 by default and users can change it, but this might still mess up the t-tests, since the estimates for the standard deviation will be based on the ddof that the user chooses. - fixed ddof for the meandiff ttest, now matches scipy.stats.ttest_ind Note: scipy has now a separate, pooled variance option in ttest, but I have not compared yet. """ import numpy as np from scipy import stats from statsmodels.tools.decorators import cache_readonly class DescrStatsW(object): """ Descriptive statistics and tests with weights for case weights Assumes that the data is 1d or 2d with (nobs, nvars) observations in rows, variables in columns, and that the same weight applies to each column. If degrees of freedom correction is used, then weights should add up to the number of observations. ttest also assumes that the sum of weights corresponds to the sample size. This is essentially the same as replicating each observations by its weight, if the weights are integers, often called case or frequency weights. Parameters ---------- data : array_like, 1-D or 2-D dataset weights : None or 1-D ndarray weights for each observation, with same length as zero axis of data ddof : int default ddof=0, degrees of freedom correction used for second moments, var, std, cov, corrcoef. However, statistical tests are independent of `ddof`, based on the standard formulas. Examples -------- >>> import numpy as np >>> np.random.seed(0) >>> x1_2d = 1.0 + np.random.randn(20, 3) >>> w1 = np.random.randint(1, 4, 20) >>> d1 = DescrStatsW(x1_2d, weights=w1) >>> d1.mean array([ 1.42739844, 1.23174284, 1.083753 ]) >>> d1.var array([ 0.94855633, 0.52074626, 1.12309325]) >>> d1.std_mean array([ 0.14682676, 0.10878944, 0.15976497]) >>> tstat, pval, df = d1.ttest_mean(0) >>> tstat; pval; df array([ 9.72165021, 11.32226471, 6.78342055]) array([ 1.58414212e-12, 1.26536887e-14, 2.37623126e-08]) 44.0 >>> tstat, pval, df = d1.ttest_mean([0, 1, 1]) >>> tstat; pval; df array([ 9.72165021, 2.13019609, 0.52422632]) array([ 1.58414212e-12, 3.87842808e-02, 6.02752170e-01]) 44.0 # if weights are integers, then asrepeats can be used >>> x1r = d1.asrepeats() >>> x1r.shape ... >>> stats.ttest_1samp(x1r, [0, 1, 1]) ... """ def __init__(self, data, weights=None, ddof=0): self.data = np.asarray(data) if weights is None: self.weights = np.ones(self.data.shape[0]) else: self.weights = np.asarray(weights).astype(float) # TODO: why squeeze? if len(self.weights.shape) > 1 and len(self.weights) > 1: self.weights = self.weights.squeeze() self.ddof = ddof @cache_readonly def sum_weights(self): """Sum of weights""" return self.weights.sum(0) @cache_readonly def nobs(self): """alias for number of observations/cases, equal to sum of weights """ return self.sum_weights @cache_readonly def sum(self): """weighted sum of data""" return np.dot(self.data.T, self.weights) @cache_readonly def mean(self): """weighted mean of data""" return self.sum / self.sum_weights @cache_readonly def demeaned(self): """data with weighted mean subtracted""" return self.data - self.mean @cache_readonly def sumsquares(self): """weighted sum of squares of demeaned data""" return np.dot((self.demeaned ** 2).T, self.weights) # need memoize instead of cache decorator def var_ddof(self, ddof=0): """variance of data given ddof Parameters ---------- ddof : int, float degrees of freedom correction, independent of attribute ddof Returns ------- var : float, ndarray variance with denominator ``sum_weights - ddof`` """ return self.sumsquares / (self.sum_weights - ddof) def std_ddof(self, ddof=0): """standard deviation of data with given ddof Parameters ---------- ddof : int, float degrees of freedom correction, independent of attribute ddof Returns ------- std : float, ndarray standard deviation with denominator ``sum_weights - ddof`` """ return np.sqrt(self.var_ddof(ddof=ddof)) @cache_readonly def var(self): """variance with default degrees of freedom correction """ return self.sumsquares / (self.sum_weights - self.ddof) @cache_readonly def _var(self): """variance without degrees of freedom correction used for statistical tests with controlled ddof """ return self.sumsquares / self.sum_weights @cache_readonly def std(self): """standard deviation with default degrees of freedom correction """ return np.sqrt(self.var) @cache_readonly def cov(self): """weighted covariance of data if data is 2 dimensional assumes variables in columns and observations in rows uses default ddof """ cov_ = np.dot(self.weights * self.demeaned.T, self.demeaned) cov_ /= self.sum_weights - self.ddof return cov_ @cache_readonly def corrcoef(self): """weighted correlation with default ddof assumes variables in columns and observations in rows """ return self.cov / self.std / self.std[:, None] @cache_readonly def std_mean(self): """standard deviation of weighted mean """ std = self.std if self.ddof != 0: # ddof correction, (need copy of std) std = std * np.sqrt( (self.sum_weights - self.ddof) / self.sum_weights ) return std / np.sqrt(self.sum_weights - 1) def quantile(self, probs, return_pandas=True): """ Compute quantiles for a weighted sample. Parameters ---------- probs : array_like A vector of probability points at which to calculate the quantiles. Each element of `probs` should fall in [0, 1]. return_pandas : bool If True, return value is a Pandas DataFrame or Series. Otherwise returns a ndarray. Returns ------- quantiles : Series, DataFrame, or ndarray If `return_pandas` = True, returns one of the following: * data are 1d, `return_pandas` = True: a Series indexed by the probability points. * data are 2d, `return_pandas` = True: a DataFrame with the probability points as row index and the variables as column index. If `return_pandas` = False, returns an ndarray containing the same values as the Series/DataFrame. Notes ----- To compute the quantiles, first, the weights are summed over exact ties yielding distinct data values y_1 < y_2 < ..., and corresponding weights w_1, w_2, .... Let s_j denote the sum of the first j weights, and let W denote the sum of all the weights. For a probability point p, if pW falls strictly between s_j and s_{j+1} then the estimated quantile is y_{j+1}. If pW = s_j then the estimated quantile is (y_j + y_{j+1})/2. If pW < p_1 then the estimated quantile is y_1. References ---------- SAS documentation for weighted quantiles: https://support.sas.com/documentation/cdl/en/procstat/63104/HTML/default/viewer.htm#procstat_univariate_sect028.htm """ import pandas as pd probs = np.asarray(probs) probs = np.atleast_1d(probs) if self.data.ndim == 1: rslt = self._quantile(self.data, probs) if return_pandas: rslt = pd.Series(rslt, index=probs) else: rslt = [] for vec in self.data.T: rslt.append(self._quantile(vec, probs)) rslt = np.column_stack(rslt) if return_pandas: columns = ["col%d" % (j + 1) for j in range(rslt.shape[1])] rslt = pd.DataFrame(data=rslt, columns=columns, index=probs) if return_pandas: rslt.index.name = "p" return rslt def _quantile(self, vec, probs): # Helper function to calculate weighted quantiles for one column. # Follows definition from SAS documentation. # Returns ndarray import pandas as pd # Aggregate over ties df = pd.DataFrame(index=np.arange(len(self.weights))) df["weights"] = self.weights df["vec"] = vec dfg = df.groupby("vec").agg(np.sum) weights = dfg.values[:, 0] values = np.asarray(dfg.index) cweights = np.cumsum(weights) totwt = cweights[-1] targets = probs * totwt ii = np.searchsorted(cweights, targets) rslt = values[ii] # Exact hits jj = np.flatnonzero(np.abs(targets - cweights[ii]) < 1e-10) jj = jj[ii[jj] < len(cweights) - 1] rslt[jj] = (values[ii[jj]] + values[ii[jj] + 1]) / 2 return rslt def tconfint_mean(self, alpha=0.05, alternative="two-sided"): """two-sided confidence interval for weighted mean of data If the data is 2d, then these are separate confidence intervals for each column. Parameters ---------- alpha : float significance level for the confidence interval, coverage is ``1-alpha`` alternative : str This specifies the alternative hypothesis for the test that corresponds to the confidence interval. The alternative hypothesis, H1, has to be one of the following 'two-sided': H1: mean not equal to value (default) 'larger' : H1: mean larger than value 'smaller' : H1: mean smaller than value Returns ------- lower, upper : floats or ndarrays lower and upper bound of confidence interval Notes ----- In a previous version, statsmodels 0.4, alpha was the confidence level, e.g. 0.95 """ # TODO: add asymmetric dof = self.sum_weights - 1 ci = _tconfint_generic( self.mean, self.std_mean, dof, alpha, alternative ) return ci def zconfint_mean(self, alpha=0.05, alternative="two-sided"): """two-sided confidence interval for weighted mean of data Confidence interval is based on normal distribution. If the data is 2d, then these are separate confidence intervals for each column. Parameters ---------- alpha : float significance level for the confidence interval, coverage is ``1-alpha`` alternative : str This specifies the alternative hypothesis for the test that corresponds to the confidence interval. The alternative hypothesis, H1, has to be one of the following 'two-sided': H1: mean not equal to value (default) 'larger' : H1: mean larger than value 'smaller' : H1: mean smaller than value Returns ------- lower, upper : floats or ndarrays lower and upper bound of confidence interval Notes ----- In a previous version, statsmodels 0.4, alpha was the confidence level, e.g. 0.95 """ return _zconfint_generic(self.mean, self.std_mean, alpha, alternative) def ttest_mean(self, value=0, alternative="two-sided"): """ttest of Null hypothesis that mean is equal to value. The alternative hypothesis H1 is defined by the following - 'two-sided': H1: mean not equal to value - 'larger' : H1: mean larger than value - 'smaller' : H1: mean smaller than value Parameters ---------- value : float or array the hypothesized value for the mean alternative : str The alternative hypothesis, H1, has to be one of the following: - 'two-sided': H1: mean not equal to value (default) - 'larger' : H1: mean larger than value - 'smaller' : H1: mean smaller than value Returns ------- tstat : float test statistic pvalue : float pvalue of the t-test df : int or float """ # TODO: check direction with R, smaller=less, larger=greater tstat = (self.mean - value) / self.std_mean dof = self.sum_weights - 1 # TODO: use outsourced if alternative == "two-sided": pvalue = stats.t.sf(np.abs(tstat), dof) * 2 elif alternative == "larger": pvalue = stats.t.sf(tstat, dof) elif alternative == "smaller": pvalue = stats.t.cdf(tstat, dof) return tstat, pvalue, dof def ttost_mean(self, low, upp): """test of (non-)equivalence of one sample TOST: two one-sided t tests null hypothesis: m < low or m > upp alternative hypothesis: low < m < upp where m is the expected value of the sample (mean of the population). If the pvalue is smaller than a threshold, say 0.05, then we reject the hypothesis that the expected value of the sample (mean of the population) is outside of the interval given by thresholds low and upp. Parameters ---------- low, upp : float equivalence interval low < mean < upp Returns ------- pvalue : float pvalue of the non-equivalence test t1, pv1, df1 : tuple test statistic, pvalue and degrees of freedom for lower threshold test t2, pv2, df2 : tuple test statistic, pvalue and degrees of freedom for upper threshold test """ t1, pv1, df1 = self.ttest_mean(low, alternative="larger") t2, pv2, df2 = self.ttest_mean(upp, alternative="smaller") return np.maximum(pv1, pv2), (t1, pv1, df1), (t2, pv2, df2) def ztest_mean(self, value=0, alternative="two-sided"): """z-test of Null hypothesis that mean is equal to value. The alternative hypothesis H1 is defined by the following 'two-sided': H1: mean not equal to value 'larger' : H1: mean larger than value 'smaller' : H1: mean smaller than value Parameters ---------- value : float or array the hypothesized value for the mean alternative : str The alternative hypothesis, H1, has to be one of the following 'two-sided': H1: mean not equal to value (default) 'larger' : H1: mean larger than value 'smaller' : H1: mean smaller than value Returns ------- tstat : float test statistic pvalue : float pvalue of the t-test Notes ----- This uses the same degrees of freedom correction as the t-test in the calculation of the standard error of the mean, i.e it uses `(sum_weights - 1)` instead of `sum_weights` in the denominator. See Examples below for the difference. Examples -------- z-test on a proportion, with 20 observations, 15 of those are our event >>> import statsmodels.api as sm >>> x1 = [0, 1] >>> w1 = [5, 15] >>> d1 = sm.stats.DescrStatsW(x1, w1) >>> d1.ztest_mean(0.5) (2.5166114784235836, 0.011848940928347452) This differs from the proportions_ztest because of the degrees of freedom correction: >>> sm.stats.proportions_ztest(15, 20.0, value=0.5) (2.5819888974716112, 0.009823274507519247). We can replicate the results from ``proportions_ztest`` if we increase the weights to have artificially one more observation: >>> sm.stats.DescrStatsW(x1, np.array(w1)*21./20).ztest_mean(0.5) (2.5819888974716116, 0.0098232745075192366) """ tstat = (self.mean - value) / self.std_mean # TODO: use outsourced if alternative == "two-sided": pvalue = stats.norm.sf(np.abs(tstat)) * 2 elif alternative == "larger": pvalue = stats.norm.sf(tstat) elif alternative == "smaller": pvalue = stats.norm.cdf(tstat) return tstat, pvalue def ztost_mean(self, low, upp): """test of (non-)equivalence of one sample, based on z-test TOST: two one-sided z-tests null hypothesis: m < low or m > upp alternative hypothesis: low < m < upp where m is the expected value of the sample (mean of the population). If the pvalue is smaller than a threshold, say 0.05, then we reject the hypothesis that the expected value of the sample (mean of the population) is outside of the interval given by thresholds low and upp. Parameters ---------- low, upp : float equivalence interval low < mean < upp Returns ------- pvalue : float pvalue of the non-equivalence test t1, pv1 : tuple test statistic and p-value for lower threshold test t2, pv2 : tuple test statistic and p-value for upper threshold test """ t1, pv1 = self.ztest_mean(low, alternative="larger") t2, pv2 = self.ztest_mean(upp, alternative="smaller") return np.maximum(pv1, pv2), (t1, pv1), (t2, pv2) def get_compare(self, other, weights=None): """return an instance of CompareMeans with self and other Parameters ---------- other : array_like or instance of DescrStatsW If array_like then this creates an instance of DescrStatsW with the given weights. weights : None or array weights are only used if other is not an instance of DescrStatsW Returns ------- cm : instance of CompareMeans the instance has self attached as d1 and other as d2. See Also -------- CompareMeans """ if not isinstance(other, self.__class__): d2 = DescrStatsW(other, weights) else: d2 = other return CompareMeans(self, d2) def asrepeats(self): """get array that has repeats given by floor(weights) observations with weight=0 are dropped """ w_int = np.floor(self.weights).astype(int) return np.repeat(self.data, w_int, axis=0) def _tstat_generic(value1, value2, std_diff, dof, alternative, diff=0): """generic ttest based on summary statistic The test statistic is : tstat = (value1 - value2 - diff) / std_diff and is assumed to be t-distributed with ``dof`` degrees of freedom. Parameters ---------- value1 : float or ndarray Value, for example mean, of the first sample. value2 : float or ndarray Value, for example mean, of the second sample. std_diff : float or ndarray Standard error of the difference value1 - value2 dof : int or float Degrees of freedom alternative : str The alternative hypothesis, H1, has to be one of the following * 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0. * 'larger' : H1: ``value1 - value2 - diff > 0`` * 'smaller' : H1: ``value1 - value2 - diff < 0`` diff : float value of difference ``value1 - value2`` under the null hypothesis Returns ------- tstat : float or ndarray Test statistic. pvalue : float or ndarray P-value of the hypothesis test assuming that the test statistic is t-distributed with ``df`` degrees of freedom. """ tstat = (value1 - value2 - diff) / std_diff if alternative in ["two-sided", "2-sided", "2s"]: pvalue = stats.t.sf(np.abs(tstat), dof) * 2 elif alternative in ["larger", "l"]: pvalue = stats.t.sf(tstat, dof) elif alternative in ["smaller", "s"]: pvalue = stats.t.cdf(tstat, dof) else: raise ValueError("invalid alternative") return tstat, pvalue def _tconfint_generic(mean, std_mean, dof, alpha, alternative): """generic t-confint based on summary statistic Parameters ---------- mean : float or ndarray Value, for example mean, of the first sample. std_mean : float or ndarray Standard error of the difference value1 - value2 dof : int or float Degrees of freedom alpha : float Significance level for the confidence interval, coverage is ``1-alpha``. alternative : str The alternative hypothesis, H1, has to be one of the following * 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0. * 'larger' : H1: ``value1 - value2 - diff > 0`` * 'smaller' : H1: ``value1 - value2 - diff < 0`` Returns ------- lower : float or ndarray Lower confidence limit. This is -inf for the one-sided alternative "smaller". upper : float or ndarray Upper confidence limit. This is inf for the one-sided alternative "larger". """ if alternative in ["two-sided", "2-sided", "2s"]: tcrit = stats.t.ppf(1 - alpha / 2.0, dof) lower = mean - tcrit * std_mean upper = mean + tcrit * std_mean elif alternative in ["larger", "l"]: tcrit = stats.t.ppf(alpha, dof) lower = mean + tcrit * std_mean upper = np.inf elif alternative in ["smaller", "s"]: tcrit = stats.t.ppf(1 - alpha, dof) lower = -np.inf upper = mean + tcrit * std_mean else: raise ValueError("invalid alternative") return lower, upper def _zstat_generic(value1, value2, std_diff, alternative, diff=0): """generic (normal) z-test based on summary statistic The test statistic is : tstat = (value1 - value2 - diff) / std_diff and is assumed to be normally distributed. Parameters ---------- value1 : float or ndarray Value, for example mean, of the first sample. value2 : float or ndarray Value, for example mean, of the second sample. std_diff : float or ndarray Standard error of the difference value1 - value2 alternative : str The alternative hypothesis, H1, has to be one of the following * 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0. * 'larger' : H1: ``value1 - value2 - diff > 0`` * 'smaller' : H1: ``value1 - value2 - diff < 0`` diff : float value of difference ``value1 - value2`` under the null hypothesis Returns ------- tstat : float or ndarray Test statistic. pvalue : float or ndarray P-value of the hypothesis test assuming that the test statistic is t-distributed with ``df`` degrees of freedom. """ zstat = (value1 - value2 - diff) / std_diff if alternative in ["two-sided", "2-sided", "2s"]: pvalue = stats.norm.sf(np.abs(zstat)) * 2 elif alternative in ["larger", "l"]: pvalue = stats.norm.sf(zstat) elif alternative in ["smaller", "s"]: pvalue = stats.norm.cdf(zstat) else: raise ValueError("invalid alternative") return zstat, pvalue def _zstat_generic2(value, std, alternative): """generic (normal) z-test based on summary statistic The test statistic is : zstat = value / std and is assumed to be normally distributed with standard deviation ``std``. Parameters ---------- value : float or ndarray Value of a sample statistic, for example mean. value2 : float or ndarray Value, for example mean, of the second sample. std : float or ndarray Standard error of the sample statistic value. alternative : str The alternative hypothesis, H1, has to be one of the following * 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0. * 'larger' : H1: ``value1 - value2 - diff > 0`` * 'smaller' : H1: ``value1 - value2 - diff < 0`` Returns ------- zstat : float or ndarray Test statistic. pvalue : float or ndarray P-value of the hypothesis test assuming that the test statistic is normally distributed. """ zstat = value / std if alternative in ["two-sided", "2-sided", "2s"]: pvalue = stats.norm.sf(np.abs(zstat)) * 2 elif alternative in ["larger", "l"]: pvalue = stats.norm.sf(zstat) elif alternative in ["smaller", "s"]: pvalue = stats.norm.cdf(zstat) else: raise ValueError("invalid alternative") return zstat, pvalue def _zconfint_generic(mean, std_mean, alpha, alternative): """generic normal-confint based on summary statistic Parameters ---------- mean : float or ndarray Value, for example mean, of the first sample. std_mean : float or ndarray Standard error of the difference value1 - value2 alpha : float Significance level for the confidence interval, coverage is ``1-alpha`` alternative : str The alternative hypothesis, H1, has to be one of the following * 'two-sided' : H1: ``value1 - value2 - diff`` not equal to 0. * 'larger' : H1: ``value1 - value2 - diff > 0`` * 'smaller' : H1: ``value1 - value2 - diff < 0`` Returns ------- lower : float or ndarray Lower confidence limit. This is -inf for the one-sided alternative "smaller". upper : float or ndarray Upper confidence limit. This is inf for the one-sided alternative "larger". """ if alternative in ["two-sided", "2-sided", "2s"]: zcrit = stats.norm.ppf(1 - alpha / 2.0) lower = mean - zcrit * std_mean upper = mean + zcrit * std_mean elif alternative in ["larger", "l"]: zcrit = stats.norm.ppf(alpha) lower = mean + zcrit * std_mean upper = np.inf elif alternative in ["smaller", "s"]: zcrit = stats.norm.ppf(1 - alpha) lower = -np.inf upper = mean + zcrit * std_mean else: raise ValueError("invalid alternative") return lower, upper class CompareMeans(object): """class for two sample comparison The tests and the confidence interval work for multi-endpoint comparison: If d1 and d2 have the same number of rows, then each column of the data in d1 is compared with the corresponding column in d2. Parameters ---------- d1, d2 : instances of DescrStatsW Notes ----- The result for the statistical tests and the confidence interval are independent of the user specified ddof. TODO: Extend to any number of groups or write a version that works in that case, like in SAS and SPSS. """ def __init__(self, d1, d2): """assume d1, d2 hold the relevant attributes """ self.d1 = d1 self.d2 = d2 # assume nobs is available # if not hasattr(self.d1, 'nobs'): # d1.nobs1 = d1.sum_weights.astype(float) #float just to make sure # self.nobs2 = d2.sum_weights.astype(float) @classmethod def from_data( cls, data1, data2, weights1=None, weights2=None, ddof1=0, ddof2=0 ): """construct a CompareMeans object from data Parameters ---------- data1, data2 : array_like, 1-D or 2-D compared datasets weights1, weights2 : None or 1-D ndarray weights for each observation of data1 and data2 respectively, with same length as zero axis of corresponding dataset. ddof1, ddof2 : int default ddof1=0, ddof2=0, degrees of freedom for data1, data2 respectively. Returns ------- A CompareMeans instance. """ return cls( DescrStatsW(data1, weights=weights1, ddof=ddof1), DescrStatsW(data2, weights=weights2, ddof=ddof2), ) def summary(self, use_t=True, alpha=0.05, usevar="pooled", value=0): """summarize the results of the hypothesis test Parameters ---------- use_t : bool, optional if use_t is True, then t test results are returned if use_t is False, then z test results are returned alpha : float significance level for the confidence interval, coverage is ``1-alpha`` usevar : str, 'pooled' or 'unequal' If ``pooled``, then the standard deviation of the samples is assumed to be the same. If ``unequal``, then the variance of Welsh ttest will be used, and the degrees of freedom are those of Satterthwaite if ``use_t`` is True. value : float difference between the means under the Null hypothesis. Returns ------- smry : SimpleTable """ d1 = self.d1 d2 = self.d2 confint_percents = 100 - alpha * 100 if use_t: tstat, pvalue, _ = self.ttest_ind(usevar=usevar, value=value) lower, upper = self.tconfint_diff(alpha=alpha, usevar=usevar) else: tstat, pvalue = self.ztest_ind(usevar=usevar, value=value) lower, upper = self.zconfint_diff(alpha=alpha, usevar=usevar) if usevar == "pooled": std_err = self.std_meandiff_pooledvar else: std_err = self.std_meandiff_separatevar std_err = np.atleast_1d(std_err) tstat = np.atleast_1d(tstat) pvalue = np.atleast_1d(pvalue) lower = np.atleast_1d(lower) upper = np.atleast_1d(upper) conf_int = np.column_stack((lower, upper)) params = np.atleast_1d(d1.mean - d2.mean - value) title = "Test for equality of means" yname = "y" # not used in params_frame xname = ["subset #%d" % (ii + 1) for ii in range(tstat.shape[0])] from statsmodels.iolib.summary import summary_params return summary_params( (None, params, std_err, tstat, pvalue, conf_int), alpha=alpha, use_t=use_t, yname=yname, xname=xname, title=title, ) @cache_readonly def std_meandiff_separatevar(self): # this uses ``_var`` to use ddof=0 for formula d1 = self.d1 d2 = self.d2 return np.sqrt(d1._var / (d1.nobs - 1) + d2._var / (d2.nobs - 1)) @cache_readonly def std_meandiff_pooledvar(self): """variance assuming equal variance in both data sets """ # this uses ``_var`` to use ddof=0 for formula d1 = self.d1 d2 = self.d2 # could make var_pooled into attribute var_pooled = ( (d1.sumsquares + d2.sumsquares) / # (d1.nobs - d1.ddof + d2.nobs - d2.ddof)) (d1.nobs - 1 + d2.nobs - 1) ) return np.sqrt(var_pooled * (1.0 / d1.nobs + 1.0 / d2.nobs)) def dof_satt(self): """degrees of freedom of Satterthwaite for unequal variance """ d1 = self.d1 d2 = self.d2 # this follows blindly the SPSS manual # except I use ``_var`` which has ddof=0 sem1 = d1._var / (d1.nobs - 1) sem2 = d2._var / (d2.nobs - 1) semsum = sem1 + sem2 z1 = (sem1 / semsum) ** 2 / (d1.nobs - 1) z2 = (sem2 / semsum) ** 2 / (d2.nobs - 1) dof = 1.0 / (z1 + z2) return dof def ttest_ind(self, alternative="two-sided", usevar="pooled", value=0): """ttest for the null hypothesis of identical means this should also be the same as onewaygls, except for ddof differences Parameters ---------- x1 : array_like, 1-D or 2-D first of the two independent samples, see notes for 2-D case x2 : array_like, 1-D or 2-D second of the two independent samples, see notes for 2-D case alternative : str The alternative hypothesis, H1, has to be one of the following 'two-sided': H1: difference in means not equal to value (default) 'larger' : H1: difference in means larger than value 'smaller' : H1: difference in means smaller than value usevar : str, 'pooled' or 'unequal' If ``pooled``, then the standard deviation of the samples is assumed to be the same. If ``unequal``, then Welsh ttest with Satterthwait degrees of freedom is used value : float difference between the means under the Null hypothesis. Returns ------- tstat : float test statistic pvalue : float pvalue of the t-test df : int or float degrees of freedom used in the t-test Notes ----- The result is independent of the user specified ddof. """ d1 = self.d1 d2 = self.d2 if usevar == "pooled": stdm = self.std_meandiff_pooledvar dof = d1.nobs - 1 + d2.nobs - 1 elif usevar == "unequal": stdm = self.std_meandiff_separatevar dof = self.dof_satt() else: raise ValueError('usevar can only be "pooled" or "unequal"') tstat, pval = _tstat_generic( d1.mean, d2.mean, stdm, dof, alternative, diff=value ) return tstat, pval, dof def ztest_ind(self, alternative="two-sided", usevar="pooled", value=0): """z-test for the null hypothesis of identical means Parameters ---------- x1 : array_like, 1-D or 2-D first of the two independent samples, see notes for 2-D case x2 : array_like, 1-D or 2-D second of the two independent samples, see notes for 2-D case alternative : str The alternative hypothesis, H1, has to be one of the following 'two-sided': H1: difference in means not equal to value (default) 'larger' : H1: difference in means larger than value 'smaller' : H1: difference in means smaller than value usevar : str, 'pooled' or 'unequal' If ``pooled``, then the standard deviation of the samples is assumed to be the same. If ``unequal``, then the standard deviations of the samples may be different. value : float difference between the means under the Null hypothesis. Returns ------- tstat : float test statistic pvalue : float pvalue of the z-test """ d1 = self.d1 d2 = self.d2 if usevar == "pooled": stdm = self.std_meandiff_pooledvar elif usevar == "unequal": stdm = self.std_meandiff_separatevar else: raise ValueError('usevar can only be "pooled" or "unequal"') tstat, pval = _zstat_generic( d1.mean, d2.mean, stdm, alternative, diff=value ) return tstat, pval def tconfint_diff( self, alpha=0.05, alternative="two-sided", usevar="pooled" ): """confidence interval for the difference in means Parameters ---------- alpha : float significance level for the confidence interval, coverage is ``1-alpha`` alternative : str This specifies the alternative hypothesis for the test that corresponds to the confidence interval. The alternative hypothesis, H1, has to be one of the following : 'two-sided': H1: difference in means not equal to value (default) 'larger' : H1: difference in means larger than value 'smaller' : H1: difference in means smaller than value usevar : str, 'pooled' or 'unequal' If ``pooled``, then the standard deviation of the samples is assumed to be the same. If ``unequal``, then Welsh ttest with Satterthwait degrees of freedom is used Returns ------- lower, upper : floats lower and upper limits of the confidence interval Notes ----- The result is independent of the user specified ddof. """ d1 = self.d1 d2 = self.d2 diff = d1.mean - d2.mean if usevar == "pooled": std_diff = self.std_meandiff_pooledvar dof = d1.nobs - 1 + d2.nobs - 1 elif usevar == "unequal": std_diff = self.std_meandiff_separatevar dof = self.dof_satt() else: raise ValueError('usevar can only be "pooled" or "unequal"') res = _tconfint_generic( diff, std_diff, dof, alpha=alpha, alternative=alternative ) return res def zconfint_diff( self, alpha=0.05, alternative="two-sided", usevar="pooled" ): """confidence interval for the difference in means Parameters ---------- alpha : float significance level for the confidence interval, coverage is ``1-alpha`` alternative : str This specifies the alternative hypothesis for the test that corresponds to the confidence interval. The alternative hypothesis, H1, has to be one of the following : 'two-sided': H1: difference in means not equal to value (default) 'larger' : H1: difference in means larger than value 'smaller' : H1: difference in means smaller than value usevar : str, 'pooled' or 'unequal' If ``pooled``, then the standard deviation of the samples is assumed to be the same. If ``unequal``, then Welsh ttest with Satterthwait degrees of freedom is used Returns ------- lower, upper : floats lower and upper limits of the confidence interval Notes ----- The result is independent of the user specified ddof. """ d1 = self.d1 d2 = self.d2 diff = d1.mean - d2.mean if usevar == "pooled": std_diff = self.std_meandiff_pooledvar elif usevar == "unequal": std_diff = self.std_meandiff_separatevar else: raise ValueError('usevar can only be "pooled" or "unequal"') res = _zconfint_generic( diff, std_diff, alpha=alpha, alternative=alternative ) return res def ttost_ind(self, low, upp, usevar="pooled"): """ test of equivalence for two independent samples, base on t-test Parameters ---------- low, upp : float equivalence interval low < m1 - m2 < upp usevar : str, 'pooled' or 'unequal' If ``pooled``, then the standard deviation of the samples is assumed to be the same. If ``unequal``, then Welsh ttest with Satterthwait degrees of freedom is used Returns ------- pvalue : float pvalue of the non-equivalence test t1, pv1 : tuple of floats test statistic and pvalue for lower threshold test t2, pv2 : tuple of floats test statistic and pvalue for upper threshold test """ tt1 = self.ttest_ind(alternative="larger", usevar=usevar, value=low) tt2 = self.ttest_ind(alternative="smaller", usevar=usevar, value=upp) # TODO: remove tuple return, use same as for function tost_ind return np.maximum(tt1[1], tt2[1]), (tt1, tt2) def ztost_ind(self, low, upp, usevar="pooled"): """ test of equivalence for two independent samples, based on z-test Parameters ---------- low, upp : float equivalence interval low < m1 - m2 < upp usevar : str, 'pooled' or 'unequal' If ``pooled``, then the standard deviation of the samples is assumed to be the same. If ``unequal``, then Welsh ttest with Satterthwait degrees of freedom is used Returns ------- pvalue : float pvalue of the non-equivalence test t1, pv1 : tuple of floats test statistic and pvalue for lower threshold test t2, pv2 : tuple of floats test statistic and pvalue for upper threshold test """ tt1 = self.ztest_ind(alternative="larger", usevar=usevar, value=low) tt2 = self.ztest_ind(alternative="smaller", usevar=usevar, value=upp) # TODO: remove tuple return, use same as for function tost_ind return np.maximum(tt1[1], tt2[1]), tt1, tt2 # tost.__doc__ = tost_ind.__doc__ # does not work for 2d, does not take weights into account ## def test_equal_var(self): ## """Levene test for independence ## ## """ ## d1 = self.d1 ## d2 = self.d2 ## #rewrite this, for now just use scipy.stats ## return stats.levene(d1.data, d2.data) def ttest_ind( x1, x2, alternative="two-sided", usevar="pooled", weights=(None, None), value=0, ): """ttest independent sample Convenience function that uses the classes and throws away the intermediate results, compared to scipy stats: drops axis option, adds alternative, usevar, and weights option. Parameters ---------- x1 : array_like, 1-D or 2-D first of the two independent samples, see notes for 2-D case x2 : array_like, 1-D or 2-D second of the two independent samples, see notes for 2-D case alternative : str The alternative hypothesis, H1, has to be one of the following * 'two-sided' (default): H1: difference in means not equal to value * 'larger' : H1: difference in means larger than value * 'smaller' : H1: difference in means smaller than value usevar : str, 'pooled' or 'unequal' If ``pooled``, then the standard deviation of the samples is assumed to be the same. If ``unequal``, then Welsh ttest with Satterthwait degrees of freedom is used weights : tuple of None or ndarrays Case weights for the two samples. For details on weights see ``DescrStatsW`` value : float difference between the means under the Null hypothesis. Returns ------- tstat : float test statistic pvalue : float pvalue of the t-test df : int or float degrees of freedom used in the t-test """ cm = CompareMeans( DescrStatsW(x1, weights=weights[0], ddof=0), DescrStatsW(x2, weights=weights[1], ddof=0), ) tstat, pval, dof = cm.ttest_ind( alternative=alternative, usevar=usevar, value=value ) return tstat, pval, dof def ttost_ind( x1, x2, low, upp, usevar="pooled", weights=(None, None), transform=None ): """test of (non-)equivalence for two independent samples TOST: two one-sided t tests null hypothesis: m1 - m2 < low or m1 - m2 > upp alternative hypothesis: low < m1 - m2 < upp where m1, m2 are the means, expected values of the two samples. If the pvalue is smaller than a threshold, say 0.05, then we reject the hypothesis that the difference between the two samples is larger than the the thresholds given by low and upp. Parameters ---------- x1 : array_like, 1-D or 2-D first of the two independent samples, see notes for 2-D case x2 : array_like, 1-D or 2-D second of the two independent samples, see notes for 2-D case low, upp : float equivalence interval low < m1 - m2 < upp usevar : str, 'pooled' or 'unequal' If ``pooled``, then the standard deviation of the samples is assumed to be the same. If ``unequal``, then Welsh ttest with Satterthwait degrees of freedom is used weights : tuple of None or ndarrays Case weights for the two samples. For details on weights see ``DescrStatsW`` transform : None or function If None (default), then the data is not transformed. Given a function, sample data and thresholds are transformed. If transform is log, then the equivalence interval is in ratio: low < m1 / m2 < upp Returns ------- pvalue : float pvalue of the non-equivalence test t1, pv1 : tuple of floats test statistic and pvalue for lower threshold test t2, pv2 : tuple of floats test statistic and pvalue for upper threshold test Notes ----- The test rejects if the 2*alpha confidence interval for the difference is contained in the ``(low, upp)`` interval. This test works also for multi-endpoint comparisons: If d1 and d2 have the same number of columns, then each column of the data in d1 is compared with the corresponding column in d2. This is the same as comparing each of the corresponding columns separately. Currently no multi-comparison correction is used. The raw p-values reported here can be correction with the functions in ``multitest``. """ if transform: if transform is np.log: # avoid hstack in special case x1 = transform(x1) x2 = transform(x2) else: # for transforms like rankdata that will need both datasets # concatenate works for stacking 1d and 2d arrays xx = transform(np.concatenate((x1, x2), 0)) x1 = xx[: len(x1)] x2 = xx[len(x1) :] low = transform(low) upp = transform(upp) cm = CompareMeans( DescrStatsW(x1, weights=weights[0], ddof=0), DescrStatsW(x2, weights=weights[1], ddof=0), ) pval, res = cm.ttost_ind(low, upp, usevar=usevar) return pval, res[0], res[1] def ttost_paired(x1, x2, low, upp, transform=None, weights=None): """test of (non-)equivalence for two dependent, paired sample TOST: two one-sided t tests null hypothesis: md < low or md > upp alternative hypothesis: low < md < upp where md is the mean, expected value of the difference x1 - x2 If the pvalue is smaller than a threshold,say 0.05, then we reject the hypothesis that the difference between the two samples is larger than the the thresholds given by low and upp. Parameters ---------- x1 : array_like first of the two independent samples x2 : array_like second of the two independent samples low, upp : float equivalence interval low < mean of difference < upp weights : None or ndarray case weights for the two samples. For details on weights see ``DescrStatsW`` transform : None or function If None (default), then the data is not transformed. Given a function sample data and thresholds are transformed. If transform is log the the equivalence interval is in ratio: low < x1 / x2 < upp Returns ------- pvalue : float pvalue of the non-equivalence test t1, pv1, df1 : tuple test statistic, pvalue and degrees of freedom for lower threshold test t2, pv2, df2 : tuple test statistic, pvalue and degrees of freedom for upper threshold test """ if transform: if transform is np.log: # avoid hstack in special case x1 = transform(x1) x2 = transform(x2) else: # for transforms like rankdata that will need both datasets # concatenate works for stacking 1d and 2d arrays xx = transform(np.concatenate((x1, x2), 0)) x1 = xx[: len(x1)] x2 = xx[len(x1) :] low = transform(low) upp = transform(upp) dd = DescrStatsW(x1 - x2, weights=weights, ddof=0) t1, pv1, df1 = dd.ttest_mean(low, alternative="larger") t2, pv2, df2 = dd.ttest_mean(upp, alternative="smaller") return np.maximum(pv1, pv2), (t1, pv1, df1), (t2, pv2, df2) def ztest( x1, x2=None, value=0, alternative="two-sided", usevar="pooled", ddof=1.0 ): """test for mean based on normal distribution, one or two samples In the case of two samples, the samples are assumed to be independent. Parameters ---------- x1 : array_like, 1-D or 2-D first of the two independent samples x2 : array_like, 1-D or 2-D second of the two independent samples value : float In the one sample case, value is the mean of x1 under the Null hypothesis. In the two sample case, value is the difference between mean of x1 and mean of x2 under the Null hypothesis. The test statistic is `x1_mean - x2_mean - value`. alternative : str The alternative hypothesis, H1, has to be one of the following 'two-sided': H1: difference in means not equal to value (default) 'larger' : H1: difference in means larger than value 'smaller' : H1: difference in means smaller than value usevar : str, 'pooled' Currently, only 'pooled' is implemented. If ``pooled``, then the standard deviation of the samples is assumed to be the same. see CompareMeans.ztest_ind for different options. ddof : int Degrees of freedom use in the calculation of the variance of the mean estimate. In the case of comparing means this is one, however it can be adjusted for testing other statistics (proportion, correlation) Returns ------- tstat : float test statistic pvalue : float pvalue of the t-test Notes ----- usevar not implemented, is always pooled in two sample case use CompareMeans instead. """ # TODO: this should delegate to CompareMeans like ttest_ind # However that does not implement ddof # usevar is not used, always pooled if usevar != "pooled": raise NotImplementedError('only usevar="pooled" is implemented') x1 = np.asarray(x1) nobs1 = x1.shape[0] x1_mean = x1.mean(0) x1_var = x1.var(0) if x2 is not None: x2 = np.asarray(x2) nobs2 = x2.shape[0] x2_mean = x2.mean(0) x2_var = x2.var(0) var_pooled = nobs1 * x1_var + nobs2 * x2_var var_pooled /= nobs1 + nobs2 - 2 * ddof var_pooled *= 1.0 / nobs1 + 1.0 / nobs2 else: var_pooled = x1_var / (nobs1 - ddof) x2_mean = 0 std_diff = np.sqrt(var_pooled) # stat = x1_mean - x2_mean - value return _zstat_generic(x1_mean, x2_mean, std_diff, alternative, diff=value) def zconfint( x1, x2=None, value=0, alpha=0.05, alternative="two-sided", usevar="pooled", ddof=1.0, ): """confidence interval based on normal distribution z-test Parameters ---------- x1 : array_like, 1-D or 2-D first of the two independent samples, see notes for 2-D case x2 : array_like, 1-D or 2-D second of the two independent samples, see notes for 2-D case value : float In the one sample case, value is the mean of x1 under the Null hypothesis. In the two sample case, value is the difference between mean of x1 and mean of x2 under the Null hypothesis. The test statistic is `x1_mean - x2_mean - value`. usevar : str, 'pooled' Currently, only 'pooled' is implemented. If ``pooled``, then the standard deviation of the samples is assumed to be the same. see CompareMeans.ztest_ind for different options. ddof : int Degrees of freedom use in the calculation of the variance of the mean estimate. In the case of comparing means this is one, however it can be adjusted for testing other statistics (proportion, correlation) Notes ----- checked only for 1 sample case usevar not implemented, is always pooled in two sample case ``value`` shifts the confidence interval so it is centered at `x1_mean - x2_mean - value` See Also -------- ztest CompareMeans """ # usevar is not used, always pooled # mostly duplicate code from ztest if usevar != "pooled": raise NotImplementedError('only usevar="pooled" is implemented') x1 = np.asarray(x1) nobs1 = x1.shape[0] x1_mean = x1.mean(0) x1_var = x1.var(0) if x2 is not None: x2 = np.asarray(x2) nobs2 = x2.shape[0] x2_mean = x2.mean(0) x2_var = x2.var(0) var_pooled = nobs1 * x1_var + nobs2 * x2_var var_pooled /= nobs1 + nobs2 - 2 * ddof var_pooled *= 1.0 / nobs1 + 1.0 / nobs2 else: var_pooled = x1_var / (nobs1 - ddof) x2_mean = 0 std_diff = np.sqrt(var_pooled) ci = _zconfint_generic( x1_mean - x2_mean - value, std_diff, alpha, alternative ) return ci def ztost(x1, low, upp, x2=None, usevar="pooled", ddof=1.0): """Equivalence test based on normal distribution Parameters ---------- x1 : array_like one sample or first sample for 2 independent samples low, upp : float equivalence interval low < m1 - m2 < upp x1 : array_like or None second sample for 2 independent samples test. If None, then a one-sample test is performed. usevar : str, 'pooled' If `pooled`, then the standard deviation of the samples is assumed to be the same. Only `pooled` is currently implemented. Returns ------- pvalue : float pvalue of the non-equivalence test t1, pv1 : tuple of floats test statistic and pvalue for lower threshold test t2, pv2 : tuple of floats test statistic and pvalue for upper threshold test Notes ----- checked only for 1 sample case """ tt1 = ztest( x1, x2, alternative="larger", usevar=usevar, value=low, ddof=ddof ) tt2 = ztest( x1, x2, alternative="smaller", usevar=usevar, value=upp, ddof=ddof ) return ( np.maximum(tt1[1], tt2[1]), tt1, tt2, ) statsmodels-0.12.2/statsmodels/tests/000077500000000000000000000000001400612667500176515ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tests/__init__.py000066400000000000000000000000601400612667500217560ustar00rootroot00000000000000# Tests for the package behavior of statsmodels statsmodels-0.12.2/statsmodels/tests/test_package.py000066400000000000000000000015221400612667500226550ustar00rootroot00000000000000import subprocess import sys def test_lazy_imports(): # Check that when statsmodels.api is imported, matplotlib is _not_ imported cmd = ("import statsmodels.api as sm; " "import sys; " "mods = [x for x in sys.modules if 'matplotlib.pyplot' in x]; " "assert not mods, mods") cmd = sys.executable + ' -c "' + cmd + '"' p = subprocess.Popen(cmd, shell=True, close_fds=True) p.wait() rc = p.returncode assert rc == 0 def test_docstring_optimization_compat(): # GH#5235 check that importing with stripped docstrings does not raise cmd = sys.executable + ' -OO -c "import statsmodels.api as sm"' p = subprocess.Popen(cmd, shell=True, stdout=subprocess.PIPE, stderr=subprocess.PIPE) out = p.communicate() rc = p.returncode assert rc == 0, out statsmodels-0.12.2/statsmodels/tools/000077500000000000000000000000001400612667500176475ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tools/__init__.py000066400000000000000000000002531400612667500217600ustar00rootroot00000000000000from .tools import add_constant, categorical from statsmodels.tools._testing import PytestTester __all__ = ['test', 'add_constant', 'categorical'] test = PytestTester() statsmodels-0.12.2/statsmodels/tools/_testing.py000066400000000000000000000144101400612667500220350ustar00rootroot00000000000000"""Testing helper functions Warning: current status experimental, mostly copy paste Warning: these functions will be changed without warning as the need during refactoring arises. The first group of functions provide consistency checks """ from statsmodels.compat.pandas import assert_equal import os import sys from distutils.version import LooseVersion import numpy as np from numpy.testing import assert_allclose, assert_ import pandas as pd class PytestTester(object): def __init__(self, package_path=None): f = sys._getframe(1) if package_path is None: package_path = f.f_locals.get('__file__', None) if package_path is None: raise ValueError('Unable to determine path') self.package_path = os.path.dirname(package_path) self.package_name = f.f_locals.get('__name__', None) def __call__(self, extra_args=None, exit=False): try: import pytest if not LooseVersion(pytest.__version__) >= LooseVersion('3.0'): raise ImportError if extra_args is None: extra_args = ['--tb=short', '--disable-pytest-warnings'] cmd = [self.package_path] + extra_args print('Running pytest ' + ' '.join(cmd)) status = pytest.main(cmd) if exit: sys.exit(status) except ImportError: raise ImportError('pytest>=3 required to run the test') def check_ttest_tvalues(results): # test that t_test has same results a params, bse, tvalues, ... res = results mat = np.eye(len(res.params)) tt = res.t_test(mat) assert_allclose(tt.effect, res.params, rtol=1e-12) # TODO: tt.sd and tt.tvalue are 2d also for single regressor, squeeze assert_allclose(np.squeeze(tt.sd), res.bse, rtol=1e-10) assert_allclose(np.squeeze(tt.tvalue), res.tvalues, rtol=1e-12) assert_allclose(tt.pvalue, res.pvalues, rtol=5e-10) assert_allclose(tt.conf_int(), res.conf_int(), rtol=1e-10) # test params table frame returned by t_test table_res = np.column_stack((res.params, res.bse, res.tvalues, res.pvalues, res.conf_int())) table2 = tt.summary_frame().values assert_allclose(table2, table_res, rtol=1e-12) # TODO: move this to test_attributes ? assert_(hasattr(res, 'use_t')) tt = res.t_test(mat[0]) tt.summary() # smoke test for #1323 assert_allclose(tt.pvalue, res.pvalues[0], rtol=5e-10) # TODO: Adapt more of test_generic_methods.test_ttest_values here? def check_ftest_pvalues(results): """ Check that the outputs of `res.wald_test` produces pvalues that match res.pvalues. Check that the string representations of `res.summary()` and (possibly) `res.summary2()` correctly label either the t or z-statistic. Parameters ---------- results : Results Raises ------ AssertionError """ res = results use_t = res.use_t k_vars = len(res.params) # check default use_t pvals = [res.wald_test(np.eye(k_vars)[k], use_f=use_t).pvalue for k in range(k_vars)] assert_allclose(pvals, res.pvalues, rtol=5e-10, atol=1e-25) # automatic use_f based on results class use_t pvals = [res.wald_test(np.eye(k_vars)[k]).pvalue for k in range(k_vars)] assert_allclose(pvals, res.pvalues, rtol=5e-10, atol=1e-25) # TODO: Separate these out into summary/summary2 tests? # label for pvalues in summary string_use_t = 'P>|z|' if use_t is False else 'P>|t|' summ = str(res.summary()) assert_(string_use_t in summ) # try except for models that do not have summary2 try: summ2 = str(res.summary2()) except AttributeError: pass else: assert_(string_use_t in summ2) def check_fitted(results): import pytest # ignore wrapper for isinstance check from statsmodels.genmod.generalized_linear_model import GLMResults from statsmodels.discrete.discrete_model import DiscreteResults # possibly unwrap -- GEE has no wrapper results = getattr(results, '_results', results) if isinstance(results, (GLMResults, DiscreteResults)): pytest.skip('Not supported for {0}'.format(type(results))) res = results fitted = res.fittedvalues assert_allclose(res.model.endog - fitted, res.resid, rtol=1e-12) assert_allclose(fitted, res.predict(), rtol=1e-12) def check_predict_types(results): """ Check that the `predict` method of the given results object produces the correct output type. Parameters ---------- results : Results Raises ------ AssertionError """ res = results # squeeze to make 1d for single regressor test case p_exog = np.squeeze(np.asarray(res.model.exog[:2])) # ignore wrapper for isinstance check from statsmodels.genmod.generalized_linear_model import GLMResults from statsmodels.discrete.discrete_model import DiscreteResults # possibly unwrap -- GEE has no wrapper results = getattr(results, '_results', results) if isinstance(results, (GLMResults, DiscreteResults)): # SMOKE test only TODO: mark this somehow res.predict(p_exog) res.predict(p_exog.tolist()) res.predict(p_exog[0].tolist()) else: fitted = res.fittedvalues[:2] assert_allclose(fitted, res.predict(p_exog), rtol=1e-12) # this needs reshape to column-vector: assert_allclose(fitted, res.predict(np.squeeze(p_exog).tolist()), rtol=1e-12) # only one prediction: assert_allclose(fitted[:1], res.predict(p_exog[0].tolist()), rtol=1e-12) assert_allclose(fitted[:1], res.predict(p_exog[0]), rtol=1e-12) # Check that pandas wrapping works as expected exog_index = range(len(p_exog)) predicted = res.predict(p_exog) cls = pd.Series if p_exog.ndim == 1 else pd.DataFrame predicted_pandas = res.predict(cls(p_exog, index=exog_index)) # predicted.ndim may not match p_exog.ndim because it may be squeezed # if p_exog has only one column cls = pd.Series if predicted.ndim == 1 else pd.DataFrame predicted_expected = cls(predicted, index=exog_index) assert_equal(predicted_expected, predicted_pandas) statsmodels-0.12.2/statsmodels/tools/catadd.py000066400000000000000000000017621400612667500214470ustar00rootroot00000000000000import numpy as np def add_indep(x, varnames, dtype=None): ''' construct array with independent columns x is either iterable (list, tuple) or instance of ndarray or a subclass of it. If x is an ndarray, then each column is assumed to represent a variable with observations in rows. ''' # TODO: this needs tests for subclasses if isinstance(x, np.ndarray) and x.ndim == 2: x = x.T nvars_orig = len(x) nobs = len(x[0]) if not dtype: dtype = np.asarray(x[0]).dtype xout = np.zeros((nobs, nvars_orig), dtype=dtype) count = 0 rank_old = 0 varnames_new = [] varnames_dropped = [] keepindx = [] for (xi, ni) in zip(x, varnames): xout[:, count] = xi rank_new = np.linalg.matrix_rank(xout) if rank_new > rank_old: varnames_new.append(ni) rank_old = rank_new count += 1 else: varnames_dropped.append(ni) return xout[:, :count], varnames_new statsmodels-0.12.2/statsmodels/tools/data.py000066400000000000000000000072021400612667500211330ustar00rootroot00000000000000""" Compatibility tools for various data structure inputs """ import numpy as np import pandas as pd def _check_period_index(x, freq="M"): from pandas import PeriodIndex, DatetimeIndex if not isinstance(x.index, (DatetimeIndex, PeriodIndex)): raise ValueError("The index must be a DatetimeIndex or PeriodIndex") if x.index.freq is not None: inferred_freq = x.index.freqstr else: inferred_freq = pd.infer_freq(x.index) if not inferred_freq.startswith(freq): raise ValueError("Expected frequency {}. Got {}".format(inferred_freq, freq)) def is_data_frame(obj): return isinstance(obj, pd.DataFrame) def is_design_matrix(obj): from patsy import DesignMatrix return isinstance(obj, DesignMatrix) def _is_structured_ndarray(obj): return isinstance(obj, np.ndarray) and obj.dtype.names is not None def interpret_data(data, colnames=None, rownames=None): """ Convert passed data structure to form required by estimation classes Parameters ---------- data : array_like colnames : sequence or None May be part of data structure rownames : sequence or None Returns ------- (values, colnames, rownames) : (homogeneous ndarray, list) """ if isinstance(data, np.ndarray): if _is_structured_ndarray(data): import warnings from statsmodels.tools.sm_exceptions import recarray_warning warnings.warn(recarray_warning, FutureWarning) if colnames is None: colnames = data.dtype.names values = struct_to_ndarray(data) else: values = data if colnames is None: colnames = ['Y_%d' % i for i in range(values.shape[1])] elif is_data_frame(data): # XXX: hack data = data.dropna() values = data.values colnames = data.columns rownames = data.index else: # pragma: no cover raise TypeError('Cannot handle input type {typ}' .format(typ=type(data).__name__)) if not isinstance(colnames, list): colnames = list(colnames) # sanity check if len(colnames) != values.shape[1]: raise ValueError('length of colnames does not match number ' 'of columns in data') if rownames is not None and len(rownames) != len(values): raise ValueError('length of rownames does not match number ' 'of rows in data') return values, colnames, rownames def struct_to_ndarray(arr): return arr.view((float, (len(arr.dtype.names),)), type=np.ndarray) def _is_using_ndarray_type(endog, exog): return (type(endog) is np.ndarray and (type(exog) is np.ndarray or exog is None)) def _is_using_ndarray(endog, exog): return (isinstance(endog, np.ndarray) and (isinstance(exog, np.ndarray) or exog is None)) def _is_using_pandas(endog, exog): from statsmodels.compat.pandas import data_klasses as klasses return (isinstance(endog, klasses) or isinstance(exog, klasses)) def _is_array_like(endog, exog): try: # do it like this in case of mixed types, ie., ndarray and list endog = np.asarray(endog) exog = np.asarray(exog) return True except: return False def _is_using_patsy(endog, exog): # we get this when a structured array is passed through a formula return (is_design_matrix(endog) and (is_design_matrix(exog) or exog is None)) def _is_recarray(data): """ Returns true if data is a recarray """ return isinstance(data, np.core.recarray) statsmodels-0.12.2/statsmodels/tools/decorators.py000066400000000000000000000104211400612667500223640ustar00rootroot00000000000000from statsmodels.tools.sm_exceptions import CacheWriteWarning from statsmodels.compat.pandas import cache_readonly as PandasCacheReadonly import warnings __all__ = ['cache_readonly', 'cache_writable', 'deprecated_alias', 'ResettableCache'] class ResettableCache(dict): """DO NOT USE. BACKWARD COMPAT ONLY""" def __init__(self, *args, **kwargs): super(ResettableCache, self).__init__(*args, **kwargs) self.__dict__ = self def deprecated_alias(old_name, new_name, remove_version=None, msg=None, warning=FutureWarning): """ Deprecate attribute in favor of alternative name. Parameters ---------- old_name : str Old, deprecated name new_name : str New name remove_version : str, optional Version that the alias will be removed msg : str, optional Message to show. Default is `old_name` is a deprecated alias for `new_name` warning : Warning, optional Warning class to give. Default is FutureWarning. Notes ----- Older or less-used classes may not conform to statsmodels naming conventions. `deprecated_alias` lets us bring them into conformance without breaking backward-compatibility. Example ------- Instances of the `Foo` class have a `nvars` attribute, but it _should_ be called `neqs`: class Foo(object): nvars = deprecated_alias('nvars', 'neqs') def __init__(self, neqs): self.neqs = neqs >>> foo = Foo(3) >>> foo.nvars __main__:1: FutureWarning: nvars is a deprecated alias for neqs 3 """ if msg is None: msg = '%s is a deprecated alias for %s' % (old_name, new_name) if remove_version is not None: msg += ', will be removed in version %s' % remove_version def fget(self): warnings.warn(msg, warning, stacklevel=2) return getattr(self, new_name) def fset(self, value): warnings.warn(msg, warning, stacklevel=2) setattr(self, new_name, value) res = property(fget=fget, fset=fset) return res class CachedAttribute(object): def __init__(self, func, cachename=None): self.fget = func self.name = func.__name__ self.cachename = cachename or '_cache' def __get__(self, obj, type=None): if obj is None: return self.fget # Get the cache or set a default one if needed _cachename = self.cachename _cache = getattr(obj, _cachename, None) if _cache is None: setattr(obj, _cachename, {}) _cache = getattr(obj, _cachename) # Get the name of the attribute to set and cache name = self.name _cachedval = _cache.get(name, None) if _cachedval is None: _cachedval = self.fget(obj) _cache[name] = _cachedval return _cachedval def __set__(self, obj, value): errmsg = "The attribute '%s' cannot be overwritten" % self.name warnings.warn(errmsg, CacheWriteWarning) class CachedWritableAttribute(CachedAttribute): def __set__(self, obj, value): _cache = getattr(obj, self.cachename) name = self.name _cache[name] = value class _cache_readonly(property): """ Decorator for CachedAttribute """ def __init__(self, cachename=None): self.func = None self.cachename = cachename def __call__(self, func): return CachedAttribute(func, cachename=self.cachename) class cache_writable(_cache_readonly): """ Decorator for CachedWritableAttribute """ def __call__(self, func): return CachedWritableAttribute(func, cachename=self.cachename) # Use pandas since it works with docs correctly cache_readonly = PandasCacheReadonly # cached_value and cached_data behave identically to cache_readonly, but # are used by `remove_data` to # a) identify array-like attributes to remove (cached_data) # b) make sure certain values are evaluated before caching (cached_value) # TODO: Disabled since the subclasses break doc strings # class cached_data(PandasCacheReadonly): # pass cached_data = PandasCacheReadonly # class cached_value(PandasCacheReadonly): # pass cached_value = PandasCacheReadonly statsmodels-0.12.2/statsmodels/tools/docstring.py000066400000000000000000000510051400612667500222160ustar00rootroot00000000000000""" Substantially copied from NumpyDoc 1.0pre. """ import copy import inspect import re import textwrap from collections import namedtuple from collections.abc import Mapping from statsmodels.tools.sm_exceptions import ParseError def dedent_lines(lines): """Deindent a list of lines maximally""" return textwrap.dedent("\n".join(lines)).split("\n") def strip_blank_lines(line): """Remove leading and trailing blank lines from a list of lines""" while line and not line[0].strip(): del line[0] while line and not line[-1].strip(): del line[-1] return line class Reader(object): """ A line-based string reader. """ def __init__(self, data): """ Parameters ---------- data : str String with lines separated by '\n'. """ if isinstance(data, list): self._str = data else: self._str = data.split('\n') # store string as list of lines self.reset() def __getitem__(self, n): return self._str[n] def reset(self): self._line_num = 0 # current line nr def read(self): if not self.eof(): out = self[self._line_num] self._line_num += 1 return out else: return '' def seek_next_non_empty_line(self): for line in self[self._line_num:]: if line.strip(): break else: self._line_num += 1 def eof(self): return self._line_num >= len(self._str) def read_to_condition(self, condition_func): start = self._line_num for line in self[start:]: if condition_func(line): return self[start:self._line_num] self._line_num += 1 if self.eof(): return self[start:self._line_num + 1] return [] def read_to_next_empty_line(self): self.seek_next_non_empty_line() def is_empty(line): return not line.strip() return self.read_to_condition(is_empty) def read_to_next_unindented_line(self): def is_unindented(line): return (line.strip() and (len(line.lstrip()) == len(line))) return self.read_to_condition(is_unindented) def peek(self, n=0): if self._line_num + n < len(self._str): return self[self._line_num + n] else: return '' def is_empty(self): return not ''.join(self._str).strip() Parameter = namedtuple('Parameter', ['name', 'type', 'desc']) class NumpyDocString(Mapping): """Parses a numpydoc string to an abstract representation Instances define a mapping from section title to structured data. """ sections = { 'Signature': '', 'Summary': [''], 'Extended Summary': [], 'Parameters': [], 'Returns': [], 'Yields': [], 'Receives': [], 'Raises': [], 'Warns': [], 'Other Parameters': [], 'Attributes': [], 'Methods': [], 'See Also': [], 'Notes': [], 'Warnings': [], 'References': '', 'Examples': '', 'index': {} } def __init__(self, docstring): orig_docstring = docstring docstring = textwrap.dedent(docstring).split('\n') self._doc = Reader(docstring) self._parsed_data = copy.deepcopy(self.sections) try: self._parse() except ParseError as e: e.docstring = orig_docstring raise def __getitem__(self, key): return self._parsed_data[key] def __setitem__(self, key, val): if key not in self._parsed_data: self._error_location("Unknown section %s" % key) else: self._parsed_data[key] = val def __iter__(self): return iter(self._parsed_data) def __len__(self): return len(self._parsed_data) def _is_at_section(self): self._doc.seek_next_non_empty_line() if self._doc.eof(): return False l1 = self._doc.peek().strip() # e.g. Parameters if l1.startswith('.. index::'): return True l2 = self._doc.peek(1).strip() # ---------- or ========== return l2.startswith('-' * len(l1)) or l2.startswith('=' * len(l1)) def _strip(self, doc): i = 0 j = 0 for i, line in enumerate(doc): if line.strip(): break for j, line in enumerate(doc[::-1]): if line.strip(): break return doc[i:len(doc) - j] def _read_to_next_section(self): section = self._doc.read_to_next_empty_line() while not self._is_at_section() and not self._doc.eof(): if not self._doc.peek(-1).strip(): # previous line was empty section += [''] section += self._doc.read_to_next_empty_line() return section def _read_sections(self): while not self._doc.eof(): data = self._read_to_next_section() name = data[0].strip() if name.startswith('..'): # index section yield name, data[1:] elif len(data) < 2: yield StopIteration else: yield name, self._strip(data[2:]) def _parse_param_list(self, content, single_element_is_type=False): r = Reader(content) params = [] while not r.eof(): header = r.read().strip() if ' : ' in header: arg_name, arg_type = header.split(' : ')[:2] else: if single_element_is_type: arg_name, arg_type = '', header else: arg_name, arg_type = header, '' desc = r.read_to_next_unindented_line() desc = dedent_lines(desc) desc = strip_blank_lines(desc) params.append(Parameter(arg_name, arg_type, desc)) return params # See also supports the following formats. # # # SPACE* COLON SPACE+ SPACE* # ( COMMA SPACE+ )+ (COMMA | PERIOD)? SPACE* # ( COMMA SPACE+ )* SPACE* COLON SPACE+ SPACE* # is one of # # COLON COLON BACKTICK BACKTICK # where # is a legal function name, and # is any nonempty sequence of word characters. # Examples: func_f1 :meth:`func_h1` :obj:`~baz.obj_r` :class:`class_j` # is a string describing the function. _role = r":(?P\w+):" _funcbacktick = r"`(?P(?:~\w+\.)?[a-zA-Z0-9_\.-]+)`" _funcplain = r"(?P[a-zA-Z0-9_\.-]+)" _funcname = r"(" + _role + _funcbacktick + r"|" + _funcplain + r")" _funcnamenext = _funcname.replace('role', 'rolenext') _funcnamenext = _funcnamenext.replace('name', 'namenext') _description = r"(?P\s*:(\s+(?P\S+.*))?)?\s*$" _func_rgx = re.compile(r"^\s*" + _funcname + r"\s*") _line_rgx = re.compile( r"^\s*" + r"(?P" + # group for all function names _funcname + r"(?P([,]\s+" + _funcnamenext + r")*)" + r")" + # end of "allfuncs" # Some function lists have a trailing comma (or period) r"(?P[,\.])?" + _description) # Empty elements are replaced with '..' empty_description = '..' def _parse_see_also(self, content): """ func_name : Descriptive text continued text another_func_name : Descriptive text func_name1, func_name2, :meth:`func_name`, func_name3 """ items = [] def parse_item_name(text): """Match ':role:`name`' or 'name'.""" m = self._func_rgx.match(text) if not m: raise ParseError(f"{text} is not a item name") role = m.group('role') name = m.group('name') if role else m.group('name2') return name, role, m.end() rest = [] for line in content: if not line.strip(): continue line_match = self._line_rgx.match(line) description = None if line_match: description = line_match.group('desc') if line_match.group('trailing') and description: self._error_location( 'Unexpected comma or period after function list at ' 'index %d of line ' '"%s"' % (line_match.end('trailing'), line)) if not description and line.startswith(' '): rest.append(line.strip()) elif line_match: funcs = [] text = line_match.group('allfuncs') while True: if not text.strip(): break name, role, match_end = parse_item_name(text) funcs.append((name, role)) text = text[match_end:].strip() if text and text[0] == ',': text = text[1:].strip() rest = list(filter(None, [description])) items.append((funcs, rest)) else: raise ParseError(f"{line} is not a item name") return items def _parse_index(self, section, content): """ .. index: default :refguide: something, else, and more """ def strip_each_in(lst): return [s.strip() for s in lst] out = {} section = section.split('::') if len(section) > 1: out['default'] = strip_each_in(section[1].split(','))[0] for line in content: line = line.split(':') if len(line) > 2: out[line[1]] = strip_each_in(line[2].split(',')) return out def _parse_summary(self): """Grab signature (if given) and summary""" if self._is_at_section(): return # If several signatures present, take the last one while True: summary = self._doc.read_to_next_empty_line() summary_str = " ".join([s.strip() for s in summary]).strip() compiled = re.compile(r'^([\w., ]+=)?\s*[\w\.]+\(.*\)$') if compiled.match(summary_str): self['Signature'] = summary_str if not self._is_at_section(): continue break if summary is not None: self['Summary'] = summary if not self._is_at_section(): self['Extended Summary'] = self._read_to_next_section() def _parse(self): self._doc.reset() self._parse_summary() sections = list(self._read_sections()) section_names = set([section for section, content in sections]) has_returns = 'Returns' in section_names has_yields = 'Yields' in section_names # We could do more tests, but we are not. Arbitrarily. if has_returns and has_yields: msg = 'Docstring contains both a Returns and Yields section.' raise ValueError(msg) if not has_yields and 'Receives' in section_names: msg = 'Docstring contains a Receives section but not Yields.' raise ValueError(msg) for (section, content) in sections: if not section.startswith('..'): section = (s.capitalize() for s in section.split(' ')) section = ' '.join(section) if self.get(section): self._error_location("The section %s appears twice" % section) if section in ('Parameters', 'Other Parameters', 'Attributes', 'Methods'): self[section] = self._parse_param_list(content) elif section in ( 'Returns', 'Yields', 'Raises', 'Warns', 'Receives'): self[section] = self._parse_param_list( content, single_element_is_type=True) elif section.startswith('.. index::'): self['index'] = self._parse_index(section, content) elif section == 'See Also': self['See Also'] = self._parse_see_also(content) else: self[section] = content def _error_location(self, msg): if hasattr(self, '_obj'): # we know where the docs came from: try: filename = inspect.getsourcefile(self._obj) except TypeError: filename = None msg = msg + (" in the docstring of %s in %s." % (self._obj, filename)) raise ValueError(msg) # string conversion routines def _str_header(self, name, symbol='-'): return [name, len(name) * symbol] def _str_indent(self, doc, indent=4): out = [] for line in doc: out += [' ' * indent + line] return out def _str_signature(self): if self['Signature']: return [self['Signature'].replace('*', r'\*')] + [''] else: return [''] def _str_summary(self): if self['Summary']: return self['Summary'] + [''] else: return [] def _str_extended_summary(self): if self['Extended Summary']: return self['Extended Summary'] + [''] else: return [] def _str_param_list(self, name): out = [] if self[name]: out += self._str_header(name) for param in self[name]: parts = [] if param.name: parts.append(param.name) if param.type: parts.append(param.type) out += [' : '.join(parts)] if param.desc and ''.join(param.desc).strip(): out += self._str_indent(param.desc) out += [''] return out def _str_section(self, name): out = [] if self[name]: out += self._str_header(name) out += self[name] out += [''] return out def _str_see_also(self, func_role): if not self['See Also']: return [] out = [] out += self._str_header("See Also") last_had_desc = True for funcs, desc in self['See Also']: assert isinstance(funcs, list) links = [] for func, role in funcs: if role: link = ':%s:`%s`' % (role, func) elif func_role: link = ':%s:`%s`' % (func_role, func) else: link = "%s" % func links.append(link) link = ', '.join(links) out += [link] if desc: out += self._str_indent([' '.join(desc)]) last_had_desc = True else: last_had_desc = False out += self._str_indent([self.empty_description]) if last_had_desc: out += [''] return out def _str_index(self): idx = self['index'] out = [] output_index = False default_index = idx.get('default', '') if default_index: output_index = True out += ['.. index:: %s' % default_index] for section, references in idx.items(): if section == 'default': continue output_index = True out += [' :%s: %s' % (section, ', '.join(references))] if output_index: return out else: return '' def __str__(self, func_role=''): out = [] out += self._str_signature() out += self._str_summary() out += self._str_extended_summary() for param_list in ('Parameters', 'Returns', 'Yields', 'Receives', 'Other Parameters', 'Raises', 'Warns'): out += self._str_param_list(param_list) out += self._str_section('Warnings') out += self._str_see_also(func_role) for s in ('Notes', 'References', 'Examples'): out += self._str_section(s) for param_list in ('Attributes', 'Methods'): out += self._str_param_list(param_list) out += self._str_index() return '\n'.join(out) class Docstring(object): """ Docstring modification. Parameters ---------- docstring : str The docstring to modify. """ def __init__(self, docstring): self._ds = None self._docstring = docstring if docstring is None: return self._ds = NumpyDocString(docstring) def remove_parameters(self, parameters): """ Parameters ---------- parameters : str, list[str] The names of the parameters to remove. """ if self._docstring is None: # Protection against -oo execution return if isinstance(parameters, str): parameters = [parameters] repl = [param for param in self._ds['Parameters'] if param.name not in parameters] if len(repl) + len(parameters) != len(self._ds['Parameters']): raise ValueError('One or more parameters were not found.') self._ds['Parameters'] = repl def insert_parameters(self, after, parameters): """ Parameters ---------- after : {None, str} If None, inset the parameters before the first parameter in the docstring. parameters : Parameter, list[Parameter] A Parameter of a list of Parameters. """ if self._docstring is None: # Protection against -oo execution return if isinstance(parameters, Parameter): parameters = [parameters] if after is None: self._ds['Parameters'] = parameters + self._ds['Parameters'] else: loc = -1 for i, param in enumerate(self._ds['Parameters']): if param.name == after: loc = i+1 break if loc < 0: raise ValueError() params = self._ds['Parameters'][:loc] + parameters params += self._ds['Parameters'][loc:] self._ds['Parameters'] = params def replace_block(self, block_name, block): """ Parameters ---------- block_name : str Name of the block to replace, e.g., 'Summary'. block : object The replacement block. The structure of the replacement block must match how the block is stored by NumpyDocString. """ if self._docstring is None: # Protection against -oo execution return block_name = ' '.join(map(str.capitalize, block_name.split(' '))) if block_name not in self._ds: raise ValueError('{0} is not a block in the ' 'docstring'.format(block_name)) if not isinstance(block, list) and \ isinstance(self._ds[block_name], list): block = [block] self._ds[block_name] = block def extract_parameters(self, parameters, indent=0): if self._docstring is None: # Protection against -oo execution return if isinstance(parameters, str): parameters = [parameters] ds_params = {param.name: param for param in self._ds['Parameters']} missing = set(parameters).difference(ds_params.keys()) if missing: raise ValueError('{0} were not found in the ' 'docstring'.format(','.join(missing))) final = [ds_params[param] for param in parameters] ds = copy.deepcopy(self._ds) for key in ds: if key != 'Parameters': ds[key] = [] if key != 'index' else {} else: ds[key] = final out = str(ds).strip() if indent: out = textwrap.indent(out, ' ' * indent) out = '\n'.join(out.split('\n')[2:]) return out def __str__(self): return str(self._ds) def remove_parameters(docstring, parameters): """ Parameters ---------- docstring : str The docstring to modify. parameters : str, list[str] The names of the parameters to remove. Returns ------- str The modified docstring. """ if docstring is None: return ds = Docstring(docstring) ds.remove_parameters(parameters) return str(ds) statsmodels-0.12.2/statsmodels/tools/eval_measures.py000066400000000000000000000363371400612667500230700ustar00rootroot00000000000000# -*- coding: utf-8 -*- """some measures for evaluation of prediction, tests and model selection Created on Tue Nov 08 15:23:20 2011 Updated on Wed Jun 03 10:42:20 2020 Authors: Josef Perktold & Peter Prescott License: BSD-3 """ import numpy as np from statsmodels.tools.validation import array_like def mse(x1, x2, axis=0): """mean squared error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- mse : ndarray or float mean squared error along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass, for example numpy matrices will silently produce an incorrect result. """ x1 = np.asanyarray(x1) x2 = np.asanyarray(x2) return np.mean((x1 - x2) ** 2, axis=axis) def rmse(x1, x2, axis=0): """root mean squared error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- rmse : ndarray or float root mean squared error along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass, for example numpy matrices will silently produce an incorrect result. """ x1 = np.asanyarray(x1) x2 = np.asanyarray(x2) return np.sqrt(mse(x1, x2, axis=axis)) def rmspe(y, y_hat, axis=0, zeros=np.nan): """ Root Mean Squared Percentage Error Parameters ---------- y : array_like The actual value. y_hat : array_like The predicted value. axis : int Axis along which the summary statistic is calculated zeros : float Value to assign to error where y is zero Returns ------- rmspe : ndarray or float Root Mean Squared Percentage Error along given axis. """ y_hat = np.asarray(y_hat) y = np.asarray(y) error = y - y_hat loc = y != 0 loc = loc.ravel() percentage_error = np.full_like(error, zeros) percentage_error.flat[loc] = error.flat[loc] / y.flat[loc] mspe = np.nanmean(percentage_error ** 2, axis=axis) * 100 return np.sqrt(mspe) def maxabs(x1, x2, axis=0): """maximum absolute error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- maxabs : ndarray or float maximum absolute difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. """ x1 = np.asanyarray(x1) x2 = np.asanyarray(x2) return np.max(np.abs(x1 - x2), axis=axis) def meanabs(x1, x2, axis=0): """mean absolute error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- meanabs : ndarray or float mean absolute difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. """ x1 = np.asanyarray(x1) x2 = np.asanyarray(x2) return np.mean(np.abs(x1 - x2), axis=axis) def medianabs(x1, x2, axis=0): """median absolute error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- medianabs : ndarray or float median absolute difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. """ x1 = np.asanyarray(x1) x2 = np.asanyarray(x2) return np.median(np.abs(x1 - x2), axis=axis) def bias(x1, x2, axis=0): """bias, mean error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- bias : ndarray or float bias, or mean difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. """ x1 = np.asanyarray(x1) x2 = np.asanyarray(x2) return np.mean(x1 - x2, axis=axis) def medianbias(x1, x2, axis=0): """median bias, median error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- medianbias : ndarray or float median bias, or median difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. """ x1 = np.asanyarray(x1) x2 = np.asanyarray(x2) return np.median(x1 - x2, axis=axis) def vare(x1, x2, ddof=0, axis=0): """variance of error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- vare : ndarray or float variance of difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. """ x1 = np.asanyarray(x1) x2 = np.asanyarray(x2) return np.var(x1 - x2, ddof=ddof, axis=axis) def stde(x1, x2, ddof=0, axis=0): """standard deviation of error Parameters ---------- x1, x2 : array_like The performance measure depends on the difference between these two arrays. axis : int axis along which the summary statistic is calculated Returns ------- stde : ndarray or float standard deviation of difference along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they need to broadcast. This uses ``numpy.asanyarray`` to convert the input. Whether this is the desired result or not depends on the array subclass. """ x1 = np.asanyarray(x1) x2 = np.asanyarray(x2) return np.std(x1 - x2, ddof=ddof, axis=axis) def iqr(x1, x2, axis=0): """ Interquartile range of error Parameters ---------- x1 : array_like One of the inputs into the IQR calculation. x2 : array_like The other input into the IQR calculation. axis : {None, int} axis along which the summary statistic is calculated Returns ------- irq : {float, ndarray} Interquartile range along given axis. Notes ----- If ``x1`` and ``x2`` have different shapes, then they must broadcast. """ x1 = array_like(x1, "x1", dtype=None, ndim=None) x2 = array_like(x2, "x1", dtype=None, ndim=None) if axis is None: x1 = x1.ravel() x2 = x2.ravel() axis = 0 xdiff = np.sort(x1 - x2, axis=axis) nobs = x1.shape[axis] idx = np.round((nobs - 1) * np.array([0.25, 0.75])).astype(int) sl = [slice(None)] * xdiff.ndim sl[axis] = idx iqr = np.diff(xdiff[tuple(sl)], axis=axis) iqr = np.squeeze(iqr) # drop reduced dimension return iqr # Information Criteria # --------------------- def aic(llf, nobs, df_modelwc): """ Akaike information criterion Parameters ---------- llf : {float, array_like} value of the loglikelihood nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- aic : float information criterion References ---------- https://en.wikipedia.org/wiki/Akaike_information_criterion """ return -2.0 * llf + 2.0 * df_modelwc def aicc(llf, nobs, df_modelwc): """ Akaike information criterion (AIC) with small sample correction Parameters ---------- llf : {float, array_like} value of the loglikelihood nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- aicc : float information criterion References ---------- https://en.wikipedia.org/wiki/Akaike_information_criterion#AICc """ return -2.0 * llf + 2.0 * df_modelwc * nobs / (nobs - df_modelwc - 1.0) def bic(llf, nobs, df_modelwc): """ Bayesian information criterion (BIC) or Schwarz criterion Parameters ---------- llf : {float, array_like} value of the loglikelihood nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- bic : float information criterion References ---------- https://en.wikipedia.org/wiki/Bayesian_information_criterion """ return -2.0 * llf + np.log(nobs) * df_modelwc def hqic(llf, nobs, df_modelwc): """ Hannan-Quinn information criterion (HQC) Parameters ---------- llf : {float, array_like} value of the loglikelihood nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- hqic : float information criterion References ---------- Wikipedia does not say much """ return -2.0 * llf + 2 * np.log(np.log(nobs)) * df_modelwc # IC based on residual sigma def aic_sigma(sigma2, nobs, df_modelwc, islog=False): r""" Akaike information criterion Parameters ---------- sigma2 : float estimate of the residual variance or determinant of Sigma_hat in the multivariate case. If islog is true, then it is assumed that sigma is already log-ed, for example logdetSigma. nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- aic : float information criterion Notes ----- A constant has been dropped in comparison to the loglikelihood base information criteria. The information criteria should be used to compare only comparable models. For example, AIC is defined in terms of the loglikelihood as :math:`-2 llf + 2 k` in terms of :math:`\hat{\sigma}^2` :math:`log(\hat{\sigma}^2) + 2 k / n` in terms of the determinant of :math:`\hat{\Sigma}` :math:`log(\|\hat{\Sigma}\|) + 2 k / n` Note: In our definition we do not divide by n in the log-likelihood version. TODO: Latex math reference for example lecture notes by Herman Bierens See Also -------- References ---------- https://en.wikipedia.org/wiki/Akaike_information_criterion """ if not islog: sigma2 = np.log(sigma2) return sigma2 + aic(0, nobs, df_modelwc) / nobs def aicc_sigma(sigma2, nobs, df_modelwc, islog=False): """Akaike information criterion (AIC) with small sample correction Parameters ---------- sigma2 : float estimate of the residual variance or determinant of Sigma_hat in the multivariate case. If islog is true, then it is assumed that sigma is already log-ed, for example logdetSigma. nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- aicc : float information criterion Notes ----- A constant has been dropped in comparison to the loglikelihood base information criteria. These should be used to compare for comparable models. References ---------- https://en.wikipedia.org/wiki/Akaike_information_criterion#AICc """ if not islog: sigma2 = np.log(sigma2) return sigma2 + aicc(0, nobs, df_modelwc) / nobs def bic_sigma(sigma2, nobs, df_modelwc, islog=False): """Bayesian information criterion (BIC) or Schwarz criterion Parameters ---------- sigma2 : float estimate of the residual variance or determinant of Sigma_hat in the multivariate case. If islog is true, then it is assumed that sigma is already log-ed, for example logdetSigma. nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- bic : float information criterion Notes ----- A constant has been dropped in comparison to the loglikelihood base information criteria. These should be used to compare for comparable models. References ---------- https://en.wikipedia.org/wiki/Bayesian_information_criterion """ if not islog: sigma2 = np.log(sigma2) return sigma2 + bic(0, nobs, df_modelwc) / nobs def hqic_sigma(sigma2, nobs, df_modelwc, islog=False): """Hannan-Quinn information criterion (HQC) Parameters ---------- sigma2 : float estimate of the residual variance or determinant of Sigma_hat in the multivariate case. If islog is true, then it is assumed that sigma is already log-ed, for example logdetSigma. nobs : int number of observations df_modelwc : int number of parameters including constant Returns ------- hqic : float information criterion Notes ----- A constant has been dropped in comparison to the loglikelihood base information criteria. These should be used to compare for comparable models. References ---------- xxx """ if not islog: sigma2 = np.log(sigma2) return sigma2 + hqic(0, nobs, df_modelwc) / nobs # from var_model.py, VAR only? separates neqs and k_vars per equation # def fpe_sigma(): # ((nobs + self.df_model) / self.df_resid) ** neqs * np.exp(ld) __all__ = [ maxabs, meanabs, medianabs, medianbias, mse, rmse, rmspe, stde, vare, aic, aic_sigma, aicc, aicc_sigma, bias, bic, bic_sigma, hqic, hqic_sigma, iqr, ] statsmodels-0.12.2/statsmodels/tools/grouputils.py000066400000000000000000000434631400612667500224500ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Tools for working with groups This provides several functions to work with groups and a Group class that keeps track of the different representations and has methods to work more easily with groups. Author: Josef Perktold, Author: Nathaniel Smith, recipe for sparse_dummies on scipy user mailing list Created on Tue Nov 29 15:44:53 2011 : sparse_dummies Created on Wed Nov 30 14:28:24 2011 : combine_indices changes: add Group class Notes ~~~~~ This reverses the class I used before, where the class was for the data and the group was auxiliary. Here, it is only the group, no data is kept. sparse_dummies needs checking for corner cases, e.g. what if a category level has zero elements? This can happen with subset selection even if the original groups where defined as arange. Not all methods and options have been tried out yet after refactoring need more efficient loop if groups are sorted -> see GroupSorted.group_iter """ from statsmodels.compat.python import lrange, lzip import numpy as np import pandas as pd import statsmodels.tools.data as data_util from pandas import Index, MultiIndex def combine_indices(groups, prefix='', sep='.', return_labels=False): """use np.unique to get integer group indices for product, intersection """ if isinstance(groups, tuple): groups = np.column_stack(groups) else: groups = np.asarray(groups) dt = groups.dtype is2d = (groups.ndim == 2) # need to store if is2d: ncols = groups.shape[1] if not groups.flags.c_contiguous: groups = np.array(groups, order='C') groups_ = groups.view([('', groups.dtype)] * groups.shape[1]) else: groups_ = groups uni, uni_idx, uni_inv = np.unique(groups_, return_index=True, return_inverse=True) if is2d: uni = uni.view(dt).reshape(-1, ncols) # avoiding a view would be # for t in uni.dtype.fields.values(): # assert (t[0] == dt) # # uni.dtype = dt # uni.shape = (uni.size//ncols, ncols) if return_labels: label = [(prefix+sep.join(['%s']*len(uni[0]))) % tuple(ii) for ii in uni] return uni_inv, uni_idx, uni, label else: return uni_inv, uni_idx, uni # written for and used in try_covariance_grouploop.py def group_sums(x, group, use_bincount=True): """simple bincount version, again group : ndarray, integer assumed to be consecutive integers no dtype checking because I want to raise in that case uses loop over columns of x for comparison, simple python loop """ x = np.asarray(x) if x.ndim == 1: x = x[:, None] elif x.ndim > 2 and use_bincount: raise ValueError('not implemented yet') if use_bincount: # re-label groups or bincount takes too much memory if np.max(group) > 2 * x.shape[0]: group = pd.factorize(group)[0] return np.array([np.bincount(group, weights=x[:, col]) for col in range(x.shape[1])]) else: uniques = np.unique(group) result = np.zeros([len(uniques)] + list(x.shape[1:])) for ii, cat in enumerate(uniques): result[ii] = x[group == cat].sum(0) return result def group_sums_dummy(x, group_dummy): """sum by groups given group dummy variable group_dummy can be either ndarray or sparse matrix """ if data_util._is_using_ndarray_type(group_dummy, None): return np.dot(x.T, group_dummy) else: # check for sparse return x.T * group_dummy # TODO: See if this can be entirely replaced by Grouping.dummy_sparse; # see GH#5687 def dummy_sparse(groups): """create a sparse indicator from a group array with integer labels Parameters ---------- groups : ndarray, int, 1d (nobs,) an array of group indicators for each observation. Group levels are assumed to be defined as consecutive integers, i.e. range(n_groups) where n_groups is the number of group levels. A group level with no observations for it will still produce a column of zeros. Returns ------- indi : ndarray, int8, 2d (nobs, n_groups) an indicator array with one row per observation, that has 1 in the column of the group level for that observation Examples -------- >>> g = np.array([0, 0, 2, 1, 1, 2, 0]) >>> indi = dummy_sparse(g) >>> indi <7x3 sparse matrix of type '' with 7 stored elements in Compressed Sparse Row format> >>> indi.todense() matrix([[1, 0, 0], [1, 0, 0], [0, 0, 1], [0, 1, 0], [0, 1, 0], [0, 0, 1], [1, 0, 0]], dtype=int8) current behavior with missing groups >>> g = np.array([0, 0, 2, 0, 2, 0]) >>> indi = dummy_sparse(g) >>> indi.todense() matrix([[1, 0, 0], [1, 0, 0], [0, 0, 1], [1, 0, 0], [0, 0, 1], [1, 0, 0]], dtype=int8) """ from scipy import sparse indptr = np.arange(len(groups)+1) data = np.ones(len(groups), dtype=np.int8) indi = sparse.csr_matrix((data, groups, indptr)) return indi class Group(object): def __init__(self, group, name=''): # self.group = np.asarray(group) # TODO: use checks in combine_indices self.name = name uni, uni_idx, uni_inv = combine_indices(group) # TODO: rename these to something easier to remember self.group_int, self.uni_idx, self.uni = uni, uni_idx, uni_inv self.n_groups = len(self.uni) # put this here so they can be overwritten before calling labels self.separator = '.' self.prefix = self.name if self.prefix: self.prefix = self.prefix + '=' # cache decorator def counts(self): return np.bincount(self.group_int) # cache_decorator def labels(self): # is this only needed for product of groups (intersection)? prefix = self.prefix uni = self.uni sep = self.separator if uni.ndim > 1: label = [(prefix+sep.join(['%s']*len(uni[0]))) % tuple(ii) for ii in uni] else: label = [prefix + '%s' % ii for ii in uni] return label def dummy(self, drop_idx=None, sparse=False, dtype=int): """ drop_idx is only available if sparse=False drop_idx is supposed to index into uni """ uni = self.uni if drop_idx is not None: idx = lrange(len(uni)) del idx[drop_idx] uni = uni[idx] group = self.group if not sparse: return (group[:, None] == uni[None, :]).astype(dtype) else: return dummy_sparse(self.group_int) def interaction(self, other): if isinstance(other, self.__class__): other = other.group return self.__class__((self, other)) def group_sums(self, x, use_bincount=True): return group_sums(x, self.group_int, use_bincount=use_bincount) def group_demean(self, x, use_bincount=True): nobs = float(len(x)) means_g = group_sums(x / nobs, self.group_int, use_bincount=use_bincount) x_demeaned = x - means_g[self.group_int] # check reverse_index? return x_demeaned, means_g class GroupSorted(Group): def __init__(self, group, name=''): super(self.__class__, self).__init__(group, name=name) idx = (np.nonzero(np.diff(group))[0]+1).tolist() self.groupidx = lzip([0] + idx, idx + [len(group)]) def group_iter(self): for low, upp in self.groupidx: yield slice(low, upp) def lag_indices(self, lag): """return the index array for lagged values Warning: if k is larger then the number of observations for an individual, then no values for that individual are returned. TODO: for the unbalanced case, I should get the same truncation for the array with lag=0. From the return of lag_idx we would not know which individual is missing. TODO: do I want the full equivalent of lagmat in tsa? maxlag or lag or lags. not tested yet """ lag_idx = np.asarray(self.groupidx)[:, 1] - lag # asarray or already? mask_ok = (lag <= lag_idx) # still an observation that belongs to the same individual return lag_idx[mask_ok] def _is_hierarchical(x): """ Checks if the first item of an array-like object is also array-like If so, we have a MultiIndex and returns True. Else returns False. """ item = x[0] # is there a better way to do this? if isinstance(item, (list, tuple, np.ndarray, pd.Series, pd.DataFrame)): return True else: return False def _make_hierarchical_index(index, names): return MultiIndex.from_tuples(*[index], names=names) def _make_generic_names(index): n_names = len(index.names) pad = str(len(str(n_names))) # number of digits return [("group{0:0"+pad+"}").format(i) for i in range(n_names)] class Grouping(object): def __init__(self, index, names=None): """ index : index-like Can be pandas MultiIndex or Index or array-like. If array-like and is a MultipleIndex (more than one grouping variable), groups are expected to be in each row. E.g., [('red', 1), ('red', 2), ('green', 1), ('green', 2)] names : list or str, optional The names to use for the groups. Should be a str if only one grouping variable is used. Notes ----- If index is already a pandas Index then there is no copy. """ if isinstance(index, (Index, MultiIndex)): if names is not None: if hasattr(index, 'set_names'): # newer pandas index.set_names(names, inplace=True) else: index.names = names self.index = index else: # array_like if _is_hierarchical(index): self.index = _make_hierarchical_index(index, names) else: self.index = Index(index, name=names) if names is None: names = _make_generic_names(self.index) if hasattr(self.index, 'set_names'): self.index.set_names(names, inplace=True) else: self.index.names = names self.nobs = len(self.index) self.nlevels = len(self.index.names) self.slices = None @property def index_shape(self): if hasattr(self.index, 'levshape'): return self.index.levshape else: return self.index.shape @property def levels(self): if hasattr(self.index, 'levels'): return self.index.levels else: return pd.Categorical(self.index).levels @property def labels(self): # this was index_int, but that's not a very good name... codes = getattr(self.index, 'codes', None) if codes is None: if hasattr(self.index, 'labels'): codes = self.index.labels else: codes = pd.Categorical(self.index).codes[None] return codes @property def group_names(self): return self.index.names def reindex(self, index=None, names=None): """ Resets the index in-place. """ # NOTE: this is not of much use if the rest of the data does not change # This needs to reset cache if names is None: names = self.group_names self = Grouping(index, names) def get_slices(self, level=0): """ Sets the slices attribute to be a list of indices of the sorted groups for the first index level. I.e., self.slices[0] is the index where each observation is in the first (sorted) group. """ # TODO: refactor this groups = self.index.get_level_values(level).unique() groups = np.array(groups) groups.sort() if isinstance(self.index, MultiIndex): self.slices = [self.index.get_loc_level(x, level=level)[0] for x in groups] else: self.slices = [self.index.get_loc(x) for x in groups] def count_categories(self, level=0): """ Sets the attribute counts to equal the bincount of the (integer-valued) labels. """ # TODO: refactor this not to set an attribute. Why would we do this? self.counts = np.bincount(self.labels[level]) def check_index(self, is_sorted=True, unique=True, index=None): """Sanity checks""" if not index: index = self.index if is_sorted: test = pd.DataFrame(lrange(len(index)), index=index) test_sorted = test.sort() if not test.index.equals(test_sorted.index): raise Exception('Data is not be sorted') if unique: if len(index) != len(index.unique()): raise Exception('Duplicate index entries') def sort(self, data, index=None): """Applies a (potentially hierarchical) sort operation on a numpy array or pandas series/dataframe based on the grouping index or a user-supplied index. Returns an object of the same type as the original data as well as the matching (sorted) Pandas index. """ if index is None: index = self.index if data_util._is_using_ndarray_type(data, None): if data.ndim == 1: out = pd.Series(data, index=index, copy=True) out = out.sort_index() else: out = pd.DataFrame(data, index=index) out = out.sort_index(inplace=False) # copies return np.array(out), out.index elif data_util._is_using_pandas(data, None): out = data out = out.reindex(index) # copies? out = out.sort_index() return out, out.index else: msg = 'data must be a Numpy array or a Pandas Series/DataFrame' raise ValueError(msg) def transform_dataframe(self, dataframe, function, level=0, **kwargs): """Apply function to each column, by group Assumes that the dataframe already has a proper index""" if dataframe.shape[0] != self.nobs: raise Exception('dataframe does not have the same shape as index') out = dataframe.groupby(level=level).apply(function, **kwargs) if 1 in out.shape: return np.ravel(out) else: return np.array(out) def transform_array(self, array, function, level=0, **kwargs): """Apply function to each column, by group """ if array.shape[0] != self.nobs: raise Exception('array does not have the same shape as index') dataframe = pd.DataFrame(array, index=self.index) return self.transform_dataframe(dataframe, function, level=level, **kwargs) def transform_slices(self, array, function, level=0, **kwargs): """Apply function to each group. Similar to transform_array but does not coerce array to a DataFrame and back and only works on a 1D or 2D numpy array. function is called function(group, group_idx, **kwargs). """ array = np.asarray(array) if array.shape[0] != self.nobs: raise Exception('array does not have the same shape as index') # always reset because level is given. need to refactor this. self.get_slices(level=level) processed = [] for s in self.slices: if array.ndim == 2: subset = array[s, :] elif array.ndim == 1: subset = array[s] processed.append(function(subset, s, **kwargs)) processed = np.array(processed) return processed.reshape(-1, processed.shape[-1]) # TODO: this is not general needs to be a PanelGrouping object def dummies_time(self): self.dummy_sparse(level=1) return self._dummies def dummies_groups(self, level=0): self.dummy_sparse(level=level) return self._dummies def dummy_sparse(self, level=0): """create a sparse indicator from a group array with integer labels Parameters ---------- groups : ndarray, int, 1d (nobs,) An array of group indicators for each observation. Group levels are assumed to be defined as consecutive integers, i.e. range(n_groups) where n_groups is the number of group levels. A group level with no observations for it will still produce a column of zeros. Returns ------- indi : ndarray, int8, 2d (nobs, n_groups) an indicator array with one row per observation, that has 1 in the column of the group level for that observation Examples -------- >>> g = np.array([0, 0, 2, 1, 1, 2, 0]) >>> indi = dummy_sparse(g) >>> indi <7x3 sparse matrix of type '' with 7 stored elements in Compressed Sparse Row format> >>> indi.todense() matrix([[1, 0, 0], [1, 0, 0], [0, 0, 1], [0, 1, 0], [0, 1, 0], [0, 0, 1], [1, 0, 0]], dtype=int8) current behavior with missing groups >>> g = np.array([0, 0, 2, 0, 2, 0]) >>> indi = dummy_sparse(g) >>> indi.todense() matrix([[1, 0, 0], [1, 0, 0], [0, 0, 1], [1, 0, 0], [0, 0, 1], [1, 0, 0]], dtype=int8) """ indi = dummy_sparse(self.labels[level]) self._dummies = indi statsmodels-0.12.2/statsmodels/tools/linalg.py000066400000000000000000000113051400612667500214670ustar00rootroot00000000000000""" Linear Algebra solvers and other helpers """ import numpy as np __all__ = ["logdet_symm", "stationary_solve", "transf_constraints", "matrix_sqrt"] def logdet_symm(m, check_symm=False): """ Return log(det(m)) asserting positive definiteness of m. Parameters ---------- m : array_like 2d array that is positive-definite (and symmetric) Returns ------- logdet : float The log-determinant of m. """ from scipy import linalg if check_symm: if not np.all(m == m.T): # would be nice to short-circuit check raise ValueError("m is not symmetric.") c, _ = linalg.cho_factor(m, lower=True) return 2*np.sum(np.log(c.diagonal())) def stationary_solve(r, b): """ Solve a linear system for a Toeplitz correlation matrix. A Toeplitz correlation matrix represents the covariance of a stationary series with unit variance. Parameters ---------- r : array_like A vector describing the coefficient matrix. r[0] is the first band next to the diagonal, r[1] is the second band, etc. b : array_like The right-hand side for which we are solving, i.e. we solve Tx = b and return b, where T is the Toeplitz coefficient matrix. Returns ------- The solution to the linear system. """ db = r[0:1] dim = b.ndim if b.ndim == 1: b = b[:, None] x = b[0:1, :] for j in range(1, len(b)): rf = r[0:j][::-1] a = (b[j, :] - np.dot(rf, x)) / (1 - np.dot(rf, db[::-1])) z = x - np.outer(db[::-1], a) x = np.concatenate((z, a[None, :]), axis=0) if j == len(b) - 1: break rn = r[j] a = (rn - np.dot(rf, db)) / (1 - np.dot(rf, db[::-1])) z = db - a*db[::-1] db = np.concatenate((z, np.r_[a])) if dim == 1: x = x[:, 0] return x def transf_constraints(constraints): """use QR to get transformation matrix to impose constraint Parameters ---------- constraints : ndarray, 2-D restriction matrix with one constraints in rows Returns ------- transf : ndarray transformation matrix to reparameterize so that constraint is imposed Notes ----- This is currently and internal helper function for GAM. API not stable and will most likely change. The code for this function was taken from patsy spline handling, and corresponds to the reparameterization used by Wood in R's mgcv package. See Also -------- statsmodels.base._constraints.TransformRestriction : class to impose constraints by reparameterization used by `_fit_constrained`. """ from scipy import linalg m = constraints.shape[0] q, _ = linalg.qr(np.transpose(constraints)) transf = q[:, m:] return transf def matrix_sqrt(mat, inverse=False, full=False, nullspace=False, threshold=1e-15): """matrix square root for symmetric matrices Usage is for decomposing a covariance function S into a square root R such that R' R = S if inverse is False, or R' R = pinv(S) if inverse is True Parameters ---------- mat : array_like, 2-d square symmetric square matrix for which square root or inverse square root is computed. There is no checking for whether the matrix is symmetric. A warning is issued if some singular values are negative, i.e. below the negative of the threshold. inverse : bool If False (default), then the matrix square root is returned. If inverse is True, then the matrix square root of the inverse matrix is returned. full : bool If full is False (default, then the square root has reduce number of rows if the matrix is singular, i.e. has singular values below the threshold. nullspace : bool If nullspace is true, then the matrix square root of the null space of the matrix is returned. threshold : float Singular values below the threshold are dropped. Returns ------- msqrt : ndarray matrix square root or square root of inverse matrix. """ # see also scipy.linalg null_space u, s, v = np.linalg.svd(mat) if np.any(s < -threshold): import warnings warnings.warn('some singular values are negative') if not nullspace: mask = s > threshold s[s < threshold] = 0 else: mask = s < threshold s[s > threshold] = 0 sqrt_s = np.sqrt(s[mask]) if inverse: sqrt_s = 1 / np.sqrt(s[mask]) if full: b = np.dot(u[:, mask], np.dot(np.diag(sqrt_s), v[mask])) else: b = np.dot(np.diag(sqrt_s), v[mask]) return b statsmodels-0.12.2/statsmodels/tools/numdiff.py000066400000000000000000000271331400612667500216570ustar00rootroot00000000000000"""numerical differentiation function, gradient, Jacobian, and Hessian Author : josef-pkt License : BSD Notes ----- These are simple forward differentiation, so that we have them available without dependencies. * Jacobian should be faster than numdifftools because it does not use loop over observations. * numerical precision will vary and depend on the choice of stepsizes """ # TODO: # * some cleanup # * check numerical accuracy (and bugs) with numdifftools and analytical # derivatives # - linear least squares case: (hess - 2*X'X) is 1e-8 or so # - gradient and Hessian agree with numdifftools when evaluated away from # minimum # - forward gradient, Jacobian evaluated at minimum is inaccurate, centered # (+/- epsilon) is ok # * dot product of Jacobian is different from Hessian, either wrong example or # a bug (unlikely), or a real difference # # # What are the conditions that Jacobian dotproduct and Hessian are the same? # # See also: # # BHHH: Greene p481 17.4.6, MLE Jacobian = d loglike / d beta , where loglike # is vector for each observation # see also example 17.4 when J'J is very different from Hessian # also does it hold only at the minimum, what's relationship to covariance # of Jacobian matrix # http://projects.scipy.org/scipy/ticket/1157 # https://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm # objective: sum((y-f(beta,x)**2), Jacobian = d f/d beta # and not d objective/d beta as in MLE Greene # similar: http://crsouza.blogspot.com/2009/11/neural-network-learning-by-levenberg_18.html#hessian # # in example: if J = d x*beta / d beta then J'J == X'X # similar to https://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm import numpy as np from statsmodels.compat.pandas import Appender, Substitution # NOTE: we only do double precision internally so far EPS = np.MachAr().eps _hessian_docs = """ Calculate Hessian with finite difference derivative approximation Parameters ---------- x : array_like value at which function derivative is evaluated f : function function of one array f(x, `*args`, `**kwargs`) epsilon : float or array_like, optional Stepsize used, if None, then stepsize is automatically chosen according to EPS**(1/%(scale)s)*x. args : tuple Arguments for function `f`. kwargs : dict Keyword arguments for function `f`. %(extra_params)s Returns ------- hess : ndarray array of partial second derivatives, Hessian %(extra_returns)s Notes ----- Equation (%(equation_number)s) in Ridout. Computes the Hessian as:: %(equation)s where e[j] is a vector with element j == 1 and the rest are zero and d[i] is epsilon[i]. References ----------: Ridout, M.S. (2009) Statistical applications of the complex-step method of numerical differentiation. The American Statistician, 63, 66-74 """ def _get_epsilon(x, s, epsilon, n): if epsilon is None: h = EPS**(1. / s) * np.maximum(np.abs(x), 0.1) else: if np.isscalar(epsilon): h = np.empty(n) h.fill(epsilon) else: # pragma : no cover h = np.asarray(epsilon) if h.shape != x.shape: raise ValueError("If h is not a scalar it must have the same" " shape as x.") return h def approx_fprime(x, f, epsilon=None, args=(), kwargs={}, centered=False): ''' Gradient of function, or Jacobian if function f returns 1d array Parameters ---------- x : ndarray parameters at which the derivative is evaluated f : function `f(*((x,)+args), **kwargs)` returning either one value or 1d array epsilon : float, optional Stepsize, if None, optimal stepsize is used. This is EPS**(1/2)*x for `centered` == False and EPS**(1/3)*x for `centered` == True. args : tuple Tuple of additional arguments for function `f`. kwargs : dict Dictionary of additional keyword arguments for function `f`. centered : bool Whether central difference should be returned. If not, does forward differencing. Returns ------- grad : ndarray gradient or Jacobian Notes ----- If f returns a 1d array, it returns a Jacobian. If a 2d array is returned by f (e.g., with a value for each observation), it returns a 3d array with the Jacobian of each observation with shape xk x nobs x xk. I.e., the Jacobian of the first observation would be [:, 0, :] ''' n = len(x) # TODO: add scaled stepsize f0 = f(*((x,)+args), **kwargs) dim = np.atleast_1d(f0).shape # it could be a scalar grad = np.zeros((n,) + dim, np.promote_types(float, x.dtype)) ei = np.zeros((n,), float) if not centered: epsilon = _get_epsilon(x, 2, epsilon, n) for k in range(n): ei[k] = epsilon[k] grad[k, :] = (f(*((x+ei,) + args), **kwargs) - f0)/epsilon[k] ei[k] = 0.0 else: epsilon = _get_epsilon(x, 3, epsilon, n) / 2. for k in range(len(x)): ei[k] = epsilon[k] grad[k, :] = (f(*((x+ei,)+args), **kwargs) - f(*((x-ei,)+args), **kwargs))/(2 * epsilon[k]) ei[k] = 0.0 return grad.squeeze().T def approx_fprime_cs(x, f, epsilon=None, args=(), kwargs={}): ''' Calculate gradient or Jacobian with complex step derivative approximation Parameters ---------- x : ndarray parameters at which the derivative is evaluated f : function `f(*((x,)+args), **kwargs)` returning either one value or 1d array epsilon : float, optional Stepsize, if None, optimal stepsize is used. Optimal step-size is EPS*x. See note. args : tuple Tuple of additional arguments for function `f`. kwargs : dict Dictionary of additional keyword arguments for function `f`. Returns ------- partials : ndarray array of partial derivatives, Gradient or Jacobian Notes ----- The complex-step derivative has truncation error O(epsilon**2), so truncation error can be eliminated by choosing epsilon to be very small. The complex-step derivative avoids the problem of round-off error with small epsilon because there is no subtraction. ''' # From Guilherme P. de Freitas, numpy mailing list # May 04 2010 thread "Improvement of performance" # http://mail.scipy.org/pipermail/numpy-discussion/2010-May/050250.html n = len(x) epsilon = _get_epsilon(x, 1, epsilon, n) increments = np.identity(n) * 1j * epsilon # TODO: see if this can be vectorized, but usually dim is small partials = [f(x+ih, *args, **kwargs).imag / epsilon[i] for i, ih in enumerate(increments)] return np.array(partials).T def approx_hess_cs(x, f, epsilon=None, args=(), kwargs={}): '''Calculate Hessian with complex-step derivative approximation Parameters ---------- x : array_like value at which function derivative is evaluated f : function function of one array f(x) epsilon : float stepsize, if None, then stepsize is automatically chosen Returns ------- hess : ndarray array of partial second derivatives, Hessian Notes ----- based on equation 10 in M. S. RIDOUT: Statistical Applications of the Complex-step Method of Numerical Differentiation, University of Kent, Canterbury, Kent, U.K. The stepsize is the same for the complex and the finite difference part. ''' # TODO: might want to consider lowering the step for pure derivatives n = len(x) h = _get_epsilon(x, 3, epsilon, n) ee = np.diag(h) hess = np.outer(h, h) n = len(x) for i in range(n): for j in range(i, n): hess[i, j] = (f(*((x + 1j*ee[i, :] + ee[j, :],) + args), **kwargs) - f(*((x + 1j*ee[i, :] - ee[j, :],)+args), **kwargs)).imag/2./hess[i, j] hess[j, i] = hess[i, j] return hess @Substitution( scale="3", extra_params="""return_grad : bool Whether or not to also return the gradient """, extra_returns="""grad : nparray Gradient if return_grad == True """, equation_number="7", equation="""1/(d_j*d_k) * ((f(x + d[j]*e[j] + d[k]*e[k]) - f(x + d[j]*e[j]))) """ ) @Appender(_hessian_docs) def approx_hess1(x, f, epsilon=None, args=(), kwargs={}, return_grad=False): n = len(x) h = _get_epsilon(x, 3, epsilon, n) ee = np.diag(h) f0 = f(*((x,)+args), **kwargs) # Compute forward step g = np.zeros(n) for i in range(n): g[i] = f(*((x+ee[i, :],)+args), **kwargs) hess = np.outer(h, h) # this is now epsilon**2 # Compute "double" forward step for i in range(n): for j in range(i, n): hess[i, j] = (f(*((x + ee[i, :] + ee[j, :],) + args), **kwargs) - g[i] - g[j] + f0)/hess[i, j] hess[j, i] = hess[i, j] if return_grad: grad = (g - f0)/h return hess, grad else: return hess @Substitution( scale="3", extra_params="""return_grad : bool Whether or not to also return the gradient """, extra_returns="""grad : ndarray Gradient if return_grad == True """, equation_number="8", equation="""1/(2*d_j*d_k) * ((f(x + d[j]*e[j] + d[k]*e[k]) - f(x + d[j]*e[j])) - (f(x + d[k]*e[k]) - f(x)) + (f(x - d[j]*e[j] - d[k]*e[k]) - f(x + d[j]*e[j])) - (f(x - d[k]*e[k]) - f(x))) """ ) @Appender(_hessian_docs) def approx_hess2(x, f, epsilon=None, args=(), kwargs={}, return_grad=False): # n = len(x) # NOTE: ridout suggesting using eps**(1/4)*theta h = _get_epsilon(x, 3, epsilon, n) ee = np.diag(h) f0 = f(*((x,)+args), **kwargs) # Compute forward step g = np.zeros(n) gg = np.zeros(n) for i in range(n): g[i] = f(*((x+ee[i, :],)+args), **kwargs) gg[i] = f(*((x-ee[i, :],)+args), **kwargs) hess = np.outer(h, h) # this is now epsilon**2 # Compute "double" forward step for i in range(n): for j in range(i, n): hess[i, j] = (f(*((x + ee[i, :] + ee[j, :],) + args), **kwargs) - g[i] - g[j] + f0 + f(*((x - ee[i, :] - ee[j, :],) + args), **kwargs) - gg[i] - gg[j] + f0)/(2 * hess[i, j]) hess[j, i] = hess[i, j] if return_grad: grad = (g - f0)/h return hess, grad else: return hess @Substitution( scale="4", extra_params="", extra_returns="", equation_number="9", equation="""1/(4*d_j*d_k) * ((f(x + d[j]*e[j] + d[k]*e[k]) - f(x + d[j]*e[j] - d[k]*e[k])) - (f(x - d[j]*e[j] + d[k]*e[k]) - f(x - d[j]*e[j] - d[k]*e[k]))""" ) @Appender(_hessian_docs) def approx_hess3(x, f, epsilon=None, args=(), kwargs={}): n = len(x) h = _get_epsilon(x, 4, epsilon, n) ee = np.diag(h) hess = np.outer(h,h) for i in range(n): for j in range(i, n): hess[i, j] = (f(*((x + ee[i, :] + ee[j, :],) + args), **kwargs) - f(*((x + ee[i, :] - ee[j, :],) + args), **kwargs) - (f(*((x - ee[i, :] + ee[j, :],) + args), **kwargs) - f(*((x - ee[i, :] - ee[j, :],) + args), **kwargs)) )/(4.*hess[i, j]) hess[j, i] = hess[i, j] return hess approx_hess = approx_hess3 approx_hess.__doc__ += "\n This is an alias for approx_hess3" statsmodels-0.12.2/statsmodels/tools/parallel.py000066400000000000000000000041451400612667500220210ustar00rootroot00000000000000"""Parallel utility function using joblib copied from https://github.com/mne-tools/mne-python Author: Alexandre Gramfort License: Simplified BSD changes for statsmodels (Josef Perktold) - try import from joblib directly, (does not import all of sklearn) """ from statsmodels.tools.sm_exceptions import (ModuleUnavailableWarning, module_unavailable_doc) def parallel_func(func, n_jobs, verbose=5): """Return parallel instance with delayed function Util function to use joblib only if available Parameters ---------- func : callable A function n_jobs : int Number of jobs to run in parallel verbose : int Verbosity level Returns ------- parallel : instance of joblib.Parallel or list The parallel object my_func : callable func if not parallel or delayed(func) n_jobs : int Number of jobs >= 0 Examples -------- >>> from math import sqrt >>> from statsmodels.tools.parallel import parallel_func >>> parallel, p_func, n_jobs = parallel_func(sqrt, n_jobs=-1, verbose=0) >>> print(n_jobs) >>> parallel(p_func(i**2) for i in range(10)) """ try: try: from joblib import Parallel, delayed except ImportError: from sklearn.externals.joblib import Parallel, delayed parallel = Parallel(n_jobs, verbose=verbose) my_func = delayed(func) if n_jobs == -1: try: import multiprocessing n_jobs = multiprocessing.cpu_count() except (ImportError, NotImplementedError): import warnings warnings.warn(module_unavailable_doc.format('multiprocessing'), ModuleUnavailableWarning) n_jobs = 1 except ImportError: import warnings warnings.warn(module_unavailable_doc.format('joblib'), ModuleUnavailableWarning) n_jobs = 1 my_func = func parallel = list return parallel, my_func, n_jobs statsmodels-0.12.2/statsmodels/tools/print_version.py000077500000000000000000000205511400612667500231300ustar00rootroot00000000000000#!/usr/bin/env python from functools import reduce import sys from os.path import dirname def safe_version(module, attr='__version__', *others): if not isinstance(attr, list): attr = [attr] try: return reduce(getattr, [module] + attr) except AttributeError: if others: return safe_version(module, others[0], *others[1:]) return "Cannot detect version" def _show_versions_only(): print("\nINSTALLED VERSIONS") print("------------------") print("Python: %d.%d.%d.%s.%s" % sys.version_info[:]) try: import os (sysname, nodename, release, version, machine) = os.uname() print("OS: %s %s %s %s" % (sysname, release, version, machine)) print("byteorder: %s" % sys.byteorder) print("LC_ALL: %s" % os.environ.get('LC_ALL', "None")) print("LANG: %s" % os.environ.get('LANG', "None")) except: pass try: import statsmodels has_sm = True except ImportError: has_sm = False print('\nstatsmodels\n===========\n') if has_sm: print('Installed: %s' % safe_version(statsmodels)) else: print('Not installed') print("\nRequired Dependencies\n=====================\n") try: import Cython print("cython: %s" % safe_version(Cython)) except ImportError: print("cython: Not installed") try: import numpy print("numpy: %s" % safe_version(numpy, ['version', 'version'])) except ImportError: print("numpy: Not installed") try: import scipy print("scipy: %s" % safe_version(scipy, ['version', 'version'])) except ImportError: print("scipy: Not installed") try: import pandas print("pandas: %s" % safe_version(pandas)) except ImportError: print("pandas: Not installed") try: import dateutil print(" dateutil: %s" % safe_version(dateutil)) except ImportError: print(" dateutil: not installed") try: import patsy print("patsy: %s" % safe_version(patsy)) except ImportError: print("patsy: Not installed") print("\nOptional Dependencies\n=====================\n") try: import matplotlib as mpl print("matplotlib: %s" % safe_version(mpl)) except ImportError: print("matplotlib: Not installed") try: from cvxopt import info print("cvxopt: %s" % safe_version(info, 'version')) except ImportError: print("cvxopt: Not installed") try: import joblib print("joblib: %s " % (safe_version(joblib))) except ImportError: print("joblib: Not installed") print("\nDeveloper Tools\n================\n") try: import IPython print("IPython: %s" % safe_version(IPython)) except ImportError: print("IPython: Not installed") try: import jinja2 print(" jinja2: %s" % safe_version(jinja2)) except ImportError: print(" jinja2: Not installed") try: import sphinx print("sphinx: %s" % safe_version(sphinx)) except ImportError: print("sphinx: Not installed") try: import pygments print(" pygments: %s" % safe_version(pygments)) except ImportError: print(" pygments: Not installed") try: import pytest print("pytest: %s (%s)" % (safe_version(pytest), dirname(pytest.__file__))) except ImportError: print("pytest: Not installed") try: import virtualenv print("virtualenv: %s" % safe_version(virtualenv)) except ImportError: print("virtualenv: Not installed") print("\n") def show_versions(show_dirs=True): """ List the versions of statsmodels and any installed dependencies Parameters ---------- show_dirs : bool Flag indicating to show module locations """ if not show_dirs: _show_versions_only() print("\nINSTALLED VERSIONS") print("------------------") print("Python: %d.%d.%d.%s.%s" % sys.version_info[:]) try: import os (sysname, nodename, release, version, machine) = os.uname() print("OS: %s %s %s %s" % (sysname, release, version, machine)) print("byteorder: %s" % sys.byteorder) print("LC_ALL: %s" % os.environ.get('LC_ALL', "None")) print("LANG: %s" % os.environ.get('LANG', "None")) except: pass try: import statsmodels has_sm = True except ImportError: has_sm = False print('\nstatsmodels\n===========\n') if has_sm: print('Installed: %s (%s)' % (safe_version(statsmodels), dirname(statsmodels.__file__))) else: print('Not installed') print("\nRequired Dependencies\n=====================\n") try: import Cython print("cython: %s (%s)" % (safe_version(Cython), dirname(Cython.__file__))) except ImportError: print("cython: Not installed") try: import numpy print("numpy: %s (%s)" % (safe_version(numpy, ['version', 'version']), dirname(numpy.__file__))) except ImportError: print("numpy: Not installed") try: import scipy print("scipy: %s (%s)" % (safe_version(scipy, ['version', 'version']), dirname(scipy.__file__))) except ImportError: print("scipy: Not installed") try: import pandas print("pandas: %s (%s)" % (safe_version(pandas, ['version', 'version'], '__version__'), dirname(pandas.__file__))) except ImportError: print("pandas: Not installed") try: import dateutil print(" dateutil: %s (%s)" % (safe_version(dateutil), dirname(dateutil.__file__))) except ImportError: print(" dateutil: not installed") try: import patsy print("patsy: %s (%s)" % (safe_version(patsy), dirname(patsy.__file__))) except ImportError: print("patsy: Not installed") print("\nOptional Dependencies\n=====================\n") try: import matplotlib as mpl print("matplotlib: %s (%s)" % (safe_version(mpl), dirname(mpl.__file__))) print(" backend: %s " % mpl.rcParams['backend']) except ImportError: print("matplotlib: Not installed") try: from cvxopt import info print("cvxopt: %s (%s)" % (safe_version(info, 'version'), dirname(info.__file__))) except ImportError: print("cvxopt: Not installed") try: import joblib print("joblib: %s (%s)" % (safe_version(joblib), dirname(joblib.__file__))) except ImportError: print("joblib: Not installed") print("\nDeveloper Tools\n================\n") try: import IPython print("IPython: %s (%s)" % (safe_version(IPython), dirname(IPython.__file__))) except ImportError: print("IPython: Not installed") try: import jinja2 print(" jinja2: %s (%s)" % (safe_version(jinja2), dirname(jinja2.__file__))) except ImportError: print(" jinja2: Not installed") try: import sphinx print("sphinx: %s (%s)" % (safe_version(sphinx), dirname(sphinx.__file__))) except ImportError: print("sphinx: Not installed") try: import pygments print(" pygments: %s (%s)" % (safe_version(pygments), dirname(pygments.__file__))) except ImportError: print(" pygments: Not installed") try: import pytest print("pytest: %s (%s)" % (safe_version(pytest), dirname(pytest.__file__))) except ImportError: print("pytest: Not installed") try: import virtualenv print("virtualenv: %s (%s)" % (safe_version(virtualenv), dirname(virtualenv.__file__))) except ImportError: print("virtualenv: Not installed") print("\n") if __name__ == "__main__": show_versions() statsmodels-0.12.2/statsmodels/tools/rootfinding.py000066400000000000000000000164141400612667500225510ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Mon Mar 18 15:48:23 2013 Author: Josef Perktold TODO: - test behavior if nans or infs are encountered during the evaluation. now partially robust to nans, if increasing can be determined or is given. - rewrite core loop to use for...except instead of while. """ import numpy as np from scipy import optimize DEBUG = False # based on scipy.stats.distributions._ppf_single_call def brentq_expanding(func, low=None, upp=None, args=(), xtol=1e-5, start_low=None, start_upp=None, increasing=None, max_it=100, maxiter_bq=100, factor=10, full_output=False): '''find the root of a function in one variable by expanding and brentq Assumes function ``func`` is monotonic. Parameters ---------- func : callable function for which we find the root ``x`` such that ``func(x) = 0`` low : float or None lower bound for brentq upp : float or None upper bound for brentq args : tuple optional additional arguments for ``func`` xtol : float parameter x tolerance given to brentq start_low : float (positive) or None starting bound for expansion with increasing ``x``. It needs to be positive. If None, then it is set to 1. start_upp : float (negative) or None starting bound for expansion with decreasing ``x``. It needs to be negative. If None, then it is set to -1. increasing : bool or None If None, then the function is evaluated at the initial bounds to determine wether the function is increasing or not. If increasing is True (False), then it is assumed that the function is monotonically increasing (decreasing). max_it : int maximum number of expansion steps. maxiter_bq : int maximum number of iterations of brentq. factor : float expansion factor for step of shifting the bounds interval, default is 10. full_output : bool, optional If full_output is False, the root is returned. If full_output is True, the return value is (x, r), where x is the root, and r is a RootResults object. Returns ------- x : float root of the function, value at which ``func(x) = 0``. info : RootResult (optional) returned if ``full_output`` is True. attributes: - start_bounds : starting bounds for expansion stage - brentq_bounds : bounds used with ``brentq`` - iterations_expand : number of iterations in expansion stage - converged : True if brentq converged. - flag : return status, 'converged' if brentq converged - function_calls : number of function calls by ``brentq`` - iterations : number of iterations in ``brentq`` Notes ----- If increasing is None, then whether the function is monotonically increasing or decreasing is inferred from evaluating the function at the initial bounds. This can fail if there is numerically no variation in the data in this range. In this case, using different starting bounds or directly specifying ``increasing`` can make it possible to move the expansion in the right direction. If ''' # TODO: rtol is missing, what does it do? left, right = low, upp # alias # start_upp first because of possible sl = -1 > upp if upp is not None: su = upp elif start_upp is not None: if start_upp < 0: raise ValueError('start_upp needs to be positive') su = start_upp else: su = 1. if low is not None: sl = low elif start_low is not None: if start_low > 0: raise ValueError('start_low needs to be negative') sl = start_low else: sl = min(-1., su - 1.) # need sl < su if upp is None: su = max(su, sl + 1.) # increasing or not ? if ((low is None) or (upp is None)) and increasing is None: assert sl < su # check during development f_low = func(sl, *args) f_upp = func(su, *args) # special case for F-distribution (symmetric around zero for effect # size) # chisquare also takes an indefinite time (did not wait see if it # returns) if np.max(np.abs(f_upp - f_low)) < 1e-15 and sl == -1 and su == 1: sl = 1e-8 f_low = func(sl, *args) increasing = (f_low < f_upp) # possibly func returns nan delta = su - sl if np.isnan(f_low): # try just 3 points to find ``increasing`` # do not change sl because brentq can handle one nan bound for fraction in [0.25, 0.5, 0.75]: sl_ = sl + fraction * delta f_low = func(sl_, *args) if not np.isnan(f_low): break else: raise ValueError('could not determine whether function is ' + 'increasing based on starting interval.' + '\nspecify increasing or change starting ' + 'bounds') if np.isnan(f_upp): for fraction in [0.25, 0.5, 0.75]: su_ = su + fraction * delta f_upp = func(su_, *args) if not np.isnan(f_upp): break else: raise ValueError('could not determine whether function is' + 'increasing based on starting interval.' + '\nspecify increasing or change starting ' + 'bounds') increasing = (f_low < f_upp) if not increasing: sl, su = su, sl left, right = right, left n_it = 0 if left is None and sl != 0: left = sl while func(left, *args) > 0: # condition is also false if func returns nan right = left left *= factor if n_it >= max_it: break n_it += 1 # left is now such that func(left) < q if right is None and su != 0: right = su while func(right, *args) < 0: left = right right *= factor if n_it >= max_it: break n_it += 1 # right is now such that func(right) > q if n_it >= max_it: # print('Warning: max_it reached') # TODO: use Warnings, Note: brentq might still work even with max_it f_low = func(sl, *args) f_upp = func(su, *args) if np.isnan(f_low) and np.isnan(f_upp): # can we still get here? raise ValueError('max_it reached' + '\nthe function values at boths bounds are NaN' + '\nchange the starting bounds, set bounds' + 'or increase max_it') res = optimize.brentq(func, left, right, args=args, xtol=xtol, maxiter=maxiter_bq, full_output=full_output) if full_output: val = res[0] info = res[1] info.iterations_expand = n_it info.start_bounds = (sl, su) info.brentq_bounds = (left, right) info.increasing = increasing return val, info else: return res statsmodels-0.12.2/statsmodels/tools/sequences.py000066400000000000000000000151051400612667500222160ustar00rootroot00000000000000"""Low discrepancy sequence tools.""" import numpy as np def discrepancy(sample, bounds=None): """Discrepancy. Compute the centered discrepancy on a given sample. It is a measure of the uniformity of the points in the parameter space. The lower the value is, the better the coverage of the parameter space is. Parameters ---------- sample : array_like (n_samples, k_vars) The sample to compute the discrepancy from. bounds : tuple or array_like ([min, k_vars], [max, k_vars]) Desired range of transformed data. The transformation apply the bounds on the sample and not the theoretical space, unit cube. Thus min and max values of the sample will coincide with the bounds. Returns ------- discrepancy : float Centered discrepancy. References ---------- [1] Fang et al. "Design and modeling for computer experiments", Computer Science and Data Analysis Series Science and Data Analysis Series, 2006. """ sample = np.asarray(sample) n_sample, dim = sample.shape # Sample scaling from bounds to unit hypercube if bounds is not None: min_ = bounds.min(axis=0) max_ = bounds.max(axis=0) sample = (sample - min_) / (max_ - min_) abs_ = abs(sample - 0.5) disc1 = np.sum(np.prod(1 + 0.5 * abs_ - 0.5 * abs_ ** 2, axis=1)) prod_arr = 1 for i in range(dim): s0 = sample[:, i] prod_arr *= (1 + 0.5 * abs(s0[:, None] - 0.5) + 0.5 * abs(s0 - 0.5) - 0.5 * abs(s0[:, None] - s0)) disc2 = prod_arr.sum() c2 = ((13.0 / 12.0) ** dim - 2.0 / n_sample * disc1 + 1.0 / (n_sample ** 2) * disc2) return c2 def primes_from_2_to(n): """Prime numbers from 2 to *n*. Parameters ---------- n : int Sup bound with ``n >= 6``. Returns ------- primes : list(int) Primes in ``2 <= p < n``. References ---------- [1] `StackOverflow `_. """ sieve = np.ones(n // 3 + (n % 6 == 2), dtype=bool) for i in range(1, int(n ** 0.5) // 3 + 1): if sieve[i]: k = 3 * i + 1 | 1 sieve[k * k // 3::2 * k] = False sieve[k * (k - 2 * (i & 1) + 4) // 3::2 * k] = False return np.r_[2, 3, ((3 * np.nonzero(sieve)[0][1:] + 1) | 1)] def n_primes(n): """List of the n-first prime numbers. Parameters ---------- n : int Number of prime numbers wanted. Returns ------- primes : list(int) List of primes. """ primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997][:n] if len(primes) < n: big_number = 10 while 'Not enought primes': primes = primes_from_2_to(big_number)[:n] if len(primes) == n: break big_number += 1000 return primes def van_der_corput(n_sample, base=2, start_index=0): """Van der Corput sequence. Pseudo-random number generator based on a b-adic expansion. Parameters ---------- n_sample : int Number of element of the sequence. base : int Base of the sequence. start_index : int Index to start the sequence from. Returns ------- sequence : list (n_samples,) Sequence of Van der Corput. """ sequence = [] for i in range(start_index, start_index + n_sample): n_th_number, denom = 0., 1. quotient = i while quotient > 0: quotient, remainder = divmod(quotient, base) denom *= base n_th_number += remainder / denom sequence.append(n_th_number) return sequence def halton(dim, n_sample, bounds=None, start_index=0): """Halton sequence. Pseudo-random number generator that generalize the Van der Corput sequence for multiple dimensions. Halton sequence use base-two Van der Corput sequence for the first dimension, base-three for its second and base-n for its n-dimension. Parameters ---------- dim : int Dimension of the parameter space. n_sample : int Number of samples to generate in the parametr space. bounds : tuple or array_like ([min, k_vars], [max, k_vars]) Desired range of transformed data. The transformation apply the bounds on the sample and not the theoretical space, unit cube. Thus min and max values of the sample will coincide with the bounds. start_index : int Index to start the sequence from. Returns ------- sequence : array_like (n_samples, k_vars) Sequence of Halton. References ---------- [1] Halton, "On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals", Numerische Mathematik, 1960. Examples -------- Generate samples from a low discrepancy sequence of Halton. >>> from statsmodels.tools import sequences >>> sample = sequences.halton(dim=2, n_sample=5) Compute the quality of the sample using the discrepancy criterion. >>> uniformity = sequences.discrepancy(sample) If some wants to continue an existing design, extra points can be obtained. >>> sample_continued = sequences.halton(dim=2, n_sample=5, start_index=5) """ base = n_primes(dim) # Generate a sample using a Van der Corput sequence per dimension. sample = [van_der_corput(n_sample + 1, bdim, start_index) for bdim in base] sample = np.array(sample).T[1:] # Sample scaling from unit hypercube to feature range if bounds is not None: min_ = bounds.min(axis=0) max_ = bounds.max(axis=0) sample = sample * (max_ - min_) + min_ return sample statsmodels-0.12.2/statsmodels/tools/sm_exceptions.py000066400000000000000000000104421400612667500231020ustar00rootroot00000000000000""" Contains custom errors and warnings. Errors should derive from Exception or another custom error. Custom errors are only needed it standard errors, for example ValueError or TypeError, are not accurate descriptions of the reason for the error. Warnings should derive from either an existing warning or another custom warning, and should usually be accompanied by a sting using the format warning_name_doc that services as a generic message to use when the warning is raised. """ import warnings # Errors class PerfectSeparationError(Exception): """ Error due to perfect prediction in discrete models """ pass class MissingDataError(Exception): """ Error raised if variables contain missing values when forbidden """ pass class X13NotFoundError(Exception): """ Error locating the X13 binary """ pass class X13Error(Exception): """ Error when running modes using X13 """ pass class ParseError(Exception): """ Error when parsing a docstring. """ def __str__(self): message = self.args[0] if hasattr(self, "docstring"): message = f"{message} in {self.docstring}" return message # Warning class X13Warning(Warning): """ Unexpected conditions when using X13 """ pass class IOWarning(RuntimeWarning): """ Resource not deleted """ pass class ModuleUnavailableWarning(Warning): """ Non-fatal import error """ pass module_unavailable_doc = """ The module {0} is not available. Cannot run in parallel. """ class ModelWarning(UserWarning): """ Base internal Warning class to simplify end-user filtering """ pass class ConvergenceWarning(ModelWarning): """ Nonlinear optimizer failed to converge to a unique solution """ pass convergence_doc = """ Failed to converge on a solution. """ class CacheWriteWarning(ModelWarning): """ Attempting to write to a read-only cached value """ pass class IterationLimitWarning(ModelWarning): """ Iteration limit reached without convergence """ pass iteration_limit_doc = """ Maximum iteration reached. """ class InvalidTestWarning(ModelWarning): """ Test not applicable to model """ pass class NotImplementedWarning(ModelWarning): """ Non-fatal function non-implementation """ pass class OutputWarning(ModelWarning): """ Function output contains atypical values """ pass class DomainWarning(ModelWarning): """ Variables are not compliant with required domain constraints """ pass class ValueWarning(ModelWarning): """ Non-fatal out-of-range value given """ pass class EstimationWarning(ModelWarning): """ Unexpected condition encountered during estimation """ pass class SingularMatrixWarning(ModelWarning): """ Non-fatal matrix inversion affects output results """ pass class HypothesisTestWarning(ModelWarning): """ Issue occurred when performing hypothesis test """ pass class InterpolationWarning(ModelWarning): """ Table granularity and limits restrict interpolation """ pass class PrecisionWarning(ModelWarning): """ Numerical implementation affects precision """ pass class SpecificationWarning(ModelWarning): """ Non-fatal model specification issue """ pass class HessianInversionWarning(ModelWarning): """ Hessian noninvertible and standard errors unavailable """ pass class CollinearityWarning(ModelWarning): """ Variables are highly collinear """ pass class InfeasibleTestError(RuntimeError): """ Test statistic cannot be computed """ pass recarray_warning = """\ recarray support has been deprecated and will be removed after 0.12. Please \ use pandas DataFrames and Series for structured data. You can suppress this warning using from warnings import filterwarnings filterwarnings("ignore", message="recarray support", category=FutureWarning) """ warnings.simplefilter("always", ModelWarning) warnings.simplefilter("always", ConvergenceWarning) warnings.simplefilter("always", CacheWriteWarning) warnings.simplefilter("always", IterationLimitWarning) warnings.simplefilter("always", InvalidTestWarning) statsmodels-0.12.2/statsmodels/tools/testing.py000066400000000000000000000042611400612667500217010ustar00rootroot00000000000000"""assert functions from numpy and pandas testing """ from statsmodels.compat.pandas import testing as pdt import numpy.testing as npt import pandas from statsmodels.tools.tools import Bunch # Standard list for parsing tables PARAM_LIST = ['params', 'bse', 'tvalues', 'pvalues'] def bunch_factory(attribute, columns): """ Generates a special purpose Bunch class Parameters ---------- attribute: str Attribute to access when splitting columns: List[str] List of names to use when splitting the columns of attribute Notes ----- After the class is initialized as a Bunch, the columne of attribute are split so that Bunch has the keys in columns and bunch[column[i]] = bunch[attribute][:, i] """ class FactoryBunch(Bunch): def __init__(self, *args, **kwargs): super(FactoryBunch, self).__init__(*args, **kwargs) if not hasattr(self, attribute): raise AttributeError('{0} is required and must be passed to ' 'the constructor'.format(attribute)) for i, att in enumerate(columns): self[att] = getattr(self, attribute)[:, i] return FactoryBunch ParamsTableTestBunch = bunch_factory('params_table', PARAM_LIST) MarginTableTestBunch = bunch_factory('margins_table', PARAM_LIST) class Holder(object): """ Test-focused class to simplify accessing values by attribute """ def __init__(self, **kwds): self.__dict__.update(kwds) def __str__(self): ss = "\n".join(str(k) + " = " + str(v) for k, v in vars(self).items()) return ss def __repr__(self): ss = str(self.__class__) + "\n" + self.__str__() return ss # adjusted functions def assert_equal(actual, desired, err_msg='', verbose=True, **kwds): if isinstance(desired, pandas.Index): pdt.assert_index_equal(actual, desired) elif isinstance(desired, pandas.Series): pdt.assert_series_equal(actual, desired, **kwds) elif isinstance(desired, pandas.DataFrame): pdt.assert_frame_equal(actual, desired, **kwds) else: npt.assert_equal(actual, desired, err_msg='', verbose=True) statsmodels-0.12.2/statsmodels/tools/tests/000077500000000000000000000000001400612667500210115ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tools/tests/__init__.py000066400000000000000000000000001400612667500231100ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tools/tests/test_catadd.py000066400000000000000000000012411400612667500236400ustar00rootroot00000000000000 import numpy as np from numpy.testing import assert_equal from statsmodels.tools.catadd import add_indep from scipy import linalg def test_add_indep(): x1 = np.array([0,0,0,0,0,1,1,1,2,2,2]) x2 = np.array([0,0,0,0,0,1,1,1,1,1,1]) x0 = np.ones(len(x2)) x = np.column_stack([x0, x1[:,None]*np.arange(3), x2[:,None]*np.arange(2)]) varnames = ['const'] + ['var1_%d' %i for i in np.arange(3)] \ + ['var2_%d' %i for i in np.arange(2)] xo, vo = add_indep(x, varnames) assert_equal(xo, np.column_stack((x0, x1, x2))) assert_equal((linalg.svdvals(x) > 1e-12).sum(), 3) assert_equal(vo, ['const', 'var1_1', 'var2_1']) statsmodels-0.12.2/statsmodels/tools/tests/test_data.py000066400000000000000000000035641400612667500233430ustar00rootroot00000000000000import pandas import numpy as np import pytest from statsmodels.tools import data def test_missing_data_pandas(): """ Fixes GH: #144 """ X = np.random.random((10,5)) X[1,2] = np.nan df = pandas.DataFrame(X) vals, cnames, rnames = data.interpret_data(df) np.testing.assert_equal(rnames.tolist(), [0,2,3,4,5,6,7,8,9]) def test_structarray(): X = np.random.random((9,)).view([('var1', 'f8'), ('var2', 'f8'), ('var3', 'f8')]) with pytest.warns(FutureWarning, match="recarray support"): vals, cnames, rnames = data.interpret_data(X) np.testing.assert_equal(cnames, X.dtype.names) np.testing.assert_equal(vals, X.view((float,3))) np.testing.assert_equal(rnames, None) def test_recarray(): X = np.random.random((9,)).view([('var1', 'f8'), ('var2', 'f8'), ('var3', 'f8')]) with pytest.warns(FutureWarning, match="recarray support"): vals, cnames, rnames = data.interpret_data(X.view(np.recarray)) np.testing.assert_equal(cnames, X.dtype.names) np.testing.assert_equal(vals, X.view((float,3))) np.testing.assert_equal(rnames, None) def test_dataframe(): X = np.random.random((10,5)) df = pandas.DataFrame(X) vals, cnames, rnames = data.interpret_data(df) np.testing.assert_equal(vals, df.values) np.testing.assert_equal(rnames.tolist(), df.index.tolist()) np.testing.assert_equal(cnames, df.columns.tolist()) def test_patsy_577(): X = np.random.random((10, 2)) df = pandas.DataFrame(X, columns=["var1", "var2"]) from patsy import dmatrix endog = dmatrix("var1 - 1", df) np.testing.assert_(data._is_using_patsy(endog, None)) exog = dmatrix("var2 - 1", df) np.testing.assert_(data._is_using_patsy(endog, exog)) statsmodels-0.12.2/statsmodels/tools/tests/test_decorators.py000066400000000000000000000036461400612667500246000ustar00rootroot00000000000000# -*- coding: utf-8 -*- import pytest from numpy.testing import assert_equal from statsmodels.tools.decorators import (cache_readonly, deprecated_alias) def test_cache_readonly(): class Example(object): def __init__(self): self._cache = {} self.a = 0 @cache_readonly def b(self): return 1 ex = Example() # Try accessing/setting a readonly attribute assert_equal(ex.__dict__, dict(a=0, _cache={})) b = ex.b assert_equal(b, 1) assert_equal(ex.__dict__, dict(a=0, _cache=dict(b=1,))) # assert_equal(ex.__dict__, dict(a=0, b=1, _cache=dict(b=1))) with pytest.raises(AttributeError): ex.b = -1 assert_equal(ex._cache, dict(b=1,)) def dummy_factory(msg, remove_version, warning): class Dummy(object): y = deprecated_alias('y', 'x', remove_version=remove_version, msg=msg, warning=warning) def __init__(self, y): self.x = y return Dummy(1) @pytest.mark.parametrize('warning', [FutureWarning, UserWarning]) @pytest.mark.parametrize('remove_version', [None, '0.11']) @pytest.mark.parametrize('msg', ['test message', None]) def test_deprecated_alias(msg, remove_version, warning): dummy_set = dummy_factory(msg, remove_version, warning) with pytest.warns(warning) as w: dummy_set.y = 2 assert dummy_set.x == 2 assert warning.__class__ is w[0].category.__class__ dummy_get = dummy_factory(msg, remove_version, warning) with pytest.warns(warning) as w: x = dummy_get.y assert x == 1 assert warning.__class__ is w[0].category.__class__ message = str(w[0].message) if not msg: if remove_version: assert 'will be removed' in message else: assert 'will be removed' not in message else: assert msg in message statsmodels-0.12.2/statsmodels/tools/tests/test_docstring.py000066400000000000000000000062641400612667500244260ustar00rootroot00000000000000import pytest from statsmodels.tools.docstring import Docstring, remove_parameters, Parameter good = """ This is the summary. This is the extended summary. Parameters ---------- x : int The first parameter. y : float The second parameter. z : {int, float, None} The final parameter. Returns ------- float Some floating point value. See Also -------- statsmodels.api The main API location. Notes ----- This is where the notes go. .. index: default :refguide: something, else, and more References ---------- .. [*] Reference 1 here Examples -------- Using the API is simple >>> import statsmodels.api """ bad = """ Returns ------- float Some floating point value. Unknown ------- I don't know what this section does. """ repeat = """ Returns ------- float Some floating point value. Returns ------- float Some floating point value. """ bad_yields = """ Returns ------- float The return. Yields ------ float Can't also yield. """ with_sig = """ func(x) func(x, y) func(x, y, z=1) """ + good def test_remove_parameter(): ds = Docstring(good) ds.remove_parameters('x') assert 'x : int' not in str(ds) ds = Docstring(good) ds.remove_parameters(['x', 'y']) assert 'x : int' not in str(ds) assert 'y : float' not in str(ds) with pytest.raises(ValueError): Docstring(good).remove_parameters(['w']) ds = remove_parameters(good, 'x') assert 'x : int' not in ds assert isinstance(ds, str) def test_insert_parameters(): new = Parameter('w', 'ndarray', ['An array input.']) ds = Docstring(good) ds.insert_parameters('y', new) assert 'w : ndarray' in str(ds) assert 'An array input.' in str(ds) other = Parameter('q', 'DataFrame', ['A pandas dataframe.']) ds = Docstring(good) ds.insert_parameters(None, [new, other]) assert 'w : ndarray' in str(ds) assert 'An array input.' in str(ds) assert 'q : DataFrame' in str(ds) assert 'A pandas dataframe.' in str(ds) assert '---\nw : ndarray' in str(ds) ds = Docstring(good) with pytest.raises(ValueError): ds.insert_parameters('unknown', new) def test_set_unknown(): ds = Docstring(good) with pytest.raises(ValueError): ds._ds['Unknown'] = ['unknown'] def test_replace_block(): ds = Docstring(good) ds.replace_block('summary', ['The is the new summary.']) assert 'The is the new summary.' in str(ds) ds = Docstring(good) ds.replace_block('summary', 'The is the new summary.') assert 'The is the new summary.' in str(ds) with pytest.raises(ValueError): ds.replace_block('unknown', ['The is the new summary.']) def test_repeat(): with pytest.raises(ValueError): Docstring(repeat) def test_bad(): with pytest.raises(ValueError): Docstring(bad) def test_empty_ds(): ds = Docstring(None) ds.replace_block('summary', ['The is the new summary.']) ds.remove_parameters('x') new = Parameter('w', 'ndarray', ['An array input.']) ds.insert_parameters('y', new) assert str(ds) == 'None' def test_yield_return(): with pytest.raises(ValueError): Docstring(bad_yields) def test_multiple_sig(): Docstring(with_sig) statsmodels-0.12.2/statsmodels/tools/tests/test_eval_measures.py000066400000000000000000000100011400612667500252450ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Tue Nov 08 22:28:48 2011 @author: josef """ import numpy as np from numpy.testing import assert_almost_equal, assert_equal import pytest from statsmodels.tools.eval_measures import ( aic, aic_sigma, aicc, aicc_sigma, bias, bic, bic_sigma, hqic, hqic_sigma, iqr, maxabs, meanabs, medianabs, medianbias, mse, rmse, rmspe, vare, ) def test_eval_measures(): # mainly regression tests x = np.arange(20).reshape(4, 5) y = np.ones((4, 5)) assert_equal(iqr(x, y), 5 * np.ones(5)) assert_equal(iqr(x, y, axis=1), 2 * np.ones(4)) assert_equal(iqr(x, y, axis=None), 9) assert_equal(mse(x, y), np.array([73.5, 87.5, 103.5, 121.5, 141.5])) assert_equal(mse(x, y, axis=1), np.array([3.0, 38.0, 123.0, 258.0])) assert_almost_equal( rmse(x, y), np.array( [8.5732141, 9.35414347, 10.17349497, 11.02270384, 11.89537725] ), ) assert_almost_equal( rmse(x, y, axis=1), np.array([1.73205081, 6.164414, 11.09053651, 16.0623784]), ) err = x - y loc = np.where(x != 0) err[loc] /= x[loc] err[np.where(x == 0)] = np.nan expected = np.sqrt(np.nanmean(err ** 2, 0) * 100) assert_almost_equal(rmspe(x, y), expected) err[np.where(np.isnan(err))] = 0.0 expected = np.sqrt(np.nanmean(err ** 2, 0) * 100) assert_almost_equal(rmspe(x, y, zeros=0), expected) assert_equal(maxabs(x, y), np.array([14.0, 15.0, 16.0, 17.0, 18.0])) assert_equal(maxabs(x, y, axis=1), np.array([3.0, 8.0, 13.0, 18.0])) assert_equal(meanabs(x, y), np.array([7.0, 7.5, 8.5, 9.5, 10.5])) assert_equal(meanabs(x, y, axis=1), np.array([1.4, 6.0, 11.0, 16.0])) assert_equal(meanabs(x, y, axis=0), np.array([7.0, 7.5, 8.5, 9.5, 10.5])) assert_equal(medianabs(x, y), np.array([6.5, 7.5, 8.5, 9.5, 10.5])) assert_equal(medianabs(x, y, axis=1), np.array([1.0, 6.0, 11.0, 16.0])) assert_equal(bias(x, y), np.array([6.5, 7.5, 8.5, 9.5, 10.5])) assert_equal(bias(x, y, axis=1), np.array([1.0, 6.0, 11.0, 16.0])) assert_equal(medianbias(x, y), np.array([6.5, 7.5, 8.5, 9.5, 10.5])) assert_equal(medianbias(x, y, axis=1), np.array([1.0, 6.0, 11.0, 16.0])) assert_equal(vare(x, y), np.array([31.25, 31.25, 31.25, 31.25, 31.25])) assert_equal(vare(x, y, axis=1), np.array([2.0, 2.0, 2.0, 2.0])) ics = [aic, aicc, bic, hqic] ics_sig = [aic_sigma, aicc_sigma, bic_sigma, hqic_sigma] @pytest.mark.parametrize("ic,ic_sig", zip(ics, ics_sig)) def test_ic_equivalence(ic, ic_sig): # consistency check assert ic(np.array(2), 10, 2).dtype == float assert ic_sig(np.array(2), 10, 2).dtype == float assert_almost_equal( ic(-10.0 / 2.0 * np.log(2.0), 10, 2) / 10, ic_sig(2, 10, 2), decimal=14 ) assert_almost_equal( ic_sig(np.log(2.0), 10, 2, islog=True), ic_sig(2, 10, 2), decimal=14 ) def test_ic(): # test information criteria # examples penalty directly from formula n = 10 k = 2 assert_almost_equal(aic(0, 10, 2), 2 * k, decimal=14) # next see Wikipedia assert_almost_equal( aicc(0, 10, 2), aic(0, n, k) + 2 * k * (k + 1.0) / (n - k - 1.0), decimal=14, ) assert_almost_equal(bic(0, 10, 2), np.log(n) * k, decimal=14) assert_almost_equal(hqic(0, 10, 2), 2 * np.log(np.log(n)) * k, decimal=14) def test_iqr_axis(reset_randomstate): x1 = np.random.standard_normal((100, 100)) x2 = np.random.standard_normal((100, 100)) ax_none = iqr(x1, x2, axis=None) ax_none_direct = iqr(x1.ravel(), x2.ravel()) assert_equal(ax_none, ax_none_direct) ax_0 = iqr(x1, x2, axis=0) assert ax_0.shape == (100,) ax_0_direct = [iqr(x1[:, i], x2[:, i]) for i in range(100)] assert_almost_equal(ax_0, np.array(ax_0_direct)) ax_1 = iqr(x1, x2, axis=1) assert ax_1.shape == (100,) ax_1_direct = [iqr(x1[i, :], x2[i, :]) for i in range(100)] assert_almost_equal(ax_1, np.array(ax_1_direct)) assert any(ax_0 != ax_1) statsmodels-0.12.2/statsmodels/tools/tests/test_grouputils.py000066400000000000000000000336631400612667500246520ustar00rootroot00000000000000from statsmodels.compat.pandas import assert_frame_equal, assert_series_equal import numpy as np from numpy.testing import assert_equal import pandas as pd import pytest from scipy import sparse from statsmodels.tools.grouputils import (dummy_sparse, Grouping, Group, combine_indices, group_sums) from statsmodels.datasets import grunfeld, anes96 class CheckGrouping(object): @pytest.mark.smoke def test_reindex(self): self.grouping.reindex(self.grouping.index) def test_count_categories(self): self.grouping.count_categories(level=0) np.testing.assert_equal(self.grouping.counts, self.expected_counts) def test_sort(self): # data frame sorted_data, index = self.grouping.sort(self.data) expected_sorted_data = self.data.sort_index() assert_frame_equal(sorted_data, expected_sorted_data) np.testing.assert_(isinstance(sorted_data, pd.DataFrame)) np.testing.assert_(not index.equals(self.grouping.index)) # make sure it copied if hasattr(sorted_data, 'equals'): # newer pandas np.testing.assert_(not sorted_data.equals(self.data)) # 2d arrays sorted_data, index = self.grouping.sort(self.data.values) np.testing.assert_array_equal(sorted_data, expected_sorted_data.values) np.testing.assert_(isinstance(sorted_data, np.ndarray)) # 1d series series = self.data[self.data.columns[0]] sorted_data, index = self.grouping.sort(series) expected_sorted_data = series.sort_index() assert_series_equal(sorted_data, expected_sorted_data) np.testing.assert_(isinstance(sorted_data, pd.Series)) if hasattr(sorted_data, 'equals'): np.testing.assert_(not sorted_data.equals(series)) # 1d array array = series.values sorted_data, index = self.grouping.sort(array) expected_sorted_data = series.sort_index().values np.testing.assert_array_equal(sorted_data, expected_sorted_data) np.testing.assert_(isinstance(sorted_data, np.ndarray)) def test_transform_dataframe(self): names = self.data.index.names transformed_dataframe = self.grouping.transform_dataframe( self.data, lambda x : x.mean(), level=0) grouped = self.data.reset_index().groupby(names[0]) expected = grouped.apply(lambda x : x.mean())[self.data.columns] np.testing.assert_allclose(transformed_dataframe, expected.values) if len(names) > 1: transformed_dataframe = self.grouping.transform_dataframe( self.data, lambda x : x.mean(), level=1) grouped = self.data.reset_index().groupby(names[1]) expected = grouped.apply(lambda x: x.mean())[self.data.columns] np.testing.assert_allclose(transformed_dataframe, expected.values) def test_transform_array(self): names = self.data.index.names transformed_array = self.grouping.transform_array( self.data.values, lambda x : x.mean(), level=0) grouped = self.data.reset_index().groupby(names[0]) expected = grouped.apply(lambda x: x.mean())[self.data.columns] np.testing.assert_allclose(transformed_array, expected.values) if len(names) > 1: transformed_array = self.grouping.transform_array( self.data.values, lambda x : x.mean(), level=1) grouped = self.data.reset_index().groupby(names[1]) expected = grouped.apply(lambda x: x.mean())[self.data.columns] np.testing.assert_allclose(transformed_array, expected.values) def test_transform_slices(self): names = self.data.index.names transformed_slices = self.grouping.transform_slices( self.data.values, lambda x, idx : x.mean(0), level=0) expected = self.data.reset_index().groupby(names[0]).mean()[ self.data.columns] np.testing.assert_allclose(transformed_slices, expected.values, rtol=1e-12, atol=1e-25) if len(names) > 1: transformed_slices = self.grouping.transform_slices( self.data.values, lambda x, idx : x.mean(0), level=1) expected = self.data.reset_index().groupby(names[1] ).mean()[ self.data.columns] np.testing.assert_allclose(transformed_slices, expected.values, rtol=1e-12, atol=1e-25) @pytest.mark.smoke def test_dummies_groups(self): # calls dummy_sparse under the hood self.grouping.dummies_groups() if len(self.grouping.group_names) > 1: self.grouping.dummies_groups(level=1) def test_dummy_sparse(self): data = self.data self.grouping.dummy_sparse() values = data.index.get_level_values(0).values expected = pd.get_dummies(pd.Series(values, dtype="category"), drop_first=False) np.testing.assert_equal(self.grouping._dummies.toarray(), expected) if len(self.grouping.group_names) > 1: self.grouping.dummy_sparse(level=1) values = data.index.get_level_values(1).values expected = pd.get_dummies(pd.Series(values, dtype="category"), drop_first=False) np.testing.assert_equal(self.grouping._dummies.toarray(), expected) class TestMultiIndexGrouping(CheckGrouping): @classmethod def setup_class(cls): grun_data = grunfeld.load_pandas().data multi_index_data = grun_data.set_index(['firm', 'year']) multi_index_panel = multi_index_data.index cls.grouping = Grouping(multi_index_panel) cls.data = multi_index_data cls.expected_counts = [20] * 11 class TestIndexGrouping(CheckGrouping): @classmethod def setup_class(cls): grun_data = grunfeld.load_pandas().data index_data = grun_data.set_index(['firm']) index_group = index_data.index cls.grouping = Grouping(index_group) cls.data = index_data cls.expected_counts = [20] * 11 def test_init_api(): # make a multi-index panel grun_data = grunfeld.load_pandas().data multi_index_panel = grun_data.set_index(['firm', 'year']).index grouping = Grouping(multi_index_panel) # check group_names np.testing.assert_array_equal(grouping.group_names, ['firm', 'year']) # check shape np.testing.assert_array_equal(grouping.index_shape, (11, 20)) # check index_int np.testing.assert_array_equal(grouping.labels, [[ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]]) grouping = Grouping(multi_index_panel, names=['firms', 'year']) np.testing.assert_array_equal(grouping.group_names, ['firms', 'year']) # make a multi-index grouping anes_data = anes96.load_pandas().data multi_index_groups = anes_data.set_index(['educ', 'income', 'TVnews']).index grouping = Grouping(multi_index_groups) np.testing.assert_array_equal(grouping.group_names, ['educ', 'income', 'TVnews']) np.testing.assert_array_equal(grouping.index_shape, (7, 24, 8)) # make a list multi-index panel list_panel = multi_index_panel.tolist() grouping = Grouping(list_panel, names=['firms', 'year']) np.testing.assert_array_equal(grouping.group_names, ['firms', 'year']) np.testing.assert_array_equal(grouping.index_shape, (11, 20)) # make a list multi-index grouping list_groups = multi_index_groups.tolist() grouping = Grouping(list_groups, names=['educ', 'income', 'TVnews']) np.testing.assert_array_equal(grouping.group_names, ['educ', 'income', 'TVnews']) np.testing.assert_array_equal(grouping.index_shape, (7, 24, 8)) # single-variable index grouping index_group = multi_index_panel.get_level_values(0) grouping = Grouping(index_group) # the original multi_index_panel had it's name changed inplace above np.testing.assert_array_equal(grouping.group_names, ['firms']) np.testing.assert_array_equal(grouping.index_shape, (220,)) # single variable list grouping list_group = multi_index_panel.get_level_values(0).tolist() grouping = Grouping(list_group) np.testing.assert_array_equal(grouping.group_names, ["group0"]) np.testing.assert_array_equal(grouping.index_shape, 11*20) # test generic group names grouping = Grouping(list_groups) np.testing.assert_array_equal(grouping.group_names, ['group0', 'group1', 'group2']) def test_combine_indices(): # Moved from grouputils __main__ section np.random.seed(985367) groups = np.random.randint(0, 2, size=(10, 2)) uv, ux, u, label = combine_indices(groups, return_labels=True) uv, ux, u, label = combine_indices(groups, prefix='g1,g2=', sep=',', return_labels=True) group0 = np.array(['sector0', 'sector1'])[groups[:, 0]] group1 = np.array(['region0', 'region1'])[groups[:, 1]] uv, ux, u, label = combine_indices((group0, group1), prefix='sector,region=', sep=',', return_labels=True) uv, ux, u, label = combine_indices((group0, group1), prefix='', sep='.', return_labels=True) group_joint = np.array(label)[uv] group_joint_expected = np.array(['sector1.region0', 'sector0.region1', 'sector0.region0', 'sector0.region1', 'sector1.region1', 'sector0.region0', 'sector1.region0', 'sector1.region0', 'sector0.region1', 'sector0.region0'], dtype='|U15') assert_equal(group_joint, group_joint_expected) @pytest.mark.smoke def test_group_sums(): # Moved from grouputils __main__ section g = np.array([0, 0, 1, 2, 1, 1, 2, 0]) group_sums(np.arange(len(g)*3*2).reshape(len(g), 3, 2), g, use_bincount=False).T group_sums(np.arange(len(g)*3*2).reshape(len(g), 3, 2)[:, :, 0], g) group_sums(np.arange(len(g)*3*2).reshape(len(g), 3, 2)[:, :, 1], g) @pytest.mark.smoke def test_group_class(): # Moved from grouputils __main__ section g = np.array([0, 0, 1, 2, 1, 1, 2, 0]) x = np.arange(len(g)*3).reshape(len(g), 3, order='F') mygroup = Group(g) mygroup.group_int mygroup.group_sums(x) mygroup.labels() def test_dummy_sparse(): # See GH#5687 g = np.array([0, 0, 2, 1, 1, 2, 0]) indi = dummy_sparse(g) assert isinstance(indi, sparse.csr.csr_matrix) result = indi.todense() expected = np.matrix([[1, 0, 0], [1, 0, 0], [0, 0, 1], [0, 1, 0], [0, 1, 0], [0, 0, 1], [1, 0, 0]], dtype=np.int8) assert_equal(result, expected) # current behavior with missing groups g = np.array([0, 0, 2, 0, 2, 0]) indi = dummy_sparse(g) result = indi.todense() expected = np.matrix([[1, 0, 0], [1, 0, 0], [0, 0, 1], [1, 0, 0], [0, 0, 1], [1, 0, 0]], dtype=np.int8) assert_equal(result, expected) statsmodels-0.12.2/statsmodels/tools/tests/test_linalg.py000066400000000000000000000013331400612667500236700ustar00rootroot00000000000000from statsmodels.tools import linalg import numpy as np from numpy.testing import assert_allclose from scipy.linalg import toeplitz def test_stationary_solve_1d(): b = np.random.uniform(size=10) r = np.random.uniform(size=9) t = np.concatenate((np.r_[1], r)) tmat = toeplitz(t) soln = np.linalg.solve(tmat, b) soln1 = linalg.stationary_solve(r, b) assert_allclose(soln, soln1, rtol=1e-5, atol=1e-5) def test_stationary_solve_2d(): b = np.random.uniform(size=(10, 2)) r = np.random.uniform(size=9) t = np.concatenate((np.r_[1], r)) tmat = toeplitz(t) soln = np.linalg.solve(tmat, b) soln1 = linalg.stationary_solve(r, b) assert_allclose(soln, soln1, rtol=1e-5, atol=1e-5) statsmodels-0.12.2/statsmodels/tools/tests/test_numdiff.py000066400000000000000000000335261400612667500240630ustar00rootroot00000000000000'''Testing numerical differentiation Still some problems, with API (args tuple versus *args) finite difference Hessian has some problems that I did not look at yet Should Hessian also work per observation, if fun returns 2d ''' import numpy as np from numpy.testing import assert_almost_equal, assert_allclose import statsmodels.api as sm from statsmodels.tools import numdiff from statsmodels.tools.numdiff import (approx_fprime, approx_fprime_cs, approx_hess_cs) DEC3 = 3 DEC4 = 4 DEC5 = 5 DEC6 = 6 DEC8 = 8 DEC13 = 13 DEC14 = 14 def maxabs(x,y): return np.abs(x-y).max() def fun(beta, x): return np.dot(x, beta).sum(0) def fun1(beta, y, x): #print(beta.shape, x.shape) xb = np.dot(x, beta) return (y-xb)**2 #(xb-xb.mean(0))**2 def fun2(beta, y, x): #print(beta.shape, x.shape) return fun1(beta, y, x).sum(0) #ravel() added because of MNLogit 2d params class CheckGradLoglikeMixin(object): def test_score(self): for test_params in self.params: sc = self.mod.score(test_params) scfd = numdiff.approx_fprime(test_params.ravel(), self.mod.loglike) assert_almost_equal(sc, scfd, decimal=1) sccs = numdiff.approx_fprime_cs(test_params.ravel(), self.mod.loglike) assert_almost_equal(sc, sccs, decimal=11) def test_hess(self): for test_params in self.params: he = self.mod.hessian(test_params) hefd = numdiff.approx_fprime_cs(test_params, self.mod.score) assert_almost_equal(he, hefd, decimal=DEC8) #NOTE: notice the accuracy below assert_almost_equal(he, hefd, decimal=7) hefd = numdiff.approx_fprime(test_params, self.mod.score, centered=True) assert_allclose(he, hefd, rtol=1e-9) hefd = numdiff.approx_fprime(test_params, self.mod.score, centered=False) assert_almost_equal(he, hefd, decimal=4) hescs = numdiff.approx_fprime_cs(test_params.ravel(), self.mod.score) assert_allclose(he, hescs, rtol=1e-13) hecs = numdiff.approx_hess_cs(test_params.ravel(), self.mod.loglike) assert_allclose(he, hecs, rtol=1e-9) #NOTE: Look at the lack of precision - default epsilon not always #best grad = self.mod.score(test_params) hecs, gradcs = numdiff.approx_hess1(test_params, self.mod.loglike, 1e-6, return_grad=True) assert_almost_equal(he, hecs, decimal=1) assert_almost_equal(grad, gradcs, decimal=1) hecs, gradcs = numdiff.approx_hess2(test_params, self.mod.loglike, 1e-4, return_grad=True) assert_almost_equal(he, hecs, decimal=3) assert_almost_equal(grad, gradcs, decimal=1) hecs = numdiff.approx_hess3(test_params, self.mod.loglike, 1e-5) assert_almost_equal(he, hecs, decimal=4) class TestGradMNLogit(CheckGradLoglikeMixin): @classmethod def setup_class(cls): #from .results.results_discrete import Anes data = sm.datasets.anes96.load(as_pandas=False) exog = data.exog exog = sm.add_constant(exog, prepend=False) cls.mod = sm.MNLogit(data.endog, exog) #def loglikeflat(cls, params): #reshapes flattened params # return cls.loglike(params.reshape(6,6)) #cls.mod.loglike = loglikeflat #need instance method #cls.params = [np.ones((6,6)).ravel()] res = cls.mod.fit(disp=0) cls.params = [res.params.ravel('F')] def test_hess(self): #NOTE: I had to overwrite this to lessen the tolerance for test_params in self.params: he = self.mod.hessian(test_params) hefd = numdiff.approx_fprime_cs(test_params, self.mod.score) assert_almost_equal(he, hefd, decimal=DEC8) #NOTE: notice the accuracy below and the epsilon changes # this does not work well for score -> hessian with non-cs step # it's a little better around the optimum assert_almost_equal(he, hefd, decimal=7) hefd = numdiff.approx_fprime(test_params, self.mod.score, centered=True) assert_almost_equal(he, hefd, decimal=4) hefd = numdiff.approx_fprime(test_params, self.mod.score, 1e-9, centered=False) assert_almost_equal(he, hefd, decimal=2) hescs = numdiff.approx_fprime_cs(test_params, self.mod.score) assert_almost_equal(he, hescs, decimal=DEC8) hecs = numdiff.approx_hess_cs(test_params, self.mod.loglike) assert_almost_equal(he, hecs, decimal=5) #NOTE: these just do not work well #hecs = numdiff.approx_hess1(test_params, self.mod.loglike, 1e-3) #assert_almost_equal(he, hecs, decimal=1) #hecs = numdiff.approx_hess2(test_params, self.mod.loglike, 1e-4) #assert_almost_equal(he, hecs, decimal=0) hecs = numdiff.approx_hess3(test_params, self.mod.loglike, 1e-4) assert_almost_equal(he, hecs, decimal=0) class TestGradLogit(CheckGradLoglikeMixin): @classmethod def setup_class(cls): data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) #mod = sm.Probit(data.endog, data.exog) cls.mod = sm.Logit(data.endog, data.exog) #res = mod.fit(method="newton") cls.params = [np.array([1,0.25,1.4,-7])] ##loglike = mod.loglike ##score = mod.score ##hess = mod.hessian class CheckDerivativeMixin(object): @classmethod def setup_class(cls): nobs = 200 #x = np.arange(nobs*3).reshape(nobs,-1) np.random.seed(187678) x = np.random.randn(nobs,3) xk = np.array([1,2,3]) xk = np.array([1.,1.,1.]) #xk = np.zeros(3) beta = xk y = np.dot(x, beta) + 0.1*np.random.randn(nobs) xkols = np.dot(np.linalg.pinv(x),y) cls.x = x cls.y = y cls.params = [np.array([1.,1.,1.]), xkols] cls.init() @classmethod def init(cls): pass def test_grad_fun1_fd(self): for test_params in self.params: #gtrue = self.x.sum(0) gtrue = self.gradtrue(test_params) fun = self.fun() epsilon = 1e-6 gfd = numdiff.approx_fprime(test_params, fun, epsilon=epsilon, args=self.args) gfd += numdiff.approx_fprime(test_params, fun, epsilon=-epsilon, args=self.args) gfd /= 2. assert_almost_equal(gtrue, gfd, decimal=DEC6) def test_grad_fun1_fdc(self): for test_params in self.params: #gtrue = self.x.sum(0) gtrue = self.gradtrue(test_params) fun = self.fun() # default epsilon of 1e-6 is not precise enough here gfd = numdiff.approx_fprime(test_params, fun, epsilon=1e-8, args=self.args, centered=True) assert_almost_equal(gtrue, gfd, decimal=DEC5) def test_grad_fun1_cs(self): for test_params in self.params: #gtrue = self.x.sum(0) gtrue = self.gradtrue(test_params) fun = self.fun() gcs = numdiff.approx_fprime_cs(test_params, fun, args=self.args) assert_almost_equal(gtrue, gcs, decimal=DEC13) def test_hess_fun1_fd(self): for test_params in self.params: #hetrue = 0 hetrue = self.hesstrue(test_params) if hetrue is not None: #Hessian does not work for 2d return of fun fun = self.fun() #default works, epsilon 1e-6 or 1e-8 is not precise enough hefd = numdiff.approx_hess1(test_params, fun, #epsilon=1e-8, # TODO: should be kwds args=self.args) assert_almost_equal(hetrue, hefd, decimal=DEC3) #TODO: I reduced precision to DEC3 from DEC4 because of # TestDerivativeFun hefd = numdiff.approx_hess2(test_params, fun, #epsilon=1e-8, # TODO: should be kwds args=self.args) assert_almost_equal(hetrue, hefd, decimal=DEC3) hefd = numdiff.approx_hess3(test_params, fun, #epsilon=1e-8, # TODO: should be kwds args=self.args) assert_almost_equal(hetrue, hefd, decimal=DEC3) def test_hess_fun1_cs(self): for test_params in self.params: #hetrue = 0 hetrue = self.hesstrue(test_params) if hetrue is not None: #Hessian does not work for 2d return of fun fun = self.fun() hecs = numdiff.approx_hess_cs(test_params, fun, args=self.args) assert_almost_equal(hetrue, hecs, decimal=DEC6) class TestDerivativeFun(CheckDerivativeMixin): @classmethod def setup_class(cls): super(TestDerivativeFun,cls).setup_class() xkols = np.dot(np.linalg.pinv(cls.x), cls.y) cls.params = [np.array([1.,1.,1.]), xkols] cls.args = (cls.x,) def fun(self): return fun def gradtrue(self, params): return self.x.sum(0) def hesstrue(self, params): return np.zeros((3,3)) #make it (3,3), because test fails with scalar 0 #why is precision only DEC3 class TestDerivativeFun2(CheckDerivativeMixin): @classmethod def setup_class(cls): super(TestDerivativeFun2,cls).setup_class() xkols = np.dot(np.linalg.pinv(cls.x), cls.y) cls.params = [np.array([1.,1.,1.]), xkols] cls.args = (cls.y, cls.x) def fun(self): return fun2 def gradtrue(self, params): y, x = self.y, self.x return (-x*2*(y-np.dot(x, params))[:,None]).sum(0) #2*(y-np.dot(x, params)).sum(0) def hesstrue(self, params): x = self.x return 2*np.dot(x.T, x) class TestDerivativeFun1(CheckDerivativeMixin): @classmethod def setup_class(cls): super(TestDerivativeFun1, cls).setup_class() xkols = np.dot(np.linalg.pinv(cls.x), cls.y) cls.params = [np.array([1.,1.,1.]), xkols] cls.args = (cls.y, cls.x) def fun(self): return fun1 def gradtrue(self, params): y, x = self.y, self.x return (-x*2*(y-np.dot(x, params))[:,None]) def hesstrue(self, params): return None y, x = self.y, self.x return (-x*2*(y-np.dot(x, params))[:,None]) #TODO: check shape def test_dtypes(): def f(x): return 2*x desired = np.array([[2, 0], [0, 2]]) assert_allclose(approx_fprime(np.array([1, 2]), f), desired) assert_allclose(approx_fprime(np.array([1., 2.]), f), desired) assert_allclose(approx_fprime(np.array([1.+0j, 2.+0j]), f), desired) if __name__ == '__main__': # FIXME: turn into tests or move/remove epsilon = 1e-6 nobs = 200 x = np.arange(nobs*3).reshape(nobs,-1) x = np.random.randn(nobs,3) xk = np.array([1,2,3]) xk = np.array([1.,1.,1.]) #xk = np.zeros(3) beta = xk y = np.dot(x, beta) + 0.1*np.random.randn(nobs) xkols = np.dot(np.linalg.pinv(x),y) print(approx_fprime((1,2,3),fun,epsilon,x)) gradtrue = x.sum(0) print(x.sum(0)) gradcs = approx_fprime_cs((1,2,3), fun, (x,), h=1.0e-20) print(gradcs, maxabs(gradcs, gradtrue)) print(approx_hess_cs((1,2,3), fun, (x,), h=1.0e-20)) #this is correctly zero print(approx_hess_cs((1,2,3), fun2, (y,x), h=1.0e-20)-2*np.dot(x.T, x)) print(numdiff.approx_hess(xk,fun2,1e-3, (y,x))[0] - 2*np.dot(x.T, x)) gt = (-x*2*(y-np.dot(x, [1,2,3]))[:,None]) g = approx_fprime_cs((1,2,3), fun1, (y,x), h=1.0e-20)#.T #this should not be transposed gd = numdiff.approx_fprime((1,2,3),fun1,epsilon,(y,x)) print(maxabs(g, gt)) print(maxabs(gd, gt)) data = sm.datasets.spector.load(as_pandas=False) data.exog = sm.add_constant(data.exog, prepend=False) #mod = sm.Probit(data.endog, data.exog) mod = sm.Logit(data.endog, data.exog) #res = mod.fit(method="newton") test_params = [1,0.25,1.4,-7] loglike = mod.loglike score = mod.score hess = mod.hessian #cs does not work for Probit because special.ndtr does not support complex #maybe calculating ndtr for real and imag parts separately, if we need it #and if it still works in this case print('sm', score(test_params)) print('fd', numdiff.approx_fprime(test_params,loglike,epsilon)) print('cs', numdiff.approx_fprime_cs(test_params,loglike)) print('sm', hess(test_params)) print('fd', numdiff.approx_fprime(test_params,score,epsilon)) print('cs', numdiff.approx_fprime_cs(test_params, score)) hesscs = numdiff.approx_hess_cs(test_params, loglike) print('cs', hesscs) print(maxabs(hess(test_params), hesscs)) data = sm.datasets.anes96.load(as_pandas=False) exog = data.exog exog = sm.add_constant(exog, prepend=False) res1 = sm.MNLogit(data.endog, exog).fit(method="newton", disp=0) datap = sm.datasets.randhie.load(as_pandas=False) nobs = len(datap.endog) exogp = sm.add_constant(datap.exog.view(float).reshape(nobs,-1), prepend=False) modp = sm.Poisson(datap.endog, exogp) resp = modp.fit(method='newton', disp=0) statsmodels-0.12.2/statsmodels/tools/tests/test_parallel.py000066400000000000000000000006241400612667500242200ustar00rootroot00000000000000import warnings from statsmodels.tools.parallel import parallel_func from numpy import arange, testing from math import sqrt def test_parallel(): x = arange(10.) with warnings.catch_warnings(): warnings.simplefilter("ignore") parallel, p_func, n_jobs = parallel_func(sqrt, n_jobs=-1, verbose=0) y = parallel(p_func(i**2) for i in range(10)) testing.assert_equal(x,y) statsmodels-0.12.2/statsmodels/tools/tests/test_rootfinding.py000066400000000000000000000056201400612667500247470ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Sat Mar 23 13:34:19 2013 Author: Josef Perktold """ import numpy as np from statsmodels.tools.rootfinding import brentq_expanding from numpy.testing import (assert_allclose, assert_equal, assert_raises, assert_array_less) def func(x, a): f = (x - a)**3 return f def func_nan(x, a, b): x = np.atleast_1d(x) f = (x - 1.*a)**3 f[x < b] = np.nan return f def funcn(x, a): f = -(x - a)**3 return f def test_brentq_expanding(): cases = [ (0, {}), (50, {}), (-50, {}), (500000, dict(low=10000)), (-50000, dict(upp=-1000)), (500000, dict(low=300000, upp=700000)), (-50000, dict(low= -70000, upp=-1000)) ] funcs = [(func, None), (func, True), (funcn, None), (funcn, False)] for f, inc in funcs: for a, kwds in cases: kw = {'increasing':inc} kw.update(kwds) res = brentq_expanding(f, args=(a,), **kwds) #print '%10d'%a, ['dec', 'inc'][f is func], res - a assert_allclose(res, a, rtol=1e-5) # wrong sign for start bounds # does not raise yet during development TODO: activate this # it kind of works in some cases, but not correctly or in a useful way #assert_raises(ValueError, brentq_expanding, func, args=(-500,), start_upp=-1000) #assert_raises(ValueError, brentq_expanding, func, args=(500,), start_low=1000) # low upp given, but does not bound root, leave brentq exception # ValueError: f(a) and f(b) must have different signs assert_raises(ValueError, brentq_expanding, funcn, args=(-50000,), low= -40000, upp=-10000) # max_it too low to find root bounds # ValueError: f(a) and f(b) must have different signs assert_raises(ValueError, brentq_expanding, func, args=(-50000,), max_it=2) # maxiter_bq too low # RuntimeError: Failed to converge after 3 iterations. assert_raises(RuntimeError, brentq_expanding, func, args=(-50000,), maxiter_bq=3) # cannot determine whether increasing, all 4 low trial points return nan assert_raises(ValueError, brentq_expanding, func_nan, args=(-20, 0.6)) # test for full_output a = 500 val, info = brentq_expanding(func, args=(a,), full_output=True) assert_allclose(val, a, rtol=1e-5) info1 = {'iterations': 63, 'start_bounds': (-1, 1), 'brentq_bounds': (100, 1000), 'flag': 'converged', 'function_calls': 64, 'iterations_expand': 3, 'converged': True} # adjustments for scipy 0.8.0 with changed convergence criteria assert_array_less(info.__dict__['iterations'], 70) assert_array_less(info.__dict__['function_calls'], 70) for k in info1: if k in ['iterations', 'function_calls']: continue assert_equal(info1[k], info.__dict__[k]) assert_allclose(info.root, a, rtol=1e-5) statsmodels-0.12.2/statsmodels/tools/tests/test_sequences.py000066400000000000000000000031441400612667500244170ustar00rootroot00000000000000import numpy as np import numpy.testing as npt from statsmodels.tools import sequences def test_discrepancy(): space_0 = [[0.1, 0.5], [0.2, 0.4], [0.3, 0.3], [0.4, 0.2], [0.5, 0.1]] space_1 = [[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]] space_2 = [[1, 5], [2, 4], [3, 3], [4, 2], [5, 1], [6, 6]] corners = np.array([[0.5, 0.5], [6.5, 6.5]]) npt.assert_allclose(sequences.discrepancy(space_0), 0.1353, atol=1e-4) # From Fang et al. Design and modeling for computer experiments, 2006 npt.assert_allclose(sequences.discrepancy(space_1, corners), 0.0081, atol=1e-4) npt.assert_allclose(sequences.discrepancy(space_2, corners), 0.0105, atol=1e-4) def test_van_der_corput(): sample = sequences.van_der_corput(10) out = [0., 0.5, 0.25, 0.75, 0.125, 0.625, 0.375, 0.875, 0.0625, 0.5625] npt.assert_almost_equal(sample, out) sample = sequences.van_der_corput(5, start_index=3) out = [0.75, 0.125, 0.625, 0.375, 0.875] npt.assert_almost_equal(sample, out) def test_primes(): primes = sequences.primes_from_2_to(50) out = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47] npt.assert_allclose(primes, out) def test_halton(): corners = np.array([[0, 2], [10, 5]]) sample = sequences.halton(dim=2, n_sample=5, bounds=corners) out = np.array([[5., 3.], [2.5, 4.], [7.5, 2.3], [1.25, 3.3], [6.25, 4.3]]) npt.assert_almost_equal(sample, out, decimal=1) sample = sequences.halton(dim=2, n_sample=3, bounds=corners, start_index=2) out = np.array([[7.5, 2.3], [1.25, 3.3], [6.25, 4.3]]) npt.assert_almost_equal(sample, out, decimal=1) statsmodels-0.12.2/statsmodels/tools/tests/test_testing.py000066400000000000000000000014011400612667500240730ustar00rootroot00000000000000import pytest import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch, \ MarginTableTestBunch, Holder @pytest.mark.parametrize('attribute, bunch_type', (('params_table', ParamsTableTestBunch), ('margins_table', MarginTableTestBunch))) def check_params_table_classes(attribute, bunch_type): table = np.empty((10, 4)) bunch = bunch_type(**{attribute: table}) assert attribute in bunch def test_bad_table(): table = np.empty((10, 4)) with pytest.raises(AttributeError): ParamsTableTestBunch(margins_table=table) def test_holder(): holder = Holder() holder.new_attr = 1 assert hasattr(holder, 'new_attr') assert getattr(holder, 'new_attr') == 1 statsmodels-0.12.2/statsmodels/tools/tests/test_tools.py000066400000000000000000000634761400612667500236020ustar00rootroot00000000000000""" Test functions for models.tools """ from statsmodels.compat.pandas import assert_frame_equal, assert_series_equal from statsmodels.compat.python import lrange import string import numpy as np from numpy.random import standard_normal from numpy.testing import (assert_equal, assert_array_equal, assert_almost_equal, assert_string_equal) import pandas as pd import pytest from statsmodels.datasets import longley from statsmodels.tools import tools from statsmodels.tools.tools import pinv_extended # Ignore future warnings from test code pytestmark = pytest.mark.filterwarnings("ignore:categorical is deprecated:FutureWarning") @pytest.fixture(scope='module') def string_var(): string_var = [string.ascii_lowercase[0:5], string.ascii_lowercase[5:10], string.ascii_lowercase[10:15], string.ascii_lowercase[15:20], string.ascii_lowercase[20:25]] string_var *= 5 string_var = np.asarray(sorted(string_var)) series = pd.Series(string_var, name='string_var') return series class TestTools(object): def test_add_constant_list(self): x = lrange(1,5) x = tools.add_constant(x) y = np.asarray([[1,1,1,1],[1,2,3,4.]]).T assert_equal(x, y) def test_add_constant_1d(self): x = np.arange(1,5) x = tools.add_constant(x) y = np.asarray([[1,1,1,1],[1,2,3,4.]]).T assert_equal(x, y) def test_add_constant_has_constant1d(self): x = np.ones(5) x = tools.add_constant(x, has_constant='skip') assert_equal(x, np.ones((5,1))) with pytest.raises(ValueError): tools.add_constant(x, has_constant='raise') assert_equal(tools.add_constant(x, has_constant='add'), np.ones((5, 2))) def test_add_constant_has_constant2d(self): x = np.asarray([[1,1,1,1],[1,2,3,4.]]).T y = tools.add_constant(x, has_constant='skip') assert_equal(x, y) with pytest.raises(ValueError): tools.add_constant(x, has_constant='raise') assert_equal(tools.add_constant(x, has_constant='add'), np.column_stack((np.ones(4), x))) def test_add_constant_recarray(self): dt = np.dtype([('', int), ('', '>> import numpy as np >>> import statsmodels.api as sm Univariate examples >>> import string >>> string_var = [string.ascii_lowercase[0:5], ... string.ascii_lowercase[5:10], ... string.ascii_lowercase[10:15], ... string.ascii_lowercase[15:20], ... string.ascii_lowercase[20:25]] >>> string_var *= 5 >>> string_var = np.asarray(sorted(string_var)) >>> design = sm.tools.categorical(string_var, drop=True) Or for a numerical categorical variable >>> instr = np.floor(np.arange(10,60, step=2)/10) >>> design = sm.tools.categorical(instr, drop=True) With a structured array >>> num = np.random.randn(25,2) >>> struct_ar = np.zeros((25,1), ... dtype=[('var1', 'f4'),('var2', 'f4'), ... ('instrument','f4'),('str_instr','a5')]) >>> struct_ar['var1'] = num[:,0][:,None] >>> struct_ar['var2'] = num[:,1][:,None] >>> struct_ar['instrument'] = instr[:,None] >>> struct_ar['str_instr'] = string_var[:,None] >>> design = sm.tools.categorical(struct_ar, col='instrument', drop=True) Or >>> design2 = sm.tools.categorical(struct_ar, col='str_instr', drop=True) """ import warnings warnings.warn( "categorical is deprecated. Use pandas Categorical to represent " "categorical data and can get_dummies to construct dummy arrays. " "It will be removed after release 0.13.", FutureWarning ) # TODO: add a NameValidator function if isinstance(col, (list, tuple)): if len(col) == 1: col = col[0] else: raise ValueError("Can only convert one column at a time") if (not isinstance(data, (pd.DataFrame, pd.Series)) and not isinstance(col, (str, int)) and col is not None): raise TypeError('col must be a str, int or None') # Pull out a Series from a DataFrame if provided if isinstance(data, pd.DataFrame): if col is None: raise TypeError('col must be a str or int when using a DataFrame') elif col not in data: raise ValueError('Column \'{0}\' not found in data'.format(col)) data = data[col] # Set col to None since we not have a Series col = None if isinstance(data, pd.Series): if col is not None and data.name != col: raise ValueError('data.name does not match col ' '\'{0}\''.format(col)) data_cat = pd.Categorical(data) dummies = pd.get_dummies(data_cat) col_map = {i: cat for i, cat in enumerate(data_cat.categories) if cat in dummies} if not drop: dummies.columns = list(dummies.columns) dummies = pd.concat([dummies, data], 1) if dictnames: return dummies, col_map return dummies # catch recarrays and structured arrays elif data.dtype.names or data.__class__ is np.recarray: # deprecated: remove path after 0.12 import warnings from statsmodels.tools.sm_exceptions import recarray_warning warnings.warn(recarray_warning, FutureWarning) if not col and np.squeeze(data).ndim > 1: raise IndexError("col is None and the input array is not 1d") if isinstance(col, int): col = data.dtype.names[col] if col is None and data.dtype.names and len(data.dtype.names) == 1: col = data.dtype.names[0] tmp_arr = np.unique(data[col]) # if the cols are shape (#,) vs (#,1) need to add an axis and flip _swap = True if data[col].ndim == 1: tmp_arr = tmp_arr[:, None] _swap = False tmp_dummy = (tmp_arr == data[col]).astype(float) if _swap: tmp_dummy = np.squeeze(tmp_dummy).swapaxes(1, 0) if not tmp_arr.dtype.names: # how do we get to this code path? tmp_arr = [asstr2(item) for item in np.squeeze(tmp_arr)] elif tmp_arr.dtype.names: tmp_arr = [asstr2(item) for item in np.squeeze(tmp_arr.tolist())] # prepend the varname and underscore, if col is numeric attribute # lookup is lost for recarrays... if col is None: try: col = data.dtype.names[0] except: col = 'var' # TODO: the above needs to be made robust because there could be many # var_yes, var_no varaibles for instance. tmp_arr = [col + '_' + item for item in tmp_arr] # TODO: test this for rec and structured arrays!!! if drop is True: if len(data.dtype) <= 1: if tmp_dummy.shape[0] < tmp_dummy.shape[1]: tmp_dummy = np.squeeze(tmp_dummy).swapaxes(1, 0) dt = lzip(tmp_arr, [tmp_dummy.dtype.str]*len(tmp_arr)) # preserve array type return np.array(lmap(tuple, tmp_dummy.tolist()), dtype=dt).view(type(data)) data = nprf.drop_fields(data, col, usemask=False, asrecarray=type(data) is np.recarray) data = nprf.append_fields(data, tmp_arr, data=tmp_dummy, usemask=False, asrecarray=type(data) is np.recarray) return data # Catch array_like for an error elif not isinstance(data, np.ndarray): raise NotImplementedError("array_like objects are not supported") else: if isinstance(col, int): offset = data.shape[1] # need error catching here? tmp_arr = np.unique(data[:, col]) tmp_dummy = (tmp_arr[:, np.newaxis] == data[:, col]).astype(float) tmp_dummy = tmp_dummy.swapaxes(1, 0) if drop is True: offset -= 1 data = np.delete(data, col, axis=1).astype(float) data = np.column_stack((data, tmp_dummy)) if dictnames is True: col_map = _make_dictnames(tmp_arr, offset) return data, col_map return data elif col is None and np.squeeze(data).ndim == 1: tmp_arr = np.unique(data) tmp_dummy = (tmp_arr[:, None] == data).astype(float) tmp_dummy = tmp_dummy.swapaxes(1, 0) if drop is True: if dictnames is True: col_map = _make_dictnames(tmp_arr) return tmp_dummy, col_map return tmp_dummy else: data = np.column_stack((data, tmp_dummy)) if dictnames is True: col_map = _make_dictnames(tmp_arr, offset=1) return data, col_map return data else: raise IndexError("The index %s is not understood" % col) # TODO: add an axis argument to this for sysreg def add_constant(data, prepend=True, has_constant='skip'): """ Add a column of ones to an array. Parameters ---------- data : array_like A column-ordered design matrix. prepend : bool If true, the constant is in the first column. Else the constant is appended (last column). has_constant : str {'raise', 'add', 'skip'} Behavior if ``data`` already has a constant. The default will return data without adding another constant. If 'raise', will raise an error if any column has a constant value. Using 'add' will add a column of 1s if a constant column is present. Returns ------- array_like The original values with a constant (column of ones) as the first or last column. Returned value type depends on input type. Notes ----- When the input is recarray or a pandas Series or DataFrame, the added column's name is 'const'. """ if _is_using_pandas(data, None) or _is_recarray(data): if _is_recarray(data): # deprecated: remove recarray support after 0.12 import warnings from statsmodels.tools.sm_exceptions import recarray_warning warnings.warn(recarray_warning, FutureWarning) from statsmodels.tsa.tsatools import add_trend return add_trend(data, trend='c', prepend=prepend, has_constant=has_constant) # Special case for NumPy x = np.asanyarray(data) ndim = x.ndim if ndim == 1: x = x[:, None] elif x.ndim > 2: raise ValueError('Only implemented for 2-dimensional arrays') is_nonzero_const = np.ptp(x, axis=0) == 0 is_nonzero_const &= np.all(x != 0.0, axis=0) if is_nonzero_const.any(): if has_constant == 'skip': return x elif has_constant == 'raise': if ndim == 1: raise ValueError("data is constant.") else: columns = np.arange(x.shape[1]) cols = ",".join([str(c) for c in columns[is_nonzero_const]]) raise ValueError(f"Column(s) {cols} are constant.") x = [np.ones(x.shape[0]), x] x = x if prepend else x[::-1] return np.column_stack(x) def isestimable(c, d): """ True if (Q, P) contrast `c` is estimable for (N, P) design `d`. From an Q x P contrast matrix `C` and an N x P design matrix `D`, checks if the contrast `C` is estimable by looking at the rank of ``vstack([C,D])`` and verifying it is the same as the rank of `D`. Parameters ---------- c : array_like A contrast matrix with shape (Q, P). If 1 dimensional assume shape is (1, P). d : array_like The design matrix, (N, P). Returns ------- bool True if the contrast `c` is estimable on design `d`. Examples -------- >>> d = np.array([[1, 1, 1, 0, 0, 0], ... [0, 0, 0, 1, 1, 1], ... [1, 1, 1, 1, 1, 1]]).T >>> isestimable([1, 0, 0], d) False >>> isestimable([1, -1, 0], d) True """ c = array_like(c, 'c', maxdim=2) d = array_like(d, 'd', ndim=2) c = c[None, :] if c.ndim == 1 else c if c.shape[1] != d.shape[1]: raise ValueError('Contrast should have %d columns' % d.shape[1]) new = np.vstack([c, d]) if np.linalg.matrix_rank(new) != np.linalg.matrix_rank(d): return False return True def pinv_extended(x, rcond=1e-15): """ Return the pinv of an array X as well as the singular values used in computation. Code adapted from numpy. """ x = np.asarray(x) x = x.conjugate() u, s, vt = np.linalg.svd(x, False) s_orig = np.copy(s) m = u.shape[0] n = vt.shape[1] cutoff = rcond * np.maximum.reduce(s) for i in range(min(n, m)): if s[i] > cutoff: s[i] = 1./s[i] else: s[i] = 0. res = np.dot(np.transpose(vt), np.multiply(s[:, np.core.newaxis], np.transpose(u))) return res, s_orig def recipr(x): """ Reciprocal of an array with entries less than or equal to 0 set to 0. Parameters ---------- x : array_like The input array. Returns ------- ndarray The array with 0-filled reciprocals. """ x = np.asarray(x) out = np.zeros_like(x, dtype=np.float64) nans = np.isnan(x.flat) pos = ~nans pos[pos] = pos[pos] & (x.flat[pos] > 0) out.flat[pos] = 1.0 / x.flat[pos] out.flat[nans] = np.nan return out def recipr0(x): """ Reciprocal of an array with entries less than 0 set to 0. Parameters ---------- x : array_like The input array. Returns ------- ndarray The array with 0-filled reciprocals. """ x = np.asarray(x) out = np.zeros_like(x, dtype=np.float64) nans = np.isnan(x.flat) non_zero = ~nans non_zero[non_zero] = non_zero[non_zero] & (x.flat[non_zero] != 0) out.flat[non_zero] = 1.0 / x.flat[non_zero] out.flat[nans] = np.nan return out def clean0(matrix): """ Erase columns of zeros: can save some time in pseudoinverse. Parameters ---------- matrix : ndarray The array to clean. Returns ------- ndarray The cleaned array. """ colsum = np.add.reduce(matrix**2, 0) val = [matrix[:, i] for i in np.flatnonzero(colsum)] return np.array(np.transpose(val)) def fullrank(x, r=None): """ Return an array whose column span is the same as x. Parameters ---------- x : ndarray The array to adjust, 2d. r : int, optional The rank of x. If not provided, determined by `np.linalg.matrix_rank`. Returns ------- ndarray The array adjusted to have full rank. Notes ----- If the rank of x is known it can be specified as r -- no check is made to ensure that this really is the rank of x. """ if r is None: r = np.linalg.matrix_rank(x) v, d, u = np.linalg.svd(x, full_matrices=False) order = np.argsort(d) order = order[::-1] value = [] for i in range(r): value.append(v[:, order[i]]) return np.asarray(np.transpose(value)).astype(np.float64) def unsqueeze(data, axis, oldshape): """ Unsqueeze a collapsed array. Parameters ---------- data : ndarray The data to unsqueeze. axis : int The axis to unsqueeze. oldshape : tuple[int] The original shape before the squeeze or reduce operation. Returns ------- ndarray The unsqueezed array. Examples -------- >>> from numpy import mean >>> from numpy.random import standard_normal >>> x = standard_normal((3,4,5)) >>> m = mean(x, axis=1) >>> m.shape (3, 5) >>> m = unsqueeze(m, 1, x.shape) >>> m.shape (3, 1, 5) >>> """ newshape = list(oldshape) newshape[axis] = 1 return data.reshape(newshape) def nan_dot(A, B): """ Returns np.dot(left_matrix, right_matrix) with the convention that nan * 0 = 0 and nan * x = nan if x != 0. Parameters ---------- A, B : ndarray """ # Find out who should be nan due to nan * nonzero should_be_nan_1 = np.dot(np.isnan(A), (B != 0)) should_be_nan_2 = np.dot((A != 0), np.isnan(B)) should_be_nan = should_be_nan_1 + should_be_nan_2 # Multiply after setting all nan to 0 # This is what happens if there were no nan * nonzero conflicts C = np.dot(np.nan_to_num(A), np.nan_to_num(B)) C[should_be_nan] = np.nan return C def maybe_unwrap_results(results): """ Gets raw results back from wrapped results. Can be used in plotting functions or other post-estimation type routines. """ return getattr(results, '_results', results) class Bunch(dict): """ Returns a dict-like object with keys accessible via attribute lookup. Parameters ---------- *args Arguments passed to dict constructor, tuples (key, value). **kwargs Keyword agument passed to dict constructor, key=value. """ def __init__(self, *args, **kwargs): super(Bunch, self).__init__(*args, **kwargs) self.__dict__ = self def _ensure_2d(x, ndarray=False): """ Parameters ---------- x : ndarray, Series, DataFrame or None Input to verify dimensions, and to transform as necesary ndarray : bool Flag indicating whether to always return a NumPy array. Setting False will return an pandas DataFrame when the input is a Series or a DataFrame. Returns ------- out : ndarray, DataFrame or None array or DataFrame with 2 dimensiona. One dimensional arrays are returned as nobs by 1. None is returned if x is None. names : list of str or None list containing variables names when the input is a pandas datatype. Returns None if the input is an ndarray. Notes ----- Accepts None for simplicity """ if x is None: return x is_pandas = _is_using_pandas(x, None) if x.ndim == 2: if is_pandas: return x, x.columns else: return x, None elif x.ndim > 2: raise ValueError('x mst be 1 or 2-dimensional.') name = x.name if is_pandas else None if ndarray: return np.asarray(x)[:, None], name else: return pd.DataFrame(x), name def matrix_rank(m, tol=None, method="qr"): """ Matrix rank calculation using QR or SVD Parameters ---------- m : array_like A 2-d array-like object to test tol : float, optional The tolerance to use when testing the matrix rank. If not provided an appropriate value is selected. method : {"ip", "qr", "svd"} The method used. "ip" uses the inner-product of a normalized version of m and then computes the rank using NumPy's matrix_rank. "qr" uses a QR decomposition and is the default. "svd" defers to NumPy's matrix_rank. Returns ------- int The rank of m. Notes ----- When using a QR factorization, the rank is determined by the number of elements on the leading diagonal of the R matrix that are above tol in absolute value. """ m = array_like(m, "m", ndim=2) if method == "ip": m = m[:, np.any(m != 0, axis=0)] m = m / np.sqrt((m ** 2).sum(0)) m = m.T @ m return np.linalg.matrix_rank(m, tol=tol, hermitian=True) elif method == "qr": r, = scipy.linalg.qr(m, mode="r") abs_diag = np.abs(np.diag(r)) if tol is None: tol = abs_diag[0] * m.shape[1] * np.finfo(float).eps return int((abs_diag > tol).sum()) else: return np.linalg.matrix_rank(m, tol=tol) statsmodels-0.12.2/statsmodels/tools/transform_model.py000066400000000000000000000054061400612667500234210ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Tue May 27 13:23:24 2014 Author: Josef Perktold License: BSD-3 """ import numpy as np class StandardizeTransform(object): """class to reparameterize a model for standardized exog Parameters ---------- data : array_like data that is standardized along axis=0 ddof : None or int degrees of freedom for calculation of standard deviation. default is 1, in contrast to numpy.std const_idx : None or int If None, then the presence of a constant is detected if the standard deviation of a column is **equal** to zero. A constant column is not transformed. If this is an integer, then the corresponding column will not be transformed. demean : bool, default is True If demean is true, then the data will be demeaned, otherwise it will only be rescaled. Notes ----- Warning: Not all options are tested and it is written for one use case. API changes are expected. This can be used to transform only the design matrix, exog, in a model, which is required in some discrete models when the endog cannot be rescaled or demeaned. The transformation is full rank and does not drop the constant. """ def __init__(self, data, ddof=1, const_idx=None, demean=True): data = np.asarray(data) self.mean = data.mean(0) self.scale = data.std(0, ddof=1) # do not transform a constant if const_idx is None: const_idx = np.nonzero(self.scale == 0)[0] if len(const_idx) == 0: const_idx = 'nc' else: const_idx = int(const_idx) if const_idx != 'nc': self.mean[const_idx] = 0 self.scale[const_idx] = 1 if demean is False: self.mean = None self.const_idx = const_idx def transform(self, data): """standardize the data using the stored transformation """ # could use scipy.stats.zscore instead if self.mean is None: return np.asarray(data) / self.scale else: return (np.asarray(data) - self.mean) / self.scale def transform_params(self, params): """Transform parameters of the standardized model to the original model Parameters ---------- params : ndarray parameters estimated with the standardized model Returns ------- params_new : ndarray parameters transformed to the parameterization of the original model """ params_new = params / self.scale if self.const_idx != 'nc': params_new[self.const_idx] -= (params_new * self.mean).sum() return params_new __call__ = transform statsmodels-0.12.2/statsmodels/tools/validation/000077500000000000000000000000001400612667500220015ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tools/validation/__init__.py000066400000000000000000000005121400612667500241100ustar00rootroot00000000000000from .validation import ( array_like, bool_like, dict_like, float_like, int_like, PandasWrapper, required_int_like, string_like, ) __all__ = [ "array_like", "bool_like", "dict_like", "float_like", "int_like", "PandasWrapper", "required_int_like", "string_like", ] statsmodels-0.12.2/statsmodels/tools/validation/decorators.py000066400000000000000000000017311400612667500245220ustar00rootroot00000000000000from functools import wraps import numpy as np import statsmodels.tools.validation.validation as v def array_like( pos, name, dtype=np.double, ndim=None, maxdim=None, shape=None, order="C", contiguous=False, ): def inner(func): @wraps(func) def wrapper(*args, **kwargs): if pos < len(args): arg = args[pos] arg = v.array_like( arg, name, dtype, ndim, maxdim, shape, order, contiguous ) if pos == 0: args = (arg,) + args[1:] else: args = args[:pos] + (arg,) + args[pos + 1:] else: arg = kwargs[name] arg = v.array_like( arg, name, dtype, ndim, maxdim, shape, order, contiguous ) kwargs[name] = arg return func(*args, **kwargs) return wrapper return inner statsmodels-0.12.2/statsmodels/tools/validation/tests/000077500000000000000000000000001400612667500231435ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tools/validation/tests/__init__.py000066400000000000000000000000001400612667500252420ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tools/validation/tests/test_validation.py000066400000000000000000000304551400612667500267150ustar00rootroot00000000000000from collections import OrderedDict import numpy as np import pandas as pd import pytest from statsmodels.tools.validation import ( array_like, PandasWrapper, bool_like, dict_like, float_like, int_like, string_like, ) from statsmodels.tools.validation.validation import _right_squeeze @pytest.fixture(params=[True, False]) def use_pandas(request): return request.param def gen_data(dim, use_pandas): if dim == 1: out = np.empty(10,) if use_pandas: out = pd.Series(out) elif dim == 2: out = np.empty((20, 10)) if use_pandas: out = pd.DataFrame(out) else: out = np.empty(np.arange(5, 5 + dim)) return out class TestArrayLike(object): def test_1d(self, use_pandas): data = gen_data(1, use_pandas) a = array_like(data, "a") assert a.ndim == 1 assert a.shape == (10,) assert type(a) is np.ndarray a = array_like(data, "a", ndim=1) assert a.ndim == 1 a = array_like(data, "a", shape=(10,)) assert a.shape == (10,) a = array_like(data, "a", ndim=1, shape=(None,)) assert a.ndim == 1 a = array_like(data, "a", ndim=2, shape=(10, 1)) assert a.ndim == 2 assert a.shape == (10, 1) with pytest.raises(ValueError, match="a is required to have shape"): array_like(data, "a", shape=(5,)) def test_2d(self, use_pandas): data = gen_data(2, use_pandas) a = array_like(data, "a", ndim=2) assert a.ndim == 2 assert a.shape == (20, 10) assert type(a) is np.ndarray a = array_like(data, "a", ndim=2) assert a.ndim == 2 a = array_like(data, "a", ndim=2, shape=(20, None)) assert a.shape == (20, 10) a = array_like(data, "a", ndim=2, shape=(20,)) assert a.shape == (20, 10) a = array_like(data, "a", ndim=2, shape=(None, 10)) assert a.shape == (20, 10) a = array_like(data, "a", ndim=2, shape=(None, None)) assert a.ndim == 2 a = array_like(data, "a", ndim=3) assert a.ndim == 3 assert a.shape == (20, 10, 1) with pytest.raises(ValueError, match="a is required to have shape"): array_like(data, "a", ndim=2, shape=(10,)) with pytest.raises(ValueError, match="a is required to have shape"): array_like(data, "a", ndim=2, shape=(20, 20)) with pytest.raises(ValueError, match="a is required to have shape"): array_like(data, "a", ndim=2, shape=(None, 20)) match = "a is required to have ndim 1 but has ndim 2" with pytest.raises(ValueError, match=match): array_like(data, "a", ndim=1) match = "a must have ndim <= 1" with pytest.raises(ValueError, match=match): array_like(data, "a", maxdim=1) def test_3d(self): data = gen_data(3, False) a = array_like(data, "a", ndim=3) assert a.shape == (5, 6, 7) assert a.ndim == 3 assert type(a) is np.ndarray a = array_like(data, "a", ndim=3, shape=(5, None, 7)) assert a.shape == (5, 6, 7) a = array_like(data, "a", ndim=3, shape=(None, None, 7)) assert a.shape == (5, 6, 7) a = array_like(data, "a", ndim=5) assert a.shape == (5, 6, 7, 1, 1) with pytest.raises(ValueError, match="a is required to have shape"): array_like(data, "a", ndim=3, shape=(10,)) with pytest.raises(ValueError, match="a is required to have shape"): array_like(data, "a", ndim=3, shape=(None, None, 5)) match = "a is required to have ndim 2 but has ndim 3" with pytest.raises(ValueError, match=match): array_like(data, "a", ndim=2) match = "a must have ndim <= 1" with pytest.raises(ValueError, match=match): array_like(data, "a", maxdim=1) match = "a must have ndim <= 2" with pytest.raises(ValueError, match=match): array_like(data, "a", maxdim=2) def test_right_squeeze_and_pad(self): data = np.empty((2, 1, 2)) a = array_like(data, "a", ndim=3) assert a.shape == (2, 1, 2) data = np.empty((2)) a = array_like(data, "a", ndim=3) assert a.shape == (2, 1, 1) data = np.empty((2, 1)) a = array_like(data, "a", ndim=3) assert a.shape == (2, 1, 1) data = np.empty((2, 1, 1, 1)) a = array_like(data, "a", ndim=3) assert a.shape == (2, 1, 1) data = np.empty((2, 1, 1, 2, 1, 1)) with pytest.raises(ValueError): array_like(data, "a", ndim=3) def test_contiguous(self): x = np.arange(10) y = x[::2] a = array_like(y, "a", contiguous=True) assert not y.flags["C_CONTIGUOUS"] assert a.flags["C_CONTIGUOUS"] def test_dtype(self): x = np.arange(10) a = array_like(x, "a", dtype=np.float32) assert a.dtype == np.float32 a = array_like(x, "a", dtype=np.uint8) assert a.dtype == np.uint8 @pytest.mark.xfail(reason="Failing for now") def test_dot(self, use_pandas): data = gen_data(2, use_pandas) a = array_like(data, "a") assert not isinstance(a.T.dot(data), array_like) assert not isinstance(a.T.dot(a), array_like) def test_slice(self, use_pandas): data = gen_data(2, use_pandas) a = array_like(data, "a", ndim=2) assert type(a[1:]) is np.ndarray def test_right_squeeze(): x = np.empty((10, 1, 10)) y = _right_squeeze(x) assert y.shape == (10, 1, 10) x = np.empty((10, 10, 1)) y = _right_squeeze(x) assert y.shape == (10, 10) x = np.empty((10, 10, 1, 1, 1, 1, 1)) y = _right_squeeze(x) assert y.shape == (10, 10) x = np.empty((10, 1, 10, 1, 1, 1, 1, 1)) y = _right_squeeze(x) assert y.shape == (10, 1, 10) def test_wrap_pandas(use_pandas): a = gen_data(1, use_pandas) b = gen_data(1, False) wrapped = PandasWrapper(a).wrap(b) expected_type = pd.Series if use_pandas else np.ndarray assert isinstance(wrapped, expected_type) assert not use_pandas or wrapped.name is None wrapped = PandasWrapper(a).wrap(b, columns="name") assert isinstance(wrapped, expected_type) assert not use_pandas or wrapped.name == "name" wrapped = PandasWrapper(a).wrap(b, columns=["name"]) assert isinstance(wrapped, expected_type) assert not use_pandas or wrapped.name == "name" expected_type = pd.DataFrame if use_pandas else np.ndarray wrapped = PandasWrapper(a).wrap(b[:, None]) assert isinstance(wrapped, expected_type) assert not use_pandas or wrapped.columns[0] == 0 wrapped = PandasWrapper(a).wrap(b[:, None], columns=["name"]) assert isinstance(wrapped, expected_type) assert not use_pandas or wrapped.columns == ["name"] if use_pandas: match = "Can only wrap 1 or 2-d array_like" with pytest.raises(ValueError, match=match): PandasWrapper(a).wrap(b[:, None, None]) match = "obj must have the same number of elements in axis 0 as" with pytest.raises(ValueError, match=match): PandasWrapper(a).wrap(b[: b.shape[0] // 2]) def test_wrap_pandas_append(): a = gen_data(1, True) a.name = "apple" b = gen_data(1, False) wrapped = PandasWrapper(a).wrap(b, append="appended") expected = "apple_appended" assert wrapped.name == expected a = gen_data(2, True) a.columns = ["apple_" + str(i) for i in range(a.shape[1])] b = gen_data(2, False) wrapped = PandasWrapper(a).wrap(b, append="appended") expected = [c + "_appended" for c in a.columns] assert list(wrapped.columns) == expected def test_wrap_pandas_append_non_string(): # GH 6826 a = gen_data(1, True) a.name = 7 b = gen_data(1, False) wrapped = PandasWrapper(a).wrap(b, append="appended") expected = "7_appended" assert wrapped.name == expected a = gen_data(2, True) a.columns = [i for i in range(a.shape[1])] b = gen_data(2, False) wrapped = PandasWrapper(a).wrap(b, append="appended") expected = [f"{c}_appended" for c in a.columns] assert list(wrapped.columns) == expected class CustomDict(dict): pass @pytest.fixture(params=(dict, OrderedDict, CustomDict, None)) def dict_type(request): return request.param def test_optional_dict_like(dict_type): val = dict_type() if dict_type is not None else dict_type out = dict_like(val, "value", optional=True) assert isinstance(out, type(val)) def test_optional_dict_like_error(): match = r"value must be a dict or dict_like \(i.e., a Mapping\)" with pytest.raises(TypeError, match=match): dict_like([], "value", optional=True) with pytest.raises(TypeError, match=match): dict_like({"a"}, "value", optional=True) with pytest.raises(TypeError, match=match): dict_like("a", "value", optional=True) def test_string(): out = string_like("apple", "value") assert out == "apple" out = string_like("apple", "value", options=("apple", "banana", "cherry")) assert out == "apple" with pytest.raises(TypeError, match="value must be a string"): string_like(1, "value") with pytest.raises(TypeError, match="value must be a string"): string_like(b"4", "value") with pytest.raises( ValueError, match="value must be one of: 'apple'," " 'banana', 'cherry'", ): string_like("date", "value", options=("apple", "banana", "cherry")) def test_optional_string(): out = string_like("apple", "value") assert out == "apple" out = string_like("apple", "value", options=("apple", "banana", "cherry")) assert out == "apple" out = string_like(None, "value", optional=True) assert out is None out = string_like( None, "value", optional=True, options=("apple", "banana", "cherry") ) assert out is None with pytest.raises(TypeError, match="value must be a string"): string_like(1, "value", optional=True) with pytest.raises(TypeError, match="value must be a string"): string_like(b"4", "value", optional=True) @pytest.fixture(params=(1.0, 1.1, np.float32(1.2), np.array([1.2]), 1.2 + 0j)) def floating(request): return request.param @pytest.fixture(params=(np.empty(2), 1.2 + 1j, True, "3.2", None)) def not_floating(request): return request.param def test_float_like(floating): assert isinstance(float_like(floating, "floating"), float) assert isinstance(float_like(floating, "floating", optional=True), float) assert float_like(None, "floating", optional=True) is None if isinstance(floating, (int, np.integer, float, np.inexact)): assert isinstance(float_like(floating, "floating", strict=True), float) assert float_like(None, "floating", optional=True, strict=True) is None def test_not_float_like(not_floating): with pytest.raises(TypeError): float_like(not_floating, "floating") @pytest.fixture(params=(1.0, 2, np.float32(3.0), np.array([4.0]))) def integer(request): return request.param @pytest.fixture( params=( 3.2, np.float32(3.2), 3 + 2j, complex(2.3 + 0j), "apple", 1.0 + 0j, np.timedelta64(2), ) ) def not_integer(request): return request.param def test_int_like(integer): assert isinstance(int_like(integer, "integer"), int) assert isinstance(int_like(integer, "integer", optional=True), int) assert int_like(None, "floating", optional=True) is None if isinstance(integer, (int, np.integer)): assert isinstance(int_like(integer, "integer", strict=True), int) assert int_like(None, "floating", optional=True, strict=True) is None def test_not_int_like(not_integer): with pytest.raises(TypeError): int_like(not_integer, "integer") @pytest.fixture(params=[True, False, 1, 1.2, "a", ""]) def boolean(request): return request.param def test_bool_like(boolean): assert isinstance(bool_like(boolean, "boolean"), bool) assert bool_like(None, "boolean", optional=True) is None if isinstance(boolean, bool): assert isinstance(bool_like(boolean, "boolean", strict=True), bool) else: with pytest.raises(TypeError): bool_like(boolean, "boolean", strict=True) def test_not_bool_like(): with pytest.raises(TypeError): bool_like(np.array([True, True]), boolean) statsmodels-0.12.2/statsmodels/tools/validation/validation.py000066400000000000000000000340141400612667500245070ustar00rootroot00000000000000from typing import Any, Optional from collections.abc import Mapping import numpy as np import pandas as pd def _right_squeeze(arr, stop_dim=0): """ Remove trailing singleton dimensions Parameters ---------- arr : ndarray Input array stop_dim : int Dimension where checking should stop so that shape[i] is not checked for i < stop_dim Returns ------- squeezed : ndarray Array with all trailing singleton dimensions (0 or 1) removed. Singleton dimensions for dimension < stop_dim are retained. """ last = arr.ndim for s in reversed(arr.shape): if s > 1: break last -= 1 last = max(last, stop_dim) return arr.reshape(arr.shape[:last]) def array_like( obj, name, dtype=np.double, ndim=1, maxdim=None, shape=None, order=None, contiguous=False, optional=False, ): """ Convert array-like to a ndarray and check conditions Parameters ---------- obj : array_like An array, any object exposing the array interface, an object whose __array__ method returns an array, or any (nested) sequence. name : str Name of the variable to use in exceptions dtype : {None, numpy.dtype, str} Required dtype. Default is double. If None, does not change the dtype of obj (if present) or uses NumPy to automatically detect the dtype ndim : {int, None} Required number of dimensions of obj. If None, no check is performed. If the numebr of dimensions of obj is less than ndim, additional axes are inserted on the right. See examples. maxdim : {int, None} Maximum allowed dimension. Use ``maxdim`` instead of ``ndim`` when inputs are allowed to have ndim 1, 2, ..., or maxdim. shape : {tuple[int], None} Required shape obj. If None, no check is performed. Partially restricted shapes can be checked using None. See examples. order : {'C', 'F', None} Order of the array contiguous : bool Ensure that the array's data is contiguous with order ``order`` optional : bool Flag indicating whether None is allowed Returns ------- ndarray The converted input. Examples -------- Convert a list or pandas series to an array >>> import pandas as pd >>> x = [0, 1, 2, 3] >>> a = array_like(x, 'x', ndim=1) >>> a.shape (4,) >>> a = array_like(pd.Series(x), 'x', ndim=1) >>> a.shape (4,) >>> type(a.orig) pandas.core.series.Series Squeezes singleton dimensions when required >>> x = np.array(x).reshape((4, 1)) >>> a = array_like(x, 'x', ndim=1) >>> a.shape (4,) Right-appends when required size is larger than actual >>> x = [0, 1, 2, 3] >>> a = array_like(x, 'x', ndim=2) >>> a.shape (4, 1) Check only the first and last dimension of the input >>> x = np.arange(4*10*4).reshape((4, 10, 4)) >>> y = array_like(x, 'x', ndim=3, shape=(4, None, 4)) Check only the first two dimensions >>> z = array_like(x, 'x', ndim=3, shape=(4, 10)) Raises ValueError if constraints are not satisfied >>> z = array_like(x, 'x', ndim=2) Traceback (most recent call last): ... ValueError: x is required to have ndim 2 but has ndim 3 >>> z = array_like(x, 'x', shape=(10, 4, 4)) Traceback (most recent call last): ... ValueError: x is required to have shape (10, 4, 4) but has shape (4, 10, 4) >>> z = array_like(x, 'x', shape=(None, 4, 4)) Traceback (most recent call last): ... ValueError: x is required to have shape (*, 4, 4) but has shape (4, 10, 4) """ if optional and obj is None: return None arr = np.asarray(obj, dtype=dtype, order=order) if maxdim is not None: if arr.ndim > maxdim: msg = "{0} must have ndim <= {1}".format(name, maxdim) raise ValueError(msg) elif ndim is not None: if arr.ndim > ndim: arr = _right_squeeze(arr, stop_dim=ndim) elif arr.ndim < ndim: arr = np.reshape(arr, arr.shape + (1,) * (ndim - arr.ndim)) if arr.ndim != ndim: msg = "{0} is required to have ndim {1} but has ndim {2}" raise ValueError(msg.format(name, ndim, arr.ndim)) if shape is not None: for actual, req in zip(arr.shape, shape): if req is not None and actual != req: req_shape = str(shape).replace("None, ", "*, ") msg = "{0} is required to have shape {1} but has shape {2}" raise ValueError(msg.format(name, req_shape, arr.shape)) if contiguous: arr = np.ascontiguousarray(arr, dtype=dtype) return arr class PandasWrapper(object): """ Wrap array_like using the index from the original input, if pandas Parameters ---------- pandas_obj : {Series, DataFrame} Object to extract the index from for wrapping Notes ----- Raises if ``orig`` is a pandas type but obj and and ``orig`` have different numbers of elements in axis 0. Also raises if the ndim of obj is larger than 2. """ def __init__(self, pandas_obj): self._pandas_obj = pandas_obj self._is_pandas = isinstance(pandas_obj, (pd.Series, pd.DataFrame)) def wrap(self, obj, columns=None, append=None, trim_start=0, trim_end=0): """ Parameters ---------- obj : {array_like} The value to wrap like to a pandas Series or DataFrame. columns : {str, list[str]} Column names or series name, if obj is 1d. append : str String to append to the columns to create a new column name. trim_start : int The number of observations to drop from the start of the index, so that the index applied is index[trim_start:]. trim_end : int The number of observations to drop from the end of the index , so that the index applied is index[:nobs - trim_end]. Returns ------- array_like A pandas Series or DataFrame, depending on the shape of obj. """ obj = np.asarray(obj) if not self._is_pandas: return obj if obj.shape[0] + trim_start + trim_end != self._pandas_obj.shape[0]: raise ValueError( "obj must have the same number of elements in " "axis 0 as orig" ) index = self._pandas_obj.index index = index[trim_start: index.shape[0] - trim_end] if obj.ndim == 1: if columns is None: name = getattr(self._pandas_obj, "name", None) elif isinstance(columns, str): name = columns else: name = columns[0] if append is not None: name = append if name is None else f"{name}_{append}" return pd.Series(obj, name=name, index=index) elif obj.ndim == 2: if columns is None: columns = getattr(self._pandas_obj, "columns", None) if append is not None: new = [] for c in columns: new.append(append if c is None else f"{c}_{append}") columns = new return pd.DataFrame(obj, columns=columns, index=index) else: raise ValueError("Can only wrap 1 or 2-d array_like") def bool_like(value, name, optional=False, strict=False): """ Convert to bool or raise if not bool_like Parameters ---------- value : object Value to verify name : str Variable name for exceptions optional : bool Flag indicating whether None is allowed strict : bool If True, then only allow bool. If False, allow types that support casting to bool. Returns ------- converted : bool value converted to a bool """ if optional and value is None: return value extra_text = " or None" if optional else "" if strict: if isinstance(value, bool): return value else: raise TypeError("{0} must be a bool{1}".format(name, extra_text)) if hasattr(value, "squeeze") and callable(value.squeeze): value = value.squeeze() try: return bool(value) except Exception: raise TypeError( "{0} must be a bool (or bool-compatible)" "{1}".format(name, extra_text) ) def int_like( value: Any, name: str, optional: bool = False, strict: bool = False ) -> Optional[int]: """ Convert to int or raise if not int_like Parameters ---------- value : object Value to verify name : str Variable name for exceptions optional : bool Flag indicating whether None is allowed strict : bool If True, then only allow int or np.integer that are not bool. If False, allow types that support integer division by 1 and conversion to int. Returns ------- converted : int value converted to a int """ if optional and value is None: return None is_bool_timedelta = isinstance(value, (bool, np.timedelta64)) if hasattr(value, "squeeze") and callable(value.squeeze): value = value.squeeze() if isinstance(value, (int, np.integer)) and not is_bool_timedelta: return int(value) elif not strict and not is_bool_timedelta: try: if value == (value // 1): return int(value) except Exception: pass extra_text = " or None" if optional else "" raise TypeError( "{0} must be integer_like (int or np.integer, but not bool" " or timedelta64){1}".format(name, extra_text) ) def required_int_like(value: Any, name: str, strict: bool = False) -> int: """ Convert to int or raise if not int_like Parameters ---------- value : object Value to verify name : str Variable name for exceptions optional : bool Flag indicating whether None is allowed strict : bool If True, then only allow int or np.integer that are not bool. If False, allow types that support integer division by 1 and conversion to int. Returns ------- converted : int value converted to a int """ _int = int_like(value, name, optional=False, strict=strict) assert _int is not None return _int def float_like(value, name, optional=False, strict=False): """ Convert to float or raise if not float_like Parameters ---------- value : object Value to verify name : str Variable name for exceptions optional : bool Flag indicating whether None is allowed strict : bool If True, then only allow int, np.integer, float or np.inexact that are not bool or complex. If False, allow complex types with 0 imag part or any other type that is float like in the sense that it support multiplication by 1.0 and conversion to float. Returns ------- converted : float value converted to a float """ if optional and value is None: return None is_bool = isinstance(value, bool) is_complex = isinstance(value, (complex, np.complexfloating)) if hasattr(value, "squeeze") and callable(value.squeeze): value = value.squeeze() if isinstance(value, (int, np.integer, float, np.inexact)) and not ( is_bool or is_complex ): return float(value) elif not strict and is_complex: imag = np.imag(value) if imag == 0: return float(np.real(value)) elif not strict and not is_bool: try: return float(value / 1.0) except Exception: pass extra_text = " or None" if optional else "" raise TypeError( "{0} must be float_like (float or np.inexact)" "{1}".format(name, extra_text) ) def string_like(value, name, optional=False, options=None, lower=True): """ Check if object is string-like and raise if not Parameters ---------- value : object Value to verify. name : str Variable name for exceptions. optional : bool Flag indicating whether None is allowed. options : tuple[str] Allowed values for input parameter `value`. lower : bool Convert all case-based characters in `value` into lowercase. Returns ------- str The validated input Raises ------ TypeError If the value is not a string or None when optional is True. ValueError If the input is not in ``options`` when ``options`` is set. """ if value is None: return None if not isinstance(value, str): extra_text = " or None" if optional else "" raise TypeError("{0} must be a string{1}".format(name, extra_text)) if lower: value = value.lower() if options is not None and value not in options: extra_text = "If not None, " if optional else "" options_text = "'" + "', '".join(options) + "'" msg = "{0}{1} must be one of: {2}".format( extra_text, name, options_text ) raise ValueError(msg) return value def dict_like(value, name, optional=False, strict=True): """ Check if dict_like (dict, Mapping) or raise if not Parameters ---------- value : object Value to verify name : str Variable name for exceptions optional : bool Flag indicating whether None is allowed strict : bool If True, then only allow dict. If False, allow any Mapping-like object. Returns ------- converted : dict_like value """ if optional and value is None: return None if not isinstance(value, Mapping) or ( strict and not (isinstance(value, dict)) ): extra_text = "If not None, " if optional else "" strict_text = " or dict_like (i.e., a Mapping)" if strict else "" msg = "{0}{1} must be a dict{2}".format(extra_text, name, strict_text) raise TypeError(msg) return value statsmodels-0.12.2/statsmodels/tools/web.py000066400000000000000000000044301400612667500207770ustar00rootroot00000000000000""" Provides a function to open the system browser to either search or go directly to a function's reference """ from statsmodels.compat.pandas import deprecate_kwarg import webbrowser from urllib.parse import urlencode from statsmodels import __version__ BASE_URL = 'https://www.statsmodels.org/' def _generate_url(func, stable): """ Parse inputs and return a correctly formatted URL or raises ValueError if the input is not understandable """ url = BASE_URL if stable: url += 'stable/' else: url += 'devel/' if func is None: return url elif isinstance(func, str): url += 'search.html?' url += urlencode({'q': func}) url += '&check_keywords=yes&area=default' else: try: func = func func_name = func.__name__ func_module = func.__module__ if not func_module.startswith('statsmodels.'): raise ValueError('Function must be from statsmodels') url += 'generated/' url += func_module + '.' + func_name + '.html' except AttributeError: raise ValueError('Input not understood') return url @deprecate_kwarg('arg', 'func') def webdoc(func=None, stable=None): """ Opens a browser and displays online documentation Parameters ---------- func : {str, callable} Either a string to search the documentation or a function stable : bool Flag indicating whether to use the stable documentation (True) or the development documentation (False). If not provided, opens the stable documentation if the current version of statsmodels is a release Examples -------- >>> import statsmodels.api as sm Documentation site >>> sm.webdoc() Search for glm in docs >>> sm.webdoc('glm') Go to current generated help for OLS >>> sm.webdoc(sm.OLS, stable=False) Notes ----- By default, open stable documentation if the current version of statsmodels is a release. Otherwise opens the development documentation. Uses the default system browser. """ stable = __version__ if 'dev' not in __version__ else stable url_or_error = _generate_url(func, stable) webbrowser.open(url_or_error) return None statsmodels-0.12.2/statsmodels/tsa/000077500000000000000000000000001400612667500172765ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/__init__.py000066400000000000000000000001131400612667500214020ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/tsa/_bds.py000066400000000000000000000163501400612667500205640ustar00rootroot00000000000000""" BDS test for IID time series References ---------- Broock, W. A., J. A. Scheinkman, W. D. Dechert, and B. LeBaron. 1996. "A Test for Independence Based on the Correlation Dimension." Econometric Reviews 15 (3): 197-235. Kanzler, Ludwig. 1999. "Very Fast and Correctly Sized Estimation of the BDS Statistic". SSRN Scholarly Paper ID 151669. Rochester, NY: Social Science Research Network. LeBaron, Blake. 1997. "A Fast Algorithm for the BDS Statistic." Studies in Nonlinear Dynamics & Econometrics 2 (2) (January 1). """ import numpy as np from scipy import stats from statsmodels.tools.validation import array_like def distance_indicators(x, epsilon=None, distance=1.5): """ Calculate all pairwise threshold distance indicators for a time series Parameters ---------- x : 1d array observations of time series for which heaviside distance indicators are calculated epsilon : scalar, optional the threshold distance to use in calculating the heaviside indicators distance : scalar, optional if epsilon is omitted, specifies the distance multiplier to use when computing it Returns ------- indicators : 2d array matrix of distance threshold indicators Notes ----- Since this can be a very large matrix, use np.int8 to save some space. """ x = array_like(x, 'x') if epsilon is not None and epsilon <= 0: raise ValueError("Threshold distance must be positive if specified." " Got epsilon of %f" % epsilon) if distance <= 0: raise ValueError("Threshold distance must be positive." " Got distance multiplier %f" % distance) # TODO: add functionality to select epsilon optimally # TODO: and/or compute for a range of epsilons in [0.5*s, 2.0*s]? # or [1.5*s, 2.0*s]? if epsilon is None: epsilon = distance * x.std(ddof=1) return np.abs(x[:, None] - x) < epsilon def correlation_sum(indicators, embedding_dim): """ Calculate a correlation sum Useful as an estimator of a correlation integral Parameters ---------- indicators : 2d array matrix of distance threshold indicators embedding_dim : int embedding dimension Returns ------- corrsum : float Correlation sum indicators_joint matrix of joint-distance-threshold indicators """ if not indicators.ndim == 2: raise ValueError('Indicators must be a matrix') if not indicators.shape[0] == indicators.shape[1]: raise ValueError('Indicator matrix must be symmetric (square)') if embedding_dim == 1: indicators_joint = indicators else: corrsum, indicators = correlation_sum(indicators, embedding_dim - 1) indicators_joint = indicators[1:, 1:]*indicators[:-1, :-1] nobs = len(indicators_joint) corrsum = np.mean(indicators_joint[np.triu_indices(nobs, 1)]) return corrsum, indicators_joint def correlation_sums(indicators, max_dim): """ Calculate all correlation sums for embedding dimensions 1:max_dim Parameters ---------- indicators : 2d array matrix of distance threshold indicators max_dim : int maximum embedding dimension Returns ------- corrsums : 1d array Correlation sums """ corrsums = np.zeros((1, max_dim)) corrsums[0, 0], indicators = correlation_sum(indicators, 1) for i in range(1, max_dim): corrsums[0, i], indicators = correlation_sum(indicators, 2) return corrsums def _var(indicators, max_dim): """ Calculate the variance of a BDS effect Parameters ---------- indicators : 2d array matrix of distance threshold indicators max_dim : int maximum embedding dimension Returns ------- variances : float Variance of BDS effect """ nobs = len(indicators) corrsum_1dim, _ = correlation_sum(indicators, 1) k = ((indicators.sum(1)**2).sum() - 3*indicators.sum() + 2*nobs) / (nobs * (nobs - 1) * (nobs - 2)) variances = np.zeros((1, max_dim - 1)) for embedding_dim in range(2, max_dim + 1): tmp = 0 for j in range(1, embedding_dim): tmp += (k**(embedding_dim - j))*(corrsum_1dim**(2 * j)) variances[0, embedding_dim-2] = 4 * ( k**embedding_dim + 2 * tmp + ((embedding_dim - 1)**2) * (corrsum_1dim**(2 * embedding_dim)) - (embedding_dim**2) * k * (corrsum_1dim**(2 * embedding_dim - 2))) return variances, k def bds(x, max_dim=2, epsilon=None, distance=1.5): """ BDS Test Statistic for Independence of a Time Series Parameters ---------- x : ndarray Observations of time series for which bds statistics is calculated. max_dim : int The maximum embedding dimension. epsilon : {float, None}, optional The threshold distance to use in calculating the correlation sum. distance : float, optional Specifies the distance multiplier to use when computing the test statistic if epsilon is omitted. Returns ------- bds_stat : float The BDS statistic. pvalue : float The p-values associated with the BDS statistic. Notes ----- The null hypothesis of the test statistic is for an independent and identically distributed (i.i.d.) time series, and an unspecified alternative hypothesis. This test is often used as a residual diagnostic. The calculation involves matrices of size (nobs, nobs), so this test will not work with very long datasets. Implementation conditions on the first m-1 initial values, which are required to calculate the m-histories: x_t^m = (x_t, x_{t-1}, ... x_{t-(m-1)}) """ x = array_like(x, 'x', ndim=1) nobs_full = len(x) if max_dim < 2 or max_dim >= nobs_full: raise ValueError("Maximum embedding dimension must be in the range" " [2,len(x)-1]. Got %d." % max_dim) # Cache the indicators indicators = distance_indicators(x, epsilon, distance) # Get estimates of m-dimensional correlation integrals corrsum_mdims = correlation_sums(indicators, max_dim) # Get variance of effect variances, k = _var(indicators, max_dim) stddevs = np.sqrt(variances) bds_stats = np.zeros((1, max_dim - 1)) pvalues = np.zeros((1, max_dim - 1)) for embedding_dim in range(2, max_dim+1): ninitial = (embedding_dim - 1) nobs = nobs_full - ninitial # Get estimates of 1-dimensional correlation integrals # (see Kanzler footnote 10 for why indicators are truncated) corrsum_1dim, _ = correlation_sum(indicators[ninitial:, ninitial:], 1) corrsum_mdim = corrsum_mdims[0, embedding_dim - 1] # Get the intermediate values for the statistic effect = corrsum_mdim - (corrsum_1dim**embedding_dim) sd = stddevs[0, embedding_dim - 2] # Calculate the statistic: bds_stat ~ N(0,1) bds_stats[0, embedding_dim - 2] = np.sqrt(nobs) * effect / sd # Calculate the p-value (two-tailed test) pvalue = 2*stats.norm.sf(np.abs(bds_stats[0, embedding_dim - 2])) pvalues[0, embedding_dim - 2] = pvalue return np.squeeze(bds_stats), np.squeeze(pvalues) statsmodels-0.12.2/statsmodels/tsa/_innovations.pyx000066400000000000000000000122731400612667500225530ustar00rootroot00000000000000#cython: language_level=3, wraparound=False, cdivision=True, boundscheck=False import numpy as np from statsmodels.tools.validation import (array_like, PandasWrapper, int_like, float_like) def innovations_algo(acov, nobs=None, rtol=None): """ innovations_algo(acov, nobs=None, rtol=None) Innovations algorithm to convert autocovariances to MA parameters. Parameters ---------- acov : array_like Array containing autocovariances including lag 0. nobs : int, optional Number of periods to run the algorithm. If not provided, nobs is equal to the length of acovf. rtol : float, optional Tolerance used to check for convergence. Default value is 0 which will never prematurely end the algorithm. Checks after 10 iterations and stops if sigma2[i] - sigma2[i - 10] < rtol * sigma2[0]. When the stopping condition is met, the remaining values in theta and sigma2 are forward filled using the value of the final iteration. Returns ------- theta : ndarray Innovation coefficients of MA representation. Array is (nobs, q) where q is the largest index of a non-zero autocovariance. theta corresponds to the first q columns of the coefficient matrix in the common description of the innovation algorithm. sigma2 : ndarray The prediction error variance (nobs,). See Also -------- innovations_filter : Filter a series using the innovations algorithm. References ---------- .. [*] Brockwell, P.J. and Davis, R.A., 2016. Introduction to time series and forecasting. Springer. Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.macrodata.load_pandas() >>> rgdpg = data.data['realgdp'].pct_change().dropna() >>> acov = sm.tsa.acovf(rgdpg) >>> nobs = activity.shape[0] >>> theta, sigma2 = innovations_algo(acov[:4], nobs=nobs) """ cdef double[::1] v, _acov cdef double[:, ::1] theta cdef Py_ssize_t i, j, k, max_lag cdef double sub, _rtol acov = array_like(acov, 'acov', contiguous=True, ndim=1) nobs = int_like(nobs, 'nobs', optional=True) rtol = float_like(rtol, 'rtol', optional=True) _acov = acov rtol = 0.0 if rtol is None else rtol if not rtol >= 0: raise ValueError('rtol must be a non-negative float or None.') _rtol = rtol if nobs is not None and nobs < 1: raise ValueError('nobs must be a positive integer') n = acov.shape[0] if nobs is None else nobs max_lag = int(np.max(np.argwhere(acov != 0))) v = np.zeros(n + 1) v[0] = _acov[0] # Retain only the relevant columns of theta theta = np.zeros((n + 1, max_lag + 1)) for i in range(1, n): for k in range(max(i - max_lag, 0), i): sub = 0 for j in range(max(i - max_lag, 0), k): sub += theta[k, k - j] * theta[i, i - j] * v[j] theta[i, i - k] = 1. / v[k] * (_acov[i - k] - sub) v[i] = _acov[0] for j in range(max(i - max_lag, 0), i): v[i] -= theta[i, i - j] ** 2 * v[j] # Break if v has converged if i >= 10: if v[i - 10] - v[i] < v[0] * _rtol: # Forward fill all remaining values v[i + 1:] = v[i] theta[i + 1:] = theta[i] break return np.asarray(theta[:n, 1:]), np.asarray(v[:n]) def innovations_filter(endog, theta): """ innovations_filter(endog, theta) Filter observations using the innovations algorithm. Parameters ---------- endog : array_like The time series to filter (nobs,). Should be demeaned if not mean 0. theta : ndarray Innovation coefficients of MA representation. Array must be (nobs, q) where q order of the MA. Returns ------- ndarray Array of filtered innovations. See Also -------- innovations_algo : Convert autocovariances to MA parameters. References ---------- .. [*] Brockwell, P.J. and Davis, R.A., 2016. Introduction to time series and forecasting. Springer. Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.macrodata.load_pandas() >>> rgdpg = data.data['realgdp'].pct_change().dropna() >>> acov = sm.tsa.acovf(rgdpg) >>> nobs = activity.shape[0] >>> theta, sigma2 = innovations_algo(acov[:4], nobs=nobs) >>> resid = innovations_filter(rgdpg, theta) """ cdef Py_ssize_t i, j, k, n_theta, nobs cdef double[::1] _endog, u cdef double[:, ::1] _theta cdef double hat pw = PandasWrapper(endog) endog = array_like(endog, 'endog', contiguous=True, ndim=1) theta = array_like(theta, 'theta', contiguous=True, ndim=2) nobs = endog.shape[0] n_theta, k = theta.shape if nobs != n_theta: raise ValueError('theta must be (nobs, q) where q is the moder order') _endog = endog _theta = theta u = np.empty(nobs) u[0] = _endog[0] for i in range(1, nobs): hat = 0.0 for j in range(min(i, k)): hat += _theta[i, j] * u[i - j - 1] u[i] = _endog[i] - hat _u = np.asarray(u) return pw.wrap(_u) statsmodels-0.12.2/statsmodels/tsa/_stl.pyx000066400000000000000000000575241400612667500210160ustar00rootroot00000000000000#cython: language_level=3, boundscheck=False, cdivision=True, wraparound=False, initializedcheck=False """ (c) 2019 Kevin Sheppard License: NCSA/BSD-3 Clause Based on NETLIB STL code Notes: See file _stl_py.py in Git history for a pure python port for the STL FORTRAN code R.B. Cleveland, W.S.Cleveland, J.E. McRae, and I. Terpenning, STL: A Seasonal-Trend Decomposition Procedure Based on Loess, Statistics Research Report, AT&T Bell Laboratories. """ """ Notes: Docstring from STL PURPOSE STL decomposes a time series into seasonal and trend components. It returns the components and robustness weights. SYNOPSIS stl(y, n, np, ns, nt, nl, isdeg, itdeg, ildeg, nsjump, ntjump, nljump, ni, no, rw, season, trend, work) integer n, np, ns, nt, nl, isdeg, itdeg, ildeg, nsjump, ntjump, nljump, ni, no real y(n), rw(n), season(n), trend(n), work(n+2*np,5) ARGUMENTS y input, time series to be decomposed. n input, number of values in y. np input, the period of the seasonal component. For example, if the time series is monthly with a yearly cycle, then np=12. ns input, length of the seasonal smoother. The value of ns should be an odd integer greater than or equal to 3; ns>6 is recommended. As ns increases the values of the seasonal component at a given point in the seasonal cycle (e.g., January values of a monthly series with a yearly cycle) become smoother. nt input, length of the trend smoother. The value of nt should be an odd integer greater than or equal to 3; a value of nt between 1.5*np and 2*np is recommended. As nt increases the values of the trend component become smoother. nl input, length of the low-pass filter. The value of nl should be an odd integer greater than or equal to 3; the smallest odd integer greater than or equal to np is recommended. isdeg input, degree of locally-fitted polynomial in seasonal smoothing. The value is 0 or 1. itdeg input, degree of locally-fitted polynomial in trend smoothing. The value is 0 or 1. ildeg input, degree of locally-fitted polynomial in low-pass smoothing. The value is 0 or 1. nsjump input, skipping value for seasonal smoothing. The seasonal smoother skips ahead nsjump points and then linearly interpolates in between. The value of nsjump should be a positive integer; if nsjump=1, a seasonal smooth is calculated at all n points. To make the procedure run faster, a reasonable choice for nsjump is 10%-20% of ns. ntjump input, skipping value for trend smoothing. nljump input, skipping value for the low-pass filter. ni input, number of loops for updating the seasonal and trend components. The value of ni should be a positive integer. See the next argument for advice on the choice of ni. no input, number of iterations of robust fitting. The value of no should be a nonnegative integer. If the data are well behaved without outliers, then robustness iterations are not needed. In this case set no=0, and set ni=2 to 5 depending on how much security you want that the seasonal-trend looping converges. If outliers are present then no=3 is a very secure value unless the outliers are radical, in which case no=5 or even 10 might be better. If no>0 then set ni to 1 or 2. rw output, final robustness weights. All rw are 1 if no=0. season output, seasonal component. trend output, trend component. work workspace of (n+2*np)*5 locations. """ from typing import Dict, Union import pandas as pd import numpy as np from libc.math cimport fabs, sqrt, isnan, NAN from statsmodels.tsa.tsatools import freq_to_period def _is_pos_int(x, odd): valid = (isinstance(x, (int, np.integer)) and not isinstance(x, np.timedelta64)) valid = valid and not isinstance(x, (float, np.floating)) try: valid = valid and x > 0 except Exception: valid = False if valid and odd: valid = valid & (x % 2) == 1 return valid cdef class STL(object): """ STL(endog, period=None, seasonal=7, trend=None, low_pass=None, seasonal_deg=0, trend_deg=0, low_pass_deg=0, robust=False, seasonal_jump=1, trend_jump=1, low_pass_jump=1) Season-Trend decomposition using LOESS. Parameters ---------- endog : array_like Data to be decomposed. Must be squeezable to 1-d. period : {int, None}, optional Periodicity of the sequence. If None and endog is a pandas Series or DataFrame, attempts to determine from endog. If endog is a ndarray, period must be provided. seasonal : int, optional Length of the seasonal smoother. Must be an odd integer, and should normally be >= 7 (default). trend : {int, None}, optional Length of the trend smoother. Must be an odd integer. If not provided uses the smallest odd integer greater than 1.5 * period / (1 - 1.5 / seasonal), following the suggestion in the original implementation. low_pass : {int, None}, optional Length of the low-pass filter. Must be an odd integer >=3. If not provided, uses the smallest odd integer > period. seasonal_deg : int, optional Degree of seasonal LOESS. 0 (constant) or 1 (constant and trend). trend_deg : int, optional Degree of trend LOESS. 0 (constant) or 1 (constant and trend). low_pass_deg : int, optional Degree of low pass LOESS. 0 (constant) or 1 (constant and trend). robust : bool, optional Flag indicating whether to use a weighted version that is robust to some forms of outliers. seasonal_jump : int, optional Positive integer determining the linear interpolation step. If larger than 1, the LOESS is used every seasonal_jump points and linear interpolation is between fitted points. Higher values reduce estimation time. trend_jump : int, optional Positive integer determining the linear interpolation step. If larger than 1, the LOESS is used every trend_jump points and values between the two are linearly interpolated. Higher values reduce estimation time. low_pass_jump : int, optional Positive integer determining the linear interpolation step. If larger than 1, the LOESS is used every low_pass_jump points and values between the two are linearly interpolated. Higher values reduce estimation time. See Also -------- statsmodels.tsa.seasonal.DecomposeResult statsmodels.tsa.seasonal.seasonal_decompose Notes ----- Derived from the NETLIB fortran written by [1]_. The original code contains a bug that appears in the determination of the median that is used in the robust weighting. This version matches the fixed version that uses a correct partitioned sort to determine the median. References ---------- .. [1] R. B. Cleveland, W. S. Cleveland, J.E. McRae, and I. Terpenning (1990) STL: A Seasonal-Trend Decomposition Procedure Based on LOESS. Journal of Official Statistics, 6, 3-73. Examples -------- The original example uses STL to decompose CO2 data into level, season and a residual. Start by aggregating to monthly, and filling any missing values >>> from statsmodels.datasets import co2 >>> import matplotlib.pyplot as plt >>> from pandas.plotting import register_matplotlib_converters >>> register_matplotlib_converters() >>> data = co2.load(True).data >>> data = data.resample('M').mean().ffill() The period (12) is automatically detected from the data's frequency ('M'). >>> from statsmodels.tsa.seasonal import STL >>> res = STL(data).fit() >>> res.plot() >>> plt.show() .. plot:: plots/stl_plot.py """ cdef object endog cdef Py_ssize_t nobs cdef int _period, seasonal, trend, low_pass, seasonal_deg, trend_deg cdef int low_pass_deg, low_pass_jump, trend_jump, seasonal_jump cdef bint robust, _use_rw cdef double[::1] _ya, _trend, _season, _rw cdef double[:, ::1] _work def __init__(self, endog, period=None, seasonal=7, trend=None, low_pass=None, seasonal_deg=1, trend_deg=1, low_pass_deg=1, robust=False, seasonal_jump=1, trend_jump=1, low_pass_jump=1): self.endog = endog y = np.ascontiguousarray(np.squeeze(np.asarray(endog)), dtype=np.double) if y.ndim != 1: raise ValueError('y must be a 1d array') self._ya = y self.nobs = y.shape[0] # n if period is None: freq = None if isinstance(endog, (pd.Series, pd.DataFrame)): freq = getattr(endog.index, 'inferred_freq', None) if freq is None: raise ValueError('Unable to determine period from endog') period = freq_to_period(freq) if not _is_pos_int(period, False) or period < 2: raise ValueError('period must be a positive integer >= 2') self._period = period # np if not _is_pos_int(seasonal, True) or seasonal < 3: raise ValueError('seasonal must be an odd positive integer >= 3') self.seasonal = seasonal # ns if trend is None: trend = int(np.ceil(1.5 * self._period / (1 - 1.5 / self.seasonal))) # ensure odd trend += ((trend % 2) == 0) if not _is_pos_int(trend, True) or trend < 3 or trend <= period: raise ValueError('trend must be an odd positive integer ' '>= 3 where trend > period') self.trend = trend # nt if low_pass is None: low_pass = self._period + 1 low_pass += ((low_pass % 2) == 0) if not _is_pos_int(low_pass, True) or \ low_pass < 3 or low_pass <= period: raise ValueError('low_pass must be an odd positive integer >= 3 ' 'where low_pass > period') self.low_pass = low_pass # nl self.seasonal_deg = seasonal_deg # isdeg self.trend_deg = trend_deg # itdeg self.low_pass_deg = low_pass_deg # ildeg self.robust = robust if not _is_pos_int(low_pass_jump, False): raise ValueError('low_pass_jump must be a positve integer') if not _is_pos_int(seasonal_jump, False): raise ValueError('seasonal_jump must be a positve integer') if not _is_pos_int(trend_jump, False): raise ValueError('trend_jump must be a positve integer') self.low_pass_jump = low_pass_jump self.seasonal_jump = seasonal_jump self.trend_jump = trend_jump self._use_rw = False self._trend = np.zeros(self.nobs) self._season = np.zeros(self.nobs) self._rw = np.ones(self.nobs) self._work = np.zeros((7, self.nobs + 2 * period)) def __reduce__(self): args = ( self.endog, self._period, self.seasonal, self.trend, self.low_pass, self.seasonal_deg, self.trend_deg, self.low_pass_deg, self.robust, self.seasonal_jump, self.trend_jump, self.low_pass_jump, ) return (STL, args) @property def period(self) -> int: """The period length of the time series""" return self._period @property def config(self) -> Dict[str, Union[int, bool]]: """ The parameters used in the model. Returns ------- dict[str, Union[int, bool]] The values used in the STL decomposition. """ return dict(period=self._period, seasonal=self.seasonal, seasonal_deg=self.seasonal_deg, seasonal_jump=self.seasonal_jump, trend=self.trend, trend_deg=self.trend_deg, trend_jump=self.trend_jump, low_pass=self.low_pass, low_pass_deg=self.low_pass_deg, low_pass_jump=self.low_pass_jump, robust=self.robust) def fit(self, inner_iter=None, outer_iter=None): """ fit(inner_iter=None, outer_iter=None) Estimate season, trend and residuals components. Parameters ---------- inner_iter : {int, None}, optional Number of iterations to perform in the inner loop. If not provided uses 2 if ``robust`` is True, or 5 if not. outer_iter : {int, None}, optional Number of iterations to perform in the outer loop. If not provided uses 15 if ``robust`` is True, or 0 if not. Returns ------- DecomposeResult Estimation results. """ cdef Py_ssize_t i if inner_iter is None: inner_iter = 2 if self.robust else 5 if outer_iter is None: outer_iter = 15 if self.robust else 0 self._use_rw = False k = 0 for i in range(self.nobs): self._season[i] = self._trend[i] = 0.0 self._rw[i] = 1.0 while True: self._onestp(inner_iter) k = k + 1 if k > outer_iter: break for i in range(self.nobs): self._work[0, i] = self._trend[i] + self._season[i] self._rwts() self._use_rw = True # Return pandas if pandas season = np.asarray(self._season) trend = np.asarray(self._trend) rw = np.asarray(self._rw) resid = self._ya - season - trend if isinstance(self.endog, (pd.Series, pd.DataFrame)): index = self.endog.index resid = pd.Series(resid, index=index, name='resid') season = pd.Series(season, index=index, name='season') trend = pd.Series(trend, index=index, name='trend') rw = pd.Series(rw, index=index, name='robust_weight') # Avoid circular imports from statsmodels.tsa.seasonal import DecomposeResult return DecomposeResult(self.endog, season, trend, resid, rw) cdef void _onestp(self, int inner_iter): """ y, n, np, ns, nt, nl, isdeg, itdeg, ildeg, nsjump, ntjump, nljump, ni, userw, rw, season, trend, work -> self._ya, self.nobs, self._period, self.seasonal, self.trend, self.low_pass, self.seasonal_deg, self.trend_deg, self.low_pass_deg, self.seasonal_jump, self.trend_jump, self.low_pass_jump, inner_iter, userw, self._rw, self._season, self._trend, self._work """ cdef Py_ssize_t i, j, np cdef double[:, ::1] work cdef double[::1] y, season, trend, rw # Original variable names work = self._work y = self._ya trend = self._trend n = self.nobs nl = self.low_pass ildeg = self.low_pass_deg nljump = self.low_pass_jump np = self._period season = self._season nt = self.trend itdeg = self.trend_deg ntjump = self.trend_jump rw = self._rw for j in range(inner_iter): for i in range(self.nobs): work[0, i] = y[i] - trend[i] self._ss() self._fts() self._ess(work[2, :], n, nl, ildeg, nljump, False, work[3, :], work[0, :], work[4, :]) for i in range(self.nobs): season[i] = work[1, np+i] - work[0, i] work[0, i] = y[i] - season[i] self._ess(work[0, :], n, nt, itdeg, ntjump, self._use_rw, rw, trend, work[2, :]) cdef double _est(self, double[::1] y, int n, int len_, int ideg, int xs, int nleft, int nright, double[::1] w, bint userw, double[::1] rw): cdef double rng, a, b, c, h, h1, h9, r, ys cdef Py_ssize_t j # Removed ok and ys, which are scalar return values rng = n - 1.0 h = max(xs - nleft, nright - xs) if len_ > n: h += (len_ - n) // 2.0 h9 = .999 * h h1 = .001 * h a = 0.0 for j in range(nleft - 1, nright): w[j] = 0. r = fabs(j + 1 - xs) if r <= h9: if r <= h1: w[j] = 1.0 else: w[j] = (1.0 - (r / h) ** 3) ** 3 if userw: w[j] = w[j] * rw[j] a = a + w[j] if a <= 0: return NAN for j in range(nleft - 1, nright): w[j] = w[j] / a if h > 0 and ideg > 0: a = 0.0 for j in range(nleft - 1, nright): a = a + w[j] * (j + 1) b = xs - a c = 0.0 for j in range(nleft - 1, nright): c = c + w[j] * (j + 1 - a) ** 2 if sqrt(c) > .001 * rng: b = b / c for j in range(nleft - 1, nright): w[j] = w[j] * (b * (j + 1 - a) + 1.0) ys = 0.0 for j in range(nleft - 1, nright): ys = ys + w[j] * y[j] return ys cdef void _ess(self, double[::1] y, int n, int len_, int ideg, int njump, bint userw, double[::1] rw, double[::1] ys, double[::1] res): # TODO: Try with 1 data point!!? Establish minimums cdef Py_ssize_t i, j, k cdef double delta cdef int newnj, nleft, nright, nsh cdef bint ok if n < 2: ys[0] = y[0] return newnj = min(njump, n - 1) if len_ >= n: nleft = 1 nright = n i = 0 while i < n: # formerly: for i in range(0, n, newnj): ys[i] = self._est(y, n, len_, ideg, i + 1, nleft, nright, res, userw, rw) if isnan(ys[i]): ys[i] = y[i] i += newnj elif newnj == 1: nsh = (len_ + 2) // 2 nleft = 1 nright = len_ for i in range(n): if (i + 1) > nsh and nright != n: nleft = nleft + 1 nright = nright + 1 ys[i] = self._est(y, n, len_, ideg, i + 1, nleft, nright, res, userw, rw) if isnan(ys[i]): ys[i] = y[i] else: nsh = (len_ + 1) // 2 i = 0 while i < n: # formerly: for i in range(0, n, newnj): if (i + 1) < nsh: nleft = 1 nright = len_ elif (i + 1) >= (n - nsh + 1): nleft = n - len_ + 1 nright = n else: nleft = i + 1 - nsh + 1 nright = len_ + i + 1 - nsh ys[i] = self._est(y, n, len_, ideg, i + 1, nleft, nright, res, userw, rw) if isnan(ys[i]): ys[i] = y[i] i += newnj if newnj == 1: return # newnj > 1 i = 0 while i < (n - newnj): # Formerly: for i in range(0, n - newnj, newnj): delta = (ys[i + newnj] - ys[i]) / newnj for j in range(i, i + newnj): ys[j] = ys[i] + delta * ((j + 1) - (i + 1)) i += newnj k = ((n - 1) // newnj) * newnj + 1 if k != n: ys[n - 1] = self._est(y, n, len_, ideg, n, nleft, nright, res, userw, rw) if isnan(ys[n - 1]): ys[n - 1] = y[n - 1] if k != (n - 1): delta = (ys[n - 1] - ys[k - 1]) / (n - k) for j in range(k, n): ys[j] = ys[k - 1] + delta * ((j + 1) - k) cdef void _ma(self, double[::1] x, int n, int len_, double[::1] ave): cdef int newn cdef double flen, v cdef Py_ssize_t i, j, k, m newn = n - len_ + 1 flen = float(len_) v = 0.0 for i in range(len_): v = v + x[i] ave[0] = v / flen k = len_ m = 0 for j in range(1, newn): v += x[k] - x[m] ave[j] = v / flen k += 1 m += 1 cdef void _fts(self): """ Original def: _fts(self, x, n, np, trend, work) Only call: fts(work[1, :], n + 2 * np, np, work[2, :], work[0, :]) """ cdef double[::1] x, trend, work cdef int n, np x = self._work[1, :] n = self.nobs + 2 * self._period np = self._period trend = self._work[2, :] work = self._work[0, :] self._ma(x, n, np, trend) self._ma(trend, n - np + 1, np, work) self._ma(work, n - 2 * np + 2, 3, trend) cdef void _ss(self): """ _ss(self, y, n, np, ns, isdeg, nsjump, userw, rw, season, work1, work2, work3, work4) ss(work[0, :], n, np, ns, isdeg, nsjump, userw, rw, work[1, :], work[2, :], work[3, :], work[4, :], season) """ cdef Py_ssize_t i, j, m cdef int n, np, ns, isdef, nsjump, k cdef bint userw cdef double[::1] y, work1, work2, work3, work4, rw, season # Original variable names y = self._work[0, :] n = self.nobs np = self._period ns = self.seasonal isdeg = self.seasonal_deg nsjump = self.seasonal_jump rw = self._rw season = self._work[1, :] work1 = self._work[2, :] work2 = self._work[3, :] work3 = self._work[4, :] work4 = self._season userw = self._use_rw for j in range(np): k = (n - (j + 1)) // np + 1 for i in range(k): work1[i] = y[i * np + j] if userw: for i in range(k): work3[i] = rw[i * np + j] self._ess(work1, k, ns, isdeg, nsjump, userw, work3, work2[1:], work4) xs = 0 nright = min(ns, k) work2[0] = self._est(work1, k, ns, isdeg, xs, 1, nright, work4, userw, work3) if isnan(work2[0]): work2[0] = work2[1] xs = k + 1 nleft = max(1, k - ns + 1) work2[k + 1] = self._est(work1, k, ns, isdeg, xs, nleft, k, work4, userw, work3) if isnan(work2[k + 1]): work2[k + 1] = work2[k] for m in range(k + 2): season[m * np + j] = work2[m] cdef void _rwts(self): """ y, n, fit, rw -> self._ya, self.nobs, self._work[0, :], self._rw """ cdef Py_ssize_t i cdef double [::1] y, fit, rw cdef double cmad, c1, c9 cdef int n # Original variable names y = self._ya n = self.nobs fit = self._work[0, :] rw = self._rw for i in range(self.nobs): rw[i] = fabs(y[i] - fit[i]) mid = np.empty(2, dtype=int) mid[0] = n // 2 mid[1] = n - mid[0] - 1 rw_part = np.partition(rw, mid) cmad = 3.0 * (rw_part[mid[0]] + rw_part[mid[1]]) if cmad == 0: for i in range(self.nobs): rw[i] = 1 return c9 = .999 * cmad c1 = .001 * cmad for i in range(self.nobs): if rw[i] <= c1: rw[i] = 1.0 elif rw[i] <= c9: rw[i] = (1.0 - (rw[i] / cmad) ** 2) ** 2 else: rw[i] = 0.0 statsmodels-0.12.2/statsmodels/tsa/adfvalues.py000066400000000000000000000376331400612667500216360ustar00rootroot00000000000000from scipy.stats import norm from numpy import array, polyval, inf, asarray __all__ = ['mackinnonp', 'mackinnoncrit'] # These are the cut-off values for the left-tail vs. the rest of the # tau distribution, for getting the p-values tau_star_nc = [-1.04, -1.53, -2.68, -3.09, -3.07, -3.77] tau_min_nc = [-19.04, -19.62, -21.21, -23.25, -21.63, -25.74] tau_max_nc = [inf, 1.51, 0.86, 0.88, 1.05, 1.24] tau_star_c = [-1.61, -2.62, -3.13, -3.47, -3.78, -3.93] tau_min_c = [-18.83, -18.86, -23.48, -28.07, -25.96, -23.27] tau_max_c = [2.74, 0.92, 0.55, 0.61, 0.79, 1] tau_star_ct = [-2.89, -3.19, -3.50, -3.65, -3.80, -4.36] tau_min_ct = [-16.18, -21.15, -25.37, -26.63, -26.53, -26.18] tau_max_ct = [0.7, 0.63, 0.71, 0.93, 1.19, 1.42] tau_star_ctt = [-3.21, -3.51, -3.81, -3.83, -4.12, -4.63] tau_min_ctt = [-17.17, -21.1, -24.33, -24.03, -24.33, -28.22] tau_max_ctt = [0.54, 0.79, 1.08, 1.43, 3.49, 1.92] _tau_maxs = { "nc": tau_max_nc, "c": tau_max_c, "ct": tau_max_ct, "ctt": tau_max_ctt, } _tau_mins = { "nc": tau_min_nc, "c": tau_min_c, "ct": tau_min_ct, "ctt": tau_min_ctt, } _tau_stars = { "nc": tau_star_nc, "c": tau_star_c, "ct": tau_star_ct, "ctt": tau_star_ctt, } small_scaling = array([1, 1, 1e-2]) tau_nc_smallp = [ [0.6344, 1.2378, 3.2496], [1.9129, 1.3857, 3.5322], [2.7648, 1.4502, 3.4186], [3.4336, 1.4835, 3.19], [4.0999, 1.5533, 3.59], [4.5388, 1.5344, 2.9807]] tau_nc_smallp = asarray(tau_nc_smallp)*small_scaling tau_c_smallp = [ [2.1659, 1.4412, 3.8269], [2.92, 1.5012, 3.9796], [3.4699, 1.4856, 3.164], [3.9673, 1.4777, 2.6315], [4.5509, 1.5338, 2.9545], [5.1399, 1.6036, 3.4445]] tau_c_smallp = asarray(tau_c_smallp)*small_scaling tau_ct_smallp = [ [3.2512, 1.6047, 4.9588], [3.6646, 1.5419, 3.6448], [4.0983, 1.5173, 2.9898], [4.5844, 1.5338, 2.8796], [5.0722, 1.5634, 2.9472], [5.53, 1.5914, 3.0392]] tau_ct_smallp = asarray(tau_ct_smallp)*small_scaling tau_ctt_smallp = [ [4.0003, 1.658, 4.8288], [4.3534, 1.6016, 3.7947], [4.7343, 1.5768, 3.2396], [5.214, 1.6077, 3.3449], [5.6481, 1.6274, 3.3455], [5.9296, 1.5929, 2.8223]] tau_ctt_smallp = asarray(tau_ctt_smallp)*small_scaling _tau_smallps = { "nc": tau_nc_smallp, "c": tau_c_smallp, "ct": tau_ct_smallp, "ctt": tau_ctt_smallp, } large_scaling = array([1, 1e-1, 1e-1, 1e-2]) tau_nc_largep = [ [0.4797, 9.3557, -0.6999, 3.3066], [1.5578, 8.558, -2.083, -3.3549], [2.2268, 6.8093, -3.2362, -5.4448], [2.7654, 6.4502, -3.0811, -4.4946], [3.2684, 6.8051, -2.6778, -3.4972], [3.7268, 7.167, -2.3648, -2.8288]] tau_nc_largep = asarray(tau_nc_largep)*large_scaling tau_c_largep = [ [1.7339, 9.3202, -1.2745, -1.0368], [2.1945, 6.4695, -2.9198, -4.2377], [2.5893, 4.5168, -3.6529, -5.0074], [3.0387, 4.5452, -3.3666, -4.1921], [3.5049, 5.2098, -2.9158, -3.3468], [3.9489, 5.8933, -2.5359, -2.721]] tau_c_largep = asarray(tau_c_largep)*large_scaling tau_ct_largep = [ [2.5261, 6.1654, -3.7956, -6.0285], [2.85, 5.272, -3.6622, -5.1695], [3.221, 5.255, -3.2685, -4.1501], [3.652, 5.9758, -2.7483, -3.2081], [4.0712, 6.6428, -2.3464, -2.546], [4.4735, 7.1757, -2.0681, -2.1196]] tau_ct_largep = asarray(tau_ct_largep)*large_scaling tau_ctt_largep = [ [3.0778, 4.9529, -4.1477, -5.9359], [3.4713, 5.967, -3.2507, -4.2286], [3.8637, 6.7852, -2.6286, -3.1381], [4.2736, 7.6199, -2.1534, -2.4026], [4.6679, 8.2618, -1.822, -1.9147], [5.0009, 8.3735, -1.6994, -1.6928]] tau_ctt_largep = asarray(tau_ctt_largep)*large_scaling _tau_largeps = { "nc": tau_nc_largep, "c": tau_c_largep, "ct": tau_ct_largep, "ctt": tau_ctt_largep, } # NOTE: The Z-statistic is used when lags are included to account for # serial correlation in the error term z_star_nc = [-2.9, -8.7, -14.8, -20.9, -25.7, -30.5] z_star_c = [-8.9, -14.3, -19.5, -25.1, -29.6, -34.4] z_star_ct = [-15.0, -19.6, -25.3, -29.6, -31.8, -38.4] z_star_ctt = [-20.7, -25.3, -29.9, -34.4, -38.5, -44.2] # These are Table 5 from MacKinnon (1994) # small p is defined as p in .005 to .150 ie p = .005 up to z_star # Z* is the largest value for which it is appropriate to use these # approximations # the left tail approximation is # p = norm.cdf(d_0 + d_1*log(abs(z)) + d_2*log(abs(z))**2 + d_3*log(abs(z))**3) # there is no Z-min, ie., it is well-behaved in the left tail z_nc_smallp = array([ [.0342, -.6376, 0, -.03872], [1.3426, -.7680, 0, -.04104], [3.8607, -2.4159, .51293, -.09835], [6.1072, -3.7250, .85887, -.13102], [7.7800, -4.4579, 1.00056, -.14014], [4.0253, -.8815, 0, -.04887]]) z_c_smallp = array([ [2.2142, -1.7863, .32828, -.07727], [1.1662, .1814, -.36707, 0], [6.6584, -4.3486, 1.04705, -.15011], [3.3249, -.8456, 0, -.04818], [4.0356, -.9306, 0, -.04776], [13.9959, -8.4314, 1.97411, -.22234]]) z_ct_smallp = array([ [4.6476, -2.8932, 0.5832, -0.0999], [7.2453, -4.7021, 1.127, -.15665], [3.4893, -0.8914, 0, -.04755], [1.6604, 1.0375, -0.53377, 0], [2.006, 1.1197, -0.55315, 0], [11.1626, -5.6858, 1.21479, -.15428]]) z_ctt_smallp = array([ [3.6739, -1.1549, 0, -0.03947], [3.9783, -1.0619, 0, -0.04394], [2.0062, 0.8907, -0.51708, 0], [4.9218, -1.0663, 0, -0.04691], [5.1433, -0.9877, 0, -0.04993], [23.6812, -14.6485, 3.42909, -.33794]]) # These are Table 6 from MacKinnon (1994). # These are well-behaved in the right tail. # the approximation function is # p = norm.cdf(d_0 + d_1 * z + d_2*z**2 + d_3*z**3 + d_4*z**4) z_large_scaling = array([1, 1e-1, 1e-2, 1e-3, 1e-5]) z_nc_largep = array([ [0.4927, 6.906, 13.2331, 12.099, 0], [1.5167, 4.6859, 4.2401, 2.7939, 7.9601], [2.2347, 3.9465, 2.2406, 0.8746, 1.4239], [2.8239, 3.6265, 1.6738, 0.5408, 0.7449], [3.3174, 3.3492, 1.2792, 0.3416, 0.3894], [3.729, 3.0611, 0.9579, 0.2087, 0.1943]]) z_nc_largep *= z_large_scaling z_c_largep = array([ [1.717, 5.5243, 4.3463, 1.6671, 0], [2.2394, 4.2377, 2.432, 0.9241, 0.4364], [2.743, 3.626, 1.5703, 0.4612, 0.567], [3.228, 3.3399, 1.2319, 0.3162, 0.3482], [3.6583, 3.0934, 0.9681, 0.2111, 0.1979], [4.0379, 2.8735, 0.7694, 0.1433, 0.1146]]) z_c_largep *= z_large_scaling z_ct_largep = array([ [2.7117, 4.5731, 2.2868, 0.6362, 0.5], [3.0972, 4.0873, 1.8982, 0.5796, 0.7384], [3.4594, 3.6326, 1.4284, 0.3813, 0.4325], [3.806, 3.2634, 1.0689, 0.2402, 0.2304], [4.1402, 2.9867, 0.8323, 0.16, 0.1315], [4.4497, 2.7534, 0.6582, 0.1089, 0.0773]]) z_ct_largep *= z_large_scaling z_ctt_largep = array([ [3.4671, 4.3476, 1.9231, 0.5381, 0.6216], [3.7827, 3.9421, 1.5699, 0.4093, 0.4485], [4.052, 3.4947, 1.1772, 0.2642, 0.2502], [4.3311, 3.1625, 0.9126, 0.1775, 0.1462], [4.594, 2.8739, 0.707, 0.1181, 0.0838], [4.8479, 2.6447, 0.5647, 0.0827, 0.0518]]) z_ctt_largep *= z_large_scaling # TODO: finish this and then integrate them into adf function def mackinnonp(teststat, regression="c", N=1, lags=None): """ Returns MacKinnon's approximate p-value for teststat. Parameters ---------- teststat : float "T-value" from an Augmented Dickey-Fuller regression. regression : str {"c", "nc", "ct", "ctt"} This is the method of regression that was used. Following MacKinnon's notation, this can be "c" for constant, "nc" for no constant, "ct" for constant and trend, and "ctt" for constant, trend, and trend-squared. N : int The number of series believed to be I(1). For (Augmented) Dickey- Fuller N = 1. Returns ------- p-value : float The p-value for the ADF statistic estimated using MacKinnon 1994. References ---------- .. [*] MacKinnon, J.G. 1994 "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests." Journal of Business & Economics Statistics, 12.2, 167-76. Notes ----- For (A)DF H_0: AR coefficient = 1 H_a: AR coefficient < 1 """ maxstat = _tau_maxs[regression] minstat = _tau_mins[regression] starstat = _tau_stars[regression] if teststat > maxstat[N-1]: return 1.0 elif teststat < minstat[N-1]: return 0.0 if teststat <= starstat[N-1]: tau_coef = _tau_smallps[regression][N-1] else: # Note: above is only for z stats tau_coef = _tau_largeps[regression][N-1] return norm.cdf(polyval(tau_coef[::-1], teststat)) # These are the new estimates from MacKinnon 2010 # the first axis is N -1 # the second axis is 1 %, 5 %, 10 % # the last axis is the coefficients tau_nc_2010 = [[ [-2.56574, -2.2358, -3.627, 0], # N = 1 [-1.94100, -0.2686, -3.365, 31.223], [-1.61682, 0.2656, -2.714, 25.364]]] tau_nc_2010 = asarray(tau_nc_2010) tau_c_2010 = [ [[-3.43035, -6.5393, -16.786, -79.433], # N = 1, 1% [-2.86154, -2.8903, -4.234, -40.040], # 5 % [-2.56677, -1.5384, -2.809, 0]], # 10 % [[-3.89644, -10.9519, -33.527, 0], # N = 2 [-3.33613, -6.1101, -6.823, 0], [-3.04445, -4.2412, -2.720, 0]], [[-4.29374, -14.4354, -33.195, 47.433], # N = 3 [-3.74066, -8.5632, -10.852, 27.982], [-3.45218, -6.2143, -3.718, 0]], [[-4.64332, -18.1031, -37.972, 0], # N = 4 [-4.09600, -11.2349, -11.175, 0], [-3.81020, -8.3931, -4.137, 0]], [[-4.95756, -21.8883, -45.142, 0], # N = 5 [-4.41519, -14.0405, -12.575, 0], [-4.13157, -10.7417, -3.784, 0]], [[-5.24568, -25.6688, -57.737, 88.639], # N = 6 [-4.70693, -16.9178, -17.492, 60.007], [-4.42501, -13.1875, -5.104, 27.877]], [[-5.51233, -29.5760, -69.398, 164.295], # N = 7 [-4.97684, -19.9021, -22.045, 110.761], [-4.69648, -15.7315, -5.104, 27.877]], [[-5.76202, -33.5258, -82.189, 256.289], # N = 8 [-5.22924, -23.0023, -24.646, 144.479], [-4.95007, -18.3959, -7.344, 94.872]], [[-5.99742, -37.6572, -87.365, 248.316], # N = 9 [-5.46697, -26.2057, -26.627, 176.382], [-5.18897, -21.1377, -9.484, 172.704]], [[-6.22103, -41.7154, -102.680, 389.33], # N = 10 [-5.69244, -29.4521, -30.994, 251.016], [-5.41533, -24.0006, -7.514, 163.049]], [[-6.43377, -46.0084, -106.809, 352.752], # N = 11 [-5.90714, -32.8336, -30.275, 249.994], [-5.63086, -26.9693, -4.083, 151.427]], [[-6.63790, -50.2095, -124.156, 579.622], # N = 12 [-6.11279, -36.2681, -32.505, 314.802], [-5.83724, -29.9864, -2.686, 184.116]]] tau_c_2010 = asarray(tau_c_2010) tau_ct_2010 = [ [[-3.95877, -9.0531, -28.428, -134.155], # N = 1 [-3.41049, -4.3904, -9.036, -45.374], [-3.12705, -2.5856, -3.925, -22.380]], [[-4.32762, -15.4387, -35.679, 0], # N = 2 [-3.78057, -9.5106, -12.074, 0], [-3.49631, -7.0815, -7.538, 21.892]], [[-4.66305, -18.7688, -49.793, 104.244], # N = 3 [-4.11890, -11.8922, -19.031, 77.332], [-3.83511, -9.0723, -8.504, 35.403]], [[-4.96940, -22.4694, -52.599, 51.314], # N = 4 [-4.42871, -14.5876, -18.228, 39.647], [-4.14633, -11.2500, -9.873, 54.109]], [[-5.25276, -26.2183, -59.631, 50.646], # N = 5 [-4.71537, -17.3569, -22.660, 91.359], [-4.43422, -13.6078, -10.238, 76.781]], [[-5.51727, -29.9760, -75.222, 202.253], # N = 6 [-4.98228, -20.3050, -25.224, 132.03], [-4.70233, -16.1253, -9.836, 94.272]], [[-5.76537, -33.9165, -84.312, 245.394], # N = 7 [-5.23299, -23.3328, -28.955, 182.342], [-4.95405, -18.7352, -10.168, 120.575]], [[-6.00003, -37.8892, -96.428, 335.92], # N = 8 [-5.46971, -26.4771, -31.034, 220.165], [-5.19183, -21.4328, -10.726, 157.955]], [[-6.22288, -41.9496, -109.881, 466.068], # N = 9 [-5.69447, -29.7152, -33.784, 273.002], [-5.41738, -24.2882, -8.584, 169.891]], [[-6.43551, -46.1151, -120.814, 566.823], # N = 10 [-5.90887, -33.0251, -37.208, 346.189], [-5.63255, -27.2042, -6.792, 177.666]], [[-6.63894, -50.4287, -128.997, 642.781], # N = 11 [-6.11404, -36.4610, -36.246, 348.554], [-5.83850, -30.1995, -5.163, 210.338]], [[-6.83488, -54.7119, -139.800, 736.376], # N = 12 [-6.31127, -39.9676, -37.021, 406.051], [-6.03650, -33.2381, -6.606, 317.776]]] tau_ct_2010 = asarray(tau_ct_2010) tau_ctt_2010 = [ [[-4.37113, -11.5882, -35.819, -334.047], # N = 1 [-3.83239, -5.9057, -12.490, -118.284], [-3.55326, -3.6596, -5.293, -63.559]], [[-4.69276, -20.2284, -64.919, 88.884], # N =2 [-4.15387, -13.3114, -28.402, 72.741], [-3.87346, -10.4637, -17.408, 66.313]], [[-4.99071, -23.5873, -76.924, 184.782], # N = 3 [-4.45311, -15.7732, -32.316, 122.705], [-4.17280, -12.4909, -17.912, 83.285]], [[-5.26780, -27.2836, -78.971, 137.871], # N = 4 [-4.73244, -18.4833, -31.875, 111.817], [-4.45268, -14.7199, -17.969, 101.92]], [[-5.52826, -30.9051, -92.490, 248.096], # N = 5 [-4.99491, -21.2360, -37.685, 194.208], [-4.71587, -17.0820, -18.631, 136.672]], [[-5.77379, -34.7010, -105.937, 393.991], # N = 6 [-5.24217, -24.2177, -39.153, 232.528], [-4.96397, -19.6064, -18.858, 174.919]], [[-6.00609, -38.7383, -108.605, 365.208], # N = 7 [-5.47664, -27.3005, -39.498, 246.918], [-5.19921, -22.2617, -17.910, 208.494]], [[-6.22758, -42.7154, -119.622, 421.395], # N = 8 [-5.69983, -30.4365, -44.300, 345.48], [-5.42320, -24.9686, -19.688, 274.462]], [[-6.43933, -46.7581, -136.691, 651.38], # N = 9 [-5.91298, -33.7584, -42.686, 346.629], [-5.63704, -27.8965, -13.880, 236.975]], [[-6.64235, -50.9783, -145.462, 752.228], # N = 10 [-6.11753, -37.056, -48.719, 473.905], [-5.84215, -30.8119, -14.938, 316.006]], [[-6.83743, -55.2861, -152.651, 792.577], # N = 11 [-6.31396, -40.5507, -46.771, 487.185], [-6.03921, -33.8950, -9.122, 285.164]], [[-7.02582, -59.6037, -166.368, 989.879], # N = 12 [-6.50353, -44.0797, -47.242, 543.889], [-6.22941, -36.9673, -10.868, 418.414]]] tau_ctt_2010 = asarray(tau_ctt_2010) tau_2010s = { "nc": tau_nc_2010, "c": tau_c_2010, "ct": tau_ct_2010, "ctt": tau_ctt_2010, } def mackinnoncrit(N=1, regression="c", nobs=inf): """ Returns the critical values for cointegrating and the ADF test. In 2010 MacKinnon updated the values of his 1994 paper with critical values for the augmented Dickey-Fuller tests. These new values are to be preferred and are used here. Parameters ---------- N : int The number of series of I(1) series for which the null of non-cointegration is being tested. For N > 12, the critical values are linearly interpolated (not yet implemented). For the ADF test, N = 1. reg : str {'c', 'tc', 'ctt', 'nc'} Following MacKinnon (1996), these stand for the type of regression run. 'c' for constant and no trend, 'tc' for constant with a linear trend, 'ctt' for constant with a linear and quadratic trend, and 'nc' for no constant. The values for the no constant case are taken from the 1996 paper, as they were not updated for 2010 due to the unrealistic assumptions that would underlie such a case. nobs : int or np.inf This is the sample size. If the sample size is numpy.inf, then the asymptotic critical values are returned. References ---------- .. [*] MacKinnon, J.G. 1994 "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests." Journal of Business & Economics Statistics, 12.2, 167-76. .. [*] MacKinnon, J.G. 2010. "Critical Values for Cointegration Tests." Queen's University, Dept of Economics Working Papers 1227. http://ideas.repec.org/p/qed/wpaper/1227.html """ reg = regression if reg not in ['c', 'ct', 'nc', 'ctt']: raise ValueError("regression keyword %s not understood" % reg) tau = tau_2010s[reg] if nobs is inf: return tau[N-1, :, 0] else: val = tau[N-1, :, ::-1] return polyval(val.T, 1./nobs) statsmodels-0.12.2/statsmodels/tsa/api.py000066400000000000000000000046561400612667500204340ustar00rootroot00000000000000__all__ = ['AR', 'arima', 'AutoReg', 'ARMA', 'ARIMA', 'var', 'VAR', 'VECM', 'SVAR', 'filters', 'innovations', 'tsatools', 'add_trend', 'detrend', 'lagmat', 'lagmat2ds', 'add_lag', 'interp', 'stattools', 'acovf', 'acf', 'pacf', 'pacf_yw', 'pacf_ols', 'ccovf', 'ccf', 'q_stat', 'coint', 'arma_order_select_ic', 'adfuller', 'kpss', 'bds', 'datetools', 'seasonal_decompose', 'graphics', 'x13_arima_select_order', 'x13_arima_analysis', 'statespace', 'SARIMAX', 'UnobservedComponents', 'VARMAX', 'DynamicFactor', 'DynamicFactorMQ', 'MarkovRegression', 'MarkovAutoregression', 'ETSModel', 'ExponentialSmoothing', 'SimpleExpSmoothing', 'Holt', 'arma_generate_sample', 'ArmaProcess', 'STL', 'STLForecast', 'bk_filter', 'cf_filter', 'hp_filter'] from .ar_model import AR, AutoReg from .arima import api as arima from .arima_model import ARMA, ARIMA from . import vector_ar as var from .arima_process import arma_generate_sample, ArmaProcess from .vector_ar.var_model import VAR from .vector_ar.vecm import VECM from .vector_ar.svar_model import SVAR from .filters import api as filters from . import tsatools from .tsatools import (add_trend, detrend, lagmat, lagmat2ds, add_lag) from . import interp from . import stattools from .stattools import ( acovf, acf, pacf, pacf_yw, pacf_ols, ccovf, ccf, q_stat, coint, arma_order_select_ic, adfuller, kpss, bds) from .base import datetools from .seasonal import seasonal_decompose from ..graphics import tsaplots as graphics from .x13 import x13_arima_select_order from .x13 import x13_arima_analysis from .statespace import api as statespace from .statespace.sarimax import SARIMAX from .statespace.structural import UnobservedComponents from .statespace.varmax import VARMAX from .statespace.dynamic_factor import DynamicFactor from .statespace.dynamic_factor_mq import DynamicFactorMQ from .regime_switching.markov_regression import MarkovRegression from .regime_switching.markov_autoregression import MarkovAutoregression from .exponential_smoothing.ets import ETSModel from .holtwinters import ExponentialSmoothing, SimpleExpSmoothing, Holt from .innovations import api as innovations from .seasonal import STL from .forecasting.stl import STLForecast from .filters import bk_filter, cf_filter, hp_filter statsmodels-0.12.2/statsmodels/tsa/ar_model.py000066400000000000000000002757441400612667500214550ustar00rootroot00000000000000# -*- coding: utf-8 -*- from statsmodels.compat.pandas import Appender, Substitution, to_numpy from collections.abc import Iterable import copy import datetime as dt from types import SimpleNamespace import warnings import numpy as np from numpy.linalg import inv, slogdet import pandas as pd from scipy.stats import gaussian_kde, norm import statsmodels.base.model as base from statsmodels.tsa.base.prediction import PredictionResults import statsmodels.base.wrapper as wrap from statsmodels.iolib.summary import Summary from statsmodels.regression.linear_model import OLS from statsmodels.tools.decorators import cache_readonly, cache_writable from statsmodels.tools.docstring import Docstring, remove_parameters from statsmodels.tools.numdiff import approx_fprime, approx_hess from statsmodels.tools.validation import ( array_like, bool_like, int_like, string_like, ) from statsmodels.tsa.arima_process import arma2ma from statsmodels.tsa.base import tsa_model from statsmodels.tsa.deterministic import ( DeterministicProcess, Seasonality, TimeTrend, ) from statsmodels.tsa.kalmanf.kalmanfilter import KalmanFilter from statsmodels.tsa.tsatools import ( _ar_invtransparams, _ar_transparams, add_trend, freq_to_period, lagmat, ) from statsmodels.tsa.vector_ar import util __all__ = ["AR", "AutoReg"] AR_DEPRECATION_WARN = """ statsmodels.tsa.AR has been deprecated in favor of statsmodels.tsa.AutoReg and statsmodels.tsa.SARIMAX. AutoReg adds the ability to specify exogenous variables, include time trends, and add seasonal dummies. The AutoReg API differs from AR since the model is treated as immutable, and so the entire specification including the lag length must be specified when creating the model. This change is too substantial to incorporate into the existing AR api. The function ar_select_order performs lag length selection for AutoReg models. AutoReg only estimates parameters using conditional MLE (OLS). Use SARIMAX to estimate ARX and related models using full MLE via the Kalman Filter. To silence this warning and continue using AR until it is removed, use: import warnings warnings.filterwarnings('ignore', 'statsmodels.tsa.ar_model.AR', FutureWarning) """ REPEATED_FIT_ERROR = """ Model has been fit using maxlag={0}, method={1}, ic={2}, trend={3}. These cannot be changed in subsequent calls to `fit`. Instead, use a new instance of AR. """ def sumofsq(x, axis=0): """Helper function to calculate sum of squares along first axis""" return np.sum(x ** 2, axis=axis) def _ar_predict_out_of_sample(y, params, k_ar, k_trend, steps, start=0): mu = params[:k_trend] if k_trend else 0 # only have to worry constant arparams = params[k_trend:][::-1] # reverse for dot # dynamic endogenous variable endog = np.zeros(k_ar + steps) # this is one too big but does not matter if start: endog[:k_ar] = y[start - k_ar : start] else: endog[:k_ar] = y[-k_ar:] forecast = np.zeros(steps) for i in range(steps): fcast = mu + np.dot(arparams, endog[i : i + k_ar]) forecast[i] = fcast endog[i + k_ar] = fcast return forecast class AutoReg(tsa_model.TimeSeriesModel): """ Autoregressive AR-X(p) model. Estimate an AR-X model using Conditional Maximum Likelihood (OLS). Parameters ---------- endog : array_like A 1-d endogenous response variable. The dependent variable. lags : {int, list[int]} The number of lags to include in the model if an integer or the list of lag indices to include. For example, [1, 4] will only include lags 1 and 4 while lags=4 will include lags 1, 2, 3, and 4. trend : {'n', 'c', 't', 'ct'} The trend to include in the model: * 'n' - No trend. * 'c' - Constant only. * 't' - Time trend only. * 'ct' - Constant and time trend. seasonal : bool Flag indicating whether to include seasonal dummies in the model. If seasonal is True and trend includes 'c', then the first period is excluded from the seasonal terms. exog : array_like, optional Exogenous variables to include in the model. Must have the same number of observations as endog and should be aligned so that endog[i] is regressed on exog[i]. hold_back : {None, int} Initial observations to exclude from the estimation sample. If None, then hold_back is equal to the maximum lag in the model. Set to a non-zero value to produce comparable models with different lag length. For example, to compare the fit of a model with lags=3 and lags=1, set hold_back=3 which ensures that both models are estimated using observations 3,...,nobs. hold_back must be >= the maximum lag in the model. period : {None, int} The period of the data. Only used if seasonal is True. This parameter can be omitted if using a pandas object for endog that contains a recognized frequency. missing : str Available options are 'none', 'drop', and 'raise'. If 'none', no nan checking is done. If 'drop', any observations with nans are dropped. If 'raise', an error is raised. Default is 'none'. deterministic : DeterministicProcess A deterministic process. If provided, trend and seasonal are ignored. A warning is raised if trend is not "n" and seasonal is not False. old_names : bool Flag indicating whether to use the v0.11 names or the v0.12+ names. After v0.12 is released, the default names will change to the new names. See Also -------- statsmodels.tsa.statespace.sarimax.SARIMAX Estimation of SARIMAX models using exact likelihood and the Kalman Filter. Examples -------- >>> import statsmodels.api as sm >>> from statsmodels.tsa.ar_model import AutoReg >>> data = sm.datasets.sunspots.load_pandas().data['SUNACTIVITY'] >>> out = 'AIC: {0:0.3f}, HQIC: {1:0.3f}, BIC: {2:0.3f}' Start by fitting an unrestricted Seasonal AR model >>> res = AutoReg(data, lags = [1, 11, 12]).fit() >>> print(out.format(res.aic, res.hqic, res.bic)) AIC: 5.945, HQIC: 5.970, BIC: 6.007 An alternative used seasonal dummies >>> res = AutoReg(data, lags=1, seasonal=True, period=11).fit() >>> print(out.format(res.aic, res.hqic, res.bic)) AIC: 6.017, HQIC: 6.080, BIC: 6.175 Finally, both the seasonal AR structure and dummies can be included >>> res = AutoReg(data, lags=[1, 11, 12], seasonal=True, period=11).fit() >>> print(out.format(res.aic, res.hqic, res.bic)) AIC: 5.884, HQIC: 5.959, BIC: 6.071 """ def __init__( self, endog, lags, trend="c", seasonal=False, exog=None, hold_back=None, period=None, missing="none", *, deterministic=None, old_names=None ): super(AutoReg, self).__init__(endog, exog, None, None, missing=missing) self._trend = string_like( trend, "trend", options=("n", "c", "t", "ct") ) self._seasonal = bool_like(seasonal, "seasonal") self._period = int_like(period, "period", optional=True) if self._period is None and self._seasonal: if self.data.freq: self._period = freq_to_period(self._index_freq) else: err = ( "freq cannot be inferred from endog and model includes" " seasonal terms. The number of periods must be " "explicitly set when the endog's index does not " "contain a frequency." ) raise ValueError(err) terms = [TimeTrend.from_string(self._trend)] if seasonal: terms.append(Seasonality(self._period)) if hasattr(self.data.orig_endog, "index"): index = self.data.orig_endog.index else: index = np.arange(self.data.endog.shape[0]) self._user_deterministic = False if deterministic is not None: if not isinstance(deterministic, DeterministicProcess): raise TypeError("deterministic must be a DeterministicProcess") self._deterministics = deterministic self._user_deterministic = True else: self._deterministics = DeterministicProcess( index, additional_terms=terms ) self._lags = lags self._exog_names = [] self._k_ar = 0 self._hold_back = int_like(hold_back, "hold_back", optional=True) self._old_names = bool_like(old_names, "old_names", optional=True) if deterministic is not None: self._old_names = False if self._trend != "n" or self._seasonal: warnings.warn( 'When using deterministic, trend must be "n" and ' "seasonal must be False.", RuntimeWarning, ) if self._old_names is None: warnings.warn( "The parameter names will change after 0.12 is " "released. Set old_names to False to use the new names " "now. Set old_names to True to use the old names. ", FutureWarning, ) self._old_names = True self._check_lags() self._setup_regressors() self.nobs = self._y.shape[0] self.data.xnames = self.exog_names @property def ar_lags(self): """The autoregressive lags included in the model""" return self._lags @property def hold_back(self): """The number of initial obs. excluded from the estimation sample.""" return self._hold_back @property def seasonal(self): """Flag indicating that the model contains a seasonal component.""" return self._seasonal @property def df_model(self): """The model degrees of freedom.""" return self._x.shape[1] @property def exog_names(self): """Names of exogenous variables included in model""" return self._exog_names def initialize(self): """Initialize the model (no-op).""" pass def _check_lags(self): lags = self._lags if isinstance(lags, Iterable): lags = np.array(sorted([int_like(lag, "lags") for lag in lags])) self._lags = lags if np.any(lags < 1) or np.unique(lags).shape[0] != lags.shape[0]: raise ValueError( "All values in lags must be positive and " "distinct." ) self._maxlag = np.max(lags) else: self._maxlag = int_like(lags, "lags") if self._maxlag < 0: raise ValueError("lags must be a positive scalar.") self._lags = np.arange(1, self._maxlag + 1) if self._hold_back is None: self._hold_back = self._maxlag if self._hold_back < self._maxlag: raise ValueError( "hold_back must be >= lags if lags is an int or" "max(lags) if lags is array_like." ) def _setup_regressors(self): maxlag = self._maxlag hold_back = self._hold_back exog_names = [] endog_names = self.endog_names x, y = lagmat(self.endog, maxlag, original="sep") exog_names.extend( [endog_names + ".L{0}".format(lag) for lag in self._lags] ) if len(self._lags) < maxlag: x = x[:, self._lags - 1] self._k_ar = x.shape[1] deterministic = self._deterministics.in_sample() if deterministic.shape[1]: x = np.c_[to_numpy(deterministic), x] if self._old_names: deterministic_names = [] if "c" in self._trend: deterministic_names.append("intercept") if "t" in self._trend: deterministic_names.append("trend") if self._seasonal: period = self._period names = ["seasonal.{0}".format(i) for i in range(period)] if "c" in self._trend: names = names[1:] deterministic_names.extend(names) else: deterministic_names = list(deterministic.columns) exog_names = deterministic_names + exog_names if self.exog is not None: x = np.c_[x, self.exog] exog_names.extend(self.data.param_names) y = y[hold_back:] x = x[hold_back:] if y.shape[0] < x.shape[1]: reg = x.shape[1] period = self._period trend = 0 if self._trend == "n" else len(self._trend) seas = 0 if not self._seasonal else period - ("c" in self._trend) lags = self._lags.shape[0] nobs = y.shape[0] raise ValueError( "The model specification cannot be estimated. " "The model contains {0} regressors ({1} trend, " "{2} seasonal, {3} lags) but after adjustment " "for hold_back and creation of the lags, there " "are only {4} data points available to estimate " "parameters.".format(reg, trend, seas, lags, nobs) ) self._y, self._x = y, x self._exog_names = exog_names def fit(self, cov_type="nonrobust", cov_kwds=None, use_t=False): """ Estimate the model parameters. Parameters ---------- cov_type : str The covariance estimator to use. The most common choices are listed below. Supports all covariance estimators that are available in ``OLS.fit``. * 'nonrobust' - The class OLS covariance estimator that assumes homoskedasticity. * 'HC0', 'HC1', 'HC2', 'HC3' - Variants of White's (or Eiker-Huber-White) covariance estimator. `HC0` is the standard implementation. The other make corrections to improve the finite sample performance of the heteroskedasticity robust covariance estimator. * 'HAC' - Heteroskedasticity-autocorrelation robust covariance estimation. Supports cov_kwds. - `maxlags` integer (required) : number of lags to use. - `kernel` callable or str (optional) : kernel currently available kernels are ['bartlett', 'uniform'], default is Bartlett. - `use_correction` bool (optional) : If true, use small sample correction. cov_kwds : dict, optional A dictionary of keyword arguments to pass to the covariance estimator. `nonrobust` and `HC#` do not support cov_kwds. use_t : bool, optional A flag indicating that inference should use the Student's t distribution that accounts for model degree of freedom. If False, uses the normal distribution. If None, defers the choice to the cov_type. It also removes degree of freedom corrections from the covariance estimator when cov_type is 'nonrobust'. Returns ------- AutoRegResults Estimation results. See Also -------- statsmodels.regression.linear_model.OLS Ordinary Least Squares estimation. statsmodels.regression.linear_model.RegressionResults See ``get_robustcov_results`` for a detailed list of available covariance estimators and options. Notes ----- Use ``OLS`` to estimate model parameters and to estimate parameter covariance. """ # TODO: Determine correction for degree-of-freedom # Special case parameterless model if self._x.shape[1] == 0: return AutoRegResultsWrapper( AutoRegResults(self, np.empty(0), np.empty((0, 0))) ) ols_mod = OLS(self._y, self._x) ols_res = ols_mod.fit( cov_type=cov_type, cov_kwds=cov_kwds, use_t=use_t ) cov_params = ols_res.cov_params() use_t = ols_res.use_t if cov_type == "nonrobust" and not use_t: nobs = self._y.shape[0] k = self._x.shape[1] scale = nobs / (nobs - k) cov_params /= scale res = AutoRegResults( self, ols_res.params, cov_params, ols_res.normalized_cov_params ) return AutoRegResultsWrapper(res) def _resid(self, params): params = array_like(params, "params", ndim=2) resid = self._y - self._x @ params return resid.squeeze() def loglike(self, params): """ Log-likelihood of model. Parameters ---------- params : ndarray The model parameters used to compute the log-likelihood. Returns ------- float The log-likelihood value. """ nobs = self.nobs resid = self._resid(params) ssr = resid @ resid llf = -(nobs / 2) * (np.log(2 * np.pi) + np.log(ssr / nobs) + 1) return llf def score(self, params): """ Score vector of model. The gradient of logL with respect to each parameter. Parameters ---------- params : ndarray The parameters to use when evaluating the Hessian. Returns ------- ndarray The score vector evaluated at the parameters. """ resid = self._resid(params) return self._x.T @ resid def information(self, params): """ Fisher information matrix of model. Returns -1 * Hessian of the log-likelihood evaluated at params. Parameters ---------- params : ndarray The model parameters. Returns ------- ndarray The information matrix. """ resid = self._resid(params) sigma2 = resid @ resid / self.nobs return sigma2 * (self._x.T @ self._x) def hessian(self, params): """ The Hessian matrix of the model. Parameters ---------- params : ndarray The parameters to use when evaluating the Hessian. Returns ------- ndarray The hessian evaluated at the parameters. """ return -self.information(params) def _setup_oos_forecast(self, add_forecasts, exog_oos): x = np.zeros((add_forecasts, self._x.shape[1])) oos_exog = self._deterministics.out_of_sample(steps=add_forecasts) n_deterministic = oos_exog.shape[1] x[:, :n_deterministic] = to_numpy(oos_exog) # skip the AR columns loc = n_deterministic + len(self._lags) if self.exog is not None: x[:, loc:] = exog_oos[:add_forecasts] return x def _wrap_prediction(self, prediction, start, end): n_values = end - start if not isinstance(self.data.orig_endog, (pd.Series, pd.DataFrame)): return prediction[-n_values:] index = self._index if end > self.endog.shape[0]: freq = getattr(index, "freq", None) if freq: if isinstance(index, pd.PeriodIndex): index = pd.period_range(index[0], freq=freq, periods=end) else: index = pd.date_range(index[0], freq=freq, periods=end) else: index = pd.RangeIndex(end) index = index[start:end] prediction = prediction[-n_values:] return pd.Series(prediction, index=index) def _dynamic_predict( self, params, start, end, dynamic, num_oos, exog, exog_oos ): """ :param params: :param start: :param end: :param dynamic: :param num_oos: :param exog: :param exog_oos: :return: """ reg = [] hold_back = self._hold_back if (start - hold_back) <= self.nobs: is_loc = slice(start - hold_back, end + 1 - hold_back) x = self._x[is_loc] if exog is not None: x = x.copy() # Replace final columns x[:, -exog.shape[1] :] = exog[start : end + 1] reg.append(x) if num_oos > 0: reg.append(self._setup_oos_forecast(num_oos, exog_oos)) reg = np.vstack(reg) det_col_idx = self._x.shape[1] - len(self._lags) det_col_idx -= 0 if self.exog is None else self.exog.shape[1] # + 1 is due t0 inclusiveness of predict functions adj_dynamic = dynamic - start + 1 forecasts = np.empty(reg.shape[0]) forecasts[:adj_dynamic] = reg[:adj_dynamic] @ params for h in range(adj_dynamic, reg.shape[0]): # Fill in regressor matrix for j, lag in enumerate(self._lags): fcast_loc = h - lag if fcast_loc >= 0: val = forecasts[fcast_loc] else: # If before the start of the forecasts, use actual values val = self.endog[start + fcast_loc] reg[h, det_col_idx + j] = val forecasts[h] = reg[h : h + 1] @ params return self._wrap_prediction(forecasts, start, end + 1 + num_oos) def _static_oos_predict(self, params, num_oos, exog_oos): new_x = self._setup_oos_forecast(num_oos, exog_oos) if self._maxlag == 0: return new_x @ params forecasts = np.empty(num_oos) nexog = 0 if self.exog is None else self.exog.shape[1] ar_offset = self._x.shape[1] - nexog - self._lags.shape[0] for i in range(num_oos): for j, lag in enumerate(self._lags): loc = i - lag val = self._y[loc] if loc < 0 else forecasts[loc] new_x[i, ar_offset + j] = val forecasts[i] = new_x[i : i + 1] @ params return forecasts def _static_predict(self, params, start, end, num_oos, exog, exog_oos): """ Path for static predictions Parameters ---------- start : int Index of first observation end : int Index of last in-sample observation. Inclusive, so start:end+1 in slice notation. num_oos : int Number of out-of-sample observations, so that the returned size is num_oos + (end - start + 1). exog : ndarray Array containing replacement exog values exog_oos : ndarray Containing forecast exog values """ hold_back = self._hold_back nobs = self.endog.shape[0] x = np.empty((0, self._x.shape[1])) if start <= nobs: is_loc = slice(start - hold_back, end + 1 - hold_back) x = self._x[is_loc] if exog is not None: x = x.copy() # Replace final columns x[:, -exog.shape[1] :] = exog[start : end + 1] in_sample = x @ params if num_oos == 0: # No out of sample return self._wrap_prediction(in_sample, start, end + 1) out_of_sample = self._static_oos_predict(params, num_oos, exog_oos) prediction = np.hstack((in_sample, out_of_sample)) return self._wrap_prediction(prediction, start, end + 1 + num_oos) def predict( self, params, start=None, end=None, dynamic=False, exog=None, exog_oos=None, ): """ In-sample prediction and out-of-sample forecasting. Parameters ---------- params : array_like The fitted model parameters. start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, i.e., the last forecast is end. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out-of-sample prediction. Default is the last observation in the sample. Unlike standard python slices, end is inclusive so that all the predictions [start, start+1, ..., end-1, end] are returned. dynamic : {bool, int, str, datetime, Timestamp}, optional Integer offset relative to `start` at which to begin dynamic prediction. Prior to this observation, true endogenous values will be used for prediction; starting with this observation and continuing through the end of prediction, forecasted endogenous values will be used instead. Datetime-like objects are not interpreted as offsets. They are instead used to find the index location of `dynamic` which is then used to to compute the offset. exog : array_like A replacement exogenous array. Must have the same shape as the exogenous data array used when the model was created. exog_oos : array_like An array containing out-of-sample values of the exogenous variable. Must has the same number of columns as the exog used when the model was created, and at least as many rows as the number of out-of-sample forecasts. Returns ------- predictions : {ndarray, Series} Array of out of in-sample predictions and / or out-of-sample forecasts. """ params = array_like(params, "params") exog = array_like(exog, "exog", ndim=2, optional=True) exog_oos = array_like(exog_oos, "exog_oos", ndim=2, optional=True) start = 0 if start is None else start end = self._index[-1] if end is None else end start, end, num_oos, _ = self._get_prediction_index(start, end) start = max(start, self._hold_back) if self.exog is None and (exog is not None or exog_oos is not None): raise ValueError( "exog and exog_oos cannot be used when the model " "does not contains exogenous regressors." ) elif self.exog is not None: if exog is not None and exog.shape != self.exog.shape: msg = ( "The shape of exog {0} must match the shape of the " "exog variable used to create the model {1}." ) raise ValueError(msg.format(exog.shape, self.exog.shape)) if ( exog_oos is not None and exog_oos.shape[1] != self.exog.shape[1] ): msg = ( "The number of columns in exog_oos ({0}) must match " "the number of columns in the exog variable used to " "create the model ({1})." ) raise ValueError( msg.format(exog_oos.shape[1], self.exog.shape[1]) ) if num_oos > 0 and exog_oos is None: raise ValueError( "exog_oos must be provided when producing " "out-of-sample forecasts." ) elif exog_oos is not None and num_oos > exog_oos.shape[0]: msg = ( "start and end indicate that {0} out-of-sample " "predictions must be computed. exog_oos has {1} rows " "but must have at least {0}." ) raise ValueError(msg.format(num_oos, exog_oos.shape[0])) if (isinstance(dynamic, bool) and not dynamic) or self._maxlag == 0: # If model has no lags, static and dynamic are identical return self._static_predict( params, start, end, num_oos, exog, exog_oos ) if isinstance(dynamic, (str, bytes, pd.Timestamp, dt.datetime)): dynamic, _, _ = self._get_index_loc(dynamic) offset = dynamic - start elif dynamic is True: # if True, all forecasts are dynamic, except start offset = 0 else: offset = int(dynamic) dynamic = start + offset if dynamic < 0: raise ValueError( "Dynamic prediction cannot begin prior to the" " first observation in the sample." ) return self._dynamic_predict( params, start, end, dynamic, num_oos, exog, exog_oos ) class AR(tsa_model.TimeSeriesModel): __doc__ = tsa_model._tsa_doc % { "model": """\ Autoregressive AR(p) model. .. deprecated:: 0.11 To be removed after 0.12 is released. Use statsmodels.tsa.ar_model.AutoReg instead.""", "params": """endog : array_like A 1-d endogenous response variable. The independent variable.""", "extra_params": base._missing_param_doc, "extra_sections": "", } def __init__(self, endog, dates=None, freq=None, missing="none"): warnings.warn(AR_DEPRECATION_WARN, FutureWarning) super(AR, self).__init__(endog, None, dates, freq, missing=missing) endog = self.endog # original might not have been an ndarray if endog.ndim == 1: endog = endog[:, None] self.endog = endog # to get shapes right elif endog.ndim > 1 and endog.shape[1] != 1: raise ValueError("Only the univariate case is implemented") self._fit_params = None def initialize(self): """Initialization of the model (no-op).""" pass def _transparams(self, params): """ Transforms params to induce stationarity/invertability. Reference --------- Jones(1980) """ p = self.k_ar k = self.k_trend newparams = params.copy() newparams[k : k + p] = _ar_transparams(params[k : k + p].copy()) return newparams def _invtransparams(self, start_params): """ Inverse of the Jones reparameterization """ p = self.k_ar k = self.k_trend newparams = start_params.copy() newparams[k : k + p] = _ar_invtransparams( start_params[k : k + p].copy() ) return newparams def _presample_fit(self, params, start, p, end, y, predictedvalues): """ Return the pre-sample predicted values using the Kalman Filter Notes ----- See predict method for how to use start and p. """ k = self.k_trend # build system matrices T_mat = KalmanFilter.T(params, p, k, p) R_mat = KalmanFilter.R(params, p, k, 0, p) # Initial State mean and variance alpha = np.zeros((p, 1)) Q_0 = np.dot( inv(np.identity(p ** 2) - np.kron(T_mat, T_mat)), np.dot(R_mat, R_mat.T).ravel("F"), ) Q_0 = Q_0.reshape(p, p, order="F") # TODO: order might need to be p+k P = Q_0 Z_mat = KalmanFilter.Z(p) for i in range(end): # iterate p-1 times to fit presample v_mat = y[i] - np.dot(Z_mat, alpha) F_mat = np.dot(np.dot(Z_mat, P), Z_mat.T) Finv = 1.0 / F_mat # inv. always scalar K = np.dot(np.dot(np.dot(T_mat, P), Z_mat.T), Finv) # update state alpha = np.dot(T_mat, alpha) + np.dot(K, v_mat) L = T_mat - np.dot(K, Z_mat) P = np.dot(np.dot(T_mat, P), L.T) + np.dot(R_mat, R_mat.T) if i >= start - 1: # only record if we ask for it predictedvalues[i + 1 - start] = np.dot(Z_mat, alpha) def _get_prediction_index(self, start, end, dynamic, index=None): method = getattr(self, "method", "mle") k_ar = getattr(self, "k_ar", 0) if start is None: if method == "mle" and not dynamic: start = 0 else: # cannot do presample fit for cmle or dynamic start = k_ar start = self._index[start] if end is None: end = self._index[-1] start, end, out_of_sample, prediction_index = super( AR, self )._get_prediction_index(start, end, index) # Other validation if (method == "cmle" or dynamic) and start < k_ar: raise ValueError( "Start must be >= k_ar for conditional MLE " "or dynamic forecast. Got %d" % start ) return start, end, out_of_sample, prediction_index def predict(self, params, start=None, end=None, dynamic=False): """ Construct in-sample and out-of-sample prediction. Parameters ---------- params : ndarray The fitted model parameters. start : int, str, or datetime Zero-indexed observation number at which to start forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. end : int, str, or datetime Zero-indexed observation number at which to end forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. dynamic : bool The `dynamic` keyword affects in-sample prediction. If dynamic is False, then the in-sample lagged values are used for prediction. If `dynamic` is True, then in-sample forecasts are used in place of lagged dependent variables. The first forecasted value is `start`. Returns ------- array_like An array containing the predicted values. Notes ----- The linear Gaussian Kalman filter is used to return pre-sample fitted values. The exact initial Kalman Filter is used. See Durbin and Koopman in the references for more information. """ if not (hasattr(self, "k_ar") and hasattr(self, "k_trend")): raise RuntimeError("Model must be fit before calling predict") # will return an index of a date start, end, out_of_sample, _ = self._get_prediction_index( start, end, dynamic ) k_ar = self.k_ar k_trend = self.k_trend method = self.method endog = self.endog.squeeze() if dynamic: out_of_sample += end - start + 1 return _ar_predict_out_of_sample( endog, params, k_ar, k_trend, out_of_sample, start ) predictedvalues = np.zeros(end + 1 - start) # fit pre-sample if method == "mle": # use Kalman Filter to get initial values if k_trend: mu = params[0] / (1 - np.sum(params[k_trend:])) else: mu = 0 # modifies predictedvalues in place if start < k_ar: self._presample_fit( params, start, k_ar, min(k_ar - 1, end), endog[:k_ar] - mu, predictedvalues, ) predictedvalues[: k_ar - start] += mu if end < k_ar: return predictedvalues # just do the whole thing and truncate fittedvalues = np.dot(self.X, params) pv_start = max(k_ar - start, 0) fv_start = max(start - k_ar, 0) fv_end = min(len(fittedvalues), end - k_ar + 1) predictedvalues[pv_start:] = fittedvalues[fv_start:fv_end] if out_of_sample: forecastvalues = _ar_predict_out_of_sample( endog, params, k_ar, k_trend, out_of_sample ) predictedvalues = np.r_[predictedvalues, forecastvalues] return predictedvalues def _presample_varcov(self, params): """ Returns the inverse of the presample variance-covariance. Notes ----- See Hamilton p. 125 """ k = self.k_trend p = self.k_ar # get inv(Vp) Hamilton 5.3.7 params0 = np.r_[-1, params[k:]] Vpinv = np.zeros((p, p), dtype=params.dtype) for i in range(1, p + 1): Vpinv[i - 1, i - 1 :] = np.correlate(params0, params0[:i])[:-1] Vpinv[i - 1, i - 1 :] -= np.correlate(params0[-i:], params0)[:-1] Vpinv = Vpinv + Vpinv.T - np.diag(Vpinv.diagonal()) return Vpinv def _loglike_css(self, params): """ Loglikelihood of AR(p) process using conditional sum of squares """ nobs = self.nobs Y = self.Y X = self.X ssr = sumofsq(Y.squeeze() - np.dot(X, params)) sigma2 = ssr / nobs return -nobs / 2 * (np.log(2 * np.pi) + np.log(sigma2) + 1) def _loglike_mle(self, params): """ Loglikelihood of AR(p) process using exact maximum likelihood """ nobs = self.nobs X = self.X endog = self.endog k_ar = self.k_ar k_trend = self.k_trend # reparameterize according to Jones (1980) like in ARMA/Kalman Filter if self.transparams: params = self._transparams(params) # get mean and variance for pre-sample lags yp = endog[:k_ar].copy() if k_trend: c = [params[0]] * k_ar else: c = [0] mup = np.asarray(c / (1 - np.sum(params[k_trend:]))) diffp = yp - mup[:, None] # get inv(Vp) Hamilton 5.3.7 Vpinv = self._presample_varcov(params) diffpVpinv = np.dot(np.dot(diffp.T, Vpinv), diffp).item() ssr = sumofsq(endog[k_ar:].squeeze() - np.dot(X, params)) # concentrating the likelihood means that sigma2 is given by sigma2 = 1.0 / nobs * (diffpVpinv + ssr) self.sigma2 = sigma2 logdet = slogdet(Vpinv)[1] # TODO: add check for singularity loglike = ( -1 / 2.0 * ( nobs * (np.log(2 * np.pi) + np.log(sigma2)) - logdet + diffpVpinv / sigma2 + ssr / sigma2 ) ) return loglike def loglike(self, params): r""" The loglikelihood of an AR(p) process. Parameters ---------- params : ndarray The fitted parameters of the AR model. Returns ------- float The loglikelihood evaluated at `params`. Notes ----- Contains constant term. If the model is fit by OLS then this returns the conditional maximum likelihood. .. math:: \frac{\left(n-p\right)}{2}\left(\log\left(2\pi\right) +\log\left(\sigma^{2}\right)\right) -\frac{1}{\sigma^{2}}\sum_{i}\epsilon_{i}^{2} If it is fit by MLE then the (exact) unconditional maximum likelihood is returned. .. math:: -\frac{n}{2}log\left(2\pi\right) -\frac{n}{2}\log\left(\sigma^{2}\right) +\frac{1}{2}\left|V_{p}^{-1}\right| -\frac{1}{2\sigma^{2}}\left(y_{p} -\mu_{p}\right)^{\prime}V_{p}^{-1}\left(y_{p}-\mu_{p}\right) -\frac{1}{2\sigma^{2}}\sum_{t=p+1}^{n}\epsilon_{i}^{2} where :math:`\mu_{p}` is a (`p` x 1) vector with each element equal to the mean of the AR process and :math:`\sigma^{2}V_{p}` is the (`p` x `p`) variance-covariance matrix of the first `p` observations. """ # Math is on Hamilton ~pp 124-5 if self.method == "cmle": return self._loglike_css(params) else: return self._loglike_mle(params) def score(self, params): """ Compute the gradient of the log-likelihood at params. Parameters ---------- params : array_like The parameter values at which to evaluate the score function. Returns ------- ndarray The gradient computed using numerical methods. """ loglike = self.loglike return approx_fprime(params, loglike, epsilon=1e-8) def information(self, params): """ Not implemented. Parameters ---------- params : ndarray The model parameters. """ return def hessian(self, params): """ Compute the hessian using a numerical approximation. Parameters ---------- params : ndarray The model parameters. Returns ------- ndarray The hessian evaluated at params. """ loglike = self.loglike return approx_hess(params, loglike) def _stackX(self, k_ar, trend): """ Private method to build the RHS matrix for estimation. Columns are trend terms then lags. """ endog = self.endog X = lagmat(endog, maxlag=k_ar, trim="both") k_trend = util.get_trendorder(trend) if k_trend: X = add_trend(X, prepend=True, trend=trend, has_constant="raise") self.k_trend = k_trend return X def select_order(self, maxlag, ic, trend="c", method="mle"): """ Select the lag order according to the information criterion. Parameters ---------- maxlag : int The highest lag length tried. See `AR.fit`. ic : {'aic','bic','hqic','t-stat'} Criterion used for selecting the optimal lag length. See `AR.fit`. trend : {'c','nc'} Whether to include a constant or not. 'c' - include constant. 'nc' - no constant. method : {'cmle', 'mle'}, optional The method to use in estimation. * 'cmle' - Conditional maximum likelihood using OLS * 'mle' - Unconditional (exact) maximum likelihood. See `solver` and the Notes. Returns ------- int Best lag according to the information criteria. """ endog = self.endog # make Y and X with same nobs to compare ICs Y = endog[maxlag:] self.Y = Y # attach to get correct fit stats X = self._stackX(maxlag, trend) # sets k_trend self.X = X k = self.k_trend # k_trend set in _stackX k = max(1, k) # handle if startlag is 0 results = {} if ic != "t-stat": for lag in range(k, maxlag + 1): # have to reinstantiate the model to keep comparable models endog_tmp = endog[maxlag - lag :] fit = AR(endog_tmp).fit( maxlag=lag, method=method, full_output=0, trend=trend, maxiter=100, disp=0, ) results[lag] = getattr(fit, ic) bestic, bestlag = min((res, k) for k, res in results.items()) else: # choose by last t-stat. stop = 1.6448536269514722 # for t-stat, norm.ppf(.95) for lag in range(maxlag, k - 1, -1): # have to reinstantiate the model to keep comparable models endog_tmp = endog[maxlag - lag :] fit = AR(endog_tmp).fit( maxlag=lag, method=method, full_output=0, trend=trend, maxiter=35, disp=-1, ) bestlag = 0 if np.abs(fit.tvalues[-1]) >= stop: bestlag = lag break return bestlag def fit( self, maxlag=None, method="cmle", ic=None, trend="c", transparams=True, start_params=None, solver="lbfgs", maxiter=35, full_output=1, disp=1, callback=None, **kwargs ): """ Fit the unconditional maximum likelihood of an AR(p) process. Parameters ---------- maxlag : int If `ic` is None, then maxlag is the lag length used in fit. If `ic` is specified then maxlag is the highest lag order used to select the correct lag order. If maxlag is None, the default is round(12*(nobs/100.)**(1/4.)). method : {'cmle', 'mle'}, optional The method to use in estimation. * 'cmle' - Conditional maximum likelihood using OLS * 'mle' - Unconditional (exact) maximum likelihood. See `solver` and the Notes. ic : {'aic','bic','hic','t-stat'} Criterion used for selecting the optimal lag length. * 'aic' - Akaike Information Criterion * 'bic' - Bayes Information Criterion * 't-stat' - Based on last lag * 'hqic' - Hannan-Quinn Information Criterion If any of the information criteria are selected, the lag length which results in the lowest value is selected. If t-stat, the model starts with maxlag and drops a lag until the highest lag has a t-stat that is significant at the 95 % level. trend : {'c','nc'} Whether to include a constant or not. * 'c' - include constant. * 'nc' - no constant. transparams : bool, optional Whether or not to transform the parameters to ensure stationarity. Uses the transformation suggested in Jones (1980). start_params : array_like, optional A first guess on the parameters. Default is cmle estimates. solver : str or None, optional Solver to be used if method is 'mle'. The default is 'lbfgs' (limited memory Broyden-Fletcher-Goldfarb-Shanno). Other choices are 'bfgs', 'newton' (Newton-Raphson), 'nm' (Nelder-Mead), 'cg' - (conjugate gradient), 'ncg' (non-conjugate gradient), and 'powell'. maxiter : int, optional The maximum number of function evaluations. Default is 35. full_output : bool, optional If True, all output from solver will be available in the Results object's mle_retvals attribute. Output is dependent on the solver. See Notes for more information. disp : bool, optional If True, convergence information is output. callback : function, optional Called after each iteration as callback(xk) where xk is the current parameter vector. **kwargs See LikelihoodModel.fit for keyword arguments that can be passed to fit. Returns ------- ARResults Results instance. See Also -------- statsmodels.base.model.LikelihoodModel.fit Base fit class with further details about options. Notes ----- The parameters after `trend` are only used when method is 'mle'. References ---------- .. [*] Jones, R.H. 1980 "Maximum likelihood fitting of ARMA models to time series with missing observations." `Technometrics`. 22.3. 389-95. """ start_params = array_like( start_params, "start_params", ndim=1, optional=True ) method = method.lower() if method not in ["cmle", "mle"]: raise ValueError("Method %s not recognized" % method) self.method = method self.trend = trend self.transparams = transparams nobs = len(self.endog) # overwritten if method is 'cmle' endog = self.endog # The parameters are no longer allowed to change in an instance fit_params = (maxlag, method, ic, trend) if self._fit_params is not None and self._fit_params != fit_params: raise RuntimeError(REPEATED_FIT_ERROR.format(*self._fit_params)) if maxlag is None: maxlag = int(round(12 * (nobs / 100.0) ** (1 / 4.0))) k_ar = maxlag # stays this if ic is None # select lag length if ic is not None: ic = ic.lower() if ic not in ["aic", "bic", "hqic", "t-stat"]: raise ValueError("ic option %s not understood" % ic) k_ar = self.select_order(k_ar, ic, trend, method) self.k_ar = k_ar # change to what was chosen by ic # redo estimation for best lag # make LHS Y = endog[k_ar:, :] # make lagged RHS X = self._stackX(k_ar, trend) # sets self.k_trend k_trend = self.k_trend self.exog_names = util.make_lag_names(self.endog_names, k_ar, k_trend) self.Y = Y self.X = X if method == "cmle": # do OLS arfit = OLS(Y, X).fit() params = arfit.params self.nobs = nobs - k_ar self.sigma2 = arfit.ssr / arfit.nobs # needed for predict fcasterr else: # method == "mle" solver = solver.lower() self.nobs = nobs if start_params is None: start_params = OLS(Y, X).fit().params else: if len(start_params) != k_trend + k_ar: raise ValueError( "Length of start params is %d. There" " are %d parameters." % (len(start_params), k_trend + k_ar) ) start_params = self._invtransparams(start_params) if solver == "lbfgs": kwargs.setdefault("pgtol", 1e-8) kwargs.setdefault("factr", 1e2) kwargs.setdefault("m", 12) kwargs.setdefault("approx_grad", True) mlefit = super(AR, self).fit( start_params=start_params, method=solver, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, **kwargs ) params = mlefit.params if self.transparams: params = self._transparams(params) self.transparams = False # turn off now for other results pinv_exog = np.linalg.pinv(X) normalized_cov_params = np.dot(pinv_exog, pinv_exog.T) arfit = ARResults(copy.copy(self), params, normalized_cov_params) if method == "mle" and full_output: arfit.mle_retvals = mlefit.mle_retvals arfit.mle_settings = mlefit.mle_settings # Set fit params since completed the fit if self._fit_params is None: self._fit_params = fit_params return ARResultsWrapper(arfit) class ARResults(tsa_model.TimeSeriesModelResults): """ Class to hold results from fitting an AR model. Parameters ---------- model : AR Model instance Reference to the model that is fit. params : ndarray The fitted parameters from the AR Model. normalized_cov_params : ndarray The array inv(dot(x.T,x)) where x contains the regressors in the model. scale : float, optional An estimate of the scale of the model. Attributes ---------- k_ar : float Lag length. Sometimes used as `p` in the docs. k_trend : float The number of trend terms included. 'nc'=0, 'c'=1. llf : float The loglikelihood of the model evaluated at `params`. See `AR.loglike` model : AR model instance A reference to the fitted AR model. nobs : float The number of available observations `nobs` - `k_ar` n_totobs : float The number of total observations in `endog`. Sometimes `n` in the docs. params : ndarray The fitted parameters of the model. scale : float Same as sigma2 sigma2 : float The variance of the innovations (residuals). trendorder : int The polynomial order of the trend. 'nc' = None, 'c' or 't' = 0, 'ct' = 1, etc. """ _cache = {} # for scale setter def __init__(self, model, params, normalized_cov_params=None, scale=1.0): super(ARResults, self).__init__( model, params, normalized_cov_params, scale ) self._cache = {} self.nobs = model.nobs n_totobs = len(model.endog) self.n_totobs = n_totobs self.X = model.X # copy? self.Y = model.Y k_ar = model.k_ar self.k_ar = k_ar k_trend = model.k_trend self.k_trend = k_trend trendorder = None if k_trend > 0: trendorder = k_trend - 1 self.trendorder = trendorder # TODO: cmle vs mle? self.df_model = k_ar + k_trend self.df_resid = self.model.df_resid = n_totobs - self.df_model @cache_writable() def sigma2(self): model = self.model if model.method == "cmle": # do DOF correction return 1.0 / self.nobs * sumofsq(self.resid) else: return self.model.sigma2 @cache_writable() # for compatability with RegressionResults def scale(self): return self.sigma2 @cache_readonly def bse(self): # allow user to specify? """ The standard errors of the estimated parameters. If `method` is 'cmle', then the standard errors that are returned are the OLS standard errors of the coefficients. If the `method` is 'mle' then they are computed using the numerical Hessian. """ if self.model.method == "cmle": # uses different scale/sigma def. resid = self.resid ssr = np.dot(resid, resid) ols_scale = ssr / (self.nobs - self.k_ar - self.k_trend) return np.sqrt(np.diag(self.cov_params(scale=ols_scale))) else: hess = approx_hess(self.params, self.model.loglike) return np.sqrt(np.diag(-np.linalg.inv(hess))) @cache_readonly def pvalues(self): """The p values associated with the standard errors.""" return norm.sf(np.abs(self.tvalues)) * 2 @cache_readonly def aic(self): """ Akaike Information Criterion using Lutkepohl's definition. :math:`log(sigma) + 2*(1 + k_ar + k_trend)/nobs` """ # TODO: this is based on loglike with dropped constant terms ? # Lutkepohl # return np.log(self.sigma2) + 1./self.model.nobs * self.k_ar # Include constant as estimated free parameter and double the loss return np.log(self.sigma2) + 2 * (1 + self.df_model) / self.nobs # Stata defintion # nobs = self.nobs # return -2 * self.llf/nobs + 2 * (self.k_ar+self.k_trend)/nobs @cache_readonly def hqic(self): r""" Hannan-Quinn Information Criterion using Lutkepohl's definition. :math:`\ln(\sigma) + (1 + df_{model}) 2 \ln(\ln(nobs))/nobs` """ nobs = self.nobs # Lutkepohl # return np.log(self.sigma2)+ 2 * np.log(np.log(nobs))/nobs * self.k_ar # R uses all estimated parameters rather than just lags return np.log(self.sigma2) + 2 * np.log(np.log(nobs)) / nobs * ( 1 + self.df_model ) # Stata # nobs = self.nobs # return -2 * self.llf/nobs + 2 * np.log(np.log(nobs))/nobs * \ # (self.k_ar + self.k_trend) @cache_readonly def fpe(self): """ Final prediction error using Lütkepohl's definition. ((n_totobs+k_trend)/(n_totobs-k_ar-k_trend))*sigma """ nobs = self.nobs df_model = self.df_model # Lutkepohl return ((nobs + df_model) / (nobs - df_model)) * self.sigma2 @cache_readonly def bic(self): r""" Bayes Information Criterion :math:`\ln(\sigma) + (1 + df_{model}) \ln(nobs)/nobs` """ nobs = self.nobs # Lutkepohl # return np.log(self.sigma2) + np.log(nobs)/nobs * self.k_ar # Include constant as est. free parameter return np.log(self.sigma2) + (1 + self.df_model) * np.log(nobs) / nobs # Stata # return -2 * self.llf/nobs + np.log(nobs)/nobs * (self.k_ar + \ # self.k_trend) @cache_readonly def resid(self): """ The residuals of the model. If the model is fit by 'mle' then the pre-sample residuals are calculated using fittedvalues from the Kalman Filter. """ # NOTE: uses fittedvalues because it calculate presample values for mle model = self.model endog = model.endog.squeeze() if model.method == "cmle": # elimate pre-sample return endog[self.k_ar :] - self.fittedvalues else: return model.endog.squeeze() - self.fittedvalues @cache_readonly def roots(self): """ The roots of the AR process. The roots are the solution to (1 - arparams[0]*z - arparams[1]*z**2 -...- arparams[p-1]*z**k_ar) = 0. Stability requires that the roots in modulus lie outside the unit circle. """ k = self.k_trend return np.roots(np.r_[1, -self.params[k:]]) ** -1 @cache_readonly def arfreq(self): r""" Returns the frequency of the AR roots. This is the solution, x, to z = abs(z)*exp(2j*np.pi*x) where z are the roots. """ z = self.roots return np.arctan2(z.imag, z.real) / (2 * np.pi) @cache_readonly def fittedvalues(self): """ The in-sample predicted values of the fitted AR model. The `k_ar` initial values are computed via the Kalman Filter if the model is fit by `mle`. """ return self.model.predict(self.params) @Appender(remove_parameters(AR.predict.__doc__, "params")) def predict(self, start=None, end=None, dynamic=False): params = self.params predictedvalues = self.model.predict(params, start, end, dynamic) return predictedvalues # TODO: consider returning forecast errors and confidence intervals? def summary(self, alpha=0.05): """Summarize the Model Parameters ---------- alpha : float, optional Significance level for the confidence intervals. Returns ------- smry : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary """ model = self.model title = model.__class__.__name__ + " Model Results" method = model.method # get sample start = 0 if "mle" in method else self.k_ar if self.data.dates is not None: dates = self.data.dates sample = [dates[start].strftime("%m-%d-%Y")] sample += ["- " + dates[-1].strftime("%m-%d-%Y")] else: sample = str(start) + " - " + str(len(self.data.orig_endog)) k_ar = self.k_ar order = "({0})".format(k_ar) dep_name = str(self.model.endog_names) top_left = [ ("Dep. Variable:", dep_name), ("Model:", [model.__class__.__name__ + order]), ("Method:", [method]), ("Date:", None), ("Time:", None), ("Sample:", [sample[0]]), ("", [sample[1]]), ] top_right = [ ("No. Observations:", [str(len(self.model.endog))]), ("Log Likelihood", ["%#5.3f" % self.llf]), ("S.D. of innovations", ["%#5.3f" % self.sigma2 ** 0.5]), ("AIC", ["%#5.3f" % self.aic]), ("BIC", ["%#5.3f" % self.bic]), ("HQIC", ["%#5.3f" % self.hqic]), ] smry = Summary() smry.add_table_2cols( self, gleft=top_left, gright=top_right, title=title ) smry.add_table_params(self, alpha=alpha, use_t=False) # Make the roots table from statsmodels.iolib.table import SimpleTable if k_ar: arstubs = ["AR.%d" % i for i in range(1, k_ar + 1)] stubs = arstubs roots = self.roots freq = self.arfreq else: # AR(0) model stubs = [] if len(stubs): # not AR(0) modulus = np.abs(roots) data = np.column_stack((roots.real, roots.imag, modulus, freq)) roots_table = SimpleTable( [ ( "%17.4f" % row[0], "%+17.4fj" % row[1], "%17.4f" % row[2], "%17.4f" % row[3], ) for row in data ], headers=[ " Real", " Imaginary", " Modulus", " Frequency", ], title="Roots", stubs=stubs, ) smry.tables.append(roots_table) return smry class ARResultsWrapper(wrap.ResultsWrapper): _attrs = {} _wrap_attrs = wrap.union_dicts( tsa_model.TimeSeriesResultsWrapper._wrap_attrs, _attrs ) _methods = {} _wrap_methods = wrap.union_dicts( tsa_model.TimeSeriesResultsWrapper._wrap_methods, _methods ) wrap.populate_wrapper(ARResultsWrapper, ARResults) doc = Docstring(AutoReg.predict.__doc__) _predict_params = doc.extract_parameters( ["start", "end", "dynamic", "exog", "exog_oos"], 8 ) class AutoRegResults(tsa_model.TimeSeriesModelResults): """ Class to hold results from fitting an AutoReg model. Parameters ---------- model : AutoReg Reference to the model that is fit. params : ndarray The fitted parameters from the AR Model. cov_params : ndarray The estimated covariance matrix of the model parameters. normalized_cov_params : ndarray The array inv(dot(x.T,x)) where x contains the regressors in the model. scale : float, optional An estimate of the scale of the model. """ _cache = {} # for scale setter def __init__( self, model, params, cov_params, normalized_cov_params=None, scale=1.0 ): super(AutoRegResults, self).__init__( model, params, normalized_cov_params, scale ) self._cache = {} self._params = params self._nobs = model.nobs self._n_totobs = model.endog.shape[0] self._df_model = model.df_model self._ar_lags = model.ar_lags self._max_lag = 0 if self._ar_lags.shape[0] > 0: self._max_lag = self._ar_lags.max() self._hold_back = self.model.hold_back self.cov_params_default = cov_params def initialize(self, model, params, **kwargs): """ Initialize (possibly re-initialize) a Results instance. Parameters ---------- model : Model The model instance. params : ndarray The model parameters. **kwargs Any additional keyword arguments required to initialize the model. """ self._params = params self.model = model @property def ar_lags(self): """The autoregressive lags included in the model""" return self._ar_lags @property def params(self): """The estimated parameters.""" return self._params @property def df_model(self): """The degrees of freedom consumed by the model.""" return self._df_model @property def df_resid(self): """The remaining degrees of freedom in the residuals.""" return self.nobs - self._df_model @property def nobs(self): """ The number of observations after adjusting for losses due to lags. """ return self._nobs @cache_writable() def sigma2(self): return 1.0 / self.nobs * sumofsq(self.resid) @cache_writable() # for compatability with RegressionResults def scale(self): return self.sigma2 @cache_readonly def bse(self): # allow user to specify? """ The standard errors of the estimated parameters. If `method` is 'cmle', then the standard errors that are returned are the OLS standard errors of the coefficients. If the `method` is 'mle' then they are computed using the numerical Hessian. """ return np.sqrt(np.diag(self.cov_params())) @cache_readonly def aic(self): """ Akaike Information Criterion using Lutkepohl's definition. :math:`log(sigma) + 2*(1 + df_model) / nobs` """ # This is based on loglike with dropped constant terms ? # Lutkepohl # return np.log(self.sigma2) + 1./self.model.nobs * self.k_ar # Include constant as estimated free parameter and double the loss # Stata defintion # nobs = self.nobs # return -2 * self.llf/nobs + 2 * (self.k_ar+self.k_trend)/nobs return np.log(self.sigma2) + 2 * (1 + self.df_model) / self.nobs @cache_readonly def hqic(self): r""" Hannan-Quinn Information Criterion using Lutkepohl's definition. :math:`\ln(\sigma) + (1 + df_{model}) 2 \ln(\ln(nobs))/nobs` """ # Lutkepohl # return np.log(self.sigma2)+ 2 * np.log(np.log(nobs))/nobs * self.k_ar # R uses all estimated parameters rather than just lags # Stata # nobs = self.nobs # return -2 * self.llf/nobs + 2 * np.log(np.log(nobs))/nobs * \ # (self.k_ar + self.k_trend) nobs = self.nobs loglog_n = np.log(np.log(nobs)) log_sigma2 = np.log(self.sigma2) return log_sigma2 + 2 * loglog_n / nobs * (1 + self.df_model) @cache_readonly def fpe(self): """ Final prediction error using Lütkepohl's definition. ((n_totobs+k_trend)/(n_totobs-k_ar-k_trend))*sigma """ nobs = self.nobs df_model = self.df_model # Lutkepohl return ((nobs + df_model) / (nobs - df_model)) * self.sigma2 @cache_readonly def bic(self): r""" Bayes Information Criterion :math:`\ln(\sigma) + (1 + df_{model}) \ln(nobs)/nobs` """ # Lutkepohl # np.log(self.sigma2) + np.log(nobs)/nobs * self.k_ar # Include constant as est. free parameter # Stata # -2 * self.llf/nobs + np.log(nobs)/nobs * (self.k_ar + self.k_trend) nobs = self.nobs return np.log(self.sigma2) + (1 + self.df_model) * np.log(nobs) / nobs @cache_readonly def resid(self): """ The residuals of the model. """ model = self.model endog = model.endog.squeeze() return endog[self._hold_back :] - self.fittedvalues def _lag_repr(self): """Returns poly repr of an AR, (1 -phi1 L -phi2 L^2-...)""" k_ar = len(self.ar_lags) ar_params = np.zeros(self._max_lag + 1) ar_params[0] = 1 df_model = self._df_model exog = self.model.exog k_exog = exog.shape[1] if exog is not None else 0 params = self._params[df_model - k_ar - k_exog : df_model - k_exog] for i, lag in enumerate(self._ar_lags): ar_params[lag] = -params[i] return ar_params @cache_readonly def roots(self): """ The roots of the AR process. The roots are the solution to (1 - arparams[0]*z - arparams[1]*z**2 -...- arparams[p-1]*z**k_ar) = 0. Stability requires that the roots in modulus lie outside the unit circle. """ lag_repr = self._lag_repr() if lag_repr.shape[0] == 1: return np.empty(0) return np.roots(lag_repr) ** -1 @cache_readonly def arfreq(self): r""" Returns the frequency of the AR roots. This is the solution, x, to z = abs(z)*exp(2j*np.pi*x) where z are the roots. """ z = self.roots return np.arctan2(z.imag, z.real) / (2 * np.pi) @cache_readonly def fittedvalues(self): """ The in-sample predicted values of the fitted AR model. The `k_ar` initial values are computed via the Kalman Filter if the model is fit by `mle`. """ return self.model.predict(self.params) def test_serial_correlation(self, lags=None, model_df=None): """ Ljung-Box test for residual serial correlation Parameters ---------- lags : int The maximum number of lags to use in the test. Jointly tests that all autocorrelations up to and including lag j are zero for j = 1, 2, ..., lags. If None, uses lag=12*(nobs/100)^{1/4}. After 0.12 the number of lags will change to min(10, nobs // 5). model_df : int The model degree of freedom to use when adjusting computing the test statistic to account for parameter estimation. If None, uses the number of AR lags included in the model. Returns ------- output : DataFrame DataFrame containing three columns: the test statistic, the p-value of the test, and the degree of freedom used in the test. Notes ----- Null hypothesis is no serial correlation. The the test degree-of-freedom is 0 or negative once accounting for model_df, then the test statistic's p-value is missing. See Also -------- statsmodels.stats.diagnostic.acorr_ljungbox Ljung-Box test for serial correlation. """ # Deferred to prevent circular import from statsmodels.stats.diagnostic import acorr_ljungbox lags = int_like(lags, "lags", optional=True) model_df = int_like(model_df, "df_model", optional=True) model_df = len(self.ar_lags) if model_df is None else model_df nobs_effective = self.resid.shape[0] # Default lags for acorr_ljungbox is 40, but may not always have # that many observations if lags is None: # TODO: Switch to min(10, nobs//5) after 0.12 warnings.warn( "The default value of lags is changing. After 0.12," " this value will become min(10, nobs//5). Directly " "set lags to silence this warning.", FutureWarning, ) # Future # lags = min(nobs // 5, 10) lags = int( min(12 * (nobs_effective / 100) ** (1 / 4), nobs_effective - 1) ) test_stats = acorr_ljungbox( self.resid, lags=lags, boxpierce=False, model_df=model_df, return_df=False, ) cols = ["Ljung-Box", "LB P-value", "DF"] if lags == 1: test_stats = [list(test_stats) + [max(0, 1 - model_df)]] else: df = np.clip(np.arange(1, lags + 1) - model_df, 0, np.inf).astype( np.int ) test_stats = list(test_stats) + [df] test_stats = [ [test_stats[i][j] for i in range(3)] for j in range(lags) ] index = pd.RangeIndex(1, lags + 1, name="Lag") return pd.DataFrame(test_stats, columns=cols, index=index) def test_normality(self): """ Test for normality of standardized residuals. Returns ------- Series Series containing four values, the test statistic and its p-value, the skewness and the kurtosis. Notes ----- Null hypothesis is normality. See Also -------- statsmodels.stats.stattools.jarque_bera The Jarque-Bera test of normality. """ # Deferred to prevent circular import from statsmodels.stats.stattools import jarque_bera index = ["Jarque-Bera", "P-value", "Skewness", "Kurtosis"] return pd.Series(jarque_bera(self.resid), index=index) def test_heteroskedasticity(self, lags=None): """ ARCH-LM test of residual heteroskedasticity Parameters ---------- lags : int The maximum number of lags to use in the test. Jointly tests that all squared autocorrelations up to and including lag j are zero for j = 1, 2, ..., lags. If None, uses lag=12*(nobs/100)^{1/4}. Returns ------- Series Series containing the test statistic and its p-values. See Also -------- statsmodels.stats.diagnostic.het_arch ARCH-LM test. statsmodels.stats.diagnostic.acorr_lm LM test for autocorrelation. """ from statsmodels.stats.diagnostic import het_arch lags = int_like(lags, "lags", optional=True) nobs_effective = self.resid.shape[0] if lags is None: max_lag = (nobs_effective - 1) // 2 lags = int(min(12 * (nobs_effective / 100) ** (1 / 4), max_lag)) out = [] for lag in range(1, lags + 1): res = het_arch(self.resid, nlags=lag, autolag=None) out.append([res[0], res[1], lag]) index = pd.RangeIndex(1, lags + 1, name="Lag") cols = ["ARCH-LM", "P-value", "DF"] return pd.DataFrame(out, columns=cols, index=index) def diagnostic_summary(self): """ Returns a summary containing standard model diagnostic tests Returns ------- Summary A summary instance with panels for serial correlation tests, normality tests and heteroskedasticity tests. See Also -------- test_serial_correlation Test models residuals for serial correlation. test_normality Test models residuals for deviations from normality. test_heteroskedasticity Test models residuals for conditional heteroskedasticity. """ from statsmodels.iolib.table import SimpleTable spacer = SimpleTable([""]) smry = Summary() sc = self.test_serial_correlation() sc = sc.loc[sc.DF > 0] values = [[i + 1] + row for i, row in enumerate(sc.values.tolist())] data_fmts = ("%10d", "%10.3f", "%10.3f", "%10d") if sc.shape[0]: tab = SimpleTable( values, headers=["Lag"] + list(sc.columns), title="Test of No Serial Correlation", header_align="r", data_fmts=data_fmts, ) smry.tables.append(tab) smry.tables.append(spacer) jb = self.test_normality() data_fmts = ("%10.3f", "%10.3f", "%10.3f", "%10.3f") tab = SimpleTable( [jb.values], headers=list(jb.index), title="Test of Normality", header_align="r", data_fmts=data_fmts, ) smry.tables.append(tab) smry.tables.append(spacer) arch_lm = self.test_heteroskedasticity() values = [ [i + 1] + row for i, row in enumerate(arch_lm.values.tolist()) ] data_fmts = ("%10d", "%10.3f", "%10.3f", "%10d") tab = SimpleTable( values, headers=["Lag"] + list(arch_lm.columns), title="Test of Conditional Homoskedasticity", header_align="r", data_fmts=data_fmts, ) smry.tables.append(tab) return smry @Appender(remove_parameters(AutoReg.predict.__doc__, "params")) def predict( self, start=None, end=None, dynamic=False, exog=None, exog_oos=None ): return self.model.predict( self._params, start=start, end=end, dynamic=dynamic, exog=exog, exog_oos=exog_oos, ) def get_prediction( self, start=None, end=None, dynamic=False, exog=None, exog_oos=None ): """ Predictions and prediction intervals Parameters ---------- params : array_like The fitted model parameters. start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, i.e., the last forecast is end. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out-of-sample prediction. Default is the last observation in the sample. Unlike standard python slices, end is inclusive so that all the predictions [start, start+1, ..., end-1, end] are returned. dynamic : {bool, int, str, datetime, Timestamp}, optional Integer offset relative to `start` at which to begin dynamic prediction. Prior to this observation, true endogenous values will be used for prediction; starting with this observation and continuing through the end of prediction, forecasted endogenous values will be used instead. Datetime-like objects are not interpreted as offsets. They are instead used to find the index location of `dynamic` which is then used to to compute the offset. exog : array_like A replacement exogenous array. Must have the same shape as the exogenous data array used when the model was created. exog_oos : array_like An array containing out-of-sample values of the exogenous variable. Must has the same number of columns as the exog used when the model was created, and at least as many rows as the number of out-of-sample forecasts. Returns ------- PredictionResults Prediction results with mean and prediction intervals """ mean = self.predict( start=start, end=end, dynamic=dynamic, exog=exog, exog_oos=exog_oos ) mean_var = np.zeros_like(mean) start = 0 if start is None else start end = self.model._index[-1] if end is None else end _, _, oos, _ = self.model._get_prediction_index(start, end) if oos > 0: ar_params = self._lag_repr() ma = arma2ma(ar_params, np.ones(1), lags=oos) mean_var[-oos:] = self.sigma2 * np.cumsum(ma ** 2) if isinstance(mean, pd.Series): mean_var = pd.Series(mean_var, index=mean.index) return PredictionResults(mean, mean_var) def forecast(self, steps=1, exog=None): """ Out-of-sample forecasts Parameters ---------- steps : {int, str, datetime}, default 1 If an integer, the number of steps to forecast from the end of the sample. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, steps must be an integer. exog : {ndarray, Series} A replacement exogenous array. Must have the same shape as the exogenous data array used when the model was created. Returns ------- array_like Array of out of in-sample predictions and / or out-of-sample forecasts. See Also -------- AutoRegResults.predict In- and out-of-sample predictions """ start = self.model.data.orig_endog.shape[0] if isinstance(steps, (int, np.integer)): end = start + steps - 1 else: end = steps return self.predict( start=start, end=end, dynamic=False, exog_oos=exog ) @Substitution(predict_params=_predict_params) def plot_predict( self, start=None, end=None, dynamic=False, exog=None, exog_oos=None, alpha=0.05, in_sample=True, fig=None, figsize=None, ): """ Plot in- and out-of-sample predictions Parameters ---------- %(predict_params)s alpha : {float, None} The tail probability not covered by the confidence interval. Must be in (0, 1). Confidence interval is constructed assuming normally distributed shocks. If None, figure will not show the confidence interval. in_sample : bool Flag indicating whether to include the in-sample period in the plot. fig : Figure An existing figure handle. If not provided, a new figure is created. figsize: tuple[float, float] Tuple containing the figure size values. Returns ------- Figure Figure handle containing the plot. """ from statsmodels.graphics.utils import _import_mpl, create_mpl_fig _import_mpl() fig = create_mpl_fig(fig, figsize) predictions = self.get_prediction( start=start, end=end, dynamic=dynamic, exog=exog, exog_oos=exog_oos ) start = 0 if start is None else start end = self.model._index[-1] if end is None else end _, _, oos, _ = self.model._get_prediction_index(start, end) ax = fig.add_subplot(111) mean = predictions.predicted_mean if not in_sample and oos: if isinstance(mean, pd.Series): mean = mean.iloc[-oos:] elif not in_sample: raise ValueError( "in_sample is False but there are no" "out-of-sample forecasts to plot." ) ax.plot(mean, zorder=2) if oos and alpha is not None: ci = np.asarray(predictions.conf_int(alpha)) lower, upper = ci[-oos:, 0], ci[-oos:, 1] label = "{0:.0%} confidence interval".format(1 - alpha) x = ax.get_lines()[-1].get_xdata() ax.fill_between( x[-oos:], lower, upper, color="gray", alpha=0.5, label=label, zorder=1, ) ax.legend(loc="best") return fig def plot_diagnostics(self, lags=10, fig=None, figsize=None): """ Diagnostic plots for standardized residuals Parameters ---------- lags : int, optional Number of lags to include in the correlogram. Default is 10. fig : Figure, optional If given, subplots are created in this figure instead of in a new figure. Note that the 2x2 grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Notes ----- Produces a 2x2 plot grid with the following plots (ordered clockwise from top left): 1. Standardized residuals over time 2. Histogram plus estimated density of standardized residuals, along with a Normal(0,1) density plotted for reference. 3. Normal Q-Q plot, with Normal reference line. 4. Correlogram See Also -------- statsmodels.graphics.gofplots.qqplot statsmodels.graphics.tsaplots.plot_acf """ from statsmodels.graphics.utils import _import_mpl, create_mpl_fig _import_mpl() fig = create_mpl_fig(fig, figsize) # Eliminate residuals associated with burned or diffuse likelihoods resid = self.resid # Top-left: residuals vs time ax = fig.add_subplot(221) if hasattr(self.model.data, "dates") and self.data.dates is not None: x = self.model.data.dates._mpl_repr() x = x[self.model.hold_back :] else: hold_back = self.model.hold_back x = hold_back + np.arange(self.resid.shape[0]) std_resid = resid / np.sqrt(self.sigma2) ax.plot(x, std_resid) ax.hlines(0, x[0], x[-1], alpha=0.5) ax.set_xlim(x[0], x[-1]) ax.set_title("Standardized residual") # Top-right: histogram, Gaussian kernel density, Normal density # Can only do histogram and Gaussian kernel density on the non-null # elements std_resid_nonmissing = std_resid[~(np.isnan(resid))] ax = fig.add_subplot(222) # gh5792: Remove except after support for matplotlib>2.1 required try: ax.hist(std_resid_nonmissing, density=True, label="Hist") except AttributeError: ax.hist(std_resid_nonmissing, normed=True, label="Hist") kde = gaussian_kde(std_resid) xlim = (-1.96 * 2, 1.96 * 2) x = np.linspace(xlim[0], xlim[1]) ax.plot(x, kde(x), label="KDE") ax.plot(x, norm.pdf(x), label="N(0,1)") ax.set_xlim(xlim) ax.legend() ax.set_title("Histogram plus estimated density") # Bottom-left: QQ plot ax = fig.add_subplot(223) from statsmodels.graphics.gofplots import qqplot qqplot(std_resid, line="s", ax=ax) ax.set_title("Normal Q-Q") # Bottom-right: Correlogram ax = fig.add_subplot(224) from statsmodels.graphics.tsaplots import plot_acf plot_acf(resid, ax=ax, lags=lags) ax.set_title("Correlogram") ax.set_ylim(-1, 1) return fig def summary(self, alpha=0.05): """ Summarize the Model Parameters ---------- alpha : float, optional Significance level for the confidence intervals. Returns ------- smry : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary """ model = self.model title = model.__class__.__name__ + " Model Results" method = "Conditional MLE" # get sample start = self._hold_back if self.data.dates is not None: dates = self.data.dates sample = [dates[start].strftime("%m-%d-%Y")] sample += ["- " + dates[-1].strftime("%m-%d-%Y")] else: sample = [str(start), str(len(self.data.orig_endog))] model = model.__class__.__name__ if self.model.seasonal: model = "Seas. " + model if len(self.ar_lags) < self._max_lag: model = "Restr. " + model if self.model.exog is not None: model += "-X" order = "({0})".format(self._max_lag) dep_name = str(self.model.endog_names) top_left = [ ("Dep. Variable:", [dep_name]), ("Model:", [model + order]), ("Method:", [method]), ("Date:", None), ("Time:", None), ("Sample:", [sample[0]]), ("", [sample[1]]), ] top_right = [ ("No. Observations:", [str(len(self.model.endog))]), ("Log Likelihood", ["%#5.3f" % self.llf]), ("S.D. of innovations", ["%#5.3f" % self.sigma2 ** 0.5]), ("AIC", ["%#5.3f" % self.aic]), ("BIC", ["%#5.3f" % self.bic]), ("HQIC", ["%#5.3f" % self.hqic]), ] smry = Summary() smry.add_table_2cols( self, gleft=top_left, gright=top_right, title=title ) smry.add_table_params(self, alpha=alpha, use_t=False) # Make the roots table from statsmodels.iolib.table import SimpleTable if self._max_lag: arstubs = ["AR.%d" % i for i in range(1, self._max_lag + 1)] stubs = arstubs roots = self.roots freq = self.arfreq modulus = np.abs(roots) data = np.column_stack((roots.real, roots.imag, modulus, freq)) roots_table = SimpleTable( [ ( "%17.4f" % row[0], "%+17.4fj" % row[1], "%17.4f" % row[2], "%17.4f" % row[3], ) for row in data ], headers=[ " Real", " Imaginary", " Modulus", " Frequency", ], title="Roots", stubs=stubs, ) smry.tables.append(roots_table) return smry class AutoRegResultsWrapper(wrap.ResultsWrapper): _attrs = {} _wrap_attrs = wrap.union_dicts( tsa_model.TimeSeriesResultsWrapper._wrap_attrs, _attrs ) _methods = {} _wrap_methods = wrap.union_dicts( tsa_model.TimeSeriesResultsWrapper._wrap_methods, _methods ) wrap.populate_wrapper(AutoRegResultsWrapper, AutoRegResults) doc = Docstring(AutoReg.__doc__) _auto_reg_params = doc.extract_parameters( [ "trend", "seasonal", "exog", "hold_back", "period", "missing", "old_names", ], 4, ) @Substitution(auto_reg_params=_auto_reg_params) def ar_select_order( endog, maxlag, ic="bic", glob=False, trend="c", seasonal=False, exog=None, hold_back=None, period=None, missing="none", old_names=None, ): """ Autoregressive AR-X(p) model order selection. Parameters ---------- endog : array_like A 1-d endogenous response variable. The independent variable. maxlag : int The maximum lag to consider. ic : {'aic', 'hqic', 'bic'} The information criterion to use in the selection. glob : bool Flag indicating where to use a global search across all combinations of lags. In practice, this option is not computational feasible when maxlag is larger than 15 (or perhaps 20) since the global search requires fitting 2**maxlag models. %(auto_reg_params)s Returns ------- AROrderSelectionResults A results holder containing the model and the complete set of information criteria for all models fit. Examples -------- >>> from statsmodels.tsa.ar_model import ar_select_order >>> data = sm.datasets.sunspots.load_pandas().data['SUNACTIVITY'] Determine the optimal lag structure >>> mod = ar_select_order(data, maxlag=13) >>> mod.ar_lags array([1, 2, 3, 4, 5, 6, 7, 8, 9]) Determine the optimal lag structure with seasonal terms >>> mod = ar_select_order(data, maxlag=13, seasonal=True, period=12) >>> mod.ar_lags array([1, 2, 3, 4, 5, 6, 7, 8, 9]) Globally determine the optimal lag structure >>> mod = ar_select_order(data, maxlag=13, glob=True) >>> mod.ar_lags array([1, 2, 9]) """ full_mod = AutoReg( endog, maxlag, trend=trend, seasonal=seasonal, exog=exog, hold_back=hold_back, period=period, missing=missing, old_names=old_names, ) nexog = full_mod.exog.shape[1] if full_mod.exog is not None else 0 y, x = full_mod._y, full_mod._x base_col = x.shape[1] - nexog - maxlag sel = np.ones(x.shape[1], dtype=bool) ics = [] def compute_ics(res): nobs = res.nobs df_model = res.df_model sigma2 = 1.0 / nobs * sumofsq(res.resid) res = SimpleNamespace(nobs=nobs, df_model=df_model, sigma2=sigma2) aic = AutoRegResults.aic.func(res) bic = AutoRegResults.bic.func(res) hqic = AutoRegResults.hqic.func(res) return aic, bic, hqic def ic_no_data(): """Fake mod and results to handle no regressor case""" mod = SimpleNamespace( nobs=y.shape[0], endog=y, exog=np.empty((y.shape[0], 0)) ) llf = OLS.loglike(mod, np.empty(0)) res = SimpleNamespace( resid=y, nobs=y.shape[0], llf=llf, df_model=0, k_constant=0 ) return compute_ics(res) if not glob: sel[base_col : base_col + maxlag] = False for i in range(maxlag + 1): sel[base_col : base_col + i] = True if not np.any(sel): ics.append((0, ic_no_data())) continue res = OLS(y, x[:, sel]).fit() lags = tuple(j for j in range(1, i + 1)) lags = 0 if not lags else lags ics.append((lags, compute_ics(res))) else: bits = np.arange(2 ** maxlag, dtype=np.int32)[:, None] bits = bits.view(np.uint8) bits = np.unpackbits(bits).reshape(-1, 32) for i in range(4): bits[:, 8 * i : 8 * (i + 1)] = bits[:, 8 * i : 8 * (i + 1)][ :, ::-1 ] masks = bits[:, :maxlag] for mask in masks: sel[base_col : base_col + maxlag] = mask if not np.any(sel): ics.append((0, ic_no_data())) continue res = OLS(y, x[:, sel]).fit() lags = tuple(np.where(mask)[0] + 1) lags = 0 if not lags else lags ics.append((lags, compute_ics(res))) key_loc = {"aic": 0, "bic": 1, "hqic": 2}[ic] ics = sorted(ics, key=lambda x: x[1][key_loc]) selected_model = ics[0][0] mod = AutoReg( endog, selected_model, trend=trend, seasonal=seasonal, exog=exog, hold_back=hold_back, period=period, missing=missing, old_names=old_names, ) return AROrderSelectionResults(mod, ics, trend, seasonal, period) class AROrderSelectionResults(object): """ Results from an AR order selection Contains the information criteria for all fitted model orders. """ def __init__(self, model, ics, trend, seasonal, period): self._model = model self._ics = ics self._trend = trend self._seasonal = seasonal self._period = period aic = sorted(ics, key=lambda r: r[1][0]) self._aic = dict([(key, val[0]) for key, val in aic]) bic = sorted(ics, key=lambda r: r[1][1]) self._bic = dict([(key, val[1]) for key, val in bic]) hqic = sorted(ics, key=lambda r: r[1][2]) self._hqic = dict([(key, val[2]) for key, val in hqic]) @property def model(self): """The model selected using the chosen information criterion.""" return self._model @property def seasonal(self): """Flag indicating if a seasonal component is included.""" return self._seasonal @property def trend(self): """The trend included in the model selection.""" return self._trend @property def period(self): """The period of the seasonal component.""" return self._period @property def aic(self): """ The Akaike information criterion for the models fit. Returns ------- dict[tuple, float] """ return self._aic @property def bic(self): """ The Bayesian (Schwarz) information criteria for the models fit. Returns ------- dict[tuple, float] """ return self._bic @property def hqic(self): """ The Hannan-Quinn information criteria for the models fit. Returns ------- dict[tuple, float] """ return self._hqic @property def ar_lags(self): """The lags included in the selected model.""" return self._model.ar_lags statsmodels-0.12.2/statsmodels/tsa/arima/000077500000000000000000000000001400612667500203675ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/__init__.py000066400000000000000000000000001400612667500224660ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/api.py000066400000000000000000000000561400612667500215130ustar00rootroot00000000000000__all__ = ["ARIMA"] from .model import ARIMA statsmodels-0.12.2/statsmodels/tsa/arima/datasets/000077500000000000000000000000001400612667500221775ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/datasets/__init__.py000066400000000000000000000000001400612667500242760ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/datasets/brockwell_davis_2002/000077500000000000000000000000001400612667500260145ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/datasets/brockwell_davis_2002/__init__.py000077500000000000000000000005651400612667500301360ustar00rootroot00000000000000__all__ = ['dowj', 'lake', 'oshorts', 'sbl'] from statsmodels.tsa.arima.datasets.brockwell_davis_2002.data.dowj import dowj from statsmodels.tsa.arima.datasets.brockwell_davis_2002.data.lake import lake from statsmodels.tsa.arima.datasets.brockwell_davis_2002.data.oshorts import ( oshorts) from statsmodels.tsa.arima.datasets.brockwell_davis_2002.data.sbl import sbl statsmodels-0.12.2/statsmodels/tsa/arima/datasets/brockwell_davis_2002/data/000077500000000000000000000000001400612667500267255ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/datasets/brockwell_davis_2002/data/__init__.py000066400000000000000000000000001400612667500310240ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/datasets/brockwell_davis_2002/data/dowj.py000066400000000000000000000025331400612667500302450ustar00rootroot00000000000000""" Dow-Jones Utilities Index, Aug.28--Dec.18, 1972. Dataset described in [1]_ and included as a part of the ITSM2000 software [2]_. Downloaded on April 22, 2019 from: http://www.springer.com/cda/content/document/cda_downloaddocument/ITSM2000.zip See also https://finance.yahoo.com/quote/%5EDJU/history?period1=83822400&period2=93502800&interval=1d&filter=history&frequency=1d TODO: Add the correct business days index for this data (freq='B' does not work) References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. .. [2] Brockwell, Peter J., and Richard A. Davis. n.d. ITSM2000. """ # noqa:E501 import pandas as pd dowj = pd.Series([ 110.94, 110.69, 110.43, 110.56, 110.75, 110.84, 110.46, 110.56, 110.46, 110.05, 109.6, 109.31, 109.31, 109.25, 109.02, 108.54, 108.77, 109.02, 109.44, 109.38, 109.53, 109.89, 110.56, 110.56, 110.72, 111.23, 111.48, 111.58, 111.9, 112.19, 112.06, 111.96, 111.68, 111.36, 111.42, 112, 112.22, 112.7, 113.15, 114.36, 114.65, 115.06, 115.86, 116.4, 116.44, 116.88, 118.07, 118.51, 119.28, 119.79, 119.7, 119.28, 119.66, 120.14, 120.97, 121.13, 121.55, 121.96, 122.26, 123.79, 124.11, 124.14, 123.37, 123.02, 122.86, 123.02, 123.11, 123.05, 123.05, 122.83, 123.18, 122.67, 122.73, 122.86, 122.67, 122.09, 122, 121.23]) statsmodels-0.12.2/statsmodels/tsa/arima/datasets/brockwell_davis_2002/data/lake.py000077500000000000000000000023041400612667500302150ustar00rootroot00000000000000""" Lake level of Lake Huron in feet (reduced by 570), 1875--1972. Dataset described in [1]_ and included as a part of the ITSM2000 software [2]_. Downloaded on April 22, 2019 from: http://www.springer.com/cda/content/document/cda_downloaddocument/ITSM2000.zip References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. .. [2] Brockwell, Peter J., and Richard A. Davis. n.d. ITSM2000. """ import pandas as pd lake = pd.Series([ 10.38, 11.86, 10.97, 10.8, 9.79, 10.39, 10.42, 10.82, 11.4, 11.32, 11.44, 11.68, 11.17, 10.53, 10.01, 9.91, 9.14, 9.16, 9.55, 9.67, 8.44, 8.24, 9.1, 9.09, 9.35, 8.82, 9.32, 9.01, 9, 9.8, 9.83, 9.72, 9.89, 10.01, 9.37, 8.69, 8.19, 8.67, 9.55, 8.92, 8.09, 9.37, 10.13, 10.14, 9.51, 9.24, 8.66, 8.86, 8.05, 7.79, 6.75, 6.75, 7.82, 8.64, 10.58, 9.48, 7.38, 6.9, 6.94, 6.24, 6.84, 6.85, 6.9, 7.79, 8.18, 7.51, 7.23, 8.42, 9.61, 9.05, 9.26, 9.22, 9.38, 9.1, 7.95, 8.12, 9.75, 10.85, 10.41, 9.96, 9.61, 8.76, 8.18, 7.21, 7.13, 9.1, 8.25, 7.91, 6.89, 5.96, 6.8, 7.68, 8.38, 8.52, 9.74, 9.31, 9.89, 9.96], index=pd.period_range(start='1875', end='1972', freq='A').to_timestamp()) statsmodels-0.12.2/statsmodels/tsa/arima/datasets/brockwell_davis_2002/data/oshorts.py000066400000000000000000000014631400612667500310040ustar00rootroot00000000000000""" 57 consecutive daily overshorts from an underground gasoline tank at a filling station in Colorado Dataset described in [1]_ and included as a part of the ITSM2000 software [2]_. Downloaded on April 22, 2019 from: http://www.springer.com/cda/content/document/cda_downloaddocument/ITSM2000.zip References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. .. [2] Brockwell, Peter J., and Richard A. Davis. n.d. ITSM2000. """ import pandas as pd oshorts = pd.Series([ 78, -58, 53, -65, 13, -6, -16, -14, 3, -72, 89, -48, -14, 32, 56, -86, -66, 50, 26, 59, -47, -83, 2, -1, 124, -106, 113, -76, -47, -32, 39, -30, 6, -73, 18, 2, -24, 23, -38, 91, -56, -58, 1, 14, -4, 77, -127, 97, 10, -28, -17, 23, -2, 48, -131, 65, -17]) statsmodels-0.12.2/statsmodels/tsa/arima/datasets/brockwell_davis_2002/data/sbl.py000066400000000000000000000025671400612667500300710ustar00rootroot00000000000000""" The number of car drivers killed or seriously injured monthly in Great Britain for ten years beginning in January 1975 Dataset described in [1]_ and included as a part of the ITSM2000 software [2]_. Downloaded on April 22, 2019 from: http://www.springer.com/cda/content/document/cda_downloaddocument/ITSM2000.zip References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. .. [2] Brockwell, Peter J., and Richard A. Davis. n.d. ITSM2000. """ import pandas as pd sbl = pd.Series([ 1577, 1356, 1652, 1382, 1519, 1421, 1442, 1543, 1656, 1561, 1905, 2199, 1473, 1655, 1407, 1395, 1530, 1309, 1526, 1327, 1627, 1748, 1958, 2274, 1648, 1401, 1411, 1403, 1394, 1520, 1528, 1643, 1515, 1685, 2000, 2215, 1956, 1462, 1563, 1459, 1446, 1622, 1657, 1638, 1643, 1683, 2050, 2262, 1813, 1445, 1762, 1461, 1556, 1431, 1427, 1554, 1645, 1653, 2016, 2207, 1665, 1361, 1506, 1360, 1453, 1522, 1460, 1552, 1548, 1827, 1737, 1941, 1474, 1458, 1542, 1404, 1522, 1385, 1641, 1510, 1681, 1938, 1868, 1726, 1456, 1445, 1456, 1365, 1487, 1558, 1488, 1684, 1594, 1850, 1998, 2079, 1494, 1057, 1218, 1168, 1236, 1076, 1174, 1139, 1427, 1487, 1483, 1513, 1357, 1165, 1282, 1110, 1297, 1185, 1222, 1284, 1444, 1575, 1737, 1763], index=pd.date_range(start='1975-01-01', end='1984-12-01', freq='MS')) statsmodels-0.12.2/statsmodels/tsa/arima/estimators/000077500000000000000000000000001400612667500225615ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/estimators/__init__.py000066400000000000000000000000001400612667500246600ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/estimators/burg.py000066400000000000000000000043571400612667500241030ustar00rootroot00000000000000""" Burg's method for estimating AR(p) model parameters. Author: Chad Fulton License: BSD-3 """ import numpy as np from statsmodels.tools.tools import Bunch from statsmodels.regression import linear_model from statsmodels.tsa.arima.specification import SARIMAXSpecification from statsmodels.tsa.arima.params import SARIMAXParams def burg(endog, ar_order=0, demean=True): """ Estimate AR parameters using Burg technique. Parameters ---------- endog : array_like or SARIMAXSpecification Input time series array, assumed to be stationary. ar_order : int, optional Autoregressive order. Default is 0. demean : bool, optional Whether to estimate and remove the mean from the process prior to fitting the autoregressive coefficients. Returns ------- parameters : SARIMAXParams object Contains the parameter estimates from the final iteration. other_results : Bunch Includes one component, `spec`, which is the `SARIMAXSpecification` instance corresponding to the input arguments. Notes ----- The primary reference is [1]_, section 5.1.2. This procedure assumes that the series is stationary. This function is a light wrapper around `statsmodels.linear_model.burg`. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. """ spec = SARIMAXSpecification(endog, ar_order=ar_order) endog = spec.endog # Workaround for statsmodels.tsa.stattools.pacf_burg which does not work # on integer input # TODO: remove when possible if np.issubdtype(endog.dtype, np.dtype(int)): endog = endog * 1.0 if not spec.is_ar_consecutive: raise ValueError('Burg estimation unavailable for models with' ' seasonal or otherwise non-consecutive AR orders.') p = SARIMAXParams(spec=spec) if ar_order == 0: p.sigma2 = np.var(endog) else: p.ar_params, p.sigma2 = linear_model.burg(endog, order=ar_order, demean=demean) # Construct other results other_results = Bunch({ 'spec': spec, }) return p, other_results statsmodels-0.12.2/statsmodels/tsa/arima/estimators/durbin_levinson.py000066400000000000000000000067651400612667500263510ustar00rootroot00000000000000""" Durbin-Levinson recursions for estimating AR(p) model parameters. Author: Chad Fulton License: BSD-3 """ from statsmodels.compat.pandas import deprecate_kwarg import numpy as np from statsmodels.tools.tools import Bunch from statsmodels.tsa.arima.params import SARIMAXParams from statsmodels.tsa.arima.specification import SARIMAXSpecification from statsmodels.tsa.stattools import acovf @deprecate_kwarg("unbiased", "adjusted") def durbin_levinson(endog, ar_order=0, demean=True, adjusted=False): """ Estimate AR parameters at multiple orders using Durbin-Levinson recursions. Parameters ---------- endog : array_like or SARIMAXSpecification Input time series array, assumed to be stationary. ar_order : int, optional Autoregressive order. Default is 0. demean : bool, optional Whether to estimate and remove the mean from the process prior to fitting the autoregressive coefficients. Default is True. adjusted : bool, optional Whether to use the "adjusted" autocovariance estimator, which uses n - h degrees of freedom rather than n. This option can result in a non-positive definite autocovariance matrix. Default is False. Returns ------- parameters : list of SARIMAXParams objects List elements correspond to estimates at different `ar_order`. For example, parameters[0] is an `SARIMAXParams` instance corresponding to `ar_order=0`. other_results : Bunch Includes one component, `spec`, containing the `SARIMAXSpecification` instance corresponding to the input arguments. Notes ----- The primary reference is [1]_, section 2.5.1. This procedure assumes that the series is stationary. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. """ max_spec = SARIMAXSpecification(endog, ar_order=ar_order) endog = max_spec.endog # Make sure we have a consecutive process if not max_spec.is_ar_consecutive: raise ValueError('Durbin-Levinson estimation unavailable for models' ' with seasonal or otherwise non-consecutive AR' ' orders.') gamma = acovf(endog, adjusted=adjusted, fft=True, demean=demean, nlag=max_spec.ar_order) # If no AR component, just a variance computation if max_spec.ar_order == 0: ar_params = [None] sigma2 = [gamma[0]] # Otherwise, AR model else: Phi = np.zeros((max_spec.ar_order, max_spec.ar_order)) v = np.zeros(max_spec.ar_order + 1) Phi[0, 0] = gamma[1] / gamma[0] v[0] = gamma[0] v[1] = v[0] * (1 - Phi[0, 0]**2) for i in range(1, max_spec.ar_order): tmp = Phi[i-1, :i] Phi[i, i] = (gamma[i + 1] - np.dot(tmp, gamma[i:0:-1])) / v[i] Phi[i, :i] = (tmp - Phi[i, i] * tmp[::-1]) v[i + 1] = v[i] * (1 - Phi[i, i]**2) ar_params = [None] + [Phi[i, :i + 1] for i in range(max_spec.ar_order)] sigma2 = v # Compute output out = [] for i in range(max_spec.ar_order + 1): spec = SARIMAXSpecification(ar_order=i) p = SARIMAXParams(spec=spec) if i == 0: p.params = sigma2[i] else: p.params = np.r_[ar_params[i], sigma2[i]] out.append(p) # Construct other results other_results = Bunch({ 'spec': spec, }) return out, other_results statsmodels-0.12.2/statsmodels/tsa/arima/estimators/gls.py000066400000000000000000000314151400612667500237240ustar00rootroot00000000000000""" Feasible generalized least squares for regression with SARIMA errors. Author: Chad Fulton License: BSD-3 """ import numpy as np import warnings from statsmodels.tools.tools import add_constant, Bunch from statsmodels.regression.linear_model import OLS from statsmodels.tsa.innovations import arma_innovations from statsmodels.tsa.statespace.tools import diff from statsmodels.tsa.arima.estimators.yule_walker import yule_walker from statsmodels.tsa.arima.estimators.burg import burg from statsmodels.tsa.arima.estimators.hannan_rissanen import hannan_rissanen from statsmodels.tsa.arima.estimators.innovations import ( innovations, innovations_mle) from statsmodels.tsa.arima.estimators.statespace import statespace from statsmodels.tsa.arima.specification import SARIMAXSpecification from statsmodels.tsa.arima.params import SARIMAXParams def gls(endog, exog=None, order=(0, 0, 0), seasonal_order=(0, 0, 0, 0), include_constant=None, n_iter=None, max_iter=50, tolerance=1e-8, arma_estimator='innovations_mle', arma_estimator_kwargs=None): """ Estimate ARMAX parameters by GLS. Parameters ---------- endog : array_like Input time series array. exog : array_like, optional Array of exogenous regressors. If not included, then `include_constant` must be True, and then `exog` will only include the constant column. order : tuple, optional The (p,d,q) order of the ARIMA model. Default is (0, 0, 0). seasonal_order : tuple, optional The (P,D,Q,s) order of the seasonal ARIMA model. Default is (0, 0, 0, 0). include_constant : bool, optional Whether to add a constant term in `exog` if it's not already there. The estimate of the constant will then appear as one of the `exog` parameters. If `exog` is None, then the constant will represent the mean of the process. Default is True if the specified model does not include integration and False otherwise. n_iter : int, optional Optionally iterate feasible GSL a specific number of times. Default is to iterate to convergence. If set, this argument overrides the `max_iter` and `tolerance` arguments. max_iter : int, optional Maximum number of feasible GLS iterations. Default is 50. If `n_iter` is set, it overrides this argument. tolerance : float, optional Tolerance for determining convergence of feasible GSL iterations. If `iter` is set, this argument has no effect. Default is 1e-8. arma_estimator : str, optional The estimator used for estimating the ARMA model. This option should not generally be used, unless the default method is failing or is otherwise unsuitable. Not all values will be valid, depending on the specified model orders (`order` and `seasonal_order`). Possible values are: * 'innovations_mle' - can be used with any specification * 'statespace' - can be used with any specification * 'hannan_rissanen' - can be used with any ARMA non-seasonal model * 'yule_walker' - only non-seasonal consecutive autoregressive (AR) models * 'burg' - only non-seasonal, consecutive autoregressive (AR) models * 'innovations' - only non-seasonal, consecutive moving average (MA) models. The default is 'innovations_mle'. arma_estimator_kwargs : dict, optional Arguments to pass to the ARMA estimator. Returns ------- parameters : SARIMAXParams object Contains the parameter estimates from the final iteration. other_results : Bunch Includes eight components: `spec`, `params`, `converged`, `differences`, `iterations`, `arma_estimator`, 'arma_estimator_kwargs', and `arma_results`. Notes ----- The primary reference is [1]_, section 6.6. In particular, the implementation follows the iterative procedure described in section 6.6.2. Construction of the transformed variables used to compute the GLS estimator described in section 6.6.1 is done via an application of the innovations algorithm (rather than explicit construction of the transformation matrix). Note that if the specified model includes integration, both the `endog` and `exog` series will be differenced prior to estimation and a warning will be issued to alert the user. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. """ # Handle n_iter if n_iter is not None: max_iter = n_iter tolerance = np.inf # Default for include_constant is True if there is no integration and # False otherwise integrated = order[1] > 0 or seasonal_order[1] > 0 if include_constant is None: include_constant = not integrated elif include_constant and integrated: raise ValueError('Cannot include a constant in an integrated model.') # Handle including the constant (need to do it now so that the constant # parameter can be included in the specification as part of `exog`.) if include_constant: exog = np.ones_like(endog) if exog is None else add_constant(exog) # Create the SARIMAX specification spec = SARIMAXSpecification(endog, exog=exog, order=order, seasonal_order=seasonal_order) endog = spec.endog exog = spec.exog # Handle integration if spec.is_integrated: # TODO: this is the approach suggested by BD (see Remark 1 in # section 6.6.2 and Example 6.6.3), but maybe there are some cases # where we don't want to force this behavior on the user? warnings.warn('Provided `endog` and `exog` series have been' ' differenced to eliminate integration prior to GLS' ' parameter estimation.') endog = diff(endog, k_diff=spec.diff, k_seasonal_diff=spec.seasonal_diff, seasonal_periods=spec.seasonal_periods) exog = diff(exog, k_diff=spec.diff, k_seasonal_diff=spec.seasonal_diff, seasonal_periods=spec.seasonal_periods) augmented = np.c_[endog, exog] # Validate arma_estimator spec.validate_estimator(arma_estimator) if arma_estimator_kwargs is None: arma_estimator_kwargs = {} # Step 1: OLS mod_ols = OLS(endog, exog) res_ols = mod_ols.fit() exog_params = res_ols.params resid = res_ols.resid # 0th iteration parameters p = SARIMAXParams(spec=spec) p.exog_params = exog_params if spec.max_ar_order > 0: p.ar_params = np.zeros(spec.k_ar_params) if spec.max_seasonal_ar_order > 0: p.seasonal_ar_params = np.zeros(spec.k_seasonal_ar_params) if spec.max_ma_order > 0: p.ma_params = np.zeros(spec.k_ma_params) if spec.max_seasonal_ma_order > 0: p.seasonal_ma_params = np.zeros(spec.k_seasonal_ma_params) p.sigma2 = res_ols.scale ar_params = p.ar_params seasonal_ar_params = p.seasonal_ar_params ma_params = p.ma_params seasonal_ma_params = p.seasonal_ma_params sigma2 = p.sigma2 # Step 2 - 4: iterate feasible GLS to convergence arma_results = [None] differences = [None] parameters = [p] converged = False if n_iter is None else None i = 0 for i in range(1, max_iter + 1): prev = exog_params # Step 2: ARMA # TODO: allow estimator-specific kwargs? if arma_estimator == 'yule_walker': p_arma, res_arma = yule_walker( resid, ar_order=spec.ar_order, demean=False, **arma_estimator_kwargs) elif arma_estimator == 'burg': p_arma, res_arma = burg(resid, ar_order=spec.ar_order, demean=False, **arma_estimator_kwargs) elif arma_estimator == 'innovations': out, res_arma = innovations(resid, ma_order=spec.ma_order, demean=False, **arma_estimator_kwargs) p_arma = out[-1] elif arma_estimator == 'hannan_rissanen': p_arma, res_arma = hannan_rissanen( resid, ar_order=spec.ar_order, ma_order=spec.ma_order, demean=False, **arma_estimator_kwargs) else: # For later iterations, use a "warm start" for parameter estimates # (speeds up estimation and convergence) start_params = ( None if i == 1 else np.r_[ar_params, ma_params, seasonal_ar_params, seasonal_ma_params, sigma2]) # Note: in each case, we do not pass in the order of integration # since we have already differenced the series tmp_order = (spec.order[0], 0, spec.order[2]) tmp_seasonal_order = (spec.seasonal_order[0], 0, spec.seasonal_order[2], spec.seasonal_order[3]) if arma_estimator == 'innovations_mle': p_arma, res_arma = innovations_mle( resid, order=tmp_order, seasonal_order=tmp_seasonal_order, demean=False, start_params=start_params, **arma_estimator_kwargs) else: p_arma, res_arma = statespace( resid, order=tmp_order, seasonal_order=tmp_seasonal_order, include_constant=False, start_params=start_params, **arma_estimator_kwargs) ar_params = p_arma.ar_params seasonal_ar_params = p_arma.seasonal_ar_params ma_params = p_arma.ma_params seasonal_ma_params = p_arma.seasonal_ma_params sigma2 = p_arma.sigma2 arma_results.append(res_arma) # Step 3: GLS # Compute transformed variables that satisfy OLS assumptions # Note: In section 6.1.1 of Brockwell and Davis (2016), these # transformations are developed as computed by left multiplcation # by a matrix T. However, explicitly constructing T and then # performing the left-multiplications does not scale well when nobs is # large. Instead, we can retrieve the transformed variables as the # residuals of the innovations algorithm (the `normalize=True` # argument applies a Prais-Winsten-type normalization to the first few # observations to ensure homoskedasticity). Brockwell and Davis # mention that they also take this approach in practice. # GH-6540: AR must be stationary if not p_arma.is_stationary: raise ValueError( "Roots of the autoregressive parameters indicate that data is" "non-stationary. GLS cannot be used with non-stationary " "parameters. You should consider differencing the model data" "or applying a nonlinear transformation (e.g., natural log)." ) tmp, _ = arma_innovations.arma_innovations( augmented, ar_params=ar_params, ma_params=ma_params, normalize=True) u = tmp[:, 0] x = tmp[:, 1:] # OLS on transformed variables mod_gls = OLS(u, x) res_gls = mod_gls.fit() exog_params = res_gls.params resid = endog - np.dot(exog, exog_params) # Construct the parameter vector for the iteration p = SARIMAXParams(spec=spec) p.exog_params = exog_params if spec.max_ar_order > 0: p.ar_params = ar_params if spec.max_seasonal_ar_order > 0: p.seasonal_ar_params = seasonal_ar_params if spec.max_ma_order > 0: p.ma_params = ma_params if spec.max_seasonal_ma_order > 0: p.seasonal_ma_params = seasonal_ma_params p.sigma2 = sigma2 parameters.append(p) # Check for convergence difference = np.abs(exog_params - prev) differences.append(difference) if n_iter is None and np.all(difference < tolerance): converged = True break else: if n_iter is None: warnings.warn('Feasible GLS failed to converge in %d iterations.' ' Consider increasing the maximum number of' ' iterations using the `max_iter` argument or' ' reducing the required tolerance using the' ' `tolerance` argument.' % max_iter) # Construct final results p = parameters[-1] other_results = Bunch({ 'spec': spec, 'params': parameters, 'converged': converged, 'differences': differences, 'iterations': i, 'arma_estimator': arma_estimator, 'arma_estimator_kwargs': arma_estimator_kwargs, 'arma_results': arma_results, }) return p, other_results statsmodels-0.12.2/statsmodels/tsa/arima/estimators/hannan_rissanen.py000066400000000000000000000207761400612667500263140ustar00rootroot00000000000000""" Hannan-Rissanen procedure for estimating ARMA(p,q) model parameters. Author: Chad Fulton License: BSD-3 """ import numpy as np from scipy.signal import lfilter from statsmodels.tools.tools import Bunch from statsmodels.regression.linear_model import OLS, yule_walker from statsmodels.tsa.tsatools import lagmat from statsmodels.tsa.arima.specification import SARIMAXSpecification from statsmodels.tsa.arima.params import SARIMAXParams def hannan_rissanen(endog, ar_order=0, ma_order=0, demean=True, initial_ar_order=None, unbiased=None): """ Estimate ARMA parameters using Hannan-Rissanen procedure. Parameters ---------- endog : array_like Input time series array, assumed to be stationary. ar_order : int Autoregressive order ma_order : int Moving average order demean : bool, optional Whether to estimate and remove the mean from the process prior to fitting the ARMA coefficients. Default is True. initial_ar_order : int, optional Order of long autoregressive process used for initial computation of residuals. unbiased : bool, optional Whether or not to apply the bias correction step. Default is True if the estimated coefficients from the previous step imply a stationary and invertible process and False otherwise. Returns ------- parameters : SARIMAXParams object other_results : Bunch Includes three components: `spec`, containing the `SARIMAXSpecification` instance corresponding to the input arguments; `initial_ar_order`, containing the autoregressive lag order used in the first step; and `resid`, which contains the computed residuals from the last step. Notes ----- The primary reference is [1]_, section 5.1.4, which describes a three-step procedure that we implement here. 1. Fit a large-order AR model via Yule-Walker to estimate residuals 2. Compute AR and MA estimates via least squares 3. (Unless the estimated coefficients from step (2) are non-stationary / non-invertible or `unbiased=False`) Perform bias correction The order used for the AR model in the first step may be given as an argument. If it is not, we compute it as suggested by [2]_. The estimate of the variance that we use is computed from the residuals of the least-squares regression and not from the innovations algorithm. This is because our fast implementation of the innovations algorithm is only valid for stationary processes, and the Hannan-Rissanen procedure may produce estimates that imply non-stationary processes. To avoid inconsistency, we never compute this latter variance here, even if it is possible. See test_hannan_rissanen::test_brockwell_davis_example_517 for an example of how to compute this variance manually. This procedure assumes that the series is stationary, but if this is not true, it is still possible that this procedure will return parameters that imply a non-stationary / non-invertible process. Note that the third stage will only be applied if the parameters from the second stage imply a stationary / invertible model. If `unbiased=True` is given, then non-stationary / non-invertible parameters in the second stage will throw an exception. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. .. [2] Gomez, Victor, and Agustin Maravall. 2001. "Automatic Modeling Methods for Univariate Series." A Course in Time Series Analysis, 171–201. """ spec = SARIMAXSpecification(endog, ar_order=ar_order, ma_order=ma_order) endog = spec.endog if demean: endog = endog - endog.mean() p = SARIMAXParams(spec=spec) nobs = len(endog) max_ar_order = spec.max_ar_order max_ma_order = spec.max_ma_order # Default initial_ar_order is as suggested by Gomez and Maravall (2001) if initial_ar_order is None: initial_ar_order = max(np.floor(np.log(nobs)**2).astype(int), 2 * max(max_ar_order, max_ma_order)) # Create a spec, just to validate the initial autoregressive order _ = SARIMAXSpecification(endog, ar_order=initial_ar_order) # Compute lagged endog # (`ar_ix`, and `ma_ix` below, are to account for non-consecutive lags; # for indexing purposes, must have dtype int) ar_ix = np.array(spec.ar_lags, dtype=int) - 1 lagged_endog = lagmat(endog, max_ar_order, trim='both')[:, ar_ix] # If no AR or MA components, this is just a variance computation if max_ma_order == 0 and max_ar_order == 0: p.sigma2 = np.var(endog, ddof=0) resid = endog.copy() # If no MA component, this is just CSS elif max_ma_order == 0: mod = OLS(endog[max_ar_order:], lagged_endog) res = mod.fit() resid = res.resid p.ar_params = res.params p.sigma2 = res.scale # Otherwise ARMA model else: # Step 1: Compute long AR model via Yule-Walker, get residuals initial_ar_params, _ = yule_walker( endog, order=initial_ar_order, method='mle') X = lagmat(endog, initial_ar_order, trim='both') y = endog[initial_ar_order:] resid = y - X.dot(initial_ar_params) # Get lagged residuals for `exog` in least-squares regression ma_ix = np.array(spec.ma_lags, dtype=int) - 1 lagged_resid = lagmat(resid, max_ma_order, trim='both')[:, ma_ix] # Step 2: estimate ARMA model via least squares ix = initial_ar_order + max_ma_order - max_ar_order mod = OLS(endog[initial_ar_order + max_ma_order:], np.c_[lagged_endog[ix:], lagged_resid]) res = mod.fit() p.ar_params = res.params[:spec.k_ar_params] p.ma_params = res.params[spec.k_ar_params:] resid = res.resid p.sigma2 = res.scale # Step 3: bias correction (if requested) if unbiased is True or unbiased is None: if p.is_stationary and p.is_invertible: Z = np.zeros_like(endog) V = np.zeros_like(endog) W = np.zeros_like(endog) ar_coef = p.ar_poly.coef ma_coef = p.ma_poly.coef for t in range(nobs): if t >= max(max_ar_order, max_ma_order): # Note: in the case of non-consecutive lag orders, the # polynomials have the appropriate zeros so we don't # need to subset `endog[t - max_ar_order:t]` or # Z[t - max_ma_order:t] tmp_ar = np.dot( -ar_coef[1:], endog[t - max_ar_order:t][::-1]) tmp_ma = np.dot(ma_coef[1:], Z[t - max_ma_order:t][::-1]) Z[t] = endog[t] - tmp_ar - tmp_ma V = lfilter([1], ar_coef, Z) W = lfilter(np.r_[1, -ma_coef[1:]], [1], Z) lagged_V = lagmat(V, max_ar_order, trim='both') lagged_W = lagmat(W, max_ma_order, trim='both') exog = np.c_[ lagged_V[max(max_ma_order - max_ar_order, 0):, ar_ix], lagged_W[max(max_ar_order - max_ma_order, 0):, ma_ix]] mod_unbias = OLS(Z[max(max_ar_order, max_ma_order):], exog) res_unbias = mod_unbias.fit() p.ar_params = ( p.ar_params + res_unbias.params[:spec.k_ar_params]) p.ma_params = ( p.ma_params + res_unbias.params[spec.k_ar_params:]) # Recompute sigma2 resid = mod.endog - mod.exog.dot( np.r_[p.ar_params, p.ma_params]) p.sigma2 = np.inner(resid, resid) / len(resid) elif unbiased is True: raise ValueError('Cannot perform third step of Hannan-Rissanen' ' estimation to remove parameter bias,' ' because parameters estimated from the' ' second step are non-stationary or' ' non-invertible') # TODO: Gomez and Maravall (2001) or Gomez (1998) # propose one more step here to further improve MA estimates # Construct results other_results = Bunch({ 'spec': spec, 'initial_ar_order': initial_ar_order, 'resid': resid }) return p, other_results statsmodels-0.12.2/statsmodels/tsa/arima/estimators/innovations.py000066400000000000000000000226731400612667500255140ustar00rootroot00000000000000""" Innovations algorithm for MA(q) and SARIMA(p,d,q)x(P,D,Q,s) model parameters. Author: Chad Fulton License: BSD-3 """ import warnings import numpy as np from scipy.optimize import minimize from statsmodels.tools.tools import Bunch from statsmodels.tsa.innovations import arma_innovations from statsmodels.tsa.stattools import acovf, innovations_algo from statsmodels.tsa.statespace.tools import diff from statsmodels.tsa.arima.specification import SARIMAXSpecification from statsmodels.tsa.arima.params import SARIMAXParams from statsmodels.tsa.arima.estimators.hannan_rissanen import hannan_rissanen def innovations(endog, ma_order=0, demean=True): """ Estimate MA parameters using innovations algorithm. Parameters ---------- endog : array_like or SARIMAXSpecification Input time series array, assumed to be stationary. ma_order : int, optional Maximum moving average order. Default is 0. demean : bool, optional Whether to estimate and remove the mean from the process prior to fitting the moving average coefficients. Default is True. Returns ------- parameters : list of SARIMAXParams objects List elements correspond to estimates at different `ma_order`. For example, parameters[0] is an `SARIMAXParams` instance corresponding to `ma_order=0`. other_results : Bunch Includes one component, `spec`, containing the `SARIMAXSpecification` instance corresponding to the input arguments. Notes ----- The primary reference is [1]_, section 5.1.3. This procedure assumes that the series is stationary. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. """ max_spec = SARIMAXSpecification(endog, ma_order=ma_order) endog = max_spec.endog if demean: endog = endog - endog.mean() if not max_spec.is_ma_consecutive: raise ValueError('Innovations estimation unavailable for models with' ' seasonal or otherwise non-consecutive MA orders.') sample_acovf = acovf(endog, fft=True) theta, v = innovations_algo(sample_acovf, nobs=max_spec.ma_order + 1) ma_params = [theta[i, :i] for i in range(1, max_spec.ma_order + 1)] sigma2 = v out = [] for i in range(max_spec.ma_order + 1): spec = SARIMAXSpecification(ma_order=i) p = SARIMAXParams(spec=spec) if i == 0: p.params = sigma2[i] else: p.params = np.r_[ma_params[i - 1], sigma2[i]] out.append(p) # Construct other results other_results = Bunch({ 'spec': spec, }) return out, other_results def innovations_mle(endog, order=(0, 0, 0), seasonal_order=(0, 0, 0, 0), demean=True, enforce_invertibility=True, start_params=None, minimize_kwargs=None): """ Estimate SARIMA parameters by MLE using innovations algorithm. Parameters ---------- endog : array_like Input time series array. order : tuple, optional The (p,d,q) order of the model for the number of AR parameters, differences, and MA parameters. Default is (0, 0, 0). seasonal_order : tuple, optional The (P,D,Q,s) order of the seasonal component of the model for the AR parameters, differences, MA parameters, and periodicity. Default is (0, 0, 0, 0). demean : bool, optional Whether to estimate and remove the mean from the process prior to fitting the SARIMA coefficients. Default is True. enforce_invertibility : bool, optional Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. Default is True. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The AR polynomial must be stationary. If `enforce_invertibility=True` the MA poylnomial must be invertible. If not provided, default starting parameters are computed using the Hannan-Rissanen method. minimize_kwargs : dict, optional Arguments to pass to scipy.optimize.minimize. Returns ------- parameters : SARIMAXParams object other_results : Bunch Includes four components: `spec`, containing the `SARIMAXSpecification` instance corresponding to the input arguments; `minimize_kwargs`, containing any keyword arguments passed to `minimize`; `start_params`, containing the untransformed starting parameters passed to `minimize`; and `minimize_results`, containing the output from `minimize`. Notes ----- The primary reference is [1]_, section 5.2. Note: we do not include `enforce_stationarity` as an argument, because this function requires stationarity. TODO: support concentrating out the scale (should be easy: use sigma2=1 and then compute sigma2=np.sum(u**2 / v) / len(u); would then need to redo llf computation in the Cython function). TODO: add support for fixed parameters TODO: add support for secondary optimization that does not enforce stationarity / invertibility, starting from first step's parameters References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. """ spec = SARIMAXSpecification( endog, order=order, seasonal_order=seasonal_order, enforce_stationarity=True, enforce_invertibility=enforce_invertibility) endog = spec.endog if spec.is_integrated: warnings.warn('Provided `endog` series has been differenced to' ' eliminate integration prior to ARMA parameter' ' estimation.') endog = diff(endog, k_diff=spec.diff, k_seasonal_diff=spec.seasonal_diff, seasonal_periods=spec.seasonal_periods) if demean: endog = endog - endog.mean() p = SARIMAXParams(spec=spec) if start_params is None: sp = SARIMAXParams(spec=spec) # Estimate starting parameters via Hannan-Rissanen hr, hr_results = hannan_rissanen(endog, ar_order=spec.ar_order, ma_order=spec.ma_order, demean=False) if spec.seasonal_periods == 0: # If no seasonal component, then `hr` gives starting parameters sp.params = hr.params else: # If we do have a seasonal component, estimate starting parameters # for the seasonal lags using the residuals from the previous step _ = SARIMAXSpecification( endog, seasonal_order=seasonal_order, enforce_stationarity=True, enforce_invertibility=enforce_invertibility) ar_order = np.array(spec.seasonal_ar_lags) * spec.seasonal_periods ma_order = np.array(spec.seasonal_ma_lags) * spec.seasonal_periods seasonal_hr, seasonal_hr_results = hannan_rissanen( hr_results.resid, ar_order=ar_order, ma_order=ma_order, demean=False) # Set the starting parameters sp.ar_params = hr.ar_params sp.ma_params = hr.ma_params sp.seasonal_ar_params = seasonal_hr.ar_params sp.seasonal_ma_params = seasonal_hr.ma_params sp.sigma2 = seasonal_hr.sigma2 # Then, require starting parameters to be stationary and invertible if not sp.is_stationary: sp.ar_params = [0] * sp.k_ar_params sp.seasonal_ar_params = [0] * sp.k_seasonal_ar_params if not sp.is_invertible and spec.enforce_invertibility: sp.ma_params = [0] * sp.k_ma_params sp.seasonal_ma_params = [0] * sp.k_seasonal_ma_params start_params = sp.params else: sp = SARIMAXParams(spec=spec) sp.params = start_params if not sp.is_stationary: raise ValueError('Given starting parameters imply a non-stationary' ' AR process. Innovations algorithm requires a' ' stationary process.') if spec.enforce_invertibility and not sp.is_invertible: raise ValueError('Given starting parameters imply a non-invertible' ' MA process with `enforce_invertibility=True`.') def obj(params): p.params = spec.constrain_params(params) return -arma_innovations.arma_loglike( endog, ar_params=-p.reduced_ar_poly.coef[1:], ma_params=p.reduced_ma_poly.coef[1:], sigma2=p.sigma2) # Untransform the starting parameters unconstrained_start_params = spec.unconstrain_params(start_params) # Perform the minimization if minimize_kwargs is None: minimize_kwargs = {} if 'options' not in minimize_kwargs: minimize_kwargs['options'] = {} minimize_kwargs['options'].setdefault('maxiter', 100) minimize_results = minimize(obj, unconstrained_start_params, **minimize_kwargs) # TODO: show warning if convergence failed. # Reverse the transformation to get the optimal parameters p.params = spec.constrain_params(minimize_results.x) # Construct other results other_results = Bunch({ 'spec': spec, 'minimize_results': minimize_results, 'minimize_kwargs': minimize_kwargs, 'start_params': start_params }) return p, other_results statsmodels-0.12.2/statsmodels/tsa/arima/estimators/statespace.py000066400000000000000000000115261400612667500252740ustar00rootroot00000000000000""" State space approach to estimating SARIMAX models. Author: Chad Fulton License: BSD-3 """ import numpy as np from statsmodels.tools.tools import add_constant, Bunch from statsmodels.tsa.statespace.sarimax import SARIMAX from statsmodels.tsa.arima.specification import SARIMAXSpecification from statsmodels.tsa.arima.params import SARIMAXParams def statespace(endog, exog=None, order=(0, 0, 0), seasonal_order=(0, 0, 0, 0), include_constant=True, enforce_stationarity=True, enforce_invertibility=True, concentrate_scale=False, start_params=None, fit_kwargs=None): """ Estimate SARIMAX parameters using state space methods. Parameters ---------- endog : array_like Input time series array. order : tuple, optional The (p,d,q) order of the model for the number of AR parameters, differences, and MA parameters. Default is (0, 0, 0). seasonal_order : tuple, optional The (P,D,Q,s) order of the seasonal component of the model for the AR parameters, differences, MA parameters, and periodicity. Default is (0, 0, 0, 0). include_constant : bool, optional Whether to add a constant term in `exog` if it's not already there. The estimate of the constant will then appear as one of the `exog` parameters. If `exog` is None, then the constant will represent the mean of the process. enforce_stationarity : bool, optional Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. Default is True. enforce_invertibility : bool, optional Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. Default is True. concentrate_scale : bool, optional Whether or not to concentrate the scale (variance of the error term) out of the likelihood. This reduces the number of parameters estimated by maximum likelihood by one. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The AR polynomial must be stationary. If `enforce_invertibility=True` the MA poylnomial must be invertible. If not provided, default starting parameters are computed using the Hannan-Rissanen method. fit_kwargs : dict, optional Arguments to pass to the state space model's `fit` method. Returns ------- parameters : SARIMAXParams object other_results : Bunch Includes two components, `spec`, containing the `SARIMAXSpecification` instance corresponding to the input arguments; and `state_space_results`, corresponding to the results from the underlying state space model and Kalman filter / smoother. Notes ----- The primary reference is [1]_. References ---------- .. [1] Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods: Second Edition. Oxford University Press. """ # Handle including the constant (need to do it now so that the constant # parameter can be included in the specification as part of `exog`.) if include_constant: exog = np.ones_like(endog) if exog is None else add_constant(exog) # Create the specification spec = SARIMAXSpecification( endog, exog=exog, order=order, seasonal_order=seasonal_order, enforce_stationarity=enforce_stationarity, enforce_invertibility=enforce_invertibility, concentrate_scale=concentrate_scale) endog = spec.endog exog = spec.exog p = SARIMAXParams(spec=spec) # Check start parameters if start_params is not None: sp = SARIMAXParams(spec=spec) sp.params = start_params if spec.enforce_stationarity and not sp.is_stationary: raise ValueError('Given starting parameters imply a non-stationary' ' AR process with `enforce_stationarity=True`.') if spec.enforce_invertibility and not sp.is_invertible: raise ValueError('Given starting parameters imply a non-invertible' ' MA process with `enforce_invertibility=True`.') # Create and fit the state space model mod = SARIMAX(endog, exog=exog, order=spec.order, seasonal_order=spec.seasonal_order, enforce_stationarity=spec.enforce_stationarity, enforce_invertibility=spec.enforce_invertibility, concentrate_scale=spec.concentrate_scale) if fit_kwargs is None: fit_kwargs = {} fit_kwargs.setdefault('disp', 0) res_ss = mod.fit(start_params=start_params, **fit_kwargs) # Construct results p.params = res_ss.params res = Bunch({ 'spec': spec, 'statespace_results': res_ss, }) return p, res statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/000077500000000000000000000000001400612667500237235ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/__init__.py000066400000000000000000000000001400612667500260220ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/results/000077500000000000000000000000001400612667500254245ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/results/results_burg.R000066400000000000000000000014701400612667500302710ustar00rootroot00000000000000library(itsmr) options(digits=10) # Test Burg's method on lake dataset using itsmr::burg # Python test is: test_burg::test_itsmr res <- burg(lake, 10) print(res$phi) # [1] 1.05853631096 -0.32639150878 0.04784765122 0.02620476111 0.04444511374 # [6] -0.04134010262 0.02251178970 -0.01427524694 0.22223486915 -0.20935524387 print(res$sigma2) # [1] 0.4458956354 # Test Burg's method on non-stationary dataset using stats::ar.burg res <- ar.burg(x = (1:11) * 1, aic = FALSE, order.max = 2, demean = FALSE, var.method = 2) print(res$ar) # [1] 1.9669331547 -0.9892846679 print(res$var.pred) # [1] 0.02143066427 res <- ar.burg(x = (1:11) * 1, aic = FALSE, order.max = 2, demean = FALSE, var.method = 1) print(res$ar) # [1] 1.9669331547 -0.9892846679 print(res$var.pred) # [1] 0.02143066427 statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/results/results_hr.R000066400000000000000000000004331400612667500277410ustar00rootroot00000000000000library(itsmr) options(digits=10) # Test Hannan-Rissanen method on lake dataset using itsmr::hannan # Python test is: test_hannan_rissanen::test_itsmr res <- hannan(lake, 1, 1) print(res$phi) # [1] 0.69607715 print(res$theta) # [1] 0.3787969217 print(res$sigma2) # [1] 0.4773580109 statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/results/results_innovations_ma.R000066400000000000000000000005471400612667500323620ustar00rootroot00000000000000library(itsmr) options(digits=10) # Test innovation method on lake dataset using itsmr::ia # Python test is: test_innovations::test_itsmr res <- ia(lake, 10, 10) print(res$theta) # [1] 1.0816255264 0.7781248438 0.5367164430 0.3291559246 0.3160039850 # [6] 0.2513754550 0.2051536531 0.1441070313 0.3431868340 0.1827400798 print(res$sigma2) # [1] 0.4523684344 statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/results/results_yw_dl.R000066400000000000000000000014301400612667500304440ustar00rootroot00000000000000library(itsmr) options(digits=10) # Test Yule-Walker method on lake dataset using itsmr::yw # Python test is: test_yule_walker::test_itsmr for(i in 1:5) { res <- yw(lake, i) print(res$phi) print(res$sigma2) } # [1] 0.8319112104 # [1] 0.5098608429 # [1] 1.0538248798 -0.2667516276 # [1] 0.4790561946 # [1] 1.0887037577 -0.4045435867 0.1307541335 # [1] 0.4730073172 # [1] 1.08425065810 -0.39076602696 0.09367609911 0.03405704644 # [1] 0.4715119356 # [1] 1.08213598501 -0.39658257147 0.11793957728 -0.03326633983 0.06209208707 # [1] 0.4716322564 # Test Yule-Walker method on non-stationary dataset using stats::ar.yw res <- ar.yw(x = (1:11) * 1, aic = FALSE, order.max = 2, demean = FALSE) print(res$ar) # [1] 0.92318534179 -0.06166314306 print(res$var.pred) # [1] 15.36526603 statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/test_burg.py000066400000000000000000000076011400612667500262770ustar00rootroot00000000000000import numpy as np import pytest from numpy.testing import assert_allclose, assert_equal, assert_raises from statsmodels.tsa.innovations.arma_innovations import arma_innovations from statsmodels.tsa.arima.datasets.brockwell_davis_2002 import dowj, lake from statsmodels.tsa.arima.estimators.burg import burg @pytest.mark.low_precision('Test against Example 5.1.3 in Brockwell and Davis' ' (2016)') def test_brockwell_davis_example_513(): # Test against Example 5.1.3 in Brockwell and Davis (2016) # (low-precision test, since we are testing against values printed in the # textbook) # Difference and demean the series endog = dowj.diff().iloc[1:] # Burg res, _ = burg(endog, ar_order=1, demean=True) assert_allclose(res.ar_params, [0.4371], atol=1e-4) assert_allclose(res.sigma2, 0.1423, atol=1e-4) @pytest.mark.low_precision('Test against Example 5.1.4 in Brockwell and Davis' ' (2016)') def test_brockwell_davis_example_514(): # Test against Example 5.1.4 in Brockwell and Davis (2016) # (low-precision test, since we are testing against values printed in the # textbook) # Get the lake data endog = lake.copy() # Should have 98 observations assert_equal(len(endog), 98) desired = 9.0041 assert_allclose(endog.mean(), desired, atol=1e-4) # Burg res, _ = burg(endog, ar_order=2, demean=True) assert_allclose(res.ar_params, [1.0449, -0.2456], atol=1e-4) assert_allclose(res.sigma2, 0.4706, atol=1e-4) def check_itsmr(lake): # Test against R itsmr::burg; see results/results_burg.R res, _ = burg(lake, 10, demean=True) desired_ar_params = [ 1.05853631096, -0.32639150878, 0.04784765122, 0.02620476111, 0.04444511374, -0.04134010262, 0.02251178970, -0.01427524694, 0.22223486915, -0.20935524387] assert_allclose(res.ar_params, desired_ar_params) # itsmr always returns the innovations algorithm estimate of sigma2, # whereas we return Burg's estimate u, v = arma_innovations(np.array(lake) - np.mean(lake), ar_params=res.ar_params, sigma2=1) desired_sigma2 = 0.4458956354 assert_allclose(np.sum(u**2 / v) / len(u), desired_sigma2) def test_itsmr(): # Note: apparently itsmr automatically demeans (there is no option to # control this) endog = lake.copy() check_itsmr(endog) # Pandas series check_itsmr(endog.values) # Numpy array check_itsmr(endog.tolist()) # Python list def test_nonstationary_series(): # Test against R stats::ar.burg; see results/results_burg.R endog = np.arange(1, 12) * 1.0 res, _ = burg(endog, 2, demean=False) desired_ar_params = [1.9669331547, -0.9892846679] assert_allclose(res.ar_params, desired_ar_params) desired_sigma2 = 0.02143066427 assert_allclose(res.sigma2, desired_sigma2) # With var.method = 1, stats::ar.burg also returns something equivalent to # the innovations algorithm estimate of sigma2 u, v = arma_innovations(endog, ar_params=res.ar_params, sigma2=1) desired_sigma2 = 0.02191056906 assert_allclose(np.sum(u**2 / v) / len(u), desired_sigma2) def test_invalid(): endog = np.arange(2) * 1.0 assert_raises(ValueError, burg, endog, ar_order=2) assert_raises(ValueError, burg, endog, ar_order=-1) assert_raises(ValueError, burg, endog, ar_order=1.5) endog = np.arange(10) * 1.0 assert_raises(ValueError, burg, endog, ar_order=[1, 3]) def test_misc(): # Test defaults (order = 0, demean=True) endog = lake.copy() res, _ = burg(endog) assert_allclose(res.params, np.var(endog)) # Test that integer input gives the same result as float-coerced input. endog = np.array([1, 2, 5, 3, -2, 1, -3, 5, 2, 3, -1], dtype=int) res_int, _ = burg(endog, 2) res_float, _ = burg(endog * 1.0, 2) assert_allclose(res_int.params, res_float.params) statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/test_durbin_levinson.py000066400000000000000000000077031400612667500305430ustar00rootroot00000000000000import numpy as np import pytest from numpy.testing import assert_allclose, assert_raises from statsmodels.tsa.innovations.arma_innovations import arma_innovations from statsmodels.tsa.arima.datasets.brockwell_davis_2002 import dowj, lake from statsmodels.tsa.arima.estimators.durbin_levinson import durbin_levinson @pytest.mark.low_precision('Test against Example 5.1.1 in Brockwell and Davis' ' (2016)') def test_brockwell_davis_example_511(): # Note: this example is primarily tested in # test_yule_walker::test_brockwell_davis_example_511. # Difference the series endog = dowj.diff().iloc[1:] # Durbin-Levinson dl, _ = durbin_levinson(endog, ar_order=2, demean=True) assert_allclose(dl[0].params, np.var(endog)) assert_allclose(dl[1].params, [0.4219, 0.1479], atol=1e-4) assert_allclose(dl[2].params, [0.3739, 0.1138, 0.1460], atol=1e-4) def check_itsmr(lake): # Test against R itsmr::yw; see results/results_yw_dl.R dl, _ = durbin_levinson(lake, 5) assert_allclose(dl[0].params, np.var(lake)) assert_allclose(dl[1].ar_params, [0.8319112104]) assert_allclose(dl[2].ar_params, [1.0538248798, -0.2667516276]) desired = [1.0887037577, -0.4045435867, 0.1307541335] assert_allclose(dl[3].ar_params, desired) desired = [1.08425065810, -0.39076602696, 0.09367609911, 0.03405704644] assert_allclose(dl[4].ar_params, desired) desired = [1.08213598501, -0.39658257147, 0.11793957728, -0.03326633983, 0.06209208707] assert_allclose(dl[5].ar_params, desired) # itsmr::yw returns the innovations algorithm estimate of the variance # we'll just check for p=5 u, v = arma_innovations(np.array(lake) - np.mean(lake), ar_params=dl[5].ar_params, sigma2=1) desired_sigma2 = 0.4716322564 assert_allclose(np.sum(u**2 / v) / len(u), desired_sigma2) def test_itsmr(): # Note: apparently itsmr automatically demeans (there is no option to # control this) endog = lake.copy() check_itsmr(endog) # Pandas series check_itsmr(endog.values) # Numpy array check_itsmr(endog.tolist()) # Python list def test_nonstationary_series(): # Test against R stats::ar.yw; see results/results_yw_dl.R endog = np.arange(1, 12) * 1.0 res, _ = durbin_levinson(endog, 2, demean=False) desired_ar_params = [0.92318534179, -0.06166314306] assert_allclose(res[2].ar_params, desired_ar_params) @pytest.mark.xfail(reason='Different computation of variances') def test_nonstationary_series_variance(): # See `test_nonstationary_series`. This part of the test has been broken # out as an xfail because we compute a different estimate of the variance # from stats::ar.yw, but keeping the test in case we want to also implement # that variance estimate in the future. endog = np.arange(1, 12) * 1.0 res, _ = durbin_levinson(endog, 2, demean=False) desired_sigma2 = 15.36526603 assert_allclose(res[2].sigma2, desired_sigma2) def test_invalid(): endog = np.arange(2) * 1.0 assert_raises(ValueError, durbin_levinson, endog, ar_order=2) assert_raises(ValueError, durbin_levinson, endog, ar_order=-1) assert_raises(ValueError, durbin_levinson, endog, ar_order=1.5) endog = np.arange(10) * 1.0 assert_raises(ValueError, durbin_levinson, endog, ar_order=[1, 3]) def test_misc(): # Test defaults (order = 0, demean=True) endog = lake.copy() res, _ = durbin_levinson(endog) assert_allclose(res[0].params, np.var(endog)) # Test that integer input gives the same result as float-coerced input. endog = np.array([1, 2, 5, 3, -2, 1, -3, 5, 2, 3, -1], dtype=int) res_int, _ = durbin_levinson(endog, 2, demean=False) res_float, _ = durbin_levinson(endog * 1.0, 2, demean=False) assert_allclose(res_int[0].params, res_float[0].params) assert_allclose(res_int[1].params, res_float[1].params) assert_allclose(res_int[2].params, res_float[2].params) statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/test_gls.py000066400000000000000000000203431400612667500261230ustar00rootroot00000000000000import numpy as np import pytest from numpy.testing import ( assert_, assert_allclose, assert_equal, assert_warns, assert_raises) from statsmodels.tsa.arima.datasets.brockwell_davis_2002 import lake, oshorts from statsmodels.tsa.arima.estimators.gls import gls @pytest.mark.low_precision('Test against Example 6.6.1 in Brockwell and Davis' ' (2016)') def test_brockwell_davis_example_661(): endog = oshorts.copy() exog = np.ones_like(endog) # Here we restrict the iterations to 1 and test against the values in the # text (set tolerance=1 to suppress to warning that it didn't converge) res, _ = gls(endog, exog, order=(0, 0, 1), max_iter=1, tolerance=1) assert_allclose(res.exog_params, -4.745, atol=1e-3) assert_allclose(res.ma_params, -0.818, atol=1e-3) assert_allclose(res.sigma2, 2041, atol=1) # Here we do not restrict the iterations and test against the values in # the last row of Table 6.2 (note: this table does not report sigma2) res, _ = gls(endog, exog, order=(0, 0, 1)) assert_allclose(res.exog_params, -4.780, atol=1e-3) assert_allclose(res.ma_params, -0.848, atol=1e-3) @pytest.mark.low_precision('Test against Example 6.6.2 in Brockwell and Davis' ' (2016)') def test_brockwell_davis_example_662(): endog = lake.copy() exog = np.c_[np.ones_like(endog), np.arange(1, len(endog) + 1) * 1.0] res, _ = gls(endog, exog, order=(2, 0, 0)) # Parameter values taken from Table 6.3 row 2, except for sigma2 and the # last digit of the exog_params[0], which were given in the text assert_allclose(res.exog_params, [10.091, -.0216], atol=1e-3) assert_allclose(res.ar_params, [1.005, -.291], atol=1e-3) assert_allclose(res.sigma2, .4571, atol=1e-3) def test_integrated(): # Get the lake data endog1 = lake.copy() exog1 = np.c_[np.ones_like(endog1), np.arange(1, len(endog1) + 1) * 1.0] endog2 = np.r_[0, np.cumsum(endog1)] exog2 = np.c_[[0, 0], np.cumsum(exog1, axis=0).T].T # Estimate without integration p1, _ = gls(endog1, exog1, order=(1, 0, 0)) # Estimate with integration with assert_warns(UserWarning): p2, _ = gls(endog2, exog2, order=(1, 1, 0)) assert_allclose(p1.params, p2.params) def test_integrated_invalid(): # Test for invalid versions of integrated model # - include_constant=True is invalid if integration is present endog = lake.copy() exog = np.arange(1, len(endog) + 1) * 1.0 assert_raises(ValueError, gls, endog, exog, order=(1, 1, 0), include_constant=True) def test_results(): endog = lake.copy() exog = np.c_[np.ones_like(endog), np.arange(1, len(endog) + 1) * 1.0] # Test for results output p, res = gls(endog, exog, order=(1, 0, 0)) assert_('params' in res) assert_('converged' in res) assert_('differences' in res) assert_('iterations' in res) assert_('arma_estimator' in res) assert_('arma_results' in res) assert_(res.converged) assert_(res.iterations > 0) assert_equal(res.arma_estimator, 'innovations_mle') assert_equal(len(res.params), res.iterations + 1) assert_equal(len(res.differences), res.iterations + 1) assert_equal(len(res.arma_results), res.iterations + 1) assert_equal(res.params[-1], p) def test_iterations(): endog = lake.copy() exog = np.c_[np.ones_like(endog), np.arange(1, len(endog) + 1) * 1.0] # Test for n_iter usage _, res = gls(endog, exog, order=(1, 0, 0), n_iter=1) assert_equal(res.iterations, 1) assert_equal(res.converged, None) def test_misc(): endog = lake.copy() exog = np.c_[np.ones_like(endog), np.arange(1, len(endog) + 1) * 1.0] # Test for warning if iterations fail to converge assert_warns(UserWarning, gls, endog, exog, order=(2, 0, 0), max_iter=0) @pytest.mark.todo('Low priority: test full GLS against another package') @pytest.mark.smoke def test_alternate_arma_estimators_valid(): # Test that we can use (valid) alternate ARMA estimators # Note that this does not test the results of the alternative estimators, # and so it is labeled as a smoke test / TODO. However, assuming those # estimators are tested elsewhere, the main testable concern from their # inclusion in the feasible GLS step is that produce results at all. # Thus, for example, we specify n_iter=1, and ignore the actual results. # Nonetheless, it would be good to test against another package. endog = lake.copy() exog = np.c_[np.ones_like(endog), np.arange(1, len(endog) + 1) * 1.0] _, res_yw = gls(endog, exog=exog, order=(1, 0, 0), arma_estimator='yule_walker', n_iter=1) assert_equal(res_yw.arma_estimator, 'yule_walker') _, res_b = gls(endog, exog=exog, order=(1, 0, 0), arma_estimator='burg', n_iter=1) assert_equal(res_b.arma_estimator, 'burg') _, res_i = gls(endog, exog=exog, order=(0, 0, 1), arma_estimator='innovations', n_iter=1) assert_equal(res_i.arma_estimator, 'innovations') _, res_hr = gls(endog, exog=exog, order=(1, 0, 1), arma_estimator='hannan_rissanen', n_iter=1) assert_equal(res_hr.arma_estimator, 'hannan_rissanen') _, res_ss = gls(endog, exog=exog, order=(1, 0, 1), arma_estimator='statespace', n_iter=1) assert_equal(res_ss.arma_estimator, 'statespace') # Finally, default method is innovations _, res_imle = gls(endog, exog=exog, order=(1, 0, 1), n_iter=1) assert_equal(res_imle.arma_estimator, 'innovations_mle') def test_alternate_arma_estimators_invalid(): # Test that specifying an invalid ARMA estimators raises an error endog = lake.copy() exog = np.c_[np.ones_like(endog), np.arange(1, len(endog) + 1) * 1.0] # Test for invalid estimator assert_raises(ValueError, gls, endog, exog, order=(0, 0, 1), arma_estimator='invalid_estimator') # Yule-Walker, Burg can only handle consecutive AR assert_raises(ValueError, gls, endog, exog, order=(0, 0, 1), arma_estimator='yule_walker') assert_raises(ValueError, gls, endog, exog, order=(0, 0, 0), seasonal_order=(1, 0, 0, 4), arma_estimator='yule_walker') assert_raises(ValueError, gls, endog, exog, order=([0, 1], 0, 0), arma_estimator='yule_walker') assert_raises(ValueError, gls, endog, exog, order=(0, 0, 1), arma_estimator='burg') assert_raises(ValueError, gls, endog, exog, order=(0, 0, 0), seasonal_order=(1, 0, 0, 4), arma_estimator='burg') assert_raises(ValueError, gls, endog, exog, order=([0, 1], 0, 0), arma_estimator='burg') # Innovations (MA) can only handle consecutive MA assert_raises(ValueError, gls, endog, exog, order=(1, 0, 0), arma_estimator='innovations') assert_raises(ValueError, gls, endog, exog, order=(0, 0, 0), seasonal_order=(0, 0, 1, 4), arma_estimator='innovations') assert_raises(ValueError, gls, endog, exog, order=(0, 0, [0, 1]), arma_estimator='innovations') # Hannan-Rissanen can't handle seasonal components assert_raises(ValueError, gls, endog, exog, order=(0, 0, 0), seasonal_order=(0, 0, 1, 4), arma_estimator='hannan_rissanen') def test_arma_kwargs(): endog = lake.copy() exog = np.c_[np.ones_like(endog), np.arange(1, len(endog) + 1) * 1.0] # Test with the default method for scipy.optimize.minimize (BFGS) _, res1_imle = gls(endog, exog=exog, order=(1, 0, 1), n_iter=1) assert_equal(res1_imle.arma_estimator_kwargs, {}) assert_equal(res1_imle.arma_results[1].minimize_results.message, 'Optimization terminated successfully.') # Now specify a different method (L-BFGS-B) arma_estimator_kwargs = {'minimize_kwargs': {'method': 'L-BFGS-B'}} _, res2_imle = gls(endog, exog=exog, order=(1, 0, 1), n_iter=1, arma_estimator_kwargs=arma_estimator_kwargs) assert_equal(res2_imle.arma_estimator_kwargs, arma_estimator_kwargs) msg = res2_imle.arma_results[1].minimize_results.message if isinstance(msg, bytes): msg = msg.decode("utf-8") assert_equal(msg, 'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH') statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/test_hannan_rissanen.py000066400000000000000000000107761400612667500305140ustar00rootroot00000000000000import numpy as np import pytest from numpy.testing import assert_allclose from statsmodels.tsa.innovations.arma_innovations import arma_innovations from statsmodels.tsa.arima.datasets.brockwell_davis_2002 import lake from statsmodels.tsa.arima.estimators.hannan_rissanen import hannan_rissanen @pytest.mark.low_precision('Test against Example 5.1.7 in Brockwell and Davis' ' (2016)') def test_brockwell_davis_example_517(): # Get the lake data endog = lake.copy() # BD do not implement the "bias correction" third step that they describe, # so we can't use their results to test that. Thus here `unbiased=False`. # Note: it's not clear why BD use initial_order=22 (and they don't mention # that they do this), but it is the value that allows the test to pass. hr, _ = hannan_rissanen(endog, ar_order=1, ma_order=1, demean=True, initial_ar_order=22, unbiased=False) assert_allclose(hr.ar_params, [0.6961], atol=1e-4) assert_allclose(hr.ma_params, [0.3788], atol=1e-4) # Because our fast implementation of the innovations algorithm does not # allow for non-stationary processes, the estimate of the variance returned # by `hannan_rissanen` is based on the residuals from the least-squares # regression, rather than (as reported by BD) based on the innovations # algorithm output. Since the estimates here do correspond to a stationary # series, we can compute the innovations variance manually to check # against BD. u, v = arma_innovations(endog - endog.mean(), hr.ar_params, hr.ma_params, sigma2=1) tmp = u / v**0.5 assert_allclose(np.inner(tmp, tmp) / len(u), 0.4774, atol=1e-4) def test_itsmr(): # This is essentially a high precision version of # test_brockwell_davis_example_517, where the desired values were computed # from R itsmr::hannan; see results/results_hr.R endog = lake.copy() hr, _ = hannan_rissanen(endog, ar_order=1, ma_order=1, demean=True, initial_ar_order=22, unbiased=False) assert_allclose(hr.ar_params, [0.69607715], atol=1e-4) assert_allclose(hr.ma_params, [0.3787969217], atol=1e-4) # Because our fast implementation of the innovations algorithm does not # allow for non-stationary processes, the estimate of the variance returned # by `hannan_rissanen` is based on the residuals from the least-squares # regression, rather than (as reported by BD) based on the innovations # algorithm output. Since the estimates here do correspond to a stationary # series, we can compute the innovations variance manually to check # against BD. u, v = arma_innovations(endog - endog.mean(), hr.ar_params, hr.ma_params, sigma2=1) tmp = u / v**0.5 assert_allclose(np.inner(tmp, tmp) / len(u), 0.4773580109, atol=1e-4) @pytest.mark.xfail(reason='TODO: improve checks on valid order parameters.') def test_initial_order(): endog = np.arange(20) * 1.0 # TODO: shouldn't allow initial_ar_order <= ar_order hannan_rissanen(endog, ar_order=2, ma_order=0, initial_ar_order=1) # TODO: shouldn't allow initial_ar_order <= ma_order hannan_rissanen(endog, ar_order=0, ma_order=2, initial_ar_order=1) # TODO: shouldn't allow initial_ar_order >= dataset hannan_rissanen(endog, ar_order=0, ma_order=2, initial_ar_order=20) @pytest.mark.xfail(reason='TODO: improve checks on valid order parameters.') def test_invalid_orders(): endog = np.arange(2) * 1.0 # TODO: shouldn't allow ar_order >= dataset hannan_rissanen(endog, ar_order=2) # TODO: shouldn't allow ma_order >= dataset hannan_rissanen(endog, ma_order=2) @pytest.mark.todo('Improve checks on valid order parameters.') @pytest.mark.smoke def test_nonconsecutive_lags(): endog = np.arange(20) * 1.0 hannan_rissanen(endog, ar_order=[1, 4]) hannan_rissanen(endog, ma_order=[1, 3]) hannan_rissanen(endog, ar_order=[1, 4], ma_order=[1, 3]) hannan_rissanen(endog, ar_order=[0, 0, 1]) hannan_rissanen(endog, ma_order=[0, 0, 1]) hannan_rissanen(endog, ar_order=[0, 0, 1], ma_order=[0, 0, 1]) hannan_rissanen(endog, ar_order=0, ma_order=0) def test_unbiased_error(): # Test that we get the appropriate error when we specify unbiased=True # but the second-stage yields non-stationary parameters. endog = (np.arange(1000) * 1.0) with pytest.raises(ValueError, match='Cannot perform third step'): hannan_rissanen(endog, ar_order=1, ma_order=1, unbiased=True) statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/test_innovations.py000066400000000000000000000313431400612667500277070ustar00rootroot00000000000000import numpy as np import pytest from numpy.testing import ( assert_, assert_allclose, assert_warns, assert_raises) from statsmodels.tsa.innovations.arma_innovations import arma_innovations from statsmodels.tsa.statespace import sarimax from statsmodels.tsa.arima.datasets.brockwell_davis_2002 import ( dowj, lake, oshorts) from statsmodels.tsa.arima.estimators.burg import burg from statsmodels.tsa.arima.estimators.hannan_rissanen import hannan_rissanen from statsmodels.tsa.arima.estimators.innovations import ( innovations, innovations_mle) @pytest.mark.low_precision('Test against Example 5.1.5 in Brockwell and Davis' ' (2016)') def test_brockwell_davis_example_515(): # Difference and demean the series endog = dowj.diff().iloc[1:] # Innvations algorithm (MA) p, _ = innovations(endog, ma_order=17, demean=True) # First BD show the MA(2) coefficients resulting from the m=17 computations assert_allclose(p[17].ma_params[:2], [.4269, .2704], atol=1e-4) assert_allclose(p[17].sigma2, 0.1122, atol=1e-4) # Then they separately show the full MA(17) coefficients desired = [.4269, .2704, .1183, .1589, .1355, .1568, .1284, -.0060, .0148, -.0017, .1974, -.0463, .2023, .1285, -.0213, -.2575, .0760] assert_allclose(p[17].ma_params, desired, atol=1e-4) def check_innovations_ma_itsmr(lake): # Test against R itsmr::ia; see results/results_innovations.R ia, _ = innovations(lake, 10, demean=True) desired = [ 1.0816255264, 0.7781248438, 0.5367164430, 0.3291559246, 0.3160039850, 0.2513754550, 0.2051536531, 0.1441070313, 0.3431868340, 0.1827400798] assert_allclose(ia[10].ma_params, desired) # itsmr::ia returns the innovations algorithm estimate of the variance u, v = arma_innovations(np.array(lake) - np.mean(lake), ma_params=ia[10].ma_params, sigma2=1) desired_sigma2 = 0.4523684344 assert_allclose(np.sum(u**2 / v) / len(u), desired_sigma2) def test_innovations_ma_itsmr(): # Note: apparently itsmr automatically demeans (there is no option to # control this) endog = lake.copy() check_innovations_ma_itsmr(endog) # Pandas series check_innovations_ma_itsmr(endog.values) # Numpy array check_innovations_ma_itsmr(endog.tolist()) # Python list def test_innovations_ma_invalid(): endog = np.arange(2) assert_raises(ValueError, innovations, endog, ma_order=2) assert_raises(ValueError, innovations, endog, ma_order=-1) assert_raises(ValueError, innovations, endog, ma_order=1.5) endog = np.arange(10) assert_raises(ValueError, innovations, endog, ma_order=[1, 3]) @pytest.mark.low_precision('Test against Example 5.2.4 in Brockwell and Davis' ' (2016)') def test_brockwell_davis_example_524(): # Difference and demean the series endog = dowj.diff().iloc[1:] # Use Burg method to get initial coefficients for MLE initial, _ = burg(endog, ar_order=1, demean=True) # Fit MLE via innovations algorithm p, _ = innovations_mle(endog, order=(1, 0, 0), demean=True, start_params=initial.params) assert_allclose(p.ar_params, 0.4471, atol=1e-4) @pytest.mark.low_precision('Test against Example 5.2.4 in Brockwell and Davis' ' (2016)') @pytest.mark.xfail(reason='Suspicious result reported in Brockwell and Davis' ' (2016).') def test_brockwell_davis_example_524_variance(): # See `test_brockwell_davis_example_524` for the main test # TODO: the test for sigma2 fails, but the value reported by BD (0.02117) # is suspicious. For example, the Burg results have an AR coefficient of # 0.4371 and sigma2 = 0.1423. It seems unlikely that the small difference # in AR coefficient would result in an order of magniture reduction in # sigma2 (see test_burg::test_brockwell_davis_example_513). Should run # this in the ITSM program to check its output. endog = dowj.diff().iloc[1:] # Use Burg method to get initial coefficients for MLE initial, _ = burg(endog, ar_order=1, demean=True) # Fit MLE via innovations algorithm p, _ = innovations_mle(endog, order=(1, 0, 0), demean=True, start_params=initial.params) assert_allclose(p.sigma2, 0.02117, atol=1e-4) @pytest.mark.low_precision('Test against Example 5.2.5 in Brockwell and Davis' ' (2016)') def test_brockwell_davis_example_525(): # Difference and demean the series endog = lake.copy() # Use HR method to get initial coefficients for MLE initial, _ = hannan_rissanen(endog, ar_order=1, ma_order=1, demean=True) # Fit MLE via innovations algorithm p, _ = innovations_mle(endog, order=(1, 0, 1), demean=True, start_params=initial.params) assert_allclose(p.params, [0.7446, 0.3213, 0.4750], atol=1e-4) # Fit MLE via innovations algorithm, with default starting parameters p, _ = innovations_mle(endog, order=(1, 0, 1), demean=True) assert_allclose(p.params, [0.7446, 0.3213, 0.4750], atol=1e-4) @pytest.mark.low_precision('Test against Example 5.4.1 in Brockwell and Davis' ' (2016)') def test_brockwell_davis_example_541(): # Difference and demean the series endog = oshorts.copy() # Use innovations MA method to get initial coefficients for MLE initial, _ = innovations(endog, ma_order=1, demean=True) # Fit MLE via innovations algorithm p, _ = innovations_mle(endog, order=(0, 0, 1), demean=True, start_params=initial[1].params) assert_allclose(p.ma_params, -0.818, atol=1e-3) # TODO: the test for sigma2 fails; we get 2040.85 whereas BD reports # 2040.75. Unclear if this is optimizers finding different maxima, or a # reporting error by BD (i.e. typo where the 8 got reported as a 7). Should # check this out with ITSM program. NB: state space also finds 2040.85 as # the MLE value. # assert_allclose(p.sigma2, 2040.75, atol=1e-2) def test_innovations_mle_statespace(): # Test innovations output against state-space output. endog = lake.copy() endog = endog - endog.mean() start_params = [0, 0, np.var(endog)] p, mleres = innovations_mle(endog, order=(1, 0, 1), demean=False, start_params=start_params) mod = sarimax.SARIMAX(endog, order=(1, 0, 1)) # Test that the maximized log-likelihood found via applications of the # innovations algorithm matches the log-likelihood found by the Kalman # filter at the same parameters res = mod.filter(p.params) assert_allclose(-mleres.minimize_results.fun, res.llf) # Test MLE fitting # To avoid small numerical differences with MLE fitting, start at the # parameters found from innovations_mle res2 = mod.fit(start_params=p.params, disp=0) # Test that the state space approach confirms the MLE values found by # innovations_mle assert_allclose(p.params, res2.params) # Test that starting parameter estimation succeeds and isn't terrible # (i.e. leads to the same MLE) p2, _ = innovations_mle(endog, order=(1, 0, 1), demean=False) # (does not need to be high-precision test since it's okay if different # starting parameters give slightly different MLE) assert_allclose(p.params, p2.params, atol=1e-5) def test_innovations_mle_statespace_seasonal(): # Test innovations output against state-space output. endog = lake.copy() endog = endog - endog.mean() start_params = [0, np.var(endog)] p, mleres = innovations_mle(endog, seasonal_order=(1, 0, 0, 4), demean=False, start_params=start_params) mod = sarimax.SARIMAX(endog, order=(0, 0, 0), seasonal_order=(1, 0, 0, 4)) # Test that the maximized log-likelihood found via applications of the # innovations algorithm matches the log-likelihood found by the Kalman # filter at the same parameters res = mod.filter(p.params) assert_allclose(-mleres.minimize_results.fun, res.llf) # Test MLE fitting # To avoid small numerical differences with MLE fitting, start at the # parameters found from innovations_mle res2 = mod.fit(start_params=p.params, disp=0) # Test that the state space approach confirms the MLE values found by # innovations_mle assert_allclose(p.params, res2.params) # Test that starting parameter estimation succeeds and isn't terrible # (i.e. leads to the same MLE) p2, _ = innovations_mle(endog, seasonal_order=(1, 0, 0, 4), demean=False) # (does not need to be high-precision test since it's okay if different # starting parameters give slightly different MLE) assert_allclose(p.params, p2.params, atol=1e-5) def test_innovations_mle_statespace_nonconsecutive(): # Test innovations output against state-space output. endog = lake.copy() endog = endog - endog.mean() start_params = [0, 0, np.var(endog)] p, mleres = innovations_mle(endog, order=([0, 1], 0, [0, 1]), demean=False, start_params=start_params) mod = sarimax.SARIMAX(endog, order=([0, 1], 0, [0, 1])) # Test that the maximized log-likelihood found via applications of the # innovations algorithm matches the log-likelihood found by the Kalman # filter at the same parameters res = mod.filter(p.params) assert_allclose(-mleres.minimize_results.fun, res.llf) # Test MLE fitting # To avoid small numerical differences with MLE fitting, start at the # parameters found from innovations_mle res2 = mod.fit(start_params=p.params, disp=0) # Test that the state space approach confirms the MLE values found by # innovations_mle assert_allclose(p.params, res2.params) # Test that starting parameter estimation succeeds and isn't terrible # (i.e. leads to the same MLE) p2, _ = innovations_mle(endog, order=([0, 1], 0, [0, 1]), demean=False) # (does not need to be high-precision test since it's okay if different # starting parameters give slightly different MLE) assert_allclose(p.params, p2.params, atol=1e-5) def test_innovations_mle_integrated(): endog = np.r_[0, np.cumsum(lake.copy())] start_params = [0, np.var(lake.copy())] with assert_warns(UserWarning): p, mleres = innovations_mle(endog, order=(1, 1, 0), demean=False, start_params=start_params) mod = sarimax.SARIMAX(endog, order=(1, 1, 0), simple_differencing=True) # Test that the maximized log-likelihood found via applications of the # innovations algorithm matches the log-likelihood found by the Kalman # filter at the same parameters res = mod.filter(p.params) assert_allclose(-mleres.minimize_results.fun, res.llf) # Test MLE fitting # To avoid small numerical differences with MLE fitting, start at the # parameters found from innovations_mle res2 = mod.fit(start_params=p.params, disp=0) # Test that the state space approach confirms the MLE values found by # innovations_mle # Note: atol is required only due to precision issues on Windows assert_allclose(p.params, res2.params, atol=1e-6) # Test that the result is equivalent to order=(1, 0, 0) on the differenced # data p2, _ = innovations_mle(lake.copy(), order=(1, 0, 0), demean=False, start_params=start_params) # (does not need to be high-precision test since it's okay if different # starting parameters give slightly different MLE) assert_allclose(p.params, p2.params, atol=1e-5) def test_innovations_mle_misc(): endog = np.arange(20)**2 * 1.0 # Check that when Hannan-Rissanen estimates non-stationary starting # parameters, innovations_mle sets it to zero hr, _ = hannan_rissanen(endog, ar_order=1, demean=False) assert_(hr.ar_params[0] > 1) _, res = innovations_mle(endog, order=(1, 0, 0)) assert_allclose(res.start_params[0], 0) # Check that when Hannan-Rissanen estimates non-invertible starting # parameters, innovations_mle sets it to zero hr, _ = hannan_rissanen(endog, ma_order=1, demean=False) assert_(hr.ma_params[0] > 1) _, res = innovations_mle(endog, order=(0, 0, 1)) assert_allclose(res.start_params[0], 0) def test_innovations_mle_invalid(): endog = np.arange(2) * 1.0 assert_raises(ValueError, innovations_mle, endog, order=(0, 0, 2)) assert_raises(ValueError, innovations_mle, endog, order=(0, 0, -1)) assert_raises(ValueError, innovations_mle, endog, order=(0, 0, 1.5)) endog = lake.copy() assert_raises(ValueError, innovations_mle, endog, order=(1, 0, 0), start_params=[1., 1.]) assert_raises(ValueError, innovations_mle, endog, order=(0, 0, 1), start_params=[1., 1.]) statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/test_statespace.py000066400000000000000000000042251400612667500274730ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_allclose, assert_raises from statsmodels.tools.tools import add_constant from statsmodels.tsa.statespace import sarimax from statsmodels.tsa.arima.datasets.brockwell_davis_2002 import lake from statsmodels.tsa.arima.estimators.statespace import statespace def test_basic(): endog = lake.copy() exog = np.arange(1, len(endog) + 1) * 1.0 # Test default options (include_constant=True, concentrate_scale=False) p, res = statespace(endog, exog=exog, order=(1, 0, 0), include_constant=True, concentrate_scale=False) mod_ss = sarimax.SARIMAX(endog, exog=add_constant(exog), order=(1, 0, 0)) res_ss = mod_ss.filter(p.params) assert_allclose(res.statespace_results.llf, res_ss.llf) # Test include_constant=False p, res = statespace(endog, exog=exog, order=(1, 0, 0), include_constant=False, concentrate_scale=False) mod_ss = sarimax.SARIMAX(endog, exog=exog, order=(1, 0, 0)) res_ss = mod_ss.filter(p.params) assert_allclose(res.statespace_results.llf, res_ss.llf) # Test concentrate_scale=True p, res = statespace(endog, exog=exog, order=(1, 0, 0), include_constant=True, concentrate_scale=True) mod_ss = sarimax.SARIMAX(endog, exog=add_constant(exog), order=(1, 0, 0), concentrate_scale=True) res_ss = mod_ss.filter(p.params) assert_allclose(res.statespace_results.llf, res_ss.llf) def test_start_params(): endog = lake.copy() # Test for valid use of starting parameters p, _ = statespace(endog, order=(1, 0, 0), start_params=[0, 0, 1.]) p, _ = statespace(endog, order=(1, 0, 0), start_params=[0, 1., 1.], enforce_stationarity=False) p, _ = statespace(endog, order=(0, 0, 1), start_params=[0, 1., 1.], enforce_invertibility=False) # Test for invalid use of starting parameters assert_raises(ValueError, statespace, endog, order=(1, 0, 0), start_params=[0, 1., 1.]) assert_raises(ValueError, statespace, endog, order=(0, 0, 1), start_params=[0, 1., 1.]) statsmodels-0.12.2/statsmodels/tsa/arima/estimators/tests/test_yule_walker.py000066400000000000000000000056411400612667500276650ustar00rootroot00000000000000import numpy as np import pytest from numpy.testing import assert_allclose, assert_equal, assert_raises from statsmodels.tsa.stattools import acovf from statsmodels.tsa.innovations.arma_innovations import arma_innovations from statsmodels.tsa.arima.datasets.brockwell_davis_2002 import dowj, lake from statsmodels.tsa.arima.estimators.yule_walker import yule_walker @pytest.mark.low_precision('Test against Example 5.1.1 in Brockwell and Davis' ' (2016)') def test_brockwell_davis_example_511(): # Make the series stationary endog = dowj.diff().iloc[1:] # Should have 77 observations assert_equal(len(endog), 77) # Autocovariances desired = [0.17992, 0.07590, 0.04885] assert_allclose(acovf(endog, fft=True, nlag=2), desired, atol=1e-5) # Yule-Walker yw, _ = yule_walker(endog, ar_order=1, demean=True) assert_allclose(yw.ar_params, [0.4219], atol=1e-4) assert_allclose(yw.sigma2, 0.1479, atol=1e-4) @pytest.mark.low_precision('Test against Example 5.1.4 in Brockwell and Davis' ' (2016)') def test_brockwell_davis_example_514(): # Note: this example is primarily tested in # test_burg::test_brockwell_davis_example_514. # Get the lake data, demean endog = lake.copy() # Yule-Walker res, _ = yule_walker(endog, ar_order=2, demean=True) assert_allclose(res.ar_params, [1.0538, -0.2668], atol=1e-4) assert_allclose(res.sigma2, 0.4920, atol=1e-4) def check_itsmr(lake): # Test against R itsmr::yw; see results/results_yw_dl.R yw, _ = yule_walker(lake, 5) desired = [1.08213598501, -0.39658257147, 0.11793957728, -0.03326633983, 0.06209208707] assert_allclose(yw.ar_params, desired) # stats::ar.yw return the innovations algorithm estimate of the variance u, v = arma_innovations(np.array(lake) - np.mean(lake), ar_params=yw.ar_params, sigma2=1) desired_sigma2 = 0.4716322564 assert_allclose(np.sum(u**2 / v) / len(u), desired_sigma2) def test_itsmr(): # Note: apparently itsmr automatically demeans (there is no option to # control this) endog = lake.copy() check_itsmr(endog) # Pandas series check_itsmr(endog.values) # Numpy array check_itsmr(endog.tolist()) # Python list def test_invalid(): endog = np.arange(2) * 1.0 assert_raises(ValueError, yule_walker, endog, ar_order=-1) assert_raises(ValueError, yule_walker, endog, ar_order=1.5) endog = np.arange(10) * 1.0 assert_raises(ValueError, yule_walker, endog, ar_order=[1, 3]) @pytest.mark.xfail(reason='TODO: this does not raise an error due to the way' ' linear_model.yule_walker works.') def test_invalid_xfail(): endog = np.arange(2) * 1.0 # TODO: this does not raise an error due to the way Statsmodels' # yule_walker function works assert_raises(ValueError, yule_walker, endog, ar_order=2) statsmodels-0.12.2/statsmodels/tsa/arima/estimators/yule_walker.py000066400000000000000000000047251400612667500254660ustar00rootroot00000000000000""" Yule-Walker method for estimating AR(p) model parameters. Author: Chad Fulton License: BSD-3 """ from statsmodels.compat.pandas import deprecate_kwarg from statsmodels.regression import linear_model from statsmodels.tools.tools import Bunch from statsmodels.tsa.arima.params import SARIMAXParams from statsmodels.tsa.arima.specification import SARIMAXSpecification @deprecate_kwarg("unbiased", "adjusted") def yule_walker(endog, ar_order=0, demean=True, adjusted=False): """ Estimate AR parameters using Yule-Walker equations. Parameters ---------- endog : array_like or SARIMAXSpecification Input time series array, assumed to be stationary. ar_order : int, optional Autoregressive order. Default is 0. demean : bool, optional Whether to estimate and remove the mean from the process prior to fitting the autoregressive coefficients. Default is True. adjusted : bool, optional Whether to use the adjusted autocovariance estimator, which uses n - h degrees of freedom rather than n. For some processes this option may result in a non-positive definite autocovariance matrix. Default is False. Returns ------- parameters : SARIMAXParams object Contains the parameter estimates from the final iteration. other_results : Bunch Includes one component, `spec`, which is the `SARIMAXSpecification` instance corresponding to the input arguments. Notes ----- The primary reference is [1]_, section 5.1.1. This procedure assumes that the series is stationary. For a description of the effect of the adjusted estimate of the autocovariance function, see 2.4.2 of [1]_. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. """ spec = SARIMAXSpecification(endog, ar_order=ar_order) endog = spec.endog p = SARIMAXParams(spec=spec) if not spec.is_ar_consecutive: raise ValueError('Yule-Walker estimation unavailable for models with' ' seasonal or non-consecutive AR orders.') # Estimate parameters method = 'adjusted' if adjusted else 'mle' p.ar_params, sigma = linear_model.yule_walker( endog, order=ar_order, demean=demean, method=method) p.sigma2 = sigma**2 # Construct other results other_results = Bunch({ 'spec': spec, }) return p, other_results statsmodels-0.12.2/statsmodels/tsa/arima/model.py000066400000000000000000000562731400612667500220560ustar00rootroot00000000000000""" ARIMA model class. Author: Chad Fulton License: BSD-3 """ from statsmodels.compat.pandas import Appender import warnings import numpy as np from statsmodels.tools.data import _is_using_pandas from statsmodels.tsa.statespace import sarimax from statsmodels.tsa.statespace.kalman_filter import MEMORY_CONSERVE from statsmodels.tsa.statespace.tools import diff import statsmodels.base.wrapper as wrap from statsmodels.tsa.arima.estimators.yule_walker import yule_walker from statsmodels.tsa.arima.estimators.burg import burg from statsmodels.tsa.arima.estimators.hannan_rissanen import hannan_rissanen from statsmodels.tsa.arima.estimators.innovations import ( innovations, innovations_mle) from statsmodels.tsa.arima.estimators.gls import gls as estimate_gls from statsmodels.tsa.arima.specification import SARIMAXSpecification class ARIMA(sarimax.SARIMAX): """ Autoregressive Integrated Moving Average (ARIMA) model, and extensions This model is the basic interface for ARIMA-type models, including those with exogenous regressors and those with seasonal components. The most general form of the model is SARIMAX(p, d, q)x(P, D, Q, s). It also allows all specialized cases, including - autoregressive models: AR(p) - moving average models: MA(q) - mixed autoregressive moving average models: ARMA(p, q) - integration models: ARIMA(p, d, q) - seasonal models: SARIMA(P, D, Q, s) - regression with errors that follow one of the above ARIMA-type models Parameters ---------- endog : array_like, optional The observed time-series process :math:`y`. exog : array_like, optional Array of exogenous regressors. order : tuple, optional The (p,d,q) order of the model for the autoregressive, differences, and moving average components. d is always an integer, while p and q may either be integers or lists of integers. seasonal_order : tuple, optional The (P,D,Q,s) order of the seasonal component of the model for the AR parameters, differences, MA parameters, and periodicity. Default is (0, 0, 0, 0). D and s are always integers, while P and Q may either be integers or lists of positive integers. trend : str{'n','c','t','ct'} or iterable, optional Parameter controlling the deterministic trend. Can be specified as a string where 'c' indicates a constant term, 't' indicates a linear trend in time, and 'ct' includes both. Can also be specified as an iterable defining a polynomial, as in `numpy.poly1d`, where `[1,1,0,1]` would denote :math:`a + bt + ct^3`. Default is 'c' for models without integration, and no trend for models with integration. enforce_stationarity : bool, optional Whether or not to require the autoregressive parameters to correspond to a stationarity process. enforce_invertibility : bool, optional Whether or not to require the moving average parameters to correspond to an invertible process. concentrate_scale : bool, optional Whether or not to concentrate the scale (variance of the error term) out of the likelihood. This reduces the number of parameters by one. This is only applicable when considering estimation by numerical maximum likelihood. trend_offset : int, optional The offset at which to start time trend values. Default is 1, so that if `trend='t'` the trend is equal to 1, 2, ..., nobs. Typically is only set when the model created by extending a previous dataset. dates : array_like of datetime, optional If no index is given by `endog` or `exog`, an array-like object of datetime objects can be provided. freq : str, optional If no index is given by `endog` or `exog`, the frequency of the time-series may be specified here as a Pandas offset or offset string. missing : str Available options are 'none', 'drop', and 'raise'. If 'none', no nan checking is done. If 'drop', any observations with nans are dropped. If 'raise', an error is raised. Default is 'none'. Notes ----- This model incorporates both exogenous regressors and trend components through "regression with ARIMA errors". `enforce_stationarity` and `enforce_invertibility` are specified in the constructor because they affect loglikelihood computations, and so should not be changed on the fly. This is why they are not instead included as arguments to the `fit` method. TODO: should we use concentrate_scale=True by default? Examples -------- >>> mod = sm.tsa.arima.ARIMA(endog, order=(1, 0, 0)) >>> res = mod.fit() >>> print(res.summary()) """ def __init__(self, endog, exog=None, order=(0, 0, 0), seasonal_order=(0, 0, 0, 0), trend=None, enforce_stationarity=True, enforce_invertibility=True, concentrate_scale=False, trend_offset=1, dates=None, freq=None, missing='none', validate_specification=True): # Default for trend # 'c' if there is no integration and 'n' otherwise # TODO: if trend='c', then we could alternatively use `demean=True` in # the estimation methods rather than setting up `exog` and using GLS. # Not sure if it's worth the trouble though. integrated = order[1] > 0 or seasonal_order[1] > 0 if trend is None and not integrated: trend = 'c' elif trend is None: trend = 'n' # Construct the specification # (don't pass specific values of enforce stationarity/invertibility, # because we don't actually want to restrict the estimators based on # this criteria. Instead, we'll just make sure that the parameter # estimates from those methods satisfy the criteria.) self._spec_arima = SARIMAXSpecification( endog, exog=exog, order=order, seasonal_order=seasonal_order, trend=trend, enforce_stationarity=None, enforce_invertibility=None, concentrate_scale=concentrate_scale, trend_offset=trend_offset, dates=dates, freq=freq, missing=missing, validate_specification=validate_specification) exog = self._spec_arima._model.data.orig_exog # Raise an error if we have a constant in an integrated model has_trend = len(self._spec_arima.trend_terms) > 0 if has_trend: lowest_trend = np.min(self._spec_arima.trend_terms) if lowest_trend < order[1] + seasonal_order[1]: raise ValueError( 'In models with integration (`d > 0`) or seasonal' ' integration (`D > 0`), trend terms of lower order than' ' `d + D` cannot be (as they would be eliminated due to' ' the differencing operation). For example, a constant' ' cannot be included in an ARIMA(1, 1, 1) model, but' ' including a linear trend, which would have the same' ' effect as fitting a constant to the differenced data,' ' is allowed.') # Keep the given `exog` by removing the prepended trend variables input_exog = None if exog is not None: if _is_using_pandas(exog, None): input_exog = exog.iloc[:, self._spec_arima.k_trend:] else: input_exog = exog[:, self._spec_arima.k_trend:] # Initialize the base SARIMAX class # Note: we don't pass in a trend value to the base class, since ARIMA # standardizes the trend to always be part of exog, while the base # SARIMAX class puts it in the transition equation. super(ARIMA, self).__init__( endog, exog, trend=None, order=order, seasonal_order=seasonal_order, enforce_stationarity=enforce_stationarity, enforce_invertibility=enforce_invertibility, concentrate_scale=concentrate_scale, dates=dates, freq=freq, missing=missing, validate_specification=validate_specification) self.trend = trend # Save the input exog and input exog names, so that we can refer to # them later (see especially `ARIMAResults.append`) self._input_exog = input_exog if exog is not None: self._input_exog_names = self.exog_names[self._spec_arima.k_trend:] else: self._input_exog_names = None # Override the public attributes for k_exog and k_trend to reflect the # distinction here (for the purpose of the superclass, these are both # combined as `k_exog`) self.k_exog = self._spec_arima.k_exog self.k_trend = self._spec_arima.k_trend # Remove some init kwargs that aren't used in this model unused = ['measurement_error', 'time_varying_regression', 'mle_regression', 'simple_differencing', 'hamilton_representation'] self._init_keys = [key for key in self._init_keys if key not in unused] @property def _res_classes(self): return {'fit': (ARIMAResults, ARIMAResultsWrapper)} def fit(self, start_params=None, transformed=True, includes_fixed=False, method=None, method_kwargs=None, gls=None, gls_kwargs=None, cov_type=None, cov_kwds=None, return_params=False, low_memory=False): """ Fit (estimate) the parameters of the model. Parameters ---------- start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. If None, the default is given by Model.start_params. transformed : bool, optional Whether or not `start_params` is already transformed. Default is True. includes_fixed : bool, optional If parameters were previously fixed with the `fix_params` method, this argument describes whether or not `start_params` also includes the fixed parameters, in addition to the free parameters. Default is False. method : str, optional The method used for estimating the parameters of the model. Valid options include 'statespace', 'innovations_mle', 'hannan_rissanen', 'burg', 'innovations', and 'yule_walker'. Not all options are available for every specification (for example 'yule_walker' can only be used with AR(p) models). method_kwargs : dict, optional Arguments to pass to the fit function for the parameter estimator described by the `method` argument. gls : bool, optional Whether or not to use generalized least squares (GLS) to estimate regression effects. The default is False if `method='statespace'` and is True otherwise. gls_kwargs : dict, optional Arguments to pass to the GLS estimation fit method. Only applicable if GLS estimation is used (see `gls` argument for details). cov_type : str, optional The `cov_type` keyword governs the method for calculating the covariance matrix of parameter estimates. Can be one of: - 'opg' for the outer product of gradient estimator - 'oim' for the observed information matrix estimator, calculated using the method of Harvey (1989) - 'approx' for the observed information matrix estimator, calculated using a numerical approximation of the Hessian matrix. - 'robust' for an approximate (quasi-maximum likelihood) covariance matrix that may be valid even in the presence of some misspecifications. Intermediate calculations use the 'oim' method. - 'robust_approx' is the same as 'robust' except that the intermediate calculations use the 'approx' method. - 'none' for no covariance matrix calculation. Default is 'opg' unless memory conservation is used to avoid computing the loglikelihood values for each observation, in which case the default is 'oim'. cov_kwds : dict or None, optional A dictionary of arguments affecting covariance matrix computation. **opg, oim, approx, robust, robust_approx** - 'approx_complex_step' : bool, optional - If True, numerical approximations are computed using complex-step methods. If False, numerical approximations are computed using finite difference methods. Default is True. - 'approx_centered' : bool, optional - If True, numerical approximations computed using finite difference methods use a centered approximation. Default is False. return_params : bool, optional Whether or not to return only the array of maximizing parameters. Default is False. low_memory : bool, optional If set to True, techniques are applied to substantially reduce memory usage. If used, some features of the results object will not be available (including smoothed results and in-sample prediction), although out-of-sample forecasting is possible. Default is False. Returns ------- ARIMAResults Examples -------- >>> mod = sm.tsa.arima.ARIMA(endog, order=(1, 0, 0)) >>> res = mod.fit() >>> print(res.summary()) """ # Determine which method to use # 1. If method is specified, make sure it is valid if method is not None: self._spec_arima.validate_estimator(method) # 2. Otherwise, use state space # TODO: may want to consider using innovations (MLE) if possible here, # (since in some cases it may be faster than state space), but it is # less tested. else: method = 'statespace' # Can only use fixed parameters with method='statespace' if self._has_fixed_params and method != 'statespace': raise ValueError('When parameters have been fixed, only the method' ' "statespace" can be used; got "%s".' % method) # Handle kwargs related to the fit method if method_kwargs is None: method_kwargs = {} required_kwargs = [] if method == 'statespace': required_kwargs = ['enforce_stationarity', 'enforce_invertibility', 'concentrate_scale'] elif method == 'innovations_mle': required_kwargs = ['enforce_invertibility'] for name in required_kwargs: if name in method_kwargs: raise ValueError('Cannot override model level value for "%s"' ' when method="%s".' % (name, method)) method_kwargs[name] = getattr(self, name) # Handle kwargs related to GLS estimation if gls_kwargs is None: gls_kwargs = {} # Handle starting parameters # TODO: maybe should have standard way of computing starting # parameters in this class? if start_params is not None: if method not in ['statespace', 'innovations_mle']: raise ValueError('Estimation method "%s" does not use starting' ' parameters, but `start_params` argument was' ' given.' % method) method_kwargs['start_params'] = start_params method_kwargs['transformed'] = transformed method_kwargs['includes_fixed'] = includes_fixed # Perform estimation, depending on whether we have exog or not p = None fit_details = None has_exog = self._spec_arima.exog is not None if has_exog or method == 'statespace': # Use GLS if it was explicitly requested (`gls = True`) or if it # was left at the default (`gls = None`) and the ARMA estimator is # anything but statespace. # Note: both GLS and statespace are able to handle models with # integration, so we don't need to difference endog or exog here. if has_exog and (gls or (gls is None and method != 'statespace')): p, fit_details = estimate_gls( self.endog, exog=self.exog, order=self.order, seasonal_order=self.seasonal_order, include_constant=False, arma_estimator=method, arma_estimator_kwargs=method_kwargs, **gls_kwargs) elif method != 'statespace': raise ValueError('If `exog` is given and GLS is disabled' ' (`gls=False`), then the only valid' " method is 'statespace'. Got '%s'." % method) else: method_kwargs.setdefault('disp', 0) res = super(ARIMA, self).fit( return_params=return_params, low_memory=low_memory, cov_type=cov_type, cov_kwds=cov_kwds, **method_kwargs) if not return_params: res.fit_details = res.mlefit else: # Handle differencing if we have an integrated model # (these methods do not support handling integration internally, # so we need to manually do the differencing) endog = self.endog order = self._spec_arima.order seasonal_order = self._spec_arima.seasonal_order if self._spec_arima.is_integrated: warnings.warn('Provided `endog` series has been differenced' ' to eliminate integration prior to parameter' ' estimation by method "%s".' % method) endog = diff( endog, k_diff=self._spec_arima.diff, k_seasonal_diff=self._spec_arima.seasonal_diff, seasonal_periods=self._spec_arima.seasonal_periods) if order[1] > 0: order = (order[0], 0, order[2]) if seasonal_order[1] > 0: seasonal_order = (seasonal_order[0], 0, seasonal_order[2], seasonal_order[3]) # Now, estimate parameters if method == 'yule_walker': p, fit_details = yule_walker( endog, ar_order=order[0], demean=False, **method_kwargs) elif method == 'burg': p, fit_details = burg(endog, ar_order=order[0], demean=False, **method_kwargs) elif method == 'hannan_rissanen': p, fit_details = hannan_rissanen( endog, ar_order=order[0], ma_order=order[2], demean=False, **method_kwargs) elif method == 'innovations': p, fit_details = innovations( endog, ma_order=order[2], demean=False, **method_kwargs) # innovations computes estimates through the given order, so # we want to take the estimate associated with the given order p = p[-1] elif method == 'innovations_mle': p, fit_details = innovations_mle( endog, order=order, seasonal_order=seasonal_order, demean=False, **method_kwargs) # In all cases except method='statespace', we now need to extract the # parameters and, optionally, create a new results object if p is not None: # Need to check that fitted parameters satisfy given restrictions if (self.enforce_stationarity and self._spec_arima.max_reduced_ar_order > 0 and not p.is_stationary): raise ValueError('Non-stationary autoregressive parameters' ' found with `enforce_stationarity=True`.' ' Consider setting it to False or using a' ' different estimation method, such as' ' method="statespace".') if (self.enforce_invertibility and self._spec_arima.max_reduced_ma_order > 0 and not p.is_invertible): raise ValueError('Non-invertible moving average parameters' ' found with `enforce_invertibility=True`.' ' Consider setting it to False or using a' ' different estimation method, such as' ' method="statespace".') # Build the requested results if return_params: res = p.params else: # Handle memory conservation option if low_memory: conserve_memory = self.ssm.conserve_memory self.ssm.set_conserve_memory(MEMORY_CONSERVE) # Perform filtering / smoothing if (self.ssm.memory_no_predicted or self.ssm.memory_no_gain or self.ssm.memory_no_smoothing): func = self.filter else: func = self.smooth res = func(p.params, transformed=True, includes_fixed=True, cov_type=cov_type, cov_kwds=cov_kwds) # Save any details from the fit method res.fit_details = fit_details # Reset memory conservation if low_memory: self.ssm.set_conserve_memory(conserve_memory) return res @Appender(sarimax.SARIMAXResults.__doc__) class ARIMAResults(sarimax.SARIMAXResults): @Appender(sarimax.SARIMAXResults.append.__doc__) def append(self, endog, exog=None, refit=False, fit_kwargs=None, **kwargs): # MLEResults.append will concatenate the given `exog` here with # `data.orig_exog`. However, `data.orig_exog` already has had any # trend variables prepended to it, while the `exog` given here should # not. Instead, we need to temporarily replace `orig_exog` and # `exog_names` with the ones that correspond to those that were input # by the user. if exog is not None: orig_exog = self.model.data.orig_exog exog_names = self.model.exog_names self.model.data.orig_exog = self.model._input_exog self.model.exog_names = self.model._input_exog_names # Perform the appending procedure out = super().append(endog, exog=exog, refit=refit, fit_kwargs=fit_kwargs, **kwargs) # Now we reverse the temporary change made above if exog is not None: self.model.data.orig_exog = orig_exog self.model.exog_names = exog_names return out class ARIMAResultsWrapper(sarimax.SARIMAXResultsWrapper): _attrs = {} _wrap_attrs = wrap.union_dicts( sarimax.SARIMAXResultsWrapper._wrap_attrs, _attrs) _methods = {} _wrap_methods = wrap.union_dicts( sarimax.SARIMAXResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(ARIMAResultsWrapper, ARIMAResults) # noqa:E305 statsmodels-0.12.2/statsmodels/tsa/arima/params.py000066400000000000000000000354251400612667500222350ustar00rootroot00000000000000""" SARIMAX parameters class. Author: Chad Fulton License: BSD-3 """ import numpy as np import pandas as pd from numpy.polynomial import Polynomial from statsmodels.tsa.statespace.tools import is_invertible from statsmodels.tsa.arima.tools import validate_basic class SARIMAXParams(object): """ SARIMAX parameters. Parameters ---------- spec : SARIMAXSpecification Specification of the SARIMAX model. Attributes ---------- spec : SARIMAXSpecification Specification of the SARIMAX model. exog_names : list of str Names associated with exogenous parameters. ar_names : list of str Names associated with (non-seasonal) autoregressive parameters. ma_names : list of str Names associated with (non-seasonal) moving average parameters. seasonal_ar_names : list of str Names associated with seasonal autoregressive parameters. seasonal_ma_names : list of str Names associated with seasonal moving average parameters. param_names :list of str Names of all model parameters. k_exog_params : int Number of parameters associated with exogenous variables. k_ar_params : int Number of parameters associated with (non-seasonal) autoregressive lags. k_ma_params : int Number of parameters associated with (non-seasonal) moving average lags. k_seasonal_ar_params : int Number of parameters associated with seasonal autoregressive lags. k_seasonal_ma_params : int Number of parameters associated with seasonal moving average lags. k_params : int Total number of model parameters. """ def __init__(self, spec): self.spec = spec # Local copies of relevant attributes self.exog_names = spec.exog_names self.ar_names = spec.ar_names self.ma_names = spec.ma_names self.seasonal_ar_names = spec.seasonal_ar_names self.seasonal_ma_names = spec.seasonal_ma_names self.param_names = spec.param_names self.k_exog_params = spec.k_exog_params self.k_ar_params = spec.k_ar_params self.k_ma_params = spec.k_ma_params self.k_seasonal_ar_params = spec.k_seasonal_ar_params self.k_seasonal_ma_params = spec.k_seasonal_ma_params self.k_params = spec.k_params # Cache for holding parameter values self._params_split = spec.split_params( np.zeros(self.k_params) * np.nan, allow_infnan=True) self._params = None @property def exog_params(self): """(array) Parameters associated with exogenous variables.""" return self._params_split['exog_params'] @exog_params.setter def exog_params(self, value): if np.isscalar(value): value = [value] * self.k_exog_params self._params_split['exog_params'] = validate_basic( value, self.k_exog_params, title='exogenous coefficients') self._params = None @property def ar_params(self): """(array) Autoregressive (non-seasonal) parameters.""" return self._params_split['ar_params'] @ar_params.setter def ar_params(self, value): if np.isscalar(value): value = [value] * self.k_ar_params self._params_split['ar_params'] = validate_basic( value, self.k_ar_params, title='AR coefficients') self._params = None @property def ar_poly(self): """(Polynomial) Autoregressive (non-seasonal) lag polynomial.""" coef = np.zeros(self.spec.max_ar_order + 1) coef[0] = 1 ix = self.spec.ar_lags coef[ix] = -self._params_split['ar_params'] return Polynomial(coef) @ar_poly.setter def ar_poly(self, value): # Convert from the polynomial to the parameters, and set that way if isinstance(value, Polynomial): value = value.coef value = validate_basic(value, self.spec.max_ar_order + 1, title='AR polynomial') if value[0] != 1: raise ValueError('AR polynomial constant must be equal to 1.') ar_params = [] for i in range(1, self.spec.max_ar_order + 1): if i in self.spec.ar_lags: ar_params.append(-value[i]) elif value[i] != 0: raise ValueError('AR polynomial includes non-zero values' ' for lags that are excluded in the' ' specification.') self.ar_params = ar_params @property def ma_params(self): """(array) Moving average (non-seasonal) parameters.""" return self._params_split['ma_params'] @ma_params.setter def ma_params(self, value): if np.isscalar(value): value = [value] * self.k_ma_params self._params_split['ma_params'] = validate_basic( value, self.k_ma_params, title='MA coefficients') self._params = None @property def ma_poly(self): """(Polynomial) Moving average (non-seasonal) lag polynomial.""" coef = np.zeros(self.spec.max_ma_order + 1) coef[0] = 1 ix = self.spec.ma_lags coef[ix] = self._params_split['ma_params'] return Polynomial(coef) @ma_poly.setter def ma_poly(self, value): # Convert from the polynomial to the parameters, and set that way if isinstance(value, Polynomial): value = value.coef value = validate_basic(value, self.spec.max_ma_order + 1, title='MA polynomial') if value[0] != 1: raise ValueError('MA polynomial constant must be equal to 1.') ma_params = [] for i in range(1, self.spec.max_ma_order + 1): if i in self.spec.ma_lags: ma_params.append(value[i]) elif value[i] != 0: raise ValueError('MA polynomial includes non-zero values' ' for lags that are excluded in the' ' specification.') self.ma_params = ma_params @property def seasonal_ar_params(self): """(array) Seasonal autoregressive parameters.""" return self._params_split['seasonal_ar_params'] @seasonal_ar_params.setter def seasonal_ar_params(self, value): if np.isscalar(value): value = [value] * self.k_seasonal_ar_params self._params_split['seasonal_ar_params'] = validate_basic( value, self.k_seasonal_ar_params, title='seasonal AR coefficients') self._params = None @property def seasonal_ar_poly(self): """(Polynomial) Seasonal autoregressive lag polynomial.""" # Need to expand the polynomial according to the season s = self.spec.seasonal_periods coef = [1] if s > 0: expanded = np.zeros(self.spec.max_seasonal_ar_order) ix = np.array(self.spec.seasonal_ar_lags, dtype=int) - 1 expanded[ix] = -self._params_split['seasonal_ar_params'] coef = np.r_[1, np.pad(np.reshape(expanded, (-1, 1)), [(0, 0), (s - 1, 0)], 'constant').flatten()] return Polynomial(coef) @seasonal_ar_poly.setter def seasonal_ar_poly(self, value): s = self.spec.seasonal_periods # Note: assume that we are given coefficients from the full polynomial # Convert from the polynomial to the parameters, and set that way if isinstance(value, Polynomial): value = value.coef value = validate_basic(value, 1 + s * self.spec.max_seasonal_ar_order, title='seasonal AR polynomial') if value[0] != 1: raise ValueError('Polynomial constant must be equal to 1.') seasonal_ar_params = [] for i in range(1, self.spec.max_seasonal_ar_order + 1): if i in self.spec.seasonal_ar_lags: seasonal_ar_params.append(-value[s * i]) elif value[s * i] != 0: raise ValueError('AR polynomial includes non-zero values' ' for lags that are excluded in the' ' specification.') self.seasonal_ar_params = seasonal_ar_params @property def seasonal_ma_params(self): """(array) Seasonal moving average parameters.""" return self._params_split['seasonal_ma_params'] @seasonal_ma_params.setter def seasonal_ma_params(self, value): if np.isscalar(value): value = [value] * self.k_seasonal_ma_params self._params_split['seasonal_ma_params'] = validate_basic( value, self.k_seasonal_ma_params, title='seasonal MA coefficients') self._params = None @property def seasonal_ma_poly(self): """(Polynomial) Seasonal moving average lag polynomial.""" # Need to expand the polynomial according to the season s = self.spec.seasonal_periods coef = np.array([1]) if s > 0: expanded = np.zeros(self.spec.max_seasonal_ma_order) ix = np.array(self.spec.seasonal_ma_lags, dtype=int) - 1 expanded[ix] = self._params_split['seasonal_ma_params'] coef = np.r_[1, np.pad(np.reshape(expanded, (-1, 1)), [(0, 0), (s - 1, 0)], 'constant').flatten()] return Polynomial(coef) @seasonal_ma_poly.setter def seasonal_ma_poly(self, value): s = self.spec.seasonal_periods # Note: assume that we are given coefficients from the full polynomial # Convert from the polynomial to the parameters, and set that way if isinstance(value, Polynomial): value = value.coef value = validate_basic(value, 1 + s * self.spec.max_seasonal_ma_order, title='seasonal MA polynomial',) if value[0] != 1: raise ValueError('Polynomial constant must be equal to 1.') seasonal_ma_params = [] for i in range(1, self.spec.max_seasonal_ma_order + 1): if i in self.spec.seasonal_ma_lags: seasonal_ma_params.append(value[s * i]) elif value[s * i] != 0: raise ValueError('MA polynomial includes non-zero values' ' for lags that are excluded in the' ' specification.') self.seasonal_ma_params = seasonal_ma_params @property def sigma2(self): """(float) Innovation variance.""" return self._params_split['sigma2'] @sigma2.setter def sigma2(self, params): length = int(not self.spec.concentrate_scale) self._params_split['sigma2'] = validate_basic( params, length, title='sigma2').item() self._params = None @property def reduced_ar_poly(self): """(Polynomial) Reduced form autoregressive lag polynomial.""" return self.ar_poly * self.seasonal_ar_poly @property def reduced_ma_poly(self): """(Polynomial) Reduced form moving average lag polynomial.""" return self.ma_poly * self.seasonal_ma_poly @property def params(self): """(array) Complete parameter vector.""" if self._params is None: self._params = self.spec.join_params(**self._params_split) return self._params.copy() @params.setter def params(self, value): self._params_split = self.spec.split_params(value) self._params = None @property def is_complete(self): """(bool) Are current parameter values all filled in (i.e. not NaN).""" return not np.any(np.isnan(self.params)) @property def is_valid(self): """(bool) Are current parameter values valid (e.g. variance > 0).""" valid = True try: self.spec.validate_params(self.params) except ValueError: valid = False return valid @property def is_stationary(self): """(bool) Is the reduced autoregressive lag poylnomial stationary.""" validate_basic(self.ar_params, self.k_ar_params, title='AR coefficients') validate_basic(self.seasonal_ar_params, self.k_seasonal_ar_params, title='seasonal AR coefficients') ar_stationary = True seasonal_ar_stationary = True if self.k_ar_params > 0: ar_stationary = is_invertible(self.ar_poly.coef) if self.k_seasonal_ar_params > 0: seasonal_ar_stationary = is_invertible(self.seasonal_ar_poly.coef) return ar_stationary and seasonal_ar_stationary @property def is_invertible(self): """(bool) Is the reduced moving average lag poylnomial invertible.""" # Short-circuit if there is no MA component validate_basic(self.ma_params, self.k_ma_params, title='MA coefficients') validate_basic(self.seasonal_ma_params, self.k_seasonal_ma_params, title='seasonal MA coefficients') ma_stationary = True seasonal_ma_stationary = True if self.k_ma_params > 0: ma_stationary = is_invertible(self.ma_poly.coef) if self.k_seasonal_ma_params > 0: seasonal_ma_stationary = is_invertible(self.seasonal_ma_poly.coef) return ma_stationary and seasonal_ma_stationary def to_dict(self): """ Return the parameters split by type into a dictionary. Returns ------- split_params : dict Dictionary with keys 'exog_params', 'ar_params', 'ma_params', 'seasonal_ar_params', 'seasonal_ma_params', and (unless `concentrate_scale=True`) 'sigma2'. Values are the parameters associated with the key, based on the `params` argument. """ return self._params_split.copy() def to_pandas(self): """ Return the parameters as a Pandas series. Returns ------- series : pd.Series Pandas series with index set to the parameter names. """ return pd.Series(self.params, index=self.param_names) def __repr__(self): """Represent SARIMAXParams object as a string.""" components = [] if self.k_exog_params: components.append('exog=%s' % str(self.exog_params)) if self.k_ar_params: components.append('ar=%s' % str(self.ar_params)) if self.k_ma_params: components.append('ma=%s' % str(self.ma_params)) if self.k_seasonal_ar_params: components.append('seasonal_ar=%s' % str(self.seasonal_ar_params)) if self.k_seasonal_ma_params: components.append('seasonal_ma=%s' % str(self.seasonal_ma_params)) if not self.spec.concentrate_scale: components.append('sigma2=%s' % self.sigma2) return 'SARIMAXParams(%s)' % ', '.join(components) statsmodels-0.12.2/statsmodels/tsa/arima/specification.py000066400000000000000000001324141400612667500235660ustar00rootroot00000000000000""" SARIMAX specification class. Author: Chad Fulton License: BSD-3 """ import numpy as np import pandas as pd from statsmodels.tools.data import _is_using_pandas from statsmodels.tsa.base.tsa_model import TimeSeriesModel from statsmodels.tsa.statespace.tools import ( is_invertible, constrain_stationary_univariate as constrain, unconstrain_stationary_univariate as unconstrain, prepare_exog, prepare_trend_spec, prepare_trend_data) from statsmodels.tsa.arima.tools import standardize_lag_order, validate_basic class SARIMAXSpecification(object): """ SARIMAX specification. Parameters ---------- endog : array_like, optional The observed time-series process :math:`y`. exog : array_like, optional Array of exogenous regressors. order : tuple, optional The (p,d,q) order of the model for the autoregressive, differences, and moving average components. d is always an integer, while p and q may either be integers or lists of integers. May not be used in combination with the arguments `ar_order`, `diff`, or `ma_order`. seasonal_order : tuple, optional The (P,D,Q,s) order of the seasonal component of the model for the AR parameters, differences, MA parameters, and periodicity. Default is (0, 0, 0, 0). D and s are always integers, while P and Q may either be integers or lists of positive integers. May not be used in combination with the arguments `seasonal_ar_order`, `seasonal_diff`, or `seasonal_ma_order`. ar_order : int or list of int The autoregressive order of the model. May be an integer, in which case all autoregressive lags up to and including it will be included. Alternatively, may be a list of integers specifying which lag orders are included. May not be used in combination with `order`. diff : int The order of integration of the model. May not be used in combination with `order`. ma_order : int or list of int The moving average order of the model. May be an integer or list of integers. See the documentation for `ar_order` for details. May not be used in combination with `order`. seasonal_ar_order : int or list of int The seasonal autoregressive order of the model. May be an integer or list of integers. See the documentation for `ar_order` for examples. Note that if `seasonal_periods = 4` and `seasonal_ar_order = 2`, then this implies that the overall model will include lags 4 and 8. May not be used in combination with `seasonal_order`. seasonal_diff : int The order of seasonal integration of the model. May not be used in combination with `seasonal_order`. seasonal_ma_order : int or list of int The moving average order of the model. May be an integer or list of integers. See the documentation for `ar_order` and `seasonal_ar_order` for additional details. May not be used in combination with `seasonal_order`. seasonal_periods : int Number of periods in a season. May not be used in combination with `seasonal_order`. enforce_stationarity : bool, optional Whether or not to require the autoregressive parameters to correspond to a stationarity process. This is only possible in estimation by numerical maximum likelihood. enforce_invertibility : bool, optional Whether or not to require the moving average parameters to correspond to an invertible process. This is only possible in estimation by numerical maximum likelihood. concentrate_scale : bool, optional Whether or not to concentrate the scale (variance of the error term) out of the likelihood. This reduces the number of parameters by one. This is only applicable when considering estimation by numerical maximum likelihood. dates : array_like of datetime, optional If no index is given by `endog` or `exog`, an array-like object of datetime objects can be provided. freq : str, optional If no index is given by `endog` or `exog`, the frequency of the time-series may be specified here as a Pandas offset or offset string. missing : str Available options are 'none', 'drop', and 'raise'. If 'none', no nan checking is done. If 'drop', any observations with nans are dropped. If 'raise', an error is raised. Default is 'none'. Attributes ---------- order : tuple, optional The (p,d,q) order of the model for the autoregressive, differences, and moving average components. d is always an integer, while p and q may either be integers or lists of integers. seasonal_order : tuple, optional The (P,D,Q,s) order of the seasonal component of the model for the AR parameters, differences, MA parameters, and periodicity. Default is (0, 0, 0, 0). D and s are always integers, while P and Q may either be integers or lists of positive integers. ar_order : int or list of int The autoregressive order of the model. May be an integer, in which case all autoregressive lags up to and including it will be included. For example, if `ar_order = 3`, then the model will include lags 1, 2, and 3. Alternatively, may be a list of integers specifying exactly which lag orders are included. For example, if `ar_order = [1, 3]`, then the model will include lags 1 and 3 but will exclude lag 2. diff : int The order of integration of the model. ma_order : int or list of int The moving average order of the model. May be an integer or list of integers. See the documentation for `ar_order` for examples. seasonal_ar_order : int or list of int The seasonal autoregressive order of the model. May be an integer or list of integers. See the documentation for `ar_order` for examples. Note that if `seasonal_periods = 4` and `seasonal_ar_order = 2`, then this implies that the overall model will include lags 4 and 8. seasonal_diff : int The order of seasonal integration of the model. seasonal_ma_order : int or list of int The moving average order of the model. May be an integer or list of integers. See the documentation for `ar_order` and `seasonal_ar_order` for additional details. seasonal_periods : int Number of periods in a season. trend : str{'n','c','t','ct'} or iterable, optional Parameter controlling the deterministic trend polynomial :math:`A(t)`. Can be specified as a string where 'c' indicates a constant (i.e. a degree zero component of the trend polynomial), 't' indicates a linear trend with time, and 'ct' is both. Can also be specified as an iterable defining the polynomial as in `numpy.poly1d`, where `[1,1,0,1]` would denote :math:`a + bt + ct^3`. Default is to not include a trend component. ar_lags : list of int List of included autoregressive lags. If `ar_order` is a list, then `ar_lags == ar_order`. If `ar_lags = [1, 2]`, then the overall model will include the 1st and 2nd autoregressive lags. ma_lags : list of int List of included moving average lags. If `ma_order` is a list, then `ma_lags == ma_order`. If `ma_lags = [1, 2]`, then the overall model will include the 1st and 2nd moving average lags. seasonal_ar_lags : list of int List of included seasonal autoregressive lags. If `seasonal_ar_order` is a list, then `seasonal_ar_lags == seasonal_ar_order`. If `seasonal_periods = 4` and `seasonal_ar_lags = [1, 2]`, then the overall model will include the 4th and 8th autoregressive lags. seasonal_ma_lags : list of int List of included seasonal moving average lags. If `seasonal_ma_order` is a list, then `seasonal_ma_lags == seasonal_ma_order`. See the documentation to `seasonal_ar_lags` for examples. max_ar_order : int Largest included autoregressive lag. max_ma_order : int Largest included moving average lag. max_seasonal_ar_order : int Largest included seasonal autoregressive lag. max_seasonal_ma_order : int Largest included seasonal moving average lag. max_reduced_ar_order : int Largest lag in the reduced autoregressive polynomial. Equal to `max_ar_order + max_seasonal_ar_order * seasonal_periods`. max_reduced_ma_order : int Largest lag in the reduced moving average polynomial. Equal to `max_ma_order + max_seasonal_ma_order * seasonal_periods`. enforce_stationarity : bool Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. This is only possible in estimation by numerical maximum likelihood. enforce_invertibility : bool Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. This is only possible in estimation by numerical maximum likelihood. concentrate_scale : bool Whether or not to concentrate the variance (scale term) out of the log-likelihood function. This is only applicable when considering estimation by numerical maximum likelihood. is_ar_consecutive is_ma_consecutive is_integrated is_seasonal k_exog_params k_ar_params k_ma_params k_seasonal_ar_params k_seasonal_ma_params k_params exog_names ar_names ma_names seasonal_ar_names seasonal_ma_names param_names Examples -------- >>> SARIMAXSpecification(order=(1, 0, 2)) SARIMAXSpecification(endog=y, order=(1, 0, 2)) >>> spec = SARIMAXSpecification(ar_order=1, ma_order=2) SARIMAXSpecification(endog=y, order=(1, 0, 2)) >>> spec = SARIMAXSpecification(ar_order=1, seasonal_order=(1, 0, 0, 4)) SARIMAXSpecification(endog=y, order=(1, 0, 0), seasonal_order=(1, 0, 0, 4)) """ def __init__(self, endog=None, exog=None, order=None, seasonal_order=None, ar_order=None, diff=None, ma_order=None, seasonal_ar_order=None, seasonal_diff=None, seasonal_ma_order=None, seasonal_periods=None, trend=None, enforce_stationarity=None, enforce_invertibility=None, concentrate_scale=None, trend_offset=1, dates=None, freq=None, missing='none', validate_specification=True): # Basic parameters self.enforce_stationarity = enforce_stationarity self.enforce_invertibility = enforce_invertibility self.concentrate_scale = concentrate_scale self.trend_offset = trend_offset # Validate that we were not given conflicting specifications has_order = order is not None has_specific_order = (ar_order is not None or diff is not None or ma_order is not None) has_seasonal_order = seasonal_order is not None has_specific_seasonal_order = (seasonal_ar_order is not None or seasonal_diff is not None or seasonal_ma_order is not None or seasonal_periods is not None) if has_order and has_specific_order: raise ValueError('Cannot specify both `order` and either of' ' `ar_order` or `ma_order`.') if has_seasonal_order and has_specific_seasonal_order: raise ValueError('Cannot specify both `seasonal_order` and any of' ' `seasonal_ar_order`, `seasonal_ma_order`,' ' or `seasonal_periods`.') # Compute `order` if has_specific_order: ar_order = 0 if ar_order is None else ar_order diff = 0 if diff is None else diff ma_order = 0 if ma_order is None else ma_order order = (ar_order, diff, ma_order) elif not has_order: order = (0, 0, 0) # Compute `seasonal_order` if has_specific_seasonal_order: seasonal_ar_order = ( 0 if seasonal_ar_order is None else seasonal_ar_order) seasonal_diff = 0 if seasonal_diff is None else seasonal_diff seasonal_ma_order = ( 0 if seasonal_ma_order is None else seasonal_ma_order) seasonal_periods = ( 0 if seasonal_periods is None else seasonal_periods) seasonal_order = (seasonal_ar_order, seasonal_diff, seasonal_ma_order, seasonal_periods) elif not has_seasonal_order: seasonal_order = (0, 0, 0, 0) # Validate shapes of `order`, `seasonal_order` if len(order) != 3: raise ValueError('`order` argument must be an iterable with three' ' elements.') if len(seasonal_order) != 4: raise ValueError('`seasonal_order` argument must be an iterable' ' with four elements.') # Validate differencing parameters if validate_specification: if order[1] < 0: raise ValueError('Cannot specify negative differencing.') if order[1] != int(order[1]): raise ValueError('Cannot specify fractional differencing.') if seasonal_order[1] < 0: raise ValueError('Cannot specify negative seasonal' ' differencing.') if seasonal_order[1] != int(seasonal_order[1]): raise ValueError('Cannot specify fractional seasonal' ' differencing.') if seasonal_order[3] < 0: raise ValueError('Cannot specify negative seasonal' ' periodicity.') # Standardize to integers or lists of integers order = ( standardize_lag_order(order[0], 'AR'), int(order[1]), standardize_lag_order(order[2], 'MA')) seasonal_order = ( standardize_lag_order(seasonal_order[0], 'seasonal AR'), int(seasonal_order[1]), standardize_lag_order(seasonal_order[2], 'seasonal MA'), int(seasonal_order[3])) # Validate seasonals if validate_specification: if seasonal_order[3] == 1: raise ValueError('Seasonal periodicity must be greater' ' than 1.') if ((seasonal_order[0] != 0 or seasonal_order[1] != 0 or seasonal_order[2] != 0) and seasonal_order[3] == 0): raise ValueError('Must include nonzero seasonal periodicity if' ' including seasonal AR, MA, or' ' differencing.') # Basic order self.order = order self.ar_order, self.diff, self.ma_order = order self.seasonal_order = seasonal_order (self.seasonal_ar_order, self.seasonal_diff, self.seasonal_ma_order, self.seasonal_periods) = seasonal_order # Lists of included lags if isinstance(self.ar_order, list): self.ar_lags = self.ar_order else: self.ar_lags = np.arange(1, self.ar_order + 1).tolist() if isinstance(self.ma_order, list): self.ma_lags = self.ma_order else: self.ma_lags = np.arange(1, self.ma_order + 1).tolist() if isinstance(self.seasonal_ar_order, list): self.seasonal_ar_lags = self.seasonal_ar_order else: self.seasonal_ar_lags = ( np.arange(1, self.seasonal_ar_order + 1).tolist()) if isinstance(self.seasonal_ma_order, list): self.seasonal_ma_lags = self.seasonal_ma_order else: self.seasonal_ma_lags = ( np.arange(1, self.seasonal_ma_order + 1).tolist()) # Maximum lag orders self.max_ar_order = self.ar_lags[-1] if self.ar_lags else 0 self.max_ma_order = self.ma_lags[-1] if self.ma_lags else 0 self.max_seasonal_ar_order = ( self.seasonal_ar_lags[-1] if self.seasonal_ar_lags else 0) self.max_seasonal_ma_order = ( self.seasonal_ma_lags[-1] if self.seasonal_ma_lags else 0) self.max_reduced_ar_order = ( self.max_ar_order + self.max_seasonal_ar_order * self.seasonal_periods) self.max_reduced_ma_order = ( self.max_ma_order + self.max_seasonal_ma_order * self.seasonal_periods) # Check that we don't have duplicate AR or MA lags from the seasonal # component ar_lags = set(self.ar_lags) seasonal_ar_lags = set(np.array(self.seasonal_ar_lags) * self.seasonal_periods) duplicate_ar_lags = ar_lags.intersection(seasonal_ar_lags) if validate_specification and len(duplicate_ar_lags) > 0: raise ValueError('Invalid model: autoregressive lag(s) %s are' ' in both the seasonal and non-seasonal' ' autoregressive components.' % duplicate_ar_lags) ma_lags = set(self.ma_lags) seasonal_ma_lags = set(np.array(self.seasonal_ma_lags) * self.seasonal_periods) duplicate_ma_lags = ma_lags.intersection(seasonal_ma_lags) if validate_specification and len(duplicate_ma_lags) > 0: raise ValueError('Invalid model: moving average lag(s) %s are' ' in both the seasonal and non-seasonal' ' moving average components.' % duplicate_ma_lags) # Handle trend self.trend = trend self.trend_poly, _ = prepare_trend_spec(trend) # Check for a constant column in the provided exog exog_is_pandas = _is_using_pandas(exog, None) if (validate_specification and exog is not None and len(self.trend_poly) > 0 and self.trend_poly[0] == 1): # Figure out if we have any constant columns x = np.asanyarray(exog) ptp0 = np.ptp(x, axis=0) col_is_const = ptp0 == 0 nz_const = col_is_const & (x[0] != 0) col_const = nz_const # If we already have a constant column, raise an error if np.any(col_const): raise ValueError('A constant trend was included in the model' ' specification, but the `exog` data already' ' contains a column of constants.') # This contains the included exponents of the trend polynomial, # where e.g. the constant term has exponent 0, a linear trend has # exponent 1, etc. self.trend_terms = np.where(self.trend_poly == 1)[0] # Trend order is either the degree of the trend polynomial, if all # exponents are included, or a list of included exponents. Here we need # to make a distinction between a degree zero polynomial (i.e. a # constant) and the zero polynomial (i.e. not even a constant). The # former has `trend_order = 0`, while the latter has # `trend_order = None`. self.k_trend = len(self.trend_terms) if len(self.trend_terms) == 0: self.trend_order = None self.trend_degree = None elif np.all(self.trend_terms == np.arange(len(self.trend_terms))): self.trend_order = self.trend_terms[-1] self.trend_degree = self.trend_terms[-1] else: self.trend_order = self.trend_terms self.trend_degree = self.trend_terms[-1] # Handle endog / exog # Standardize exog self.k_exog, exog = prepare_exog(exog) # Standardize endog (including creating a faux endog if necessary) faux_endog = endog is None if endog is None: endog = [] if exog is None else np.zeros(len(exog)) * np.nan # Add trend data into exog nobs = len(endog) if exog is None else len(exog) if self.trend_order is not None: # Add in the data trend_data = self.construct_trend_data(nobs, trend_offset) if exog is None: exog = trend_data elif exog_is_pandas: trend_data = pd.DataFrame(trend_data, index=exog.index, columns=self.construct_trend_names()) exog = pd.concat([trend_data, exog], axis=1) else: exog = np.c_[trend_data, exog] # Create an underlying time series model, to handle endog / exog, # especially validating shapes, retrieving names, and potentially # providing us with a time series index self._model = TimeSeriesModel(endog, exog=exog, dates=dates, freq=freq, missing=missing) self.endog = None if faux_endog else self._model.endog self.exog = self._model.exog # Validate endog shape if (validate_specification and not faux_endog and self.endog.ndim > 1 and self.endog.shape[1] > 1): raise ValueError('SARIMAX models require univariate `endog`. Got' ' shape %s.' % str(self.endog.shape)) self._has_missing = ( None if faux_endog else np.any(np.isnan(self.endog))) @property def is_ar_consecutive(self): """ (bool) Is autoregressive lag polynomial consecutive. I.e. does it include all lags up to and including the maximum lag. """ return (self.max_seasonal_ar_order == 0 and not isinstance(self.ar_order, list)) @property def is_ma_consecutive(self): """ (bool) Is moving average lag polynomial consecutive. I.e. does it include all lags up to and including the maximum lag. """ return (self.max_seasonal_ma_order == 0 and not isinstance(self.ma_order, list)) @property def is_integrated(self): """ (bool) Is the model integrated. I.e. does it have a nonzero `diff` or `seasonal_diff`. """ return self.diff > 0 or self.seasonal_diff > 0 @property def is_seasonal(self): """(bool) Does the model include a seasonal component.""" return self.seasonal_periods != 0 @property def k_exog_params(self): """(int) Number of parameters associated with exogenous variables.""" return len(self.exog_names) @property def k_ar_params(self): """(int) Number of autoregressive (non-seasonal) parameters.""" return len(self.ar_lags) @property def k_ma_params(self): """(int) Number of moving average (non-seasonal) parameters.""" return len(self.ma_lags) @property def k_seasonal_ar_params(self): """(int) Number of seasonal autoregressive parameters.""" return len(self.seasonal_ar_lags) @property def k_seasonal_ma_params(self): """(int) Number of seasonal moving average parameters.""" return len(self.seasonal_ma_lags) @property def k_params(self): """(int) Total number of model parameters.""" k_params = (self.k_exog_params + self.k_ar_params + self.k_ma_params + self.k_seasonal_ar_params + self.k_seasonal_ma_params) if not self.concentrate_scale: k_params += 1 return k_params @property def exog_names(self): """(list of str) Names associated with exogenous parameters.""" exog_names = self._model.exog_names return [] if exog_names is None else exog_names @property def ar_names(self): """(list of str) Names of (non-seasonal) autoregressive parameters.""" return ['ar.L%d' % i for i in self.ar_lags] @property def ma_names(self): """(list of str) Names of (non-seasonal) moving average parameters.""" return ['ma.L%d' % i for i in self.ma_lags] @property def seasonal_ar_names(self): """(list of str) Names of seasonal autoregressive parameters.""" s = self.seasonal_periods return ['ar.S.L%d' % (i * s) for i in self.seasonal_ar_lags] @property def seasonal_ma_names(self): """(list of str) Names of seasonal moving average parameters.""" s = self.seasonal_periods return ['ma.S.L%d' % (i * s) for i in self.seasonal_ma_lags] @property def param_names(self): """(list of str) Names of all model parameters.""" names = (self.exog_names + self.ar_names + self.ma_names + self.seasonal_ar_names + self.seasonal_ma_names) if not self.concentrate_scale: names.append('sigma2') return names @property def valid_estimators(self): """ (list of str) Estimators that could be used with specification. Note: does not consider the presense of `exog` in determining valid estimators. If there are exogenous variables, then feasible Generalized Least Squares should be used through the `gls` estimator, and the `valid_estimators` are the estimators that could be passed as the `arma_estimator` argument to `gls`. """ estimators = set(['yule_walker', 'burg', 'innovations', 'hannan_rissanen', 'innovations_mle', 'statespace']) # Properties has_ar = self.max_ar_order != 0 has_ma = self.max_ma_order != 0 has_seasonal = self.seasonal_periods != 0 # Only state space can handle missing data or concentrated scale if self._has_missing: estimators.intersection_update(['statespace']) # Only numerical MLE estimators can enforce restrictions if ((self.enforce_stationarity and self.max_ar_order > 0) or (self.enforce_invertibility and self.max_ma_order > 0)): estimators.intersection_update(['innovations_mle', 'statespace']) # Innovations: no AR, non-consecutive MA, seasonal if has_ar or not self.is_ma_consecutive or has_seasonal: estimators.discard('innovations') # Yule-Walker/Burg: no MA, non-consecutive AR, seasonal if has_ma or not self.is_ar_consecutive or has_seasonal: estimators.discard('yule_walker') estimators.discard('burg') # Hannan-Rissanen: no seasonal if has_seasonal: estimators.discard('hannan_rissanen') # Innovations MLE: cannot have enforce_stationary=False or # concentratre_scale=True if self.enforce_stationarity is False or self.concentrate_scale: estimators.discard('innovations_mle') return estimators def validate_estimator(self, estimator): """ Validate an SARIMA estimator. Parameters ---------- estimator : str Name of the estimator to validate against the current state of the specification. Possible values are: 'yule_walker', 'burg', 'innovations', 'hannan_rissanen', 'innovoations_mle', 'statespace'. Notes ----- This method will raise a `ValueError` if an invalid method is passed, and otherwise will return None. This method does not consider the presense of `exog` in determining valid estimators. If there are exogenous variables, then feasible Generalized Least Squares should be used through the `gls` estimator, and a "valid" estimator is one that could be passed as the `arma_estimator` argument to `gls`. This method only uses the attributes `enforce_stationarity` and `concentrate_scale` to determine the validity of numerical maximum likelihood estimators. These only include 'innovations_mle' (which does not support `enforce_stationarity=False` or `concentrate_scale=True`) and 'statespace' (which supports all combinations of each). Examples -------- >>> spec = SARIMAXSpecification(order=(1, 0, 2)) >>> spec.validate_estimator('yule_walker') ValueError: Yule-Walker estimator does not support moving average components. >>> spec.validate_estimator('burg') ValueError: Burg estimator does not support moving average components. >>> spec.validate_estimator('innovations') ValueError: Burg estimator does not support autoregressive components. >>> spec.validate_estimator('hannan_rissanen') # returns None >>> spec.validate_estimator('innovations_mle') # returns None >>> spec.validate_estimator('statespace') # returns None >>> spec.validate_estimator('not_an_estimator') ValueError: "not_an_estimator" is not a valid estimator. """ has_ar = self.max_ar_order != 0 has_ma = self.max_ma_order != 0 has_seasonal = self.seasonal_periods != 0 has_missing = self._has_missing titles = { 'yule_walker': 'Yule-Walker', 'burg': 'Burg', 'innovations': 'Innovations', 'hannan_rissanen': 'Hannan-Rissanen', 'innovations_mle': 'Innovations MLE', 'statespace': 'State space' } # Only state space form can support missing data if estimator != 'statespace': if has_missing: raise ValueError('%s estimator does not support missing' ' values in `endog`.' % titles[estimator]) # Only state space and innovations MLE can enforce parameter # restrictions if estimator not in ['innovations_mle', 'statespace']: if self.max_ar_order > 0 and self.enforce_stationarity: raise ValueError('%s estimator cannot enforce a stationary' ' autoregressive lag polynomial.' % titles[estimator]) if self.max_ma_order > 0 and self.enforce_invertibility: raise ValueError('%s estimator cannot enforce an invertible' ' moving average lag polynomial.' % titles[estimator]) # Now go through specific disqualifications for each estimator if estimator in ['yule_walker', 'burg']: if has_seasonal: raise ValueError('%s estimator does not support seasonal' ' components.' % titles[estimator]) if not self.is_ar_consecutive: raise ValueError('%s estimator does not support' ' non-consecutive autoregressive lags.' % titles[estimator]) if has_ma: raise ValueError('%s estimator does not support moving average' ' components.' % titles[estimator]) elif estimator == 'innovations': if has_seasonal: raise ValueError('Innovations estimator does not support' ' seasonal components.') if not self.is_ma_consecutive: raise ValueError('Innovations estimator does not support' ' non-consecutive moving average lags.') if has_ar: raise ValueError('Innovations estimator does not support' ' autoregressive components.') elif estimator == 'hannan_rissanen': if has_seasonal: raise ValueError('Hannan-Rissanen estimator does not support' ' seasonal components.') elif estimator == 'innovations_mle': if self.enforce_stationarity is False: raise ValueError('Innovations MLE estimator does not support' ' non-stationary autoregressive components,' ' but `enforce_stationarity` is set to False') if self.concentrate_scale: raise ValueError('Innovations MLE estimator does not support' ' concentrating the scale out of the' ' log-likelihood function') elif estimator == 'statespace': # State space form supports all variations of SARIMAX. pass else: raise ValueError('"%s" is not a valid estimator.' % estimator) def split_params(self, params, allow_infnan=False): """ Split parameter array by type into dictionary. Parameters ---------- params : array_like Array of model parameters. allow_infnan : bool, optional Whether or not to allow `params` to contain -np.Inf, np.Inf, and np.nan. Default is False. Returns ------- split_params : dict Dictionary with keys 'exog_params', 'ar_params', 'ma_params', 'seasonal_ar_params', 'seasonal_ma_params', and (unless `concentrate_scale=True`) 'sigma2'. Values are the parameters associated with the key, based on the `params` argument. Examples -------- >>> spec = SARIMAXSpecification(ar_order=1) >>> spec.split_params([0.5, 4]) {'exog_params': array([], dtype=float64), 'ar_params': array([0.5]), 'ma_params': array([], dtype=float64), 'seasonal_ar_params': array([], dtype=float64), 'seasonal_ma_params': array([], dtype=float64), 'sigma2': 4.0} """ params = validate_basic(params, self.k_params, allow_infnan=allow_infnan, title='joint parameters') ix = [self.k_exog_params, self.k_ar_params, self.k_ma_params, self.k_seasonal_ar_params, self.k_seasonal_ma_params] names = ['exog_params', 'ar_params', 'ma_params', 'seasonal_ar_params', 'seasonal_ma_params'] if not self.concentrate_scale: ix.append(1) names.append('sigma2') ix = np.cumsum(ix) out = dict(zip(names, np.split(params, ix))) if 'sigma2' in out: out['sigma2'] = out['sigma2'].item() return out def join_params(self, exog_params=None, ar_params=None, ma_params=None, seasonal_ar_params=None, seasonal_ma_params=None, sigma2=None): """ Join parameters into a single vector. Parameters ---------- exog_params : array_like, optional Parameters associated with exogenous regressors. Required if `exog` is part of specification. ar_params : array_like, optional Parameters associated with (non-seasonal) autoregressive component. Required if this component is part of the specification. ma_params : array_like, optional Parameters associated with (non-seasonal) moving average component. Required if this component is part of the specification. seasonal_ar_params : array_like, optional Parameters associated with seasonal autoregressive component. Required if this component is part of the specification. seasonal_ma_params : array_like, optional Parameters associated with seasonal moving average component. Required if this component is part of the specification. sigma2 : array_like, optional Innovation variance parameter. Required unless `concentrated_scale=True`. Returns ------- params : ndarray Array of parameters. Examples -------- >>> spec = SARIMAXSpecification(ar_order=1) >>> spec.join_params(ar_params=0.5, sigma2=4) array([0.5, 4. ]) """ definitions = [ ('exogenous variables', self.k_exog_params, exog_params), ('AR terms', self.k_ar_params, ar_params), ('MA terms', self.k_ma_params, ma_params), ('seasonal AR terms', self.k_seasonal_ar_params, seasonal_ar_params), ('seasonal MA terms', self.k_seasonal_ma_params, seasonal_ma_params), ('variance', int(not self.concentrate_scale), sigma2)] params_list = [] for title, k, params in definitions: if k > 0: # Validate if params is None: raise ValueError('Specification includes %s, but no' ' parameters were provided.' % title) params = np.atleast_1d(np.squeeze(params)) if not params.shape == (k,): raise ValueError('Specification included %d %s, but' ' parameters with shape %s were provided.' % (k, title, params.shape)) # Otherwise add to the list params_list.append(params) return np.concatenate(params_list) def validate_params(self, params): """ Validate parameter vector by raising ValueError on invalid values. Parameters ---------- params : array_like Array of model parameters. Notes ----- Primarily checks that the parameters have the right shape and are not NaN or infinite. Also checks if parameters are consistent with a stationary process if `enforce_stationarity=True` and that they are consistent with an invertible process if `enforce_invertibility=True`. Finally, checks that the variance term is positive, unless `concentrate_scale=True`. Examples -------- >>> spec = SARIMAXSpecification(ar_order=1) >>> spec.validate_params([-0.5, 4.]) # returns None >>> spec.validate_params([-0.5, -2]) ValueError: Non-positive variance term. >>> spec.validate_params([-1.5, 4.]) ValueError: Non-stationary autoregressive polynomial. """ # Note: split_params includes basic validation params = self.split_params(params) # Specific checks if self.enforce_stationarity: if self.k_ar_params: ar_poly = np.r_[1, -params['ar_params']] if not is_invertible(ar_poly): raise ValueError('Non-stationary autoregressive' ' polynomial.') if self.k_seasonal_ar_params: seasonal_ar_poly = np.r_[1, -params['seasonal_ar_params']] if not is_invertible(seasonal_ar_poly): raise ValueError('Non-stationary seasonal autoregressive' ' polynomial.') if self.enforce_invertibility: if self.k_ma_params: ma_poly = np.r_[1, params['ma_params']] if not is_invertible(ma_poly): raise ValueError('Non-invertible moving average' ' polynomial.') if self.k_seasonal_ma_params: seasonal_ma_poly = np.r_[1, params['seasonal_ma_params']] if not is_invertible(seasonal_ma_poly): raise ValueError('Non-invertible seasonal moving average' ' polynomial.') if not self.concentrate_scale: if params['sigma2'] <= 0: raise ValueError('Non-positive variance term.') def constrain_params(self, unconstrained): """ Constrain parameter values to be valid through transformations. Parameters ---------- unconstrained : array_like Array of model unconstrained parameters. Returns ------- constrained : ndarray Array of model parameters transformed to produce a valid model. Notes ----- This is usually only used when performing numerical minimization of the log-likelihood function. This function is necessary because the minimizers consider values over the entire real space, while SARIMAX models require parameters in subspaces (for example positive variances). Examples -------- >>> spec = SARIMAXSpecification(ar_order=1) >>> spec.constrain_params([10, -2]) array([-0.99504, 4. ]) """ unconstrained = self.split_params(unconstrained) params = {} if self.k_exog_params: params['exog_params'] = unconstrained['exog_params'] if self.k_ar_params: if self.enforce_stationarity: params['ar_params'] = constrain(unconstrained['ar_params']) else: params['ar_params'] = unconstrained['ar_params'] if self.k_ma_params: if self.enforce_invertibility: params['ma_params'] = -constrain(unconstrained['ma_params']) else: params['ma_params'] = unconstrained['ma_params'] if self.k_seasonal_ar_params: if self.enforce_stationarity: params['seasonal_ar_params'] = ( constrain(unconstrained['seasonal_ar_params'])) else: params['seasonal_ar_params'] = ( unconstrained['seasonal_ar_params']) if self.k_seasonal_ma_params: if self.enforce_invertibility: params['seasonal_ma_params'] = ( -constrain(unconstrained['seasonal_ma_params'])) else: params['seasonal_ma_params'] = ( unconstrained['seasonal_ma_params']) if not self.concentrate_scale: params['sigma2'] = unconstrained['sigma2']**2 return self.join_params(**params) def unconstrain_params(self, constrained): """ Reverse transformations used to constrain parameter values to be valid. Parameters ---------- constrained : array_like Array of model parameters. Returns ------- unconstrained : ndarray Array of parameters with constraining transformions reversed. Notes ----- This is usually only used when performing numerical minimization of the log-likelihood function. This function is the (approximate) inverse of `constrain_params`. Examples -------- >>> spec = SARIMAXSpecification(ar_order=1) >>> spec.unconstrain_params([-0.5, 4.]) array([0.57735, 2. ]) """ constrained = self.split_params(constrained) params = {} if self.k_exog_params: params['exog_params'] = constrained['exog_params'] if self.k_ar_params: if self.enforce_stationarity: params['ar_params'] = unconstrain(constrained['ar_params']) else: params['ar_params'] = constrained['ar_params'] if self.k_ma_params: if self.enforce_invertibility: params['ma_params'] = unconstrain(-constrained['ma_params']) else: params['ma_params'] = constrained['ma_params'] if self.k_seasonal_ar_params: if self.enforce_stationarity: params['seasonal_ar_params'] = ( unconstrain(constrained['seasonal_ar_params'])) else: params['seasonal_ar_params'] = ( constrained['seasonal_ar_params']) if self.k_seasonal_ma_params: if self.enforce_invertibility: params['seasonal_ma_params'] = ( unconstrain(-constrained['seasonal_ma_params'])) else: params['seasonal_ma_params'] = ( constrained['seasonal_ma_params']) if not self.concentrate_scale: params['sigma2'] = constrained['sigma2']**0.5 return self.join_params(**params) def construct_trend_data(self, nobs, offset=1): if self.trend_order is None: trend_data = None else: trend_data = prepare_trend_data( self.trend_poly, int(np.sum(self.trend_poly)), nobs, offset) return trend_data def construct_trend_names(self): names = [] for i in self.trend_terms: if i == 0: names.append('const') elif i == 1: names.append('drift') else: names.append('trend.%d' % i) return names def __repr__(self): """Represent SARIMAXSpecification object as a string.""" components = [] if self.endog is not None: components.append('endog=%s' % self._model.endog_names) if self.k_exog_params: components.append('exog=%s' % self.exog_names) components.append('order=%s' % str(self.order)) if self.seasonal_periods > 0: components.append('seasonal_order=%s' % str(self.seasonal_order)) if self.enforce_stationarity is not None: components.append('enforce_stationarity=%s' % self.enforce_stationarity) if self.enforce_invertibility is not None: components.append('enforce_invertibility=%s' % self.enforce_invertibility) if self.concentrate_scale is not None: components.append('concentrate_scale=%s' % self.concentrate_scale) return 'SARIMAXSpecification(%s)' % ', '.join(components) statsmodels-0.12.2/statsmodels/tsa/arima/tests/000077500000000000000000000000001400612667500215315ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/tests/__init__.py000066400000000000000000000000001400612667500236300ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/arima/tests/test_model.py000066400000000000000000000332551400612667500242520ustar00rootroot00000000000000""" Tests for ARIMA model. Tests are primarily limited to checking that the model is constructed correctly and that it is calling the appropriate parameter estimators correctly. Tests of correctness of parameter estimation routines are left to the individual estimators' test functions. Author: Chad Fulton License: BSD-3 """ from statsmodels.compat.platform import PLATFORM_WIN32 import io import numpy as np import pandas as pd import pytest from numpy.testing import assert_equal, assert_allclose, assert_raises, assert_ from statsmodels.datasets import macrodata from statsmodels.tsa.arima.model import ARIMA from statsmodels.tsa.arima.estimators.yule_walker import yule_walker from statsmodels.tsa.arima.estimators.burg import burg from statsmodels.tsa.arima.estimators.hannan_rissanen import hannan_rissanen from statsmodels.tsa.arima.estimators.innovations import ( innovations, innovations_mle) from statsmodels.tsa.arima.estimators.statespace import statespace dta = macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-07-01', freq='QS') def test_default_trend(): # Test that we are setting the trend default correctly endog = dta['infl'].iloc[:50] # Defaults when only endog is specified mod = ARIMA(endog) # with no integration, default trend a constant assert_equal(mod._spec_arima.trend_order, 0) assert_allclose(mod.exog, np.ones((mod.nobs, 1))) # Defaults with integrated model mod = ARIMA(endog, order=(0, 1, 0)) # with no integration, default trend is none assert_equal(mod._spec_arima.trend_order, None) assert_equal(mod.exog, None) def test_invalid(): # Tests that invalid options raise errors # (note that this is only invalid options specific to `ARIMA`, and not # invalid options that would raise errors in SARIMAXSpecification). endog = dta['infl'].iloc[:50] mod = ARIMA(endog, order=(1, 0, 0)) # Need valid method assert_raises(ValueError, mod.fit, method='not_a_method') # Can only use 'statespace' with fixed parameters with mod.fix_params({'ar.L1': 0.5}): assert_raises(ValueError, mod.fit, method='yule_walker') # Cannot override model-level values in fit assert_raises(ValueError, mod.fit, method='statespace', method_kwargs={ 'enforce_stationarity': False}) # start_params only valid for MLE methods assert_raises(ValueError, mod.fit, method='yule_walker', start_params=[0.5, 1.]) # has_exog and gls=False with non-statespace method mod2 = ARIMA(endog, order=(1, 0, 0), trend='c') assert_raises(ValueError, mod2.fit, method='yule_walker', gls=False) # non-stationary parameters mod3 = ARIMA(np.arange(100) * 1.0, order=(1, 0, 0), trend='n') assert_raises(ValueError, mod3.fit, method='hannan_rissanen') # non-invertible parameters mod3 = ARIMA(np.arange(20) * 1.0, order=(0, 0, 1), trend='n') assert_raises(ValueError, mod3.fit, method='hannan_rissanen') def test_yule_walker(): # Test for basic use of Yule-Walker estimation endog = dta['infl'].iloc[:50] # AR(2), no trend (since trend would imply GLS estimation) desired_p, _ = yule_walker(endog, ar_order=2, demean=False) mod = ARIMA(endog, order=(2, 0, 0), trend='n') res = mod.fit(method='yule_walker') assert_allclose(res.params, desired_p.params) def test_burg(): # Test for basic use of Yule-Walker estimation endog = dta['infl'].iloc[:50] # AR(2), no trend (since trend would imply GLS estimation) desired_p, _ = burg(endog, ar_order=2, demean=False) mod = ARIMA(endog, order=(2, 0, 0), trend='n') res = mod.fit(method='burg') assert_allclose(res.params, desired_p.params) def test_hannan_rissanen(): # Test for basic use of Hannan-Rissanen estimation endog = dta['infl'].diff().iloc[1:101] # ARMA(1, 1), no trend (since trend would imply GLS estimation) desired_p, _ = hannan_rissanen( endog, ar_order=1, ma_order=1, demean=False) mod = ARIMA(endog, order=(1, 0, 1), trend='n') res = mod.fit(method='hannan_rissanen') assert_allclose(res.params, desired_p.params) def test_innovations(): # Test for basic use of Yule-Walker estimation endog = dta['infl'].iloc[:50] # MA(2), no trend (since trend would imply GLS estimation) desired_p, _ = innovations(endog, ma_order=2, demean=False) mod = ARIMA(endog, order=(0, 0, 2), trend='n') res = mod.fit(method='innovations') assert_allclose(res.params, desired_p[-1].params) def test_innovations_mle(): # Test for basic use of Yule-Walker estimation endog = dta['infl'].iloc[:100] # ARMA(1, 1), no trend (since trend would imply GLS estimation) desired_p, _ = innovations_mle( endog, order=(1, 0, 1), demean=False) mod = ARIMA(endog, order=(1, 0, 1), trend='n') res = mod.fit(method='innovations_mle') # Note: atol is required only due to precision issues on Windows assert_allclose(res.params, desired_p.params, atol=1e-5) # SARMA(1, 0)x(1, 0)4, no trend (since trend would imply GLS estimation) desired_p, _ = innovations_mle( endog, order=(1, 0, 0), seasonal_order=(1, 0, 0, 4), demean=False) mod = ARIMA(endog, order=(1, 0, 0), seasonal_order=(1, 0, 0, 4), trend='n') res = mod.fit(method='innovations_mle') # Note: atol is required only due to precision issues on Windows assert_allclose(res.params, desired_p.params, atol=1e-5) def test_statespace(): # Test for basic use of Yule-Walker estimation endog = dta['infl'].iloc[:100] # ARMA(1, 1), no trend desired_p, _ = statespace(endog, order=(1, 0, 1), include_constant=False) mod = ARIMA(endog, order=(1, 0, 1), trend='n') res = mod.fit(method='statespace') # Note: tol changes required due to precision issues on Windows rtol = 1e-7 if not PLATFORM_WIN32 else 1e-3 assert_allclose(res.params, desired_p.params, rtol=rtol, atol=1e-4) # ARMA(1, 2), with trend desired_p, _ = statespace(endog, order=(1, 0, 2), include_constant=True) mod = ARIMA(endog, order=(1, 0, 2), trend='c') res = mod.fit(method='statespace') # Note: atol is required only due to precision issues on Windows assert_allclose(res.params, desired_p.params, atol=1e-4) # SARMA(1, 0)x(1, 0)4, no trend desired_p, _spec = statespace(endog, order=(1, 0, 0), seasonal_order=(1, 0, 0, 4), include_constant=False) mod = ARIMA(endog, order=(1, 0, 0), seasonal_order=(1, 0, 0, 4), trend='n') res = mod.fit(method='statespace') # Note: atol is required only due to precision issues on Windows assert_allclose(res.params, desired_p.params, atol=1e-4) def test_low_memory(): # Basic test that the low_memory option is working endog = dta['infl'].iloc[:50] mod = ARIMA(endog, order=(1, 0, 0), concentrate_scale=True) res1 = mod.fit() res2 = mod.fit(low_memory=True) # Check that the models produce the same results assert_allclose(res2.params, res1.params) assert_allclose(res2.llf, res1.llf) # Check that the model's basic memory conservation option was not changed assert_equal(mod.ssm.memory_conserve, 0) # Check that low memory was actually used (just check a couple) assert_(res2.llf_obs is None) assert_(res2.predicted_state is None) assert_(res2.filtered_state is None) assert_(res2.smoothed_state is None) def check_cloned(mod, endog, exog=None): mod_c = mod.clone(endog, exog=exog) assert_allclose(mod.nobs, mod_c.nobs) assert_(mod._index.equals(mod_c._index)) assert_equal(mod.k_params, mod_c.k_params) assert_allclose(mod.start_params, mod_c.start_params) p = mod.start_params assert_allclose(mod.loglike(p), mod_c.loglike(p)) assert_allclose(mod.concentrate_scale, mod_c.concentrate_scale) def test_clone(): endog = dta['infl'].iloc[:50] exog = np.arange(endog.shape[0]) # Basic model check_cloned(ARIMA(endog), endog) check_cloned(ARIMA(endog.values), endog.values) # With trends check_cloned(ARIMA(endog, trend='c'), endog) check_cloned(ARIMA(endog, trend='t'), endog) check_cloned(ARIMA(endog, trend='ct'), endog) # With exog check_cloned(ARIMA(endog, exog=exog), endog, exog=exog) check_cloned(ARIMA(endog, exog=exog, trend='c'), endog, exog=exog) # Concentrated scale check_cloned(ARIMA(endog, exog=exog, trend='c', concentrate_scale=True), endog, exog=exog) # Higher order (use a different dataset to avoid warnings about # non-invertible start params) endog = dta['realgdp'].iloc[:100] exog = np.arange(endog.shape[0]) check_cloned(ARIMA(endog, order=(2, 1, 1), seasonal_order=(1, 1, 2, 4), exog=exog, trend=[0, 0, 1], concentrate_scale=True), endog, exog=exog) def test_constant_integrated_model_error(): with pytest.raises(ValueError, match="In models with integration"): ARIMA(np.ones(100), order=(1, 1, 0), trend='c') with pytest.raises(ValueError, match="In models with integration"): ARIMA(np.ones(100), order=(1, 0, 0), seasonal_order=(1, 1, 0, 6), trend='c') with pytest.raises(ValueError, match="In models with integration"): ARIMA(np.ones(100), order=(1, 2, 0), trend='t') with pytest.raises(ValueError, match="In models with integration"): ARIMA(np.ones(100), order=(1, 1, 0), seasonal_order=(1, 1, 0, 6), trend='t') def test_forecast(): # Numpy endog = dta['infl'].iloc[:100].values mod = ARIMA(endog[:50], order=(1, 1, 0), trend='t') res = mod.filter([0.2, 0.3, 1.0]) endog2 = endog.copy() endog2[50:] = np.nan mod2 = mod.clone(endog2) res2 = mod2.filter(res.params) assert_allclose(res.forecast(50), res2.fittedvalues[-50:]) def test_forecast_with_exog(): # Numpy endog = dta['infl'].iloc[:100].values exog = np.arange(len(endog))**2 mod = ARIMA(endog[:50], order=(1, 1, 0), exog=exog[:50], trend='t') res = mod.filter([0.2, 0.05, 0.3, 1.0]) endog2 = endog.copy() endog2[50:] = np.nan mod2 = mod.clone(endog2, exog=exog) print(mod.param_names) print(mod2.param_names) res2 = mod2.filter(res.params) assert_allclose(res.forecast(50, exog=exog[50:]), res2.fittedvalues[-50:]) def test_append(): endog = dta['infl'].iloc[:100].values mod = ARIMA(endog[:50], trend='c') res = mod.fit() res_e = res.append(endog[50:]) mod2 = ARIMA(endog) res2 = mod2.filter(res_e.params) assert_allclose(res2.llf, res_e.llf) def test_append_with_exog(): # Numpy endog = dta['infl'].iloc[:100].values exog = np.arange(len(endog)) mod = ARIMA(endog[:50], exog=exog[:50], trend='c') res = mod.fit() res_e = res.append(endog[50:], exog=exog[50:]) mod2 = ARIMA(endog, exog=exog, trend='c') res2 = mod2.filter(res_e.params) assert_allclose(res2.llf, res_e.llf) def test_append_with_exog_and_trend(): # Numpy endog = dta['infl'].iloc[:100].values exog = np.arange(len(endog))**2 mod = ARIMA(endog[:50], exog=exog[:50], trend='ct') res = mod.fit() res_e = res.append(endog[50:], exog=exog[50:]) mod2 = ARIMA(endog, exog=exog, trend='ct') res2 = mod2.filter(res_e.params) assert_allclose(res2.llf, res_e.llf) def test_append_with_exog_pandas(): # Pandas endog = dta['infl'].iloc[:100] exog = pd.Series(np.arange(len(endog)), index=endog.index) mod = ARIMA(endog.iloc[:50], exog=exog.iloc[:50], trend='c') res = mod.fit() res_e = res.append(endog.iloc[50:], exog=exog.iloc[50:]) mod2 = ARIMA(endog, exog=exog, trend='c') res2 = mod2.filter(res_e.params) assert_allclose(res2.llf, res_e.llf) def test_cov_type_none(): endog = dta['infl'].iloc[:100].values mod = ARIMA(endog[:50], trend='c') res = mod.fit(cov_type='none') assert_allclose(res.cov_params(), np.nan) def test_nonstationary_gls_error(): # GH-6540 endog = pd.read_csv( io.StringIO( """\ data\n 9.112\n9.102\n9.103\n9.099\n9.094\n9.090\n9.108\n9.088\n9.091\n9.083\n9.095\n 9.090\n9.098\n9.093\n9.087\n9.088\n9.083\n9.095\n9.077\n9.082\n9.082\n9.081\n 9.081\n9.079\n9.088\n9.096\n9.081\n9.098\n9.081\n9.094\n9.091\n9.095\n9.097\n 9.108\n9.104\n9.098\n9.085\n9.093\n9.094\n9.092\n9.093\n9.106\n9.097\n9.108\n 9.100\n9.106\n9.114\n9.111\n9.097\n9.099\n9.108\n9.108\n9.110\n9.101\n9.111\n 9.114\n9.111\n9.126\n9.124\n9.112\n9.120\n9.142\n9.136\n9.131\n9.106\n9.112\n 9.119\n9.125\n9.123\n9.138\n9.133\n9.133\n9.137\n9.133\n9.138\n9.136\n9.128\n 9.127\n9.143\n9.128\n9.135\n9.133\n9.131\n9.136\n9.120\n9.127\n9.130\n9.116\n 9.132\n9.128\n9.119\n9.119\n9.110\n9.132\n9.130\n9.124\n9.130\n9.135\n9.135\n 9.119\n9.119\n9.136\n9.126\n9.122\n9.119\n9.123\n9.121\n9.130\n9.121\n9.119\n 9.106\n9.118\n9.124\n9.121\n9.127\n9.113\n9.118\n9.103\n9.112\n9.110\n9.111\n 9.108\n9.113\n9.117\n9.111\n9.100\n9.106\n9.109\n9.113\n9.110\n9.101\n9.113\n 9.111\n9.101\n9.097\n9.102\n9.100\n9.110\n9.110\n9.096\n9.095\n9.090\n9.104\n 9.097\n9.099\n9.095\n9.096\n9.085\n9.097\n9.098\n9.090\n9.080\n9.093\n9.085\n 9.075\n9.067\n9.072\n9.062\n9.068\n9.053\n9.051\n9.049\n9.052\n9.059\n9.070\n 9.058\n9.074\n9.063\n9.057\n9.062\n9.058\n9.049\n9.047\n9.062\n9.052\n9.052\n 9.044\n9.060\n9.062\n9.055\n9.058\n9.054\n9.044\n9.047\n9.050\n9.048\n9.041\n 9.055\n9.051\n9.028\n9.030\n9.029\n9.027\n9.016\n9.023\n9.031\n9.042\n9.035\n """ ), index_col=None, ) mod = ARIMA( endog, order=(18, 0, 39), enforce_stationarity=False, enforce_invertibility=False, ) with pytest.raises(ValueError, match="Roots of the autoregressive"): mod.fit(method="hannan_rissanen", low_memory=True, cov_type="none") statsmodels-0.12.2/statsmodels/tsa/arima/tests/test_params.py000066400000000000000000000536461400612667500244430ustar00rootroot00000000000000import numpy as np import pandas as pd from numpy.testing import assert_, assert_equal, assert_allclose, assert_raises from statsmodels.tsa.arima import specification, params def test_init(): # Test initialization of the params # Basic test, with 1 of each parameter exog = pd.DataFrame([[0]], columns=['a']) spec = specification.SARIMAXSpecification( exog=exog, order=(1, 1, 1), seasonal_order=(1, 1, 1, 4)) p = params.SARIMAXParams(spec=spec) # Test things copied over from spec assert_equal(p.spec, spec) assert_equal(p.exog_names, ['a']) assert_equal(p.ar_names, ['ar.L1']) assert_equal(p.ma_names, ['ma.L1']) assert_equal(p.seasonal_ar_names, ['ar.S.L4']) assert_equal(p.seasonal_ma_names, ['ma.S.L4']) assert_equal(p.param_names, ['a', 'ar.L1', 'ma.L1', 'ar.S.L4', 'ma.S.L4', 'sigma2']) assert_equal(p.k_exog_params, 1) assert_equal(p.k_ar_params, 1) assert_equal(p.k_ma_params, 1) assert_equal(p.k_seasonal_ar_params, 1) assert_equal(p.k_seasonal_ma_params, 1) assert_equal(p.k_params, 6) # Initial parameters should all be NaN assert_equal(p.params, np.nan) assert_equal(p.ar_params, [np.nan]) assert_equal(p.ma_params, [np.nan]) assert_equal(p.seasonal_ar_params, [np.nan]) assert_equal(p.seasonal_ma_params, [np.nan]) assert_equal(p.sigma2, np.nan) assert_equal(p.ar_poly.coef, np.r_[1, np.nan]) assert_equal(p.ma_poly.coef, np.r_[1, np.nan]) assert_equal(p.seasonal_ar_poly.coef, np.r_[1, 0, 0, 0, np.nan]) assert_equal(p.seasonal_ma_poly.coef, np.r_[1, 0, 0, 0, np.nan]) assert_equal(p.reduced_ar_poly.coef, np.r_[1, [np.nan] * 5]) assert_equal(p.reduced_ma_poly.coef, np.r_[1, [np.nan] * 5]) # Test other properties, methods assert_(not p.is_complete) assert_(not p.is_valid) assert_raises(ValueError, p.__getattribute__, 'is_stationary') assert_raises(ValueError, p.__getattribute__, 'is_invertible') desired = { 'exog_params': [np.nan], 'ar_params': [np.nan], 'ma_params': [np.nan], 'seasonal_ar_params': [np.nan], 'seasonal_ma_params': [np.nan], 'sigma2': np.nan} assert_equal(p.to_dict(), desired) desired = pd.Series([np.nan] * spec.k_params, index=spec.param_names) assert_allclose(p.to_pandas(), desired) # Test with different numbers of parameters for each exog = pd.DataFrame([[0, 0]], columns=['a', 'b']) spec = specification.SARIMAXSpecification( exog=exog, order=(3, 1, 2), seasonal_order=(5, 1, 6, 4)) p = params.SARIMAXParams(spec=spec) # No real need to test names here, since they are already tested above for # the 1-param case, and tested more extensively in test for # SARIMAXSpecification assert_equal(p.k_exog_params, 2) assert_equal(p.k_ar_params, 3) assert_equal(p.k_ma_params, 2) assert_equal(p.k_seasonal_ar_params, 5) assert_equal(p.k_seasonal_ma_params, 6) assert_equal(p.k_params, 2 + 3 + 2 + 5 + 6 + 1) def test_set_params_single(): # Test setting parameters directly (i.e. we test setting the AR/MA # parameters by setting the lag polynomials elsewhere) # Here each type has only a single parameters exog = pd.DataFrame([[0]], columns=['a']) spec = specification.SARIMAXSpecification( exog=exog, order=(1, 1, 1), seasonal_order=(1, 1, 1, 4)) p = params.SARIMAXParams(spec=spec) def check(is_stationary='raise', is_invertible='raise'): assert_(not p.is_complete) assert_(not p.is_valid) if is_stationary == 'raise': assert_raises(ValueError, p.__getattribute__, 'is_stationary') else: assert_equal(p.is_stationary, is_stationary) if is_invertible == 'raise': assert_raises(ValueError, p.__getattribute__, 'is_invertible') else: assert_equal(p.is_invertible, is_invertible) # Set params one at a time, as scalars p.exog_params = -6. check() p.ar_params = -5. check() p.ma_params = -4. check() p.seasonal_ar_params = -3. check(is_stationary=False) p.seasonal_ma_params = -2. check(is_stationary=False, is_invertible=False) p.sigma2 = -1. # Finally, we have a complete set. assert_(p.is_complete) # But still not valid assert_(not p.is_valid) assert_equal(p.params, [-6, -5, -4, -3, -2, -1]) assert_equal(p.exog_params, [-6]) assert_equal(p.ar_params, [-5]) assert_equal(p.ma_params, [-4]) assert_equal(p.seasonal_ar_params, [-3]) assert_equal(p.seasonal_ma_params, [-2]) assert_equal(p.sigma2, -1.) # Lag polynomials assert_equal(p.ar_poly.coef, np.r_[1, 5]) assert_equal(p.ma_poly.coef, np.r_[1, -4]) assert_equal(p.seasonal_ar_poly.coef, np.r_[1, 0, 0, 0, 3]) assert_equal(p.seasonal_ma_poly.coef, np.r_[1, 0, 0, 0, -2]) # (1 - a L) (1 - b L^4) = (1 - a L - b L^4 + a b L^5) assert_equal(p.reduced_ar_poly.coef, np.r_[1, 5, 0, 0, 3, 15]) # (1 + a L) (1 + b L^4) = (1 + a L + b L^4 + a b L^5) assert_equal(p.reduced_ma_poly.coef, np.r_[1, -4, 0, 0, -2, 8]) # Override again, one at a time, now using lists p.exog_params = [1.] p.ar_params = [2.] p.ma_params = [3.] p.seasonal_ar_params = [4.] p.seasonal_ma_params = [5.] p.sigma2 = [6.] p.params = [1, 2, 3, 4, 5, 6] assert_equal(p.params, [1, 2, 3, 4, 5, 6]) assert_equal(p.exog_params, [1]) assert_equal(p.ar_params, [2]) assert_equal(p.ma_params, [3]) assert_equal(p.seasonal_ar_params, [4]) assert_equal(p.seasonal_ma_params, [5]) assert_equal(p.sigma2, 6.) # Override again, one at a time, now using arrays p.exog_params = np.array(6.) p.ar_params = np.array(5.) p.ma_params = np.array(4.) p.seasonal_ar_params = np.array(3.) p.seasonal_ma_params = np.array(2.) p.sigma2 = np.array(1.) assert_equal(p.params, [6, 5, 4, 3, 2, 1]) assert_equal(p.exog_params, [6]) assert_equal(p.ar_params, [5]) assert_equal(p.ma_params, [4]) assert_equal(p.seasonal_ar_params, [3]) assert_equal(p.seasonal_ma_params, [2]) assert_equal(p.sigma2, 1.) # Override again, now setting params all at once p.params = [1, 2, 3, 4, 5, 6] assert_equal(p.params, [1, 2, 3, 4, 5, 6]) assert_equal(p.exog_params, [1]) assert_equal(p.ar_params, [2]) assert_equal(p.ma_params, [3]) assert_equal(p.seasonal_ar_params, [4]) assert_equal(p.seasonal_ma_params, [5]) assert_equal(p.sigma2, 6.) # Lag polynomials assert_equal(p.ar_poly.coef, np.r_[1, -2]) assert_equal(p.ma_poly.coef, np.r_[1, 3]) assert_equal(p.seasonal_ar_poly.coef, np.r_[1, 0, 0, 0, -4]) assert_equal(p.seasonal_ma_poly.coef, np.r_[1, 0, 0, 0, 5]) # (1 - a L) (1 - b L^4) = (1 - a L - b L^4 + a b L^5) assert_equal(p.reduced_ar_poly.coef, np.r_[1, -2, 0, 0, -4, 8]) # (1 + a L) (1 + b L^4) = (1 + a L + b L^4 + a b L^5) assert_equal(p.reduced_ma_poly.coef, np.r_[1, 3, 0, 0, 5, 15]) def test_set_params_single_nonconsecutive(): # Test setting parameters directly (i.e. we test setting the AR/MA # parameters by setting the lag polynomials elsewhere) # Here each type has only a single parameters but has non-consecutive # lag orders exog = pd.DataFrame([[0]], columns=['a']) spec = specification.SARIMAXSpecification( exog=exog, order=([0, 1], 1, [0, 1]), seasonal_order=([0, 1], 1, [0, 1], 4)) p = params.SARIMAXParams(spec=spec) def check(is_stationary='raise', is_invertible='raise'): assert_(not p.is_complete) assert_(not p.is_valid) if is_stationary == 'raise': assert_raises(ValueError, p.__getattribute__, 'is_stationary') else: assert_equal(p.is_stationary, is_stationary) if is_invertible == 'raise': assert_raises(ValueError, p.__getattribute__, 'is_invertible') else: assert_equal(p.is_invertible, is_invertible) # Set params one at a time, as scalars p.exog_params = -6. check() p.ar_params = -5. check() p.ma_params = -4. check() p.seasonal_ar_params = -3. check(is_stationary=False) p.seasonal_ma_params = -2. check(is_stationary=False, is_invertible=False) p.sigma2 = -1. # Finally, we have a complete set. assert_(p.is_complete) # But still not valid assert_(not p.is_valid) assert_equal(p.params, [-6, -5, -4, -3, -2, -1]) assert_equal(p.exog_params, [-6]) assert_equal(p.ar_params, [-5]) assert_equal(p.ma_params, [-4]) assert_equal(p.seasonal_ar_params, [-3]) assert_equal(p.seasonal_ma_params, [-2]) assert_equal(p.sigma2, -1.) # Lag polynomials assert_equal(p.ar_poly.coef, [1, 0, 5]) assert_equal(p.ma_poly.coef, [1, 0, -4]) assert_equal(p.seasonal_ar_poly.coef, [1, 0, 0, 0, 0, 0, 0, 0, 3]) assert_equal(p.seasonal_ma_poly.coef, [1, 0, 0, 0, 0, 0, 0, 0, -2]) # (1 - a L^2) (1 - b L^8) = (1 - a L^2 - b L^8 + a b L^10) assert_equal(p.reduced_ar_poly.coef, [1, 0, 5, 0, 0, 0, 0, 0, 3, 0, 15]) # (1 + a L^2) (1 + b L^4) = (1 + a L^2 + b L^8 + a b L^10) assert_equal(p.reduced_ma_poly.coef, [1, 0, -4, 0, 0, 0, 0, 0, -2, 0, 8]) # Override again, now setting params all at once p.params = [1, 2, 3, 4, 5, 6] assert_equal(p.params, [1, 2, 3, 4, 5, 6]) assert_equal(p.exog_params, [1]) assert_equal(p.ar_params, [2]) assert_equal(p.ma_params, [3]) assert_equal(p.seasonal_ar_params, [4]) assert_equal(p.seasonal_ma_params, [5]) assert_equal(p.sigma2, 6.) # Lag polynomials assert_equal(p.ar_poly.coef, np.r_[1, 0, -2]) assert_equal(p.ma_poly.coef, np.r_[1, 0, 3]) assert_equal(p.seasonal_ar_poly.coef, [1, 0, 0, 0, 0, 0, 0, 0, -4]) assert_equal(p.seasonal_ma_poly.coef, [1, 0, 0, 0, 0, 0, 0, 0, 5]) # (1 - a L^2) (1 - b L^8) = (1 - a L^2 - b L^8 + a b L^10) assert_equal(p.reduced_ar_poly.coef, [1, 0, -2, 0, 0, 0, 0, 0, -4, 0, 8]) # (1 + a L^2) (1 + b L^4) = (1 + a L^2 + b L^8 + a b L^10) assert_equal(p.reduced_ma_poly.coef, [1, 0, 3, 0, 0, 0, 0, 0, 5, 0, 15]) def test_set_params_multiple(): # Test setting parameters directly (i.e. we test setting the AR/MA # parameters by setting the lag polynomials elsewhere) # Here each type has multiple a single parameters exog = pd.DataFrame([[0, 0]], columns=['a', 'b']) spec = specification.SARIMAXSpecification( exog=exog, order=(2, 1, 2), seasonal_order=(2, 1, 2, 4)) p = params.SARIMAXParams(spec=spec) p.params = [-1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11] assert_equal(p.params, [-1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11]) assert_equal(p.exog_params, [-1, 2]) assert_equal(p.ar_params, [-3, 4]) assert_equal(p.ma_params, [-5, 6]) assert_equal(p.seasonal_ar_params, [-7, 8]) assert_equal(p.seasonal_ma_params, [-9, 10]) assert_equal(p.sigma2, -11) # Lag polynomials assert_equal(p.ar_poly.coef, np.r_[1, 3, -4]) assert_equal(p.ma_poly.coef, np.r_[1, -5, 6]) assert_equal(p.seasonal_ar_poly.coef, np.r_[1, 0, 0, 0, 7, 0, 0, 0, -8]) assert_equal(p.seasonal_ma_poly.coef, np.r_[1, 0, 0, 0, -9, 0, 0, 0, 10]) # (1 - a_1 L - a_2 L^2) (1 - b_1 L^4 - b_2 L^8) = # (1 - b_1 L^4 - b_2 L^8) + # (-a_1 L + a_1 b_1 L^5 + a_1 b_2 L^9) + # (-a_2 L^2 + a_2 b_1 L^6 + a_2 b_2 L^10) = # 1 - a_1 L - a_2 L^2 - b_1 L^4 + a_1 b_1 L^5 + # a_2 b_1 L^6 - b_2 L^8 + a_1 b_2 L^9 + a_2 b_2 L^10 assert_equal(p.reduced_ar_poly.coef, [1, 3, -4, 0, 7, (-3 * -7), (4 * -7), 0, -8, (-3 * 8), 4 * 8]) # (1 + a_1 L + a_2 L^2) (1 + b_1 L^4 + b_2 L^8) = # (1 + b_1 L^4 + b_2 L^8) + # (a_1 L + a_1 b_1 L^5 + a_1 b_2 L^9) + # (a_2 L^2 + a_2 b_1 L^6 + a_2 b_2 L^10) = # 1 + a_1 L + a_2 L^2 + b_1 L^4 + a_1 b_1 L^5 + # a_2 b_1 L^6 + b_2 L^8 + a_1 b_2 L^9 + a_2 b_2 L^10 assert_equal(p.reduced_ma_poly.coef, [1, -5, 6, 0, -9, (-5 * -9), (6 * -9), 0, 10, (-5 * 10), (6 * 10)]) def test_set_poly_short_lags(): # Basic example (short lag orders) exog = pd.DataFrame([[0, 0]], columns=['a', 'b']) spec = specification.SARIMAXSpecification( exog=exog, order=(1, 1, 1), seasonal_order=(1, 1, 1, 4)) p = params.SARIMAXParams(spec=spec) # Valid polynomials p.ar_poly = [1, -0.5] assert_equal(p.ar_params, [0.5]) p.ar_poly = np.polynomial.Polynomial([1, -0.55]) assert_equal(p.ar_params, [0.55]) p.ma_poly = [1, 0.3] assert_equal(p.ma_params, [0.3]) p.ma_poly = np.polynomial.Polynomial([1, 0.35]) assert_equal(p.ma_params, [0.35]) p.seasonal_ar_poly = [1, 0, 0, 0, -0.2] assert_equal(p.seasonal_ar_params, [0.2]) p.seasonal_ar_poly = np.polynomial.Polynomial([1, 0, 0, 0, -0.25]) assert_equal(p.seasonal_ar_params, [0.25]) p.seasonal_ma_poly = [1, 0, 0, 0, 0.1] assert_equal(p.seasonal_ma_params, [0.1]) p.seasonal_ma_poly = np.polynomial.Polynomial([1, 0, 0, 0, 0.15]) assert_equal(p.seasonal_ma_params, [0.15]) # Invalid polynomials # Must have 1 in the initial position assert_raises(ValueError, p.__setattr__, 'ar_poly', [2, -0.5]) assert_raises(ValueError, p.__setattr__, 'ma_poly', [2, 0.3]) assert_raises(ValueError, p.__setattr__, 'seasonal_ar_poly', [2, 0, 0, 0, -0.2]) assert_raises(ValueError, p.__setattr__, 'seasonal_ma_poly', [2, 0, 0, 0, 0.1]) # Too short assert_raises(ValueError, p.__setattr__, 'ar_poly', 1) assert_raises(ValueError, p.__setattr__, 'ar_poly', [1]) assert_raises(ValueError, p.__setattr__, 'ma_poly', 1) assert_raises(ValueError, p.__setattr__, 'ma_poly', [1]) assert_raises(ValueError, p.__setattr__, 'seasonal_ar_poly', 1) assert_raises(ValueError, p.__setattr__, 'seasonal_ar_poly', [1]) assert_raises(ValueError, p.__setattr__, 'seasonal_ar_poly', [1, 0, 0, 0]) assert_raises(ValueError, p.__setattr__, 'seasonal_ma_poly', 1) assert_raises(ValueError, p.__setattr__, 'seasonal_ma_poly', [1]) assert_raises(ValueError, p.__setattr__, 'seasonal_ma_poly', [1, 0, 0, 0]) # Too long assert_raises(ValueError, p.__setattr__, 'ar_poly', [1, -0.5, 0.2]) assert_raises(ValueError, p.__setattr__, 'ma_poly', [1, 0.3, 0.2]) assert_raises(ValueError, p.__setattr__, 'seasonal_ar_poly', [1, 0, 0, 0, 0.1, 0]) assert_raises(ValueError, p.__setattr__, 'seasonal_ma_poly', [1, 0, 0, 0, 0.1, 0]) # Number in invalid location (only for seasonal polynomials) assert_raises(ValueError, p.__setattr__, 'seasonal_ar_poly', [1, 1, 0, 0, 0, -0.2]) assert_raises(ValueError, p.__setattr__, 'seasonal_ma_poly', [1, 1, 0, 0, 0, 0.1]) def test_set_poly_short_lags_nonconsecutive(): # Short but non-consecutive lag orders exog = pd.DataFrame([[0, 0]], columns=['a', 'b']) spec = specification.SARIMAXSpecification( exog=exog, order=([0, 1], 1, [0, 1]), seasonal_order=([0, 1], 1, [0, 1], 4)) p = params.SARIMAXParams(spec=spec) # Valid polynomials p.ar_poly = [1, 0, -0.5] assert_equal(p.ar_params, [0.5]) p.ar_poly = np.polynomial.Polynomial([1, 0, -0.55]) assert_equal(p.ar_params, [0.55]) p.ma_poly = [1, 0, 0.3] assert_equal(p.ma_params, [0.3]) p.ma_poly = np.polynomial.Polynomial([1, 0, 0.35]) assert_equal(p.ma_params, [0.35]) p.seasonal_ar_poly = [1, 0, 0, 0, 0, 0, 0, 0, -0.2] assert_equal(p.seasonal_ar_params, [0.2]) p.seasonal_ar_poly = ( np.polynomial.Polynomial([1, 0, 0, 0, 0, 0, 0, 0, -0.25])) assert_equal(p.seasonal_ar_params, [0.25]) p.seasonal_ma_poly = [1, 0, 0, 0, 0, 0, 0, 0, 0.1] assert_equal(p.seasonal_ma_params, [0.1]) p.seasonal_ma_poly = ( np.polynomial.Polynomial([1, 0, 0, 0, 0, 0, 0, 0, 0.15])) assert_equal(p.seasonal_ma_params, [0.15]) # Invalid polynomials # Number in invalid (i.e. an excluded lag) location # (now also for non-seasonal polynomials) assert_raises(ValueError, p.__setattr__, 'ar_poly', [1, 1, -0.5]) assert_raises(ValueError, p.__setattr__, 'ma_poly', [1, 1, 0.3]) assert_raises(ValueError, p.__setattr__, 'seasonal_ar_poly', [1, 0, 0, 0, 1., 0, 0, 0, -0.2]) assert_raises(ValueError, p.__setattr__, 'seasonal_ma_poly', [1, 0, 0, 0, 1., 0, 0, 0, 0.1]) def test_set_poly_longer_lags(): # Test with higher order polynomials exog = pd.DataFrame([[0, 0]], columns=['a', 'b']) spec = specification.SARIMAXSpecification( exog=exog, order=(2, 1, 2), seasonal_order=(2, 1, 2, 4)) p = params.SARIMAXParams(spec=spec) # Setup the non-AR/MA values p.exog_params = [-1, 2] p.sigma2 = -11 # Lag polynomials p.ar_poly = np.r_[1, 3, -4] p.ma_poly = np.r_[1, -5, 6] p.seasonal_ar_poly = np.r_[1, 0, 0, 0, 7, 0, 0, 0, -8] p.seasonal_ma_poly = np.r_[1, 0, 0, 0, -9, 0, 0, 0, 10] # Test that parameters were set correctly assert_equal(p.params, [-1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11]) assert_equal(p.exog_params, [-1, 2]) assert_equal(p.ar_params, [-3, 4]) assert_equal(p.ma_params, [-5, 6]) assert_equal(p.seasonal_ar_params, [-7, 8]) assert_equal(p.seasonal_ma_params, [-9, 10]) assert_equal(p.sigma2, -11) def test_is_stationary(): # Tests for the `is_stationary` property spec = specification.SARIMAXSpecification( order=(1, 1, 1), seasonal_order=(1, 1, 1, 4)) p = params.SARIMAXParams(spec=spec) # Test stationarity assert_raises(ValueError, p.__getattribute__, 'is_stationary') p.ar_params = [0.5] p.seasonal_ar_params = [0] assert_(p.is_stationary) p.ar_params = [1.0] assert_(not p.is_stationary) p.ar_params = [0] p.seasonal_ar_params = [0.5] assert_(p.is_stationary) p.seasonal_ar_params = [1.0] assert_(not p.is_stationary) p.ar_params = [0.2] p.seasonal_ar_params = [0.2] assert_(p.is_stationary) p.ar_params = [0.99] p.seasonal_ar_params = [0.99] assert_(p.is_stationary) p.ar_params = [1.] p.seasonal_ar_params = [1.] assert_(not p.is_stationary) def test_is_invertible(): # Tests for the `is_invertible` property spec = specification.SARIMAXSpecification( order=(1, 1, 1), seasonal_order=(1, 1, 1, 4)) p = params.SARIMAXParams(spec=spec) # Test invertibility assert_raises(ValueError, p.__getattribute__, 'is_invertible') p.ma_params = [0.5] p.seasonal_ma_params = [0] assert_(p.is_invertible) p.ma_params = [1.0] assert_(not p.is_invertible) p.ma_params = [0] p.seasonal_ma_params = [0.5] assert_(p.is_invertible) p.seasonal_ma_params = [1.0] assert_(not p.is_invertible) p.ma_params = [0.2] p.seasonal_ma_params = [0.2] assert_(p.is_invertible) p.ma_params = [0.99] p.seasonal_ma_params = [0.99] assert_(p.is_invertible) p.ma_params = [1.] p.seasonal_ma_params = [1.] assert_(not p.is_invertible) def test_is_valid(): # Additional tests for the `is_valid` property (tests for NaN checks were # already done in `test_set_params_single`). spec = specification.SARIMAXSpecification( order=(1, 1, 1), seasonal_order=(1, 1, 1, 4), enforce_stationarity=True, enforce_invertibility=True) p = params.SARIMAXParams(spec=spec) # Doesn't start out as valid assert_(not p.is_valid) # Given stationary / invertible values, it is valid p.params = [0.5, 0.5, 0.5, 0.5, 1.] assert_(p.is_valid) # With either non-stationary or non-invertible values, not valid p.params = [1., 0.5, 0.5, 0.5, 1.] assert_(not p.is_valid) p.params = [0.5, 1., 0.5, 0.5, 1.] assert_(not p.is_valid) p.params = [0.5, 0.5, 1., 0.5, 1.] assert_(not p.is_valid) p.params = [0.5, 0.5, 0.5, 1., 1.] assert_(not p.is_valid) def test_repr_str(): exog = pd.DataFrame([[0, 0]], columns=['a', 'b']) spec = specification.SARIMAXSpecification( exog=exog, order=(1, 1, 1), seasonal_order=(1, 1, 1, 4)) p = params.SARIMAXParams(spec=spec) # Check when we haven't given any parameters assert_equal(repr(p), 'SARIMAXParams(exog=[nan nan], ar=[nan], ma=[nan],' ' seasonal_ar=[nan], seasonal_ma=[nan], sigma2=nan)') # assert_equal(str(p), '[nan nan nan nan nan nan nan]') p.exog_params = [1, 2] assert_equal(repr(p), 'SARIMAXParams(exog=[1. 2.], ar=[nan], ma=[nan],' ' seasonal_ar=[nan], seasonal_ma=[nan], sigma2=nan)') # assert_equal(str(p), '[ 1. 2. nan nan nan nan nan]') p.ar_params = [0.5] assert_equal(repr(p), 'SARIMAXParams(exog=[1. 2.], ar=[0.5], ma=[nan],' ' seasonal_ar=[nan], seasonal_ma=[nan], sigma2=nan)') # assert_equal(str(p), '[1. 2. 0.5 nan nan nan nan]') p.ma_params = [0.2] assert_equal(repr(p), 'SARIMAXParams(exog=[1. 2.], ar=[0.5], ma=[0.2],' ' seasonal_ar=[nan], seasonal_ma=[nan], sigma2=nan)') # assert_equal(str(p), '[1. 2. 0.5 0.2 nan nan nan]') p.seasonal_ar_params = [0.001] assert_equal(repr(p), 'SARIMAXParams(exog=[1. 2.], ar=[0.5], ma=[0.2],' ' seasonal_ar=[0.001], seasonal_ma=[nan],' ' sigma2=nan)') # assert_equal(str(p), # '[1.e+00 2.e+00 5.e-01 2.e-01 1.e-03 nan nan]') p.seasonal_ma_params = [-0.001] assert_equal(repr(p), 'SARIMAXParams(exog=[1. 2.], ar=[0.5], ma=[0.2],' ' seasonal_ar=[0.001], seasonal_ma=[-0.001],' ' sigma2=nan)') # assert_equal(str(p), '[ 1.e+00 2.e+00 5.e-01 2.e-01 1.e-03' # ' -1.e-03 nan]') p.sigma2 = 10.123 assert_equal(repr(p), 'SARIMAXParams(exog=[1. 2.], ar=[0.5], ma=[0.2],' ' seasonal_ar=[0.001], seasonal_ma=[-0.001],' ' sigma2=10.123)') # assert_equal(str(p), '[ 1.0000e+00 2.0000e+00 5.0000e-01 2.0000e-01' # ' 1.0000e-03 -1.0000e-03\n 1.0123e+01]') statsmodels-0.12.2/statsmodels/tsa/arima/tests/test_specification.py000066400000000000000000000571231400612667500257720ustar00rootroot00000000000000import numpy as np import pandas as pd import pytest from numpy.testing import assert_equal, assert_allclose, assert_raises from statsmodels.tsa.statespace.tools import ( constrain_stationary_univariate as constrain, unconstrain_stationary_univariate as unconstrain) from statsmodels.tsa.arima import specification def check_attributes(spec, order, seasonal_order, enforce_stationarity, enforce_invertibility, concentrate_scale): p, d, q = order P, D, Q, s = seasonal_order assert_equal(spec.order, (p, d, q)) assert_equal(spec.seasonal_order, (P, D, Q, s)) assert_equal(spec.ar_order, p) assert_equal(spec.diff, d) assert_equal(spec.ma_order, q) assert_equal(spec.seasonal_ar_order, P) assert_equal(spec.seasonal_diff, D) assert_equal(spec.seasonal_ma_order, Q) assert_equal(spec.seasonal_periods, s) assert_equal(spec.ar_lags, (p if isinstance(p, list) else np.arange(1, p + 1))) assert_equal(spec.ma_lags, (q if isinstance(q, list) else np.arange(1, q + 1))) assert_equal(spec.seasonal_ar_lags, (P if isinstance(P, list) else np.arange(1, P + 1))) assert_equal(spec.seasonal_ma_lags, (Q if isinstance(Q, list) else np.arange(1, Q + 1))) max_ar_order = p[-1] if isinstance(p, list) else p max_ma_order = q[-1] if isinstance(q, list) else q max_seasonal_ar_order = P[-1] if isinstance(P, list) else P max_seasonal_ma_order = Q[-1] if isinstance(Q, list) else Q assert_equal(spec.max_ar_order, max_ar_order) assert_equal(spec.max_ma_order, max_ma_order) assert_equal(spec.max_seasonal_ar_order, max_seasonal_ar_order) assert_equal(spec.max_seasonal_ma_order, max_seasonal_ma_order) assert_equal(spec.max_reduced_ar_order, max_ar_order + max_seasonal_ar_order * s) assert_equal(spec.max_reduced_ma_order, max_ma_order + max_seasonal_ma_order * s) assert_equal(spec.enforce_stationarity, enforce_stationarity) assert_equal(spec.enforce_invertibility, enforce_invertibility) assert_equal(spec.concentrate_scale, concentrate_scale) def check_properties(spec, order, seasonal_order, enforce_stationarity, enforce_invertibility, concentrate_scale, is_ar_consecutive, is_ma_consecutive, exog_names, ar_names, ma_names, seasonal_ar_names, seasonal_ma_names): p, d, q = order P, D, Q, s = seasonal_order k_exog_params = len(exog_names) k_ar_params = len(p) if isinstance(p, list) else p k_ma_params = len(q) if isinstance(q, list) else q k_seasonal_ar_params = len(P) if isinstance(P, list) else P k_seasonal_ma_params = len(Q) if isinstance(Q, list) else Q k_variance_params = int(not concentrate_scale) param_names = (exog_names + ar_names + ma_names + seasonal_ar_names + seasonal_ma_names) if not concentrate_scale: param_names.append('sigma2') assert_equal(spec.is_ar_consecutive, is_ar_consecutive) assert_equal(spec.is_ma_consecutive, is_ma_consecutive) assert_equal(spec.is_integrated, d + D > 0) assert_equal(spec.is_seasonal, s > 0) assert_equal(spec.k_exog_params, k_exog_params) assert_equal(spec.k_ar_params, k_ar_params) assert_equal(spec.k_ma_params, k_ma_params) assert_equal(spec.k_seasonal_ar_params, k_seasonal_ar_params) assert_equal(spec.k_seasonal_ma_params, k_seasonal_ma_params) assert_equal(spec.k_params, k_exog_params + k_ar_params + k_ma_params + k_seasonal_ar_params + k_seasonal_ma_params + k_variance_params) assert_equal(spec.exog_names, exog_names) assert_equal(spec.ar_names, ar_names) assert_equal(spec.ma_names, ma_names) assert_equal(spec.seasonal_ar_names, seasonal_ar_names) assert_equal(spec.seasonal_ma_names, seasonal_ma_names) assert_equal(spec.param_names, param_names) def check_methods(spec, order, seasonal_order, enforce_stationarity, enforce_invertibility, concentrate_scale, exog_params, ar_params, ma_params, seasonal_ar_params, seasonal_ma_params, sigma2): params = np.r_[exog_params, ar_params, ma_params, seasonal_ar_params, seasonal_ma_params, sigma2] # Test methods desired = { 'exog_params': exog_params, 'ar_params': ar_params, 'ma_params': ma_params, 'seasonal_ar_params': seasonal_ar_params, 'seasonal_ma_params': seasonal_ma_params} if not concentrate_scale: desired['sigma2'] = sigma2 assert_equal(spec.split_params(params), desired) assert_equal(spec.join_params(**desired), params) assert_equal(spec.validate_params(params), None) # Wrong shape assert_raises(ValueError, spec.validate_params, []) # Wrong dtype assert_raises(ValueError, spec.validate_params, ['a'] + params[1:].tolist()) # NaN / Infinity assert_raises(ValueError, spec.validate_params, np.r_[np.inf, params[1:]]) assert_raises(ValueError, spec.validate_params, np.r_[np.nan, params[1:]]) # Non-stationary / non-invertible if spec.max_ar_order > 0: params = np.r_[exog_params, np.ones_like(ar_params), ma_params, np.zeros_like(seasonal_ar_params), seasonal_ma_params, sigma2] if enforce_stationarity: assert_raises(ValueError, spec.validate_params, params) else: assert_equal(spec.validate_params(params), None) if spec.max_ma_order > 0: params = np.r_[exog_params, ar_params, np.ones_like(ma_params), seasonal_ar_params, np.zeros_like(seasonal_ma_params), sigma2] if enforce_invertibility: assert_raises(ValueError, spec.validate_params, params) else: assert_equal(spec.validate_params(params), None) if spec.max_seasonal_ar_order > 0: params = np.r_[exog_params, np.zeros_like(ar_params), ma_params, np.ones_like(seasonal_ar_params), seasonal_ma_params, sigma2] if enforce_stationarity: assert_raises(ValueError, spec.validate_params, params) else: assert_equal(spec.validate_params(params), None) if spec.max_seasonal_ma_order > 0: params = np.r_[exog_params, ar_params, np.zeros_like(ma_params), seasonal_ar_params, np.ones_like(seasonal_ma_params), sigma2] if enforce_invertibility: assert_raises(ValueError, spec.validate_params, params) else: assert_equal(spec.validate_params(params), None) # Invalid variances if not concentrate_scale: params = np.r_[exog_params, ar_params, ma_params, seasonal_ar_params, seasonal_ma_params, 0.] assert_raises(ValueError, spec.validate_params, params) params = np.r_[exog_params, ar_params, ma_params, seasonal_ar_params, seasonal_ma_params, -1] assert_raises(ValueError, spec.validate_params, params) # Constrain / unconstrain unconstrained_ar_params = ar_params unconstrained_ma_params = ma_params unconstrained_seasonal_ar_params = seasonal_ar_params unconstrained_seasonal_ma_params = seasonal_ma_params unconstrained_sigma2 = sigma2 if spec.max_ar_order > 0 and enforce_stationarity: unconstrained_ar_params = unconstrain(np.array(ar_params)) if spec.max_ma_order > 0 and enforce_invertibility: unconstrained_ma_params = unconstrain(-np.array(ma_params)) if spec.max_seasonal_ar_order > 0 and enforce_stationarity: unconstrained_seasonal_ar_params = ( unconstrain(np.array(seasonal_ar_params))) if spec.max_seasonal_ma_order > 0 and enforce_invertibility: unconstrained_seasonal_ma_params = ( unconstrain(-np.array(unconstrained_seasonal_ma_params))) if not concentrate_scale: unconstrained_sigma2 = unconstrained_sigma2**0.5 unconstrained_params = np.r_[ exog_params, unconstrained_ar_params, unconstrained_ma_params, unconstrained_seasonal_ar_params, unconstrained_seasonal_ma_params, unconstrained_sigma2] params = np.r_[exog_params, ar_params, ma_params, seasonal_ar_params, seasonal_ma_params, sigma2] assert_allclose(spec.unconstrain_params(params), unconstrained_params) assert_allclose(spec.constrain_params(unconstrained_params), params) assert_allclose( spec.constrain_params(spec.unconstrain_params(params)), params) @pytest.mark.parametrize("n,d,D,s,params,which", [ # AR models (0, 0, 0, 0, np.array([1.]), 'p'), (1, 0, 0, 0, np.array([0.5, 1.]), 'p'), (1, 0, 0, 0, np.array([-0.2, 100.]), 'p'), (2, 0, 0, 0, np.array([-0.2, 0.5, 100.]), 'p'), (20, 0, 0, 0, np.array([0] * 20 + [100.]), 'p'), # ARI models (0, 1, 0, 0, np.array([1.]), 'p'), (0, 1, 1, 4, np.array([1.]), 'p'), (1, 1, 0, 0, np.array([0.5, 1.]), 'p'), (1, 1, 1, 4, np.array([0.5, 1.]), 'p'), # MA models (0, 0, 0, 0, np.array([1.]), 'q'), (1, 0, 0, 0, np.array([0.5, 1.]), 'q'), (1, 0, 0, 0, np.array([-0.2, 100.]), 'q'), (2, 0, 0, 0, np.array([-0.2, 0.5, 100.]), 'q'), (20, 0, 0, 0, np.array([0] * 20 + [100.]), 'q'), # IMA models (0, 1, 0, 0, np.array([1.]), 'q'), (0, 1, 1, 4, np.array([1.]), 'q'), (1, 1, 0, 0, np.array([0.5, 1.]), 'q'), (1, 1, 1, 4, np.array([0.5, 1.]), 'q'), ]) def test_specification_ar_or_ma(n, d, D, s, params, which): if which == 'p': p, d, q = n, d, 0 ar_names = ['ar.L%d' % i for i in range(1, p + 1)] ma_names = [] else: p, d, q = 0, d, n ar_names = [] ma_names = ['ma.L%d' % i for i in range(1, q + 1)] ar_params = params[:p] ma_params = params[p:-1] sigma2 = params[-1] P, D, Q, s = 0, D, 0, s args = ((p, d, q), (P, D, Q, s)) kwargs = { 'enforce_stationarity': None, 'enforce_invertibility': None, 'concentrate_scale': None } properties_kwargs = kwargs.copy() properties_kwargs.update({ 'is_ar_consecutive': True, 'is_ma_consecutive': True, 'exog_names': [], 'ar_names': ar_names, 'ma_names': ma_names, 'seasonal_ar_names': [], 'seasonal_ma_names': []}) methods_kwargs = kwargs.copy() methods_kwargs.update({ 'exog_params': [], 'ar_params': ar_params, 'ma_params': ma_params, 'seasonal_ar_params': [], 'seasonal_ma_params': [], 'sigma2': sigma2}) # Test the spec created with order, seasonal_order spec = specification.SARIMAXSpecification( order=(p, d, q), seasonal_order=(P, D, Q, s)) check_attributes(spec, *args, **kwargs) check_properties(spec, *args, **properties_kwargs) check_methods(spec, *args, **methods_kwargs) # Test the spec created with ar_order, etc. spec = specification.SARIMAXSpecification( ar_order=p, diff=d, ma_order=q, seasonal_ar_order=P, seasonal_diff=D, seasonal_ma_order=Q, seasonal_periods=s) check_attributes(spec, *args, **kwargs) check_properties(spec, *args, **properties_kwargs) check_methods(spec, *args, **methods_kwargs) @pytest.mark.parametrize(("endog,exog,p,d,q,P,D,Q,s," "enforce_stationarity,enforce_invertibility," "concentrate_scale"), [ (None, None, 0, 0, 0, 0, 0, 0, 0, True, True, False), (None, None, 1, 0, 1, 0, 0, 0, 0, True, True, False), (None, None, 1, 1, 1, 0, 0, 0, 0, True, True, False), (None, None, 1, 0, 0, 0, 0, 0, 4, True, True, False), (None, None, 0, 0, 0, 1, 1, 1, 4, True, True, False), (None, None, 1, 0, 0, 1, 0, 0, 4, True, True, False), (None, None, 1, 0, 0, 1, 1, 1, 4, True, True, False), (None, None, 2, 1, 3, 4, 1, 3, 12, True, True, False), # Non-consecutive lag orders (None, None, [1, 3], 0, 0, 1, 0, 0, 4, True, True, False), (None, None, 0, 0, 0, 0, 0, [1, 3], 4, True, True, False), (None, None, [2], 0, [1, 3], [1, 3], 0, [1, 4], 4, True, True, False), # Modify enforce / concentrate (None, None, 2, 1, 3, 4, 1, 3, 12, False, False, True), (None, None, 2, 1, 3, 4, 1, 3, 12, True, False, True), (None, None, 2, 1, 3, 4, 1, 3, 12, False, True, True), # Endog / exog (True, None, 2, 1, 3, 4, 1, 3, 12, False, True, True), (None, 2, 2, 1, 3, 4, 1, 3, 12, False, True, True), (True, 2, 2, 1, 3, 4, 1, 3, 12, False, True, True), ('y', None, 2, 1, 3, 4, 1, 3, 12, False, True, True), (None, ['x1'], 2, 1, 3, 4, 1, 3, 12, False, True, True), ('y', ['x1'], 2, 1, 3, 4, 1, 3, 12, False, True, True), ('y', ['x1', 'x2'], 2, 1, 3, 4, 1, 3, 12, False, True, True), (True, ['x1', 'x2'], 2, 1, 3, 4, 1, 3, 12, False, True, True), ('y', 2, 2, 1, 3, 4, 1, 3, 12, False, True, True), ]) def test_specification(endog, exog, p, d, q, P, D, Q, s, enforce_stationarity, enforce_invertibility, concentrate_scale): # Assumptions: # - p, q, P, Q are either integers or lists of non-consecutive integers # (i.e. we are not testing boolean lists or consecutive lists here, which # should be tested in the `standardize_lag_order` tests) # Construct the specification if isinstance(p, list): k_ar_params = len(p) max_ar_order = p[-1] else: k_ar_params = max_ar_order = p if isinstance(q, list): k_ma_params = len(q) max_ma_order = q[-1] else: k_ma_params = max_ma_order = q if isinstance(P, list): k_seasonal_ar_params = len(P) max_seasonal_ar_order = P[-1] else: k_seasonal_ar_params = max_seasonal_ar_order = P if isinstance(Q, list): k_seasonal_ma_params = len(Q) max_seasonal_ma_order = Q[-1] else: k_seasonal_ma_params = max_seasonal_ma_order = Q # Get endog / exog nobs = d + D * s + max(3 * max_ma_order + 1, 3 * max_seasonal_ma_order * s + 1, max_ar_order, max_seasonal_ar_order * s) + 1 if endog is True: endog = np.arange(nobs) * 1.0 elif isinstance(endog, str): endog = pd.Series(np.arange(nobs) * 1.0, name=endog) elif endog is not None: raise ValueError('Invalid `endog` in test setup.') if isinstance(exog, int): exog_names = ['x%d' % (i + 1) for i in range(exog)] exog = np.arange(nobs * len(exog_names)).reshape(nobs, len(exog_names)) elif isinstance(exog, list): exog_names = exog exog = np.arange(nobs * len(exog_names)).reshape(nobs, len(exog_names)) exog = pd.DataFrame(exog, columns=exog_names) elif exog is None: exog_names = [] else: raise ValueError('Invalid `exog` in test setup.') # Setup args, kwargs args = ((p, d, q), (P, D, Q, s)) kwargs = { 'enforce_stationarity': enforce_stationarity, 'enforce_invertibility': enforce_invertibility, 'concentrate_scale': concentrate_scale } properties_kwargs = kwargs.copy() is_ar_consecutive = not isinstance(p, list) and max_seasonal_ar_order == 0 is_ma_consecutive = not isinstance(q, list) and max_seasonal_ma_order == 0 properties_kwargs.update({ 'is_ar_consecutive': is_ar_consecutive, 'is_ma_consecutive': is_ma_consecutive, 'exog_names': exog_names, 'ar_names': [ 'ar.L%d' % i for i in (p if isinstance(p, list) else range(1, p + 1))], 'ma_names': [ 'ma.L%d' % i for i in (q if isinstance(q, list) else range(1, q + 1))], 'seasonal_ar_names': [ 'ar.S.L%d' % (i * s) for i in (P if isinstance(P, list) else range(1, P + 1))], 'seasonal_ma_names': [ 'ma.S.L%d' % (i * s) for i in (Q if isinstance(Q, list) else range(1, Q + 1))]}) methods_kwargs = kwargs.copy() methods_kwargs.update({ 'exog_params': np.arange(len(exog_names)), 'ar_params': ( [] if k_ar_params == 0 else constrain(np.arange(k_ar_params) / 10)), 'ma_params': ( [] if k_ma_params == 0 else constrain((np.arange(k_ma_params) + 10) / 100)), 'seasonal_ar_params': ( [] if k_seasonal_ar_params == 0 else constrain(np.arange(k_seasonal_ar_params) - 4)), 'seasonal_ma_params': ( [] if k_seasonal_ma_params == 0 else constrain((np.arange(k_seasonal_ma_params) - 10) / 100)), 'sigma2': [] if concentrate_scale else 2.3424}) # Test the spec created with order, seasonal_order spec = specification.SARIMAXSpecification( endog, exog=exog, order=(p, d, q), seasonal_order=(P, D, Q, s), enforce_stationarity=enforce_stationarity, enforce_invertibility=enforce_invertibility, concentrate_scale=concentrate_scale) check_attributes(spec, *args, **kwargs) check_properties(spec, *args, **properties_kwargs) check_methods(spec, *args, **methods_kwargs) # Test the spec created with ar_order, etc. spec = specification.SARIMAXSpecification( endog, exog=exog, ar_order=p, diff=d, ma_order=q, seasonal_ar_order=P, seasonal_diff=D, seasonal_ma_order=Q, seasonal_periods=s, enforce_stationarity=enforce_stationarity, enforce_invertibility=enforce_invertibility, concentrate_scale=concentrate_scale) check_attributes(spec, *args, **kwargs) check_properties(spec, *args, **properties_kwargs) check_methods(spec, *args, **methods_kwargs) def test_misc(): # Check that no arguments results in all zero orders spec = specification.SARIMAXSpecification() assert_equal(spec.order, (0, 0, 0)) assert_equal(spec.seasonal_order, (0, 0, 0, 0)) # Check for repr spec = specification.SARIMAXSpecification( endog=pd.Series([0], name='y'), exog=pd.DataFrame([[0, 0]], columns=['x1', 'x2']), order=(1, 1, 2), seasonal_order=(2, 1, 0, 12), enforce_stationarity=False, enforce_invertibility=False, concentrate_scale=True) desired = ("SARIMAXSpecification(endog=y, exog=['x1', 'x2']," " order=(1, 1, 2), seasonal_order=(2, 1, 0, 12)," " enforce_stationarity=False, enforce_invertibility=False," " concentrate_scale=True)") assert_equal(repr(spec), desired) def test_invalid(): assert_raises(ValueError, specification.SARIMAXSpecification, order=(1, 0, 0), ar_order=1) assert_raises(ValueError, specification.SARIMAXSpecification, seasonal_order=(1, 0, 0), seasonal_ar_order=1) assert_raises(ValueError, specification.SARIMAXSpecification, order=(-1, 0, 0)) assert_raises(ValueError, specification.SARIMAXSpecification, order=(1.5, 0, 0)) assert_raises(ValueError, specification.SARIMAXSpecification, order=(0, -1, 0)) assert_raises(ValueError, specification.SARIMAXSpecification, order=(0, 1.5, 0)) assert_raises(ValueError, specification.SARIMAXSpecification, order=(0,)) assert_raises(ValueError, specification.SARIMAXSpecification, seasonal_order=(0, 1.5, 0, 4)) assert_raises(ValueError, specification.SARIMAXSpecification, seasonal_order=(-1, 0, 0, 4)) assert_raises(ValueError, specification.SARIMAXSpecification, seasonal_order=(1.5, 0, 0, 4)) assert_raises(ValueError, specification.SARIMAXSpecification, seasonal_order=(0, -1, 0, 4)) assert_raises(ValueError, specification.SARIMAXSpecification, seasonal_order=(0, 1.5, 0, 4)) assert_raises(ValueError, specification.SARIMAXSpecification, seasonal_order=(1, 0, 0, 0)) assert_raises(ValueError, specification.SARIMAXSpecification, seasonal_order=(1, 0, 0, -1)) assert_raises(ValueError, specification.SARIMAXSpecification, seasonal_order=(1, 0, 0, 1)) assert_raises(ValueError, specification.SARIMAXSpecification, seasonal_order=(1,)) assert_raises(ValueError, specification.SARIMAXSpecification, order=(1, 0, 0), endog=np.zeros((10, 2))) spec = specification.SARIMAXSpecification(ar_order=1) assert_raises(ValueError, spec.join_params) assert_raises(ValueError, spec.join_params, ar_params=[0.2, 0.3]) @pytest.mark.parametrize( "order,seasonal_order,enforce_stationarity," "enforce_invertibility,concentrate_scale,valid", [ # Different orders ((0, 0, 0), (0, 0, 0, 0), None, None, None, ['yule_walker', 'burg', 'innovations', 'hannan_rissanen', 'innovations_mle', 'statespace']), ((1, 0, 0), (0, 0, 0, 0), None, None, None, ['yule_walker', 'burg', 'hannan_rissanen', 'innovations_mle', 'statespace']), ((0, 0, 1), (0, 0, 0, 0), None, None, None, ['innovations', 'hannan_rissanen', 'innovations_mle', 'statespace']), ((1, 0, 1), (0, 0, 0, 0), None, None, None, ['hannan_rissanen', 'innovations_mle', 'statespace']), ((0, 0, 0), (1, 0, 0, 4), None, None, None, ['innovations_mle', 'statespace']), # Different options ((1, 0, 0), (0, 0, 0, 0), True, None, None, ['innovations_mle', 'statespace']), ((1, 0, 0), (0, 0, 0, 0), False, None, None, ['yule_walker', 'burg', 'hannan_rissanen', 'statespace']), ((1, 0, 0), (0, 0, 0, 0), None, True, None, ['yule_walker', 'burg', 'hannan_rissanen', 'innovations_mle', 'statespace']), ((1, 0, 0), (0, 0, 0, 0), None, False, None, ['yule_walker', 'burg', 'hannan_rissanen', 'innovations_mle', 'statespace']), ((1, 0, 0), (0, 0, 0, 0), None, None, True, ['yule_walker', 'burg', 'hannan_rissanen', 'statespace']), ]) def test_valid_estimators(order, seasonal_order, enforce_stationarity, enforce_invertibility, concentrate_scale, valid): # Basic specification spec = specification.SARIMAXSpecification( order=order, seasonal_order=seasonal_order, enforce_stationarity=enforce_stationarity, enforce_invertibility=enforce_invertibility, concentrate_scale=concentrate_scale) estimators = set(['yule_walker', 'burg', 'innovations', 'hannan_rissanen', 'innovations_mle', 'statespace']) desired = set(valid) assert_equal(spec.valid_estimators, desired) for estimator in desired: assert_equal(spec.validate_estimator(estimator), None) for estimator in estimators.difference(desired): print(estimator, enforce_stationarity) assert_raises(ValueError, spec.validate_estimator, estimator) # Now try specification with missing values in endog spec = specification.SARIMAXSpecification( endog=[np.nan], order=order, seasonal_order=seasonal_order, enforce_stationarity=enforce_stationarity, enforce_invertibility=enforce_invertibility, concentrate_scale=concentrate_scale) assert_equal(spec.valid_estimators, set(['statespace'])) assert_equal(spec.validate_estimator('statespace'), None) for estimator in estimators.difference(['statespace']): assert_raises(ValueError, spec.validate_estimator, estimator) def test_invalid_estimator(): spec = specification.SARIMAXSpecification() assert_raises(ValueError, spec.validate_estimator, 'not_an_estimator') statsmodels-0.12.2/statsmodels/tsa/arima/tests/test_tools.py000066400000000000000000000064631400612667500243130ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_equal, assert_raises from statsmodels.tsa.arima.tools import ( standardize_lag_order, validate_basic) def test_standardize_lag_order_int(): # Integer input assert_equal(standardize_lag_order(0, title='test'), 0) assert_equal(standardize_lag_order(3), 3) def test_standardize_lag_order_list_int(): # List input, lags assert_equal(standardize_lag_order([]), 0) assert_equal(standardize_lag_order([1, 2]), 2) assert_equal(standardize_lag_order([1, 3]), [1, 3]) def test_standardize_lag_order_tuple_int(): # Non-list iterable input, lags assert_equal(standardize_lag_order((1, 2)), 2) assert_equal(standardize_lag_order((1, 3)), [1, 3]) def test_standardize_lag_order_ndarray_int(): assert_equal(standardize_lag_order(np.array([1, 2])), 2) assert_equal(standardize_lag_order(np.array([1, 3])), [1, 3]) def test_standardize_lag_order_list_bool(): # List input, booleans assert_equal(standardize_lag_order([0]), 0) assert_equal(standardize_lag_order([1]), 1) assert_equal(standardize_lag_order([0, 1]), [2]) assert_equal(standardize_lag_order([0, 1, 0, 1]), [2, 4]) def test_standardize_lag_order_tuple_bool(): # Non-list iterable input, lags assert_equal(standardize_lag_order((0)), 0) assert_equal(standardize_lag_order((1)), 1) assert_equal(standardize_lag_order((0, 1)), [2]) assert_equal(standardize_lag_order((0, 1, 0, 1)), [2, 4]) def test_standardize_lag_order_ndarray_bool(): assert_equal(standardize_lag_order(np.array([0])), 0) assert_equal(standardize_lag_order(np.array([1])), 1) assert_equal(standardize_lag_order(np.array([0, 1])), [2]) assert_equal(standardize_lag_order(np.array([0, 1, 0, 1])), [2, 4]) def test_standardize_lag_order_misc(): # Misc. assert_equal(standardize_lag_order(np.array([[1], [3]])), [1, 3]) def test_standardize_lag_order_invalid(): # Invalid input assert_raises(TypeError, standardize_lag_order, None) assert_raises(ValueError, standardize_lag_order, 1.2) assert_raises(ValueError, standardize_lag_order, -1) assert_raises(ValueError, standardize_lag_order, np.arange(4).reshape(2, 2)) # Boolean list can't have 2, lag order list can't have 0 assert_raises(ValueError, standardize_lag_order, [0, 2]) # Can't have duplicates assert_raises(ValueError, standardize_lag_order, [1, 1, 2]) def test_validate_basic(): # Valid parameters assert_equal(validate_basic([], 0, title='test'), []) assert_equal(validate_basic(0, 1), [0]) assert_equal(validate_basic([0], 1), [0]) assert_equal(validate_basic(np.array([1.2, 0.5 + 1j]), 2), np.array([1.2, 0.5 + 1j])) assert_equal( validate_basic([np.nan, -np.inf, np.inf], 3, allow_infnan=True), [np.nan, -np.inf, np.inf]) # Invalid parameters assert_raises(ValueError, validate_basic, [], 1, title='test') assert_raises(ValueError, validate_basic, 0, 0) assert_raises(ValueError, validate_basic, 'a', 1) assert_raises(ValueError, validate_basic, None, 1) assert_raises(ValueError, validate_basic, np.nan, 1) assert_raises(ValueError, validate_basic, np.inf, 1) assert_raises(ValueError, validate_basic, -np.inf, 1) assert_raises(ValueError, validate_basic, [1, 2], 1) statsmodels-0.12.2/statsmodels/tsa/arima/tools.py000066400000000000000000000122661400612667500221100ustar00rootroot00000000000000""" SARIMAX tools. Author: Chad Fulton License: BSD-3 """ import numpy as np def standardize_lag_order(order, title=None): """ Standardize lag order input. Parameters ---------- order : int or array_like Maximum lag order (if integer) or iterable of specific lag orders. title : str, optional Description of the order (e.g. "autoregressive") to use in error messages. Returns ------- order : int or list of int Maximum lag order if consecutive lag orders were specified, otherwise a list of integer lag orders. Notes ----- It is ambiguous if order=[1] is meant to be a boolean list or a list of lag orders to include, but this is irrelevant because either interpretation gives the same result. Order=[0] would be ambiguous, except that 0 is not a valid lag order to include, so there is no harm in interpreting as a boolean list, in which case it is the same as order=0, which seems like reasonable behavior. Examples -------- >>> standardize_lag_order(3) 3 >>> standardize_lag_order(np.arange(1, 4)) 3 >>> standardize_lag_order([1, 3]) [1, 3] """ order = np.array(order) title = 'order' if title is None else '%s order' % title # Only integer orders are valid if not np.all(order == order.astype(int)): raise ValueError('Invalid %s. Non-integer order (%s) given.' % (title, order)) order = order.astype(int) # Only positive integers are valid if np.any(order < 0): raise ValueError('Terms in the %s cannot be negative.' % title) # Try to squeeze out an irrelevant trailing dimension if order.ndim == 2 and order.shape[1] == 1: order = order[:, 0] elif order.ndim > 1: raise ValueError('Invalid %s. Must be an integer or' ' 1-dimensional array-like object (e.g. list,' ' ndarray, etc.). Got %s.' % (title, order)) # Option 1: the typical integer response (implies including all # lags up through and including the value) if order.ndim == 0: order = order.item() elif len(order) == 0: order = 0 else: # Option 2: boolean list has_zeros = (0 in order) has_multiple_ones = np.sum(order == 1) > 1 has_gt_one = np.any(order > 1) if has_zeros or has_multiple_ones: if has_gt_one: raise ValueError('Invalid %s. Appears to be a boolean list' ' (since it contains a 0 element and/or' ' multiple elements) but also contains' ' elements greater than 1 like a list of' ' lag orders.' % title) order = (np.where(order == 1)[0] + 1) # (Default) Option 3: list of lag orders to include else: order = np.sort(order) # If we have an empty list, set order to zero if len(order) == 0: order = 0 # If we actually were given consecutive lag orders, just use integer elif np.all(order == np.arange(1, len(order) + 1)): order = order[-1] # Otherwise, convert to list else: order = order.tolist() # Check for duplicates has_duplicate = isinstance(order, list) and np.any(np.diff(order) == 0) if has_duplicate: raise ValueError('Invalid %s. Cannot have duplicate elements.' % title) return order def validate_basic(params, length, allow_infnan=False, title=None): """ Validate parameter vector for basic correctness. Parameters ---------- params : array_like Array of parameters to validate. length : int Expected length of the parameter vector. allow_infnan : bool, optional Whether or not to allow `params` to contain -np.Inf, np.Inf, and np.nan. Default is False. title : str, optional Description of the parameters (e.g. "autoregressive") to use in error messages. Returns ------- params : ndarray Array of validated parameters. Notes ----- Basic check that the parameters are numeric and that they are the right shape. Optionally checks for NaN / infinite values. """ title = '' if title is None else ' for %s' % title # Check for invalid type and coerce to non-integer try: params = np.array(params) * 1.0 except TypeError: raise ValueError('Parameters vector%s includes invalid values.' % title) # Check for NaN, inf if not allow_infnan and (np.any(np.isnan(params)) or np.any(np.isinf(params))): raise ValueError('Parameters vector%s includes NaN or Inf values.' % title) params = np.atleast_1d(np.squeeze(params)) # Check for right number of parameters if params.shape != (length,): plural = '' if length == 1 else 's' raise ValueError('Specification%s implies %d parameter%s, but' ' values with shape %s were provided.' % (title, length, plural, params.shape)) return params statsmodels-0.12.2/statsmodels/tsa/arima_model.py000066400000000000000000002367011400612667500221320ustar00rootroot00000000000000# Note: The information criteria add 1 to the number of parameters # whenever the model has an AR or MA term since, in principle, # the variance could be treated as a free parameter and restricted # This code does not allow this, but it adds consistency with other # packages such as gretl and X12-ARIMA import copy from datetime import datetime import numpy as np import pandas as pd from numpy import dot, log, zeros, pi from numpy.linalg import inv from scipy import optimize from scipy.signal import lfilter from scipy.stats import norm from statsmodels.compat.pandas import Appender import statsmodels.base.wrapper as wrap from statsmodels.regression.linear_model import yule_walker, OLS from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.numdiff import approx_hess_cs, approx_fprime_cs from statsmodels.tools.sm_exceptions import SpecificationWarning from statsmodels.tools.validation import array_like, string_like from statsmodels.tsa.ar_model import AutoReg, ar_select_order from statsmodels.tsa.arima_process import arma2ma from statsmodels.tsa.base import tsa_model from statsmodels.tsa.kalmanf import KalmanFilter from statsmodels.tsa.tsatools import (lagmat, add_trend, _ar_transparams, _ar_invtransparams, _ma_transparams, _ma_invtransparams, unintegrate, unintegrate_levels) from statsmodels.tsa.vector_ar import util ARIMA_DEPRECATION_WARN = """ statsmodels.tsa.arima_model.ARMA and statsmodels.tsa.arima_model.ARIMA have been deprecated in favor of statsmodels.tsa.arima.model.ARIMA (note the . between arima and model) and statsmodels.tsa.SARIMAX. These will be removed after the 0.12 release. statsmodels.tsa.arima.model.ARIMA makes use of the statespace framework and is both well tested and maintained. To silence this warning and continue using ARMA and ARIMA until they are removed, use: import warnings warnings.filterwarnings('ignore', 'statsmodels.tsa.arima_model.ARMA', FutureWarning) warnings.filterwarnings('ignore', 'statsmodels.tsa.arima_model.ARIMA', FutureWarning) """ REPEATED_FIT_ERROR = """ Model has been fit using trend={0} and method={1}. These cannot be changed in subsequent calls to `fit`. Instead, use a new instance of {mod}. """ _armax_notes = r""" Notes ----- If exogenous variables are given, then the model that is fit is .. math:: \phi(L)(y_t - X_t\beta) = \theta(L)\epsilon_t where :math:`\phi` and :math:`\theta` are polynomials in the lag operator, :math:`L`. This is the regression model with ARMA errors, or ARMAX model. This specification is used, whether or not the model is fit using conditional sum of square or maximum-likelihood, using the `method` argument in :meth:`statsmodels.tsa.arima_model.%(Model)s.fit`. Therefore, for now, `css` and `mle` refer to estimation methods only. This may change for the case of the `css` model in future versions. """ _arma_params = """endog : array_like The endogenous variable. order : iterable The (p,q) order of the model for the number of AR parameters, and MA parameters to use. exog : array_like, optional An optional array of exogenous variables. This should *not* include a constant or trend. You can specify this in the `fit` method.""" _arma_model = """\ Autoregressive Moving Average ARMA(p,q) Model .. deprecated:: 0.12 Use statsmodels.tsa.arima.model.ARIMA instead""" _arima_model = """\ Autoregressive Integrated Moving Average ARIMA(p,d,q) Model .. deprecated:: 0.12 Use statsmodels.tsa.arima.model.ARIMA instead""" _arima_params = """endog : array_like The endogenous variable. order : iterable The (p,d,q) order of the model for the number of AR parameters, differences, and MA parameters to use. exog : array_like, optional An optional array of exogenous variables. This should *not* include a constant or trend. You can specify this in the `fit` method.""" _predict_notes = """ Notes ----- Use the results predict method instead. """ _results_notes = """ Notes ----- It is recommended to use dates with the time-series models, as the below will probably make clear. However, if ARIMA is used without dates and/or `start` and `end` are given as indices, then these indices are in terms of the *original*, undifferenced series. Ie., given some undifferenced observations:: 1970Q1, 1 1970Q2, 1.5 1970Q3, 1.25 1970Q4, 2.25 1971Q1, 1.2 1971Q2, 4.1 1970Q1 is observation 0 in the original series. However, if we fit an ARIMA(p,1,q) model then we lose this first observation through differencing. Therefore, the first observation we can forecast (if using exact MLE) is index 1. In the differenced series this is index 0, but we refer to it as 1 from the original series. """ _predict = """ %(Model)s model in-sample and out-of-sample prediction Parameters ---------- %(params)s start : int, str, or datetime Zero-indexed observation number at which to start forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. end : int, str, or datetime Zero-indexed observation number at which to end forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. exog : array_like, optional If the model is an ARMAX and out-of-sample forecasting is requested, exog must be given. exog must be aligned so that exog[0] is used to produce the first out-of-sample forecast. The number of observation in exog should match the number of out-of-sample forecasts produced. If the length of exog does not match the number of forecasts, a SpecificationWarning is produced. dynamic : bool, optional The `dynamic` keyword affects in-sample prediction. If dynamic is False, then the in-sample lagged values are used for prediction. If `dynamic` is True, then in-sample forecasts are used in place of lagged dependent variables. The first forecast value is `start`. %(extra_params)s Returns ------- %(returns)s %(extra_section)s """ _predict_returns = """predict : ndarray The predicted values. """ _arma_predict = _predict % {"Model": "ARMA", "params": """params : array_like The fitted parameters of the model.""", "extra_params": "", "returns": _predict_returns, "extra_section": _predict_notes} _arma_results_predict = _predict % {"Model": "ARMA", "params": "", "extra_params": "", "returns": _predict_returns, "extra_section": _results_notes} _arima_extras = """typ : str {'linear', 'levels'} - 'linear' : Linear prediction in terms of the differenced endogenous variables. - 'levels' : Predict the levels of the original endogenous variables.\n""" _arima_predict = _predict % {"Model": "ARIMA", "params": """params : array_like The fitted parameters of the model.""", "extra_params": _arima_extras, "returns": _predict_returns, "extra_section": _predict_notes} _arima_results_predict = _predict % {"Model": "ARIMA", "params": "", "extra_params": _arima_extras, "returns": _predict_returns, "extra_section": _results_notes} _arima_plot_predict_example = """ Examples -------- >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> import pandas as pd >>> >>> dta = sm.datasets.sunspots.load_pandas().data[['SUNACTIVITY']] >>> dta.index = pd.date_range(start='1700', end='2009', freq='A') >>> res = sm.tsa.ARMA(dta, (3, 0)).fit() >>> fig, ax = plt.subplots() >>> ax = dta.loc['1950':].plot(ax=ax) >>> fig = res.plot_predict('1990', '2012', dynamic=True, ax=ax, ... plot_insample=False) >>> plt.show() .. plot:: plots/arma_predict_plot.py """ _plot_extras = """alpha : float, optional The confidence intervals for the forecasts are (1 - alpha)% plot_insample : bool, optional Whether to plot the in-sample series. Default is True. ax : matplotlib.Axes, optional Existing axes to plot with.""" _plot_predict = (""" Plot forecasts """ + '\n'.join(_predict.split('\n')[2:])) % { "params": "", "extra_params": _plot_extras, "returns": """fig : Figure The plotted Figure instance""", "extra_section": ('\n' + _arima_plot_predict_example + '\n' + _results_notes) } _arima_plot_predict = (""" Plot forecasts """ + '\n'.join(_predict.split('\n')[2:])) % { "params": "", "extra_params": _plot_extras, "returns": """fig : Figure The plotted Figure instance""", "extra_section": ('\n' + _arima_plot_predict_example + '\n' + '\n'.join(_results_notes.split('\n')[:3]) + (""" This is hard-coded to only allow plotting of the forecasts in levels. """) + '\n'.join(_results_notes.split('\n')[3:])) } def cumsum_n(x, n): for _ in range(n): x = np.cumsum(x) return x def _prediction_adjust_exog(exog, row_labels, dynamic, end): """ Adjust exog if exog has dates that align with endog Parameters ---------- exog : {array_like, None} The exog values row_labels : {pd.DatetimeIndex, None} Row labels from endog dynamic : bool Flag indicating whether dynamic forecasts are expected end : int Index of final in-sample observation """ if exog is None: return None exog_start = 0 exog_index = getattr(exog, 'index', None) exog_dates = isinstance(exog_index, pd.DatetimeIndex) endog_dates = isinstance(row_labels, pd.DatetimeIndex) date_adj = endog_dates and exog_dates and not dynamic if date_adj and row_labels.isin(exog_index).all(): end_label = row_labels[end] exog_start = exog.index.get_loc(end_label) + 1 exog = array_like(exog, 'exog', ndim=2) return exog[exog_start:] def _check_arima_start(start, k_ar, k_diff, method, dynamic): if start < 0: raise ValueError("The start index %d of the original series " "has been differenced away" % start) elif (dynamic or 'mle' not in method) and start < k_ar: raise ValueError("Start must be >= k_ar for conditional MLE " "or dynamic forecast. Got %d" % start) def _get_predict_out_of_sample(endog, p, q, k_trend, k_exog, start, errors, trendparam, exparams, arparams, maparams, steps, method, exog=None): """ Returns endog, resid, mu of appropriate length for out of sample prediction. """ if q: resid = np.zeros(q) if start and 'mle' in method or (start == p and not start == 0): resid[:q] = errors[start - q:start] elif start: resid[:q] = errors[start - q - p:start - p] else: resid[:q] = errors[-q:] else: resid = None y = endog if k_trend == 1: # use expectation not constant if k_exog > 0: # TODO: technically should only hold for MLE not # conditional model. See #274. # ensure 2-d for conformability if np.ndim(exog) == 1 and k_exog == 1: # have a 1d series of observations -> 2d exog = exog[:, None] elif np.ndim(exog) == 1: # should have a 1d row of exog -> 2d if len(exog) != k_exog: raise ValueError("1d exog given and len(exog) != k_exog") exog = exog[None, :] X = lagmat(np.dot(exog, exparams), p, original='in', trim='both') mu = trendparam * (1 - arparams.sum()) # arparams were reversed in unpack for ease later mu = mu + (np.r_[1, -arparams[::-1]] * X).sum(1)[:, None] else: mu = trendparam * (1 - arparams.sum()) mu = np.array([mu] * steps) elif k_exog > 0: X = np.dot(exog, exparams) X = lagmat(X, p, original='in', trim='both') mu = (np.r_[1, -arparams[::-1]] * X).sum(1)[:, None] else: mu = np.zeros(steps) endog = np.zeros(p + steps - 1) if p and start: endog[:p] = y[start - p:start] elif p: endog[:p] = y[-p:] return endog, resid, mu def _arma_predict_out_of_sample(params, steps, errors, p, q, k_trend, k_exog, endog, exog=None, start=0, method='mle'): (trendparam, exparams, arparams, maparams) = _unpack_params(params, (p, q), k_trend, k_exog, reverse=True) endog, resid, mu = _get_predict_out_of_sample(endog, p, q, k_trend, k_exog, start, errors, trendparam, exparams, arparams, maparams, steps, method, exog) forecast = np.zeros(steps) if steps == 1: if q: return mu[0] + np.dot(arparams, endog[:p]) + np.dot(maparams, resid[:q]) else: return mu[0] + np.dot(arparams, endog[:p]) if q: i = 0 # if q == 1 else: i = -1 for i in range(min(q, steps - 1)): fcast = (mu[i] + np.dot(arparams, endog[i:i + p]) + np.dot(maparams[:q - i], resid[i:i + q])) forecast[i] = fcast endog[i + p] = fcast for i in range(i + 1, steps - 1): fcast = mu[i] + np.dot(arparams, endog[i:i + p]) forecast[i] = fcast endog[i + p] = fcast # need to do one more without updating endog forecast[steps - 1] = mu[steps - 1] + np.dot(arparams, endog[steps - 1:]) return forecast def _arma_predict_in_sample(start, end, endog, resid, k_ar, method): """ Pre- and in-sample fitting for ARMA. """ if 'mle' in method: fittedvalues = endog - resid # get them all then trim else: fittedvalues = endog[k_ar:] - resid fv_start = start if 'mle' not in method: fv_start -= k_ar # start is in terms of endog index fv_end = min(len(fittedvalues), end + 1) return fittedvalues[fv_start:fv_end] def _unpack_params(params, order, k_trend, k_exog, reverse=False): p, q = order k = k_trend + k_exog maparams = params[k + p:] arparams = params[k:k + p] trend = params[:k_trend] exparams = params[k_trend:k] if reverse: return trend, exparams, arparams[::-1], maparams[::-1] return trend, exparams, arparams, maparams def _make_arma_names(data, k_trend, order, exog_names): k_ar, k_ma = order exog_names = exog_names or [] ar_lag_names = util.make_lag_names([data.ynames], k_ar, 0) ar_lag_names = [''.join(('ar.', i)) for i in ar_lag_names] ma_lag_names = util.make_lag_names([data.ynames], k_ma, 0) ma_lag_names = [''.join(('ma.', i)) for i in ma_lag_names] trend_name = util.make_lag_names('', 0, k_trend) exog_names = trend_name + exog_names + ar_lag_names + ma_lag_names return exog_names def _make_arma_exog(endog, exog, trend): k_trend = 1 # overwritten if no constant if exog is None and trend == 'c': # constant only exog = np.ones((len(endog), 1)) elif exog is not None and trend == 'c': # constant plus exogenous exog = add_trend(exog, trend='c', prepend=True, has_constant='raise') elif trend == 'nc': k_trend = 0 return k_trend, exog def _check_estimable(nobs, n_params): if nobs <= n_params: raise ValueError("Insufficient degrees of freedom to estimate") class ARMA(tsa_model.TimeSeriesModel): __doc__ = tsa_model._tsa_doc % {"model": _arma_model, "params": _arma_params, "extra_params": "", "extra_sections": _armax_notes % {"Model": "ARMA"}} def __init__(self, endog, order, exog=None, dates=None, freq=None, missing='none'): import warnings warnings.warn(ARIMA_DEPRECATION_WARN, FutureWarning) super(ARMA, self).__init__(endog, exog, dates, freq, missing=missing) # GH 2575 array_like(endog, 'endog') exog = array_like(self.data.exog, 'exog', ndim=2, optional=True) _check_estimable(len(self.endog), sum(order)) self.k_ar = k_ar = order[0] self.k_ma = k_ma = order[1] self.k_lags = max(k_ar, k_ma + 1) if exog is not None: k_exog = exog.shape[1] # number of exog. variables excl. const else: k_exog = 0 self.k_exog = k_exog self._orig_exog_names = self.exog_names self._fit_params = None def _fit_start_params_hr(self, order, start_ar_lags=None): """ Get starting parameters for fit. Parameters ---------- order : iterable (p,q,k) - AR lags, MA lags, and number of exogenous variables including the constant. start_ar_lags : int, optional If start_ar_lags is not None, rather than fitting an AR process according to best BIC, fits an AR process with a lag length equal to start_ar_lags. Returns ------- start_params : ndarray A first guess at the starting parameters. Notes ----- If necessary, fits an AR process with the laglength start_ar_lags, or selected according to best BIC if start_ar_lags is None. Obtain the residuals. Then fit an ARMA(p,q) model via OLS using these residuals for a first approximation. Uses a separate OLS regression to find the coefficients of exogenous variables. References ---------- Hannan, E.J. and Rissanen, J. 1982. "Recursive estimation of mixed autoregressive-moving average order." `Biometrika`. 69.1. Durbin, J. 1960. "The Fitting of Time-Series Models." `Review of the International Statistical Institute`. Vol. 28, No. 3 """ p, q, k = order start_params = zeros((p + q + k)) # make copy of endog because overwritten endog = np.array(self.endog, np.float64) exog = self.exog if k != 0: ols_params = OLS(endog, exog).fit().params start_params[:k] = ols_params endog -= np.dot(exog, ols_params).squeeze() if q != 0: if p != 0: # make sure we do not run into small data problems in AR fit nobs = len(endog) if start_ar_lags is None: maxlag = int(round(12 * (nobs / 100.) ** (1 / 4.))) if maxlag >= nobs: maxlag = nobs - 1 mod = ar_select_order(endog, maxlag, trend='n', old_names=False).model armod = mod.fit() else: if start_ar_lags >= nobs: start_ar_lags = nobs - 1 armod = AutoReg(endog, start_ar_lags, trend='n', old_names=False).fit() arcoefs_tmp = armod.params p_tmp = len(armod.ar_lags) # it's possible in small samples that optimal lag-order # does not leave enough obs. No consistent way to fix. if p_tmp + q >= len(endog): raise ValueError("Proper starting parameters cannot" " be found for this order with this " "number of observations. Use the " "start_params argument, or set " "start_ar_lags to an integer less than " "len(endog) - q.") resid = endog[p_tmp:] - np.dot(lagmat(endog, p_tmp, trim='both'), arcoefs_tmp) if p < p_tmp + q: endog_start = p_tmp + q - p resid_start = 0 else: endog_start = 0 resid_start = p - p_tmp - q lag_endog = lagmat(endog, p, 'both')[endog_start:] lag_resid = lagmat(resid, q, 'both')[resid_start:] # stack ar lags and resids X = np.column_stack((lag_endog, lag_resid)) coefs = OLS(endog[max(p_tmp + q, p):], X).fit().params start_params[k:k + p + q] = coefs else: ar_coeffs = yule_walker(endog, order=q)[0] ar = np.r_[[1], -ar_coeffs.squeeze()] start_params[k + p:k + p + q] = arma2ma(ar, [1], lags=q+1)[1:] if q == 0 and p != 0: arcoefs = yule_walker(endog, order=p)[0] start_params[k:k + p] = arcoefs # check AR coefficients if p and not np.all(np.abs(np.roots(np.r_[1, -start_params[k:k + p]] )) < 1): raise ValueError("The computed initial AR coefficients are not " "stationary\nYou should induce stationarity, " "choose a different model order, or you can\n" "pass your own start_params.") # check MA coefficients elif q and not np.all(np.abs(np.roots(np.r_[1, start_params[k + p:]] )) < 1): raise ValueError("The computed initial MA coefficients are not " "invertible\nYou should induce invertibility, " "choose a different model order, or you can\n" "pass your own start_params.") # check MA coefficients return start_params def _fit_start_params(self, order, method, start_ar_lags=None): if method != 'css-mle': # use Hannan-Rissanen to get start params start_params = self._fit_start_params_hr(order, start_ar_lags) else: # use CSS to get start params def func(params): return -self.loglike_css(params) start_params = self._fit_start_params_hr(order, start_ar_lags) if self.transparams: start_params = self._invtransparams(start_params) bounds = [(None,) * 2] * sum(order) mlefit = optimize.fmin_l_bfgs_b(func, start_params, approx_grad=True, m=12, pgtol=1e-7, factr=1e3, bounds=bounds, iprint=-1) start_params = mlefit[0] if self.transparams: start_params = self._transparams(start_params) return start_params def score(self, params): """ Compute the score function at params. Notes ----- This is a numerical approximation. """ return approx_fprime_cs(params, self.loglike, args=(False,)) def hessian(self, params): """ Compute the Hessian at params, Notes ----- This is a numerical approximation. """ return approx_hess_cs(params, self.loglike, args=(False,)) def _transparams(self, params): """ Transforms params to induce stationarity/invertability. Reference --------- Jones(1980) """ k_ar, k_ma = self.k_ar, self.k_ma k = self.k_exog + self.k_trend newparams = np.zeros_like(params) # just copy exogenous parameters if k != 0: newparams[:k] = params[:k] # AR Coeffs if k_ar != 0: newparams[k:k + k_ar] = _ar_transparams(params[k:k + k_ar].copy()) # MA Coeffs if k_ma != 0: newparams[k + k_ar:] = _ma_transparams(params[k + k_ar:].copy()) return newparams def _invtransparams(self, start_params): """ Inverse of the Jones reparameterization """ k_ar, k_ma = self.k_ar, self.k_ma k = self.k_exog + self.k_trend newparams = start_params.copy() arcoefs = newparams[k:k + k_ar] macoefs = newparams[k + k_ar:] # AR coeffs if k_ar != 0: newparams[k:k + k_ar] = _ar_invtransparams(arcoefs) # MA coeffs if k_ma != 0: newparams[k + k_ar:k + k_ar + k_ma] = _ma_invtransparams(macoefs) return newparams def _get_prediction_index(self, start, end, dynamic, index=None): method = getattr(self, 'method', 'mle') k_ar = getattr(self, 'k_ar', 0) k_diff = getattr(self, 'k_diff', 0) if start is None: if 'mle' in method and not dynamic: start = 0 else: start = k_ar start = self._index[start] start, end, out_of_sample, prediction_index = ( super(ARMA, self)._get_prediction_index(start, end, index)) # This replaces the _validate() call if 'mle' not in method and start < k_ar - k_diff: raise ValueError("Start must be >= k_ar for conditional " "MLE or dynamic forecast. Got %s" % start) # Other validation _check_arima_start(start, k_ar, k_diff, method, dynamic) return start, end, out_of_sample, prediction_index def geterrors(self, params): """ Get the errors of the ARMA process. Parameters ---------- params : array_like The fitted ARMA parameters order : array_like 3 item iterable, with the number of AR, MA, and exogenous parameters, including the trend """ # start, end, out_of_sample, prediction_index = ( # self._get_prediction_index(start, end, index)) params = np.asarray(params) k_ar, k_ma = self.k_ar, self.k_ma k = self.k_exog + self.k_trend method = getattr(self, 'method', 'mle') if 'mle' in method: # use KalmanFilter to get errors (y, k, nobs, k_ar, k_ma, k_lags, newparams, Z_mat, m, R_mat, T_mat, paramsdtype) = KalmanFilter._init_kalman_state(params, self) errors = KalmanFilter.geterrors(y, k, k_ar, k_ma, k_lags, nobs, Z_mat, m, R_mat, T_mat, paramsdtype) else: # use scipy.signal.lfilter y = self.endog.copy() k = self.k_exog + self.k_trend if k > 0: y -= dot(self.exog, params[:k]) k_ar = self.k_ar k_ma = self.k_ma (trendparams, exparams, arparams, maparams) = _unpack_params(params, (k_ar, k_ma), self.k_trend, self.k_exog, reverse=False) b, a = np.r_[1, -arparams], np.r_[1, maparams] zi = zeros((max(k_ar, k_ma))) for i in range(k_ar): zi[i] = sum(-b[:i + 1][::-1] * y[:i + 1]) e = lfilter(b, a, y, zi=zi) errors = e[0][k_ar:] return errors.squeeze() @Appender(_arma_predict) def predict(self, params, start=None, end=None, exog=None, dynamic=False, **kwargs): if kwargs and 'typ' not in kwargs: raise TypeError('Unknown extra arguments') if not (hasattr(self, 'k_ar') and hasattr(self, 'k_trend')): raise RuntimeError('Model must be fit before calling predict') params = array_like(params, 'params') method = getattr(self, 'method', 'mle') # do not assume fit # will return an index of a date start, end, out_of_sample, _ = ( self._get_prediction_index(start, end, dynamic)) if out_of_sample and (exog is None and self.k_exog > 0): raise ValueError("You must provide exog for ARMAX") endog = self.endog resid = self.geterrors(params) k_ar = self.k_ar # Adjust exog if exog has dates that align with endog row_labels = self.data.row_labels exog = _prediction_adjust_exog(exog, row_labels, dynamic, end) if out_of_sample != 0 and self.k_exog > 0: # we need the last k_ar exog for the lag-polynomial if self.k_exog > 0 and k_ar > 0 and not dynamic: # need the last k_ar exog for the lag-polynomial exog = np.vstack((self.exog[-k_ar:, self.k_trend:], exog)) if dynamic: if self.k_exog > 0: # need the last k_ar exog for the lag-polynomial exog_insample = self.exog[start - k_ar:, self.k_trend:] if exog is not None: exog = np.vstack((exog_insample, exog)) else: exog = exog_insample # TODO: now that predict does dynamic in-sample it should # also return error estimates and confidence intervals # but how? len(endog) is not tot_obs out_of_sample += end - start + 1 return _arma_predict_out_of_sample(params, out_of_sample, resid, k_ar, self.k_ma, self.k_trend, self.k_exog, endog, exog, start, method) predictedvalues = _arma_predict_in_sample(start, end, endog, resid, k_ar, method) if out_of_sample: forecastvalues = _arma_predict_out_of_sample(params, out_of_sample, resid, k_ar, self.k_ma, self.k_trend, self.k_exog, endog, exog, method=method) if (exog is not None and (exog.shape[0] - k_ar) != forecastvalues.shape[0]): import warnings msg = """ The number of observations in exog does not match the number of out-of-sample observations. This might indicate that exog is not correctly aligned. exog should be aligned so that the exog[0] is used for the first out-of-sample forecast, and exog[-1] is used for the last out-of-sample forecast. exog is not used for in-sample observations which are the fitted values. To silence this warning, ensure the number of observation in exog ({0}) matches the number of out-of-sample forecasts ({1})' """ msg = msg.format(exog.shape[0], forecastvalues.shape[0]) warnings.warn(msg, SpecificationWarning) predictedvalues = np.r_[predictedvalues, forecastvalues] return predictedvalues def loglike(self, params, set_sigma2=True): """ Compute the log-likelihood for ARMA(p,q) model Notes ----- Likelihood used depends on the method set in fit """ method = self.method if method in ['mle', 'css-mle']: return self.loglike_kalman(params, set_sigma2) elif method == 'css': return self.loglike_css(params, set_sigma2) else: raise ValueError("Method %s not understood" % method) def loglike_kalman(self, params, set_sigma2=True): """ Compute exact loglikelihood for ARMA(p,q) model by the Kalman Filter. """ return KalmanFilter.loglike(params, self, set_sigma2) def loglike_css(self, params, set_sigma2=True): """ Conditional Sum of Squares likelihood function. """ k_ar = self.k_ar k_ma = self.k_ma k = self.k_exog + self.k_trend y = self.endog.copy().astype(params.dtype) nobs = self.nobs # how to handle if empty? if self.transparams: newparams = self._transparams(params) else: newparams = params if k > 0: y -= dot(self.exog, newparams[:k]) # the order of p determines how many zeros errors to set for lfilter b, a = np.r_[1, -newparams[k:k + k_ar]], np.r_[1, newparams[k + k_ar:]] zi = np.zeros((max(k_ar, k_ma)), dtype=params.dtype) for i in range(k_ar): zi[i] = sum(-b[:i + 1][::-1] * y[:i + 1]) errors = lfilter(b, a, y, zi=zi)[0][k_ar:] ssr = np.dot(errors, errors) sigma2 = ssr / nobs if set_sigma2: self.sigma2 = sigma2 llf = -nobs / 2. * (log(2 * pi) + log(sigma2)) - ssr / (2 * sigma2) return llf def fit(self, start_params=None, trend='c', method="css-mle", transparams=True, solver='lbfgs', maxiter=500, full_output=1, disp=5, callback=None, start_ar_lags=None, **kwargs): """ Fits ARMA(p,q) model using exact maximum likelihood via Kalman filter. Parameters ---------- start_params : array_like, optional Starting parameters for ARMA(p,q). If None, the default is given by ARMA._fit_start_params. See there for more information. transparams : bool, optional Whether or not to transform the parameters to ensure stationarity. Uses the transformation suggested in Jones (1980). If False, no checking for stationarity or invertibility is done. method : str {'css-mle','mle','css'} This is the loglikelihood to maximize. If "css-mle", the conditional sum of squares likelihood is maximized and its values are used as starting values for the computation of the exact likelihood via the Kalman filter. If "mle", the exact likelihood is maximized via the Kalman Filter. If "css" the conditional sum of squares likelihood is maximized. All three methods use `start_params` as starting parameters. See above for more information. trend : str {'c','nc'} Whether to include a constant or not. 'c' includes constant, 'nc' no constant. solver : str or None, optional Solver to be used. The default is 'lbfgs' (limited memory Broyden-Fletcher-Goldfarb-Shanno). Other choices are 'bfgs', 'newton' (Newton-Raphson), 'nm' (Nelder-Mead), 'cg' - (conjugate gradient), 'ncg' (non-conjugate gradient), and 'powell'. By default, the limited memory BFGS uses m=12 to approximate the Hessian, projected gradient tolerance of 1e-8 and factr = 1e2. You can change these by using kwargs. maxiter : int, optional The maximum number of function evaluations. Default is 500. tol : float The convergence tolerance. Default is 1e-08. full_output : bool, optional If True, all output from solver will be available in the Results object's mle_retvals attribute. Output is dependent on the solver. See Notes for more information. disp : int, optional If True, convergence information is printed. For the default l_bfgs_b solver, disp controls the frequency of the output during the iterations. disp < 0 means no output in this case. callback : function, optional Called after each iteration as callback(xk) where xk is the current parameter vector. start_ar_lags : int, optional Parameter for fitting start_params. When fitting start_params, residuals are obtained from an AR fit, then an ARMA(p,q) model is fit via OLS using these residuals. If start_ar_lags is None, fit an AR process according to best BIC. If start_ar_lags is not None, fits an AR process with a lag length equal to start_ar_lags. See ARMA._fit_start_params_hr for more information. **kwargs See Notes for keyword arguments that can be passed to fit. Returns ------- statsmodels.tsa.arima_model.ARMAResults class See Also -------- statsmodels.base.model.LikelihoodModel.fit : for more information on using the solvers. ARMAResults : results class returned by fit Notes ----- If fit by 'mle', it is assumed for the Kalman Filter that the initial unknown state is zero, and that the initial variance is P = dot(inv(identity(m**2)-kron(T,T)),dot(R,R.T).ravel('F')).reshape(r, r, order = 'F') """ trend = string_like(trend, 'trend', options=('nc', 'c')) if self._fit_params is not None: fp = (trend, method) if self._fit_params != fp: raise RuntimeError(REPEATED_FIT_ERROR.format(*fp, mod='ARMA')) k_ar = self.k_ar k_ma = self.k_ma # enforce invertibility self.transparams = transparams endog, exog = self.endog, self.exog k_exog = self.k_exog self.nobs = len(endog) # this is overwritten if method is 'css' # (re)set trend and handle exogenous variables # always pass original exog if hasattr(self, 'k_trend'): k_trend = self.k_trend exog = self.exog else: # Ensures only call once per ARMA instance k_trend, exog = _make_arma_exog(endog, self.exog, trend) # Check has something to estimate if k_ar == 0 and k_ma == 0 and k_trend == 0 and k_exog == 0: raise ValueError("Estimation requires the inclusion of least one " "AR term, MA term, a constant or an exogenous " "variable.") # check again now that we know the trend _check_estimable(len(endog), k_ar + k_ma + k_exog + k_trend) self.k_trend = k_trend self.exog = exog # overwrites original exog from __init__ # (re)set names for this model self.exog_names = _make_arma_names(self.data, k_trend, (k_ar, k_ma), self._orig_exog_names) k = k_trend + k_exog # choose objective function if k_ma == 0 and k_ar == 0: method = "css" # Always CSS when no AR or MA terms self.method = method = method.lower() # adjust nobs for css if method == 'css': self.nobs = len(self.endog) - k_ar if start_params is not None: start_params = array_like(start_params, 'start_params') else: # estimate starting parameters start_params = self._fit_start_params((k_ar, k_ma, k), method, start_ar_lags) if transparams: # transform initial parameters to ensure invertibility start_params = self._invtransparams(start_params) if solver == 'lbfgs': kwargs.setdefault('pgtol', 1e-8) kwargs.setdefault('factr', 1e2) kwargs.setdefault('m', 12) kwargs.setdefault('approx_grad', True) mlefit = super(ARMA, self).fit(start_params, method=solver, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, **kwargs) params = mlefit.params if transparams: # transform parameters back params = self._transparams(params) self.transparams = False # so methods do not expect transf. normalized_cov_params = None # TODO: fix this armafit = ARMAResults(copy.copy(self), params, normalized_cov_params) armafit.mle_retvals = mlefit.mle_retvals armafit.mle_settings = mlefit.mle_settings # Save core fit parameters for future checks self._fit_params = (trend, method) return ARMAResultsWrapper(armafit) @classmethod def from_formula(cls, formula, data, subset=None, drop_cols=None, *args, **kwargs): raise NotImplementedError("from_formula is not supported" " for ARMA models.") # TODO: the length of endog changes when we give a difference to fit # so model methods are not the same on unfit models as fit ones # starting to think that order of model should be put in instantiation... class ARIMA(ARMA): __doc__ = tsa_model._tsa_doc % {"model": _arima_model, "params": _arima_params, "extra_params": "", "extra_sections": _armax_notes % {"Model": "ARIMA"}} def __new__(cls, endog, order, exog=None, dates=None, freq=None, missing='none'): p, d, q = order if d == 0: # then we just use an ARMA model return ARMA(endog, (p, q), exog, dates, freq, missing) else: mod = super(ARIMA, cls).__new__(cls) mod.__init__(endog, order, exog, dates, freq, missing) return mod def __getnewargs__(self): # using same defaults as in __init__ dates = getattr(self, 'dates', None) freq = getattr(self, 'freq', None) missing = getattr(self, 'missing', 'none') return ((self.endog), (self.k_lags, self.k_diff, self.k_ma), self.exog, dates, freq, missing) def __init__(self, endog, order, exog=None, dates=None, freq=None, missing='none'): p, d, q = order if d > 2: # TODO: to make more general, need to address the d == 2 stuff # in the predict method raise ValueError("d > 2 is not supported") super(ARIMA, self).__init__(endog, (p, q), exog, dates, freq, missing) self.k_diff = d self._first_unintegrate = unintegrate_levels(self.endog[:d], d) self.endog = np.diff(self.endog, n=d) # NOTE: will check in ARMA but check again since differenced now _check_estimable(len(self.endog), p + q) if exog is not None: self.exog = self.exog[d:] if d == 1: self.data.ynames = 'D.' + self.endog_names else: self.data.ynames = 'D{0:d}.'.format(d) + self.endog_names # what about exog, should we difference it automatically before # super call? # Reset index orig_length = len(self._index) new_length = self.endog.shape[0] if self.data.row_labels is not None: self.data._cache['row_labels'] = ( self.data.row_labels[orig_length - new_length:]) if self._index is not None: if self._index_generated: self._index = self._index[:-(orig_length - new_length)] else: self._index = self._index[orig_length - new_length:] def _get_prediction_index(self, start, end, dynamic, index=None): method = getattr(self, 'method', 'mle') k_ar = getattr(self, 'k_ar', 0) k_diff = getattr(self, 'k_diff', 0) if start is None: if 'mle' in method and not dynamic: start = 0 else: start = k_ar start = self._index[start] elif isinstance(start, (int, np.integer)): start -= k_diff if start < 0: raise ValueError('The start index %d of the original series ' ' has been differenced away' % start) if isinstance(end, (int, np.integer)): end -= k_diff start, end, out_of_sample, prediction_index = ( super(ARIMA, self)._get_prediction_index(start, end, index)) # From _get_predict_end if 'mle' not in self.method and not dynamic: end -= k_ar # This replaces the _validate() call if 'mle' not in method and start < k_ar - k_diff: raise ValueError("Start must be >= k_ar for conditional " "MLE or dynamic forecast. Got %s" % start) # Other validation _check_arima_start(start, k_ar, k_diff, method, dynamic) return start, end, out_of_sample, prediction_index def fit(self, start_params=None, trend='c', method="css-mle", transparams=True, solver='lbfgs', maxiter=500, full_output=1, disp=5, callback=None, start_ar_lags=None, **kwargs): """ Fits ARIMA(p,d,q) model by exact maximum likelihood via Kalman filter. Parameters ---------- start_params : array_like, optional Starting parameters for ARMA(p,q). If None, the default is given by ARMA._fit_start_params. See there for more information. transparams : bool, optional Whether or not to transform the parameters to ensure stationarity. Uses the transformation suggested in Jones (1980). If False, no checking for stationarity or invertibility is done. method : str {'css-mle','mle','css'} This is the loglikelihood to maximize. If "css-mle", the conditional sum of squares likelihood is maximized and its values are used as starting values for the computation of the exact likelihood via the Kalman filter. If "mle", the exact likelihood is maximized via the Kalman Filter. If "css" the conditional sum of squares likelihood is maximized. All three methods use `start_params` as starting parameters. See above for more information. trend : str {'c','nc'} Whether to include a constant or not. 'c' includes constant, 'nc' no constant. solver : str or None, optional Solver to be used. The default is 'lbfgs' (limited memory Broyden-Fletcher-Goldfarb-Shanno). Other choices are 'bfgs', 'newton' (Newton-Raphson), 'nm' (Nelder-Mead), 'cg' - (conjugate gradient), 'ncg' (non-conjugate gradient), and 'powell'. By default, the limited memory BFGS uses m=12 to approximate the Hessian, projected gradient tolerance of 1e-8 and factr = 1e2. You can change these by using kwargs. maxiter : int, optional The maximum number of function evaluations. Default is 500. tol : float The convergence tolerance. Default is 1e-08. full_output : bool, optional If True, all output from solver will be available in the Results object's mle_retvals attribute. Output is dependent on the solver. See Notes for more information. disp : int, optional If True, convergence information is printed. For the default l_bfgs_b solver, disp controls the frequency of the output during the iterations. disp < 0 means no output in this case. callback : function, optional Called after each iteration as callback(xk) where xk is the current parameter vector. start_ar_lags : int, optional Parameter for fitting start_params. When fitting start_params, residuals are obtained from an AR fit, then an ARMA(p,q) model is fit via OLS using these residuals. If start_ar_lags is None, fit an AR process according to best BIC. If start_ar_lags is not None, fits an AR process with a lag length equal to start_ar_lags. See ARMA._fit_start_params_hr for more information. **kwargs See Notes for keyword arguments that can be passed to fit. Returns ------- `statsmodels.tsa.arima.ARIMAResults` class See Also -------- statsmodels.base.model.LikelihoodModel.fit : for more information on using the solvers. ARIMAResults : results class returned by fit Notes ----- If fit by 'mle', it is assumed for the Kalman Filter that the initial unknown state is zero, and that the initial variance is P = dot(inv(identity(m**2)-kron(T,T)),dot(R,R.T).ravel('F')).reshape(r, r, order = 'F') """ mlefit = super(ARIMA, self).fit(start_params, trend, method, transparams, solver, maxiter, full_output, disp, callback, start_ar_lags, **kwargs) normalized_cov_params = None # TODO: fix this? arima_fit = ARIMAResults(self, mlefit._results.params, normalized_cov_params) arima_fit.k_diff = self.k_diff arima_fit.mle_retvals = mlefit.mle_retvals arima_fit.mle_settings = mlefit.mle_settings return ARIMAResultsWrapper(arima_fit) @Appender(_arima_predict) def predict(self, params, start=None, end=None, exog=None, typ='linear', dynamic=False): if not (hasattr(self, 'k_ar') and hasattr(self, 'k_trend')): raise RuntimeError('Model must be fit before calling predict') # go ahead and convert to an index for easier checking if isinstance(start, (str, datetime)): start, _, _ = self._get_index_label_loc(start) if isinstance(start, slice): start = start.start # Adjustment since _index was already changed to fit the # differenced endog. start += self.k_diff if typ == 'linear': if not dynamic or (start != self.k_ar + self.k_diff and start is not None): return super(ARIMA, self).predict(params, start, end, exog, dynamic) else: # need to assume pre-sample residuals are zero # do this by a hack q = self.k_ma self.k_ma = 0 predictedvalues = super(ARIMA, self).predict(params, start, end, exog, dynamic) self.k_ma = q return predictedvalues elif typ == 'levels': endog = self.data.endog if not dynamic: predict = super(ARIMA, self).predict(params, start, end, exog, dynamic) start, end, out_of_sample, _ = ( self._get_prediction_index(start, end, dynamic)) d = self.k_diff if 'mle' in self.method: start += d - 1 # for case where d == 2 end += d - 1 # add each predicted diff to lagged endog if out_of_sample: fv = predict[:-out_of_sample] + endog[start:end + 1] if d == 2: # TODO: make a general solution to this fv += np.diff(endog[start - 1:end + 1]) levels = unintegrate_levels(endog[-d:], d) fv = np.r_[fv, unintegrate(predict[-out_of_sample:], levels)[d:]] else: fv = predict + endog[start:end + 1] if d == 2: fv += np.diff(endog[start - 1:end + 1]) else: k_ar = self.k_ar if out_of_sample: fv = (predict[:-out_of_sample] + endog[max(start, self.k_ar - 1):end + k_ar + 1]) if d == 2: fv += np.diff(endog[start - 1:end + 1]) levels = unintegrate_levels(endog[-d:], d) fv = np.r_[fv, unintegrate(predict[-out_of_sample:], levels)[d:]] else: fv = predict + endog[max(start, k_ar):end + k_ar + 1] if d == 2: fv += np.diff(endog[start - 1:end + 1]) else: # IFF we need to use pre-sample values assume pre-sample # residuals are zero, do this by a hack if start == self.k_ar + self.k_diff or start is None: # do the first k_diff+1 separately p = self.k_ar q = self.k_ma k_exog = self.k_exog k_trend = self.k_trend k_diff = self.k_diff (trendparam, exparams, arparams, maparams) = _unpack_params(params, (p, q), k_trend, k_exog, reverse=True) # this is the hack self.k_ma = 0 predict = super(ARIMA, self).predict(params, start, end, exog, dynamic) if not start: start, _, _, _ = self._get_prediction_index( start, end, dynamic) start += k_diff self.k_ma = q return endog[start - 1] + np.cumsum(predict) else: predict = super(ARIMA, self).predict(params, start, end, exog, dynamic) return endog[start - 1] + np.cumsum(predict) return fv else: # pragma : no cover raise ValueError("typ %s not understood" % typ) class ARMAResults(tsa_model.TimeSeriesModelResults): """ Class to hold results from fitting an ARMA model. Parameters ---------- model : ARMA instance The fitted model instance params : ndarray Fitted parameters normalized_cov_params : ndarray, optional The normalized variance covariance matrix scale : float, optional Optional argument to scale the variance covariance matrix. Attributes ---------- aic : float Akaike Information Criterion :math:`-2*llf+2* df_model` where `df_model` includes all AR parameters, MA parameters, constant terms parameters on constant terms and the variance. arparams : ndarray The parameters associated with the AR coefficients in the model. arroots : ndarray The roots of the AR coefficients are the solution to (1 - arparams[0]*z - arparams[1]*z**2 -...- arparams[p-1]*z**k_ar) = 0 Stability requires that the roots in modulus lie outside the unit circle. bic : float Bayes Information Criterion -2*llf + log(nobs)*df_model Where if the model is fit using conditional sum of squares, the number of observations `nobs` does not include the `p` pre-sample observations. bse : ndarray The standard errors of the parameters. These are computed using the numerical Hessian. df_model : ndarray The model degrees of freedom = `k_exog` + `k_trend` + `k_ar` + `k_ma` df_resid : ndarray The residual degrees of freedom = `nobs` - `df_model` fittedvalues : ndarray The predicted values of the model. hqic : float Hannan-Quinn Information Criterion -2*llf + 2*(`df_model`)*log(log(nobs)) Like `bic` if the model is fit using conditional sum of squares then the `k_ar` pre-sample observations are not counted in `nobs`. k_ar : int The number of AR coefficients in the model. k_exog : int The number of exogenous variables included in the model. Does not include the constant. k_ma : int The number of MA coefficients. k_trend : int This is 0 for no constant or 1 if a constant is included. llf : float The value of the log-likelihood function evaluated at `params`. maparams : ndarray The value of the moving average coefficients. maroots : ndarray The roots of the MA coefficients are the solution to (1 + maparams[0]*z + maparams[1]*z**2 + ... + maparams[q-1]*z**q) = 0 Stability requires that the roots in modules lie outside the unit circle. model : ARMA instance A reference to the model that was fit. nobs : float The number of observations used to fit the model. If the model is fit using exact maximum likelihood this is equal to the total number of observations, `n_totobs`. If the model is fit using conditional maximum likelihood this is equal to `n_totobs` - `k_ar`. n_totobs : float The total number of observations for `endog`. This includes all observations, even pre-sample values if the model is fit using `css`. params : ndarray The parameters of the model. The order of variables is the trend coefficients and the `k_exog` exogenous coefficients, then the `k_ar` AR coefficients, and finally the `k_ma` MA coefficients. pvalues : ndarray The p-values associated with the t-values of the coefficients. Note that the coefficients are assumed to have a Student's T distribution. resid : ndarray The model residuals. If the model is fit using 'mle' then the residuals are created via the Kalman Filter. If the model is fit using 'css' then the residuals are obtained via `scipy.signal.lfilter` adjusted such that the first `k_ma` residuals are zero. These zero residuals are not returned. scale : float This is currently set to 1.0 and not used by the model or its results. sigma2 : float The variance of the residuals. If the model is fit by 'css', sigma2 = ssr/nobs, where ssr is the sum of squared residuals. If the model is fit by 'mle', then sigma2 = 1/nobs * sum(v**2 / F) where v is the one-step forecast error and F is the forecast error variance. See `nobs` for the difference in definitions depending on the fit. """ _cache = {} def __init__(self, model, params, normalized_cov_params=None, scale=1.): super(ARMAResults, self).__init__(model, params, normalized_cov_params, scale) self.sigma2 = model.sigma2 nobs = model.nobs self.nobs = nobs k_exog = model.k_exog self.k_exog = k_exog k_trend = model.k_trend self.k_trend = k_trend k_ar = model.k_ar self.k_ar = k_ar self.n_totobs = len(model.endog) k_ma = model.k_ma self.k_ma = k_ma df_model = k_exog + k_trend + k_ar + k_ma self._ic_df_model = df_model + 1 self.df_model = df_model self.df_resid = self.nobs - df_model self._cache = {} @cache_readonly def arroots(self): return np.roots(np.r_[1, -self.arparams]) ** -1 @cache_readonly def maroots(self): return np.roots(np.r_[1, self.maparams]) ** -1 @cache_readonly def arfreq(self): r""" Returns the frequency of the AR roots. This is the solution, x, to z = abs(z)*exp(2j*np.pi*x) where z are the roots. """ z = self.arroots return np.arctan2(z.imag, z.real) / (2 * pi) @cache_readonly def mafreq(self): r""" Returns the frequency of the MA roots. This is the solution, x, to z = abs(z)*exp(2j*np.pi*x) where z are the roots. """ z = self.maroots return np.arctan2(z.imag, z.real) / (2 * pi) @cache_readonly def arparams(self): k = self.k_exog + self.k_trend return self.params[k:k + self.k_ar] @cache_readonly def maparams(self): k = self.k_exog + self.k_trend k_ar = self.k_ar return self.params[k + k_ar:] @cache_readonly def llf(self): return self.model.loglike(self.params) @cache_readonly def bse(self): params = self.params hess = self.model.hessian(params) if len(params) == 1: # cannot take an inverse, ensure 1d return np.sqrt(-1. / hess[0]) return np.sqrt(np.diag(-inv(hess))) @cache_readonly def cov_params_default(self): hess = self.model.hessian(self.params) return -inv(hess) @cache_readonly def aic(self): return -2 * self.llf + 2 * self._ic_df_model @cache_readonly def bic(self): nobs = self.nobs return -2 * self.llf + np.log(nobs) * self._ic_df_model @cache_readonly def hqic(self): nobs = self.nobs return -2 * self.llf + 2 * np.log(np.log(nobs)) * self._ic_df_model @cache_readonly def fittedvalues(self): model = self.model endog = model.endog.copy() k_ar = self.k_ar exog = model.exog # this is a copy if exog is not None: if model.method == "css" and k_ar > 0: exog = exog[k_ar:] if model.method == "css" and k_ar > 0: endog = endog[k_ar:] fv = endog - self.resid return fv @cache_readonly def resid(self): return self.model.geterrors(self.params) @Appender(_arma_results_predict) def predict(self, start=None, end=None, exog=None, dynamic=False, **kwargs): return self.model.predict(self.params, start, end, exog, dynamic, **kwargs) def _forecast_error(self, steps): sigma2 = self.sigma2 ma_rep = arma2ma(np.r_[1, -self.arparams], np.r_[1, self.maparams], lags=steps) fcasterr = np.sqrt(sigma2 * np.cumsum(ma_rep ** 2)) return fcasterr def _forecast_conf_int(self, forecast, fcasterr, alpha): const = norm.ppf(1 - alpha / 2.) conf_int = np.c_[forecast - const * fcasterr, forecast + const * fcasterr] return conf_int def forecast(self, steps=1, exog=None, alpha=.05): """ Out-of-sample forecasts Parameters ---------- steps : int The number of out of sample forecasts from the end of the sample. exog : ndarray If the model is an ARMAX, you must provide out of sample values for the exogenous variables. This should not include the constant. The number of observation in exog must match the value of steps. alpha : float The confidence intervals for the forecasts are (1 - alpha) % Returns ------- forecast : ndarray Array of out of sample forecasts stderr : ndarray Array of the standard error of the forecasts. conf_int : ndarray 2d array of the confidence interval for the forecast """ if exog is not None: exog = array_like(exog, 'exog', maxdim=2) if self.k_exog == 1 and exog.ndim == 1: exog = exog[:, None] elif exog.ndim == 1: if len(exog) != self.k_exog: raise ValueError("1d exog given and len(exog) != k_exog") exog = exog[None, :] if exog.shape[0] != steps: raise ValueError("new exog needed for each step") if self.k_exog != exog.shape[1]: raise ValueError('exog must contain the same number of ' 'variables as in the estimated model.') # prepend in-sample exog observations if self.k_ar > 0: exog = np.vstack((self.model.exog[-self.k_ar:, self.k_trend:], exog)) else: if self.k_exog: raise ValueError('Forecast values for exog are required when ' 'the model contains exogenous regressors.') forecast = _arma_predict_out_of_sample(self.params, steps, self.resid, self.k_ar, self.k_ma, self.k_trend, self.k_exog, self.model.endog, exog, method=self.model.method) # compute the standard errors fcasterr = self._forecast_error(steps) conf_int = self._forecast_conf_int(forecast, fcasterr, alpha) return forecast, fcasterr, conf_int def summary(self, alpha=.05): """Summarize the Model Parameters ---------- alpha : float, optional Significance level for the confidence intervals. Returns ------- smry : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary """ from statsmodels.iolib.summary import Summary model = self.model title = model.__class__.__name__ + ' Model Results' method = model.method # get sample TODO: make better sample machinery for estimation k_diff = getattr(self, 'k_diff', 0) if 'mle' in method: start = k_diff else: start = k_diff + self.k_ar if self.data.dates is not None: dates = self.data.dates sample = [dates[start].strftime('%m-%d-%Y')] sample += ['- ' + dates[-1].strftime('%m-%d-%Y')] else: sample = str(start) + ' - ' + str(len(self.data.orig_endog)) k_ar, k_ma = self.k_ar, self.k_ma if not k_diff: order = str((k_ar, k_ma)) else: order = str((k_ar, k_diff, k_ma)) top_left = [('Dep. Variable:', None), ('Model:', [model.__class__.__name__ + order]), ('Method:', [method]), ('Date:', None), ('Time:', None), ('Sample:', [sample[0]]), ('', [sample[1]]) ] top_right = [ ('No. Observations:', [str(len(self.model.endog))]), ('Log Likelihood', ["%#5.3f" % self.llf]), ('S.D. of innovations', ["%#5.3f" % self.sigma2 ** .5]), ('AIC', ["%#5.3f" % self.aic]), ('BIC', ["%#5.3f" % self.bic]), ('HQIC', ["%#5.3f" % self.hqic])] smry = Summary() smry.add_table_2cols(self, gleft=top_left, gright=top_right, title=title) smry.add_table_params(self, alpha=alpha, use_t=False) # Make the roots table from statsmodels.iolib.table import SimpleTable if k_ma and k_ar: arstubs = ["AR.%d" % i for i in range(1, k_ar + 1)] mastubs = ["MA.%d" % i for i in range(1, k_ma + 1)] stubs = arstubs + mastubs roots = np.r_[self.arroots, self.maroots] freq = np.r_[self.arfreq, self.mafreq] elif k_ma: mastubs = ["MA.%d" % i for i in range(1, k_ma + 1)] stubs = mastubs roots = self.maroots freq = self.mafreq elif k_ar: arstubs = ["AR.%d" % i for i in range(1, k_ar + 1)] stubs = arstubs roots = self.arroots freq = self.arfreq else: # 0,0 model stubs = [] if len(stubs): # not 0, 0 modulus = np.abs(roots) data = np.column_stack((roots.real, roots.imag, modulus, freq)) roots_table = SimpleTable([('%17.4f' % row[0], '%+17.4fj' % row[1], '%17.4f' % row[2], '%17.4f' % row[3]) for row in data], headers=[' Real', ' Imaginary', ' Modulus', ' Frequency'], title="Roots", stubs=stubs) smry.tables.append(roots_table) return smry def summary2(self, title=None, alpha=.05, float_format="%.4f"): """ Experimental summary function for ARIMA Results Parameters ---------- title : str, optional Title for the top table. If not None, then this replaces the default title alpha : float, optional significance level for the confidence intervals float_format : str, optional print format for floats in parameters summary Returns ------- smry : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary2.Summary : class to hold summary results """ from pandas import DataFrame # get sample TODO: make better sample machinery for estimation k_diff = getattr(self, 'k_diff', 0) if 'mle' in self.model.method: start = k_diff else: start = k_diff + self.k_ar if self.data.dates is not None: dates = self.data.dates sample = [dates[start].strftime('%m-%d-%Y')] sample += [dates[-1].strftime('%m-%d-%Y')] else: sample = str(start) + ' - ' + str(len(self.data.orig_endog)) k_ar, k_ma = self.k_ar, self.k_ma # Roots table if k_ma and k_ar: arstubs = ["AR.%d" % i for i in range(1, k_ar + 1)] mastubs = ["MA.%d" % i for i in range(1, k_ma + 1)] stubs = arstubs + mastubs roots = np.r_[self.arroots, self.maroots] freq = np.r_[self.arfreq, self.mafreq] elif k_ma: mastubs = ["MA.%d" % i for i in range(1, k_ma + 1)] stubs = mastubs roots = self.maroots freq = self.mafreq elif k_ar: arstubs = ["AR.%d" % i for i in range(1, k_ar + 1)] stubs = arstubs roots = self.arroots freq = self.arfreq else: # 0, 0 order stubs = [] if len(stubs): modulus = np.abs(roots) data = np.column_stack((roots.real, roots.imag, modulus, freq)) data = DataFrame(data) data.columns = ['Real', 'Imaginary', 'Modulus', 'Frequency'] data.index = stubs # Summary from statsmodels.iolib import summary2 smry = summary2.Summary() # Model info model_info = summary2.summary_model(self) model_info['Method:'] = self.model.method model_info['Sample:'] = sample[0] model_info[' '] = sample[-1] model_info['S.D. of innovations:'] = "%#5.3f" % self.sigma2 ** .5 model_info['HQIC:'] = "%#5.3f" % self.hqic model_info['No. Observations:'] = str(len(self.model.endog)) # Parameters params = summary2.summary_params(self) smry.add_dict(model_info) smry.add_df(params, float_format=float_format) if len(stubs): smry.add_df(data, float_format="%17.4f") smry.add_title(results=self, title=title) return smry @Appender(_plot_predict) def plot_predict(self, start=None, end=None, exog=None, dynamic=False, alpha=.05, plot_insample=True, ax=None): from statsmodels.graphics.utils import _import_mpl, create_mpl_ax _ = _import_mpl() fig, ax = create_mpl_ax(ax) # use predict so you set dates forecast = self.predict(start, end, exog, dynamic) # doing this twice. just add a plot keyword to predict? start, end, out_of_sample, _ = ( self.model._get_prediction_index(start, end, dynamic=False)) if out_of_sample: steps = out_of_sample fc_error = self._forecast_error(steps) conf_int = self._forecast_conf_int(forecast[-steps:], fc_error, alpha) if hasattr(self.data, "predict_dates"): from pandas import Series forecast = Series(forecast, index=self.data.predict_dates) ax = forecast.plot(ax=ax, label='forecast') else: ax.plot(forecast) x = ax.get_lines()[-1].get_xdata() if out_of_sample: label = "{0:.0%} confidence interval".format(1 - alpha) ax.fill_between(x[-out_of_sample:], conf_int[:, 0], conf_int[:, 1], color='gray', alpha=.5, label=label) if plot_insample: ax.plot(x[:end + 1 - start], self.model.endog[start:end + 1], label=self.model.endog_names) ax.legend(loc='best') return fig class ARMAResultsWrapper(wrap.ResultsWrapper): _attrs = {} _wrap_attrs = wrap.union_dicts( tsa_model.TimeSeriesResultsWrapper._wrap_attrs, _attrs) _methods = {} _wrap_methods = wrap.union_dicts( tsa_model.TimeSeriesResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(ARMAResultsWrapper, ARMAResults) # noqa:E305 class ARIMAResults(ARMAResults): @Appender(_arima_results_predict) def predict(self, start=None, end=None, exog=None, typ='linear', dynamic=False): return self.model.predict(self.params, start, end, exog, typ, dynamic) def _forecast_error(self, steps): sigma2 = self.sigma2 ma_rep = arma2ma(np.r_[1, -self.arparams], np.r_[1, self.maparams], lags=steps) fcerr = np.sqrt(np.cumsum(cumsum_n(ma_rep, self.k_diff) ** 2) * sigma2) return fcerr def _forecast_conf_int(self, forecast, fcerr, alpha): const = norm.ppf(1 - alpha / 2.) conf_int = np.c_[forecast - const * fcerr, forecast + const * fcerr] return conf_int def forecast(self, steps=1, exog=None, alpha=.05): """ Out-of-sample forecasts Parameters ---------- steps : int The number of out of sample forecasts from the end of the sample. exog : ndarray If the model is an ARIMAX, you must provide out of sample values for the exogenous variables. This should not include the constant. The number of observation in exog must match the value of steps. alpha : float The confidence intervals for the forecasts are (1 - alpha) % Returns ------- forecast : ndarray Array of out of sample forecasts stderr : ndarray Array of the standard error of the forecasts. conf_int : ndarray 2d array of the confidence interval for the forecast Notes ----- Prediction is done in the levels of the original endogenous variable. If you would like prediction of differences in levels use `predict`. """ if exog is not None: exog = array_like(exog, 'exog', ndim=2) if exog.shape[0] != steps: raise ValueError("new exog needed for each step") if self.k_exog != exog.shape[1]: raise ValueError('exog must contain the same number of ' 'variables as in the estimated model.') # prepend in-sample exog observations if self.k_ar > 0: exog = np.vstack((self.model.exog[-self.k_ar:, self.k_trend:], exog)) else: if self.k_exog: raise ValueError('Forecast values for exog are required when ' 'the model contains exogenous regressors.') forecast = _arma_predict_out_of_sample(self.params, steps, self.resid, self.k_ar, self.k_ma, self.k_trend, self.k_exog, self.model.endog, exog, method=self.model.method) d = self.model.k_diff endog = self.model.data.endog[-d:] forecast = unintegrate(forecast, unintegrate_levels(endog, d))[d:] # get forecast errors fcerr = self._forecast_error(steps) conf_int = self._forecast_conf_int(forecast, fcerr, alpha) return forecast, fcerr, conf_int @Appender(_arima_plot_predict) def plot_predict(self, start=None, end=None, exog=None, dynamic=False, alpha=.05, plot_insample=True, ax=None): from statsmodels.graphics.utils import _import_mpl, create_mpl_ax _ = _import_mpl() fig, ax = create_mpl_ax(ax) # use predict so you set dates forecast = self.predict(start, end, exog, 'levels', dynamic) # doing this twice. just add a plot keyword to predict? start, end, out_of_sample, _ = ( self.model._get_prediction_index(start, end, dynamic)) if out_of_sample: steps = out_of_sample fc_error = self._forecast_error(steps) conf_int = self._forecast_conf_int(forecast[-steps:], fc_error, alpha) if hasattr(self.data, "predict_dates"): from pandas import Series forecast = Series(forecast, index=self.data.predict_dates) ax = forecast.plot(ax=ax, label='forecast') else: ax.plot(forecast) x = ax.get_lines()[-1].get_xdata() if out_of_sample: label = "{0:.0%} confidence interval".format(1 - alpha) ax.fill_between(x[-out_of_sample:], conf_int[:, 0], conf_int[:, 1], color='gray', alpha=.5, label=label) if plot_insample: import re k_diff = self.k_diff label = re.sub(r"D\d*\.", "", self.model.endog_names) levels = unintegrate(self.model.endog, self.model._first_unintegrate) ax.plot(x[:end + 1 - start], levels[start + k_diff:end + k_diff + 1], label=label) ax.legend(loc='best') return fig class ARIMAResultsWrapper(ARMAResultsWrapper): pass wrap.populate_wrapper(ARIMAResultsWrapper, ARIMAResults) # noqa:E305 statsmodels-0.12.2/statsmodels/tsa/arima_process.py000066400000000000000000000677431400612667500225200ustar00rootroot00000000000000"""ARMA process and estimation with scipy.signal.lfilter Notes ----- * written without textbook, works but not sure about everything briefly checked and it looks to be standard least squares, see below * theoretical autocorrelation function of general ARMA Done, relatively easy to guess solution, time consuming to get theoretical test cases, example file contains explicit formulas for acovf of MA(1), MA(2) and ARMA(1,1) Properties: Judge, ... (1985): The Theory and Practise of Econometrics Author: josefpktd License: BSD """ import numpy as np from scipy import signal, optimize, linalg from statsmodels.compat.pandas import Appender from statsmodels.tools.docstring import remove_parameters, Docstring from statsmodels.tools.validation import array_like __all__ = ['arma_acf', 'arma_acovf', 'arma_generate_sample', 'arma_impulse_response', 'arma2ar', 'arma2ma', 'deconvolve', 'lpol2index', 'index2lpol'] NONSTATIONARY_ERROR = """\ The model's autoregressive parameters (ar) indicate that the process is non-stationary. arma_acovf can only be used with stationary processes. """ def arma_generate_sample(ar, ma, nsample, scale=1, distrvs=None, axis=0, burnin=0): """ Simulate data from an ARMA. Parameters ---------- ar : array_like The coefficient for autoregressive lag polynomial, including zero lag. ma : array_like The coefficient for moving-average lag polynomial, including zero lag. nsample : int or tuple of ints If nsample is an integer, then this creates a 1d timeseries of length size. If nsample is a tuple, creates a len(nsample) dimensional time series where time is indexed along the input variable ``axis``. All series are unless ``distrvs`` generates dependent data. scale : float The standard deviation of noise. distrvs : function, random number generator A function that generates the random numbers, and takes ``size`` as argument. The default is np.random.standard_normal. axis : int See nsample for details. burnin : int Number of observation at the beginning of the sample to drop. Used to reduce dependence on initial values. Returns ------- ndarray Random sample(s) from an ARMA process. Notes ----- As mentioned above, both the AR and MA components should include the coefficient on the zero-lag. This is typically 1. Further, due to the conventions used in signal processing used in signal.lfilter vs. conventions in statistics for ARMA processes, the AR parameters should have the opposite sign of what you might expect. See the examples below. Examples -------- >>> import numpy as np >>> np.random.seed(12345) >>> arparams = np.array([.75, -.25]) >>> maparams = np.array([.65, .35]) >>> ar = np.r_[1, -arparams] # add zero-lag and negate >>> ma = np.r_[1, maparams] # add zero-lag >>> y = sm.tsa.arma_generate_sample(ar, ma, 250) >>> model = sm.tsa.ARMA(y, (2, 2)).fit(trend='nc', disp=0) >>> model.params array([ 0.79044189, -0.23140636, 0.70072904, 0.40608028]) """ distrvs = np.random.standard_normal if distrvs is None else distrvs if np.ndim(nsample) == 0: nsample = [nsample] if burnin: # handle burin time for nd arrays # maybe there is a better trick in scipy.fft code newsize = list(nsample) newsize[axis] += burnin newsize = tuple(newsize) fslice = [slice(None)] * len(newsize) fslice[axis] = slice(burnin, None, None) fslice = tuple(fslice) else: newsize = tuple(nsample) fslice = tuple([slice(None)] * np.ndim(newsize)) eta = scale * distrvs(size=newsize) return signal.lfilter(ma, ar, eta, axis=axis)[fslice] def arma_acovf(ar, ma, nobs=10, sigma2=1, dtype=None): """ Theoretical autocovariances of stationary ARMA processes Parameters ---------- ar : array_like, 1d The coefficients for autoregressive lag polynomial, including zero lag. ma : array_like, 1d The coefficients for moving-average lag polynomial, including zero lag. nobs : int The number of terms (lags plus zero lag) to include in returned acovf. sigma2 : float Variance of the innovation term. Returns ------- ndarray The autocovariance of ARMA process given by ar, ma. See Also -------- arma_acf : Autocorrelation function for ARMA processes. acovf : Sample autocovariance estimation. References ---------- .. [*] Brockwell, Peter J., and Richard A. Davis. 2009. Time Series: Theory and Methods. 2nd ed. 1991. New York, NY: Springer. """ if dtype is None: dtype = np.common_type(np.array(ar), np.array(ma), np.array(sigma2)) p = len(ar) - 1 q = len(ma) - 1 m = max(p, q) + 1 if sigma2.real < 0: raise ValueError('Must have positive innovation variance.') # Short-circuit for trivial corner-case if p == q == 0: out = np.zeros(nobs, dtype=dtype) out[0] = sigma2 return out elif p > 0 and np.max(np.abs(np.roots(ar))) >= 1: raise ValueError(NONSTATIONARY_ERROR) # Get the moving average representation coefficients that we need ma_coeffs = arma2ma(ar, ma, lags=m) # Solve for the first m autocovariances via the linear system # described by (BD, eq. 3.3.8) A = np.zeros((m, m), dtype=dtype) b = np.zeros((m, 1), dtype=dtype) # We need a zero-right-padded version of ar params tmp_ar = np.zeros(m, dtype=dtype) tmp_ar[:p + 1] = ar for k in range(m): A[k, :(k + 1)] = tmp_ar[:(k + 1)][::-1] A[k, 1:m - k] += tmp_ar[(k + 1):m] b[k] = sigma2 * np.dot(ma[k:q + 1], ma_coeffs[:max((q + 1 - k), 0)]) acovf = np.zeros(max(nobs, m), dtype=dtype) try: acovf[:m] = np.linalg.solve(A, b)[:, 0] except np.linalg.LinAlgError: raise ValueError(NONSTATIONARY_ERROR) # Iteratively apply (BD, eq. 3.3.9) to solve for remaining autocovariances if nobs > m: zi = signal.lfiltic([1], ar, acovf[:m:][::-1]) acovf[m:] = signal.lfilter([1], ar, np.zeros(nobs - m, dtype=dtype), zi=zi)[0] return acovf[:nobs] def arma_acf(ar, ma, lags=10): """ Theoretical autocorrelation function of an ARMA process. Parameters ---------- ar : array_like Coefficients for autoregressive lag polynomial, including zero lag. ma : array_like Coefficients for moving-average lag polynomial, including zero lag. lags : int The number of terms (lags plus zero lag) to include in returned acf. Returns ------- ndarray The autocorrelations of ARMA process given by ar and ma. See Also -------- arma_acovf : Autocovariances from ARMA processes. acf : Sample autocorrelation function estimation. acovf : Sample autocovariance function estimation. """ acovf = arma_acovf(ar, ma, lags) return acovf / acovf[0] def arma_pacf(ar, ma, lags=10): """ Theoretical partial autocorrelation function of an ARMA process. Parameters ---------- ar : array_like, 1d The coefficients for autoregressive lag polynomial, including zero lag. ma : array_like, 1d The coefficients for moving-average lag polynomial, including zero lag. lags : int The number of terms (lags plus zero lag) to include in returned pacf. Returns ------- ndarrray The partial autocorrelation of ARMA process given by ar and ma. Notes ----- Solves yule-walker equation for each lag order up to nobs lags. not tested/checked yet """ # TODO: Should use rank 1 inverse update apacf = np.zeros(lags) acov = arma_acf(ar, ma, lags=lags + 1) apacf[0] = 1. for k in range(2, lags + 1): r = acov[:k] apacf[k - 1] = linalg.solve(linalg.toeplitz(r[:-1]), r[1:])[-1] return apacf def arma_periodogram(ar, ma, worN=None, whole=0): """ Periodogram for ARMA process given by lag-polynomials ar and ma. Parameters ---------- ar : array_like The autoregressive lag-polynomial with leading 1 and lhs sign. ma : array_like The moving average lag-polynomial with leading 1. worN : {None, int}, optional An option for scipy.signal.freqz (read "w or N"). If None, then compute at 512 frequencies around the unit circle. If a single integer, the compute at that many frequencies. Otherwise, compute the response at frequencies given in worN. whole : {0,1}, optional An options for scipy.signal.freqz/ Normally, frequencies are computed from 0 to pi (upper-half of unit-circle. If whole is non-zero compute frequencies from 0 to 2*pi. Returns ------- w : ndarray The frequencies. sd : ndarray The periodogram, also known as the spectral density. Notes ----- Normalization ? This uses signal.freqz, which does not use fft. There is a fft version somewhere. """ w, h = signal.freqz(ma, ar, worN=worN, whole=whole) sd = np.abs(h) ** 2 / np.sqrt(2 * np.pi) if np.any(np.isnan(h)): # this happens with unit root or seasonal unit root' import warnings warnings.warn('Warning: nan in frequency response h, maybe a unit ' 'root', RuntimeWarning) return w, sd def arma_impulse_response(ar, ma, leads=100): """ Compute the impulse response function (MA representation) for ARMA process. Parameters ---------- ar : array_like, 1d The auto regressive lag polynomial. ma : array_like, 1d The moving average lag polynomial. leads : int The number of observations to calculate. Returns ------- ndarray The impulse response function with nobs elements. Notes ----- This is the same as finding the MA representation of an ARMA(p,q). By reversing the role of ar and ma in the function arguments, the returned result is the AR representation of an ARMA(p,q), i.e ma_representation = arma_impulse_response(ar, ma, leads=100) ar_representation = arma_impulse_response(ma, ar, leads=100) Fully tested against matlab Examples -------- AR(1) >>> arma_impulse_response([1.0, -0.8], [1.], leads=10) array([ 1. , 0.8 , 0.64 , 0.512 , 0.4096 , 0.32768 , 0.262144 , 0.2097152 , 0.16777216, 0.13421773]) this is the same as >>> 0.8**np.arange(10) array([ 1. , 0.8 , 0.64 , 0.512 , 0.4096 , 0.32768 , 0.262144 , 0.2097152 , 0.16777216, 0.13421773]) MA(2) >>> arma_impulse_response([1.0], [1., 0.5, 0.2], leads=10) array([ 1. , 0.5, 0.2, 0. , 0. , 0. , 0. , 0. , 0. , 0. ]) ARMA(1,2) >>> arma_impulse_response([1.0, -0.8], [1., 0.5, 0.2], leads=10) array([ 1. , 1.3 , 1.24 , 0.992 , 0.7936 , 0.63488 , 0.507904 , 0.4063232 , 0.32505856, 0.26004685]) """ impulse = np.zeros(leads) impulse[0] = 1. return signal.lfilter(ma, ar, impulse) def arma2ma(ar, ma, lags=100): """ A finite-lag approximate MA representation of an ARMA process. Parameters ---------- ar : ndarray The auto regressive lag polynomial. ma : ndarray The moving average lag polynomial. lags : int The number of coefficients to calculate. Returns ------- ndarray The coefficients of AR lag polynomial with nobs elements. Notes ----- Equivalent to ``arma_impulse_response(ma, ar, leads=100)`` """ return arma_impulse_response(ar, ma, leads=lags) def arma2ar(ar, ma, lags=100): """ A finite-lag AR approximation of an ARMA process. Parameters ---------- ar : array_like The auto regressive lag polynomial. ma : array_like The moving average lag polynomial. lags : int The number of coefficients to calculate. Returns ------- ndarray The coefficients of AR lag polynomial with nobs elements. Notes ----- Equivalent to ``arma_impulse_response(ma, ar, leads=100)`` """ return arma_impulse_response(ma, ar, leads=lags) # moved from sandbox.tsa.try_fi def ar2arma(ar_des, p, q, n=20, mse='ar', start=None): """ Find arma approximation to ar process. This finds the ARMA(p,q) coefficients that minimize the integrated squared difference between the impulse_response functions (MA representation) of the AR and the ARMA process. This does not check whether the MA lag polynomial of the ARMA process is invertible, neither does it check the roots of the AR lag polynomial. Parameters ---------- ar_des : array_like The coefficients of original AR lag polynomial, including lag zero. p : int The length of desired AR lag polynomials. q : int The length of desired MA lag polynomials. n : int The number of terms of the impulse_response function to include in the objective function for the approximation. mse : str, 'ar' Not used. start : ndarray Initial values to use when finding the approximation. Returns ------- ar_app : ndarray The coefficients of the AR lag polynomials of the approximation. ma_app : ndarray The coefficients of the MA lag polynomials of the approximation. res : tuple The result of optimize.leastsq. Notes ----- Extension is possible if we want to match autocovariance instead of impulse response function. """ # TODO: convert MA lag polynomial, ma_app, to be invertible, by mirroring # TODO: roots outside the unit interval to ones that are inside. How to do # TODO: this? # p,q = pq def msear_err(arma, ar_des): ar, ma = np.r_[1, arma[:p - 1]], np.r_[1, arma[p - 1:]] ar_approx = arma_impulse_response(ma, ar, n) return (ar_des - ar_approx) # ((ar - ar_approx)**2).sum() if start is None: arma0 = np.r_[-0.9 * np.ones(p - 1), np.zeros(q - 1)] else: arma0 = start res = optimize.leastsq(msear_err, arma0, ar_des, maxfev=5000) arma_app = np.atleast_1d(res[0]) ar_app = np.r_[1, arma_app[:p - 1]], ma_app = np.r_[1, arma_app[p - 1:]] return ar_app, ma_app, res _arma_docs = {'ar': arma2ar.__doc__, 'ma': arma2ma.__doc__} def lpol2index(ar): """ Remove zeros from lag polynomial Parameters ---------- ar : array_like coefficients of lag polynomial Returns ------- coeffs : ndarray non-zero coefficients of lag polynomial index : ndarray index (lags) of lag polynomial with non-zero elements """ ar = array_like(ar, 'ar') index = np.nonzero(ar)[0] coeffs = ar[index] return coeffs, index def index2lpol(coeffs, index): """ Expand coefficients to lag poly Parameters ---------- coeffs : ndarray non-zero coefficients of lag polynomial index : ndarray index (lags) of lag polynomial with non-zero elements Returns ------- ar : array_like coefficients of lag polynomial """ n = max(index) ar = np.zeros(n + 1) ar[index] = coeffs return ar def lpol_fima(d, n=20): """MA representation of fractional integration .. math:: (1-L)^{-d} for |d|<0.5 or |d|<1 (?) Parameters ---------- d : float fractional power n : int number of terms to calculate, including lag zero Returns ------- ma : ndarray coefficients of lag polynomial """ # hide import inside function until we use this heavily from scipy.special import gammaln j = np.arange(n) return np.exp(gammaln(d + j) - gammaln(j + 1) - gammaln(d)) # moved from sandbox.tsa.try_fi def lpol_fiar(d, n=20): """AR representation of fractional integration .. math:: (1-L)^{d} for |d|<0.5 or |d|<1 (?) Parameters ---------- d : float fractional power n : int number of terms to calculate, including lag zero Returns ------- ar : ndarray coefficients of lag polynomial Notes: first coefficient is 1, negative signs except for first term, ar(L)*x_t """ # hide import inside function until we use this heavily from scipy.special import gammaln j = np.arange(n) ar = - np.exp(gammaln(-d + j) - gammaln(j + 1) - gammaln(-d)) ar[0] = 1 return ar # moved from sandbox.tsa.try_fi def lpol_sdiff(s): """return coefficients for seasonal difference (1-L^s) just a trivial convenience function Parameters ---------- s : int number of periods in season Returns ------- sdiff : list, length s+1 """ return [1] + [0] * (s - 1) + [-1] def deconvolve(num, den, n=None): """Deconvolves divisor out of signal, division of polynomials for n terms calculates den^{-1} * num Parameters ---------- num : array_like signal or lag polynomial denom : array_like coefficients of lag polynomial (linear filter) n : None or int number of terms of quotient Returns ------- quot : ndarray quotient or filtered series rem : ndarray remainder Notes ----- If num is a time series, then this applies the linear filter den^{-1}. If both num and den are both lag polynomials, then this calculates the quotient polynomial for n terms and also returns the remainder. This is copied from scipy.signal.signaltools and added n as optional parameter. """ num = np.atleast_1d(num) den = np.atleast_1d(den) N = len(num) D = len(den) if D > N and n is None: quot = [] rem = num else: if n is None: n = N - D + 1 input = np.zeros(n, float) input[0] = 1 quot = signal.lfilter(num, den, input) num_approx = signal.convolve(den, quot, mode='full') if len(num) < len(num_approx): # 1d only ? num = np.concatenate((num, np.zeros(len(num_approx) - len(num)))) rem = num - num_approx return quot, rem _generate_sample_doc = Docstring(arma_generate_sample.__doc__) _generate_sample_doc.remove_parameters(['ar', 'ma']) _generate_sample_doc.replace_block('Notes', []) _generate_sample_doc.replace_block('Examples', []) class ArmaProcess(object): r""" Theoretical properties of an ARMA process for specified lag-polynomials. Parameters ---------- ar : array_like Coefficient for autoregressive lag polynomial, including zero lag. Must be entered using the signs from the lag polynomial representation. See the notes for more information about the sign. ma : array_like Coefficient for moving-average lag polynomial, including zero lag. nobs : int, optional Length of simulated time series. Used, for example, if a sample is generated. See example. Notes ----- Both the AR and MA components must include the coefficient on the zero-lag. In almost all cases these values should be 1. Further, due to using the lag-polynomial representation, the AR parameters should have the opposite sign of what one would write in the ARMA representation. See the examples below. The ARMA(p,q) process is described by .. math:: y_{t}=\phi_{1}y_{t-1}+\ldots+\phi_{p}y_{t-p}+\theta_{1}\epsilon_{t-1} +\ldots+\theta_{q}\epsilon_{t-q}+\epsilon_{t} and the parameterization used in this function uses the lag-polynomial representation, .. math:: \left(1-\phi_{1}L-\ldots-\phi_{p}L^{p}\right)y_{t} = \left(1+\theta_{1}L+\ldots+\theta_{q}L^{q}\right)\epsilon_{t} Examples -------- ARMA(2,2) with AR coefficients 0.75 and -0.25, and MA coefficients 0.65 and 0.35 >>> import statsmodels.api as sm >>> import numpy as np >>> np.random.seed(12345) >>> arparams = np.array([.75, -.25]) >>> maparams = np.array([.65, .35]) >>> ar = np.r_[1, -arparams] # add zero-lag and negate >>> ma = np.r_[1, maparams] # add zero-lag >>> arma_process = sm.tsa.ArmaProcess(ar, ma) >>> arma_process.isstationary True >>> arma_process.isinvertible True >>> arma_process.arroots array([1.5-1.32287566j, 1.5+1.32287566j]) >>> y = arma_process.generate_sample(250) >>> model = sm.tsa.ARMA(y, (2, 2)).fit(trend='nc', disp=0) >>> model.params array([ 0.79044189, -0.23140636, 0.70072904, 0.40608028]) The same ARMA(2,2) Using the from_coeffs class method >>> arma_process = sm.tsa.ArmaProcess.from_coeffs(arparams, maparams) >>> arma_process.arroots array([1.5-1.32287566j, 1.5+1.32287566j]) """ # TODO: Check unit root behavior def __init__(self, ar=None, ma=None, nobs=100): if ar is None: ar = np.array([1.]) if ma is None: ma = np.array([1.]) self.ar = array_like(ar, 'ar') self.ma = array_like(ma, 'ma') self.arcoefs = -self.ar[1:] self.macoefs = self.ma[1:] self.arpoly = np.polynomial.Polynomial(self.ar) self.mapoly = np.polynomial.Polynomial(self.ma) self.nobs = nobs @classmethod def from_coeffs(cls, arcoefs=None, macoefs=None, nobs=100): """ Create ArmaProcess from an ARMA representation. Parameters ---------- arcoefs : array_like Coefficient for autoregressive lag polynomial, not including zero lag. The sign is inverted to conform to the usual time series representation of an ARMA process in statistics. See the class docstring for more information. macoefs : array_like Coefficient for moving-average lag polynomial, excluding zero lag. nobs : int, optional Length of simulated time series. Used, for example, if a sample is generated. Returns ------- ArmaProcess Class instance initialized with arcoefs and macoefs. Examples -------- >>> arparams = [.75, -.25] >>> maparams = [.65, .35] >>> arma_process = sm.tsa.ArmaProcess.from_coeffs(ar, ma) >>> arma_process.isstationary True >>> arma_process.isinvertible True """ arcoefs = [] if arcoefs is None else arcoefs macoefs = [] if macoefs is None else macoefs return cls(np.r_[1, -np.asarray(arcoefs)], np.r_[1, np.asarray(macoefs)], nobs=nobs) @classmethod def from_estimation(cls, model_results, nobs=None): """ Create an ArmaProcess from the results of an ARMA estimation. Parameters ---------- model_results : ARMAResults instance A fitted model. nobs : int, optional If None, nobs is taken from the results. Returns ------- ArmaProcess Class instance initialized from model_results. """ arcoefs = model_results.arparams macoefs = model_results.maparams nobs = nobs or model_results.nobs return cls(np.r_[1, -arcoefs], np.r_[1, macoefs], nobs=nobs) def __mul__(self, oth): if isinstance(oth, self.__class__): ar = (self.arpoly * oth.arpoly).coef ma = (self.mapoly * oth.mapoly).coef else: try: aroth, maoth = oth arpolyoth = np.polynomial.Polynomial(aroth) mapolyoth = np.polynomial.Polynomial(maoth) ar = (self.arpoly * arpolyoth).coef ma = (self.mapoly * mapolyoth).coef except: raise TypeError('Other type is not a valid type') return self.__class__(ar, ma, nobs=self.nobs) def __repr__(self): msg = 'ArmaProcess({0}, {1}, nobs={2}) at {3}' return msg.format(self.ar.tolist(), self.ma.tolist(), self.nobs, hex(id(self))) def __str__(self): return 'ArmaProcess\nAR: {0}\nMA: {1}'.format(self.ar.tolist(), self.ma.tolist()) @Appender(remove_parameters(arma_acovf.__doc__, ['ar', 'ma', 'sigma2'])) def acovf(self, nobs=None): nobs = nobs or self.nobs return arma_acovf(self.ar, self.ma, nobs=nobs) @Appender(remove_parameters(arma_acf.__doc__, ['ar', 'ma'])) def acf(self, lags=None): lags = lags or self.nobs return arma_acf(self.ar, self.ma, lags=lags) @Appender(remove_parameters(arma_pacf.__doc__, ['ar', 'ma'])) def pacf(self, lags=None): lags = lags or self.nobs return arma_pacf(self.ar, self.ma, lags=lags) @Appender(remove_parameters(arma_periodogram.__doc__, ['ar', 'ma', 'worN', 'whole'])) def periodogram(self, nobs=None): nobs = nobs or self.nobs return arma_periodogram(self.ar, self.ma, worN=nobs) @Appender(remove_parameters(arma_impulse_response.__doc__, ['ar', 'ma'])) def impulse_response(self, leads=None): leads = leads or self.nobs return arma_impulse_response(self.ar, self.ma, leads=leads) @Appender(remove_parameters(arma2ma.__doc__, ['ar', 'ma'])) def arma2ma(self, lags=None): lags = lags or self.lags return arma2ma(self.ar, self.ma, lags=lags) @Appender(remove_parameters(arma2ar.__doc__, ['ar', 'ma'])) def arma2ar(self, lags=None): lags = lags or self.lags return arma2ar(self.ar, self.ma, lags=lags) @property def arroots(self): """Roots of autoregressive lag-polynomial""" return self.arpoly.roots() @property def maroots(self): """Roots of moving average lag-polynomial""" return self.mapoly.roots() @property def isstationary(self): """ Arma process is stationary if AR roots are outside unit circle. Returns ------- bool True if autoregressive roots are outside unit circle. """ if np.all(np.abs(self.arroots) > 1.0): return True else: return False @property def isinvertible(self): """ Arma process is invertible if MA roots are outside unit circle. Returns ------- bool True if moving average roots are outside unit circle. """ if np.all(np.abs(self.maroots) > 1): return True else: return False def invertroots(self, retnew=False): """ Make MA polynomial invertible by inverting roots inside unit circle. Parameters ---------- retnew : bool If False (default), then return the lag-polynomial as array. If True, then return a new instance with invertible MA-polynomial. Returns ------- manew : ndarray A new invertible MA lag-polynomial, returned if retnew is false. wasinvertible : bool True if the MA lag-polynomial was already invertible, returned if retnew is false. armaprocess : new instance of class If retnew is true, then return a new instance with invertible MA-polynomial. """ # TODO: variable returns like this? pr = self.maroots mainv = self.ma invertible = self.isinvertible if not invertible: pr[np.abs(pr) < 1] = 1. / pr[np.abs(pr) < 1] pnew = np.polynomial.Polynomial.fromroots(pr) mainv = pnew.coef / pnew.coef[0] if retnew: return self.__class__(self.ar, mainv, nobs=self.nobs) else: return mainv, invertible @Appender(str(_generate_sample_doc)) def generate_sample(self, nsample=100, scale=1., distrvs=None, axis=0, burnin=0): return arma_generate_sample(self.ar, self.ma, nsample, scale, distrvs, axis=axis, burnin=burnin) statsmodels-0.12.2/statsmodels/tsa/arma_mle.py000066400000000000000000000322041400612667500214260ustar00rootroot00000000000000""" Created on Sun Oct 10 14:57:50 2010 Author: josef-pktd, Skipper Seabold License: BSD TODO: check everywhere initialization of signal.lfilter """ import numpy as np from scipy import signal, optimize from statsmodels.base.model import GenericLikelihoodModel #copied from sandbox/regression/mle.py #rename until merge of classes is complete class Arma(GenericLikelihoodModel): #switch to generic mle """ univariate Autoregressive Moving Average model, conditional on initial values The ARMA model is estimated either with conditional Least Squares or with conditional Maximum Likelihood. The implementation is using scipy.filter.lfilter which makes it faster than the Kalman Filter Implementation. The Kalman Filter Implementation however uses the exact Maximum Likelihood and will be more accurate, statistically more efficent in small samples. In large samples conditional LS, conditional MLE and exact MLE should be very close to each other, they are equivalent asymptotically. Notes ----- this can subclass TSMLEModel TODO: - CondLS return raw estimation results - needs checking that there is no wrong state retained, when running fit several times with different options - still needs consistent order options. - Currently assumes that the mean is zero, no mean or effect of exogenous variables are included in the estimation. """ def __init__(self, endog, exog=None): #need to override p,q (nar,nma) correctly super(Arma, self).__init__(endog, exog) #set default arma(1,1) self.nar = 1 self.nma = 1 #self.initialize() def initialize(self): pass def geterrors(self, params): #copied from sandbox.tsa.arima.ARIMA p, q = self.nar, self.nma ar = np.concatenate(([1], -params[:p])) ma = np.concatenate(([1], params[p:p+q])) #lfilter_zi requires same length for ar and ma maxlag = 1+max(p,q) armax = np.zeros(maxlag) armax[:p+1] = ar mamax = np.zeros(maxlag) mamax[:q+1] = ma #remove zi again to match better with Skipper's version #zi = signal.lfilter_zi(armax, mamax) #errorsest = signal.lfilter(rhoy, rhoe, self.endog, zi=zi)[0] #zi is also returned errorsest = signal.lfilter(ar, ma, self.endog) return errorsest def loglike(self, params): """ Loglikelihood for arma model Notes ----- The ancillary parameter is assumed to be the last element of the params vector """ # #copied from sandbox.tsa.arima.ARIMA # p = self.nar # rhoy = np.concatenate(([1], params[:p])) # rhoe = np.concatenate(([1], params[p:-1])) # errorsest = signal.lfilter(rhoy, rhoe, self.endog) errorsest = self.geterrors(params) sigma2 = np.maximum(params[-1]**2, 1e-6) axis = 0 nobs = len(errorsest) #this does not help for exploding paths #errorsest[np.isnan(errorsest)] = 100 # llike = -0.5 * (np.sum(np.log(sigma2),axis) # + np.sum((errorsest**2)/sigma2, axis) # + nobs*np.log(2*np.pi)) llike = -0.5 * (nobs*np.log(sigma2) + np.sum((errorsest**2)/sigma2, axis) + nobs*np.log(2*np.pi)) return llike #add for Jacobian calculation bsejac in GenericMLE, copied from loglike def nloglikeobs(self, params): """ Loglikelihood for arma model Notes ----- The ancillary parameter is assumed to be the last element of the params vector """ # #copied from sandbox.tsa.arima.ARIMA # p = self.nar # rhoy = np.concatenate(([1], params[:p])) # rhoe = np.concatenate(([1], params[p:-1])) # errorsest = signal.lfilter(rhoy, rhoe, self.endog) errorsest = self.geterrors(params) sigma2 = np.maximum(params[-1]**2, 1e-6) axis = 0 nobs = len(errorsest) #this does not help for exploding paths #errorsest[np.isnan(errorsest)] = 100 # llike = -0.5 * (np.sum(np.log(sigma2),axis) # + np.sum((errorsest**2)/sigma2, axis) # + nobs*np.log(2*np.pi)) llike = 0.5 * (np.log(sigma2) + (errorsest**2)/sigma2 + np.log(2*np.pi)) return llike #use generic instead # def score(self, params): # """ # Score vector for Arma model # """ # #return None # #print params # jac = ndt.Jacobian(self.loglike, stepMax=1e-4) # return jac(params)[-1] #use generic instead # def hessian(self, params): # """ # Hessian of arma model. Currently uses numdifftools # """ # #return None # Hfun = ndt.Jacobian(self.score, stepMax=1e-4) # return Hfun(params)[-1] #copied from arima.ARIMA, needs splitting out of method specific code def fit(self, order=(0,0), start_params=None, method="ls", **optkwds): ''' Estimate lag coefficients of an ARIMA process. Parameters ---------- order : sequence p,d,q where p is the number of AR lags, d is the number of differences to induce stationarity, and q is the number of MA lags to estimate. method : str {"ls", "ssm"} Method of estimation. LS is conditional least squares. SSM is state-space model and the Kalman filter is used to maximize the exact likelihood. rhoy0, rhoe0 : array_like (optional) starting values for estimation Returns ------- (rh, cov_x, infodict, mesg, ier) : output of scipy.optimize.leastsq rh : estimate of lag parameters, concatenated [rhoy, rhoe] cov_x : unscaled (!) covariance matrix of coefficient estimates ''' if not hasattr(order, '__iter__'): raise ValueError("order must be an iterable sequence. Got type \ %s instead" % type(order)) p,q = order self.nar = p # needed for geterrors, needs cleanup self.nma = q ## if d > 0: ## raise ValueError("Differencing not implemented yet") ## # assume no constant, ie mu = 0 ## # unless overwritten then use w_bar for mu ## Y = np.diff(endog, d, axis=0) #TODO: handle lags? x = self.endog.squeeze() # remove the squeeze might be needed later # def errfn( rho): # #rhoy, rhoe = rho # rhoy = np.concatenate(([1], rho[:p])) # rhoe = np.concatenate(([1], rho[p:])) # etahatr = signal.lfilter(rhoy, rhoe, x) # #print rho,np.sum(etahatr*etahatr) # return etahatr #replace with start_params if start_params is None: arcoefs0 = 0.5 * np.ones(p) macoefs0 = 0.5 * np.ones(q) start_params = np.r_[arcoefs0, macoefs0] method = method.lower() if method == "ls": #update optim_kwds = dict(ftol=1e-10, full_output=True) optim_kwds.update(optkwds) #changes: use self.geterrors (nobs,): # rh, cov_x, infodict, mesg, ier = \ # optimize.leastsq(errfn, np.r_[rhoy0, rhoe0],ftol=1e-10,full_output=True) rh, cov_x, infodict, mesg, ier = \ optimize.leastsq(self.geterrors, start_params, **optim_kwds) #TODO: need missing parameter estimates for LS, scale, residual-sdt #TODO: integrate this into the MLE.fit framework? elif method == "ssm": pass else: #this is also conditional least squares # fmin_bfgs is slow or does not work yet errfnsum = lambda rho : np.sum(self.geterrors(rho)**2) #xopt, {fopt, gopt, Hopt, func_calls, grad_calls optim_kwds = dict(maxiter=2, full_output=True) optim_kwds.update(optkwds) rh, fopt, gopt, cov_x, _,_, ier = \ optimize.fmin_bfgs(errfnsum, start_params, **optim_kwds) infodict, mesg = None, None self.params = rh self.ar_est = np.concatenate(([1], -rh[:p])) self.ma_est = np.concatenate(([1], rh[p:p+q])) #rh[-q:])) doesnt work for q=0, added p+q as endpoint for safety if var is included self.error_estimate = self.geterrors(rh) return rh, cov_x, infodict, mesg, ier #renamed and needs check with other fit def fit_mle(self, order=(0,0), start_params=None, method='nm', maxiter=5000, tol=1e-08, **kwds): '''Estimate an ARMA model with given order using Conditional Maximum Likelihood Parameters ---------- order : tuple, 2 elements specifies the number of lags(nar, nma) to include, not including lag 0 start_params : array_like, 1d, (nar+nma+1,) start parameters for the optimization, the length needs to be equal to the number of ar plus ma coefficients plus 1 for the residual variance method : str optimization method, as described in LikelihoodModel maxiter : int maximum number of iteration in the optimization tol : float tolerance (?) for the optimization Returns ------- mlefit : instance of (GenericLikelihood ?)Result class contains estimation results and additional statistics ''' nar, nma = p, q = order self.nar, self.nma = nar, nma if start_params is None: start_params = np.concatenate((0.05*np.ones(nar + nma), [1])) mlefit = super(Arma, self).fit(start_params=start_params, maxiter=maxiter, method=method, tol=tol, **kwds) #bug fix: running ls and then mle did not overwrite this rh = mlefit.params self.params = rh self.ar_est = np.concatenate(([1], -rh[:p])) self.ma_est = np.concatenate(([1], rh[p:p+q])) self.error_estimate = self.geterrors(rh) return mlefit #copied from arima.ARIMA def predicted(self, ar=None, ma=None): '''past predicted values of time series just added, not checked yet ''' # #ar, ma not used, not useful as arguments for predicted pattern # #need it for prediction for other time series, endog # if ar is None: # ar = self.ar_est # if ma is None: # ma = self.ma_est return self.endog - self.error_estimate #copied from arima.ARIMA def forecast(self, ar=None, ma=None, nperiod=10): '''nperiod ahead forecast at the end of the data period forecast is based on the error estimates ''' eta = np.r_[self.error_estimate, np.zeros(nperiod)] if ar is None: ar = self.ar_est if ma is None: ma = self.ma_est return signal.lfilter(ma, ar, eta) def forecast2(self, step_ahead=1, start=None, end=None, endog=None): '''rolling h-period ahead forecast without reestimation, 1 period ahead only in construction: uses loop to go over data and not sure how to get (finite) forecast polynomial for h-step Notes ----- just the idea: To improve performance with expanding arrays, specify total period by endog and the conditional forecast period by step_ahead This should be used by/with results which should contain predicted error or noise. Could be either a recursive loop or lfilter with a h-step ahead forecast filter, but then I need to calculate that one. ??? further extension: allow reestimation option question: return h-step ahead or range(h)-step ahead ? ''' if step_ahead != 1: raise NotImplementedError p,q = self.nar, self.nma k = 0 errors = self.error_estimate y = self.endog #this is for 1step ahead only, still need h-step predictive polynomial arcoefs_rev = self.params[k:k+p][::-1] macoefs_rev = self.params[k+p:k+p+q][::-1] predicted = [] # create error vector iteratively for i in range(start, end): predicted.append(sum(arcoefs_rev*y[i-p:i]) + sum(macoefs_rev * errors[i-p:i])) return np.asarray(predicted) def forecast3(self, step_ahead=1, start=None): #, end=None): '''another try for h-step ahead forecasting ''' from .arima_process import arma2ma p,q = self.nar, self.nma k=0 ar = self.params[k:k+p] ma = self.params[k+p:k+p+q] marep = arma2ma(ar,ma, start)[step_ahead+1:] #truncated ma representation errors = self.error_estimate forecasts = np.convolve(errors, marep) return forecasts#[-(errors.shape[0] - start-5):] #get 5 overlapping for testing #copied from arima.ARIMA #TODO: is this needed as a method at all? #JP: not needed in this form, but can be replace with using the parameters @classmethod def generate_sample(cls, ar, ma, nsample, std=1): eta = std * np.random.randn(nsample) return signal.lfilter(ma, ar, eta) statsmodels-0.12.2/statsmodels/tsa/base/000077500000000000000000000000001400612667500202105ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/base/__init__.py000066400000000000000000000001131400612667500223140ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/tsa/base/datetools.py000066400000000000000000000131721400612667500225640ustar00rootroot00000000000000""" Tools for working with dates """ from statsmodels.compat.python import lrange, lzip, lmap, asstr import re import datetime from pandas import to_datetime import numpy as np _quarter_to_day = { "1" : (3, 31), "2" : (6, 30), "3" : (9, 30), "4" : (12, 31), "I" : (3, 31), "II" : (6, 30), "III" : (9, 30), "IV" : (12, 31) } _mdays = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31] _months_with_days = lzip(lrange(1,13), _mdays) _month_to_day = dict(zip(map(str,lrange(1,13)), _months_with_days)) _month_to_day.update(dict(zip(["I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX", "X", "XI", "XII"], _months_with_days))) # regex patterns _y_pattern = r'^\d?\d?\d?\d$' _q_pattern = r''' ^ # beginning of string \d?\d?\d?\d # match any number 1-9999, includes leading zeros (:?q) # use q or a : as a separator ([1-4]|(I{1,3}V?)) # match 1-4 or I-IV roman numerals $ # end of string ''' _m_pattern = r''' ^ # beginning of string \d?\d?\d?\d # match any number 1-9999, includes leading zeros (:?m) # use m or a : as a separator (([1-9][0-2]?)|(I?XI{0,2}|I?VI{0,3}|I{1,3})) # match 1-12 or # I-XII roman numerals $ # end of string ''' #NOTE: see also ts.extras.isleapyear, which accepts a sequence def _is_leap(year): year = int(year) return year % 4 == 0 and (year % 100 != 0 or year % 400 == 0) def date_parser(timestr, parserinfo=None, **kwargs): """ Uses dateutil.parser.parse, but also handles monthly dates of the form 1999m4, 1999:m4, 1999:mIV, 1999mIV and the same for quarterly data with q instead of m. It is not case sensitive. The default for annual data is the end of the year, which also differs from dateutil. """ flags = re.IGNORECASE | re.VERBOSE if re.search(_q_pattern, timestr, flags): y,q = timestr.replace(":","").lower().split('q') month, day = _quarter_to_day[q.upper()] year = int(y) elif re.search(_m_pattern, timestr, flags): y,m = timestr.replace(":","").lower().split('m') month, day = _month_to_day[m.upper()] year = int(y) if _is_leap(y) and month == 2: day += 1 elif re.search(_y_pattern, timestr, flags): month, day = 12, 31 year = int(timestr) else: return to_datetime(timestr, **kwargs) return datetime.datetime(year, month, day) def date_range_str(start, end=None, length=None): """ Returns a list of abbreviated date strings. Parameters ---------- start : str The first abbreviated date, for instance, '1965q1' or '1965m1' end : str, optional The last abbreviated date if length is None. length : int, optional The length of the returned array of end is None. Returns ------- date_range : list List of strings """ flags = re.IGNORECASE | re.VERBOSE #_check_range_inputs(end, length, freq) start = start.lower() if re.search(_m_pattern, start, flags): annual_freq = 12 split = 'm' elif re.search(_q_pattern, start, flags): annual_freq = 4 split = 'q' elif re.search(_y_pattern, start, flags): annual_freq = 1 start += 'a1' # hack if end: end += 'a1' split = 'a' else: raise ValueError("Date %s not understood" % start) yr1, offset1 = lmap(int, start.replace(":","").split(split)) if end is not None: end = end.lower() yr2, offset2 = lmap(int, end.replace(":","").split(split)) length = (yr2 - yr1) * annual_freq + offset2 elif length: yr2 = yr1 + length // annual_freq offset2 = length % annual_freq + (offset1 - 1) years = np.repeat(lrange(yr1+1, yr2), annual_freq).tolist() years = np.r_[[str(yr1)]*(annual_freq+1-offset1), years] # tack on first year years = np.r_[years, [str(yr2)]*offset2] # tack on last year if split != 'a': offset = np.tile(np.arange(1, annual_freq+1), yr2-yr1-1) offset = np.r_[np.arange(offset1, annual_freq+1).astype('a2'), offset] offset = np.r_[offset, np.arange(1,offset2+1).astype('a2')] date_arr_range = [''.join([i, split, asstr(j)]) for i,j in zip(years, offset)] else: date_arr_range = years.tolist() return date_arr_range def dates_from_str(dates): """ Turns a sequence of date strings and returns a list of datetime. Parameters ---------- dates : array_like A sequence of abbreviated dates as string. For instance, '1996m1' or '1996Q1'. The datetime dates are at the end of the period. Returns ------- date_list : ndarray A list of datetime types. """ return lmap(date_parser, dates) def dates_from_range(start, end=None, length=None): """ Turns a sequence of date strings and returns a list of datetime. Parameters ---------- start : str The first abbreviated date, for instance, '1965q1' or '1965m1' end : str, optional The last abbreviated date if length is None. length : int, optional The length of the returned array of end is None. Examples -------- >>> import statsmodels.api as sm >>> import pandas as pd >>> dates = pd.date_range('1960m1', length=nobs) Returns ------- date_list : ndarray A list of datetime types. """ dates = date_range_str(start, end, length) return dates_from_str(dates) statsmodels-0.12.2/statsmodels/tsa/base/prediction.py000066400000000000000000000140231400612667500227220ustar00rootroot00000000000000import pandas as pd import numpy as np from scipy import stats class PredictionResults(object): """ Prediction results Parameters ---------- predicted_mean : {ndarray, Series, DataFrame} The predicted mean values var_pred_mean : {ndarray, Series, DataFrame} The variance of the predicted mean values dist : {None, "norm", "t", rv_frozen} The distribution to use when constructing prediction intervals. Default is normal. df : int, optional The degree of freedom parameter for the t. Not used if dist is None, "norm" or a callable. row_labels : {Sequence[Hashable], pd.Index} Row labels to use for the summary frame. If None, attempts to read the index of ``predicted_mean`` """ def __init__( self, predicted_mean, var_pred_mean, dist=None, df=None, row_labels=None, ): self._predicted_mean = np.asarray(predicted_mean) self._var_pred_mean = np.asarray(var_pred_mean) self._df = df self._row_labels = row_labels if row_labels is None: self._row_labels = getattr(predicted_mean, "index", None) self._use_pandas = self._row_labels is not None if dist != "t" and df is not None: raise ValueError('df must be None when dist is not "t"') if dist is None or dist == "norm": self.dist = stats.norm self.dist_args = () elif dist == "t": self.dist = stats.t self.dist_args = (self._df,) elif isinstance(dist, stats.distributions.rv_frozen): self.dist = dist self.dist_args = () else: raise ValueError('dist must be a None, "norm", "t" or a callable.') def _wrap_pandas(self, value, name=None, columns=None): if not self._use_pandas: return value if value.ndim == 1: return pd.Series(value, index=self._row_labels, name=name) return pd.DataFrame(value, index=self._row_labels, columns=columns) @property def row_labels(self): """The row labels used in pandas-types.""" return self._row_labels @property def predicted_mean(self): """The predicted mean""" return self._wrap_pandas(self._predicted_mean, "predicted_mean") @property def var_pred_mean(self): """The variance of the predicted mean""" if self._var_pred_mean.ndim > 2: return self._var_pred_mean return self._wrap_pandas(self._var_pred_mean, "var_pred_mean") @property def se_mean(self): """The standard deviation of the predicted mean""" ndim = self._var_pred_mean.ndim if ndim == 1: values = np.sqrt(self._var_pred_mean) elif ndim == 3: values = np.sqrt(self._var_pred_mean.T.diagonal()) else: raise NotImplementedError("var_pre_mean must be 1 or 3 dim") return self._wrap_pandas(values, "mean_se") @property def tvalues(self): """The ratio of the predicted mean to its standard deviation""" val = self.predicted_mean / self.se_mean if isinstance(val, pd.Series): val.name = "tvalues" return val def t_test(self, value=0, alternative="two-sided"): """ z- or t-test for hypothesis that mean is equal to value Parameters ---------- value : array_like value under the null hypothesis alternative : str 'two-sided', 'larger', 'smaller' Returns ------- stat : ndarray test statistic pvalue : ndarray p-value of the hypothesis test, the distribution is given by the attribute of the instance, specified in `__init__`. Default if not specified is the normal distribution. """ # assumes symmetric distribution stat = (self.predicted_mean - value) / self.se_mean if alternative in ["two-sided", "2-sided", "2s"]: pvalue = self.dist.sf(np.abs(stat), *self.dist_args) * 2 elif alternative in ["larger", "l"]: pvalue = self.dist.sf(stat, *self.dist_args) elif alternative in ["smaller", "s"]: pvalue = self.dist.cdf(stat, *self.dist_args) else: raise ValueError("invalid alternative") return stat, pvalue def conf_int(self, alpha=0.05): """ Confidence interval construction for the predicted mean. This is currently only available for t and z tests. Parameters ---------- alpha : float, optional The significance level for the prediction interval. The default `alpha` = .05 returns a 95% confidence interval. Returns ------- pi : {ndarray, DataFrame} The array has the lower and the upper limit of the prediction interval in the columns. """ se = self.se_mean q = self.dist.ppf(1 - alpha / 2.0, *self.dist_args) lower = self.predicted_mean - q * se upper = self.predicted_mean + q * se ci = np.column_stack((lower, upper)) if self._use_pandas: return self._wrap_pandas(ci, columns=["lower", "upper"]) return ci def summary_frame(self, alpha=0.05): """ Summary frame of mean, variance and confidence interval. Returns ------- DataFrame DataFrame containing four columns: * mean * mean_se * mean_ci_lower * mean_ci_upper Notes ----- Fixes alpha to 0.05 so that the confidence interval should have 95% coverage. """ ci_mean = np.asarray(self.conf_int(alpha=alpha)) lower, upper = ci_mean[:, 0], ci_mean[:, 1] to_include = { "mean": self.predicted_mean, "mean_se": self.se_mean, "mean_ci_lower": lower, "mean_ci_upper": upper, } return pd.DataFrame(to_include) statsmodels-0.12.2/statsmodels/tsa/base/tests/000077500000000000000000000000001400612667500213525ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/base/tests/__init__.py000066400000000000000000000000001400612667500234510ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/base/tests/test_base.py000066400000000000000000000072051400612667500237010ustar00rootroot00000000000000from datetime import datetime import numpy as np import numpy.testing as npt import pandas as pd import pytest from statsmodels.tsa.base.tsa_model import TimeSeriesModel from statsmodels.tools.testing import assert_equal from statsmodels.tools.sm_exceptions import ValueWarning def test_pandas_nodates_index(): data = [988, 819, 964] dates = ['a', 'b', 'c'] s = pd.Series(data, index=dates) # TODO: Remove this, this is now valid # npt.assert_raises(ValueError, TimeSeriesModel, s) # Test with a non-date index that does not raise an exception because it # can be coerced into a nanosecond DatetimeIndex data = [988, 819, 964] # index=pd.date_range('1970-01-01', periods=3, freq='QS') index = pd.to_datetime([100, 101, 102]) s = pd.Series(data, index=index) actual_str = (index[0].strftime('%Y-%m-%d %H:%M:%S.%f') + str(index[0].value)) assert_equal(actual_str, '1970-01-01 00:00:00.000000100') with pytest.warns(ValueWarning, match="No frequency information"): mod = TimeSeriesModel(s) start, end, out_of_sample, _ = mod._get_prediction_index(0, 4) assert_equal(len(mod.data.predict_dates), 5) def test_predict_freq(): # test that predicted dates have same frequency x = np.arange(1,36.) # there's a bug in pandas up to 0.10.2 for YearBegin #dates = date_range("1972-4-1", "2007-4-1", freq="AS-APR") dates = pd.date_range("1972-4-30", "2006-4-30", freq="A-APR") series = pd.Series(x, index=dates) model = TimeSeriesModel(series) #npt.assert_(model.data.freq == "AS-APR") assert_equal(model._index.freqstr, "A-APR") start, end, out_of_sample, _ = ( model._get_prediction_index("2006-4-30", "2016-4-30")) predict_dates = model.data.predict_dates #expected_dates = date_range("2006-12-31", "2016-12-31", # freq="AS-APR") expected_dates = pd.date_range("2006-4-30", "2016-4-30", freq="A-APR") assert_equal(predict_dates, expected_dates) #ptesting.assert_series_equal(predict_dates, expected_dates) def test_keyerror_start_date(): x = np.arange(1,36.) # dates = date_range("1972-4-1", "2007-4-1", freq="AS-APR") dates = pd.date_range("1972-4-30", "2006-4-30", freq="A-APR") series = pd.Series(x, index=dates) model = TimeSeriesModel(series) npt.assert_raises(KeyError, model._get_prediction_index, "1970-4-30", None) def test_period_index(): # test 1285 dates = pd.period_range(start="1/1/1990", periods=20, freq="M") x = np.arange(1, 21.) model = TimeSeriesModel(pd.Series(x, index=dates)) assert_equal(model._index.freqstr, "M") model = TimeSeriesModel(pd.Series(x, index=dates)) npt.assert_(model.data.freq == "M") def test_pandas_dates(): data = [988, 819, 964] dates = ['2016-01-01 12:00:00', '2016-02-01 12:00:00', '2016-03-01 12:00:00'] datetime_dates = pd.to_datetime(dates) result = pd.Series(data=data, index=datetime_dates, name='price') df = pd.DataFrame(data={'price': data}, index=pd.DatetimeIndex(dates, freq='MS')) model = TimeSeriesModel(df['price']) assert_equal(model.data.dates, result.index) def test_get_predict_start_end(): index = pd.date_range(start='1970-01-01', end='1990-01-01', freq='AS') endog = pd.Series(np.zeros(10), index[:10]) model = TimeSeriesModel(endog) predict_starts = [1, '1971-01-01', datetime(1971, 1, 1), index[1]] predict_ends = [20, '1990-01-01', datetime(1990, 1, 1), index[-1]] desired = (1, 9, 11) for start in predict_starts: for end in predict_ends: assert_equal(model._get_prediction_index(start, end)[:3], desired) statsmodels-0.12.2/statsmodels/tsa/base/tests/test_datetools.py000066400000000000000000000061521400612667500247650ustar00rootroot00000000000000from datetime import datetime import numpy.testing as npt from statsmodels.tsa.base.datetools import ( date_parser, dates_from_range) def test_regex_matching_month(): t1 = "1999m4" t2 = "1999:m4" t3 = "1999:mIV" t4 = "1999mIV" result = datetime(1999, 4, 30) npt.assert_equal(date_parser(t1), result) npt.assert_equal(date_parser(t2), result) npt.assert_equal(date_parser(t3), result) npt.assert_equal(date_parser(t4), result) def test_regex_matching_quarter(): t1 = "1999q4" t2 = "1999:q4" t3 = "1999:qIV" t4 = "1999qIV" result = datetime(1999, 12, 31) npt.assert_equal(date_parser(t1), result) npt.assert_equal(date_parser(t2), result) npt.assert_equal(date_parser(t3), result) npt.assert_equal(date_parser(t4), result) def test_dates_from_range(): results = [datetime(1959, 3, 31, 0, 0), datetime(1959, 6, 30, 0, 0), datetime(1959, 9, 30, 0, 0), datetime(1959, 12, 31, 0, 0), datetime(1960, 3, 31, 0, 0), datetime(1960, 6, 30, 0, 0), datetime(1960, 9, 30, 0, 0), datetime(1960, 12, 31, 0, 0), datetime(1961, 3, 31, 0, 0), datetime(1961, 6, 30, 0, 0), datetime(1961, 9, 30, 0, 0), datetime(1961, 12, 31, 0, 0), datetime(1962, 3, 31, 0, 0), datetime(1962, 6, 30, 0, 0)] dt_range = dates_from_range('1959q1', '1962q2') npt.assert_(results == dt_range) # test with starting period not the first with length results = results[2:] dt_range = dates_from_range('1959q3', length=len(results)) npt.assert_(results == dt_range) # check month results = [datetime(1959, 3, 31, 0, 0), datetime(1959, 4, 30, 0, 0), datetime(1959, 5, 31, 0, 0), datetime(1959, 6, 30, 0, 0), datetime(1959, 7, 31, 0, 0), datetime(1959, 8, 31, 0, 0), datetime(1959, 9, 30, 0, 0), datetime(1959, 10, 31, 0, 0), datetime(1959, 11, 30, 0, 0), datetime(1959, 12, 31, 0, 0), datetime(1960, 1, 31, 0, 0), datetime(1960, 2, 28, 0, 0), datetime(1960, 3, 31, 0, 0), datetime(1960, 4, 30, 0, 0), datetime(1960, 5, 31, 0, 0), datetime(1960, 6, 30, 0, 0), datetime(1960, 7, 31, 0, 0), datetime(1960, 8, 31, 0, 0), datetime(1960, 9, 30, 0, 0), datetime(1960, 10, 31, 0, 0), datetime(1960, 12, 31, 0, 0), datetime(1961, 1, 31, 0, 0), datetime(1961, 2, 28, 0, 0), datetime(1961, 3, 31, 0, 0), datetime(1961, 4, 30, 0, 0), datetime(1961, 5, 31, 0, 0), datetime(1961, 6, 30, 0, 0), datetime(1961, 7, 31, 0, 0), datetime(1961, 8, 31, 0, 0), datetime(1961, 9, 30, 0, 0), datetime(1961, 10, 31, 0, 0)] dt_range = dates_from_range("1959m3", length=len(results)) statsmodels-0.12.2/statsmodels/tsa/base/tests/test_prediction.py000066400000000000000000000027071400612667500251310ustar00rootroot00000000000000import numpy as np import pandas as pd import pytest from scipy import stats from statsmodels.tsa.base.prediction import PredictionResults @pytest.fixture(params=[True, False]) def data(request): mean = np.arange(10.0) variance = np.arange(1, 11.0) if not request.param: return mean, variance idx = pd.date_range("2000-1-1", periods=10, freq="M") return pd.Series(mean, index=idx), pd.Series(variance, index=idx) def test_basic(data): is_pandas = isinstance(data[0], pd.Series) pred = PredictionResults(data[0], data[1]) np.testing.assert_allclose(data[0], pred.predicted_mean) np.testing.assert_allclose(data[1], pred.var_pred_mean) if is_pandas: assert isinstance(pred.predicted_mean, pd.Series) assert isinstance(pred.var_pred_mean, pd.Series) assert isinstance(pred.se_mean, pd.Series) frame = pred.summary_frame() assert isinstance(frame, pd.DataFrame) assert list( frame.columns == ["mean", "mean_se", "mean_ci_lower", "mean_ci_upper"] ) @pytest.mark.parametrize("dist", [None, "norm", "t", stats.norm()]) def test_dist(data, dist): df = 10 if dist == "t" else None pred = PredictionResults(data[0], data[1], dist=dist, df=df) basic = PredictionResults(data[0], data[1]) ci = pred.conf_int() basic_ci = basic.conf_int() if dist == "t": assert np.all(np.asarray(ci != basic_ci)) else: assert np.all(np.asarray(ci == basic_ci)) statsmodels-0.12.2/statsmodels/tsa/base/tests/test_tsa_indexes.py000066400000000000000000001274661400612667500253110ustar00rootroot00000000000000""" Test index support in time series models 1. Test support for passing / constructing the underlying index in __init__ 2. Test wrapping of output using the underlying index 3. Test wrapping of prediction / forecasting using the underlying index or extensions of it. Author: Chad Fulton License: BSD-3 """ import pytest import warnings import numpy as np import pandas as pd from numpy.testing import assert_equal, assert_raises from statsmodels.tsa.base import tsa_model from statsmodels.tools.sm_exceptions import ValueWarning nobs = 5 base_dta = np.arange(nobs) dta = [ base_dta.tolist(), base_dta, pd.Series(base_dta), pd.DataFrame(base_dta) ] base_date_indexes = [ # (usual candidates) pd.date_range(start='1950-01-01', periods=nobs, freq='D'), pd.date_range(start='1950-01-01', periods=nobs, freq='W'), pd.date_range(start='1950-01-01', periods=nobs, freq='M'), pd.date_range(start='1950-01-01', periods=nobs, freq='Q'), pd.date_range(start='1950-01-01', periods=nobs, freq='A'), # (some more complicated frequencies) pd.date_range(start='1950-01-01', periods=nobs, freq='2Q'), pd.date_range(start='1950-01-01', periods=nobs, freq='2QS'), pd.date_range(start='1950-01-01', periods=nobs, freq='5s'), pd.date_range(start='1950-01-01', periods=nobs, freq='1D10min')] # Note: we separate datetime indexes and period indexes because the # date coercion does not handle string versions of PeriodIndex objects # most of the time. base_period_indexes = [ pd.period_range(start='1950-01-01', periods=nobs, freq='D'), pd.period_range(start='1950-01-01', periods=nobs, freq='W'), pd.period_range(start='1950-01-01', periods=nobs, freq='M'), pd.period_range(start='1950-01-01', periods=nobs, freq='Q'), pd.period_range(start='1950-01-01', periods=nobs, freq='A')] try: # Only later versions of pandas support these base_period_indexes += [ pd.period_range(start='1950-01-01', periods=nobs, freq='2Q'), pd.period_range(start='1950-01-01', periods=nobs, freq='5s'), pd.period_range(start='1950-01-01', periods=nobs, freq='1D10min')] except AttributeError: pass date_indexes = [ (x, None) for x in base_date_indexes] period_indexes = [ (x, None) for x in base_period_indexes] numpy_datestr_indexes = [ (x.map(str), x.freq) for x in base_date_indexes] list_datestr_indexes = [ (x.tolist(), y) for x, y in numpy_datestr_indexes] series_datestr_indexes = [ (pd.Series(x), y) for x, y in list_datestr_indexes] numpy_datetime_indexes = [ (pd.to_datetime(x).to_pydatetime(), x.freq) for x in base_date_indexes] list_datetime_indexes = [ (x.tolist(), y) for x, y in numpy_datetime_indexes] series_datetime_indexes = [ (pd.Series(x, dtype=object), y) for x, y in list_datetime_indexes] series_timestamp_indexes = [ (pd.Series(x), x.freq) for x in base_date_indexes] # Supported increment indexes supported_increment_indexes = [ (pd.Int64Index(np.arange(nobs)), None), (pd.RangeIndex(start=0, stop=nobs, step=1), None), (pd.RangeIndex(start=-5, stop=nobs - 5, step=1), None), (pd.RangeIndex(start=0, stop=nobs * 6, step=6), None)] # Supported date indexes # Only the Int64Index and the `date_indexes` are valid without # frequency information supported_date_indexes = ( numpy_datestr_indexes + list_datestr_indexes + series_datestr_indexes + numpy_datetime_indexes + list_datetime_indexes + series_datetime_indexes + series_timestamp_indexes) # Unsupported (but still valid) indexes unsupported_indexes = [ # Non-incrementing-from-zero indexes (np.arange(1, nobs+1), None), (np.arange(nobs)[::-1], None), # Float indexes, even if they increment from zero (np.arange(nobs) * 1.0, None), # Non-date-string indexes ([x for x in 'abcde'], None), # Non-date-object indexes ([str, 1, 'a', -30.1, {}], None), ] # Unsupported date indexes (i.e. those without inferrable frequency) unsupported_date_indexes = [ (['1950', '1952', '1941', '1954', '1991'], None), (['1950-01-01', '1950-01-02', '1950-01-03', '1950-01-04', '1950-01-06'], None) ] def test_instantiation_valid(): tsa_model.__warningregistry__ = {} # The primary goal of this test function is to make sure the # combinations that are supposed to be valid are actually valid, and # that valid but unsupported options give the appropriate warning # Secondarily, it also has some tests that invalid combinations raise # exceptions, although it's not intended to be comprehensive. # # Each of `endog`, `exog` can be in the following categories: # 0. None (only for exog) # 1. list # 2. numpy array # 3. pandas series # 4. pandas dataframe # # Each pandas index (of `endog`, `exog`, or passed to `dates`) can be: # 0. None # 1. RangeIndex (if applicable; i.e. if Pandas >= 0.18) # 2. Int64Index with values exactly equal to 0, 1, ..., nobs-1 # 3. DatetimeIndex with frequency # 4. PeriodIndex with frequency # 5. Anything that does not fall into the above categories also should # only raise an exception if it was passed to dates, and may trigger # a warning otherwise. # # `date` can be one of the following: # 0. None # 2. Pandas index #2 # 3. Pandas index #3 # 4. List of date strings (requires freq) # 5. List of datetime objects (requires freq) # 6. Array of date strings (requires freq) # 7. Array of datetime objects (requires freq) # 8. Series of date strings (requires freq) # 9. Series of datetime objects (requires freq) # 10. Series of pandas timestamps (requires freq) # 11. Anything that does not fall into the above categories should raise # an exception. # # `freq` can be: # 0. None # 1. Something that can be passed to `pd.to_offset` # 2. Anything that cannot should raise an Exception # # Each test will be denoted by: # endog.index:exog.index/date/freq where the corresponding # location is the integer from above; e.g. 1.0:0.0/9/1 corresponds to # - List endog (with no index) # - No exog # - Series of datetime objects # - Something valid for `pd.to_offset` (e.g. 'D', if that works with # dates) # # Notice that the endog.index:exog.index really collapses to a single # element, which is the evaluated `row_label`. This is first the exog # index, if exists, then the endog index, if it exists, or None # otherwise. **Thus, we will not test `exog` here.** # # Example valid combinations of row_label/date/freq include: # - */0/0 (i.e. anything is valid if date and freq are not passed) # - */%/% where %/% denotes a valid date/freq combination (i.e. any # row_label is valid if a valid date/freq combination is given) # # Example invalid combinations include: # - [1-2],[3-4].4/0/[1-2] (i.e. if have freq, then must have, or # coerce, a date index) # - */[4-10]/0 (i.e. for some types of dates, freq must be passed) # Baseline: list, numpy endog with no dates, no freq for endog in dta[:2]: # No indexes, should not raise warnings with warnings.catch_warnings(): warnings.simplefilter('error') mod = tsa_model.TimeSeriesModel(endog) assert_equal(isinstance(mod._index, (pd.Int64Index, pd.RangeIndex)), True) assert_equal(mod._index_none, True) assert_equal(mod._index_dates, False) assert_equal(mod._index_generated, True) assert_equal(mod.data.dates, None) assert_equal(mod.data.freq, None) # Test list, numpy endog, pandas w/o index; with dates / freq argument for endog in dta: # Supported date indexes, should not raise warnings, do not need freq with warnings.catch_warnings(): warnings.simplefilter('error') for ix, freq in date_indexes + period_indexes: mod = tsa_model.TimeSeriesModel(endog, dates=ix) if freq is None: freq = ix.freq if not isinstance(freq, str): freq = freq.freqstr assert_equal( isinstance(mod._index, (pd.DatetimeIndex, pd.PeriodIndex)), True) assert_equal(mod._index_none, False) assert_equal(mod._index_dates, True) assert_equal(mod._index_generated, False) assert_equal(mod._index.freq, mod._index_freq) assert_equal(mod.data.dates.equals(mod._index), True) assert_equal(mod.data.freq, freq) # Supported date indexes, should not raise warnings, can use valid freq with warnings.catch_warnings(): warnings.simplefilter('error') for ix, freq in date_indexes + period_indexes: mod = tsa_model.TimeSeriesModel(endog, dates=ix, freq=freq) if freq is None: freq = ix.freq if not isinstance(freq, str): freq = freq.freqstr assert_equal( isinstance(mod._index, (pd.DatetimeIndex, pd.PeriodIndex)), True) assert_equal(mod._index_none, False) assert_equal(mod._index_dates, True) assert_equal(mod._index_generated, False) assert_equal(mod._index.freq, mod._index_freq) assert_equal(mod.data.dates.equals(mod._index), True) assert_equal(mod.data.freq, freq) # Other supported indexes, with valid freq, should not raise warnings with warnings.catch_warnings(): warnings.simplefilter('error') for ix, freq in supported_date_indexes: mod = tsa_model.TimeSeriesModel(endog, dates=ix, freq=freq) if freq is None: freq = ix.freq if not isinstance(freq, str): freq = freq.freqstr assert_equal( isinstance(mod._index, (pd.DatetimeIndex, pd.PeriodIndex)), True) assert_equal(mod._index_none, False) assert_equal(mod._index_dates, True) assert_equal(mod._index_generated, False) assert_equal(mod._index.freq, mod._index_freq) assert_equal(mod.data.dates.equals(mod._index), True) assert_equal(mod.data.freq, freq) # Since only supported indexes are valid `dates` arguments, everything # else is invalid here for ix, freq in supported_increment_indexes + unsupported_indexes: assert_raises(ValueError, tsa_model.TimeSeriesModel, endog, dates=ix) # Test pandas (Series, DataFrame); with index (no dates/freq argument) for base_endog in dta[2:4]: # DatetimeIndex and PeriodIndex, should not raise warnings with warnings.catch_warnings(): warnings.simplefilter('error') for ix, freq in date_indexes + period_indexes: endog = base_endog.copy() endog.index = ix mod = tsa_model.TimeSeriesModel(endog) if freq is None: freq = ix.freq if not isinstance(freq, str): freq = freq.freqstr assert_equal( isinstance(mod._index, (pd.DatetimeIndex, pd.PeriodIndex)), True) assert_equal(mod._index_none, False) assert_equal(mod._index_dates, True) assert_equal(mod._index_generated, False) assert_equal(mod._index.freq, mod._index_freq) assert_equal(mod.data.dates.equals(mod._index), True) assert_equal(mod.data.freq, freq) # Increment index (this is a "supported" index in the sense that it # does not raise a warning, but obviously not a date index) endog = base_endog.copy() endog.index = supported_increment_indexes[0][0] mod = tsa_model.TimeSeriesModel(endog) assert_equal(type(mod._index) == pd.Int64Index, True) assert_equal(mod._index_none, False) assert_equal(mod._index_dates, False) assert_equal(mod._index_generated, False) assert_equal(mod._index_freq, None) assert_equal(mod.data.dates, None) assert_equal(mod.data.freq, None) # RangeIndex (start=0, end=nobs, so equivalent to increment index) endog = base_endog.copy() endog.index = supported_increment_indexes[1][0] mod = tsa_model.TimeSeriesModel(endog) assert_equal(type(mod._index) == pd.RangeIndex, True) assert_equal(mod._index_none, False) assert_equal(mod._index_dates, False) assert_equal(mod._index_generated, False) assert_equal(mod._index_freq, None) assert_equal(mod.data.dates, None) assert_equal(mod.data.freq, None) # Supported indexes *when a freq is given*, should not raise a warning with warnings.catch_warnings(): warnings.simplefilter('error') for ix, freq in supported_date_indexes: endog = base_endog.copy() endog.index = ix mod = tsa_model.TimeSeriesModel(endog, freq=freq) if freq is None: freq = ix.freq if not isinstance(freq, str): freq = freq.freqstr assert_equal( isinstance(mod._index, (pd.DatetimeIndex, pd.PeriodIndex)), True) assert_equal(mod._index_none, False) assert_equal(mod._index_dates, True) assert_equal(mod._index_generated, False) assert_equal(mod._index.freq, mod._index_freq) assert_equal(mod.data.dates.equals(mod._index), True) assert_equal(mod.data.freq, freq) # Unsupported (or any) indexes to the given series, *when a supported # date and freq is given*, should not raise a warning with warnings.catch_warnings(): warnings.simplefilter('error') for ix, freq in supported_date_indexes: endog = base_endog.copy() endog.index = unsupported_indexes[0][0] mod = tsa_model.TimeSeriesModel(endog, dates=ix, freq=freq) if freq is None: freq = ix.freq if not isinstance(freq, str): freq = freq.freqstr assert_equal( isinstance(mod._index, (pd.DatetimeIndex, pd.PeriodIndex)), True) assert_equal(mod._index_none, False) assert_equal(mod._index_dates, True) assert_equal(mod._index_generated, False) assert_equal(mod._index.freq, mod._index_freq) assert_equal(mod.data.dates.equals(mod._index), True) assert_equal(mod.data.freq, freq) # Date indexes with inferrable freq, but no given freq, should all give # warnings message = ('No frequency information was provided,' ' so inferred frequency %s will be used.') with warnings.catch_warnings(record=True) as w: warnings.simplefilter('always') for ix, freq in supported_date_indexes: endog = base_endog.copy() endog.index = ix mod = tsa_model.TimeSeriesModel(endog) if freq is None: freq = ix.freq if not isinstance(freq, str): freq = freq.freqstr assert_equal(type(mod._index) == pd.DatetimeIndex, True) assert_equal(mod._index_none, False) assert_equal(mod._index_dates, True) assert_equal(mod._index_generated, False) assert_equal(mod._index.freq, mod._index_freq) assert_equal(mod.data.dates.equals(mod._index), True) # Note: here, we need to hedge the test a little bit because # inferred frequencies are not always the same as the original # frequency. From the examples above, when the actual freq is # 2QS-OCT, the inferred freq is 2QS-JAN. This is an issue with # inferred frequencies, but since we are warning the user, it's # not a failure of the code. Thus we only test the "major" part # of the freq, and just test that the right message is given # (even though it will not have the actual freq of the data in # it). assert_equal(mod.data.freq.split('-')[0], freq.split('-')[0]) assert_equal(str(w[-1].message), message % mod.data.freq) # Unsupported (but valid) indexes, should all give warnings message = ('An unsupported index was provided and will be' ' ignored when e.g. forecasting.') with warnings.catch_warnings(record=True) as w: warnings.simplefilter('always') for ix, freq in unsupported_indexes: endog = base_endog.copy() endog.index = ix mod = tsa_model.TimeSeriesModel(endog) assert_equal(isinstance(mod._index, (pd.Int64Index, pd.RangeIndex)), True) assert_equal(mod._index_none, False) assert_equal(mod._index_dates, False) assert_equal(mod._index_generated, True) assert_equal(mod._index_freq, None) assert_equal(mod.data.dates, None) assert_equal(mod.data.freq, None) assert_equal(str(w[0].message), message) # Date indexes without inferrable freq, and with no given freq, should # all give warnings message = ('A date index has been provided, but it has no' ' associated frequency information and so will be' ' ignored when e.g. forecasting.') with warnings.catch_warnings(record=True) as w: warnings.simplefilter('always') for ix, freq in unsupported_date_indexes: endog = base_endog.copy() endog.index = ix mod = tsa_model.TimeSeriesModel(endog) assert_equal(isinstance(mod._index, (pd.Int64Index, pd.RangeIndex)), True) assert_equal(mod._index_none, False) assert_equal(mod._index_dates, False) assert_equal(mod._index_generated, True) assert_equal(mod._index_freq, None) assert_equal(mod.data.dates, None) assert_equal(mod.data.freq, None) assert_equal(str(w[0].message), message) # Test (invalid) freq with no index endog = dta[0] assert_raises(ValueError, tsa_model.TimeSeriesModel, endog, freq=date_indexes[1][0].freq) # Test conflicting index, freq specifications endog = dta[2].copy() endog.index = date_indexes[0][0] assert_raises(ValueError, tsa_model.TimeSeriesModel, endog, freq=date_indexes[1][0].freq) # Test unsupported index, but a freq specification endog = dta[2].copy() endog.index = unsupported_indexes[0][0] assert_raises(ValueError, tsa_model.TimeSeriesModel, endog, freq=date_indexes[1][0].freq) # Test index that can coerce to date time but incorrect freq endog = dta[2].copy() endog.index = numpy_datestr_indexes[0][0] assert_raises(ValueError, tsa_model.TimeSeriesModel, endog, freq=date_indexes[1][0].freq) def test_prediction_increment_unsupported(): # a. Generated from unsupported index endog = dta[2].copy() endog.index = unsupported_indexes[-2][0] with warnings.catch_warnings(record=True) as w: warnings.simplefilter('ignore') mod = tsa_model.TimeSeriesModel(endog) # Tests three common use cases: basic prediction, negative indexes, and # out-of-sample indexes. # Basic prediction: [0, end]; notice that since this is an in-sample # prediction, the index returned is the (unsupported) original index start_key = 0 end_key = None start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 0) assert_equal(end, nobs-1) assert_equal(out_of_sample, 0) assert_equal(prediction_index.equals(mod.data.row_labels), True) # Negative index: [-2, end]; notice that since this is an in-sample # prediction, the index returned is a piece of the (unsupported) # original index start_key = -2 end_key = -1 start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 3) assert_equal(end, 4) assert_equal(out_of_sample, 0) assert_equal(prediction_index.equals(mod.data.row_labels[3:]), True) # Forecasting: [1, 5], notice that since an unsupported index was given, # a warning will be issued start_key = 1 end_key = nobs message = ('No supported index is available.' ' Prediction results will be given with' ' an integer index beginning at `start`.') with warnings.catch_warnings(record=True) as w: warnings.simplefilter('always') start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(str(w[0].message), message) assert_equal(start, 1) assert_equal(end, 4) assert_equal(out_of_sample, 1) assert_equal(prediction_index.equals(pd.Index(np.arange(1, 6))), True) # Test getting a location that exists in the (internal) index loc, index, index_was_expanded = mod._get_index_loc(2) assert_equal(loc, 2) desired_index = pd.RangeIndex(start=0, stop=3, step=1) assert_equal(index.equals(desired_index), True) assert_equal(index_was_expanded, False) # Test getting a location that exists in the (internal) index # when using the function that alternatively falls back to the row labels loc, index, index_was_expanded = mod._get_index_label_loc(2) assert_equal(loc, 2) desired_index = pd.RangeIndex(start=0, stop=3, step=1) assert_equal(index.equals(desired_index), True) assert_equal(index_was_expanded, False) # Test getting a location that exists in the given (unsupported) index # Note that the returned index is now like the row labels loc, index, index_was_expanded = mod._get_index_label_loc('c') assert_equal(loc, 2) desired_index = mod.data.row_labels[:3] assert_equal(index.equals(desired_index), True) assert_equal(index_was_expanded, False) def test_prediction_increment_nonpandas(): endog = dta[0] mod = tsa_model.TimeSeriesModel(endog) # Tests three common use cases: basic prediction, negative indexes, and # out-of-sample indexes. # Basic prediction: [0, end]; since there was no index at all and the data # is not Pandas, the returned prediction_index is None start_key = 0 end_key = None start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 0) assert_equal(end, nobs-1) assert_equal(out_of_sample, 0) assert_equal(prediction_index is None, True) # Negative index: [-2, end]; since there was no index at all and the data # is not Pandas, the returned prediction_index is None start_key = -2 end_key = -1 start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 3) assert_equal(end, 4) assert_equal(out_of_sample, 0) assert_equal(prediction_index is None, True) # Forecasting: [1, 5]; since there was no index at all and the data # is not Pandas, the returned prediction_index is None start_key = 1 end_key = nobs start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 1) assert_equal(end, 4) assert_equal(out_of_sample, 1) assert_equal(prediction_index is None, True) # Test getting a location that exists in the (internal) index loc, index, index_was_expanded = mod._get_index_loc(2) assert_equal(loc, 2) desired_index = pd.RangeIndex(start=0, stop=3, step=1) assert_equal(index.equals(desired_index), True) assert_equal(index_was_expanded, False) # Test getting a location that exists in the (internal) index # when using the function that alternatively falls back to the row labels loc, index, index_was_expanded = mod._get_index_label_loc(2) assert_equal(loc, 2) desired_index = pd.RangeIndex(start=0, stop=3, step=1) assert_equal(index.equals(desired_index), True) assert_equal(index_was_expanded, False) def test_prediction_increment_pandas_noindex(): endog = dta[2].copy() mod = tsa_model.TimeSeriesModel(endog) # Tests three common use cases: basic prediction, negative indexes, and # out-of-sample indexes. # Basic prediction: [0, end]; since there was no index and the data is # Pandas, the index is the generated incrementing index, and no warning is # issued start_key = 0 end_key = None start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 0) assert_equal(end, nobs-1) assert_equal(out_of_sample, 0) assert_equal(prediction_index.equals(mod._index), True) # Negative index: [-2, end]; since there was no index and the data is # Pandas, the index is the generated incrementing index, and no warning is # issued start_key = -2 end_key = -1 start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 3) assert_equal(end, 4) assert_equal(out_of_sample, 0) assert_equal(prediction_index.equals(mod._index[3:]), True) # Forecasting: [1, 5]; since there was no index and the data is # Pandas, the index is the generated incrementing index, and no warning is # issued start_key = 1 end_key = nobs start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 1) assert_equal(end, 4) assert_equal(out_of_sample, 1) assert_equal(prediction_index.equals(pd.Index(np.arange(1, 6))), True) def test_prediction_increment_pandas_dates_daily(): # Date-based index endog = dta[2].copy() endog.index = date_indexes[0][0] # Daily, 1950-01-01, 1950-01-02, ... mod = tsa_model.TimeSeriesModel(endog) # Tests three common use cases: basic prediction, negative indexes, and # out-of-sample indexes. # Basic prediction: [0, end]; the index is the date index start_key = 0 end_key = None start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 0) assert_equal(end, nobs-1) assert_equal(out_of_sample, 0) assert type(prediction_index) is type(endog.index) # noqa: E721 assert_equal(prediction_index.equals(mod._index), True) # In-sample prediction: [0, 3]; the index is a subset of the date index start_key = 0 end_key = 3 start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 0) assert_equal(end, 3) assert_equal(out_of_sample, 0) assert type(prediction_index) is type(endog.index) # noqa: E721 assert_equal(prediction_index.equals(mod._index[:4]), True) # Negative index: [-2, end] start_key = -2 end_key = -1 start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 3) assert_equal(end, 4) assert_equal(out_of_sample, 0) assert type(prediction_index) is type(endog.index) # noqa: E721 assert_equal(prediction_index.equals(mod._index[3:]), True) # Forecasting: [1, 5]; the index is an extended version of the date index start_key = 1 end_key = nobs start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 1) assert_equal(end, 4) assert_equal(out_of_sample, 1) desired_index = pd.date_range(start='1950-01-02', periods=5, freq='D') assert_equal(prediction_index.equals(desired_index), True) # Date-based keys # In-sample prediction (equivalent to [1, 3]) start_key = '1950-01-02' end_key = '1950-01-04' start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 1) assert_equal(end, 3) assert_equal(out_of_sample, 0) assert type(prediction_index) is type(endog.index) # noqa: E721 assert_equal(prediction_index.equals(mod._index[1:4]), True) # Out-of-sample forecasting (equivalent to [0, 5]) start_key = '1950-01-01' end_key = '1950-01-08' start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 0) assert_equal(end, 4) assert_equal(out_of_sample, 3) desired_index = pd.date_range(start='1950-01-01', periods=8, freq='D') assert_equal(prediction_index.equals(desired_index), True) # Test getting a location that exists in the (internal) index loc, index, index_was_expanded = mod._get_index_loc(2) assert_equal(loc, 2) desired_index = pd.date_range(start='1950-01-01', periods=3, freq='D') assert_equal(index.equals(desired_index), True) assert_equal(index_was_expanded, False) # Test getting a location that exists in the (internal) index # when using the function that alternatively falls back to the row labels loc, index, index_was_expanded = mod._get_index_label_loc(2) assert_equal(loc, 2) desired_index = pd.date_range(start='1950-01-01', periods=3, freq='D') assert_equal(index.equals(desired_index), True) assert_equal(index_was_expanded, False) # Test getting a location that exists in the given (unsupported) index # Note that the returned index is now like the row labels loc, index, index_was_expanded = mod._get_index_label_loc('1950-01-03') assert_equal(loc, 2) desired_index = mod.data.row_labels[:3] assert_equal(index.equals(desired_index), True) assert_equal(index_was_expanded, False) def test_prediction_increment_pandas_dates_monthly(): # Date-based index endog = dta[2].copy() endog.index = date_indexes[2][0] # Monthly, 1950-01, 1950-02, ... mod = tsa_model.TimeSeriesModel(endog) # Tests three common use cases: basic prediction, negative indexes, and # out-of-sample indexes. # Basic prediction: [0, end]; the index is the date index start_key = 0 end_key = None start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 0) assert_equal(end, nobs-1) assert_equal(out_of_sample, 0) assert type(prediction_index) is type(endog.index) # noqa: E721 assert_equal(prediction_index.equals(mod._index), True) # In-sample prediction: [0, 3]; the index is a subset of the date index start_key = 0 end_key = 3 start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 0) assert_equal(end, 3) assert_equal(out_of_sample, 0) assert type(prediction_index) is type(endog.index) # noqa: E721 assert_equal(prediction_index.equals(mod._index[:4]), True) # Negative index: [-2, end] start_key = -2 end_key = -1 start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 3) assert_equal(end, 4) assert_equal(out_of_sample, 0) assert type(prediction_index) is type(endog.index) # noqa: E721 assert_equal(prediction_index.equals(mod._index[3:]), True) # Forecasting: [1, 5]; the index is an extended version of the date index start_key = 1 end_key = nobs start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 1) assert_equal(end, 4) assert_equal(out_of_sample, 1) desired_index = pd.date_range(start='1950-02', periods=5, freq='M') assert_equal(prediction_index.equals(desired_index), True) # Date-based keys # In-sample prediction (equivalent to [1, 3]) start_key = '1950-02' end_key = '1950-04' start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 1) assert_equal(end, 3) assert_equal(out_of_sample, 0) assert type(prediction_index) is type(endog.index) # noqa: E721 assert_equal(prediction_index.equals(mod._index[1:4]), True) # Out-of-sample forecasting (equivalent to [0, 5]) start_key = '1950-01' end_key = '1950-08' start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 0) assert_equal(end, 4) assert_equal(out_of_sample, 3) desired_index = pd.date_range(start='1950-01', periods=8, freq='M') assert_equal(prediction_index.equals(desired_index), True) # Test getting a location that exists in the (internal) index loc, index, index_was_expanded = mod._get_index_loc(2) assert_equal(loc, 2) desired_index = pd.date_range(start='1950-01', periods=3, freq='M') assert_equal(index.equals(desired_index), True) assert_equal(index_was_expanded, False) # Test getting a location that exists in the (internal) index # when using the function that alternatively falls back to the row labels loc, index, index_was_expanded = mod._get_index_label_loc(2) assert_equal(loc, 2) desired_index = pd.date_range(start='1950-01', periods=3, freq='M') assert_equal(index.equals(desired_index), True) assert_equal(index_was_expanded, False) # Test getting a location that exists in the given (unsupported) index # Note that the returned index is now like the row labels loc, index, index_was_expanded = mod._get_index_label_loc('1950-03') assert_equal(loc, slice(2, 3, None)) desired_index = mod.data.row_labels[:3] assert_equal(index.equals(desired_index), True) assert_equal(index_was_expanded, False) def test_prediction_increment_pandas_dates_nanosecond(): # Date-based index endog = dta[2].copy() endog.index = pd.date_range(start='1970-01-01', periods=len(endog), freq='N') mod = tsa_model.TimeSeriesModel(endog) # Tests three common use cases: basic prediction, negative indexes, and # out-of-sample indexes. # Basic prediction: [0, end]; the index is the date index start_key = 0 end_key = None start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 0) assert_equal(end, nobs-1) assert_equal(out_of_sample, 0) assert type(prediction_index) is type(endog.index) # noqa: E721 assert_equal(prediction_index.equals(mod._index), True) # Negative index: [-2, end] start_key = -2 end_key = -1 start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 3) assert_equal(end, 4) assert_equal(out_of_sample, 0) assert type(prediction_index) is type(endog.index) # noqa: E721 assert_equal(prediction_index.equals(mod._index[3:]), True) # Forecasting: [1, 5]; the index is an extended version of the date index start_key = 1 end_key = nobs start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 1) assert_equal(end, 4) assert_equal(out_of_sample, 1) desired_index = pd.date_range(start='1970-01-01', periods=6, freq='N')[1:] assert_equal(prediction_index.equals(desired_index), True) # Date-based keys start_key = pd.Timestamp('1970-01-01') end_key = pd.Timestamp(start_key.value + 7) start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 0) assert_equal(end, 4) assert_equal(out_of_sample, 3) desired_index = pd.date_range(start='1970-01-01', periods=8, freq='N') assert_equal(prediction_index.equals(desired_index), True) def test_range_index(): tsa_model.__warningregistry__ = {} endog = pd.Series(np.random.normal(size=5)) assert_equal(isinstance(endog.index, pd.RangeIndex), True) # Warning should not be given with warnings.catch_warnings(record=True) as w: warnings.simplefilter('always') mod = tsa_model.TimeSeriesModel(endog) assert_equal(len(w), 0) def test_prediction_rangeindex(): index = supported_increment_indexes[2][0] endog = pd.Series(dta[0], index=index) mod = tsa_model.TimeSeriesModel(endog) # Tests three common use cases: basic prediction, negative indexes, and # out-of-sample indexes. # Basic prediction: [0, end] start_key = 0 end_key = None start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 0) assert_equal(end, nobs - 1) assert_equal(out_of_sample, 0) desired_index = pd.RangeIndex(start=-5, stop=0, step=1) assert_equal(prediction_index.equals(desired_index), True) # Negative index: [-2, end] start_key = -2 end_key = -1 start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 3) assert_equal(end, 4) assert_equal(out_of_sample, 0) desired_index = pd.RangeIndex(start=-2, stop=0, step=1) assert_equal(prediction_index.equals(desired_index), True) # Forecasting: [1, 5] start_key = 1 end_key = nobs start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 1) assert_equal(end, 4) assert_equal(out_of_sample, 1) desired_index = pd.RangeIndex(start=-4, stop=1, step=1) assert_equal(prediction_index.equals(desired_index), True) def test_prediction_rangeindex_withstep(): index = supported_increment_indexes[3][0] endog = pd.Series(dta[0], index=index) mod = tsa_model.TimeSeriesModel(endog) # Tests three common use cases: basic prediction, negative indexes, and # out-of-sample indexes. # Basic prediction: [0, end] start_key = 0 end_key = None start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 0) assert_equal(end, nobs - 1) assert_equal(out_of_sample, 0) desired_index = pd.RangeIndex(start=0, stop=nobs * 6, step=6) assert_equal(prediction_index.equals(desired_index), True) # Negative index: [-2, end] start_key = -2 end_key = -1 start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 3) assert_equal(end, 4) assert_equal(out_of_sample, 0) desired_index = pd.RangeIndex(start=3 * 6, stop=nobs * 6, step=6) assert_equal(prediction_index.equals(desired_index), True) # Forecasting: [1, 5] start_key = 1 end_key = nobs start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(start, 1) assert_equal(end, 4) assert_equal(out_of_sample, 1) desired_index = pd.RangeIndex(start=1 * 6, stop=(nobs + 1) * 6, step=6) assert_equal(prediction_index.equals(desired_index), True) # Test getting a location that exists in the index loc, index, index_was_expanded = mod._get_index_loc(2) assert_equal(loc, 2) desired_index = pd.RangeIndex(start=0, stop=3 * 6, step=6) assert_equal(index.equals(desired_index), True) assert_equal(index_was_expanded, False) def test_custom_index(): tsa_model.__warningregistry__ = {} endog = pd.Series(np.random.normal(size=5), index=['a', 'b', 'c', 'd', 'e']) message = ('An unsupported index was provided and will be ignored when' ' e.g. forecasting.') with warnings.catch_warnings(record=True) as w: warnings.simplefilter('always') mod = tsa_model.TimeSeriesModel(endog) assert_equal(str(w[0].message), message) start_key = -2 end_key = -1 start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) # Test the default output index assert_equal(prediction_index.equals(pd.Index(['d', 'e'])), True) # Test custom output index start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key, index=['f', 'g'])) assert_equal(prediction_index.equals(pd.Index(['f', 'g'])), True) # Test getting a location in the index w/o fallback to row labels loc, index, index_was_expanded = mod._get_index_loc(2) assert_equal(loc, 2) assert_equal(index.equals(pd.RangeIndex(0, 3)), True) assert_equal(index_was_expanded, False) assert_equal(index_was_expanded, False) # Test getting an invalid location in the index w/ fallback to row labels with pytest.raises(KeyError): mod._get_index_loc('c') # Test getting a location in the index w/ fallback to row labels loc, index, index_was_expanded = mod._get_index_label_loc('c') assert_equal(loc, 2) assert_equal(index.equals(pd.Index(['a', 'b', 'c'])), True) assert_equal(index_was_expanded, False) # Test getting an invalid location in the index w/ fallback to row labels with pytest.raises(KeyError): mod._get_index_label_loc('aa') # Test out-of-sample start_key = 4 end_key = 5 message = ('No supported index is available.' ' Prediction results will be given with' ' an integer index beginning at `start`.') with warnings.catch_warnings(record=True) as w: warnings.simplefilter('always') start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key)) assert_equal(prediction_index.equals(pd.Index([4, 5])), True) assert_equal(str(w[0].message), message) # Test out-of-sample custom index start, end, out_of_sample, prediction_index = ( mod._get_prediction_index(start_key, end_key, index=['f', 'g'])) assert_equal(prediction_index.equals(pd.Index(['f', 'g'])), True) # Test invalid custom index assert_raises(ValueError, mod._get_prediction_index, start_key, end_key, index=['f', 'g', 'h']) def test_nonmonotonic_periodindex(): # Create a nonmonotonic period index tmp = pd.period_range(start=2000, end=2002, freq='A') index = tmp.tolist() + tmp.tolist() endog = pd.Series(np.zeros(len(index)), index=index) message = ('A date index has been provided, but it is not' ' monotonic and so will be ignored when e.g.' ' forecasting.') with pytest.warns(ValueWarning, match=message): tsa_model.TimeSeriesModel(endog) @pytest.mark.xfail(reason='Pandas PeriodIndex.is_full does not yet work for' ' all frequencies (e.g. frequencies with a' ' multiplier, like "2Q").') def test_nonfull_periodindex(): index = pd.PeriodIndex(['2000-01', '2000-03'], freq='M') endog = pd.Series(np.zeros(len(index)), index=index) message = ('A Period index has been provided, but it is not' ' full and so will be ignored when e.g.' ' forecasting.') with pytest.warns(ValueWarning, match=message): tsa_model.TimeSeriesModel(endog) def test_get_index_loc_quarterly(): # See GH#6339 ix = pd.date_range('2000Q1', periods=8, freq='QS') endog = pd.Series(np.zeros(8), index=ix) mod = tsa_model.TimeSeriesModel(endog) loc, index, _ = mod._get_index_loc('2003Q2') assert_equal(index[loc], pd.Timestamp('2003Q2')) statsmodels-0.12.2/statsmodels/tsa/base/tsa_model.py000066400000000000000000001035061400612667500225360ustar00rootroot00000000000000from statsmodels.compat.pandas import is_numeric_dtype import numbers import warnings import numpy as np from pandas import (to_datetime, Int64Index, DatetimeIndex, Period, PeriodIndex, RangeIndex, Timestamp, Series, Index, Float64Index, date_range, period_range) from pandas.tseries.frequencies import to_offset from statsmodels.base.data import PandasData import statsmodels.base.model as base import statsmodels.base.wrapper as wrap from statsmodels.tools.sm_exceptions import ValueWarning _tsa_doc = """ %(model)s Parameters ---------- %(params)s dates : array_like, optional An array-like object of datetime objects. If a pandas object is given for endog or exog, it is assumed to have a DateIndex. freq : str, optional The frequency of the time-series. A Pandas offset or 'B', 'D', 'W', 'M', 'A', or 'Q'. This is optional if dates are given. %(extra_params)s %(extra_sections)s""" _model_doc = "Timeseries model base class" _generic_params = base._model_params_doc _missing_param_doc = base._missing_param_doc def get_index_loc(key, index): """ Get the location of a specific key in an index Parameters ---------- key : label The key for which to find the location if the underlying index is a DateIndex or a location if the underlying index is a RangeIndex or an Int64Index. index : pd.Index The index to search. Returns ------- loc : int The location of the key index : pd.Index The index including the key; this is a copy of the original index unless the index had to be expanded to accommodate `key`. index_was_expanded : bool Whether or not the index was expanded to accommodate `key`. Notes ----- If `key` is past the end of of the given index, and the index is either an Int64Index or a date index, this function extends the index up to and including key, and then returns the location in the new index. """ base_index = index index = base_index date_index = isinstance(base_index, (PeriodIndex, DatetimeIndex)) int_index = isinstance(base_index, Int64Index) range_index = isinstance(base_index, RangeIndex) index_class = type(base_index) nobs = len(index) # Special handling for RangeIndex if range_index and isinstance(key, (int, np.integer)): # Negative indices (that lie in the Index) if key < 0 and -key <= nobs: key = nobs + key # Out-of-sample (note that we include key itself in the new index) elif key > nobs - 1: # See gh5835. Remove the except after pandas 0.25 required. try: base_index_start = base_index.start base_index_step = base_index.step except AttributeError: base_index_start = base_index._start base_index_step = base_index._step stop = base_index_start + (key + 1) * base_index_step index = RangeIndex(start=base_index_start, stop=stop, step=base_index_step) # Special handling for Int64Index if (not range_index and int_index and not date_index and isinstance(key, (int, np.integer))): # Negative indices (that lie in the Index) if key < 0 and -key <= nobs: key = nobs + key # Out-of-sample (note that we include key itself in the new index) elif key > base_index[-1]: index = Int64Index(np.arange(base_index[0], int(key + 1))) # Special handling for date indexes if date_index: # Use index type to choose creation function if index_class is DatetimeIndex: index_fn = date_range else: index_fn = period_range # Integer key (i.e. already given a location) if isinstance(key, (int, np.integer)): # Negative indices (that lie in the Index) if key < 0 and -key < nobs: key = index[nobs + key] # Out-of-sample (note that we include key itself in the new # index) elif key > len(base_index) - 1: index = index_fn(start=base_index[0], periods=int(key + 1), freq=base_index.freq) key = index[-1] else: key = index[key] # Other key types (i.e. string date or some datetime-like object) else: # Covert the key to the appropriate date-like object if index_class is PeriodIndex: date_key = Period(key, freq=base_index.freq) else: date_key = Timestamp(key, freq=base_index.freq) # Out-of-sample if date_key > base_index[-1]: # First create an index that may not always include `key` index = index_fn(start=base_index[0], end=date_key, freq=base_index.freq) # Now make sure we include `key` if not index[-1] == date_key: index = index_fn(start=base_index[0], periods=len(index) + 1, freq=base_index.freq) # To avoid possible inconsistencies with `get_loc` below, # set the key directly equal to the last index location key = index[-1] # Get the location if date_index: # (note that get_loc will throw a KeyError if key is invalid) loc = index.get_loc(key) elif int_index or range_index: # For Int64Index and RangeIndex, key is assumed to be the location # and not an index value (this assumption is required to support # RangeIndex) try: index[key] # We want to raise a KeyError in this case, to keep the exception # consistent across index types. # - Attempting to index with an out-of-bound location (e.g. # index[10] on an index of length 9) will raise an IndexError # (as of Pandas 0.22) # - Attemtping to index with a type that cannot be cast to integer # (e.g. a non-numeric string) will raise a ValueError if the # index is RangeIndex (otherwise will raise an IndexError) # (as of Pandas 0.22) except (IndexError, ValueError) as e: raise KeyError(str(e)) loc = key else: loc = index.get_loc(key) # Check if we now have a modified index index_was_expanded = index is not base_index # Return the index through the end of the loc / slice if isinstance(loc, slice): end = loc.stop - 1 else: end = loc return loc, index[:end + 1], index_was_expanded def get_index_label_loc(key, index, row_labels): """ Get the location of a specific key in an index or model row labels Parameters ---------- key : label The key for which to find the location if the underlying index is a DateIndex or is only being used as row labels, or a location if the underlying index is a RangeIndex or an Int64Index. index : pd.Index The index to search. row_labels : pd.Index Row labels to search if key not found in index Returns ------- loc : int The location of the key index : pd.Index The index including the key; this is a copy of the original index unless the index had to be expanded to accommodate `key`. index_was_expanded : bool Whether or not the index was expanded to accommodate `key`. Notes ----- This function expands on `get_index_loc` by first trying the given base index (or the model's index if the base index was not given) and then falling back to try again with the model row labels as the base index. """ try: loc, index, index_was_expanded = get_index_loc(key, index) except KeyError as e: try: if not isinstance(key, (int, np.integer)): loc = row_labels.get_loc(key) else: raise # Require scalar # Pandas may return a slice if there are multiple matching # locations that are monotonic increasing (otherwise it may # return an array of integer locations, see below). if isinstance(loc, slice): loc = loc.start if isinstance(loc, np.ndarray): # Pandas may return a mask (boolean array), for e.g.: # pd.Index(list('abcb')).get_loc('b') if loc.dtype == bool: # Return the first True value # (we know there is at least one True value if we're # here because otherwise the get_loc call would have # raised an exception) loc = np.argmax(loc) # Finally, Pandas may return an integer array of # locations that match the given value, for e.g. # pd.DatetimeIndex(['2001-02', '2001-01']).get_loc('2001') # (this appears to be slightly undocumented behavior, since # only int, slice, and mask are mentioned in docs for # pandas.Index.get_loc as of 0.23.4) else: loc = loc[0] if not isinstance(loc, numbers.Integral): raise index = row_labels[:loc + 1] index_was_expanded = False except: raise e return loc, index, index_was_expanded def get_prediction_index(start, end, nobs, base_index, index=None, silent=False, index_none=False, index_generated=None, data=None): """ Get the location of a specific key in an index or model row labels Parameters ---------- start : label The key at which to start prediction. Depending on the underlying model's index, may be an integer, a date (string, datetime object, pd.Timestamp, or pd.Period object), or some other object in the model's row labels. end : label The key at which to end prediction (note that this key will be *included* in prediction). Depending on the underlying model's index, may be an integer, a date (string, datetime object, pd.Timestamp, or pd.Period object), or some other object in the model's row labels. nobs : int base_index : pd.Index index : pd.Index, optional Optionally an index to associate the predicted results to. If None, an attempt is made to create an index for the predicted results from the model's index or model's row labels. silent : bool, optional Argument to silence warnings. Returns ------- start : int The index / observation location at which to begin prediction. end : int The index / observation location at which to end in-sample prediction. The maximum value for this is nobs-1. out_of_sample : int The number of observations to forecast after the end of the sample. prediction_index : pd.Index or None The index associated with the prediction results. This index covers the range [start, end + out_of_sample]. If the model has no given index and no given row labels (i.e. endog/exog is not Pandas), then this will be None. Notes ----- The arguments `start` and `end` behave differently, depending on if they are integer or not. If either is an integer, then it is assumed to refer to a *location* in the index, not to an index value. On the other hand, if it is a date string or some other type of object, then it is assumed to refer to an index *value*. In all cases, the returned `start` and `end` values refer to index *locations* (so in the former case, the given location is validated and returned whereas in the latter case a location is found that corresponds to the given index value). This difference in behavior is necessary to support `RangeIndex`. This is because integers for a RangeIndex could refer either to index values or to index locations in an ambiguous way (while for `Int64Index`, since we have required them to be full indexes, there is no ambiguity). """ # Convert index keys (start, end) to index locations and get associated # indexes. try: start, _, start_oos = get_index_label_loc(start, base_index, data.row_labels) except KeyError: raise KeyError('The `start` argument could not be matched to a' ' location related to the index of the data.') if end is None: end = max(start, len(base_index) - 1) try: end, end_index, end_oos = get_index_label_loc(end, base_index, data.row_labels) except KeyError: raise KeyError('The `end` argument could not be matched to a' ' location related to the index of the data.') # Handle slices (if the given index keys cover more than one date) if isinstance(start, slice): start = start.start if isinstance(end, slice): end = end.stop - 1 # Get the actual index for the prediction prediction_index = end_index[start:] # Validate prediction options if end < start: raise ValueError('Prediction must have `end` after `start`.') # Handle custom prediction index # First, if we were given an index, check that it's the right size and # use it if so if index is not None: if not len(prediction_index) == len(index): raise ValueError('Invalid `index` provided in prediction.' ' Must have length consistent with `start`' ' and `end` arguments.') # But if we weren't given Pandas input, this index will not be # used because the data will not be wrapped; in that case, issue # a warning if not isinstance(data, PandasData) and not silent: warnings.warn('Because the model data (`endog`, `exog`) were' ' not given as Pandas objects, the prediction' ' output will be Numpy arrays, and the given' ' `index` argument will only be used' ' internally.', ValueWarning) prediction_index = Index(index) # Now, if we *do not* have a supported index, but we were given some # kind of index... elif index_generated and not index_none: # If we are in sample, and have row labels, use them if data.row_labels is not None and not (start_oos or end_oos): prediction_index = data.row_labels[start:end + 1] # Otherwise, warn the user that they will get an Int64Index else: if not silent: warnings.warn('No supported index is available.' ' Prediction results will be given with' ' an integer index beginning at `start`.', ValueWarning) warnings.warn('No supported index is available. In the next' ' version, calling this method in a model' ' without a supported index will result in an' ' exception.', DeprecationWarning) elif index_none: prediction_index = None # For backwards compatibility, set `predict_*` values if prediction_index is not None: data.predict_start = prediction_index[0] data.predict_end = prediction_index[-1] data.predict_dates = prediction_index else: data.predict_start = None data.predict_end = None data.predict_dates = None # Compute out-of-sample observations out_of_sample = max(end - (nobs - 1), 0) end -= out_of_sample return start, end, out_of_sample, prediction_index class TimeSeriesModel(base.LikelihoodModel): __doc__ = _tsa_doc % {"model": _model_doc, "params": _generic_params, "extra_params": _missing_param_doc, "extra_sections": ""} def __init__(self, endog, exog=None, dates=None, freq=None, missing='none', **kwargs): super(TimeSeriesModel, self).__init__(endog, exog, missing=missing, **kwargs) # Date handling in indexes self._init_dates(dates, freq) def _init_dates(self, dates=None, freq=None): """ Initialize dates Parameters ---------- dates : array_like, optional An array like object containing dates. freq : str, tuple, datetime.timedelta, DateOffset or None, optional A frequency specification for either `dates` or the row labels from the endog / exog data. Notes ----- Creates `self._index` and related attributes. `self._index` is always a Pandas index, and it is always Int64Index, DatetimeIndex, or PeriodIndex. If Pandas objects, endog / exog may have any type of index. If it is an Int64Index with values 0, 1, ..., nobs-1 or if it is (coerceable to) a DatetimeIndex or PeriodIndex *with an associated frequency*, then it is called a "supported" index. Otherwise it is called an "unsupported" index. Supported indexes are standardized (i.e. a list of date strings is converted to a DatetimeIndex) and the result is put in `self._index`. Unsupported indexes are ignored, and a supported Int64Index is generated and put in `self._index`. Warnings are issued in this case to alert the user if the returned index from some operation (e.g. forecasting) is different from the original data's index. However, whenever possible (e.g. purely in-sample prediction), the original index is returned. The benefit of supported indexes is that they allow *forecasting*, i.e. it is possible to extend them in a reasonable way. Thus every model must have an underlying supported index, even if it is just a generated Int64Index. """ # Get our index from `dates` if available, otherwise from whatever # Pandas index we might have retrieved from endog, exog if dates is not None: index = dates else: index = self.data.row_labels # Sanity check that we do not have a `freq` without an index if index is None and freq is not None: raise ValueError('Frequency provided without associated index.') # If an index is available, see if it is a date-based index or if it # can be coerced to one. (If it cannot we'll fall back, below, to an # internal, 0, 1, ... nobs-1 integer index for modeling purposes) inferred_freq = False if index is not None: # Try to coerce to date-based index if not isinstance(index, (DatetimeIndex, PeriodIndex)): try: # Only try to coerce non-numeric index types (string, # list of date-times, etc.) # Note that np.asarray(Float64Index([...])) yields an # object dtype array in earlier versions of Pandas (and so # will not have is_numeric_dtype == True), so explicitly # check for it here. But note also that in very early # Pandas (~0.12), Float64Index does not exist (and so the # statsmodels compat makes it an empty tuple, so in that # case also check if the first element is a float. _index = np.asarray(index) if (is_numeric_dtype(_index) or isinstance(index, Float64Index) or (Float64Index == tuple() and isinstance(_index[0], float))): raise ValueError('Numeric index given') # If a non-index Pandas series was given, only keep its # values (because we must have a pd.Index type, below, and # pd.to_datetime will return a Series when passed # non-list-like objects) if isinstance(index, Series): index = index.values # All coercion is done via pd.to_datetime # Note: date coercion via pd.to_datetime does not handle # string versions of PeriodIndex objects most of the time. _index = to_datetime(index) # Older versions of Pandas can sometimes fail here and # return a numpy array - check to make sure it's an index if not isinstance(_index, Index): raise ValueError('Could not coerce to date index') index = _index except: # Only want to actually raise an exception if `dates` was # provided but cannot be coerced. If we got the index from # the row_labels, we'll just ignore it and use the integer # index below if dates is not None: raise ValueError('Non-date index index provided to' ' `dates` argument.') # Now, if we were given, or coerced, a date-based index, make sure # it has an associated frequency if isinstance(index, (DatetimeIndex, PeriodIndex)): # If no frequency, try to get an inferred frequency if freq is None and index.freq is None: freq = index.inferred_freq # If we got an inferred frequncy, alert the user if freq is not None: inferred_freq = True if freq is not None: warnings.warn('No frequency information was' ' provided, so inferred frequency %s' ' will be used.' % freq, ValueWarning) # Convert the passed freq to a pandas offset object if freq is not None: freq = to_offset(freq) # Now, if no frequency information is available from the index # itself or from the `freq` argument, raise an exception if freq is None and index.freq is None: # But again, only want to raise the exception if `dates` # was provided. if dates is not None: raise ValueError('No frequency information was' ' provided with date index and no' ' frequency could be inferred.') # However, if the index itself has no frequency information but # the `freq` argument is available (or was inferred), construct # a new index with an associated frequency elif freq is not None and index.freq is None: resampled_index = date_range( start=index[0], end=index[-1], freq=freq) if not inferred_freq and not resampled_index.equals(index): raise ValueError('The given frequency argument could' ' not be matched to the given index.') index = resampled_index # Finally, if the index itself has a frequency and there was # also a given frequency, raise an exception if they are not # equal elif (freq is not None and not inferred_freq and not (index.freq == freq)): raise ValueError('The given frequency argument is' ' incompatible with the given index.') # Finally, raise an exception if we could not coerce to date-based # but we were given a frequency argument elif freq is not None: raise ValueError('Given index could not be coerced to dates' ' but `freq` argument was provided.') # Get attributes of the index has_index = index is not None date_index = isinstance(index, (DatetimeIndex, PeriodIndex)) period_index = isinstance(index, PeriodIndex) int_index = isinstance(index, Int64Index) range_index = isinstance(index, RangeIndex) has_freq = index.freq is not None if date_index else None increment = Index(range(self.endog.shape[0])) is_increment = index.equals(increment) if int_index else None is_monotonic = index.is_monotonic if date_index else None # Issue warnings for unsupported indexes if has_index and not (date_index or range_index or is_increment): warnings.warn('An unsupported index was provided and will be' ' ignored when e.g. forecasting.', ValueWarning) if date_index and not has_freq: warnings.warn('A date index has been provided, but it has no' ' associated frequency information and so will be' ' ignored when e.g. forecasting.', ValueWarning) if date_index and not is_monotonic: warnings.warn('A date index has been provided, but it is not' ' monotonic and so will be ignored when e.g.' ' forecasting.', ValueWarning) # Construct the internal index index_generated = False valid_index = ((date_index and has_freq and is_monotonic) or (int_index and is_increment) or range_index) if valid_index: _index = index else: _index = increment index_generated = True self._index = _index self._index_generated = index_generated self._index_none = index is None self._index_int64 = int_index and not range_index and not date_index self._index_dates = date_index and not index_generated self._index_freq = self._index.freq if self._index_dates else None self._index_inferred_freq = inferred_freq # For backwards compatibility, set data.dates, data.freq self.data.dates = self._index if self._index_dates else None self.data.freq = self._index.freqstr if self._index_dates else None def _get_index_loc(self, key, base_index=None): """ Get the location of a specific key in an index Parameters ---------- key : label The key for which to find the location if the underlying index is a DateIndex or a location if the underlying index is a RangeIndex or an Int64Index. base_index : pd.Index, optional Optionally the base index to search. If None, the model's index is searched. Returns ------- loc : int The location of the key index : pd.Index The index including the key; this is a copy of the original index unless the index had to be expanded to accommodate `key`. index_was_expanded : bool Whether or not the index was expanded to accommodate `key`. Notes ----- If `key` is past the end of of the given index, and the index is either an Int64Index or a date index, this function extends the index up to and including key, and then returns the location in the new index. """ if base_index is None: base_index = self._index return get_index_loc(key, base_index) def _get_index_label_loc(self, key, base_index=None): """ Get the location of a specific key in an index or model row labels Parameters ---------- key : label The key for which to find the location if the underlying index is a DateIndex or is only being used as row labels, or a location if the underlying index is a RangeIndex or an Int64Index. base_index : pd.Index, optional Optionally the base index to search. If None, the model's index is searched. Returns ------- loc : int The location of the key index : pd.Index The index including the key; this is a copy of the original index unless the index had to be expanded to accommodate `key`. index_was_expanded : bool Whether or not the index was expanded to accommodate `key`. Notes ----- This method expands on `_get_index_loc` by first trying the given base index (or the model's index if the base index was not given) and then falling back to try again with the model row labels as the base index. """ if base_index is None: base_index = self._index return get_index_label_loc(key, base_index, self.data.row_labels) def _get_prediction_index(self, start, end, index=None, silent=False): """ Get the location of a specific key in an index or model row labels Parameters ---------- start : label The key at which to start prediction. Depending on the underlying model's index, may be an integer, a date (string, datetime object, pd.Timestamp, or pd.Period object), or some other object in the model's row labels. end : label The key at which to end prediction (note that this key will be *included* in prediction). Depending on the underlying model's index, may be an integer, a date (string, datetime object, pd.Timestamp, or pd.Period object), or some other object in the model's row labels. index : pd.Index, optional Optionally an index to associate the predicted results to. If None, an attempt is made to create an index for the predicted results from the model's index or model's row labels. silent : bool, optional Argument to silence warnings. Returns ------- start : int The index / observation location at which to begin prediction. end : int The index / observation location at which to end in-sample prediction. The maximum value for this is nobs-1. out_of_sample : int The number of observations to forecast after the end of the sample. prediction_index : pd.Index or None The index associated with the prediction results. This index covers the range [start, end + out_of_sample]. If the model has no given index and no given row labels (i.e. endog/exog is not Pandas), then this will be None. Notes ----- The arguments `start` and `end` behave differently, depending on if they are integer or not. If either is an integer, then it is assumed to refer to a *location* in the index, not to an index value. On the other hand, if it is a date string or some other type of object, then it is assumed to refer to an index *value*. In all cases, the returned `start` and `end` values refer to index *locations* (so in the former case, the given location is validated and returned whereas in the latter case a location is found that corresponds to the given index value). This difference in behavior is necessary to support `RangeIndex`. This is because integers for a RangeIndex could refer either to index values or to index locations in an ambiguous way (while for `Int64Index`, since we have required them to be full indexes, there is no ambiguity). """ nobs = len(self.endog) return get_prediction_index(start, end, nobs, base_index=self._index, index=index, silent=silent, index_none=self._index_none, index_generated=self._index_generated, data=self.data) def _get_exog_names(self): return self.data.xnames def _set_exog_names(self, vals): if not isinstance(vals, list): vals = [vals] self.data.xnames = vals # overwrite with writable property for (V)AR models exog_names = property(_get_exog_names, _set_exog_names, None, 'The names of the exogenous variables.') class TimeSeriesModelResults(base.LikelihoodModelResults): def __init__(self, model, params, normalized_cov_params, scale=1.): self.data = model.data super(TimeSeriesModelResults, self).__init__(model, params, normalized_cov_params, scale) class TimeSeriesResultsWrapper(wrap.ResultsWrapper): _attrs = {} _wrap_attrs = wrap.union_dicts(base.LikelihoodResultsWrapper._wrap_attrs, _attrs) _methods = {'predict' : 'dates'} _wrap_methods = wrap.union_dicts(base.LikelihoodResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(TimeSeriesResultsWrapper, # noqa:E305 TimeSeriesModelResults) if __name__ == "__main__": import statsmodels.api as sm import pandas mdata = sm.datasets.macrodata.load(as_pandas=False) #make a DataFrame #TODO: attach a DataFrame to some of the datasets, for quicker use dates = [str(int(x[0])) +':'+ str(int(x[1])) \ for x in mdata.data[['year','quarter']]] df = pandas.DataFrame(mdata.data[['realgdp','realinv','realcons']], index=dates) ex_mod = TimeSeriesModel(df) statsmodels-0.12.2/statsmodels/tsa/coint_tables.py000066400000000000000000000162561400612667500223300ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Created on Thu Aug 30 12:26:38 2012 Author: Josef Perktold function jc = c_sja(n,p) % PURPOSE: find critical values for Johansen maximum eigenvalue statistic % ------------------------------------------------------------ % USAGE: jc = c_sja(n,p) % where: n = dimension of the VAR system % p = order of time polynomial in the null-hypothesis % p = -1, no deterministic part % p = 0, for constant term % p = 1, for constant plus time-trend % p > 1 returns no critical values % ------------------------------------------------------------ % RETURNS: a (3x1) vector of percentiles for the maximum eigenvalue % statistic for: [90% 95% 99%] % ------------------------------------------------------------ % NOTES: for n > 12, the function returns a (3x1) vector of zeros. % The values returned by the function were generated using % a method described in MacKinnon (1996), using his FORTRAN % program johdist.f % ------------------------------------------------------------ % SEE ALSO: johansen() % ------------------------------------------------------------ % References: MacKinnon, Haug, Michelis (1996) 'Numerical distribution % functions of likelihood ratio tests for cointegration', % Queen's University Institute for Economic Research Discussion paper. % ------------------------------------------------------- % written by: % James P. LeSage, Dept of Economics % University of Toledo % 2801 W. Bancroft St, % Toledo, OH 43606 % jlesage@spatial-econometrics.com """ import numpy as np ss_ejcp0 = '''\ 2.9762 4.1296 6.9406 9.4748 11.2246 15.0923 15.7175 17.7961 22.2519 21.8370 24.1592 29.0609 27.9160 30.4428 35.7359 33.9271 36.6301 42.2333 39.9085 42.7679 48.6606 45.8930 48.8795 55.0335 51.8528 54.9629 61.3449 57.7954 61.0404 67.6415 63.7248 67.0756 73.8856 69.6513 73.0946 80.0937''' ss_ejcp1 = '''\ 2.7055 3.8415 6.6349 12.2971 14.2639 18.5200 18.8928 21.1314 25.8650 25.1236 27.5858 32.7172 31.2379 33.8777 39.3693 37.2786 40.0763 45.8662 43.2947 46.2299 52.3069 49.2855 52.3622 58.6634 55.2412 58.4332 64.9960 61.2041 64.5040 71.2525 67.1307 70.5392 77.4877 73.0563 76.5734 83.7105''' ss_ejcp2 = '''\ 2.7055 3.8415 6.6349 15.0006 17.1481 21.7465 21.8731 24.2522 29.2631 28.2398 30.8151 36.1930 34.4202 37.1646 42.8612 40.5244 43.4183 49.4095 46.5583 49.5875 55.8171 52.5858 55.7302 62.1741 58.5316 61.8051 68.5030 64.5292 67.9040 74.7434 70.4630 73.9355 81.0678 76.4081 79.9878 87.2395''' ejcp0 = np.array(ss_ejcp0.split(),float).reshape(-1,3) ejcp1 = np.array(ss_ejcp1.split(),float).reshape(-1,3) ejcp2 = np.array(ss_ejcp2.split(),float).reshape(-1,3) def c_sja(n, p): if ((p > 1) or (p < -1)): jc = np.full(3, np.nan) elif ((n > 12) or (n < 1)): jc = np.full(3, np.nan) elif p == -1: jc = ejcp0[n-1,:] elif p == 0: jc = ejcp1[n-1,:] elif p == 1: jc = ejcp2[n-1,:] return jc ''' function jc = c_sjt(n,p) % PURPOSE: find critical values for Johansen trace statistic % ------------------------------------------------------------ % USAGE: jc = c_sjt(n,p) % where: n = dimension of the VAR system % NOTE: routine does not work for n > 12 % p = order of time polynomial in the null-hypothesis % p = -1, no deterministic part % p = 0, for constant term % p = 1, for constant plus time-trend % p > 1 returns no critical values % ------------------------------------------------------------ % RETURNS: a (3x1) vector of percentiles for the trace % statistic for [90% 95% 99%] % ------------------------------------------------------------ % NOTES: for n > 12, the function returns a (3x1) vector of zeros. % The values returned by the function were generated using % a method described in MacKinnon (1996), using his FORTRAN % program johdist.f % ------------------------------------------------------------ % SEE ALSO: johansen() % ------------------------------------------------------------ % % References: MacKinnon, Haug, Michelis (1996) 'Numerical distribution % functions of likelihood ratio tests for cointegration', % Queen's University Institute for Economic Research Discussion paper. % ------------------------------------------------------- % written by: % James P. LeSage, Dept of Economics % University of Toledo % 2801 W. Bancroft St, % Toledo, OH 43606 % jlesage@spatial-econometrics.com % these are the values from Johansen's 1995 book % for comparison to the MacKinnon values %jcp0 = [ 2.98 4.14 7.02 % 10.35 12.21 16.16 % 21.58 24.08 29.19 % 36.58 39.71 46.00 % 55.54 59.24 66.71 % 78.30 86.36 91.12 % 104.93 109.93 119.58 % 135.16 140.74 151.70 % 169.30 175.47 187.82 % 207.21 214.07 226.95 % 248.77 256.23 270.47 % 293.83 301.95 318.14]; % ''' ss_tjcp0 = '''\ 2.9762 4.1296 6.9406 10.4741 12.3212 16.3640 21.7781 24.2761 29.5147 37.0339 40.1749 46.5716 56.2839 60.0627 67.6367 79.5329 83.9383 92.7136 106.7351 111.7797 121.7375 137.9954 143.6691 154.7977 173.2292 179.5199 191.8122 212.4721 219.4051 232.8291 255.6732 263.2603 277.9962 302.9054 311.1288 326.9716''' ss_tjcp1 = '''\ 2.7055 3.8415 6.6349 13.4294 15.4943 19.9349 27.0669 29.7961 35.4628 44.4929 47.8545 54.6815 65.8202 69.8189 77.8202 91.1090 95.7542 104.9637 120.3673 125.6185 135.9825 153.6341 159.5290 171.0905 190.8714 197.3772 210.0366 232.1030 239.2468 253.2526 277.3740 285.1402 300.2821 326.5354 334.9795 351.2150''' ss_tjcp2 = '''\ 2.7055 3.8415 6.6349 16.1619 18.3985 23.1485 32.0645 35.0116 41.0815 51.6492 55.2459 62.5202 75.1027 79.3422 87.7748 102.4674 107.3429 116.9829 133.7852 139.2780 150.0778 169.0618 175.1584 187.1891 208.3582 215.1268 228.2226 251.6293 259.0267 273.3838 298.8836 306.8988 322.4264 350.1125 358.7190 375.3203''' tjcp0 = np.array(ss_tjcp0.split(),float).reshape(-1,3) tjcp1 = np.array(ss_tjcp1.split(),float).reshape(-1,3) tjcp2 = np.array(ss_tjcp2.split(),float).reshape(-1,3) def c_sjt(n, p): if ((p > 1) or (p < -1)): jc = np.full(3, np.nan) elif ((n > 12) or (n < 1)): jc = np.full(3, np.nan) elif p == -1: jc = tjcp0[n-1,:] elif p == 0: jc = tjcp1[n-1,:] elif p == 1: jc = tjcp2[n-1,:] else: raise ValueError('invalid p') return jc if __name__ == '__main__': for p in range(-2, 3, 1): for n in range(12): print(n, p) print(c_sja(n, p)) print(c_sjt(n, p)) statsmodels-0.12.2/statsmodels/tsa/descriptivestats.py000066400000000000000000000043771400612667500232630ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Descriptive Statistics for Time Series Created on Sat Oct 30 14:24:08 2010 Author: josef-pktd License: BSD(3clause) """ import numpy as np from . import stattools as stt #todo: check subclassing for descriptive stats classes class TsaDescriptive(object): '''collection of descriptive statistical methods for time series ''' def __init__(self, data, label=None, name=''): self.data = data self.label = label self.name = name def filter(self, num, den): from scipy.signal import lfilter xfiltered = lfilter(num, den, self.data) return self.__class__(xfiltered, self.label, self.name + '_filtered') def detrend(self, order=1): from . import tsatools xdetrended = tsatools.detrend(self.data, order=order) return self.__class__(xdetrended, self.label, self.name + '_detrended') def fit(self, order=(1,0,1), **kwds): from .arima_model import ARMA self.mod = ARMA(self.data) self.res = self.mod.fit(order=order, **kwds) #self.estimated_process = return self.res def acf(self, nlags=40): return stt.acf(self.data, nlags=nlags) def pacf(self, nlags=40): return stt.pacf(self.data, nlags=nlags) def periodogram(self): #does not return frequesncies return stt.periodogram(self.data) # copied from fftarma.py def plot4(self, fig=None, nobs=100, nacf=20, nfreq=100): data = self.data acf = self.acf(nacf) pacf = self.pacf(nacf) w = np.linspace(0, np.pi, nfreq, endpoint=False) spdr = self.periodogram()[:nfreq] #(w) if fig is None: import matplotlib.pyplot as plt fig = plt.figure() ax = fig.add_subplot(2,2,1) namestr = ' for %s' % self.name if self.name else '' ax.plot(data) ax.set_title('Time series' + namestr) ax = fig.add_subplot(2,2,2) ax.plot(acf) ax.set_title('Autocorrelation' + namestr) ax = fig.add_subplot(2,2,3) ax.plot(spdr) # (wr, spdr) ax.set_title('Power Spectrum' + namestr) ax = fig.add_subplot(2,2,4) ax.plot(pacf) ax.set_title('Partial Autocorrelation' + namestr) return fig statsmodels-0.12.2/statsmodels/tsa/deterministic.py000066400000000000000000001434071400612667500225240ustar00rootroot00000000000000from statsmodels.compat.pandas import Appender, to_numpy from abc import ABC, abstractmethod import datetime as dt from typing import Hashable, List, Optional, Sequence, Set, Tuple, Type, Union import numpy as np import pandas as pd from scipy.linalg import qr from statsmodels.iolib.summary import d_or_f from statsmodels.tools.validation import ( bool_like, float_like, required_int_like, string_like, ) from statsmodels.tsa.tsatools import freq_to_period DateLike = Union[dt.datetime, pd.Timestamp, np.datetime64] IntLike = Union[int, np.integer] START_BEFORE_INDEX_ERR = """\ start is less than the first observation in the index. Values can only be \ created for observations after the start of the index. """ class DeterministicTerm(ABC): """Abstract Base Class for all Deterministic Terms""" # Set _is_dummy if the term is a dummy variable process _is_dummy = False @property def is_dummy(self) -> bool: """Flag indicating whether the values produced are dummy variables""" return self._is_dummy @abstractmethod def in_sample(self, index: Sequence[Hashable]) -> pd.DataFrame: """ Produce deterministic trends for in-sample fitting. Parameters ---------- index : index_like An index-like object. If not an index, it is converted to an index. Returns ------- DataFrame A DataFrame containing the deterministic terms. """ @abstractmethod def out_of_sample( self, steps: int, index: Sequence[Hashable], forecast_index: Optional[Sequence[Hashable]] = None, ) -> pd.DataFrame: """ Produce deterministic trends for out-of-sample forecasts Parameters ---------- steps : int The number of steps to forecast index : index_like An index-like object. If not an index, it is converted to an index. forecast_index : index_like An Index or index-like object to use for the forecasts. If provided must have steps elements. Returns ------- DataFrame A DataFrame containing the deterministic terms. """ @abstractmethod def __str__(self) -> str: """A meaningful string representation of the term""" def __hash__(self) -> int: name: Tuple[Hashable, ...] = (type(self).__name__,) return hash(name + self._eq_attr) @property @abstractmethod def _eq_attr(self) -> Tuple[Hashable, ...]: """tuple of attributes that are used for equality comparison""" @staticmethod def _index_like(index: Sequence[Hashable]) -> pd.Index: if isinstance(index, pd.Index): return index try: return pd.Index(index) except Exception: raise TypeError("index must be a pandas Index or index-like") @staticmethod def _extend_index( index: pd.Index, steps: int, forecast_index: Optional[Sequence[Hashable]] = None, ) -> pd.Index: """Extend the forecast index""" if forecast_index is not None: forecast_index = DeterministicTerm._index_like(forecast_index) assert isinstance(forecast_index, pd.Index) if forecast_index.shape[0] != steps: raise ValueError( f"The number of values in forecast_index " f"({forecast_index.shape[0]}) must match steps ({steps})." ) return forecast_index if isinstance(index, pd.PeriodIndex): return pd.period_range( index[-1] + 1, periods=steps, freq=index.freq ) elif isinstance(index, pd.DatetimeIndex) and index.freq is not None: next_obs = pd.date_range(index[-1], freq=index.freq, periods=2)[1] return pd.date_range(next_obs, freq=index.freq, periods=steps) elif isinstance(index, pd.RangeIndex): assert isinstance(index, pd.RangeIndex) try: step = index.step start = index.stop except AttributeError: # TODO: Remove after pandas min ver is 1.0.0+ step = index[-1] - index[-2] if len(index) > 1 else 1 start = index[-1] + step stop = start + step * steps return pd.RangeIndex(start, stop, step=step) elif isinstance(index, pd.Int64Index) and np.all(np.diff(index) == 1): idx_arr = np.arange(index[-1] + 1, index[-1] + steps + 1) return pd.Int64Index(idx_arr) # default range index import warnings warnings.warn( "Only PeriodIndexes, DatetimeIndexes with a frequency set, " "RangesIndexes, and Int64Indexes with a unit increment support " "extending. The index is set will contain the position relative " "to the data length.", UserWarning, ) nobs = index.shape[0] return pd.RangeIndex(nobs + 1, nobs + steps + 1) def __repr__(self) -> str: return self.__str__() + f" at 0x{id(self):0x}" def __eq__(self, other: object) -> bool: if isinstance(other, type(self)): own_attr = self._eq_attr oth_attr = other._eq_attr if len(own_attr) != len(oth_attr): return False return all([a == b for a, b in zip(own_attr, oth_attr)]) else: return False class TimeTrendDeterministicTerm(DeterministicTerm, ABC): """Abstract Base Class for all Time Trend Deterministic Terms""" def __init__(self, constant: bool = True, order: int = 0) -> None: self._constant = bool_like(constant, "constant") self._order = required_int_like(order, "order") @property def constant(self) -> bool: """Flag indicating that a constant is included""" return self._constant @property def order(self) -> int: """Order of the time trend""" return self._order @property def _columns(self) -> List[str]: columns = [] trend_names = {1: "trend", 2: "trend_squared", 3: "trend_cubed"} if self._constant: columns.append("const") for power in range(1, self._order + 1): if power in trend_names: columns.append(trend_names[power]) else: columns.append(f"trend**{power}") return columns def _get_terms(self, locs: np.ndarray) -> np.ndarray: nterms = int(self._constant) + self._order terms = np.tile(locs, (1, nterms)) power = np.zeros((1, nterms), dtype=int) power[0, int(self._constant) :] = np.arange(1, self._order + 1) terms **= power return terms def __str__(self) -> str: terms = [] if self._constant: terms.append("Constant") if self._order: terms.append(f"Powers 1 to {self._order + 1}") if not terms: terms = ["Empty"] terms_str = ",".join(terms) return f"TimeTrend({terms_str})" class TimeTrend(TimeTrendDeterministicTerm): """ Constant and time trend determinstic terms Parameters ---------- constant : bool Flag indicating whether a constant should be included. order : int A non-negative int containing the powers to include (1, 2, ..., order). See Also -------- DeterministicProcess Seasonality Fourier CalendarTimeTrend Examples -------- >>> from statsmodels.datasets import sunspots >>> from statsmodels.tsa.deterministic import TimeTrend >>> data = sunspots.load_pandas().data >>> trend_gen = TimeTrend(True, 3) >>> trend_gen.in_sample(data.index) """ def __init__(self, constant: bool = True, order: int = 0) -> None: super().__init__(constant, order) @classmethod def from_string(cls, trend: str) -> "TimeTrend": """ Create a TimeTrend from a string description. Provided for compatibility with common string names. Parameters ---------- trend : {"n", "c", "t", "ct", "ctt"} The string representation of the time trend. The terms are: * "n": No trend terms * "c": A constant only * "t": Linear time trend only * "ct": A constant and a time trend * "ctt": A constant, a time trend and a quadratic time trend Returns ------- TimeTrend The TimeTrend instance. """ constant = trend.startswith("c") order = 0 if "tt" in trend: order = 2 elif "t" in trend: order = 1 return cls(constant=constant, order=order) @Appender(DeterministicTerm.in_sample.__doc__) def in_sample( self, index: Union[Sequence[Hashable], pd.Index] ) -> pd.DataFrame: index = self._index_like(index) nobs = index.shape[0] locs = np.arange(1, nobs + 1, dtype=np.double)[:, None] terms = self._get_terms(locs) return pd.DataFrame(terms, columns=self._columns, index=index) @Appender(DeterministicTerm.out_of_sample.__doc__) def out_of_sample( self, steps: int, index: Union[Sequence[Hashable], pd.Index], forecast_index: Optional[Sequence[Hashable]] = None, ) -> pd.DataFrame: index = self._index_like(index) nobs = index.shape[0] fcast_index = self._extend_index(index, steps, forecast_index) locs = np.arange(nobs + 1, nobs + steps + 1, dtype=np.double)[:, None] terms = self._get_terms(locs) return pd.DataFrame(terms, columns=self._columns, index=fcast_index) @property def _eq_attr(self) -> Tuple[Hashable, ...]: return self._constant, self._order class Seasonality(DeterministicTerm): """ Seasonal dummy deterministic terms Parameters ---------- period : int The length of a full cycle. Must be >= 2. initial_period : int The seasonal index of the first observation. 1-indexed so must be in {1, 2, ..., period}. See Also -------- DeterministicProcess TimeTrend Fourier CalendarSeasonality Examples -------- Solar data has an 11-year cycle >>> from statsmodels.datasets import sunspots >>> from statsmodels.tsa.deterministic import Seasonality >>> data = sunspots.load_pandas().data >>> seas_gen = Seasonality(11) >>> seas_gen.in_sample(data.index) To start at a season other than 1 >>> seas_gen = Seasonality(11, initial_period=4) >>> seas_gen.in_sample(data.index) """ _is_dummy = True def __init__(self, period: int, initial_period: int = 1) -> None: self._period = required_int_like(period, "period") self._initial_period = required_int_like( initial_period, "initial_period" ) if period < 2: raise ValueError("period must be >= 2") if not 1 <= self._initial_period <= period: raise ValueError("initial_period must be in {1, 2, ..., period}") @property def period(self) -> int: """The period of the seasonality""" return self._period @property def initial_period(self) -> int: """The seasonal index of the first observation""" return self._initial_period @classmethod def from_index( cls, index: Union[Sequence[Hashable], pd.DatetimeIndex, pd.PeriodIndex] ) -> "Seasonality": """ Construct a seasonality directly from an index using its frequency. Parameters ---------- index : {DatetimeIndex, PeriodIndex} An index with its frequency (`freq`) set. Returns ------- Seasonality The initialized Seasonality instance. """ index = cls._index_like(index) if isinstance(index, pd.PeriodIndex): freq = index.freq elif isinstance(index, pd.DatetimeIndex): freq = index.freq if index.freq else index.inferred_freq else: raise TypeError("index must be a DatetimeIndex or PeriodIndex") if freq is None: raise ValueError("index must have a freq or inferred_freq set") period = freq_to_period(freq) return cls(period=period) @property def _eq_attr(self) -> Tuple[Hashable, ...]: return self._period, self._initial_period def __str__(self) -> str: return f"Seasonality(period={self._period})" @property def _columns(self) -> List[str]: period = self._period columns = [] for i in range(1, period + 1): columns.append(f"s({i},{period})") return columns @Appender(DeterministicTerm.in_sample.__doc__) def in_sample( self, index: Union[Sequence[Hashable], pd.Index] ) -> pd.DataFrame: index = self._index_like(index) nobs = index.shape[0] period = self._period term = np.zeros((nobs, period)) offset = self._initial_period - 1 for i in range(period): col = (i + offset) % period term[i::period, col] = 1 return pd.DataFrame(term, columns=self._columns, index=index) @Appender(DeterministicTerm.out_of_sample.__doc__) def out_of_sample( self, steps: int, index: Union[Sequence[Hashable], pd.Index], forecast_index: Optional[Sequence[Hashable]] = None, ) -> pd.DataFrame: index = self._index_like(index) fcast_index = self._extend_index(index, steps, forecast_index) nobs = index.shape[0] period = self._period term = np.zeros((steps, period)) offset = self._initial_period - 1 for i in range(period): col_loc = (nobs + offset + i) % period term[i::period, col_loc] = 1 return pd.DataFrame(term, columns=self._columns, index=fcast_index) class FourierDeterministicTerm(DeterministicTerm, ABC): """Abstract Base Class for all Fourier Deterministic Terms""" def __init__(self, order: int) -> None: self._order = required_int_like(order, "terms") @property def order(self) -> int: """The order of the Fourier terms included""" return self._order def _get_terms(self, locs: np.ndarray) -> np.ndarray: locs = 2 * np.pi * locs.astype(np.double) terms = np.empty((locs.shape[0], 2 * self._order)) for i in range(self._order): for j, func in enumerate((np.sin, np.cos)): terms[:, 2 * i + j] = func((i + 1) * locs) return terms class Fourier(FourierDeterministicTerm): r""" Fourier series deterministic terms Parameters ---------- period : int The length of a full cycle. Must be >= 2. order : int The number of Fourier components to include. Must be <= 2*period. See Also -------- DeterministicProcess TimeTrend Seasonality CalendarFourier Notes ----- Both a sine and a cosine term are included for each i=1, ..., order .. math:: f_{i,s,t} & = \sin\left(2 \pi i \times \frac{t}{m} \right) \\ f_{i,c,t} & = \cos\left(2 \pi i \times \frac{t}{m} \right) where m is the length of the period. Examples -------- Solar data has an 11-year cycle >>> from statsmodels.datasets import sunspots >>> from statsmodels.tsa.deterministic import Seasonality >>> data = sunspots.load_pandas().data >>> fourier_gen = Fourier(11, order=2) >>> fourier_gen.in_sample(data.index) """ _is_dummy = False def __init__(self, period: float, order: int): super().__init__(order) self._period = float_like(period, "period") if 2 * self._order > self._period: raise ValueError("2 * order must be <= period") @property def period(self) -> float: """The period of the Fourier terms""" return self._period @property def _columns(self) -> List[str]: period = self._period fmt_period = d_or_f(period).strip() columns = [] for i in range(1, self._order + 1): for typ in ("sin", "cos"): columns.append(f"{typ}({i},{fmt_period})") return columns @Appender(DeterministicTerm.in_sample.__doc__) def in_sample( self, index: Union[Sequence[Hashable], pd.Index] ) -> pd.DataFrame: index = self._index_like(index) nobs = index.shape[0] terms = self._get_terms(np.arange(nobs) / self._period) return pd.DataFrame(terms, index=index, columns=self._columns) @Appender(DeterministicTerm.out_of_sample.__doc__) def out_of_sample( self, steps: int, index: Union[Sequence[Hashable], pd.Index], forecast_index: Optional[Sequence[Hashable]] = None, ) -> pd.DataFrame: index = self._index_like(index) fcast_index = self._extend_index(index, steps, forecast_index) nobs = index.shape[0] terms = self._get_terms(np.arange(nobs, nobs + steps) / self._period) return pd.DataFrame(terms, index=fcast_index, columns=self._columns) @property def _eq_attr(self) -> Tuple[Hashable, ...]: return self._period, self._order def __str__(self) -> str: return f"Fourier(period={self._period}, order={self._order})" class CalendarDeterministicTerm(DeterministicTerm, ABC): """Abstract Base Class for calendar deterministic terms""" def __init__(self, freq: str) -> None: try: index = pd.date_range("2020-01-01", freq=freq, periods=1) self._freq = index.freq except ValueError: raise ValueError("freq is not understood by pandas") @property def freq(self) -> str: """The frequency of the deterministic terms""" return self._freq.freqstr def _compute_ratio( self, index: Union[pd.DatetimeIndex, pd.PeriodIndex] ) -> np.ndarray: if isinstance(index, pd.PeriodIndex): index = index.to_timestamp() delta = index - index.to_period(self._freq).to_timestamp() pi = index.to_period(self._freq) gap = (pi + 1).to_timestamp() - pi.to_timestamp() return to_numpy(delta) / to_numpy(gap) def _check_index_type( self, index: pd.Index, allowed: Union[Type, Tuple[Type, ...]] = ( pd.DatetimeIndex, pd.PeriodIndex, ), ) -> Union[pd.DatetimeIndex, pd.PeriodIndex]: if isinstance(allowed, type): allowed = (allowed,) if not isinstance(index, allowed): if len(allowed) == 1: allowed_types = "a " + allowed[0].__name__ else: allowed_types = ", ".join(a.__name__ for a in allowed[:-1]) if len(allowed) > 2: allowed_types += "," allowed_types += " and " + allowed[-1].__name__ msg = ( f"{type(self).__name__} terms can only be computed from " f"{allowed_types}" ) raise TypeError(msg) assert isinstance(index, (pd.DatetimeIndex, pd.PeriodIndex)) return index class CalendarFourier(CalendarDeterministicTerm, FourierDeterministicTerm): r""" Fourier series deterministic terms based on calendar time Parameters ---------- freq : str A string convertible to a pandas frequency. order : int The number of Fourier components to include. Must be <= 2*period. See Also -------- DeterministicProcess CalendarTimeTrend CalendarSeasonality Fourier Notes ----- Both a sine and a cosine term are included for each i=1, ..., order .. math:: f_{i,s,t} & = \sin\left(2 \pi i \tau_t \right) \\ f_{i,c,t} & = \cos\left(2 \pi i \tau_t \right) where m is the length of the period and :math:`\tau_t` is the frequency normalized time. For example, when freq is "D" then an observation with a timestamp of 12:00:00 would have :math:`\tau_t=0.5`. Examples -------- Here we simulate irregularly spaced hourly data and construct the calendar Fourier terms for the data. >>> import numpy as np >>> import pandas as pd >>> base = pd.Timestamp("2020-1-1") >>> gen = np.random.default_rng() >>> gaps = np.cumsum(gen.integers(0, 1800, size=1000)) >>> times = [base + pd.Timedelta(gap, unit="s") for gap in gaps] >>> index = pd.DatetimeIndex(pd.to_datetime(times)) >>> from statsmodels.tsa.deterministic import CalendarFourier >>> cal_fourier_gen = CalendarFourier("D", 2) >>> cal_fourier_gen.in_sample(index) """ def __init__(self, freq: str, order: int) -> None: super().__init__(freq) FourierDeterministicTerm.__init__(self, order) self._order = required_int_like(order, "terms") @property def _columns(self) -> List[str]: columns = [] for i in range(1, self._order + 1): for typ in ("sin", "cos"): columns.append(f"{typ}({i},freq={self._freq.freqstr})") return columns @Appender(DeterministicTerm.in_sample.__doc__) def in_sample( self, index: Union[Sequence[Hashable], pd.Index] ) -> pd.DataFrame: index = self._index_like(index) index = self._check_index_type(index) ratio = self._compute_ratio(index) terms = self._get_terms(ratio) return pd.DataFrame(terms, index=index, columns=self._columns) @Appender(DeterministicTerm.out_of_sample.__doc__) def out_of_sample( self, steps: int, index: Union[Sequence[Hashable], pd.Index], forecast_index: Optional[Sequence[Hashable]] = None, ) -> pd.DataFrame: index = self._index_like(index) fcast_index = self._extend_index(index, steps, forecast_index) self._check_index_type(fcast_index) assert isinstance(fcast_index, (pd.DatetimeIndex, pd.PeriodIndex)) ratio = self._compute_ratio(fcast_index) terms = self._get_terms(ratio) return pd.DataFrame(terms, index=fcast_index, columns=self._columns) @property def _eq_attr(self) -> Tuple[Hashable, ...]: return self._freq.freqstr, self._order def __str__(self) -> str: return f"Fourier(freq={self._freq.freqstr}, order={self._order})" class CalendarSeasonality(CalendarDeterministicTerm): """ Seasonal dummy deterministic terms based on calendar time Parameters ---------- freq : str The frequency of the seasonal effect. period : str The pandas frequency string describing the full period. See Also -------- DeterministicProcess CalendarTimeTrend CalendarFourier Seasonality Examples -------- Here we simulate irregularly spaced data (in time) and hourly seasonal dummies for the data. >>> import numpy as np >>> import pandas as pd >>> base = pd.Timestamp("2020-1-1") >>> gen = np.random.default_rng() >>> gaps = np.cumsum(gen.integers(0, 1800, size=1000)) >>> times = [base + pd.Timedelta(gap, unit="s") for gap in gaps] >>> index = pd.DatetimeIndex(pd.to_datetime(times)) >>> from statsmodels.tsa.deterministic import CalendarSeasonality >>> cal_seas_gen = CalendarSeasonality("H", "D") >>> cal_seas_gen.in_sample(index) """ _is_dummy = True # out_of: freq _supported = { "W": {"H": 24 * 7, "B": 5, "D": 7}, "D": {"H": 24}, "Q": {"M": 3}, "A": {"M": 12, "Q": 4}, } def __init__(self, freq: str, period: str) -> None: freq_options: Set[str] = set() freq_options.update( *[list(val.keys()) for val in self._supported.values()] ) period_options = list(self._supported.keys()) freq = string_like( freq, "freq", options=tuple(freq_options), lower=False ) period = string_like( period, "period", options=period_options, lower=False ) if freq not in self._supported[period]: raise ValueError( f"The combination of freq={freq} and " f"period={period} is not supported." ) super().__init__(freq) self._period = period self._freq_str = self._freq.freqstr.split("-")[0] @property def freq(self) -> str: """The frequency of the deterministic terms""" return self._freq.freqstr @property def period(self) -> str: """The full period""" return self._period def _weekly_to_loc( self, index: Union[pd.DatetimeIndex, pd.PeriodIndex] ) -> np.ndarray: if self._freq.freqstr == "H": return index.hour + 24 * index.dayofweek elif self._freq.freqstr == "D": return index.dayofweek else: # "B" bdays = pd.bdate_range("2000-1-1", periods=10).dayofweek.unique() loc = index.dayofweek if not loc.isin(bdays).all(): raise ValueError( "freq is B but index contains days that are not business " "days." ) return loc def _daily_to_loc( self, index: Union[pd.DatetimeIndex, pd.PeriodIndex] ) -> np.ndarray: return index.hour def _quarterly_to_loc( self, index: Union[pd.DatetimeIndex, pd.PeriodIndex] ) -> np.ndarray: return (index.month - 1) % 3 def _annual_to_loc( self, index: Union[pd.DatetimeIndex, pd.PeriodIndex] ) -> np.ndarray: if self._freq.freqstr == "M": return index.month - 1 else: # "Q" return index.quarter - 1 def _get_terms( self, index: Union[pd.DatetimeIndex, pd.PeriodIndex] ) -> np.ndarray: if self._period == "D": locs = self._daily_to_loc(index) elif self._period == "W": locs = self._weekly_to_loc(index) elif self._period == "Q": locs = self._quarterly_to_loc(index) else: # "A": locs = self._annual_to_loc(index) full_cycle = self._supported[self._period][self._freq_str] terms = np.zeros((locs.shape[0], full_cycle)) terms[np.arange(locs.shape[0]), locs] = 1 return terms @property def _columns(self) -> List[str]: columns = [] count = self._supported[self._period][self._freq_str] for i in range(count): columns.append( f"s({self._freq_str}={i + 1}, period={self._period})" ) return columns @Appender(DeterministicTerm.in_sample.__doc__) def in_sample( self, index: Union[Sequence[Hashable], pd.Index] ) -> pd.DataFrame: index = self._index_like(index) index = self._check_index_type(index) terms = self._get_terms(index) return pd.DataFrame(terms, index=index, columns=self._columns) @Appender(DeterministicTerm.out_of_sample.__doc__) def out_of_sample( self, steps: int, index: Union[Sequence[Hashable], pd.Index], forecast_index: Optional[Sequence[Hashable]] = None, ) -> pd.DataFrame: index = self._index_like(index) fcast_index = self._extend_index(index, steps, forecast_index) self._check_index_type(fcast_index) assert isinstance(fcast_index, (pd.DatetimeIndex, pd.PeriodIndex)) terms = self._get_terms(fcast_index) return pd.DataFrame(terms, index=fcast_index, columns=self._columns) @property def _eq_attr(self) -> Tuple[Hashable, ...]: return self._period, self._freq_str def __str__(self) -> str: return f"Seasonal(freq={self._freq_str})" class CalendarTimeTrend(CalendarDeterministicTerm, TimeTrendDeterministicTerm): r""" Constant and time trend determinstic terms based on calendar time Parameters ---------- freq : str A string convertible to a pandas frequency. constant : bool Flag indicating whether a constant should be included. order : int A non-negative int containing the powers to include (1, 2, ..., order). base_period : {str, pd.Timestamp}, default None The base period to use when computing the time stamps. This value is treated as 1 and so all other time indices are defined as the number of periods since or before this time stamp. If not provided, defaults to pandas base period for a PeriodIndex. See Also -------- DeterministicProcess CalendarFourier CalendarSeasonality TimeTrend Notes ----- The time stamp, :math:`\tau_t`, is the number of periods that have elapsed since the base_period. :math:`\tau_t` may be fractional. Examples -------- Here we simulate irregularly spaced hourly data and construct the calendar time trend terms for the data. >>> import numpy as np >>> import pandas as pd >>> base = pd.Timestamp("2020-1-1") >>> gen = np.random.default_rng() >>> gaps = np.cumsum(gen.integers(0, 1800, size=1000)) >>> times = [base + pd.Timedelta(gap, unit="s") for gap in gaps] >>> index = pd.DatetimeIndex(pd.to_datetime(times)) >>> from statsmodels.tsa.deterministic import CalendarTimeTrend >>> cal_trend_gen = CalendarTimeTrend("D", True, order=1) >>> cal_trend_gen.in_sample(index) Next, we normalize using the first time stamp >>> cal_trend_gen = CalendarTimeTrend("D", True, order=1, ... base_period=index[0]) >>> cal_trend_gen.in_sample(index) """ def __init__( self, freq: str, constant: bool = True, order: int = 0, *, base_period: Optional[Union[str, DateLike]] = None, ) -> None: super().__init__(freq) TimeTrendDeterministicTerm.__init__( self, constant=constant, order=order ) self._ref_i8 = 0 if base_period is not None: pr = pd.period_range(base_period, periods=1, freq=self._freq) self._ref_i8 = pr.asi8[0] self._base_period = None if base_period is None else str(base_period) @property def base_period(self) -> Optional[str]: """The base period""" return self._base_period @classmethod def from_string( cls, freq: str, trend: str, base_period: Optional[Union[str, DateLike]] = None, ) -> "CalendarTimeTrend": """ Create a TimeTrend from a string description. Provided for compatibility with common string names. Parameters ---------- freq : str A string convertible to a pandas frequency. trend : {"n", "c", "t", "ct", "ctt"} The string representation of the time trend. The terms are: * "n": No trend terms * "c": A constant only * "t": Linear time trend only * "ct": A constant and a time trend * "ctt": A constant, a time trend and a quadratic time trend base_period : {str, pd.Timestamp}, default None The base period to use when computing the time stamps. This value is treated as 1 and so all other time indices are defined as the number of periods since or before this time stamp. If not provided, defaults to pandas base period for a PeriodIndex. Returns ------- TimeTrend The TimeTrend instance. """ constant = trend.startswith("c") order = 0 if "tt" in trend: order = 2 elif "t" in trend: order = 1 return cls(freq, constant, order, base_period=base_period) def _terms( self, index: Union[pd.DatetimeIndex, pd.PeriodIndex], ratio: np.ndarray ) -> pd.DataFrame: if isinstance(index, pd.DatetimeIndex): index = index.to_period(self._freq) index_i8 = index.asi8 index_i8 = index_i8 - self._ref_i8 + 1 time = index_i8.astype(np.double) + ratio time = time[:, None] terms = self._get_terms(time) return pd.DataFrame(terms, columns=self._columns, index=index) @Appender(DeterministicTerm.in_sample.__doc__) def in_sample( self, index: Union[Sequence[Hashable], pd.Index] ) -> pd.DataFrame: index = self._index_like(index) index = self._check_index_type(index) ratio = self._compute_ratio(index) return self._terms(index, ratio) @Appender(DeterministicTerm.out_of_sample.__doc__) def out_of_sample( self, steps: int, index: Union[Sequence[Hashable], pd.Index], forecast_index: Optional[Sequence[Hashable]] = None, ) -> pd.DataFrame: index = self._index_like(index) fcast_index = self._extend_index(index, steps, forecast_index) self._check_index_type(fcast_index) assert isinstance(fcast_index, (pd.PeriodIndex, pd.DatetimeIndex)) ratio = self._compute_ratio(fcast_index) return self._terms(fcast_index, ratio) @property def _eq_attr(self) -> Tuple[Hashable, ...]: attr: Tuple[Hashable, ...] = ( self._constant, self._order, self._freq.freqstr, ) if self._base_period is not None: attr += (self._base_period,) return attr def __str__(self) -> str: value = TimeTrendDeterministicTerm.__str__(self) value = "Calendar" + value[:-1] + f", freq={self._freq.freqstr})" if self._base_period is not None: value = value[:-1] + f"base_period={self._base_period})" return value class DeterministicProcess: """ Container class for deterministic terms. Directly supports constants, time trends, and either seasonal dummies or fourier terms for a single cycle. Additional deterministic terms beyond the set that can be directly initialized through the constructor can be added. Parameters ---------- index : {Sequence[Hashable], pd.Index} The index of the process. Should usually be the "in-sample" index when used in forecasting applications. period : {float, int}, default None The period of the seasonal or fourier components. Must be an int for seasonal dummies. If not provided, freq is read from index if available. constant : bool, default False Whether to include a constant. order : int, default 0 The order of the tim trend to include. For example, 2 will include both linear and quadratic terms. 0 exclude time trend terms. seasonal : bool = False Whether to include seasonal dummies fourier : int = 0 The order of the fourier terms to included. additional_terms : Sequence[DeterministicTerm] A sequence of additional deterministic terms to include in the process. drop : bool, default False A flag indicating to check for perfect collinearity and to drop any linearly dependent terms. See Also -------- TimeTrend Seasonality Fourier CalendarTimeTrend CalendarSeasonality CalendarFourier Examples -------- >>> from statsmodels.tsa.deterministic import DeterministicProcess >>> from pandas import date_range >>> index = date_range("2000-1-1", freq="M", periods=240) First a determinstic process with a constant and quadratic time trend. >>> dp = DeterministicProcess(index, constant=True, order=2) >>> dp.in_sample().head(3) const trend trend_squared 2000-01-31 1.0 1.0 1.0 2000-02-29 1.0 2.0 4.0 2000-03-31 1.0 3.0 9.0 Seasonal dummies are included by setting seasonal to True. >>> dp = DeterministicProcess(index, constant=True, seasonal=True) >>> dp.in_sample().iloc[:3,:5] const s(2,12) s(3,12) s(4,12) s(5,12) 2000-01-31 1.0 0.0 0.0 0.0 0.0 2000-02-29 1.0 1.0 0.0 0.0 0.0 2000-03-31 1.0 0.0 1.0 0.0 0.0 Fourier components can be used to alternatively capture seasonal patterns, >>> dp = DeterministicProcess(index, constant=True, fourier=2) >>> dp.in_sample().head(3) const sin(1,12) cos(1,12) sin(2,12) cos(2,12) 2000-01-31 1.0 0.000000 1.000000 0.000000 1.0 2000-02-29 1.0 0.500000 0.866025 0.866025 0.5 2000-03-31 1.0 0.866025 0.500000 0.866025 -0.5 Multiple Seasonalities can be captured using additional terms. >>> from statsmodels.tsa.deterministic import Fourier >>> index = date_range("2000-1-1", freq="D", periods=5000) >>> fourier = Fourier(period=365.25, order=1) >>> dp = DeterministicProcess(index, period=3, constant=True, ... seasonal=True, additional_terms=[fourier]) >>> dp.in_sample().head(3) const s(2,3) s(3,3) sin(1,365.25) cos(1,365.25) 2000-01-01 1.0 0.0 0.0 0.000000 1.000000 2000-01-02 1.0 1.0 0.0 0.017202 0.999852 2000-01-03 1.0 0.0 1.0 0.034398 0.999408 """ def __init__( self, index: Union[Sequence[Hashable], pd.Index], *, period: Optional[Union[float, int]] = None, constant: bool = False, order: int = 0, seasonal: bool = False, fourier: int = 0, additional_terms: Sequence[DeterministicTerm] = (), drop: bool = False, ): if not isinstance(index, pd.Index): index = pd.Index(index) self._index = index self._deterministic_terms: List[DeterministicTerm] = [] self._extendable = False self._index_freq = None self._validate_index() period = float_like(period, "period", optional=True) self._constant = constant = bool_like(constant, "constant") self._order = required_int_like(order, "order") self._seasonal = seasonal = bool_like(seasonal, "seasonal") self._fourier = required_int_like(fourier, "fourier") additional_terms = tuple(additional_terms) self._cached_in_sample = None self._drop = bool_like(drop, "drop") self._additional_terms = additional_terms if constant or order: self._deterministic_terms.append(TimeTrend(constant, order)) if seasonal and fourier: raise ValueError( """seasonal and fourier can be initialized through the constructor since\ these will be necessarily perfectly collinear. Instead, you can pass \ additional components using the additional_terms input.""" ) if (seasonal or fourier) and period is None: if period is None: self._period = period = freq_to_period(self._index_freq) if seasonal: period = required_int_like(period, "period") self._deterministic_terms.append(Seasonality(period)) elif fourier: period = float_like(period, "period") assert period is not None self._deterministic_terms.append(Fourier(period, order=fourier)) for term in additional_terms: if not isinstance(term, DeterministicTerm): raise TypeError( "All additional terms must be instances of subsclasses " "of DeterministicTerm" ) if term not in self._deterministic_terms: self._deterministic_terms.append(term) else: raise ValueError( "One or more terms in additional_terms has been added " "through the parameters of the constructor. Terms must " "be unique." ) self._period = period self._retain_cols: Optional[List[Hashable]] = None @property def index(self) -> pd.Index: """The index of the process""" return self._index @property def terms(self) -> List[DeterministicTerm]: """The deterministic terms included in the process""" return self._deterministic_terms def _adjust_dummies(self, terms: List[pd.DataFrame]) -> List[pd.DataFrame]: has_const: Optional[bool] = None for dterm in self._deterministic_terms: if isinstance(dterm, (TimeTrend, CalendarTimeTrend)): has_const = has_const or dterm.constant if has_const is None: has_const = False for term in terms: const_col = (term == term.iloc[0]).all() & (term.iloc[0] != 0) has_const = has_const or const_col.any() drop_first = has_const for i, dterm in enumerate(self._deterministic_terms): is_dummy = dterm.is_dummy if is_dummy and drop_first: # drop first terms[i] = terms[i].iloc[:, 1:] drop_first = drop_first or is_dummy return terms def _remove_zeros_ones(self, terms: pd.DataFrame) -> pd.DataFrame: all_zero = np.all(terms == 0, axis=0) if np.any(all_zero): terms = terms.loc[:, ~all_zero] is_constant = terms.max(axis=0) == terms.min(axis=0) if np.sum(is_constant) > 1: # Retain first const_locs = np.where(is_constant)[0] is_constant[const_locs[:1]] = False terms = terms.loc[:, ~is_constant] return terms @Appender(DeterministicTerm.in_sample.__doc__) def in_sample(self) -> pd.DataFrame: if self._cached_in_sample is not None: return self._cached_in_sample index = self._index if not self._deterministic_terms: return pd.DataFrame(np.empty((index.shape[0], 0)), index=index) raw_terms = [] for term in self._deterministic_terms: raw_terms.append(term.in_sample(index)) raw_terms = self._adjust_dummies(raw_terms) terms: pd.DataFrame = pd.concat(raw_terms, axis=1) terms = self._remove_zeros_ones(terms) if self._drop: terms_arr = to_numpy(terms) res = qr(terms_arr, mode="r", pivoting=True) r = res[0] p = res[-1] abs_diag = np.abs(np.diag(r)) tol = abs_diag[0] * terms_arr.shape[1] * np.finfo(float).eps rank = int(np.sum(abs_diag > tol)) rpx = r.T @ terms_arr keep = [0] last_rank = 1 # Find the left-most columns that produce full rank for i in range(1, terms_arr.shape[1]): curr_rank = np.linalg.matrix_rank(rpx[: i + 1, : i + 1]) if curr_rank > last_rank: keep.append(i) last_rank = curr_rank if curr_rank == rank: break if len(keep) == rank: terms = terms.iloc[:, keep] else: terms = terms.iloc[:, np.sort(p[:rank])] self._retain_cols = terms.columns self._cached_in_sample = terms return terms @Appender(DeterministicTerm.out_of_sample.__doc__) def out_of_sample( self, steps: int, forecast_index: Optional[Union[Sequence[Hashable], pd.Index]] = None, ) -> pd.DataFrame: steps = required_int_like(steps, "steps") if self._drop and self._retain_cols is None: self.in_sample() index = self._index if not self._deterministic_terms: return pd.DataFrame(np.empty((index.shape[0], 0)), index=index) raw_terms = [] for term in self._deterministic_terms: raw_terms.append(term.out_of_sample(steps, index, forecast_index)) terms: pd.DataFrame = pd.concat(raw_terms, axis=1) assert self._retain_cols is not None if terms.shape[1] != len(self._retain_cols): terms = terms[self._retain_cols] return terms def _extend_time_index( self, stop: pd.Timestamp, ) -> Union[pd.DatetimeIndex, pd.PeriodIndex]: index = self._index if isinstance(index, pd.PeriodIndex): return pd.period_range(index[0], end=stop, freq=index.freq) return pd.date_range(start=index[0], end=stop, freq=self._index_freq) def _range_from_range_index(self, start: int, stop: int) -> pd.DataFrame: index = self._index is_int64_index = type(index) is pd.Int64Index assert isinstance(index, (pd.RangeIndex, pd.Int64Index)) if start < index[0]: raise ValueError(START_BEFORE_INDEX_ERR) if is_int64_index: idx_step = 1 else: try: idx_step = index.step except AttributeError: # TODO: Remove after pandas min ver is 1.0.0+ idx_step = index[-1] - index[-2] if len(index) > 1 else 1 if idx_step != 1 and ((start - index[0]) % idx_step) != 0: raise ValueError( f"The step of the index is not 1 (actual step={idx_step})." " start must be in the sequence that would have been " "generated by the index." ) if is_int64_index: new_idx = pd.Int64Index(np.arange(start, stop)) else: new_idx = pd.RangeIndex(start, stop, step=idx_step) if new_idx[-1] <= self._index[-1]: # In-sample only in_sample = self.in_sample() in_sample = in_sample.loc[new_idx] return in_sample elif new_idx[0] > self._index[-1]: # Out of-sample only next_value = index[-1] + idx_step if new_idx[0] != next_value: tmp = pd.RangeIndex(next_value, stop, step=idx_step) oos = self.out_of_sample(tmp.shape[0], forecast_index=tmp) return oos.loc[new_idx] return self.out_of_sample(new_idx.shape[0], forecast_index=new_idx) # Using some from each in and out of sample in_sample_loc = new_idx <= self._index[-1] in_sample_idx = new_idx[in_sample_loc] out_of_sample_idx = new_idx[~in_sample_loc] in_sample_exog = self.in_sample().loc[in_sample_idx] oos_exog = self.out_of_sample( steps=out_of_sample_idx.shape[0], forecast_index=out_of_sample_idx ) return pd.concat([in_sample_exog, oos_exog], axis=0) def _range_from_time_index( self, start: pd.Timestamp, stop: pd.Timestamp ) -> pd.DataFrame: index = self._index if isinstance(self._index, pd.PeriodIndex): if isinstance(start, pd.Timestamp): start = start.to_period(freq=self._index_freq) if isinstance(stop, pd.Timestamp): stop = stop.to_period(freq=self._index_freq) if start < index[0]: raise ValueError(START_BEFORE_INDEX_ERR) if stop <= self._index[-1]: return self.in_sample().loc[start:stop] new_idx = self._extend_time_index(stop) oos_idx = new_idx[new_idx > index[-1]] oos = self.out_of_sample(oos_idx.shape[0], oos_idx) if start >= oos_idx[0]: return oos.loc[start:stop] both = pd.concat([self.in_sample(), oos], axis=0) return both.loc[start:stop] def _int_to_timestamp(self, value: int, name: str) -> pd.Timestamp: if value < 0: raise ValueError(f"{name} must be non-negative.") if value < self._index.shape[0]: return self._index[value] add_periods = value - (self._index.shape[0] - 1) + 1 index = self._index if isinstance(self._index, pd.PeriodIndex): pr = pd.period_range( index[-1], freq=self._index_freq, periods=add_periods ) return pr[-1].to_timestamp() dr = pd.date_range( index[-1], freq=self._index_freq, periods=add_periods ) return dr[-1] def range( self, start: Union[IntLike, DateLike, str], stop: Union[IntLike, DateLike, str], ) -> pd.DataFrame: """ Deterministic terms spanning a range of observations Parameters ---------- start : {int, str, dt.datetime, pd.Timestamp, np.datetime64} The first observation. stop : {int, str, dt.datetime, pd.Timestamp, np.datetime64} The final observation. Inclusive to match most prediction function in statsmodels. Returns ------- DataFrame A data frame of deterministic terms """ if not self._extendable: raise TypeError( """The index in the deterministic process does not \ support extension. Only PeriodIndex, DatetimeIndex with a frequency, \ RangeIndex, and Int64Index that start at 0 and have only unit differences \ can be extended when producing out-of-sample forecasts. """ ) if type(self._index) in (pd.RangeIndex, pd.Int64Index): start = required_int_like(start, "start") stop = required_int_like(stop, "stop") # Add 1 to ensure that the end point is inclusive stop += 1 return self._range_from_range_index(start, stop) if isinstance(start, (int, np.integer)): start = self._int_to_timestamp(start, "start") else: start = pd.Timestamp(start) if isinstance(stop, (int, np.integer)): stop = self._int_to_timestamp(stop, "stop") else: stop = pd.Timestamp(stop) return self._range_from_time_index(start, stop) def _validate_index(self) -> None: if isinstance(self._index, pd.PeriodIndex): self._index_freq = self._index.freq self._extendable = True elif isinstance(self._index, pd.DatetimeIndex): self._index_freq = self._index.freq or self._index.inferred_freq self._extendable = self._index_freq is not None elif isinstance(self._index, pd.RangeIndex): self._extendable = True elif isinstance(self._index, pd.Int64Index): self._extendable = self._index[0] == 0 and np.all( np.diff(self._index) == 1 ) statsmodels-0.12.2/statsmodels/tsa/exponential_smoothing/000077500000000000000000000000001400612667500237135ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/exponential_smoothing/__init__.py000066400000000000000000000000001400612667500260120ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/exponential_smoothing/_ets_smooth.pyx000066400000000000000000000165351400612667500270120ustar00rootroot00000000000000#!python #cython: wraparound=False, boundscheck=False, cdivision=True from cpython cimport bool import numpy as np cimport numpy as np np.import_array() ctypedef fused numeric: np.float32_t np.float64_t np.complex64_t np.complex128_t cpdef _initialize_ets_smooth( numeric [:] params, numeric[:,:] xhat, long [:] is_fixed, numeric [:] fixed_values, bool use_beta_star=False, bool use_gamma_star=False, ): """Extracts parameters and initializes states xhat""" cdef numeric [:] full_params cdef numeric alpha, beta, gamma, phi, beta_star, gamma_star cdef Py_ssize_t idx_all, idx_params, n_all, m, n n_all = len(is_fixed) full_params = np.empty_like(fixed_values) idx_params = 0 for idx_all in range(n_all): if not is_fixed[idx_all]: full_params[idx_all] = params[idx_params] idx_params += 1 else: full_params[idx_all] = fixed_values[idx_all] # get params alpha, beta, gamma, phi = full_params[0:4] m = len(full_params[6:]) n = len(xhat) # calculate beta_star and gamma_star # if the use flags are true, the parameters are already the starred versions if use_beta_star: beta_star = beta else: beta_star = beta/alpha if use_gamma_star: gamma_star = gamma else: gamma_star = gamma / (1 - alpha) # initialize states # l = xhat[:,0], b = xhat[:,1], s = xhat[:,2:2+m] # seasons are sorted such that xhat[:,2+m-1] contains s[-m] xhat[n-1, :] = full_params[4:] return alpha, beta_star, gamma_star, phi, m, n def _ets_smooth_add_add(numeric [:] params, numeric [:] y, numeric [:] yhat, numeric [:,:] xhat, long [:] is_fixed, numeric [:] fixed_values, bool use_beta_star=False, bool use_gamma_star=False): """Smoothing with additive trend and additive season""" cdef numeric alpha, beta_star, gamma_star, phi cdef Py_ssize_t i, n, m, prev # get params alpha, beta_star, gamma_star, phi, m, n = _initialize_ets_smooth( params, xhat, is_fixed, fixed_values, use_beta_star, use_gamma_star ) # smooth for i in range(n): prev = (n+i-1) % n # s[t-m] = xhat[prev, 2+m-1] yhat[i] = xhat[prev, 0] + phi * xhat[prev, 1] + xhat[prev, 2+m-1] # l_t = a * (y_t - s_t-m) + (1-a) * (l_t-1 + phi*b_t-1) xhat[i, 0] = (alpha * (y[i] - xhat[prev, 2+m-1]) + (1 - alpha) * (xhat[prev, 0] + phi * xhat[prev, 1])) # b_t = (b*) * (l_t - l_t-1) + (1 - (b*)) * phi * b_t-1 xhat[i, 1] = (beta_star * (xhat[i, 0] - xhat[prev, 0]) + (1 - beta_star) * phi * xhat[prev, 1]) # s_t = (g*) * (y_t - l_t) + (1 - (g*)) * s_t-m xhat[i, 2] = (gamma_star * (y[i] - xhat[i, 0]) + (1 - gamma_star) * xhat[prev, 2+m-1]) xhat[i, 3:] = xhat[prev, 2:2+m-1] def _ets_smooth_add_mul(numeric [:] params, numeric [:] y, numeric [:] yhat, numeric [:,:] xhat, long [:] is_fixed, numeric [:] fixed_values, bool use_beta_star=False, bool use_gamma_star=False): """Smoothing with additive trend and multiplicative season""" cdef numeric alpha, beta_star, gamma_star, phi cdef Py_ssize_t i, n, m, prev # get params alpha, beta_star, gamma_star, phi, m, n = _initialize_ets_smooth( params, xhat, is_fixed, fixed_values, use_beta_star, use_gamma_star ) # smooth for i in range(n): prev = (n+i-1) % n # s[t-m] = xhat[prev, 2+m-1] yhat[i] = (xhat[prev, 0] + phi * xhat[prev, 1]) * xhat[prev, 2+m-1] # l_t = a * (y_t / s_t-m) + (1-a) * (l_t-1 + phi*b_t-1) xhat[i, 0] = (alpha * (y[i] / xhat[prev, 2+m-1]) + (1 - alpha) * (xhat[prev, 0] + phi * xhat[prev, 1])) # b_t = (b*) * (l_t - l_t-1) + (1 - (b*)) * phi * b_t-1 xhat[i, 1] = (beta_star * (xhat[i, 0] - xhat[prev, 0]) + (1 - beta_star) * phi * xhat[prev, 1]) # s_t = g * (y_t / (l_t-1 - phi*b_t-1)) + (1 - g) * s_t-m xhat[i, 2] = (gamma_star * (y[i] / xhat[i, 0]) + (1 - gamma_star) * xhat[prev, 2+m-1]) xhat[i, 3:] = xhat[prev, 2:2+m-1] def _ets_smooth_mul_add(numeric [:] params, numeric [:] y, numeric [:] yhat, numeric [:,:] xhat, long [:] is_fixed, numeric [:] fixed_values, bool use_beta_star=False, bool use_gamma_star=False): """Smoothing with multiplicative trend and additive season""" cdef numeric alpha, beta_star, gamma_star, phi cdef Py_ssize_t i, n, m, prev # get params alpha, beta_star, gamma_star, phi, m, n = _initialize_ets_smooth( params, xhat, is_fixed, fixed_values, use_beta_star, use_gamma_star ) # smooth for i in range(n): prev = (n+i-1) % n # s[t-m] = xhat[prev, 2+m-1] yhat[i] = (xhat[prev, 0] * xhat[prev, 1]**phi) + xhat[prev, 2+m-1] # l_t = a * (y_t - s_t-m) + (1-a) * (l_t-1 * b_t-1**phi) xhat[i, 0] = (alpha * (y[i] - xhat[prev, 2+m-1]) + (1 - alpha) * (xhat[prev, 0] * xhat[prev, 1]**phi)) # b_t = (b*) * (l_t / l_t-1) + (1 - (b*)) * b_t-1**phi xhat[i, 1] = (beta_star * (xhat[i, 0] / xhat[prev, 0]) + (1 - beta_star) * xhat[prev, 1]**phi) # s_t = g * (y_t - (l_t-1 * b_t-1**phi)) + (1 - g) * s_t-m xhat[i, 2] = (gamma_star * (y[i] - xhat[i, 0]) + (1 - gamma_star) * xhat[prev, 2+m-1]) xhat[i, 3:] = xhat[prev, 2:2+m-1] def _ets_smooth_mul_mul(numeric [:] params, numeric [:] y, numeric [:] yhat, numeric [:,:] xhat, long [:] is_fixed, numeric [:] fixed_values, bool use_beta_star=False, bool use_gamma_star=False): """Smoothing with multiplicative trend and multiplicative season""" cdef numeric alpha, beta_star, gamma_star, phi cdef Py_ssize_t i, n, m, prev # get params alpha, beta_star, gamma_star, phi, m, n = _initialize_ets_smooth( params, xhat, is_fixed, fixed_values, use_beta_star, use_gamma_star ) # smooth for i in range(n): prev = (n+i-1) % n # s[t-m] = xhat[prev, 2+m-1] yhat[i] = (xhat[prev, 0] * xhat[prev, 1]**phi) * xhat[prev, 2+m-1] # l_t = a * (y_t / s_t-m) + (1-a) * (l_t-1 * b_t-1**phi) xhat[i, 0] = (alpha * (y[i] / xhat[prev, 2+m-1]) + (1 - alpha) * (xhat[prev, 0] * xhat[prev, 1]**phi)) # b_t = (b*) * (l_t / l_t-1) + (1 - (b*)) * b_t-1**phi xhat[i, 1] = (beta_star * (xhat[i, 0] / xhat[prev, 0]) + (1 - beta_star) * xhat[prev, 1]**phi) # s_t = g * (y_t / (l_t-1 * b_t-1**phi)) + (1 - g) * s_t-m xhat[i, 2] = (gamma_star * y[i] / xhat[i, 0] + (1 - gamma_star) * xhat[prev, 2+m-1]) xhat[i, 3:] = xhat[prev, 2:2+m-1] statsmodels-0.12.2/statsmodels/tsa/exponential_smoothing/base.py000066400000000000000000001071301400612667500252010ustar00rootroot00000000000000from collections import OrderedDict import contextlib import warnings import numpy as np import pandas as pd from scipy.stats import norm from statsmodels.base.data import PandasData from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.eval_measures import aic, aicc, bic, hqic from statsmodels.tools.sm_exceptions import PrecisionWarning from statsmodels.tools.numdiff import ( _get_epsilon, approx_fprime, approx_fprime_cs, approx_hess_cs, ) from statsmodels.tools.tools import pinv_extended import statsmodels.tsa.base.tsa_model as tsbase class StateSpaceMLEModel(tsbase.TimeSeriesModel): """ This is a temporary base model from ETS, here I just copy everything I need from statespace.mlemodel.MLEModel """ def __init__( self, endog, exog=None, dates=None, freq=None, missing="none", **kwargs ): # TODO: this was changed from the original, requires some work when # using this as base class for state space and exponential smoothing super().__init__( endog=endog, exog=exog, dates=dates, freq=freq, missing=missing ) # Store kwargs to recreate model self._init_kwargs = kwargs # Prepared the endog array: C-ordered, shape=(nobs x k_endog) self.endog, self.exog = self.prepare_data(self.data) self.use_pandas = isinstance(self.data, PandasData) # Dimensions self.nobs = self.endog.shape[0] # Setup holder for fixed parameters self._has_fixed_params = False self._fixed_params = None self._params_index = None self._fixed_params_index = None self._free_params_index = None @staticmethod def prepare_data(data): raise NotImplementedError def clone(self, endog, exog=None, **kwargs): raise NotImplementedError def _validate_can_fix_params(self, param_names): for param_name in param_names: if param_name not in self.param_names: raise ValueError( 'Invalid parameter name passed: "%s".' % param_name ) @property def k_params(self): return len(self.param_names) @contextlib.contextmanager def fix_params(self, params): """ Fix parameters to specific values (context manager) Parameters ---------- params : dict Dictionary describing the fixed parameter values, of the form `param_name: fixed_value`. See the `param_names` property for valid parameter names. Examples -------- >>> mod = sm.tsa.SARIMAX(endog, order=(1, 0, 1)) >>> with mod.fix_params({'ar.L1': 0.5}): res = mod.fit() """ # Initialization (this is done here rather than in the constructor # because param_names may not be available at that point) if self._fixed_params is None: self._fixed_params = {} self._params_index = OrderedDict( zip(self.param_names, np.arange(self.k_params)) ) # Cache the current fixed parameters cache_fixed_params = self._fixed_params.copy() cache_has_fixed_params = self._has_fixed_params cache_fixed_params_index = self._fixed_params_index cache_free_params_index = self._free_params_index # Validate parameter names and values self._validate_can_fix_params(set(params.keys())) # Set the new fixed parameters, keeping the order as given by # param_names self._fixed_params.update(params) self._fixed_params = OrderedDict( [ (name, self._fixed_params[name]) for name in self.param_names if name in self._fixed_params ] ) # Update associated values self._has_fixed_params = True self._fixed_params_index = [ self._params_index[key] for key in self._fixed_params.keys() ] self._free_params_index = list( set(np.arange(self.k_params)).difference(self._fixed_params_index) ) try: yield finally: # Reset the fixed parameters self._has_fixed_params = cache_has_fixed_params self._fixed_params = cache_fixed_params self._fixed_params_index = cache_fixed_params_index self._free_params_index = cache_free_params_index def fit_constrained(self, constraints, start_params=None, **fit_kwds): """ Fit the model with some parameters subject to equality constraints. Parameters ---------- constraints : dict Dictionary of constraints, of the form `param_name: fixed_value`. See the `param_names` property for valid parameter names. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. If None, the default is given by Model.start_params. **fit_kwds : keyword arguments fit_kwds are used in the optimization of the remaining parameters. Returns ------- results : Results instance Examples -------- >>> mod = sm.tsa.SARIMAX(endog, order=(1, 0, 1)) >>> res = mod.fit_constrained({'ar.L1': 0.5}) """ with self.fix_params(constraints): res = self.fit(start_params, **fit_kwds) return res @property def start_params(self): """ (array) Starting parameters for maximum likelihood estimation. """ if hasattr(self, "_start_params"): return self._start_params else: raise NotImplementedError @property def param_names(self): """ (list of str) List of human readable parameter names (for parameters actually included in the model). """ if hasattr(self, "_param_names"): return self._param_names else: try: names = ["param.%d" % i for i in range(len(self.start_params))] except NotImplementedError: names = [] return names @classmethod def from_formula( cls, formula, data, subset=None, drop_cols=None, *args, **kwargs ): """ Not implemented for state space models """ raise NotImplementedError def _wrap_data(self, data, start_idx, end_idx, names=None): # TODO: check if this is reasonable for statespace # squeezing data: data may be: # - m x n: m dates, n simulations -> squeeze does nothing # - m x 1: m dates, 1 simulation -> squeeze removes last dimension # - 1 x n: don't squeeze, already fine # - 1 x 1: squeeze only second axis if data.ndim > 1 and data.shape[1] == 1: data = np.squeeze(data, axis=1) if self.use_pandas: _, _, _, index = self._get_prediction_index(start_idx, end_idx) if data.ndim < 2: data = pd.Series(data, index=index, name=names) else: data = pd.DataFrame(data, index=index, columns=names) return data def _wrap_results( self, params, result, return_raw, cov_type=None, cov_kwds=None, results_class=None, wrapper_class=None, ): if not return_raw: # Wrap in a results object result_kwargs = {} if cov_type is not None: result_kwargs["cov_type"] = cov_type if cov_kwds is not None: result_kwargs["cov_kwds"] = cov_kwds if results_class is None: results_class = self._res_classes["fit"][0] if wrapper_class is None: wrapper_class = self._res_classes["fit"][1] res = results_class(self, params, result, **result_kwargs) result = wrapper_class(res) return result def _score_complex_step(self, params, **kwargs): # the default epsilon can be too small # inversion_method = INVERT_UNIVARIATE | SOLVE_LU epsilon = _get_epsilon(params, 2., None, len(params)) kwargs['transformed'] = True kwargs['complex_step'] = True return approx_fprime_cs(params, self.loglike, epsilon=epsilon, kwargs=kwargs) def _score_finite_difference(self, params, approx_centered=False, **kwargs): kwargs['transformed'] = True return approx_fprime(params, self.loglike, kwargs=kwargs, centered=approx_centered) def _hessian_finite_difference(self, params, approx_centered=False, **kwargs): params = np.array(params, ndmin=1) warnings.warn('Calculation of the Hessian using finite differences' ' is usually subject to substantial approximation' ' errors.', PrecisionWarning) if not approx_centered: epsilon = _get_epsilon(params, 3, None, len(params)) else: epsilon = _get_epsilon(params, 4, None, len(params)) / 2 hessian = approx_fprime(params, self._score_finite_difference, epsilon=epsilon, kwargs=kwargs, centered=approx_centered) # TODO: changed this to nobs_effective, has to be changed when merging # with statespace mlemodel return hessian / (self.nobs_effective) def _hessian_complex_step(self, params, **kwargs): """ Hessian matrix computed by second-order complex-step differentiation on the `loglike` function. """ # the default epsilon can be too small epsilon = _get_epsilon(params, 3., None, len(params)) kwargs['transformed'] = True kwargs['complex_step'] = True hessian = approx_hess_cs( params, self.loglike, epsilon=epsilon, kwargs=kwargs) # TODO: changed this to nobs_effective, has to be changed when merging # with statespace mlemodel return hessian / (self.nobs_effective) class StateSpaceMLEResults(tsbase.TimeSeriesModelResults): r""" Class to hold results from fitting a state space model. Parameters ---------- model : MLEModel instance The fitted model instance params : ndarray Fitted parameters Attributes ---------- model : Model instance A reference to the model that was fit. nobs : float The number of observations used to fit the model. params : ndarray The parameters of the model. """ def __init__(self, model, params, scale=1.0): self.data = model.data self.endog = model.data.orig_endog super().__init__(model, params, None, scale=scale) # Save the fixed parameters self._has_fixed_params = self.model._has_fixed_params self._fixed_params_index = self.model._fixed_params_index self._free_params_index = self.model._free_params_index # TODO: seems like maybe self.fixed_params should be the dictionary # itself, not just the keys? if self._has_fixed_params: self._fixed_params = self.model._fixed_params.copy() self.fixed_params = list(self._fixed_params.keys()) else: self._fixed_params = None self.fixed_params = [] self.param_names = [ "%s (fixed)" % name if name in self.fixed_params else name for name in (self.data.param_names or []) ] # Dimensions self.nobs = self.model.nobs self.k_params = self.model.k_params self._rank = None @cache_readonly def nobs_effective(self): raise NotImplementedError @cache_readonly def df_resid(self): return self.nobs_effective - self.df_model @cache_readonly def aic(self): """ (float) Akaike Information Criterion """ return aic(self.llf, self.nobs_effective, self.df_model) @cache_readonly def aicc(self): """ (float) Akaike Information Criterion with small sample correction """ return aicc(self.llf, self.nobs_effective, self.df_model) @cache_readonly def bic(self): """ (float) Bayes Information Criterion """ return bic(self.llf, self.nobs_effective, self.df_model) @cache_readonly def fittedvalues(self): # TODO raise NotImplementedError @cache_readonly def hqic(self): """ (float) Hannan-Quinn Information Criterion """ # return (-2 * self.llf + # 2 * np.log(np.log(self.nobs_effective)) * self.df_model) return hqic(self.llf, self.nobs_effective, self.df_model) @cache_readonly def llf(self): """ (float) The value of the log-likelihood function evaluated at `params`. """ raise NotImplementedError @cache_readonly def mae(self): """ (float) Mean absolute error """ return np.mean(np.abs(self.resid)) @cache_readonly def mse(self): """ (float) Mean squared error """ return self.sse / self.nobs @cache_readonly def pvalues(self): """ (array) The p-values associated with the z-statistics of the coefficients. Note that the coefficients are assumed to have a Normal distribution. """ pvalues = np.zeros_like(self.zvalues) * np.nan mask = np.ones_like(pvalues, dtype=bool) mask[self._free_params_index] = True mask &= ~np.isnan(self.zvalues) pvalues[mask] = norm.sf(np.abs(self.zvalues[mask])) * 2 return pvalues @cache_readonly def resid(self): raise NotImplementedError @cache_readonly def sse(self): """ (float) Sum of squared errors """ return np.sum(self.resid ** 2) @cache_readonly def zvalues(self): """ (array) The z-statistics for the coefficients. """ return self.params / self.bse def _get_prediction_start_index(self, anchor): """Returns a valid numeric start index for predictions/simulations""" if anchor is None or anchor == "start": iloc = 0 elif anchor == "end": iloc = self.nobs else: iloc, _, _ = self.model._get_index_loc(anchor) if isinstance(iloc, slice): iloc = iloc.start iloc += 1 # anchor is one before start of prediction/simulation if iloc < 0: iloc = self.nobs + iloc if iloc > self.nobs: raise ValueError("Cannot anchor simulation outside of the sample.") return iloc def _cov_params_approx( self, approx_complex_step=True, approx_centered=False ): evaluated_hessian = self.nobs_effective * self.model.hessian( params=self.params, transformed=True, includes_fixed=True, method="approx", approx_complex_step=approx_complex_step, approx_centered=approx_centered, ) # TODO: Case with "not approx_complex_step" is not hit in # tests as of 2017-05-19 if len(self.fixed_params) > 0: mask = np.ix_(self._free_params_index, self._free_params_index) if len(self.fixed_params) < self.k_params: (tmp, singular_values) = pinv_extended(evaluated_hessian[mask]) else: tmp, singular_values = np.nan, [np.nan] neg_cov = np.zeros_like(evaluated_hessian) * np.nan neg_cov[mask] = tmp else: (neg_cov, singular_values) = pinv_extended(evaluated_hessian) self.model.update(self.params, transformed=True, includes_fixed=True) if self._rank is None: self._rank = np.linalg.matrix_rank(np.diag(singular_values)) return -neg_cov @cache_readonly def cov_params_approx(self): """ (array) The variance / covariance matrix. Computed using the numerical Hessian approximated by complex step or finite differences methods. """ return self._cov_params_approx( self._cov_approx_complex_step, self._cov_approx_centered ) def test_serial_correlation(self, method, lags=None): """ Ljung-Box test for no serial correlation of standardized residuals Null hypothesis is no serial correlation. Parameters ---------- method : {'ljungbox','boxpierece', None} The statistical test for serial correlation. If None, an attempt is made to select an appropriate test. lags : None, int or array_like If lags is an integer then this is taken to be the largest lag that is included, the test result is reported for all smaller lag length. If lags is a list or array, then all lags are included up to the largest lag in the list, however only the tests for the lags in the list are reported. If lags is None, then the default maxlag is 12*(nobs/100)^{1/4} Returns ------- output : ndarray An array with `(test_statistic, pvalue)` for each endogenous variable and each lag. The array is then sized `(k_endog, 2, lags)`. If the method is called as `ljungbox = res.test_serial_correlation()`, then `ljungbox[i]` holds the results of the Ljung-Box test (as would be returned by `statsmodels.stats.diagnostic.acorr_ljungbox`) for the `i` th endogenous variable. See Also -------- statsmodels.stats.diagnostic.acorr_ljungbox Ljung-Box test for serial correlation. Notes ----- For statespace models: let `d` = max(loglikelihood_burn, nobs_diffuse); this test is calculated ignoring the first `d` residuals. Output is nan for any endogenous variable which has missing values. """ if method is None: method = 'ljungbox' if self.standardized_forecasts_error is None: raise ValueError('Cannot compute test statistic when standardized' ' forecast errors have not been computed.') if method == 'ljungbox' or method == 'boxpierce': from statsmodels.stats.diagnostic import acorr_ljungbox if hasattr(self, "loglikelihood_burn"): d = np.maximum(self.loglikelihood_burn, self.nobs_diffuse) # This differs from self.nobs_effective because here we want to # exclude exact diffuse periods, whereas self.nobs_effective # only excludes explicitly burned (usually approximate diffuse) # periods. nobs_effective = self.nobs - d else: nobs_effective = self.nobs_effective output = [] # Default lags for acorr_ljungbox is 40, but may not always have # that many observations if lags is None: seasonal_periods = getattr(self.model, "seasonal_periods", 0) if seasonal_periods: lags = min(2 * seasonal_periods, nobs_effective // 5) else: lags = min(10, nobs_effective // 5) warnings.warn( "The default value of lags is changing. After 0.12, " "this value will become min(10, nobs//5) for non-seasonal " "time series and min (2*m, nobs//5) for seasonal time " "series. Directly set lags to silence this warning.", FutureWarning ) for i in range(self.model.k_endog): if hasattr(self, "filter_results"): x = self.filter_results.standardized_forecasts_error[i][d:] else: x = self.standardized_forecasts_error results = acorr_ljungbox( x, lags=lags, boxpierce=(method == 'boxpierce'), return_df=False) if method == 'ljungbox': output.append(results[0:2]) else: output.append(results[2:]) output = np.c_[output] else: raise NotImplementedError('Invalid serial correlation test' ' method.') return output def test_heteroskedasticity(self, method, alternative='two-sided', use_f=True): r""" Test for heteroskedasticity of standardized residuals Tests whether the sum-of-squares in the first third of the sample is significantly different than the sum-of-squares in the last third of the sample. Analogous to a Goldfeld-Quandt test. The null hypothesis is of no heteroskedasticity. Parameters ---------- method : {'breakvar', None} The statistical test for heteroskedasticity. Must be 'breakvar' for test of a break in the variance. If None, an attempt is made to select an appropriate test. alternative : str, 'increasing', 'decreasing' or 'two-sided' This specifies the alternative for the p-value calculation. Default is two-sided. use_f : bool, optional Whether or not to compare against the asymptotic distribution (chi-squared) or the approximate small-sample distribution (F). Default is True (i.e. default is to compare against an F distribution). Returns ------- output : ndarray An array with `(test_statistic, pvalue)` for each endogenous variable. The array is then sized `(k_endog, 2)`. If the method is called as `het = res.test_heteroskedasticity()`, then `het[0]` is an array of size 2 corresponding to the first endogenous variable, where `het[0][0]` is the test statistic, and `het[0][1]` is the p-value. Notes ----- The null hypothesis is of no heteroskedasticity. That means different things depending on which alternative is selected: - Increasing: Null hypothesis is that the variance is not increasing throughout the sample; that the sum-of-squares in the later subsample is *not* greater than the sum-of-squares in the earlier subsample. - Decreasing: Null hypothesis is that the variance is not decreasing throughout the sample; that the sum-of-squares in the earlier subsample is *not* greater than the sum-of-squares in the later subsample. - Two-sided: Null hypothesis is that the variance is not changing throughout the sample. Both that the sum-of-squares in the earlier subsample is not greater than the sum-of-squares in the later subsample *and* that the sum-of-squares in the later subsample is not greater than the sum-of-squares in the earlier subsample. For :math:`h = [T/3]`, the test statistic is: .. math:: H(h) = \sum_{t=T-h+1}^T \tilde v_t^2 \Bigg / \sum_{t=d+1}^{d+1+h} \tilde v_t^2 where :math:`d` = max(loglikelihood_burn, nobs_diffuse)` (usually corresponding to diffuse initialization under either the approximate or exact approach). This statistic can be tested against an :math:`F(h,h)` distribution. Alternatively, :math:`h H(h)` is asymptotically distributed according to :math:`\chi_h^2`; this second test can be applied by passing `asymptotic=True` as an argument. See section 5.4 of [1]_ for the above formula and discussion, as well as additional details. TODO - Allow specification of :math:`h` References ---------- .. [1] Harvey, Andrew C. 1990. *Forecasting, Structural Time Series* *Models and the Kalman Filter.* Cambridge University Press. """ if method is None: method = 'breakvar' if self.standardized_forecasts_error is None: raise ValueError('Cannot compute test statistic when standardized' ' forecast errors have not been computed.') if method == 'breakvar': # Store some values if hasattr(self, "filter_results"): squared_resid = ( self.filter_results.standardized_forecasts_error**2 ) d = np.maximum(self.loglikelihood_burn, self.nobs_diffuse) # This differs from self.nobs_effective because here we want to # exclude exact diffuse periods, whereas self.nobs_effective # only excludes explicitly burned (usually approximate diffuse) # periods. nobs_effective = self.nobs - d else: squared_resid = self.standardized_forecasts_error**2 if squared_resid.ndim == 1: squared_resid = np.asarray(squared_resid) squared_resid = squared_resid[np.newaxis, :] nobs_effective = self.nobs_effective d = 0 squared_resid = np.asarray(squared_resid) test_statistics = [] p_values = [] for i in range(self.model.k_endog): h = int(np.round(nobs_effective / 3)) numer_resid = squared_resid[i, -h:] numer_resid = numer_resid[~np.isnan(numer_resid)] numer_dof = len(numer_resid) denom_resid = squared_resid[i, d:d + h] denom_resid = denom_resid[~np.isnan(denom_resid)] denom_dof = len(denom_resid) if numer_dof < 2: warnings.warn('Early subset of data for variable %d' ' has too few non-missing observations to' ' calculate test statistic.' % i) numer_resid = np.nan if denom_dof < 2: warnings.warn('Later subset of data for variable %d' ' has too few non-missing observations to' ' calculate test statistic.' % i) denom_resid = np.nan test_statistic = np.sum(numer_resid) / np.sum(denom_resid) # Setup functions to calculate the p-values if use_f: from scipy.stats import f pval_lower = lambda test_statistics: f.cdf( # noqa:E731 test_statistics, numer_dof, denom_dof) pval_upper = lambda test_statistics: f.sf( # noqa:E731 test_statistics, numer_dof, denom_dof) else: from scipy.stats import chi2 pval_lower = lambda test_statistics: chi2.cdf( # noqa:E731 numer_dof * test_statistics, denom_dof) pval_upper = lambda test_statistics: chi2.sf( # noqa:E731 numer_dof * test_statistics, denom_dof) # Calculate the one- or two-sided p-values alternative = alternative.lower() if alternative in ['i', 'inc', 'increasing']: p_value = pval_upper(test_statistic) elif alternative in ['d', 'dec', 'decreasing']: test_statistic = 1. / test_statistic p_value = pval_upper(test_statistic) elif alternative in ['2', '2-sided', 'two-sided']: p_value = 2 * np.minimum( pval_lower(test_statistic), pval_upper(test_statistic) ) else: raise ValueError('Invalid alternative.') test_statistics.append(test_statistic) p_values.append(p_value) output = np.c_[test_statistics, p_values] else: raise NotImplementedError('Invalid heteroskedasticity test' ' method.') return output def test_normality(self, method): """ Test for normality of standardized residuals. Null hypothesis is normality. Parameters ---------- method : {'jarquebera', None} The statistical test for normality. Must be 'jarquebera' for Jarque-Bera normality test. If None, an attempt is made to select an appropriate test. See Also -------- statsmodels.stats.stattools.jarque_bera The Jarque-Bera test of normality. Notes ----- For statespace models: let `d` = max(loglikelihood_burn, nobs_diffuse); this test is calculated ignoring the first `d` residuals. In the case of missing data, the maintained hypothesis is that the data are missing completely at random. This test is then run on the standardized residuals excluding those corresponding to missing observations. """ if method is None: method = 'jarquebera' if self.standardized_forecasts_error is None: raise ValueError('Cannot compute test statistic when standardized' ' forecast errors have not been computed.') if method == 'jarquebera': from statsmodels.stats.stattools import jarque_bera if hasattr(self, "loglikelihood_burn"): d = np.maximum(self.loglikelihood_burn, self.nobs_diffuse) else: d = 0 output = [] for i in range(self.model.k_endog): if hasattr(self, "fiter_results"): resid = self.filter_results.standardized_forecasts_error[ i, d: ] else: resid = self.standardized_forecasts_error mask = ~np.isnan(resid) output.append(jarque_bera(resid[mask])) else: raise NotImplementedError('Invalid normality test method.') return np.array(output) def summary( self, alpha=0.05, start=None, title=None, model_name=None, display_params=True, ): """ Summarize the Model Parameters ---------- alpha : float, optional Significance level for the confidence intervals. Default is 0.05. start : int, optional Integer of the start observation. Default is 0. model_name : str The name of the model used. Default is to use model class name. Returns ------- summary : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary """ from statsmodels.iolib.summary import Summary # Model specification results model = self.model if title is None: title = "Statespace Model Results" if start is None: start = 0 if self.model._index_dates: ix = self.model._index d = ix[start] sample = ["%02d-%02d-%02d" % (d.month, d.day, d.year)] d = ix[-1] sample += ["- " + "%02d-%02d-%02d" % (d.month, d.day, d.year)] else: sample = [str(start), " - " + str(self.nobs)] # Standardize the model name as a list of str if model_name is None: model_name = model.__class__.__name__ # Diagnostic tests results try: het = self.test_heteroskedasticity(method="breakvar") except Exception: # FIXME: catch something specific het = np.array([[np.nan] * 2]) try: with warnings.catch_warnings(): warnings.simplefilter("ignore", FutureWarning) lb = self.test_serial_correlation(method="ljungbox") except Exception: # FIXME: catch something specific lb = np.array([[np.nan] * 2]).reshape(1, 2, 1) try: jb = self.test_normality(method="jarquebera") except Exception: # FIXME: catch something specific jb = np.array([[np.nan] * 4]) # Create the tables if not isinstance(model_name, list): model_name = [model_name] top_left = [("Dep. Variable:", None)] top_left.append(("Model:", [model_name[0]])) for i in range(1, len(model_name)): top_left.append(("", ["+ " + model_name[i]])) top_left += [ ("Date:", None), ("Time:", None), ("Sample:", [sample[0]]), ("", [sample[1]]), ] top_right = [ ("No. Observations:", [self.nobs]), ("Log Likelihood", ["%#5.3f" % self.llf]), ] if hasattr(self, "rsquared"): top_right.append(("R-squared:", ["%#8.3f" % self.rsquared])) top_right += [ ("AIC", ["%#5.3f" % self.aic]), ("BIC", ["%#5.3f" % self.bic]), ("HQIC", ["%#5.3f" % self.hqic]), ] if hasattr(self, "filter_results"): if ( self.filter_results is not None and self.filter_results.filter_concentrated ): top_right.append(("Scale", ["%#5.3f" % self.scale])) else: top_right.append(("Scale", ["%#5.3f" % self.scale])) if hasattr(self, "cov_type"): top_left.append(("Covariance Type:", [self.cov_type])) format_str = lambda array: [ # noqa:E731 ", ".join(["{0:.2f}".format(i) for i in array]) ] diagn_left = [ ("Ljung-Box (Q):", format_str(lb[:, 0, -1])), ("Prob(Q):", format_str(lb[:, 1, -1])), ("Heteroskedasticity (H):", format_str(het[:, 0])), ("Prob(H) (two-sided):", format_str(het[:, 1])), ] diagn_right = [ ("Jarque-Bera (JB):", format_str(jb[:, 0])), ("Prob(JB):", format_str(jb[:, 1])), ("Skew:", format_str(jb[:, 2])), ("Kurtosis:", format_str(jb[:, 3])), ] summary = Summary() summary.add_table_2cols( self, gleft=top_left, gright=top_right, title=title ) if len(self.params) > 0 and display_params: summary.add_table_params( self, alpha=alpha, xname=self.param_names, use_t=False ) summary.add_table_2cols( self, gleft=diagn_left, gright=diagn_right, title="" ) # Add warnings/notes, added to text format only etext = [] if hasattr(self, "cov_type") and "description" in self.cov_kwds: etext.append(self.cov_kwds["description"]) if self._rank < (len(self.params) - len(self.fixed_params)): cov_params = self.cov_params() if len(self.fixed_params) > 0: mask = np.ix_(self._free_params_index, self._free_params_index) cov_params = cov_params[mask] etext.append( "Covariance matrix is singular or near-singular," " with condition number %6.3g. Standard errors may be" " unstable." % np.linalg.cond(cov_params) ) if etext: etext = [ "[{0}] {1}".format(i + 1, text) for i, text in enumerate(etext) ] etext.insert(0, "Warnings:") summary.add_extra_txt(etext) return summary statsmodels-0.12.2/statsmodels/tsa/exponential_smoothing/ets.py000066400000000000000000002517111400612667500250670ustar00rootroot00000000000000r""" ETS models for time series analysis. The ETS models are a family of time series models. They can be seen as a generalization of simple exponential smoothing to time series that contain trends and seasonalities. Additionally, they have an underlying state space model. An ETS model is specified by an error type (E; additive or multiplicative), a trend type (T; additive or multiplicative, both damped or undamped, or none), and a seasonality type (S; additive or multiplicative or none). The following gives a very short summary, a more thorough introduction can be found in [1]_. Denote with :math:`\circ_b` the trend operation (addition or multiplication), with :math:`\circ_d` the operation linking trend and dampening factor :math:`\phi` (multiplication if trend is additive, power if trend is multiplicative), and with :math:`\circ_s` the seasonality operation (addition or multiplication). Furthermore, let :math:`\ominus` be the respective inverse operation (subtraction or division). With this, it is possible to formulate the ETS models as a forecast equation and 3 smoothing equations. The former is used to forecast observations, the latter are used to update the internal state. .. math:: \hat{y}_{t|t-1} &= (l_{t-1} \circ_b (b_{t-1}\circ_d \phi))\circ_s s_{t-m}\\ l_{t} &= \alpha (y_{t} \ominus_s s_{t-m}) + (1 - \alpha) (l_{t-1} \circ_b (b_{t-1} \circ_d \phi))\\ b_{t} &= \beta/\alpha (l_{t} \ominus_b l_{t-1}) + (1 - \beta/\alpha) b_{t-1}\\ s_{t} &= \gamma (y_t \ominus_s (l_{t-1} \circ_b (b_{t-1}\circ_d\phi)) + (1 - \gamma) s_{t-m} The notation here follows [1]_; :math:`l_t` denotes the level at time :math:`t`, `b_t` the trend, and `s_t` the seasonal component. :math:`m` is the number of seasonal periods, and :math:`\phi` a trend damping factor. The parameters :math:`\alpha, \beta, \gamma` are the smoothing parameters, which are called ``smoothing_level``, ``smoothing_trend``, and ``smoothing_seasonal``, respectively. Note that the formulation above as forecast and smoothing equation does not distinguish different error models -- it is the same for additive and multiplicative errors. But the different error models lead to different likelihood models, and therefore will lead to different fit results. The error models specify how the true values :math:`y_t` are updated. In the additive error model, .. math:: y_t = \hat{y}_{t|t-1} + e_t, in the multiplicative error model, .. math:: y_t = \hat{y}_{t|t-1}\cdot (1 + e_t). Using these error models, it is possible to formulate state space equations for the ETS models: .. math:: y_t &= Y_t + \eta \cdot e_t\\ l_t &= L_t + \alpha \cdot (M_e \cdot L_t + \kappa_l) \cdot e_t\\ b_t &= B_t + \beta \cdot (M_e \cdot B_t + \kappa_b) \cdot e_t\\ s_t &= S_t + \gamma \cdot (M_e \cdot S_t+\kappa_s)\cdot e_t\\ with .. math:: B_t &= b_{t-1} \circ_d \phi\\ L_t &= l_{t-1} \circ_b B_t\\ S_t &= s_{t-m}\\ Y_t &= L_t \circ_s S_t, and .. math:: \eta &= \begin{cases} Y_t\quad\text{if error is multiplicative}\\ 1\quad\text{else} \end{cases}\\ M_e &= \begin{cases} 1\quad\text{if error is multiplicative}\\ 0\quad\text{else} \end{cases}\\ and, when using the additive error model, .. math:: \kappa_l &= \begin{cases} \frac{1}{S_t}\quad \text{if seasonality is multiplicative}\\ 1\quad\text{else} \end{cases}\\ \kappa_b &= \begin{cases} \frac{\kappa_l}{l_{t-1}}\quad \text{if trend is multiplicative}\\ \kappa_l\quad\text{else} \end{cases}\\ \kappa_s &= \begin{cases} \frac{1}{L_t}\quad\text{if seasonality is multiplicative}\\ 1\quad\text{else} \end{cases} When using the multiplicative error model .. math:: \kappa_l &= \begin{cases} 0\quad \text{if seasonality is multiplicative}\\ S_t\quad\text{else} \end{cases}\\ \kappa_b &= \begin{cases} \frac{\kappa_l}{l_{t-1}}\quad \text{if trend is multiplicative}\\ \kappa_l + l_{t-1}\quad\text{else} \end{cases}\\ \kappa_s &= \begin{cases} 0\quad\text{if seasonality is multiplicative}\\ L_t\quad\text{else} \end{cases} When fitting an ETS model, the parameters :math:`\alpha, \beta`, \gamma, \phi` and the initial states `l_{-1}, b_{-1}, s_{-1}, \ldots, s_{-m}` are selected as maximizers of log likelihood. References ---------- .. [1] Hyndman, R.J., & Athanasopoulos, G. (2019) *Forecasting: principles and practice*, 3rd edition, OTexts: Melbourne, Australia. OTexts.com/fpp3. Accessed on April 19th 2020. """ from collections import OrderedDict import contextlib import datetime as dt import numpy as np import pandas as pd from scipy.stats import _distn_infrastructure, norm, rv_continuous, rv_discrete from statsmodels.base.covtype import descriptions import statsmodels.base.wrapper as wrap from statsmodels.iolib.summary import forg from statsmodels.iolib.table import SimpleTable from statsmodels.iolib.tableformatting import fmt_params from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.tools import Bunch from statsmodels.tools.validation import ( array_like, bool_like, int_like, string_like, ) import statsmodels.tsa.base.tsa_model as tsbase from statsmodels.tsa.exponential_smoothing import base import statsmodels.tsa.exponential_smoothing._ets_smooth as smooth from statsmodels.tsa.exponential_smoothing.initialization import ( _initialization_heuristic, ) from statsmodels.tsa.tsatools import freq_to_period # Implementation details: # * The smoothing equations are implemented only for models having all # components (trend, dampening, seasonality). When using other models, the # respective parameters (smoothing and initial parameters) are set to values # that lead to the reduced model (often zero). # The internal model is needed for smoothing (called from fit and loglike), # forecasts, and simulations. # * Somewhat related to above: There are 2 sets of parameters: model/external # params, and internal params. # - model params are all parameters necessary for a model, and are for # example passed as argument to the likelihood function or as start_params # to fit # - internal params are what is used internally in the smoothing equations # * Regarding fitting, bounds, fixing parameters, and internal parameters, the # overall workflow is the following: # - get start parameters in the form of external parameters (includes fixed # parameters) # - transform external parameters to internal parameters, bounding all that # are missing -> now we have some missing parameters, but potentially also # some user-specified bounds # - set bounds for fixed parameters # - make sure that starting parameters are within bounds # - set up the constraint bounds and function # * Since the traditional bounds are nonlinear for beta and gamma, if no bounds # are given, we internally use beta_star and gamma_star for fitting # * When estimating initial level and initial seasonal values, one of them has # to be removed in order to have a well posed problem. I am solving this by # fixing the last initial seasonal value to 0 (for additive seasonality) or 1 # (for multiplicative seasonality). # For the additive models, this means I have to subtract the last initial # seasonal value from all initial seasonal values and add it to the initial # level; for the multiplicative models I do the same with division and # multiplication class ETSModel(base.StateSpaceMLEModel): r""" ETS models. Parameters ---------- endog : array_like The observed time-series process :math:`y` error : str, optional The error model. "add" (default) or "mul". trend : str or None, optional The trend component model. "add", "mul", or None (default). damped_trend : bool, optional Whether or not an included trend component is damped. Default is False. seasonal : str, optional The seasonality model. "add", "mul", or None (default). seasonal_periods : int, optional The number of periods in a complete seasonal cycle for seasonal (Holt-Winters) models. For example, 4 for quarterly data with an annual cycle or 7 for daily data with a weekly cycle. Required if `seasonal` is not None. initialization_method : str, optional Method for initialization of the state space model. One of: * 'estimated' (default) * 'heuristic' * 'known' If 'known' initialization is used, then `initial_level` must be passed, as well as `initial_trend` and `initial_seasonal` if applicable. 'heuristic' uses a heuristic based on the data to estimate initial level, trend, and seasonal state. 'estimated' uses the same heuristic as initial guesses, but then estimates the initial states as part of the fitting process. Default is 'estimated'. initial_level : float, optional The initial level component. Only used if initialization is 'known'. initial_trend : float, optional The initial trend component. Only used if initialization is 'known'. initial_seasonal : array_like, optional The initial seasonal component. An array of length `seasonal_periods`. Only used if initialization is 'known'. bounds : dict or None, optional A dictionary with parameter names as keys and the respective bounds intervals as values (lists/tuples/arrays). The available parameter names are, depending on the model and initialization method: * "smoothing_level" * "smoothing_trend" * "smoothing_seasonal" * "damping_trend" * "initial_level" * "initial_trend" * "initial_seasonal.0", ..., "initial_seasonal." The default option is ``None``, in which case the traditional (nonlinear) bounds as described in [1]_ are used. Notes ----- The ETS models are a family of time series models. They can be seen as a generalization of simple exponential smoothing to time series that contain trends and seasonalities. Additionally, they have an underlying state space model. An ETS model is specified by an error type (E; additive or multiplicative), a trend type (T; additive or multiplicative, both damped or undamped, or none), and a seasonality type (S; additive or multiplicative or none). The following gives a very short summary, a more thorough introduction can be found in [1]_. Denote with :math:`\circ_b` the trend operation (addition or multiplication), with :math:`\circ_d` the operation linking trend and dampening factor :math:`\phi` (multiplication if trend is additive, power if trend is multiplicative), and with :math:`\circ_s` the seasonality operation (addition or multiplication). Furthermore, let :math:`\ominus` be the respective inverse operation (subtraction or division). With this, it is possible to formulate the ETS models as a forecast equation and 3 smoothing equations. The former is used to forecast observations, the latter are used to update the internal state. .. math:: \hat{y}_{t|t-1} &= (l_{t-1} \circ_b (b_{t-1}\circ_d \phi)) \circ_s s_{t-m}\\ l_{t} &= \alpha (y_{t} \ominus_s s_{t-m}) + (1 - \alpha) (l_{t-1} \circ_b (b_{t-1} \circ_d \phi))\\ b_{t} &= \beta/\alpha (l_{t} \ominus_b l_{t-1}) + (1 - \beta/\alpha) b_{t-1}\\ s_{t} &= \gamma (y_t \ominus_s (l_{t-1} \circ_b (b_{t-1}\circ_d\phi)) + (1 - \gamma) s_{t-m} The notation here follows [1]_; :math:`l_t` denotes the level at time :math:`t`, `b_t` the trend, and `s_t` the seasonal component. :math:`m` is the number of seasonal periods, and :math:`\phi` a trend damping factor. The parameters :math:`\alpha, \beta, \gamma` are the smoothing parameters, which are called ``smoothing_level``, ``smoothing_trend``, and ``smoothing_seasonal``, respectively. Note that the formulation above as forecast and smoothing equation does not distinguish different error models -- it is the same for additive and multiplicative errors. But the different error models lead to different likelihood models, and therefore will lead to different fit results. The error models specify how the true values :math:`y_t` are updated. In the additive error model, .. math:: y_t = \hat{y}_{t|t-1} + e_t, in the multiplicative error model, .. math:: y_t = \hat{y}_{t|t-1}\cdot (1 + e_t). Using these error models, it is possible to formulate state space equations for the ETS models: .. math:: y_t &= Y_t + \eta \cdot e_t\\ l_t &= L_t + \alpha \cdot (M_e \cdot L_t + \kappa_l) \cdot e_t\\ b_t &= B_t + \beta \cdot (M_e \cdot B_t + \kappa_b) \cdot e_t\\ s_t &= S_t + \gamma \cdot (M_e \cdot S_t+\kappa_s)\cdot e_t\\ with .. math:: B_t &= b_{t-1} \circ_d \phi\\ L_t &= l_{t-1} \circ_b B_t\\ S_t &= s_{t-m}\\ Y_t &= L_t \circ_s S_t, and .. math:: \eta &= \begin{cases} Y_t\quad\text{if error is multiplicative}\\ 1\quad\text{else} \end{cases}\\ M_e &= \begin{cases} 1\quad\text{if error is multiplicative}\\ 0\quad\text{else} \end{cases}\\ and, when using the additive error model, .. math:: \kappa_l &= \begin{cases} \frac{1}{S_t}\quad \text{if seasonality is multiplicative}\\ 1\quad\text{else} \end{cases}\\ \kappa_b &= \begin{cases} \frac{\kappa_l}{l_{t-1}}\quad \text{if trend is multiplicative}\\ \kappa_l\quad\text{else} \end{cases}\\ \kappa_s &= \begin{cases} \frac{1}{L_t}\quad\text{if seasonality is multiplicative}\\ 1\quad\text{else} \end{cases} When using the multiplicative error model .. math:: \kappa_l &= \begin{cases} 0\quad \text{if seasonality is multiplicative}\\ S_t\quad\text{else} \end{cases}\\ \kappa_b &= \begin{cases} \frac{\kappa_l}{l_{t-1}}\quad \text{if trend is multiplicative}\\ \kappa_l + l_{t-1}\quad\text{else} \end{cases}\\ \kappa_s &= \begin{cases} 0\quad\text{if seasonality is multiplicative}\\ L_t\quad\text{else} \end{cases} When fitting an ETS model, the parameters :math:`\alpha, \beta`, \gamma, \phi` and the initial states `l_{-1}, b_{-1}, s_{-1}, \ldots, s_{-m}` are selected as maximizers of log likelihood. References ---------- .. [1] Hyndman, R.J., & Athanasopoulos, G. (2019) *Forecasting: principles and practice*, 3rd edition, OTexts: Melbourne, Australia. OTexts.com/fpp3. Accessed on April 19th 2020. """ def __init__( self, endog, error="add", trend=None, damped_trend=False, seasonal=None, seasonal_periods=None, initialization_method="estimated", initial_level=None, initial_trend=None, initial_seasonal=None, bounds=None, dates=None, freq=None, missing="none", ): super().__init__( endog, exog=None, dates=dates, freq=freq, missing=missing ) # MODEL DEFINITION # ================ options = ("add", "mul", "additive", "multiplicative") # take first three letters of option -> either "add" or "mul" self.error = string_like(error, "error", options=options)[:3] self.trend = string_like( trend, "trend", options=options, optional=True ) if self.trend is not None: self.trend = self.trend[:3] self.damped_trend = bool_like(damped_trend, "damped_trend") self.seasonal = string_like( seasonal, "seasonal", options=options, optional=True ) if self.seasonal is not None: self.seasonal = self.seasonal[:3] self.has_trend = self.trend is not None self.has_seasonal = self.seasonal is not None if self.has_seasonal: self.seasonal_periods = int_like( seasonal_periods, "seasonal_periods", optional=True ) if seasonal_periods is None: self.seasonal_periods = freq_to_period(self._index_freq) if self.seasonal_periods <= 1: raise ValueError("seasonal_periods must be larger than 1.") else: # in case the model has no seasonal component, we internally handle # this as if it had an additive seasonal component with # seasonal_periods=1, but restrict the smoothing parameter to 0 and # set the initial seasonal to 0. self.seasonal_periods = 1 # reject invalid models if np.any(self.endog <= 0) and ( self.error == "mul" or self.trend == "mul" or self.seasonal == "mul" ): raise ValueError( "endog must be strictly positive when using" "multiplicative error, trend or seasonal components." ) if self.damped_trend and not self.has_trend: raise ValueError("Can only dampen the trend component") # INITIALIZATION METHOD # ===================== self.set_initialization_method( initialization_method, initial_level, initial_trend, initial_seasonal, ) # BOUNDS # ====== self.set_bounds(bounds) # SMOOTHER # ======== if self.trend == "add" or self.trend is None: if self.seasonal == "add" or self.seasonal is None: self._smoothing_func = smooth._ets_smooth_add_add else: self._smoothing_func = smooth._ets_smooth_add_mul else: if self.seasonal == "add" or self.seasonal is None: self._smoothing_func = smooth._ets_smooth_mul_add else: self._smoothing_func = smooth._ets_smooth_mul_mul def set_initialization_method( self, initialization_method, initial_level=None, initial_trend=None, initial_seasonal=None, ): """ Sets a new initialization method for the state space model. Parameters ---------- initialization_method : str, optional Method for initialization of the state space model. One of: * 'estimated' (default) * 'heuristic' * 'known' If 'known' initialization is used, then `initial_level` must be passed, as well as `initial_trend` and `initial_seasonal` if applicable. 'heuristic' uses a heuristic based on the data to estimate initial level, trend, and seasonal state. 'estimated' uses the same heuristic as initial guesses, but then estimates the initial states as part of the fitting process. Default is 'estimated'. initial_level : float, optional The initial level component. Only used if initialization is 'known'. initial_trend : float, optional The initial trend component. Only used if initialization is 'known'. initial_seasonal : array_like, optional The initial seasonal component. An array of length `seasonal_periods`. Only used if initialization is 'known'. """ self.initialization_method = string_like( initialization_method, "initialization_method", options=("estimated", "known", "heuristic"), ) if self.initialization_method == "known": if initial_level is None: raise ValueError( "`initial_level` argument must be provided" ' when initialization method is set to "known".' ) if self.has_trend and initial_trend is None: raise ValueError( "`initial_trend` argument must be provided" " for models with a trend component when" ' initialization method is set to "known".' ) if self.has_seasonal and initial_seasonal is None: raise ValueError( "`initial_seasonal` argument must be provided" " for models with a seasonal component when" ' initialization method is set to "known".' ) elif ( self.initialization_method == "heuristic" or self.initialization_method == "estimated" ): ( initial_level, initial_trend, initial_seasonal, ) = _initialization_heuristic( self.endog, trend=self.trend, seasonal=self.seasonal, seasonal_periods=self.seasonal_periods, ) if not self.has_trend: initial_trend = 0 if not self.has_seasonal: initial_seasonal = 0 self.initial_level = initial_level self.initial_trend = initial_trend self.initial_seasonal = initial_seasonal # we also have to reset the params index dictionaries self._internal_params_index = OrderedDict( zip(self._internal_param_names, np.arange(self._k_params_internal)) ) self._params_index = OrderedDict( zip(self.param_names, np.arange(self.k_params)) ) def set_bounds(self, bounds): """ Set bounds for parameter estimation. Parameters ---------- bounds : dict or None, optional A dictionary with parameter names as keys and the respective bounds intervals as values (lists/tuples/arrays). The available parameter names are in ``self.param_names``. The default option is ``None``, in which case the traditional (nonlinear) bounds as described in [1]_ are used. References ---------- .. [1] Hyndman, R.J., & Athanasopoulos, G. (2019) *Forecasting: principles and practice*, 3rd edition, OTexts: Melbourne, Australia. OTexts.com/fpp3. Accessed on April 19th 2020. """ if bounds is None: self.bounds = {} else: if not isinstance(bounds, (dict, OrderedDict)): raise ValueError("bounds must be a dictionary") for key in bounds: if key not in self.param_names: raise ValueError( f"Invalid key: {key} in bounds dictionary" ) bounds[key] = array_like( bounds[key], f"bounds[{key}]", shape=(2,) ) self.bounds = bounds @staticmethod def prepare_data(data): """ Prepare data for use in the state space representation """ endog = np.array(data.orig_endog, order="C") if endog.ndim != 1: raise ValueError("endog must be 1-dimensional") return endog, None @property def nobs_effective(self): return self.nobs @property def k_endog(self): return 1 @property def short_name(self): name = "".join( [ str(s)[0].upper() for s in [self.error, self.trend, self.seasonal] ] ) if self.damped_trend: name = name[0:2] + "d" + name[2] return name @property def _param_names(self): param_names = ["smoothing_level"] if self.has_trend: param_names += ["smoothing_trend"] if self.has_seasonal: param_names += ["smoothing_seasonal"] if self.damped_trend: param_names += ["damping_trend"] # Initialization if self.initialization_method == "estimated": param_names += ["initial_level"] if self.has_trend: param_names += ["initial_trend"] if self.has_seasonal: param_names += [ f"initial_seasonal.{i}" for i in range(self.seasonal_periods) ] return param_names @property def state_names(self): names = ["level"] if self.has_trend: names += ["trend"] if self.has_seasonal: names += ["seasonal"] return names @property def initial_state_names(self): names = ["initial_level"] if self.has_trend: names += ["initial_trend"] if self.has_seasonal: names += [ f"initial_seasonal.{i}" for i in range(self.seasonal_periods) ] return names @property def _smoothing_param_names(self): return [ "smoothing_level", "smoothing_trend", "smoothing_seasonal", "damping_trend", ] @property def _internal_initial_state_names(self): param_names = [ "initial_level", "initial_trend", ] param_names += [ f"initial_seasonal.{i}" for i in range(self.seasonal_periods) ] return param_names @property def _internal_param_names(self): return self._smoothing_param_names + self._internal_initial_state_names @property def _k_states(self): return 1 + int(self.has_trend) + int(self.has_seasonal) # level @property def _k_states_internal(self): return 2 + self.seasonal_periods @property def _k_smoothing_params(self): return self._k_states + int(self.damped_trend) @property def _k_initial_states(self): return ( 1 + int(self.has_trend) + +int(self.has_seasonal) * self.seasonal_periods ) @property def k_params(self): k = self._k_smoothing_params if self.initialization_method == "estimated": k += self._k_initial_states return k @property def _k_params_internal(self): return 4 + 2 + self.seasonal_periods def _internal_params(self, params): """ Converts a parameter array passed from outside to the internally used full parameter array. """ # internal params that are not needed are all set to zero, except phi, # which is one internal = np.zeros(self._k_params_internal, dtype=params.dtype) for i, name in enumerate(self.param_names): internal_idx = self._internal_params_index[name] internal[internal_idx] = params[i] if not self.damped_trend: internal[3] = 1 # phi is 4th parameter if self.initialization_method != "estimated": internal[4] = self.initial_level internal[5] = self.initial_trend internal[6:] = self.initial_seasonal return internal def _model_params(self, internal): """ Converts internal parameters to model parameters """ params = np.empty(self.k_params) for i, name in enumerate(self.param_names): internal_idx = self._internal_params_index[name] params[i] = internal[internal_idx] return params @property def _seasonal_index(self): return 1 + int(self.has_trend) def _get_states(self, xhat): states = np.empty((self.nobs, self._k_states)) all_names = ["level", "trend", "seasonal"] for i, name in enumerate(self.state_names): idx = all_names.index(name) states[:, i] = xhat[:, idx] return states def _get_internal_states(self, states, params): """ Converts a state matrix/dataframe to the (nobs, 2+m) matrix used internally """ internal_params = self._internal_params(params) if isinstance(states, (pd.Series, pd.DataFrame)): states = states.values internal_states = np.zeros((self.nobs, 2 + self.seasonal_periods)) internal_states[:, 0] = states[:, 0] if self.has_trend: internal_states[:, 1] = states[:, 1] if self.has_seasonal: for j in range(self.seasonal_periods): internal_states[j:, 2 + j] = states[ 0 : self.nobs - j, self._seasonal_index ] internal_states[0:j, 2 + j] = internal_params[6 : 6 + j][::-1] return internal_states @property def _default_start_params(self): return { "smoothing_level": 0.1, "smoothing_trend": 0.01, "smoothing_seasonal": 0.01, "damping_trend": 0.98, } @property def _start_params(self): """ Default start params in the format of external parameters. This should not be called directly, but by calling ``self.start_params``. """ params = [] for p in self._smoothing_param_names: if p in self.param_names: params.append(self._default_start_params[p]) if self.initialization_method == "estimated": lvl_idx = len(params) params += [self.initial_level] if self.has_trend: params += [self.initial_trend] if self.has_seasonal: # we have to adapt the seasonal values a bit to make sure the # problem is well posed (see implementation notes above) initial_seasonal = self.initial_seasonal if self.seasonal == "mul": params[lvl_idx] *= initial_seasonal[-1] initial_seasonal /= initial_seasonal[-1] else: params[lvl_idx] += initial_seasonal[-1] initial_seasonal -= initial_seasonal[-1] params += initial_seasonal.tolist() return np.array(params) def _convert_and_bound_start_params(self, params): """ This converts start params to internal params, sets internal-only parameters as bounded, sets bounds for fixed parameters, and then makes sure that all start parameters are within the specified bounds. """ internal_params = self._internal_params(params) # set bounds for missing and fixed for p in self._internal_param_names: idx = self._internal_params_index[p] if p not in self.param_names: # any missing parameters are set to the value they got from the # call to _internal_params self.bounds[p] = [internal_params[idx]] * 2 elif self._has_fixed_params and p in self._fixed_params: self.bounds[p] = [self._fixed_params[p]] * 2 # make sure everything is within bounds if p in self.bounds: internal_params[idx] = np.clip( internal_params[idx] + 1e-3, # try not to start on boundary *self.bounds[p], ) return internal_params def _setup_bounds(self): # By default, we are using the traditional constraints for the # smoothing parameters if nothing else is specified # # 0 < alpha < 1 # 0 < beta/alpha < 1 # 0 < gamma + alpha < 1 # 0.8 < phi < 0.98 # # For initial states, no bounds are the default setting. # # Since the bounds for beta and gamma are not in the simple form of a # constant interval, we will use the parameters beta_star=beta/alpha # and gamma_star=gamma+alpha during fitting. lb = np.zeros(self._k_params_internal) + 1e-4 ub = np.ones(self._k_params_internal) - 1e-4 # other bounds for phi and initial states lb[3], ub[3] = 0.8, 0.98 if self.initialization_method == "estimated": lb[4:-1] = -np.inf ub[4:-1] = np.inf # fix the last initial_seasonal to 0 or 1, otherwise the equation # is underdetermined if self.seasonal == "mul": lb[-1], ub[-1] = 1, 1 else: lb[-1], ub[-1] = 0, 0 # set lb and ub for parameters with bounds for p in self._internal_param_names: idx = self._internal_params_index[p] if p in self.bounds: lb[idx], ub[idx] = self.bounds[p] return [(lb[i], ub[i]) for i in range(self._k_params_internal)] def fit( self, start_params=None, maxiter=1000, full_output=True, disp=True, callback=None, return_params=False, **kwargs, ): r""" Fit an ETS model by maximizing log-likelihood. Log-likelihood is a function of the model parameters :math:`\alpha, \beta, \gamma, \phi` (depending on the chosen model), and, if `initialization_method` was set to `'estimated'` in the constructor, also the initial states :math:`l_{-1}, b_{-1}, s_{-1}, \ldots, s_{-m}`. The fit is performed using the L-BFGS algorithm. Parameters ---------- start_params : array_like, optional Initial values for parameters that will be optimized. If this is ``None``, default values will be used. The length of this depends on the chosen model. This should contain the parameters in the following order, skipping parameters that do not exist in the chosen model. * `smoothing_level` (:math:`\alpha`) * `smoothing_trend` (:math:`\beta`) * `smoothing_seasonal` (:math:`\gamma`) * `damping_trend` (:math:`\phi`) If ``initialization_method`` was set to ``'estimated'`` (the default), additionally, the parameters * `initial_level` (:math:`l_{-1}`) * `initial_trend` (:math:`l_{-1}`) * `initial_seasonal.0` (:math:`s_{-1}`) * ... * `initial_seasonal.` (:math:`s_{-m}`) also have to be specified. maxiter : int, optional The maximum number of iterations to perform. full_output : bool, optional Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. disp : bool, optional Set to True to print convergence messages. callback : callable callback(xk), optional Called after each iteration, as callback(xk), where xk is the current parameter vector. return_params : bool, optional Whether or not to return only the array of maximizing parameters. Default is False. **kwargs Additional keyword arguments to pass to the optimizer. Returns ------- results : ETSResults """ if start_params is None: start_params = self.start_params else: start_params = np.asarray(start_params) if self._has_fixed_params and len(self._free_params_index) == 0: final_params = np.asarray(list(self._fixed_params.values())) mlefit = Bunch( params=start_params, mle_retvals=None, mle_settings=None ) else: internal_start_params = self._convert_and_bound_start_params( start_params ) bounds = self._setup_bounds() # check if we need to use the starred parameters use_beta_star = "smoothing_trend" not in self.bounds if use_beta_star: internal_start_params[1] /= internal_start_params[0] use_gamma_star = "smoothing_seasonal" not in self.bounds if use_gamma_star: internal_start_params[2] /= 1 - internal_start_params[0] # check if we have fixed parameters and remove them from the # parameter vector is_fixed = np.zeros(self._k_params_internal, dtype=int) fixed_values = np.empty_like(internal_start_params) params_without_fixed = [] kwargs["bounds"] = [] for i in range(self._k_params_internal): if bounds[i][0] == bounds[i][1]: is_fixed[i] = True fixed_values[i] = bounds[i][0] else: params_without_fixed.append(internal_start_params[i]) kwargs["bounds"].append(bounds[i]) params_without_fixed = np.asarray(params_without_fixed) # pre-allocate memory for smoothing results yhat = np.zeros(self.nobs) xhat = np.zeros((self.nobs, self._k_states_internal)) kwargs["approx_grad"] = True with self.use_internal_loglike(): mlefit = super().fit( params_without_fixed, fargs=( yhat, xhat, is_fixed, fixed_values, use_beta_star, use_gamma_star, ), method="lbfgs", maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, skip_hessian=True, **kwargs, ) # convert params back # first, insert fixed params fitted_params = np.empty_like(internal_start_params) idx_without_fixed = 0 for i in range(self._k_params_internal): if is_fixed[i]: fitted_params[i] = fixed_values[i] else: fitted_params[i] = mlefit.params[idx_without_fixed] idx_without_fixed += 1 if use_beta_star: fitted_params[1] *= fitted_params[0] if use_gamma_star: fitted_params[2] *= 1 - fitted_params[0] final_params = self._model_params(fitted_params) if return_params: return final_params else: result = self.smooth(final_params) result.mlefit = mlefit result.mle_retvals = mlefit.mle_retvals result.mle_settings = mlefit.mle_settings return result def _loglike_internal( self, params, yhat, xhat, is_fixed=None, fixed_values=None, use_beta_star=False, use_gamma_star=False, ): """ Log-likelihood function to be called from fit to avoid reallocation of memory. Parameters ---------- params : np.ndarray of np.float Model parameters: (alpha, beta, gamma, phi, l[-1], b[-1], s[-1], ..., s[-m]). If there are no fixed values this must be in the format of internal parameters. Otherwise the fixed values are skipped. yhat : np.ndarray Array of size (n,) where fitted values will be written to. xhat : np.ndarray Array of size (n, _k_states_internal) where fitted states will be written to. is_fixed : np.ndarray or None Boolean array indicating values which are fixed during fitting. This must have the full length of internal parameters. fixed_values : np.ndarray or None Array of fixed values (arbitrary values for non-fixed parameters) This must have the full length of internal parameters. use_beta_star : boolean Whether to internally use beta_star as parameter use_gamma_star : boolean Whether to internally use gamma_star as parameter """ if np.iscomplexobj(params): data = np.asarray(self.endog, dtype=complex) else: data = self.endog if is_fixed is None: is_fixed = np.zeros(self._k_params_internal, dtype=int) fixed_values = np.empty( self._k_params_internal, dtype=params.dtype ) self._smoothing_func( params, data, yhat, xhat, is_fixed, fixed_values, use_beta_star, use_gamma_star, ) res = self._residuals(yhat, data=data) logL = -self.nobs / 2 * (np.log(2 * np.pi * np.mean(res ** 2)) + 1) if self.error == "mul": logL -= np.sum(np.log(yhat)) if np.isnan(logL): logL = np.inf return logL @contextlib.contextmanager def use_internal_loglike(self): external_loglike = self.loglike self.loglike = self._loglike_internal try: yield finally: self.loglike = external_loglike def loglike(self, params, **kwargs): r""" Log-likelihood of model. Parameters ---------- params : np.ndarray of np.float Model parameters: (alpha, beta, gamma, phi, l[-1], b[-1], s[-1], ..., s[-m]) Notes ----- The log-likelihood of a exponential smoothing model is [1]_: .. math:: l(\theta, x_0|y) = - \frac{n}{2}(\log(2\pi s^2) + 1) - \sum\limits_{t=1}^n \log(k_t) with .. math:: s^2 = \frac{1}{n}\sum\limits_{t=1}^n \frac{\hat{y}_t - y_t}{k_t} where :math:`k_t = 1` for the additive error model and :math:`k_t = y_t` for the multiplicative error model. References ---------- .. [1] J. K. Ord, A. B. Koehler R. D. and Snyder (1997). Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models. *Journal of the American Statistical Association*, 92(440), 1621-1629 """ params = self._internal_params(np.asarray(params)) yhat = np.zeros(self.nobs, dtype=params.dtype) xhat = np.zeros( (self.nobs, self._k_states_internal), dtype=params.dtype ) return self._loglike_internal(np.asarray(params), yhat, xhat) def _residuals(self, yhat, data=None): """Calculates residuals of a prediction""" if data is None: data = self.endog if self.error == "mul": return (data - yhat) / yhat else: return data - yhat def _smooth(self, params): """ Exponential smoothing with given parameters Parameters ---------- params : array_like Model parameters Returns ------- yhat : pd.Series or np.ndarray Predicted values from exponential smoothing. If original data was a ``pd.Series``, returns a ``pd.Series``, else a ``np.ndarray``. xhat : pd.DataFrame or np.ndarray Internal states of exponential smoothing. If original data was a ``pd.Series``, returns a ``pd.DataFrame``, else a ``np.ndarray``. """ internal_params = self._internal_params(params) yhat = np.zeros(self.nobs) xhat = np.zeros((self.nobs, self._k_states_internal)) is_fixed = np.zeros(self._k_params_internal, dtype=int) fixed_values = np.empty(self._k_params_internal, dtype=params.dtype) self._smoothing_func( internal_params, self.endog, yhat, xhat, is_fixed, fixed_values ) # remove states that are only internal states = self._get_states(xhat) if self.use_pandas: _, _, _, index = self._get_prediction_index(0, self.nobs - 1) yhat = pd.Series(yhat, index=index) statenames = ["level"] if self.has_trend: statenames += ["trend"] if self.has_seasonal: statenames += ["seasonal"] states = pd.DataFrame(states, index=index, columns=statenames) return yhat, states def smooth(self, params, return_raw=False): """ Exponential smoothing with given parameters Parameters ---------- params : array_like Model parameters return_raw : bool, optional Whether to return only the state space results or the full results object. Default is ``False``. Returns ------- result : ETSResultsWrapper or tuple If ``return_raw=False``, returns a ETSResultsWrapper object. Otherwise a tuple of arrays or pandas objects, depending on the format of the endog data. """ params = np.asarray(params) results = self._smooth(params) return self._wrap_results(params, results, return_raw) @property def _res_classes(self): return {"fit": (ETSResults, ETSResultsWrapper)} def hessian( self, params, approx_centered=False, approx_complex_step=True, **kwargs ): r""" Hessian matrix of the likelihood function, evaluated at the given parameters Parameters ---------- params : array_like Array of parameters at which to evaluate the hessian. approx_centered : bool Whether to use a centered scheme for finite difference approximation approx_complex_step : bool Whether to use complex step differentiation for approximation Returns ------- hessian : ndarray Hessian matrix evaluated at `params` Notes ----- This is a numerical approximation. """ method = kwargs.get("method", "approx") if method == "approx": if approx_complex_step: hessian = self._hessian_complex_step(params, **kwargs) else: hessian = self._hessian_finite_difference( params, approx_centered=approx_centered, **kwargs ) else: raise NotImplementedError("Invalid Hessian calculation method.") return hessian def score( self, params, approx_centered=False, approx_complex_step=True, **kwargs ): method = kwargs.get("method", "approx") if method == "approx": if approx_complex_step: score = self._score_complex_step(params, **kwargs) else: score = self._score_finite_difference( params, approx_centered=approx_centered, **kwargs ) else: raise NotImplementedError("Invalid score method.") return score def update(params, *args, **kwargs): # Dummy method to make methods copied from statespace.MLEModel work ... class ETSResults(base.StateSpaceMLEResults): """ Results from an error, trend, seasonal (ETS) exponential smoothing model """ def __init__(self, model, params, results): yhat, xhat = results self._llf = model.loglike(params) self._residuals = model._residuals(yhat) self._fittedvalues = yhat # scale is concentrated in this model formulation and corresponds to # mean squared residuals, see docstring of model.loglike scale = np.mean(self._residuals ** 2) super().__init__(model, params, scale=scale) # get model definition model_definition_attrs = [ "short_name", "error", "trend", "seasonal", "damped_trend", "has_trend", "has_seasonal", "seasonal_periods", "initialization_method", ] for attr in model_definition_attrs: setattr(self, attr, getattr(model, attr)) self.param_names = [ "%s (fixed)" % name if name in self.fixed_params else name for name in (self.model.param_names or []) ] # get fitted states and parameters internal_params = self.model._internal_params(params) self.states = xhat if self.model.use_pandas: states = self.states.iloc else: states = self.states self.initial_state = np.zeros(model._k_initial_states) self.level = states[:, 0] self.initial_level = internal_params[4] self.initial_state[0] = self.initial_level self.alpha = self.params[0] self.smoothing_level = self.alpha if self.has_trend: self.slope = states[:, 1] self.initial_trend = internal_params[5] self.initial_state[1] = self.initial_trend self.beta = self.params[1] self.smoothing_trend = self.beta if self.has_seasonal: self.season = states[:, self.model._seasonal_index] self.initial_seasonal = internal_params[6:] self.initial_state[ self.model._seasonal_index : ] = self.initial_seasonal self.gamma = self.params[self.model._seasonal_index] self.smoothing_seasonal = self.gamma if self.damped_trend: self.phi = internal_params[3] self.damping_trend = self.phi # degrees of freedom of model k_free_params = self.k_params - len(self.fixed_params) self.df_model = k_free_params + 1 # standardized forecasting error self.mean_resid = np.mean(self.resid) self.scale_resid = np.std(self.resid, ddof=1) self.standardized_forecasts_error = ( self.resid - self.mean_resid ) / self.scale_resid # Setup covariance matrix notes dictionary # For now, only support "approx" if not hasattr(self, "cov_kwds"): self.cov_kwds = {} self.cov_type = "approx" # Setup the cache self._cache = {} # Handle covariance matrix calculation self._cov_approx_complex_step = True self._cov_approx_centered = False approx_type_str = "complex-step" try: self._rank = None if self.k_params == 0: self.cov_params_default = np.zeros((0, 0)) self._rank = 0 self.cov_kwds["description"] = "No parameters estimated." else: self.cov_params_default = self.cov_params_approx self.cov_kwds["description"] = descriptions["approx"].format( approx_type=approx_type_str ) except np.linalg.LinAlgError: self._rank = 0 k_params = len(self.params) self.cov_params_default = np.zeros((k_params, k_params)) * np.nan self.cov_kwds["cov_type"] = ( "Covariance matrix could not be calculated: singular." " information matrix." ) @cache_readonly def nobs_effective(self): return self.nobs @cache_readonly def fittedvalues(self): return self._fittedvalues @cache_readonly def resid(self): return self._residuals @cache_readonly def llf(self): """ log-likelihood function evaluated at the fitted params """ return self._llf def _get_prediction_params(self, start_idx): """ Returns internal parameter representation of smoothing parameters and "initial" states for prediction/simulation, that is the states just before the first prediction/simulation step. """ internal_params = self.model._internal_params(self.params) if start_idx == 0: return internal_params else: internal_states = self.model._get_internal_states( self.states, self.params ) start_state = np.empty(6 + self.seasonal_periods) start_state[0:4] = internal_params[0:4] start_state[4:] = internal_states[start_idx - 1, :] return start_state def _relative_forecast_variance(self, steps): """ References ---------- .. [1] Hyndman, R.J., & Athanasopoulos, G. (2019) *Forecasting: principles and practice*, 3rd edition, OTexts: Melbourne, Australia. OTexts.com/fpp3. Accessed on April 19th 2020. """ h = steps alpha = self.smoothing_level if self.has_trend: beta = self.smoothing_trend if self.has_seasonal: gamma = self.smoothing_seasonal m = self.seasonal_periods k = np.asarray((h - 1) / m, dtype=int) if self.damped_trend: phi = self.damping_trend model = self.model.short_name if model == "ANN": return 1 + alpha ** 2 * (h - 1) elif model == "AAN": return 1 + (h - 1) * ( alpha ** 2 + alpha * beta * h + beta ** 2 * h / 6 * (2 * h - 1) ) elif model == "AAdN": return ( 1 + alpha ** 2 * (h - 1) + ( (beta * phi * h) / ((1 - phi) ** 2) * (2 * alpha * (1 - phi) + beta * phi) ) - ( (beta * phi * (1 - phi ** h)) / ((1 - phi) ** 2 * (1 - phi ** 2)) * ( 2 * alpha * (1 - phi ** 2) + beta * phi * (1 + 2 * phi - phi ** h) ) ) ) elif model == "ANA": return 1 + alpha ** 2 * (h - 1) + gamma * k * (2 * alpha + gamma) elif model == "AAA": return ( 1 + (h - 1) * ( alpha ** 2 + alpha * beta * h + (beta ** 2) / 6 * h * (2 * h - 1) ) + gamma * k * (2 * alpha + gamma + beta * m * (k + 1)) ) elif model == "AAdA": return ( 1 + alpha ** 2 * (h - 1) + gamma * k * (2 * alpha + gamma) + (beta * phi * h) / ((1 - phi) ** 2) * (2 * alpha * (1 - phi) + beta * phi) - ( (beta * phi * (1 - phi ** h)) / ((1 - phi) ** 2 * (1 - phi ** 2)) * ( 2 * alpha * (1 - phi ** 2) + beta * phi * (1 + 2 * phi - phi ** h) ) ) + ( (2 * beta * gamma * phi) / ((1 - phi) * (1 - phi ** m)) * (k * (1 - phi ** m) - phi ** m * (1 - phi ** (m * k))) ) ) else: raise NotImplementedError def simulate( self, nsimulations, anchor=None, repetitions=1, random_errors=None, random_state=None, ): r""" Random simulations using the state space formulation. Parameters ---------- nsimulations : int The number of simulation steps. anchor : int, str, or datetime, optional First period for simulation. The simulation will be conditional on all existing datapoints prior to the `anchor`. Type depends on the index of the given `endog` in the model. Two special cases are the strings 'start' and 'end'. `start` refers to beginning the simulation at the first period of the sample (i.e. using the initial values as simulation anchor), and `end` refers to beginning the simulation at the first period after the sample. Integer values can run from 0 to `nobs`, or can be negative to apply negative indexing. Finally, if a date/time index was provided to the model, then this argument can be a date string to parse or a datetime type. Default is 'start'. Note: `anchor` corresponds to the observation right before the `start` observation in the `predict` method. repetitions : int, optional Number of simulated paths to generate. Default is 1 simulated path. random_errors : optional Specifies how the random errors should be obtained. Can be one of the following: * ``None``: Random normally distributed values with variance estimated from the fit errors drawn from numpy's standard RNG (can be seeded with the `random_state` argument). This is the default option. * A distribution function from ``scipy.stats``, e.g. ``scipy.stats.norm``: Fits the distribution function to the fit errors and draws from the fitted distribution. Note the difference between ``scipy.stats.norm`` and ``scipy.stats.norm()``, the latter one is a frozen distribution function. * A frozen distribution function from ``scipy.stats``, e.g. ``scipy.stats.norm(scale=2)``: Draws from the frozen distribution function. * A ``np.ndarray`` with shape (`nsimulations`, `repetitions`): Uses the given values as random errors. * ``"bootstrap"``: Samples the random errors from the fit errors. random_state : int or np.random.RandomState, optional A seed for the random number generator or a ``np.random.RandomState`` object. Only used if `random_errors` is ``None``. Default is ``None``. Returns ------- sim : pd.Series, pd.DataFrame or np.ndarray An ``np.ndarray``, ``pd.Series``, or ``pd.DataFrame`` of simulated values. If the original data was a ``pd.Series`` or ``pd.DataFrame``, `sim` will be a ``pd.Series`` if `repetitions` is 1, and a ``pd.DataFrame`` of shape (`nsimulations`, `repetitions`) else. Otherwise, if `repetitions` is 1, a ``np.ndarray`` of shape (`nsimulations`,) is returned, and if `repetitions` is not 1 a ``np.ndarray`` of shape (`nsimulations`, `repetitions`) is returned. """ r""" Implementation notes -------------------- The simulation is based on the state space model of the Holt-Winter's methods. The state space model assumes that the true value at time :math:`t` is randomly distributed around the prediction value. If using the additive error model, this means: .. math:: y_t &= \hat{y}_{t|t-1} + e_t\\ e_t &\sim \mathcal{N}(0, \sigma^2) Using the multiplicative error model: .. math:: y_t &= \hat{y}_{t|t-1} \cdot (1 + e_t)\\ e_t &\sim \mathcal{N}(0, \sigma^2) Inserting these equations into the smoothing equation formulation leads to the state space equations. The notation used here follows [1]_. Additionally, .. math:: B_t = b_{t-1} \circ_d \phi\\ L_t = l_{t-1} \circ_b B_t\\ S_t = s_{t-m}\\ Y_t = L_t \circ_s S_t, where :math:`\circ_d` is the operation linking trend and damping parameter (multiplication if the trend is additive, power if the trend is multiplicative), :math:`\circ_b` is the operation linking level and trend (addition if the trend is additive, multiplication if the trend is multiplicative), and :math:'\circ_s` is the operation linking seasonality to the rest. The state space equations can then be formulated as .. math:: y_t = Y_t + \eta \cdot e_t\\ l_t = L_t + \alpha \cdot (M_e \cdot L_t + \kappa_l) \cdot e_t\\ b_t = B_t + \beta \cdot (M_e \cdot B_t+\kappa_b) \cdot e_t\\ s_t = S_t + \gamma \cdot (M_e \cdot S_t + \kappa_s) \cdot e_t\\ with .. math:: \eta &= \begin{cases} Y_t\quad\text{if error is multiplicative}\\ 1\quad\text{else} \end{cases}\\ M_e &= \begin{cases} 1\quad\text{if error is multiplicative}\\ 0\quad\text{else} \end{cases}\\ and, when using the additive error model, .. math:: \kappa_l &= \begin{cases} \frac{1}{S_t}\quad \text{if seasonality is multiplicative}\\ 1\quad\text{else} \end{cases}\\ \kappa_b &= \begin{cases} \frac{\kappa_l}{l_{t-1}}\quad \text{if trend is multiplicative}\\ \kappa_l\quad\text{else} \end{cases}\\ \kappa_s &= \begin{cases} \frac{1}{L_t}\quad \text{if seasonality is multiplicative}\\ 1\quad\text{else} \end{cases} When using the multiplicative error model .. math:: \kappa_l &= \begin{cases} 0\quad \text{if seasonality is multiplicative}\\ S_t\quad\text{else} \end{cases}\\ \kappa_b &= \begin{cases} \frac{\kappa_l}{l_{t-1}}\quad \text{if trend is multiplicative}\\ \kappa_l + l_{t-1}\quad\text{else} \end{cases}\\ \kappa_s &= \begin{cases} 0\quad\text{if seasonality is multiplicative}\\ L_t\quad\text{else} \end{cases} References ---------- .. [1] Hyndman, R.J., & Athanasopoulos, G. (2018) *Forecasting: principles and practice*, 2nd edition, OTexts: Melbourne, Australia. OTexts.com/fpp2. Accessed on February 28th 2020. """ # Get the starting location start_idx = self._get_prediction_start_index(anchor) # set initial values and obtain parameters start_params = self._get_prediction_params(start_idx) x = np.zeros((nsimulations, self.model._k_states_internal)) # is fixed and fixed values are dummy arguments is_fixed = np.zeros(len(start_params), dtype=int) fixed_values = np.zeros_like(start_params) ( alpha, beta_star, gamma_star, phi, m, _, ) = smooth._initialize_ets_smooth( start_params, x, is_fixed, fixed_values ) beta = alpha * beta_star gamma = (1 - alpha) * gamma_star # make x a 3 dimensional matrix: first dimension is nsimulations # (number of steps), next is number of states, innermost is repetitions nstates = x.shape[1] x = np.tile(np.reshape(x, (nsimulations, nstates, 1)), repetitions) y = np.empty((nsimulations, repetitions)) # get random error eps sigma = np.sqrt(self.scale) if isinstance(random_errors, np.ndarray): if random_errors.shape != (nsimulations, repetitions): raise ValueError( "If random is an ndarray, it must have shape " "(nsimulations, repetitions)!" ) eps = random_errors elif random_errors == "bootstrap": eps = np.random.choice( self.resid, size=(nsimulations, repetitions), replace=True ) elif random_errors is None: if random_state is None: eps = np.random.randn(nsimulations, repetitions) * sigma elif isinstance(random_state, int): rng = np.random.RandomState(random_state) eps = rng.randn(nsimulations, repetitions) * sigma elif isinstance(random_state, np.random.RandomState): eps = random_state.randn(nsimulations, repetitions) * sigma else: raise ValueError( "Argument random_state must be None, an integer, " "or an instance of np.random.RandomState" ) elif isinstance(random_errors, (rv_continuous, rv_discrete)): params = random_errors.fit(self.resid) eps = random_errors.rvs(*params, size=(nsimulations, repetitions)) elif isinstance(random_errors, _distn_infrastructure.rv_frozen): eps = random_errors.rvs(size=(nsimulations, repetitions)) else: raise ValueError("Argument random_errors has unexpected value!") # get model settings mul_seasonal = self.seasonal == "mul" mul_trend = self.trend == "mul" mul_error = self.error == "mul" # define trend, damping and seasonality operations if mul_trend: op_b = np.multiply op_d = np.power else: op_b = np.add op_d = np.multiply if mul_seasonal: op_s = np.multiply else: op_s = np.add # x translation: # - x[t, 0, :] is level[t] # - x[t, 1, :] is trend[t] # - x[t, 2, :] is seasonal[t] # - x[t, 3, :] is seasonal[t-1] # - x[t, 2+j, :] is seasonal[t-j] # - similarly: x[t-1, 2+m-1, :] is seasonal[t-m] for t in range(nsimulations): B = op_d(x[t - 1, 1, :], phi) L = op_b(x[t - 1, 0, :], B) S = x[t - 1, 2 + m - 1, :] Y = op_s(L, S) if self.error == "add": eta = 1 kappa_l = 1 / S if mul_seasonal else 1 kappa_b = kappa_l / x[t - 1, 0, :] if mul_trend else kappa_l kappa_s = 1 / L if mul_seasonal else 1 else: eta = Y kappa_l = 0 if mul_seasonal else S kappa_b = ( kappa_l / x[t - 1, 0, :] if mul_trend else kappa_l + x[t - 1, 0, :] ) kappa_s = 0 if mul_seasonal else L y[t, :] = Y + eta * eps[t, :] x[t, 0, :] = L + alpha * (mul_error * L + kappa_l) * eps[t, :] x[t, 1, :] = B + beta * (mul_error * B + kappa_b) * eps[t, :] x[t, 2, :] = S + gamma * (mul_error * S + kappa_s) * eps[t, :] # update seasonals by shifting previous seasonal right x[t, 3:, :] = x[t - 1, 2:-1, :] # Wrap data / squeeze where appropriate if repetitions > 1: names = ["simulation.%d" % num for num in range(repetitions)] else: names = "simulation" return self.model._wrap_data( y, start_idx, start_idx + nsimulations - 1, names=names ) def forecast(self, steps=1): """ Out-of-sample forecasts Parameters ---------- steps : int, str, or datetime, optional If an integer, the number of steps to forecast from the end of the sample. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, steps must be an integer. Default Returns ------- forecast : ndarray Array of out of sample forecasts. A (steps x k_endog) array. """ return self._forecast(steps, "end") def _forecast(self, steps, anchor): """ Dynamic prediction/forecasting """ # forecast is the same as simulation without errors return self.simulate( steps, anchor=anchor, random_errors=np.zeros((steps, 1)) ) def _handle_prediction_index(self, start, dynamic, end, index): if start is None: start = 0 # Handle start, end, dynamic start, end, out_of_sample, _ = self.model._get_prediction_index( start, end, index ) # if end was outside of the sample, it is now the last point in the # sample if start > end + out_of_sample + 1: raise ValueError( "Prediction start cannot lie outside of the sample." ) # Handle `dynamic` if isinstance(dynamic, (str, dt.datetime, pd.Timestamp)): dynamic, _, _ = self.model._get_index_loc(dynamic) # Convert to offset relative to start dynamic = dynamic - start elif isinstance(dynamic, bool): if dynamic: dynamic = 0 else: dynamic = end + 1 - start # start : index of first predicted value # dynamic : offset to first dynamically predicted value # -> if dynamic == 0, only dynamic simulations if dynamic == 0: start_smooth = None end_smooth = None nsmooth = 0 start_dynamic = start else: # dynamic simulations from start + dynamic start_smooth = start end_smooth = min(start + dynamic - 1, end) nsmooth = max(end_smooth - start_smooth + 1, 0) start_dynamic = start + dynamic # anchor for simulations is one before start_dynamic if start_dynamic == 0: anchor_dynamic = "start" else: anchor_dynamic = start_dynamic - 1 # end is last point in sample, out_of_sample gives number of # simulations out of sample end_dynamic = end + out_of_sample ndynamic = end_dynamic - start_dynamic + 1 return ( start, end, start_smooth, end_smooth, anchor_dynamic, start_dynamic, end_dynamic, nsmooth, ndynamic, index, ) def predict(self, start=None, end=None, dynamic=False, index=None): """ In-sample prediction and out-of-sample forecasting Parameters ---------- start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, i.e., the last forecast is end. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. dynamic : bool, int, str, or datetime, optional Integer offset relative to `start` at which to begin dynamic prediction. Can also be an absolute date string to parse or a datetime type (these are not interpreted as offsets). Prior to this observation, true endogenous values will be used for prediction; starting with this observation and continuing through the end of prediction, forecasted endogenous values will be used instead. index : pd.Index, optional Optionally an index to associate the predicted results to. If None, an attempt is made to create an index for the predicted results from the model's index or model's row labels. Returns ------- forecast : array_like or pd.Series. Array of out of in-sample predictions and / or out-of-sample forecasts. An (npredict,) array. If original data was a pd.Series or DataFrame, a pd.Series is returned. """ ( start, end, start_smooth, end_smooth, anchor_dynamic, _, end_dynamic, nsmooth, ndynamic, index, ) = self._handle_prediction_index(start, dynamic, end, index) y = np.empty(nsmooth + ndynamic) # In sample nondynamic prediction: smoothing if nsmooth > 0: y[0:nsmooth] = self.fittedvalues[start_smooth : end_smooth + 1] # Out of sample/dynamic prediction: forecast if ndynamic > 0: y[nsmooth:] = self._forecast(ndynamic, anchor_dynamic) # when we are doing out of sample only prediction, start > end + 1, and # we only want to output beginning at start if start > end + 1: ndiscard = start - (end + 1) y = y[ndiscard:] # Wrap data / squeeze where appropriate return self.model._wrap_data(y, start, end_dynamic) def get_prediction( self, start=None, end=None, dynamic=False, index=None, method=None, simulate_repetitions=1000, **simulate_kwargs, ): """ Calculates mean prediction and prediction intervals. Parameters ---------- start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, i.e., the last forecast is end. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. dynamic : bool, int, str, or datetime, optional Integer offset relative to `start` at which to begin dynamic prediction. Can also be an absolute date string to parse or a datetime type (these are not interpreted as offsets). Prior to this observation, true endogenous values will be used for prediction; starting with this observation and continuing through the end of prediction, forecasted endogenous values will be used instead. index : pd.Index, optional Optionally an index to associate the predicted results to. If None, an attempt is made to create an index for the predicted results from the model's index or model's row labels. method : str or None, optional Method to use for calculating prediction intervals. 'exact' (default, if available) or 'simulated'. simulate_repetitions : int, optional Number of simulation repetitions for calculating prediction intervals when ``method='simulated'``. Default is 1000. **simulate_kwargs : Additional arguments passed to the ``simulate`` method. Returns ------- PredictionResults Predicted mean values and prediction intervals """ return PredictionResultsWrapper( PredictionResults( self, start, end, dynamic, index, method, simulate_repetitions, **simulate_kwargs, ) ) def summary(self, alpha=0.05, start=None): """ Summarize the fitted model Parameters ---------- alpha : float, optional Significance level for the confidence intervals. Default is 0.05. start : int, optional Integer of the start observation. Default is 0. Returns ------- summary : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary """ model_name = f"ETS({self.short_name})" summary = super().summary( alpha=alpha, start=start, title="ETS Results", model_name=model_name, ) if self.model.initialization_method != "estimated": params = np.array(self.initial_state) if params.ndim > 1: params = params[0] names = self.model.initial_state_names param_header = [ "initialization method: %s" % self.model.initialization_method ] params_stubs = names params_data = [ [forg(params[i], prec=4)] for i in range(len(params)) ] initial_state_table = SimpleTable( params_data, param_header, params_stubs, txt_fmt=fmt_params ) summary.tables.insert(-1, initial_state_table) return summary class ETSResultsWrapper(wrap.ResultsWrapper): _attrs = { "fittedvalues": "rows", "level": "rows", "resid": "rows", "season": "rows", "slope": "rows", } _wrap_attrs = wrap.union_dicts( tsbase.TimeSeriesResultsWrapper._wrap_attrs, _attrs ) _methods = {"predict": "dates", "forecast": "dates"} _wrap_methods = wrap.union_dicts( tsbase.TimeSeriesResultsWrapper._wrap_methods, _methods ) wrap.populate_wrapper(ETSResultsWrapper, ETSResults) class PredictionResults: """ ETS mean prediction and prediction intervals Parameters ---------- results : ETSResults Model estimation results. start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, i.e., the last forecast is end. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. dynamic : bool, int, str, or datetime, optional Integer offset relative to `start` at which to begin dynamic prediction. Can also be an absolute date string to parse or a datetime type (these are not interpreted as offsets). Prior to this observation, true endogenous values will be used for prediction; starting with this observation and continuing through the end of prediction, forecasted endogenous values will be used instead. index : pd.Index, optional Optionally an index to associate the predicted results to. If None, an attempt is made to create an index for the predicted results from the model's index or model's row labels. method : str or None, optional Method to use for calculating prediction intervals. 'exact' (default, if available) or 'simulated'. simulate_repetitions : int, optional Number of simulation repetitions for calculating prediction intervals. Default is 1000. **simulate_kwargs : Additional arguments passed to the ``simulate`` method. """ def __init__( self, results, start=None, end=None, dynamic=False, index=None, method=None, simulate_repetitions=1000, **simulate_kwargs, ): self.use_pandas = results.model.use_pandas if method is None: exact_available = ["ANN", "AAN", "AAdN", "ANA", "AAA", "AAdA"] if results.model.short_name in exact_available: method = "exact" else: method = "simulated" self.method = method ( start, end, start_smooth, _, anchor_dynamic, start_dynamic, end_dynamic, nsmooth, ndynamic, index, ) = results._handle_prediction_index(start, dynamic, end, index) self.predicted_mean = results.predict( start=start, end=end_dynamic, dynamic=dynamic, index=index ) self.row_labels = self.predicted_mean.index self.endog = np.empty(nsmooth + ndynamic) * np.nan if nsmooth > 0: self.endog[0: (end - start + 1)] = results.data.endog[ start: (end + 1) ] self.model = Bunch( data=results.model.data.__class__( endog=self.endog, predict_dates=self.row_labels ) ) if self.method == "simulated": sim_results = [] # first, perform "non-dynamic" simulations, i.e. simulations of # only one step, based on the previous step if nsmooth > 1: if start_smooth == 0: anchor = "start" else: anchor = start_smooth - 1 for i in range(nsmooth): sim_results.append( results.simulate( 1, anchor=anchor, repetitions=simulate_repetitions, **simulate_kwargs, ) ) # anchor anchor = start_smooth + i sim_results.append( results.simulate( ndynamic, anchor=anchor_dynamic, repetitions=simulate_repetitions, **simulate_kwargs, ) ) self.simulation_results = np.concatenate(sim_results, axis=0) # if self.use_pandas: # self.simulation_results = pd.DataFrame( # self.simulation_results, index=self.row_labels, # columns=sim_results[0].columns # ) else: # method == 'exact' steps = np.ones(ndynamic + nsmooth) if ndynamic > 0: steps[ (start_dynamic - min(start_dynamic, start)): ] = range(1, ndynamic + 1) # when we are doing out of sample only prediction, # start > end + 1, and # we only want to output beginning at start if start > end + 1: ndiscard = start - (end + 1) steps = steps[ndiscard:] self.forecast_variance = ( results.mse * results._relative_forecast_variance(steps) ) @property def var_pred_mean(self): """The variance of the predicted mean""" return self.forecast_variance def pred_int(self, alpha=0.05): """ Calculates prediction intervals by performing multiple simulations. Parameters ---------- alpha : float, optional The significance level for the prediction interval. Default is 0.05, that is, a 95% prediction interval. """ if self.method == "simulated": simulated_upper_pi = np.quantile( self.simulation_results, 1 - alpha / 2, axis=1 ) simulated_lower_pi = np.quantile( self.simulation_results, alpha / 2, axis=1 ) pred_int = np.vstack((simulated_lower_pi, simulated_upper_pi)).T else: q = norm.ppf(1 - alpha / 2) half_interval_size = q * np.sqrt(self.forecast_variance) pred_int = np.vstack( ( self.predicted_mean - half_interval_size, self.predicted_mean + half_interval_size, ) ).T if self.use_pandas: pred_int = pd.DataFrame(pred_int, index=self.row_labels) names = [ f"lower PI (alpha={alpha:f})", f"upper PI (alpha={alpha:f})", ] pred_int.columns = names return pred_int def summary_frame(self, endog=0, alpha=0.05): pred_int = np.asarray(self.pred_int(alpha=alpha)) to_include = {} to_include["mean"] = self.predicted_mean if self.method == "simulated": to_include["mean_numerical"] = np.mean( self.simulation_results, axis=1 ) to_include["pi_lower"] = pred_int[:, 0] to_include["pi_upper"] = pred_int[:, 1] res = pd.DataFrame( to_include, index=self.row_labels, columns=list(to_include.keys()) ) return res class PredictionResultsWrapper(wrap.ResultsWrapper): _attrs = { "predicted_mean": "dates", "simulation_results": "dates", "endog": "dates", } _wrap_attrs = wrap.union_dicts(_attrs) _methods = {} _wrap_methods = wrap.union_dicts(_methods) wrap.populate_wrapper(PredictionResultsWrapper, PredictionResults) # noqa:E305 statsmodels-0.12.2/statsmodels/tsa/exponential_smoothing/initialization.py000066400000000000000000000101461400612667500273160ustar00rootroot00000000000000""" Initialization methods for states of exponential smoothing models """ import numpy as np import pandas as pd def _initialization_simple(endog, trend=False, seasonal=False, seasonal_periods=None): # See Section 7.6 of Hyndman and Athanasopoulos initial_trend = None initial_seasonal = None # Non-seasonal if seasonal is None: initial_level = endog[0] if trend == 'add': initial_trend = endog[1] - endog[0] elif trend == 'mul': initial_trend = endog[1] / endog[0] # Seasonal else: initial_level = np.mean(endog[:seasonal_periods]) m = seasonal_periods if trend is not None: initial_trend = (pd.Series(endog).diff(m)[m:2 * m] / m).mean() if seasonal == 'add': initial_seasonal = endog[:m] - initial_level elif seasonal == 'mul': initial_seasonal = endog[:m] / initial_level return initial_level, initial_trend, initial_seasonal def _initialization_heuristic(endog, trend=False, seasonal=False, seasonal_periods=None): # See Section 2.6 of Hyndman et al. endog = endog.copy() nobs = len(endog) if nobs < 10: raise ValueError('Cannot use heuristic method with less than 10' ' observations.') # Seasonal component initial_seasonal = None if seasonal: # Calculate the number of full cycles to use if nobs < 2 * seasonal_periods: raise ValueError('Cannot compute initial seasonals using' ' heuristic method with less than two full' ' seasonal cycles in the data.') # We need at least 10 periods for the level initialization # and we will lose self.seasonal_periods // 2 values at the # beginning and end of the sample, so we need at least # 10 + 2 * (self.seasonal_periods // 2) values min_obs = 10 + 2 * (seasonal_periods // 2) if nobs < min_obs: raise ValueError('Cannot use heuristic method to compute' ' initial seasonal and levels with less' ' than 10 + 2 * (seasonal_periods // 2)' ' datapoints.') # In some datasets we may only have 2 full cycles (but this may # still satisfy the above restriction that we will end up with # 10 seasonally adjusted observations) k_cycles = min(5, nobs // seasonal_periods) # In other datasets, 3 full cycles may not be enough to end up # with 10 seasonally adjusted observations k_cycles = max(k_cycles, int(np.ceil(min_obs / seasonal_periods))) # Compute the moving average series = pd.Series(endog[:seasonal_periods * k_cycles]) initial_trend = series.rolling(seasonal_periods, center=True).mean() if seasonal_periods % 2 == 0: initial_trend = initial_trend.shift(-1).rolling(2).mean() # Detrend if seasonal == 'add': detrended = series - initial_trend elif seasonal == 'mul': detrended = series / initial_trend # Average seasonal effect tmp = np.zeros(k_cycles * seasonal_periods) * np.nan tmp[:len(detrended)] = detrended.values initial_seasonal = np.nanmean( tmp.reshape(k_cycles, seasonal_periods).T, axis=1) # Normalize the seasonals if seasonal == 'add': initial_seasonal -= np.mean(initial_seasonal) elif seasonal == 'mul': initial_seasonal /= np.mean(initial_seasonal) # Replace the data with the trend endog = initial_trend.dropna().values # Trend / Level exog = np.c_[np.ones(10), np.arange(10) + 1] if endog.ndim == 1: endog = np.atleast_2d(endog).T beta = np.squeeze(np.linalg.pinv(exog).dot(endog[:10])) initial_level = beta[0] initial_trend = None if trend == 'add': initial_trend = beta[1] elif trend == 'mul': initial_trend = 1 + beta[1] / beta[0] return initial_level, initial_trend, initial_seasonal statsmodels-0.12.2/statsmodels/tsa/filters/000077500000000000000000000000001400612667500207465ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/filters/__init__.py000066400000000000000000000001131400612667500230520ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/tsa/filters/_utils.py000066400000000000000000000056371400612667500226320ustar00rootroot00000000000000from functools import wraps from statsmodels.tools.data import _is_using_pandas from statsmodels.tsa.tsatools import freq_to_period def _get_pandas_wrapper(X, trim_head=None, trim_tail=None, names=None): index = X.index #TODO: allow use index labels if trim_head is None and trim_tail is None: index = index elif trim_tail is None: index = index[trim_head:] elif trim_head is None: index = index[:-trim_tail] else: index = index[trim_head:-trim_tail] if hasattr(X, "columns"): if names is None: names = X.columns return lambda x : X.__class__(x, index=index, columns=names) else: if names is None: names = X.name return lambda x : X.__class__(x, index=index, name=names) def pandas_wrapper(func, trim_head=None, trim_tail=None, names=None, *args, **kwargs): @wraps(func) def new_func(X, *args, **kwargs): # quick pass-through for do nothing case if not _is_using_pandas(X, None): return func(X, *args, **kwargs) wrapper_func = _get_pandas_wrapper(X, trim_head, trim_tail, names) ret = func(X, *args, **kwargs) ret = wrapper_func(ret) return ret return new_func def pandas_wrapper_bunch(func, trim_head=None, trim_tail=None, names=None, *args, **kwargs): @wraps(func) def new_func(X, *args, **kwargs): # quick pass-through for do nothing case if not _is_using_pandas(X, None): return func(X, *args, **kwargs) wrapper_func = _get_pandas_wrapper(X, trim_head, trim_tail, names) ret = func(X, *args, **kwargs) ret = wrapper_func(ret) return ret return new_func def pandas_wrapper_predict(func, trim_head=None, trim_tail=None, columns=None, *args, **kwargs): raise NotImplementedError def pandas_wrapper_freq(func, trim_head=None, trim_tail=None, freq_kw='freq', columns=None, *args, **kwargs): """ Return a new function that catches the incoming X, checks if it's pandas, calls the functions as is. Then wraps the results in the incoming index. Deals with frequencies. Expects that the function returns a tuple, a Bunch object, or a pandas-object. """ @wraps(func) def new_func(X, *args, **kwargs): # quick pass-through for do nothing case if not _is_using_pandas(X, None): return func(X, *args, **kwargs) wrapper_func = _get_pandas_wrapper(X, trim_head, trim_tail, columns) index = X.index freq = index.inferred_freq kwargs.update({freq_kw : freq_to_period(freq)}) ret = func(X, *args, **kwargs) ret = wrapper_func(ret) return ret return new_func statsmodels-0.12.2/statsmodels/tsa/filters/api.py000066400000000000000000000004401400612667500220670ustar00rootroot00000000000000__all__ = ["bkfilter", "hpfilter", "cffilter", "miso_lfilter", "convolution_filter", "recursive_filter"] from .bk_filter import bkfilter from .hp_filter import hpfilter from .cf_filter import cffilter from .filtertools import miso_lfilter, convolution_filter, recursive_filter statsmodels-0.12.2/statsmodels/tsa/filters/bk_filter.py000066400000000000000000000065751400612667500232760ustar00rootroot00000000000000 import numpy as np from scipy.signal import fftconvolve from statsmodels.tools.validation import array_like, PandasWrapper def bkfilter(x, low=6, high=32, K=12): """ Filter a time series using the Baxter-King bandpass filter. Parameters ---------- x : array_like A 1 or 2d ndarray. If 2d, variables are assumed to be in columns. low : float Minimum period for oscillations, ie., Baxter and King suggest that the Burns-Mitchell U.S. business cycle has 6 for quarterly data and 1.5 for annual data. high : float Maximum period for oscillations BK suggest that the U.S. business cycle has 32 for quarterly data and 8 for annual data. K : int Lead-lag length of the filter. Baxter and King propose a truncation length of 12 for quarterly data and 3 for annual data. Returns ------- ndarray The cyclical component of x. See Also -------- statsmodels.tsa.filters.cf_filter.cffilter The Christiano Fitzgerald asymmetric, random walk filter. statsmodels.tsa.filters.bk_filter.hpfilter Hodrick-Prescott filter. statsmodels.tsa.seasonal.seasonal_decompose Decompose a time series using moving averages. statsmodels.tsa.seasonal.STL Season-Trend decomposition using LOESS. Notes ----- Returns a centered weighted moving average of the original series. Where the weights a[j] are computed :: a[j] = b[j] + theta, for j = 0, +/-1, +/-2, ... +/- K b[0] = (omega_2 - omega_1)/pi b[j] = 1/(pi*j)(sin(omega_2*j)-sin(omega_1*j), for j = +/-1, +/-2,... and theta is a normalizing constant :: theta = -sum(b)/(2K+1) References ---------- Baxter, M. and R. G. King. "Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series." *Review of Economics and Statistics*, 1999, 81(4), 575-593. Examples -------- >>> import statsmodels.api as sm >>> import pandas as pd >>> dta = sm.datasets.macrodata.load_pandas().data >>> index = pd.DatetimeIndex(start='1959Q1', end='2009Q4', freq='Q') >>> dta.set_index(index, inplace=True) >>> cycles = sm.tsa.filters.bkfilter(dta[['realinv']], 6, 24, 12) >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> cycles.plot(ax=ax, style=['r--', 'b-']) >>> plt.show() .. plot:: plots/bkf_plot.py """ # TODO: change the docstring to ..math::? # TODO: allow windowing functions to correct for Gibb's Phenomenon? # adjust bweights (symmetrically) by below before demeaning # Lancosz Sigma Factors np.sinc(2*j/(2.*K+1)) pw = PandasWrapper(x) x = array_like(x, 'x', maxdim=2) omega_1 = 2. * np.pi / high # convert from freq. to periodicity omega_2 = 2. * np.pi / low bweights = np.zeros(2 * K + 1) bweights[K] = (omega_2 - omega_1) / np.pi # weight at zero freq. j = np.arange(1, int(K) + 1) weights = 1 / (np.pi * j) * (np.sin(omega_2 * j) - np.sin(omega_1 * j)) bweights[K + j] = weights # j is an idx bweights[:K] = weights[::-1] # make symmetric weights bweights -= bweights.mean() # make sure weights sum to zero if x.ndim == 2: bweights = bweights[:, None] x = fftconvolve(x, bweights, mode='valid') # get a centered moving avg/convolution return pw.wrap(x, append='cycle', trim_start=K, trim_end=K) statsmodels-0.12.2/statsmodels/tsa/filters/cf_filter.py000066400000000000000000000071341400612667500232620ustar00rootroot00000000000000import numpy as np from statsmodels.tools.validation import array_like, PandasWrapper # the data is sampled quarterly, so cut-off frequency of 18 # Wn is normalized cut-off freq #Cutoff frequency is that frequency where the magnitude response of the filter # is sqrt(1/2.). For butter, the normalized cutoff frequency Wn must be a # number between 0 and 1, where 1 corresponds to the Nyquist frequency, p # radians per sample. # NOTE: uses a loop, could probably be sped-up for very large datasets def cffilter(x, low=6, high=32, drift=True): """ Christiano Fitzgerald asymmetric, random walk filter. Parameters ---------- x : array_like The 1 or 2d array to filter. If 2d, variables are assumed to be in columns. low : float Minimum period of oscillations. Features below low periodicity are filtered out. Default is 6 for quarterly data, giving a 1.5 year periodicity. high : float Maximum period of oscillations. Features above high periodicity are filtered out. Default is 32 for quarterly data, giving an 8 year periodicity. drift : bool Whether or not to remove a trend from the data. The trend is estimated as np.arange(nobs)*(x[-1] - x[0])/(len(x)-1). Returns ------- cycle : array_like The features of x between the periodicities low and high. trend : array_like The trend in the data with the cycles removed. See Also -------- statsmodels.tsa.filters.bk_filter.bkfilter Baxter-King filter. statsmodels.tsa.filters.bk_filter.hpfilter Hodrick-Prescott filter. statsmodels.tsa.seasonal.seasonal_decompose Decompose a time series using moving averages. statsmodels.tsa.seasonal.STL Season-Trend decomposition using LOESS. Examples -------- >>> dta = sm.datasets.macrodata.load_pandas().data >>> index = pd.DatetimeIndex(start='1959Q1', end='2009Q4', freq='Q') >>> dta.set_index(index, inplace=True) >>> cf_cycles, cf_trend = sm.tsa.filters.cffilter(dta[["infl", "unemp"]]) >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> cf_cycles.plot(ax=ax, style=['r--', 'b-']) >>> plt.show() .. plot:: plots/cff_plot.py """ #TODO: cythonize/vectorize loop?, add ability for symmetric filter, # and estimates of theta other than random walk. if low < 2: raise ValueError("low must be >= 2") pw = PandasWrapper(x) x = array_like(x, 'x', ndim=2) nobs, nseries = x.shape a = 2*np.pi/high b = 2*np.pi/low if drift: # get drift adjusted series x = x - np.arange(nobs)[:, None] * (x[-1] - x[0]) / (nobs - 1) J = np.arange(1, nobs + 1) Bj = (np.sin(b * J) - np.sin(a * J)) / (np.pi * J) B0 = (b - a) / np.pi Bj = np.r_[B0, Bj][:, None] y = np.zeros((nobs, nseries)) for i in range(nobs): B = -.5 * Bj[0] - np.sum(Bj[1:-i - 2]) A = -Bj[0] - np.sum(Bj[1:-i - 2]) - np.sum(Bj[1:i]) - B y[i] = (Bj[0] * x[i] + np.dot(Bj[1:-i - 2].T, x[i + 1:-1]) + B * x[-1] + np.dot(Bj[1:i].T, x[1:i][::-1]) + A * x[0]) y = y.squeeze() cycle, trend = y.squeeze(), x.squeeze() - y return pw.wrap(cycle, append='cycle'), pw.wrap(trend, append='trend') if __name__ == "__main__": import statsmodels as sm dta = sm.datasets.macrodata.load(as_pandas=False).data[['infl','tbilrate']].view((float,2))[1:] cycle, trend = cffilter(dta, 6, 32, drift=True) dta = sm.datasets.macrodata.load(as_pandas=False).data['tbilrate'][1:] cycle2, trend2 = cffilter(dta, 6, 32, drift=True) statsmodels-0.12.2/statsmodels/tsa/filters/filtertools.py000066400000000000000000000271441400612667500236760ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Linear Filters for time series analysis and testing TODO: * check common sequence in signature of filter functions (ar,ma,x) or (x,ar,ma) Created on Sat Oct 23 17:18:03 2010 Author: Josef-pktd """ # not original copied from various experimental scripts # version control history is there import numpy as np import scipy.fftpack as fft from scipy import signal from scipy.signal.signaltools import _centered as trim_centered from statsmodels.tools.validation import array_like, PandasWrapper def _pad_nans(x, head=None, tail=None): if np.ndim(x) == 1: if head is None and tail is None: return x elif head and tail: return np.r_[[np.nan] * head, x, [np.nan] * tail] elif tail is None: return np.r_[[np.nan] * head, x] elif head is None: return np.r_[x, [np.nan] * tail] elif np.ndim(x) == 2: if head is None and tail is None: return x elif head and tail: return np.r_[[[np.nan] * x.shape[1]] * head, x, [[np.nan] * x.shape[1]] * tail] elif tail is None: return np.r_[[[np.nan] * x.shape[1]] * head, x] elif head is None: return np.r_[x, [[np.nan] * x.shape[1]] * tail] else: raise ValueError("Nan-padding for ndim > 2 not implemented") #original changes and examples in sandbox.tsa.try_var_convolve # do not do these imports, here just for copied fftconvolve #get rid of these imports #from scipy.fftpack import fft, ifft, ifftshift, fft2, ifft2, fftn, \ # ifftn, fftfreq #from numpy import product,array # previous location in sandbox.tsa.try_var_convolve def fftconvolveinv(in1, in2, mode="full"): """ Convolve two N-dimensional arrays using FFT. See convolve. copied from scipy.signal.signaltools, but here used to try out inverse filter. does not work or I cannot get it to work 2010-10-23: looks ok to me for 1d, from results below with padded data array (fftp) but it does not work for multidimensional inverse filter (fftn) original signal.fftconvolve also uses fftn """ s1 = np.array(in1.shape) s2 = np.array(in2.shape) complex_result = (np.issubdtype(in1.dtype, np.complex) or np.issubdtype(in2.dtype, np.complex)) size = s1+s2-1 # Always use 2**n-sized FFT fsize = 2**np.ceil(np.log2(size)) IN1 = fft.fftn(in1,fsize) #IN1 *= fftn(in2,fsize) #JP: this looks like the only change I made IN1 /= fft.fftn(in2,fsize) # use inverse filter # note the inverse is elementwise not matrix inverse # is this correct, NO does not seem to work for VARMA fslice = tuple([slice(0, int(sz)) for sz in size]) ret = fft.ifftn(IN1)[fslice].copy() del IN1 if not complex_result: ret = ret.real if mode == "full": return ret elif mode == "same": if np.product(s1,axis=0) > np.product(s2,axis=0): osize = s1 else: osize = s2 return trim_centered(ret,osize) elif mode == "valid": return trim_centered(ret,abs(s2-s1)+1) #code duplication with fftconvolveinv def fftconvolve3(in1, in2=None, in3=None, mode="full"): """ Convolve two N-dimensional arrays using FFT. See convolve. For use with arma (old version: in1=num in2=den in3=data * better for consistency with other functions in1=data in2=num in3=den * note in2 and in3 need to have consistent dimension/shape since I'm using max of in2, in3 shapes and not the sum copied from scipy.signal.signaltools, but here used to try out inverse filter does not work or I cannot get it to work 2010-10-23 looks ok to me for 1d, from results below with padded data array (fftp) but it does not work for multidimensional inverse filter (fftn) original signal.fftconvolve also uses fftn """ if (in2 is None) and (in3 is None): raise ValueError('at least one of in2 and in3 needs to be given') s1 = np.array(in1.shape) if in2 is not None: s2 = np.array(in2.shape) else: s2 = 0 if in3 is not None: s3 = np.array(in3.shape) s2 = max(s2, s3) # try this looks reasonable for ARMA #s2 = s3 complex_result = (np.issubdtype(in1.dtype, np.complex) or np.issubdtype(in2.dtype, np.complex)) size = s1+s2-1 # Always use 2**n-sized FFT fsize = 2**np.ceil(np.log2(size)) #convolve shorter ones first, not sure if it matters if in2 is not None: IN1 = fft.fftn(in2, fsize) if in3 is not None: IN1 /= fft.fftn(in3, fsize) # use inverse filter # note the inverse is elementwise not matrix inverse # is this correct, NO does not seem to work for VARMA IN1 *= fft.fftn(in1, fsize) fslice = tuple([slice(0, int(sz)) for sz in size]) ret = fft.ifftn(IN1)[fslice].copy() del IN1 if not complex_result: ret = ret.real if mode == "full": return ret elif mode == "same": if np.product(s1,axis=0) > np.product(s2,axis=0): osize = s1 else: osize = s2 return trim_centered(ret,osize) elif mode == "valid": return trim_centered(ret,abs(s2-s1)+1) #original changes and examples in sandbox.tsa.try_var_convolve #examples and tests are there def recursive_filter(x, ar_coeff, init=None): """ Autoregressive, or recursive, filtering. Parameters ---------- x : array_like Time-series data. Should be 1d or n x 1. ar_coeff : array_like AR coefficients in reverse time order. See Notes for details. init : array_like Initial values of the time-series prior to the first value of y. The default is zero. Returns ------- array_like Filtered array, number of columns determined by x and ar_coeff. If x is a pandas object than a Series is returned. Notes ----- Computes the recursive filter :: y[n] = ar_coeff[0] * y[n-1] + ... + ar_coeff[n_coeff - 1] * y[n - n_coeff] + x[n] where n_coeff = len(n_coeff). """ pw = PandasWrapper(x) x = array_like(x, 'x') ar_coeff = array_like(ar_coeff, 'ar_coeff') if init is not None: # integer init are treated differently in lfiltic init = array_like(init, 'init') if len(init) != len(ar_coeff): raise ValueError("ar_coeff must be the same length as init") if init is not None: zi = signal.lfiltic([1], np.r_[1, -ar_coeff], init, x) else: zi = None y = signal.lfilter([1.], np.r_[1, -ar_coeff], x, zi=zi) if init is not None: result = y[0] else: result = y return pw.wrap(result) def convolution_filter(x, filt, nsides=2): """ Linear filtering via convolution. Centered and backward displaced moving weighted average. Parameters ---------- x : array_like data array, 1d or 2d, if 2d then observations in rows filt : array_like Linear filter coefficients in reverse time-order. Should have the same number of dimensions as x though if 1d and ``x`` is 2d will be coerced to 2d. nsides : int, optional If 2, a centered moving average is computed using the filter coefficients. If 1, the filter coefficients are for past values only. Both methods use scipy.signal.convolve. Returns ------- y : ndarray, 2d Filtered array, number of columns determined by x and filt. If a pandas object is given, a pandas object is returned. The index of the return is the exact same as the time period in ``x`` Notes ----- In nsides == 1, x is filtered :: y[n] = filt[0]*x[n-1] + ... + filt[n_filt-1]*x[n-n_filt] where n_filt is len(filt). If nsides == 2, x is filtered around lag 0 :: y[n] = filt[0]*x[n - n_filt/2] + ... + filt[n_filt / 2] * x[n] + ... + x[n + n_filt/2] where n_filt is len(filt). If n_filt is even, then more of the filter is forward in time than backward. If filt is 1d or (nlags,1) one lag polynomial is applied to all variables (columns of x). If filt is 2d, (nlags, nvars) each series is independently filtered with its own lag polynomial, uses loop over nvar. This is different than the usual 2d vs 2d convolution. Filtering is done with scipy.signal.convolve, so it will be reasonably fast for medium sized data. For large data fft convolution would be faster. """ # for nsides shift the index instead of using 0 for 0 lag this # allows correct handling of NaNs if nsides == 1: trim_head = len(filt) - 1 trim_tail = None elif nsides == 2: trim_head = int(np.ceil(len(filt)/2.) - 1) or None trim_tail = int(np.ceil(len(filt)/2.) - len(filt) % 2) or None else: # pragma : no cover raise ValueError("nsides must be 1 or 2") pw = PandasWrapper(x) x = array_like(x, 'x', maxdim=2) filt = array_like(filt, 'filt', ndim=x.ndim) if filt.ndim == 1 or min(filt.shape) == 1: result = signal.convolve(x, filt, mode='valid') elif filt.ndim == 2: nlags = filt.shape[0] nvar = x.shape[1] result = np.zeros((x.shape[0] - nlags + 1, nvar)) if nsides == 2: for i in range(nvar): # could also use np.convolve, but easier for swiching to fft result[:, i] = signal.convolve(x[:, i], filt[:, i], mode='valid') elif nsides == 1: for i in range(nvar): result[:, i] = signal.convolve(x[:, i], np.r_[0, filt[:, i]], mode='valid') result = _pad_nans(result, trim_head, trim_tail) return pw.wrap(result) # previously located in sandbox.tsa.garch def miso_lfilter(ar, ma, x, useic=False): """ Filter multiple time series into a single time series. Uses a convolution to merge inputs, and then lfilter to produce output. Parameters ---------- ar : array_like The coefficients of autoregressive lag polynomial including lag zero, ar(L) in the expression ar(L)y_t. ma : array_like, same ndim as x, currently 2d The coefficient of the moving average lag polynomial, ma(L) in ma(L)x_t. x : array_like The 2-d input data series, time in rows, variables in columns. useic : bool Flag indicating whether to use initial conditions. Returns ------- y : ndarray The filtered output series. inp : ndarray, 1d The combined input series. Notes ----- currently for 2d inputs only, no choice of axis Use of signal.lfilter requires that ar lag polynomial contains floating point numbers does not cut off invalid starting and final values miso_lfilter find array y such that: ar(L)y_t = ma(L)x_t with shapes y (nobs,), x (nobs, nvars), ar (narlags,), and ma (narlags, nvars). """ ma = array_like(ma, 'ma') ar = array_like(ar, 'ar') inp = signal.correlate(x, ma[::-1, :])[:, (x.shape[1] + 1) // 2] # for testing 2d equivalence between convolve and correlate # inp2 = signal.convolve(x, ma[:,::-1])[:, (x.shape[1]+1)//2] # np.testing.assert_almost_equal(inp2, inp) nobs = x.shape[0] # cut of extra values at end # TODO: initialize also x for correlate if useic: return signal.lfilter([1], ar, inp, zi=signal.lfiltic(np.array([1., 0.]), ar, useic))[0][:nobs], inp[:nobs] else: return signal.lfilter([1], ar, inp)[:nobs], inp[:nobs] statsmodels-0.12.2/statsmodels/tsa/filters/hp_filter.py000066400000000000000000000062501400612667500232770ustar00rootroot00000000000000 import numpy as np from scipy import sparse from scipy.sparse.linalg import spsolve from statsmodels.tools.validation import array_like, PandasWrapper def hpfilter(x, lamb=1600): """ Hodrick-Prescott filter. Parameters ---------- x : array_like The time series to filter, 1-d. lamb : float The Hodrick-Prescott smoothing parameter. A value of 1600 is suggested for quarterly data. Ravn and Uhlig suggest using a value of 6.25 (1600/4**4) for annual data and 129600 (1600*3**4) for monthly data. Returns ------- cycle : ndarray The estimated cycle in the data given lamb. trend : ndarray The estimated trend in the data given lamb. See Also -------- statsmodels.tsa.filters.bk_filter.bkfilter Baxter-King filter. statsmodels.tsa.filters.cf_filter.cffilter The Christiano Fitzgerald asymmetric, random walk filter. statsmodels.tsa.seasonal.seasonal_decompose Decompose a time series using moving averages. statsmodels.tsa.seasonal.STL Season-Trend decomposition using LOESS. Notes ----- The HP filter removes a smooth trend, `T`, from the data `x`. by solving min sum((x[t] - T[t])**2 + lamb*((T[t+1] - T[t]) - (T[t] - T[t-1]))**2) T t Here we implemented the HP filter as a ridge-regression rule using scipy.sparse. In this sense, the solution can be written as T = inv(I + lamb*K'K)x where I is a nobs x nobs identity matrix, and K is a (nobs-2) x nobs matrix such that K[i,j] = 1 if i == j or i == j + 2 K[i,j] = -2 if i == j + 1 K[i,j] = 0 otherwise References ---------- Hodrick, R.J, and E. C. Prescott. 1980. "Postwar U.S. Business Cycles: An Empirical Investigation." `Carnegie Mellon University discussion paper no. 451`. Ravn, M.O and H. Uhlig. 2002. "Notes On Adjusted the Hodrick-Prescott Filter for the Frequency of Observations." `The Review of Economics and Statistics`, 84(2), 371-80. Examples -------- >>> import statsmodels.api as sm >>> import pandas as pd >>> dta = sm.datasets.macrodata.load_pandas().data >>> index = pd.period_range('1959Q1', '2009Q3', freq='Q') >>> dta.set_index(index, inplace=True) >>> cycle, trend = sm.tsa.filters.hpfilter(dta.realgdp, 1600) >>> gdp_decomp = dta[['realgdp']] >>> gdp_decomp["cycle"] = cycle >>> gdp_decomp["trend"] = trend >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> gdp_decomp[["realgdp", "trend"]]["2000-03-31":].plot(ax=ax, ... fontsize=16) >>> plt.show() .. plot:: plots/hpf_plot.py """ pw = PandasWrapper(x) x = array_like(x, 'x', ndim=1) nobs = len(x) I = sparse.eye(nobs, nobs) # noqa:E741 offsets = np.array([0, 1, 2]) data = np.repeat([[1.], [-2.], [1.]], nobs, axis=1) K = sparse.dia_matrix((data, offsets), shape=(nobs - 2, nobs)) use_umfpack = True trend = spsolve(I+lamb*K.T.dot(K), x, use_umfpack=use_umfpack) cycle = x - trend return pw.wrap(cycle, append='cycle'), pw.wrap(trend, append='trend') statsmodels-0.12.2/statsmodels/tsa/filters/tests/000077500000000000000000000000001400612667500221105ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/filters/tests/__init__.py000066400000000000000000000000001400612667500242070ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/filters/tests/results/000077500000000000000000000000001400612667500236115ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/filters/tests/results/__init__.py000066400000000000000000000000001400612667500257100ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/filters/tests/results/filter.R000066400000000000000000000032241400612667500252220ustar00rootroot00000000000000library(R2nparray) x <- c(-50, 175, 149, 214, 247, 237, 225, 329, 729, 809, 530, 489, 540, 457, 195, 176, 337, 239, 128, 102, 232, 429, 3, 98, 43, -141, -77, -13, 125, 361, -45, 184) x <- ts(x, start=c(1951, 1), frequency=4) conv2 <- filter(x, c(.75, .25), method="convolution") conv1 <- filter(x, c(.75, .25), method="convolution", sides=1) recurse <- filter(x, c(.75, .25), method="recursive") recurse.init <- filter(x, c(.75, .25), method="recursive", init=c(150, 100)) conv2.odd <- filter(x, c(.75, .5, .3, .2, .1), method="convolution", sides=2) conv1.odd <- filter(x, c(.75, .5, .3, .2, .1), method="convolution", sides=1) recurse.odd <- filter(x, c(.75, .5, .3, .2, .1), method="recursive", init=c(150, 100, 125, 135, 145)) # missing values x[10] = NaN conv2.na <- filter(x, c(.75, .25), method="convolution") conv1.na <- filter(x, c(.75, .25), method="convolution", sides=1) recurse.na <- filter(x, c(.75, .25), method="recursive") recurse.init.na <- filter(x, c(.75, .25), method="recursive", init=c(150, 100)) options(digits=12) R2nparray(list(conv2=as.numeric(conv2), conv1=as.numeric(conv1), recurse=as.numeric(recurse), recurse_init=as.numeric(recurse.init), conv2_na=as.numeric(conv2.na), conv1_na=as.numeric(conv1.na), recurse_na=as.numeric(recurse.na), recurse_init_na=as.numeric(recurse.init.na), conv2_odd=as.numeric(conv2.odd), conv1_odd=as.numeric(conv1.odd), recurse_odd=as.numeric(recurse.odd)), fname="filter_results.py") statsmodels-0.12.2/statsmodels/tsa/filters/tests/results/filter_results.py000066400000000000000000000074261400612667500272420ustar00rootroot00000000000000import numpy as np conv2 = np.array([ 118.75, 155.5, 197.75, 238.75, 239.5, 228, 303, 629, 789, 599.75, 499.25, 527.25, 477.75, 260.5, 180.75, 296.75, 263.5, 155.75, 108.5, 199.5, 379.75, 109.5, 74.25, 56.75, -95, -93, -29, 90.5, 302, 56.5, 126.75, np.nan]) conv1 = np.array([ np.nan, 118.75, 155.5, 197.75, 238.75, 239.5, 228, 303, 629, 789, 599.75, 499.25, 527.25, 477.75, 260.5, 180.75, 296.75, 263.5, 155.75, 108.5, 199.5, 379.75, 109.5, 74.25, 56.75, -95, -93, -29, 90.5, 302, 56.5, 126.75]) recurse = np.array([ -50, 137.5, 239.625, 428.09375, 627.9765625, 815.005859375, 993.248535156, 1277.68786621, 1935.57803345, 2580.10549164, 2948.97362709, 3345.75659323, 3786.56085169, 4133.35978708, 4241.66005323, 4390.58498669, 4690.35375333, 4854.41156167, 4941.39710958, 5021.6507226, 5233.58731935, 5609.60317016, 5518.59920746, 5639.35019814, 5652.16245047, 5507.95938738, 5467.01015315, 5464.24746171, 5589.93813457, 5919.51546636, 5792.12113341, 6007.96971665]) recurse_init = np.array([ 87.5, 278.125, 379.46875, 568.1328125, 767.966796875, 955.008300781, 1133.2479248, 1417.6880188, 2075.5779953, 2720.10550117, 3088.97362471, 3485.75659382, 3926.56085154, 4273.35978711, 4381.66005322, 4530.58498669, 4830.35375333, 4994.41156167, 5081.39710958, 5161.6507226, 5373.58731935, 5749.60317016, 5658.59920746, 5779.35019814, 5792.16245047, 5647.95938738, 5607.01015315, 5604.24746171, 5729.93813457, 6059.51546636, 5932.12113341, 6147.96971665]) conv2_na = np.array([ 118.75, 155.5, 197.75, 238.75, 239.5, 228, 303, 629, np.nan, np.nan, 499.25, 527.25, 477.75, 260.5, 180.75, 296.75, 263.5, 155.75, 108.5, 199.5, 379.75, 109.5, 74.25, 56.75, -95, -93, -29, 90.5, 302, 56.5, 126.75, np.nan]) conv1_na = np.array([ np.nan, 118.75, 155.5, 197.75, 238.75, 239.5, 228, 303, 629, np.nan, np.nan, 499.25, 527.25, 477.75, 260.5, 180.75, 296.75, 263.5, 155.75, 108.5, 199.5, 379.75, 109.5, 74.25, 56.75, -95, -93, -29, 90.5, 302, 56.5, 126.75]) recurse_na = np.array([ -50, 137.5, 239.625, 428.09375, 627.9765625, 815.005859375, 993.248535156, 1277.68786621, 1935.57803345, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan]) recurse_init_na = np.array([ 87.5, 278.125, 379.46875, 568.1328125, 767.966796875, 955.008300781, 1133.2479248, 1417.6880188, 2075.5779953, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan]) conv2_odd = np.array([ np.nan, np.nan, 366.95, 412.75, 419.05, 501.15, 850.85, 1138.65, 1109, 1053.15, 1043.2, 946.35, 687.55, 523.5, 544.65, 485.25, 371.3, 297.2, 344.9, 517.85, 319.55, 260.3, 191.15, -11.35, -95.45, -72.15, 40.25, 299.85, 173.95, 247.5, np.nan, np.nan]) conv1_odd = np.array([ np.nan, np.nan, np.nan, np.nan, 366.95, 412.75, 419.05, 501.15, 850.85, 1138.65, 1109, 1053.15, 1043.2, 946.35, 687.55, 523.5, 544.65, 485.25, 371.3, 297.2, 344.9, 517.85, 319.55, 260.3, 191.15, -11.35, -95.45, -72.15, 40.25, 299.85, 173.95, 247.5]) recurse_odd = np.array([ 191.5, 462.125, 668.84375, 1044.1453125, 1556.46835938, 2238.65205078, 3175.44806152, 4572.56601685, 6833.45236176, 9776.38394429, 13509.7387615, 18791.5897613, 26145.4239591, 36153.4065035, 49699.8299323, 68480.4947171, 94501.551723, 130110.583827, 179061.168784, 246469.715955, 339396.406323, 467401.785292, 643016.749056, 885080.436404, 1218108.49028, 1676305.60832, 2307074.11064, 3175195.69641, 4370080.25182, 6014713.24095, 8277634.14851, 11392536.8578]) statsmodels-0.12.2/statsmodels/tsa/filters/tests/test_filters.py000066400000000000000000001144501400612667500251760ustar00rootroot00000000000000from statsmodels.compat.pandas import assert_frame_equal, make_dataframe from datetime import datetime import numpy as np from numpy.testing import (assert_almost_equal, assert_equal, assert_allclose, assert_raises, assert_) from numpy import array, column_stack from statsmodels.tsa.filters._utils import pandas_wrapper from statsmodels.datasets import macrodata from pandas import DataFrame, date_range, concat from statsmodels.tsa.filters.api import (bkfilter, hpfilter, cffilter, convolution_filter, recursive_filter) def test_bking1d(): # Test Baxter King band-pass filter. Results are taken from Stata bking_results = array([ 7.320813, 2.886914, -6.818976, -13.49436, -13.27936, -9.405913, -5.691091, -5.133076, -7.273468, -9.243364, -8.482916, -4.447764, 2.406559, 10.68433, 19.46414, 28.09749, 34.11066, 33.48468, 24.64598, 9.952399, -4.265528, -12.59471, -13.46714, -9.049501, -3.011248, .5655082, 2.897976, 7.406077, 14.67959, 18.651, 13.05891, -2.945415, -24.08659, -41.86147, -48.68383, -43.32689, -31.66654, -20.38356, -13.76411, -9.978693, -3.7704, 10.27108, 31.02847, 51.87613, 66.93117, 73.51951, 73.4053, 69.17468, 59.8543, 38.23899, -.2604809, -49.0107, -91.1128, -112.1574, -108.3227, -86.51453, -59.91258, -40.01185, -29.70265, -22.76396, -13.08037, 1.913622, 20.44045, 37.32873, 46.79802, 51.95937, 59.67393, 70.50803, 81.27311, 83.53191, 67.72536, 33.78039, -6.509092, -37.31579, -46.05207, -29.81496, 1.416417, 28.31503, 32.90134, 8.949259, -35.41895, -84.65775, -124.4288, -144.6036, -140.2204, -109.2624, -53.6901, 15.07415, 74.44268, 104.0403, 101.0725, 76.58291, 49.27925, 36.15751, 36.48799, 37.60897, 27.75998, 4.216643, -23.20579, -39.33292, -36.6134, -20.90161, -4.143123, 5.48432, 9.270075, 13.69573, 22.16675, 33.01987, 41.93186, 47.12222, 48.62164, 47.30701, 40.20537, 22.37898, -7.133002, -43.3339, -78.51229, -101.3684, -105.2179, -90.97147, -68.30824, -48.10113, -35.60709, -31.15775, -31.82346, -32.49278, -28.22499, -14.42852, 10.1827, 36.64189, 49.43468, 38.75517, 6.447761, -33.15883, -62.60446, -72.87829, -66.54629, -52.61205, -38.06676, -26.19963, -16.51492, -7.007577, .6125674, 7.866972, 14.8123, 22.52388, 30.65265, 39.47801, 49.05027, 59.02925, 72.88999, 95.08865, 125.8983, 154.4283, 160.7638, 130.6092, 67.84406, -7.070272, -68.08128, -99.39944, -104.911, -100.2372, -98.11596, -104.2051, -114.0125, -113.3475, -92.98669, -51.91707, -.7313812, 43.22938, 64.62762, 64.07226, 59.35707, 67.06026, 91.87247, 124.4591, 151.2402, 163.0648, 154.6432]) X = macrodata.load_pandas().data['realinv'].values Y = bkfilter(X, 6, 32, 12) assert_almost_equal(Y, bking_results, 4) def test_bking2d(): # Test Baxter-King band-pass filter with 2d input bking_results = array([ [7.320813, -.0374475], [2.886914, -.0430094], [-6.818976, -.053456], [-13.49436, -.0620739], [-13.27936, -.0626929], [-9.405913, -.0603022], [-5.691091, -.0630016], [-5.133076, -.0832268], [-7.273468, -.1186448], [-9.243364, -.1619868], [-8.482916, -.2116604], [-4.447764, -.2670747], [2.406559, -.3209931], [10.68433, -.3583075], [19.46414, -.3626742], [28.09749, -.3294618], [34.11066, -.2773388], [33.48468, -.2436127], [24.64598, -.2605531], [9.952399, -.3305166], [-4.265528, -.4275561], [-12.59471, -.5076068], [-13.46714, -.537573], [-9.049501, -.5205845], [-3.011248, -.481673], [.5655082, -.4403994], [2.897976, -.4039957], [7.406077, -.3537394], [14.67959, -.2687359], [18.651, -.1459743], [13.05891, .0014926], [-2.945415, .1424277], [-24.08659, .2451936], [-41.86147, .288541], [-48.68383, .2727282], [-43.32689, .1959127], [-31.66654, .0644874], [-20.38356, -.1158372], [-13.76411, -.3518627], [-9.978693, -.6557535], [-3.7704, -1.003754], [10.27108, -1.341632], [31.02847, -1.614486], [51.87613, -1.779089], [66.93117, -1.807459], [73.51951, -1.679688], [73.4053, -1.401012], [69.17468, -.9954996], [59.8543, -.511261], [38.23899, -.0146745], [-.2604809, .4261311], [-49.0107, .7452514], [-91.1128, .8879492], [-112.1574, .8282748], [-108.3227, .5851508], [-86.51453, .2351699], [-59.91258, -.1208998], [-40.01185, -.4297895], [-29.70265, -.6821963], [-22.76396, -.9234254], [-13.08037, -1.217539], [1.913622, -1.57367], [20.44045, -1.927008], [37.32873, -2.229565], [46.79802, -2.463154], [51.95937, -2.614697], [59.67393, -2.681357], [70.50803, -2.609654], [81.27311, -2.301618], [83.53191, -1.720974], [67.72536, -.9837123], [33.78039, -.2261613], [-6.509092, .4546985], [-37.31579, 1.005751], [-46.05207, 1.457224], [-29.81496, 1.870815], [1.416417, 2.263313], [28.31503, 2.599906], [32.90134, 2.812282], [8.949259, 2.83358], [-35.41895, 2.632667], [-84.65775, 2.201077], [-124.4288, 1.598951], [-144.6036, .9504762], [-140.2204, .4187932], [-109.2624, .1646726], [-53.6901, .2034265], [15.07415, .398165], [74.44268, .5427476], [104.0403, .5454975], [101.0725, .4723354], [76.58291, .4626823], [49.27925, .5840143], [36.15751, .7187981], [36.48799, .6058422], [37.60897, .1221227], [27.75998, -.5891272], [4.216643, -1.249841], [-23.20579, -1.594972], [-39.33292, -1.545968], [-36.6134, -1.275494], [-20.90161, -1.035783], [-4.143123, -.9971732], [5.48432, -1.154264], [9.270075, -1.29987], [13.69573, -1.240559], [22.16675, -.9662656], [33.01987, -.6420301], [41.93186, -.4698712], [47.12222, -.4527797], [48.62164, -.4407153], [47.30701, -.2416076], [40.20537, .2317583], [22.37898, .8710276], [-7.133002, 1.426177], [-43.3339, 1.652785], [-78.51229, 1.488021], [-101.3684, 1.072096], [-105.2179, .6496446], [-90.97147, .4193682], [-68.30824, .41847], [-48.10113, .5253419], [-35.60709, .595076], [-31.15775, .5509905], [-31.82346, .3755519], [-32.49278, .1297979], [-28.22499, -.0916165], [-14.42852, -.2531037], [10.1827, -.3220784], [36.64189, -.2660561], [49.43468, -.1358522], [38.75517, -.0279508], [6.447761, .0168735], [-33.15883, .0315687], [-62.60446, .0819507], [-72.87829, .2274033], [-66.54629, .4641401], [-52.61205, .7211093], [-38.06676, .907773], [-26.19963, .9387103], [-16.51492, .7940786], [-7.007577, .5026631], [.6125674, .1224996], [7.866972, -.2714422], [14.8123, -.6273921], [22.52388, -.9124271], [30.65265, -1.108861], [39.47801, -1.199206], [49.05027, -1.19908], [59.02925, -1.139046], [72.88999, -.9775021], [95.08865, -.6592603], [125.8983, -.1609712], [154.4283, .4796201], [160.7638, 1.100565], [130.6092, 1.447148], [67.84406, 1.359608], [-7.070272, .8931825], [-68.08128, .2619787], [-99.39944, -.252208], [-104.911, -.4703874], [-100.2372, -.4430657], [-98.11596, -.390683], [-104.2051, -.5647846], [-114.0125, -.9397582], [-113.3475, -1.341633], [-92.98669, -1.567337], [-51.91707, -1.504943], [-.7313812, -1.30576], [43.22938, -1.17151], [64.62762, -1.136151], [64.07226, -1.050555], [59.35707, -.7308369], [67.06026, -.1766731], [91.87247, .3898467], [124.4591, .8135461], [151.2402, .9644226], [163.0648, .6865934], [154.6432, .0115685]]) mdata = macrodata.load_pandas() X = mdata.data[['realinv', 'cpi']].values.astype(float) Y = bkfilter(X, 6, 32, 12) assert_almost_equal(Y, bking_results, 4) def test_hpfilter(): # Test Hodrick-Prescott Filter. Results taken from Stata. hpfilt_res = array([ [3.951191484487844718e+01, 2.670837085155121713e+03], [8.008853245681075350e+01, 2.698712467543189177e+03], [4.887545512195401898e+01, 2.726612544878045810e+03], [3.059193256079834100e+01, 2.754612067439201837e+03], [6.488266733421960453e+01, 2.782816332665780465e+03], [2.304024204546703913e+01, 2.811349757954532834e+03], [-1.355312369487364776e+00, 2.840377312369487299e+03], [-6.746236512580753697e+01, 2.870078365125807522e+03], [-8.136743836853429457e+01, 2.900631438368534418e+03], [-6.016789026443257171e+01, 2.932172890264432681e+03], [-4.636922433138215638e+01, 2.964788224331382025e+03], [-2.069533915570400495e+01, 2.998525339155703932e+03], [-2.162152558595607843e+00, 3.033403152558595593e+03], [-4.718647774311648391e+00, 3.069427647774311481e+03], [-1.355645669169007306e+01, 3.106603456691690099e+03], [-4.436926204475639679e+01, 3.144932262044756499e+03], [-4.332027378211660107e+01, 3.184407273782116590e+03], [-4.454697106352068658e+01, 3.224993971063520803e+03], [-2.629875787765286077e+01, 3.266630757877652741e+03], [-4.426119635629265758e+01, 3.309228196356292756e+03], [-1.443441190762496262e+01, 3.352680411907625057e+03], [-2.026686669186437939e+01, 3.396853866691864368e+03], [-1.913700136208899494e+01, 3.441606001362089046e+03], [-5.482458977940950717e+01, 3.486781589779409387e+03], [-1.596244517937793717e+01, 3.532213445179378141e+03], [-1.374011542874541192e+01, 3.577700115428745448e+03], [1.325482813403914406e+01, 3.623030171865960710e+03], [5.603040174253828809e+01, 3.667983598257461836e+03], [1.030743373627105939e+02, 3.712348662637289181e+03], [7.217534795943993231e+01, 3.755948652040559864e+03], [5.462972503693208637e+01, 3.798671274963067845e+03], [4.407065050666142270e+01, 3.840449349493338559e+03], [3.749016270204992907e+01, 3.881249837297949853e+03], [-1.511244199923112319e+00, 3.921067244199923152e+03], [-9.093507374079763395e+00, 3.959919507374079785e+03], [-1.685361946760258434e+01, 3.997823619467602384e+03], [2.822211031434289907e+01, 4.034790889685657021e+03], [6.117590627896424849e+01, 4.070822093721035344e+03], [5.433135391434370831e+01, 4.105935646085656117e+03], [3.810480376716623141e+01, 4.140188196232833434e+03], [7.042964928802848590e+01, 4.173670350711971878e+03], [4.996346842507591646e+01, 4.206496531574924120e+03], [4.455282059571254649e+01, 4.238825179404287155e+03], [-7.584961950576143863e+00, 4.270845961950576566e+03], [-4.620339247697120300e+01, 4.302776392476971523e+03], [-7.054024364552969928e+01, 4.334829243645529459e+03], [-6.492941099801464588e+01, 4.367188410998014660e+03], [-1.433567024239555394e+02, 4.399993702423955256e+03], [-5.932834493089012540e+01, 4.433344344930889747e+03], [-6.842096758743628016e+01, 4.467249967587436004e+03], [-6.774011924654860195e+01, 4.501683119246548813e+03], [-9.030958565658056614e+01, 4.536573585656580690e+03], [-4.603981499136807543e+01, 4.571808814991368308e+03], [2.588118806672991923e+01, 4.607219811933269739e+03], [3.489419371912299539e+01, 4.642608806280876706e+03], [7.675179642495095322e+01, 4.677794203575049323e+03], [1.635497817724171910e+02, 4.712616218227582976e+03], [1.856079654765617306e+02, 4.746963034523438182e+03], [1.254269446392718237e+02, 4.780825055360728584e+03], [1.387413113837174024e+02, 4.814308688616282780e+03], [6.201826599282230745e+01, 4.847598734007177882e+03], [4.122129542972197669e+01, 4.880966704570278125e+03], [-4.120287475842360436e+01, 4.914722874758424041e+03], [-9.486328233441963675e+01, 4.949203282334419782e+03], [-1.894232132641573116e+02, 4.984718213264157384e+03], [-1.895766639620087517e+02, 5.021518663962008759e+03], [-1.464092413342650616e+02, 5.059737241334265491e+03], [-1.218770668721217589e+02, 5.099388066872122181e+03], [-4.973075629078175552e+01, 5.140393756290781312e+03], [-5.365375213897277717e+01, 5.182600752138972894e+03], [-7.175241524251214287e+01, 5.225824415242512259e+03], [-7.834757283225462743e+01, 5.269846572832254424e+03], [-6.264220687943907251e+01, 5.314404206879438789e+03], [-3.054332122210325906e+00, 5.359185332122210639e+03], [4.808218808024685131e+01, 5.403838811919753425e+03], [2.781399326736391231e+00, 5.448011600673263274e+03], [-2.197570415173231595e+01, 5.491380704151732061e+03], [1.509441335012807031e+02, 5.533624866498719712e+03], [1.658909029574851957e+02, 5.574409097042514986e+03], [2.027292548049981633e+02, 5.613492745195001589e+03], [1.752101578176061594e+02, 5.650738842182393455e+03], [1.452808749847536092e+02, 5.686137125015246056e+03], [1.535481629475025329e+02, 5.719786837052497503e+03], [1.376169777998875361e+02, 5.751878022200112355e+03], [1.257703080340770612e+02, 5.782696691965922582e+03], [-2.524186846895645431e+01, 5.812614868468956047e+03], [-6.546618027042404719e+01, 5.842083180270424236e+03], [1.192352023580315290e+01, 5.871536479764196883e+03], [1.043482970188742911e+02, 5.901368702981125352e+03], 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[6.052940492147536133e+01, 6.895388595078524304e+03], [6.029518881462354329e+01, 6.962461811185376064e+03], [2.187042136652689805e+01, 7.029098578633473153e+03], [2.380067926824722235e+01, 7.095149320731752596e+03], [-7.119129802169481991e+00, 7.160478129802169860e+03], [-3.194497359120850888e+01, 7.224963973591208742e+03], [-1.897137038934124575e+01, 7.288481370389341464e+03], [-1.832687287845146784e+01, 7.350884872878451461e+03], [4.600482336597542599e+01, 7.412017176634024509e+03], [2.489047706403016491e+01, 7.471709522935970199e+03], [6.305909392127250612e+01, 7.529821906078727807e+03], [4.585212309498183458e+01, 7.586229876905018500e+03], [9.314260180878318351e+01, 7.640848398191216802e+03], [1.129819097095369216e+02, 7.693621090290463144e+03], [1.204662123176703972e+02, 7.744549787682329224e+03], [1.336860614601246198e+02, 7.793706938539875409e+03], [1.034567175813735957e+02, 7.841240282418626521e+03], [1.403118873372050075e+02, 7.887381112662795204e+03], [1.271726169351004501e+02, 7.932425383064899506e+03], [8.271925765282139764e+01, 7.976756742347178260e+03], [-3.197432211752584408e+01, 8.020838322117525422e+03], [-1.150209535194062482e+02, 8.065184953519406008e+03], [-1.064694837456772802e+02, 8.110291483745677397e+03], [-1.190428718925368230e+02, 8.156580871892536379e+03], [-1.353635336292991269e+02, 8.204409533629299403e+03], [-9.644348283027102298e+01, 8.254059482830271008e+03], [-6.143413116116607853e+01, 8.305728131161165948e+03], [-3.019161311097923317e+01, 8.359552613110980019e+03], [1.384333163552582846e+00, 8.415631666836447039e+03], [-4.156016073666614830e+01, 8.474045160736666730e+03], [-4.843882841860977351e+01, 8.534873828418609264e+03], [-6.706442838867042155e+01, 8.598172428388670596e+03], [-2.019644488579979225e+01, 8.663965444885800025e+03], [-4.316446881084630149e+00, 8.732235446881084499e+03], [4.435061943264736328e+01, 8.802952380567352520e+03], [2.820550564155564643e+01, 8.876083494358445023e+03], [5.155624419490777655e+01, 8.951623755805092514e+03], [-4.318760899315748247e+00, 9.029585760899315574e+03], [-6.534632828542271454e+01, 9.110014328285422380e+03], [-7.226757738268497633e+01, 9.192951577382684263e+03], [-9.412378615444868046e+01, 9.278398786154448317e+03], [-1.191240653288368776e+02, 9.366312065328836979e+03], [-4.953669826751865912e+01, 9.456588698267518339e+03], [-6.017251579067487910e+01, 9.549051515790675694e+03], [-5.103438828313483100e+01, 9.643492388283135369e+03], [-7.343057830678117170e+01, 9.739665578306781754e+03], [-2.774245193054957781e+01, 9.837293451930549054e+03], [-3.380481112519191811e+00, 9.936052481112519672e+03], [-2.672779877794346248e+01, 1.003560179877794326e+04], [-3.217342505148371856e+01, 1.013559842505148299e+04], [-4.140567518359966925e+01, 1.023568267518359971e+04], [-6.687756033938057953e+00, 1.033547475603393832e+04], [7.300600408459467872e+01, 1.043456899591540605e+04], [6.862345670680042531e+01, 1.053255554329319966e+04], [5.497882461487461114e+01, 1.062907017538512628e+04], [9.612244093055960548e+01, 1.072379155906944106e+04], [1.978212770103891671e+02, 1.081643272298961165e+04], [1.362772276848754700e+02, 1.090676677231512440e+04], [2.637635494867263333e+02, 1.099469045051327339e+04], [1.876813256815166824e+02, 1.108018567431848351e+04], [1.711447873158413131e+02, 1.116339921268415856e+04], [5.257586460826678376e+01, 1.124459513539173349e+04], [4.710652228531762375e+01, 1.132414447771468258e+04], [-6.237613484241046535e+01, 1.140245113484241119e+04], [-9.982044354035315337e+01, 1.147994844354035376e+04], [-7.916275548997509759e+01, 1.155703075548997549e+04], [-9.526003459472303803e+01, 1.163403003459472347e+04], [-1.147987680369169539e+02, 1.171122876803691724e+04], [-1.900259054765901965e+02, 1.178884990547659072e+04], [-2.212256473439556430e+02, 1.186704464734395515e+04], [-2.071394278781845060e+02, 1.194584542787818464e+04], [-8.968541528904825100e+01, 1.202514641528904758e+04], [-6.189531564415665343e+01, 1.210471231564415575e+04], [-5.662878162551714922e+01, 1.218425178162551674e+04], [-4.961678134413705266e+01, 1.226343478134413635e+04], [-3.836288992144181975e+01, 1.234189588992144127e+04], [-8.956671991456460091e+00, 1.241923867199145570e+04], [3.907028461866866564e+01, 1.249504271538133071e+04], [1.865299000184495526e+01, 1.256888200999815490e+04], [4.279803532226833340e+01, 1.264035496467773191e+04], [3.962735362631610769e+01, 1.270907164637368442e+04], [1.412691291877854383e+02, 1.277466887081221466e+04], [1.256537791844366438e+02, 1.283680822081556289e+04], [7.067642758858892194e+01, 1.289523957241141034e+04], [1.108876647603192396e+02, 1.294979133523968085e+04], [9.956490829291760747e+01, 1.300033609170708223e+04], [1.571612709880937473e+02, 1.304681572901190702e+04], [2.318746375812715996e+02, 1.308923436241872878e+04], [2.635546670125277160e+02, 1.312769433298747208e+04], [2.044220965739259555e+02, 1.316244290342607383e+04], [2.213739418903714977e+02, 1.319389205810962812e+04], [1.020184547767112235e+02, 1.322258154522328914e+04], [-1.072694716663390864e+02, 1.324918947166633916e+04], [-3.490477058718843182e+02, 1.327445770587188417e+04], [-3.975570728533530200e+02, 1.329906107285335383e+04], [-3.331152428080622485e+02, 1.332345624280806260e+04]]) dta = macrodata.load_pandas().data['realgdp'].values res = column_stack((hpfilter(dta, 1600))) assert_almost_equal(res, hpfilt_res, 6) def test_cfitz_filter(): # Test Christiano-Fitzgerald Filter. Results taken from R. # NOTE: The Stata mata code and the matlab code it's based on are wrong. cfilt_res = array([ [0.712599537179426, 0.439563468233128], [1.06824041304411, 0.352886666575907], [1.19422467791128, 0.257297004260607], [0.970845473140327, 0.114504692143872], [0.467026976628563, -0.070734782329146], [-0.089153511514031, -0.238609685132605], [-0.452339254128573, -0.32376584042956], [-0.513231214461187, -0.314288554228112], [-0.352372578720063, -0.258815055101336], [-0.160282602521333, -0.215076844089567], [-0.0918782593827686, -0.194120745417214], [-0.168083823205437, -0.158327420072693], [-0.291595204965808, -0.0742727139742986], [-0.348638756841307, 0.037008291163602], [-0.304328040874631, 0.108196527328748], [-0.215933150969686, 0.0869231107437175], [-0.165632621390694, -0.0130556619786275], [-0.182326839507151, -0.126570926191824], [-0.223737786804725, -0.205535321806185], [-0.228939291453403, -0.269110078201836], [-0.185518327227038, -0.375976507132174], [-0.143900152461529, -0.53760115656157], [-0.162749541550174, -0.660065018626038], [-0.236263634756884, -0.588542352053736], [-0.275785854309211, -0.236867929421996], [-0.173666515108109, 0.303436335579219], [0.0963135720251639, 0.779772338801993], [0.427070069032285, 0.929108075350647], [0.629034743259998, 0.658330841002647], [0.557941248993624, 0.118500049361018], [0.227866624051603, -0.385048321099911], [-0.179878859883227, -0.582223992561493], [-0.428263000051965, -0.394053702908091], [-0.381640684645912, 0.0445437406977307], [-0.0942745548364887, 0.493997792757968], [0.238132391504895, 0.764519811304315], [0.431293754256291, 0.814755206427316], [0.455010435813661, 0.745567043101108], [0.452800768971269, 0.709401694610443], [0.615754619329312, 0.798293251119636], [1.00256335412457, 0.975856845059388], [1.44841039351691, 1.09097252730799], [1.64651971120370, 0.967823457118036], [1.35534532901802, 0.522397724737059], [0.580492790312048, -0.16941343361609], [-0.410746188031773, -0.90760401289056], [-1.26148406066881, -1.49592867122591], [-1.75784179124566, -1.87404167409849], [-1.94478553960064, -2.14586210891112], [-2.03751202708559, -2.465855239868], [-2.20376059354166, -2.86294187189049], [-2.39722338315852, -3.15004697654831], [-2.38032366161537, -3.01390466643222], [-1.91798022532025, -2.23395210271226], [-0.982318490353716, -0.861346053067472], [0.199047030343412, 0.790266582335616], [1.28582776574786, 2.33731327460104], [2.03565905376430, 3.54085486821911], [2.41201557412526, 4.36519456268955], [2.52011070482927, 4.84810517685452], [2.45618479815452, 4.92906708807477], [2.22272146945388, 4.42591058990048], [1.78307567169034, 3.20962906108388], [1.18234431860844, 1.42568060336985], [0.590069172333348, -0.461896808688991], [0.19662302949837, -1.89020992539465], [0.048307034171166, -2.53490571941987], [-0.0141956981899000, -2.50020338531674], [-0.230505187108187, -2.20625973569823], [-0.700947410386801, -2.06643697511048], [-1.27085123163060, -2.21536883679783], [-1.64082547897928, -2.49016921117735], [-1.62286182971254, -2.63948740221362], [-1.31609762181362, -2.54685250637904], [-1.03085567704873, -2.27157435428923], [-1.01100120380112, -1.90404507430561], [-1.19823958399826, -1.4123209792214], [-1.26398933608383, -0.654000086153317], [-0.904710628949692, 0.447960016248203], [-0.151340093679588, 1.73970411237156], [0.592926881165989, 2.85741581650685], [0.851660587507523, 3.4410446351716], [0.480324393352127, 3.36870271362297], [-0.165153230782417, 2.82003806696544], [-0.459235919375844, 2.12858991660866], [0.0271158842479935, 1.55840980891556], [1.18759188180671, 1.17980298478623], [2.43238266962309, 0.904011534980672], [3.08277213720132, 0.595286911949837], [2.79953663720953, 0.148014782859571], [1.73694442845833, -0.496297332023011], [0.357638079951977, -1.33108149877570], [-0.891418825216945, -2.22650083183366], [-1.77646467793627, -2.89359299718574], [-2.24614790863088, -2.97921619243347], [-2.29048879096607, -2.30003092779280], [-1.87929656465888, -1.05298381273274], [-1.04510101454788, 0.215837488618531], [0.00413338508394524, 0.937866257924888], [0.906870625251025, 0.92664365343019], [1.33869057593416, 0.518564571494679], [1.22659678454440, 0.288096869652890], [0.79380139656044, 0.541053084632774], [0.38029431865832, 1.01905199983437], [0.183929413600038, 1.10529586616777], [0.140045425897033, 0.393618564826736], [0.0337313182352219, -0.86431819007665], [-0.269208622829813, -1.85638085246792], [-0.687276639992166, -1.82275359004533], [-1.00161592325614, -0.692695765071617], [-1.06320089194036, 0.803577361347341], [-0.927152307196776, 1.67366338751788], [-0.786802101366614, 1.42564362251793], [-0.772970884572502, 0.426446388877964], [-0.81275662801789, -0.437721213831647], [-0.686831250382476, -0.504255468075149], [-0.237936463020255, 0.148656301898438], [0.459631879129522, 0.832925905720478], [1.12717379822508, 0.889455302576383], [1.48640453200855, 0.268042676202216], [1.46515245776211, -0.446505038539178], [1.22993484959115, -0.563868578181134], [1.0272100765927, 0.0996849952196907], [0.979191212438404, 1.05053652824665], [1.00733490030391, 1.51658415000556], [0.932192535457706, 1.06262774912638], [0.643374300839414, -0.0865180803476065], [0.186885168954461, -1.24799408923277], [-0.290842337365465, -1.80035611156538], [-0.669446735516495, -1.58847333561510], [-0.928915624595538, -0.932116966867929], [-1.11758635926997, -0.307879396807850], [-1.26832454569756, -0.00856199983957032], [-1.35755577149251, -0.0303537516690989], [-1.34244112665546, -0.196807620887435], [-1.22227976023299, -0.342062643495923], [-1.04601473486818, -0.390474392372016], [-0.85158508717846, -0.322164402093596], [-0.605033439160543, -0.126930141915954], [-0.218304303942818, 0.179551077808122], [0.352173017779006, 0.512327303000081], [1.01389600097229, 0.733397490572755], [1.55149778750607, 0.748740387440165], [1.75499674757591, 0.601759717901009], [1.56636057468633, 0.457705308377562], [1.12239792537274, 0.470849913286519], [0.655802600286141, 0.646142040378738], [0.335285115340180, 0.824103600255079], [0.173454596506888, 0.808068498175582], [0.0666753011315252, 0.521488214487996], [-0.0842367474816212, 0.0583493276173476], [-0.285604762631464, -0.405958418332253], [-0.465735422869919, -0.747800086512926], [-0.563586691231348, -0.94982272350799], [-0.598110322024572, -1.04736894794361], [-0.65216025756061, -1.04858365218822], [-0.789663117801624, -0.924145633093637], [-0.984704045337959, -0.670740724179446], [-1.12449565589348, -0.359476803003931], [-1.07878318723543, -0.092290938944355], [-0.775555435407062, 0.102132527529259], [-0.231610677329856, 0.314409560305622], [0.463192794235131, 0.663523546243286], [1.17416973448423, 1.13156902460931], [1.74112278814906, 1.48967153067024], [2.00320855757084, 1.42571085941843], [1.8529912317336, 0.802460519079555], [1.30747261947211, -0.169219078629572], [0.540237070403222, -1.01621539672694], [-0.177136817092375, -1.3130784867977], [-0.611981468823591, -0.982477824460773], [-0.700240028737747, -0.344919609255406], [-0.572396497740112, 0.125083535035390], [-0.450934466600975, 0.142553112732280], [-0.494020014254326, -0.211429053871656], [-0.701707589094918, -0.599602868825992], [-0.94721339346157, -0.710669870591623], [-1.09297139748946, -0.47846194092245], [-1.08850658866583, -0.082258450179988], [-0.976082880696692, 0.235758921309309], [-0.81885695346771, 0.365298185204303], [-0.63165529525553, 0.384725179378064], [-0.37983149226421, 0.460240196164378], [-0.0375551354277652, 0.68580913832794], [0.361996927427804, 0.984470835955107], [0.739920615366072, 1.13195975020298], [1.03583478061534, 0.88812510421667], [1.25614938962160, 0.172561520611839], [1.45295030231799, -0.804979390544485], [1.64887158748426, -1.55662011197859], [1.78022721495313, -1.52921975346218], [1.71945683859668, -0.462240366424548], [1.36728880239190, 1.31213774341268], [0.740173894315912, 2.88362740582926], [-0.0205364331835904, 3.20319080963167], [-0.725643970956428, 1.75222466531151], [-1.23900506689782, -0.998432917440275], [-1.52651897508678, -3.72752870885448], [-1.62857516631435, -5.00551707196292], [-1.59657420180451, -4.18499132634584], [-1.45489013276495, -1.81759097305637], [-1.21309542313047, 0.722029457352468]]) dta = macrodata.load_pandas().data[['tbilrate', 'infl']].values[1:] cyc, trend = cffilter(dta) assert_almost_equal(cyc, cfilt_res, 8) # do 1d cyc, trend = cffilter(dta[:, 1]) assert_almost_equal(cyc, cfilt_res[:, 1], 8) def test_bking_pandas(): # 1d dta = macrodata.load_pandas().data index = date_range(start='1959-01-01', end='2009-10-01', freq='Q') dta.index = index filtered = bkfilter(dta["infl"]) nd_filtered = bkfilter(dta['infl'].values) assert_equal(filtered.values, nd_filtered) assert_equal(filtered.index[0], datetime(1962, 3, 31)) assert_equal(filtered.index[-1], datetime(2006, 9, 30)) assert_equal(filtered.name, "infl_cycle") # 2d filtered = bkfilter(dta[["infl", "unemp"]]) nd_filtered = bkfilter(dta[['infl', 'unemp']].values) assert_equal(filtered.values, nd_filtered) assert_equal(filtered.index[0], datetime(1962, 3, 31)) assert_equal(filtered.index[-1], datetime(2006, 9, 30)) assert_equal(filtered.columns.values, ["infl_cycle", "unemp_cycle"]) def test_cfitz_pandas(): # 1d dta = macrodata.load_pandas().data index = date_range(start='1959-01-01', end='2009-10-01', freq='Q') dta.index = index cycle, trend = cffilter(dta["infl"]) ndcycle, ndtrend = cffilter(dta['infl'].values) assert_allclose(cycle.values, ndcycle, rtol=1e-14) assert_equal(cycle.index[0], datetime(1959, 3, 31)) assert_equal(cycle.index[-1], datetime(2009, 9, 30)) assert_equal(cycle.name, "infl_cycle") # 2d cycle, trend = cffilter(dta[["infl", "unemp"]]) ndcycle, ndtrend = cffilter(dta[['infl', 'unemp']].values) assert_allclose(cycle.values, ndcycle, rtol=1e-14) assert_equal(cycle.index[0], datetime(1959, 3, 31)) assert_equal(cycle.index[-1], datetime(2009, 9, 30)) assert_equal(cycle.columns.values, ["infl_cycle", "unemp_cycle"]) def test_hpfilter_pandas(): dta = macrodata.load_pandas().data index = date_range(start='1959-01-01', end='2009-10-01', freq='Q') dta.index = index cycle, trend = hpfilter(dta["realgdp"]) ndcycle, ndtrend = hpfilter(dta['realgdp'].values) assert_equal(cycle.values, ndcycle) assert_equal(cycle.index[0], datetime(1959, 3, 31)) assert_equal(cycle.index[-1], datetime(2009, 9, 30)) assert_equal(cycle.name, "realgdp_cycle") class TestFilters(object): @classmethod def setup_class(cls): # even data = [-50, 175, 149, 214, 247, 237, 225, 329, 729, 809, 530, 489, 540, 457, 195, 176, 337, 239, 128, 102, 232, 429, 3, 98, 43, -141, -77, -13, 125, 361, -45, 184] cls.data = DataFrame(data, date_range(start='1/1/1951', periods=len(data), freq='Q')) data[9] = np.nan cls.datana = DataFrame(data, date_range(start='1/1/1951', periods=len(data), freq='Q')) from .results import filter_results cls.expected = filter_results def test_convolution(self): x = self.data.values.squeeze() res = convolution_filter(x, [.75, .25]) expected = self.expected.conv2 np.testing.assert_almost_equal(res, expected) res = convolution_filter(x, [.75, .25], nsides=1) expected = self.expected.conv1 np.testing.assert_almost_equal(res, expected) x = self.datana.values.squeeze() res = convolution_filter(x, [.75, .25]) expected = self.expected.conv2_na np.testing.assert_almost_equal(res, expected) res = convolution_filter(x, [.75, .25], nsides=1) expected = self.expected.conv1_na np.testing.assert_almost_equal(res, expected) def test_convolution2d(self): x = self.data.values res = convolution_filter(x, [[.75], [.25]]) expected = self.expected.conv2 np.testing.assert_almost_equal(res, expected[:, None]) res = convolution_filter(np.c_[x, x], [[.75, .75], [.25, .25]]) np.testing.assert_almost_equal(res, np.c_[expected, expected]) res = convolution_filter(x, [[.75], [.25]], nsides=1) expected = self.expected.conv1 np.testing.assert_almost_equal(res, expected[:, None]) x = self.datana.values res = convolution_filter(x, [[.75], [.25]]) expected = self.expected.conv2_na np.testing.assert_almost_equal(res, expected[:, None]) res = convolution_filter(x, [[.75], [.25]], nsides=1) expected = self.expected.conv1_na np.testing.assert_almost_equal(res, expected[:, None]) def test_recursive(self): x = self.data.values.squeeze() res = recursive_filter(x, [.75, .25]) expected = self.expected.recurse np.testing.assert_almost_equal(res, expected) res = recursive_filter(x, [.75, .25], init=[150, 100]) expected = self.expected.recurse_init np.testing.assert_almost_equal(res, expected) x = self.datana.values.squeeze() res = recursive_filter(x, [.75, .25]) expected = self.expected.recurse_na np.testing.assert_almost_equal(res, expected) res = recursive_filter(x, [.75, .25], init=[150, 100]) expected = self.expected.recurse_init_na np.testing.assert_almost_equal(res, expected) assert_raises(ValueError, recursive_filter, x, [.75, .25, .5], [150, 100]) def test_pandas(self): start = datetime(1951, 3, 31) end = datetime(1958, 12, 31) x = self.data[0] res = convolution_filter(x, [.75, .25]) assert_(res.index[0] == start) assert_(res.index[-1] == end) res = convolution_filter(x, [.75, .25], nsides=1) assert_(res.index[0] == start) # with no nan-padding q1 if not assert_(res.index[-1] == end) res = recursive_filter(x, [.75, .25]) assert_(res.index[0] == start) assert_(res.index[-1] == end) x = self.datana res = recursive_filter(x, [.75, .25]) assert_(res.index[0] == start) assert_(res.index[-1] == end) def test_pandas2d(self): start = datetime(1951, 3, 31) end = datetime(1958, 12, 31) x = concat((self.data[0], self.data[0]), axis=1) res = convolution_filter(x, [[.75, .75], [.25, .25]]) assert_(res.index[0] == start) assert_(res.index[-1] == end) def test_odd_length_filter(self): start = datetime(1951, 3, 31) end = datetime(1958, 12, 31) x = self.data[0] res = convolution_filter(x, [.75, .5, .3, .2, .1]) expected = self.expected.conv2_odd np.testing.assert_almost_equal(res.values.squeeze(), expected) np.testing.assert_(res.index[0] == start) np.testing.assert_(res.index[-1] == end) res = convolution_filter(x, [.75, .5, .3, .2, .1], nsides=1) expected = self.expected.conv1_odd np.testing.assert_almost_equal(res.values.squeeze(), expected) np.testing.assert_(res.index[0] == start) np.testing.assert_(res.index[-1] == end) # with no NAs # not a stable filter res = recursive_filter(x, [.75, .5, .3, .2, .1], init=[150, 100, 125, 135, 145]) expected = self.expected.recurse_odd # only have 12 characters in R and this blows up and gets big np.testing.assert_almost_equal(res.values.squeeze(), expected, 4) np.testing.assert_(res.index[0] == start) np.testing.assert_(res.index[-1] == end) def dummy_func(x): return x def dummy_func_array(x): return x.values def dummy_func_pandas_columns(x): return x.values def dummy_func_pandas_series(x): return x['A'] def test_pandas_freq_decorator(): x = make_dataframe() # in x, get a function back that returns an x with the same columns func = pandas_wrapper(dummy_func) np.testing.assert_equal(func(x.values), x) func = pandas_wrapper(dummy_func_array) assert_frame_equal(func(x), x) expected = x.rename(columns=dict(zip('ABCD', 'EFGH'))) func = pandas_wrapper(dummy_func_array, names=list('EFGH')) assert_frame_equal(func(x), expected) statsmodels-0.12.2/statsmodels/tsa/forecasting/000077500000000000000000000000001400612667500216025ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/forecasting/__init__.py000066400000000000000000000000001400612667500237010ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/forecasting/stl.py000066400000000000000000000426471400612667500227730ustar00rootroot00000000000000from statsmodels.compat.pandas import Substitution import datetime as dt from textwrap import indent from typing import Any, Dict, Optional, Union import numpy as np import pandas as pd from statsmodels.base.data import PandasData from statsmodels.iolib.summary import SimpleTable, Summary from statsmodels.tools.docstring import Docstring, Parameter from statsmodels.tsa.base.prediction import PredictionResults from statsmodels.tsa.base.tsa_model import get_index_loc, get_prediction_index from statsmodels.tsa.seasonal import STL, DecomposeResult from statsmodels.tsa.statespace.kalman_filter import _check_dynamic DateLike = Union[int, str, dt.datetime, pd.Timestamp, np.datetime64] ds = Docstring(STL.__doc__) ds.insert_parameters( "endog", Parameter( "model", "Model", [ "The model used to forecast endog after the seasonality has been " "removed using STL" ], ), ) ds.insert_parameters( "model", Parameter( "model_kwargs", "Dict[str, Any]", [ "Any additional arguments needed to initialized the model using " "the residuals produced by subtracting the seasonality." ], ), ) _stl_forecast_params = ds.extract_parameters( [ "endog", "model", "model_kwargs", "period", "seasonal", "trend", "low_pass", "seasonal_deg", "trend_deg", "low_pass_deg", "robust", "seasonal_jump", "trend_jump", "low_pass_jump", ] ) ds = Docstring(STL.fit.__doc__) _fit_params = ds.extract_parameters(["inner_iter", "outer_iter"]) @Substitution(stl_forecast_params=indent(_stl_forecast_params, " ")) class STLForecast: r""" Model-based forecasting using STL to remove seasonality Forecasts are produced by first subtracting the seasonality estimated using STL, then forecasting the deseasonalized data using a time-series model, for example, ARIMA. Parameters ---------- %(stl_forecast_params)s See Also -------- statsmodels.tsa.arima.model.ARIMA ARIMA modeling. statsmodels.tsa.ar_model.AutoReg Autoregressive modeling supporting complex deterministics. statsmodels.tsa.exponential_smoothing.ets.ETSModel Additive and multiplicative exponential smoothing with trend. statsmodels.tsa.statespace.exponential_smoothing.ExponentialSmoothing Additive exponential smoothing with trend. Notes ----- If :math:`\hat{S}_t` is the seasonal component, then the deseasonalize series is constructed as .. math:: Y_t - \hat{S}_t The trend component is not removed, and so the time series model should be capable of adequately fitting and forecasting the trend if present. The out-of-sample forecasts of the seasonal component are produced as .. math:: \hat{S}_{T + h} = \hat{S}_{T - k} where :math:`k = m - h + m \lfloor (h-1)/m \rfloor` tracks the period offset in the full cycle of 1, 2, ..., m where m is the period length. This class is mostly a convenience wrapper around ``STL`` and a user-specified model. The model is assumed to follow the standard statsmodels pattern: * ``fit`` is used to estimate parameters and returns a results instance, ``results``. * ``results`` must exposes a method ``forecast(steps, **kwargs)`` that produces out-of-sample forecasts. * ``results`` may also exposes a method ``get_prediction`` that produces both in- and out-of-sample predictions. Examples -------- >>> import numpy as np >>> import pandas as pd >>> from statsmodels.tsa.api import STLForecast >>> from statsmodels.tsa.arima.model import ARIMA >>> from statsmodels.datasets import macrodata >>> ds = macrodata.load_pandas() >>> data = np.log(ds.data.m1) >>> base_date = f"{int(ds.data.year[0])}-{3*int(ds.data.quarter[0])+1}-1" >>> data.index = pd.date_range(base_date, periods=data.shape[0], freq="QS") Generate forecasts from an ARIMA >>> stlf = STLForecast(data, ARIMA, model_kwargs={"order": (2, 1, 0)}) >>> res = stlf.fit() >>> forecasts = res.forecast(12) Generate forecasts from an Exponential Smoothing model with trend >>> from statsmodels.tsa.statespace import exponential_smoothing >>> ES = exponential_smoothing.ExponentialSmoothing >>> config = {"trend": True} >>> stlf = STLForecast(data, ES, model_kwargs=config) >>> res = stlf.fit() >>> forecasts = res.forecast(12) """ def __init__( self, endog, model, *, model_kwargs=None, period=None, seasonal=7, trend=None, low_pass=None, seasonal_deg=1, trend_deg=1, low_pass_deg=1, robust=False, seasonal_jump=1, trend_jump=1, low_pass_jump=1, ): self._endog = endog self._stl_kwargs = dict( period=period, seasonal=seasonal, trend=trend, low_pass=low_pass, seasonal_deg=seasonal_deg, trend_deg=trend_deg, low_pass_deg=low_pass_deg, robust=robust, seasonal_jump=seasonal_jump, trend_jump=trend_jump, low_pass_jump=low_pass_jump, ) self._model = model self._model_kwargs = {} if model_kwargs is None else model_kwargs if not hasattr(model, "fit"): raise AttributeError("model must expose a ``fit`` method.") @Substitution(fit_params=indent(_fit_params, " " * 8)) def fit(self, *, inner_iter=None, outer_iter=None, fit_kwargs=None): """ Estimate STL and forecasting model parameters. Parameters ---------- %(fit_params)s fit_kwargs : Dict[str, Any] Any additional keyword arguments to pass to ``model``'s ``fit`` method when estimating the model on the decomposed residuals. Returns ------- STLForecastResults Results with forecasting methods. """ fit_kwargs = {} if fit_kwargs is None else fit_kwargs stl = STL(self._endog, **self._stl_kwargs) stl_fit: DecomposeResult = stl.fit( inner_iter=inner_iter, outer_iter=outer_iter ) model_endog = stl_fit.trend + stl_fit.resid mod = self._model(model_endog, **self._model_kwargs) res = mod.fit(**fit_kwargs) if not hasattr(res, "forecast"): raise AttributeError( "The model's result must expose a ``forecast`` method." ) return STLForecastResults(stl, stl_fit, mod, res, self._endog) class STLForecastResults: """ Results for forecasting using STL to remove seasonality Parameters ---------- stl : STL The STL instance used to decompose the data. result : DecomposeResult The result of applying STL to the data. model : Model The time series model used to model the non-seasonal dynamics. model_result : Results Model results instance supporting, at a minimum, ``forecast``. """ def __init__( self, stl: STL, result: DecomposeResult, model, model_result, endog ) -> None: self._stl = stl self._result = result self._model = model self._model_result = model_result self._endog = np.asarray(endog) self._nobs = self._endog.shape[0] self._index = getattr(endog, "index", pd.RangeIndex(self._nobs)) if not isinstance( self._index, (pd.Int64Index, pd.DatetimeIndex, pd.PeriodIndex) ): try: self._index = pd.to_datetime(self._index) except ValueError: self._index = pd.RangeIndex(self._nobs) @property def period(self) -> int: """The period of the seasonal component""" return self._stl.period @property def stl(self) -> STL: """The STL instance used to decompose the time series""" return self._stl @property def result(self) -> DecomposeResult: """The result of applying STL to the data""" return self._result @property def model(self) -> Any: """The model fit to the additively deseasonalized data""" return self._model @property def model_result(self) -> Any: """The result class from the estimated model""" return self._model_result def summary(self) -> Summary: """ Summary of both the STL decomposition and the model fit. Returns ------- Summary The summary of the model fit and the STL decomposition. Notes ----- Requires that the model's result class supports ``summary`` and returns a ``Summary`` object. """ if not hasattr(self._model_result, "summary"): raise AttributeError( "The model result does not have a summary attribute." ) summary: Summary = self._model_result.summary() if not isinstance(summary, Summary): raise TypeError( "The model result's summary is not a Summary object." ) summary.tables[0].title = ( "STL Decomposition and " + summary.tables[0].title ) config = self._stl.config left_keys = ("period", "seasonal", "robust") left_data = [] left_stubs = [] right_data = [] right_stubs = [] for key in config: new = key.capitalize() new = new.replace("_", " ") if new in ("Trend", "Low Pass"): new += " Length" is_left = any(key.startswith(val) for val in left_keys) new += ":" stub = f"{new:<23s}" val = f"{str(config[key]):>13s}" if is_left: left_stubs.append(stub) left_data.append([val]) else: right_stubs.append(" " * 6 + stub) right_data.append([val]) tab = SimpleTable( left_data, stubs=tuple(left_stubs), title="STL Configuration" ) tab.extend_right(SimpleTable(right_data, stubs=right_stubs)) summary.tables.append(tab) return summary def _get_seasonal_prediction( self, start: Optional[DateLike], end: Optional[DateLike], dynamic: Union[bool, DateLike], ) -> np.ndarray: """ Get STLs seasonal in- and out-of-sample predictions Parameters ---------- start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, i.e., the last forecast is end. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. dynamic : bool, int, str, or datetime, optional Integer offset relative to `start` at which to begin dynamic prediction. Can also be an absolute date string to parse or a datetime type (these are not interpreted as offsets). Prior to this observation, true endogenous values will be used for prediction; starting with this observation and continuing through the end of prediction, forecasted endogenous values will be used instead. Returns ------- ndarray Array containing the seasibak predictions. """ data = PandasData(pd.Series(self._endog), index=self._index) (start, end, out_of_sample, prediction_index,) = get_prediction_index( start, end, self._nobs, self._index, data=data ) if isinstance(dynamic, (str, dt.datetime, pd.Timestamp)): dynamic, _, _ = get_index_loc(dynamic, self._index) dynamic = dynamic - start elif dynamic is True: dynamic = 0 elif dynamic is False: # If `dynamic=False`, then no dynamic predictions dynamic = None nobs = self._nobs dynamic, _ = _check_dynamic(dynamic, start, end, nobs) in_sample_end = end + 1 if dynamic is None else dynamic seasonal = np.asarray(self._result.seasonal) predictions = seasonal[start:in_sample_end] oos = np.empty((0,)) if dynamic is not None: num = out_of_sample + end + 1 - dynamic oos = self._seasonal_forecast(num, None, offset=dynamic) elif out_of_sample: oos = self._seasonal_forecast(out_of_sample, None) oos_start = max(start - nobs, 0) oos = oos[oos_start:] predictions = np.r_[predictions, oos] return predictions def _seasonal_forecast( self, steps: int, index: Optional[pd.Index], offset=None ) -> Union[pd.Series, np.ndarray]: """ Get the seasonal component of the forecast Parameters ---------- steps : int The number of steps required. index : pd.Index A pandas index to use. If None, returns an ndarray. offset : int The index of the first out-of-sample observation. If None, uses nobs. Returns ------- seasonal : {ndarray, Series} The seasonal component. """ period = self.period seasonal = np.asarray(self._result.seasonal) offset = self._nobs if offset is None else offset seasonal = seasonal[offset - period : offset] seasonal = np.tile(seasonal, steps // period + ((steps % period) != 0)) seasonal = seasonal[:steps] if index is not None: seasonal = pd.Series(seasonal, index=index) return seasonal def forecast( self, steps: int = 1, **kwargs: Dict[str, Any] ) -> Union[np.ndarray, pd.Series]: """ Out-of-sample forecasts Parameters ---------- steps : int, str, or datetime, optional If an integer, the number of steps to forecast from the end of the sample. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, steps must be an integer. Default **kwargs Additional arguments may required for forecasting beyond the end of the sample. These arguments are passed into the time series model results' ``forecast`` method. Returns ------- forecast : {ndarray, Series} Out of sample forecasts """ forecast = self._model_result.forecast(steps=steps, **kwargs) index = forecast.index if isinstance(forecast, pd.Series) else None return forecast + self._seasonal_forecast(steps, index) def get_prediction( self, start: Optional[DateLike] = None, end: Optional[DateLike] = None, dynamic: Union[bool, DateLike] = False, **kwargs: Dict[str, Any], ): """ In-sample prediction and out-of-sample forecasting Parameters ---------- start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, i.e., the last forecast is end. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. dynamic : bool, int, str, or datetime, optional Integer offset relative to `start` at which to begin dynamic prediction. Can also be an absolute date string to parse or a datetime type (these are not interpreted as offsets). Prior to this observation, true endogenous values will be used for prediction; starting with this observation and continuing through the end of prediction, forecasted endogenous values will be used instead. **kwargs Additional arguments may required for forecasting beyond the end of the sample. These arguments are passed into the time series model results' ``get_prediction`` method. Returns ------- PredictionResults PredictionResults instance containing in-sample predictions, out-of-sample forecasts, and prediction intervals. """ pred = self._model_result.get_prediction( start=start, end=end, dynamic=dynamic, **kwargs ) seasonal_prediction = self._get_seasonal_prediction( start, end, dynamic ) mean = pred.predicted_mean + seasonal_prediction return PredictionResults( mean, pred.var_pred_mean, dist="norm", row_labels=pred.row_labels, ) statsmodels-0.12.2/statsmodels/tsa/forecasting/tests/000077500000000000000000000000001400612667500227445ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/forecasting/tests/__init__.py000066400000000000000000000000001400612667500250430ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/forecasting/tests/test_stl.py000066400000000000000000000106041400612667500251600ustar00rootroot00000000000000import numpy as np from numpy.testing import assert_allclose import pandas as pd import pytest from statsmodels.tsa.ar_model import AutoReg from statsmodels.tsa.arima.model import ARIMA from statsmodels.tsa.base.prediction import PredictionResults from statsmodels.tsa.deterministic import Fourier from statsmodels.tsa.exponential_smoothing.ets import ETSModel from statsmodels.tsa.forecasting.stl import STLForecast from statsmodels.tsa.seasonal import STL, DecomposeResult from statsmodels.tsa.statespace.exponential_smoothing import ( ExponentialSmoothing, ) @pytest.fixture(scope="module") def data(request): rs = np.random.RandomState(987654321) err = rs.standard_normal(500) index = pd.date_range("1980-1-1", freq="M", periods=500) fourier = Fourier(12, 1) terms = fourier.in_sample(index) det = np.squeeze(np.asarray(terms @ np.array([[2], [1]]))) for i in range(1, 500): err[i] += 0.9 * err[i - 1] + det[i] return pd.Series(err, index=index) def test_smoke(data): stlf = STLForecast(data, ARIMA, model_kwargs={"order": (2, 0, 0)}) res = stlf.fit(fit_kwargs={}) res.forecast(37) assert isinstance(res.summary().as_text(), str) assert isinstance(res.stl, STL) assert isinstance(res.result, DecomposeResult) assert isinstance(res.model, ARIMA) assert hasattr(res.model_result, "forecast") MODELS = [ (ARIMA, {"order": (2, 0, 0), "trend": "c"}), (ExponentialSmoothing, {"trend": True}), (AutoReg, {"lags": 2, "old_names": False}), (ETSModel, {}), ] MODELS = MODELS[-1:] IDS = [str(c[0]).split(".")[-1][:-2] for c in MODELS] @pytest.mark.parametrize("config", MODELS, ids=IDS) @pytest.mark.parametrize("horizon", [1, 7, 23]) def test_equivalence_forecast(data, config, horizon): model, kwargs = config stl = STL(data) stl_fit = stl.fit() resids = data - stl_fit.seasonal mod = model(resids, **kwargs) fit_kwarg = {} if model is ETSModel: fit_kwarg["disp"] = False res = mod.fit(**fit_kwarg) stlf = STLForecast(data, model, model_kwargs=kwargs).fit(fit_kwargs=fit_kwarg) seasonal = np.asarray(stl_fit.seasonal)[-12:] seasonal = np.tile(seasonal, 1 + horizon // 12) fcast = res.forecast(horizon) + seasonal[:horizon] actual = stlf.forecast(horizon) assert_allclose(actual, fcast, rtol=1e-4) if not hasattr(res, "get_prediction"): return pred = stlf.get_prediction(data.shape[0], data.shape[0] + horizon - 1) assert isinstance(pred, PredictionResults) assert_allclose(pred.predicted_mean, fcast, rtol=1e-4) half = data.shape[0] // 2 stlf.get_prediction(half, data.shape[0] + horizon - 1) stlf.get_prediction(half, data.shape[0] + horizon - 1, dynamic=True) stlf.get_prediction(half, data.shape[0] + horizon - 1, dynamic=half // 2) if hasattr(data, "index"): loc = data.index[half + half // 2] a = stlf.get_prediction( half, data.shape[0] + horizon - 1, dynamic=loc.strftime("%Y-%m-%d") ) b = stlf.get_prediction( half, data.shape[0] + horizon - 1, dynamic=loc.to_pydatetime() ) c = stlf.get_prediction(half, data.shape[0] + horizon - 1, dynamic=loc) assert_allclose(a.predicted_mean, b.predicted_mean, rtol=1e-4) assert_allclose(a.predicted_mean, c.predicted_mean, rtol=1e-4) def test_exceptions(data): class BadModel: def __init__(self, *args, **kwargs): pass with pytest.raises(AttributeError, match="model must expose"): STLForecast(data, BadModel) class NoForecast(BadModel): def fit(self, *args, **kwargs): return BadModel() with pytest.raises(AttributeError, match="The model's result"): STLForecast(data, NoForecast).fit() class BadResult: def forecast(self, *args, **kwargs): pass class FakeModel(BadModel): def fit(self, *args, **kwargs): return BadResult() with pytest.raises(AttributeError, match="The model result does not"): STLForecast(data, FakeModel).fit().summary() class BadResultSummary(BadResult): def summary(self, *args, **kwargs): return object() class FakeModelSummary(BadModel): def fit(self, *args, **kwargs): return BadResultSummary() with pytest.raises(TypeError, match="The model result's summary"): STLForecast(data, FakeModelSummary).fit().summary() statsmodels-0.12.2/statsmodels/tsa/forecasting/tests/test_theta.py000066400000000000000000000100401400612667500254550ustar00rootroot00000000000000from itertools import product import numpy as np import pandas as pd import pytest from statsmodels.tsa.forecasting.theta import ThetaModel SMOKE_PARAMS = list(product(["array", "dataframe", "series"], [True, False])) SMOKE_IDS = [f"type: {typ}, exponential: {exp}" for typ, exp in SMOKE_PARAMS] @pytest.fixture(params=SMOKE_PARAMS, ids=SMOKE_IDS) def data(request): rs = np.random.RandomState([3290328901, 323293105, 121029109]) scale = 0.01 if request.param[1] else 1 y = np.cumsum(scale + scale * rs.standard_normal((300))) if request.param[1]: y = np.exp(y) index = pd.date_range("2000-01-01", periods=300) if request.param[0] == "array": return y elif request.param[0] == "dataframe": return pd.DataFrame(y[:, None], columns=["y"], index=index) else: return pd.Series(y, name="y", index=index) @pytest.fixture(params=["datetime", "period", "range", "nofreq"]) def indexed_data(request): rs = np.random.RandomState([3290328901, 323293105, 121029109]) scale = 0.01 y = np.cumsum(scale + scale * rs.standard_normal((300))) y = np.exp(y) if request.param == "datetime": index = pd.date_range("2000-1-1", periods=300) elif request.param == "period": index = pd.period_range("2000-1-1", periods=300, freq="M") elif request.param == "range": index = pd.RangeIndex(100, 100 + 2 * 300, 2) else: # request.param == "nofreq" index = pd.date_range("2000-1-1", periods=1000) locs = np.unique(rs.randint(0, 1000, size=500)) index = index[locs[:300]] return pd.Series(y, index=index, name=f"y_{request.param}") @pytest.mark.smoke @pytest.mark.parametrize("period", [None, 4, 12]) @pytest.mark.parametrize("use_mle", [True, False]) @pytest.mark.parametrize("deseasonalize", [True, False]) @pytest.mark.parametrize("use_test", [True, False]) @pytest.mark.parametrize("diff", [True, False]) @pytest.mark.parametrize("model", ["auto", "additive", "multiplicative"]) def test_smoke(data, period, use_mle, deseasonalize, use_test, diff, model): if period is None and isinstance(data, np.ndarray): return res = ThetaModel( data, period=period, deseasonalize=deseasonalize, use_test=use_test, difference=diff, method=model, ).fit(use_mle=use_mle) assert "b0" in str(res.summary()) res.forecast(36) res.forecast_components(47) assert res.model.use_test is (use_test and res.model.deseasonalize) assert res.model.difference is diff @pytest.mark.smoke def test_alt_index(indexed_data): idx = indexed_data.index date_like = not hasattr(idx, "freq") or getattr(idx, "freq", None) is None period = 12 if date_like else None res = ThetaModel(indexed_data, period=period).fit() if hasattr(idx, "freq") and idx.freq is None: with pytest.warns(UserWarning): res.forecast_components(37) with pytest.warns(UserWarning): res.forecast(23) else: res.forecast_components(37) res.forecast(23) def test_no_freq(): idx = pd.date_range("2000-1-1", periods=300) locs = [] for i in range(100): locs.append(2 * i + int((i % 2) == 1)) y = pd.Series(np.random.standard_normal(100), index=idx[locs]) with pytest.raises(ValueError, match="You must specify a period or"): ThetaModel(y) def test_forecast_errors(data): res = ThetaModel(data, period=12).fit() with pytest.raises(ValueError, match="steps must be a positive integer"): res.forecast(-1) with pytest.raises(ValueError, match="theta must be a float"): res.forecast(7, theta=0.99) with pytest.raises(ValueError, match="steps must be a positive integer"): res.forecast_components(0) def test_pi_width(): # GH 7075 rs = np.random.RandomState(1233091) y = np.arange(100) + rs.standard_normal(100) th = ThetaModel(y, period=12, deseasonalize=False) res = th.fit() pi = res.prediction_intervals(24) d = np.squeeze(np.diff(np.asarray(pi), axis=1)) assert np.all(np.diff(d) > 0) statsmodels-0.12.2/statsmodels/tsa/forecasting/theta.py000066400000000000000000000551061400612667500232700ustar00rootroot00000000000000r""" Implementation of the Theta forecasting method of Assimakopoulos, V., & Nikolopoulos, K. (2000). The theta model: a decomposition approach to forecasting. International journal of forecasting, 16(4), 521-530. and updates in Hyndman, R. J., & Billah, B. (2003). Unmasking the Theta method. International Journal of Forecasting, 19(2), 287-290. Fioruci, J. A., Pellegrini, T. R., Louzada, F., & Petropoulos, F. (2015). The optimized theta method. arXiv preprint arXiv:1503.03529. """ from typing import TYPE_CHECKING, Optional, Tuple import numpy as np import pandas as pd from scipy import stats from statsmodels.iolib.summary import Summary from statsmodels.iolib.table import SimpleTable from statsmodels.tools.validation import ( array_like, bool_like, float_like, int_like, string_like, ) from statsmodels.tsa.deterministic import DeterministicTerm from statsmodels.tsa.seasonal import seasonal_decompose from statsmodels.tsa.statespace.exponential_smoothing import ( ExponentialSmoothing, ) from statsmodels.tsa.statespace.sarimax import SARIMAX from statsmodels.tsa.stattools import acf from statsmodels.tsa.tsatools import add_trend, freq_to_period if TYPE_CHECKING: import matplotlib.figure def extend_index(steps: int, index: pd.Index) -> pd.Index: return DeterministicTerm._extend_index(index, steps) class ThetaModel: r""" The Theta forecasting model of Assimakopoulos and Nikolopoulos (2000) Parameters ---------- endog : array_like, 1d The data to forecast. period : int, default None The period of the data that is used in the seasonality test and adjustment. If None then the period is determined from y's index, if available. deseasonalize : bool, default True A flag indicating whether the deseasonalize the data. If True and use_test is True, the data is only deseasonalized if the null of no seasonal component is rejected. use_test : bool, default True A flag indicating whether test the period-th autocorrelation. If this test rejects using a size of 10%, then decomposition is used. Set to False to skip the test. method : {"auto", "additive", "multiplicative"}, default "auto" The model used for the seasonal decomposition. "auto" uses a multiplicative if y is non-negative and all estimated seasonal components are positive. If either of these conditions is False, then it uses an additive decomposition. difference : bool, default False A flag indicating to difference the data before testing for seasonality. See Also -------- statsmodels.tsa.statespace.exponential_smoothing.ExponentialSmoothing Exponential smoothing parameter estimation and forecasting statsmodels.tsa.statespace.sarimax.SARIMAX Seasonal ARIMA parameter estimation and forecasting Notes ----- The Theta model forecasts the future as a weighted combination of two Theta lines. This class supports combinations of models with two thetas: 0 and a user-specified choice (default 2). The forecasts are then .. math:: \hat{X}_{T+h|T} = \frac{\theta-1}{\theta} b_0 \left[h - 1 + \frac{1}{\alpha} - \frac{(1-\alpha)^T}{\alpha} \right] + \tilde{X}_{T+h|T} where :math:`\tilde{X}_{T+h|T}` is the SES forecast of the endogenous variable using the parameter :math:`\alpha`. :math:`b_0` is the slope of a time trend line fitted to X using the terms 0, 1, ..., T-1. The model is estimated in steps: 1. Test for seasonality 2. Deseasonalize if seasonality detected 3. Estimate :math:`\alpha` by fitting a SES model to the data and :math:`b_0` by OLS. 4. Forecast the series 5. Reseasonalize if the data was deseasonalized. The seasonality test examines where the autocorrelation at the seasonal period is different from zero. The seasonality is then removed using a seasonal decomposition with a multiplicative trend. If the seasonality estimate is non-positive then an additive trend is used instead. The default deseasonalizing method can be changed using the options. References ---------- .. [1] Assimakopoulos, V., & Nikolopoulos, K. (2000). The theta model: a decomposition approach to forecasting. International Journal of Forecasting, 16(4), 521-530. .. [2] Hyndman, R. J., & Billah, B. (2003). Unmasking the Theta method. International Journal of Forecasting, 19(2), 287-290. .. [3] Fioruci, J. A., Pellegrini, T. R., Louzada, F., & Petropoulos, F. (2015). The optimized theta method. arXiv preprint arXiv:1503.03529. """ def __init__( self, endog, *, period: Optional[int] = None, deseasonalize: bool = True, use_test: bool = True, method: str = "auto", difference: bool = False ) -> None: self._y = array_like(endog, "endog", ndim=1) if isinstance(endog, pd.DataFrame): self.endog_orig = endog.iloc[:, 0] else: self.endog_orig = endog self._period = int_like(period, "period", optional=True) self._deseasonalize = bool_like(deseasonalize, "deseasonalize") self._use_test = ( bool_like(use_test, "use_test") and self._deseasonalize ) self._diff = bool_like(difference, "difference") self._method = string_like( method, "model", options=("auto", "additive", "multiplicative", "mul", "add"), ) if self._period is None and self._deseasonalize: idx = getattr(endog, "index", None) pfreq = None if idx is not None: pfreq = getattr(idx, "freq", None) if pfreq is None: pfreq = getattr(idx, "inferred_freq", None) if pfreq is not None: self._period = freq_to_period(pfreq) else: raise ValueError( "You must specify a period or endog must be a " "pandas object with a DatetimeIndex with " "a freq not set to None" ) self._has_seasonality = self._deseasonalize def _test_seasonality(self) -> None: y = self._y if self._diff: y = np.diff(y) rho = acf(y, nlags=self._period, fft=True) nobs = y.shape[0] stat = nobs * rho[-1] ** 2 / np.sum(rho[:-1] ** 2) # CV is 10% from a chi2(1), 1.645**2 self._has_seasonality = stat > 2.705543454095404 def _deseasonalize_data(self) -> Tuple[np.ndarray, np.ndarray]: y = self._y if not self._has_seasonality: return self._y, np.empty(0) self._method = ( "mul" if self._method == "auto" and self._y.min() > 0 else "add" ) res = seasonal_decompose(y, model=self._method, period=self._period) if res.seasonal.min() <= 0: self._method = "add" res = seasonal_decompose(y, model="add", period=self._period) return y - res.seasonal, res.seasonal[: self._period] else: return y / res.seasonal, res.seasonal[: self._period] def fit( self, use_mle: bool = False, disp: bool = False ) -> "ThetaModelResults": r""" Estimate model parameters. Parameters ---------- use_mle : bool, default False Estimate the parameters using MLE by fitting an ARIMA(0,1,1) with a drift. If False (the default), estimates parameters using OLS of a constant and a time-trend and by fitting a SES to the model data. disp : bool, default True Display iterative output from fitting the model. Notes ----- When using MLE, the parameters are estimated from the ARIMA(0,1,1) .. math:: X_t = X_{t-1} + b_0 + (\alpha-1)\epsilon_{t-1} + \epsilon_t When estimating the model using 2-step estimation, the model parameters are estimated using the OLS regression .. math:: X_t = a_0 + b_0 (t-1) + \eta_t and the SES .. math:: \tilde{X}_{t+1} = \alpha X_{t} + (1-\alpha)\tilde{X}_{t} Returns ------- ThetaModelResult Model results and forecasting """ if self._deseasonalize and self._use_test: self._test_seasonality() y, seasonal = self._deseasonalize_data() if use_mle: mod = SARIMAX(y, order=(0, 1, 1), trend="c") res = mod.fit(disp=disp) params = np.asarray(res.params) alpha = params[1] + 1 if alpha > 1: alpha = 0.9998 res = mod.fit_constrained({"ma.L1": alpha - 1}) params = np.asarray(res.params) b0 = params[0] sigma2 = params[-1] one_step = res.forecast(1) - b0 else: ct = add_trend(y, "ct", prepend=True)[:, :2] ct[:, 1] -= 1 _, b0 = np.linalg.lstsq(ct, y, rcond=None)[0] res = ExponentialSmoothing( y, initial_level=y[0], initialization_method="known" ).fit(disp=disp) alpha = res.params[0] sigma2 = None one_step = res.forecast(1) return ThetaModelResults( b0, alpha, sigma2, one_step, seasonal, use_mle, self ) @property def deseasonalize(self) -> bool: """Whether to deseasonalize the data""" return self._deseasonalize @property def period(self) -> int: """The period of the seasonality""" return self._period @property def use_test(self) -> bool: """Whether to test the data for seasonality""" return self._use_test @property def difference(self) -> bool: """Whether the data is differenced in the seasonality test""" return self._diff @property def method(self) -> str: """The method used to deseasonalize the data""" return self._method class ThetaModelResults: """ Results class from estimated Theta Models. Parameters ---------- b0 : float The estimated trend slope. alpha : float The estimated SES parameter. sigma2 : float The estimated residual variance from the SES/IMA model. one_step : float The one-step forecast from the SES. seasonal : ndarray An array of estimated seasonal terms. use_mle : bool A flag indicating that the parameters were estimated using MLE. model : ThetaModel The model used to produce the results. """ def __init__( self, b0: float, alpha: float, sigma2: Optional[float], one_step: float, seasonal: np.ndarray, use_mle: bool, model: ThetaModel, ) -> None: self._b0 = b0 self._alpha = alpha self._sigma2 = sigma2 self._one_step = one_step self._nobs = model.endog_orig.shape[0] self._model = model self._seasonal = seasonal self._use_mle = use_mle @property def params(self) -> pd.Series: """The forecasting model parameters""" return pd.Series([self._b0, self._alpha], index=["b0", "alpha"]) @property def sigma2(self) -> float: """The estimated residual variance""" if self._sigma2 is None: mod = SARIMAX(self.model._y, order=(0, 1, 1), trend="c") res = mod.fit(disp=False) self._sigma2 = np.asarray(res.params)[-1] assert self._sigma2 is not None return self._sigma2 @property def model(self) -> ThetaModel: """The model used to produce the results""" return self._model def forecast(self, steps: int = 1, theta: float = 2) -> pd.Series: r""" Forecast the model for a given theta Parameters ---------- steps : int The number of steps ahead to compute the forecast components. theta : float The theta value to use when computing the weight to combine the trend and the SES forecasts. Returns ------- Series A Series containing the forecasts Notes ----- The forecast is computed as .. math:: \hat{X}_{T+h|T} = \frac{\theta-1}{\theta} b_0 \left[h - 1 + \frac{1}{\alpha} - \frac{(1-\alpha)^T}{\alpha} \right] + \tilde{X}_{T+h|T} where :math:`\tilde{X}_{T+h|T}` is the SES forecast of the endogenous variable using the parameter :math:`\alpha`. :math:`b_0` is the slope of a time trend line fitted to X using the terms 0, 1, ..., T-1. This expression follows from [1]_ and [2]_ when the combination weights are restricted to be (theta-1)/theta and 1/theta. This nests the original implementation when theta=2 and the two weights are both 1/2. References ---------- .. [1] Hyndman, R. J., & Billah, B. (2003). Unmasking the Theta method. International Journal of Forecasting, 19(2), 287-290. .. [2] Fioruci, J. A., Pellegrini, T. R., Louzada, F., & Petropoulos, F. (2015). The optimized theta method. arXiv preprint arXiv:1503.03529. """ steps = int_like(steps, "steps") if steps < 1: raise ValueError("steps must be a positive integer") theta = float_like(theta, "theta") if theta < 1: raise ValueError("theta must be a float >= 1") thresh = 4.0 / np.finfo(np.double).eps trend_weight = (theta - 1) / theta if theta < thresh else 1.0 comp = self.forecast_components(steps=steps) fcast = trend_weight * comp.trend + np.asarray(comp.ses) # Re-seasonalize if needed if self.model.deseasonalize: seasonal = np.asarray(comp.seasonal) if self.model.method.startswith("mul"): fcast *= seasonal else: fcast += seasonal fcast.name = "forecast" return fcast def forecast_components(self, steps: int = 1) -> pd.DataFrame: r""" Compute the three components of the Theta model forecast Parameters ---------- steps : int The number of steps ahead to compute the forecast components. Returns ------- DataFrame A DataFrame with three columns: trend, ses and seasonal containing the forecast values of each of the three components. Notes ----- For a given value of :math:`\theta`, the deseasonalized forecast is `fcast = w * trend + ses` where :math:`w = \frac{theta - 1}{theta}`. The reseasonalized forecasts are then `seasonal * fcast` if the seasonality is multiplicative or `seasonal + fcast` if the seasonality is additive. """ steps = int_like(steps, "steps") if steps < 1: raise ValueError("steps must be a positive integer") alpha = self._alpha b0 = self._b0 nobs = self._nobs h = np.arange(1, steps + 1, dtype=np.float64) - 1 if alpha > 0: h += 1 / alpha - ((1 - alpha) ** nobs / alpha) trend = b0 * h ses = self._one_step * np.ones(steps) if self.model.method.startswith("add"): season = np.zeros(steps) else: season = np.ones(steps) # Re-seasonalize if self.model.deseasonalize: seasonal = self._seasonal period = self.model.period oos_idx = nobs + np.arange(1, steps + 1) seasonal_locs = oos_idx % period if seasonal.shape[0]: season[:] = seasonal[seasonal_locs] index = getattr(self.model.endog_orig, "index", None) if index is None: index = pd.RangeIndex(0, self.model.endog_orig.shape[0]) index = extend_index(steps, index) df = pd.DataFrame( {"trend": trend, "ses": ses, "seasonal": season}, index=index ) return df def summary(self) -> Summary: """ Summarize the model Returns ------- Summary This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary """ model = self.model smry = Summary() model_name = type(model).__name__ title = model_name + " Results" method = "MLE" if self._use_mle else "OLS/SES" is_series = isinstance(model.endog_orig, pd.Series) index = getattr(model.endog_orig, "index", None) if is_series and isinstance(index, (pd.DatetimeIndex, pd.PeriodIndex)): sample = [index[0].strftime("%m-%d-%Y")] sample += ["- " + index[-1].strftime("%m-%d-%Y")] else: sample = [str(0), str(model.endog_orig.shape[0])] dep_name = getattr(model.endog_orig, "name", "endog") or "endog" top_left = [ ("Dep. Variable:", [dep_name]), ("Method:", [method]), ("Date:", None), ("Time:", None), ("Sample:", [sample[0]]), ("", [sample[1]]), ] method = ( "Multiplicative" if model.method.startswith("mul") else "Additive" ) top_right = [ ("No. Observations:", [str(self._nobs)]), ("Deseasonalized:", [str(model.deseasonalize)]), ] if model.deseasonalize: top_right.extend( [ ("Deseas. Method:", [method]), ("Period:", [str(model.period)]), ("", [""]), ("", [""]), ] ) else: top_right.extend([("", [""])] * 4) smry.add_table_2cols( self, gleft=top_left, gright=top_right, title=title ) table_fmt = {"data_fmts": ["%s", "%#0.4g"], "data_aligns": "r"} data = np.asarray(self.params)[:, None] st = SimpleTable( data, ["Parameters", "Estimate"], list(self.params.index), title="Parameter Estimates", txt_fmt=table_fmt, ) smry.tables.append(st) return smry def prediction_intervals( self, steps: int = 1, theta: float = 2, alpha: float = 0.05 ) -> pd.DataFrame: r""" Parameters ---------- steps : int, default 1 The number of steps ahead to compute the forecast components. theta : float, default 2 The theta value to use when computing the weight to combine the trend and the SES forecasts. alpha : float, default 0.05 Significance level for the confidence intervals. Returns ------- DataFrame DataFrame with columns lower and upper Notes ----- The variance of the h-step forecast is assumed to follow from the integrated Moving Average structure of the Theta model, and so is :math:`\sigma^2(1 + (h-1)(1 + (\alpha-1)^2)`. The prediction interval assumes that innovations are normally distributed. """ model_alpha = self.params[1] sigma2_h = ( 1 + np.arange(steps) * (1 + (model_alpha - 1) ** 2) ) * self.sigma2 sigma_h = np.sqrt(sigma2_h) quantile = stats.norm.ppf(alpha / 2) predictions = self.forecast(steps, theta) return pd.DataFrame( { "lower": predictions + sigma_h * quantile, "upper": predictions + sigma_h * -quantile, } ) def plot_predict( self, steps: int = 1, theta: float = 2, alpha: Optional[float] = 0.05, in_sample: bool = False, fig: Optional["matplotlib.figure.Figure"] = None, figsize: Tuple[float, float] = None, ) -> "matplotlib.figure.Figure": r""" Plot forecasts, prediction intervals and in-sample values Parameters ---------- steps : int, default 1 The number of steps ahead to compute the forecast components. theta : float, default 2 The theta value to use when computing the weight to combine the trend and the SES forecasts. alpha : {float, None}, default 0.05 The tail probability not covered by the confidence interval. Must be in (0, 1). Confidence interval is constructed assuming normally distributed shocks. If None, figure will not show the confidence interval. in_sample : bool, default False Flag indicating whether to include the in-sample period in the plot. fig : Figure, default None An existing figure handle. If not provided, a new figure is created. figsize: tuple[float, float], default None Tuple containing the figure size. Returns ------- Figure Figure handle containing the plot. Notes ----- The variance of the h-step forecast is assumed to follow from the integrated Moving Average structure of the Theta model, and so is :math:`\sigma^2(\alpha^2 + (h-1))`. The prediction interval assumes that innovations are normally distributed. """ from statsmodels.graphics.utils import _import_mpl, create_mpl_fig _import_mpl() fig = create_mpl_fig(fig, figsize) assert fig is not None predictions = self.forecast(steps, theta) pred_index = predictions.index ax = fig.add_subplot(111) nobs = self.model.endog_orig.shape[0] index = pd.Int64Index(np.arange(nobs)) if in_sample: if isinstance(self.model.endog_orig, pd.Series): index = self.model.endog_orig.index ax.plot(index, self.model.endog_orig) ax.plot(pred_index, predictions) if alpha is not None: pi = self.prediction_intervals(steps, theta, alpha) label = "{0:.0%} confidence interval".format(1 - alpha) ax.fill_between( pred_index, pi["lower"], pi["upper"], color="gray", alpha=0.5, label=label, ) ax.legend(loc="best", frameon=False) fig.tight_layout(pad=1.0) return fig statsmodels-0.12.2/statsmodels/tsa/holtwinters/000077500000000000000000000000001400612667500216605ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/holtwinters/__init__.py000066400000000000000000000005421400612667500237720ustar00rootroot00000000000000from statsmodels.tsa.holtwinters.model import ( PY_SMOOTHERS, SMOOTHERS, ExponentialSmoothing, Holt, SimpleExpSmoothing, ) from statsmodels.tsa.holtwinters.results import HoltWintersResults __all__ = [ "ExponentialSmoothing", "SimpleExpSmoothing", "Holt", "HoltWintersResults", "SMOOTHERS", "PY_SMOOTHERS", ] statsmodels-0.12.2/statsmodels/tsa/holtwinters/_exponential_smoothers.pyx000066400000000000000000000275141400612667500272230ustar00rootroot00000000000000#!python #cython: language_level=3, wraparound=False, boundscheck=False, cdivision=True import numpy as np cimport numpy as np np.import_array() cdef double LOWER_BOUND = np.sqrt(np.finfo(float).eps) cdef class HoltWintersArgs: cdef long[::1] _xi cdef double[::1] _p, _y, _l, _b, _s cdef double[:, ::1] _bounds cdef Py_ssize_t _m, _n cdef bint _transform def __init__( self, long[::1] xi, double[::1] p, double[:, ::1] bounds, double[::1] y, Py_ssize_t m, Py_ssize_t n, bint transform=False, ): self._xi = xi self._p = p self._bounds = bounds self._y = y self._l = np.empty(n) self._b = np.empty(n) self._s = np.empty(n + m - 1) self._m = m self._n = n self._transform = transform @property def xi(self): return np.asarray(self._xi) @xi.setter def xi(self, value): self._xi = value @property def p(self): return np.asarray(self._p) @property def bounds(self): return np.asarray(self._bounds) @property def y(self): return np.asarray(self._y) @property def lvl(self): return np.asarray(self._l) @property def b(self): return np.asarray(self._b) @property def s(self): return np.asarray(self._s) @property def m(self): return self._m @property def n(self): return self._n @property def transform(self): return self._transform @transform.setter def transform(self, value): self._transform = value cdef to_restricted(double[::1] p, long[::1] sel, double[:, ::1] bounds): """ Transform parameters from the unrestricted [0,1] space Parameters ---------- p : ndarray The parameters to transform sel : ndarray Array indicating whether a parameter is being estiamted bounds : ndarray 2-d array of bounds where bound for element i is in row i and stored as [lb, ub] Returns ------- """ cdef double a, b, g, ub, lb a = p[0] b = p[1] g = p[2] if sel[0]: lb = max(LOWER_BOUND, bounds[0, 0]) ub = min(1 - LOWER_BOUND, bounds[0, 1]) a = lb + a * (ub - lb) if sel[1]: lb = bounds[1, 0] ub = min(a, bounds[1, 1]) b = lb + b * (ub - lb) if sel[2]: lb = bounds[2, 0] ub = min(1. - a, bounds[2, 1]) g = lb + g * (ub - lb) return a, b, g def _test_to_restricted(p, sel, bounds): """Testing harness""" return to_restricted(p, sel, bounds) # noinspection PyProtectedMember cdef object holt_init(double[::1] x, HoltWintersArgs hw_args): """Initialization for the Holt Models""" cdef double alpha, beta, phi, alphac, betac, l0, b0, _ cdef Py_ssize_t i, n, idx = 0 cdef double[::1] p cdef long[::1] xi p = hw_args._p xi = hw_args._xi n = p.shape[0] for i in range(n): if xi[i]: p[i] = x[idx] idx += 1 if hw_args._transform: alpha, beta, _ = to_restricted(p, xi, hw_args._bounds) else: alpha = p[0] beta = p[1] l0 = p[3] b0 = p[4] phi = p[5] alphac = 1 - alpha betac = 1 - beta hw_args._l[0] = l0 hw_args._b[0] = b0 return alpha, beta, phi, alphac, betac # noinspection PyProtectedMember def holt__(double[::1] x, HoltWintersArgs hw_args): """ Compute the sum of squared residuals for Simple Exponential Smoothing Returns ------- ndarray Array containing model errors """ cdef double alpha, beta, phi, betac, alphac cdef double[::1] err, l, y cdef Py_ssize_t i l = hw_args._l y = hw_args._y err = np.empty(hw_args._n) alpha, beta, phi, alphac, betac = holt_init(x, hw_args) err[0] = y[0] - l[0] for i in range(1, hw_args._n): l[i] = (alpha * y[i - 1]) + (alphac * l[i - 1]) err[i] = y[i] - l[i] return np.asarray(err) # noinspection PyProtectedMember def holt_mul_dam(double[::1] x, HoltWintersArgs hw_args): """ Multiplicative and Multiplicative Damped Minimization Function (M,) & (Md,) """ cdef double alpha, beta, phi, betac, alphac cdef double[::1] err, l, b, y cdef Py_ssize_t i err = np.empty(hw_args._n) alpha, beta, phi, alphac, betac = holt_init(x, hw_args) y = hw_args._y l = hw_args._l b = hw_args._b err[0] = y[0] - (l[0] * b[0]**phi) for i in range(1, hw_args._n): l[i] = (alpha * y[i - 1]) + (alphac * (l[i - 1] * b[i - 1]**phi)) b[i] = (beta * (l[i] / l[i - 1])) + (betac * b[i - 1]**phi) err[i] = y[i] - (l[i] * b[i]**phi) return np.asarray(err) # noinspection PyProtectedMember def holt_add_dam(double[::1] x, HoltWintersArgs hw_args): """ Additive and Additive Damped Minimization Function (A,) & (Ad,) """ cdef double alpha, beta, phi, betac, alphac cdef double[::1] err, l, b, y cdef Py_ssize_t i err = np.empty(hw_args._n) alpha, beta, phi, alphac, betac = holt_init(x, hw_args) y = hw_args._y l = hw_args._l b = hw_args._b err[0] = y[0] - (l[0] + phi * b[0]) for i in range(1, hw_args._n): l[i] = (alpha * y[i - 1]) + (alphac * (l[i - 1] + phi * b[i - 1])) b[i] = (beta * (l[i] - l[i - 1])) + (betac * phi * b[i - 1]) err[i] = y[i] - (l[i] + phi * b[i]) return np.asarray(err) # noinspection PyProtectedMember cdef object holt_win_init(double[::1] x, HoltWintersArgs hw_args): """Initialization for the Holt Winters Seasonal Models""" cdef double alpha, beta, gamma, phi, alphac, betac, l0, b0 cdef Py_ssize_t i, n, idx = 0 cdef double[::1] p, s cdef long[::1] xi p = hw_args._p xi = hw_args._xi n = p.shape[0] for i in range(n): if xi[i]: p[i] = x[idx] idx += 1 if hw_args._transform: alpha, beta, gamma = to_restricted(p, xi, hw_args._bounds) else: alpha = p[0] beta = p[1] gamma = p[2] l0 = p[3] b0 = p[4] phi = p[5] alphac = 1 - alpha betac = 1 - beta gammac = 1 - gamma hw_args._l[0] = l0 hw_args._b[0] = b0 s = hw_args._s for i in range(hw_args._m): s[i] = p[6+i] return alpha, beta, gamma, phi, alphac, betac, gammac # noinspection PyProtectedMember def holt_win_add_add_dam(double[::1] x, HoltWintersArgs hw_args): """ Additive and Additive Damped with Additive Seasonal Minimization Function (A,A) & (Ad,A) """ cdef double alpha, beta, gamma, phi, alphac, betac, gammac cdef double[::1] err, l, s, b, y cdef Py_ssize_t i, m err = np.empty(hw_args._n) alpha, beta, gamma, phi, alphac, betac, gammac = holt_win_init(x, hw_args) y = hw_args._y l = hw_args._l b = hw_args._b s = hw_args._s m = hw_args._m err[0] = y[0] - (l[0] + phi * b[0] + s[0]) for i in range(1, hw_args._n): l[i] = (alpha * y[i - 1]) - (alpha * s[i - 1]) + \ (alphac * (l[i - 1] + phi * b[i - 1])) b[i] = (beta * (l[i] - l[i - 1])) + (betac * phi * b[i - 1]) s[i + m - 1] = gamma * y[i - 1] - \ (gamma * (l[i - 1] + phi * b[i - 1])) + (gammac * s[i - 1]) err[i] = y[i] - (l[i] + phi * b[i] + s[i]) return np.asarray(err) # noinspection PyProtectedMember def holt_win__add(double[::1] x, HoltWintersArgs hw_args): """ Additive Seasonal Minimization Function (,A) """ cdef double alpha, beta, gamma, phi, alphac, betac, gammac cdef double[::1] err, y, l, s cdef Py_ssize_t i, m err = np.empty(hw_args._n) alpha, beta, gamma, phi, alphac, betac, gammac= holt_win_init(x, hw_args) y = hw_args._y l = hw_args._l s = hw_args._s m = hw_args._m err[0] = y[0] - (l[0] + s[0]) for i in range(1, hw_args._n): l[i] = (alpha * y[i - 1]) - (alpha * s[i - 1]) + (alphac * (l[i - 1])) s[i + m - 1] = gamma * y[i - 1] - \ (gamma * (l[i - 1])) + (gammac * s[i - 1]) err[i] = y[i] - (l[i] + s[i]) return np.asarray(err) # noinspection PyProtectedMember def holt_win__mul(double[::1] x, HoltWintersArgs hw_args): """ Multiplicative Seasonal Minimization Function (,M) """ cdef double alpha, beta, gamma, phi, alphac, betac, gammac cdef double[::1] err, y, l, s cdef Py_ssize_t i, m err = np.empty(hw_args._n) alpha, beta, gamma, phi, alphac, betac, gammac= holt_win_init(x, hw_args) y = hw_args._y l = hw_args._l s = hw_args._s m = hw_args._m err[0] = y[0] - (l[0] * s[0]) for i in range(1, hw_args._n): l[i] = (alpha * y[i - 1] / s[i - 1]) + (alphac * (l[i - 1])) s[i + m - 1] = (gamma * y[i - 1] / (l[i - 1])) + (gammac * s[i - 1]) err[i] = y[i] - (l[i] * s[i]) return np.asarray(err) # noinspection PyProtectedMember def holt_win_mul_mul_dam(double[::1] x, HoltWintersArgs hw_args): """ Multiplicative and Multiplicative Damped with Multiplicative Seasonal Minimization Function (M,M) & (Md,M) """ cdef double alpha, beta, gamma, phi, alphac, betac, gammac cdef double[::1] err, y, l, b, s cdef Py_ssize_t i, m err = np.empty(hw_args._n) alpha, beta, gamma, phi, alphac, betac, gammac= holt_win_init(x, hw_args) y = hw_args._y l = hw_args._l b = hw_args._b s = hw_args._s m = hw_args._m err[0] = y[0] - ((l[0] * b[0]**phi) * s[0]) for i in range(1, hw_args._n): l[i] = (alpha * y[i - 1] / s[i - 1]) + \ (alphac * (l[i - 1] * b[i - 1]**phi)) b[i] = (beta * (l[i] / l[i - 1])) + (betac * b[i - 1]**phi) s[i + m - 1] = (gamma * y[i - 1] / (l[i - 1] * b[i - 1]**phi)) + (gammac * s[i - 1]) err[i] = y[i] - ((l[i] * b[i]**phi) * s[i]) return np.asarray(err) # noinspection PyProtectedMember def holt_win_add_mul_dam(double[::1] x, HoltWintersArgs hw_args): """ Additive and Additive Damped with Multiplicative Seasonal Minimization Function (A,M) & (Ad,M) """ cdef double alpha, beta, gamma, phi, alphac, betac, gammac cdef double[::1] err, l, s, b, y cdef Py_ssize_t i, m err = np.empty(hw_args._n) alpha, beta, gamma, phi, alphac, betac, gammac= holt_win_init(x, hw_args) y = hw_args._y l = hw_args._l b = hw_args._b s = hw_args._s m = hw_args._m err[0] = y[0] - ((l[0] + phi * b[0]) * s[0]) for i in range(1, hw_args._n): l[i] = (alpha * y[i - 1] / s[i - 1]) + \ (alphac * (l[i - 1] + phi * b[i - 1])) b[i] = (beta * (l[i] - l[i - 1])) + (betac * phi * b[i - 1]) s[i + m - 1] = (gamma * y[i - 1] / (l[i - 1] + phi * b[i - 1])) + (gammac * s[i - 1]) err[i] = y[i] - ((l[i] + phi * b[i]) * s[i]) return np.asarray(err) # noinspection PyProtectedMember def holt_win_mul_add_dam(double[::1] x, HoltWintersArgs hw_args): """ Multiplicative and Multiplicative Damped with Additive Seasonal Minimization Function (M,A) & (M,Ad) """ cdef double alpha, beta, gamma, phi, alphac, betac, gammac cdef double[::1] err, l, s, b, y cdef Py_ssize_t i, m err = np.empty(hw_args._n) alpha, beta, gamma, phi, alphac, betac, gammac= holt_win_init(x, hw_args) y = hw_args._y l = hw_args._l b = hw_args._b s = hw_args._s m = hw_args._m err[0] = y[0] - ((l[0] * phi * b[0]) + s[0]) for i in range(1, hw_args._n): l[i] = (alpha * y[i - 1]) - (alpha * s[i - 1]) + \ (alphac * (l[i - 1] * b[i - 1]**phi)) b[i] = (beta * (l[i] / l[i - 1])) + (betac * b[i - 1]**phi) s[i + m - 1] = gamma * y[i - 1] - \ (gamma * (l[i - 1] * b[i - 1]**phi)) + (gammac * s[i - 1]) err[i] = y[i] - ((l[i] * phi * b[i]) + s[i]) return np.asarray(err) statsmodels-0.12.2/statsmodels/tsa/holtwinters/_smoothers.py000066400000000000000000000236321400612667500244220ustar00rootroot00000000000000import numpy as np LOWER_BOUND = np.sqrt(np.finfo(float).eps) class HoltWintersArgs: def __init__(self, xi, p, bounds, y, m, n, transform=False): self._xi = xi self._p = p self._bounds = bounds self._y = y self._lvl = np.empty(n) self._b = np.empty(n) self._s = np.empty(n + m - 1) self._m = m self._n = n self._transform = transform @property def xi(self): return self._xi @xi.setter def xi(self, value): self._xi = value @property def p(self): return self._p @property def bounds(self): return self._bounds @property def y(self): return self._y @property def lvl(self): return self._lvl @property def b(self): return self._b @property def s(self): return self._s @property def m(self): return self._m @property def n(self): return self._n @property def transform(self): return self._transform @transform.setter def transform(self, value): self._transform = value def to_restricted(p, sel, bounds): """ Transform parameters from the unrestricted [0,1] space to satisfy both the bounds and the 2 constraints beta <= alpha and gamma <= (1-alpha) Parameters ---------- p : ndarray The parameters to transform sel : ndarray Array indicating whether a parameter is being estimated. If not estimated, not transformed. bounds : ndarray 2-d array of bounds where bound for element i is in row i and stored as [lb, ub] Returns ------- """ a, b, g = p[:3] if sel[0]: lb = max(LOWER_BOUND, bounds[0, 0]) ub = min(1 - LOWER_BOUND, bounds[0, 1]) a = lb + a * (ub - lb) if sel[1]: lb = bounds[1, 0] ub = min(a, bounds[1, 1]) b = lb + b * (ub - lb) if sel[2]: lb = bounds[2, 0] ub = min(1.0 - a, bounds[2, 1]) g = lb + g * (ub - lb) return a, b, g def to_unrestricted(p, sel, bounds): """ Transform parameters to the unrestricted [0,1] space Parameters ---------- p : ndarray Parameters that strictly satisfy the constraints Returns ------- ndarray Parameters all in (0,1) """ # eps < a < 1 - eps # eps < b <= a # eps < g <= 1 - a a, b, g = p[:3] if sel[0]: lb = max(LOWER_BOUND, bounds[0, 0]) ub = min(1 - LOWER_BOUND, bounds[0, 1]) a = (a - lb) / (ub - lb) if sel[1]: lb = bounds[1, 0] ub = min(p[0], bounds[1, 1]) b = (b - lb) / (ub - lb) if sel[2]: lb = bounds[2, 0] ub = min(1.0 - p[0], bounds[2, 1]) g = (g - lb) / (ub - lb) return a, b, g def holt_init(x, hw_args: HoltWintersArgs): """ Initialization for the Holt Models """ # Map back to the full set of parameters hw_args.p[hw_args.xi.astype(bool)] = x # Ensure alpha and beta satisfy the requirements if hw_args.transform: alpha, beta, _ = to_restricted(hw_args.p, hw_args.xi, hw_args.bounds) else: alpha, beta = hw_args.p[:2] # Level, trend and dampening l0, b0, phi = hw_args.p[3:6] # Save repeated calculations alphac = 1 - alpha betac = 1 - beta # Setup alpha * y y_alpha = alpha * hw_args.y # In-place operations hw_args.lvl[0] = l0 hw_args.b[0] = b0 return alpha, beta, phi, alphac, betac, y_alpha def holt__(x, hw_args: HoltWintersArgs): """ Simple Exponential Smoothing Minimization Function (,) """ _, _, _, alphac, _, y_alpha = holt_init(x, hw_args) n = hw_args.n lvl = hw_args.lvl for i in range(1, n): lvl[i] = (y_alpha[i - 1]) + (alphac * (lvl[i - 1])) return hw_args.y - lvl def holt_mul_dam(x, hw_args: HoltWintersArgs): """ Multiplicative and Multiplicative Damped Minimization Function (M,) & (Md,) """ _, beta, phi, alphac, betac, y_alpha = holt_init(x, hw_args) lvl = hw_args.lvl b = hw_args.b for i in range(1, hw_args.n): lvl[i] = (y_alpha[i - 1]) + (alphac * (lvl[i - 1] * b[i - 1] ** phi)) b[i] = (beta * (lvl[i] / lvl[i - 1])) + (betac * b[i - 1] ** phi) return hw_args.y - lvl * b ** phi def holt_add_dam(x, hw_args: HoltWintersArgs): """ Additive and Additive Damped Minimization Function (A,) & (Ad,) """ _, beta, phi, alphac, betac, y_alpha = holt_init(x, hw_args) lvl = hw_args.lvl b = hw_args.b for i in range(1, hw_args.n): lvl[i] = (y_alpha[i - 1]) + (alphac * (lvl[i - 1] + phi * b[i - 1])) b[i] = (beta * (lvl[i] - lvl[i - 1])) + (betac * phi * b[i - 1]) return hw_args.y - (lvl + phi * b) def holt_win_init(x, hw_args: HoltWintersArgs): """Initialization for the Holt Winters Seasonal Models""" hw_args.p[hw_args.xi.astype(bool)] = x if hw_args.transform: alpha, beta, gamma = to_restricted( hw_args.p, hw_args.xi, hw_args.bounds ) else: alpha, beta, gamma = hw_args.p[:3] l0, b0, phi = hw_args.p[3:6] s0 = hw_args.p[6:] alphac = 1 - alpha betac = 1 - beta gammac = 1 - gamma y_alpha = alpha * hw_args.y y_gamma = gamma * hw_args.y hw_args.lvl[:] = 0 hw_args.b[:] = 0 hw_args.s[:] = 0 hw_args.lvl[0] = l0 hw_args.b[0] = b0 hw_args.s[: hw_args.m] = s0 return alpha, beta, gamma, phi, alphac, betac, gammac, y_alpha, y_gamma def holt_win__mul(x, hw_args: HoltWintersArgs): """ Multiplicative Seasonal Minimization Function (,M) """ (_, _, _, _, alphac, _, gammac, y_alpha, y_gamma) = holt_win_init( x, hw_args ) lvl = hw_args.lvl s = hw_args.s m = hw_args.m for i in range(1, hw_args.n): lvl[i] = (y_alpha[i - 1] / s[i - 1]) + (alphac * (lvl[i - 1])) s[i + m - 1] = (y_gamma[i - 1] / (lvl[i - 1])) + (gammac * s[i - 1]) return hw_args.y - lvl * s[: -(m - 1)] def holt_win__add(x, hw_args: HoltWintersArgs): """ Additive Seasonal Minimization Function (,A) """ (alpha, _, gamma, _, alphac, _, gammac, y_alpha, y_gamma) = holt_win_init( x, hw_args ) lvl = hw_args.lvl s = hw_args.s m = hw_args.m for i in range(1, hw_args.n): lvl[i] = ( (y_alpha[i - 1]) - (alpha * s[i - 1]) + (alphac * (lvl[i - 1])) ) s[i + m - 1] = ( y_gamma[i - 1] - (gamma * (lvl[i - 1])) + (gammac * s[i - 1]) ) return hw_args.y - lvl - s[: -(m - 1)] def holt_win_add_mul_dam(x, hw_args: HoltWintersArgs): """ Additive and Additive Damped with Multiplicative Seasonal Minimization Function (A,M) & (Ad,M) """ ( _, beta, _, phi, alphac, betac, gammac, y_alpha, y_gamma, ) = holt_win_init(x, hw_args) lvl = hw_args.lvl b = hw_args.b s = hw_args.s m = hw_args.m for i in range(1, hw_args.n): lvl[i] = (y_alpha[i - 1] / s[i - 1]) + ( alphac * (lvl[i - 1] + phi * b[i - 1]) ) b[i] = (beta * (lvl[i] - lvl[i - 1])) + (betac * phi * b[i - 1]) s[i + m - 1] = (y_gamma[i - 1] / (lvl[i - 1] + phi * b[i - 1])) + ( gammac * s[i - 1] ) return hw_args.y - (lvl + phi * b) * s[: -(m - 1)] def holt_win_mul_mul_dam(x, hw_args: HoltWintersArgs): """ Multiplicative and Multiplicative Damped with Multiplicative Seasonal Minimization Function (M,M) & (Md,M) """ ( _, beta, _, phi, alphac, betac, gammac, y_alpha, y_gamma, ) = holt_win_init(x, hw_args) lvl = hw_args.lvl s = hw_args.s b = hw_args.b m = hw_args.m for i in range(1, hw_args.n): lvl[i] = (y_alpha[i - 1] / s[i - 1]) + ( alphac * (lvl[i - 1] * b[i - 1] ** phi) ) b[i] = (beta * (lvl[i] / lvl[i - 1])) + (betac * b[i - 1] ** phi) s[i + m - 1] = (y_gamma[i - 1] / (lvl[i - 1] * b[i - 1] ** phi)) + ( gammac * s[i - 1] ) return hw_args.y - (lvl * b ** phi) * s[: -(m - 1)] def holt_win_add_add_dam(x, hw_args: HoltWintersArgs): """ Additive and Additive Damped with Additive Seasonal Minimization Function (A,A) & (Ad,A) """ ( alpha, beta, gamma, phi, alphac, betac, gammac, y_alpha, y_gamma, ) = holt_win_init(x, hw_args) lvl = hw_args.lvl s = hw_args.s b = hw_args.b m = hw_args.m for i in range(1, hw_args.n): lvl[i] = ( (y_alpha[i - 1]) - (alpha * s[i - 1]) + (alphac * (lvl[i - 1] + phi * b[i - 1])) ) b[i] = (beta * (lvl[i] - lvl[i - 1])) + (betac * phi * b[i - 1]) s[i + m - 1] = ( y_gamma[i - 1] - (gamma * (lvl[i - 1] + phi * b[i - 1])) + (gammac * s[i - 1]) ) return hw_args.y - ((lvl + phi * b) + s[: -(m - 1)]) def holt_win_mul_add_dam(x, hw_args: HoltWintersArgs): """ Multiplicative and Multiplicative Damped with Additive Seasonal Minimization Function (M,A) & (M,Ad) """ ( alpha, beta, gamma, phi, alphac, betac, gammac, y_alpha, y_gamma, ) = holt_win_init(x, hw_args) lvl = hw_args.lvl s = hw_args.s b = hw_args.b m = hw_args.m for i in range(1, hw_args.n): lvl[i] = ( (y_alpha[i - 1]) - (alpha * s[i - 1]) + (alphac * (lvl[i - 1] * b[i - 1] ** phi)) ) b[i] = (beta * (lvl[i] / lvl[i - 1])) + (betac * b[i - 1] ** phi) s[i + m - 1] = ( y_gamma[i - 1] - (gamma * (lvl[i - 1] * b[i - 1] ** phi)) + (gammac * s[i - 1]) ) return hw_args.y - ((lvl * phi * b) + s[: -(m - 1)]) statsmodels-0.12.2/statsmodels/tsa/holtwinters/model.py000066400000000000000000002071171400612667500233420ustar00rootroot00000000000000""" Notes ----- Code written using below textbook as a reference. Results are checked against the expected outcomes in the text book. Properties: Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. Author: Terence L van Zyl Modified: Kevin Sheppard """ from statsmodels.compat.pandas import deprecate_kwarg import contextlib from typing import Any, Hashable, Sequence import warnings import numpy as np import pandas as pd from scipy.optimize import basinhopping, least_squares, minimize from scipy.special import inv_boxcox from scipy.stats import boxcox from statsmodels.tools.validation import ( array_like, bool_like, dict_like, float_like, int_like, string_like, ) from statsmodels.tsa.base.tsa_model import TimeSeriesModel from statsmodels.tsa.exponential_smoothing.ets import _initialization_heuristic from statsmodels.tsa.holtwinters import ( _exponential_smoothers as smoothers, _smoothers as py_smoothers, ) from statsmodels.tsa.holtwinters._exponential_smoothers import HoltWintersArgs from statsmodels.tsa.holtwinters._smoothers import ( to_restricted, to_unrestricted, ) from statsmodels.tsa.holtwinters.results import ( HoltWintersResults, HoltWintersResultsWrapper, ) from statsmodels.tsa.tsatools import freq_to_period SMOOTHERS = { ("mul", "add"): smoothers.holt_win_add_mul_dam, ("mul", "mul"): smoothers.holt_win_mul_mul_dam, ("mul", None): smoothers.holt_win__mul, ("add", "add"): smoothers.holt_win_add_add_dam, ("add", "mul"): smoothers.holt_win_mul_add_dam, ("add", None): smoothers.holt_win__add, (None, "add"): smoothers.holt_add_dam, (None, "mul"): smoothers.holt_mul_dam, (None, None): smoothers.holt__, } PY_SMOOTHERS = { ("mul", "add"): py_smoothers.holt_win_add_mul_dam, ("mul", "mul"): py_smoothers.holt_win_mul_mul_dam, ("mul", None): py_smoothers.holt_win__mul, ("add", "add"): py_smoothers.holt_win_add_add_dam, ("add", "mul"): py_smoothers.holt_win_mul_add_dam, ("add", None): py_smoothers.holt_win__add, (None, "add"): py_smoothers.holt_add_dam, (None, "mul"): py_smoothers.holt_mul_dam, (None, None): py_smoothers.holt__, } def opt_wrapper(func): def f(*args, **kwargs): err = func(*args, **kwargs) if isinstance(err, np.ndarray): return err.T @ err return err return f class _OptConfig(object): alpha: float beta: float phi: float gamma: float level: float trend: float seasonal: np.ndarray y: np.ndarray params: np.ndarray mask: np.ndarray mle_retvals: Any def unpack_parameters(self, params) -> "_OptConfig": self.alpha = params[0] self.beta = params[1] self.gamma = params[2] self.level = params[3] self.trend = params[4] self.phi = params[5] self.seasonal = params[6:] return self class ExponentialSmoothing(TimeSeriesModel): """ Holt Winter's Exponential Smoothing Parameters ---------- endog : array_like The time series to model. trend : {"add", "mul", "additive", "multiplicative", None}, optional Type of trend component. damped_trend : bool, optional Should the trend component be damped. seasonal : {"add", "mul", "additive", "multiplicative", None}, optional Type of seasonal component. seasonal_periods : int, optional The number of periods in a complete seasonal cycle, e.g., 4 for quarterly data or 7 for daily data with a weekly cycle. initialization_method : str, optional Method for initialize the recursions. One of: * None * 'estimated' * 'heuristic' * 'legacy-heuristic' * 'known' None defaults to the pre-0.12 behavior where initial values are passed as part of ``fit``. If any of the other values are passed, then the initial values must also be set when constructing the model. If 'known' initialization is used, then `initial_level` must be passed, as well as `initial_trend` and `initial_seasonal` if applicable. Default is 'estimated'. "legacy-heuristic" uses the same values that were used in statsmodels 0.11 and earlier. initial_level : float, optional The initial level component. Required if estimation method is "known". If set using either "estimated" or "heuristic" this value is used. This allows one or more of the initial values to be set while deferring to the heuristic for others or estimating the unset parameters. initial_trend : float, optional The initial trend component. Required if estimation method is "known". If set using either "estimated" or "heuristic" this value is used. This allows one or more of the initial values to be set while deferring to the heuristic for others or estimating the unset parameters. initial_seasonal : array_like, optional The initial seasonal component. An array of length `seasonal` or length `seasonal - 1` (in which case the last initial value is computed to make the average effect zero). Only used if initialization is 'known'. Required if estimation method is "known". If set using either "estimated" or "heuristic" this value is used. This allows one or more of the initial values to be set while deferring to the heuristic for others or estimating the unset parameters. use_boxcox : {True, False, 'log', float}, optional Should the Box-Cox transform be applied to the data first? If 'log' then apply the log. If float then use the value as lambda. bounds : dict[str, tuple[float, float]], optional An dictionary containing bounds for the parameters in the model, excluding the initial values if estimated. The keys of the dictionary are the variable names, e.g., smoothing_level or initial_slope. The initial seasonal variables are labeled initial_seasonal. for j=0,...,m-1 where m is the number of period in a full season. Use None to indicate a non-binding constraint, e.g., (0, None) constrains a parameter to be non-negative. dates : array_like of datetime, optional An array-like object of datetime objects. If a Pandas object is given for endog, it is assumed to have a DateIndex. freq : str, optional The frequency of the time-series. A Pandas offset or 'B', 'D', 'W', 'M', 'A', or 'Q'. This is optional if dates are given. missing : str Available options are 'none', 'drop', and 'raise'. If 'none', no nan checking is done. If 'drop', any observations with nans are dropped. If 'raise', an error is raised. Default is 'none'. Notes ----- This is a full implementation of the holt winters exponential smoothing as per [1]_. This includes all the unstable methods as well as the stable methods. The implementation of the library covers the functionality of the R library as much as possible whilst still being Pythonic. References ---------- .. [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. """ @deprecate_kwarg("damped", "damped_trend") def __init__( self, endog, trend=None, damped_trend=False, seasonal=None, *, seasonal_periods=None, initialization_method=None, # Future: 'estimated', initial_level=None, initial_trend=None, initial_seasonal=None, use_boxcox=None, bounds=None, dates=None, freq=None, missing="none", ): super(ExponentialSmoothing, self).__init__( endog, None, dates, freq, missing=missing ) self._y = self._data = array_like( endog, "endog", contiguous=True, order="C" ) options = ("add", "mul", "additive", "multiplicative") trend = string_like(trend, "trend", options=options, optional=True) if trend in ["additive", "multiplicative"]: trend = {"additive": "add", "multiplicative": "mul"}[trend] self.trend = trend self.damped_trend = bool_like(damped_trend, "damped_trend") seasonal = string_like( seasonal, "seasonal", options=options, optional=True ) if seasonal in ["additive", "multiplicative"]: seasonal = {"additive": "add", "multiplicative": "mul"}[seasonal] self.seasonal = seasonal self.has_trend = trend in ["mul", "add"] self.has_seasonal = seasonal in ["mul", "add"] if (self.trend == "mul" or self.seasonal == "mul") and not np.all( self._data > 0.0 ): raise ValueError( "endog must be strictly positive when using" "multiplicative trend or seasonal components." ) if self.damped_trend and not self.has_trend: raise ValueError("Can only dampen the trend component") if self.has_seasonal: self.seasonal_periods = int_like( seasonal_periods, "seasonal_periods", optional=True ) if seasonal_periods is None: try: self.seasonal_periods = freq_to_period(self._index_freq) except Exception: raise ValueError( "seasonal_periods has not been provided and index " "does not have a known freq. You must provide " "seasonal_periods" ) if self.seasonal_periods <= 1: raise ValueError("seasonal_periods must be larger than 1.") assert self.seasonal_periods is not None else: self.seasonal_periods = 0 self.nobs = len(self.endog) options = ("known", "estimated", "heuristic", "legacy-heuristic") self._initialization_method = string_like( initialization_method, "initialization_method", optional=True, options=options, ) self._initial_level = float_like( initial_level, "initial_level", optional=True ) self._initial_trend = float_like( initial_trend, "initial_trend", optional=True ) self._initial_seasonal = array_like( initial_seasonal, "initial_seasonal", optional=True ) estimated = self._initialization_method in (None, "estimated") self._estimate_level = estimated self._estimate_trend = estimated and self.trend self._estimate_seasonal = estimated and self.seasonal self._bounds = self._check_bounds(bounds) self._use_boxcox = use_boxcox self._lambda = np.nan self._y = self._boxcox() self._initialize() self._fixed_parameters = {} def _check_bounds(self, bounds): bounds = dict_like(bounds, "bounds", optional=True) if bounds is None: return msg = ( "bounds must be a dictionary of 2-element tuples of the form" " (lb, ub) where lb < ub, lb>=0 and ub<=1" ) variables = self._ordered_names() for key in bounds: if key not in variables: supported = ", ".join(variables[:-1]) supported += ", and " + variables[-1] raise KeyError( f"{key} does not match the list of supported variables " f"names: {supported}." ) bound = bounds[key] if not isinstance(bound, tuple): raise TypeError(msg) lb = bound[0] if bound[0] is not None else -np.inf ub = bound[1] if bound[1] is not None else np.inf if len(bound) != 2 or lb >= ub: raise ValueError(msg) if ("smoothing" in key or "damp" in key) and ( bound[0] < 0.0 or bound[1] > 1.0 ): raise ValueError( f"{key} must have a lower bound >= 0.0 and <= 1.0" ) return bounds def _boxcox(self): if ( self._use_boxcox is not None and self._initialization_method is None ): raise ValueError( "initialization_method must be set when use_boxcox has" "been set." ) if self._use_boxcox is None or self._use_boxcox is False: self._lambda = np.nan return self._y if self._use_boxcox is True: y, self._lambda = boxcox(self._y) elif isinstance(self._use_boxcox, (int, float)): self._lambda = float(self._use_boxcox) y = boxcox(self._y, self._use_boxcox) else: raise TypeError("use_boxcox must be True, False or a float.") return y @contextlib.contextmanager def fix_params(self, values): """ Temporarily fix parameters for estimation. Parameters ---------- values : dict Values to fix. The key is the parameter name and the value is the fixed value. Yields ------ None No value returned. Examples -------- >>> from statsmodels.datasets.macrodata import load_pandas >>> data = load_pandas() >>> import statsmodels.tsa.api as tsa >>> mod = tsa.ExponentialSmoothing(data.data.realcons, trend="add", ... initialization_method="estimated") >>> with mod.fix_params({"smoothing_level": 0.2}): ... mod.fit() """ values = dict_like(values, "values") valid_keys = ("smoothing_level",) if self.has_trend: valid_keys += ("smoothing_trend",) if self.has_seasonal: valid_keys += ("smoothing_seasonal",) m = self.seasonal_periods valid_keys += tuple([f"initial_seasonal.{i}" for i in range(m)]) if self.damped_trend: valid_keys += ("damping_trend",) if self._initialization_method in ("estimated", None): extra_keys = [ key.replace("smoothing_", "initial_") for key in valid_keys if "smoothing_" in key ] valid_keys += tuple(extra_keys) for key in values: if key not in valid_keys: valid = ", ".join(valid_keys[:-1]) + ", and " + valid_keys[-1] raise KeyError( f"{key} if not allowed. Only {valid} are supported in " f"this specification." ) if "smoothing_level" in values: alpha = values["smoothing_level"] if alpha <= 0.0: raise ValueError("smoothing_level must be in (0, 1)") beta = values.get("smoothing_trend", 0.0) if beta > alpha: raise ValueError("smoothing_trend must be <= smoothing_level") gamma = values.get("smoothing_seasonal", 0.0) if gamma > 1 - alpha: raise ValueError( "smoothing_seasonal must be <= 1 - smoothing_level" ) try: self._fixed_parameters = values yield finally: self._fixed_parameters = {} def _initialize(self): if self._initialization_method is None: msg = "initial_{0} given but no initialization method specified." if self._initial_level is not None: raise ValueError(msg.format("level")) if self._initial_trend is not None: raise ValueError(msg.format("trend")) if self._initial_seasonal is not None: raise ValueError(msg.format("seasonal")) warnings.warn( "After 0.13 initialization must be handled at model creation", FutureWarning, ) return if self._initialization_method == "known": return self._initialize_known() msg = ( f"initialization method is {self._initialization_method} but " "initial_{0} has been set." ) if self._initial_level is not None: raise ValueError(msg.format("level")) if self._initial_trend is not None: raise ValueError(msg.format("trend")) if self._initial_seasonal is not None: raise ValueError(msg.format("seasonal")) if self._initialization_method == "legacy-heuristic": return self._initialize_legacy() elif self._initialization_method in ("heuristic", "estimated"): return self._initialize_heuristic() def _initialize_heuristic(self): trend = self.trend if self.has_trend else False seasonal = self.seasonal if self.has_seasonal else False lvl, trend, seas = _initialization_heuristic( self._y, trend, seasonal, self.seasonal_periods ) self._initial_level = lvl self._initial_trend = trend self._initial_seasonal = seas def _initialize_legacy(self): lvl, trend, seasonal = self.initial_values(force=True) self._initial_level = lvl self._initial_trend = trend self._initial_seasonal = seasonal def _initialize_known(self): msg = "initialization is 'known' but initial_{0} not given" if self._initial_level is None: raise ValueError(msg.format("level")) excess = "initial_{0} set but model has no {0} component" if self.has_trend and self._initial_trend is None: raise ValueError(msg.format("trend")) elif not self.has_trend and self._initial_trend is not None: raise ValueError(excess.format("trend")) if self.has_seasonal and self._initial_seasonal is None: raise ValueError(msg.format("seasonal")) elif not self.has_seasonal and self._initial_seasonal is not None: raise ValueError(excess.format("seasonal")) def predict(self, params, start=None, end=None): """ In-sample and out-of-sample prediction. Parameters ---------- params : ndarray The fitted model parameters. start : int, str, or datetime Zero-indexed observation number at which to start forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. end : int, str, or datetime Zero-indexed observation number at which to end forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. Returns ------- ndarray The predicted values. """ if start is None: freq = getattr(self._index, "freq", 1) if isinstance(freq, int): start = self._index.shape[0] + freq else: start = self._index[-1] + freq start, end, out_of_sample, _ = self._get_prediction_index( start=start, end=end ) if out_of_sample > 0: res = self._predict(h=out_of_sample, **params) else: res = self._predict(h=0, **params) return res.fittedfcast[start : end + out_of_sample + 1] def _enforce_bounds(self, p, sel, lb, ub): initial_p = p[sel] # Ensure strictly inbounds loc = initial_p <= lb upper = ub[loc].copy() upper[~np.isfinite(upper)] = 100.0 eps = 1e-4 initial_p[loc] = lb[loc] + eps * (upper - lb[loc]) loc = initial_p >= ub lower = lb[loc].copy() lower[~np.isfinite(lower)] = -100.0 eps = 1e-4 initial_p[loc] = ub[loc] - eps * (ub[loc] - lower) return initial_p @staticmethod def _check_blocked_keywords( d: dict, keys: Sequence[Hashable], name="kwargs" ): for key in keys: if key in d: raise ValueError(f"{name} must not contain '{key}'") def _check_bound_feasibility(self, bounds): if bounds[1][0] > bounds[0][1]: raise ValueError( "The bounds for smoothing_trend and smoothing_level are " "incompatible since smoothing_trend <= smoothing_level." ) if bounds[2][0] > (1 - bounds[0][1]): raise ValueError( "The bounds for smoothing_seasonal and smoothing_level " "are incompatible since smoothing_seasonal <= " "1 - smoothing_level." ) @staticmethod def _setup_brute(sel, bounds, alpha): # More points when fewer parameters ns = 87 // sel[:3].sum() if not sel[0]: # Easy case since no cross-constraints nparams = int(sel[1]) + int(sel[2]) args = [] for i in range(1, 3): if sel[i]: bound = bounds[i] step = bound[1] - bound[0] lb = bound[0] + 0.005 * step if i == 1: ub = min(bound[1], alpha) - 0.005 * step else: ub = min(bound[1], 1 - alpha) - 0.005 * step args.append(np.linspace(lb, ub, ns)) points = np.stack(np.meshgrid(*args)) points = points.reshape((nparams, -1)).T return np.ascontiguousarray(points) bound = bounds[0] step = 0.005 * (bound[1] - bound[0]) points = np.linspace(bound[0] + step, bound[1] - step, ns) if not sel[1] and not sel[2]: return points[:, None] combined = [] b_bounds = bounds[1] g_bounds = bounds[2] if sel[1] and sel[2]: for a in points: b_lb = b_bounds[0] b_ub = min(b_bounds[1], a) g_lb = g_bounds[0] g_ub = min(g_bounds[1], 1 - a) if b_lb > b_ub or g_lb > g_ub: # infeasible point continue nb = int(np.ceil(ns * np.sqrt(a))) ng = int(np.ceil(ns * np.sqrt(1 - a))) b = np.linspace(b_lb, b_ub, nb) g = np.linspace(g_lb, g_ub, ng) both = np.stack(np.meshgrid(b, g)).reshape(2, -1).T final = np.empty((both.shape[0], 3)) final[:, 0] = a final[:, 1:] = both combined.append(final) elif sel[1]: for a in points: b_lb = b_bounds[0] b_ub = min(b_bounds[1], a) if b_lb > b_ub: # infeasible point continue nb = int(np.ceil(ns * np.sqrt(a))) final = np.empty((nb, 2)) final[:, 0] = a final[:, 1] = np.linspace(b_lb, b_ub, nb) combined.append(final) else: # sel[2] for a in points: g_lb = g_bounds[0] g_ub = min(g_bounds[1], 1 - a) if g_lb > g_ub: # infeasible point continue ng = int(np.ceil(ns * np.sqrt(1 - a))) final = np.empty((ng, 2)) final[:, 1] = np.linspace(g_lb, g_ub, ng) final[:, 0] = a combined.append(final) return np.vstack(combined) def _ordered_names(self): names = ( "smoothing_level", "smoothing_trend", "smoothing_seasonal", "initial_level", "initial_trend", "damping_trend", ) m = self.seasonal_periods names += tuple([f"initial_seasonal.{i}" for i in range(m)]) return names def _update_for_fixed(self, sel, alpha, beta, gamma, phi, l0, b0, s0): if self._fixed_parameters: fixed = self._fixed_parameters names = self._ordered_names() not_fixed = np.array([name not in fixed for name in names]) if (~sel[~not_fixed]).any(): invalid = [] for name, s, nf in zip(names, sel, not_fixed): if not s and not nf: invalid.append(name) invalid_names = ", ".join(invalid) raise ValueError( "Cannot fix a parameter that is not being " f"estimated: {invalid_names}" ) sel &= not_fixed alpha = fixed.get("smoothing_level", alpha) beta = fixed.get("smoothing_trend", beta) gamma = fixed.get("smoothing_seasonal", gamma) phi = fixed.get("damping_trend", phi) l0 = fixed.get("initial_level", l0) b0 = fixed.get("initial_trend", l0) for i in range(self.seasonal_periods): s0[i] = fixed.get(f"initial_seasonal.{i}", s0[i]) return sel, alpha, beta, gamma, phi, l0, b0, s0 def _construct_bounds(self): trend_lb = 0.0 if self.trend == "mul" else None season_lb = 0.0 if self.seasonal == "mul" else None lvl_lb = None if trend_lb is None and season_lb is None else 0.0 bounds = [ (0.0, 1.0), # alpha (0.0, 1.0), # beta (0.0, 1.0), # gamma (lvl_lb, None), # level (trend_lb, None), # trend (0.8, 0.995), # phi ] bounds += [(season_lb, None)] * self.seasonal_periods if self._bounds is not None: assert isinstance(self._bounds, dict) for i, name in enumerate(self._ordered_names()): bounds[i] = self._bounds.get(name, bounds[i]) # Update bounds to account for fixed parameters fixed = self._fixed_parameters if "smoothing_level" in fixed: # Update bounds if fixed alpha alpha = fixed["smoothing_level"] # beta <= alpha if bounds[1][1] > alpha: bounds[1] = (bounds[1][0], alpha) # gamma <= 1 - alpha if bounds[2][1] > (1 - alpha): bounds[2] = (bounds[2][0], 1 - alpha) # gamma <= 1 - alpha if "smoothing_trend" in fixed: # beta <= alpha beta = fixed["smoothing_trend"] bounds[0] = (max(beta, bounds[0][0]), bounds[0][1]) if "smoothing_seasonal" in fixed: gamma = fixed["smoothing_seasonal"] # gamma <= 1 - alpha => alpha <= 1 - gamma bounds[0] = (bounds[0][0], min(1 - gamma, bounds[0][1])) # Ensure bounds are feasible for i, name in enumerate(self._ordered_names()): lb = bounds[i][0] if bounds[i][0] is not None else -np.inf ub = bounds[i][1] if bounds[i][1] is not None else np.inf if lb >= ub: raise ValueError( "After adjusting for user-provided bounds fixed values, " f"the resulting set of bounds for {name}, {bounds[i]}, " "are infeasible." ) self._check_bound_feasibility(bounds) return bounds def _get_starting_values( self, params, start_params, use_brute, sel, hw_args, bounds, alpha, func, ): if start_params is None and use_brute and np.any(sel[:3]): # Have a quick look in the region for a good starting place for # alpha, beta & gamma using fixed values for initial m = self.seasonal_periods sv_sel = np.array([False] * (6 + m)) sv_sel[:3] = True sv_sel &= sel hw_args.xi = sv_sel.astype(int) hw_args.transform = False # Setup the grid points, respecting constraints points = self._setup_brute(sv_sel, bounds, alpha) opt = opt_wrapper(func) best_val = np.inf best_params = points[0] for point in points: val = opt(point, hw_args) if val < best_val: best_params = point best_val = val params[sv_sel] = best_params elif start_params is not None: if len(start_params) != sel.sum(): msg = "start_params must have {0} values but has {1}." nxi, nsp = len(sel), len(start_params) raise ValueError(msg.format(nxi, nsp)) params[sel] = start_params return params def _optimize_parameters( self, data: _OptConfig, use_brute, method, kwargs ) -> _OptConfig: # Prepare starting values alpha = data.alpha beta = data.beta phi = data.phi gamma = data.gamma initial_level = data.level initial_trend = data.trend y = data.y start_params = data.params has_seasonal = self.has_seasonal has_trend = self.has_trend trend = self.trend seasonal = self.seasonal damped_trend = self.damped_trend m = self.seasonal_periods params = np.zeros(6 + m) l0, b0, s0 = self.initial_values( initial_level=data.level, initial_trend=data.trend ) init_alpha = alpha if alpha is not None else 0.5 / max(m, 1) init_beta = beta if beta is None and has_trend: init_beta = 0.1 * init_alpha init_gamma = gamma if has_seasonal and gamma is None: init_gamma = 0.05 * (1 - init_alpha) init_phi = phi if phi is not None else 0.99 # Selection of parameters to optimize sel = np.array( [ alpha is None, has_trend and beta is None, has_seasonal and gamma is None, initial_level is None, has_trend and initial_trend is None, damped_trend and phi is None, ] + [has_seasonal] * m, ) ( sel, init_alpha, init_beta, init_gamma, init_phi, l0, b0, s0, ) = self._update_for_fixed( sel, init_alpha, init_beta, init_gamma, init_phi, l0, b0, s0 ) func = SMOOTHERS[(seasonal, trend)] params[:6] = [init_alpha, init_beta, init_gamma, l0, b0, init_phi] if m: params[-m:] = s0 if not np.any(sel): from statsmodels.tools.sm_exceptions import EstimationWarning message = ( "Model has no free parameters to estimate. Set " "optimized=False to suppress this warning" ) warnings.warn(message, EstimationWarning) data = data.unpack_parameters(params) data.params = params data.mask = sel return data orig_bounds = self._construct_bounds() bounds = np.array(orig_bounds[:3], dtype=float) hw_args = HoltWintersArgs( sel.astype(int), params, bounds, y, m, self.nobs ) params = self._get_starting_values( params, start_params, use_brute, sel, hw_args, bounds, init_alpha, func, ) # We always use [0, 1] for a, b and g and handle transform inside mod_bounds = [(0, 1)] * 3 + orig_bounds[3:] relevant_bounds = [bnd for bnd, flag in zip(mod_bounds, sel) if flag] bounds = np.array(relevant_bounds, dtype=float) lb, ub = bounds.T lb[np.isnan(lb)] = -np.inf ub[np.isnan(ub)] = np.inf hw_args.xi = sel.astype(int) # Ensure strictly inbounds initial_p = self._enforce_bounds(params, sel, lb, ub) # Transform to unrestricted space params[sel] = initial_p params[:3] = to_unrestricted(params, sel, hw_args.bounds) initial_p = params[sel] # Ensure parameters are transformed internally hw_args.transform = True if method in ("least_squares", "ls"): # Least squares uses a different format for bounds ls_bounds = lb, ub self._check_blocked_keywords(kwargs, ("args", "bounds")) res = least_squares( func, initial_p, bounds=ls_bounds, args=(hw_args,), **kwargs ) success = res.success elif method in ("basinhopping", "bh"): # Take a deeper look in the local minimum we are in to find the # best solution to parameters, maybe hop around to try escape the # local minimum we may be in. minimizer_kwargs = {"args": (hw_args,), "bounds": relevant_bounds} kwargs = kwargs.copy() if "minimizer_kwargs" in kwargs: self._check_blocked_keywords( kwargs["minimizer_kwargs"], ("args", "bounds"), name="kwargs['minimizer_kwargs']", ) minimizer_kwargs.update(kwargs["minimizer_kwargs"]) del kwargs["minimizer_kwargs"] default_kwargs = { "minimizer_kwargs": minimizer_kwargs, "stepsize": 0.01, } default_kwargs.update(kwargs) obj = opt_wrapper(func) res = basinhopping(obj, initial_p, **default_kwargs) success = res.lowest_optimization_result.success else: obj = opt_wrapper(func) self._check_blocked_keywords(kwargs, ("args", "bounds", "method")) res = minimize( obj, initial_p, args=(hw_args,), bounds=relevant_bounds, method=method, **kwargs, ) success = res.success # finally transform to restricted space params[sel] = res.x params[:3] = to_restricted(params, sel, hw_args.bounds) res.x = params[sel] if not success: from statsmodels.tools.sm_exceptions import ConvergenceWarning warnings.warn( "Optimization failed to converge. Check mle_retvals.", ConvergenceWarning, ) params[sel] = res.x data.unpack_parameters(params) data.params = params data.mask = sel data.mle_retvals = res return data @deprecate_kwarg("smoothing_slope", "smoothing_trend") @deprecate_kwarg("initial_slope", "initial_trend") @deprecate_kwarg("damping_slope", "damping_trend") def fit( self, smoothing_level=None, smoothing_trend=None, smoothing_seasonal=None, damping_trend=None, *, optimized=True, remove_bias=False, start_params=None, method=None, minimize_kwargs=None, use_brute=True, use_boxcox=None, use_basinhopping=None, initial_level=None, initial_trend=None, ): """ Fit the model Parameters ---------- smoothing_level : float, optional The alpha value of the simple exponential smoothing, if the value is set then this value will be used as the value. smoothing_trend : float, optional The beta value of the Holt's trend method, if the value is set then this value will be used as the value. smoothing_seasonal : float, optional The gamma value of the holt winters seasonal method, if the value is set then this value will be used as the value. damping_trend : float, optional The phi value of the damped method, if the value is set then this value will be used as the value. optimized : bool, optional Estimate model parameters by maximizing the log-likelihood. remove_bias : bool, optional Remove bias from forecast values and fitted values by enforcing that the average residual is equal to zero. start_params : array_like, optional Starting values to used when optimizing the fit. If not provided, starting values are determined using a combination of grid search and reasonable values based on the initial values of the data. See the notes for the structure of the model parameters. method : str, default "L-BFGS-B" The minimizer used. Valid options are "L-BFGS-B" , "TNC", "SLSQP" (default), "Powell", "trust-constr", "basinhopping" (also "bh") and "least_squares" (also "ls"). basinhopping tries multiple starting values in an attempt to find a global minimizer in non-convex problems, and so is slower than the others. minimize_kwargs : dict[str, Any] A dictionary of keyword arguments passed to SciPy's minimize function if method is one of "L-BFGS-B", "TNC", "SLSQP", "Powell", or "trust-constr", or SciPy's basinhopping or least_squares functions. The valid keywords are optimizer specific. Consult SciPy's documentation for the full set of options. use_brute : bool, optional Search for good starting values using a brute force (grid) optimizer. If False, a naive set of starting values is used. use_boxcox : {True, False, 'log', float}, optional Should the Box-Cox transform be applied to the data first? If 'log' then apply the log. If float then use the value as lambda. .. deprecated:: 0.12 Set use_boxcox when constructing the model use_basinhopping : bool, optional Deprecated. Using Basin Hopping optimizer to find optimal values. Use ``method`` instead. .. deprecated:: 0.12 Use ``method`` instead. initial_level : float, optional Value to use when initializing the fitted level. .. deprecated:: 0.12 Set initial_level when constructing the model initial_trend : float, optional Value to use when initializing the fitted trend. .. deprecated:: 0.12 Set initial_trend when constructing the model or set initialization_method. Returns ------- HoltWintersResults See statsmodels.tsa.holtwinters.HoltWintersResults. Notes ----- This is a full implementation of the holt winters exponential smoothing as per [1]. This includes all the unstable methods as well as the stable methods. The implementation of the library covers the functionality of the R library as much as possible whilst still being Pythonic. The parameters are ordered [alpha, beta, gamma, initial_level, initial_trend, phi] which are then followed by m seasonal values if the model contains a seasonal smoother. Any parameter not relevant for the model is omitted. For example, a model that has a level and a seasonal component, but no trend and is not damped, would have starting values [alpha, gamma, initial_level, s0, s1, ..., s] where sj is the initial value for seasonal component j. References ---------- [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. """ # Variable renames to alpha,beta, etc as this helps with following the # mathematical notation in general alpha = float_like(smoothing_level, "smoothing_level", True) beta = float_like(smoothing_trend, "smoothing_trend", True) gamma = float_like(smoothing_seasonal, "smoothing_seasonal", True) phi = float_like(damping_trend, "damping_trend", True) initial_level = float_like(initial_level, "initial_level", True) initial_trend = float_like(initial_trend, "initial_trend", True) start_params = array_like(start_params, "start_params", optional=True) minimize_kwargs = dict_like( minimize_kwargs, "minimize_kwargs", optional=True ) minimize_kwargs = {} if minimize_kwargs is None else minimize_kwargs use_basinhopping = bool_like( use_basinhopping, "use_basinhopping", optional=True ) supported_methods = ("basinhopping", "bh") supported_methods += ("least_squares", "ls") supported_methods += ( "L-BFGS-B", "TNC", "SLSQP", "Powell", "trust-constr", ) method = string_like( method, "method", options=supported_methods, lower=False, optional=True, ) if initial_level is not None or initial_trend is not None: if self._initialization_method is not None: raise ValueError( "Initial values were set during model construction. These " "cannot be changed during fit." ) warnings.warn( "Setting initial values during fit is deprecated and will be " "removed after 0.13. These should be set during model " "initialization.", FutureWarning, ) if use_boxcox is not None: if self._use_boxcox is not None: raise ValueError( "use_boxcox was set at model initialization and cannot " "be changed" ) warnings.warn( "Setting use_boxcox during fit has been deprecated and will " "be removed after 0.13. It must be set during model " "initialization.", FutureWarning, ) elif self._use_boxcox is None: use_boxcox = False else: use_boxcox = self._use_boxcox if use_basinhopping is not None: if method is not None: raise ValueError( "use_basinhopping has been deprecated and method has " "also been set. These both cannot be used. Use only " "method instead." ) if use_basinhopping: method = "basinhopping" warnings.warn( "use_basinhopping is deprecated. Set optimization method " "using 'method'. This option will be removed after 0.13 " "is released.", FutureWarning, ) data = self._data damped = self.damped_trend phi = phi if damped else 1.0 if self._use_boxcox is None: if use_boxcox == "log": lamda = 0.0 y = boxcox(data, lamda) elif isinstance(use_boxcox, float): lamda = use_boxcox y = boxcox(data, lamda) elif use_boxcox: y, lamda = boxcox(data) # use_boxcox = lamda else: y = data.squeeze() else: y = self._y self._y = y res = _OptConfig() res.alpha = alpha res.beta = beta res.phi = phi res.gamma = gamma res.level = initial_level res.trend = initial_trend res.seasonal = None res.y = y res.params = start_params res.mle_retvals = res.mask = None method = "SLSQP" if method is None else method if optimized: res = self._optimize_parameters( res, use_brute, method, minimize_kwargs ) else: l0, b0, s0 = self.initial_values( initial_level=initial_level, initial_trend=initial_trend ) res.level = l0 res.trend = b0 res.seasonal = s0 if self._fixed_parameters: fp = self._fixed_parameters res.alpha = fp.get("smoothing_level", res.alpha) res.beta = fp.get("smoothing_trend", res.beta) res.gamma = fp.get("smoothing_seasonal", res.gamma) res.phi = fp.get("damping_trend", res.phi) res.level = fp.get("initial_level", res.level) res.trend = fp.get("initial_trend", res.trend) res.seasonal = fp.get("initial_seasonal", res.seasonal) hwfit = self._predict( h=0, smoothing_level=res.alpha, smoothing_trend=res.beta, smoothing_seasonal=res.gamma, damping_trend=res.phi, initial_level=res.level, initial_trend=res.trend, initial_seasons=res.seasonal, use_boxcox=use_boxcox, remove_bias=remove_bias, is_optimized=res.mask, ) hwfit._results.mle_retvals = res.mle_retvals return hwfit def initial_values( self, initial_level=None, initial_trend=None, force=False ): """ Compute initial values used in the exponential smoothing recursions. Parameters ---------- initial_level : {float, None} The initial value used for the level component. initial_trend : {float, None} The initial value used for the trend component. force : bool Force the calculation even if initial values exist. Returns ------- initial_level : float The initial value used for the level component. initial_trend : {float, None} The initial value used for the trend component. initial_seasons : list The initial values used for the seasonal components. Notes ----- Convenience function the exposes the values used to initialize the recursions. When optimizing parameters these are used as starting values. Method used to compute the initial value depends on when components are included in the model. In a simple exponential smoothing model without trend or a seasonal components, the initial value is set to the first observation. When a trend is added, the trend is initialized either using y[1]/y[0], if multiplicative, or y[1]-y[0]. When the seasonal component is added the initialization adapts to account for the modified structure. """ if self._initialization_method is not None and not force: return ( self._initial_level, self._initial_trend, self._initial_seasonal, ) y = self._y trend = self.trend seasonal = self.seasonal has_seasonal = self.has_seasonal has_trend = self.has_trend m = self.seasonal_periods l0 = initial_level b0 = initial_trend if has_seasonal: l0 = y[np.arange(self.nobs) % m == 0].mean() if l0 is None else l0 if b0 is None and has_trend: # TODO: Fix for short m lead, lag = y[m : m + m], y[:m] if trend == "mul": b0 = np.exp((np.log(lead.mean()) - np.log(lag.mean())) / m) else: b0 = ((lead - lag) / m).mean() s0 = list(y[:m] / l0) if seasonal == "mul" else list(y[:m] - l0) elif has_trend: l0 = y[0] if l0 is None else l0 if b0 is None: b0 = y[1] / y[0] if trend == "mul" else y[1] - y[0] s0 = [] else: if l0 is None: l0 = y[0] b0 = None s0 = [] return l0, b0, s0 @deprecate_kwarg("smoothing_slope", "smoothing_trend") @deprecate_kwarg("damping_slope", "damping_trend") def _predict( self, h=None, smoothing_level=None, smoothing_trend=None, smoothing_seasonal=None, initial_level=None, initial_trend=None, damping_trend=None, initial_seasons=None, use_boxcox=None, lamda=None, remove_bias=None, is_optimized=None, ): """ Helper prediction function Parameters ---------- h : int, optional The number of time steps to forecast ahead. """ # Variable renames to alpha, beta, etc as this helps with following the # mathematical notation in general alpha = smoothing_level beta = smoothing_trend gamma = smoothing_seasonal phi = damping_trend # Start in sample and out of sample predictions data = self.endog damped = self.damped_trend has_seasonal = self.has_seasonal has_trend = self.has_trend trend = self.trend seasonal = self.seasonal m = self.seasonal_periods phi = phi if damped else 1.0 if use_boxcox == "log": lamda = 0.0 y = boxcox(data, 0.0) elif isinstance(use_boxcox, float): lamda = use_boxcox y = boxcox(data, lamda) elif use_boxcox: y, lamda = boxcox(data) else: lamda = None y = data.squeeze() if np.ndim(y) != 1: raise NotImplementedError("Only 1 dimensional data supported") y_alpha = np.zeros((self.nobs,)) y_gamma = np.zeros((self.nobs,)) alphac = 1 - alpha y_alpha[:] = alpha * y betac = 1 - beta if beta is not None else 0 gammac = 1 - gamma if gamma is not None else 0 if has_seasonal: y_gamma[:] = gamma * y lvls = np.zeros((self.nobs + h + 1,)) b = np.zeros((self.nobs + h + 1,)) s = np.zeros((self.nobs + h + m + 1,)) lvls[0] = initial_level b[0] = initial_trend s[:m] = initial_seasons phi_h = ( np.cumsum(np.repeat(phi, h + 1) ** np.arange(1, h + 1 + 1)) if damped else np.arange(1, h + 1 + 1) ) trended = {"mul": np.multiply, "add": np.add, None: lambda l, b: l}[ trend ] detrend = {"mul": np.divide, "add": np.subtract, None: lambda l, b: 0}[ trend ] dampen = {"mul": np.power, "add": np.multiply, None: lambda b, phi: 0}[ trend ] nobs = self.nobs if seasonal == "mul": for i in range(1, nobs + 1): lvls[i] = y_alpha[i - 1] / s[i - 1] + ( alphac * trended(lvls[i - 1], dampen(b[i - 1], phi)) ) if has_trend: b[i] = (beta * detrend(lvls[i], lvls[i - 1])) + ( betac * dampen(b[i - 1], phi) ) s[i + m - 1] = y_gamma[i - 1] / trended( lvls[i - 1], dampen(b[i - 1], phi) ) + (gammac * s[i - 1]) _trend = b[1 : nobs + 1].copy() season = s[m : nobs + m].copy() lvls[nobs:] = lvls[nobs] if has_trend: b[:nobs] = dampen(b[:nobs], phi) b[nobs:] = dampen(b[nobs], phi_h) trend = trended(lvls, b) s[nobs + m - 1 :] = [ s[(nobs - 1) + j % m] for j in range(h + 1 + 1) ] fitted = trend * s[:-m] elif seasonal == "add": for i in range(1, nobs + 1): lvls[i] = ( y_alpha[i - 1] - (alpha * s[i - 1]) + (alphac * trended(lvls[i - 1], dampen(b[i - 1], phi))) ) if has_trend: b[i] = (beta * detrend(lvls[i], lvls[i - 1])) + ( betac * dampen(b[i - 1], phi) ) s[i + m - 1] = ( y_gamma[i - 1] - (gamma * trended(lvls[i - 1], dampen(b[i - 1], phi))) + (gammac * s[i - 1]) ) _trend = b[1 : nobs + 1].copy() season = s[m : nobs + m].copy() lvls[nobs:] = lvls[nobs] if has_trend: b[:nobs] = dampen(b[:nobs], phi) b[nobs:] = dampen(b[nobs], phi_h) trend = trended(lvls, b) s[nobs + m - 1 :] = [ s[(nobs - 1) + j % m] for j in range(h + 1 + 1) ] fitted = trend + s[:-m] else: for i in range(1, nobs + 1): lvls[i] = y_alpha[i - 1] + ( alphac * trended(lvls[i - 1], dampen(b[i - 1], phi)) ) if has_trend: b[i] = (beta * detrend(lvls[i], lvls[i - 1])) + ( betac * dampen(b[i - 1], phi) ) _trend = b[1 : nobs + 1].copy() season = s[m : nobs + m].copy() lvls[nobs:] = lvls[nobs] if has_trend: b[:nobs] = dampen(b[:nobs], phi) b[nobs:] = dampen(b[nobs], phi_h) trend = trended(lvls, b) fitted = trend level = lvls[1 : nobs + 1].copy() if use_boxcox or use_boxcox == "log" or isinstance(use_boxcox, float): fitted = inv_boxcox(fitted, lamda) err = fitted[: -h - 1] - data sse = err.T @ err # (s0 + gamma) + (b0 + beta) + (l0 + alpha) + phi k = m * has_seasonal + 2 * has_trend + 2 + 1 * damped aic = self.nobs * np.log(sse / self.nobs) + k * 2 if self.nobs - k - 3 > 0: aicc_penalty = (2 * (k + 2) * (k + 3)) / (self.nobs - k - 3) else: aicc_penalty = np.inf aicc = aic + aicc_penalty bic = self.nobs * np.log(sse / self.nobs) + k * np.log(self.nobs) resid = data - fitted[: -h - 1] if remove_bias: fitted += resid.mean() self.params = { "smoothing_level": alpha, "smoothing_trend": beta, "smoothing_seasonal": gamma, "damping_trend": phi if damped else np.nan, "initial_level": lvls[0], "initial_trend": b[0] / phi if phi > 0 else 0, "initial_seasons": s[:m], "use_boxcox": use_boxcox, "lamda": lamda, "remove_bias": remove_bias, } # Format parameters into a DataFrame codes = ["alpha", "beta", "gamma", "l.0", "b.0", "phi"] codes += ["s.{0}".format(i) for i in range(m)] idx = [ "smoothing_level", "smoothing_trend", "smoothing_seasonal", "initial_level", "initial_trend", "damping_trend", ] idx += ["initial_seasons.{0}".format(i) for i in range(m)] formatted = [alpha, beta, gamma, lvls[0], b[0], phi] formatted += s[:m].tolist() formatted = list(map(lambda v: np.nan if v is None else v, formatted)) formatted = np.array(formatted) if is_optimized is None: optimized = np.zeros(len(codes), dtype=bool) else: optimized = is_optimized.astype(bool) included = [True, has_trend, has_seasonal, True, has_trend, damped] included += [True] * m formatted = pd.DataFrame( [[c, f, o] for c, f, o in zip(codes, formatted, optimized)], columns=["name", "param", "optimized"], index=idx, ) formatted = formatted.loc[included] hwfit = HoltWintersResults( self, self.params, fittedfcast=fitted, fittedvalues=fitted[: -h - 1], fcastvalues=fitted[-h - 1 :], sse=sse, level=level, trend=_trend, season=season, aic=aic, bic=bic, aicc=aicc, resid=resid, k=k, params_formatted=formatted, optimized=optimized, ) return HoltWintersResultsWrapper(hwfit) class SimpleExpSmoothing(ExponentialSmoothing): """ Simple Exponential Smoothing Parameters ---------- endog : array_like The time series to model. initialization_method : str, optional Method for initialize the recursions. One of: * None * 'estimated' * 'heuristic' * 'legacy-heuristic' * 'known' None defaults to the pre-0.12 behavior where initial values are passed as part of ``fit``. If any of the other values are passed, then the initial values must also be set when constructing the model. If 'known' initialization is used, then `initial_level` must be passed, as well as `initial_trend` and `initial_seasonal` if applicable. Default is 'estimated'. "legacy-heuristic" uses the same values that were used in statsmodels 0.11 and earlier. initial_level : float, optional The initial level component. Required if estimation method is "known". If set using either "estimated" or "heuristic" this value is used. This allows one or more of the initial values to be set while deferring to the heuristic for others or estimating the unset parameters. See Also -------- ExponentialSmoothing Exponential smoothing with trend and seasonal components. Holt Exponential smoothing with a trend component. Notes ----- This is a full implementation of the simple exponential smoothing as per [1]_. `SimpleExpSmoothing` is a restricted version of :class:`ExponentialSmoothing`. References ---------- .. [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. """ def __init__( self, endog, initialization_method=None, # Future: 'estimated', initial_level=None, ): super(SimpleExpSmoothing, self).__init__( endog, initialization_method=initialization_method, initial_level=initial_level, ) def fit( self, smoothing_level=None, *, optimized=True, start_params=None, initial_level=None, use_brute=True, use_boxcox=None, remove_bias=False, method=None, minimize_kwargs=None, ): """ Fit the model Parameters ---------- smoothing_level : float, optional The smoothing_level value of the simple exponential smoothing, if the value is set then this value will be used as the value. optimized : bool, optional Estimate model parameters by maximizing the log-likelihood. start_params : ndarray, optional Starting values to used when optimizing the fit. If not provided, starting values are determined using a combination of grid search and reasonable values based on the initial values of the data. initial_level : float, optional Value to use when initializing the fitted level. use_brute : bool, optional Search for good starting values using a brute force (grid) optimizer. If False, a naive set of starting values is used. use_boxcox : {True, False, 'log', float}, optional Should the Box-Cox transform be applied to the data first? If 'log' then apply the log. If float then use the value as lambda. remove_bias : bool, optional Remove bias from forecast values and fitted values by enforcing that the average residual is equal to zero. method : str, default "L-BFGS-B" The minimizer used. Valid options are "L-BFGS-B" (default), "TNC", "SLSQP", "Powell", "trust-constr", "basinhopping" (also "bh") and "least_squares" (also "ls"). basinhopping tries multiple starting values in an attempt to find a global minimizer in non-convex problems, and so is slower than the others. minimize_kwargs : dict[str, Any] A dictionary of keyword arguments passed to SciPy's minimize function if method is one of "L-BFGS-B" (default), "TNC", "SLSQP", "Powell", or "trust-constr", or SciPy's basinhopping or least_squares. The valid keywords are optimizer specific. Consult SciPy's documentation for the full set of options. Returns ------- HoltWintersResults See statsmodels.tsa.holtwinters.HoltWintersResults. Notes ----- This is a full implementation of the simple exponential smoothing as per [1]. References ---------- [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. """ return super(SimpleExpSmoothing, self).fit( smoothing_level=smoothing_level, optimized=optimized, start_params=start_params, initial_level=initial_level, use_brute=use_brute, remove_bias=remove_bias, use_boxcox=use_boxcox, method=method, minimize_kwargs=minimize_kwargs, ) class Holt(ExponentialSmoothing): """ Holt's Exponential Smoothing Parameters ---------- endog : array_like The time series to model. exponential : bool, optional Type of trend component. damped_trend : bool, optional Should the trend component be damped. initialization_method : str, optional Method for initialize the recursions. One of: * None * 'estimated' * 'heuristic' * 'legacy-heuristic' * 'known' None defaults to the pre-0.12 behavior where initial values are passed as part of ``fit``. If any of the other values are passed, then the initial values must also be set when constructing the model. If 'known' initialization is used, then `initial_level` must be passed, as well as `initial_trend` and `initial_seasonal` if applicable. Default is 'estimated'. "legacy-heuristic" uses the same values that were used in statsmodels 0.11 and earlier. initial_level : float, optional The initial level component. Required if estimation method is "known". If set using either "estimated" or "heuristic" this value is used. This allows one or more of the initial values to be set while deferring to the heuristic for others or estimating the unset parameters. initial_trend : float, optional The initial trend component. Required if estimation method is "known". If set using either "estimated" or "heuristic" this value is used. This allows one or more of the initial values to be set while deferring to the heuristic for others or estimating the unset parameters. See Also -------- ExponentialSmoothing Exponential smoothing with trend and seasonal components. SimpleExpSmoothing Basic exponential smoothing with only a level component. Notes ----- This is a full implementation of the Holt's exponential smoothing as per [1]_. `Holt` is a restricted version of :class:`ExponentialSmoothing`. References ---------- .. [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. """ @deprecate_kwarg("damped", "damped_trend") def __init__( self, endog, exponential=False, damped_trend=False, initialization_method=None, # Future: 'estimated', initial_level=None, initial_trend=None, ): trend = "mul" if exponential else "add" super(Holt, self).__init__( endog, trend=trend, damped_trend=damped_trend, initialization_method=initialization_method, initial_level=initial_level, initial_trend=initial_trend, ) @deprecate_kwarg("smoothing_slope", "smoothing_trend") @deprecate_kwarg("initial_slope", "initial_trend") @deprecate_kwarg("damping_slope", "damping_trend") def fit( self, smoothing_level=None, smoothing_trend=None, *, damping_trend=None, optimized=True, start_params=None, initial_level=None, initial_trend=None, use_brute=True, use_boxcox=None, remove_bias=False, method=None, minimize_kwargs=None, ): """ Fit the model Parameters ---------- smoothing_level : float, optional The alpha value of the simple exponential smoothing, if the value is set then this value will be used as the value. smoothing_trend : float, optional The beta value of the Holt's trend method, if the value is set then this value will be used as the value. damping_trend : float, optional The phi value of the damped method, if the value is set then this value will be used as the value. optimized : bool, optional Estimate model parameters by maximizing the log-likelihood. start_params : ndarray, optional Starting values to used when optimizing the fit. If not provided, starting values are determined using a combination of grid search and reasonable values based on the initial values of the data. initial_level : float, optional Value to use when initializing the fitted level. .. deprecated:: 0.12 Set initial_level when constructing the model initial_trend : float, optional Value to use when initializing the fitted trend. .. deprecated:: 0.12 Set initial_trend when constructing the model use_brute : bool, optional Search for good starting values using a brute force (grid) optimizer. If False, a naive set of starting values is used. use_boxcox : {True, False, 'log', float}, optional Should the Box-Cox transform be applied to the data first? If 'log' then apply the log. If float then use the value as lambda. remove_bias : bool, optional Remove bias from forecast values and fitted values by enforcing that the average residual is equal to zero. method : str, default "L-BFGS-B" The minimizer used. Valid options are "L-BFGS-B" (default), "TNC", "SLSQP", "Powell", "trust-constr", "basinhopping" (also "bh") and "least_squares" (also "ls"). basinhopping tries multiple starting values in an attempt to find a global minimizer in non-convex problems, and so is slower than the others. minimize_kwargs : dict[str, Any] A dictionary of keyword arguments passed to SciPy's minimize function if method is one of "L-BFGS-B" (default), "TNC", "SLSQP", "Powell", or "trust-constr", or SciPy's basinhopping or least_squares. The valid keywords are optimizer specific. Consult SciPy's documentation for the full set of options. Returns ------- HoltWintersResults See statsmodels.tsa.holtwinters.HoltWintersResults. Notes ----- This is a full implementation of the Holt's exponential smoothing as per [1]. References ---------- [1] Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014. """ return super(Holt, self).fit( smoothing_level=smoothing_level, smoothing_trend=smoothing_trend, damping_trend=damping_trend, optimized=optimized, start_params=start_params, initial_level=initial_level, initial_trend=initial_trend, use_brute=use_brute, use_boxcox=use_boxcox, remove_bias=remove_bias, method=method, minimize_kwargs=minimize_kwargs, ) statsmodels-0.12.2/statsmodels/tsa/holtwinters/results.py000066400000000000000000000632731400612667500237460ustar00rootroot00000000000000import numpy as np import pandas as pd from scipy.special import inv_boxcox from scipy.stats import ( _distn_infrastructure, boxcox, rv_continuous, rv_discrete, ) from statsmodels.base.data import PandasData from statsmodels.base.model import Results from statsmodels.base.wrapper import ( ResultsWrapper, populate_wrapper, union_dicts, ) class HoltWintersResults(Results): """ Results from fitting Exponential Smoothing models. Parameters ---------- model : ExponentialSmoothing instance The fitted model instance. params : dict All the parameters for the Exponential Smoothing model. sse : float The sum of squared errors. aic : float The Akaike information criterion. aicc : float AIC with a correction for finite sample sizes. bic : float The Bayesian information criterion. optimized : bool Flag indicating whether the model parameters were optimized to fit the data. level : ndarray An array of the levels values that make up the fitted values. trend : ndarray An array of the trend values that make up the fitted values. season : ndarray An array of the seasonal values that make up the fitted values. params_formatted : pd.DataFrame DataFrame containing all parameters, their short names and a flag indicating whether the parameter's value was optimized to fit the data. resid : ndarray An array of the residuals of the fittedvalues and actual values. k : int The k parameter used to remove the bias in AIC, BIC etc. fittedvalues : ndarray An array of the fitted values. Fitted by the Exponential Smoothing model. fittedfcast : ndarray An array of both the fitted values and forecast values. fcastvalues : ndarray An array of the forecast values forecast by the Exponential Smoothing model. mle_retvals : {None, scipy.optimize.optimize.OptimizeResult} Optimization results if the parameters were optimized to fit the data. """ def __init__( self, model, params, sse, aic, aicc, bic, optimized, level, trend, season, params_formatted, resid, k, fittedvalues, fittedfcast, fcastvalues, mle_retvals=None, ): self.data = model.data super(HoltWintersResults, self).__init__(model, params) self._model = model self._sse = sse self._aic = aic self._aicc = aicc self._bic = bic self._optimized = optimized self._level = level self._trend = trend self._season = season self._params_formatted = params_formatted self._fittedvalues = fittedvalues self._fittedfcast = fittedfcast self._fcastvalues = fcastvalues self._resid = resid self._k = k self._mle_retvals = mle_retvals @property def aic(self): """ The Akaike information criterion. """ return self._aic @property def aicc(self): """ AIC with a correction for finite sample sizes. """ return self._aicc @property def bic(self): """ The Bayesian information criterion. """ return self._bic @property def sse(self): """ The sum of squared errors between the data and the fittted value. """ return self._sse @property def model(self): """ The model used to produce the results instance. """ return self._model @model.setter def model(self, value): self._model = value @property def level(self): """ An array of the levels values that make up the fitted values. """ return self._level @property def optimized(self): """ Flag indicating if model parameters were optimized to fit the data. """ return self._optimized @property def slope(self): """ An array of the slope values that make up the fitted values. .. deprecated:: 0.12 Use the trend property instead. """ import warnings warnings.warn( "slope is deprecated and will be removed after 0.13", FutureWarning ) return self._trend @property def trend(self): """ An array of the trend values that make up the fitted values. """ return self._trend @property def season(self): """ An array of the seasonal values that make up the fitted values. """ return self._season @property def params_formatted(self): """ DataFrame containing all parameters Contains short names and a flag indicating whether the parameter's value was optimized to fit the data. """ return self._params_formatted @property def fittedvalues(self): """ An array of the fitted values """ return self._fittedvalues @property def fittedfcast(self): """ An array of both the fitted values and forecast values. """ return self._fittedfcast @property def fcastvalues(self): """ An array of the forecast values """ return self._fcastvalues @property def resid(self): """ An array of the residuals of the fittedvalues and actual values. """ return self._resid @property def k(self): """ The k parameter used to remove the bias in AIC, BIC etc. """ return self._k @property def mle_retvals(self): """ Optimization results if the parameters were optimized to fit the data. """ return self._mle_retvals @mle_retvals.setter def mle_retvals(self, value): self._mle_retvals = value def predict(self, start=None, end=None): """ In-sample prediction and out-of-sample forecasting Parameters ---------- start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. Returns ------- forecast : ndarray Array of out of sample forecasts. """ return self.model.predict(self.params, start, end) def forecast(self, steps=1): """ Out-of-sample forecasts Parameters ---------- steps : int The number of out of sample forecasts from the end of the sample. Returns ------- forecast : ndarray Array of out of sample forecasts """ try: freq = getattr(self.model._index, "freq", 1) if isinstance(freq, int): start = self.model._index.shape[0] end = start + steps - 1 else: start = self.model._index[-1] + freq end = self.model._index[-1] + steps * freq return self.model.predict(self.params, start=start, end=end) except (AttributeError, ValueError): # May occur when the index does not have a freq return self.model._predict(h=steps, **self.params).fcastvalues def summary(self): """ Summarize the fitted Model Returns ------- smry : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary """ from statsmodels.iolib.summary import Summary from statsmodels.iolib.table import SimpleTable model = self.model title = model.__class__.__name__ + " Model Results" dep_variable = "endog" orig_endog = self.model.data.orig_endog if isinstance(orig_endog, pd.DataFrame): dep_variable = orig_endog.columns[0] elif isinstance(orig_endog, pd.Series): dep_variable = orig_endog.name seasonal_periods = ( None if self.model.seasonal is None else self.model.seasonal_periods ) lookup = { "add": "Additive", "additive": "Additive", "mul": "Multiplicative", "multiplicative": "Multiplicative", None: "None", } transform = self.params["use_boxcox"] box_cox_transform = True if transform else False box_cox_coeff = ( transform if isinstance(transform, str) else self.params["lamda"] ) if isinstance(box_cox_coeff, float): box_cox_coeff = "{:>10.5f}".format(box_cox_coeff) top_left = [ ("Dep. Variable:", [dep_variable]), ("Model:", [model.__class__.__name__]), ("Optimized:", [str(np.any(self.optimized))]), ("Trend:", [lookup[self.model.trend]]), ("Seasonal:", [lookup[self.model.seasonal]]), ("Seasonal Periods:", [str(seasonal_periods)]), ("Box-Cox:", [str(box_cox_transform)]), ("Box-Cox Coeff.:", [str(box_cox_coeff)]), ] top_right = [ ("No. Observations:", [str(len(self.model.endog))]), ("SSE", ["{:5.3f}".format(self.sse)]), ("AIC", ["{:5.3f}".format(self.aic)]), ("BIC", ["{:5.3f}".format(self.bic)]), ("AICC", ["{:5.3f}".format(self.aicc)]), ("Date:", None), ("Time:", None), ] smry = Summary() smry.add_table_2cols( self, gleft=top_left, gright=top_right, title=title ) formatted = self.params_formatted # type: pd.DataFrame def _fmt(x): abs_x = np.abs(x) scale = 1 if abs_x != 0: scale = int(np.log10(abs_x)) if scale > 4 or scale < -3: return "{:>20.5g}".format(x) dec = min(7 - scale, 7) fmt = "{{:>20.{0}f}}".format(dec) return fmt.format(x) tab = [] for _, vals in formatted.iterrows(): tab.append( [ _fmt(vals.iloc[1]), "{0:>20}".format(vals.iloc[0]), "{0:>20}".format(str(bool(vals.iloc[2]))), ] ) params_table = SimpleTable( tab, headers=["coeff", "code", "optimized"], title="", stubs=list(formatted.index), ) smry.tables.append(params_table) return smry def simulate( self, nsimulations, anchor=None, repetitions=1, error="add", random_errors=None, random_state=None, ): r""" Random simulations using the state space formulation. Parameters ---------- nsimulations : int The number of simulation steps. anchor : int, str, or datetime, optional First period for simulation. The simulation will be conditional on all existing datapoints prior to the `anchor`. Type depends on the index of the given `endog` in the model. Two special cases are the strings 'start' and 'end'. `start` refers to beginning the simulation at the first period of the sample, and `end` refers to beginning the simulation at the first period after the sample. Integer values can run from 0 to `nobs`, or can be negative to apply negative indexing. Finally, if a date/time index was provided to the model, then this argument can be a date string to parse or a datetime type. Default is 'end'. repetitions : int, optional Number of simulated paths to generate. Default is 1 simulated path. error : {"add", "mul", "additive", "multiplicative"}, optional Error model for state space formulation. Default is ``"add"``. random_errors : optional Specifies how the random errors should be obtained. Can be one of the following: * ``None``: Random normally distributed values with variance estimated from the fit errors drawn from numpy's standard RNG (can be seeded with the `random_state` argument). This is the default option. * A distribution function from ``scipy.stats``, e.g. ``scipy.stats.norm``: Fits the distribution function to the fit errors and draws from the fitted distribution. Note the difference between ``scipy.stats.norm`` and ``scipy.stats.norm()``, the latter one is a frozen distribution function. * A frozen distribution function from ``scipy.stats``, e.g. ``scipy.stats.norm(scale=2)``: Draws from the frozen distribution function. * A ``np.ndarray`` with shape (`nsimulations`, `repetitions`): Uses the given values as random errors. * ``"bootstrap"``: Samples the random errors from the fit errors. random_state : int or np.random.RandomState, optional A seed for the random number generator or a ``np.random.RandomState`` object. Only used if `random_errors` is ``None``. Default is ``None``. Returns ------- sim : pd.Series, pd.DataFrame or np.ndarray An ``np.ndarray``, ``pd.Series``, or ``pd.DataFrame`` of simulated values. If the original data was a ``pd.Series`` or ``pd.DataFrame``, `sim` will be a ``pd.Series`` if `repetitions` is 1, and a ``pd.DataFrame`` of shape (`nsimulations`, `repetitions`) else. Otherwise, if `repetitions` is 1, a ``np.ndarray`` of shape (`nsimulations`,) is returned, and if `repetitions` is not 1 a ``np.ndarray`` of shape (`nsimulations`, `repetitions`) is returned. Notes ----- The simulation is based on the state space model of the Holt-Winter's methods. The state space model assumes that the true value at time :math:`t` is randomly distributed around the prediction value. If using the additive error model, this means: .. math:: y_t &= \hat{y}_{t|t-1} + e_t\\ e_t &\sim \mathcal{N}(0, \sigma^2) Using the multiplicative error model: .. math:: y_t &= \hat{y}_{t|t-1} \cdot (1 + e_t)\\ e_t &\sim \mathcal{N}(0, \sigma^2) Inserting these equations into the smoothing equation formulation leads to the state space equations. The notation used here follows [1]_. Additionally, .. math:: B_t &= b_{t-1} \circ_d \phi\\ L_t &= l_{t-1} \circ_b B_t\\ S_t &= s_{t-m}\\ Y_t &= L_t \circ_s S_t, where :math:`\circ_d` is the operation linking trend and damping parameter (multiplication if the trend is additive, power if the trend is multiplicative), :math:`\circ_b` is the operation linking level and trend (addition if the trend is additive, multiplication if the trend is multiplicative), and :math:`\circ_s` is the operation linking seasonality to the rest. The state space equations can then be formulated as .. math:: y_t &= Y_t + \eta \cdot e_t\\ l_t &= L_t + \alpha \cdot (M_e \cdot L_t + \kappa_l) \cdot e_t\\ b_t &= B_t + \beta \cdot (M_e \cdot B_t + \kappa_b) \cdot e_t\\ s_t &= S_t + \gamma \cdot (M_e \cdot S_t + \kappa_s) \cdot e_t\\ with .. math:: \eta &= \begin{cases} Y_t\quad\text{if error is multiplicative}\\ 1\quad\text{else} \end{cases}\\ M_e &= \begin{cases} 1\quad\text{if error is multiplicative}\\ 0\quad\text{else} \end{cases}\\ and, when using the additive error model, .. math:: \kappa_l &= \begin{cases} \frac{1}{S_t}\quad \text{if seasonality is multiplicative}\\ 1\quad\text{else} \end{cases}\\ \kappa_b &= \begin{cases} \frac{\kappa_l}{l_{t-1}}\quad \text{if trend is multiplicative}\\ \kappa_l\quad\text{else} \end{cases}\\ \kappa_s &= \begin{cases} \frac{1}{L_t}\quad\text{if seasonality is multiplicative}\\ 1\quad\text{else} \end{cases} When using the multiplicative error model .. math:: \kappa_l &= \begin{cases} 0\quad \text{if seasonality is multiplicative}\\ S_t\quad\text{else} \end{cases}\\ \kappa_b &= \begin{cases} \frac{\kappa_l}{l_{t-1}}\quad \text{if trend is multiplicative}\\ \kappa_l + l_{t-1}\quad\text{else} \end{cases}\\ \kappa_s &= \begin{cases} 0\quad\text{if seasonality is multiplicative}\\ L_t\quad\text{else} \end{cases} References ---------- .. [1] Hyndman, R.J., & Athanasopoulos, G. (2018) *Forecasting: principles and practice*, 2nd edition, OTexts: Melbourne, Australia. OTexts.com/fpp2. Accessed on February 28th 2020. """ # check inputs if error in ["additive", "multiplicative"]: error = {"additive": "add", "multiplicative": "mul"}[error] if error not in ["add", "mul"]: raise ValueError("error must be 'add' or 'mul'!") # Get the starting location if anchor is None or anchor == "end": start_idx = self.model.nobs elif anchor == "start": start_idx = 0 else: start_idx, _, _ = self.model._get_index_loc(anchor) if isinstance(start_idx, slice): start_idx = start_idx.start if start_idx < 0: start_idx += self.model.nobs if start_idx > self.model.nobs: raise ValueError("Cannot anchor simulation outside of the sample.") # get Holt-Winters settings and parameters trend = self.model.trend damped = self.model.damped_trend seasonal = self.model.seasonal use_boxcox = self.params["use_boxcox"] lamda = self.params["lamda"] alpha = self.params["smoothing_level"] beta = self.params["smoothing_trend"] gamma = self.params["smoothing_seasonal"] phi = self.params["damping_trend"] # if model has no seasonal component, use 1 as period length m = max(self.model.seasonal_periods, 1) n_params = ( 2 + 2 * self.model.has_trend + (m + 1) * self.model.has_seasonal + damped ) mul_seasonal = seasonal == "mul" mul_trend = trend == "mul" mul_error = error == "mul" # define trend, damping and seasonality operations if mul_trend: op_b = np.multiply op_d = np.power neutral_b = 1 else: op_b = np.add op_d = np.multiply neutral_b = 0 if mul_seasonal: op_s = np.multiply neutral_s = 1 else: op_s = np.add neutral_s = 0 # set initial values level = self.level _trend = self.trend season = self.season # (notation as in https://otexts.com/fpp2/ets.html) y = np.empty((nsimulations, repetitions)) # lvl instead of l because of E741 lvl = np.empty((nsimulations + 1, repetitions)) b = np.empty((nsimulations + 1, repetitions)) s = np.empty((nsimulations + m, repetitions)) # the following uses python's index wrapping if start_idx == 0: lvl[-1, :] = self.params["initial_level"] b[-1, :] = self.params["initial_trend"] else: lvl[-1, :] = level[start_idx - 1] b[-1, :] = _trend[start_idx - 1] if 0 <= start_idx and start_idx <= m: initial_seasons = self.params["initial_seasons"] _s = np.concatenate( (initial_seasons[start_idx:], season[:start_idx]) ) s[-m:, :] = np.tile(_s, (repetitions, 1)).T else: s[-m:, :] = np.tile( season[start_idx - m : start_idx], (repetitions, 1) ).T # set neutral values for unused features if trend is None: b[:, :] = neutral_b phi = 1 beta = 0 if seasonal is None: s[:, :] = neutral_s gamma = 0 if not damped: phi = 1 # calculate residuals for error covariance estimation if use_boxcox: fitted = boxcox(self.fittedvalues, lamda) else: fitted = self.fittedvalues if error == "add": resid = self.model._y - fitted else: resid = (self.model._y - fitted) / fitted sigma = np.sqrt(np.sum(resid ** 2) / (len(resid) - n_params)) # get random error eps if isinstance(random_errors, np.ndarray): if random_errors.shape != (nsimulations, repetitions): raise ValueError( "If random_errors is an ndarray, it must have shape " "(nsimulations, repetitions)" ) eps = random_errors elif random_errors == "bootstrap": eps = np.random.choice( resid, size=(nsimulations, repetitions), replace=True ) elif random_errors is None: if random_state is None: eps = np.random.randn(nsimulations, repetitions) * sigma elif isinstance(random_state, int): rng = np.random.RandomState(random_state) eps = rng.randn(nsimulations, repetitions) * sigma elif isinstance(random_state, np.random.RandomState): eps = random_state.randn(nsimulations, repetitions) * sigma else: raise ValueError( "Argument random_state must be None, an integer, " "or an instance of np.random.RandomState" ) elif isinstance(random_errors, (rv_continuous, rv_discrete)): params = random_errors.fit(resid) eps = random_errors.rvs(*params, size=(nsimulations, repetitions)) elif isinstance(random_errors, _distn_infrastructure.rv_frozen): eps = random_errors.rvs(size=(nsimulations, repetitions)) else: raise ValueError("Argument random_errors has unexpected value!") for t in range(nsimulations): b0 = op_d(b[t - 1, :], phi) l0 = op_b(lvl[t - 1, :], b0) s0 = s[t - m, :] y0 = op_s(l0, s0) if error == "add": eta = 1 kappa_l = 1 / s0 if mul_seasonal else 1 kappa_b = kappa_l / lvl[t - 1, :] if mul_trend else kappa_l kappa_s = 1 / l0 if mul_seasonal else 1 else: eta = y0 kappa_l = 0 if mul_seasonal else s0 kappa_b = ( kappa_l / lvl[t - 1, :] if mul_trend else kappa_l + lvl[t - 1, :] ) kappa_s = 0 if mul_seasonal else l0 y[t, :] = y0 + eta * eps[t, :] lvl[t, :] = l0 + alpha * (mul_error * l0 + kappa_l) * eps[t, :] b[t, :] = b0 + beta * (mul_error * b0 + kappa_b) * eps[t, :] s[t, :] = s0 + gamma * (mul_error * s0 + kappa_s) * eps[t, :] if use_boxcox: y = inv_boxcox(y, lamda) sim = np.atleast_1d(np.squeeze(y)) if y.shape[0] == 1 and y.size > 1: sim = sim[None, :] # Wrap data / squeeze where appropriate if not isinstance(self.model.data, PandasData): return sim _, _, _, index = self.model._get_prediction_index( start_idx, start_idx + nsimulations - 1 ) if repetitions == 1: sim = pd.Series(sim, index=index, name=self.model.endog_names) else: sim = pd.DataFrame(sim, index=index) return sim class HoltWintersResultsWrapper(ResultsWrapper): _attrs = { "fittedvalues": "rows", "level": "rows", "resid": "rows", "season": "rows", "trend": "rows", "slope": "rows", } _wrap_attrs = union_dicts(ResultsWrapper._wrap_attrs, _attrs) _methods = {"predict": "dates", "forecast": "dates"} _wrap_methods = union_dicts(ResultsWrapper._wrap_methods, _methods) populate_wrapper(HoltWintersResultsWrapper, HoltWintersResults) statsmodels-0.12.2/statsmodels/tsa/holtwinters/tests/000077500000000000000000000000001400612667500230225ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/holtwinters/tests/__init__.py000066400000000000000000000000001400612667500251210ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/holtwinters/tests/results/000077500000000000000000000000001400612667500245235ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/holtwinters/tests/results/__init__.py000066400000000000000000000000001400612667500266220ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/holtwinters/tests/results/housing-data.csv000066400000000000000000000272161400612667500276330ustar00rootroot00000000000000DATE,HOUSTNSA 1959-01-01,96.2 1959-02-01,99.0 1959-03-01,127.7 1959-04-01,150.8 1959-05-01,152.5 1959-06-01,147.8 1959-07-01,148.1 1959-08-01,138.2 1959-09-01,136.4 1959-10-01,120.0 1959-11-01,104.7 1959-12-01,95.6 1960-01-01,86.0 1960-02-01,90.7 1960-03-01,90.5 1960-04-01,123.0 1960-05-01,130.2 1960-06-01,122.8 1960-07-01,114.3 1960-08-01,130.3 1960-09-01,96.9 1960-10-01,110.4 1960-11-01,92.8 1960-12-01,64.2 1961-01-01,70.4 1961-02-01,74.1 1961-03-01,104.2 1961-04-01,112.8 1961-05-01,127.6 1961-06-01,134.8 1961-07-01,126.6 1961-08-01,127.1 1961-09-01,125.4 1961-10-01,124.8 1961-11-01,103.0 1961-12-01,82.2 1962-01-01,81.2 1962-02-01,77.1 1962-03-01,116.2 1962-04-01,147.8 1962-05-01,155.2 1962-06-01,136.8 1962-07-01,136.5 1962-08-01,147.7 1962-09-01,114.3 1962-10-01,135.2 1962-11-01,120.9 1962-12-01,93.9 1963-01-01,79.0 1963-02-01,89.6 1963-03-01,124.8 1963-04-01,164.2 1963-05-01,172.7 1963-06-01,154.2 1963-07-01,151.3 1963-08-01,144.0 1963-09-01,143.7 1963-10-01,165.3 1963-11-01,119.3 1963-12-01,95.0 1964-01-01,97.9 1964-02-01,101.3 1964-03-01,129.1 1964-04-01,147.1 1964-05-01,152.8 1964-06-01,157.2 1964-07-01,140.6 1964-08-01,138.3 1964-09-01,119.8 1964-10-01,141.2 1964-11-01,110.6 1964-12-01,93.0 1965-01-01,81.7 1965-02-01,80.9 1965-03-01,119.9 1965-04-01,148.6 1965-05-01,153.3 1965-06-01,151.8 1965-07-01,139.1 1965-08-01,128.3 1965-09-01,124.6 1965-10-01,133.1 1965-11-01,110.5 1965-12-01,101.1 1966-01-01,79.4 1966-02-01,76.2 1966-03-01,118.1 1966-04-01,140.9 1966-05-01,130.0 1966-06-01,120.6 1966-07-01,99.2 1966-08-01,101.8 1966-09-01,89.1 1966-10-01,76.6 1966-11-01,72.8 1966-12-01,60.2 1967-01-01,59.1 1967-02-01,61.4 1967-03-01,91.5 1967-04-01,113.7 1967-05-01,132.0 1967-06-01,125.4 1967-07-01,125.3 1967-08-01,127.4 1967-09-01,121.9 1967-10-01,135.4 1967-11-01,118.4 1967-12-01,80.1 1968-01-01,80.5 1968-02-01,84.6 1968-03-01,126.6 1968-04-01,162.0 1968-05-01,140.9 1968-06-01,137.9 1968-07-01,139.8 1968-08-01,136.6 1968-09-01,134.2 1968-10-01,140.8 1968-11-01,127.1 1968-12-01,96.4 1969-01-01,101.5 1969-02-01,90.1 1969-03-01,131.9 1969-04-01,159.0 1969-05-01,155.5 1969-06-01,147.3 1969-07-01,125.2 1969-08-01,124.9 1969-09-01,129.3 1969-10-01,123.4 1969-11-01,94.6 1969-12-01,84.1 1970-01-01,66.4 1970-02-01,74.3 1970-03-01,114.7 1970-04-01,128.4 1970-05-01,125.0 1970-06-01,135.2 1970-07-01,140.8 1970-08-01,128.7 1970-09-01,130.9 1970-10-01,140.9 1970-11-01,126.9 1970-12-01,121.4 1971-01-01,110.6 1971-02-01,102.2 1971-03-01,167.9 1971-04-01,201.1 1971-05-01,198.5 1971-06-01,193.8 1971-07-01,194.3 1971-08-01,204.5 1971-09-01,173.8 1971-10-01,179.7 1971-11-01,173.7 1971-12-01,152.1 1972-01-01,149.1 1972-02-01,152.2 1972-03-01,203.9 1972-04-01,211.6 1972-05-01,225.8 1972-06-01,223.1 1972-07-01,206.5 1972-08-01,228.6 1972-09-01,203.0 1972-10-01,216.5 1972-11-01,185.7 1972-12-01,150.5 1973-01-01,146.6 1973-02-01,138.0 1973-03-01,200.0 1973-04-01,205.0 1973-05-01,234.0 1973-06-01,202.6 1973-07-01,202.6 1973-08-01,197.2 1973-09-01,148.4 1973-10-01,147.1 1973-11-01,133.3 1973-12-01,90.4 1974-01-01,84.5 1974-02-01,109.4 1974-03-01,124.8 1974-04-01,159.5 1974-05-01,149.0 1974-06-01,147.6 1974-07-01,126.6 1974-08-01,111.1 1974-09-01,98.3 1974-10-01,96.7 1974-11-01,75.1 1974-12-01,55.1 1975-01-01,56.1 1975-02-01,54.7 1975-03-01,80.2 1975-04-01,97.9 1975-05-01,116.1 1975-06-01,110.3 1975-07-01,119.3 1975-08-01,117.3 1975-09-01,111.9 1975-10-01,123.6 1975-11-01,96.9 1975-12-01,76.1 1976-01-01,72.5 1976-02-01,89.9 1976-03-01,118.4 1976-04-01,137.2 1976-05-01,147.9 1976-06-01,154.2 1976-07-01,136.6 1976-08-01,145.9 1976-09-01,151.8 1976-10-01,148.4 1976-11-01,127.1 1976-12-01,107.4 1977-01-01,81.3 1977-02-01,112.5 1977-03-01,173.6 1977-04-01,182.2 1977-05-01,201.3 1977-06-01,197.6 1977-07-01,189.8 1977-08-01,194.0 1977-09-01,177.7 1977-10-01,193.1 1977-11-01,154.8 1977-12-01,129.2 1978-01-01,88.6 1978-02-01,101.3 1978-03-01,172.1 1978-04-01,197.5 1978-05-01,211.0 1978-06-01,216.0 1978-07-01,192.2 1978-08-01,190.9 1978-09-01,180.5 1978-10-01,192.1 1978-11-01,158.6 1978-12-01,119.5 1979-01-01,88.2 1979-02-01,84.5 1979-03-01,152.9 1979-04-01,161.0 1979-05-01,189.1 1979-06-01,191.8 1979-07-01,164.2 1979-08-01,170.3 1979-09-01,163.7 1979-10-01,169.0 1979-11-01,118.7 1979-12-01,91.6 1980-01-01,73.1 1980-02-01,79.9 1980-03-01,85.1 1980-04-01,96.2 1980-05-01,91.7 1980-06-01,116.4 1980-07-01,120.1 1980-08-01,129.9 1980-09-01,138.3 1980-10-01,152.7 1980-11-01,112.9 1980-12-01,95.9 1981-01-01,84.5 1981-02-01,71.9 1981-03-01,107.8 1981-04-01,123.0 1981-05-01,109.9 1981-06-01,105.8 1981-07-01,99.9 1981-08-01,86.3 1981-09-01,84.1 1981-10-01,87.2 1981-11-01,64.6 1981-12-01,59.1 1982-01-01,47.2 1982-02-01,51.3 1982-03-01,78.2 1982-04-01,84.1 1982-05-01,98.8 1982-06-01,91.1 1982-07-01,106.8 1982-08-01,96.0 1982-09-01,106.4 1982-10-01,110.5 1982-11-01,108.9 1982-12-01,82.9 1983-01-01,91.3 1983-02-01,96.3 1983-03-01,134.6 1983-04-01,135.8 1983-05-01,174.9 1983-06-01,173.2 1983-07-01,161.6 1983-08-01,176.8 1983-09-01,154.9 1983-10-01,159.3 1983-11-01,136.0 1983-12-01,108.3 1984-01-01,109.1 1984-02-01,130.0 1984-03-01,137.5 1984-04-01,172.7 1984-05-01,180.7 1984-06-01,184.0 1984-07-01,162.1 1984-08-01,147.4 1984-09-01,148.5 1984-10-01,152.3 1984-11-01,126.2 1984-12-01,98.9 1985-01-01,105.4 1985-02-01,95.4 1985-03-01,145.0 1985-04-01,175.8 1985-05-01,170.2 1985-06-01,163.2 1985-07-01,160.7 1985-08-01,160.7 1985-09-01,147.7 1985-10-01,173.0 1985-11-01,124.1 1985-12-01,120.5 1986-01-01,115.6 1986-02-01,107.2 1986-03-01,151.0 1986-04-01,188.2 1986-05-01,186.6 1986-06-01,183.6 1986-07-01,172.0 1986-08-01,163.8 1986-09-01,154.0 1986-10-01,154.8 1986-11-01,115.6 1986-12-01,113.0 1987-01-01,105.1 1987-02-01,102.8 1987-03-01,141.2 1987-04-01,159.3 1987-05-01,158.0 1987-06-01,162.9 1987-07-01,152.4 1987-08-01,143.6 1987-09-01,152.0 1987-10-01,139.1 1987-11-01,118.8 1987-12-01,85.4 1988-01-01,78.2 1988-02-01,90.2 1988-03-01,128.8 1988-04-01,153.2 1988-05-01,140.2 1988-06-01,150.2 1988-07-01,137.0 1988-08-01,136.8 1988-09-01,131.1 1988-10-01,135.1 1988-11-01,113.0 1988-12-01,94.2 1989-01-01,100.1 1989-02-01,85.8 1989-03-01,117.8 1989-04-01,129.4 1989-05-01,131.7 1989-06-01,143.2 1989-07-01,134.7 1989-08-01,122.4 1989-09-01,109.3 1989-10-01,130.1 1989-11-01,96.6 1989-12-01,75.0 1990-01-01,99.2 1990-02-01,86.9 1990-03-01,108.5 1990-04-01,119.0 1990-05-01,121.1 1990-06-01,117.8 1990-07-01,111.2 1990-08-01,102.8 1990-09-01,93.1 1990-10-01,94.2 1990-11-01,81.4 1990-12-01,57.4 1991-01-01,52.5 1991-02-01,59.1 1991-03-01,73.8 1991-04-01,99.7 1991-05-01,97.7 1991-06-01,103.4 1991-07-01,103.5 1991-08-01,94.7 1991-09-01,86.6 1991-10-01,101.8 1991-11-01,75.6 1991-12-01,65.6 1992-01-01,71.6 1992-02-01,78.8 1992-03-01,111.6 1992-04-01,107.6 1992-05-01,115.2 1992-06-01,117.8 1992-07-01,106.2 1992-08-01,109.9 1992-09-01,106.0 1992-10-01,111.8 1992-11-01,84.5 1992-12-01,78.6 1993-01-01,70.5 1993-02-01,74.6 1993-03-01,95.5 1993-04-01,117.8 1993-05-01,120.9 1993-06-01,128.5 1993-07-01,115.3 1993-08-01,121.8 1993-09-01,118.5 1993-10-01,123.3 1993-11-01,102.3 1993-12-01,98.7 1994-01-01,76.2 1994-02-01,83.5 1994-03-01,134.3 1994-04-01,137.6 1994-05-01,148.8 1994-06-01,136.4 1994-07-01,127.8 1994-08-01,139.8 1994-09-01,130.1 1994-10-01,130.6 1994-11-01,113.4 1994-12-01,98.5 1995-01-01,84.5 1995-02-01,81.6 1995-03-01,103.8 1995-04-01,116.9 1995-05-01,130.5 1995-06-01,123.4 1995-07-01,129.1 1995-08-01,135.8 1995-09-01,122.4 1995-10-01,126.2 1995-11-01,107.2 1995-12-01,92.8 1996-01-01,90.7 1996-02-01,95.9 1996-03-01,116.0 1996-04-01,146.6 1996-05-01,143.9 1996-06-01,138.0 1996-07-01,137.5 1996-08-01,144.2 1996-09-01,128.7 1996-10-01,130.8 1996-11-01,111.5 1996-12-01,93.1 1997-01-01,82.2 1997-02-01,94.7 1997-03-01,120.4 1997-04-01,142.3 1997-05-01,136.3 1997-06-01,140.4 1997-07-01,134.6 1997-08-01,126.5 1997-09-01,139.2 1997-10-01,139.0 1997-11-01,112.4 1997-12-01,106.0 1998-01-01,91.2 1998-02-01,101.1 1998-03-01,132.6 1998-04-01,144.9 1998-05-01,143.3 1998-06-01,159.6 1998-07-01,156.0 1998-08-01,147.5 1998-09-01,141.5 1998-10-01,155.5 1998-11-01,124.2 1998-12-01,119.6 1999-01-01,106.8 1999-02-01,110.2 1999-03-01,147.3 1999-04-01,144.6 1999-05-01,153.2 1999-06-01,149.4 1999-07-01,152.6 1999-08-01,152.9 1999-09-01,140.3 1999-10-01,142.9 1999-11-01,127.4 1999-12-01,113.6 2000-01-01,104.0 2000-02-01,119.7 2000-03-01,133.4 2000-04-01,149.5 2000-05-01,152.9 2000-06-01,146.3 2000-07-01,135.0 2000-08-01,141.4 2000-09-01,128.9 2000-10-01,139.7 2000-11-01,117.1 2000-12-01,100.7 2001-01-01,106.4 2001-02-01,108.2 2001-03-01,133.2 2001-04-01,151.3 2001-05-01,154.0 2001-06-01,155.2 2001-07-01,154.6 2001-08-01,141.5 2001-09-01,133.1 2001-10-01,139.8 2001-11-01,121.0 2001-12-01,104.6 2002-01-01,110.4 2002-02-01,120.4 2002-03-01,138.2 2002-04-01,148.8 2002-05-01,165.5 2002-06-01,160.3 2002-07-01,155.9 2002-08-01,147.0 2002-09-01,155.6 2002-10-01,146.8 2002-11-01,133.0 2002-12-01,123.1 2003-01-01,117.8 2003-02-01,109.7 2003-03-01,147.2 2003-04-01,151.2 2003-05-01,165.0 2003-06-01,174.5 2003-07-01,175.8 2003-08-01,163.8 2003-09-01,171.3 2003-10-01,173.5 2003-11-01,153.7 2003-12-01,144.2 2004-01-01,124.5 2004-02-01,126.4 2004-03-01,173.8 2004-04-01,179.5 2004-05-01,187.6 2004-06-01,172.3 2004-07-01,182.0 2004-08-01,185.9 2004-09-01,164.0 2004-10-01,181.3 2004-11-01,138.1 2004-12-01,140.2 2005-01-01,142.9 2005-02-01,149.1 2005-03-01,156.2 2005-04-01,184.6 2005-05-01,197.9 2005-06-01,192.8 2005-07-01,187.6 2005-08-01,192.0 2005-09-01,187.9 2005-10-01,180.4 2005-11-01,160.7 2005-12-01,136.0 2006-01-01,153.0 2006-02-01,145.1 2006-03-01,165.9 2006-04-01,160.5 2006-05-01,190.2 2006-06-01,170.2 2006-07-01,160.9 2006-08-01,146.8 2006-09-01,150.1 2006-10-01,130.6 2006-11-01,115.2 2006-12-01,112.4 2007-01-01,95.0 2007-02-01,103.1 2007-03-01,123.8 2007-04-01,135.6 2007-05-01,136.5 2007-06-01,137.8 2007-07-01,127.9 2007-08-01,121.2 2007-09-01,101.5 2007-10-01,115.0 2007-11-01,88.8 2007-12-01,68.9 2008-01-01,70.8 2008-02-01,78.4 2008-03-01,82.2 2008-04-01,89.5 2008-05-01,91.7 2008-06-01,102.5 2008-07-01,86.7 2008-08-01,76.4 2008-09-01,73.9 2008-10-01,68.2 2008-11-01,47.5 2008-12-01,37.7 2009-01-01,31.9 2009-02-01,39.8 2009-03-01,42.7 2009-04-01,42.5 2009-05-01,52.2 2009-06-01,59.1 2009-07-01,56.8 2009-08-01,52.9 2009-09-01,52.6 2009-10-01,44.5 2009-11-01,42.3 2009-12-01,36.6 2010-01-01,38.9 2010-02-01,40.7 2010-03-01,54.7 2010-04-01,62.0 2010-05-01,56.2 2010-06-01,53.8 2010-07-01,51.5 2010-08-01,56.3 2010-09-01,53.0 2010-10-01,45.4 2010-11-01,40.6 2010-12-01,33.8 2011-01-01,40.2 2011-02-01,35.4 2011-03-01,49.9 2011-04-01,49.0 2011-05-01,54.0 2011-06-01,60.5 2011-07-01,57.6 2011-08-01,54.5 2011-09-01,58.8 2011-10-01,53.2 2011-11-01,53.0 2011-12-01,42.7 2012-01-01,47.2 2012-02-01,49.7 2012-03-01,58.0 2012-04-01,66.8 2012-05-01,67.8 2012-06-01,74.7 2012-07-01,69.2 2012-08-01,69.0 2012-09-01,75.8 2012-10-01,77.0 2012-11-01,62.2 2012-12-01,63.2 2013-01-01,58.7 2013-02-01,66.1 2013-03-01,83.3 2013-04-01,76.3 2013-05-01,87.2 2013-06-01,80.7 2013-07-01,84.0 2013-08-01,80.4 2013-09-01,78.4 2013-10-01,78.4 2013-11-01,83.8 2013-12-01,67.6 2014-01-01,60.7 2014-02-01,65.1 2014-03-01,80.2 2014-04-01,94.9 2014-05-01,92.5 2014-06-01,87.3 2014-07-01,101.0 2014-08-01,86.2 2014-09-01,94.2 2014-10-01,92.0 2014-11-01,75.8 2014-12-01,73.4 2015-01-01,73.0 2015-02-01,61.9 2015-03-01,79.7 2015-04-01,108.5 2015-05-01,99.6 2015-06-01,112.3 2015-07-01,107.2 2015-08-01,99.2 2015-09-01,111.6 2015-10-01,90.9 2015-11-01,89.9 2015-12-01,78.1 2016-01-01,74.3 2016-02-01,84.1 2016-03-01,90.7 2016-04-01,106.2 2016-05-01,105.0 2016-06-01,111.6 2016-07-01,115.2 2016-08-01,102.8 2016-09-01,95.0 2016-10-01,114.5 2016-11-01,87.8 2016-12-01,86.5 2017-01-01,82.3 2017-02-01,87.8 2017-03-01,97.1 2017-04-01,105.2 2017-05-01,106.0 2017-06-01,116.3 2017-07-01,112.3 2017-08-01,102.6 2017-09-01,104.4 2017-10-01,109.6 2017-11-01,97.9 2017-12-01,81.4 2018-01-01,91.6 2018-02-01,89.7 2018-03-01,107.2 2018-04-01,117.5 2018-05-01,123.8 2018-06-01,111.5 statsmodels-0.12.2/statsmodels/tsa/holtwinters/tests/test_holtwinters.py000066400000000000000000001735601400612667500270310ustar00rootroot00000000000000""" Author: Terence L van Zyl Modified: Kevin Sheppard """ import os import re import warnings import numpy as np from numpy.testing import assert_allclose, assert_almost_equal import pandas as pd import pytest import scipy.stats from statsmodels.tools.sm_exceptions import ( ConvergenceWarning, EstimationWarning, ValueWarning, ) from statsmodels.tsa.holtwinters import ( PY_SMOOTHERS, SMOOTHERS, ExponentialSmoothing, Holt, SimpleExpSmoothing, ) from statsmodels.tsa.holtwinters._exponential_smoothers import ( HoltWintersArgs, _test_to_restricted, ) from statsmodels.tsa.holtwinters._smoothers import ( HoltWintersArgs as PyHoltWintersArgs, to_restricted, to_unrestricted, ) base, _ = os.path.split(os.path.abspath(__file__)) housing_data = pd.read_csv( os.path.join(base, "results", "housing-data.csv"), index_col="DATE", parse_dates=True, ) housing_data = housing_data.asfreq("MS") SEASONALS = ("add", "mul", None) TRENDS = ("add", "mul", None) @pytest.fixture(scope="module") def ses(): rs = np.random.RandomState(0) e = rs.standard_normal(1200) y = e.copy() for i in range(1, 1200): y[i] = y[i - 1] + e[i] - 0.2 * e[i - 1] y = y[200:] index = pd.date_range("2000-1-1", periods=y.shape[0], freq="M") return pd.Series(y, index=index, name="y") def _simple_dbl_exp_smoother(x, alpha, beta, l0, b0, nforecast=0): """ Simple, slow, direct implementation of double exp smoothing for testing """ n = x.shape[0] lvals = np.zeros(n) b = np.zeros(n) xhat = np.zeros(n) f = np.zeros(nforecast) lvals[0] = l0 b[0] = b0 # Special case the 0 observations since index -1 is not available xhat[0] = l0 + b0 lvals[0] = alpha * x[0] + (1 - alpha) * (l0 + b0) b[0] = beta * (lvals[0] - l0) + (1 - beta) * b0 for t in range(1, n): # Obs in index t is the time t forecast for t + 1 lvals[t] = alpha * x[t] + (1 - alpha) * (lvals[t - 1] + b[t - 1]) b[t] = beta * (lvals[t] - lvals[t - 1]) + (1 - beta) * b[t - 1] xhat[1:] = lvals[0:-1] + b[0:-1] f[:] = lvals[-1] + np.arange(1, nforecast + 1) * b[-1] err = x - xhat return lvals, b, f, err, xhat class TestHoltWinters(object): @classmethod def setup_class(cls): # Changed for backwards compatibility with pandas # oildata_oil = pd.read_json(oildata_oil_json, # typ='Series').sort_index() data = [ 446.65652290000003, 454.47330649999998, 455.66297400000002, 423.63223879999998, 456.27132790000002, 440.58805009999998, 425.33252010000001, 485.14944789999998, 506.04816210000001, 526.79198329999997, 514.26888899999994, 494.21101929999998, ] index = [ "1996-12-31 00:00:00", "1997-12-31 00:00:00", "1998-12-31 00:00:00", "1999-12-31 00:00:00", "2000-12-31 00:00:00", "2001-12-31 00:00:00", "2002-12-31 00:00:00", "2003-12-31 00:00:00", "2004-12-31 00:00:00", "2005-12-31 00:00:00", "2006-12-31 00:00:00", "2007-12-31 00:00:00", ] oildata_oil = pd.Series(data, index) oildata_oil.index = pd.DatetimeIndex( oildata_oil.index, freq=pd.infer_freq(oildata_oil.index) ) cls.oildata_oil = oildata_oil # air_ausair = pd.read_json(air_ausair_json, # typ='Series').sort_index() data = [ 17.5534, 21.860099999999999, 23.886600000000001, 26.929300000000001, 26.888500000000001, 28.831399999999999, 30.075099999999999, 30.953499999999998, 30.185700000000001, 31.579699999999999, 32.577568999999997, 33.477398000000001, 39.021580999999998, 41.386431999999999, 41.596552000000003, ] index = [ "1990-12-31 00:00:00", "1991-12-31 00:00:00", "1992-12-31 00:00:00", "1993-12-31 00:00:00", "1994-12-31 00:00:00", "1995-12-31 00:00:00", "1996-12-31 00:00:00", "1997-12-31 00:00:00", "1998-12-31 00:00:00", "1999-12-31 00:00:00", "2000-12-31 00:00:00", "2001-12-31 00:00:00", "2002-12-31 00:00:00", "2003-12-31 00:00:00", "2004-12-31 00:00:00", ] air_ausair = pd.Series(data, index) air_ausair.index = pd.DatetimeIndex( air_ausair.index, freq=pd.infer_freq(air_ausair.index) ) cls.air_ausair = air_ausair # livestock2_livestock = pd.read_json(livestock2_livestock_json, # typ='Series').sort_index() data = [ 263.91774700000002, 268.30722200000002, 260.662556, 266.63941899999998, 277.51577800000001, 283.834045, 290.30902800000001, 292.474198, 300.83069399999999, 309.28665699999999, 318.33108099999998, 329.37239, 338.88399800000002, 339.24412599999999, 328.60063200000002, 314.25538499999999, 314.45969500000001, 321.41377899999998, 329.78929199999999, 346.38516499999997, 352.29788200000002, 348.37051500000001, 417.56292200000001, 417.12356999999997, 417.749459, 412.233904, 411.94681700000001, 394.69707499999998, 401.49927000000002, 408.27046799999999, 414.24279999999999, ] index = [ "1970-12-31 00:00:00", "1971-12-31 00:00:00", "1972-12-31 00:00:00", "1973-12-31 00:00:00", "1974-12-31 00:00:00", "1975-12-31 00:00:00", "1976-12-31 00:00:00", "1977-12-31 00:00:00", "1978-12-31 00:00:00", "1979-12-31 00:00:00", "1980-12-31 00:00:00", "1981-12-31 00:00:00", "1982-12-31 00:00:00", "1983-12-31 00:00:00", "1984-12-31 00:00:00", "1985-12-31 00:00:00", "1986-12-31 00:00:00", "1987-12-31 00:00:00", "1988-12-31 00:00:00", "1989-12-31 00:00:00", "1990-12-31 00:00:00", "1991-12-31 00:00:00", "1992-12-31 00:00:00", "1993-12-31 00:00:00", "1994-12-31 00:00:00", "1995-12-31 00:00:00", "1996-12-31 00:00:00", "1997-12-31 00:00:00", "1998-12-31 00:00:00", "1999-12-31 00:00:00", "2000-12-31 00:00:00", ] livestock2_livestock = pd.Series(data, index) livestock2_livestock.index = pd.DatetimeIndex( livestock2_livestock.index, freq=pd.infer_freq(livestock2_livestock.index), ) cls.livestock2_livestock = livestock2_livestock # aust = pd.read_json(aust_json, typ='Series').sort_index() data = [ 41.727457999999999, 24.04185, 32.328102999999999, 37.328707999999999, 46.213152999999998, 29.346326000000001, 36.482909999999997, 42.977719, 48.901524999999999, 31.180221, 37.717880999999998, 40.420211000000002, 51.206862999999998, 31.887228, 40.978262999999998, 43.772491000000002, 55.558566999999996, 33.850915000000001, 42.076383, 45.642291999999998, 59.766779999999997, 35.191876999999998, 44.319737000000003, 47.913736, ] index = [ "2005-03-01 00:00:00", "2005-06-01 00:00:00", "2005-09-01 00:00:00", "2005-12-01 00:00:00", "2006-03-01 00:00:00", "2006-06-01 00:00:00", "2006-09-01 00:00:00", "2006-12-01 00:00:00", "2007-03-01 00:00:00", "2007-06-01 00:00:00", "2007-09-01 00:00:00", "2007-12-01 00:00:00", "2008-03-01 00:00:00", "2008-06-01 00:00:00", "2008-09-01 00:00:00", "2008-12-01 00:00:00", "2009-03-01 00:00:00", "2009-06-01 00:00:00", "2009-09-01 00:00:00", "2009-12-01 00:00:00", "2010-03-01 00:00:00", "2010-06-01 00:00:00", "2010-09-01 00:00:00", "2010-12-01 00:00:00", ] aust = pd.Series(data, index) aust.index = pd.DatetimeIndex( aust.index, freq=pd.infer_freq(aust.index) ) cls.aust = aust cls.start_params = [ 1.5520372162082909e-09, 2.066338221674873e-18, 1.727109018250519e-09, 50.568333479425036, 0.9129273810171223, 0.83535867, 0.50297119, 0.62439273, 0.67723128, ] def test_predict(self): fit1 = ExponentialSmoothing( self.aust, seasonal_periods=4, trend="add", seasonal="mul", initialization_method="estimated", ).fit(start_params=self.start_params) fit2 = ExponentialSmoothing( self.aust, seasonal_periods=4, trend="add", seasonal="mul", initialization_method="estimated", ).fit(start_params=self.start_params) # fit3 = ExponentialSmoothing(self.aust, seasonal_periods=4, # trend='add', seasonal='mul').fit(remove_bias=True, # use_basinhopping=True) assert_almost_equal( fit1.predict("2011-03-01 00:00:00", "2011-12-01 00:00:00"), [61.3083, 37.3730, 46.9652, 51.5578], 3, ) assert_almost_equal( fit2.predict(end="2011-12-01 00:00:00"), [61.3083, 37.3730, 46.9652, 51.5578], 3, ) # assert_almost_equal(fit3.predict('2010-10-01 00:00:00', # '2010-10-01 00:00:00'), # [49.087], 3) def test_ndarray(self): fit1 = ExponentialSmoothing( self.aust.values, seasonal_periods=4, trend="add", seasonal="mul", initialization_method="estimated", ).fit(start_params=self.start_params) assert_almost_equal( fit1.forecast(4), [61.3083, 37.3730, 46.9652, 51.5578], 3 ) # FIXME: this is passing 2019-05-22 on some platforms; what has changed? @pytest.mark.xfail(reason="Optimizer does not converge", strict=False) def test_forecast(self): fit1 = ExponentialSmoothing( self.aust, seasonal_periods=4, trend="add", seasonal="add", ).fit(method="bh", use_brute=True) assert_almost_equal( fit1.forecast(steps=4), [60.9542, 36.8505, 46.1628, 50.1272], 3 ) def test_simple_exp_smoothing(self): fit1 = SimpleExpSmoothing( self.oildata_oil, initialization_method="legacy-heuristic" ).fit(0.2, optimized=False) fit2 = SimpleExpSmoothing( self.oildata_oil, initialization_method="legacy-heuristic" ).fit(0.6, optimized=False) fit3 = SimpleExpSmoothing( self.oildata_oil, initialization_method="estimated" ).fit() assert_almost_equal(fit1.forecast(1), [484.802468], 4) assert_almost_equal( fit1.level, [ 446.65652290, 448.21987962, 449.7084985, 444.49324656, 446.84886283, 445.59670028, 441.54386424, 450.26498098, 461.4216172, 474.49569042, 482.45033014, 484.80246797, ], 4, ) assert_almost_equal(fit2.forecast(1), [501.837461], 4) assert_almost_equal(fit3.forecast(1), [496.493543], 4) assert_almost_equal(fit3.params["smoothing_level"], 0.891998, 4) assert_almost_equal(fit3.params["initial_level"], 447.478440, 3) def test_holt(self): fit1 = Holt( self.air_ausair, initialization_method="legacy-heuristic" ).fit(smoothing_level=0.8, smoothing_trend=0.2, optimized=False) fit2 = Holt( self.air_ausair, exponential=True, initialization_method="legacy-heuristic", ).fit(smoothing_level=0.8, smoothing_trend=0.2, optimized=False) fit3 = Holt( self.air_ausair, damped_trend=True, initialization_method="estimated", ).fit(smoothing_level=0.8, smoothing_trend=0.2) assert_almost_equal( fit1.forecast(5), [43.76, 45.59, 47.43, 49.27, 51.10], 2 ) assert_almost_equal( fit1.trend, [ 3.617628, 3.59006512, 3.33438212, 3.23657639, 2.69263502, 2.46388914, 2.2229097, 1.95959226, 1.47054601, 1.3604894, 1.28045881, 1.20355193, 1.88267152, 2.09564416, 1.83655482, ], 4, ) assert_almost_equal( fit1.fittedfcast, [ 21.8601, 22.032368, 25.48461872, 27.54058587, 30.28813356, 30.26106173, 31.58122149, 32.599234, 33.24223906, 32.26755382, 33.07776017, 33.95806605, 34.77708354, 40.05535303, 43.21586036, 43.75696849, ], 4, ) assert_almost_equal( fit2.forecast(5), [44.60, 47.24, 50.04, 53.01, 56.15], 2 ) assert_almost_equal( fit3.forecast(5), [42.85, 43.81, 44.66, 45.41, 46.06], 2 ) @pytest.mark.smoke def test_holt_damp_fit(self): # Smoke test for parameter estimation fit1 = SimpleExpSmoothing( self.livestock2_livestock, initialization_method="estimated" ).fit() mod4 = Holt( self.livestock2_livestock, damped_trend=True, initialization_method="estimated", ) fit4 = mod4.fit(damping_trend=0.98, method="least_squares") mod5 = Holt( self.livestock2_livestock, exponential=True, damped_trend=True, initialization_method="estimated", ) fit5 = mod5.fit() # We accept the below values as we getting a better SSE than text book assert_almost_equal(fit1.params["smoothing_level"], 1.00, 2) assert_almost_equal(fit1.params["smoothing_trend"], np.NaN, 2) assert_almost_equal(fit1.params["damping_trend"], np.NaN, 2) assert_almost_equal(fit1.params["initial_level"], 263.96, 1) assert_almost_equal(fit1.params["initial_trend"], np.NaN, 2) assert_almost_equal(fit1.sse, 6761.35, 2) # 6080.26 assert_almost_equal(fit4.params["smoothing_level"], 0.98, 2) assert_almost_equal(fit4.params["smoothing_trend"], 0.00, 2) assert_almost_equal(fit4.params["damping_trend"], 0.98, 2) assert_almost_equal(fit4.params["initial_level"], 257.36, 2) assert_almost_equal(fit4.params["initial_trend"], 6.64, 2) assert_almost_equal(fit4.sse, 6036.56, 2) # 6080.26 assert_almost_equal(fit5.params["smoothing_level"], 0.97, 2) assert_almost_equal(fit5.params["smoothing_trend"], 0.00, 2) assert_almost_equal(fit5.params["damping_trend"], 0.98, 2) assert_almost_equal(fit5.params["initial_level"], 258.95, 1) assert_almost_equal(fit5.params["initial_trend"], 1.04, 2) assert_almost_equal(fit5.sse, 6082.00, 0) # 6100.11 def test_holt_damp_r(self): # Test the damping parameters against the R forecast packages `ets` # library(ets) # livestock2_livestock <- c(...) # res <- ets(livestock2_livestock, model='AAN', damped_trend=TRUE, # phi=0.98) with pytest.warns(FutureWarning): mod = Holt(self.livestock2_livestock, damped_trend=True) params = { "smoothing_level": 0.97402626, "smoothing_trend": 0.00010006, "damping_trend": 0.98, "initial_level": 252.59039965, "initial_trend": 6.90265918, } with mod.fix_params(params): fit = mod.fit(optimized=False) # Check that we captured the parameters correctly for key in params.keys(): assert_allclose(fit.params[key], params[key]) # Summary output # print(res$mse) assert_allclose(fit.sse / mod.nobs, 195.4397924865488, atol=1e-3) # print(res$aicc) # TODO: this fails - different AICC definition? # assert_allclose(fit.aicc, 282.386426659408, atol=1e-3) # print(res$bic) # TODO: this fails - different BIC definition? # assert_allclose(fit.bic, 287.1563626818338) # print(res$states[,'l']) # note: this array includes the initial level desired = [ 252.5903996514365, 263.7992355246843, 268.3623324350207, 261.0312983437606, 266.6590942700923, 277.3958197247272, 283.8256217863908, 290.2962560621914, 292.5701438129583, 300.7655919939834, 309.2118057241649, 318.2377698496536, 329.2238709362550, 338.7709778307978, 339.3669793596703, 329.0127022356033, 314.7684267018998, 314.5948077575944, 321.3612035017972, 329.6924360833211, 346.0712138652086, 352.2534120008911, 348.5862874190927, 415.8839400693967, 417.2018843196238, 417.8435306633725, 412.4857261252961, 412.0647865321129, 395.2500605270393, 401.4367438266322, 408.1907701386275, 414.1814574903921, ] assert_allclose(np.r_[fit.params["initial_level"], fit.level], desired) # print(res$states[,'b']) # note: this array includes the initial slope desired = [ 6.902659175332394, 6.765062519124909, 6.629548973536494, 6.495537532917715, 6.365550989616566, 6.238702070454378, 6.113960476763530, 5.991730467006233, 5.871526257315264, 5.754346516684953, 5.639547926790058, 5.527116419415724, 5.417146212898857, 5.309238662451385, 5.202580636191761, 5.096941655567694, 4.993026494493987, 4.892645486210410, 4.794995106664251, 4.699468310763351, 4.606688340205792, 4.514725879754355, 4.423600168391240, 4.341595902295941, 4.254462303550087, 4.169010676686062, 4.084660399498803, 4.002512751871354, 3.920332298146730, 3.842166514133902, 3.765630194200260, 3.690553892582855, ] # TODO: not sure why the precision is so low here... assert_allclose( np.r_[fit.params["initial_trend"], fit.trend], desired, atol=1e-3 ) # print(res$fitted) desired = [ 259.3550056432622, 270.4289967934267, 274.8592904290865, 267.3969251260200, 272.8973342399166, 283.5097477537724, 289.8173030536191, 296.1681519198575, 298.3242395451272, 306.4048515803347, 314.7385626924191, 323.6543439406810, 334.5326742248959, 343.9740317200002, 344.4655083831382, 334.0077050580596, 319.6615926665040, 319.3896003340806, 326.0602987063282, 334.2979150278692, 350.5857684386102, 356.6778433630504, 352.9214155841161, 420.1387040536467, 421.3712573771029, 421.9291611265248, 416.4886933168049, 415.9872490289468, 399.0919861792231, 405.2020670104834, 411.8810877289437, ] assert_allclose(fit.fittedvalues, desired, atol=1e-3) # print(forecast(res)$mean) desired = [ 417.7982003051233, 421.3426082635598, 424.8161280628277, 428.2201774661102, 431.5561458813270, 434.8253949282395, 438.0292589942138, 441.1690457788685, 444.2460368278302, 447.2614880558126, ] assert_allclose(fit.forecast(10), desired, atol=1e-4) def test_hw_seasonal(self): mod = ExponentialSmoothing( self.aust, seasonal_periods=4, trend="additive", seasonal="additive", initialization_method="estimated", use_boxcox=True, ) fit1 = mod.fit() assert_almost_equal( fit1.forecast(8), [59.96, 38.63, 47.48, 51.89, 62.81, 41.0, 50.06, 54.57], 2, ) def test_hw_seasonal_add_mul(self): mod2 = ExponentialSmoothing( self.aust, seasonal_periods=4, trend="add", seasonal="mul", initialization_method="estimated", use_boxcox=True, ) fit2 = mod2.fit() assert_almost_equal( fit2.forecast(8), [61.69, 37.37, 47.22, 52.03, 65.08, 39.34, 49.72, 54.79], 2, ) ExponentialSmoothing( self.aust, seasonal_periods=4, trend="mul", seasonal="add", initialization_method="estimated", use_boxcox=0.0, ).fit() ExponentialSmoothing( self.aust, seasonal_periods=4, trend="multiplicative", seasonal="multiplicative", initialization_method="estimated", use_boxcox=0.0, ).fit() # Skip since estimator is unstable # assert_almost_equal(fit5.forecast(1), [60.60], 2) # assert_almost_equal(fit6.forecast(1), [61.47], 2) def test_hw_seasonal_buggy(self): fit3 = ExponentialSmoothing( self.aust, seasonal_periods=4, seasonal="add", initialization_method="estimated", use_boxcox=True, ).fit() assert_almost_equal( fit3.forecast(8), [ 59.487190, 35.758854, 44.600641, 47.751384, 59.487190, 35.758854, 44.600641, 47.751384, ], 2, ) fit4 = ExponentialSmoothing( self.aust, seasonal_periods=4, seasonal="mul", initialization_method="estimated", use_boxcox=True, ).fit() assert_almost_equal( fit4.forecast(8), [ 59.26155037, 35.27811302, 44.00438543, 47.97732693, 59.26155037, 35.27811302, 44.00438543, 47.97732693, ], 2, ) @pytest.mark.parametrize( "trend_seasonal", (("mul", None), (None, "mul"), ("mul", "mul")) ) def test_negative_multipliative(trend_seasonal): trend, seasonal = trend_seasonal y = -np.ones(100) with pytest.raises(ValueError): ExponentialSmoothing( y, trend=trend, seasonal=seasonal, seasonal_periods=10 ) @pytest.mark.parametrize("seasonal", SEASONALS) def test_dampen_no_trend(seasonal): with pytest.raises(TypeError): ExponentialSmoothing( housing_data, trend=False, seasonal=seasonal, damped_trend=True, seasonal_periods=10, ) @pytest.mark.parametrize("seasonal", ("add", "mul")) def test_invalid_seasonal(seasonal): y = pd.Series( -np.ones(100), index=pd.date_range("2000-1-1", periods=100, freq="MS") ) with pytest.raises(ValueError): ExponentialSmoothing(y, seasonal=seasonal, seasonal_periods=1) def test_2d_data(): with pytest.raises(ValueError): ExponentialSmoothing(pd.concat([housing_data, housing_data], 1)).fit() def test_infer_freq(): hd2 = housing_data.copy() hd2.index = list(hd2.index) with warnings.catch_warnings(record=True) as w: mod = ExponentialSmoothing( hd2, trend="add", seasonal="add", initialization_method="estimated" ) assert len(w) == 1 assert "ValueWarning" in str(w[0]) assert mod.seasonal_periods == 12 @pytest.mark.parametrize("trend", TRENDS) @pytest.mark.parametrize("seasonal", SEASONALS) def test_start_params(trend, seasonal): mod = ExponentialSmoothing( housing_data, trend=trend, seasonal=seasonal, initialization_method="estimated", ) res = mod.fit() res2 = mod.fit( method="basinhopping", minimize_kwargs={"minimizer_kwargs": {"method": "SLSQP"}}, ) assert res2.sse < 1.01 * res.sse assert isinstance(res2.params, dict) def test_no_params_to_optimize(): with pytest.warns(FutureWarning): mod = ExponentialSmoothing(housing_data) with pytest.warns(EstimationWarning): mod.fit(smoothing_level=0.5, initial_level=housing_data.iloc[0]) def test_invalid_start_param_length(): mod = ExponentialSmoothing(housing_data, initialization_method="estimated") with pytest.raises(ValueError): mod.fit(start_params=np.array([0.5])) def test_basin_hopping(reset_randomstate): mod = ExponentialSmoothing( housing_data, trend="add", initialization_method="estimated" ) res = mod.fit() with pytest.warns(FutureWarning): res2 = mod.fit(use_basinhopping=True) # Basin hopping occasionally produces a slightly larger objective tol = 1e-5 assert res2.sse <= res.sse + tol res3 = mod.fit(method="basinhopping") assert_almost_equal(res2.sse, res3.sse, decimal=2) def test_debiased(): mod = ExponentialSmoothing( housing_data, trend="add", initialization_method="estimated" ) res = mod.fit() res2 = mod.fit(remove_bias=True) assert np.any(res.fittedvalues != res2.fittedvalues) err2 = housing_data.iloc[:, 0] - res2.fittedvalues assert_almost_equal(err2.mean(), 0.0) @pytest.mark.smoke @pytest.mark.parametrize("trend", TRENDS) @pytest.mark.parametrize("seasonal", SEASONALS) def test_float_boxcox(trend, seasonal): res = ExponentialSmoothing( housing_data, trend=trend, seasonal=seasonal, initialization_method="estimated", use_boxcox=0.5, ).fit() assert_allclose(res.params["use_boxcox"], 0.5) with pytest.warns(FutureWarning): res = ExponentialSmoothing( housing_data, trend=trend, seasonal=seasonal, ).fit(use_boxcox=0.5) assert_allclose(res.params["use_boxcox"], 0.5) @pytest.mark.parametrize("trend", TRENDS) @pytest.mark.parametrize("seasonal", SEASONALS) def test_equivalence_cython_python(trend, seasonal): mod = ExponentialSmoothing( housing_data, trend=trend, seasonal=seasonal, initialization_method="estimated", ) with pytest.warns(None): # Overflow in mul-mul case fixed res = mod.fit() res.summary() # Smoke test params = res.params nobs = housing_data.shape[0] y = np.squeeze(np.asarray(housing_data)) m = 12 if seasonal else 0 p = np.zeros(6 + m) alpha = params["smoothing_level"] beta = params["smoothing_trend"] gamma = params["smoothing_seasonal"] phi = params["damping_trend"] phi = 1.0 if np.isnan(phi) else phi l0 = params["initial_level"] b0 = params["initial_trend"] p[:6] = alpha, beta, gamma, l0, b0, phi if seasonal: p[6:] = params["initial_seasons"] xi = np.ones_like(p).astype(int) p_copy = p.copy() bounds = np.array([[0.0, 1.0]] * 3) py_func = PY_SMOOTHERS[(seasonal, trend)] cy_func = SMOOTHERS[(seasonal, trend)] py_hw_args = PyHoltWintersArgs(xi, p_copy, bounds, y, m, nobs, False) cy_hw_args = HoltWintersArgs(xi, p_copy, bounds, y, m, nobs, False) sse_cy = cy_func(p, cy_hw_args) sse_py = py_func(p, py_hw_args) assert_allclose(sse_py, sse_cy) sse_py = py_func(p, cy_hw_args) assert_allclose(sse_py, sse_cy) def test_direct_holt_add(): mod = SimpleExpSmoothing(housing_data, initialization_method="estimated") res = mod.fit() x = np.squeeze(np.asarray(mod.endog)) alpha = res.params["smoothing_level"] l, b, f, _, xhat = _simple_dbl_exp_smoother( x, alpha, beta=0.0, l0=res.params["initial_level"], b0=0.0, nforecast=5 ) assert_allclose(l, res.level) assert_allclose(f, res.level.iloc[-1] * np.ones(5)) assert_allclose(f, res.forecast(5)) mod = ExponentialSmoothing( housing_data, trend="add", initialization_method="estimated" ) res = mod.fit() x = np.squeeze(np.asarray(mod.endog)) alpha = res.params["smoothing_level"] beta = res.params["smoothing_trend"] l, b, f, _, xhat = _simple_dbl_exp_smoother( x, alpha, beta=beta, l0=res.params["initial_level"], b0=res.params["initial_trend"], nforecast=5, ) assert_allclose(xhat, res.fittedvalues) assert_allclose(l + b, res.level + res.trend) assert_allclose(l, res.level) assert_allclose(b, res.trend) assert_allclose( f, res.level.iloc[-1] + res.trend.iloc[-1] * np.array([1, 2, 3, 4, 5]) ) assert_allclose(f, res.forecast(5)) def test_integer_array(reset_randomstate): rs = np.random.RandomState(12345) e = 10 * rs.standard_normal((1000, 2)) y_star = np.cumsum(e[:, 0]) y = y_star + e[:, 1] y = y.astype(int) res = ExponentialSmoothing( y, trend="add", initialization_method="estimated" ).fit() assert res.params["smoothing_level"] != 0.0 def test_damping_trend_zero(): endog = np.arange(10) mod = ExponentialSmoothing( endog, trend="add", damped_trend=True, initialization_method="estimated", ) res1 = mod.fit(smoothing_level=1, smoothing_trend=0.0, damping_trend=1e-20) pred1 = res1.predict(start=0) assert_allclose(pred1, np.r_[0.0, np.arange(9)], atol=1e-10) res2 = mod.fit(smoothing_level=1, smoothing_trend=0.0, damping_trend=0) pred2 = res2.predict(start=0) assert_allclose(pred2, np.r_[0.0, np.arange(9)], atol=1e-10) assert_allclose(pred1, pred2, atol=1e-10) @pytest.fixture def austourists(): # austourists dataset from fpp2 package # https://cran.r-project.org/web/packages/fpp2/index.html data = [ 30.05251, 19.14850, 25.31769, 27.59144, 32.07646, 23.48796, 28.47594, 35.12375, 36.83848, 25.00702, 30.72223, 28.69376, 36.64099, 23.82461, 29.31168, 31.77031, 35.17788, 19.77524, 29.60175, 34.53884, 41.27360, 26.65586, 28.27986, 35.19115, 42.20566, 24.64917, 32.66734, 37.25735, 45.24246, 29.35048, 36.34421, 41.78208, 49.27660, 31.27540, 37.85063, 38.83704, 51.23690, 31.83855, 41.32342, 42.79900, 55.70836, 33.40714, 42.31664, 45.15712, 59.57608, 34.83733, 44.84168, 46.97125, 60.01903, 38.37118, 46.97586, 50.73380, 61.64687, 39.29957, 52.67121, 54.33232, 66.83436, 40.87119, 51.82854, 57.49191, 65.25147, 43.06121, 54.76076, 59.83447, 73.25703, 47.69662, 61.09777, 66.05576, ] index = pd.date_range("1999-03-01", "2015-12-01", freq="3MS") return pd.Series(data, index) @pytest.fixture def simulate_expected_results_r(): """ obtained from ets.simulate in the R package forecast, data is from fpp2 package. library(magrittr) library(fpp2) library(forecast) concat <- function(...) { return(paste(..., sep="")) } error <- c("A", "M") trend <- c("A", "M", "N") seasonal <- c("A", "M", "N") models <- outer(error, trend, FUN = "concat") %>% outer(seasonal, FUN = "concat") %>% as.vector # innov from np.random.seed(0); np.random.randn(4) innov <- c(1.76405235, 0.40015721, 0.97873798, 2.2408932) params <- expand.grid(models, c(TRUE, FALSE)) results <- apply(params, 1, FUN = function(p) { tryCatch( simulate(ets(austourists, model = p[1], damped = as.logical(p[2])), innov = innov), error = function(e) c(NA, NA, NA, NA)) }) %>% t rownames(results) <- apply(params, 1, FUN = function(x) paste(x[1], x[2])) """ damped = { "AAA": [77.84173, 52.69818, 65.83254, 71.85204], "MAA": [207.81653, 136.97700, 253.56234, 588.95800], "MAM": [215.83822, 127.17132, 269.09483, 704.32105], "MMM": [216.52591, 132.47637, 283.04889, 759.08043], "AAN": [62.51423, 61.87381, 63.14735, 65.11360], "MAN": [168.25189, 90.46201, 133.54769, 232.81738], "MMN": [167.97747, 90.59675, 134.20300, 235.64502], } undamped = { "AAA": [77.10860, 51.51669, 64.46857, 70.36349], "MAA": [209.23158, 149.62943, 270.65579, 637.03828], "ANA": [77.09320, 51.52384, 64.36231, 69.84786], "MNA": [207.86986, 169.42706, 313.97960, 793.97948], "MAM": [214.45750, 106.19605, 211.61304, 492.12223], "MMM": [221.01861, 158.55914, 403.22625, 1389.33384], "MNM": [215.00997, 140.93035, 309.92465, 875.07985], "AAN": [63.66619, 63.09571, 64.45832, 66.51967], "MAN": [172.37584, 91.51932, 134.11221, 230.98970], "MMN": [169.88595, 97.33527, 142.97017, 252.51834], "ANN": [60.53589, 59.51851, 60.17570, 61.63011], "MNN": [163.01575, 112.58317, 172.21992, 338.93918], } return {True: damped, False: undamped} @pytest.fixture def simulate_fit_state_r(): """ The final state from the R model fits to get an exact comparison Obtained with this R script: library(magrittr) library(fpp2) library(forecast) concat <- function(...) { return(paste(..., sep="")) } as_dict_string <- function(named) { string <- '{' for (name in names(named)) { string <- concat(string, "\"", name, "\": ", named[name], ", ") } string <- concat(string, '}') return(string) } get_var <- function(named, name) { if (name %in% names(named)) val <- c(named[name]) else val <- c(NaN) names(val) <- c(name) return(val) } error <- c("A", "M") trend <- c("A", "M", "N") seasonal <- c("A", "M", "N") models <- outer(error, trend, FUN = "concat") %>% outer(seasonal, FUN = "concat") %>% as.vector # innov from np.random.seed(0); np.random.randn(4) innov <- c(1.76405235, 0.40015721, 0.97873798, 2.2408932) n <- length(austourists) + 1 # print fit parameters and final states for (damped in c(TRUE, FALSE)) { print(paste("damped =", damped)) for (model in models) { state <- tryCatch((function(){ fit <- ets(austourists, model = model, damped = damped) pars <- c() # alpha, beta, gamma, phi for (name in c("alpha", "beta", "gamma", "phi")) { pars <- c(pars, get_var(fit$par, name)) } # l, b, s1, s2, s3, s4 states <- c() for (name in c("l", "b", "s1", "s2", "s3", "s4")) states <- c(states, get_var(fit$states[n,], name)) c(pars, states) })(), error = function(e) rep(NA, 10)) cat(concat("\"", model, "\": ", as_dict_string(state), ",\n")) } } """ damped = { "AAA": { "alpha": 0.35445427317618, "beta": 0.0320074905894167, "gamma": 0.399933869627979, "phi": 0.979999965983533, "l": 62.003405788717, "b": 0.706524957599738, "s1": 3.58786406600866, "s2": -0.0747450283892903, "s3": -11.7569356589817, "s4": 13.3818805055271, }, "MAA": { "alpha": 0.31114284033284, "beta": 0.0472138763848083, "gamma": 0.309502324693322, "phi": 0.870889202791893, "l": 59.2902342851514, "b": 0.62538315801909, "s1": 5.66660224738038, "s2": 2.16097311633352, "s3": -9.20020909069337, "s4": 15.3505801601698, }, "MAM": { "alpha": 0.483975835390643, "beta": 0.00351728130401287, "gamma": 0.00011309784353818, "phi": 0.979999998322032, "l": 63.0042707536293, "b": 0.275035160634846, "s1": 1.03531670491486, "s2": 0.960515682506077, "s3": 0.770086097577864, "s4": 1.23412213281709, }, "MMM": { "alpha": 0.523526123191035, "beta": 0.000100021136675999, "gamma": 0.000100013723372502, "phi": 0.971025672907157, "l": 63.2030316675533, "b": 1.00458391644788, "s1": 1.03476354353096, "s2": 0.959953222294316, "s3": 0.771346403552048, "s4": 1.23394845160922, }, "AAN": { "alpha": 0.014932817259302, "beta": 0.0149327068053362, "gamma": np.nan, "phi": 0.979919958387887, "l": 60.0651024395378, "b": 0.699112782133822, "s1": np.nan, "s2": np.nan, "s3": np.nan, "s4": np.nan, }, "MAN": { "alpha": 0.0144217343786778, "beta": 0.0144216994589862, "gamma": np.nan, "phi": 0.979999719878659, "l": 60.1870032363649, "b": 0.698421913047609, "s1": np.nan, "s2": np.nan, "s3": np.nan, "s4": np.nan, }, "MMN": { "alpha": 0.015489181776072, "beta": 0.0154891632646377, "gamma": np.nan, "phi": 0.975139118496093, "l": 60.1855946424729, "b": 1.00999589024928, "s1": np.nan, "s2": np.nan, "s3": np.nan, "s4": np.nan, }, } undamped = { "AAA": { "alpha": 0.20281951627363, "beta": 0.000169786227368617, "gamma": 0.464523797585052, "phi": np.nan, "l": 62.5598121416791, "b": 0.578091734736357, "s1": 2.61176734723357, "s2": -1.24386240029203, "s3": -12.9575427049515, "s4": 12.2066400808086, }, "MAA": { "alpha": 0.416371920801538, "beta": 0.000100008012920072, "gamma": 0.352943901103959, "phi": np.nan, "l": 62.0497742976079, "b": 0.450130087198346, "s1": 3.50368220490457, "s2": -0.0544297321113539, "s3": -11.6971093199679, "s4": 13.1974985095916, }, "ANA": { "alpha": 0.54216694759434, "beta": np.nan, "gamma": 0.392030170511872, "phi": np.nan, "l": 57.606831186929, "b": np.nan, "s1": 8.29613785790501, "s2": 4.6033791939889, "s3": -7.43956343440823, "s4": 17.722316385643, }, "MNA": { "alpha": 0.532842556756286, "beta": np.nan, "gamma": 0.346387433608713, "phi": np.nan, "l": 58.0372808528325, "b": np.nan, "s1": 7.70802088750111, "s2": 4.14885814748503, "s3": -7.72115936226225, "s4": 17.1674660340923, }, "MAM": { "alpha": 0.315621390571192, "beta": 0.000100011993615961, "gamma": 0.000100051297784532, "phi": np.nan, "l": 62.4082004238551, "b": 0.513327867101983, "s1": 1.03713425342421, "s2": 0.959607104686072, "s3": 0.770172817592091, "s4": 1.23309264451638, }, "MMM": { "alpha": 0.546068965886, "beta": 0.0737816453485457, "gamma": 0.000100031693302807, "phi": np.nan, "l": 63.8203866275649, "b": 1.01833305374778, "s1": 1.03725227137871, "s2": 0.961177239042923, "s3": 0.771173487523454, "s4": 1.23036313932852, }, "MNM": { "alpha": 0.608993139624813, "beta": np.nan, "gamma": 0.000167258612971303, "phi": np.nan, "l": 63.1472153330648, "b": np.nan, "s1": 1.0384840572776, "s2": 0.961456755855531, "s3": 0.768427399477366, "s4": 1.23185085956321, }, "AAN": { "alpha": 0.0097430554119077, "beta": 0.00974302759255084, "gamma": np.nan, "phi": np.nan, "l": 61.1430969243248, "b": 0.759041621012503, "s1": np.nan, "s2": np.nan, "s3": np.nan, "s4": np.nan, }, "MAN": { "alpha": 0.0101749952821338, "beta": 0.0101749138539332, "gamma": np.nan, "phi": np.nan, "l": 61.6020426238699, "b": 0.761407500773051, "s1": np.nan, "s2": np.nan, "s3": np.nan, "s4": np.nan, }, "MMN": { "alpha": 0.0664382968951546, "beta": 0.000100001678373356, "gamma": np.nan, "phi": np.nan, "l": 60.7206911970871, "b": 1.01221899136391, "s1": np.nan, "s2": np.nan, "s3": np.nan, "s4": np.nan, }, "ANN": { "alpha": 0.196432515825523, "beta": np.nan, "gamma": np.nan, "phi": np.nan, "l": 58.7718395431632, "b": np.nan, "s1": np.nan, "s2": np.nan, "s3": np.nan, "s4": np.nan, }, "MNN": { "alpha": 0.205985314333856, "beta": np.nan, "gamma": np.nan, "phi": np.nan, "l": 58.9770839944419, "b": np.nan, "s1": np.nan, "s2": np.nan, "s3": np.nan, "s4": np.nan, }, } return {True: damped, False: undamped} @pytest.mark.parametrize("trend", TRENDS) @pytest.mark.parametrize("seasonal", SEASONALS) @pytest.mark.parametrize("damped", (True, False)) @pytest.mark.parametrize("error", ("add", "mul")) def test_simulate_expected_r( trend, seasonal, damped, error, austourists, simulate_expected_results_r, simulate_fit_state_r, ): """ Test for :meth:``statsmodels.tsa.holtwinters.HoltWintersResults``. The tests are using the implementation in the R package ``forecast`` as reference, and example data is taken from ``fpp2`` (package and book). """ short_name = {"add": "A", "mul": "M", None: "N"} model_name = short_name[error] + short_name[trend] + short_name[seasonal] if model_name in simulate_expected_results_r[damped]: expected = np.asarray(simulate_expected_results_r[damped][model_name]) state = simulate_fit_state_r[damped][model_name] else: return # create HoltWintersResults object with same parameters as in R with pytest.warns(FutureWarning): fit = ExponentialSmoothing( austourists, seasonal_periods=4, trend=trend, seasonal=seasonal, damped_trend=damped, ).fit( smoothing_level=state["alpha"], smoothing_trend=state["beta"], smoothing_seasonal=state["gamma"], damping_trend=state["phi"], optimized=False, ) # set the same final state as in R fit.level[-1] = state["l"] fit.trend[-1] = state["b"] fit.season[-1] = state["s1"] fit.season[-2] = state["s2"] fit.season[-3] = state["s3"] fit.season[-4] = state["s4"] # for MMM with damped trend the fit fails if np.any(np.isnan(fit.fittedvalues)): return innov = np.asarray([[1.76405235, 0.40015721, 0.97873798, 2.2408932]]).T sim = fit.simulate(4, repetitions=1, error=error, random_errors=innov) assert_almost_equal(expected, sim.values, 5) def test_simulate_keywords(austourists): """ check whether all keywords are accepted and work without throwing errors. """ fit = ExponentialSmoothing( austourists, seasonal_periods=4, trend="add", seasonal="add", damped_trend=True, initialization_method="estimated", ).fit() # test anchor assert_almost_equal( fit.simulate(4, anchor=0, random_state=0).values, fit.simulate(4, anchor="start", random_state=0).values, ) assert_almost_equal( fit.simulate(4, anchor=-1, random_state=0).values, fit.simulate(4, anchor="2015-12-01", random_state=0).values, ) assert_almost_equal( fit.simulate(4, anchor="end", random_state=0).values, fit.simulate(4, anchor="2016-03-01", random_state=0).values, ) # test different random error options fit.simulate(4, repetitions=10, random_errors=scipy.stats.norm) fit.simulate(4, repetitions=10, random_errors=scipy.stats.norm()) fit.simulate(4, repetitions=10, random_errors=np.random.randn(4, 10)) fit.simulate(4, repetitions=10, random_errors="bootstrap") # test seeding res = fit.simulate(4, repetitions=10, random_state=10).values res2 = fit.simulate( 4, repetitions=10, random_state=np.random.RandomState(10) ).values assert np.all(res == res2) def test_simulate_boxcox(austourists): """ check if simulation results with boxcox fits are reasonable """ fit = ExponentialSmoothing( austourists, seasonal_periods=4, trend="add", seasonal="mul", damped_trend=False, initialization_method="estimated", use_boxcox=True, ).fit() expected = fit.forecast(4).values res = fit.simulate(4, repetitions=10, random_state=0).values mean = np.mean(res, axis=1) assert np.all(np.abs(mean - expected) < 5) @pytest.mark.parametrize("ix", [10, 100, 1000, 2000]) def test_forecast_index(ix): # GH 6549 ts_1 = pd.Series( [85601, 89662, 85122, 84400, 78250, 84434, 71072, 70357, 72635, 73210], index=range(ix, ix + 10), ) with pytest.warns(ConvergenceWarning): model = ExponentialSmoothing( ts_1, trend="add", damped_trend=False ).fit() index = model.forecast(steps=10).index assert index[0] == ix + 10 assert index[-1] == ix + 19 def test_error_dampen(): with pytest.raises(ValueError, match="Can only dampen the"): ExponentialSmoothing(np.ones(100), damped_trend=True) def test_error_boxcox(): y = np.random.standard_normal(100) with pytest.raises(TypeError, match="use_boxcox must be True"): ExponentialSmoothing(y, use_boxcox="a", initialization_method="known") with pytest.raises(ValueError, match="initialization_method must be set"): ExponentialSmoothing(y, use_boxcox=True) mod = ExponentialSmoothing( y ** 2, use_boxcox=True, initialization_method="legacy-heuristic" ) with pytest.raises(ValueError, match="use_boxcox was set"): mod.fit(use_boxcox=False) def test_error_initialization(ses): with pytest.raises( ValueError, match="initialization is 'known' but initial_level" ): ExponentialSmoothing(ses, initialization_method="known") with pytest.raises(ValueError, match="initial_trend set but model"): ExponentialSmoothing( ses, initialization_method="known", initial_level=1.0, initial_trend=1.0, ) with pytest.raises(ValueError, match="initial_seasonal set but model"): ExponentialSmoothing( ses, initialization_method="known", initial_level=1.0, initial_seasonal=[0.2, 0.3, 0.4, 0.5], ) with pytest.raises(ValueError): ExponentialSmoothing(ses, initial_level=1.0) with pytest.raises(ValueError): ExponentialSmoothing(ses, initial_trend=1.0) with pytest.raises(ValueError): ExponentialSmoothing(ses, initial_seasonal=[1.0, 0.2, 0.05, 4]) with pytest.raises(ValueError): ExponentialSmoothing( ses, trend="add", initialization_method="known", initial_level=1.0, ) with pytest.raises(ValueError): ExponentialSmoothing( ses, trend="add", seasonal="add", initialization_method="known", initial_level=1.0, initial_trend=2.0, ) mod = ExponentialSmoothing( ses, initialization_method="known", initial_level=1.0 ) with pytest.raises(ValueError): mod.fit(initial_level=2.0) with pytest.raises(ValueError): mod.fit(use_basinhopping=True, method="least_squares") @pytest.mark.parametrize( "method", [ "least_squares", "basinhopping", "L-BFGS-B", "TNC", "SLSQP", "Powell", "trust-constr", ], ) def test_alternative_minimizers(method, ses): sv = np.array([0.77, 11.00]) minimize_kwargs = {} mod = ExponentialSmoothing(ses, initialization_method="estimated") res = mod.fit( method=method, start_params=sv, minimize_kwargs=minimize_kwargs ) assert_allclose(res.params["smoothing_level"], 0.77232545, rtol=1e-3) assert_allclose(res.params["initial_level"], 11.00359693, rtol=1e-3) def test_minimizer_kwargs_error(ses): mod = ExponentialSmoothing(ses, initialization_method="estimated") kwargs = {"args": "anything"} with pytest.raises(ValueError): mod.fit(minimize_kwargs=kwargs) with pytest.raises(ValueError): mod.fit(method="least_squares", minimize_kwargs=kwargs) kwargs = {"minimizer_kwargs": {"args": "anything"}} with pytest.raises(ValueError): mod.fit(method="basinhopping", minimize_kwargs=kwargs) kwargs = {"minimizer_kwargs": {"method": "SLSQP"}} res = mod.fit(method="basinhopping", minimize_kwargs=kwargs) assert isinstance(res.params, dict) @pytest.mark.parametrize( "params", [[0.8, 0.3, 0.9], [0.3, 0.8, 0.2], [0.5, 0.6, 0.6]] ) def test_to_restricted_equiv(params): params = np.array(params) sel = np.array([True] * 3) bounds = np.array([[0.0, 1.0]] * 3) assert_allclose( to_restricted(params, sel, bounds), _test_to_restricted(params, sel.astype(int), bounds), ) @pytest.mark.parametrize( "params", [[0.8, 0.3, 0.1], [0.3, 0.2, 0.6], [0.5, 0.5, 0.5]] ) def test_restricted_round_tip(params): params = np.array(params) sel = np.array([True] * 3) bounds = np.array([[0.0, 1.0]] * 3) assert_allclose( params, to_unrestricted(to_restricted(params, sel, bounds), sel, bounds), ) def test_bad_bounds(ses): bounds = {"bad_key": (0.0, 1.0)} with pytest.raises(KeyError): ExponentialSmoothing(ses, bounds=bounds) bounds = {"smoothing_level": [0.0, 1.0]} with pytest.raises(TypeError): ExponentialSmoothing(ses, bounds=bounds) bounds = {"smoothing_level": (0.0, 1.0, 2.0)} with pytest.raises(ValueError): ExponentialSmoothing(ses, bounds=bounds) bounds = {"smoothing_level": (1.0, 0.0)} with pytest.raises(ValueError): ExponentialSmoothing(ses, bounds=bounds) bounds = {"smoothing_level": (-1.0, 2.0)} with pytest.raises(ValueError): ExponentialSmoothing(ses, bounds=bounds) def test_valid_bounds(ses): bounds = {"smoothing_level": (0.1, 1.0)} res = ExponentialSmoothing( ses, bounds=bounds, initialization_method="estimated" ).fit(method="least_squares") res2 = ExponentialSmoothing(ses, initialization_method="estimated").fit( method="least_squares" ) assert_allclose( res.params["smoothing_level"], res2.params["smoothing_level"], rtol=1e-4, ) def test_fixed_basic(ses): mod = ExponentialSmoothing(ses, initialization_method="estimated") with mod.fix_params({"smoothing_level": 0.3}): res = mod.fit() assert res.params["smoothing_level"] == 0.3 mod = ExponentialSmoothing( ses, trend="add", damped_trend=True, initialization_method="estimated" ) with mod.fix_params({"damping_trend": 0.98}): res = mod.fit() assert res.params["damping_trend"] == 0.98 mod = ExponentialSmoothing( ses, trend="add", seasonal="add", initialization_method="estimated" ) with mod.fix_params({"smoothing_seasonal": 0.1, "smoothing_level": 0.2}): res = mod.fit() assert res.params["smoothing_seasonal"] == 0.1 assert res.params["smoothing_level"] == 0.2 def test_fixed_errors(ses): mod = ExponentialSmoothing(ses, initialization_method="estimated") with pytest.raises(KeyError): with mod.fix_params({"smoothing_trend": 0.3}): pass with pytest.raises(ValueError): with mod.fix_params({"smoothing_level": -0.3}): pass mod = ExponentialSmoothing( ses, trend="add", initialization_method="estimated" ) with pytest.raises(ValueError): with mod.fix_params({"smoothing_level": 0.3, "smoothing_trend": 0.4}): pass mod = ExponentialSmoothing( ses, trend="add", seasonal="add", initialization_method="estimated" ) with pytest.raises(ValueError): with mod.fix_params( {"smoothing_level": 0.3, "smoothing_seasonal": 0.8} ): pass bounds = {"smoothing_level": (0.4, 0.8), "smoothing_seasonal": (0.7, 0.9)} mod = ExponentialSmoothing( ses, trend="add", seasonal="add", bounds=bounds, initialization_method="estimated", ) with pytest.raises(ValueError, match="After adjusting for user-provided"): with mod.fix_params( {"smoothing_trend": 0.3, "smoothing_seasonal": 0.6} ): mod.fit() @pytest.mark.parametrize("trend", ["add", None]) @pytest.mark.parametrize("seasonal", ["add", None]) def test_brute(ses, trend, seasonal): mod = ExponentialSmoothing( ses, trend=trend, seasonal=seasonal, initialization_method="estimated" ) res = mod.fit(use_brute=True) assert res.mle_retvals.success with mod.fix_params({"smoothing_level": 0.1}): res = mod.fit(use_brute=True) assert res.mle_retvals.success def test_fix_set_parameters(ses): with pytest.raises(ValueError): ExponentialSmoothing( ses, initial_level=1.0, initialization_method="heuristic" ) with pytest.raises(ValueError): ExponentialSmoothing( ses, trend="add", initial_trend=1.0, initialization_method="legacy-heuristic", ) with pytest.raises(ValueError): ExponentialSmoothing( ses, seasonal="add", initial_seasonal=np.ones(12), initialization_method="estimated", ) def test_fix_unfixable(ses): mod = ExponentialSmoothing(ses, initialization_method="estimated") with pytest.raises(ValueError, match="Cannot fix a parameter"): with mod.fix_params({"smoothing_level": 0.25}): mod.fit(smoothing_level=0.2) def test_infeasible_bounds(ses): bounds = {"smoothing_level": (0.1, 0.2), "smoothing_trend": (0.3, 0.4)} with pytest.raises(ValueError, match="The bounds for smoothing_trend"): ExponentialSmoothing( ses, trend="add", bounds=bounds, initialization_method="estimated" ).fit() bounds = {"smoothing_level": (0.3, 0.5), "smoothing_seasonal": (0.7, 0.8)} with pytest.raises(ValueError, match="The bounds for smoothing_seasonal"): ExponentialSmoothing( ses, seasonal="add", bounds=bounds, initialization_method="estimated", ).fit() @pytest.mark.parametrize( "method", ["estimated", "heuristic", "legacy-heuristic"] ) @pytest.mark.parametrize("trend", [None, "add"]) @pytest.mark.parametrize("seasonal", [None, "add"]) def test_initialization_methods(ses, method, trend, seasonal): mod = ExponentialSmoothing( ses, trend=trend, seasonal=seasonal, initialization_method=method ) res = mod.fit() assert res.mle_retvals.success def test_attributes(ses): res = ExponentialSmoothing(ses, initialization_method="estimated").fit() with pytest.warns(FutureWarning): assert_allclose(res.trend, res.slope) assert res.k > 0 assert res.resid.shape[0] == ses.shape[0] assert_allclose(res.fcastvalues, res.fittedfcast[-1:]) def test_summary_boxcox(ses): mod = ExponentialSmoothing( ses ** 2, use_boxcox=True, initialization_method="heuristic" ) with pytest.raises(ValueError, match="use_boxcox was set at model"): mod.fit(use_boxcox=True) res = mod.fit() summ = str(res.summary()) assert re.findall(r"Box-Cox:[\s]*True", summ) def test_simulate(ses): mod = ExponentialSmoothing( np.asarray(ses), initialization_method="heuristic" ) res = mod.fit() with pytest.raises(ValueError, match="error must be"): res.simulate(10, error="unknown") with pytest.raises(ValueError, match="If random"): res.simulate(10, error="additive", random_errors=np.empty((20, 20))) res.simulate(10, error="additive", anchor=100) with pytest.raises(ValueError, match="Cannot anchor"): res.simulate(10, error="additive", anchor=2000) with pytest.raises(ValueError, match="Argument random_state"): res.simulate( 10, error="additive", anchor=100, random_state="bad_value" ) with pytest.raises(ValueError, match="Argument random_errors"): res.simulate(10, error="additive", random_errors="bad_values") @pytest.mark.parametrize( "index_typ", ["date_range", "period", "range", "irregular"] ) def test_forecast_index_types(ses, index_typ): nobs = ses.shape[0] kwargs = {} warning = None fcast_index = None if index_typ == "period": index = pd.period_range("2000-1-1", periods=nobs + 36, freq="M") elif index_typ == "date_range": index = pd.date_range("2000-1-1", periods=nobs + 36, freq="M") elif index_typ == "range": index = pd.RangeIndex(nobs + 36) kwargs["seasonal_periods"] = 12 elif index_typ == "irregular": rs = np.random.RandomState(0) index = pd.Index(np.cumsum(rs.randint(0, 4, size=nobs + 36))) warning = ValueWarning kwargs["seasonal_periods"] = 12 fcast_index = pd.RangeIndex(start=1000, stop=1036, step=1) if fcast_index is None: fcast_index = index[-36:] ses = ses.copy() ses.index = index[:-36] with pytest.warns(warning): res = ExponentialSmoothing( ses, trend="add", seasonal="add", initialization_method="heuristic", **kwargs ).fit() with pytest.warns(warning): fcast = res.forecast(36) assert isinstance(fcast, pd.Series) pd.testing.assert_index_equal(fcast.index, fcast_index) def test_boxcox_components(ses): mod = ExponentialSmoothing( ses + 1 - ses.min(), initialization_method="estimated", use_boxcox=True ) res = mod.fit() with pytest.raises(AssertionError): # Must be different since level is not transformed assert_allclose(res.level, res.fittedvalues) assert not hasattr(res, "_untransformed_level") assert not hasattr(res, "_untransformed_trend") assert not hasattr(res, "_untransformed_seasonal") @pytest.mark.parametrize("repetitions", [1, 10]) @pytest.mark.parametrize("random_errors", [None, "bootstrap"]) def test_forecast_1_simulation(austourists, random_errors, repetitions): # GH 7053 fit = ExponentialSmoothing( austourists, seasonal_periods=4, trend="add", seasonal="add", damped_trend=True, initialization_method="estimated", ).fit() sim = fit.simulate( 1, anchor=0, random_errors=random_errors, repetitions=repetitions ) expected_shape = (1,) if repetitions == 1 else (1, repetitions) assert sim.shape == expected_shape sim = fit.simulate( 10, anchor=0, random_errors=random_errors, repetitions=repetitions ) expected_shape = (10,) if repetitions == 1 else (10, repetitions) assert sim.shape == expected_shape statsmodels-0.12.2/statsmodels/tsa/innovations/000077500000000000000000000000001400612667500216455ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/innovations/__init__.py000066400000000000000000000001131400612667500237510ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/tsa/innovations/_arma_innovations.pyx.in000066400000000000000000000401101400612667500265160ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ Innovations algorithm Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("cnp.float32_t", "np.float32", "cnp.NPY_FLOAT32"), "d": ("cnp.float64_t", "float", "cnp.NPY_FLOAT64"), "c": ("cnp.complex64_t", "np.complex64", "cnp.NPY_COMPLEX64"), "z": ("cnp.complex128_t", "complex", "cnp.NPY_COMPLEX128"), } }} # Typical imports import numpy as np import warnings from statsmodels.tsa import arima_process from statsmodels.src.math cimport NPY_PI, dlog, zlog cimport numpy as cnp cimport cython cnp.import_array() cdef int C = 0 {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} cdef {{prefix}}toeplitz(int n, int offset0, int offset1, {{cython_type}} [:] in_column, {{cython_type}} [:, :] out_matrix): """ toeplitz(int n, int o0, int o1, {{cython_type}} [:] in_column, {{cython_type}} [:, :] out_matrix Construct a Toeplitz block in a matrix in place Parameters ---------- n : int The number of entries of `in_column` to use. offset0 : int The row offset for `out_matrix` at which to begin writing the Toeplitz block. offset1 : int The column offset for `out_matrix` at which to begin writing the Toeplitz block. in_column : ndarray The column used to construct the Toeplitz block. out_matrix : ndarray The matrix in which to write a Toeplitz block Notes ----- This function constructs the Toeplitz block in-place and does not return any output. """ cdef Py_ssize_t i, j for i in range(n): for j in range(i + 1): out_matrix[offset0 + i, offset1 + j] = in_column[i - j] if i != j: # Note: scipy by default does complex conjugate, but not # necessary here since we're only dealing with covariances, # which will be real (except in the case of complex-step # differentiation, but in that case we do not want to apply # the conjugation anyway) out_matrix[offset0 + j, offset1 + i] = in_column[i - j] cpdef {{prefix}}arma_transformed_acovf_fast({{cython_type}} [:] ar, {{cython_type}} [:] ma, {{cython_type}} [:] arma_acovf): """ arma_transformed_acovf_fast({{cython_type}} [:] ar, {{cython_type}} [:] ma, {{cython_type}} [:] arma_acovf) Quickly construct the autocovariance matrix for a transformed process. Using the autocovariance function for an ARMA process, constructs the autocovariances associated with the transformed process described in equation (3.3.1) of _[1] in a memory efficient, and so fast, way. Parameters ---------- ar : ndarray Autoregressive coefficients, including the zero lag, where the sign convention assumes the coefficients are part of the lag polynomial on the left-hand-side of the ARMA definition (i.e. they have the opposite sign from the usual econometrics convention in which the coefficients are on the right-hand-side of the ARMA definition). ma : ndarray Moving average coefficients, including the zero lag, where the sign convention assumes the coefficients are part of the lag polynomial on the right-hand-side of the ARMA definition (i.e. they have the same sign from the usual econometrics convention in which the coefficients are on the right-hand-side of the ARMA definition). arma_acovf : ndarray The vector of autocovariances of the ARMA process. Returns ------- acovf : ndarray A matrix containing the autocovariances of the portion of the transformed process with time-varying autocovariances. Its dimension is equal to `min(m * 2, n)` where `m = max(len(ar) - 1, len(ma) - 1)` and `n` is the length of the input array `arma_acovf`. It is important to note that only the values in the first `m` columns or `m` rows are valid. In particular, the entries in the block `acovf[m:, m:]` should not be used in any case (and in fact will always be equal to zeros). acovf2 : ndarray An array containing the autocovariance function of the portion of the transformed process with time-invariant autocovariances. Its dimension is equal to `max(n - m, 0)` where `n` is the length of the input array `arma_acovf`. Notes ----- The definition of this autocovariance matrix is from _[1] equation 3.3.3. This function assumes that the variance of the ARMA innovation term is equal to one. If this is not true, then the calling program should replace `arma_acovf` with `arma_acovf / sigma2`, where sigma2 is that variance. This function is relatively fast even when `arma_acovf` is large, since it only constructs the full autocovariance matrix for a generally small subset of observations. The trade-off is that the output of this function is somewhat more difficult to use. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2009. Time Series: Theory and Methods. 2nd ed. 1991. New York, NY: Springer. """ cdef Py_ssize_t nobs, p, q, m, m2, n, i, j, r, tmp_ix cdef cnp.npy_intp dim1[1] cdef cnp.npy_intp dim2[2] cdef {{cython_type}} [:, :] acovf cdef {{cython_type}} [:] acovf2 nobs = arma_acovf.shape[0] p = len(ar) - 1 q = len(ma) - 1 m = max(p, q) m2 = 2 * m n = min(m2, nobs) dim2[0] = m2; dim2[1] = m2; acovf = cnp.PyArray_ZEROS(2, dim2, {{typenum}}, C) dim1[0] = max(nobs - m, 0); acovf2 = cnp.PyArray_ZEROS(1, dim1, {{typenum}}, C) # Set i, j = 1, ..., m (which is then done) {{prefix}}toeplitz(m, 0, 0, arma_acovf, acovf) # Set i = 1, ..., m; j = m + 1, ..., 2 m # and i = m + 1, ..., 2 m; j = 1, ..., m if nobs > m: for j in range(m): for i in range(m, m2): acovf[i, j] = arma_acovf[i - j] for r in range(1, p + 1): tmp_ix = abs(r - (i - j)) acovf[i, j] = acovf[i, j] - (-ar[r] * arma_acovf[tmp_ix]) acovf[:m, m:m2] = acovf[m:m2, :m].T # Set values for |i - j| <= q, min(i, j) = m + 1, and max(i, j) <= nobs if nobs > m: for i in range(nobs - m): for r in range(q + 1 - i): acovf2[i] = acovf2[i] + ma[r] * ma[r + i] return acovf[:n, :n], acovf2 cpdef {{prefix}}arma_innovations_algo_fast(int nobs, {{cython_type}} [:] ar_params, {{cython_type}} [:] ma_params, {{cython_type}} [:, :] acovf, {{cython_type}} [:] acovf2): """ arma_innovations_algo_fast(int nobs, {{cython_type}} [:] ar_params, {{cython_type}} [:] ma_params, {{cython_type}} [:, :] acovf, {{cython_type}} [:] acovf2) Quickly apply innovations algorithm for an ARMA process. Parameters ---------- ar_params : ndarray Autoregressive parameters. ma_params : ndarray Moving average parameters. acovf : ndarray An `m * 2` x `m * 2` autocovariance matrix at least the first `m` columns filled in, where `m = max(len(ar_params), ma_params)` (see `arma_transformed_acovf_fast`). acovf2 : ndarray A `max(0, nobs - m)` length vector containing the autocovariance function associated with the final `nobs - m` observations. Returns ------- theta : ndarray The matrix of moving average coefficients from the innovations algorithm. v : ndarray The vector of mean squared errors. Notes ----- The innovations algorithm is presented in _[1], section 2.5.2. Details of the innovations algorithm applied to ARMA processes is given in _[1] section 3.3 and in section 5.2.7. This function is relatively fast even with a large number of observations since we can exploit a number of known zeros in the theta array. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2009. Time Series: Theory and Methods. 2nd ed. 1991. New York, NY: Springer. """ cdef Py_ssize_t i, j, k, n, _n, m, m2, p, q, start, start2 cdef cnp.npy_intp dim1[1] cdef cnp.npy_intp dim2[2] cdef {{cython_type}} [:, :] theta cdef {{cython_type}} [:] v p = len(ar_params) q = len(ma_params) m = max(p, q) m2 = 2 * m dim1[0] = nobs; v = cnp.PyArray_ZEROS(1, dim1, {{typenum}}, C) dim2[0] = nobs; dim2[1] = m + 1; theta = cnp.PyArray_ZEROS(2, dim2, {{typenum}}, C) if m > 0: v[0] = acovf[0, 0] else: # (handle the corner case where p = q = 0) v[0] = acovf2[0] for n in range(nobs - 1): _n = n + 1 start = 0 if n < m else n + 1 - q for k in range(start, n + 1): # See Brockwell and Davis, p. 100-101 # (here we have weak rather than strict inequality due to Python's # zero indexing) if n >= m and n - k >= q: continue if n + 1 < m2 and k < m: theta[_n, n - k] = acovf[n + 1, k] else: theta[_n, n - k] = acovf2[n + 1 - k] start2 = 0 if n < m else n - m for j in range(start2, k): if n - j < m + 1: theta[_n, n - k] = theta[_n, n - k] - theta[k - 1 + 1, k - j - 1] * theta[_n, n - j] * v[j] theta[_n, n - k] = theta[_n, n - k] / v[k] if n + 1 < m: v[n + 1] = acovf[n + 1, n + 1] else: v[n + 1] = acovf2[0] start = max(0, n - (m + 1) + 2) for i in range(start, n + 1): v[n + 1] = v[n + 1] - theta[_n, n - i]**2 * v[i] return theta, v cpdef {{prefix}}arma_innovations_filter({{cython_type}} [:] endog, {{cython_type}} [:] ar_params, {{cython_type}} [:] ma_params, {{cython_type}} [:, :] theta): """ arma_innovations_filter({{cython_type}} [:] endog, {{cython_type}} [:] ar_params, {{cython_type}} [:] ma_params, {{cython_type}} [:, :] theta): Innovations filter for an ARMA process. Parameters ---------- endog : ndarray The observed time-series process. ar_params : ndarray Autoregressive parameters. ma_params : ndarray Moving average parameters. theta : ndarray The matrix of moving average coefficients from the innovations algorithm (see `arma_innovations_algo` or `arma_innovations_algo_fast`) Returns ------- u : ndarray The vector of innovations: the one-step-ahead prediction errors from applying the innovations algorithm. Notes ----- The innovations algorithm is presented in _[1], section 2.5.2. Details of the innovations algorithm applied to ARMA processes is given in _[1] section 3.3 and in section 5.2.7. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2009. Time Series: Theory and Methods. 2nd ed. 1991. New York, NY: Springer. """ cdef Py_ssize_t nobs, i, k, j, m, p, q cdef cnp.npy_intp dim1[1] cdef {{cython_type}} [:] u cdef {{cython_type}} hat p = len(ar_params) q = len(ma_params) m = max(p, q) nobs = theta.shape[0] k = theta.shape[1] dim1[0] = nobs; u = cnp.PyArray_ZEROS(1, dim1, {{typenum}}, C) u[0] = endog[0] for i in range(1, nobs): hat = 0 if i < m: for j in range(i): hat = hat + theta[i, j] * u[i - j - 1] else: for j in range(p): hat = hat + ar_params[j] * endog[i - j - 1] for j in range(q): hat = hat + theta[i, j] * u[i - j - 1] u[i] = endog[i] - hat return u cpdef {{prefix}}arma_innovations({{cython_type}} [:] endog, {{cython_type}} [:] ar_params, {{cython_type}} [:] ma_params, {{cython_type}} sigma2): """ arma_innovations({{cython_type}} [:] endog, {{cython_type}} [:] ar_params, {{cython_type}} [:] ma_params): Compute innovations and variances based on an ARMA process. Parameters ---------- endog : ndarray The observed time-series process. ar_params : ndarray Autoregressive parameters. ma_params : ndarray Moving average parameters. sigma2 : ndarray The ARMA innovation variance. Returns ------- u : ndarray The vector of innovations: the one-step-ahead prediction errors from applying the innovations algorithm. v : ndarray The vector of innovation variances. Notes ----- The innovations algorithm is presented in _[1], section 2.5.2. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2009. Time Series: Theory and Methods. 2nd ed. 1991. New York, NY: Springer. """ cdef Py_ssize_t nobs = len(endog), i cdef {{cython_type}} const cdef {{cython_type}} [:] ar, ma, arma_acovf, llf_obs, acovf2, u, v cdef {{cython_type}} [:, :] acovf cdef cnp.npy_intp dim1[1] dim1[0] = len(ar_params) + 1; ar = cnp.PyArray_ZEROS(1, dim1, {{typenum}}, C) dim1[0] = len(ma_params) + 1; ma = cnp.PyArray_ZEROS(1, dim1, {{typenum}}, C) ar[0] = 1 for i in range(1, len(ar_params) + 1): ar[i] = -1 * ar_params[i - 1] ma[0] = 1 ma[1:] = ma_params arma_acovf = arima_process.arma_acovf(ar, ma, nobs, sigma2, dtype={{dtype}}) / sigma2 acovf, acovf2 = {{prefix}}arma_transformed_acovf_fast(ar, ma, arma_acovf) theta, v = {{prefix}}arma_innovations_algo_fast(nobs, ar_params, ma_params, acovf, acovf2) u = {{prefix}}arma_innovations_filter(endog, ar_params, ma_params, theta) return u, v cpdef {{prefix}}arma_loglikeobs_fast({{cython_type}} [:] endog, {{cython_type}} [:] ar_params, {{cython_type}} [:] ma_params, {{cython_type}} sigma2): """ {{prefix}}arma_loglikeobs_fast({{cython_type}} [:] endog, {{cython_type}} [:] ar_params, {{cython_type}} [:] ma_params, {{cython_type}} sigma2) Quickly calculate the loglikelihood of each observation for an ARMA process Parameters ---------- endog : ndarray The observed time-series process. ar_params : ndarray Autoregressive parameters. ma_params : ndarray Moving average parameters. sigma2 : ndarray The ARMA innovation variance. Returns ------- loglike : ndarray of float Array of loglikelihood values for each observation. Notes ----- Details related to computing the loglikelihood associated with an ARMA process using the innovations algorithm are given in _[1] section 5.2. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2009. Time Series: Theory and Methods. 2nd ed. 1991. New York, NY: Springer. """ cdef Py_ssize_t nobs = len(endog), i cdef {{cython_type}} const cdef {{cython_type}} [:] llf_obs, u, v cdef cnp.npy_intp dim1[1] u, v = {{prefix}}arma_innovations(endog, ar_params, ma_params, sigma2) dim1[0] = nobs; llf_obs = cnp.PyArray_ZEROS(1, dim1, {{typenum}}, C) const = {{combined_prefix}}log(2*NPY_PI) for i in range(nobs): llf_obs[i] = -0.5 * u[i]**2 / (sigma2 * v[i]) - 0.5 * (const + {{combined_prefix}}log(sigma2 * v[i])) return np.array(llf_obs, dtype={{dtype}}) {{endfor}} statsmodels-0.12.2/statsmodels/tsa/innovations/api.py000066400000000000000000000001761400612667500227740ustar00rootroot00000000000000from .arma_innovations import ( # noqa: F401 arma_innovations, arma_loglike, arma_loglikeobs, arma_score, arma_scoreobs) statsmodels-0.12.2/statsmodels/tsa/innovations/arma_innovations.py000066400000000000000000000230761400612667500255760ustar00rootroot00000000000000import numpy as np from statsmodels.tsa import arima_process from statsmodels.tsa.statespace.tools import prefix_dtype_map from statsmodels.tools.numdiff import _get_epsilon, approx_fprime_cs from scipy.linalg.blas import find_best_blas_type from . import _arma_innovations NON_STATIONARY_ERROR = """\ The model's autoregressive parameters (ar_params) indicate that the process is non-stationary. The innovations algorithm cannot be used. """ def arma_innovations(endog, ar_params=None, ma_params=None, sigma2=1, normalize=False, prefix=None): """ Compute innovations using a given ARMA process. Parameters ---------- endog : ndarray The observed time-series process, may be univariate or multivariate. ar_params : ndarray, optional Autoregressive parameters. ma_params : ndarray, optional Moving average parameters. sigma2 : ndarray, optional The ARMA innovation variance. Default is 1. normalize : bool, optional Whether or not to normalize the returned innovations. Default is False. prefix : str, optional The BLAS prefix associated with the datatype. Default is to find the best datatype based on given input. This argument is typically only used internally. Returns ------- innovations : ndarray Innovations (one-step-ahead prediction errors) for the given `endog` series with predictions based on the given ARMA process. If `normalize=True`, then the returned innovations have been "whitened" by dividing through by the square root of the mean square error. innovations_mse : ndarray Mean square error for the innovations. """ # Parameters endog = np.array(endog) squeezed = endog.ndim == 1 if squeezed: endog = endog[:, None] ar_params = np.atleast_1d([] if ar_params is None else ar_params) ma_params = np.atleast_1d([] if ma_params is None else ma_params) nobs, k_endog = endog.shape ar = np.r_[1, -ar_params] ma = np.r_[1, ma_params] # Get BLAS prefix if prefix is None: prefix, dtype, _ = find_best_blas_type( [endog, ar_params, ma_params, np.array(sigma2)]) dtype = prefix_dtype_map[prefix] # Make arrays contiguous for BLAS calls endog = np.asfortranarray(endog, dtype=dtype) ar_params = np.asfortranarray(ar_params, dtype=dtype) ma_params = np.asfortranarray(ma_params, dtype=dtype) sigma2 = dtype(sigma2).item() # Get the appropriate functions arma_transformed_acovf_fast = getattr( _arma_innovations, prefix + 'arma_transformed_acovf_fast') arma_innovations_algo_fast = getattr( _arma_innovations, prefix + 'arma_innovations_algo_fast') arma_innovations_filter = getattr( _arma_innovations, prefix + 'arma_innovations_filter') # Run the innovations algorithm for ARMA coefficients arma_acovf = arima_process.arma_acovf(ar, ma, sigma2=sigma2, nobs=nobs) / sigma2 acovf, acovf2 = arma_transformed_acovf_fast(ar, ma, arma_acovf) theta, v = arma_innovations_algo_fast(nobs, ar_params, ma_params, acovf, acovf2) v = np.array(v) if (np.any(v < 0) or not np.isfinite(theta).all() or not np.isfinite(v).all()): # This is defensive code that is hard to hit raise ValueError(NON_STATIONARY_ERROR) # Run the innovations filter across each series u = [] for i in range(k_endog): u_i = np.array(arma_innovations_filter(endog[:, i], ar_params, ma_params, theta)) u.append(u_i) u = np.vstack(u).T if normalize: u /= v[:, None]**0.5 # Post-processing if squeezed: u = u.squeeze() return u, v def arma_loglike(endog, ar_params=None, ma_params=None, sigma2=1, prefix=None): """ Compute the log-likelihood of the given data assuming an ARMA process. Parameters ---------- endog : ndarray The observed time-series process. ar_params : ndarray, optional Autoregressive parameters. ma_params : ndarray, optional Moving average parameters. sigma2 : ndarray, optional The ARMA innovation variance. Default is 1. prefix : str, optional The BLAS prefix associated with the datatype. Default is to find the best datatype based on given input. This argument is typically only used internally. Returns ------- float The joint loglikelihood. """ llf_obs = arma_loglikeobs(endog, ar_params=ar_params, ma_params=ma_params, sigma2=sigma2, prefix=prefix) return np.sum(llf_obs) def arma_loglikeobs(endog, ar_params=None, ma_params=None, sigma2=1, prefix=None): """ Compute the log-likelihood for each observation assuming an ARMA process. Parameters ---------- endog : ndarray The observed time-series process. ar_params : ndarray, optional Autoregressive parameters. ma_params : ndarray, optional Moving average parameters. sigma2 : ndarray, optional The ARMA innovation variance. Default is 1. prefix : str, optional The BLAS prefix associated with the datatype. Default is to find the best datatype based on given input. This argument is typically only used internally. Returns ------- ndarray Array of loglikelihood values for each observation. """ endog = np.array(endog) ar_params = np.atleast_1d([] if ar_params is None else ar_params) ma_params = np.atleast_1d([] if ma_params is None else ma_params) if prefix is None: prefix, dtype, _ = find_best_blas_type( [endog, ar_params, ma_params, np.array(sigma2)]) dtype = prefix_dtype_map[prefix] endog = np.ascontiguousarray(endog, dtype=dtype) ar_params = np.asfortranarray(ar_params, dtype=dtype) ma_params = np.asfortranarray(ma_params, dtype=dtype) sigma2 = dtype(sigma2).item() func = getattr(_arma_innovations, prefix + 'arma_loglikeobs_fast') return func(endog, ar_params, ma_params, sigma2) def arma_score(endog, ar_params=None, ma_params=None, sigma2=1, prefix=None): """ Compute the score (gradient of the log-likelihood function). Parameters ---------- endog : ndarray The observed time-series process. ar_params : ndarray, optional Autoregressive coefficients, not including the zero lag. ma_params : ndarray, optional Moving average coefficients, not including the zero lag, where the sign convention assumes the coefficients are part of the lag polynomial on the right-hand-side of the ARMA definition (i.e. they have the same sign from the usual econometrics convention in which the coefficients are on the right-hand-side of the ARMA definition). sigma2 : ndarray, optional The ARMA innovation variance. Default is 1. prefix : str, optional The BLAS prefix associated with the datatype. Default is to find the best datatype based on given input. This argument is typically only used internally. Returns --------- ndarray Score, evaluated at the given parameters. Notes ----- This is a numerical approximation, calculated using first-order complex step differentiation on the `arma_loglike` method. """ ar_params = [] if ar_params is None else ar_params ma_params = [] if ma_params is None else ma_params p = len(ar_params) q = len(ma_params) def func(params): return arma_loglike(endog, params[:p], params[p:p + q], params[p + q:]) params0 = np.r_[ar_params, ma_params, sigma2] epsilon = _get_epsilon(params0, 2., None, len(params0)) return approx_fprime_cs(params0, func, epsilon) def arma_scoreobs(endog, ar_params=None, ma_params=None, sigma2=1, prefix=None): """ Compute the score (gradient) per observation. Parameters ---------- endog : ndarray The observed time-series process. ar_params : ndarray, optional Autoregressive coefficients, not including the zero lag. ma_params : ndarray, optional Moving average coefficients, not including the zero lag, where the sign convention assumes the coefficients are part of the lag polynomial on the right-hand-side of the ARMA definition (i.e. they have the same sign from the usual econometrics convention in which the coefficients are on the right-hand-side of the ARMA definition). sigma2 : ndarray, optional The ARMA innovation variance. Default is 1. prefix : str, optional The BLAS prefix associated with the datatype. Default is to find the best datatype based on given input. This argument is typically only used internally. Returns --------- ndarray Score per observation, evaluated at the given parameters. Notes ----- This is a numerical approximation, calculated using first-order complex step differentiation on the `arma_loglike` method. """ ar_params = [] if ar_params is None else ar_params ma_params = [] if ma_params is None else ma_params p = len(ar_params) q = len(ma_params) def func(params): return arma_loglikeobs(endog, params[:p], params[p:p + q], params[p + q:]) params0 = np.r_[ar_params, ma_params, sigma2] epsilon = _get_epsilon(params0, 2., None, len(params0)) return approx_fprime_cs(params0, func, epsilon) statsmodels-0.12.2/statsmodels/tsa/innovations/tests/000077500000000000000000000000001400612667500230075ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/innovations/tests/__init__.py000066400000000000000000000000001400612667500251060ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/innovations/tests/test_arma_innovations.py000066400000000000000000000041321400612667500277670ustar00rootroot00000000000000""" Tests for ARMA innovations algorithm wrapper """ import numpy as np import pytest from numpy.testing import assert_allclose from statsmodels.tsa.innovations import arma_innovations from statsmodels.tsa.statespace.sarimax import SARIMAX @pytest.mark.parametrize("ar_params,ma_params,sigma2", [ (np.array([]), np.array([]), 1), (np.array([0.]), np.array([0.]), 1), (np.array([0.9]), np.array([]), 1), (np.array([]), np.array([0.9]), 1), (np.array([0.2, -0.4, 0.1, 0.1]), np.array([0.5, 0.1]), 1.123), (np.array([0.5, 0.1]), np.array([0.2, -0.4, 0.1, 0.1]), 1.123), ]) def test_innovations_algo_filter_kalman_filter(ar_params, ma_params, sigma2): # Test the innovations algorithm and filter against the Kalman filter # for exact likelihood evaluation of an ARMA process np.random.seed(42) endog = np.random.normal(size=100) # Innovations algorithm approach llf = arma_innovations.arma_loglike(endog, ar_params, ma_params, sigma2) llf_obs = arma_innovations.arma_loglikeobs(endog, ar_params, ma_params, sigma2) score = arma_innovations.arma_score(endog, ar_params, ma_params, sigma2) score_obs = arma_innovations.arma_scoreobs(endog, ar_params, ma_params, sigma2) # Kalman filter apparoach mod = SARIMAX(endog, order=(len(ar_params), 0, len(ma_params))) params = np.r_[ar_params, ma_params, sigma2] # Test that the two approaches are the same assert_allclose(llf, mod.loglike(params)) assert_allclose(llf_obs, mod.loglikeobs(params)) # Note: the tolerance on the two gets worse as more nobs are added assert_allclose(score, mod.score(params), atol=1e-5) assert_allclose(score_obs, mod.score_obs(params), atol=1e-5) @pytest.mark.parametrize("ar_params", ([1.9, -0.8], [1.0], [2.0, -1.0])) def test_innovations_nonstationary(ar_params): np.random.seed(42) endog = np.random.normal(size=100) with pytest.raises(ValueError, match="The model's autoregressive"): arma_innovations.arma_innovations(endog, ar_params=ar_params) statsmodels-0.12.2/statsmodels/tsa/innovations/tests/test_cython_arma_innovations_fast.py000066400000000000000000000330671400612667500324010ustar00rootroot00000000000000""" Tests for fast version of ARMA innovations algorithm """ import numpy as np import pytest from numpy.testing import assert_equal, assert_allclose from statsmodels.tsa.arima_process import arma_acovf from statsmodels.tsa.innovations import _arma_innovations, arma_innovations from statsmodels.tsa.statespace.sarimax import SARIMAX def test_brockwell_davis_ex533(): # See Brockwell and Davis (2009) - Time Series Theory and Methods # Example 5.3.3: ARMA(1, 1) process, p.g. 177 nobs = 10 ar_params = np.array([0.2]) ma_params = np.array([0.4]) sigma2 = 8.92 p = len(ar_params) q = len(ma_params) m = max(p, q) ar = np.r_[1, -ar_params] ma = np.r_[1, ma_params] # First, get the autocovariance of the process arma_process_acovf = arma_acovf(ar, ma, nobs=nobs, sigma2=sigma2) unconditional_variance = ( sigma2 * (1 + 2 * ar_params[0] * ma_params[0] + ma_params[0]**2) / (1 - ar_params[0]**2)) assert_allclose(arma_process_acovf[0], unconditional_variance) # Next, get the autocovariance of the transformed process # Note: as required by {{prefix}}arma_transformed_acovf, we first divide # through by sigma^2 arma_process_acovf /= sigma2 unconditional_variance /= sigma2 transformed_acovf = _arma_innovations.darma_transformed_acovf_fast( ar, ma, arma_process_acovf) acovf, acovf2 = (np.array(arr) for arr in transformed_acovf) # `acovf` is an m^2 x m^2 matrix, where m = max(p, q) # but it is only valid for the autocovariances of the first m observations # (this means in particular that the block `acovf[m:, m:]` should *not* be # used) # `acovf2` then contains the (time invariant) autocovariance terms for # the observations m + 1, ..., nobs - since the autocovariance is the same # for these terms, to save space we do not construct the autocovariance # matrix as we did for the first m terms. Thus `acovf2[0]` is the variance, # `acovf2[1]` is the first autocovariance, etc. # Test the autocovariance function for observations m + 1, ..., nobs # (it is time invariant here) assert_equal(acovf2.shape, (nobs - m,)) assert_allclose(acovf2[0], 1 + ma_params[0]**2) assert_allclose(acovf2[1], ma_params[0]) assert_allclose(acovf2[2:], 0) # Test the autocovariance function for observations 1, ..., m # (it is time varying here) assert_equal(acovf.shape, (m * 2, m * 2)) # (we need to check `acovf[:m * 2, :m]`, i.e. `acovf[:2, :1])` ix = np.diag_indices_from(acovf) ix_lower = (ix[0][:-1] + 1, ix[1][:-1]) # acovf[ix] is the diagonal, and we want to check the first m # elements of the diagonal assert_allclose(acovf[ix][:m], unconditional_variance) # acovf[ix_lower] is the first lower off-diagonal assert_allclose(acovf[ix_lower][:m], ma_params[0]) # Now, check that we compute the moving average coefficients and the # associated variances correctly out = _arma_innovations.darma_innovations_algo_fast( nobs, ar_params, ma_params, acovf, acovf2) theta = np.array(out[0]) v = np.array(out[1]) # Test v (see eq. 5.3.13) desired_v = np.zeros(nobs) desired_v[0] = unconditional_variance for i in range(1, nobs): desired_v[i] = 1 + (1 - 1 / desired_v[i - 1]) * ma_params[0]**2 assert_allclose(v, desired_v) # Test theta (see eq. 5.3.13) # Note that they will have shape (nobs, m + 1) here, not (nobs, nobs - 1) # as in the original (non-fast) version assert_equal(theta.shape, (nobs, m + 1)) desired_theta = np.zeros(nobs) for i in range(1, nobs): desired_theta[i] = ma_params[0] / desired_v[i - 1] assert_allclose(theta[:, 0], desired_theta) assert_allclose(theta[:, 1:], 0) # Test against Table 5.3.1 endog = np.array([ -1.1, 0.514, 0.116, -0.845, 0.872, -0.467, -0.977, -1.699, -1.228, -1.093]) u = _arma_innovations.darma_innovations_filter(endog, ar_params, ma_params, theta) # Note: Table 5.3.1 has \hat X_n+1 = -0.5340 for n = 1, but this seems to # be a typo, since equation 5.3.12 gives the form of the prediction # equation as \hat X_n+1 = \phi X_n + \theta_n1 (X_n - \hat X_n) # Then for n = 1 we have: # \hat X_n+1 = 0.2 (-1.1) + (0.2909) (-1.1 - 0) = -0.5399 # And for n = 2 if we use what we have computed, then we get: # \hat X_n+1 = 0.2 (0.514) + (0.3833) (0.514 - (-0.54)) = 0.5068 # as desired, whereas if we used the book's number for n=1 we would get: # \hat X_n+1 = 0.2 (0.514) + (0.3833) (0.514 - (-0.534)) = 0.5045 # which is not what Table 5.3.1 shows. desired_hat = np.array([ 0, -0.540, 0.5068, -0.1321, -0.4539, 0.7046, -0.5620, -0.3614, -0.8748, -0.3869]) desired_u = endog - desired_hat assert_allclose(u, desired_u, atol=1e-4) def test_brockwell_davis_ex534(): # See Brockwell and Davis (2009) - Time Series Theory and Methods # Example 5.3.4: ARMA(1, 1) process, p.g. 178 nobs = 10 ar_params = np.array([1, -0.24]) ma_params = np.array([0.4, 0.2, 0.1]) sigma2 = 1 p = len(ar_params) q = len(ma_params) m = max(p, q) ar = np.r_[1, -ar_params] ma = np.r_[1, ma_params] # First, get the autocovariance of the process arma_process_acovf = arma_acovf(ar, ma, nobs=nobs, sigma2=sigma2) assert_allclose(arma_process_acovf[:3], [7.17133, 6.44139, 5.06027], atol=1e-5) # Next, get the autocovariance of the transformed process transformed_acovf = _arma_innovations.darma_transformed_acovf_fast( ar, ma, arma_process_acovf) acovf, acovf2 = (np.array(arr) for arr in transformed_acovf) # See test_brockwell_davis_ex533 for details on acovf vs acovf2 # Test acovf assert_equal(acovf.shape, (m * 2, m * 2)) ix = np.diag_indices_from(acovf) ix_lower1 = (ix[0][:-1] + 1, ix[1][:-1]) ix_lower2 = (ix[0][:-2] + 2, ix[1][:-2]) ix_lower3 = (ix[0][:-3] + 3, ix[1][:-3]) ix_lower4 = (ix[0][:-4] + 4, ix[1][:-4]) assert_allclose(acovf[ix][:m], 7.17133, atol=1e-5) desired = [6.44139, 6.44139, 0.816] assert_allclose(acovf[ix_lower1][:m], desired, atol=1e-5) assert_allclose(acovf[ix_lower2][0], 5.06027, atol=1e-5) assert_allclose(acovf[ix_lower2][1:m], 0.34, atol=1e-5) assert_allclose(acovf[ix_lower3][:m], 0.1, atol=1e-5) assert_allclose(acovf[ix_lower4][:m], 0, atol=1e-5) # Test acovf2 assert_equal(acovf2.shape, (nobs - m,)) assert_allclose(acovf2[:4], [1.21, 0.5, 0.24, 0.1]) assert_allclose(acovf2[4:], 0) # Test innovations algorithm output out = _arma_innovations.darma_innovations_algo_fast( nobs, ar_params, ma_params, acovf, acovf2) theta = np.array(out[0]) v = np.array(out[1]) # Test v (see Table 5.3.2) desired_v = [7.1713, 1.3856, 1.0057, 1.0019, 1.0016, 1.0005, 1.0000, 1.0000, 1.0000, 1.0000] assert_allclose(v, desired_v, atol=1e-4) # Test theta (see Table 5.3.2) assert_equal(theta.shape, (nobs, m + 1)) desired_theta = np.array([ [0, 0.8982, 1.3685, 0.4008, 0.3998, 0.3992, 0.4000, 0.4000, 0.4000, 0.4000], [0, 0, 0.7056, 0.1806, 0.2020, 0.1995, 0.1997, 0.2000, 0.2000, 0.2000], [0, 0, 0, 0.0139, 0.0722, 0.0994, 0.0998, 0.0998, 0.0999, 0.1]]).T assert_allclose(theta[:, :m], desired_theta, atol=1e-4) assert_allclose(theta[:, m:], 0) # Test innovations filter output endog = np.array([1.704, 0.527, 1.041, 0.942, 0.555, -1.002, -0.585, 0.010, -0.638, 0.525]) u = _arma_innovations.darma_innovations_filter(endog, ar_params, ma_params, theta) desired_hat = np.array([ 0, 1.5305, -0.1710, 1.2428, 0.7443, 0.3138, -1.7293, -0.1688, 0.3193, -0.8731]) desired_u = endog - desired_hat assert_allclose(u, desired_u, atol=1e-4) @pytest.mark.parametrize("ar_params,ma_params,sigma2", [ (np.array([]), np.array([]), 1), (np.array([0.]), np.array([0.]), 1), (np.array([0.9]), np.array([]), 1), (np.array([]), np.array([0.9]), 1), (np.array([0.2, -0.4, 0.1, 0.1]), np.array([0.5, 0.1]), 1.123), (np.array([0.5, 0.1]), np.array([0.2, -0.4, 0.1, 0.1]), 1.123), ]) def test_innovations_algo_filter_kalman_filter(ar_params, ma_params, sigma2): # Test the innovations algorithm and filter against the Kalman filter # for exact likelihood evaluation of an ARMA process ar = np.r_[1, -ar_params] ma = np.r_[1, ma_params] endog = np.random.normal(size=10) nobs = len(endog) # Innovations algorithm approach arma_process_acovf = arma_acovf(ar, ma, nobs=nobs, sigma2=sigma2) transformed_acov = _arma_innovations.darma_transformed_acovf_fast( ar, ma, arma_process_acovf / sigma2) acovf, acovf2 = (np.array(mv) for mv in transformed_acov) theta, r = _arma_innovations.darma_innovations_algo_fast( nobs, ar_params, ma_params, acovf, acovf2) u = _arma_innovations.darma_innovations_filter(endog, ar_params, ma_params, theta) v = np.array(r) * sigma2 u = np.array(u) llf_obs = -0.5 * u**2 / v - 0.5 * np.log(2 * np.pi * v) # Kalman filter apparoach mod = SARIMAX(endog, order=(len(ar_params), 0, len(ma_params))) res = mod.filter(np.r_[ar_params, ma_params, sigma2]) # Test that the two approaches are identical assert_allclose(u, res.forecasts_error[0]) # assert_allclose(theta[1:, 0], res.filter_results.kalman_gain[0, 0, :-1]) assert_allclose(llf_obs, res.llf_obs) # Get llf_obs directly llf_obs2 = _arma_innovations.darma_loglikeobs_fast( endog, ar_params, ma_params, sigma2) assert_allclose(llf_obs2, res.llf_obs) @pytest.mark.parametrize("ar_params,ma_params,sigma2", [ (np.array([]), np.array([]), 1), (np.array([0.]), np.array([0.]), 1), (np.array([0.9]), np.array([]), 1), (np.array([]), np.array([0.9]), 1), (np.array([0.2, -0.4, 0.1, 0.1]), np.array([0.5, 0.1]), 1.123), (np.array([0.5, 0.1]), np.array([0.2, -0.4, 0.1, 0.1]), 1.123), ]) def test_innovations_algo_direct_filter_kalman_filter(ar_params, ma_params, sigma2): # Test the innovations algorithm and filter against the Kalman filter # for exact likelihood evaluation of an ARMA process, using the direct # function. endog = np.random.normal(size=10) # Innovations algorithm approach u, r = arma_innovations.arma_innovations(endog, ar_params, ma_params, sigma2) v = np.array(r) * sigma2 u = np.array(u) llf_obs = -0.5 * u**2 / v - 0.5 * np.log(2 * np.pi * v) # Kalman filter apparoach mod = SARIMAX(endog, order=(len(ar_params), 0, len(ma_params))) res = mod.filter(np.r_[ar_params, ma_params, sigma2]) # Test that the two approaches are identical assert_allclose(u, res.forecasts_error[0]) # assert_allclose(theta[1:, 0], res.filter_results.kalman_gain[0, 0, :-1]) assert_allclose(llf_obs, res.llf_obs) # Get llf_obs directly llf_obs2 = _arma_innovations.darma_loglikeobs_fast( endog, ar_params, ma_params, sigma2) assert_allclose(llf_obs2, res.llf_obs) @pytest.mark.parametrize("ar_params,diff,ma_params,sigma2", [ (np.array([]), 1, np.array([]), 1), (np.array([0.]), 1, np.array([0.]), 1), (np.array([0.9]), 1, np.array([]), 1), (np.array([]), 1, np.array([0.9]), 1), (np.array([0.2, -0.4, 0.1, 0.1]), 1, np.array([0.5, 0.1]), 1.123), (np.array([0.5, 0.1]), 1, np.array([0.2, -0.4, 0.1, 0.1]), 1.123), (np.array([0.5, 0.1]), 2, np.array([0.2, -0.4, 0.1, 0.1]), 1.123), ]) def test_integrated_process(ar_params, diff, ma_params, sigma2): # Test loglikelihood computation when model has integration nobs = 100 endog = np.cumsum(np.random.normal(size=nobs)) # Innovations algorithm approach llf_obs = arma_innovations.arma_loglikeobs( np.diff(endog, diff), ar_params, ma_params, sigma2) # Kalman filter apparoach mod = SARIMAX(endog, order=(len(ar_params), diff, len(ma_params)), simple_differencing=True) res = mod.filter(np.r_[ar_params, ma_params, sigma2]) # Test that the two approaches are identical assert_allclose(llf_obs, res.llf_obs) @pytest.mark.parametrize("ar_params,ma_params,sigma2", [ (np.array([]), np.array([]), 1), (np.array([0.]), np.array([0.]), 1), (np.array([0.9]), np.array([]), 1), (np.array([]), np.array([0.9]), 1), (np.array([0.2, -0.4, 0.1, 0.1]), np.array([0.5, 0.1]), 1.123), (np.array([0.5, 0.1]), np.array([0.2, -0.4, 0.1, 0.1]), 1.123), ]) def test_regression_with_arma_errors(ar_params, ma_params, sigma2): # Test loglikelihood computation when model has regressors nobs = 100 eps = np.random.normal(nobs) exog = np.c_[np.ones(nobs), np.random.uniform(size=nobs)] beta = [5, -0.2] endog = np.dot(exog, beta) + eps # Innovations algorithm approach beta_hat = np.squeeze(np.linalg.pinv(exog).dot(endog)) demeaned = endog - np.dot(exog, beta_hat) llf_obs = arma_innovations.arma_loglikeobs( demeaned, ar_params, ma_params, sigma2) # Kalman filter approach # (this works since we impose here that the regression coefficients are # beta_hat - in practice, the MLE estimates will not necessarily match # the OLS estimates beta_hat) mod = SARIMAX(endog, exog=exog, order=(len(ar_params), 0, len(ma_params))) res = mod.filter(np.r_[beta_hat, ar_params, ma_params, sigma2]) # Test that the two approaches are identical assert_allclose(llf_obs, res.llf_obs) statsmodels-0.12.2/statsmodels/tsa/interp/000077500000000000000000000000001400612667500205775ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/interp/__init__.py000066400000000000000000000002051400612667500227050ustar00rootroot00000000000000__all__ = ['dentonm', 'test'] from .denton import dentonm from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/tsa/interp/denton.py000066400000000000000000000251001400612667500224360ustar00rootroot00000000000000 import numpy as np from numpy import (dot, eye, diag_indices, zeros, ones, diag, asarray, r_) from numpy.linalg import solve # def denton(indicator, benchmark, freq="aq", **kwarg): # """ # Denton's method to convert low-frequency to high frequency data. # # Parameters # ---------- # benchmark : array_like # The higher frequency benchmark. A 1d or 2d data series in columns. # If 2d, then M series are assumed. # indicator # A low-frequency indicator series. It is assumed that there are no # pre-sample indicators. Ie., the first indicators line up with # the first benchmark. # freq : str {"aq","qm", "other"} # "aq" - Benchmarking an annual series to quarterly. # "mq" - Benchmarking a quarterly series to monthly. # "other" - Custom stride. A kwarg, k, must be supplied. # kwargs : # k : int # The number of high-frequency observations that sum to make an # aggregate low-frequency observation. `k` is used with # `freq` == "other". # Returns # ------- # benchmarked series : ndarray # # Notes # ----- # Denton's method minimizes the distance given by the penalty function, in # a least squares sense, between the unknown benchmarked series and the # indicator series subject to the condition that the sum of the benchmarked # series is equal to the benchmark. # # # References # ---------- # Bloem, A.M, Dippelsman, R.J. and Maehle, N.O. 2001 Quarterly National # Accounts Manual--Concepts, Data Sources, and Compilation. IMF. # http://www.imf.org/external/pubs/ft/qna/2000/Textbook/index.htm # Denton, F.T. 1971. "Adjustment of monthly or quarterly series to annual # totals: an approach based on quadratic minimization." Journal of the # American Statistical Association. 99-102. # # """ # # check arrays and make 2d # indicator = np.asarray(indicator) # if indicator.ndim == 1: # indicator = indicator[:,None] # benchmark = np.asarray(benchmark) # if benchmark.ndim == 1: # benchmark = benchmark[:,None] # # # get dimensions # N = len(indicator) # total number of high-freq # m = len(benchmark) # total number of low-freq # # # number of low-freq observations for aggregate measure # # 4 for annual to quarter and 3 for quarter to monthly # if freq == "aq": # k = 4 # elif freq == "qm": # k = 3 # elif freq == "other": # k = kwargs.get("k") # if not k: # raise ValueError("k must be supplied with freq=\"other\"") # else: # raise ValueError("freq %s not understood" % freq) # # n = k*m # number of indicator series with a benchmark for back-series # # if k*m != n, then we are going to extrapolate q observations # # B = block_diag(*(np.ones((k,1)),)*m) # # r = benchmark - B.T.dot(indicator) #TODO: take code in the string at the end and implement Denton's original # method with a few of the penalty functions. def dentonm(indicator, benchmark, freq="aq", **kwargs): """ Modified Denton's method to convert low-frequency to high-frequency data. Uses proportionate first-differences as the penalty function. See notes. Parameters ---------- indicator : array_like A low-frequency indicator series. It is assumed that there are no pre-sample indicators. Ie., the first indicators line up with the first benchmark. benchmark : array_like The higher frequency benchmark. A 1d or 2d data series in columns. If 2d, then M series are assumed. freq : str {"aq","qm", "other"} The frequency to use in the conversion. * "aq" - Benchmarking an annual series to quarterly. * "mq" - Benchmarking a quarterly series to monthly. * "other" - Custom stride. A kwarg, k, must be supplied. **kwargs Additional keyword argument. For example: * k, an int, the number of high-frequency observations that sum to make an aggregate low-frequency observation. `k` is used with `freq` == "other". Returns ------- transformed : ndarray The transformed series. Examples -------- >>> indicator = [50,100,150,100] * 5 >>> benchmark = [500,400,300,400,500] >>> benchmarked = dentonm(indicator, benchmark, freq="aq") Notes ----- Denton's method minimizes the distance given by the penalty function, in a least squares sense, between the unknown benchmarked series and the indicator series subject to the condition that the sum of the benchmarked series is equal to the benchmark. The modification allows that the first value not be pre-determined as is the case with Denton's original method. If the there is no benchmark provided for the last few indicator observations, then extrapolation is performed using the last benchmark-indicator ratio of the previous period. Minimizes sum((X[t]/I[t] - X[t-1]/I[t-1])**2) s.t. sum(X) = A, for each period. Where X is the benchmarked series, I is the indicator, and A is the benchmark. References ---------- Bloem, A.M, Dippelsman, R.J. and Maehle, N.O. 2001 Quarterly National Accounts Manual--Concepts, Data Sources, and Compilation. IMF. http://www.imf.org/external/pubs/ft/qna/2000/Textbook/index.htm Cholette, P. 1988. "Benchmarking systems of socio-economic time series." Statistics Canada, Time Series Research and Analysis Division, Working Paper No TSRA-88-017E. Denton, F.T. 1971. "Adjustment of monthly or quarterly series to annual totals: an approach based on quadratic minimization." Journal of the American Statistical Association. 99-102. """ # penalty : str # Penalty function. Can be "D1", "D2", "D3", "D4", "D5". # X is the benchmarked series and I is the indicator. # D1 - sum((X[t] - X[t-1]) - (I[t] - I[ti-1])**2) # D2 - sum((ln(X[t]/X[t-1]) - ln(I[t]/I[t-1]))**2) # D3 - sum((X[t]/X[t-1] / I[t]/I[t-1])**2) # D4 - sum((X[t]/I[t] - X[t-1]/I[t-1])**2) # D5 - sum((X[t]/I[t] / X[t-1]/I[t-1] - 1)**2) #NOTE: only D4 is the only one implemented, see IMF chapter 6. # check arrays and make 2d indicator = asarray(indicator) if indicator.ndim == 1: indicator = indicator[:,None] benchmark = asarray(benchmark) if benchmark.ndim == 1: benchmark = benchmark[:,None] # get dimensions N = len(indicator) # total number of high-freq m = len(benchmark) # total number of low-freq # number of low-freq observations for aggregate measure # 4 for annual to quarter and 3 for quarter to monthly if freq == "aq": k = 4 elif freq == "qm": k = 3 elif freq == "other": k = kwargs.get("k") if not k: raise ValueError("k must be supplied with freq=\"other\"") else: raise ValueError("freq %s not understood" % freq) n = k*m # number of indicator series with a benchmark for back-series # if k*m != n, then we are going to extrapolate q observations if N > n: q = N - n else: q = 0 # make the aggregator matrix #B = block_diag(*(ones((k,1)),)*m) B = np.kron(np.eye(m), ones((k,1))) # following the IMF paper, we can do Zinv = diag(1./indicator.squeeze()[:n]) # this is D in Denton's notation (not using initial value correction) # D = eye(n) # make off-diagonal = -1 # D[((np.diag_indices(n)[0])[:-1]+1,(np.diag_indices(n)[1])[:-1])] = -1 # account for starting conditions # H = D[1:,:] # HTH = dot(H.T,H) # just make HTH HTH = eye(n) diag_idx0, diag_idx1 = diag_indices(n) HTH[diag_idx0[1:-1], diag_idx1[1:-1]] += 1 HTH[diag_idx0[:-1]+1, diag_idx1[:-1]] = -1 HTH[diag_idx0[:-1], diag_idx1[:-1]+1] = -1 W = dot(dot(Zinv,HTH),Zinv) # make partitioned matrices # TODO: break this out so that we can simplify the linalg? I = zeros((n+m, n+m)) # noqa:E741 I[:n,:n] = W I[:n,n:] = B I[n:,:n] = B.T A = zeros((m+n,1)) # zero first-order constraints A[-m:] = benchmark # adding up constraints X = solve(I,A) X = X[:-m] # drop the lagrange multipliers # handle extrapolation if q > 0: # get last Benchmark-Indicator ratio bi = X[n-1]/indicator[n-1] extrapolated = bi * indicator[n:] X = r_[X,extrapolated] return X.squeeze() if __name__ == "__main__": #these will be the tests # from IMF paper # quarterly data indicator = np.array([98.2, 100.8, 102.2, 100.8, 99.0, 101.6, 102.7, 101.5, 100.5, 103.0, 103.5, 101.5]) # two annual observations benchmark = np.array([4000.,4161.4]) x_imf = dentonm(indicator, benchmark, freq="aq") imf_stata = np.array([969.8, 998.4, 1018.3, 1013.4, 1007.2, 1042.9, 1060.3, 1051.0, 1040.6, 1066.5, 1071.7, 1051.0]) np.testing.assert_almost_equal(imf_stata, x_imf, 1) # Denton example zQ = np.array([50,100,150,100] * 5) Y = np.array([500,400,300,400,500]) x_denton = dentonm(zQ, Y, freq="aq") x_stata = np.array([64.334796,127.80616,187.82379,120.03526,56.563894, 105.97568,147.50144,89.958987,40.547201,74.445963, 108.34473,76.66211,42.763347,94.14664,153.41596, 109.67405,58.290761,122.62556,190.41409,128.66959]) """ # Examples from the Denton 1971 paper k = 4 m = 5 n = m*k zQ = [50,100,150,100] * m Y = [500,400,300,400,500] A = np.eye(n) B = block_diag(*(np.ones((k,1)),)*m) r = Y - B.T.dot(zQ) #Ainv = inv(A) Ainv = A # shortcut for identity C = Ainv.dot(B).dot(inv(B.T.dot(Ainv).dot(B))) x = zQ + C.dot(r) # minimize first difference d(x-z) R = linalg.tri(n, dtype=float) # R is tril so actually R.T in paper Ainv = R.dot(R.T) C = Ainv.dot(B).dot(inv(B.T.dot(Ainv).dot(B))) x1 = zQ + C.dot(r) # minimize the second difference d**2(x-z) Ainv = R.dot(Ainv).dot(R.T) C = Ainv.dot(B).dot(inv(B.T.dot(Ainv).dot(B))) x12 = zQ + C.dot(r) # # do it proportionately (x-z)/z Z = np.diag(zQ) Ainv = np.eye(n) C = Z.dot(Ainv).dot(Z).dot(B).dot(inv(B.T.dot(Z).dot(Ainv).dot(Z).dot(B))) x11 = zQ + C.dot(r) # do it proportionately with differencing d((x-z)/z) Ainv = R.dot(R.T) C = Z.dot(Ainv).dot(Z).dot(B).dot(inv(B.T.dot(Z).dot(Ainv).dot(Z).dot(B))) x111 = zQ + C.dot(r) x_stata = np.array([64.334796,127.80616,187.82379,120.03526,56.563894, 105.97568,147.50144,89.958987,40.547201,74.445963, 108.34473,76.66211,42.763347,94.14664,153.41596, 109.67405,58.290761,122.62556,190.41409,128.66959]) """ statsmodels-0.12.2/statsmodels/tsa/interp/tests/000077500000000000000000000000001400612667500217415ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/interp/tests/__init__.py000066400000000000000000000000001400612667500240400ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/interp/tests/test_denton.py000066400000000000000000000023201400612667500246360ustar00rootroot00000000000000import numpy as np from statsmodels.tsa.interp import dentonm def test_denton_quarterly(): # Data and results taken from IMF paper indicator = np.array([98.2, 100.8, 102.2, 100.8, 99.0, 101.6, 102.7, 101.5, 100.5, 103.0, 103.5, 101.5]) benchmark = np.array([4000.,4161.4]) x_imf = dentonm(indicator, benchmark, freq="aq") imf_stata = np.array([969.8, 998.4, 1018.3, 1013.4, 1007.2, 1042.9, 1060.3, 1051.0, 1040.6, 1066.5, 1071.7, 1051.0]) np.testing.assert_almost_equal(imf_stata, x_imf, 1) def test_denton_quarterly2(): # Test denton vs stata. Higher precision than other test. zQ = np.array([50,100,150,100] * 5) Y = np.array([500,400,300,400,500]) x_denton = dentonm(zQ, Y, freq="aq") x_stata = np.array([64.334796,127.80616,187.82379,120.03526,56.563894, 105.97568,147.50144,89.958987,40.547201,74.445963, 108.34473,76.66211,42.763347,94.14664,153.41596, 109.67405,58.290761,122.62556,190.41409,128.66959]) np.testing.assert_almost_equal(x_denton, x_stata, 5) if __name__ == "__main__": import pytest pytest.main([__file__, '-vvs', '-x', '--pdb']) statsmodels-0.12.2/statsmodels/tsa/kalmanf/000077500000000000000000000000001400612667500207075ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/kalmanf/__init__.py000066400000000000000000000002251400612667500230170ustar00rootroot00000000000000__all__ = ['KalmanFilter', 'test'] from .kalmanfilter import KalmanFilter from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/tsa/kalmanf/kalman_loglike.pyx000066400000000000000000000324611400612667500244300ustar00rootroot00000000000000from numpy cimport float64_t, ndarray, complex128_t from numpy import log as nplog from numpy import (identity, dot, kron, pi, sum, zeros_like, ones, asfortranarray) from numpy.linalg import pinv cimport cython cimport numpy as cnp cnp.import_array() # included in Cython numpy headers from numpy cimport PyArray_ZEROS from scipy.linalg.cython_blas cimport dgemm, dgemv, zgemm, zgemv ctypedef float64_t DOUBLE ctypedef complex128_t dcomplex cdef int FORTRAN = 1 cdef extern from "math.h": double log(double x) @cython.boundscheck(False) @cython.wraparound(False) @cython.cdivision(True) def kalman_filter_double(double[:] y not None, unsigned int k, unsigned int p, unsigned int q, int r, unsigned int nobs, double[::1, :] Z_mat, double[::1, :] R_mat, double[::1, :] T_mat): """ Cython version of the Kalman filter recursions for an ARMA process. """ cdef cnp.npy_intp yshape[2] yshape[0] = nobs yshape[1] = 1 cdef cnp.npy_intp mshape[2] mshape[0] = r mshape[1] = 1 cdef cnp.npy_intp r2shape[2] r2shape[0] = r r2shape[1] = r cdef: int one = 1 # univariate filter int ldz = Z_mat.strides[1] / sizeof(DOUBLE) int ldt = T_mat.strides[1] / sizeof(DOUBLE) int ldr = R_mat.strides[1] / sizeof(DOUBLE) # forecast errors ndarray[DOUBLE, ndim=2] v = PyArray_ZEROS(2, yshape, cnp.NPY_DOUBLE, FORTRAN) # store variance of forecast errors double[::1, :] F = ones((nobs,1), order='F') # variance of forecast errors double loglikelihood = 0 int i = 0 # initial state double[::1, :] alpha = PyArray_ZEROS(2, mshape, cnp.NPY_DOUBLE, FORTRAN) int lda = alpha.strides[1] / sizeof(DOUBLE) # initial variance double[::1, :] P = asfortranarray(dot(pinv(identity(r**2) - kron(T_mat, T_mat)), dot(R_mat, R_mat.T).ravel('F') ).reshape(r, r, order='F')) int ldp = P.strides[1] / sizeof(DOUBLE) double F_mat = 0. double Finv = 0. double v_mat = 0 double[::1, :] K = PyArray_ZEROS(2, r2shape, cnp.NPY_DOUBLE, FORTRAN) int ldk = K.strides[1] / sizeof(DOUBLE) # pre-allocate some tmp arrays for the dgemm calls # T_mat rows x P cols double[::1, :] tmp1 = PyArray_ZEROS(2, r2shape, cnp.NPY_DOUBLE, FORTRAN) int ldt1 = tmp1.strides[1] / sizeof(DOUBLE) double[::1, :] tmp2 = zeros_like(alpha, order='F') # K rows x v_mat cols int ldt2 = tmp2.strides[1] / sizeof(DOUBLE) double[::1, :] L = zeros_like(T_mat, order='F') int ldl = L.strides[1] / sizeof(DOUBLE) # T_mat rows x P cols double[::1, :] tmp3 = PyArray_ZEROS(2, r2shape, cnp.NPY_DOUBLE, FORTRAN) int ldt3 = tmp3.strides[1] / sizeof(DOUBLE) double alph = 1.0 double beta = 0.0 # NOTE: not sure about just checking F_mat[0, 0], did not appear to work while not F_mat == 1. and i < nobs: # Predict # Z_mat is just a selector matrix v_mat = y[i] - alpha[0, 0] v[i, 0] = v_mat # one-step forecast error covariance # Z_mat is just a selector matrix F_mat = P[0, 0] F[i,0] = F_mat Finv = 1. / F_mat # always scalar for univariate series # compute Kalman Gain, K equivalent to: # K = np.dot(np.dot(np.dot(T_mat, P), Z_mat.T), Finv) # in two steps: # tmp1 = np.dot(T_mat, P) # K = Finv * tmp1.dot(Z_mat.T) dgemm("N", "N", &r, &r, &r, &alph, &T_mat[0, 0], &ldt, &P[0, 0], &ldp, &beta, &tmp1[0, 0], &ldt1) dgemv("N", &r, &r, &Finv, &tmp1[0, 0], &ldt1, &Z_mat[0, 0], &one, &beta, &K[0, 0], &one) # update state; equivalent to: # alpha = np.dot(T_mat, alpha) + np.dot(K, v_mat) # in two steps: # tmp2 = np.dot(T_mat, alpha) # alpha = tmp2 + np.dot(K, v_mat) dgemv("N", &r, &r, &alph, &T_mat[0, 0], &ldt, &alpha[0, 0], &one, &beta, &tmp2[0, 0], &one) for ii in range(r): alpha[ii, 0] = K[ii, 0] * v_mat + tmp2[ii, 0] # The next block is equivalent to: # L = T_mat - np.dot(K, Z_mat) # in two steps: # L = np.dot(K, Z_mat) # L = T_mat - L dgemm("N", "N", &r, &r, &one, &alph, &K[0, 0], &ldk, &Z_mat[0, 0], &ldz, &beta, &L[0, 0], &ldl) for jj in range(r): for kk in range(r): L[jj, kk] = T_mat[jj, kk] - L[jj, kk] # The next block computes P equivalent to: # P = np.dot(np.dot(T_mat, P), L.T) + np.dot(R_mat, R_mat.T) # in three steps: # tmp5 = np.dot(R_mat, R_mat.T) # tmp3 = np.dot(T_mat, P) # P = np.dot(tmp3, L.T) + tmp5 dgemm("N", "N", &r, &r, &r, &alph, &T_mat[0, 0], &ldt, &P[0, 0], &ldp, &beta, &tmp3[0, 0], &ldt3) dgemm("N", "T", &r, &r, &one, &alph, &R_mat[0, 0], &ldr, &R_mat[0, 0], &ldr, &beta, &P[0, 0], &ldp) dgemm("N", "T", &r, &r, &r, &alph, &tmp3[0, 0], &ldt3, &L[0, 0], &ldl, &alph, &P[0, 0], &ldp) loglikelihood += log(F_mat) i += 1 for i in xrange(i,nobs): v_mat = y[i] - alpha[0, 0] v[i, 0] = v_mat # The next block is equivalent to: # alpha = np.dot(T_mat, alpha) + np.dot(K, v_mat) # in two steps: # tmp2 = np.dot(T_mat, alpha) # alpha = np.dot(K, v_mat) + tmp2 dgemm("N", "N", &r, &one, &r, &alph, &T_mat[0, 0], &ldt, &alpha[0, 0], &lda, &beta, &tmp2[0, 0], &ldt2) for ii in range(r): alpha[ii, 0] = K[ii, 0] * v_mat + tmp2[ii, 0] return v, F, loglikelihood @cython.boundscheck(False) @cython.wraparound(False) @cython.cdivision(True) def kalman_filter_complex(dcomplex[:] y, unsigned int k, unsigned int p, unsigned int q, int r, unsigned int nobs, dcomplex[::1, :] Z_mat, dcomplex[::1, :] R_mat, dcomplex[::1, :] T_mat): """ Cython version of the Kalman filter recursions for an ARMA process. """ cdef cnp.npy_intp yshape[2] yshape[0] = nobs yshape[1] = 1 cdef cnp.npy_intp mshape[2] mshape[0] = r mshape[1] = 1 cdef cnp.npy_intp r2shape[2] r2shape[0] = r r2shape[1] = r cdef: int one = 1 int ldz = Z_mat.strides[1] / sizeof(dcomplex) int ldt = T_mat.strides[1] / sizeof(dcomplex) int ldr = R_mat.strides[1] / sizeof(dcomplex) # forecast errors ndarray[complex, ndim=2] v = PyArray_ZEROS(2, yshape, cnp.NPY_CDOUBLE, FORTRAN) # store variance of forecast errors dcomplex[::1, :] F = ones((nobs, 1), dtype=complex, order='F') dcomplex loglikelihood = 0 + 0j int i = 0 # initial state dcomplex[::1, :] alpha = PyArray_ZEROS(2, mshape, cnp.NPY_CDOUBLE, FORTRAN) int lda = alpha.strides[1] / sizeof(dcomplex) # initial variance dcomplex[::1, :] P = asfortranarray(dot(pinv(identity(r**2) - kron(T_mat, T_mat)), dot(R_mat, R_mat.T).ravel('F')).reshape(r, r, order='F')) int ldp = P.strides[1] / sizeof(dcomplex) dcomplex F_mat = 0 dcomplex Finv = 0 dcomplex v_mat = 0 dcomplex[::1, :] K = PyArray_ZEROS(2, mshape, cnp.NPY_CDOUBLE, FORTRAN) int ldk = K.strides[1] / sizeof(dcomplex) # pre-allocate some tmp arrays for the dgemm calls dcomplex[::1, :] tmp1 = PyArray_ZEROS(2, r2shape, cnp.NPY_CDOUBLE, FORTRAN) int ldt1 = tmp1.strides[1] / sizeof(dcomplex) dcomplex[::1, :] tmp2 = zeros_like(alpha, order='F') int ldt2 = tmp2.strides[1] / sizeof(dcomplex) dcomplex[::1, :] L = zeros_like(T_mat, dtype=complex, order='F') int ldl = L.strides[1] / sizeof(dcomplex) # T_mat rows x P cols dcomplex[::1, :] tmp3 = PyArray_ZEROS(2, r2shape, cnp.NPY_CDOUBLE, FORTRAN) int ldt3 = tmp3.strides[1] / sizeof(dcomplex) dcomplex alph = 1 + 0j dcomplex beta = 0 while F_mat != 1 and i < nobs: # Z_mat is just a selector matrix v_mat = y[i] - alpha[0,0] v[i, 0] = v_mat # one-step forecast error covariance # Z_mat is just a selctor matrix so the below is equivalent F_mat = P[0, 0] F[i, 0] = F_mat Finv = 1. / F_mat # always scalar for univariate series # compute Kalman Gain K, equivalent to: # K = np.dot(np.dot(np.dot(T_mat, P), Z_mat.T), Finv) # in two steps: # tmp1 = np.dot(T_mat, P) # K = Finv * tmp1.dot(Z_mat.T) zgemm("N", "N", &r, &r, &r, &alph, &T_mat[0, 0], &ldt, &P[0, 0], &ldp, &beta, &tmp1[0, 0], &ldt1) zgemv("N", &r, &r, &Finv, &tmp1[0, 0], &ldt1, &Z_mat[0, 0], &one, &beta, &K[0, 0], &one) # update state, equivalent to: # alpha = np.dot(T_mat, alpha) + np.dot(K, v_mat) # in two steps: # tmp2 = np.dot(T_mat, alpha) # alpha = tmp2 + np.dot(K, v_mat) zgemv("N", &r, &r, &alph, &T_mat[0, 0], &ldt, &alpha[0, 0], &one, &beta, &tmp2[0, 0], &one) for ii in range(r): alpha[ii, 0] = K[ii, 0] * v_mat + tmp2[ii, 0] # The next block is equivalent to: # L = T_mat - np.dot(K, Z_mat) # in two steps: # L = np.dot(K, Z_mat) # L = T_mat - L zgemm("N", "N", &r, &r, &one, &alph, &K[0, 0], &ldk, &Z_mat[0, 0], &ldz, &beta, &L[0, 0], &ldl) for jj in range(r): for kk in range(r): L[jj, kk] = T_mat[jj, kk] - L[jj, kk] # The next block computes P equivalent to: # P = np.dot(np.dot(T_mat, P), L.T) + np.dot(R_mat, R_mat.T) # in three steps: # tmp5 = np.dot(R_mat, R_mat.T) # tmp3 = np.dot(T_mat, P) # P = np.dot(tmp3, L.T) + tmp5 zgemm("N", "N", &r, &r, &r, &alph, &T_mat[0, 0], &ldt, &P[0, 0], &ldp, &beta, &tmp3[0, 0], &ldt3) zgemm("N", "T", &r, &r, &one, &alph, &R_mat[0, 0], &ldr, &R_mat[0, 0], &ldr, &beta, &P[0, 0], &ldp) zgemm("N", "T", &r, &r, &r, &alph, &tmp3[0, 0], &ldt3, &L[0, 0], &ldl, &alph, &P[0, 0], &ldp) loglikelihood += nplog(F_mat) i += 1 for i in xrange(i, nobs): # Z_mat is just a selector v_mat = y[i] - alpha[0, 0] v[i, 0] = v_mat # The next block is equivalent to: # alpha = np.dot(T_mat, alpha) + np.dot(K, v_mat) # in two steps: # tmp2 = np.dot(T_mat, alpha) # alpha = np.dot(K, v_mat) + tmp2 zgemm("N", "N", &r, &one, &r, &alph, &T_mat[0, 0], &ldt, &alpha[0, 0], &lda, &beta, &tmp2[0, 0], &ldt2) for ii in range(r): alpha[ii, 0] = K[ii, 0] * v_mat + tmp2[ii, 0] return v, F, loglikelihood @cython.boundscheck(False) @cython.wraparound(False) @cython.cdivision(True) def kalman_loglike_double(double[:] y, unsigned int k, unsigned int p, unsigned int q, int r, unsigned int nobs, double[::1, :] Z_mat, double[::1, :] R_mat, double[::1, :] T_mat): """ Cython version of the Kalman filter recursions for an ARMA process. """ v, F, loglikelihood = kalman_filter_double(y, k, p, q, r, nobs, Z_mat, R_mat, T_mat) sigma2 = 1. / nobs * sum(v**2 / F) loglike = -.5 * (loglikelihood + nobs * log(sigma2)) loglike -= nobs / 2. * (log(2 * pi) + 1) return loglike, sigma2 @cython.boundscheck(False) @cython.wraparound(False) @cython.cdivision(True) def kalman_loglike_complex(dcomplex[:] y, unsigned int k, unsigned int p, unsigned int q, int r, unsigned int nobs, dcomplex[::1, :] Z_mat, dcomplex[::1, :] R_mat, dcomplex[::1, :] T_mat): """ Cython version of the Kalman filter recursions for an ARMA process. """ v, F, loglikelihood = kalman_filter_complex(y, k, p, q, r, nobs, Z_mat, R_mat, T_mat) sigma2 = 1. / nobs * sum(v**2 / F) loglike = -.5 * (loglikelihood + nobs * nplog(sigma2)) loglike -= nobs / 2. * (log(2 * pi) + 1) return loglike, sigma2 statsmodels-0.12.2/statsmodels/tsa/kalmanf/kalmanfilter.py000066400000000000000000000175771400612667500237530ustar00rootroot00000000000000""" State Space Analysis using the Kalman Filter References ----------- Durbin., J and Koopman, S.J. `Time Series Analysis by State Space Methods`. Oxford, 2001. Hamilton, J.D. `Time Series Analysis`. Princeton, 1994. Harvey, A.C. `Forecasting, Structural Time Series Models and the Kalman Filter`. Cambridge, 1989. Notes ----- This file follows Hamilton's notation pretty closely. The ARMA Model class follows Durbin and Koopman notation. Harvey uses Durbin and Koopman notation. """ # noqa:E501 # Anderson and Moore `Optimal Filtering` provides a more efficient algorithm # namely the information filter # if the number of series is much greater than the number of states # e.g., with a DSGE model. See Also # http://www.federalreserve.gov/pubs/oss/oss4/aimindex.html # Harvey notes that the square root filter will keep P_t pos. def. but # is not strictly needed outside of the engineering (long series) import numpy as np from . import kalman_loglike # Fast filtering and smoothing for multivariate state space models # and The Riksbank -- Strid and Walentin (2008) # Block Kalman filtering for large-scale DSGE models # but this is obviously macro model specific class KalmanFilter(object): r""" Kalman Filter code intended for use with the ARMA model. Notes ----- The notation for the state-space form follows Durbin and Koopman (2001). The observation equations is .. math:: y_{t} = Z_{t}\alpha_{t} + \epsilon_{t} The state equation is .. math:: \alpha_{t+1} = T_{t}\alpha_{t} + R_{t}\eta_{t} For the present purposed \epsilon_{t} is assumed to always be zero. """ @classmethod def T(cls, params, r, k, p): # F in Hamilton """ The coefficient matrix for the state vector in the state equation. Its dimension is r+k x r+k. Parameters ---------- r : int In the context of the ARMA model r is max(p,q+1) where p is the AR order and q is the MA order. k : int The number of exogenous variables in the ARMA model, including the constant if appropriate. p : int The AR coefficient in an ARMA model. References ---------- Durbin and Koopman Section 3.7. """ arr = np.zeros((r, r), dtype=params.dtype, order="F") # allows for complex-step derivative params_padded = np.zeros(r, dtype=params.dtype, order="F") # handle zero coefficients if necessary # NOTE: squeeze added for cg optimizer params_padded[:p] = params[k:p + k] arr[:, 0] = params_padded # first p params are AR coeffs w/ short params arr[:-1, 1:] = np.eye(r - 1) return arr @classmethod def R(cls, params, r, k, q, p): # R is H in Hamilton """ The coefficient matrix for the state vector in the observation equation. Its dimension is r+k x 1. Parameters ---------- r : int In the context of the ARMA model r is max(p,q+1) where p is the AR order and q is the MA order. k : int The number of exogenous variables in the ARMA model, including the constant if appropriate. q : int The MA order in an ARMA model. p : int The AR order in an ARMA model. References ---------- Durbin and Koopman Section 3.7. """ arr = np.zeros((r, 1), dtype=params.dtype, order="F") # this allows zero coefficients # dtype allows for compl. der. arr[1:q + 1, :] = params[p + k:p + k + q][:, None] arr[0] = 1.0 return arr @classmethod def Z(cls, r): """ Returns the Z selector matrix in the observation equation. Parameters ---------- r : int In the context of the ARMA model r is max(p,q+1) where p is the AR order and q is the MA order. Notes ----- Currently only returns a 1 x r vector [1,0,0,...0]. Will need to be generalized when the Kalman Filter becomes more flexible. """ arr = np.zeros((1, r), order="F") arr[:, 0] = 1. return arr @classmethod def geterrors(cls, y, k, k_ar, k_ma, k_lags, nobs, Z_mat, m, R_mat, T_mat, paramsdtype): """ Returns just the errors of the Kalman Filter """ if np.issubdtype(paramsdtype, np.float64): return kalman_loglike.kalman_filter_double( y, k, k_ar, k_ma, k_lags, int(nobs), Z_mat, R_mat, T_mat)[0] elif np.issubdtype(paramsdtype, np.complex128): return kalman_loglike.kalman_filter_complex( y, k, k_ar, k_ma, k_lags, int(nobs), Z_mat, R_mat, T_mat)[0] else: raise TypeError("dtype %s is not supported " "Please file a bug report" % paramsdtype) @classmethod def _init_kalman_state(cls, params, arma_model): """ Returns the system matrices and other info needed for the Kalman Filter recursions """ paramsdtype = params.dtype y = arma_model.endog.copy().astype(paramsdtype) k = arma_model.k_exog + arma_model.k_trend nobs = arma_model.nobs k_ar = arma_model.k_ar k_ma = arma_model.k_ma k_lags = arma_model.k_lags if arma_model.transparams: newparams = arma_model._transparams(params) else: newparams = params # do not need a copy if not modified. if k > 0: y -= np.dot(arma_model.exog, newparams[:k]) # system matrices Z_mat = cls.Z(k_lags) m = Z_mat.shape[1] # r R_mat = cls.R(newparams, k_lags, k, k_ma, k_ar) T_mat = cls.T(newparams, k_lags, k, k_ar) return (y, k, nobs, k_ar, k_ma, k_lags, newparams, Z_mat, m, R_mat, T_mat, paramsdtype) @classmethod def loglike(cls, params, arma_model, set_sigma2=True): """ The loglikelihood for an ARMA model using the Kalman Filter recursions. Parameters ---------- params : ndarray The coefficients of the ARMA model, assumed to be in the order of trend variables and `k` exogenous coefficients, the `p` AR coefficients, then the `q` MA coefficients. arma_model : `statsmodels.tsa.arima.ARMA` instance A reference to the ARMA model instance. set_sigma2 : bool, optional True if arma_model.sigma2 should be set. Note that sigma2 will be computed in any case, but it will be discarded if set_sigma2 is False. Notes ----- This works for both real valued and complex valued parameters. The complex values being used to compute the numerical derivative. If available will use a Cython version of the Kalman Filter. """ # TODO: see section 3.4.6 in Harvey for computing the derivatives in # the recursion itself. # TODO: this will not work for time-varying parameters (y, k, nobs, k_ar, k_ma, k_lags, newparams, Z_mat, m, R_mat, T_mat, paramsdtype) = cls._init_kalman_state(params, arma_model) if np.issubdtype(paramsdtype, np.float64): loglike, sigma2 = kalman_loglike.kalman_loglike_double( y, k, k_ar, k_ma, k_lags, int(nobs), Z_mat, R_mat, T_mat) elif np.issubdtype(paramsdtype, np.complex128): loglike, sigma2 = kalman_loglike.kalman_loglike_complex( y, k, k_ar, k_ma, k_lags, int(nobs), Z_mat.astype(complex), R_mat, T_mat) else: raise TypeError("This dtype %s is not supported " " Please files a bug report." % paramsdtype) if set_sigma2: arma_model.sigma2 = sigma2 return loglike statsmodels-0.12.2/statsmodels/tsa/mlemodel.py000066400000000000000000000042051400612667500214470ustar00rootroot00000000000000"""Base Classes for Likelihood Models in time series analysis Warning: imports numdifftools Created on Sun Oct 10 15:00:47 2010 Author: josef-pktd License: BSD """ try: import numdifftools as ndt except ImportError: pass from statsmodels.base.model import LikelihoodModel #copied from sandbox/regression/mle.py #TODO: I take it this is only a stub and should be included in another # model class? class TSMLEModel(LikelihoodModel): """ univariate time series model for estimation with maximum likelihood Note: This is not working yet """ def __init__(self, endog, exog=None): #need to override p,q (nar,nma) correctly super(TSMLEModel, self).__init__(endog, exog) #set default arma(1,1) self.nar = 1 self.nma = 1 #self.initialize() def geterrors(self, params): raise NotImplementedError def loglike(self, params): """ Loglikelihood for timeseries model Parameters ---------- params : array_like The model parameters Notes ----- needs to be overwritten by subclass """ raise NotImplementedError def score(self, params): """ Score vector for Arma model """ #return None #print params jac = ndt.Jacobian(self.loglike, stepMax=1e-4) return jac(params)[-1] def hessian(self, params): """ Hessian of arma model. Currently uses numdifftools """ #return None Hfun = ndt.Jacobian(self.score, stepMax=1e-4) return Hfun(params)[-1] def fit(self, start_params=None, maxiter=5000, method='fmin', tol=1e-08): '''estimate model by minimizing negative loglikelihood does this need to be overwritten ? ''' if start_params is None and hasattr(self, '_start_params'): start_params = self._start_params #start_params = np.concatenate((0.05*np.ones(self.nar + self.nma), [1])) mlefit = super(TSMLEModel, self).fit(start_params=start_params, maxiter=maxiter, method=method, tol=tol) return mlefit statsmodels-0.12.2/statsmodels/tsa/regime_switching/000077500000000000000000000000001400612667500226255ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/regime_switching/__init__.py000066400000000000000000000001131400612667500247310ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/tsa/regime_switching/_hamilton_filter.pxd000066400000000000000000000064431400612667500266700ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ Hamilton filter declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np cdef void shamilton_filter_log_iteration(int t, int k_regimes, int order, np.float32_t [:,:] transition, np.float32_t [:] weighted_likelihoods, np.float32_t [:] prev_filtered_marginalized_probabilities, np.float32_t [:] conditional_likelihoods, np.float32_t [:] joint_likelihoods, np.float32_t [:] curr_predicted_joint_probabilities, np.float32_t [:] prev_filtered_joint_probabilities, np.float32_t [:] curr_filtered_joint_probabilities, np.float32_t [:] tmp_predicted_joint_probabilities) nogil cdef void dhamilton_filter_log_iteration(int t, int k_regimes, int order, np.float64_t [:,:] transition, np.float64_t [:] weighted_likelihoods, np.float64_t [:] prev_filtered_marginalized_probabilities, np.float64_t [:] conditional_likelihoods, np.float64_t [:] joint_likelihoods, np.float64_t [:] curr_predicted_joint_probabilities, np.float64_t [:] prev_filtered_joint_probabilities, np.float64_t [:] curr_filtered_joint_probabilities, np.float64_t [:] tmp_predicted_joint_probabilities) nogil cdef void chamilton_filter_log_iteration(int t, int k_regimes, int order, np.complex64_t [:,:] transition, np.complex64_t [:] weighted_likelihoods, np.complex64_t [:] prev_filtered_marginalized_probabilities, np.complex64_t [:] conditional_likelihoods, np.complex64_t [:] joint_likelihoods, np.complex64_t [:] curr_predicted_joint_probabilities, np.complex64_t [:] prev_filtered_joint_probabilities, np.complex64_t [:] curr_filtered_joint_probabilities, np.complex64_t [:] tmp_predicted_joint_probabilities) nogil cdef void zhamilton_filter_log_iteration(int t, int k_regimes, int order, np.complex128_t [:,:] transition, np.complex128_t [:] weighted_likelihoods, np.complex128_t [:] prev_filtered_marginalized_probabilities, np.complex128_t [:] conditional_likelihoods, np.complex128_t [:] joint_likelihoods, np.complex128_t [:] curr_predicted_joint_probabilities, np.complex128_t [:] prev_filtered_joint_probabilities, np.complex128_t [:] curr_filtered_joint_probabilities, np.complex128_t [:] tmp_predicted_joint_probabilities) nogil statsmodels-0.12.2/statsmodels/tsa/regime_switching/_hamilton_filter.pyx.in000066400000000000000000000213351400612667500273170ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ Hamilton filter Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # Typical imports import numpy as np import warnings cimport numpy as np cimport cython from statsmodels.src.math cimport dlog, zlog, dexp, zexp cdef int FORTRAN = 1 {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} def {{prefix}}hamilton_filter_log(int nobs, int k_regimes, int order, {{cython_type}} [:,:,:] regime_transition, {{cython_type}} [:,:] conditional_likelihoods, {{cython_type}} [:] joint_likelihoods, {{cython_type}} [:,:] predicted_joint_probabilities, {{cython_type}} [:,:] filtered_joint_probabilities): cdef int t, i, j, k, ix, regime_transition_t = 0, time_varying_regime_transition cdef: # k_regimes_order_m1 is not used when order == 0. int k_regimes_order_m1 = k_regimes**max(order - 1, 0) int k_regimes_order = k_regimes**order int k_regimes_order_p1 = k_regimes**(order + 1) {{cython_type}} [:] weighted_likelihoods, tmp_filtered_marginalized_probabilities, tmp_predicted_joint_probabilities np.float64_t tmp_max_real {{cython_type}} tmp_max time_varying_regime_transition = regime_transition.shape[2] > 1 weighted_likelihoods = np.zeros(k_regimes_order_p1, dtype={{dtype}}) # tmp_filtered_marginalized_probabilities is not used if order == 0. tmp_filtered_marginalized_probabilities = np.zeros(k_regimes_order, dtype={{dtype}}) tmp_predicted_joint_probabilities = np.zeros(k_regimes, dtype={{dtype}}) with nogil: for t in range(nobs): if time_varying_regime_transition: regime_transition_t = t if order > 0: # Collapse filtered joint probabilities over the last dimension # Pr[S_{t-1}, ..., S_{t-r} | t-1] = \sum_{ S_{t-r-1} } Pr[S_{t-1}, ..., S_{t-r}, S_{t-r-1} | t-1] ix = 0 # tmp_filtered_marginalized_probabilities[:] = 0 for j in range(k_regimes_order): # This is logsumexp, so we use the maximum trick tmp_max_real = filtered_joint_probabilities[ix, t]{{if combined_prefix == 'z'}}.real{{endif}} tmp_max = filtered_joint_probabilities[ix, t] for i in range(k_regimes): if filtered_joint_probabilities[ix + i, t]{{if combined_prefix == 'z'}}.real{{endif}} > tmp_max_real: tmp_max_real = filtered_joint_probabilities[ix + i, t]{{if combined_prefix == 'z'}}.real{{endif}} tmp_max = filtered_joint_probabilities[ix + i, t] tmp_filtered_marginalized_probabilities[j] = 0 for i in range(k_regimes): tmp_filtered_marginalized_probabilities[j] = ( tmp_filtered_marginalized_probabilities[j] + {{combined_prefix}}exp(filtered_joint_probabilities[ix, t] - tmp_max)) ix = ix + 1 tmp_filtered_marginalized_probabilities[j] = (tmp_max + {{combined_prefix}}log(tmp_filtered_marginalized_probabilities[j])) {{prefix}}hamilton_filter_log_iteration(t, k_regimes, order, regime_transition[:, :, regime_transition_t], weighted_likelihoods, tmp_filtered_marginalized_probabilities, conditional_likelihoods[:, t], joint_likelihoods, predicted_joint_probabilities[:, t], filtered_joint_probabilities[:, t], filtered_joint_probabilities[:, t+1], tmp_predicted_joint_probabilities) cdef void {{prefix}}hamilton_filter_log_iteration(int t, int k_regimes, int order, {{cython_type}} [:,:] regime_transition, {{cython_type}} [:] weighted_likelihoods, {{cython_type}} [:] prev_filtered_marginalized_probabilities, {{cython_type}} [:] conditional_likelihoods, {{cython_type}} [:] joint_likelihoods, {{cython_type}} [:] curr_predicted_joint_probabilities, {{cython_type}} [:] prev_filtered_joint_probabilities, {{cython_type}} [:] curr_filtered_joint_probabilities, {{cython_type}} [:] tmp_predicted_joint_probabilities) nogil: cdef int i, j, k, ix cdef: int k_regimes_order_m1 = k_regimes**(order - 1) int k_regimes_order = k_regimes**order int k_regimes_order_p1 = k_regimes**(order + 1) np.float64_t tmp_max_real {{cython_type}} tmp_max # Compute predicted joint probabilities # Pr[S_t, S_{t-1}, ..., S_{t-r} | t-1] = Pr[S_t | S_{t-1}] * Pr[S_{t-1}, ..., S_{t-r} | t-1] if order > 0: ix = 0 for i in range(k_regimes): for j in range(k_regimes): for k in range(k_regimes_order_m1): curr_predicted_joint_probabilities[ix] = ( prev_filtered_marginalized_probabilities[j * k_regimes_order_m1 + k] + regime_transition[i, j]) ix += 1 else: curr_predicted_joint_probabilities[:] = 0 for i in range(k_regimes): # Again, this is logsumexp, so we use the maximum trick tmp_max_real = 0 tmp_max = 0 for j in range(k_regimes): tmp_predicted_joint_probabilities[j] = ( prev_filtered_joint_probabilities[j] + regime_transition[i, j]) if tmp_predicted_joint_probabilities[j]{{if combined_prefix == 'z'}}.real{{endif}} > tmp_max_real: tmp_max_real = tmp_predicted_joint_probabilities[j]{{if combined_prefix == 'z'}}.real{{endif}} tmp_max = tmp_predicted_joint_probabilities[j] curr_predicted_joint_probabilities[i] = 0 for j in range(k_regimes): curr_predicted_joint_probabilities[i] = ( curr_predicted_joint_probabilities[i] + {{combined_prefix}}exp(tmp_predicted_joint_probabilities[j] - tmp_max)) curr_predicted_joint_probabilities[i] = (tmp_max + {{combined_prefix}}log(curr_predicted_joint_probabilities[i])) # Compute weighted likelihoods f(y_t | S_t, S_{t-1}, ..., S_{t-r}, t-1) * Pr[S_t, S_{t-1}, ..., S_{t-r} | t-1] tmp_max_real = 0 tmp_max = 0 for i in range(k_regimes_order_p1): weighted_likelihoods[i] = ( curr_predicted_joint_probabilities[i] + conditional_likelihoods[i]) # Compute the maximum for use below in logsumexp if weighted_likelihoods[i]{{if combined_prefix == 'z'}}.real{{endif}} > tmp_max_real: tmp_max_real = weighted_likelihoods[i]{{if combined_prefix == 'z'}}.real{{endif}} tmp_max = weighted_likelihoods[i] # Compute the joint likelihood f(y_t | t-1) # Again, this is logsumexp, so we use the maximum trick (where the # maximum was just computed above) joint_likelihoods[t] = 0 for i in range(k_regimes_order_p1): joint_likelihoods[t] = ( joint_likelihoods[t] + {{combined_prefix}}exp(weighted_likelihoods[i] - tmp_max)) joint_likelihoods[t] = tmp_max + {{combined_prefix}}log(joint_likelihoods[t]) # Compute filtered joint probabilities # Pr[S_t, S_{t-1}, ..., S_{t-r} | t] = ( # f(y_t | S_t, S_{t-1}, ..., S_{t-r}, t-1) * # Pr[S_t, S_{t-1}, ..., S_{t-r} | t-1] / # f(y_t | t-1)) for i in range(k_regimes_order_p1): # TODO: do I need to worry about some value for joint_likelihoods? curr_filtered_joint_probabilities[i] = ( weighted_likelihoods[i] - joint_likelihoods[t]) {{endfor}} statsmodels-0.12.2/statsmodels/tsa/regime_switching/_kim_smoother.pxd000066400000000000000000000072431400612667500262070ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ Kim smoother declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np cpdef skim_smoother_log(int nobs, int k_regimes, int order, np.float32_t [:, :, :] regime_transition, np.float32_t [:, :] predicted_joint_probabilities, np.float32_t [:, :] filtered_joint_probabilities, np.float32_t [:, :] smoothed_joint_probabilities) cpdef dkim_smoother_log(int nobs, int k_regimes, int order, np.float64_t [:, :, :] regime_transition, np.float64_t [:, :] predicted_joint_probabilities, np.float64_t [:, :] filtered_joint_probabilities, np.float64_t [:, :] smoothed_joint_probabilities) cpdef ckim_smoother_log(int nobs, int k_regimes, int order, np.complex64_t [:, :, :] regime_transition, np.complex64_t [:, :] predicted_joint_probabilities, np.complex64_t [:, :] filtered_joint_probabilities, np.complex64_t [:, :] smoothed_joint_probabilities) cpdef zkim_smoother_log(int nobs, int k_regimes, int order, np.complex128_t [:, :, :] regime_transition, np.complex128_t [:, :] predicted_joint_probabilities, np.complex128_t [:, :] filtered_joint_probabilities, np.complex128_t [:, :] smoothed_joint_probabilities) cdef void skim_smoother_log_iteration(int tt, int k_regimes, int order, np.float32_t [:] tmp_joint_probabilities, np.float32_t [:] tmp_probabilities_fraction, np.float32_t [:, :] regime_transition, np.float32_t [:] predicted_joint_probabilities, np.float32_t [:] filtered_joint_probabilities, np.float32_t [:] prev_smoothed_joint_probabilities, np.float32_t [:] next_smoothed_joint_probabilities) nogil cdef void dkim_smoother_log_iteration(int tt, int k_regimes, int order, np.float64_t [:] tmp_joint_probabilities, np.float64_t [:] tmp_probabilities_fraction, np.float64_t [:, :] regime_transition, np.float64_t [:] predicted_joint_probabilities, np.float64_t [:] filtered_joint_probabilities, np.float64_t [:] prev_smoothed_joint_probabilities, np.float64_t [:] next_smoothed_joint_probabilities) nogil cdef void ckim_smoother_log_iteration(int tt, int k_regimes, int order, np.complex64_t [:] tmp_joint_probabilities, np.complex64_t [:] tmp_probabilities_fraction, np.complex64_t [:, :] regime_transition, np.complex64_t [:] predicted_joint_probabilities, np.complex64_t [:] filtered_joint_probabilities, np.complex64_t [:] prev_smoothed_joint_probabilities, np.complex64_t [:] next_smoothed_joint_probabilities) nogil cdef void zkim_smoother_log_iteration(int tt, int k_regimes, int order, np.complex128_t [:] tmp_joint_probabilities, np.complex128_t [:] tmp_probabilities_fraction, np.complex128_t [:, :] regime_transition, np.complex128_t [:] predicted_joint_probabilities, np.complex128_t [:] filtered_joint_probabilities, np.complex128_t [:] prev_smoothed_joint_probabilities, np.complex128_t [:] next_smoothed_joint_probabilities) nogil statsmodels-0.12.2/statsmodels/tsa/regime_switching/_kim_smoother.pyx.in000066400000000000000000000132461400612667500266410ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ Kim smoother Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # Typical imports import numpy as np import warnings cimport numpy as np cimport cython from statsmodels.src.math cimport dlog, zlog, dexp, zexp cdef int FORTRAN = 1 {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} cpdef {{prefix}}kim_smoother_log(int nobs, int k_regimes, int order, {{cython_type}} [:, :, :] regime_transition, {{cython_type}} [:, :] predicted_joint_probabilities, {{cython_type}} [:, :] filtered_joint_probabilities, {{cython_type}} [:, :] smoothed_joint_probabilities): cdef int t, i, j, k, ix, regime_transition_t = 0, time_varying_regime_transition cdef: int k_regimes_order_m1 = k_regimes**(order - 1) int k_regimes_order = k_regimes**order int k_regimes_order_p1 = k_regimes**(order + 1) int k_regimes_order_p2 = k_regimes**(order + 2) {{cython_type}} [:] tmp_joint_probabilities, tmp_probabilities_fraction time_varying_regime_transition = regime_transition.shape[2] > 1 tmp_joint_probabilities = np.zeros(k_regimes_order_p2, dtype={{dtype}}) tmp_probabilities_fraction = np.zeros(k_regimes_order_p1, dtype={{dtype}}) # S_T, S_{T-1}, ..., S_{T-r} | T smoothed_joint_probabilities[:, nobs-1] = filtered_joint_probabilities[:, nobs-1] with nogil: for t in range(nobs - 2, -1, -1): if time_varying_regime_transition: regime_transition_t = t + 1 {{prefix}}kim_smoother_log_iteration(t, k_regimes, order, tmp_joint_probabilities, tmp_probabilities_fraction, regime_transition[:, :, regime_transition_t], predicted_joint_probabilities[:, t+1], filtered_joint_probabilities[:, t], smoothed_joint_probabilities[:, t+1], smoothed_joint_probabilities[:, t]) cdef void {{prefix}}kim_smoother_log_iteration(int tt, int k_regimes, int order, {{cython_type}} [:] tmp_joint_probabilities, {{cython_type}} [:] tmp_probabilities_fraction, {{cython_type}} [:, :] regime_transition, {{cython_type}} [:] predicted_joint_probabilities, {{cython_type}} [:] filtered_joint_probabilities, {{cython_type}} [:] prev_smoothed_joint_probabilities, {{cython_type}} [:] next_smoothed_joint_probabilities) nogil: cdef int t, i, j, k, ix cdef: int k_regimes_order_m1 = k_regimes**(order - 1) int k_regimes_order = k_regimes**order int k_regimes_order_p1 = k_regimes**(order + 1) int k_regimes_order_p2 = k_regimes**(order + 2) cdef np.float64_t tmp_max_real cdef {{cython_type}} tmp_max # Pr[S_{t+1}, S_t, ..., S_{t-r+1} | t] = Pr[S_{t+1} | S_t] * Pr[S_t, ..., S_{t-r+1} | t] ix = 0 for i in range(k_regimes): for j in range(k_regimes): for k in range(k_regimes_order): tmp_joint_probabilities[ix] = ( filtered_joint_probabilities[j * k_regimes_order + k] + regime_transition[i, j]) ix += 1 # S_{t+1}, S_t, ..., S_{t-r+2} | T / S_{t+1}, S_t, ..., S_{t-r+2} | t for i in range(k_regimes_order_p1): # TODO: do I need to worry about some value for predicted_joint_probabilities? tmp_probabilities_fraction[i] = ( prev_smoothed_joint_probabilities[i] - predicted_joint_probabilities[i]) # S_{t+1}, S_t, ..., S_{t-r+1} | T ix = 0 for i in range(k_regimes_order_p1): for j in range(k_regimes): tmp_joint_probabilities[ix] = ( tmp_probabilities_fraction[i] + tmp_joint_probabilities[ix]) ix = ix + 1 for i in range(k_regimes_order_p1): tmp_max_real = tmp_joint_probabilities[i]{{if combined_prefix == 'z'}}.real{{endif}} tmp_max = tmp_joint_probabilities[i] for j in range(k_regimes): ix = j * k_regimes_order_p1 + i if tmp_joint_probabilities[ix]{{if combined_prefix == 'z'}}.real{{endif}} > tmp_max_real: tmp_max_real = tmp_joint_probabilities[ix]{{if combined_prefix == 'z'}}.real{{endif}} tmp_max = tmp_joint_probabilities[ix] next_smoothed_joint_probabilities[i] = 0 for j in range(k_regimes): ix = j * k_regimes_order_p1 + i next_smoothed_joint_probabilities[i] = ( next_smoothed_joint_probabilities[i] + {{combined_prefix}}exp(tmp_joint_probabilities[ix] - tmp_max)) next_smoothed_joint_probabilities[i] = (tmp_max + {{combined_prefix}}log(next_smoothed_joint_probabilities[i])) {{endfor}} statsmodels-0.12.2/statsmodels/tsa/regime_switching/markov_autoregression.py000066400000000000000000000431271400612667500276360ustar00rootroot00000000000000""" Markov switching autoregression models Author: Chad Fulton License: BSD-3 """ import numpy as np import statsmodels.base.wrapper as wrap from statsmodels.tsa.tsatools import lagmat from statsmodels.tsa.regime_switching import ( markov_switching, markov_regression) from statsmodels.tsa.statespace.tools import ( constrain_stationary_univariate, unconstrain_stationary_univariate) class MarkovAutoregression(markov_regression.MarkovRegression): r""" Markov switching regression model Parameters ---------- endog : array_like The endogenous variable. k_regimes : int The number of regimes. order : int The order of the autoregressive lag polynomial. trend : {'nc', 'c', 't', 'ct'} Whether or not to include a trend. To include an constant, time trend, or both, set `trend='c'`, `trend='t'`, or `trend='ct'`. For no trend, set `trend='nc'`. Default is a constant. exog : array_like, optional Array of exogenous regressors, shaped nobs x k. exog_tvtp : array_like, optional Array of exogenous or lagged variables to use in calculating time-varying transition probabilities (TVTP). TVTP is only used if this variable is provided. If an intercept is desired, a column of ones must be explicitly included in this array. switching_ar : bool or iterable, optional If a boolean, sets whether or not all autoregressive coefficients are switching across regimes. If an iterable, should be of length equal to `order`, where each element is a boolean describing whether the corresponding coefficient is switching. Default is True. switching_trend : bool or iterable, optional If a boolean, sets whether or not all trend coefficients are switching across regimes. If an iterable, should be of length equal to the number of trend variables, where each element is a boolean describing whether the corresponding coefficient is switching. Default is True. switching_exog : bool or iterable, optional If a boolean, sets whether or not all regression coefficients are switching across regimes. If an iterable, should be of length equal to the number of exogenous variables, where each element is a boolean describing whether the corresponding coefficient is switching. Default is True. switching_variance : bool, optional Whether or not there is regime-specific heteroskedasticity, i.e. whether or not the error term has a switching variance. Default is False. Notes ----- This model is new and API stability is not guaranteed, although changes will be made in a backwards compatible way if possible. The model can be written as: .. math:: y_t = a_{S_t} + x_t' \beta_{S_t} + \phi_{1, S_t} (y_{t-1} - a_{S_{t-1}} - x_{t-1}' \beta_{S_{t-1}}) + \dots + \phi_{p, S_t} (y_{t-p} - a_{S_{t-p}} - x_{t-p}' \beta_{S_{t-p}}) + \varepsilon_t \\ \varepsilon_t \sim N(0, \sigma_{S_t}^2) i.e. the model is an autoregression with where the autoregressive coefficients, the mean of the process (possibly including trend or regression effects) and the variance of the error term may be switching across regimes. The `trend` is accommodated by prepending columns to the `exog` array. Thus if `trend='c'`, the passed `exog` array should not already have a column of ones. References ---------- Kim, Chang-Jin, and Charles R. Nelson. 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications". MIT Press Books. The MIT Press. """ def __init__(self, endog, k_regimes, order, trend='c', exog=None, exog_tvtp=None, switching_ar=True, switching_trend=True, switching_exog=False, switching_variance=False, dates=None, freq=None, missing='none'): # Properties self.switching_ar = switching_ar # Switching options if self.switching_ar is True or self.switching_ar is False: self.switching_ar = [self.switching_ar] * order elif not len(self.switching_ar) == order: raise ValueError('Invalid iterable passed to `switching_ar`.') # Initialize the base model super(MarkovAutoregression, self).__init__( endog, k_regimes, trend=trend, exog=exog, order=order, exog_tvtp=exog_tvtp, switching_trend=switching_trend, switching_exog=switching_exog, switching_variance=switching_variance, dates=dates, freq=freq, missing=missing) # Sanity checks if self.nobs <= self.order: raise ValueError('Must have more observations than the order of' ' the autoregression.') # Autoregressive exog self.exog_ar = lagmat(endog, self.order)[self.order:] # Reshape other datasets self.nobs -= self.order self.orig_endog = self.endog self.endog = self.endog[self.order:] if self._k_exog > 0: self.orig_exog = self.exog self.exog = self.exog[self.order:] # Reset the ModelData datasets self.data.endog, self.data.exog = ( self.data._convert_endog_exog(self.endog, self.exog)) # Reset indexes, if provided if self.data.row_labels is not None: self.data._cache['row_labels'] = ( self.data.row_labels[self.order:]) if self._index is not None: if self._index_generated: self._index = self._index[:-self.order] else: self._index = self._index[self.order:] # Parameters self.parameters['autoregressive'] = self.switching_ar # Cache an array for holding slices self._predict_slices = [slice(None, None, None)] * (self.order + 1) def predict_conditional(self, params): """ In-sample prediction, conditional on the current and previous regime Parameters ---------- params : array_like Array of parameters at which to create predictions. Returns ------- predict : array_like Array of predictions conditional on current, and possibly past, regimes """ params = np.array(params, ndmin=1) # Prediction is based on: # y_t = x_t beta^{(S_t)} + # \phi_1^{(S_t)} (y_{t-1} - x_{t-1} beta^{(S_t-1)}) + ... # \phi_p^{(S_t)} (y_{t-p} - x_{t-p} beta^{(S_t-p)}) + eps_t if self._k_exog > 0: xb = [] for i in range(self.k_regimes): coeffs = params[self.parameters[i, 'exog']] xb.append(np.dot(self.orig_exog, coeffs)) predict = np.zeros( (self.k_regimes,) * (self.order + 1) + (self.nobs,), dtype=np.promote_types(np.float64, params.dtype)) # Iterate over S_{t} = i for i in range(self.k_regimes): ar_coeffs = params[self.parameters[i, 'autoregressive']] # y_t - x_t beta^{(S_t)} ix = self._predict_slices[:] ix[0] = i ix = tuple(ix) if self._k_exog > 0: predict[ix] += xb[i][self.order:] # Iterate over j = 2, .., p for j in range(1, self.order + 1): for k in range(self.k_regimes): # This gets a specific time-period / regime slice: # S_{t} = i, S_{t-j} = k, across all other time-period / # regime slices. ix = self._predict_slices[:] ix[0] = i ix[j] = k ix = tuple(ix) start = self.order - j end = -j if self._k_exog > 0: predict[ix] += ar_coeffs[j-1] * ( self.orig_endog[start:end] - xb[k][start:end]) else: predict[ix] += ar_coeffs[j-1] * ( self.orig_endog[start:end]) return predict def _resid(self, params): return self.endog - self.predict_conditional(params) def _conditional_loglikelihoods(self, params): """ Compute loglikelihoods conditional on the current period's regime and the last `self.order` regimes. """ # Get the residuals resid = self._resid(params) # Compute the conditional likelihoods variance = params[self.parameters['variance']].squeeze() if self.switching_variance: variance = np.reshape(variance, (self.k_regimes, 1, 1)) conditional_loglikelihoods = ( -0.5 * resid**2 / variance - 0.5 * np.log(2 * np.pi * variance)) return conditional_loglikelihoods @property def _res_classes(self): return {'fit': (MarkovAutoregressionResults, MarkovAutoregressionResultsWrapper)} def _em_iteration(self, params0): """ EM iteration """ # Inherited parameters result, params1 = markov_switching.MarkovSwitching._em_iteration( self, params0) tmp = np.sqrt(result.smoothed_marginal_probabilities) # Regression coefficients coeffs = None if self._k_exog > 0: coeffs = self._em_exog(result, self.endog, self.exog, self.parameters.switching['exog'], tmp) for i in range(self.k_regimes): params1[self.parameters[i, 'exog']] = coeffs[i] # Autoregressive if self.order > 0: if self._k_exog > 0: ar_coeffs, variance = self._em_autoregressive( result, coeffs) else: ar_coeffs = self._em_exog( result, self.endog, self.exog_ar, self.parameters.switching['autoregressive']) variance = self._em_variance( result, self.endog, self.exog_ar, ar_coeffs, tmp) for i in range(self.k_regimes): params1[self.parameters[i, 'autoregressive']] = ar_coeffs[i] params1[self.parameters['variance']] = variance return result, params1 def _em_autoregressive(self, result, betas, tmp=None): """ EM step for autoregressive coefficients and variances """ if tmp is None: tmp = np.sqrt(result.smoothed_marginal_probabilities) resid = np.zeros((self.k_regimes, self.nobs + self.order)) resid[:] = self.orig_endog if self._k_exog > 0: for i in range(self.k_regimes): resid[i] -= np.dot(self.orig_exog, betas[i]) # The difference between this and `_em_exog` is that here we have a # different endog and exog for each regime coeffs = np.zeros((self.k_regimes,) + (self.order,)) variance = np.zeros((self.k_regimes,)) exog = np.zeros((self.nobs, self.order)) for i in range(self.k_regimes): endog = resid[i, self.order:] exog = lagmat(resid[i], self.order)[self.order:] tmp_endog = tmp[i] * endog tmp_exog = tmp[i][:, None] * exog coeffs[i] = np.dot(np.linalg.pinv(tmp_exog), tmp_endog) if self.switching_variance: tmp_resid = endog - np.dot(exog, coeffs[i]) variance[i] = (np.sum( tmp_resid**2 * result.smoothed_marginal_probabilities[i]) / np.sum(result.smoothed_marginal_probabilities[i])) else: tmp_resid = tmp_endog - np.dot(tmp_exog, coeffs[i]) variance[i] = np.sum(tmp_resid**2) # Variances if not self.switching_variance: variance = variance.sum() / self.nobs return coeffs, variance @property def start_params(self): """ (array) Starting parameters for maximum likelihood estimation. """ # Inherited parameters params = markov_switching.MarkovSwitching.start_params.fget(self) # OLS for starting parameters endog = self.endog.copy() if self._k_exog > 0 and self.order > 0: exog = np.c_[self.exog, self.exog_ar] elif self._k_exog > 0: exog = self.exog elif self.order > 0: exog = self.exog_ar if self._k_exog > 0 or self.order > 0: beta = np.dot(np.linalg.pinv(exog), endog) variance = np.var(endog - np.dot(exog, beta)) else: variance = np.var(endog) # Regression coefficients if self._k_exog > 0: if np.any(self.switching_coeffs): for i in range(self.k_regimes): params[self.parameters[i, 'exog']] = ( beta[:self._k_exog] * (i / self.k_regimes)) else: params[self.parameters['exog']] = beta[:self._k_exog] # Autoregressive if self.order > 0: if np.any(self.switching_ar): for i in range(self.k_regimes): params[self.parameters[i, 'autoregressive']] = ( beta[self._k_exog:] * (i / self.k_regimes)) else: params[self.parameters['autoregressive']] = beta[self._k_exog:] # Variance if self.switching_variance: params[self.parameters['variance']] = ( np.linspace(variance / 10., variance, num=self.k_regimes)) else: params[self.parameters['variance']] = variance return params @property def param_names(self): """ (list of str) List of human readable parameter names (for parameters actually included in the model). """ # Inherited parameters param_names = np.array( markov_regression.MarkovRegression.param_names.fget(self), dtype=object) # Autoregressive if np.any(self.switching_ar): for i in range(self.k_regimes): param_names[self.parameters[i, 'autoregressive']] = [ 'ar.L%d[%d]' % (j+1, i) for j in range(self.order)] else: param_names[self.parameters['autoregressive']] = [ 'ar.L%d' % (j+1) for j in range(self.order)] return param_names.tolist() def transform_params(self, unconstrained): """ Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation Parameters ---------- unconstrained : array_like Array of unconstrained parameters used by the optimizer, to be transformed. Returns ------- constrained : array_like Array of constrained parameters which may be used in likelihood evaluation. """ # Inherited parameters constrained = super(MarkovAutoregression, self).transform_params( unconstrained) # Autoregressive # TODO may provide unexpected results when some coefficients are not # switching for i in range(self.k_regimes): s = self.parameters[i, 'autoregressive'] constrained[s] = constrain_stationary_univariate( unconstrained[s]) return constrained def untransform_params(self, constrained): """ Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer Parameters ---------- constrained : array_like Array of constrained parameters used in likelihood evaluation, to be transformed. Returns ------- unconstrained : array_like Array of unconstrained parameters used by the optimizer. """ # Inherited parameters unconstrained = super(MarkovAutoregression, self).untransform_params( constrained) # Autoregressive # TODO may provide unexpected results when some coefficients are not # switching for i in range(self.k_regimes): s = self.parameters[i, 'autoregressive'] unconstrained[s] = unconstrain_stationary_univariate( constrained[s]) return unconstrained class MarkovAutoregressionResults(markov_regression.MarkovRegressionResults): r""" Class to hold results from fitting a Markov switching autoregression model Parameters ---------- model : MarkovAutoregression instance The fitted model instance params : ndarray Fitted parameters filter_results : HamiltonFilterResults or KimSmootherResults instance The underlying filter and, optionally, smoother output cov_type : str The type of covariance matrix estimator to use. Can be one of 'approx', 'opg', 'robust', or 'none'. Attributes ---------- model : Model instance A reference to the model that was fit. filter_results : HamiltonFilterResults or KimSmootherResults instance The underlying filter and, optionally, smoother output nobs : float The number of observations used to fit the model. params : ndarray The parameters of the model. scale : float This is currently set to 1.0 and not used by the model or its results. """ pass class MarkovAutoregressionResultsWrapper( markov_regression.MarkovRegressionResultsWrapper): pass wrap.populate_wrapper(MarkovAutoregressionResultsWrapper, # noqa:E305 MarkovAutoregressionResults) statsmodels-0.12.2/statsmodels/tsa/regime_switching/markov_regression.py000066400000000000000000000400061400612667500267360ustar00rootroot00000000000000""" Markov switching regression models Author: Chad Fulton License: BSD-3 """ import numpy as np import statsmodels.base.wrapper as wrap from statsmodels.tsa.regime_switching import markov_switching class MarkovRegression(markov_switching.MarkovSwitching): r""" First-order k-regime Markov switching regression model Parameters ---------- endog : array_like The endogenous variable. k_regimes : int The number of regimes. trend : {'nc', 'c', 't', 'ct'} Whether or not to include a trend. To include an intercept, time trend, or both, set `trend='c'`, `trend='t'`, or `trend='ct'`. For no trend, set `trend='nc'`. Default is an intercept. exog : array_like, optional Array of exogenous regressors, shaped nobs x k. order : int, optional The order of the model describes the dependence of the likelihood on previous regimes. This depends on the model in question and should be set appropriately by subclasses. exog_tvtp : array_like, optional Array of exogenous or lagged variables to use in calculating time-varying transition probabilities (TVTP). TVTP is only used if this variable is provided. If an intercept is desired, a column of ones must be explicitly included in this array. switching_trend : bool or iterable, optional If a boolean, sets whether or not all trend coefficients are switching across regimes. If an iterable, should be of length equal to the number of trend variables, where each element is a boolean describing whether the corresponding coefficient is switching. Default is True. switching_exog : bool or iterable, optional If a boolean, sets whether or not all regression coefficients are switching across regimes. If an iterable, should be of length equal to the number of exogenous variables, where each element is a boolean describing whether the corresponding coefficient is switching. Default is True. switching_variance : bool, optional Whether or not there is regime-specific heteroskedasticity, i.e. whether or not the error term has a switching variance. Default is False. Notes ----- This model is new and API stability is not guaranteed, although changes will be made in a backwards compatible way if possible. The model can be written as: .. math:: y_t = a_{S_t} + x_t' \beta_{S_t} + \varepsilon_t \\ \varepsilon_t \sim N(0, \sigma_{S_t}^2) i.e. the model is a dynamic linear regression where the coefficients and the variance of the error term may be switching across regimes. The `trend` is accommodated by prepending columns to the `exog` array. Thus if `trend='c'`, the passed `exog` array should not already have a column of ones. References ---------- Kim, Chang-Jin, and Charles R. Nelson. 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications". MIT Press Books. The MIT Press. """ def __init__(self, endog, k_regimes, trend='c', exog=None, order=0, exog_tvtp=None, switching_trend=True, switching_exog=True, switching_variance=False, dates=None, freq=None, missing='none'): # Properties self.trend = trend self.switching_trend = switching_trend self.switching_exog = switching_exog self.switching_variance = switching_variance # Exogenous data self.k_exog, exog = markov_switching.prepare_exog(exog) # Trend nobs = len(endog) self.k_trend = 0 self._k_exog = self.k_exog trend_exog = None if trend == 'c': trend_exog = np.ones((nobs, 1)) self.k_trend = 1 elif trend == 't': trend_exog = (np.arange(nobs) + 1)[:, np.newaxis] self.k_trend = 1 elif trend == 'ct': trend_exog = np.c_[np.ones((nobs, 1)), (np.arange(nobs) + 1)[:, np.newaxis]] self.k_trend = 2 if trend_exog is not None: exog = trend_exog if exog is None else np.c_[trend_exog, exog] self._k_exog += self.k_trend # Initialize the base model super(MarkovRegression, self).__init__( endog, k_regimes, order=order, exog_tvtp=exog_tvtp, exog=exog, dates=dates, freq=freq, missing=missing) # Switching options if self.switching_trend is True or self.switching_trend is False: self.switching_trend = [self.switching_trend] * self.k_trend elif not len(self.switching_trend) == self.k_trend: raise ValueError('Invalid iterable passed to `switching_trend`.') if self.switching_exog is True or self.switching_exog is False: self.switching_exog = [self.switching_exog] * self.k_exog elif not len(self.switching_exog) == self.k_exog: raise ValueError('Invalid iterable passed to `switching_exog`.') self.switching_coeffs = ( np.r_[self.switching_trend, self.switching_exog].astype(bool).tolist()) # Parameters self.parameters['exog'] = self.switching_coeffs self.parameters['variance'] = [1] if self.switching_variance else [0] def predict_conditional(self, params): """ In-sample prediction, conditional on the current regime Parameters ---------- params : array_like Array of parameters at which to perform prediction. Returns ------- predict : array_like Array of predictions conditional on current, and possibly past, regimes """ params = np.array(params, ndmin=1) # Since in the base model the values are the same across columns, we # only compute a single column, and then expand it below. predict = np.zeros((self.k_regimes, self.nobs), dtype=params.dtype) for i in range(self.k_regimes): # Predict if self._k_exog > 0: coeffs = params[self.parameters[i, 'exog']] predict[i] = np.dot(self.exog, coeffs) return predict[:, None, :] def _resid(self, params): predict = np.repeat(self.predict_conditional(params), self.k_regimes, axis=1) return self.endog - predict def _conditional_loglikelihoods(self, params): """ Compute loglikelihoods conditional on the current period's regime """ # Get residuals resid = self._resid(params) # Compute the conditional likelihoods variance = params[self.parameters['variance']].squeeze() if self.switching_variance: variance = np.reshape(variance, (self.k_regimes, 1, 1)) conditional_loglikelihoods = ( -0.5 * resid**2 / variance - 0.5 * np.log(2 * np.pi * variance)) return conditional_loglikelihoods @property def _res_classes(self): return {'fit': (MarkovRegressionResults, MarkovRegressionResultsWrapper)} def _em_iteration(self, params0): """ EM iteration Notes ----- This uses the inherited _em_iteration method for computing the non-TVTP transition probabilities and then performs the EM step for regression coefficients and variances. """ # Inherited parameters result, params1 = super(MarkovRegression, self)._em_iteration(params0) tmp = np.sqrt(result.smoothed_marginal_probabilities) # Regression coefficients coeffs = None if self._k_exog > 0: coeffs = self._em_exog(result, self.endog, self.exog, self.parameters.switching['exog'], tmp) for i in range(self.k_regimes): params1[self.parameters[i, 'exog']] = coeffs[i] # Variances params1[self.parameters['variance']] = self._em_variance( result, self.endog, self.exog, coeffs, tmp) # params1[self.parameters['variance']] = 0.33282116 return result, params1 def _em_exog(self, result, endog, exog, switching, tmp=None): """ EM step for regression coefficients """ k_exog = exog.shape[1] coeffs = np.zeros((self.k_regimes, k_exog)) # First, estimate non-switching coefficients if not np.all(switching): nonswitching_exog = exog[:, ~switching] nonswitching_coeffs = ( np.dot(np.linalg.pinv(nonswitching_exog), endog)) coeffs[:, ~switching] = nonswitching_coeffs endog = endog - np.dot(nonswitching_exog, nonswitching_coeffs) # Next, get switching coefficients if np.any(switching): switching_exog = exog[:, switching] if tmp is None: tmp = np.sqrt(result.smoothed_marginal_probabilities) for i in range(self.k_regimes): tmp_endog = tmp[i] * endog tmp_exog = tmp[i][:, np.newaxis] * switching_exog coeffs[i, switching] = ( np.dot(np.linalg.pinv(tmp_exog), tmp_endog)) return coeffs def _em_variance(self, result, endog, exog, betas, tmp=None): """ EM step for variances """ k_exog = 0 if exog is None else exog.shape[1] if self.switching_variance: variance = np.zeros(self.k_regimes) for i in range(self.k_regimes): if k_exog > 0: resid = endog - np.dot(exog, betas[i]) else: resid = endog variance[i] = ( np.sum(resid**2 * result.smoothed_marginal_probabilities[i]) / np.sum(result.smoothed_marginal_probabilities[i])) else: variance = 0 if tmp is None: tmp = np.sqrt(result.smoothed_marginal_probabilities) for i in range(self.k_regimes): tmp_endog = tmp[i] * endog if k_exog > 0: tmp_exog = tmp[i][:, np.newaxis] * exog resid = tmp_endog - np.dot(tmp_exog, betas[i]) else: resid = tmp_endog variance += np.sum(resid**2) variance /= self.nobs return variance @property def start_params(self): """ (array) Starting parameters for maximum likelihood estimation. Notes ----- These are not very sophisticated and / or good. We set equal transition probabilities and interpolate regression coefficients between zero and the OLS estimates, where the interpolation is based on the regime number. We rely heavily on the EM algorithm to quickly find much better starting parameters, which are then used by the typical scoring approach. """ # Inherited parameters params = markov_switching.MarkovSwitching.start_params.fget(self) # Regression coefficients if self._k_exog > 0: beta = np.dot(np.linalg.pinv(self.exog), self.endog) variance = np.var(self.endog - np.dot(self.exog, beta)) if np.any(self.switching_coeffs): for i in range(self.k_regimes): params[self.parameters[i, 'exog']] = ( beta * (i / self.k_regimes)) else: params[self.parameters['exog']] = beta else: variance = np.var(self.endog) # Variances if self.switching_variance: params[self.parameters['variance']] = ( np.linspace(variance / 10., variance, num=self.k_regimes)) else: params[self.parameters['variance']] = variance return params @property def param_names(self): """ (list of str) List of human readable parameter names (for parameters actually included in the model). """ # Inherited parameters param_names = np.array( markov_switching.MarkovSwitching.param_names.fget(self), dtype=object) # Regression coefficients if np.any(self.switching_coeffs): for i in range(self.k_regimes): param_names[self.parameters[i, 'exog']] = [ '%s[%d]' % (exog_name, i) for exog_name in self.exog_names] else: param_names[self.parameters['exog']] = self.exog_names # Variances if self.switching_variance: for i in range(self.k_regimes): param_names[self.parameters[i, 'variance']] = 'sigma2[%d]' % i else: param_names[self.parameters['variance']] = 'sigma2' return param_names.tolist() def transform_params(self, unconstrained): """ Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation Parameters ---------- unconstrained : array_like Array of unconstrained parameters used by the optimizer, to be transformed. Returns ------- constrained : array_like Array of constrained parameters which may be used in likelihood evaluation. """ # Inherited parameters constrained = super(MarkovRegression, self).transform_params( unconstrained) # Nothing to do for regression coefficients constrained[self.parameters['exog']] = ( unconstrained[self.parameters['exog']]) # Force variances to be positive constrained[self.parameters['variance']] = ( unconstrained[self.parameters['variance']]**2) return constrained def untransform_params(self, constrained): """ Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer Parameters ---------- constrained : array_like Array of constrained parameters used in likelihood evaluation, to be transformed. Returns ------- unconstrained : array_like Array of unconstrained parameters used by the optimizer. """ # Inherited parameters unconstrained = super(MarkovRegression, self).untransform_params( constrained) # Nothing to do for regression coefficients unconstrained[self.parameters['exog']] = ( constrained[self.parameters['exog']]) # Force variances to be positive unconstrained[self.parameters['variance']] = ( constrained[self.parameters['variance']]**0.5) return unconstrained class MarkovRegressionResults(markov_switching.MarkovSwitchingResults): r""" Class to hold results from fitting a Markov switching regression model Parameters ---------- model : MarkovRegression instance The fitted model instance params : ndarray Fitted parameters filter_results : HamiltonFilterResults or KimSmootherResults instance The underlying filter and, optionally, smoother output cov_type : str The type of covariance matrix estimator to use. Can be one of 'approx', 'opg', 'robust', or 'none'. Attributes ---------- model : Model instance A reference to the model that was fit. filter_results : HamiltonFilterResults or KimSmootherResults instance The underlying filter and, optionally, smoother output nobs : float The number of observations used to fit the model. params : ndarray The parameters of the model. scale : float This is currently set to 1.0 and not used by the model or its results. """ pass class MarkovRegressionResultsWrapper( markov_switching.MarkovSwitchingResultsWrapper): pass wrap.populate_wrapper(MarkovRegressionResultsWrapper, # noqa:E305 MarkovRegressionResults) statsmodels-0.12.2/statsmodels/tsa/regime_switching/markov_switching.py000066400000000000000000002422531400612667500265650ustar00rootroot00000000000000""" Markov switching models Author: Chad Fulton License: BSD-3 """ import warnings import numpy as np import pandas as pd from scipy.special import logsumexp from statsmodels.tools.tools import Bunch from statsmodels.tools.numdiff import approx_fprime_cs, approx_hess_cs from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.eval_measures import aic, bic, hqic from statsmodels.tools.tools import pinv_extended from statsmodels.tools.sm_exceptions import EstimationWarning import statsmodels.base.wrapper as wrap from statsmodels.base.data import PandasData import statsmodels.tsa.base.tsa_model as tsbase from statsmodels.tsa.statespace.tools import find_best_blas_type, prepare_exog from statsmodels.tsa.regime_switching._hamilton_filter import ( shamilton_filter_log, dhamilton_filter_log, chamilton_filter_log, zhamilton_filter_log) from statsmodels.tsa.regime_switching._kim_smoother import ( skim_smoother_log, dkim_smoother_log, ckim_smoother_log, zkim_smoother_log) prefix_hamilton_filter_log_map = { 's': shamilton_filter_log, 'd': dhamilton_filter_log, 'c': chamilton_filter_log, 'z': zhamilton_filter_log } prefix_kim_smoother_log_map = { 's': skim_smoother_log, 'd': dkim_smoother_log, 'c': ckim_smoother_log, 'z': zkim_smoother_log } def _logistic(x): """ Note that this is not a vectorized function """ x = np.array(x) # np.exp(x) / (1 + np.exp(x)) if x.ndim == 0: y = np.reshape(x, (1, 1, 1)) # np.exp(x[i]) / (1 + np.sum(np.exp(x[:]))) elif x.ndim == 1: y = np.reshape(x, (len(x), 1, 1)) # np.exp(x[i,t]) / (1 + np.sum(np.exp(x[:,t]))) elif x.ndim == 2: y = np.reshape(x, (x.shape[0], 1, x.shape[1])) # np.exp(x[i,j,t]) / (1 + np.sum(np.exp(x[:,j,t]))) elif x.ndim == 3: y = x else: raise NotImplementedError tmp = np.c_[np.zeros((y.shape[-1], y.shape[1], 1)), y.T].T evaluated = np.reshape(np.exp(y - logsumexp(tmp, axis=0)), x.shape) return evaluated def _partials_logistic(x): """ Note that this is not a vectorized function """ tmp = _logistic(x) # k if tmp.ndim == 0: return tmp - tmp**2 # k x k elif tmp.ndim == 1: partials = np.diag(tmp - tmp**2) # k x k x t elif tmp.ndim == 2: partials = [np.diag(tmp[:, t] - tmp[:, t]**2) for t in range(tmp.shape[1])] shape = tmp.shape[1], tmp.shape[0], tmp.shape[0] partials = np.concatenate(partials).reshape(shape).transpose((1, 2, 0)) # k x k x j x t else: partials = [[np.diag(tmp[:, j, t] - tmp[:, j, t]**2) for t in range(tmp.shape[2])] for j in range(tmp.shape[1])] shape = tmp.shape[1], tmp.shape[2], tmp.shape[0], tmp.shape[0] partials = np.concatenate(partials).reshape(shape).transpose( (2, 3, 0, 1)) for i in range(tmp.shape[0]): for j in range(i): partials[i, j, ...] = -tmp[i, ...] * tmp[j, ...] partials[j, i, ...] = partials[i, j, ...] return partials def cy_hamilton_filter_log(initial_probabilities, regime_transition, conditional_loglikelihoods, model_order): """ Hamilton filter in log space using Cython inner loop. Parameters ---------- initial_probabilities : ndarray Array of initial probabilities, shaped (k_regimes,) giving the distribution of the regime process at time t = -order where order is a nonnegative integer. regime_transition : ndarray Matrix of regime transition probabilities, shaped either (k_regimes, k_regimes, 1) or if there are time-varying transition probabilities (k_regimes, k_regimes, nobs + order). Entry [i, j, t] contains the probability of moving from j at time t-1 to i at time t, so each matrix regime_transition[:, :, t] should be left stochastic. The first order entries and initial_probabilities are used to produce the initial joint distribution of dimension order + 1 at time t=0. conditional_loglikelihoods : ndarray Array of loglikelihoods conditional on the last `order+1` regimes, shaped (k_regimes,)*(order + 1) + (nobs,). Returns ------- filtered_marginal_probabilities : ndarray Array containing Pr[S_t=s_t | Y_t] - the probability of being in each regime conditional on time t information. Shaped (k_regimes, nobs). predicted_joint_probabilities : ndarray Array containing Pr[S_t=s_t, ..., S_{t-order}=s_{t-order} | Y_{t-1}] - the joint probability of the current and previous `order` periods being in each combination of regimes conditional on time t-1 information. Shaped (k_regimes,) * (order + 1) + (nobs,). joint_loglikelihoods : ndarray Array of loglikelihoods condition on time t information, shaped (nobs,). filtered_joint_probabilities : ndarray Array containing Pr[S_t=s_t, ..., S_{t-order}=s_{t-order} | Y_{t}] - the joint probability of the current and previous `order` periods being in each combination of regimes conditional on time t information. Shaped (k_regimes,) * (order + 1) + (nobs,). """ # Dimensions k_regimes = len(initial_probabilities) nobs = conditional_loglikelihoods.shape[-1] order = conditional_loglikelihoods.ndim - 2 dtype = conditional_loglikelihoods.dtype # Check for compatible shapes. incompatible_shapes = ( regime_transition.shape[-1] not in (1, nobs + model_order) or regime_transition.shape[:2] != (k_regimes, k_regimes) or conditional_loglikelihoods.shape[0] != k_regimes) if incompatible_shapes: raise ValueError('Arguments do not have compatible shapes') # Convert to log space initial_probabilities = np.log(initial_probabilities) regime_transition = np.log(np.maximum(regime_transition, 1e-20)) # Storage # Pr[S_t = s_t | Y_t] filtered_marginal_probabilities = ( np.zeros((k_regimes, nobs), dtype=dtype)) # Pr[S_t = s_t, ... S_{t-r} = s_{t-r} | Y_{t-1}] # Has k_regimes^(order+1) elements predicted_joint_probabilities = np.zeros( (k_regimes,) * (order + 1) + (nobs,), dtype=dtype) # log(f(y_t | Y_{t-1})) joint_loglikelihoods = np.zeros((nobs,), dtype) # Pr[S_t = s_t, ... S_{t-r+1} = s_{t-r+1} | Y_t] # Has k_regimes^order elements filtered_joint_probabilities = np.zeros( (k_regimes,) * (order + 1) + (nobs + 1,), dtype=dtype) # Initial probabilities filtered_marginal_probabilities[:, 0] = initial_probabilities tmp = np.copy(initial_probabilities) shape = (k_regimes, k_regimes) transition_t = 0 for i in range(order): if regime_transition.shape[-1] > 1: transition_t = i tmp = np.reshape(regime_transition[..., transition_t], shape + (1,) * i) + tmp filtered_joint_probabilities[..., 0] = tmp # Get appropriate subset of transition matrix if regime_transition.shape[-1] > 1: regime_transition = regime_transition[..., model_order:] # Run Cython filter iterations prefix, dtype, _ = find_best_blas_type(( regime_transition, conditional_loglikelihoods, joint_loglikelihoods, predicted_joint_probabilities, filtered_joint_probabilities)) func = prefix_hamilton_filter_log_map[prefix] func(nobs, k_regimes, order, regime_transition, conditional_loglikelihoods.reshape(k_regimes**(order+1), nobs), joint_loglikelihoods, predicted_joint_probabilities.reshape(k_regimes**(order+1), nobs), filtered_joint_probabilities.reshape(k_regimes**(order+1), nobs+1)) # Save log versions for smoother predicted_joint_probabilities_log = predicted_joint_probabilities filtered_joint_probabilities_log = filtered_joint_probabilities # Convert out of log scale predicted_joint_probabilities = np.exp(predicted_joint_probabilities) filtered_joint_probabilities = np.exp(filtered_joint_probabilities) # S_t | t filtered_marginal_probabilities = filtered_joint_probabilities[..., 1:] for i in range(1, filtered_marginal_probabilities.ndim - 1): filtered_marginal_probabilities = np.sum( filtered_marginal_probabilities, axis=-2) return (filtered_marginal_probabilities, predicted_joint_probabilities, joint_loglikelihoods, filtered_joint_probabilities[..., 1:], predicted_joint_probabilities_log, filtered_joint_probabilities_log[..., 1:]) def cy_kim_smoother_log(regime_transition, predicted_joint_probabilities, filtered_joint_probabilities): """ Kim smoother in log space using Cython inner loop. Parameters ---------- regime_transition : ndarray Matrix of regime transition probabilities, shaped either (k_regimes, k_regimes, 1) or if there are time-varying transition probabilities (k_regimes, k_regimes, nobs). predicted_joint_probabilities : ndarray Array containing Pr[S_t=s_t, ..., S_{t-order}=s_{t-order} | Y_{t-1}] - the joint probability of the current and previous `order` periods being in each combination of regimes conditional on time t-1 information. Shaped (k_regimes,) * (order + 1) + (nobs,). filtered_joint_probabilities : ndarray Array containing Pr[S_t=s_t, ..., S_{t-order}=s_{t-order} | Y_{t}] - the joint probability of the current and previous `order` periods being in each combination of regimes conditional on time t information. Shaped (k_regimes,) * (order + 1) + (nobs,). Returns ------- smoothed_joint_probabilities : ndarray Array containing Pr[S_t=s_t, ..., S_{t-order}=s_{t-order} | Y_T] - the joint probability of the current and previous `order` periods being in each combination of regimes conditional on all information. Shaped (k_regimes,) * (order + 1) + (nobs,). smoothed_marginal_probabilities : ndarray Array containing Pr[S_t=s_t | Y_T] - the probability of being in each regime conditional on all information. Shaped (k_regimes, nobs). """ # Dimensions k_regimes = filtered_joint_probabilities.shape[0] nobs = filtered_joint_probabilities.shape[-1] order = filtered_joint_probabilities.ndim - 2 dtype = filtered_joint_probabilities.dtype # Storage smoothed_joint_probabilities = np.zeros( (k_regimes,) * (order + 1) + (nobs,), dtype=dtype) # Get appropriate subset of transition matrix if regime_transition.shape[-1] == nobs + order: regime_transition = regime_transition[..., order:] # Convert to log space regime_transition = np.log(np.maximum(regime_transition, 1e-20)) # Run Cython smoother iterations prefix, dtype, _ = find_best_blas_type(( regime_transition, predicted_joint_probabilities, filtered_joint_probabilities)) func = prefix_kim_smoother_log_map[prefix] func(nobs, k_regimes, order, regime_transition, predicted_joint_probabilities.reshape(k_regimes**(order+1), nobs), filtered_joint_probabilities.reshape(k_regimes**(order+1), nobs), smoothed_joint_probabilities.reshape(k_regimes**(order+1), nobs)) # Convert back from log space smoothed_joint_probabilities = np.exp(smoothed_joint_probabilities) # Get smoothed marginal probabilities S_t | T by integrating out # S_{t-k+1}, S_{t-k+2}, ..., S_{t-1} smoothed_marginal_probabilities = smoothed_joint_probabilities for i in range(1, smoothed_marginal_probabilities.ndim - 1): smoothed_marginal_probabilities = np.sum( smoothed_marginal_probabilities, axis=-2) return smoothed_joint_probabilities, smoothed_marginal_probabilities class MarkovSwitchingParams(object): """ Class to hold parameters in Markov switching models Parameters ---------- k_regimes : int The number of regimes between which parameters may switch. Notes ----- The purpose is to allow selecting parameter indexes / slices based on parameter type, regime number, or both. Parameters are lexicographically ordered in the following way: 1. Named type string (e.g. "autoregressive") 2. Number (e.g. the first autoregressive parameter, then the second) 3. Regime (if applicable) Parameter blocks are set using dictionary setter notation where the key is the named type string and the value is a list of boolean values indicating whether a given parameter is switching or not. For example, consider the following code: parameters = MarkovSwitchingParams(k_regimes=2) parameters['regime_transition'] = [1,1] parameters['exog'] = [0, 1] This implies the model has 7 parameters: 4 "regime_transition"-related parameters (2 parameters that each switch according to regimes) and 3 "exog"-related parameters (1 parameter that does not switch, and one 1 that does). The order of parameters is then: 1. The first "regime_transition" parameter, regime 0 2. The first "regime_transition" parameter, regime 1 3. The second "regime_transition" parameter, regime 1 4. The second "regime_transition" parameter, regime 1 5. The first "exog" parameter 6. The second "exog" parameter, regime 0 7. The second "exog" parameter, regime 1 Retrieving indexes / slices is done through dictionary getter notation. There are three options for the dictionary key: - Regime number (zero-indexed) - Named type string (e.g. "autoregressive") - Regime number and named type string In the above example, consider the following getters: >>> parameters[0] array([0, 2, 4, 6]) >>> parameters[1] array([1, 3, 5, 6]) >>> parameters['exog'] slice(4, 7, None) >>> parameters[0, 'exog'] [4, 6] >>> parameters[1, 'exog'] [4, 7] Notice that in the last two examples, both lists of indexes include 4. That's because that is the index of the the non-switching first "exog" parameter, which should be selected regardless of the regime. In addition to the getter, the `k_parameters` attribute is an dict with the named type strings as the keys. It can be used to get the total number of parameters of each type: >>> parameters.k_parameters['regime_transition'] 4 >>> parameters.k_parameters['exog'] 3 """ def __init__(self, k_regimes): self.k_regimes = k_regimes self.k_params = 0 self.k_parameters = {} self.switching = {} self.slices_purpose = {} self.relative_index_regime_purpose = [ {} for i in range(self.k_regimes)] self.index_regime_purpose = [ {} for i in range(self.k_regimes)] self.index_regime = [[] for i in range(self.k_regimes)] def __getitem__(self, key): _type = type(key) # Get a slice for a block of parameters by purpose if _type is str: return self.slices_purpose[key] # Get a slice for a block of parameters by regime elif _type is int: return self.index_regime[key] elif _type is tuple: if not len(key) == 2: raise IndexError('Invalid index') if type(key[1]) == str and type(key[0]) == int: return self.index_regime_purpose[key[0]][key[1]] elif type(key[0]) == str and type(key[1]) == int: return self.index_regime_purpose[key[1]][key[0]] else: raise IndexError('Invalid index') else: raise IndexError('Invalid index') def __setitem__(self, key, value): _type = type(key) if _type is str: value = np.array(value, dtype=bool, ndmin=1) k_params = self.k_params self.k_parameters[key] = ( value.size + np.sum(value) * (self.k_regimes - 1)) self.k_params += self.k_parameters[key] self.switching[key] = value self.slices_purpose[key] = np.s_[k_params:self.k_params] for j in range(self.k_regimes): self.relative_index_regime_purpose[j][key] = [] self.index_regime_purpose[j][key] = [] offset = 0 for i in range(value.size): switching = value[i] for j in range(self.k_regimes): # Non-switching parameters if not switching: self.relative_index_regime_purpose[j][key].append( offset) # Switching parameters else: self.relative_index_regime_purpose[j][key].append( offset + j) offset += 1 if not switching else self.k_regimes for j in range(self.k_regimes): offset = 0 indices = [] for k, v in self.relative_index_regime_purpose[j].items(): v = (np.r_[v] + offset).tolist() self.index_regime_purpose[j][k] = v indices.append(v) offset += self.k_parameters[k] self.index_regime[j] = np.concatenate(indices).astype(int) else: raise IndexError('Invalid index') class MarkovSwitching(tsbase.TimeSeriesModel): """ First-order k-regime Markov switching model Parameters ---------- endog : array_like The endogenous variable. k_regimes : int The number of regimes. order : int, optional The order of the model describes the dependence of the likelihood on previous regimes. This depends on the model in question and should be set appropriately by subclasses. exog_tvtp : array_like, optional Array of exogenous or lagged variables to use in calculating time-varying transition probabilities (TVTP). TVTP is only used if this variable is provided. If an intercept is desired, a column of ones must be explicitly included in this array. Notes ----- This model is new and API stability is not guaranteed, although changes will be made in a backwards compatible way if possible. References ---------- Kim, Chang-Jin, and Charles R. Nelson. 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications". MIT Press Books. The MIT Press. """ def __init__(self, endog, k_regimes, order=0, exog_tvtp=None, exog=None, dates=None, freq=None, missing='none'): # Properties self.k_regimes = k_regimes self.tvtp = exog_tvtp is not None # The order of the model may be overridden in subclasses self.order = order # Exogenous data # TODO add checks for exog_tvtp consistent shape and indices self.k_tvtp, self.exog_tvtp = prepare_exog(exog_tvtp) # Initialize the base model super(MarkovSwitching, self).__init__(endog, exog, dates=dates, freq=freq, missing=missing) # Dimensions self.nobs = self.endog.shape[0] # Sanity checks if self.endog.ndim > 1 and self.endog.shape[1] > 1: raise ValueError('Must have univariate endogenous data.') if self.k_regimes < 2: raise ValueError('Markov switching models must have at least two' ' regimes.') if not(self.exog_tvtp is None or self.exog_tvtp.shape[0] == self.nobs): raise ValueError('Time-varying transition probabilities exogenous' ' array must have the same number of observations' ' as the endogenous array.') # Parameters self.parameters = MarkovSwitchingParams(self.k_regimes) k_transition = self.k_regimes - 1 if self.tvtp: k_transition *= self.k_tvtp self.parameters['regime_transition'] = [1] * k_transition # Internal model properties: default is steady-state initialization self._initialization = 'steady-state' self._initial_probabilities = None @property def k_params(self): """ (int) Number of parameters in the model """ return self.parameters.k_params def initialize_steady_state(self): """ Set initialization of regime probabilities to be steady-state values Notes ----- Only valid if there are not time-varying transition probabilities. """ if self.tvtp: raise ValueError('Cannot use steady-state initialization when' ' the regime transition matrix is time-varying.') self._initialization = 'steady-state' self._initial_probabilities = None def initialize_known(self, probabilities, tol=1e-8): """ Set initialization of regime probabilities to use known values """ self._initialization = 'known' probabilities = np.array(probabilities, ndmin=1) if not probabilities.shape == (self.k_regimes,): raise ValueError('Initial probabilities must be a vector of shape' ' (k_regimes,).') if not np.abs(np.sum(probabilities) - 1) < tol: raise ValueError('Initial probabilities vector must sum to one.') self._initial_probabilities = probabilities def initial_probabilities(self, params, regime_transition=None): """ Retrieve initial probabilities """ params = np.array(params, ndmin=1) if self._initialization == 'steady-state': if regime_transition is None: regime_transition = self.regime_transition_matrix(params) if regime_transition.ndim == 3: regime_transition = regime_transition[..., 0] m = regime_transition.shape[0] A = np.c_[(np.eye(m) - regime_transition).T, np.ones(m)].T try: probabilities = np.linalg.pinv(A)[:, -1] except np.linalg.LinAlgError: raise RuntimeError('Steady-state probabilities could not be' ' constructed.') elif self._initialization == 'known': probabilities = self._initial_probabilities else: raise RuntimeError('Invalid initialization method selected.') # Slightly bound probabilities away from zero (for filters in log # space) probabilities = np.maximum(probabilities, 1e-20) return probabilities def _regime_transition_matrix_tvtp(self, params, exog_tvtp=None): if exog_tvtp is None: exog_tvtp = self.exog_tvtp nobs = len(exog_tvtp) regime_transition_matrix = np.zeros( (self.k_regimes, self.k_regimes, nobs), dtype=np.promote_types(np.float64, params.dtype)) # Compute the predicted values from the regression for i in range(self.k_regimes): coeffs = params[self.parameters[i, 'regime_transition']] regime_transition_matrix[:-1, i, :] = np.dot( exog_tvtp, np.reshape(coeffs, (self.k_regimes-1, self.k_tvtp)).T).T # Perform the logistic transformation tmp = np.c_[np.zeros((nobs, self.k_regimes, 1)), regime_transition_matrix[:-1, :, :].T].T regime_transition_matrix[:-1, :, :] = np.exp( regime_transition_matrix[:-1, :, :] - logsumexp(tmp, axis=0)) # Compute the last column of the transition matrix regime_transition_matrix[-1, :, :] = ( 1 - np.sum(regime_transition_matrix[:-1, :, :], axis=0)) return regime_transition_matrix def regime_transition_matrix(self, params, exog_tvtp=None): """ Construct the left-stochastic transition matrix Notes ----- This matrix will either be shaped (k_regimes, k_regimes, 1) or if there are time-varying transition probabilities, it will be shaped (k_regimes, k_regimes, nobs). The (i,j)th element of this matrix is the probability of transitioning from regime j to regime i; thus the previous regime is represented in a column and the next regime is represented by a row. It is left-stochastic, meaning that each column sums to one (because it is certain that from one regime (j) you will transition to *some other regime*). """ params = np.array(params, ndmin=1) if not self.tvtp: regime_transition_matrix = np.zeros( (self.k_regimes, self.k_regimes, 1), dtype=np.promote_types(np.float64, params.dtype)) regime_transition_matrix[:-1, :, 0] = np.reshape( params[self.parameters['regime_transition']], (self.k_regimes-1, self.k_regimes)) regime_transition_matrix[-1, :, 0] = ( 1 - np.sum(regime_transition_matrix[:-1, :, 0], axis=0)) else: regime_transition_matrix = ( self._regime_transition_matrix_tvtp(params, exog_tvtp)) return regime_transition_matrix def predict(self, params, start=None, end=None, probabilities=None, conditional=False): """ In-sample prediction and out-of-sample forecasting Parameters ---------- params : ndarray Parameters at which to form predictions start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, i.e., the last forecast is end. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. probabilities : str or array_like, optional Specifies the weighting probabilities used in constructing the prediction as a weighted average. If a string, can be 'predicted', 'filtered', or 'smoothed'. Otherwise can be an array of probabilities to use. Default is smoothed. conditional : bool or int, optional Whether or not to return predictions conditional on current or past regimes. If False, returns a single vector of weighted predictions. If True or 1, returns predictions conditional on the current regime. For larger integers, returns predictions conditional on the current regime and some number of past regimes. Returns ------- predict : ndarray Array of out of in-sample predictions and / or out-of-sample forecasts. """ if start is None: start = self._index[0] # Handle start, end start, end, out_of_sample, prediction_index = ( self._get_prediction_index(start, end)) if out_of_sample > 0: raise NotImplementedError # Perform in-sample prediction predict = self.predict_conditional(params) squeezed = np.squeeze(predict) # Check if we need to do weighted averaging if squeezed.ndim - 1 > conditional: # Determine in-sample weighting probabilities if probabilities is None or probabilities == 'smoothed': results = self.smooth(params, return_raw=True) probabilities = results.smoothed_joint_probabilities elif probabilities == 'filtered': results = self.filter(params, return_raw=True) probabilities = results.filtered_joint_probabilities elif probabilities == 'predicted': results = self.filter(params, return_raw=True) probabilities = results.predicted_joint_probabilities # Compute weighted average predict = (predict * probabilities) for i in range(predict.ndim - 1 - int(conditional)): predict = np.sum(predict, axis=-2) else: predict = squeezed return predict[start:end + out_of_sample + 1] def predict_conditional(self, params): """ In-sample prediction, conditional on the current, and possibly past, regimes Parameters ---------- params : array_like Array of parameters at which to perform prediction. Returns ------- predict : array_like Array of predictions conditional on current, and possibly past, regimes """ raise NotImplementedError def _conditional_loglikelihoods(self, params): """ Compute likelihoods conditional on the current period's regime (and the last self.order periods' regimes if self.order > 0). Must be implemented in subclasses. """ raise NotImplementedError def _filter(self, params, regime_transition=None): # Get the regime transition matrix if not provided if regime_transition is None: regime_transition = self.regime_transition_matrix(params) # Get the initial probabilities initial_probabilities = self.initial_probabilities( params, regime_transition) # Compute the conditional likelihoods conditional_loglikelihoods = self._conditional_loglikelihoods(params) # Apply the filter return ((regime_transition, initial_probabilities, conditional_loglikelihoods) + cy_hamilton_filter_log( initial_probabilities, regime_transition, conditional_loglikelihoods, self.order)) def filter(self, params, transformed=True, cov_type=None, cov_kwds=None, return_raw=False, results_class=None, results_wrapper_class=None): """ Apply the Hamilton filter Parameters ---------- params : array_like Array of parameters at which to perform filtering. transformed : bool, optional Whether or not `params` is already transformed. Default is True. cov_type : str, optional See `fit` for a description of covariance matrix types for results object. cov_kwds : dict or None, optional See `fit` for a description of required keywords for alternative covariance estimators return_raw : bool,optional Whether or not to return only the raw Hamilton filter output or a full results object. Default is to return a full results object. results_class : type, optional A results class to instantiate rather than `MarkovSwitchingResults`. Usually only used internally by subclasses. results_wrapper_class : type, optional A results wrapper class to instantiate rather than `MarkovSwitchingResults`. Usually only used internally by subclasses. Returns ------- MarkovSwitchingResults """ params = np.array(params, ndmin=1) if not transformed: params = self.transform_params(params) # Save the parameter names self.data.param_names = self.param_names # Get the result names = ['regime_transition', 'initial_probabilities', 'conditional_loglikelihoods', 'filtered_marginal_probabilities', 'predicted_joint_probabilities', 'joint_loglikelihoods', 'filtered_joint_probabilities', 'predicted_joint_probabilities_log', 'filtered_joint_probabilities_log'] result = HamiltonFilterResults( self, Bunch(**dict(zip(names, self._filter(params))))) # Wrap in a results object return self._wrap_results(params, result, return_raw, cov_type, cov_kwds, results_class, results_wrapper_class) def _smooth(self, params, predicted_joint_probabilities_log, filtered_joint_probabilities_log, regime_transition=None): # Get the regime transition matrix if regime_transition is None: regime_transition = self.regime_transition_matrix(params) # Apply the smoother return cy_kim_smoother_log(regime_transition, predicted_joint_probabilities_log, filtered_joint_probabilities_log) @property def _res_classes(self): return {'fit': (MarkovSwitchingResults, MarkovSwitchingResultsWrapper)} def _wrap_results(self, params, result, return_raw, cov_type=None, cov_kwds=None, results_class=None, wrapper_class=None): if not return_raw: # Wrap in a results object result_kwargs = {} if cov_type is not None: result_kwargs['cov_type'] = cov_type if cov_kwds is not None: result_kwargs['cov_kwds'] = cov_kwds if results_class is None: results_class = self._res_classes['fit'][0] if wrapper_class is None: wrapper_class = self._res_classes['fit'][1] res = results_class(self, params, result, **result_kwargs) result = wrapper_class(res) return result def smooth(self, params, transformed=True, cov_type=None, cov_kwds=None, return_raw=False, results_class=None, results_wrapper_class=None): """ Apply the Kim smoother and Hamilton filter Parameters ---------- params : array_like Array of parameters at which to perform filtering. transformed : bool, optional Whether or not `params` is already transformed. Default is True. cov_type : str, optional See `fit` for a description of covariance matrix types for results object. cov_kwds : dict or None, optional See `fit` for a description of required keywords for alternative covariance estimators return_raw : bool,optional Whether or not to return only the raw Hamilton filter output or a full results object. Default is to return a full results object. results_class : type, optional A results class to instantiate rather than `MarkovSwitchingResults`. Usually only used internally by subclasses. results_wrapper_class : type, optional A results wrapper class to instantiate rather than `MarkovSwitchingResults`. Usually only used internally by subclasses. Returns ------- MarkovSwitchingResults """ params = np.array(params, ndmin=1) if not transformed: params = self.transform_params(params) # Save the parameter names self.data.param_names = self.param_names # Hamilton filter # TODO add option to filter to return logged values so that we do not # need to re-log them for smoother names = ['regime_transition', 'initial_probabilities', 'conditional_loglikelihoods', 'filtered_marginal_probabilities', 'predicted_joint_probabilities', 'joint_loglikelihoods', 'filtered_joint_probabilities', 'predicted_joint_probabilities_log', 'filtered_joint_probabilities_log'] result = Bunch(**dict(zip(names, self._filter(params)))) # Kim smoother out = self._smooth(params, result.predicted_joint_probabilities_log, result.filtered_joint_probabilities_log) result['smoothed_joint_probabilities'] = out[0] result['smoothed_marginal_probabilities'] = out[1] result = KimSmootherResults(self, result) # Wrap in a results object return self._wrap_results(params, result, return_raw, cov_type, cov_kwds, results_class, results_wrapper_class) def loglikeobs(self, params, transformed=True): """ Loglikelihood evaluation for each period Parameters ---------- params : array_like Array of parameters at which to evaluate the loglikelihood function. transformed : bool, optional Whether or not `params` is already transformed. Default is True. """ params = np.array(params, ndmin=1) if not transformed: params = self.transform_params(params) results = self._filter(params) return results[5] def loglike(self, params, transformed=True): """ Loglikelihood evaluation Parameters ---------- params : array_like Array of parameters at which to evaluate the loglikelihood function. transformed : bool, optional Whether or not `params` is already transformed. Default is True. """ return np.sum(self.loglikeobs(params, transformed)) def score(self, params, transformed=True): """ Compute the score function at params. Parameters ---------- params : array_like Array of parameters at which to evaluate the score function. transformed : bool, optional Whether or not `params` is already transformed. Default is True. """ params = np.array(params, ndmin=1) return approx_fprime_cs(params, self.loglike, args=(transformed,)) def score_obs(self, params, transformed=True): """ Compute the score per observation, evaluated at params Parameters ---------- params : array_like Array of parameters at which to evaluate the score function. transformed : bool, optional Whether or not `params` is already transformed. Default is True. """ params = np.array(params, ndmin=1) return approx_fprime_cs(params, self.loglikeobs, args=(transformed,)) def hessian(self, params, transformed=True): """ Hessian matrix of the likelihood function, evaluated at the given parameters Parameters ---------- params : array_like Array of parameters at which to evaluate the Hessian function. transformed : bool, optional Whether or not `params` is already transformed. Default is True. """ params = np.array(params, ndmin=1) return approx_hess_cs(params, self.loglike) def fit(self, start_params=None, transformed=True, cov_type='approx', cov_kwds=None, method='bfgs', maxiter=100, full_output=1, disp=0, callback=None, return_params=False, em_iter=5, search_reps=0, search_iter=5, search_scale=1., **kwargs): """ Fits the model by maximum likelihood via Hamilton filter. Parameters ---------- start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. If None, the default is given by Model.start_params. transformed : bool, optional Whether or not `start_params` is already transformed. Default is True. cov_type : str, optional The type of covariance matrix estimator to use. Can be one of 'approx', 'opg', 'robust', or 'none'. Default is 'approx'. cov_kwds : dict or None, optional Keywords for alternative covariance estimators method : str, optional The `method` determines which solver from `scipy.optimize` is used, and it can be chosen from among the following strings: - 'newton' for Newton-Raphson, 'nm' for Nelder-Mead - 'bfgs' for Broyden-Fletcher-Goldfarb-Shanno (BFGS) - 'lbfgs' for limited-memory BFGS with optional box constraints - 'powell' for modified Powell's method - 'cg' for conjugate gradient - 'ncg' for Newton-conjugate gradient - 'basinhopping' for global basin-hopping solver The explicit arguments in `fit` are passed to the solver, with the exception of the basin-hopping solver. Each solver has several optional arguments that are not the same across solvers. See the notes section below (or scipy.optimize) for the available arguments and for the list of explicit arguments that the basin-hopping solver supports. maxiter : int, optional The maximum number of iterations to perform. full_output : bool, optional Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. disp : bool, optional Set to True to print convergence messages. callback : callable callback(xk), optional Called after each iteration, as callback(xk), where xk is the current parameter vector. return_params : bool, optional Whether or not to return only the array of maximizing parameters. Default is False. em_iter : int, optional Number of initial EM iteration steps used to improve starting parameters. search_reps : int, optional Number of randomly drawn search parameters that are drawn around `start_params` to try and improve starting parameters. Default is 0. search_iter : int, optional Number of initial EM iteration steps used to improve each of the search parameter repetitions. search_scale : float or array, optional. Scale of variates for random start parameter search. **kwargs Additional keyword arguments to pass to the optimizer. Returns ------- MarkovSwitchingResults """ if start_params is None: start_params = self.start_params transformed = True else: start_params = np.array(start_params, ndmin=1) # Random search for better start parameters if search_reps > 0: start_params = self._start_params_search( search_reps, start_params=start_params, transformed=transformed, em_iter=search_iter, scale=search_scale) transformed = True # Get better start params through EM algorithm if em_iter and not self.tvtp: start_params = self._fit_em(start_params, transformed=transformed, maxiter=em_iter, tolerance=0, return_params=True) transformed = True if transformed: start_params = self.untransform_params(start_params) # Maximum likelihood estimation by scoring fargs = (False,) mlefit = super(MarkovSwitching, self).fit(start_params, method=method, fargs=fargs, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, skip_hessian=True, **kwargs) # Just return the fitted parameters if requested if return_params: result = self.transform_params(mlefit.params) # Otherwise construct the results class if desired else: result = self.smooth(mlefit.params, transformed=False, cov_type=cov_type, cov_kwds=cov_kwds) result.mlefit = mlefit result.mle_retvals = mlefit.mle_retvals result.mle_settings = mlefit.mle_settings return result def _fit_em(self, start_params=None, transformed=True, cov_type='none', cov_kwds=None, maxiter=50, tolerance=1e-6, full_output=True, return_params=False, **kwargs): """ Fits the model using the Expectation-Maximization (EM) algorithm Parameters ---------- start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. If None, the default is given by `start_params`. transformed : bool, optional Whether or not `start_params` is already transformed. Default is True. cov_type : str, optional The type of covariance matrix estimator to use. Can be one of 'approx', 'opg', 'robust', or 'none'. Default is 'none'. cov_kwds : dict or None, optional Keywords for alternative covariance estimators maxiter : int, optional The maximum number of iterations to perform. tolerance : float, optional The iteration stops when the difference between subsequent loglikelihood values is less than this tolerance. full_output : bool, optional Set to True to have all available output in the Results object's mle_retvals attribute. This includes all intermediate values for parameters and loglikelihood values return_params : bool, optional Whether or not to return only the array of maximizing parameters. Default is False. **kwargs Additional keyword arguments to pass to the optimizer. Notes ----- This is a private method for finding good starting parameters for MLE by scoring. It has not been tested for a thoroughly correct EM implementation in all cases. It does not support TVTP transition probabilities. Returns ------- MarkovSwitchingResults """ if start_params is None: start_params = self.start_params transformed = True else: start_params = np.array(start_params, ndmin=1) if not transformed: start_params = self.transform_params(start_params) # Perform expectation-maximization llf = [] params = [start_params] i = 0 delta = 0 while i < maxiter and (i < 2 or (delta > tolerance)): out = self._em_iteration(params[-1]) llf.append(out[0].llf) params.append(out[1]) if i > 0: delta = 2 * (llf[-1] - llf[-2]) / np.abs((llf[-1] + llf[-2])) i += 1 # Just return the fitted parameters if requested if return_params: result = params[-1] # Otherwise construct the results class if desired else: result = self.filter(params[-1], transformed=True, cov_type=cov_type, cov_kwds=cov_kwds) # Save the output if full_output: em_retvals = Bunch(**{'params': np.array(params), 'llf': np.array(llf), 'iter': i}) em_settings = Bunch(**{'tolerance': tolerance, 'maxiter': maxiter}) else: em_retvals = None em_settings = None result.mle_retvals = em_retvals result.mle_settings = em_settings return result def _em_iteration(self, params0): """ EM iteration Notes ----- The EM iteration in this base class only performs the EM step for non-TVTP transition probabilities. """ params1 = np.zeros(params0.shape, dtype=np.promote_types(np.float64, params0.dtype)) # Smooth at the given parameters result = self.smooth(params0, transformed=True, return_raw=True) # The EM with TVTP is not yet supported, just return the previous # iteration parameters if self.tvtp: params1[self.parameters['regime_transition']] = ( params0[self.parameters['regime_transition']]) else: regime_transition = self._em_regime_transition(result) for i in range(self.k_regimes): params1[self.parameters[i, 'regime_transition']] = ( regime_transition[i]) return result, params1 def _em_regime_transition(self, result): """ EM step for regime transition probabilities """ # Marginalize the smoothed joint probabilites to just S_t, S_{t-1} | T tmp = result.smoothed_joint_probabilities for i in range(tmp.ndim - 3): tmp = np.sum(tmp, -2) smoothed_joint_probabilities = tmp # Transition parameters (recall we're not yet supporting TVTP here) k_transition = len(self.parameters[0, 'regime_transition']) regime_transition = np.zeros((self.k_regimes, k_transition)) for i in range(self.k_regimes): # S_{t_1} for j in range(self.k_regimes - 1): # S_t regime_transition[i, j] = ( np.sum(smoothed_joint_probabilities[j, i]) / np.sum(result.smoothed_marginal_probabilities[i])) # It may be the case that due to rounding error this estimates # transition probabilities that sum to greater than one. If so, # re-scale the probabilities and warn the user that something # is not quite right delta = np.sum(regime_transition[i]) - 1 if delta > 0: warnings.warn('Invalid regime transition probabilities' ' estimated in EM iteration; probabilities have' ' been re-scaled to continue estimation.', EstimationWarning) regime_transition[i] /= 1 + delta + 1e-6 return regime_transition def _start_params_search(self, reps, start_params=None, transformed=True, em_iter=5, scale=1.): """ Search for starting parameters as random permutations of a vector Parameters ---------- reps : int Number of random permutations to try. start_params : ndarray, optional Starting parameter vector. If not given, class-level start parameters are used. transformed : bool, optional If `start_params` was provided, whether or not those parameters are already transformed. Default is True. em_iter : int, optional Number of EM iterations to apply to each random permutation. scale : array or float, optional Scale of variates for random start parameter search. Can be given as an array of length equal to the number of parameters or as a single scalar. Notes ----- This is a private method for finding good starting parameters for MLE by scoring, where the defaults have been set heuristically. """ if start_params is None: start_params = self.start_params transformed = True else: start_params = np.array(start_params, ndmin=1) # Random search is over untransformed space if transformed: start_params = self.untransform_params(start_params) # Construct the standard deviations scale = np.array(scale, ndmin=1) if scale.size == 1: scale = np.ones(self.k_params) * scale if not scale.size == self.k_params: raise ValueError('Scale of variates for random start' ' parameter search must be given for each' ' parameter or as a single scalar.') # Construct the random variates variates = np.zeros((reps, self.k_params)) for i in range(self.k_params): variates[:, i] = scale[i] * np.random.uniform(-0.5, 0.5, size=reps) llf = self.loglike(start_params, transformed=False) params = start_params for i in range(reps): with warnings.catch_warnings(): warnings.simplefilter("ignore") try: proposed_params = self._fit_em( start_params + variates[i], transformed=False, maxiter=em_iter, return_params=True) proposed_llf = self.loglike(proposed_params) if proposed_llf > llf: llf = proposed_llf params = self.untransform_params(proposed_params) except Exception: # FIXME: catch something specific pass # Return transformed parameters return self.transform_params(params) @property def start_params(self): """ (array) Starting parameters for maximum likelihood estimation. """ params = np.zeros(self.k_params, dtype=np.float64) # Transition probabilities if self.tvtp: params[self.parameters['regime_transition']] = 0. else: params[self.parameters['regime_transition']] = 1. / self.k_regimes return params @property def param_names(self): """ (list of str) List of human readable parameter names (for parameters actually included in the model). """ param_names = np.zeros(self.k_params, dtype=object) # Transition probabilities if self.tvtp: # TODO add support for exog_tvtp_names param_names[self.parameters['regime_transition']] = [ 'p[%d->%d].tvtp%d' % (j, i, k) for i in range(self.k_regimes-1) for k in range(self.k_tvtp) for j in range(self.k_regimes) ] else: param_names[self.parameters['regime_transition']] = [ 'p[%d->%d]' % (j, i) for i in range(self.k_regimes-1) for j in range(self.k_regimes)] return param_names.tolist() def transform_params(self, unconstrained): """ Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation Parameters ---------- unconstrained : array_like Array of unconstrained parameters used by the optimizer, to be transformed. Returns ------- constrained : array_like Array of constrained parameters which may be used in likelihood evaluation. Notes ----- In the base class, this only transforms the transition-probability- related parameters. """ constrained = np.array(unconstrained, copy=True) constrained = constrained.astype( np.promote_types(np.float64, constrained.dtype)) # Nothing to do for transition probabilities if TVTP if self.tvtp: constrained[self.parameters['regime_transition']] = ( unconstrained[self.parameters['regime_transition']]) # Otherwise do logistic transformation else: # Transition probabilities for i in range(self.k_regimes): tmp1 = unconstrained[self.parameters[i, 'regime_transition']] tmp2 = np.r_[0, tmp1] constrained[self.parameters[i, 'regime_transition']] = np.exp( tmp1 - logsumexp(tmp2)) # Do not do anything for the rest of the parameters return constrained def _untransform_logistic(self, unconstrained, constrained): """ Function to allow using a numerical root-finder to reverse the logistic transform. """ resid = np.zeros(unconstrained.shape, dtype=unconstrained.dtype) exp = np.exp(unconstrained) sum_exp = np.sum(exp) for i in range(len(unconstrained)): resid[i] = (unconstrained[i] - np.log(1 + sum_exp - exp[i]) + np.log(1 / constrained[i] - 1)) return resid def untransform_params(self, constrained): """ Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer Parameters ---------- constrained : array_like Array of constrained parameters used in likelihood evaluation, to be transformed. Returns ------- unconstrained : array_like Array of unconstrained parameters used by the optimizer. Notes ----- In the base class, this only untransforms the transition-probability- related parameters. """ unconstrained = np.array(constrained, copy=True) unconstrained = unconstrained.astype( np.promote_types(np.float64, unconstrained.dtype)) # Nothing to do for transition probabilities if TVTP if self.tvtp: unconstrained[self.parameters['regime_transition']] = ( constrained[self.parameters['regime_transition']]) # Otherwise reverse logistic transformation else: for i in range(self.k_regimes): s = self.parameters[i, 'regime_transition'] if self.k_regimes == 2: unconstrained[s] = -np.log(1. / constrained[s] - 1) else: from scipy.optimize import root out = root(self._untransform_logistic, np.zeros(unconstrained[s].shape, unconstrained.dtype), args=(constrained[s],)) if not out['success']: raise ValueError('Could not untransform parameters.') unconstrained[s] = out['x'] # Do not do anything for the rest of the parameters return unconstrained class HamiltonFilterResults(object): """ Results from applying the Hamilton filter to a state space model. Parameters ---------- model : Representation A Statespace representation Attributes ---------- nobs : int Number of observations. k_endog : int The dimension of the observation series. k_regimes : int The number of unobserved regimes. regime_transition : ndarray The regime transition matrix. initialization : str Initialization method for regime probabilities. initial_probabilities : ndarray Initial regime probabilities conditional_loglikelihoods : ndarray The loglikelihood values at each time period, conditional on regime. predicted_joint_probabilities : ndarray Predicted joint probabilities at each time period. filtered_marginal_probabilities : ndarray Filtered marginal probabilities at each time period. filtered_joint_probabilities : ndarray Filtered joint probabilities at each time period. joint_loglikelihoods : ndarray The likelihood values at each time period. llf_obs : ndarray The loglikelihood values at each time period. """ def __init__(self, model, result): self.model = model self.nobs = model.nobs self.order = model.order self.k_regimes = model.k_regimes attributes = ['regime_transition', 'initial_probabilities', 'conditional_loglikelihoods', 'predicted_joint_probabilities', 'filtered_marginal_probabilities', 'filtered_joint_probabilities', 'joint_loglikelihoods'] for name in attributes: setattr(self, name, getattr(result, name)) self.initialization = model._initialization self.llf_obs = self.joint_loglikelihoods self.llf = np.sum(self.llf_obs) # Subset transition if necessary (e.g. for Markov autoregression) if self.regime_transition.shape[-1] > 1 and self.order > 0: self.regime_transition = self.regime_transition[..., self.order:] # Cache for predicted marginal probabilities self._predicted_marginal_probabilities = None @property def predicted_marginal_probabilities(self): if self._predicted_marginal_probabilities is None: self._predicted_marginal_probabilities = ( self.predicted_joint_probabilities) for i in range(self._predicted_marginal_probabilities.ndim - 2): self._predicted_marginal_probabilities = np.sum( self._predicted_marginal_probabilities, axis=-2) return self._predicted_marginal_probabilities @property def expected_durations(self): """ (array) Expected duration of a regime, possibly time-varying. """ # It is possible that we will have a degenerate system, so that there # is no possibility of transitioning to a different state. In that # case, we do want the expected duration of one state to be np.inf, # and the expected duration of the other states to be np.nan diag = np.diagonal(self.regime_transition) expected_durations = np.zeros_like(diag) degenerate = np.any(diag == 1, axis=1) # For non-degenerate states, use the usual computation expected_durations[~degenerate] = 1 / (1 - diag[~degenerate]) # For degenerate states, everything is np.nan, except for the one # state that is np.inf. expected_durations[degenerate] = np.nan expected_durations[diag == 1] = np.inf return expected_durations.squeeze() class KimSmootherResults(HamiltonFilterResults): """ Results from applying the Kim smoother to a Markov switching model. Parameters ---------- model : MarkovSwitchingModel The model object. result : dict A dictionary containing two keys: 'smoothd_joint_probabilities' and 'smoothed_marginal_probabilities'. Attributes ---------- nobs : int Number of observations. k_endog : int The dimension of the observation series. k_states : int The dimension of the unobserved state process. """ def __init__(self, model, result): super(KimSmootherResults, self).__init__(model, result) attributes = ['smoothed_joint_probabilities', 'smoothed_marginal_probabilities'] for name in attributes: setattr(self, name, getattr(result, name)) class MarkovSwitchingResults(tsbase.TimeSeriesModelResults): r""" Class to hold results from fitting a Markov switching model Parameters ---------- model : MarkovSwitching instance The fitted model instance params : ndarray Fitted parameters filter_results : HamiltonFilterResults or KimSmootherResults instance The underlying filter and, optionally, smoother output cov_type : str The type of covariance matrix estimator to use. Can be one of 'approx', 'opg', 'robust', or 'none'. Attributes ---------- model : Model instance A reference to the model that was fit. filter_results : HamiltonFilterResults or KimSmootherResults instance The underlying filter and, optionally, smoother output nobs : float The number of observations used to fit the model. params : ndarray The parameters of the model. scale : float This is currently set to 1.0 and not used by the model or its results. """ use_t = False def __init__(self, model, params, results, cov_type='opg', cov_kwds=None, **kwargs): self.data = model.data tsbase.TimeSeriesModelResults.__init__(self, model, params, normalized_cov_params=None, scale=1.) # Save the filter / smoother output self.filter_results = results if isinstance(results, KimSmootherResults): self.smoother_results = results else: self.smoother_results = None # Dimensions self.nobs = model.nobs self.order = model.order self.k_regimes = model.k_regimes # Setup covariance matrix notes dictionary if not hasattr(self, 'cov_kwds'): self.cov_kwds = {} self.cov_type = cov_type # Setup the cache self._cache = {} # Handle covariance matrix calculation if cov_kwds is None: cov_kwds = {} self._cov_approx_complex_step = ( cov_kwds.pop('approx_complex_step', True)) self._cov_approx_centered = cov_kwds.pop('approx_centered', False) try: self._rank = None self._get_robustcov_results(cov_type=cov_type, use_self=True, **cov_kwds) except np.linalg.LinAlgError: self._rank = 0 k_params = len(self.params) self.cov_params_default = np.zeros((k_params, k_params)) * np.nan self.cov_kwds['cov_type'] = ( 'Covariance matrix could not be calculated: singular.' ' information matrix.') # Copy over arrays attributes = ['regime_transition', 'initial_probabilities', 'conditional_loglikelihoods', 'predicted_marginal_probabilities', 'predicted_joint_probabilities', 'filtered_marginal_probabilities', 'filtered_joint_probabilities', 'joint_loglikelihoods', 'expected_durations'] for name in attributes: setattr(self, name, getattr(self.filter_results, name)) attributes = ['smoothed_joint_probabilities', 'smoothed_marginal_probabilities'] for name in attributes: if self.smoother_results is not None: setattr(self, name, getattr(self.smoother_results, name)) else: setattr(self, name, None) # Reshape some arrays to long-format self.predicted_marginal_probabilities = ( self.predicted_marginal_probabilities.T) self.filtered_marginal_probabilities = ( self.filtered_marginal_probabilities.T) if self.smoother_results is not None: self.smoothed_marginal_probabilities = ( self.smoothed_marginal_probabilities.T) # Make into Pandas arrays if using Pandas data if isinstance(self.data, PandasData): index = self.data.row_labels if self.expected_durations.ndim > 1: self.expected_durations = pd.DataFrame( self.expected_durations, index=index) self.predicted_marginal_probabilities = pd.DataFrame( self.predicted_marginal_probabilities, index=index) self.filtered_marginal_probabilities = pd.DataFrame( self.filtered_marginal_probabilities, index=index) if self.smoother_results is not None: self.smoothed_marginal_probabilities = pd.DataFrame( self.smoothed_marginal_probabilities, index=index) def _get_robustcov_results(self, cov_type='opg', **kwargs): from statsmodels.base.covtype import descriptions use_self = kwargs.pop('use_self', False) if use_self: res = self else: raise NotImplementedError res = self.__class__( self.model, self.params, normalized_cov_params=self.normalized_cov_params, scale=self.scale) # Set the new covariance type res.cov_type = cov_type res.cov_kwds = {} approx_type_str = 'complex-step' # Calculate the new covariance matrix k_params = len(self.params) if k_params == 0: res.cov_params_default = np.zeros((0, 0)) res._rank = 0 res.cov_kwds['description'] = 'No parameters estimated.' elif cov_type == 'custom': res.cov_type = kwargs['custom_cov_type'] res.cov_params_default = kwargs['custom_cov_params'] res.cov_kwds['description'] = kwargs['custom_description'] res._rank = np.linalg.matrix_rank(res.cov_params_default) elif cov_type == 'none': res.cov_params_default = np.zeros((k_params, k_params)) * np.nan res._rank = np.nan res.cov_kwds['description'] = descriptions['none'] elif self.cov_type == 'approx': res.cov_params_default = res.cov_params_approx res.cov_kwds['description'] = descriptions['approx'].format( approx_type=approx_type_str) elif self.cov_type == 'opg': res.cov_params_default = res.cov_params_opg res.cov_kwds['description'] = descriptions['OPG'].format( approx_type=approx_type_str) elif self.cov_type == 'robust': res.cov_params_default = res.cov_params_robust res.cov_kwds['description'] = descriptions['robust'].format( approx_type=approx_type_str) else: raise NotImplementedError('Invalid covariance matrix type.') return res @cache_readonly def aic(self): """ (float) Akaike Information Criterion """ # return -2*self.llf + 2*self.params.shape[0] return aic(self.llf, self.nobs, self.params.shape[0]) @cache_readonly def bic(self): """ (float) Bayes Information Criterion """ # return -2*self.llf + self.params.shape[0]*np.log(self.nobs) return bic(self.llf, self.nobs, self.params.shape[0]) @cache_readonly def cov_params_approx(self): """ (array) The variance / covariance matrix. Computed using the numerical Hessian approximated by complex step or finite differences methods. """ evaluated_hessian = self.model.hessian(self.params, transformed=True) neg_cov, singular_values = pinv_extended(evaluated_hessian) if self._rank is None: self._rank = np.linalg.matrix_rank(np.diag(singular_values)) return -neg_cov @cache_readonly def cov_params_opg(self): """ (array) The variance / covariance matrix. Computed using the outer product of gradients method. """ score_obs = self.model.score_obs(self.params, transformed=True).T cov_params, singular_values = pinv_extended( np.inner(score_obs, score_obs)) if self._rank is None: self._rank = np.linalg.matrix_rank(np.diag(singular_values)) return cov_params @cache_readonly def cov_params_robust(self): """ (array) The QMLE variance / covariance matrix. Computed using the numerical Hessian as the evaluated hessian. """ cov_opg = self.cov_params_opg evaluated_hessian = self.model.hessian(self.params, transformed=True) cov_params, singular_values = pinv_extended( np.dot(np.dot(evaluated_hessian, cov_opg), evaluated_hessian) ) if self._rank is None: self._rank = np.linalg.matrix_rank(np.diag(singular_values)) return cov_params @cache_readonly def fittedvalues(self): """ (array) The predicted values of the model. An (nobs x k_endog) array. """ return self.model.predict(self.params) @cache_readonly def hqic(self): """ (float) Hannan-Quinn Information Criterion """ # return -2*self.llf + 2*np.log(np.log(self.nobs))*self.params.shape[0] return hqic(self.llf, self.nobs, self.params.shape[0]) @cache_readonly def llf_obs(self): """ (float) The value of the log-likelihood function evaluated at `params`. """ return self.model.loglikeobs(self.params) @cache_readonly def llf(self): """ (float) The value of the log-likelihood function evaluated at `params`. """ return self.model.loglike(self.params) @cache_readonly def resid(self): """ (array) The model residuals. An (nobs x k_endog) array. """ return self.model.endog - self.fittedvalues @property def joint_likelihoods(self): return np.exp(self.joint_loglikelihoods) def predict(self, start=None, end=None, probabilities=None, conditional=False): """ In-sample prediction and out-of-sample forecasting Parameters ---------- start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, i.e., the last forecast is end. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. probabilities : str or array_like, optional Specifies the weighting probabilities used in constructing the prediction as a weighted average. If a string, can be 'predicted', 'filtered', or 'smoothed'. Otherwise can be an array of probabilities to use. Default is smoothed. conditional : bool or int, optional Whether or not to return predictions conditional on current or past regimes. If False, returns a single vector of weighted predictions. If True or 1, returns predictions conditional on the current regime. For larger integers, returns predictions conditional on the current regime and some number of past regimes. Returns ------- predict : ndarray Array of out of in-sample predictions and / or out-of-sample forecasts. An (npredict x k_endog) array. """ return self.model.predict(self.params, start=start, end=end, probabilities=probabilities, conditional=conditional) def forecast(self, steps=1, **kwargs): """ Out-of-sample forecasts Parameters ---------- steps : int, str, or datetime, optional If an integer, the number of steps to forecast from the end of the sample. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, steps must be an integer. Default **kwargs Additional arguments may required for forecasting beyond the end of the sample. See `FilterResults.predict` for more details. Returns ------- forecast : ndarray Array of out of sample forecasts. A (steps x k_endog) array. """ raise NotImplementedError def summary(self, alpha=.05, start=None, title=None, model_name=None, display_params=True): """ Summarize the Model Parameters ---------- alpha : float, optional Significance level for the confidence intervals. Default is 0.05. start : int, optional Integer of the start observation. Default is 0. title : str, optional The title of the summary table. model_name : str The name of the model used. Default is to use model class name. display_params : bool, optional Whether or not to display tables of estimated parameters. Default is True. Usually only used internally. Returns ------- summary : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary """ from statsmodels.iolib.summary import Summary # Model specification results model = self.model if title is None: title = 'Markov Switching Model Results' if start is None: start = 0 if self.data.dates is not None: dates = self.data.dates d = dates[start] sample = ['%02d-%02d-%02d' % (d.month, d.day, d.year)] d = dates[-1] sample += ['- ' + '%02d-%02d-%02d' % (d.month, d.day, d.year)] else: sample = [str(start), ' - ' + str(self.model.nobs)] # Standardize the model name as a list of str if model_name is None: model_name = model.__class__.__name__ # Create the tables if not isinstance(model_name, list): model_name = [model_name] top_left = [('Dep. Variable:', None)] top_left.append(('Model:', [model_name[0]])) for i in range(1, len(model_name)): top_left.append(('', ['+ ' + model_name[i]])) top_left += [ ('Date:', None), ('Time:', None), ('Sample:', [sample[0]]), ('', [sample[1]]) ] top_right = [ ('No. Observations:', [self.model.nobs]), ('Log Likelihood', ["%#5.3f" % self.llf]), ('AIC', ["%#5.3f" % self.aic]), ('BIC', ["%#5.3f" % self.bic]), ('HQIC', ["%#5.3f" % self.hqic]) ] if hasattr(self, 'cov_type'): top_left.append(('Covariance Type:', [self.cov_type])) summary = Summary() summary.add_table_2cols(self, gleft=top_left, gright=top_right, title=title) # Make parameters tables for each regime from statsmodels.iolib.summary import summary_params import re def make_table(self, mask, title, strip_end=True): res = (self, self.params[mask], self.bse[mask], self.tvalues[mask], self.pvalues[mask], self.conf_int(alpha)[mask]) param_names = [ re.sub(r'\[\d+\]$', '', name) for name in np.array(self.data.param_names)[mask].tolist() ] return summary_params(res, yname=None, xname=param_names, alpha=alpha, use_t=False, title=title) params = model.parameters regime_masks = [[] for i in range(model.k_regimes)] other_masks = {} for key, switching in params.switching.items(): k_params = len(switching) if key == 'regime_transition': continue other_masks[key] = [] for i in range(k_params): if switching[i]: for j in range(self.k_regimes): regime_masks[j].append(params[j, key][i]) else: other_masks[key].append(params[0, key][i]) for i in range(self.k_regimes): mask = regime_masks[i] if len(mask) > 0: table = make_table(self, mask, 'Regime %d parameters' % i) summary.tables.append(table) mask = [] for key, _mask in other_masks.items(): mask.extend(_mask) if len(mask) > 0: table = make_table(self, mask, 'Non-switching parameters') summary.tables.append(table) # Transition parameters mask = params['regime_transition'] table = make_table(self, mask, 'Regime transition parameters') summary.tables.append(table) # Add warnings/notes, added to text format only etext = [] if hasattr(self, 'cov_type') and 'description' in self.cov_kwds: etext.append(self.cov_kwds['description']) if self._rank < len(self.params): etext.append("Covariance matrix is singular or near-singular," " with condition number %6.3g. Standard errors may be" " unstable." % np.linalg.cond(self.cov_params())) if etext: etext = ["[{0}] {1}".format(i + 1, text) for i, text in enumerate(etext)] etext.insert(0, "Warnings:") summary.add_extra_txt(etext) return summary class MarkovSwitchingResultsWrapper(wrap.ResultsWrapper): _attrs = { 'cov_params_approx': 'cov', 'cov_params_default': 'cov', 'cov_params_opg': 'cov', 'cov_params_robust': 'cov', } _wrap_attrs = wrap.union_dicts(tsbase.TimeSeriesResultsWrapper._wrap_attrs, _attrs) _methods = { 'forecast': 'dates', } _wrap_methods = wrap.union_dicts( tsbase.TimeSeriesResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(MarkovSwitchingResultsWrapper, # noqa:E305 MarkovSwitchingResults) 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.3570154,.6429846,.0027989,.9972011,.0035125,.9964876,-.2296742,1.026684,.5781449,1.023168,1.395377 .3565186,.6434814,.1375207,.8624793,.1369265,.8630735,.132511,1.19744,.8177727,1.05099,1.492269 .3598582,.6401418,.2749309,.7250692,.6349947,.3650052,.3607773,.7020003,.5792084,.6081876,.8663656 .3632645,.6367355,.0747665,.9252335,.04608,.9539199,.2392728,.9091664,.6658179,.8590808,1.638283 .3583026,.6416974,.3430003,.6569996,.2439876,.7560124,.3945461,1.222072,.9255675,.9382305,1.486441 .3649519,.6350481,.2784336,.7215664,.2026928,.7973073,.5596761,.5065153,.5259164,.521317,.917065 .3633513,.6366487,.4820935,.5179065,.4820935,.5179065,.0647946,.6038795,.4080022,.3439901,.4402459 statsmodels-0.12.2/statsmodels/tsa/regime_switching/tests/test_markov_autoregression.py000066400000000000000000001203751400612667500320400ustar00rootroot00000000000000""" Tests for Markov Autoregression models Author: Chad Fulton License: BSD-3 """ import warnings import os import numpy as np from numpy.testing import assert_equal, assert_allclose import pandas as pd import pytest from statsmodels.tools import add_constant from statsmodels.tsa.regime_switching import markov_autoregression current_path = os.path.dirname(os.path.abspath(__file__)) rgnp = [2.59316421, 2.20217133, 0.45827562, 0.9687438, -0.24130757, 0.89647478, 2.05393219, 1.73353648, 0.93871289, -0.46477833, -0.80983406, -1.39763689, -0.39886093, 1.1918416, 1.45620048, 2.11808228, 1.08957863, 1.32390273, 0.87296367, -0.19773273, 0.45420215, 0.07221876, 1.1030364, 0.82097489, -0.05795795, 0.58447772, -1.56192672, -2.05041027, 0.53637183, 2.33676839, 2.34014559, 1.2339263, 1.8869648, -0.45920792, 0.84940469, 1.70139849, -0.28756312, 0.09594627, -0.86080289, 1.03447127, 1.23685944, 1.42004502, 2.22410631, 1.30210173, 1.03517699, 0.9253425, -0.16559951, 1.3444382, 1.37500131, 1.73222184, 0.71605635, 2.21032143, 0.85333031, 1.00238776, 0.42725441, 2.14368343, 1.43789184, 1.57959926, 2.27469826, 1.95962656, 0.25992399, 1.01946914, 0.49016398, 0.5636338, 0.5959546, 1.43082857, 0.56230122, 1.15388393, 1.68722844, 0.77438205, -0.09647045, 1.39600146, 0.13646798, 0.55223715, -0.39944872, -0.61671102, -0.08722561, 1.2101835, -0.90729755, 2.64916158, -0.0080694, 0.51111895, -0.00401437, 2.16821432, 1.92586732, 1.03504717, 1.85897219, 2.32004929, 0.25570789, -0.09855274, 0.89073682, -0.55896485, 0.28350255, -1.31155407, -0.88278776, -1.97454941, 1.01275265, 1.68264723, 1.38271284, 1.86073637, 0.4447377, 0.41449001, 0.99202275, 1.36283576, 1.59970522, 1.98845816, -0.25684232, 0.87786949, 3.1095655, 0.85324478, 1.23337317, 0.00314302, -0.09433369, 0.89883322, -0.19036628, 0.99772376, -2.39120054, 0.06649673, 1.26136017, 1.91637838, -0.3348029, 0.44207108, -1.40664911, -1.52129889, 0.29919869, -0.80197448, 0.15204792, 0.98585027, 2.13034606, 1.34397924, 1.61550522, 2.70930099, 1.24461412, 0.50835466, 0.14802167] rec = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0] def test_predict(): # AR(1) without mean, k_regimes=2 endog = np.ones(10) mod = markov_autoregression.MarkovAutoregression( endog, k_regimes=2, order=1, trend='nc') assert_equal(mod.nobs, 9) assert_equal(mod.endog, np.ones(9)) params = np.r_[0.5, 0.5, 1., 0.1, 0.5] mod_resid = mod._resid(params) resids = np.zeros((2, 2, mod.nobs)) # Resids when: S_{t} = 0 resids[0, :, :] = np.ones(9) - 0.1 * np.ones(9) assert_allclose(mod_resid[0, :, :], resids[0, :, :]) # Resids when: S_{t} = 1 resids[1, :, :] = np.ones(9) - 0.5 * np.ones(9) assert_allclose(mod_resid[1, :, :], resids[1, :, :]) # AR(1) with mean, k_regimes=2 endog = np.arange(10) mod = markov_autoregression.MarkovAutoregression( endog, k_regimes=2, order=1) assert_equal(mod.nobs, 9) assert_equal(mod.endog, np.arange(1, 10)) params = np.r_[0.5, 0.5, 2., 3., 1., 0.1, 0.5] mod_resid = mod._resid(params) resids = np.zeros((2, 2, mod.nobs)) # Resids when: S_t = 0, S_{t-1} = 0 resids[0, 0, :] = (np.arange(1, 10) - 2.) - 0.1 * (np.arange(9) - 2.) assert_allclose(mod_resid[0, 0, :], resids[0, 0, :]) # Resids when: S_t = 0, S_{t-1} = 1 resids[0, 1, :] = (np.arange(1, 10) - 2.) - 0.1 * (np.arange(9) - 3.) assert_allclose(mod_resid[0, 1, :], resids[0, 1, :]) # Resids when: S_t = 1, S_{t-1} = 0 resids[1, 0, :] = (np.arange(1, 10) - 3.) - 0.5 * (np.arange(9) - 2.) assert_allclose(mod_resid[1, 0, :], resids[1, 0, :]) # Resids when: S_t = 1, S_{t-1} = 1 resids[1, 1, :] = (np.arange(1, 10) - 3.) - 0.5 * (np.arange(9) - 3.) assert_allclose(mod_resid[1, 1, :], resids[1, 1, :]) # AR(2) with mean, k_regimes=3 endog = np.arange(10) mod = markov_autoregression.MarkovAutoregression( endog, k_regimes=3, order=2) assert_equal(mod.nobs, 8) assert_equal(mod.endog, np.arange(2, 10)) params = np.r_[[0.3] * 6, 2., 3., 4, 1., 0.1, 0.5, 0.8, -0.05, -0.25, -0.4] mod_resid = mod._resid(params) resids = np.zeros((3, 3, 3, mod.nobs)) # Resids when: S_t = 0, S_{t-1} = 0, S_{t-2} = 0 resids[0, 0, 0, :] = ( (np.arange(2, 10) - 2.) - 0.1 * (np.arange(1, 9) - 2.) - (-0.05) * (np.arange(8) - 2.)) assert_allclose(mod_resid[0, 0, 0, :], resids[0, 0, 0, :]) # Resids when: S_t = 1, S_{t-1} = 0, S_{t-2} = 0 resids[1, 0, 0, :] = ( (np.arange(2, 10) - 3.) - 0.5 * (np.arange(1, 9) - 2.) - (-0.25) * (np.arange(8) - 2.)) assert_allclose(mod_resid[1, 0, 0, :], resids[1, 0, 0, :]) # Resids when: S_t = 0, S_{t-1} = 2, S_{t-2} = 1 resids[0, 2, 1, :] = ( (np.arange(2, 10) - 2.) - 0.1 * (np.arange(1, 9) - 4.) - (-0.05) * (np.arange(8) - 3.)) assert_allclose(mod_resid[0, 2, 1, :], resids[0, 2, 1, :]) # AR(1) with mean + non-switching exog endog = np.arange(10) exog = np.r_[0.4, 5, 0.2, 1.2, -0.3, 2.5, 0.2, -0.7, 2., -1.1] mod = markov_autoregression.MarkovAutoregression( endog, k_regimes=2, order=1, exog=exog) assert_equal(mod.nobs, 9) assert_equal(mod.endog, np.arange(1, 10)) params = np.r_[0.5, 0.5, 2., 3., 1.5, 1., 0.1, 0.5] mod_resid = mod._resid(params) resids = np.zeros((2, 2, mod.nobs)) # Resids when: S_t = 0, S_{t-1} = 0 resids[0, 0, :] = ( (np.arange(1, 10) - 2. - 1.5 * exog[1:]) - 0.1 * (np.arange(9) - 2. - 1.5 * exog[:-1])) assert_allclose(mod_resid[0, 0, :], resids[0, 0, :]) # Resids when: S_t = 0, S_{t-1} = 1 resids[0, 1, :] = ( (np.arange(1, 10) - 2. - 1.5 * exog[1:]) - 0.1 * (np.arange(9) - 3. - 1.5 * exog[:-1])) assert_allclose(mod_resid[0, 1, :], resids[0, 1, :]) # Resids when: S_t = 1, S_{t-1} = 0 resids[1, 0, :] = ( (np.arange(1, 10) - 3. - 1.5 * exog[1:]) - 0.5 * (np.arange(9) - 2. - 1.5 * exog[:-1])) assert_allclose(mod_resid[1, 0, :], resids[1, 0, :]) # Resids when: S_t = 1, S_{t-1} = 1 resids[1, 1, :] = ( (np.arange(1, 10) - 3. - 1.5 * exog[1:]) - 0.5 * (np.arange(9) - 3. - 1.5 * exog[:-1])) assert_allclose(mod_resid[1, 1, :], resids[1, 1, :]) def test_conditional_loglikelihoods(): # AR(1) without mean, k_regimes=2, non-switching variance endog = np.ones(10) mod = markov_autoregression.MarkovAutoregression( endog, k_regimes=2, order=1) assert_equal(mod.nobs, 9) assert_equal(mod.endog, np.ones(9)) params = np.r_[0.5, 0.5, 2., 3., 2., 0.1, 0.5] resid = mod._resid(params) conditional_likelihoods = ( np.exp(-0.5 * resid**2 / 2) / np.sqrt(2 * np.pi * 2)) assert_allclose(mod._conditional_loglikelihoods(params), np.log(conditional_likelihoods)) # AR(1) without mean, k_regimes=3, switching variance endog = np.ones(10) mod = markov_autoregression.MarkovAutoregression( endog, k_regimes=3, order=1, switching_variance=True) assert_equal(mod.nobs, 9) assert_equal(mod.endog, np.ones(9)) params = np.r_[[0.3]*6, 2., 3., 4., 1.5, 3., 4.5, 0.1, 0.5, 0.8] mod_conditional_loglikelihoods = mod._conditional_loglikelihoods(params) conditional_likelihoods = mod._resid(params) # S_t = 0 conditional_likelihoods[0, :, :] = ( np.exp(-0.5 * conditional_likelihoods[0, :, :]**2 / 1.5) / np.sqrt(2 * np.pi * 1.5)) assert_allclose(mod_conditional_loglikelihoods[0, :, :], np.log(conditional_likelihoods[0, :, :])) # S_t = 1 conditional_likelihoods[1, :, :] = ( np.exp(-0.5 * conditional_likelihoods[1, :, :]**2 / 3.) / np.sqrt(2 * np.pi * 3.)) assert_allclose(mod_conditional_loglikelihoods[1, :, :], np.log(conditional_likelihoods[1, :, :])) # S_t = 2 conditional_likelihoods[2, :, :] = ( np.exp(-0.5 * conditional_likelihoods[2, :, :]**2 / 4.5) / np.sqrt(2 * np.pi * 4.5)) assert_allclose(mod_conditional_loglikelihoods[2, :, :], np.log(conditional_likelihoods[2, :, :])) class MarkovAutoregression(object): @classmethod def setup_class(cls, true, endog, atol=1e-5, rtol=1e-7, **kwargs): cls.model = markov_autoregression.MarkovAutoregression(endog, **kwargs) cls.true = true cls.result = cls.model.smooth(cls.true['params']) cls.atol = atol cls.rtol = rtol def test_llf(self): assert_allclose(self.result.llf, self.true['llf'], atol=self.atol, rtol=self.rtol) def test_fit(self, **kwargs): # Test fitting against Stata with warnings.catch_warnings(): warnings.simplefilter("ignore") res = self.model.fit(disp=False, **kwargs) assert_allclose(res.llf, self.true['llf_fit'], atol=self.atol, rtol=self.rtol) @pytest.mark.smoke def test_fit_em(self, **kwargs): # Test EM fitting (smoke test) res_em = self.model._fit_em(**kwargs) assert_allclose(res_em.llf, self.true['llf_fit_em'], atol=self.atol, rtol=self.rtol) hamilton_ar2_short_filtered_joint_probabilities = np.array([ [[[4.99506987e-02, 6.44048275e-04, 6.22227140e-05, 4.45756755e-06, 5.26645567e-07, 7.99846146e-07, 1.19425705e-05, 6.87762063e-03], [1.95930395e-02, 3.25884335e-04, 1.12955091e-04, 3.38537103e-04, 9.81927968e-06, 2.71696750e-05, 5.83828290e-03, 7.64261509e-02]], [[1.97113193e-03, 9.50372207e-05, 1.98390978e-04, 1.88188953e-06, 4.83449400e-07, 1.14872860e-05, 4.02918239e-06, 4.35015431e-04], [2.24870443e-02, 1.27331172e-03, 9.62155856e-03, 4.04178695e-03, 2.75516282e-04, 1.18179572e-02, 5.99778157e-02, 1.48149567e-01]]], [[[6.70912859e-02, 1.84223872e-02, 2.55621792e-04, 4.48500688e-05, 7.80481515e-05, 2.73734559e-06, 7.59835896e-06, 1.42930726e-03], [2.10053328e-02, 7.44036383e-03, 3.70388879e-04, 2.71878370e-03, 1.16152088e-03, 7.42182691e-05, 2.96490192e-03, 1.26774695e-02]], [[8.09335679e-02, 8.31016518e-02, 2.49149080e-02, 5.78825626e-04, 2.19019941e-03, 1.20179130e-03, 7.83659430e-05, 2.76363377e-03], [7.36967899e-01, 8.88697316e-01, 9.64463954e-01, 9.92270877e-01, 9.96283886e-01, 9.86863839e-01, 9.31117063e-01, 7.51241236e-01]]]]) hamilton_ar2_short_predicted_joint_probabilities = np.array([[ [[[1.20809334e-01, 3.76964436e-02, 4.86045844e-04, 4.69578023e-05, 3.36400588e-06, 3.97445190e-07, 6.03622290e-07, 9.01273552e-06], [3.92723623e-02, 1.47863379e-02, 2.45936108e-04, 8.52441571e-05, 2.55484811e-04, 7.41034525e-06, 2.05042201e-05, 4.40599447e-03]], [[4.99131230e-03, 1.48756005e-03, 7.17220245e-05, 1.49720314e-04, 1.42021122e-06, 3.64846209e-07, 8.66914462e-06, 3.04071516e-06], [4.70476003e-02, 1.69703652e-02, 9.60933974e-04, 7.26113047e-03, 3.05022748e-03, 2.07924699e-04, 8.91869322e-03, 4.52636381e-02]]], [[[4.99131230e-03, 6.43506069e-03, 1.76698327e-03, 2.45179642e-05, 4.30179435e-06, 7.48598845e-06, 2.62552503e-07, 7.28796600e-07], [1.62256192e-03, 2.01472650e-03, 7.13642497e-04, 3.55258493e-05, 2.60772139e-04, 1.11407276e-04, 7.11864528e-06, 2.84378568e-04]], [[5.97950448e-03, 7.76274317e-03, 7.97069493e-03, 2.38971340e-03, 5.55180599e-05, 2.10072977e-04, 1.15269812e-04, 7.51646942e-06], [5.63621989e-02, 7.06862760e-02, 8.52394030e-02, 9.25065601e-02, 9.51736612e-02, 9.55585689e-02, 9.46550451e-02, 8.93080931e-02]]]], [[[[3.92723623e-02, 1.22542551e-02, 1.58002431e-04, 1.52649118e-05, 1.09356167e-06, 1.29200377e-07, 1.96223855e-07, 2.92983500e-06], [1.27665503e-02, 4.80670161e-03, 7.99482261e-05, 2.77109335e-05, 8.30522919e-05, 2.40893443e-06, 6.66545485e-06, 1.43228843e-03]], [[1.62256192e-03, 4.83571884e-04, 2.33151963e-05, 4.86706634e-05, 4.61678312e-07, 1.18603191e-07, 2.81814142e-06, 9.88467229e-07], [1.52941031e-02, 5.51667911e-03, 3.12377744e-04, 2.36042810e-03, 9.91559466e-04, 6.75915830e-05, 2.89926399e-03, 1.47141776e-02]]], [[[4.70476003e-02, 6.06562252e-02, 1.66554040e-02, 2.31103828e-04, 4.05482745e-05, 7.05621631e-05, 2.47479309e-06, 6.86956236e-06], [1.52941031e-02, 1.89906063e-02, 6.72672133e-03, 3.34863029e-04, 2.45801156e-03, 1.05011361e-03, 6.70996238e-05, 2.68052335e-03]], [[5.63621989e-02, 7.31708248e-02, 7.51309569e-02, 2.25251946e-02, 5.23307566e-04, 1.98012644e-03, 1.08652148e-03, 7.08494735e-05], [5.31264334e-01, 6.66281623e-01, 8.03457913e-01, 8.71957394e-01, 8.97097216e-01, 9.00725317e-01, 8.92208794e-01, 8.41808970e-01]]]]]) hamilton_ar2_short_smoothed_joint_probabilities = np.array([ [[[1.29898189e-02, 1.66298475e-04, 1.29822987e-05, 9.95268382e-07, 1.84473346e-07, 7.18761267e-07, 1.69576494e-05, 6.87762063e-03], [5.09522472e-03, 8.41459714e-05, 2.35672254e-05, 7.55872505e-05, 3.43949612e-06, 2.44153330e-05, 8.28997024e-03, 7.64261509e-02]], [[5.90021731e-04, 2.55342733e-05, 4.50698224e-05, 5.30734135e-07, 1.80741761e-07, 1.11483792e-05, 5.98539007e-06, 4.35015431e-04], [6.73107901e-03, 3.42109009e-04, 2.18579464e-03, 1.13987259e-03, 1.03004157e-04, 1.14692946e-02, 8.90976350e-02, 1.48149567e-01]]], [[[6.34648123e-02, 1.79187451e-02, 2.37462147e-04, 3.55542558e-05, 7.63980455e-05, 2.90520820e-06, 8.17644492e-06, 1.42930726e-03], [1.98699352e-02, 7.23695477e-03, 3.44076057e-04, 2.15527721e-03, 1.13696383e-03, 7.87695658e-05, 3.19047276e-03, 1.26774695e-02]], [[8.81925054e-02, 8.33092133e-02, 2.51106301e-02, 5.81007470e-04, 2.19065072e-03, 1.20221350e-03, 7.56893839e-05, 2.76363377e-03], [8.03066603e-01, 8.90916999e-01, 9.72040418e-01, 9.96011175e-01, 9.96489179e-01, 9.87210535e-01, 8.99315113e-01, 7.51241236e-01]]]]) class TestHamiltonAR2Short(MarkovAutoregression): # This is just a set of regression tests @classmethod def setup_class(cls): true = { 'params': np.r_[0.754673, 0.095915, -0.358811, 1.163516, np.exp(-0.262658)**2, 0.013486, -0.057521], 'llf': -10.14066, 'llf_fit': -4.0523073, 'llf_fit_em': -8.885836 } super(TestHamiltonAR2Short, cls).setup_class( true, rgnp[-10:], k_regimes=2, order=2, switching_ar=False) def test_fit_em(self): with warnings.catch_warnings(): warnings.simplefilter("ignore") super(TestHamiltonAR2Short, self).test_fit_em() def test_filter_output(self, **kwargs): res = self.result # Filtered assert_allclose(res.filtered_joint_probabilities, hamilton_ar2_short_filtered_joint_probabilities) # Predicted desired = hamilton_ar2_short_predicted_joint_probabilities if desired.ndim > res.predicted_joint_probabilities.ndim: desired = desired.sum(axis=-2) assert_allclose(res.predicted_joint_probabilities, desired) def test_smoother_output(self, **kwargs): res = self.result # Filtered assert_allclose(res.filtered_joint_probabilities, hamilton_ar2_short_filtered_joint_probabilities) # Predicted desired = hamilton_ar2_short_predicted_joint_probabilities if desired.ndim > res.predicted_joint_probabilities.ndim: desired = desired.sum(axis=-2) assert_allclose(res.predicted_joint_probabilities, desired) # Smoothed, entry-by-entry assert_allclose( res.smoothed_joint_probabilities[..., -1], hamilton_ar2_short_smoothed_joint_probabilities[..., -1]) assert_allclose( res.smoothed_joint_probabilities[..., -2], hamilton_ar2_short_smoothed_joint_probabilities[..., -2]) assert_allclose( res.smoothed_joint_probabilities[..., -3], hamilton_ar2_short_smoothed_joint_probabilities[..., -3]) assert_allclose( res.smoothed_joint_probabilities[..., :-3], hamilton_ar2_short_smoothed_joint_probabilities[..., :-3]) hamilton_ar4_filtered = [ 0.776712, 0.949192, 0.996320, 0.990258, 0.940111, 0.537442, 0.140001, 0.008942, 0.048480, 0.614097, 0.910889, 0.995463, 0.979465, 0.992324, 0.984561, 0.751038, 0.776268, 0.522048, 0.814956, 0.821786, 0.472729, 0.673567, 0.029031, 0.001556, 0.433276, 0.985463, 0.995025, 0.966067, 0.998445, 0.801467, 0.960997, 0.996431, 0.461365, 0.199357, 0.027398, 0.703626, 0.946388, 0.985321, 0.998244, 0.989567, 0.984510, 0.986811, 0.793788, 0.973675, 0.984848, 0.990418, 0.918427, 0.998769, 0.977647, 0.978742, 0.927635, 0.998691, 0.988934, 0.991654, 0.999288, 0.999073, 0.918636, 0.987710, 0.966876, 0.910015, 0.826150, 0.969451, 0.844049, 0.941525, 0.993363, 0.949978, 0.615206, 0.970915, 0.787585, 0.707818, 0.200476, 0.050835, 0.140723, 0.809850, 0.086422, 0.990344, 0.785963, 0.817425, 0.659152, 0.996578, 0.992860, 0.948501, 0.996883, 0.999712, 0.906694, 0.725013, 0.963690, 0.386960, 0.241302, 0.009078, 0.015789, 0.000896, 0.541530, 0.928686, 0.953704, 0.992741, 0.935877, 0.918958, 0.977316, 0.987941, 0.987300, 0.996769, 0.645469, 0.921285, 0.999917, 0.949335, 0.968914, 0.886025, 0.777141, 0.904381, 0.368277, 0.607429, 0.002491, 0.227610, 0.871284, 0.987717, 0.288705, 0.512124, 0.030329, 0.005177, 0.256183, 0.020955, 0.051620, 0.549009, 0.991715, 0.987892, 0.995377, 0.999833, 0.993756, 0.956164, 0.927714] hamilton_ar4_smoothed = [ 0.968096, 0.991071, 0.998559, 0.958534, 0.540652, 0.072784, 0.010999, 0.006228, 0.172144, 0.898574, 0.989054, 0.998293, 0.986434, 0.993248, 0.976868, 0.858521, 0.847452, 0.675670, 0.596294, 0.165407, 0.035270, 0.127967, 0.007414, 0.004944, 0.815829, 0.998128, 0.998091, 0.993227, 0.999283, 0.921100, 0.977171, 0.971757, 0.124680, 0.063710, 0.114570, 0.954701, 0.994852, 0.997302, 0.999345, 0.995817, 0.996218, 0.994580, 0.933990, 0.996054, 0.998151, 0.996976, 0.971489, 0.999786, 0.997362, 0.996755, 0.993053, 0.999947, 0.998469, 0.997987, 0.999830, 0.999360, 0.953176, 0.992673, 0.975235, 0.938121, 0.946784, 0.986897, 0.905792, 0.969755, 0.995379, 0.914480, 0.772814, 0.931385, 0.541742, 0.394596, 0.063428, 0.027829, 0.124527, 0.286105, 0.069362, 0.995950, 0.961153, 0.962449, 0.945022, 0.999855, 0.998943, 0.980041, 0.999028, 0.999838, 0.863305, 0.607421, 0.575983, 0.013300, 0.007562, 0.000635, 0.001806, 0.002196, 0.803550, 0.972056, 0.984503, 0.998059, 0.985211, 0.988486, 0.994452, 0.994498, 0.998873, 0.999192, 0.870482, 0.976282, 0.999961, 0.984283, 0.973045, 0.786176, 0.403673, 0.275418, 0.115199, 0.257560, 0.004735, 0.493936, 0.907360, 0.873199, 0.052959, 0.076008, 0.001653, 0.000847, 0.062027, 0.021257, 0.219547, 0.955654, 0.999851, 0.997685, 0.998324, 0.999939, 0.996858, 0.969209, 0.927714] class TestHamiltonAR4(MarkovAutoregression): @classmethod def setup_class(cls): # Results from E-views: # Dependent variable followed by a list of switching regressors: # rgnp c # List of non-switching regressors: # ar(1) ar(2) ar(3) ar(4) # Do not check "Regime specific error variances" # Switching type: Markov # Number of Regimes: 2 # Probability regressors: # c # Method SWITCHREG # Sample 1951q1 1984q4 true = { 'params': np.r_[0.754673, 0.095915, -0.358811, 1.163516, np.exp(-0.262658)**2, 0.013486, -0.057521, -0.246983, -0.212923], 'llf': -181.26339, 'llf_fit': -181.26339, 'llf_fit_em': -183.85444, 'bse_oim': np.r_[.0965189, .0377362, .2645396, .0745187, np.nan, .1199942, .137663, .1069103, .1105311, ] } super(TestHamiltonAR4, cls).setup_class( true, rgnp, k_regimes=2, order=4, switching_ar=False) def test_filtered_regimes(self): res = self.result assert_equal(len(res.filtered_marginal_probabilities[:, 1]), self.model.nobs) assert_allclose(res.filtered_marginal_probabilities[:, 1], hamilton_ar4_filtered, atol=1e-5) def test_smoothed_regimes(self): res = self.result assert_equal(len(res.smoothed_marginal_probabilities[:, 1]), self.model.nobs) assert_allclose(res.smoothed_marginal_probabilities[:, 1], hamilton_ar4_smoothed, atol=1e-5) def test_bse(self): # Cannot compare middle element of bse because we estimate sigma^2 # rather than sigma bse = self.result.cov_params_approx.diagonal()**0.5 assert_allclose(bse[:4], self.true['bse_oim'][:4], atol=1e-6) assert_allclose(bse[6:], self.true['bse_oim'][6:], atol=1e-6) class TestHamiltonAR2Switch(MarkovAutoregression): # Results from Stata, see http://www.stata.com/manuals14/tsmswitch.pdf @classmethod def setup_class(cls): path = os.path.join(current_path, 'results', 'results_predict_rgnp.csv') results = pd.read_csv(path) true = { 'params': np.r_[.3812383, .3564492, -.0055216, 1.195482, .6677098**2, .3710719, .4621503, .7002937, -.3206652], 'llf': -179.32354, 'llf_fit': -179.38684, 'llf_fit_em': -184.99606, 'bse_oim': np.r_[.1424841, .0994742, .2057086, .1225987, np.nan, .1754383, .1652473, .187409, .1295937], 'smoothed0': results.iloc[3:]['switchar2_sm1'], 'smoothed1': results.iloc[3:]['switchar2_sm2'], 'predict0': results.iloc[3:]['switchar2_yhat1'], 'predict1': results.iloc[3:]['switchar2_yhat2'], 'predict_predicted': results.iloc[3:]['switchar2_pyhat'], 'predict_filtered': results.iloc[3:]['switchar2_fyhat'], 'predict_smoothed': results.iloc[3:]['switchar2_syhat'], } super(TestHamiltonAR2Switch, cls).setup_class( true, rgnp, k_regimes=2, order=2) def test_smoothed_marginal_probabilities(self): assert_allclose(self.result.smoothed_marginal_probabilities[:, 0], self.true['smoothed0'], atol=1e-6) assert_allclose(self.result.smoothed_marginal_probabilities[:, 1], self.true['smoothed1'], atol=1e-6) def test_predict(self): # Smoothed actual = self.model.predict( self.true['params'], probabilities='smoothed') assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6) actual = self.model.predict( self.true['params'], probabilities=None) assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6) actual = self.result.predict(probabilities='smoothed') assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6) actual = self.result.predict(probabilities=None) assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6) def test_bse(self): # Cannot compare middle element of bse because we estimate sigma^2 # rather than sigma bse = self.result.cov_params_approx.diagonal()**0.5 assert_allclose(bse[:4], self.true['bse_oim'][:4], atol=1e-7) assert_allclose(bse[6:], self.true['bse_oim'][6:], atol=1e-7) hamilton_ar1_switch_filtered = [ 0.840288, 0.730337, 0.900234, 0.596492, 0.921618, 0.983828, 0.959039, 0.898366, 0.477335, 0.251089, 0.049367, 0.386782, 0.942868, 0.965632, 0.982857, 0.897603, 0.946986, 0.916413, 0.640912, 0.849296, 0.778371, 0.954420, 0.929906, 0.723930, 0.891196, 0.061163, 0.004806, 0.977369, 0.997871, 0.977950, 0.896580, 0.963246, 0.430539, 0.906586, 0.974589, 0.514506, 0.683457, 0.276571, 0.956475, 0.966993, 0.971618, 0.987019, 0.916670, 0.921652, 0.930265, 0.655554, 0.965858, 0.964981, 0.976790, 0.868267, 0.983240, 0.852052, 0.919150, 0.854467, 0.987868, 0.935840, 0.958138, 0.979535, 0.956541, 0.716322, 0.919035, 0.866437, 0.899609, 0.914667, 0.976448, 0.867252, 0.953075, 0.977850, 0.884242, 0.688299, 0.968461, 0.737517, 0.870674, 0.559413, 0.380339, 0.582813, 0.941311, 0.240020, 0.999349, 0.619258, 0.828343, 0.729726, 0.991009, 0.966291, 0.899148, 0.970798, 0.977684, 0.695877, 0.637555, 0.915824, 0.434600, 0.771277, 0.113756, 0.144002, 0.008466, 0.994860, 0.993173, 0.961722, 0.978555, 0.789225, 0.836283, 0.940383, 0.968368, 0.974473, 0.980248, 0.518125, 0.904086, 0.993023, 0.802936, 0.920906, 0.685445, 0.666524, 0.923285, 0.643861, 0.938184, 0.008862, 0.945406, 0.990061, 0.991500, 0.486669, 0.805039, 0.089036, 0.025067, 0.863309, 0.352784, 0.733295, 0.928710, 0.984257, 0.926597, 0.959887, 0.984051, 0.872682, 0.824375, 0.780157] hamilton_ar1_switch_smoothed = [ 0.900074, 0.758232, 0.914068, 0.637248, 0.901951, 0.979905, 0.958935, 0.888641, 0.261602, 0.148761, 0.056919, 0.424396, 0.932184, 0.954962, 0.983958, 0.895595, 0.949519, 0.923473, 0.678898, 0.848793, 0.807294, 0.958868, 0.942936, 0.809137, 0.960892, 0.032947, 0.007127, 0.967967, 0.996551, 0.979278, 0.896181, 0.987462, 0.498965, 0.908803, 0.986893, 0.488720, 0.640492, 0.325552, 0.951996, 0.959703, 0.960914, 0.986989, 0.916779, 0.924570, 0.935348, 0.677118, 0.960749, 0.958966, 0.976974, 0.838045, 0.986562, 0.847774, 0.908866, 0.821110, 0.984965, 0.915302, 0.938196, 0.976518, 0.973780, 0.744159, 0.922006, 0.873292, 0.904035, 0.917547, 0.978559, 0.870915, 0.948420, 0.979747, 0.884791, 0.711085, 0.973235, 0.726311, 0.828305, 0.446642, 0.411135, 0.639357, 0.973151, 0.141707, 0.999805, 0.618207, 0.783239, 0.672193, 0.987618, 0.964655, 0.877390, 0.962437, 0.989002, 0.692689, 0.699370, 0.937934, 0.522535, 0.824567, 0.058746, 0.146549, 0.009864, 0.994072, 0.992084, 0.956945, 0.984297, 0.795926, 0.845698, 0.935364, 0.963285, 0.972767, 0.992168, 0.528278, 0.826349, 0.996574, 0.811431, 0.930873, 0.680756, 0.721072, 0.937977, 0.731879, 0.996745, 0.016121, 0.951187, 0.989820, 0.996968, 0.592477, 0.889144, 0.036015, 0.040084, 0.858128, 0.418984, 0.746265, 0.907990, 0.980984, 0.900449, 0.934741, 0.986807, 0.872818, 0.812080, 0.780157] class TestHamiltonAR1Switch(MarkovAutoregression): @classmethod def setup_class(cls): # Results from E-views: # Dependent variable followed by a list of switching regressors: # rgnp c ar(1) # List of non-switching regressors: # Do not check "Regime specific error variances" # Switching type: Markov # Number of Regimes: 2 # Probability regressors: # c # Method SWITCHREG # Sample 1951q1 1984q4 true = { 'params': np.r_[0.85472458, 0.53662099, 1.041419, -0.479157, np.exp(-0.231404)**2, 0.243128, 0.713029], 'llf': -186.7575, 'llf_fit': -186.7575, 'llf_fit_em': -189.25446 } super(TestHamiltonAR1Switch, cls).setup_class( true, rgnp, k_regimes=2, order=1) def test_filtered_regimes(self): assert_allclose(self.result.filtered_marginal_probabilities[:, 0], hamilton_ar1_switch_filtered, atol=1e-5) def test_smoothed_regimes(self): assert_allclose(self.result.smoothed_marginal_probabilities[:, 0], hamilton_ar1_switch_smoothed, atol=1e-5) def test_expected_durations(self): expected_durations = [6.883477, 1.863513] assert_allclose(self.result.expected_durations, expected_durations, atol=1e-5) hamilton_ar1_switch_tvtp_filtered = [ 0.999996, 0.999211, 0.999849, 0.996007, 0.999825, 0.999991, 0.999981, 0.999819, 0.041745, 0.001116, 1.74e-05, 0.000155, 0.999976, 0.999958, 0.999993, 0.999878, 0.999940, 0.999791, 0.996553, 0.999486, 0.998485, 0.999894, 0.999765, 0.997657, 0.999619, 0.002853, 1.09e-05, 0.999884, 0.999996, 0.999997, 0.999919, 0.999987, 0.989762, 0.999807, 0.999978, 0.050734, 0.010660, 0.000217, 0.006174, 0.999977, 0.999954, 0.999995, 0.999934, 0.999867, 0.999824, 0.996783, 0.999941, 0.999948, 0.999981, 0.999658, 0.999994, 0.999753, 0.999859, 0.999330, 0.999993, 0.999956, 0.999970, 0.999996, 0.999991, 0.998674, 0.999869, 0.999432, 0.999570, 0.999600, 0.999954, 0.999499, 0.999906, 0.999978, 0.999712, 0.997441, 0.999948, 0.998379, 0.999578, 0.994745, 0.045936, 0.006816, 0.027384, 0.000278, 1.000000, 0.996382, 0.999541, 0.998130, 0.999992, 0.999990, 0.999860, 0.999986, 0.999997, 0.998520, 0.997777, 0.999821, 0.033353, 0.011629, 6.95e-05, 4.52e-05, 2.04e-06, 0.999963, 0.999977, 0.999949, 0.999986, 0.999240, 0.999373, 0.999858, 0.999946, 0.999972, 0.999991, 0.994039, 0.999817, 0.999999, 0.999715, 0.999924, 0.997763, 0.997944, 0.999825, 0.996592, 0.695147, 0.000161, 0.999665, 0.999928, 0.999988, 0.992742, 0.374214, 0.001569, 2.16e-05, 0.000941, 4.32e-05, 0.000556, 0.999955, 0.999993, 0.999942, 0.999973, 0.999999, 0.999919, 0.999438, 0.998738] hamilton_ar1_switch_tvtp_smoothed = [ 0.999997, 0.999246, 0.999918, 0.996118, 0.999740, 0.999990, 0.999984, 0.999783, 0.035454, 0.000958, 1.53e-05, 0.000139, 0.999973, 0.999939, 0.999994, 0.999870, 0.999948, 0.999884, 0.997243, 0.999668, 0.998424, 0.999909, 0.999860, 0.998037, 0.999559, 0.002533, 1.16e-05, 0.999801, 0.999993, 0.999997, 0.999891, 0.999994, 0.990096, 0.999753, 0.999974, 0.048495, 0.009289, 0.000542, 0.005991, 0.999974, 0.999929, 0.999995, 0.999939, 0.999880, 0.999901, 0.996221, 0.999937, 0.999935, 0.999985, 0.999450, 0.999995, 0.999768, 0.999897, 0.998930, 0.999992, 0.999949, 0.999954, 0.999995, 0.999994, 0.998687, 0.999902, 0.999547, 0.999653, 0.999538, 0.999966, 0.999485, 0.999883, 0.999982, 0.999831, 0.996940, 0.999968, 0.998678, 0.999780, 0.993895, 0.055372, 0.020421, 0.022913, 0.000127, 1.000000, 0.997072, 0.999715, 0.996893, 0.999990, 0.999991, 0.999811, 0.999978, 0.999998, 0.999100, 0.997866, 0.999787, 0.034912, 0.009932, 5.91e-05, 3.99e-05, 1.77e-06, 0.999954, 0.999976, 0.999932, 0.999991, 0.999429, 0.999393, 0.999845, 0.999936, 0.999961, 0.999995, 0.994246, 0.999570, 1.000000, 0.999702, 0.999955, 0.998611, 0.998019, 0.999902, 0.998486, 0.673991, 0.000205, 0.999627, 0.999902, 0.999994, 0.993707, 0.338707, 0.001359, 2.36e-05, 0.000792, 4.47e-05, 0.000565, 0.999932, 0.999993, 0.999931, 0.999950, 0.999999, 0.999940, 0.999626, 0.998738] expected_durations = [ [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [1.223309, 1864.084], [1.223309, 1864.084], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [1.223309, 1864.084], [1.223309, 1864.084], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084], [1.223309, 1864.084], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391], [710.7573, 1.000391]] class TestHamiltonAR1SwitchTVTP(MarkovAutoregression): @classmethod def setup_class(cls): # Results from E-views: # Dependent variable followed by a list of switching regressors: # rgnp c ar(1) # List of non-switching regressors: # Do not check "Regime specific error variances" # Switching type: Markov # Number of Regimes: 2 # Probability regressors: # c recession # Method SWITCHREG # Sample 1951q1 1984q4 true = { 'params': np.r_[6.564923, 7.846371, -8.064123, -15.37636, 1.027190, -0.719760, np.exp(-0.217003)**2, 0.161489, 0.022536], 'llf': -163.914049, 'llf_fit': -161.786477, 'llf_fit_em': -163.914049 } exog_tvtp = np.c_[np.ones(len(rgnp)), rec] super(TestHamiltonAR1SwitchTVTP, cls).setup_class( true, rgnp, k_regimes=2, order=1, exog_tvtp=exog_tvtp) @pytest.mark.skip # TODO(ChadFulton): give reason for skip def test_fit_em(self): pass def test_filtered_regimes(self): assert_allclose(self.result.filtered_marginal_probabilities[:, 0], hamilton_ar1_switch_tvtp_filtered, atol=1e-5) def test_smoothed_regimes(self): assert_allclose(self.result.smoothed_marginal_probabilities[:, 0], hamilton_ar1_switch_tvtp_smoothed, atol=1e-5) def test_expected_durations(self): assert_allclose(self.result.expected_durations, expected_durations, rtol=1e-5, atol=1e-7) class TestFilardo(MarkovAutoregression): @classmethod def setup_class(cls): path = os.path.join(current_path, 'results', 'mar_filardo.csv') cls.mar_filardo = pd.read_csv(path) true = { 'params': np.r_[4.35941747, -1.6493936, 1.7702123, 0.9945672, 0.517298, -0.865888, np.exp(-0.362469)**2, 0.189474, 0.079344, 0.110944, 0.122251], 'llf': -586.5718, 'llf_fit': -586.5718, 'llf_fit_em': -586.5718 } endog = cls.mar_filardo['dlip'].iloc[1:].values exog_tvtp = add_constant( cls.mar_filardo['dmdlleading'].iloc[:-1].values) super(TestFilardo, cls).setup_class( true, endog, k_regimes=2, order=4, switching_ar=False, exog_tvtp=exog_tvtp) @pytest.mark.skip # TODO(ChadFulton): give reason for skip def test_fit(self, **kwargs): pass @pytest.mark.skip # TODO(ChadFulton): give reason for skip def test_fit_em(self): pass def test_filtered_regimes(self): assert_allclose(self.result.filtered_marginal_probabilities[:, 0], self.mar_filardo['filtered_0'].iloc[5:], atol=1e-5) def test_smoothed_regimes(self): assert_allclose(self.result.smoothed_marginal_probabilities[:, 0], self.mar_filardo['smoothed_0'].iloc[5:], atol=1e-5) def test_expected_durations(self): assert_allclose(self.result.expected_durations, self.mar_filardo[['duration0', 'duration1']].iloc[5:], rtol=1e-5, atol=1e-7) class TestFilardoPandas(MarkovAutoregression): @classmethod def setup_class(cls): path = os.path.join(current_path, 'results', 'mar_filardo.csv') cls.mar_filardo = pd.read_csv(path) cls.mar_filardo.index = pd.date_range('1948-02-01', '1991-04-01', freq='MS') true = { 'params': np.r_[4.35941747, -1.6493936, 1.7702123, 0.9945672, 0.517298, -0.865888, np.exp(-0.362469)**2, 0.189474, 0.079344, 0.110944, 0.122251], 'llf': -586.5718, 'llf_fit': -586.5718, 'llf_fit_em': -586.5718 } endog = cls.mar_filardo['dlip'].iloc[1:] exog_tvtp = add_constant( cls.mar_filardo['dmdlleading'].iloc[:-1]) super(TestFilardoPandas, cls).setup_class( true, endog, k_regimes=2, order=4, switching_ar=False, exog_tvtp=exog_tvtp) @pytest.mark.skip # TODO(ChadFulton): give reason for skip def test_fit(self, **kwargs): pass @pytest.mark.skip # TODO(ChadFulton): give reason for skip def test_fit_em(self): pass def test_filtered_regimes(self): assert_allclose(self.result.filtered_marginal_probabilities[0], self.mar_filardo['filtered_0'].iloc[5:], atol=1e-5) def test_smoothed_regimes(self): assert_allclose(self.result.smoothed_marginal_probabilities[0], self.mar_filardo['smoothed_0'].iloc[5:], atol=1e-5) def test_expected_durations(self): assert_allclose(self.result.expected_durations, self.mar_filardo[['duration0', 'duration1']].iloc[5:], rtol=1e-5, atol=1e-7) statsmodels-0.12.2/statsmodels/tsa/regime_switching/tests/test_markov_regression.py000066400000000000000000002106451400612667500311470ustar00rootroot00000000000000""" Tests for Markov Regression models Author: Chad Fulton License: BSD-3 """ import os import warnings import numpy as np from numpy.testing import assert_allclose, assert_raises import pandas as pd import pytest from statsmodels.tsa.regime_switching import (markov_switching, markov_regression) current_path = os.path.dirname(os.path.abspath(__file__)) # See https://www.stata-press.com/data/r14/usmacro fedfunds = [1.03, 0.99, 1.34, 1.5, 1.94, 2.36, 2.48, 2.69, 2.81, 2.93, 2.93, 3.0, 3.23, 3.25, 1.86, 0.94, 1.32, 2.16, 2.57, 3.08, 3.58, 3.99, 3.93, 3.7, 2.94, 2.3, 2.0, 1.73, 1.68, 2.4, 2.46, 2.61, 2.85, 2.92, 2.97, 2.96, 3.33, 3.45, 3.46, 3.49, 3.46, 3.58, 3.97, 4.08, 4.07, 4.17, 4.56, 4.91, 5.41, 5.56, 4.82, 3.99, 3.89, 4.17, 4.79, 5.98, 5.94, 5.92, 6.57, 8.33, 8.98, 8.94, 8.57, 7.88, 6.7, 5.57, 3.86, 4.56, 5.47, 4.75, 3.54, 4.3, 4.74, 5.14, 6.54, 7.82, 10.56, 10.0, 9.32, 11.25, 12.09, 9.35, 6.3, 5.42, 6.16, 5.41, 4.83, 5.2, 5.28, 4.87, 4.66, 5.16, 5.82, 6.51, 6.76, 7.28, 8.1, 9.58, 10.07, 10.18, 10.95, 13.58, 15.05, 12.69, 9.84, 15.85, 16.57, 17.78, 17.58, 13.59, 14.23, 14.51, 11.01, 9.29, 8.65, 8.8, 9.46, 9.43, 9.69, 10.56, 11.39, 9.27, 8.48, 7.92, 7.9, 8.1, 7.83, 6.92, 6.21, 6.27, 6.22, 6.65, 6.84, 6.92, 6.66, 7.16, 7.98, 8.47, 9.44, 9.73, 9.08, 8.61, 8.25, 8.24, 8.16, 7.74, 6.43, 5.86, 5.64, 4.82, 4.02, 3.77, 3.26, 3.04, 3.04, 3.0, 3.06, 2.99, 3.21, 3.94, 4.49, 5.17, 5.81, 6.02, 5.8, 5.72, 5.36, 5.24, 5.31, 5.28, 5.28, 5.52, 5.53, 5.51, 5.52, 5.5, 5.53, 4.86, 4.73, 4.75, 5.09, 5.31, 5.68, 6.27, 6.52, 6.47, 5.59, 4.33, 3.5, 2.13, 1.73, 1.75, 1.74, 1.44, 1.25, 1.25, 1.02, 1.0, 1.0, 1.01, 1.43, 1.95, 2.47, 2.94, 3.46, 3.98, 4.46, 4.91, 5.25, 5.25, 5.26, 5.25, 5.07, 4.5, 3.18, 2.09, 1.94, 0.51, 0.18, 0.18, 0.16, 0.12, 0.13, 0.19, 0.19, 0.19] # See https://www.stata-press.com/data/r14/usmacro ogap = [-0.53340107, 0.72974336, 2.93532324, 3.58194304, 4.15760183, 4.28775644, 3.01683831, 2.64185619, 1.82473528, 2.37461162, 2.39338565, 1.24197006, 1.1370815, -1.28657401, -4.46665335, -4.79258966, -3.06711817, -1.3212384, -0.54485309, 0.86588413, -0.2469136, -0.75004685, 0.7417022, -0.71350163, -1.5151515, -3.80444455, -4.02601957, -3.17873883, -2.48841596, -1.42372882, -0.61779928, -0.6430338, -0.73277968, -1.38330388, -1.31537247, -0.95626277, 0., -0.15248552, 0.93233085, 1.03888392, 1.27174389, 0.63400578, 2.13007665, 2.44789481, 3.37605071, 4.72771597, 6.20753956, 5.39234877, 5.0825758, 4.8605876, 4.65116262, 3.52755141, 3.35122228, 3.09326482, 4.10191917, 4.69641066, 4.38452244, 3.79841614, 4.38338947, 3.63766766, 3.24129653, 1.84967709, 0.75554705, -0.02802691, -0.03673432, -1.90527546, -0.14918824, -0.42940569, -0.46382189, -0.97892815, -0.12142799, 1.37281513, 1.5143193, 2.47730422, 3.9762032, 4.08987427, 2.62857127, 2.90107131, 0.97277576, 0.42547619, -1.60488391, -2.97784758, -4.98650694, -5.03382635, -4.25698328, -3.74993205, -2.39661908, -2.41223454, -2.66694117, -2.62232494, -2.29969597, -1.38809109, -0.67855304, -1.08100712, -1.82682908, 0.92868561, 0.87040615, 1.32669306, 0.56407404, -0.13848817, -0.13089494, -0.58975571, -1.00534534, -3.55482054, -4.20365095, -2.97225475, -1.57762408, -2.77206445, -2.32418823, -4.01929235, -6.25393772, -6.46356869, -7.47437572, -8.06377602, -7.57157278, -6.14639282, -5.00167227, -3.74511886, -2.54788184, -1.64858043, -1.47994602, -1.44707143, -1.31824112, -1.20102882, -0.57691002, -0.64480144, -0.57239723, -0.93083948, -0.8392899, -1.19972074, -1.18918467, -0.87174636, -0.78151888, 0.10762761, -0.10596547, 0.40488175, 0.17958413, 0.67704558, 0.99767941, 1.00495291, 0.98304421, 0.47067845, 0.80427116, 0.45058677, -0.26300991, -1.84629929, -2.99437666, -2.90482664, -3.09490418, -3.32399321, -2.87384319, -2.47262239, -2.19618678, -1.91843009, -2.46574545, -2.58180451, -2.72212362, -2.17548561, -1.96046102, -1.3287729, -1.42521954, -1.04951096, -1.47037697, -1.87099183, -1.72912872, -1.76828432, -1.85885167, -0.9193368, -0.95776832, -0.62119246, -0.53508854, -0.04090983, 0.47511154, 0.41246772, 0.57928383, 0.67604625, 1.1378212, 1.96481478, 2.05066752, 1.93714142, 2.34412026, 3.16807413, 2.57455897, 3.59218717, 2.79711962, 2.41787243, 1.19362748, 0.82524049, -0.36692095, -1.00542021, -0.89346135, -1.23166943, -1.56921482, -2.29188299, -2.56877398, -2.37549472, -1.4183135, -1.00017595, -1.03901041, -0.86736482, -0.63541794, -0.38296556, 0.11404825, 0.07249562, 0.30608681, 0.27121997, 0.90333837, 0.595429, 0.08057959, 0.25154814, -0.27741581, -0.14053501, -0.06035376, -0.2722317, -1.5122633, -1.5272249, -2.5325017, -5.14671373, -6.88223982, -7.36753035, -7.43927145, -6.89403868, -6.8306222, -6.26507998, -5.93287086, -5.59370756] # See https://www.stata-press.com/data/r14/usmacro inf = [np.nan, np.nan, np.nan, np.nan, -0.2347243, 0.37373397, 0.25006533, 1.04645514, 2.01665616, 2.58033299, 3.41399837, 3.60986805, 3.46304512, 3.08529949, 3.45609665, 3.27347994, 2.29982662, 1.91197193, 0.89083761, 0.390598, 0.96842253, 1.47531354, 1.39343977, 1.82488036, 1.35991514, 1.39598227, 1.50695646, 0.8690359, 1.20648873, 0.70517123, 0.89477205, 1.30740857, 1.20212376, 1.30043352, 1.22895002, 1.03573787, 1.36272156, 1.39236343, 1.48636675, 1.46398985, 1.07421875, 1.26611042, 1.1639185, 1.64622331, 1.71658623, 1.78565705, 2.41930342, 2.6897428, 3.27391338, 3.5685041, 2.87078357, 2.56671929, 2.70717716, 2.99242783, 3.74010396, 4.11855173, 4.47761202, 4.62397051, 4.87426901, 5.50198364, 5.52285719, 5.83354473, 6.22577858, 6.03848171, 5.68597221, 5.60000038, 4.81102371, 4.31496382, 4.27074528, 3.53535342, 3.50587225, 3.22580624, 3.02948403, 3.33414626, 4.1129365, 5.60817289, 6.83709764, 8.41692829, 9.91564655, 10.54788017, 11.45758915, 12.04798317, 11.13530636, 9.53939915, 8.67963028, 7.38337183, 6.34047985, 6.01503754, 5.58903217, 5.18573475, 5.90339899, 6.79609919, 6.57417107, 6.59522104, 6.47466183, 7.02936935, 8.02397346, 8.9289465, 9.78376389, 10.75433922, 11.72252846, 12.64148235, 14.20953751, 14.42577076, 12.93487072, 12.53929329, 11.26111889, 9.87392902, 10.85386753, 9.5831337, 7.58190918, 6.90676928, 5.81573057, 4.44292784, 3.59408045, 3.29905081, 2.52680969, 3.23384356, 4.62551022, 4.40519285, 4.29570436, 4.1543026, 3.64175439, 3.60676312, 3.35249043, 3.5137701, 3.1053853, 1.67858768, 1.66821122, 1.34587157, 2.03802228, 3.69979739, 4.16317225, 4.40493536, 3.96511626, 3.97994113, 4.1420536, 4.3066597, 4.67509222, 5.15961123, 4.70588255, 4.62759781, 5.23231459, 4.58372736, 5.56420517, 6.27646685, 5.25958157, 4.84686804, 3.85226536, 2.96485686, 2.89388347, 3.07301927, 3.07467055, 3.12198234, 3.17306924, 3.12524581, 2.8174715, 2.76977897, 2.53936958, 2.38237333, 2.85493255, 2.60332823, 2.84049082, 3.09557867, 2.66420412, 2.62607908, 2.78390908, 2.8270874, 2.8999064, 3.23162007, 2.94453382, 2.30179024, 2.22504783, 1.89075232, 1.48277605, 1.58312511, 1.59639311, 1.5253576, 1.68703699, 2.11280179, 2.34625125, 2.61982656, 3.25799918, 3.29342604, 3.46889949, 3.44350553, 3.40975904, 3.32491398, 2.67803454, 1.87507534, 1.23194993, 1.31765401, 1.57628381, 2.25352097, 2.97640777, 2.00593972, 2.21688938, 2.00165296, 1.81766617, 2.78586531, 2.67522621, 3.38513398, 3.0353508, 2.92293549, 3.81956744, 3.6745038, 3.69086194, 3.92426181, 3.34028482, 1.96539891, 2.43147993, 2.66511655, 2.34880662, 4.03147316, 4.13719845, 4.31058264, 5.25250196, 1.59580016, -0.1842365, -0.94229329, -1.60695589, 1.48749816, 2.33687115, 1.78588998, 1.22873163, 1.21550024] # See https://www.stata-press.com/data/r14/snp500 areturns = [1.60864139, 0.6581642, 0.91177338, 1.88970506, 0.76378739, 0.10790635, 0.29509732, 0.16913767, 1.30772412, 0.85901159, 0.92307973, 0.9833895, 0.9116146, 2.58575296, 0.36441925, 1.89720023, 0.65161127, 1.17255056, 0.53518051, 0.00534112, 1.25064528, 2.00023437, 0.79801333, 1.42980587, 0.02078664, 2.31948757, 2.78705025, 1.36003578, 0.15257211, 0.30815724, 0.40030465, 0.89941251, 0.36925647, 0.75660467, 0.87896836, 1.07261622, 0.1137321, 1.32838523, 1.03085732, 1.33930087, 0.66706187, 0.94959277, 1.07173061, 0.80687243, 1.35347247, 1.56781077, 0.71599048, 0.50293237, 0.33926481, 2.94415998, 0.72026408, 0.28967711, 1.05362082, 0.3702977, 2.05277085, 0.49342933, 0.03423685, 0.34392089, 1.01741159, 1.43457139, 0.03759775, 1.54626679, 1.07742834, 0.28664029, 0.72592038, 0.91093767, 0.06915179, 0.88005662, 0.47802091, 1.2907486, 0.57604247, 0.71046084, 0.81753206, 0.26241753, 2.57300162, 0.16590172, 0.2918649, 0.96136051, 1.6711514, 0.94229084, 1.83614326, 0.28854966, 0.35050908, 0.04593768, 0.07599987, 0.09888303, 0.12907109, 2.0099268, 0.23006552, 1.18803704, 0.99970037, 1.32702613, 0.45646569, 1.43720019, 0.04425191, 0.53156406, 0.45951003, 1.26583254, 0.26994073, 0.1238014, 0.53068936, 0.21927625, 0.73882329, 0.13153869, 0.97837049, 2.36890459, 2.29313374, 0.75562358, 0.08656374, 2.4979558, 0.64189923, 0.22916116, 2.27840376, 0.46641645, 2.02508688, 1.25530422, 1.27711689, 0.07773363, 0.23380435, 1.58663058, 0.19108967, 0.52218717, 0.18055375, 1.18262017, 0.47418493, 0.88282752, 0.98944044, 1.04560554, 0.65470523, 0.2604697, 0.14658713, 0.77688956, 1.10911596, 0.69967973, 1.04578161, 0.29641318, 0.98087156, 0.46531865, 0.11846001, 0.44440377, 1.11066306, 0.02238905, 0.19865835, 1.48028743, 0.27695858, 0.9391492, 1.70575404, 2.94507742, 0.35386264, 0.72816408, 1.80369282, 0.12440593, 1.04197288, 1.2957871, 1.35031664, 0.55384284, 1.13915396, 0.29186234, 1.21344364, 0.23005128, 0.85578758, 1.80613887, 1.55996382, 1.46395147, 0.59826899, 0.65880769, 1.68974137, 1.12778795, 4.19566727, 0.14379959, 2.09945345, 0.29264972, 1.25936544, 0.84738803, 0.54094779, 2.27655816, 1.48392296, 1.13808954, 1.16038692, 0.46204364, 2.09433556, 1.16782069, 2.0192802, 2.6190269, 1.63471925, 0.25279006, 2.64083171, 1.64290273, 2.42852569, 1.54714262, 1.14975035, 3.59362221, 1.16689992, 5.11030865, 1.81326246, 0.93489766, 1.38605726, 0.53841805, 1.02298951, 2.03038621, 2.8340385, 0.13691254, 3.18769765, 0.23076122, 1.95332313, 1.63122225, 2.66484141, 0.86377442, 1.1782372, 0.57231718, 1.11979997, 2.07001758, 0.08726255, 1.71130466, 1.04979181, 1.9825747, 3.43235064, 1.50204682, 1.75699294, 2.56816769, 0.75786251, 0.93131924, 1.45494628, 0.49975556, 0.32756457, 0.47183469, 3.3737793, 2.25759649, 0.34138981, 3.09048033, 10.32189178, 10.15319347, 0.12398402, 4.65263939, 7.62032652, 7.04052448, 4.55579329, 3.52704573, 3.38968754, 3.00466204, 0.46617937, 1.42808878, 1.00660408, 4.65142584, 5.20996618, 4.80301046, 0.99780792, 1.15280604, 1.87296033, 4.60985804, 5.41294718, 6.06733084, 3.18375754, 10.0548315, 4.22182512, 1.24640226, 2.66358495, 2.60049844, 0.00352026, 1.02208447, 4.09924603, 1.27764511, 0.90124834, 0.5303241, 3.84383249, 1.24640775, 1.39796948, 2.34609175, 1.7742399, 3.56689548, 1.27681601, 5.32056713, 3.19770503, 1.89575887, 0.59274858, 0.64010525, 2.65920091, 0.81912726, 0.4868626, 3.13063931, 1.3960743, 1.03451502, 1.28983963, 3.27489519, 1.41772103, 2.00014663, 2.02787399, 3.50289273, 1.65296888, 0.02450024, 0.04084374, 0.17252181, 0.78132814, 0.20216605, 1.48436368, 0.3301619, 1.12080252, 0.00699845, 3.87074757, 0.84627002, 2.26680374, 2.07992935, 1.62452054, 0.66078293, 2.26608515, 1.58540344, 0.98763937, 0.25370923, 1.2576412, 1.07146478, 0.48786601, 0.02327727, 1.29385257, 3.52217674, 1.05305433, 5.13598871, 1.43351507, 2.12951326, 3.03700447, 0.65843326, 4.28524971, 2.3428576, 4.72853422, 0.58606911, 2.70345545, 0.8207835, 0.16228235, 2.80714321, 1.97183621, 0.5928334, 3.61601782, 1.82700455, 1.52638936, 0.72525144, 0.6499536, 1.58741212, 0.72647524, 0.65064299, 0.43771812, 2.68048692, 2.20902133, 0.0988697, 0.31138307, 2.79860616, 1.13209391, 0.91427463, 0.69550049, 0.68990183, 0.65359998, 1.04932129, 0.00310441, 0.48663121, 1.68144464, 0.99051267, 0.22263506, 0.97846323, 0.55040002, 2.56734443, 0.12510587, 2.15363359, 1.18440747, 0.66974002, 0.48981813, 2.08285856, 1.03952742, 1.00747502, 0.52523118, 0.81593889, 0.22168602, 2.73786068, 1.21678591, 0.235705, 0.56248677, 3.66057348, 0.35822684, 0.97550339, 1.21677041, 4.03415823, 9.10342026, 2.24355674, 3.6120553, 4.36456299, 0.83891636, 1.07712805, 2.28685427, 4.04548168, 1.67408013, 4.57762337, 2.47123241, 1.88890803, 1.62245703, 0.02149973, 0.48483402, 4.40716505, 0.28621164, 4.56798553, 1.6255945, 0.6124717, 2.72943926, 0.80645156, 1.26738918, 0.91451788, 1.59959269, 0.0356785, 1.93719864, 0.42164543, 0.87313241, 0.52508104, 0.44771862, 1.38226497, 1.83891225, 0.00711749, 0.26621303, 2.25254321, 0.27307722, 0.26436633, 1.80608702, 2.29477572, 2.0931437, 2.2915051, 0.82041657, 2.09074521, 1.87793779, 2.15142703, 1.549685, 2.44940472, 0.45297864, 0.35515305, 0.23224437, 1.77138305, 0.98827285, 0.98435384, 0.80031335, 0.49445853, 0.36061874, 2.15444446, 1.92558503, 0.75404048, 0.31921348, 0.32092738, 0.48054051, 0.98650485, 1.1810472, 0.28533801, 3.02953291, 0.16818592, 2.20164418, 0.3911584, 0.6942575, 0.55016953, 0.06157291, 0.19509397, 2.3744297, 0.73775989, 1.12842739, 0.87197775, 0.30168825, 0.71310955, 0.27689508, 1.13476491, 1.60331428, 1.56165123, 0.31513214, 0.02698154, 0.49029687, 0.17265303, 0.36386153, 0.56225872, 1.59077382, 1.84919345, 1.4230696, 1.28607559, 0.57890779, 1.14760947, 0.22594096, 0.43510813, 2.90668917, 1.49716794, 1.9549973, 2.10786223, 0.71948445, 0.19396119, 0.86563414, 0.63498968, 2.3593328, 0.18950517, 0.45737442, 1.82937241, 1.72589195, 0.29414186, 0.74434268, 1.22564518, 2.01444268, 2.32068515, 0.98414028, 0.1174908, 0.22450124, 1.24669802, 0.70953292, 0.21857196, 0.11119327, 0.60500813, 2.04446197, 1.146896, 0.54849964, 0.23402978, 0.32219616, 2.7076292, 1.57800817, 2.08260155, 1.81090641, 0.45189673, 1.01260054, 0.65379494, 0.94736898, 0.37556711, 0.44287458, 0.34578958, 1.48449266, 1.95924711, 0.09717447] # See https://www.stata-press.com/data/r14/mumpspc # Note that this has already been seasonally differenced at period 12 mumpspc = [0.29791319, 0.41467956, 1.13061404, 1.23267496, 1.55659747, 1.41078568, 0.45335022, 0.1419628, 0.03802268, 0.04621375, 0.01261204, 0.04653099, 0.10195512, 0.18079406, -0.1898452, -0.24501109, -0.71440864, -0.82188988, -0.32300544, -0.07680188, -0.0183593, -0.02145147, -0.14442876, -0.13897884, -0.41970083, -0.53978181, -0.81733, -0.77516699, -0.6827361, -0.27539611, 0.01427381, -0.02352227, 0.00223821, -0.00509738, 0.03753691, 0.05826023, 0.34700248, 0.53648567, 0.56336415, 0.73740566, 0.68290168, 0.80702746, 0.47288245, 0.22873914, 0.1323263, 0.18721257, 0.38872179, 0.5571546, 0.62545192, 0.51162982, 1.28496778, 0.91240239, 0.44763446, -0.34558165, -0.32126725, -0.13707247, -0.11812115, -0.14246191, -0.33914241, -0.59595251, -0.76603931, -0.95292002, -1.69234133, -1.44532502, -0.8163048, -0.27210402, -0.05841839, 0.02669862, 0.06060357, 0.04068814, 0.17806116, 0.25716701, 0.58398741, 0.95062274, 2.00101161, 2.05761814, 1.74057662, 0.76864243, 0.3566184, 0.01938879, 0.01129906, -0.00691494, -0.11471844, -0.12220788, -0.46378085, -0.76668882, -1.8203615, -1.80084801, -1.58501005, -0.5208298, -0.27426577, -0.01387694, -0.04243414, -0.07133579, -0.10209171, -0.04366681, -0.06109473, -0.03943163, 0.3148942, 0.57496029, 0.60446811, 0.73262405, 0.37140131, 0.18555129, 0.08227628, 0.11913572, 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-0.10721764, -0.05092888, -0.04520934, 0.01234692, -0.03137775, -0.01226076, 0.00540099, 0.0410589, -0.06418979, -0.23792684, -0.19889355, 0.15362859, 0.19808075, 0.09901999, 0.08383148, 0.1328882, 0.1155429, 0.06566355, 0.13103351, -0.00214756, 0.11389524, 0.60455656, 0.43063915, -0.11312306, 0.00848174, -0.04416773, -0.03458966, -0.11635408, -0.09985384, -0.10910749, -0.03021795, 0.00818002, -0.20921308, -0.42517149, -0.26740992, 0.21723568, 0.19341183, 0.03723881, 0.0800474, 0.1313054, 0.17315492, 0.60613275, 0.88496959, 1.29391515, 1.67872524, 1.1444242, 0.56303668, 0.21097398, -0.29172775, -0.07173294, -0.10594339, -0.13427913, -0.23306128, -0.63841069, -1.01829767, -1.37716746, -1.74518943, -1.48689389, -1.00245714, -0.67613804, -0.09916437, 0.01034598, 0.00059676, -0.02620511, 0.07644644, 0.21421635, 0.36779583, 0.44090557, 0.65572244, 0.69319898, 1.03741217, 1.03150916, 0.48106751, 0.19878693, 0.08993446, 0.10016203, 0.08885416, 0.01304582, 0.01628131, -0.16743767, -0.3889482, -0.25320077, -0.41278255, -0.64387393, -0.24642634, -0.09595281, 0.00029226, -0.03017606, -0.09989822, -0.10608336, -0.12089968, -0.02303368, -0.07865107, -0.07976627, -0.27282, -0.00616729, 0.12162459, 0.01441428, 0.01936977, 0.04224043, 0.10971794, 0.31981739, 0.37371701, 0.21740788, 0.66436541, 0.8377074, 1.11139965, 0.89899027, 0.63889956, 0.26021931, 0.10602421, 0.05764158, 0.03996068, 0.13342732, -0.01258349, 0.20526713, -0.05639255, -0.51611507, -1.10225511, -1.04906142, -0.82814342, -0.32945809, -0.16659749, -0.13606755, -0.156371, -0.44539213, -0.54849428, -0.57765388, -0.46875834, -0.20867264, 0.11628377, 0.30508852, 0.18076879, 0.15996796, 0.09090945, 0.13049443, 0.37585843, 0.47701722, 0.8886351, 1.12534606, 1.0532701, 1.1787746, 1.19929063, 0.67156017, 0.26693404, 0.08880523, -0.0367229, 0.01958427, -0.2178995, -0.35959432, -0.61479795, -1.12488365, -1.24093127, -1.37260103, -1.34592342, -1.1085875, -0.48515847, -0.22466549, -0.01377375, -0.15326615, -0.20697775, -0.21839607, -0.37820193, -0.18108195, -0.23839343, 0.00777894, -0.01658171, 0.14208788, 0.21352491, 0.08116969, 0.0220954, 0.05151662, 0.15160444, 0.46347663, 0.59711337, 0.69609326, 0.85816896, 0.44160861, 0.29913878, 0.35687125, 0.02410281, -0.00206721, 0.04784113, 0.01441422, 0.01972398, -0.19168586, -0.31085777, -0.38792318, -0.59203249, -0.4652282, -0.36413753, -0.41189915, -0.27989927, -0.06170946, -0.09512204, -0.05406281, -0.04524729, -0.19567066, -0.19209856, -0.30510414, -0.21937585, -0.34253049, -0.08848315, 0.0628857, 0.12370691, 0.08033729, 0.02536885, 0.06512444, -0.00683796, 0.01617461, 0.09414208, 0.17485267, 0.01436073, 0.15278709, 0.21909434, -0.13190985, 0.1297549, 0.00458425, 0.00097814, 0.0419029, 0.09299085, 0.30784416, 0.3420583, 0.31633973, 0.6052171, 0.59994769, 0.19161701, 0.14463156, -0.00356764, 0.03013593, -0.00030272, -0.04639405, -0.11171955, -0.26541206, -0.46245131, -0.59785151, -0.93805957, -1.02102923, -0.85468853, -0.57457525, -0.43376198, -0.22778665, -0.08325937, -0.07688884, -0.10757375, -0.04266521, -0.07971251, 0.19849321, 0.46367952, 0.45219129, 0.5286305, 0.82308269, 0.62806904, 0.44585282, 0.2649036, 0.18073915, 0.24439827, 0.33583486, 0.36763605, 0.31510991, 0.44708037, 0.27008474, 0.06621343, -0.20664448, -0.34370041, -0.30381745, -0.18254732, -0.16462031, -0.20288868, -0.47805107, -0.42589119, -0.52396262, -0.80304122, -0.54068702, -0.32430774, -0.41455108, -0.18256193, -0.11230741, -0.05113308, -0.00785848, -0.00410898, 0.02002721, 0.04911622, 0.11129829, 0.03739616, 0.23160917, 0.09051466, 0.0703001, 0.15306205, 0.092351, 0.04038295, -0.00022292, -0.0345473, -0.104352, -0.14002147, -0.25555477, -0.15546834, -0.12915748, -0.00736588, 0.18039131, 0.03981721, 0.05406788, -0.00028329, 0.12522104, 0.09731361, 0.29498664, 0.20997131, 0.16853192, 0.07126871, 0.02766478, -0.13036358, -0.26429421, -0.18460721, -0.17133695, -0.06757163, -0.16766661, -0.17020702, -0.26582304, -0.23111637, -0.16535208, -0.13117793, -0.28425765, -0.30206084, -0.16778651, -0.0795947, -0.0456669, -0.01921733, -0.02716412, 0.01525059, 0.01458484, 0.00587094, 0.01239279, -0.03418982, -0.09835899, 0.05628902, 0.00924054] class MarkovRegression(object): @classmethod def setup_class(cls, true, endog, atol=1e-5, rtol=1e-7, **kwargs): cls.model = markov_regression.MarkovRegression(endog, **kwargs) cls.true = true cls.result = cls.model.smooth(cls.true['params']) cls.atol = atol cls.rtol = rtol @pytest.mark.smoke def test_summary(self): self.result.summary() def test_llf(self): assert_allclose(self.result.llf, self.true['llf'], atol=self.atol, rtol=self.rtol) def test_fit(self, **kwargs): # Test fitting against Stata with warnings.catch_warnings(): warnings.simplefilter("ignore") res = self.model.fit(disp=False, **kwargs) assert_allclose(res.llf, self.true['llf_fit'], atol=self.atol, rtol=self.rtol) @pytest.mark.smoke def test_fit_em(self, **kwargs): # Test EM fitting (smoke test) res_em = self.model._fit_em(**kwargs) assert_allclose(res_em.llf, self.true['llf_fit_em'], atol=self.atol, rtol=self.rtol) fedfunds_const_filtered_joint_probabilities = np.array([ [[9.81875427e-01, 9.99977639e-01, 9.99982269e-01, 9.99977917e-01, 9.99961064e-01, 9.99932206e-01, 9.99919386e-01, 9.99894144e-01, 9.99875287e-01, 9.99853807e-01, 9.99852600e-01, 9.99839056e-01, 9.99783848e-01, 9.99774884e-01, 9.99954588e-01, 9.99988082e-01, 9.99982757e-01, 9.99948590e-01, 9.99910525e-01, 9.99825195e-01, 9.99660841e-01, 9.99411534e-01, 9.99435921e-01, 9.99578212e-01, 9.99835797e-01, 9.99931424e-01, 9.99955815e-01, 9.99969158e-01, 9.99971638e-01, 9.99929247e-01, 9.99921198e-01, 9.99904441e-01, 9.99869417e-01, 9.99855264e-01, 9.99845124e-01, 9.99846496e-01, 9.99755048e-01, 9.99708382e-01, 9.99701905e-01, 9.99690188e-01, 9.99700859e-01, 9.99653041e-01, 9.99426220e-01, 9.99320494e-01, 9.99321052e-01, 9.99230758e-01, 9.98727025e-01, 9.97930031e-01, 9.95880407e-01, 9.94433855e-01, 9.97574246e-01, 9.99263821e-01, 9.99459141e-01, 9.99242937e-01, 9.98291614e-01, 9.91580774e-01, 9.89101309e-01, 9.88455096e-01, 9.73457493e-01, 7.07858812e-01, 9.84830417e-02, 5.48777905e-03, 6.48064326e-04, 9.48013715e-04, 1.00281851e-02, 1.69325148e-01, 8.57820523e-01, 9.93211456e-01, 9.94962561e-01, 9.97835285e-01, 9.99559280e-01, 9.99122588e-01, 9.98381004e-01, 9.97159054e-01, 9.81694661e-01, 8.52237392e-01, 2.98185003e-02, 3.80317793e-04, 3.03223798e-05, 3.72338821e-06, 9.81252727e-08, 1.16279423e-06, 2.19178686e-03, 2.54688430e-01, 5.45485941e-01, 8.49963514e-01, 9.79591871e-01, 9.94535520e-01, 9.95920695e-01, 9.97652340e-01, 9.98379085e-01, 9.97097840e-01, 9.92715379e-01, 9.78668900e-01, 9.54978984e-01, 8.70032440e-01, 4.73445558e-01, 1.87649267e-02, 2.26217560e-04, 7.75338336e-06, 1.77410820e-06, 2.00686803e-08, 9.02595322e-11, 2.90324859e-10, 2.76383741e-07, 4.31669137e-09, 6.21472832e-13, 4.82334762e-14, 1.27598134e-14, 3.17409414e-12, 2.61276609e-10, 7.78226008e-11, 5.39702646e-09, 5.20281165e-06, 1.16430050e-04, 2.28275630e-04, 8.20520602e-05, 3.54392208e-05, 2.52690630e-05, 5.71223049e-06, 6.04760361e-07, 3.25802367e-06, 1.49189117e-04, 9.03616681e-04, 2.05169327e-03, 1.79174202e-03, 2.00293091e-03, 8.80162479e-03, 6.98800266e-02, 2.10894169e-01, 3.78257683e-01, 4.16997707e-01, 3.74555143e-01, 3.09162817e-01, 3.19673213e-01, 2.13371614e-01, 5.00408396e-02, 5.65131400e-03, 2.67174854e-04, 2.77281533e-05, 3.81188091e-05, 1.64157087e-04, 4.99719207e-04, 8.42437704e-04, 9.94072768e-04, 1.92236077e-03, 1.77274131e-02, 1.80694204e-01, 5.59064015e-01, 9.22767369e-01, 9.95149639e-01, 9.99418123e-01, 9.99755674e-01, 9.99825956e-01, 9.99829396e-01, 9.99837748e-01, 9.99825597e-01, 9.99839509e-01, 9.99789371e-01, 9.99458023e-01, 9.98857894e-01, 9.97136330e-01, 9.92814933e-01, 9.88571000e-01, 9.89824082e-01, 9.91277010e-01, 9.94688346e-01, 9.96090383e-01, 9.96010189e-01, 9.96126138e-01, 9.96152552e-01, 9.94805484e-01, 9.94365920e-01, 9.94404335e-01, 9.94350015e-01, 9.94473588e-01, 9.94298374e-01, 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4.39360698e-04, 9.96435388e-04, 3.66366176e-03, 1.21697619e-02, 2.12118606e-02, 8.85040895e-03, 6.31975856e-04, 2.36270150e-05, 8.19945322e-07, 7.50841896e-08, 4.48888835e-08, 4.54342381e-08, 3.02100160e-08, 1.58478237e-08, 1.23342395e-08, 9.10969133e-09, 6.55477183e-09, 6.38307937e-09, 6.46757155e-09, 1.13921361e-08, 3.92715328e-08, 1.54492028e-07, 5.69351898e-07, 2.10015832e-06, 8.28479101e-06, 3.11191703e-05, 1.07326014e-04, 3.11263455e-04, 5.09327027e-04, 5.47428437e-04, 5.52354866e-04, 4.31919788e-04, 1.60904664e-04, 1.29332277e-05, 5.04162769e-07, 9.33695004e-08, 1.15650115e-08, 1.13921931e-09, 7.36511886e-10, 7.17294041e-10, 6.62811758e-10, 6.37139329e-10, 6.98642410e-10, 7.56071871e-10, 7.56083358e-10]]]) class TestFedFundsConst(MarkovRegression): # Results from Stata, see http://www.stata.com/manuals14/tsmswitch.pdf @classmethod def setup_class(cls): path = os.path.join(current_path, 'results', 'results_predict_fedfunds.csv') results = pd.read_csv(path) true = { 'params': np.r_[.9820939, .0503587, 3.70877, 9.556793, 2.107562**2], 'llf': -508.63592, 'llf_fit': -508.63592, 'llf_fit_em': -508.65852, 'bse_oim': np.r_[.0104002, .0268434, .1767083, .2999889, np.nan], 'smoothed0': results['const_sm1'], 'smoothed1': results['const_sm2'], 'predict0': results['const_yhat1'], 'predict1': results['const_yhat2'], 'predict_predicted': results['const_pyhat'], 'predict_filtered': results['const_fyhat'], 'predict_smoothed': results['const_syhat'], } super(TestFedFundsConst, cls).setup_class(true, fedfunds, k_regimes=2) def test_filter_output(self, **kwargs): res = self.result assert_allclose(res.filtered_joint_probabilities, fedfunds_const_filtered_joint_probabilities) def test_smoothed_marginal_probabilities(self): assert_allclose(self.result.smoothed_marginal_probabilities[:, 0], self.true['smoothed0'], atol=1e-6) assert_allclose(self.result.smoothed_marginal_probabilities[:, 1], self.true['smoothed1'], atol=1e-6) def test_predict(self): # Predictions conditional on regime (the same no matter which # probabilities are selected) for name in ['predicted', 'filtered', 'smoothed', None]: actual = self.model.predict( self.true['params'], probabilities=name, conditional=True) assert_allclose(actual[0], self.true['predict0'], atol=1e-6) assert_allclose(actual[1], self.true['predict1'], atol=1e-6) # Predicted actual = self.model.predict( self.true['params'], probabilities='predicted') assert_allclose(actual, self.true['predict_predicted'], atol=1e-5) # Filtered actual = self.model.predict( self.true['params'], probabilities='filtered') assert_allclose(self.model.predict(self.true['params'], probabilities='filtered'), self.true['predict_filtered'], atol=1e-5) # Smoothed actual = self.model.predict( self.true['params'], probabilities='smoothed') assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6) actual = self.model.predict( self.true['params'], probabilities=None) assert_allclose(actual, self.true['predict_smoothed'], atol=1e-6) def test_bse(self): # Cannot compare last element of bse because we estimate sigma^2 rather # than sigma^2 bse = self.result.cov_params_approx.diagonal()**0.5 assert_allclose(bse[:-1], self.true['bse_oim'][:-1], atol=1e-7) fedfunds_const_short_filtered_joint_probabilities = np.array([ [[9.81370301e-01, 9.99956215e-01, 9.99995966e-01, 9.99996082e-01, 9.99996179e-01, 9.99996370e-01, 9.99996334e-01, 9.99996045e-01, 9.99996030e-01, 9.99996030e-01], [1.78929069e-02, 3.78065881e-05, 3.06546640e-07, 1.91118379e-07, 1.91095611e-07, 1.86129447e-07, 1.76579974e-07, 1.78918351e-07, 1.93625709e-07, 1.93628651e-07]], [[3.71038873e-05, 5.75327472e-06, 3.72600443e-06, 3.72600486e-06, 3.62917375e-06, 3.44299546e-06, 3.48862495e-06, 3.77538503e-06, 3.77538498e-06, 3.77538498e-06], [6.99688113e-04, 2.24977302e-07, 1.18135050e-09, 7.36520203e-10, 7.17294043e-10, 6.62811758e-10, 6.37139329e-10, 6.98642410e-10, 7.56071871e-10, 7.56083358e-10]]]) fedfunds_const_short_predicted_joint_probabilities = np.array([ [[[7.11514435e-01, 9.63797786e-01, 9.82050899e-01, 9.82089938e-01, 9.82090052e-01, 9.82090147e-01, 9.82090335e-01, 9.82090300e-01, 9.82090016e-01, 9.82090001e-01], [1.29727398e-02, 1.75725147e-02, 3.71296195e-05, 3.01057585e-07, 1.87696195e-07, 1.87673833e-07, 1.82796594e-07, 1.73418115e-07, 1.75714621e-07, 1.90158628e-07]], [[6.65201476e-04, 1.86850353e-06, 2.89727435e-07, 1.87636739e-07, 1.87636761e-07, 1.82760472e-07, 1.73384775e-07, 1.75682617e-07, 1.90123482e-07, 1.90123479e-07], [1.25440648e-02, 3.52353838e-05, 1.13295645e-08, 5.94912755e-11, 3.70902000e-11, 3.61219955e-11, 3.33783385e-11, 3.20855083e-11, 3.51827235e-11, 3.80747965e-11]]], [[[1.29727398e-02, 1.75725147e-02, 1.79053160e-02, 1.79060278e-02, 1.79060298e-02, 1.79060316e-02, 1.79060350e-02, 1.79060344e-02, 1.79060292e-02, 1.79060289e-02], [2.36526442e-04, 3.20392181e-04, 6.76968547e-07, 5.48905479e-09, 3.42218481e-09, 3.42177711e-09, 3.33285249e-09, 3.16185867e-09, 3.20372988e-09, 3.46708131e-09]], [[1.25440648e-02, 3.52353838e-05, 5.46354728e-06, 3.53836769e-06, 3.53836810e-06, 3.44641328e-06, 3.26961068e-06, 3.31294233e-06, 3.58526155e-06, 3.58526150e-06], [2.36550228e-01, 6.64452729e-04, 2.13647738e-07, 1.12185923e-09, 6.99430003e-10, 6.81172047e-10, 6.29433420e-10, 6.05053821e-10, 6.63459686e-10, 7.17997074e-10]]]]) fedfunds_const_short_smoothed_joint_probabilities = np.array([ [[9.82056759e-01, 9.99961887e-01, 9.99999502e-01, 9.99999618e-01, 9.99999623e-01, 9.99999637e-01, 9.99999644e-01, 9.99999627e-01, 9.99999612e-01, 9.99996030e-01], [1.79054228e-02, 3.78068025e-05, 3.06547724e-07, 1.91119055e-07, 1.91096269e-07, 1.86130055e-07, 1.76580558e-07, 1.78918992e-07, 1.93626403e-07, 1.93628651e-07]], [[1.90448249e-06, 2.95069837e-07, 1.91096241e-07, 1.91095282e-07, 1.86127261e-07, 1.76579242e-07, 1.78922146e-07, 1.93629492e-07, 1.94345814e-07, 3.77538498e-06], [3.59138585e-05, 1.15384749e-08, 6.05881299e-11, 3.77738466e-11, 3.67874300e-11, 3.39933060e-11, 3.26771544e-11, 3.58315175e-11, 3.89203762e-11, 7.56083358e-10]]]) class TestFedFundsConstShort(MarkovRegression): # This is just a set of regression tests @classmethod def setup_class(cls): true = { 'params': np.r_[.9820939, .0503587, 3.70877, 9.556793, 2.107562**2], 'llf': -29.909297, 'llf_fit': -7.8553370, 'llf_fit_em': -7.8554974 } super(TestFedFundsConstShort, cls).setup_class(true, fedfunds[-10:], k_regimes=2) def test_filter_output(self, **kwargs): res = self.result # Filtered assert_allclose(res.filtered_joint_probabilities, fedfunds_const_short_filtered_joint_probabilities) # Predicted desired = fedfunds_const_short_predicted_joint_probabilities if desired.ndim > res.predicted_joint_probabilities.ndim: desired = desired.sum(axis=-2) assert_allclose(res.predicted_joint_probabilities, desired) def test_smoother_output(self, **kwargs): res = self.result # Filtered assert_allclose(res.filtered_joint_probabilities, fedfunds_const_short_filtered_joint_probabilities) # Predicted desired = fedfunds_const_short_predicted_joint_probabilities if desired.ndim > res.predicted_joint_probabilities.ndim: desired = desired.sum(axis=-2) assert_allclose(res.predicted_joint_probabilities, desired) # Smoothed, last entry assert_allclose(res.smoothed_joint_probabilities, fedfunds_const_short_smoothed_joint_probabilities) def test_hamilton_filter_order_zero(self): k_regimes = 3 nobs = 4 initial_probabilities = np.ones(k_regimes) / k_regimes # We do not actually transition between the 3 regimes. regime_transition = np.eye(k_regimes)[:, :, np.newaxis] # Regime i correponds to a sequence of iid draws from discrete # random variables that are equally likely to be -1 and i for i=0, # 1, 2. We observe the sequence -1, -1, 1, -1. The first two # observations tell us nothing, but the third lets us know that we # are in regime 1 the whole time. conditional_likelihoods = np.ones((k_regimes, nobs)) / 2 conditional_likelihoods[:, 2] = [0, 1, 0] expected_marginals = np.empty((k_regimes, nobs)) expected_marginals[:, :2] = [[1/3], [1/3], [1/3]] expected_marginals[:, 2:] = [[0], [1], [0]] cy_results = markov_switching.cy_hamilton_filter_log( initial_probabilities, regime_transition, np.log(conditional_likelihoods + 1e-20), model_order=0) assert_allclose(cy_results[0], expected_marginals, atol=1e-15) def test_hamilton_filter_order_zero_with_tvtp(self): k_regimes = 3 nobs = 8 initial_probabilities = np.ones(k_regimes) / k_regimes # We do not actually transition between the 3 regimes except from # t=3 to t=4 where we reset to regimes 1 and 2 being equally # likely. regime_transition = np.zeros((k_regimes, k_regimes, nobs)) regime_transition[...] = np.eye(k_regimes)[:, :, np.newaxis] regime_transition[..., 4] = [[0, 0, 0], [1/2, 1/2, 1/2], [1/2, 1/2, 1/2]] # Regime i correponds to a sequence of iid draws from discrete # random variables that are equally likely to be -1, i, and i + 1 # for i = 0, 1, 2. We observe the sequence: # # t = 0, 1, 2, 3, 4, 5, 6, 7 # X_t = -1, 1, 2, -1, -1, 2, 3, -1 # # The first observations tell us nothing, the second tells us that # regime 0 and 1 are equally likely, and the third tells us that we # must be in regime 1 for t = 0, 1, 2, 3. At t=4 we transition to # state 1 or 2. In this case, neither a -1 or 2 changes our view # that these states are equally likely, but a 3 tells we must be in # state 2 for the second four timestamps. conditional_likelihoods = np.empty((k_regimes, nobs)) conditional_likelihoods[:, 0] = [1/3, 1/3, 1/3] conditional_likelihoods[:, 1] = [1/3, 1/3, 0] conditional_likelihoods[:, 2] = [0, 1/3, 1/3] conditional_likelihoods[:, 3:5] = [[1/3], [1/3], [1/3]] conditional_likelihoods[:, 5] = [0, 1/3, 1/3] conditional_likelihoods[:, 6] = [0, 0, 1/3] conditional_likelihoods[:, 7] = [1/3, 1/3, 1/3] expected_marginals = np.empty((k_regimes, nobs)) expected_marginals[:, 0] = [1/3, 1/3, 1/3] expected_marginals[:, 1] = [1/2, 1/2, 0] expected_marginals[:, 2:4] = [[0], [1], [0]] expected_marginals[:, 4:6] = [[0], [1/2], [1/2]] expected_marginals[:, 6:8] = [[0], [0], [1]] cy_results = markov_switching.cy_hamilton_filter_log( initial_probabilities, regime_transition, np.log(conditional_likelihoods + 1e-20), model_order=0) assert_allclose(cy_results[0], expected_marginals, atol=1e-15) def test_hamilton_filter_shape_checks(self): k_regimes = 3 nobs = 8 order = 3 initial_probabilities = np.ones(k_regimes) / k_regimes regime_transition = np.ones((k_regimes, k_regimes, nobs)) / k_regimes conditional_loglikelihoods = np.ones(order * (k_regimes,) + (nobs,)) with assert_raises(ValueError): markov_switching.cy_hamilton_filter_log( initial_probabilities, regime_transition, conditional_loglikelihoods, model_order=order) class TestFedFundsConstL1(MarkovRegression): # Results from Stata, see http://www.stata.com/manuals14/tsmswitch.pdf @classmethod def setup_class(cls): true = { 'params': np.r_[.6378175, .1306295, .724457, -.0988764, .7631424, 1.061174, .6915759**2], 'llf': -264.71069, 'llf_fit': -264.71069, 'llf_fit_em': -264.71153, 'bse_oim': np.r_[.1202616, .0495924, .2886657, .1183838, .0337234, .0185031, np.nan] } super(TestFedFundsConstL1, cls).setup_class( true, fedfunds[1:], k_regimes=2, exog=fedfunds[:-1]) def test_bse(self): # Cannot compare last element of bse because we estimate sigma^2 rather # than sigma^2 bse = self.result.cov_params_approx.diagonal()**0.5 assert_allclose(bse[:-1], self.true['bse_oim'][:-1], atol=1e-6) class TestFedFundsConstL1Exog(MarkovRegression): # Results from Stata, see http://www.stata.com/manuals14/tsmswitch.pdf @classmethod def setup_class(cls): path = os.path.join(current_path, 'results', 'results_predict_fedfunds.csv') results = pd.read_csv(path) true = { 'params': np.r_[.7279288, .2114578, .6554954, -.0944924, .8314458, .9292574, .1355425, .0343072, -.0273928, .2125275, .5764495**2], 'llf': -229.25614, 'llf_fit': -229.25614, 'llf_fit_em': -229.25624, 'bse_oim': np.r_[.0929915, .0641179, .1373889, .1279231, .0333236, .0270852, .0294113, .0240138, .0408057, .0297351, np.nan], 'predict0': results.iloc[4:]['constL1exog_syhat1'], 'predict1': results.iloc[4:]['constL1exog_syhat2'], 'predict_smoothed': results.iloc[4:]['constL1exog_syhat'], } super(TestFedFundsConstL1Exog, cls).setup_class( true, fedfunds[4:], k_regimes=2, exog=np.c_[fedfunds[3:-1], ogap[4:], inf[4:]]) def test_fit(self, **kwargs): kwargs.setdefault('em_iter', 10) kwargs.setdefault('maxiter', 100) super(TestFedFundsConstL1Exog, self).test_fit(**kwargs) def test_predict(self): # Predictions conditional on regime (the same no matter which # probabilities are selected) for name in ['predicted', 'filtered', 'smoothed', None]: actual = self.model.predict( self.true['params'], probabilities=name, conditional=True) assert_allclose(actual[0], self.true['predict0'], atol=1e-5) assert_allclose(actual[1], self.true['predict1'], atol=1e-5) # Smoothed actual = self.model.predict( self.true['params'], probabilities='smoothed') assert_allclose(actual, self.true['predict_smoothed'], atol=1e-5) actual = self.model.predict( self.true['params'], probabilities=None) assert_allclose(actual, self.true['predict_smoothed'], atol=1e-5) actual = self.result.predict(probabilities='smoothed') assert_allclose(actual, self.true['predict_smoothed'], atol=1e-5) actual = self.result.predict(probabilities=None) assert_allclose(actual, self.true['predict_smoothed'], atol=1e-5) def test_bse(self): # Cannot compare last element of bse because we estimate sigma^2 rather # than sigma^2 bse = self.result.cov_params_approx.diagonal()**0.5 assert_allclose(bse[:-1], self.true['bse_oim'][:-1], atol=1e-7) class TestFedFundsConstL1Exog3(MarkovRegression): # Results from Stata, see http://www.stata.com/manuals14/tsmswitch.pdf @classmethod def setup_class(cls): true = { 'params': np.r_[.7253684, .1641252, .6178282, .2564055, .7994204, .3821718, .5261292, -.0034106, .6015991, .8464551, .9690088, .4178913, .1201952, .0464136, .1075357, -.0425603, .1298906, .9099168, .438375**2], 'llf': -189.89493, 'llf_fit': -182.27188, 'llf_fit_em': -226.88581 } super(TestFedFundsConstL1Exog3, cls).setup_class( true, fedfunds[4:], k_regimes=3, exog=np.c_[fedfunds[3:-1], ogap[4:], inf[4:]]) def test_fit(self, **kwargs): kwargs['search_reps'] = 20 np.random.seed(1234) super(TestFedFundsConstL1Exog3, self).test_fit(**kwargs) class TestAreturnsConstL1Variance(MarkovRegression): # Results from Stata, see http://www.stata.com/manuals14/tsmswitch.pdf @classmethod def setup_class(cls): true = { 'params': np.r_[.7530865, .6825357, .7641424, 1.972771, .0790744, .527953, .5895792**2, 1.605333**2], 'llf': -745.7977, 'llf_fit': -745.7977, 'llf_fit_em': -745.83654, 'bse_oim': np.r_[.0634387, .0662574, .0782852, .2784204, .0301862, .0857841, np.nan, np.nan] } super(TestAreturnsConstL1Variance, cls).setup_class( true, areturns[1:], k_regimes=2, exog=areturns[:-1], switching_variance=True) def test_fit(self, **kwargs): kwargs.setdefault('em_iter', 10) kwargs.setdefault('maxiter', 100) super(TestAreturnsConstL1Variance, self).test_fit(**kwargs) def test_bse(self): # Cannot compare last two element of bse because we estimate sigma^2 # rather than sigma bse = self.result.cov_params_approx.diagonal()**0.5 assert_allclose(bse[:-2], self.true['bse_oim'][:-2], atol=1e-7) class TestMumpspcNoconstL1Variance(MarkovRegression): # Results from Stata, see http://www.stata.com/manuals14/tsmswitch.pdf @classmethod def setup_class(cls): true = { 'params': np.r_[.762733, .1473767, .420275, .9847369, .0562405**2, .2611362**2], 'llf': 131.7225, 'llf_fit': 131.7225, 'llf_fit_em': 131.7175 } super(TestMumpspcNoconstL1Variance, cls).setup_class( true, mumpspc[1:], k_regimes=2, trend='nc', exog=mumpspc[:-1], switching_variance=True, atol=1e-4) gh5380_series = [ -2.28833689e-04, -4.83175915e-05, -4.93236435e-04, -2.92251109e-04, -4.03295179e-04, -2.01009784e-04, 2.85109215e-04, 1.85710827e-04, -2.04503930e-04, -9.06050944e-05, 1.06177818e-03, -4.97251569e-04, 7.16669183e-04, 1.81161945e-04, -6.87139289e-04, -4.85979721e-05, -1.68387973e-05, -4.43257154e-04, 5.37457383e-04, -8.17822909e-04, 6.06814040e-04, -1.05481968e-05, -1.15698730e-04, -8.57638924e-04, 8.98143953e-05, 1.70216877e-04, -2.84874742e-04, -2.81999910e-05, -3.43787510e-04, -5.74808548e-04, -6.47844682e-05, 1.08667397e-04, -1.28790034e-04, 7.07615608e-05, 1.17633886e-04, 8.98163443e-07, 1.03860559e-05, -2.50298430e-06, -9.09673045e-07, -1.94645227e-05, -5.21373877e-05, -1.38431813e-04, 1.11092157e-04, 3.09541647e-05, -1.57756488e-04, 4.93176285e-05, -4.87488913e-05, 2.08097182e-04, -7.08581132e-05, -8.12182224e-06, 8.03090891e-05, -1.02981093e-05, 2.07550066e-05, 3.75383116e-05, -3.96307514e-05, -1.12007982e-05, -4.00958429e-05, 2.01206738e-05, -2.95802891e-05, 1.26422639e-04, -3.95617289e-05, 1.94523738e-04, 4.63964270e-05, 2.07712951e-05, 2.92417981e-04, 2.15111259e-04, 1.23762736e-04, 7.78305555e-05, -3.44022033e-04, -2.84249114e-05, -1.08351559e-04, -1.76944408e-04, 7.99332875e-05, 5.09785758e-04, 3.24506365e-04, -2.47943721e-04, 2.22346033e-04, -6.66164024e-05, 2.00911206e-04, 4.58750048e-04, -1.55390954e-04, 3.67913831e-04, 1.08274314e-04, -1.27400351e-04, 1.50654063e-04, 2.69976025e-04, 4.51532804e-05, -2.21579419e-04, 1.54792373e-04, 1.98397630e-04, 3.96943388e-04, 6.18663277e-04, 8.86151537e-04, 6.16949774e-04, 5.44538857e-03, 7.33282114e-05, 3.93393013e-03, 6.66556165e-04, 6.18815111e-03, -6.40775088e-03, -1.98864768e-03, -3.42828364e-05, -7.92023127e-04, -1.64656177e-03, -3.31112273e-03, -2.63499766e-03, -2.55118821e-04, -3.63858500e-04, -6.58065806e-04, -3.38492405e-04, -1.10458161e-03, -2.08228620e-07, -7.21562092e-05, 7.92946105e-05, 1.25472212e-05, -1.27190212e-04, 3.94913196e-05, -1.87353437e-05, -6.57929565e-06, 1.61597869e-05, 1.90031845e-05, 8.76129739e-03, -8.34566734e-03, -5.82053353e-05, 1.28770725e-04, 2.38160836e-04, -1.84590083e-05, 3.10903734e-05, 1.89366264e-05, 7.61985181e-05, 3.20208326e-04, -6.90388272e-05, 2.09928647e-05, -3.14720707e-05, 1.32614437e-04, 1.10385710e-04, -4.91256074e-05, -1.16967974e-04, 4.88977021e-05, 6.19231048e-05, 2.95994863e-04, 1.91592526e-03, -2.22511393e-04, -8.04871984e-04, -6.66886069e-04, -3.80754506e-04, -4.06613941e-05, -4.66164600e-04, -1.48077847e-04, 1.31787219e-04, 5.12392307e-05, -2.61346302e-05, -1.46071993e-04, -3.17839957e-04, -2.52143621e-04, -1.73768102e-04, -6.88107229e-05, -2.14130430e-05, 5.25348170e-07, -9.80972737e-05, -6.90120785e-05, -1.28208365e-04, 2.09816018e-05, 1.02199123e-05, 2.08633684e-05, 1.05609818e-05, 1.35835269e-05, 1.50357742e-04, 5.72303827e-05, 1.27501839e-04, 1.20706157e-04, 8.27340411e-06, 3.77430540e-05, 8.10426523e-05, 9.99617511e-05, 1.21103273e-04, 1.10255996e-04, 6.89558159e-05, 3.22442426e-05, 8.49416109e-05, 4.05396296e-04, 1.69699170e-04, 1.10892701e-04, 7.21186150e-05, 1.24978570e-04, -2.91922347e-04, 5.50447651e-05, -1.68467417e-04, -7.06084859e-05, -3.73250482e-04, -1.49829854e-04, -7.23752254e-05, -9.80670951e-05, -3.00179050e-05, 4.15704679e-05, 2.87503307e-05, -5.09988933e-05, -9.55791344e-06, -2.74369249e-05, -2.23330122e-05, 9.74727035e-06, -8.58146574e-06, 2.97704340e-05, -1.12990428e-05, -5.90507361e-05, 9.50772649e-07, -7.35502474e-07, 5.66683332e-07, -9.81320792e-06, -6.60845729e-07, -3.19848073e-05, -1.10779191e-04] @pytest.mark.smoke def test_avoid_underflow(): # See GH5380 for example and dataset demonstrating underflow. This test is # the "Example 1" given there. # The underlying problem was an underflow error in computing the smoothed # states, which resulted in NaN values in e.g. smoothed_joint_probabilities # This causes NaNs in the EM algorithm (e.g. _em_regime_transition), and # so the _fit_em method would return NaN parameters, as would the fit # method. # This test runs the smoother at the last set of good parameter values # (i.e. these parameters were generated by _fit_em and did not have any # NaN values in them, but the smoothed_joint_probabilities computed at # those parameters have NaNs in them, so that the next set of parameters # would have NaNs). The test then checks that the underflow problem has # been resolved, i.e. that there are no NaNs in the predicted, filtered, # and smoothed joint probabilities. m = markov_regression.MarkovRegression( gh5380_series, k_regimes=2, switching_variance=True) # To get these params, the following command was used: # params = m._fit_em(maxiter=1).params params = np.array([ 6.97337611e-01, 6.26116329e-01, -6.41266551e-06, 3.81141202e-06, 4.72462327e-08, 4.45291473e-06]) res = m.smooth(params) assert not np.any(np.isnan(res.predicted_joint_probabilities)) assert not np.any(np.isnan(res.filtered_joint_probabilities)) assert not np.any(np.isnan(res.smoothed_joint_probabilities)) def test_exog_tvtp(): exog = np.ones_like(fedfunds) mod1 = markov_regression.MarkovRegression(fedfunds, k_regimes=2) mod2 = markov_regression.MarkovRegression(fedfunds, k_regimes=2, exog_tvtp=exog) params = np.r_[0.98209618, 0.05036498, 3.70877542, 9.55676298, 4.44181911] params_tvtp = params.copy() params_tvtp[0] = mod2._untransform_logistic( np.r_[0.], np.r_[1 - params[0]]) params_tvtp[1] = mod2._untransform_logistic( np.r_[0.], np.r_[1 - params[1]]) res1 = mod1.smooth(params) res2 = mod2.smooth(params_tvtp) assert_allclose(res2.llf_obs, res1.llf_obs) assert_allclose(res2.regime_transition - res1.regime_transition, 0, atol=1e-15) assert_allclose(res2.predicted_joint_probabilities, res1.predicted_joint_probabilities) assert_allclose(res2.filtered_joint_probabilities, res1.filtered_joint_probabilities) assert_allclose(res2.smoothed_joint_probabilities, res1.smoothed_joint_probabilities) statsmodels-0.12.2/statsmodels/tsa/regime_switching/tests/test_markov_switching.py000066400000000000000000000277231400612667500307710ustar00rootroot00000000000000""" General tests for Markov switching models Author: Chad Fulton License: BSD-3 """ import numpy as np from numpy.testing import assert_equal, assert_allclose, assert_raises import pandas as pd from statsmodels.tools.numdiff import approx_fprime_cs from statsmodels.tsa.regime_switching import markov_switching def test_params(): def check_transtion_2(params): assert_equal(params['regime_transition'], np.s_[0:2]) assert_equal(params[0, 'regime_transition'], [0]) assert_equal(params[1, 'regime_transition'], [1]) assert_equal(params['regime_transition', 0], [0]) assert_equal(params['regime_transition', 1], [1]) def check_transition_3(params): assert_equal(params['regime_transition'], np.s_[0:6]) assert_equal(params[0, 'regime_transition'], [0, 3]) assert_equal(params[1, 'regime_transition'], [1, 4]) assert_equal(params[2, 'regime_transition'], [2, 5]) assert_equal(params['regime_transition', 0], [0, 3]) assert_equal(params['regime_transition', 1], [1, 4]) assert_equal(params['regime_transition', 2], [2, 5]) params = markov_switching.MarkovSwitchingParams(k_regimes=2) params['regime_transition'] = [1] assert_equal(params.k_params, 1 * 2) assert_equal(params[0], [0]) assert_equal(params[1], [1]) check_transtion_2(params) params['exog'] = [0, 1] assert_equal(params.k_params, 1 * 2 + 1 + 1 * 2) assert_equal(params[0], [0, 2, 3]) assert_equal(params[1], [1, 2, 4]) check_transtion_2(params) assert_equal(params['exog'], np.s_[2:5]) assert_equal(params[0, 'exog'], [2, 3]) assert_equal(params[1, 'exog'], [2, 4]) assert_equal(params['exog', 0], [2, 3]) assert_equal(params['exog', 1], [2, 4]) params = markov_switching.MarkovSwitchingParams(k_regimes=3) params['regime_transition'] = [1, 1] assert_equal(params.k_params, 2 * 3) assert_equal(params[0], [0, 3]) assert_equal(params[1], [1, 4]) assert_equal(params[2], [2, 5]) check_transition_3(params) # Test for invalid parameter setting assert_raises(IndexError, params.__setitem__, None, [1, 1]) # Test for invalid parameter selection assert_raises(IndexError, params.__getitem__, None) assert_raises(IndexError, params.__getitem__, (0, 0)) assert_raises(IndexError, params.__getitem__, ('exog', 'exog')) assert_raises(IndexError, params.__getitem__, ('exog', 0, 1)) def test_init_endog(): index = pd.date_range(start='1950-01-01', periods=10, freq='D') endog = [ np.ones(10), pd.Series(np.ones(10), index=index), np.ones((10, 1)), pd.DataFrame(np.ones((10, 1)), index=index) ] for _endog in endog: mod = markov_switching.MarkovSwitching(_endog, k_regimes=2) assert_equal(mod.nobs, 10) assert_equal(mod.endog, _endog.squeeze()) assert_equal(mod.k_regimes, 2) assert_equal(mod.tvtp, False) assert_equal(mod.k_tvtp, 0) assert_equal(mod.k_params, 2) # Invalid: k_regimes < 2 endog = np.ones(10) assert_raises(ValueError, markov_switching.MarkovSwitching, endog, k_regimes=1) # Invalid: multiple endog columns endog = np.ones((10, 2)) assert_raises(ValueError, markov_switching.MarkovSwitching, endog, k_regimes=2) def test_init_exog_tvtp(): endog = np.ones(10) exog_tvtp = np.c_[np.ones((10, 1)), (np.arange(10) + 1)[:, np.newaxis]] mod = markov_switching.MarkovSwitching(endog, k_regimes=2, exog_tvtp=exog_tvtp) assert_equal(mod.tvtp, True) assert_equal(mod.k_tvtp, 2) # Invalid exog_tvtp (too many obs) exog_tvtp = np.c_[np.ones((11, 1)), (np.arange(11) + 1)[:, np.newaxis]] assert_raises(ValueError, markov_switching.MarkovSwitching, endog, k_regimes=2, exog_tvtp=exog_tvtp) def test_transition_matrix(): # k_regimes = 2 endog = np.ones(10) mod = markov_switching.MarkovSwitching(endog, k_regimes=2) params = np.r_[0., 0., 1.] transition_matrix = np.zeros((2, 2, 1)) transition_matrix[1, :] = 1. assert_allclose(mod.regime_transition_matrix(params), transition_matrix) # k_regimes = 3 endog = np.ones(10) mod = markov_switching.MarkovSwitching(endog, k_regimes=3) params = np.r_[[0]*3, [0.2]*3, 1.] transition_matrix = np.zeros((3, 3, 1)) transition_matrix[1, :, 0] = 0.2 transition_matrix[2, :, 0] = 0.8 assert_allclose(mod.regime_transition_matrix(params), transition_matrix) # k_regimes = 2, tvtp endog = np.ones(10) exog_tvtp = np.c_[np.ones((10, 1)), (np.arange(10) + 1)[:, np.newaxis]] mod = markov_switching.MarkovSwitching(endog, k_regimes=2, exog_tvtp=exog_tvtp) # If all TVTP regression coefficients are zero, then the logit transform # results in exp(0) / (1 + exp(0)) = 0.5 for all parameters; since it's # k_regimes=2 the remainder calculation is also 0.5. params = np.r_[0, 0, 0, 0] assert_allclose(mod.regime_transition_matrix(params), 0.5) # Manually compute the TVTP coefficients params = np.r_[1, 2, 1, 2] transition_matrix = np.zeros((2, 2, 10)) coeffs0 = np.sum(exog_tvtp, axis=1) p11 = np.exp(coeffs0) / (1 + np.exp(coeffs0)) transition_matrix[0, 0, :] = p11 transition_matrix[1, 0, :] = 1 - p11 coeffs1 = np.sum(2 * exog_tvtp, axis=1) p21 = np.exp(coeffs1) / (1 + np.exp(coeffs1)) transition_matrix[0, 1, :] = p21 transition_matrix[1, 1, :] = 1 - p21 assert_allclose(mod.regime_transition_matrix(params), transition_matrix, atol=1e-10) # k_regimes = 3, tvtp endog = np.ones(10) exog_tvtp = np.c_[np.ones((10, 1)), (np.arange(10) + 1)[:, np.newaxis]] mod = markov_switching.MarkovSwitching( endog, k_regimes=3, exog_tvtp=exog_tvtp) # If all TVTP regression coefficients are zero, then the logit transform # results in exp(0) / (1 + exp(0) + exp(0)) = 1/3 for all parameters; # since it's k_regimes=3 the remainder calculation is also 1/3. params = np.r_[[0]*12] assert_allclose(mod.regime_transition_matrix(params), 1 / 3) # Manually compute the TVTP coefficients for the first column params = np.r_[[0]*6, [2]*6] transition_matrix = np.zeros((3, 3, 10)) p11 = np.zeros(10) p12 = 2 * np.sum(exog_tvtp, axis=1) tmp = np.exp(np.c_[p11, p12]).T transition_matrix[:2, 0, :] = tmp / (1 + np.sum(tmp, axis=0)) transition_matrix[2, 0, :] = ( 1 - np.sum(transition_matrix[:2, 0, :], axis=0)) assert_allclose(mod.regime_transition_matrix(params)[:, 0, :], transition_matrix[:, 0, :], atol=1e-10) def test_initial_probabilities(): endog = np.ones(10) mod = markov_switching.MarkovSwitching(endog, k_regimes=2) params = np.r_[0.5, 0.5, 1.] # Valid known initial probabilities mod.initialize_known([0.2, 0.8]) assert_allclose(mod.initial_probabilities(params), [0.2, 0.8]) # Invalid known initial probabilities (too many elements) assert_raises(ValueError, mod.initialize_known, [0.2, 0.2, 0.6]) # Invalid known initial probabilities (does not sum to 1) assert_raises(ValueError, mod.initialize_known, [0.2, 0.2]) # Valid steady-state probabilities mod.initialize_steady_state() assert_allclose(mod.initial_probabilities(params), [0.5, 0.5]) # Invalid steady-state probabilities (when mod has tvtp) endog = np.ones(10) mod = markov_switching.MarkovSwitching(endog, k_regimes=2, exog_tvtp=endog) assert_raises(ValueError, mod.initialize_steady_state) def test_logistic(): logistic = markov_switching._logistic # For a number, logistic(x) = np.exp(x) / (1 + np.exp(x)) cases = [0, 10., -4] for x in cases: # Have to use allclose b/c logistic() actually uses logsumexp, so # they're not equal assert_allclose(logistic(x), np.exp(x) / (1 + np.exp(x))) # For a vector, logistic(x) returns # np.exp(x[i]) / (1 + np.sum(np.exp(x[:]))) for each i # but squeezed cases = [[1.], [0, 1.], [-2, 3., 1.2, -30.]] for x in cases: actual = logistic(x) desired = [np.exp(i) / (1 + np.sum(np.exp(x))) for i in x] assert_allclose(actual, desired) # For a 2-dim, logistic(x) returns # np.exp(x[i, t]) / (1 + np.sum(np.exp(x[:, t]))) for each i, each t # but squeezed case = [[1.]] actual = logistic(case) assert_equal(actual.shape, (1, 1)) assert_allclose(actual, np.exp(1) / (1 + np.exp(1))) # Here, np.array(case) is 2x1, so it is interpreted as i=0, 1 and t=0 case = [[0], [1.]] actual = logistic(case) desired = [np.exp(i) / (1 + np.sum(np.exp(case))) for i in case] assert_allclose(actual, desired) # Here, np.array(case) is 1x2, so it is interpreted as i=0 and t=0, 1 case = [[0, 1.]] actual = logistic(case) desired = np.exp(case) / (1 + np.exp(case)) assert_allclose(actual, desired) # For a 3-dim, logistic(x) returns # np.exp(x[i, j, t]) / (1 + np.sum(np.exp(x[:, j, t]))) # for each i, each j, each t case = np.arange(2*3*4).reshape(2, 3, 4) actual = logistic(case) for j in range(3): assert_allclose(actual[:, j, :], logistic(case[:, j, :])) def test_partials_logistic(): # Here we compare to analytic derivatives and to finite-difference # approximations logistic = markov_switching._logistic partials_logistic = markov_switching._partials_logistic # For a number, logistic(x) = np.exp(x) / (1 + np.exp(x)) # Then d/dx = logistix(x) - logistic(x)**2 cases = [0, 10., -4] for x in cases: assert_allclose(partials_logistic(x), logistic(x) - logistic(x)**2) assert_allclose(partials_logistic(x), approx_fprime_cs([x], logistic)) # For a vector, logistic(x) returns # np.exp(x[i]) / (1 + np.sum(np.exp(x[:]))) for each i # Then d logistic(x[i]) / dx[i] = (logistix(x) - logistic(x)**2)[i] # And d logistic(x[i]) / dx[j] = -(logistic(x[i]) * logistic[x[j]]) cases = [[1.], [0, 1.], [-2, 3., 1.2, -30.]] for x in cases: evaluated = np.atleast_1d(logistic(x)) partials = np.diag(evaluated - evaluated**2) for i in range(len(x)): for j in range(i): partials[i, j] = partials[j, i] = -evaluated[i] * evaluated[j] assert_allclose(partials_logistic(x), partials) assert_allclose(partials_logistic(x), approx_fprime_cs(x, logistic)) # For a 2-dim, logistic(x) returns # np.exp(x[i, t]) / (1 + np.sum(np.exp(x[:, t]))) for each i, each t # but squeezed case = [[1.]] evaluated = logistic(case) partial = [evaluated - evaluated**2] assert_allclose(partials_logistic(case), partial) assert_allclose(partials_logistic(case), approx_fprime_cs(case, logistic)) # # Here, np.array(case) is 2x1, so it is interpreted as i=0, 1 and t=0 case = [[0], [1.]] evaluated = logistic(case)[:, 0] partials = np.diag(evaluated - evaluated**2) partials[0, 1] = partials[1, 0] = -np.multiply(*evaluated) assert_allclose(partials_logistic(case)[:, :, 0], partials) assert_allclose(partials_logistic(case), approx_fprime_cs(np.squeeze(case), logistic)[..., None]) # Here, np.array(case) is 1x2, so it is interpreted as i=0 and t=0, 1 case = [[0, 1.]] evaluated = logistic(case) partials = (evaluated - evaluated**2)[None, ...] assert_allclose(partials_logistic(case), partials) assert_allclose(partials_logistic(case), approx_fprime_cs(case, logistic).T) # For a 3-dim, logistic(x) returns # np.exp(x[i, j, t]) / (1 + np.sum(np.exp(x[:, j, t]))) # for each i, each j, each t case = np.arange(2*3*4).reshape(2, 3, 4) evaluated = logistic(case) partials = partials_logistic(case) for t in range(4): for j in range(3): desired = np.diag(evaluated[:, j, t] - evaluated[:, j, t]**2) desired[0, 1] = desired[1, 0] = -np.multiply(*evaluated[:, j, t]) assert_allclose(partials[..., j, t], desired) statsmodels-0.12.2/statsmodels/tsa/seasonal.py000066400000000000000000000247211400612667500214630ustar00rootroot00000000000000""" Seasonal Decomposition by Moving Averages """ from statsmodels.compat.pandas import deprecate_kwarg import numpy as np import pandas as pd from pandas.core.nanops import nanmean as pd_nanmean from statsmodels.tools.validation import PandasWrapper, array_like from statsmodels.tsa._stl import STL from statsmodels.tsa.filters.filtertools import convolution_filter from statsmodels.tsa.tsatools import freq_to_period __all__ = ['STL', 'seasonal_decompose', 'seasonal_mean', 'DecomposeResult'] def _extrapolate_trend(trend, npoints): """ Replace nan values on trend's end-points with least-squares extrapolated values with regression considering npoints closest defined points. """ front = next(i for i, vals in enumerate(trend) if not np.any(np.isnan(vals))) back = trend.shape[0] - 1 - next(i for i, vals in enumerate(trend[::-1]) if not np.any(np.isnan(vals))) front_last = min(front + npoints, back) back_first = max(front, back - npoints) k, n = np.linalg.lstsq( np.c_[np.arange(front, front_last), np.ones(front_last - front)], trend[front:front_last], rcond=-1)[0] extra = (np.arange(0, front) * np.c_[k] + np.c_[n]).T if trend.ndim == 1: extra = extra.squeeze() trend[:front] = extra k, n = np.linalg.lstsq( np.c_[np.arange(back_first, back), np.ones(back - back_first)], trend[back_first:back], rcond=-1)[0] extra = (np.arange(back + 1, trend.shape[0]) * np.c_[k] + np.c_[n]).T if trend.ndim == 1: extra = extra.squeeze() trend[back + 1:] = extra return trend @deprecate_kwarg('freq', 'period') def seasonal_mean(x, period): """ Return means for each period in x. period is an int that gives the number of periods per cycle. E.g., 12 for monthly. NaNs are ignored in the mean. """ return np.array([pd_nanmean(x[i::period], axis=0) for i in range(period)]) @deprecate_kwarg('freq', 'period') def seasonal_decompose(x, model="additive", filt=None, period=None, two_sided=True, extrapolate_trend=0): """ Seasonal decomposition using moving averages. Parameters ---------- x : array_like Time series. If 2d, individual series are in columns. x must contain 2 complete cycles. model : {"additive", "multiplicative"}, optional Type of seasonal component. Abbreviations are accepted. filt : array_like, optional The filter coefficients for filtering out the seasonal component. The concrete moving average method used in filtering is determined by two_sided. period : int, optional Period of the series. Must be used if x is not a pandas object or if the index of x does not have a frequency. Overrides default periodicity of x if x is a pandas object with a timeseries index. two_sided : bool, optional The moving average method used in filtering. If True (default), a centered moving average is computed using the filt. If False, the filter coefficients are for past values only. extrapolate_trend : int or 'freq', optional If set to > 0, the trend resulting from the convolution is linear least-squares extrapolated on both ends (or the single one if two_sided is False) considering this many (+1) closest points. If set to 'freq', use `freq` closest points. Setting this parameter results in no NaN values in trend or resid components. Returns ------- DecomposeResult A object with seasonal, trend, and resid attributes. See Also -------- statsmodels.tsa.filters.bk_filter.bkfilter Baxter-King filter. statsmodels.tsa.filters.cf_filter.cffilter Christiano-Fitzgerald asymmetric, random walk filter. statsmodels.tsa.filters.hp_filter.hpfilter Hodrick-Prescott filter. statsmodels.tsa.filters.convolution_filter Linear filtering via convolution. statsmodels.tsa.seasonal.STL Season-Trend decomposition using LOESS. Notes ----- This is a naive decomposition. More sophisticated methods should be preferred. The additive model is Y[t] = T[t] + S[t] + e[t] The multiplicative model is Y[t] = T[t] * S[t] * e[t] The results are obtained by first estimating the trend by applying a convolution filter to the data. The trend is then removed from the series and the average of this de-trended series for each period is the returned seasonal component. """ pfreq = period pw = PandasWrapper(x) if period is None: pfreq = getattr(getattr(x, 'index', None), 'inferred_freq', None) x = array_like(x, 'x', maxdim=2) nobs = len(x) if not np.all(np.isfinite(x)): raise ValueError("This function does not handle missing values") if model.startswith('m'): if np.any(x <= 0): raise ValueError("Multiplicative seasonality is not appropriate " "for zero and negative values") if period is None: if pfreq is not None: pfreq = freq_to_period(pfreq) period = pfreq else: raise ValueError("You must specify a period or x must be a " "pandas object with a DatetimeIndex with " "a freq not set to None") if x.shape[0] < 2 * pfreq: raise ValueError('x must have 2 complete cycles requires {0} ' 'observations. x only has {1} ' 'observation(s)'.format(2 * pfreq, x.shape[0])) if filt is None: if period % 2 == 0: # split weights at ends filt = np.array([.5] + [1] * (period - 1) + [.5]) / period else: filt = np.repeat(1. / period, period) nsides = int(two_sided) + 1 trend = convolution_filter(x, filt, nsides) if extrapolate_trend == 'freq': extrapolate_trend = period - 1 if extrapolate_trend > 0: trend = _extrapolate_trend(trend, extrapolate_trend + 1) if model.startswith('m'): detrended = x / trend else: detrended = x - trend period_averages = seasonal_mean(detrended, period) if model.startswith('m'): period_averages /= np.mean(period_averages, axis=0) else: period_averages -= np.mean(period_averages, axis=0) seasonal = np.tile(period_averages.T, nobs // period + 1).T[:nobs] if model.startswith('m'): resid = x / seasonal / trend else: resid = detrended - seasonal results = [] for s, name in zip((seasonal, trend, resid, x), ('seasonal', 'trend', 'resid', None)): results.append(pw.wrap(s.squeeze(), columns=name)) return DecomposeResult(seasonal=results[0], trend=results[1], resid=results[2], observed=results[3]) class DecomposeResult(object): """ Results class for seasonal decompositions Parameters ---------- observed : array_like The data series that has been decomposed. seasonal : array_like The seasonal component of the data series. trend : array_like The trend component of the data series. resid : array_like The residual component of the data series. weights : array_like, optional The weights used to reduce outlier influence. """ def __init__(self, observed, seasonal, trend, resid, weights=None): self._seasonal = seasonal self._trend = trend if weights is None: weights = np.ones_like(observed) if isinstance(observed, pd.Series): weights = pd.Series(weights, index=observed.index, name='weights') self._weights = weights self._resid = resid self._observed = observed @property def observed(self): """Observed data""" return self._observed @property def seasonal(self): """The estimated seasonal component""" return self._seasonal @property def trend(self): """The estimated trend component""" return self._trend @property def resid(self): """The estimated residuals""" return self._resid @property def weights(self): """The weights used in the robust estimation""" return self._weights @property def nobs(self): """Number of observations""" return self._observed.shape def plot(self, observed=True, seasonal=True, trend=True, resid=True, weights=False): """ Plot estimated components Parameters ---------- observed : bool Include the observed series in the plot seasonal : bool Include the seasonal component in the plot trend : bool Include the trend component in the plot resid : bool Include the residual in the plot weights : bool Include the weights in the plot (if any) Returns ------- matplotlib.figure.Figure The figure instance that containing the plot. """ from statsmodels.graphics.utils import _import_mpl from pandas.plotting import register_matplotlib_converters plt = _import_mpl() register_matplotlib_converters() series = [(self._observed, 'Observed')] if observed else [] series += [(self.trend, 'trend')] if trend else [] series += [(self.seasonal, 'seasonal')] if seasonal else [] series += [(self.resid, 'residual')] if resid else [] series += [(self.weights, 'weights')] if weights else [] if isinstance(self._observed, (pd.DataFrame, pd.Series)): nobs = self._observed.shape[0] xlim = self._observed.index[0], self._observed.index[nobs - 1] else: xlim = (0, self._observed.shape[0] - 1) fig, axs = plt.subplots(len(series), 1) for i, (ax, (series, def_name)) in enumerate(zip(axs, series)): if def_name != 'residual': ax.plot(series) else: ax.plot(series, marker='o', linestyle='none') ax.plot(xlim, (0, 0), color='#000000', zorder=-3) name = getattr(series, 'name', def_name) if def_name != 'Observed': name = name.capitalize() title = ax.set_title if i == 0 and observed else ax.set_ylabel title(name) ax.set_xlim(xlim) fig.tight_layout() return fig statsmodels-0.12.2/statsmodels/tsa/statespace/000077500000000000000000000000001400612667500214325ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/__init__.py000066400000000000000000000001131400612667500235360ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/tsa/statespace/_cfa_simulation_smoother.pxd000066400000000000000000000105121400612667500272220ustar00rootroot00000000000000""" State Space Model CFA simulation smoother declarations Author: Chad Fulton License: BSD-3 """ # Typical imports cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace) cdef class sCFASimulationSmoother(object): # Statespace object cdef readonly sStatespace model cdef readonly int order, lower_bandwidth cdef readonly int k_states, k_states2 cdef readonly np.float32_t [::1, :] prior_mean, posterior_mean cdef readonly np.float32_t [::1, :] posterior_cov_inv_chol, K cdef readonly np.float32_t [::1, :] initial_state_cov_inv, obs_cov_fac, selected_state_cov_inv cdef readonly np.float32_t [::1, :] QiT, TQiT, TQiTpQ, ZHiZ, HiZ cdef readonly np.float32_t [:] ymd cdef np.float32_t * _K cdef np.float32_t * _initial_state_cov_inv cdef np.float32_t * _obs_cov_fac cdef np.float32_t * _selected_state_cov_inv cdef np.float32_t * _QiT cdef np.float32_t * _TQiT cdef np.float32_t * _TQiTpQ cdef np.float32_t * _ZHiZ cdef np.float32_t * _HiZ cdef np.float32_t * _ymd cdef void _reinitialize_pointers(self) except * cpdef int update_sparse_posterior_moments(self) except * cpdef simulate(self, variates=*) cdef class dCFASimulationSmoother(object): # Statespace object cdef readonly dStatespace model cdef readonly int order, lower_bandwidth cdef readonly int k_states, k_states2 cdef readonly np.float64_t [::1, :] prior_mean, posterior_mean cdef readonly np.float64_t [::1, :] posterior_cov_inv_chol, K cdef readonly np.float64_t [::1, :] initial_state_cov_inv, obs_cov_fac, selected_state_cov_inv cdef readonly np.float64_t [::1, :] QiT, TQiT, TQiTpQ, ZHiZ, HiZ cdef readonly np.float64_t [:] ymd cdef np.float64_t * _K cdef np.float64_t * _initial_state_cov_inv cdef np.float64_t * _obs_cov_fac cdef np.float64_t * _selected_state_cov_inv cdef np.float64_t * _QiT cdef np.float64_t * _TQiT cdef np.float64_t * _TQiTpQ cdef np.float64_t * _ZHiZ cdef np.float64_t * _HiZ cdef np.float64_t * _ymd cdef void _reinitialize_pointers(self) except * cpdef int update_sparse_posterior_moments(self) except * cpdef simulate(self, variates=*) cdef class cCFASimulationSmoother(object): # Statespace object cdef readonly cStatespace model cdef readonly int order, lower_bandwidth cdef readonly int k_states, k_states2 cdef readonly np.complex64_t [::1, :] prior_mean, posterior_mean cdef readonly np.complex64_t [::1, :] posterior_cov_inv_chol, K cdef readonly np.complex64_t [::1, :] initial_state_cov_inv, obs_cov_fac, selected_state_cov_inv cdef readonly np.complex64_t [::1, :] QiT, TQiT, TQiTpQ, ZHiZ, HiZ cdef readonly np.complex64_t [:] ymd cdef np.complex64_t * _K cdef np.complex64_t * _initial_state_cov_inv cdef np.complex64_t * _obs_cov_fac cdef np.complex64_t * _selected_state_cov_inv cdef np.complex64_t * _QiT cdef np.complex64_t * _TQiT cdef np.complex64_t * _TQiTpQ cdef np.complex64_t * _ZHiZ cdef np.complex64_t * _HiZ cdef np.complex64_t * _ymd cdef void _reinitialize_pointers(self) except * cpdef int update_sparse_posterior_moments(self) except * cpdef simulate(self, variates=*) cdef class zCFASimulationSmoother(object): # Statespace object cdef readonly zStatespace model cdef readonly int order, lower_bandwidth cdef readonly int k_states, k_states2 cdef readonly np.complex128_t [::1, :] prior_mean, posterior_mean cdef readonly np.complex128_t [::1, :] posterior_cov_inv_chol, K cdef readonly np.complex128_t [::1, :] initial_state_cov_inv, obs_cov_fac, selected_state_cov_inv cdef readonly np.complex128_t [::1, :] QiT, TQiT, TQiTpQ, ZHiZ, HiZ cdef readonly np.complex128_t [:] ymd cdef np.complex128_t * _K cdef np.complex128_t * _initial_state_cov_inv cdef np.complex128_t * _obs_cov_fac cdef np.complex128_t * _selected_state_cov_inv cdef np.complex128_t * _QiT cdef np.complex128_t * _TQiT cdef np.complex128_t * _TQiTpQ cdef np.complex128_t * _ZHiZ cdef np.complex128_t * _HiZ cdef np.complex128_t * _ymd cdef void _reinitialize_pointers(self) except * cpdef int update_sparse_posterior_moments(self) except * cpdef simulate(self, variates=*) statsmodels-0.12.2/statsmodels/tsa/statespace/_cfa_simulation_smoother.pyx.in000066400000000000000000000471551400612667500276710ustar00rootroot00000000000000#cython: profile=False #cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ "Cholesky Factor Algorithm" (CFA) simulation smoothing TODO: - Allow fewer simulations than nobs / unlimited simulations in time-varying case References ---------- .. [*] McCausland, William J., Shirley Miller, and Denis Pelletier. "Simulation smoothing for state-space models: A computational efficiency analysis." Computational Statistics & Data Analysis 55, no. 1 (2011): 199-212. .. [*] Chan, Joshua CC, and Ivan Jeliazkov. "Efficient simulation and integrated likelihood estimation in state space models." International Journal of Mathematical Modelling and Numerical Optimisation 1, no. 1-2 (2009): 101-120. Author: Chad Fulton License: BSD-3 """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # Typical imports import numpy as np import warnings cimport numpy as np cimport cython np.import_array() cimport scipy.linalg.cython_blas as blas cimport scipy.linalg.cython_lapack as lapack cimport statsmodels.tsa.statespace._tools as tools cdef int FORTRAN = 1 {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} cdef class {{prefix}}CFASimulationSmoother(object): """ Notes ----- Currently not implemented (but could be): - Diffuse initialization - Support for collapsed observation vector Cannot be implemented: - Degenerate initial state distribution - Degenerate observation shock vector - Degenerate state shock vector """ def __init__(self, {{prefix}}Statespace model): cdef int inc = 1 cdef: np.npy_intp dim1[1] np.npy_intp dim2[2] self.model = model self.k_states = model.k_states self.k_states2 = self.k_states**2 self.order = self.model.nobs * self.k_states self.lower_bandwidth = 2 * self.k_states - 1 # Validate that our model is acceptable if self.model.nobs == 1: # TODO: this is probably easily fixable raise NotImplementedError('Cannot use CFA simulation smoothing' ' with a single observation.') # Posterior mean vector # Note: we'll define this as two-dimensional, although we'll want to # access it though it is a "one-dimensional" stacked vector at one # point. But that's not a problem given the column-major ordering here, # we can just pretend it's a one-dimensional array of length # k_states * nobs dim2[0] = self.k_states; dim2[1] = self.model.nobs; self.prior_mean = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self.posterior_mean = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Sparse storage for Cholesky factor of posterior covariance matrix dim2[0] = self.lower_bandwidth + 1; dim2[1] = self.order; self.posterior_cov_inv_chol = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self.K = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Intermediate computation arrays dim2[0] = self.k_states; dim2[1] = self.k_states; self.initial_state_cov_inv = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = self.model.k_endog; dim2[1] = self.model.k_endog; self.obs_cov_fac = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = self.k_states; dim2[1] = self.k_states; self.selected_state_cov_inv = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Temporary arrays dim2[0] = self.k_states; dim2[1] = self.k_states; self.QiT = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self.TQiT = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self.TQiTpQ = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self.ZHiZ = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = self.model.k_endog; dim2[1] = self.k_states; self.HiZ = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim1[0] = self.model.k_endog; self.ymd = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) # Pointers self._K = &self.K[0, 0] self._initial_state_cov_inv = &self.initial_state_cov_inv[0, 0] self._obs_cov_fac = &self.obs_cov_fac[0, 0] self._selected_state_cov_inv = &self.selected_state_cov_inv[0, 0] self._QiT = &self.QiT[0, 0] self._TQiT = &self.TQiT[0, 0] self._TQiTpQ = &self.TQiTpQ[0, 0] self._ZHiZ = &self.ZHiZ[0, 0] self._HiZ = &self.HiZ[0, 0] self._ymd = &self.ymd[0] def __reduce__(self): args = (self.model,) state = {'order': self.order, 'lower_bandwidth': self.lower_bandwidth, 'prior_mean': np.array(self.prior_mean, copy=True, order='F'), 'posterior_mean': np.array(self.posterior_mean, copy=True, order='F'), 'posterior_cov_inv_chol': np.array(self.posterior_cov_inv_chol, copy=True, order='F'), 'K': np.array(self.K, copy=True, order='F'), 'initial_state_cov_inv': np.array(self.initial_state_cov_inv, copy=True, order='F'), 'obs_cov_fac': np.array(self.obs_cov_fac, copy=True, order='F'), 'selected_state_cov_inv': np.array(self.selected_state_cov_inv, copy=True, order='F'), 'QiT': np.array(self.QiT, copy=True, order='F'), 'TQiT': np.array(self.TQiT, copy=True, order='F'), 'TQiTpQ': np.array(self.TQiTpQ, copy=True, order='F'), 'ZHiZ': np.array(self.ZHiZ, copy=True, order='F'), 'HiZ': np.array(self.HiZ, copy=True, order='F'), 'ymd': np.array(self.ymd, copy=True, order='F'), } return (self.__class__, args, state) def __setstate__(self, state): self.order = state['order'] self.lower_bandwidth = state['lower_bandwidth'] self.prior_mean = state['prior_mean'] self.posterior_mean = state['posterior_mean'] self.posterior_cov_inv_chol = state['posterior_cov_inv_chol'] self.K = state['K'] self.initial_state_cov_inv = state['initial_state_cov_inv'] self.obs_cov_fac = state['obs_cov_fac'] self.selected_state_cov_inv = state['selected_state_cov_inv'] self.QiT = state['QiT'] self.TQiT = state['TQiT'] self.TQiTpQ = state['TQiTpQ'] self.ZHiZ = state['ZHiZ'] self.HiZ = state['HiZ'] self.ymd = state['ymd'] self._reinitialize_pointers() cdef void _reinitialize_pointers(self) except *: self._K = &self.K[0, 0] self._initial_state_cov_inv = &self.initial_state_cov_inv[0, 0] self._obs_cov_fac = &self.obs_cov_fac[0, 0] self._selected_state_cov_inv = &self.selected_state_cov_inv[0, 0] self._QiT = &self.QiT[0, 0] self._TQiT = &self.TQiT[0, 0] self._TQiTpQ = &self.TQiTpQ[0, 0] self._ZHiZ = &self.ZHiZ[0, 0] self._HiZ = &self.HiZ[0, 0] self._ymd = &self.ymd[0] cpdef int update_sparse_posterior_moments(self) except *: # Update the computation of posterior moments for the entire state # vector, with the covariance matrix represented in what Scipy calls # "lower diagonal ordered form" - see e.g. Scipy's documentation page # for linalg.cholesky_banded for details of the storage format cdef: int t, i, j, rows, ld, info int reset_missing = 0 int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 int time_varying_obs_intercept = self.model.obs_intercept.shape[1] > 1 int time_varying_design = self.model.design.shape[2] > 1 int time_varying_obs_cov = self.model.obs_cov.shape[2] > 1 int time_varying_state_intercept = self.model.state_intercept.shape[1] > 1 int time_varying_transition = self.model.transition.shape[2] > 1 int time_varying_selection = self.model.selection.shape[2] > 1 int time_varying_state_cov = self.model.state_cov.shape[2] > 1 int time_varying_selected_state_cov = time_varying_selection or time_varying_state_cov self.model.seek(0, False, False) # Invert initial state covariance matrix # (we actually need the inverse here) if self.model.initialized_diffuse: self.initial_state_cov_inv[:] = 0. else: blas.{{prefix}}copy(&self.k_states2, self.model._initial_state_cov, &inc, self._initial_state_cov_inv, &inc) lapack.{{prefix}}potrf("L", &self.k_states, self._initial_state_cov_inv, &self.k_states, &info) if info > 0: raise np.linalg.LinAlgError('Non-positive-definite initial state covariance matrix.') elif info < 0: raise np.linalg.LinAlgError('Invalid value in initial state covariance matrix.') lapack.{{prefix}}potri("L", &self.k_states, self._initial_state_cov_inv, &self.k_states, &info) # Iterate over periods j = 0 # this will be a column counter for t in range(self.model.nobs): # Update the model representation to the current time point self.model.seek(t, False, False) # Check if we need to reset arrays based on Z for missing data reset_missing = 0 if t > 0: for i in range(self.model.k_endog): reset_missing = reset_missing + (not self.model.missing[i,t] == self.model.missing[i, t - 1]) # Invert selected_state_cov # (again, we actually need the inverse itself) if t == 0 or time_varying_selected_state_cov: blas.{{prefix}}copy(&self.k_states2, self.model._selected_state_cov, &inc, self._selected_state_cov_inv, &inc) lapack.{{prefix}}potrf("L", &self.k_states, self._selected_state_cov_inv, &self.k_states, &info) if info > 0: raise np.linalg.LinAlgError('Non-positive-definite selected state covariance matrix encountered at period %d' % t) elif info < 0: raise np.linalg.LinAlgError('Invalid value in selected state covariance matrix encountered at period %d' % t) lapack.{{prefix}}potri("L", &self.k_states, self._selected_state_cov_inv, &self.k_states, &info) # T(RQRi)T + (RQRi) if (t == 0 or time_varying_transition or time_varying_selected_state_cov): # QiT = (RQRi) @ T blas.{{prefix}}symm("L", "L", &self.k_states, &self.k_states, &alpha, self._selected_state_cov_inv, &self.k_states, self.model._transition, &self.k_states, &beta, self._QiT, &self.k_states) # TQiT = T.T @ QiT blas.{{prefix}}gemm("T", "N", &self.k_states, &self.k_states, &self.k_states, &alpha, self.model._transition, &self.k_states, self._QiT, &self.k_states, &beta, self._TQiT, &self.k_states) # TQiTpQ = TQiT + RQRi # Note: there will not be correct entries in the upper triangle, because # selected_state_cov was only set in the lower triangle. However, that's # okay because we only reference the lower triangle, below blas.{{prefix}}copy(&self.k_states2, self._selected_state_cov_inv, &inc, self._TQiTpQ, &inc) blas.{{prefix}}axpy(&self.k_states2, &alpha, self._TQiT, &inc, self._TQiTpQ, &inc) # Z (Hi) Z if t == 0 or reset_missing or time_varying_design or time_varying_obs_cov: # Cholesky of obs_cov if t == 0 or reset_missing or time_varying_obs_cov: blas.{{prefix}}copy(&self.model._k_endog2, self.model._obs_cov, &inc, self._obs_cov_fac, &inc) lapack.{{prefix}}potrf("L", &self.model._k_endog, self._obs_cov_fac, &self.model._k_endog, &info) if info > 0: raise np.linalg.LinAlgError('Non-positive-definite observation covariance matrix encountered at period %d' % t) elif info < 0: raise np.linalg.LinAlgError('Invalid value in observation covariance matrix encountered at period %d' % t) # HiZ = Hi Z blas.{{prefix}}copy(&self.model._k_endogstates, self.model._design, &inc, self._HiZ, &inc) lapack.{{prefix}}potrs("L", &self.model._k_endog, &self.k_states, self._obs_cov_fac, &self.model._k_endog, self._HiZ, &self.model._k_endog, &info) # ZHiZ = Z.T @ HiZ blas.{{prefix}}gemm("T", "N", &self.k_states, &self.k_states, &self.model._k_endog, &alpha, self.model._design, &self.model._k_endog, self._HiZ, &self.model._k_endog, &beta, self._ZHiZ, &self.k_states) # Fill in K and posterior_cov_inv_chol (which is right now just # going to contain posterior_cov_inv, and then we will take the # sparse Cholesky after the loop), prior mean # Iterate over columns in this (*, k_states) "block" of K, P for i in range(self.k_states): rows = self.k_states - i if t < self.model.nobs - 1: if t == 0: # K[:q - i, col] = (TQiT + P0i)[i:, i] blas.{{prefix}}copy(&rows, &self.TQiT[i, i], &inc, &self.K[0, j], &inc) blas.{{prefix}}axpy(&rows, &alpha, &self.initial_state_cov_inv[i, i], &inc, &self.K[0, j], &inc) else: # K[:q - i, col] = TQiTpQ[i:, i] blas.{{prefix}}copy(&rows, &self.TQiTpQ[i, i], &inc, &self.K[0, j], &inc) # P[:q - i, col] = K[:q - i, col] + ZHiZ[i:, i] blas.{{prefix}}copy(&rows, &self.K[0, j], &inc, &self.posterior_cov_inv_chol[0, j], &inc) blas.{{prefix}}axpy(&rows, &alpha, &self.ZHiZ[i, i], &inc, &self.posterior_cov_inv_chol[0, j], &inc) # K[q - i:q + q - i, col] = -QiT[:q, i] blas.{{prefix}}copy(&self.k_states, &self.QiT[0, i], &inc, &self.K[rows, j], &inc) blas.{{prefix}}scal(&self.k_states, &gamma, &self.K[rows, j], &inc) # P[q - i:q + q - i, col] = -QiT[:q, i] blas.{{prefix}}copy(&self.k_states, &self.K[rows, j], &inc, &self.posterior_cov_inv_chol[rows, j], &inc) # Last period is different elif t == self.model.nobs - 1: # K[:q - i, col] = RQRi[i:, i] blas.{{prefix}}copy(&rows, &self.selected_state_cov_inv[i, i], &inc, &self.K[0, j], &inc) # P[:q - i, col] = K[:q - i, col] + ZHiZ[i:, i] blas.{{prefix}}copy(&rows, &self.K[0, j], &inc, &self.posterior_cov_inv_chol[0, j], &inc) blas.{{prefix}}axpy(&rows, &alpha, &self.ZHiZ[i, i], &inc, &self.posterior_cov_inv_chol[0, j], &inc) # Advance the column counter j = j + 1 # Prior mean if t == 0: # prior_mean[:, 0] = initial_state blas.{{prefix}}copy(&self.k_states, self.model._initial_state, &inc, &self.prior_mean[0, 0], &inc) else: # prior_mean[:, t] = c[:, t] + T @ prior_mean[:, t-1] blas.{{prefix}}copy(&self.k_states, self.model._state_intercept, &inc, &self.prior_mean[0, t], &inc) blas.{{prefix}}gemv("N", &self.k_states, &self.k_states, &alpha, self.model._transition, &self.k_states, &self.prior_mean[0, t - 1], &inc, &alpha, &self.prior_mean[0, t], &inc) # (Hi Z)' (y - d) if self.model.nmissing[t] == self.model.k_endog: self.posterior_mean[:, t] = 0 else: blas.{{prefix}}copy(&self.model._k_endog, self.model._obs, &inc, &self.ymd[0], &inc) blas.{{prefix}}axpy(&self.model._k_endog, &gamma, self.model._obs_intercept, &inc, &self.ymd[0], &inc) blas.{{prefix}}gemv("T", &self.model._k_endog, &self.k_states, &alpha, self._HiZ, &self.model._k_endog, &self.ymd[0], &inc, &beta, &self.posterior_mean[0, t], &inc) # Orders of sparse matrices order = self.model.nobs * self.k_states ld = self.lower_bandwidth + 1 # Compute the sparse Cholesky factor of posterior cov lapack.{{prefix}}pbtrf("L", &self.order, &self.lower_bandwidth, &self.posterior_cov_inv_chol[0, 0], &ld, &info) if info > 0: raise np.linalg.LinAlgError('Non-positive-definite joint posterior covariance matrix encountered.') elif info < 0: raise np.linalg.LinAlgError('Invalid value in joint posterior covariance matrix encountered.') # Compute the posterior mean # posterior_mean = P^{-1} (K prior_mean + ZHimd) blas.{{prefix}}{{if combined_prefix == 'd'}}s{{else}}h{{endif}}bmv("L", &self.order, &self.lower_bandwidth, &alpha, self._K, &ld, &self.prior_mean[0, 0], &inc, &alpha, &self.posterior_mean[0, 0], &inc) lapack.{{prefix}}pbtrs("L", &self.order, &self.lower_bandwidth, &inc, &self.posterior_cov_inv_chol[0, 0], &ld, &self.posterior_mean[0, 0], &self.order, &info) cpdef simulate(self, variates=None): cdef int inc = 1 cdef int ld = self.lower_bandwidth + 1 cdef {{cython_type}} alpha = 1.0 cdef {{cython_type}} [:] u # Sample u from N(0, I) if variates is None: u = np.random.normal(size=self.order).astype({{dtype}}) else: u = variates tools.validate_vector_shape('variates', &u.shape[0], self.order, None) # Solve L' x = u to get x \sim N(0, P^{-1}) # (L = posterior_cov_inv_chol is lower triangular) blas.{{prefix}}tbsv("L", "T", "N", &self.order, &self.lower_bandwidth, &self.posterior_cov_inv_chol[0, 0], &ld, &u[0], &inc) # Add in the posterior mean blas.{{prefix}}axpy(&self.order, &alpha, &self.posterior_mean[0, 0], &inc, &u[0], &inc) return np.array(u).reshape(self.model.nobs, self.k_states).T {{endfor}} statsmodels-0.12.2/statsmodels/tsa/statespace/_filters/000077500000000000000000000000001400612667500232415ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/_filters/__init__.py000066400000000000000000000000001400612667500253400ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/_filters/_conventional.pxd000066400000000000000000000107301400612667500266150ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models - Conventional Kalman Filter declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace ) from statsmodels.tsa.statespace._kalman_filter cimport ( sKalmanFilter, dKalmanFilter, cKalmanFilter, zKalmanFilter ) # Single precision cdef int sforecast_missing_conventional(sKalmanFilter kfilter, sStatespace model) cdef int supdating_missing_conventional(sKalmanFilter kfilter, sStatespace model) cdef np.float32_t sinverse_missing_conventional(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) except * cdef np.float32_t sloglikelihood_missing_conventional(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) cdef np.float32_t sscale_missing_conventional(sKalmanFilter kfilter, sStatespace model) cdef int sforecast_conventional(sKalmanFilter kfilter, sStatespace model) cdef int schandrasekhar_recursion(sKalmanFilter kfilter, sStatespace model) cdef int supdating_conventional(sKalmanFilter kfilter, sStatespace model) cdef int sprediction_conventional(sKalmanFilter kfilter, sStatespace model) cdef np.float32_t sloglikelihood_conventional(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) cdef np.float32_t sscale_conventional(sKalmanFilter kfilter, sStatespace model) # Double precision cdef int dforecast_missing_conventional(dKalmanFilter kfilter, dStatespace model) cdef int dupdating_missing_conventional(dKalmanFilter kfilter, dStatespace model) cdef np.float64_t dinverse_missing_conventional(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) except * cdef np.float64_t dloglikelihood_missing_conventional(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) cdef np.float64_t dscale_missing_conventional(dKalmanFilter kfilter, dStatespace model) cdef int dforecast_conventional(dKalmanFilter kfilter, dStatespace model) cdef int dchandrasekhar_recursion(dKalmanFilter kfilter, dStatespace model) cdef int dupdating_conventional(dKalmanFilter kfilter, dStatespace model) cdef int dprediction_conventional(dKalmanFilter kfilter, dStatespace model) cdef np.float64_t dloglikelihood_conventional(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) cdef np.float64_t dscale_conventional(dKalmanFilter kfilter, dStatespace model) # Single precision complex cdef int cforecast_missing_conventional(cKalmanFilter kfilter, cStatespace model) cdef int cupdating_missing_conventional(cKalmanFilter kfilter, cStatespace model) cdef np.complex64_t cinverse_missing_conventional(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) except * cdef np.complex64_t cloglikelihood_missing_conventional(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) cdef np.complex64_t cscale_missing_conventional(cKalmanFilter kfilter, cStatespace model) cdef int cforecast_conventional(cKalmanFilter kfilter, cStatespace model) cdef int cupdating_conventional(cKalmanFilter kfilter, cStatespace model) cdef int cchandrasekhar_recursion(cKalmanFilter kfilter, cStatespace model) cdef int cprediction_conventional(cKalmanFilter kfilter, cStatespace model) cdef np.complex64_t cloglikelihood_conventional(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) cdef np.complex64_t cscale_conventional(cKalmanFilter kfilter, cStatespace model) # Double precision complex cdef int zforecast_missing_conventional(zKalmanFilter kfilter, zStatespace model) cdef int zupdating_missing_conventional(zKalmanFilter kfilter, zStatespace model) cdef np.complex128_t zinverse_missing_conventional(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) except * cdef np.complex128_t zloglikelihood_missing_conventional(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) cdef np.complex128_t zscale_missing_conventional(zKalmanFilter kfilter, zStatespace model) cdef int zforecast_conventional(zKalmanFilter kfilter, zStatespace model) cdef int zchandrasekhar_recursion(zKalmanFilter kfilter, zStatespace model) cdef int zupdating_conventional(zKalmanFilter kfilter, zStatespace model) cdef int zprediction_conventional(zKalmanFilter kfilter, zStatespace model) cdef np.complex128_t zloglikelihood_conventional(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) cdef np.complex128_t zscale_conventional(zKalmanFilter kfilter, zStatespace model) statsmodels-0.12.2/statsmodels/tsa/statespace/_filters/_conventional.pyx.in000066400000000000000000000425351400612667500272570ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # Typical imports import numpy as np cimport numpy as np from statsmodels.src.math cimport * cimport scipy.linalg.cython_blas as blas cimport scipy.linalg.cython_lapack as lapack from statsmodels.tsa.statespace._kalman_filter cimport ( MEMORY_NO_FORECAST_COV, FILTER_CONCENTRATED, FILTER_CHANDRASEKHAR) {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} # ### Missing Observation Conventional Kalman filter # # See Durbin and Koopman (2012) Chapter 4.10 # # Here k_endog is the same as usual, but the design matrix and observation # covariance matrix are enforced to be zero matrices, and the loglikelihood # is defined to be zero. cdef int {{prefix}}forecast_missing_conventional({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef int i, j cdef int inc = 1, design_t = 0 cdef {{cython_type}} alpha = 1 # #### Forecast for time t # `forecast` $= Z_t a_t + d_t$ # Just set to zeros, see below (this means if forecasts are required for # this part, they must be done in the wrappe) # #### Forecast error for time t # It is undefined here, since obs is nan # Note: use kfilter dimensions since we just want to set the whole array # to zero for i in range(kfilter.k_endog): kfilter._forecast[i] = 0 kfilter._forecast_error[i] = 0 # #### Forecast error covariance matrix for time t # $F_t \equiv 0$ # Note: use kfilter dimensions since we just want to set the whole array # to zeros for i in range(kfilter.k_endog): # columns for j in range(kfilter.k_endog): # rows kfilter._forecast_error_cov[j + i*kfilter.k_endog] = 0 cdef int {{prefix}}updating_missing_conventional({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef int inc = 1 # Simply copy over the input arrays ($a_t, P_t$) to the filtered arrays # ($a_{t|t}, P_{t|t}$) # Note: use kfilter dimensions since we just want to copy whole arrays; blas.{{prefix}}copy(&kfilter.k_states, kfilter._input_state, &inc, kfilter._filtered_state, &inc) blas.{{prefix}}copy(&kfilter.k_states2, kfilter._input_state_cov, &inc, kfilter._filtered_state_cov, &inc) cdef {{cython_type}} {{prefix}}inverse_missing_conventional({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant) except *: # Since the inverse of the forecast error covariance matrix is not # stored, we do not need to fill it (e.g. with NPY_NAN values). Instead, # just do a noop here and return a zero determinant ($|0|$). return -np.inf cdef {{cython_type}} {{prefix}}loglikelihood_missing_conventional({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant): return 0.0 cdef {{cython_type}} {{prefix}}scale_missing_conventional({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): return 0.0 # ### Conventional Kalman filter # # The following are the above routines as defined in the conventional Kalman # filter. # # See Durbin and Koopman (2012) Chapter 4 cdef int {{prefix}}forecast_conventional({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): # Constants cdef: int inc = 1, ld, i, j {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # #### Forecast for time t # `forecast` $= Z_t a_t + d_t$ # # *Note*: $a_t$ is given from the initialization (for $t = 0$) or # from the previous iteration of the filter (for $t > 0$). # $\\# = d_t$ blas.{{prefix}}copy(&model._k_endog, model._obs_intercept, &inc, kfilter._forecast, &inc) # `forecast` $= 1.0 * Z_t a_t + 1.0 * \\#$ # $(p \times 1) = (p \times m) (m \times 1) + (p \times 1)$ blas.{{prefix}}gemv("N", &model._k_endog, &model._k_states, &alpha, model._design, &model._k_endog, kfilter._input_state, &inc, &alpha, kfilter._forecast, &inc) # #### Forecast error for time t # `forecast_error` $\equiv v_t = y_t -$ `forecast` # $\\# = y_t$ blas.{{prefix}}copy(&model._k_endog, model._obs, &inc, kfilter._forecast_error, &inc) # $v_t = -1.0 * $ `forecast` $ + \\#$ # $(p \times 1) = (p \times 1) + (p \times 1)$ blas.{{prefix}}axpy(&model._k_endog, &gamma, kfilter._forecast, &inc, kfilter._forecast_error, &inc) # *Intermediate calculation* (used just below and then once more) # `tmp1` array used here, dimension $(m \times p)$ # $\\#_1 = P_t Z_t'$ # $(m \times p) = (m \times m) (p \times m)'$ blas.{{prefix}}gemm("N", "T", &model._k_states, &model._k_endog, &model._k_states, &alpha, kfilter._input_state_cov, &kfilter.k_states, model._design, &model._k_endog, &beta, kfilter._tmp1, &kfilter.k_states) # #### Forecast error covariance matrix for time t # $F_t \equiv Z_t P_t Z_t' + H_t$ # # *Note*: this and does nothing at all to `forecast_error_cov` if # converged == True # TODO make sure when converged, the copies are made correctly if not kfilter.converged: # $\\# = H_t$ # blas.{{prefix}}copy(&kfilter.k_endog2, kfilter._obs_cov, &inc, kfilter._forecast_error_cov, &inc) for i in range(model._k_endog): # columns for j in range(model._k_endog): # rows kfilter._forecast_error_cov[j + i*kfilter.k_endog] = model._obs_cov[j + i*model._k_endog] # $F_t = 1.0 * Z_t \\#_1 + 1.0 * \\#$ blas.{{prefix}}gemm("N", "N", &model._k_endog, &model._k_endog, &model._k_states, &alpha, model._design, &model._k_endog, kfilter._tmp1, &kfilter.k_states, &alpha, kfilter._forecast_error_cov, &kfilter.k_endog) return 0 cdef int {{prefix}}chandrasekhar_recursion({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): # Constants cdef: int info int inc = 1 int j, k {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # Chandrasekhar recursion # Initialization of the recursions if kfilter.t == 0: # Initialize M blas.{{prefix}}copy(&model._k_endog2, kfilter._forecast_error_cov, &inc, &kfilter.CM[0, 0], &inc) lapack.{{prefix}}getrf(&model._k_endog, &model._k_endog, &kfilter.CM[0, 0], &kfilter.k_endog, kfilter._forecast_error_ipiv, &info) lapack.{{prefix}}getri(&model._k_endog, &kfilter.CM[0, 0], &kfilter.k_endog, kfilter._forecast_error_ipiv, kfilter._forecast_error_work, &kfilter.ldwork, &info) blas.{{prefix}}scal(&model._k_endog2, &gamma, &kfilter.CM[0, 0], &inc) # Initialize W # Our Kalman gain is T P Z' F^{-1} but we need to initialize # W = T P Z', so we need to multiply by F # (not particularly efficient way to do this, but it's only # done for one time step so it's probably okay) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_endog, &model._k_endog, &alpha, kfilter._kalman_gain, &kfilter.k_states, kfilter._forecast_error_cov, &kfilter.k_endog, &beta, &kfilter.CW[0, 0], &kfilter.k_states) else: # Compute M = M + M @ W.T @ Z.T @ Fi_prev @ Z @ W @ M # = M + (M @ W.T) @ Z.T @ (Fi_prev @ Z) @ (W @ M) # M @ W.T: (p x p) (p x m) -> (p x m) blas.{{prefix}}gemm("N", "T", &model._k_endog, &model._k_states, &model._k_endog, &alpha, &kfilter.CM[0, 0], &kfilter.k_endog, &kfilter.CW[0, 0], &kfilter.k_states, &beta, &kfilter.CMW[0, 0], &kfilter.k_endog) # (Fi_prev @ Z) @ (W @ M): (p x m) (m x p) -> (p x p) blas.{{prefix}}gemm("N", "T", &model._k_endog, &model._k_endog, &model._k_states, &alpha, &kfilter.CprevFiZ[0, 0], &kfilter.k_endog, &kfilter.CMW[0, 0], &kfilter.k_endog, &beta, &kfilter.CtmpM[0, 0], &kfilter.k_endog) # (M @ W.T) @ Z.T: (p x m) (m x p) -> (p x p) blas.{{prefix}}gemm("N", "T", &model._k_endog, &model._k_endog, &model._k_states, &alpha, &kfilter.CMW[0, 0], &kfilter.k_endog, model._design, &model._k_endog, &beta, &kfilter.CMWZ[0, 0], &kfilter.k_endog) # M + (M @ W.T @ Z.T) (Fi_prev @ Z @ W @ M) : (p x p) (p x p) -> (p x p) blas.{{prefix}}gemm("N", "N", &model._k_endog, &model._k_endog, &model._k_endog, &alpha, &kfilter.CMWZ[0, 0], &kfilter.k_endog, &kfilter.CtmpM[0, 0], &model._k_endog, &alpha, &kfilter.CM[0, 0], &kfilter.k_endog) # Compute W = (T - Kg @ Z) @ W # W -> tmpW blas.{{prefix}}copy(&model._k_endogstates, &kfilter.CW[0, 0], &inc, &kfilter.CtmpW[0, 0], &inc) # T -> tmp00 blas.{{prefix}}copy(&model._k_states2, model._transition, &inc, kfilter._tmp00, &inc) # T - K @ Z: (m x p) (p x m) -> (m x m) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_endog, &gamma, kfilter._kalman_gain, &kfilter.k_states, model._design, &model._k_endog, &alpha, kfilter._tmp00, &kfilter.k_states) # (T - T @ K @ Z[i]) @ tmpW -> W blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_endog, &model._k_states, &alpha, kfilter._tmp00, &kfilter.k_states, &kfilter.CtmpW[0, 0], &kfilter.k_states, &beta, &kfilter.CW[0, 0], &kfilter.k_states) # Save F^{-1} Z (this period's value used in next iteration) blas.{{prefix}}copy(&model._k_endogstates, kfilter._tmp3, &inc, &kfilter.CprevFiZ[0, 0], &inc) cdef int {{prefix}}updating_conventional({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): # Constants cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # #### Filtered state for time t # $a_{t|t} = a_t + P_t Z_t' F_t^{-1} v_t$ # $a_{t|t} = 1.0 * \\#_1 \\#_2 + 1.0 a_t$ blas.{{prefix}}copy(&kfilter.k_states, kfilter._input_state, &inc, kfilter._filtered_state, &inc) blas.{{prefix}}gemv("N", &model._k_states, &model._k_endog, &alpha, kfilter._tmp1, &kfilter.k_states, kfilter._tmp2, &inc, &alpha, kfilter._filtered_state, &inc) # #### Filtered state covariance for time t # Temporary computation used below if not kfilter.converged: # P_t Z_t' F_t^{-1} # $(m \times p) = (m \times m) (m \times p)$ blas.{{prefix}}gemm("N", "T", &model._k_states, &model._k_endog, &model._k_states, &alpha, kfilter._input_state_cov, &kfilter.k_states, kfilter._tmp3, &kfilter.k_endog, &beta, &kfilter.CtmpW[0, 0], &kfilter.k_states) # $P_{t|t} = P_t - P_t Z_t' F_t^{-1} Z_t P_t$ # $P_{t|t} = P_t - \\#_1 \\#_3 P_t$ # # *Note*: this and does nothing at all to `filtered_state_cov` if # converged == True if not kfilter.converged: blas.{{prefix}}copy(&kfilter.k_states2, kfilter._input_state_cov, &inc, kfilter._filtered_state_cov, &inc) # $P_{t|t} = - 1.0 * \\# P_t + 1.0 * P_t$ # $(m \times m) = (m \times p) (p \times m) + (m \times m)$ blas.{{prefix}}gemm("N", "T", &model._k_states, &model._k_states, &model._k_endog, &gamma, &kfilter.CtmpW[0, 0], &kfilter.k_states, kfilter._tmp1, &kfilter.k_states, &alpha, kfilter._filtered_state_cov, &kfilter.k_states) # #### Kalman gain for time t # $K_t = T_t P_t Z_t' F_t^{-1}$ # # *Note*: this and does nothing at all to `kalman_gain` if # converged == True # *Note*: Kim and Nelson (1999) have a different version of the Kalman # gain, defined as $P_t Z_t' F_t^{-1}$. That is not adopted here. if not kfilter.converged: # T_t P_t Z_t' F_t^{-1} # $(m \times p) = (m \times m) (m \times p)$ blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_endog, &model._k_states, &alpha, model._transition, &kfilter.k_states, &kfilter.CtmpW[0, 0], &kfilter.k_states, &beta, kfilter._kalman_gain, &kfilter.k_states) return 0 cdef int {{prefix}}prediction_conventional({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): # Constants cdef: int inc = 1 int forecast_cov_t = kfilter.t {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 if kfilter.conserve_memory & MEMORY_NO_FORECAST_COV > 0: forecast_cov_t = 1 # #### Predicted state for time t+1 # $a_{t+1} = T_t a_{t|t} + c_t$ blas.{{prefix}}copy(&model._k_states, model._state_intercept, &inc, kfilter._predicted_state, &inc) blas.{{prefix}}gemv("N", &model._k_states, &model._k_states, &alpha, model._transition, &model._k_states, kfilter._filtered_state, &inc, &alpha, kfilter._predicted_state, &inc) # #### Predicted state covariance matrix for time t+1 # $P_{t+1} = T_t P_{t|t} T_t' + Q_t^*$ # # *Note*: this and does nothing at all to `predicted_state_cov` if # converged == True if not kfilter.converged: blas.{{prefix}}copy(&model._k_states2, model._selected_state_cov, &inc, kfilter._predicted_state_cov, &inc) # `tmp0` array used here, dimension $(m \times m)$ if kfilter.filter_method & FILTER_CHANDRASEKHAR: # Chandrasekhar_recursion {{prefix}}chandrasekhar_recursion(kfilter, model) # Chandrasekhar-based prediction step blas.{{prefix}}copy(&model._k_states2, kfilter._input_state_cov, &inc, kfilter._predicted_state_cov, &inc) # M @ W.T. (p x p) (p x m) blas.{{prefix}}gemm("N", "T", &model._k_endog, &model._k_states, &model._k_endog, &alpha, &kfilter.CM[0, 0], &kfilter.k_endog, &kfilter.CW[0, 0], &kfilter.k_states, &beta, &kfilter.CMW[0, 0], &kfilter.k_endog) # P = P + W M W.T blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_endog, &alpha, &kfilter.CW[0, 0], &kfilter.k_states, &kfilter.CMW[0, 0], &kfilter.k_endog, &alpha, kfilter._predicted_state_cov, &kfilter.k_states) else: # Kalman filter prediction step # $\\#_0 = T_t P_{t|t} $ # $(m \times m) = (m \times m) (m \times m)$ blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, model._transition, &model._k_states, kfilter._filtered_state_cov, &kfilter.k_states, &beta, kfilter._tmp0, &kfilter.k_states) # $P_{t+1} = 1.0 \\#_0 T_t' + 1.0 \\#$ # $(m \times m) = (m \times m) (m \times m) + (m \times m)$ blas.{{prefix}}gemm("N", "T", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmp0, &kfilter.k_states, model._transition, &model._k_states, &alpha, kfilter._predicted_state_cov, &kfilter.k_states) return 0 cdef {{cython_type}} {{prefix}}loglikelihood_conventional({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant): # Constants cdef: {{cython_type}} loglikelihood int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 loglikelihood = -0.5*(model._k_endog*{{combined_prefix}}log(2*NPY_PI) + determinant) if not kfilter.filter_method & FILTER_CONCENTRATED: {{if combined_prefix == 'd'}} loglikelihood = loglikelihood - 0.5*blas.{{prefix}}dot(&model._k_endog, kfilter._forecast_error, &inc, kfilter._tmp2, &inc) {{else}} blas.{{prefix}}gemv("N", &inc, &model._k_endog, &alpha, kfilter._forecast_error, &inc, kfilter._tmp2, &inc, &beta, kfilter._tmp0, &inc) loglikelihood = loglikelihood - 0.5 * kfilter._tmp0[0] {{endif}} return loglikelihood cdef {{cython_type}} {{prefix}}scale_conventional({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): # Constants cdef: {{cython_type}} scale int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{if combined_prefix == 'd'}} scale = blas.{{prefix}}dot(&model._k_endog, kfilter._forecast_error, &inc, kfilter._tmp2, &inc) {{else}} blas.{{prefix}}gemv("N", &inc, &model._k_endog, &alpha, kfilter._forecast_error, &inc, kfilter._tmp2, &inc, &beta, kfilter._tmp0, &inc) scale = kfilter._tmp0[0] {{endif}} return scale {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/_filters/_inversions.pxd000066400000000000000000000071751400612667500263260ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models - Inversion methods declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace ) from statsmodels.tsa.statespace._kalman_filter cimport ( sKalmanFilter, dKalmanFilter, cKalmanFilter, zKalmanFilter ) # Single precision cdef np.float32_t sinverse_univariate(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) except * cdef np.float32_t sfactorize_cholesky(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) except * cdef np.float32_t sfactorize_lu(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) except * cdef np.float32_t sinverse_cholesky(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) except * cdef np.float32_t sinverse_lu(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) except * cdef np.float32_t ssolve_cholesky(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) except * cdef np.float32_t ssolve_lu(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) except * # Double precision cdef np.float64_t dinverse_univariate(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) except * cdef np.float64_t dfactorize_cholesky(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) except * cdef np.float64_t dfactorize_lu(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) except * cdef np.float64_t dinverse_cholesky(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) except * cdef np.float64_t dinverse_lu(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) except * cdef np.float64_t dsolve_cholesky(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) except * cdef np.float64_t dsolve_lu(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) except * # Single precision complex cdef np.complex64_t cinverse_univariate(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) except * cdef np.complex64_t cfactorize_cholesky(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) except * cdef np.complex64_t cfactorize_lu(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) except * cdef np.complex64_t cinverse_cholesky(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) except * cdef np.complex64_t cinverse_lu(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) except * cdef np.complex64_t csolve_cholesky(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) except * cdef np.complex64_t csolve_lu(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) except * # Double precision complex cdef np.complex128_t zinverse_univariate(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) except * cdef np.complex128_t zfactorize_cholesky(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) except * cdef np.complex128_t zfactorize_lu(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) except * cdef np.complex128_t zinverse_cholesky(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) except * cdef np.complex128_t zinverse_lu(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) except * cdef np.complex128_t zsolve_cholesky(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) except * cdef np.complex128_t zsolve_lu(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) except * statsmodels-0.12.2/statsmodels/tsa/statespace/_filters/_inversions.pyx.in000066400000000000000000000444661400612667500267640ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} cimport numpy as np import numpy as np from statsmodels.src.math cimport * cimport scipy.linalg.cython_blas as blas cimport scipy.linalg.cython_lapack as lapack from statsmodels.tsa.statespace._kalman_filter cimport ( MEMORY_NO_SMOOTHING, MEMORY_NO_STD_FORECAST) {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} # ## Forecast error covariance inversion # # The following are routines that can calculate the inverse of the forecast # error covariance matrix (defined in `forecast_`). # # These routines are aware of the possibility that the Kalman filter may have # converged to a steady state, in which case they do not need to perform the # inversion or calculate the determinant. cdef {{cython_type}} {{prefix}}inverse_univariate({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant) except *: """ Factorize the forecast error covariance matrix using simple division in the case that the observations are univariate. If the model has converged to a steady-state, this is a NOOP and simply returns the determinant that was passed in. """ # TODO it's not a noop if converged, but the docstring says it is... # #### Intermediate values cdef: int inc = 1 {{cython_type}} scalar # Take the inverse of the forecast error covariance matrix if not kfilter.converged: determinant = {{combined_prefix}}log(kfilter._forecast_error_cov[0]) try: # If we're close to singular, switch to univariate version even if the # following doesn't trigger a ZeroDivisionError if kfilter._forecast_error_cov[0]{{if combined_prefix == 'z'}}.real{{endif}} < 1e-12: raise Exception scalar = 1.0 / kfilter._forecast_error_cov[0] except: raise np.linalg.LinAlgError('Non-positive-definite forecast error' ' covariance matrix encountered at' ' period %d' % kfilter.t) kfilter._tmp2[0] = scalar * kfilter._forecast_error[0] blas.{{prefix}}copy(&model._k_endogstates, model._design, &inc, kfilter._tmp3, &inc) blas.{{prefix}}scal(&model._k_endogstates, &scalar, kfilter._tmp3, &inc) if not (kfilter.conserve_memory & MEMORY_NO_STD_FORECAST > 0): kfilter._standardized_forecast_error[0] = kfilter._forecast_error[0] * scalar**0.5 if not (kfilter.conserve_memory & MEMORY_NO_SMOOTHING > 0): kfilter._tmp4[0] = scalar * model._obs_cov[0] return determinant cdef {{cython_type}} {{prefix}}factorize_cholesky({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant) except *: """ Factorize the forecast error covariance matrix using a Cholesky decomposition. Called by either of the `solve_cholesky` or `invert_cholesky` routines. Requires a positive definite matrix, but is faster than an LU decomposition. If the model has converged to a steady-state, this is a NOOP and simply returns the determinant that was passed in. """ cdef: int inc = 1 int info int i if not kfilter.converged or not (kfilter.conserve_memory & MEMORY_NO_STD_FORECAST > 0): blas.{{prefix}}copy(&kfilter.k_endog2, kfilter._forecast_error_cov, &inc, kfilter._forecast_error_fac, &inc) lapack.{{prefix}}potrf("U", &model._k_endog, kfilter._forecast_error_fac, &kfilter.k_endog, &info) if info < 0: raise np.linalg.LinAlgError('Illegal value in forecast error' ' covariance matrix encountered at' ' period %d' % kfilter.t) if info > 0: raise np.linalg.LinAlgError('Non-positive-definite forecast error' ' covariance matrix encountered at' ' period %d' % kfilter.t) # Calculate the determinant (just the squared product of the # diagonals, in the Cholesky decomposition case) determinant = 0.0 for i in range(model._k_endog): determinant = determinant + {{combined_prefix}}log(kfilter.forecast_error_fac[i, i]) determinant = 2 * determinant return determinant cdef {{cython_type}} {{prefix}}factorize_lu({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant) except *: """ Factorize the forecast error covariance matrix using an LU decomposition. Called by either of the `solve_lu` or `invert_lu` routines. Is slower than a Cholesky decomposition, but does not require a positive definite matrix. If the model has converged to a steady-state, this is a NOOP and simply returns the determinant that was passed in. """ cdef: int inc = 1 int info int i if not kfilter.converged: # Perform LU decomposition into `forecast_error_fac` blas.{{prefix}}copy(&kfilter.k_endog2, kfilter._forecast_error_cov, &inc, kfilter._forecast_error_fac, &inc) lapack.{{prefix}}getrf(&model._k_endog, &model._k_endog, kfilter._forecast_error_fac, &kfilter.k_endog, kfilter._forecast_error_ipiv, &info) if info < 0: raise np.linalg.LinAlgError('Illegal value in forecast error' ' covariance matrix encountered at' ' period %d' % kfilter.t) if info > 0: raise np.linalg.LinAlgError('Singular forecast error covariance' ' matrix encountered at period %d' % kfilter.t) # Calculate the determinant (product of the diagonals, but with # sign modifications according to the permutation matrix) determinant = 1 for i in range(model._k_endog): if not kfilter._forecast_error_ipiv[i] == i+1: determinant *= -1*kfilter.forecast_error_fac[i, i] else: determinant *= kfilter.forecast_error_fac[i, i] determinant = {{combined_prefix}}log(determinant) return determinant cdef {{cython_type}} {{prefix}}inverse_cholesky({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant) except *: """ inverse_cholesky(self, determinant) If the model has converged to a steady-state, this is a NOOP and simply returns the determinant that was passed in. """ cdef: int info int inc = 1 int i, j {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 if not kfilter.converged or not (kfilter.conserve_memory & MEMORY_NO_STD_FORECAST > 0): # Perform the Cholesky decomposition and get the determinant determinant = {{prefix}}factorize_cholesky(kfilter, model, determinant) # Use the Cholesky factor to get standardized forecast errors, if desired # (in the notation of DK, kfilter._forecast_error_fac holds L_t', and # we want to solve the equation L_t' v_t^s = v_t) if not (kfilter.conserve_memory & MEMORY_NO_STD_FORECAST > 0): blas.{{prefix}}copy(&kfilter.k_endog, kfilter._forecast_error, &inc, kfilter._standardized_forecast_error, &inc) lapack.{{prefix}}trtrs("U", "T", "N", &model._k_endog, &inc, kfilter._forecast_error_fac, &kfilter.k_endog, kfilter._standardized_forecast_error, &kfilter.k_endog, &info) if info != 0: raise np.linalg.LinAlgError('Error computing standardized' ' forecast error at period %d' % kfilter.t) # Continue taking the inverse lapack.{{prefix}}potri("U", &model._k_endog, kfilter._forecast_error_fac, &kfilter.k_endog, &info) # ?potri only fills in the upper triangle of the symmetric array, and # since the ?symm and ?symv routines are not available as of scipy # 0.11.0, we cannot use them, so we must fill in the lower triangle # by hand for i in range(model._k_endog): # columns for j in range(i): # rows kfilter.forecast_error_fac[i,j] = kfilter.forecast_error_fac[j,i] # Get `tmp2` and `tmp3` via matrix multiplications # `tmp2` array used here, dimension $(p \times 1)$ # $\\#_2 = F_t^{-1} v_t$ #blas.{{prefix}}symv("U", &model._k_endog, &alpha, kfilter._forecast_error_fac, &kfilter.k_endog, # kfilter._forecast_error, &inc, &beta, kfilter._tmp2, &inc) blas.{{prefix}}gemv("N", &model._k_endog, &model._k_endog, &alpha, kfilter._forecast_error_fac, &kfilter.k_endog, kfilter._forecast_error, &inc, &beta, kfilter._tmp2, &inc) # `tmp3` array used here, dimension $(p \times m)$ # $\\#_3 = F_t^{-1} Z_t$ #blas.{{prefix}}symm("L", "U", &kfilter.k_endog, &kfilter.k_states, # &alpha, kfilter._forecast_error_fac, &kfilter.k_endog, # kfilter._design, &kfilter.k_endog, # &beta, kfilter._tmp3, &kfilter.k_endog) blas.{{prefix}}gemm("N", "N", &model._k_endog, &model._k_states, &model._k_endog, &alpha, kfilter._forecast_error_fac, &kfilter.k_endog, model._design, &model._k_endog, &beta, kfilter._tmp3, &kfilter.k_endog) if not (kfilter.conserve_memory & MEMORY_NO_SMOOTHING > 0): # `tmp4` array used here, dimension $(p \times p)$ # $\\#_4 = F_t^{-1} H_t$ #blas.{{prefix}}symm("L", "U", &kfilter.k_endog, &kfilter.k_endog, # &alpha, kfilter._forecast_error_fac, &kfilter.k_endog, # kfilter._obs_cov, &kfilter.k_endog, # &beta, kfilter._tmp4, &kfilter.k_endog) blas.{{prefix}}gemm("N", "N", &model._k_endog, &model._k_endog, &model._k_endog, &alpha, kfilter._forecast_error_fac, &kfilter.k_endog, model._obs_cov, &model._k_endog, &beta, kfilter._tmp4, &kfilter.k_endog) return determinant cdef {{cython_type}} {{prefix}}inverse_lu({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant) except *: """ inverse_cholesky(self, determinant) If the model has converged to a steady-state, this is a NOOP and simply returns the determinant that was passed in. """ cdef: int info int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 if not kfilter.converged: # Perform the Cholesky decomposition and get the determinant determinant = {{prefix}}factorize_lu(kfilter, model, determinant) # Continue taking the inverse lapack.{{prefix}}getri(&model._k_endog, kfilter._forecast_error_fac, &kfilter.k_endog, kfilter._forecast_error_ipiv, kfilter._forecast_error_work, &kfilter.ldwork, &info) # Get `tmp2` and `tmp3` via matrix multiplications # `tmp2` array used here, dimension $(p \times 1)$ # $\\#_2 = F_t^{-1} v_t$ blas.{{prefix}}gemv("N", &model._k_endog, &model._k_endog, &alpha, kfilter._forecast_error_fac, &kfilter.k_endog, kfilter._forecast_error, &inc, &beta, kfilter._tmp2, &inc) # `tmp3` array used here, dimension $(p \times m)$ # $\\#_3 = F_t^{-1} Z_t$ blas.{{prefix}}gemm("N", "N", &model._k_endog, &model._k_states, &model._k_endog, &alpha, kfilter._forecast_error_fac, &kfilter.k_endog, model._design, &model._k_endog, &beta, kfilter._tmp3, &kfilter.k_endog) if not (kfilter.conserve_memory & MEMORY_NO_SMOOTHING > 0): # `tmp4` array used here, dimension $(p \times p)$ # $\\#_4 = F_t^{-1} H_t$ blas.{{prefix}}gemm("N", "N", &model._k_endog, &model._k_endog, &model._k_endog, &alpha, kfilter._forecast_error_fac, &kfilter.k_endog, model._obs_cov, &model._k_endog, &beta, kfilter._tmp4, &kfilter.k_endog) return determinant cdef {{cython_type}} {{prefix}}solve_cholesky({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant) except *: """ solve_cholesky(self, determinant) If the model has converged to a steady-state, this is a NOOP and simply returns the determinant that was passed in. """ cdef: int info, i, j int inc = 1 if not kfilter.converged: # Perform the Cholesky decomposition and get the determinant determinant = {{prefix}}factorize_cholesky(kfilter, model, determinant) # Use the Cholesky factor to get standardized forecast errors, if desired # (in the notation of DK, kfilter._forecast_error_fac holds L_t', and # we want to solve the equation L_t' v_t^s = v_t) if not (kfilter.conserve_memory & MEMORY_NO_STD_FORECAST > 0): blas.{{prefix}}copy(&kfilter.k_endog, kfilter._forecast_error, &inc, kfilter._standardized_forecast_error, &inc) lapack.{{prefix}}trtrs("U", "T", "N", &model._k_endog, &inc, kfilter._forecast_error_fac, &kfilter.k_endog, kfilter._standardized_forecast_error, &kfilter.k_endog, &info) if info != 0: raise np.linalg.LinAlgError('Error computing standardized' ' forecast error at period %d' % kfilter.t) # Solve the linear systems # `tmp2` array used here, dimension $(p \times 1)$ # $F_t \\#_2 = v_t$ blas.{{prefix}}copy(&kfilter.k_endog, kfilter._forecast_error, &inc, kfilter._tmp2, &inc) lapack.{{prefix}}potrs("U", &model._k_endog, &inc, kfilter._forecast_error_fac, &kfilter.k_endog, kfilter._tmp2, &kfilter.k_endog, &info) # `tmp3` array used here, dimension $(p \times m)$ # $F_t \\#_3 = Z_t$ if model._k_states == model.k_states and model._k_endog == model.k_endog: blas.{{prefix}}copy(&kfilter.k_endogstates, model._design, &inc, kfilter._tmp3, &inc) else: for i in range(model._k_states): # columns for j in range(model._k_endog): # rows kfilter._tmp3[j + i*kfilter.k_endog] = model._design[j + i*model._k_endog] lapack.{{prefix}}potrs("U", &model._k_endog, &model._k_states, kfilter._forecast_error_fac, &kfilter.k_endog, kfilter._tmp3, &kfilter.k_endog, &info) if not (kfilter.conserve_memory & MEMORY_NO_SMOOTHING > 0): # `tmp4` array used here, dimension $(p \times p)$ # $F_t \\#_4 = H_t$ if model._k_states == model.k_states and model._k_endog == model.k_endog: blas.{{prefix}}copy(&kfilter.k_endog2, model._obs_cov, &inc, kfilter._tmp4, &inc) else: for i in range(model._k_endog): # columns for j in range(model._k_endog): # rows kfilter._tmp4[j + i*kfilter.k_endog] = model._obs_cov[j + i*model._k_endog] lapack.{{prefix}}potrs("U", &model._k_endog, &model._k_endog, kfilter._forecast_error_fac, &kfilter.k_endog, kfilter._tmp4, &kfilter.k_endog, &info) return determinant cdef {{cython_type}} {{prefix}}solve_lu({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant) except *: """ inverse_cholesky(self, determinant) If the model has converged to a steady-state, this is a NOOP and simply returns the determinant that was passed in. """ cdef: int info int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 if not kfilter.converged: # Perform the Cholesky decomposition and get the determinant determinant = {{prefix}}factorize_lu(kfilter, model, determinant) # Solve the linear systems # `tmp2` array used here, dimension $(p \times 1)$ # $F_t \\#_2 = v_t$ blas.{{prefix}}copy(&kfilter.k_endog, kfilter._forecast_error, &inc, kfilter._tmp2, &inc) lapack.{{prefix}}getrs("N", &model._k_endog, &inc, kfilter._forecast_error_fac, &kfilter.k_endog, kfilter._forecast_error_ipiv, kfilter._tmp2, &kfilter.k_endog, &info) # `tmp3` array used here, dimension $(p \times m)$ # $F_t \\#_3 = Z_t$ if model._k_states == model.k_states and model._k_endog == model.k_endog: blas.{{prefix}}copy(&kfilter.k_endogstates, model._design, &inc, kfilter._tmp3, &inc) else: for i in range(model._k_states): # columns for j in range(model._k_endog): # rows kfilter._tmp3[j + i*kfilter.k_endog] = model._design[j + i*model._k_endog] lapack.{{prefix}}getrs("N", &model._k_endog, &model._k_states, kfilter._forecast_error_fac, &kfilter.k_endog, kfilter._forecast_error_ipiv, kfilter._tmp3, &kfilter.k_endog, &info) if not (kfilter.conserve_memory & MEMORY_NO_SMOOTHING > 0): # `tmp4` array used here, dimension $(p \times p)$ # $F_t \\#_4 = H_t$ if model._k_states == model.k_states and model._k_endog == model.k_endog: blas.{{prefix}}copy(&kfilter.k_endog2, model._obs_cov, &inc, kfilter._tmp4, &inc) else: for i in range(model._k_endog): # columns for j in range(model._k_endog): # rows kfilter._tmp4[j + i*kfilter.k_endog] = model._obs_cov[j + i*model._k_endog] lapack.{{prefix}}getrs("N", &model._k_endog, &model._k_endog, kfilter._forecast_error_fac, &kfilter.k_endog, kfilter._forecast_error_ipiv, kfilter._tmp4, &kfilter.k_endog, &info) return determinant {{endfor}} statsmodels-0.12.2/statsmodels/tsa/statespace/_filters/_univariate.pxd000066400000000000000000000155361400612667500262760ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models - Conventional Kalman Filter declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace ) from statsmodels.tsa.statespace._kalman_filter cimport ( sKalmanFilter, dKalmanFilter, cKalmanFilter, zKalmanFilter ) # Single precision cdef int sforecast_univariate(sKalmanFilter kfilter, sStatespace model) cdef int supdating_univariate(sKalmanFilter kfilter, sStatespace model) cdef int sprediction_univariate(sKalmanFilter kfilter, sStatespace model) cdef np.float32_t sinverse_noop_univariate(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) except * cdef np.float32_t sloglikelihood_univariate(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) cdef np.float32_t sscale_univariate(sKalmanFilter kfilter, sStatespace model) cdef void sforecast_error(sKalmanFilter kfilter, sStatespace model, int i) cdef np.float32_t sforecast_error_cov(sKalmanFilter kfilter, sStatespace model, int i) cdef void stemp_arrays(sKalmanFilter kfilter, sStatespace model, int i, np.float32_t forecast_error_cov_inv) cdef void sfiltered_state(sKalmanFilter kfilter, sStatespace model, int i, np.float32_t forecast_error_cov_inv) cdef void sfiltered_state_cov(sKalmanFilter kfilter, sStatespace model, int i, np.float32_t forecast_error_cov_inv) cdef void schandrasekhar_recursion(sKalmanFilter kfilter, sStatespace model, int i, np.float32_t forecast_error_cov, np.float32_t forecast_error_cov_inv, np.float32_t forecast_error_cov_inv_prev) cdef void spredicted_state(sKalmanFilter kfilter, sStatespace model) cdef void spredicted_state_cov(sKalmanFilter kfilter, sStatespace model) cdef void spredicted_state_cov_chandrasekhar(sKalmanFilter kfilter, sStatespace model) cdef void sloglikelihood(sKalmanFilter kfilter, sStatespace model, int i, np.float32_t forecast_error_cov, np.float32_t forecast_error_cov_inv) # Double precision cdef int dforecast_univariate(dKalmanFilter kfilter, dStatespace model) cdef int dupdating_univariate(dKalmanFilter kfilter, dStatespace model) cdef int dprediction_univariate(dKalmanFilter kfilter, dStatespace model) cdef np.float64_t dinverse_noop_univariate(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) except * cdef np.float64_t dloglikelihood_univariate(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) cdef np.float64_t dscale_univariate(dKalmanFilter kfilter, dStatespace model) cdef void dforecast_error(dKalmanFilter kfilter, dStatespace model, int i) cdef np.float64_t dforecast_error_cov(dKalmanFilter kfilter, dStatespace model, int i) cdef void dtemp_arrays(dKalmanFilter kfilter, dStatespace model, int i, np.float64_t forecast_error_cov_inv) cdef void dfiltered_state(dKalmanFilter kfilter, dStatespace model, int i, np.float64_t forecast_error_cov_inv) cdef void dfiltered_state_cov(dKalmanFilter kfilter, dStatespace model, int i, np.float64_t forecast_error_cov_inv) cdef void dchandrasekhar_recursion(dKalmanFilter kfilter, dStatespace model, int i, np.float64_t forecast_error_cov, np.float64_t forecast_error_cov_inv, np.float64_t forecast_error_cov_inv_prev) cdef void dpredicted_state(dKalmanFilter kfilter, dStatespace model) cdef void dpredicted_state_cov(dKalmanFilter kfilter, dStatespace model) cdef void dpredicted_state_cov_chandrasekhar(dKalmanFilter kfilter, dStatespace model) cdef void dloglikelihood(dKalmanFilter kfilter, dStatespace model, int i, np.float64_t forecast_error_cov, np.float64_t forecast_error_cov_inv) # Single precision complex cdef int cforecast_univariate(cKalmanFilter kfilter, cStatespace model) cdef int cupdating_univariate(cKalmanFilter kfilter, cStatespace model) cdef int cprediction_univariate(cKalmanFilter kfilter, cStatespace model) cdef np.complex64_t cinverse_noop_univariate(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) except * cdef np.complex64_t cloglikelihood_univariate(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) cdef np.complex64_t cscale_univariate(cKalmanFilter kfilter, cStatespace model) cdef void cforecast_error(cKalmanFilter kfilter, cStatespace model, int i) cdef np.complex64_t cforecast_error_cov(cKalmanFilter kfilter, cStatespace model, int i) cdef void ctemp_arrays(cKalmanFilter kfilter, cStatespace model, int i, np.complex64_t forecast_error_cov_inv) cdef void cfiltered_state(cKalmanFilter kfilter, cStatespace model, int i, np.complex64_t forecast_error_cov_inv) cdef void cfiltered_state_cov(cKalmanFilter kfilter, cStatespace model, int i, np.complex64_t forecast_error_cov_inv) cdef void cchandrasekhar_recursion(cKalmanFilter kfilter, cStatespace model, int i, np.complex64_t forecast_error_cov, np.complex64_t forecast_error_cov_inv, np.complex64_t forecast_error_cov_inv_prev) cdef void cpredicted_state(cKalmanFilter kfilter, cStatespace model) cdef void cpredicted_state_cov(cKalmanFilter kfilter, cStatespace model) cdef void cpredicted_state_cov_chandrasekhar(cKalmanFilter kfilter, cStatespace model) cdef void cloglikelihood(cKalmanFilter kfilter, cStatespace model, int i, np.complex64_t forecast_error_cov, np.complex64_t forecast_error_cov_inv) # Double precision complex cdef int zforecast_univariate(zKalmanFilter kfilter, zStatespace model) cdef int zupdating_univariate(zKalmanFilter kfilter, zStatespace model) cdef int zprediction_univariate(zKalmanFilter kfilter, zStatespace model) cdef np.complex128_t zinverse_noop_univariate(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) except * cdef np.complex128_t zloglikelihood_univariate(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) cdef np.complex128_t zscale_univariate(zKalmanFilter kfilter, zStatespace model) cdef void zforecast_error(zKalmanFilter kfilter, zStatespace model, int i) cdef np.complex128_t zforecast_error_cov(zKalmanFilter kfilter, zStatespace model, int i) cdef void ztemp_arrays(zKalmanFilter kfilter, zStatespace model, int i, np.complex128_t forecast_error_cov_inv) cdef void zfiltered_state(zKalmanFilter kfilter, zStatespace model, int i, np.complex128_t forecast_error_cov_inv) cdef void zfiltered_state_cov(zKalmanFilter kfilter, zStatespace model, int i, np.complex128_t forecast_error_cov_inv) cdef void zchandrasekhar_recursion(zKalmanFilter kfilter, zStatespace model, int i, np.complex128_t forecast_error_cov, np.complex128_t forecast_error_cov_inv, np.complex128_t forecast_error_cov_inv_prev) cdef void zpredicted_state(zKalmanFilter kfilter, zStatespace model) cdef void zpredicted_state_cov(zKalmanFilter kfilter, zStatespace model) cdef void zpredicted_state_cov_chandrasekhar(zKalmanFilter kfilter, zStatespace model) cdef void zloglikelihood(zKalmanFilter kfilter, zStatespace model, int i, np.complex128_t forecast_error_cov, np.complex128_t forecast_error_cov_inv) statsmodels-0.12.2/statsmodels/tsa/statespace/_filters/_univariate.pyx.in000066400000000000000000000651611400612667500267270ustar00rootroot00000000000000#cython: profile=False #cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # Typical imports cimport numpy as np import numpy as np from statsmodels.src.math cimport * cimport scipy.linalg.cython_blas as blas cimport scipy.linalg.cython_lapack as lapack from statsmodels.tsa.statespace._kalman_filter cimport ( MEMORY_NO_LIKELIHOOD, MEMORY_NO_FORECAST_COV, MEMORY_NO_STD_FORECAST, MEMORY_NO_SMOOTHING, FILTER_CONCENTRATED, FILTER_CHANDRASEKHAR) {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' combined_suffix = '' if combined_prefix == 'z': combined_suffix = 'u' }} # ### Univariate Kalman filter # # The following are the routines as defined in the univariate Kalman filter. # # See Durbin and Koopman (2012) Chapter 6.4 cdef int {{prefix}}forecast_univariate({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): # Constants cdef: int i, j, k int inc = 1 int forecast_cov_t = kfilter.t int check {{cython_type}} forecast_error_cov {{cython_type}} forecast_error_cov_inv {{cython_type}} forecast_error_cov_inv_prev = 0.0 if kfilter.conserve_memory & MEMORY_NO_FORECAST_COV > 0: forecast_cov_t = 1 # Initialize the filtered states {{prefix}}initialize_filtered(kfilter, model) # Make sure the loglikelihood is set to zero if necessary # Iterate over the observations at time t for i in range(model._k_endog): # #### Forecast for time t # `forecast` $= Z_{t,i} a_{t,i} + d_{t,i}$ # Note: $Z_{t,i}$ is a row vector starting at [i,0,t] and ending at # [i,k_states,t] # Note: zdot and cdot are broken, so have to use gemv for those # #### Forecast error for time t # `forecast_error` $\equiv v_t = y_t -$ `forecast` {{prefix}}forecast_error(kfilter, model, i) # #### Forecast error covariance matrix for time t # $F_{t,i} \equiv Z_{t,i} P_{t,i} Z_{t,i}' + H_{t,i}$ # TODO what about Kalman convergence? # Note: zdot and cdot are broken, so have to use gemv for those if not kfilter.converged: forecast_error_cov = {{prefix}}forecast_error_cov(kfilter, model, i) else: forecast_error_cov = kfilter._forecast_error_cov[i + i*kfilter.k_endog] # Handle numerical issues that can cause a very small negative # forecast_error_cov check = {{prefix}}check1(kfilter, forecast_error_cov) if check: kfilter._forecast_error_cov[i + i*kfilter.k_endog] = 0 forecast_error_cov = 0 # If we have a non-zero variance # (if we have a zero-variance then we are done with this iteration) check = {{prefix}}check2(kfilter, i, forecast_error_cov) if check: forecast_error_cov_inv = {{prefix}}forecast_error_cov_inv(kfilter, model, i, forecast_error_cov) {{prefix}}standardized_forecast_error(kfilter, model, i, forecast_error_cov_inv) # Save temporary array data {{prefix}}temp_arrays(kfilter, model, i, forecast_error_cov_inv) # #### Filtered state for time t # $a_{t,i+1} = a_{t,i} + P_{t,i} Z_{t,i}' F_{t,i}^{-1} v_{t,i}$ # Make a new temporary array # K_{t,i} = P_{t,i} Z_{t,i}' F_{t,i}^{-1} {{prefix}}filtered_state(kfilter, model, i, forecast_error_cov_inv) # Chandrasekhar arrays if not kfilter.converged and (kfilter.filter_method & FILTER_CHANDRASEKHAR > 0): if kfilter.t > 0: forecast_error_cov_inv_prev = 1.0 / kfilter.forecast_error_cov[i, i, forecast_cov_t - 1] {{prefix}}chandrasekhar_recursion(kfilter, model, i, forecast_error_cov, forecast_error_cov_inv, forecast_error_cov_inv_prev) # #### Filtered state covariance for time t # $P_{t,i+1} = P_{t,i} - P_{t,i} Z_{t,i}' F_{t,i}^{-1} Z_{t,i} P_{t,i}'$ if not kfilter.converged: {{prefix}}filtered_state_cov(kfilter, model, i, forecast_error_cov_inv) # #### Loglikelihood {{prefix}}loglikelihood(kfilter, model, i, forecast_error_cov, forecast_error_cov_inv) else: # Otherwise, we need to record that this observation is not associated # with a loglikelihood step (so that it can be excluded in the denominator # when computing the scale) kfilter.nobs_kendog_univariate_singular = kfilter.nobs_kendog_univariate_singular + 1 {{prefix}}symmetry(kfilter, model) return 0 cdef void {{prefix}}initialize_filtered({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef int inc = 1 blas.{{prefix}}copy(&kfilter.k_states, kfilter._input_state, &inc, kfilter._filtered_state, &inc) if not kfilter.converged: blas.{{prefix}}copy(&kfilter.k_states2, kfilter._input_state_cov, &inc, kfilter._filtered_state_cov, &inc) cdef int {{prefix}}check1({{prefix}}KalmanFilter kfilter, {{cython_type}} forecast_error_cov): if not kfilter.converged: return forecast_error_cov{{if combined_prefix == 'z'}}.real{{endif}} < 0 else: return False cdef int {{prefix}}check2({{prefix}}KalmanFilter kfilter, int i, {{cython_type}} forecast_error_cov): if not kfilter.converged: kfilter.forecast_error_ipiv[i] = forecast_error_cov{{if combined_prefix == 'z'}}.real{{endif}} > kfilter.tolerance_diffuse return kfilter.forecast_error_ipiv[i] cdef {{cython_type}} {{prefix}}forecast_error_cov_inv({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, int i, {{cython_type}} forecast_error_cov): if not kfilter.converged: kfilter.forecast_error_fac[i, i] = 1.0 / forecast_error_cov return kfilter.forecast_error_fac[i, i] cdef void {{prefix}}standardized_forecast_error({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, int i, {{cython_type}} forecast_error_cov_inv): if not (kfilter.conserve_memory & MEMORY_NO_STD_FORECAST > 0): kfilter._standardized_forecast_error[i] = ( kfilter._forecast_error[i] * forecast_error_cov_inv**0.5) cdef void {{prefix}}symmetry({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef int j, k # Make final filtered_state_cov symmetric (is not currently symmetric # due to use of ?syr or ?her) if not kfilter.converged: for j in range(model._k_states): # columns for k in range(model._k_states): # rows if k > j: # row > column => in lower triangle kfilter._filtered_state_cov[j + k*kfilter.k_states] = kfilter._filtered_state_cov[k + j*kfilter.k_states] cdef void {{prefix}}forecast_error({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, int i): cdef: int inc = 1 {{cython_type}} alpha = 1 {{cython_type}} beta = 0 int k_states = model._k_states # Adjust for a VAR transition (i.e. design = [#, 0], where the zeros # correspond to all states except the first k_posdef states) if model.subset_design: k_states = model._k_posdef # `forecast` $= Z_{t,i} a_{t,i} + d_{t,i}$ {{if combined_prefix == 'd'}} kfilter._forecast[i] = ( model._obs_intercept[i] + blas.{{prefix}}dot(&k_states, &model._design[i], &model._k_endog, kfilter._filtered_state, &inc) ) {{else}} blas.{{prefix}}gemv("N", &inc, &k_states, &alpha, kfilter._filtered_state, &inc, &model._design[i], &model._k_endog, &beta, kfilter._tmp0, &inc) kfilter._forecast[i] = model._obs_intercept[i] + kfilter._tmp0[0] {{endif}} # `forecast_error` $\equiv v_t = y_t -$ `forecast` kfilter._forecast_error[i] = model._obs[i] - kfilter._forecast[i] cdef {{cython_type}} {{prefix}}forecast_error_cov({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, int i): cdef: int inc = 1 {{cython_type}} alpha = 1 {{cython_type}} beta = 0 {{cython_type}} forecast_error_cov int k_states = model._k_states # Adjust for a VAR transition (i.e. design = [#, 0], where the zeros # correspond to all states except the first k_posdef states) if model.subset_design: k_states = model._k_posdef # *Intermediate calculation* (used just below and then once more) # $M_{t,i} = P_{t,i} Z_{t,i}'$ # $(m \times 1) = (m \times m) (1 \times m)'$ # blas.{{prefix}}gemv("N", &model._k_states, &k_states, # &alpha, kfilter._filtered_state_cov, &kfilter.k_states, # &model._design[i], &model._k_endog, # &beta, &kfilter._M[i*kfilter.k_states], &inc) # $F_{t,i} \equiv Z_{t,i} P_{t,i} Z_{t,i}' + H_{t,i}$ {{if combined_prefix == 'd'}} blas.{{prefix}}symv("L", &model._k_states, &alpha, kfilter._filtered_state_cov, &kfilter.k_states, &model._design[i], &model._k_endog, &beta, &kfilter._M[i*kfilter.k_states], &inc) forecast_error_cov = ( model._obs_cov[i + i*model._k_endog] + blas.{{prefix}}dot(&k_states, &model._design[i], &model._k_endog, &kfilter._M[i*kfilter.k_states], &inc) ) {{else}} blas.{{prefix}}symm("R", "L", &inc, &model._k_states, &alpha, kfilter._filtered_state_cov, &kfilter.k_states, &model._design[i], &model._k_endog, &beta, &kfilter._M[i*kfilter.k_states], &inc) blas.{{prefix}}gemv("N", &inc, &k_states, &alpha, &kfilter._M[i*kfilter.k_states], &inc, &model._design[i], &model._k_endog, &beta, kfilter._tmp0, &inc) forecast_error_cov = model._obs_cov[i + i*model._k_endog] + kfilter._tmp0[0] {{endif}} kfilter._forecast_error_cov[i + i*kfilter.k_endog] = forecast_error_cov return forecast_error_cov cdef void {{prefix}}temp_arrays({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, int i, {{cython_type}} forecast_error_cov_inv): cdef: int k_states = model._k_states tmp_1 = 0 # Adjust for a VAR transition (i.e. design = [#, 0], where the zeros # correspond to all states except the first k_posdef states) if model.subset_design: k_states = model._k_posdef # $\\#_1 = P_{t,i} Z_{t,i}'$ - set above # $\\#_2 = v_{t,i} / F_{t,i}$ kfilter._tmp2[i] = kfilter._forecast_error[i] * forecast_error_cov_inv # $\\#_3 = Z_{t,i} / F_{t,i}$ # $\\#_4 = H_{t,i} / F_{t,i}$ if not kfilter.converged: blas.{{prefix}}copy(&k_states, &model._design[i], &model._k_endog, &kfilter._tmp3[i], &kfilter.k_endog) blas.{{prefix}}scal(&k_states, &forecast_error_cov_inv, &kfilter._tmp3[i], &kfilter.k_endog) kfilter._tmp4[i + i*kfilter.k_endog] = model._obs_cov[i + i*model._k_endog] * forecast_error_cov_inv elif kfilter.conserve_memory & MEMORY_NO_SMOOTHING > 0: # If we're converged and we're not storing these arrays, then we # already have the converged values and there's nothing more to do pass else: # If we're converged and we are storing these arrays, then we # just need to copy them from the previous iteration blas.{{prefix}}copy(&k_states, &kfilter.tmp3[i, 0, kfilter.t - 1], &kfilter.k_endog, &kfilter._tmp3[i], &kfilter.k_endog) kfilter._tmp4[i + i*kfilter.k_endog] = kfilter.tmp4[i, i, kfilter.t - 1] cdef void {{prefix}}filtered_state({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, int i, {{cython_type}} forecast_error_cov_inv): cdef int j # $a_{t,i+1} = a_{t,i} + P_{t,i} Z_{t,i}' F_{t,i}^{-1} v_{t,i}$ for j in range(model._k_states): if not kfilter.converged: kfilter._kalman_gain[j + i*kfilter.k_states] = kfilter._M[j + i*kfilter.k_states] * forecast_error_cov_inv kfilter._filtered_state[j] = ( kfilter._filtered_state[j] + kfilter._forecast_error[i] * kfilter._kalman_gain[j + i*kfilter.k_states] ) cdef void {{prefix}}filtered_state_cov({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, int i, {{cython_type}} forecast_error_cov_inv): cdef: int inc = 1, j, k {{cython_type}} scalar = -1.0 * forecast_error_cov_inv {{cython_type}} alpha = 1.0 {{cython_type}} gamma = -1.0 int k_states = model._k_states int k_states1 = model._k_states # Adjust for a VAR transition (i.e. design = [#, 0], where the zeros # correspond to all states except the first k_posdef states) if model.subset_design: k_states = model._k_posdef if model._k_posdef > model._k_states: k_states1 = model._k_posdef + 1 # $P_{t,i+1} = P_{t,i} - P_{t,i} Z_{t,i}' F_{t,i}^{-1} Z_{t,i} P_{t,i}'$ # blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, # &gamma, &kfilter._M[i*kfilter.k_states], &inc, # &kfilter._kalman_gain[i*kfilter.k_states], &inc, # kfilter._filtered_state_cov, &kfilter.k_states # ) {{if combined_prefix == 'd'}} blas.{{prefix}}syr("L", &model._k_states, &scalar, &kfilter._M[i*kfilter.k_states], &inc, kfilter._filtered_state_cov, &kfilter.k_states ) {{else}} blas.{{prefix}}syrk("L", "N", &model._k_states, &inc, &scalar, &kfilter._M[i*kfilter.k_states], &kfilter.k_states, &alpha, kfilter._filtered_state_cov, &kfilter.k_states) {{endif}} cdef void {{prefix}}chandrasekhar_recursion({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, int i, {{cython_type}} forecast_error_cov, {{cython_type}} forecast_error_cov_inv, {{cython_type}} forecast_error_cov_inv_prev): # Constants cdef: int inc = 1 int j, k {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # Initialization if kfilter.t == 0: if i == 0: kfilter.CM[:] = 0 # W[:, i:i+1] = T @ (P @ Z[i].T) # W[:, i:i+1] = T @ K @ F[i, i] # Note: we scale by forecast error cov here b/c kalman_gain was # computed above as K = P @ Z[i].T @ (1 / F[i, i]) blas.{{prefix}}gemv("N", &model._k_states, &model._k_states, &forecast_error_cov, model._transition, &model._k_states, &kfilter._kalman_gain[i * kfilter.k_states], &inc, &beta, &kfilter.CW[0, i], &inc) # M[i, i] = Finv[i, i] kfilter.CM[i, i] = -forecast_error_cov_inv # Updating else: # M.T @ W.T. (p x p) (p x m) blas.{{prefix}}gemm("T", "T", &model._k_endog, &model._k_states, &model._k_endog, &alpha, &kfilter.CM[0, 0], &kfilter.k_endog, &kfilter.CW[0, 0], &kfilter.k_states, &beta, &kfilter.CMW[0, 0], &kfilter.k_endog) # MW @ Z[i].T (p x m) (m x 1) -> (p x 1) blas.{{prefix}}gemv("N", &model._k_endog, &model._k_states, &alpha, &kfilter.CMW[0, 0], &kfilter.k_endog, &model._design[i], &model._k_endog, &beta, &kfilter.CMWZ[0, 0], &inc) # M = M + MWZ @ MWZ.T / F_prev[i, i] # Note: syr / syrk only fills in lower triangle here {{if combined_prefix == 'd'}} blas.{{prefix}}syr("L", &model._k_endog, &forecast_error_cov_inv_prev, &kfilter.CMWZ[0, 0], &inc, &kfilter.CM[0, 0], &kfilter.k_endog) {{else}} blas.{{prefix}}syrk("L", "N", &model._k_endog, &inc, &forecast_error_cov_inv_prev, &kfilter.CMWZ[0, 0], &kfilter.k_endog, &alpha, &kfilter.CM[0, 0], &kfilter.k_endog) {{endif}} # Fill in the upper triangle for j in range(model._k_endog): # columns for k in range(model._k_endog): # rows if k > j: # row > column => in lower triangle kfilter.CM[j, k] = kfilter.CM[k, j] # Compute W # W -> tmpW blas.{{prefix}}copy(&model._k_endogstates, &kfilter.CW[0, 0], &inc, &kfilter.CtmpW[0, 0], &inc) if i == model.k_endog - 1: # W = (T - T @ K @ Z[i]) @ W # Compute T @ K: (m x m) (m x 1) -> (m x 1) # Note: we previously copied CW -> CtmpW, so overwriting CW is okay blas.{{prefix}}gemv("N", &model._k_states, &model._k_states, &alpha, model._transition, &model._k_states, &kfilter._kalman_gain[i*kfilter.k_states], &inc, &beta, &kfilter.CW[0, 0], &inc) # T -> tmp00 blas.{{prefix}}copy(&model._k_states2, model._transition, &inc, kfilter._tmp00, &inc) # T - (T @ K) @ Z[i]: (m x 1) (1 x m) -> (m x m) blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &gamma, &kfilter.CW[0, 0], &inc, &model._design[i], &model._k_endog, kfilter._tmp00, &kfilter.k_states) # (T - T @ K @ Z[i]) @ tmpW -> W blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_endog, &model._k_states, &alpha, kfilter._tmp00, &kfilter.k_states, &kfilter.CtmpW[0, 0], &kfilter.k_states, &beta, &kfilter.CW[0, 0], &kfilter.k_states) else: # W = (I - I @ K @ Z[i]) @ W # K @ Z[i] (m x 1) (1 x m) -> (m x m) kfilter.tmp0[:] = 0 blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &alpha, &kfilter._kalman_gain[i*kfilter.k_states], &inc, &model._design[i], &model._k_endog, kfilter._tmp0, &kfilter.k_states) # W = - K @ Z[i] @ W + W blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_endog, &model._k_states, &gamma, kfilter._tmp0, &kfilter.k_states, &kfilter.CtmpW[0, 0], &kfilter.k_states, &alpha, &kfilter.CW[0, 0], &kfilter.k_states) cdef void {{prefix}}loglikelihood({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, int i, {{cython_type}} forecast_error_cov, {{cython_type}} forecast_error_cov_inv): kfilter._loglikelihood[0] = ( kfilter._loglikelihood[0] - 0.5*( {{combined_prefix}}log(2 * NPY_PI * forecast_error_cov) ) ) if kfilter.filter_method & FILTER_CONCENTRATED: kfilter._scale[0] = kfilter._scale[0] + kfilter._forecast_error[i]**2 * forecast_error_cov_inv else: kfilter._loglikelihood[0] = kfilter._loglikelihood[0] - 0.5 * (kfilter._forecast_error[i]**2 * forecast_error_cov_inv) cdef int {{prefix}}updating_univariate({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): # the updating step was performed in the forecast_univariate step return 0 cdef int {{prefix}}prediction_univariate({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): # Constants cdef: int inc = 1 int i, j {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # #### Predicted state for time t+1 # $a_{t+1} = T_t a_{t,n} + c_t$ # #### Predicted state covariance matrix for time t+1 # $P_{t+1} = T_t P_{t,n} T_t' + Q_t^*$ # # TODO check behavior during convergence if not model.companion_transition: {{prefix}}predicted_state(kfilter, model) if not kfilter.converged: if kfilter.filter_method & FILTER_CHANDRASEKHAR > 0: {{prefix}}predicted_state_cov_chandrasekhar(kfilter, model) else: {{prefix}}predicted_state_cov(kfilter, model) else: {{prefix}}companion_predicted_state(kfilter, model) if not kfilter.converged: {{prefix}}companion_predicted_state_cov(kfilter, model) # #### Kalman gain for time t # $K_t = T_t P_t Z_t' F_t^{-1}$ # Kalman gain calculation done in forecasting step. return 0 cdef void {{prefix}}predicted_state({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef: int inc = 1 {{cython_type}} alpha = 1.0 # $a_{t+1} = T_t a_{t,n} + c_t$ blas.{{prefix}}copy(&model._k_states, model._state_intercept, &inc, kfilter._predicted_state, &inc) blas.{{prefix}}gemv("N", &model._k_states, &model._k_states, &alpha, model._transition, &model._k_states, kfilter._filtered_state, &inc, &alpha, kfilter._predicted_state, &inc) cdef void {{prefix}}predicted_state_cov({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 # $P_{t+1} = T_t P_{t,n} T_t' + Q_t^*$ blas.{{prefix}}copy(&model._k_states2, model._selected_state_cov, &inc, kfilter._predicted_state_cov, &inc) # `tmp0` array used here, dimension $(m \times m)$ # $\\#_0 = T_t P_{t|t} $ # $(m \times m) = (m \times m) (m \times m)$ # blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, # &alpha, model._transition, &model._k_states, # kfilter._filtered_state_cov, &kfilter.k_states, # &beta, kfilter._tmp0, &kfilter.k_states) blas.{{prefix}}symm("R", "L", &model._k_states, &model._k_states, &alpha, kfilter._filtered_state_cov, &kfilter.k_states, model._transition, &model._k_states, &beta, kfilter._tmp0, &kfilter.k_states) # $P_{t+1} = 1.0 \\#_0 T_t' + 1.0 \\#$ # $(m \times m) = (m \times m) (m \times m) + (m \times m)$ blas.{{prefix}}gemm("N", "T", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmp0, &kfilter.k_states, model._transition, &model._k_states, &alpha, kfilter._predicted_state_cov, &kfilter.k_states) cdef void {{prefix}}predicted_state_cov_chandrasekhar({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): # Constants cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 blas.{{prefix}}copy(&model._k_states2, kfilter._input_state_cov, &inc, kfilter._predicted_state_cov, &inc) # M @ W.T. (p x p) (p x m) blas.{{prefix}}gemm("N", "T", &model._k_endog, &model._k_states, &model._k_endog, &alpha, &kfilter.CM[0, 0], &kfilter.k_endog, &kfilter.CW[0, 0], &kfilter.k_states, &beta, &kfilter.CMW[0, 0], &kfilter.k_endog) # P = P + W M W.T blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_endog, &alpha, &kfilter.CW[0, 0], &kfilter.k_states, &kfilter.CMW[0, 0], &kfilter.k_endog, &alpha, kfilter._predicted_state_cov, &kfilter.k_states) cdef void {{prefix}}companion_predicted_state({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef: int i int inc = 1 {{cython_type}} alpha = 1.0 # $a_{t+1} = T_t a_{t,n} + c_t$ blas.{{prefix}}copy(&model._k_states, model._state_intercept, &inc, kfilter._predicted_state, &inc) blas.{{prefix}}gemv("N", &model._k_posdef, &model._k_states, &alpha, model._transition, &model._k_states, kfilter._filtered_state, &inc, &alpha, kfilter._predicted_state, &inc) for i in range(model._k_posdef, model._k_states): kfilter._predicted_state[i] = kfilter._predicted_state[i] + kfilter._filtered_state[i - model._k_posdef] cdef void {{prefix}}companion_predicted_state_cov({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef: int i, j, idx int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} tmp # $P_{t+1} = T_t P_{t,n} T_t' + Q_t^*$ # `tmp0` array used here, dimension $(p \times m)$ # $\\#_0 = \phi_t P_{t|t} $ # $(p \times m) = (p \times m) (m \times m)$ # TODO: symm? blas.{{prefix}}gemm("N", "N", &model._k_posdef, &model._k_states, &model._k_states, &alpha, model._transition, &model._k_states, kfilter._filtered_state_cov, &kfilter.k_states, &beta, kfilter._tmp0, &kfilter.k_states) # $P_{t+1} = 1.0 \\#_0 \phi_t' + 1.0 \\#$ # $(m \times m) = (p \times m) (m \times p) + (m \times m)$ blas.{{prefix}}gemm("N", "T", &model._k_posdef, &model._k_posdef, &model._k_states, &alpha, kfilter._tmp0, &kfilter.k_states, model._transition, &model._k_states, &beta, kfilter._predicted_state_cov, &kfilter.k_states) # Fill in the basic matrix blocks for i in range(kfilter.k_states): # columns for j in range(kfilter.k_states): # rows idx = j + i*kfilter.k_states # Add the Q matrix to the upper-left block if i < model._k_posdef and j < model._k_posdef: kfilter._predicted_state_cov[idx] = ( kfilter._predicted_state_cov[idx] + model._state_cov[j + i*model._k_posdef] ) # Set the upper-right block to be the first m-p columns of # \phi _t P_{t|t}, and the lower-left block to the its transpose elif i >= model._k_posdef and j < model._k_posdef: tmp = kfilter._tmp0[j + (i-model._k_posdef)*kfilter.k_states] kfilter._predicted_state_cov[idx] = tmp kfilter._predicted_state_cov[i + j*model._k_states] = tmp # Set the lower-right block elif i >= model._k_posdef and j >= model._k_posdef: kfilter._predicted_state_cov[idx] = ( kfilter._filtered_state_cov[(j - model._k_posdef) + (i - model._k_posdef)*kfilter.k_states] ) cdef {{cython_type}} {{prefix}}inverse_noop_univariate({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant) except *: return -np.inf cdef {{cython_type}} {{prefix}}loglikelihood_univariate({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant): return 0 cdef {{cython_type}} {{prefix}}scale_univariate({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): return 0 {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/_filters/_univariate_diffuse.pxd000066400000000000000000000062511400612667500277750ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models - Conventional Kalman Filter declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace ) from statsmodels.tsa.statespace._kalman_filter cimport ( sKalmanFilter, dKalmanFilter, cKalmanFilter, zKalmanFilter ) # Single precision cdef int sforecast_univariate_diffuse(sKalmanFilter kfilter, sStatespace model) cdef int supdating_univariate_diffuse(sKalmanFilter kfilter, sStatespace model) cdef int sprediction_univariate_diffuse(sKalmanFilter kfilter, sStatespace model) cdef np.float32_t sinverse_noop_univariate_diffuse(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) except * cdef np.float32_t sloglikelihood_univariate_diffuse(sKalmanFilter kfilter, sStatespace model, np.float32_t determinant) cdef np.float32_t sforecast_error_diffuse_cov(sKalmanFilter kfilter, sStatespace model, int i) cdef void spredicted_diffuse_state_cov(sKalmanFilter kfilter, sStatespace model) # Double precision cdef int dforecast_univariate_diffuse(dKalmanFilter kfilter, dStatespace model) cdef int dupdating_univariate_diffuse(dKalmanFilter kfilter, dStatespace model) cdef int dprediction_univariate_diffuse(dKalmanFilter kfilter, dStatespace model) cdef np.float64_t dinverse_noop_univariate_diffuse(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) except * cdef np.float64_t dloglikelihood_univariate_diffuse(dKalmanFilter kfilter, dStatespace model, np.float64_t determinant) cdef np.float64_t dforecast_error_diffuse_cov(dKalmanFilter kfilter, dStatespace model, int i) cdef void dpredicted_diffuse_state_cov(dKalmanFilter kfilter, dStatespace model) # Single precision complex cdef int cforecast_univariate_diffuse(cKalmanFilter kfilter, cStatespace model) cdef int cupdating_univariate_diffuse(cKalmanFilter kfilter, cStatespace model) cdef int cprediction_univariate_diffuse(cKalmanFilter kfilter, cStatespace model) cdef np.complex64_t cinverse_noop_univariate_diffuse(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) except * cdef np.complex64_t cloglikelihood_univariate_diffuse(cKalmanFilter kfilter, cStatespace model, np.complex64_t determinant) cdef np.complex64_t cforecast_error_diffuse_cov(cKalmanFilter kfilter, cStatespace model, int i) cdef void cpredicted_diffuse_state_cov(cKalmanFilter kfilter, cStatespace model) # Double precision complex cdef int zforecast_univariate_diffuse(zKalmanFilter kfilter, zStatespace model) cdef int zupdating_univariate_diffuse(zKalmanFilter kfilter, zStatespace model) cdef int zprediction_univariate_diffuse(zKalmanFilter kfilter, zStatespace model) cdef np.complex128_t zinverse_noop_univariate_diffuse(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) except * cdef np.complex128_t zloglikelihood_univariate_diffuse(zKalmanFilter kfilter, zStatespace model, np.complex128_t determinant) cdef np.complex128_t zforecast_error_diffuse_cov(zKalmanFilter kfilter, zStatespace model, int i) cdef void zpredicted_diffuse_state_cov(zKalmanFilter kfilter, zStatespace model) statsmodels-0.12.2/statsmodels/tsa/statespace/_filters/_univariate_diffuse.pyx.in000066400000000000000000000335141400612667500304310ustar00rootroot00000000000000#cython: profile=False #cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # Typical imports cimport numpy as np import numpy as np from statsmodels.src.math cimport * cimport scipy.linalg.cython_blas as blas cimport scipy.linalg.cython_lapack as lapack from statsmodels.tsa.statespace._kalman_filter cimport ( FILTER_CONCENTRATED, MEMORY_NO_LIKELIHOOD, MEMORY_NO_STD_FORECAST) {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' combined_suffix = '' if combined_prefix == 'z': combined_suffix = 'u' }} from statsmodels.tsa.statespace._filters._univariate cimport ( {{prefix}}forecast_error, {{prefix}}forecast_error_cov, {{prefix}}temp_arrays, {{prefix}}predicted_state, {{prefix}}predicted_state_cov) # ### Univariate Kalman filter # # The following are the routines as defined in the univariate Kalman filter. # # See Durbin and Koopman (2012) Chapter 6.4 cdef int {{prefix}}forecast_univariate_diffuse({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): # Constants cdef: int i, j, k int inc = 1 {{cython_type}} forecast_error_cov, forecast_error_cov_inv, forecast_error_diffuse_cov, forecast_error_diffuse_cov_inv, F1, F12 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # Initialize the filtered states blas.{{prefix}}copy(&kfilter.k_states, kfilter._input_state, &inc, kfilter._filtered_state, &inc) blas.{{prefix}}copy(&kfilter.k_states2, kfilter._input_state_cov, &inc, kfilter._filtered_state_cov, &inc) blas.{{prefix}}copy(&kfilter.k_states2, kfilter._input_diffuse_state_cov, &inc, kfilter._predicted_diffuse_state_cov, &inc) # Iterate over endogenous variables for i in range(model._k_endog): # forecast_t, v_t, {{prefix}}forecast_error(kfilter, model, i) # F_{*,t} forecast_error_cov = {{prefix}}forecast_error_cov(kfilter, model, i) if forecast_error_cov{{if combined_prefix == 'z'}}.real{{endif}} < 0: kfilter._forecast_error_cov[i + i*kfilter.k_endog] = 0 forecast_error_cov = 0 # Save temporary array data if not forecast_error_cov == 0: forecast_error_cov_inv = 1.0 / forecast_error_cov {{prefix}}temp_arrays(kfilter, model, i, forecast_error_cov_inv) # F_{\infty,t} forecast_error_diffuse_cov = {{prefix}}forecast_error_diffuse_cov(kfilter, model, i) if forecast_error_diffuse_cov{{if combined_prefix == 'z'}}.real{{endif}} < 0: kfilter._forecast_error_diffuse_cov[i + i*kfilter.k_endog] = 0 forecast_error_diffuse_cov = 0 # F_{\infty, i, i, t} > 0 if forecast_error_diffuse_cov{{if combined_prefix == 'z'}}.real{{endif}} > kfilter.tolerance_diffuse: forecast_error_diffuse_cov_inv = 1.0 / forecast_error_diffuse_cov F1 = forecast_error_diffuse_cov_inv # Usually F2 = -forecast_error_cov * forecast_error_diffuse_cov_inv**2 # but this version is more convenient for the *axpy call F12 = -forecast_error_cov * forecast_error_diffuse_cov_inv # K0 = M_inf[:, i:i+1] * F1 blas.{{prefix}}copy(&kfilter.k_states, &kfilter._M_inf[i * kfilter.k_states], &inc, kfilter._tmpK0, &inc) blas.{{prefix}}scal(&kfilter.k_states, &F1, kfilter._tmpK0, &inc) # K1 = M[:, i:i+1] * F1 + M_inf[:, i:i+1] * F2 # K1 = M[:, i:i+1] * F1 + K0 * F12 blas.{{prefix}}copy(&kfilter.k_states, &kfilter._M[i*kfilter.k_states], &inc, kfilter._tmpK1, &inc) blas.{{prefix}}scal(&kfilter.k_states, &F1, kfilter._tmpK1, &inc) blas.{{prefix}}axpy(&kfilter.k_states, &F12, kfilter._tmpK0, &inc, kfilter._tmpK1, &inc) # L0 = np.eye(m) - np.dot(K0, Zi) kfilter.tmpL0[:] = 0 blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &gamma, kfilter._tmpK0, &inc, &model._design[i], &model._k_endog, kfilter._tmpL0, &kfilter.k_states) for j in range(kfilter.k_states): kfilter._tmpL0[j + j*kfilter.k_states] = kfilter._tmpL0[j + j*kfilter.k_states] + 1 # L1 = -np.dot(K1, Zi) kfilter.tmpL1[:] = 0 blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &gamma, kfilter._tmpK1, &inc, &model._design[i], &model._k_endog, kfilter._tmpL1, &kfilter.k_states) # a_t = a_t + K0[:, 0] * v[i] blas.{{prefix}}axpy(&kfilter.k_states, &kfilter._forecast_error[i], kfilter._tmpK0, &inc, kfilter._filtered_state, &inc) # P_t = np.dot(P_t_inf, L1.T) + np.dot(P_t, L0.T) # `tmp0` array used here, dimension $(m \times m)$ blas.{{prefix}}copy(&kfilter.k_states2, kfilter._filtered_state_cov, &inc, kfilter._tmp0, &inc) blas.{{prefix}}gemm("N", "T", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmp0, &kfilter.k_states, kfilter._tmpL0, &kfilter.k_states, &beta, kfilter._filtered_state_cov, &kfilter.k_states) blas.{{prefix}}gemm("N", "T", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._predicted_diffuse_state_cov, &kfilter.k_states, kfilter._tmpL1, &kfilter.k_states, &alpha, kfilter._filtered_state_cov, &kfilter.k_states) # P_t_inf = np.dot(P_t_inf, L0.T) blas.{{prefix}}copy(&kfilter.k_states2, kfilter._predicted_diffuse_state_cov, &inc, kfilter._tmp0, &inc) blas.{{prefix}}gemm("N", "T", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmp0, &kfilter.k_states, kfilter._tmpL0, &kfilter.k_states, &beta, kfilter._predicted_diffuse_state_cov, &kfilter.k_states) # Loglikelihood kfilter._loglikelihood[0] = ( kfilter._loglikelihood[0] - 0.5*( {{combined_prefix}}log(2 * NPY_PI * forecast_error_diffuse_cov))) elif forecast_error_cov{{if combined_prefix == 'z'}}.real{{endif}} > kfilter.tolerance_diffuse: kfilter.nobs_kendog_diffuse_nonsingular = kfilter.nobs_kendog_diffuse_nonsingular + 1 forecast_error_cov_inv = 1.0 / forecast_error_cov # Standardized forecasts error if not (kfilter.conserve_memory & MEMORY_NO_STD_FORECAST > 0): kfilter._standardized_forecast_error[i] = ( kfilter._forecast_error[i] * forecast_error_cov_inv**0.5) # K0 = M[:, i:i+1] / F[i, i] blas.{{prefix}}copy(&kfilter.k_states, &kfilter._M[i*kfilter.k_states], &inc, kfilter._tmpK0, &inc) blas.{{prefix}}scal(&kfilter.k_states, &forecast_error_cov_inv, kfilter._tmpK0, &inc) # L0 = np.eye(m) - np.dot(K0, Zi) kfilter.tmpL0[:] = 0 blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &gamma, kfilter._tmpK0, &inc, &model._design[i], &model._k_endog, kfilter._tmpL0, &kfilter.k_states) for j in range(kfilter.k_states): kfilter._tmpL0[j + j*kfilter.k_states] = kfilter._tmpL0[j + j*kfilter.k_states] + 1 # a_t = a_t + K0[:, 0] * v[i] blas.{{prefix}}axpy(&kfilter.k_states, &kfilter._forecast_error[i], kfilter._tmpK0, &inc, kfilter._filtered_state, &inc) # P_t = np.dot(P_t, L0) blas.{{prefix}}copy(&kfilter.k_states2, kfilter._filtered_state_cov, &inc, kfilter._tmp0, &inc) blas.{{prefix}}gemm("N", "T", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmp0, &kfilter.k_states, kfilter._tmpL0, &kfilter.k_states, &beta, kfilter._filtered_state_cov, &kfilter.k_states) # P_t_inf = P_t_inf # (noop) # Loglikelihood if not forecast_error_cov == 0: kfilter._loglikelihood[0] = ( kfilter._loglikelihood[0] - 0.5*( {{combined_prefix}}log(2 * NPY_PI * forecast_error_cov))) if kfilter.filter_method & FILTER_CONCENTRATED: kfilter._scale[0] = kfilter._scale[0] + kfilter._forecast_error[i]**2 * forecast_error_cov_inv else: kfilter._loglikelihood[0] = kfilter._loglikelihood[0] - 0.5 * (kfilter._forecast_error[i]**2 * forecast_error_cov_inv) # Kalman gain blas.{{prefix}}copy(&kfilter.k_states, kfilter._tmpK0, &inc, &kfilter._kalman_gain[i * kfilter.k_states], &inc) # Prediction (done below) # a_t1[:] = np.dot(T, a_tt) # P_t1[:] = np.dot(np.dot(T, P_tt), T.T) + RQR # P_t1_inf[:] = np.dot(np.dot(T, P_t_inf), T.T) return 0 cdef {{cython_type}} {{prefix}}forecast_error_diffuse_cov({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, int i): cdef: int inc = 1 {{cython_type}} alpha = 1 {{cython_type}} beta = 0 {{cython_type}} forecast_error_diffuse_cov int k_states = model._k_states # Adjust for a VAR transition (i.e. design = [#, 0], where the zeros # correspond to all states except the first k_posdef states) if model.subset_design: k_states = model._k_posdef # *Intermediate calculation* # `M_inf` array used here, dimension $(m \times 1)$ # $M_{i, \infty} = P_{t,i,\infty} Z_{t,i}'$ # $(m \times 1) = (m \times m) (1 \times m)'$ blas.{{prefix}}gemv("N", &model._k_states, &model._k_states, &alpha, kfilter._predicted_diffuse_state_cov, &kfilter.k_states, &model._design[i], &model._k_endog, &beta, &kfilter._M_inf[i * kfilter.k_states], &inc) # $F_{t,i,\infty} \equiv Z_{t,i} P_{t,i,\infty} Z_{t,i}'$ {{if combined_prefix == 'd'}} # blas.{{prefix}}symv("U", &model._k_states, # &alpha, kfilter._filtered_state_cov, &kfilter.k_states, # &model._design[i], &model._k_endog, # &beta, &kfilter._M_inf[i * kfilter.k_states], &inc) forecast_error_diffuse_cov = ( blas.{{prefix}}dot(&k_states, &model._design[i], &model._k_endog, &kfilter._M_inf[i * kfilter.k_states], &inc) ) {{else}} # blas.{{prefix}}gemv("N", &model._k_states, &k_states, # &alpha, kfilter._filtered_state_cov, &kfilter.k_states, # &model._design[i], &model._k_endog, # &beta, &kfilter._M_inf[i * kfilter.k_states], &inc) blas.{{prefix}}gemv("N", &inc, &k_states, &alpha, &kfilter._M_inf[i * kfilter.k_states], &inc, &model._design[i], &model._k_endog, &beta, kfilter._tmp0, &inc) forecast_error_diffuse_cov = kfilter._tmp0[0] {{endif}} kfilter._forecast_error_diffuse_cov[i + i*kfilter.k_endog] = forecast_error_diffuse_cov return forecast_error_diffuse_cov cdef int {{prefix}}prediction_univariate_diffuse({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): # Constants cdef: int inc = 1 int i, j {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 {{prefix}}predicted_state(kfilter, model) {{prefix}}predicted_state_cov(kfilter, model) {{prefix}}predicted_diffuse_state_cov(kfilter, model) return 0 cdef void {{prefix}}predicted_diffuse_state_cov({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 # Need special handling for the completely missing case, since the # conventional Kalman filter routines are used in this case and they do not # copy over the predicted diffuse state cov if model._nmissing == model.k_endog: blas.{{prefix}}copy(&kfilter.k_states2, kfilter._input_diffuse_state_cov, &inc, kfilter._predicted_diffuse_state_cov, &inc) # P_t1_inf[:] = np.dot(np.dot(T, P_t_inf), T.T) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, model._transition, &model._k_states, kfilter._predicted_diffuse_state_cov, &kfilter.k_states, &beta, kfilter._tmp0, &kfilter.k_states) # $P_{t+1} = 1.0 \\#_0 T_t' + 1.0 \\#$ # $(m \times m) = (m \times m) (m \times m) + (m \times m)$ blas.{{prefix}}gemm("N", "T", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmp0, &kfilter.k_states, model._transition, &model._k_states, &beta, kfilter._predicted_diffuse_state_cov, &kfilter.k_states) # Note: updating, inverse, loglikelihood are all performed in prior steps cdef int {{prefix}}updating_univariate_diffuse({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): return 0 cdef {{cython_type}} {{prefix}}inverse_noop_univariate_diffuse({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant) except *: return -np.inf cdef {{cython_type}} {{prefix}}loglikelihood_univariate_diffuse({{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, {{cython_type}} determinant): return 0 {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/_initialization.pxd000066400000000000000000000154021400612667500253370ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models - Initialization declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace ) cdef class sInitialization(object): cdef readonly int k_states cdef public np.float64_t approximate_diffuse_variance cdef np.float32_t [:] constant cdef np.float32_t [::1, :] stationary_cov cdef np.float32_t [::1, :] _tmp_transition cdef np.float32_t [::1, :] _tmp_selected_state_cov cpdef int initialize(self, inititialization_type, int offset, sStatespace model, np.float32_t [:] initial_state_mean, np.float32_t [::1, :] initial_diffuse_state_cov, np.float32_t [::1, :] initial_stationary_state_cov, int complex_step=*) except 1 cdef int clear_constant(self, int offset, np.float32_t [:] initial_state_mean) except 1 cdef int clear_cov(self, int offset, np.float32_t [::1, :] cov) except 1 cdef int initialize_known_constant(self, int offset, np.float32_t [:] initial_state_mean) except 1 cdef int initialize_known_stationary_cov(self, int offset, np.float32_t [::1, :] initial_stationary_state_cov) except 1 cdef int initialize_diffuse(self, int offset, np.float32_t [::1, :] initial_diffuse_state_cov) except 1 cdef int initialize_approximate_diffuse(self, int offset, np.float32_t [::1, :] initial_stationary_state_cov) except 1 cdef int initialize_stationary_constant(self, int offset, sStatespace model, np.float32_t [:] initial_state_mean, int complex_step=*) except 1 cdef int initialize_stationary_stationary_cov(self, int offset, sStatespace model, np.float32_t [::1, :] initial_stationary_state_cov, int complex_step=*) except 1 cdef class dInitialization(object): cdef readonly int k_states cdef public np.float64_t approximate_diffuse_variance cdef np.float64_t [:] constant cdef np.float64_t [::1, :] stationary_cov cdef np.float64_t [::1, :] _tmp_transition cdef np.float64_t [::1, :] _tmp_selected_state_cov cpdef int initialize(self, inititialization_type, int offset, dStatespace model, np.float64_t [:] initial_state_mean, np.float64_t [::1, :] initial_diffuse_state_cov, np.float64_t [::1, :] initial_stationary_state_cov, int complex_step=*) except 1 cdef int clear_constant(self, int offset, np.float64_t [:] initial_state_mean) except 1 cdef int clear_cov(self, int offset, np.float64_t [::1, :] cov) except 1 cdef int initialize_known_constant(self, int offset, np.float64_t [:] initial_state_mean) except 1 cdef int initialize_known_stationary_cov(self, int offset, np.float64_t [::1, :] initial_stationary_state_cov) except 1 cdef int initialize_diffuse(self, int offset, np.float64_t [::1, :] initial_diffuse_state_cov) except 1 cdef int initialize_approximate_diffuse(self, int offset, np.float64_t [::1, :] initial_stationary_state_cov) except 1 cdef int initialize_stationary_constant(self, int offset, dStatespace model, np.float64_t [:] initial_state_mean, int complex_step=*) except 1 cdef int initialize_stationary_stationary_cov(self, int offset, dStatespace model, np.float64_t [::1, :] initial_stationary_state_cov, int complex_step=*) except 1 cdef class cInitialization(object): cdef readonly int k_states cdef public np.float64_t approximate_diffuse_variance cdef np.complex64_t [:] constant cdef np.complex64_t [::1, :] stationary_cov cdef np.complex64_t [::1, :] _tmp_transition cdef np.complex64_t [::1, :] _tmp_selected_state_cov cpdef int initialize(self, inititialization_type, int offset, cStatespace model, np.complex64_t [:] initial_state_mean, np.complex64_t [::1, :] initial_diffuse_state_cov, np.complex64_t [::1, :] initial_stationary_state_cov, int complex_step=*) except 1 cdef int clear_constant(self, int offset, np.complex64_t [:] initial_state_mean) except 1 cdef int clear_cov(self, int offset, np.complex64_t [::1, :] cov) except 1 cdef int initialize_known_constant(self, int offset, np.complex64_t [:] initial_state_mean) except 1 cdef int initialize_known_stationary_cov(self, int offset, np.complex64_t [::1, :] initial_stationary_state_cov) except 1 cdef int initialize_diffuse(self, int offset, np.complex64_t [::1, :] initial_diffuse_state_cov) except 1 cdef int initialize_approximate_diffuse(self, int offset, np.complex64_t [::1, :] initial_stationary_state_cov) except 1 cdef int initialize_stationary_constant(self, int offset, cStatespace model, np.complex64_t [:] initial_state_mean, int complex_step=*) except 1 cdef int initialize_stationary_stationary_cov(self, int offset, cStatespace model, np.complex64_t [::1, :] initial_stationary_state_cov, int complex_step=*) except 1 cdef class zInitialization(object): cdef readonly int k_states cdef public np.float64_t approximate_diffuse_variance cdef np.complex128_t [:] constant cdef np.complex128_t [::1, :] stationary_cov cdef np.complex128_t [::1, :] _tmp_transition cdef np.complex128_t [::1, :] _tmp_selected_state_cov cpdef int initialize(self, inititialization_type, int offset, zStatespace model, np.complex128_t [:] initial_state_mean, np.complex128_t [::1, :] initial_diffuse_state_cov, np.complex128_t [::1, :] initial_stationary_state_cov, int complex_step=*) except 1 cdef int clear_constant(self, int offset, np.complex128_t [:] initial_state_mean) except 1 cdef int clear_cov(self, int offset, np.complex128_t [::1, :] cov) except 1 cdef int initialize_known_constant(self, int offset, np.complex128_t [:] initial_state_mean) except 1 cdef int initialize_known_stationary_cov(self, int offset, np.complex128_t [::1, :] initial_stationary_state_cov) except 1 cdef int initialize_diffuse(self, int offset, np.complex128_t [::1, :] initial_diffuse_state_cov) except 1 cdef int initialize_approximate_diffuse(self, int offset, np.complex128_t [::1, :] initial_stationary_state_cov) except 1 cdef int initialize_stationary_constant(self, int offset, zStatespace model, np.complex128_t [:] initial_state_mean, int complex_step=*) except 1 cdef int initialize_stationary_stationary_cov(self, int offset, zStatespace model, np.complex128_t [::1, :] initial_stationary_state_cov, int complex_step=*) except 1 statsmodels-0.12.2/statsmodels/tsa/statespace/_initialization.pyx.in000066400000000000000000000250311400612667500257700ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models - Initialization Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # Typical imports import numpy as np import warnings cimport numpy as np cimport cython np.import_array() from statsmodels.src.math cimport * cimport scipy.linalg.cython_blas as blas cimport scipy.linalg.cython_lapack as lapack cimport statsmodels.tsa.statespace._tools as tools {{for prefix, types in TYPES.items()}} from statsmodels.tsa.statespace._representation cimport {{prefix}}Statespace {{endfor}} cdef int FORTRAN = 1 {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} ## State Space Initialization cdef class {{prefix}}Initialization(object): def __init__(self, int k_states, {{cython_type}} [:] constant, {{cython_type}} [::1, :] stationary_cov, np.float64_t approximate_diffuse_variance=1e6): cdef: int k np.npy_intp dim1[1] np.npy_intp dim2[2] self.k_states = k_states self.constant = constant self.stationary_cov = stationary_cov self.approximate_diffuse_variance = approximate_diffuse_variance # Validate tools.validate_vector_shape('known constant', &self.constant.shape[0], self.k_states, None) tools.validate_matrix_shape('known covariance', &self.stationary_cov.shape[0], self.k_states, self.k_states, None) # Internal temporary matrices dim2[0] = self.k_states; dim2[1] = self.k_states; self._tmp_transition = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = self.k_states; dim2[1] = self.k_states; self._tmp_selected_state_cov = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) def __reduce__(self): init = (self.k_states, np.array(self.constant), np.array(self.stationary_cov), self.approximate_diffuse_variance) state = {'_tmp_transition': np.array(self._tmp_transition, copy=True, order='F'), '_tmp_selected_state_cov': np.array(self._tmp_selected_state_cov, copy=True, order='F')} return (self.__class__, init, state) def __setstate__(self, state): self._tmp_transition = state['_tmp_transition'] self._tmp_selected_state_cov = state['_tmp_selected_state_cov'] cpdef int initialize(self, initialization_type, int offset, {{prefix}}Statespace model, {{cython_type}} [:] initial_state_mean, {{cython_type}} [::1, :] initial_diffuse_state_cov, {{cython_type}} [::1, :] initial_stationary_state_cov, int complex_step=False) except 1: if offset + self.k_states > model.k_states: raise ValueError('Invalid offset.') tools.validate_vector_shape('initial state mean', &initial_state_mean.shape[0], model.k_states, None) tools.validate_matrix_shape('initial diffuse state cov', &initial_diffuse_state_cov.shape[0], model.k_states, model.k_states, None) tools.validate_matrix_shape('initial stationary state cov', &initial_stationary_state_cov.shape[0], model.k_states, model.k_states, None) if initialization_type == 'known': self.initialize_known_constant(offset, initial_state_mean) self.initialize_known_stationary_cov(offset, initial_stationary_state_cov) self.clear_cov(offset, initial_diffuse_state_cov) elif initialization_type == 'diffuse': self.initialize_diffuse(offset, initial_diffuse_state_cov) self.clear_constant(offset, initial_state_mean) self.clear_cov(offset, initial_stationary_state_cov) elif initialization_type == 'approximate_diffuse': self.initialize_known_constant(offset, initial_state_mean) self.initialize_approximate_diffuse(offset, initial_stationary_state_cov) self.clear_cov(offset, initial_diffuse_state_cov) elif initialization_type == 'stationary': self.initialize_stationary_constant(offset, model, initial_state_mean, complex_step) self.initialize_stationary_stationary_cov(offset, model, initial_stationary_state_cov, complex_step) self.clear_cov(offset, initial_diffuse_state_cov) else: raise ValueError('Invalid initialization type') return 0 cdef int clear_constant(self, int offset, {{cython_type}} [:] initial_state_mean) except 1: initial_state_mean[offset:offset + self.k_states] = 0 return 0 cdef int clear_cov(self, int offset, {{cython_type}} [::1, :] cov) except 1: cov[offset:offset + self.k_states, offset:offset + self.k_states] = 0 return 0 cdef int initialize_known_constant(self, int offset, {{cython_type}} [:] initial_state_mean) except 1: cdef int inc = 1 blas.{{prefix}}copy(&self.k_states, &self.constant[0], &inc, &initial_state_mean[offset], &inc) return 0 cdef int initialize_known_stationary_cov(self, int offset, {{cython_type}} [::1, :] initial_stationary_state_cov) except 1: cdef int i, inc = 1 # Copy columns for i in range(self.k_states): blas.{{prefix}}copy(&self.k_states, &self.stationary_cov[0, i], &inc, &initial_stationary_state_cov[offset, offset + i], &inc) return 0 cdef int initialize_diffuse(self, int offset, {{cython_type}} [::1, :] initial_diffuse_state_cov) except 1: cdef int i for i in range(offset, offset + self.k_states): initial_diffuse_state_cov[i, i] = 1 return 0 cdef int initialize_approximate_diffuse(self, int offset, {{cython_type}} [::1, :] initial_stationary_state_cov) except 1: cdef int i for i in range(offset, offset + self.k_states): initial_stationary_state_cov[i, i] = self.approximate_diffuse_variance return 0 cdef int initialize_stationary_constant(self, int offset, {{prefix}}Statespace model, {{cython_type}} [:] initial_state_mean, int complex_step=False) except 1: cdef: np.npy_intp dim2[2] int i, info, inc = 1 int k_states2 = self.k_states**2 np.float64_t asum, tol = 1e-9 cdef {{cython_type}} scalar cdef int [::1,:] ipiv # Clear the unconditional mean (for this block) initial_state_mean[offset:offset + self.k_states] = 0 # Check if the state intercept is all zeros; if it is, then the # unconditional mean is also all zeros {{if combined_prefix == 'd'}} asum = blas.{{prefix}}asum(&model.k_states, &model.state_intercept[0, 0], &inc) {{elif prefix == 'c'}} asum = blas.scasum(&model.k_states, &model.state_intercept[0, 0], &inc) {{else}} asum = blas.dzasum(&model.k_states, &model.state_intercept[0, 0], &inc) {{endif}} # If the state intercept is non-zero, compute the mean if asum > tol: dim2[0] = self.k_states dim2[1] = self.k_states ipiv = np.PyArray_ZEROS(2, dim2, np.NPY_INT32, FORTRAN) # Create T - I # (copy colummns) for i in range(self.k_states): blas.{{prefix}}copy(&self.k_states, &model.transition[offset,offset + i,0], &inc, &self._tmp_transition[0,i], &inc) self._tmp_transition[i, i] = self._tmp_transition[i, i] - 1 # Multiply by -1 to get I - T scalar = -1.0 blas.{{prefix}}scal(&k_states2, &scalar, &self._tmp_transition[0, 0], &inc) # c blas.{{prefix}}copy(&self.k_states, &model.state_intercept[offset,0], &inc, &initial_state_mean[offset], &inc) # Solve (I - T) x = c lapack.{{prefix}}getrf(&self.k_states, &self.k_states, &self._tmp_transition[0, 0], &self.k_states, &ipiv[0, 0], &info) lapack.{{prefix}}getrs('N', &self.k_states, &inc, &self._tmp_transition[0, 0], &self.k_states, &ipiv[0, 0], &initial_state_mean[offset], &self.k_states, &info) return 0 cdef int initialize_stationary_stationary_cov(self, int offset, {{prefix}}Statespace model, {{cython_type}} [::1, :] initial_stationary_state_cov, int complex_step=False) except 1: cdef: int i, inc = 1 int k_states2 = self.k_states**2 # Create selected state covariance matrix tools._{{prefix}}select_cov(self.k_states, model.k_posdef, model.k_states, &model.tmp[0,0], &model.selection[offset,0,0], &model.state_cov[0,0,0], &self._tmp_selected_state_cov[0,0]) # Create a copy of the transition matrix # (copy colummns) for i in range(self.k_states): blas.{{prefix}}copy(&self.k_states, &model.transition[offset,offset + i,0], &inc, &self._tmp_transition[0,i], &inc) # Solve the discrete Lyapunov equation to the get initial state # covariance matrix tools._{{prefix}}solve_discrete_lyapunov( &self._tmp_transition[0,0], &self._tmp_selected_state_cov[0,0], self.k_states, complex_step) # Copy into initial_stationary_state_cov # (copy colummns) for i in range(self.k_states): blas.{{prefix}}copy(&self.k_states, &self._tmp_selected_state_cov[0,i], &inc, &initial_stationary_state_cov[offset,offset + i], &inc) return 0 {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/_kalman_filter.pxd000066400000000000000000000602121400612667500251170ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ Kalman Filter declarations Author: Chad Fulton License: Simplified-BSD """ # ## Constants # ### Filters cdef int FILTER_CONVENTIONAL # Durbin and Koopman (2012), Chapter 4 cdef int FILTER_EXACT_INITIAL # ibid., Chapter 5.6 cdef int FILTER_AUGMENTED # ibid., Chapter 5.7 cdef int FILTER_SQUARE_ROOT # ibid., Chapter 6.3 cdef int FILTER_UNIVARIATE # ibid., Chapter 6.4 cdef int FILTER_COLLAPSED # ibid., Chapter 6.5 cdef int FILTER_EXTENDED # ibid., Chapter 10.2 cdef int FILTER_UNSCENTED # ibid., Chapter 10.3 cdef int FILTER_CONCENTRATED # Harvey (1989), Chapter 3.4 cdef int FILTER_CHANDRASEKHAR # Herbst (2015) # ### Inversion methods # Methods by which the terms using the inverse of the forecast error # covariance matrix are solved. cdef int INVERT_UNIVARIATE cdef int SOLVE_LU cdef int INVERT_LU cdef int SOLVE_CHOLESKY cdef int INVERT_CHOLESKY # ### Numerical Stability methods # Methods to improve numerical stability cdef int STABILITY_FORCE_SYMMETRY # ### Memory conservation options cdef int MEMORY_STORE_ALL cdef int MEMORY_NO_FORECAST_MEAN cdef int MEMORY_NO_FORECAST_COV cdef int MEMORY_NO_FORECAST cdef int MEMORY_NO_PREDICTED_MEAN cdef int MEMORY_NO_PREDICTED_COV cdef int MEMORY_NO_PREDICTED cdef int MEMORY_NO_FILTERED_MEAN cdef int MEMORY_NO_FILTERED_COV cdef int MEMORY_NO_FILTERED cdef int MEMORY_NO_LIKELIHOOD cdef int MEMORY_NO_GAIN cdef int MEMORY_NO_SMOOTHING cdef int MEMORY_NO_STD_FORECAST cdef int MEMORY_CONSERVE # ### Timing options cdef int TIMING_INIT_FILTERED cdef int TIMING_INIT_PREDICTED # Typical imports cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace ) # Single precision cdef class sKalmanFilter(object): # Statespace object cdef readonly sStatespace model # ### Filter parameters cdef readonly int t cdef public np.float64_t tolerance, tolerance_diffuse cdef readonly int nobs_diffuse cdef readonly int nobs_kendog_diffuse_nonsingular cdef readonly int nobs_kendog_univariate_singular cdef readonly int converged cdef readonly int period_converged cdef readonly int time_invariant cdef readonly int filter_method cdef public int inversion_method cdef public int stability_method cdef readonly int conserve_memory cdef public int filter_timing cdef readonly int loglikelihood_burn cdef public int [:] univariate_filter # ### Kalman filter properties cdef readonly np.float32_t [:] loglikelihood, scale cdef readonly np.float32_t [::1,:] filtered_state, predicted_state, forecast, forecast_error, standardized_forecast_error cdef readonly np.float32_t [::1,:,:] filtered_state_cov, predicted_state_cov, forecast_error_cov, predicted_diffuse_state_cov, forecast_error_diffuse_cov, M, M_inf cdef readonly np.float32_t [::1,:,:] kalman_gain # ### Steady State Values cdef readonly np.float32_t [::1,:] converged_forecast_error_cov cdef readonly np.float32_t [::1,:] converged_filtered_state_cov cdef readonly np.float32_t [::1,:] converged_predicted_state_cov cdef readonly np.float32_t [::1,:] converged_kalman_gain cdef readonly np.float32_t [::1,:] converged_M cdef readonly np.float32_t converged_determinant # ### Temporary arrays cdef readonly np.float32_t [::1,:] forecast_error_fac cdef readonly int [:] forecast_error_ipiv cdef readonly np.float32_t [::1,:] forecast_error_work cdef readonly np.float32_t [::1,:] tmp0, tmp00 cdef readonly np.float32_t [::1,:] tmp2 cdef readonly np.float32_t [::1,:,:] tmp1, tmp3, tmp4 cdef readonly np.float32_t [:] tmpK0, tmpK1 cdef readonly np.float32_t [::1,:] tmpL0, tmpL1 cdef readonly np.float32_t [::1,:] CW, CtmpW, CMW, CM, CprevFiZ, CtmpM, CMWZ cdef readonly np.float32_t determinant # ### Pointers to current-iteration arrays # cdef np.float32_t * _obs # cdef np.float32_t * _design # cdef np.float32_t * _obs_intercept # cdef np.float32_t * _obs_cov # cdef np.float32_t * _transition # cdef np.float32_t * _state_intercept # cdef np.float32_t * _selection # cdef np.float32_t * _state_cov # cdef np.float32_t * _selected_state_cov # cdef np.float32_t * _initial_state # cdef np.float32_t * _initial_state_cov cdef np.float32_t * _input_state cdef np.float32_t * _input_state_cov cdef np.float32_t * _input_diffuse_state_cov cdef np.float32_t * _forecast cdef np.float32_t * _forecast_error cdef np.float32_t * _standardized_forecast_error cdef np.float32_t * _forecast_error_cov cdef np.float32_t * _filtered_state cdef np.float32_t * _filtered_state_cov cdef np.float32_t * _predicted_state cdef np.float32_t * _predicted_state_cov cdef np.float32_t * _forecast_error_diffuse_cov cdef np.float32_t * _predicted_diffuse_state_cov cdef np.float32_t * _M cdef np.float32_t * _M_inf cdef np.float32_t * _kalman_gain cdef np.float32_t * _loglikelihood cdef np.float32_t * _scale cdef np.float32_t * _converged_forecast_error_cov cdef np.float32_t * _converged_filtered_state_cov cdef np.float32_t * _converged_predicted_state_cov cdef np.float32_t * _converged_kalman_gain cdef np.float32_t * _converged_M cdef np.float32_t * _forecast_error_fac cdef int * _forecast_error_ipiv cdef np.float32_t * _forecast_error_work cdef np.float32_t * _tmp0 cdef np.float32_t * _tmp00 cdef np.float32_t * _tmp1 cdef np.float32_t * _tmp2 cdef np.float32_t * _tmp3 cdef np.float32_t * _tmp4 cdef np.float32_t * _tmpM_inf cdef np.float32_t * _tmpK0 cdef np.float32_t * _tmpK1 cdef np.float32_t * _tmpL0 cdef np.float32_t * _tmpL1 # ### Pointers to current-iteration Kalman filtering functions cdef int (*forecasting)( sKalmanFilter, sStatespace ) cdef np.float32_t (*inversion)( sKalmanFilter, sStatespace, np.float32_t ) except * cdef int (*updating)( sKalmanFilter, sStatespace ) cdef np.float32_t (*calculate_loglikelihood)( sKalmanFilter, sStatespace, np.float32_t ) cdef np.float32_t (*calculate_scale)( sKalmanFilter, sStatespace ) cdef int (*prediction)( sKalmanFilter, sStatespace ) # ### Define some constants cdef readonly int k_endog, k_states, k_posdef, k_endog2, k_states2, k_posdef2, k_endogstates, k_statesposdef cdef readonly int ldwork cdef allocate_arrays(self) cdef void set_dimensions(self) cpdef set_filter_method(self, int filter_method, int force_reset=*) cpdef seek(self, unsigned int t, int reset=*) cdef void initialize_statespace_object_pointers(self) except * cdef void initialize_filter_object_pointers(self) cdef void initialize_function_pointers(self) except * cdef void post_convergence(self) cdef void numerical_stability(self) cdef int check_diffuse(self) cdef void check_convergence(self) cdef void migrate_storage(self) cdef void _reinitialize_pointers(self) except * cdef void _forecasting(self) cdef np.float32_t _inversion(self) cdef void _updating(self) cdef np.float32_t _calculate_loglikelihood(self) cdef void _prediction(self) # Double precision cdef class dKalmanFilter(object): # Statespace object cdef readonly dStatespace model # ### Filter parameters cdef readonly int t cdef public np.float64_t tolerance, tolerance_diffuse cdef readonly int nobs_diffuse cdef readonly int nobs_kendog_diffuse_nonsingular cdef readonly int nobs_kendog_univariate_singular cdef readonly int converged cdef readonly int period_converged cdef readonly int time_invariant cdef readonly int filter_method cdef public int inversion_method cdef public int stability_method cdef readonly int conserve_memory cdef public int filter_timing cdef readonly int loglikelihood_burn cdef public int [:] univariate_filter # ### Kalman filter properties cdef readonly np.float64_t [:] loglikelihood, scale cdef readonly np.float64_t [::1,:] filtered_state, predicted_state, forecast, forecast_error, standardized_forecast_error cdef readonly np.float64_t [::1,:,:] filtered_state_cov, predicted_state_cov, forecast_error_cov, predicted_diffuse_state_cov, forecast_error_diffuse_cov, M, M_inf cdef readonly np.float64_t [::1,:,:] kalman_gain # ### Steady State Values cdef readonly np.float64_t [::1,:] converged_forecast_error_cov cdef readonly np.float64_t [::1,:] converged_filtered_state_cov cdef readonly np.float64_t [::1,:] converged_predicted_state_cov cdef readonly np.float64_t [::1,:] converged_kalman_gain cdef readonly np.float64_t [::1,:] converged_M cdef readonly np.float64_t converged_determinant # ### Temporary arrays cdef readonly np.float64_t [::1,:] forecast_error_fac cdef readonly int [:] forecast_error_ipiv cdef readonly np.float64_t [::1,:] forecast_error_work cdef readonly np.float64_t [::1,:] tmp0, tmp00 cdef readonly np.float64_t [::1,:] tmp2 cdef readonly np.float64_t [::1,:,:] tmp1, tmp3, tmp4 cdef readonly np.float64_t [:] tmpM_inf, tmpK0, tmpK1 cdef readonly np.float64_t [::1,:] tmpL0, tmpL1 cdef readonly np.float64_t [::1,:] CW, CtmpW, CMW, CM, CprevFiZ, CtmpM, CMWZ cdef readonly np.float64_t determinant # ### Pointers to current-iteration arrays # cdef np.float64_t * _obs # cdef np.float64_t * _design # cdef np.float64_t * _obs_intercept # cdef np.float64_t * _obs_cov # cdef np.float64_t * _transition # cdef np.float64_t * _state_intercept # cdef np.float64_t * _selection # cdef np.float64_t * _state_cov # cdef np.float64_t * _selected_state_cov # cdef np.float64_t * _initial_state # cdef np.float64_t * _initial_state_cov cdef np.float64_t * _input_state cdef np.float64_t * _input_state_cov cdef np.float64_t * _input_diffuse_state_cov cdef np.float64_t * _forecast cdef np.float64_t * _forecast_error cdef np.float64_t * _standardized_forecast_error cdef np.float64_t * _forecast_error_cov cdef np.float64_t * _filtered_state cdef np.float64_t * _filtered_state_cov cdef np.float64_t * _predicted_state cdef np.float64_t * _predicted_state_cov cdef np.float64_t * _forecast_error_diffuse_cov cdef np.float64_t * _predicted_diffuse_state_cov cdef np.float64_t * _M cdef np.float64_t * _M_inf cdef np.float64_t * _kalman_gain cdef np.float64_t * _loglikelihood cdef np.float64_t * _scale cdef np.float64_t * _converged_forecast_error_cov cdef np.float64_t * _converged_filtered_state_cov cdef np.float64_t * _converged_predicted_state_cov cdef np.float64_t * _converged_kalman_gain cdef np.float64_t * _converged_M cdef np.float64_t * _forecast_error_fac cdef int * _forecast_error_ipiv cdef np.float64_t * _forecast_error_work cdef np.float64_t * _tmp0 cdef np.float64_t * _tmp00 cdef np.float64_t * _tmp1 cdef np.float64_t * _tmp2 cdef np.float64_t * _tmp3 cdef np.float64_t * _tmp4 cdef np.float64_t * _tmpM_inf cdef np.float64_t * _tmpK0 cdef np.float64_t * _tmpK1 cdef np.float64_t * _tmpL0 cdef np.float64_t * _tmpL1 # ### Pointers to current-iteration Kalman filtering functions cdef int (*forecasting)( dKalmanFilter, dStatespace ) cdef np.float64_t (*inversion)( dKalmanFilter, dStatespace, np.float64_t ) except * cdef int (*updating)( dKalmanFilter, dStatespace ) cdef np.float64_t (*calculate_loglikelihood)( dKalmanFilter, dStatespace, np.float64_t ) cdef np.float64_t (*calculate_scale)( dKalmanFilter, dStatespace ) cdef int (*prediction)( dKalmanFilter, dStatespace ) # ### Define some constants cdef readonly int k_endog, k_states, k_posdef, k_endog2, k_states2, k_posdef2, k_endogstates, k_statesposdef cdef readonly int ldwork cdef allocate_arrays(self) cdef void set_dimensions(self) cpdef set_filter_method(self, int filter_method, int force_reset=*) cpdef seek(self, unsigned int t, int reset=*) cdef void initialize_statespace_object_pointers(self) except * cdef void initialize_filter_object_pointers(self) cdef void initialize_function_pointers(self) except * cdef void post_convergence(self) cdef void numerical_stability(self) cdef int check_diffuse(self) cdef void check_convergence(self) cdef void migrate_storage(self) cdef void _reinitialize_pointers(self) except * cdef void _forecasting(self) cdef np.float64_t _inversion(self) cdef void _updating(self) cdef np.float64_t _calculate_loglikelihood(self) cdef void _prediction(self) # Single precision complex cdef class cKalmanFilter(object): # Statespace object cdef readonly cStatespace model # ### Filter parameters cdef readonly int t cdef public np.float64_t tolerance, tolerance_diffuse cdef readonly int nobs_diffuse cdef readonly int nobs_kendog_diffuse_nonsingular cdef readonly int nobs_kendog_univariate_singular cdef readonly int converged cdef readonly int period_converged cdef readonly int time_invariant cdef readonly int filter_method cdef public int inversion_method cdef public int stability_method cdef readonly int conserve_memory cdef public int filter_timing cdef readonly int loglikelihood_burn cdef public int [:] univariate_filter # ### Kalman filter properties cdef readonly np.complex64_t [:] loglikelihood, scale cdef readonly np.complex64_t [::1,:] filtered_state, predicted_state, forecast, forecast_error, standardized_forecast_error cdef readonly np.complex64_t [::1,:,:] filtered_state_cov, predicted_state_cov, forecast_error_cov, predicted_diffuse_state_cov, forecast_error_diffuse_cov, M, M_inf cdef readonly np.complex64_t [::1,:,:] kalman_gain # ### Steady State Values cdef readonly np.complex64_t [::1,:] converged_forecast_error_cov cdef readonly np.complex64_t [::1,:] converged_filtered_state_cov cdef readonly np.complex64_t [::1,:] converged_predicted_state_cov cdef readonly np.complex64_t [::1,:] converged_kalman_gain cdef readonly np.complex64_t [::1,:] converged_M cdef readonly np.complex64_t converged_determinant # ### Temporary arrays cdef readonly np.complex64_t [::1,:] forecast_error_fac cdef readonly int [:] forecast_error_ipiv cdef readonly np.complex64_t [::1,:] forecast_error_work cdef readonly np.complex64_t [::1,:] tmp0, tmp00 cdef readonly np.complex64_t [::1,:] tmp2 cdef readonly np.complex64_t [::1,:,:] tmp1, tmp3, tmp4 cdef readonly np.complex64_t [:] tmpM_inf, tmpK0, tmpK1 cdef readonly np.complex64_t [::1,:] tmpL0, tmpL1 cdef readonly np.complex64_t [::1,:] CW, CtmpW, CMW, CM, CprevFiZ, CtmpM, CMWZ cdef readonly np.complex64_t determinant # ### Pointers to current-iteration arrays # cdef np.complex64_t * _obs # cdef np.complex64_t * _design # cdef np.complex64_t * _obs_intercept # cdef np.complex64_t * _obs_cov # cdef np.complex64_t * _transition # cdef np.complex64_t * _state_intercept # cdef np.complex64_t * _selection # cdef np.complex64_t * _state_cov # cdef np.complex64_t * _selected_state_cov # cdef np.complex64_t * _initial_state # cdef np.complex64_t * _initial_state_cov cdef np.complex64_t * _input_state cdef np.complex64_t * _input_state_cov cdef np.complex64_t * _input_diffuse_state_cov cdef np.complex64_t * _forecast cdef np.complex64_t * _forecast_error cdef np.complex64_t * _standardized_forecast_error cdef np.complex64_t * _forecast_error_cov cdef np.complex64_t * _filtered_state cdef np.complex64_t * _filtered_state_cov cdef np.complex64_t * _predicted_state cdef np.complex64_t * _predicted_state_cov cdef np.complex64_t * _forecast_error_diffuse_cov cdef np.complex64_t * _predicted_diffuse_state_cov cdef np.complex64_t * _M cdef np.complex64_t * _M_inf cdef np.complex64_t * _kalman_gain cdef np.complex64_t * _loglikelihood cdef np.complex64_t * _scale cdef np.complex64_t * _converged_forecast_error_cov cdef np.complex64_t * _converged_filtered_state_cov cdef np.complex64_t * _converged_predicted_state_cov cdef np.complex64_t * _converged_kalman_gain cdef np.complex64_t * _converged_M cdef np.complex64_t * _forecast_error_fac cdef int * _forecast_error_ipiv cdef np.complex64_t * _forecast_error_work cdef np.complex64_t * _tmp0 cdef np.complex64_t * _tmp00 cdef np.complex64_t * _tmp1 cdef np.complex64_t * _tmp2 cdef np.complex64_t * _tmp3 cdef np.complex64_t * _tmp4 cdef np.complex64_t * _tmpM_inf cdef np.complex64_t * _tmpK0 cdef np.complex64_t * _tmpK1 cdef np.complex64_t * _tmpL0 cdef np.complex64_t * _tmpL1 # ### Pointers to current-iteration Kalman filtering functions cdef int (*forecasting)( cKalmanFilter, cStatespace ) cdef np.complex64_t (*inversion)( cKalmanFilter, cStatespace, np.complex64_t ) except * cdef int (*updating)( cKalmanFilter, cStatespace ) cdef np.complex64_t (*calculate_loglikelihood)( cKalmanFilter, cStatespace, np.complex64_t ) cdef np.complex64_t (*calculate_scale)( cKalmanFilter, cStatespace ) cdef int (*prediction)( cKalmanFilter, cStatespace ) # ### Define some constants cdef readonly int k_endog, k_states, k_posdef, k_endog2, k_states2, k_posdef2, k_endogstates, k_statesposdef cdef readonly int ldwork cdef allocate_arrays(self) cdef void set_dimensions(self) cpdef set_filter_method(self, int filter_method, int force_reset=*) cpdef seek(self, unsigned int t, int reset=*) cdef void initialize_statespace_object_pointers(self) except * cdef void initialize_filter_object_pointers(self) cdef void initialize_function_pointers(self) except * cdef void post_convergence(self) cdef void numerical_stability(self) cdef int check_diffuse(self) cdef void check_convergence(self) cdef void migrate_storage(self) cdef void _reinitialize_pointers(self) except * cdef void _forecasting(self) cdef np.complex64_t _inversion(self) cdef void _updating(self) cdef np.complex64_t _calculate_loglikelihood(self) cdef void _prediction(self) # Double precision complex cdef class zKalmanFilter(object): # Statespace object cdef readonly zStatespace model # ### Filter parameters cdef readonly int t cdef public np.float64_t tolerance, tolerance_diffuse cdef readonly int nobs_diffuse cdef readonly int nobs_kendog_diffuse_nonsingular cdef readonly int nobs_kendog_univariate_singular cdef readonly int converged cdef readonly int period_converged cdef readonly int time_invariant cdef readonly int filter_method cdef public int inversion_method cdef public int stability_method cdef readonly int conserve_memory cdef public int filter_timing cdef readonly int loglikelihood_burn cdef public int [:] univariate_filter # ### Kalman filter properties cdef readonly np.complex128_t [:] loglikelihood, scale cdef readonly np.complex128_t [::1,:] filtered_state, predicted_state, forecast, forecast_error, standardized_forecast_error cdef readonly np.complex128_t [::1,:,:] filtered_state_cov, predicted_state_cov, forecast_error_cov, predicted_diffuse_state_cov, forecast_error_diffuse_cov, M, M_inf cdef readonly np.complex128_t [::1,:,:] kalman_gain # ### Steady State Values cdef readonly np.complex128_t [::1,:] converged_forecast_error_cov cdef readonly np.complex128_t [::1,:] converged_filtered_state_cov cdef readonly np.complex128_t [::1,:] converged_predicted_state_cov cdef readonly np.complex128_t [::1,:] converged_kalman_gain cdef readonly np.complex128_t [::1,:] converged_M cdef readonly np.complex128_t converged_determinant # ### Temporary arrays cdef readonly np.complex128_t [::1,:] forecast_error_fac cdef readonly int [:] forecast_error_ipiv cdef readonly np.complex128_t [::1,:] forecast_error_work cdef readonly np.complex128_t [::1,:] tmp0, tmp00 cdef readonly np.complex128_t [::1,:] tmp2 cdef readonly np.complex128_t [::1,:,:] tmp1, tmp3, tmp4 cdef readonly np.complex128_t [:] tmpM_inf, tmpK0, tmpK1 cdef readonly np.complex128_t [::1,:] tmpL0, tmpL1 cdef readonly np.complex128_t [::1,:] CW, CtmpW, CMW, CM, CprevFiZ, CtmpM, CMWZ cdef readonly np.complex128_t determinant # ### Pointers to current-iteration arrays # cdef np.complex128_t * _obs # cdef np.complex128_t * _design # cdef np.complex128_t * _obs_intercept # cdef np.complex128_t * _obs_cov # cdef np.complex128_t * _transition # cdef np.complex128_t * _state_intercept # cdef np.complex128_t * _selection # cdef np.complex128_t * _state_cov # cdef np.complex128_t * _selected_state_cov # cdef np.complex128_t * _initial_state # cdef np.complex128_t * _initial_state_cov cdef np.complex128_t * _input_state cdef np.complex128_t * _input_state_cov cdef np.complex128_t * _input_diffuse_state_cov cdef np.complex128_t * _forecast cdef np.complex128_t * _forecast_error cdef np.complex128_t * _standardized_forecast_error cdef np.complex128_t * _forecast_error_cov cdef np.complex128_t * _filtered_state cdef np.complex128_t * _filtered_state_cov cdef np.complex128_t * _predicted_state cdef np.complex128_t * _predicted_state_cov cdef np.complex128_t * _forecast_error_diffuse_cov cdef np.complex128_t * _predicted_diffuse_state_cov cdef np.complex128_t * _M cdef np.complex128_t * _M_inf cdef np.complex128_t * _kalman_gain cdef np.complex128_t * _loglikelihood cdef np.complex128_t * _scale cdef np.complex128_t * _converged_forecast_error_cov cdef np.complex128_t * _converged_filtered_state_cov cdef np.complex128_t * _converged_predicted_state_cov cdef np.complex128_t * _converged_kalman_gain cdef np.complex128_t * _converged_M cdef np.complex128_t * _forecast_error_fac cdef int * _forecast_error_ipiv cdef np.complex128_t * _forecast_error_work cdef np.complex128_t * _tmp0 cdef np.complex128_t * _tmp00 cdef np.complex128_t * _tmp1 cdef np.complex128_t * _tmp2 cdef np.complex128_t * _tmp3 cdef np.complex128_t * _tmp4 cdef np.complex128_t * _tmpM_inf cdef np.complex128_t * _tmpK0 cdef np.complex128_t * _tmpK1 cdef np.complex128_t * _tmpL0 cdef np.complex128_t * _tmpL1 # ### Pointers to current-iteration Kalman filtering functions cdef int (*forecasting)( zKalmanFilter, zStatespace ) cdef np.complex128_t (*inversion)( zKalmanFilter, zStatespace, np.complex128_t ) except * cdef int (*updating)( zKalmanFilter, zStatespace ) cdef np.complex128_t (*calculate_loglikelihood)( zKalmanFilter, zStatespace, np.complex128_t ) cdef np.complex128_t (*calculate_scale)( zKalmanFilter, zStatespace ) cdef int (*prediction)( zKalmanFilter, zStatespace ) # ### Define some constants cdef readonly int k_endog, k_states, k_posdef, k_endog2, k_states2, k_posdef2, k_endogstates, k_statesposdef cdef readonly int ldwork cdef allocate_arrays(self) cdef void set_dimensions(self) cpdef set_filter_method(self, int filter_method, int force_reset=*) cpdef seek(self, unsigned int t, int reset=*) cdef void initialize_statespace_object_pointers(self) except * cdef void initialize_filter_object_pointers(self) cdef void initialize_function_pointers(self) except * cdef void post_convergence(self) cdef void numerical_stability(self) cdef int check_diffuse(self) cdef void check_convergence(self) cdef void migrate_storage(self) cdef void _reinitialize_pointers(self) except * cdef void _forecasting(self) cdef np.complex128_t _inversion(self) cdef void _updating(self) cdef np.complex128_t _calculate_loglikelihood(self) cdef void _prediction(self) statsmodels-0.12.2/statsmodels/tsa/statespace/_kalman_filter.pyx.in000066400000000000000000001763771400612667500255750ustar00rootroot00000000000000""" Kalman Filter Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # ## Constants # ### Filters cdef int FILTER_CONVENTIONAL = 0x01 # Durbin and Koopman (2012), Chapter 4 cdef int FILTER_EXACT_INITIAL = 0x02 # ibid., Chapter 5.6 cdef int FILTER_AUGMENTED = 0x04 # ibid., Chapter 5.7 not implemented cdef int FILTER_SQUARE_ROOT = 0x08 # ibid., Chapter 6.3 not implemented cdef int FILTER_UNIVARIATE = 0x10 # ibid., Chapter 6.4 cdef int FILTER_COLLAPSED = 0x20 # ibid., Chapter 6.5 cdef int FILTER_EXTENDED = 0x40 # ibid., Chapter 10.2 not implemented cdef int FILTER_UNSCENTED = 0x80 # ibid., Chapter 10.3 not implemented cdef int FILTER_CONCENTRATED = 0x100 # Harvey (1989), Chapter 3.4 cdef int FILTER_CHANDRASEKHAR = 0x200 # Herbst (2015) # ### Inversion methods # Methods by which the terms using the inverse of the forecast error # covariance matrix are solved. cdef int INVERT_UNIVARIATE = 0x01 cdef int SOLVE_LU = 0x02 cdef int INVERT_LU = 0x04 cdef int SOLVE_CHOLESKY = 0x08 cdef int INVERT_CHOLESKY = 0x10 # ### Numerical Stability methods # Methods to improve numerical stability cdef int STABILITY_FORCE_SYMMETRY = 0x01 # ### Memory conservation options cdef int MEMORY_STORE_ALL = 0 cdef int MEMORY_NO_FORECAST_MEAN = 0x01 cdef int MEMORY_NO_FORECAST_COV = 0x02 cdef int MEMORY_NO_FORECAST = MEMORY_NO_FORECAST_MEAN | MEMORY_NO_FORECAST_COV cdef int MEMORY_NO_PREDICTED_MEAN = 0x04 cdef int MEMORY_NO_PREDICTED_COV = 0x08 cdef int MEMORY_NO_PREDICTED = ( MEMORY_NO_PREDICTED_MEAN | MEMORY_NO_PREDICTED_COV) cdef int MEMORY_NO_FILTERED_MEAN = 0x10 cdef int MEMORY_NO_FILTERED_COV = 0x20 cdef int MEMORY_NO_FILTERED = MEMORY_NO_FILTERED_MEAN | MEMORY_NO_FILTERED_COV cdef int MEMORY_NO_LIKELIHOOD = 0x40 cdef int MEMORY_NO_GAIN = 0x80 cdef int MEMORY_NO_SMOOTHING = 0x100 cdef int MEMORY_NO_STD_FORECAST = 0x200 cdef int MEMORY_CONSERVE = ( MEMORY_NO_FORECAST | MEMORY_NO_PREDICTED | MEMORY_NO_FILTERED | MEMORY_NO_LIKELIHOOD | MEMORY_NO_GAIN | MEMORY_NO_SMOOTHING | MEMORY_NO_STD_FORECAST ) # ### Timing options # By default, assume filter is initialized with predicted values (as in # Durbin and Koopman 2012) # # Alternately, assume filter is initialized with filtered values (as in # Kim and Nelson 1999) cdef int TIMING_INIT_PREDICTED = 0 cdef int TIMING_INIT_FILTERED = 1 # Typical imports import numpy as np import warnings cimport numpy as np cimport cython np.import_array() from statsmodels.src.math cimport * cimport scipy.linalg.cython_blas as blas cimport scipy.linalg.cython_lapack as lapack cimport statsmodels.tsa.statespace._tools as tools {{for prefix, types in TYPES.items()}} from statsmodels.tsa.statespace._representation cimport {{prefix}}Statespace from statsmodels.tsa.statespace._filters._conventional cimport ( {{prefix}}forecast_missing_conventional, {{prefix}}updating_missing_conventional, {{prefix}}inverse_missing_conventional, {{prefix}}loglikelihood_missing_conventional, {{prefix}}scale_missing_conventional, {{prefix}}forecast_conventional, {{prefix}}updating_conventional, {{prefix}}prediction_conventional, {{prefix}}loglikelihood_conventional, {{prefix}}scale_conventional ) from statsmodels.tsa.statespace._filters._univariate cimport ( {{prefix}}forecast_univariate, {{prefix}}updating_univariate, {{prefix}}inverse_noop_univariate, {{prefix}}prediction_univariate, {{prefix}}loglikelihood_univariate, {{prefix}}scale_univariate ) from statsmodels.tsa.statespace._filters._univariate_diffuse cimport ( {{prefix}}forecast_univariate_diffuse, {{prefix}}updating_univariate_diffuse, {{prefix}}inverse_noop_univariate_diffuse, {{prefix}}prediction_univariate_diffuse, {{prefix}}loglikelihood_univariate_diffuse ) from statsmodels.tsa.statespace._filters._inversions cimport ( {{prefix}}inverse_univariate, {{prefix}}factorize_cholesky, {{prefix}}factorize_lu, {{prefix}}inverse_cholesky, {{prefix}}inverse_lu, {{prefix}}solve_cholesky, {{prefix}}solve_lu ) {{endfor}} cdef int FORTRAN = 1 {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} # ## Kalman filter cdef class {{prefix}}KalmanFilter(object): """ {{prefix}}KalmanFilter(model, filter_method=FILTER_CONVENTIONAL, inversion_method=INVERT_UNIVARIATE | SOLVE_CHOLESKY, stability_method=STABILITY_FORCE_SYMMETRY, filter_timing=TIMING_INIT_PREDICTED, tolerance=1e-19) A representation of the Kalman filter recursions. While the filter is mathematically represented as a recursion, it is here translated into Python as a stateful iterator. Because there are actually several types of Kalman filter depending on the state space model of interest, this class only handles the *iteration* aspect of filtering, and delegates the actual operations to four general workhorse routines, which can be implemented separately for each type of Kalman filter. In order to maintain a consistent interface, and because these four general routines may be quite different across filter types, their argument is only the stateful ?KalmanFilter object. Furthermore, in order to allow the different types of filter to substitute alternate matrices, this class defines a set of pointers to the various state space arrays and the filtering output arrays. For example, handling missing observations requires not only substituting `obs`, `design`, and `obs_cov` matrices, but the new matrices actually have different dimensions than the originals. This can be flexibly accommodated simply by replacing e.g. the `obs` pointer to the substituted `obs` array and replacing `k_endog` for that iteration. Then in the next iteration, when the `obs` vector may be missing different elements (or none at all), it can again be redefined. Each iteration of the filter (see `__next__`) proceeds in a number of steps. `initialize_object_pointers` initializes pointers to current-iteration objects (i.e. the state space arrays and filter output arrays). `initialize_function_pointers` initializes pointers to the appropriate Kalman filtering routines (i.e. `forecast_conventional` or `forecast_exact_initial`, etc.). `select_arrays` converts the base arrays into "selected" arrays using selection matrices. In particular, it handles the state covariance matrix and redefined matrices based on missing values. `post_convergence` handles copying arrays from time $t-1$ to time $t$ when the Kalman filter has converged and they do not need to be re-calculated. `forecasting` calls the Kalman filter `forcasting_` routine `inversion` calls the appropriate function to invert the forecast error covariance matrix. `updating` calls the Kalman filter `updating_` routine `loglikelihood` calls the Kalman filter `loglikelihood_` routine `prediction` calls the Kalman filter `prediction_` routine `numerical_stability` performs end-of-iteration tasks to improve the numerical stability of the filter `check_convergence` checks for convergence of the filter to steady-state. """ # ### Statespace model # cdef readonly {{prefix}}Statespace model # ### Filter parameters # Holds the time-iteration state of the filter # *Note*: must be changed using the `seek` method # cdef readonly int t # Holds the tolerance parameter for convergence # cdef public np.float64_t tolerance # Holds the convergence to steady-state status of the filter # *Note*: is by default reset each time `seek` is called # cdef readonly int converged # cdef readonly int period_converged # Holds whether or not the model is time-invariant # *Note*: is by default reset each time `seek` is called # cdef readonly int time_invariant # The Kalman filter procedure to use # cdef readonly int filter_method # The method by which the terms using the inverse of the forecast # error covariance matrix are solved. # cdef public int inversion_method # Methods to improve numerical stability # cdef public int stability_method # Whether or not to conserve memory # If True, only stores filtered states and covariance matrices # cdef readonly int conserve_memory # Whether or not to use alternate timing # If True, uses the Kim and Nelson (1999) timing # cdef readonly int filter_timing # If conserving loglikelihood, the number of periods to "burn" # before starting to record the loglikelihood # cdef readonly int loglikelihood_burn # ### Kalman filter properties # `loglikelihood` $\equiv \log p(y_t | Y_{t-1})$ # cdef readonly {{cython_type}} [:] loglikelihood # `filtered_state` $\equiv a_{t|t} = E(\alpha_t | Y_t)$ is the **filtered estimator** of the state $(m \times T)$ # `predicted_state` $\equiv a_{t+1} = E(\alpha_{t+1} | Y_t)$ is the **one-step ahead predictor** of the state $(m \times T-1)$ # `forecast` $\equiv E(y_t|Y_{t-1})$ is the **forecast** of the next observation $(p \times T)$ # `forecast_error` $\equiv v_t = y_t - E(y_t|Y_{t-1})$ is the **one-step ahead forecast error** of the next observation $(p \times T)$ # # *Note*: Actual values in `filtered_state` will be from 1 to `nobs`+1. Actual # values in `predicted_state` will be from 0 to `nobs`+1 because the initialization # is copied over to the zeroth entry, and similar for the covariances, below. # # *Old notation: beta_tt, beta_tt1, y_tt1, eta_tt1* # cdef readonly {{cython_type}} [::1,:] filtered_state, predicted_state, forecast, forecast_error # `filtered_state_cov` $\equiv P_{t|t} = Var(\alpha_t | Y_t)$ is the **filtered state covariance matrix** $(m \times m \times T)$ # `predicted_state_cov` $\equiv P_{t+1} = Var(\alpha_{t+1} | Y_t)$ is the **predicted state covariance matrix** $(m \times m \times T)$ # `forecast_error_cov` $\equiv F_t = Var(v_t | Y_{t-1})$ is the **forecast error covariance matrix** $(p \times p \times T)$ # # *Old notation: P_tt, P_tt1, f_tt1* # cdef readonly {{cython_type}} [::1,:,:] filtered_state_cov, predicted_state_cov, forecast_error_cov # `kalman_gain` $\equiv K_{t} = T_t P_t Z_t' F_t^{-1}$ is the **Kalman gain** $(m \times p \times T)$ # cdef readonly {{cython_type}} [::1,:,:] kalman_gain # ### Steady State Values # These matrices are used to hold the converged matrices after the Kalman # filter has reached steady-state # cdef readonly {{cython_type}} [::1,:] converged_forecast_error_cov # cdef readonly {{cython_type}} [::1,:] converged_filtered_state_cov # cdef readonly {{cython_type}} [::1,:] converged_predicted_state_cov # cdef readonly {{cython_type}} [::1,:] converged_kalman_gain # cdef readonly {{cython_type}} converged_determinant # ### Temporary arrays # These matrices are used to temporarily hold selected observation vectors, # design matrices, and observation covariance matrices in the case of # missing data. # `forecast_error_fac` is a forecast error covariance matrix **factorization** $(p \times p)$. # Depending on the method for handling the inverse of the forecast error covariance matrix, it may be: # - a Cholesky factorization if `cholesky_solve` is used # - an inverse calculated via Cholesky factorization if `cholesky_inverse` is used # - an LU factorization if `lu_solve` is used # - an inverse calculated via LU factorization if `lu_inverse` is used # cdef readonly {{cython_type}} [::1,:] forecast_error_fac # `forecast_error_ipiv` holds pivot indices if an LU decomposition is used # cdef readonly int [:] forecast_error_ipiv # `forecast_error_work` is a work array for matrix inversion if an LU # decomposition is used # cdef readonly {{cython_type}} [::1,:] forecast_error_work # These hold the memory allocations of the anonymous temporary arrays # cdef readonly {{cython_type}} [::1,:] tmp0, tmp00 # These hold the memory allocations of the named temporary arrays # (these are all time-varying in the last dimension) # cdef readonly {{cython_type}} [::1,:] tmp2 # cdef readonly {{cython_type}} [::1,:,:] tmp1, tmp3 # Holds the determinant across calculations (this is done because after # convergence, it does not need to be re-calculated anymore) # cdef readonly {{cython_type}} determinant # ### Pointers to current-iteration arrays # cdef {{cython_type}} * _obs # cdef {{cython_type}} * _design # cdef {{cython_type}} * _obs_intercept # cdef {{cython_type}} * _obs_cov # cdef {{cython_type}} * _transition # cdef {{cython_type}} * _state_intercept # cdef {{cython_type}} * _selection # cdef {{cython_type}} * _state_cov # cdef {{cython_type}} * _selected_state_cov # cdef {{cython_type}} * _initial_state # cdef {{cython_type}} * _initial_state_cov # cdef {{cython_type}} * _input_state # cdef {{cython_type}} * _input_state_cov # cdef {{cython_type}} * _forecast # cdef {{cython_type}} * _forecast_error # cdef {{cython_type}} * _forecast_error_cov # cdef {{cython_type}} * _filtered_state # cdef {{cython_type}} * _filtered_state_cov # cdef {{cython_type}} * _predicted_state # cdef {{cython_type}} * _predicted_state_cov # cdef {{cython_type}} * _kalman_gain # cdef {{cython_type}} * _loglikelihood # cdef {{cython_type}} * _converged_forecast_error_cov # cdef {{cython_type}} * _converged_filtered_state_cov # cdef {{cython_type}} * _converged_predicted_state_cov # cdef {{cython_type}} * _converged_kalman_gain # cdef {{cython_type}} * _forecast_error_fac # cdef int * _forecast_error_ipiv # cdef {{cython_type}} * _forecast_error_work # cdef {{cython_type}} * _tmp0 # cdef {{cython_type}} * _tmp00 # cdef {{cython_type}} * _tmp1 # cdef {{cython_type}} * _tmp2 # cdef {{cython_type}} * _tmp3 # ### Pointers to current-iteration Kalman filtering functions # cdef int (*forecasting)( # {{prefix}}KalmanFilter, {{prefix}}Statespace # ) # cdef {{cython_type}} (*inversion)( # {{prefix}}KalmanFilter, {{prefix}}Statespace, {{cython_type}} # ) except * # cdef int (*updating)( # {{prefix}}KalmanFilter, {{prefix}}Statespace # ) # cdef {{cython_type}} (*calculate_loglikelihood)( # {{prefix}}KalmanFilter, {{prefix}}Statespace, {{cython_type}} # ) # cdef int (*prediction)( # {{prefix}}KalmanFilter, {{prefix}}Statespace # ) # ### Define some constants # cdef readonly int k_endog, k_states, k_posdef, k_endog2, k_states2, k_endogstates # cdef readonly ldwork def __init__(self, {{prefix}}Statespace model, int filter_method=FILTER_CONVENTIONAL, int inversion_method=INVERT_UNIVARIATE | SOLVE_CHOLESKY, int stability_method=STABILITY_FORCE_SYMMETRY, int conserve_memory=MEMORY_STORE_ALL, int filter_timing=TIMING_INIT_PREDICTED, np.float64_t tolerance=1e-19, int loglikelihood_burn=0): # Save the model self.model = model # Initialize filter parameters self.tolerance = tolerance self.tolerance_diffuse = 1e-10 # TODO replace hardcode with argument self.inversion_method = inversion_method self.stability_method = stability_method self.conserve_memory = conserve_memory self.filter_timing = filter_timing self.loglikelihood_burn = loglikelihood_burn # Initialize the constant values self.time_invariant = self.model.time_invariant # TODO replace with optimal work array size self.ldwork = self.model.k_endog # Set the filter method self.set_dimensions() self.set_filter_method(filter_method, True) # Initialize time and convergence status self.t = 0 self.nobs_diffuse = 0 self.converged = 0 self.period_converged = 0 def __reduce__(self): args = (self.model, self.filter_method, self.inversion_method, self.stability_method, self.conserve_memory, self.filter_timing, self.tolerance, self.loglikelihood_burn) state = {'t': self.t, 'nobs_diffuse' : self.nobs_diffuse, 'converged' : self.converged, 'converged_determinant' : self.converged_determinant, 'determinant' : self.determinant, 'period_converged' : self.period_converged, 'converged_filtered_state_cov': np.array(self.converged_filtered_state_cov, copy=True, order='F'), 'converged_forecast_error_cov': np.array(self.converged_forecast_error_cov, copy=True, order='F'), 'converged_kalman_gain': np.array(self.converged_kalman_gain, copy=True, order='F'), 'converged_M': np.array(self.converged_M, copy=True, order='F'), 'converged_predicted_state_cov': np.array(self.converged_predicted_state_cov, copy=True, order='F'), 'filtered_state': np.array(self.filtered_state, copy=True, order='F'), 'filtered_state_cov': np.array(self.filtered_state_cov, copy=True, order='F'), 'forecast': np.array(self.forecast, copy=True, order='F'), 'forecast_error': np.array(self.forecast_error, copy=True, order='F'), 'forecast_error_cov': np.array(self.forecast_error_cov, copy=True, order='F'), 'forecast_error_fac': np.array(self.forecast_error_fac, copy=True, order='F'), 'forecast_error_ipiv': np.array(self.forecast_error_ipiv, copy=True, order='F'), 'forecast_error_work': np.array(self.forecast_error_work, copy=True, order='F'), 'kalman_gain': np.array(self.kalman_gain, copy=True, order='F'), 'univariate_filter': np.array(self.univariate_filter, copy=True, order='F'), 'loglikelihood': np.array(self.loglikelihood, copy=True, order='F'), 'predicted_state': np.array(self.predicted_state, copy=True, order='F'), 'predicted_state_cov': np.array(self.predicted_state_cov, copy=True, order='F'), 'standardized_forecast_error': np.array(self.standardized_forecast_error, copy=True, order='F'), 'predicted_diffuse_state_cov': np.array(self.predicted_diffuse_state_cov, copy=True, order='F'), 'forecast_error_diffuse_cov': np.array(self.forecast_error_diffuse_cov, copy=True, order='F'), 'tmp0': np.array(self.tmp0, copy=True, order='F'), 'tmp00': np.array(self.tmp00, copy=True, order='F'), 'tmp1': np.array(self.tmp1, copy=True, order='F'), 'tmp2': np.array(self.tmp2, copy=True, order='F'), 'tmp3': np.array(self.tmp3, copy=True, order='F'), 'tmp4': np.array(self.tmp4, copy=True, order='F'), 'M': np.array(self.M, copy=True, order='F'), 'M_inf': np.array(self.M_inf, copy=True, order='F'), 'tmpK0': np.array(self.tmpK0, copy=True, order='F'), 'tmpK1': np.array(self.tmpK1, copy=True, order='F'), 'tmpL0': np.array(self.tmpL0, copy=True, order='F'), 'tmpL1': np.array(self.tmpL1, copy=True, order='F') } return (self.__class__, args, state) def __setstate__(self, state): self.t = state['t'] self.nobs_diffuse = state['nobs_diffuse'] self.converged = state['converged'] self.converged_determinant = state['converged_determinant'] self.determinant = state['determinant'] self.period_converged = state['period_converged'] self.converged_filtered_state_cov = state['converged_filtered_state_cov'] self.converged_forecast_error_cov = state['converged_forecast_error_cov'] self.converged_kalman_gain = state['converged_kalman_gain'] self.converged_M = state['converged_M'] self.converged_predicted_state_cov = state['converged_predicted_state_cov'] self.filtered_state = state['filtered_state'] self.filtered_state_cov = state['filtered_state_cov'] self.forecast = state['forecast'] self.forecast_error = state['forecast_error'] self.forecast_error_cov = state['forecast_error_cov'] self.forecast_error_fac = state['forecast_error_fac'] self.forecast_error_ipiv = state['forecast_error_ipiv'] self.forecast_error_work = state['forecast_error_work'] self.kalman_gain = state['kalman_gain'] self.univariate_filter = state['univariate_filter'] self.loglikelihood = state['loglikelihood'] self.predicted_state = state['predicted_state'] self.predicted_state_cov = state['predicted_state_cov'] self.standardized_forecast_error = state['standardized_forecast_error'] self.predicted_diffuse_state_cov = state['predicted_diffuse_state_cov'] self.forecast_error_diffuse_cov = state['forecast_error_diffuse_cov'] self.tmp0 = state['tmp0'] self.tmp00 = state['tmp00'] self.tmp1 = state['tmp1'] self.tmp2 = state['tmp2'] self.tmp3 = state['tmp3'] self.tmp4 = state['tmp4'] self.M = state['M'] self.M_inf = state['M_inf'] self.tmpK0 = state['tmpK0'] self.tmpK1 = state['tmpK1'] self.tmpL0 = state['tmpL0'] self.tmpL1 = state['tmpL1'] self._reinitialize_pointers() cdef void _reinitialize_pointers(self) except *: self._converged_forecast_error_cov = &self.converged_forecast_error_cov[0,0] self._converged_filtered_state_cov = &self.converged_filtered_state_cov[0,0] self._converged_predicted_state_cov = &self.converged_predicted_state_cov[0,0] self._converged_kalman_gain = &self.converged_kalman_gain[0,0] self._converged_M = &self.converged_M[0,0] self._forecast_error_fac = &self.forecast_error_fac[0,0] self._forecast_error_work = &self.forecast_error_work[0,0] self._forecast_error_ipiv = &self.forecast_error_ipiv[0] self._tmp0 = &self.tmp0[0, 0] self._tmp00 = &self.tmp00[0, 0] self._tmpK0 = &self.tmpK0[0] self._tmpK1 = &self.tmpK1[0] self._tmpL0 = &self.tmpL0[0,0] self._tmpL1 = &self.tmpL1[0,0] cdef allocate_arrays(self): # Local variables cdef: np.npy_intp dim1[1] np.npy_intp dim2[2] np.npy_intp dim3[3] cdef int storage # #### Allocate arrays for calculations dim1[0] = self.model.nobs; self.univariate_filter = np.PyArray_ZEROS(1, dim1, np.NPY_INT32, FORTRAN) # Arrays for Kalman filter output # Forecast if self.conserve_memory & MEMORY_NO_FORECAST_MEAN: storage = 2 else: storage = self.model.nobs dim2[0] = self.k_endog; dim2[1] = storage; self.forecast = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self.forecast_error = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) if self.conserve_memory & MEMORY_NO_FORECAST_COV: storage = 2 else: storage = self.model.nobs dim3[0] = self.k_endog; dim3[1] = self.k_endog; dim3[2] = storage; self.forecast_error_cov = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) # Standardized forecast errors if self.conserve_memory & MEMORY_NO_STD_FORECAST > 0: storage = 1 else: storage = self.model.nobs dim2[0] = self.k_endog; dim2[1] = storage; self.standardized_forecast_error = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Filtered if self.conserve_memory & MEMORY_NO_FILTERED_MEAN > 0: storage = 2 else: storage = self.model.nobs dim2[0] = self.k_states; dim2[1] = storage; self.filtered_state = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) if self.conserve_memory & MEMORY_NO_FILTERED_COV > 0: storage = 2 else: storage = self.model.nobs dim3[0] = self.k_states; dim3[1] = self.k_states; dim3[2] = storage; self.filtered_state_cov = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) # Predicted if self.conserve_memory & MEMORY_NO_PREDICTED_MEAN > 0: storage = 2 else: storage = self.model.nobs dim2[0] = self.k_states; dim2[1] = storage+1; self.predicted_state = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) if self.conserve_memory & MEMORY_NO_PREDICTED_COV > 0: storage = 2 else: storage = self.model.nobs dim3[0] = self.k_states; dim3[1] = self.k_states; dim3[2] = storage+1; self.predicted_state_cov = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) # Exact diffuse initialization # TODO: only create full nobs-length arrays if necessary if self.conserve_memory & MEMORY_NO_FORECAST_COV: storage = 2 else: storage = self.model.nobs dim3[0] = self.k_endog; dim3[1] = self.k_endog; dim3[2] = storage; self.forecast_error_diffuse_cov = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) if self.conserve_memory & MEMORY_NO_PREDICTED_COV > 0: storage = 2 else: storage = self.model.nobs dim3[0] = self.k_states; dim3[1] = self.k_states; dim3[2] = storage+1; self.predicted_diffuse_state_cov = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) dim3[0] = self.k_states; dim3[1] = self.k_endog; dim3[2] = storage; self.M = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) self.M_inf = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) dim1[0] = self.k_states; self.tmpK0 = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) self._tmpK0 = &self.tmpK0[0] self.tmpK1 = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) self._tmpK1 = &self.tmpK1[0] dim2[0] = self.k_states; dim2[1] = self.k_states; self.tmpL0 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._tmpL0 = &self.tmpL0[0,0] self.tmpL1 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._tmpL1 = &self.tmpL1[0,0] # Kalman Gain if self.conserve_memory & MEMORY_NO_GAIN > 0: storage = 1 else: storage = self.model.nobs dim3[0] = self.k_states; dim3[1] = self.k_endog; dim3[2] = storage; self.kalman_gain = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) # Likelihood if self.conserve_memory & MEMORY_NO_LIKELIHOOD > 0: storage = 1 else: storage = self.model.nobs dim1[0] = storage self.loglikelihood = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) self.scale = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) # Converged matrices dim2[0] = self.k_endog; dim2[1] = self.k_endog; self.converged_forecast_error_cov = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._converged_forecast_error_cov = &self.converged_forecast_error_cov[0,0] dim2[0] = self.k_states; dim2[1] = self.k_states; self.converged_filtered_state_cov = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._converged_filtered_state_cov = &self.converged_filtered_state_cov[0,0] dim2[0] = self.k_states; dim2[1] = self.k_states; self.converged_predicted_state_cov = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._converged_predicted_state_cov = &self.converged_predicted_state_cov[0,0] dim2[0] = self.k_states; dim2[1] = self.k_endog; self.converged_kalman_gain = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._converged_kalman_gain = &self.converged_kalman_gain[0,0] dim2[0] = self.k_states; dim2[1] = self.k_endog; self.converged_M = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._converged_M = &self.converged_M[0,0] # #### Arrays for temporary calculations # *Note*: in math notation below, a $\\#$ will represent a generic # temporary array, and a $\\#_i$ will represent a named temporary array. # Arrays related to matrix factorizations / inverses dim2[0] = self.k_endog; dim2[1] = self.k_endog; self.forecast_error_fac = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._forecast_error_fac = &self.forecast_error_fac[0,0] dim2[0] = self.ldwork; dim2[1] = self.ldwork; self.forecast_error_work = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._forecast_error_work = &self.forecast_error_work[0,0] dim1[0] = self.k_endog; self.forecast_error_ipiv = np.PyArray_ZEROS(1, dim1, np.NPY_INT, FORTRAN) self._forecast_error_ipiv = &self.forecast_error_ipiv[0] # Holds arrays of dimension $(m \times m)$ and $(m \times r)$ dim2[0] = self.k_states; dim2[1] = self.k_states; self.tmp0 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._tmp0 = &self.tmp0[0, 0] dim2[0] = self.k_states; dim2[1] = self.k_states; self.tmp00 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._tmp00 = &self.tmp00[0, 0] # Optionally we may not want to store temporary arrays required # for smoothing if self.conserve_memory & MEMORY_NO_SMOOTHING > 0: storage = 1 else: storage = self.model.nobs # Holds arrays of dimension $(m \times p \times T)$ # $\\#_1 = P_t Z_t'$ # Also known as the matrix M dim3[0] = self.k_states; dim3[1] = self.k_endog; dim3[2] = storage; self.tmp1 = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) # Holds arrays of dimension $(p \times T)$ # $\\#_2 = F_t^{-1} v_t$ dim2[0] = self.k_endog; dim2[1] = storage; self.tmp2 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Holds arrays of dimension $(p \times m \times T)$ # $\\#_3 = F_t^{-1} Z_t$ dim3[0] = self.k_endog; dim3[1] = self.k_states; dim3[2] = storage; self.tmp3 = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) # Holds arrays of dimension $(p \times p \times T)$ # $\\#_4 = F_t^{-1} H_t$ dim3[0] = self.k_endog; dim3[1] = self.k_endog; dim3[2] = storage; self.tmp4 = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) # Arrays for Chandrasekhar recursions # W $(m \times p)$ (W1 = T @ P @ Z[i].T) dim2[0] = self.k_states; dim2[1] = self.k_endog; self.CW = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # temporary array for W (m \times p) self.CtmpW = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Previous version of `tmp3` array: F_{t-1}^{-1} Z dim2[0] = self.k_endog; dim2[1] = self.k_states; self.CprevFiZ = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # M @ W.T $(p \times m)$ dim2[0] = self.k_endog; dim2[1] = self.k_states; self.CMW = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # M.T @ W.T @ Z.T $(p \times p)$ # or in univariate case: M.T @ W.T @ Z[i] $(p \times 1)$ dim2[0] = self.k_endog; dim2[1] = self.k_endog; self.CMWZ = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # M $(p \times p)$ (M1 = -F^{-1}) dim2[0] = self.k_endog; dim2[1] = self.k_endog; self.CM = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # temporary array for M (p \times p) self.CtmpM = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) cdef void set_dimensions(self): """ Set dimensions for the Kalman filter These are used *only* to define the shapes of the Kalman filter output and temporary arrays in memory. They will not change between iterations of the filter. They only differ from the {{prefix}}Statespace versions in the case that the FILTER_COLLAPSED flag is set, in which case model.k_endog and kfilter.k_endog will be different (since kfilter.k_endog = model.k_states). Across *iterations* of the Kalman filter, both model.k_* and kfilter.k_* are fixed, although model._k_* may be different from either when there is missing data in a given period's observations. The actual dimension of the *data* being considered at a given iteration is always given by model._k_* variables, which take into account both FILTER_COLLAPSED and missing data. But, the dimension *in memory* of the Kalman filter arrays will always be given by kfilter.k_*. The following relations will always hold: kfilter.k_endog = model.k_states if self.filter_method & FILTER_COLLAPSED else model.k_endog kfilter.k_endog = model._k_endog + model._nmissing """ self.k_endog = self.model.k_states if self.filter_method & FILTER_COLLAPSED else self.model.k_endog self.k_states = self.model.k_states self.k_posdef = self.model.k_posdef self.k_endog2 = self.k_endog**2 self.k_states2 = self.k_states**2 self.k_posdef2 = self.k_posdef**2 self.k_endogstates = self.k_endog * self.k_states self.k_statesposdef = self.k_states * self.k_posdef cpdef set_filter_method(self, int filter_method, int force_reset=True): """ set_filter_method(self, filter_method, force_reset=True) Change the filter method. """ cdef int time_invariant if not filter_method == self.filter_method or force_reset: # Check for invalid filter methods if filter_method & FILTER_COLLAPSED and self.k_endog <= self.k_states: raise RuntimeError('Cannot collapse observation vector if the' ' state dimension is equal to or larger than the' ' dimension of the observation vector.') if filter_method & FILTER_COLLAPSED and filter_method & FILTER_CONCENTRATED: raise RuntimeError('Cannot apply a concentrated likelihood function' ' with a collapsed observation vector.') if filter_method & FILTER_CHANDRASEKHAR: # Check for missing data if self.model.has_missing: raise RuntimeError('Cannot use Chandrasekhar recursions' ' with missing data.') # Note: would like to check for stationary initialization, but # we can't do that here b/c self.model does not store the # initialization object for us to inspect. # TODO: however, we can set a new flag in self.model.initialize # noting the type of initialization (stationary, diffuse, # mixed, etc.) and then check the value here. if self.filter_timing == TIMING_INIT_FILTERED: raise RuntimeError('Cannot use Chandrasekhar recursions' ' with filtered timing.') # Check for a time-invariant model time_invariant = ( self.model.design.shape[2] == 1 and self.model.obs_cov.shape[2] == 1 and self.model.transition.shape[2] == 1 and self.model.selection.shape[2] == 1 and self.model.state_cov.shape[2] == 1) if not time_invariant: raise RuntimeError('Cannot use Chandrasekhar recursions' ' with time-varying system matrices' ' (except for intercept terms).') # Change the smoother output flag self.filter_method = filter_method # Reset dimensions self.set_dimensions() # Reset matrices self.allocate_arrays() # Reset the flag for using the univariate method if filter_method & FILTER_UNIVARIATE: self.univariate_filter[:] = 1 else: self.univariate_filter[:] = 0 # Seek to the beginning self.seek(0, True) cpdef seek(self, unsigned int t, int reset=True): """ seek(self, t, reset = True) Change the time-state of the filter Is usually called to reset the filter to the beginning. """ if not t == 0 and t >= self.model.nobs: raise IndexError("Observation index out of range") self.t = t if reset: self.nobs_diffuse = 0 self.nobs_kendog_diffuse_nonsingular = 0 self.nobs_kendog_univariate_singular = 0 self.converged = 0 self.period_converged = 0 if self.filter_method & FILTER_UNIVARIATE: self.univariate_filter[:] = 1 else: self.univariate_filter[:] = 0 def __iter__(self): return self def __call__(self, int filter_method=-1): """ Iterate the filter across the entire set of observations. """ cdef int i # Reset the filter method if necessary if not filter_method == -1: self.set_filter_method(filter_method) # Reset the filter self.seek(0, True) # Perform forward filtering iterations for i in range(self.model.nobs): next(self) def __next__(self): """ Perform an iteration of the Kalman filter """ cdef int inc = 1 cdef int filtered_mean_t = self.t cdef int filtered_cov_t = self.t cdef int predicted_mean_t = self.t cdef int predicted_cov_t = self.t if self.conserve_memory & MEMORY_NO_FILTERED_MEAN > 0: filtered_mean_t = 1 if self.conserve_memory & MEMORY_NO_FILTERED_COV > 0: filtered_cov_t = 1 if self.conserve_memory & MEMORY_NO_PREDICTED_MEAN > 0: predicted_mean_t = 1 if self.conserve_memory & MEMORY_NO_PREDICTED_COV > 0: predicted_cov_t = 1 # Get time subscript, and stop the iterator if at the end if not self.t < self.model.nobs: raise StopIteration # Clear values if self.t == 0 or not (self.conserve_memory & MEMORY_NO_LIKELIHOOD): self.loglikelihood[self.t] = 0 self.scale[self.t] = 0 # Clear convergence flag if we've just switched the filter type # (this should only happen in contrived cases though, since after we've # successfully converged, the inversion step won't fail anymore) if (self.converged and self.univariate_filter[self.t] != self.univariate_filter[self.t - 1]): self.converged = 0 self.period_converged = 0 # Initialize pointers to current-iteration objects self.initialize_statespace_object_pointers() self.initialize_filter_object_pointers() # Initialize pointers to appropriate Kalman filtering functions self.initialize_function_pointers() # Convert base arrays into "selected" arrays # - State covariance matrix? $Q_t \to R_t Q_t R_t`$ # - Missing values: $y_t \to W_t y_t$, $Z_t \to W_t Z_t$, $H_t \to W_t H_t$ # self.select_state_cov() # self.select_missing() # self.transform() # Post-convergence: copy previous iteration arrays self.post_convergence() # Prediction step (alternate timing) if self.filter_timing == TIMING_INIT_FILTERED: # We need to shift back to the previous filtered_* arrays, or to # the initial_* arrays if we're at time t==0 if self.t == 0: self._filtered_state = self.model._initial_state self._filtered_state_cov = self.model._initial_state_cov self._input_diffuse_state_cov = self.model._initial_diffuse_state_cov if self.check_diffuse(): raise NotImplementedError('Cannot use alternate ("filtered")' ' timing with exact diffuse' ' initialization.') else: self._filtered_state = &self.filtered_state[0, filtered_mean_t-1] self._filtered_state_cov = &self.filtered_state_cov[0, 0, filtered_cov_t-1] # Perform the prediction step self.prediction(self, self.model) # self._prediction() # Aids to numerical stability self.numerical_stability() # Now shift back to the current filtered_* arrays (so they can be # set in the updating step) self._filtered_state = &self.filtered_state[0, filtered_mean_t] self._filtered_state_cov = &self.filtered_state_cov[0, 0, filtered_cov_t] # Clear `forecasts_error_cov` if we switched from multivariate to # univariate (because we might have off-diagonal elements stored from # a previous multivariate run that wouldn't have been cleared yet) if self.univariate_filter[self.t] == 1 and (self.t == 0 or self.univariate_filter[self.t - 1] == 0): self.forecast_error_cov[..., self.t:] = 0 # Form forecasts self.forecasting(self, self.model) # self._forecasting() # Perform `forecast_error_cov` inversion (or decomposition) try: self.determinant = self.inversion(self, self.model, self.determinant) except np.linalg.LinAlgError: # If the multivariate filter fails here due to a singular forecast # error covariance matrix, then we can try to fall back to the # univariate filter # If we were already using the univariate filter, raise the # exception if not ((self.inversion_method & INVERT_UNIVARIATE) or (self.inversion_method & SOLVE_CHOLESKY)): raise NotImplementedError( 'Singular forecast error covariance matrix detected, but' ' multivariate filter cannot fall back to univariate' ' filter when the inversion method is set to anything' ' other than INVERT_UNIVARIATE or SOLVE_CHOLESKY.') elif self.univariate_filter[self.t]: raise else: self.univariate_filter[self.t] = 1 next(self) return # self.determinant = self._inversion() # Updating step self.updating(self, self.model) # self._updating() # Retrieve the loglikelihood if not self.conserve_memory & MEMORY_NO_LIKELIHOOD or self.t >= self.loglikelihood_burn: self._loglikelihood[0] = ( self._loglikelihood[0] + self.calculate_loglikelihood(self, self.model, self.determinant) + # self._calculate_loglikelihood() + self.model.collapse_loglikelihood ) if self.filter_method & FILTER_CONCENTRATED: self._scale[0] = self._scale[0] + self.calculate_scale(self, self.model) # Prediction step (default timing) if self.filter_timing == TIMING_INIT_PREDICTED: self.prediction(self, self.model) # self._prediction() # Aids to numerical stability self.numerical_stability() # Last prediction step (alternate timing) if self.filter_timing == TIMING_INIT_FILTERED and self.t == self.model.nobs-1: self._predicted_state = &self.predicted_state[0, predicted_mean_t+1] self._predicted_state_cov = &self.predicted_state_cov[0, 0, predicted_cov_t+1] self._predicted_diffuse_state_cov = &self.predicted_diffuse_state_cov[0, 0, predicted_cov_t+1] self.prediction(self, self.model) # Check for convergence self.check_convergence() # If conserving memory, migrate storage: t->t-1, t+1->t self.migrate_storage() # Advance the time self.t += 1 cdef void _forecasting(self): {{prefix}}forecast_univariate(self, self.model) cdef {{cython_type}} _inversion(self): {{prefix}}inverse_noop_univariate(self, self.model, self.determinant) cdef void _updating(self): {{prefix}}updating_univariate(self, self.model) cdef {{cython_type}} _calculate_loglikelihood(self): return {{prefix}}loglikelihood_univariate(self, self.model, self.determinant) cdef void _prediction(self): {{prefix}}prediction_univariate(self, self.model) cdef void initialize_statespace_object_pointers(self) except *: cdef: int transform_diagonalize = 0 int transform_generalized_collapse = 0 int reset = 0 # Determine which transformations need to be made transform_generalized_collapse = self.filter_method & FILTER_COLLAPSED transform_diagonalize = self.univariate_filter[self.t] if self.t > 0: reset = self.univariate_filter[self.t] != self.univariate_filter[self.t - 1] # Initialize object-level pointers to statespace arrays #self.model.initialize_object_pointers(self.t) self.model.seek(self.t, transform_diagonalize, transform_generalized_collapse, reset) # Handle missing data if self.model._nmissing > 0 or (self.model.has_missing and self.filter_method & FILTER_UNIVARIATE): # TODO there is likely a way to allow convergence and the univariate filter, but it # does not work "out-of-the-box" right now self.converged = 0 cdef void initialize_filter_object_pointers(self): cdef: int t = self.t int inc = 1 # Indices for arrays that may or may not be stored completely cdef: int forecast_mean_t = t int forecast_cov_t = t int filtered_mean_t = t int filtered_cov_t = t int predicted_mean_t = t int predicted_cov_t = t int gain_t = t int smoothing_t = t int loglikelihood_t = t int std_forecast_t = t if self.conserve_memory & MEMORY_NO_FORECAST_MEAN > 0: forecast_mean_t = 1 if self.conserve_memory & MEMORY_NO_FORECAST_COV > 0: forecast_cov_t = 1 if self.conserve_memory & MEMORY_NO_FILTERED_MEAN > 0: filtered_mean_t = 1 if self.conserve_memory & MEMORY_NO_FILTERED_COV > 0: filtered_cov_t = 1 if self.conserve_memory & MEMORY_NO_PREDICTED_MEAN > 0: predicted_mean_t = 1 if self.conserve_memory & MEMORY_NO_PREDICTED_COV > 0: predicted_cov_t = 1 if self.conserve_memory & MEMORY_NO_GAIN > 0: gain_t = 0 if self.conserve_memory & MEMORY_NO_SMOOTHING > 0: smoothing_t = 0 if self.conserve_memory & MEMORY_NO_LIKELIHOOD > 0: loglikelihood_t = 0 if self.conserve_memory & MEMORY_NO_STD_FORECAST > 0: std_forecast_t = 0 # Initialize object-level pointers to input arrays self._input_state = &self.predicted_state[0, predicted_mean_t] self._input_state_cov = &self.predicted_state_cov[0, 0, predicted_cov_t] self._input_diffuse_state_cov = &self.predicted_diffuse_state_cov[0, 0, predicted_cov_t] # Copy initialization arrays to input arrays if we're starting the # filter if t == 0 and self.filter_timing == TIMING_INIT_PREDICTED: # `predicted_state[:,0]` $= a_1 =$ `initial_state` # `predicted_state_cov[:,:,0]` $= P_1 =$ `initial_state_cov` # Under the default timing assumption (TIMING_INIT_PREDICTED), the # recursion takes $a_t, P_t$ as input, and as a last step computes # $a_{t+1}, P_{t+1}$, which can be input for the next recursion. # This means that the filter ends by computing $a_{T+1}, P_{T+1}$, # so that the predicted_* arrays have time-dimension T+1, rather than # T like all the other arrays. # Note that $a_{T+1}, P_{T+1}$ should not be in use anywhere. # TODO phase out any use of these, and eventually stop computing it # This means that the zeroth entry in the time-dimension can hold the # input array (even though it is no different than what is held in the # initial_state_* arrays). blas.{{prefix}}copy(&self.model._k_states, self.model._initial_state, &inc, self._input_state, &inc) blas.{{prefix}}copy(&self.model._k_states2, self.model._initial_state_cov, &inc, self._input_state_cov, &inc) blas.{{prefix}}copy(&self.model._k_states2, self.model._initial_diffuse_state_cov, &inc, self._input_diffuse_state_cov, &inc) # Now we can check if we are in a diffuse period. If we are but we are # not using the univariate method, then we may need to perform the # diagonalization transformation (since in diffuse periods we always # use the univariate method) if not self.univariate_filter[self.t] and self.check_diffuse(): self.model.transform_diagonalize(self.model.t, self.model._previous_t) # Initialize object-level pointers to output arrays self._forecast = &self.forecast[0, forecast_mean_t] self._forecast_error = &self.forecast_error[0, forecast_mean_t] self._forecast_error_cov = &self.forecast_error_cov[0, 0, forecast_cov_t] self._forecast_error_diffuse_cov = &self.forecast_error_diffuse_cov[0, 0, forecast_cov_t] self._standardized_forecast_error = &self.standardized_forecast_error[0, std_forecast_t] self._filtered_state = &self.filtered_state[0, filtered_mean_t] self._filtered_state_cov = &self.filtered_state_cov[0, 0, filtered_cov_t] if self.filter_timing == TIMING_INIT_PREDICTED: self._predicted_state = &self.predicted_state[0, predicted_mean_t+1] self._predicted_state_cov = &self.predicted_state_cov[0, 0, predicted_cov_t+1] self._predicted_diffuse_state_cov = &self.predicted_diffuse_state_cov[0, 0, predicted_cov_t+1] else: self._predicted_state = &self.predicted_state[0, predicted_mean_t] self._predicted_state_cov = &self.predicted_state_cov[0, 0, predicted_cov_t] self._predicted_diffuse_state_cov = &self.predicted_diffuse_state_cov[0, 0, predicted_cov_t] self._M = &self.M[0, 0, predicted_cov_t] self._M_inf = &self.M_inf[0, 0, predicted_cov_t] self._kalman_gain = &self.kalman_gain[0, 0, gain_t] self._loglikelihood = &self.loglikelihood[loglikelihood_t] self._scale = &self.scale[loglikelihood_t] # Initialize object-level pointers to named temporary arrays self._tmp1 = &self.tmp1[0, 0, smoothing_t] self._tmp2 = &self.tmp2[0, smoothing_t] self._tmp3 = &self.tmp3[0, 0, smoothing_t] self._tmp4 = &self.tmp4[0, 0, smoothing_t] cdef void initialize_function_pointers(self) except *: cdef int diffuse = self.check_diffuse() # Filtering method # Must use univariate diffuse method if we are at a diffuse observation if diffuse: self.forecasting = {{prefix}}forecast_univariate_diffuse self.updating = {{prefix}}updating_univariate_diffuse self.inversion = {{prefix}}inverse_noop_univariate_diffuse self.calculate_loglikelihood = {{prefix}}loglikelihood_univariate_diffuse self.calculate_scale = {{prefix}}scale_univariate self.prediction = {{prefix}}prediction_univariate_diffuse # Univariate method elif self.univariate_filter[self.t]: self.forecasting = {{prefix}}forecast_univariate self.updating = {{prefix}}updating_univariate self.inversion = {{prefix}}inverse_noop_univariate self.calculate_loglikelihood = {{prefix}}loglikelihood_univariate self.calculate_scale = {{prefix}}scale_univariate self.prediction = {{prefix}}prediction_univariate # Conventional method elif self.filter_method & FILTER_CONVENTIONAL: self.forecasting = {{prefix}}forecast_conventional self.updating = {{prefix}}updating_conventional self.calculate_loglikelihood = {{prefix}}loglikelihood_conventional self.calculate_scale = {{prefix}}scale_conventional self.prediction = {{prefix}}prediction_conventional # Inversion method if self.inversion_method & INVERT_UNIVARIATE and self.k_endog == 1: self.inversion = {{prefix}}inverse_univariate elif self.inversion_method & SOLVE_CHOLESKY: self.inversion = {{prefix}}solve_cholesky elif self.inversion_method & SOLVE_LU: self.inversion = {{prefix}}solve_lu elif self.inversion_method & INVERT_CHOLESKY: self.inversion = {{prefix}}inverse_cholesky elif self.inversion_method & INVERT_LU: self.inversion = {{prefix}}inverse_lu else: raise NotImplementedError("Invalid inversion method") else: raise NotImplementedError("Invalid filtering method") # Handle completely missing data, can always just use conventional # methods if self.model._nmissing == self.model.k_endog: # Change the forecasting step to set the forecast at the intercept # $d_t$, so that the forecast error is $v_t = y_t - d_t$. self.forecasting = {{prefix}}forecast_missing_conventional # Change the updating step to just copy $a_{t|t} = a_t$ and # $P_{t|t} = P_t$ self.updating = {{prefix}}updating_missing_conventional # Change the inversion step to inverse to nans. self.inversion = {{prefix}}inverse_missing_conventional # Change the loglikelihood calculation to give zero. self.calculate_loglikelihood = {{prefix}}loglikelihood_missing_conventional self.calculate_scale = {{prefix}}scale_missing_conventional # The prediction step is the same as the conventional Kalman # filter cdef void post_convergence(self): # Constants cdef: int inc = 1 if self.converged: # $F_t$ blas.{{prefix}}copy(&self.k_endog2, self._converged_forecast_error_cov, &inc, self._forecast_error_cov, &inc) # $P_{t|t}$ blas.{{prefix}}copy(&self.k_states2, self._converged_filtered_state_cov, &inc, self._filtered_state_cov, &inc) # $P_t$ blas.{{prefix}}copy(&self.k_states2, self._converged_predicted_state_cov, &inc, self._predicted_state_cov, &inc) # $K_t$ blas.{{prefix}}copy(&self.k_endogstates, self._converged_kalman_gain, &inc, self._kalman_gain, &inc) # $|F_t|$ self.determinant = self.converged_determinant # $M_t$ blas.{{prefix}}copy(&self.k_endogstates, self._converged_M, &inc, self._M, &inc) cdef void numerical_stability(self): cdef int inc = 1 cdef int k_states cdef int i, j cdef int predicted_cov_t = self.t cdef {{cython_type}} alpha = 1.0 cdef {{cython_type}} scalar = 0.5 if self.conserve_memory & MEMORY_NO_PREDICTED_COV: predicted_cov_t = 1 if self.filter_timing == TIMING_INIT_PREDICTED: predicted_cov_t += 1 if self.stability_method & STABILITY_FORCE_SYMMETRY: # Enforce symmetry of predicted covariance matrix # $P_{t+1} = 0.5 * (P_{t+1} + P_{t+1}')$ # See Grewal (2001), Section 6.3.1.1 for i in range(self.k_states): k_states = self.k_states - i blas.{{prefix}}axpy(&k_states, &alpha, &self.predicted_state_cov[i, i, predicted_cov_t], &self.k_states, &self.predicted_state_cov[i, i, predicted_cov_t], &inc) blas.{{prefix}}copy(&k_states, &self.predicted_state_cov[i, i, predicted_cov_t], &inc, &self.predicted_state_cov[i, i, predicted_cov_t], &self.k_states) blas.{{prefix}}scal(&self.k_states2, &scalar, &self.predicted_state_cov[0, 0, predicted_cov_t], &inc) cdef int check_diffuse(self): cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} scalar if self.t == self.nobs_diffuse: {{if combined_prefix == 'd'}} if blas.{{prefix}}dot(&self.k_states2, self._input_diffuse_state_cov, &inc, self._input_diffuse_state_cov, &inc) > self.tolerance_diffuse: self.nobs_diffuse = self.nobs_diffuse + 1 {{else}} blas.{{prefix}}gemv("N", &inc, &self.k_states2, &alpha, self._input_diffuse_state_cov, &inc, self._input_diffuse_state_cov, &inc, &beta, self._tmp00, &inc) if {{combined_prefix}}abs(self._tmp00[0]) > self.tolerance_diffuse: self.nobs_diffuse = self.nobs_diffuse + 1 {{endif}} return self.t < self.nobs_diffuse cdef void check_convergence(self): # Constants cdef: int inc = 1, missing_flag = 0 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # Indices for arrays that may or may not be stored completely cdef: int forecast_cov_t = self.t int filtered_cov_t = self.t int predicted_cov_t = self.t int gain_t = self.t if self.conserve_memory & MEMORY_NO_FORECAST_COV > 0: forecast_cov_t = 1 if self.conserve_memory & MEMORY_NO_FILTERED_COV > 0: filtered_cov_t = 1 if self.conserve_memory & MEMORY_NO_PREDICTED_COV > 0: predicted_cov_t = 1 if self.conserve_memory & MEMORY_NO_GAIN > 0: gain_t = 0 # Figure out if there is a missing value if self.model.nmissing[self.t] > 0 or (not self.t == 0 and self.model.nmissing[self.t-1] > 0): missing_flag = 1 if self.time_invariant and not self.converged and not missing_flag and not self.t < self.nobs_diffuse + 1: # #### Check for steady-state convergence # # `tmp0` array used here, dimension $(m \times m)$ # `tmp00` array used here, dimension $(1 \times 1)$ if self.filter_timing == TIMING_INIT_PREDICTED: blas.{{prefix}}copy(&self.k_states2, self._input_state_cov, &inc, self._tmp0, &inc) blas.{{prefix}}axpy(&self.k_states2, &gamma, self._predicted_state_cov, &inc, self._tmp0, &inc) elif self.t > 0: blas.{{prefix}}copy(&self.k_states2, &self.predicted_state_cov[0,0,predicted_cov_t], &inc, self._tmp0, &inc) blas.{{prefix}}axpy(&self.k_states2, &gamma, &self.predicted_state_cov[0,0,predicted_cov_t-1], &inc, self._tmp0, &inc) else: return {{if combined_prefix == 'd'}} if blas.{{prefix}}dot(&self.k_states2, self._tmp0, &inc, self._tmp0, &inc) < self.tolerance: self.converged = 1 self.period_converged = self.t {{else}} blas.{{prefix}}gemv("N", &inc, &self.k_states2, &alpha, self._tmp0, &inc, self._tmp0, &inc, &beta, self._tmp00, &inc) if {{combined_prefix}}abs(self._tmp00[0]) < self.tolerance: self.converged = 1 self.period_converged = self.t {{endif}} # If we just converged, copy the current iteration matrices to the # converged storage if self.converged == 1: # $F_t$ blas.{{prefix}}copy(&self.k_endog2, &self.forecast_error_cov[0, 0, forecast_cov_t], &inc, self._converged_forecast_error_cov, &inc) # $P_{t|t}$ blas.{{prefix}}copy(&self.k_states2, &self.filtered_state_cov[0, 0, filtered_cov_t], &inc, self._converged_filtered_state_cov, &inc) # $P_t$ blas.{{prefix}}copy(&self.k_states2, &self.predicted_state_cov[0, 0, predicted_cov_t], &inc, self._converged_predicted_state_cov, &inc) # $|F_t|$ self.converged_determinant = self.determinant # $K_t$ blas.{{prefix}}copy(&self.k_endogstates, &self.kalman_gain[0, 0, gain_t], &inc, self._converged_kalman_gain, &inc) # $M_t$ blas.{{prefix}}copy(&self.k_endogstates, &self.M[0, 0, predicted_cov_t], &inc, self._converged_M, &inc) cdef void migrate_storage(self): cdef: int inc = 1 int diffuse = self.check_diffuse() # Forecast: 1 -> 0 if self.conserve_memory & MEMORY_NO_FORECAST_MEAN > 0: blas.{{prefix}}copy(&self.k_endog, &self.forecast[0, 1], &inc, &self.forecast[0, 0], &inc) blas.{{prefix}}copy(&self.k_endog, &self.forecast_error[0, 1], &inc, &self.forecast_error[0, 0], &inc) if self.conserve_memory & MEMORY_NO_FORECAST_COV > 0: blas.{{prefix}}copy(&self.k_endog2, &self.forecast_error_cov[0, 0, 1], &inc, &self.forecast_error_cov[0, 0, 0], &inc) # Filtered: 1 -> 0 if self.conserve_memory & MEMORY_NO_FILTERED_MEAN > 0: blas.{{prefix}}copy(&self.k_states, &self.filtered_state[0, 1], &inc, &self.filtered_state[0, 0], &inc) if self.conserve_memory & MEMORY_NO_FILTERED_COV > 0: blas.{{prefix}}copy(&self.k_states2, &self.filtered_state_cov[0, 0, 1], &inc, &self.filtered_state_cov[0, 0, 0], &inc) if self.conserve_memory & MEMORY_NO_PREDICTED_MEAN > 0: # Predicted: 1 -> 0 blas.{{prefix}}copy(&self.k_states, &self.predicted_state[0, 1], &inc, &self.predicted_state[0, 0], &inc) # Predicted: 2 -> 1 if self.filter_timing == TIMING_INIT_PREDICTED: blas.{{prefix}}copy(&self.k_states, &self.predicted_state[0, 2], &inc, &self.predicted_state[0, 1], &inc) if self.conserve_memory & MEMORY_NO_PREDICTED_COV > 0: # Predicted: 1 -> 0 blas.{{prefix}}copy(&self.k_states2, &self.predicted_state_cov[0, 0, 1], &inc, &self.predicted_state_cov[0, 0, 0], &inc) if diffuse: blas.{{prefix}}copy(&self.k_states2, &self.predicted_diffuse_state_cov[0, 0, 1], &inc, &self.predicted_diffuse_state_cov[0, 0, 0], &inc) # Predicted: 2 -> 1 if self.filter_timing == TIMING_INIT_PREDICTED: blas.{{prefix}}copy(&self.k_states2, &self.predicted_state_cov[0, 0, 2], &inc, &self.predicted_state_cov[0, 0, 1], &inc) if diffuse: blas.{{prefix}}copy(&self.k_states2, &self.predicted_diffuse_state_cov[0, 0, 2], &inc, &self.predicted_diffuse_state_cov[0, 0, 1], &inc) {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/_kalman_smoother.pxd000066400000000000000000000451111400612667500254730ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Model Smoother declarations Author: Chad Fulton License: Simplified-BSD """ cdef int SMOOTHER_STATE # Durbin and Koopman (2012), Chapter 4.4.2 cdef int SMOOTHER_STATE_COV # Durbin and Koopman (2012), Chapter 4.4.3 cdef int SMOOTHER_DISTURBANCE # Durbin and Koopman (2012), Chapter 4.5 cdef int SMOOTHER_DISTURBANCE_COV # Durbin and Koopman (2012), Chapter 4.5 cdef int SMOOTHER_STATE_AUTOCOV # Durbin and Koopman (2012), Chapter 4.7 cdef int SMOOTHER_ALL cdef int SMOOTH_CONVENTIONAL cdef int SMOOTH_CLASSICAL cdef int SMOOTH_ALTERNATIVE cdef int SMOOTH_UNIVARIATE # Typical imports cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace ) from statsmodels.tsa.statespace._kalman_filter cimport ( sKalmanFilter, dKalmanFilter, cKalmanFilter, zKalmanFilter ) # Single precision cdef class sKalmanSmoother(object): # Statespace object cdef readonly sStatespace model # Kalman filter cdef readonly sKalmanFilter kfilter cdef readonly int t cdef readonly int smoother_output cdef readonly int smooth_method cdef readonly int _smooth_method cdef readonly int filter_method cdef readonly np.float32_t [::1,:] scaled_smoothed_estimator cdef readonly np.float32_t [::1,:,:] scaled_smoothed_estimator_cov cdef readonly np.float32_t [::1,:] smoothing_error cdef readonly np.float32_t [::1,:] smoothed_state cdef readonly np.float32_t [::1,:,:] smoothed_state_cov cdef readonly np.float32_t [::1,:] smoothed_measurement_disturbance cdef readonly np.float32_t [::1,:] smoothed_state_disturbance cdef readonly np.float32_t [::1,:,:] smoothed_measurement_disturbance_cov cdef readonly np.float32_t [::1,:,:] smoothed_state_disturbance_cov cdef readonly np.float32_t [::1,:,:] smoothed_state_autocov, innovations_transition cdef readonly np.float32_t [::1,:] tmp_autocov cdef readonly np.float32_t [::1,:] scaled_smoothed_diffuse_estimator cdef readonly np.float32_t [::1,:,:] scaled_smoothed_diffuse1_estimator_cov cdef readonly np.float32_t [::1,:,:] scaled_smoothed_diffuse2_estimator_cov cdef readonly np.float32_t [:] selected_design cdef readonly np.float32_t [:] selected_obs_cov cdef readonly np.float32_t [::1,:] tmpL, tmpL2, tmp0, tmp00, tmp000 # Statespace # cdef np.float32_t * _design # cdef np.float32_t * _obs_cov # cdef np.float32_t * _transition # cdef np.float32_t * _selection # cdef np.float32_t * _state_cov # Kalman filter # cdef np.float32_t * _predicted_state # cdef np.float32_t * _predicted_state_cov # cdef np.float32_t * _kalman_gain # cdef np.float32_t * _tmp1 # cdef np.float32_t * _tmp2 # cdef np.float32_t * _tmp3 # cdef np.float32_t * _tmp4 # Kalman smoother cdef np.float32_t * _input_scaled_smoothed_estimator cdef np.float32_t * _input_scaled_smoothed_estimator_cov cdef np.float32_t * _scaled_smoothed_estimator cdef np.float32_t * _scaled_smoothed_estimator_cov cdef np.float32_t * _smoothing_error cdef np.float32_t * _smoothed_state cdef np.float32_t * _smoothed_state_cov cdef np.float32_t * _smoothed_measurement_disturbance cdef np.float32_t * _smoothed_state_disturbance cdef np.float32_t * _smoothed_measurement_disturbance_cov cdef np.float32_t * _smoothed_state_disturbance_cov cdef np.float32_t * _innovations_transition cdef np.float32_t * _smoothed_state_autocov cdef np.float32_t * _tmp_autocov cdef np.float32_t * _input_scaled_smoothed_diffuse_estimator cdef np.float32_t * _input_scaled_smoothed_diffuse1_estimator_cov cdef np.float32_t * _input_scaled_smoothed_diffuse2_estimator_cov cdef np.float32_t * _scaled_smoothed_diffuse_estimator cdef np.float32_t * _scaled_smoothed_diffuse1_estimator_cov cdef np.float32_t * _scaled_smoothed_diffuse2_estimator_cov # Temporary cdef np.float32_t * _tmpL cdef np.float32_t * _tmpL2 cdef np.float32_t * _tmp0 cdef np.float32_t * _tmp00 cdef np.float32_t * _tmp000 # Functions cdef int (*smooth_estimators_measurement)( sKalmanSmoother, sKalmanFilter, sStatespace ) except * cdef int (*smooth_estimators_time)( sKalmanSmoother, sKalmanFilter, sStatespace ) cdef int (*smooth_state)( sKalmanSmoother, sKalmanFilter, sStatespace ) cdef int (*smooth_disturbances)( sKalmanSmoother, sKalmanFilter, sStatespace ) # cdef readonly int k_endog, k_states, k_posdef, k_endog2, k_states2, k_posdef2, k_endogstates, k_statesposdef cdef allocate_arrays(self) cdef int check_filter_method_changed(self) cdef int reset_filter_method(self, int force_reset=*) cpdef set_smoother_output(self, int smoother_output, int force_reset=*) cpdef set_smooth_method(self, int smooth_method) cpdef reset(self, int force_reset=*) cpdef seek(self, unsigned int t) cdef void initialize_statespace_object_pointers(self) except * cdef void initialize_filter_object_pointers(self) cdef void initialize_smoother_object_pointers(self) except * cdef void initialize_function_pointers(self) except * cdef void _initialize_temp_pointers(self) except * # Double precision cdef class dKalmanSmoother(object): # Statespace object cdef readonly dStatespace model # Kalman filter cdef readonly dKalmanFilter kfilter cdef readonly int t cdef readonly int smoother_output cdef readonly int smooth_method cdef readonly int _smooth_method cdef readonly int filter_method cdef readonly np.float64_t [::1,:] scaled_smoothed_estimator cdef readonly np.float64_t [::1,:,:] scaled_smoothed_estimator_cov cdef readonly np.float64_t [::1,:] smoothing_error cdef readonly np.float64_t [::1,:] smoothed_state cdef readonly np.float64_t [::1,:,:] smoothed_state_cov cdef readonly np.float64_t [::1,:] smoothed_measurement_disturbance cdef readonly np.float64_t [::1,:] smoothed_state_disturbance cdef readonly np.float64_t [::1,:,:] smoothed_measurement_disturbance_cov cdef readonly np.float64_t [::1,:,:] smoothed_state_disturbance_cov cdef readonly np.float64_t [::1,:,:] smoothed_state_autocov, innovations_transition cdef readonly np.float64_t [::1,:] tmp_autocov cdef readonly np.float64_t [::1,:] scaled_smoothed_diffuse_estimator cdef readonly np.float64_t [::1,:,:] scaled_smoothed_diffuse1_estimator_cov cdef readonly np.float64_t [::1,:,:] scaled_smoothed_diffuse2_estimator_cov cdef readonly np.float64_t [:] selected_design cdef readonly np.float64_t [:] selected_obs_cov cdef readonly np.float64_t [::1,:] tmpL, tmpL2, tmp0, tmp00, tmp000 # Statespace # cdef np.float64_t * _design # cdef np.float64_t * _obs_cov # cdef np.float64_t * _transition # cdef np.float64_t * _selection # cdef np.float64_t * _state_cov # Kalman filter # cdef np.float64_t * _predicted_state # cdef np.float64_t * _predicted_state_cov # cdef np.float64_t * _kalman_gain # cdef np.float64_t * _tmp1 # cdef np.float64_t * _tmp2 # cdef np.float64_t * _tmp3 # cdef np.float64_t * _tmp4 # Kalman smoother cdef np.float64_t * _input_scaled_smoothed_estimator cdef np.float64_t * _input_scaled_smoothed_estimator_cov cdef np.float64_t * _scaled_smoothed_estimator cdef np.float64_t * _scaled_smoothed_estimator_cov cdef np.float64_t * _smoothing_error cdef np.float64_t * _smoothed_state cdef np.float64_t * _smoothed_state_cov cdef np.float64_t * _smoothed_measurement_disturbance cdef np.float64_t * _smoothed_state_disturbance cdef np.float64_t * _smoothed_measurement_disturbance_cov cdef np.float64_t * _smoothed_state_disturbance_cov cdef np.float64_t * _innovations_transition cdef np.float64_t * _smoothed_state_autocov cdef np.float64_t * _tmp_autocov cdef np.float64_t * _input_scaled_smoothed_diffuse_estimator cdef np.float64_t * _input_scaled_smoothed_diffuse1_estimator_cov cdef np.float64_t * _input_scaled_smoothed_diffuse2_estimator_cov cdef np.float64_t * _scaled_smoothed_diffuse_estimator cdef np.float64_t * _scaled_smoothed_diffuse1_estimator_cov cdef np.float64_t * _scaled_smoothed_diffuse2_estimator_cov # Temporary cdef np.float64_t * _tmpL cdef np.float64_t * _tmpL2 cdef np.float64_t * _tmp0 cdef np.float64_t * _tmp00 cdef np.float64_t * _tmp000 # Functions cdef int (*smooth_estimators_measurement)( dKalmanSmoother, dKalmanFilter, dStatespace ) except * cdef int (*smooth_estimators_time)( dKalmanSmoother, dKalmanFilter, dStatespace ) cdef int (*smooth_state)( dKalmanSmoother, dKalmanFilter, dStatespace ) cdef int (*smooth_disturbances)( dKalmanSmoother, dKalmanFilter, dStatespace ) # cdef readonly int k_endog, k_states, k_posdef, k_endog2, k_states2, k_posdef2, k_endogstates, k_statesposdef cdef allocate_arrays(self) cdef int check_filter_method_changed(self) cdef int reset_filter_method(self, int force_reset=*) cpdef set_smoother_output(self, int smoother_output, int force_reset=*) cpdef set_smooth_method(self, int smooth_method) cpdef reset(self, int force_reset=*) cpdef seek(self, unsigned int t) cdef void initialize_statespace_object_pointers(self) except * cdef void initialize_filter_object_pointers(self) cdef void initialize_smoother_object_pointers(self) except * cdef void initialize_function_pointers(self) except * cdef void _initialize_temp_pointers(self) except * # Single precision complex cdef class cKalmanSmoother(object): # Statespace object cdef readonly cStatespace model # Kalman filter cdef readonly cKalmanFilter kfilter cdef readonly int t cdef readonly int smoother_output cdef readonly int smooth_method cdef readonly int _smooth_method cdef readonly int filter_method cdef readonly np.complex64_t [::1,:] scaled_smoothed_estimator cdef readonly np.complex64_t [::1,:,:] scaled_smoothed_estimator_cov cdef readonly np.complex64_t [::1,:] smoothing_error cdef readonly np.complex64_t [::1,:] smoothed_state cdef readonly np.complex64_t [::1,:,:] smoothed_state_cov cdef readonly np.complex64_t [::1,:] smoothed_measurement_disturbance cdef readonly np.complex64_t [::1,:] smoothed_state_disturbance cdef readonly np.complex64_t [::1,:,:] smoothed_measurement_disturbance_cov cdef readonly np.complex64_t [::1,:,:] smoothed_state_disturbance_cov cdef readonly np.complex64_t [::1,:,:] smoothed_state_autocov, innovations_transition cdef readonly np.complex64_t [::1,:] tmp_autocov cdef readonly np.complex64_t [::1,:] scaled_smoothed_diffuse_estimator cdef readonly np.complex64_t [::1,:,:] scaled_smoothed_diffuse1_estimator_cov cdef readonly np.complex64_t [::1,:,:] scaled_smoothed_diffuse2_estimator_cov cdef readonly np.complex64_t [:] selected_design cdef readonly np.complex64_t [:] selected_obs_cov cdef readonly np.complex64_t [::1,:] tmpL, tmpL2, tmp0, tmp00, tmp000 # Statespace # cdef np.complex64_t * _design # cdef np.complex64_t * _obs_cov # cdef np.complex64_t * _transition # cdef np.complex64_t * _selection # cdef np.complex64_t * _state_cov # Kalman filter # cdef np.complex64_t * _predicted_state # cdef np.complex64_t * _predicted_state_cov # cdef np.complex64_t * _kalman_gain # cdef np.complex64_t * _tmp1 # cdef np.complex64_t * _tmp2 # cdef np.complex64_t * _tmp3 # cdef np.complex64_t * _tmp4 # Kalman smoother cdef np.complex64_t * _input_scaled_smoothed_estimator cdef np.complex64_t * _input_scaled_smoothed_estimator_cov cdef np.complex64_t * _scaled_smoothed_estimator cdef np.complex64_t * _scaled_smoothed_estimator_cov cdef np.complex64_t * _smoothing_error cdef np.complex64_t * _smoothed_state cdef np.complex64_t * _smoothed_state_cov cdef np.complex64_t * _smoothed_measurement_disturbance cdef np.complex64_t * _smoothed_state_disturbance cdef np.complex64_t * _smoothed_measurement_disturbance_cov cdef np.complex64_t * _smoothed_state_disturbance_cov cdef np.complex64_t * _innovations_transition cdef np.complex64_t * _smoothed_state_autocov cdef np.complex64_t * _tmp_autocov cdef np.complex64_t * _input_scaled_smoothed_diffuse_estimator cdef np.complex64_t * _input_scaled_smoothed_diffuse1_estimator_cov cdef np.complex64_t * _input_scaled_smoothed_diffuse2_estimator_cov cdef np.complex64_t * _scaled_smoothed_diffuse_estimator cdef np.complex64_t * _scaled_smoothed_diffuse1_estimator_cov cdef np.complex64_t * _scaled_smoothed_diffuse2_estimator_cov # Temporary cdef np.complex64_t * _tmpL cdef np.complex64_t * _tmpL2 cdef np.complex64_t * _tmp0 cdef np.complex64_t * _tmp00 cdef np.complex64_t * _tmp000 # Functions cdef int (*smooth_estimators_measurement)( cKalmanSmoother, cKalmanFilter, cStatespace ) except * cdef int (*smooth_estimators_time)( cKalmanSmoother, cKalmanFilter, cStatespace ) cdef int (*smooth_state)( cKalmanSmoother, cKalmanFilter, cStatespace ) cdef int (*smooth_disturbances)( cKalmanSmoother, cKalmanFilter, cStatespace ) # cdef readonly int k_endog, k_states, k_posdef, k_endog2, k_states2, k_posdef2, k_endogstates, k_statesposdef cdef allocate_arrays(self) cdef int check_filter_method_changed(self) cdef int reset_filter_method(self, int force_reset=*) cpdef set_smoother_output(self, int smoother_output, int force_reset=*) cpdef set_smooth_method(self, int smooth_method) cpdef reset(self, int force_reset=*) cpdef seek(self, unsigned int t) cdef void initialize_statespace_object_pointers(self) except * cdef void initialize_filter_object_pointers(self) cdef void initialize_smoother_object_pointers(self) except * cdef void initialize_function_pointers(self) except * cdef void _initialize_temp_pointers(self) except * # Double precision complex cdef class zKalmanSmoother(object): # Statespace object cdef readonly zStatespace model # Kalman filter cdef readonly zKalmanFilter kfilter cdef readonly int t cdef readonly int smoother_output cdef readonly int smooth_method cdef readonly int _smooth_method cdef readonly int filter_method cdef readonly np.complex128_t [::1,:] scaled_smoothed_estimator cdef readonly np.complex128_t [::1,:,:] scaled_smoothed_estimator_cov cdef readonly np.complex128_t [::1,:] smoothing_error cdef readonly np.complex128_t [::1,:] smoothed_state cdef readonly np.complex128_t [::1,:,:] smoothed_state_cov cdef readonly np.complex128_t [::1,:] smoothed_measurement_disturbance cdef readonly np.complex128_t [::1,:] smoothed_state_disturbance cdef readonly np.complex128_t [::1,:,:] smoothed_measurement_disturbance_cov cdef readonly np.complex128_t [::1,:,:] smoothed_state_disturbance_cov cdef readonly np.complex128_t [::1,:,:] smoothed_state_autocov, innovations_transition cdef readonly np.complex128_t [::1,:] tmp_autocov cdef readonly np.complex128_t [::1,:] scaled_smoothed_diffuse_estimator cdef readonly np.complex128_t [::1,:,:] scaled_smoothed_diffuse1_estimator_cov cdef readonly np.complex128_t [::1,:,:] scaled_smoothed_diffuse2_estimator_cov cdef readonly np.complex128_t [:] selected_design cdef readonly np.complex128_t [:] selected_obs_cov cdef readonly np.complex128_t [::1,:] tmpL, tmpL2, tmp0, tmp00, tmp000 # Statespace # cdef np.complex128_t * _design # cdef np.complex128_t * _obs_cov # cdef np.complex128_t * _transition # cdef np.complex128_t * _selection # cdef np.complex128_t * _state_cov # Kalman filter # cdef np.complex128_t * _predicted_state # cdef np.complex128_t * _predicted_state_cov # cdef np.complex128_t * _kalman_gain # cdef np.complex128_t * _tmp1 # cdef np.complex128_t * _tmp2 # cdef np.complex128_t * _tmp3 # cdef np.complex128_t * _tmp4 # Kalman smoother cdef np.complex128_t * _input_scaled_smoothed_estimator cdef np.complex128_t * _input_scaled_smoothed_estimator_cov cdef np.complex128_t * _scaled_smoothed_estimator cdef np.complex128_t * _scaled_smoothed_estimator_cov cdef np.complex128_t * _smoothing_error cdef np.complex128_t * _smoothed_state cdef np.complex128_t * _smoothed_state_cov cdef np.complex128_t * _smoothed_measurement_disturbance cdef np.complex128_t * _smoothed_state_disturbance cdef np.complex128_t * _smoothed_measurement_disturbance_cov cdef np.complex128_t * _smoothed_state_disturbance_cov cdef np.complex128_t * _innovations_transition cdef np.complex128_t * _smoothed_state_autocov cdef np.complex128_t * _tmp_autocov cdef np.complex128_t * _input_scaled_smoothed_diffuse_estimator cdef np.complex128_t * _input_scaled_smoothed_diffuse1_estimator_cov cdef np.complex128_t * _input_scaled_smoothed_diffuse2_estimator_cov cdef np.complex128_t * _scaled_smoothed_diffuse_estimator cdef np.complex128_t * _scaled_smoothed_diffuse1_estimator_cov cdef np.complex128_t * _scaled_smoothed_diffuse2_estimator_cov # Temporary cdef np.complex128_t * _tmpL cdef np.complex128_t * _tmpL2 cdef np.complex128_t * _tmp0 cdef np.complex128_t * _tmp00 cdef np.complex128_t * _tmp000 # Functions cdef int (*smooth_estimators_measurement)( zKalmanSmoother, zKalmanFilter, zStatespace ) except * cdef int (*smooth_estimators_time)( zKalmanSmoother, zKalmanFilter, zStatespace ) cdef int (*smooth_state)( zKalmanSmoother, zKalmanFilter, zStatespace ) cdef int (*smooth_disturbances)( zKalmanSmoother, zKalmanFilter, zStatespace ) # cdef readonly int k_endog, k_states, k_posdef, k_endog2, k_states2, k_posdef2, k_endogstates, k_statesposdef cdef allocate_arrays(self) cdef int check_filter_method_changed(self) cdef int reset_filter_method(self, int force_reset=*) cpdef set_smoother_output(self, int smoother_output, int force_reset=*) cpdef set_smooth_method(self, int smooth_method) cpdef reset(self, int force_reset=*) cpdef seek(self, unsigned int t) cdef void initialize_statespace_object_pointers(self) except * cdef void initialize_filter_object_pointers(self) cdef void initialize_smoother_object_pointers(self) except * cdef void initialize_function_pointers(self) except * cdef void _initialize_temp_pointers(self) except * statsmodels-0.12.2/statsmodels/tsa/statespace/_kalman_smoother.pyx.in000066400000000000000000001150321400612667500261250ustar00rootroot00000000000000#cython: profile=False #cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # ## Constants # ### Smoothers cdef int SMOOTHER_STATE = 0x01 # Durbin and Koopman (2012), Chapter 4.4.2 cdef int SMOOTHER_STATE_COV = 0x02 # Durbin and Koopman (2012), Chapter 4.4.3 cdef int SMOOTHER_DISTURBANCE = 0x04 # Durbin and Koopman (2012), Chapter 4.5 cdef int SMOOTHER_DISTURBANCE_COV = 0x08 # Durbin and Koopman (2012), Chapter 4.5 cdef int SMOOTHER_STATE_AUTOCOV = 0x10 # Durbin and Koopman (2012), Chapter 4.7 cdef int SMOOTHER_ALL = ( SMOOTHER_STATE | SMOOTHER_STATE_COV | SMOOTHER_STATE_AUTOCOV | SMOOTHER_DISTURBANCE | SMOOTHER_DISTURBANCE_COV ) cdef int SMOOTH_CONVENTIONAL = 0x01 cdef int SMOOTH_CLASSICAL = 0x02 cdef int SMOOTH_ALTERNATIVE = 0x04 cdef int SMOOTH_UNIVARIATE = 0x08 from statsmodels.tsa.statespace._kalman_filter cimport ( FILTER_CONVENTIONAL, FILTER_UNIVARIATE, FILTER_COLLAPSED, MEMORY_NO_PREDICTED, MEMORY_NO_GAIN, MEMORY_NO_SMOOTHING ) # Typical imports import numpy as np import warnings cimport numpy as np cimport cython np.import_array() cimport scipy.linalg.cython_blas as blas cdef int FORTRAN = 1 {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} from statsmodels.tsa.statespace._smoothers._conventional cimport ( {{prefix}}smoothed_estimators_missing_conventional, {{prefix}}smoothed_disturbances_missing_conventional, {{prefix}}smoothed_estimators_measurement_conventional, {{prefix}}smoothed_estimators_time_conventional, {{prefix}}smoothed_state_conventional, {{prefix}}smoothed_state_autocov_conventional, {{prefix}}smoothed_disturbances_conventional ) from statsmodels.tsa.statespace._smoothers._univariate cimport ( {{prefix}}smoothed_estimators_measurement_univariate, {{prefix}}smoothed_estimators_time_univariate, {{prefix}}smoothed_disturbances_univariate ) from statsmodels.tsa.statespace._smoothers._univariate_diffuse cimport ( {{prefix}}smoothed_estimators_measurement_univariate_diffuse, {{prefix}}smoothed_estimators_time_univariate_diffuse, {{prefix}}smoothed_state_univariate_diffuse, {{prefix}}smoothed_disturbances_univariate_diffuse, {{prefix}}smoothed_state_autocov_univariate_diffuse ) from statsmodels.tsa.statespace._smoothers._classical cimport ( {{prefix}}smoothed_estimators_measurement_classical, {{prefix}}smoothed_estimators_time_classical, {{prefix}}smoothed_state_classical ) from statsmodels.tsa.statespace._smoothers._alternative cimport ( {{prefix}}smoothed_estimators_measurement_alternative, {{prefix}}smoothed_estimators_time_alternative, {{prefix}}smoothed_state_alternative, {{prefix}}smoothed_disturbances_alternative ) # ## Kalman filter cdef class {{prefix}}KalmanSmoother(object): """ {{prefix}}KalmanSmoother(model, kfilter, smoother_output=SMOOTHING_ALL) A representation of the Kalman smoother recursions; it performs a single backwards pass through the data (after the forwards pass via the Kalman filter has already been completed). In all cases, it calculates: - `scaled_smoothed_estimator` - `smoothing_error` it can optionally peform three types of smoothing: - State smoothing provides `smoothed_state` and `smoothed_state_cov` - Disturbance smoothing provides `smoothed_measurement_disturbance` and `smoothed_state_disturbance` - Simulation smoothing provides `sampled_measurement_disturbance` and `sampled_state_disturbance` (note that this requires Disturbance smoothing as well). Note: this output arrays in this class are always defined in-memory according to the original dimensions in the {{prefix}}Statespace object. Note: if the `filter_method` of the underlying {{prefix}}KalmanFilter changes, the smoother *must* be reset using the object callable (__call__) or the `reset` method. This is because when the filter method is changed, the filter output arrays are reset. """ # ### Statespace model # cdef readonly {{prefix}}Statespace model # ### Kalman filter # cdef readonly {{prefix}}KalmanFilter kfilter # ### Smoother parameters # Holds the time-iteration state of the filter # *Note*: must be changed using the `seek` method # cdef readonly int t # cdef readonly int smoother_output # Keep track of the filter method against which the arrays were created # so that we can re-allocate memory if the filter method changes. # cdef readonly int filter_method # ### Kalman smoother properties # `scaled_smoothed_estimator` $\equiv r_t$ is the **scaled smoothed estimator** of $\eta_t$ $(m \times T)$ # cdef readonly {{cython_type}} [::1,:] scaled_smoothed_estimator # `scaled_smoothed_estimator_cov` $\equiv N_t$ is the **scaled smoothed estimator covariance matrix** $(m \times m \times T)$ # cdef readonly {{cython_type}} [::1,:,:] scaled_smoothed_estimator_cov # `smoothing_error` $\equiv u_t = F_{t}^{-1} v_t - K_t' r_t$ is the **smoothing error** $(p \times T)$ # cdef readonly {{cython_type}} [::1,:] smoothing_error # `smoothed_state` $\equiv \hat \alpha_t = E(\alpha_t | Y_n)$ is the **smoothed estimator** of the state $(m \times T)$ # cdef readonly {{cython_type}} [::1,:] smoothed_state # `smoothed_state_cov` $\equiv V_t = Var(\alpha_t | Y_n)$ is the **smoothed state covariance matrix** $(m \times m \times T)$ # cdef readonly {{cython_type}} [::1,:,:] smoothed_state_cov # `smoothed_measurement_disturbance` $\equiv \hat \varepsilon_t = E(\varepsilon_t | Y_n)$ is the **smoothed measurement disturbance** $(p \times T)$ # cdef readonly {{cython_type}} [::1,:] smoothed_measurement_disturbance # `smoothed_state_disturbance` $\equiv \hat \eta_t = E(\eta_t | Y_n)$ is the **smoothed state disturbance** $(r \times T)$ # cdef readonly {{cython_type}} [::1,:] smoothed_state_disturbance # `smoothed_measurement_disturbance_cov` $\equiv Var (\varepsilon_t | Y_n)$ is the **smoothed measurement disturbance covariance matrix** $(p \times p \times T)$ # cdef readonly {{cython_type}} [::1,:,:] smoothed_measurement_disturbance_cov # `smoothed_state_disturbance` $\equiv Var (\eta_t | Y_n)$ is the **smoothed state disturbance covariance matrix** $(r \times r \times T)$ # cdef readonly {{cython_type}} [::1,:,:] smoothed_state_disturbance_cov # ### Temporary arrays # These matrices are used to temporarily hold selected observation vectors, # design matrices, and observation covariance matrices in the case of # missing data. # The following are contiguous memory segments which are then used to # store the data in the above matrices. # cdef readonly {{cython_type}} [:] selected_design # cdef readonly {{cython_type}} [:] selected_obs_cov # These hold the memory allocations of the unnamed temporary arrays # cdef readonly {{cython_type}} [::1,:] tmpL, tmpL2, tmp0, tmp00, tmp000 # ### Pointers to current-iteration arrays # Statespace # cdef {{cython_type}} * _design # cdef {{cython_type}} * _obs_cov # cdef {{cython_type}} * _transition # cdef {{cython_type}} * _selection # cdef {{cython_type}} * _state_cov # Kalman filter # cdef {{cython_type}} * _predicted_state # cdef {{cython_type}} * _predicted_state_cov # cdef {{cython_type}} * _kalman_gain # cdef {{cython_type}} * _tmp1 # cdef {{cython_type}} * _tmp2 # cdef {{cython_type}} * _tmp3 # cdef {{cython_type}} * _tmp4 # Kalman smoother # cdef {{cython_type}} * _input_scaled_smoothed_estimator # cdef {{cython_type}} * _input_scaled_smoothed_estimator_cov # cdef {{cython_type}} * _scaled_smoothed_estimator # cdef {{cython_type}} * _scaled_smoothed_estimator_cov # cdef {{cython_type}} * _smoothing_error # cdef {{cython_type}} * _smoothed_state # cdef {{cython_type}} * _smoothed_state_cov # cdef {{cython_type}} * _smoothed_measurement_disturbance # cdef {{cython_type}} * _smoothed_state_disturbance # cdef {{cython_type}} * _smoothed_measurement_disturbance_cov # cdef {{cython_type}} * _smoothed_state_disturbance_cov # cdef {{cython_type}} * _tmpL # cdef {{cython_type}} * _tmpL2 # cdef {{cython_type}} * _tmp0 # cdef {{cython_type}} * _tmp00 # cdef {{cython_type}} * _tmp000 # ### Pointers to current-iteration Kalman smoothing functions # cdef int (*smooth_estimators)( # {{prefix}}KalmanSmoother, {{prefix}}KalmanFilter, {{prefix}}Statespace # ) # cdef int (*smooth_state)( # {{prefix}}KalmanSmoother, {{prefix}}KalmanFilter, {{prefix}}Statespace # ) # cdef int (*smooth_disturbances)( # {{prefix}}KalmanSmoother, {{prefix}}KalmanFilter, {{prefix}}Statespace # ) # ### Define some constants # cdef readonly int k_endog, k_states, k_posdef, k_endog2, k_states2, k_posdef2, k_endogstates, k_statesposdef def __init__(self, {{prefix}}Statespace model, {{prefix}}KalmanFilter kfilter, int smoother_output=SMOOTHER_ALL, int smooth_method=0): # Save the model self.model = model self.kfilter = kfilter # Save the parameters self.filter_method = kfilter.filter_method # Make sure the appropriate output has been stored in the filter if self.kfilter.conserve_memory & MEMORY_NO_PREDICTED: raise ValueError('Cannot perform smoothing without all predicted states') if self.kfilter.conserve_memory & MEMORY_NO_GAIN: raise ValueError('Cannot perform smoothing without all Kalman gains') if self.kfilter.conserve_memory & MEMORY_NO_SMOOTHING: raise ValueError('Cannot perform smoothing without all smoothing variables') # Set smoothing output and initialize output arrays self.set_smoother_output(smoother_output) self.set_smooth_method(smooth_method) cdef allocate_arrays(self): cdef: np.npy_intp dim1[1] np.npy_intp dim2[2] np.npy_intp dim3[3] # #### Allocate arrays for calculations # Note: these are defined in memory according to the kfilter dimensions # In the case of FILTERED_COLLAPSED, the smoothed measurement # output describes only the component of transformed observations # that is related to the states. # Arrays for Kalman smoother output dim2[0] = self.kfilter.k_states; dim2[1] = self.model.nobs+1; self.scaled_smoothed_estimator = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim3[0] = self.kfilter.k_states; dim3[1] = self.kfilter.k_states; dim3[2] = self.model.nobs+1; self.scaled_smoothed_estimator_cov = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) dim2[0] = self.kfilter.k_endog; dim2[1] = self.model.nobs; self.smoothing_error = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = self.kfilter.k_states; dim2[1] = self.model.nobs; self.smoothed_state = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim3[0] = self.kfilter.k_states; dim3[1] = self.kfilter.k_states; dim3[2] = self.model.nobs; self.smoothed_state_cov = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) dim2[0] = self.kfilter.k_endog; dim2[1] = self.model.nobs; self.smoothed_measurement_disturbance = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = self.kfilter.k_posdef; dim2[1] = self.model.nobs; self.smoothed_state_disturbance = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim3[0] = self.kfilter.k_endog; dim3[1] = self.kfilter.k_endog; dim3[2] = self.model.nobs; self.smoothed_measurement_disturbance_cov = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) dim3[0] = self.kfilter.k_posdef; dim3[1] = self.kfilter.k_posdef; dim3[2] = self.model.nobs; self.smoothed_state_disturbance_cov = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) # Innovations transition matrix (L_t = T_t - K_t Z_t) dim3[0] = self.kfilter.k_states; dim3[1] = self.kfilter.k_states; dim3[2] = self.model.nobs self.innovations_transition = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) # Smoothed state autocovariance arrays dim3[0] = self.kfilter.k_states; dim3[1] = self.kfilter.k_states; dim3[2] = self.model.nobs self.smoothed_state_autocov = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) dim2[0] = self.kfilter.k_states; dim2[1] = self.kfilter.k_states; self.tmp_autocov = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._tmp_autocov = &self.tmp_autocov[0, 0] # Diffuse output dim2[0] = self.kfilter.k_states; dim2[1] = self.model.nobs+1; self.scaled_smoothed_diffuse_estimator = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim3[0] = self.kfilter.k_states; dim3[1] = self.kfilter.k_states; dim3[2] = self.model.nobs+1; self.scaled_smoothed_diffuse1_estimator_cov = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) self.scaled_smoothed_diffuse2_estimator_cov = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) # #### Arrays for temporary calculations # *Note*: in math notation below, a $\\#$ will represent a generic # temporary array, and a $\\#_i$ will represent a named temporary array. # # $L_t$ $(m \times m)$, also holds $(m \times r)$ sometimes dim2[0] = self.kfilter.k_states; dim2[1] = max(self.kfilter.k_states, self.kfilter.k_posdef); self.tmpL = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._tmpL = &self.tmpL[0, 0] self.tmpL2 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._tmpL2 = &self.tmpL2[0, 0] # # Holds arrays of dimension $(m \times m)$ and $(m \times r)$ dim2[0] = self.kfilter.k_states; dim2[1] = max(self.kfilter.k_states, self.kfilter.k_posdef); self.tmp0 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._tmp0 = &self.tmp0[0, 0] # # Holds arrays of dimension $(m \times p)$ dim2[0] = self.kfilter.k_states; dim2[1] = self.kfilter.k_endog; self.tmp00 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._tmp00 = &self.tmp00[0, 0] # # Holds arrays of dimension $(m \times p)$ dim2[0] = self.kfilter.k_states; dim2[1] = self.kfilter.k_endog; self.tmp000 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self._tmp000 = &self.tmp000[0, 0] # Arrays for missing data # dim1[0] = self.kfilter.k_endog * self.kfilter.k_states; # self.selected_design = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) # dim1[0] = self.kfilter.k_endog2; # self.selected_obs_cov = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) def __reduce__(self): state = { 't': self.t, '_smooth_method': self._smooth_method, 'scaled_smoothed_estimator': np.array(self.scaled_smoothed_estimator, copy=True, order='F'), 'scaled_smoothed_estimator_cov': np.array(self.scaled_smoothed_estimator_cov, copy=True, order='F'), 'smoothing_error': np.array(self.smoothing_error, copy=True, order='F'), 'smoothed_state': np.array(self.smoothed_state, copy=True, order='F'), 'smoothed_state_cov': np.array(self.smoothed_state_cov, copy=True, order='F'), 'smoothed_measurement_disturbance': np.array(self.smoothed_measurement_disturbance, copy=True, order='F'), 'smoothed_state_disturbance': np.array(self.smoothed_state_disturbance, copy=True, order='F'), 'smoothed_measurement_disturbance_cov': np.array(self.smoothed_measurement_disturbance_cov, copy=True, order='F'), 'smoothed_state_disturbance_cov': np.array(self.smoothed_state_disturbance_cov, copy=True, order='F'), 'smoothed_state_autocov': np.array(self.smoothed_state_autocov, copy=True, order='F'), 'innovations_transition': np.array(self.smoothed_state_autocov, copy=True, order='F'), 'tmp_autocov': np.array(self.tmp_autocov, copy=True, order='F'), 'scaled_smoothed_diffuse_estimator': np.array(self.scaled_smoothed_diffuse_estimator, copy=True, order='F'), 'scaled_smoothed_diffuse1_estimator_cov': np.array(self.scaled_smoothed_diffuse1_estimator_cov, copy=True, order='F'), 'scaled_smoothed_diffuse2_estimator_cov': np.array(self.scaled_smoothed_diffuse2_estimator_cov, copy=True, order='F'), 'tmpL': np.array(self.tmpL, copy=True, order='F'), 'tmpL2': np.array(self.tmpL2, copy=True, order='F'), 'tmp0': np.array(self.tmp0, copy=True, order='F'), 'tmp00': np.array(self.tmp00, copy=True, order='F'), 'tmp000': np.array(self.tmp000, copy=True, order='F') } args = (self.model, self.kfilter, self.smoother_output, self.smooth_method) return (self.__class__, args, state) def __setstate__(self, state): self.t = state['t'] self._smooth_method = state['_smooth_method'] self.scaled_smoothed_estimator = state['scaled_smoothed_estimator'] self.scaled_smoothed_estimator_cov = state['scaled_smoothed_estimator_cov'] self.smoothing_error = state['smoothing_error'] self.smoothed_state = state['smoothed_state'] self.smoothed_state_cov = state['smoothed_state_cov'] self.smoothed_measurement_disturbance = state['smoothed_measurement_disturbance'] self.smoothed_state_disturbance = state['smoothed_state_disturbance'] self.smoothed_measurement_disturbance_cov = state['smoothed_measurement_disturbance_cov'] self.smoothed_state_disturbance_cov = state['smoothed_state_disturbance_cov'] self.smoothed_state_autocov = state['smoothed_state_autocov'] self.innovations_transition = state['innovations_transition'] self.tmp_autocov = state['tmp_autocov'] self.scaled_smoothed_diffuse_estimator = state['scaled_smoothed_diffuse_estimator'] self.scaled_smoothed_diffuse1_estimator_cov = state['scaled_smoothed_diffuse1_estimator_cov'] self.scaled_smoothed_diffuse2_estimator_cov = state['scaled_smoothed_diffuse2_estimator_cov'] self.tmpL = state['tmpL'] self.tmpL2 = state['tmpL2'] self.tmp0 = state['tmp0'] self.tmp00 = state['tmp00'] self.tmp000 = state['tmp000'] self.initialize_smoother_object_pointers() self._initialize_temp_pointers() cdef void _initialize_temp_pointers(self) except *: self._tmpL = &self.tmpL[0, 0] self._tmpL2 = &self.tmpL2[0, 0] self._tmp0 = &self.tmp0[0, 0] self._tmp00 = &self.tmp00[0, 0] self._tmp000 = &self.tmp000[0, 0] self._tmp_autocov = &self.tmp_autocov[0, 0] cdef int check_filter_method_changed(self): return not self.kfilter.filter_method == self.filter_method cdef int reset_filter_method(self, int force_reset=True): cdef int changed = self.check_filter_method_changed() if changed or force_reset: # Save the new method self.filter_method = self.kfilter.filter_method # Reset matrices self.allocate_arrays() # Reset the smooth method (in case it was based on the filter # method) self.set_smooth_method(self.smooth_method) return changed cpdef set_smoother_output(self, int smoother_output, int force_reset=True): if not smoother_output == self.smoother_output or force_reset: # Change the smoother output flag self.smoother_output = smoother_output # Reset matrices self.reset(True) cpdef set_smooth_method(self, int smooth_method): cdef int _smooth_method self.smooth_method = smooth_method # If no smooth method provided, use default for the filter type if self.smooth_method == 0: self.reset_filter_method(False) if self.kfilter.filter_method & FILTER_UNIVARIATE: _smooth_method = SMOOTH_UNIVARIATE else: _smooth_method = SMOOTH_CONVENTIONAL else: _smooth_method = self.smooth_method # Make sure we do not have an invalid smooth method for our filter # method if((_smooth_method & SMOOTH_UNIVARIATE) and not (self.filter_method & FILTER_UNIVARIATE) or (self.filter_method & FILTER_UNIVARIATE) and not (_smooth_method & SMOOTH_UNIVARIATE)): raise ValueError('Invalid smoothing method: can only use' ' univariate smoothing when univariate filtering' ' has been used previously.') self._smooth_method = _smooth_method cpdef reset(self, int force_reset=False): """ reset(self) Reset the smoother. """ # Reset the filter method (if necessary) self.reset_filter_method(force_reset) # Set the time self.t = self.model.nobs-1 cpdef seek(self, unsigned int t): """ seek(self, t) Change the time-state of the smoother Notes ----- Between seek calls, the `filter_method` parameter of the associated Kalman filter object is not allowed to change. If the `filter_method` has changed, either recall the smoother using the object callable or explicitly reset the smoother using the `reset` method. """ # Make sure the seek location is valid if not t == 0 and t >= self.model.nobs: raise IndexError("Observation index out of range") # Make sure we have not changed filter methods in-between seeking if self.check_filter_method_changed(): raise RuntimeError("Filter method in associated Kalman filter was" " changed in between smoother seek() calls." " If the filter method is changed, the smoother" " must be called from the beginning. Use the" " object callable (`__call__`) or the `reset`" " method.") self.t = t def __iter__(self): return self def __call__(self, int smoother_output=-1): """ Iterate the smoother across the entire set of observations. """ cdef int i # Reset the smoother self.reset() # Perform backwards smoothing iterations for i in range(self.model.nobs-1,-1,-1): next(self) def __next__(self): """ Perform an iteration of the Kalman smoother """ cdef int t, inc = 1 cdef int diffuse = self.t < self.kfilter.nobs_diffuse # Get time subscript, and stop the iterator if at the end if not self.t >= 0: raise StopIteration # Make sure we have not changed filter methods in-between iterations if self.check_filter_method_changed(): raise RuntimeError("Filter method in associated Kalman filter was" " changed in between smoother iterations." " If the filter method is changed, the smoother" " must be called from the beginning. Use the" " object callable (`__call__`) or the `reset`" " method.") # Initialize pointers to current-iteration objects self.initialize_statespace_object_pointers() self.initialize_filter_object_pointers() self.initialize_smoother_object_pointers() # Initialize pointers to appropriate Kalman smoothing functions self.initialize_function_pointers() # Clear measurement disturbance variables` if we switched from # multivariate to univariate (because we might have off-diagonal # elements stored from a previous multivariate run that wouldn't have # been cleared yet) if self.t > 0 and self.kfilter.univariate_filter[self.t] == 0 and self.kfilter.univariate_filter[self.t - 1] == 1: if self._smooth_method & SMOOTH_CLASSICAL: raise NotImplementedError( 'Cannot use classical smoothing when the multivariate' ' filter has fallen back to univariate filtering.') if self._smooth_method & SMOOTH_ALTERNATIVE: raise NotImplementedError( 'Cannot use alternative smoothing when the multivariate' ' filter has fallen back to univariate filtering.') self.smoothing_error[..., :self.t] = 0 self.smoothed_measurement_disturbance_cov[..., :self.t] = 0 self.innovations_transition[..., :self.t] = 0 # Conventional timing of the measurement step of the scaled smoothed # estimator and covariance matrix, smoothing error # $L_t, r_{t-1}, N_{t-1}, u_t$ if diffuse or self._smooth_method & (SMOOTH_CONVENTIONAL | SMOOTH_CLASSICAL | SMOOTH_UNIVARIATE): self.smooth_estimators_measurement(self, self.kfilter, self.model) # Smoothed state and covariance matrix # $\hat \alpha_t, V_t$ if self.smoother_output & (SMOOTHER_STATE | SMOOTHER_STATE_COV): self.smooth_state(self, self.kfilter, self.model) # Modified Byrson-Frazier timing of the measurement step of the scaled # smoothed estimator and covariance matrix, smoothing error # $L_t, r_{t-1}, N_{t-1}, u_t$ if not diffuse and self._smooth_method & SMOOTH_ALTERNATIVE: self.smooth_estimators_measurement(self, self.kfilter, self.model) # Smoothed state autocovariance matrix if diffuse: blas.{{prefix}}copy(&self.kfilter.k_states2, self.kfilter._tmpL0, &inc, self._innovations_transition, &inc) else: blas.{{prefix}}copy(&self.kfilter.k_states2, self._tmpL, &inc, self._innovations_transition, &inc) if self.smoother_output & SMOOTHER_STATE_AUTOCOV: if diffuse: {{prefix}}smoothed_state_autocov_univariate_diffuse(self, self.kfilter, self.model) else: if self.smooth_method & SMOOTH_ALTERNATIVE: self._input_scaled_smoothed_estimator_cov = &self.scaled_smoothed_estimator_cov[0, 0, self.t+1] {{prefix}}smoothed_state_autocov_conventional(self, self.kfilter, self.model) if self.smooth_method & SMOOTH_ALTERNATIVE: self._input_scaled_smoothed_estimator_cov = &self.scaled_smoothed_estimator_cov[0, 0, self.t] # Smoothed disturbances # $\hat \eta_t, \hat \varepsilon_t, Var(\eta_t | Y_n), Var(\varepsilon_t | Y_n)$ if self.smoother_output & SMOOTHER_DISTURBANCE: self.smooth_disturbances(self, self.kfilter, self.model) # Time step of the scaled smoothed estimator and covariance matrix self.smooth_estimators_time(self, self.kfilter, self.model) # When switching from the non-univariate filtering methods to the # univariate filtering method, we need to run one or more # univariate time smoothing steps to get the appropriate values (e.g. # for scaled_smoothed_estimator). Moreover, the alternative and # classical methods have different timing. # This happens in two cases: # 1. Exact diffuse filtering and smoothing only uses the univariate # method, so if non-univariate filtering methods are used for # the remaining filtering and smoothing then we need to run this. # 2. If the multivariate filtering method failed in a particular time # step (due to a singular forecast error covariance matrix) and # the univariate method was used as a fallback, then we need to run # this. if ((self.kfilter.nobs_diffuse > 0 and self.t == self.kfilter.nobs_diffuse) or (self.t > 0 and self.kfilter.univariate_filter[self.t] == 0 and self.kfilter.univariate_filter[self.t-1] == 1)): t = self.t if self._smooth_method & SMOOTH_CONVENTIONAL: {{prefix}}smoothed_estimators_time_univariate(self, self.kfilter, self.model) if self._smooth_method & SMOOTH_ALTERNATIVE: self.t = self.t - 1 self.initialize_statespace_object_pointers() self.initialize_filter_object_pointers() self.initialize_smoother_object_pointers() self.initialize_function_pointers() {{prefix}}smoothed_estimators_time_univariate(self, self.kfilter, self.model) self.t = t elif self._smooth_method & SMOOTH_CLASSICAL: self.t = t - 1 self.initialize_statespace_object_pointers() self.initialize_filter_object_pointers() self.initialize_smoother_object_pointers() self.initialize_function_pointers() {{prefix}}smoothed_estimators_measurement_classical(self, self.kfilter, self.model) self.t = t self.initialize_statespace_object_pointers() self.initialize_filter_object_pointers() self.initialize_smoother_object_pointers() self.initialize_function_pointers() {{prefix}}smoothed_estimators_time_univariate(self, self.kfilter, self.model) # Note: the above diffuse handling for alternative and classical # handling modifies the pointers, and should be the last part of this # function # Advance the smoother self.t -= 1 cdef void initialize_statespace_object_pointers(self) except *: cdef: int transform_diagonalize = 0 int transform_generalized_collapse = 0 int collapse_occurred = 0 # Determine which transformations (would) need to be made transform_generalized_collapse = self.kfilter.filter_method & FILTER_COLLAPSED if not transform_generalized_collapse: transform_diagonalize = self.kfilter.univariate_filter[self.t] # Initialize object-level pointers to statespace arrays # Note: does not matter what transformations were required for the # filter; we do not need to perform them for the smoother # TODO actually we do, to get _design, _obs_cov, etc. However we do not # need it to recalculate the selected_obs and loglikelihood, so # need to decouple those parts from the generalized collapse self.model.seek(self.t, transform_diagonalize, transform_generalized_collapse) # Initialize object-level pointers to statespace arrays # self._design = self.model._design # self._obs_cov = self.model._obs_cov # self._transition = self.model._transition # self._selection = self.model._selection # self._state_cov = self.model._state_cov # A collapse would not actually occur in a given iteration, even with # the FILTER_COLLAPSED flag, in the case that there was enough missing # data that k_endog - nmissing <= k_states # collapse_occurred = ( # transform_generalized_collapse and # self.model.k_endog - self.model._nmissing > self.model.k_states # ) # If a collapse should have occurred, the dimensions need to be # adjusted (because we did not tell the model about the collapse in the # seek() call above) # if collapse_occurred: # self.model.set_dimensions(self.model.k_states, # self.model.k_states, # self.model.k_posdef) cdef void initialize_filter_object_pointers(self): # cdef: # int t = self.t # int inc = 1 # # Initialize object-level pointers to output arrays # self._predicted_state = &self.kfilter.predicted_state[0, t] # self._predicted_state_cov = &self.kfilter.predicted_state_cov[0, 0, t] # self._kalman_gain = &self.kfilter.kalman_gain[0, 0, t] # # Initialize object-level pointers to named temporary arrays # self._tmp1 = &self.kfilter.tmp1[0, 0, t] # self._tmp2 = &self.kfilter.tmp2[0, t] # self._tmp3 = &self.kfilter.tmp3[0, 0, t] # self._tmp4 = &self.kfilter.tmp4[0, 0, t] self.kfilter.seek(self.t, False) self.kfilter.initialize_filter_object_pointers() cdef void initialize_smoother_object_pointers(self) except *: cdef: int t = self.t int inc = 1 int diffuse = self.t < self.kfilter.nobs_diffuse # Initialize object-level pointers to output arrays if diffuse or self._smooth_method & (SMOOTH_CONVENTIONAL | SMOOTH_CLASSICAL | SMOOTH_UNIVARIATE): self._input_scaled_smoothed_estimator = &self.scaled_smoothed_estimator[0, t+1] self._input_scaled_smoothed_estimator_cov = &self.scaled_smoothed_estimator_cov[0, 0, t+1] self._scaled_smoothed_estimator = &self.scaled_smoothed_estimator[0, t] self._scaled_smoothed_estimator_cov = &self.scaled_smoothed_estimator_cov[0, 0, t] else: # if self._smooth_method & SMOOTH_ALTERNATIVE self._input_scaled_smoothed_estimator = &self.scaled_smoothed_estimator[0, t] self._input_scaled_smoothed_estimator_cov = &self.scaled_smoothed_estimator_cov[0, 0, t] self._scaled_smoothed_estimator = &self.scaled_smoothed_estimator[0, t-1] self._scaled_smoothed_estimator_cov = &self.scaled_smoothed_estimator_cov[0, 0, t-1] self._smoothing_error = &self.smoothing_error[0, t] self._smoothed_state = &self.smoothed_state[0, t] self._smoothed_state_cov = &self.smoothed_state_cov[0, 0, t] self._smoothed_measurement_disturbance = &self.smoothed_measurement_disturbance[0, t] self._smoothed_state_disturbance = &self.smoothed_state_disturbance[0, t] self._smoothed_measurement_disturbance_cov = &self.smoothed_measurement_disturbance_cov[0, 0, t] self._smoothed_state_disturbance_cov = &self.smoothed_state_disturbance_cov[0, 0, t] self._innovations_transition = &self.innovations_transition[0, 0, t] self._smoothed_state_autocov = &self.smoothed_state_autocov[0, 0, t] # Diffuse if diffuse: self._input_scaled_smoothed_diffuse_estimator = &self.scaled_smoothed_diffuse_estimator[0, t+1] self._input_scaled_smoothed_diffuse1_estimator_cov = &self.scaled_smoothed_diffuse1_estimator_cov[0, 0, t+1] self._input_scaled_smoothed_diffuse2_estimator_cov = &self.scaled_smoothed_diffuse2_estimator_cov[0, 0, t+1] self._scaled_smoothed_diffuse_estimator = &self.scaled_smoothed_diffuse_estimator[0, t] self._scaled_smoothed_diffuse1_estimator_cov = &self.scaled_smoothed_diffuse1_estimator_cov[0, 0, t] self._scaled_smoothed_diffuse2_estimator_cov = &self.scaled_smoothed_diffuse2_estimator_cov[0, 0, t] cdef void initialize_function_pointers(self) except *: cdef int diffuse = self.t < self.kfilter.nobs_diffuse # Diffuse smoother if diffuse: self.smooth_estimators_measurement = {{prefix}}smoothed_estimators_measurement_univariate_diffuse self.smooth_estimators_time = {{prefix}}smoothed_estimators_time_univariate_diffuse self.smooth_state = {{prefix}}smoothed_state_univariate_diffuse self.smooth_disturbances = {{prefix}}smoothed_disturbances_univariate_diffuse # Univariate (modified Bryson-Frazier) smoother elif (self._smooth_method & SMOOTH_UNIVARIATE) or self.kfilter.univariate_filter[self.t]: self.smooth_estimators_measurement = {{prefix}}smoothed_estimators_measurement_univariate self.smooth_estimators_time = {{prefix}}smoothed_estimators_time_univariate self.smooth_state = {{prefix}}smoothed_state_conventional self.smooth_disturbances = {{prefix}}smoothed_disturbances_univariate # Multivariate modified Bryson-Frazier smoother elif self._smooth_method & SMOOTH_ALTERNATIVE: self.smooth_estimators_measurement = {{prefix}}smoothed_estimators_measurement_alternative self.smooth_estimators_time = {{prefix}}smoothed_estimators_time_alternative self.smooth_state = {{prefix}}smoothed_state_alternative self.smooth_disturbances = {{prefix}}smoothed_disturbances_alternative # Multivariate classical (Anderson and Moore) smoother elif self._smooth_method & SMOOTH_CLASSICAL: self.smooth_estimators_measurement = {{prefix}}smoothed_estimators_measurement_classical self.smooth_estimators_time = {{prefix}}smoothed_estimators_time_classical self.smooth_state = {{prefix}}smoothed_state_classical self.smooth_disturbances = {{prefix}}smoothed_disturbances_conventional # Multivariate conventional (Durbin and Koopman) smoother elif self._smooth_method & SMOOTH_CONVENTIONAL: self.smooth_estimators_measurement = {{prefix}}smoothed_estimators_measurement_conventional self.smooth_estimators_time = {{prefix}}smoothed_estimators_time_conventional self.smooth_state = {{prefix}}smoothed_state_conventional self.smooth_disturbances = {{prefix}}smoothed_disturbances_conventional else: raise NotImplementedError("Smoother method not available.") # Handle completely missing data # (All methods except the conventional method can use the same routines in this case) # This is essentially just an application of the smoothed_estimators_time_* step. if not diffuse and self._smooth_method & SMOOTH_CONVENTIONAL and self.model._nmissing == self.model.k_endog: # Change the smoothing functions to take into account a missing observation self.smooth_estimators_measurement = {{prefix}}smoothed_estimators_missing_conventional # (no need to change the state smoothing recursion) # self.smooth_state = {{prefix}}smoothed_state_missing_conventional self.smooth_disturbances = {{prefix}}smoothed_disturbances_missing_conventional {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/_pykalman_smoother.py000066400000000000000000000254251400612667500257070ustar00rootroot00000000000000""" Kalman Smoother Author: Chad Fulton License: Simplified-BSD """ import numpy as np SMOOTHER_STATE = 0x01 # Durbin and Koopman (2012), Chapter 4.4.2 SMOOTHER_STATE_COV = 0x02 # ibid., Chapter 4.4.3 SMOOTHER_DISTURBANCE = 0x04 # ibid., Chapter 4.5 SMOOTHER_DISTURBANCE_COV = 0x08 # ibid., Chapter 4.5 SMOOTHER_ALL = ( SMOOTHER_STATE | SMOOTHER_STATE_COV | SMOOTHER_DISTURBANCE | SMOOTHER_DISTURBANCE_COV ) class _KalmanSmoother(object): def __init__(self, model, kfilter, smoother_output): # Save values self.model = model self.kfilter = kfilter self._kfilter = model._kalman_filter self.smoother_output = smoother_output # Create storage self.scaled_smoothed_estimator = None self.scaled_smoothed_estimator_cov = None self.smoothing_error = None self.smoothed_state = None self.smoothed_state_cov = None self.smoothed_state_disturbance = None self.smoothed_state_disturbance_cov = None self.smoothed_measurement_disturbance = None self.smoothed_measurement_disturbance_cov = None # Intermediate values self.tmp_L = np.zeros((model.k_states, model.k_states, model.nobs), dtype=kfilter.dtype) if smoother_output & (SMOOTHER_STATE | SMOOTHER_DISTURBANCE): self.scaled_smoothed_estimator = ( np.zeros((model.k_states, model.nobs+1), dtype=kfilter.dtype)) self.smoothing_error = ( np.zeros((model.k_endog, model.nobs), dtype=kfilter.dtype)) if smoother_output & (SMOOTHER_STATE_COV | SMOOTHER_DISTURBANCE_COV): self.scaled_smoothed_estimator_cov = ( np.zeros((model.k_states, model.k_states, model.nobs + 1), dtype=kfilter.dtype)) # State smoothing if smoother_output & SMOOTHER_STATE: self.smoothed_state = np.zeros((model.k_states, model.nobs), dtype=kfilter.dtype) if smoother_output & SMOOTHER_STATE_COV: self.smoothed_state_cov = ( np.zeros((model.k_states, model.k_states, model.nobs), dtype=kfilter.dtype)) # Disturbance smoothing if smoother_output & SMOOTHER_DISTURBANCE: self.smoothed_state_disturbance = ( np.zeros((model.k_posdef, model.nobs), dtype=kfilter.dtype)) self.smoothed_measurement_disturbance = ( np.zeros((model.k_endog, model.nobs), dtype=kfilter.dtype)) if smoother_output & SMOOTHER_DISTURBANCE_COV: self.smoothed_state_disturbance_cov = ( np.zeros((model.k_posdef, model.k_posdef, model.nobs), dtype=kfilter.dtype)) self.smoothed_measurement_disturbance_cov = ( np.zeros((model.k_endog, model.k_endog, model.nobs), dtype=kfilter.dtype)) def seek(self, t): if t >= self.model.nobs: raise IndexError("Observation index out of range") self.t = t def __iter__(self): return self def __call__(self): self.seek(self.model.nobs-1) # Perform backwards smoothing iterations for i in range(self.model.nobs-1, -1, -1): next(self) def next(self): # next() is required for compatibility with Python2.7. return self.__next__() def __next__(self): # Check for valid iteration if not self.t >= 0: raise StopIteration # Get local copies of variables t = self.t kfilter = self.kfilter _kfilter = self._kfilter model = self.model smoother_output = self.smoother_output scaled_smoothed_estimator = self.scaled_smoothed_estimator scaled_smoothed_estimator_cov = self.scaled_smoothed_estimator_cov smoothing_error = self.smoothing_error smoothed_state = self.smoothed_state smoothed_state_cov = self.smoothed_state_cov smoothed_state_disturbance = self.smoothed_state_disturbance smoothed_state_disturbance_cov = self.smoothed_state_disturbance_cov smoothed_measurement_disturbance = ( self.smoothed_measurement_disturbance) smoothed_measurement_disturbance_cov = ( self.smoothed_measurement_disturbance_cov) tmp_L = self.tmp_L # Seek the Cython Kalman filter to the right place, setup matrices _kfilter.seek(t, False) _kfilter.initialize_statespace_object_pointers() _kfilter.initialize_filter_object_pointers() _kfilter.select_missing() missing_entire_obs = ( _kfilter.model.nmissing[t] == _kfilter.model.k_endog) missing_partial_obs = ( not missing_entire_obs and _kfilter.model.nmissing[t] > 0) # Get the appropriate (possibly time-varying) indices design_t = 0 if kfilter.design.shape[2] == 1 else t obs_cov_t = 0 if kfilter.obs_cov.shape[2] == 1 else t transition_t = 0 if kfilter.transition.shape[2] == 1 else t selection_t = 0 if kfilter.selection.shape[2] == 1 else t state_cov_t = 0 if kfilter.state_cov.shape[2] == 1 else t # Get endog dimension (can vary if there missing data) k_endog = _kfilter.k_endog # Get references to representation matrices and Kalman filter output transition = model.transition[:, :, transition_t] selection = model.selection[:, :, selection_t] state_cov = model.state_cov[:, :, state_cov_t] predicted_state = kfilter.predicted_state[:, t] predicted_state_cov = kfilter.predicted_state_cov[:, :, t] mask = ~kfilter.missing[:, t].astype(bool) if missing_partial_obs: design = np.array( _kfilter.selected_design[:k_endog*model.k_states], copy=True ).reshape(k_endog, model.k_states, order='F') obs_cov = np.array( _kfilter.selected_obs_cov[:k_endog**2], copy=True ).reshape(k_endog, k_endog) kalman_gain = kfilter.kalman_gain[:, mask, t] forecasts_error_cov = np.array( _kfilter.forecast_error_cov[:, :, t], copy=True ).ravel(order='F')[:k_endog**2].reshape(k_endog, k_endog) forecasts_error = np.array( _kfilter.forecast_error[:k_endog, t], copy=True) F_inv = np.linalg.inv(forecasts_error_cov) else: if missing_entire_obs: design = np.zeros(model.design.shape[:-1]) else: design = model.design[:, :, design_t] obs_cov = model.obs_cov[:, :, obs_cov_t] kalman_gain = kfilter.kalman_gain[:, :, t] forecasts_error_cov = kfilter.forecasts_error_cov[:, :, t] forecasts_error = kfilter.forecasts_error[:, t] F_inv = np.linalg.inv(forecasts_error_cov) # Create a temporary matrix tmp_L[:, :, t] = transition - kalman_gain.dot(design) L = tmp_L[:, :, t] # Perform the recursion # Intermediate values if smoother_output & (SMOOTHER_STATE | SMOOTHER_DISTURBANCE): if missing_entire_obs: # smoothing_error is undefined here, keep it as zeros scaled_smoothed_estimator[:, t - 1] = ( transition.transpose().dot(scaled_smoothed_estimator[:, t]) ) else: smoothing_error[:k_endog, t] = ( F_inv.dot(forecasts_error) - kalman_gain.transpose().dot( scaled_smoothed_estimator[:, t]) ) scaled_smoothed_estimator[:, t - 1] = ( design.transpose().dot(smoothing_error[:k_endog, t]) + transition.transpose().dot(scaled_smoothed_estimator[:, t]) ) if smoother_output & (SMOOTHER_STATE_COV | SMOOTHER_DISTURBANCE_COV): if missing_entire_obs: scaled_smoothed_estimator_cov[:, :, t - 1] = ( L.transpose().dot( scaled_smoothed_estimator_cov[:, :, t] ).dot(L) ) else: scaled_smoothed_estimator_cov[:, :, t - 1] = ( design.transpose().dot(F_inv).dot(design) + L.transpose().dot( scaled_smoothed_estimator_cov[:, :, t] ).dot(L) ) # State smoothing if smoother_output & SMOOTHER_STATE: smoothed_state[:, t] = ( predicted_state + predicted_state_cov.dot(scaled_smoothed_estimator[:, t - 1]) ) if smoother_output & SMOOTHER_STATE_COV: smoothed_state_cov[:, :, t] = ( predicted_state_cov - predicted_state_cov.dot( scaled_smoothed_estimator_cov[:, :, t - 1] ).dot(predicted_state_cov) ) # Disturbance smoothing if smoother_output & (SMOOTHER_DISTURBANCE | SMOOTHER_DISTURBANCE_COV): QR = state_cov.dot(selection.transpose()) if smoother_output & SMOOTHER_DISTURBANCE: smoothed_state_disturbance[:, t] = ( QR.dot(scaled_smoothed_estimator[:, t]) ) # measurement disturbance is set to zero when all missing # (unconditional distribution) if not missing_entire_obs: smoothed_measurement_disturbance[mask, t] = ( obs_cov.dot(smoothing_error[:k_endog, t]) ) if smoother_output & SMOOTHER_DISTURBANCE_COV: smoothed_state_disturbance_cov[:, :, t] = ( state_cov - QR.dot( scaled_smoothed_estimator_cov[:, :, t] ).dot(QR.transpose()) ) if missing_entire_obs: smoothed_measurement_disturbance_cov[:, :, t] = obs_cov else: # For non-missing portion, calculate as usual ix = np.ix_(mask, mask, [t]) smoothed_measurement_disturbance_cov[ix] = ( obs_cov - obs_cov.dot( F_inv + kalman_gain.transpose().dot( scaled_smoothed_estimator_cov[:, :, t] ).dot(kalman_gain) ).dot(obs_cov) )[:, :, np.newaxis] # For missing portion, use unconditional distribution ix = np.ix_(~mask, ~mask, [t]) mod_ix = np.ix_(~mask, ~mask, [0]) smoothed_measurement_disturbance_cov[ix] = np.copy( model.obs_cov[:, :, obs_cov_t:obs_cov_t+1])[mod_ix] # Advance the smoother self.t -= 1 statsmodels-0.12.2/statsmodels/tsa/statespace/_quarterly_ar1.py000066400000000000000000000163011400612667500247370ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ (Internal) AR(1) model for monthly growth rates aggregated to quarterly freq. Author: Chad Fulton License: BSD-3 """ import warnings import numpy as np from statsmodels.tools.tools import Bunch from statsmodels.tsa.statespace import mlemodel, initialization from statsmodels.tsa.statespace.kalman_smoother import ( SMOOTHER_STATE, SMOOTHER_STATE_COV, SMOOTHER_STATE_AUTOCOV) from statsmodels.tsa.statespace.tools import ( constrain_stationary_univariate, unconstrain_stationary_univariate) class QuarterlyAR1(mlemodel.MLEModel): r""" AR(1) model for monthly growth rates aggregated to quarterly frequency Parameters ---------- endog : array_like The observed time-series process :math:`y` Notes ----- This model is internal, used to estimate starting parameters for the DynamicFactorMQ class. The model is: .. math:: y_t & = \begin{bmatrix} 1 & 2 & 3 & 2 & 1 \end{bmatrix} \alpha_t \\ \alpha_t & = \begin{bmatrix} \phi & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ \end{bmatrix} + \begin{bmatrix} 1 \\ 0 \\ 0 \\ 0 \\ 0 \end{bmatrix} \varepsilon_t The two parameters to be estimated are :math:`\phi` and :math:`\sigma^2`. It supports fitting via the usual quasi-Newton methods, as well as using the EM algorithm. """ def __init__(self, endog): super().__init__(endog, k_states=5, k_posdef=1, initialization='stationary') self['design'] = [1, 2, 3, 2, 1] self['transition', 1:, :-1] = np.eye(4) self['selection', 0, 0] = 1. @property def param_names(self): return ['phi', 'sigma2'] @property def start_params(self): return np.array([0, np.nanvar(self.endog) / 19]) def fit(self, *args, **kwargs): # Don't show warnings with warnings.catch_warnings(): warnings.simplefilter("ignore") out = super().fit(*args, **kwargs) return out def fit_em(self, start_params=None, transformed=True, cov_type='none', cov_kwds=None, maxiter=500, tolerance=1e-6, em_initialization=True, mstep_method=None, full_output=True, return_params=False, low_memory=False): if self._has_fixed_params: raise NotImplementedError('Cannot fit using the EM algorithm while' ' holding some parameters fixed.') if low_memory: raise ValueError('Cannot fit using the EM algorithm when using' ' low_memory option.') if start_params is None: start_params = self.start_params transformed = True else: start_params = np.array(start_params, ndmin=1) if not transformed: start_params = self.transform_params(start_params) # Perform expectation-maximization llf = [] params = [start_params] init = None i = 0 delta = 0 while i < maxiter and (i < 2 or (delta > tolerance)): out = self._em_iteration(params[-1], init=init, mstep_method=mstep_method) llf.append(out[0].llf_obs.sum()) params.append(out[1]) if em_initialization: init = initialization.Initialization( self.k_states, 'known', constant=out[0].smoothed_state[..., 0], stationary_cov=out[0].smoothed_state_cov[..., 0]) if i > 0: delta = (2 * (llf[-1] - llf[-2]) / (np.abs(llf[-1]) + np.abs(llf[-2]))) i += 1 # Just return the fitted parameters if requested if return_params: result = params[-1] # Otherwise construct the results class if desired else: if em_initialization: base_init = self.ssm.initialization self.ssm.initialization = init result = self.smooth(params[-1], transformed=True, cov_type=cov_type, cov_kwds=cov_kwds) if em_initialization: self.ssm.initialization = base_init # Save the output if full_output: em_retvals = Bunch(**{'params': np.array(params), 'llf': np.array(llf), 'iter': i}) em_settings = Bunch(**{'tolerance': tolerance, 'maxiter': maxiter}) else: em_retvals = None em_settings = None result.mle_retvals = em_retvals result.mle_settings = em_settings return result def _em_iteration(self, params0, init=None, mstep_method=None): # (E)xpectation step res = self._em_expectation_step(params0, init=init) # (M)aximization step params1 = self._em_maximization_step(res, params0, mstep_method=mstep_method) return res, params1 def _em_expectation_step(self, params0, init=None): # (E)xpectation step self.update(params0) # Re-initialize state, if new initialization is given if init is not None: base_init = self.ssm.initialization self.ssm.initialization = init # Perform smoothing, only saving what is required res = self.ssm.smooth( SMOOTHER_STATE | SMOOTHER_STATE_COV | SMOOTHER_STATE_AUTOCOV, update_filter=False) res.llf_obs = np.array( self.ssm._kalman_filter.loglikelihood, copy=True) # Reset initialization if init is not None: self.ssm.initialization = base_init return res def _em_maximization_step(self, res, params0, mstep_method=None): a = res.smoothed_state.T[..., None] cov_a = res.smoothed_state_cov.transpose(2, 0, 1) acov_a = res.smoothed_state_autocov.transpose(2, 0, 1) # E[a_t a_t'], t = 0, ..., T Eaa = cov_a.copy() + np.matmul(a, a.transpose(0, 2, 1)) # E[a_t a_{t-1}'], t = 1, ..., T Eaa1 = acov_a[:-1] + np.matmul(a[1:], a[:-1].transpose(0, 2, 1)) # Factor VAR and covariance A = Eaa[:-1, :1, :1].sum(axis=0) B = Eaa1[:, :1, :1].sum(axis=0) C = Eaa[1:, :1, :1].sum(axis=0) nobs = Eaa.shape[0] - 1 f_A = B / A f_Q = (C - f_A @ B.T) / nobs params1 = np.zeros_like(params0) params1[0] = f_A[0, 0] params1[1] = f_Q[0, 0] return params1 def transform_params(self, unconstrained): return np.array([ constrain_stationary_univariate(unconstrained[:1]), unconstrained[1]**2]) def untransform_params(self, constrained): return np.array([ unconstrain_stationary_univariate(constrained[:1]), constrained[1]**0.5]) def update(self, params, **kwargs): super().update(params, **kwargs) self['transition', 0, 0] = params[0] self['state_cov', 0, 0] = params[1] statsmodels-0.12.2/statsmodels/tsa/statespace/_representation.pxd000066400000000000000000000353621400612667500253610ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np cdef class sStatespace(object): # Statespace dimensions cdef readonly int nobs, k_endog, k_states, k_posdef # Statespace representation matrices cdef readonly np.float32_t [::1,:] obs, obs_intercept, state_intercept cdef readonly np.float32_t [:] initial_state cdef readonly np.float32_t [::1,:] initial_state_cov, initial_diffuse_state_cov cdef readonly np.float32_t [::1,:,:] design, obs_cov, transition, selection, state_cov, selected_state_cov cdef readonly int [::1,:] missing cdef readonly int [:] nmissing cdef readonly int has_missing # Flags cdef readonly int time_invariant cdef readonly int initialized, initialized_diffuse, initialized_stationary cdef public int diagonal_obs_cov cdef readonly int _diagonal_obs_cov cdef public int subset_design cdef public int companion_transition # Temporary arrays cdef np.float32_t [::1,:] tmp # Temporary selection arrays cdef readonly np.float32_t [:] selected_obs cdef readonly np.float32_t [:] selected_obs_intercept cdef readonly np.float32_t [:] selected_design cdef readonly np.float32_t [:] selected_obs_cov # Temporary transformation arrays cdef readonly np.float32_t [::1,:] transform_cholesky cdef readonly np.float32_t [::1,:] transform_obs_cov cdef readonly np.float32_t [::1,:] transform_design cdef readonly np.float32_t [:] transform_obs_intercept cdef readonly np.float32_t transform_determinant cdef readonly np.float32_t [:] collapse_obs cdef readonly np.float32_t [:] collapse_obs_tmp cdef readonly np.float32_t [::1,:] collapse_design cdef readonly np.float32_t [::1,:] collapse_obs_cov cdef readonly np.float32_t [::1,:] collapse_cholesky cdef readonly np.float32_t collapse_loglikelihood # Pointers cdef np.float32_t * _obs cdef np.float32_t * _design cdef np.float32_t * _obs_intercept cdef np.float32_t * _obs_cov cdef np.float32_t * _transition cdef np.float32_t * _state_intercept cdef np.float32_t * _selection cdef np.float32_t * _state_cov cdef np.float32_t * _selected_state_cov cdef np.float32_t * _initial_state cdef np.float32_t * _initial_state_cov cdef np.float32_t * _initial_diffuse_state_cov # Current location cdef readonly int t cdef readonly int _previous_t cdef readonly int _k_endog, _k_states, _k_posdef, _k_endog2, _k_states2, _k_posdef2, _k_endogstates, _k_statesposdef cdef readonly int _nmissing # Functions cpdef seek(self, unsigned int t, unsigned int transform_diagonalize, unsigned int transform_generalized_collapse, unsigned int reset=*) cdef void set_dimensions(self, unsigned int k_endog, unsigned int k_states, unsigned int k_posdef) cdef void select_state_cov(self, unsigned int t) cdef int select_missing(self, unsigned int t) cdef void _select_missing_entire_obs(self, unsigned int t) cdef void _select_missing_partial_obs(self, unsigned int t) cdef void transform(self, unsigned int t, unsigned int previous_t, unsigned int transform_diagonalize, unsigned int transform_generalized_collapse, unsigned int reset=*) except * cdef void transform_diagonalize(self, unsigned int t, unsigned int previous_t, unsigned int reset=*) except * cdef int transform_generalized_collapse(self, unsigned int t, unsigned int previous_t, unsigned int reset=*) except * cdef class dStatespace(object): # Statespace dimensions cdef readonly int nobs, k_endog, k_states, k_posdef # Statespace representation matrices cdef readonly np.float64_t [::1,:] obs, obs_intercept, state_intercept cdef readonly np.float64_t [:] initial_state cdef readonly np.float64_t [::1,:] initial_state_cov, initial_diffuse_state_cov cdef readonly np.float64_t [::1,:,:] design, obs_cov, transition, selection, state_cov, selected_state_cov cdef readonly int [::1,:] missing cdef readonly int [:] nmissing cdef readonly int has_missing # Flags cdef readonly int time_invariant cdef readonly int initialized, initialized_diffuse, initialized_stationary cdef public int diagonal_obs_cov cdef readonly int _diagonal_obs_cov cdef public int subset_design cdef public int companion_transition # Temporary arrays cdef np.float64_t [::1,:] tmp # Temporary selection arrays cdef readonly np.float64_t [:] selected_obs cdef readonly np.float64_t [:] selected_obs_intercept cdef readonly np.float64_t [:] selected_design cdef readonly np.float64_t [:] selected_obs_cov # Temporary transformation arrays cdef readonly np.float64_t [::1,:] transform_cholesky cdef readonly np.float64_t [::1,:] transform_obs_cov cdef readonly np.float64_t [::1,:] transform_design cdef readonly np.float64_t [:] transform_obs_intercept cdef readonly np.float64_t transform_determinant cdef readonly np.float64_t [:] collapse_obs cdef readonly np.float64_t [:] collapse_obs_tmp cdef readonly np.float64_t [::1,:] collapse_design cdef readonly np.float64_t [::1,:] collapse_obs_cov cdef readonly np.float64_t [::1,:] collapse_cholesky cdef readonly np.float64_t collapse_loglikelihood # Pointers cdef np.float64_t * _obs cdef np.float64_t * _design cdef np.float64_t * _obs_intercept cdef np.float64_t * _obs_cov cdef np.float64_t * _transition cdef np.float64_t * _state_intercept cdef np.float64_t * _selection cdef np.float64_t * _state_cov cdef np.float64_t * _selected_state_cov cdef np.float64_t * _initial_state cdef np.float64_t * _initial_state_cov cdef np.float64_t * _initial_diffuse_state_cov # Current location cdef readonly int t cdef readonly int _previous_t cdef readonly int _k_endog, _k_states, _k_posdef, _k_endog2, _k_states2, _k_posdef2, _k_endogstates, _k_statesposdef cdef readonly int _nmissing # Functions cpdef seek(self, unsigned int t, unsigned int transform_diagonalize, unsigned int transform_generalized_collapse, unsigned int reset=*) cdef void set_dimensions(self, unsigned int k_endog, unsigned int k_states, unsigned int k_posdef) cdef void select_state_cov(self, unsigned int t) cdef int select_missing(self, unsigned int t) cdef void _select_missing_entire_obs(self, unsigned int t) cdef void _select_missing_partial_obs(self, unsigned int t) cdef void transform(self, unsigned int t, unsigned int previous_t, unsigned int transform_diagonalize, unsigned int transform_generalized_collapse, unsigned int reset=*) except * cdef void transform_diagonalize(self, unsigned int t, unsigned int previous_t, unsigned int reset=*) except * cdef int transform_generalized_collapse(self, unsigned int t, unsigned int previous_t, unsigned int reset=*) except * cdef class cStatespace(object): # Statespace dimensions cdef readonly int nobs, k_endog, k_states, k_posdef # Statespace representation matrices cdef readonly np.complex64_t [::1,:] obs, obs_intercept, state_intercept cdef readonly np.complex64_t [:] initial_state cdef readonly np.complex64_t [::1,:] initial_state_cov, initial_diffuse_state_cov cdef readonly np.complex64_t [::1,:,:] design, obs_cov, transition, selection, state_cov, selected_state_cov cdef readonly int [::1,:] missing cdef readonly int [:] nmissing cdef readonly int has_missing # Flags cdef readonly int time_invariant cdef readonly int initialized, initialized_diffuse, initialized_stationary cdef public int diagonal_obs_cov cdef readonly int _diagonal_obs_cov cdef public int subset_design cdef public int companion_transition # Temporary arrays cdef np.complex64_t [::1,:] tmp # Temporary selection arrays cdef readonly np.complex64_t [:] selected_obs cdef readonly np.complex64_t [:] selected_obs_intercept cdef readonly np.complex64_t [:] selected_design cdef readonly np.complex64_t [:] selected_obs_cov # Temporary transformation arrays cdef readonly np.complex64_t [::1,:] transform_cholesky cdef readonly np.complex64_t [::1,:] transform_obs_cov cdef readonly np.complex64_t [::1,:] transform_design cdef readonly np.complex64_t [:] transform_obs_intercept cdef readonly np.complex64_t transform_determinant cdef readonly np.complex64_t [:] collapse_obs cdef readonly np.complex64_t [:] collapse_obs_tmp cdef readonly np.complex64_t [::1,:] collapse_design cdef readonly np.complex64_t [::1,:] collapse_obs_cov cdef readonly np.complex64_t [::1,:] collapse_cholesky cdef readonly np.complex64_t collapse_loglikelihood # Pointers cdef np.complex64_t * _obs cdef np.complex64_t * _design cdef np.complex64_t * _obs_intercept cdef np.complex64_t * _obs_cov cdef np.complex64_t * _transition cdef np.complex64_t * _state_intercept cdef np.complex64_t * _selection cdef np.complex64_t * _state_cov cdef np.complex64_t * _selected_state_cov cdef np.complex64_t * _initial_state cdef np.complex64_t * _initial_state_cov cdef np.complex64_t * _initial_diffuse_state_cov # Current location cdef readonly int t cdef readonly int _previous_t cdef readonly int _k_endog, _k_states, _k_posdef, _k_endog2, _k_states2, _k_posdef2, _k_endogstates, _k_statesposdef cdef readonly int _nmissing # Functions cpdef seek(self, unsigned int t, unsigned int transform_diagonalize, unsigned int transform_generalized_collapse, unsigned int reset=*) cdef void set_dimensions(self, unsigned int k_endog, unsigned int k_states, unsigned int k_posdef) cdef void select_state_cov(self, unsigned int t) cdef int select_missing(self, unsigned int t) cdef void _select_missing_entire_obs(self, unsigned int t) cdef void _select_missing_partial_obs(self, unsigned int t) cdef void transform(self, unsigned int t, unsigned int previous_t, unsigned int transform_diagonalize, unsigned int transform_generalized_collapse, unsigned int reset=*) except * cdef void transform_diagonalize(self, unsigned int t, unsigned int previous_t, unsigned int reset=*) except * cdef int transform_generalized_collapse(self, unsigned int t, unsigned int previous_t, unsigned int reset=*) except * cdef class zStatespace(object): # Statespace dimensions cdef readonly int nobs, k_endog, k_states, k_posdef # Statespace representation matrices cdef readonly np.complex128_t [::1,:] obs, obs_intercept, state_intercept cdef readonly np.complex128_t [:] initial_state cdef readonly np.complex128_t [::1,:] initial_state_cov, initial_diffuse_state_cov cdef readonly np.complex128_t [::1,:,:] design, obs_cov, transition, selection, state_cov, selected_state_cov cdef readonly int [::1,:] missing cdef readonly int [:] nmissing cdef readonly int has_missing # Flags cdef readonly int time_invariant cdef readonly int initialized, initialized_diffuse, initialized_stationary cdef public int diagonal_obs_cov cdef readonly int _diagonal_obs_cov cdef public int subset_design cdef public int companion_transition # Temporary arrays cdef np.complex128_t [::1,:] tmp # Temporary selection arrays cdef readonly np.complex128_t [:] selected_obs cdef readonly np.complex128_t [:] selected_obs_intercept cdef readonly np.complex128_t [:] selected_design cdef readonly np.complex128_t [:] selected_obs_cov # Temporary transformation arrays cdef readonly np.complex128_t [::1,:] transform_cholesky cdef readonly np.complex128_t [::1,:] transform_obs_cov cdef readonly np.complex128_t [::1,:] transform_design cdef readonly np.complex128_t [:] transform_obs_intercept cdef readonly np.complex128_t transform_determinant cdef readonly np.complex128_t [:] collapse_obs cdef readonly np.complex128_t [:] collapse_obs_tmp cdef readonly np.complex128_t [::1,:] collapse_design cdef readonly np.complex128_t [::1,:] collapse_obs_cov cdef readonly np.complex128_t [::1,:] collapse_cholesky cdef readonly np.complex128_t collapse_loglikelihood # Pointers cdef np.complex128_t * _obs cdef np.complex128_t * _design cdef np.complex128_t * _obs_intercept cdef np.complex128_t * _obs_cov cdef np.complex128_t * _transition cdef np.complex128_t * _state_intercept cdef np.complex128_t * _selection cdef np.complex128_t * _state_cov cdef np.complex128_t * _selected_state_cov cdef np.complex128_t * _initial_state cdef np.complex128_t * _initial_state_cov cdef np.complex128_t * _initial_diffuse_state_cov # Current location cdef readonly int t cdef readonly int _previous_t cdef readonly int _k_endog, _k_states, _k_posdef, _k_endog2, _k_states2, _k_posdef2, _k_endogstates, _k_statesposdef cdef readonly int _nmissing # Functions cpdef seek(self, unsigned int t, unsigned int transform_diagonalize, unsigned int transform_generalized_collapse, unsigned int reset=*) cdef void set_dimensions(self, unsigned int k_endog, unsigned int k_states, unsigned int k_posdef) cdef void select_state_cov(self, unsigned int t) cdef int select_missing(self, unsigned int t) cdef void _select_missing_entire_obs(self, unsigned int t) cdef void _select_missing_partial_obs(self, unsigned int t) cdef void transform(self, unsigned int t, unsigned int previous_t, unsigned int transform_diagonalize, unsigned int transform_generalized_collapse, unsigned int reset=*) except * cdef void transform_diagonalize(self, unsigned int t, unsigned int previous_t, unsigned int reset=*) except * cdef int transform_generalized_collapse(self, unsigned int t, unsigned int previous_t, unsigned int reset=*) except * cdef int sselect_cov(int k, int k_posdef, np.float32_t * tmp, np.float32_t * selection, np.float32_t * cov, np.float32_t * selected_cov) cdef int dselect_cov(int k, int k_posdef, np.float64_t * tmp, np.float64_t * selection, np.float64_t * cov, np.float64_t * selected_cov) cdef int cselect_cov(int k, int k_posdef, np.complex64_t * tmp, np.complex64_t * selection, np.complex64_t * cov, np.complex64_t * selected_cov) cdef int zselect_cov(int k, int k_posdef, np.complex128_t * tmp, np.complex128_t * selection, np.complex128_t * cov, np.complex128_t * selected_cov) statsmodels-0.12.2/statsmodels/tsa/statespace/_representation.pyx.in000066400000000000000000001404161400612667500260100ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # Typical imports import numpy as np import warnings cimport numpy as np cimport cython np.import_array() from statsmodels.src.math cimport * cimport scipy.linalg.cython_blas as blas cimport scipy.linalg.cython_lapack as lapack cimport statsmodels.tsa.statespace._tools as tools {{for prefix, types in TYPES.items()}} from statsmodels.tsa.statespace._initialization cimport {{prefix}}Initialization {{endfor}} cdef int FORTRAN = 1 {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} ## State Space Representation cdef class {{prefix}}Statespace(object): """ {{prefix}}Statespace(obs, design, obs_intercept, obs_cov, transition, state_intercept, selection, state_cov) *See Durbin and Koopman (2012), Chapter 4 for all notation* """ # ### State space representation # # $$ # \begin{align} # y_t & = Z_t \alpha_t + d_t + \varepsilon_t \hspace{3em} & \varepsilon_t & \sim N(0, H_t) \\\\ # \alpha_{t+1} & = T_t \alpha_t + c_t + R_t \eta_t & \eta_t & \sim N(0, Q_t) \\\\ # & & \alpha_1 & \sim N(a_1, P_1) # \end{align} # $$ # # $y_t$ is $p \times 1$ # $\varepsilon_t$ is $p \times 1$ # $\alpha_t$ is $m \times 1$ # $\eta_t$ is $r \times 1$ # $t = 1, \dots, T$ # `nobs` $\equiv T$ is the length of the time-series # `k_endog` $\equiv p$ is dimension of observation space # `k_states` $\equiv m$ is the dimension of the state space # `k_posdef` $\equiv r$ is the dimension of the state shocks # *Old notation: T, n, k, g* # cdef readonly int nobs, k_endog, k_states, k_posdef # `obs` $\equiv y_t$ is the **observation vector** $(p \times T)$ # `design` $\equiv Z_t$ is the **design vector** $(p \times m \times T)$ # `obs_intercept` $\equiv d_t$ is the **observation intercept** $(p \times T)$ # `obs_cov` $\equiv H_t$ is the **observation covariance matrix** $(p \times p \times T)$ # `transition` $\equiv T_t$ is the **transition matrix** $(m \times m \times T)$ # `state_intercept` $\equiv c_t$ is the **state intercept** $(m \times T)$ # `selection` $\equiv R_t$ is the **selection matrix** $(m \times r \times T)$ # `state_cov` $\equiv Q_t$ is the **state covariance matrix** $(r \times r \times T)$ # `selected_state_cov` $\equiv R Q_t R'$ is the **selected state covariance matrix** $(m \times m \times T)$ # `initial_state` $\equiv a_1$ is the **initial state mean** $(m \times 1)$ # `initial_state_cov` $\equiv P_1$ is the **initial state covariance matrix** $(m \times m)$ # `initial_state_cov` $\equiv P_\inf$ is the **initial diffuse state covariance matrix** $(m \times m)$ # # With the exception of `obs`, these are *optionally* time-varying. If they are instead time-invariant, # then the dimension of length $T$ is instead of length $1$. # # *Note*: the initial vectors' notation 1-indexed as in Durbin and Koopman, # but in the recursions below it will be 0-indexed in the Python arrays. # # *Old notation: y, -, mu, beta_tt_init, P_tt_init* # cdef readonly {{cython_type}} [::1,:] obs, obs_intercept, state_intercept # cdef readonly {{cython_type}} [:] initial_state # cdef readonly {{cython_type}} [::1,:] initial_state_cov # *Old notation: H, R, F, G, Q*, G Q* G'* # cdef readonly {{cython_type}} [::1,:,:] design, obs_cov, transition, selection, state_cov, selected_state_cov # `missing` is a $(p \times T)$ boolean matrix where a row is a $(p \times 1)$ vector # in which the $i$th position is $1$ if $y_{i,t}$ is to be considered a missing value. # *Note:* This is created as the output of np.isnan(obs). # cdef readonly int [::1,:] missing # `nmissing` is an `T \times 0` integer vector holding the number of *missing* observations # $p - p_t$ # cdef readonly int [:] nmissing # Flag for a time-invariant model, which requires that *all* of the # possibly time-varying arrays are time-invariant. # cdef readonly int time_invariant # Flag for initialization. # cdef readonly int initialized # Flags for performance improvements # TODO need to add this to the UI in representation # cdef public int diagonal_obs_cov # cdef public int subset_design # cdef public int companion_transition # Temporary arrays # cdef {{cython_type}} [::1,:] tmp # Temporary selection arrays # cdef readonly {{cython_type}} [:] selected_obs # The following are contiguous memory segments which are then used to # store the data in the above matrices. # cdef readonly {{cython_type}} [:] selected_design # cdef readonly {{cython_type}} [:] selected_obs_cov # Temporary transformation arrays # cdef readonly {{cython_type}} [::1,:] transform_cholesky # cdef readonly {{cython_type}} [::1,:] transform_obs_cov # cdef readonly {{cython_type}} [::1,:] transform_design # cdef readonly {{cython_type}} transform_determinant # cdef readonly {{cython_type}} [:] collapse_obs # cdef readonly {{cython_type}} [:] collapse_obs_tmp # cdef readonly {{cython_type}} [::1,:] collapse_design # cdef readonly {{cython_type}} [::1,:] collapse_obs_cov # cdef readonly {{cython_type}} [::1,:] collapse_cholesky # cdef readonly {{cython_type}} collapse_loglikelihood # Pointers # cdef {{cython_type}} * _obs # cdef {{cython_type}} * _design # cdef {{cython_type}} * _obs_intercept # cdef {{cython_type}} * _obs_cov # cdef {{cython_type}} * _transition # cdef {{cython_type}} * _state_intercept # cdef {{cython_type}} * _selection # cdef {{cython_type}} * _state_cov # cdef {{cython_type}} * _selected_state_cov # cdef {{cython_type}} * _initial_state # cdef {{cython_type}} * _initial_state_cov # Current location dimensions # cdef int _k_endog, _k_states, _k_posdef, _k_endog2, _k_states2, _k_posdef2, _k_endogstates, _k_statesposdef # cdef int _nmissing # ### Initialize state space model # *Note*: The initial state and state covariance matrix must be provided. def __init__(self, {{cython_type}} [::1,:] obs, {{cython_type}} [::1,:,:] design, {{cython_type}} [::1,:] obs_intercept, {{cython_type}} [::1,:,:] obs_cov, {{cython_type}} [::1,:,:] transition, {{cython_type}} [::1,:] state_intercept, {{cython_type}} [::1,:,:] selection, {{cython_type}} [::1,:,:] state_cov, diagonal_obs_cov=-1): # Local variables cdef: int t, i, j np.npy_intp dim1[1] np.npy_intp dim2[2] np.npy_intp dim3[3] # #### State space representation variables # **Note**: these arrays share data with the versions defined in # Python and passed to this constructor, so if they are updated in # Python they will also be updated here. self.obs = obs self.design = design self.obs_intercept = obs_intercept self.obs_cov = obs_cov self.transition = transition self.state_intercept = state_intercept self.selection = selection self.state_cov = state_cov # Dimensions self.k_endog = obs.shape[0] self.k_states = selection.shape[0] self.k_posdef = selection.shape[1] self.nobs = obs.shape[1] # #### Validate matrix dimensions # # Make sure that the given state-space matrices have consistent sizes tools.validate_matrix_shape('design', &self.design.shape[0], self.k_endog, self.k_states, self.nobs) tools.validate_vector_shape('observation intercept', &self.obs_intercept.shape[0], self.k_endog, self.nobs) tools.validate_matrix_shape('observation covariance matrix', &self.obs_cov.shape[0], self.k_endog, self.k_endog, self.nobs) tools.validate_matrix_shape('transition', &self.transition.shape[0], self.k_states, self.k_states, self.nobs) tools.validate_vector_shape('state intercept', &self.state_intercept.shape[0], self.k_states, self.nobs) tools.validate_matrix_shape('state covariance matrix', &self.state_cov.shape[0], self.k_posdef, self.k_posdef, self.nobs) # Check for a time-invariant model self.time_invariant = ( self.design.shape[2] == 1 and self.obs_intercept.shape[1] == 1 and self.obs_cov.shape[2] == 1 and self.transition.shape[2] == 1 and self.state_intercept.shape[1] == 1 and self.selection.shape[2] == 1 and self.state_cov.shape[2] == 1 ) # Set the flags for initialization to be false self.initialized = False self.initialized_diffuse = False self.initialized_stationary = False self.diagonal_obs_cov = diagonal_obs_cov self._diagonal_obs_cov = -1 # Allocate selected state covariance matrix dim3[0] = self.k_states; dim3[1] = self.k_states; dim3[2] = 1; # (we only allocate memory for time-varying array if necessary) if self.state_cov.shape[2] > 1 or self.selection.shape[2] > 1: dim3[2] = self.nobs self.selected_state_cov = np.PyArray_ZEROS(3, dim3, {{typenum}}, FORTRAN) # Handle missing data self.missing = np.array(np.isnan(obs), dtype=np.int32, order="F") self.nmissing = np.array(np.sum(self.missing, axis=0), dtype=np.int32) self.has_missing = np.sum(self.nmissing) > 0 # Create the temporary array # Holds arrays of dimension $(m \times m)$ dim2[0] = self.k_states; dim2[1] = max(self.k_states, self.k_posdef); self.tmp = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Arrays for initialization dim1[0] = self.k_states; self.initial_state = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) dim2[0] = self.k_states; dim2[1] = self.k_states; self.initial_state_cov = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = self.k_states; dim2[1] = self.k_states; self.initial_diffuse_state_cov = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Arrays for missing data dim1[0] = self.k_endog; self.selected_obs = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) dim1[0] = self.k_endog; self.selected_obs_intercept = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) dim1[0] = self.k_endog * self.k_states; self.selected_design = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) dim1[0] = self.k_endog**2; self.selected_obs_cov = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) # Arrays for transformations dim2[0] = self.k_endog; dim2[1] = self.k_endog; self.transform_cholesky = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self.transform_obs_cov = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = self.k_endog; dim2[1] = self.k_states; self.transform_design = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim1[0] = self.k_endog; self.transform_obs_intercept = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) dim1[0] = self.k_states; self.collapse_obs = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) self.collapse_obs_tmp = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) dim2[0] = self.k_states; dim2[1] = self.k_states; self.collapse_design = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self.collapse_obs_cov = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self.collapse_cholesky = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Initialize location self.t = 0 self._previous_t = 0 # Initialize dimensions self.set_dimensions(self.k_endog, self.k_states, self.k_posdef) def __reduce__(self): init = (np.array(self.obs, copy=True, order='F'), np.array(self.design, copy=True, order='F'), np.array(self.obs_intercept, copy=True, order='F'), np.array(self.obs_cov, copy=True, order='F'), np.array(self.transition, copy=True, order='F'), np.array(self.state_intercept, copy=True, order='F'), np.array(self.selection, copy=True, order='F'), np.array(self.state_cov, copy=True, order='F'), self.diagonal_obs_cov) state = {'initialized': self.initialized, 'initialized_diffuse': self.initialized_diffuse, 'initialized_stationary': self.initialized_stationary, 'initial_state': None, 'initial_state_cov': None, 'initial_diffuse_state_cov': None, 'missing': np.array(self.missing, copy=True, order='F'), 'nmissing': np.array(self.nmissing, copy=True, order='F'), 'has_missing': self.has_missing, 'tmp': np.array(self.tmp, copy=True, order='F'), 'selected_state_cov': np.array(self.selected_state_cov, copy=True, order='F'), 'selected_obs': np.array(self.selected_obs, copy=True, order='F'), 'selected_obs_intercept': np.array(self.selected_obs_intercept, copy=True, order='F'), 'selected_design': np.array(self.selected_design, copy=True, order='F'), 'selected_obs_cov': np.array(self.selected_obs_cov, copy=True, order='F'), 'transform_cholesky': np.array(self.transform_cholesky, copy=True, order='F'), 'transform_obs_cov': np.array(self.transform_obs_cov, copy=True, order='F'), 'transform_design': np.array(self.transform_design, copy=True, order='F'), 'collapse_obs': np.array(self.collapse_obs, copy=True, order='F'), 'collapse_obs_tmp': np.array(self.collapse_obs_tmp, copy=True, order='F'), 'collapse_design': np.array(self.collapse_design, copy=True, order='F'), 'collapse_obs_cov': np.array(self.collapse_obs_cov, copy=True, order='F'), 'collapse_cholesky': np.array(self.collapse_cholesky, copy=True, order='F'), 't': self.t, 'collapse_loglikelihood': self.collapse_loglikelihood, 'companion_transition': self.companion_transition, 'transform_determinant': self.transform_determinant, } if self.initialized: state['initial_state'] = np.array(self.initial_state, copy=True, order='F') state['initial_state_cov'] = np.array(self.initial_state_cov, copy=True, order='F') state['initial_diffuse_state_cov'] = np.array(self.initial_diffuse_state_cov, copy=True, order='F') return (self.__class__, init, state) def __setstate__(self, state): self.initial_state = state['initial_state'] self.initial_state_cov = state['initial_state_cov'] self.initial_diffuse_state_cov = state['initial_diffuse_state_cov'] self.initialized = state['initialized'] self.initialized_diffuse = state['initialized_diffuse'] self.initialized_stationary = state['initialized_stationary'] self.selected_state_cov = state['selected_state_cov'] self.missing = state['missing'] self.nmissing =state['nmissing'] self.has_missing = state['has_missing'] self.tmp = state['tmp'] self.selected_obs = state['selected_obs'] self.selected_obs_intercept = state['selected_obs_intercept'] self.selected_design = state['selected_design'] self.selected_obs_cov =state['selected_obs_cov'] self.transform_cholesky = state['transform_cholesky'] self.transform_obs_cov = state['transform_obs_cov'] self.transform_design = state['transform_design'] self.collapse_obs = state['collapse_obs'] self.collapse_obs_tmp = state['collapse_obs_tmp'] self.collapse_design = state['collapse_design'] self.collapse_obs_cov = state['collapse_obs_cov'] self.collapse_cholesky = state['collapse_cholesky'] self.t = state['t'] self.collapse_loglikelihood = state['collapse_loglikelihood'] self.companion_transition = state['companion_transition'] self.transform_determinant = state['transform_determinant'] def initialize(self, init, offset=0, complex_step=False, clear=True): cdef {{prefix}}Initialization _init # Clear initial arrays if clear: self.initial_state[:] = 0 self.initial_diffuse_state_cov[:] = 0 self.initial_state_cov[:] = 0 # If using global initialization, compute the actual elements and # return them self.initialized_diffuse = False self.initialized_stationary = False if init.initialization_type is not None: init._initialize_initialization(prefix='{{prefix}}') _init = init._initializations['{{prefix}}'] _init.initialize(init.initialization_type, offset, self, self.initial_state, self.initial_diffuse_state_cov, self.initial_state_cov, complex_step) if init.initialization_type == 'diffuse': self.initialized_diffuse = True if init.initialization_type == 'stationary': self.initialized_stationary = True # Otherwise, if using blocks, initialize each of the blocks else: for block_index, block_init in init.blocks.items(): self.initialize(block_init, offset=offset + block_index[0], complex_step=complex_step, clear=False) if not self.initialized: self.initialized = True # ## Initialize: known values # # Initialize the filter with specific values, assumed to be known with # certainty or else as filled with parameters from a maximum likelihood # estimation run. def initialize_known(self, {{cython_type}} [:] initial_state, {{cython_type}} [::1,:] initial_state_cov): """ initialize_known(initial_state, initial_state_cov) """ tools.validate_vector_shape('initial state', &initial_state.shape[0], self.k_states, None) tools.validate_matrix_shape('initial state covariance', &initial_state_cov.shape[0], self.k_states, self.k_states, None) self.initial_state = initial_state self.initial_state_cov = initial_state_cov self.initial_diffuse_state_cov[:] = 0 self.initialized = True # ## Initialize: approximate diffuse priors # # Durbin and Koopman note that this initialization should only be coupled # with the standard Kalman filter for "approximate exploratory work" and # can lead to "large rounding errors" (p. 125). # # *Note:* see Durbin and Koopman section 5.6.1 def initialize_approximate_diffuse(self, {{cython_type}} variance=1e2): """ initialize_approximate_diffuse(variance=1e2) """ cdef np.npy_intp dim[1] dim[0] = self.k_states self.initial_state = np.PyArray_ZEROS(1, dim, {{typenum}}, FORTRAN) self.initial_state_cov = np.eye(self.k_states, dtype={{dtype}}).T * variance self.initial_diffuse_state_cov[:] = 0 self.initialized = True # ## Initialize: stationary process # *Note:* see Durbin and Koopman section 5.6.2 def initialize_stationary(self, complex_step=False): """ initialize_stationary() """ cdef np.npy_intp dim1[1] cdef np.npy_intp dim2[2] cdef int i, info, inc = 1 cdef int k_states2 = self.k_states**2 cdef np.float64_t asum, tol = 1e-9 cdef {{cython_type}} scalar cdef int [::1,:] ipiv # Create selected state covariance matrix {{prefix}}select_cov(self.k_states, self.k_posdef, &self.tmp[0,0], &self.selection[0,0,0], &self.state_cov[0,0,0], &self.selected_state_cov[0,0,0]) # Initial state mean {{if combined_prefix == 'd'}} asum = blas.{{prefix}}asum(&self.k_states, &self.state_intercept[0, 0], &inc) {{elif prefix == 'c'}} asum = blas.scasum(&self.k_states, &self.state_intercept[0, 0], &inc) {{else}} asum = blas.dzasum(&self.k_states, &self.state_intercept[0, 0], &inc) {{endif}} dim1[0] = self.k_states self.initial_state = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) if asum > tol: dim2[0] = self.k_states dim2[1] = self.k_states ipiv = np.PyArray_ZEROS(2, dim2, np.NPY_INT32, FORTRAN) # I - T blas.{{prefix}}copy(&k_states2, &self.transition[0,0,0], &inc, &self.tmp[0,0], &inc) scalar = -1.0 blas.{{prefix}}scal(&k_states2, &scalar, &self.tmp[0, 0], &inc) for i in range(self.k_states): self.tmp[i, i] = self.tmp[i, i] + 1 # c blas.{{prefix}}copy(&self.k_states, &self.state_intercept[0,0], &inc, &self.initial_state[0], &inc) # Solve (I - T) x = c lapack.{{prefix}}getrf(&self.k_states, &self.k_states, &self.tmp[0, 0], &self.k_states, &ipiv[0, 0], &info) lapack.{{prefix}}getrs('N', &self.k_states, &inc, &self.tmp[0, 0], &self.k_states, &ipiv[0, 0], &self.initial_state[0], &self.k_states, &info) dim2[0] = self.k_states; dim2[1] = self.k_states; self.initial_state_cov = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Create a copy of the transition matrix (to avoid overwriting it) blas.{{prefix}}copy(&k_states2, &self.transition[0,0,0], &inc, &self.tmp[0,0], &inc) # Copy the selected state covariance to the initial state covariance # (it will be overwritten with the appropriate matrix) blas.{{prefix}}copy(&k_states2, &self.selected_state_cov[0,0,0], &inc, &self.initial_state_cov[0,0], &inc) # Solve the discrete Lyapunov equation to the get initial state # covariance matrix tools._{{prefix}}solve_discrete_lyapunov(&self.tmp[0,0], &self.initial_state_cov[0,0], self.k_states, complex_step) self.initial_diffuse_state_cov[:] = 0 self.initialized = True def __iter__(self): return self def __next__(self): """ Advance to the next location """ if self.t >= self.nobs: raise StopIteration else: self.seek(self.t+1, 0, 0) cpdef seek(self, unsigned int t, unsigned int transform_diagonalize, unsigned int transform_generalized_collapse, unsigned int reset=False): self._previous_t = self.t # Set the global time indicator, if valid if t >= self.nobs: raise IndexError("Observation index out of range") self.t = t # Indices for possibly time-varying arrays cdef: int k_endog int design_t = 0 int obs_intercept_t = 0 int obs_cov_t = 0 int transition_t = 0 int state_intercept_t = 0 int selection_t = 0 int state_cov_t = 0 # Get indices for possibly time-varying arrays if not self.time_invariant: if self.design.shape[2] > 1: design_t = t if self.obs_intercept.shape[1] > 1: obs_intercept_t = t if self.obs_cov.shape[2] > 1: obs_cov_t = t if self.transition.shape[2] > 1: transition_t = t if self.state_intercept.shape[1] > 1: state_intercept_t = t if self.selection.shape[2] > 1: selection_t = t if self.state_cov.shape[2] > 1: state_cov_t = t # Initialize object-level pointers to statespace arrays self._obs = &self.obs[0, t] self._design = &self.design[0, 0, design_t] self._obs_intercept = &self.obs_intercept[0, obs_intercept_t] self._obs_cov = &self.obs_cov[0, 0, obs_cov_t] self._transition = &self.transition[0, 0, transition_t] self._state_intercept = &self.state_intercept[0, state_intercept_t] self._selection = &self.selection[0, 0, selection_t] self._state_cov = &self.state_cov[0, 0, state_cov_t] # Initialize object-level pointers to initialization if not self.initialized: raise RuntimeError("Statespace model not initialized.") self._initial_state = &self.initial_state[0] self._initial_state_cov = &self.initial_state_cov[0,0] self._initial_diffuse_state_cov = &self.initial_diffuse_state_cov[0,0] # Create the selected state covariance matrix self.select_state_cov(t) # Handle missing data # Note: this modifies object pointers and _* dimensions k_endog = self.select_missing(t) # Set dimensions self.set_dimensions(k_endog, self.k_states, self.k_posdef) # Handle transformations self.transform(t, self._previous_t, transform_diagonalize, transform_generalized_collapse, reset) cdef void set_dimensions(self, unsigned int k_endog, unsigned int k_states, unsigned int k_posdef): self._k_endog = k_endog self._k_states = k_states self._k_posdef = k_posdef self._k_endog2 = k_endog**2 self._k_states2 = k_states**2 self._k_posdef2 = k_posdef**2 self._k_endogstates = k_endog * k_states self._k_statesposdef = k_states * k_posdef cdef void select_state_cov(self, unsigned int t): cdef int selected_state_cov_t = 0 # ### Get selected state covariance matrix if t == 0 or self.selected_state_cov.shape[2] > 1: selected_state_cov_t = t self._selected_state_cov = &self.selected_state_cov[0, 0, selected_state_cov_t] {{prefix}}select_cov(self.k_states, self.k_posdef, &self.tmp[0,0], self._selection, self._state_cov, self._selected_state_cov) else: self._selected_state_cov = &self.selected_state_cov[0, 0, 0] cdef int select_missing(self, unsigned int t): # Note: this assumes that object pointers are already initialized # Note: this assumes that transform_... will be done *later* cdef int k_endog = self.k_endog # Set the current iteration nmissing self._nmissing = self.nmissing[t] # ### Perform missing selections # In Durbin and Koopman (2012), these are represented as matrix # multiplications, i.e. $Z_t^* = W_t Z_t$ where $W_t$ is a row # selection matrix (it contains a subset of rows of the identity # matrix). # # It's more efficient, though, to just copy over the data directly, # which is what is done here. Note that the `selected_*` arrays are # defined as single-dimensional, so the assignment indexes below are # set such that the arrays can be interpreted by the BLAS and LAPACK # functions as two-dimensional, column-major arrays. # # In the case that all data is missing (e.g. this is what happens in # forecasting), we actually set do not change the dimension, but we set # the design matrix to the zeros array. if self._nmissing == self.k_endog: self._select_missing_entire_obs(t) elif self._nmissing > 0: self._select_missing_partial_obs(t) k_endog = self.k_endog - self._nmissing # Return the number of non-missing endogenous variables return k_endog cdef void _select_missing_entire_obs(self, unsigned int t): cdef: int i, j # Design matrix is set to zeros for i in range(self.k_states): for j in range(self.k_endog): self.selected_design[j + i*self.k_endog] = 0.0 self._design = &self.selected_design[0] cdef void _select_missing_partial_obs(self, unsigned int t): cdef: int i, j, k, l int inc = 1 int design_t = 0 int obs_cov_t = 0 int k_endog = self.k_endog - self._nmissing k = 0 for i in range(self.k_endog): if not self.missing[i, t]: self.selected_obs[k] = self._obs[i] self.selected_obs_intercept[k] = self._obs_intercept[i] # i is rows, k is rows blas.{{prefix}}copy(&self.k_states, &self._design[i], &self.k_endog, &self.selected_design[k], &k_endog) # i, k is columns, j, l is rows l = 0 for j in range(self.k_endog): if not self.missing[j, t]: self.selected_obs_cov[l + k*k_endog] = self._obs_cov[j + i*self.k_endog] l += 1 k += 1 self._obs = &self.selected_obs[0] self._obs_intercept = &self.selected_obs_intercept[0] self._design = &self.selected_design[0] self._obs_cov = &self.selected_obs_cov[0] cdef void transform(self, unsigned int t, unsigned int previous_t, unsigned int transform_diagonalize, unsigned int transform_generalized_collapse, unsigned int reset=False) except *: # Reset the collapsed loglikelihood self.collapse_loglikelihood = 0 if transform_generalized_collapse and not self._k_endog <= self._k_states: k_endog = self.transform_generalized_collapse(t, previous_t, reset) # Reset dimensions self.set_dimensions(k_endog, self._k_states, self._k_posdef) elif transform_diagonalize and not (self.diagonal_obs_cov == 1): self.transform_diagonalize(t, previous_t, reset) cdef void transform_diagonalize(self, unsigned int t, unsigned int previous_t, unsigned int reset=False) except *: # Note: this assumes that initialize_object_pointers has *already* been done # Note: this assumes that select_missing has *already* been done # TODO need unit tests, especially for the missing case # TODO need to also transform observation intercept cdef: int i, j, inc=1 int obs_cov_t = 0 int info int reset_missing int diagonal_obs_cov {{cython_type}} * _transform_obs_cov = &self.transform_obs_cov[0, 0] {{cython_type}} * _transform_cholesky = &self.transform_cholesky[0, 0] if self.obs_cov.shape[2] > 1: obs_cov_t = t # Handle missing data if self.nmissing[t] == self.k_endog: return reset_missing = 0 for i in range(self.k_endog): reset_missing = reset_missing + (not self.missing[i,t] == self.missing[i,previous_t]) # If the flag for a diagonal covariancem matrix is not set globally in # the model one way or the other, then we need to check diagonal_obs_cov = self.diagonal_obs_cov if diagonal_obs_cov == -1: # We don't need to check for a diagonal covariance matrix each t, # except in the following cases: if self._diagonal_obs_cov == -1 or t == 0 or self.obs_cov.shape[2] > 1 or reset_missing or reset: diagonal_obs_cov = 1 for i in range(self.k_endog): for j in range(self.k_endog): if i == j: continue if not ({{combined_prefix}}abs(self.obs_cov[i, j, obs_cov_t]) < 1e-9): diagonal_obs_cov = 0 break # Otherwise, we use whatever value was produced last period else: diagonal_obs_cov = self._diagonal_obs_cov self._diagonal_obs_cov = diagonal_obs_cov if diagonal_obs_cov == 1: return # If we have a non-diagonal obs cov, we need to compute the cholesky # decomposition of *self._obs_cov if t == 0 or self.obs_cov.shape[2] > 1 or reset_missing or reset: # LDL decomposition blas.{{prefix}}copy(&self._k_endog2, self._obs_cov, &inc, _transform_cholesky, &inc) info = tools._{{prefix}}ldl(_transform_cholesky, self._k_endog) # Check for errors if info > 0: warnings.warn("Positive semi-definite observation covariance matrix encountered at period %d" % t) elif info < 0: raise np.linalg.LinAlgError('Invalid value in LDL factorization of observation covariance matrix encountered at period %d' % t) # Currently both L and D are stored in transform_cholesky for i in range(self._k_endog): # i is rows for j in range(self._k_endog): # j is columns # Diagonal elements come from the diagonal if i == j: _transform_obs_cov[i + i * self._k_endog] = _transform_cholesky[i + i * self._k_endog] # Other elements are zero else: _transform_obs_cov[i + j * self._k_endog] = 0 # Zero out the upper triangle of the cholesky if j > i: _transform_cholesky[i + j * self._k_endog] = 0 # Convert from L to C simply by setting the diagonal elements to ones _transform_cholesky[i + i * self._k_endog] = 1 # Solve for y_t^* # (unless this is a completely missing observation) # TODO: note that this can cause problems if this function is run twice if not self._nmissing == self.k_endog: # If we have some missing elements, selected_obs is already populated if self._nmissing == 0: blas.{{prefix}}copy(&self._k_endog, &self.obs[0,t], &inc, &self.selected_obs[0], &inc) lapack.{{prefix}}trtrs("L", "N", "U", &self._k_endog, &inc, _transform_cholesky, &self.k_endog, &self.selected_obs[0], &self._k_endog, &info) # Check for errors if info > 0: raise np.linalg.LinAlgError('Singular factorization of observation covariance matrix encountered at period %d' % t) elif info < 0: raise np.linalg.LinAlgError('Invalid value in factorization of observation covariance matrix encountered at period %d' % t) # Setup the pointer self._obs = &self.selected_obs[0] # Solve for d_t^*, if necessary if t == 0 or self.obs_intercept.shape[1] > 1 or reset_missing or reset: blas.{{prefix}}copy(&self._k_endog, self._obs_intercept, &inc, &self.transform_obs_intercept[0], &inc) lapack.{{prefix}}trtrs("L", "N", "U", &self._k_endog, &inc, _transform_cholesky, &self.k_endog, &self.transform_obs_intercept[0], &self._k_endog, &info) # Solve for Z_t^*, if necessary if t == 0 or self.design.shape[2] > 1 or reset_missing or reset: blas.{{prefix}}copy(&self._k_endogstates, self._design, &inc, &self.transform_design[0,0], &inc) lapack.{{prefix}}trtrs("L", "N", "U", &self._k_endog, &self._k_states, _transform_cholesky, &self.k_endog, &self.transform_design[0,0], &self._k_endog, &info) # Check for errors if info > 0: raise np.linalg.LinAlgError('Singular factorization of observation covariance matrix encountered at period %d' % t) elif info < 0: raise np.linalg.LinAlgError('Invalid value in factorization of observation covariance matrix encountered at period %d' % t) # Setup final pointers self._design = &self.transform_design[0,0] self._obs_cov = &self.transform_obs_cov[0,0] self._obs_intercept = &self.transform_obs_intercept[0] cdef int transform_generalized_collapse(self, unsigned int t, unsigned int previous_t, unsigned int reset=True) except *: # Note: this assumes that initialize_object_pointers has *already* been done # Note: this assumes that select_missing has *already* been done # TODO need unit tests, especially for the missing case cdef: int i, j, k, l, inc=1 int obs_cov_t, design_t int info int reset_missing {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 int k_states = self._k_states int k_states2 = self._k_states2 int k_endogstates = self._k_endogstates # $y_t^* = \bar A^* y_t = C_t Z_t' H_t^{-1} y_t$ # $Z_t^* = C_t^{-1}$ # $H_t^* = I_m$ # Make sure we have enough observations to perform collapse if self.k_endog < self.k_states: raise RuntimeError('Cannot collapse observation vector it the' ' state dimension is larger than the dimension' ' of the observation vector.') # Adjust for a VAR transition (i.e. design = [#, 0], where the zeros # correspond to all states except the first k_posdef states) if self.subset_design: k_states = self._k_posdef k_states2 = self._k_posdef2 k_endogstates = self._k_endog * self._k_posdef # Handle missing data if self.nmissing[t] == self.k_endog: return self.k_states reset_missing = 0 for i in range(self.k_endog): reset_missing = reset_missing + (not self.missing[i,t] == self.missing[i,previous_t]) # Initialize the transformation if self.collapse_obs_cov[0,0] == 0: # Set H_t^* to identity for i in range(k_states): self.collapse_obs_cov[i,i] = 1 # Make sure we do not have an observation intercept if not np.sum(self.obs_intercept) == 0 or self.obs_intercept.shape[2] > 1: raise RuntimeError('The observation collapse transformation' ' does not currently support an observation' ' intercept.') # Perform the Cholesky decomposition of H_t, if necessary if t == 0 or self.obs_cov.shape[2] > 1 or reset_missing or reset: # Cholesky decomposition: $H = L L'$ blas.{{prefix}}copy(&self._k_endog2, self._obs_cov, &inc, &self.transform_cholesky[0,0], &inc) lapack.{{prefix}}potrf("L", &self._k_endog, &self.transform_cholesky[0,0], &self._k_endog, &info) # Check for errors if info > 0: raise np.linalg.LinAlgError('Non-positive-definite observation covariance matrix encountered at period %d' % t) elif info < 0: raise np.linalg.LinAlgError('Invalid value in observation covariance matrix encountered at period %d' % t) # Calculate the determinant (just the squared product of the # diagonals, in the Cholesky decomposition case) self.transform_determinant = 0. for i in range(self._k_endog): j = i * (self._k_endog + 1) k = j % self.k_endog l = j // self.k_endog if not self.transform_cholesky[k, l] == 0: self.transform_determinant = self.transform_determinant + {{combined_prefix}}log(self.transform_cholesky[k, l]) self.transform_determinant = 2 * self.transform_determinant # Get $Z_t \equiv C^{-1}$, if necessary if t == 0 or self.obs_cov.shape[2] > 1 or self.design.shape[2] > 1 or reset_missing or reset: # Calculate $H_t^{-1} Z_t \equiv (Z_t' H_t^{-1})'$ via Cholesky solver blas.{{prefix}}copy(&self._k_endogstates, self._design, &inc, &self.transform_design[0,0], &inc) lapack.{{prefix}}potrs("L", &self._k_endog, &k_states, &self.transform_cholesky[0,0], &self._k_endog, &self.transform_design[0,0], &self._k_endog, &info) # Check for errors if not info == 0: raise np.linalg.LinAlgError('Invalid value in calculation of H_t^{-1}Z matrix encountered at period %d' % t) # Calculate $(H_t^{-1} Z_t)' Z_t$ # $(m \times m) = (m \times p) (p \times p) (p \times m)$ blas.{{prefix}}gemm("T", "N", &k_states, &k_states, &self._k_endog, &alpha, self._design, &self._k_endog, &self.transform_design[0,0], &self._k_endog, &beta, &self.collapse_cholesky[0,0], &self._k_states) # Calculate $(Z_t' H_t^{-1} Z_t)^{-1}$ via Cholesky inversion lapack.{{prefix}}potrf("U", &k_states, &self.collapse_cholesky[0,0], &self.k_states, &info) # Check for errors if info > 0: raise np.linalg.LinAlgError('Non-positive-definite ZHZ matrix encountered at period %d' % t) elif info < 0: raise np.linalg.LinAlgError('Invalid value in ZHZ matrix encountered at period %d' % t) lapack.{{prefix}}potri("U", &k_states, &self.collapse_cholesky[0,0], &self.k_states, &info) # Calculate $C_t$ (the upper triangular cholesky decomposition of $(Z_t' H_t^{-1} Z_t)^{-1}$) lapack.{{prefix}}potrf("U", &k_states, &self.collapse_cholesky[0,0], &self.k_states, &info) # Check for errors if info > 0: raise np.linalg.LinAlgError('Non-positive-definite C matrix encountered at period %d' % t) elif info < 0: raise np.linalg.LinAlgError('Invalid value in C matrix encountered at period %d' % t) # Calculate $C_t'^{-1} \equiv Z_t$ # Do so by solving the system: $C_t' x = I$ # (Recall that collapse_obs_cov is an identity matrix) blas.{{prefix}}copy(&self._k_states2, &self.collapse_obs_cov[0,0], &inc, &self.collapse_design[0,0], &inc) lapack.{{prefix}}trtrs("U", "T", "N", &k_states, &k_states, &self.collapse_cholesky[0,0], &self._k_states, &self.collapse_design[0,0], &self._k_states, &info) # Calculate $\bar y_t^* = \bar A_t^* y_t = C_t Z_t' H_t^{-1} y_t$ # (unless this is a completely missing observation) self.collapse_loglikelihood = 0 if not self._nmissing == self.k_endog: # If we have some missing elements, selected_obs is already populated if self._nmissing == 0: blas.{{prefix}}copy(&self.k_endog, &self.obs[0,t], &inc, &self.selected_obs[0], &inc) # $\\# = Z_t' H_t^{-1} y_t$ blas.{{prefix}}gemv("T", &self._k_endog, &k_states, &alpha, &self.transform_design[0,0], &self._k_endog, &self.selected_obs[0], &inc, &beta, &self.collapse_obs[0], &inc) # $y_t^* = C_t \\#$ blas.{{prefix}}trmv("U", "N", "N", &k_states, &self.collapse_cholesky[0,0], &self._k_states, &self.collapse_obs[0], &inc) # Get residuals for loglikelihood calculation # Note: Durbin and Koopman (2012) appears to have an error in the # formula here. They have $e_t = y_t - Z_t \bar y_t^*$, whereas it # should be: $e_t = y_t - Z_t C_t' \bar y_t^*$ # See Jungbacker and Koopman (2014), section 2.5 where $e_t$ is # defined. In this case, $Z_t^dagger = Z_t C_t$ where # $C_t C_t' = (Z_t' \Sigma_\varepsilon^{-1} Z_t)^{-1}$. # # $ \\# = C_t' y_t^*$ blas.{{prefix}}copy(&k_states, &self.collapse_obs[0], &inc, &self.collapse_obs_tmp[0], &inc) blas.{{prefix}}trmv("U", "T", "N", &k_states, &self.collapse_cholesky[0,0], &self._k_states, &self.collapse_obs_tmp[0], &inc) # $e_t = - Z_t C_t' y_t^* + y_t$ blas.{{prefix}}gemv("N", &self._k_endog, &k_states, &gamma, self._design, &self._k_endog, &self.collapse_obs_tmp[0], &inc, &alpha, &self.selected_obs[0], &inc) # Calculate e_t' H_t^{-1} e_t via Cholesky solver # $H_t^{-1} = (L L')^{-1} = L^{-1}' L^{-1}$ # So we want $e_t' L^{-1}' L^{-1} e_t = (L^{-1} e_t)' L^{-1} e_t$ # We have $L$ in `transform_cholesky`, so we want to do a linear # solve of $L x = e_t$ where L is lower triangular lapack.{{prefix}}trtrs("L", "N", "N", &self._k_endog, &inc, &self.transform_cholesky[0,0], &self._k_endog, &self.selected_obs[0], &self._k_endog, &info) # Calculate loglikelihood contribution of this observation # $e_t' H_t^{-1} e_t = (L^{-1} e_t)' L^{-1} e_t = \sum_i e_{i,t}**2$ self.collapse_loglikelihood = 0 for i in range(self._k_endog): self.collapse_loglikelihood = self.collapse_loglikelihood + self.selected_obs[i]**2 # (p-m) log( 2*pi) + log( |H_t| ) self.collapse_loglikelihood = ( self.collapse_loglikelihood + (self._k_endog - k_states)*{{combined_prefix}}log(2*NPY_PI) + self.transform_determinant ) # -0.5 * ... self.collapse_loglikelihood = -0.5 * self.collapse_loglikelihood # Set pointers self._obs = &self.collapse_obs[0] self._design = &self.collapse_design[0,0] self._obs_cov = &self.collapse_obs_cov[0,0] # TODO can I replace this with k_states? I think I should be able to return self._k_states # ### Selected covariance matrice cdef int {{prefix}}select_cov(int k, int k_posdef, {{cython_type}} * tmp, {{cython_type}} * selection, {{cython_type}} * cov, {{cython_type}} * selected_cov): cdef: {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 # Only need to do something if there is a covariance matrix # (i.e k_posdof == 0) if k_posdef > 0: # #### Calculate selected state covariance matrix # $Q_t^* = R_t Q_t R_t'$ # # Combine a selection matrix and a covariance matrix to get # a simplified (but possibly singular) "selected" covariance # matrix (see e.g. Durbin and Koopman p. 43) # `tmp0` array used here, dimension $(m \times r)$ # TODO this does not require two ?gemm calls, since we know that it # is just selection rows and columns of the Q matrix # $\\#_0 = 1.0 * R_t Q_t$ # $(m \times r) = (m \times r) (r \times r)$ blas.{{prefix}}gemm("N", "N", &k, &k_posdef, &k_posdef, &alpha, selection, &k, cov, &k_posdef, &beta, tmp, &k) # $Q_t^* = 1.0 * \\#_0 R_t'$ # $(m \times m) = (m \times r) (m \times r)'$ blas.{{prefix}}gemm("N", "T", &k, &k, &k_posdef, &alpha, tmp, &k, selection, &k, &beta, selected_cov, &k) {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/_simulation_smoother.pxd000066400000000000000000000274221400612667500264210ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Model Smoother declarations Author: Chad Fulton License: Simplified-BSD """ cdef int SMOOTHER_STATE # Durbin and Koopman (2012), Chapter 4.4.2 cdef int SMOOTHER_STATE_COV # Durbin and Koopman (2012), Chapter 4.4.3 cdef int SMOOTHER_DISTURBANCE # Durbin and Koopman (2012), Chapter 4.5 cdef int SMOOTHER_DISTURBANCE_COV # Durbin and Koopman (2012), Chapter 4.5 cdef int SMOOTHER_ALL # Typical imports cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace ) from statsmodels.tsa.statespace._kalman_filter cimport ( sKalmanFilter, dKalmanFilter, cKalmanFilter, zKalmanFilter ) from statsmodels.tsa.statespace._kalman_smoother cimport ( sKalmanSmoother, dKalmanSmoother, cKalmanSmoother, zKalmanSmoother ) # Single precision cdef class sSimulationSmoother(object): # ### Statespace model cdef readonly sStatespace model # ### Kalman filter cdef readonly sKalmanFilter kfilter # ### Kalman smoother cdef readonly sKalmanSmoother smoother # ### Simulated Statespace model cdef readonly sStatespace simulated_model # ### Simulated Kalman filter cdef readonly sKalmanFilter simulated_kfilter # ### Simulated Kalman smoother cdef readonly sKalmanSmoother simulated_smoother # ### Simulated Statespace model cdef readonly sStatespace secondary_simulated_model # ### Simulated Kalman filter cdef readonly sKalmanFilter secondary_simulated_kfilter # ### Simulated Kalman smoother cdef readonly sKalmanSmoother secondary_simulated_smoother # ### Simulation parameters cdef public int simulation_output cdef public int has_missing # ### Random variates cdef int n_disturbance_variates cdef readonly np.float32_t [:] disturbance_variates cdef int n_initial_state_variates cdef readonly np.float32_t [:] initial_state_variates # ### Simulated Data cdef readonly np.float32_t [::1,:] simulated_measurement_disturbance cdef readonly np.float32_t [::1,:] simulated_state_disturbance cdef readonly np.float32_t [::1,:] simulated_state # ### Generated Data cdef readonly np.float32_t [::1,:] generated_obs cdef readonly np.float32_t [::1,:] generated_state # ### Temporary arrays cdef readonly np.float32_t [::1,:] tmp0, tmp1, tmp2 # ### Pointers cdef np.float32_t * _tmp0 cdef np.float32_t * _tmp1 cdef np.float32_t * _tmp2 # ### Parameters cdef readonly int nobs cdef readonly int pretransformed_disturbance_variates cdef readonly int pretransformed_initial_state_variates cdef readonly int fixed_initial_state cpdef draw_disturbance_variates(self) cpdef draw_initial_state_variates(self) cpdef set_disturbance_variates(self, np.float32_t [:] variates, int pretransformed=*) cpdef set_initial_state_variates(self, np.float32_t [:] variates, int pretransformed=*) cpdef set_initial_state(self, np.float32_t [:] initial_state) cpdef simulate(self, int simulation_output=*) cdef np.float32_t generate_obs(self, int t, np.float32_t * obs, np.float32_t * state, np.float32_t * variates) cdef np.float32_t generate_state(self, int t, np.float32_t * state, np.float32_t * input_state, np.float32_t * variates) cdef void cholesky(self, np.float32_t * source, np.float32_t * destination, int n) cdef void transform_variates(self, np.float32_t * variates, np.float32_t * cholesky_factor, int n) cdef void _reinitialize_temp_pointers(self) except * # Double precision cdef class dSimulationSmoother(object): # ### Statespace model cdef readonly dStatespace model # ### Kalman filter cdef readonly dKalmanFilter kfilter # ### Kalman smoother cdef readonly dKalmanSmoother smoother # ### Simulated Statespace model cdef readonly dStatespace simulated_model # ### Simulated Kalman filter cdef readonly dKalmanFilter simulated_kfilter # ### Simulated Kalman smoother cdef readonly dKalmanSmoother simulated_smoother # ### Simulated Statespace model cdef readonly dStatespace secondary_simulated_model # ### Simulated Kalman filter cdef readonly dKalmanFilter secondary_simulated_kfilter # ### Simulated Kalman smoother cdef readonly dKalmanSmoother secondary_simulated_smoother # ### Simulation parameters cdef public int simulation_output cdef public int has_missing # ### Random variates cdef int n_disturbance_variates cdef readonly np.float64_t [:] disturbance_variates cdef int n_initial_state_variates cdef readonly np.float64_t [:] initial_state_variates # ### Simulated Data cdef readonly np.float64_t [::1,:] simulated_measurement_disturbance cdef readonly np.float64_t [::1,:] simulated_state_disturbance cdef readonly np.float64_t [::1,:] simulated_state # ### Generated Data cdef readonly np.float64_t [::1,:] generated_obs cdef readonly np.float64_t [::1,:] generated_state # ### Temporary arrays cdef readonly np.float64_t [::1,:] tmp0, tmp1, tmp2 # ### Pointers cdef np.float64_t * _tmp0 cdef np.float64_t * _tmp1 cdef np.float64_t * _tmp2 # ### Parameters cdef readonly int nobs cdef readonly int pretransformed_disturbance_variates cdef readonly int pretransformed_initial_state_variates cdef readonly int fixed_initial_state cpdef draw_disturbance_variates(self) cpdef draw_initial_state_variates(self) cpdef set_disturbance_variates(self, np.float64_t [:] variates, int pretransformed=*) cpdef set_initial_state_variates(self, np.float64_t [:] variates, int pretransformed=*) cpdef set_initial_state(self, np.float64_t [:] initial_state) cpdef simulate(self, int simulation_output=*) cdef np.float64_t generate_obs(self, int t, np.float64_t * obs, np.float64_t * state, np.float64_t * variates) cdef np.float64_t generate_state(self, int t, np.float64_t * state, np.float64_t * input_state, np.float64_t * variates) cdef void cholesky(self, np.float64_t * source, np.float64_t * destination, int n) cdef void transform_variates(self, np.float64_t * variates, np.float64_t * cholesky_factor, int n) cdef void _reinitialize_temp_pointers(self) except * # Single precision complex cdef class cSimulationSmoother(object): # ### Statespace model cdef readonly cStatespace model # ### Kalman filter cdef readonly cKalmanFilter kfilter # ### Kalman smoother cdef readonly cKalmanSmoother smoother # ### Simulated Statespace model cdef readonly cStatespace simulated_model # ### Simulated Kalman filter cdef readonly cKalmanFilter simulated_kfilter # ### Simulated Kalman smoother cdef readonly cKalmanSmoother simulated_smoother # ### Simulated Statespace model cdef readonly cStatespace secondary_simulated_model # ### Simulated Kalman filter cdef readonly cKalmanFilter secondary_simulated_kfilter # ### Simulated Kalman smoother cdef readonly cKalmanSmoother secondary_simulated_smoother # ### Simulation parameters cdef public int simulation_output cdef public int has_missing # ### Random variates cdef int n_disturbance_variates cdef readonly np.complex64_t [:] disturbance_variates cdef int n_initial_state_variates cdef readonly np.complex64_t [:] initial_state_variates # ### Simulated Data cdef readonly np.complex64_t [::1,:] simulated_measurement_disturbance cdef readonly np.complex64_t [::1,:] simulated_state_disturbance cdef readonly np.complex64_t [::1,:] simulated_state # ### Generated Data cdef readonly np.complex64_t [::1,:] generated_obs cdef readonly np.complex64_t [::1,:] generated_state # ### Temporary arrays cdef readonly np.complex64_t [::1,:] tmp0, tmp1, tmp2 # ### Pointers cdef np.complex64_t * _tmp0 cdef np.complex64_t * _tmp1 cdef np.complex64_t * _tmp2 # ### Parameters cdef readonly int nobs cdef readonly int pretransformed_disturbance_variates cdef readonly int pretransformed_initial_state_variates cdef readonly int fixed_initial_state cpdef draw_disturbance_variates(self) cpdef draw_initial_state_variates(self) cpdef set_disturbance_variates(self, np.complex64_t [:] variates, int pretransformed=*) cpdef set_initial_state_variates(self, np.complex64_t [:] variates, int pretransformed=*) cpdef set_initial_state(self, np.complex64_t [:] initial_state) cpdef simulate(self, int simulation_output=*) cdef np.complex64_t generate_obs(self, int t, np.complex64_t * obs, np.complex64_t * state, np.complex64_t * variates) cdef np.complex64_t generate_state(self, int t, np.complex64_t * state, np.complex64_t * input_state, np.complex64_t * variates) cdef void cholesky(self, np.complex64_t * source, np.complex64_t * destination, int n) cdef void transform_variates(self, np.complex64_t * variates, np.complex64_t * cholesky_factor, int n) cdef void _reinitialize_temp_pointers(self) except * # Double precision complex cdef class zSimulationSmoother(object): # ### Statespace model cdef readonly zStatespace model # ### Kalman filter cdef readonly zKalmanFilter kfilter # ### Kalman smoother cdef readonly zKalmanSmoother smoother # ### Simulated Statespace model cdef readonly zStatespace simulated_model # ### Simulated Kalman filter cdef readonly zKalmanFilter simulated_kfilter # ### Simulated Kalman smoother cdef readonly zKalmanSmoother simulated_smoother # ### Simulated Statespace model cdef readonly zStatespace secondary_simulated_model # ### Simulated Kalman filter cdef readonly zKalmanFilter secondary_simulated_kfilter # ### Simulated Kalman smoother cdef readonly zKalmanSmoother secondary_simulated_smoother # ### Simulation parameters cdef public int simulation_output cdef public int has_missing # ### Random variates cdef int n_disturbance_variates cdef readonly np.complex128_t [:] disturbance_variates cdef int n_initial_state_variates cdef readonly np.complex128_t [:] initial_state_variates # ### Simulated Data cdef readonly np.complex128_t [::1,:] simulated_measurement_disturbance cdef readonly np.complex128_t [::1,:] simulated_state_disturbance cdef readonly np.complex128_t [::1,:] simulated_state # ### Generated Data cdef readonly np.complex128_t [::1,:] generated_obs cdef readonly np.complex128_t [::1,:] generated_state # ### Temporary arrays cdef readonly np.complex128_t [::1,:] tmp0, tmp1, tmp2 # ### Pointers cdef np.complex128_t * _tmp0 cdef np.complex128_t * _tmp1 cdef np.complex128_t * _tmp2 # ### Parameters cdef readonly int nobs cdef readonly int pretransformed_disturbance_variates cdef readonly int pretransformed_initial_state_variates cdef readonly int fixed_initial_state cpdef draw_disturbance_variates(self) cpdef draw_initial_state_variates(self) cpdef set_disturbance_variates(self, np.complex128_t [:] variates, int pretransformed=*) cpdef set_initial_state_variates(self, np.complex128_t [:] variates, int pretransformed=*) cpdef set_initial_state(self, np.complex128_t [:] initial_state) cpdef simulate(self, int simulation_output=*) cdef np.complex128_t generate_obs(self, int t, np.complex128_t * obs, np.complex128_t * state, np.complex128_t * variates) cdef np.complex128_t generate_state(self, int t, np.complex128_t * state, np.complex128_t * input_state, np.complex128_t * variates) cdef void cholesky(self, np.complex128_t * source, np.complex128_t * destination, int n) cdef void transform_variates(self, np.complex128_t * variates, np.complex128_t * cholesky_factor, int n) cdef void _reinitialize_temp_pointers(self) except *statsmodels-0.12.2/statsmodels/tsa/statespace/_simulation_smoother.pyx.in000066400000000000000000001000141400612667500270400ustar00rootroot00000000000000#cython: profile=False #cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # ## Constants # ### Simulation smoothers # TODO actually just copy the values from SMOOTHING_STATE, SMOOTHING_DISTURBANCE # because we always want them to be identical cdef int SIMULATE_STATE = 0x01 # Durbin and Koopman (2012), Chapter 4.9.1 cdef int SIMULATE_DISTURBANCE = 0x04 # Durbin and Koopman (2012), Chapter 4.9.2 cdef int SIMULATE_ALL = ( SIMULATE_STATE | SIMULATE_DISTURBANCE ) from statsmodels.tsa.statespace._kalman_filter cimport ( FILTER_CONVENTIONAL, FILTER_COLLAPSED, FILTER_UNIVARIATE, INVERT_UNIVARIATE, SOLVE_CHOLESKY, TIMING_INIT_PREDICTED, STABILITY_FORCE_SYMMETRY, MEMORY_STORE_ALL ) from statsmodels.tsa.statespace._kalman_smoother cimport ( SMOOTHER_ALL ) # Typical imports import numpy as np import warnings cimport numpy as np cimport cython np.import_array() cimport scipy.linalg.cython_blas as blas cimport scipy.linalg.cython_lapack as lapack cimport statsmodels.tsa.statespace._tools as tools cdef int FORTRAN = 1 {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} cdef class {{prefix}}SimulationSmoother(object): # ### Statespace model # cdef readonly {{prefix}}Statespace model # ### Kalman filter # cdef readonly {{prefix}}KalmanFilter kfilter # ### Kalman smoother # cdef readonly {{prefix}}KalmanSmoother smoother # ### Simulated Statespace model # cdef readonly {{prefix}}Statespace simulated_model # ### Simulated Kalman filter # cdef readonly {{prefix}}KalmanFilter simulated_kfilter # ### Simulated Kalman smoother # cdef readonly {{prefix}}KalmanSmoother simulated_smoother # ### Secondary Simulated Statespace model # Note: currently only used in the case of missing data # cdef readonly {{prefix}}Statespace secondary_simulated_model # ### Simulated Kalman filter # cdef readonly {{prefix}}KalmanFilter secondary_simulated_kfilter # ### Simulated Kalman smoother # cdef readonly {{prefix}}KalmanSmoother secondary_simulated_smoother # ### Simulation parameters # cdef public int simulation_output # cdef readonly int has_missing # ### Random variates # cdef int n_disturbance_variates # cdef readonly {{cython_type}} [:] disturbance_variates # cdef int n_initial_state_variates # cdef readonly {{cython_type}} [:] initial_state_variates # ### Simulated Data # cdef readonly {{cython_type}} [::1,:] simulated_measurement_disturbance # cdef readonly {{cython_type}} [::1,:] simulated_state_disturbance # cdef readonly {{cython_type}} [::1,:] simulated_state # ### Generated Data # cdef readonly {{cython_type}} [::1,:] generated_obs # cdef readonly {{cython_type}} [::1,:] generated_state # ### Temporary arrays # cdef readonly {{cython_type}} [::1,:] tmp0, tmp1, tmp2 # ### Pointers # cdef {{cython_type}} * _tmp0 # cdef {{cython_type}} * _tmp1 # cdef {{cython_type}} * _tmp2 def __init__(self, {{prefix}}Statespace model, int filter_method=FILTER_CONVENTIONAL, int inversion_method=INVERT_UNIVARIATE | SOLVE_CHOLESKY, int stability_method=STABILITY_FORCE_SYMMETRY, int conserve_memory=MEMORY_STORE_ALL, int filter_timing=TIMING_INIT_PREDICTED, np.float64_t tolerance=1e-19, int loglikelihood_burn=0, int smoother_output=SMOOTHER_ALL, int simulation_output=SIMULATE_ALL, int nobs=-1): cdef int inc = 1 cdef: np.npy_intp dim1[1] np.npy_intp dim2[2] cdef {{cython_type}} [::1,:] obs cdef {{cython_type}} [::1,:] secondary_obs cdef int nobs_endog # Use model nobs by default if nobs == -1: nobs = model.nobs # Only allow more nobs if a time-invariant model elif nobs > model.nobs and model.time_invariant == 0: raise ValueError('In a time-varying model, cannot create more' ' simulations than there are observations.') elif nobs <= 0: raise ValueError('Invalid number of simulations; must be' ' positive.') self.nobs = nobs nobs_endog = self.nobs * model.k_endog self.pretransformed_disturbance_variates = False self.pretransformed_initial_state_variates = False self.fixed_initial_state = False # Model objects self.model = model # self.kfilter = {{prefix}}KalmanFilter( # self.model, filter_method, inversion_method, # stability_method, conserve_memory, # tolerance, loglikelihood_burn # ) # self.smoother = {{prefix}}KalmanSmoother( # self.model, self.kfilter, smoother_output # ) # Simulated model objects dim2[0] = model.k_endog; dim2[1] = self.nobs; obs = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) self.simulated_model = {{prefix}}Statespace( obs, model.design, model.obs_intercept, model.obs_cov, model.transition, model.state_intercept, model.selection, model.state_cov ) self.simulated_kfilter = {{prefix}}KalmanFilter( self.simulated_model, filter_method, inversion_method, stability_method, conserve_memory, filter_timing, tolerance, loglikelihood_burn ) self.simulated_smoother = {{prefix}}KalmanSmoother( self.simulated_model, self.simulated_kfilter, smoother_output ) # Secondary simulated model objects # Currently only used if there is missing data (since then the # approach in which the Kalman filter only has to be run over the # series y_t^* = y_t - y_t^+ is infeasible), although it could also # allow drawing multiple samples at the same time, see Durbin and # Koopman (2002). self.has_missing = model.has_missing if self.has_missing: dim2[0] = model.k_endog; dim2[1] = self.nobs; secondary_obs = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) blas.{{prefix}}copy(&nobs_endog, &model.obs[0,0], &inc, &secondary_obs[0,0], &inc) self.secondary_simulated_model = {{prefix}}Statespace( secondary_obs, model.design, model.obs_intercept, model.obs_cov, model.transition, model.state_intercept, model.selection, model.state_cov ) self.secondary_simulated_kfilter = {{prefix}}KalmanFilter( self.secondary_simulated_model, filter_method, inversion_method, stability_method, conserve_memory, filter_timing, tolerance, loglikelihood_burn ) self.secondary_simulated_smoother = {{prefix}}KalmanSmoother( self.secondary_simulated_model, self.secondary_simulated_kfilter, smoother_output ) # In the case of non-missing data, the Kalman filter will actually # be run over y_t^* = y_t - y_t^+, which means the observation equation # intercept should be zero; make sure that it is else: dim2[0] = self.model.k_endog; dim2[1] = self.model.obs_intercept.shape[1]; self.simulated_model.obs_intercept = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = self.model.k_states; dim2[1] = self.model.state_intercept.shape[1]; self.simulated_model.state_intercept = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Initialize the simulated model memoryviews # Note: the actual initialization is replaced in the simulate() # function below, but will complain if the memoryviews have not been # first initialized, which this call does. self.simulated_model.initialize_approximate_diffuse() if self.has_missing: self.secondary_simulated_model.initialize_approximate_diffuse() # Parameters self.simulation_output = simulation_output self.n_disturbance_variates = self.nobs * (self.model.k_endog + self.model.k_posdef) self.n_initial_state_variates = self.model.k_states # Random variates dim1[0] = self.n_disturbance_variates; self.disturbance_variates = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) dim1[0] = self.n_initial_state_variates; self.initial_state_variates = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) # Simulated data (\tilde eta_t, \tilde eps_t, \tilde alpha_t) # Note that these are (k_endog x nobs), (k_posdef x nobs), (k_states x nobs) if filter_method & FILTER_COLLAPSED: dim2[0] = self.model.k_states; dim2[1] = self.nobs; else: dim2[0] = self.model.k_endog; dim2[1] = self.nobs; self.simulated_measurement_disturbance = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = self.model.k_posdef; dim2[1] = self.nobs; self.simulated_state_disturbance = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = self.model.k_states; dim2[1] = self.nobs; self.simulated_state = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Generated data (y_t^+, alpha_t^+) dim2[0] = self.model.k_endog; dim2[1] = self.nobs; self.generated_obs = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = self.model.k_states; dim2[1] = self.nobs+1; self.generated_state = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Temporary arrays dim2[0] = self.model.k_states; dim2[1] = self.model.k_states; self.tmp0 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # chol(P_1) dim2[0] = self.model.k_posdef; dim2[1] = self.model.k_posdef; self.tmp2 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # chol(Q_t) dim2[0] = self.model.k_endog; dim2[1] = self.model.k_endog; self.tmp1 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # chol(H_t) # Pointers self._tmp0 = &self.tmp0[0,0] self._tmp1 = &self.tmp1[0,0] self._tmp2 = &self.tmp2[0,0] def __reduce__(self): args = (self.model, self.model.filter_method, self.model.inversion_method, self.model.stability_method, self.model.conserve_memory, self.model.filter_timing, self.model.tolerance, self.model.loglikelihood_burn, self.simulated_smoother.smoother_output, self.simulation_output, self.nobs, self.pretransformed_variates) state = { 'disturbance_variates': np.array(self.disturbance_variates, copy=True, order='F'), 'initial_state_variates': np.array(self.initial_state_variates, copy=True, order='F'), 'simulated_measurement_disturbance': np.array(self.simulated_measurement_disturbance, copy=True, order='F'), 'simulated_state_disturbance': np.array(self.simulated_state_disturbance, copy=True, order='F'), 'simulated_state': np.array(self.simulated_state, copy=True, order='F'), 'generated_obs': np.array(self.generated_obs, copy=True, order='F'), 'generated_state': np.array(self.generated_state, copy=True, order='F'), 'tmp0': np.array(self.tmp0, copy=True, order='F'), 'tmp2': np.array(self.tmp2, copy=True, order='F'), 'tmp1': np.array(self.tmp1, copy=True, order='F') } return (self.__class__, args, state) def __setstate__(self, state): self.disturbance_variates = state['disturbance_variates'] self.initial_state_variates = state['initial_state_variates'] self.simulated_measurement_disturbance = state['simulated_measurement_disturbance'] self.simulated_state_disturbance = state['simulated_state_disturbance'] self.simulated_state = state['simulated_state'] self.generated_obs = state['generated_obs'] self.generated_state = state['generated_state'] self.tmp0 = state['tmp0'] self.tmp2 = state['tmp2'] self.tmp1 = state['tmp1'] cdef void _reinitialize_temp_pointers(self) except *: self._tmp0 = &self.tmp0[0,0] self._tmp1 = &self.tmp1[0,0] self._tmp2 = &self.tmp2[0,0] cpdef draw_disturbance_variates(self): self.disturbance_variates = np.random.normal(size=self.n_disturbance_variates) self.pretransformed_disturbance_variates = False cpdef draw_initial_state_variates(self): self.initial_state_variates = np.random.normal(size=self.n_initial_state_variates) self.pretransformed_initial_state_variates = False self.fixed_initial_state = False cpdef set_disturbance_variates(self, {{cython_type}} [:] variates, int pretransformed=0): # TODO allow variates to be an iterator or callback tools.validate_vector_shape('disturbance variates', &variates.shape[0], self.n_disturbance_variates) self.disturbance_variates = variates self.pretransformed_disturbance_variates = pretransformed cpdef set_initial_state_variates(self, {{cython_type}} [:] variates, int pretransformed=0): # Note that the initial state is set to be: # initial_state = mod.initial_state + initial_state_variate * cholesky(mod.initial_state_cov) # so is can be difficult to set the initial state itself via this method; # see instead set_initial_state # TODO allow variates to be an iterator or callback tools.validate_vector_shape('initial state variates', &variates.shape[0], self.n_initial_state_variates) self.initial_state_variates = variates self.pretransformed_initial_state_variates = pretransformed self.fixed_initial_state = False cpdef set_initial_state(self, {{cython_type}} [:] initial_state): # Using this method sets a flag that indicates the self.initial_state_variates # variable should be interpreted as the actual initial_state. # TODO allow variates to be an iterator or callback tools.validate_vector_shape('initial state', &initial_state.shape[0], self.n_initial_state_variates) self.initial_state_variates = initial_state self.pretransformed_initial_state_variates = True self.fixed_initial_state = True cpdef simulate(self, int simulation_output=-1): """ Draw a simulation """ cdef: int inc = 1 int info int measurement_idx, state_idx, t int k_endog = self.model.k_endog int k_states = self.model.k_states int k_states2 = self.model.k_states**2 int k_posdef = self.model.k_posdef int k_posdef2 = self.model.k_posdef**2 int nobs_endog = self.nobs * self.model.k_endog int nobs_kstates = self.nobs * self.model.k_states int nobs1_kstates = (self.nobs+1) * self.model.k_states int nobs_posdef = self.nobs * self.model.k_posdef cdef: {{cython_type}} alpha = 1.0 {{cython_type}} gamma = -1.0 cdef {{prefix}}Statespace collapsing_model cdef {{cython_type}} [:,:] collapsing_obs cdef np.npy_intp dim2[2] if simulation_output == -1: simulation_output = self.simulation_output # Forwards recursion # 0. Statespace initialization if not self.model.initialized: raise RuntimeError("Statespace model not initialized.") blas.{{prefix}}copy(&k_states, &self.model.initial_state[0], &inc, &self.simulated_model.initial_state[0], &inc) blas.{{prefix}}copy(&k_states2, &self.model.initial_state_cov[0,0], &inc, &self.simulated_model.initial_state_cov[0,0], &inc) blas.{{prefix}}copy(&k_states2, &self.model.initial_diffuse_state_cov[0,0], &inc, &self.simulated_model.initial_diffuse_state_cov[0,0], &inc) if self.has_missing: blas.{{prefix}}copy(&k_states, &self.model.initial_state[0], &inc, &self.secondary_simulated_model.initial_state[0], &inc) blas.{{prefix}}copy(&k_states2, &self.model.initial_state_cov[0,0], &inc, &self.secondary_simulated_model.initial_state_cov[0,0], &inc) blas.{{prefix}}copy(&k_states2, &self.model.initial_diffuse_state_cov[0,0], &inc, &self.secondary_simulated_model.initial_diffuse_state_cov[0,0], &inc) # 0. Kalman filter initialization: get alpha_1^+ ~ N(a_1, P_1) # Usually, this means transforming the N(0,1) random variate # into a N(initial_state, initial_state_cov) random variate. # alpha_1^+ = initial_state + variate * chol(initial_state_cov) # If pretransformed_variates is True, then the variates should already # be N(0, initial_state_cov), and then we just need: # alpha_1^+ = initial_state + variate # However, if fixed_initial_state is True, then we just set: # alpha_1^+ = variate blas.{{prefix}}copy(&k_states, &self.initial_state_variates[0], &inc, &self.generated_state[0,0], &inc) if not self.fixed_initial_state: self.cholesky(&self.model.initial_state_cov[0,0], self._tmp0, k_states) if not self.pretransformed_initial_state_variates: self.transform_variates(&self.generated_state[0,0], self._tmp0, k_states) # In the case of no missing data, we want to keep the initial state at zero if self.has_missing: blas.{{prefix}}axpy(&k_states, &alpha, &self.model.initial_state[0], &inc, &self.generated_state[0,0], &inc) self.simulated_kfilter.seek(0) # reset the filter if self.has_missing: self.secondary_simulated_kfilter.seek(0) # reset the filter measurement_idx = 0 state_idx = nobs_endog # Note: it is only when we are simulating a series that we might have # self.model.nobs != self.simulated_model.nobs, and in that case we do # not need to copy over the observations. # TODO: Need more explicit support for the pure simulation case, both # to avoid errors (like the copy statement below) and because we can # probably speed up the process by not running the filter parts. if not self.has_missing and (self.model.nobs == self.simulated_model.nobs): # reset the obs data in the primary simulated model # (but only if there is not missing data - in that case we will # combine the actual data with the generated data in the primary # model, so copy the actual data here and subtract data below) blas.{{prefix}}copy(&nobs_endog, &self.model.obs[0,0], &inc, &self.simulated_model.obs[0,0], &inc) for t in range(self.nobs): # 1. Transform independent draws to w_t^+: eps_t^+ = ind_eps * chol(H_t) # eta_t^+ = ind_eta * chol(Q_t) # 2. Construct y_t^+ = d_t + Z_t alpha_t^+ + eps_t^+ # alpha_{t+1}^+ = c_t + T_t alpha_t^+ + eta_t^+ # Measurement disturbance (eps) # self._tmp1 = chol(H_t) if t == 0 or self.model.obs_cov.shape[2] > 1: self.cholesky(&self.model.obs_cov[0,0,t], self._tmp1, k_endog) # eps_t^+ = ind_eps * chol(H_t) if not self.pretransformed_disturbance_variates: self.transform_variates(&self.disturbance_variates[measurement_idx], self._tmp1, k_endog) # y_t^+ self.generate_obs(t, &self.generated_obs[0,t], &self.generated_state[0,t], &self.disturbance_variates[measurement_idx]) measurement_idx += k_endog # State disturbance (eta) # self._tmp1 = chol(Q_t) if t == 0 or self.model.state_cov.shape[2] > 1: self.cholesky(&self.model.state_cov[0,0,t], self._tmp2, k_posdef) # eta_t^+ = ind_eta * chol(Q_t) if not self.pretransformed_disturbance_variates: self.transform_variates(&self.disturbance_variates[state_idx], self._tmp2, k_posdef) # alpha_t+1^+ self.generate_state(t, &self.generated_state[0,t+1], &self.generated_state[0,t], &self.disturbance_variates[state_idx]) state_idx += k_posdef # If we are just generating new series (i.e. all we want is # generated_obs, generated_state), go to the next iteration if self.simulation_output == 0: continue # Typically, rather than running the Kalman filter separately for # y_t^+ and y_t, we can instead run it over y_t^* = y_t - y_t^+ if not self.has_missing: # Construct y_t^* = - y_t^+ + y_t blas.{{prefix}}axpy(&k_endog, &gamma, &self.generated_obs[0,t], &inc, &self.simulated_model.obs[0, t], &inc) # 3. Iterate Kalman filter, based on y_t^* # (this will give us alpha_t+1^*) next(self.simulated_kfilter) # In the case of missing data, we have to run them separately else: # 3-1. Iterate the Kalman filter on the y_t^+ data # to get alpha_t+1^+ blas.{{prefix}}copy(&k_endog, &self.generated_obs[0,t], &inc, &self.simulated_model.obs[0, t], &inc) next(self.simulated_kfilter) # 3-2. Iterate the Kalman filter on the y_t data # to get alpha_t+1 next(self.secondary_simulated_kfilter) # If we are just generating new series (i.e. all we want is # generated_obs, generated_state), return now if self.simulation_output == 0: return # Backwards recursion # This gives us \hat w_t^* = \hat w_t - \hat w_t^+ (simulation_output & SIMULATE_DISTURBANCE) # \hat alpha_t+1^* = \hat alpha_t+1 - \hat alpha_t+1^+ (simulation_output & SIMULATE_STATE) # or if there is missing data: # this gives us \hat w_t^+ # \hat alpha_t+1 # and we construct starred versions below self.simulated_smoother.smoother_output = simulation_output self.simulated_smoother() # In the FILTER_COLLAPSED case, we now need to replace nobs_endog with # nobs_kstates if self.simulated_kfilter.filter_method & FILTER_COLLAPSED: nobs_endog = nobs_kstates if self.has_missing: # This gives us \hat w_t # \hat alpha_t+1 self.secondary_simulated_smoother.smoother_output = simulation_output self.secondary_simulated_smoother() # Construct \hat w_t^* = \hat w_t - \hat w_t^+ # \hat alpha_t+1^* = \hat alpha_t+1 - \hat alpha_t+1^+ # Note: this overwrites the values in self.simulated_smoother, # so that the steps below will be the same regardless of whether or # not there was missing data if self.simulation_output & SIMULATE_DISTURBANCE: # If there are partially missing entries, we need to re-order # the smoothed measurment disturbances. tools.{{prefix}}reorder_missing_vector(self.secondary_simulated_smoother.smoothed_measurement_disturbance, self.model.missing) blas.{{prefix}}swap(&nobs_endog, &self.simulated_smoother.smoothed_measurement_disturbance[0,0], &inc, &self.secondary_simulated_smoother.smoothed_measurement_disturbance[0,0], &inc) blas.{{prefix}}axpy(&nobs_endog, &gamma, &self.secondary_simulated_smoother.smoothed_measurement_disturbance[0,0], &inc, &self.simulated_smoother.smoothed_measurement_disturbance[0,0], &inc) blas.{{prefix}}swap(&nobs_posdef, &self.simulated_smoother.smoothed_state_disturbance[0,0], &inc, &self.secondary_simulated_smoother.smoothed_state_disturbance[0,0], &inc) blas.{{prefix}}axpy(&nobs_posdef, &gamma, &self.secondary_simulated_smoother.smoothed_state_disturbance[0,0], &inc, &self.simulated_smoother.smoothed_state_disturbance[0,0], &inc) if self.simulation_output & SIMULATE_STATE: blas.{{prefix}}swap(&nobs_kstates, &self.simulated_smoother.smoothed_state[0,0], &inc, &self.secondary_simulated_smoother.smoothed_state[0,0], &inc) blas.{{prefix}}axpy(&nobs_kstates, &gamma, &self.secondary_simulated_smoother.smoothed_state[0,0], &inc, &self.simulated_smoother.smoothed_state[0,0], &inc) # Construct the final simulated variables # This gives us \tilde w_t = \hat w_t^* + w_t^+ (simulation_output & SIMULATE_DISTURBANCE) # \tilde alpha_t+1 = \hat alpha_t^* + alpha_t^+ (simulation_output & SIMULATE_STATE) if self.simulation_output & SIMULATE_DISTURBANCE: # \tilde eps_t = \hat eps_t^* + eps_t^+ # In the FILTER_COLLAPSED case, we have to use a collapsed version of the disturbance variates, # so we construct a new representation that can perform the collapse on the variates if self.simulated_kfilter.filter_method & FILTER_COLLAPSED: dim2[0] = k_endog; dim2[1] = self.nobs; collapsing_obs = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) nobs_endog = k_endog * self.nobs blas.{{prefix}}copy(&nobs_endog, &self.disturbance_variates[0], &inc, &collapsing_obs[0, 0], &inc) nobs_endog = nobs_kstates collapsing_model = {{prefix}}Statespace( collapsing_obs, self.model.design, self.model.obs_intercept, self.model.obs_cov, self.model.transition, self.model.state_intercept, self.model.selection, self.model.state_cov ) collapsing_model.initialized = True for t in range(self.nobs): collapsing_model.seek(t, self.simulated_kfilter.univariate_filter[t], self.simulated_kfilter.filter_method & FILTER_COLLAPSED) blas.{{prefix}}copy(&k_states, &collapsing_model.collapse_obs[0], &inc, &self.simulated_measurement_disturbance[0,t], &inc) else: blas.{{prefix}}copy(&nobs_endog, &self.disturbance_variates[0], &inc, &self.simulated_measurement_disturbance[0,0], &inc) blas.{{prefix}}axpy(&nobs_endog, &alpha, &self.simulated_smoother.smoothed_measurement_disturbance[0,0], &inc, &self.simulated_measurement_disturbance[0,0], &inc) # \tilde eta_t = \hat eta_t^* + eta_t^+ blas.{{prefix}}copy(&nobs_posdef, &self.disturbance_variates[k_endog * self.nobs], &inc, &self.simulated_state_disturbance[0,0], &inc) blas.{{prefix}}axpy(&nobs_posdef, &alpha, &self.simulated_smoother.smoothed_state_disturbance[0,0], &inc, &self.simulated_state_disturbance[0,0], &inc) if self.simulation_output & SIMULATE_STATE: # \tilde alpha_t = \hat alpha_t^* + alpha_t^+ blas.{{prefix}}copy(&nobs_kstates, &self.generated_state[0,0], &inc, &self.simulated_state[0,0], &inc) blas.{{prefix}}axpy(&nobs_kstates, &alpha, &self.simulated_smoother.smoothed_state[0,0], &inc, &self.simulated_state[0,0], &inc) cdef {{cython_type}} generate_obs(self, int t, {{cython_type}} * obs, {{cython_type}} * state, {{cython_type}} * variates): cdef: int inc = 1 int k_endog = self.model.k_endog int k_states = self.model.k_states int design_t = 0 int obs_intercept_t = 0 cdef: {{cython_type}} alpha = 1.0 # Get indices for possibly time-varying arrays # Note that this would be problematic if simulating a # time-varying system if the number of simulated observations was # greater than the number of observations in the model (because then # e.g. self.model.design[0,0,design_t] would be an invalid memory # location). # However, this problem is ruled out in the constructor since for # time-varying systems, the number of simulated observations must be # less than the number of observations in the model. if not self.model.time_invariant: if self.model.design.shape[2] > 1: design_t = t if self.model.obs_intercept.shape[1] > 1: obs_intercept_t = t # \\# = d_t + \varepsilon_t blas.{{prefix}}copy(&k_endog, variates, &inc, obs, &inc) blas.{{prefix}}axpy(&k_endog, &alpha, &self.model.obs_intercept[0,obs_intercept_t], &inc, obs, &inc) # y_t = \\# + Z_t alpha_t blas.{{prefix}}gemv("N", &k_endog, &k_states, &alpha, &self.model.design[0,0,design_t], &k_endog, state, &inc, &alpha, obs, &inc) cdef {{cython_type}} generate_state(self, int t, {{cython_type}} * state, {{cython_type}} * input_state, {{cython_type}} * variates): cdef: int inc = 1 int k_states = self.model.k_states int k_posdef = self.model.k_posdef int state_intercept_t = 0 int transition_t = 0 int selection_t = 0 cdef: {{cython_type}} alpha = 1.0 # Get indices for possibly time-varying arrays if not self.model.time_invariant: if self.model.state_intercept.shape[1] > 1: state_intercept_t = t if self.model.transition.shape[2] > 1: transition_t = t if self.model.selection.shape[2] > 1: selection_t = t # \\# = R_t eta_t + c_t blas.{{prefix}}copy(&k_states, &self.model.state_intercept[0,state_intercept_t], &inc, state, &inc) blas.{{prefix}}gemv("N", &k_states, &k_posdef, &alpha, &self.model.selection[0,0,selection_t], &k_states, variates, &inc, &alpha, state, &inc) # alpha_{t+1} = T_t alpha_t + \\# blas.{{prefix}}gemv("N", &k_states, &k_states, &alpha, &self.model.transition[0,0,transition_t], &k_states, input_state, &inc, &alpha, state, &inc) cdef void cholesky(self, {{cython_type}} * source, {{cython_type}} * destination, int n): cdef: int inc = 1 int n2 = n**2 int info if n == 1: destination[0] = source[0]**0.5 else: blas.{{prefix}}copy(&n2, source, &inc, destination, &inc) lapack.{{prefix}}potrf("L", &n, destination, &n, &info) cdef void transform_variates(self, {{cython_type}} * variates, {{cython_type}} * cholesky_factor, int n): cdef: int inc = 1 # Overwrites variate if n == 1: variates[0] = cholesky_factor[0] * variates[0] else: blas.{{prefix}}trmv("L", "N", "N", &n, cholesky_factor, &n, variates, &inc) {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/_smoothers/000077500000000000000000000000001400612667500236145ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/_smoothers/__init__.py000066400000000000000000000000001400612667500257130ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/_smoothers/_alternative.pxd000066400000000000000000000047441400612667500270170ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models - Conventional Kalman Filter declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace ) from statsmodels.tsa.statespace._kalman_filter cimport ( sKalmanFilter, dKalmanFilter, cKalmanFilter, zKalmanFilter ) from statsmodels.tsa.statespace._kalman_smoother cimport ( sKalmanSmoother, dKalmanSmoother, cKalmanSmoother, zKalmanSmoother ) # Single precision cdef int ssmoothed_estimators_measurement_alternative(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) except * cdef int ssmoothed_estimators_time_alternative(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) cdef int ssmoothed_state_alternative(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) cdef int ssmoothed_disturbances_alternative(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) # Double precision cdef int dsmoothed_estimators_measurement_alternative(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) except * cdef int dsmoothed_estimators_time_alternative(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) cdef int dsmoothed_state_alternative(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) cdef int dsmoothed_disturbances_alternative(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) # Single precision complex cdef int csmoothed_estimators_measurement_alternative(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) except * cdef int csmoothed_estimators_time_alternative(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) cdef int csmoothed_state_alternative(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) cdef int csmoothed_disturbances_alternative(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) # Double precision complex cdef int zsmoothed_estimators_measurement_alternative(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) except * cdef int zsmoothed_estimators_time_alternative(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) cdef int zsmoothed_state_alternative(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) cdef int zsmoothed_disturbances_alternative(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) statsmodels-0.12.2/statsmodels/tsa/statespace/_smoothers/_alternative.pyx.in000066400000000000000000000344341400612667500274500ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # Typical imports import numpy as np cimport numpy as np from statsmodels.src.math cimport * cimport scipy.linalg.cython_blas as blas from statsmodels.tsa.statespace._kalman_smoother cimport ( SMOOTHER_STATE, SMOOTHER_STATE_COV, SMOOTHER_DISTURBANCE, SMOOTHER_DISTURBANCE_COV ) {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} # ### Alternative conventional Kalman smoother # # The following are the above routines as defined in the conventional Kalman # smoother. # # See Durbin and Koopman (2012) Chapter 4 cdef int {{prefix}}smoothed_estimators_measurement_alternative({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model) except *: cdef: int i int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 if model._nmissing == model.k_endog: # $L_t = T_t$ blas.{{prefix}}copy(&model._k_states2, model._transition, &inc, smoother._tmpL, &inc) return 1 # $C_t = (I - P_t Z_t' F_t^{-1} Z_t)$ # $C_t = (I - \\#_1 \\#_3)$ # $(m \times m) = (m \times m) + (m \times p) (p \times m)$ # (this is required for any type of smoothing) blas.{{prefix}}copy(&model._k_states2, model._transition, &inc, smoother._tmpL, &inc) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_endog, &gamma, kfilter._tmp1, &kfilter.k_states, kfilter._tmp3, &kfilter.k_endog, &beta, smoother._tmpL, &kfilter.k_states) for i in range(model._k_states): smoother.tmpL[i,i] = smoother.tmpL[i,i] + 1 # Scaled smoothed estimator # $\tilde r_{t} = Z_n' F_n^{-1} v_n + C_t' \hat r_n$ # $\tilde r_{t} = \\#_3' v_n + C_t' \hat r_n$ # $(m \times 1) = (m \times p) (p \times 1) + (m \times m) (m \times 1)$ if smoother.smoother_output & (SMOOTHER_STATE | SMOOTHER_DISTURBANCE): blas.{{prefix}}gemv("T", &model._k_states, &model._k_states, &alpha, smoother._tmpL, &kfilter.k_states, smoother._input_scaled_smoothed_estimator, &inc, &beta, smoother._tmp0, &inc) blas.{{prefix}}copy(&model._k_states, smoother._tmp0, &inc, smoother._input_scaled_smoothed_estimator, &inc) blas.{{prefix}}gemv("T", &model._k_endog, &model._k_states, &alpha, kfilter._tmp3, &kfilter.k_endog, &kfilter.forecast_error[0, smoother.t], &inc, &alpha, smoother._input_scaled_smoothed_estimator, &inc) # Scaled smoothed estimator covariance matrix # $\tilde N_{t} = Z_t' F_t^{-1} Z_t + C_t' \hat N_t C_t$ # $\tilde N_{t} = Z_t' \\#_3 + C_t' \hat N_t C_t$ # $(m \times m) = (m \times p) (p \times m) + (m \times m) (m \times m) (m \times m)$ if smoother.smoother_output & (SMOOTHER_STATE_COV | SMOOTHER_DISTURBANCE_COV): blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, smoother._tmpL, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmpL, &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states) blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_endog, &alpha, model._design, &model._k_endog, kfilter._tmp3, &kfilter.k_endog, &alpha, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states) # $L_t = T_t C_t$ # $(m \times m) = (m \times m) (m \times m)$ blas.{{prefix}}copy(&model._k_states2, smoother._tmpL, &inc, smoother._tmp0, &inc) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, model._transition, &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._tmpL, &kfilter.k_states) # Smoothing error # $u_t = \\#_2 - K_t' \tilde r_{t+1}$ # $(p \times 1) = (p \times 1) - (p \times m) (m \times 1)$ if smoother.smoother_output & (SMOOTHER_DISTURBANCE): blas.{{prefix}}copy(&kfilter.k_endog, kfilter._tmp2, &inc, smoother._smoothing_error, &inc) if smoother.t < model.nobs - 1: blas.{{prefix}}gemv("T", &model._k_states, &model._k_endog, &gamma, kfilter._kalman_gain, &kfilter.k_states, &smoother.scaled_smoothed_estimator[0, smoother.t+1], &inc, &alpha, smoother._smoothing_error, &inc) cdef int {{prefix}}smoothed_estimators_time_alternative({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef: int i int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 if smoother.t == 0: return 1 # Scaled smoothed estimator # $\hat r_{t-1} = T_t' \tilde r_t$ # $(m \times 1) = (m \times m) (m \times 1) if smoother.smoother_output & (SMOOTHER_STATE | SMOOTHER_DISTURBANCE): blas.{{prefix}}gemv("T", &model._k_states, &model._k_states, &alpha, model._transition, &kfilter.k_states, smoother._input_scaled_smoothed_estimator, &inc, &beta, smoother._scaled_smoothed_estimator, &inc) # Scaled smoothed estimator covariance matrix # $\hat N_{t-1} = T_t' \tilde N_t T_t$ # $(m \times m) = (m \times p) (m \times m) (m \times m)$ if smoother.smoother_output & (SMOOTHER_STATE_COV | SMOOTHER_DISTURBANCE_COV): blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, model._transition, &kfilter.k_states, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, model._transition, &kfilter.k_states, &beta, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states) cdef int {{prefix}}smoothed_state_alternative({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef int i, j cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # Need to clear out the scaled_smoothed_estimator and # scaled_smoothed_estimator_cov in case we're re-running the filter if smoother.t == model.nobs - 1: smoother.scaled_smoothed_estimator[:, model.nobs-1] = 0 smoother.scaled_smoothed_estimator_cov[:, :, model.nobs-1] = 0 # Smoothed state if smoother.smoother_output & SMOOTHER_STATE: # $\hat \alpha_t = a_t|t + P_t|t \hat r_t$ # $(m \times 1) = (m \times 1) + (m \times m) (m \times 1)$ blas.{{prefix}}copy(&kfilter.k_states, &kfilter.filtered_state[0,smoother.t], &inc, smoother._smoothed_state, &inc) blas.{{prefix}}gemv("N", &model._k_states, &model._k_states, &alpha, &kfilter.filtered_state_cov[0, 0, smoother.t], &kfilter.k_states, smoother._input_scaled_smoothed_estimator, &inc, &alpha, smoother._smoothed_state, &inc) # Smoothed state covariance if smoother.smoother_output & SMOOTHER_STATE_COV: # $V_t = P_t|t [I - \hat N_t P_t|t]$ # $(m \times m) = (m \times m) [(m \times m) - (m \times m) (m \times m)]$ blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &gamma, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, &kfilter.filtered_state_cov[0, 0, smoother.t], &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) for i in range(kfilter.k_states): smoother.tmp0[i,i] = 1 + smoother.tmp0[i,i] blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, &kfilter.filtered_state_cov[0,0,smoother.t], &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._smoothed_state_cov, &kfilter.k_states) cdef int {{prefix}}smoothed_disturbances_alternative({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef int i, j cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # At this point $\tilde r_t$ has been computed, and is stored in # scaled_smoothed_estimator[:, t] but $\varepsilon_t$ depends # on $\tilde r_{t+1}$, which is stored in scaled_smoothed_estimator[:, t+1] # Temporary arrays # $\\#_0 = R_t Q_t$ # $(m \times r) = (m \times r) (r \times r)$ if smoother.smoother_output & (SMOOTHER_DISTURBANCE | SMOOTHER_DISTURBANCE_COV): blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_posdef, &model._k_posdef, &alpha, model._selection, &model._k_states, model._state_cov, &model._k_posdef, &beta, smoother._tmp0, &kfilter.k_states) if smoother.smoother_output & SMOOTHER_DISTURBANCE: # Smoothed measurement disturbance # $\hat \varepsilon_t = H_t u_t$ # $(p \times 1) = (p \times p) (p \times 1)$ blas.{{prefix}}gemv("N", &model._k_endog, &model._k_endog, &alpha, model._obs_cov, &model._k_endog, smoother._smoothing_error, &inc, &beta, smoother._smoothed_measurement_disturbance, &inc) # Smoothed state disturbance # $\hat \eta_t = \\#_0' \tilde r_{t+1}$ # $(r \times 1) = (r \times m) (m \times 1)$ blas.{{prefix}}gemv("T", &model._k_states, &model._k_posdef, &alpha, smoother._tmp0, &kfilter.k_states, &smoother.scaled_smoothed_estimator[0, smoother.t+1], &inc, &beta, smoother._smoothed_state_disturbance, &inc) if smoother.smoother_output & SMOOTHER_DISTURBANCE_COV: # $\\#_00 = K_t H_t$ # $(m \times p) = (m \times p) (p \times p)$ blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_endog, &model._k_endog, &alpha, kfilter._kalman_gain, &kfilter.k_states, model._obs_cov, &model._k_endog, &beta, smoother._tmp00, &kfilter.k_states) # Smoothed measurement disturbance covariance matrix # $Var(\varepsilon_t | Y_n) = H_t - H_t \\#_4 - \\#_00' \tilde N_t \\#_00$ # $(p \times p) = (p \times p) - (p \times p) (p \times p) - (p \times m) (m \times m) (m \times p)$ blas.{{prefix}}gemm("N", "N", &model._k_endog, &model._k_endog, &model._k_endog, &gamma, model._obs_cov, &model._k_endog, kfilter._tmp4, &kfilter.k_endog, &beta, smoother._smoothed_measurement_disturbance_cov, &kfilter.k_endog) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_endog, &model._k_states, &alpha, &smoother.scaled_smoothed_estimator_cov[0, 0, smoother.t+1], &kfilter.k_states, smoother._tmp00, &kfilter.k_states, &beta, smoother._tmp000, &kfilter.k_states) blas.{{prefix}}gemm("T", "N", &model._k_endog, &model._k_endog, &model._k_states, &gamma, smoother._tmp00, &kfilter.k_states, smoother._tmp000, &kfilter.k_states, &alpha, smoother._smoothed_measurement_disturbance_cov, &kfilter.k_endog) # blas.{{prefix}}axpy(&model._k_endog2, &alpha, # model._obs_cov, &inc, # smoother._smoothed_measurement_disturbance_cov, &inc) for i in range(kfilter.k_endog): for j in range(i+1): smoother._smoothed_measurement_disturbance_cov[i + j*kfilter.k_endog] = model._obs_cov[i + j*model._k_endog] + smoother._smoothed_measurement_disturbance_cov[i + j*kfilter.k_endog] if not i == j: smoother._smoothed_measurement_disturbance_cov[j + i*kfilter.k_endog] = model._obs_cov[j + i*model._k_endog] + smoother._smoothed_measurement_disturbance_cov[j + i*kfilter.k_endog] # Smoothed state disturbance covariance matrix # $Var(\eta_t | Y_n) = Q_t - \\#_0' \tilde N_t \\#_0$ # $(r \times r) = (r \times r) - (r \times m) (m \times m) (m \times r)$ blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_posdef, &model._k_states, &alpha, &smoother.scaled_smoothed_estimator_cov[0, 0, smoother.t+1], &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._tmpL, &kfilter.k_states) blas.{{prefix}}copy(&model._k_posdef2, model._state_cov, &inc, smoother._smoothed_state_disturbance_cov, &inc) blas.{{prefix}}gemm("T", "N", &model._k_posdef, &model._k_posdef, &model._k_states, &gamma, smoother._tmp0, &kfilter.k_states, smoother._tmpL, &kfilter.k_states, &alpha, smoother._smoothed_state_disturbance_cov, &kfilter.k_posdef) {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/_smoothers/_classical.pxd000066400000000000000000000040141400612667500264250ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models - Conventional Kalman Filter declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace ) from statsmodels.tsa.statespace._kalman_filter cimport ( sKalmanFilter, dKalmanFilter, cKalmanFilter, zKalmanFilter ) from statsmodels.tsa.statespace._kalman_smoother cimport ( sKalmanSmoother, dKalmanSmoother, cKalmanSmoother, zKalmanSmoother ) # Single precision cdef int ssmoothed_estimators_measurement_classical(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) except * cdef int ssmoothed_estimators_time_classical(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) cdef int ssmoothed_state_classical(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) # Double precision cdef int dsmoothed_estimators_measurement_classical(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) except * cdef int dsmoothed_estimators_time_classical(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) cdef int dsmoothed_state_classical(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) # Single precision complex cdef int csmoothed_estimators_measurement_classical(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) except * cdef int csmoothed_estimators_time_classical(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) cdef int csmoothed_state_classical(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) # Double precision complex cdef int zsmoothed_estimators_measurement_classical(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) except * cdef int zsmoothed_estimators_time_classical(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) cdef int zsmoothed_state_classical(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) statsmodels-0.12.2/statsmodels/tsa/statespace/_smoothers/_classical.pyx.in000066400000000000000000000260561400612667500270710ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models Author: Chad Fulton License: Simplified-BSD Notes ----- The dimensions used in all the BLAS / LAPACK calls below use the following convention: - The dimensions of the arrays *as they are to be manipulated* are all defined as model._k_* - If the array in question is defined in the Statespace object (obs, obs_intercept, design, obs_cov, state_intercept, transition, selection, state_cov, selected_state_cov), then the dimension in-memory is defined as model._k_* This is because the in-memory shape of matrices changes according to whether or not data is missing and whether or not the generalized collapse transform is applied. - If the array in question is defined in the Kalman filter object (forecast_*, filtered_*, predicted_*, etc.), then the dimension in-memory is defined as kfilter.k_* This is because the in-memory shape of matrices only changes according to filter_method. - If the array in question is defined in the Kalman smoother object (smoothed_*, etc.), then the dimension in-memory is defined as kfilter.k_* This is because the in-memory shape of matrices only changes according to filter_method. Thus, for example, a ?gemm call has the following signature: dgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc) - m, n, and k are the dimensions *as they are to be manipulated*, and are always defined as model._k_* - lda, ldb, and ldc are the *in-memory* dimension, and they are set as model._k_* if the array is defined in the Statespace object, otherwise (in either the filter or smoother cases) they are set as kfilter.k_* Note that for ?copy calls, the number of elements to be copied is defined to be the dimension in memory of the array that is being copied *from*. """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # Typical imports import numpy as np cimport numpy as np from statsmodels.src.math cimport * cimport scipy.linalg.cython_blas as blas cimport scipy.linalg.cython_lapack as lapack from statsmodels.tsa.statespace._kalman_smoother cimport ( SMOOTHER_STATE, SMOOTHER_STATE_COV, SMOOTHER_DISTURBANCE, SMOOTHER_DISTURBANCE_COV ) {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} # ### Classical Kalman smoother # # The following are the above routines as defined in the conventional Kalman # smoother. # # See Durbin and Koopman (2012) Chapter 4.6.1 cdef int {{prefix}}smoothed_estimators_measurement_classical({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model) except *: cdef: int i, j, info int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 {{cython_type}} tmp # Factorize the predicted state covariance matrix blas.{{prefix}}copy(&kfilter.k_states2, &kfilter.predicted_state_cov[0,0,smoother.t+1], &inc, smoother._tmpL, &inc) lapack.{{prefix}}potrf("L", &kfilter.k_states, smoother._tmpL, &kfilter.k_states, &info) if info < 0: raise np.linalg.LinAlgError('Illegal value in predicted state' ' covariance matrix encountered at' ' period %d' % smoother.t) if info > 0: raise np.linalg.LinAlgError('Singular predicted state covariance' ' matrix encountered at period %d' % smoother.t) # Scaled smoothed estimator # $r_t = P_{t+1}^{-1} (\hat \alpha_{t+1} - a_{t+1})$ # $(m \times 1) = (m \times m) [(m \times 1) - (m \times 1)]$ # Note: save $r_t$ as _input_scaled_smoothed_estimator not as # _scaled_smoothed_estimator if smoother.t < model.nobs-1 and smoother.smoother_output & (SMOOTHER_STATE | SMOOTHER_DISTURBANCE): blas.{{prefix}}copy(&kfilter.k_states, &smoother.smoothed_state[0, smoother.t+1], &inc, smoother._input_scaled_smoothed_estimator, &inc) blas.{{prefix}}axpy(&kfilter.k_states, &gamma, &kfilter.predicted_state[0,smoother.t+1], &inc, smoother._input_scaled_smoothed_estimator, &inc) lapack.{{prefix}}potrs("L", &kfilter.k_states, &inc, smoother._tmpL, &kfilter.k_states, smoother._input_scaled_smoothed_estimator, &kfilter.k_states, &info) if info < 0: raise np.linalg.LinAlgError('Illegal value in predicted state' ' covariance matrix encountered at' ' period %d' % smoother.t) # Scaled smoothed estimator covariance matrix # $N_t = P_{t+1}^{-1} (P_{t+1} - V_{t+1}) P_{t+1}^{-1} # $(m \times m) = (m \times p) (p \times m) + (m \times m) (m \times m) (m \times m)$ # Note: save $N_t$ as _input_scaled_smoothed_estimator_cov not as # _scaled_smoothed_estimator_cov if smoother.t < model.nobs-1 and smoother.smoother_output & (SMOOTHER_STATE_COV | SMOOTHER_DISTURBANCE_COV): blas.{{prefix}}copy(&kfilter.k_states2, &kfilter.predicted_state_cov[0, 0, smoother.t+1], &inc, smoother._input_scaled_smoothed_estimator_cov, &inc) blas.{{prefix}}axpy(&kfilter.k_states2, &gamma, &smoother.smoothed_state_cov[0, 0, smoother.t+1], &inc, smoother._input_scaled_smoothed_estimator_cov, &inc) lapack.{{prefix}}potrs("L", &kfilter.k_states, &kfilter.k_states, smoother._tmpL, &kfilter.k_states, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, &info) if info < 0: raise np.linalg.LinAlgError('Illegal value in predicted state' ' covariance matrix encountered at' ' period %d' % smoother.t) # transpose for i in range(kfilter.k_states): for j in range(i, kfilter.k_states): if i == j: continue tmp = smoother.scaled_smoothed_estimator_cov[i,j,smoother.t+1] smoother.scaled_smoothed_estimator_cov[i,j,smoother.t+1] = smoother.scaled_smoothed_estimator_cov[j,i,smoother.t+1] smoother.scaled_smoothed_estimator_cov[j,i,smoother.t+1] = tmp lapack.{{prefix}}potrs("L", &kfilter.k_states, &kfilter.k_states, smoother._tmpL, &kfilter.k_states, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, &info) if info < 0: raise np.linalg.LinAlgError('Illegal value in predicted state' ' covariance matrix encountered at' ' period %d' % smoother.t) # Smoothing error # $u_t = \\#_2 - K_t' r_t$ # $(p \times 1) = (p \times 1) - (p \times m) (m \times 1)$ if smoother.smoother_output & (SMOOTHER_DISTURBANCE): if not model._nmissing == model.k_endog: blas.{{prefix}}copy(&kfilter.k_endog, kfilter._tmp2, &inc, smoother._smoothing_error, &inc) blas.{{prefix}}gemv("T", &model._k_states, &model._k_endog, &gamma, kfilter._kalman_gain, &kfilter.k_states, smoother._input_scaled_smoothed_estimator, &inc, &alpha, smoother._smoothing_error, &inc) # $L_t = (T_t - K_t Z_t)$ # $(m \times m) = (m \times m) + (m \times p) (p \times m)$ # (this is required for any type of smoothing) blas.{{prefix}}copy(&model._k_states2, model._transition, &inc, smoother._tmpL, &inc) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_endog, &gamma, kfilter._kalman_gain, &kfilter.k_states, model._design, &model._k_endog, &alpha, smoother._tmpL, &kfilter.k_states) cdef int {{prefix}}smoothed_estimators_time_classical({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): pass cdef int {{prefix}}smoothed_state_classical({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef int i, j cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 if (smoother.smoother_output & SMOOTHER_STATE) or (smoother.smoother_output & SMOOTHER_STATE_COV): blas.{{prefix}}gemm("N", "T", &model._k_states, &model._k_states, &model._k_states, &alpha, &kfilter.filtered_state_cov[0, 0, smoother.t], &kfilter.k_states, model._transition, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) # Smoothed state if smoother.smoother_output & SMOOTHER_STATE: # $\hat \alpha_t = a_t|t + P_t|t T_t' r_t$ # $(m \times 1) = (m \times 1) + (m \times m) (m \times 1)$ blas.{{prefix}}copy(&kfilter.k_states, &kfilter.filtered_state[0,smoother.t], &inc, smoother._smoothed_state, &inc) blas.{{prefix}}gemv("N", &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, smoother._input_scaled_smoothed_estimator, &inc, &alpha, smoother._smoothed_state, &inc) # Smoothed state covariance if smoother.smoother_output & SMOOTHER_STATE_COV: # $V_t = P_t|t [I - T_t' N_t T_t P_t|t]$ # $(m \times m) = (m \times m) [(m \times m) - (m \times m) (m \times m)]$ blas.{{prefix}}gemm("N", "T", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._tmpL2, &kfilter.k_states) blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &gamma, model._transition, &kfilter.k_states, smoother._tmpL2, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) for i in range(kfilter.k_states): smoother.tmp0[i,i] = 1 + smoother.tmp0[i,i] blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, &kfilter.filtered_state_cov[0,0,smoother.t], &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._smoothed_state_cov, &kfilter.k_states) {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/_smoothers/_conventional.pxd000066400000000000000000000076441400612667500272020ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models - Conventional Kalman Filter declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace ) from statsmodels.tsa.statespace._kalman_filter cimport ( sKalmanFilter, dKalmanFilter, cKalmanFilter, zKalmanFilter ) from statsmodels.tsa.statespace._kalman_smoother cimport ( sKalmanSmoother, dKalmanSmoother, cKalmanSmoother, zKalmanSmoother ) # Single precision cdef int ssmoothed_estimators_missing_conventional(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) except * cdef int ssmoothed_disturbances_missing_conventional(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) cdef int ssmoothed_estimators_measurement_conventional(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) except * cdef int ssmoothed_estimators_time_conventional(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) cdef int ssmoothed_state_conventional(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) cdef int ssmoothed_state_autocov_conventional(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) cdef int ssmoothed_disturbances_conventional(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) # Double precision cdef int dsmoothed_estimators_missing_conventional(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) except * cdef int dsmoothed_disturbances_missing_conventional(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) cdef int dsmoothed_estimators_measurement_conventional(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) except * cdef int dsmoothed_estimators_time_conventional(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) cdef int dsmoothed_state_conventional(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) cdef int dsmoothed_state_autocov_conventional(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) cdef int dsmoothed_disturbances_conventional(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) # Single precision complex cdef int csmoothed_estimators_missing_conventional(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) except * cdef int csmoothed_disturbances_missing_conventional(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) cdef int csmoothed_estimators_measurement_conventional(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) except * cdef int csmoothed_estimators_time_conventional(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) cdef int csmoothed_state_conventional(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) cdef int csmoothed_state_autocov_conventional(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) cdef int csmoothed_disturbances_conventional(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) # Double precision complex cdef int zsmoothed_estimators_missing_conventional(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) except * cdef int zsmoothed_disturbances_missing_conventional(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) cdef int zsmoothed_estimators_measurement_conventional(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) except * cdef int zsmoothed_estimators_time_conventional(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) cdef int zsmoothed_state_conventional(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) cdef int zsmoothed_state_autocov_conventional(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) cdef int zsmoothed_disturbances_conventional(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) statsmodels-0.12.2/statsmodels/tsa/statespace/_smoothers/_conventional.pyx.in000066400000000000000000000507261400612667500276330ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models Author: Chad Fulton License: Simplified-BSD Notes ----- The dimensions used in all the BLAS / LAPACK calls below use the following convention: - The dimensions of the arrays *as they are to be manipulated* are all defined as model._k_* - If the array in question is defined in the Statespace object (obs, obs_intercept, design, obs_cov, state_intercept, transition, selection, state_cov, selected_state_cov), then the dimension in-memory is defined as model._k_* This is because the in-memory shape of matrices changes according to whether or not data is missing and whether or not the generalized collapse transform is applied. - If the array in question is defined in the Kalman filter object (forecast_*, filtered_*, predicted_*, etc.), then the dimension in-memory is defined as kfilter.k_* This is because the in-memory shape of matrices only changes according to filter_method. - If the array in question is defined in the Kalman smoother object (smoothed_*, etc.), then the dimension in-memory is defined as kfilter.k_* This is because the in-memory shape of matrices only changes according to filter_method. Thus, for example, a ?gemm call has the following signature: dgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc) - m, n, and k are the dimensions *as they are to be manipulated*, and are always defined as model._k_* - lda, ldb, and ldc are the *in-memory* dimension, and they are set as model._k_* if the array is defined in the Statespace object, otherwise (in either the filter or smoother cases) they are set as kfilter.k_* Note that for ?copy calls, the number of elements to be copied is defined to be the dimension in memory of the array that is being copied *from*. """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # Typical imports import numpy as np cimport numpy as np from statsmodels.src.math cimport * cimport scipy.linalg.cython_blas as blas from statsmodels.tsa.statespace._kalman_smoother cimport ( SMOOTHER_STATE, SMOOTHER_STATE_COV, SMOOTHER_DISTURBANCE, SMOOTHER_DISTURBANCE_COV ) {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} # ### Missing Observation Conventional Kalman smoother # # See Durbin and Koopman (2012) Chapter 4.10 # # Here k_endog is the same as usual, but the design matrix and observation # covariance matrix are enforced to be zero matrices. cdef int {{prefix}}smoothed_estimators_missing_conventional({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model) except *: cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # Scaled smoothed estimator # $r_{t-1} = T_t' r_t$ # $(m \times 1) = (m \times m) (m \times 1)$ # Note: save $r_{t-1}$ as scaled_smoothed_estimator[t] rather than # as scaled_smoothed_estimator[t-1] because we actually need to store # T+1 of them (r_{T-1} to r_{-1} -> r_T to r_0) if smoother.smoother_output & (SMOOTHER_STATE | SMOOTHER_DISTURBANCE): blas.{{prefix}}gemv("T", &model._k_states, &model._k_states, &alpha, model._transition, &model._k_states, smoother._input_scaled_smoothed_estimator, &inc, &beta, smoother._scaled_smoothed_estimator, &inc) # Scaled smoothed estimator covariance matrix # $N_{t-1} = T_t' N_t T_t$ # $(m \times m) = (m \times m) (m \times m) (m \times m)$ # Note: save $N_{t-1}$ as scaled_smoothed_estimator_cov[t] rather # than as scaled_smoothed_estimator_cov[t-1] because we actually # need to store T+1 of them (N_{T-1} to N_{-1} -> N_T to N_0) if smoother.smoother_output & (SMOOTHER_STATE_COV | SMOOTHER_DISTURBANCE_COV): blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, model._transition, &model._k_states, &beta, smoother._tmp0, &kfilter.k_states) blas.{{prefix}}gemm("T", "N", &kfilter.k_states, &kfilter.k_states, &kfilter.k_states, &alpha, model._transition, &model._k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states) # $L_t = T_t$ blas.{{prefix}}copy(&model._k_states2, model._transition, &inc, smoother._tmpL, &inc) # Smoothing error # It is undefined here, since F_t^{-1} is nan # for i in range(kfilter.k_endog): # smoother._smoothing_error[i] = 0 # Smoothing error # $u_t = - K_t' r_t$ # $(p \times 1) = (p \times 1) - (p \times m) (m \times 1)$ # TODO in the missing case, I think K_t is defined to be zeros, so this # would be unnecessary if smoother.smoother_output & (SMOOTHER_DISTURBANCE): blas.{{prefix}}gemv("T", &model._k_states, &model._k_endog, &gamma, kfilter._kalman_gain, &kfilter.k_states, smoother._input_scaled_smoothed_estimator, &inc, &beta, smoother._smoothing_error, &inc) cdef int {{prefix}}smoothed_disturbances_missing_conventional({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # Temporary arrays # $\\#_0 = R_t Q_t$ # $(m \times r) = (m \times r) (r \times r)$ if smoother.smoother_output & (SMOOTHER_DISTURBANCE | SMOOTHER_DISTURBANCE_COV): blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_posdef, &model._k_posdef, &alpha, model._selection, &model._k_states, model._state_cov, &model._k_posdef, &beta, smoother._tmp0, &kfilter.k_states) if smoother.smoother_output & SMOOTHER_DISTURBANCE: # Smoothed state disturbance # $\hat \eta_t = \\#_0' r_t$ # $(r \times 1) = (r \times m) (m \times 1)$ blas.{{prefix}}gemv("T", &kfilter.k_states, &kfilter.k_posdef, &alpha, smoother._tmp0, &kfilter.k_states, smoother._input_scaled_smoothed_estimator, &inc, &beta, smoother._smoothed_state_disturbance, &inc) if smoother.smoother_output & SMOOTHER_DISTURBANCE_COV: # Smoothed state disturbance covariance matrix # $Var(\eta_t | Y_n) = Q_t - \\#_0' N_t \\#_0$ # $(r \times r) = (r \times r) - (r \times m) (m \times m) (m \times r)$ blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_posdef, &model._k_states, &alpha, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._tmpL, &kfilter.k_states) blas.{{prefix}}copy(&model._k_posdef2, model._state_cov, &inc, smoother._smoothed_state_disturbance_cov, &inc) blas.{{prefix}}gemm("T", "N", &model._k_posdef, &model._k_posdef, &model._k_states, &gamma, smoother._tmp0, &kfilter.k_states, smoother._tmpL, &kfilter.k_states, &alpha, smoother._smoothed_state_disturbance_cov, &kfilter.k_posdef) # Just return the unconditional distribution for the measurement # disturbances corresponding to a missing observation # TODO this is not explicitly addressed in Durbin and Koopman Chapter 4 # or in Koopman (1993) - need to find a source for if this is correct # Note: this is what the MATLAB ssm toolbox does, also # Smoothed measurement disturbances have unconditional expected # value of 0, so no need to do anything # Smoothed measurement and state disturbances have unconditional covariance # matrix of $H_t, Q_t$, respectively blas.{{prefix}}copy(&model._k_endog2, model._obs_cov, &inc, smoother._smoothed_measurement_disturbance_cov, &inc) # ### Conventional Kalman smoother # # The following are the above routines as defined in the conventional Kalman # smoother. # # See Durbin and Koopman (2012) Chapter 4 cdef int {{prefix}}smoothed_estimators_measurement_conventional({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model) except *: cdef: int i int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # Smoothing error # $u_t = \\#_2 - K_t' r_t$ # $(p \times 1) = (p \times 1) - (p \times m) (m \times 1)$ if smoother.smoother_output & (SMOOTHER_DISTURBANCE): blas.{{prefix}}copy(&model._k_endog, kfilter._tmp2, &inc, smoother._smoothing_error, &inc) blas.{{prefix}}gemv("T", &model._k_states, &model._k_endog, &gamma, kfilter._kalman_gain, &kfilter.k_states, smoother._input_scaled_smoothed_estimator, &inc, &alpha, smoother._smoothing_error, &inc) # $L_t = (T_t - K_t Z_t)$ # $(m \times m) = (m \times m) + (m \times p) (p \times m)$ # (this is required for any type of smoothing) blas.{{prefix}}copy(&model._k_states2, model._transition, &inc, smoother._tmpL, &inc) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_endog, &gamma, kfilter._kalman_gain, &kfilter.k_states, model._design, &model._k_endog, &alpha, smoother._tmpL, &kfilter.k_states) # Scaled smoothed estimator # $r_{t-1} = Z_t' \\#_2 + L_t' r_t$ # $(m \times 1) = (m \times p) (p \times 1) + (m \times m) (m \times 1)$ # Note: save $r_{t-1}$ as scaled_smoothed_estimator[t] rather than # as scaled_smoothed_estimator[t-1] because we actually need to store # T+1 of them (r_{T-1} to r_{-1} -> r_T to r_0) if smoother.smoother_output & (SMOOTHER_STATE | SMOOTHER_DISTURBANCE): blas.{{prefix}}gemv("T", &model._k_states, &model._k_states, &alpha, smoother._tmpL, &kfilter.k_states, smoother._input_scaled_smoothed_estimator, &inc, &beta, smoother._scaled_smoothed_estimator, &inc) blas.{{prefix}}gemv("T", &model._k_endog, &model._k_states, &alpha, model._design, &model._k_endog, kfilter._tmp2, &inc, &alpha, smoother._scaled_smoothed_estimator, &inc) # Scaled smoothed estimator covariance matrix # $N_{t-1} = Z_t' \\#_3 + L_t' N_t L_t$ # $(m \times m) = (m \times p) (p \times m) + (m \times m) (m \times m) (m \times m)$ # Note: save $N_{t-1}$ as scaled_smoothed_estimator_cov[t] rather # than as scaled_smoothed_estimator_cov[t-1] because we actually # need to store T+1 of them (N_{T-1} to N_{-1} -> N_T to N_0) if smoother.smoother_output & (SMOOTHER_STATE_COV | SMOOTHER_DISTURBANCE_COV): blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, smoother._tmpL, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmpL, &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states) blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_endog, &alpha, model._design, &model._k_endog, kfilter._tmp3, &kfilter.k_endog, &alpha, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states) cdef int {{prefix}}smoothed_estimators_time_conventional({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): pass cdef int {{prefix}}smoothed_state_conventional({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef int i, j cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # Smoothed state if smoother.smoother_output & SMOOTHER_STATE: # $\hat \alpha_t = a_t + P_t r_{t-1}$ # $(m \times 1) = (m \times 1) + (m \times m) (m \times 1)$ blas.{{prefix}}copy(&kfilter.k_states, &kfilter.predicted_state[0,smoother.t], &inc, smoother._smoothed_state, &inc) blas.{{prefix}}gemv("N", &model._k_states, &model._k_states, &alpha, &kfilter.predicted_state_cov[0,0,smoother.t], &kfilter.k_states, smoother._scaled_smoothed_estimator, &inc, &alpha, smoother._smoothed_state, &inc) # Smoothed state covariance if smoother.smoother_output & SMOOTHER_STATE_COV: # $V_t = P_t [I - N_{t-1} P_t]$ # $(m \times m) = (m \times m) [(m \times m) - (m \times m) (m \times m)]$ blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &gamma, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states, &kfilter.predicted_state_cov[0,0,smoother.t], &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) for i in range(kfilter.k_states): smoother.tmp0[i,i] = 1 + smoother.tmp0[i,i] blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, &kfilter.predicted_state_cov[0,0,smoother.t], &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._smoothed_state_cov, &kfilter.k_states) cdef int {{prefix}}smoothed_state_autocov_conventional({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef: int i int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # This function computes Cov(alpha_{t+1}, alpha_t) = Cov(alpha_t, alpha_{t+1})' # From Durbin and Koopman, 2012, Chapter 4.7 # Cov(alpha_{t+1}, alpha_t) = (I - P_{t+1} N_{t}) L_t P_t blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &gamma, &kfilter.predicted_state_cov[0,0,smoother.t+1], &kfilter.k_states, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) for i in range(kfilter.k_states): smoother.tmp0[i,i] = 1 + smoother.tmp0[i,i] blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &alpha, smoother._tmpL, &kfilter.k_states, &kfilter.predicted_state_cov[0,0,smoother.t], &kfilter.k_states, &beta, smoother._tmp_autocov, &kfilter.k_states) blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &alpha, smoother._tmp0, &kfilter.k_states, smoother._tmp_autocov, &kfilter.k_states, &beta, smoother._smoothed_state_autocov, &kfilter.k_states) cdef int {{prefix}}smoothed_disturbances_conventional({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef int i, j cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # Temporary arrays # $\\#_0 = R_t Q_t$ # $(m \times r) = (m \times r) (r \times r)$ if smoother.smoother_output & (SMOOTHER_DISTURBANCE | SMOOTHER_DISTURBANCE_COV): blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_posdef, &model._k_posdef, &alpha, model._selection, &model._k_states, model._state_cov, &model._k_posdef, &beta, smoother._tmp0, &kfilter.k_states) if smoother.smoother_output & SMOOTHER_DISTURBANCE: # Smoothed measurement disturbance # $\hat \varepsilon_t = H_t u_t$ # $(p \times 1) = (p \times p) (p \times 1)$ blas.{{prefix}}gemv("N", &model._k_endog, &model._k_endog, &alpha, model._obs_cov, &model._k_endog, smoother._smoothing_error, &inc, &beta, smoother._smoothed_measurement_disturbance, &inc) # Smoothed state disturbance # $\hat \eta_t = \\#_0' r_t$ # $(r \times 1) = (r \times m) (m \times 1)$ blas.{{prefix}}gemv("T", &model._k_states, &model._k_posdef, &alpha, smoother._tmp0, &kfilter.k_states, smoother._input_scaled_smoothed_estimator, &inc, &beta, smoother._smoothed_state_disturbance, &inc) if smoother.smoother_output & SMOOTHER_DISTURBANCE_COV: # $\\#_00 = K_t H_t$ # $(m \times p) = (m \times p) (p \times p)$ blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_endog, &model._k_endog, &alpha, kfilter._kalman_gain, &kfilter.k_states, model._obs_cov, &model._k_endog, &beta, smoother._tmp00, &kfilter.k_states) # Smoothed measurement disturbance covariance matrix # $Var(\varepsilon_t | Y_n) = H_t - H_t \\#_4 - \\#_00' N_t \\#_00$ # $(p \times p) = (p \times p) - (p \times p) (p \times p) - (p \times m) (m \times m) (m \times p)$ blas.{{prefix}}gemm("N", "N", &model._k_endog, &model._k_endog, &model._k_endog, &gamma, model._obs_cov, &model._k_endog, kfilter._tmp4, &kfilter.k_endog, &beta, smoother._smoothed_measurement_disturbance_cov, &kfilter.k_endog) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_endog, &model._k_states, &alpha, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, smoother._tmp00, &kfilter.k_states, &beta, smoother._tmp000, &kfilter.k_states) blas.{{prefix}}gemm("T", "N", &model._k_endog, &model._k_endog, &model._k_states, &gamma, smoother._tmp00, &kfilter.k_states, smoother._tmp000, &kfilter.k_states, &alpha, smoother._smoothed_measurement_disturbance_cov, &kfilter.k_endog) # blas.{{prefix}}axpy(&model._k_endog2, &alpha, # model._obs_cov, &inc, # smoother._smoothed_measurement_disturbance_cov, &inc) for i in range(kfilter.k_endog): for j in range(i+1): smoother._smoothed_measurement_disturbance_cov[i + j*kfilter.k_endog] = model._obs_cov[i + j*model._k_endog] + smoother._smoothed_measurement_disturbance_cov[i + j*kfilter.k_endog] if not i == j: smoother._smoothed_measurement_disturbance_cov[j + i*kfilter.k_endog] = model._obs_cov[j + i*model._k_endog] + smoother._smoothed_measurement_disturbance_cov[j + i*kfilter.k_endog] # Smoothed state disturbance covariance matrix # $Var(\eta_t | Y_n) = Q_t - \\#_0' N_t \\#_0$ # $(r \times r) = (r \times r) - (r \times m) (m \times m) (m \times r)$ blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_posdef, &model._k_states, &alpha, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._tmpL, &kfilter.k_states) blas.{{prefix}}copy(&model._k_posdef2, model._state_cov, &inc, smoother._smoothed_state_disturbance_cov, &inc) blas.{{prefix}}gemm("T", "N", &model._k_posdef, &model._k_posdef, &model._k_states, &gamma, smoother._tmp0, &kfilter.k_states, smoother._tmpL, &kfilter.k_states, &alpha, smoother._smoothed_state_disturbance_cov, &kfilter.k_posdef) {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/_smoothers/_univariate.pxd000066400000000000000000000040641400612667500266430ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models - Conventional Kalman Filter declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace ) from statsmodels.tsa.statespace._kalman_filter cimport ( sKalmanFilter, dKalmanFilter, cKalmanFilter, zKalmanFilter ) from statsmodels.tsa.statespace._kalman_smoother cimport ( sKalmanSmoother, dKalmanSmoother, cKalmanSmoother, zKalmanSmoother ) # Single precision cdef int ssmoothed_estimators_measurement_univariate(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) except * cdef int ssmoothed_estimators_time_univariate(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) cdef int ssmoothed_disturbances_univariate(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) # Double precision cdef int dsmoothed_estimators_measurement_univariate(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) except * cdef int dsmoothed_estimators_time_univariate(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) cdef int dsmoothed_disturbances_univariate(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) # Single precision complex cdef int csmoothed_estimators_measurement_univariate(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) except * cdef int csmoothed_estimators_time_univariate(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) cdef int csmoothed_disturbances_univariate(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) # Double precision complex cdef int zsmoothed_estimators_measurement_univariate(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) except * cdef int zsmoothed_estimators_time_univariate(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) cdef int zsmoothed_disturbances_univariate(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) statsmodels-0.12.2/statsmodels/tsa/statespace/_smoothers/_univariate.pyx.in000066400000000000000000000642211400612667500272760ustar00rootroot00000000000000#cython: profile=False #cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models Note: there is a typo in Durbin and Koopman (2012) in the equations for the univariate smoothed measurement disturbances and smoothed measurement disturbance covariances. In each equation (p157), the Kalman gain vector K_{t,i} is used, but in fact these should be multiplied by the forecast error covariance F_{t,i}. The original paper on the univariate approach, Koopman and Durbin (2000) has the correct form. The typo arose because the original paper defines the Kalman gain as K_{t,i} = P_{t,i} Z_{t,i}' but the book defines it as K_{t,i} = P_{t,i} Z_{t,i}' F_{t,i}^{-1}, and the book does not correct the disturbances formulas for this change. Furthermore, in analogy to the disturbance smoother from chapter 4, the formula for the univariate covariance ought to be subtracted from the observation covariance. So, what we ought to have is: \hat \varepsilon_{t,i} = \sigma_{t,i}^2 F_{t,i}^{-1} (v_{t,i} - F_{t,i} K_{t,i}' r_{t,i}) Var(\hat \varepsilon_{t,i}) = \sigma_{t,i}^2 - \sigma_{t,i}^4 F_{t,i}^{-2} (v_{t,i} - F_{t,i} K_{t,i}' r_{t,i}) Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # Typical imports import numpy as np cimport numpy as np from statsmodels.src.math cimport * cimport scipy.linalg.cython_blas as blas from statsmodels.tsa.statespace._kalman_smoother cimport ( SMOOTHER_STATE, SMOOTHER_STATE_COV, SMOOTHER_STATE_AUTOCOV, SMOOTHER_DISTURBANCE, SMOOTHER_DISTURBANCE_COV ) {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' combined_suffix = '' if combined_prefix == 'z': combined_suffix = 'u' }} # ### Univariate Kalman smoother # # The following are the routines as defined in the univariate Kalman filter. # # The only modification to the conventional Kalman smoother is the recursive # definition of the scaled smoothing error and the scaled smoothing error # covariance matrix. # # See Durbin and Koopman (2012) Chapter 6.4 cdef int {{prefix}}smoothed_estimators_measurement_univariate({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model) except *: cdef: int i, j, k, inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 {{cython_type}} scalar int k_states = model._k_states # {{cython_type}} [::1, :] tmpL # {{cython_type}} * _tmpL # dim2[0] = self.kfilter.k_states; dim2[1] = self.kfilter.k_states; # self.tmpL = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # Adjust for a VAR transition (i.e. design = [#, 0], where the zeros # correspond to all states except the first k_posdef states) if model.subset_design: k_states = model._k_posdef # Need to clear out the scaled_smoothed_estimator and # scaled_smoothed_estimator_cov in case we're re-running the filter if smoother.t == model.nobs - 1: smoother.scaled_smoothed_estimator[:, model.nobs-1] = 0 smoother.scaled_smoothed_estimator_cov[:, :, model.nobs-1] = 0 # Smoothing error # (not used in the univariate approach) # Given r_{t,0}: # calculate r_{t-1,p}, ..., r_{t-1, 0} and N_{t-1,p}, ..., N_{t-1,0} # Iterate for i in range(kfilter.k_endog-1,-1,-1): if smoother.smoother_output & (SMOOTHER_STATE | SMOOTHER_DISTURBANCE): # K_{t,i}' r_{t,i} (also will need these later for smoothed # disturbances) # Note: zdot and cdot are broken, so have to use gemv for those {{if combined_prefix == 'd'}} smoother._smoothed_measurement_disturbance[i] = ( blas.{{prefix}}dot(&model._k_states, &kfilter._kalman_gain[i*kfilter.k_states], &inc, smoother._scaled_smoothed_estimator, &inc) ) {{else}} blas.{{prefix}}gemv("N", &inc, &model._k_states, &alpha, smoother._scaled_smoothed_estimator, &inc, &kfilter._kalman_gain[i*kfilter.k_states], &inc, &beta, &smoother._smoothed_measurement_disturbance[i], &inc) {{endif}} if smoother.smoother_output & (SMOOTHER_STATE_COV | SMOOTHER_DISTURBANCE_COV): # K_{t,i}' N_{t,i} K_{t,i} (also will need these later for smoothed # disturbance covs) # Note: uses tmp0 # blas.{{prefix}}gemv("N", &model._k_states, &model._k_states, # &alpha, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states, # &kfilter._kalman_gain[i*kfilter.k_states], &inc, # &beta, smoother._tmp0, &inc) blas.{{prefix}}{{if combined_prefix == 'z'}}he{{else}}sy{{endif}}mv("U", &model._k_states, &alpha, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states, &kfilter._kalman_gain[i*kfilter.k_states], &inc, &beta, smoother._tmp0, &inc) # Note: zdot and cdot are broken, so have to use gemv for those {{if combined_prefix == 'd'}} smoother._smoothed_measurement_disturbance_cov[i + i*kfilter.k_endog] = ( blas.{{prefix}}dot(&model._k_states, &kfilter._kalman_gain[i*kfilter.k_states], &inc, smoother._tmp0, &inc) ) {{else}} blas.{{prefix}}gemv("N", &inc, &model._k_states, &alpha, smoother._tmp0, &inc, &kfilter._kalman_gain[i*kfilter.k_states], &inc, &beta, &smoother._smoothed_measurement_disturbance_cov[i*kfilter.k_endog + i], &inc) {{endif}} # In most cases we can use an optimized version of these iterations # that e.g. reduces the number of (m x m) matrix multiplications. # However, it can suffer from catestrophic cancellation (especially for # the first period in the approximate diffuse case, and even more so if # the initial variance is increased to e.g. 1e9), and as a result we # fall back to the more-precise-but-slower version (maybe 4x slower # for large state vectors) when numerical problems seems likely. if smoother.t >= kfilter.loglikelihood_burn and kfilter._forecast_error_cov[i*kfilter.k_endog + i]{{if combined_prefix == 'z'}}.real{{endif}} < 1e5: {{prefix}}fast_iter_smoothed_estimators_measurement_univariate(smoother, kfilter, model, i, k_states) else: {{prefix}}precise_iter_smoothed_estimators_measurement_univariate(smoother, kfilter, model, i, k_states) # Transition for L blas.{{prefix}}copy(&kfilter.k_states2, smoother._tmpL, &inc, smoother._tmpL2, &inc) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, model._transition, &kfilter.k_states, smoother._tmpL2, &kfilter.k_states, &beta, smoother._tmpL, &kfilter.k_states) cdef int {{prefix}}fast_iter_smoothed_estimators_measurement_univariate({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, int i, int k_states): """ Faster version of univariate smoother iteration Uses the following decompositions: $$ \begin{aligned} L_{t,i} & = I_m - K_{t,i} Z_{t,i} \\ r_{t, i-1} & = Z_{t,i}' F_{t,i}^{-1} v_{t,i} + L_{t,i}' r_{t,i} \\ & = Z_{t,i}' F_{t,i}^{-1} v_{t,i} + r_{t,i} - Z_{t,i}' K_{t,i}' r_{t,i} \\ & = r_{t,i} + Z_{t,i}' (F_{t,i}^{-1} v_{t,i} - K_{t,i}' r_{t,i}) \\ N_{t, i-1} & = Z_{t,i}' F_{t,i}^{-1} Z_{t,i} + L_{t,i}' N_{t,i} L_{t,i} \\ & = Z_{t,i}' F_{t,i}^{-1} Z_{t,i} + (I_m - K_{t,i} Z_{t,i})' N_{t,i} (I_m - K_{t,i} Z_{t,i}) \\ & = Z_{t,i}' F_{t,i}^{-1} Z_{t,i} + N_{t,i} - Z_{t,i}' K_{t,i}' N_{t,i} - N_{t,i} K_{t,i} Z_{t,i} + Z_{t,i}' K_{t,i}' N_{t,i} K_{t,i} Z_{t,i} \\ \end{aligned} $$ and $$ \begin{aligned} L_{t,i} & = I_m - K_{t,i} Z_{t,i} \\ L_{t} & = L_{t,n} L_{t,n-1} \dots L_{t,1} \\ L_{t}^n & = L_{t,n} \\ L_{t}^{n-1} & = L_{t,n} L_{t,n-1} \\ & = L_{t,n} (I_m - K_{t,i} Z_{t,i}) \\ & = L_{t,n} - L_{t,n} K_{t,i} Z_{t,i} \\ L_{t}^{n-2} & = L_{t,n} L_{t,n-1} L_{t,n-2} \\ & = L_{t}^{n-1} L_{t,n-2} \\ & = L_{t}^{n-1} - L_{t}^{n-1} K_{t,i} Z_{t,i} \\ \end{aligned} $$ """ cdef: int j, k, inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 {{cython_type}} scalar # Accumulate L_{t,i} so that at the end of the iteration we have L_t # L_{t}^n = L_{t,n} if i == kfilter.k_endog - 1: # Zero the temporary matrix smoother.tmpL[:,:k_states] = 0 # blas.{{prefix}}scal(&kfilter.k_states2, &beta, smoother._tmpL, &inc) # Create the K_{t,i} Z_{t,i} component # (m x p) (m x 1) x (1 x p) blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &k_states, &gamma, &kfilter._kalman_gain[i*kfilter.k_states], &inc, &model._design[i], &model._k_endog, smoother._tmpL, &kfilter.k_states) # Add the identity matrix for j in range(k_states): smoother._tmpL[j + j*kfilter.k_states] = smoother._tmpL[j + j*kfilter.k_states] + 1 # L_{t}^{i} = L_{t,i+1} - (L_{t,i+1} K_{t, i}) Z_{t, i} else: # blas.{{prefix}}copy(&kfilter.k_states2, smoother._tmpL, &inc, smoother._tmp0, &inc) # L_t^i K_{t,i} -> tmpL2 (m x m) (m x 1) blas.{{prefix}}gemv("N", &model._k_states, &model._k_states, &alpha, smoother._tmpL, &kfilter.k_states, &kfilter._kalman_gain[i*kfilter.k_states], &inc, &beta, smoother._tmpL2, &inc) # L_t^i - (L_t^i K_{t,i}) Z_{t,i} -> tmpL (m x 1) (1 x m) # blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &inc, # &gamma, smoother._tmpL2, &kfilter.k_states, # &model._design[i], &model._k_endog, # &alpha, smoother._tmpL, &kfilter.k_states) blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &gamma, smoother._tmpL2, &inc, &model._design[i], &model._k_endog, smoother._tmpL, &kfilter.k_states) # Scaled smoothed estimator # $r_{t,i-1} = Z_{t,i}' v_{t,i} / F_{t,i} + L_{t,i}' r_{t,i}$ # [or] # $r_{t,i-1} = r_{t,i} + Z_{t,i}' (v_{t,i} / F_{t,i} - K_{t,i}' r_{t,i})$ # Note: save $r_{t-1}$ as scaled_smoothed_estimator[t] rather than # as scaled_smoothed_estimator[t-1] because we actually need to store # T+1 of them (r_{T-1} to r_{-1} -> r_T to r_0) if smoother.smoother_output & (SMOOTHER_STATE | SMOOTHER_DISTURBANCE): scalar = kfilter._tmp2[i] - smoother._smoothed_measurement_disturbance[i] blas.{{prefix}}axpy(&k_states, &scalar, &model._design[i], &model._k_endog, smoother._scaled_smoothed_estimator, &inc) if smoother.smoother_output & (SMOOTHER_STATE_COV | SMOOTHER_DISTURBANCE_COV): # Scaled smoothed estimator covariance matrix # $N_{t,i-1} = Z_{t,i}' Z_{t,i} / F_{t,i} + L_{t,i}' N_{t,i} L_{t,i}$ # [or] # $N_{t,i-1} = N_{t,i} + Z_{t,i}' Z_{t,i} (K_{t,i}' N_{t, i} K_{t,i} + 1 / F_{t,i}) - (N_{t,i} K_{t,i} Z_{t,i}) - (N_{t,i} K_{t,i} Z_{t,i})' $ # Note: save $N_{t-1}$ as scaled_smoothed_estimator_cov[t] rather # than as scaled_smoothed_estimator_cov[t-1] because we actually # need to store T+1 of them (N_{T-1} to N_{-1} -> N_T to N_0) # Clear tmpL2 (because ?ger doesn't clear it) smoother.tmpL2[:] = 0 # (N_{t,i} K_{t,i} Z_{t,i}) blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &alpha, smoother._tmp0, &inc, &model._design[i], &model._k_endog, smoother._tmpL2, &kfilter.k_states) # (N_{t,i} K_{t,i} Z_{t,i}) + (N_{t,i} K_{t,i} Z_{t,i})' # for j in range(kfilter.k_states): # k = kfilter.k_states - j # blas.{{prefix}}axpy(&k, &alpha, &smoother.tmpL2[j, j], &kfilter.k_states, # &smoother.tmpL2[j, j], &inc) # blas.{{prefix}}copy(&k, &smoother.tmpL2[j, j], &inc, # &smoother.tmpL2[j, j], &kfilter.k_states) # N_{t,i} - [(N_{t,i} K_{t,i} Z_{t,i}) + (N_{t,i} K_{t,i} Z_{t,i})'] # blas.{{prefix}}axpy(&kfilter.k_states2, &gamma, smoother._tmpL2, &inc, # smoother._scaled_smoothed_estimator_cov, &inc) # Below is a faster way to do these ^ two steps for j in range(kfilter.k_states): k = kfilter.k_states - j blas.{{prefix}}axpy(&k, &gamma, &smoother.tmpL2[j, j], &inc, &smoother._scaled_smoothed_estimator_cov[j+j*kfilter.k_states], &inc) blas.{{prefix}}axpy(&k, &gamma, &smoother.tmpL2[j, j], &kfilter.k_states, &smoother._scaled_smoothed_estimator_cov[j+j*kfilter.k_states], &inc) blas.{{prefix}}copy(&k, &smoother._scaled_smoothed_estimator_cov[j+j*kfilter.k_states], &inc, &smoother._scaled_smoothed_estimator_cov[j+j*kfilter.k_states], &kfilter.k_states) # N_{t,i-1} scalar = smoother._smoothed_measurement_disturbance_cov[i*kfilter.k_endog + i] if kfilter._forecast_error_cov[i*kfilter.k_endog + i]{{if combined_prefix == 'z'}}.real{{endif}} > kfilter.tolerance_diffuse: scalar = scalar + 1 / kfilter._forecast_error_cov[i*kfilter.k_endog + i] # TODO: replace with syr + fill in upper triangle? blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &scalar, &model._design[i], &model._k_endog, &model._design[i], &model._k_endog, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states) # {{if combined_prefix == 'd'}} # blas.{{prefix}}syr("L", &model._k_states, # &scalar, &model._design[i], &model._k_endog, # smoother._scaled_smoothed_estimator_cov, &kfilter.k_states) # {{else}} # blas.{{prefix}}syrk("L", "N", &model._k_states, &inc, # &scalar, &model._design[i], &model._k_endog, # &alpha, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states) # {{endif}} # for j in range(model._k_states): # columns # for k in range(model._k_states): # rows # if k > j: # row > column => in lower triangle # smoother._scaled_smoothed_estimator_cov[j + k*kfilter.k_states] = smoother._scaled_smoothed_estimator_cov[k + j*kfilter.k_states] cdef int {{prefix}}precise_iter_smoothed_estimators_measurement_univariate({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model, int i, int k_states): cdef: int j, k, inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 {{cython_type}} scalar # $L_{t,i} = (I_m - K_{t,i} Z_{t,i})$ # $(m \times m) = (m \times m) - (m \times 1) (1 \times m)$ # blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &inc, # &gamma, &kfilter._kalman_gain[i*kfilter.k_states], &kfilter.k_states, # &model._design[i], &model._k_endog, # &beta, smoother._tmpL, &kfilter.k_states) # Zero the temporary matrix # blas.{{prefix}}scal(&kfilter.k_states2, &beta, smoother._tmpL, &inc) smoother.tmpL2[:,:k_states] = 0 # Create the K_{t,i} Z_{t,i} component # (m x p) (m x 1) x (1 x p) blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &k_states, &gamma, &kfilter._kalman_gain[i*kfilter.k_states], &inc, &model._design[i], &model._k_endog, smoother._tmpL2, &kfilter.k_states) # Add the identity matrix for j in range(k_states): smoother._tmpL2[j + j*kfilter.k_states] = smoother._tmpL2[j + j*kfilter.k_states] + 1 # Accumulate L_{t,i} into L_{t} = L_{t,n} L_{t,n-1} ... L_{t,1} if i == kfilter.k_endog-1: blas.{{prefix}}copy(&kfilter.k_states2, smoother._tmpL2, &inc, smoother._tmpL, &inc) else: blas.{{prefix}}copy(&kfilter.k_states2, smoother._tmpL, &inc, smoother._tmp0, &inc) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, smoother._tmpL2, &kfilter.k_states, &beta, smoother._tmpL, &kfilter.k_states) # Scaled smoothed estimator # $r_{t,i-1} = Z_{t,i}' v_{t,i} / F_{t,i} + L_{t,i}' r_{t,i}$ # $(m \times 1) = (m \times 1) (1 \times 1) + (m \times m) (m \times 1)$ # Note: save $r_{t-1}$ as scaled_smoothed_estimator[t] rather than # as scaled_smoothed_estimator[t-1] because we actually need to store # T+1 of them (r_{T-1} to r_{-1} -> r_T to r_0) if smoother.smoother_output & (SMOOTHER_STATE | SMOOTHER_DISTURBANCE): #blas.{{prefix}}scal(&kfilter.k_states, &beta, smoother._tmp0, &inc) blas.{{prefix}}gemv("T", &model._k_states, &k_states, &alpha, smoother._tmpL2, &kfilter.k_states, smoother._scaled_smoothed_estimator, &inc, &beta, smoother._tmp0, &inc) blas.{{prefix}}swap(&k_states, smoother._tmp0, &inc, smoother._scaled_smoothed_estimator, &inc) blas.{{prefix}}axpy(&k_states, &kfilter._tmp2[i], &model._design[i], &model._k_endog, smoother._scaled_smoothed_estimator, &inc) if smoother.smoother_output & (SMOOTHER_STATE_COV | SMOOTHER_DISTURBANCE_COV): # Scaled smoothed estimator covariance matrix # $N_{t,i-1} = Z_{t,i}' Z_{t,i} / F_{t,i} + L_{t,i}' N_{t,i} L_{t,i}$ # $(m \times m) = (m \times p) (p \times m) + (m \times m) (m \times m) (m \times m)$ # Note: save $N_{t-1}$ as scaled_smoothed_estimator_cov[t] rather # than as scaled_smoothed_estimator_cov[t-1] because we actually # need to store T+1 of them (N_{T-1} to N_{-1} -> N_T to N_0) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states, smoother._tmpL2, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmpL2, &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states) blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &alpha, &model._design[i], &model._k_endog, &kfilter._tmp3[i], &kfilter.k_endog, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states) cdef int {{prefix}}smoothed_estimators_time_univariate({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef: int i, j, inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 {{cython_type}} scalar int k_states = model._k_states {{cython_type}} * _transition if smoother.t == 0: return 1 # r_{t-1,p} = T_{t-1}' r_{t,0} if model.transition.shape[2] > 1: _transition = &model.transition[0, 0, smoother.t-1] else: _transition = &model.transition[0, 0, 0] if smoother.smoother_output & (SMOOTHER_STATE | SMOOTHER_DISTURBANCE): blas.{{prefix}}gemv("T", &model._k_states, &model._k_states, &alpha, _transition, &model._k_states, smoother._scaled_smoothed_estimator, &inc, &beta, &smoother.scaled_smoothed_estimator[0, smoother.t-1], &inc) # N_{t-1,p} = T_{t-1}' N_{t,0} T_{t-1} if smoother.smoother_output & (SMOOTHER_STATE_COV | SMOOTHER_DISTURBANCE_COV): blas.{{prefix}}copy(&kfilter.k_states2, smoother._scaled_smoothed_estimator_cov, &inc, &smoother.scaled_smoothed_estimator_cov[0, 0, smoother.t-1], &inc) blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, _transition, &model._k_states, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, _transition, &model._k_states, &beta, &smoother.scaled_smoothed_estimator_cov[0, 0, smoother.t-1], &kfilter.k_states) cdef int {{prefix}}smoothed_disturbances_univariate({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): # Note: this only differs from the conventional version in the # definition of the smoothed measurement disturbance and cov cdef int i, j cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # Temporary arrays # $\\#_0 = R_t Q_t$ # $(m \times r) = (m \times r) (r \times r)$ blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_posdef, &model._k_posdef, &alpha, model._selection, &model._k_states, model._state_cov, &model._k_posdef, &beta, smoother._tmp0, &kfilter.k_states) if smoother.smoother_output & SMOOTHER_DISTURBANCE: for i in range(model._k_endog): # Smoothed measurement disturbance # $\hat \varepsilon_t = (H_{t,i} / F_{t,i}) (v_{t,i} - F_{t,i} K_{t,i}' r_{t,i})$ # Note: K_{t,i}' r_{t,i} was stored in _smoothed_measurement_disturbance[i] # in smoothed_estimators_univariate, above, so we just need to implement # $\hat \varepsilon_t = (H_{t,i} / F_{t,i}) (v_{t,i} - \\#)$ here # (this is because we do not otherwise store the r_{t,i} values) # $(p \times 1) = (p \times p) (p \times 1)$ smoother._smoothed_measurement_disturbance[i] = ( kfilter._tmp4[i + i*kfilter.k_endog] * ( kfilter._forecast_error[i] - kfilter._forecast_error_cov[i + i*kfilter.k_endog] * smoother._smoothed_measurement_disturbance[i] ) ) # Smoothed state disturbance # $\hat \eta_t = \\#_0' r_t$ # $(r \times 1) = (r \times m) (m \times 1)$ blas.{{prefix}}gemv("T", &model._k_states, &model._k_posdef, &alpha, smoother._tmp0, &kfilter.k_states, smoother._input_scaled_smoothed_estimator, &inc, &beta, smoother._smoothed_state_disturbance, &inc) if smoother.smoother_output & SMOOTHER_DISTURBANCE_COV: for i in range(model._k_endog): # Smoothed measurement disturbance covariance matrix # $Var(\varepsilon_{t,i} | Y_n) = H_{t,i} - (H_{t,i} / F_{t,i})^2 * (F_{t,i} + F_{t,i}^2 K_{t,i}' N_{t,i} K_{t,i})$ # Note: K_{t,i}' N_{t,i} K_{t,i} was stored in _smoothed_measurement_disturbance_cov[i,i] # in smoothed_estimators_univariate, above, so we just need to implement # $Var(\varepsilon_{t,i} | Y_n) = H_{t,i} - (H_{t,i} / F_{t,i})^2 * (F_{t,i} + F_{t,i}^2 * \\#)$ here # (this is because we do not otherwise store the N_{t,i} values) # $(1 \times 1) = (p \times p) - (p \times p) (p \times p) - (p \times m) (m \times m) (m \times p)$ smoother._smoothed_measurement_disturbance_cov[i + i*kfilter.k_endog] = model._obs_cov[i + i*model._k_endog] - ( (kfilter._tmp4[i + i*kfilter.k_endog]**2) * ( kfilter._forecast_error_cov[i + i*kfilter.k_endog] + kfilter._forecast_error_cov[i + i*kfilter.k_endog]**2 * smoother._smoothed_measurement_disturbance_cov[i + i*kfilter.k_endog] ) ) # Smoothed state disturbance covariance matrix # $Var(\eta_t | Y_n) = Q_t - \\#_0' N_t \\#_0$ # $(r \times r) = (r \times r) - (r \times m) (m \times m) (m \times r)$ blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_posdef, &model._k_states, &alpha, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._tmpL, &kfilter.k_states) blas.{{prefix}}copy(&model._k_posdef2, model._state_cov, &inc, smoother._smoothed_state_disturbance_cov, &inc) blas.{{prefix}}gemm("T", "N", &kfilter.k_posdef, &kfilter.k_posdef, &kfilter.k_states, &gamma, smoother._tmp0, &kfilter.k_states, smoother._tmpL, &kfilter.k_states, &alpha, smoother._smoothed_state_disturbance_cov, &kfilter.k_posdef) {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/_smoothers/_univariate_diffuse.pxd000066400000000000000000000060641400612667500303520ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models - Conventional Kalman Filter declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np from statsmodels.tsa.statespace._representation cimport ( sStatespace, dStatespace, cStatespace, zStatespace ) from statsmodels.tsa.statespace._kalman_filter cimport ( sKalmanFilter, dKalmanFilter, cKalmanFilter, zKalmanFilter ) from statsmodels.tsa.statespace._kalman_smoother cimport ( sKalmanSmoother, dKalmanSmoother, cKalmanSmoother, zKalmanSmoother ) # Single precision cdef int ssmoothed_estimators_measurement_univariate_diffuse(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) except * cdef int ssmoothed_estimators_time_univariate_diffuse(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) cdef int ssmoothed_state_univariate_diffuse(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) cdef int ssmoothed_disturbances_univariate_diffuse(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) cdef int ssmoothed_state_autocov_univariate_diffuse(sKalmanSmoother smoother, sKalmanFilter kfilter, sStatespace model) # Double precision cdef int dsmoothed_estimators_measurement_univariate_diffuse(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) except * cdef int dsmoothed_estimators_time_univariate_diffuse(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) cdef int dsmoothed_state_univariate_diffuse(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) cdef int dsmoothed_disturbances_univariate_diffuse(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) cdef int dsmoothed_state_autocov_univariate_diffuse(dKalmanSmoother smoother, dKalmanFilter kfilter, dStatespace model) # Single precision complex cdef int csmoothed_estimators_measurement_univariate_diffuse(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) except * cdef int csmoothed_estimators_time_univariate_diffuse(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) cdef int csmoothed_state_univariate_diffuse(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) cdef int csmoothed_disturbances_univariate_diffuse(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) cdef int csmoothed_state_autocov_univariate_diffuse(cKalmanSmoother smoother, cKalmanFilter kfilter, cStatespace model) # Double precision complex cdef int zsmoothed_estimators_measurement_univariate_diffuse(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) except * cdef int zsmoothed_estimators_time_univariate_diffuse(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) cdef int zsmoothed_state_univariate_diffuse(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) cdef int zsmoothed_disturbances_univariate_diffuse(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) cdef int zsmoothed_state_autocov_univariate_diffuse(zKalmanSmoother smoother, zKalmanFilter kfilter, zStatespace model) statsmodels-0.12.2/statsmodels/tsa/statespace/_smoothers/_univariate_diffuse.pyx.in000066400000000000000000001162011400612667500307770ustar00rootroot00000000000000#cython: profile=False #cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models Note: some of the calls below are not fully optimized (in the sense that some things are re-computed rather than stored) but since these iterations will almost always only be for a very few periods, gains from further optimization are likely to be small. Note: there is a typo in Durbin and Koopman (2012) in the equations for the univariate smoothed measurement disturbances and smoothed measurement disturbance covariances. In each equation (p157), the Kalman gain vector K_{t,i} is used, but in fact these should be multiplied by the forecast error covariance F_{t,i}. The original paper on the univariate approach, Koopman and Durbin (2000) has the correct form. The typo arose because the original paper defines the Kalman gain as K_{t,i} = P_{t,i} Z_{t,i}' but the book defines it as K_{t,i} = P_{t,i} Z_{t,i}' F_{t,i}^{-1}, and the book does not correct the disturbances formulas for this change. Furthermore, in analogy to the disturbance smoother from chapter 4, the formula for the univariate covariance ought to be subtracted from the observation covariance. So, what we ought to have is: \hat \varepsilon_{t,i} = \sigma_{t,i}^2 F_{t,i}^{-1} (v_{t,i} - F_{t,i} K_{t,i}' r_{t,i}) Var(\hat \varepsilon_{t,i}) = \sigma_{t,i}^2 - \sigma_{t,i}^4 F_{t,i}^{-2} (v_{t,i} - F_{t,i} K_{t,i}' r_{t,i}) Author: Chad Fulton License: Simplified-BSD """ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} # Typical imports import numpy as np cimport numpy as np from statsmodels.src.math cimport * cimport scipy.linalg.cython_blas as blas from statsmodels.tsa.statespace._kalman_smoother cimport ( SMOOTHER_STATE, SMOOTHER_STATE_COV, SMOOTHER_STATE_AUTOCOV, SMOOTHER_DISTURBANCE, SMOOTHER_DISTURBANCE_COV ) {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' combined_suffix = '' if combined_prefix == 'z': combined_suffix = 'u' }} # ### Univariate diffuse Kalman smoother # # See Durbin and Koopman (2012) Chapter 5.3 cdef int {{prefix}}smoothed_estimators_measurement_univariate_diffuse({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model) except *: cdef: int i, j, inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 {{cython_type}} scalar int k_states = model._k_states {{cython_type}} forecast_error_cov, forecast_error_cov_inv, forecast_error_diffuse_cov, forecast_error_diffuse_cov_inv, F1, F12, F2 # Adjust for a VAR transition (i.e. design = [#, 0], where the zeros # correspond to all states except the first k_posdef states) if model.subset_design: k_states = model._k_posdef # Need to clear out the scaled_smoothed_estimator and # scaled_smoothed_estimator_cov in case we're re-running the filter if smoother.t == model.nobs - 1: smoother.scaled_smoothed_estimator[:, model.nobs-1] = 0 smoother.scaled_smoothed_estimator_cov[:, :, model.nobs-1] = 0 smoother.scaled_smoothed_diffuse_estimator[:, model.nobs-1] = 0 smoother.scaled_smoothed_diffuse1_estimator_cov[:, :, model.nobs-1] = 0 smoother.scaled_smoothed_diffuse2_estimator_cov[:, :, model.nobs-1] = 0 # Smoothing error # (not used in the univariate approach) # Given r_{t,0}: # calculate r_{t-1,p}, ..., r_{t-1, 0} and N_{t-1,p}, ..., N_{t-1,0} # Clear temporary arrays used for cumulation of L0 and L1 smoother.tmpL[:] = 0 smoother.tmpL2[:] = 0 for i in range(kfilter.k_states): smoother.tmpL[i, i] = 1 smoother.tmpL2[i, i] = 1 # Iterate for i in range(kfilter.k_endog-1,-1,-1): # Forecast error covariance and diffuse forecast error covariance # F_{*,t} forecast_error_cov = kfilter._forecast_error_cov[i + i*kfilter.k_endog] # F_{\infty,t} forecast_error_diffuse_cov = kfilter._forecast_error_diffuse_cov[i + i*kfilter.k_endog] # Intermediate computations (must be done first so we can set the # measurement disturbance variables correctly) if {{combined_prefix}}abs(forecast_error_diffuse_cov) > kfilter.tolerance_diffuse: forecast_error_diffuse_cov_inv = 1.0 / forecast_error_diffuse_cov F1 = forecast_error_diffuse_cov_inv # Usually F2 = -forecast_error_cov * forecast_error_diffuse_cov_inv**2 # but this version is more convenient for the *axpy call F12 = -forecast_error_cov * forecast_error_diffuse_cov_inv F2 = F12 * forecast_error_diffuse_cov_inv # K0 = M_inf[:, i:i+1] * F1 blas.{{prefix}}copy(&kfilter.k_states, &kfilter._M_inf[i * kfilter.k_states], &inc, kfilter._tmpK0, &inc) blas.{{prefix}}scal(&kfilter.k_states, &F1, kfilter._tmpK0, &inc) # K1 = M[:, i:i+1] * F1 + M_inf[:, i:i+1] * F2 # K1 = M[:, i:i+1] * F1 + K0 * F12 blas.{{prefix}}copy(&kfilter.k_states, &kfilter._M[i*kfilter.k_states], &inc, kfilter._tmpK1, &inc) blas.{{prefix}}scal(&kfilter.k_states, &F1, kfilter._tmpK1, &inc) blas.{{prefix}}axpy(&kfilter.k_states, &F12, kfilter._tmpK0, &inc, kfilter._tmpK1, &inc) # L0 = np.eye(m) - np.dot(K0, Zi) kfilter.tmpL0[:] = 0 blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &gamma, kfilter._tmpK0, &inc, &model._design[i], &model._k_endog, kfilter._tmpL0, &kfilter.k_states) for j in range(kfilter.k_states): kfilter._tmpL0[j + j*kfilter.k_states] = kfilter._tmpL0[j + j*kfilter.k_states] + 1 # L1 = -np.dot(K1, Zi) kfilter.tmpL1[:] = 0 blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &gamma, kfilter._tmpK1, &inc, &model._design[i], &model._k_endog, kfilter._tmpL1, &kfilter.k_states) elif not forecast_error_cov == 0: forecast_error_cov_inv = 1.0 / forecast_error_cov # K0 = M[:, i:i+1] / F[i, i] blas.{{prefix}}copy(&kfilter.k_states, &kfilter._M[i*kfilter.k_states], &inc, kfilter._tmpK0, &inc) blas.{{prefix}}scal(&kfilter.k_states, &forecast_error_cov_inv, kfilter._tmpK0, &inc) # L0 = np.eye(m) - np.dot(K0, Zi) kfilter.tmpL0[:] = 0 blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &gamma, kfilter._tmpK0, &inc, &model._design[i], &model._k_endog, kfilter._tmpL0, &kfilter.k_states) for j in range(kfilter.k_states): kfilter._tmpL0[j + j*kfilter.k_states] = kfilter._tmpL0[j + j*kfilter.k_states] + 1 else: kfilter.tmpK0[:] = 0 kfilter.tmpL0[:] = 0 for j in range(kfilter.k_states): kfilter._tmpL0[j + j*kfilter.k_states] = 1 # Cumulate L0 and L1 blas.{{prefix}}copy(&kfilter.k_states2, smoother._tmpL, &inc, smoother._tmp0, &inc) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, kfilter._tmpL0, &kfilter.k_states, &beta, smoother._tmpL, &kfilter.k_states) if {{combined_prefix}}abs(forecast_error_diffuse_cov) > kfilter.tolerance_diffuse: blas.{{prefix}}copy(&kfilter.k_states2, smoother._tmpL2, &inc, smoother._tmp0, &inc) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, kfilter._tmpL1, &kfilter.k_states, &beta, smoother._tmpL2, &kfilter.k_states) # Store values for measurement disturbance smoothing # np.dot(K0.T, rt) if smoother.smoother_output & SMOOTHER_DISTURBANCE: # Note: zdot and cdot are broken, so have to use gemv for those {{if combined_prefix == 'd'}} smoother._smoothed_measurement_disturbance[i] = ( blas.{{prefix}}dot(&model._k_states, kfilter._tmpK0, &inc, smoother._scaled_smoothed_estimator, &inc) ) {{else}} blas.{{prefix}}gemv("N", &inc, &model._k_states, &alpha, smoother._scaled_smoothed_estimator, &inc, kfilter._tmpK0, &inc, &beta, &smoother._smoothed_measurement_disturbance[i], &inc) {{endif}} # Store values for measurement disturbance covariance smoothing # np.dot(np.dot(K0.T, Nt), K0) if smoother.smoother_output & SMOOTHER_DISTURBANCE_COV: blas.{{prefix}}gemv("N", &model._k_states, &model._k_states, &alpha, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states, kfilter._tmpK0, &inc, &beta, smoother._tmp0, &inc) # Note: zdot and cdot are broken, so have to use gemv for those {{if combined_prefix == 'd'}} smoother._smoothed_measurement_disturbance_cov[i + i*kfilter.k_endog] = ( blas.{{prefix}}dot(&model._k_states, kfilter._tmpK0, &inc, smoother._tmp0, &inc) ) {{else}} blas.{{prefix}}gemv("N", &inc, &model._k_states, &alpha, smoother._tmp0, &inc, kfilter._tmpK0, &inc, &beta, &smoother._smoothed_measurement_disturbance_cov[i*kfilter.k_endog + i], &inc) {{endif}} # F_{\infty, i, i, t} > 0 if {{combined_prefix}}abs(forecast_error_diffuse_cov) > kfilter.tolerance_diffuse: # Update # rt_inf[:] = Zi.T[:, 0] * v[i] * F1 + np.dot(L0.T, rt_inf) + np.dot(L1.T, rt) blas.{{prefix}}copy(&model._k_states, smoother._scaled_smoothed_diffuse_estimator, &inc, smoother._tmp0, &inc) blas.{{prefix}}copy(&model._k_states, &model._design[i], &model._k_endog, smoother._scaled_smoothed_diffuse_estimator, &inc) scalar = F1 * kfilter._forecast_error[i] blas.{{prefix}}gemv("T", &model._k_states, &model._k_states, &alpha, kfilter._tmpL0, &kfilter.k_states, smoother._tmp0, &inc, &scalar, smoother._scaled_smoothed_diffuse_estimator, &inc) blas.{{prefix}}gemv("T", &model._k_states, &model._k_states, &alpha, kfilter._tmpL1, &kfilter.k_states, smoother._scaled_smoothed_estimator, &inc, &alpha, smoother._scaled_smoothed_diffuse_estimator, &inc) # rt[:] = np.dot(L0.T, rt) blas.{{prefix}}copy(&model._k_states, smoother._scaled_smoothed_estimator, &inc, smoother._tmp0, &inc) blas.{{prefix}}gemv("T", &model._k_states, &model._k_states, &alpha, kfilter._tmpL0, &kfilter.k_states, smoother._tmp0, &inc, &beta, smoother._scaled_smoothed_estimator, &inc) # Nt_inf2[:] = ZiTZi * F2 + np.dot(np.dot(L0.T, Nt_inf2), L0) + np.dot(np.dot(L0.T, Nt_inf1), L1) + np.dot(np.dot(L1.T, Nt_inf1.T), L0) + np.dot(np.dot(L1.T, Nt), L1) # Nt_inf2[:] = ZiTZi * F2 + np.dot(np.dot(L0.T, Nt_inf2), L0) + np.dot(np.dot(L0.T, Nt_inf1), L1) + np.dot(np.dot(L1.T, Nt_inf1.T), L0) + np.dot(np.dot(L1.T, Nt), L1) # : np.dot(L0.T, Nt_inf2) -> tmp0 blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmpL0, &kfilter.k_states, smoother._scaled_smoothed_diffuse2_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) # : np.dot(tmp0, L0) -> scaled_smoothed_diffuse2_estimator_cov blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, kfilter._tmpL0, &kfilter.k_states, &beta, smoother._scaled_smoothed_diffuse2_estimator_cov, &kfilter.k_states) # : np.dot(L0.T, Nt_inf1) -> tmp0 blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmpL0, &kfilter.k_states, smoother._scaled_smoothed_diffuse1_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) # : np.dot(tmp0, L1) -> scaled_smoothed_diffuse2_estimator_cov blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, kfilter._tmpL1, &kfilter.k_states, &alpha, smoother._scaled_smoothed_diffuse2_estimator_cov, &kfilter.k_states) # : np.dot(L1.T, Nt_inf1.T) -> tmp0 blas.{{prefix}}gemm("T", "T", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmpL1, &kfilter.k_states, smoother._scaled_smoothed_diffuse1_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) # : np.dot(tmp0, L0) -> scaled_smoothed_diffuse2_estimator_cov blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, kfilter._tmpL0, &kfilter.k_states, &alpha, smoother._scaled_smoothed_diffuse2_estimator_cov, &kfilter.k_states) # : np.dot(L1.T, Nt) -> tmp0 blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmpL1, &kfilter.k_states, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) # : np.dot(tmp0, L1) -> scaled_smoothed_diffuse2_estimator_cov blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, kfilter._tmpL1, &kfilter.k_states, &alpha, smoother._scaled_smoothed_diffuse2_estimator_cov, &kfilter.k_states) # Note: still need to add ZiTZi * F2 to Nt_inf2, which is done below. # Nt_inf1[:] = ZiTZi * F1 + np.dot(np.dot(L0.T, Nt_inf1), L0) + np.dot(np.dot(L1.T, Nt), L0) # : np.dot(L0.T, Nt_inf1) -> tmp0 blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmpL0, &kfilter.k_states, smoother._scaled_smoothed_diffuse1_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) # : np.dot(tmp0, L0) -> scaled_smoothed_diffuse2_estimator_cov blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, kfilter._tmpL0, &kfilter.k_states, &beta, smoother._scaled_smoothed_diffuse1_estimator_cov, &kfilter.k_states) # : np.dot(L1.T, Nt) -> tmp0 blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmpL1, &kfilter.k_states, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) # : np.dot(tmp0, L0) -> scaled_smoothed_diffuse2_estimator_cov blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, kfilter._tmpL0, &kfilter.k_states, &alpha, smoother._scaled_smoothed_diffuse1_estimator_cov, &kfilter.k_states) # # : np.dot(L0.T, Nt) -> tmp0 # blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, # &alpha, kfilter._tmpL0, &kfilter.k_states, # smoother._scaled_smoothed_estimator_cov, &kfilter.k_states, # &beta, smoother._tmp0, &kfilter.k_states) # # : np.dot(tmp0, L1) -> scaled_smoothed_diffuse2_estimator_cov # blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, # &alpha, smoother._tmp0, &kfilter.k_states, # kfilter._tmpL1, &kfilter.k_states, # &alpha, smoother._scaled_smoothed_diffuse1_estimator_cov, &kfilter.k_states) # Note: still need to add ZiTZi * F1 to Nt_inf1, which is done below. # Now add in ZiTZi # ZiTZi smoother.tmp0[:] = 0 blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &alpha, &model._design[i], &model._k_endog, &model._design[i], &model._k_endog, smoother._tmp0, &kfilter.k_states) # : Nt_inf2 += ZiTZi * F2 blas.{{prefix}}axpy(&kfilter.k_states2, &F2, smoother._tmp0, &inc, smoother._scaled_smoothed_diffuse2_estimator_cov, &inc) # : Nt_inf1 += ZiTZi * F1 blas.{{prefix}}axpy(&kfilter.k_states2, &F1, smoother._tmp0, &inc, smoother._scaled_smoothed_diffuse1_estimator_cov, &inc) # Nt[:] = np.dot(np.dot(L0.T, Nt), L0) # : np.dot(L0.T, Nt) -> tmp0 blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmpL0, &kfilter.k_states, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) # : np.dot(tmp0, L0) -> scaled_smoothed_estimator_cov blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, kfilter._tmpL0, &kfilter.k_states, &beta, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states) # F_{\infty, i, i, t} = 0 elif not forecast_error_cov == 0: # Update # Note: Koopman and Durbin (2003) subtract the latter term, # but they use a different definition of the smoothing # recursion in general than the book Durbin and Koopman; this # version is consistent with the definition of the smoothing # recursion in the book. # rt[:] = Zi.T[:, 0] * v[i] / F[i, i] + np.dot(L0.T, rt) blas.{{prefix}}copy(&model._k_states, smoother._scaled_smoothed_estimator, &inc, smoother._tmp0, &inc) blas.{{prefix}}copy(&model._k_states, &model._design[i], &model._k_endog, smoother._scaled_smoothed_estimator, &inc) scalar = forecast_error_cov_inv * kfilter._forecast_error[i] blas.{{prefix}}gemv("T", &model._k_states, &model._k_states, &alpha, kfilter._tmpL0, &kfilter.k_states, smoother._tmp0, &inc, &scalar, smoother._scaled_smoothed_estimator, &inc) # rt_inf[:] = rt_inf[:] # Nt[:] = ZiTZi / F[i, i] + np.dot(np.dot(L0.T, Nt), L0) # : np.dot(L0.T, Nt) -> tmp0 blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, kfilter._tmpL0, &kfilter.k_states, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) # : np.dot(tmp0, L0) -> scaled_smoothed_diffuse2_estimator_cov blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, kfilter._tmpL0, &kfilter.k_states, &beta, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states) blas.{{prefix}}ger{{combined_suffix}}(&model._k_states, &model._k_states, &forecast_error_cov_inv, &model._design[i], &model._k_endog, &model._design[i], &model._k_endog, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states) # Nt_inf1[:] = np.dot(Nt_inf1, L0) blas.{{prefix}}copy(&model._k_states2, smoother._scaled_smoothed_diffuse1_estimator_cov, &inc, smoother._tmp0, &inc) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, kfilter._tmpL0, &kfilter.k_states, &beta, smoother._scaled_smoothed_diffuse1_estimator_cov, &kfilter.k_states) # Nt_inf2[:] = Nt_inf2 # Finalize the cumulated L0 and L1 by premultiplying by T # (and put them into kfilter.tmpL0 and kfilter.tmpL1) blas.{{prefix}}copy(&kfilter.k_states2, smoother._tmpL, &inc, smoother._tmp0, &inc) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, model._transition, &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, kfilter._tmpL0, &kfilter.k_states) blas.{{prefix}}copy(&kfilter.k_states2, smoother._tmpL2, &inc, smoother._tmp0, &inc) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, model._transition, &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, kfilter._tmpL1, &kfilter.k_states) cdef int {{prefix}}smoothed_estimators_time_univariate_diffuse({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef: int i, j, inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 {{cython_type}} scalar int k_states = model._k_states if smoother.t == 0: return 1 # TODO check that this is the right transition matrix to use in the case # of time-varying matrices # rt1[:] = np.dot(T1.T, rt) blas.{{prefix}}gemv("T", &model._k_states, &model._k_states, &alpha, model._transition, &model._k_states, smoother._scaled_smoothed_estimator, &inc, &beta, &smoother.scaled_smoothed_estimator[0, smoother.t-1], &inc) # rt1_inf[:] = np.dot(T1.T, rt_inf) blas.{{prefix}}gemv("T", &model._k_states, &model._k_states, &alpha, model._transition, &model._k_states, smoother._scaled_smoothed_diffuse_estimator, &inc, &beta, &smoother.scaled_smoothed_diffuse_estimator[0, smoother.t-1], &inc) # Nt1 = np.dot(np.dot(T1.T, Nt1), T1) blas.{{prefix}}copy(&kfilter.k_states2, smoother._scaled_smoothed_estimator_cov, &inc, &smoother.scaled_smoothed_estimator_cov[0, 0, smoother.t-1], &inc) blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, model._transition, &model._k_states, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, model._transition, &model._k_states, &beta, &smoother.scaled_smoothed_estimator_cov[0, 0, smoother.t-1], &kfilter.k_states) # Nt1_inf1 = np.dot(np.dot(T1.T, Nt1_inf1), T1) blas.{{prefix}}copy(&kfilter.k_states2, smoother._scaled_smoothed_diffuse1_estimator_cov, &inc, &smoother.scaled_smoothed_diffuse1_estimator_cov[0, 0, smoother.t-1], &inc) blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, model._transition, &model._k_states, smoother._scaled_smoothed_diffuse1_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, model._transition, &model._k_states, &beta, &smoother.scaled_smoothed_diffuse1_estimator_cov[0, 0, smoother.t-1], &kfilter.k_states) # Nt1_inf2 = np.dot(np.dot(T1.T, Nt1_inf2), T1) blas.{{prefix}}copy(&kfilter.k_states2, smoother._scaled_smoothed_diffuse2_estimator_cov, &inc, &smoother.scaled_smoothed_diffuse2_estimator_cov[0, 0, smoother.t-1], &inc) blas.{{prefix}}gemm("T", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, model._transition, &model._k_states, smoother._scaled_smoothed_diffuse2_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, smoother._tmp0, &kfilter.k_states, model._transition, &model._k_states, &beta, &smoother.scaled_smoothed_diffuse2_estimator_cov[0, 0, smoother.t-1], &kfilter.k_states) cdef int {{prefix}}smoothed_state_univariate_diffuse({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef: int i, j, inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 {{cython_type}} scalar int k_states = model._k_states # Smoothed state if smoother.smoother_output & SMOOTHER_STATE: # alpha_hat[:] = a_t + np.dot(P_t, rt) + np.dot(P_t_inf, rt_inf) blas.{{prefix}}copy(&kfilter.k_states, &kfilter.predicted_state[0,smoother.t], &inc, smoother._smoothed_state, &inc) blas.{{prefix}}gemv("N", &model._k_states, &model._k_states, &alpha, &kfilter.predicted_state_cov[0,0,smoother.t], &kfilter.k_states, smoother._scaled_smoothed_estimator, &inc, &alpha, smoother._smoothed_state, &inc) blas.{{prefix}}gemv("N", &model._k_states, &model._k_states, &alpha, &kfilter.predicted_diffuse_state_cov[0,0,smoother.t], &kfilter.k_states, smoother._scaled_smoothed_diffuse_estimator, &inc, &alpha, smoother._smoothed_state, &inc) # Smoothed state covariance if smoother.smoother_output & SMOOTHER_STATE_COV: # V[:] = P_t - np.dot(np.dot(P_t, Nt), P_t) - np.dot(np.dot(P_t, Nt_inf1), P_t_inf) - np.dot(np.dot(P_t_inf, Nt_inf1), P_t).T - np.dot(np.dot(P_t_inf, Nt_inf2), P_t_inf) # : P_t [ I - N_t P_t] blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &gamma, smoother._scaled_smoothed_estimator_cov, &kfilter.k_states, &kfilter.predicted_state_cov[0,0,smoother.t], &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) for i in range(kfilter.k_states): smoother.tmp0[i,i] = 1 + smoother.tmp0[i,i] blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, &kfilter.predicted_state_cov[0,0,smoother.t], &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._smoothed_state_cov, &kfilter.k_states) # : - np.dot(np.dot(P_t_inf, Nt_inf1), P_t) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, &kfilter.predicted_diffuse_state_cov[0,0,smoother.t], &kfilter.k_states, smoother._scaled_smoothed_diffuse1_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &gamma, smoother._tmp0, &kfilter.k_states, &kfilter.predicted_state_cov[0,0,smoother.t], &kfilter.k_states, &alpha, smoother._smoothed_state_cov, &kfilter.k_states) # : - np.dot(np.dot(P_t_inf, Nt_inf1), P_t).T # [or] # : - np.dot(np.dot(P_t, Nt_inf1.T), P_t_inf) blas.{{prefix}}gemm("N", "T", &model._k_states, &model._k_states, &model._k_states, &alpha, &kfilter.predicted_state_cov[0,0,smoother.t], &kfilter.k_states, smoother._scaled_smoothed_diffuse1_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &gamma, smoother._tmp0, &kfilter.k_states, &kfilter.predicted_diffuse_state_cov[0,0,smoother.t], &kfilter.k_states, &alpha, smoother._smoothed_state_cov, &kfilter.k_states) # - np.dot(np.dot(P_t_inf, Nt_inf2), P_t_inf) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &alpha, &kfilter.predicted_diffuse_state_cov[0,0,smoother.t], &kfilter.k_states, smoother._scaled_smoothed_diffuse2_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_states, &model._k_states, &gamma, smoother._tmp0, &kfilter.k_states, &kfilter.predicted_diffuse_state_cov[0,0,smoother.t], &kfilter.k_states, &alpha, smoother._smoothed_state_cov, &kfilter.k_states) cdef int {{prefix}}smoothed_disturbances_univariate_diffuse({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): # Note: this only differs from the conventional version in the # definition of the smoothed measurement disturbance and cov cdef int i, j cdef: int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 {{cython_type}} forecast_error_cov, forecast_error_cov_inv, forecast_error_diffuse_cov, forecast_error_diffuse_cov_inv, obs_cov # Temporary arrays # $\\#_0 = R_t Q_t$ # $(m \times r) = (m \times r) (r \times r)$ blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_posdef, &model._k_posdef, &alpha, model._selection, &model._k_states, model._state_cov, &model._k_posdef, &beta, smoother._tmp0, &kfilter.k_states) for i in range(model._k_endog): forecast_error_cov = kfilter._forecast_error_cov[i + i*kfilter.k_endog] forecast_error_diffuse_cov = kfilter._forecast_error_diffuse_cov[i + i*kfilter.k_endog] obs_cov = model._obs_cov[i + i*model._k_endog] # Smoothed measurement disturbance if smoother.smoother_output & SMOOTHER_DISTURBANCE: if {{combined_prefix}}abs(forecast_error_diffuse_cov) > kfilter.tolerance_diffuse: smoother._smoothed_measurement_disturbance[i] = -obs_cov * smoother._smoothed_measurement_disturbance[i] elif not forecast_error_cov == 0: smoother._smoothed_measurement_disturbance[i] = obs_cov * ( kfilter._forecast_error[i] / forecast_error_cov - smoother._smoothed_measurement_disturbance[i]) else: smoother._smoothed_measurement_disturbance[i] = 0 # Smoothed measurement disturbance covariance matrix if smoother.smoother_output & SMOOTHER_DISTURBANCE_COV: if {{combined_prefix}}abs(forecast_error_diffuse_cov) > kfilter.tolerance_diffuse: smoother._smoothed_measurement_disturbance_cov[i + i*kfilter.k_endog] = ( obs_cov * (1 - obs_cov * smoother._smoothed_measurement_disturbance_cov[i + i*kfilter.k_endog])) elif not forecast_error_cov == 0: smoother._smoothed_measurement_disturbance_cov[i + i*kfilter.k_endog] = ( obs_cov * (1 - obs_cov * (1. / forecast_error_cov + smoother._smoothed_measurement_disturbance_cov[i + i*kfilter.k_endog]))) else: smoother._smoothed_measurement_disturbance_cov[i + i*kfilter.k_endog] = obs_cov # Smoothed state disturbance if smoother.smoother_output & SMOOTHER_DISTURBANCE: blas.{{prefix}}gemv("T", &model._k_states, &model._k_posdef, &alpha, smoother._tmp0, &kfilter.k_states, smoother._input_scaled_smoothed_estimator, &inc, &beta, smoother._smoothed_state_disturbance, &inc) # Smoothed state disturbance covariance matrix if smoother.smoother_output & SMOOTHER_DISTURBANCE_COV: blas.{{prefix}}gemm("N", "N", &model._k_states, &model._k_posdef, &model._k_states, &alpha, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &beta, smoother._tmpL, &kfilter.k_states) blas.{{prefix}}copy(&model._k_posdef2, model._state_cov, &inc, smoother._smoothed_state_disturbance_cov, &inc) blas.{{prefix}}gemm("T", "N", &kfilter.k_posdef, &kfilter.k_posdef, &kfilter.k_states, &gamma, smoother._tmp0, &kfilter.k_states, smoother._tmpL, &kfilter.k_states, &alpha, smoother._smoothed_state_disturbance_cov, &kfilter.k_posdef) cdef int {{prefix}}smoothed_state_autocov_univariate_diffuse({{prefix}}KalmanSmoother smoother, {{prefix}}KalmanFilter kfilter, {{prefix}}Statespace model): cdef: int i int inc = 1 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 # The below code was a test to see if the diffuse autocov could be # relatively simply computed (i.e. which required certain terms to cancel # out), but it appears that it cannot (i.e. it requires the computation of # L2, which is nontrivial and not described by Durbin and Koopman). return 0 # -P_t1 N0t -> tmp0 blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &gamma, &kfilter.predicted_state_cov[0,0,smoother.t+1], &kfilter.k_states, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) # - P_t1_inf N2t - P_t1 N0t -> tmpL blas.{{prefix}}copy(&kfilter.k_states2, smoother._tmp0, &inc, smoother._tmpL, &inc) blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &gamma, &kfilter.predicted_diffuse_state_cov[0,0,smoother.t+1], &kfilter.k_states, smoother._input_scaled_smoothed_diffuse2_estimator_cov, &kfilter.k_states, &alpha, smoother._tmpL, &kfilter.k_states) # I - P_t1_inf N1t - P_t1 N0t -> tmp0 blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &gamma, &kfilter.predicted_diffuse_state_cov[0,0,smoother.t+1], &kfilter.k_states, smoother._input_scaled_smoothed_diffuse1_estimator_cov, &kfilter.k_states, &alpha, smoother._tmp0, &kfilter.k_states) for i in range(kfilter.k_states): smoother.tmp0[i,i] = 1 + smoother.tmp0[i,i] # L0t P_t -> tmpL2 blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &alpha, kfilter._tmpL0, &kfilter.k_states, &kfilter.predicted_state_cov[0, 0, smoother.t], &kfilter.k_states, &beta, smoother._tmpL2, &kfilter.k_states) # L0t P_t + L1t P_t_inf -> tmpL2 blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &alpha, kfilter._tmpL1, &kfilter.k_states, &kfilter.predicted_diffuse_state_cov[0, 0, smoother.t], &kfilter.k_states, &alpha, smoother._tmpL2, &kfilter.k_states) # [I - P_t1_inf N1t - P_t1 N0t] (L1t P_t_inf + L0t P_t) -> smoothed_state_autocov blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &alpha, smoother._tmp0, &kfilter.k_states, smoother._tmpL2, &kfilter.k_states, &beta, smoother._smoothed_state_autocov, &kfilter.k_states) # L0t P_t_inf -> tmp0 blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &alpha, kfilter._tmpL0, &kfilter.k_states, &kfilter.predicted_diffuse_state_cov[0, 0, smoother.t], &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) # [- P_t1_inf N2t - P_t1 N0t] L0t P_t_inf +-> smoothed_state_autocov blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &alpha, smoother._tmpL, &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &alpha, smoother._smoothed_state_autocov, &kfilter.k_states) # [- P_t1_inf N0t ] -> tmpL blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &gamma, &kfilter.predicted_diffuse_state_cov[0,0,smoother.t+1], &kfilter.k_states, smoother._input_scaled_smoothed_estimator_cov, &kfilter.k_states, &beta, smoother._tmpL, &kfilter.k_states) # L1t P_t -> tmp0 blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &alpha, kfilter._tmpL1, &kfilter.k_states, &kfilter.predicted_state_cov[0, 0, smoother.t], &kfilter.k_states, &beta, smoother._tmp0, &kfilter.k_states) # [- P_t1_inf N0t ] L1t P_t +-> smoothed_state_autocov blas.{{prefix}}gemm("N", "N", &model.k_states, &model.k_states, &model.k_states, &alpha, smoother._tmpL, &kfilter.k_states, smoother._tmp0, &kfilter.k_states, &alpha, smoother._smoothed_state_autocov, &kfilter.k_states) {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/_tools.pxd000066400000000000000000000125561400612667500234570ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Models - Cython Tools declarations Author: Chad Fulton License: Simplified-BSD """ cimport numpy as np cdef validate_matrix_shape(str name, Py_ssize_t *shape, int nrows, int ncols, object nobs=*) cdef validate_vector_shape(str name, Py_ssize_t *shape, int nrows, object nobs=*) cdef int _ssolve_discrete_lyapunov(np.float32_t * a, np.float32_t * q, int n, int complex_step=*) except * cdef int _dsolve_discrete_lyapunov(np.float64_t * a, np.float64_t * q, int n, int complex_step=*) except * cdef int _csolve_discrete_lyapunov(np.complex64_t * a, np.complex64_t * q, int n, int complex_step=*) except * cdef int _zsolve_discrete_lyapunov(np.complex128_t * a, np.complex128_t * q, int n, int complex_step=*) except * cdef int _sldl(np.float32_t * A, int n) except * cdef int _dldl(np.float64_t * A, int n) except * cdef int _cldl(np.complex64_t * A, int n) except * cdef int _zldl(np.complex128_t * A, int n) except * cpdef int sldl(np.float32_t [::1, :] A) except * cpdef int dldl(np.float64_t [::1, :] A) except * cpdef int cldl(np.complex64_t [::1, :] A) except * cpdef int zldl(np.complex128_t [::1, :] A) except * cpdef int sreorder_missing_matrix(np.float32_t [::1, :, :] A, int [::1, :] missing, int reorder_rows, int reorder_cols, int diagonal) except * cpdef int dreorder_missing_matrix(np.float64_t [::1, :, :] A, int [::1, :] missing, int reorder_rows, int reorder_cols, int diagonal) except * cpdef int creorder_missing_matrix(np.complex64_t [::1, :, :] A, int [::1, :] missing, int reorder_rows, int reorder_cols, int diagonal) except * cpdef int zreorder_missing_matrix(np.complex128_t [::1, :, :] A, int [::1, :] missing, int reorder_rows, int reorder_cols, int diagonal) except * cpdef int sreorder_missing_vector(np.float32_t [::1, :] A, int [::1, :] missing) except * cpdef int dreorder_missing_vector(np.float64_t [::1, :] A, int [::1, :] missing) except * cpdef int creorder_missing_vector(np.complex64_t [::1, :] A, int [::1, :] missing) except * cpdef int zreorder_missing_vector(np.complex128_t [::1, :] A, int [::1, :] missing) except * cpdef int scopy_missing_matrix(np.float32_t [::1, :, :] A, np.float32_t [::1, :, :] B, int [::1, :] missing, int copy_rows, int copy_cols, int diagonal) except * cpdef int dcopy_missing_matrix(np.float64_t [::1, :, :] A, np.float64_t [::1, :, :] B, int [::1, :] missing, int copy_rows, int copy_cols, int diagonal) except * cpdef int ccopy_missing_matrix(np.complex64_t [::1, :, :] A, np.complex64_t [::1, :, :] B, int [::1, :] missing, int copy_rows, int copy_cols, int diagonal) except * cpdef int zcopy_missing_matrix(np.complex128_t [::1, :, :] A, np.complex128_t [::1, :, :] B, int [::1, :] missing, int copy_rows, int copy_cols, int diagonal) except * cpdef int scopy_missing_vector(np.float32_t [::1, :] A, np.float32_t [::1, :] B, int [::1, :] missing) except * cpdef int dcopy_missing_vector(np.float64_t [::1, :] A, np.float64_t [::1, :] B, int [::1, :] missing) except * cpdef int ccopy_missing_vector(np.complex64_t [::1, :] A, np.complex64_t [::1, :] B, int [::1, :] missing) except * cpdef int zcopy_missing_vector(np.complex128_t [::1, :] A, np.complex128_t [::1, :] B, int [::1, :] missing) except * cpdef int scopy_index_matrix(np.float32_t [::1, :, :] A, np.float32_t [::1, :, :] B, int [::1, :] index, int copy_rows, int copy_cols, int diagonal) except * cpdef int dcopy_index_matrix(np.float64_t [::1, :, :] A, np.float64_t [::1, :, :] B, int [::1, :] index, int copy_rows, int copy_cols, int diagonal) except * cpdef int ccopy_index_matrix(np.complex64_t [::1, :, :] A, np.complex64_t [::1, :, :] B, int [::1, :] index, int copy_rows, int copy_cols, int diagonal) except * cpdef int zcopy_index_matrix(np.complex128_t [::1, :, :] A, np.complex128_t [::1, :, :] B, int [::1, :] index, int copy_rows, int copy_cols, int diagonal) except * cpdef int scopy_index_vector(np.float32_t [::1, :] A, np.float32_t [::1, :] B, int [::1, :] index) except * cpdef int dcopy_index_vector(np.float64_t [::1, :] A, np.float64_t [::1, :] B, int [::1, :] index) except * cpdef int ccopy_index_vector(np.complex64_t [::1, :] A, np.complex64_t [::1, :] B, int [::1, :] index) except * cpdef int zcopy_index_vector(np.complex128_t [::1, :] A, np.complex128_t [::1, :] B, int [::1, :] index) except * cdef int _sselect_cov(int k_states, int k_posdef, int k_states_total, np.float32_t * tmp, np.float32_t * selection, np.float32_t * cov, np.float32_t * selected_cov) cdef int _dselect_cov(int k_states, int k_posdef, int k_states_total, np.float64_t * tmp, np.float64_t * selection, np.float64_t * cov, np.float64_t * selected_cov) cdef int _cselect_cov(int k_states, int k_posdef, int k_states_total, np.complex64_t * tmp, np.complex64_t * selection, np.complex64_t * cov, np.complex64_t * selected_cov) cdef int _zselect_cov(int k_states, int k_posdef, int k_states_total, np.complex128_t * tmp, np.complex128_t * selection, np.complex128_t * cov, np.complex128_t * selected_cov) statsmodels-0.12.2/statsmodels/tsa/statespace/_tools.pyx.in000066400000000000000000001241631400612667500241070ustar00rootroot00000000000000#cython: boundscheck=False #cython: wraparound=False #cython: cdivision=False """ State Space Model - Cython tools Author: Chad Fulton License: Simplified-BSD """ # Typical imports cimport numpy as np cimport cython import numpy as np np.import_array() from statsmodels.src.math cimport * cimport scipy.linalg.cython_blas as blas cimport scipy.linalg.cython_lapack as lapack cdef FORTRAN = 1 ctypedef fused sm_type_t: np.float64_t np.float32_t np.complex64_t np.complex128_t # ------------------------------------------------------------------------ # Array shape validation cdef validate_matrix_shape(str name, Py_ssize_t *shape, int nrows, int ncols, nobs=None): if not shape[0] == nrows: raise ValueError('Invalid shape for %s matrix: requires %d rows,' ' got %d' % (name, nrows, shape[0])) if not shape[1] == ncols: raise ValueError('Invalid shape for %s matrix: requires %d columns,' 'got %d' % (name, shape[1], shape[1])) if nobs is not None and shape[2] not in [1, nobs]: raise ValueError('Invalid time-varying dimension for %s matrix:' ' requires 1 or %d, got %d' % (name, nobs, shape[2])) cdef validate_vector_shape(str name, Py_ssize_t *shape, int nrows, nobs = None): if not shape[0] == nrows: raise ValueError('Invalid shape for %s vector: requires %d rows,' ' got %d' % (name, nrows, shape[0])) if nobs is not None and not shape[1] in [1, nobs]: raise ValueError('Invalid time-varying dimension for %s vector:' ' requires 1 or %d got %d' % (name, nobs, shape[1])) # ------------------------------------------------------------------------ # Blas Wrapping cdef inline copy(int size, sm_type_t* src_arr, sm_type_t* target, int incx=1, int incy=1): """ Parameters ---------- size : int number of elements in vectors `src_arr` and `target` src_arr : sm_type_t* Pointer to Array that we are copying _from_ target : sm_type_t* Pointer to Array that we are copying _to_ incx : int, default 1 Specifies the increment for the elements of `src_arr` incy : int, default 1 Specifies the increment for the elements of `target` References ---------- https://software.intel.com/en-us/mkl-developer-reference-c-cblas-copy """ if sm_type_t is np.float32_t: blas.scopy(&size, src_arr, &incx, target, &incy) elif sm_type_t is np.float64_t: blas.dcopy(&size, src_arr, &incx, target, &incy) elif sm_type_t is np.complex64_t: blas.ccopy(&size, src_arr, &incx, target, &incy) elif sm_type_t is np.complex128_t: blas.zcopy(&size, src_arr, &incx, target, &incy) cdef inline swap(int size, sm_type_t* src_arr, sm_type_t* target, int incx=1, int incy=1): """ Parameters ---------- size : int number of elements in vectors `src_arr` and `target` src_arr : sm_type_t* Pointer to first of two arrays being swapped target : sm_type_t* Pointer to second of two arrays being swapped incx : int, default 1 Specifies the increment for the elements of `src_arr` incy : int, default 1 Specifies the increment for the elements of `target` References ---------- https://software.intel.com/en-us/mkl-developer-reference-c-cblas-swap """ if sm_type_t is np.float32_t: blas.sswap(&size, src_arr, &incx, target, &incy) elif sm_type_t is np.float64_t: blas.dswap(&size, src_arr, &incx, target, &incy) elif sm_type_t is np.complex64_t: blas.cswap(&size, src_arr, &incx, target, &incy) elif sm_type_t is np.complex128_t: blas.zswap(&size, src_arr, &incx, target, &incy) # ------------------------------------------------------------------------ {{py: TYPES = { "s": ("np.float32_t", "np.float32", "np.NPY_FLOAT32"), "d": ("np.float64_t", "float", "np.NPY_FLOAT64"), "c": ("np.complex64_t", "np.complex64", "np.NPY_COMPLEX64"), "z": ("np.complex128_t", "complex", "np.NPY_COMPLEX128"), } }} {{for prefix, types in TYPES.items()}} {{py:cython_type, dtype, typenum = types}} {{py: combined_prefix = prefix combined_cython_type = cython_type if prefix == 'c': combined_prefix = 'z' combined_cython_type = 'np.complex128_t' if prefix == 's': combined_prefix = 'd' combined_cython_type = 'np.float64_t' }} cdef bint _{{prefix}}select1({{cython_type}} * a): return 0 cdef bint _{{prefix}}select2({{cython_type}} * a, {{cython_type}} * b): return 0 cdef int _{{prefix}}solve_discrete_lyapunov({{cython_type}} * a, {{cython_type}} * q, int n, int complex_step=False) except *: # Note: some of this code (esp. the Sylvester solving part) cribbed from # https://raw.githubusercontent.com/scipy/scipy/master/scipy/linalg/_solvers.py # Solve an equation of the form $A'XA-X=-Q$ # a: input / output # q: input / output cdef: int i, j int info int inc = 1 int n2 = n**2 {{if prefix == 's' or prefix == 'c'}} np.float32_t scale = 0.0 {{else}} np.float64_t scale = 0.0 {{endif}} {{cython_type}} tmp = 0.0 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} delta = -2.0 char trans cdef np.npy_intp dim[2] cdef {{cython_type}} [::1,:] apI, capI, u, v cdef int [::1,:] ipiv # Dummy selection function, will not actually be referenced since we do not # need to order the eigenvalues in the ?gees call. cdef: int sdim int lwork = 3*n bint bwork cdef np.npy_intp dim1[1] cdef {{cython_type}} [::1,:] work cdef {{cython_type}} [:] wr {{if prefix == 's' or prefix == 'c'}} cdef np.float32_t [:] wi {{else}} cdef np.float64_t [:] wi {{endif}} # Initialize arrays dim[0] = n; dim[1] = n; apI = np.PyArray_ZEROS(2, dim, {{typenum}}, FORTRAN) capI = np.PyArray_ZEROS(2, dim, {{typenum}}, FORTRAN) u = np.PyArray_ZEROS(2, dim, {{typenum}}, FORTRAN) v = np.PyArray_ZEROS(2, dim, {{typenum}}, FORTRAN) ipiv = np.PyArray_ZEROS(2, dim, np.NPY_INT32, FORTRAN) dim1[0] = n; wr = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) {{if prefix == 's'}} wi = np.PyArray_ZEROS(1, dim1, {{typenum}}, FORTRAN) {{else}} wi = np.PyArray_ZEROS(1, dim1, np.NPY_FLOAT64, FORTRAN) {{endif}} #vs = np.PyArray_ZEROS(2, dim, {{typenum}}, FORTRAN) dim[0] = lwork; dim[1] = lwork; work = np.PyArray_ZEROS(2, dim, {{typenum}}, FORTRAN) # - Solve for b.conj().transpose() -------- # Get apI = a + I (stored in apI) # = (a + eye) # For: c = 2*np.dot(np.dot(inv(a + eye), q), aHI_inv) copy(n2, a, &apI[0, 0]) # (for loop below adds the identity) # Get conj(a) + I (stored in capI) # a^H + I -> capI # For: aHI_inv = inv(aH + eye) copy(n2, a, &capI[0, 0]) # (for loop below adds the identity) # Get conj(a) - I (stored in a) # a^H - I -> a # For: b = np.dot(aH - eye, aHI_inv) # (for loop below subtracts the identity) # Add / subtract identity matrix for i in range(n): apI[i,i] = apI[i,i] + 1 # apI -> a + eye capI[i,i] = capI[i,i] + 1 # aH + eye a[i + i*n] = a[i + i*n] - 1 # a - eye # Solve [conj(a) + I] b' = [conj(a) - I] (result stored in a) # For: b = np.dot(aH - eye, aHI_inv) # Where: aHI_inv = inv(aH + eye) # where b = (a^H - eye) (a^H + eye)^{-1} # or b^H = (a + eye)^{-1} (a - eye) # or (a + eye) b^H = (a - eye) lapack.{{prefix}}getrf(&n, &n, &capI[0,0], &n, &ipiv[0,0], &info) if not info == 0: raise np.linalg.LinAlgError('LU decomposition error.') lapack.{{prefix}}getrs("N", &n, &n, &capI[0,0], &n, &ipiv[0,0], a, &n, &info) if not info == 0: raise np.linalg.LinAlgError('LU solver error.') # Now we have b^H; we could take the conjugate transpose to get b, except # that the input to the continuous Lyapunov equation is exactly # b^H, so we already have the quantity we need. # - Solve for (-c) -------- # where c = 2*np.dot(np.dot(inv(a + eye), q), aHI_inv) # = 2*(a + eye)^{-1} q (a^H + eye)^{-1} # and with q Hermitian # consider x = (a + eye)^{-1} q (a^H + eye)^{-1} # this can be done in two linear solving steps: # 1. consider y = q (a^H + eye)^{-1} # or y (a^H + eye) = q # or (a^H + eye)^H y^H = q^H # or (a + eye) y^H = q # 2. Then consider x = (a + eye)^{-1} y # or (a + eye) x = y # Solve [conj(a) + I] tmp' = q (result stored in q) # For: y = q (a^H + eye)^{-1} => (a + eye) y^H = q lapack.{{prefix}}getrs("N", &n, &n, &capI[0,0], &n, &ipiv[0,0], q, &n, &info) if not info == 0: raise np.linalg.LinAlgError('LU solver error.') # Replace the result (stored in q) with its (conjugate) transpose for j in range(1, n): for i in range(j): tmp = q[i + j*n] q[i + j*n] = q[j + i*n] q[j + i*n] = tmp {{if combined_prefix == 'z'}} if not complex_step: for i in range(n2): q[i] = q[i] - q[i].imag * 2.0j {{endif}} lapack.{{prefix}}getrs("N", &n, &n, &capI[0,0], &n, &ipiv[0,0], q, &n, &info) if not info == 0: raise np.linalg.LinAlgError('LU solver error.') # q -> -2.0 * q blas.{{prefix}}scal(&n2, &delta, q, &inc) # - Solve continuous time Lyapunov -------- # Now solve the continuous time Lyapunov equation (AX + XA^H = Q), on the # transformed inputs ... # ... which requires solving the continuous time Sylvester equation # (AX + XB = Q) where B = A^H # Compute the real Schur decomposition of a (unordered) # TODO compute the optimal lwork rather than always using 3*n {{if combined_prefix == 'd'}} # a is now the Schur form of A; (r) # u is now the unitary Schur transformation matrix for A; (u) # In the usual case, we will also have: # r = s, so s is also stored in a # u = v, so v is also stored in u # In the complex-step case, we will instead have: # r = s.conj() # u = v.conj() lapack.{{prefix}}gees("V", "N", &_{{prefix}}select2, &n, a, &n, &sdim, &wr[0], &wi[0], &u[0,0], &n, &work[0,0], &lwork, &bwork, &info) {{else}} lapack.{{prefix}}gees("V", "N", &_{{prefix}}select1, &n, a, &n, &sdim, &wr[0], &u[0,0], &n, &work[0,0], &lwork, &wi[0], &bwork, &info) {{endif}} if not info == 0: raise np.linalg.LinAlgError('Schur decomposition solver error.') # Get v (so that in the complex step case we can take the conjugate) copy(n2, &u[0, 0], &v[0, 0]) # If complex step, take the conjugate {{if combined_prefix == 'z'}} if complex_step: for i in range(n): for j in range(n): v[i,j] = v[i,j] - v[i,j].imag * 2.0j {{endif}} # Construct f = u^H*q*u (result overwrites q) # In the usual case, v = u # In the complex step case, v = u.conj() blas.{{prefix}}gemm("N", "N", &n, &n, &n, &alpha, q, &n, &v[0,0], &n, &beta, &capI[0,0], &n) blas.{{prefix}}gemm("C", "N", &n, &n, &n, &alpha, &u[0,0], &n, &capI[0,0], &n, &beta, q, &n) # DTRYSL Solve op(A)*X + X*op(B) = scale*C which is here: # r*X + X*r = scale*q # results overwrite q copy(n2, a, &apI[0, 0]) {{if combined_prefix == 'z'}} if complex_step: for i in range(n): for j in range(n): apI[j,i] = apI[j,i] - apI[j,i].imag * 2.0j {{endif}} lapack.{{prefix}}trsyl("N", "C", &inc, &n, &n, a, &n, &apI[0,0], &n, q, &n, &scale, &info) # Scale q by scale if not scale == 1.0: blas.{{prefix}}scal(&n2, <{{cython_type}}*> &scale, q, &inc) # Calculate the solution: u * q * v^H (results overwrite q) # In the usual case, v = u # In the complex step case, v = u.conj() blas.{{prefix}}gemm("N", "C", &n, &n, &n, &alpha, q, &n, &v[0,0], &n, &beta, &capI[0,0], &n) blas.{{prefix}}gemm("N", "N", &n, &n, &n, &alpha, &u[0,0], &n, &capI[0,0], &n, &beta, q, &n) cpdef _{{prefix}}compute_coefficients_from_multivariate_pacf({{cython_type}} [::1,:] partial_autocorrelations, {{cython_type}} [::1,:] error_variance, int transform_variance, int order, int k_endog): """ Notes ----- This uses the ?trmm BLAS functions which are not available in Scipy v0.11.0 """ # Constants cdef: {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 {{cython_type}} gamma = -1.0 int k_endog2 = k_endog**2 int k_endog_order = k_endog * order int k_endog_order1 = k_endog * (order+1) int info, s, k # Local variables cdef: np.npy_intp dim2[2] {{cython_type}} [::1, :] initial_variance {{cython_type}} [::1, :] forward_variance {{cython_type}} [::1, :] backward_variance {{cython_type}} [::1, :] autocovariances {{cython_type}} [::1, :] forwards1 {{cython_type}} [::1, :] forwards2 {{cython_type}} [::1, :] backwards1 {{cython_type}} [::1, :] backwards2 {{cython_type}} [::1, :] forward_factors {{cython_type}} [::1, :] backward_factors {{cython_type}} [::1, :] tmp {{cython_type}} [::1, :] tmp2 # Pointers cdef: {{cython_type}} * forwards {{cython_type}} * prev_forwards {{cython_type}} * backwards {{cython_type}} * prev_backwards # ?trmm # cdef {{prefix}}trmm_t *{{prefix}}trmm = <{{prefix}}trmm_t*>Capsule_AsVoidPtr(blas.{{prefix}}trmm._cpointer) # dim2[0] = self.k_endog; dim2[1] = storage; # self.forecast = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # If we want to keep the provided variance but with the constrained # coefficient matrices, we need to make a copy here, and then after the # main loop we will transform the coefficients to match the passed variance if not transform_variance: initial_variance = np.asfortranarray(error_variance.copy()) # Need to make the input variance large enough that the recursions # do not lead to zero-matrices due to roundoff error, which would case # exceptions from the Cholesky decompositions. # Note that this will still not always ensure positive definiteness, # and for k_endog, order large enough an exception may still be raised error_variance = np.asfortranarray(np.eye(k_endog, dtype={{dtype}}) * (order + k_endog)**10) # Initialize matrices dim2[0] = k_endog; dim2[1] = k_endog; forward_variance = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) backward_variance = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) forward_factors = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) backward_factors = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) tmp = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) tmp2 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = k_endog; dim2[1] = k_endog_order; # \phi_{s,k}, s = 1, ..., p # k = 1, ..., s+1 forwards1 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) forwards2 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) # \phi_{s,k}^* backwards1 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) backwards2 = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = k_endog; dim2[1] = k_endog_order1; autocovariances = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) copy(k_endog2, &error_variance[0, 0], &forward_variance[0, 0]) # \Sigma_s copy(k_endog2, &error_variance[0, 0], &backward_variance[0, 0]) # \Sigma_s^*, s = 0, ..., p copy(k_endog2, &error_variance[0, 0], &autocovariances[0, 0]) # \Gamma_s # error_variance_factor = linalg.cholesky(error_variance, lower=True) copy(k_endog2, &error_variance[0, 0], &forward_factors[0,0]) lapack.{{prefix}}potrf("L", &k_endog, &forward_factors[0,0], &k_endog, &info) copy(k_endog2, &forward_factors[0, 0], &backward_factors[0, 0]) # We fill in the entries as follows: # [1,1] # [2,2], [2,1] # [3,3], [3,1], [3,2] # ... # [p,p], [p,1], ..., [p,p-1] # the last row, correctly ordered, is then used as the coefficients for s in range(order): # s = 0, ..., p-1 if s % 2 == 0: forwards = &forwards1[0, 0] prev_forwards = &forwards2[0, 0] backwards = &backwards1[0, 0] prev_backwards = &backwards2[0, 0] else: forwards = &forwards2[0, 0] prev_forwards = &forwards1[0, 0] backwards = &backwards2[0, 0] prev_backwards = &backwards1[0, 0] # Create the "last" (k = s+1) matrix # Note: this is for k = s+1. However, below we then have to fill # in for k = 1, ..., s in order. # P L*^{-1} = x # x L* = P # L*' x' = P' # forwards[:, s*k_endog:(s+1)*k_endog] = np.dot( # forward_factors, # linalg.solve_triangular( # backward_factors, partial_autocorrelations[:, s*k_endog:(s+1)*k_endog].T, # lower=True, trans='T').T # ) for k in range(k_endog): copy(k_endog, &partial_autocorrelations[k, s*k_endog], &tmp[0, k], k_endog) lapack.{{prefix}}trtrs("L", "T", "N", &k_endog, &k_endog, &backward_factors[0,0], &k_endog, &tmp[0, 0], &k_endog, &info) # {{prefix}}gemm("N", "T", &k_endog, &k_endog, &k_endog, # &alpha, &forward_factors[0,0], &k_endog, # &tmp[0, 0], &k_endog, # &beta, &forwards[s*k_endog2], &k_endog) blas.{{prefix}}trmm("R", "L", "T", "N", &k_endog, &k_endog, &alpha, &forward_factors[0,0], &k_endog, &tmp[0, 0], &k_endog) for k in range(k_endog): copy(k_endog, &tmp[k, 0], &forwards[s*k_endog2 + k*k_endog], k_endog) # P' L^{-1} = x # x L = P' # L' x' = P # backwards[:, s*k_endog:(s+1)*k_endog] = np.dot( # backward_factors, # linalg.solve_triangular( # forward_factors, partial_autocorrelations[:, s*k_endog:(s+1)*k_endog], # lower=True, trans='T').T # ) copy(k_endog2, &partial_autocorrelations[0, s*k_endog], &tmp[0, 0]) lapack.{{prefix}}trtrs("L", "T", "N", &k_endog, &k_endog, &forward_factors[0, 0], &k_endog, &tmp[0, 0], &k_endog, &info) # {{prefix}}gemm("N", "T", &k_endog, &k_endog, &k_endog, # &alpha, &backward_factors[0, 0], &k_endog, # &tmp[0, 0], &k_endog, # &beta, &backwards[s * k_endog2], &k_endog) blas.{{prefix}}trmm("R", "L", "T", "N", &k_endog, &k_endog, &alpha, &backward_factors[0,0], &k_endog, &tmp[0, 0], &k_endog) for k in range(k_endog): copy(k_endog, &tmp[k, 0], &backwards[s*k_endog2 + k*k_endog], k_endog) # Update the variance # Note: if s >= 1, this will be further updated in the for loop # below # Also, this calculation will be re-used in the forward variance # tmp = np.dot(forwards[:, s*k_endog:(s+1)*k_endog], backward_variance) # tmpT = np.dot(backward_variance.T, forwards[:, s*k_endog:(s+1)*k_endog].T) blas.{{prefix}}gemm("T", "T", &k_endog, &k_endog, &k_endog, &alpha, &backward_variance[0, 0], &k_endog, &forwards[s * k_endog2], &k_endog, &beta, &tmp[0, 0], &k_endog) # autocovariances[:, (s+1)*k_endog:(s+2)*k_endog] = tmp.copy().T copy(k_endog2, &tmp[0, 0], &autocovariances[0, (s+1)*k_endog]) # Create the remaining k = 1, ..., s matrices, # only has an effect if s >= 1 for k in range(s): # forwards[:, k*k_endog:(k+1)*k_endog] = ( # prev_forwards[:, k*k_endog:(k+1)*k_endog] - # np.dot( # forwards[:, s*k_endog:(s+1)*k_endog], # prev_backwards[:, (s-k-1)*k_endog:(s-k)*k_endog] # ) # ) copy(k_endog2, &prev_forwards[k * k_endog2], &forwards[k * k_endog2]) blas.{{prefix}}gemm("N", "N", &k_endog, &k_endog, &k_endog, &gamma, &forwards[s * k_endog2], &k_endog, &prev_backwards[(s - k - 1) * k_endog2], &k_endog, &alpha, &forwards[k * k_endog2], &k_endog) # backwards[:, k*k_endog:(k+1)*k_endog] = ( # prev_backwards[:, k*k_endog:(k+1)*k_endog] - # np.dot( # backwards[:, s*k_endog:(s+1)*k_endog], # prev_forwards[:, (s-k-1)*k_endog:(s-k)*k_endog] # ) # ) copy(k_endog2, &prev_backwards[k * k_endog2], &backwards[k * k_endog2]) blas.{{prefix}}gemm("N", "N", &k_endog, &k_endog, &k_endog, &gamma, &backwards[s * k_endog2], &k_endog, &prev_forwards[(s - k - 1) * k_endog2], &k_endog, &alpha, &backwards[k * k_endog2], &k_endog) # autocovariances[:, (s+1)*k_endog:(s+2)*k_endog] += np.dot( # autocovariances[:, (k+1)*k_endog:(k+2)*k_endog], # prev_forwards[:, (s-k-1)*k_endog:(s-k)*k_endog].T # ) blas.{{prefix}}gemm("N", "T", &k_endog, &k_endog, &k_endog, &alpha, &autocovariances[0, (k+1)*k_endog], &k_endog, &prev_forwards[(s - k - 1) * k_endog2], &k_endog, &alpha, &autocovariances[0, (s+1)*k_endog], &k_endog) # Create forward and backwards variances # backward_variance = ( # backward_variance - # np.dot( # np.dot(backwards[:, s*k_endog:(s+1)*k_endog], forward_variance), # backwards[:, s*k_endog:(s+1)*k_endog].T # ) # ) blas.{{prefix}}gemm("N", "N", &k_endog, &k_endog, &k_endog, &alpha, &backwards[s * k_endog2], &k_endog, &forward_variance[0, 0], &k_endog, &beta, &tmp2[0, 0], &k_endog) blas.{{prefix}}gemm("N", "T", &k_endog, &k_endog, &k_endog, &gamma, &tmp2[0, 0], &k_endog, &backwards[s * k_endog2], &k_endog, &alpha, &backward_variance[0, 0], &k_endog) # forward_variance = ( # forward_variance - # np.dot(tmp, forwards[:, s*k_endog:(s+1)*k_endog].T) # ) # forward_variance = ( # forward_variance - # np.dot(tmpT.T, forwards[:, s*k_endog:(s+1)*k_endog].T) # ) blas.{{prefix}}gemm("T", "T", &k_endog, &k_endog, &k_endog, &gamma, &tmp[0, 0], &k_endog, &forwards[s * k_endog2], &k_endog, &alpha, &forward_variance[0, 0], &k_endog) # Cholesky factors # forward_factors = linalg.cholesky(forward_variance, lower=True) # backward_factors = linalg.cholesky(backward_variance, lower=True) copy(k_endog2, &forward_variance[0, 0], &forward_factors[0, 0]) lapack.{{prefix}}potrf("L", &k_endog, &forward_factors[0,0], &k_endog, &info) copy(k_endog2, &backward_variance[0, 0], &backward_factors[0, 0]) lapack.{{prefix}}potrf("L", &k_endog, &backward_factors[0,0], &k_endog, &info) # If we do not want to use the transformed variance, we need to # adjust the constrained matrices, as presented in Lemma 2.3, see above if not transform_variance: if order % 2 == 0: forwards = &forwards2[0,0] else: forwards = &forwards1[0,0] # Here, we need to construct T such that: # variance = T * initial_variance * T' # To do that, consider the Cholesky of variance (L) and # input_variance (M) to get: # L L' = T M M' T' = (TM) (TM)' # => L = T M # => L M^{-1} = T # initial_variance_factor = np.linalg.cholesky(initial_variance) # L' lapack.{{prefix}}potrf("U", &k_endog, &initial_variance[0,0], &k_endog, &info) # transformed_variance_factor = np.linalg.cholesky(variance) # M' copy(k_endog2, &forward_variance[0, 0], &tmp[0, 0]) lapack.{{prefix}}potrf("U", &k_endog, &tmp[0,0], &k_endog, &info) # {{prefix}}potri("L", &k_endog, &tmp[0,0], &k_endog, &info) # We need to zero out the lower triangle of L', because ?trtrs only # knows that M' is upper triangular for s in range(k_endog - 1): # column for k in range(s+1, k_endog): # row initial_variance[k, s] = 0 # Note that T is lower triangular # L M^{-1} = T # M' T' = L' # transform = np.dot(initial_variance_factor, # np.linalg.inv(transformed_variance_factor)) lapack.{{prefix}}trtrs("U", "N", "N", &k_endog, &k_endog, &tmp[0,0], &k_endog, &initial_variance[0, 0], &k_endog, &info) # Now: # initial_variance = T' for s in range(order): # forwards[:, s*k_endog:(s+1)*k_endog] = ( # np.dot( # np.dot(transform, forwards[:, s*k_endog:(s+1)*k_endog]), # inv_transform # ) # ) # TF T^{-1} = x # TF = x T # (TF)' = T' x' # Get TF copy(k_endog2, &forwards[s * k_endog2], &tmp2[0, 0]) blas.{{prefix}}trmm("L", "U", "T", "N", &k_endog, &k_endog, &alpha, &initial_variance[0, 0], &k_endog, &tmp2[0, 0], &k_endog) for k in range(k_endog): copy(k_endog, &tmp2[k, 0], &tmp[0, k], k_endog) # Get x' lapack.{{prefix}}trtrs("U", "N", "N", &k_endog, &k_endog, &initial_variance[0,0], &k_endog, &tmp[0, 0], &k_endog, &info) # Get x for k in range(k_endog): copy(k_endog, &tmp[k, 0], &forwards[s * k_endog2 + k*k_endog], k_endog) if order % 2 == 0: return forwards2, forward_variance else: return forwards1, forward_variance cpdef _{{prefix}}constrain_sv_less_than_one({{cython_type}} [::1,:] unconstrained, int order, int k_endog): """ Transform arbitrary matrices to matrices with singular values less than one. Corresponds to Lemma 2.2 in Ansley and Kohn (1986). See `constrain_stationary_multivariate` for more details. """ # Constants cdef: {{cython_type}} alpha = 1.0 int k_endog2 = k_endog**2 int info, i # Local variables cdef: np.npy_intp dim2[2] {{cython_type}} [::1, :] constrained {{cython_type}} [::1, :] tmp {{cython_type}} [::1, :] eye dim2[0] = k_endog; dim2[1] = k_endog * order; constrained = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) dim2[0] = k_endog; dim2[1] = k_endog; tmp = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) eye = np.PyArray_ZEROS(2, dim2, {{typenum}}, FORTRAN) eye = np.asfortranarray(np.eye(k_endog, dtype={{dtype}})) for i in range(order): copy(k_endog2, &eye[0, 0], &tmp[0, 0]) blas.{{prefix}}gemm("N", "T", &k_endog, &k_endog, &k_endog, &alpha, &unconstrained[0, i*k_endog], &k_endog, &unconstrained[0, i*k_endog], &k_endog, &alpha, &tmp[0, 0], &k_endog) lapack.{{prefix}}potrf("L", &k_endog, &tmp[0, 0], &k_endog, &info) copy(k_endog2, &unconstrained[0, i*k_endog], &constrained[0, i*k_endog]) # constrained.append(linalg.solve_triangular(B, A, lower=lower)) lapack.{{prefix}}trtrs("L", "N", "N", &k_endog, &k_endog, &tmp[0, 0], &k_endog, &constrained[0, i*k_endog], &k_endog, &info) return constrained cdef int _{{prefix}}ldl({{cython_type}} * A, int n) except *: # See Golub and Van Loan, Algorithm 4.1.2 cdef: int info = 0 int j, i, k np.npy_intp dim[1] np.float64_t tol = 1e-15 {{cython_type}} [:] v dim[0] = n v = np.PyArray_ZEROS(1, dim, {{typenum}}, FORTRAN) for j in range(n): # Compute v(1:j) v[j] = A[j + j*n] # Positive definite element: use Golub and Van Loan algorithm if v[j].real < -tol: info = -j break elif v[j].real > tol: for i in range(j): v[i] = A[j + i*n] * A[i + i*n] v[j] = v[j] - A[j + i*n] * v[i] # Store d(j) and compute L(j+1:n,j) A[j + j*n] = v[j] for i in range(j+1, n): for k in range(j): A[i + j*n] = A[i + j*n] - A[i + k*n] * v[k] A[i + j*n] = A[i + j*n] / v[j] # Positive semi-definite element: zero the appropriate column else: info = 1 for i in range(j, n): A[i + j*n] return info cpdef int {{prefix}}ldl({{cython_type}} [::1, :] A) except *: _{{prefix}}ldl(&A[0,0], A.shape[0]) cdef int _{{prefix}}reorder_missing_diagonal({{cython_type}} * a, int * missing, int n): """ a is a pointer to an n x n diagonal array A missing is a pointer to an n x 1 array n is the dimension of A """ cdef int i, j, k, nobs nobs = n # Construct the non-missing index for i in range(n): nobs = nobs - missing[i] # Perform replacement k = nobs-1 for i in range(n-1,-1,-1): if not missing[i]: a[i + i*n] = a[k + k*n] k = k - 1 else: a[i + i*n] = 0 cdef int _{{prefix}}reorder_missing_submatrix({{cython_type}} * a, int * missing, int n): """ a is a pointer to an n x n array A missing is a pointer to an n x 1 array n is the dimension of A """ cdef int i, j, k, nobs _{{prefix}}reorder_missing_rows(a, missing, n, n) _{{prefix}}reorder_missing_cols(a, missing, n, n) cdef int _{{prefix}}reorder_missing_rows({{cython_type}} * a, int * missing, int n, int m): """ a is a pointer to an n x m array A missing is a pointer to an n x 1 array n is the number of rows of A m is the number of columns of A """ cdef int i, j, k, nobs nobs = n # Construct the non-missing index for i in range(n): nobs = nobs - missing[i] # Perform replacement k = nobs-1 for i in range(n-1,-1,-1): if not missing[i]: swap(m, &a[i], &a[k], n, n) k = k - 1 cdef int _{{prefix}}reorder_missing_cols({{cython_type}} * a, int * missing, int n, int m): """ a is a pointer to an n x m array A missing is a pointer to an m x 1 array n is the number of rows of A m is the number of columns of A """ cdef int i, k, nobs nobs = m # Construct the non-missing index for i in range(m): nobs = nobs - missing[i] # Perform replacement k = nobs-1 for i in range(m-1,-1,-1): if not missing[i]: swap(n, &a[i*n], &a[k*n]) k = k - 1 cpdef int {{prefix}}reorder_missing_matrix({{cython_type}} [::1, :, :] A, int [::1, :] missing, int reorder_rows, int reorder_cols, int diagonal) except *: cdef int n, m, T, t n, m, T = A.shape[0:3] if reorder_rows and reorder_cols: if not n == m: raise RuntimeError('Reordering a submatrix requires n = m') if diagonal: for t in range(T): _{{prefix}}reorder_missing_diagonal(&A[0, 0, t], &missing[0, t], n) else: for t in range(T): _{{prefix}}reorder_missing_submatrix(&A[0, 0, t], &missing[0, t], n) elif diagonal: raise RuntimeError('`diagonal` argument only valid with reordering a submatrix') elif reorder_rows: for t in range(T): _{{prefix}}reorder_missing_rows(&A[0, 0, t], &missing[0, t], n, m) elif reorder_cols: for t in range(T): _{{prefix}}reorder_missing_cols(&A[0, 0, t], &missing[0, t], n, m) cpdef int {{prefix}}reorder_missing_vector({{cython_type}} [::1, :] A, int [::1, :] missing) except *: cdef int i, k, t, n, T, nobs n, T = A.shape[0:2] for t in range(T): _{{prefix}}reorder_missing_rows(&A[0, t], &missing[0, t], n, 1) cdef int _{{prefix}}copy_missing_diagonal({{cython_type}} * a, {{cython_type}} * b, int * missing, int n): """ Copy the non-missing block of diagonal entries a is a pointer to an n x n diagonal array A (copy from) b is a pointer to an n x n diagonal array B (copy to) missing is a pointer to an n x 1 array n is the dimension of A, B """ cdef int i, j, k, nobs nobs = n # Construct the non-missing index for i in range(n): nobs = nobs - missing[i] # Perform replacement k = nobs-1 for i in range(nobs): b[i + i*n] = a[i + i*n] cdef int _{{prefix}}copy_missing_submatrix({{cython_type}} * a, {{cython_type}} * b, int * missing, int n): """ Copy the non-missing submatrix a is a pointer to an n x n diagonal array A (copy from) b is a pointer to an n x n diagonal array B (copy to) missing is a pointer to an n x 1 array n is the dimension of A, B """ cdef int i, j, nobs nobs = n # Construct the non-missing index for i in range(n): nobs = nobs - missing[i] # Perform replacement for i in range(nobs): copy(nobs, &a[i*n], &b[i*n]) cdef int _{{prefix}}copy_missing_rows({{cython_type}} * a, {{cython_type}} * b, int * missing, int n, int m): """ a is a pointer to an n x m array A b is a pointer to an n x n diagonal array B (copy to) missing is a pointer to an n x 1 array n is the number of rows of A m is the number of columns of A """ cdef int i, j, k, nobs nobs = n # Construct the non-missing index for i in range(n): nobs = nobs - missing[i] # Perform replacement for i in range(nobs): copy(m, &a[i], &b[i], n, n) cdef int _{{prefix}}copy_missing_cols({{cython_type}} * a, {{cython_type}} * b, int * missing, int n, int m): """ a is a pointer to an n x m array A b is a pointer to an n x n diagonal array B (copy to) missing is a pointer to an m x 1 array n is the number of rows of A m is the number of columns of A """ cdef int i, j, nobs nobs = m # Construct the non-missing index for i in range(m): nobs = nobs - missing[i] # Perform replacement for i in range(nobs): copy(n, &a[i*n], &b[i*n]) cpdef int {{prefix}}copy_missing_matrix({{cython_type}} [::1, :, :] A, {{cython_type}} [::1, :, :] B, int [::1, :] missing, int missing_rows, int missing_cols, int diagonal) except *: cdef int n, m, T, t, A_T, A_t = 0, time_varying n, m, T = B.shape[0:3] A_T = A.shape[2] time_varying = (A_T == T) if missing_rows and missing_cols: if not n == m: raise RuntimeError('Copying a submatrix requires n = m') if diagonal: for t in range(T): if time_varying: A_t = t _{{prefix}}copy_missing_diagonal(&A[0, 0, A_t], &B[0, 0, t], &missing[0, t], n) else: for t in range(T): if time_varying: A_t = t _{{prefix}}copy_missing_submatrix(&A[0, 0, A_t], &B[0, 0, t], &missing[0, t], n) elif diagonal: raise RuntimeError('`diagonal` argument only valid with copying a submatrix') elif missing_rows: for t in range(T): if time_varying: A_t = t _{{prefix}}copy_missing_rows(&A[0, 0, A_t], &B[0, 0, t], &missing[0, t], n, m) elif missing_cols: for t in range(T): if time_varying: A_t = t _{{prefix}}copy_missing_cols(&A[0, 0, A_t], &B[0, 0, t], &missing[0, t], n, m) pass cpdef int {{prefix}}copy_missing_vector({{cython_type}} [::1, :] A, {{cython_type}} [::1, :] B, int [::1, :] missing) except *: cdef int n, t, T, A_t = 0, A_T n, T = B.shape[0:2] A_T = A.shape[1] time_varying = (A_T == T) for t in range(T): if time_varying: A_t = t _{{prefix}}copy_missing_rows(&A[0, A_t], &B[0, t], &missing[0, t], n, 1) cdef int _{{prefix}}copy_index_diagonal({{cython_type}} * a, {{cython_type}} * b, int * index, int n): """ Copy the non-index block of diagonal entries a is a pointer to an n x n diagonal array A (copy from) b is a pointer to an n x n diagonal array B (copy to) index is a pointer to an n x 1 array n is the dimension of A, B """ cdef int i, j, k, nobs # Perform replacement for i in range(n): if index[i]: b[i + i*n] = a[i + i*n] cdef int _{{prefix}}copy_index_submatrix({{cython_type}} * a, {{cython_type}} * b, int * index, int n): """ Copy the non-index submatrix a is a pointer to an n x n diagonal array A (copy from) b is a pointer to an n x n diagonal array B (copy to) index is a pointer to an n x 1 array n is the dimension of A, B """ _{{prefix}}copy_index_rows(a, b, index, n, n) _{{prefix}}copy_index_cols(a, b, index, n, n) cdef int _{{prefix}}copy_index_rows({{cython_type}} * a, {{cython_type}} * b, int * index, int n, int m): """ a is a pointer to an n x m array A b is a pointer to an n x n diagonal array B (copy to) index is a pointer to an n x 1 array n is the number of rows of A m is the number of columns of A """ cdef int i # Perform replacement for i in range(n): if index[i]: copy(m, &a[i], &b[i], n, n) cdef int _{{prefix}}copy_index_cols({{cython_type}} * a, {{cython_type}} * b, int * index, int n, int m): """ a is a pointer to an n x m array A b is a pointer to an n x n diagonal array B (copy to) index is a pointer to an m x 1 array n is the number of rows of A m is the number of columns of A """ cdef int i, j, k, nobs # Perform replacement for i in range(m): if index[i]: copy(n, &a[i*n], &b[i*n]) cpdef int {{prefix}}copy_index_matrix({{cython_type}} [::1, :, :] A, {{cython_type}} [::1, :, :] B, int [::1, :] index, int index_rows, int index_cols, int diagonal) except *: cdef int n, m, T, t, A_T, A_t = 0, time_varying n, m, T = B.shape[0:3] A_T = A.shape[2] time_varying = (A_T == T) if index_rows and index_cols: if not n == m: raise RuntimeError('Copying a submatrix requires n = m') if diagonal: for t in range(T): if time_varying: A_t = t _{{prefix}}copy_index_diagonal(&A[0, 0, A_t], &B[0, 0, t], &index[0, t], n) else: for t in range(T): if time_varying: A_t = t _{{prefix}}copy_index_submatrix(&A[0, 0, A_t], &B[0, 0, t], &index[0, t], n) elif diagonal: raise RuntimeError('`diagonal` argument only valid with copying a submatrix') elif index_rows: for t in range(T): if time_varying: A_t = t _{{prefix}}copy_index_rows(&A[0, 0, A_t], &B[0, 0, t], &index[0, t], n, m) elif index_cols: for t in range(T): if time_varying: A_t = t _{{prefix}}copy_index_cols(&A[0, 0, A_t], &B[0, 0, t], &index[0, t], n, m) cpdef int {{prefix}}copy_index_vector({{cython_type}} [::1, :] A, {{cython_type}} [::1, :] B, int [::1, :] index) except *: cdef int n, t, T, A_t = 0, A_T n, T = B.shape[0:2] A_T = A.shape[1] time_varying = (A_T == T) for t in range(T): if time_varying: A_t = t _{{prefix}}copy_index_rows(&A[0, A_t], &B[0, t], &index[0, t], n, 1) cdef int _{{prefix}}select_cov(int k_states, int k_posdef, int k_states_total, {{cython_type}} * tmp, {{cython_type}} * selection, {{cython_type}} * cov, {{cython_type}} * selected_cov): cdef: int i, k_states2 = k_states**2 {{cython_type}} alpha = 1.0 {{cython_type}} beta = 0.0 # Only need to do something if there is a covariance matrix # (i.e k_posdof == 0) if k_posdef > 0: # #### Calculate selected state covariance matrix # $Q_t^* = R_t Q_t R_t'$ # # Combine a selection matrix and a covariance matrix to get # a simplified (but possibly singular) "selected" covariance # matrix (see e.g. Durbin and Koopman p. 43) # `tmp0` array used here, dimension $(m \times r)$ # $\\#_0 = 1.0 * R_t Q_t$ # $(m \times r) = (m \times r) (r \times r)$ blas.{{prefix}}gemm("N", "N", &k_states, &k_posdef, &k_posdef, &alpha, selection, &k_states_total, cov, &k_posdef, &beta, tmp, &k_states) # $Q_t^* = 1.0 * \\#_0 R_t'$ # $(m \times m) = (m \times r) (m \times r)'$ blas.{{prefix}}gemm("N", "T", &k_states, &k_states, &k_posdef, &alpha, tmp, &k_states, selection, &k_states_total, &beta, selected_cov, &k_states) else: for i in range(k_states2): selected_cov[i] = 0 {{endfor}}statsmodels-0.12.2/statsmodels/tsa/statespace/api.py000066400000000000000000000004551400612667500225610ustar00rootroot00000000000000__all__ = ["SARIMAX", "ExponentialSmoothing", "MLEModel", "MLEResults", "tools", "Initialization"] from .sarimax import SARIMAX from .exponential_smoothing import ExponentialSmoothing from .mlemodel import MLEModel, MLEResults from .initialization import Initialization from . import tools statsmodels-0.12.2/statsmodels/tsa/statespace/cfa_simulation_smoother.py000066400000000000000000000240531400612667500267250ustar00rootroot00000000000000""" "Cholesky Factor Algorithm" (CFA) simulation smoothing for state space models Author: Chad Fulton License: BSD-3 """ import numpy as np from . import tools class CFASimulationSmoother(object): r""" "Cholesky Factor Algorithm" (CFA) simulation smoother Parameters ---------- model : Representation The state space model. Notes ----- This class allows simulation smoothing by the "Cholesky Factor Algorithm" (CFA) described in [1]_ and [2]_, which essentially takes advantage of the existence of an efficient sparse Cholesky factor algorithm for banded matrices that are held in a sparse matrix format. In particular, this simulation smoother computes the joint posterior mean and covariance matrix for the unobserved state vector all at once, rather than using the recursive computations of the Kalman filter and smoother. It then uses these posterior moments to sample directly from this joint posterior. For some models, it can be more computationally efficient than the simulation smoother based on the Kalman filter and smoother. **Important caveat**: However, this simulation smoother cannot be used with all state space models, including several of the most popular. In particular, the CFA algorithm cannot support degenerate distributions (i.e. positive semi-definite covariance matrices) for the initial state (which is the prior for the first state) or the observation or state innovations. One practical problem with this algorithm is that an autoregressive term with order higher than one is typically put into state space form by augmenting the states using identities. As identities, these augmenting terms will not be subject to random innovations, and so the state innovation will be degenerate. It is possible to take these higher order terms directly into account when constructing the posterior covariance matrix, but this has not yet been implemented. Similarly, some state space forms of SARIMA and VARMA models make the observation equation an identity, which is not compatible with the CFA simulation smoothing approach. This simulation smoother has so-far found most of its use with dynamic factor and stochastic volatility models, which satisfy the restrictions described above. **Not-yet-implemented**: There are several features that are not yet available with this simulation smoother: - It does not yet allow diffuse initialization of the state vector. - It produces simulated states only for exactly the observations in the model (i.e. it cannot produce simulations for a subset of the model observations or for observations outside the model). References ---------- .. [1] McCausland, William J., Shirley Miller, and Denis Pelletier. "Simulation smoothing for state-space models: A computational efficiency analysis." Computational Statistics & Data Analysis 55, no. 1 (2011): 199-212. .. [2] Chan, Joshua CC, and Ivan Jeliazkov. "Efficient simulation and integrated likelihood estimation in state space models." International Journal of Mathematical Modelling and Numerical Optimisation 1, no. 1-2 (2009): 101-120. """ def __init__(self, model, cfa_simulation_smoother_classes=None): self.model = model # Get the simulation smoother classes self.prefix_simulation_smoother_map = ( cfa_simulation_smoother_classes if cfa_simulation_smoother_classes is not None else tools.prefix_cfa_simulation_smoother_map.copy()) self._simulation_smoothers = {} self._posterior_mean = None self._posterior_cov_inv_chol = None self._posterior_cov = None self._simulated_state = None @property def _simulation_smoother(self): prefix = self.model.prefix if prefix in self._simulation_smoothers: return self._simulation_smoothers[prefix] return None @property def posterior_mean(self): r""" Posterior mean of the states conditional on the data Notes ----- .. math:: \hat \alpha_t = E[\alpha_t \mid Y^n ] This posterior mean is identical to the `smoothed_state` computed by the Kalman smoother. """ if self._posterior_mean is None: self._posterior_mean = np.array( self._simulation_smoother.posterior_mean, copy=True) return self._posterior_mean @property def posterior_cov_inv_chol_sparse(self): r""" Sparse Cholesky factor of inverse posterior covariance matrix Notes ----- This attribute holds in sparse diagonal banded storage the Cholesky factor of the inverse of the posterior covariance matrix. If we denote :math:`P = Var[\alpha \mid Y^n ]`, then the this attribute holds the lower Cholesky factor :math:`L`, defined from :math:`L L' = P^{-1}`. This attribute uses the sparse diagonal banded storage described in the documentation of, for example, the SciPy function `scipy.linalg.solveh_banded`. """ if self._posterior_cov_inv_chol is None: self._posterior_cov_inv_chol = np.array( self._simulation_smoother.posterior_cov_inv_chol, copy=True) return self._posterior_cov_inv_chol @property def posterior_cov(self): r""" Posterior covariance of the states conditional on the data Notes ----- **Warning**: the matrix computed when accessing this property can be extremely large: it is shaped `(nobs * k_states, nobs * k_states)`. In most cases, it is better to use the `posterior_cov_inv_chol_sparse` property if possible, which holds in sparse diagonal banded storage the Cholesky factor of the inverse of the posterior covariance matrix. .. math:: Var[\alpha \mid Y^n ] This posterior covariance matrix is *not* identical to the `smoothed_state_cov` attribute produced by the Kalman smoother, because it additionally contains all cross-covariance terms. Instead, `smoothed_state_cov` contains the `(k_states, k_states)` block diagonal entries of this posterior covariance matrix. """ if self._posterior_cov is None: from scipy.linalg import cho_solve_banded inv_chol = self.posterior_cov_inv_chol_sparse self._posterior_cov = cho_solve_banded( (inv_chol, True), np.eye(inv_chol.shape[1])) return self._posterior_cov def simulate(self, variates=None, update_posterior=True): r""" Perform simulation smoothing (via Cholesky factor algorithm) Does not return anything, but populates the object's `simulated_state` attribute, and also makes available the attributes `posterior_mean`, `posterior_cov`, and `posterior_cov_inv_chol_sparse`. Parameters ---------- variates : array_like, optional Random variates, distributed standard Normal. Usually only specified if results are to be replicated (e.g. to enforce a seed) or for testing. If not specified, random variates are drawn. Must be shaped (nobs, k_states). Notes ----- The first step in simulating from the joint posterior of the state vector conditional on the data is to compute the two relevant moments of the joint posterior distribution: .. math:: \alpha \mid Y_n \sim N(\hat \alpha, Var(\alpha \mid Y_n)) Let :math:`L L' = Var(\alpha \mid Y_n)^{-1}`. Then simulation proceeds according to the following steps: 1. Draw :math:`u \sim N(0, I)` 2. Compute :math:`x = \hat \alpha + (L')^{-1} u` And then :math:`x` is a draw from the joint posterior of the states. The output of the function is as follows: - The simulated draw :math:`x` is held in the `simulated_state` attribute. - The posterior mean :math:`\hat \alpha` is held in the `posterior_mean` attribute. - The (lower triangular) Cholesky factor of the inverse posterior covariance matrix, :math:`L`, is held in sparse diagonal banded storage in the `posterior_cov_inv_chol` attribute. - The posterior covariance matrix :math:`Var(\alpha \mid Y_n)` can be computed on demand by accessing the `posterior_cov` property. Note that this matrix can be extremely large, so care must be taken when accessing this property. In most cases, it will be preferred to make use of the `posterior_cov_inv_chol` attribute rather than the `posterior_cov` attribute. """ # (Re) initialize the _statespace representation prefix, dtype, create = self.model._initialize_representation() # Validate variates and get in required datatype if variates is not None: tools.validate_matrix_shape('variates', variates.shape, self.model.k_states, self.model.nobs, 1) variates = np.ravel(variates, order='F').astype(dtype) # (Re) initialize the state self.model._initialize_state(prefix=prefix) # Construct the Cython simulation smoother instance, if necessary if create or prefix not in self._simulation_smoothers: cls = self.prefix_simulation_smoother_map[prefix] self._simulation_smoothers[prefix] = cls( self.model._statespaces[prefix]) sim = self._simulation_smoothers[prefix] # Update posterior moments, if requested if update_posterior: sim.update_sparse_posterior_moments() self._posterior_mean = None self._posterior_cov_inv_chol = None self._posterior_cov = None # Perform simulation smoothing self.simulated_state = sim.simulate(variates=variates) statsmodels-0.12.2/statsmodels/tsa/statespace/dynamic_factor.py000066400000000000000000001523461400612667500250010ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Dynamic factor model Author: Chad Fulton License: Simplified-BSD """ import numpy as np from .mlemodel import MLEModel, MLEResults, MLEResultsWrapper from .tools import ( is_invertible, prepare_exog, constrain_stationary_univariate, unconstrain_stationary_univariate, constrain_stationary_multivariate, unconstrain_stationary_multivariate ) from statsmodels.multivariate.pca import PCA from statsmodels.regression.linear_model import OLS from statsmodels.tsa.vector_ar.var_model import VAR from statsmodels.tsa.arima.model import ARIMA from statsmodels.tools.tools import Bunch from statsmodels.tools.data import _is_using_pandas from statsmodels.tsa.tsatools import lagmat from statsmodels.tools.decorators import cache_readonly import statsmodels.base.wrapper as wrap from statsmodels.compat.pandas import Appender class DynamicFactor(MLEModel): r""" Dynamic factor model Parameters ---------- endog : array_like The observed time-series process :math:`y` exog : array_like, optional Array of exogenous regressors for the observation equation, shaped nobs x k_exog. k_factors : int The number of unobserved factors. factor_order : int The order of the vector autoregression followed by the factors. error_cov_type : {'scalar', 'diagonal', 'unstructured'}, optional The structure of the covariance matrix of the observation error term, where "unstructured" puts no restrictions on the matrix, "diagonal" requires it to be any diagonal matrix (uncorrelated errors), and "scalar" requires it to be a scalar times the identity matrix. Default is "diagonal". error_order : int, optional The order of the vector autoregression followed by the observation error component. Default is None, corresponding to white noise errors. error_var : bool, optional Whether or not to model the errors jointly via a vector autoregression, rather than as individual autoregressions. Has no effect unless `error_order` is set. Default is False. enforce_stationarity : bool, optional Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. Default is True. **kwargs Keyword arguments may be used to provide default values for state space matrices or for Kalman filtering options. See `Representation`, and `KalmanFilter` for more details. Attributes ---------- exog : array_like, optional Array of exogenous regressors for the observation equation, shaped nobs x k_exog. k_factors : int The number of unobserved factors. factor_order : int The order of the vector autoregression followed by the factors. error_cov_type : {'diagonal', 'unstructured'} The structure of the covariance matrix of the error term, where "unstructured" puts no restrictions on the matrix and "diagonal" requires it to be a diagonal matrix (uncorrelated errors). error_order : int The order of the vector autoregression followed by the observation error component. error_var : bool Whether or not to model the errors jointly via a vector autoregression, rather than as individual autoregressions. Has no effect unless `error_order` is set. enforce_stationarity : bool, optional Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. Default is True. Notes ----- The dynamic factor model considered here is in the so-called static form, and is specified: .. math:: y_t & = \Lambda f_t + B x_t + u_t \\ f_t & = A_1 f_{t-1} + \dots + A_p f_{t-p} + \eta_t \\ u_t & = C_1 u_{t-1} + \dots + C_q u_{t-q} + \varepsilon_t where there are `k_endog` observed series and `k_factors` unobserved factors. Thus :math:`y_t` is a `k_endog` x 1 vector and :math:`f_t` is a `k_factors` x 1 vector. :math:`x_t` are optional exogenous vectors, shaped `k_exog` x 1. :math:`\eta_t` and :math:`\varepsilon_t` are white noise error terms. In order to identify the factors, :math:`Var(\eta_t) = I`. Denote :math:`Var(\varepsilon_t) \equiv \Sigma`. Options related to the unobserved factors: - `k_factors`: this is the dimension of the vector :math:`f_t`, above. To exclude factors completely, set `k_factors = 0`. - `factor_order`: this is the number of lags to include in the factor evolution equation, and corresponds to :math:`p`, above. To have static factors, set `factor_order = 0`. Options related to the observation error term :math:`u_t`: - `error_order`: the number of lags to include in the error evolution equation; corresponds to :math:`q`, above. To have white noise errors, set `error_order = 0` (this is the default). - `error_cov_type`: this controls the form of the covariance matrix :math:`\Sigma`. If it is "dscalar", then :math:`\Sigma = \sigma^2 I`. If it is "diagonal", then :math:`\Sigma = \text{diag}(\sigma_1^2, \dots, \sigma_n^2)`. If it is "unstructured", then :math:`\Sigma` is any valid variance / covariance matrix (i.e. symmetric and positive definite). - `error_var`: this controls whether or not the errors evolve jointly according to a VAR(q), or individually according to separate AR(q) processes. In terms of the formulation above, if `error_var = False`, then the matrices :math:C_i` are diagonal, otherwise they are general VAR matrices. References ---------- .. [*] Lütkepohl, Helmut. 2007. New Introduction to Multiple Time Series Analysis. Berlin: Springer. """ def __init__(self, endog, k_factors, factor_order, exog=None, error_order=0, error_var=False, error_cov_type='diagonal', enforce_stationarity=True, **kwargs): # Model properties self.enforce_stationarity = enforce_stationarity # Factor-related properties self.k_factors = k_factors self.factor_order = factor_order # Error-related properties self.error_order = error_order self.error_var = error_var and error_order > 0 self.error_cov_type = error_cov_type # Exogenous data (self.k_exog, exog) = prepare_exog(exog) # Note: at some point in the future might add state regression, as in # SARIMAX. self.mle_regression = self.k_exog > 0 # We need to have an array or pandas at this point if not _is_using_pandas(endog, None): endog = np.asanyarray(endog, order='C') # Save some useful model orders, internally used k_endog = endog.shape[1] if endog.ndim > 1 else 1 self._factor_order = max(1, self.factor_order) * self.k_factors self._error_order = self.error_order * k_endog # Calculate the number of states k_states = self._factor_order k_posdef = self.k_factors if self.error_order > 0: k_states += self._error_order k_posdef += k_endog # We can still estimate the model with no dynamic state (e.g. SUR), we # just need to have one state that does nothing. self._unused_state = False if k_states == 0: k_states = 1 k_posdef = 1 self._unused_state = True # Test for non-multivariate endog if k_endog < 2: raise ValueError('The dynamic factors model is only valid for' ' multivariate time series.') # Test for too many factors if self.k_factors >= k_endog: raise ValueError('Number of factors must be less than the number' ' of endogenous variables.') # Test for invalid error_cov_type if self.error_cov_type not in ['scalar', 'diagonal', 'unstructured']: raise ValueError('Invalid error covariance matrix type' ' specification.') # By default, initialize as stationary kwargs.setdefault('initialization', 'stationary') # Initialize the state space model super(DynamicFactor, self).__init__( endog, exog=exog, k_states=k_states, k_posdef=k_posdef, **kwargs ) # Set as time-varying model if we have exog if self.k_exog > 0: self.ssm._time_invariant = False # Initialize the components self.parameters = {} self._initialize_loadings() self._initialize_exog() self._initialize_error_cov() self._initialize_factor_transition() self._initialize_error_transition() self.k_params = sum(self.parameters.values()) # Cache parameter vector slices def _slice(key, offset): length = self.parameters[key] param_slice = np.s_[offset:offset + length] offset += length return param_slice, offset offset = 0 self._params_loadings, offset = _slice('factor_loadings', offset) self._params_exog, offset = _slice('exog', offset) self._params_error_cov, offset = _slice('error_cov', offset) self._params_factor_transition, offset = ( _slice('factor_transition', offset)) self._params_error_transition, offset = ( _slice('error_transition', offset)) # Update _init_keys attached by super self._init_keys += ['k_factors', 'factor_order', 'error_order', 'error_var', 'error_cov_type', 'enforce_stationarity'] + list(kwargs.keys()) def _initialize_loadings(self): # Initialize the parameters self.parameters['factor_loadings'] = self.k_endog * self.k_factors # Setup fixed components of state space matrices if self.error_order > 0: start = self._factor_order end = self._factor_order + self.k_endog self.ssm['design', :, start:end] = np.eye(self.k_endog) # Setup indices of state space matrices self._idx_loadings = np.s_['design', :, :self.k_factors] def _initialize_exog(self): # Initialize the parameters self.parameters['exog'] = self.k_exog * self.k_endog # If we have exog effects, then the obs intercept needs to be # time-varying if self.k_exog > 0: self.ssm['obs_intercept'] = np.zeros((self.k_endog, self.nobs)) # Setup indices of state space matrices self._idx_exog = np.s_['obs_intercept', :self.k_endog, :] def _initialize_error_cov(self): if self.error_cov_type == 'scalar': self._initialize_error_cov_diagonal(scalar=True) elif self.error_cov_type == 'diagonal': self._initialize_error_cov_diagonal(scalar=False) elif self.error_cov_type == 'unstructured': self._initialize_error_cov_unstructured() def _initialize_error_cov_diagonal(self, scalar=False): # Initialize the parameters self.parameters['error_cov'] = 1 if scalar else self.k_endog # Setup fixed components of state space matrices # Setup indices of state space matrices k_endog = self.k_endog k_factors = self.k_factors idx = np.diag_indices(k_endog) if self.error_order > 0: matrix = 'state_cov' idx = (idx[0] + k_factors, idx[1] + k_factors) else: matrix = 'obs_cov' self._idx_error_cov = (matrix,) + idx def _initialize_error_cov_unstructured(self): # Initialize the parameters k_endog = self.k_endog self.parameters['error_cov'] = int(k_endog * (k_endog + 1) / 2) # Setup fixed components of state space matrices # Setup indices of state space matrices self._idx_lower_error_cov = np.tril_indices(self.k_endog) if self.error_order > 0: start = self.k_factors end = self.k_factors + self.k_endog self._idx_error_cov = ( np.s_['state_cov', start:end, start:end]) else: self._idx_error_cov = np.s_['obs_cov', :, :] def _initialize_factor_transition(self): order = self.factor_order * self.k_factors k_factors = self.k_factors # Initialize the parameters self.parameters['factor_transition'] = ( self.factor_order * self.k_factors**2) # Setup fixed components of state space matrices # VAR(p) for factor transition if self.k_factors > 0: if self.factor_order > 0: self.ssm['transition', k_factors:order, :order - k_factors] = ( np.eye(order - k_factors)) self.ssm['selection', :k_factors, :k_factors] = np.eye(k_factors) # Identification requires constraining the state covariance to an # identity matrix self.ssm['state_cov', :k_factors, :k_factors] = np.eye(k_factors) # Setup indices of state space matrices self._idx_factor_transition = np.s_['transition', :k_factors, :order] def _initialize_error_transition(self): # Initialize the appropriate situation if self.error_order == 0: self._initialize_error_transition_white_noise() else: # Generic setup fixed components of state space matrices # VAR(q) for error transition # (in the individual AR case, we still have the VAR(q) companion # matrix structure, but force the coefficient matrices to be # diagonal) k_endog = self.k_endog k_factors = self.k_factors _factor_order = self._factor_order _error_order = self._error_order _slice = np.s_['selection', _factor_order:_factor_order + k_endog, k_factors:k_factors + k_endog] self.ssm[_slice] = np.eye(k_endog) _slice = np.s_[ 'transition', _factor_order + k_endog:_factor_order + _error_order, _factor_order:_factor_order + _error_order - k_endog] self.ssm[_slice] = np.eye(_error_order - k_endog) # Now specialized setups if self.error_var: self._initialize_error_transition_var() else: self._initialize_error_transition_individual() def _initialize_error_transition_white_noise(self): # Initialize the parameters self.parameters['error_transition'] = 0 # No fixed components of state space matrices # Setup indices of state space matrices (just an empty slice) self._idx_error_transition = np.s_['transition', 0:0, 0:0] def _initialize_error_transition_var(self): k_endog = self.k_endog _factor_order = self._factor_order _error_order = self._error_order # Initialize the parameters self.parameters['error_transition'] = _error_order * k_endog # Fixed components already setup above # Setup indices of state space matrices # Here we want to set all of the elements of the coefficient matrices, # the same as in a VAR specification self._idx_error_transition = np.s_[ 'transition', _factor_order:_factor_order + k_endog, _factor_order:_factor_order + _error_order] def _initialize_error_transition_individual(self): k_endog = self.k_endog _error_order = self._error_order # Initialize the parameters self.parameters['error_transition'] = _error_order # Fixed components already setup above # Setup indices of state space matrices # Here we want to set only the diagonal elements of the coefficient # matrices, and we want to set them in order by equation, not by # matrix (i.e. set the first element of the first matrix's diagonal, # then set the first element of the second matrix's diagonal, then...) # The basic setup is a tiled list of diagonal indices, one for each # coefficient matrix idx = np.tile(np.diag_indices(k_endog), self.error_order) # Now we need to shift the rows down to the correct location row_shift = self._factor_order # And we need to shift the columns in an increasing way col_inc = self._factor_order + np.repeat( [i * k_endog for i in range(self.error_order)], k_endog) idx[0] += row_shift idx[1] += col_inc # Make a copy (without the row shift) so that we can easily get the # diagonal parameters back out of a generic coefficients matrix array idx_diag = idx.copy() idx_diag[0] -= row_shift idx_diag[1] -= self._factor_order idx_diag = idx_diag[:, np.lexsort((idx_diag[1], idx_diag[0]))] self._idx_error_diag = (idx_diag[0], idx_diag[1]) # Finally, we want to fill the entries in in the correct order, which # is to say we want to fill in lexicographically, first by row then by # column idx = idx[:, np.lexsort((idx[1], idx[0]))] self._idx_error_transition = np.s_['transition', idx[0], idx[1]] def clone(self, endog, exog=None, **kwargs): return self._clone_from_init_kwds(endog, exog=exog, **kwargs) @property def _res_classes(self): return {'fit': (DynamicFactorResults, DynamicFactorResultsWrapper)} @property def start_params(self): params = np.zeros(self.k_params, dtype=np.float64) endog = self.endog.copy() mask = ~np.any(np.isnan(endog), axis=1) endog = endog[mask] if self.k_exog > 0: exog = self.exog[mask] # 1. Factor loadings (estimated via PCA) if self.k_factors > 0: # Use principal components + OLS as starting values res_pca = PCA(endog, ncomp=self.k_factors) mod_ols = OLS(endog, res_pca.factors) res_ols = mod_ols.fit() # Using OLS params for the loadings tends to gives higher starting # log-likelihood. params[self._params_loadings] = res_ols.params.T.ravel() # params[self._params_loadings] = res_pca.loadings.ravel() # However, using res_ols.resid tends to causes non-invertible # starting VAR coefficients for error VARs # endog = res_ols.resid endog = endog - np.dot(res_pca.factors, res_pca.loadings.T) # 2. Exog (OLS on residuals) if self.k_exog > 0: mod_ols = OLS(endog, exog=exog) res_ols = mod_ols.fit() # In the form: beta.x1.y1, beta.x2.y1, beta.x1.y2, ... params[self._params_exog] = res_ols.params.T.ravel() endog = res_ols.resid # 3. Factors (VAR on res_pca.factors) stationary = True if self.k_factors > 1 and self.factor_order > 0: # 3a. VAR transition (OLS on factors estimated via PCA) mod_factors = VAR(res_pca.factors) res_factors = mod_factors.fit(maxlags=self.factor_order, ic=None, trend='nc') # Save the parameters params[self._params_factor_transition] = ( res_factors.params.T.ravel()) # Test for stationarity coefficient_matrices = ( params[self._params_factor_transition].reshape( self.k_factors * self.factor_order, self.k_factors ).T ).reshape(self.k_factors, self.k_factors, self.factor_order).T stationary = is_invertible([1] + list(-coefficient_matrices)) elif self.k_factors > 0 and self.factor_order > 0: # 3b. AR transition Y = res_pca.factors[self.factor_order:] X = lagmat(res_pca.factors, self.factor_order, trim='both') params_ar = np.linalg.pinv(X).dot(Y) stationary = is_invertible(np.r_[1, -params_ar.squeeze()]) params[self._params_factor_transition] = params_ar[:, 0] # Check for stationarity if not stationary and self.enforce_stationarity: raise ValueError('Non-stationary starting autoregressive' ' parameters found with `enforce_stationarity`' ' set to True.') # 4. Errors if self.error_order == 0: if self.error_cov_type == 'scalar': params[self._params_error_cov] = endog.var(axis=0).mean() elif self.error_cov_type == 'diagonal': params[self._params_error_cov] = endog.var(axis=0) elif self.error_cov_type == 'unstructured': cov_factor = np.diag(endog.std(axis=0)) params[self._params_error_cov] = ( cov_factor[self._idx_lower_error_cov].ravel()) elif self.error_var: mod_errors = VAR(endog) res_errors = mod_errors.fit(maxlags=self.error_order, ic=None, trend='nc') # Test for stationarity coefficient_matrices = ( np.array(res_errors.params.T).ravel().reshape( self.k_endog * self.error_order, self.k_endog ).T ).reshape(self.k_endog, self.k_endog, self.error_order).T stationary = is_invertible([1] + list(-coefficient_matrices)) if not stationary and self.enforce_stationarity: raise ValueError('Non-stationary starting error autoregressive' ' parameters found with' ' `enforce_stationarity` set to True.') # Get the error autoregressive parameters params[self._params_error_transition] = ( np.array(res_errors.params.T).ravel()) # Get the error covariance parameters if self.error_cov_type == 'scalar': params[self._params_error_cov] = ( res_errors.sigma_u.diagonal().mean()) elif self.error_cov_type == 'diagonal': params[self._params_error_cov] = res_errors.sigma_u.diagonal() elif self.error_cov_type == 'unstructured': try: cov_factor = np.linalg.cholesky(res_errors.sigma_u) except np.linalg.LinAlgError: cov_factor = np.eye(res_errors.sigma_u.shape[0]) * ( res_errors.sigma_u.diagonal().mean()**0.5) cov_factor = np.eye(res_errors.sigma_u.shape[0]) * ( res_errors.sigma_u.diagonal().mean()**0.5) params[self._params_error_cov] = ( cov_factor[self._idx_lower_error_cov].ravel()) else: error_ar_params = [] error_cov_params = [] for i in range(self.k_endog): mod_error = ARIMA(endog[:, i], order=(self.error_order, 0, 0), trend='n', enforce_stationarity=True) res_error = mod_error.fit(method='burg') error_ar_params += res_error.params[:self.error_order].tolist() error_cov_params += res_error.params[-1:].tolist() params[self._params_error_transition] = np.r_[error_ar_params] params[self._params_error_cov] = np.r_[error_cov_params] return params @property def param_names(self): param_names = [] endog_names = self.endog_names # 1. Factor loadings param_names += [ 'loading.f%d.%s' % (j+1, endog_names[i]) for i in range(self.k_endog) for j in range(self.k_factors) ] # 2. Exog # Recall these are in the form: beta.x1.y1, beta.x2.y1, beta.x1.y2, ... param_names += [ 'beta.%s.%s' % (self.exog_names[j], endog_names[i]) for i in range(self.k_endog) for j in range(self.k_exog) ] # 3. Error covariances if self.error_cov_type == 'scalar': param_names += ['sigma2'] elif self.error_cov_type == 'diagonal': param_names += [ 'sigma2.%s' % endog_names[i] for i in range(self.k_endog) ] elif self.error_cov_type == 'unstructured': param_names += [ 'cov.chol[%d,%d]' % (i + 1, j + 1) for i in range(self.k_endog) for j in range(i+1) ] # 4. Factor transition VAR param_names += [ 'L%d.f%d.f%d' % (i+1, k+1, j+1) for j in range(self.k_factors) for i in range(self.factor_order) for k in range(self.k_factors) ] # 5. Error transition VAR if self.error_var: param_names += [ 'L%d.e(%s).e(%s)' % (i+1, endog_names[k], endog_names[j]) for j in range(self.k_endog) for i in range(self.error_order) for k in range(self.k_endog) ] else: param_names += [ 'L%d.e(%s).e(%s)' % (i+1, endog_names[j], endog_names[j]) for j in range(self.k_endog) for i in range(self.error_order) ] return param_names @property def state_names(self): names = [] endog_names = self.endog_names # Factors and lags names += [ (('f%d' % (j + 1)) if i == 0 else ('f%d.L%d' % (j + 1, i))) for i in range(max(1, self.factor_order)) for j in range(self.k_factors)] if self.error_order > 0: names += [ (('e(%s)' % endog_names[j]) if i == 0 else ('e(%s).L%d' % (endog_names[j], i))) for i in range(self.error_order) for j in range(self.k_endog)] if self._unused_state: names += ['dummy'] return names def transform_params(self, unconstrained): """ Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation Parameters ---------- unconstrained : array_like Array of unconstrained parameters used by the optimizer, to be transformed. Returns ------- constrained : array_like Array of constrained parameters which may be used in likelihood evaluation. Notes ----- Constrains the factor transition to be stationary and variances to be positive. """ unconstrained = np.array(unconstrained, ndmin=1) dtype = unconstrained.dtype constrained = np.zeros(unconstrained.shape, dtype=dtype) # 1. Factor loadings # The factor loadings do not need to be adjusted constrained[self._params_loadings] = ( unconstrained[self._params_loadings]) # 2. Exog # The regression coefficients do not need to be adjusted constrained[self._params_exog] = ( unconstrained[self._params_exog]) # 3. Error covariances # If we have variances, force them to be positive if self.error_cov_type in ['scalar', 'diagonal']: constrained[self._params_error_cov] = ( unconstrained[self._params_error_cov]**2) # Otherwise, nothing needs to be done elif self.error_cov_type == 'unstructured': constrained[self._params_error_cov] = ( unconstrained[self._params_error_cov]) # 4. Factor transition VAR # VAR transition: optionally force to be stationary if self.enforce_stationarity and self.factor_order > 0: # Transform the parameters unconstrained_matrices = ( unconstrained[self._params_factor_transition].reshape( self.k_factors, self._factor_order)) # This is always an identity matrix, but because the transform # done prior to update (where the ssm representation matrices # change), it may be complex cov = self.ssm['state_cov', :self.k_factors, :self.k_factors].real coefficient_matrices, variance = ( constrain_stationary_multivariate(unconstrained_matrices, cov)) constrained[self._params_factor_transition] = ( coefficient_matrices.ravel()) else: constrained[self._params_factor_transition] = ( unconstrained[self._params_factor_transition]) # 5. Error transition VAR # VAR transition: optionally force to be stationary if self.enforce_stationarity and self.error_order > 0: # Joint VAR specification if self.error_var: unconstrained_matrices = ( unconstrained[self._params_error_transition].reshape( self.k_endog, self._error_order)) start = self.k_factors end = self.k_factors + self.k_endog cov = self.ssm['state_cov', start:end, start:end].real coefficient_matrices, variance = ( constrain_stationary_multivariate( unconstrained_matrices, cov)) constrained[self._params_error_transition] = ( coefficient_matrices.ravel()) # Separate AR specifications else: coefficients = ( unconstrained[self._params_error_transition].copy()) for i in range(self.k_endog): start = i * self.error_order end = (i + 1) * self.error_order coefficients[start:end] = constrain_stationary_univariate( coefficients[start:end]) constrained[self._params_error_transition] = coefficients else: constrained[self._params_error_transition] = ( unconstrained[self._params_error_transition]) return constrained def untransform_params(self, constrained): """ Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer. Parameters ---------- constrained : array_like Array of constrained parameters used in likelihood evaluation, to be transformed. Returns ------- unconstrained : array_like Array of unconstrained parameters used by the optimizer. """ constrained = np.array(constrained, ndmin=1) dtype = constrained.dtype unconstrained = np.zeros(constrained.shape, dtype=dtype) # 1. Factor loadings # The factor loadings do not need to be adjusted unconstrained[self._params_loadings] = ( constrained[self._params_loadings]) # 2. Exog # The regression coefficients do not need to be adjusted unconstrained[self._params_exog] = ( constrained[self._params_exog]) # 3. Error covariances # If we have variances, force them to be positive if self.error_cov_type in ['scalar', 'diagonal']: unconstrained[self._params_error_cov] = ( constrained[self._params_error_cov]**0.5) # Otherwise, nothing needs to be done elif self.error_cov_type == 'unstructured': unconstrained[self._params_error_cov] = ( constrained[self._params_error_cov]) # 3. Factor transition VAR # VAR transition: optionally force to be stationary if self.enforce_stationarity and self.factor_order > 0: # Transform the parameters constrained_matrices = ( constrained[self._params_factor_transition].reshape( self.k_factors, self._factor_order)) cov = self.ssm['state_cov', :self.k_factors, :self.k_factors].real coefficient_matrices, variance = ( unconstrain_stationary_multivariate( constrained_matrices, cov)) unconstrained[self._params_factor_transition] = ( coefficient_matrices.ravel()) else: unconstrained[self._params_factor_transition] = ( constrained[self._params_factor_transition]) # 5. Error transition VAR # VAR transition: optionally force to be stationary if self.enforce_stationarity and self.error_order > 0: # Joint VAR specification if self.error_var: constrained_matrices = ( constrained[self._params_error_transition].reshape( self.k_endog, self._error_order)) start = self.k_factors end = self.k_factors + self.k_endog cov = self.ssm['state_cov', start:end, start:end].real coefficient_matrices, variance = ( unconstrain_stationary_multivariate( constrained_matrices, cov)) unconstrained[self._params_error_transition] = ( coefficient_matrices.ravel()) # Separate AR specifications else: coefficients = ( constrained[self._params_error_transition].copy()) for i in range(self.k_endog): start = i * self.error_order end = (i + 1) * self.error_order coefficients[start:end] = ( unconstrain_stationary_univariate( coefficients[start:end])) unconstrained[self._params_error_transition] = coefficients else: unconstrained[self._params_error_transition] = ( constrained[self._params_error_transition]) return unconstrained def _validate_can_fix_params(self, param_names): super(DynamicFactor, self)._validate_can_fix_params(param_names) ix = np.cumsum(list(self.parameters.values()))[:-1] (_, _, _, factor_transition_names, error_transition_names) = [ arr.tolist() for arr in np.array_split(self.param_names, ix)] if self.enforce_stationarity and self.factor_order > 0: if self.k_factors > 1 or self.factor_order > 1: fix_all = param_names.issuperset(factor_transition_names) fix_any = ( len(param_names.intersection(factor_transition_names)) > 0) if fix_any and not fix_all: raise ValueError( 'Cannot fix individual factor transition parameters' ' when `enforce_stationarity=True`. In this case,' ' must either fix all factor transition parameters or' ' none.') if self.enforce_stationarity and self.error_order > 0: if self.error_var or self.error_order > 1: fix_all = param_names.issuperset(error_transition_names) fix_any = ( len(param_names.intersection(error_transition_names)) > 0) if fix_any and not fix_all: raise ValueError( 'Cannot fix individual error transition parameters' ' when `enforce_stationarity=True`. In this case,' ' must either fix all error transition parameters or' ' none.') def update(self, params, transformed=True, includes_fixed=False, complex_step=False): """ Update the parameters of the model Updates the representation matrices to fill in the new parameter values. Parameters ---------- params : array_like Array of new parameters. transformed : bool, optional Whether or not `params` is already transformed. If set to False, `transform_params` is called. Default is True.. Returns ------- params : array_like Array of parameters. Notes ----- Let `n = k_endog`, `m = k_factors`, and `p = factor_order`. Then the `params` vector has length :math:`[n \times m] + [n] + [m^2 \times p]`. It is expanded in the following way: - The first :math:`n \times m` parameters fill out the factor loading matrix, starting from the [0,0] entry and then proceeding along rows. These parameters are not modified in `transform_params`. - The next :math:`n` parameters provide variances for the error_cov errors in the observation equation. They fill in the diagonal of the observation covariance matrix, and are constrained to be positive by `transofrm_params`. - The next :math:`m^2 \times p` parameters are used to create the `p` coefficient matrices for the vector autoregression describing the factor transition. They are transformed in `transform_params` to enforce stationarity of the VAR(p). They are placed so as to make the transition matrix a companion matrix for the VAR. In particular, we assume that the first :math:`m^2` parameters fill the first coefficient matrix (starting at [0,0] and filling along rows), the second :math:`m^2` parameters fill the second matrix, etc. """ params = self.handle_params(params, transformed=transformed, includes_fixed=includes_fixed) # 1. Factor loadings # Update the design / factor loading matrix self.ssm[self._idx_loadings] = ( params[self._params_loadings].reshape(self.k_endog, self.k_factors) ) # 2. Exog if self.k_exog > 0: exog_params = params[self._params_exog].reshape( self.k_endog, self.k_exog).T self.ssm[self._idx_exog] = np.dot(self.exog, exog_params).T # 3. Error covariances if self.error_cov_type in ['scalar', 'diagonal']: self.ssm[self._idx_error_cov] = ( params[self._params_error_cov]) elif self.error_cov_type == 'unstructured': error_cov_lower = np.zeros((self.k_endog, self.k_endog), dtype=params.dtype) error_cov_lower[self._idx_lower_error_cov] = ( params[self._params_error_cov]) self.ssm[self._idx_error_cov] = ( np.dot(error_cov_lower, error_cov_lower.T)) # 4. Factor transition VAR self.ssm[self._idx_factor_transition] = ( params[self._params_factor_transition].reshape( self.k_factors, self.factor_order * self.k_factors)) # 5. Error transition VAR if self.error_var: self.ssm[self._idx_error_transition] = ( params[self._params_error_transition].reshape( self.k_endog, self._error_order)) else: self.ssm[self._idx_error_transition] = ( params[self._params_error_transition]) class DynamicFactorResults(MLEResults): """ Class to hold results from fitting an DynamicFactor model. Parameters ---------- model : DynamicFactor instance The fitted model instance Attributes ---------- specification : dictionary Dictionary including all attributes from the DynamicFactor model instance. coefficient_matrices_var : ndarray Array containing autoregressive lag polynomial coefficient matrices, ordered from lowest degree to highest. See Also -------- statsmodels.tsa.statespace.kalman_filter.FilterResults statsmodels.tsa.statespace.mlemodel.MLEResults """ def __init__(self, model, params, filter_results, cov_type=None, **kwargs): super(DynamicFactorResults, self).__init__(model, params, filter_results, cov_type, **kwargs) self.df_resid = np.inf # attribute required for wald tests self.specification = Bunch(**{ # Model properties 'k_endog': self.model.k_endog, 'enforce_stationarity': self.model.enforce_stationarity, # Factor-related properties 'k_factors': self.model.k_factors, 'factor_order': self.model.factor_order, # Error-related properties 'error_order': self.model.error_order, 'error_var': self.model.error_var, 'error_cov_type': self.model.error_cov_type, # Other properties 'k_exog': self.model.k_exog }) # Polynomials / coefficient matrices self.coefficient_matrices_var = None if self.model.factor_order > 0: ar_params = ( np.array(self.params[self.model._params_factor_transition])) k_factors = self.model.k_factors factor_order = self.model.factor_order self.coefficient_matrices_var = ( ar_params.reshape(k_factors * factor_order, k_factors).T ).reshape(k_factors, k_factors, factor_order).T self.coefficient_matrices_error = None if self.model.error_order > 0: ar_params = ( np.array(self.params[self.model._params_error_transition])) k_endog = self.model.k_endog error_order = self.model.error_order if self.model.error_var: self.coefficient_matrices_error = ( ar_params.reshape(k_endog * error_order, k_endog).T ).reshape(k_endog, k_endog, error_order).T else: mat = np.zeros((k_endog, k_endog * error_order)) mat[self.model._idx_error_diag] = ar_params self.coefficient_matrices_error = ( mat.T.reshape(error_order, k_endog, k_endog)) @property def factors(self): """ Estimates of unobserved factors Returns ------- out : Bunch Has the following attributes shown in Notes. Notes ----- The output is a bunch of the following format: - `filtered`: a time series array with the filtered estimate of the component - `filtered_cov`: a time series array with the filtered estimate of the variance/covariance of the component - `smoothed`: a time series array with the smoothed estimate of the component - `smoothed_cov`: a time series array with the smoothed estimate of the variance/covariance of the component - `offset`: an integer giving the offset in the state vector where this component begins """ # If present, level is always the first component of the state vector out = None spec = self.specification if spec.k_factors > 0: offset = 0 end = spec.k_factors res = self.filter_results out = Bunch( filtered=res.filtered_state[offset:end], filtered_cov=res.filtered_state_cov[offset:end, offset:end], smoothed=None, smoothed_cov=None, offset=offset) if self.smoothed_state is not None: out.smoothed = self.smoothed_state[offset:end] if self.smoothed_state_cov is not None: out.smoothed_cov = ( self.smoothed_state_cov[offset:end, offset:end]) return out @cache_readonly def coefficients_of_determination(self): """ Coefficients of determination (:math:`R^2`) from regressions of individual estimated factors on endogenous variables. Returns ------- coefficients_of_determination : ndarray A `k_endog` x `k_factors` array, where `coefficients_of_determination[i, j]` represents the :math:`R^2` value from a regression of factor `j` and a constant on endogenous variable `i`. Notes ----- Although it can be difficult to interpret the estimated factor loadings and factors, it is often helpful to use the coefficients of determination from univariate regressions to assess the importance of each factor in explaining the variation in each endogenous variable. In models with many variables and factors, this can sometimes lend interpretation to the factors (for example sometimes one factor will load primarily on real variables and another on nominal variables). See Also -------- plot_coefficients_of_determination """ from statsmodels.tools import add_constant spec = self.specification coefficients = np.zeros((spec.k_endog, spec.k_factors)) which = 'filtered' if self.smoothed_state is None else 'smoothed' for i in range(spec.k_factors): exog = add_constant(self.factors[which][i]) for j in range(spec.k_endog): endog = self.filter_results.endog[j] coefficients[j, i] = OLS(endog, exog).fit().rsquared return coefficients def plot_coefficients_of_determination(self, endog_labels=None, fig=None, figsize=None): """ Plot the coefficients of determination Parameters ---------- endog_labels : bool, optional Whether or not to label the endogenous variables along the x-axis of the plots. Default is to include labels if there are 5 or fewer endogenous variables. fig : Figure, optional If given, subplots are created in this figure instead of in a new figure. Note that the grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Notes ----- Produces a `k_factors` x 1 plot grid. The `i`th plot shows a bar plot of the coefficients of determination associated with factor `i`. The endogenous variables are arranged along the x-axis according to their position in the `endog` array. See Also -------- coefficients_of_determination """ from statsmodels.graphics.utils import _import_mpl, create_mpl_fig _import_mpl() fig = create_mpl_fig(fig, figsize) spec = self.specification # Should we label endogenous variables? if endog_labels is None: endog_labels = spec.k_endog <= 5 # Plot the coefficients of determination coefficients_of_determination = self.coefficients_of_determination plot_idx = 1 locations = np.arange(spec.k_endog) for coeffs in coefficients_of_determination.T: # Create the new axis ax = fig.add_subplot(spec.k_factors, 1, plot_idx) ax.set_ylim((0, 1)) ax.set(title='Factor %i' % plot_idx, ylabel=r'$R^2$') bars = ax.bar(locations, coeffs) if endog_labels: width = bars[0].get_width() ax.xaxis.set_ticks(locations + width / 2) ax.xaxis.set_ticklabels(self.model.endog_names) else: ax.set(xlabel='Endogenous variables') ax.xaxis.set_ticks([]) plot_idx += 1 return fig @Appender(MLEResults.summary.__doc__) def summary(self, alpha=.05, start=None, separate_params=True): from statsmodels.iolib.summary import summary_params spec = self.specification # Create the model name model_name = [] if spec.k_factors > 0: if spec.factor_order > 0: model_type = ('DynamicFactor(factors=%d, order=%d)' % (spec.k_factors, spec.factor_order)) else: model_type = 'StaticFactor(factors=%d)' % spec.k_factors model_name.append(model_type) if spec.k_exog > 0: model_name.append('%d regressors' % spec.k_exog) else: model_name.append('SUR(%d regressors)' % spec.k_exog) if spec.error_order > 0: error_type = 'VAR' if spec.error_var else 'AR' model_name.append('%s(%d) errors' % (error_type, spec.error_order)) summary = super(DynamicFactorResults, self).summary( alpha=alpha, start=start, model_name=model_name, display_params=not separate_params ) if separate_params: indices = np.arange(len(self.params)) def make_table(self, mask, title, strip_end=True): res = (self, self.params[mask], self.bse[mask], self.zvalues[mask], self.pvalues[mask], self.conf_int(alpha)[mask]) param_names = [ '.'.join(name.split('.')[:-1]) if strip_end else name for name in np.array(self.data.param_names)[mask].tolist() ] return summary_params(res, yname=None, xname=param_names, alpha=alpha, use_t=False, title=title) k_endog = self.model.k_endog k_exog = self.model.k_exog k_factors = self.model.k_factors factor_order = self.model.factor_order _factor_order = self.model._factor_order _error_order = self.model._error_order # Add parameter tables for each endogenous variable loading_indices = indices[self.model._params_loadings] loading_masks = [] exog_indices = indices[self.model._params_exog] exog_masks = [] for i in range(k_endog): # 1. Factor loadings # Recall these are in the form: # 'loading.f1.y1', 'loading.f2.y1', 'loading.f1.y2', ... loading_mask = ( loading_indices[i * k_factors:(i + 1) * k_factors]) loading_masks.append(loading_mask) # 2. Exog # Recall these are in the form: # beta.x1.y1, beta.x2.y1, beta.x1.y2, ... exog_mask = exog_indices[i * k_exog:(i + 1) * k_exog] exog_masks.append(exog_mask) # Create the table mask = np.concatenate([loading_mask, exog_mask]) title = "Results for equation %s" % self.model.endog_names[i] table = make_table(self, mask, title) summary.tables.append(table) # Add parameter tables for each factor factor_indices = indices[self.model._params_factor_transition] factor_masks = [] if factor_order > 0: for i in range(k_factors): start = i * _factor_order factor_mask = factor_indices[start: start + _factor_order] factor_masks.append(factor_mask) # Create the table title = "Results for factor equation f%d" % (i+1) table = make_table(self, factor_mask, title) summary.tables.append(table) # Add parameter tables for error transitions error_masks = [] if spec.error_order > 0: error_indices = indices[self.model._params_error_transition] for i in range(k_endog): if spec.error_var: start = i * _error_order end = (i + 1) * _error_order else: start = i * spec.error_order end = (i + 1) * spec.error_order error_mask = error_indices[start:end] error_masks.append(error_mask) # Create the table title = ("Results for error equation e(%s)" % self.model.endog_names[i]) table = make_table(self, error_mask, title) summary.tables.append(table) # Error covariance terms error_cov_mask = indices[self.model._params_error_cov] table = make_table(self, error_cov_mask, "Error covariance matrix", strip_end=False) summary.tables.append(table) # Add a table for all other parameters masks = [] for m in (loading_masks, exog_masks, factor_masks, error_masks, [error_cov_mask]): m = np.array(m).flatten() if len(m) > 0: masks.append(m) masks = np.concatenate(masks) inverse_mask = np.array(list(set(indices).difference(set(masks)))) if len(inverse_mask) > 0: table = make_table(self, inverse_mask, "Other parameters", strip_end=False) summary.tables.append(table) return summary class DynamicFactorResultsWrapper(MLEResultsWrapper): _attrs = {} _wrap_attrs = wrap.union_dicts(MLEResultsWrapper._wrap_attrs, _attrs) _methods = {} _wrap_methods = wrap.union_dicts(MLEResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(DynamicFactorResultsWrapper, # noqa:E305 DynamicFactorResults) statsmodels-0.12.2/statsmodels/tsa/statespace/dynamic_factor_mq.py000066400000000000000000005534071400612667500255010ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Dynamic factor model. Author: Chad Fulton License: BSD-3 """ from collections import OrderedDict from warnings import warn import numpy as np import pandas as pd from scipy.linalg import cho_factor, cho_solve, LinAlgError from statsmodels.tools.data import _is_using_pandas from statsmodels.tools.validation import int_like from statsmodels.tools.decorators import cache_readonly from statsmodels.regression.linear_model import OLS from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.multivariate.pca import PCA from statsmodels.tsa.statespace.sarimax import SARIMAX from statsmodels.tsa.statespace._quarterly_ar1 import QuarterlyAR1 from statsmodels.tsa.vector_ar.var_model import VAR from statsmodels.tools.tools import Bunch from statsmodels.tools.validation import string_like from statsmodels.tsa.tsatools import lagmat from statsmodels.tsa.statespace import mlemodel, initialization from statsmodels.tsa.statespace.tools import ( companion_matrix, is_invertible, constrain_stationary_univariate, constrain_stationary_multivariate, unconstrain_stationary_univariate, unconstrain_stationary_multivariate) from statsmodels.tsa.statespace.kalman_smoother import ( SMOOTHER_STATE, SMOOTHER_STATE_COV, SMOOTHER_STATE_AUTOCOV) from statsmodels.base.data import PandasData from statsmodels.iolib.table import SimpleTable from statsmodels.iolib.summary import Summary from statsmodels.iolib.tableformatting import fmt_params class FactorBlock(dict): """ Helper class for describing and indexing a block of factors. Parameters ---------- factor_names : tuple of str Tuple of factor names in the block (in the order that they will appear in the state vector). factor_order : int Order of the vector autoregression governing the factor block dynamics. endog_factor_map : pd.DataFrame Mapping from endog variable names to factor names. state_offset : int Offset of this factor block in the state vector. has_endog_Q : bool Flag if the model contains quarterly data. Notes ----- The goal of this class is, in particular, to make it easier to retrieve indexes of subsets of the state vector that are associated with a particular block of factors. - `factors_ix` is a matrix of indices, with rows corresponding to factors in the block and columns corresponding to lags - `factors` is vec(factors_ix) (i.e. it stacks columns, so that it is `factors_ix.ravel(order='F')`). Thinking about a VAR system, the first k*p elements correspond to the equation for the first variable. The next k*p elements correspond to the equation for the second variable, and so on. It contains all of the lags in the state vector, which is max(5, p) - `factors_ar` is the subset of `factors` that have nonzero coefficients, so it contains lags up to p. - `factors_L1` only contains the first lag of the factors - `factors_L1_5` contains the first - fifth lags of the factors """ def __init__(self, factor_names, factor_order, endog_factor_map, state_offset, k_endog_Q): self.factor_names = factor_names self.k_factors = len(self.factor_names) self.factor_order = factor_order self.endog_factor_map = endog_factor_map.loc[:, factor_names] self.state_offset = state_offset self.k_endog_Q = k_endog_Q if self.k_endog_Q > 0: self._factor_order = max(5, self.factor_order) else: self._factor_order = self.factor_order self.k_states = self.k_factors * self._factor_order # Save items self['factors'] = self.factors self['factors_ar'] = self.factors_ar self['factors_ix'] = self.factors_ix self['factors_L1'] = self.factors_L1 self['factors_L1_5'] = self.factors_L1_5 @property def factors_ix(self): """Factor state index array, shaped (k_factors, lags).""" # i.e. the position in the state vector of the second lag of the third # factor is factors_ix[2, 1] # ravel(order='F') gives e.g (f0.L1, f1.L1, f0.L2, f1.L2, f0.L3, ...) # while # ravel(order='C') gives e.g (f0.L1, f0.L2, f0.L3, f1.L1, f1.L2, ...) o = self.state_offset return np.reshape(o + np.arange(self.k_factors * self._factor_order), (self._factor_order, self.k_factors)).T @property def factors(self): """Factors and all lags in the state vector (max(5, p)).""" # Note that this is equivalent to factors_ix with ravel(order='F') o = self.state_offset return np.s_[o:o + self.k_factors * self._factor_order] @property def factors_ar(self): """Factors and all lags used in the factor autoregression (p).""" o = self.state_offset return np.s_[o:o + self.k_factors * self.factor_order] @property def factors_L1(self): """Factors (first block / lag only).""" o = self.state_offset return np.s_[o:o + self.k_factors] @property def factors_L1_5(self): """Factors plus four lags.""" o = self.state_offset return np.s_[o:o + self.k_factors * 5] class DynamicFactorMQStates(dict): """ Helper class for describing and indexing the state vector. Parameters ---------- k_endog_M : int Number of monthly (or non-time-specific, if k_endog_Q=0) variables. k_endog_Q : int Number of quarterly variables. endog_names : list Names of the endogenous variables. factors : int, list, or dict Integer giving the number of (global) factors, a list with the names of (global) factors, or a dictionary with: - keys : names of endogenous variables - values : lists of factor names. If this is an integer, then the factor names will be 0, 1, .... factor_orders : int or dict Integer describing the order of the vector autoregression (VAR) governing all factor block dynamics or dictionary with: - keys : factor name or tuples of factor names in a block - values : integer describing the VAR order for that factor block If a dictionary, this defines the order of the factor blocks in the state vector. Otherwise, factors are ordered so that factors that load on more variables come first (and then alphabetically, to break ties). factor_multiplicities : int or dict This argument provides a convenient way to specify multiple factors that load identically on variables. For example, one may want two "global" factors (factors that load on all variables) that evolve jointly according to a VAR. One could specify two global factors in the `factors` argument and specify that they are in the same block in the `factor_orders` argument, but it is easier to specify a single global factor in the `factors` argument, and set the order in the `factor_orders` argument, and then set the factor multiplicity to 2. This argument must be an integer describing the factor multiplicity for all factors or dictionary with: - keys : factor name - values : integer describing the factor multiplicity for the factors in the given block idiosyncratic_ar1 : bool Whether or not to model the idiosyncratic component for each series as an AR(1) process. If False, the idiosyncratic component is instead modeled as white noise. Attributes ---------- k_endog : int Total number of endogenous variables. k_states : int Total number of state variables (those associated with the factors and those associated with the idiosyncratic disturbances). k_posdef : int Total number of state disturbance terms (those associated with the factors and those associated with the idiosyncratic disturbances). k_endog_M : int Number of monthly (or non-time-specific, if k_endog_Q=0) variables. k_endog_Q : int Number of quarterly variables. k_factors : int Total number of factors. Note that factor multiplicities will have already been expanded. k_states_factors : int The number of state variables associated with factors (includes both factors and lags of factors included in the state vector). k_posdef_factors : int The number of state disturbance terms associated with factors. k_states_idio : int Total number of state variables associated with idiosyncratic disturbances. k_posdef_idio : int Total number of state disturbance terms associated with idiosyncratic disturbances. k_states_idio_M : int The number of state variables associated with idiosyncratic disturbances for monthly (or non-time-specific if there are no quarterly variables) variables. If the disturbances are AR(1), then this will be equal to `k_endog_M`, otherwise it will be equal to zero. k_states_idio_Q : int The number of state variables associated with idiosyncratic disturbances for quarterly variables. This will always be equal to `k_endog_Q * 5`, even if the disturbances are not AR(1). k_posdef_idio_M : int The number of state disturbance terms associated with idiosyncratic disturbances for monthly (or non-time-specific if there are no quarterly variables) variables. If the disturbances are AR(1), then this will be equal to `k_endog_M`, otherwise it will be equal to zero. k_posdef_idio_Q : int The number of state disturbance terms associated with idiosyncratic disturbances for quarterly variables. This will always be equal to `k_endog_Q`, even if the disturbances are not AR(1). idiosyncratic_ar1 : bool Whether or not to model the idiosyncratic component for each series as an AR(1) process. factor_blocks : list of FactorBlock List of `FactorBlock` helper instances for each factor block. factor_names : list of str List of factor names. factors : dict Dictionary with: - keys : names of endogenous variables - values : lists of factor names. Note that factor multiplicities will have already been expanded. factor_orders : dict Dictionary with: - keys : tuple of factor names - values : integer describing autoregression order Note that factor multiplicities will have already been expanded. max_factor_order : int Maximum autoregression order across all factor blocks. factor_block_orders : pd.Series Series containing lag orders, with the factor block (a tuple of factor names) as the index. factor_multiplicities : dict Dictionary with: - keys : factor name - values : integer describing the factor multiplicity for the factors in the given block endog_factor_map : dict Dictionary with: - keys : endog name - values : list of factor names loading_counts : pd.Series Series containing number of endogenous variables loading on each factor, with the factor name as the index. block_loading_counts : dict Dictionary with: - keys : tuple of factor names - values : average number of endogenous variables loading on the block (note that average is over the factors in the block) Notes ----- The goal of this class is, in particular, to make it easier to retrieve indexes of subsets of the state vector. Note that the ordering of the factor blocks in the state vector is determined by the `factor_orders` argument if a dictionary. Otherwise, factors are ordered so that factors that load on more variables come first (and then alphabetically, to break ties). - `factors_L1` is an array with the indexes of first lag of the factors from each block. Ordered first by block, and then by lag. - `factors_L1_5` is an array with the indexes contains the first - fifth lags of the factors from each block. Ordered first by block, and then by lag. - `factors_L1_5_ix` is an array shaped (5, k_factors) with the indexes of the first - fifth lags of the factors from each block. - `idio_ar_L1` is an array with the indexes of the first lag of the idiosyncratic AR states, both monthly (if appliable) and quarterly. - `idio_ar_M` is a slice with the indexes of the idiosyncratic disturbance states for the monthly (or non-time-specific if there are no quarterly variables) variables. It is an empty slice if `idiosyncratic_ar1 = False`. - `idio_ar_Q` is a slice with the indexes of the idiosyncratic disturbance states and all lags, for the quarterly variables. It is an empty slice if there are no quarterly variable. - `idio_ar_Q_ix` is an array shaped (k_endog_Q, 5) with the indexes of the first - fifth lags of the idiosyncratic disturbance states for the quarterly variables. - `endog_factor_iloc` is a list of lists, with entries for each endogenous variable. The entry for variable `i`, `endog_factor_iloc[i]` is a list of indexes of the factors that variable `i` loads on. This does not include any lags, but it can be used with e.g. `factors_L1_5_ix` to get lags. """ def __init__(self, k_endog_M, k_endog_Q, endog_names, factors, factor_orders, factor_multiplicities, idiosyncratic_ar1): # Save model parameterization self.k_endog_M = k_endog_M self.k_endog_Q = k_endog_Q self.k_endog = self.k_endog_M + self.k_endog_Q self.idiosyncratic_ar1 = idiosyncratic_ar1 # Validate factor-related inputs factors_is_int = np.issubdtype(type(factors), np.integer) factors_is_list = isinstance(factors, (list, tuple)) orders_is_int = np.issubdtype(type(factor_orders), np.integer) if factor_multiplicities is None: factor_multiplicities = 1 mult_is_int = np.issubdtype(type(factor_multiplicities), np.integer) if not (factors_is_int or factors_is_list or isinstance(factors, dict)): raise ValueError('`factors` argument must an integer number of' ' factors, a list of global factor names, or a' ' dictionary, mapping observed variables to' ' factors.') if not (orders_is_int or isinstance(factor_orders, dict)): raise ValueError('`factor_orders` argument must either be an' ' integer or a dictionary.') if not (mult_is_int or isinstance(factor_multiplicities, dict)): raise ValueError('`factor_multiplicities` argument must either be' ' an integer or a dictionary.') # Expand integers # If `factors` is an integer, we assume that it denotes the number of # global factors (factors that load on each variable) if factors_is_int or factors_is_list: # Validate this here for a more informative error message if ((factors_is_int and factors == 0) or (factors_is_list and len(factors) == 0)): raise ValueError('The model must contain at least one factor.') if factors_is_list: factor_names = list(factors) else: factor_names = [f'{i}' for i in range(factors)] factors = {name: factor_names[:] for name in endog_names} factor_names = set(np.concatenate(list(factors.values()))) if orders_is_int: factor_orders = {factor_name: factor_orders for factor_name in factor_names} if mult_is_int: factor_multiplicities = {factor_name: factor_multiplicities for factor_name in factor_names} # Apply the factor multiplities factors, factor_orders = self._apply_factor_multiplicities( factors, factor_orders, factor_multiplicities) # Save the (potentially expanded) variables self.factors = factors self.factor_orders = factor_orders self.factor_multiplicities = factor_multiplicities # Get the mapping between endog and factors self.endog_factor_map = self._construct_endog_factor_map( factors, endog_names) self.k_factors = self.endog_factor_map.shape[1] # Validate number of factors # TODO: could do more extensive validation here. if self.k_factors > self.k_endog_M: raise ValueError(f'Number of factors ({self.k_factors}) cannot be' ' greater than the number of monthly endogenous' f' variables ({self.k_endog_M}).') # Get `loading_counts`: factor -> # endog loading on the factor self.loading_counts = ( self.endog_factor_map.sum(axis=0).rename('count') .reset_index().sort_values(['count', 'factor'], ascending=[False, True]) .set_index('factor')) # `block_loading_counts`: block -> average of (# loading on factor) # across each factor in the block block_loading_counts = { block: np.atleast_1d( self.loading_counts.loc[list(block), 'count']).mean(axis=0) for block in factor_orders.keys()} ix = pd.Index(block_loading_counts.keys(), tupleize_cols=False, name='block') self.block_loading_counts = pd.Series( list(block_loading_counts.values()), index=ix, name='count').to_frame().sort_values( ['count', 'block'], ascending=[False, True])['count'] # Get the mapping between factor blocks and VAR order # `factor_block_orders`: pd.Series of factor block -> lag order ix = pd.Index(factor_orders.keys(), tupleize_cols=False, name='block') self.factor_block_orders = pd.Series( list(factor_orders.values()), index=ix, name='order') # If the `factor_orders` variable was an integer, then it did not # define an ordering for the factor blocks. In this case, we use the # loading counts to do so. This ensures that e.g. global factors are # listed first. if orders_is_int: keys = self.block_loading_counts.keys() self.factor_block_orders = self.factor_block_orders.loc[keys] self.factor_block_orders.index.name = 'block' # Define factor_names based on factor_block_orders (instead of on those # from `endog_factor_map`) to (a) make sure that factors are allocated # to only one block, and (b) order the factor names to be consistent # with the block definitions. factor_names = pd.Series( np.concatenate(list(self.factor_block_orders.index))) missing = [name for name in self.endog_factor_map.columns if name not in factor_names.tolist()] if len(missing): ix = pd.Index([(factor_name,) for factor_name in missing], tupleize_cols=False, name='block') default_block_orders = pd.Series(np.ones(len(ix), dtype=int), index=ix, name='order') self.factor_block_orders = ( self.factor_block_orders.append(default_block_orders)) factor_names = pd.Series( np.concatenate(list(self.factor_block_orders.index))) duplicates = factor_names.duplicated() if duplicates.any(): duplicate_names = set(factor_names[duplicates]) raise ValueError('Each factor can be assigned to at most one' ' block of factors in `factor_orders`.' f' Duplicate entries for {duplicate_names}') self.factor_names = factor_names.tolist() self.max_factor_order = np.max(self.factor_block_orders) # Re-order the columns of the endog factor mapping to reflect the # orderings of endog_names and factor_names self.endog_factor_map = ( self.endog_factor_map.loc[endog_names, factor_names]) # Create factor block helpers, and get factor-related state and posdef # dimensions self.k_states_factors = 0 self.k_posdef_factors = 0 state_offset = 0 self.factor_blocks = [] for factor_names, factor_order in self.factor_block_orders.items(): block = FactorBlock(factor_names, factor_order, self.endog_factor_map, state_offset, self.k_endog_Q) self.k_states_factors += block.k_states self.k_posdef_factors += block.k_factors state_offset += block.k_states self.factor_blocks.append(block) # Idiosyncratic state dimensions self.k_states_idio_M = self.k_endog_M if idiosyncratic_ar1 else 0 self.k_states_idio_Q = self.k_endog_Q * 5 self.k_states_idio = self.k_states_idio_M + self.k_states_idio_Q # Idiosyncratic posdef dimensions self.k_posdef_idio_M = self.k_endog_M if self.idiosyncratic_ar1 else 0 self.k_posdef_idio_Q = self.k_endog_Q self.k_posdef_idio = self.k_posdef_idio_M + self.k_posdef_idio_Q # Total states, posdef self.k_states = self.k_states_factors + self.k_states_idio self.k_posdef = self.k_posdef_factors + self.k_posdef_idio # Cache self._endog_factor_iloc = None def _apply_factor_multiplicities(self, factors, factor_orders, factor_multiplicities): """ Expand `factors` and `factor_orders` to account for factor multiplity. For example, if there is a `global` factor with multiplicity 2, then this method expands that into `global.1` and `global.2` in both the `factors` and `factor_orders` dictionaries. Parameters ---------- factors : dict Dictionary of {endog_name: list of factor names} factor_orders : dict Dictionary of {tuple of factor names: factor order} factor_multiplicities : dict Dictionary of {factor name: factor multiplicity} Returns ------- new_factors : dict Dictionary of {endog_name: list of factor names}, with factor names expanded to incorporate multiplicities. new_factors : dict Dictionary of {tuple of factor names: factor order}, with factor names in each tuple expanded to incorporate multiplicities. """ # Expand the factors to account for the multiplicities new_factors = {} for endog_name, factors_list in factors.items(): new_factor_list = [] for factor_name in factors_list: n = factor_multiplicities.get(factor_name, 1) if n > 1: new_factor_list += [f'{factor_name}.{i + 1}' for i in range(n)] else: new_factor_list.append(factor_name) new_factors[endog_name] = new_factor_list # Expand the factor orders to account for the multiplicities new_factor_orders = {} for block, factor_order in factor_orders.items(): if not isinstance(block, tuple): block = (block,) new_block = [] for factor_name in block: n = factor_multiplicities.get(factor_name, 1) if n > 1: new_block += [f'{factor_name}.{i + 1}' for i in range(n)] else: new_block += [factor_name] new_factor_orders[tuple(new_block)] = factor_order return new_factors, new_factor_orders def _construct_endog_factor_map(self, factors, endog_names): """ Construct mapping of observed variables to factors. Parameters ---------- factors : dict Dictionary of {endog_name: list of factor names} endog_names : list of str List of the names of the observed variables. Returns ------- endog_factor_map : pd.DataFrame Boolean dataframe with `endog_names` as the index and the factor names (computed from the `factors` input) as the columns. Each cell is True if the associated factor is allowed to load on the associated observed variable. """ # Validate that all entries in the factors dictionary have associated # factors missing = [] for key, value in factors.items(): if not isinstance(value, (list, tuple)) or len(value) == 0: missing.append(key) if len(missing): raise ValueError('Each observed variable must be mapped to at' ' least one factor in the `factors` dictionary.' f' Variables missing factors are: {missing}.') # Validate that we have been told about the factors for each endog # variable. This is because it doesn't make sense to include an # observed variable that doesn't load on any factor missing = set(endog_names).difference(set(factors.keys())) if len(missing): raise ValueError('If a `factors` dictionary is provided, then' ' it must include entries for each observed' f' variable. Missing variables are: {missing}.') # Figure out the set of factor names # (0 is just a dummy value for the dict - we just do it this way to # collect the keys, in order, without duplicates.) factor_names = {} for key, value in factors.items(): if isinstance(value, str): factor_names[value] = 0 else: factor_names.update({v: 0 for v in value}) factor_names = list(factor_names.keys()) k_factors = len(factor_names) endog_factor_map = pd.DataFrame( np.zeros((self.k_endog, k_factors), dtype=bool), index=pd.Index(endog_names, name='endog'), columns=pd.Index(factor_names, name='factor')) for key, value in factors.items(): endog_factor_map.loc[key, value] = True return endog_factor_map @property def factors_L1(self): """Factors.""" ix = np.arange(self.k_states_factors) iloc = tuple(ix[block.factors_L1] for block in self.factor_blocks) return np.concatenate(iloc) @property def factors_L1_5_ix(self): """Factors plus any lags, index shaped (5, k_factors).""" ix = np.arange(self.k_states_factors) iloc = [] for block in self.factor_blocks: iloc.append(ix[block.factors_L1_5].reshape(5, block.k_factors)) return np.concatenate(iloc, axis=1) @property def idio_ar_L1(self): """Idiosyncratic AR states, (first block / lag only).""" ix1 = self.k_states_factors if self.idiosyncratic_ar1: ix2 = ix1 + self.k_endog else: ix2 = ix1 + self.k_endog_Q return np.s_[ix1:ix2] @property def idio_ar_M(self): """Idiosyncratic AR states for monthly variables.""" ix1 = self.k_states_factors ix2 = ix1 if self.idiosyncratic_ar1: ix2 += self.k_endog_M return np.s_[ix1:ix2] @property def idio_ar_Q(self): """Idiosyncratic AR states and all lags for quarterly variables.""" # Note that this is equivalent to idio_ar_Q_ix with ravel(order='F') ix1 = self.k_states_factors if self.idiosyncratic_ar1: ix1 += self.k_endog_M ix2 = ix1 + self.k_endog_Q * 5 return np.s_[ix1:ix2] @property def idio_ar_Q_ix(self): """Idiosyncratic AR (quarterly) state index, (k_endog_Q, lags).""" # i.e. the position in the state vector of the second lag of the third # quarterly variable is idio_ar_Q_ix[2, 1] # ravel(order='F') gives e.g (y1.L1, y2.L1, y1.L2, y2.L3, y1.L3, ...) # while # ravel(order='C') gives e.g (y1.L1, y1.L2, y1.L3, y2.L1, y2.L2, ...) start = self.k_states_factors if self.idiosyncratic_ar1: start += self.k_endog_M return (start + np.reshape( np.arange(5 * self.k_endog_Q), (5, self.k_endog_Q)).T) @property def endog_factor_iloc(self): """List of list of int, factor indexes for each observed variable.""" # i.e. endog_factor_iloc[i] is a list of integer locations of the # factors that load on the ith observed variable if self._endog_factor_iloc is None: ilocs = [] for i in range(self.k_endog): ilocs.append(np.where(self.endog_factor_map.iloc[i])[0]) self._endog_factor_iloc = ilocs return self._endog_factor_iloc def __getitem__(self, key): """ Use square brackets to access index / slice elements. This is convenient in highlighting the indexing / slice quality of these attributes in the code below. """ if key in ['factors_L1', 'factors_L1_5_ix', 'idio_ar_L1', 'idio_ar_M', 'idio_ar_Q', 'idio_ar_Q_ix']: return getattr(self, key) else: raise KeyError(key) class DynamicFactorMQ(mlemodel.MLEModel): r""" Dynamic factor model with EM algorithm; option for monthly/quarterly data. Implementation of the dynamic factor model of Bańbura and Modugno (2014) ([1]_) and Bańbura, Giannone, and Reichlin (2011) ([2]_). Uses the EM algorithm for parameter fitting, and so can accommodate a large number of left-hand-side variables. Specifications can include any collection of blocks of factors, including different factor autoregression orders, and can include AR(1) processes for idiosyncratic disturbances. Can incorporate monthly/quarterly mixed frequency data along the lines of Mariano and Murasawa (2011) ([4]_). A special case of this model is the Nowcasting model of Bok et al. (2017) ([3]_). Moreover, this model can be used to compute the news associated with updated data releases. Parameters ---------- endog : array_like Observed time-series process :math:`y`. See the "Notes" section for details on how to set up a model with monthly/quarterly mixed frequency data. k_endog_monthly : int, optional If specifying a monthly/quarterly mixed frequency model in which the provided `endog` dataset contains both the monthly and quarterly data, this variable should be used to indicate how many of the variables are monthly. Note that when using the `k_endog_monthly` argument, the columns with monthly variables in `endog` should be ordered first, and the columns with quarterly variables should come afterwards. See the "Notes" section for details on how to set up a model with monthly/quarterly mixed frequency data. factors : int, list, or dict, optional Integer giving the number of (global) factors, a list with the names of (global) factors, or a dictionary with: - keys : names of endogenous variables - values : lists of factor names. If this is an integer, then the factor names will be 0, 1, .... The default is a single factor that loads on all variables. Note that there cannot be more factors specified than there are monthly variables. factor_orders : int or dict, optional Integer describing the order of the vector autoregression (VAR) governing all factor block dynamics or dictionary with: - keys : factor name or tuples of factor names in a block - values : integer describing the VAR order for that factor block If a dictionary, this defines the order of the factor blocks in the state vector. Otherwise, factors are ordered so that factors that load on more variables come first (and then alphabetically, to break ties). factor_multiplicities : int or dict, optional This argument provides a convenient way to specify multiple factors that load identically on variables. For example, one may want two "global" factors (factors that load on all variables) that evolve jointly according to a VAR. One could specify two global factors in the `factors` argument and specify that they are in the same block in the `factor_orders` argument, but it is easier to specify a single global factor in the `factors` argument, and set the order in the `factor_orders` argument, and then set the factor multiplicity to 2. This argument must be an integer describing the factor multiplicity for all factors or dictionary with: - keys : factor name - values : integer describing the factor multiplicity for the factors in the given block idiosyncratic_ar1 : bool Whether or not to model the idiosyncratic component for each series as an AR(1) process. If False, the idiosyncratic component is instead modeled as white noise. standardize : bool or tuple, optional If a boolean, whether or not to standardize each endogenous variable to have mean zero and standard deviation 1 before fitting the model. See "Notes" for details about how this option works with postestimation output. If a tuple (usually only used internally), then the tuple must have length 2, with each element containing a Pandas series with index equal to the names of the endogenous variables. The first element should contain the mean values and the second element should contain the standard deviations. Default is True. endog_quarterly : pandas.Series or pandas.DataFrame Observed quarterly variables. If provided, must be a Pandas Series or DataFrame with a DatetimeIndex or PeriodIndex at the quarterly frequency. See the "Notes" section for details on how to set up a model with monthly/quarterly mixed frequency data. init_t0 : bool, optional If True, this option initializes the Kalman filter with the distribution for :math:`\alpha_0` rather than :math:`\alpha_1`. See the "Notes" section for more details. This option is rarely used except for testing. Default is False. obs_cov_diag : bool, optional If True and if `idiosyncratic_ar1 is True`, then this option puts small positive values in the observation disturbance covariance matrix. This is not required for estimation and is rarely used except for testing. (It is sometimes used to prevent numerical errors, for example those associated with a positive semi-definite forecast error covariance matrix at the first time step when using EM initialization, but state space models in Statsmodels switch to the univariate approach in those cases, and so do not need to use this trick). Default is False. Notes ----- The basic model is: .. math:: y_t & = \Lambda f_t + \epsilon_t \\ f_t & = A_1 f_{t-1} + \dots + A_p f_{t-p} + u_t where: - :math:`y_t` is observed data at time t - :math:`\epsilon_t` is idiosyncratic disturbance at time t (see below for details, including modeling serial correlation in this term) - :math:`f_t` is the unobserved factor at time t - :math:`u_t \sim N(0, Q)` is the factor disturbance at time t and: - :math:`\Lambda` is referred to as the matrix of factor loadings - :math:`A_i` are matrices of autoregression coefficients Furthermore, we allow the idiosyncratic disturbances to be serially correlated, so that, if `idiosyncratic_ar1=True`, :math:`\epsilon_{i,t} = \rho_i \epsilon_{i,t-1} + e_{i,t}`, where :math:`e_{i,t} \sim N(0, \sigma_i^2)`. If `idiosyncratic_ar1=False`, then we instead have :math:`\epsilon_{i,t} = e_{i,t}`. This basic setup can be found in [1]_, [2]_, [3]_, and [4]_. We allow for two generalizations of this model: 1. Following [2]_, we allow multiple "blocks" of factors, which are independent from the other blocks of factors. Different blocks can be set to load on different subsets of the observed variables, and can be specified with different lag orders. 2. Following [4]_ and [2]_, we allow mixed frequency models in which both monthly and quarterly data are used. See the section on "Mixed frequency models", below, for more details. Additional notes: - The observed data may contain arbitrary patterns of missing entries. **EM algorithm** This model contains a potentially very large number of parameters, and it can be difficult and take a prohibitively long time to numerically optimize the likelihood function using quasi-Newton methods. Instead, the default fitting method in this model uses the EM algorithm, as detailed in [1]_. As a result, the model can accommodate datasets with hundreds of observed variables. **Mixed frequency data** This model can handle mixed frequency data in two ways. In this section, we only briefly describe this, and refer readers to [2]_ and [4]_ for all details. First, because there can be arbitrary patterns of missing data in the observed vector, one can simply include lower frequency variables as observed in a particular higher frequency period, and missing otherwise. For example, in a monthly model, one could include quarterly data as occurring on the third month of each quarter. To use this method, one simply needs to combine the data into a single dataset at the higher frequency that can be passed to this model as the `endog` argument. However, depending on the type of variables used in the analysis and the assumptions about the data generating process, this approach may not be valid. For example, suppose that we are interested in the growth rate of real GDP, which is measured at a quarterly frequency. If the basic factor model is specified at a monthly frequency, then the quarterly growth rate in the third month of each quarter -- which is what we actually observe -- is approximated by a particular weighted average of unobserved monthly growth rates. We need to take this particular weight moving average into account in constructing our model, and this is what the second approach does. The second approach follows [2]_ and [4]_ in constructing a state space form to explicitly model the quarterly growth rates in terms of the unobserved monthly growth rates. To use this approach, there are two methods: 1. Combine the monthly and quarterly data into a single dataset at the monthly frequency, with the monthly data in the first columns and the quarterly data in the last columns. Pass this dataset to the model as the `endog` argument and give the number of the variables that are monthly as the `k_endog_monthly` argument. 2. Construct a monthly dataset as a Pandas DataFrame with a DatetimeIndex or PeriodIndex at the monthly frequency and separately construct a quarterly dataset as a Pandas DataFrame with a DatetimeIndex or PeriodIndex at the quarterly frequency. Pass the monthly DataFrame to the model as the `endog` argument and pass the quarterly DataFrame to the model as the `endog_quarterly` argument. Note that this only incorporates one particular type of mixed frequency data. See also Banbura et al. (2013). "Now-Casting and the Real-Time Data Flow." for discussion about other types of mixed frequency data that are not supported by this framework. **Nowcasting and the news** Through its support for monthly/quarterly mixed frequency data, this model can allow for the nowcasting of quarterly variables based on monthly observations. In particular, [2]_ and [3]_ use this model to construct nowcasts of real GDP and analyze the impacts of "the news", derived from incoming data on a real-time basis. This latter functionality can be accessed through the `news` method of the results object. **Standardizing data** As is often the case in formulating a dynamic factor model, we do not explicitly account for the mean of each observed variable. Instead, the default behavior is to standardize each variable prior to estimation. Thus if :math:`y_t` are the given observed data, the dynamic factor model is actually estimated on the standardized data defined by: .. math:: x_{i, t} = (y_{i, t} - \bar y_i) / s_i where :math:`\bar y_i` is the sample mean and :math:`s_i` is the sample standard deviation. By default, if standardization is applied prior to estimation, results such as in-sample predictions, out-of-sample forecasts, and the computation of the "news" are reported in the scale of the original data (i.e. the model output has the reverse transformation applied before it is returned to the user). Standardization can be disabled by passing `standardization=False` to the model constructor. **Identification of factors and loadings** The estimated factors and the factor loadings in this model are only identified up to an invertible transformation. As described in (the working paper version of) [2]_, while it is possible to impose normalizations to achieve identification, the EM algorithm does will converge regardless. Moreover, for nowcasting and forecasting purposes, identification is not required. This model does not impose any normalization to identify the factors and the factor loadings. **Miscellaneous** There are two arguments available in the model constructor that are rarely used but which deserve a brief mention: `init_t0` and `obs_cov_diag`. These arguments are provided to allow exactly matching the output of other packages that have slight differences in how the underlying state space model is set up / applied. - `init_t0`: state space models in Statsmodels follow Durbin and Koopman in initializing the model with :math:`\alpha_1 \sim N(a_1, P_1)`. Other implementations sometimes initialize instead with :math:`\alpha_0 \sim N(a_0, P_0)`. We can accommodate this by prepending a row of NaNs to the observed dataset. - `obs_cov_diag`: the state space form in [1]_ incorporates non-zero (but very small) diagonal elements for the observation disturbance covariance matrix. Examples -------- Constructing and fitting a `DynamicFactorMQ` model. >>> data = sm.datasets.macrodata.load_pandas().data.iloc[-100:] >>> data.index = pd.period_range(start='1984Q4', end='2009Q3', freq='Q') >>> endog = data[['infl', 'tbilrate']].resample('M').last() >>> endog_Q = np.log(data[['realgdp', 'realcons']]).diff().iloc[1:] * 400 **Basic usage** In the simplest case, passing only the `endog` argument results in a model with a single factor that follows an AR(1) process. Note that because we are not also providing an `endog_quarterly` dataset, `endog` can be a numpy array or Pandas DataFrame with any index (it does not have to be monthly). The `summary` method can be useful in checking the model specification. >>> mod = sm.tsa.DynamicFactorMQ(endog) >>> print(mod.summary()) Model Specification: Dynamic Factor Model ========================================================================== Model: Dynamic Factor Model # of monthly variables: 2 + 1 factors in 1 blocks # of factors: 1 + AR(1) idiosyncratic Idiosyncratic disturbances: AR(1) Sample: 1984-10 Standardize variables: True - 2009-09 Observed variables / factor loadings ======================== Dep. variable 0 ------------------------ infl X tbilrate X Factor blocks: ===================== block order --------------------- 0 1 ===================== **Factors** With `factors=2`, there will be two independent factors that will each evolve according to separate AR(1) processes. >>> mod = sm.tsa.DynamicFactorMQ(endog, factors=2) >>> print(mod.summary()) Model Specification: Dynamic Factor Model ========================================================================== Model: Dynamic Factor Model # of monthly variables: 2 + 2 factors in 2 blocks # of factors: 2 + AR(1) idiosyncratic Idiosyncratic disturbances: AR(1) Sample: 1984-10 Standardize variables: True - 2009-09 Observed variables / factor loadings =================================== Dep. variable 0 1 ----------------------------------- infl X X tbilrate X X Factor blocks: ===================== block order --------------------- 0 1 1 1 ===================== **Factor multiplicities** By instead specifying `factor_multiplicities=2`, we would still have two factors, but they would be dependent and would evolve jointly according to a VAR(1) process. >>> mod = sm.tsa.DynamicFactorMQ(endog, factor_multiplicities=2) >>> print(mod.summary()) Model Specification: Dynamic Factor Model ========================================================================== Model: Dynamic Factor Model # of monthly variables: 2 + 2 factors in 1 blocks # of factors: 2 + AR(1) idiosyncratic Idiosyncratic disturbances: AR(1) Sample: 1984-10 Standardize variables: True - 2009-09 Observed variables / factor loadings =================================== Dep. variable 0.1 0.2 ----------------------------------- infl X X tbilrate X X Factor blocks: ===================== block order --------------------- 0.1, 0.2 1 ===================== **Factor orders** In either of the above cases, we could extend the order of the (vector) autoregressions by using the `factor_orders` argument. For example, the below model would contain two independent factors that each evolve according to a separate AR(2) process: >>> mod = sm.tsa.DynamicFactorMQ(endog, factors=2, factor_orders=2) >>> print(mod.summary()) Model Specification: Dynamic Factor Model ========================================================================== Model: Dynamic Factor Model # of monthly variables: 2 + 2 factors in 2 blocks # of factors: 2 + AR(1) idiosyncratic Idiosyncratic disturbances: AR(1) Sample: 1984-10 Standardize variables: True - 2009-09 Observed variables / factor loadings =================================== Dep. variable 0 1 ----------------------------------- infl X X tbilrate X X Factor blocks: ===================== block order --------------------- 0 2 1 2 ===================== **Serial correlation in the idiosyncratic disturbances** By default, the model allows each idiosyncratic disturbance terms to evolve according to an AR(1) process. If preferred, they can instead be specified to be serially independent by passing `ididosyncratic_ar1=False`. >>> mod = sm.tsa.DynamicFactorMQ(endog, idiosyncratic_ar1=False) >>> print(mod.summary()) Model Specification: Dynamic Factor Model ========================================================================== Model: Dynamic Factor Model # of monthly variables: 2 + 1 factors in 1 blocks # of factors: 1 + iid idiosyncratic Idiosyncratic disturbances: iid Sample: 1984-10 Standardize variables: True - 2009-09 Observed variables / factor loadings ======================== Dep. variable 0 ------------------------ infl X tbilrate X Factor blocks: ===================== block order --------------------- 0 1 ===================== *Monthly / Quarterly mixed frequency* To specify a monthly / quarterly mixed frequency model see the (Notes section for more details about these models): >>> mod = sm.tsa.DynamicFactorMQ(endog, endog_quarterly=endog_Q) >>> print(mod.summary()) Model Specification: Dynamic Factor Model ========================================================================== Model: Dynamic Factor Model # of monthly variables: 2 + 1 factors in 1 blocks # of quarterly variables: 2 + Mixed frequency (M/Q) # of factors: 1 + AR(1) idiosyncratic Idiosyncratic disturbances: AR(1) Sample: 1984-10 Standardize variables: True - 2009-09 Observed variables / factor loadings ======================== Dep. variable 0 ------------------------ infl X tbilrate X realgdp X realcons X Factor blocks: ===================== block order --------------------- 0 1 ===================== *Customize observed variable / factor loadings* To specify that certain that certain observed variables only load on certain factors, it is possible to pass a dictionary to the `factors` argument. >>> factors = {'infl': ['global'] ... 'tbilrate': ['global'] ... 'realgdp': ['global', 'real'] ... 'realcons': ['global', 'real']} >>> mod = sm.tsa.DynamicFactorMQ(endog, endog_quarterly=endog_Q) >>> print(mod.summary()) Model Specification: Dynamic Factor Model ========================================================================== Model: Dynamic Factor Model # of monthly variables: 2 + 2 factors in 2 blocks # of quarterly variables: 2 + Mixed frequency (M/Q) # of factor blocks: 2 + AR(1) idiosyncratic Idiosyncratic disturbances: AR(1) Sample: 1984-10 Standardize variables: True - 2009-09 Observed variables / factor loadings =================================== Dep. variable global real ----------------------------------- infl X tbilrate X realgdp X X realcons X X Factor blocks: ===================== block order --------------------- global 1 real 1 ===================== **Fitting parameters** To fit the model, use the `fit` method. This method uses the EM algorithm by default. >>> mod = sm.tsa.DynamicFactorMQ(endog) >>> res = mod.fit() >>> print(res.summary()) Dynamic Factor Results ========================================================================== Dep. Variable: ['infl', 'tbilrate'] No. Observations: 300 Model: Dynamic Factor Model Log Likelihood -127.909 + 1 factors in 1 blocks AIC 271.817 + AR(1) idiosyncratic BIC 301.447 Date: Tue, 04 Aug 2020 HQIC 283.675 Time: 15:59:11 EM Iterations 83 Sample: 10-31-1984 - 09-30-2009 Covariance Type: Not computed Observation equation: ============================================================== Factor loadings: 0 idiosyncratic: AR(1) var. -------------------------------------------------------------- infl -0.67 0.39 0.73 tbilrate -0.63 0.99 0.01 Transition: Factor block 0 ======================================= L1.0 error variance --------------------------------------- 0 0.98 0.01 ======================================= Warnings: [1] Covariance matrix not calculated. *Displaying iteration progress* To display information about the EM iterations, use the `disp` argument. >>> mod = sm.tsa.DynamicFactorMQ(endog) >>> res = mod.fit(disp=10) EM start iterations, llf=-291.21 EM iteration 10, llf=-157.17, convergence criterion=0.053801 EM iteration 20, llf=-128.99, convergence criterion=0.0035545 EM iteration 30, llf=-127.97, convergence criterion=0.00010224 EM iteration 40, llf=-127.93, convergence criterion=1.3281e-05 EM iteration 50, llf=-127.92, convergence criterion=5.4725e-06 EM iteration 60, llf=-127.91, convergence criterion=2.8665e-06 EM iteration 70, llf=-127.91, convergence criterion=1.6999e-06 EM iteration 80, llf=-127.91, convergence criterion=1.1085e-06 EM converged at iteration 83, llf=-127.91, convergence criterion=9.9004e-07 < tolerance=1e-06 **Results: forecasting, impulse responses, and more** One the model is fitted, there are a number of methods available from the results object. Some examples include: *Forecasting* >>> mod = sm.tsa.DynamicFactorMQ(endog) >>> res = mod.fit() >>> print(res.forecast(steps=5)) infl tbilrate 2009-10 1.784169 0.260401 2009-11 1.735848 0.305981 2009-12 1.730674 0.350968 2010-01 1.742110 0.395369 2010-02 1.759786 0.439194 *Impulse responses* >>> mod = sm.tsa.DynamicFactorMQ(endog) >>> res = mod.fit() >>> print(res.impulse_responses(steps=5)) infl tbilrate 0 -1.511956 -1.341498 1 -1.483172 -1.315960 2 -1.454937 -1.290908 3 -1.427240 -1.266333 4 -1.400069 -1.242226 5 -1.373416 -1.218578 For other available methods (including in-sample prediction, simulation of time series, extending the results to incorporate new data, and the news), see the documentation for state space models. References ---------- .. [1] Bańbura, Marta, and Michele Modugno. "Maximum likelihood estimation of factor models on datasets with arbitrary pattern of missing data." Journal of Applied Econometrics 29, no. 1 (2014): 133-160. .. [2] Bańbura, Marta, Domenico Giannone, and Lucrezia Reichlin. "Nowcasting." The Oxford Handbook of Economic Forecasting. July 8, 2011. .. [3] Bok, Brandyn, Daniele Caratelli, Domenico Giannone, Argia M. Sbordone, and Andrea Tambalotti. 2018. "Macroeconomic Nowcasting and Forecasting with Big Data." Annual Review of Economics 10 (1): 615-43. https://doi.org/10.1146/annurev-economics-080217-053214. .. [4] Mariano, Roberto S., and Yasutomo Murasawa. "A coincident index, common factors, and monthly real GDP." Oxford Bulletin of Economics and Statistics 72, no. 1 (2010): 27-46. """ def __init__(self, endog, k_endog_monthly=None, factors=1, factor_orders=1, factor_multiplicities=None, idiosyncratic_ar1=True, standardize=True, endog_quarterly=None, init_t0=False, obs_cov_diag=False, **kwargs): # Handle endog variables if endog_quarterly is not None: if k_endog_monthly is not None: raise ValueError('If `endog_quarterly` is specified, then' ' `endog` must contain only monthly' ' variables, and so `k_endog_monthly` cannot' ' be specified since it will be inferred from' ' the shape of `endog`.') endog, k_endog_monthly = self.construct_endog( endog, endog_quarterly) endog_is_pandas = _is_using_pandas(endog, None) if endog_is_pandas: if isinstance(endog, pd.Series): endog = endog.to_frame() else: if np.ndim(endog) < 2: endog = np.atleast_2d(endog).T if k_endog_monthly is None: k_endog_monthly = endog.shape[1] if endog_is_pandas: endog_names = endog.columns.tolist() else: if endog.shape[1] == 1: endog_names = ['y'] else: endog_names = [f'y{i + 1}' for i in range(endog.shape[1])] self.k_endog_M = int_like(k_endog_monthly, 'k_endog_monthly') self.k_endog_Q = endog.shape[1] - self.k_endog_M # Compute helper for handling factors / state indexing s = self._s = DynamicFactorMQStates( self.k_endog_M, self.k_endog_Q, endog_names, factors, factor_orders, factor_multiplicities, idiosyncratic_ar1) # Save parameterization self.factors = factors self.factor_orders = factor_orders self.factor_multiplicities = factor_multiplicities self.endog_factor_map = self._s.endog_factor_map self.factor_block_orders = self._s.factor_block_orders self.factor_names = self._s.factor_names self.k_factors = self._s.k_factors self.k_factor_blocks = len(self.factor_block_orders) self.max_factor_order = self._s.max_factor_order self.idiosyncratic_ar1 = idiosyncratic_ar1 self.init_t0 = init_t0 self.obs_cov_diag = obs_cov_diag if self.init_t0: # TODO: test each of these options if endog_is_pandas: ix = pd.period_range(endog.index[0] - 1, endog.index[-1], freq='M') endog = endog.reindex(ix) else: endog = np.c_[[np.nan] * endog.shape[1], endog.T].T # Standardize endog, if requested # Note: endog_mean and endog_std will always each be 1-dimensional with # length equal to the number of endog variables if isinstance(standardize, tuple) and len(standardize) == 2: endog_mean, endog_std = standardize # Validate the input n = endog.shape[1] if (isinstance(endog_mean, pd.Series) and not endog_mean.index.equals(pd.Index(endog_names))): raise ValueError('Invalid value passed for `standardize`:' ' if a Pandas Series, must have index' f' {endog_names}. Got {endog_mean.index}.') else: endog_mean = np.atleast_1d(endog_mean) if (isinstance(endog_std, pd.Series) and not endog_std.index.equals(pd.Index(endog_names))): raise ValueError('Invalid value passed for `standardize`:' ' if a Pandas Series, must have index' f' {endog_names}. Got {endog_std.index}.') else: endog_std = np.atleast_1d(endog_std) if (np.shape(endog_mean) != (n,) or np.shape(endog_std) != (n,)): raise ValueError('Invalid value passed for `standardize`: each' f' element must be shaped ({n},).') standardize = True # Make sure we have Pandas if endog is Pandas if endog_is_pandas: endog_mean = pd.Series(endog_mean, index=endog_names) endog_std = pd.Series(endog_std, index=endog_names) elif standardize in [1, True]: endog_mean = endog.mean(axis=0) endog_std = endog.std(axis=0) elif standardize in [0, False]: endog_mean = np.zeros(endog.shape[1]) endog_std = np.ones(endog.shape[1]) else: raise ValueError('Invalid value passed for `standardize`.') self._endog_mean = endog_mean self._endog_std = endog_std self.standardize = standardize if np.any(self._endog_std < 1e-10): ix = np.where(self._endog_std < 1e-10) names = np.array(endog_names)[ix[0]].tolist() raise ValueError('Constant variable(s) found in observed' ' variables, but constants cannot be included' f' in this model. These variables are: {names}.') if self.standardize: endog = (endog - self._endog_mean) / self._endog_std # Observation / states slices o = self._o = { 'M': np.s_[:self.k_endog_M], 'Q': np.s_[self.k_endog_M:]} # Construct the basic state space representation super().__init__(endog, k_states=s.k_states, k_posdef=s.k_posdef, **kwargs) # Revert the standardization for orig_endog if self.standardize: self.data.orig_endog = ( self.data.orig_endog * self._endog_std + self._endog_mean) # State initialization # Note: we could just initialize the entire thing as stationary, but # doing each block separately should be faster and avoid numerical # issues if 'initialization' not in kwargs: self.ssm.initialize(self._default_initialization()) # Fixed components of the state space representation # > design if self.idiosyncratic_ar1: self['design', o['M'], s['idio_ar_M']] = np.eye(self.k_endog_M) multipliers = [1, 2, 3, 2, 1] for i in range(len(multipliers)): m = multipliers[i] self['design', o['Q'], s['idio_ar_Q_ix'][:, i]] = ( m * np.eye(self.k_endog_Q)) # > obs cov if self.obs_cov_diag: self['obs_cov'] = np.eye(self.k_endog) * 1e-4 # > transition for block in s.factor_blocks: if block.k_factors == 1: tmp = 0 else: tmp = np.zeros((block.k_factors, block.k_factors)) self['transition', block['factors'], block['factors']] = ( companion_matrix([1] + [tmp] * block._factor_order).T) if self.k_endog_Q == 1: tmp = 0 else: tmp = np.zeros((self.k_endog_Q, self.k_endog_Q)) self['transition', s['idio_ar_Q'], s['idio_ar_Q']] = ( companion_matrix([1] + [tmp] * 5).T) # > selection ix1 = ix2 = 0 for block in s.factor_blocks: ix2 += block.k_factors self['selection', block['factors_ix'][:, 0], ix1:ix2] = ( np.eye(block.k_factors)) ix1 = ix2 if self.idiosyncratic_ar1: ix2 = ix1 + self.k_endog_M self['selection', s['idio_ar_M'], ix1:ix2] = np.eye(self.k_endog_M) ix1 = ix2 ix2 = ix1 + self.k_endog_Q self['selection', s['idio_ar_Q_ix'][:, 0], ix1:ix2] = ( np.eye(self.k_endog_Q)) # Parameters self.params = OrderedDict([ ('loadings', np.sum(self.endog_factor_map.values)), ('factor_ar', np.sum([block.k_factors**2 * block.factor_order for block in s.factor_blocks])), ('factor_cov', np.sum([block.k_factors * (block.k_factors + 1) // 2 for block in s.factor_blocks])), ('idiosyncratic_ar1', self.k_endog if self.idiosyncratic_ar1 else 0), ('idiosyncratic_var', self.k_endog)]) self.k_params = np.sum(list(self.params.values())) # Parameter slices ix = np.split(np.arange(self.k_params), np.cumsum(list(self.params.values()))[:-1]) self._p = dict(zip(self.params.keys(), ix)) # Cache self._loading_constraints = {} # Initialization kwarg keys, e.g. for cloning self._init_keys += [ 'factors', 'factor_orders', 'factor_multiplicities', 'idiosyncratic_ar1', 'standardize', 'init_t0', 'obs_cov_diag'] + list(kwargs.keys()) @classmethod def construct_endog(cls, endog_monthly, endog_quarterly): """ Construct a combined dataset from separate monthly and quarterly data. Parameters ---------- endog_monthly : array_like Monthly dataset. If a quarterly dataset is given, then this must be a Pandas object with a PeriodIndex or DatetimeIndex at a monthly frequency. endog_quarterly : array_like or None Quarterly dataset. If not None, then this must be a Pandas object with a PeriodIndex or DatetimeIndex at a quarterly frequency. Returns ------- endog : array_like If both endog_monthly and endog_quarterly were given, this is a Pandas DataFrame with a PeriodIndex at the monthly frequency, with all of the columns from `endog_monthly` ordered first and the columns from `endog_quarterly` ordered afterwards. Otherwise it is simply the input `endog_monthly` dataset. k_endog_monthly : int The number of monthly variables (which are ordered first) in the returned `endog` dataset. """ # Create combined dataset if endog_quarterly is not None: # Validate endog_monthly base_msg = ('If given both monthly and quarterly data' ' then the monthly dataset must be a Pandas' ' object with a date index at a monthly frequency.') if not isinstance(endog_monthly, (pd.Series, pd.DataFrame)): raise ValueError('Given monthly dataset is not a' ' Pandas object. ' + base_msg) elif endog_monthly.index.inferred_type not in ( "datetime64", "period", ): raise ValueError('Given monthly dataset has an' ' index with non-date values. ' + base_msg) elif not getattr(endog_monthly.index, 'freqstr', 'N')[0] == 'M': freqstr = getattr(endog_monthly.index, 'freqstr', 'None') raise ValueError('Index of given monthly dataset has a' ' non-monthly frequency (to check this,' ' examine the `freqstr` attribute of the' ' index of the dataset - it should start with' ' M if it is monthly).' f' Got {freqstr}. ' + base_msg) # Validate endog_quarterly base_msg = ('If a quarterly dataset is given, then it must be a' ' Pandas object with a date index at a quarterly' ' frequency.') if not isinstance(endog_quarterly, (pd.Series, pd.DataFrame)): raise ValueError('Given quarterly dataset is not a' ' Pandas object. ' + base_msg) elif endog_quarterly.index.inferred_type not in ( "datetime64", "period", ): raise ValueError('Given quarterly dataset has an' ' index with non-date values. ' + base_msg) elif not getattr(endog_quarterly.index, 'freqstr', 'N')[0] == 'Q': freqstr = getattr(endog_quarterly.index, 'freqstr', 'None') raise ValueError('Index of given quarterly dataset' ' has a non-quarterly frequency (to check' ' this, examine the `freqstr` attribute of' ' the index of the dataset - it should start' ' with Q if it is quarterly).' f' Got {freqstr}. ' + base_msg) # Convert to PeriodIndex, if applicable if hasattr(endog_monthly.index, 'to_period'): endog_monthly = endog_monthly.to_period('M') if hasattr(endog_quarterly.index, 'to_period'): endog_quarterly = endog_quarterly.to_period('Q') # Combine the datasets endog = pd.concat([ endog_monthly, endog_quarterly.resample('M', convention='end').first()], axis=1) # Make sure we didn't accidentally get duplicate column names column_counts = endog.columns.value_counts() if column_counts.max() > 1: columns = endog.columns.values.astype(object) for name in column_counts.index: count = column_counts.loc[name] if count == 1: continue mask = columns == name columns[mask] = [f'{name}{i + 1}' for i in range(count)] endog.columns = columns else: endog = endog_monthly.copy() shape = endog_monthly.shape k_endog_monthly = shape[1] if len(shape) == 2 else 1 return endog, k_endog_monthly def clone(self, endog, k_endog_monthly=None, endog_quarterly=None, retain_standardization=False, **kwargs): """ Clone state space model with new data and optionally new specification. Parameters ---------- endog : array_like The observed time-series process :math:`y` k_endog_monthly : int, optional If specifying a monthly/quarterly mixed frequency model in which the provided `endog` dataset contains both the monthly and quarterly data, this variable should be used to indicate how many of the variables are monthly. endog_quarterly : array_like, optional Observations of quarterly variables. If provided, must be a Pandas Series or DataFrame with a DatetimeIndex or PeriodIndex at the quarterly frequency. kwargs Keyword arguments to pass to the new model class to change the model specification. Returns ------- model : DynamicFactorMQ instance """ if retain_standardization and self.standardize: kwargs['standardize'] = (self._endog_mean, self._endog_std) mod = self._clone_from_init_kwds( endog, k_endog_monthly=k_endog_monthly, endog_quarterly=endog_quarterly, **kwargs) return mod @property def _res_classes(self): return {'fit': (DynamicFactorMQResults, mlemodel.MLEResultsWrapper)} def _default_initialization(self): s = self._s init = initialization.Initialization(self.k_states) for block in s.factor_blocks: init.set(block['factors'], 'stationary') if self.idiosyncratic_ar1: for i in range(s['idio_ar_M'].start, s['idio_ar_M'].stop): init.set(i, 'stationary') init.set(s['idio_ar_Q'], 'stationary') return init def _get_endog_names(self, truncate=None, as_string=None): if truncate is None: truncate = False if as_string is False or self.k_endog == 1 else 24 if as_string is False and truncate is not False: raise ValueError('Can only truncate endog names if they' ' are returned as a string.') if as_string is None: as_string = truncate is not False # The base `endog_names` property is only a list if there are at least # two variables; often, we need it to be a list endog_names = self.endog_names if not isinstance(endog_names, list): endog_names = [endog_names] if as_string: endog_names = [str(name) for name in endog_names] if truncate is not False: n = truncate endog_names = [name if len(name) <= n else name[:n] + '...' for name in endog_names] return endog_names @property def _model_name(self): model_name = [ 'Dynamic Factor Model', f'{self.k_factors} factors in {self.k_factor_blocks} blocks'] if self.k_endog_Q > 0: model_name.append('Mixed frequency (M/Q)') error_type = 'AR(1)' if self.idiosyncratic_ar1 else 'iid' model_name.append(f'{error_type} idiosyncratic') return model_name def summary(self, truncate_endog_names=None): """ Create a summary table describing the model. Parameters ---------- truncate_endog_names : int, optional The number of characters to show for names of observed variables. Default is 24 if there is more than one observed variable, or an unlimited number of there is only one. """ # Get endog names endog_names = self._get_endog_names(truncate=truncate_endog_names, as_string=True) title = 'Model Specification: Dynamic Factor Model' if self._index_dates: ix = self._index d = ix[0] sample = ['%s' % d] d = ix[-1] sample += ['- ' + '%s' % d] else: sample = [str(0), ' - ' + str(self.nobs)] # Standardize the model name as a list of str model_name = self._model_name # - Top summary table ------------------------------------------------ top_left = [] top_left.append(('Model:', [model_name[0]])) for i in range(1, len(model_name)): top_left.append(('', ['+ ' + model_name[i]])) top_left += [ ('Sample:', [sample[0]]), ('', [sample[1]])] top_right = [] if self.k_endog_Q > 0: top_right += [ ('# of monthly variables:', [self.k_endog_M]), ('# of quarterly variables:', [self.k_endog_Q])] else: top_right += [('# of observed variables:', [self.k_endog])] if self.k_factor_blocks == 1: top_right += [('# of factors:', [self.k_factors])] else: top_right += [('# of factor blocks:', [self.k_factor_blocks])] top_right += [('Idiosyncratic disturbances:', ['AR(1)' if self.idiosyncratic_ar1 else 'iid']), ('Standardize variables:', [self.standardize])] summary = Summary() self.model = self summary.add_table_2cols(self, gleft=top_left, gright=top_right, title=title) table_ix = 1 del self.model # - Endog / factor map ----------------------------------------------- data = self.endog_factor_map.replace({True: 'X', False: ''}) data.index = endog_names for name, col in data.iteritems(): data[name] = data[name] + (' ' * (len(name) // 2)) data.index.name = 'Dep. variable' data = data.reset_index() params_data = data.values params_header = data.columns.map(str).tolist() params_stubs = None title = 'Observed variables / factor loadings' table = SimpleTable( params_data, params_header, params_stubs, txt_fmt=fmt_params, title=title) summary.tables.insert(table_ix, table) table_ix += 1 # - Factor blocks summary table -------------------------------------- data = self.factor_block_orders.reset_index() data['block'] = data['block'].map( lambda factor_names: ', '.join(factor_names)) data[['order']] = ( data[['order']].applymap(str)) params_data = data.values params_header = data.columns.map(str).tolist() params_stubs = None title = 'Factor blocks:' table = SimpleTable( params_data, params_header, params_stubs, txt_fmt=fmt_params, title=title) summary.tables.insert(table_ix, table) table_ix += 1 return summary def __str__(self): """Summary tables showing model specification.""" return str(self.summary()) @property def state_names(self): """(list of str) List of human readable names for unobserved states.""" # Factors state_names = [] for block in self._s.factor_blocks: state_names += [f'{name}' for name in block.factor_names[:]] for s in range(1, block._factor_order): state_names += [f'L{s}.{name}' for name in block.factor_names] # Monthly error endog_names = self._get_endog_names() if self.idiosyncratic_ar1: endog_names_M = endog_names[self._o['M']] state_names += [f'eps_M.{name}' for name in endog_names_M] endog_names_Q = endog_names[self._o['Q']] # Quarterly error state_names += [f'eps_Q.{name}' for name in endog_names_Q] for s in range(1, 5): state_names += [f'L{s}.eps_Q.{name}' for name in endog_names_Q] return state_names @property def param_names(self): """(list of str) List of human readable parameter names.""" param_names = [] # Loadings # So that Lambda = params[ix].reshape(self.k_endog, self.k_factors) # (where Lambda stacks Lambda_M and Lambda_Q) endog_names = self._get_endog_names(as_string=False) for endog_name in endog_names: for block in self._s.factor_blocks: for factor_name in block.factor_names: if self.endog_factor_map.loc[endog_name, factor_name]: param_names.append( f'loading.{factor_name}->{endog_name}') # Factor VAR for block in self._s.factor_blocks: for to_factor in block.factor_names: param_names += [f'L{i}.{from_factor}->{to_factor}' for i in range(1, block.factor_order + 1) for from_factor in block.factor_names] # Factor covariance for i in range(len(self._s.factor_blocks)): block = self._s.factor_blocks[i] param_names += [f'fb({i}).cov.chol[{j + 1},{k + 1}]' for j in range(block.k_factors) for k in range(j + 1)] # Error AR(1) if self.idiosyncratic_ar1: endog_names_M = endog_names[self._o['M']] param_names += [f'L1.eps_M.{name}' for name in endog_names_M] endog_names_Q = endog_names[self._o['Q']] param_names += [f'L1.eps_Q.{name}' for name in endog_names_Q] # Error innovation variances param_names += [f'sigma2.{name}' for name in endog_names] return param_names @property def start_params(self): """(array) Starting parameters for maximum likelihood estimation.""" params = np.zeros(self.k_params, dtype=np.float64) # (1) estimate factors one at a time, where the first step uses # PCA on all `endog` variables that load on the first factor, and # subsequent steps use residuals from the previous steps. # TODO: what about factors that only load on quarterly variables? endog_factor_map_M = self.endog_factor_map.iloc[:self.k_endog_M] factors = [] endog = (pd.DataFrame(self.endog).interpolate() .fillna(method='backfill') .values) for name in self.factor_names: # Try to retrieve this from monthly variables, which is most # consistent endog_ix = np.where(endog_factor_map_M.loc[:, name])[0] # But fall back to quarterly if necessary if len(endog_ix) == 0: endog_ix = np.where(self.endog_factor_map.loc[:, name])[0] factor_endog = endog[:, endog_ix] res_pca = PCA(factor_endog, ncomp=1, method='eig', normalize=False) factors.append(res_pca.factors) endog[:, endog_ix] -= res_pca.projection factors = np.concatenate(factors, axis=1) # (2) Estimate coefficients for each endog, one at a time (OLS for # monthly variables, restricted OLS for quarterly). Also, compute # residuals. loadings = [] resid = [] for i in range(self.k_endog_M): factor_ix = self._s.endog_factor_iloc[i] factor_exog = factors[:, factor_ix] mod_ols = OLS(self.endog[:, i], exog=factor_exog, missing='drop') res_ols = mod_ols.fit() loadings += res_ols.params.tolist() resid.append(res_ols.resid) for i in range(self.k_endog_M, self.k_endog): factor_ix = self._s.endog_factor_iloc[i] factor_exog = lagmat(factors[:, factor_ix], 4, original='in') mod_glm = GLM(self.endog[:, i], factor_exog, missing='drop') res_glm = mod_glm.fit_constrained(self.loading_constraints(i)) loadings += res_glm.params[:len(factor_ix)].tolist() resid.append(res_glm.resid_response) params[self._p['loadings']] = loadings # (3) For each factor block, use an AR or VAR model to get coefficients # and covariance estimate # Factor transitions stationary = True factor_ar = [] factor_cov = [] i = 0 for block in self._s.factor_blocks: factors_endog = factors[:, i:i + block.k_factors] i += block.k_factors if block.factor_order == 0: continue if block.k_factors == 1: mod_factors = SARIMAX(factors_endog, order=(block.factor_order, 0, 0)) sp = mod_factors.start_params block_factor_ar = sp[:-1] block_factor_cov = sp[-1:] coefficient_matrices = mod_factors.start_params[:-1] elif block.k_factors > 1: mod_factors = VAR(factors_endog) res_factors = mod_factors.fit( maxlags=block.factor_order, ic=None, trend='nc') block_factor_ar = res_factors.params.T.ravel() L = np.linalg.cholesky(res_factors.sigma_u) block_factor_cov = L[np.tril_indices_from(L)] coefficient_matrices = np.transpose( np.reshape(block_factor_ar, (block.k_factors, block.k_factors, block.factor_order)), (2, 0, 1)) # Test for stationarity stationary = is_invertible([1] + list(-coefficient_matrices)) # Check for stationarity if not stationary: warn('Non-stationary starting factor autoregressive' ' parameters found for factor block' f' {block.factor_names}. Using zeros as starting' ' parameters.') block_factor_ar[:] = 0 cov_factor = np.diag(factors_endog.std(axis=0)) block_factor_cov = ( cov_factor[np.tril_indices(block.k_factors)]) factor_ar += block_factor_ar.tolist() factor_cov += block_factor_cov.tolist() params[self._p['factor_ar']] = factor_ar params[self._p['factor_cov']] = factor_cov # (4) Use residuals from step (2) to estimate the idiosyncratic # component # Idiosyncratic component if self.idiosyncratic_ar1: idio_ar1 = [] idio_var = [] for i in range(self.k_endog_M): mod_idio = SARIMAX(resid[i], order=(1, 0, 0), trend='c') sp = mod_idio.start_params idio_ar1.append(np.clip(sp[1], -0.99, 0.99)) idio_var.append(np.clip(sp[-1], 1e-5, np.inf)) for i in range(self.k_endog_M, self.k_endog): y = self.endog[:, i].copy() y[~np.isnan(y)] = resid[i] mod_idio = QuarterlyAR1(y) res_idio = mod_idio.fit(maxiter=10, return_params=True, disp=False) res_idio = mod_idio.fit_em(res_idio, maxiter=5, return_params=True) idio_ar1.append(np.clip(res_idio[0], -0.99, 0.99)) idio_var.append(np.clip(res_idio[1], 1e-5, np.inf)) params[self._p['idiosyncratic_ar1']] = idio_ar1 params[self._p['idiosyncratic_var']] = idio_var else: idio_var = [np.var(resid[i]) for i in range(self.k_endog_M)] for i in range(self.k_endog_M, self.k_endog): y = self.endog[:, i].copy() y[~np.isnan(y)] = resid[i] mod_idio = QuarterlyAR1(y) res_idio = mod_idio.fit(return_params=True, disp=False) idio_var.append(np.clip(res_idio[1], 1e-5, np.inf)) params[self._p['idiosyncratic_var']] = idio_var return params def transform_params(self, unconstrained): """ Transform parameters from optimizer space to model space. Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation. Parameters ---------- unconstrained : array_like Array of unconstrained parameters used by the optimizer, to be transformed. Returns ------- constrained : array_like Array of constrained parameters which may be used in likelihood evaluation. """ constrained = unconstrained.copy() # Stationary factor VAR unconstrained_factor_ar = unconstrained[self._p['factor_ar']] constrained_factor_ar = [] i = 0 for block in self._s.factor_blocks: length = block.k_factors**2 * block.factor_order tmp_coeff = np.reshape( unconstrained_factor_ar[i:i + length], (block.k_factors, block.k_factors * block.factor_order)) tmp_cov = np.eye(block.k_factors) tmp_coeff, _ = constrain_stationary_multivariate(tmp_coeff, tmp_cov) constrained_factor_ar += tmp_coeff.ravel().tolist() i += length constrained[self._p['factor_ar']] = constrained_factor_ar # Stationary idiosyncratic AR(1) if self.idiosyncratic_ar1: idio_ar1 = unconstrained[self._p['idiosyncratic_ar1']] constrained[self._p['idiosyncratic_ar1']] = [ constrain_stationary_univariate(idio_ar1[i:i + 1])[0] for i in range(self.k_endog)] # Positive idiosyncratic variances constrained[self._p['idiosyncratic_var']] = ( constrained[self._p['idiosyncratic_var']]**2) return constrained def untransform_params(self, constrained): """ Transform parameters from model space to optimizer space. Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer. Parameters ---------- constrained : array_like Array of constrained parameters used in likelihood evaluation, to be transformed. Returns ------- unconstrained : array_like Array of unconstrained parameters used by the optimizer. """ unconstrained = constrained.copy() # Stationary factor VAR constrained_factor_ar = constrained[self._p['factor_ar']] unconstrained_factor_ar = [] i = 0 for block in self._s.factor_blocks: length = block.k_factors**2 * block.factor_order tmp_coeff = np.reshape( constrained_factor_ar[i:i + length], (block.k_factors, block.k_factors * block.factor_order)) tmp_cov = np.eye(block.k_factors) tmp_coeff, _ = unconstrain_stationary_multivariate(tmp_coeff, tmp_cov) unconstrained_factor_ar += tmp_coeff.ravel().tolist() i += length unconstrained[self._p['factor_ar']] = unconstrained_factor_ar # Stationary idiosyncratic AR(1) if self.idiosyncratic_ar1: idio_ar1 = constrained[self._p['idiosyncratic_ar1']] unconstrained[self._p['idiosyncratic_ar1']] = [ unconstrain_stationary_univariate(idio_ar1[i:i + 1])[0] for i in range(self.k_endog)] # Positive idiosyncratic variances unconstrained[self._p['idiosyncratic_var']] = ( unconstrained[self._p['idiosyncratic_var']]**0.5) return unconstrained def update(self, params, **kwargs): """ Update the parameters of the model. Parameters ---------- params : array_like Array of new parameters. transformed : bool, optional Whether or not `params` is already transformed. If set to False, `transform_params` is called. Default is True. """ params = super().update(params, **kwargs) # Local copies o = self._o s = self._s p = self._p # Loadings loadings = params[p['loadings']] start = 0 for i in range(self.k_endog_M): iloc = self._s.endog_factor_iloc[i] k_factors = len(iloc) factor_ix = s['factors_L1'][iloc] self['design', i, factor_ix] = loadings[start:start + k_factors] start += k_factors multipliers = np.array([1, 2, 3, 2, 1])[:, None] for i in range(self.k_endog_M, self.k_endog): iloc = self._s.endog_factor_iloc[i] k_factors = len(iloc) factor_ix = s['factors_L1_5_ix'][:, iloc] self['design', i, factor_ix.ravel()] = np.ravel( loadings[start:start + k_factors] * multipliers) start += k_factors # Factor VAR factor_ar = params[p['factor_ar']] start = 0 for block in s.factor_blocks: k_params = block.k_factors**2 * block.factor_order A = np.reshape( factor_ar[start:start + k_params], (block.k_factors, block.k_factors * block.factor_order)) start += k_params self['transition', block['factors_L1'], block['factors_ar']] = A # Factor covariance factor_cov = params[p['factor_cov']] start = 0 ix1 = 0 for block in s.factor_blocks: k_params = block.k_factors * (block.k_factors + 1) // 2 L = np.zeros((block.k_factors, block.k_factors), dtype=params.dtype) L[np.tril_indices_from(L)] = factor_cov[start:start + k_params] start += k_params Q = L @ L.T ix2 = ix1 + block.k_factors self['state_cov', ix1:ix2, ix1:ix2] = Q ix1 = ix2 # Error AR(1) if self.idiosyncratic_ar1: alpha = np.diag(params[p['idiosyncratic_ar1']]) self['transition', s['idio_ar_L1'], s['idio_ar_L1']] = alpha # Error variances if self.idiosyncratic_ar1: self['state_cov', self.k_factors:, self.k_factors:] = ( np.diag(params[p['idiosyncratic_var']])) else: idio_var = params[p['idiosyncratic_var']] self['obs_cov', o['M'], o['M']] = np.diag(idio_var[o['M']]) self['state_cov', self.k_factors:, self.k_factors:] = ( np.diag(idio_var[o['Q']])) @property def loglike_constant(self): """ Constant term in the joint log-likelihood function. Useful in facilitating comparisons to other packages that exclude the constant from the log-likelihood computation. """ return -0.5 * (1 - np.isnan(self.endog)).sum() * np.log(2 * np.pi) def loading_constraints(self, i): r""" Matrix formulation of quarterly variables' factor loading constraints. Parameters ---------- i : int Index of the `endog` variable to compute constraints for. Returns ------- R : array (k_constraints, k_factors * 5) q : array (k_constraints,) Notes ----- If the factors were known, then the factor loadings for the ith quarterly variable would be computed by a linear regression of the form y_i = A_i' f + B_i' L1.f + C_i' L2.f + D_i' L3.f + E_i' L4.f where: - f is (k_i x 1) and collects all of the factors that load on y_i - L{j}.f is (k_i x 1) and collects the jth lag of each factor - A_i, ..., E_i are (k_i x 1) and collect factor loadings As the observed variable is quarterly while the factors are monthly, we want to restrict the estimated regression coefficients to be: y_i = A_i f + 2 A_i L1.f + 3 A_i L2.f + 2 A_i L3.f + A_i L4.f Stack the unconstrained coefficients: \Lambda_i = [A_i' B_i' ... E_i']' Then the constraints can be written as follows, for l = 1, ..., k_i - 2 A_{i,l} - B_{i,l} = 0 - 3 A_{i,l} - C_{i,l} = 0 - 2 A_{i,l} - D_{i,l} = 0 - A_{i,l} - E_{i,l} = 0 So that k_constraints = 4 * k_i. In matrix form the constraints are: .. math:: R \Lambda_i = q where :math:`\Lambda_i` is shaped `(k_i * 5,)`, :math:`R` is shaped `(k_constraints, k_i * 5)`, and :math:`q` is shaped `(k_constraints,)`. For example, for the case that k_i = 2, we can write: | 2 0 -1 0 0 0 0 0 0 0 | | A_{i,1} | | 0 | | 0 2 0 -1 0 0 0 0 0 0 | | A_{i,2} | | 0 | | 3 0 0 0 -1 0 0 0 0 0 | | B_{i,1} | | 0 | | 0 3 0 0 0 -1 0 0 0 0 | | B_{i,2} | | 0 | | 2 0 0 0 0 0 -1 0 0 0 | | C_{i,1} | = | 0 | | 0 2 0 0 0 0 0 -1 0 0 | | C_{i,2} | | 0 | | 1 0 0 0 0 0 0 0 -1 0 | | D_{i,1} | | 0 | | 0 1 0 0 0 0 0 0 0 -1 | | D_{i,2} | | 0 | | E_{i,1} | | 0 | | E_{i,2} | | 0 | """ if i < self.k_endog_M: raise ValueError('No constraints for monthly variables.') if i not in self._loading_constraints: k_factors = self.endog_factor_map.iloc[i].sum() R = np.zeros((k_factors * 4, k_factors * 5)) q = np.zeros(R.shape[0]) # Let R = [R_1 R_2] # Then R_1 is multiples of the identity matrix multipliers = np.array([1, 2, 3, 2, 1]) R[:, :k_factors] = np.reshape( (multipliers[1:] * np.eye(k_factors)[..., None]).T, (k_factors * 4, k_factors)) # And R_2 is the identity R[:, k_factors:] = np.diag([-1] * (k_factors * 4)) self._loading_constraints[i] = (R, q) return self._loading_constraints[i] def fit(self, start_params=None, transformed=True, includes_fixed=False, cov_type='none', cov_kwds=None, method='em', maxiter=500, tolerance=1e-6, em_initialization=True, mstep_method=None, full_output=1, disp=False, callback=None, return_params=False, optim_score=None, optim_complex_step=None, optim_hessian=None, flags=None, low_memory=False, llf_decrease_action='revert', llf_decrease_tolerance=1e-4, **kwargs): """ Fits the model by maximum likelihood via Kalman filter. Parameters ---------- start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. If None, the default is given by Model.start_params. transformed : bool, optional Whether or not `start_params` is already transformed. Default is True. includes_fixed : bool, optional If parameters were previously fixed with the `fix_params` method, this argument describes whether or not `start_params` also includes the fixed parameters, in addition to the free parameters. Default is False. cov_type : str, optional The `cov_type` keyword governs the method for calculating the covariance matrix of parameter estimates. Can be one of: - 'opg' for the outer product of gradient estimator - 'oim' for the observed information matrix estimator, calculated using the method of Harvey (1989) - 'approx' for the observed information matrix estimator, calculated using a numerical approximation of the Hessian matrix. - 'robust' for an approximate (quasi-maximum likelihood) covariance matrix that may be valid even in the presence of some misspecifications. Intermediate calculations use the 'oim' method. - 'robust_approx' is the same as 'robust' except that the intermediate calculations use the 'approx' method. - 'none' for no covariance matrix calculation. Default is 'none', since computing this matrix can be very slow when there are a large number of parameters. cov_kwds : dict or None, optional A dictionary of arguments affecting covariance matrix computation. **opg, oim, approx, robust, robust_approx** - 'approx_complex_step' : bool, optional - If True, numerical approximations are computed using complex-step methods. If False, numerical approximations are computed using finite difference methods. Default is True. - 'approx_centered' : bool, optional - If True, numerical approximations computed using finite difference methods use a centered approximation. Default is False. method : str, optional The `method` determines which solver from `scipy.optimize` is used, and it can be chosen from among the following strings: - 'em' for the EM algorithm - 'newton' for Newton-Raphson - 'nm' for Nelder-Mead - 'bfgs' for Broyden-Fletcher-Goldfarb-Shanno (BFGS) - 'lbfgs' for limited-memory BFGS with optional box constraints - 'powell' for modified Powell's method - 'cg' for conjugate gradient - 'ncg' for Newton-conjugate gradient - 'basinhopping' for global basin-hopping solver The explicit arguments in `fit` are passed to the solver, with the exception of the basin-hopping solver. Each solver has several optional arguments that are not the same across solvers. See the notes section below (or scipy.optimize) for the available arguments and for the list of explicit arguments that the basin-hopping solver supports. maxiter : int, optional The maximum number of iterations to perform. full_output : bool, optional Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. disp : bool, optional Set to True to print convergence messages. callback : callable callback(xk), optional Called after each iteration, as callback(xk), where xk is the current parameter vector. return_params : bool, optional Whether or not to return only the array of maximizing parameters. Default is False. optim_score : {'harvey', 'approx'} or None, optional The method by which the score vector is calculated. 'harvey' uses the method from Harvey (1989), 'approx' uses either finite difference or complex step differentiation depending upon the value of `optim_complex_step`, and None uses the built-in gradient approximation of the optimizer. Default is None. This keyword is only relevant if the optimization method uses the score. optim_complex_step : bool, optional Whether or not to use complex step differentiation when approximating the score; if False, finite difference approximation is used. Default is True. This keyword is only relevant if `optim_score` is set to 'harvey' or 'approx'. optim_hessian : {'opg','oim','approx'}, optional The method by which the Hessian is numerically approximated. 'opg' uses outer product of gradients, 'oim' uses the information matrix formula from Harvey (1989), and 'approx' uses numerical approximation. This keyword is only relevant if the optimization method uses the Hessian matrix. low_memory : bool, optional If set to True, techniques are applied to substantially reduce memory usage. If used, some features of the results object will not be available (including smoothed results and in-sample prediction), although out-of-sample forecasting is possible. Note that this option is not available when using the EM algorithm (which is the default for this model). Default is False. llf_decrease_action : {'ignore', 'warn', 'revert'}, optional Action to take if the log-likelihood decreases in an EM iteration. 'ignore' continues the iterations, 'warn' issues a warning but continues the iterations, while 'revert' ends the iterations and returns the result from the last good iteration. Default is 'warn'. llf_decrease_tolerance : float, optional Minimum size of the log-likelihood decrease required to trigger a warning or to end the EM iterations. Setting this value slightly larger than zero allows small decreases in the log-likelihood that may be caused by numerical issues. If set to zero, then any decrease will trigger the `llf_decrease_action`. Default is 1e-4. **kwargs Additional keyword arguments to pass to the optimizer. Returns ------- MLEResults See Also -------- statsmodels.base.model.LikelihoodModel.fit statsmodels.tsa.statespace.mlemodel.MLEResults """ if method == 'em': return self.fit_em( start_params=start_params, transformed=transformed, cov_type=cov_type, cov_kwds=cov_kwds, maxiter=maxiter, tolerance=tolerance, em_initialization=em_initialization, mstep_method=mstep_method, full_output=full_output, disp=disp, return_params=return_params, low_memory=low_memory, llf_decrease_action=llf_decrease_action, llf_decrease_tolerance=llf_decrease_tolerance, **kwargs) else: return super().fit( start_params=start_params, transformed=transformed, includes_fixed=includes_fixed, cov_type=cov_type, cov_kwds=cov_kwds, method=method, maxiter=maxiter, tolerance=tolerance, full_output=full_output, disp=disp, callback=callback, return_params=return_params, optim_score=optim_score, optim_complex_step=optim_complex_step, optim_hessian=optim_hessian, flags=flags, low_memory=low_memory, **kwargs) def fit_em(self, start_params=None, transformed=True, cov_type='none', cov_kwds=None, maxiter=500, tolerance=1e-6, disp=False, em_initialization=True, mstep_method=None, full_output=True, return_params=False, low_memory=False, llf_decrease_action='revert', llf_decrease_tolerance=1e-4): """ Fits the model by maximum likelihood via the EM algorithm. Parameters ---------- start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is to use `DynamicFactorMQ.start_params`. transformed : bool, optional Whether or not `start_params` is already transformed. Default is True. cov_type : str, optional The `cov_type` keyword governs the method for calculating the covariance matrix of parameter estimates. Can be one of: - 'opg' for the outer product of gradient estimator - 'oim' for the observed information matrix estimator, calculated using the method of Harvey (1989) - 'approx' for the observed information matrix estimator, calculated using a numerical approximation of the Hessian matrix. - 'robust' for an approximate (quasi-maximum likelihood) covariance matrix that may be valid even in the presence of some misspecifications. Intermediate calculations use the 'oim' method. - 'robust_approx' is the same as 'robust' except that the intermediate calculations use the 'approx' method. - 'none' for no covariance matrix calculation. Default is 'none', since computing this matrix can be very slow when there are a large number of parameters. cov_kwds : dict or None, optional A dictionary of arguments affecting covariance matrix computation. **opg, oim, approx, robust, robust_approx** - 'approx_complex_step' : bool, optional - If True, numerical approximations are computed using complex-step methods. If False, numerical approximations are computed using finite difference methods. Default is True. - 'approx_centered' : bool, optional - If True, numerical approximations computed using finite difference methods use a centered approximation. Default is False. maxiter : int, optional The maximum number of EM iterations to perform. tolerance : float, optional Parameter governing convergence of the EM algorithm. The `tolerance` is the minimum relative increase in the likelihood for which convergence will be declared. A smaller value for the `tolerance` will typically yield more precise parameter estimates, but will typically require more EM iterations. Default is 1e-6. disp : int or bool, optional Controls printing of EM iteration progress. If an integer, progress is printed at every `disp` iterations. A value of True is interpreted as the value of 1. Default is False (nothing will be printed). em_initialization : bool, optional Whether or not to also update the Kalman filter initialization using the EM algorithm. Default is True. mstep_method : {None, 'missing', 'nonmissing'}, optional The EM algorithm maximization step. If there are no NaN values in the dataset, this can be set to "nonmissing" (which is slightly faster) or "missing", otherwise it must be "missing". Default is "nonmissing" if there are no NaN values or "missing" if there are. full_output : bool, optional Set to True to have all available output from EM iterations in the Results object's mle_retvals attribute. return_params : bool, optional Whether or not to return only the array of maximizing parameters. Default is False. low_memory : bool, optional This option cannot be used with the EM algorithm and will raise an error if set to True. Default is False. llf_decrease_action : {'ignore', 'warn', 'revert'}, optional Action to take if the log-likelihood decreases in an EM iteration. 'ignore' continues the iterations, 'warn' issues a warning but continues the iterations, while 'revert' ends the iterations and returns the result from the last good iteration. Default is 'warn'. llf_decrease_tolerance : float, optional Minimum size of the log-likelihood decrease required to trigger a warning or to end the EM iterations. Setting this value slightly larger than zero allows small decreases in the log-likelihood that may be caused by numerical issues. If set to zero, then any decrease will trigger the `llf_decrease_action`. Default is 1e-4. Returns ------- DynamicFactorMQResults See Also -------- statsmodels.tsa.statespace.mlemodel.MLEModel.fit statsmodels.tsa.statespace.mlemodel.MLEResults """ if self._has_fixed_params: raise NotImplementedError('Cannot fit using the EM algorithm while' ' holding some parameters fixed.') if low_memory: raise ValueError('Cannot fit using the EM algorithm when using' ' low_memory option.') if start_params is None: start_params = self.start_params transformed = True else: start_params = np.array(start_params, ndmin=1) if not transformed: start_params = self.transform_params(start_params) llf_decrease_action = string_like( llf_decrease_action, 'llf_decrease_action', options=['ignore', 'warn', 'revert']) disp = int(disp) # Perform expectation-maximization s = self._s llf = [] params = [start_params] init = None inits = [self.ssm.initialization] i = 0 delta = 0 terminate = False # init_stationary = None if em_initialization else True while i < maxiter and not terminate and (i < 1 or (delta > tolerance)): out = self._em_iteration(params[-1], init=init, mstep_method=mstep_method) new_llf = out[0].llf_obs.sum() # If we are not using EM initialization, then we need to check for # non-stationary parameters if not em_initialization: self.update(out[1]) switch_init = [] T = self['transition'] init = self.ssm.initialization iloc = np.arange(self.k_states) # We may only have global initialization if we have no # quarterly variables and idiosyncratic_ar1=False if self.k_endog_Q == 0 and not self.idiosyncratic_ar1: block = s.factor_blocks[0] if init.initialization_type == 'stationary': Tb = T[block['factors'], block['factors']] if not np.all(np.linalg.eigvals(Tb) < (1 - 1e-10)): init.set(block['factors'], 'diffuse') switch_init.append( 'factor block:' f' {tuple(block.factor_names)}') else: # Factor blocks for block in s.factor_blocks: b = tuple(iloc[block['factors']]) init_type = init.blocks[b].initialization_type if init_type == 'stationary': Tb = T[block['factors'], block['factors']] if not np.all(np.linalg.eigvals(Tb) < (1 - 1e-10)): init.set(block['factors'], 'diffuse') switch_init.append( 'factor block:' f' {tuple(block.factor_names)}') if self.idiosyncratic_ar1: endog_names = self._get_endog_names(as_string=True) # Monthly variables for j in range(s['idio_ar_M'].start, s['idio_ar_M'].stop): init_type = init.blocks[(j,)].initialization_type if init_type == 'stationary': if not np.abs(T[j, j]) < (1 - 1e-10): init.set(j, 'diffuse') name = endog_names[j - s['idio_ar_M'].start] switch_init.append( 'idiosyncratic AR(1) for monthly' f' variable: {name}') # Quarterly variables if self.k_endog_Q > 0: b = tuple(iloc[s['idio_ar_Q']]) init_type = init.blocks[b].initialization_type if init_type == 'stationary': Tb = T[s['idio_ar_Q'], s['idio_ar_Q']] if not np.all(np.linalg.eigvals(Tb) < (1 - 1e-10)): init.set(s['idio_ar_Q'], 'diffuse') switch_init.append( 'idiosyncratic AR(1) for the' ' block of quarterly variables') if len(switch_init) > 0: warn('Non-stationary parameters found at EM iteration' f' {i + 1}, which is not compatible with' ' stationary initialization. Initialization was' ' switched to diffuse for the following: ' f' {switch_init}, and fitting was restarted.') results = self.fit_em( start_params=params[-1], transformed=transformed, cov_type=cov_type, cov_kwds=cov_kwds, maxiter=maxiter, tolerance=tolerance, em_initialization=em_initialization, mstep_method=mstep_method, full_output=full_output, disp=disp, return_params=return_params, low_memory=low_memory, llf_decrease_action=llf_decrease_action, llf_decrease_tolerance=llf_decrease_tolerance) self.ssm.initialize(self._default_initialization()) return results # Check for decrease in the log-likelihood # Note: allow a little numerical error before declaring a decrease llf_decrease = ( i > 0 and (new_llf - llf[-1]) < -llf_decrease_tolerance) if llf_decrease_action == 'revert' and llf_decrease: warn(f'Log-likelihood decreased at EM iteration {i + 1}.' f' Reverting to the results from EM iteration {i}' ' (prior to the decrease) and returning the solution.') # Terminated iteration i -= 1 terminate = True else: if llf_decrease_action == 'warn' and llf_decrease: warn(f'Log-likelihood decreased at EM iteration {i + 1},' ' which can indicate numerical issues.') llf.append(new_llf) params.append(out[1]) if em_initialization: init = initialization.Initialization( self.k_states, 'known', constant=out[0].smoothed_state[..., 0], stationary_cov=out[0].smoothed_state_cov[..., 0]) inits.append(init) if i > 0: delta = (2 * np.abs(llf[-1] - llf[-2]) / (np.abs(llf[-1]) + np.abs(llf[-2]))) else: delta = np.inf # If `disp` is not False, display the first iteration if disp and i == 0: print(f'EM start iterations, llf={llf[-1]:.5g}') # Print output every `disp` observations elif disp and ((i + 1) % disp) == 0: print(f'EM iteration {i + 1}, llf={llf[-1]:.5g},' f' convergence criterion={delta:.5g}') # Advance the iteration counter i += 1 # Check for convergence not_converged = (i == maxiter and delta > tolerance) # If no convergence without explicit termination, warn users if not_converged: warn(f'EM reached maximum number of iterations ({maxiter}),' f' without achieving convergence: llf={llf[-1]:.5g},' f' convergence criterion={delta:.5g}' f' (while specified tolerance was {tolerance:.5g})') # If `disp` is not False, display the final iteration if disp: if terminate: print(f'EM terminated at iteration {i}, llf={llf[-1]:.5g},' f' convergence criterion={delta:.5g}' f' (while specified tolerance was {tolerance:.5g})') elif not_converged: print(f'EM reached maximum number of iterations ({maxiter}),' f' without achieving convergence: llf={llf[-1]:.5g},' f' convergence criterion={delta:.5g}' f' (while specified tolerance was {tolerance:.5g})') else: print(f'EM converged at iteration {i}, llf={llf[-1]:.5g},' f' convergence criterion={delta:.5g}' f' < tolerance={tolerance:.5g}') # Just return the fitted parameters if requested if return_params: result = params[-1] # Otherwise construct the results class if desired else: if em_initialization: base_init = self.ssm.initialization self.ssm.initialization = init # Note that because we are using params[-1], we are actually using # the results from one additional iteration compared to the # iteration at which we declared convergence. result = self.smooth(params[-1], transformed=True, cov_type=cov_type, cov_kwds=cov_kwds) if em_initialization: self.ssm.initialization = base_init # Save the output if full_output: llf.append(result.llf) em_retvals = Bunch(**{'params': np.array(params), 'llf': np.array(llf), 'iter': i, 'inits': inits}) em_settings = Bunch(**{'method': 'em', 'tolerance': tolerance, 'maxiter': maxiter}) else: em_retvals = None em_settings = None result._results.mle_retvals = em_retvals result._results.mle_settings = em_settings return result def _em_iteration(self, params0, init=None, mstep_method=None): """EM iteration.""" # (E)xpectation step res = self._em_expectation_step(params0, init=init) # (M)aximization step params1 = self._em_maximization_step(res, params0, mstep_method=mstep_method) return res, params1 def _em_expectation_step(self, params0, init=None): """EM expectation step.""" # (E)xpectation step self.update(params0) # Re-initialize state, if new initialization is given if init is not None: base_init = self.ssm.initialization self.ssm.initialization = init # Perform smoothing, only saving what is required res = self.ssm.smooth( SMOOTHER_STATE | SMOOTHER_STATE_COV | SMOOTHER_STATE_AUTOCOV, update_filter=False) res.llf_obs = np.array( self.ssm._kalman_filter.loglikelihood, copy=True) # Reset initialization if init is not None: self.ssm.initialization = base_init return res def _em_maximization_step(self, res, params0, mstep_method=None): """EM maximization step.""" s = self._s a = res.smoothed_state.T[..., None] cov_a = res.smoothed_state_cov.transpose(2, 0, 1) acov_a = res.smoothed_state_autocov.transpose(2, 0, 1) # E[a_t a_t'], t = 0, ..., T Eaa = cov_a.copy() + np.matmul(a, a.transpose(0, 2, 1)) # E[a_t a_{t-1}'], t = 1, ..., T Eaa1 = acov_a[:-1] + np.matmul(a[1:], a[:-1].transpose(0, 2, 1)) # Observation equation has_missing = np.any(res.nmissing) if mstep_method is None: mstep_method = 'missing' if has_missing else 'nonmissing' mstep_method = mstep_method.lower() if mstep_method == 'nonmissing' and has_missing: raise ValueError('Cannot use EM algorithm option' ' `mstep_method="nonmissing"` with missing data.') if mstep_method == 'nonmissing': func = self._em_maximization_obs_nonmissing elif mstep_method == 'missing': func = self._em_maximization_obs_missing else: raise ValueError('Invalid maximization step method: "%s".' % mstep_method) # TODO: compute H is pretty slow Lambda, H = func(res, Eaa, a, compute_H=(not self.idiosyncratic_ar1)) # Factor VAR and covariance factor_ar = [] factor_cov = [] for b in s.factor_blocks: A = Eaa[:-1, b['factors_ar'], b['factors_ar']].sum(axis=0) B = Eaa1[:, b['factors_L1'], b['factors_ar']].sum(axis=0) C = Eaa[1:, b['factors_L1'], b['factors_L1']].sum(axis=0) nobs = Eaa.shape[0] - 1 # want: x = B A^{-1}, so solve: x A = B or solve: A' x' = B' try: f_A = cho_solve(cho_factor(A), B.T).T except LinAlgError: # Fall back to general solver if there are problems with # postive-definiteness f_A = np.linalg.solve(A, B.T).T f_Q = (C - f_A @ B.T) / nobs factor_ar += f_A.ravel().tolist() factor_cov += ( np.linalg.cholesky(f_Q)[np.tril_indices_from(f_Q)].tolist()) # Idiosyncratic AR(1) and variances if self.idiosyncratic_ar1: ix = s['idio_ar_L1'] Ad = Eaa[:-1, ix, ix].sum(axis=0).diagonal() Bd = Eaa1[:, ix, ix].sum(axis=0).diagonal() Cd = Eaa[1:, ix, ix].sum(axis=0).diagonal() nobs = Eaa.shape[0] - 1 alpha = Bd / Ad sigma2 = (Cd - alpha * Bd) / nobs else: ix = s['idio_ar_L1'] C = Eaa[:, ix, ix].sum(axis=0) sigma2 = np.r_[H.diagonal()[self._o['M']], C.diagonal() / Eaa.shape[0]] # Save parameters params1 = np.zeros_like(params0) loadings = [] for i in range(self.k_endog): iloc = self._s.endog_factor_iloc[i] factor_ix = s['factors_L1'][iloc] loadings += Lambda[i, factor_ix].tolist() params1[self._p['loadings']] = loadings params1[self._p['factor_ar']] = factor_ar params1[self._p['factor_cov']] = factor_cov if self.idiosyncratic_ar1: params1[self._p['idiosyncratic_ar1']] = alpha params1[self._p['idiosyncratic_var']] = sigma2 return params1 def _em_maximization_obs_nonmissing(self, res, Eaa, a, compute_H=False): """EM maximization step, observation equation without missing data.""" s = self._s dtype = Eaa.dtype # Observation equation (non-missing) # Note: we only compute loadings for monthly variables because # quarterly variables will always have missing entries, so we would # never choose this method in that case k = s.k_states_factors Lambda = np.zeros((self.k_endog, k), dtype=dtype) for i in range(self.k_endog): y = self.endog[:, i:i + 1] iloc = self._s.endog_factor_iloc[i] factor_ix = s['factors_L1'][iloc] ix = (np.s_[:],) + np.ix_(factor_ix, factor_ix) A = Eaa[ix].sum(axis=0) B = y.T @ a[:, factor_ix, 0] if self.idiosyncratic_ar1: ix1 = s.k_states_factors + i ix2 = ix1 + 1 B -= Eaa[:, ix1:ix2, factor_ix].sum(axis=0) # want: x = B A^{-1}, so solve: x A = B or solve: A' x' = B' try: Lambda[i, factor_ix] = cho_solve(cho_factor(A), B.T).T except LinAlgError: # Fall back to general solver if there are problems with # postive-definiteness Lambda[i, factor_ix] = np.linalg.solve(A, B.T).T # Compute new obs cov # Note: this is unnecessary if `idiosyncratic_ar1=True`. # This is written in a slightly more general way than # Banbura and Modugno (2014), equation (7); see instead equation (13) # of Wu et al. (1996) # "An algorithm for estimating parameters of state-space models" if compute_H: Z = self['design'].copy() Z[:, :k] = Lambda BL = self.endog.T @ a[..., 0] @ Z.T C = self.endog.T @ self.endog H = (C + -BL - BL.T + Z @ Eaa.sum(axis=0) @ Z.T) / self.nobs else: H = np.zeros((self.k_endog, self.k_endog), dtype=dtype) * np.nan return Lambda, H def _em_maximization_obs_missing(self, res, Eaa, a, compute_H=False): """EM maximization step, observation equation with missing data.""" s = self._s dtype = Eaa.dtype # Observation equation (missing) k = s.k_states_factors Lambda = np.zeros((self.k_endog, k), dtype=dtype) W = (1 - res.missing.T) mask = W.astype(bool) # Compute design for monthly # Note: the relevant A changes for each i for i in range(self.k_endog_M): iloc = self._s.endog_factor_iloc[i] factor_ix = s['factors_L1'][iloc] m = mask[:, i] yt = self.endog[m, i:i + 1] ix = np.ix_(m, factor_ix, factor_ix) Ai = Eaa[ix].sum(axis=0) Bi = yt.T @ a[np.ix_(m, factor_ix)][..., 0] if self.idiosyncratic_ar1: ix1 = s.k_states_factors + i ix2 = ix1 + 1 Bi -= Eaa[m, ix1:ix2][..., factor_ix].sum(axis=0) # want: x = B A^{-1}, so solve: x A = B or solve: A' x' = B' try: Lambda[i, factor_ix] = cho_solve(cho_factor(Ai), Bi.T).T except LinAlgError: # Fall back to general solver if there are problems with # postive-definiteness Lambda[i, factor_ix] = np.linalg.solve(Ai, Bi.T).T # Compute unrestricted design for quarterly # See Banbura at al. (2011), where this is described in Appendix C, # between equations (13) and (14). if self.k_endog_Q > 0: # Note: the relevant A changes for each i multipliers = np.array([1, 2, 3, 2, 1])[:, None] for i in range(self.k_endog_M, self.k_endog): iloc = self._s.endog_factor_iloc[i] factor_ix = s['factors_L1_5_ix'][:, iloc].ravel().tolist() R, _ = self.loading_constraints(i) iQ = i - self.k_endog_M m = mask[:, i] yt = self.endog[m, i:i + 1] ix = np.ix_(m, factor_ix, factor_ix) Ai = Eaa[ix].sum(axis=0) BiQ = yt.T @ a[np.ix_(m, factor_ix)][..., 0] if self.idiosyncratic_ar1: ix = (np.s_[:],) + np.ix_(s['idio_ar_Q_ix'][iQ], factor_ix) Eepsf = Eaa[ix] BiQ -= (multipliers * Eepsf[m].sum(axis=0)).sum(axis=0) # Note that there was a typo in Banbura et al. (2011) for # the formula applying the restrictions. In their notation, # they show (C D C')^{-1} while it should be (C D^{-1} C')^{-1} # Note: in reality, this is: # unrestricted - Aii @ R.T @ RARi @ (R @ unrestricted - q) # where the restrictions are defined as: R @ unrestricted = q # However, here q = 0, so we can simplify. try: L_and_lower = cho_factor(Ai) # x = BQ A^{-1}, or x A = BQ, so solve A' x' = (BQ)' unrestricted = cho_solve(L_and_lower, BiQ.T).T[0] AiiRT = cho_solve(L_and_lower, R.T) L_and_lower = cho_factor(R @ AiiRT) RAiiRTiR = cho_solve(L_and_lower, R) restricted = unrestricted - AiiRT @ RAiiRTiR @ unrestricted except LinAlgError: # Fall back to slower method if there are problems with # postive-definiteness Aii = np.linalg.inv(Ai) unrestricted = (BiQ @ Aii)[0] RARi = np.linalg.inv(R @ Aii @ R.T) restricted = (unrestricted - Aii @ R.T @ RARi @ R @ unrestricted) Lambda[i, factor_ix] = restricted # Compute new obs cov # Note: this is unnecessary if `idiosyncratic_ar1=True`. # See Banbura and Modugno (2014), equation (12) # This does not literally follow their formula, e.g. multiplying by the # W_t selection matrices, because those formulas require loops that are # relatively slow. The formulation here is vectorized. if compute_H: Z = self['design'].copy() Z[:, :Lambda.shape[1]] = Lambda y = np.nan_to_num(self.endog) C = y.T @ y W = W[..., None] IW = 1 - W WL = W * Z WLT = WL.transpose(0, 2, 1) BL = y[..., None] @ a.transpose(0, 2, 1) @ WLT A = Eaa BLT = BL.transpose(0, 2, 1) IWT = IW.transpose(0, 2, 1) H = (C + (-BL - BLT + WL @ A @ WLT + IW * self['obs_cov'] * IWT).sum(axis=0)) / self.nobs else: H = np.zeros((self.k_endog, self.k_endog), dtype=dtype) * np.nan return Lambda, H def smooth(self, params, transformed=True, includes_fixed=False, complex_step=False, cov_type='none', cov_kwds=None, return_ssm=False, results_class=None, results_wrapper_class=None, **kwargs): """ Kalman smoothing. Parameters ---------- params : array_like Array of parameters at which to evaluate the loglikelihood function. transformed : bool, optional Whether or not `params` is already transformed. Default is True. return_ssm : bool,optional Whether or not to return only the state space output or a full results object. Default is to return a full results object. cov_type : str, optional See `MLEResults.fit` for a description of covariance matrix types for results object. Default is None. cov_kwds : dict or None, optional See `MLEResults.get_robustcov_results` for a description required keywords for alternative covariance estimators **kwargs Additional keyword arguments to pass to the Kalman filter. See `KalmanFilter.filter` for more details. """ return super().smooth( params, transformed=transformed, includes_fixed=includes_fixed, complex_step=complex_step, cov_type=cov_type, cov_kwds=cov_kwds, return_ssm=return_ssm, results_class=results_class, results_wrapper_class=results_wrapper_class, **kwargs) def filter(self, params, transformed=True, includes_fixed=False, complex_step=False, cov_type='none', cov_kwds=None, return_ssm=False, results_class=None, results_wrapper_class=None, low_memory=False, **kwargs): """ Kalman filtering. Parameters ---------- params : array_like Array of parameters at which to evaluate the loglikelihood function. transformed : bool, optional Whether or not `params` is already transformed. Default is True. return_ssm : bool,optional Whether or not to return only the state space output or a full results object. Default is to return a full results object. cov_type : str, optional See `MLEResults.fit` for a description of covariance matrix types for results object. Default is 'none'. cov_kwds : dict or None, optional See `MLEResults.get_robustcov_results` for a description required keywords for alternative covariance estimators low_memory : bool, optional If set to True, techniques are applied to substantially reduce memory usage. If used, some features of the results object will not be available (including in-sample prediction), although out-of-sample forecasting is possible. Default is False. **kwargs Additional keyword arguments to pass to the Kalman filter. See `KalmanFilter.filter` for more details. """ return super().filter( params, transformed=transformed, includes_fixed=includes_fixed, complex_step=complex_step, cov_type=cov_type, cov_kwds=cov_kwds, return_ssm=return_ssm, results_class=results_class, results_wrapper_class=results_wrapper_class, **kwargs) def simulate(self, params, nsimulations, measurement_shocks=None, state_shocks=None, initial_state=None, anchor=None, repetitions=None, exog=None, extend_model=None, extend_kwargs=None, transformed=True, includes_fixed=False, original_scale=True, **kwargs): r""" Simulate a new time series following the state space model. Parameters ---------- params : array_like Array of parameters to use in constructing the state space representation to use when simulating. nsimulations : int The number of observations to simulate. If the model is time-invariant this can be any number. If the model is time-varying, then this number must be less than or equal to the number of observations. measurement_shocks : array_like, optional If specified, these are the shocks to the measurement equation, :math:`\varepsilon_t`. If unspecified, these are automatically generated using a pseudo-random number generator. If specified, must be shaped `nsimulations` x `k_endog`, where `k_endog` is the same as in the state space model. state_shocks : array_like, optional If specified, these are the shocks to the state equation, :math:`\eta_t`. If unspecified, these are automatically generated using a pseudo-random number generator. If specified, must be shaped `nsimulations` x `k_posdef` where `k_posdef` is the same as in the state space model. initial_state : array_like, optional If specified, this is the initial state vector to use in simulation, which should be shaped (`k_states` x 1), where `k_states` is the same as in the state space model. If unspecified, but the model has been initialized, then that initialization is used. This must be specified if `anchor` is anything other than "start" or 0 (or else you can use the `simulate` method on a results object rather than on the model object). anchor : int, str, or datetime, optional First period for simulation. The simulation will be conditional on all existing datapoints prior to the `anchor`. Type depends on the index of the given `endog` in the model. Two special cases are the strings 'start' and 'end'. `start` refers to beginning the simulation at the first period of the sample, and `end` refers to beginning the simulation at the first period after the sample. Integer values can run from 0 to `nobs`, or can be negative to apply negative indexing. Finally, if a date/time index was provided to the model, then this argument can be a date string to parse or a datetime type. Default is 'start'. repetitions : int, optional Number of simulated paths to generate. Default is 1 simulated path. exog : array_like, optional New observations of exogenous regressors, if applicable. transformed : bool, optional Whether or not `params` is already transformed. Default is True. includes_fixed : bool, optional If parameters were previously fixed with the `fix_params` method, this argument describes whether or not `params` also includes the fixed parameters, in addition to the free parameters. Default is False. original_scale : bool, optional If the model specification standardized the data, whether or not to return simulations in the original scale of the data (i.e. before it was standardized by the model). Default is True. Returns ------- simulated_obs : ndarray An array of simulated observations. If `repetitions=None`, then it will be shaped (nsimulations x k_endog) or (nsimulations,) if `k_endog=1`. Otherwise it will be shaped (nsimulations x k_endog x repetitions). If the model was given Pandas input then the output will be a Pandas object. If `k_endog > 1` and `repetitions` is not None, then the output will be a Pandas DataFrame that has a MultiIndex for the columns, with the first level containing the names of the `endog` variables and the second level containing the repetition number. """ # Get usual simulations (in the possibly-standardized scale) sim = super().simulate( params, nsimulations, measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state, anchor=anchor, repetitions=repetitions, exog=exog, extend_model=extend_model, extend_kwargs=extend_kwargs, transformed=transformed, includes_fixed=includes_fixed, **kwargs) # If applicable, convert predictions back to original space if self.standardize and original_scale: use_pandas = isinstance(self.data, PandasData) shape = sim.shape if use_pandas: # pd.Series (k_endog=1, replications=None) if len(shape) == 1: sim = sim * self._endog_std[0] + self._endog_mean[0] # pd.DataFrame (k_endog > 1, replications=None) # [or] # pd.DataFrame with MultiIndex (replications > 0) elif len(shape) == 2: sim = (sim.multiply(self._endog_std, axis=1, level=0) .add(self._endog_mean, axis=1, level=0)) else: # 1-dim array (k_endog=1, replications=None) if len(shape) == 1: sim = sim * self._endog_std + self._endog_mean # 2-dim array (k_endog > 1, replications=None) elif len(shape) == 2: sim = sim * self._endog_std + self._endog_mean # 3-dim array with MultiIndex (replications > 0) else: # Get arrays into the form that can be used for # broadcasting std = np.atleast_2d(self._endog_std)[..., None] mean = np.atleast_2d(self._endog_mean)[..., None] sim = sim * std + mean return sim def impulse_responses(self, params, steps=1, impulse=0, orthogonalized=False, cumulative=False, anchor=None, exog=None, extend_model=None, extend_kwargs=None, transformed=True, includes_fixed=False, original_scale=True, **kwargs): """ Impulse response function. Parameters ---------- params : array_like Array of model parameters. steps : int, optional The number of steps for which impulse responses are calculated. Default is 1. Note that for time-invariant models, the initial impulse is not counted as a step, so if `steps=1`, the output will have 2 entries. impulse : int or array_like If an integer, the state innovation to pulse; must be between 0 and `k_posdef-1`. Alternatively, a custom impulse vector may be provided; must be shaped `k_posdef x 1`. orthogonalized : bool, optional Whether or not to perform impulse using orthogonalized innovations. Note that this will also affect custum `impulse` vectors. Default is False. cumulative : bool, optional Whether or not to return cumulative impulse responses. Default is False. anchor : int, str, or datetime, optional Time point within the sample for the state innovation impulse. Type depends on the index of the given `endog` in the model. Two special cases are the strings 'start' and 'end', which refer to setting the impulse at the first and last points of the sample, respectively. Integer values can run from 0 to `nobs - 1`, or can be negative to apply negative indexing. Finally, if a date/time index was provided to the model, then this argument can be a date string to parse or a datetime type. Default is 'start'. exog : array_like, optional New observations of exogenous regressors for our-of-sample periods, if applicable. transformed : bool, optional Whether or not `params` is already transformed. Default is True. includes_fixed : bool, optional If parameters were previously fixed with the `fix_params` method, this argument describes whether or not `params` also includes the fixed parameters, in addition to the free parameters. Default is False. original_scale : bool, optional If the model specification standardized the data, whether or not to return impulse responses in the original scale of the data (i.e. before it was standardized by the model). Default is True. **kwargs If the model has time-varying design or transition matrices and the combination of `anchor` and `steps` implies creating impulse responses for the out-of-sample period, then these matrices must have updated values provided for the out-of-sample steps. For example, if `design` is a time-varying component, `nobs` is 10, `anchor=1`, and `steps` is 15, a (`k_endog` x `k_states` x 7) matrix must be provided with the new design matrix values. Returns ------- impulse_responses : ndarray Responses for each endogenous variable due to the impulse given by the `impulse` argument. For a time-invariant model, the impulse responses are given for `steps + 1` elements (this gives the "initial impulse" followed by `steps` responses for the important cases of VAR and SARIMAX models), while for time-varying models the impulse responses are only given for `steps` elements (to avoid having to unexpectedly provide updated time-varying matrices). """ # Get usual simulations (in the possibly-standardized scale) irfs = super().impulse_responses( params, steps=steps, impulse=impulse, orthogonalized=orthogonalized, cumulative=cumulative, anchor=anchor, exog=exog, extend_model=extend_model, extend_kwargs=extend_kwargs, transformed=transformed, includes_fixed=includes_fixed, original_scale=original_scale, **kwargs) # If applicable, convert predictions back to original space if self.standardize and original_scale: use_pandas = isinstance(self.data, PandasData) shape = irfs.shape if use_pandas: # pd.Series (k_endog=1, replications=None) if len(shape) == 1: irfs = irfs * self._endog_std[0] # pd.DataFrame (k_endog > 1) # [or] # pd.DataFrame with MultiIndex (replications > 0) elif len(shape) == 2: irfs = irfs.multiply(self._endog_std, axis=1, level=0) else: # 1-dim array (k_endog=1) if len(shape) == 1: irfs = irfs * self._endog_std # 2-dim array (k_endog > 1) elif len(shape) == 2: irfs = irfs * self._endog_std return irfs class DynamicFactorMQResults(mlemodel.MLEResults): """ Results from fitting a dynamic factor model """ def __init__(self, model, params, filter_results, cov_type=None, **kwargs): super(DynamicFactorMQResults, self).__init__( model, params, filter_results, cov_type, **kwargs) @property def factors(self): """ Estimates of unobserved factors. Returns ------- out : Bunch Has the following attributes shown in Notes. Notes ----- The output is a bunch of the following format: - `filtered`: a time series array with the filtered estimate of the component - `filtered_cov`: a time series array with the filtered estimate of the variance/covariance of the component - `smoothed`: a time series array with the smoothed estimate of the component - `smoothed_cov`: a time series array with the smoothed estimate of the variance/covariance of the component - `offset`: an integer giving the offset in the state vector where this component begins """ out = None if self.model.k_factors > 0: iloc = self.model._s.factors_L1 ix = np.array(self.model.state_names)[iloc].tolist() out = Bunch( filtered=self.states.filtered.loc[:, ix], filtered_cov=self.states.filtered_cov.loc[np.s_[ix, :], ix], smoothed=None, smoothed_cov=None) if self.smoothed_state is not None: out.smoothed = self.states.smoothed.loc[:, ix] if self.smoothed_state_cov is not None: out.smoothed_cov = ( self.states.smoothed_cov.loc[np.s_[ix, :], ix]) return out def get_coefficients_of_determination(self, method='individual', which=None): """ Get coefficients of determination (R-squared) for variables / factors. Parameters ---------- method : {'individual', 'joint', 'cumulative'}, optional The type of R-squared values to generate. "individual" plots the R-squared of each variable on each factor; "joint" plots the R-squared of each variable on each factor that it loads on; "cumulative" plots the successive R-squared values as each additional factor is added to the regression, for each variable. Default is 'individual'. which: {None, 'filtered', 'smoothed'}, optional Whether to compute R-squared values based on filtered or smoothed estimates of the factors. Default is 'smoothed' if smoothed results are available and 'filtered' otherwise. Returns ------- rsquared : pd.DataFrame or pd.Series The R-squared values from regressions of observed variables on one or more of the factors. If method='individual' or method='cumulative', this will be a Pandas DataFrame with observed variables as the index and factors as the columns . If method='joint', will be a Pandas Series with observed variables as the index. See Also -------- plot_coefficients_of_determination coefficients_of_determination """ from statsmodels.tools import add_constant method = string_like(method, 'method', options=['individual', 'joint', 'cumulative']) if which is None: which = 'filtered' if self.smoothed_state is None else 'smoothed' k_endog = self.model.k_endog k_factors = self.model.k_factors ef_map = self.model._s.endog_factor_map endog_names = self.model.endog_names factor_names = self.model.factor_names if method == 'individual': coefficients = np.zeros((k_endog, k_factors)) for i in range(k_factors): exog = add_constant(self.factors[which].iloc[:, i]) for j in range(k_endog): if ef_map.iloc[j, i]: endog = self.filter_results.endog[j] coefficients[j, i] = ( OLS(endog, exog, missing='drop').fit().rsquared) else: coefficients[j, i] = np.nan coefficients = pd.DataFrame(coefficients, index=endog_names, columns=factor_names) elif method == 'joint': coefficients = np.zeros((k_endog,)) exog = add_constant(self.factors[which]) for j in range(k_endog): endog = self.filter_results.endog[j] ix = np.r_[True, ef_map.iloc[j]].tolist() X = exog.loc[:, ix] coefficients[j] = ( OLS(endog, X, missing='drop').fit().rsquared) coefficients = pd.Series(coefficients, index=endog_names) elif method == 'cumulative': coefficients = np.zeros((k_endog, k_factors)) exog = add_constant(self.factors[which]) for j in range(k_endog): endog = self.filter_results.endog[j] for i in range(k_factors): if self.model._s.endog_factor_map.iloc[j, i]: ix = np.r_[True, ef_map.iloc[j, :i + 1], [False] * (k_factors - i - 1)] X = exog.loc[:, ix.astype(bool).tolist()] coefficients[j, i] = ( OLS(endog, X, missing='drop').fit().rsquared) else: coefficients[j, i] = np.nan coefficients = pd.DataFrame(coefficients, index=endog_names, columns=factor_names) return coefficients @cache_readonly def coefficients_of_determination(self): """ Individual coefficients of determination (:math:`R^2`). Coefficients of determination (:math:`R^2`) from regressions of endogenous variables on individual estimated factors. Returns ------- coefficients_of_determination : ndarray A `k_endog` x `k_factors` array, where `coefficients_of_determination[i, j]` represents the :math:`R^2` value from a regression of factor `j` and a constant on endogenous variable `i`. Notes ----- Although it can be difficult to interpret the estimated factor loadings and factors, it is often helpful to use the coefficients of determination from univariate regressions to assess the importance of each factor in explaining the variation in each endogenous variable. In models with many variables and factors, this can sometimes lend interpretation to the factors (for example sometimes one factor will load primarily on real variables and another on nominal variables). See Also -------- get_coefficients_of_determination plot_coefficients_of_determination """ return self.get_coefficients_of_determination(method='individual') def plot_coefficients_of_determination(self, method='individual', which=None, endog_labels=None, fig=None, figsize=None): """ Plot coefficients of determination (R-squared) for variables / factors. Parameters ---------- method : {'individual', 'joint', 'cumulative'}, optional The type of R-squared values to generate. "individual" plots the R-squared of each variable on each factor; "joint" plots the R-squared of each variable on each factor that it loads on; "cumulative" plots the successive R-squared values as each additional factor is added to the regression, for each variable. Default is 'individual'. which: {None, 'filtered', 'smoothed'}, optional Whether to compute R-squared values based on filtered or smoothed estimates of the factors. Default is 'smoothed' if smoothed results are available and 'filtered' otherwise. endog_labels : bool, optional Whether or not to label the endogenous variables along the x-axis of the plots. Default is to include labels if there are 5 or fewer endogenous variables. fig : Figure, optional If given, subplots are created in this figure instead of in a new figure. Note that the grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Notes ----- The endogenous variables are arranged along the x-axis according to their position in the model's `endog` array. See Also -------- get_coefficients_of_determination """ from statsmodels.graphics.utils import _import_mpl, create_mpl_fig _import_mpl() fig = create_mpl_fig(fig, figsize) method = string_like(method, 'method', options=['individual', 'joint', 'cumulative']) # Should we label endogenous variables? if endog_labels is None: endog_labels = self.model.k_endog <= 5 # Plot the coefficients of determination rsquared = self.get_coefficients_of_determination(method=method, which=which) if method in ['individual', 'cumulative']: plot_idx = 1 for factor_name, coeffs in rsquared.T.iterrows(): # Create the new axis ax = fig.add_subplot(self.model.k_factors, 1, plot_idx) ax.set_ylim((0, 1)) ax.set(title=f'{factor_name}', ylabel=r'$R^2$') coeffs.plot(ax=ax, kind='bar') if plot_idx < len(rsquared.columns) or not endog_labels: ax.xaxis.set_ticklabels([]) plot_idx += 1 elif method == 'joint': ax = fig.add_subplot(1, 1, 1) ax.set_ylim((0, 1)) ax.set(title=r'$R^2$ - regression on all loaded factors', ylabel=r'$R^2$') rsquared.plot(ax=ax, kind='bar') if not endog_labels: ax.xaxis.set_ticklabels([]) return fig def get_prediction(self, start=None, end=None, dynamic=False, index=None, exog=None, extend_model=None, extend_kwargs=None, original_scale=True, **kwargs): """ In-sample prediction and out-of-sample forecasting. Parameters ---------- start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, i.e., the last forecast is end. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. dynamic : bool, int, str, or datetime, optional Integer offset relative to `start` at which to begin dynamic prediction. Can also be an absolute date string to parse or a datetime type (these are not interpreted as offsets). Prior to this observation, true endogenous values will be used for prediction; starting with this observation and continuing through the end of prediction, forecasted endogenous values will be used instead. original_scale : bool, optional If the model specification standardized the data, whether or not to return predictions in the original scale of the data (i.e. before it was standardized by the model). Default is True. **kwargs Additional arguments may required for forecasting beyond the end of the sample. See `FilterResults.predict` for more details. Returns ------- forecast : ndarray Array of out of in-sample predictions and / or out-of-sample forecasts. An (npredict x k_endog) array. """ # Get usual predictions (in the possibly-standardized scale) res = super().get_prediction(start=start, end=end, dynamic=dynamic, index=index, exog=exog, extend_model=extend_model, extend_kwargs=extend_kwargs, **kwargs) # If applicable, convert predictions back to original space if self.model.standardize and original_scale: prediction_results = res.prediction_results k_endog, nobs = prediction_results.endog.shape mean = np.array(self.model._endog_mean) std = np.array(self.model._endog_std) if self.model.k_endog > 1: mean = mean[None, :] std = std[None, :] if not prediction_results.results.memory_no_forecast_mean: res._results._predicted_mean = ( res._results._predicted_mean * std + mean) if not prediction_results.results.memory_no_forecast_cov: if k_endog == 1: res._results._var_pred_mean *= std**2 else: res._results._var_pred_mean = ( std * res._results._var_pred_mean * std.T) return res def news(self, comparison, impact_date=None, impacted_variable=None, start=None, end=None, periods=None, exog=None, comparison_type=None, return_raw=False, tolerance=1e-10, endog_quarterly=None, original_scale=True, **kwargs): """ Compute impacts from updated data (news and revisions). Parameters ---------- comparison : array_like or MLEResults An updated dataset with updated and/or revised data from which the news can be computed, or an updated or previous results object to use in computing the news. impact_date : int, str, or datetime, optional A single specific period of impacts from news and revisions to compute. Can also be a date string to parse or a datetime type. This argument cannot be used in combination with `start`, `end`, or `periods`. Default is the first out-of-sample observation. impacted_variable : str, list, array, or slice, optional Observation variable label or slice of labels specifying that only specific impacted variables should be shown in the News output. The impacted variable(s) describe the variables that were *affected* by the news. If you do not know the labels for the variables, check the `endog_names` attribute of the model instance. start : int, str, or datetime, optional The first period of impacts from news and revisions to compute. Can also be a date string to parse or a datetime type. Default is the first out-of-sample observation. end : int, str, or datetime, optional The last period of impacts from news and revisions to compute. Can also be a date string to parse or a datetime type. Default is the first out-of-sample observation. periods : int, optional The number of periods of impacts from news and revisions to compute. exog : array_like, optional Array of exogenous regressors for the out-of-sample period, if applicable. comparison_type : {None, 'previous', 'updated'} This denotes whether the `comparison` argument represents a *previous* results object or dataset or an *updated* results object or dataset. If not specified, then an attempt is made to determine the comparison type. return_raw : bool, optional Whether or not to return only the specific output or a full results object. Default is to return a full results object. tolerance : float, optional The numerical threshold for determining zero impact. Default is that any impact less than 1e-10 is assumed to be zero. endog_quarterly : array_like, optional New observations of quarterly variables, if `comparison` was provided as an updated monthly dataset. If this argument is provided, it must be a Pandas Series or DataFrame with a DatetimeIndex or PeriodIndex at the quarterly frequency. References ---------- .. [1] Bańbura, Marta, and Michele Modugno. "Maximum likelihood estimation of factor models on datasets with arbitrary pattern of missing data." Journal of Applied Econometrics 29, no. 1 (2014): 133-160. .. [2] Bańbura, Marta, Domenico Giannone, and Lucrezia Reichlin. "Nowcasting." The Oxford Handbook of Economic Forecasting. July 8, 2011. .. [3] Bańbura, Marta, Domenico Giannone, Michele Modugno, and Lucrezia Reichlin. "Now-casting and the real-time data flow." In Handbook of economic forecasting, vol. 2, pp. 195-237. Elsevier, 2013. """ news_results = super().news( comparison, impact_date=impact_date, impacted_variable=impacted_variable, start=start, end=end, periods=periods, exog=exog, comparison_type=comparison_type, return_raw=return_raw, tolerance=tolerance, endog_quarterly=endog_quarterly, **kwargs) # If we have standardized the data, we may want to report the news in # the original scale. If so, we need to modify the data to "undo" the # standardization. if not return_raw and self.model.standardize and original_scale: endog_mean = self.model._endog_mean endog_std = self.model._endog_std # Don't need to add in the mean for the impacts, since they are # the difference of two forecasts news_results.total_impacts = ( news_results.total_impacts * endog_std) news_results.update_impacts = ( news_results.update_impacts * endog_std) if news_results.revision_impacts is not None: news_results.revision_impacts = ( news_results.revision_impacts * endog_std) # Update forecasts for name in ['prev_impacted_forecasts', 'news', 'update_realized', 'update_forecasts', 'post_impacted_forecasts']: dta = getattr(news_results, name) # for pd.Series, dta.multiply(...) removes the name attribute; # save it now so that we can add it back in orig_name = None if hasattr(dta, 'name'): orig_name = dta.name dta = dta.multiply(endog_std, level=1) # add back in the name attribute if it was removed if orig_name is not None: dta.name = orig_name if name != 'news': dta = dta.add(endog_mean, level=1) setattr(news_results, name, dta) # For the weights: rows correspond to update (date, variable) and # columns correspond to the impacted variable. # 1. Because we have modified the updates (realized, forecasts, and # forecast errors) to be in the scale of the original updated # variable, we need to essentially reverse that change for each # row of the weights by dividing by the standard deviation of # that row's updated variable # 2. Because we want the impacts to be in the scale of the original # impacted variable, we need to multiply each column by the # standard deviation of that column's impacted variable news_results.weights = ( news_results.weights.divide(endog_std, axis=0, level=1) .multiply(endog_std, axis=1, level=1)) return news_results def append(self, endog, endog_quarterly=None, refit=False, fit_kwargs=None, copy_initialization=True, retain_standardization=True, **kwargs): """ Recreate the results object with new data appended to original data. Creates a new result object applied to a dataset that is created by appending new data to the end of the model's original data. The new results can then be used for analysis or forecasting. Parameters ---------- endog : array_like New observations from the modeled time-series process. endog_quarterly : array_like, optional New observations of quarterly variables. If provided, must be a Pandas Series or DataFrame with a DatetimeIndex or PeriodIndex at the quarterly frequency. refit : bool, optional Whether to re-fit the parameters, based on the combined dataset. Default is False (so parameters from the current results object are used to create the new results object). fit_kwargs : dict, optional Keyword arguments to pass to `fit` (if `refit=True`) or `filter` / `smooth`. copy_initialization : bool, optional Whether or not to copy the initialization from the current results set to the new model. Default is True. retain_standardization : bool, optional Whether or not to use the mean and standard deviations that were used to standardize the data in the current model in the new model. Default is True. **kwargs Keyword arguments may be used to modify model specification arguments when created the new model object. Returns ------- results Updated Results object, that includes results from both the original dataset and the new dataset. Notes ----- The `endog` and `exog` arguments to this method must be formatted in the same way (e.g. Pandas Series versus Numpy array) as were the `endog` and `exog` arrays passed to the original model. The `endog` (and, if applicable, `endog_quarterly`) arguments to this method should consist of new observations that occurred directly after the last element of `endog`. For any other kind of dataset, see the `apply` method. This method will apply filtering to all of the original data as well as to the new data. To apply filtering only to the new data (which can be much faster if the original dataset is large), see the `extend` method. See Also -------- extend apply """ # Construct the combined dataset, if necessary endog, k_endog_monthly = DynamicFactorMQ.construct_endog( endog, endog_quarterly) # Check for compatible dimensions k_endog = endog.shape[1] if len(endog.shape) == 2 else 1 if (k_endog_monthly != self.model.k_endog_M or k_endog != self.model.k_endog): raise ValueError('Cannot append data of a different dimension to' ' a model.') kwargs['k_endog_monthly'] = k_endog_monthly return super().append( endog, refit=refit, fit_kwargs=fit_kwargs, copy_initialization=copy_initialization, retain_standardization=retain_standardization, **kwargs) def extend(self, endog, endog_quarterly=None, fit_kwargs=None, retain_standardization=True, **kwargs): """ Recreate the results object for new data that extends original data. Creates a new result object applied to a new dataset that is assumed to follow directly from the end of the model's original data. The new results can then be used for analysis or forecasting. Parameters ---------- endog : array_like New observations from the modeled time-series process. endog_quarterly : array_like, optional New observations of quarterly variables. If provided, must be a Pandas Series or DataFrame with a DatetimeIndex or PeriodIndex at the quarterly frequency. fit_kwargs : dict, optional Keyword arguments to pass to `filter` or `smooth`. retain_standardization : bool, optional Whether or not to use the mean and standard deviations that were used to standardize the data in the current model in the new model. Default is True. **kwargs Keyword arguments may be used to modify model specification arguments when created the new model object. Returns ------- results Updated Results object, that includes results only for the new dataset. See Also -------- append apply Notes ----- The `endog` argument to this method should consist of new observations that occurred directly after the last element of the model's original `endog` array. For any other kind of dataset, see the `apply` method. This method will apply filtering only to the new data provided by the `endog` argument, which can be much faster than re-filtering the entire dataset. However, the returned results object will only have results for the new data. To retrieve results for both the new data and the original data, see the `append` method. """ # Construct the combined dataset, if necessary endog, k_endog_monthly = DynamicFactorMQ.construct_endog( endog, endog_quarterly) # Check for compatible dimensions k_endog = endog.shape[1] if len(endog.shape) == 2 else 1 if (k_endog_monthly != self.model.k_endog_M or k_endog != self.model.k_endog): raise ValueError('Cannot append data of a different dimension to' ' a model.') kwargs['k_endog_monthly'] = k_endog_monthly return super().extend( endog, fit_kwargs=fit_kwargs, retain_standardization=retain_standardization, **kwargs) def apply(self, endog, k_endog_monthly=None, endog_quarterly=None, refit=False, fit_kwargs=None, copy_initialization=False, retain_standardization=True, **kwargs): """ Apply the fitted parameters to new data unrelated to the original data. Creates a new result object using the current fitted parameters, applied to a completely new dataset that is assumed to be unrelated to the model's original data. The new results can then be used for analysis or forecasting. Parameters ---------- endog : array_like New observations from the modeled time-series process. k_endog_monthly : int, optional If specifying a monthly/quarterly mixed frequency model in which the provided `endog` dataset contains both the monthly and quarterly data, this variable should be used to indicate how many of the variables are monthly. endog_quarterly : array_like, optional New observations of quarterly variables. If provided, must be a Pandas Series or DataFrame with a DatetimeIndex or PeriodIndex at the quarterly frequency. refit : bool, optional Whether to re-fit the parameters, using the new dataset. Default is False (so parameters from the current results object are used to create the new results object). fit_kwargs : dict, optional Keyword arguments to pass to `fit` (if `refit=True`) or `filter` / `smooth`. copy_initialization : bool, optional Whether or not to copy the initialization from the current results set to the new model. Default is False. retain_standardization : bool, optional Whether or not to use the mean and standard deviations that were used to standardize the data in the current model in the new model. Default is True. **kwargs Keyword arguments may be used to modify model specification arguments when created the new model object. Returns ------- results Updated Results object, that includes results only for the new dataset. See Also -------- statsmodels.tsa.statespace.mlemodel.MLEResults.append statsmodels.tsa.statespace.mlemodel.MLEResults.apply Notes ----- The `endog` argument to this method should consist of new observations that are not necessarily related to the original model's `endog` dataset. For observations that continue that original dataset by follow directly after its last element, see the `append` and `extend` methods. """ mod = self.model.clone(endog, k_endog_monthly=k_endog_monthly, endog_quarterly=endog_quarterly, retain_standardization=retain_standardization, **kwargs) if copy_initialization: res = self.filter_results init = initialization.Initialization( self.model.k_states, 'known', constant=res.initial_state, stationary_cov=res.initial_state_cov) mod.ssm.initialization = init res = self._apply(mod, refit=refit, fit_kwargs=fit_kwargs, **kwargs) return res def summary(self, alpha=.05, start=None, title=None, model_name=None, display_params=True, display_diagnostics=False, display_params_as_list=False, truncate_endog_names=None, display_max_endog=3): """ Summarize the Model. Parameters ---------- alpha : float, optional Significance level for the confidence intervals. Default is 0.05. start : int, optional Integer of the start observation. Default is 0. title : str, optional The title used for the summary table. model_name : str, optional The name of the model used. Default is to use model class name. Returns ------- summary : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary """ mod = self.model # Default title / model name if title is None: title = 'Dynamic Factor Results' if model_name is None: model_name = self.model._model_name # Get endog names endog_names = self.model._get_endog_names( truncate=truncate_endog_names) # Get extra elements for top summary table extra_top_left = None extra_top_right = [] mle_retvals = getattr(self, 'mle_retvals', None) mle_settings = getattr(self, 'mle_settings', None) if mle_settings is not None and mle_settings.method == 'em': extra_top_right += [('EM Iterations', [f'{mle_retvals.iter}'])] # Get the basic summary tables summary = super().summary( alpha=alpha, start=start, title=title, model_name=model_name, display_params=(display_params and display_params_as_list), display_diagnostics=display_diagnostics, truncate_endog_names=truncate_endog_names, display_max_endog=display_max_endog, extra_top_left=extra_top_left, extra_top_right=extra_top_right) # Get tables of parameters table_ix = 1 if not display_params_as_list: # Observation equation table data = pd.DataFrame( self.filter_results.design[:, mod._s['factors_L1'], 0], index=endog_names, columns=mod.factor_names) data = data.applymap(lambda s: '%.2f' % s) # Idiosyncratic terms # data[' '] = ' ' k_idio = 1 if mod.idiosyncratic_ar1: data[' idiosyncratic: AR(1)'] = ( self.params[mod._p['idiosyncratic_ar1']]) k_idio += 1 data['var.'] = self.params[mod._p['idiosyncratic_var']] data.iloc[:, -k_idio:] = data.iloc[:, -k_idio:].applymap( lambda s: '%.2f' % s) data.index.name = 'Factor loadings:' # Clear entries for non-loading factors base_iloc = np.arange(mod.k_factors) for i in range(mod.k_endog): iloc = [j for j in base_iloc if j not in mod._s.endog_factor_iloc[i]] data.iloc[i, iloc] = '.' data = data.reset_index() # Build the table params_data = data.values params_header = data.columns.tolist() params_stubs = None title = 'Observation equation:' table = SimpleTable( params_data, params_header, params_stubs, txt_fmt=fmt_params, title=title) summary.tables.insert(table_ix, table) table_ix += 1 # Factor transitions ix1 = 0 ix2 = 0 for i in range(len(mod._s.factor_blocks)): block = mod._s.factor_blocks[i] ix2 += block.k_factors T = self.filter_results.transition lag_names = [] for j in range(block.factor_order): lag_names += [f'L{j + 1}.{name}' for name in block.factor_names] data = pd.DataFrame(T[block.factors_L1, block.factors_ar, 0], index=block.factor_names, columns=lag_names) data.index.name = '' data = data.applymap(lambda s: '%.2f' % s) Q = self.filter_results.state_cov # data[' '] = '' if block.k_factors == 1: data[' error variance'] = Q[ix1, ix1] else: data[' error covariance'] = block.factor_names for j in range(block.k_factors): data[block.factor_names[j]] = Q[ix1:ix2, ix1 + j] data.iloc[:, -block.k_factors:] = ( data.iloc[:, -block.k_factors:].applymap( lambda s: '%.2f' % s)) data = data.reset_index() params_data = data.values params_header = data.columns.tolist() params_stubs = None title = f'Transition: Factor block {i}' table = SimpleTable( params_data, params_header, params_stubs, txt_fmt=fmt_params, title=title) summary.tables.insert(table_ix, table) table_ix += 1 ix1 = ix2 return summary statsmodels-0.12.2/statsmodels/tsa/statespace/exponential_smoothing.py000066400000000000000000000651131400612667500264270ustar00rootroot00000000000000""" Linear exponential smoothing models Author: Chad Fulton License: BSD-3 """ import numpy as np import pandas as pd from statsmodels.base.data import PandasData from statsmodels.genmod.generalized_linear_model import GLM from statsmodels.tools.validation import (array_like, bool_like, float_like, string_like, int_like) from statsmodels.tsa.exponential_smoothing import initialization as es_init from statsmodels.tsa.statespace import initialization as ss_init from statsmodels.tsa.statespace.kalman_filter import ( MEMORY_CONSERVE, MEMORY_NO_FORECAST) from statsmodels.compat.pandas import Appender import statsmodels.base.wrapper as wrap from statsmodels.iolib.summary import forg from statsmodels.iolib.table import SimpleTable from statsmodels.iolib.tableformatting import fmt_params from .mlemodel import MLEModel, MLEResults, MLEResultsWrapper class ExponentialSmoothing(MLEModel): """ Linear exponential smoothing models Parameters ---------- endog : array_like The observed time-series process :math:`y` trend : bool, optional Whether or not to include a trend component. Default is False. damped_trend : bool, optional Whether or not an included trend component is damped. Default is False. seasonal : int, optional The number of periods in a complete seasonal cycle for seasonal (Holt-Winters) models. For example, 4 for quarterly data with an annual cycle or 7 for daily data with a weekly cycle. Default is no seasonal effects. initialization_method : str, optional Method for initialize the recursions. One of: * 'estimated' * 'concentrated' * 'heuristic' * 'known' If 'known' initialization is used, then `initial_level` must be passed, as well as `initial_slope` and `initial_seasonal` if applicable. Default is 'estimated'. initial_level : float, optional The initial level component. Only used if initialization is 'known'. initial_trend : float, optional The initial trend component. Only used if initialization is 'known'. initial_seasonal : array_like, optional The initial seasonal component. An array of length `seasonal` or length `seasonal - 1` (in which case the last initial value is computed to make the average effect zero). Only used if initialization is 'known'. bounds : iterable[tuple], optional An iterable containing bounds for the parameters. Must contain four elements, where each element is a tuple of the form (lower, upper). Default is (0.0001, 0.9999) for the level, trend, and seasonal smoothing parameters and (0.8, 0.98) for the trend damping parameter. concentrate_scale : bool, optional Whether or not to concentrate the scale (variance of the error term) out of the likelihood. Notes ----- The parameters and states of this model are estimated by setting up the exponential smoothing equations as a special case of a linear Gaussian state space model and applying the Kalman filter. As such, it has slightly worse performance than the dedicated exponential smoothing model, :class:`statsmodels.tsa.holtwinters.ExponentialSmoothing`, and it does not support multiplicative (nonlinear) exponential smoothing models. However, as a subclass of the state space models, this model class shares a consistent set of functionality with those models, which can make it easier to work with. In addition, it supports computing confidence intervals for forecasts and it supports concentrating the initial state out of the likelihood function. References ---------- [1] Hyndman, Rob, Anne B. Koehler, J. Keith Ord, and Ralph D. Snyder. Forecasting with exponential smoothing: the state space approach. Springer Science & Business Media, 2008. """ def __init__(self, endog, trend=False, damped_trend=False, seasonal=None, initialization_method='estimated', initial_level=None, initial_trend=None, initial_seasonal=None, bounds=None, concentrate_scale=True, dates=None, freq=None, missing='none'): # Model definition self.trend = bool_like(trend, 'trend') self.damped_trend = bool_like(damped_trend, 'damped_trend') self.seasonal_periods = int_like(seasonal, 'seasonal', optional=True) self.seasonal = self.seasonal_periods is not None self.initialization_method = string_like( initialization_method, 'initialization_method').lower() self.concentrate_scale = bool_like(concentrate_scale, 'concentrate_scale') # TODO: add validation for bounds (e.g. have all bounds, upper > lower) # TODO: add `bounds_method` argument to choose between "usual" and # "admissible" as in Hyndman et al. (2008) self.bounds = bounds if self.bounds is None: self.bounds = [(1e-4, 1-1e-4)] * 3 + [(0.8, 0.98)] # Validation if self.seasonal_periods == 1: raise ValueError('Cannot have a seasonal period of 1.') if self.seasonal and self.seasonal_periods is None: raise NotImplementedError('Unable to detect season automatically;' ' please specify `seasonal_periods`.') if self.initialization_method not in ['concentrated', 'estimated', 'simple', 'heuristic', 'known']: raise ValueError('Invalid initialization method "%s".' % initialization_method) if self.initialization_method == 'known': if initial_level is None: raise ValueError('`initial_level` argument must be provided' ' when initialization method is set to' ' "known".') if initial_trend is None and self.trend: raise ValueError('`initial_trend` argument must be provided' ' for models with a trend component when' ' initialization method is set to "known".') if initial_seasonal is None and self.seasonal: raise ValueError('`initial_seasonal` argument must be provided' ' for models with a seasonal component when' ' initialization method is set to "known".') # Initialize the state space model if not self.seasonal or self.seasonal_periods is None: self._seasonal_periods = 0 else: self._seasonal_periods = self.seasonal_periods k_states = 2 + int(self.trend) + self._seasonal_periods k_posdef = 1 init = ss_init.Initialization(k_states, 'known', constant=[0] * k_states) super(ExponentialSmoothing, self).__init__( endog, k_states=k_states, k_posdef=k_posdef, initialization=init, dates=dates, freq=freq, missing=missing) # Concentrate the scale out of the likelihood function if self.concentrate_scale: self.ssm.filter_concentrated = True # Setup fixed elements of the system matrices # Observation error self.ssm['design', 0, 0] = 1. self.ssm['selection', 0, 0] = 1. self.ssm['state_cov', 0, 0] = 1. # Level self.ssm['design', 0, 1] = 1. self.ssm['transition', 1, 1] = 1. # Trend if self.trend: self.ssm['transition', 1:3, 2] = 1. # Seasonal if self.seasonal: k = 2 + int(self.trend) self.ssm['design', 0, k] = 1. self.ssm['transition', k, -1] = 1. self.ssm['transition', k + 1:k_states, k:k_states - 1] = ( np.eye(self.seasonal_periods - 1)) # Initialization of the states if self.initialization_method != 'known': msg = ('Cannot give `%%s` argument when initialization is "%s"' % initialization_method) if initial_level is not None: raise ValueError(msg % 'initial_level') if initial_trend is not None: raise ValueError(msg % 'initial_trend') if initial_seasonal is not None: raise ValueError(msg % 'initial_seasonal') if self.initialization_method == 'simple': initial_level, initial_trend, initial_seasonal = ( es_init._initialization_simple( self.endog[:, 0], trend='add' if self.trend else None, seasonal='add' if self.seasonal else None, seasonal_periods=self.seasonal_periods)) elif self.initialization_method == 'heuristic': initial_level, initial_trend, initial_seasonal = ( es_init._initialization_heuristic( self.endog[:, 0], trend='add' if self.trend else None, seasonal='add' if self.seasonal else None, seasonal_periods=self.seasonal_periods)) elif self.initialization_method == 'known': initial_level = float_like(initial_level, 'initial_level') if self.trend: initial_trend = float_like(initial_trend, 'initial_trend') if self.seasonal: initial_seasonal = array_like(initial_seasonal, 'initial_seasonal') if len(initial_seasonal) == self.seasonal_periods - 1: initial_seasonal = np.r_[initial_seasonal, 0 - np.sum(initial_seasonal)] if len(initial_seasonal) != self.seasonal_periods: raise ValueError( 'Invalid length of initial seasonal values. Must be' ' one of s or s-1, where s is the number of seasonal' ' periods.') self._initial_level = initial_level self._initial_trend = initial_trend self._initial_seasonal = initial_seasonal self._initial_state = None # Initialize now if possible (if we have a damped trend, then # initialization will depend on the phi parameter, and so has to be # done at each `update`) methods = ['simple', 'heuristic', 'known'] if not self.damped_trend and self.initialization_method in methods: self._initialize_constant_statespace(initial_level, initial_trend, initial_seasonal) # Save keys for kwarg initialization self._init_keys += ['trend', 'damped_trend', 'seasonal', 'initialization_method', 'initial_level', 'initial_trend', 'initial_seasonal', 'bounds', 'concentrate_scale', 'dates', 'freq', 'missing'] def _get_init_kwds(self): kwds = super()._get_init_kwds() kwds['seasonal'] = self.seasonal_periods return kwds @property def _res_classes(self): return {'fit': (ExponentialSmoothingResults, ExponentialSmoothingResultsWrapper)} def clone(self, endog, exog=None, **kwargs): if exog is not None: raise NotImplementedError( 'ExponentialSmoothing does not support `exog`.') return self._clone_from_init_kwds(endog, **kwargs) @property def state_names(self): state_names = ['error', 'level'] if self.trend: state_names += ['trend'] if self.seasonal: state_names += ['seasonal.%d' % i for i in range(self.seasonal_periods)] return state_names @property def param_names(self): param_names = ['smoothing_level'] if self.trend: param_names += ['smoothing_trend'] if self.seasonal: param_names += ['smoothing_seasonal'] if self.damped_trend: param_names += ['damping_trend'] if not self.concentrate_scale: param_names += ['sigma2'] # Initialization if self.initialization_method == 'estimated': param_names += ['initial_level'] if self.trend: param_names += ['initial_trend'] if self.seasonal: param_names += ['initial_seasonal.%d' % i for i in range(self.seasonal_periods - 1)] return param_names @property def start_params(self): # Make sure starting parameters aren't beyond or right on the bounds bounds = [(x[0] + 1e-3, x[1] - 1e-3) for x in self.bounds] # See Hyndman p.24 start_params = [np.clip(0.1, *bounds[0])] if self.trend: start_params += [np.clip(0.01, *bounds[1])] if self.seasonal: start_params += [np.clip(0.01, *bounds[2])] if self.damped_trend: start_params += [np.clip(0.98, *bounds[3])] if not self.concentrate_scale: start_params += [np.var(self.endog)] # Initialization if self.initialization_method == 'estimated': initial_level, initial_trend, initial_seasonal = ( es_init._initialization_simple( self.endog[:, 0], trend='add' if self.trend else None, seasonal='add' if self.seasonal else None, seasonal_periods=self.seasonal_periods)) start_params += [initial_level] if self.trend: start_params += [initial_trend] if self.seasonal: start_params += initial_seasonal.tolist()[:-1] return np.array(start_params) @property def k_params(self): k_params = ( 1 + int(self.trend) + int(self.seasonal) + int(not self.concentrate_scale) + int(self.damped_trend)) if self.initialization_method == 'estimated': k_params += ( 1 + int(self.trend) + int(self.seasonal) * (self._seasonal_periods - 1)) return k_params def transform_params(self, unconstrained): unconstrained = np.array(unconstrained, ndmin=1) constrained = np.zeros_like(unconstrained) # Alpha in (0, 1) low, high = self.bounds[0] constrained[0] = ( 1 / (1 + np.exp(-unconstrained[0])) * (high - low) + low) i = 1 # Beta in (0, alpha) if self.trend: low, high = self.bounds[1] high = min(high, constrained[0]) constrained[i] = ( 1 / (1 + np.exp(-unconstrained[i])) * (high - low) + low) i += 1 # Gamma in (0, 1 - alpha) if self.seasonal: low, high = self.bounds[2] high = min(high, 1 - constrained[0]) constrained[i] = ( 1 / (1 + np.exp(-unconstrained[i])) * (high - low) + low) i += 1 # Phi in bounds (e.g. default is [0.8, 0.98]) if self.damped_trend: low, high = self.bounds[3] constrained[i] = ( 1 / (1 + np.exp(-unconstrained[i])) * (high - low) + low) i += 1 # sigma^2 positive if not self.concentrate_scale: constrained[i] = unconstrained[i]**2 i += 1 # Initial parameters are as-is if self.initialization_method == 'estimated': constrained[i:] = unconstrained[i:] return constrained def untransform_params(self, constrained): constrained = np.array(constrained, ndmin=1) unconstrained = np.zeros_like(constrained) # Alpha in (0, 1) low, high = self.bounds[0] tmp = (constrained[0] - low) / (high - low) unconstrained[0] = np.log(tmp / (1 - tmp)) i = 1 # Beta in (0, alpha) if self.trend: low, high = self.bounds[1] high = min(high, constrained[0]) tmp = (constrained[i] - low) / (high - low) unconstrained[i] = np.log(tmp / (1 - tmp)) i += 1 # Gamma in (0, 1 - alpha) if self.seasonal: low, high = self.bounds[2] high = min(high, 1 - constrained[0]) tmp = (constrained[i] - low) / (high - low) unconstrained[i] = np.log(tmp / (1 - tmp)) i += 1 # Phi in bounds (e.g. default is [0.8, 0.98]) if self.damped_trend: low, high = self.bounds[3] tmp = (constrained[i] - low) / (high - low) unconstrained[i] = np.log(tmp / (1 - tmp)) i += 1 # sigma^2 positive if not self.concentrate_scale: unconstrained[i] = constrained[i]**0.5 i += 1 # Initial parameters are as-is if self.initialization_method == 'estimated': unconstrained[i:] = constrained[i:] return unconstrained def _initialize_constant_statespace(self, initial_level, initial_trend=None, initial_seasonal=None): # Note: this should be run after `update` has already put any new # parameters into the transition matrix, since it uses the transition # matrix explicitly. # Due to timing differences, the state space representation integrates # the trend into the level in the "predicted_state" (only the # "filtered_state" corresponds to the timing of the exponential # smoothing models) # Initial values are interpreted as "filtered" values constant = np.array([0., initial_level]) if self.trend and initial_trend is not None: constant = np.r_[constant, initial_trend] if self.seasonal and initial_seasonal is not None: constant = np.r_[constant, initial_seasonal] self._initial_state = constant[1:] # Apply the prediction step to get to what we need for our Kalman # filter implementation constant = np.dot(self.ssm['transition'], constant) self.initialization.constant = constant def _initialize_stationary_cov_statespace(self): R = self.ssm['selection'] Q = self.ssm['state_cov'] self.initialization.stationary_cov = R.dot(Q).dot(R.T) def update(self, params, transformed=True, includes_fixed=False, complex_step=False): params = self.handle_params(params, transformed=transformed, includes_fixed=includes_fixed) # State space system matrices self.ssm['selection', 0, 0] = 1 - params[0] self.ssm['selection', 1, 0] = params[0] i = 1 if self.trend: self.ssm['selection', 2, 0] = params[i] i += 1 if self.seasonal: self.ssm['selection', 0, 0] -= params[i] self.ssm['selection', i + 1, 0] = params[i] i += 1 if self.damped_trend: self.ssm['transition', 1:3, 2] = params[i] i += 1 if not self.concentrate_scale: self.ssm['state_cov', 0, 0] = params[i] i += 1 # State initialization if self.initialization_method == 'estimated': initial_level = params[i] i += 1 initial_trend = None initial_seasonal = None if self.trend: initial_trend = params[i] i += 1 if self.seasonal: initial_seasonal = params[i: i + self.seasonal_periods - 1] initial_seasonal = np.r_[initial_seasonal, 0 - np.sum(initial_seasonal)] self._initialize_constant_statespace(initial_level, initial_trend, initial_seasonal) methods = ['simple', 'heuristic', 'known'] if self.damped_trend and self.initialization_method in methods: self._initialize_constant_statespace( self._initial_level, self._initial_trend, self._initial_seasonal) self._initialize_stationary_cov_statespace() def _compute_concentrated_states(self, params, *args, **kwargs): # Apply the usual filter, but keep forecasts kwargs['conserve_memory'] = MEMORY_CONSERVE & ~MEMORY_NO_FORECAST super().loglike(params, *args, **kwargs) # Compute the initial state vector y_tilde = np.array(self.ssm._kalman_filter.forecast_error[0], copy=True) # Need to modify our state space system matrices slightly to get them # back into the form of the innovations framework of # De Livera et al. (2011) T = self['transition', 1:, 1:] R = self['selection', 1:] Z = self['design', :, 1:].copy() i = 1 if self.trend: Z[0, i] = 1. i += 1 if self.seasonal: Z[0, i] = 0. Z[0, -1] = 1. # Now compute the regression components as described in # De Livera et al. (2011), equation (10). D = T - R.dot(Z) w = np.zeros((self.nobs, self.k_states - 1), dtype=D.dtype) w[0] = Z for i in range(self.nobs - 1): w[i + 1] = w[i].dot(D) mod_ols = GLM(y_tilde, w) # If we have seasonal parameters, constrain them to sum to zero # (otherwise the initial level gets confounded with the sum of the # seasonals). if self.seasonal: R = np.zeros_like(Z) R[0, -self.seasonal_periods:] = 1. q = np.zeros((1, 1)) res_ols = mod_ols.fit_constrained((R, q)) else: res_ols = mod_ols.fit() # Separate into individual components initial_level = res_ols.params[0] initial_trend = res_ols.params[1] if self.trend else None initial_seasonal = ( res_ols.params[-self.seasonal_periods:] if self.seasonal else None) return initial_level, initial_trend, initial_seasonal @Appender(MLEModel.loglike.__doc__) def loglike(self, params, *args, **kwargs): if self.initialization_method == 'concentrated': self._initialize_constant_statespace( *self._compute_concentrated_states(params, *args, **kwargs)) llf = self.ssm.loglike() self.ssm.initialization.constant = np.zeros(self.k_states) else: llf = super().loglike(params, *args, **kwargs) return llf @Appender(MLEModel.filter.__doc__) def filter(self, params, cov_type=None, cov_kwds=None, return_ssm=False, results_class=None, results_wrapper_class=None, *args, **kwargs): if self.initialization_method == 'concentrated': self._initialize_constant_statespace( *self._compute_concentrated_states(params, *args, **kwargs)) results = super().filter( params, cov_type=cov_type, cov_kwds=cov_kwds, return_ssm=return_ssm, results_class=results_class, results_wrapper_class=results_wrapper_class, *args, **kwargs) if self.initialization_method == 'concentrated': self.ssm.initialization.constant = np.zeros(self.k_states) return results @Appender(MLEModel.smooth.__doc__) def smooth(self, params, cov_type=None, cov_kwds=None, return_ssm=False, results_class=None, results_wrapper_class=None, *args, **kwargs): if self.initialization_method == 'concentrated': self._initialize_constant_statespace( *self._compute_concentrated_states(params, *args, **kwargs)) results = super().smooth( params, cov_type=cov_type, cov_kwds=cov_kwds, return_ssm=return_ssm, results_class=results_class, results_wrapper_class=results_wrapper_class, *args, **kwargs) if self.initialization_method == 'concentrated': self.ssm.initialization.constant = np.zeros(self.k_states) return results class ExponentialSmoothingResults(MLEResults): """ Results from fitting a linear exponential smoothing model """ def __init__(self, model, params, filter_results, cov_type=None, **kwargs): super().__init__(model, params, filter_results, cov_type, **kwargs) # Save the states self.initial_state = model._initial_state if isinstance(self.data, PandasData): index = self.data.row_labels self.initial_state = pd.DataFrame( [model._initial_state], columns=model.state_names[1:]) if model._index_dates and model._index_freq is not None: self.initial_state.index = index.shift(-1)[:1] @Appender(MLEResults.summary.__doc__) def summary(self, alpha=.05, start=None): specification = ['A'] if self.model.trend and self.model.damped_trend: specification.append('Ad') elif self.model.trend: specification.append('A') else: specification.append('N') if self.model.seasonal: specification.append('A') else: specification.append('N') model_name = 'ETS(' + ', '.join(specification) + ')' summary = super(ExponentialSmoothingResults, self).summary( alpha=alpha, start=start, title='Exponential Smoothing Results', model_name=model_name) if self.model.initialization_method != 'estimated': params = np.array(self.initial_state) if params.ndim > 1: params = params[0] names = self.model.state_names param_header = ['initialization method: %s' % self.model.initialization_method] params_stubs = names params_data = [[forg(params[i], prec=4)] for i in range(len(params))] initial_state_table = SimpleTable(params_data, param_header, params_stubs, txt_fmt=fmt_params) summary.tables.insert(-1, initial_state_table) return summary class ExponentialSmoothingResultsWrapper(MLEResultsWrapper): _attrs = {} _wrap_attrs = wrap.union_dicts(MLEResultsWrapper._wrap_attrs, _attrs) _methods = {} _wrap_methods = wrap.union_dicts(MLEResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(ExponentialSmoothingResultsWrapper, # noqa:E305 ExponentialSmoothingResults) statsmodels-0.12.2/statsmodels/tsa/statespace/initialization.py000066400000000000000000000645201400612667500250420ustar00rootroot00000000000000""" State Space Representation - Initialization Author: Chad Fulton License: Simplified-BSD """ import warnings import numpy as np from . import tools class Initialization(object): r""" State space initialization Parameters ---------- k_states : int exact_diffuse_initialization : bool, optional Whether or not to use exact diffuse initialization; only has an effect if some states are initialized as diffuse. Default is True. approximate_diffuse_variance : float, optional If using approximate diffuse initialization, the initial variance used. Default is 1e6. Notes ----- As developed in Durbin and Koopman (2012), the state space recursions must be initialized for the first time period. The general form of this initialization is: .. math:: \alpha_1 & = a + A \delta + R_0 \eta_0 \\ \delta & \sim N(0, \kappa I), \kappa \to \infty \\ \eta_0 & \sim N(0, Q_0) Thus the state vector can be initialized with a known constant part (elements of :math:`a`), with part modeled as a diffuse initial distribution (as a part of :math:`\delta`), and with a part modeled as a known (proper) initial distribution (as a part of :math:`\eta_0`). There are two important restrictions: 1. An element of the state vector initialized as diffuse cannot be also modeled with a stationary component. In the `validate` method, violations of this cause an exception to be raised. 2. If an element of the state vector is initialized with both a known constant part and with a diffuse initial distribution, the effect of the diffuse initialization will essentially ignore the given known constant value. In the `validate` method, violations of this cause a warning to be given, since it is not technically invalid but may indicate user error. The :math:`\eta_0` compoenent is also referred to as the stationary part because it is often set to the unconditional distribution of a stationary process. Initialization is specified for blocks (consecutive only, for now) of the state vector, with the entire state vector and individual elements as special cases. Denote the block in question as :math:`\alpha_1^{(i)}`. It can be initialized in the following ways: - 'known' - 'diffuse' or 'exact_diffuse' or 'approximate_diffuse' - 'stationary' - 'mixed' In the first three cases, the block's initialization is specified as an instance of the `Initialization` class, with the `initialization_type` attribute set to one of those three string values. In the 'mixed' cases, the initialization is also an instance of the `Initialization` class, but it will itself contain sub-blocks. Details of each type follow. Regardless of the type, for each block, the following must be defined: the `constant` array, an array `diffuse` with indices corresponding to diffuse elements, an array `stationary` with indices corresponding to stationary elements, and `stationary_cov`, a matrix with order equal to the number of stationary elements in the block. **Known** If a block is initialized as known, then a known (possibly degenerate) distribution is used; in particular, the block of states is understood to be distributed :math:`\alpha_1^{(i)} \sim N(a^{(i)}, Q_0^{(i)})`. Here, is is possible to set :math:`a^{(i)} = 0`, and it is also possible that :math:`Q_0^{(i)}` is only positive-semidefinite; i.e. :math:`\alpha_1^{(i)}` may be degenerate. One particular example is that if the entire block's initial values are known, then :math:`R_0^{(i)} = 0`, and so `Var(\alpha_1^{(i)}) = 0`. Here, `constant` must be provided (although it can be zeros), and `stationary_cov` is optional (by default it is a matrix of zeros). **Diffuse** If a block is initialized as diffuse, then set :math:`\alpha_1^{(i)} \sim N(a^{(i)}, \kappa^{(i)} I)`. If the block is initialized using the exact diffuse initialization procedure, then it is understood that :math:`\kappa^{(i)} \to \infty`. If the block is initialized using the approximate diffuse initialization procedure, then `\kappa^{(i)}` is set to some large value rather than driven to infinity. In the approximate diffuse initialization case, it is possible, although unlikely, that a known constant value may have some effect on initialization if :math:`\kappa^{(i)}` is not set large enough. Here, `constant` may be provided, and `approximate_diffuse_variance` may be provided. **Stationary** If a block is initialized as stationary, then the block of states is understood to have the distribution :math:`\alpha_1^{(i)} \sim N(a^{(i)}, Q_0^{(i)})`. :math:`a^{(i)}` is the unconditional mean of the block, computed as :math:`(I - T^{(i)})^{-1} c_t`. :math:`Q_0^{(i)}` is the unconditional variance of the block, computed as the solution to the discrete Lyapunov equation: .. math:: T^{(i)} Q_0^{(i)} T^{(i)} + (R Q R')^{(i)} = Q_0^{(i)} :math:`T^{(i)}` and :math:`(R Q R')^{(i)}` are the submatrices of the corresponding state space system matrices corresponding to the given block of states. Here, no values can be provided. **Mixed** In this case, the block can be further broken down into sub-blocks. Usually, only the top-level `Initialization` instance will be of 'mixed' type, and in many cases, even the top-level instance will be purely 'known', 'diffuse', or 'stationary'. For a block of type mixed, suppose that it has `J` sub-blocks, :math:`\alpha_1^{(i,j)}`. Then :math:`\alpha_1^{(i)} = a^{(i)} + A^{(i)} \delta + R_0^{(i)} \eta_0^{(i)}`. Examples -------- Basic examples have one specification for all of the states: >>> Initialization(k_states=2, 'known', constant=[0, 1]) >>> Initialization(k_states=2, 'known', stationary_cov=np.eye(2)) >>> Initialization(k_states=2, 'known', constant=[0, 1], stationary_cov=np.eye(2)) >>> Initialization(k_states=2, 'diffuse') >>> Initialization(k_states=2, 'approximate_diffuse', approximate_diffuse_variance=1e6) >>> Initialization(k_states=2, 'stationary') More complex examples initialize different blocks of states separately >>> init = Initialization(k_states=3) >>> init.set((0, 1), 'known', constant=[0, 1]) >>> init.set((0, 1), 'known', stationary_cov=np.eye(2)) >>> init.set((0, 1), 'known', constant=[0, 1], stationary_cov=np.eye(2)) >>> init.set((0, 1), 'diffuse') >>> init.set((0, 1), 'approximate_diffuse', approximate_diffuse_variance=1e6) >>> init.set((0, 1), 'stationary') A still more complex example initializes a block using a previously created `Initialization` object: >>> init1 = Initialization(k_states=2, 'known', constant=[0, 1]) >>> init2 = Initialization(k_states=3) >>> init2.set((1, 2), init1) """ def __init__(self, k_states, initialization_type=None, initialization_classes=None, approximate_diffuse_variance=1e6, constant=None, stationary_cov=None): # Parameters self.k_states = k_states # Attributes handling blocks of states with different initializations self._states = tuple(np.arange(k_states)) self._initialization = np.array([None] * k_states) self.blocks = {} # Attributes handling initialization of the entire set of states # `constant` is a vector of constant values (i.e. it is the vector # a from DK) self.initialization_type = None self.constant = np.zeros(self.k_states) self.stationary_cov = np.zeros((self.k_states, self.k_states)) self.approximate_diffuse_variance = approximate_diffuse_variance # Cython interface attributes self.prefix_initialization_map = ( initialization_classes if initialization_classes is not None else tools.prefix_initialization_map.copy()) self._representations = {} self._initializations = {} # If given a global initialization, use it now if initialization_type is not None: self.set(None, initialization_type, constant=constant, stationary_cov=stationary_cov) def __setitem__(self, index, initialization_type): self.set(index, initialization_type) def _initialize_initialization(self, prefix): dtype = tools.prefix_dtype_map[prefix] # If the dtype-specific representation matrices do not exist, create # them if prefix not in self._representations: # Copy the statespace representation matrices self._representations[prefix] = { 'constant': self.constant.astype(dtype), 'stationary_cov': np.asfortranarray( self.stationary_cov.astype(dtype)), } # If they do exist, update them else: self._representations[prefix]['constant'][:] = ( self.constant.astype(dtype)[:]) self._representations[prefix]['stationary_cov'][:] = ( self.stationary_cov.astype(dtype)[:]) # Create if necessary if prefix not in self._initializations: # Setup the base statespace object cls = self.prefix_initialization_map[prefix] self._initializations[prefix] = cls( self.k_states, self._representations[prefix]['constant'], self._representations[prefix]['stationary_cov'], self.approximate_diffuse_variance) # Otherwise update else: self._initializations[prefix].approximate_diffuse_variance = ( self.approximate_diffuse_variance) return prefix, dtype def set(self, index, initialization_type, constant=None, stationary_cov=None, approximate_diffuse_variance=None): r""" Set initialization for states, either globally or for a block Parameters ---------- index : tuple or int or None Arguments used to create a `slice` of states. Can be a tuple with `(start, stop)` (note that for `slice`, stop is not inclusive), or an integer (to select a specific state), or None (to select all the states). initialization_type : str The type of initialization used for the states selected by `index`. Must be one of 'known', 'diffuse', 'approximate_diffuse', or 'stationary'. constant : array_like, optional A vector of constant values, denoted :math:`a`. Most often used with 'known' initialization, but may also be used with 'approximate_diffuse' (although it will then likely have little effect). stationary_cov : array_like, optional The covariance matrix of the stationary part, denoted :math:`Q_0`. Only used with 'known' initialization. approximate_diffuse_variance : float, optional The approximate diffuse variance, denoted :math:`\kappa`. Only applicable with 'approximate_diffuse' initialization. Default is 1e6. """ # Construct the index, using a slice object as an intermediate step # to enforce regularity if not isinstance(index, slice): if isinstance(index, (int, np.integer)): index = int(index) if index < 0 or index >= self.k_states: raise ValueError('Invalid index.') index = (index, index + 1) elif index is None: index = (index,) elif not isinstance(index, tuple): raise ValueError('Invalid index.') if len(index) > 2: raise ValueError('Cannot include a slice step in `index`.') index = slice(*index) index = self._states[index] # Compatibility with zero-length slices (can make it easier to set up # initialization without lots of if statements) if len(index) == 0: return # Make sure that we are not setting a block when global initialization # was previously set if self.initialization_type is not None and not index == self._states: raise ValueError('Cannot set initialization for the block of' ' states %s because initialization was' ' previously performed globally. You must either' ' re-initialize globally or' ' else unset the global initialization before' ' initializing specific blocks of states.' % str(index)) # Make sure that we are not setting a block that *overlaps* with # another block (although we are free to *replace* an entire block) uninitialized = np.equal(self._initialization[index, ], None) if index not in self.blocks and not np.all(uninitialized): raise ValueError('Cannot set initialization for the state(s) %s' ' because they are a subset of a previously' ' initialized block. You must either' ' re-initialize the entire block as a whole or' ' else unset the entire block before' ' re-initializing the subset.' % str(np.array(index)[~uninitialized])) # If setting for all states, set this object's initialization # attributes k_states = len(index) if k_states == self.k_states: self.initialization_type = initialization_type # General validation if (approximate_diffuse_variance is not None and not initialization_type == 'approximate_diffuse'): raise ValueError('`approximate_diffuse_variance` can only be' ' provided when using approximate diffuse' ' initialization.') if (stationary_cov is not None and not initialization_type == 'known'): raise ValueError('`stationary_cov` can only be provided when' ' using known initialization.') # Specific initialization handling if initialization_type == 'known': # Make sure we were given some known initialization if constant is None and stationary_cov is None: raise ValueError('Must specify either the constant vector' ' or the stationary covariance matrix' ' (or both) if using known' ' initialization.') # Defaults if stationary_cov is None: stationary_cov = np.zeros((k_states, k_states)) else: stationary_cov = np.array(stationary_cov) # Validate if not stationary_cov.shape == (k_states, k_states): raise ValueError('Invalid stationary covariance matrix;' ' given shape %s but require shape %s.' % (str(stationary_cov.shape), str((k_states, k_states)))) # Set values self.stationary_cov = stationary_cov elif initialization_type == 'diffuse': if constant is not None: warnings.warn('Constant values provided, but they are' ' ignored in exact diffuse initialization.') elif initialization_type == 'approximate_diffuse': if approximate_diffuse_variance is not None: self.approximate_diffuse_variance = ( approximate_diffuse_variance) elif initialization_type == 'stationary': if constant is not None: raise ValueError('Constant values cannot be provided for' ' stationary initialization.') else: raise ValueError('Invalid initialization type.') # Handle constant if constant is None: constant = np.zeros(k_states) else: constant = np.array(constant) if not constant.shape == (k_states,): raise ValueError('Invalid constant vector; given shape %s' ' but require shape %s.' % (str(constant.shape), str((k_states,)))) self.constant = constant # Otherwise, if setting a sub-block, construct the new initialization # object else: if isinstance(initialization_type, Initialization): init = initialization_type else: if approximate_diffuse_variance is None: approximate_diffuse_variance = ( self.approximate_diffuse_variance) init = Initialization( k_states, initialization_type, constant=constant, stationary_cov=stationary_cov, approximate_diffuse_variance=approximate_diffuse_variance) self.blocks[index] = init for i in index: self._initialization[i] = index def unset(self, index): """ Unset initialization for states, either globally or for a block Parameters ---------- index : tuple or int or None Arguments used to create a `slice` of states. Can be a tuple with `(start, stop)` (note that for `slice`, stop is not inclusive), or an integer (to select a specific state), or None (to select all the states). Notes ----- Note that this specifically unsets initializations previously created using `set` with this same index. Thus you cannot use `index=None` to unset all initializations, but only to unset a previously set global initialization. To unset all initializations (including both global and block level), use the `clear` method. """ if isinstance(index, (int, np.integer)): index = int(index) if index < 0 or index > self.k_states: raise ValueError('Invalid index.') index = (index, index + 1) elif index is None: index = (index,) elif not isinstance(index, tuple): raise ValueError('Invalid index.') if len(index) > 2: raise ValueError('Cannot include a slice step in `index`.') index = self._states[slice(*index)] # Compatibility with zero-length slices (can make it easier to set up # initialization without lots of if statements) if len(index) == 0: return # Unset the values k_states = len(index) if k_states == self.k_states and self.initialization_type is not None: self.initialization_type = None self.constant[:] = 0 self.stationary_cov[:] = 0 elif index in self.blocks: for i in index: self._initialization[i] = None del self.blocks[index] else: raise ValueError('The given index does not correspond to a' ' previously initialized block.') def clear(self): """ Clear all previously set initializations, either global or block level """ # Clear initializations for i in self._states: self._initialization[i] = None # Delete block initializations keys = list(self.blocks.keys()) for key in keys: del self.blocks[key] # Clear global attributes self.initialization_type = None self.constant[:] = 0 self.stationary_cov[:] = 0 @property def initialized(self): return not (self.initialization_type is None and np.any(np.equal(self._initialization, None))) def __call__(self, index=None, model=None, initial_state_mean=None, initial_diffuse_state_cov=None, initial_stationary_state_cov=None, complex_step=False): r""" Construct initialization representation Parameters ---------- model : Representation, optional A state space model representation object, optional if 'stationary' initialization is used and ignored otherwise. See notes for details in the stationary initialization case. model_index : ndarray, optional The base index of the block in the model. initial_state_mean : ndarray, optional An array (or more usually view) in which to place the initial state mean. initial_diffuse_state_cov : ndarray, optional An array (or more usually view) in which to place the diffuse component of initial state covariance matrix. initial_stationary_state_cov : ndarray, optional An array (or more usually view) in which to place the stationary component of initial state covariance matrix. Returns ------- initial_state_mean : ndarray Initial state mean, :math:`a_1^{(0)} = a` initial_diffuse_state_cov : ndarray Diffuse component of initial state covariance matrix, :math:`P_\infty = A A'` initial_stationary_state_cov : ndarray Stationary component of initial state covariance matrix, :math:`P_* = R_0 Q_0 R_0'` Notes ----- If stationary initialization is used either globally or for any block of states, then either `model` or all of `state_intercept`, `transition`, `selection`, and `state_cov` must be provided. """ # Check that all states are initialized somehow if (self.initialization_type is None and np.any(np.equal(self._initialization, None))): raise ValueError('Cannot construct initialization representation' ' because not all states have been initialized.') # Setup indexes if index is None: index = self._states ix1 = np.s_[:] ix2 = np.s_[:, :] else: ix1 = np.s_[index[0]:index[-1] + 1] ix2 = np.ix_(index, index) # Retrieve state_intercept, etc. if `model` was given if model is not None: state_intercept = model['state_intercept', ix1, 0] transition = model[('transition',) + ix2 + (0,)] selection = model['selection', ix1, :, 0] state_cov = model['state_cov', :, :, 0] selected_state_cov = np.dot(selection, state_cov).dot(selection.T) # Create output arrays if not given if initial_state_mean is None: initial_state_mean = np.zeros(self.k_states) cov_shape = (self.k_states, self.k_states) if initial_diffuse_state_cov is None: initial_diffuse_state_cov = np.zeros(cov_shape) if initial_stationary_state_cov is None: initial_stationary_state_cov = np.zeros(cov_shape) # If using global initialization, compute the actual elements and # return them if self.initialization_type is not None: eye = np.eye(self.k_states) zeros = np.zeros((self.k_states, self.k_states)) # General validation if self.initialization_type == 'stationary' and model is None: raise ValueError('Stationary initialization requires passing' ' either the `model` argument or all of the' ' individual transition equation arguments.') if self.initialization_type == 'stationary': # TODO performance eigvals = np.linalg.eigvals(transition) threshold = 1. - 1e-10 if not np.max(np.abs(eigvals)) < threshold: raise ValueError('Transition equation is not stationary,' ' and so stationary initialization cannot' ' be used.') # Set the initial state mean if self.initialization_type == 'stationary': # TODO performance initial_state_mean[ix1] = np.linalg.solve(eye - transition, state_intercept) else: initial_state_mean[ix1] = self.constant # Set the diffuse component if self.initialization_type == 'diffuse': initial_diffuse_state_cov[ix2] = np.eye(self.k_states) else: initial_diffuse_state_cov[ix2] = zeros # Set the stationary component if self.initialization_type == 'known': initial_stationary_state_cov[ix2] = self.stationary_cov elif self.initialization_type == 'diffuse': initial_stationary_state_cov[ix2] = zeros elif self.initialization_type == 'approximate_diffuse': initial_stationary_state_cov[ix2] = ( eye * self.approximate_diffuse_variance) elif self.initialization_type == 'stationary': # TODO performance initial_stationary_state_cov[ix2] = ( tools.solve_discrete_lyapunov(transition, selected_state_cov, complex_step=complex_step)) else: # Otherwise, if using blocks, recursively initialize # them (values will be set in-place) for block_index, init in self.blocks.items(): init(index=tuple(np.array(index)[block_index, ]), model=model, initial_state_mean=initial_state_mean, initial_diffuse_state_cov=initial_diffuse_state_cov, initial_stationary_state_cov=initial_stationary_state_cov) return (initial_state_mean, initial_diffuse_state_cov, initial_stationary_state_cov) statsmodels-0.12.2/statsmodels/tsa/statespace/kalman_filter.py000066400000000000000000002765711400612667500246360ustar00rootroot00000000000000""" State Space Representation and Kalman Filter Author: Chad Fulton License: Simplified-BSD """ import contextlib from warnings import warn import numpy as np from .representation import OptionWrapper, Representation, FrozenRepresentation from .tools import reorder_missing_matrix, reorder_missing_vector from . import tools from statsmodels.tools.sm_exceptions import ValueWarning # Define constants FILTER_CONVENTIONAL = 0x01 # Durbin and Koopman (2012), Chapter 4 FILTER_EXACT_INITIAL = 0x02 # ibid., Chapter 5.6 FILTER_AUGMENTED = 0x04 # ibid., Chapter 5.7 FILTER_SQUARE_ROOT = 0x08 # ibid., Chapter 6.3 FILTER_UNIVARIATE = 0x10 # ibid., Chapter 6.4 FILTER_COLLAPSED = 0x20 # ibid., Chapter 6.5 FILTER_EXTENDED = 0x40 # ibid., Chapter 10.2 FILTER_UNSCENTED = 0x80 # ibid., Chapter 10.3 FILTER_CONCENTRATED = 0x100 # Harvey (1989), Chapter 3.4 FILTER_CHANDRASEKHAR = 0x200 # Herbst (2015) INVERT_UNIVARIATE = 0x01 SOLVE_LU = 0x02 INVERT_LU = 0x04 SOLVE_CHOLESKY = 0x08 INVERT_CHOLESKY = 0x10 STABILITY_FORCE_SYMMETRY = 0x01 MEMORY_STORE_ALL = 0 MEMORY_NO_FORECAST_MEAN = 0x01 MEMORY_NO_FORECAST_COV = 0x02 MEMORY_NO_FORECAST = MEMORY_NO_FORECAST_MEAN | MEMORY_NO_FORECAST_COV MEMORY_NO_PREDICTED_MEAN = 0x04 MEMORY_NO_PREDICTED_COV = 0x08 MEMORY_NO_PREDICTED = MEMORY_NO_PREDICTED_MEAN | MEMORY_NO_PREDICTED_COV MEMORY_NO_FILTERED_MEAN = 0x10 MEMORY_NO_FILTERED_COV = 0x20 MEMORY_NO_FILTERED = MEMORY_NO_FILTERED_MEAN | MEMORY_NO_FILTERED_COV MEMORY_NO_LIKELIHOOD = 0x40 MEMORY_NO_GAIN = 0x80 MEMORY_NO_SMOOTHING = 0x100 MEMORY_NO_STD_FORECAST = 0x200 MEMORY_CONSERVE = ( MEMORY_NO_FORECAST_COV | MEMORY_NO_PREDICTED | MEMORY_NO_FILTERED | MEMORY_NO_LIKELIHOOD | MEMORY_NO_GAIN | MEMORY_NO_SMOOTHING ) TIMING_INIT_PREDICTED = 0 TIMING_INIT_FILTERED = 1 class KalmanFilter(Representation): r""" State space representation of a time series process, with Kalman filter Parameters ---------- k_endog : {array_like, int} The observed time-series process :math:`y` if array like or the number of variables in the process if an integer. k_states : int The dimension of the unobserved state process. k_posdef : int, optional The dimension of a guaranteed positive definite covariance matrix describing the shocks in the transition equation. Must be less than or equal to `k_states`. Default is `k_states`. loglikelihood_burn : int, optional The number of initial periods during which the loglikelihood is not recorded. Default is 0. tolerance : float, optional The tolerance at which the Kalman filter determines convergence to steady-state. Default is 1e-19. results_class : class, optional Default results class to use to save filtering output. Default is `FilterResults`. If specified, class must extend from `FilterResults`. **kwargs Keyword arguments may be used to provide values for the filter, inversion, and stability methods. See `set_filter_method`, `set_inversion_method`, and `set_stability_method`. Keyword arguments may be used to provide default values for state space matrices. See `Representation` for more details. See Also -------- FilterResults statsmodels.tsa.statespace.representation.Representation Notes ----- There are several types of options available for controlling the Kalman filter operation. All options are internally held as bitmasks, but can be manipulated by setting class attributes, which act like boolean flags. For more information, see the `set_*` class method documentation. The options are: filter_method The filtering method controls aspects of which Kalman filtering approach will be used. inversion_method The Kalman filter may contain one matrix inversion: that of the forecast error covariance matrix. The inversion method controls how and if that inverse is performed. stability_method The Kalman filter is a recursive algorithm that may in some cases suffer issues with numerical stability. The stability method controls what, if any, measures are taken to promote stability. conserve_memory By default, the Kalman filter computes a number of intermediate matrices at each iteration. The memory conservation options control which of those matrices are stored. filter_timing By default, the Kalman filter follows Durbin and Koopman, 2012, in initializing the filter with predicted values. Kim and Nelson, 1999, instead initialize the filter with filtered values, which is essentially just a different timing convention. The `filter_method` and `inversion_method` options intentionally allow the possibility that multiple methods will be indicated. In the case that multiple methods are selected, the underlying Kalman filter will attempt to select the optional method given the input data. For example, it may be that INVERT_UNIVARIATE and SOLVE_CHOLESKY are indicated (this is in fact the default case). In this case, if the endogenous vector is 1-dimensional (`k_endog` = 1), then INVERT_UNIVARIATE is used and inversion reduces to simple division, and if it has a larger dimension, the Cholesky decomposition along with linear solving (rather than explicit matrix inversion) is used. If only SOLVE_CHOLESKY had been set, then the Cholesky decomposition method would *always* be used, even in the case of 1-dimensional data. """ filter_methods = [ 'filter_conventional', 'filter_exact_initial', 'filter_augmented', 'filter_square_root', 'filter_univariate', 'filter_collapsed', 'filter_extended', 'filter_unscented', 'filter_concentrated', 'filter_chandrasekhar' ] filter_conventional = OptionWrapper('filter_method', FILTER_CONVENTIONAL) """ (bool) Flag for conventional Kalman filtering. """ filter_exact_initial = OptionWrapper('filter_method', FILTER_EXACT_INITIAL) """ (bool) Flag for exact initial Kalman filtering. Not implemented. """ filter_augmented = OptionWrapper('filter_method', FILTER_AUGMENTED) """ (bool) Flag for augmented Kalman filtering. Not implemented. """ filter_square_root = OptionWrapper('filter_method', FILTER_SQUARE_ROOT) """ (bool) Flag for square-root Kalman filtering. Not implemented. """ filter_univariate = OptionWrapper('filter_method', FILTER_UNIVARIATE) """ (bool) Flag for univariate filtering of multivariate observation vector. """ filter_collapsed = OptionWrapper('filter_method', FILTER_COLLAPSED) """ (bool) Flag for Kalman filtering with collapsed observation vector. """ filter_extended = OptionWrapper('filter_method', FILTER_EXTENDED) """ (bool) Flag for extended Kalman filtering. Not implemented. """ filter_unscented = OptionWrapper('filter_method', FILTER_UNSCENTED) """ (bool) Flag for unscented Kalman filtering. Not implemented. """ filter_concentrated = OptionWrapper('filter_method', FILTER_CONCENTRATED) """ (bool) Flag for Kalman filtering with concentrated log-likelihood. """ filter_chandrasekhar = OptionWrapper('filter_method', FILTER_CHANDRASEKHAR) """ (bool) Flag for filtering with Chandrasekhar recursions. """ inversion_methods = [ 'invert_univariate', 'solve_lu', 'invert_lu', 'solve_cholesky', 'invert_cholesky' ] invert_univariate = OptionWrapper('inversion_method', INVERT_UNIVARIATE) """ (bool) Flag for univariate inversion method (recommended). """ solve_lu = OptionWrapper('inversion_method', SOLVE_LU) """ (bool) Flag for LU and linear solver inversion method. """ invert_lu = OptionWrapper('inversion_method', INVERT_LU) """ (bool) Flag for LU inversion method. """ solve_cholesky = OptionWrapper('inversion_method', SOLVE_CHOLESKY) """ (bool) Flag for Cholesky and linear solver inversion method (recommended). """ invert_cholesky = OptionWrapper('inversion_method', INVERT_CHOLESKY) """ (bool) Flag for Cholesky inversion method. """ stability_methods = ['stability_force_symmetry'] stability_force_symmetry = ( OptionWrapper('stability_method', STABILITY_FORCE_SYMMETRY) ) """ (bool) Flag for enforcing covariance matrix symmetry """ memory_options = [ 'memory_store_all', 'memory_no_forecast_mean', 'memory_no_forecast_cov', 'memory_no_forecast', 'memory_no_predicted_mean', 'memory_no_predicted_cov', 'memory_no_predicted', 'memory_no_filtered_mean', 'memory_no_filtered_cov', 'memory_no_filtered', 'memory_no_likelihood', 'memory_no_gain', 'memory_no_smoothing', 'memory_no_std_forecast', 'memory_conserve' ] memory_store_all = OptionWrapper('conserve_memory', MEMORY_STORE_ALL) """ (bool) Flag for storing all intermediate results in memory (default). """ memory_no_forecast_mean = OptionWrapper( 'conserve_memory', MEMORY_NO_FORECAST_MEAN) """ (bool) Flag to prevent storing forecasts and forecast errors. """ memory_no_forecast_cov = OptionWrapper( 'conserve_memory', MEMORY_NO_FORECAST_COV) """ (bool) Flag to prevent storing forecast error covariance matrices. """ @property def memory_no_forecast(self): """ (bool) Flag to prevent storing all forecast-related output. """ return self.memory_no_forecast_mean or self.memory_no_forecast_cov @memory_no_forecast.setter def memory_no_forecast(self, value): if bool(value): self.memory_no_forecast_mean = True self.memory_no_forecast_cov = True else: self.memory_no_forecast_mean = False self.memory_no_forecast_cov = False memory_no_predicted_mean = OptionWrapper( 'conserve_memory', MEMORY_NO_PREDICTED_MEAN) """ (bool) Flag to prevent storing predicted states. """ memory_no_predicted_cov = OptionWrapper( 'conserve_memory', MEMORY_NO_PREDICTED_COV) """ (bool) Flag to prevent storing predicted state covariance matrices. """ @property def memory_no_predicted(self): """ (bool) Flag to prevent storing predicted state and covariance matrices. """ return self.memory_no_predicted_mean or self.memory_no_predicted_cov @memory_no_predicted.setter def memory_no_predicted(self, value): if bool(value): self.memory_no_predicted_mean = True self.memory_no_predicted_cov = True else: self.memory_no_predicted_mean = False self.memory_no_predicted_cov = False memory_no_filtered_mean = OptionWrapper( 'conserve_memory', MEMORY_NO_FILTERED_MEAN) """ (bool) Flag to prevent storing filtered states. """ memory_no_filtered_cov = OptionWrapper( 'conserve_memory', MEMORY_NO_FILTERED_COV) """ (bool) Flag to prevent storing filtered state covariance matrices. """ @property def memory_no_filtered(self): """ (bool) Flag to prevent storing filtered state and covariance matrices. """ return self.memory_no_filtered_mean or self.memory_no_filtered_cov @memory_no_filtered.setter def memory_no_filtered(self, value): if bool(value): self.memory_no_filtered_mean = True self.memory_no_filtered_cov = True else: self.memory_no_filtered_mean = False self.memory_no_filtered_cov = False memory_no_likelihood = ( OptionWrapper('conserve_memory', MEMORY_NO_LIKELIHOOD) ) """ (bool) Flag to prevent storing likelihood values for each observation. """ memory_no_gain = OptionWrapper('conserve_memory', MEMORY_NO_GAIN) """ (bool) Flag to prevent storing the Kalman gain matrices. """ memory_no_smoothing = OptionWrapper('conserve_memory', MEMORY_NO_SMOOTHING) """ (bool) Flag to prevent storing likelihood values for each observation. """ memory_no_std_forecast = ( OptionWrapper('conserve_memory', MEMORY_NO_STD_FORECAST)) """ (bool) Flag to prevent storing standardized forecast errors. """ memory_conserve = OptionWrapper('conserve_memory', MEMORY_CONSERVE) """ (bool) Flag to conserve the maximum amount of memory. """ timing_options = [ 'timing_init_predicted', 'timing_init_filtered' ] timing_init_predicted = OptionWrapper('filter_timing', TIMING_INIT_PREDICTED) """ (bool) Flag for the default timing convention (Durbin and Koopman, 2012). """ timing_init_filtered = OptionWrapper('filter_timing', TIMING_INIT_FILTERED) """ (bool) Flag for the alternate timing convention (Kim and Nelson, 2012). """ # Default filter options filter_method = FILTER_CONVENTIONAL """ (int) Filtering method bitmask. """ inversion_method = INVERT_UNIVARIATE | SOLVE_CHOLESKY """ (int) Inversion method bitmask. """ stability_method = STABILITY_FORCE_SYMMETRY """ (int) Stability method bitmask. """ conserve_memory = MEMORY_STORE_ALL """ (int) Memory conservation bitmask. """ filter_timing = TIMING_INIT_PREDICTED """ (int) Filter timing. """ def __init__(self, k_endog, k_states, k_posdef=None, loglikelihood_burn=0, tolerance=1e-19, results_class=None, kalman_filter_classes=None, **kwargs): super(KalmanFilter, self).__init__( k_endog, k_states, k_posdef, **kwargs ) # Setup the underlying Kalman filter storage self._kalman_filters = {} # Filter options self.loglikelihood_burn = loglikelihood_burn self.results_class = ( results_class if results_class is not None else FilterResults ) # Options self.prefix_kalman_filter_map = ( kalman_filter_classes if kalman_filter_classes is not None else tools.prefix_kalman_filter_map.copy()) self.set_filter_method(**kwargs) self.set_inversion_method(**kwargs) self.set_stability_method(**kwargs) self.set_conserve_memory(**kwargs) self.set_filter_timing(**kwargs) self.tolerance = tolerance # Internal flags # The _scale internal flag is used because we may want to # use a fixed scale, in which case we want the flag to the Cython # Kalman filter to indicate that the scale should not be concentrated # out, so that self.filter_concentrated = False, but we still want to # alert the results object that we are viewing the model as one in # which the scale had been concentrated out for e.g. degree of freedom # computations. # This value should always be None, except within the fixed_scale # context, and should not be modified by users or anywhere else. self._scale = None def _clone_kwargs(self, endog, **kwargs): # See Representation._clone_kwargs for docstring kwargs = super(KalmanFilter, self)._clone_kwargs(endog, **kwargs) # Get defaults for options kwargs.setdefault('filter_method', self.filter_method) kwargs.setdefault('inversion_method', self.inversion_method) kwargs.setdefault('stability_method', self.stability_method) kwargs.setdefault('conserve_memory', self.conserve_memory) kwargs.setdefault('filter_timing', self.filter_timing) kwargs.setdefault('tolerance', self.tolerance) kwargs.setdefault('loglikelihood_burn', self.loglikelihood_burn) return kwargs @property def _kalman_filter(self): prefix = self.prefix if prefix in self._kalman_filters: return self._kalman_filters[prefix] return None def _initialize_filter(self, filter_method=None, inversion_method=None, stability_method=None, conserve_memory=None, tolerance=None, filter_timing=None, loglikelihood_burn=None): if filter_method is None: filter_method = self.filter_method if inversion_method is None: inversion_method = self.inversion_method if stability_method is None: stability_method = self.stability_method if conserve_memory is None: conserve_memory = self.conserve_memory if loglikelihood_burn is None: loglikelihood_burn = self.loglikelihood_burn if filter_timing is None: filter_timing = self.filter_timing if tolerance is None: tolerance = self.tolerance # Make sure we have endog if self.endog is None: raise RuntimeError('Must bind a dataset to the model before' ' filtering or smoothing.') # Initialize the representation matrices prefix, dtype, create_statespace = self._initialize_representation() # Determine if we need to (re-)create the filter # (definitely need to recreate if we recreated the _statespace object) create_filter = create_statespace or prefix not in self._kalman_filters if not create_filter: kalman_filter = self._kalman_filters[prefix] create_filter = ( not kalman_filter.conserve_memory == conserve_memory or not kalman_filter.loglikelihood_burn == loglikelihood_burn ) # If the dtype-specific _kalman_filter does not exist (or if we need # to re-create it), create it if create_filter: if prefix in self._kalman_filters: # Delete the old filter del self._kalman_filters[prefix] # Setup the filter cls = self.prefix_kalman_filter_map[prefix] self._kalman_filters[prefix] = cls( self._statespaces[prefix], filter_method, inversion_method, stability_method, conserve_memory, filter_timing, tolerance, loglikelihood_burn ) # Otherwise, update the filter parameters else: kalman_filter = self._kalman_filters[prefix] kalman_filter.set_filter_method(filter_method, False) kalman_filter.inversion_method = inversion_method kalman_filter.stability_method = stability_method kalman_filter.filter_timing = filter_timing kalman_filter.tolerance = tolerance # conserve_memory and loglikelihood_burn changes always lead to # re-created filters return prefix, dtype, create_filter, create_statespace def set_filter_method(self, filter_method=None, **kwargs): r""" Set the filtering method The filtering method controls aspects of which Kalman filtering approach will be used. Parameters ---------- filter_method : int, optional Bitmask value to set the filter method to. See notes for details. **kwargs Keyword arguments may be used to influence the filter method by setting individual boolean flags. See notes for details. Notes ----- The filtering method is defined by a collection of boolean flags, and is internally stored as a bitmask. The methods available are: FILTER_CONVENTIONAL Conventional Kalman filter. FILTER_UNIVARIATE Univariate approach to Kalman filtering. Overrides conventional method if both are specified. FILTER_COLLAPSED Collapsed approach to Kalman filtering. Will be used *in addition* to conventional or univariate filtering. FILTER_CONCENTRATED Use the concentrated log-likelihood function. Will be used *in addition* to the other options. Note that only the first method is available if using a Scipy version older than 0.16. If the bitmask is set directly via the `filter_method` argument, then the full method must be provided. If keyword arguments are used to set individual boolean flags, then the lowercase of the method must be used as an argument name, and the value is the desired value of the boolean flag (True or False). Note that the filter method may also be specified by directly modifying the class attributes which are defined similarly to the keyword arguments. The default filtering method is FILTER_CONVENTIONAL. Examples -------- >>> mod = sm.tsa.statespace.SARIMAX(range(10)) >>> mod.ssm.filter_method 1 >>> mod.ssm.filter_conventional True >>> mod.ssm.filter_univariate = True >>> mod.ssm.filter_method 17 >>> mod.ssm.set_filter_method(filter_univariate=False, ... filter_collapsed=True) >>> mod.ssm.filter_method 33 >>> mod.ssm.set_filter_method(filter_method=1) >>> mod.ssm.filter_conventional True >>> mod.ssm.filter_univariate False >>> mod.ssm.filter_collapsed False >>> mod.ssm.filter_univariate = True >>> mod.ssm.filter_method 17 """ if filter_method is not None: self.filter_method = filter_method for name in KalmanFilter.filter_methods: if name in kwargs: setattr(self, name, kwargs[name]) def set_inversion_method(self, inversion_method=None, **kwargs): r""" Set the inversion method The Kalman filter may contain one matrix inversion: that of the forecast error covariance matrix. The inversion method controls how and if that inverse is performed. Parameters ---------- inversion_method : int, optional Bitmask value to set the inversion method to. See notes for details. **kwargs Keyword arguments may be used to influence the inversion method by setting individual boolean flags. See notes for details. Notes ----- The inversion method is defined by a collection of boolean flags, and is internally stored as a bitmask. The methods available are: INVERT_UNIVARIATE If the endogenous time series is univariate, then inversion can be performed by simple division. If this flag is set and the time series is univariate, then division will always be used even if other flags are also set. SOLVE_LU Use an LU decomposition along with a linear solver (rather than ever actually inverting the matrix). INVERT_LU Use an LU decomposition along with typical matrix inversion. SOLVE_CHOLESKY Use a Cholesky decomposition along with a linear solver. INVERT_CHOLESKY Use an Cholesky decomposition along with typical matrix inversion. If the bitmask is set directly via the `inversion_method` argument, then the full method must be provided. If keyword arguments are used to set individual boolean flags, then the lowercase of the method must be used as an argument name, and the value is the desired value of the boolean flag (True or False). Note that the inversion method may also be specified by directly modifying the class attributes which are defined similarly to the keyword arguments. The default inversion method is `INVERT_UNIVARIATE | SOLVE_CHOLESKY` Several things to keep in mind are: - If the filtering method is specified to be univariate, then simple division is always used regardless of the dimension of the endogenous time series. - Cholesky decomposition is about twice as fast as LU decomposition, but it requires that the matrix be positive definite. While this should generally be true, it may not be in every case. - Using a linear solver rather than true matrix inversion is generally faster and is numerically more stable. Examples -------- >>> mod = sm.tsa.statespace.SARIMAX(range(10)) >>> mod.ssm.inversion_method 1 >>> mod.ssm.solve_cholesky True >>> mod.ssm.invert_univariate True >>> mod.ssm.invert_lu False >>> mod.ssm.invert_univariate = False >>> mod.ssm.inversion_method 8 >>> mod.ssm.set_inversion_method(solve_cholesky=False, ... invert_cholesky=True) >>> mod.ssm.inversion_method 16 """ if inversion_method is not None: self.inversion_method = inversion_method for name in KalmanFilter.inversion_methods: if name in kwargs: setattr(self, name, kwargs[name]) def set_stability_method(self, stability_method=None, **kwargs): r""" Set the numerical stability method The Kalman filter is a recursive algorithm that may in some cases suffer issues with numerical stability. The stability method controls what, if any, measures are taken to promote stability. Parameters ---------- stability_method : int, optional Bitmask value to set the stability method to. See notes for details. **kwargs Keyword arguments may be used to influence the stability method by setting individual boolean flags. See notes for details. Notes ----- The stability method is defined by a collection of boolean flags, and is internally stored as a bitmask. The methods available are: STABILITY_FORCE_SYMMETRY = 0x01 If this flag is set, symmetry of the predicted state covariance matrix is enforced at each iteration of the filter, where each element is set to the average of the corresponding elements in the upper and lower triangle. If the bitmask is set directly via the `stability_method` argument, then the full method must be provided. If keyword arguments are used to set individual boolean flags, then the lowercase of the method must be used as an argument name, and the value is the desired value of the boolean flag (True or False). Note that the stability method may also be specified by directly modifying the class attributes which are defined similarly to the keyword arguments. The default stability method is `STABILITY_FORCE_SYMMETRY` Examples -------- >>> mod = sm.tsa.statespace.SARIMAX(range(10)) >>> mod.ssm.stability_method 1 >>> mod.ssm.stability_force_symmetry True >>> mod.ssm.stability_force_symmetry = False >>> mod.ssm.stability_method 0 """ if stability_method is not None: self.stability_method = stability_method for name in KalmanFilter.stability_methods: if name in kwargs: setattr(self, name, kwargs[name]) def set_conserve_memory(self, conserve_memory=None, **kwargs): r""" Set the memory conservation method By default, the Kalman filter computes a number of intermediate matrices at each iteration. The memory conservation options control which of those matrices are stored. Parameters ---------- conserve_memory : int, optional Bitmask value to set the memory conservation method to. See notes for details. **kwargs Keyword arguments may be used to influence the memory conservation method by setting individual boolean flags. See notes for details. Notes ----- The memory conservation method is defined by a collection of boolean flags, and is internally stored as a bitmask. The methods available are: MEMORY_STORE_ALL Store all intermediate matrices. This is the default value. MEMORY_NO_FORECAST_MEAN Do not store the forecast or forecast errors. If this option is used, the `predict` method from the results class is unavailable. MEMORY_NO_FORECAST_COV Do not store the forecast error covariance matrices. MEMORY_NO_FORECAST Do not store the forecast, forecast error, or forecast error covariance matrices. If this option is used, the `predict` method from the results class is unavailable. MEMORY_NO_PREDICTED_MEAN Do not store the predicted state. MEMORY_NO_PREDICTED_COV Do not store the predicted state covariance matrices. MEMORY_NO_PREDICTED Do not store the predicted state or predicted state covariance matrices. MEMORY_NO_FILTERED_MEAN Do not store the filtered state. MEMORY_NO_FILTERED_COV Do not store the filtered state covariance matrices. MEMORY_NO_FILTERED Do not store the filtered state or filtered state covariance matrices. MEMORY_NO_LIKELIHOOD Do not store the vector of loglikelihood values for each observation. Only the sum of the loglikelihood values is stored. MEMORY_NO_GAIN Do not store the Kalman gain matrices. MEMORY_NO_SMOOTHING Do not store temporary variables related to Kalman smoothing. If this option is used, smoothing is unavailable. MEMORY_NO_STD_FORECAST Do not store standardized forecast errors. MEMORY_CONSERVE Do not store any intermediate matrices. If the bitmask is set directly via the `conserve_memory` argument, then the full method must be provided. If keyword arguments are used to set individual boolean flags, then the lowercase of the method must be used as an argument name, and the value is the desired value of the boolean flag (True or False). Note that the memory conservation method may also be specified by directly modifying the class attributes which are defined similarly to the keyword arguments. The default memory conservation method is `MEMORY_STORE_ALL`, so that all intermediate matrices are stored. Examples -------- >>> mod = sm.tsa.statespace.SARIMAX(range(10)) >>> mod.ssm..conserve_memory 0 >>> mod.ssm.memory_no_predicted False >>> mod.ssm.memory_no_predicted = True >>> mod.ssm.conserve_memory 2 >>> mod.ssm.set_conserve_memory(memory_no_filtered=True, ... memory_no_forecast=True) >>> mod.ssm.conserve_memory 7 """ if conserve_memory is not None: self.conserve_memory = conserve_memory for name in KalmanFilter.memory_options: if name in kwargs: setattr(self, name, kwargs[name]) def set_filter_timing(self, alternate_timing=None, **kwargs): r""" Set the filter timing convention By default, the Kalman filter follows Durbin and Koopman, 2012, in initializing the filter with predicted values. Kim and Nelson, 1999, instead initialize the filter with filtered values, which is essentially just a different timing convention. Parameters ---------- alternate_timing : int, optional Whether or not to use the alternate timing convention. Default is unspecified. **kwargs Keyword arguments may be used to influence the memory conservation method by setting individual boolean flags. See notes for details. """ if alternate_timing is not None: self.filter_timing = int(alternate_timing) if 'timing_init_predicted' in kwargs: self.filter_timing = int(not kwargs['timing_init_predicted']) if 'timing_init_filtered' in kwargs: self.filter_timing = int(kwargs['timing_init_filtered']) @contextlib.contextmanager def fixed_scale(self, scale): """ fixed_scale(scale) Context manager for fixing the scale when FILTER_CONCENTRATED is set Parameters ---------- scale : numeric Scale of the model. Notes ----- This a no-op if scale is None. This context manager is most useful in models which are explicitly concentrating out the scale, so that the set of parameters they are estimating does not include the scale. """ # If a scale was provided, use it and do not concentrate it out of the # loglikelihood if scale is not None and scale != 1: if not self.filter_concentrated: raise ValueError('Cannot provide scale if filter method does' ' not include FILTER_CONCENTRATED.') self.filter_concentrated = False self._scale = scale obs_cov = self['obs_cov'] state_cov = self['state_cov'] self['obs_cov'] = scale * obs_cov self['state_cov'] = scale * state_cov try: yield finally: # If a scale was provided, reset the model if scale is not None and scale != 1: self['state_cov'] = state_cov self['obs_cov'] = obs_cov self.filter_concentrated = True self._scale = None def _filter(self, filter_method=None, inversion_method=None, stability_method=None, conserve_memory=None, filter_timing=None, tolerance=None, loglikelihood_burn=None, complex_step=False): # Initialize the filter prefix, dtype, create_filter, create_statespace = ( self._initialize_filter( filter_method, inversion_method, stability_method, conserve_memory, filter_timing, tolerance, loglikelihood_burn ) ) kfilter = self._kalman_filters[prefix] # Initialize the state self._initialize_state(prefix=prefix, complex_step=complex_step) # Run the filter kfilter() return kfilter def filter(self, filter_method=None, inversion_method=None, stability_method=None, conserve_memory=None, filter_timing=None, tolerance=None, loglikelihood_burn=None, complex_step=False): r""" Apply the Kalman filter to the statespace model. Parameters ---------- filter_method : int, optional Determines which Kalman filter to use. Default is conventional. inversion_method : int, optional Determines which inversion technique to use. Default is by Cholesky decomposition. stability_method : int, optional Determines which numerical stability techniques to use. Default is to enforce symmetry of the predicted state covariance matrix. conserve_memory : int, optional Determines what output from the filter to store. Default is to store everything. filter_timing : int, optional Determines the timing convention of the filter. Default is that from Durbin and Koopman (2012), in which the filter is initialized with predicted values. tolerance : float, optional The tolerance at which the Kalman filter determines convergence to steady-state. Default is 1e-19. loglikelihood_burn : int, optional The number of initial periods during which the loglikelihood is not recorded. Default is 0. Notes ----- This function by default does not compute variables required for smoothing. """ # Handle memory conservation if conserve_memory is None: conserve_memory = self.conserve_memory | MEMORY_NO_SMOOTHING conserve_memory_cache = self.conserve_memory self.set_conserve_memory(conserve_memory) # Run the filter kfilter = self._filter( filter_method, inversion_method, stability_method, conserve_memory, filter_timing, tolerance, loglikelihood_burn, complex_step) # Create the results object results = self.results_class(self) results.update_representation(self) results.update_filter(kfilter) # Resent memory conservation self.set_conserve_memory(conserve_memory_cache) return results def loglike(self, **kwargs): r""" Calculate the loglikelihood associated with the statespace model. Parameters ---------- **kwargs Additional keyword arguments to pass to the Kalman filter. See `KalmanFilter.filter` for more details. Returns ------- loglike : float The joint loglikelihood. """ kwargs.setdefault('conserve_memory', MEMORY_CONSERVE ^ MEMORY_NO_LIKELIHOOD) kfilter = self._filter(**kwargs) loglikelihood_burn = kwargs.get('loglikelihood_burn', self.loglikelihood_burn) if not (kwargs['conserve_memory'] & MEMORY_NO_LIKELIHOOD): loglike = np.sum(kfilter.loglikelihood[loglikelihood_burn:]) else: loglike = np.sum(kfilter.loglikelihood) # Need to modify the computed log-likelihood to incorporate the # MLE scale. if self.filter_method & FILTER_CONCENTRATED: d = max(loglikelihood_burn, kfilter.nobs_diffuse) nobs_k_endog = np.sum( self.k_endog - np.array(self._statespace.nmissing)[d:]) # In the univariate case, we need to subtract observations # associated with a singular forecast error covariance matrix nobs_k_endog -= kfilter.nobs_kendog_univariate_singular if not (kwargs['conserve_memory'] & MEMORY_NO_LIKELIHOOD): scale = np.sum(kfilter.scale[d:]) / nobs_k_endog else: scale = kfilter.scale[0] / nobs_k_endog loglike += -0.5 * nobs_k_endog # Now need to modify this for diffuse initialization, since for # diffuse periods we only need to add in the scale value part if # the diffuse forecast error covariance matrix element was singular if kfilter.nobs_diffuse > 0: nobs_k_endog -= kfilter.nobs_kendog_diffuse_nonsingular loglike += -0.5 * nobs_k_endog * np.log(scale) return loglike def loglikeobs(self, **kwargs): r""" Calculate the loglikelihood for each observation associated with the statespace model. Parameters ---------- **kwargs Additional keyword arguments to pass to the Kalman filter. See `KalmanFilter.filter` for more details. Notes ----- If `loglikelihood_burn` is positive, then the entries in the returned loglikelihood vector are set to be zero for those initial time periods. Returns ------- loglike : array of float Array of loglikelihood values for each observation. """ if self.memory_no_likelihood: raise RuntimeError('Cannot compute loglikelihood if' ' MEMORY_NO_LIKELIHOOD option is selected.') if not self.filter_method & FILTER_CONCENTRATED: kwargs.setdefault('conserve_memory', MEMORY_CONSERVE ^ MEMORY_NO_LIKELIHOOD) else: kwargs.setdefault( 'conserve_memory', MEMORY_CONSERVE ^ (MEMORY_NO_FORECAST | MEMORY_NO_LIKELIHOOD)) kfilter = self._filter(**kwargs) llf_obs = np.array(kfilter.loglikelihood, copy=True) loglikelihood_burn = kwargs.get('loglikelihood_burn', self.loglikelihood_burn) # If the scale was concentrated out of the log-likelihood function, # then the llf_obs above is: # -0.5 * k_endog * log 2 * pi - 0.5 * log |F_t| # and we need to add in the effect of the scale: # -0.5 * k_endog * log scale - 0.5 v' F_t^{-1} v / scale # and note that v' F_t^{-1} is in the _kalman_filter.scale array # Also note that we need to adjust the nobs and k_endog in both the # denominator of the scale computation and in the llf_obs adjustment # to take into account missing values. if self.filter_method & FILTER_CONCENTRATED: d = max(loglikelihood_burn, kfilter.nobs_diffuse) nmissing = np.array(self._statespace.nmissing) nobs_k_endog = np.sum(self.k_endog - nmissing[d:]) # In the univariate case, we need to subtract observations # associated with a singular forecast error covariance matrix nobs_k_endog -= kfilter.nobs_kendog_univariate_singular scale = np.sum(kfilter.scale[d:]) / nobs_k_endog # Need to modify this for diffuse initialization, since for # diffuse periods we only need to add in the scale value if the # diffuse forecast error covariance matrix element was singular nsingular = 0 if kfilter.nobs_diffuse > 0: d = kfilter.nobs_diffuse Finf = kfilter.forecast_error_diffuse_cov singular = np.diagonal(Finf).real <= kfilter.tolerance_diffuse nsingular = np.sum(~singular, axis=1) scale_obs = np.array(kfilter.scale, copy=True) llf_obs += -0.5 * ( (self.k_endog - nmissing - nsingular) * np.log(scale) + scale_obs / scale) # Set any burned observations to have zero likelihood llf_obs[:loglikelihood_burn] = 0 return llf_obs def simulate(self, nsimulations, measurement_shocks=None, state_shocks=None, initial_state=None): r""" Simulate a new time series following the state space model Parameters ---------- nsimulations : int The number of observations to simulate. If the model is time-invariant this can be any number. If the model is time-varying, then this number must be less than or equal to the number measurement_shocks : array_like, optional If specified, these are the shocks to the measurement equation, :math:`\varepsilon_t`. If unspecified, these are automatically generated using a pseudo-random number generator. If specified, must be shaped `nsimulations` x `k_endog`, where `k_endog` is the same as in the state space model. state_shocks : array_like, optional If specified, these are the shocks to the state equation, :math:`\eta_t`. If unspecified, these are automatically generated using a pseudo-random number generator. If specified, must be shaped `nsimulations` x `k_posdef` where `k_posdef` is the same as in the state space model. initial_state : array_like, optional If specified, this is the state vector at time zero, which should be shaped (`k_states` x 1), where `k_states` is the same as in the state space model. If unspecified, but the model has been initialized, then that initialization is used. If unspecified and the model has not been initialized, then a vector of zeros is used. Note that this is not included in the returned `simulated_states` array. Returns ------- simulated_obs : ndarray An (nsimulations x k_endog) array of simulated observations. simulated_states : ndarray An (nsimulations x k_states) array of simulated states. """ time_invariant = self.time_invariant # Check for valid number of simulations if not time_invariant and nsimulations > self.nobs: raise ValueError('In a time-varying model, cannot create more' ' simulations than there are observations.') # Check / generate measurement shocks if measurement_shocks is not None: measurement_shocks = np.array(measurement_shocks) if measurement_shocks.ndim == 0: measurement_shocks = measurement_shocks[np.newaxis, np.newaxis] elif measurement_shocks.ndim == 1: measurement_shocks = measurement_shocks[:, np.newaxis] required_shape = (nsimulations, self.k_endog) try: measurement_shocks = measurement_shocks.reshape(required_shape) except ValueError: raise ValueError('Provided measurement shocks are not of the' ' appropriate shape. Required %s, got %s.' % (str(required_shape), str(measurement_shocks.shape))) elif self.shapes['obs_cov'][-1] == 1: measurement_shocks = np.random.multivariate_normal( mean=np.zeros(self.k_endog), cov=self['obs_cov'], size=nsimulations) # Check / generate state shocks if state_shocks is not None: state_shocks = np.array(state_shocks) if state_shocks.ndim == 0: state_shocks = state_shocks[np.newaxis, np.newaxis] elif state_shocks.ndim == 1: state_shocks = state_shocks[:, np.newaxis] required_shape = (nsimulations, self.k_posdef) try: state_shocks = state_shocks.reshape(required_shape) except ValueError: raise ValueError('Provided state shocks are not of the' ' appropriate shape. Required %s, got %s.' % (str(required_shape), str(state_shocks.shape))) elif self.shapes['state_cov'][-1] == 1: state_shocks = np.random.multivariate_normal( mean=np.zeros(self.k_posdef), cov=self['state_cov'], size=nsimulations) # Handle time-varying case tvp = (self.shapes['obs_cov'][-1] > 1 or self.shapes['state_cov'][-1] > 1) if tvp and measurement_shocks is None: measurement_shocks = np.zeros((nsimulations, self.k_endog)) for i in range(nsimulations): measurement_shocks[i] = np.random.multivariate_normal( mean=np.zeros(self.k_endog), cov=self['obs_cov', ..., i]) if tvp and state_shocks is None: state_shocks = np.zeros((nsimulations, self.k_posdef)) for i in range(nsimulations): state_shocks[i] = np.random.multivariate_normal( mean=np.zeros(self.k_posdef), cov=self['state_cov', ..., i]) # Get the initial states if initial_state is not None: initial_state = np.array(initial_state) if initial_state.ndim == 0: initial_state = initial_state[np.newaxis] elif (initial_state.ndim > 1 and not initial_state.shape == (self.k_states, 1)): raise ValueError('Invalid shape of provided initial state' ' vector. Required (%d, 1)' % self.k_states) elif self.initialization is not None: out = self.initialization(model=self) initial_state = out[0] + np.random.multivariate_normal( np.zeros_like(out[0]), out[2]) else: # TODO: deprecate this, since we really should not be simulating # unless we have an initialization. initial_state = np.zeros(self.k_states) return self._simulate(nsimulations, measurement_shocks, state_shocks, initial_state) def _simulate(self, nsimulations, measurement_shocks, state_shocks, initial_state): raise NotImplementedError('Simulation only available through' ' the simulation smoother.') def impulse_responses(self, steps=10, impulse=0, orthogonalized=False, cumulative=False, direct=False): r""" Impulse response function Parameters ---------- steps : int, optional The number of steps for which impulse responses are calculated. Default is 10. Note that the initial impulse is not counted as a step, so if `steps=1`, the output will have 2 entries. impulse : int or array_like If an integer, the state innovation to pulse; must be between 0 and `k_posdef-1` where `k_posdef` is the same as in the state space model. Alternatively, a custom impulse vector may be provided; must be a column vector with shape `(k_posdef, 1)`. orthogonalized : bool, optional Whether or not to perform impulse using orthogonalized innovations. Note that this will also affect custum `impulse` vectors. Default is False. cumulative : bool, optional Whether or not to return cumulative impulse responses. Default is False. Returns ------- impulse_responses : ndarray Responses for each endogenous variable due to the impulse given by the `impulse` argument. A (steps + 1 x k_endog) array. Notes ----- Intercepts in the measurement and state equation are ignored when calculating impulse responses. TODO: add note about how for time-varying systems this is - perhaps counter-intuitively - returning the impulse response within the given model (i.e. starting at period 0 defined by the model) and it is *not* doing impulse responses after the end of the model. To compute impulse responses from arbitrary time points, it is necessary to clone a new model with the appropriate system matrices. """ # We need to add an additional step, since the first simulated value # will always be zeros (note that we take this value out at the end). steps += 1 # For time-invariant models, add an additional `step`. This is the # default for time-invariant models based on the expected behavior for # ARIMA and VAR models: we want to record the initial impulse and also # `steps` values of the responses afterwards. if (self._design.shape[2] == 1 and self._transition.shape[2] == 1 and self._selection.shape[2] == 1): steps += 1 # Check for what kind of impulse we want if type(impulse) == int: if impulse >= self.k_posdef or impulse < 0: raise ValueError('Invalid value for `impulse`. Must be the' ' index of one of the state innovations.') # Create the (non-orthogonalized) impulse vector idx = impulse impulse = np.zeros(self.k_posdef) impulse[idx] = 1 else: impulse = np.array(impulse) if impulse.ndim > 1: impulse = np.squeeze(impulse) if not impulse.shape == (self.k_posdef,): raise ValueError('Invalid impulse vector. Must be shaped' ' (%d,)' % self.k_posdef) # Orthogonalize the impulses, if requested, using Cholesky on the # first state covariance matrix if orthogonalized: state_chol = np.linalg.cholesky(self.state_cov[:, :, 0]) impulse = np.dot(state_chol, impulse) # If we have time-varying design, transition, or selection matrices, # then we can't produce more IRFs than we have time points time_invariant_irf = ( self._design.shape[2] == self._transition.shape[2] == self._selection.shape[2] == 1) # Note: to generate impulse responses following the end of a # time-varying model, one should `clone` the state space model with the # new time-varying model, and then compute the IRFs using the cloned # model if not time_invariant_irf and steps > self.nobs: raise ValueError('In a time-varying model, cannot create more' ' impulse responses than there are' ' observations') # Impulse responses only depend on the design, transition, and # selection matrices. We set the others to zeros because they must be # set in the call to `clone`. # Note: we don't even need selection after the first point, because # the state shocks will be zeros in every period except the first. sim_model = self.clone( endog=np.zeros((steps, self.k_endog), dtype=self.dtype), obs_intercept=np.zeros(self.k_endog), design=self['design', :, :, :steps], obs_cov=np.zeros((self.k_endog, self.k_endog)), state_intercept=np.zeros(self.k_states), transition=self['transition', :, :, :steps], selection=self['selection', :, :, :steps], state_cov=np.zeros((self.k_posdef, self.k_posdef))) # Get the impulse response function via simulation of the state # space model, but with other shocks set to zero measurement_shocks = np.zeros((steps, self.k_endog)) state_shocks = np.zeros((steps, self.k_posdef)) state_shocks[0] = impulse initial_state = np.zeros((self.k_states,)) irf, _ = sim_model.simulate( steps, measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # Get the cumulative response if requested if cumulative: irf = np.cumsum(irf, axis=0) # Here we ignore the first value, because it is always zeros (we added # an additional `step` at the top to account for this). return irf[1:] class FilterResults(FrozenRepresentation): """ Results from applying the Kalman filter to a state space model. Parameters ---------- model : Representation A Statespace representation Attributes ---------- nobs : int Number of observations. nobs_diffuse : int Number of observations under the diffuse Kalman filter. k_endog : int The dimension of the observation series. k_states : int The dimension of the unobserved state process. k_posdef : int The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation. dtype : dtype Datatype of representation matrices prefix : str BLAS prefix of representation matrices shapes : dictionary of name,tuple A dictionary recording the shapes of each of the representation matrices as tuples. endog : ndarray The observation vector. design : ndarray The design matrix, :math:`Z`. obs_intercept : ndarray The intercept for the observation equation, :math:`d`. obs_cov : ndarray The covariance matrix for the observation equation :math:`H`. transition : ndarray The transition matrix, :math:`T`. state_intercept : ndarray The intercept for the transition equation, :math:`c`. selection : ndarray The selection matrix, :math:`R`. state_cov : ndarray The covariance matrix for the state equation :math:`Q`. missing : array of bool An array of the same size as `endog`, filled with boolean values that are True if the corresponding entry in `endog` is NaN and False otherwise. nmissing : array of int An array of size `nobs`, where the ith entry is the number (between 0 and `k_endog`) of NaNs in the ith row of the `endog` array. time_invariant : bool Whether or not the representation matrices are time-invariant initialization : str Kalman filter initialization method. initial_state : array_like The state vector used to initialize the Kalamn filter. initial_state_cov : array_like The state covariance matrix used to initialize the Kalamn filter. initial_diffuse_state_cov : array_like Diffuse state covariance matrix used to initialize the Kalamn filter. filter_method : int Bitmask representing the Kalman filtering method inversion_method : int Bitmask representing the method used to invert the forecast error covariance matrix. stability_method : int Bitmask representing the methods used to promote numerical stability in the Kalman filter recursions. conserve_memory : int Bitmask representing the selected memory conservation method. filter_timing : int Whether or not to use the alternate timing convention. tolerance : float The tolerance at which the Kalman filter determines convergence to steady-state. loglikelihood_burn : int The number of initial periods during which the loglikelihood is not recorded. converged : bool Whether or not the Kalman filter converged. period_converged : int The time period in which the Kalman filter converged. filtered_state : ndarray The filtered state vector at each time period. filtered_state_cov : ndarray The filtered state covariance matrix at each time period. predicted_state : ndarray The predicted state vector at each time period. predicted_state_cov : ndarray The predicted state covariance matrix at each time period. forecast_error_diffuse_cov : ndarray Diffuse forecast error covariance matrix at each time period. predicted_diffuse_state_cov : ndarray The predicted diffuse state covariance matrix at each time period. kalman_gain : ndarray The Kalman gain at each time period. forecasts : ndarray The one-step-ahead forecasts of observations at each time period. forecasts_error : ndarray The forecast errors at each time period. forecasts_error_cov : ndarray The forecast error covariance matrices at each time period. llf_obs : ndarray The loglikelihood values at each time period. """ _filter_attributes = [ 'filter_method', 'inversion_method', 'stability_method', 'conserve_memory', 'filter_timing', 'tolerance', 'loglikelihood_burn', 'converged', 'period_converged', 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'tmp1', 'tmp2', 'tmp3', 'tmp4', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'llf', 'llf_obs', 'collapsed_forecasts', 'collapsed_forecasts_error', 'collapsed_forecasts_error_cov', 'scale' ] _filter_options = ( KalmanFilter.filter_methods + KalmanFilter.stability_methods + KalmanFilter.inversion_methods + KalmanFilter.memory_options ) _attributes = FrozenRepresentation._model_attributes + _filter_attributes def __init__(self, model): super(FilterResults, self).__init__(model) # Setup caches for uninitialized objects self._kalman_gain = None self._standardized_forecasts_error = None def update_representation(self, model, only_options=False): """ Update the results to match a given model Parameters ---------- model : Representation The model object from which to take the updated values. only_options : bool, optional If set to true, only the filter options are updated, and the state space representation is not updated. Default is False. Notes ----- This method is rarely required except for internal usage. """ if not only_options: super(FilterResults, self).update_representation(model) # Save the options as boolean variables for name in self._filter_options: setattr(self, name, getattr(model, name, None)) def update_filter(self, kalman_filter): """ Update the filter results Parameters ---------- kalman_filter : statespace.kalman_filter.KalmanFilter The model object from which to take the updated values. Notes ----- This method is rarely required except for internal usage. """ # State initialization self.initial_state = np.array( kalman_filter.model.initial_state, copy=True ) self.initial_state_cov = np.array( kalman_filter.model.initial_state_cov, copy=True ) # Save Kalman filter parameters self.filter_method = kalman_filter.filter_method self.inversion_method = kalman_filter.inversion_method self.stability_method = kalman_filter.stability_method self.conserve_memory = kalman_filter.conserve_memory self.filter_timing = kalman_filter.filter_timing self.tolerance = kalman_filter.tolerance self.loglikelihood_burn = kalman_filter.loglikelihood_burn # Save Kalman filter output self.converged = bool(kalman_filter.converged) self.period_converged = kalman_filter.period_converged self.filtered_state = np.array(kalman_filter.filtered_state, copy=True) self.filtered_state_cov = np.array( kalman_filter.filtered_state_cov, copy=True ) self.predicted_state = np.array( kalman_filter.predicted_state, copy=True ) self.predicted_state_cov = np.array( kalman_filter.predicted_state_cov, copy=True ) # Reset caches has_missing = np.sum(self.nmissing) > 0 if not (self.memory_no_std_forecast or self.invert_lu or self.solve_lu or self.filter_collapsed): if has_missing: self._standardized_forecasts_error = np.array( reorder_missing_vector( kalman_filter.standardized_forecast_error, self.missing, prefix=self.prefix)) else: self._standardized_forecasts_error = np.array( kalman_filter.standardized_forecast_error, copy=True) else: self._standardized_forecasts_error = None # In the partially missing data case, all entries will # be in the upper left submatrix rather than the correct placement # Re-ordering does not make sense in the collapsed case. if has_missing and (not self.memory_no_gain and not self.filter_collapsed): self._kalman_gain = np.array(reorder_missing_matrix( kalman_filter.kalman_gain, self.missing, reorder_cols=True, prefix=self.prefix)) self.tmp1 = np.array(reorder_missing_matrix( kalman_filter.tmp1, self.missing, reorder_cols=True, prefix=self.prefix)) self.tmp2 = np.array(reorder_missing_vector( kalman_filter.tmp2, self.missing, prefix=self.prefix)) self.tmp3 = np.array(reorder_missing_matrix( kalman_filter.tmp3, self.missing, reorder_rows=True, prefix=self.prefix)) self.tmp4 = np.array(reorder_missing_matrix( kalman_filter.tmp4, self.missing, reorder_cols=True, reorder_rows=True, prefix=self.prefix)) else: if not self.memory_no_gain: self._kalman_gain = np.array( kalman_filter.kalman_gain, copy=True) self.tmp1 = np.array(kalman_filter.tmp1, copy=True) self.tmp2 = np.array(kalman_filter.tmp2, copy=True) self.tmp3 = np.array(kalman_filter.tmp3, copy=True) self.tmp4 = np.array(kalman_filter.tmp4, copy=True) self.M = np.array(kalman_filter.M, copy=True) self.M_diffuse = np.array(kalman_filter.M_inf, copy=True) # Note: use forecasts rather than forecast, so as not to interfer # with the `forecast` methods in subclasses self.forecasts = np.array(kalman_filter.forecast, copy=True) self.forecasts_error = np.array( kalman_filter.forecast_error, copy=True ) self.forecasts_error_cov = np.array( kalman_filter.forecast_error_cov, copy=True ) # Note: below we will set self.llf, and in the memory_no_likelihood # case we will replace self.llf_obs = None at that time. self.llf_obs = np.array(kalman_filter.loglikelihood, copy=True) # Diffuse objects self.nobs_diffuse = kalman_filter.nobs_diffuse self.initial_diffuse_state_cov = None self.forecasts_error_diffuse_cov = None self.predicted_diffuse_state_cov = None if self.nobs_diffuse > 0: self.initial_diffuse_state_cov = np.array( kalman_filter.model.initial_diffuse_state_cov, copy=True) self.predicted_diffuse_state_cov = np.array( kalman_filter.predicted_diffuse_state_cov, copy=True) if has_missing and not self.filter_collapsed: self.forecasts_error_diffuse_cov = np.array( reorder_missing_matrix( kalman_filter.forecast_error_diffuse_cov, self.missing, reorder_cols=True, reorder_rows=True, prefix=self.prefix)) else: self.forecasts_error_diffuse_cov = np.array( kalman_filter.forecast_error_diffuse_cov, copy=True) # If there was missing data, save the original values from the Kalman # filter output, since below will set the values corresponding to # the missing observations to nans. self.missing_forecasts = None self.missing_forecasts_error = None self.missing_forecasts_error_cov = None if np.sum(self.nmissing) > 0: # Copy the provided arrays (which are as the Kalman filter dataset) # into new variables self.missing_forecasts = np.copy(self.forecasts) self.missing_forecasts_error = np.copy(self.forecasts_error) self.missing_forecasts_error_cov = ( np.copy(self.forecasts_error_cov) ) # Save the collapsed values self.collapsed_forecasts = None self.collapsed_forecasts_error = None self.collapsed_forecasts_error_cov = None if self.filter_collapsed: # Copy the provided arrays (which are from the collapsed dataset) # into new variables self.collapsed_forecasts = self.forecasts[:self.k_states, :] self.collapsed_forecasts_error = ( self.forecasts_error[:self.k_states, :] ) self.collapsed_forecasts_error_cov = ( self.forecasts_error_cov[:self.k_states, :self.k_states, :] ) # Recreate the original arrays (which should be from the original # dataset) in the appropriate dimension dtype = self.collapsed_forecasts.dtype self.forecasts = np.zeros((self.k_endog, self.nobs), dtype=dtype) self.forecasts_error = np.zeros((self.k_endog, self.nobs), dtype=dtype) self.forecasts_error_cov = ( np.zeros((self.k_endog, self.k_endog, self.nobs), dtype=dtype) ) # Fill in missing values in the forecast, forecast error, and # forecast error covariance matrix (this is required due to how the # Kalman filter implements observations that are either partly or # completely missing) # Construct the predictions, forecasts can_compute_mean = not (self.memory_no_forecast_mean or self.memory_no_predicted_mean) can_compute_cov = not (self.memory_no_forecast_cov or self.memory_no_predicted_cov) if can_compute_mean or can_compute_cov: for t in range(self.nobs): design_t = 0 if self.design.shape[2] == 1 else t obs_cov_t = 0 if self.obs_cov.shape[2] == 1 else t obs_intercept_t = 0 if self.obs_intercept.shape[1] == 1 else t # For completely missing observations, the Kalman filter will # produce forecasts, but forecast errors and the forecast # error covariance matrix will be zeros - make them nan to # improve clarity of results. if self.nmissing[t] > 0: mask = ~self.missing[:, t].astype(bool) # We can recover forecasts # For partially missing observations, the Kalman filter # will produce all elements (forecasts, forecast errors, # forecast error covariance matrices) as usual, but their # dimension will only be equal to the number of non-missing # elements, and their location in memory will be in the # first blocks (e.g. for the forecasts_error, the first # k_endog - nmissing[t] columns will be filled in), # regardless of which endogenous variables they refer to # (i.e. the non- missing endogenous variables for that # observation). Furthermore, the forecast error covariance # matrix is only valid for those elements. What is done is # to set all elements to nan for these observations so that # they are flagged as missing. The variables # missing_forecasts, etc. then provide the forecasts, etc. # provided by the Kalman filter, from which the data can be # retrieved if desired. if can_compute_mean: self.forecasts[:, t] = np.dot( self.design[:, :, design_t], self.predicted_state[:, t] ) + self.obs_intercept[:, obs_intercept_t] self.forecasts_error[:, t] = np.nan self.forecasts_error[mask, t] = ( self.endog[mask, t] - self.forecasts[mask, t]) # TODO: We should only fill in the non-masked elements of # this array. Also, this will give the multivariate version # even if univariate filtering was selected. Instead, we # should use the reordering methods and then replace the # masked values with NaNs if can_compute_cov: self.forecasts_error_cov[:, :, t] = np.dot( np.dot(self.design[:, :, design_t], self.predicted_state_cov[:, :, t]), self.design[:, :, design_t].T ) + self.obs_cov[:, :, obs_cov_t] # In the collapsed case, everything just needs to be rebuilt # for the original observed data, since the Kalman filter # produced these values for the collapsed data. elif self.filter_collapsed: if can_compute_mean: self.forecasts[:, t] = np.dot( self.design[:, :, design_t], self.predicted_state[:, t] ) + self.obs_intercept[:, obs_intercept_t] self.forecasts_error[:, t] = ( self.endog[:, t] - self.forecasts[:, t] ) if can_compute_cov: self.forecasts_error_cov[:, :, t] = np.dot( np.dot(self.design[:, :, design_t], self.predicted_state_cov[:, :, t]), self.design[:, :, design_t].T ) + self.obs_cov[:, :, obs_cov_t] # Note: if we concentrated out the scale, need to adjust the # loglikelihood values and all of the covariance matrices and the # values that depend on the covariance matrices # Note: concentrated computation is not permitted with collapsed # version, so we do not need to modify collapsed arrays. self.scale = 1. if self.filter_concentrated and self.model._scale is None: d = max(self.loglikelihood_burn, self.nobs_diffuse) # Compute the scale nmissing = np.array(kalman_filter.model.nmissing) nobs_k_endog = np.sum(self.k_endog - nmissing[d:]) # In the univariate case, we need to subtract observations # associated with a singular forecast error covariance matrix nobs_k_endog -= kalman_filter.nobs_kendog_univariate_singular scale_obs = np.array(kalman_filter.scale, copy=True) if not self.memory_no_likelihood: self.scale = np.sum(scale_obs[d:]) / nobs_k_endog else: self.scale = scale_obs[0] / nobs_k_endog # Need to modify this for diffuse initialization, since for # diffuse periods we only need to add in the scale value if the # diffuse forecast error covariance matrix element was singular nsingular = 0 if kalman_filter.nobs_diffuse > 0: Finf = kalman_filter.forecast_error_diffuse_cov singular = (np.diagonal(Finf).real <= kalman_filter.tolerance_diffuse) nsingular = np.sum(~singular, axis=1) # Adjust the loglikelihood obs (see `KalmanFilter.loglikeobs` for # defaults on the adjustment) if not self.memory_no_likelihood: self.llf_obs += -0.5 * ( (self.k_endog - nmissing - nsingular) * np.log(self.scale) + scale_obs / self.scale) else: self.llf_obs[0] += -0.5 * (np.sum( (self.k_endog - nmissing - nsingular) * np.log(self.scale)) + scale_obs / self.scale) # Scale the filter output self.obs_cov = self.obs_cov * self.scale self.state_cov = self.state_cov * self.scale self.initial_state_cov = self.initial_state_cov * self.scale self.predicted_state_cov = self.predicted_state_cov * self.scale self.filtered_state_cov = self.filtered_state_cov * self.scale self.forecasts_error_cov = self.forecasts_error_cov * self.scale if self.missing_forecasts_error_cov is not None: self.missing_forecasts_error_cov = ( self.missing_forecasts_error_cov * self.scale) # Note: do not have to adjust the Kalman gain or tmp4 self.tmp1 = self.tmp1 * self.scale self.tmp2 = self.tmp2 / self.scale self.tmp3 = self.tmp3 / self.scale if not (self.memory_no_std_forecast or self.invert_lu or self.solve_lu or self.filter_collapsed): self._standardized_forecasts_error = ( self._standardized_forecasts_error / self.scale**0.5) # The self.model._scale value is only not None within a fixed_scale # context, in which case it is set and indicates that we should # generally view this results object as using a concentrated scale # (e.g. for d.o.f. computations), but because the fixed scale was # actually applied to the model prior to filtering, we do not need to # make any adjustments to the filter output, etc. elif self.model._scale is not None: self.filter_concentrated = True self.scale = self.model._scale # Now, save self.llf, and handle the memory_no_likelihood case if not self.memory_no_likelihood: self.llf = np.sum(self.llf_obs[self.loglikelihood_burn:]) else: self.llf = self.llf_obs[0] self.llf_obs = None @property def kalman_gain(self): """ Kalman gain matrices """ if self._kalman_gain is None: # k x n self._kalman_gain = np.zeros( (self.k_states, self.k_endog, self.nobs), dtype=self.dtype) for t in range(self.nobs): # In the case of entirely missing observations, let the Kalman # gain be zeros. if self.nmissing[t] == self.k_endog: continue design_t = 0 if self.design.shape[2] == 1 else t transition_t = 0 if self.transition.shape[2] == 1 else t if self.nmissing[t] == 0: self._kalman_gain[:, :, t] = np.dot( np.dot( self.transition[:, :, transition_t], self.predicted_state_cov[:, :, t] ), np.dot( np.transpose(self.design[:, :, design_t]), np.linalg.inv(self.forecasts_error_cov[:, :, t]) ) ) else: mask = ~self.missing[:, t].astype(bool) F = self.forecasts_error_cov[np.ix_(mask, mask, [t])] self._kalman_gain[:, mask, t] = np.dot( np.dot( self.transition[:, :, transition_t], self.predicted_state_cov[:, :, t] ), np.dot( np.transpose(self.design[mask, :, design_t]), np.linalg.inv(F[:, :, 0]) ) ) return self._kalman_gain @property def standardized_forecasts_error(self): r""" Standardized forecast errors Notes ----- The forecast errors produced by the Kalman filter are .. math:: v_t \sim N(0, F_t) Hypothesis tests are usually applied to the standardized residuals .. math:: v_t^s = B_t v_t \sim N(0, I) where :math:`B_t = L_t^{-1}` and :math:`F_t = L_t L_t'`; then :math:`F_t^{-1} = (L_t')^{-1} L_t^{-1} = B_t' B_t`; :math:`B_t` and :math:`L_t` are lower triangular. Finally, :math:`B_t v_t \sim N(0, B_t F_t B_t')` and :math:`B_t F_t B_t' = L_t^{-1} L_t L_t' (L_t')^{-1} = I`. Thus we can rewrite :math:`v_t^s = L_t^{-1} v_t` or :math:`L_t v_t^s = v_t`; the latter equation is the form required to use a linear solver to recover :math:`v_t^s`. Since :math:`L_t` is lower triangular, we can use a triangular solver (?TRTRS). """ if (self._standardized_forecasts_error is None and not self.memory_no_forecast): if self.k_endog == 1: self._standardized_forecasts_error = ( self.forecasts_error / self.forecasts_error_cov[0, 0, :]**0.5) else: from scipy import linalg self._standardized_forecasts_error = np.zeros( self.forecasts_error.shape, dtype=self.dtype) for t in range(self.forecasts_error_cov.shape[2]): if self.nmissing[t] > 0: self._standardized_forecasts_error[:, t] = np.nan if self.nmissing[t] < self.k_endog: mask = ~self.missing[:, t].astype(bool) F = self.forecasts_error_cov[np.ix_(mask, mask, [t])] try: upper, _ = linalg.cho_factor(F[:, :, 0]) self._standardized_forecasts_error[mask, t] = ( linalg.solve_triangular( upper, self.forecasts_error[mask, t], trans=1)) except linalg.LinAlgError: self._standardized_forecasts_error[mask, t] = ( np.nan) return self._standardized_forecasts_error def predict(self, start=None, end=None, dynamic=None, **kwargs): r""" In-sample and out-of-sample prediction for state space models generally Parameters ---------- start : int, optional Zero-indexed observation number at which to start prediction, i.e., the first prediction will be at start. end : int, optional Zero-indexed observation number at which to end prediction, i.e., the last prediction will be at end. dynamic : int, optional Offset relative to `start` at which to begin dynamic prediction. Prior to this observation, true endogenous values will be used for prediction; starting with this observation and continuing through the end of prediction, predicted endogenous values will be used instead. **kwargs If the prediction range is outside of the sample range, any of the state space representation matrices that are time-varying must have updated values provided for the out-of-sample range. For example, of `obs_intercept` is a time-varying component and the prediction range extends 10 periods beyond the end of the sample, a (`k_endog` x 10) matrix must be provided with the new intercept values. Returns ------- results : kalman_filter.PredictionResults A PredictionResults object. Notes ----- All prediction is performed by applying the deterministic part of the measurement equation using the predicted state variables. Out-of-sample prediction first applies the Kalman filter to missing data for the number of periods desired to obtain the predicted states. """ # Get the start and the end of the entire prediction range if start is None: start = 0 elif start < 0: raise ValueError('Cannot predict values previous to the sample.') if end is None: end = self.nobs # Prediction and forecasting is performed by iterating the Kalman # Kalman filter through the entire range [0, end] # Then, everything is returned corresponding to the range [start, end]. # In order to perform the calculations, the range is separately split # up into the following categories: # - static: (in-sample) the Kalman filter is run as usual # - dynamic: (in-sample) the Kalman filter is run, but on missing data # - forecast: (out-of-sample) the Kalman filter is run, but on missing # data # Short-circuit if end is before start if end <= start: raise ValueError('End of prediction must be after start.') # Get the number of forecasts to make after the end of the sample nforecast = max(0, end - self.nobs) # Get the number of dynamic prediction periods # If `dynamic=True`, then assume that we want to begin dynamic # prediction at the start of the sample prediction. if dynamic is True: dynamic = 0 # If `dynamic=False`, then assume we want no dynamic prediction if dynamic is False: dynamic = None # Check validity of dynamic and warn or error if issues dynamic, ndynamic = _check_dynamic(dynamic, start, end, self.nobs) # Get the number of in-sample static predictions if dynamic is None: nstatic = min(end, self.nobs) - min(start, self.nobs) else: # (use max(., 0), since dynamic can be prior to start) nstatic = max(dynamic - start, 0) # Cannot do in-sample prediction if we do not have appropriate # arrays (we can do out-of-sample forecasting, however) if nstatic > 0 and self.memory_no_forecast_mean: raise ValueError('In-sample prediction is not available if memory' ' conservation has been used to avoid storing' ' forecast means.') # Cannot do dynamic in-sample prediction if we do not have appropriate # arrays (we can do out-of-sample forecasting, however) if ndynamic > 0 and self.memory_no_predicted: raise ValueError('In-sample dynamic prediction is not available if' ' memory conservation has been used to avoid' ' storing forecasted or predicted state means' ' or covariances.') # Construct the predicted state and covariance matrix for each time # period depending on whether that time period corresponds to # one-step-ahead prediction, dynamic prediction, or out-of-sample # forecasting. # If we only have simple prediction, then we can use the already saved # Kalman filter output if ndynamic == 0 and nforecast == 0: results = self # If we have dynamic prediction or forecasting, then we need to # re-apply the Kalman filter else: # Figure out the period for which we need to run the Kalman filter if dynamic is not None: kf_start = min(start, dynamic, self.nobs) else: kf_start = min(start, self.nobs) kf_end = end # Make start, end consistent with the results that we're generating start = max(start - kf_start, 0) end = kf_end - kf_start # We must at least store forecasts and predictions kwargs['conserve_memory'] = ( self.conserve_memory & ~MEMORY_NO_FORECAST & ~MEMORY_NO_PREDICTED) # Can't use Chandrasekhar recursions for prediction kwargs['filter_method'] = ( self.model.filter_method & ~FILTER_CHANDRASEKHAR) # Even if we have not stored all predicted values (means and covs), # we can still do pure out-of-sample forecasting because we will # always have stored the last predicted values. In this case, we # will initialize the forecasting filter with these values if self.memory_no_predicted: constant = self.predicted_state[..., -1] stationary_cov = self.predicted_state_cov[..., -1] # Otherwise initialize with the predicted state / cov from the # existing results, at index kf_start (note that the time # dimension of predicted_state and predicted_state_cov is # self.nobs + 1; so e.g. in the case of pure forecasting we should # be using the very last predicted state and predicted state cov # elements, and kf_start will equal self.nobs which is correct) else: constant = self.predicted_state[..., kf_start] stationary_cov = self.predicted_state_cov[..., kf_start] kwargs.update({'initialization': 'known', 'constant': constant, 'stationary_cov': stationary_cov}) # Construct the new endogenous array. endog = np.zeros((nforecast, self.k_endog)) * np.nan model = self.model.extend( endog, start=kf_start, end=kf_end - nforecast, **kwargs) # Have to retroactively modify the model's endog if ndynamic > 0: model.endog[:, -(ndynamic + nforecast):] = np.nan with model.fixed_scale(self.scale): results = model.filter() return PredictionResults(results, start, end, nstatic, ndynamic, nforecast) class PredictionResults(FilterResults): r""" Results of in-sample and out-of-sample prediction for state space models generally Parameters ---------- results : FilterResults Output from filtering, corresponding to the prediction desired start : int Zero-indexed observation number at which to start forecasting, i.e., the first forecast will be at start. end : int Zero-indexed observation number at which to end forecasting, i.e., the last forecast will be at end. nstatic : int Number of in-sample static predictions (these are always the first elements of the prediction output). ndynamic : int Number of in-sample dynamic predictions (these always follow the static predictions directly, and are directly followed by the forecasts). nforecast : int Number of in-sample forecasts (these always follow the dynamic predictions directly). Attributes ---------- npredictions : int Number of observations in the predicted series; this is not necessarily the same as the number of observations in the original model from which prediction was performed. start : int Zero-indexed observation number at which to start prediction, i.e., the first predict will be at `start`; this is relative to the original model from which prediction was performed. end : int Zero-indexed observation number at which to end prediction, i.e., the last predict will be at `end`; this is relative to the original model from which prediction was performed. nstatic : int Number of in-sample static predictions. ndynamic : int Number of in-sample dynamic predictions. nforecast : int Number of in-sample forecasts. endog : ndarray The observation vector. design : ndarray The design matrix, :math:`Z`. obs_intercept : ndarray The intercept for the observation equation, :math:`d`. obs_cov : ndarray The covariance matrix for the observation equation :math:`H`. transition : ndarray The transition matrix, :math:`T`. state_intercept : ndarray The intercept for the transition equation, :math:`c`. selection : ndarray The selection matrix, :math:`R`. state_cov : ndarray The covariance matrix for the state equation :math:`Q`. filtered_state : ndarray The filtered state vector at each time period. filtered_state_cov : ndarray The filtered state covariance matrix at each time period. predicted_state : ndarray The predicted state vector at each time period. predicted_state_cov : ndarray The predicted state covariance matrix at each time period. forecasts : ndarray The one-step-ahead forecasts of observations at each time period. forecasts_error : ndarray The forecast errors at each time period. forecasts_error_cov : ndarray The forecast error covariance matrices at each time period. Notes ----- The provided ranges must be conformable, meaning that it must be that `end - start == nstatic + ndynamic + nforecast`. This class is essentially a view to the FilterResults object, but returning the appropriate ranges for everything. """ representation_attributes = [ 'endog', 'design', 'design', 'obs_intercept', 'obs_cov', 'transition', 'state_intercept', 'selection', 'state_cov' ] filter_attributes = [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov' ] def __init__(self, results, start, end, nstatic, ndynamic, nforecast): # Save the filter results object self.results = results # Save prediction ranges self.npredictions = start - end self.start = start self.end = end self.nstatic = nstatic self.ndynamic = ndynamic self.nforecast = nforecast def clear(self): attributes = (['endog'] + self.representation_attributes + self.filter_attributes) for attr in attributes: _attr = '_' + attr if hasattr(self, _attr): delattr(self, _attr) def __getattr__(self, attr): """ Provide access to the representation and filtered output in the appropriate range (`start` - `end`). """ # Prevent infinite recursive lookups if attr[0] == '_': raise AttributeError("'%s' object has no attribute '%s'" % (self.__class__.__name__, attr)) _attr = '_' + attr # Cache the attribute if not hasattr(self, _attr): if attr == 'endog' or attr in self.filter_attributes: # Get a copy value = getattr(self.results, attr).copy() # Subset to the correct time frame value = value[..., self.start:self.end] elif attr in self.representation_attributes: value = getattr(self.results, attr).copy() # If a time-invariant matrix, return it. Otherwise, subset to # the correct period. if value.shape[-1] == 1: value = value[..., 0] else: value = value[..., self.start:self.end] else: raise AttributeError("'%s' object has no attribute '%s'" % (self.__class__.__name__, attr)) setattr(self, _attr, value) return getattr(self, _attr) def _check_dynamic(dynamic, start, end, nobs): """ Verify dynamic and warn or error if issues Parameters ---------- dynamic : {int, None} The offset relative to start of the dynamic forecasts. None if no dynamic forecasts are required. start : int The location of the first forecast. end : int The location of the final forecast (inclusive). nobs : int The number of observations in the time series. Returns ------- dynamic : {int, None} The start location of the first dynamic forecast. None if there are no in-sample dynamic forecasts. ndynamic : int The number of dynamic forecasts """ if dynamic is None: return dynamic, 0 # Replace the relative dynamic offset with an absolute offset dynamic = start + dynamic # Validate the `dynamic` parameter if dynamic < 0: raise ValueError('Dynamic prediction cannot begin prior to the' ' first observation in the sample.') elif dynamic > end: warn('Dynamic prediction specified to begin after the end of' ' prediction, and so has no effect.', ValueWarning) return None, 0 elif dynamic > nobs: warn('Dynamic prediction specified to begin during' ' out-of-sample forecasting period, and so has no' ' effect.', ValueWarning) return None, 0 # Get the total size of the desired dynamic forecasting component # Note: the first `dynamic` periods of prediction are actually # *not* dynamic, because dynamic prediction begins at observation # `dynamic`. ndynamic = max(0, min(end, nobs) - dynamic) return dynamic, ndynamic statsmodels-0.12.2/statsmodels/tsa/statespace/kalman_smoother.py000066400000000000000000001756071400612667500252070ustar00rootroot00000000000000""" State Space Representation and Kalman Filter, Smoother Author: Chad Fulton License: Simplified-BSD """ import numpy as np from types import SimpleNamespace from statsmodels.tsa.statespace.representation import OptionWrapper from statsmodels.tsa.statespace.kalman_filter import (KalmanFilter, FilterResults) from statsmodels.tsa.statespace.tools import ( reorder_missing_matrix, reorder_missing_vector, copy_index_matrix) from statsmodels.tsa.statespace import tools SMOOTHER_STATE = 0x01 # Durbin and Koopman (2012), Chapter 4.4.2 SMOOTHER_STATE_COV = 0x02 # ibid., Chapter 4.4.3 SMOOTHER_DISTURBANCE = 0x04 # ibid., Chapter 4.5 SMOOTHER_DISTURBANCE_COV = 0x08 # ibid., Chapter 4.5 SMOOTHER_STATE_AUTOCOV = 0x10 # ibid., Chapter 4.7 SMOOTHER_ALL = ( SMOOTHER_STATE | SMOOTHER_STATE_COV | SMOOTHER_DISTURBANCE | SMOOTHER_DISTURBANCE_COV | SMOOTHER_STATE_AUTOCOV ) SMOOTH_CONVENTIONAL = 0x01 SMOOTH_CLASSICAL = 0x02 SMOOTH_ALTERNATIVE = 0x04 SMOOTH_UNIVARIATE = 0x08 class KalmanSmoother(KalmanFilter): r""" State space representation of a time series process, with Kalman filter and smoother. Parameters ---------- k_endog : {array_like, int} The observed time-series process :math:`y` if array like or the number of variables in the process if an integer. k_states : int The dimension of the unobserved state process. k_posdef : int, optional The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation. Must be less than or equal to `k_states`. Default is `k_states`. results_class : class, optional Default results class to use to save filtering output. Default is `SmootherResults`. If specified, class must extend from `SmootherResults`. **kwargs Keyword arguments may be used to provide default values for state space matrices, for Kalman filtering options, or for Kalman smoothing options. See `Representation` for more details. """ smoother_outputs = [ 'smoother_state', 'smoother_state_cov', 'smoother_state_autocov', 'smoother_disturbance', 'smoother_disturbance_cov', 'smoother_all', ] smoother_state = OptionWrapper('smoother_output', SMOOTHER_STATE) smoother_state_cov = OptionWrapper('smoother_output', SMOOTHER_STATE_COV) smoother_disturbance = ( OptionWrapper('smoother_output', SMOOTHER_DISTURBANCE) ) smoother_disturbance_cov = ( OptionWrapper('smoother_output', SMOOTHER_DISTURBANCE_COV) ) smoother_state_autocov = ( OptionWrapper('smoother_output', SMOOTHER_STATE_AUTOCOV) ) smoother_all = OptionWrapper('smoother_output', SMOOTHER_ALL) smooth_methods = [ 'smooth_conventional', 'smooth_alternative', 'smooth_classical' ] smooth_conventional = OptionWrapper('smooth_method', SMOOTH_CONVENTIONAL) """ (bool) Flag for conventional (Durbin and Koopman, 2012) Kalman smoothing. """ smooth_alternative = OptionWrapper('smooth_method', SMOOTH_ALTERNATIVE) """ (bool) Flag for alternative (modified Bryson-Frazier) smoothing. """ smooth_classical = OptionWrapper('smooth_method', SMOOTH_CLASSICAL) """ (bool) Flag for classical (see e.g. Anderson and Moore, 1979) smoothing. """ smooth_univariate = OptionWrapper('smooth_method', SMOOTH_UNIVARIATE) """ (bool) Flag for univariate smoothing (uses modified Bryson-Frazier timing). """ # Default smoother options smoother_output = SMOOTHER_ALL smooth_method = 0 def __init__(self, k_endog, k_states, k_posdef=None, results_class=None, kalman_smoother_classes=None, **kwargs): # Set the default results class if results_class is None: results_class = SmootherResults super(KalmanSmoother, self).__init__( k_endog, k_states, k_posdef, results_class=results_class, **kwargs ) # Options self.prefix_kalman_smoother_map = ( kalman_smoother_classes if kalman_smoother_classes is not None else tools.prefix_kalman_smoother_map.copy()) # Setup the underlying Kalman smoother storage self._kalman_smoothers = {} # Set the smoother options self.set_smoother_output(**kwargs) self.set_smooth_method(**kwargs) def _clone_kwargs(self, endog, **kwargs): # See Representation._clone_kwargs for docstring kwargs = super(KalmanSmoother, self)._clone_kwargs(endog, **kwargs) # Get defaults for options kwargs.setdefault('smoother_output', self.smoother_output) kwargs.setdefault('smooth_method', self.smooth_method) return kwargs @property def _kalman_smoother(self): prefix = self.prefix if prefix in self._kalman_smoothers: return self._kalman_smoothers[prefix] return None def _initialize_smoother(self, smoother_output=None, smooth_method=None, prefix=None, **kwargs): if smoother_output is None: smoother_output = self.smoother_output if smooth_method is None: smooth_method = self.smooth_method # Make sure we have the required Kalman filter prefix, dtype, create_filter, create_statespace = ( self._initialize_filter(prefix, **kwargs) ) # Determine if we need to (re-)create the smoother # (definitely need to recreate if we recreated the filter) create_smoother = (create_filter or prefix not in self._kalman_smoothers) if not create_smoother: kalman_smoother = self._kalman_smoothers[prefix] create_smoother = (kalman_smoother.kfilter is not self._kalman_filters[prefix]) # If the dtype-specific _kalman_smoother does not exist (or if we # need to re-create it), create it if create_smoother: # Setup the smoother cls = self.prefix_kalman_smoother_map[prefix] self._kalman_smoothers[prefix] = cls( self._statespaces[prefix], self._kalman_filters[prefix], smoother_output, smooth_method ) # Otherwise, update the smoother parameters else: self._kalman_smoothers[prefix].set_smoother_output( smoother_output, False) self._kalman_smoothers[prefix].set_smooth_method(smooth_method) return prefix, dtype, create_smoother, create_filter, create_statespace def set_smoother_output(self, smoother_output=None, **kwargs): """ Set the smoother output The smoother can produce several types of results. The smoother output variable controls which are calculated and returned. Parameters ---------- smoother_output : int, optional Bitmask value to set the smoother output to. See notes for details. **kwargs Keyword arguments may be used to influence the smoother output by setting individual boolean flags. See notes for details. Notes ----- The smoother output is defined by a collection of boolean flags, and is internally stored as a bitmask. The methods available are: SMOOTHER_STATE = 0x01 Calculate and return the smoothed states. SMOOTHER_STATE_COV = 0x02 Calculate and return the smoothed state covariance matrices. SMOOTHER_STATE_AUTOCOV = 0x10 Calculate and return the smoothed state lag-one autocovariance matrices. SMOOTHER_DISTURBANCE = 0x04 Calculate and return the smoothed state and observation disturbances. SMOOTHER_DISTURBANCE_COV = 0x08 Calculate and return the covariance matrices for the smoothed state and observation disturbances. SMOOTHER_ALL Calculate and return all results. If the bitmask is set directly via the `smoother_output` argument, then the full method must be provided. If keyword arguments are used to set individual boolean flags, then the lowercase of the method must be used as an argument name, and the value is the desired value of the boolean flag (True or False). Note that the smoother output may also be specified by directly modifying the class attributes which are defined similarly to the keyword arguments. The default smoother output is SMOOTHER_ALL. If performance is a concern, only those results which are needed should be specified as any results that are not specified will not be calculated. For example, if the smoother output is set to only include SMOOTHER_STATE, the smoother operates much more quickly than if all output is required. Examples -------- >>> import statsmodels.tsa.statespace.kalman_smoother as ks >>> mod = ks.KalmanSmoother(1,1) >>> mod.smoother_output 15 >>> mod.set_smoother_output(smoother_output=0) >>> mod.smoother_state = True >>> mod.smoother_output 1 >>> mod.smoother_state True """ if smoother_output is not None: self.smoother_output = smoother_output for name in KalmanSmoother.smoother_outputs: if name in kwargs: setattr(self, name, kwargs[name]) def set_smooth_method(self, smooth_method=None, **kwargs): r""" Set the smoothing method The smoothing method can be used to override the Kalman smoother approach used. By default, the Kalman smoother used depends on the Kalman filter method. Parameters ---------- smooth_method : int, optional Bitmask value to set the filter method to. See notes for details. **kwargs Keyword arguments may be used to influence the filter method by setting individual boolean flags. See notes for details. Notes ----- The smoothing method is defined by a collection of boolean flags, and is internally stored as a bitmask. The methods available are: SMOOTH_CONVENTIONAL = 0x01 Default Kalman smoother, as presented in Durbin and Koopman, 2012 chapter 4. SMOOTH_CLASSICAL = 0x02 Classical Kalman smoother, as presented in Anderson and Moore, 1979 or Durbin and Koopman, 2012 chapter 4.6.1. SMOOTH_ALTERNATIVE = 0x04 Modified Bryson-Frazier Kalman smoother method; this is identical to the conventional method of Durbin and Koopman, 2012, except that an additional intermediate step is included. SMOOTH_UNIVARIATE = 0x08 Univariate Kalman smoother, as presented in Durbin and Koopman, 2012 chapter 6, except with modified Bryson-Frazier timing. Practically speaking, these methods should all produce the same output but different computational implications, numerical stability implications, or internal timing assumptions. Note that only the first method is available if using a Scipy version older than 0.16. If the bitmask is set directly via the `smooth_method` argument, then the full method must be provided. If keyword arguments are used to set individual boolean flags, then the lowercase of the method must be used as an argument name, and the value is the desired value of the boolean flag (True or False). Note that the filter method may also be specified by directly modifying the class attributes which are defined similarly to the keyword arguments. The default filtering method is SMOOTH_CONVENTIONAL. Examples -------- >>> mod = sm.tsa.statespace.SARIMAX(range(10)) >>> mod.smooth_method 1 >>> mod.filter_conventional True >>> mod.filter_univariate = True >>> mod.smooth_method 17 >>> mod.set_smooth_method(filter_univariate=False, filter_collapsed=True) >>> mod.smooth_method 33 >>> mod.set_smooth_method(smooth_method=1) >>> mod.filter_conventional True >>> mod.filter_univariate False >>> mod.filter_collapsed False >>> mod.filter_univariate = True >>> mod.smooth_method 17 """ if smooth_method is not None: self.smooth_method = smooth_method for name in KalmanSmoother.smooth_methods: if name in kwargs: setattr(self, name, kwargs[name]) def _smooth(self, smoother_output=None, smooth_method=None, prefix=None, complex_step=False, results=None, **kwargs): # Initialize the smoother prefix, dtype, create_smoother, create_filter, create_statespace = ( self._initialize_smoother( smoother_output, smooth_method, prefix=prefix, **kwargs )) # Check that the filter and statespace weren't just recreated if create_filter or create_statespace: raise ValueError('Passed settings forced re-creation of the' ' Kalman filter. Please run `_filter` before' ' running `_smooth`.') # Get the appropriate smoother smoother = self._kalman_smoothers[prefix] # Run the smoother smoother() return smoother def smooth(self, smoother_output=None, smooth_method=None, results=None, run_filter=True, prefix=None, complex_step=False, update_representation=True, update_filter=True, update_smoother=True, **kwargs): """ Apply the Kalman smoother to the statespace model. Parameters ---------- smoother_output : int, optional Determines which Kalman smoother output calculate. Default is all (including state, disturbances, and all covariances). results : class or object, optional If a class, then that class is instantiated and returned with the result of both filtering and smoothing. If an object, then that object is updated with the smoothing data. If None, then a SmootherResults object is returned with both filtering and smoothing results. run_filter : bool, optional Whether or not to run the Kalman filter prior to smoothing. Default is True. prefix : str The prefix of the datatype. Usually only used internally. Returns ------- SmootherResults object """ # Run the filter kfilter = self._filter(**kwargs) # Create the results object results = self.results_class(self) if update_representation: results.update_representation(self) if update_filter: results.update_filter(kfilter) else: # (even if we don't update all filter results, still need to # update this) results.nobs_diffuse = kfilter.nobs_diffuse # Run the smoother if smoother_output is None: smoother_output = self.smoother_output smoother = self._smooth(smoother_output, results=results, **kwargs) # Update the results if update_smoother: results.update_smoother(smoother) return results class SmootherResults(FilterResults): r""" Results from applying the Kalman smoother and/or filter to a state space model. Parameters ---------- model : Representation A Statespace representation Attributes ---------- nobs : int Number of observations. k_endog : int The dimension of the observation series. k_states : int The dimension of the unobserved state process. k_posdef : int The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation. dtype : dtype Datatype of representation matrices prefix : str BLAS prefix of representation matrices shapes : dictionary of name:tuple A dictionary recording the shapes of each of the representation matrices as tuples. endog : ndarray The observation vector. design : ndarray The design matrix, :math:`Z`. obs_intercept : ndarray The intercept for the observation equation, :math:`d`. obs_cov : ndarray The covariance matrix for the observation equation :math:`H`. transition : ndarray The transition matrix, :math:`T`. state_intercept : ndarray The intercept for the transition equation, :math:`c`. selection : ndarray The selection matrix, :math:`R`. state_cov : ndarray The covariance matrix for the state equation :math:`Q`. missing : array of bool An array of the same size as `endog`, filled with boolean values that are True if the corresponding entry in `endog` is NaN and False otherwise. nmissing : array of int An array of size `nobs`, where the ith entry is the number (between 0 and k_endog) of NaNs in the ith row of the `endog` array. time_invariant : bool Whether or not the representation matrices are time-invariant initialization : str Kalman filter initialization method. initial_state : array_like The state vector used to initialize the Kalamn filter. initial_state_cov : array_like The state covariance matrix used to initialize the Kalamn filter. filter_method : int Bitmask representing the Kalman filtering method inversion_method : int Bitmask representing the method used to invert the forecast error covariance matrix. stability_method : int Bitmask representing the methods used to promote numerical stability in the Kalman filter recursions. conserve_memory : int Bitmask representing the selected memory conservation method. tolerance : float The tolerance at which the Kalman filter determines convergence to steady-state. loglikelihood_burn : int The number of initial periods during which the loglikelihood is not recorded. converged : bool Whether or not the Kalman filter converged. period_converged : int The time period in which the Kalman filter converged. filtered_state : ndarray The filtered state vector at each time period. filtered_state_cov : ndarray The filtered state covariance matrix at each time period. predicted_state : ndarray The predicted state vector at each time period. predicted_state_cov : ndarray The predicted state covariance matrix at each time period. kalman_gain : ndarray The Kalman gain at each time period. forecasts : ndarray The one-step-ahead forecasts of observations at each time period. forecasts_error : ndarray The forecast errors at each time period. forecasts_error_cov : ndarray The forecast error covariance matrices at each time period. loglikelihood : ndarray The loglikelihood values at each time period. collapsed_forecasts : ndarray If filtering using collapsed observations, stores the one-step-ahead forecasts of collapsed observations at each time period. collapsed_forecasts_error : ndarray If filtering using collapsed observations, stores the one-step-ahead forecast errors of collapsed observations at each time period. collapsed_forecasts_error_cov : ndarray If filtering using collapsed observations, stores the one-step-ahead forecast error covariance matrices of collapsed observations at each time period. standardized_forecast_error : ndarray The standardized forecast errors smoother_output : int Bitmask representing the generated Kalman smoothing output scaled_smoothed_estimator : ndarray The scaled smoothed estimator at each time period. scaled_smoothed_estimator_cov : ndarray The scaled smoothed estimator covariance matrices at each time period. smoothing_error : ndarray The smoothing error covariance matrices at each time period. smoothed_state : ndarray The smoothed state at each time period. smoothed_state_cov : ndarray The smoothed state covariance matrices at each time period. smoothed_state_autocov : ndarray The smoothed state lago-one autocovariance matrices at each time period: :math:`Cov(\alpha_{t+1}, \alpha_t)`. smoothed_measurement_disturbance : ndarray The smoothed measurement at each time period. smoothed_state_disturbance : ndarray The smoothed state at each time period. smoothed_measurement_disturbance_cov : ndarray The smoothed measurement disturbance covariance matrices at each time period. smoothed_state_disturbance_cov : ndarray The smoothed state disturbance covariance matrices at each time period. """ _smoother_attributes = [ 'smoother_output', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov', 'innovations_transition' ] _smoother_options = KalmanSmoother.smoother_outputs _attributes = FilterResults._model_attributes + _smoother_attributes def update_representation(self, model, only_options=False): """ Update the results to match a given model Parameters ---------- model : Representation The model object from which to take the updated values. only_options : bool, optional If set to true, only the smoother and filter options are updated, and the state space representation is not updated. Default is False. Notes ----- This method is rarely required except for internal usage. """ super(SmootherResults, self).update_representation(model, only_options) # Save the options as boolean variables for name in self._smoother_options: setattr(self, name, getattr(model, name, None)) # Initialize holders for smoothed forecasts self._smoothed_forecasts = None self._smoothed_forecasts_error = None self._smoothed_forecasts_error_cov = None def update_smoother(self, smoother): """ Update the smoother results Parameters ---------- smoother : KalmanSmoother The model object from which to take the updated values. Notes ----- This method is rarely required except for internal usage. """ # Copy the appropriate output attributes = [] # Since update_representation will already have been called, we can # use the boolean options smoother_* and know they match the smoother # itself if self.smoother_state or self.smoother_disturbance: attributes.append('scaled_smoothed_estimator') if self.smoother_state_cov or self.smoother_disturbance_cov: attributes.append('scaled_smoothed_estimator_cov') if self.smoother_state: attributes.append('smoothed_state') if self.smoother_state_cov: attributes.append('smoothed_state_cov') if self.smoother_state_autocov: attributes.append('smoothed_state_autocov') if self.smoother_disturbance: attributes += [ 'smoothing_error', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance' ] if self.smoother_disturbance_cov: attributes += [ 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov' ] has_missing = np.sum(self.nmissing) > 0 for name in self._smoother_attributes: if name == 'smoother_output': pass elif name in attributes: if name in ['smoothing_error', 'smoothed_measurement_disturbance']: vector = getattr(smoother, name, None) if vector is not None and has_missing: vector = np.array(reorder_missing_vector( vector, self.missing, prefix=self.prefix)) else: vector = np.array(vector, copy=True) setattr(self, name, vector) elif name == 'smoothed_measurement_disturbance_cov': matrix = getattr(smoother, name, None) if matrix is not None and has_missing: matrix = reorder_missing_matrix( matrix, self.missing, reorder_rows=True, reorder_cols=True, prefix=self.prefix) # In the missing data case, we want to set the missing # components equal to their unconditional distribution copy_index_matrix( self.obs_cov, matrix, self.missing, index_rows=True, index_cols=True, inplace=True, prefix=self.prefix) else: matrix = np.array(matrix, copy=True) setattr(self, name, matrix) else: setattr(self, name, np.array(getattr(smoother, name, None), copy=True)) else: setattr(self, name, None) self.innovations_transition = ( np.array(smoother.innovations_transition, copy=True)) # Diffuse objects self.scaled_smoothed_diffuse_estimator = None self.scaled_smoothed_diffuse1_estimator_cov = None self.scaled_smoothed_diffuse2_estimator_cov = None if self.nobs_diffuse > 0: self.scaled_smoothed_diffuse_estimator = np.array( smoother.scaled_smoothed_diffuse_estimator, copy=True) self.scaled_smoothed_diffuse1_estimator_cov = np.array( smoother.scaled_smoothed_diffuse1_estimator_cov, copy=True) self.scaled_smoothed_diffuse2_estimator_cov = np.array( smoother.scaled_smoothed_diffuse2_estimator_cov, copy=True) # Adjustments # For r_t (and similarly for N_t), what was calculated was # r_T, ..., r_{-1}. We only want r_0, ..., r_T # so exclude the appropriate element so that the time index is # consistent with the other returned output # r_t stored such that scaled_smoothed_estimator[0] == r_{-1} start = 1 end = None if 'scaled_smoothed_estimator' in attributes: self.scaled_smoothed_estimator = ( self.scaled_smoothed_estimator[:, start:end] ) if 'scaled_smoothed_estimator_cov' in attributes: self.scaled_smoothed_estimator_cov = ( self.scaled_smoothed_estimator_cov[:, :, start:end] ) # Clear the smoothed forecasts self._smoothed_forecasts = None self._smoothed_forecasts_error = None self._smoothed_forecasts_error_cov = None # Note: if we concentrated out the scale, need to adjust the # loglikelihood values and all of the covariance matrices and the # values that depend on the covariance matrices if self.filter_concentrated and self.model._scale is None: self.smoothed_state_cov *= self.scale self.smoothed_state_autocov *= self.scale self.smoothed_state_disturbance_cov *= self.scale self.smoothed_measurement_disturbance_cov *= self.scale self.scaled_smoothed_estimator /= self.scale self.scaled_smoothed_estimator_cov /= self.scale self.smoothing_error /= self.scale # Cache self.__smoothed_state_autocovariance = {} def _smoothed_state_autocovariance(self, shift, start, end, extend_kwargs=None): """ Compute "forward" autocovariances, Cov(t, t+j) Parameters ---------- shift : int The number of period to shift forwards when computing the autocovariance. This has the opposite sign as `lag` from the `smoothed_state_autocovariance` method. start : int, optional The start of the interval (inclusive) of autocovariances to compute and return. end : int, optional The end of the interval (exclusive) autocovariances to compute and return. Note that since it is an exclusive endpoint, the returned autocovariances do not include the value at this index. extend_kwargs : dict, optional Keyword arguments containing updated state space system matrices for handling out-of-sample autocovariance computations in time-varying state space models. """ if extend_kwargs is None: extend_kwargs = {} # Size of returned array in the time dimension n = end - start # Get number of post-sample periods we need to create an extended # model to compute if shift == 0: max_insample = self.nobs - shift else: max_insample = self.nobs - shift + 1 n_postsample = max(0, end - max_insample) # Get full in-sample arrays if shift != 0: L = self.innovations_transition P = self.predicted_state_cov N = self.scaled_smoothed_estimator_cov else: acov = self.smoothed_state_cov # If applicable, append out-of-sample arrays if n_postsample > 0: # Note: we need 1 less than the number of post endog = np.zeros((n_postsample, self.k_endog)) * np.nan mod = self.model.extend(endog, start=self.nobs, **extend_kwargs) mod.initialize_known(self.predicted_state[..., self.nobs], self.predicted_state_cov[..., self.nobs]) res = mod.smooth() if shift != 0: start_insample = max(0, start) L = np.concatenate((L[..., start_insample:], res.innovations_transition), axis=2) P = np.concatenate((P[..., start_insample:], res.predicted_state_cov[..., 1:]), axis=2) N = np.concatenate((N[..., start_insample:], res.scaled_smoothed_estimator_cov), axis=2) end -= start_insample start -= start_insample else: acov = np.concatenate((acov, res.predicted_state_cov), axis=2) if shift != 0: # Subset to appropriate start, end start_insample = max(0, start) LT = L[..., start_insample:end + shift - 1].T P = P[..., start_insample:end + shift].T N = N[..., start_insample:end + shift - 1].T # Intermediate computations tmpLT = np.eye(self.k_states)[None, :, :] length = P.shape[0] - shift # this is the required length of LT for i in range(1, shift + 1): tmpLT = LT[shift - i:length + shift - i] @ tmpLT eye = np.eye(self.k_states)[None, ...] # Compute the autocovariance acov = np.zeros((n, self.k_states, self.k_states)) acov[:start_insample - start] = np.nan acov[start_insample - start:] = ( P[:-shift] @ tmpLT @ (eye - N[shift - 1:] @ P[shift:])) else: acov = acov.T[start:end] return acov def smoothed_state_autocovariance(self, lag=1, t=None, start=None, end=None, extend_kwargs=None): r""" Compute state vector autocovariances, conditional on the full dataset Computes: .. math:: Cov(\alpha_t - \hat \alpha_t, \alpha_{t - j} - \hat \alpha_{t - j}) where the `lag` argument gives the value for :math:`j`. Thus when the `lag` argument is positive, the autocovariance is between the current and previous periods, while if `lag` is negative the autocovariance is between the current and future periods. Parameters ---------- lag : int, optional The number of period to shift when computing the autocovariance. Default is 1. t : int, optional A specific period for which to compute and return the autocovariance. Cannot be used in combination with `start` or `end`. See the Returns section for details on how this parameter affects what is what is returned. start : int, optional The start of the interval (inclusive) of autocovariances to compute and return. Cannot be used in combination with the `t` argument. See the Returns section for details on how this parameter affects what is what is returned. Default is 0. end : int, optional The end of the interval (exclusive) autocovariances to compute and return. Note that since it is an exclusive endpoint, the returned autocovariances do not include the value at this index. Cannot be used in combination with the `t` argument. See the Returns section for details on how this parameter affects what is what is returned and what the default value is. extend_kwargs : dict, optional Keyword arguments containing updated state space system matrices for handling out-of-sample autocovariance computations in time-varying state space models. Returns ------- acov : ndarray Array of autocovariance matrices. If the argument `t` is not provided, then it is shaped `(k_states, k_states, n)`, while if `t` given then the third axis is dropped and the array is shaped `(k_states, k_states)`. The output under the default case differs somewhat based on the state space model and the sign of the lag. To see how these cases differ, denote the output at each time point as Cov(t, t-j). Then: - If `lag > 0` (and the model is either time-varying or time-invariant), then the returned array is shaped `(*, *, nobs)` and each entry [:, :, t] contains Cov(t, t-j). However, the model does not have enough information to compute autocovariances in the pre-sample period, so that we cannot compute Cov(1, 1-lag), Cov(2, 2-lag), ..., Cov(lag, 0). Thus the first `lag` entries have all values set to NaN. - If the model is time-invariant and `lag < -1` or if `lag` is 0 or -1, and the model is either time-invariant or time-varying, then the returned array is shaped `(*, *, nobs)` and each entry [:, :, t] contains Cov(t, t+j). Moreover, all entries are available (i.e. there are no NaNs). - If the model is time-varying and `lag < -1` and `extend_kwargs` is not provided, then the returned array is shaped `(*, *, nobs - lag + 1)`. - However, if the model is time-varying and `lag < -1`, then `extend_kwargs` can be provided with `lag - 1` additional matrices so that the returned array is shaped `(*, *, nobs)` as usual. More generally, the dimension of the last axis will be `start - end`. Notes ----- This method computes: .. math:: Cov(\alpha_t - \hat \alpha_t, \alpha_{t - j} - \hat \alpha_{t - j}) where the `lag` argument determines the autocovariance order :math:`j`, and `lag` is an integer (positive, zero, or negative). This method cannot compute values associated with time points prior to the sample, and so it returns a matrix of NaN values for these time points. For example, if `start=0` and `lag=2`, then assuming the output is assigned to the variable `acov`, we will have `acov[..., 0]` and `acov[..., 1]` as matrices filled with NaN values. Based only on the "current" results object (i.e. the Kalman smoother applied to the sample), there is not enough information to compute Cov(t, t+j) for the last `lag - 1` observations of the sample. However, the values can be computed for these time points using the transition equation of the state space representation, and so for time-invariant state space models we do compute these values. For time-varying models, this can also be done, but updated state space matrices for the out-of-sample time points must be provided via the `extend_kwargs` argument. See [1]_, Chapter 4.7, for all details about how these autocovariances are computed. The `t` and `start`/`end` parameters compute and return only the requested autocovariances. As a result, using these parameters is recommended to reduce the computational burden, particularly if the number of observations and/or the dimension of the state vector is large. References ---------- .. [1] Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods: Second Edition. Oxford University Press. """ # We can cache the results for time-invariant models cache_key = None if extend_kwargs is None or len(extend_kwargs) == 0: cache_key = (lag, t, start, end) # Short-circuit for a cache-hit if (cache_key is not None and cache_key in self.__smoothed_state_autocovariance): return self.__smoothed_state_autocovariance[cache_key] # Switch to only positive values for `lag` forward_autocovariances = False if lag < 0: lag = -lag forward_autocovariances = True # Handle `t` if t is not None and (start is not None or end is not None): raise ValueError('Cannot specify both `t` and `start` or `end`.') if t is not None: start = t end = t + 1 # Defaults if start is None: start = 0 if end is None: if forward_autocovariances and lag > 1 and extend_kwargs is None: end = self.nobs - lag + 1 else: end = self.nobs if extend_kwargs is None: extend_kwargs = {} # Sanity checks if start < 0 or end < 0: raise ValueError('Negative `t`, `start`, or `end` is not allowed.') if end < start: raise ValueError('`end` must be after `start`') if lag == 0 and self.smoothed_state_cov is None: raise RuntimeError('Cannot return smoothed state covariances' ' if those values have not been computed by' ' Kalman smoothing.') # We already have in-sample (+1 out-of-sample) smoothed covariances if lag == 0 and end <= self.nobs + 1: acov = self.smoothed_state_cov if end == self.nobs + 1: acov = np.concatenate( (acov[..., start:], self.predicted_state_cov[..., -1:]), axis=2).T else: acov = acov.T[start:end] # In-sample, we can compute up to Cov(T, T+1) or Cov(T+1, T) and down # to Cov(1, 2) or Cov(2, 1). So: # - For lag=1 we set Cov(1, 0) = np.nan and then can compute up to T-1 # in-sample values Cov(2, 1), ..., Cov(T, T-1) and the first # out-of-sample value Cov(T+1, T) elif (lag == 1 and self.smoothed_state_autocov is not None and not forward_autocovariances and end <= self.nobs + 1): # nans = np.zeros((self.k_states, self.k_states, lag)) * np.nan # acov = np.concatenate((nans, self.smoothed_state_autocov), # axis=2).transpose(2, 0, 1)[start:end] if start == 0: nans = np.zeros((self.k_states, self.k_states, lag)) * np.nan acov = np.concatenate( (nans, self.smoothed_state_autocov[..., :end - 1]), axis=2) else: acov = self.smoothed_state_autocov[..., start - 1:end - 1] acov = acov.transpose(2, 0, 1) # - For lag=-1 we can compute T in-sample values, Cov(1, 2), ..., # Cov(T, T+1) but we cannot compute the first out-of-sample value # Cov(T+1, T+2). elif (lag == 1 and self.smoothed_state_autocov is not None and forward_autocovariances and end < self.nobs + 1): acov = self.smoothed_state_autocov.T[start:end] # Otherwise, we need to compute additional values at the end of the # sample else: if forward_autocovariances: # Cov(t, t + lag), t = start, ..., end acov = self._smoothed_state_autocovariance( lag, start, end, extend_kwargs=extend_kwargs) else: # Cov(t, t + lag)' = Cov(t + lag, t), # with t = start - lag, ..., end - lag out = self._smoothed_state_autocovariance( lag, start - lag, end - lag, extend_kwargs=extend_kwargs) acov = out.transpose(0, 2, 1) # Squeeze the last axis or else reshape to have the same axis # definitions as e.g. smoothed_state_cov if t is not None: acov = acov[0] else: acov = acov.transpose(1, 2, 0) # Fill in the cache, if applicable if cache_key is not None: self.__smoothed_state_autocovariance[cache_key] = acov return acov def news(self, previous, t=None, start=None, end=None, revised=None, design=None): r""" Compute the news and impacts associated with a data release Parameters ---------- previous : SmootherResults Prior results object relative to which to compute the news. This results object must have identical state space representation for the prior sample period so that the only difference is that this results object has updates to the observed data. t : int, optional A specific period for which to compute the news. Cannot be used in combination with `start` or `end`. start : int, optional The start of the interval (inclusive) of news to compute. Cannot be used in combination with the `t` argument. Default is the last period of the sample (`nobs - 1`). end : int, optional The end of the interval (exclusive) of news to compute. Note that since it is an exclusive endpoint, the returned news do not include the value at this index. Cannot be used in combination with the `t` argument. design : array, optional Design matrix for the period `t` in time-varying models. If this model has a time-varying design matrix, and the argument `t` is out of this model's sample, then a new design matrix for period `t` must be provided. Unused otherwise. Returns ------- news_results : SimpleNamespace News and impacts associated with a data release. Includes the following attributes: - `update_impacts`: update to forecasts of impacted variables from the news. It is equivalent to E[y^i | post] - E[y^i | revision], where y^i are the variables of interest. In [1]_, this is described as "revision" in equation (17). - `revision_impacts`: update to forecasts of variables impacted variables from data revisions. It is E[y^i | revision] - E[y^i | previous], and does not have a specific notation in [1]_, since there for simplicity they assume that there are no revisions. - `news`: the unexpected component of the updated data. Denoted I = y^u - E[y^u | previous], where y^u are the data points that were newly incorporated in a data release (but not including revisions to data points that already existed in the previous release). In [1]_, this is described as "news" in equation (17). - `gain`: the gain matrix associated with the "Kalman-like" update from the news, E[y I'] E[I I']^{-1}. In [1]_, this can be found in the equation For E[y_{k,t_k} \mid I_{v+1}] in the middle of page 17. - `update_forecasts`: forecasts of the updated periods used to construct the news, E[y^u | previous]. - `update_realized`: realizations of the updated periods used to construct the news, y^u. - `prev_impacted_forecasts`: previous forecast of the periods of interest, E[y^i | previous]. - `post_impacted_forecasts`: forecast of the periods of interest after taking into account both revisions and updates, E[y^i | post]. - `revision_results`: results object that updates the `previous` results to take into account data revisions. - `revisions_ix`: list of `(t, i)` positions of revisions in endog - `updates_ix`: list of `(t, i)` positions of updates to endog Notes ----- This method computes the effect of new data (e.g. from a new data release) on smoothed forecasts produced by a state space model, as described in [1]_. References ---------- .. [1] Bańbura, Marta and Modugno, Michele. 2010. "Maximum likelihood estimation of factor models on data sets with arbitrary pattern of missing data." No 1189, Working Paper Series, European Central Bank. https://EconPapers.repec.org/RePEc:ecb:ecbwps:20101189. .. [2] Bańbura, Marta, and Michele Modugno. "Maximum likelihood estimation of factor models on datasets with arbitrary pattern of missing data." Journal of Applied Econometrics 29, no. 1 (2014): 133-160. """ # Handle `t` if t is not None and (start is not None or end is not None): raise ValueError('Cannot specify both `t` and `start` or `end`.') if t is not None: start = t end = t + 1 # Defaults if start is None: start = self.nobs - 1 if end is None: end = self.nobs # Sanity checks if start < 0 or end < 0: raise ValueError('Negative `t`, `start`, or `end` is not allowed.') if end <= start: raise ValueError('`end` must be after `start`') if self.smoothed_state_cov is None: raise ValueError('Cannot compute news without having applied the' ' Kalman smoother first.') error_ss = ('This results object has %s and so it does not appear to' ' by an extension of `previous`. Can only compute the' ' news by comparing this results set to previous results' ' objects.') if self.nobs < previous.nobs: raise ValueError(error_ss % 'fewer observations than' ' `previous`') if not (self.k_endog == previous.k_endog and self.k_states == previous.k_states and self.k_posdef == previous.k_posdef): raise ValueError(error_ss % 'different state space dimensions than' ' `previous`') for key in self.model.shapes.keys(): if key == 'obs': continue tv = getattr(self, key).shape[-1] > 1 tv_prev = getattr(previous, key).shape[-1] > 1 if tv and not tv_prev: raise ValueError(error_ss % f'time-varying {key} while' ' `previous` does not') if not tv and tv_prev: raise ValueError(error_ss % f'time-invariant {key} while' ' `previous` does not') # We cannot forecast out-of-sample periods in a time-varying models if end > self.nobs and not self.model.time_invariant: raise RuntimeError('Cannot compute the impacts of news on periods' ' outside of the sample in time-varying' ' models.') # For time-varying case, figure out extension kwargs extend_kwargs = {} for key in self.model.shapes.keys(): if key == 'obs': continue mat = getattr(self, key) prev_mat = getattr(previous, key) if mat.shape[-1] > prev_mat.shape[-1]: extend_kwargs[key] = mat[..., prev_mat.shape[-1]:] # Figure out which indices have changed revisions_ix, updates_ix = previous.model.diff_endog(self.endog.T) # Compute prev / post impact forecasts prev_impacted_forecasts = ( previous.smoothed_forecasts[..., start:end]) if end > previous.nobs: predict_start = max(start, previous.nobs) p = previous.predict( start=predict_start, end=end, **extend_kwargs) prev_impacted_forecasts = np.concatenate( (prev_impacted_forecasts, p.forecasts), axis=1) post_impacted_forecasts = ( self.smoothed_forecasts[..., start:end]) if end > self.nobs: predict_start = max(start, self.nobs) p = self.predict(start=predict_start, end=end, **extend_kwargs) post_impacted_forecasts = np.concatenate( (post_impacted_forecasts, p.forecasts), axis=1) # If we have revisions to previous data, then we need to construct a # new results set that only includes those revisions if len(revisions_ix) > 0 and revised is None: # Copy time-varying matrices (required by clone) clone_kwargs = {} for key in self.model.shapes.keys(): if key == 'obs': continue prev_mat = getattr(previous, key) if prev_mat.shape[-1] > 1: clone_kwargs[key] = prev_mat rev_endog = self.endog.T[:previous.nobs].copy() rev_endog[previous.missing.astype(bool).T] = np.nan rev_mod = previous.model.clone(rev_endog, **clone_kwargs) # TODO: performance: can get a performance improvement for large # models with `update_filter=False, update_smoother=False`, # but then will need to manually populate the fields that we # need for what we do below (i.e. we call # `smoothed_forecasts` and `predict`) # TODO: performance: we don't need to smooth back through the # entire sample for what we're doing, since we only need # smoothed_forecasts for the impact period revised = rev_mod.smooth() # Compute impacts from the revisions, if any if len(revisions_ix) > 0: # Compute the effect of revisions on forecasts of the impacted # variables revised_impact_forecasts = ( revised.smoothed_forecasts[..., start:end]) if end > revised.nobs: predict_start = max(start, revised.nobs) p = revised.predict( start=predict_start, end=end, **extend_kwargs) revised_impact_forecasts = np.concatenate( (revised_impact_forecasts, p.forecasts), axis=1) revision_impacts = (revised_impact_forecasts - prev_impacted_forecasts).T if t is not None: revision_impacts = revision_impacts[0] else: revised = previous revision_impacts = None # Now handle updates if len(updates_ix) > 0: # Figure out which time points we need forecast errors for update_t, update_k = zip(*updates_ix) update_start_t = np.min(update_t) update_end_t = np.max(update_t) update_end_insample_t = np.minimum(revised.nobs - 1, update_end_t) update_nforecast = update_end_t - update_end_insample_t # For the in-sample periods, get out the smoothed forecasts for # the updated variables for each relevant time period i1 = update_start_t i2 = update_end_insample_t + 1 if i2 > i1: forecasts_insample = revised.smoothed_forecasts[:, i1:i2] else: forecasts_insample = np.zeros((self.k_endog, 0)) # For the out-of-sample periods, predicted and smoothed forecasts # for the updated variables are the same if update_nforecast > 0: forecast_start = previous.nobs forecast_end = forecast_start + update_nforecast p = revised.predict( start=forecast_start, end=forecast_end, **extend_kwargs) forecasts_oos = p.forecasts else: forecasts_oos = np.zeros((self.k_endog, 0)) forecasts = np.c_[forecasts_insample, forecasts_oos].T realized = self.endog.T[update_start_t:update_end_t + 1] forecasts_error = realized - forecasts # Now subset forecast errors to only the (time, endog) elements # that are updates ix_t = update_t - update_start_t update_realized = realized[ix_t, update_k] update_forecasts = forecasts[ix_t, update_k] update_forecasts_error = forecasts_error[ix_t, update_k] # Get the gains associated with each of the periods if self.design.shape[2] == 1: design = self.design[..., 0][None, ...] elif end <= self.nobs: design = self.design[..., start:end].transpose(2, 0, 1) else: if design is None: raise ValueError('Model has time-varying design matrix, so' ' an updated time-varying matrix for' ' period `t` is required.') elif design.ndim == 2: design = design[None, ...] else: design = design.transpose(2, 0, 1) state_gain = revised.smoothed_state_gain( updates_ix, start=start, end=end, extend_kwargs=extend_kwargs) obs_gain = design @ state_gain # Get the news update_impacts = obs_gain @ update_forecasts_error # Squeeze if `t` argument used if t is not None: obs_gain = obs_gain[0] update_impacts = update_impacts[0] else: update_impacts = None update_forecasts = None update_realized = None update_forecasts_error = None obs_gain = None # Results out = SimpleNamespace( # update to forecast of impacted variables from news # = E[y^i | post] - E[y^i | revision] = weight @ news update_impacts=update_impacts, # update to forecast of variables of interest from revisions # = E[y^i | revision] - E[y^i | previous] revision_impacts=revision_impacts, # news = A = y^u - E[y^u | previous] news=update_forecasts_error, # gain matrix = E[y A'] E[A A']^{-1} gain=obs_gain, # forecasts of the updated periods used to construct the news # = E[y^u | previous] update_forecasts=update_forecasts, # realizations of the updated periods used to construct the news # = y^u update_realized=update_realized, # previous forecast of the periods of interest, E[y^i | previous] prev_impacted_forecasts=prev_impacted_forecasts, # post. forecast of the periods of interest, E[y^i | post] post_impacted_forecasts=post_impacted_forecasts, # results object associated with the revision revision_results=None, # list of (x, y) positions of revisions to endog revisions_ix=revisions_ix, # list of (x, y) positions of updates to endog updates_ix=updates_ix) if len(revisions_ix) > 0: out.revision_results = revised return out def smoothed_state_gain(self, updates_ix, t=None, start=None, end=None, extend_kwargs=None): r""" Cov(\tilde \alpha_{t}, I) Var(I, I)^{-1} where I is a vector of forecast errors associated with `update_indices`. Parameters ---------- updates_ix : list List of indices `(t, i)`, where `t` denotes a zero-indexed time location and `i` denotes a zero-indexed endog variable. """ # Handle `t` if t is not None and (start is not None or end is not None): raise ValueError('Cannot specify both `t` and `start` or `end`.') if t is not None: start = t end = t + 1 # Defaults if start is None: start = self.nobs - 1 if end is None: end = self.nobs if extend_kwargs is None: extend_kwargs = {} # Sanity checks if start < 0 or end < 0: raise ValueError('Negative `t`, `start`, or `end` is not allowed.') if end <= start: raise ValueError('`end` must be after `start`') # Dimensions n_periods = end - start n_updates = len(updates_ix) # Helper to get possibly matrix that is possibly time-varying def get_mat(which, t): mat = getattr(self, which) if mat.shape[-1] > 1: if t < self.nobs: out = mat[..., t] else: if (which not in extend_kwargs or extend_kwargs[which].shape[-1] <= t - self.nobs): raise ValueError(f'Model has time-varying {which}' ' matrix, so an updated time-varying' ' matrix for the extension period is' ' required.') out = extend_kwargs[which][..., t - self.nobs] else: out = mat[..., 0] return out # Helper to get Cov(\tilde \alpha_{t}, I) def get_cov_state_revision(t): tmp1 = np.zeros((self.k_states, n_updates)) for i in range(n_updates): t_i, k_i = updates_ix[i] acov = self.smoothed_state_autocovariance( lag=t - t_i, t=t, extend_kwargs=extend_kwargs) Z_i = get_mat('design', t_i) tmp1[:, i:i + 1] = acov @ Z_i[k_i:k_i + 1].T return tmp1 # Compute Cov(\tilde \alpha_{t}, I) tmp1 = np.zeros((n_periods, self.k_states, n_updates)) for s in range(start, end): tmp1[s - start] = get_cov_state_revision(s) # Compute Var(I) tmp2 = np.zeros((n_updates, n_updates)) for i in range(n_updates): t_i, k_i = updates_ix[i] for j in range(i + 1): t_j, k_j = updates_ix[j] Z_i = get_mat('design', t_i) Z_j = get_mat('design', t_j) acov = self.smoothed_state_autocovariance( lag=t_i - t_j, t=t_i, extend_kwargs=extend_kwargs) tmp2[i, j] = tmp2[j, i] = ( Z_i[k_i:k_i + 1] @ acov @ Z_j[k_j:k_j + 1].T) if t_i == t_j: H = get_mat('obs_cov', t_i) if i == j: tmp2[i, j] += H[k_i, k_j] else: tmp2[i, j] += H[k_i, k_j] tmp2[j, i] += H[k_i, k_j] # Gain gain = tmp1 @ np.linalg.inv(tmp2) if t is not None: gain = gain[0] return gain def _get_smoothed_forecasts(self): if self._smoothed_forecasts is None: # Initialize empty arrays self._smoothed_forecasts = np.zeros(self.forecasts.shape, dtype=self.dtype) self._smoothed_forecasts_error = ( np.zeros(self.forecasts_error.shape, dtype=self.dtype) ) self._smoothed_forecasts_error_cov = ( np.zeros(self.forecasts_error_cov.shape, dtype=self.dtype) ) for t in range(self.nobs): design_t = 0 if self.design.shape[2] == 1 else t obs_cov_t = 0 if self.obs_cov.shape[2] == 1 else t obs_intercept_t = 0 if self.obs_intercept.shape[1] == 1 else t mask = ~self.missing[:, t].astype(bool) # We can recover forecasts self._smoothed_forecasts[:, t] = np.dot( self.design[:, :, design_t], self.smoothed_state[:, t] ) + self.obs_intercept[:, obs_intercept_t] if self.nmissing[t] > 0: self._smoothed_forecasts_error[:, t] = np.nan self._smoothed_forecasts_error[mask, t] = ( self.endog[mask, t] - self._smoothed_forecasts[mask, t] ) self._smoothed_forecasts_error_cov[:, :, t] = np.dot( np.dot(self.design[:, :, design_t], self.smoothed_state_cov[:, :, t]), self.design[:, :, design_t].T ) + self.obs_cov[:, :, obs_cov_t] return ( self._smoothed_forecasts, self._smoothed_forecasts_error, self._smoothed_forecasts_error_cov ) @property def smoothed_forecasts(self): return self._get_smoothed_forecasts()[0] @property def smoothed_forecasts_error(self): return self._get_smoothed_forecasts()[1] @property def smoothed_forecasts_error_cov(self): return self._get_smoothed_forecasts()[2] statsmodels-0.12.2/statsmodels/tsa/statespace/mlemodel.py000066400000000000000000006011511400612667500236060ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ State Space Model Author: Chad Fulton License: Simplified-BSD """ import contextlib import warnings import datetime as dt from types import SimpleNamespace import numpy as np import pandas as pd from scipy.stats import norm from statsmodels.tools.tools import pinv_extended, Bunch from statsmodels.tools.sm_exceptions import PrecisionWarning, ValueWarning from statsmodels.tools.numdiff import (_get_epsilon, approx_hess_cs, approx_fprime_cs, approx_fprime) from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.eval_measures import aic, aicc, bic, hqic import statsmodels.base.wrapper as wrap import statsmodels.tsa.base.prediction as pred from statsmodels.base.data import PandasData import statsmodels.tsa.base.tsa_model as tsbase from .news import NewsResults from .simulation_smoother import SimulationSmoother from .kalman_smoother import SmootherResults from .kalman_filter import INVERT_UNIVARIATE, SOLVE_LU, MEMORY_CONSERVE from .initialization import Initialization from .tools import prepare_exog, concat def _handle_args(names, defaults, *args, **kwargs): output_args = [] # We need to handle positional arguments in two ways, in case this was # called by a Scipy optimization routine if len(args) > 0: # the fit() method will pass a dictionary if isinstance(args[0], dict): flags = args[0] # otherwise, a user may have just used positional arguments... else: flags = dict(zip(names, args)) for i in range(len(names)): output_args.append(flags.get(names[i], defaults[i])) for name, value in flags.items(): if name in kwargs: raise TypeError("loglike() got multiple values for keyword" " argument '%s'" % name) else: for i in range(len(names)): output_args.append(kwargs.pop(names[i], defaults[i])) return tuple(output_args) + (kwargs,) def _check_index(desired_index, dta, title='data'): given_index = None if isinstance(dta, (pd.Series, pd.DataFrame)): given_index = dta.index if given_index is not None and not desired_index.equals(given_index): desired_freq = getattr(desired_index, 'freq', None) given_freq = getattr(given_index, 'freq', None) if ((desired_freq is not None or given_freq is not None) and desired_freq != given_freq): raise ValueError('Given %s does not have an index' ' that extends the index of the' ' model. Expected index frequency is' ' "%s", but got "%s".' % (title, desired_freq, given_freq)) else: raise ValueError('Given %s does not have an index' ' that extends the index of the' ' model.' % title) class MLEModel(tsbase.TimeSeriesModel): r""" State space model for maximum likelihood estimation Parameters ---------- endog : array_like The observed time-series process :math:`y` k_states : int The dimension of the unobserved state process. exog : array_like, optional Array of exogenous regressors, shaped nobs x k. Default is no exogenous regressors. dates : array_like of datetime, optional An array-like object of datetime objects. If a Pandas object is given for endog, it is assumed to have a DateIndex. freq : str, optional The frequency of the time-series. A Pandas offset or 'B', 'D', 'W', 'M', 'A', or 'Q'. This is optional if dates are given. **kwargs Keyword arguments may be used to provide default values for state space matrices or for Kalman filtering options. See `Representation`, and `KalmanFilter` for more details. Attributes ---------- ssm : statsmodels.tsa.statespace.kalman_filter.KalmanFilter Underlying state space representation. See Also -------- statsmodels.tsa.statespace.mlemodel.MLEResults statsmodels.tsa.statespace.kalman_filter.KalmanFilter statsmodels.tsa.statespace.representation.Representation Notes ----- This class wraps the state space model with Kalman filtering to add in functionality for maximum likelihood estimation. In particular, it adds the concept of updating the state space representation based on a defined set of parameters, through the `update` method or `updater` attribute (see below for more details on which to use when), and it adds a `fit` method which uses a numerical optimizer to select the parameters that maximize the likelihood of the model. The `start_params` `update` method must be overridden in the child class (and the `transform` and `untransform` methods, if needed). """ def __init__(self, endog, k_states, exog=None, dates=None, freq=None, **kwargs): # Initialize the model base super(MLEModel, self).__init__(endog=endog, exog=exog, dates=dates, freq=freq, missing='none') # Store kwargs to recreate model self._init_kwargs = kwargs # Prepared the endog array: C-ordered, shape=(nobs x k_endog) self.endog, self.exog = self.prepare_data() # Dimensions self.nobs = self.endog.shape[0] self.k_states = k_states # Initialize the state-space representation self.initialize_statespace(**kwargs) # Setup holder for fixed parameters self._has_fixed_params = False self._fixed_params = None self._params_index = None self._fixed_params_index = None self._free_params_index = None def prepare_data(self): """ Prepare data for use in the state space representation """ endog = np.array(self.data.orig_endog, order='C') exog = self.data.orig_exog if exog is not None: exog = np.array(exog) # Base class may allow 1-dim data, whereas we need 2-dim if endog.ndim == 1: endog.shape = (endog.shape[0], 1) # this will be C-contiguous return endog, exog def initialize_statespace(self, **kwargs): """ Initialize the state space representation Parameters ---------- **kwargs Additional keyword arguments to pass to the state space class constructor. """ # (Now self.endog is C-ordered and in long format (nobs x k_endog). To # get F-ordered and in wide format just need to transpose) endog = self.endog.T # Instantiate the state space object self.ssm = SimulationSmoother(endog.shape[0], self.k_states, nobs=endog.shape[1], **kwargs) # Bind the data to the model self.ssm.bind(endog) # Other dimensions, now that `ssm` is available self.k_endog = self.ssm.k_endog def _get_index_with_final_state(self): # The index we inherit from `TimeSeriesModel` will only cover the # data sample itself, but we will also need an index value for the # final state which is the next time step to the last datapoint. # This method figures out an appropriate value for the three types of # supported indexes: date-based, Int64Index, or RangeIndex if self._index_dates: if isinstance(self._index, pd.DatetimeIndex): index = pd.date_range( start=self._index[0], periods=len(self._index) + 1, freq=self._index.freq) elif isinstance(self._index, pd.PeriodIndex): index = pd.period_range( start=self._index[0], periods=len(self._index) + 1, freq=self._index.freq) else: raise NotImplementedError elif isinstance(self._index, pd.RangeIndex): # COMPAT: pd.RangeIndex does not have start, stop, step prior to # pandas 0.25 try: start = self._index.start stop = self._index.stop step = self._index.step except AttributeError: start = self._index._start stop = self._index._stop step = self._index._step index = pd.RangeIndex(start, stop + step, step) elif isinstance(self._index, pd.Int64Index): # The only valid Int64Index is a full, incrementing index, so this # is general value = self._index[-1] + 1 index = pd.Int64Index(self._index.tolist() + [value]) else: raise NotImplementedError return index def __setitem__(self, key, value): return self.ssm.__setitem__(key, value) def __getitem__(self, key): return self.ssm.__getitem__(key) def _get_init_kwds(self): # Get keywords based on model attributes kwds = super(MLEModel, self)._get_init_kwds() for key, value in kwds.items(): if value is None and hasattr(self.ssm, key): kwds[key] = getattr(self.ssm, key) return kwds def clone(self, endog, exog=None, **kwargs): """ Clone state space model with new data and optionally new specification Parameters ---------- endog : array_like The observed time-series process :math:`y` k_states : int The dimension of the unobserved state process. exog : array_like, optional Array of exogenous regressors, shaped nobs x k. Default is no exogenous regressors. kwargs Keyword arguments to pass to the new model class to change the model specification. Returns ------- model : MLEModel subclass Notes ----- This method must be implemented """ raise NotImplementedError('This method is not implemented in the base' ' class and must be set up by each specific' ' model.') def _clone_from_init_kwds(self, endog, **kwargs): # Cannot make this the default, because there is extra work required # for subclasses to make _get_init_kwds useful. use_kwargs = self._get_init_kwds() use_kwargs.update(kwargs) # Check for `exog` if getattr(self, 'k_exog', 0) > 0 and kwargs.get('exog', None) is None: raise ValueError('Cloning a model with an exogenous component' ' requires specifying a new exogenous array using' ' the `exog` argument.') mod = self.__class__(endog, **use_kwargs) return mod def set_filter_method(self, filter_method=None, **kwargs): """ Set the filtering method The filtering method controls aspects of which Kalman filtering approach will be used. Parameters ---------- filter_method : int, optional Bitmask value to set the filter method to. See notes for details. **kwargs Keyword arguments may be used to influence the filter method by setting individual boolean flags. See notes for details. Notes ----- This method is rarely used. See the corresponding function in the `KalmanFilter` class for details. """ self.ssm.set_filter_method(filter_method, **kwargs) def set_inversion_method(self, inversion_method=None, **kwargs): """ Set the inversion method The Kalman filter may contain one matrix inversion: that of the forecast error covariance matrix. The inversion method controls how and if that inverse is performed. Parameters ---------- inversion_method : int, optional Bitmask value to set the inversion method to. See notes for details. **kwargs Keyword arguments may be used to influence the inversion method by setting individual boolean flags. See notes for details. Notes ----- This method is rarely used. See the corresponding function in the `KalmanFilter` class for details. """ self.ssm.set_inversion_method(inversion_method, **kwargs) def set_stability_method(self, stability_method=None, **kwargs): """ Set the numerical stability method The Kalman filter is a recursive algorithm that may in some cases suffer issues with numerical stability. The stability method controls what, if any, measures are taken to promote stability. Parameters ---------- stability_method : int, optional Bitmask value to set the stability method to. See notes for details. **kwargs Keyword arguments may be used to influence the stability method by setting individual boolean flags. See notes for details. Notes ----- This method is rarely used. See the corresponding function in the `KalmanFilter` class for details. """ self.ssm.set_stability_method(stability_method, **kwargs) def set_conserve_memory(self, conserve_memory=None, **kwargs): """ Set the memory conservation method By default, the Kalman filter computes a number of intermediate matrices at each iteration. The memory conservation options control which of those matrices are stored. Parameters ---------- conserve_memory : int, optional Bitmask value to set the memory conservation method to. See notes for details. **kwargs Keyword arguments may be used to influence the memory conservation method by setting individual boolean flags. Notes ----- This method is rarely used. See the corresponding function in the `KalmanFilter` class for details. """ self.ssm.set_conserve_memory(conserve_memory, **kwargs) def set_smoother_output(self, smoother_output=None, **kwargs): """ Set the smoother output The smoother can produce several types of results. The smoother output variable controls which are calculated and returned. Parameters ---------- smoother_output : int, optional Bitmask value to set the smoother output to. See notes for details. **kwargs Keyword arguments may be used to influence the smoother output by setting individual boolean flags. Notes ----- This method is rarely used. See the corresponding function in the `KalmanSmoother` class for details. """ self.ssm.set_smoother_output(smoother_output, **kwargs) def initialize_known(self, initial_state, initial_state_cov): """Initialize known""" self.ssm.initialize_known(initial_state, initial_state_cov) def initialize_approximate_diffuse(self, variance=None): """Initialize approximate diffuse""" self.ssm.initialize_approximate_diffuse(variance) def initialize_stationary(self): """Initialize stationary""" self.ssm.initialize_stationary() @property def initialization(self): return self.ssm.initialization @initialization.setter def initialization(self, value): self.ssm.initialization = value @property def initial_variance(self): return self.ssm.initial_variance @initial_variance.setter def initial_variance(self, value): self.ssm.initial_variance = value @property def loglikelihood_burn(self): return self.ssm.loglikelihood_burn @loglikelihood_burn.setter def loglikelihood_burn(self, value): self.ssm.loglikelihood_burn = value @property def tolerance(self): return self.ssm.tolerance @tolerance.setter def tolerance(self, value): self.ssm.tolerance = value def _validate_can_fix_params(self, param_names): for param_name in param_names: if param_name not in self.param_names: raise ValueError('Invalid parameter name passed: "%s".' % param_name) @contextlib.contextmanager def fix_params(self, params): """ Fix parameters to specific values (context manager) Parameters ---------- params : dict Dictionary describing the fixed parameter values, of the form `param_name: fixed_value`. See the `param_names` property for valid parameter names. Examples -------- >>> mod = sm.tsa.SARIMAX(endog, order=(1, 0, 1)) >>> with mod.fix_params({'ar.L1': 0.5}): res = mod.fit() """ k_params = len(self.param_names) # Initialization (this is done here rather than in the constructor # because param_names may not be available at that point) if self._fixed_params is None: self._fixed_params = {} self._params_index = dict( zip(self.param_names, np.arange(k_params))) # Cache the current fixed parameters cache_fixed_params = self._fixed_params.copy() cache_has_fixed_params = self._has_fixed_params cache_fixed_params_index = self._fixed_params_index cache_free_params_index = self._free_params_index # Validate parameter names and values self._validate_can_fix_params(set(params.keys())) # Set the new fixed parameters, keeping the order as given by # param_names self._fixed_params.update(params) self._fixed_params = dict([ (name, self._fixed_params[name]) for name in self.param_names if name in self._fixed_params]) # Update associated values self._has_fixed_params = True self._fixed_params_index = [self._params_index[key] for key in self._fixed_params.keys()] self._free_params_index = list( set(np.arange(k_params)).difference(self._fixed_params_index)) try: yield finally: # Reset the fixed parameters self._has_fixed_params = cache_has_fixed_params self._fixed_params = cache_fixed_params self._fixed_params_index = cache_fixed_params_index self._free_params_index = cache_free_params_index def fit(self, start_params=None, transformed=True, includes_fixed=False, cov_type=None, cov_kwds=None, method='lbfgs', maxiter=50, full_output=1, disp=5, callback=None, return_params=False, optim_score=None, optim_complex_step=None, optim_hessian=None, flags=None, low_memory=False, **kwargs): """ Fits the model by maximum likelihood via Kalman filter. Parameters ---------- start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. If None, the default is given by Model.start_params. transformed : bool, optional Whether or not `start_params` is already transformed. Default is True. includes_fixed : bool, optional If parameters were previously fixed with the `fix_params` method, this argument describes whether or not `start_params` also includes the fixed parameters, in addition to the free parameters. Default is False. cov_type : str, optional The `cov_type` keyword governs the method for calculating the covariance matrix of parameter estimates. Can be one of: - 'opg' for the outer product of gradient estimator - 'oim' for the observed information matrix estimator, calculated using the method of Harvey (1989) - 'approx' for the observed information matrix estimator, calculated using a numerical approximation of the Hessian matrix. - 'robust' for an approximate (quasi-maximum likelihood) covariance matrix that may be valid even in the presence of some misspecifications. Intermediate calculations use the 'oim' method. - 'robust_approx' is the same as 'robust' except that the intermediate calculations use the 'approx' method. - 'none' for no covariance matrix calculation. Default is 'opg' unless memory conservation is used to avoid computing the loglikelihood values for each observation, in which case the default is 'approx'. cov_kwds : dict or None, optional A dictionary of arguments affecting covariance matrix computation. **opg, oim, approx, robust, robust_approx** - 'approx_complex_step' : bool, optional - If True, numerical approximations are computed using complex-step methods. If False, numerical approximations are computed using finite difference methods. Default is True. - 'approx_centered' : bool, optional - If True, numerical approximations computed using finite difference methods use a centered approximation. Default is False. method : str, optional The `method` determines which solver from `scipy.optimize` is used, and it can be chosen from among the following strings: - 'newton' for Newton-Raphson - 'nm' for Nelder-Mead - 'bfgs' for Broyden-Fletcher-Goldfarb-Shanno (BFGS) - 'lbfgs' for limited-memory BFGS with optional box constraints - 'powell' for modified Powell's method - 'cg' for conjugate gradient - 'ncg' for Newton-conjugate gradient - 'basinhopping' for global basin-hopping solver The explicit arguments in `fit` are passed to the solver, with the exception of the basin-hopping solver. Each solver has several optional arguments that are not the same across solvers. See the notes section below (or scipy.optimize) for the available arguments and for the list of explicit arguments that the basin-hopping solver supports. maxiter : int, optional The maximum number of iterations to perform. full_output : bool, optional Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. disp : bool, optional Set to True to print convergence messages. callback : callable callback(xk), optional Called after each iteration, as callback(xk), where xk is the current parameter vector. return_params : bool, optional Whether or not to return only the array of maximizing parameters. Default is False. optim_score : {'harvey', 'approx'} or None, optional The method by which the score vector is calculated. 'harvey' uses the method from Harvey (1989), 'approx' uses either finite difference or complex step differentiation depending upon the value of `optim_complex_step`, and None uses the built-in gradient approximation of the optimizer. Default is None. This keyword is only relevant if the optimization method uses the score. optim_complex_step : bool, optional Whether or not to use complex step differentiation when approximating the score; if False, finite difference approximation is used. Default is True. This keyword is only relevant if `optim_score` is set to 'harvey' or 'approx'. optim_hessian : {'opg','oim','approx'}, optional The method by which the Hessian is numerically approximated. 'opg' uses outer product of gradients, 'oim' uses the information matrix formula from Harvey (1989), and 'approx' uses numerical approximation. This keyword is only relevant if the optimization method uses the Hessian matrix. low_memory : bool, optional If set to True, techniques are applied to substantially reduce memory usage. If used, some features of the results object will not be available (including smoothed results and in-sample prediction), although out-of-sample forecasting is possible. Default is False. **kwargs Additional keyword arguments to pass to the optimizer. Returns ------- MLEResults See Also -------- statsmodels.base.model.LikelihoodModel.fit statsmodels.tsa.statespace.mlemodel.MLEResults """ if start_params is None: start_params = self.start_params transformed = True includes_fixed = True # Update the score method if optim_score is None and method == 'lbfgs': kwargs.setdefault('approx_grad', True) kwargs.setdefault('epsilon', 1e-5) elif optim_score is None: optim_score = 'approx' # Check for complex step differentiation if optim_complex_step is None: optim_complex_step = not self.ssm._complex_endog elif optim_complex_step and self.ssm._complex_endog: raise ValueError('Cannot use complex step derivatives when data' ' or parameters are complex.') # Standardize starting parameters start_params = self.handle_params(start_params, transformed=True, includes_fixed=includes_fixed) # Unconstrain the starting parameters if transformed: start_params = self.untransform_params(start_params) # Remove any fixed parameters if self._has_fixed_params: start_params = start_params[self._free_params_index] # If all parameters are fixed, we are done if self._has_fixed_params and len(start_params) == 0: mlefit = Bunch(params=[], mle_retvals=None, mle_settings=None) else: # Maximum likelihood estimation if flags is None: flags = {} flags.update({ 'transformed': False, 'includes_fixed': False, 'score_method': optim_score, 'approx_complex_step': optim_complex_step }) if optim_hessian is not None: flags['hessian_method'] = optim_hessian fargs = (flags,) mlefit = super(MLEModel, self).fit(start_params, method=method, fargs=fargs, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, skip_hessian=True, **kwargs) # Just return the fitted parameters if requested if return_params: return self.handle_params(mlefit.params, transformed=False, includes_fixed=False) # Otherwise construct the results class if desired else: # Handle memory conservation option if low_memory: conserve_memory = self.ssm.conserve_memory self.ssm.set_conserve_memory(MEMORY_CONSERVE) # Perform filtering / smoothing if (self.ssm.memory_no_predicted or self.ssm.memory_no_gain or self.ssm.memory_no_smoothing): func = self.filter else: func = self.smooth res = func(mlefit.params, transformed=False, includes_fixed=False, cov_type=cov_type, cov_kwds=cov_kwds) res.mlefit = mlefit res.mle_retvals = mlefit.mle_retvals res.mle_settings = mlefit.mle_settings # Reset memory conservation if low_memory: self.ssm.set_conserve_memory(conserve_memory) return res def fit_constrained(self, constraints, start_params=None, **fit_kwds): """ Fit the model with some parameters subject to equality constraints. Parameters ---------- constraints : dict Dictionary of constraints, of the form `param_name: fixed_value`. See the `param_names` property for valid parameter names. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. If None, the default is given by Model.start_params. **fit_kwds : keyword arguments fit_kwds are used in the optimization of the remaining parameters. Returns ------- results : Results instance Examples -------- >>> mod = sm.tsa.SARIMAX(endog, order=(1, 0, 1)) >>> res = mod.fit_constrained({'ar.L1': 0.5}) """ with self.fix_params(constraints): res = self.fit(start_params, **fit_kwds) return res @property def _res_classes(self): return {'fit': (MLEResults, MLEResultsWrapper)} def _wrap_results(self, params, result, return_raw, cov_type=None, cov_kwds=None, results_class=None, wrapper_class=None): if not return_raw: # Wrap in a results object result_kwargs = {} if cov_type is not None: result_kwargs['cov_type'] = cov_type if cov_kwds is not None: result_kwargs['cov_kwds'] = cov_kwds if results_class is None: results_class = self._res_classes['fit'][0] if wrapper_class is None: wrapper_class = self._res_classes['fit'][1] res = results_class(self, params, result, **result_kwargs) result = wrapper_class(res) return result def filter(self, params, transformed=True, includes_fixed=False, complex_step=False, cov_type=None, cov_kwds=None, return_ssm=False, results_class=None, results_wrapper_class=None, low_memory=False, **kwargs): """ Kalman filtering Parameters ---------- params : array_like Array of parameters at which to evaluate the loglikelihood function. transformed : bool, optional Whether or not `params` is already transformed. Default is True. return_ssm : bool,optional Whether or not to return only the state space output or a full results object. Default is to return a full results object. cov_type : str, optional See `MLEResults.fit` for a description of covariance matrix types for results object. cov_kwds : dict or None, optional See `MLEResults.get_robustcov_results` for a description required keywords for alternative covariance estimators low_memory : bool, optional If set to True, techniques are applied to substantially reduce memory usage. If used, some features of the results object will not be available (including in-sample prediction), although out-of-sample forecasting is possible. Default is False. **kwargs Additional keyword arguments to pass to the Kalman filter. See `KalmanFilter.filter` for more details. """ params = self.handle_params(params, transformed=transformed, includes_fixed=includes_fixed) self.update(params, transformed=True, includes_fixed=True, complex_step=complex_step) # Save the parameter names self.data.param_names = self.param_names if complex_step: kwargs['inversion_method'] = INVERT_UNIVARIATE | SOLVE_LU # Handle memory conservation if low_memory: kwargs['conserve_memory'] = MEMORY_CONSERVE # Get the state space output result = self.ssm.filter(complex_step=complex_step, **kwargs) # Wrap in a results object return self._wrap_results(params, result, return_ssm, cov_type, cov_kwds, results_class, results_wrapper_class) def smooth(self, params, transformed=True, includes_fixed=False, complex_step=False, cov_type=None, cov_kwds=None, return_ssm=False, results_class=None, results_wrapper_class=None, **kwargs): """ Kalman smoothing Parameters ---------- params : array_like Array of parameters at which to evaluate the loglikelihood function. transformed : bool, optional Whether or not `params` is already transformed. Default is True. return_ssm : bool,optional Whether or not to return only the state space output or a full results object. Default is to return a full results object. cov_type : str, optional See `MLEResults.fit` for a description of covariance matrix types for results object. cov_kwds : dict or None, optional See `MLEResults.get_robustcov_results` for a description required keywords for alternative covariance estimators **kwargs Additional keyword arguments to pass to the Kalman filter. See `KalmanFilter.filter` for more details. """ params = self.handle_params(params, transformed=transformed, includes_fixed=includes_fixed) self.update(params, transformed=True, includes_fixed=True, complex_step=complex_step) # Save the parameter names self.data.param_names = self.param_names if complex_step: kwargs['inversion_method'] = INVERT_UNIVARIATE | SOLVE_LU # Get the state space output result = self.ssm.smooth(complex_step=complex_step, **kwargs) # Wrap in a results object return self._wrap_results(params, result, return_ssm, cov_type, cov_kwds, results_class, results_wrapper_class) _loglike_param_names = ['transformed', 'includes_fixed', 'complex_step'] _loglike_param_defaults = [True, False, False] def loglike(self, params, *args, **kwargs): """ Loglikelihood evaluation Parameters ---------- params : array_like Array of parameters at which to evaluate the loglikelihood function. transformed : bool, optional Whether or not `params` is already transformed. Default is True. **kwargs Additional keyword arguments to pass to the Kalman filter. See `KalmanFilter.filter` for more details. See Also -------- update : modifies the internal state of the state space model to reflect new params Notes ----- [1]_ recommend maximizing the average likelihood to avoid scale issues; this is done automatically by the base Model fit method. References ---------- .. [1] Koopman, Siem Jan, Neil Shephard, and Jurgen A. Doornik. 1999. Statistical Algorithms for Models in State Space Using SsfPack 2.2. Econometrics Journal 2 (1): 107-60. doi:10.1111/1368-423X.00023. """ transformed, includes_fixed, complex_step, kwargs = _handle_args( MLEModel._loglike_param_names, MLEModel._loglike_param_defaults, *args, **kwargs) params = self.handle_params(params, transformed=transformed, includes_fixed=includes_fixed) self.update(params, transformed=True, includes_fixed=True, complex_step=complex_step) if complex_step: kwargs['inversion_method'] = INVERT_UNIVARIATE | SOLVE_LU loglike = self.ssm.loglike(complex_step=complex_step, **kwargs) # Koopman, Shephard, and Doornik recommend maximizing the average # likelihood to avoid scale issues, but the averaging is done # automatically in the base model `fit` method return loglike def loglikeobs(self, params, transformed=True, includes_fixed=False, complex_step=False, **kwargs): """ Loglikelihood evaluation Parameters ---------- params : array_like Array of parameters at which to evaluate the loglikelihood function. transformed : bool, optional Whether or not `params` is already transformed. Default is True. **kwargs Additional keyword arguments to pass to the Kalman filter. See `KalmanFilter.filter` for more details. See Also -------- update : modifies the internal state of the Model to reflect new params Notes ----- [1]_ recommend maximizing the average likelihood to avoid scale issues; this is done automatically by the base Model fit method. References ---------- .. [1] Koopman, Siem Jan, Neil Shephard, and Jurgen A. Doornik. 1999. Statistical Algorithms for Models in State Space Using SsfPack 2.2. Econometrics Journal 2 (1): 107-60. doi:10.1111/1368-423X.00023. """ params = self.handle_params(params, transformed=transformed, includes_fixed=includes_fixed) # If we're using complex-step differentiation, then we cannot use # Cholesky factorization if complex_step: kwargs['inversion_method'] = INVERT_UNIVARIATE | SOLVE_LU self.update(params, transformed=True, includes_fixed=True, complex_step=complex_step) return self.ssm.loglikeobs(complex_step=complex_step, **kwargs) def simulation_smoother(self, simulation_output=None, **kwargs): r""" Retrieve a simulation smoother for the state space model. Parameters ---------- simulation_output : int, optional Determines which simulation smoother output is calculated. Default is all (including state and disturbances). **kwargs Additional keyword arguments, used to set the simulation output. See `set_simulation_output` for more details. Returns ------- SimulationSmoothResults """ return self.ssm.simulation_smoother( simulation_output=simulation_output, **kwargs) def _forecasts_error_partial_derivatives(self, params, transformed=True, includes_fixed=False, approx_complex_step=None, approx_centered=False, res=None, **kwargs): params = np.array(params, ndmin=1) # We cannot use complex-step differentiation with non-transformed # parameters if approx_complex_step is None: approx_complex_step = transformed if not transformed and approx_complex_step: raise ValueError("Cannot use complex-step approximations to" " calculate the observed_information_matrix" " with untransformed parameters.") # If we're using complex-step differentiation, then we cannot use # Cholesky factorization if approx_complex_step: kwargs['inversion_method'] = INVERT_UNIVARIATE | SOLVE_LU # Get values at the params themselves if res is None: self.update(params, transformed=transformed, includes_fixed=includes_fixed, complex_step=approx_complex_step) res = self.ssm.filter(complex_step=approx_complex_step, **kwargs) # Setup n = len(params) # Compute partial derivatives w.r.t. forecast error and forecast # error covariance partials_forecasts_error = ( np.zeros((self.k_endog, self.nobs, n)) ) partials_forecasts_error_cov = ( np.zeros((self.k_endog, self.k_endog, self.nobs, n)) ) if approx_complex_step: epsilon = _get_epsilon(params, 2, None, n) increments = np.identity(n) * 1j * epsilon for i, ih in enumerate(increments): self.update(params + ih, transformed=transformed, includes_fixed=includes_fixed, complex_step=True) _res = self.ssm.filter(complex_step=True, **kwargs) partials_forecasts_error[:, :, i] = ( _res.forecasts_error.imag / epsilon[i] ) partials_forecasts_error_cov[:, :, :, i] = ( _res.forecasts_error_cov.imag / epsilon[i] ) elif not approx_centered: epsilon = _get_epsilon(params, 2, None, n) ei = np.zeros((n,), float) for i in range(n): ei[i] = epsilon[i] self.update(params + ei, transformed=transformed, includes_fixed=includes_fixed, complex_step=False) _res = self.ssm.filter(complex_step=False, **kwargs) partials_forecasts_error[:, :, i] = ( _res.forecasts_error - res.forecasts_error) / epsilon[i] partials_forecasts_error_cov[:, :, :, i] = ( _res.forecasts_error_cov - res.forecasts_error_cov) / epsilon[i] ei[i] = 0.0 else: epsilon = _get_epsilon(params, 3, None, n) / 2. ei = np.zeros((n,), float) for i in range(n): ei[i] = epsilon[i] self.update(params + ei, transformed=transformed, includes_fixed=includes_fixed, complex_step=False) _res1 = self.ssm.filter(complex_step=False, **kwargs) self.update(params - ei, transformed=transformed, includes_fixed=includes_fixed, complex_step=False) _res2 = self.ssm.filter(complex_step=False, **kwargs) partials_forecasts_error[:, :, i] = ( (_res1.forecasts_error - _res2.forecasts_error) / (2 * epsilon[i])) partials_forecasts_error_cov[:, :, :, i] = ( (_res1.forecasts_error_cov - _res2.forecasts_error_cov) / (2 * epsilon[i])) ei[i] = 0.0 return partials_forecasts_error, partials_forecasts_error_cov def observed_information_matrix(self, params, transformed=True, includes_fixed=False, approx_complex_step=None, approx_centered=False, **kwargs): """ Observed information matrix Parameters ---------- params : array_like, optional Array of parameters at which to evaluate the loglikelihood function. **kwargs Additional keyword arguments to pass to the Kalman filter. See `KalmanFilter.filter` for more details. Notes ----- This method is from Harvey (1989), which shows that the information matrix only depends on terms from the gradient. This implementation is partially analytic and partially numeric approximation, therefore, because it uses the analytic formula for the information matrix, with numerically computed elements of the gradient. References ---------- Harvey, Andrew C. 1990. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press. """ params = np.array(params, ndmin=1) # Setup n = len(params) # We cannot use complex-step differentiation with non-transformed # parameters if approx_complex_step is None: approx_complex_step = transformed if not transformed and approx_complex_step: raise ValueError("Cannot use complex-step approximations to" " calculate the observed_information_matrix" " with untransformed parameters.") # Get values at the params themselves params = self.handle_params(params, transformed=transformed, includes_fixed=includes_fixed) self.update(params, transformed=True, includes_fixed=True, complex_step=approx_complex_step) # If we're using complex-step differentiation, then we cannot use # Cholesky factorization if approx_complex_step: kwargs['inversion_method'] = INVERT_UNIVARIATE | SOLVE_LU res = self.ssm.filter(complex_step=approx_complex_step, **kwargs) dtype = self.ssm.dtype # Save this for inversion later inv_forecasts_error_cov = res.forecasts_error_cov.copy() partials_forecasts_error, partials_forecasts_error_cov = ( self._forecasts_error_partial_derivatives( params, transformed=transformed, includes_fixed=includes_fixed, approx_complex_step=approx_complex_step, approx_centered=approx_centered, res=res, **kwargs)) # Compute the information matrix tmp = np.zeros((self.k_endog, self.k_endog, self.nobs, n), dtype=dtype) information_matrix = np.zeros((n, n), dtype=dtype) d = np.maximum(self.ssm.loglikelihood_burn, res.nobs_diffuse) for t in range(d, self.nobs): inv_forecasts_error_cov[:, :, t] = ( np.linalg.inv(res.forecasts_error_cov[:, :, t]) ) for i in range(n): tmp[:, :, t, i] = np.dot( inv_forecasts_error_cov[:, :, t], partials_forecasts_error_cov[:, :, t, i] ) for i in range(n): for j in range(n): information_matrix[i, j] += ( 0.5 * np.trace(np.dot(tmp[:, :, t, i], tmp[:, :, t, j])) ) information_matrix[i, j] += np.inner( partials_forecasts_error[:, t, i], np.dot(inv_forecasts_error_cov[:, :, t], partials_forecasts_error[:, t, j]) ) return information_matrix / (self.nobs - self.ssm.loglikelihood_burn) def opg_information_matrix(self, params, transformed=True, includes_fixed=False, approx_complex_step=None, **kwargs): """ Outer product of gradients information matrix Parameters ---------- params : array_like, optional Array of parameters at which to evaluate the loglikelihood function. **kwargs Additional arguments to the `loglikeobs` method. References ---------- Berndt, Ernst R., Bronwyn Hall, Robert Hall, and Jerry Hausman. 1974. Estimation and Inference in Nonlinear Structural Models. NBER Chapters. National Bureau of Economic Research, Inc. """ # We cannot use complex-step differentiation with non-transformed # parameters if approx_complex_step is None: approx_complex_step = transformed if not transformed and approx_complex_step: raise ValueError("Cannot use complex-step approximations to" " calculate the observed_information_matrix" " with untransformed parameters.") score_obs = self.score_obs(params, transformed=transformed, includes_fixed=includes_fixed, approx_complex_step=approx_complex_step, **kwargs).transpose() return ( np.inner(score_obs, score_obs) / (self.nobs - self.ssm.loglikelihood_burn) ) def _score_complex_step(self, params, **kwargs): # the default epsilon can be too small # inversion_method = INVERT_UNIVARIATE | SOLVE_LU epsilon = _get_epsilon(params, 2., None, len(params)) kwargs['transformed'] = True kwargs['complex_step'] = True return approx_fprime_cs(params, self.loglike, epsilon=epsilon, kwargs=kwargs) def _score_finite_difference(self, params, approx_centered=False, **kwargs): kwargs['transformed'] = True return approx_fprime(params, self.loglike, kwargs=kwargs, centered=approx_centered) def _score_harvey(self, params, approx_complex_step=True, **kwargs): score_obs = self._score_obs_harvey( params, approx_complex_step=approx_complex_step, **kwargs) return np.sum(score_obs, axis=0) def _score_obs_harvey(self, params, approx_complex_step=True, approx_centered=False, includes_fixed=False, **kwargs): """ Score Parameters ---------- params : array_like, optional Array of parameters at which to evaluate the loglikelihood function. **kwargs Additional keyword arguments to pass to the Kalman filter. See `KalmanFilter.filter` for more details. Notes ----- This method is from Harvey (1989), section 3.4.5 References ---------- Harvey, Andrew C. 1990. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press. """ params = np.array(params, ndmin=1) n = len(params) # Get values at the params themselves self.update(params, transformed=True, includes_fixed=includes_fixed, complex_step=approx_complex_step) if approx_complex_step: kwargs['inversion_method'] = INVERT_UNIVARIATE | SOLVE_LU if 'transformed' in kwargs: del kwargs['transformed'] res = self.ssm.filter(complex_step=approx_complex_step, **kwargs) # Get forecasts error partials partials_forecasts_error, partials_forecasts_error_cov = ( self._forecasts_error_partial_derivatives( params, transformed=True, includes_fixed=includes_fixed, approx_complex_step=approx_complex_step, approx_centered=approx_centered, res=res, **kwargs)) # Compute partial derivatives w.r.t. likelihood function partials = np.zeros((self.nobs, n)) k_endog = self.k_endog for t in range(self.nobs): inv_forecasts_error_cov = np.linalg.inv( res.forecasts_error_cov[:, :, t]) for i in range(n): partials[t, i] += np.trace(np.dot( np.dot(inv_forecasts_error_cov, partials_forecasts_error_cov[:, :, t, i]), (np.eye(k_endog) - np.dot(inv_forecasts_error_cov, np.outer(res.forecasts_error[:, t], res.forecasts_error[:, t]))))) # 2 * dv / di * F^{-1} v_t # where x = F^{-1} v_t or F x = v partials[t, i] += 2 * np.dot( partials_forecasts_error[:, t, i], np.dot(inv_forecasts_error_cov, res.forecasts_error[:, t])) return -partials / 2. _score_param_names = ['transformed', 'includes_fixed', 'score_method', 'approx_complex_step', 'approx_centered'] _score_param_defaults = [True, False, 'approx', None, False] def score(self, params, *args, **kwargs): """ Compute the score function at params. Parameters ---------- params : array_like Array of parameters at which to evaluate the score. *args Additional positional arguments to the `loglike` method. **kwargs Additional keyword arguments to the `loglike` method. Returns ------- score : ndarray Score, evaluated at `params`. Notes ----- This is a numerical approximation, calculated using first-order complex step differentiation on the `loglike` method. Both args and kwargs are necessary because the optimizer from `fit` must call this function and only supports passing arguments via args (for example `scipy.optimize.fmin_l_bfgs`). """ (transformed, includes_fixed, method, approx_complex_step, approx_centered, kwargs) = ( _handle_args(MLEModel._score_param_names, MLEModel._score_param_defaults, *args, **kwargs)) # For fit() calls, the method is called 'score_method' (to distinguish # it from the method used for fit) but generally in kwargs the method # will just be called 'method' if 'method' in kwargs: method = kwargs.pop('method') if approx_complex_step is None: approx_complex_step = not self.ssm._complex_endog if approx_complex_step and self.ssm._complex_endog: raise ValueError('Cannot use complex step derivatives when data' ' or parameters are complex.') out = self.handle_params( params, transformed=transformed, includes_fixed=includes_fixed, return_jacobian=not transformed) if transformed: params = out else: params, transform_score = out if method == 'harvey': kwargs['includes_fixed'] = True score = self._score_harvey( params, approx_complex_step=approx_complex_step, **kwargs) elif method == 'approx' and approx_complex_step: kwargs['includes_fixed'] = True score = self._score_complex_step(params, **kwargs) elif method == 'approx': kwargs['includes_fixed'] = True score = self._score_finite_difference( params, approx_centered=approx_centered, **kwargs) else: raise NotImplementedError('Invalid score method.') if not transformed: score = np.dot(transform_score, score) if self._has_fixed_params and not includes_fixed: score = score[self._free_params_index] return score def score_obs(self, params, method='approx', transformed=True, includes_fixed=False, approx_complex_step=None, approx_centered=False, **kwargs): """ Compute the score per observation, evaluated at params Parameters ---------- params : array_like Array of parameters at which to evaluate the score. **kwargs Additional arguments to the `loglike` method. Returns ------- score : ndarray Score per observation, evaluated at `params`. Notes ----- This is a numerical approximation, calculated using first-order complex step differentiation on the `loglikeobs` method. """ if not transformed and approx_complex_step: raise ValueError("Cannot use complex-step approximations to" " calculate the score at each observation" " with untransformed parameters.") if approx_complex_step is None: approx_complex_step = not self.ssm._complex_endog if approx_complex_step and self.ssm._complex_endog: raise ValueError('Cannot use complex step derivatives when data' ' or parameters are complex.') params = self.handle_params(params, transformed=True, includes_fixed=includes_fixed) kwargs['transformed'] = transformed kwargs['includes_fixed'] = True if method == 'harvey': score = self._score_obs_harvey( params, approx_complex_step=approx_complex_step, **kwargs) elif method == 'approx' and approx_complex_step: # the default epsilon can be too small epsilon = _get_epsilon(params, 2., None, len(params)) kwargs['complex_step'] = True score = approx_fprime_cs(params, self.loglikeobs, epsilon=epsilon, kwargs=kwargs) elif method == 'approx': score = approx_fprime(params, self.loglikeobs, kwargs=kwargs, centered=approx_centered) else: raise NotImplementedError('Invalid scoreobs method.') return score _hessian_param_names = ['transformed', 'hessian_method', 'approx_complex_step', 'approx_centered'] _hessian_param_defaults = [True, 'approx', None, False] def hessian(self, params, *args, **kwargs): r""" Hessian matrix of the likelihood function, evaluated at the given parameters Parameters ---------- params : array_like Array of parameters at which to evaluate the hessian. *args Additional positional arguments to the `loglike` method. **kwargs Additional keyword arguments to the `loglike` method. Returns ------- hessian : ndarray Hessian matrix evaluated at `params` Notes ----- This is a numerical approximation. Both args and kwargs are necessary because the optimizer from `fit` must call this function and only supports passing arguments via args (for example `scipy.optimize.fmin_l_bfgs`). """ transformed, method, approx_complex_step, approx_centered, kwargs = ( _handle_args(MLEModel._hessian_param_names, MLEModel._hessian_param_defaults, *args, **kwargs)) # For fit() calls, the method is called 'hessian_method' (to # distinguish it from the method used for fit) but generally in kwargs # the method will just be called 'method' if 'method' in kwargs: method = kwargs.pop('method') if not transformed and approx_complex_step: raise ValueError("Cannot use complex-step approximations to" " calculate the hessian with untransformed" " parameters.") if approx_complex_step is None: approx_complex_step = not self.ssm._complex_endog if approx_complex_step and self.ssm._complex_endog: raise ValueError('Cannot use complex step derivatives when data' ' or parameters are complex.') if method == 'oim': hessian = self._hessian_oim( params, transformed=transformed, approx_complex_step=approx_complex_step, approx_centered=approx_centered, **kwargs) elif method == 'opg': hessian = self._hessian_opg( params, transformed=transformed, approx_complex_step=approx_complex_step, approx_centered=approx_centered, **kwargs) elif method == 'approx' and approx_complex_step: hessian = self._hessian_complex_step( params, transformed=transformed, **kwargs) elif method == 'approx': hessian = self._hessian_finite_difference( params, transformed=transformed, approx_centered=approx_centered, **kwargs) else: raise NotImplementedError('Invalid Hessian calculation method.') return hessian def _hessian_oim(self, params, **kwargs): """ Hessian matrix computed using the Harvey (1989) information matrix """ return -self.observed_information_matrix(params, **kwargs) def _hessian_opg(self, params, **kwargs): """ Hessian matrix computed using the outer product of gradients information matrix """ return -self.opg_information_matrix(params, **kwargs) def _hessian_finite_difference(self, params, approx_centered=False, **kwargs): params = np.array(params, ndmin=1) warnings.warn('Calculation of the Hessian using finite differences' ' is usually subject to substantial approximation' ' errors.', PrecisionWarning) if not approx_centered: epsilon = _get_epsilon(params, 3, None, len(params)) else: epsilon = _get_epsilon(params, 4, None, len(params)) / 2 hessian = approx_fprime(params, self._score_finite_difference, epsilon=epsilon, kwargs=kwargs, centered=approx_centered) return hessian / (self.nobs - self.ssm.loglikelihood_burn) def _hessian_complex_step(self, params, **kwargs): """ Hessian matrix computed by second-order complex-step differentiation on the `loglike` function. """ # the default epsilon can be too small epsilon = _get_epsilon(params, 3., None, len(params)) kwargs['transformed'] = True kwargs['complex_step'] = True hessian = approx_hess_cs( params, self.loglike, epsilon=epsilon, kwargs=kwargs) return hessian / (self.nobs - self.ssm.loglikelihood_burn) @property def start_params(self): """ (array) Starting parameters for maximum likelihood estimation. """ if hasattr(self, '_start_params'): return self._start_params else: raise NotImplementedError @property def param_names(self): """ (list of str) List of human readable parameter names (for parameters actually included in the model). """ if hasattr(self, '_param_names'): return self._param_names else: try: names = ['param.%d' % i for i in range(len(self.start_params))] except NotImplementedError: names = [] return names @property def state_names(self): """ (list of str) List of human readable names for unobserved states. """ if hasattr(self, '_state_names'): return self._state_names else: names = ['state.%d' % i for i in range(self.k_states)] return names def transform_jacobian(self, unconstrained, approx_centered=False): """ Jacobian matrix for the parameter transformation function Parameters ---------- unconstrained : array_like Array of unconstrained parameters used by the optimizer. Returns ------- jacobian : ndarray Jacobian matrix of the transformation, evaluated at `unconstrained` See Also -------- transform_params Notes ----- This is a numerical approximation using finite differences. Note that in general complex step methods cannot be used because it is not guaranteed that the `transform_params` method is a real function (e.g. if Cholesky decomposition is used). """ return approx_fprime(unconstrained, self.transform_params, centered=approx_centered) def transform_params(self, unconstrained): """ Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation Parameters ---------- unconstrained : array_like Array of unconstrained parameters used by the optimizer, to be transformed. Returns ------- constrained : array_like Array of constrained parameters which may be used in likelihood evaluation. Notes ----- This is a noop in the base class, subclasses should override where appropriate. """ return np.array(unconstrained, ndmin=1) def untransform_params(self, constrained): """ Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer Parameters ---------- constrained : array_like Array of constrained parameters used in likelihood evaluation, to be transformed. Returns ------- unconstrained : array_like Array of unconstrained parameters used by the optimizer. Notes ----- This is a noop in the base class, subclasses should override where appropriate. """ return np.array(constrained, ndmin=1) def handle_params(self, params, transformed=True, includes_fixed=False, return_jacobian=False): params = np.array(params, ndmin=1) # Never want integer dtype, so convert to floats if np.issubdtype(params.dtype, np.integer): params = params.astype(np.float64) if not includes_fixed and self._has_fixed_params: k_params = len(self.param_names) new_params = np.zeros(k_params, dtype=params.dtype) * np.nan new_params[self._free_params_index] = params params = new_params if not transformed: # It may be the case that the transformation relies on having # "some" (non-NaN) values for the fixed parameters, even if we will # not actually be transforming the fixed parameters (as they will) # be set below regardless if not includes_fixed and self._has_fixed_params: params[self._fixed_params_index] = ( list(self._fixed_params.values())) if return_jacobian: transform_score = self.transform_jacobian(params) params = self.transform_params(params) if not includes_fixed and self._has_fixed_params: params[self._fixed_params_index] = ( list(self._fixed_params.values())) return (params, transform_score) if return_jacobian else params def update(self, params, transformed=True, includes_fixed=False, complex_step=False): """ Update the parameters of the model Parameters ---------- params : array_like Array of new parameters. transformed : bool, optional Whether or not `params` is already transformed. If set to False, `transform_params` is called. Default is True. Returns ------- params : array_like Array of parameters. Notes ----- Since Model is a base class, this method should be overridden by subclasses to perform actual updating steps. """ return self.handle_params(params=params, transformed=transformed, includes_fixed=includes_fixed) def _validate_out_of_sample_exog(self, exog, out_of_sample): """ Validate given `exog` as satisfactory for out-of-sample operations Parameters ---------- exog : array_like or None New observations of exogenous regressors, if applicable. out_of_sample : int Number of new observations required. Returns ------- exog : array or None A numpy array of shape (out_of_sample, k_exog) if the model contains an `exog` component, or None if it does not. """ if out_of_sample and self.k_exog > 0: if exog is None: raise ValueError('Out-of-sample operations in a model' ' with a regression component require' ' additional exogenous values via the' ' `exog` argument.') exog = np.array(exog) required_exog_shape = (out_of_sample, self.k_exog) try: exog = exog.reshape(required_exog_shape) except ValueError: raise ValueError('Provided exogenous values are not of the' ' appropriate shape. Required %s, got %s.' % (str(required_exog_shape), str(exog.shape))) elif self.k_exog > 0: exog = None warnings.warn('Exogenous array provided, but additional data' ' is not required. `exog` argument ignored.', ValueWarning) return exog def _get_extension_time_varying_matrices( self, params, exog, out_of_sample, extend_kwargs=None, transformed=True, includes_fixed=False, **kwargs): """ Get updated time-varying state space system matrices Parameters ---------- params : array_like Array of parameters used to construct the time-varying system matrices. exog : array_like or None New observations of exogenous regressors, if applicable. out_of_sample : int Number of new observations required. extend_kwargs : dict, optional Dictionary of keyword arguments to pass to the state space model constructor. For example, for an SARIMAX state space model, this could be used to pass the `concentrate_scale=True` keyword argument. Any arguments that are not explicitly set in this dictionary will be copied from the current model instance. transformed : bool, optional Whether or not `start_params` is already transformed. Default is True. includes_fixed : bool, optional If parameters were previously fixed with the `fix_params` method, this argument describes whether or not `start_params` also includes the fixed parameters, in addition to the free parameters. Default is False. """ # Get the appropriate exog for the extended sample exog = self._validate_out_of_sample_exog(exog, out_of_sample) # Create extended model if extend_kwargs is None: extend_kwargs = {} # Handle trend offset for extended model if getattr(self, 'k_trend', 0) > 0 and hasattr(self, 'trend_offset'): extend_kwargs.setdefault( 'trend_offset', self.trend_offset + self.nobs) mod_extend = self.clone( endog=np.zeros((out_of_sample, self.k_endog)), exog=exog, **extend_kwargs) mod_extend.update(params, transformed=transformed, includes_fixed=includes_fixed) # Retrieve the extensions to the time-varying system matrices and # put them in kwargs for name in self.ssm.shapes.keys(): if name == 'obs' or name in kwargs: continue if getattr(self.ssm, name).shape[-1] > 1: mat = getattr(mod_extend.ssm, name) kwargs[name] = mat[..., -out_of_sample:] return kwargs def simulate(self, params, nsimulations, measurement_shocks=None, state_shocks=None, initial_state=None, anchor=None, repetitions=None, exog=None, extend_model=None, extend_kwargs=None, transformed=True, includes_fixed=False, **kwargs): r""" Simulate a new time series following the state space model Parameters ---------- params : array_like Array of parameters to use in constructing the state space representation to use when simulating. nsimulations : int The number of observations to simulate. If the model is time-invariant this can be any number. If the model is time-varying, then this number must be less than or equal to the number of observations. measurement_shocks : array_like, optional If specified, these are the shocks to the measurement equation, :math:`\varepsilon_t`. If unspecified, these are automatically generated using a pseudo-random number generator. If specified, must be shaped `nsimulations` x `k_endog`, where `k_endog` is the same as in the state space model. state_shocks : array_like, optional If specified, these are the shocks to the state equation, :math:`\eta_t`. If unspecified, these are automatically generated using a pseudo-random number generator. If specified, must be shaped `nsimulations` x `k_posdef` where `k_posdef` is the same as in the state space model. initial_state : array_like, optional If specified, this is the initial state vector to use in simulation, which should be shaped (`k_states` x 1), where `k_states` is the same as in the state space model. If unspecified, but the model has been initialized, then that initialization is used. This must be specified if `anchor` is anything other than "start" or 0 (or else you can use the `simulate` method on a results object rather than on the model object). anchor : int, str, or datetime, optional First period for simulation. The simulation will be conditional on all existing datapoints prior to the `anchor`. Type depends on the index of the given `endog` in the model. Two special cases are the strings 'start' and 'end'. `start` refers to beginning the simulation at the first period of the sample, and `end` refers to beginning the simulation at the first period after the sample. Integer values can run from 0 to `nobs`, or can be negative to apply negative indexing. Finally, if a date/time index was provided to the model, then this argument can be a date string to parse or a datetime type. Default is 'start'. repetitions : int, optional Number of simulated paths to generate. Default is 1 simulated path. exog : array_like, optional New observations of exogenous regressors, if applicable. transformed : bool, optional Whether or not `params` is already transformed. Default is True. includes_fixed : bool, optional If parameters were previously fixed with the `fix_params` method, this argument describes whether or not `params` also includes the fixed parameters, in addition to the free parameters. Default is False. Returns ------- simulated_obs : ndarray An array of simulated observations. If `repetitions=None`, then it will be shaped (nsimulations x k_endog) or (nsimulations,) if `k_endog=1`. Otherwise it will be shaped (nsimulations x k_endog x repetitions). If the model was given Pandas input then the output will be a Pandas object. If `k_endog > 1` and `repetitions` is not None, then the output will be a Pandas DataFrame that has a MultiIndex for the columns, with the first level containing the names of the `endog` variables and the second level containing the repetition number. """ # Make sure the model class has the current parameters self.update(params, transformed=transformed, includes_fixed=includes_fixed) # Get the starting location if anchor is None or anchor == 'start': iloc = 0 elif anchor == 'end': iloc = self.nobs else: iloc, _, _ = self._get_index_loc(anchor) if isinstance(iloc, slice): iloc = iloc.start if iloc < 0: iloc = self.nobs + iloc if iloc > self.nobs: raise ValueError('Cannot anchor simulation outside of the sample.') if iloc > 0 and initial_state is None: raise ValueError('If `anchor` is after the start of the sample,' ' must provide a value for `initial_state`.') # Get updated time-varying system matrices in **kwargs, if necessary out_of_sample = max(iloc + nsimulations - self.nobs, 0) if extend_model is None: extend_model = self.exog is not None or not self.ssm.time_invariant if out_of_sample and extend_model: kwargs = self._get_extension_time_varying_matrices( params, exog, out_of_sample, extend_kwargs, transformed=transformed, includes_fixed=includes_fixed, **kwargs) # Standardize the dimensions of the initial state if initial_state is not None: initial_state = np.array(initial_state) if initial_state.ndim < 2: initial_state = np.atleast_2d(initial_state).T # Construct a model that represents the simulation period end = min(self.nobs, iloc + nsimulations) nextend = iloc + nsimulations - end sim_model = self.ssm.extend(np.empty((nextend, self.k_endog)), start=iloc, end=end, **kwargs) # Simulate the data _repetitions = 1 if repetitions is None else repetitions sim = np.zeros((nsimulations, self.k_endog, _repetitions)) for i in range(_repetitions): initial_state_variates = None if initial_state is not None: if initial_state.shape[1] == 1: initial_state_variates = initial_state[:, 0] else: initial_state_variates = initial_state[:, i] # TODO: allow specifying measurement / state shocks for each # repetition? out, _ = sim_model.simulate( nsimulations, measurement_shocks, state_shocks, initial_state_variates) sim[:, :, i] = out # Wrap data / squeeze where appropriate use_pandas = isinstance(self.data, PandasData) index = None if use_pandas: _, _, _, index = self._get_prediction_index( iloc, iloc + nsimulations - 1) # If `repetitions` isn't set, we squeeze the last dimension(s) if repetitions is None: if self.k_endog == 1: sim = sim[:, 0, 0] if use_pandas: sim = pd.Series(sim, index=index, name=self.endog_names) else: sim = sim[:, :, 0] if use_pandas: sim = pd.DataFrame(sim, index=index, columns=self.endog_names) elif use_pandas: shape = sim.shape endog_names = self.endog_names if not isinstance(endog_names, list): endog_names = [endog_names] columns = pd.MultiIndex.from_product([endog_names, np.arange(shape[2])]) sim = pd.DataFrame(sim.reshape(shape[0], shape[1] * shape[2]), index=index, columns=columns) return sim def impulse_responses(self, params, steps=1, impulse=0, orthogonalized=False, cumulative=False, anchor=None, exog=None, extend_model=None, extend_kwargs=None, transformed=True, includes_fixed=False, **kwargs): """ Impulse response function Parameters ---------- params : array_like Array of model parameters. steps : int, optional The number of steps for which impulse responses are calculated. Default is 1. Note that for time-invariant models, the initial impulse is not counted as a step, so if `steps=1`, the output will have 2 entries. impulse : int or array_like If an integer, the state innovation to pulse; must be between 0 and `k_posdef-1`. Alternatively, a custom impulse vector may be provided; must be shaped `k_posdef x 1`. orthogonalized : bool, optional Whether or not to perform impulse using orthogonalized innovations. Note that this will also affect custum `impulse` vectors. Default is False. cumulative : bool, optional Whether or not to return cumulative impulse responses. Default is False. anchor : int, str, or datetime, optional Time point within the sample for the state innovation impulse. Type depends on the index of the given `endog` in the model. Two special cases are the strings 'start' and 'end', which refer to setting the impulse at the first and last points of the sample, respectively. Integer values can run from 0 to `nobs - 1`, or can be negative to apply negative indexing. Finally, if a date/time index was provided to the model, then this argument can be a date string to parse or a datetime type. Default is 'start'. exog : array_like, optional New observations of exogenous regressors for our-of-sample periods, if applicable. transformed : bool, optional Whether or not `params` is already transformed. Default is True. includes_fixed : bool, optional If parameters were previously fixed with the `fix_params` method, this argument describes whether or not `params` also includes the fixed parameters, in addition to the free parameters. Default is False. **kwargs If the model has time-varying design or transition matrices and the combination of `anchor` and `steps` implies creating impulse responses for the out-of-sample period, then these matrices must have updated values provided for the out-of-sample steps. For example, if `design` is a time-varying component, `nobs` is 10, `anchor=1`, and `steps` is 15, a (`k_endog` x `k_states` x 7) matrix must be provided with the new design matrix values. Returns ------- impulse_responses : ndarray Responses for each endogenous variable due to the impulse given by the `impulse` argument. For a time-invariant model, the impulse responses are given for `steps + 1` elements (this gives the "initial impulse" followed by `steps` responses for the important cases of VAR and SARIMAX models), while for time-varying models the impulse responses are only given for `steps` elements (to avoid having to unexpectedly provide updated time-varying matrices). Notes ----- Intercepts in the measurement and state equation are ignored when calculating impulse responses. TODO: add an option to allow changing the ordering for the orthogonalized option. Will require permuting matrices when constructing the extended model. """ # Make sure the model class has the current parameters self.update(params, transformed=transformed, includes_fixed=includes_fixed) # For time-invariant models, add an additional `step`. This is the # default for time-invariant models based on the expected behavior for # ARIMA and VAR models: we want to record the initial impulse and also # `steps` values of the responses afterwards. # Note: we don't modify `steps` itself, because # `KalmanFilter.impulse_responses` also adds an additional step in this # case (this is so that there isn't different behavior when calling # this method versus that method). We just need to also keep track of # this here because we need to generate the correct extended model. additional_steps = 0 if (self.ssm._design.shape[2] == 1 and self.ssm._transition.shape[2] == 1 and self.ssm._selection.shape[2] == 1): additional_steps = 1 # Get the starting location if anchor is None or anchor == 'start': iloc = 0 elif anchor == 'end': iloc = self.nobs - 1 else: iloc, _, _ = self._get_index_loc(anchor) if isinstance(iloc, slice): iloc = iloc.start if iloc < 0: iloc = self.nobs + iloc if iloc >= self.nobs: raise ValueError('Cannot anchor impulse responses outside of the' ' sample.') time_invariant = ( self.ssm._design.shape[2] == self.ssm._obs_cov.shape[2] == self.ssm._transition.shape[2] == self.ssm._selection.shape[2] == self.ssm._state_cov.shape[2] == 1) # Get updated time-varying system matrices in **kwargs, if necessary # (Note: KalmanFilter adds 1 to steps to account for the first impulse) out_of_sample = max( iloc + (steps + additional_steps + 1) - self.nobs, 0) if extend_model is None: extend_model = self.exog is not None and not time_invariant if out_of_sample and extend_model: kwargs = self._get_extension_time_varying_matrices( params, exog, out_of_sample, extend_kwargs, transformed=transformed, includes_fixed=includes_fixed, **kwargs) # Special handling for matrix terms that are time-varying but # irrelevant for impulse response functions. Must be set since # ssm.extend() requires that we pass new matrices for these, but they # are ignored for IRF purposes. end = min(self.nobs, iloc + steps + additional_steps) nextend = iloc + (steps + additional_steps + 1) - end if ('obs_intercept' not in kwargs and self.ssm._obs_intercept.shape[1] > 1): kwargs['obs_intercept'] = np.zeros((self.k_endog, nextend)) if ('state_intercept' not in kwargs and self.ssm._state_intercept.shape[1] > 1): kwargs['state_intercept'] = np.zeros((self.k_states, nextend)) if 'obs_cov' not in kwargs and self.ssm._obs_cov.shape[2] > 1: kwargs['obs_cov'] = np.zeros((self.k_endog, self.k_endog, nextend)) # Special handling for matrix terms that are time-varying but # only the value at the anchor matters for IRF purposes. if 'state_cov' not in kwargs and self.ssm._state_cov.shape[2] > 1: tmp = np.zeros((self.ssm.k_posdef, self.ssm.k_posdef, nextend)) tmp[:] = self['state_cov', :, :, iloc:iloc + 1] kwargs['state_cov'] = tmp if 'selection' not in kwargs and self.ssm._selection.shape[2] > 1: tmp = np.zeros((self.k_states, self.ssm.k_posdef, nextend)) tmp[:] = self['selection', :, :, iloc:iloc + 1] kwargs['selection'] = tmp # Construct a model that represents the simulation period sim_model = self.ssm.extend(np.empty((nextend, self.k_endog)), start=iloc, end=end, **kwargs) # Compute the impulse responses irfs = sim_model.impulse_responses( steps, impulse, orthogonalized, cumulative) # IRF is (nobs x k_endog); do not want to squeeze in case of steps = 1 if irfs.shape[1] == 1: irfs = irfs[:, 0] # Wrap data / squeeze where appropriate use_pandas = isinstance(self.data, PandasData) if use_pandas: if self.k_endog == 1: irfs = pd.Series(irfs, name=self.endog_names) else: irfs = pd.DataFrame(irfs, columns=self.endog_names) return irfs @classmethod def from_formula(cls, formula, data, subset=None): """ Not implemented for state space models """ raise NotImplementedError class MLEResults(tsbase.TimeSeriesModelResults): r""" Class to hold results from fitting a state space model. Parameters ---------- model : MLEModel instance The fitted model instance params : ndarray Fitted parameters filter_results : KalmanFilter instance The underlying state space model and Kalman filter output Attributes ---------- model : Model instance A reference to the model that was fit. filter_results : KalmanFilter instance The underlying state space model and Kalman filter output nobs : float The number of observations used to fit the model. params : ndarray The parameters of the model. scale : float This is currently set to 1.0 unless the model uses concentrated filtering. See Also -------- MLEModel statsmodels.tsa.statespace.kalman_filter.FilterResults statsmodels.tsa.statespace.representation.FrozenRepresentation """ def __init__(self, model, params, results, cov_type=None, cov_kwds=None, **kwargs): self.data = model.data scale = results.scale tsbase.TimeSeriesModelResults.__init__(self, model, params, normalized_cov_params=None, scale=scale) # Save the fixed parameters self._has_fixed_params = self.model._has_fixed_params self._fixed_params_index = self.model._fixed_params_index self._free_params_index = self.model._free_params_index # TODO: seems like maybe self.fixed_params should be the dictionary # itself, not just the keys? if self._has_fixed_params: self._fixed_params = self.model._fixed_params.copy() self.fixed_params = list(self._fixed_params.keys()) else: self._fixed_params = None self.fixed_params = [] self.param_names = [ '%s (fixed)' % name if name in self.fixed_params else name for name in (self.data.param_names or [])] # Save the state space representation output self.filter_results = results if isinstance(results, SmootherResults): self.smoother_results = results else: self.smoother_results = None # Dimensions self.nobs = self.filter_results.nobs self.nobs_diffuse = self.filter_results.nobs_diffuse if self.nobs_diffuse > 0 and self.loglikelihood_burn > 0: warnings.warn('Care should be used when applying a loglikelihood' ' burn to a model with exact diffuse initialization.' ' Some results objects, e.g. degrees of freedom,' ' expect only one of the two to be set.') # This only excludes explicitly burned (usually approximate diffuse) # periods but does not exclude exact diffuse periods. This is # because the loglikelihood remains valid for the initial periods in # the exact diffuse case (see DK, 2012, section 7.2) and so also do # e.g. information criteria (see DK, 2012, section 7.4) and the score # vector (see DK, 2012, section 7.3.3, equation 7.15). # However, other objects should be excluded in the diffuse periods # (e.g. the diffuse forecast errors, so in some cases a different # nobs_effective will have to be computed and used) self.nobs_effective = self.nobs - self.loglikelihood_burn P = self.filter_results.initial_diffuse_state_cov self.k_diffuse_states = 0 if P is None else np.sum(np.diagonal(P) == 1) # Degrees of freedom (see DK 2012, section 7.4) k_free_params = self.params.size - len(self.fixed_params) self.df_model = (k_free_params + self.k_diffuse_states + self.filter_results.filter_concentrated) self.df_resid = self.nobs_effective - self.df_model # Setup covariance matrix notes dictionary if not hasattr(self, 'cov_kwds'): self.cov_kwds = {} if cov_type is None: cov_type = 'approx' if results.memory_no_likelihood else 'opg' self.cov_type = cov_type # Setup the cache self._cache = {} # Handle covariance matrix calculation if cov_kwds is None: cov_kwds = {} self._cov_approx_complex_step = ( cov_kwds.pop('approx_complex_step', True)) self._cov_approx_centered = cov_kwds.pop('approx_centered', False) try: self._rank = None self._get_robustcov_results(cov_type=cov_type, use_self=True, **cov_kwds) except np.linalg.LinAlgError: self._rank = 0 k_params = len(self.params) self.cov_params_default = np.zeros((k_params, k_params)) * np.nan self.cov_kwds['cov_type'] = ( 'Covariance matrix could not be calculated: singular.' ' information matrix.') self.model.update(self.params, transformed=True, includes_fixed=True) # References of filter and smoother output extra_arrays = [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov'] for name in extra_arrays: setattr(self, name, getattr(self.filter_results, name, None)) # Remove too-short results when memory conservation was used if self.filter_results.memory_no_forecast_mean: self.forecasts = None self.forecasts_error = None if self.filter_results.memory_no_forecast_cov: self.forecasts_error_cov = None if self.filter_results.memory_no_predicted_mean: self.predicted_state = None if self.filter_results.memory_no_predicted_cov: self.predicted_state_cov = None if self.filter_results.memory_no_filtered_mean: self.filtered_state = None if self.filter_results.memory_no_filtered_cov: self.filtered_state_cov = None if self.filter_results.memory_no_gain: pass if self.filter_results.memory_no_smoothing: pass if self.filter_results.memory_no_std_forecast: self.standardized_forecasts_error = None # Save more convenient access to states # (will create a private attribute _states here and provide actual # access via a getter, so that we can e.g. issue a warning in the case # that a useless Pandas index was given in the model specification) self._states = SimpleNamespace() use_pandas = isinstance(self.data, PandasData) index = self.model._index columns = self.model.state_names # Predicted states # Note: a complication here is that we also include the initial values # here, so that we need an extended index in the Pandas case if (self.predicted_state is None or self.filter_results.memory_no_predicted_mean): self._states.predicted = None elif use_pandas: extended_index = self.model._get_index_with_final_state() self._states.predicted = pd.DataFrame( self.predicted_state.T, index=extended_index, columns=columns) else: self._states.predicted = self.predicted_state.T if (self.predicted_state_cov is None or self.filter_results.memory_no_predicted_cov): self._states.predicted_cov = None elif use_pandas: extended_index = self.model._get_index_with_final_state() tmp = np.transpose(self.predicted_state_cov, (2, 0, 1)) self._states.predicted_cov = pd.DataFrame( np.reshape(tmp, (tmp.shape[0] * tmp.shape[1], tmp.shape[2])), index=pd.MultiIndex.from_product( [extended_index, columns]).swaplevel(), columns=columns) else: self._states.predicted_cov = np.transpose( self.predicted_state_cov, (2, 0, 1)) # Filtered states if (self.filtered_state is None or self.filter_results.memory_no_filtered_mean): self._states.filtered = None elif use_pandas: self._states.filtered = pd.DataFrame( self.filtered_state.T, index=index, columns=columns) else: self._states.filtered = self.filtered_state.T if (self.filtered_state_cov is None or self.filter_results.memory_no_filtered_cov): self._states.filtered_cov = None elif use_pandas: tmp = np.transpose(self.filtered_state_cov, (2, 0, 1)) self._states.filtered_cov = pd.DataFrame( np.reshape(tmp, (tmp.shape[0] * tmp.shape[1], tmp.shape[2])), index=pd.MultiIndex.from_product([index, columns]).swaplevel(), columns=columns) else: self._states.filtered_cov = np.transpose( self.filtered_state_cov, (2, 0, 1)) # Smoothed states if self.smoothed_state is None: self._states.smoothed = None elif use_pandas: self._states.smoothed = pd.DataFrame( self.smoothed_state.T, index=index, columns=columns) else: self._states.smoothed = self.smoothed_state.T if self.smoothed_state_cov is None: self._states.smoothed_cov = None elif use_pandas: tmp = np.transpose(self.smoothed_state_cov, (2, 0, 1)) self._states.smoothed_cov = pd.DataFrame( np.reshape(tmp, (tmp.shape[0] * tmp.shape[1], tmp.shape[2])), index=pd.MultiIndex.from_product([index, columns]).swaplevel(), columns=columns) else: self._states.smoothed_cov = np.transpose( self.smoothed_state_cov, (2, 0, 1)) # Handle removing data self._data_attr_model = getattr(self, '_data_attr_model', []) self._data_attr_model.extend(['ssm']) self._data_attr.extend(extra_arrays) self._data_attr.extend(['filter_results', 'smoother_results']) def _get_robustcov_results(self, cov_type='opg', **kwargs): """ Create new results instance with specified covariance estimator as default Note: creating new results instance currently not supported. Parameters ---------- cov_type : str the type of covariance matrix estimator to use. See Notes below kwargs : depends on cov_type Required or optional arguments for covariance calculation. See Notes below. Returns ------- results : results instance This method creates a new results instance with the requested covariance as the default covariance of the parameters. Inferential statistics like p-values and hypothesis tests will be based on this covariance matrix. Notes ----- The following covariance types and required or optional arguments are currently available: - 'opg' for the outer product of gradient estimator - 'oim' for the observed information matrix estimator, calculated using the method of Harvey (1989) - 'approx' for the observed information matrix estimator, calculated using a numerical approximation of the Hessian matrix. Uses complex step approximation by default, or uses finite differences if `approx_complex_step=False` in the `cov_kwds` dictionary. - 'robust' for an approximate (quasi-maximum likelihood) covariance matrix that may be valid even in the presence of some misspecifications. Intermediate calculations use the 'oim' method. - 'robust_approx' is the same as 'robust' except that the intermediate calculations use the 'approx' method. - 'none' for no covariance matrix calculation. """ from statsmodels.base.covtype import descriptions use_self = kwargs.pop('use_self', False) if use_self: res = self else: raise NotImplementedError res = self.__class__( self.model, self.params, normalized_cov_params=self.normalized_cov_params, scale=self.scale) # Set the new covariance type res.cov_type = cov_type res.cov_kwds = {} # Calculate the new covariance matrix approx_complex_step = self._cov_approx_complex_step if approx_complex_step: approx_type_str = 'complex-step' elif self._cov_approx_centered: approx_type_str = 'centered finite differences' else: approx_type_str = 'finite differences' k_params = len(self.params) if k_params == 0: res.cov_params_default = np.zeros((0, 0)) res._rank = 0 res.cov_kwds['description'] = 'No parameters estimated.' elif cov_type == 'custom': res.cov_type = kwargs['custom_cov_type'] res.cov_params_default = kwargs['custom_cov_params'] res.cov_kwds['description'] = kwargs['custom_description'] if len(self.fixed_params) > 0: mask = np.ix_(self._free_params_index, self._free_params_index) else: mask = np.s_[...] res._rank = np.linalg.matrix_rank(res.cov_params_default[mask]) elif cov_type == 'none': res.cov_params_default = np.zeros((k_params, k_params)) * np.nan res._rank = np.nan res.cov_kwds['description'] = descriptions['none'] elif self.cov_type == 'approx': res.cov_params_default = res.cov_params_approx res.cov_kwds['description'] = descriptions['approx'].format( approx_type=approx_type_str) elif self.cov_type == 'oim': res.cov_params_default = res.cov_params_oim res.cov_kwds['description'] = descriptions['OIM'].format( approx_type=approx_type_str) elif self.cov_type == 'opg': res.cov_params_default = res.cov_params_opg res.cov_kwds['description'] = descriptions['OPG'].format( approx_type=approx_type_str) elif self.cov_type == 'robust' or self.cov_type == 'robust_oim': res.cov_params_default = res.cov_params_robust_oim res.cov_kwds['description'] = descriptions['robust-OIM'].format( approx_type=approx_type_str) elif self.cov_type == 'robust_approx': res.cov_params_default = res.cov_params_robust_approx res.cov_kwds['description'] = descriptions['robust-approx'].format( approx_type=approx_type_str) else: raise NotImplementedError('Invalid covariance matrix type.') return res @cache_readonly def aic(self): """ (float) Akaike Information Criterion """ return aic(self.llf, self.nobs_effective, self.df_model) @cache_readonly def aicc(self): """ (float) Akaike Information Criterion with small sample correction """ return aicc(self.llf, self.nobs_effective, self.df_model) @cache_readonly def bic(self): """ (float) Bayes Information Criterion """ return bic(self.llf, self.nobs_effective, self.df_model) def _cov_params_approx(self, approx_complex_step=True, approx_centered=False): evaluated_hessian = self.nobs_effective * self.model.hessian( params=self.params, transformed=True, includes_fixed=True, method='approx', approx_complex_step=approx_complex_step, approx_centered=approx_centered) # TODO: Case with "not approx_complex_step" is not hit in # tests as of 2017-05-19 if len(self.fixed_params) > 0: mask = np.ix_(self._free_params_index, self._free_params_index) (tmp, singular_values) = pinv_extended(evaluated_hessian[mask]) neg_cov = np.zeros_like(evaluated_hessian) * np.nan neg_cov[mask] = tmp else: (neg_cov, singular_values) = pinv_extended(evaluated_hessian) self.model.update(self.params, transformed=True, includes_fixed=True) if self._rank is None: self._rank = np.linalg.matrix_rank(np.diag(singular_values)) return -neg_cov @cache_readonly def cov_params_approx(self): """ (array) The variance / covariance matrix. Computed using the numerical Hessian approximated by complex step or finite differences methods. """ return self._cov_params_approx(self._cov_approx_complex_step, self._cov_approx_centered) def _cov_params_oim(self, approx_complex_step=True, approx_centered=False): evaluated_hessian = self.nobs_effective * self.model.hessian( self.params, hessian_method='oim', transformed=True, includes_fixed=True, approx_complex_step=approx_complex_step, approx_centered=approx_centered) if len(self.fixed_params) > 0: mask = np.ix_(self._free_params_index, self._free_params_index) (tmp, singular_values) = pinv_extended(evaluated_hessian[mask]) neg_cov = np.zeros_like(evaluated_hessian) * np.nan neg_cov[mask] = tmp else: (neg_cov, singular_values) = pinv_extended(evaluated_hessian) self.model.update(self.params, transformed=True, includes_fixed=True) if self._rank is None: self._rank = np.linalg.matrix_rank(np.diag(singular_values)) return -neg_cov @cache_readonly def cov_params_oim(self): """ (array) The variance / covariance matrix. Computed using the method from Harvey (1989). """ return self._cov_params_oim(self._cov_approx_complex_step, self._cov_approx_centered) def _cov_params_opg(self, approx_complex_step=True, approx_centered=False): evaluated_hessian = self.nobs_effective * self.model._hessian_opg( self.params, transformed=True, includes_fixed=True, approx_complex_step=approx_complex_step, approx_centered=approx_centered) no_free_params = (self._free_params_index is not None and len(self._free_params_index) == 0) if no_free_params: neg_cov = np.zeros_like(evaluated_hessian) * np.nan singular_values = np.empty(0) elif len(self.fixed_params) > 0: mask = np.ix_(self._free_params_index, self._free_params_index) (tmp, singular_values) = pinv_extended(evaluated_hessian[mask]) neg_cov = np.zeros_like(evaluated_hessian) * np.nan neg_cov[mask] = tmp else: (neg_cov, singular_values) = pinv_extended(evaluated_hessian) self.model.update(self.params, transformed=True, includes_fixed=True) if self._rank is None: if no_free_params: self._rank = 0 else: self._rank = np.linalg.matrix_rank(np.diag(singular_values)) return -neg_cov @cache_readonly def cov_params_opg(self): """ (array) The variance / covariance matrix. Computed using the outer product of gradients method. """ return self._cov_params_opg(self._cov_approx_complex_step, self._cov_approx_centered) @cache_readonly def cov_params_robust(self): """ (array) The QMLE variance / covariance matrix. Alias for `cov_params_robust_oim` """ return self.cov_params_robust_oim def _cov_params_robust_oim(self, approx_complex_step=True, approx_centered=False): cov_opg = self._cov_params_opg(approx_complex_step=approx_complex_step, approx_centered=approx_centered) evaluated_hessian = self.nobs_effective * self.model.hessian( self.params, hessian_method='oim', transformed=True, includes_fixed=True, approx_complex_step=approx_complex_step, approx_centered=approx_centered) if len(self.fixed_params) > 0: mask = np.ix_(self._free_params_index, self._free_params_index) cov_params = np.zeros_like(evaluated_hessian) * np.nan cov_opg = cov_opg[mask] evaluated_hessian = evaluated_hessian[mask] tmp, singular_values = pinv_extended( np.dot(np.dot(evaluated_hessian, cov_opg), evaluated_hessian)) cov_params[mask] = tmp else: (cov_params, singular_values) = pinv_extended( np.dot(np.dot(evaluated_hessian, cov_opg), evaluated_hessian)) self.model.update(self.params, transformed=True, includes_fixed=True) if self._rank is None: self._rank = np.linalg.matrix_rank(np.diag(singular_values)) return cov_params @cache_readonly def cov_params_robust_oim(self): """ (array) The QMLE variance / covariance matrix. Computed using the method from Harvey (1989) as the evaluated hessian. """ return self._cov_params_robust_oim(self._cov_approx_complex_step, self._cov_approx_centered) def _cov_params_robust_approx(self, approx_complex_step=True, approx_centered=False): cov_opg = self._cov_params_opg(approx_complex_step=approx_complex_step, approx_centered=approx_centered) evaluated_hessian = self.nobs_effective * self.model.hessian( self.params, transformed=True, includes_fixed=True, method='approx', approx_complex_step=approx_complex_step) # TODO: Case with "not approx_complex_step" is not # hit in tests as of 2017-05-19 if len(self.fixed_params) > 0: mask = np.ix_(self._free_params_index, self._free_params_index) cov_params = np.zeros_like(evaluated_hessian) * np.nan cov_opg = cov_opg[mask] evaluated_hessian = evaluated_hessian[mask] tmp, singular_values = pinv_extended( np.dot(np.dot(evaluated_hessian, cov_opg), evaluated_hessian)) cov_params[mask] = tmp else: (cov_params, singular_values) = pinv_extended( np.dot(np.dot(evaluated_hessian, cov_opg), evaluated_hessian)) self.model.update(self.params, transformed=True, includes_fixed=True) if self._rank is None: self._rank = np.linalg.matrix_rank(np.diag(singular_values)) return cov_params @cache_readonly def cov_params_robust_approx(self): """ (array) The QMLE variance / covariance matrix. Computed using the numerical Hessian as the evaluated hessian. """ return self._cov_params_robust_approx(self._cov_approx_complex_step, self._cov_approx_centered) def info_criteria(self, criteria, method='standard'): r""" Information criteria Parameters ---------- criteria : {'aic', 'bic', 'hqic'} The information criteria to compute. method : {'standard', 'lutkepohl'} The method for information criteria computation. Default is 'standard' method; 'lutkepohl' computes the information criteria as in Lütkepohl (2007). See Notes for formulas. Notes ----- The `'standard'` formulas are: .. math:: AIC & = -2 \log L(Y_n | \hat \psi) + 2 k \\ BIC & = -2 \log L(Y_n | \hat \psi) + k \log n \\ HQIC & = -2 \log L(Y_n | \hat \psi) + 2 k \log \log n \\ where :math:`\hat \psi` are the maximum likelihood estimates of the parameters, :math:`n` is the number of observations, and `k` is the number of estimated parameters. Note that the `'standard'` formulas are returned from the `aic`, `bic`, and `hqic` results attributes. The `'lutkepohl'` formulas are (Lütkepohl, 2010): .. math:: AIC_L & = \log | Q | + \frac{2 k}{n} \\ BIC_L & = \log | Q | + \frac{k \log n}{n} \\ HQIC_L & = \log | Q | + \frac{2 k \log \log n}{n} \\ where :math:`Q` is the state covariance matrix. Note that the Lütkepohl definitions do not apply to all state space models, and should be used with care outside of SARIMAX and VARMAX models. References ---------- .. [*] Lütkepohl, Helmut. 2007. *New Introduction to Multiple Time* *Series Analysis.* Berlin: Springer. """ criteria = criteria.lower() method = method.lower() if method == 'standard': out = getattr(self, criteria) elif method == 'lutkepohl': if self.filter_results.state_cov.shape[-1] > 1: raise ValueError('Cannot compute Lütkepohl statistics for' ' models with time-varying state covariance' ' matrix.') cov = self.filter_results.state_cov[:, :, 0] if criteria == 'aic': out = np.squeeze(np.linalg.slogdet(cov)[1] + 2 * self.df_model / self.nobs_effective) elif criteria == 'bic': out = np.squeeze(np.linalg.slogdet(cov)[1] + self.df_model * np.log(self.nobs_effective) / self.nobs_effective) elif criteria == 'hqic': out = np.squeeze(np.linalg.slogdet(cov)[1] + 2 * self.df_model * np.log(np.log(self.nobs_effective)) / self.nobs_effective) else: raise ValueError('Invalid information criteria') else: raise ValueError('Invalid information criteria computation method') return out @cache_readonly def fittedvalues(self): """ (array) The predicted values of the model. An (nobs x k_endog) array. """ # This is a (k_endog x nobs array; do not want to squeeze in case of # the corner case where nobs = 1 (mostly a concern in the predict or # forecast functions, but here also to maintain consistency) fittedvalues = self.forecasts if fittedvalues is None: pass elif fittedvalues.shape[0] == 1: fittedvalues = fittedvalues[0, :] else: fittedvalues = fittedvalues.T return fittedvalues @cache_readonly def hqic(self): """ (float) Hannan-Quinn Information Criterion """ # return (-2 * self.llf + # 2 * np.log(np.log(self.nobs_effective)) * self.df_model) return hqic(self.llf, self.nobs_effective, self.df_model) @cache_readonly def llf_obs(self): """ (float) The value of the log-likelihood function evaluated at `params`. """ return self.filter_results.llf_obs @cache_readonly def llf(self): """ (float) The value of the log-likelihood function evaluated at `params`. """ return self.filter_results.llf @cache_readonly def loglikelihood_burn(self): """ (float) The number of observations during which the likelihood is not evaluated. """ return self.filter_results.loglikelihood_burn @cache_readonly def mae(self): """ (float) Mean absolute error """ return np.mean(np.abs(self.resid)) @cache_readonly def mse(self): """ (float) Mean squared error """ return self.sse / self.nobs @cache_readonly def pvalues(self): """ (array) The p-values associated with the z-statistics of the coefficients. Note that the coefficients are assumed to have a Normal distribution. """ pvalues = np.zeros_like(self.zvalues) * np.nan mask = np.ones_like(pvalues, dtype=bool) mask[self._free_params_index] = True mask &= ~np.isnan(self.zvalues) pvalues[mask] = norm.sf(np.abs(self.zvalues[mask])) * 2 return pvalues @cache_readonly def resid(self): """ (array) The model residuals. An (nobs x k_endog) array. """ # This is a (k_endog x nobs array; do not want to squeeze in case of # the corner case where nobs = 1 (mostly a concern in the predict or # forecast functions, but here also to maintain consistency) resid = self.forecasts_error if resid is None: pass elif resid.shape[0] == 1: resid = resid[0, :] else: resid = resid.T return resid @property def states(self): if self.model._index_generated and not self.model._index_none: warnings.warn('No supported index is available. The `states`' ' DataFrame uses a generated integer index', ValueWarning) return self._states @cache_readonly def sse(self): """ (float) Sum of squared errors """ return np.sum(self.resid**2) @cache_readonly def zvalues(self): """ (array) The z-statistics for the coefficients. """ return self.params / self.bse def test_normality(self, method): """ Test for normality of standardized residuals. Null hypothesis is normality. Parameters ---------- method : {'jarquebera', None} The statistical test for normality. Must be 'jarquebera' for Jarque-Bera normality test. If None, an attempt is made to select an appropriate test. See Also -------- statsmodels.stats.stattools.jarque_bera The Jarque-Bera test of normality. Notes ----- Let `d` = max(loglikelihood_burn, nobs_diffuse); this test is calculated ignoring the first `d` residuals. In the case of missing data, the maintained hypothesis is that the data are missing completely at random. This test is then run on the standardized residuals excluding those corresponding to missing observations. """ if method is None: method = 'jarquebera' if self.standardized_forecasts_error is None: raise ValueError('Cannot compute test statistic when standardized' ' forecast errors have not been computed.') if method == 'jarquebera': from statsmodels.stats.stattools import jarque_bera d = np.maximum(self.loglikelihood_burn, self.nobs_diffuse) output = [] for i in range(self.model.k_endog): resid = self.filter_results.standardized_forecasts_error[i, d:] mask = ~np.isnan(resid) output.append(jarque_bera(resid[mask])) else: raise NotImplementedError('Invalid normality test method.') return np.array(output) def test_heteroskedasticity(self, method, alternative='two-sided', use_f=True): r""" Test for heteroskedasticity of standardized residuals Tests whether the sum-of-squares in the first third of the sample is significantly different than the sum-of-squares in the last third of the sample. Analogous to a Goldfeld-Quandt test. The null hypothesis is of no heteroskedasticity. Parameters ---------- method : {'breakvar', None} The statistical test for heteroskedasticity. Must be 'breakvar' for test of a break in the variance. If None, an attempt is made to select an appropriate test. alternative : str, 'increasing', 'decreasing' or 'two-sided' This specifies the alternative for the p-value calculation. Default is two-sided. use_f : bool, optional Whether or not to compare against the asymptotic distribution (chi-squared) or the approximate small-sample distribution (F). Default is True (i.e. default is to compare against an F distribution). Returns ------- output : ndarray An array with `(test_statistic, pvalue)` for each endogenous variable. The array is then sized `(k_endog, 2)`. If the method is called as `het = res.test_heteroskedasticity()`, then `het[0]` is an array of size 2 corresponding to the first endogenous variable, where `het[0][0]` is the test statistic, and `het[0][1]` is the p-value. Notes ----- The null hypothesis is of no heteroskedasticity. That means different things depending on which alternative is selected: - Increasing: Null hypothesis is that the variance is not increasing throughout the sample; that the sum-of-squares in the later subsample is *not* greater than the sum-of-squares in the earlier subsample. - Decreasing: Null hypothesis is that the variance is not decreasing throughout the sample; that the sum-of-squares in the earlier subsample is *not* greater than the sum-of-squares in the later subsample. - Two-sided: Null hypothesis is that the variance is not changing throughout the sample. Both that the sum-of-squares in the earlier subsample is not greater than the sum-of-squares in the later subsample *and* that the sum-of-squares in the later subsample is not greater than the sum-of-squares in the earlier subsample. For :math:`h = [T/3]`, the test statistic is: .. math:: H(h) = \sum_{t=T-h+1}^T \tilde v_t^2 \Bigg / \sum_{t=d+1}^{d+1+h} \tilde v_t^2 where :math:`d` = max(loglikelihood_burn, nobs_diffuse)` (usually corresponding to diffuse initialization under either the approximate or exact approach). This statistic can be tested against an :math:`F(h,h)` distribution. Alternatively, :math:`h H(h)` is asymptotically distributed according to :math:`\chi_h^2`; this second test can be applied by passing `asymptotic=True` as an argument. See section 5.4 of [1]_ for the above formula and discussion, as well as additional details. TODO - Allow specification of :math:`h` References ---------- .. [1] Harvey, Andrew C. 1990. *Forecasting, Structural Time Series* *Models and the Kalman Filter.* Cambridge University Press. """ if method is None: method = 'breakvar' if self.standardized_forecasts_error is None: raise ValueError('Cannot compute test statistic when standardized' ' forecast errors have not been computed.') if method == 'breakvar': # Store some values squared_resid = self.filter_results.standardized_forecasts_error**2 d = np.maximum(self.loglikelihood_burn, self.nobs_diffuse) # This differs from self.nobs_effective because here we want to # exclude exact diffuse periods, whereas self.nobs_effective only # excludes explicitly burned (usually approximate diffuse) periods. nobs_effective = self.nobs - d test_statistics = [] p_values = [] for i in range(self.model.k_endog): h = int(np.round(nobs_effective / 3)) numer_resid = squared_resid[i, -h:] numer_resid = numer_resid[~np.isnan(numer_resid)] numer_dof = len(numer_resid) denom_resid = squared_resid[i, d:d+h] denom_resid = denom_resid[~np.isnan(denom_resid)] denom_dof = len(denom_resid) if numer_dof < 2: warnings.warn('Early subset of data for variable %d' ' has too few non-missing observations to' ' calculate test statistic.' % i) numer_resid = np.nan if denom_dof < 2: warnings.warn('Later subset of data for variable %d' ' has too few non-missing observations to' ' calculate test statistic.' % i) denom_resid = np.nan test_statistic = np.sum(numer_resid) / np.sum(denom_resid) # Setup functions to calculate the p-values if use_f: from scipy.stats import f pval_lower = lambda test_statistics: f.cdf( # noqa:E731 test_statistics, numer_dof, denom_dof) pval_upper = lambda test_statistics: f.sf( # noqa:E731 test_statistics, numer_dof, denom_dof) else: from scipy.stats import chi2 pval_lower = lambda test_statistics: chi2.cdf( # noqa:E731 numer_dof * test_statistics, denom_dof) pval_upper = lambda test_statistics: chi2.sf( # noqa:E731 numer_dof * test_statistics, denom_dof) # Calculate the one- or two-sided p-values alternative = alternative.lower() if alternative in ['i', 'inc', 'increasing']: p_value = pval_upper(test_statistic) elif alternative in ['d', 'dec', 'decreasing']: test_statistic = 1. / test_statistic p_value = pval_upper(test_statistic) elif alternative in ['2', '2-sided', 'two-sided']: p_value = 2 * np.minimum( pval_lower(test_statistic), pval_upper(test_statistic) ) else: raise ValueError('Invalid alternative.') test_statistics.append(test_statistic) p_values.append(p_value) output = np.c_[test_statistics, p_values] else: raise NotImplementedError('Invalid heteroskedasticity test' ' method.') return output def test_serial_correlation(self, method, lags=None): """ Ljung-Box test for no serial correlation of standardized residuals Null hypothesis is no serial correlation. Parameters ---------- method : {'ljungbox','boxpierece', None} The statistical test for serial correlation. If None, an attempt is made to select an appropriate test. lags : None, int or array_like If lags is an integer then this is taken to be the largest lag that is included, the test result is reported for all smaller lag length. If lags is a list or array, then all lags are included up to the largest lag in the list, however only the tests for the lags in the list are reported. If lags is None, then the default maxlag is 12*(nobs/100)^{1/4}. After 0.12 the default maxlag will change to min(10, nobs // 5) for non-seasonal models and min(2*m, nobs // 5) for seasonal time series where m is the seasonal period. Returns ------- output : ndarray An array with `(test_statistic, pvalue)` for each endogenous variable and each lag. The array is then sized `(k_endog, 2, lags)`. If the method is called as `ljungbox = res.test_serial_correlation()`, then `ljungbox[i]` holds the results of the Ljung-Box test (as would be returned by `statsmodels.stats.diagnostic.acorr_ljungbox`) for the `i` th endogenous variable. See Also -------- statsmodels.stats.diagnostic.acorr_ljungbox Ljung-Box test for serial correlation. Notes ----- Let `d` = max(loglikelihood_burn, nobs_diffuse); this test is calculated ignoring the first `d` residuals. Output is nan for any endogenous variable which has missing values. """ if method is None: method = 'ljungbox' if self.standardized_forecasts_error is None: raise ValueError('Cannot compute test statistic when standardized' ' forecast errors have not been computed.') if method == 'ljungbox' or method == 'boxpierce': from statsmodels.stats.diagnostic import acorr_ljungbox d = np.maximum(self.loglikelihood_burn, self.nobs_diffuse) # This differs from self.nobs_effective because here we want to # exclude exact diffuse periods, whereas self.nobs_effective only # excludes explicitly burned (usually approximate diffuse) periods. nobs_effective = self.nobs - d output = [] # Default lags for acorr_ljungbox is 40, but may not always have # that many observations if lags is None: seasonal_periods = getattr(self.model, "seasonal_periods", 0) if seasonal_periods: lags = min(2 * seasonal_periods, nobs_effective // 5) else: lags = min(10, nobs_effective // 5) warnings.warn( "The default value of lags is changing. After 0.12, " "this value will become min(10, nobs//5) for non-seasonal " "time series and min (2*m, nobs//5) for seasonal time " "series. Directly set lags to silence this warning.", FutureWarning ) for i in range(self.model.k_endog): results = acorr_ljungbox( self.filter_results.standardized_forecasts_error[i][d:], lags=lags, boxpierce=(method == 'boxpierce'), return_df=False) if method == 'ljungbox': output.append(results[0:2]) else: output.append(results[2:]) output = np.c_[output] else: raise NotImplementedError('Invalid serial correlation test' ' method.') return output def get_prediction(self, start=None, end=None, dynamic=False, index=None, exog=None, extend_model=None, extend_kwargs=None, **kwargs): """ In-sample prediction and out-of-sample forecasting Parameters ---------- start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, i.e., the last forecast is end. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. dynamic : bool, int, str, or datetime, optional Integer offset relative to `start` at which to begin dynamic prediction. Can also be an absolute date string to parse or a datetime type (these are not interpreted as offsets). Prior to this observation, true endogenous values will be used for prediction; starting with this observation and continuing through the end of prediction, forecasted endogenous values will be used instead. **kwargs Additional arguments may required for forecasting beyond the end of the sample. See `FilterResults.predict` for more details. Returns ------- predictions : PredictionResults PredictionResults instance containing in-sample predictions and out-of-sample forecasts. """ if start is None: start = 0 # Handle start, end, dynamic start, end, out_of_sample, prediction_index = ( self.model._get_prediction_index(start, end, index)) # Handle `dynamic` if isinstance(dynamic, (str, dt.datetime, pd.Timestamp)): dynamic, _, _ = self.model._get_index_loc(dynamic) # Convert to offset relative to start dynamic = dynamic - start # If we have out-of-sample forecasting and `exog` or in general any # kind of time-varying state space model, then we need to create an # extended model to get updated state space system matrices if extend_model is None: extend_model = (self.model.exog is not None or not self.filter_results.time_invariant) if out_of_sample and extend_model: kwargs = self.model._get_extension_time_varying_matrices( self.params, exog, out_of_sample, extend_kwargs, transformed=True, includes_fixed=True, **kwargs) # Make sure the model class has the current parameters self.model.update(self.params, transformed=True, includes_fixed=True) # Perform the prediction # This is a (k_endog x npredictions) array; do not want to squeeze in # case of npredictions = 1 prediction_results = self.filter_results.predict( start, end + out_of_sample + 1, dynamic, **kwargs) # Return a new mlemodel.PredictionResults object return PredictionResultsWrapper(PredictionResults( self, prediction_results, row_labels=prediction_index)) def get_forecast(self, steps=1, **kwargs): """ Out-of-sample forecasts and prediction intervals Parameters ---------- steps : int, str, or datetime, optional If an integer, the number of steps to forecast from the end of the sample. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, steps must be an integer. Default **kwargs Additional arguments may required for forecasting beyond the end of the sample. See `FilterResults.predict` for more details. Returns ------- predictions : PredictionResults PredictionResults instance containing in-sample predictions and out-of-sample forecasts. """ if isinstance(steps, int): end = self.nobs + steps - 1 else: end = steps return self.get_prediction(start=self.nobs, end=end, **kwargs) def predict(self, start=None, end=None, dynamic=False, **kwargs): """ In-sample prediction and out-of-sample forecasting Parameters ---------- start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, i.e., the last forecast is end. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. dynamic : bool, int, str, or datetime, optional Integer offset relative to `start` at which to begin dynamic prediction. Can also be an absolute date string to parse or a datetime type (these are not interpreted as offsets). Prior to this observation, true endogenous values will be used for prediction; starting with this observation and continuing through the end of prediction, forecasted endogenous values will be used instead. **kwargs Additional arguments may required for forecasting beyond the end of the sample. See `FilterResults.predict` for more details. Returns ------- forecast : array_like Array of out of in-sample predictions and / or out-of-sample forecasts. An (npredict x k_endog) array. See Also -------- forecast Out-of-sample forecasts get_prediction Prediction results and confidence intervals """ # Perform the prediction prediction_results = self.get_prediction(start, end, dynamic, **kwargs) return prediction_results.predicted_mean def forecast(self, steps=1, **kwargs): """ Out-of-sample forecasts Parameters ---------- steps : int, str, or datetime, optional If an integer, the number of steps to forecast from the end of the sample. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, steps must be an integer. Default **kwargs Additional arguments may required for forecasting beyond the end of the sample. See `FilterResults.predict` for more details. Returns ------- forecast : PredictionResults PredictionResults instance containing in-sample predictions and out-of-sample forecasts. """ if isinstance(steps, int): end = self.nobs + steps - 1 else: end = steps return self.predict(start=self.nobs, end=end, **kwargs) def simulate(self, nsimulations, measurement_shocks=None, state_shocks=None, initial_state=None, anchor=None, repetitions=None, exog=None, extend_model=None, extend_kwargs=None, **kwargs): r""" Simulate a new time series following the state space model Parameters ---------- nsimulations : int The number of observations to simulate. If the model is time-invariant this can be any number. If the model is time-varying, then this number must be less than or equal to the number measurement_shocks : array_like, optional If specified, these are the shocks to the measurement equation, :math:`\varepsilon_t`. If unspecified, these are automatically generated using a pseudo-random number generator. If specified, must be shaped `nsimulations` x `k_endog`, where `k_endog` is the same as in the state space model. state_shocks : array_like, optional If specified, these are the shocks to the state equation, :math:`\eta_t`. If unspecified, these are automatically generated using a pseudo-random number generator. If specified, must be shaped `nsimulations` x `k_posdef` where `k_posdef` is the same as in the state space model. initial_state : array_like, optional If specified, this is the initial state vector to use in simulation, which should be shaped (`k_states` x 1), where `k_states` is the same as in the state space model. If unspecified, but the model has been initialized, then that initialization is used. This must be specified if `anchor` is anything other than "start" or 0. anchor : int, str, or datetime, optional Starting point from which to begin the simulations; type depends on the index of the given `endog` model. Two special cases are the strings 'start' and 'end', which refer to starting at the beginning and end of the sample, respectively. If a date/time index was provided to the model, then this argument can be a date string to parse or a datetime type. Otherwise, an integer index should be given. Default is 'start'. repetitions : int, optional Number of simulated paths to generate. Default is 1 simulated path. exog : array_like, optional New observations of exogenous regressors, if applicable. Returns ------- simulated_obs : ndarray An array of simulated observations. If `repetitions=None`, then it will be shaped (nsimulations x k_endog) or (nsimulations,) if `k_endog=1`. Otherwise it will be shaped (nsimulations x k_endog x repetitions). If the model was given Pandas input then the output will be a Pandas object. If `k_endog > 1` and `repetitions` is not None, then the output will be a Pandas DataFrame that has a MultiIndex for the columns, with the first level containing the names of the `endog` variables and the second level containing the repetition number. """ # Get the starting location if anchor is None or anchor == 'start': iloc = 0 elif anchor == 'end': iloc = self.nobs else: iloc, _, _ = self.model._get_index_loc(anchor) if isinstance(iloc, slice): iloc = iloc.start if iloc < 0: iloc = self.nobs + iloc if iloc > self.nobs: raise ValueError('Cannot anchor simulation outside of the sample.') # Setup the initial state if initial_state is None: initial_state_moments = ( self.predicted_state[:, iloc], self.predicted_state_cov[:, :, iloc]) _repetitions = 1 if repetitions is None else repetitions initial_state = np.random.multivariate_normal( *initial_state_moments, size=_repetitions).T scale = self.scale if self.filter_results.filter_concentrated else None with self.model.ssm.fixed_scale(scale): sim = self.model.simulate( self.params, nsimulations, measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state, anchor=anchor, repetitions=repetitions, exog=exog, transformed=True, includes_fixed=True, extend_model=extend_model, extend_kwargs=extend_kwargs, **kwargs) return sim def impulse_responses(self, steps=1, impulse=0, orthogonalized=False, cumulative=False, **kwargs): """ Impulse response function Parameters ---------- steps : int, optional The number of steps for which impulse responses are calculated. Default is 1. Note that for time-invariant models, the initial impulse is not counted as a step, so if `steps=1`, the output will have 2 entries. impulse : int or array_like If an integer, the state innovation to pulse; must be between 0 and `k_posdef-1`. Alternatively, a custom impulse vector may be provided; must be shaped `k_posdef x 1`. orthogonalized : bool, optional Whether or not to perform impulse using orthogonalized innovations. Note that this will also affect custum `impulse` vectors. Default is False. cumulative : bool, optional Whether or not to return cumulative impulse responses. Default is False. anchor : int, str, or datetime, optional Time point within the sample for the state innovation impulse. Type depends on the index of the given `endog` in the model. Two special cases are the strings 'start' and 'end', which refer to setting the impulse at the first and last points of the sample, respectively. Integer values can run from 0 to `nobs - 1`, or can be negative to apply negative indexing. Finally, if a date/time index was provided to the model, then this argument can be a date string to parse or a datetime type. Default is 'start'. exog : array_like, optional New observations of exogenous regressors, if applicable. **kwargs If the model has time-varying design or transition matrices and the combination of `anchor` and `steps` implies creating impulse responses for the out-of-sample period, then these matrices must have updated values provided for the out-of-sample steps. For example, if `design` is a time-varying component, `nobs` is 10, `anchor=1`, and `steps` is 15, a (`k_endog` x `k_states` x 7) matrix must be provided with the new design matrix values. Returns ------- impulse_responses : ndarray Responses for each endogenous variable due to the impulse given by the `impulse` argument. For a time-invariant model, the impulse responses are given for `steps + 1` elements (this gives the "initial impulse" followed by `steps` responses for the important cases of VAR and SARIMAX models), while for time-varying models the impulse responses are only given for `steps` elements (to avoid having to unexpectedly provide updated time-varying matrices). Notes ----- Intercepts in the measurement and state equation are ignored when calculating impulse responses. """ scale = self.scale if self.filter_results.filter_concentrated else None with self.model.ssm.fixed_scale(scale): irfs = self.model.impulse_responses(self.params, steps, impulse, orthogonalized, cumulative, **kwargs) # These are wrapped automatically, so just return the array if isinstance(irfs, (pd.Series, pd.DataFrame)): irfs = irfs.values return irfs def _apply(self, mod, refit=False, fit_kwargs=None, **kwargs): if fit_kwargs is None: fit_kwargs = {} if refit: fit_kwargs.setdefault('start_params', self.params) if self._has_fixed_params: fit_kwargs.setdefault('includes_fixed', True) res = mod.fit_constrained(self._fixed_params, **fit_kwargs) else: res = mod.fit(**fit_kwargs) else: if 'cov_type' in fit_kwargs: raise ValueError('Cannot specify covariance type in' ' `fit_kwargs` unless refitting' ' parameters (not available in extend).') if 'cov_kwds' in fit_kwargs: raise ValueError('Cannot specify covariance keyword arguments' ' in `fit_kwargs` unless refitting' ' parameters (not available in extend).') if self.cov_type == 'none': fit_kwargs['cov_type'] = 'none' else: fit_kwargs['cov_type'] = 'custom' fit_kwargs['cov_kwds'] = { 'custom_cov_type': self.cov_type, 'custom_cov_params': self.cov_params_default, 'custom_description': ('Parameters and standard errors' ' were estimated using a different' ' dataset and were then applied to' ' this dataset. %s' % self.cov_kwds['description'])} if self.smoother_results is not None: func = mod.smooth else: func = mod.filter if self._has_fixed_params: with mod.fix_params(self._fixed_params): fit_kwargs.setdefault('includes_fixed', True) res = func(self.params, **fit_kwargs) else: res = func(self.params, **fit_kwargs) return res def _news_previous_results(self, previous, start, end, periods): # Compute the news out = self.smoother_results.news(previous.smoother_results, start=start, end=end) return out def _news_updated_results(self, updated, start, end, periods): return updated._news_previous_results(self, start, end, periods) def _news_previous_data(self, endog, start, end, periods, exog): previous = self.apply(endog, exog=exog, copy_initialization=True) return self._news_previous_results(previous, start, end, periods) def _news_updated_data(self, endog, start, end, periods, exog): updated = self.apply(endog, exog=exog, copy_initialization=True) return self._news_updated_results(updated, start, end, periods) def news(self, comparison, impact_date=None, impacted_variable=None, start=None, end=None, periods=None, exog=None, comparison_type=None, return_raw=False, tolerance=1e-10, **kwargs): """ Compute impacts from updated data (news and revisions) Parameters ---------- comparison : array_like or MLEResults An updated dataset with updated and/or revised data from which the news can be computed, or an updated or previous results object to use in computing the news. impact_date : int, str, or datetime, optional A single specific period of impacts from news and revisions to compute. Can also be a date string to parse or a datetime type. This argument cannot be used in combination with `start`, `end`, or `periods`. Default is the first out-of-sample observation. impacted_variable : str, list, array, or slice, optional Observation variable label or slice of labels specifying that only specific impacted variables should be shown in the News output. The impacted variable(s) describe the variables that were *affected* by the news. If you do not know the labels for the variables, check the `endog_names` attribute of the model instance. start : int, str, or datetime, optional The first period of impacts from news and revisions to compute. Can also be a date string to parse or a datetime type. Default is the first out-of-sample observation. end : int, str, or datetime, optional The last period of impacts from news and revisions to compute. Can also be a date string to parse or a datetime type. Default is the first out-of-sample observation. periods : int, optional The number of periods of impacts from news and revisions to compute. exog : array_like, optional Array of exogenous regressors for the out-of-sample period, if applicable. comparison_type : {None, 'previous', 'updated'} This denotes whether the `comparison` argument represents a *previous* results object or dataset or an *updated* results object or dataset. If not specified, then an attempt is made to determine the comparison type. return_raw : bool, optional Whether or not to return only the specific output or a full results object. Default is to return a full results object. tolerance : float, optional The numerical threshold for determining zero impact. Default is that any impact less than 1e-10 is assumed to be zero. Returns ------- NewsResults Impacts of data revisions and news on estimates References ---------- .. [1] BaÅ„bura, Marta, and Michele Modugno. "Maximum likelihood estimation of factor models on datasets with arbitrary pattern of missing data." Journal of Applied Econometrics 29, no. 1 (2014): 133-160. .. [2] BaÅ„bura, Marta, Domenico Giannone, and Lucrezia Reichlin. "Nowcasting." The Oxford Handbook of Economic Forecasting. July 8, 2011. .. [3] BaÅ„bura, Marta, Domenico Giannone, Michele Modugno, and Lucrezia Reichlin. "Now-casting and the real-time data flow." In Handbook of economic forecasting, vol. 2, pp. 195-237. Elsevier, 2013. """ # Validate input if self.smoother_results is None: raise ValueError('Cannot compute news without Kalman smoother' ' results.') # If we were given data, create a new results object comparison_dataset = not isinstance( comparison, (MLEResults, MLEResultsWrapper)) if comparison_dataset: # If `exog` is longer than `comparison`, then we extend it to match nobs_endog = len(comparison) nobs_exog = len(exog) if exog is not None else nobs_endog if nobs_exog > nobs_endog: _, _, _, ix = self.model._get_prediction_index( start=0, end=nobs_exog - 1) # TODO: check that the index of `comparison` matches the model comparison = np.asarray(comparison) if comparison.ndim < 2: comparison = np.atleast_2d(comparison).T if (comparison.ndim != 2 or comparison.shape[1] != self.model.k_endog): raise ValueError('Invalid shape for `comparison`. Must' f' contain {self.model.k_endog} columns.') extra = np.zeros((nobs_exog - nobs_endog, self.model.k_endog)) * np.nan comparison = pd.DataFrame( np.concatenate([comparison, extra], axis=0), index=ix, columns=self.model.endog_names) # Get the results object comparison = self.apply(comparison, exog=exog, copy_initialization=True, **kwargs) # Now, figure out the `updated` versus `previous` results objects nmissing = self.filter_results.missing.sum() nmissing_comparison = comparison.filter_results.missing.sum() if (comparison_type == 'updated' or (comparison_type is None and ( comparison.nobs > self.nobs or (comparison.nobs == self.nobs and nmissing > nmissing_comparison)))): updated = comparison previous = self elif (comparison_type == 'previous' or (comparison_type is None and ( comparison.nobs < self.nobs or (comparison.nobs == self.nobs and nmissing < nmissing_comparison)))): updated = self previous = comparison else: raise ValueError('Could not automatically determine the type' ' of comparison requested to compute the' ' News, so it must be specified as "updated"' ' or "previous", using the `comparison_type`' ' keyword argument') # Check that the index of `updated` is a superset of the # index of `previous` # Note: the try/except block is for Pandas < 0.25, in which # `PeriodIndex.difference` raises a ValueError if the argument is not # also a `PeriodIndex`. try: diff = previous.model._index.difference(updated.model._index) except ValueError: diff = [True] if len(diff) > 0: raise ValueError('The index associated with the updated results is' ' not a superset of the index associated with the' ' previous results, and so these datasets do not' ' appear to be related. Can only compute the' ' news by comparing this results set to previous' ' results objects.') # Handle start, end, periods # There doesn't seem to be any universal defaults that both (a) make # sense for all data update combinations, and (b) work with both # time-invariant and time-varying models. So we require that the user # specify exactly two of start, end, periods. if impact_date is not None: if not (start is None and end is None and periods is None): raise ValueError('Cannot use the `impact_date` argument in' ' combination with `start`, `end`, or' ' `periods`.') start = impact_date periods = 1 if start is None and end is None and periods is None: start = previous.nobs - 1 end = previous.nobs - 1 if int(start is None) + int(end is None) + int(periods is None) != 1: raise ValueError('Of the three parameters: start, end, and' ' periods, exactly two must be specified') # If we have the `periods` object, we need to convert `start`/`end` to # integers so that we can compute the other one. That's because # _get_prediction_index doesn't support a `periods` argument elif start is not None and periods is not None: start, _, _, _ = self.model._get_prediction_index(start, start) end = start + (periods - 1) elif end is not None and periods is not None: _, end, _, _ = self.model._get_prediction_index(end, end) start = end - (periods - 1) elif start is not None and end is not None: pass # Get the integer-based start, end and the prediction index start, end, out_of_sample, prediction_index = ( updated.model._get_prediction_index(start, end)) end = end + out_of_sample # News results will always use Pandas, so if the model's data was not # from Pandas, we'll create an index, as if the model's data had been # given a default Pandas index. if prediction_index is None: prediction_index = pd.RangeIndex(start=start, stop=end + 1) # For time-varying models try to create an appended `updated` model # with NaN values. Do not extend the model if this was already done # above (i.e. the case that `comparison` was a new dataset), because # in that case `exog` and `kwargs` should have # been set with the input `comparison` dataset in mind, and so would be # useless here. Ultimately, we've already extended `updated` as far # as we can. So raise an exception in that case with a useful message. # However, we still want to try to accommodate extending the model here # if it is possible. # Note that we do not need to extend time-invariant models, because # `KalmanSmoother.news` can itself handle any impact dates for # time-invariant models. time_varying = not (previous.filter_results.time_invariant or updated.filter_results.time_invariant) if time_varying and end >= updated.nobs: # If we the given `comparison` was a dataset and either `exog` or # `kwargs` was set, then we assume that we cannot create an updated # time-varying model (because then we can't tell if `kwargs` and # `exog` arguments are meant to apply to the `comparison` dataset # or to this extension) if comparison_dataset and (exog is not None or len(kwargs) > 0): if comparison is updated: raise ValueError('If providing an updated dataset as the' ' `comparison` with a time-varying model,' ' then the `end` period cannot be beyond' ' the end of that updated dataset.') else: raise ValueError('If providing an previous dataset as the' ' `comparison` with a time-varying model,' ' then the `end` period cannot be beyond' ' the end of the (updated) results' ' object.') # Try to extend `updated` updated_orig = updated # TODO: `append` should fix this k_endog=1 issue for us # TODO: is the + 1 necessary? if self.model.k_endog > 1: extra = np.zeros((end - updated.nobs + 1, self.model.k_endog)) * np.nan else: extra = np.zeros((end - updated.nobs + 1,)) * np.nan updated = updated_orig.append(extra, exog=exog, **kwargs) # Compute the news news_results = ( updated._news_previous_results(previous, start, end + 1, periods)) if not return_raw: news_results = NewsResults( news_results, self, updated, previous, impacted_variable, tolerance, row_labels=prediction_index) return news_results def append(self, endog, exog=None, refit=False, fit_kwargs=None, copy_initialization=False, **kwargs): """ Recreate the results object with new data appended to the original data Creates a new result object applied to a dataset that is created by appending new data to the end of the model's original data. The new results can then be used for analysis or forecasting. Parameters ---------- endog : array_like New observations from the modeled time-series process. exog : array_like, optional New observations of exogenous regressors, if applicable. refit : bool, optional Whether to re-fit the parameters, based on the combined dataset. Default is False (so parameters from the current results object are used to create the new results object). copy_initialization : bool, optional Whether or not to copy the initialization from the current results set to the new model. Default is False fit_kwargs : dict, optional Keyword arguments to pass to `fit` (if `refit=True`) or `filter` / `smooth`. copy_initialization : bool, optional **kwargs Keyword arguments may be used to modify model specification arguments when created the new model object. Returns ------- results Updated Results object, that includes results from both the original dataset and the new dataset. Notes ----- The `endog` and `exog` arguments to this method must be formatted in the same way (e.g. Pandas Series versus Numpy array) as were the `endog` and `exog` arrays passed to the original model. The `endog` argument to this method should consist of new observations that occurred directly after the last element of `endog`. For any other kind of dataset, see the `apply` method. This method will apply filtering to all of the original data as well as to the new data. To apply filtering only to the new data (which can be much faster if the original dataset is large), see the `extend` method. See Also -------- statsmodels.tsa.statespace.mlemodel.MLEResults.extend statsmodels.tsa.statespace.mlemodel.MLEResults.apply Examples -------- >>> index = pd.period_range(start='2000', periods=2, freq='A') >>> original_observations = pd.Series([1.2, 1.5], index=index) >>> mod = sm.tsa.SARIMAX(original_observations) >>> res = mod.fit() >>> print(res.params) ar.L1 0.9756 sigma2 0.0889 dtype: float64 >>> print(res.fittedvalues) 2000 0.0000 2001 1.1707 Freq: A-DEC, dtype: float64 >>> print(res.forecast(1)) 2002 1.4634 Freq: A-DEC, dtype: float64 >>> new_index = pd.period_range(start='2002', periods=1, freq='A') >>> new_observations = pd.Series([0.9], index=new_index) >>> updated_res = res.append(new_observations) >>> print(updated_res.params) ar.L1 0.9756 sigma2 0.0889 dtype: float64 >>> print(updated_res.fittedvalues) 2000 0.0000 2001 1.1707 2002 1.4634 Freq: A-DEC, dtype: float64 >>> print(updated_res.forecast(1)) 2003 0.878 Freq: A-DEC, dtype: float64 """ start = self.nobs end = self.nobs + len(endog) - 1 _, _, _, append_ix = self.model._get_prediction_index(start, end) # Check the index of the new data if isinstance(self.model.data, PandasData): _check_index(append_ix, endog, '`endog`') # Concatenate the new data to original data new_endog = concat([self.model.data.orig_endog, endog], axis=0, allow_mix=True) # Handle `exog` if exog is not None: _, exog = prepare_exog(exog) _check_index(append_ix, exog, '`exog`') new_exog = concat([self.model.data.orig_exog, exog], axis=0, allow_mix=True) else: new_exog = None # Create a continuous index for the combined data if isinstance(self.model.data, PandasData): start = 0 end = len(new_endog) - 1 _, _, _, new_index = self.model._get_prediction_index(start, end) # Standardize `endog` to have the right index and columns columns = self.model.endog_names if not isinstance(columns, list): columns = [columns] new_endog = pd.DataFrame(new_endog, index=new_index, columns=columns) # Standardize `exog` to have the right index if new_exog is not None: new_exog = pd.DataFrame(new_exog, index=new_index, columns=self.model.exog_names) if copy_initialization: res = self.filter_results init = Initialization( self.model.k_states, 'known', constant=res.initial_state, stationary_cov=res.initial_state_cov) kwargs.setdefault('initialization', init) mod = self.model.clone(new_endog, exog=new_exog, **kwargs) res = self._apply(mod, refit=refit, fit_kwargs=fit_kwargs, **kwargs) return res def extend(self, endog, exog=None, fit_kwargs=None, **kwargs): """ Recreate the results object for new data that extends the original data Creates a new result object applied to a new dataset that is assumed to follow directly from the end of the model's original data. The new results can then be used for analysis or forecasting. Parameters ---------- endog : array_like New observations from the modeled time-series process. exog : array_like, optional New observations of exogenous regressors, if applicable. fit_kwargs : dict, optional Keyword arguments to pass to `filter` or `smooth`. **kwargs Keyword arguments may be used to modify model specification arguments when created the new model object. Returns ------- results Updated Results object, that includes results only for the new dataset. See Also -------- statsmodels.tsa.statespace.mlemodel.MLEResults.append statsmodels.tsa.statespace.mlemodel.MLEResults.apply Notes ----- The `endog` argument to this method should consist of new observations that occurred directly after the last element of the model's original `endog` array. For any other kind of dataset, see the `apply` method. This method will apply filtering only to the new data provided by the `endog` argument, which can be much faster than re-filtering the entire dataset. However, the returned results object will only have results for the new data. To retrieve results for both the new data and the original data, see the `append` method. Examples -------- >>> index = pd.period_range(start='2000', periods=2, freq='A') >>> original_observations = pd.Series([1.2, 1.5], index=index) >>> mod = sm.tsa.SARIMAX(original_observations) >>> res = mod.fit() >>> print(res.params) ar.L1 0.9756 sigma2 0.0889 dtype: float64 >>> print(res.fittedvalues) 2000 0.0000 2001 1.1707 Freq: A-DEC, dtype: float64 >>> print(res.forecast(1)) 2002 1.4634 Freq: A-DEC, dtype: float64 >>> new_index = pd.period_range(start='2002', periods=1, freq='A') >>> new_observations = pd.Series([0.9], index=new_index) >>> updated_res = res.extend(new_observations) >>> print(updated_res.params) ar.L1 0.9756 sigma2 0.0889 dtype: float64 >>> print(updated_res.fittedvalues) 2002 1.4634 Freq: A-DEC, dtype: float64 >>> print(updated_res.forecast(1)) 2003 0.878 Freq: A-DEC, dtype: float64 """ start = self.nobs end = self.nobs + len(endog) - 1 _, _, _, extend_ix = self.model._get_prediction_index(start, end) if isinstance(self.model.data, PandasData): _check_index(extend_ix, endog, '`endog`') # Standardize `endog` to have the right index and columns columns = self.model.endog_names if not isinstance(columns, list): columns = [columns] endog = pd.DataFrame(endog, index=extend_ix, columns=columns) # Extend the current fit result to additional data mod = self.model.clone(endog, exog=exog, **kwargs) mod.ssm.initialization = Initialization( mod.k_states, 'known', constant=self.predicted_state[..., -1], stationary_cov=self.predicted_state_cov[..., -1]) res = self._apply(mod, refit=False, fit_kwargs=fit_kwargs, **kwargs) return res def apply(self, endog, exog=None, refit=False, fit_kwargs=None, copy_initialization=False, **kwargs): """ Apply the fitted parameters to new data unrelated to the original data Creates a new result object using the current fitted parameters, applied to a completely new dataset that is assumed to be unrelated to the model's original data. The new results can then be used for analysis or forecasting. Parameters ---------- endog : array_like New observations from the modeled time-series process. exog : array_like, optional New observations of exogenous regressors, if applicable. refit : bool, optional Whether to re-fit the parameters, using the new dataset. Default is False (so parameters from the current results object are used to create the new results object). copy_initialization : bool, optional Whether or not to copy the initialization from the current results set to the new model. Default is False fit_kwargs : dict, optional Keyword arguments to pass to `fit` (if `refit=True`) or `filter` / `smooth`. **kwargs Keyword arguments may be used to modify model specification arguments when created the new model object. Returns ------- results Updated Results object, that includes results only for the new dataset. See Also -------- statsmodels.tsa.statespace.mlemodel.MLEResults.append statsmodels.tsa.statespace.mlemodel.MLEResults.apply Notes ----- The `endog` argument to this method should consist of new observations that are not necessarily related to the original model's `endog` dataset. For observations that continue that original dataset by follow directly after its last element, see the `append` and `extend` methods. Examples -------- >>> index = pd.period_range(start='2000', periods=2, freq='A') >>> original_observations = pd.Series([1.2, 1.5], index=index) >>> mod = sm.tsa.SARIMAX(original_observations) >>> res = mod.fit() >>> print(res.params) ar.L1 0.9756 sigma2 0.0889 dtype: float64 >>> print(res.fittedvalues) 2000 0.0000 2001 1.1707 Freq: A-DEC, dtype: float64 >>> print(res.forecast(1)) 2002 1.4634 Freq: A-DEC, dtype: float64 >>> new_index = pd.period_range(start='1980', periods=3, freq='A') >>> new_observations = pd.Series([1.4, 0.3, 1.2], index=new_index) >>> new_res = res.apply(new_observations) >>> print(new_res.params) ar.L1 0.9756 sigma2 0.0889 dtype: float64 >>> print(new_res.fittedvalues) 1980 1.1707 1981 1.3659 1982 0.2927 Freq: A-DEC, dtype: float64 Freq: A-DEC, dtype: float64 >>> print(new_res.forecast(1)) 1983 1.1707 Freq: A-DEC, dtype: float64 """ mod = self.model.clone(endog, exog=exog, **kwargs) if copy_initialization: res = self.filter_results init = Initialization( self.model.k_states, 'known', constant=res.initial_state, stationary_cov=res.initial_state_cov) mod.ssm.initialization = init res = self._apply(mod, refit=refit, fit_kwargs=fit_kwargs, **kwargs) return res def plot_diagnostics(self, variable=0, lags=10, fig=None, figsize=None, truncate_endog_names=24): """ Diagnostic plots for standardized residuals of one endogenous variable Parameters ---------- variable : int, optional Index of the endogenous variable for which the diagnostic plots should be created. Default is 0. lags : int, optional Number of lags to include in the correlogram. Default is 10. fig : Figure, optional If given, subplots are created in this figure instead of in a new figure. Note that the 2x2 grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Returns ------- Figure Figure instance with diagnostic plots See Also -------- statsmodels.graphics.gofplots.qqplot statsmodels.graphics.tsaplots.plot_acf Notes ----- Produces a 2x2 plot grid with the following plots (ordered clockwise from top left): 1. Standardized residuals over time 2. Histogram plus estimated density of standardized residuals, along with a Normal(0,1) density plotted for reference. 3. Normal Q-Q plot, with Normal reference line. 4. Correlogram """ from statsmodels.graphics.utils import _import_mpl, create_mpl_fig _import_mpl() fig = create_mpl_fig(fig, figsize) # Eliminate residuals associated with burned or diffuse likelihoods d = np.maximum(self.loglikelihood_burn, self.nobs_diffuse) # If given a variable name, find the index if isinstance(variable, str): variable = self.model.endog_names.index(variable) # Get residuals if hasattr(self.data, 'dates') and self.data.dates is not None: ix = self.data.dates[d:] else: ix = np.arange(self.nobs - d) resid = pd.Series( self.filter_results.standardized_forecasts_error[variable, d:], index=ix) if resid.shape[0] < max(d, lags): raise ValueError( "Length of endogenous variable must be larger the the number " "of lags used in the model and the number of observations " "burned in the log-likelihood calculation." ) # Top-left: residuals vs time ax = fig.add_subplot(221) resid.dropna().plot(ax=ax) ax.hlines(0, ix[0], ix[-1], alpha=0.5) ax.set_xlim(ix[0], ix[-1]) name = self.model.endog_names[variable] if len(name) > truncate_endog_names: name = name[:truncate_endog_names - 3] + '...' ax.set_title(f'Standardized residual for "{name}"') # Top-right: histogram, Gaussian kernel density, Normal density # Can only do histogram and Gaussian kernel density on the non-null # elements resid_nonmissing = resid.dropna() ax = fig.add_subplot(222) # gh5792: Remove except after support for matplotlib>2.1 required try: ax.hist(resid_nonmissing, density=True, label='Hist') except AttributeError: ax.hist(resid_nonmissing, normed=True, label='Hist') from scipy.stats import gaussian_kde, norm kde = gaussian_kde(resid_nonmissing) xlim = (-1.96*2, 1.96*2) x = np.linspace(xlim[0], xlim[1]) ax.plot(x, kde(x), label='KDE') ax.plot(x, norm.pdf(x), label='N(0,1)') ax.set_xlim(xlim) ax.legend() ax.set_title('Histogram plus estimated density') # Bottom-left: QQ plot ax = fig.add_subplot(223) from statsmodels.graphics.gofplots import qqplot qqplot(resid_nonmissing, line='s', ax=ax) ax.set_title('Normal Q-Q') # Bottom-right: Correlogram ax = fig.add_subplot(224) from statsmodels.graphics.tsaplots import plot_acf plot_acf(resid, ax=ax, lags=lags) ax.set_title('Correlogram') ax.set_ylim(-1, 1) return fig def summary(self, alpha=.05, start=None, title=None, model_name=None, display_params=True, display_diagnostics=True, truncate_endog_names=None, display_max_endog=None, extra_top_left=None, extra_top_right=None): """ Summarize the Model Parameters ---------- alpha : float, optional Significance level for the confidence intervals. Default is 0.05. start : int, optional Integer of the start observation. Default is 0. model_name : str The name of the model used. Default is to use model class name. Returns ------- summary : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary """ from statsmodels.iolib.summary import Summary from statsmodels.iolib.table import SimpleTable from statsmodels.iolib.tableformatting import fmt_params # Model specification results model = self.model if title is None: title = 'Statespace Model Results' if start is None: start = 0 if self.model._index_dates: ix = self.model._index d = ix[start] sample = ['%02d-%02d-%02d' % (d.month, d.day, d.year)] d = ix[-1] sample += ['- ' + '%02d-%02d-%02d' % (d.month, d.day, d.year)] else: sample = [str(start), ' - ' + str(self.nobs)] # Standardize the model name as a list of str if model_name is None: model_name = model.__class__.__name__ # Truncate endog names if truncate_endog_names is None: truncate_endog_names = False if self.model.k_endog == 1 else 24 endog_names = self.model.endog_names if not isinstance(endog_names, list): endog_names = [endog_names] endog_names = [str(name) for name in endog_names] if truncate_endog_names is not False: n = truncate_endog_names endog_names = [name if len(name) <= n else name[:n] + '...' for name in endog_names] # Shorten the endog name list if applicable if display_max_endog is None: display_max_endog = np.inf yname = None if self.model.k_endog > display_max_endog: k = self.model.k_endog - 1 yname = '"' + endog_names[0] + f'", and {k} more' # Create the tables if not isinstance(model_name, list): model_name = [model_name] top_left = [('Dep. Variable:', None)] top_left.append(('Model:', [model_name[0]])) for i in range(1, len(model_name)): top_left.append(('', ['+ ' + model_name[i]])) top_left += [ ('Date:', None), ('Time:', None), ('Sample:', [sample[0]]), ('', [sample[1]]) ] top_right = [ ('No. Observations:', [self.nobs]), ('Log Likelihood', ["%#5.3f" % self.llf]), ] if hasattr(self, 'rsquared'): top_right.append(('R-squared:', ["%#8.3f" % self.rsquared])) top_right += [ ('AIC', ["%#5.3f" % self.aic]), ('BIC', ["%#5.3f" % self.bic]), ('HQIC', ["%#5.3f" % self.hqic])] if (self.filter_results is not None and self.filter_results.filter_concentrated): top_right.append(('Scale', ["%#5.3f" % self.scale])) if hasattr(self, 'cov_type'): cov_type = self.cov_type if cov_type == 'none': cov_type = 'Not computed' top_left.append(('Covariance Type:', [cov_type])) if extra_top_left is not None: top_left += extra_top_left if extra_top_right is not None: top_right += extra_top_right summary = Summary() summary.add_table_2cols(self, gleft=top_left, gright=top_right, title=title, yname=yname) table_ix = 1 if len(self.params) > 0 and display_params: summary.add_table_params(self, alpha=alpha, xname=self.param_names, use_t=False) table_ix += 1 # Diagnostic tests results if display_diagnostics: try: het = self.test_heteroskedasticity(method='breakvar') except Exception: # FIXME: catch something specific het = np.zeros((self.model.k_endog, 2)) * np.nan try: lb = self.test_serial_correlation(method='ljungbox', lags=[1]) except Exception: # FIXME: catch something specific lb = np.zeros((self.model.k_endog, 2, 1)) * np.nan try: jb = self.test_normality(method='jarquebera') except Exception: # FIXME: catch something specific jb = np.zeros((self.model.k_endog, 4)) * np.nan if self.model.k_endog <= display_max_endog: format_str = lambda array: [ # noqa:E731 ', '.join(['{0:.2f}'.format(i) for i in array]) ] diagn_left = [ ('Ljung-Box (L1) (Q):', format_str(lb[:, 0, -1])), ('Prob(Q):', format_str(lb[:, 1, -1])), ('Heteroskedasticity (H):', format_str(het[:, 0])), ('Prob(H) (two-sided):', format_str(het[:, 1]))] diagn_right = [('Jarque-Bera (JB):', format_str(jb[:, 0])), ('Prob(JB):', format_str(jb[:, 1])), ('Skew:', format_str(jb[:, 2])), ('Kurtosis:', format_str(jb[:, 3])) ] summary.add_table_2cols(self, gleft=diagn_left, gright=diagn_right, title="") else: columns = ['LjungBox\n(L1) (Q)', 'Prob(Q)', 'Het.(H)', 'Prob(H)', 'Jarque\nBera(JB)', 'Prob(JB)', 'Skew', 'Kurtosis'] data = pd.DataFrame( np.c_[lb[:, :2, -1], het[:, :2], jb[:, :4]], index=endog_names, columns=columns).applymap( lambda num: '' if pd.isnull(num) else '%.2f' % num) data.index.name = 'Residual of\nDep. variable' data = data.reset_index() params_data = data.values params_header = data.columns.tolist() params_stubs = None title = 'Residual diagnostics:' table = SimpleTable( params_data, params_header, params_stubs, txt_fmt=fmt_params, title=title) summary.tables.insert(table_ix, table) # Add warnings/notes, added to text format only etext = [] if hasattr(self, 'cov_type') and 'description' in self.cov_kwds: etext.append(self.cov_kwds['description']) if self._rank < (len(self.params) - len(self.fixed_params)): cov_params = self.cov_params() if len(self.fixed_params) > 0: mask = np.ix_(self._free_params_index, self._free_params_index) cov_params = cov_params[mask] etext.append("Covariance matrix is singular or near-singular," " with condition number %6.3g. Standard errors may be" " unstable." % np.linalg.cond(cov_params)) if etext: etext = ["[{0}] {1}".format(i + 1, text) for i, text in enumerate(etext)] etext.insert(0, "Warnings:") summary.add_extra_txt(etext) return summary class MLEResultsWrapper(wrap.ResultsWrapper): _attrs = { 'zvalues': 'columns', 'cov_params_approx': 'cov', 'cov_params_default': 'cov', 'cov_params_oim': 'cov', 'cov_params_opg': 'cov', 'cov_params_robust': 'cov', 'cov_params_robust_approx': 'cov', 'cov_params_robust_oim': 'cov', } _wrap_attrs = wrap.union_dicts(tsbase.TimeSeriesResultsWrapper._wrap_attrs, _attrs) _methods = { 'forecast': 'dates', 'impulse_responses': 'ynames' } _wrap_methods = wrap.union_dicts( tsbase.TimeSeriesResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(MLEResultsWrapper, MLEResults) # noqa:E305 class PredictionResults(pred.PredictionResults): """ Parameters ---------- prediction_results : kalman_filter.PredictionResults instance Results object from prediction after fitting or filtering a state space model. row_labels : iterable Row labels for the predicted data. Attributes ---------- """ def __init__(self, model, prediction_results, row_labels=None): if model.model.k_endog == 1: endog = pd.Series(prediction_results.endog[0], name=model.model.endog_names) else: endog = pd.DataFrame(prediction_results.endog.T, columns=model.model.endog_names) self.model = Bunch(data=model.data.__class__( endog=endog, predict_dates=row_labels)) self.prediction_results = prediction_results # Get required values k_endog, nobs = prediction_results.endog.shape if not prediction_results.results.memory_no_forecast_mean: predicted_mean = self.prediction_results.forecasts else: predicted_mean = np.zeros((k_endog, nobs)) * np.nan if predicted_mean.shape[0] == 1: predicted_mean = predicted_mean[0, :] else: predicted_mean = predicted_mean.transpose() if not prediction_results.results.memory_no_forecast_cov: var_pred_mean = self.prediction_results.forecasts_error_cov else: var_pred_mean = np.zeros((k_endog, k_endog, nobs)) * np.nan if var_pred_mean.shape[0] == 1: var_pred_mean = var_pred_mean[0, 0, :] else: var_pred_mean = var_pred_mean.transpose() # Initialize super(PredictionResults, self).__init__(predicted_mean, var_pred_mean, dist='norm', row_labels=row_labels) @property def se_mean(self): # Replace negative values with np.nan to avoid a RuntimeWarning var_pred_mean = self.var_pred_mean.copy() var_pred_mean[var_pred_mean < 0] = np.nan if var_pred_mean.ndim == 1: se_mean = np.sqrt(var_pred_mean) else: se_mean = np.sqrt(var_pred_mean.T.diagonal()) return se_mean def conf_int(self, method='endpoint', alpha=0.05, **kwds): # TODO: this performs metadata wrapping, and that should be handled # by attach_* methods. However, they do not currently support # this use case. _use_pandas = self._use_pandas self._use_pandas = False conf_int = super(PredictionResults, self).conf_int(alpha, **kwds) self._use_pandas = _use_pandas # Create a dataframe if self._row_labels is not None: conf_int = pd.DataFrame(conf_int, index=self.row_labels) # Attach the endog names ynames = self.model.data.ynames if not type(ynames) == list: ynames = [ynames] names = (['lower {0}'.format(name) for name in ynames] + ['upper {0}'.format(name) for name in ynames]) conf_int.columns = names return conf_int def summary_frame(self, endog=0, alpha=0.05): # TODO: finish and cleanup # import pandas as pd # ci_obs = self.conf_int(alpha=alpha, obs=True) # need to split ci_mean = np.asarray(self.conf_int(alpha=alpha)) _use_pandas = self._use_pandas self._use_pandas = False to_include = {} if self.predicted_mean.ndim == 1: yname = self.model.data.ynames to_include['mean'] = self.predicted_mean to_include['mean_se'] = self.se_mean k_endog = 1 else: yname = self.model.data.ynames[endog] to_include['mean'] = self.predicted_mean[:, endog] to_include['mean_se'] = self.se_mean[:, endog] k_endog = self.predicted_mean.shape[1] self._use_pandas = _use_pandas to_include['mean_ci_lower'] = ci_mean[:, endog] to_include['mean_ci_upper'] = ci_mean[:, k_endog + endog] # pandas dict does not handle 2d_array # data = np.column_stack(list(to_include.values())) # names = .... res = pd.DataFrame(to_include, index=self._row_labels, columns=list(to_include.keys())) res.columns.name = yname return res class PredictionResultsWrapper(wrap.ResultsWrapper): _attrs = { 'predicted_mean': 'dates', 'se_mean': 'dates', 't_values': 'dates', } _wrap_attrs = wrap.union_dicts(_attrs) _methods = {} _wrap_methods = wrap.union_dicts(_methods) wrap.populate_wrapper(PredictionResultsWrapper, PredictionResults) # noqa:E305 statsmodels-0.12.2/statsmodels/tsa/statespace/news.py000066400000000000000000001402021400612667500227570ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ News for state space models Author: Chad Fulton License: BSD-3 """ import numpy as np import pandas as pd from statsmodels.iolib.table import SimpleTable from statsmodels.iolib.summary import Summary from statsmodels.iolib.tableformatting import fmt_params class NewsResults(object): """ Impacts of data revisions and news on estimates of variables of interest Parameters ---------- news_results : SimpleNamespace instance Results from `KalmanSmoother.news`. model : MLEResults The results object associated with the model from which the NewsResults was generated. updated : MLEResults The results object associated with the model containing the updated dataset. previous : MLEResults The results object associated with the model containing the previous dataset. impacted_variable : str, list, array, or slice, optional Observation variable label or slice of labels specifying particular impacted variables to display in output. The impacted variable(s) describe the variables that were *affected* by the news. If you do not know the labels for the variables, check the `endog_names` attribute of the model instance. tolerance : float, optional The numerical threshold for determining zero impact. Default is that any impact less than 1e-10 is assumed to be zero. row_labels : iterable Row labels (often dates) for the impacts of the revisions and news. Attributes ---------- total_impacts : pd.Series Updates to forecasts of impacted variables from both news and data revisions, E[y^i | post] - E[y^i | previous]. update_impacts : pd.Series Updates to forecasts of impacted variables from the news, E[y^i | post] - E[y^i | revisions] where y^i are the impacted variables of interest. revision_impacts : pd.Series Updates to forecasts of impacted variables from data revisions, E[y^i | revisions] - E[y^i | previous]. news : pd.Series The unexpected component of the updated data, E[y^u | post] - E[y^u | revisions] where y^u are the updated variables. weights : pd.Series Weights describing the effect of news on variables of interest. update_forecasts : pd.Series Forecasts based on the previous dataset of the variables that were updated, E[y^u | previous]. update_realized : pd.Series Actual observed data associated with the variables that were updated, y^u prev_impacted_forecasts : pd.Series Previous forecast of the variables of interest, E[y^i | previous]. post_impacted_forecasts : pd.Series Forecast of the variables of interest after taking into account both revisions and updates, E[y^i | post]. revisions_iloc : pd.DataFrame The integer locations of the data revisions in the dataset. revisions_ix : pd.DataFrame The label-based locations of the data revisions in the dataset. updates_iloc : pd.DataFrame The integer locations of the updated data points. updates_ix : pd.DataFrame The label-based locations of updated data points. References ---------- .. [1] BaÅ„bura, Marta, and Michele Modugno. "Maximum likelihood estimation of factor models on datasets with arbitrary pattern of missing data." Journal of Applied Econometrics 29, no. 1 (2014): 133-160. .. [2] BaÅ„bura, Marta, Domenico Giannone, and Lucrezia Reichlin. "Nowcasting." The Oxford Handbook of Economic Forecasting. July 8, 2011. .. [3] BaÅ„bura, Marta, Domenico Giannone, Michele Modugno, and Lucrezia Reichlin. "Now-casting and the real-time data flow." In Handbook of economic forecasting, vol. 2, pp. 195-237. Elsevier, 2013. """ def __init__(self, news_results, model, updated, previous, impacted_variable=None, tolerance=1e-10, row_labels=None): # Note: `model` will be the same as one of `revised` or `previous`, but # we need to save it as self.model so that the `predict_dates`, which # were generated by the `_get_prediction_index` call, will be available # for use by the base wrapping code. self.model = model self.updated = updated self.previous = previous self.news_results = news_results self._impacted_variable = impacted_variable self._tolerance = tolerance self.row_labels = row_labels self.params = [] # required for `summary` to work columns = np.atleast_1d(self.updated.model.endog_names) # E[y^i | post] self.post_impacted_forecasts = pd.DataFrame( news_results.post_impacted_forecasts.T, index=self.row_labels, columns=columns) # E[y^i | previous] self.prev_impacted_forecasts = pd.DataFrame( news_results.prev_impacted_forecasts.T, index=self.row_labels, columns=columns) # E[y^i | post] - E[y^i | revisions] self.update_impacts = pd.DataFrame( news_results.update_impacts, index=self.row_labels, columns=columns) # E[y^i | revisions] - E[y^i | previous] self.revision_impacts = pd.DataFrame( news_results.revision_impacts, index=self.row_labels, columns=columns) # E[y^i | post] - E[y^i | previous] self.total_impacts = (self.post_impacted_forecasts - self.prev_impacted_forecasts) # Indices of revisions and updates index = self.updated.model._index self.revisions_iloc = pd.DataFrame( list(zip(*news_results.revisions_ix)), index=['revision date', 'revised variable']).T iloc = self.revisions_iloc if len(iloc) > 0: self.revisions_ix = pd.DataFrame({ 'revision date': index[iloc['revision date']], 'revised variable': columns[iloc['revised variable']]}) else: self.revisions_ix = iloc.copy() self.updates_iloc = pd.DataFrame( list(zip(*news_results.updates_ix)), index=['update date', 'updated variable']).T iloc = self.updates_iloc if len(iloc) > 0: self.updates_ix = pd.DataFrame({ 'update date': index[iloc['update date']], 'updated variable': columns[iloc['updated variable']]}) else: self.updates_ix = iloc.copy() # Wrap forecasts and forecasts errors ix = pd.MultiIndex.from_arrays([self.updates_ix['update date'], self.updates_ix['updated variable']]) # E[y^u | post] - E[y^u | previous] if news_results.news is None: self.news = pd.Series([], index=ix, name='news', dtype=model.params.dtype) else: self.news = pd.Series(news_results.news, index=ix, name='news') # E[y^u | previous] if news_results.update_forecasts is None: self.update_forecasts = pd.Series([], index=ix, dtype=model.params.dtype) else: self.update_forecasts = pd.Series( news_results.update_forecasts, index=ix) # y^u if news_results.update_realized is None: self.update_realized = pd.Series([], index=ix, dtype=model.params.dtype) else: self.update_realized = pd.Series( news_results.update_realized, index=ix) cols = pd.MultiIndex.from_product([self.row_labels, columns]) # reshaped version of gain matrix E[y A'] E[A A']^{-1} if len(self.updates_iloc): weights = news_results.gain.transpose(0, 1, 2).reshape( len(cols), len(ix)) else: weights = np.zeros((len(cols), len(ix))) self.weights = pd.DataFrame(weights, index=cols, columns=ix).T self.weights.columns.names = ['impact date', 'impacted variable'] @property def impacted_variable(self): return self._impacted_variable @impacted_variable.setter def impacted_variable(self, value): self._impacted_variable = value @property def tolerance(self): return self._tolerance @tolerance.setter def tolerance(self, value): self._tolerance = value @property def data_revisions(self): """ Revisions to data points that existed in the previous dataset Returns ------- data_revisions : pd.DataFrame Index is as MultiIndex consisting of `revision date` and `revised variable`. The columns are: - `observed (prev)`: the value of the data as it was observed in the previous dataset. - `revised`: the revised value of the data, as it is observed in the new dataset See also -------- data_updates """ # Save revisions data data = self.revisions_ix.copy() data['observed (prev)'] = [ self.previous.model.endog[row[0], row[1]] for _, row in self.revisions_iloc.iterrows()] data['revised'] = [ self.updated.model.endog[row[0], row[1]] for _, row in self.revisions_iloc.iterrows()] data.index = pd.MultiIndex.from_arrays([data['revision date'], data['revised variable']]) data = data.sort_index().drop(['revision date', 'revised variable'], axis=1) return data @property def data_updates(self): """ Updated data; new entries that did not exist in the previous dataset Returns ------- data_updates : pd.DataFrame Index is as MultiIndex consisting of `update date` and `updated variable`. The columns are: - `forecast (prev)`: the previous forecast of the new entry, based on the information available in the previous dataset (recall that for these updated data points, the previous dataset had no observed value for them at all) - `observed`: the value of the new entry, as it is observed in the new dataset See also -------- data_updates """ data = pd.concat([self.update_realized, self.update_forecasts], axis=1).sort_index().reset_index() data.columns = (data.columns[:2].tolist() + ['observed', 'forecast (prev)']) data.index = pd.MultiIndex.from_arrays([data['update date'], data['updated variable']]) data = data.sort_index().drop(['update date', 'updated variable'], axis=1) return data @property def details_by_impact(self): """ Details of forecast revisions from news, organized by impacts first Returns ------- details : pd.DataFrame Index is as MultiIndex consisting of: - `impact date`: the date of the impact on the variable of interest - `impacted variable`: the variable that is being impacted - `update date`: the date of the data update, that results in `news` that impacts the forecast of variables of interest - `updated variable`: the variable being updated, that results in `news` that impacts the forecast of variables of interest The columns are: - `forecast (prev)`: the previous forecast of the new entry, based on the information available in the previous dataset - `observed`: the value of the new entry, as it is observed in the new dataset - `news`: the news associated with the update (this is just the forecast error: `observed` - `forecast (prev)`) - `weight`: the weight describing how the `news` effects the forecast of the variable of interest - `impact`: the impact of the `news` on the forecast of the variable of interest Notes ----- This table decomposes updated forecasts of variables of interest from the `news` associated with each updated datapoint from the new data release. This table does not summarize the impacts or show the effect of revisions. That information can be found in the `impacts` table. This form of the details table is organized so that the impacted dates / variables are first in the index. This is convenient for slicing by impacted variables / dates to view the details of data updates for a particular variable or date. However, since the `forecast (prev)` and `observed` columns have a lot of duplication, printing the entire table gives a result that is less easy to parse than that produced by the `details_by_update` property. `details_by_update` contains the same information but is organized to be more convenient for displaying the entire table of detailed updates. At the same time, `details_by_update` is less convenient for subsetting. See Also -------- details_by_update impacts """ df = self.weights.stack(level=[0, 1]).rename('weight').to_frame() if len(self.updates_iloc): df['forecast (prev)'] = self.update_forecasts df['observed'] = self.update_realized df['news'] = self.news df['impact'] = df['news'] * df['weight'] else: df['forecast (prev)'] = [] df['observed'] = [] df['news'] = [] df['impact'] = [] df = df[['observed', 'forecast (prev)', 'news', 'weight', 'impact']] df = df.reorder_levels([2, 3, 0, 1]).sort_index() if self.impacted_variable is not None and len(df) > 0: df = df.loc[np.s_[:, self.impacted_variable], :] mask = np.abs(df['weight']) > self.tolerance return df[mask] @property def details_by_update(self): """ Details of forecast revisions from news, organized by updates first Returns ------- details : pd.DataFrame Index is as MultiIndex consisting of: - `update date`: the date of the data update, that results in `news` that impacts the forecast of variables of interest - `updated variable`: the variable being updated, that results in `news` that impacts the forecast of variables of interest - `forecast (prev)`: the previous forecast of the new entry, based on the information available in the previous dataset - `observed`: the value of the new entry, as it is observed in the new dataset - `impact date`: the date of the impact on the variable of interest - `impacted variable`: the variable that is being impacted The columns are: - `news`: the news associated with the update (this is just the forecast error: `observed` - `forecast (prev)`) - `weight`: the weight describing how the `news` effects the forecast of the variable of interest - `impact`: the impact of the `news` on the forecast of the variable of interest Notes ----- This table decomposes updated forecasts of variables of interest from the `news` associated with each updated datapoint from the new data release. This table does not summarize the impacts or show the effect of revisions. That information can be found in the `impacts` table. This form of the details table is organized so that the updated dates / variables are first in the index, and in this table the index also contains the forecasts and observed values of the updates. This is convenient for displaying the entire table of detailed updates because it allows sparsifying duplicate entries. However, since it includes forecasts and observed values in the index of the table, it is not convenient for subsetting by the variable of interest. Instead, the `details_by_impact` property is organized to make slicing by impacted variables / dates easy. This allows, for example, viewing the details of data updates on a particular variable or date of interest. See Also -------- details_by_impact impacts """ df = self.weights.stack(level=[0, 1]).rename('weight').to_frame() if len(self.updates_iloc): df['forecast (prev)'] = self.update_forecasts df['observed'] = self.update_realized df['news'] = self.news df['impact'] = df['news'] * df['weight'] else: df['forecast (prev)'] = [] df['observed'] = [] df['news'] = [] df['impact'] = [] df = df[['forecast (prev)', 'observed', 'news', 'weight', 'impact']] df = df.reset_index() keys = ['update date', 'updated variable', 'observed', 'forecast (prev)', 'impact date', 'impacted variable'] df.index = pd.MultiIndex.from_arrays([df[key] for key in keys]) details = df.drop(keys, axis=1).sort_index() if self.impacted_variable is not None and len(df) > 0: details = details.loc[ np.s_[:, :, :, :, :, self.impacted_variable], :] mask = np.abs(details['weight']) > self.tolerance return details[mask] @property def impacts(self): """ Impacts from news and revisions on all dates / variables of interest Returns ------- impacts : pd.DataFrame Index is as MultiIndex consisting of: - `impact date`: the date of the impact on the variable of interest - `impacted variable`: the variable that is being impacted The columns are: - `estimate (prev)`: the previous estimate / forecast of the date / variable of interest. - `impact of revisions`: the impact of all data revisions on the estimate of the date / variable of interest. - `impact of news`: the impact of all news on the estimate of the date / variable of interest. - `total impact`: the total impact of both revisions and news on the estimate of the date / variable of interest. - `estimate (new)`: the new estimate / forecast of the date / variable of interest after taking into account the effects of the revisions and news. Notes ----- This table decomposes updated forecasts of variables of interest into the overall effect from revisions and news. This table does not break down the detail by the updated dates / variables. That information can be found in the `details_by_impact` `details_by_update` tables. See Also -------- details_by_impact details_by_update """ # Summary of impacts impacts = pd.concat([ self.prev_impacted_forecasts.unstack().rename('estimate (prev)'), self.revision_impacts.unstack().rename('impact of revisions'), self.update_impacts.unstack().rename('impact of news'), self.post_impacted_forecasts.unstack().rename('estimate (new)')], axis=1) impacts['impact of revisions'] = ( impacts['impact of revisions'].fillna(0)) impacts['impact of news'] = ( impacts['impact of news'].fillna(0)) impacts['total impact'] = (impacts['impact of revisions'] + impacts['impact of news']) impacts = impacts.reorder_levels([1, 0]).sort_index() impacts.index.names = ['impact date', 'impacted variable'] impacts = impacts[['estimate (prev)', 'impact of revisions', 'impact of news', 'total impact', 'estimate (new)']] if self.impacted_variable is not None: impacts = impacts.loc[np.s_[:, self.impacted_variable], :] tmp = np.abs(impacts[['impact of revisions', 'impact of news']]) mask = (tmp > self.tolerance).any(axis=1) return impacts[mask] def summary_impacts(self, impact_date=None, impacted_variable=None, groupby='impact date', show_revisions_columns=None, sparsify=True, float_format='%.2f'): """ Create summary table with detailed impacts from news; by date, variable Parameters ---------- impact_date : int, str, datetime, list, array, or slice, optional Observation index label or slice of labels specifying particular impact periods to display. The impact date(s) describe the periods in which impacted variables were *affected* by the news. If this argument is given, the output table will only show this impact date or dates. Note that this argument is passed to the Pandas `loc` accessor, and so it should correspond to the labels of the model's index. If the model was created with data in a list or numpy array, then these labels will be zero-indexes observation integers. impacted_variable : str, list, array, or slice, optional Observation variable label or slice of labels specifying particular impacted variables to display. The impacted variable(s) describe the variables that were *affected* by the news. If you do not know the labels for the variables, check the `endog_names` attribute of the model instance. groupby : {impact date, impacted date} The primary variable for grouping results in the impacts table. The default is to group by update date. show_revisions_columns : bool, optional If set to False, the impacts table will not show the impacts from data revisions or the total impacts. Default is to show the revisions and totals columns if any revisions were made and otherwise to hide them. sparsify : bool, optional, default True Set to False for the table to include every one of the multiindex keys at each row. float_format : str, optional Formatter format string syntax for converting numbers to strings. Default is '%.2f'. Returns ------- impacts_table : SimpleTable Table describing total impacts from both revisions and news. See the documentation for the `impacts` attribute for more details about the index and columns. See Also -------- impacts """ # Squeeze for univariate models if impacted_variable is None and self.updated.model.k_endog == 1: impacted_variable = self.updated.model.endog_names # Default is to only show the revisions columns if there were any # revisions (otherwise it would just be a column of zeros) if show_revisions_columns is None: show_revisions_columns = len(self.revisions_iloc) > 0 # Select only the variables / dates of interest s = list(np.s_[:, :]) if impact_date is not None: s[0] = np.s_[impact_date] if impacted_variable is not None: s[1] = np.s_[impacted_variable] s = tuple(s) impacts = self.impacts.loc[s, :] # Make the first index level the groupby level groupby = groupby.lower() if groupby in ['impacted variable', 'impacted_variable']: impacts.index = impacts.index.swaplevel(1, 0) elif groupby not in ['impact date', 'impact_date']: raise ValueError('Invalid groupby for impacts table. Valid options' ' are "impact date" or "impacted variable".' f'Got "{groupby}".') impacts = impacts.sort_index() # Drop the non-groupby level if there's only one value tmp_index = impacts.index.remove_unused_levels() k_vars = len(tmp_index.levels[1]) removed_level = None if sparsify and k_vars == 1: name = tmp_index.names[1] value = tmp_index.levels[1][0] removed_level = f'{name} = {value}' impacts.index = tmp_index.droplevel(1) impacts = impacts.applymap( lambda num: '' if pd.isnull(num) else float_format % num) impacts = impacts.reset_index() impacts.iloc[:, 0] = impacts.iloc[:, 0].map(str) else: impacts = impacts.reset_index() impacts.iloc[:, :2] = impacts.iloc[:, :2].applymap(str) impacts.iloc[:, 2:] = impacts.iloc[:, 2:].applymap( lambda num: '' if pd.isnull(num) else float_format % num) # Sparsify the groupby column if sparsify and groupby in impacts: mask = impacts[groupby] == impacts[groupby].shift(1) tmp = impacts.loc[mask, groupby] if len(tmp) > 0: impacts.loc[mask, groupby] = '' # Drop revisions and totals columns if applicable if not show_revisions_columns: impacts.drop(['impact of revisions', 'total impact'], axis=1, inplace=True) params_data = impacts.values params_header = impacts.columns.tolist() params_stubs = None title = 'Impacts' if removed_level is not None: join = 'on' if groupby == 'date' else 'for' title += f' {join} [{removed_level}]' impacts_table = SimpleTable( params_data, params_header, params_stubs, txt_fmt=fmt_params, title=title) return impacts_table def summary_details(self, impact_date=None, impacted_variable=None, update_date=None, updated_variable=None, groupby='update date', sparsify=True, float_format='%.2f', multiple_tables=False): """ Create summary table with detailed impacts from news; by date, variable Parameters ---------- impact_date : int, str, datetime, list, array, or slice, optional Observation index label or slice of labels specifying particular impact periods to display. The impact date(s) describe the periods in which impacted variables were *affected* by the news. If this argument is given, the output table will only show this impact date or dates. Note that this argument is passed to the Pandas `loc` accessor, and so it should correspond to the labels of the model's index. If the model was created with data in a list or numpy array, then these labels will be zero-indexes observation integers. impacted_variable : str, list, array, or slice, optional Observation variable label or slice of labels specifying particular impacted variables to display. The impacted variable(s) describe the variables that were *affected* by the news. If you do not know the labels for the variables, check the `endog_names` attribute of the model instance. update_date : int, str, datetime, list, array, or slice, optional Observation index label or slice of labels specifying particular updated periods to display. The updated date(s) describe the periods in which the new data points were available that generated the news). See the note on `impact_date` for details about what these labels are. updated_variable : str, list, array, or slice, optional Observation variable label or slice of labels specifying particular updated variables to display. The updated variable(s) describe the variables that were *affected* by the news. If you do not know the labels for the variables, check the `endog_names` attribute of the model instance. groupby : {update date, updated date, impact date, impacted date} The primary variable for grouping results in the details table. The default is to group by update date. sparsify : bool, optional, default True Set to False for the table to include every one of the multiindex keys at each row. float_format : str, optional Formatter format string syntax for converting numbers to strings. Default is '%.2f'. multiple_tables : bool, optional If set to True, this function will return a list of tables, one table for each of the unique `groupby` levels. Default is False, in which case this function returns a single table. Returns ------- details_table : SimpleTable or list of SimpleTable Table or list of tables describing how the news from each update (i.e. news from a particular variable / date) translates into changes to the forecasts of each impacted variable variable / date. This table contains information about the updates and about the impacts. Updates are newly observed datapoints that were not available in the previous results set. Each update leads to news, and the news may cause changes in the forecasts of the impacted variables. The amount that a particular piece of news (from an update to some variable at some date) impacts a variable at some date depends on weights that can be computed from the model results. The data contained in this table that refer to updates are: - `update date` : The date at which a new datapoint was added. - `updated variable` : The variable for which a new datapoint was added. - `forecast (prev)` : The value that had been forecast by the previous model for the given updated variable and date. - `observed` : The observed value of the new datapoint. - `news` : The news is the difference between the observed value and the previously forecast value for a given updated variable and date. The data contained in this table that refer to impacts are: - `impact date` : A date associated with an impact. - `impacted variable` : A variable that was impacted by the news. - `weight` : The weight of news from a given `update date` and `update variable` on a given `impacted variable` at a given `impact date`. - `impact` : The revision to the smoothed estimate / forecast of the impacted variable at the impact date based specifically on the news generated by the `updated variable` at the `update date`. See Also -------- details_by_impact details_by_update """ # Squeeze for univariate models if self.updated.model.k_endog == 1: if impacted_variable is None: impacted_variable = self.updated.model.endog_names if updated_variable is None: updated_variable = self.updated.model.endog_names # Select only the variables / dates of interest s = list(np.s_[:, :, :, :, :, :]) if impact_date is not None: s[0] = np.s_[impact_date] if impacted_variable is not None: s[1] = np.s_[impacted_variable] if update_date is not None: s[2] = np.s_[update_date] if updated_variable is not None: s[3] = np.s_[updated_variable] s = tuple(s) details = self.details_by_impact.loc[s, :] # Make the first index level the groupby level groupby = groupby.lower().replace('_', ' ') groupby_overall = 'impact' levels_order = [0, 1, 2, 3] if groupby == 'update date': levels_order = [2, 3, 0, 1] groupby_overall = 'update' elif groupby == 'updated variable': levels_order = [3, 2, 1, 0] groupby_overall = 'update' elif groupby == 'impacted variable': levels_order = [1, 0, 3, 2] elif groupby != 'impact date': raise ValueError('Invalid groupby for details table. Valid options' ' are "update date", "updated variable",' ' "impact date",or "impacted variable".' f' Got "{groupby}".') details.index = (details.index.reorder_levels(levels_order) .remove_unused_levels()) details = details.sort_index() # If our overall group-by is `update`, move forecast (prev) and # observed into the index base_levels = [0, 1, 2, 3] if groupby_overall == 'update': details.set_index(['observed', 'forecast (prev)'], append=True, inplace=True) details.index = details.index.reorder_levels([0, 1, 4, 5, 2, 3]) base_levels = [0, 1, 4, 5] # Drop the non-groupby levels if there's only one value tmp_index = details.index.remove_unused_levels() n_levels = len(tmp_index.levels) k_level_values = [len(tmp_index.levels[i]) for i in range(n_levels)] removed_levels = [] if sparsify: for i in sorted(base_levels)[::-1][:-1]: if k_level_values[i] == 1: name = tmp_index.names[i] value = tmp_index.levels[i][0] can_drop = ( (name == 'update date' and update_date is not None) or (name == 'updated variable' and updated_variable is not None) or (name == 'impact date' and impact_date is not None) or (name == 'impacted variable' and (impacted_variable is not None or self.impacted_variable is not None))) if can_drop or not multiple_tables: removed_levels.insert(0, f'{name} = {value}') details.index = tmp_index = tmp_index.droplevel(i) # Move everything to columns details = details.reset_index() # Function for formatting numbers def str_format(num, mark_ones=False, mark_zeroes=False): if pd.isnull(num): out = '' elif mark_ones and np.abs(1 - num) < self.tolerance: out = '1.0' elif mark_zeroes and np.abs(num) < self.tolerance: out = '0' else: out = float_format % num return out # Function to create the table def create_table(details, removed_levels): # Convert everything to strings for key in ['observed', 'forecast (prev)', 'news', 'weight', 'impact']: if key in details: args = ( # mark_ones True if key in ['weight'] else False, # mark_zeroes True if key in ['weight', 'impact'] else False) details[key] = details[key].apply(str_format, args=args) for key in ['update date', 'impact date']: if key in details: details[key] = details[key].apply(str) # Sparsify index columns if sparsify: sparsify_cols = ['update date', 'updated variable', 'impact date', 'impacted variable'] if groupby_overall == 'update': sparsify_cols += ['observed', 'forecast (prev)'] for key in sparsify_cols: if key in details: mask = details[key] == details[key].shift(1) details.loc[mask, key] = '' params_data = details.values params_header = details.columns.tolist() params_stubs = None title = 'Details' if len(removed_levels): title += ' for [' + ', '.join(removed_levels) + ']' return SimpleTable(params_data, params_header, params_stubs, txt_fmt=fmt_params, title=title) if multiple_tables: details_table = [] for item in details[groupby].unique(): mask = details[groupby] == item item_details = details[mask].drop(groupby, axis=1) item_removed_levels = [f'{groupby} = {item}'] + removed_levels details_table.append(create_table(item_details, item_removed_levels)) else: details_table = create_table(details, removed_levels) return details_table def summary_revisions(self, sparsify=True): """ Create summary table showing revisions to the previous results' data Parameters ---------- sparsify : bool, optional, default True Set to False for the table to include every one of the multiindex keys at each row. Returns ------- revisions_table : SimpleTable Table showing revisions to the previous results' data. Columns are: - `revision date` : date associated with a revised data point - `revised variable` : variable that was revised at `revision date` - `observed (prev)` : the observed value prior to the revision - `revised` : the new value after the revision """ data = self.data_revisions.sort_index().reset_index() data[['revision date', 'revised variable']] = ( data[['revision date', 'revised variable']].applymap(str)) data.iloc[:, 2:] = data.iloc[:, 2:].applymap( lambda num: '' if pd.isnull(num) else '%.2f' % num) # Sparsify the date column if sparsify: mask = data['revision date'] == data['revision date'].shift(1) data.loc[mask, 'revision date'] = '' params_data = data.values params_header = data.columns.tolist() params_stubs = None title = 'Revisions to dataset:' revisions_table = SimpleTable( params_data, params_header, params_stubs, txt_fmt=fmt_params, title=title) return revisions_table def summary_news(self, sparsify=True): """ Create summary table showing news from new data since previous results Parameters ---------- sparsify : bool, optional, default True Set to False for the table to include every one of the multiindex keys at each row. Returns ------- updates_table : SimpleTable Table showing new datapoints that were not in the previous results' data. Columns are: - `update date` : date associated with a new data point. - `updated variable` : variable for which new data was added at `update date`. - `forecast (prev)` : the forecast value for the updated variable at the update date in the previous results object (i.e. prior to the data being available). - `observed` : the observed value of the new datapoint. See Also -------- data_updates """ data = pd.merge( self.data_updates, self.news, left_index=True, right_index=True).sort_index().reset_index() data[['update date', 'updated variable']] = ( data[['update date', 'updated variable']].applymap(str)) data.iloc[:, 2:] = data.iloc[:, 2:].applymap( lambda num: '' if pd.isnull(num) else '%.2f' % num) # Sparsify the date column if sparsify: mask = data['update date'] == data['update date'].shift(1) data.loc[mask, 'update date'] = '' params_data = data.values params_header = data.columns.tolist() params_stubs = None title = 'News from updated observations:' updates_table = SimpleTable( params_data, params_header, params_stubs, txt_fmt=fmt_params, title=title) return updates_table def summary(self, impact_date=None, impacted_variable=None, update_date=None, updated_variable=None, impacts_groupby='impact date', details_groupby='update date', show_revisions_columns=None, sparsify=True, include_details_tables=None, include_revisions_tables=False, float_format='%.2f'): """ Create summary tables describing news and impacts Parameters ---------- impact_date : int, str, datetime, list, array, or slice, optional Observation index label or slice of labels specifying particular impact periods to display. The impact date(s) describe the periods in which impacted variables were *affected* by the news. If this argument is given, the impact and details tables will only show this impact date or dates. Note that this argument is passed to the Pandas `loc` accessor, and so it should correspond to the labels of the model's index. If the model was created with data in a list or numpy array, then these labels will be zero-indexes observation integers. impacted_variable : str, list, array, or slice, optional Observation variable label or slice of labels specifying particular impacted variables to display. The impacted variable(s) describe the variables that were *affected* by the news. If you do not know the labels for the variables, check the `endog_names` attribute of the model instance. update_date : int, str, datetime, list, array, or slice, optional Observation index label or slice of labels specifying particular updated periods to display. The updated date(s) describe the periods in which the new data points were available that generated the news). See the note on `impact_date` for details about what these labels are. updated_variable : str, list, array, or slice, optional Observation variable label or slice of labels specifying particular updated variables to display. The updated variable(s) describe the variables that were *affected* by the news. If you do not know the labels for the variables, check the `endog_names` attribute of the model instance. impacts_groupby : {impact date, impacted date} The primary variable for grouping results in the impacts table. The default is to group by update date. details_groupby : str One of "update date", "updated date", "impact date", or "impacted date". The primary variable for grouping results in the details table. Only used if the details tables are included. The default is to group by update date. show_revisions_columns : bool, optional If set to False, the impacts table will not show the impacts from data revisions or the total impacts. Default is to show the revisions and totals columns if any revisions were made and otherwise to hide them. sparsify : bool, optional, default True Set to False for the table to include every one of the multiindex keys at each row. include_details_tables : bool, optional If set to True, the summary will show tables describing the details of how news from specific updates translate into specific impacts. These tables can be very long, particularly in cases where there were many updates and in multivariate models. The default is to show detailed tables only for univariate models. include_revisions_tables : bool, optional If set to True, the summary will show tables describing the revisions and updates that lead to impacts on variables of interest. float_format : str, optional Formatter format string syntax for converting numbers to strings. Default is '%.2f'. Returns ------- summary_tables : Summary Summary tables describing news and impacts. Basic tables include: - A table with general information about the sample. - A table describing the impacts of revisions and news. - Tables describing revisions in the dataset since the previous results set (unless `include_revisions_tables=False`). In univariate models or if `include_details_tables=True`, one or more tables will additionally be included describing the details of how news from specific updates translate into specific impacts. See Also -------- summary_impacts summary_details summary_revisions summary_updates """ # Default for include_details_tables if include_details_tables is None: include_details_tables = self.updated.model.k_endog == 1 # Model specification results model = self.model.model title = 'News' def get_sample(model): if model._index_dates: ix = model._index d = ix[0] sample = ['%s' % d] d = ix[-1] sample += ['- ' + '%s' % d] else: sample = [str(0), ' - ' + str(model.nobs)] return sample previous_sample = get_sample(self.previous.model) revised_sample = get_sample(self.updated.model) # Standardize the model name as a list of str model_name = model.__class__.__name__ # Top summary table top_left = [('Model:', [model_name]), ('Date:', None), ('Time:', None)] top_right = [ ('Original sample:', [previous_sample[0]]), ('', [previous_sample[1]]), ('Update through:', [revised_sample[1][2:]]), ('No. Revisions:', [len(self.revisions_ix)]), ('No. New datapoints:', [len(self.updates_ix)])] summary = Summary() self.model.endog_names = self.model.model.endog_names summary.add_table_2cols(self, gleft=top_left, gright=top_right, title=title) table_ix = 1 # Impact table summary.tables.insert(table_ix, self.summary_impacts( impact_date=impact_date, impacted_variable=impacted_variable, groupby=impacts_groupby, show_revisions_columns=show_revisions_columns, sparsify=sparsify, float_format=float_format)) table_ix += 1 # News table if len(self.updates_iloc) > 0: summary.tables.insert( table_ix, self.summary_news(sparsify=sparsify)) table_ix += 1 # Detail tables multiple_tables = self.updated.model.k_endog > 1 details_tables = self.summary_details( impact_date=impact_date, impacted_variable=impacted_variable, groupby=details_groupby, sparsify=sparsify, float_format=float_format, multiple_tables=multiple_tables) if not multiple_tables: details_tables = [details_tables] if include_details_tables: for table in details_tables: summary.tables.insert(table_ix, table) table_ix += 1 # Revisions if include_revisions_tables and len(self.revisions_iloc) > 0: summary.tables.insert( table_ix, self.summary_revisions(sparsify=sparsify)) table_ix += 1 return summary statsmodels-0.12.2/statsmodels/tsa/statespace/representation.py000066400000000000000000001276451400612667500250650ustar00rootroot00000000000000""" State Space Representation Author: Chad Fulton License: Simplified-BSD """ import numpy as np from .tools import ( find_best_blas_type, validate_matrix_shape, validate_vector_shape ) from .initialization import Initialization from . import tools class OptionWrapper(object): def __init__(self, mask_attribute, mask_value): # Name of the class-level bitmask attribute self.mask_attribute = mask_attribute # Value of this option self.mask_value = mask_value def __get__(self, obj, objtype): # Return True / False based on whether the bit is set in the bitmask return bool(getattr(obj, self.mask_attribute, 0) & self.mask_value) def __set__(self, obj, value): mask_attribute_value = getattr(obj, self.mask_attribute, 0) if bool(value): value = mask_attribute_value | self.mask_value else: value = mask_attribute_value & ~self.mask_value setattr(obj, self.mask_attribute, value) class MatrixWrapper(object): def __init__(self, name, attribute): self.name = name self.attribute = attribute self._attribute = '_' + attribute def __get__(self, obj, objtype): matrix = getattr(obj, self._attribute, None) # # Remove last dimension if the array is not actually time-varying # if matrix is not None and matrix.shape[-1] == 1: # return np.squeeze(matrix, -1) return matrix def __set__(self, obj, value): value = np.asarray(value, order="F") shape = obj.shapes[self.attribute] if len(shape) == 3: value = self._set_matrix(obj, value, shape) else: value = self._set_vector(obj, value, shape) setattr(obj, self._attribute, value) obj.shapes[self.attribute] = value.shape def _set_matrix(self, obj, value, shape): # Expand 1-dimensional array if possible if (value.ndim == 1 and shape[0] == 1 and value.shape[0] == shape[1]): value = value[None, :] # Enforce that the matrix is appropriate size validate_matrix_shape( self.name, value.shape, shape[0], shape[1], obj.nobs ) # Expand time-invariant matrix if value.ndim == 2: value = np.array(value[:, :, None], order="F") return value def _set_vector(self, obj, value, shape): # Enforce that the vector has appropriate length validate_vector_shape( self.name, value.shape, shape[0], obj.nobs ) # Expand the time-invariant vector if value.ndim == 1: value = np.array(value[:, None], order="F") return value class Representation(object): r""" State space representation of a time series process Parameters ---------- k_endog : {array_like, int} The observed time-series process :math:`y` if array like or the number of variables in the process if an integer. k_states : int The dimension of the unobserved state process. k_posdef : int, optional The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation. Must be less than or equal to `k_states`. Default is `k_states`. initial_variance : float, optional Initial variance used when approximate diffuse initialization is specified. Default is 1e6. initialization : Initialization object or str, optional Initialization method for the initial state. If a string, must be one of {'diffuse', 'approximate_diffuse', 'stationary', 'known'}. initial_state : array_like, optional If `initialization='known'` is used, the mean of the initial state's distribution. initial_state_cov : array_like, optional If `initialization='known'` is used, the covariance matrix of the initial state's distribution. nobs : int, optional If an endogenous vector is not given (i.e. `k_endog` is an integer), the number of observations can optionally be specified. If not specified, they will be set to zero until data is bound to the model. dtype : np.dtype, optional If an endogenous vector is not given (i.e. `k_endog` is an integer), the default datatype of the state space matrices can optionally be specified. Default is `np.float64`. design : array_like, optional The design matrix, :math:`Z`. Default is set to zeros. obs_intercept : array_like, optional The intercept for the observation equation, :math:`d`. Default is set to zeros. obs_cov : array_like, optional The covariance matrix for the observation equation :math:`H`. Default is set to zeros. transition : array_like, optional The transition matrix, :math:`T`. Default is set to zeros. state_intercept : array_like, optional The intercept for the transition equation, :math:`c`. Default is set to zeros. selection : array_like, optional The selection matrix, :math:`R`. Default is set to zeros. state_cov : array_like, optional The covariance matrix for the state equation :math:`Q`. Default is set to zeros. **kwargs Additional keyword arguments. Not used directly. It is present to improve compatibility with subclasses, so that they can use `**kwargs` to specify any default state space matrices (e.g. `design`) without having to clean out any other keyword arguments they might have been passed. Attributes ---------- nobs : int The number of observations. k_endog : int The dimension of the observation series. k_states : int The dimension of the unobserved state process. k_posdef : int The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation. shapes : dictionary of name:tuple A dictionary recording the initial shapes of each of the representation matrices as tuples. initialization : str Kalman filter initialization method. Default is unset. initial_variance : float Initial variance for approximate diffuse initialization. Default is 1e6. Notes ----- A general state space model is of the form .. math:: y_t & = Z_t \alpha_t + d_t + \varepsilon_t \\ \alpha_t & = T_t \alpha_{t-1} + c_t + R_t \eta_t \\ where :math:`y_t` refers to the observation vector at time :math:`t`, :math:`\alpha_t` refers to the (unobserved) state vector at time :math:`t`, and where the irregular components are defined as .. math:: \varepsilon_t \sim N(0, H_t) \\ \eta_t \sim N(0, Q_t) \\ The remaining variables (:math:`Z_t, d_t, H_t, T_t, c_t, R_t, Q_t`) in the equations are matrices describing the process. Their variable names and dimensions are as follows Z : `design` :math:`(k\_endog \times k\_states \times nobs)` d : `obs_intercept` :math:`(k\_endog \times nobs)` H : `obs_cov` :math:`(k\_endog \times k\_endog \times nobs)` T : `transition` :math:`(k\_states \times k\_states \times nobs)` c : `state_intercept` :math:`(k\_states \times nobs)` R : `selection` :math:`(k\_states \times k\_posdef \times nobs)` Q : `state_cov` :math:`(k\_posdef \times k\_posdef \times nobs)` In the case that one of the matrices is time-invariant (so that, for example, :math:`Z_t = Z_{t+1} ~ \forall ~ t`), its last dimension may be of size :math:`1` rather than size `nobs`. References ---------- .. [*] Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods: Second Edition. Oxford University Press. """ endog = None r""" (array) The observation vector, alias for `obs`. """ design = MatrixWrapper('design', 'design') r""" (array) Design matrix: :math:`Z~(k\_endog \times k\_states \times nobs)` """ obs_intercept = MatrixWrapper('observation intercept', 'obs_intercept') r""" (array) Observation intercept: :math:`d~(k\_endog \times nobs)` """ obs_cov = MatrixWrapper('observation covariance matrix', 'obs_cov') r""" (array) Observation covariance matrix: :math:`H~(k\_endog \times k\_endog \times nobs)` """ transition = MatrixWrapper('transition', 'transition') r""" (array) Transition matrix: :math:`T~(k\_states \times k\_states \times nobs)` """ state_intercept = MatrixWrapper('state intercept', 'state_intercept') r""" (array) State intercept: :math:`c~(k\_states \times nobs)` """ selection = MatrixWrapper('selection', 'selection') r""" (array) Selection matrix: :math:`R~(k\_states \times k\_posdef \times nobs)` """ state_cov = MatrixWrapper('state covariance matrix', 'state_cov') r""" (array) State covariance matrix: :math:`Q~(k\_posdef \times k\_posdef \times nobs)` """ def __init__(self, k_endog, k_states, k_posdef=None, initial_variance=1e6, nobs=0, dtype=np.float64, design=None, obs_intercept=None, obs_cov=None, transition=None, state_intercept=None, selection=None, state_cov=None, statespace_classes=None, **kwargs): self.shapes = {} # Check if k_endog is actually the endog array endog = None if isinstance(k_endog, np.ndarray): endog = k_endog # If so, assume that it is either column-ordered and in wide format # or row-ordered and in long format if (endog.flags['C_CONTIGUOUS'] and (endog.shape[0] > 1 or nobs == 1)): endog = endog.T k_endog = endog.shape[0] # Endogenous array, dimensions, dtype self.k_endog = k_endog if k_endog < 1: raise ValueError('Number of endogenous variables in statespace' ' model must be a positive number.') self.nobs = nobs # Get dimensions from transition equation if k_states < 1: raise ValueError('Number of states in statespace model must be a' ' positive number.') self.k_states = k_states self.k_posdef = k_posdef if k_posdef is not None else k_states # Make sure k_posdef <= k_states # TODO: we could technically allow k_posdef > k_states, but the Cython # code needs to be more thoroughly checked to avoid seg faults. if self.k_posdef > self.k_states: raise ValueError('Dimension of state innovation `k_posdef` cannot' ' be larger than the dimension of the state.') # Bind endog, if it was given if endog is not None: self.bind(endog) # Record the shapes of all of our matrices # Note: these are time-invariant shapes; in practice the last dimension # may also be `self.nobs` for any or all of these. self.shapes = { 'obs': (self.k_endog, self.nobs), 'design': (self.k_endog, self.k_states, 1), 'obs_intercept': (self.k_endog, 1), 'obs_cov': (self.k_endog, self.k_endog, 1), 'transition': (self.k_states, self.k_states, 1), 'state_intercept': (self.k_states, 1), 'selection': (self.k_states, self.k_posdef, 1), 'state_cov': (self.k_posdef, self.k_posdef, 1), } # Representation matrices # These matrices are only used in the Python object as containers, # which will be copied to the appropriate _statespace object if a # filter is called. scope = locals() for name, shape in self.shapes.items(): if name == 'obs': continue # Create the initial storage array for each matrix setattr(self, '_' + name, np.zeros(shape, dtype=dtype, order="F")) # If we were given an initial value for the matrix, set it # (notice it is being set via the descriptor) if scope[name] is not None: setattr(self, name, scope[name]) # Options self.initial_variance = initial_variance self.prefix_statespace_map = (statespace_classes if statespace_classes is not None else tools.prefix_statespace_map.copy()) # State-space initialization data self.initialization = kwargs.get('initialization', None) basic_inits = ['diffuse', 'approximate_diffuse', 'stationary'] if self.initialization in basic_inits: self.initialize(self.initialization) elif self.initialization == 'known': if 'constant' in kwargs: constant = kwargs['constant'] elif 'initial_state' in kwargs: # TODO deprecation warning constant = kwargs['initial_state'] else: raise ValueError('Initial state must be provided when "known"' ' is the specified initialization method.') if 'stationary_cov' in kwargs: stationary_cov = kwargs['stationary_cov'] elif 'initial_state_cov' in kwargs: # TODO deprecation warning stationary_cov = kwargs['initial_state_cov'] else: raise ValueError('Initial state covariance matrix must be' ' provided when "known" is the specified' ' initialization method.') self.initialize('known', constant=constant, stationary_cov=stationary_cov) elif (not isinstance(self.initialization, Initialization) and self.initialization is not None): raise ValueError("Invalid state space initialization method.") # Matrix representations storage self._representations = {} # Setup the underlying statespace object storage self._statespaces = {} # Caches self._time_invariant = None def __getitem__(self, key): _type = type(key) # If only a string is given then we must be getting an entire matrix if _type is str: if key not in self.shapes: raise IndexError('"%s" is an invalid state space matrix name' % key) matrix = getattr(self, '_' + key) # See note on time-varying arrays, below if matrix.shape[-1] == 1: return matrix[(slice(None),)*(matrix.ndim-1) + (0,)] else: return matrix # Otherwise if we have a tuple, we want a slice of a matrix elif _type is tuple: name, slice_ = key[0], key[1:] if name not in self.shapes: raise IndexError('"%s" is an invalid state space matrix name' % name) matrix = getattr(self, '_' + name) # Since the model can support time-varying arrays, but often we # will instead have time-invariant arrays, we want to allow setting # a matrix slice like mod['transition',0,:] even though technically # it should be mod['transition',0,:,0]. Thus if the array in # question is time-invariant but the last slice was excluded, # add it in as a zero. if matrix.shape[-1] == 1 and len(slice_) <= matrix.ndim-1: slice_ = slice_ + (0,) return matrix[slice_] # Otherwise, we have only a single slice index, but it is not a string else: raise IndexError('First index must the name of a valid state space' ' matrix.') def __setitem__(self, key, value): _type = type(key) # If only a string is given then we must be setting an entire matrix if _type is str: if key not in self.shapes: raise IndexError('"%s" is an invalid state space matrix name' % key) setattr(self, key, value) # If it's a tuple (with a string as the first element) then we must be # setting a slice of a matrix elif _type is tuple: name, slice_ = key[0], key[1:] if name not in self.shapes: raise IndexError('"%s" is an invalid state space matrix name' % key[0]) # Change the dtype of the corresponding matrix dtype = np.array(value).dtype matrix = getattr(self, '_' + name) valid_types = ['f', 'd', 'F', 'D'] if not matrix.dtype == dtype and dtype.char in valid_types: matrix = getattr(self, '_' + name).real.astype(dtype) # Since the model can support time-varying arrays, but often we # will instead have time-invariant arrays, we want to allow setting # a matrix slice like mod['transition',0,:] even though technically # it should be mod['transition',0,:,0]. Thus if the array in # question is time-invariant but the last slice was excluded, # add it in as a zero. if matrix.shape[-1] == 1 and len(slice_) == matrix.ndim-1: slice_ = slice_ + (0,) # Set the new value matrix[slice_] = value setattr(self, name, matrix) # Otherwise we got a single non-string key, (e.g. mod[:]), which is # invalid else: raise IndexError('First index must the name of a valid state space' ' matrix.') def _clone_kwargs(self, endog, **kwargs): """ Construct keyword arguments for cloning a state space model Parameters ---------- endog : array_like An observed time-series process :math:`y`. **kwargs Keyword arguments to pass to the new state space representation model constructor. Those that are not specified are copied from the specification of the current state space model. """ # We always need the base dimensions, but they cannot change from # the base model when cloning (the idea is: if these need to change, # need to make a new instance manually, since it's not really cloning). kwargs['nobs'] = len(endog) kwargs['k_endog'] = self.k_endog for key in ['k_states', 'k_posdef']: val = getattr(self, key) if key not in kwargs or kwargs[key] is None: kwargs[key] = val if kwargs[key] != val: raise ValueError('Cannot change the dimension of %s when' ' cloning.' % key) # Get defaults for time-invariant system matrices, if not otherwise # provided # Time-varying matrices must be replaced. for name in self.shapes.keys(): if name == 'obs': continue if name not in kwargs: mat = getattr(self, name) if mat.shape[-1] != 1: raise ValueError('The `%s` matrix is time-varying. Cloning' ' this model requires specifying an' ' updated matrix.' % name) kwargs[name] = mat # Default is to use the same initialization kwargs.setdefault('initialization', self.initialization) return kwargs def clone(self, endog, **kwargs): """ Clone a state space representation while overriding some elements Parameters ---------- endog : array_like An observed time-series process :math:`y`. **kwargs Keyword arguments to pass to the new state space representation model constructor. Those that are not specified are copied from the specification of the current state space model. Returns ------- Representation Notes ----- If some system matrices are time-varying, then new time-varying matrices *must* be provided. """ kwargs = self._clone_kwargs(endog, **kwargs) mod = self.__class__(**kwargs) mod.bind(endog) return mod def extend(self, endog, start=None, end=None, **kwargs): """ Extend the current state space model, or a specific (time) subset Parameters ---------- endog : array_like An observed time-series process :math:`y`. start : int, optional The first period of a time-varying state space model to include in the new model. Has no effect if the state space model is time-invariant. Default is the initial period. end : int, optional The last period of a time-varying state space model to include in the new model. Has no effect if the state space model is time-invariant. Default is the final period. **kwargs Keyword arguments to pass to the new state space representation model constructor. Those that are not specified are copied from the specification of the current state space model. Returns ------- Representation Notes ----- This method does not allow replacing a time-varying system matrix with a time-invariant one (or vice-versa). If that is required, use `clone`. """ endog = np.atleast_1d(endog) if endog.ndim == 1: endog = endog[:, np.newaxis] nobs = len(endog) if start is None: start = 0 if end is None: end = self.nobs if start < 0: start = self.nobs + start if end < 0: end = self.nobs + end if start > self.nobs: raise ValueError('The `start` argument of the extension within the' ' base model cannot be after the end of the' ' base model.') if end > self.nobs: raise ValueError('The `end` argument of the extension within the' ' base model cannot be after the end of the' ' base model.') if start > end: raise ValueError('The `start` argument of the extension within the' ' base model cannot be after the `end` argument.') # Note: if start == end or if end < self.nobs, then we're just cloning # (no extension) endog = tools.concat([self.endog[:, start:end].T, endog]) # Extend any time-varying arrays error_ti = ('Model has time-invariant %s matrix, so cannot provide' ' an extended matrix.') error_tv = ('Model has time-varying %s matrix, so an updated' ' time-varying matrix for the extension period' ' is required.') for name, shape in self.shapes.items(): if name == 'obs': continue mat = getattr(self, name) # If we were *not* given an extended value for this matrix... if name not in kwargs: # If this is a time-varying matrix in the existing model if mat.shape[-1] > 1: # If we have an extension period, then raise an error # because we should have been given an extended value if end + nobs > self.nobs: raise ValueError(error_tv % name) # If we do not have an extension period, then set the new # time-varying matrix to be the portion of the existing # time-varying matrix that corresponds to the period of # interest else: kwargs[name] = mat[..., start:end + nobs] elif nobs == 0: raise ValueError('Extension is being performed within-sample' ' so cannot provide an extended matrix') # If we were given an extended value for this matrix else: # TODO: Need to add a check for ndim, and if the matrix has # one fewer dimensions than the existing matrix, add a new axis # If this is a time-invariant matrix in the existing model, # raise an error if mat.shape[-1] == 1 and self.nobs > 1: raise ValueError(error_ti % name) # Otherwise, validate the shape of the given extended value # Note: we do not validate the number of observations here # (so we pass in updated_mat.shape[-1] as the nobs argument # in the validate_* calls); instead, we check below that we # at least `nobs` values were passed in and then only take the # first of them as required. This can be useful when e.g. the # end user knows the extension values up to some maximum # endpoint, but does not know what the calling methods may # specifically require. updated_mat = np.asarray(kwargs[name]) if len(shape) == 2: validate_vector_shape(name, updated_mat.shape, shape[0], updated_mat.shape[-1]) else: validate_matrix_shape(name, updated_mat.shape, shape[0], shape[1], updated_mat.shape[-1]) if updated_mat.shape[-1] < nobs: raise ValueError(error_tv % name) else: updated_mat = updated_mat[..., :nobs] # Concatenate to get the new time-varying matrix kwargs[name] = np.c_[mat[..., start:end], updated_mat] return self.clone(endog, **kwargs) def diff_endog(self, new_endog, tolerance=1e-10): # TODO: move this function to tools? endog = self.endog.T if len(new_endog) < len(endog): raise ValueError('Given data (length %d) is too short to diff' ' against model data (length %d).' % (len(new_endog), len(endog))) if len(new_endog) > len(endog): nobs_append = len(new_endog) - len(endog) endog = np.c_[endog.T, new_endog[-nobs_append:].T * np.nan].T new_nan = np.isnan(new_endog) existing_nan = np.isnan(endog) diff = np.abs(new_endog - endog) diff[new_nan ^ existing_nan] = np.inf diff[new_nan & existing_nan] = 0. is_revision = (diff > tolerance) is_new = existing_nan & ~new_nan is_revision[is_new] = False revision_ix = list(zip(*np.where(is_revision))) new_ix = list(zip(*np.where(is_new))) return revision_ix, new_ix @property def prefix(self): """ (str) BLAS prefix of currently active representation matrices """ arrays = ( self._design, self._obs_intercept, self._obs_cov, self._transition, self._state_intercept, self._selection, self._state_cov ) if self.endog is not None: arrays = (self.endog,) + arrays return find_best_blas_type(arrays)[0] @property def dtype(self): """ (dtype) Datatype of currently active representation matrices """ return tools.prefix_dtype_map[self.prefix] @property def time_invariant(self): """ (bool) Whether or not currently active representation matrices are time-invariant """ if self._time_invariant is None: return ( self._design.shape[2] == self._obs_intercept.shape[1] == self._obs_cov.shape[2] == self._transition.shape[2] == self._state_intercept.shape[1] == self._selection.shape[2] == self._state_cov.shape[2] ) else: return self._time_invariant @property def _statespace(self): prefix = self.prefix if prefix in self._statespaces: return self._statespaces[prefix] return None @property def obs(self): r""" (array) Observation vector: :math:`y~(k\_endog \times nobs)` """ return self.endog def bind(self, endog): """ Bind data to the statespace representation Parameters ---------- endog : ndarray Endogenous data to bind to the model. Must be column-ordered ndarray with shape (`k_endog`, `nobs`) or row-ordered ndarray with shape (`nobs`, `k_endog`). Notes ----- The strict requirements arise because the underlying statespace and Kalman filtering classes require Fortran-ordered arrays in the wide format (shaped (`k_endog`, `nobs`)), and this structure is setup to prevent copying arrays in memory. By default, numpy arrays are row (C)-ordered and most time series are represented in the long format (with time on the 0-th axis). In this case, no copying or re-ordering needs to be performed, instead the array can simply be transposed to get it in the right order and shape. Although this class (Representation) has stringent `bind` requirements, it is assumed that it will rarely be used directly. """ if not isinstance(endog, np.ndarray): raise ValueError("Invalid endogenous array; must be an ndarray.") # Make sure we have a 2-dimensional array # Note: reshaping a 1-dim array into a 2-dim array by changing the # shape tuple always results in a row (C)-ordered array, so it # must be shaped (nobs, k_endog) if endog.ndim == 1: # In the case of nobs x 0 arrays if self.k_endog == 1: endog.shape = (endog.shape[0], 1) # In the case of k_endog x 0 arrays else: endog.shape = (1, endog.shape[0]) if not endog.ndim == 2: raise ValueError('Invalid endogenous array provided; must be' ' 2-dimensional.') # Check for valid column-ordered arrays if endog.flags['F_CONTIGUOUS'] and endog.shape[0] == self.k_endog: pass # Check for valid row-ordered arrays, and transpose them to be the # correct column-ordered array elif endog.flags['C_CONTIGUOUS'] and endog.shape[1] == self.k_endog: endog = endog.T # Invalid column-ordered arrays elif endog.flags['F_CONTIGUOUS']: raise ValueError('Invalid endogenous array; column-ordered' ' arrays must have first axis shape of' ' `k_endog`.') # Invalid row-ordered arrays elif endog.flags['C_CONTIGUOUS']: raise ValueError('Invalid endogenous array; row-ordered' ' arrays must have last axis shape of' ' `k_endog`.') # Non-contiguous arrays else: raise ValueError('Invalid endogenous array; must be ordered in' ' contiguous memory.') # In some corner cases (e.g. np.array(1., ndmin=2) with numpy < 1.8) # we may still have a non-fortran contiguous array, so double-check # that now if not endog.flags['F_CONTIGUOUS']: endog = np.asfortranarray(endog) # Set a flag for complex data self._complex_endog = np.iscomplexobj(endog) # Set the data self.endog = endog self.nobs = self.endog.shape[1] # Reset shapes if hasattr(self, 'shapes'): self.shapes['obs'] = self.endog.shape def initialize(self, initialization, approximate_diffuse_variance=None, constant=None, stationary_cov=None): """Create an Initialization object if necessary""" if initialization == 'known': initialization = Initialization(self.k_states, 'known', constant=constant, stationary_cov=stationary_cov) elif initialization == 'approximate_diffuse': if approximate_diffuse_variance is None: approximate_diffuse_variance = self.initial_variance initialization = Initialization( self.k_states, 'approximate_diffuse', approximate_diffuse_variance=approximate_diffuse_variance) elif initialization == 'stationary': initialization = Initialization(self.k_states, 'stationary') elif initialization == 'diffuse': initialization = Initialization(self.k_states, 'diffuse') # We must have an initialization object at this point if not isinstance(initialization, Initialization): raise ValueError("Invalid state space initialization method.") self.initialization = initialization def initialize_known(self, constant, stationary_cov): """ Initialize the statespace model with known distribution for initial state. These values are assumed to be known with certainty or else filled with parameters during, for example, maximum likelihood estimation. Parameters ---------- constant : array_like Known mean of the initial state vector. stationary_cov : array_like Known covariance matrix of the initial state vector. """ constant = np.asarray(constant, order="F") stationary_cov = np.asarray(stationary_cov, order="F") if not constant.shape == (self.k_states,): raise ValueError('Invalid dimensions for constant state vector.' ' Requires shape (%d,), got %s' % (self.k_states, str(constant.shape))) if not stationary_cov.shape == (self.k_states, self.k_states): raise ValueError('Invalid dimensions for stationary covariance' ' matrix. Requires shape (%d,%d), got %s' % (self.k_states, self.k_states, str(stationary_cov.shape))) self.initialize('known', constant=constant, stationary_cov=stationary_cov) def initialize_approximate_diffuse(self, variance=None): """ Initialize the statespace model with approximate diffuse values. Rather than following the exact diffuse treatment (which is developed for the case that the variance becomes infinitely large), this assigns an arbitrary large number for the variance. Parameters ---------- variance : float, optional The variance for approximating diffuse initial conditions. Default is 1e6. """ if variance is None: variance = self.initial_variance self.initialize('approximate_diffuse', approximate_diffuse_variance=variance) def initialize_stationary(self): """ Initialize the statespace model as stationary. """ self.initialize('stationary') def initialize_diffuse(self): """ Initialize the statespace model as stationary. """ self.initialize('diffuse') def _initialize_representation(self, prefix=None): if prefix is None: prefix = self.prefix dtype = tools.prefix_dtype_map[prefix] # If the dtype-specific representation matrices do not exist, create # them if prefix not in self._representations: # Copy the statespace representation matrices self._representations[prefix] = {} for matrix in self.shapes.keys(): if matrix == 'obs': self._representations[prefix][matrix] = ( self.obs.astype(dtype) ) else: # Note: this always makes a copy self._representations[prefix][matrix] = ( getattr(self, '_' + matrix).astype(dtype) ) # If they do exist, update them else: for matrix in self.shapes.keys(): existing = self._representations[prefix][matrix] if matrix == 'obs': # existing[:] = self.obs.astype(dtype) pass else: new = getattr(self, '_' + matrix).astype(dtype) if existing.shape == new.shape: existing[:] = new[:] else: self._representations[prefix][matrix] = new # Determine if we need to (re-)create the _statespace models # (if time-varying matrices changed) if prefix in self._statespaces: ss = self._statespaces[prefix] create = ( not ss.obs.shape[1] == self.endog.shape[1] or not ss.design.shape[2] == self.design.shape[2] or not ss.obs_intercept.shape[1] == self.obs_intercept.shape[1] or not ss.obs_cov.shape[2] == self.obs_cov.shape[2] or not ss.transition.shape[2] == self.transition.shape[2] or not (ss.state_intercept.shape[1] == self.state_intercept.shape[1]) or not ss.selection.shape[2] == self.selection.shape[2] or not ss.state_cov.shape[2] == self.state_cov.shape[2] ) else: create = True # (re-)create if necessary if create: if prefix in self._statespaces: del self._statespaces[prefix] # Setup the base statespace object cls = self.prefix_statespace_map[prefix] self._statespaces[prefix] = cls( self._representations[prefix]['obs'], self._representations[prefix]['design'], self._representations[prefix]['obs_intercept'], self._representations[prefix]['obs_cov'], self._representations[prefix]['transition'], self._representations[prefix]['state_intercept'], self._representations[prefix]['selection'], self._representations[prefix]['state_cov'] ) return prefix, dtype, create def _initialize_state(self, prefix=None, complex_step=False): # TODO once the transition to using the Initialization objects is # complete, this should be moved entirely to the _{{prefix}}Statespace # object. if prefix is None: prefix = self.prefix # (Re-)initialize the statespace model if isinstance(self.initialization, Initialization): if not self.initialization.initialized: raise RuntimeError('Initialization is incomplete.') self._statespaces[prefix].initialize(self.initialization, complex_step=complex_step) else: raise RuntimeError('Statespace model not initialized.') class FrozenRepresentation(object): """ Frozen Statespace Model Takes a snapshot of a Statespace model. Parameters ---------- model : Representation A Statespace representation Attributes ---------- nobs : int Number of observations. k_endog : int The dimension of the observation series. k_states : int The dimension of the unobserved state process. k_posdef : int The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation. dtype : dtype Datatype of representation matrices prefix : str BLAS prefix of representation matrices shapes : dictionary of name:tuple A dictionary recording the shapes of each of the representation matrices as tuples. endog : ndarray The observation vector. design : ndarray The design matrix, :math:`Z`. obs_intercept : ndarray The intercept for the observation equation, :math:`d`. obs_cov : ndarray The covariance matrix for the observation equation :math:`H`. transition : ndarray The transition matrix, :math:`T`. state_intercept : ndarray The intercept for the transition equation, :math:`c`. selection : ndarray The selection matrix, :math:`R`. state_cov : ndarray The covariance matrix for the state equation :math:`Q`. missing : array of bool An array of the same size as `endog`, filled with boolean values that are True if the corresponding entry in `endog` is NaN and False otherwise. nmissing : array of int An array of size `nobs`, where the ith entry is the number (between 0 and `k_endog`) of NaNs in the ith row of the `endog` array. time_invariant : bool Whether or not the representation matrices are time-invariant initialization : Initialization object Kalman filter initialization method. initial_state : array_like The state vector used to initialize the Kalamn filter. initial_state_cov : array_like The state covariance matrix used to initialize the Kalamn filter. """ _model_attributes = [ 'model', 'prefix', 'dtype', 'nobs', 'k_endog', 'k_states', 'k_posdef', 'time_invariant', 'endog', 'design', 'obs_intercept', 'obs_cov', 'transition', 'state_intercept', 'selection', 'state_cov', 'missing', 'nmissing', 'shapes', 'initialization', 'initial_state', 'initial_state_cov', 'initial_variance' ] _attributes = _model_attributes def __init__(self, model): # Initialize all attributes to None for name in self._attributes: setattr(self, name, None) # Update the representation attributes self.update_representation(model) def update_representation(self, model): """Update model Representation""" # Model self.model = model # Data type self.prefix = model.prefix self.dtype = model.dtype # Copy the model dimensions self.nobs = model.nobs self.k_endog = model.k_endog self.k_states = model.k_states self.k_posdef = model.k_posdef self.time_invariant = model.time_invariant # Save the state space representation at the time self.endog = model.endog self.design = model._design.copy() self.obs_intercept = model._obs_intercept.copy() self.obs_cov = model._obs_cov.copy() self.transition = model._transition.copy() self.state_intercept = model._state_intercept.copy() self.selection = model._selection.copy() self.state_cov = model._state_cov.copy() self.missing = np.array(model._statespaces[self.prefix].missing, copy=True) self.nmissing = np.array(model._statespaces[self.prefix].nmissing, copy=True) # Save the final shapes of the matrices self.shapes = dict(model.shapes) for name in self.shapes.keys(): if name == 'obs': continue self.shapes[name] = getattr(self, name).shape self.shapes['obs'] = self.endog.shape # Save the state space initialization self.initialization = model.initialization if model.initialization is not None: model._initialize_state() self.initial_state = np.array( model._statespaces[self.prefix].initial_state, copy=True) self.initial_state_cov = np.array( model._statespaces[self.prefix].initial_state_cov, copy=True) self.initial_diffuse_state_cov = np.array( model._statespaces[self.prefix].initial_diffuse_state_cov, copy=True) statsmodels-0.12.2/statsmodels/tsa/statespace/sarimax.py000066400000000000000000002436331400612667500234630ustar00rootroot00000000000000""" SARIMAX Model Author: Chad Fulton License: Simplified-BSD """ from warnings import warn import numpy as np import pandas as pd from statsmodels.compat.pandas import Appender from statsmodels.tools.tools import Bunch from statsmodels.tools.data import _is_using_pandas from statsmodels.tools.decorators import cache_readonly import statsmodels.base.wrapper as wrap from statsmodels.tsa.arima.specification import SARIMAXSpecification from statsmodels.tsa.arima.params import SARIMAXParams from statsmodels.tsa.tsatools import lagmat from .initialization import Initialization from .mlemodel import MLEModel, MLEResults, MLEResultsWrapper from .tools import ( companion_matrix, diff, is_invertible, constrain_stationary_univariate, unconstrain_stationary_univariate, prepare_exog, prepare_trend_spec, prepare_trend_data) class SARIMAX(MLEModel): r""" Seasonal AutoRegressive Integrated Moving Average with eXogenous regressors model Parameters ---------- endog : array_like The observed time-series process :math:`y` exog : array_like, optional Array of exogenous regressors, shaped nobs x k. order : iterable or iterable of iterables, optional The (p,d,q) order of the model for the number of AR parameters, differences, and MA parameters. `d` must be an integer indicating the integration order of the process, while `p` and `q` may either be an integers indicating the AR and MA orders (so that all lags up to those orders are included) or else iterables giving specific AR and / or MA lags to include. Default is an AR(1) model: (1,0,0). seasonal_order : iterable, optional The (P,D,Q,s) order of the seasonal component of the model for the AR parameters, differences, MA parameters, and periodicity. `D` must be an integer indicating the integration order of the process, while `P` and `Q` may either be an integers indicating the AR and MA orders (so that all lags up to those orders are included) or else iterables giving specific AR and / or MA lags to include. `s` is an integer giving the periodicity (number of periods in season), often it is 4 for quarterly data or 12 for monthly data. Default is no seasonal effect. trend : str{'n','c','t','ct'} or iterable, optional Parameter controlling the deterministic trend polynomial :math:`A(t)`. Can be specified as a string where 'c' indicates a constant (i.e. a degree zero component of the trend polynomial), 't' indicates a linear trend with time, and 'ct' is both. Can also be specified as an iterable defining the non-zero polynomial exponents to include, in increasing order. For example, `[1,1,0,1]` denotes :math:`a + bt + ct^3`. Default is to not include a trend component. measurement_error : bool, optional Whether or not to assume the endogenous observations `endog` were measured with error. Default is False. time_varying_regression : bool, optional Used when an explanatory variables, `exog`, are provided provided to select whether or not coefficients on the exogenous regressors are allowed to vary over time. Default is False. mle_regression : bool, optional Whether or not to use estimate the regression coefficients for the exogenous variables as part of maximum likelihood estimation or through the Kalman filter (i.e. recursive least squares). If `time_varying_regression` is True, this must be set to False. Default is True. simple_differencing : bool, optional Whether or not to use partially conditional maximum likelihood estimation. If True, differencing is performed prior to estimation, which discards the first :math:`s D + d` initial rows but results in a smaller state-space formulation. See the Notes section for important details about interpreting results when this option is used. If False, the full SARIMAX model is put in state-space form so that all datapoints can be used in estimation. Default is False. enforce_stationarity : bool, optional Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. Default is True. enforce_invertibility : bool, optional Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. Default is True. hamilton_representation : bool, optional Whether or not to use the Hamilton representation of an ARMA process (if True) or the Harvey representation (if False). Default is False. concentrate_scale : bool, optional Whether or not to concentrate the scale (variance of the error term) out of the likelihood. This reduces the number of parameters estimated by maximum likelihood by one, but standard errors will then not be available for the scale parameter. trend_offset : int, optional The offset at which to start time trend values. Default is 1, so that if `trend='t'` the trend is equal to 1, 2, ..., nobs. Typically is only set when the model created by extending a previous dataset. use_exact_diffuse : bool, optional Whether or not to use exact diffuse initialization for non-stationary states. Default is False (in which case approximate diffuse initialization is used). **kwargs Keyword arguments may be used to provide default values for state space matrices or for Kalman filtering options. See `Representation`, and `KalmanFilter` for more details. Attributes ---------- measurement_error : bool Whether or not to assume the endogenous observations `endog` were measured with error. state_error : bool Whether or not the transition equation has an error component. mle_regression : bool Whether or not the regression coefficients for the exogenous variables were estimated via maximum likelihood estimation. state_regression : bool Whether or not the regression coefficients for the exogenous variables are included as elements of the state space and estimated via the Kalman filter. time_varying_regression : bool Whether or not coefficients on the exogenous regressors are allowed to vary over time. simple_differencing : bool Whether or not to use partially conditional maximum likelihood estimation. enforce_stationarity : bool Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. enforce_invertibility : bool Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. hamilton_representation : bool Whether or not to use the Hamilton representation of an ARMA process. trend : str{'n','c','t','ct'} or iterable Parameter controlling the deterministic trend polynomial :math:`A(t)`. See the class parameter documentation for more information. polynomial_ar : ndarray Array containing autoregressive lag polynomial lags, ordered from lowest degree to highest. The polynomial begins with lag 0. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). polynomial_ma : ndarray Array containing moving average lag polynomial lags, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). polynomial_seasonal_ar : ndarray Array containing seasonal moving average lag polynomial lags, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). polynomial_seasonal_ma : ndarray Array containing seasonal moving average lag polynomial lags, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). polynomial_trend : ndarray Array containing trend polynomial coefficients, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). k_ar : int Highest autoregressive order in the model, zero-indexed. k_ar_params : int Number of autoregressive parameters to be estimated. k_diff : int Order of integration. k_ma : int Highest moving average order in the model, zero-indexed. k_ma_params : int Number of moving average parameters to be estimated. seasonal_periods : int Number of periods in a season. k_seasonal_ar : int Highest seasonal autoregressive order in the model, zero-indexed. k_seasonal_ar_params : int Number of seasonal autoregressive parameters to be estimated. k_seasonal_diff : int Order of seasonal integration. k_seasonal_ma : int Highest seasonal moving average order in the model, zero-indexed. k_seasonal_ma_params : int Number of seasonal moving average parameters to be estimated. k_trend : int Order of the trend polynomial plus one (i.e. the constant polynomial would have `k_trend=1`). k_exog : int Number of exogenous regressors. Notes ----- The SARIMA model is specified :math:`(p, d, q) \times (P, D, Q)_s`. .. math:: \phi_p (L) \tilde \phi_P (L^s) \Delta^d \Delta_s^D y_t = A(t) + \theta_q (L) \tilde \theta_Q (L^s) \zeta_t In terms of a univariate structural model, this can be represented as .. math:: y_t & = u_t + \eta_t \\ \phi_p (L) \tilde \phi_P (L^s) \Delta^d \Delta_s^D u_t & = A(t) + \theta_q (L) \tilde \theta_Q (L^s) \zeta_t where :math:`\eta_t` is only applicable in the case of measurement error (although it is also used in the case of a pure regression model, i.e. if p=q=0). In terms of this model, regression with SARIMA errors can be represented easily as .. math:: y_t & = \beta_t x_t + u_t \\ \phi_p (L) \tilde \phi_P (L^s) \Delta^d \Delta_s^D u_t & = A(t) + \theta_q (L) \tilde \theta_Q (L^s) \zeta_t this model is the one used when exogenous regressors are provided. Note that the reduced form lag polynomials will be written as: .. math:: \Phi (L) \equiv \phi_p (L) \tilde \phi_P (L^s) \\ \Theta (L) \equiv \theta_q (L) \tilde \theta_Q (L^s) If `mle_regression` is True, regression coefficients are treated as additional parameters to be estimated via maximum likelihood. Otherwise they are included as part of the state with a diffuse initialization. In this case, however, with approximate diffuse initialization, results can be sensitive to the initial variance. This class allows two different underlying representations of ARMA models as state space models: that of Hamilton and that of Harvey. Both are equivalent in the sense that they are analytical representations of the ARMA model, but the state vectors of each have different meanings. For this reason, maximum likelihood does not result in identical parameter estimates and even the same set of parameters will result in different loglikelihoods. The Harvey representation is convenient because it allows integrating differencing into the state vector to allow using all observations for estimation. In this implementation of differenced models, the Hamilton representation is not able to accommodate differencing in the state vector, so `simple_differencing` (which performs differencing prior to estimation so that the first d + sD observations are lost) must be used. Many other packages use the Hamilton representation, so that tests against Stata and R require using it along with simple differencing (as Stata does). If `filter_concentrated = True` is used, then the scale of the model is concentrated out of the likelihood. A benefit of this is that there the dimension of the parameter vector is reduced so that numerical maximization of the log-likelihood function may be faster and more stable. If this option in a model with measurement error, it is important to note that the estimated measurement error parameter will be relative to the scale, and is named "snr.measurement_error" instead of "var.measurement_error". To compute the variance of the measurement error in this case one would multiply `snr.measurement_error` parameter by the scale. If `simple_differencing = True` is used, then the `endog` and `exog` data are differenced prior to putting the model in state-space form. This has the same effect as if the user differenced the data prior to constructing the model, which has implications for using the results: - Forecasts and predictions will be about the *differenced* data, not about the original data. (while if `simple_differencing = False` is used, then forecasts and predictions will be about the original data). - If the original data has an Int64Index, a new RangeIndex will be created for the differenced data that starts from one, and forecasts and predictions will use this new index. Detailed information about state space models can be found in [1]_. Some specific references are: - Chapter 3.4 describes ARMA and ARIMA models in state space form (using the Harvey representation), and gives references for basic seasonal models and models with a multiplicative form (for example the airline model). It also shows a state space model for a full ARIMA process (this is what is done here if `simple_differencing=False`). - Chapter 3.6 describes estimating regression effects via the Kalman filter (this is performed if `mle_regression` is False), regression with time-varying coefficients, and regression with ARMA errors (recall from above that if regression effects are present, the model estimated by this class is regression with SARIMA errors). - Chapter 8.4 describes the application of an ARMA model to an example dataset. A replication of this section is available in an example IPython notebook in the documentation. References ---------- .. [1] Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods: Second Edition. Oxford University Press. """ def __init__(self, endog, exog=None, order=(1, 0, 0), seasonal_order=(0, 0, 0, 0), trend=None, measurement_error=False, time_varying_regression=False, mle_regression=True, simple_differencing=False, enforce_stationarity=True, enforce_invertibility=True, hamilton_representation=False, concentrate_scale=False, trend_offset=1, use_exact_diffuse=False, dates=None, freq=None, missing='none', validate_specification=True, **kwargs): self._spec = SARIMAXSpecification( endog, exog=exog, order=order, seasonal_order=seasonal_order, trend=trend, enforce_stationarity=None, enforce_invertibility=None, concentrate_scale=concentrate_scale, dates=dates, freq=freq, missing=missing, validate_specification=validate_specification) self._params = SARIMAXParams(self._spec) # Save given orders order = self._spec.order seasonal_order = self._spec.seasonal_order self.order = order self.seasonal_order = seasonal_order # Model parameters self.seasonal_periods = seasonal_order[3] self.measurement_error = measurement_error self.time_varying_regression = time_varying_regression self.mle_regression = mle_regression self.simple_differencing = simple_differencing self.enforce_stationarity = enforce_stationarity self.enforce_invertibility = enforce_invertibility self.hamilton_representation = hamilton_representation self.concentrate_scale = concentrate_scale self.use_exact_diffuse = use_exact_diffuse # Enforce non-MLE coefficients if time varying coefficients is # specified if self.time_varying_regression and self.mle_regression: raise ValueError('Models with time-varying regression coefficients' ' must integrate the coefficients as part of the' ' state vector, so that `mle_regression` must' ' be set to False.') # Lag polynomials self._params.ar_params = -1 self.polynomial_ar = self._params.ar_poly.coef self._polynomial_ar = self.polynomial_ar.copy() self._params.ma_params = 1 self.polynomial_ma = self._params.ma_poly.coef self._polynomial_ma = self.polynomial_ma.copy() self._params.seasonal_ar_params = -1 self.polynomial_seasonal_ar = self._params.seasonal_ar_poly.coef self._polynomial_seasonal_ar = self.polynomial_seasonal_ar.copy() self._params.seasonal_ma_params = 1 self.polynomial_seasonal_ma = self._params.seasonal_ma_poly.coef self._polynomial_seasonal_ma = self.polynomial_seasonal_ma.copy() # Deterministic trend polynomial self.trend = trend self.trend_offset = trend_offset self.polynomial_trend, self.k_trend = prepare_trend_spec(self.trend) self._polynomial_trend = self.polynomial_trend.copy() self._k_trend = self.k_trend # (we internally use _k_trend for mechanics so that the public # attribute can be overridden by subclasses) # Model orders # Note: k_ar, k_ma, k_seasonal_ar, k_seasonal_ma do not include the # constant term, so they may be zero. # Note: for a typical ARMA(p,q) model, p = k_ar_params = k_ar - 1 and # q = k_ma_params = k_ma - 1, although this may not be true for models # with arbitrary log polynomials. self.k_ar = self._spec.max_ar_order self.k_ar_params = self._spec.k_ar_params self.k_diff = int(order[1]) self.k_ma = self._spec.max_ma_order self.k_ma_params = self._spec.k_ma_params self.k_seasonal_ar = (self._spec.max_seasonal_ar_order * self._spec.seasonal_periods) self.k_seasonal_ar_params = self._spec.k_seasonal_ar_params self.k_seasonal_diff = int(seasonal_order[1]) self.k_seasonal_ma = (self._spec.max_seasonal_ma_order * self._spec.seasonal_periods) self.k_seasonal_ma_params = self._spec.k_seasonal_ma_params # Make internal copies of the differencing orders because if we use # simple differencing, then we will need to internally use zeros after # the simple differencing has been performed self._k_diff = self.k_diff self._k_seasonal_diff = self.k_seasonal_diff # We can only use the Hamilton representation if differencing is not # performed as a part of the state space if (self.hamilton_representation and not (self.simple_differencing or self._k_diff == self._k_seasonal_diff == 0)): raise ValueError('The Hamilton representation is only available' ' for models in which there is no differencing' ' integrated into the state vector. Set' ' `simple_differencing` to True or set' ' `hamilton_representation` to False') # Model order # (this is used internally in a number of locations) self._k_order = max(self.k_ar + self.k_seasonal_ar, self.k_ma + self.k_seasonal_ma + 1) if self._k_order == 1 and self.k_ar + self.k_seasonal_ar == 0: # Handle time-varying regression if self.time_varying_regression: self._k_order = 0 # Exogenous data (self._k_exog, exog) = prepare_exog(exog) # (we internally use _k_exog for mechanics so that the public attribute # can be overridden by subclasses) self.k_exog = self._k_exog # Redefine mle_regression to be true only if it was previously set to # true and there are exogenous regressors self.mle_regression = ( self.mle_regression and exog is not None and self._k_exog > 0 ) # State regression is regression with coefficients estimated within # the state vector self.state_regression = ( not self.mle_regression and exog is not None and self._k_exog > 0 ) # If all we have is a regression (so k_ar = k_ma = 0), then put the # error term as measurement error if self.state_regression and self._k_order == 0: self.measurement_error = True # Number of states k_states = self._k_order if not self.simple_differencing: k_states += (self.seasonal_periods * self._k_seasonal_diff + self._k_diff) if self.state_regression: k_states += self._k_exog # Number of positive definite elements of the state covariance matrix k_posdef = int(self._k_order > 0) # Only have an error component to the states if k_posdef > 0 self.state_error = k_posdef > 0 if self.state_regression and self.time_varying_regression: k_posdef += self._k_exog # Diffuse initialization can be more sensistive to the variance value # in the case of state regression, so set a higher than usual default # variance if self.state_regression: kwargs.setdefault('initial_variance', 1e10) # Handle non-default loglikelihood burn self._loglikelihood_burn = kwargs.get('loglikelihood_burn', None) # Number of parameters self.k_params = ( self.k_ar_params + self.k_ma_params + self.k_seasonal_ar_params + self.k_seasonal_ma_params + self._k_trend + self.measurement_error + int(not self.concentrate_scale) ) if self.mle_regression: self.k_params += self._k_exog # We need to have an array or pandas at this point self.orig_endog = endog self.orig_exog = exog if not _is_using_pandas(endog, None): endog = np.asanyarray(endog) # Update the differencing dimensions if simple differencing is applied self.orig_k_diff = self._k_diff self.orig_k_seasonal_diff = self._k_seasonal_diff if (self.simple_differencing and (self._k_diff > 0 or self._k_seasonal_diff > 0)): self._k_diff = 0 self._k_seasonal_diff = 0 # Internally used in several locations self._k_states_diff = ( self._k_diff + self.seasonal_periods * self._k_seasonal_diff ) # Set some model variables now so they will be available for the # initialize() method, below self.nobs = len(endog) self.k_states = k_states self.k_posdef = k_posdef # Initialize the statespace super(SARIMAX, self).__init__( endog, exog=exog, k_states=k_states, k_posdef=k_posdef, **kwargs ) # Set the filter to concentrate out the scale if requested if self.concentrate_scale: self.ssm.filter_concentrated = True # Set as time-varying model if we have time-trend or exog if self._k_exog > 0 or len(self.polynomial_trend) > 1: self.ssm._time_invariant = False # Initialize the fixed components of the statespace model self.ssm['design'] = self.initial_design self.ssm['state_intercept'] = self.initial_state_intercept self.ssm['transition'] = self.initial_transition self.ssm['selection'] = self.initial_selection if self.concentrate_scale: self.ssm['state_cov', 0, 0] = 1. # update _init_keys attached by super self._init_keys += ['order', 'seasonal_order', 'trend', 'measurement_error', 'time_varying_regression', 'mle_regression', 'simple_differencing', 'enforce_stationarity', 'enforce_invertibility', 'hamilton_representation', 'concentrate_scale', 'trend_offset'] + list(kwargs.keys()) # TODO: I think the kwargs or not attached, need to recover from ??? # Initialize the state if self.ssm.initialization is None: self.initialize_default() def prepare_data(self): endog, exog = super(SARIMAX, self).prepare_data() # Perform simple differencing if requested if (self.simple_differencing and (self.orig_k_diff > 0 or self.orig_k_seasonal_diff > 0)): # Save the original length orig_length = endog.shape[0] # Perform simple differencing endog = diff(endog.copy(), self.orig_k_diff, self.orig_k_seasonal_diff, self.seasonal_periods) if exog is not None: exog = diff(exog.copy(), self.orig_k_diff, self.orig_k_seasonal_diff, self.seasonal_periods) # Reset the ModelData datasets and cache self.data.endog, self.data.exog = ( self.data._convert_endog_exog(endog, exog)) # Reset indexes, if provided new_length = self.data.endog.shape[0] if self.data.row_labels is not None: self.data._cache['row_labels'] = ( self.data.row_labels[orig_length - new_length:]) if self._index is not None: if self._index_int64: self._index = pd.RangeIndex(start=1, stop=new_length + 1) elif self._index_generated: self._index = self._index[:-(orig_length - new_length)] else: self._index = self._index[orig_length - new_length:] # Reset the nobs self.nobs = endog.shape[0] # Cache the arrays for calculating the intercept from the trend # components self._trend_data = prepare_trend_data( self.polynomial_trend, self._k_trend, self.nobs, self.trend_offset) return endog, exog def initialize(self): """ Initialize the SARIMAX model. Notes ----- These initialization steps must occur following the parent class __init__ function calls. """ super(SARIMAX, self).initialize() # Cache the indexes of included polynomial orders (for update below) # (but we do not want the index of the constant term, so exclude the # first index) self._polynomial_ar_idx = np.nonzero(self.polynomial_ar)[0][1:] self._polynomial_ma_idx = np.nonzero(self.polynomial_ma)[0][1:] self._polynomial_seasonal_ar_idx = np.nonzero( self.polynomial_seasonal_ar )[0][1:] self._polynomial_seasonal_ma_idx = np.nonzero( self.polynomial_seasonal_ma )[0][1:] # Save the indices corresponding to the reduced form lag polynomial # parameters in the transition and selection matrices so that they # do not have to be recalculated for each update() start_row = self._k_states_diff end_row = start_row + self.k_ar + self.k_seasonal_ar col = self._k_states_diff if not self.hamilton_representation: self.transition_ar_params_idx = ( np.s_['transition', start_row:end_row, col] ) else: self.transition_ar_params_idx = ( np.s_['transition', col, start_row:end_row] ) start_row += 1 end_row = start_row + self.k_ma + self.k_seasonal_ma col = 0 if not self.hamilton_representation: self.selection_ma_params_idx = ( np.s_['selection', start_row:end_row, col] ) else: self.design_ma_params_idx = ( np.s_['design', col, start_row:end_row] ) # Cache indices for exog variances in the state covariance matrix if self.state_regression and self.time_varying_regression: idx = np.diag_indices(self.k_posdef) self._exog_variance_idx = ('state_cov', idx[0][-self._k_exog:], idx[1][-self._k_exog:]) def initialize_default(self, approximate_diffuse_variance=None): """Initialize default""" if approximate_diffuse_variance is None: approximate_diffuse_variance = self.ssm.initial_variance if self.use_exact_diffuse: diffuse_type = 'diffuse' else: diffuse_type = 'approximate_diffuse' # Set the loglikelihood burn parameter, if not given in constructor if self._loglikelihood_burn is None: k_diffuse_states = self.k_states if self.enforce_stationarity: k_diffuse_states -= self._k_order self.loglikelihood_burn = k_diffuse_states init = Initialization( self.k_states, approximate_diffuse_variance=approximate_diffuse_variance) if self.enforce_stationarity: # Differencing operators are at the beginning init.set((0, self._k_states_diff), diffuse_type) # Stationary component in the middle init.set((self._k_states_diff, self._k_states_diff + self._k_order), 'stationary') # Regression components at the end init.set((self._k_states_diff + self._k_order, self._k_states_diff + self._k_order + self._k_exog), diffuse_type) # If we're not enforcing a stationarity, then we cannot initialize a # stationary component else: init.set(None, diffuse_type) self.ssm.initialization = init @property def initial_design(self): """Initial design matrix""" # Basic design matrix design = np.r_[ [1] * self._k_diff, ([0] * (self.seasonal_periods - 1) + [1]) * self._k_seasonal_diff, [1] * self.state_error, [0] * (self._k_order - 1) ] if len(design) == 0: design = np.r_[0] # If we have exogenous regressors included as part of the state vector # then the exogenous data is incorporated as a time-varying component # of the design matrix if self.state_regression: if self._k_order > 0: design = np.c_[ np.reshape( np.repeat(design, self.nobs), (design.shape[0], self.nobs) ).T, self.exog ].T[None, :, :] else: design = self.exog.T[None, :, :] return design @property def initial_state_intercept(self): """Initial state intercept vector""" # TODO make this self._k_trend > 1 and adjust the update to take # into account that if the trend is a constant, it is not time-varying if self._k_trend > 0: state_intercept = np.zeros((self.k_states, self.nobs)) else: state_intercept = np.zeros((self.k_states,)) return state_intercept @property def initial_transition(self): """Initial transition matrix""" transition = np.zeros((self.k_states, self.k_states)) # Exogenous regressors component if self.state_regression: start = -self._k_exog # T_\beta transition[start:, start:] = np.eye(self._k_exog) # Autoregressive component start = -(self._k_exog + self._k_order) end = -self._k_exog if self._k_exog > 0 else None else: # Autoregressive component start = -self._k_order end = None # T_c if self._k_order > 0: transition[start:end, start:end] = companion_matrix(self._k_order) if self.hamilton_representation: transition[start:end, start:end] = np.transpose( companion_matrix(self._k_order) ) # Seasonal differencing component # T^* if self._k_seasonal_diff > 0: seasonal_companion = companion_matrix(self.seasonal_periods).T seasonal_companion[0, -1] = 1 for d in range(self._k_seasonal_diff): start = self._k_diff + d * self.seasonal_periods end = self._k_diff + (d + 1) * self.seasonal_periods # T_c^* transition[start:end, start:end] = seasonal_companion # i for i in range(d + 1, self._k_seasonal_diff): transition[start, end + self.seasonal_periods - 1] = 1 # \iota transition[start, self._k_states_diff] = 1 # Differencing component if self._k_diff > 0: idx = np.triu_indices(self._k_diff) # T^** transition[idx] = 1 # [0 1] if self.seasonal_periods > 0: start = self._k_diff end = self._k_states_diff transition[:self._k_diff, start:end] = ( ([0] * (self.seasonal_periods - 1) + [1]) * self._k_seasonal_diff) # [1 0] column = self._k_states_diff transition[:self._k_diff, column] = 1 return transition @property def initial_selection(self): """Initial selection matrix""" if not (self.state_regression and self.time_varying_regression): if self.k_posdef > 0: selection = np.r_[ [0] * (self._k_states_diff), [1] * (self._k_order > 0), [0] * (self._k_order - 1), [0] * ((1 - self.mle_regression) * self._k_exog) ][:, None] if len(selection) == 0: selection = np.zeros((self.k_states, self.k_posdef)) else: selection = np.zeros((self.k_states, 0)) else: selection = np.zeros((self.k_states, self.k_posdef)) # Typical state variance if self._k_order > 0: selection[0, 0] = 1 # Time-varying regression coefficient variances for i in range(self._k_exog, 0, -1): selection[-i, -i] = 1 return selection def clone(self, endog, exog=None, **kwargs): return self._clone_from_init_kwds(endog, exog=exog, **kwargs) @property def _res_classes(self): return {'fit': (SARIMAXResults, SARIMAXResultsWrapper)} @staticmethod def _conditional_sum_squares(endog, k_ar, polynomial_ar, k_ma, polynomial_ma, k_trend=0, trend_data=None, warning_description=None): k = 2 * k_ma r = max(k + k_ma, k_ar) k_params_ar = 0 if k_ar == 0 else len(polynomial_ar.nonzero()[0]) - 1 k_params_ma = 0 if k_ma == 0 else len(polynomial_ma.nonzero()[0]) - 1 residuals = None if k_ar + k_ma + k_trend > 0: try: # If we have MA terms, get residuals from an AR(k) model to use # as data for conditional sum of squares estimates of the MA # parameters if k_ma > 0: Y = endog[k:] X = lagmat(endog, k, trim='both') params_ar = np.linalg.pinv(X).dot(Y) residuals = Y - np.dot(X, params_ar) # Run an ARMA(p,q) model using the just computed residuals as # data Y = endog[r:] X = np.empty((Y.shape[0], 0)) if k_trend > 0: if trend_data is None: raise ValueError('Trend data must be provided if' ' `k_trend` > 0.') X = np.c_[X, trend_data[:(-r if r > 0 else None), :]] if k_ar > 0: cols = polynomial_ar.nonzero()[0][1:] - 1 X = np.c_[X, lagmat(endog, k_ar)[r:, cols]] if k_ma > 0: cols = polynomial_ma.nonzero()[0][1:] - 1 X = np.c_[X, lagmat(residuals, k_ma)[r-k:, cols]] # Get the array of [ar_params, ma_params] params = np.linalg.pinv(X).dot(Y) residuals = Y - np.dot(X, params) except ValueError: if warning_description is not None: warning_description = ' for %s' % warning_description else: warning_description = '' warn('Too few observations to estimate starting parameters%s.' ' All parameters except for variances will be set to' ' zeros.' % warning_description) # Typically this will be raised if there are not enough # observations for the `lagmat` calls. params = np.zeros(k_trend + k_ar + k_ma, dtype=endog.dtype) if len(endog) == 0: # This case usually happens when there are not even enough # observations for a complete set of differencing # operations (no hope of fitting, just set starting # variance to 1) residuals = np.ones(k_params_ma * 2 + 1, dtype=endog.dtype) else: residuals = np.r_[ np.zeros(k_params_ma * 2, dtype=endog.dtype), endog - np.mean(endog)] # Default output params_trend = [] params_ar = [] params_ma = [] params_variance = [] # Get the params offset = 0 if k_trend > 0: params_trend = params[offset:k_trend + offset] offset += k_trend if k_ar > 0: params_ar = params[offset:k_params_ar + offset] offset += k_params_ar if k_ma > 0: params_ma = params[offset:k_params_ma + offset] offset += k_params_ma if residuals is not None: if len(residuals) > 1: params_variance = (residuals[k_params_ma:] ** 2).mean() else: params_variance = np.var(endog) return (params_trend, params_ar, params_ma, params_variance) @property def start_params(self): """ Starting parameters for maximum likelihood estimation """ # Perform differencing if necessary (i.e. if simple differencing is # false so that the state-space model will use the entire dataset) trend_data = self._trend_data if not self.simple_differencing and ( self._k_diff > 0 or self._k_seasonal_diff > 0): endog = diff(self.endog, self._k_diff, self._k_seasonal_diff, self.seasonal_periods) if self.exog is not None: exog = diff(self.exog, self._k_diff, self._k_seasonal_diff, self.seasonal_periods) else: exog = None trend_data = trend_data[:endog.shape[0], :] else: endog = self.endog.copy() exog = self.exog.copy() if self.exog is not None else None endog = endog.squeeze() # Although the Kalman filter can deal with missing values in endog, # conditional sum of squares cannot if np.any(np.isnan(endog)): mask = ~np.isnan(endog).squeeze() endog = endog[mask] if exog is not None: exog = exog[mask] if trend_data is not None: trend_data = trend_data[mask] # Regression effects via OLS params_exog = [] if self._k_exog > 0: params_exog = np.linalg.pinv(exog).dot(endog) endog = endog - np.dot(exog, params_exog) if self.state_regression: params_exog = [] # Non-seasonal ARMA component and trend (params_trend, params_ar, params_ma, params_variance) = self._conditional_sum_squares( endog, self.k_ar, self.polynomial_ar, self.k_ma, self.polynomial_ma, self._k_trend, trend_data, warning_description='ARMA and trend') # If we have estimated non-stationary start parameters but enforce # stationarity is on, start with 0 parameters and warn invalid_ar = ( self.k_ar > 0 and self.enforce_stationarity and not is_invertible(np.r_[1, -params_ar]) ) if invalid_ar: warn('Non-stationary starting autoregressive parameters' ' found. Using zeros as starting parameters.') params_ar *= 0 # If we have estimated non-invertible start parameters but enforce # invertibility is on, raise an error invalid_ma = ( self.k_ma > 0 and self.enforce_invertibility and not is_invertible(np.r_[1, params_ma]) ) if invalid_ma: warn('Non-invertible starting MA parameters found.' ' Using zeros as starting parameters.') params_ma *= 0 # Seasonal Parameters _, params_seasonal_ar, params_seasonal_ma, params_seasonal_variance = ( self._conditional_sum_squares( endog, self.k_seasonal_ar, self.polynomial_seasonal_ar, self.k_seasonal_ma, self.polynomial_seasonal_ma, warning_description='seasonal ARMA')) # If we have estimated non-stationary start parameters but enforce # stationarity is on, warn and set start params to 0 invalid_seasonal_ar = ( self.k_seasonal_ar > 0 and self.enforce_stationarity and not is_invertible(np.r_[1, -params_seasonal_ar]) ) if invalid_seasonal_ar: warn('Non-stationary starting seasonal autoregressive' ' Using zeros as starting parameters.') params_seasonal_ar *= 0 # If we have estimated non-invertible start parameters but enforce # invertibility is on, raise an error invalid_seasonal_ma = ( self.k_seasonal_ma > 0 and self.enforce_invertibility and not is_invertible(np.r_[1, params_seasonal_ma]) ) if invalid_seasonal_ma: warn('Non-invertible starting seasonal moving average' ' Using zeros as starting parameters.') params_seasonal_ma *= 0 # Variances params_exog_variance = [] if self.state_regression and self.time_varying_regression: # TODO how to set the initial variance parameters? params_exog_variance = [1] * self._k_exog if (self.state_error and type(params_variance) == list and len(params_variance) == 0): if not (type(params_seasonal_variance) == list and len(params_seasonal_variance) == 0): params_variance = params_seasonal_variance elif self._k_exog > 0: params_variance = np.inner(endog, endog) else: params_variance = np.inner(endog, endog) / self.nobs params_measurement_variance = 1 if self.measurement_error else [] # We want to bound the starting variance away from zero params_variance = np.atleast_1d(max(np.array(params_variance), 1e-10)) # Remove state variance as parameter if scale is concentrated out if self.concentrate_scale: params_variance = [] # Combine all parameters return np.r_[ params_trend, params_exog, params_ar, params_ma, params_seasonal_ar, params_seasonal_ma, params_exog_variance, params_measurement_variance, params_variance ] @property def endog_names(self, latex=False): """Names of endogenous variables""" diff = '' if self.k_diff > 0: if self.k_diff == 1: diff = r'\Delta' if latex else 'D' else: diff = (r'\Delta^%d' if latex else 'D%d') % self.k_diff seasonal_diff = '' if self.k_seasonal_diff > 0: if self.k_seasonal_diff == 1: seasonal_diff = ((r'\Delta_%d' if latex else 'DS%d') % (self.seasonal_periods)) else: seasonal_diff = ((r'\Delta_%d^%d' if latex else 'D%dS%d') % (self.k_seasonal_diff, self.seasonal_periods)) endog_diff = self.simple_differencing if endog_diff and self.k_diff > 0 and self.k_seasonal_diff > 0: return (('%s%s %s' if latex else '%s.%s.%s') % (diff, seasonal_diff, self.data.ynames)) elif endog_diff and self.k_diff > 0: return (('%s %s' if latex else '%s.%s') % (diff, self.data.ynames)) elif endog_diff and self.k_seasonal_diff > 0: return (('%s %s' if latex else '%s.%s') % (seasonal_diff, self.data.ynames)) else: return self.data.ynames params_complete = [ 'trend', 'exog', 'ar', 'ma', 'seasonal_ar', 'seasonal_ma', 'exog_variance', 'measurement_variance', 'variance' ] @property def param_terms(self): """ List of parameters actually included in the model, in sorted order. TODO Make this an dict with slice or indices as the values. """ model_orders = self.model_orders # Get basic list from model orders params = [ order for order in self.params_complete if model_orders[order] > 0 ] # k_exog may be positive without associated parameters if it is in the # state vector if 'exog' in params and not self.mle_regression: params.remove('exog') return params @property def param_names(self): """ List of human readable parameter names (for parameters actually included in the model). """ params_sort_order = self.param_terms model_names = self.model_names return [ name for param in params_sort_order for name in model_names[param] ] @property def state_names(self): # TODO: we may be able to revisit these states to get somewhat more # informative names, but ultimately probably not much better. # TODO: alternatively, we may be able to get better for certain models, # like pure AR models. k_ar_states = self._k_order if not self.simple_differencing: k_ar_states += (self.seasonal_periods * self._k_seasonal_diff + self._k_diff) names = ['state.%d' % i for i in range(k_ar_states)] if self._k_exog > 0 and self.state_regression: names += ['beta.%s' % self.exog_names[i] for i in range(self._k_exog)] return names @property def model_orders(self): """ The orders of each of the polynomials in the model. """ return { 'trend': self._k_trend, 'exog': self._k_exog, 'ar': self.k_ar, 'ma': self.k_ma, 'seasonal_ar': self.k_seasonal_ar, 'seasonal_ma': self.k_seasonal_ma, 'reduced_ar': self.k_ar + self.k_seasonal_ar, 'reduced_ma': self.k_ma + self.k_seasonal_ma, 'exog_variance': self._k_exog if ( self.state_regression and self.time_varying_regression) else 0, 'measurement_variance': int(self.measurement_error), 'variance': int(self.state_error and not self.concentrate_scale), } @property def model_names(self): """ The plain text names of all possible model parameters. """ return self._get_model_names(latex=False) @property def model_latex_names(self): """ The latex names of all possible model parameters. """ return self._get_model_names(latex=True) def _get_model_names(self, latex=False): names = { 'trend': None, 'exog': None, 'ar': None, 'ma': None, 'seasonal_ar': None, 'seasonal_ma': None, 'reduced_ar': None, 'reduced_ma': None, 'exog_variance': None, 'measurement_variance': None, 'variance': None, } # Trend if self._k_trend > 0: trend_template = 't_%d' if latex else 'trend.%d' names['trend'] = [] for i in self.polynomial_trend.nonzero()[0]: if i == 0: names['trend'].append('intercept') elif i == 1: names['trend'].append('drift') else: names['trend'].append(trend_template % i) # Exogenous coefficients if self._k_exog > 0: names['exog'] = self.exog_names # Autoregressive if self.k_ar > 0: ar_template = '$\\phi_%d$' if latex else 'ar.L%d' names['ar'] = [] for i in self.polynomial_ar.nonzero()[0][1:]: names['ar'].append(ar_template % i) # Moving Average if self.k_ma > 0: ma_template = '$\\theta_%d$' if latex else 'ma.L%d' names['ma'] = [] for i in self.polynomial_ma.nonzero()[0][1:]: names['ma'].append(ma_template % i) # Seasonal Autoregressive if self.k_seasonal_ar > 0: seasonal_ar_template = ( '$\\tilde \\phi_%d$' if latex else 'ar.S.L%d' ) names['seasonal_ar'] = [] for i in self.polynomial_seasonal_ar.nonzero()[0][1:]: names['seasonal_ar'].append(seasonal_ar_template % i) # Seasonal Moving Average if self.k_seasonal_ma > 0: seasonal_ma_template = ( '$\\tilde \\theta_%d$' if latex else 'ma.S.L%d' ) names['seasonal_ma'] = [] for i in self.polynomial_seasonal_ma.nonzero()[0][1:]: names['seasonal_ma'].append(seasonal_ma_template % i) # Reduced Form Autoregressive if self.k_ar > 0 or self.k_seasonal_ar > 0: reduced_polynomial_ar = reduced_polynomial_ar = -np.polymul( self.polynomial_ar, self.polynomial_seasonal_ar ) ar_template = '$\\Phi_%d$' if latex else 'ar.R.L%d' names['reduced_ar'] = [] for i in reduced_polynomial_ar.nonzero()[0][1:]: names['reduced_ar'].append(ar_template % i) # Reduced Form Moving Average if self.k_ma > 0 or self.k_seasonal_ma > 0: reduced_polynomial_ma = np.polymul( self.polynomial_ma, self.polynomial_seasonal_ma ) ma_template = '$\\Theta_%d$' if latex else 'ma.R.L%d' names['reduced_ma'] = [] for i in reduced_polynomial_ma.nonzero()[0][1:]: names['reduced_ma'].append(ma_template % i) # Exogenous variances if self.state_regression and self.time_varying_regression: if not self.concentrate_scale: exog_var_template = ('$\\sigma_\\text{%s}^2$' if latex else 'var.%s') else: exog_var_template = ( '$\\sigma_\\text{%s}^2 / \\sigma_\\zeta^2$' if latex else 'snr.%s') names['exog_variance'] = [ exog_var_template % exog_name for exog_name in self.exog_names ] # Measurement error variance if self.measurement_error: if not self.concentrate_scale: meas_var_tpl = ( '$\\sigma_\\eta^2$' if latex else 'var.measurement_error') else: meas_var_tpl = ( '$\\sigma_\\eta^2 / \\sigma_\\zeta^2$' if latex else 'snr.measurement_error') names['measurement_variance'] = [meas_var_tpl] # State variance if self.state_error and not self.concentrate_scale: var_tpl = '$\\sigma_\\zeta^2$' if latex else 'sigma2' names['variance'] = [var_tpl] return names def transform_params(self, unconstrained): """ Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation. Used primarily to enforce stationarity of the autoregressive lag polynomial, invertibility of the moving average lag polynomial, and positive variance parameters. Parameters ---------- unconstrained : array_like Unconstrained parameters used by the optimizer. Returns ------- constrained : array_like Constrained parameters used in likelihood evaluation. Notes ----- If the lag polynomial has non-consecutive powers (so that the coefficient is zero on some element of the polynomial), then the constraint function is not onto the entire space of invertible polynomials, although it only excludes a very small portion very close to the invertibility boundary. """ unconstrained = np.array(unconstrained, ndmin=1) constrained = np.zeros(unconstrained.shape, unconstrained.dtype) start = end = 0 # Retain the trend parameters if self._k_trend > 0: end += self._k_trend constrained[start:end] = unconstrained[start:end] start += self._k_trend # Retain any MLE regression coefficients if self.mle_regression: end += self._k_exog constrained[start:end] = unconstrained[start:end] start += self._k_exog # Transform the AR parameters (phi) to be stationary if self.k_ar_params > 0: end += self.k_ar_params if self.enforce_stationarity: constrained[start:end] = ( constrain_stationary_univariate(unconstrained[start:end]) ) else: constrained[start:end] = unconstrained[start:end] start += self.k_ar_params # Transform the MA parameters (theta) to be invertible if self.k_ma_params > 0: end += self.k_ma_params if self.enforce_invertibility: constrained[start:end] = ( -constrain_stationary_univariate(unconstrained[start:end]) ) else: constrained[start:end] = unconstrained[start:end] start += self.k_ma_params # Transform the seasonal AR parameters (\tilde phi) to be stationary if self.k_seasonal_ar > 0: end += self.k_seasonal_ar_params if self.enforce_stationarity: constrained[start:end] = ( constrain_stationary_univariate(unconstrained[start:end]) ) else: constrained[start:end] = unconstrained[start:end] start += self.k_seasonal_ar_params # Transform the seasonal MA parameters (\tilde theta) to be invertible if self.k_seasonal_ma_params > 0: end += self.k_seasonal_ma_params if self.enforce_invertibility: constrained[start:end] = ( -constrain_stationary_univariate(unconstrained[start:end]) ) else: constrained[start:end] = unconstrained[start:end] start += self.k_seasonal_ma_params # Transform the standard deviation parameters to be positive if self.state_regression and self.time_varying_regression: end += self._k_exog constrained[start:end] = unconstrained[start:end]**2 start += self._k_exog if self.measurement_error: constrained[start] = unconstrained[start]**2 start += 1 end += 1 if self.state_error and not self.concentrate_scale: constrained[start] = unconstrained[start]**2 # start += 1 # end += 1 return constrained def untransform_params(self, constrained): """ Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer Used primarily to reverse enforcement of stationarity of the autoregressive lag polynomial and invertibility of the moving average lag polynomial. Parameters ---------- constrained : array_like Constrained parameters used in likelihood evaluation. Returns ------- constrained : array_like Unconstrained parameters used by the optimizer. Notes ----- If the lag polynomial has non-consecutive powers (so that the coefficient is zero on some element of the polynomial), then the constraint function is not onto the entire space of invertible polynomials, although it only excludes a very small portion very close to the invertibility boundary. """ constrained = np.array(constrained, ndmin=1) unconstrained = np.zeros(constrained.shape, constrained.dtype) start = end = 0 # Retain the trend parameters if self._k_trend > 0: end += self._k_trend unconstrained[start:end] = constrained[start:end] start += self._k_trend # Retain any MLE regression coefficients if self.mle_regression: end += self._k_exog unconstrained[start:end] = constrained[start:end] start += self._k_exog # Transform the AR parameters (phi) to be stationary if self.k_ar_params > 0: end += self.k_ar_params if self.enforce_stationarity: unconstrained[start:end] = ( unconstrain_stationary_univariate(constrained[start:end]) ) else: unconstrained[start:end] = constrained[start:end] start += self.k_ar_params # Transform the MA parameters (theta) to be invertible if self.k_ma_params > 0: end += self.k_ma_params if self.enforce_invertibility: unconstrained[start:end] = ( unconstrain_stationary_univariate(-constrained[start:end]) ) else: unconstrained[start:end] = constrained[start:end] start += self.k_ma_params # Transform the seasonal AR parameters (\tilde phi) to be stationary if self.k_seasonal_ar > 0: end += self.k_seasonal_ar_params if self.enforce_stationarity: unconstrained[start:end] = ( unconstrain_stationary_univariate(constrained[start:end]) ) else: unconstrained[start:end] = constrained[start:end] start += self.k_seasonal_ar_params # Transform the seasonal MA parameters (\tilde theta) to be invertible if self.k_seasonal_ma_params > 0: end += self.k_seasonal_ma_params if self.enforce_invertibility: unconstrained[start:end] = ( unconstrain_stationary_univariate(-constrained[start:end]) ) else: unconstrained[start:end] = constrained[start:end] start += self.k_seasonal_ma_params # Untransform the standard deviation if self.state_regression and self.time_varying_regression: end += self._k_exog unconstrained[start:end] = constrained[start:end]**0.5 start += self._k_exog if self.measurement_error: unconstrained[start] = constrained[start]**0.5 start += 1 end += 1 if self.state_error and not self.concentrate_scale: unconstrained[start] = constrained[start]**0.5 # start += 1 # end += 1 return unconstrained def _validate_can_fix_params(self, param_names): super(SARIMAX, self)._validate_can_fix_params(param_names) model_names = self.model_names items = [ ('ar', 'autoregressive', self.enforce_stationarity, '`enforce_stationarity=True`'), ('seasonal_ar', 'seasonal autoregressive', self.enforce_stationarity, '`enforce_stationarity=True`'), ('ma', 'moving average', self.enforce_invertibility, '`enforce_invertibility=True`'), ('seasonal_ma', 'seasonal moving average', self.enforce_invertibility, '`enforce_invertibility=True`')] for name, title, condition, condition_desc in items: names = set(model_names[name] or []) fix_all = param_names.issuperset(names) fix_any = len(param_names.intersection(names)) > 0 if condition and fix_any and not fix_all: raise ValueError('Cannot fix individual %s parameters when' ' %s. Must either fix all %s parameters or' ' none.' % (title, condition_desc, title)) def update(self, params, transformed=True, includes_fixed=False, complex_step=False): """ Update the parameters of the model Updates the representation matrices to fill in the new parameter values. Parameters ---------- params : array_like Array of new parameters. transformed : bool, optional Whether or not `params` is already transformed. If set to False, `transform_params` is called. Default is True.. Returns ------- params : array_like Array of parameters. """ params = self.handle_params(params, transformed=transformed, includes_fixed=includes_fixed) params_trend = None params_exog = None params_ar = None params_ma = None params_seasonal_ar = None params_seasonal_ma = None params_exog_variance = None params_measurement_variance = None params_variance = None # Extract the parameters start = end = 0 end += self._k_trend params_trend = params[start:end] start += self._k_trend if self.mle_regression: end += self._k_exog params_exog = params[start:end] start += self._k_exog end += self.k_ar_params params_ar = params[start:end] start += self.k_ar_params end += self.k_ma_params params_ma = params[start:end] start += self.k_ma_params end += self.k_seasonal_ar_params params_seasonal_ar = params[start:end] start += self.k_seasonal_ar_params end += self.k_seasonal_ma_params params_seasonal_ma = params[start:end] start += self.k_seasonal_ma_params if self.state_regression and self.time_varying_regression: end += self._k_exog params_exog_variance = params[start:end] start += self._k_exog if self.measurement_error: params_measurement_variance = params[start] start += 1 end += 1 if self.state_error and not self.concentrate_scale: params_variance = params[start] # start += 1 # end += 1 # Update lag polynomials if self.k_ar > 0: if self._polynomial_ar.dtype == params.dtype: self._polynomial_ar[self._polynomial_ar_idx] = -params_ar else: polynomial_ar = self._polynomial_ar.real.astype(params.dtype) polynomial_ar[self._polynomial_ar_idx] = -params_ar self._polynomial_ar = polynomial_ar if self.k_ma > 0: if self._polynomial_ma.dtype == params.dtype: self._polynomial_ma[self._polynomial_ma_idx] = params_ma else: polynomial_ma = self._polynomial_ma.real.astype(params.dtype) polynomial_ma[self._polynomial_ma_idx] = params_ma self._polynomial_ma = polynomial_ma if self.k_seasonal_ar > 0: idx = self._polynomial_seasonal_ar_idx if self._polynomial_seasonal_ar.dtype == params.dtype: self._polynomial_seasonal_ar[idx] = -params_seasonal_ar else: polynomial_seasonal_ar = ( self._polynomial_seasonal_ar.real.astype(params.dtype) ) polynomial_seasonal_ar[idx] = -params_seasonal_ar self._polynomial_seasonal_ar = polynomial_seasonal_ar if self.k_seasonal_ma > 0: idx = self._polynomial_seasonal_ma_idx if self._polynomial_seasonal_ma.dtype == params.dtype: self._polynomial_seasonal_ma[idx] = params_seasonal_ma else: polynomial_seasonal_ma = ( self._polynomial_seasonal_ma.real.astype(params.dtype) ) polynomial_seasonal_ma[idx] = params_seasonal_ma self._polynomial_seasonal_ma = polynomial_seasonal_ma # Get the reduced form lag polynomial terms by multiplying the regular # and seasonal lag polynomials # Note: that although the numpy np.polymul examples assume that they # are ordered from highest degree to lowest, whereas our are from # lowest to highest, it does not matter. if self.k_seasonal_ar > 0: reduced_polynomial_ar = -np.polymul( self._polynomial_ar, self._polynomial_seasonal_ar ) else: reduced_polynomial_ar = -self._polynomial_ar if self.k_seasonal_ma > 0: reduced_polynomial_ma = np.polymul( self._polynomial_ma, self._polynomial_seasonal_ma ) else: reduced_polynomial_ma = self._polynomial_ma # Observation intercept # Exogenous data with MLE estimation of parameters enters through a # time-varying observation intercept (is equivalent to simply # subtracting it out of the endogenous variable first) if self.mle_regression: self.ssm['obs_intercept'] = np.dot(self.exog, params_exog)[None, :] # State intercept (Harvey) or additional observation intercept # (Hamilton) # SARIMA trend enters through the a time-varying state intercept, # associated with the first row of the stationary component of the # state vector (i.e. the first element of the state vector following # any differencing elements) if self._k_trend > 0: data = np.dot(self._trend_data, params_trend).astype(params.dtype) if not self.hamilton_representation: self.ssm['state_intercept', self._k_states_diff, :] = data else: # The way the trend enters in the Hamilton representation means # that the parameter is not an ``intercept'' but instead the # mean of the process. The trend values in `data` are meant for # an intercept, and so must be transformed to represent the # mean instead if self.hamilton_representation: data /= np.sum(-reduced_polynomial_ar) # If we already set the observation intercept for MLE # regression, just add to it if self.mle_regression: self.ssm.obs_intercept += data[None, :] # Otherwise set it directly else: self.ssm['obs_intercept'] = data[None, :] # Observation covariance matrix if self.measurement_error: self.ssm['obs_cov', 0, 0] = params_measurement_variance # Transition matrix if self.k_ar > 0 or self.k_seasonal_ar > 0: self.ssm[self.transition_ar_params_idx] = reduced_polynomial_ar[1:] elif not self.ssm.transition.dtype == params.dtype: # This is required if the transition matrix is not really in use # (e.g. for an MA(q) process) so that it's dtype never changes as # the parameters' dtype changes. This changes the dtype manually. self.ssm['transition'] = self.ssm['transition'].real.astype( params.dtype) # Selection matrix (Harvey) or Design matrix (Hamilton) if self.k_ma > 0 or self.k_seasonal_ma > 0: if not self.hamilton_representation: self.ssm[self.selection_ma_params_idx] = ( reduced_polynomial_ma[1:] ) else: self.ssm[self.design_ma_params_idx] = reduced_polynomial_ma[1:] # State covariance matrix if self.k_posdef > 0: if not self.concentrate_scale: self['state_cov', 0, 0] = params_variance if self.state_regression and self.time_varying_regression: self.ssm[self._exog_variance_idx] = params_exog_variance return params def _get_extension_time_varying_matrices( self, params, exog, out_of_sample, extend_kwargs=None, transformed=True, includes_fixed=False, **kwargs): """ Get time-varying state space system matrices for extended model Notes ----- We need to override this method for SARIMAX because we need some special handling in the `simple_differencing=True` case. """ # Get the appropriate exog for the extended sample exog = self._validate_out_of_sample_exog(exog, out_of_sample) # Get the tmp endog, exog if self.simple_differencing: nobs = self.data.orig_endog.shape[0] + out_of_sample tmp_endog = np.zeros((nobs, self.k_endog)) if exog is not None: tmp_exog = np.c_[self.data.orig_exog.T, exog.T].T else: tmp_exog = None else: tmp_endog = np.zeros((out_of_sample, self.k_endog)) tmp_exog = exog # Create extended model if extend_kwargs is None: extend_kwargs = {} if not self.simple_differencing and self.k_trend > 0: extend_kwargs.setdefault( 'trend_offset', self.trend_offset + self.nobs) extend_kwargs.setdefault('validate_specification', False) mod_extend = self.clone( endog=tmp_endog, exog=tmp_exog, **extend_kwargs) mod_extend.update(params, transformed=transformed, includes_fixed=includes_fixed,) # Retrieve the extensions to the time-varying system matrices # and put them in kwargs for name in self.ssm.shapes.keys(): if name == 'obs': continue if getattr(self.ssm, name).shape[-1] > 1: mat = getattr(mod_extend.ssm, name) kwargs[name] = mat[..., -out_of_sample:] return kwargs class SARIMAXResults(MLEResults): """ Class to hold results from fitting an SARIMAX model. Parameters ---------- model : SARIMAX instance The fitted model instance Attributes ---------- specification : dictionary Dictionary including all attributes from the SARIMAX model instance. polynomial_ar : ndarray Array containing autoregressive lag polynomial coefficients, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). polynomial_ma : ndarray Array containing moving average lag polynomial coefficients, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). polynomial_seasonal_ar : ndarray Array containing seasonal autoregressive lag polynomial coefficients, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). polynomial_seasonal_ma : ndarray Array containing seasonal moving average lag polynomial coefficients, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). polynomial_trend : ndarray Array containing trend polynomial coefficients, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). model_orders : list of int The orders of each of the polynomials in the model. param_terms : list of str List of parameters actually included in the model, in sorted order. See Also -------- statsmodels.tsa.statespace.kalman_filter.FilterResults statsmodels.tsa.statespace.mlemodel.MLEResults """ def __init__(self, model, params, filter_results, cov_type=None, **kwargs): super(SARIMAXResults, self).__init__(model, params, filter_results, cov_type, **kwargs) self.df_resid = np.inf # attribute required for wald tests # Save _init_kwds self._init_kwds = self.model._get_init_kwds() # Save model specification self.specification = Bunch(**{ # Set additional model parameters 'seasonal_periods': self.model.seasonal_periods, 'measurement_error': self.model.measurement_error, 'time_varying_regression': self.model.time_varying_regression, 'simple_differencing': self.model.simple_differencing, 'enforce_stationarity': self.model.enforce_stationarity, 'enforce_invertibility': self.model.enforce_invertibility, 'hamilton_representation': self.model.hamilton_representation, 'concentrate_scale': self.model.concentrate_scale, 'trend_offset': self.model.trend_offset, 'order': self.model.order, 'seasonal_order': self.model.seasonal_order, # Model order 'k_diff': self.model.k_diff, 'k_seasonal_diff': self.model.k_seasonal_diff, 'k_ar': self.model.k_ar, 'k_ma': self.model.k_ma, 'k_seasonal_ar': self.model.k_seasonal_ar, 'k_seasonal_ma': self.model.k_seasonal_ma, # Param Numbers 'k_ar_params': self.model.k_ar_params, 'k_ma_params': self.model.k_ma_params, # Trend / Regression 'trend': self.model.trend, 'k_trend': self.model.k_trend, 'k_exog': self.model.k_exog, 'mle_regression': self.model.mle_regression, 'state_regression': self.model.state_regression, }) # Polynomials self.polynomial_trend = self.model._polynomial_trend self.polynomial_ar = self.model._polynomial_ar self.polynomial_ma = self.model._polynomial_ma self.polynomial_seasonal_ar = self.model._polynomial_seasonal_ar self.polynomial_seasonal_ma = self.model._polynomial_seasonal_ma self.polynomial_reduced_ar = np.polymul( self.polynomial_ar, self.polynomial_seasonal_ar ) self.polynomial_reduced_ma = np.polymul( self.polynomial_ma, self.polynomial_seasonal_ma ) # Distinguish parameters self.model_orders = self.model.model_orders self.param_terms = self.model.param_terms start = end = 0 for name in self.param_terms: if name == 'ar': k = self.model.k_ar_params elif name == 'ma': k = self.model.k_ma_params elif name == 'seasonal_ar': k = self.model.k_seasonal_ar_params elif name == 'seasonal_ma': k = self.model.k_seasonal_ma_params else: k = self.model_orders[name] end += k setattr(self, '_params_%s' % name, self.params[start:end]) start += k # Handle removing data self._data_attr_model.extend(['orig_endog', 'orig_exog']) def extend(self, endog, exog=None, **kwargs): kwargs.setdefault('trend_offset', self.nobs + 1) return super(SARIMAXResults, self).extend(endog, exog=exog, **kwargs) @cache_readonly def arroots(self): """ (array) Roots of the reduced form autoregressive lag polynomial """ return np.roots(self.polynomial_reduced_ar)**-1 @cache_readonly def maroots(self): """ (array) Roots of the reduced form moving average lag polynomial """ return np.roots(self.polynomial_reduced_ma)**-1 @cache_readonly def arfreq(self): """ (array) Frequency of the roots of the reduced form autoregressive lag polynomial """ z = self.arroots if not z.size: return return np.arctan2(z.imag, z.real) / (2 * np.pi) @cache_readonly def mafreq(self): """ (array) Frequency of the roots of the reduced form moving average lag polynomial """ z = self.maroots if not z.size: return return np.arctan2(z.imag, z.real) / (2 * np.pi) @cache_readonly def arparams(self): """ (array) Autoregressive parameters actually estimated in the model. Does not include seasonal autoregressive parameters (see `seasonalarparams`) or parameters whose values are constrained to be zero. """ return self._params_ar @cache_readonly def seasonalarparams(self): """ (array) Seasonal autoregressive parameters actually estimated in the model. Does not include nonseasonal autoregressive parameters (see `arparams`) or parameters whose values are constrained to be zero. """ return self._params_seasonal_ar @cache_readonly def maparams(self): """ (array) Moving average parameters actually estimated in the model. Does not include seasonal moving average parameters (see `seasonalmaparams`) or parameters whose values are constrained to be zero. """ return self._params_ma @cache_readonly def seasonalmaparams(self): """ (array) Seasonal moving average parameters actually estimated in the model. Does not include nonseasonal moving average parameters (see `maparams`) or parameters whose values are constrained to be zero. """ return self._params_seasonal_ma @Appender(MLEResults.summary.__doc__) def summary(self, alpha=.05, start=None): # Create the model name # See if we have an ARIMA component order = '' if self.model.k_ar + self.model.k_diff + self.model.k_ma > 0: if self.model.k_ar == self.model.k_ar_params: order_ar = self.model.k_ar else: order_ar = list(self.model._spec.ar_lags) if self.model.k_ma == self.model.k_ma_params: order_ma = self.model.k_ma else: order_ma = list(self.model._spec.ma_lags) # If there is simple differencing, then that is reflected in the # dependent variable name k_diff = 0 if self.model.simple_differencing else self.model.k_diff order = '(%s, %d, %s)' % (order_ar, k_diff, order_ma) # See if we have an SARIMA component seasonal_order = '' has_seasonal = ( self.model.k_seasonal_ar + self.model.k_seasonal_diff + self.model.k_seasonal_ma ) > 0 if has_seasonal: tmp = int(self.model.k_seasonal_ar / self.model.seasonal_periods) if tmp == self.model.k_seasonal_ar_params: order_seasonal_ar = ( int(self.model.k_seasonal_ar / self.model.seasonal_periods) ) else: order_seasonal_ar = list(self.model._spec.seasonal_ar_lags) tmp = int(self.model.k_seasonal_ma / self.model.seasonal_periods) if tmp == self.model.k_ma_params: order_seasonal_ma = tmp else: order_seasonal_ma = list(self.model._spec.seasonal_ma_lags) # If there is simple differencing, then that is reflected in the # dependent variable name k_seasonal_diff = self.model.k_seasonal_diff if self.model.simple_differencing: k_seasonal_diff = 0 seasonal_order = ('(%s, %d, %s, %d)' % (str(order_seasonal_ar), k_seasonal_diff, str(order_seasonal_ma), self.model.seasonal_periods)) if not order == '': order += 'x' model_name = ( '%s%s%s' % (self.model.__class__.__name__, order, seasonal_order) ) return super(SARIMAXResults, self).summary( alpha=alpha, start=start, title='SARIMAX Results', model_name=model_name ) class SARIMAXResultsWrapper(MLEResultsWrapper): _attrs = {} _wrap_attrs = wrap.union_dicts(MLEResultsWrapper._wrap_attrs, _attrs) _methods = {} _wrap_methods = wrap.union_dicts(MLEResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(SARIMAXResultsWrapper, SARIMAXResults) # noqa:E305 statsmodels-0.12.2/statsmodels/tsa/statespace/simulation_smoother.py000066400000000000000000000552121400612667500261150ustar00rootroot00000000000000""" State Space Representation, Kalman Filter, Smoother, and Simulation Smoother Author: Chad Fulton License: Simplified-BSD """ import numpy as np from .kalman_smoother import KalmanSmoother from .cfa_simulation_smoother import CFASimulationSmoother from . import tools SIMULATION_STATE = 0x01 SIMULATION_DISTURBANCE = 0x04 SIMULATION_ALL = ( SIMULATION_STATE | SIMULATION_DISTURBANCE ) class SimulationSmoother(KalmanSmoother): r""" State space representation of a time series process, with Kalman filter and smoother, and with simulation smoother. Parameters ---------- k_endog : {array_like, int} The observed time-series process :math:`y` if array like or the number of variables in the process if an integer. k_states : int The dimension of the unobserved state process. k_posdef : int, optional The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation. Must be less than or equal to `k_states`. Default is `k_states`. simulation_smooth_results_class : class, optional Default results class to use to save output of simulation smoothing. Default is `SimulationSmoothResults`. If specified, class must extend from `SimulationSmoothResults`. simulation_smoother_classes : dict, optional Dictionary with BLAS prefixes as keys and classes as values. **kwargs Keyword arguments may be used to provide default values for state space matrices, for Kalman filtering options, for Kalman smoothing options, or for Simulation smoothing options. See `Representation`, `KalmanFilter`, and `KalmanSmoother` for more details. """ simulation_outputs = [ 'simulate_state', 'simulate_disturbance', 'simulate_all' ] def __init__(self, k_endog, k_states, k_posdef=None, simulation_smooth_results_class=None, simulation_smoother_classes=None, **kwargs): super(SimulationSmoother, self).__init__( k_endog, k_states, k_posdef, **kwargs ) if simulation_smooth_results_class is None: simulation_smooth_results_class = SimulationSmoothResults self.simulation_smooth_results_class = simulation_smooth_results_class self.prefix_simulation_smoother_map = ( simulation_smoother_classes if simulation_smoother_classes is not None else tools.prefix_simulation_smoother_map.copy()) # Holder for an model-level simulation smoother objects, to use in # simulating new time series. self._simulators = {} def get_simulation_output(self, simulation_output=None, simulate_state=None, simulate_disturbance=None, simulate_all=None, **kwargs): r""" Get simulation output bitmask Helper method to get final simulation output bitmask from a set of optional arguments including the bitmask itself and possibly boolean flags. Parameters ---------- simulation_output : int, optional Simulation output bitmask. If this is specified, it is simply returned and the other arguments are ignored. simulate_state : bool, optional Whether or not to include the state in the simulation output. simulate_disturbance : bool, optional Whether or not to include the state and observation disturbances in the simulation output. simulate_all : bool, optional Whether or not to include all simulation output. \*\*kwargs Additional keyword arguments. Present so that calls to this method can use \*\*kwargs without clearing out additional arguments. """ # If we do not explicitly have simulation_output, try to get it from # kwargs if simulation_output is None: simulation_output = 0 if simulate_state: simulation_output |= SIMULATION_STATE if simulate_disturbance: simulation_output |= SIMULATION_DISTURBANCE if simulate_all: simulation_output |= SIMULATION_ALL # Handle case of no information in kwargs if simulation_output == 0: # If some arguments were passed, but we still do not have any # simulation output, raise an exception argument_set = not all([ simulate_state is None, simulate_disturbance is None, simulate_all is None ]) if argument_set: raise ValueError("Invalid simulation output options:" " given options would result in no" " output.") # Otherwise set simulation output to be the same as smoother # output simulation_output = self.smoother_output return simulation_output def _simulate(self, nsimulations, measurement_shocks, state_shocks, initial_state): # Initialize the filter and representation prefix, dtype, create_smoother, create_filter, create_statespace = ( self._initialize_smoother()) # Initialize the state self._initialize_state(prefix=prefix) # Create the simulator if necessary if (prefix not in self._simulators or not nsimulations == self._simulators[prefix].nobs): simulation_output = 0 # Kalman smoother parameters smoother_output = -1 # Kalman filter parameters filter_method = self.filter_method inversion_method = self.inversion_method stability_method = self.stability_method conserve_memory = self.conserve_memory filter_timing = self.filter_timing loglikelihood_burn = self.loglikelihood_burn tolerance = self.tolerance # Create a new simulation smoother object cls = self.prefix_simulation_smoother_map[prefix] self._simulators[prefix] = cls( self._statespaces[prefix], filter_method, inversion_method, stability_method, conserve_memory, filter_timing, tolerance, loglikelihood_burn, smoother_output, simulation_output, nsimulations ) simulator = self._simulators[prefix] # Set the disturbance variates if measurement_shocks is not None and state_shocks is not None: disturbance_variates = np.atleast_1d(np.array( np.r_[measurement_shocks.ravel(), state_shocks.ravel()], dtype=self.dtype ).squeeze()) simulator.set_disturbance_variates(disturbance_variates, pretransformed=True) elif measurement_shocks is None and state_shocks is None: pass elif measurement_shocks is not None: raise ValueError('Must set `state_shocks` if `measurement_shocks`' ' is set.') elif state_shocks is not None: raise ValueError('Must set `measurement_shocks` if `state_shocks`' ' is set.') # Set the intial state vector initial_state = np.atleast_1d(np.array( initial_state, dtype=self.dtype ).squeeze()) simulator.set_initial_state(initial_state) # Perform simulation smoothing # Note: simulation_output=-1 corresponds to whatever was setup when # the simulation smoother was constructed simulator.simulate(-1) simulated_obs = np.array(simulator.generated_obs, copy=True) simulated_state = np.array(simulator.generated_state, copy=True) return ( simulated_obs[:, :nsimulations].T, simulated_state[:, :nsimulations].T ) def simulation_smoother(self, simulation_output=None, method='kfs', results_class=None, prefix=None, **kwargs): r""" Retrieve a simulation smoother for the statespace model. Parameters ---------- simulation_output : int, optional Determines which simulation smoother output is calculated. Default is all (including state and disturbances). method : {'kfs', 'cfa'}, optional Method for simulation smoothing. If `method='kfs'`, then the simulation smoother is based on Kalman filtering and smoothing recursions. If `method='cfa'`, then the simulation smoother is based on the Cholesky Factor Algorithm (CFA) approach. The CFA approach is not applicable to all state space models, but can be faster for the cases in which it is supported. simulation_smooth_results_class : class, optional Default results class to use to save output of simulation smoothing. Default is `SimulationSmoothResults`. If specified, class must extend from `SimulationSmoothResults`. prefix : str The prefix of the datatype. Usually only used internally. **kwargs Additional keyword arguments, used to set the simulation output. See `set_simulation_output` for more details. Returns ------- SimulationSmoothResults """ method = method.lower() # Short-circuit for CFA if method == 'cfa': if simulation_output not in [None, 1, -1]: raise ValueError('Can only retrieve simulations of the state' ' vector using the CFA simulation smoother.') return CFASimulationSmoother(self) elif method != 'kfs': raise ValueError('Invalid simulation smoother method "%s". Valid' ' methods are "kfs" or "cfa".' % method) # Set the class to be the default results class, if None provided if results_class is None: results_class = self.simulation_smooth_results_class # Instantiate a new results object if not issubclass(results_class, SimulationSmoothResults): raise ValueError('Invalid results class provided.') # Make sure we have the required Statespace representation prefix, dtype, create_smoother, create_filter, create_statespace = ( self._initialize_smoother()) # Simulation smoother parameters simulation_output = self.get_simulation_output(simulation_output, **kwargs) # Kalman smoother parameters smoother_output = kwargs.get('smoother_output', simulation_output) # Kalman filter parameters filter_method = kwargs.get('filter_method', self.filter_method) inversion_method = kwargs.get('inversion_method', self.inversion_method) stability_method = kwargs.get('stability_method', self.stability_method) conserve_memory = kwargs.get('conserve_memory', self.conserve_memory) filter_timing = kwargs.get('filter_timing', self.filter_timing) loglikelihood_burn = kwargs.get('loglikelihood_burn', self.loglikelihood_burn) tolerance = kwargs.get('tolerance', self.tolerance) # Create a new simulation smoother object cls = self.prefix_simulation_smoother_map[prefix] simulation_smoother = cls( self._statespaces[prefix], filter_method, inversion_method, stability_method, conserve_memory, filter_timing, tolerance, loglikelihood_burn, smoother_output, simulation_output ) # Create results object results = results_class(self, simulation_smoother) return results class SimulationSmoothResults(object): r""" Results from applying the Kalman smoother and/or filter to a state space model. Parameters ---------- model : Representation A Statespace representation simulation_smoother : {{prefix}}SimulationSmoother object The Cython simulation smoother object with which to simulation smooth. Attributes ---------- model : Representation A Statespace representation dtype : dtype Datatype of representation matrices prefix : str BLAS prefix of representation matrices simulation_output : int Bitmask controlling simulation output. simulate_state : bool Flag for if the state is included in simulation output. simulate_disturbance : bool Flag for if the state and observation disturbances are included in simulation output. simulate_all : bool Flag for if simulation output should include everything. generated_measurement_disturbance : ndarray Measurement disturbance variates used to genereate the observation vector. generated_state_disturbance : ndarray State disturbance variates used to genereate the state and observation vectors. generated_obs : ndarray Generated observation vector produced as a byproduct of simulation smoothing. generated_state : ndarray Generated state vector produced as a byproduct of simulation smoothing. simulated_state : ndarray Simulated state. simulated_measurement_disturbance : ndarray Simulated measurement disturbance. simulated_state_disturbance : ndarray Simulated state disturbance. """ def __init__(self, model, simulation_smoother): self.model = model self.prefix = model.prefix self.dtype = model.dtype self._simulation_smoother = simulation_smoother # Output self._generated_measurement_disturbance = None self._generated_state_disturbance = None self._generated_obs = None self._generated_state = None self._simulated_state = None self._simulated_measurement_disturbance = None self._simulated_state_disturbance = None @property def simulation_output(self): return self._simulation_smoother.simulation_output @simulation_output.setter def simulation_output(self, value): self._simulation_smoother.simulation_output = value @property def simulate_state(self): return bool(self.simulation_output & SIMULATION_STATE) @simulate_state.setter def simulate_state(self, value): if bool(value): self.simulation_output = self.simulation_output | SIMULATION_STATE else: self.simulation_output = self.simulation_output & ~SIMULATION_STATE @property def simulate_disturbance(self): return bool(self.simulation_output & SIMULATION_DISTURBANCE) @simulate_disturbance.setter def simulate_disturbance(self, value): if bool(value): self.simulation_output = ( self.simulation_output | SIMULATION_DISTURBANCE) else: self.simulation_output = ( self.simulation_output & ~SIMULATION_DISTURBANCE) @property def simulate_all(self): return bool(self.simulation_output & SIMULATION_ALL) @simulate_all.setter def simulate_all(self, value): if bool(value): self.simulation_output = self.simulation_output | SIMULATION_ALL else: self.simulation_output = self.simulation_output & ~SIMULATION_ALL @property def generated_measurement_disturbance(self): r""" Randomly drawn measurement disturbance variates Used to construct `generated_obs`. Notes ----- .. math:: \varepsilon_t^+ ~ N(0, H_t) If `disturbance_variates` were provided to the `simulate()` method, then this returns those variates (which were N(0,1)) transformed to the distribution above. """ if self._generated_measurement_disturbance is None: end = self.model.nobs * self.model.k_endog self._generated_measurement_disturbance = np.array( self._simulation_smoother.disturbance_variates[:end], copy=True).reshape(self.model.nobs, self.model.k_endog) return self._generated_measurement_disturbance @property def generated_state_disturbance(self): r""" Randomly drawn state disturbance variates, used to construct `generated_state` and `generated_obs`. Notes ----- .. math:: \eta_t^+ ~ N(0, Q_t) If `disturbance_variates` were provided to the `simulate()` method, then this returns those variates (which were N(0,1)) transformed to the distribution above. """ if self._generated_state_disturbance is None: start = self.model.nobs * self.model.k_endog self._generated_state_disturbance = np.array( self._simulation_smoother.disturbance_variates[start:], copy=True).reshape(self.model.nobs, self.model.k_posdef) return self._generated_state_disturbance @property def generated_obs(self): r""" Generated vector of observations by iterating on the observation and transition equations, given a random initial state draw and random disturbance draws. Notes ----- .. math:: y_t^+ = d_t + Z_t \alpha_t^+ + \varepsilon_t^+ """ if self._generated_obs is None: self._generated_obs = np.array( self._simulation_smoother.generated_obs, copy=True ) return self._generated_obs @property def generated_state(self): r""" Generated vector of states by iterating on the transition equation, given a random initial state draw and random disturbance draws. Notes ----- .. math:: \alpha_{t+1}^+ = c_t + T_t \alpha_t^+ + \eta_t^+ """ if self._generated_state is None: self._generated_state = np.array( self._simulation_smoother.generated_state, copy=True ) return self._generated_state @property def simulated_state(self): r""" Random draw of the state vector from its conditional distribution. Notes ----- .. math:: \alpha ~ p(\alpha \mid Y_n) """ if self._simulated_state is None: self._simulated_state = np.array( self._simulation_smoother.simulated_state, copy=True ) return self._simulated_state @property def simulated_measurement_disturbance(self): r""" Random draw of the measurement disturbance vector from its conditional distribution. Notes ----- .. math:: \varepsilon ~ N(\hat \varepsilon, Var(\hat \varepsilon \mid Y_n)) """ if self._simulated_measurement_disturbance is None: self._simulated_measurement_disturbance = np.array( self._simulation_smoother.simulated_measurement_disturbance, copy=True ) return self._simulated_measurement_disturbance @property def simulated_state_disturbance(self): r""" Random draw of the state disturbance vector from its conditional distribution. Notes ----- .. math:: \eta ~ N(\hat \eta, Var(\hat \eta \mid Y_n)) """ if self._simulated_state_disturbance is None: self._simulated_state_disturbance = np.array( self._simulation_smoother.simulated_state_disturbance, copy=True ) return self._simulated_state_disturbance def simulate(self, simulation_output=-1, disturbance_variates=None, initial_state_variates=None, pretransformed_variates=False): r""" Perform simulation smoothing Does not return anything, but populates the object's `simulated_*` attributes, as specified by simulation output. Parameters ---------- simulation_output : int, optional Bitmask controlling simulation output. Default is to use the simulation output defined in object initialization. disturbance_variates : array_likes, optional Random values to use as disturbance variates, distributed standard Normal. Usually only specified if results are to be replicated (e.g. to enforce a seed) or for testing. If not specified, random variates are drawn. initial_state_variates : array_likes, optional Random values to use as initial state variates. Usually only specified if results are to be replicated (e.g. to enforce a seed) or for testing. If not specified, random variates are drawn. """ # Clear any previous output self._generated_measurement_disturbance = None self._generated_state_disturbance = None self._generated_state = None self._generated_obs = None self._generated_state = None self._simulated_state = None self._simulated_measurement_disturbance = None self._simulated_state_disturbance = None # Re-initialize the _statespace representation prefix, dtype, create_smoother, create_filter, create_statespace = ( self.model._initialize_smoother()) # Initialize the state self.model._initialize_state(prefix=prefix) # Draw the (independent) random variates for disturbances in the # simulation if disturbance_variates is not None: self._simulation_smoother.set_disturbance_variates( np.array(disturbance_variates, dtype=self.dtype), pretransformed=pretransformed_variates ) else: self._simulation_smoother.draw_disturbance_variates() # Draw the (independent) random variates for the initial states in the # simulation if initial_state_variates is not None: self._simulation_smoother.set_initial_state_variates( np.array(initial_state_variates, dtype=self.dtype), pretransformed=pretransformed_variates ) else: self._simulation_smoother.draw_initial_state_variates() # Perform simulation smoothing # Note: simulation_output=-1 corresponds to whatever was setup when # the simulation smoother was constructed self._simulation_smoother.simulate(simulation_output) statsmodels-0.12.2/statsmodels/tsa/statespace/structural.py000066400000000000000000002313131400612667500242170ustar00rootroot00000000000000""" Univariate structural time series models TODO: tests: "** On entry to DLASCL, parameter number 4 had an illegal value" Author: Chad Fulton License: Simplified-BSD """ from warnings import warn import numpy as np from statsmodels.compat.pandas import Appender from statsmodels.tools.tools import Bunch from statsmodels.tools.sm_exceptions import OutputWarning, SpecificationWarning import statsmodels.base.wrapper as wrap from statsmodels.tsa.filters.hp_filter import hpfilter from statsmodels.tsa.tsatools import lagmat from .mlemodel import MLEModel, MLEResults, MLEResultsWrapper from .initialization import Initialization from .tools import ( companion_matrix, constrain_stationary_univariate, unconstrain_stationary_univariate, prepare_exog) _mask_map = { 1: 'irregular', 2: 'fixed intercept', 3: 'deterministic constant', 6: 'random walk', 7: 'local level', 8: 'fixed slope', 11: 'deterministic trend', 14: 'random walk with drift', 15: 'local linear deterministic trend', 31: 'local linear trend', 27: 'smooth trend', 26: 'random trend' } class UnobservedComponents(MLEModel): r""" Univariate unobserved components time series model These are also known as structural time series models, and decompose a (univariate) time series into trend, seasonal, cyclical, and irregular components. Parameters ---------- level : {bool, str}, optional Whether or not to include a level component. Default is False. Can also be a string specification of the level / trend component; see Notes for available model specification strings. trend : bool, optional Whether or not to include a trend component. Default is False. If True, `level` must also be True. seasonal : {int, None}, optional The period of the seasonal component, if any. Default is None. freq_seasonal : {list[dict], None}, optional. Whether (and how) to model seasonal component(s) with trig. functions. If specified, there is one dictionary for each frequency-domain seasonal component. Each dictionary must have the key, value pair for 'period' -- integer and may have a key, value pair for 'harmonics' -- integer. If 'harmonics' is not specified in any of the dictionaries, it defaults to the floor of period/2. cycle : bool, optional Whether or not to include a cycle component. Default is False. autoregressive : {int, None}, optional The order of the autoregressive component. Default is None. exog : {array_like, None}, optional Exogenous variables. irregular : bool, optional Whether or not to include an irregular component. Default is False. stochastic_level : bool, optional Whether or not any level component is stochastic. Default is False. stochastic_trend : bool, optional Whether or not any trend component is stochastic. Default is False. stochastic_seasonal : bool, optional Whether or not any seasonal component is stochastic. Default is True. stochastic_freq_seasonal : list[bool], optional Whether or not each seasonal component(s) is (are) stochastic. Default is True for each component. The list should be of the same length as freq_seasonal. stochastic_cycle : bool, optional Whether or not any cycle component is stochastic. Default is False. damped_cycle : bool, optional Whether or not the cycle component is damped. Default is False. cycle_period_bounds : tuple, optional A tuple with lower and upper allowed bounds for the period of the cycle. If not provided, the following default bounds are used: (1) if no date / time information is provided, the frequency is constrained to be between zero and :math:`\pi`, so the period is constrained to be in [0.5, infinity]. (2) If the date / time information is provided, the default bounds allow the cyclical component to be between 1.5 and 12 years; depending on the frequency of the endogenous variable, this will imply different specific bounds. use_exact_diffuse : bool, optional Whether or not to use exact diffuse initialization for non-stationary states. Default is False (in which case approximate diffuse initialization is used). Notes ----- These models take the general form (see [1]_ Chapter 3.2 for all details) .. math:: y_t = \mu_t + \gamma_t + c_t + \varepsilon_t where :math:`y_t` refers to the observation vector at time :math:`t`, :math:`\mu_t` refers to the trend component, :math:`\gamma_t` refers to the seasonal component, :math:`c_t` refers to the cycle, and :math:`\varepsilon_t` is the irregular. The modeling details of these components are given below. **Trend** The trend component is a dynamic extension of a regression model that includes an intercept and linear time-trend. It can be written: .. math:: \mu_t = \mu_{t-1} + \beta_{t-1} + \eta_{t-1} \\ \beta_t = \beta_{t-1} + \zeta_{t-1} where the level is a generalization of the intercept term that can dynamically vary across time, and the trend is a generalization of the time-trend such that the slope can dynamically vary across time. Here :math:`\eta_t \sim N(0, \sigma_\eta^2)` and :math:`\zeta_t \sim N(0, \sigma_\zeta^2)`. For both elements (level and trend), we can consider models in which: - The element is included vs excluded (if the trend is included, there must also be a level included). - The element is deterministic vs stochastic (i.e. whether or not the variance on the error term is confined to be zero or not) The only additional parameters to be estimated via MLE are the variances of any included stochastic components. The level/trend components can be specified using the boolean keyword arguments `level`, `stochastic_level`, `trend`, etc., or all at once as a string argument to `level`. The following table shows the available model specifications: +----------------------------------+--------------------------------------+--------------------+--------------------------------------------------+ | Model name | Full string syntax | Abbreviated syntax | Model | +==================================+======================================+====================+==================================================+ | No trend | `'irregular'` | `'ntrend'` | .. math:: y_t &= \varepsilon_t | +----------------------------------+--------------------------------------+--------------------+--------------------------------------------------+ | Fixed intercept | `'fixed intercept'` | | .. math:: y_t &= \mu | +----------------------------------+--------------------------------------+--------------------+--------------------------------------------------+ | Deterministic constant | `'deterministic constant'` | `'dconstant'` | .. math:: y_t &= \mu + \varepsilon_t | +----------------------------------+--------------------------------------+--------------------+--------------------------------------------------+ | Local level | `'local level'` | `'llevel'` | .. math:: y_t &= \mu_t + \varepsilon_t \\ | | | | | \mu_t &= \mu_{t-1} + \eta_t | +----------------------------------+--------------------------------------+--------------------+--------------------------------------------------+ | Random walk | `'random walk'` | `'rwalk'` | .. math:: y_t &= \mu_t \\ | | | | | \mu_t &= \mu_{t-1} + \eta_t | +----------------------------------+--------------------------------------+--------------------+--------------------------------------------------+ | Fixed slope | `'fixed slope'` | | .. math:: y_t &= \mu_t \\ | | | | | \mu_t &= \mu_{t-1} + \beta | +----------------------------------+--------------------------------------+--------------------+--------------------------------------------------+ | Deterministic trend | `'deterministic trend'` | `'dtrend'` | .. math:: y_t &= \mu_t + \varepsilon_t \\ | | | | | \mu_t &= \mu_{t-1} + \beta | +----------------------------------+--------------------------------------+--------------------+--------------------------------------------------+ | Local linear deterministic trend | `'local linear deterministic trend'` | `'lldtrend'` | .. math:: y_t &= \mu_t + \varepsilon_t \\ | | | | | \mu_t &= \mu_{t-1} + \beta + \eta_t | +----------------------------------+--------------------------------------+--------------------+--------------------------------------------------+ | Random walk with drift | `'random walk with drift'` | `'rwdrift'` | .. math:: y_t &= \mu_t \\ | | | | | \mu_t &= \mu_{t-1} + \beta + \eta_t | +----------------------------------+--------------------------------------+--------------------+--------------------------------------------------+ | Local linear trend | `'local linear trend'` | `'lltrend'` | .. math:: y_t &= \mu_t + \varepsilon_t \\ | | | | | \mu_t &= \mu_{t-1} + \beta_{t-1} + \eta_t \\ | | | | | \beta_t &= \beta_{t-1} + \zeta_t | +----------------------------------+--------------------------------------+--------------------+--------------------------------------------------+ | Smooth trend | `'smooth trend'` | `'strend'` | .. math:: y_t &= \mu_t + \varepsilon_t \\ | | | | | \mu_t &= \mu_{t-1} + \beta_{t-1} \\ | | | | | \beta_t &= \beta_{t-1} + \zeta_t | +----------------------------------+--------------------------------------+--------------------+--------------------------------------------------+ | Random trend | `'random trend'` | `'rtrend'` | .. math:: y_t &= \mu_t \\ | | | | | \mu_t &= \mu_{t-1} + \beta_{t-1} \\ | | | | | \beta_t &= \beta_{t-1} + \zeta_t | +----------------------------------+--------------------------------------+--------------------+--------------------------------------------------+ Following the fitting of the model, the unobserved level and trend component time series are available in the results class in the `level` and `trend` attributes, respectively. **Seasonal (Time-domain)** The seasonal component is modeled as: .. math:: \gamma_t = - \sum_{j=1}^{s-1} \gamma_{t+1-j} + \omega_t \\ \omega_t \sim N(0, \sigma_\omega^2) The periodicity (number of seasons) is s, and the defining character is that (without the error term), the seasonal components sum to zero across one complete cycle. The inclusion of an error term allows the seasonal effects to vary over time (if this is not desired, :math:`\sigma_\omega^2` can be set to zero using the `stochastic_seasonal=False` keyword argument). This component results in one parameter to be selected via maximum likelihood: :math:`\sigma_\omega^2`, and one parameter to be chosen, the number of seasons `s`. Following the fitting of the model, the unobserved seasonal component time series is available in the results class in the `seasonal` attribute. ** Frequency-domain Seasonal** Each frequency-domain seasonal component is modeled as: .. math:: \gamma_t & = \sum_{j=1}^h \gamma_{j, t} \\ \gamma_{j, t+1} & = \gamma_{j, t}\cos(\lambda_j) + \gamma^{*}_{j, t}\sin(\lambda_j) + \omega_{j,t} \\ \gamma^{*}_{j, t+1} & = -\gamma^{(1)}_{j, t}\sin(\lambda_j) + \gamma^{*}_{j, t}\cos(\lambda_j) + \omega^{*}_{j, t}, \\ \omega^{*}_{j, t}, \omega_{j, t} & \sim N(0, \sigma_{\omega^2}) \\ \lambda_j & = \frac{2 \pi j}{s} where j ranges from 1 to h. The periodicity (number of "seasons" in a "year") is s and the number of harmonics is h. Note that h is configurable to be less than s/2, but s/2 harmonics is sufficient to fully model all seasonal variations of periodicity s. Like the time domain seasonal term (cf. Seasonal section, above), the inclusion of the error terms allows for the seasonal effects to vary over time. The argument stochastic_freq_seasonal can be used to set one or more of the seasonal components of this type to be non-random, meaning they will not vary over time. This component results in one parameter to be fitted using maximum likelihood: :math:`\sigma_{\omega^2}`, and up to two parameters to be chosen, the number of seasons s and optionally the number of harmonics h, with :math:`1 \leq h \leq \floor(s/2)`. After fitting the model, each unobserved seasonal component modeled in the frequency domain is available in the results class in the `freq_seasonal` attribute. **Cycle** The cyclical component is intended to capture cyclical effects at time frames much longer than captured by the seasonal component. For example, in economics the cyclical term is often intended to capture the business cycle, and is then expected to have a period between "1.5 and 12 years" (see Durbin and Koopman). .. math:: c_{t+1} & = \rho_c (\tilde c_t \cos \lambda_c t + \tilde c_t^* \sin \lambda_c) + \tilde \omega_t \\ c_{t+1}^* & = \rho_c (- \tilde c_t \sin \lambda_c t + \tilde c_t^* \cos \lambda_c) + \tilde \omega_t^* \\ where :math:`\omega_t, \tilde \omega_t iid N(0, \sigma_{\tilde \omega}^2)` The parameter :math:`\lambda_c` (the frequency of the cycle) is an additional parameter to be estimated by MLE. If the cyclical effect is stochastic (`stochastic_cycle=True`), then there is another parameter to estimate (the variance of the error term - note that both of the error terms here share the same variance, but are assumed to have independent draws). If the cycle is damped (`damped_cycle=True`), then there is a third parameter to estimate, :math:`\rho_c`. In order to achieve cycles with the appropriate frequencies, bounds are imposed on the parameter :math:`\lambda_c` in estimation. These can be controlled via the keyword argument `cycle_period_bounds`, which, if specified, must be a tuple of bounds on the **period** `(lower, upper)`. The bounds on the frequency are then calculated from those bounds. The default bounds, if none are provided, are selected in the following way: 1. If no date / time information is provided, the frequency is constrained to be between zero and :math:`\pi`, so the period is constrained to be in :math:`[0.5, \infty]`. 2. If the date / time information is provided, the default bounds allow the cyclical component to be between 1.5 and 12 years; depending on the frequency of the endogenous variable, this will imply different specific bounds. Following the fitting of the model, the unobserved cyclical component time series is available in the results class in the `cycle` attribute. **Irregular** The irregular components are independent and identically distributed (iid): .. math:: \varepsilon_t \sim N(0, \sigma_\varepsilon^2) **Autoregressive Irregular** An autoregressive component (often used as a replacement for the white noise irregular term) can be specified as: .. math:: \varepsilon_t = \rho(L) \varepsilon_{t-1} + \epsilon_t \\ \epsilon_t \sim N(0, \sigma_\epsilon^2) In this case, the AR order is specified via the `autoregressive` keyword, and the autoregressive coefficients are estimated. Following the fitting of the model, the unobserved autoregressive component time series is available in the results class in the `autoregressive` attribute. **Regression effects** Exogenous regressors can be pass to the `exog` argument. The regression coefficients will be estimated by maximum likelihood unless `mle_regression=False`, in which case the regression coefficients will be included in the state vector where they are essentially estimated via recursive OLS. If the regression_coefficients are included in the state vector, the recursive estimates are available in the results class in the `regression_coefficients` attribute. References ---------- .. [1] Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods: Second Edition. Oxford University Press. """ # noqa:E501 def __init__(self, endog, level=False, trend=False, seasonal=None, freq_seasonal=None, cycle=False, autoregressive=None, exog=None, irregular=False, stochastic_level=False, stochastic_trend=False, stochastic_seasonal=True, stochastic_freq_seasonal=None, stochastic_cycle=False, damped_cycle=False, cycle_period_bounds=None, mle_regression=True, use_exact_diffuse=False, **kwargs): # Model options self.level = level self.trend = trend self.seasonal_periods = seasonal if seasonal is not None else 0 self.seasonal = self.seasonal_periods > 0 if freq_seasonal: self.freq_seasonal_periods = [d['period'] for d in freq_seasonal] self.freq_seasonal_harmonics = [d.get( 'harmonics', int(np.floor(d['period'] / 2))) for d in freq_seasonal] else: self.freq_seasonal_periods = [] self.freq_seasonal_harmonics = [] self.freq_seasonal = any(x > 0 for x in self.freq_seasonal_periods) self.cycle = cycle self.ar_order = autoregressive if autoregressive is not None else 0 self.autoregressive = self.ar_order > 0 self.irregular = irregular self.stochastic_level = stochastic_level self.stochastic_trend = stochastic_trend self.stochastic_seasonal = stochastic_seasonal if stochastic_freq_seasonal is None: self.stochastic_freq_seasonal = [True] * len( self.freq_seasonal_periods) else: if len(stochastic_freq_seasonal) != len(freq_seasonal): raise ValueError( "Length of stochastic_freq_seasonal must equal length" " of freq_seasonal: {!r} vs {!r}".format( len(stochastic_freq_seasonal), len(freq_seasonal))) self.stochastic_freq_seasonal = stochastic_freq_seasonal self.stochastic_cycle = stochastic_cycle self.damped_cycle = damped_cycle self.mle_regression = mle_regression self.use_exact_diffuse = use_exact_diffuse # Check for string trend/level specification self.trend_specification = None if isinstance(self.level, str): self.trend_specification = level self.level = False # Check if any of the trend/level components have been set, and # reset everything to False trend_attributes = ['irregular', 'level', 'trend', 'stochastic_level', 'stochastic_trend'] for attribute in trend_attributes: if not getattr(self, attribute) is False: warn("Value of `%s` may be overridden when the trend" " component is specified using a model string." % attribute, SpecificationWarning) setattr(self, attribute, False) # Now set the correct specification spec = self.trend_specification if spec == 'irregular' or spec == 'ntrend': self.irregular = True self.trend_specification = 'irregular' elif spec == 'fixed intercept': self.level = True elif spec == 'deterministic constant' or spec == 'dconstant': self.irregular = True self.level = True self.trend_specification = 'deterministic constant' elif spec == 'local level' or spec == 'llevel': self.irregular = True self.level = True self.stochastic_level = True self.trend_specification = 'local level' elif spec == 'random walk' or spec == 'rwalk': self.level = True self.stochastic_level = True self.trend_specification = 'random walk' elif spec == 'fixed slope': self.level = True self.trend = True elif spec == 'deterministic trend' or spec == 'dtrend': self.irregular = True self.level = True self.trend = True self.trend_specification = 'deterministic trend' elif (spec == 'local linear deterministic trend' or spec == 'lldtrend'): self.irregular = True self.level = True self.stochastic_level = True self.trend = True self.trend_specification = 'local linear deterministic trend' elif spec == 'random walk with drift' or spec == 'rwdrift': self.level = True self.stochastic_level = True self.trend = True self.trend_specification = 'random walk with drift' elif spec == 'local linear trend' or spec == 'lltrend': self.irregular = True self.level = True self.stochastic_level = True self.trend = True self.stochastic_trend = True self.trend_specification = 'local linear trend' elif spec == 'smooth trend' or spec == 'strend': self.irregular = True self.level = True self.trend = True self.stochastic_trend = True self.trend_specification = 'smooth trend' elif spec == 'random trend' or spec == 'rtrend': self.level = True self.trend = True self.stochastic_trend = True self.trend_specification = 'random trend' else: raise ValueError("Invalid level/trend specification: '%s'" % spec) # Check for a model that makes sense if trend and not level: warn("Trend component specified without level component;" " deterministic level component added.", SpecificationWarning) self.level = True self.stochastic_level = False if not (self.irregular or (self.level and self.stochastic_level) or (self.trend and self.stochastic_trend) or (self.seasonal and self.stochastic_seasonal) or (self.freq_seasonal and any( self.stochastic_freq_seasonal)) or (self.cycle and self.stochastic_cycle) or self.autoregressive): warn("Specified model does not contain a stochastic element;" " irregular component added.", SpecificationWarning) self.irregular = True if self.seasonal and self.seasonal_periods < 2: raise ValueError('Seasonal component must have a seasonal period' ' of at least 2.') if self.freq_seasonal: for p in self.freq_seasonal_periods: if p < 2: raise ValueError( 'Frequency Domain seasonal component must have a ' 'seasonal period of at least 2.') # Create a bitmask holding the level/trend specification self.trend_mask = ( self.irregular * 0x01 | self.level * 0x02 | self.level * self.stochastic_level * 0x04 | self.trend * 0x08 | self.trend * self.stochastic_trend * 0x10 ) # Create the trend specification, if it was not given if self.trend_specification is None: # trend specification may be none, e.g. if the model is only # a stochastic cycle, etc. self.trend_specification = _mask_map.get(self.trend_mask, None) # Exogenous component (self.k_exog, exog) = prepare_exog(exog) self.regression = self.k_exog > 0 # Model parameters self._k_seasonal_states = (self.seasonal_periods - 1) * self.seasonal self._k_freq_seas_states = ( sum(2 * h for h in self.freq_seasonal_harmonics) * self.freq_seasonal) self._k_cycle_states = self.cycle * 2 k_states = ( self.level + self.trend + self._k_seasonal_states + self._k_freq_seas_states + self._k_cycle_states + self.ar_order + (not self.mle_regression) * self.k_exog ) k_posdef = ( self.stochastic_level * self.level + self.stochastic_trend * self.trend + self.stochastic_seasonal * self.seasonal + ((sum(2 * h if self.stochastic_freq_seasonal[ix] else 0 for ix, h in enumerate(self.freq_seasonal_harmonics))) * self.freq_seasonal) + self.stochastic_cycle * (self._k_cycle_states) + self.autoregressive ) # Handle non-default loglikelihood burn self._loglikelihood_burn = kwargs.get('loglikelihood_burn', None) # We can still estimate the model with just the irregular component, # just need to have one state that does nothing. self._unused_state = False if k_states == 0: if not self.irregular: raise ValueError('Model has no components specified.') k_states = 1 self._unused_state = True if k_posdef == 0: k_posdef = 1 # Setup the representation super(UnobservedComponents, self).__init__( endog, k_states, k_posdef=k_posdef, exog=exog, **kwargs ) self.setup() # Set as time-varying model if we have exog if self.k_exog > 0: self.ssm._time_invariant = False # Need to reset the MLE names (since when they were first set, `setup` # had not been run (and could not have been at that point)) self.data.param_names = self.param_names # Get bounds for the frequency of the cycle, if we know the frequency # of the data. if cycle_period_bounds is None: freq = self.data.freq[0] if self.data.freq is not None else '' if freq == 'A': cycle_period_bounds = (1.5, 12) elif freq == 'Q': cycle_period_bounds = (1.5*4, 12*4) elif freq == 'M': cycle_period_bounds = (1.5*12, 12*12) else: # If we have no information on data frequency, require the # cycle frequency to be between 0 and pi cycle_period_bounds = (2, np.inf) self.cycle_frequency_bound = ( 2*np.pi / cycle_period_bounds[1], 2*np.pi / cycle_period_bounds[0] ) # Update _init_keys attached by super self._init_keys += ['level', 'trend', 'seasonal', 'freq_seasonal', 'cycle', 'autoregressive', 'irregular', 'stochastic_level', 'stochastic_trend', 'stochastic_seasonal', 'stochastic_freq_seasonal', 'stochastic_cycle', 'damped_cycle', 'cycle_period_bounds', 'mle_regression'] + list(kwargs.keys()) # Initialize the state self.initialize_default() def _get_init_kwds(self): # Get keywords based on model attributes kwds = super(UnobservedComponents, self)._get_init_kwds() # Modifications if self.trend_specification is not None: kwds['level'] = self.trend_specification for attr in ['irregular', 'trend', 'stochastic_level', 'stochastic_trend']: kwds[attr] = False kwds['seasonal'] = self.seasonal_periods kwds['freq_seasonal'] = [ {'period': p, 'harmonics': self.freq_seasonal_harmonics[ix]} for ix, p in enumerate(self.freq_seasonal_periods)] kwds['autoregressive'] = self.ar_order return kwds def setup(self): """ Setup the structural time series representation """ # Initialize the ordered sets of parameters self.parameters = {} self.parameters_obs_intercept = {} self.parameters_obs_cov = {} self.parameters_transition = {} self.parameters_state_cov = {} # Initialize the fixed components of the state space matrices, i = 0 # state offset j = 0 # state covariance offset if self.irregular: self.parameters_obs_cov['irregular_var'] = 1 if self.level: self.ssm['design', 0, i] = 1. self.ssm['transition', i, i] = 1. if self.trend: self.ssm['transition', i, i+1] = 1. if self.stochastic_level: self.ssm['selection', i, j] = 1. self.parameters_state_cov['level_var'] = 1 j += 1 i += 1 if self.trend: self.ssm['transition', i, i] = 1. if self.stochastic_trend: self.ssm['selection', i, j] = 1. self.parameters_state_cov['trend_var'] = 1 j += 1 i += 1 if self.seasonal: n = self.seasonal_periods - 1 self.ssm['design', 0, i] = 1. self.ssm['transition', i:i + n, i:i + n] = ( companion_matrix(np.r_[1, [1] * n]).transpose() ) if self.stochastic_seasonal: self.ssm['selection', i, j] = 1. self.parameters_state_cov['seasonal_var'] = 1 j += 1 i += n if self.freq_seasonal: for ix, h in enumerate(self.freq_seasonal_harmonics): # These are the \gamma_jt and \gamma^*_jt terms in D&K (3.8) n = 2 * h p = self.freq_seasonal_periods[ix] lambda_p = 2 * np.pi / float(p) t = 0 # frequency transition matrix offset for block in range(1, h + 1): # ibid. eqn (3.7) self.ssm['design', 0, i+t] = 1. # ibid. eqn (3.8) cos_lambda_block = np.cos(lambda_p * block) sin_lambda_block = np.sin(lambda_p * block) trans = np.array([[cos_lambda_block, sin_lambda_block], [-sin_lambda_block, cos_lambda_block]]) trans_s = np.s_[i + t:i + t + 2] self.ssm['transition', trans_s, trans_s] = trans t += 2 if self.stochastic_freq_seasonal[ix]: self.ssm['selection', i:i + n, j:j + n] = np.eye(n) cov_key = 'freq_seasonal_var_{!r}'.format(ix) self.parameters_state_cov[cov_key] = 1 j += n i += n if self.cycle: self.ssm['design', 0, i] = 1. self.parameters_transition['cycle_freq'] = 1 if self.damped_cycle: self.parameters_transition['cycle_damp'] = 1 if self.stochastic_cycle: self.ssm['selection', i:i+2, j:j+2] = np.eye(2) self.parameters_state_cov['cycle_var'] = 1 j += 2 self._idx_cycle_transition = np.s_['transition', i:i+2, i:i+2] i += 2 if self.autoregressive: self.ssm['design', 0, i] = 1. self.parameters_transition['ar_coeff'] = self.ar_order self.parameters_state_cov['ar_var'] = 1 self.ssm['selection', i, j] = 1 self.ssm['transition', i:i+self.ar_order, i:i+self.ar_order] = ( companion_matrix(self.ar_order).T ) self._idx_ar_transition = ( np.s_['transition', i, i:i+self.ar_order] ) j += 1 i += self.ar_order if self.regression: if self.mle_regression: self.parameters_obs_intercept['reg_coeff'] = self.k_exog else: design = np.repeat(self.ssm['design', :, :, 0], self.nobs, axis=0) self.ssm['design'] = design.transpose()[np.newaxis, :, :] self.ssm['design', 0, i:i+self.k_exog, :] = ( self.exog.transpose()) self.ssm['transition', i:i+self.k_exog, i:i+self.k_exog] = ( np.eye(self.k_exog) ) i += self.k_exog # Update to get the actual parameter set self.parameters.update(self.parameters_obs_cov) self.parameters.update(self.parameters_state_cov) self.parameters.update(self.parameters_transition) # ordered last self.parameters.update(self.parameters_obs_intercept) self.k_obs_intercept = sum(self.parameters_obs_intercept.values()) self.k_obs_cov = sum(self.parameters_obs_cov.values()) self.k_transition = sum(self.parameters_transition.values()) self.k_state_cov = sum(self.parameters_state_cov.values()) self.k_params = sum(self.parameters.values()) # Other indices idx = np.diag_indices(self.ssm.k_posdef) self._idx_state_cov = ('state_cov', idx[0], idx[1]) # Some of the variances may be tied together (repeated parameter usage) # Use list() for compatibility with python 3.5 param_keys = list(self.parameters_state_cov.keys()) self._var_repetitions = np.ones(self.k_state_cov, dtype=int) if self.freq_seasonal: for ix, is_stochastic in enumerate(self.stochastic_freq_seasonal): if is_stochastic: num_harmonics = self.freq_seasonal_harmonics[ix] repeat_times = 2 * num_harmonics cov_key = 'freq_seasonal_var_{!r}'.format(ix) cov_ix = param_keys.index(cov_key) self._var_repetitions[cov_ix] = repeat_times if self.stochastic_cycle and self.cycle: cov_ix = param_keys.index('cycle_var') self._var_repetitions[cov_ix] = 2 self._repeat_any_var = any(self._var_repetitions > 1) def initialize_default(self, approximate_diffuse_variance=None): if approximate_diffuse_variance is None: approximate_diffuse_variance = self.ssm.initial_variance if self.use_exact_diffuse: diffuse_type = 'diffuse' else: diffuse_type = 'approximate_diffuse' # Set the loglikelihood burn parameter, if not given in constructor if self._loglikelihood_burn is None: k_diffuse_states = ( self.k_states - int(self._unused_state) - self.ar_order) self.loglikelihood_burn = k_diffuse_states init = Initialization( self.k_states, approximate_diffuse_variance=approximate_diffuse_variance) if self._unused_state: # If this flag is set, it means we have a model with just an # irregular component and nothing else. The state is then # irrelevant and we can't put it as diffuse, since then the filter # will never leave the diffuse state. init.set(0, 'known', constant=[0]) elif self.autoregressive: offset = (self.level + self.trend + self._k_seasonal_states + self._k_freq_seas_states + self._k_cycle_states) length = self.ar_order init.set((0, offset), diffuse_type) init.set((offset, offset + length), 'stationary') init.set((offset + length, self.k_states), diffuse_type) # If we do not have an autoregressive component, then everything has # a diffuse initialization else: init.set(None, diffuse_type) self.ssm.initialization = init def clone(self, endog, exog=None, **kwargs): return self._clone_from_init_kwds(endog, exog=exog, **kwargs) @property def _res_classes(self): return {'fit': (UnobservedComponentsResults, UnobservedComponentsResultsWrapper)} @property def start_params(self): if not hasattr(self, 'parameters'): return [] # Eliminate missing data to estimate starting parameters endog = self.endog exog = self.exog if np.any(np.isnan(endog)): mask = ~np.isnan(endog).squeeze() endog = endog[mask] if exog is not None: exog = exog[mask] # Level / trend variances # (Use the HP filter to get initial estimates of variances) _start_params = {} if self.level: resid, trend1 = hpfilter(endog) if self.stochastic_trend: cycle2, trend2 = hpfilter(trend1) _start_params['trend_var'] = np.std(trend2)**2 if self.stochastic_level: _start_params['level_var'] = np.std(cycle2)**2 elif self.stochastic_level: _start_params['level_var'] = np.std(trend1)**2 else: resid = self.ssm.endog[0] # Regression if self.regression and self.mle_regression: _start_params['reg_coeff'] = ( np.linalg.pinv(exog).dot(resid).tolist() ) resid = np.squeeze( resid - np.dot(exog, _start_params['reg_coeff']) ) # Autoregressive if self.autoregressive: Y = resid[self.ar_order:] X = lagmat(resid, self.ar_order, trim='both') _start_params['ar_coeff'] = np.linalg.pinv(X).dot(Y).tolist() resid = np.squeeze(Y - np.dot(X, _start_params['ar_coeff'])) _start_params['ar_var'] = np.var(resid) # The variance of the residual term can be used for all variances, # just to get something in the right order of magnitude. var_resid = np.var(resid) # Seasonal if self.stochastic_seasonal: _start_params['seasonal_var'] = var_resid # Frequency domain seasonal for ix, is_stochastic in enumerate(self.stochastic_freq_seasonal): cov_key = 'freq_seasonal_var_{!r}'.format(ix) _start_params[cov_key] = var_resid # Cyclical if self.cycle: _start_params['cycle_var'] = var_resid # Clip this to make sure it is positive and strictly stationary # (i.e. do not want negative or 1) _start_params['cycle_damp'] = np.clip( np.linalg.pinv(resid[:-1, None]).dot(resid[1:])[0], 0, 0.99 ) # Set initial period estimate to 3 year, if we know the frequency # of the data observations freq = self.data.freq[0] if self.data.freq is not None else '' if freq == 'A': _start_params['cycle_freq'] = 2 * np.pi / 3 elif freq == 'Q': _start_params['cycle_freq'] = 2 * np.pi / 12 elif freq == 'M': _start_params['cycle_freq'] = 2 * np.pi / 36 else: if not np.any(np.isinf(self.cycle_frequency_bound)): _start_params['cycle_freq'] = ( np.mean(self.cycle_frequency_bound)) elif np.isinf(self.cycle_frequency_bound[1]): _start_params['cycle_freq'] = self.cycle_frequency_bound[0] else: _start_params['cycle_freq'] = self.cycle_frequency_bound[1] # Irregular if self.irregular: _start_params['irregular_var'] = var_resid # Create the starting parameter list start_params = [] for key in self.parameters.keys(): if np.isscalar(_start_params[key]): start_params.append(_start_params[key]) else: start_params += _start_params[key] return start_params @property def param_names(self): if not hasattr(self, 'parameters'): return [] param_names = [] for key in self.parameters.keys(): if key == 'irregular_var': param_names.append('sigma2.irregular') elif key == 'level_var': param_names.append('sigma2.level') elif key == 'trend_var': param_names.append('sigma2.trend') elif key == 'seasonal_var': param_names.append('sigma2.seasonal') elif key.startswith('freq_seasonal_var_'): # There are potentially multiple frequency domain # seasonal terms idx_fseas_comp = int(key[-1]) periodicity = self.freq_seasonal_periods[idx_fseas_comp] harmonics = self.freq_seasonal_harmonics[idx_fseas_comp] freq_seasonal_name = "{p}({h})".format( p=repr(periodicity), h=repr(harmonics)) param_names.append( 'sigma2.' + 'freq_seasonal_' + freq_seasonal_name) elif key == 'cycle_var': param_names.append('sigma2.cycle') elif key == 'cycle_freq': param_names.append('frequency.cycle') elif key == 'cycle_damp': param_names.append('damping.cycle') elif key == 'ar_coeff': for i in range(self.ar_order): param_names.append('ar.L%d' % (i+1)) elif key == 'ar_var': param_names.append('sigma2.ar') elif key == 'reg_coeff': param_names += [ 'beta.%s' % self.exog_names[i] for i in range(self.k_exog) ] else: param_names.append(key) return param_names @property def state_names(self): names = [] if self.level: names.append('level') if self.trend: names.append('trend') if self.seasonal: names.append('seasonal') names += ['seasonal.L%d' % i for i in range(1, self._k_seasonal_states)] if self.freq_seasonal: names += ['freq_seasonal.%d' % i for i in range(self._k_freq_seas_states)] if self.cycle: names += ['cycle', 'cycle.auxilliary'] if self.ar_order > 0: names += ['ar.L%d' % i for i in range(1, self.ar_order + 1)] if self.k_exog > 0 and not self.mle_regression: names += ['beta.%s' % self.exog_names[i] for i in range(self.k_exog)] if self._unused_state: names += ['dummy'] return names def transform_params(self, unconstrained): """ Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation """ unconstrained = np.array(unconstrained, ndmin=1) constrained = np.zeros(unconstrained.shape, dtype=unconstrained.dtype) # Positive parameters: obs_cov, state_cov offset = self.k_obs_cov + self.k_state_cov constrained[:offset] = unconstrained[:offset]**2 # Cycle parameters if self.cycle: # Cycle frequency must be between between our bounds low, high = self.cycle_frequency_bound constrained[offset] = ( 1 / (1 + np.exp(-unconstrained[offset])) ) * (high - low) + low offset += 1 # Cycle damping (if present) must be between 0 and 1 if self.damped_cycle: constrained[offset] = ( 1 / (1 + np.exp(-unconstrained[offset])) ) offset += 1 # Autoregressive coefficients must be stationary if self.autoregressive: constrained[offset:offset + self.ar_order] = ( constrain_stationary_univariate( unconstrained[offset:offset + self.ar_order] ) ) offset += self.ar_order # Nothing to do with betas constrained[offset:offset + self.k_exog] = ( unconstrained[offset:offset + self.k_exog] ) return constrained def untransform_params(self, constrained): """ Reverse the transformation """ constrained = np.array(constrained, ndmin=1) unconstrained = np.zeros(constrained.shape, dtype=constrained.dtype) # Positive parameters: obs_cov, state_cov offset = self.k_obs_cov + self.k_state_cov unconstrained[:offset] = constrained[:offset]**0.5 # Cycle parameters if self.cycle: # Cycle frequency must be between between our bounds low, high = self.cycle_frequency_bound x = (constrained[offset] - low) / (high - low) unconstrained[offset] = np.log( x / (1 - x) ) offset += 1 # Cycle damping (if present) must be between 0 and 1 if self.damped_cycle: unconstrained[offset] = np.log( constrained[offset] / (1 - constrained[offset]) ) offset += 1 # Autoregressive coefficients must be stationary if self.autoregressive: unconstrained[offset:offset + self.ar_order] = ( unconstrain_stationary_univariate( constrained[offset:offset + self.ar_order] ) ) offset += self.ar_order # Nothing to do with betas unconstrained[offset:offset + self.k_exog] = ( constrained[offset:offset + self.k_exog] ) return unconstrained def _validate_can_fix_params(self, param_names): super(UnobservedComponents, self)._validate_can_fix_params(param_names) if 'ar_coeff' in self.parameters: ar_names = ['ar.L%d' % (i+1) for i in range(self.ar_order)] fix_all_ar = param_names.issuperset(ar_names) fix_any_ar = len(param_names.intersection(ar_names)) > 0 if fix_any_ar and not fix_all_ar: raise ValueError('Cannot fix individual autoregressive.' ' parameters. Must either fix all' ' autoregressive parameters or none.') def update(self, params, transformed=True, includes_fixed=False, complex_step=False): params = self.handle_params(params, transformed=transformed, includes_fixed=includes_fixed) offset = 0 # Observation covariance if self.irregular: self.ssm['obs_cov', 0, 0] = params[offset] offset += 1 # State covariance if self.k_state_cov > 0: variances = params[offset:offset+self.k_state_cov] if self._repeat_any_var: variances = np.repeat(variances, self._var_repetitions) self.ssm[self._idx_state_cov] = variances offset += self.k_state_cov # Cycle transition if self.cycle: cos_freq = np.cos(params[offset]) sin_freq = np.sin(params[offset]) cycle_transition = np.array( [[cos_freq, sin_freq], [-sin_freq, cos_freq]] ) if self.damped_cycle: offset += 1 cycle_transition *= params[offset] self.ssm[self._idx_cycle_transition] = cycle_transition offset += 1 # AR transition if self.autoregressive: self.ssm[self._idx_ar_transition] = ( params[offset:offset+self.ar_order] ) offset += self.ar_order # Beta observation intercept if self.regression: if self.mle_regression: self.ssm['obs_intercept'] = np.dot( self.exog, params[offset:offset+self.k_exog] )[None, :] offset += self.k_exog class UnobservedComponentsResults(MLEResults): """ Class to hold results from fitting an unobserved components model. Parameters ---------- model : UnobservedComponents instance The fitted model instance Attributes ---------- specification : dictionary Dictionary including all attributes from the unobserved components model instance. See Also -------- statsmodels.tsa.statespace.kalman_filter.FilterResults statsmodels.tsa.statespace.mlemodel.MLEResults """ def __init__(self, model, params, filter_results, cov_type=None, **kwargs): super(UnobservedComponentsResults, self).__init__( model, params, filter_results, cov_type, **kwargs) self.df_resid = np.inf # attribute required for wald tests # Save _init_kwds self._init_kwds = self.model._get_init_kwds() # Save number of states by type self._k_states_by_type = { 'seasonal': self.model._k_seasonal_states, 'freq_seasonal': self.model._k_freq_seas_states, 'cycle': self.model._k_cycle_states} # Save the model specification self.specification = Bunch(**{ # Model options 'level': self.model.level, 'trend': self.model.trend, 'seasonal_periods': self.model.seasonal_periods, 'seasonal': self.model.seasonal, 'freq_seasonal': self.model.freq_seasonal, 'freq_seasonal_periods': self.model.freq_seasonal_periods, 'freq_seasonal_harmonics': self.model.freq_seasonal_harmonics, 'cycle': self.model.cycle, 'ar_order': self.model.ar_order, 'autoregressive': self.model.autoregressive, 'irregular': self.model.irregular, 'stochastic_level': self.model.stochastic_level, 'stochastic_trend': self.model.stochastic_trend, 'stochastic_seasonal': self.model.stochastic_seasonal, 'stochastic_freq_seasonal': self.model.stochastic_freq_seasonal, 'stochastic_cycle': self.model.stochastic_cycle, 'damped_cycle': self.model.damped_cycle, 'regression': self.model.regression, 'mle_regression': self.model.mle_regression, 'k_exog': self.model.k_exog, # Check for string trend/level specification 'trend_specification': self.model.trend_specification }) @property def level(self): """ Estimates of unobserved level component Returns ------- out: Bunch Has the following attributes: - `filtered`: a time series array with the filtered estimate of the component - `filtered_cov`: a time series array with the filtered estimate of the variance/covariance of the component - `smoothed`: a time series array with the smoothed estimate of the component - `smoothed_cov`: a time series array with the smoothed estimate of the variance/covariance of the component - `offset`: an integer giving the offset in the state vector where this component begins """ # If present, level is always the first component of the state vector out = None spec = self.specification if spec.level: offset = 0 out = Bunch(filtered=self.filtered_state[offset], filtered_cov=self.filtered_state_cov[offset, offset], smoothed=None, smoothed_cov=None, offset=offset) if self.smoothed_state is not None: out.smoothed = self.smoothed_state[offset] if self.smoothed_state_cov is not None: out.smoothed_cov = self.smoothed_state_cov[offset, offset] return out @property def trend(self): """ Estimates of of unobserved trend component Returns ------- out: Bunch Has the following attributes: - `filtered`: a time series array with the filtered estimate of the component - `filtered_cov`: a time series array with the filtered estimate of the variance/covariance of the component - `smoothed`: a time series array with the smoothed estimate of the component - `smoothed_cov`: a time series array with the smoothed estimate of the variance/covariance of the component - `offset`: an integer giving the offset in the state vector where this component begins """ # If present, trend is always the second component of the state vector # (because level is always present if trend is present) out = None spec = self.specification if spec.trend: offset = int(spec.level) out = Bunch(filtered=self.filtered_state[offset], filtered_cov=self.filtered_state_cov[offset, offset], smoothed=None, smoothed_cov=None, offset=offset) if self.smoothed_state is not None: out.smoothed = self.smoothed_state[offset] if self.smoothed_state_cov is not None: out.smoothed_cov = self.smoothed_state_cov[offset, offset] return out @property def seasonal(self): """ Estimates of unobserved seasonal component Returns ------- out: Bunch Has the following attributes: - `filtered`: a time series array with the filtered estimate of the component - `filtered_cov`: a time series array with the filtered estimate of the variance/covariance of the component - `smoothed`: a time series array with the smoothed estimate of the component - `smoothed_cov`: a time series array with the smoothed estimate of the variance/covariance of the component - `offset`: an integer giving the offset in the state vector where this component begins """ # If present, seasonal always follows level/trend (if they are present) # Note that we return only the first seasonal state, but there are # in fact seasonal_periods-1 seasonal states, however latter states # are just lagged versions of the first seasonal state. out = None spec = self.specification if spec.seasonal: offset = int(spec.trend + spec.level) out = Bunch(filtered=self.filtered_state[offset], filtered_cov=self.filtered_state_cov[offset, offset], smoothed=None, smoothed_cov=None, offset=offset) if self.smoothed_state is not None: out.smoothed = self.smoothed_state[offset] if self.smoothed_state_cov is not None: out.smoothed_cov = self.smoothed_state_cov[offset, offset] return out @property def freq_seasonal(self): """ Estimates of unobserved frequency domain seasonal component(s) Returns ------- out: list of Bunch instances Each item has the following attributes: - `filtered`: a time series array with the filtered estimate of the component - `filtered_cov`: a time series array with the filtered estimate of the variance/covariance of the component - `smoothed`: a time series array with the smoothed estimate of the component - `smoothed_cov`: a time series array with the smoothed estimate of the variance/covariance of the component - `offset`: an integer giving the offset in the state vector where this component begins """ # If present, freq_seasonal components always follows level/trend # and seasonal. # There are 2 * (harmonics) seasonal states per freq_seasonal # component. # The sum of every other state enters the measurement equation. # Additionally, there can be multiple components of this type. # These facts make this property messier in implementation than the # others. # Fortunately, the states are conditionally mutually independent # (conditional on previous timestep's states), so that the calculations # of the variances are simple summations of individual variances and # the calculation of the returned state is likewise a summation. out = [] spec = self.specification if spec.freq_seasonal: previous_states_offset = int(spec.trend + spec.level + self._k_states_by_type['seasonal']) previous_f_seas_offset = 0 for ix, h in enumerate(spec.freq_seasonal_harmonics): offset = previous_states_offset + previous_f_seas_offset period = spec.freq_seasonal_periods[ix] # Only the gamma_jt terms enter the measurement equation (cf. # D&K 2012 (3.7)) states_in_sum = np.arange(0, 2 * h, 2) filtered_state = np.sum( [self.filtered_state[offset + j] for j in states_in_sum], axis=0) filtered_cov = np.sum( [self.filtered_state_cov[offset + j, offset + j] for j in states_in_sum], axis=0) item = Bunch( filtered=filtered_state, filtered_cov=filtered_cov, smoothed=None, smoothed_cov=None, offset=offset, pretty_name='seasonal {p}({h})'.format(p=repr(period), h=repr(h))) if self.smoothed_state is not None: item.smoothed = np.sum( [self.smoothed_state[offset+j] for j in states_in_sum], axis=0) if self.smoothed_state_cov is not None: item.smoothed_cov = np.sum( [self.smoothed_state_cov[offset+j, offset+j] for j in states_in_sum], axis=0) out.append(item) previous_f_seas_offset += 2 * h return out @property def cycle(self): """ Estimates of unobserved cycle component Returns ------- out: Bunch Has the following attributes: - `filtered`: a time series array with the filtered estimate of the component - `filtered_cov`: a time series array with the filtered estimate of the variance/covariance of the component - `smoothed`: a time series array with the smoothed estimate of the component - `smoothed_cov`: a time series array with the smoothed estimate of the variance/covariance of the component - `offset`: an integer giving the offset in the state vector where this component begins """ # If present, cycle always follows level/trend, seasonal, and freq # seasonal. # Note that we return only the first cyclical state, but there are # in fact 2 cyclical states. The second cyclical state is not simply # a lag of the first cyclical state, but the first cyclical state is # the one that enters the measurement equation. out = None spec = self.specification if spec.cycle: offset = int(spec.trend + spec.level + self._k_states_by_type['seasonal'] + self._k_states_by_type['freq_seasonal']) out = Bunch(filtered=self.filtered_state[offset], filtered_cov=self.filtered_state_cov[offset, offset], smoothed=None, smoothed_cov=None, offset=offset) if self.smoothed_state is not None: out.smoothed = self.smoothed_state[offset] if self.smoothed_state_cov is not None: out.smoothed_cov = self.smoothed_state_cov[offset, offset] return out @property def autoregressive(self): """ Estimates of unobserved autoregressive component Returns ------- out: Bunch Has the following attributes: - `filtered`: a time series array with the filtered estimate of the component - `filtered_cov`: a time series array with the filtered estimate of the variance/covariance of the component - `smoothed`: a time series array with the smoothed estimate of the component - `smoothed_cov`: a time series array with the smoothed estimate of the variance/covariance of the component - `offset`: an integer giving the offset in the state vector where this component begins """ # If present, autoregressive always follows level/trend, seasonal, # freq seasonal, and cyclical. # If it is an AR(p) model, then there are p associated # states, but the second - pth states are just lags of the first state. out = None spec = self.specification if spec.autoregressive: offset = int(spec.trend + spec.level + self._k_states_by_type['seasonal'] + self._k_states_by_type['freq_seasonal'] + self._k_states_by_type['cycle']) out = Bunch(filtered=self.filtered_state[offset], filtered_cov=self.filtered_state_cov[offset, offset], smoothed=None, smoothed_cov=None, offset=offset) if self.smoothed_state is not None: out.smoothed = self.smoothed_state[offset] if self.smoothed_state_cov is not None: out.smoothed_cov = self.smoothed_state_cov[offset, offset] return out @property def regression_coefficients(self): """ Estimates of unobserved regression coefficients Returns ------- out: Bunch Has the following attributes: - `filtered`: a time series array with the filtered estimate of the component - `filtered_cov`: a time series array with the filtered estimate of the variance/covariance of the component - `smoothed`: a time series array with the smoothed estimate of the component - `smoothed_cov`: a time series array with the smoothed estimate of the variance/covariance of the component - `offset`: an integer giving the offset in the state vector where this component begins """ # If present, state-vector regression coefficients always are last # (i.e. they follow level/trend, seasonal, freq seasonal, cyclical, and # autoregressive states). There is one state associated with each # regressor, and all are returned here. out = None spec = self.specification if spec.regression: if spec.mle_regression: import warnings warnings.warn('Regression coefficients estimated via maximum' ' likelihood. Estimated coefficients are' ' available in the parameters list, not as part' ' of the state vector.', OutputWarning) else: offset = int(spec.trend + spec.level + self._k_states_by_type['seasonal'] + self._k_states_by_type['freq_seasonal'] + self._k_states_by_type['cycle'] + spec.ar_order) start = offset end = offset + spec.k_exog out = Bunch( filtered=self.filtered_state[start:end], filtered_cov=self.filtered_state_cov[start:end, start:end], smoothed=None, smoothed_cov=None, offset=offset ) if self.smoothed_state is not None: out.smoothed = self.smoothed_state[start:end] if self.smoothed_state_cov is not None: out.smoothed_cov = ( self.smoothed_state_cov[start:end, start:end]) return out def plot_components(self, which=None, alpha=0.05, observed=True, level=True, trend=True, seasonal=True, freq_seasonal=True, cycle=True, autoregressive=True, legend_loc='upper right', fig=None, figsize=None): """ Plot the estimated components of the model. Parameters ---------- which : {'filtered', 'smoothed'}, or None, optional Type of state estimate to plot. Default is 'smoothed' if smoothed results are available otherwise 'filtered'. alpha : float, optional The confidence intervals for the components are (1 - alpha) % level : bool, optional Whether or not to plot the level component, if applicable. Default is True. trend : bool, optional Whether or not to plot the trend component, if applicable. Default is True. seasonal : bool, optional Whether or not to plot the seasonal component, if applicable. Default is True. freq_seasonal : bool, optional Whether or not to plot the frequency domain seasonal component(s), if applicable. Default is True. cycle : bool, optional Whether or not to plot the cyclical component, if applicable. Default is True. autoregressive : bool, optional Whether or not to plot the autoregressive state, if applicable. Default is True. fig : Figure, optional If given, subplots are created in this figure instead of in a new figure. Note that the grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Notes ----- If all options are included in the model and selected, this produces a 6x1 plot grid with the following plots (ordered top-to-bottom): 0. Observed series against predicted series 1. Level 2. Trend 3. Seasonal 4. Freq Seasonal 5. Cycle 6. Autoregressive Specific subplots will be removed if the component is not present in the estimated model or if the corresponding keyword argument is set to False. All plots contain (1 - `alpha`) % confidence intervals. """ from scipy.stats import norm from statsmodels.graphics.utils import _import_mpl, create_mpl_fig plt = _import_mpl() fig = create_mpl_fig(fig, figsize) # Determine which results we have if which is None: which = 'filtered' if self.smoothed_state is None else 'smoothed' # Determine which plots we have spec = self.specification comp = [ ('level', level and spec.level), ('trend', trend and spec.trend), ('seasonal', seasonal and spec.seasonal), ] if freq_seasonal and spec.freq_seasonal: for ix, _ in enumerate(spec.freq_seasonal_periods): key = 'freq_seasonal_{!r}'.format(ix) comp.append((key, True)) comp.extend( [('cycle', cycle and spec.cycle), ('autoregressive', autoregressive and spec.autoregressive)]) components = dict(comp) llb = self.filter_results.loglikelihood_burn # Number of plots k_plots = observed + np.sum(list(components.values())) # Get dates, if applicable if hasattr(self.data, 'dates') and self.data.dates is not None: dates = self.data.dates._mpl_repr() else: dates = np.arange(len(self.data.endog)) # Get the critical value for confidence intervals critical_value = norm.ppf(1 - alpha / 2.) plot_idx = 1 # Observed, predicted, confidence intervals if observed: ax = fig.add_subplot(k_plots, 1, plot_idx) plot_idx += 1 # Plot the observed dataset ax.plot(dates[llb:], self.model.endog[llb:], color='k', label='Observed') # Get the predicted values and confidence intervals predict = self.filter_results.forecasts[0] std_errors = np.sqrt(self.filter_results.forecasts_error_cov[0, 0]) ci_lower = predict - critical_value * std_errors ci_upper = predict + critical_value * std_errors # Plot ax.plot(dates[llb:], predict[llb:], label='One-step-ahead predictions') ci_poly = ax.fill_between( dates[llb:], ci_lower[llb:], ci_upper[llb:], alpha=0.2 ) ci_label = '$%.3g \\%%$ confidence interval' % ((1 - alpha) * 100) # Proxy artist for fill_between legend entry # See e.g. https://matplotlib.org/1.3.1/users/legend_guide.html p = plt.Rectangle((0, 0), 1, 1, fc=ci_poly.get_facecolor()[0]) # Legend handles, labels = ax.get_legend_handles_labels() handles.append(p) labels.append(ci_label) ax.legend(handles, labels, loc=legend_loc) ax.set_title('Predicted vs observed') # Plot each component for component, is_plotted in components.items(): if not is_plotted: continue ax = fig.add_subplot(k_plots, 1, plot_idx) plot_idx += 1 try: component_bunch = getattr(self, component) title = component.title() except AttributeError: # This might be a freq_seasonal component, of which there are # possibly multiple bagged up in property freq_seasonal if component.startswith('freq_seasonal_'): ix = int(component.replace('freq_seasonal_', '')) big_bunch = getattr(self, 'freq_seasonal') component_bunch = big_bunch[ix] title = component_bunch.pretty_name else: raise # Check for a valid estimation type if which not in component_bunch: raise ValueError('Invalid type of state estimate.') which_cov = '%s_cov' % which # Get the predicted values value = component_bunch[which] # Plot state_label = '%s (%s)' % (title, which) ax.plot(dates[llb:], value[llb:], label=state_label) # Get confidence intervals if which_cov in component_bunch: std_errors = np.sqrt(component_bunch['%s_cov' % which]) ci_lower = value - critical_value * std_errors ci_upper = value + critical_value * std_errors ci_poly = ax.fill_between( dates[llb:], ci_lower[llb:], ci_upper[llb:], alpha=0.2 ) ci_label = ('$%.3g \\%%$ confidence interval' % ((1 - alpha) * 100)) # Legend ax.legend(loc=legend_loc) ax.set_title('%s component' % title) # Add a note if first observations excluded if llb > 0: text = ('Note: The first %d observations are not shown, due to' ' approximate diffuse initialization.') fig.text(0.1, 0.01, text % llb, fontsize='large') return fig @Appender(MLEResults.summary.__doc__) def summary(self, alpha=.05, start=None): # Create the model name model_name = [self.specification.trend_specification] if self.specification.seasonal: seasonal_name = ('seasonal(%d)' % self.specification.seasonal_periods) if self.specification.stochastic_seasonal: seasonal_name = 'stochastic ' + seasonal_name model_name.append(seasonal_name) if self.specification.freq_seasonal: for ix, is_stochastic in enumerate( self.specification.stochastic_freq_seasonal): periodicity = self.specification.freq_seasonal_periods[ix] harmonics = self.specification.freq_seasonal_harmonics[ix] freq_seasonal_name = "freq_seasonal({p}({h}))".format( p=repr(periodicity), h=repr(harmonics)) if is_stochastic: freq_seasonal_name = 'stochastic ' + freq_seasonal_name model_name.append(freq_seasonal_name) if self.specification.cycle: cycle_name = 'cycle' if self.specification.stochastic_cycle: cycle_name = 'stochastic ' + cycle_name if self.specification.damped_cycle: cycle_name = 'damped ' + cycle_name model_name.append(cycle_name) if self.specification.autoregressive: autoregressive_name = 'AR(%d)' % self.specification.ar_order model_name.append(autoregressive_name) return super(UnobservedComponentsResults, self).summary( alpha=alpha, start=start, title='Unobserved Components Results', model_name=model_name ) class UnobservedComponentsResultsWrapper(MLEResultsWrapper): _attrs = {} _wrap_attrs = wrap.union_dicts(MLEResultsWrapper._wrap_attrs, _attrs) _methods = {} _wrap_methods = wrap.union_dicts(MLEResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(UnobservedComponentsResultsWrapper, # noqa:E305 UnobservedComponentsResults) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/000077500000000000000000000000001400612667500225745ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/__init__.py000066400000000000000000000000001400612667500246730ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/kfas_helpers.py000066400000000000000000000071371400612667500256240ustar00rootroot00000000000000# Helper functions for working with KFAS output import numpy as np import pandas as pd from statsmodels.tools.tools import Bunch def parse(path, ssm): # Dimensions n = ssm.nobs p = ssm.k_endog m = ssm.k_states r = ssm.k_posdef p2 = p**2 m2 = m**2 mp = m * p r2 = r**2 # Extract the different pieces of output from KFAS kfas = pd.read_csv(path) components = [('r', m), ('r0', m), ('r1', m), ('N', m2), ('N0', m2), ('N1', m2), ('N2', m2), ('m', p), ('v', p), ('F', p), ('Finf', p), ('K', mp), ('Kinf', mp), ('a', m), ('P', m2), ('Pinf', m2), ('att', m), ('Ptt', m2), ('alphahat', m), ('V', m2), ('muhat', p), ('V_mu', p2), ('etahat', r), ('V_eta', r2), ('epshat', p), ('V_eps', p), ('llf', 1)] dta = {} ix = 0 for key, length in components: dta[key] = kfas.iloc[:, ix:ix + length].fillna(0) dta[key].name = None ix += length # Reformat the KFAS output to compare with statsmodels output res = Bunch() d = len(kfas['Pinf_1'].dropna()) # forecasts res['forecasts'] = dta['m'].values[:n].T res['forecasts_error'] = dta['v'].values[:n].T res['forecasts_error_cov'] = np.c_[ [np.diag(x) for y, x in dta['F'].iloc[:n].iterrows()]].T res['forecasts_error_diffuse_cov'] = np.c_[ [np.diag(x) for y, x in dta['Finf'].iloc[:n].iterrows()]].T res['kalman_gain'] = dta['K'].values[:n].reshape(n, m, p, order='F').T res['Kinf'] = dta['Kinf'].values[:n].reshape(n, m, p, order='F') # filtered res['filtered_state'] = dta['att'].values[:n].T res['filtered_state_cov'] = dta['Ptt'].values[:n].reshape( n, m, m, order='F').T # predicted res['predicted_state'] = dta['a'].values.T res['predicted_state_cov'] = dta['P'].values.reshape( n + 1, m, m, order='F').T res['predicted_diffuse_state_cov'] = dta['Pinf'].values.reshape( n + 1, m, m, order='F').T # loglike # Note: KFAS only gives the total loglikelihood res['llf_obs'] = dta['llf'].values[0, 0] # smoothed res['smoothed_state'] = dta['alphahat'].values[:n].T res['smoothed_state_cov'] = dta['V'].values[:n].reshape( n, m, m, order='F').T res['smoothed_measurement_disturbance'] = dta['epshat'].values[:n].T res['smoothed_measurement_disturbance_cov'] = np.c_[ [np.diag(x) for y, x in dta['V_eps'].iloc[:n].iterrows()]].T res['smoothed_state_disturbance'] = dta['etahat'].values[:n].T res['smoothed_state_disturbance_cov'] = dta['V_eta'].values[:n].reshape( n, r, r, order='F').T # scaled smoothed estimator # Note: we store both r and r0 together as "scaled smoothed estimator" # while "scaled smoothed diffuse estimator" corresponds to r1 res['scaled_smoothed_estimator'] = np.c_[dta['r0'][:d].T, dta['r'][d:].T][..., 1:] res['scaled_smoothed_diffuse_estimator'] = dta['r1'].values.T N0 = dta['N0'].values[:d].reshape(d, m, m, order='F') N = dta['N'].values[d:].reshape(n + 1 - d, m, m, order='F') res['scaled_smoothed_estimator_cov'] = np.c_[N0.T, N.T][..., 1:] # Have to do a more precise transpose for these since they may not be # symmetric res['scaled_smoothed_diffuse1_estimator_cov'] = dta['N1'].values.reshape( n + 1, m, m, order='F').transpose(1, 2, 0) res['scaled_smoothed_diffuse2_estimator_cov'] = dta['N2'].values.reshape( n + 1, m, m, 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found at % % http://joshuachan.org/code/code_TVPVAR.html % % % % See Chan, J.C.C. and Jeliazkov, I. (2009) Efficient Simulation and % % Integrated Likelihood Estimation in State Space Models % % % % ======================================================================= % Code to generate the dataset being used is as follows: % dta = sm.datasets.macrodata.load_pandas().data % dta.index = pd.period_range('1959Q1', '2009Q3', freq='Q') % endog = np.log(dta[['realcons', 'realgdp', 'cpi']]).diff().iloc[1:13] * 400 % endog.to_csv('sp_code/macrodata.csv', index=False, header=False) clear; clc; rng(1234) load macrodata.csv; Y0 = macrodata(1:3,:); shortY = macrodata(4:12,:); [T n] = size(shortY); Y = reshape(shortY',T*n,1); p = 1; % no. of lags q = n^2*p+n; % dim of states Tq = T*q; Tn = T*n; q2 = q^2; nnp1 = n*(n+1); nloop = 1; burnin = 0; %% initialize for storage store_Omega11 = zeros(nloop-burnin,n,n); store_Omega22 = zeros(nloop-burnin,q); store_beta = zeros(nloop-burnin,Tq); %% initialize the Markov chain Omega11 = cov(macrodata); Omega22 = .01*ones(q,1); % store only the diag elements invOmega11 = Omega11\speye(n); invOmega22 = 1./Omega22; beta = zeros(Tq,1); %% prior nu01 = n+3; S01 = eye(n); nu02 = 3; S02 = .005*ones(q,1); Vbeta = 5*ones(q,1); %% construct and compute a few thigns X = zeros(T,n*p); for i=1:p X(:,(i-1)*n+1:i*n) = [Y0(3-i+1:end,:); shortY(1:T-i,:)]; end bigG = SURform([ones(n*T,1) kron(X,ones(n,1))]); H = speye(Tq,Tq) - sparse(q+1:Tq,1:(T-1)*q,ones(1,(T-1)*q),Tq,Tq); newnu1 = nu01 + T; newnu2 = nu02 + (T-1)/2; %% - Iteration 1 ---------------------------------------------------------- % sample beta invS = sparse(1:Tq,1:Tq,[1./Vbeta; repmat(invOmega22,T-1,1)]'); K = H'*invS*H; GinvOmega11 = bigG'*kron(speye(T),invOmega11); GinvOmega11G = GinvOmega11*bigG; invP = K + GinvOmega11G; C = chol(invP); % so that C'*C = invP betahat = C\(C'\(GinvOmega11*Y)); state_variates = randn(Tq,1); beta = betahat + C\state_variates; % C is upper triangular % sample Omega11 e1 = reshape(Y-bigG*beta,n,T); newS1 = S01 + e1*e1'; invOmega11 = wishrnd(newS1\speye(n),newnu1); Omega11 = invOmega11\speye(n); % sample Omega22 e2 = reshape(H*beta,q,T); newS2 = S02 + sum(e2(:,2:end).^2,2)/2; invOmega22 = gamrnd(newnu2,1./newS2); Omega22 = 1./invOmega22; % save results invP_1 = invP; posterior_mean_1 = reshape(betahat, q, T); state_variates_1 = reshape(state_variates, q, T); beta_1 = reshape(beta, q, T); S10_1 = newS1; v10_1 = newnu1; Omega11_1 = Omega11; Si0_1 = newS2; vi0_1 = newnu2; Omega22_1 = Omega22; %% - Iteration 2 ---------------------------------------------------------- % sample beta invS = sparse(1:Tq,1:Tq,[1./Vbeta; repmat(invOmega22,T-1,1)]'); K = H'*invS*H; GinvOmega11 = bigG'*kron(speye(T),invOmega11); GinvOmega11G = GinvOmega11*bigG; invP = K + GinvOmega11G; aaa = full(invP); bbb = inv(aaa); C = chol(invP); % so that C'*C = invP betahat = C\(C'\(GinvOmega11*Y)); state_variates = randn(Tq,1); beta = betahat + C\state_variates; % C is upper triangular % sample Omega11 e1 = reshape(Y-bigG*beta,n,T); newS1 = S01 + e1*e1'; invOmega11 = wishrnd(newS1\speye(n),newnu1); Omega11 = invOmega11\speye(n); % sample Omega22 e2 = reshape(H*beta,q,T); newS2 = S02 + sum(e2(:,2:end).^2,2)/2; invOmega22 = gamrnd(newnu2,1./newS2); Omega22 = 1./invOmega22; % save results invP_2 = invP; posterior_mean_2 = reshape(betahat, q, T); state_variates_2 = reshape(state_variates, q, T); beta_2 = reshape(beta, q, T); S10_2 = newS1; v10_2 = newnu1; Omega11_2 = Omega11; Si0_2 = newS2; vi0_2 = newnu2; Omega22_2 = Omega22; %% - Output --------------------------------------------------------------- invP = [full(invP_1)' full(invP_2)']'; posterior_mean = [posterior_mean_1' posterior_mean_2']'; state_variates = [state_variates_1' state_variates_2']'; beta = [beta_1' beta_2']'; S10 = [S10_1 S10_2]; v10 = [v10_1 v10_2]; Omega_11 = [Omega11_1 Omega11_2]; Si0 = [Si0_1 Si0_2]; vi0 = [vi0_1 vi0_2]; Omega_22 = [Omega22_1 Omega22_2]; dlmwrite('cfa_tvpvar_invP.csv', invP, 'precision', 15); dlmwrite('cfa_tvpvar_posterior_mean.csv', posterior_mean, 'precision', 10); dlmwrite('cfa_tvpvar_state_variates.csv', state_variates, 'precision', 10); dlmwrite('cfa_tvpvar_beta.csv', beta, 'precision', 10); dlmwrite('cfa_tvpvar_S10.csv', S10, 'precision', 10); dlmwrite('cfa_tvpvar_v10.csv', v10, 'precision', 10); dlmwrite('cfa_tvpvar_Omega_11.csv', Omega_11, 'precision', 10); dlmwrite('cfa_tvpvar_Si0.csv', Si0, 'precision', 10); dlmwrite('cfa_tvpvar_vi0.csv', vi0, 'precision', 10); dlmwrite('cfa_tvpvar_Omega_22.csv', Omega_22, 'precision', 10); statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/cfa_tvpvar_v10.csv000066400000000000000000000000061400612667500276270ustar00rootroot0000000000000014,14 statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/cfa_tvpvar_vi0.csv000066400000000000000000000000041400612667500277150ustar00rootroot000000000000007,7 statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/clark1989.csv000066400000000000000000000105221400612667500264410ustar00rootroot000000000000001239.5, 0 1247.199951, 0 1255, 0 1269.5, 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6.600000064 4867.899902, 6.833333333 4879.899902, 6.866666794 4880.799805, 7.100000064 4918.5, 7.366666794 4947.5, 7.600000064 4990.5, 7.633333206 5060.700195, 7.366666794 5075.299805, 7.133333365 5105.399902, 7.066666603 5139.399902, 6.800000032 5218, 6.633333365 5261.100098, 6.633333206 5314.100098, 6.199999968 5367, 6 5433.799805, 5.566666603 5470.100098, 5.533333302 5487.799805, 5.633333206 5544.600098, 5.633333206statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/example_ssm_wpi1.m000066400000000000000000000025471400612667500277400ustar00rootroot00000000000000% Load the dataset data = csvread('results_wpi1_ar3_stata.csv', 1, 0); % First differences dwpi1 = diff(data(:,1)); % Parameters ar = [.5270715, .0952613, .2580355]; sigma2 = .5307459; % Create the state space representation [nobs, k_endog] = size(dwpi1); k_states = 3; k_posdef = 1; obs = dwpi1'; obs_intercept = [0]; design = [1, 0, 0]; obs_cov = [0]; state_intercept = [0; 0]; transition = [ar; 1, 0, 0; 0, 1, 0]; selection = [1; 0; 0]; state_cov = [sigma2]; selected_state_cov = selection * state_cov * selection'; initial_state = [0; 0]; initial_state_cov = dlyap(conj(transition), selected_state_cov); mod = ssmodel('test', ssmat(obs_cov), ssmat(design), ssmat(transition),ssmat(selection),ssmat(state_cov)); mod.P1 = initial_state_cov; % Optionally add missing values % obs(10:20) = nan; % Estimate [a, P] = kalman(dwpi1', mod); [alphahat, V] = statesmo(dwpi1', mod); [eps, eta, epsvar, etavar] = disturbsmo(dwpi1', mod); % Note: simsmo seems to always crashes MATLAB %[alphatilde, epstilde, etatilde] = simsmo(dwpi1', mod); % Calculate determinants of variance matrices (so that we can compare % in unit tests) detP = zeros(1,nobs); detV = zeros(1,nobs); for i = 1:nobs+1; detP(i) = det(P(:,:,i)); detV(i) = det(V(:,:,i)); end; % Write output csvwrite('results_wpi1_ar3_matlab_ssm.csv', [a(:,1:end-1) detP(:,1:end-1) alphahat detV eps epsvar eta etavar]); statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/exponential_smoothing.R000066400000000000000000000150671400612667500310460ustar00rootroot00000000000000library(fpp) library(forecast) library(gdata) options(digits=16) # Simple exponential smoothing oildata <- window(oil,start=1996,end=2007) oil_fpp1 <- ses(oildata, alpha=0.2, initial="simple", h=17) oil_fpp2 <- ses(oildata, alpha=0.6, initial="simple", h=17) oil_fpp3 <- ses(oildata, h=17) oil_ets <- forecast(ets(oildata), h=17) # Holt's linear trend method air <- window(ausair,start=1990,end=2004) air_fpp1 <- holt(air, alpha=0.8, beta=0.2, damped=FALSE, initial="simple", h=14) air_fpp2 <- holt(air, alpha=0.8, beta=0.2, damped=TRUE, initial="optimal", h=14) air_ets <- forecast(ets(air, 'AAN', damped=TRUE), h=14) # Holt-Winters seasonal method aust <- window(austourists,start=2005) aust_fpp1 <- hw(aust, seasonal="additive", h=5) aust_ets1 <- forecast(ets(aust, 'AAA', damped=FALSE), h=5) aust_ets2 <- forecast(ets(aust, 'AAA', damped=TRUE), h=5) aust_ets3 <- forecast(ets(aust, 'ANA'), h=5) # Save params / output params <- data.frame( oil_fpp1=c(oil_fpp1$model$par['alpha'], NA, NA, NA, NA, oil_fpp1$model$par['l'], NA, NA, NA, NA, oil_fpp1$model$sigma2, oil_fpp1$model$SSE, NA, NA), oil_fpp2=c(oil_fpp2$model$par['alpha'], NA, NA, NA, NA, oil_fpp2$model$par['l'], NA, NA, NA, NA, oil_fpp2$model$sigma2, oil_fpp2$model$SSE, NA, NA), oil_fpp3=c(oil_fpp3$model$par['alpha'], NA, NA, NA, NA, oil_fpp3$model$par['l'], NA, NA, NA, NA, oil_fpp3$model$sigma2, NA, oil_fpp3$model$loglik, oil_fpp3$model$mse), oil_ets=c(oil_ets$model$par['alpha'], NA, NA, NA, NA, oil_ets$model$par['l'], NA, NA, NA, NA, oil_ets$model$sigma2, NA, oil_ets$model$loglik, oil_ets$model$mse), air_fpp1=c(air_fpp1$model$par[1:2], NA, NA, NA, air_fpp1$model$par[3:4], NA, NA, NA, air_fpp1$model$sigma2, air_fpp1$model$SSE, NA, NA), air_fpp2=c(air_fpp2$model$par[4], NA, air_fpp2$model$par[5], NA, air_fpp2$model$par[1:3], NA, NA, NA, air_fpp2$model$sigma2, NA, air_fpp2$model$loglik, air_fpp2$model$mse), air_ets=c(air_ets$model$par[1], NA, air_ets$model$par[2], NA, air_ets$model$par[3:5], NA, NA, NA, air_ets$model$sigma2, NA, air_ets$model$loglik, air_ets$model$mse), aust_fpp1=c(aust_fpp1$model$par[1], NA, aust_fpp1$model$par[2:3], NA, aust_fpp1$model$par[4:8], aust_fpp1$model$sigma2, NA, aust_fpp1$model$loglik, aust_fpp1$model$mse), aust_ets1=c(aust_ets1$model$par[1], NA, aust_ets1$model$par[2:3], NA, aust_ets1$model$par[4:8], aust_ets1$model$sigma2, NA, aust_ets1$model$loglik, aust_ets1$model$mse), aust_ets2=c(aust_ets2$model$par[1], NA, aust_ets2$model$par[2:9], aust_ets2$model$sigma2, NA, aust_ets2$model$loglik, aust_ets2$model$mse), aust_ets3=c(aust_ets3$model$par[1], NA, NA, aust_ets3$model$par[2], NA, aust_ets3$model$par[3], NA, aust_ets3$model$par[4:6], aust_ets3$model$sigma2, NA, aust_ets3$model$loglik, aust_ets3$model$mse)) row.names(params) <- c('alpha', 'beta_star', 'beta', 'gamma', 'phi', 'l0', 'b0', 's0_0', 's0_1', 's0_2', 'sigma2', 'sse', 'llf', 'mse') # Save predict / forecast predict <- data.frame( oil_fpp1_mean=c(oil_fpp1$fitted, oil_fpp1$mean), oil_fpp1_lower=c(rep(NA, 12), oil_fpp1$lower[,'95%']), oil_fpp1_upper=c(rep(NA, 12), oil_fpp1$upper[,'95%']), oil_fpp2_mean=c(oil_fpp2$fitted, oil_fpp2$mean), oil_fpp2_lower=c(rep(NA, 12), oil_fpp2$lower[,'95%']), oil_fpp2_upper=c(rep(NA, 12), oil_fpp2$upper[,'95%']), oil_fpp3_mean=c(oil_fpp3$fitted, oil_fpp3$mean), oil_fpp3_lower=c(rep(NA, 12), oil_fpp3$lower[,'95%']), oil_fpp3_upper=c(rep(NA, 12), oil_fpp3$upper[,'95%']), oil_ets_mean=c(oil_ets$fitted, oil_ets$mean), oil_ets_lower=c(rep(NA, 12), oil_ets$lower[,'95%']), oil_ets_upper=c(rep(NA, 12), oil_ets$upper[,'95%']), air_fpp1_mean=c(air_fpp1$fitted, air_fpp1$mean), air_fpp1_lower=c(rep(NA, 15), air_fpp1$lower[,'95%']), air_fpp1_upper=c(rep(NA, 15), air_fpp1$upper[,'95%']), air_fpp2_mean=c(air_fpp2$fitted, air_fpp2$mean), air_fpp2_lower=c(rep(NA, 15), air_fpp2$lower[,'95%']), air_fpp2_upper=c(rep(NA, 15), air_fpp2$upper[,'95%']), air_ets_mean=c(air_ets$fitted, air_ets$mean), air_ets_lower=c(rep(NA, 15), air_ets$lower[,'95%']), air_ets_upper=c(rep(NA, 15), air_ets$upper[,'95%']), aust_fpp1_mean=c(aust_fpp1$fitted, aust_fpp1$mean), aust_fpp1_lower=c(rep(NA, 24), aust_fpp1$lower[,'95%']), aust_fpp1_upper=c(rep(NA, 24), aust_fpp1$upper[,'95%']), aust_ets1_mean=c(aust_ets1$fitted, aust_ets1$mean), aust_ets1_lower=c(rep(NA, 24), aust_ets1$lower[,'95%']), aust_ets1_upper=c(rep(NA, 24), aust_ets1$upper[,'95%']), aust_ets2_mean=c(aust_ets2$fitted, aust_ets2$mean), aust_ets2_lower=c(rep(NA, 24), aust_ets2$lower[,'95%']), aust_ets2_upper=c(rep(NA, 24), aust_ets2$upper[,'95%']), aust_ets3_mean=c(aust_ets3$fitted, aust_ets3$mean), aust_ets3_lower=c(rep(NA, 24), aust_ets3$lower[,'95%']), aust_ets3_upper=c(rep(NA, 24), aust_ets3$upper[,'95%'])) # Save estimated states oil_fpp1_states <- data.frame(oil_fpp1$model$states) colnames(oil_fpp1_states) <- paste("oil_fpp1", colnames(oil_fpp1_states), sep="_") oil_fpp2_states <- data.frame(oil_fpp2$model$states) colnames(oil_fpp2_states) <- paste("oil_fpp2", colnames(oil_fpp2_states), sep="_") oil_fpp3_states <- data.frame(oil_fpp3$model$states) colnames(oil_fpp3_states) <- paste("oil_fpp3", colnames(oil_fpp3_states), sep="_") oil_ets_states <- data.frame(oil_ets$model$states) colnames(oil_ets_states) <- paste("oil_ets", colnames(oil_ets_states), sep="_") air_fpp1_states <- data.frame(air_fpp1$model$states) colnames(air_fpp1_states) <- paste("air_fpp1", colnames(air_fpp1_states), sep="_") air_fpp2_states <- data.frame(air_fpp2$model$states) colnames(air_fpp2_states) <- paste("air_fpp2", colnames(air_fpp2_states), sep="_") air_ets_states <- data.frame(air_ets$model$states) colnames(air_ets_states) <- paste("air_ets", colnames(air_ets_states), sep="_") aust_fpp1_states <- data.frame(aust_fpp1$model$states) colnames(aust_fpp1_states) <- paste("aust_fpp1", colnames(aust_fpp1_states), sep="_") aust_ets1_states <- data.frame(aust_ets1$model$states) colnames(aust_ets1_states) <- paste("aust_ets1", colnames(aust_ets1_states), sep="_") aust_ets2_states <- data.frame(aust_ets2$model$states) colnames(aust_ets2_states) <- paste("aust_ets2", colnames(aust_ets2_states), sep="_") aust_ets3_states <- data.frame(aust_ets3$model$states) colnames(aust_ets3_states) <- paste("aust_ets3", colnames(aust_ets3_states), sep="_") states <- cbindX( oil_fpp1_states, oil_fpp2_states, oil_fpp3_states, oil_ets_states, air_fpp1_states, air_fpp2_states, air_ets_states, aust_fpp1_states, aust_ets1_states, aust_ets2_states, aust_ets3_states) write.csv(params, 'exponential_smoothing_params.csv') write.csv(predict, 'exponential_smoothing_predict.csv') write.csv(states, 'exponential_smoothing_states.csv') 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statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/000077500000000000000000000000001400612667500271535ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/000077500000000000000000000000001400612667500312675ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/LICENSE000066400000000000000000000027741400612667500323060ustar00rootroot00000000000000BSD 3-Clause License Copyright (c) 2018, Federal Reserve Bank of New York All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/README.md000066400000000000000000000012551400612667500325510ustar00rootroot00000000000000The code in this folder is based on the Federal Reserve Bank of New York code found at https://github.com/FRBNY-TimeSeriesAnalysis/Nowcasting, which was downloaded as of commit 19f365cab8269e3aac3faa11ad091d6e913c5c43. Only the files from that repository which were required for generating the test results are included here. In additionm the following files from the original package have been modified (use git diff against the above repository to see the changes) - functions/dfm.m - functions/update_nowcast.m The following files are not a part of the original package: - test_DFM_blocks.m - test_DFM.m - test_news_blocks.m - test_news.m - test_spec_blocks.xls - test_spec.xls statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/__init__.py000066400000000000000000000000001400612667500333660ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/data/000077500000000000000000000000001400612667500322005ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/data/US/000077500000000000000000000000001400612667500325275ustar00rootroot000000000000002016-06-29.csv000066400000000000000000001625021400612667500342360ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/data/USDate,PAYEMS,JTSJOL,CPIAUCSL,DGORDER,HSN1F,RSAFS,UNRATE,HOUST,INDPRO,PPIFIS,DSPIC96,BOPTEXP,BOPTIMP,WHLSLRIMSA,TTLCONS,IR,CPILFESL,PCEPILFE,PCEPI,PERMIT,TCU,BUSINV,IQ,GACDISA066MSFRBNY,PCEC96,GACDFSA066MSFRBPHI,GDPC1,ULCNFB,A261RX1Q020SBEA 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10/1/88,106277,,119.9,,718,,5.4,1522,64.022,,6159.5,,,,,,125.2,64.184,62.831,1516,84.8,,,,,27.2,,, 11/1/88,106616,,120.3,,628,,5.3,1569,64.1173,,6162,,,,,,125.6,64.358,62.975,1508,84.8,,,,,27.2,,, 12/1/88,106906,,120.7,,658,,5.3,1563,64.421,,6196.4,,,,,89.3,126,64.563,63.165,1501,85.1,,93.8,,,22.7,8610.9,73.316,8625 1/1/89,107168,,121.2,,719,,5.4,1621,64.6158,,6224.8,,,,,91.1,126.5,64.881,63.482,1466,85.3,,94.9,,,28.2,,, 2/1/89,107426,,121.6,,622,,5.2,1425,64.3268,,6244.7,,,,,90.6,126.9,65.037,63.686,1383,84.8,,94.6,,,20.1,,, 3/1/89,107619,,122.2,,567,,5,1422,64.4548,,6276.6,,,,,91.3,127.4,65.227,63.919,1214,84.8,,95.2,,,17.9,8697.7,73.699,8681.7 4/1/89,107792,,123.1,,608,,5.2,1339,64.527,,6244,,,,,92,127.8,65.442,64.341,1376,84.7,,95,,,4.1,,, 5/1/89,107910,,123.7,,656,,5.2,1331,64.0662,,6215.1,,,,,92.6,128.3,65.637,64.575,1381,84,,95.4,,,-10.2,,, 6/1/89,108026,,124.1,,642,,5.3,1397,64.0963,,6232.2,,,,,91.5,128.8,65.806,64.713,1322,83.8,,95.2,,,-7.6,8766.1,73.694,8664.6 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4/1/90,109687,,128.9,,542,,5.4,1248,64.8976,,6419.2,,,,,91.6,134,67.976,66.752,1136,83,,95.1,,,-9,,, 5/1/90,109838,,129.1,,534,,5.4,1212,65.0068,,6405.2,,,,,91.2,134.4,68.176,66.896,1067,82.9,,95.3,,,-16.5,,, 6/1/90,109862,,129.9,,545,,5.2,1177,65.2286,,6419.4,,,,,90.8,135.1,68.439,67.191,1108,83,,95.1,,,-8.6,8981.7,76.727,8845.3 7/1/90,109830,,130.5,,542,,5.5,1171,65.1543,,6442.5,,,,,90.5,135.8,68.602,67.348,1078,82.8,,95.3,,,-18.1,,, 8/1/90,109614,,131.6,,528,,5.7,1115,65.3528,,6404.7,,,,,93.3,136.6,68.889,67.797,1069,82.9,,95.4,,,-18.2,,, 9/1/90,109525,,132.5,,496,,5.9,1110,65.4459,,6404,,,,,96.5,137.1,69.133,68.215,976,82.9,,95.8,,,-43.4,8983.9,77.487,8837 10/1/90,109366,,133.4,,465,,5.9,1014,64.945,,6353.2,,,,,99.3,137.6,69.364,68.602,925,82.1,,96.6,,,-48.2,,, 11/1/90,109216,,133.7,,493,,6.2,1145,64.1877,,6354.9,,,,,98.7,138,69.443,68.685,941,81.1,,96.7,,,-27.1,,, 12/1/90,109160,,134.2,,464,,6.3,969,63.7612,,6390.3,,,,,98.4,138.6,69.53,68.741,861,80.4,,96.3,,,-37.1,8907.4,78.765,8794.8 1/1/91,109040,,134.7,,401,,6.4,798,63.4795,,6369.3,,,,,97,139.5,69.869,68.996,786,80,,96.8,,,-32,,, 2/1/91,108735,,134.8,,482,,6.6,965,63.049,,6379.4,,,,,95,140.2,70.049,69.021,853,79.3,,96.7,,,-22.2,,, 3/1/91,108577,,134.8,,507,,6.8,921,62.7082,,6390.6,,,,,95,140.5,70.19,69.032,911,78.8,,96.4,,,-11.6,8865.6,79.128,8783.3 4/1/91,108366,,135.1,,508,,6.7,1001,62.8463,,6412.7,,,,,94.2,140.9,70.326,69.154,916,78.9,,96.6,,,-6.5,,, 5/1/91,108241,,135.6,,517,,6.9,996,63.4638,,6412.9,,,,,94,141.3,70.607,69.44,991,79.6,,96.4,,,3.9,,, 6/1/91,108338,,136,,516,,6.9,1036,64.0488,,6445.9,,,,,93.4,141.8,70.758,69.557,964,80.2,,96.1,,,13,8934.4,79.307,8806.3 7/1/91,108298,,136.2,,511,,6.8,1063,64.1013,,6432.8,,,,,92.8,142.3,70.973,69.667,973,80.2,,95.7,,,19.9,,, 8/1/91,108308,,136.6,,526,,6.9,1049,64.1515,,6445,,,,,93.1,142.9,71.166,69.827,944,80.2,,96,,,27,,, 9/1/91,108340,,137,,487,,6.9,1015,64.7177,,6463.7,,,,,93.3,143.4,71.449,70.067,974,80.8,,95.6,,,20,8977.3,79.664,8829.6 10/1/91,108357,,137.2,,524,,7,1079,64.6012,,6474,,,,,94.1,143.7,71.605,70.197,991,80.5,,96.6,,,9.5,,, 11/1/91,108299,,137.8,,575,,7,1103,64.5274,,6486.7,,,,,94.5,144.2,71.736,70.348,984,80.3,,96.7,,,1.3,,, 12/1/91,108325,,138.2,,558,,7.3,1079,64.2613,,6546.2,,,,,94.3,144.7,71.907,70.52,1061,79.9,,95.7,,,-18.8,9016.4,80.215,8862.7 1/1/92,108377,,138.3,,676,164083,7.3,1176,63.8916,,6616.3,50251,52277,188403,,94,145.1,72.099,70.613,1077,79.2,808281,95.7,,,-2.2,,, 2/1/92,108314,,138.6,114535,639,164260,7.4,1250,64.3381,,6649.9,51682,52513,189335,,94,145.4,72.292,70.789,1146,79.6,809588,96.3,,,0.6,,, 3/1/92,108368,,139.1,120025,553,163747,7.4,1297,64.902,,6659.6,50294,52935,190547,,93.9,145.9,72.473,70.962,1082,80.2,812709,96.2,,,15,9123,80.704,9017.6 4/1/92,108527,,139.4,124470,546,164759,7.4,1099,65.3746,,6679.4,50302,53411,189951,,93.6,146.3,72.71,71.153,1054,80.6,815477,96.4,,,20,,, 5/1/92,108653,,139.7,125822,554,165617,7.6,1214,65.5902,,6712.9,50044,53963,189115,,94,146.8,72.813,71.248,1056,80.7,815010,96.7,,,17,,, 6/1/92,108721,,140.1,122834,596,166098,7.8,1145,65.6132,,6741.7,51727,54551,192831,,94.8,147.1,72.869,71.374,1057,80.5,820470,96.5,,,15,9223.5,80.769,9091.2 7/1/92,108792,,140.5,122590,627,167305,7.7,1139,66.1891,,6736.8,52533,55313,191989,,95.3,147.6,73.144,71.609,1089,81.1,825008,96.6,,,27.5,,, 8/1/92,108930,,140.8,120411,636,167797,7.6,1226,65.8651,,6759.6,50940,55395,192602,,95.7,147.9,73.21,71.704,1075,80.5,826136,96.3,,,16.7,,, 9/1/92,108966,,141.1,120711,650,169407,7.6,1186,66.0268,,6725.8,51984,55515,193344,,95.9,148.1,73.331,71.823,1114,80.5,827501,96.6,,,21,9313.2,80.98,9120.1 10/1/92,109148,,141.7,127392,621,170681,7.3,1244,66.511,,6682.5,53035,56556,193625,,96.6,148.8,73.615,72.078,1132,81,827915,96.3,,,-4.8,,, 11/1/92,109284,,142.1,122374,614,171025,7.4,1214,66.8027,,6685.9,52246,56214,195300,,96,149.2,73.779,72.223,1118,81.2,829834,96.2,,,18.2,,, 12/1/92,109496,,142.3,126080,650,172995,7.4,1227,66.8587,,6922.8,51843,57446,196914,,94.4,149.6,73.917,72.35,1176,81.1,835800,96.3,,,25.4,9406.5,81.062,9209.7 1/1/93,109805,,142.8,121637,596,175078,7.3,1210,67.1432,,6793.6,52568,56439,197552,458080,94.3,150.1,74.129,72.524,1177,81.3,835995,96.4,,,31.1,,, 2/1/93,110047,,143.1,128854,604,173770,7.1,1210,67.4314,,6817.1,52480,56076,197207,462967,94.2,150.6,74.271,72.633,1148,81.5,838105,96.7,,,34.3,,, 3/1/93,109998,,143.3,126762,602,172328,7,1083,67.3651,,6794.6,53035,59813,198831,458399,94.7,150.8,74.431,72.781,1056,81.3,844816,96.6,,,16.2,9424.1,80.941,9171.9 4/1/93,110306,,143.8,127395,701,176766,7.1,1258,67.5583,,6825.9,53139,59584,199622,469425,95.2,151.4,74.651,72.977,1104,81.5,846790,96.8,,,23.3,,, 5/1/93,110572,,144.2,126529,626,178445,7.1,1260,67.3459,,6814.5,54229,58598,199395,468998,95.5,151.8,74.904,73.203,1112,81.1,847301,97.1,,,14.8,,, 6/1/93,110754,,144.3,130212,653,178201,7,1280,67.4753,,6800.8,52346,59275,199698,480247,95,152.1,74.976,73.229,1130,81.1,849144,96.9,,,3.5,9480.1,82.031,9284.9 7/1/93,111055,,144.5,128111,655,180759,6.9,1254,67.6707,,6817.1,52818,59200,199737,483571,94.5,152.3,75.13,73.345,1174,81.3,849350,97,,,-3.2,,, 8/1/93,111211,,144.8,129378,645,180692,6.8,1300,67.5985,,6826.9,53224,58805,201788,491494,94.4,152.8,75.272,73.471,1230,81.1,850895,97,,,-0.3,,, 9/1/93,111451,,145,127233,726,181800,6.7,1343,67.9241,,6809.3,53648,60679,202858,497297,94.5,152.9,75.387,73.55,1251,81.3,855006,96.9,,,7.3,9526.3,81.927,9300.8 10/1/93,111737,,145.6,133168,704,182910,6.8,1392,68.439,,6772.6,55476,62069,202074,492823,94.9,153.4,75.51,73.78,1287,81.8,855355,96.9,,,8.9,,, 11/1/93,112000,,146,130391,769,184746,6.6,1376,68.7289,,6791.6,54345,61361,203158,515934,94.4,153.9,75.702,73.917,1357,82,859061,97,,,18.9,,, 12/1/93,112312,,146.3,133565,812,186339,6.5,1533,69.0884,,7023.2,55552,61271,204842,533150,93.5,154.3,75.734,73.934,1461,82.3,863093,97.3,,,41.4,9653.5,82.17,9482.3 1/1/94,112583,,146.3,138498,619,185128,6.6,1272,69.3476,,6892.9,55159,61365,204844,513314,93.5,154.5,75.793,73.958,1390,82.4,863036,98,,,27.2,,, 2/1/94,112783,,146.7,137141,686,188077,6.6,1337,69.3617,,6908.4,53729,62974,206498,513196,93.9,154.8,75.956,74.127,1269,82.2,867675,98,,,21.3,,, 3/1/94,113248,,147.1,136548,747,191588,6.5,1564,70.0831,,6930.4,58307,64772,205748,521040,94,155.3,76.216,74.333,1342,82.9,868782,98.2,,,19.8,9748.2,81.373,9533.5 4/1/94,113598,,147.2,140336,692,191632,6.4,1465,70.4425,,6932.6,56436,64323,206510,528063,94.7,155.5,76.329,74.42,1392,83.1,871997,98.2,,,16.8,,, 5/1/94,113931,,147.5,142630,691,190940,6.1,1526,70.824,,7016.1,57342,65070,210080,532328,95.5,155.9,76.5,74.528,1396,83.3,882951,98.5,,,22.1,,, 6/1/94,114246,,147.9,145063,621,193196,6.1,1409,71.2811,,7002.8,58451,66831,209820,536198,96.3,156.4,76.666,74.708,1357,83.6,888685,98.5,,,25,9881.4,82.028,9683.7 7/1/94,114619,,148.4,145013,628,193763,6.1,1439,71.3953,,7008.8,58492,67230,211902,537232,97.2,156.7,76.829,74.944,1335,83.5,894306,98.7,,,17.7,,, 8/1/94,114901,,149,145884,656,196157,6,1450,71.8011,,7019.1,60407,68710,213360,537960,97.6,157.1,76.91,75.111,1377,83.7,902171,98.9,,,18.5,,, 9/1/94,115254,,149.3,145487,677,197754,5.9,1474,72.0617,,7048.2,60715,69026,215081,538215,97.2,157.5,77.027,75.195,1412,83.7,908038,99.1,,,18.4,9939.7,82.455,9774.9 10/1/94,115467,,149.4,149547,715,199579,5.8,1450,72.6829,,7113.4,59861,69019,218049,533273,97.9,157.8,77.207,75.322,1397,84.2,913451,99.7,,,26.1,,, 11/1/94,115887,,149.8,150038,646,199723,5.6,1511,73.1379,,7111.1,61532,71147,219673,539150,98.5,158.2,77.353,75.469,1340,84.4,919510,100.4,,,24.7,,, 12/1/94,116164,,150.1,152489,629,200670,5.5,1455,73.8818,,7144.2,62825,71281,221978,541794,98.4,158.3,77.38,75.519,1396,85,926431,101.1,,,23.3,10052.5,82.111,9887.4 1/1/95,116488,,150.5,150459,626,201583,5.6,1407,74.0142,,7174.2,63118,72442,224148,543930,98.7,159,77.567,75.667,1282,84.9,935671,101.9,,,8.8,,, 2/1/95,116692,,150.9,153856,559,198383,5.4,1316,73.9247,,7190.3,63077,71894,226012,537826,99.4,159.4,77.687,75.795,1254,84.5,942757,102.5,,,9.2,,, 3/1/95,116913,,151.2,152888,616,200230,5.4,1249,74.0284,,7208.3,64349,74057,228569,542715,99.9,159.9,77.872,75.931,1226,84.3,951531,103,,,2,10086.9,82.589,9934 4/1/95,117075,,151.8,151401,621,201048,5.8,1267,74.014,,7153.1,65074,74682,231002,543096,100.9,160.4,78.049,76.128,1259,84,959227,104,,,-11.2,,, 5/1/95,117060,,152.1,152838,674,202993,5.6,1314,74.2239,,7223.3,65755,74845,231862,542566,101.8,160.7,78.177,76.24,1271,83.9,965662,104.3,,,-8.5,,, 6/1/95,117294,,152.4,150051,725,205507,5.6,1281,74.4807,,7245.4,64855,75478,233297,546131,101.4,161.1,78.238,76.309,1305,83.9,969532,104.5,,,-20.7,10122.1,82.831,9991.4 7/1/95,117390,,152.6,148915,765,204959,5.7,1461,74.1902,,7259.9,66560,74247,235664,547342,101.1,161.4,78.362,76.404,1354,83.3,972755,104.8,,,-20.3,,, 8/1/95,117643,,152.9,154372,701,206529,5.7,1416,75.1211,,7265.8,67469,74173,236003,550996,100.8,161.8,78.547,76.568,1386,84,976101,104.3,,,1.2,,, 9/1/95,117887,,153.1,160175,678,206978,5.6,1369,75.4216,,7289.4,68943,74867,237075,554011,100.8,162.2,78.651,76.621,1421,84,980037,104.4,,,26.2,10208.8,83.295,10114 10/1/95,118040,,153.5,155473,696,206157,5.5,1369,75.3448,,7297.7,68105,74219,238005,555132,100.4,162.7,78.84,76.818,1400,83.6,984279,104.5,,,21.7,,, 11/1/95,118189,,153.7,156146,664,208661,5.6,1452,75.531,,7317.5,68009,74523,238149,557445,100.6,163,78.895,76.819,1430,83.4,986800,104.5,,,5.5,,, 12/1/95,118322,,153.9,163279,709,210434,5.6,1431,75.8317,,7326.1,69071,75342,238392,557953,101,163.1,79.007,76.968,1442,83.4,985410,104.4,,,19.6,10281.2,83.463,10178.4 1/1/96,118303,,154.7,155806,714,208731,5.6,1467,75.3347,,7337.5,68299,76764,239788,575138,101.2,163.7,79.102,77.143,1387,82.5,990755,104.9,,,-14.7,,, 2/1/96,118735,,155,150773,769,212011,5.5,1491,76.5148,,7394.6,69899,77217,239571,568052,101,164,79.203,77.263,1420,83.4,991286,104.7,,,4.8,,, 3/1/96,119002,,155.5,164976,721,213855,5.5,1424,76.4339,,7419.1,69797,77553,239391,574538,101.6,164.4,79.382,77.492,1437,82.9,989178,104.6,,,-3.5,10348.7,83.999,10289.1 4/1/96,119165,,156.1,156830,736,214644,5.6,1516,77.1163,,7376.4,70126,78870,242644,590464,102.5,164.6,79.487,77.721,1463,83.3,992104,105.2,,,21.3,,, 5/1/96,119487,,156.4,164502,746,216304,5.6,1504,77.695,,7470.8,71029,80288,242517,600186,101.8,165,79.624,77.854,1457,83.5,993754,105.6,,,19.6,,, 6/1/96,119774,,156.7,164599,721,216059,5.3,1467,78.3435,,7515.5,71056,78516,241659,602150,100.7,165.4,79.686,77.854,1429,83.8,993128,105.4,,,21,10529.4,83.901,10443.8 7/1/96,120023,,157,163588,770,216374,5.5,1472,78.208,,7495.6,69404,79536,241933,599899,100.6,165.7,79.837,78.02,1450,83.3,997579,104.9,,,29.4,,, 8/1/96,120202,,157.2,157310,826,216355,5.1,1557,78.6658,,7513.8,70563,80919,241755,603959,100.7,166,79.908,78.097,1413,83.4,999982,104.7,,,13.8,,, 9/1/96,120427,,157.7,165442,770,219240,5.2,1475,79.1997,,7531.8,70553,80748,240016,615466,101.8,166.5,80.142,78.31,1392,83.6,1000707,103.9,,,12.9,10626.8,84.216,10542.3 10/1/96,120677,,158.2,165266,720,221039,5.2,1392,79.1389,,7530.8,73769,80404,240734,621761,102.4,166.8,80.329,78.544,1358,83.1,1004411,103.6,,,8.2,,, 11/1/96,120976,,158.7,170783,771,220989,5.4,1489,79.8221,,7550.6,74263,81531,240909,620812,102.2,167.2,80.441,78.689,1412,83.4,1004506,103.2,,,11.1,,, 12/1/96,121147,,159.1,162332,805,221898,5.4,1370,80.3307,,7577.2,72842,83317,241058,606078,102.5,167.4,80.472,78.78,1411,83.5,1004679,103.2,,,8.1,10739.1,84.582,10673.8 1/1/97,121381,,159.4,161827,830,223524,5.3,1355,80.4255,,7602.1,72910,84179,243449,608608,102.2,167.8,80.556,78.881,1382,83.2,1007758,103.3,,,12.8,,, 2/1/97,121684,,159.7,170221,801,225409,5.2,1486,81.4045,,7624.6,75225,85001,243583,615415,101.2,168.1,80.72,79.045,1445,83.8,1010744,103.5,,,16.9,,, 3/1/97,122000,,159.8,167568,831,226136,5.2,1457,81.9717,,7659.5,77050,85433,244978,620467,100,168.4,80.91,79.126,1436,84,1010343,103.6,,,13.4,10820.9,85.598,10796 4/1/97,122292,,159.9,174054,744,224588,5.1,1492,82.0209,,7664.7,77769,85855,245342,616175,98.8,168.9,81.063,79.2,1421,83.6,1014591,103.6,,,6.5,,, 5/1/97,122552,,159.9,168586,760,222906,4.9,1442,82.5095,,7696.3,77883,86277,246725,624743,98.8,169.2,81.128,79.169,1414,83.7,1018535,103.4,,,1.1,,, 6/1/97,122818,,160.2,174828,793,226048,5,1494,82.9253,,7720.6,78889,86043,251010,626396,98.8,169.4,81.245,79.268,1402,83.6,1024701,103.2,,,18,10984.2,85.251,10923.2 7/1/97,123124,,160.4,178860,805,228738,4.9,1437,83.5464,,7751.8,80099,87132,249996,637410,98.5,169.7,81.297,79.312,1440,83.8,1026671,103.2,,,20.2,,, 8/1/97,123093,,160.8,177302,815,229317,4.8,1390,84.434,,7791.7,78622,87365,250888,639593,98.4,169.8,81.266,79.377,1449,84.2,1028029,103.2,,,17.2,,, 9/1/97,123605,,161.2,177835,840,230284,4.9,1546,85.1978,,7813,79287,88556,253166,646526,98.4,170.2,81.421,79.557,1494,84.4,1034401,102.9,,,19.1,11124,85.385,11105.9 10/1/97,123945,,161.5,177801,800,229822,4.7,1520,85.9177,,7849.7,79383,88472,254054,653196,98.6,170.6,81.543,79.66,1499,84.6,1038300,102.5,,,19.3,,, 11/1/97,124251,,161.7,191187,864,230486,4.6,1510,86.6748,,7898.4,78300,88086,256109,643710,98.1,170.8,81.576,79.67,1469,84.8,1040120,102.5,,,19.8,,, 12/1/97,124554,,161.8,173770,793,231197,4.7,1566,86.9454,,7942.9,79038,90327,258454,642021,97.2,171.2,81.627,79.657,1456,84.5,1045506,102,,,15.6,11210.3,86.564,11250.9 1/1/98,124830,,162,174288,872,231605,4.6,1525,87.3838,,8015,79008,89784,259088,645686,95.9,171.6,81.743,79.688,1555,84.4,1048287,101.3,,,18.6,,, 2/1/98,125026,,162,181270,866,231664,4.6,1584,87.482,,8067,77931,89495,261734,648121,95,171.9,81.802,79.639,1647,83.9,1055020,101,,,13.2,,, 3/1/98,125177,,162,176886,836,233043,4.7,1567,87.552,,8114,78812,91692,263439,666906,94.1,172.2,81.88,79.645,1605,83.4,1060195,100.7,,,10.5,11321.2,87.548,11371.1 4/1/98,125457,,162.2,180915,866,235976,4.3,1540,87.854,,8140.5,77626,91566,263284,674351,93.9,172.5,82.034,79.746,1547,83.2,1062374,100.3,,,8.7,,, 5/1/98,125861,,162.6,180634,887,237055,4.4,1536,88.4226,,8173.6,77147,91349,265233,674325,93.7,172.9,82.117,79.858,1554,83.2,1061523,100.4,,,13.2,,, 6/1/98,126080,,162.8,172189,923,238958,4.5,1641,87.8558,,8219.9,76961,90208,264400,703177,93.1,173.2,82.018,79.794,1551,82.2,1061963,99.9,,,24.1,11431,88.113,11534.1 7/1/98,126209,,163.2,170459,876,237423,4.5,1698,87.5421,,8234.8,76149,90098,264793,696540,92.3,173.5,82.243,79.986,1610,81.4,1063957,99.5,,,8.3,,, 8/1/98,126551,,163.4,179033,846,236412,4.5,1614,89.3341,,8261.8,75512,91540,267204,698156,92,174,82.401,80.095,1654,82.6,1066374,99,,,10.4,,, 9/1/98,126774,,163.5,181422,864,238542,4.6,1582,89.1794,,8287.3,77179,91999,268711,707561,92.2,174.2,82.382,80.044,1577,82,1070807,98.5,,,-14.2,11580.6,88.286,11697.9 10/1/98,126973,,163.9,178527,893,242531,4.5,1715,89.8907,,8301.1,79351,94166,269467,707943,92.3,174.4,82.538,80.215,1719,82.3,1073232,98.4,,,3.5,,, 11/1/98,127255,,164.1,182400,995,244307,4.4,1660,89.8458,,8335,79117,94290,271044,707845,91.8,174.8,82.549,80.217,1672,81.8,1077587,98.6,,,-4.7,,, 12/1/98,127601,,164.4,178424,949,246577,4.4,1792,90.1893,,8349.5,78382,93127,272297,706989,91,175.4,82.697,80.302,1742,81.8,1077188,98.5,,,4.6,11770.7,88.038,11805.7 1/1/99,127727,,164.7,186527,875,246891,4.3,1748,90.6043,,8381.7,78033,93980,272635,708818,91.3,175.6,82.854,80.448,1732,81.8,1077133,98.5,,7582,13.7,,, 2/1/99,128137,,164.7,185546,848,249510,4.4,1670,91.0816,,8409,77635,96421,274923,726308,91.2,175.6,82.855,80.428,1720,81.9,1082750,98.3,,7620,15.1,,, 3/1/99,128244,,164.8,184689,863,250657,4.2,1710,91.235,,8418.6,78449,96350,275847,737226,91.5,175.7,82.874,80.484,1665,81.6,1090048,97.9,,7654.1,4.3,11864.7,88.64,11952 4/1/99,128620,,165.9,182993,918,252418,4.3,1553,91.4677,,8402.6,78872,97125,276188,728788,92.4,176.3,83.069,80.856,1600,81.5,1092922,98.1,,7697.8,20.6,,, 5/1/99,128831,,166,185963,888,254738,4.2,1611,92.1525,,8420.1,78939,99168,276792,727358,93.1,176.5,83.126,80.889,1640,81.8,1095938,98.2,,7731.6,13.1,,, 6/1/99,129091,,166,182590,923,255472,4.3,1559,92.0042,,8448.9,79234,102349,276961,739167,92.9,176.6,83.16,80.906,1702,81.4,1098785,98.2,,7765.2,5.8,11962.5,88.692,12026.2 7/1/99,129417,,166.7,189083,900,257441,4.3,1669,92.5769,,8458.4,80449,103870,279948,745815,93.8,177.1,83.308,81.12,1682,81.6,1104056,98.1,,7778.8,9.8,,, 8/1/99,129577,,167.1,189414,893,260253,4.2,1648,92.9517,,8494.4,81943,104920,280588,741524,94.8,177.3,83.344,81.263,1671,81.6,1105878,98.4,,7820.9,13.8,,, 9/1/99,129791,,167.8,188910,826,261352,4.2,1635,92.5954,,8488.3,83163,106063,282127,751402,95.8,177.8,83.556,81.547,1551,81,1112276,98.5,,7858.2,13.9,12113.1,88.684,12137.4 10/1/99,130191,,168.1,194547,872,261825,4.1,1608,93.8128,,8541.3,83565,107096,285104,759906,96,178.1,83.688,81.677,1649,81.8,1115769,98.8,,7874.8,16,,, 11/1/99,130484,,168.4,186597,863,264883,4.1,1648,94.2587,,8601.7,84441,109665,288823,781199,96.7,178.4,83.769,81.749,1672,81.9,1128342,99,,7911.9,20.9,,, 12/1/99,130780,,168.8,196344,873,269876,4,1708,94.9777,,8672.2,85142,111479,290182,789431,97.4,178.7,83.888,81.951,1683,82.2,1137264,99,,8015.7,14.2,12323.3,89.052,12335.9 1/1/00,131010,,169.3,201360,873,268091,4,1636,94.9864,,8744.8,85646,112733,292768,784940,97.8,179.3,84.103,82.186,1727,81.9,1139998,99.2,,7988.5,11.2,,, 2/1/00,131140,,170,183911,856,272020,4.1,1737,95.2576,,8778.7,86142,116071,294593,793737,99.7,179.4,84.229,82.445,1692,81.9,1146461,99.6,,8065.3,14.6,,, 3/1/00,131608,,171,192130,900,275214,4,1604,95.6407,,8800.6,87368,118523,296789,809459,99.9,180,84.4,82.797,1651,81.9,1150694,100,,8110.8,19.4,12359.1,92.702,12587.7 4/1/00,131895,,170.9,195044,841,271004,3.8,1626,96.3318,,8836.9,88855,117655,299545,804766,98.5,180.3,84.445,82.72,1597,82.3,1157508,100,,8101.6,10,,, 5/1/00,132122,,171.2,188606,857,271418,4,1575,96.5139,,8869.8,88017,117830,301245,805005,98.8,180.7,84.531,82.784,1543,82.1,1163939,100.2,,8139,13.9,,, 6/1/00,132075,,172.2,219745,793,273440,4,1559,96.5856,,8890.2,90771,121737,303182,795411,100.2,181.1,84.585,83.056,1572,81.9,1174272,100.1,,8156,2.6,12592.5,91.095,12657.5 7/1/00,132251,,172.7,189265,887,272638,4,1463,96.4624,,8937.1,90421,121848,304073,783795,100.2,181.5,84.771,83.256,1542,81.6,1175346,100,,8160.6,4.7,,, 8/1/00,132241,,172.7,188730,848,272943,4.1,1541,96.1414,,8985.2,92424,122459,305053,805341,100.4,181.9,84.869,83.243,1552,81,1183272,99.8,,8203.8,17.3,,, 9/1/00,132377,,173.6,199947,912,277523,3.9,1507,96.5318,,8985.5,92347,126365,305223,814330,101.6,182.3,85.079,83.604,1570,81.1,1183439,100.4,,8269.4,5.5,12607.7,92.915,12751.6 10/1/00,132363,,173.9,186158,933,276973,3.9,1549,96.2532,,9000,91511,124734,307282,816100,101.2,182.6,85.199,83.718,1577,80.6,1189917,100.3,,8265.8,1.8,,, 11/1/00,132589,,174.2,189392,880,275923,3.9,1551,96.2769,,8994,91388,123996,309328,820054,101.2,183.1,85.344,83.83,1614,80.4,1197042,100.3,,8272.5,7.1,,, 12/1/00,132731,4736,174.6,188659,983,275736,3.9,1532,96.0165,,9004.6,90431,123885,309191,811516,100.5,183.3,85.403,83.938,1543,79.9,1195870,100.1,,8314.9,-7.8,12679.3,92.507,12729 1/1/01,132705,5385,175.6,177056,936,278916,4.2,1600,95.3542,,9054.5,90331,125148,308745,814479,100.5,183.9,85.683,84.311,1699,79.1,1197916,100.3,,8314.4,-36.6,,, 2/1/01,132777,4658,176,180276,963,278799,4.2,1625,94.7736,,9073,90181,119530,309036,813647,99.9,184.4,85.814,84.424,1656,78.4,1191628,100.2,,8326.3,-29.4,,, 3/1/01,132752,4563,176.1,182209,939,276468,4.3,1590,94.5456,,9101.3,88454,121186,309051,828057,98.3,184.7,85.898,84.427,1659,77.9,1186070,100,,8317.4,-20.8,12643.3,95.041,12876.4 4/1/01,132471,4901,176.4,171850,909,280804,4.4,1649,94.3111,,9080.8,86748,117966,310478,842392,97.8,185.1,86.044,84.584,1666,77.5,1184414,99.9,,8318.7,-10.8,,, 5/1/01,132433,4550,177.3,177749,885,281540,4.3,1605,93.6876,,9061.7,87256,114702,311619,848146,98,185.3,86.074,84.814,1665,76.8,1182107,99.6,,8351.4,-11.8,,, 6/1/01,132302,4280,177.7,176350,882,280399,4.5,1636,93.1114,,9062.4,85035,114175,309196,855730,97.6,186,86.278,84.974,1626,76.1,1173167,99.4,,8352.1,-7,12710.3,93.734,12853 7/1/01,132190,4499,177.4,170129,880,279522,4.6,1670,92.586,,9198.4,82833,112914,306252,850471,96.1,186.4,86.503,84.949,1598,75.5,1165024,99,-13.29,8368.8,-12.6,,, 8/1/01,132033,4134,177.4,170484,866,281423,4.9,1567,92.4101,,9359,83787,111958,305464,847465,96,186.7,86.554,84.946,1615,75.2,1163584,98.8,-8.01,8412.7,-18.1,,, 9/1/01,131793,3975,178.1,164123,853,276095,5,1562,92.0924,,9290.6,77367,108508,304703,837412,95.9,187.1,86.078,84.67,1565,74.8,1157220,99,-12.5,8332.2,-8.2,12670.1,93.335,12807.3 10/1/01,131468,3605,177.6,171530,871,294613,5.3,1540,91.6854,,9145.7,77883,108722,302932,845941,93.7,187.4,86.694,84.978,1566,74.3,1139069,98.3,-14.74,8531.9,-23.6,,, 11/1/01,131175,3387,177.5,163811,924,286960,5.5,1602,91.2155,,9167.5,77999,107735,299419,843911,92.3,188.1,86.869,84.921,1651,73.8,1126307,97.8,-21.51,8489.9,-17.7,,, 12/1/01,131005,3385,177.4,165304,979,283708,5.7,1568,91.2654,,9190.4,77780,104618,297536,849689,91.4,188.4,86.888,84.833,1680,73.7,1118527,97.6,-9.78,8475.6,-11,12705.3,92.997,12742.9 1/1/02,130867,3759,177.7,162604,880,283577,5.7,1698,91.7848,,9385.7,78920,108275,296625,858654,91.6,188.7,86.918,84.893,1665,74,1117593,97.5,1.43,8502.4,10.5,,, 2/1/02,130733,3372,178,171172,948,285061,5.7,1829,91.8034,,9395.5,78880,111167,294141,862338,91.6,189.1,87.083,85.035,1787,73.9,1112391,97.3,13.3,8537.6,11,,, 3/1/02,130713,3551,178.5,168666,923,284263,5.7,1642,92.5295,,9391.3,79601,110425,294220,844551,92.8,189.2,87.193,85.272,1691,74.4,1108261,97.6,13.82,8533.8,12.3,12822.3,91.42,12907.7 4/1/02,130634,3472,179.3,171197,936,288820,5.9,1592,92.9204,,9417.9,81551,115217,293147,858240,94.3,189.7,87.452,85.64,1669,74.7,1107085,98,20.18,8577.6,12.6,,, 5/1/02,130627,3596,179.5,172743,978,284994,5.8,1764,93.2998,,9438.5,81724,115645,293444,850935,94.4,190,87.565,85.709,1716,74.9,1110533,98,12.92,8543,10.1,,, 6/1/02,130684,3365,179.6,165875,957,287401,5.8,1717,94.1905,,9459,82741,117641,294407,846777,94.1,190.2,87.706,85.818,1758,75.6,1113042,98,8.91,8583.8,20.4,12893,92.157,12986.9 7/1/02,130599,3411,180,174812,956,290427,5.8,1655,93.9664,,9429.7,83036,116686,296753,847129,94.5,190.5,87.87,85.996,1738,75.4,1119183,98.3,-1.87,8633.6,5.9,,, 8/1/02,130585,3490,180.5,177665,1014,292582,5.7,1633,93.9897,,9422,83422,119165,297560,839008,94.8,191.1,88.039,86.161,1695,75.4,1120477,98.5,8.24,8645.8,-1.3,,, 9/1/02,130526,3308,180.8,167950,1044,288434,5.7,1804,94.1275,,9427.1,82744,119263,298751,832134,95.5,191.3,88.173,86.308,1803,75.5,1128501,98.8,6.33,8604.7,4.4,12955.8,91.896,13003.8 10/1/02,130652,3535,181.2,167444,1006,289634,5.7,1648,93.7988,,9448.3,82028,117199,298373,839690,95.5,191.5,88.253,86.469,1799,75.2,1130517,98.7,-3.8,8638.6,-7.6,,, 11/1/02,130662,3415,181.5,170662,1024,291475,5.9,1753,94.2885,,9469.5,83041,122665,298646,844697,94.6,191.9,88.339,86.555,1771,75.6,1132287,98.8,3.97,8665.3,7.4,,, 12/1/02,130505,2943,181.8,163155,1048,293819,6,1788,93.8334,,9497,81017,124311,301281,855921,95.2,192.1,88.407,86.625,1896,75.3,1139031,98.6,2.38,8719.2,7.2,12964,92.282,13078.9 1/1/03,130597,3824,182.6,169107,999,295294,5.8,1853,94.3584,,9500.8,82110,122850,301118,863855,96.9,192.4,88.432,86.853,1808,75.7,1140033,98.9,8.11,8727.3,5.5,,, 2/1/03,130447,3381,183.6,173001,936,291178,5.9,1629,94.6468,,9481.3,82779,122142,302246,859225,98.5,192.5,88.541,87.209,1854,76,1148945,99.5,-3.54,8684.9,-1.6,,, 3/1/03,130238,3052,183.9,173201,999,296347,5.9,1726,94.4394,,9514.9,82580,125935,303337,851132,99.1,192.5,88.671,87.421,1757,75.9,1149327,99.7,6.47,8725.5,-3.9,13031.2,91.941,13099.6 4/1/03,130194,3340,183.2,169542,1012,295643,6,1643,93.764,,9576.2,81429,123417,304070,859459,96,192.5,88.768,87.271,1803,75.3,1150311,99.6,-14.49,8779.6,-6.7,,, 5/1/03,130186,3233,182.9,171205,1078,296395,6.1,1751,93.7793,,9650.6,82172,122951,302540,866814,95.3,192.9,88.894,87.17,1835,75.4,1145242,99.7,15.66,8798.5,-0.6,,, 6/1/03,130195,3334,183.1,174113,1193,299662,6.3,1867,93.9277,,9683.2,84632,124253,301697,880865,96.2,193,88.945,87.265,1875,75.5,1142156,99.5,25.13,8850.4,3.7,13152.1,92.304,13221.5 7/1/03,130219,3270,183.7,173055,1168,302788,6.2,1897,94.3114,,9792.1,85373,126735,301837,891264,96.7,193.4,89.144,87.502,1885,75.8,1139420,99.4,19.33,8896.1,7.7,,, 8/1/03,130177,3283,184.5,174328,1206,307745,6.1,1833,94.138,,9852.8,84247,124049,301292,901839,96.7,193.6,89.225,87.778,1966,75.7,1132679,99.4,15.54,8976.4,20.3,,, 9/1/03,130281,3074,185.1,178118,1131,305916,6.1,1939,94.7363,,9739,86224,127930,302194,911589,96.2,193.7,89.319,88.026,1961,76.2,1136927,99.8,20.37,8945.7,20.7,13372.4,91.689,13348.1 10/1/03,130479,3205,184.9,183254,1144,304824,6,1967,94.8514,,9780.6,88195,129466,305106,925732,96.3,194,89.437,87.998,2012,76.3,1142942,100,36.78,8967.4,28.3,,, 11/1/03,130496,3157,185,182472,1093,308551,5.8,2083,95.6337,,9852.4,90513,130355,306146,925985,96.8,194,89.536,88.089,1918,76.9,1144972,100.5,33.97,9026,26.9,,, 12/1/03,130618,3214,185.5,180958,1129,307362,5.7,2057,95.5638,,9869.1,90164,134228,308305,948491,97.5,194.2,89.651,88.286,1987,76.9,1147613,100.8,27.36,9033,26.5,13528.7,92.037,13479.1 1/1/04,130780,3459,186.3,176855,1165,309225,5.7,1911,95.7472,,9879.9,90056,134408,308614,938826,99,194.6,89.857,88.606,1952,77.1,1148861,101.5,32.47,9071.5,36.1,,, 2/1/04,130826,3402,186.7,180727,1159,311427,5.6,1846,96.3214,,9900.7,93882,138204,312596,938656,99.4,194.9,90.026,88.815,1966,77.5,1158924,102.2,36.98,9089.3,27.8,,, 3/1/04,131158,3380,187.1,191580,1276,316935,5.8,1998,95.8684,,9936.6,96519,143003,314683,960946,100.2,195.5,90.196,88.969,2066,77.2,1168406,103,32.66,9128.5,29.6,13606.5,91.929,13581.8 4/1/04,131407,3629,187.4,184187,1186,313531,5.6,2003,96.2677,,9969.2,95754,143232,314745,967761,100.4,195.9,90.418,89.123,2070,77.5,1176107,103.7,39,9135.9,32.3,,, 5/1/04,131715,3660,188.2,183593,1241,318962,5.6,1981,97.0723,,10020.2,97259,145428,318348,974158,101.9,196.2,90.558,89.426,2150,78.2,1183322,104.1,36.95,9184.6,29,,, 6/1/04,131791,3424,188.9,185560,1180,314971,5.6,1828,96.2562,,10020.5,94853,149555,320957,983072,101.7,196.6,90.74,89.715,2020,77.6,1195490,103.4,27.05,9145.9,30.6,13706.2,92.815,13722.4 7/1/04,131835,3934,189.1,187032,1088,318532,5.5,2002,97.0032,,10036.4,96474,147767,326795,1006119,102.1,196.8,90.889,89.834,2112,78.2,1207087,103.9,34.98,9207.3,34.7,,, 8/1/04,131956,3619,189.2,185137,1175,318945,5.4,2024,97.0723,,10065.8,96909,150225,330144,1013724,103.6,196.9,90.956,89.908,2056,78.2,1216708,103.4,15.23,9226.2,25.1,,, 9/1/04,132120,3742,189.8,188132,1214,324607,5.4,1905,97.1565,,10066,98277,149765,330080,1012290,104.1,197.5,91.122,90.083,2041,78.3,1217241,103.8,28.37,9295.6,19.6,13830.8,94.098,13878.8 10/1/04,132466,3792,190.8,185578,1305,326680,5.5,2072,98.0701,,10075,99773,154734,335181,1015562,105.8,197.9,91.275,90.43,2097,79,1224943,104.4,24.54,9309.5,26.9,,, 11/1/04,132530,3238,191.7,192940,1179,327837,5.4,1782,98.2541,,10051.2,99533,158352,339295,1023210,105.5,198.3,91.421,90.734,2079,79.1,1238657,104.7,15.31,9323,19.2,,, 12/1/04,132660,3650,191.7,192834,1242,331877,5.4,2042,98.9703,,10418.5,102259,156760,340147,1037684,104,198.6,91.549,90.793,2082,79.7,1241070,104.8,21.59,9381,25.5,13950.4,94.204,13949 1/1/05,132794,3670,191.6,193240,1203,329187,5.3,2144,99.417,,10070.4,103059,158620,345077,1045913,104.6,199,91.813,90.854,2139,80,1252690,105.6,15.55,9379.8,13.4,,, 2/1/05,133033,3845,192.4,195227,1319,332847,5.4,2207,100.0955,,10074.5,103867,161321,347014,1066374,105.5,199.4,91.978,91.12,2114,80.4,1261588,105.7,17.14,9412.3,21.1,,, 3/1/05,133169,3831,193.1,187090,1328,332517,5.2,1864,99.9283,,10105.9,104805,157424,348963,1071467,107.8,200.1,92.204,91.392,2062,80.2,1269402,106.4,24.29,9435.5,15.1,14099.1,93.891,14084.9 4/1/05,133534,4243,193.7,195130,1260,337608,5.2,2061,100.0742,,10125.6,106865,163980,352174,1080952,108.8,200.2,92.321,91.655,2150,80.2,1275059,106.9,8.3,9510.4,25.3,,, 5/1/05,133708,3884,193.6,206420,1286,334551,5.1,2025,100.2414,,10167.5,106231,162495,352631,1093516,107.9,200.5,92.544,91.738,2085,80.3,1275921,106.7,-4.92,9463.2,9.3,,, 6/1/05,133955,4022,193.7,209180,1274,344034,5,2068,100.6437,,10196.8,106314,164574,354436,1105851,109.2,200.6,92.603,91.792,2178,80.5,1276189,106.7,7.8,9560.7,-1.3,14172.7,94.501,14185.8 7/1/05,134331,4319,194.9,197076,1389,346715,5,2054,100.3278,,10222.5,106679,164742,355779,1118698,110.5,200.9,92.741,92.181,2203,80.1,1270684,106.8,23.78,9620.8,8.1,,, 8/1/05,134525,4073,196.1,204803,1255,342950,4.9,2095,100.5151,,10238,107997,166385,357483,1129503,112.1,201.1,92.833,92.563,2219,80.2,1275135,106.6,23.72,9586.1,11.2,,, 9/1/05,134593,4237,198.8,204139,1244,343711,5,2151,98.6063,,10185.6,106885,171808,358681,1148733,114.4,201.3,93.046,93.458,2263,78.5,1282763,107.5,16.92,9548.8,7.1,14291.8,94.958,14310.8 10/1/05,134678,4277,199.1,209844,1336,344390,5,2065,99.8695,,10234.6,109388,176528,361610,1160818,114.5,202,93.294,93.594,2170,79.4,1291267,108.3,12.05,9573.4,4.8,,, 11/1/05,135015,4220,198.1,222564,1214,347047,5,2147,100.9014,,10304.9,110656,174746,363609,1172553,112.3,202.5,93.515,93.381,2218,80.1,1300312,107.6,18.01,9625.4,10.3,,, 12/1/05,135174,4064,198.1,220015,1239,347441,4.9,1994,101.4873,,10359.6,113277,177643,368075,1184609,112.3,202.8,93.633,93.4,2120,80.5,1313363,107.7,22.9,9665.3,12.9,14373.4,95.508,14508 1/1/06,135452,4298,199.3,207660,1174,357626,4.7,2273,101.6088,,10498.6,115061,181741,369334,1195698,113.7,203.2,93.793,93.811,2212,80.5,1322938,108.5,17.5,9701.1,5.4,,, 2/1/06,135768,4229,199.4,217661,1061,354614,4.8,2119,101.6839,,10543.4,115652,178503,372909,1205060,112.8,203.6,93.926,93.852,2141,80.4,1327296,108.6,20.89,9733.6,15.3,,, 3/1/06,136049,4493,199.7,227670,1116,356357,4.7,1969,101.8522,,10562.7,118272,180846,374669,1205018,112.7,204.3,94.153,94.007,2118,80.5,1340157,108.8,33.19,9753,14.7,14546.1,96.93,14782.8 4/1/06,136232,4680,200.7,214414,1123,357320,4.7,1821,102.2952,,10549.1,118672,181516,379473,1192849,115.1,204.8,94.39,94.398,1998,80.7,1348834,109.6,18.48,9771.1,14.2,,, 5/1/06,136255,4389,201.3,215979,1086,356423,4.6,1942,102.1531,,10539.8,120599,185444,382353,1180699,117.2,205.4,94.576,94.609,1905,80.5,1363477,110.4,18.61,9781.9,13.8,,, 6/1/06,136337,4349,201.8,221232,1074,357763,4.6,1802,102.522,,10563.3,122053,185534,385029,1172074,117.3,205.9,94.803,94.832,1867,80.6,1376219,111.2,26.5,9790.2,11.7,14589.6,97.041,14805.1 7/1/06,136544,4154,202.9,211849,965,359217,4.7,1737,102.5057,,10560.4,119803,186328,388417,1157784,118.2,206.3,94.913,95.167,1763,80.5,1381506,111.6,16.56,9836,4,,, 8/1/06,136725,4560,203.8,210303,1035,360497,4.7,1650,102.8357,,10558.6,122321,190144,392613,1146049,118.8,206.8,95.108,95.467,1722,80.6,1391671,112.1,11.72,9813.7,12.5,,, 9/1/06,136883,4516,202.8,236000,1016,358468,4.5,1720,102.6606,,10623.5,123562,188497,394472,1136144,116.2,207.2,95.272,95.232,1655,80.3,1396955,111.7,14.95,9864.5,-0.8,14602.6,97.594,14863.7 10/1/06,136887,4472,201.9,216908,941,358435,4.4,1491,102.6297,,10684.6,125646,184636,396159,1123281,113.3,207.6,95.413,94.979,1570,80.1,1401162,111.4,18.72,9911.3,2.3,,, 11/1/06,137095,4341,202,225791,1003,359256,4.5,1570,102.539,,10722.4,127445,186020,400600,1122263,113.8,207.8,95.45,95.004,1535,79.9,1406822,111.8,22.92,9927.5,4.5,,, 12/1/06,137266,4278,203.1,229389,998,364300,4.4,1649,103.6229,,10750.4,128557,190149,399056,1134855,115.1,208.1,95.632,95.393,1638,80.5,1407550,112.5,20.08,9976.5,-1.8,14716.9,98.555,14920.2 1/1/07,137506,4630,203.437,218565,891,363462,4.6,1409,103.1171,,10759.9,130079,187734,400300,1138412,113.7,208.6,95.998,95.689,1626,80,1412861,113,7.34,9983.8,7.5,,, 2/1/07,137596,4465,204.226,221337,828,364090,4.5,1480,104.172,,10788,128399,186877,402004,1138752,114.1,209.135,96.227,96.005,1598,80.6,1418881,113.9,24.5,9990.3,3.5,,, 3/1/07,137785,4666,205.288,228747,833,367714,4.4,1495,104.3501,,10820.6,133133,194930,404430,1146756,115.9,209.418,96.305,96.34,1596,80.6,1421414,114.7,13.4,9997.9,2.8,14726,100.88,14882.6 4/1/07,137864,4824,205.904,233592,887,366065,4.5,1490,105.0975,,10818.3,132458,192972,405351,1150637,117.5,209.747,96.397,96.527,1470,81,1428782,115.2,3.94,10018.8,3,,, 5/1/07,138007,4550,206.755,227743,842,370887,4.4,1415,105.1436,,10813,135183,194470,406984,1161625,118.6,210.058,96.5,96.798,1493,80.9,1438234,115.5,9.91,10030.3,3.7,,, 6/1/07,138085,4608,207.234,229855,793,367933,4.6,1448,105.1474,,10800.7,136594,196114,408454,1162937,120,210.392,96.651,96.997,1407,80.7,1445825,116,24.34,10024.7,17.3,14838.7,100.199,14904.1 7/1/07,138052,4490,207.603,238609,778,369472,4.7,1354,105.1149,,10825.1,137564,197478,408796,1155029,121.5,210.773,96.793,97.141,1361,80.6,1447601,116.1,26.18,10047.1,6.8,,, 8/1/07,138028,4555,207.667,233226,699,370982,4.6,1330,105.3166,,10831.6,140485,197490,410409,1158779,121.1,211.119,96.956,97.225,1321,80.7,1453555,116.3,22.87,10080.7,-0.5,,, 9/1/07,138116,4523,208.547,225797,686,373138,4.7,1183,105.6629,,10859.2,141276,199070,413663,1158334,121.8,211.554,97.221,97.601,1261,80.9,1461665,116.7,14.69,10079.7,7.5,14938.5,99.388,14822.4 10/1/07,138201,4300,209.19,229267,727,375048,4.7,1264,105.1595,,10839.4,144737,201274,414494,1153031,123.6,212.077,97.46,97.883,1192,80.5,1466607,117.6,25.82,10067.3,7.8,,, 11/1/07,138316,4156,210.834,232433,641,378371,4.7,1197,105.729,,10828.9,146373,206090,419444,1133745,127.5,212.66,97.619,98.373,1224,80.9,1476061,118.7,25.88,10093,6.7,,, 12/1/07,138413,4123,211.445,242879,619,375349,5,1037,105.7256,,10874.9,147269,204422,424640,1114939,127.3,213.168,97.857,98.638,1149,80.9,1486039,119.3,8.6,10085.1,-5.4,14991.8,100.034,14816.6 1/1/08,138432,4260,212.174,237274,627,375303,5,1084,105.4069,,10906.2,150167,211306,430413,1111225,129.2,213.771,98.058,98.894,1094,80.7,1501539,120.7,7.1,10074.7,-18.4,,, 2/1/08,138346,4042,212.687,233810,593,371661,4.9,1103,105.054,,10925.4,152433,216781,434859,1097981,129.5,213.939,98.173,99.11,1014,80.5,1508060,121.8,-7.4,10045.3,-20.2,,, 3/1/08,138268,4001,213.448,230770,535,371961,5.1,1005,104.7987,,10948.4,152089,212154,435828,1103225,133.5,214.42,98.394,99.416,967,80.4,1507598,123.8,-14.56,10063,-14.7,14889.5,102.035,14842.2 4/1/08,138058,4098,213.942,229958,536,373877,5,1013,104.0207,,10906.9,156756,220284,442797,1101713,137.3,214.56,98.514,99.654,1008,79.8,1516249,124.4,-3,10079.5,-21.2,,, 5/1/08,137873,3960,215.208,230207,504,375790,5.4,973,103.4941,,11431.6,158799,220950,445480,1101282,141.2,214.936,98.702,100.091,995,79.5,1518473,124.8,-3.99,10084.1,-16.1,,, 6/1/08,137708,3767,217.463,229634,487,376584,5.6,1046,103.3216,,11129.8,163609,224279,451407,1089615,145.5,215.424,98.894,100.786,1180,79.4,1529914,126.1,-8.08,10070.2,-16.8,14963.4,101.115,14832.4 7/1/08,137499,3821,219.016,223764,477,374774,5.8,923,102.7625,,10954.3,165379,232221,457317,1087047,147.5,215.965,99.029,101.218,921,78.9,1540430,128,-5.23,10028.8,-16.2,,, 8/1/08,137233,3665,218.69,216357,435,372091,6.1,844,101.2245,,10866.7,162658,224766,461590,1069121,143,216.393,99.147,101.135,858,77.7,1541344,125.9,-0.8,10026.4,-17.6,,, 9/1/08,136781,3264,218.877,210859,433,366167,6.1,820,96.8689,,10878.9,153586,214086,459693,1059904,137.8,216.713,99.27,101.236,797,74.3,1532678,124.9,-8.08,9960,2,14891.6,101.726,14767 10/1/08,136308,3292,216.995,192059,393,352900,6.5,777,97.7617,,10933,151364,211555,453086,1056692,129.6,216.788,99.261,100.684,736,74.9,1517254,122.3,-25.85,9915.6,-37.6,,, 11/1/08,135539,2956,213.153,183989,389,339942,6.8,652,96.5572,,11008.9,142400,187123,450605,1035307,120,216.947,99.255,99.545,626,74,1495985,118.4,-22.65,9896.5,-40.9,,, 12/1/08,134844,2830,211.398,173900,377,332065,7.3,560,93.7183,,10969.2,132372,174835,445208,999710,114.5,216.925,99.228,99.007,554,71.7,1464379,115.8,-25.41,9842.1,-37.6,14577,103.48,14479.5 1/1/09,134053,2767,211.933,153310,336,336977,7.8,490,91.5058,,11015.1,125294,163136,440581,969117,113,217.346,99.259,99.068,545,70,1446916,116.6,-26.66,9884.2,-31.1,,, 2/1/09,133350,2791,212.705,145602,372,335765,8.3,582,90.934,,10916,127342,155109,432272,965485,113,217.792,99.358,99.284,558,69.5,1424654,116.3,-34.53,9846.2,-39.4,,, 3/1/09,132527,2491,212.495,145571,339,330219,8.7,505,89.5012,,10916.6,125998,155161,423761,958519,113.6,218.253,99.48,99.193,513,68.3,1404704,115.5,-33.43,9822.1,-34.4,14375,100.138,14257.8 4/1/09,131841,2357,212.709,144239,337,331314,9,478,88.7058,,10976.4,124390,154095,417893,927456,114.8,218.706,99.737,99.34,521,67.7,1387702,116.1,-19.13,9806.6,-25.2,,, 5/1/09,131490,2427,213.022,150641,376,334290,9.4,540,87.7758,,11147.2,126221,151593,412663,913727,116.8,218.904,99.84,99.474,556,67,1370298,116.6,-6.2,9811.4,-22.4,,, 6/1/09,131020,2428,214.79,145782,393,339532,9.5,585,87.4125,,10958,128891,155258,406457,907196,120,219.112,99.974,100.067,601,66.7,1353860,117.8,-9.51,9801.1,0.3,14355.6,100.66,14259.2 7/1/09,130691,2196,214.726,156180,411,340286,9.5,594,88.3209,,10919.5,130848,163637,400364,906087,119.3,219.263,99.991,100.02,595,67.4,1339022,117.4,0.06,9833.3,-6.7,,, 8/1/09,130479,2306,215.445,157966,418,346705,9.6,586,89.2996,,10892.4,131438,162705,395611,893746,121.1,219.496,100.11,100.288,616,68.2,1319852,118.1,12.8,9933.4,8.8,,, 9/1/09,130260,2478,215.861,157328,386,338356,9.8,585,89.9908,,10907.1,136142,170632,391004,882793,121.3,219.92,100.291,100.454,609,68.8,1314699,117.9,20.93,9830.9,14.9,14402.5,99.899,14328.1 10/1/09,130060,2400,216.509,162553,396,341590,10,534,90.2527,,10862.6,140401,174228,392490,866972,122.3,220.501,100.581,100.764,583,69.1,1322088,117.9,33.13,9849.5,12.6,,, 11/1/09,130053,2350,217.234,161811,375,344911,9.9,588,90.6331,100.2,10888,141370,178573,398592,853896,124.1,220.666,100.666,100.997,623,69.5,1330686,118.9,25.56,9848.1,15.5,,, 12/1/09,129774,2407,217.347,159408,352,346258,9.9,581,90.8895,100.3,10925.7,144718,182700,397020,838737,124.4,220.881,100.713,101.052,664,69.8,1329577,119.7,5.2,9896.8,16.5,14541.9,99.32,14528.3 1/1/10,129802,2636,217.488,182190,345,346349,9.8,614,91.9065,101.2,10906.7,144013,181167,397177,814452,125.9,220.633,100.807,101.234,636,70.8,1331369,120.7,14.8,9881.7,12.9,,, 2/1/10,129733,2578,217.281,176104,336,346972,9.8,604,92.2135,101,10887.5,145059,186093,398452,808245,125.8,220.731,100.89,101.248,650,71.2,1338781,120.3,21.28,9911.3,14.1,,, 3/1/10,129896,2666,217.353,180182,381,354625,9.9,636,92.8133,101.1,10912,149262,189028,400709,815113,126.3,220.783,101.033,101.363,687,71.8,1347526,121.2,19.93,9960.1,14.3,14604.8,98.116,14547.3 4/1/10,130139,3220,217.403,187405,422,357086,9.9,687,93.1984,101.4,10993.2,147800,188664,401553,825199,127.7,220.822,101.061,101.349,637,72.2,1353583,122.5,27.64,9972.7,16.2,,, 5/1/10,130661,2891,217.29,186349,280,354430,9.6,583,94.6492,101.6,11067,152502,193834,403494,821833,126.7,220.962,101.182,101.392,575,73.5,1355176,123.1,17.88,10001.3,22.2,,, 6/1/10,130528,2664,217.199,186485,305,353830,9.4,536,94.8328,101.4,11071.3,152069,198626,405845,822777,125.2,221.194,101.288,101.447,587,73.8,1366683,122.2,20.09,10021.2,15.1,14745.9,98.896,14648.6 7/1/10,130458,2965,217.605,189532,283,354536,9.4,546,95.2539,101.6,11080.5,155434,195847,410771,796903,125.2,221.363,101.345,101.569,579,74.3,1378218,122,5.34,10027.4,7.5,,, 8/1/10,130424,2920,217.923,192145,282,356560,9.5,599,95.6092,101.8,11114.7,156016,200937,415843,798360,125.7,221.509,101.442,101.713,580,74.7,1389628,123,10.23,10074.8,3.6,,, 9/1/10,130372,2767,218.275,200308,317,359440,9.5,594,95.8794,102.1,11101.2,156896,200937,422512,803378,125.7,221.711,101.488,101.807,563,75,1406603,123.7,9.9,10087.1,4.1,14845.5,98.842,14839.5 10/1/10,130629,3033,219.035,194686,291,363855,9.4,543,95.6362,102.5,11128.3,162730,202727,431258,798831,127.1,221.83,101.559,102.045,558,74.9,1420992,124.7,15.5,10136.8,0.2,,, 11/1/10,130752,2914,219.59,196672,287,367352,9.8,545,95.7002,102.8,11160.8,164418,202180,434309,798208,129.2,222.149,101.665,102.211,560,75,1430814,126.6,-7.56,10175.2,19.2,,, 12/1/10,130840,2857,220.472,194933,326,369299,9.3,539,96.4959,103.1,11239,167408,208223,441058,786597,131,222.343,101.667,102.455,632,75.7,1447968,127.5,11.82,10186.4,15.4,14939,98.882,14904.9 1/1/11,130882,2939,221.187,204711,307,372041,9.1,630,96.4283,103.7,11297.4,168932,216055,444374,754710,133,222.803,101.808,102.685,576,75.7,1458858,129.1,8.96,10201.2,16.4,,, 2/1/11,131070,3056,221.898,194236,270,375003,9,517,96.0111,104.3,11329,167437,211155,449434,757019,135.3,223.213,101.983,102.966,542,75.4,1467507,130.8,11.5,10210,29.1,,, 3/1/11,131295,3130,223.046,211908,300,378472,9,600,96.8407,105,11312.4,175373,218851,454289,768276,139.3,223.454,102.131,103.356,583,76,1486908,132.7,12.67,10240.2,36.6,14881.3,101.5,14924.4 4/1/11,131641,3287,224.093,200903,310,380284,9.1,554,96.4337,105.5,11282.8,177458,219684,456729,768555,142.9,223.727,102.384,103.808,581,75.7,1500503,133.8,19.56,10235.2,13.2,,, 5/1/11,131714,3114,224.806,206091,305,380398,9,561,96.6227,105.8,11277.1,177451,224671,465920,775999,143.1,224.175,102.628,104.144,618,75.8,1516439,134.3,9.91,10229.5,6.2,,, 6/1/11,131949,3224,224.806,199884,301,383081,9.1,608,96.8573,105.9,11325.8,175611,225043,471032,797238,142.2,224.697,102.767,104.179,636,75.9,1524898,134.5,-4.81,10248.3,-0.3,14989.6,100.6,14996.1 7/1/11,132019,3475,225.395,208592,296,382966,9,623,97.3169,106.1,11371.2,180121,225810,474156,792089,142.4,225.218,102.942,104.38,621,76.2,1529735,134,-6.05,10277.2,6.8,,, 8/1/11,132126,3168,226.106,215290,299,383541,9,585,97.7956,106.3,11363.5,180455,225423,475937,805366,141.9,225.862,103.157,104.618,647,76.5,1538486,134.6,-3.7,10271.6,-19.6,,, 9/1/11,132372,3495,226.597,208277,304,387313,9,650,97.7474,106.7,11330.8,182398,225703,472095,807010,141.7,226.118,103.23,104.787,610,76.4,1533929,135.3,-4.23,10297.9,-11.2,15021.1,101.415,15093.1 10/1/11,132574,3421,226.75,208553,316,390302,8.8,610,98.4096,106.3,11340.8,181683,226645,476937,802658,141.2,226.506,103.371,104.851,671,76.8,1545524,132.6,-5.37,10326.8,6,,, 11/1/11,132720,3153,227.169,216970,328,391478,8.6,711,98.281,106.6,11329.3,179589,226633,478647,806301,142.2,226.899,103.539,104.999,706,76.5,1552965,132.7,4.62,10313.3,3.9,,, 12/1/11,132927,3369,227.223,226853,341,391695,8.5,694,98.6739,106.5,11416,180513,229973,485328,814989,142.2,227.405,103.656,105.018,697,76.7,1561441,132.1,11.77,10310.2,2.4,15190.3,99.404,15217 1/1/12,133265,3664,227.86,224549,335,395280,8.3,723,99.3787,106.9,11495.2,180073,231056,486011,823375,142.2,227.869,103.94,105.325,715,77.1,1568406,132.5,10.34,10354.4,7.4,,, 2/1/12,133522,3501,228.377,223657,366,400181,8.3,704,99.6578,107.2,11559,182640,226210,493015,825163,142.2,228.063,104.081,105.56,733,77.1,1581826,133.1,16.62,10398,10.8,,, 3/1/12,133761,3852,228.894,221505,354,401830,8.2,695,98.9579,107.4,11589,186316,236533,494501,828668,144.2,228.49,104.282,105.804,797,76.4,1588787,134.1,16.12,10384.7,9.2,15291,101.552,15500.4 4/1/12,133836,3663,229.286,219540,354,400095,8.2,753,99.8396,107.6,11620,185030,232284,497964,834951,144.1,228.915,104.461,105.943,747,76.9,1595510,134.7,8.33,10399.5,6.1,,, 5/1/12,133951,3706,228.722,217293,370,399463,8.2,708,100.0042,107.6,11632.1,185070,231041,499293,849347,142,229.241,104.588,105.868,807,76.9,1601668,134,13.52,10400.2,-0.6,,, 6/1/12,134038,3792,228.506,219155,360,395723,8.2,757,100.0318,107.3,11657.8,185286,228746,501984,859250,138.7,229.686,104.718,105.844,790,76.8,1606673,131.7,2.74,10390.3,-12.4,15362.4,101.525,15522.8 7/1/12,134181,3694,228.475,224520,369,397516,8.2,740,100.3132,107.2,11626.4,184336,227706,507164,857301,137.7,229.956,104.831,105.88,840,76.8,1618075,132.2,2.94,10422.2,-13.1,,, 8/1/12,134371,3655,229.844,202185,375,401937,8.1,754,99.8389,107.5,11605.6,183265,227372,509466,857558,139.4,230.205,104.89,106.238,832,76.3,1627178,133.4,-2.41,10405.9,-2.8,,, 9/1/12,134552,3533,230.987,215073,385,405707,7.8,847,99.9599,108.2,11660.2,188647,228711,515873,862358,140.8,230.618,105.014,106.576,921,76.3,1637311,134.5,-6.7,10444.3,-0.7,15380.8,101.793,15517.1 10/1/12,134684,3713,231.655,219319,358,405598,7.8,915,100.2146,108.3,11729.1,182988,226029,515170,870362,141.2,231.013,105.271,106.886,895,76.3,1639501,134.6,-3.87,10426.9,-1.5,,, 11/1/12,134833,3556,231.278,217917,392,407327,7.7,833,100.7651,108.4,11884.7,185747,232414,519864,866855,140.2,231.298,105.377,106.768,930,76.6,1645933,133.8,-1.13,10454.3,-10.9,,, 12/1/12,135076,3576,231.272,229811,399,409468,7.9,976,101.0382,108.5,12194.8,189591,227661,520341,865730,139.4,231.701,105.442,106.758,938,76.7,1649980,133.6,-5.59,10478.5,2.1,15384.3,104.987,15650.6 1/1/13,135266,3712,231.641,217899,442,412207,8,888,100.9614,108.7,11411.4,188751,229794,524138,857410,140.1,232.244,105.692,106.922,928,76.6,1664747,134.1,-9.31,10504.9,-1.2,,, 2/1/13,135577,3972,233.005,229948,439,416783,7.7,970,101.4781,108.9,11431,190448,233066,522415,871574,141.3,232.653,105.825,107.333,971,76.9,1665488,135.1,7.62,10519.2,-4.7,,, 3/1/13,135712,3901,232.313,211676,449,412514,7.5,999,101.6302,108.8,11451.3,188248,224197,522759,865844,141.2,232.813,105.94,107.244,932,76.9,1663571,134.4,6.45,10530.5,3.3,15457.2,102.521,15631.6 4/1/13,135904,3962,231.856,221018,451,413391,7.6,826,101.5825,108.7,11461.4,189485,228412,523862,877799,140.2,232.854,106.008,107.128,1015,76.8,1667106,133.6,5.12,10530.1,1.5,,, 5/1/13,136122,3886,231.895,231237,430,414207,7.5,920,101.6016,108.6,11517.8,188438,231277,520521,882693,139.4,233.081,106.123,107.244,1016,76.7,1663950,132.9,-2.2,10556.2,0.6,,, 6/1/13,136268,3913,232.357,239620,463,415989,7.5,852,101.8221,109,11540.4,191198,227163,521060,893248,138.8,233.429,106.29,107.479,951,76.8,1663664,132.8,6.22,10576.5,12.8,15500.2,104.076,15744.4 7/1/13,136408,3915,232.749,216297,376,417962,7.3,891,101.2443,109.3,11538.3,190614,228284,522047,909513,138.9,233.844,106.382,107.587,986,76.4,1668921,132.6,4.89,10584.6,14.7,,, 8/1/13,136677,3921,233.249,220679,380,417101,7.3,898,101.9928,109.3,11570.2,190719,228802,526015,914609,139.4,234.293,106.511,107.739,947,76.9,1677150,131.9,10.34,10582,7.5,,, 9/1/13,136862,3985,233.642,229220,399,417682,7.3,860,102.4847,109.4,11599.4,190791,232108,528707,924361,139.8,234.624,106.63,107.858,1015,77.2,1684967,132.4,7.67,10630,19.9,15614.4,103.952,15759.2 10/1/13,137051,4104,233.799,224830,444,419686,7.2,921,102.4287,109.6,11559.1,194342,232143,534357,937982,138.9,234.878,106.82,108,1031,77.1,1695757,131.6,4.71,10651,12.7,,, 11/1/13,137342,3878,234.21,236964,446,421056,6.9,1104,102.7732,109.7,11595,195830,230681,539012,948850,137.7,235.278,106.978,108.071,1042,77.4,1706023,131.8,1.77,10702.5,3.5,,, 12/1/13,137387,3742,234.847,229057,441,422891,6.7,1010,102.9513,109.8,11602.8,194591,229405,541205,961996,137.8,235.69,107.066,108.254,1013,77.5,1714804,132.3,3.3,10717.6,3,15761.5,103.655,15863.4 1/1/14,137574,3884,235.436,221834,447,419195,6.6,902,102.4621,110.1,11646.4,194756,233590,543909,973655,138.3,236.022,107.21,108.421,1001,77,1723614,132.7,10.52,10662.3,15.9,,, 2/1/14,137742,4098,235.621,229392,423,424657,6.7,948,103.2919,110.3,11704.9,193829,234654,547290,985280,139.8,236.288,107.292,108.492,1032,77.6,1731101,133.7,4.41,10732.2,3.6,,, 3/1/14,138014,4202,235.897,234525,410,429707,6.7,973,104.0896,110.6,11745,198000,238855,552444,989496,140.5,236.649,107.502,108.708,1078,78.1,1737184,134.9,5.16,10779.6,15,15724.9,105.998,15887.3 4/1/14,138324,4575,236.495,236771,401,433082,6.2,1038,104.2409,110.8,11758.1,197463,241483,557540,992914,139.7,237.103,107.698,108.907,1080,78.1,1744407,133.5,4.67,10804.7,18.3,,, 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3/1/15,140972,5180,235.859,235120,490,440394,5.5,964,105.515,109.6,12102.2,190448,238637,581609,1052899,125.3,240.797,108.952,109.015,1071,77.3,1783657,125.9,6.22,11104.4,10.7,16177.3,107.247,16408.6 4/1/15,141223,5580,236.197,231515,500,440355,5.4,1192,105.2732,109.6,12164.6,191675,232560,582432,1084961,125.1,241.392,109.123,109.085,1178,76.9,1789893,125.1,0.57,11135.1,10.8,,, 5/1/15,141496,5386,236.876,223541,507,444319,5.5,1063,105.0259,110.1,12193.2,190361,230531,585606,1107569,126.5,241.672,109.254,109.418,1266,76.6,1791225,125.7,2.22,11196.5,8.1,,, 6/1/15,141724,5168,237.423,234699,472,444890,5.3,1213,104.8599,110.4,12223.2,190347,233320,589665,1113424,126.6,242.089,109.416,109.67,1334,76.4,1804517,125.3,-2.05,11205.1,8.1,16333.6,107.769,16498 7/1/15,142001,5788,237.734,236630,498,447559,5.3,1147,105.4755,110.5,12255,190106,230006,588091,1114716,125.4,242.464,109.512,109.775,1142,76.7,1802652,124.8,0.94,11229.3,0.7,,, 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1/1/16,143314,5604,238.107,231756,526,448041,4.9,1128,104.6059,110,12485.4,179771,222079,586160,1121975,117.8,245.232,110.392,109.94,1188,75.8,1800048,118.7,-19.37,11356.1,-3.5,,, 2/1/16,143547,5608,237.707,224081,525,449226,4.9,1213,104.4165,109.6,12509.9,182159,226187,582888,1137868,117.2,245.925,110.584,109.84,1162,75.6,1798344,118.2,-16.64,11385.1,-2.8,,, 3/1/16,143733,5670,237.92,228499,522,447907,5,1113,103.3972,109.5,12545.7,180174,215709,584254,1155122,117.7,246.095,110.653,109.91,1077,74.8,1804490,118.1,0.62,11377.6,12.4,16514.6,110.504,16781.2 4/1/16,143856,5788,238.89,235971,586,453601,5,1167,103.9858,109.7,12569.6,182796,220232,587901,1133932,118.5,246.574,110.842,110.247,1130,75.3,1807098,118.7,9.56,11470.9,-1.6,,, 5/1/16,143894,,239.41,230701,551,455644,4.7,1164,103.5527,110.1,12579.3,,,,,120.2,247.074,111.022,110.431,1136,74.9,,120,-9.02,11500.2,-1.8,,, 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4/1/90,109687,,128.9,,542,,5.4,1248,64.8976,,6419.2,,,,,91.6,134,67.976,66.752,1136,83,,95.1,,,-9,,, 5/1/90,109838,,129.1,,534,,5.4,1212,65.0068,,6405.2,,,,,91.2,134.4,68.176,66.896,1067,82.9,,95.3,,,-16.5,,, 6/1/90,109862,,129.9,,545,,5.2,1177,65.2286,,6419.4,,,,,90.8,135.1,68.439,67.191,1108,83,,95.1,,,-8.6,8981.7,76.727,8845.3 7/1/90,109830,,130.5,,542,,5.5,1171,65.1543,,6442.5,,,,,90.5,135.8,68.602,67.348,1078,82.8,,95.3,,,-18.1,,, 8/1/90,109614,,131.6,,528,,5.7,1115,65.3528,,6404.7,,,,,93.3,136.6,68.889,67.797,1069,82.9,,95.4,,,-18.2,,, 9/1/90,109525,,132.5,,496,,5.9,1110,65.4459,,6404,,,,,96.5,137.1,69.133,68.215,976,82.9,,95.8,,,-43.4,8983.9,77.487,8837 10/1/90,109366,,133.4,,465,,5.9,1014,64.945,,6353.2,,,,,99.3,137.6,69.364,68.602,925,82.1,,96.6,,,-48.2,,, 11/1/90,109216,,133.7,,493,,6.2,1145,64.1877,,6354.9,,,,,98.7,138,69.443,68.685,941,81.1,,96.7,,,-27.1,,, 12/1/90,109160,,134.2,,464,,6.3,969,63.7612,,6390.3,,,,,98.4,138.6,69.53,68.741,861,80.4,,96.3,,,-37.1,8907.4,78.765,8794.8 1/1/91,109040,,134.7,,401,,6.4,798,63.4795,,6369.3,,,,,97,139.5,69.869,68.996,786,80,,96.8,,,-32,,, 2/1/91,108735,,134.8,,482,,6.6,965,63.049,,6379.4,,,,,95,140.2,70.049,69.021,853,79.3,,96.7,,,-22.2,,, 3/1/91,108577,,134.8,,507,,6.8,921,62.7082,,6390.6,,,,,95,140.5,70.19,69.032,911,78.8,,96.4,,,-11.6,8865.6,79.128,8783.3 4/1/91,108366,,135.1,,508,,6.7,1001,62.8463,,6412.7,,,,,94.2,140.9,70.326,69.154,916,78.9,,96.6,,,-6.5,,, 5/1/91,108241,,135.6,,517,,6.9,996,63.4638,,6412.9,,,,,94,141.3,70.607,69.44,991,79.6,,96.4,,,3.9,,, 6/1/91,108338,,136,,516,,6.9,1036,64.0488,,6445.9,,,,,93.4,141.8,70.758,69.557,964,80.2,,96.1,,,13,8934.4,79.307,8806.3 7/1/91,108298,,136.2,,511,,6.8,1063,64.1013,,6432.8,,,,,92.8,142.3,70.973,69.667,973,80.2,,95.7,,,19.9,,, 8/1/91,108308,,136.6,,526,,6.9,1049,64.1515,,6445,,,,,93.1,142.9,71.166,69.827,944,80.2,,96,,,27,,, 9/1/91,108340,,137,,487,,6.9,1015,64.7177,,6463.7,,,,,93.3,143.4,71.449,70.067,974,80.8,,95.6,,,20,8977.3,79.664,8829.6 10/1/91,108357,,137.2,,524,,7,1079,64.6012,,6474,,,,,94.1,143.7,71.605,70.197,991,80.5,,96.6,,,9.5,,, 11/1/91,108299,,137.8,,575,,7,1103,64.5274,,6486.7,,,,,94.5,144.2,71.736,70.348,984,80.3,,96.7,,,1.3,,, 12/1/91,108325,,138.2,,558,,7.3,1079,64.2613,,6546.2,,,,,94.3,144.7,71.907,70.52,1061,79.9,,95.7,,,-18.8,9016.4,80.215,8862.7 1/1/92,108377,,138.3,,676,164083,7.3,1176,63.8916,,6616.3,50251,52277,188403,,94,145.1,72.099,70.613,1077,79.2,808281,95.7,,,-2.2,,, 2/1/92,108314,,138.6,114535,639,164260,7.4,1250,64.3381,,6649.9,51682,52513,189335,,94,145.4,72.292,70.789,1146,79.6,809588,96.3,,,0.6,,, 3/1/92,108368,,139.1,120025,553,163747,7.4,1297,64.902,,6659.6,50294,52935,190547,,93.9,145.9,72.473,70.962,1082,80.2,812709,96.2,,,15,9123,80.704,9017.6 4/1/92,108527,,139.4,124470,546,164759,7.4,1099,65.3746,,6679.4,50302,53411,189951,,93.6,146.3,72.71,71.153,1054,80.6,815477,96.4,,,20,,, 5/1/92,108653,,139.7,125822,554,165617,7.6,1214,65.5902,,6712.9,50044,53963,189115,,94,146.8,72.813,71.248,1056,80.7,815010,96.7,,,17,,, 6/1/92,108721,,140.1,122834,596,166098,7.8,1145,65.6132,,6741.7,51727,54551,192831,,94.8,147.1,72.869,71.374,1057,80.5,820470,96.5,,,15,9223.5,80.769,9091.2 7/1/92,108792,,140.5,122590,627,167305,7.7,1139,66.1891,,6736.8,52533,55313,191989,,95.3,147.6,73.144,71.609,1089,81.1,825008,96.6,,,27.5,,, 8/1/92,108930,,140.8,120411,636,167797,7.6,1226,65.8651,,6759.6,50940,55395,192602,,95.7,147.9,73.21,71.704,1075,80.5,826136,96.3,,,16.7,,, 9/1/92,108966,,141.1,120711,650,169407,7.6,1186,66.0268,,6725.8,51984,55515,193344,,95.9,148.1,73.331,71.823,1114,80.5,827501,96.6,,,21,9313.2,80.98,9120.1 10/1/92,109148,,141.7,127392,621,170681,7.3,1244,66.511,,6682.5,53035,56556,193625,,96.6,148.8,73.615,72.078,1132,81,827915,96.3,,,-4.8,,, 11/1/92,109284,,142.1,122374,614,171025,7.4,1214,66.8027,,6685.9,52246,56214,195300,,96,149.2,73.779,72.223,1118,81.2,829834,96.2,,,18.2,,, 12/1/92,109496,,142.3,126080,650,172995,7.4,1227,66.8587,,6922.8,51843,57446,196914,,94.4,149.6,73.917,72.35,1176,81.1,835800,96.3,,,25.4,9406.5,81.062,9209.7 1/1/93,109805,,142.8,121637,596,175078,7.3,1210,67.1432,,6793.6,52568,56439,197552,458080,94.3,150.1,74.129,72.524,1177,81.3,835995,96.4,,,31.1,,, 2/1/93,110047,,143.1,128854,604,173770,7.1,1210,67.4314,,6817.1,52480,56076,197207,462967,94.2,150.6,74.271,72.633,1148,81.5,838105,96.7,,,34.3,,, 3/1/93,109998,,143.3,126762,602,172328,7,1083,67.3651,,6794.6,53035,59813,198831,458399,94.7,150.8,74.431,72.781,1056,81.3,844816,96.6,,,16.2,9424.1,80.941,9171.9 4/1/93,110306,,143.8,127395,701,176766,7.1,1258,67.5583,,6825.9,53139,59584,199622,469425,95.2,151.4,74.651,72.977,1104,81.5,846790,96.8,,,23.3,,, 5/1/93,110572,,144.2,126529,626,178445,7.1,1260,67.3459,,6814.5,54229,58598,199395,468998,95.5,151.8,74.904,73.203,1112,81.1,847301,97.1,,,14.8,,, 6/1/93,110754,,144.3,130212,653,178201,7,1280,67.4753,,6800.8,52346,59275,199698,480247,95,152.1,74.976,73.229,1130,81.1,849144,96.9,,,3.5,9480.1,82.031,9284.9 7/1/93,111055,,144.5,128111,655,180759,6.9,1254,67.6707,,6817.1,52818,59200,199737,483571,94.5,152.3,75.13,73.345,1174,81.3,849350,97,,,-3.2,,, 8/1/93,111211,,144.8,129378,645,180692,6.8,1300,67.5985,,6826.9,53224,58805,201788,491494,94.4,152.8,75.272,73.471,1230,81.1,850895,97,,,-0.3,,, 9/1/93,111451,,145,127233,726,181800,6.7,1343,67.9241,,6809.3,53648,60679,202858,497297,94.5,152.9,75.387,73.55,1251,81.3,855006,96.9,,,7.3,9526.3,81.927,9300.8 10/1/93,111737,,145.6,133168,704,182910,6.8,1392,68.439,,6772.6,55476,62069,202074,492823,94.9,153.4,75.51,73.78,1287,81.8,855355,96.9,,,8.9,,, 11/1/93,112000,,146,130391,769,184746,6.6,1376,68.7289,,6791.6,54345,61361,203158,515934,94.4,153.9,75.702,73.917,1357,82,859061,97,,,18.9,,, 12/1/93,112312,,146.3,133565,812,186339,6.5,1533,69.0884,,7023.2,55552,61271,204842,533150,93.5,154.3,75.734,73.934,1461,82.3,863093,97.3,,,41.4,9653.5,82.17,9482.3 1/1/94,112583,,146.3,138498,619,185128,6.6,1272,69.3476,,6892.9,55159,61365,204844,513314,93.5,154.5,75.793,73.958,1390,82.4,863036,98,,,27.2,,, 2/1/94,112783,,146.7,137141,686,188077,6.6,1337,69.3617,,6908.4,53729,62974,206498,513196,93.9,154.8,75.956,74.127,1269,82.2,867675,98,,,21.3,,, 3/1/94,113248,,147.1,136548,747,191588,6.5,1564,70.0831,,6930.4,58307,64772,205748,521040,94,155.3,76.216,74.333,1342,82.9,868782,98.2,,,19.8,9748.2,81.373,9533.5 4/1/94,113598,,147.2,140336,692,191632,6.4,1465,70.4425,,6932.6,56436,64323,206510,528063,94.7,155.5,76.329,74.42,1392,83.1,871997,98.2,,,16.8,,, 5/1/94,113931,,147.5,142630,691,190940,6.1,1526,70.824,,7016.1,57342,65070,210080,532328,95.5,155.9,76.5,74.528,1396,83.3,882951,98.5,,,22.1,,, 6/1/94,114246,,147.9,145063,621,193196,6.1,1409,71.2811,,7002.8,58451,66831,209820,536198,96.3,156.4,76.666,74.708,1357,83.6,888685,98.5,,,25,9881.4,82.028,9683.7 7/1/94,114619,,148.4,145013,628,193763,6.1,1439,71.3953,,7008.8,58492,67230,211902,537232,97.2,156.7,76.829,74.944,1335,83.5,894306,98.7,,,17.7,,, 8/1/94,114901,,149,145884,656,196157,6,1450,71.8011,,7019.1,60407,68710,213360,537960,97.6,157.1,76.91,75.111,1377,83.7,902171,98.9,,,18.5,,, 9/1/94,115254,,149.3,145487,677,197754,5.9,1474,72.0617,,7048.2,60715,69026,215081,538215,97.2,157.5,77.027,75.195,1412,83.7,908038,99.1,,,18.4,9939.7,82.455,9774.9 10/1/94,115467,,149.4,149547,715,199579,5.8,1450,72.6829,,7113.4,59861,69019,218049,533273,97.9,157.8,77.207,75.322,1397,84.2,913451,99.7,,,26.1,,, 11/1/94,115887,,149.8,150038,646,199723,5.6,1511,73.1379,,7111.1,61532,71147,219673,539150,98.5,158.2,77.353,75.469,1340,84.4,919510,100.4,,,24.7,,, 12/1/94,116164,,150.1,152489,629,200670,5.5,1455,73.8818,,7144.2,62825,71281,221978,541794,98.4,158.3,77.38,75.519,1396,85,926431,101.1,,,23.3,10052.5,82.111,9887.4 1/1/95,116488,,150.5,150459,626,201583,5.6,1407,74.0142,,7174.2,63118,72442,224148,543930,98.7,159,77.567,75.667,1282,84.9,935671,101.9,,,8.8,,, 2/1/95,116692,,150.9,153856,559,198383,5.4,1316,73.9247,,7190.3,63077,71894,226012,537826,99.4,159.4,77.687,75.795,1254,84.5,942757,102.5,,,9.2,,, 3/1/95,116913,,151.2,152888,616,200230,5.4,1249,74.0284,,7208.3,64349,74057,228569,542715,99.9,159.9,77.872,75.931,1226,84.3,951531,103,,,2,10086.9,82.589,9934 4/1/95,117075,,151.8,151401,621,201048,5.8,1267,74.014,,7153.1,65074,74682,231002,543096,100.9,160.4,78.049,76.128,1259,84,959227,104,,,-11.2,,, 5/1/95,117060,,152.1,152838,674,202993,5.6,1314,74.2239,,7223.3,65755,74845,231862,542566,101.8,160.7,78.177,76.24,1271,83.9,965662,104.3,,,-8.5,,, 6/1/95,117294,,152.4,150051,725,205507,5.6,1281,74.4807,,7245.4,64855,75478,233297,546131,101.4,161.1,78.238,76.309,1305,83.9,969532,104.5,,,-20.7,10122.1,82.831,9991.4 7/1/95,117390,,152.6,148915,765,204959,5.7,1461,74.1902,,7259.9,66560,74247,235664,547342,101.1,161.4,78.362,76.404,1354,83.3,972755,104.8,,,-20.3,,, 8/1/95,117643,,152.9,154372,701,206529,5.7,1416,75.1211,,7265.8,67469,74173,236003,550996,100.8,161.8,78.547,76.568,1386,84,976101,104.3,,,1.2,,, 9/1/95,117887,,153.1,160175,678,206978,5.6,1369,75.4216,,7289.4,68943,74867,237075,554011,100.8,162.2,78.651,76.621,1421,84,980037,104.4,,,26.2,10208.8,83.295,10114 10/1/95,118040,,153.5,155473,696,206157,5.5,1369,75.3448,,7297.7,68105,74219,238005,555132,100.4,162.7,78.84,76.818,1400,83.6,984279,104.5,,,21.7,,, 11/1/95,118189,,153.7,156146,664,208661,5.6,1452,75.531,,7317.5,68009,74523,238149,557445,100.6,163,78.895,76.819,1430,83.4,986800,104.5,,,5.5,,, 12/1/95,118322,,153.9,163279,709,210434,5.6,1431,75.8317,,7326.1,69071,75342,238392,557953,101,163.1,79.007,76.968,1442,83.4,985410,104.4,,,19.6,10281.2,83.463,10178.4 1/1/96,118303,,154.7,155806,714,208731,5.6,1467,75.3347,,7337.5,68299,76764,239788,575138,101.2,163.7,79.102,77.143,1387,82.5,990755,104.9,,,-14.7,,, 2/1/96,118735,,155,150773,769,212011,5.5,1491,76.5148,,7394.6,69899,77217,239571,568052,101,164,79.203,77.263,1420,83.4,991286,104.7,,,4.8,,, 3/1/96,119002,,155.5,164976,721,213855,5.5,1424,76.4339,,7419.1,69797,77553,239391,574538,101.6,164.4,79.382,77.492,1437,82.9,989178,104.6,,,-3.5,10348.7,83.999,10289.1 4/1/96,119165,,156.1,156830,736,214644,5.6,1516,77.1163,,7376.4,70126,78870,242644,590464,102.5,164.6,79.487,77.721,1463,83.3,992104,105.2,,,21.3,,, 5/1/96,119487,,156.4,164502,746,216304,5.6,1504,77.695,,7470.8,71029,80288,242517,600186,101.8,165,79.624,77.854,1457,83.5,993754,105.6,,,19.6,,, 6/1/96,119774,,156.7,164599,721,216059,5.3,1467,78.3435,,7515.5,71056,78516,241659,602150,100.7,165.4,79.686,77.854,1429,83.8,993128,105.4,,,21,10529.4,83.901,10443.8 7/1/96,120023,,157,163588,770,216374,5.5,1472,78.208,,7495.6,69404,79536,241933,599899,100.6,165.7,79.837,78.02,1450,83.3,997579,104.9,,,29.4,,, 8/1/96,120202,,157.2,157310,826,216355,5.1,1557,78.6658,,7513.8,70563,80919,241755,603959,100.7,166,79.908,78.097,1413,83.4,999982,104.7,,,13.8,,, 9/1/96,120427,,157.7,165442,770,219240,5.2,1475,79.1997,,7531.8,70553,80748,240016,615466,101.8,166.5,80.142,78.31,1392,83.6,1000707,103.9,,,12.9,10626.8,84.216,10542.3 10/1/96,120677,,158.2,165266,720,221039,5.2,1392,79.1389,,7530.8,73769,80404,240734,621761,102.4,166.8,80.329,78.544,1358,83.1,1004411,103.6,,,8.2,,, 11/1/96,120976,,158.7,170783,771,220989,5.4,1489,79.8221,,7550.6,74263,81531,240909,620812,102.2,167.2,80.441,78.689,1412,83.4,1004506,103.2,,,11.1,,, 12/1/96,121147,,159.1,162332,805,221898,5.4,1370,80.3307,,7577.2,72842,83317,241058,606078,102.5,167.4,80.472,78.78,1411,83.5,1004679,103.2,,,8.1,10739.1,84.582,10673.8 1/1/97,121381,,159.4,161827,830,223524,5.3,1355,80.4255,,7602.1,72910,84179,243449,608608,102.2,167.8,80.556,78.881,1382,83.2,1007758,103.3,,,12.8,,, 2/1/97,121684,,159.7,170221,801,225409,5.2,1486,81.4045,,7624.6,75225,85001,243583,615415,101.2,168.1,80.72,79.045,1445,83.8,1010744,103.5,,,16.9,,, 3/1/97,122000,,159.8,167568,831,226136,5.2,1457,81.9717,,7659.5,77050,85433,244978,620467,100,168.4,80.91,79.126,1436,84,1010343,103.6,,,13.4,10820.9,85.598,10796 4/1/97,122292,,159.9,174054,744,224588,5.1,1492,82.0209,,7664.7,77769,85855,245342,616175,98.8,168.9,81.063,79.2,1421,83.6,1014591,103.6,,,6.5,,, 5/1/97,122552,,159.9,168586,760,222906,4.9,1442,82.5095,,7696.3,77883,86277,246725,624743,98.8,169.2,81.128,79.169,1414,83.7,1018535,103.4,,,1.1,,, 6/1/97,122818,,160.2,174828,793,226048,5,1494,82.9253,,7720.6,78889,86043,251010,626396,98.8,169.4,81.245,79.268,1402,83.6,1024701,103.2,,,18,10984.2,85.251,10923.2 7/1/97,123124,,160.4,178860,805,228738,4.9,1437,83.5464,,7751.8,80099,87132,249996,637410,98.5,169.7,81.297,79.312,1440,83.8,1026671,103.2,,,20.2,,, 8/1/97,123093,,160.8,177302,815,229317,4.8,1390,84.434,,7791.7,78622,87365,250888,639593,98.4,169.8,81.266,79.377,1449,84.2,1028029,103.2,,,17.2,,, 9/1/97,123605,,161.2,177835,840,230284,4.9,1546,85.1978,,7813,79287,88556,253166,646526,98.4,170.2,81.421,79.557,1494,84.4,1034401,102.9,,,19.1,11124,85.385,11105.9 10/1/97,123945,,161.5,177801,800,229822,4.7,1520,85.9177,,7849.7,79383,88472,254054,653196,98.6,170.6,81.543,79.66,1499,84.6,1038300,102.5,,,19.3,,, 11/1/97,124251,,161.7,191187,864,230486,4.6,1510,86.6748,,7898.4,78300,88086,256109,643710,98.1,170.8,81.576,79.67,1469,84.8,1040120,102.5,,,19.8,,, 12/1/97,124554,,161.8,173770,793,231197,4.7,1566,86.9454,,7942.9,79038,90327,258454,642021,97.2,171.2,81.627,79.657,1456,84.5,1045506,102,,,15.6,11210.3,86.564,11250.9 1/1/98,124830,,162,174288,872,231605,4.6,1525,87.3838,,8015,79008,89784,259088,645686,95.9,171.6,81.743,79.688,1555,84.4,1048287,101.3,,,18.6,,, 2/1/98,125026,,162,181270,866,231664,4.6,1584,87.482,,8067,77931,89495,261734,648121,95,171.9,81.802,79.639,1647,83.9,1055020,101,,,13.2,,, 3/1/98,125177,,162,176886,836,233043,4.7,1567,87.552,,8114,78812,91692,263439,666906,94.1,172.2,81.88,79.645,1605,83.4,1060195,100.7,,,10.5,11321.2,87.548,11371.1 4/1/98,125457,,162.2,180915,866,235976,4.3,1540,87.854,,8140.5,77626,91566,263284,674351,93.9,172.5,82.034,79.746,1547,83.2,1062374,100.3,,,8.7,,, 5/1/98,125861,,162.6,180634,887,237055,4.4,1536,88.4226,,8173.6,77147,91349,265233,674325,93.7,172.9,82.117,79.858,1554,83.2,1061523,100.4,,,13.2,,, 6/1/98,126080,,162.8,172189,923,238958,4.5,1641,87.8558,,8219.9,76961,90208,264400,703177,93.1,173.2,82.018,79.794,1551,82.2,1061963,99.9,,,24.1,11431,88.113,11534.1 7/1/98,126209,,163.2,170459,876,237423,4.5,1698,87.5421,,8234.8,76149,90098,264793,696540,92.3,173.5,82.243,79.986,1610,81.4,1063957,99.5,,,8.3,,, 8/1/98,126551,,163.4,179033,846,236412,4.5,1614,89.3341,,8261.8,75512,91540,267204,698156,92,174,82.401,80.095,1654,82.6,1066374,99,,,10.4,,, 9/1/98,126774,,163.5,181422,864,238542,4.6,1582,89.1794,,8287.3,77179,91999,268711,707561,92.2,174.2,82.382,80.044,1577,82,1070807,98.5,,,-14.2,11580.6,88.286,11697.9 10/1/98,126973,,163.9,178527,893,242531,4.5,1715,89.8907,,8301.1,79351,94166,269467,707943,92.3,174.4,82.538,80.215,1719,82.3,1073232,98.4,,,3.5,,, 11/1/98,127255,,164.1,182400,995,244307,4.4,1660,89.8458,,8335,79117,94290,271044,707845,91.8,174.8,82.549,80.217,1672,81.8,1077587,98.6,,,-4.7,,, 12/1/98,127601,,164.4,178424,949,246577,4.4,1792,90.1893,,8349.5,78382,93127,272297,706989,91,175.4,82.697,80.302,1742,81.8,1077188,98.5,,,4.6,11770.7,88.038,11805.7 1/1/99,127727,,164.7,186527,875,246891,4.3,1748,90.6043,,8381.7,78033,93980,272635,708818,91.3,175.6,82.854,80.448,1732,81.8,1077133,98.5,,7582,13.7,,, 2/1/99,128137,,164.7,185546,848,249510,4.4,1670,91.0816,,8409,77635,96421,274923,726308,91.2,175.6,82.855,80.428,1720,81.9,1082750,98.3,,7620,15.1,,, 3/1/99,128244,,164.8,184689,863,250657,4.2,1710,91.235,,8418.6,78449,96350,275847,737226,91.5,175.7,82.874,80.484,1665,81.6,1090048,97.9,,7654.1,4.3,11864.7,88.64,11952 4/1/99,128620,,165.9,182993,918,252418,4.3,1553,91.4677,,8402.6,78872,97125,276188,728788,92.4,176.3,83.069,80.856,1600,81.5,1092922,98.1,,7697.8,20.6,,, 5/1/99,128831,,166,185963,888,254738,4.2,1611,92.1525,,8420.1,78939,99168,276792,727358,93.1,176.5,83.126,80.889,1640,81.8,1095938,98.2,,7731.6,13.1,,, 6/1/99,129091,,166,182590,923,255472,4.3,1559,92.0042,,8448.9,79234,102349,276961,739167,92.9,176.6,83.16,80.906,1702,81.4,1098785,98.2,,7765.2,5.8,11962.5,88.692,12026.2 7/1/99,129417,,166.7,189083,900,257441,4.3,1669,92.5769,,8458.4,80449,103870,279948,745815,93.8,177.1,83.308,81.12,1682,81.6,1104056,98.1,,7778.8,9.8,,, 8/1/99,129577,,167.1,189414,893,260253,4.2,1648,92.9517,,8494.4,81943,104920,280588,741524,94.8,177.3,83.344,81.263,1671,81.6,1105878,98.4,,7820.9,13.8,,, 9/1/99,129791,,167.8,188910,826,261352,4.2,1635,92.5954,,8488.3,83163,106063,282127,751402,95.8,177.8,83.556,81.547,1551,81,1112276,98.5,,7858.2,13.9,12113.1,88.684,12137.4 10/1/99,130191,,168.1,194547,872,261825,4.1,1608,93.8128,,8541.3,83565,107096,285104,759906,96,178.1,83.688,81.677,1649,81.8,1115769,98.8,,7874.8,16,,, 11/1/99,130484,,168.4,186597,863,264883,4.1,1648,94.2587,,8601.7,84441,109665,288823,781199,96.7,178.4,83.769,81.749,1672,81.9,1128342,99,,7911.9,20.9,,, 12/1/99,130780,,168.8,196344,873,269876,4,1708,94.9777,,8672.2,85142,111479,290182,789431,97.4,178.7,83.888,81.951,1683,82.2,1137264,99,,8015.7,14.2,12323.3,89.052,12335.9 1/1/00,131010,,169.3,201360,873,268091,4,1636,94.9864,,8744.8,85646,112733,292768,784940,97.8,179.3,84.103,82.186,1727,81.9,1139998,99.2,,7988.5,11.2,,, 2/1/00,131140,,170,183911,856,272020,4.1,1737,95.2576,,8778.7,86142,116071,294593,793737,99.7,179.4,84.229,82.445,1692,81.9,1146461,99.6,,8065.3,14.6,,, 3/1/00,131608,,171,192130,900,275214,4,1604,95.6407,,8800.6,87368,118523,296789,809459,99.9,180,84.4,82.797,1651,81.9,1150694,100,,8110.8,19.4,12359.1,92.702,12587.7 4/1/00,131895,,170.9,195044,841,271004,3.8,1626,96.3318,,8836.9,88855,117655,299545,804766,98.5,180.3,84.445,82.72,1597,82.3,1157508,100,,8101.6,10,,, 5/1/00,132122,,171.2,188606,857,271418,4,1575,96.5139,,8869.8,88017,117830,301245,805005,98.8,180.7,84.531,82.784,1543,82.1,1163939,100.2,,8139,13.9,,, 6/1/00,132075,,172.2,219745,793,273440,4,1559,96.5856,,8890.2,90771,121737,303182,795411,100.2,181.1,84.585,83.056,1572,81.9,1174272,100.1,,8156,2.6,12592.5,91.095,12657.5 7/1/00,132251,,172.7,189265,887,272638,4,1463,96.4624,,8937.1,90421,121848,304073,783795,100.2,181.5,84.771,83.256,1542,81.6,1175346,100,,8160.6,4.7,,, 8/1/00,132241,,172.7,188730,848,272943,4.1,1541,96.1414,,8985.2,92424,122459,305053,805341,100.4,181.9,84.869,83.243,1552,81,1183272,99.8,,8203.8,17.3,,, 9/1/00,132377,,173.6,199947,912,277523,3.9,1507,96.5318,,8985.5,92347,126365,305223,814330,101.6,182.3,85.079,83.604,1570,81.1,1183439,100.4,,8269.4,5.5,12607.7,92.915,12751.6 10/1/00,132363,,173.9,186158,933,276973,3.9,1549,96.2532,,9000,91511,124734,307282,816100,101.2,182.6,85.199,83.718,1577,80.6,1189917,100.3,,8265.8,1.8,,, 11/1/00,132589,,174.2,189392,880,275923,3.9,1551,96.2769,,8994,91388,123996,309328,820054,101.2,183.1,85.344,83.83,1614,80.4,1197042,100.3,,8272.5,7.1,,, 12/1/00,132731,4736,174.6,188659,983,275736,3.9,1532,96.0165,,9004.6,90431,123885,309191,811516,100.5,183.3,85.403,83.938,1543,79.9,1195870,100.1,,8314.9,-7.8,12679.3,92.507,12729 1/1/01,132705,5385,175.6,177056,936,278916,4.2,1600,95.3542,,9054.5,90331,125148,308745,814479,100.5,183.9,85.683,84.311,1699,79.1,1197916,100.3,,8314.4,-36.6,,, 2/1/01,132777,4658,176,180276,963,278799,4.2,1625,94.7736,,9073,90181,119530,309036,813647,99.9,184.4,85.814,84.424,1656,78.4,1191628,100.2,,8326.3,-29.4,,, 3/1/01,132752,4563,176.1,182209,939,276468,4.3,1590,94.5456,,9101.3,88454,121186,309051,828057,98.3,184.7,85.898,84.427,1659,77.9,1186070,100,,8317.4,-20.8,12643.3,95.041,12876.4 4/1/01,132471,4901,176.4,171850,909,280804,4.4,1649,94.3111,,9080.8,86748,117966,310478,842392,97.8,185.1,86.044,84.584,1666,77.5,1184414,99.9,,8318.7,-10.8,,, 5/1/01,132433,4550,177.3,177749,885,281540,4.3,1605,93.6876,,9061.7,87256,114702,311619,848146,98,185.3,86.074,84.814,1665,76.8,1182107,99.6,,8351.4,-11.8,,, 6/1/01,132302,4280,177.7,176350,882,280399,4.5,1636,93.1114,,9062.4,85035,114175,309196,855730,97.6,186,86.278,84.974,1626,76.1,1173167,99.4,,8352.1,-7,12710.3,93.734,12853 7/1/01,132190,4499,177.4,170129,880,279522,4.6,1670,92.586,,9198.4,82833,112914,306252,850471,96.1,186.4,86.503,84.949,1598,75.5,1165024,99,-13.29,8368.8,-12.6,,, 8/1/01,132033,4134,177.4,170484,866,281423,4.9,1567,92.4101,,9359,83787,111958,305464,847465,96,186.7,86.554,84.946,1615,75.2,1163584,98.8,-8.01,8412.7,-18.1,,, 9/1/01,131793,3975,178.1,164123,853,276095,5,1562,92.0924,,9290.6,77367,108508,304703,837412,95.9,187.1,86.078,84.67,1565,74.8,1157220,99,-12.5,8332.2,-8.2,12670.1,93.335,12807.3 10/1/01,131468,3605,177.6,171530,871,294613,5.3,1540,91.6854,,9145.7,77883,108722,302932,845941,93.7,187.4,86.694,84.978,1566,74.3,1139069,98.3,-14.74,8531.9,-23.6,,, 11/1/01,131175,3387,177.5,163811,924,286960,5.5,1602,91.2155,,9167.5,77999,107735,299419,843911,92.3,188.1,86.869,84.921,1651,73.8,1126307,97.8,-21.51,8489.9,-17.7,,, 12/1/01,131005,3385,177.4,165304,979,283708,5.7,1568,91.2654,,9190.4,77780,104618,297536,849689,91.4,188.4,86.888,84.833,1680,73.7,1118527,97.6,-9.78,8475.6,-11,12705.3,92.997,12742.9 1/1/02,130867,3759,177.7,162604,880,283577,5.7,1698,91.7848,,9385.7,78920,108275,296625,858654,91.6,188.7,86.918,84.893,1665,74,1117593,97.5,1.43,8502.4,10.5,,, 2/1/02,130733,3372,178,171172,948,285061,5.7,1829,91.8034,,9395.5,78880,111167,294141,862338,91.6,189.1,87.083,85.035,1787,73.9,1112391,97.3,13.3,8537.6,11,,, 3/1/02,130713,3551,178.5,168666,923,284263,5.7,1642,92.5295,,9391.3,79601,110425,294220,844551,92.8,189.2,87.193,85.272,1691,74.4,1108261,97.6,13.82,8533.8,12.3,12822.3,91.42,12907.7 4/1/02,130634,3472,179.3,171197,936,288820,5.9,1592,92.9204,,9417.9,81551,115217,293147,858240,94.3,189.7,87.452,85.64,1669,74.7,1107085,98,20.18,8577.6,12.6,,, 5/1/02,130627,3596,179.5,172743,978,284994,5.8,1764,93.2998,,9438.5,81724,115645,293444,850935,94.4,190,87.565,85.709,1716,74.9,1110533,98,12.92,8543,10.1,,, 6/1/02,130684,3365,179.6,165875,957,287401,5.8,1717,94.1905,,9459,82741,117641,294407,846777,94.1,190.2,87.706,85.818,1758,75.6,1113042,98,8.91,8583.8,20.4,12893,92.157,12986.9 7/1/02,130599,3411,180,174812,956,290427,5.8,1655,93.9664,,9429.7,83036,116686,296753,847129,94.5,190.5,87.87,85.996,1738,75.4,1119183,98.3,-1.87,8633.6,5.9,,, 8/1/02,130585,3490,180.5,177665,1014,292582,5.7,1633,93.9897,,9422,83422,119165,297560,839008,94.8,191.1,88.039,86.161,1695,75.4,1120477,98.5,8.24,8645.8,-1.3,,, 9/1/02,130526,3308,180.8,167950,1044,288434,5.7,1804,94.1275,,9427.1,82744,119263,298751,832134,95.5,191.3,88.173,86.308,1803,75.5,1128501,98.8,6.33,8604.7,4.4,12955.8,91.896,13003.8 10/1/02,130652,3535,181.2,167444,1006,289634,5.7,1648,93.7988,,9448.3,82028,117199,298373,839690,95.5,191.5,88.253,86.469,1799,75.2,1130517,98.7,-3.8,8638.6,-7.6,,, 11/1/02,130662,3415,181.5,170662,1024,291475,5.9,1753,94.2885,,9469.5,83041,122665,298646,844697,94.6,191.9,88.339,86.555,1771,75.6,1132287,98.8,3.97,8665.3,7.4,,, 12/1/02,130505,2943,181.8,163155,1048,293819,6,1788,93.8334,,9497,81017,124311,301281,855921,95.2,192.1,88.407,86.625,1896,75.3,1139031,98.6,2.38,8719.2,7.2,12964,92.282,13078.9 1/1/03,130597,3824,182.6,169107,999,295294,5.8,1853,94.3584,,9500.8,82110,122850,301118,863855,96.9,192.4,88.432,86.853,1808,75.7,1140033,98.9,8.11,8727.3,5.5,,, 2/1/03,130447,3381,183.6,173001,936,291178,5.9,1629,94.6468,,9481.3,82779,122142,302246,859225,98.5,192.5,88.541,87.209,1854,76,1148945,99.5,-3.54,8684.9,-1.6,,, 3/1/03,130238,3052,183.9,173201,999,296347,5.9,1726,94.4394,,9514.9,82580,125935,303337,851132,99.1,192.5,88.671,87.421,1757,75.9,1149327,99.7,6.47,8725.5,-3.9,13031.2,91.941,13099.6 4/1/03,130194,3340,183.2,169542,1012,295643,6,1643,93.764,,9576.2,81429,123417,304070,859459,96,192.5,88.768,87.271,1803,75.3,1150311,99.6,-14.49,8779.6,-6.7,,, 5/1/03,130186,3233,182.9,171205,1078,296395,6.1,1751,93.7793,,9650.6,82172,122951,302540,866814,95.3,192.9,88.894,87.17,1835,75.4,1145242,99.7,15.66,8798.5,-0.6,,, 6/1/03,130195,3334,183.1,174113,1193,299662,6.3,1867,93.9277,,9683.2,84632,124253,301697,880865,96.2,193,88.945,87.265,1875,75.5,1142156,99.5,25.13,8850.4,3.7,13152.1,92.304,13221.5 7/1/03,130219,3270,183.7,173055,1168,302788,6.2,1897,94.3114,,9792.1,85373,126735,301837,891264,96.7,193.4,89.144,87.502,1885,75.8,1139420,99.4,19.33,8896.1,7.7,,, 8/1/03,130177,3283,184.5,174328,1206,307745,6.1,1833,94.138,,9852.8,84247,124049,301292,901839,96.7,193.6,89.225,87.778,1966,75.7,1132679,99.4,15.54,8976.4,20.3,,, 9/1/03,130281,3074,185.1,178118,1131,305916,6.1,1939,94.7363,,9739,86224,127930,302194,911589,96.2,193.7,89.319,88.026,1961,76.2,1136927,99.8,20.37,8945.7,20.7,13372.4,91.689,13348.1 10/1/03,130479,3205,184.9,183254,1144,304824,6,1967,94.8514,,9780.6,88195,129466,305106,925732,96.3,194,89.437,87.998,2012,76.3,1142942,100,36.78,8967.4,28.3,,, 11/1/03,130496,3157,185,182472,1093,308551,5.8,2083,95.6337,,9852.4,90513,130355,306146,925985,96.8,194,89.536,88.089,1918,76.9,1144972,100.5,33.97,9026,26.9,,, 12/1/03,130618,3214,185.5,180958,1129,307362,5.7,2057,95.5638,,9869.1,90164,134228,308305,948491,97.5,194.2,89.651,88.286,1987,76.9,1147613,100.8,27.36,9033,26.5,13528.7,92.037,13479.1 1/1/04,130780,3459,186.3,176855,1165,309225,5.7,1911,95.7472,,9879.9,90056,134408,308614,938826,99,194.6,89.857,88.606,1952,77.1,1148861,101.5,32.47,9071.5,36.1,,, 2/1/04,130826,3402,186.7,180727,1159,311427,5.6,1846,96.3214,,9900.7,93882,138204,312596,938656,99.4,194.9,90.026,88.815,1966,77.5,1158924,102.2,36.98,9089.3,27.8,,, 3/1/04,131158,3380,187.1,191580,1276,316935,5.8,1998,95.8684,,9936.6,96519,143003,314683,960946,100.2,195.5,90.196,88.969,2066,77.2,1168406,103,32.66,9128.5,29.6,13606.5,91.929,13581.8 4/1/04,131407,3629,187.4,184187,1186,313531,5.6,2003,96.2677,,9969.2,95754,143232,314745,967761,100.4,195.9,90.418,89.123,2070,77.5,1176107,103.7,39,9135.9,32.3,,, 5/1/04,131715,3660,188.2,183593,1241,318962,5.6,1981,97.0723,,10020.2,97259,145428,318348,974158,101.9,196.2,90.558,89.426,2150,78.2,1183322,104.1,36.95,9184.6,29,,, 6/1/04,131791,3424,188.9,185560,1180,314971,5.6,1828,96.2562,,10020.5,94853,149555,320957,983072,101.7,196.6,90.74,89.715,2020,77.6,1195490,103.4,27.05,9145.9,30.6,13706.2,92.815,13722.4 7/1/04,131835,3934,189.1,187032,1088,318532,5.5,2002,97.0032,,10036.4,96474,147767,326795,1006119,102.1,196.8,90.889,89.834,2112,78.2,1207087,103.9,34.98,9207.3,34.7,,, 8/1/04,131956,3619,189.2,185137,1175,318945,5.4,2024,97.0723,,10065.8,96909,150225,330144,1013724,103.6,196.9,90.956,89.908,2056,78.2,1216708,103.4,15.23,9226.2,25.1,,, 9/1/04,132120,3742,189.8,188132,1214,324607,5.4,1905,97.1565,,10066,98277,149765,330080,1012290,104.1,197.5,91.122,90.083,2041,78.3,1217241,103.8,28.37,9295.6,19.6,13830.8,94.098,13878.8 10/1/04,132466,3792,190.8,185578,1305,326680,5.5,2072,98.0701,,10075,99773,154734,335181,1015562,105.8,197.9,91.275,90.43,2097,79,1224943,104.4,24.54,9309.5,26.9,,, 11/1/04,132530,3238,191.7,192940,1179,327837,5.4,1782,98.2541,,10051.2,99533,158352,339295,1023210,105.5,198.3,91.421,90.734,2079,79.1,1238657,104.7,15.31,9323,19.2,,, 12/1/04,132660,3650,191.7,192834,1242,331877,5.4,2042,98.9703,,10418.5,102259,156760,340147,1037684,104,198.6,91.549,90.793,2082,79.7,1241070,104.8,21.59,9381,25.5,13950.4,94.204,13949 1/1/05,132794,3670,191.6,193240,1203,329187,5.3,2144,99.417,,10070.4,103059,158620,345077,1045913,104.6,199,91.813,90.854,2139,80,1252690,105.6,15.55,9379.8,13.4,,, 2/1/05,133033,3845,192.4,195227,1319,332847,5.4,2207,100.0955,,10074.5,103867,161321,347014,1066374,105.5,199.4,91.978,91.12,2114,80.4,1261588,105.7,17.14,9412.3,21.1,,, 3/1/05,133169,3831,193.1,187090,1328,332517,5.2,1864,99.9283,,10105.9,104805,157424,348963,1071467,107.8,200.1,92.204,91.392,2062,80.2,1269402,106.4,24.29,9435.5,15.1,14099.1,93.891,14084.9 4/1/05,133534,4243,193.7,195130,1260,337608,5.2,2061,100.0742,,10125.6,106865,163980,352174,1080952,108.8,200.2,92.321,91.655,2150,80.2,1275059,106.9,8.3,9510.4,25.3,,, 5/1/05,133708,3884,193.6,206420,1286,334551,5.1,2025,100.2414,,10167.5,106231,162495,352631,1093516,107.9,200.5,92.544,91.738,2085,80.3,1275921,106.7,-4.92,9463.2,9.3,,, 6/1/05,133955,4022,193.7,209180,1274,344034,5,2068,100.6437,,10196.8,106314,164574,354436,1105851,109.2,200.6,92.603,91.792,2178,80.5,1276189,106.7,7.8,9560.7,-1.3,14172.7,94.501,14185.8 7/1/05,134331,4319,194.9,197076,1389,346715,5,2054,100.3278,,10222.5,106679,164742,355779,1118698,110.5,200.9,92.741,92.181,2203,80.1,1270684,106.8,23.78,9620.8,8.1,,, 8/1/05,134525,4073,196.1,204803,1255,342950,4.9,2095,100.5151,,10238,107997,166385,357483,1129503,112.1,201.1,92.833,92.563,2219,80.2,1275135,106.6,23.72,9586.1,11.2,,, 9/1/05,134593,4237,198.8,204139,1244,343711,5,2151,98.6063,,10185.6,106885,171808,358681,1148733,114.4,201.3,93.046,93.458,2263,78.5,1282763,107.5,16.92,9548.8,7.1,14291.8,94.958,14310.8 10/1/05,134678,4277,199.1,209844,1336,344390,5,2065,99.8695,,10234.6,109388,176528,361610,1160818,114.5,202,93.294,93.594,2170,79.4,1291267,108.3,12.05,9573.4,4.8,,, 11/1/05,135015,4220,198.1,222564,1214,347047,5,2147,100.9014,,10304.9,110656,174746,363609,1172553,112.3,202.5,93.515,93.381,2218,80.1,1300312,107.6,18.01,9625.4,10.3,,, 12/1/05,135174,4064,198.1,220015,1239,347441,4.9,1994,101.4873,,10359.6,113277,177643,368075,1184609,112.3,202.8,93.633,93.4,2120,80.5,1313363,107.7,22.9,9665.3,12.9,14373.4,95.508,14508 1/1/06,135452,4298,199.3,207660,1174,357626,4.7,2273,101.6088,,10498.6,115061,181741,369334,1195698,113.7,203.2,93.793,93.811,2212,80.5,1322938,108.5,17.5,9701.1,5.4,,, 2/1/06,135768,4229,199.4,217661,1061,354614,4.8,2119,101.6839,,10543.4,115652,178503,372909,1205060,112.8,203.6,93.926,93.852,2141,80.4,1327296,108.6,20.89,9733.6,15.3,,, 3/1/06,136049,4493,199.7,227670,1116,356357,4.7,1969,101.8522,,10562.7,118272,180846,374669,1205018,112.7,204.3,94.153,94.007,2118,80.5,1340157,108.8,33.19,9753,14.7,14546.1,96.93,14782.8 4/1/06,136232,4680,200.7,214414,1123,357320,4.7,1821,102.2952,,10549.1,118672,181516,379473,1192849,115.1,204.8,94.39,94.398,1998,80.7,1348834,109.6,18.48,9771.1,14.2,,, 5/1/06,136255,4389,201.3,215979,1086,356423,4.6,1942,102.1531,,10539.8,120599,185444,382353,1180699,117.2,205.4,94.576,94.609,1905,80.5,1363477,110.4,18.61,9781.9,13.8,,, 6/1/06,136337,4349,201.8,221232,1074,357763,4.6,1802,102.522,,10563.3,122053,185534,385029,1172074,117.3,205.9,94.803,94.832,1867,80.6,1376219,111.2,26.5,9790.2,11.7,14589.6,97.041,14805.1 7/1/06,136544,4154,202.9,211849,965,359217,4.7,1737,102.5057,,10560.4,119803,186328,388417,1157784,118.2,206.3,94.913,95.167,1763,80.5,1381506,111.6,16.56,9836,4,,, 8/1/06,136725,4560,203.8,210303,1035,360497,4.7,1650,102.8357,,10558.6,122321,190144,392613,1146049,118.8,206.8,95.108,95.467,1722,80.6,1391671,112.1,11.72,9813.7,12.5,,, 9/1/06,136883,4516,202.8,236000,1016,358468,4.5,1720,102.6606,,10623.5,123562,188497,394472,1136144,116.2,207.2,95.272,95.232,1655,80.3,1396955,111.7,14.95,9864.5,-0.8,14602.6,97.594,14863.7 10/1/06,136887,4472,201.9,216908,941,358435,4.4,1491,102.6297,,10684.6,125646,184636,396159,1123281,113.3,207.6,95.413,94.979,1570,80.1,1401162,111.4,18.72,9911.3,2.3,,, 11/1/06,137095,4341,202,225791,1003,359256,4.5,1570,102.539,,10722.4,127445,186020,400600,1122263,113.8,207.8,95.45,95.004,1535,79.9,1406822,111.8,22.92,9927.5,4.5,,, 12/1/06,137266,4278,203.1,229389,998,364300,4.4,1649,103.6229,,10750.4,128557,190149,399056,1134855,115.1,208.1,95.632,95.393,1638,80.5,1407550,112.5,20.08,9976.5,-1.8,14716.9,98.555,14920.2 1/1/07,137506,4630,203.437,218565,891,363462,4.6,1409,103.1171,,10759.9,130079,187734,400300,1138412,113.7,208.6,95.998,95.689,1626,80,1412861,113,7.34,9983.8,7.5,,, 2/1/07,137596,4465,204.226,221337,828,364090,4.5,1480,104.172,,10788,128399,186877,402004,1138752,114.1,209.135,96.227,96.005,1598,80.6,1418881,113.9,24.5,9990.3,3.5,,, 3/1/07,137785,4666,205.288,228747,833,367714,4.4,1495,104.3501,,10820.6,133133,194930,404430,1146756,115.9,209.418,96.305,96.34,1596,80.6,1421414,114.7,13.4,9997.9,2.8,14726,100.88,14882.6 4/1/07,137864,4824,205.904,233592,887,366065,4.5,1490,105.0975,,10818.3,132458,192972,405351,1150637,117.5,209.747,96.397,96.527,1470,81,1428782,115.2,3.94,10018.8,3,,, 5/1/07,138007,4550,206.755,227743,842,370887,4.4,1415,105.1436,,10813,135183,194470,406984,1161625,118.6,210.058,96.5,96.798,1493,80.9,1438234,115.5,9.91,10030.3,3.7,,, 6/1/07,138085,4608,207.234,229855,793,367933,4.6,1448,105.1474,,10800.7,136594,196114,408454,1162937,120,210.392,96.651,96.997,1407,80.7,1445825,116,24.34,10024.7,17.3,14838.7,100.199,14904.1 7/1/07,138052,4490,207.603,238609,778,369472,4.7,1354,105.1149,,10825.1,137564,197478,408796,1155029,121.5,210.773,96.793,97.141,1361,80.6,1447601,116.1,26.18,10047.1,6.8,,, 8/1/07,138028,4555,207.667,233226,699,370982,4.6,1330,105.3166,,10831.6,140485,197490,410409,1158779,121.1,211.119,96.956,97.225,1321,80.7,1453555,116.3,22.87,10080.7,-0.5,,, 9/1/07,138116,4523,208.547,225797,686,373138,4.7,1183,105.6629,,10859.2,141276,199070,413663,1158334,121.8,211.554,97.221,97.601,1261,80.9,1461665,116.7,14.69,10079.7,7.5,14938.5,99.388,14822.4 10/1/07,138201,4300,209.19,229267,727,375048,4.7,1264,105.1595,,10839.4,144737,201274,414494,1153031,123.6,212.077,97.46,97.883,1192,80.5,1466607,117.6,25.82,10067.3,7.8,,, 11/1/07,138316,4156,210.834,232433,641,378371,4.7,1197,105.729,,10828.9,146373,206090,419444,1133745,127.5,212.66,97.619,98.373,1224,80.9,1476061,118.7,25.88,10093,6.7,,, 12/1/07,138413,4123,211.445,242879,619,375349,5,1037,105.7256,,10874.9,147269,204422,424640,1114939,127.3,213.168,97.857,98.638,1149,80.9,1486039,119.3,8.6,10085.1,-5.4,14991.8,100.034,14816.6 1/1/08,138432,4260,212.174,237274,627,375303,5,1084,105.4069,,10906.2,150167,211306,430413,1111225,129.2,213.771,98.058,98.894,1094,80.7,1501539,120.7,7.1,10074.7,-18.4,,, 2/1/08,138346,4042,212.687,233810,593,371661,4.9,1103,105.054,,10925.4,152433,216781,434859,1097981,129.5,213.939,98.173,99.11,1014,80.5,1508060,121.8,-7.4,10045.3,-20.2,,, 3/1/08,138268,4001,213.448,230770,535,371961,5.1,1005,104.7987,,10948.4,152089,212154,435828,1103225,133.5,214.42,98.394,99.416,967,80.4,1507598,123.8,-14.56,10063,-14.7,14889.5,102.035,14842.2 4/1/08,138058,4098,213.942,229958,536,373877,5,1013,104.0207,,10906.9,156756,220284,442797,1101713,137.3,214.56,98.514,99.654,1008,79.8,1516249,124.4,-3,10079.5,-21.2,,, 5/1/08,137873,3960,215.208,230207,504,375790,5.4,973,103.4941,,11431.6,158799,220950,445480,1101282,141.2,214.936,98.702,100.091,995,79.5,1518473,124.8,-3.99,10084.1,-16.1,,, 6/1/08,137708,3767,217.463,229634,487,376584,5.6,1046,103.3216,,11129.8,163609,224279,451407,1089615,145.5,215.424,98.894,100.786,1180,79.4,1529914,126.1,-8.08,10070.2,-16.8,14963.4,101.115,14832.4 7/1/08,137499,3821,219.016,223764,477,374774,5.8,923,102.7625,,10954.3,165379,232221,457317,1087047,147.5,215.965,99.029,101.218,921,78.9,1540430,128,-5.23,10028.8,-16.2,,, 8/1/08,137233,3665,218.69,216357,435,372091,6.1,844,101.2245,,10866.7,162658,224766,461590,1069121,143,216.393,99.147,101.135,858,77.7,1541344,125.9,-0.8,10026.4,-17.6,,, 9/1/08,136781,3264,218.877,210859,433,366167,6.1,820,96.8689,,10878.9,153586,214086,459693,1059904,137.8,216.713,99.27,101.236,797,74.3,1532678,124.9,-8.08,9960,2,14891.6,101.726,14767 10/1/08,136308,3292,216.995,192059,393,352900,6.5,777,97.7617,,10933,151364,211555,453086,1056692,129.6,216.788,99.261,100.684,736,74.9,1517254,122.3,-25.85,9915.6,-37.6,,, 11/1/08,135539,2956,213.153,183989,389,339942,6.8,652,96.5572,,11008.9,142400,187123,450605,1035307,120,216.947,99.255,99.545,626,74,1495985,118.4,-22.65,9896.5,-40.9,,, 12/1/08,134844,2830,211.398,173900,377,332065,7.3,560,93.7183,,10969.2,132372,174835,445208,999710,114.5,216.925,99.228,99.007,554,71.7,1464379,115.8,-25.41,9842.1,-37.6,14577,103.48,14479.5 1/1/09,134053,2767,211.933,153310,336,336977,7.8,490,91.5058,,11015.1,125294,163136,440581,969117,113,217.346,99.259,99.068,545,70,1446916,116.6,-26.66,9884.2,-31.1,,, 2/1/09,133350,2791,212.705,145602,372,335765,8.3,582,90.934,,10916,127342,155109,432272,965485,113,217.792,99.358,99.284,558,69.5,1424654,116.3,-34.53,9846.2,-39.4,,, 3/1/09,132527,2491,212.495,145571,339,330219,8.7,505,89.5012,,10916.6,125998,155161,423761,958519,113.6,218.253,99.48,99.193,513,68.3,1404704,115.5,-33.43,9822.1,-34.4,14375,100.138,14257.8 4/1/09,131841,2357,212.709,144239,337,331314,9,478,88.7058,,10976.4,124390,154095,417893,927456,114.8,218.706,99.737,99.34,521,67.7,1387702,116.1,-19.13,9806.6,-25.2,,, 5/1/09,131490,2427,213.022,150641,376,334290,9.4,540,87.7758,,11147.2,126221,151593,412663,913727,116.8,218.904,99.84,99.474,556,67,1370298,116.6,-6.2,9811.4,-22.4,,, 6/1/09,131020,2428,214.79,145782,393,339532,9.5,585,87.4125,,10958,128891,155258,406457,907196,120,219.112,99.974,100.067,601,66.7,1353860,117.8,-9.51,9801.1,0.3,14355.6,100.66,14259.2 7/1/09,130691,2196,214.726,156180,411,340286,9.5,594,88.3209,,10919.5,130848,163637,400364,906087,119.3,219.263,99.991,100.02,595,67.4,1339022,117.4,0.06,9833.3,-6.7,,, 8/1/09,130479,2306,215.445,157966,418,346705,9.6,586,89.2996,,10892.4,131438,162705,395611,893746,121.1,219.496,100.11,100.288,616,68.2,1319852,118.1,12.8,9933.4,8.8,,, 9/1/09,130260,2478,215.861,157328,386,338356,9.8,585,89.9908,,10907.1,136142,170632,391004,882793,121.3,219.92,100.291,100.454,609,68.8,1314699,117.9,20.93,9830.9,14.9,14402.5,99.899,14328.1 10/1/09,130060,2400,216.509,162553,396,341590,10,534,90.2527,,10862.6,140401,174228,392490,866972,122.3,220.501,100.581,100.764,583,69.1,1322088,117.9,33.13,9849.5,12.6,,, 11/1/09,130053,2350,217.234,161811,375,344911,9.9,588,90.6331,100.2,10888,141370,178573,398592,853896,124.1,220.666,100.666,100.997,623,69.5,1330686,118.9,25.56,9848.1,15.5,,, 12/1/09,129774,2407,217.347,159408,352,346258,9.9,581,90.8895,100.3,10925.7,144718,182700,397020,838737,124.4,220.881,100.713,101.052,664,69.8,1329577,119.7,5.2,9896.8,16.5,14541.9,99.32,14528.3 1/1/10,129802,2636,217.488,182190,345,346349,9.8,614,91.9065,101.2,10906.7,144013,181167,397177,814452,125.9,220.633,100.807,101.234,636,70.8,1331369,120.7,14.8,9881.7,12.9,,, 2/1/10,129733,2578,217.281,176104,336,346972,9.8,604,92.2135,101,10887.5,145059,186093,398452,808245,125.8,220.731,100.89,101.248,650,71.2,1338781,120.3,21.28,9911.3,14.1,,, 3/1/10,129896,2666,217.353,180182,381,354625,9.9,636,92.8133,101.1,10912,149262,189028,400709,815113,126.3,220.783,101.033,101.363,687,71.8,1347526,121.2,19.93,9960.1,14.3,14604.8,98.116,14547.3 4/1/10,130139,3220,217.403,187405,422,357086,9.9,687,93.1984,101.4,10993.2,147800,188664,401553,825199,127.7,220.822,101.061,101.349,637,72.2,1353583,122.5,27.64,9972.7,16.2,,, 5/1/10,130661,2891,217.29,186349,280,354430,9.6,583,94.6492,101.6,11067,152502,193834,403494,821833,126.7,220.962,101.182,101.392,575,73.5,1355176,123.1,17.88,10001.3,22.2,,, 6/1/10,130528,2664,217.199,186485,305,353830,9.4,536,94.8328,101.4,11071.3,152069,198626,405845,822777,125.2,221.194,101.288,101.447,587,73.8,1366683,122.2,20.09,10021.2,15.1,14745.9,98.896,14648.6 7/1/10,130458,2965,217.605,189532,283,354536,9.4,546,95.2539,101.6,11080.5,155434,195847,410771,796903,125.2,221.363,101.345,101.569,579,74.3,1378218,122,5.34,10027.4,7.5,,, 8/1/10,130424,2920,217.923,192145,282,356560,9.5,599,95.6092,101.8,11114.7,156016,200937,415843,798360,125.7,221.509,101.442,101.713,580,74.7,1389628,123,10.23,10074.8,3.6,,, 9/1/10,130372,2767,218.275,200308,317,359440,9.5,594,95.8794,102.1,11101.2,156896,200937,422512,803378,125.7,221.711,101.488,101.807,563,75,1406603,123.7,9.9,10087.1,4.1,14845.5,98.842,14839.5 10/1/10,130629,3033,219.035,194686,291,363855,9.4,543,95.6362,102.5,11128.3,162730,202727,431258,798831,127.1,221.83,101.559,102.045,558,74.9,1420992,124.7,15.5,10136.8,0.2,,, 11/1/10,130752,2914,219.59,196672,287,367352,9.8,545,95.7002,102.8,11160.8,164418,202180,434309,798208,129.2,222.149,101.665,102.211,560,75,1430814,126.6,-7.56,10175.2,19.2,,, 12/1/10,130840,2857,220.472,194933,326,369299,9.3,539,96.4959,103.1,11239,167408,208223,441058,786597,131,222.343,101.667,102.455,632,75.7,1447968,127.5,11.82,10186.4,15.4,14939,98.882,14904.9 1/1/11,130882,2939,221.187,204711,307,372041,9.1,630,96.4283,103.7,11297.4,168932,216055,444374,754710,133,222.803,101.808,102.685,576,75.7,1458858,129.1,8.96,10201.2,16.4,,, 2/1/11,131070,3056,221.898,194236,270,375003,9,517,96.0111,104.3,11329,167437,211155,449434,757019,135.3,223.213,101.983,102.966,542,75.4,1467507,130.8,11.5,10210,29.1,,, 3/1/11,131295,3130,223.046,211908,300,378472,9,600,96.8407,105,11312.4,175373,218851,454289,768276,139.3,223.454,102.131,103.356,583,76,1486908,132.7,12.67,10240.2,36.6,14881.3,101.5,14924.4 4/1/11,131641,3287,224.093,200903,310,380284,9.1,554,96.4337,105.5,11282.8,177458,219684,456729,768555,142.9,223.727,102.384,103.808,581,75.7,1500503,133.8,19.56,10235.2,13.2,,, 5/1/11,131714,3114,224.806,206091,305,380398,9,561,96.6227,105.8,11277.1,177451,224671,465920,775999,143.1,224.175,102.628,104.144,618,75.8,1516439,134.3,9.91,10229.5,6.2,,, 6/1/11,131949,3224,224.806,199884,301,383081,9.1,608,96.8573,105.9,11325.8,175611,225043,471032,797238,142.2,224.697,102.767,104.179,636,75.9,1524898,134.5,-4.81,10248.3,-0.3,14989.6,100.6,14996.1 7/1/11,132019,3475,225.395,208592,296,382966,9,623,97.3169,106.1,11371.2,180121,225810,474156,792089,142.4,225.218,102.942,104.38,621,76.2,1529735,134,-6.05,10277.2,6.8,,, 8/1/11,132126,3168,226.106,215290,299,383541,9,585,97.7956,106.3,11363.5,180455,225423,475937,805366,141.9,225.862,103.157,104.618,647,76.5,1538486,134.6,-3.7,10271.6,-19.6,,, 9/1/11,132372,3495,226.597,208277,304,387313,9,650,97.7474,106.7,11330.8,182398,225703,472095,807010,141.7,226.118,103.23,104.787,610,76.4,1533929,135.3,-4.23,10297.9,-11.2,15021.1,101.415,15093.1 10/1/11,132574,3421,226.75,208553,316,390302,8.8,610,98.4096,106.3,11340.8,181683,226645,476937,802658,141.2,226.506,103.371,104.851,671,76.8,1545524,132.6,-5.37,10326.8,6,,, 11/1/11,132720,3153,227.169,216970,328,391478,8.6,711,98.281,106.6,11329.3,179589,226633,478647,806301,142.2,226.899,103.539,104.999,706,76.5,1552965,132.7,4.62,10313.3,3.9,,, 12/1/11,132927,3369,227.223,226853,341,391695,8.5,694,98.6739,106.5,11416,180513,229973,485328,814989,142.2,227.405,103.656,105.018,697,76.7,1561441,132.1,11.77,10310.2,2.4,15190.3,99.404,15217 1/1/12,133265,3664,227.86,224549,335,395280,8.3,723,99.3787,106.9,11495.2,180073,231056,486011,823375,142.2,227.869,103.94,105.325,715,77.1,1568406,132.5,10.34,10354.4,7.4,,, 2/1/12,133522,3501,228.377,223657,366,400181,8.3,704,99.6578,107.2,11559,182640,226210,493015,825163,142.2,228.063,104.081,105.56,733,77.1,1581826,133.1,16.62,10398,10.8,,, 3/1/12,133761,3852,228.894,221505,354,401830,8.2,695,98.9579,107.4,11589,186316,236533,494501,828668,144.2,228.49,104.282,105.804,797,76.4,1588787,134.1,16.12,10384.7,9.2,15291,101.552,15500.4 4/1/12,133836,3663,229.286,219540,354,400095,8.2,753,99.8396,107.6,11620,185030,232284,497964,834951,144.1,228.915,104.461,105.943,747,76.9,1595510,134.7,8.33,10399.5,6.1,,, 5/1/12,133951,3706,228.722,217293,370,399463,8.2,708,100.0042,107.6,11632.1,185070,231041,499293,849347,142,229.241,104.588,105.868,807,76.9,1601668,134,13.52,10400.2,-0.6,,, 6/1/12,134038,3792,228.506,219155,360,395723,8.2,757,100.0318,107.3,11657.8,185286,228746,501984,859250,138.7,229.686,104.718,105.844,790,76.8,1606673,131.7,2.74,10390.3,-12.4,15362.4,101.525,15522.8 7/1/12,134181,3694,228.475,224520,369,397516,8.2,740,100.3132,107.2,11626.4,184336,227706,507164,857301,137.7,229.956,104.831,105.88,840,76.8,1618075,132.2,2.94,10422.2,-13.1,,, 8/1/12,134371,3655,229.844,202185,375,401937,8.1,754,99.8389,107.5,11605.6,183265,227372,509466,857558,139.4,230.205,104.89,106.238,832,76.3,1627178,133.4,-2.41,10405.9,-2.8,,, 9/1/12,134552,3533,230.987,215073,385,405707,7.8,847,99.9599,108.2,11660.2,188647,228711,515873,862358,140.8,230.618,105.014,106.576,921,76.3,1637311,134.5,-6.7,10444.3,-0.7,15380.8,101.793,15517.1 10/1/12,134684,3713,231.655,219319,358,405598,7.8,915,100.2146,108.3,11729.1,182988,226029,515170,870362,141.2,231.013,105.271,106.886,895,76.3,1639501,134.6,-3.87,10426.9,-1.5,,, 11/1/12,134833,3556,231.278,217917,392,407327,7.7,833,100.7651,108.4,11884.7,185747,232414,519864,866855,140.2,231.298,105.377,106.768,930,76.6,1645933,133.8,-1.13,10454.3,-10.9,,, 12/1/12,135076,3576,231.272,229811,399,409468,7.9,976,101.0382,108.5,12194.8,189591,227661,520341,865730,139.4,231.701,105.442,106.758,938,76.7,1649980,133.6,-5.59,10478.5,2.1,15384.3,104.987,15650.6 1/1/13,135266,3712,231.641,217899,442,412207,8,888,100.9614,108.7,11411.4,188751,229794,524138,857410,140.1,232.244,105.692,106.922,928,76.6,1664747,134.1,-9.31,10504.9,-1.2,,, 2/1/13,135577,3972,233.005,229948,439,416783,7.7,970,101.4781,108.9,11431,190448,233066,522415,871574,141.3,232.653,105.825,107.333,971,76.9,1665488,135.1,7.62,10519.2,-4.7,,, 3/1/13,135712,3901,232.313,211676,449,412514,7.5,999,101.6302,108.8,11451.3,188248,224197,522759,865844,141.2,232.813,105.94,107.244,932,76.9,1663571,134.4,6.45,10530.5,3.3,15491.9,102.521,15642.7 4/1/13,135904,3962,231.856,221018,451,413391,7.6,826,101.5825,108.7,11461.4,189485,228412,523862,877799,140.2,232.854,106.008,107.128,1015,76.8,1667106,133.6,5.12,10530.1,1.5,,, 5/1/13,136122,3886,231.895,231237,430,414207,7.5,920,101.6016,108.6,11517.8,188438,231277,520521,882693,139.4,233.081,106.123,107.244,1016,76.7,1663950,132.9,-2.2,10556.2,0.6,,, 6/1/13,136268,3913,232.357,239620,463,415989,7.5,852,101.8221,109,11540.4,191198,227163,521060,893248,138.8,233.429,106.29,107.479,951,76.8,1663664,132.8,6.22,10576.5,12.8,15521.6,104.076,15719.8 7/1/13,136408,3915,232.749,216297,376,417962,7.3,891,101.2443,109.3,11538.3,190614,228284,522047,909513,138.9,233.844,106.382,107.587,986,76.4,1668921,132.6,4.89,10584.6,14.7,,, 8/1/13,136677,3921,233.249,220679,380,417101,7.3,898,101.9928,109.3,11570.2,190719,228802,526015,914609,139.4,234.293,106.511,107.739,947,76.9,1677150,131.9,10.34,10582,7.5,,, 9/1/13,136862,3985,233.642,229220,399,417682,7.3,860,102.4847,109.4,11599.4,190791,232108,528707,924361,139.8,234.624,106.63,107.858,1015,77.2,1684967,132.4,7.67,10630,19.9,15641.3,103.952,15752 10/1/13,137051,4104,233.799,224830,444,419686,7.2,921,102.4287,109.6,11559.1,194342,232143,534357,937982,138.9,234.878,106.82,108,1031,77.1,1695757,131.6,4.71,10651,12.7,,, 11/1/13,137342,3878,234.21,236964,446,421056,6.9,1104,102.7732,109.7,11595,195830,230681,539012,948850,137.7,235.278,106.978,108.071,1042,77.4,1706023,131.8,1.77,10702.5,3.5,,, 12/1/13,137387,3742,234.847,229057,441,422891,6.7,1010,102.9513,109.8,11602.8,194591,229405,541205,961996,137.8,235.69,107.066,108.254,1013,77.5,1714804,132.3,3.3,10717.6,3,15793.9,103.655,15851.3 1/1/14,137574,3884,235.436,221834,447,419195,6.6,902,102.4621,110.1,11646.4,194756,233590,543909,977072,138.3,236.022,107.21,108.421,1001,77,1723614,132.7,10.52,10662.3,15.9,,, 2/1/14,137742,4098,235.621,229392,423,424657,6.7,948,103.2919,110.3,11704.9,193829,234654,547290,984715,139.8,236.288,107.292,108.492,1032,77.6,1731101,133.7,4.41,10732.2,3.6,,, 3/1/14,138014,4202,235.897,234525,410,429707,6.7,973,104.0896,110.6,11745,198000,238855,552444,993293,140.5,236.649,107.502,108.708,1078,78.1,1737184,134.9,5.16,10779.6,15,15747,105.998,15932.3 4/1/14,138324,4575,236.495,236771,401,433082,6.2,1038,104.2409,110.8,11758.1,197463,241483,557540,1002975,139.7,237.103,107.698,108.907,1080,78.1,1744407,133.5,4.67,10804.7,18.3,,, 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8/1/15,142151,5308,237.703,229846,505,446970,5.1,1132,105.5783,110.3,12293.9,186620,231259,588696,1145216,123.2,242.753,109.603,109.753,1166,76.7,1802092,123,-12.79,11265.2,3.4,,, 9/1/15,142300,5360,237.489,223693,457,447207,5.1,1189,105.3072,109.8,12320.4,187550,228622,590904,1152122,121.9,243.224,109.794,109.691,1129,76.4,1807638,122.3,-12.86,11292.7,-3.6,16454.9,107.866,16669 10/1/15,142595,5422,237.949,234513,478,447066,5,1073,105.1649,109.6,12359,185587,227186,589595,1134381,121.5,243.701,109.86,109.774,1175,76.3,1803740,122,-11.41,11301.3,-5.9,,, 11/1/15,142875,5198,238.302,232507,508,448454,5,1171,104.4871,109.7,12381.9,183576,224698,588101,1135470,120.8,244.139,110.02,109.911,1286,75.7,1800901,121.1,-10.06,11332.3,-5.7,,, 12/1/15,143146,5281,238.041,223402,538,450448,5,1160,104.0452,109.6,12430,183074,224561,587178,1133678,119.3,244.516,110.095,109.819,1201,75.4,1801193,119.8,-6.21,11358.5,-10.2,16490.7,109.289,16730.3 1/1/16,143314,5604,238.107,231756,526,448041,4.9,1128,104.5495,110,12485.4,179771,222079,586160,1144928,117.8,245.232,110.392,109.94,1188,75.7,1800048,118.7,-19.37,11356.1,-3.5,,, 2/1/16,143547,5608,237.707,224081,525,449294,4.9,1213,104.3717,109.7,12509.9,182159,226187,582888,1157704,117.2,245.925,110.584,109.84,1162,75.6,1798344,118.2,-16.64,11385.1,-2.8,,, 3/1/16,143733,5670,237.92,228499,537,447907,5,1113,103.3557,109.5,12545.7,180174,215709,584254,1176380,117.7,246.095,110.653,109.91,1077,74.8,1804490,118.1,0.62,11377.6,12.4,16525,110.504,16766.9 4/1/16,143877,5845,238.89,235729,572,453397,5,1155,103.8246,109.7,12569.6,182668,220051,588382,1152363,118.5,246.574,110.842,110.247,1130,75.2,1807046,118.6,9.56,11470.9,-1.6,,, 5/1/16,143888,5500,239.41,229014,572,454359,4.7,1135,103.511,110.1,12579.3,182354,223498,589154,1143257,120.2,247.074,111.022,110.431,1136,74.9,1809981,120,-9.02,11500.2,-1.8,,, 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DocumentSummaryInformation8ÿÿÿÿÿÿÿÿÿÿÿÿ(statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/functions/000077500000000000000000000000001400612667500332775ustar00rootroot00000000000000__init__.py000066400000000000000000000000001400612667500353170ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/functionsstatsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/functions/dfm.m000066400000000000000000001140701400612667500342260ustar00rootroot00000000000000function Res = dfm(X,Spec,threshold,max_iter) %DFM() Runs the dynamic factor model % % Syntax: % Res = DFM(X,Par) % % Description: % DFM() inputs the organized and transformed data X and parameter structure Par. % Then, the function outputs dynamic factor model structure Res and data % summary statistics (mean and standard deviation). % % Input arguments: % X: Kalman-smoothed data where missing values are replaced by their expectation % Par: A structure containing the following parameters: % Par.blocks: Block loadings. % Par.nQ: Number of quarterly series % Par.p: Number of lags in transition matrix % Par.r: Number of common factors for each block % % Output Arguments: % % Res - structure of model results with the following fields % . X_sm | Kalman-smoothed data where missing values are replaced by their expectation % . Z | Smoothed states. Rows give time, and columns are organized according to Res.C. % . C | Observation matrix. The rows correspond % to each series, and the columns are organized as shown below: % - 1-20: These columns give the factor loadings. For example, 1-5 % give loadings for the first block and are organized in % reverse-chronological order (f^G_t, f^G_t-1, f^G_t-2, f^G_t-3, % f^G_t-4). Columns 6-10, 11-15, and 16-20 give loadings for % the second, third, and fourth blocks respectively. % .R: Covariance for observation matrix residuals % .A: Transition matrix. This is a square matrix that follows the % same organization scheme as Res.C's columns. Identity matrices are % used to account for matching terms on the left and righthand side. % For example, we place an I4 matrix to account for matching % (f_t-1; f_t-2; f_t-3; f_t-4) terms. % .Q: Covariance for transition equation residuals. % .Mx: Series mean % .Wx: Series standard deviation % .Z_0: Initial value of state % .V_0: Initial value of covariance matrix % .r: Number of common factors for each block % .p: Number of lags in transition equation % % References: % % Marta Banbura, Domenico Giannone and Lucrezia Reichlin % Nowcasting (2010) % Michael P. Clements and David F. Hendry, editors, % Oxford Handbook on Economic Forecasting. %% Store model parameters ------------------------------------------------ % DFM input specifications: See documentation for details Par.blocks = Spec.Blocks; % Block loading structure Par.nQ = sum(strcmp('q',Spec.Frequency)); % Number of quarterly series Par.p = Spec.p; % Number of lags in autoregressive of factor (same for all factors) Par.r = ones(1,size(Spec.Blocks,2)) * Spec.k; % Number of common factors for each block %Par.r(1) =2; % Display blocks try fprintf('\n\n\n'); disp('Table 3: Block Loading Structure') disp(array2table(Spec.Blocks,... 'RowNames', strrep(Spec.SeriesName,' ','_'),... 'VariableNames',Spec.BlockNames)); fprintf('\n\n\n'); catch end fprintf('Estimating the dynamic factor model (DFM) ... \n\n'); [T,N] = size(X); r = Par.r; p = Par.p; nQ = Par.nQ; blocks = Par.blocks; i_idio = logical([ones(N-nQ,1);zeros(nQ,1)]); %R*Lambda = q; Constraints on the loadings of the quartrly variables R_mat = [ 2 -1 0 0 0;... 3 0 -1 0 0;... 2 0 0 -1 0;... 1 0 0 0 -1]; q = zeros(4,1); if(nargin < 3) threshold = 1e-5; % EM loop threshold (default value) end if(nargin < 4) max_iter = 5000; % EM loop maximum number of iterations end %% Prepare data ----------------------------------------------------------- Mx = mean(X,'omitnan'); Wx = std(X,'omitnan'); xNaN = (X-repmat(Mx,T,1))./repmat(Wx,T,1); % Standardize series %% Initial Conditions ----------------------------------------------------- optNaN.method = 2; % Remove leading and closing zeros optNaN.k = 3; % Setting for filter(): See remNaN_spline [A, C, Q, R, Z_0, V_0] = InitCond(xNaN,r,p,blocks,optNaN,R_mat,q,nQ,i_idio); % Initialize EM loop values previous_loglik = -inf; num_iter = 0; LL = -inf; converged = 0; % y for the estimation is WITH missing data y = xNaN'; %% EM LOOP ---------------------------------------------------------------- %The model can be written as %y = C*Z + e; %Z = A*Z(-1) + v %where y is NxT, Z is (pr)xT, etc % Remove the leading and ending nans optNaN.method = 3; y_est = remNaNs_spline(xNaN,optNaN)'; while (num_iter < max_iter) & ~converged % Loop until converges or max iter. [C_new, R_new, A_new, Q_new, Z_0, V_0, loglik] = ... % Applying EM algorithm EMstep(y_est, A, C, Q, R, Z_0, V_0, r,p,R_mat,q,nQ,i_idio,blocks); C = C_new; R = R_new; A = A_new; Q = Q_new; if num_iter > 2 % Checking convergence [converged, decrease(num_iter + 1)] = ... em_converged(loglik, previous_loglik, threshold, 1); end if (mod(num_iter,10) == 0) && (num_iter > 0) % Print updates to command window disp(['Now running the ',num2str(num_iter),... 'th iteration of max ', num2str(max_iter)]); disp([' Loglik',' (% Change)']) disp([num2str(loglik),' (', sprintf('%6.2f',100*((loglik-previous_loglik)/previous_loglik)) '%)']) end LL = [LL loglik]; previous_loglik = loglik; num_iter = num_iter + 1; end if(num_iter < max_iter) disp(['Successful: Convergence at ', num2str(num_iter), ' iterations']) else disp('Stopped because maximum iterations reached') end % Final run of the Kalman filter [Zsmooth, Vsmooth, VVsmooth, loglik] = runKF(y, A, C, Q, R, Z_0, V_0); Zsmooth = Zsmooth'; x_sm = Zsmooth(2:end,:) * C'; % Get smoothed X %% Loading the structure with the results -------------------------------- Res.x_sm = x_sm; Res.X_sm = repmat(Wx,T,1) .* x_sm + repmat(Mx,T,1); % Unstandardized, smoothed Res.Z = Zsmooth(2:end,:); Res.C = C; Res.R = R; Res.A = A; Res.Q = Q; Res.Mx = Mx; Res.Wx = Wx; Res.Z_0 = Z_0; Res.V_0 = V_0; Res.r = r; Res.p = p; Res.loglik = loglik; Res.Vsmooth = Vsmooth; Res.VVsmooth = VVsmooth; %% Display output % Table with names and factor loadings nQ = Par.nQ; % Number of quarterly series nM = size(Spec.SeriesID,1) - nQ; % Number monthly series nLags = max(Par.p, 5); % 5 comes from monthly-quarterly aggregation nFactors = sum(Par.r); fprintf('\n\n\n'); try disp('Table 4: Factor Loadings for Monthly Series'); disp(array2table(Res.C(1:nM, 1:5:nFactors*5),... % Only select lag(0) terms 'RowNames', strrep(Spec.SeriesName(1:nM),' ','_'), ... 'VariableNames', Spec.BlockNames)); fprintf('\n\n\n'); disp('Table 5: Quarterly Loadings Sample (Global Factor)') disp(array2table(Res.C(end-nQ+1:end, 1:5), ... % Select only quarterly series 'RowNames', strrep(Spec.SeriesName(end-nQ+1:end),' ','_'), ... 'VariableNames', {'f1_lag0', 'f1_lag1', 'f1_lag2', 'f1_lag3', 'f1_lag4'})); fprintf('\n\n\n'); catch end % Table with AR model on factors (factors with AR parameter and variance of residuals) A_terms = diag(Res.A); % Transition equation terms Q_terms = diag(Res.Q); % Covariance matrix terms try disp('Table 6: Autoregressive Coefficients on Factors') disp(table(A_terms(1:5:nFactors*5), ... % Only select lag(0) terms Q_terms(1:5:nFactors*5), ... 'VariableNames', {'AR_Coefficient', 'Variance_Residual'}, ... 'RowNames', strrep(Spec.BlockNames,' ','_'))); fprintf('\n\n\n'); catch end % Table with AR model idiosyncratic errors (factors with AR parameter and variance of residuals) try disp('Table 7: Autoregressive Coefficients on Idiosyncratic Component') disp(table(A_terms([nFactors*5+1:nFactors*5+nM nFactors*5+nM+1:5:end]),... % 21:50 give monthly, 51:5:61 give quarterly Q_terms([nFactors*5+1:nFactors*5+nM nFactors*5+nM+1:5:end]), ... 'VariableNames', {'AR_Coefficient', 'Variance_Residual'}, ... 'RowNames', strrep(Spec.SeriesName,' ','_'))); catch end end %% PROCEDURES ------------------------------------------------------------- % Note: Kalman filter (runKF()) is in the 'functions' folder function [C_new, R_new, A_new, Q_new, Z_0, V_0, loglik] = EMstep(y, A, C, Q, R, Z_0, V_0, r,p,R_mat,q,nQ,i_idio,blocks) %EMstep Applies EM algorithm for parameter reestimation % % Syntax: % [C_new, R_new, A_new, Q_new, Z_0, V_0, loglik] % = EMstep(y, A, C, Q, R, Z_0, V_0, r, p, R_mat, q, nQ, i_idio, blocks) % % Description: % EMstep reestimates parameters based on the Estimation Maximization (EM) % algorithm. This is a two-step procedure: % (1) E-step: the expectation of the log-likelihood is calculated using % previous parameter estimates. % (2) M-step: Parameters are re-estimated through the maximisation of % the log-likelihood (maximize result from (1)). % % See "Maximum likelihood estimation of factor models on data sets with % arbitrary pattern of missing data" for details about parameter % derivation (Banbura & Modugno, 2010). This procedure is in much the % same spirit. % % Input: % y: Series data % A: Transition matrix % C: Observation matrix % Q: Covariance for transition equation residuals % R: Covariance for observation matrix residuals % Z_0: Initial values of factors % V_0: Initial value of factor covariance matrix % r: Number of common factors for each block (e.g. vector [1 1 1 1]) % p: Number of lags in transition equation % R_mat: Estimation structure for quarterly variables (i.e. "tent") % q: Constraints on loadings % nQ: Number of quarterly series % i_idio: Indices for monthly variables % blocks: Block structure for each series (i.e. for a series, the structure % [1 0 0 1] indicates loadings on the first and fourth factors) % % Output: % C_new: Updated observation matrix % R_new: Updated covariance matrix for residuals of observation matrix % A_new: Updated transition matrix % Q_new: Updated covariance matrix for residuals for transition matrix % Z_0: Initial value of state % V_0: Initial value of covariance matrix % loglik: Log likelihood % % References: % "Maximum likelihood estimation of factor models on data sets with % arbitrary pattern of missing data" by Banbura & Modugno (2010). % Abbreviated as BM2010 % % %% Initialize preliminary values % Store series/model values [n, T] = size(y); nM = n - nQ; % Number of monthly series pC = size(R_mat,2); ppC = max(p,pC); num_blocks = size(blocks,2); % Number of blocks %% ESTIMATION STEP: Compute the (expected) sufficient statistics for a single %Kalman filter sequence % Running the Kalman filter and smoother with current parameters % Note that log-liklihood is NOT re-estimated after the runKF step: This % effectively gives the previous iteration's log-likelihood % For more information on output, see runKF [Zsmooth, Vsmooth, VVsmooth, loglik] = runKF(y, A, C, Q, R, Z_0, V_0); %% MAXIMIZATION STEP (TRANSITION EQUATION) % See (Banbura & Modugno, 2010) for details. % Initialize output A_new = A; Q_new = Q; V_0_new = V_0; %%% 2A. UPDATE FACTOR PARAMETERS INDIVIDUALLY ---------------------------- for i = 1:num_blocks % Loop for each block: factors are uncorrelated % SETUP INDEXING r_i = r(i); % r_i = 1 if block is loaded rp = r_i*p; rp1 = sum(r(1:i-1))*ppC; b_subset = rp1+1:rp1+rp; % Subset blocks: Helps for subsetting Zsmooth, Vsmooth t_start = rp1+1; % Transition matrix factor idx start t_end = rp1+r_i*ppC; % Transition matrix factor idx end % ESTIMATE FACTOR PORTION OF Q, A % Note: EZZ, EZZ_BB, EZZ_FB are parts of equations 6 and 8 in BM 2010 % E[f_t*f_t' | Omega_T] EZZ = Zsmooth(b_subset, 2:end) * Zsmooth(b_subset, 2:end)'... +sum(Vsmooth(b_subset, b_subset, 2:end) ,3); % E[f_{t-1}*f_{t-1}' | Omega_T] EZZ_BB = Zsmooth(b_subset, 1:end-1)*Zsmooth(b_subset, 1:end-1)'... +sum(Vsmooth(b_subset, b_subset, 1:end-1), 3); % E[f_t*f_{t-1}' | Omega_T] EZZ_FB = Zsmooth(b_subset, 2:end)*Zsmooth(b_subset, 1:end-1)'... +sum(VVsmooth(b_subset, b_subset, :), 3); % Select transition matrix/covariance matrix for block i A_i = A(t_start:t_end, t_start:t_end); Q_i = Q(t_start:t_end, t_start:t_end); % Equation 6: Estimate VAR(p) for factor A_i(1:r_i,1:rp) = EZZ_FB(1:r_i,1:rp) * inv(EZZ_BB(1:rp,1:rp)); % Equation 8: Covariance matrix of residuals of VAR Q_i(1:r_i,1:r_i) = (EZZ(1:r_i,1:r_i) - A_i(1:r_i,1:rp)* EZZ_FB(1:r_i,1:rp)') / T; % Place updated results in output matrix A_new(t_start:t_end, t_start:t_end) = A_i; Q_new(t_start:t_end, t_start:t_end) = Q_i; V_0_new(t_start:t_end, t_start:t_end) =... Vsmooth(t_start:t_end, t_start:t_end,1); end %%% 2B. UPDATING PARAMETERS FOR IDIOSYNCRATIC COMPONENT ------------------ rp1 = sum(r)*ppC; % Col size of factor portion niM = sum(i_idio(1:nM)); % Number of monthly values t_start = rp1+1; % Start of idiosyncratic component index i_subset = t_start:rp1+niM; % Gives indices for monthly idiosyncratic component values % Below 3 estimate the idiosyncratic component (for eqns 6, 8 BM 2010) % E[f_t*f_t' | \Omega_T] EZZ = diag(diag(Zsmooth(t_start:end, 2:end) * Zsmooth(t_start:end, 2:end)'))... + diag(diag(sum(Vsmooth(t_start:end, t_start:end, 2:end), 3))); % E[f_{t-1}*f_{t-1}' | \Omega_T] EZZ_BB = diag(diag(Zsmooth(t_start:end, 1:end-1)* Zsmooth(t_start:end, 1:end-1)'))... + diag(diag(sum(Vsmooth(t_start:end, t_start:end, 1:end-1), 3))); % E[f_t*f_{t-1}' | \Omega_T] EZZ_FB = diag(diag(Zsmooth(t_start:end, 2:end)*Zsmooth(t_start:end, 1:end-1)'))... + diag(diag(sum(VVsmooth(t_start:end, t_start:end, :), 3))); A_i = EZZ_FB * diag(1./diag((EZZ_BB))); % Equation 6 Q_i = (EZZ - A_i*EZZ_FB') / T; % Equation 8 % Place updated results in output matrix A_new(i_subset, i_subset) = A_i(1:niM,1:niM); Q_new(i_subset, i_subset) = Q_i(1:niM,1:niM); V_0_new(i_subset, i_subset) = diag(diag(Vsmooth(i_subset, i_subset, 1))); %% 3 MAXIMIZATION STEP (observation equation) %%% INITIALIZATION AND SETUP ---------------------------------------------- Z_0 = Zsmooth(:,1); %zeros(size(Zsmooth,1),1); % V_0 = Vsmooth(:,:,1); % Set missing data series values to 0 nanY = isnan(y); y(nanY) = 0; % LOADINGS C_new = C; % Blocks bl = unique(blocks,'rows'); % Gives unique loadings n_bl = size(bl,1); % Number of unique loadings % Initialize indices: These later help with subsetting bl_idxM = []; % Indicator for monthly factor loadings bl_idxQ = []; % Indicator for quarterly factor loadings R_con = []; % Block diagonal matrix giving monthly-quarterly aggreg scheme q_con = []; % Loop through each block for i = 1:num_blocks bl_idxQ = [bl_idxQ repmat(bl(:,i),1,r(i)*ppC)]; bl_idxM = [bl_idxM repmat(bl(:,i),1,r(i)) zeros(n_bl,r(i)*(ppC-1))]; R_con = blkdiag(R_con, kron(R_mat,eye(r(i)))); q_con = [q_con;zeros(r(i)*size(R_mat,1),1)]; end % Indicator for monthly/quarterly blocks in observation matrix bl_idxM = logical(bl_idxM); bl_idxQ = logical(bl_idxQ); i_idio_M = i_idio(1:nM); % Gives 1 for monthly series n_idio_M = length(find(i_idio_M)); % Number of monthly series c_i_idio = cumsum(i_idio); % Cumulative number of monthly series for i = 1:n_bl % Loop through unique loadings (e.g. [1 0 0 0], [1 1 0 0]) bl_i = bl(i,:); rs = sum(r(logical(bl_i))); % Total num of blocks loaded idx_i = find(ismember(blocks, bl_i, 'rows')); % Indices for bl_i idx_iM = idx_i(idx_i nM); % Index for quarterly series rps = rs * ppC; % Monthly-quarterly aggregation scheme R_con_i = R_con(:,bl_idxQ(i,:)); q_con_i = q_con; no_c = ~(any(R_con_i,2)); R_con_i(no_c,:) = []; q_con_i(no_c,:) = []; % Loop through quarterly series in loading. This parallels monthly code for j = idx_iQ' % Initialization denom = zeros(rps,rps); nom = zeros(1,rps); nom2 = zeros(1,rps); idx_jQ = j-nM; % Ordinal position of quarterly variable % Loc of factor structure corresponding to quarterly var residuals i_idio_jQ = (rp1 + n_idio_M + 5*(idx_jQ-1)+1:rp1+ n_idio_M + 5*idx_jQ); % Place quarterly values in output matrix V_0_new(i_idio_jQ, i_idio_jQ) = Vsmooth(i_idio_jQ, i_idio_jQ,1); A_new(i_idio_jQ(1), i_idio_jQ(1)) = A_i(i_idio_jQ(1)-rp1, i_idio_jQ(1)-rp1); Q_new(i_idio_jQ(1), i_idio_jQ(1)) = Q_i(i_idio_jQ(1)-rp1, i_idio_jQ(1)-rp1); for t=1:T Wt = diag(~nanY(j,t)); % Selection matrix for quarterly values % Intermediate steps in BGR equation 13 denom = denom + ... kron(Zsmooth(bl_idxQ(i,:), t+1) * Zsmooth(bl_idxQ(i,:), t+1)'... + Vsmooth(bl_idxQ(i,:), bl_idxQ(i,:), t+1), Wt); nom = nom + y(j, t)*Zsmooth(bl_idxQ(i,:), t+1)'; nom = nom -... Wt * ([1 2 3 2 1] * Zsmooth(i_idio_jQ,t+1) * ... Zsmooth(bl_idxQ(i,:),t+1)'+... [1 2 3 2 1]*Vsmooth(i_idio_jQ,bl_idxQ(i,:),t+1)); nom2 = nom2 + Wt * ([1 2 3 2 1] * Zsmooth(i_idio_jQ,t+1) * ... Zsmooth(bl_idxQ(i,:),t+1)'+... [1 2 3 2 1] * Vsmooth(i_idio_jQ,bl_idxQ(i,:),t+1)); end C_i = inv(denom) * nom'; C_i_constr = C_i - ... % BGR equation 13 inv(denom) * R_con_i'*inv(R_con_i*inv(denom)*R_con_i') * (R_con_i*C_i-q_con_i); % Place updated values in output structure C_new(j,bl_idxQ(i,:)) = C_i_constr; end end %%% 3B. UPDATE COVARIANCE OF RESIDUALS FOR OBSERVATION EQUATION ----------- % Initialize covariance of residuals of observation equation R_new = zeros(n,n); for t=1:T Wt = diag(~nanY(:,t)); % Selection matrix R_new = R_new + (y(:,t) - ... % BGR equation 15 Wt * C_new * Zsmooth(:, t+1)) * (y(:,t) - Wt*C_new*Zsmooth(:,t+1))'... + Wt*C_new*Vsmooth(:,:,t+1)*C_new'*Wt + (eye(n)-Wt)*R*(eye(n)-Wt); end R_new = R_new/T; RR = diag(R_new); %RR(RR<1e-2) = 1e-2; RR(i_idio_M) = 1e-04; % Ensure non-zero measurement error. See Doz, Giannone, Reichlin (2012) for reference. RR(nM+1:end) = 1e-04; R_new = diag(RR); end %-------------------------------------------------------------------------- function [converged, decrease] = em_converged(loglik, previous_loglik, threshold, check_decreased) %em_converged checks whether EM algorithm has converged % % Syntax: % [converged, decrease] = em_converged(loglik, previous_loglik, threshold, check_increased) % % Description: % em_converged() checks whether EM has converged. Convergence occurs if % the slope of the log-likelihood function falls below 'threshold'(i.e. % f(t) - f(t-1)| / avg < threshold) where avg = (|f(t)| + |f(t-1)|)/2 % and f(t) is log lik at iteration t. 'threshold' defaults to 1e-4. % % This stopping criterion is from Numerical Recipes in C (pg. 423). % With MAP estimation (using priors), the likelihood can decrease % even if the mode of the posterior increases. % % Input arguments: % loglik: Log-likelihood from current EM iteration % previous_loglik: Log-likelihood from previous EM iteration % threshold: Convergence threshhold. The default is 1e-4. % check_decreased: Returns text output if log-likelihood decreases. % % Output: % converged (numeric): Returns 1 if convergence criteria satisfied, and 0 otherwise. % decrease (numeric): Returns 1 if loglikelihood decreased. %% Instantiate variables % Threshhold arguments: Checks default behavior if nargin < 3, threshold = 1e-4; end if nargin < 4, check_decreased = 1; end % Initialize output converged = 0; decrease = 0; %% Check if log-likelihood decreases (optional) if check_decreased if loglik - previous_loglik < -1e-3 % allow for a little imprecision fprintf(1, '******likelihood decreased from %6.4f to %6.4f!\n', previous_loglik, loglik); decrease = 1; end end %% Check convergence criteria delta_loglik = abs(loglik - previous_loglik); % Difference in loglik avg_loglik = (abs(loglik) + abs(previous_loglik) + eps)/2; if (delta_loglik / avg_loglik) < threshold, converged = 1; % Check convergence end end %-------------------------------------------------------------------------- %InitCond() Calculates initial conditions for parameter estimation % % Description: % Given standardized data and model information, InitCond() creates % initial parameter estimates. These are intial inputs in the EM % algorithm, which re-estimates these parameters using Kalman filtering % techniques. % %Inputs: % - x: Standardized data % - r: Number of common factors for each block % - p: Number of lags in transition equation % - blocks: Gives series loadings % - optNaN: Option for missing values in spline. See remNaNs_spline() for details. % - Rcon: Incorporates estimation for quarterly series (i.e. "tent structure") % - q: Constraints on loadings for quarterly variables % - NQ: Number of quarterly variables % - i_idio: Logical. Gives index for monthly variables (1) and quarterly (0) % %Output: % - A: Transition matrix % - C: Observation matrix % - Q: Covariance for transition equation residuals % - R: Covariance for observation equation residuals % - Z_0: Initial value of state % - V_0: Initial value of covariance matrix function [ A, C, Q, R, Z_0, V_0] = InitCond(x,r,p,blocks,optNaN,Rcon,q,nQ,i_idio) pC = size(Rcon,2); % Gives 'tent' structure size (quarterly to monthly) ppC = max(p,pC); n_b = size(blocks,2); % Number of blocks OPTS.disp=0; % Turns off diagnostic information for eigenvalue computation [xBal,indNaN] = remNaNs_spline(x,optNaN); % Spline without NaNs [T,N] = size(xBal); % Time T series number N nM = N-nQ; % Number of monthly series xNaN = xBal; xNaN(indNaN) = nan; % Set missing values equal to NaNs res = xBal; % Spline output equal to res: Later this is used for residuals resNaN = xNaN; % Later used for residuals % Initialize model coefficient output C = []; A = []; Q = []; V_0 = []; % Set the first observations as NaNs: For quarterly-monthly aggreg. scheme indNaN(1:pC-1,:) = true; for i = 1:n_b % Loop for each block r_i = r(i); % r_i = 1 when block is loaded %% Observation equation ----------------------------------------------- C_i = zeros(N,r_i*ppC); % Initialize state variable matrix helper idx_i = find(blocks(:,i)); % Returns series index loading block i idx_iM = idx_i(idx_inM); % Quarterly series indicies for loaded blocks % Returns eigenvector v w/largest eigenvalue d [v, d] = eigs(cov(res(:,idx_iM)), r_i, 'lm'); % Flip sign for cleaner output. Gives equivalent results without this section if(sum(v) < 0) v = -v; end % For monthly series with loaded blocks (rows), replace with eigenvector % This gives the loading C_i(idx_iM,1:r_i) = v; f = res(:,idx_iM)*v; % Data projection for eigenvector direction F = []; % Lag matrix using loading. This is later used for quarterly series for kk = 0:max(p+1,pC)-1 F = [F f(pC-kk:end-kk,:)]; end Rcon_i = kron(Rcon,eye(r_i)); % Quarterly-monthly aggregation scheme q_i = kron(q,zeros(r_i,1)); % Produces projected data with lag structure (so pC-1 fewer entries) ff = F(:, 1:r_i*pC); for j = idx_iQ' % Loop for quarterly variables % For series j, values are dropped to accommodate lag structure xx_j = resNaN(pC:end,j); if sum(~isnan(xx_j)) < size(ff,2)+2 xx_j = res(pC:end,j); % Replaces xx_j with spline if too many NaNs end ff_j = ff(~isnan(xx_j),:); xx_j = xx_j(~isnan(xx_j)); iff_j = inv(ff_j'*ff_j); Cc = iff_j*ff_j'*xx_j; % Least squares % Spline data monthly to quarterly conversion Cc = Cc - iff_j*Rcon_i'*inv(Rcon_i*iff_j*Rcon_i')*(Rcon_i*Cc-q_i); C_i(j,1:pC*r_i)=Cc'; % Place in output matrix end ff = [zeros(pC-1,pC*r_i);ff]; % Zeros in first pC-1 entries (replace dropped from lag) % Residual calculations res = res - ff*C_i'; resNaN = res; resNaN(indNaN) = nan; C = [C C_i]; % Combine past loadings together %% Transition equation ------------------------------------------------ z = F(:,1:r_i); % Projected data (no lag) Z = F(:,r_i+1:r_i*(p+1)); % Data with lag 1 A_i = zeros(r_i*ppC,r_i*ppC)'; % Initialize transition matrix A_temp = inv(Z'*Z)*Z'*z; % OLS: gives coefficient value AR(p) process A_i(1:r_i,1:r_i*p) = A_temp'; A_i(r_i+1:end,1:r_i*(ppC-1)) = eye(r_i*(ppC-1)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Q_i = zeros(ppC*r_i,ppC*r_i); e = z - Z*A_temp; % VAR residuals Q_i(1:r_i,1:r_i) = cov(e); % VAR covariance matrix initV_i = reshape(inv(eye((r_i*ppC)^2)-kron(A_i,A_i))*Q_i(:),r_i*ppC,r_i*ppC); % Gives top left block for the transition matrix A = blkdiag(A,A_i); Q = blkdiag(Q,Q_i); V_0 = blkdiag(V_0,initV_i); end eyeN = eye(N); % Used inside observation matrix eyeN(:,~i_idio) = []; C=[C eyeN]; C = [C [zeros(nM,5*nQ); kron(eye(nQ),[1 2 3 2 1])]]; % Monthly-quarterly agreggation scheme R = diag(var(resNaN,'omitnan')); % Initialize covariance matrix for transition matrix ii_idio = find(i_idio); % Indicies for monthly variables n_idio = length(ii_idio); % Number of monthly variables BM = zeros(n_idio); % Initialize monthly transition matrix values SM = zeros(n_idio); % Initialize monthly residual covariance matrix values for i = 1:n_idio; % Loop for monthly variables % Set observation equation residual covariance matrix diagonal R(ii_idio(i),ii_idio(i)) = 1e-04; % Subsetting series residuals for series i res_i = resNaN(:,ii_idio(i)); % Returns number of leading/ending zeros leadZero = max( find( (1:T)' == cumsum(isnan(res_i)) ) ); endZero = max( find( (1:T)' == cumsum(isnan(res_i(end:-1:1))) ) ); % Truncate leading and ending zeros res_i = res(:,ii_idio(i)); res_i(end-endZero + 1:end) = []; res_i(1:leadZero) = []; % Linear regression: AR 1 process for monthly series residuals BM(i,i) = inv(res_i(1:end-1)'*res_i(1:end-1))*res_i(1:end-1)'*res_i(2:end,:); SM(i,i) = cov(res_i(2:end)-res_i(1:end-1)*BM(i,i)); % Residual covariance matrix end Rdiag = diag(R); sig_e = Rdiag(nM+1:N)/19; Rdiag(nM+1:N) = 1e-04; R = diag(Rdiag); % Covariance for obs matrix residuals % For BQ, SQ rho0 = 0.1; temp = zeros(5); temp(1,1) = 1; % Blocks for covariance matrices SQ = kron(diag((1-rho0^2)*sig_e),temp); BQ = kron(eye(nQ),[[rho0 zeros(1,4)];[eye(4),zeros(4,1)]]); initViQ = reshape(inv(eye((5*nQ)^2)-kron(BQ,BQ))*SQ(:),5*nQ,5*nQ); initViM = diag(1./diag(eye(size(BM,1))-BM.^2)).*SM; % Output A = blkdiag(A, BM, BQ); % Observation matrix Q = blkdiag(Q, SM, SQ); % Residual covariance matrix (transition) Z_0 = zeros(size(A,1),1); % States V_0 = blkdiag(V_0, initViM, initViQ); % Covariance of states end function [zsmooth, Vsmooth, VVsmooth, loglik] = runKF(Y, A, C, Q, R, Z_0, V_0); %runKF() Applies Kalman filter and fixed-interval smoother % % Syntax: % [zsmooth, Vsmooth, VVsmooth, loglik] = runKF(Y, A, C, Q, R, Z_0, V_0) % % Description: % runKF() applies a Kalman filter and fixed-interval smoother. The % script uses the following model: % Y_t = C_t Z_t + e_t for e_t ~ N(0, R) % Z_t = A Z_{t-1} + mu_t for mu_t ~ N(0, Q) % Throughout this file: % 'm' denotes the number of elements in the state vector Z_t. % 'k' denotes the number of elements (observed variables) in Y_t. % 'nobs' denotes the number of time periods for which data are observed. % % Input parameters: % Y: k-by-nobs matrix of input data % A: m-by-m transition matrix % C: k-by-m observation matrix % Q: m-by-m covariance matrix for transition equation residuals (mu_t) % R: k-by-k covariance for observation matrix residuals (e_t) % Z_0: 1-by-m vector, initial value of state % V_0: m-by-m matrix, initial value of state covariance matrix % % Output parameters: % zsmooth: k-by-(nobs+1) matrix, smoothed factor estimates % (i.e. zsmooth(:,t+1) = Z_t|T) % Vsmooth: k-by-k-by-(nobs+1) array, smoothed factor covariance matrices % (i.e. Vsmooth(:,:,t+1) = Cov(Z_t|T)) % VVsmooth: k-by-k-by-nobs array, lag 1 factor covariance matrices % (i.e. Cov(Z_t,Z_t-1|T)) % loglik: scalar, log-likelihood % % References: % - QuantEcon's "A First Look at the Kalman Filter" % - Adapted from replication files for: % "Nowcasting", 2010, (by Marta Banbura, Domenico Giannone and Lucrezia % Reichlin), in Michael P. Clements and David F. Hendry, editors, Oxford % Handbook on Economic Forecasting. % % The software can be freely used in applications. % Users are kindly requested to add acknowledgements to published work and % to cite the above reference in any resulting publications S = SKF(Y, A, C, Q, R, Z_0, V_0); % Kalman filter S = FIS(A, S); % Fixed interval smoother % Organize output zsmooth = S.ZmT; Vsmooth = S.VmT; VVsmooth = S.VmT_1; loglik = S.loglik; end %______________________________________________________________________ function S = SKF(Y, A, C, Q, R, Z_0, V_0) %SKF Applies Kalman filter % % Syntax: % S = SKF(Y, A, C, Q, R, Z_0, V_0) % % Description: % SKF() applies the Kalman filter % Input parameters: % Y: k-by-nobs matrix of input data % A: m-by-m transition matrix % C: k-by-m observation matrix % Q: m-by-m covariance matrix for transition equation residuals (mu_t) % R: k-by-k covariance for observation matrix residuals (e_t) % Z_0: 1-by-m vector, initial value of state % V_0: m-by-m matrix, initial value of state covariance matrix % % Output parameters: % S.Zm: m-by-nobs matrix, prior/predicted factor state vector % (S.Zm(:,t) = Z_t|t-1) % S.ZmU: m-by-(nobs+1) matrix, posterior/updated state vector % (S.Zm(t+1) = Z_t|t) % S.Vm: m-by-m-by-nobs array, prior/predicted covariance of factor % state vector (S.Vm(:,:,t) = V_t|t-1) % S.VmU: m-by-m-by-(nobs+1) array, posterior/updated covariance of % factor state vector (S.VmU(:,:,t+1) = V_t|t) % S.loglik: scalar, value of likelihood function % S.k_t: k-by-m Kalman gain %% INITIALIZE OUTPUT VALUES --------------------------------------------- % Output structure & dimensions of state space matrix [~, m] = size(C); % Outputs time for data matrix. "number of observations" nobs = size(Y,2); % Instantiate output S.Zm = nan(m, nobs); % Z_t | t-1 (prior) S.Vm = nan(m, m, nobs); % V_t | t-1 (prior) S.ZmU = nan(m, nobs+1); % Z_t | t (posterior/updated) S.VmU = nan(m, m, nobs+1); % V_t | t (posterior/updated) S.loglik = 0; %% SET INITIAL VALUES ---------------------------------------------------- Zu = Z_0; % Z_0|0 (In below loop, Zu gives Z_t | t) Vu = V_0; % V_0|0 (In below loop, Vu guvse V_t | t) % Store initial values S.ZmU(:,1) = Zu; S.VmU(:,:,1) = Vu; %% KALMAN FILTER PROCEDURE ---------------------------------------------- for t = 1:nobs %%% CALCULATING PRIOR DISTIBUTION---------------------------------- % Use transition eqn to create prior estimate for factor % i.e. Z = Z_t|t-1 Z = A * Zu; % Prior covariance matrix of Z (i.e. V = V_t|t-1) % Var(Z) = Var(A*Z + u_t) = Var(A*Z) + Var(\epsilon) = % A*Vu*A' + Q V = A * Vu* A' + Q; V = 0.5 * (V+V'); % Trick to make symmetric %%% CALCULATING POSTERIOR DISTRIBUTION ---------------------------- % Removes missing series: These are removed from Y, C, and R [Y_t, C_t, R_t, ~] = MissData(Y(:,t), C, R); % Check if y_t contains no data. If so, replace Zu and Vu with prior. if isempty(Y_t) Zu = Z; Vu = V; else % Steps for variance and population regression coefficients: % Var(c_t*Z_t + e_t) = c_t Var(A) c_t' + Var(u) = c_t*V *c_t' + R VC = V * C_t'; iF = inv(C_t * VC + R_t); % Matrix of population regression coefficients (QuantEcon eqn #4) VCF = VC*iF; % Gives difference between actual and predicted observation % matrix values innov = Y_t - C_t*Z; % Update estimate of factor values (posterior) Zu = Z + VCF * innov; % Update covariance matrix (posterior) for time t Vu = V - VCF * VC'; Vu = 0.5 * (Vu+Vu'); % Approximation trick to make symmetric % Update log likelihood % t % llf = -0.5 * size(Y_t, 1) * log(2 * pi) - 0.5*(log(det(iF)) - innov'*iF*innov) % fprintf('----------') S.loglik = S.loglik + 0.5*(log(det(iF)) - innov'*iF*innov); end %%% STORE OUTPUT---------------------------------------------------- % Store covariance and observation values for t-1 (priors) S.Zm(:,t) = Z; S.Vm(:,:,t) = V; % Store covariance and state values for t (posteriors) % i.e. Zu = Z_t|t & Vu = V_t|t S.ZmU(:,t+1) = Zu; S.VmU(:,:,t+1) = Vu; end % Store Kalman gain k_t if isempty(Y_t) S.k_t = zeros(m,m); else S.k_t = VCF * C_t; end end %______________________________________________________________________ function S = FIS(A, S) %FIS() Applies fixed-interval smoother % % Syntax: % S = FIS(A, S) % % Description: % SKF() applies a fixed-interval smoother, and is used in conjunction % with SKF(). See page 154 of 'Forecasting, structural time series models % and the Kalman filter' for more details (Harvey, 1990). % % Input parameters: % A: m-by-m transition matrix % S: structure returned by SKF() % % Output parameters: % S: FIS() adds the following smoothed estimates to the S structure: % - S.ZmT: m-by-(nobs+1) matrix, smoothed states % (S.ZmT(:,t+1) = Z_t|T) % - S.VmT: m-by-m-by-(nobs+1) array, smoothed factor covariance % matrices (S.VmT(:,:,t+1) = V_t|T = Cov(Z_t|T)) % - S.VmT_1: m-by-m-by-nobs array, smoothed lag 1 factor covariance % matrices (S.VmT_1(:,:,t) = Cov(Z_t Z_t-1|T)) % % Model: % Y_t = C_t Z_t + e_t for e_t ~ N(0, R) % Z_t = A Z_{t-1} + mu_t for mu_t ~ N(0, Q) %% ORGANIZE INPUT --------------------------------------------------------- % Initialize output matrices [m, nobs] = size(S.Zm); S.ZmT = zeros(m,nobs+1); S.VmT = zeros(m,m,nobs+1); % Fill the final period of ZmT, VmT with SKF() posterior values S.ZmT(:,nobs+1) = squeeze(S.ZmU(:, nobs+1)); S.VmT(:,:,nobs+1) = squeeze(S.VmU(:,:, nobs+1)); % Initialize VmT_1 lag 1 covariance matrix for final period S.VmT_1(:,:,nobs) = (eye(m)-S.k_t) *A*squeeze(S.VmU(:,:,nobs)); % Used for recursion process. See companion file for details J_2 = squeeze(S.VmU(:,:,nobs)) * A' * pinv(squeeze(S.Vm(:,:,nobs))); %% RUN SMOOTHING ALGORITHM ---------------------------------------------- % Loop through time reverse-chronologically (starting at final period nobs) for t = nobs:-1:1 % Store posterior and prior factor covariance values VmU = squeeze(S.VmU(:,:,t)); Vm1 = squeeze(S.Vm(:,:,t)); % Store previous period smoothed factor covariance and lag-1 covariance V_T = squeeze(S.VmT(:,:,t+1)); V_T1 = squeeze(S.VmT_1(:,:,t)); J_1 = J_2; % Update smoothed factor estimate S.ZmT(:,t) = S.ZmU(:,t) + J_1 * (S.ZmT(:,t+1) - A * S.ZmU(:,t)) ; % Update smoothed factor covariance matrix S.VmT(:,:,t) = VmU + J_1 * (V_T - Vm1) * J_1'; if t>1 % Update weight J_2 = squeeze(S.VmU(:, :, t-1)) * A' * pinv(squeeze(S.Vm(:,:,t-1))); % Update lag 1 factor covariance matrix S.VmT_1(:,:,t-1) = VmU * J_2'+J_1 * (V_T1 - A * VmU) * J_2'; end end end function [y,C,R,L] = MissData(y,C,R) % Syntax: % Description: % Eliminates the rows in y & matrices C, R that correspond to missing % data (NaN) in y % % Input: % y: Vector of observations at time t % C: Observation matrix % R: Covariance for observation matrix residuals % % Output: % y: Vector of observations at time t (reduced) % C: Observation matrix (reduced) % R: Covariance for observation matrix residuals % L: Used to restore standard dimensions(n x #) where # is the nr of % available data in y % Returns 1 for nonmissing series ix = ~isnan(y); % Index for columns with nonmissing variables e = eye(size(y,1)); L = e(:,ix); % Removes missing series y = y(ix); % Removes missing series from observation matrix C = C(ix,:); % Removes missing series from transition matrix R = R(ix,ix); end load_data.m000066400000000000000000000110111400612667500353000ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/functionsfunction [X,Time,Z] = load_data(datafile,Spec,sample,loadExcel) %loadData Load vintage of data from file and format as structure % % Description: % % Load data from file % % Input Arguments: % % datafile - filename of Microsoft Excel workbook file % % Output Arguments: % % Data - structure with the following fields: % . X : T x N numeric array, transformed dataset % . Time : T x 1 numeric array, date number with observation dates % . Z : T x N numeric array, raw (untransformed) dataset fprintf('Loading data... \n'); if nargin < 4 loadExcel = 0; end ext = datafile(find(datafile=='.',1,'last'):end); % file extension idx = strfind(datafile,filesep); idx = idx(2); datafile_mat = fullfile(datafile(1:idx),'mat',[strtok(datafile(idx+1:end),'.') '.mat']); if exist(datafile_mat,'file')==2 && ~loadExcel % Load raw data from MATLAB formatted binary (.mat) file d = load(datafile_mat); Z = d.Z; Time = d.Time; Mnem = d.Mnem; elseif any(strcmpi(ext,{'.xlsx','.xls'})) % Read raw data from Excel file [Z,Time,Mnem] = readData(datafile); save(datafile_mat,'Z','Time','Mnem'); % Z : raw (untransformed) observed data % Time : observation periods for the time series data % Mnem : series ID for each variable else error('Only Microsoft Excel workbook files supported.'); end % Sort data based on model specification Z = sortData(Z,Mnem,Spec); clear Mnem; % since now Mnem == Spec.SeriesID % Transform data based on model specification [X,Time,Z] = transformData(Z,Time,Spec); % Drop data not in estimation sample if nargin == 3 [X,Time,Z] = dropData(X,Time,Z,sample); end end function [Z,Time,Mnem] = readData(datafile) %readData Read data from Microsoft Excel workbook file [DATA,TEXT] = xlsread(datafile,'data'); Mnem = TEXT(1,2:end); if ispc Time = datenum(TEXT(2:end,1),'mm/dd/yyyy'); Z = DATA; else Time = DATA(:,1) + datenum(1899,12,31) - 1; Z = DATA(:,2:end); end end function [Z,Mnem] = sortData(Z,Mnem,Spec) %sortData Sort series by order of model specification % Drop series not in Spec inSpec = ismember(Mnem,Spec.SeriesID); Mnem(~inSpec) = []; Z(:,~inSpec) = []; % Sort series by ordering of Spec N = length(Spec.SeriesID); permutation = NaN(1,N); for i = 1:N idxSeriesSpec = find(strcmp(Spec.SeriesID{i},Mnem)); permutation(i) = idxSeriesSpec; end Mnem = Mnem(permutation); Z = Z(:,permutation); end function [X,Time,Z] = transformData(Z,Time,Spec) %transformData Transforms each data series based on Spec.Transformation % % Input Arguments: % % Z : T x N numeric array, raw (untransformed) observed data % Spec : structure , model specification % % Output Arguments: % % X : T x N numeric array, transformed data (stationary to enter DFM) T = size(Z,1); N = size(Z,2); X = NaN(T,N); for i = 1:N formula = Spec.Transformation{i}; freq = Spec.Frequency{i}; switch freq % time step for different frequencies based on monthly time case 'm' % Monthly step = 1; case 'q' % Quarterly step = 3; end t1 = step; % assume monthly observations start at beginning of quarter n = step/12; % number of years, needed to compute annual % changes series = Spec.SeriesName{i}; switch formula case 'lin' % Levels (No Transformation) X(:,i) = Z(:,i); case 'chg' % Change (Difference) X(t1:step:T,i) = [NaN; Z(t1+step:step:T,i) - Z(t1:step:T-t1,i)]; case 'ch1' % Year over Year Change (Difference) X(12+t1:step:T,i) = Z(12+t1:step:T,i) - Z(t1:step:T-12,i); case 'pch' % Percent Change X(t1:step:T,i) = 100*[NaN; Z(t1+step:step:T,i) ./ Z(t1:step:T-t1,i) - 1]; case 'pc1' % Year over Year Percent Change X(12+t1:step:T,i) = 100*(Z(12+t1:step:T,i) ./ Z(t1:step:T-12,i) - 1); case 'pca' % Percent Change (Annual Rate) X(t1:step:T,i) = 100*[NaN; (Z(t1+step:step:T,i) ./ Z(t1:step:T-step,i)).^(1/n) - 1]; case 'log' % Natural Log X(:,i) = log(Z(:,i)); otherwise warning(['Transformation ''' formula ''' not found for ' series '. ' 'Using untransformed data.']); X(:,i) = Z(:,i); end end % Drop first quarter of observations % since transformations cause missing values Time = Time(4:end); Z = Z(4:end,:); X = X(4:end,:); end function [X,Time,Z] = dropData(X,Time,Z,sample) %dropData Remove data not in estimation sample idxDrop = Time < sample; Time(idxDrop) = []; X(idxDrop,:) = []; Z(idxDrop,:) = []; end load_spec.m000066400000000000000000000057001400612667500353310ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/functionsfunction Spec = load_spec(specfile) %loadSpec Load model specification for a dynamic factor model (DFM) % % Description: % % Load model specification 'Spec' from a Microsoft Excel workbook file % given by 'filename'. % % Input Arguments: % % filename - % % Output Arguments: % % spec - 1 x 1 structure with the following fields: % . series_id % . name % . frequency % . units % . transformation % . category % . blocks % . BlockNames % Spec = struct; [~,~,raw] = xlsread(specfile,'','','basic'); header = strrep(raw(1,:),' ',''); raw = raw(2:end,:); % Find and drop series from Spec that are not in Model Model = cell2mat(raw(:,strcmpi('Model',header))); raw(Model==0,:) = []; % Parse fields given by column names in Excel worksheet fldnms = {'SeriesID','SeriesName','Frequency','Units','Transformation','Category'}; for iField = 1:numel(fldnms) fld = fldnms{iField}; jCol = find(strcmpi(fld,header),1); if isempty(jCol) error([fld ' column missing from model specification.']); % I guess Title and Units are not necessary though else Spec.(fld) = raw(:,jCol); end end % Parse blocks. jColBlock = strncmpi('Block',header,length('Block')); Blocks = cell2mat(raw(:,jColBlock)); Blocks(isnan(Blocks)) = 0; if ~all(Blocks(:,1)==1) error('All variables must load on global block.'); else Spec.Blocks = Blocks; end % Sort all fields of 'Spec' in order of decreasing frequency frequency = {'d','w','m','q','sa','a'}; permutation = []; for iFreq = 1:numel(frequency) permutation = [permutation; find(strcmp(frequency{iFreq},Spec.Frequency))]; %#ok end fldnms = fieldnames(Spec); for iField = 1:numel(fldnms) fld = fldnms{iField}; Spec.(fld) = Spec.(fld)(permutation,:); end Spec.BlockNames = regexprep(header(jColBlock),'Block\d-',''); Spec.UnitsTransformed = Spec.Transformation; Spec.UnitsTransformed = strrep(Spec.UnitsTransformed,'lin','Levels (No Transformation)'); Spec.UnitsTransformed = strrep(Spec.UnitsTransformed,'chg','Change (Difference)'); Spec.UnitsTransformed = strrep(Spec.UnitsTransformed,'ch1','Year over Year Change (Difference)'); Spec.UnitsTransformed = strrep(Spec.UnitsTransformed,'pch','Percent Change'); Spec.UnitsTransformed = strrep(Spec.UnitsTransformed,'pc1','Year over Year Percent Change'); Spec.UnitsTransformed = strrep(Spec.UnitsTransformed,'pca','Percent Change (Annual Rate)'); Spec.UnitsTransformed = strrep(Spec.UnitsTransformed,'cch','Continuously Compounded Rate of Change'); Spec.UnitsTransformed = strrep(Spec.UnitsTransformed,'cca','Continuously Compounded Annual Rate of Change'); Spec.UnitsTransformed = strrep(Spec.UnitsTransformed,'log','Natural Log'); % Summarize model specification fprintf('Table 1: Model specification \n'); try tabular = table(Spec.SeriesID,Spec.SeriesName,Spec.Units,Spec.UnitsTransformed,... 'VariableNames',{'SeriesID','SeriesName','Units','Transformation'}); disp(tabular); catch end end remNaNs_spline.m000066400000000000000000000125431400612667500363200ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/functions%%% Replication files for: %%% ""Nowcasting", 2010, (by Marta Banbura, Domenico Giannone and Lucrezia Reichlin), %%% in Michael P. Clements and David F. Hendry, editors, Oxford Handbook on Economic Forecasting. %%% %%% The software can be freely used in applications. %%% Users are kindly requested to add acknowledgements to published work and %%% to cite the above reference in any resulting publications % %Description: % %remNaNs Treats NaNs in dataset for use in DFM. % % Syntax: % [X,indNaN] = remNaNs(X,options) % % Description: % remNaNs() processes NaNs in a data matrix X according to 5 cases (see % below for details). These are useful for running functions in the % 'DFM.m' file that do not take missing value inputs. % % Input parameters: % X (T x n): Input data where T gives time and n gives the series. % options: A structure with two elements: % options.method (numeric): % - 1: Replaces all missing values using filter(). % - 2: Replaces missing values after removing trailing and leading % zeros (a row is 'missing' if >80% is NaN) % - 3: Only removes rows with leading and closing zeros % - 4: Replaces missing values after removing trailing and leading % zeros (a row is 'missing' if all are NaN) % - 5: Replaces missing values with spline() then runs filter(). % % options.k (numeric): remNaNs() relies on MATLAB's filter function % for the 1-D filter. k controls the rational transfer function % argument's numerator (the denominator is set to 1). More % specifically, the numerator takes the form 'ones(2*k+1,1)/(2*k+1)' % For additional help, see MATLAB's documentation for filter(). % % Output parameters: % X: Outputted data. % indNaN: A matrix indicating the location for missing values (1 for NaN). function [X,indNaN] = remNaNs_spline(X,options) [T,N]=size(X); % Gives dimensions for data input k=options.k; % Inputted options indNaN=isnan(X); % Returns location of NaNs switch options.method case 1 % replace all the missing values for i = 1:N % loop through columns x = X(:,i); x(indNaN(:,i))= nan_median(x); % Replace missing values series median x_MA =filter (ones(2*k+1,1)/(2*k+1), 1, [x(1)*ones(k,1);x;x(end)*ones(k,1)]); x_MA=x_MA(2*k+1:end); % Match dimensions % Replace missing observations with filtered values x(indNaN(:,i))=x_MA(indNaN(:,i)); X(:,i)=x; % Replace vector end case 2 %replace missing values after removing leading and closing zeros % Returns row sum for NaN values. Marks true for rows with more % than 80% NaN rem1=(sum(indNaN,2)>N*0.8); nanLead =(cumsum(rem1)==(1:T)'); nanEnd =(cumsum(rem1(end:-1:1))==(1:T)'); nanEnd = nanEnd(end:-1:1); % Reverses nanEnd nanLE = (nanLead | nanEnd); % Subsets X for for X(nanLE,:) = []; indNaN = isnan(X); % Index for missing values % Loop for each series for i = 1:N x = X(:,i); isnanx = isnan(x); t1 = min(find(~isnanx)); % First non-NaN entry t2 = max(find(~isnanx)); % Last non-NaN entry % Interpolates without NaN entries in beginning and end x(t1:t2) = spline(find(~isnanx),x(~isnanx),(t1:t2)'); isnanx = isnan(x); % replace NaN observations with median x(isnanx) = median(x,'omitnan'); % Apply filter x_MA = filter (ones(2*k+1,1)/(2*k+1),1,[x(1)*ones(k,1);x;x(end)*ones(k,1)]); x_MA = x_MA(2*k+1:end); % Replace nanx with filtered observations x(isnanx) = x_MA(isnanx); X(:,i) = x; end case 3 %only remove rows with leading and closing zeros rem1=(sum(indNaN,2)==N); nanLead=(cumsum(rem1)==(1:T)'); nanEnd=(cumsum(rem1(end:-1:1))==(1:T)'); nanEnd=nanEnd(end:-1:1); nanLE=(nanLead | nanEnd); X(nanLE,:)=[]; indNaN = isnan(X); case 4 %remove rows with leading and closing zeros & replace missing values rem1=(sum(indNaN,2)==N); nanLead=(cumsum(rem1)==(1:T)'); nanEnd=(cumsum(rem1(end:-1:1))==(1:T)'); nanEnd=nanEnd(end:-1:1); nanLE=(nanLead | nanEnd); X(nanLE,:)=[]; indNaN=isnan(X); for i = 1:N x = X(:,i); isnanx = isnan(x); t1 = min(find(~isnanx)); t2 = max(find(~isnanx)); x(t1:t2) = spline(find(~isnanx),x(~isnanx),(t1:t2)'); isnanx = isnan(x); x(isnanx)=nan_median(x); x_MA =filter (ones(2*k+1,1)/(2*k+1),1,[x(1)*ones(k,1);x;x(end)*ones(k,1)]); x_MA=x_MA(2*k+1:end); x(isnanx)=x_MA(isnanx); X(:,i)=x; end case 5 %replace missing values indNaN=isnan(X); for i = 1:N x = X(:,i); isnanx = isnan(x); t1 = min(find(~isnanx)); t2 = max(find(~isnanx)); x(t1:t2) = spline(find(~isnanx),x(~isnanx),(t1:t2)'); isnanx = isnan(x); x(isnanx)=nan_median(x); x_MA =filter (ones(2*k+1,1)/(2*k+1),1,[x(1)*ones(k,1);x;x(end)*ones(k,1)]); x_MA=x_MA(2*k+1:end); x(isnanx)=x_MA(isnanx); X(:,i)=x; end end summarize.m000066400000000000000000000061141400612667500354140ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/functionsfunction summarize(X,Time,Spec,vintage) %summarize Display the detail table for data entering the DFM % % Description: % Display the detail table for the nowcast, decomposing nowcast changes % into news and impacts for released data series. % Print results to command window fprintf('\n\n\n'); fprintf('Table 2: Data Summary \n'); [T,N] = size(X); %fprintf('Vintage: %s \n',datestr(datenum(vintage,'yyyy-mm-dd'),'mmmm dd, yyyy')); fprintf('N = %4d data series \n',N); fprintf('T = %4d observations from %10s to %10s \n',T,datestr(Time(1),'yyyy-mm-dd'),datestr(Time(end),'yyyy-mm-dd')); fprintf('%30s | %17s %12s %10s %8s %8s %8s %8s \n',... 'Data Series','Observations','Units','Frequency','Mean','Std. Dev.','Min','Max'); fprintf([repmat('-',1,130) '\n']); for i = 1:N % time indexes for which there are observed values for series i t_obs = ~isnan(X(:,i)); data_series = Spec.SeriesName{i}; if length(data_series) > 30 data_series = [data_series(1:27) '...']; end series_id = Spec.SeriesID{i}; if length(series_id) > 28 series_id = [series_id(1:25) '...']; end series_id = ['[' series_id ']']; num_obs = length(X(t_obs,i)); freq = Spec.Frequency{i}; if strcmp('m',freq) format_date = 'mmm yyyy'; frequency = 'Monthly'; elseif strcmp('q',freq) format_date = 'QQ yyyy'; frequency = 'Quarterly'; end units = Spec.Units{i}; transform = Spec.Transformation{i}; % display transformed units if strfind(units,'Index') units_transformed = 'Index'; elseif strcmp('chg',transform) if strfind(units,'%') units_transformed = 'Ppt. change'; else units_transformed = 'Level change'; end elseif strcmp('pch',transform) && strcmp('m',freq) units_transformed = 'MoM%'; elseif strcmp('pca',transform) && strcmp('q',freq) units_transformed = 'QoQ% AR'; else if length([units ' (' transform ')']) > 12 units_transformed = [units(1:6) ' (' transform ')']; else units_transformed = [units ' (' transform ')']; end end t_obs_start = find(t_obs,1,'first'); t_obs_end = find(t_obs,1,'last'); obs_date_start = datestr(Time(t_obs_start),format_date); obs_date_end = datestr(Time(t_obs_end ),format_date); date_range = [obs_date_start '-' obs_date_end]; y = X(t_obs,i); d = Time(t_obs); mean_series = mean(y,'omitnan'); stdv_series = std(y,'omitnan'); [min_series,t_min] = min(y); [max_series,t_max] = max(y); min_date = datestr(d(t_min),format_date); max_date = datestr(d(t_max),format_date); fprintf('%30s | %17d %12s %10s %8.1f %8.1f %8.1f %8.1f \n',... data_series,num_obs,units_transformed,frequency,mean_series,stdv_series,min_series,max_series); fprintf('%30s | %17s %12s %10s %8s %8s %8s %8s \n',... series_id,date_range,'','','','',min_date,max_date); end fprintf('\n\n\n'); end update_nowcast.m000066400000000000000000000522341400612667500364240ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/functionsfunction [Res] = update_nowcast(X_old,X_new,Time,Spec,Res,series,period,vintage_old,vintage_new) if ~isnumeric(vintage_old) vintage_old = datenum(vintage_old,'yyyy-mm-dd'); end if ~isnumeric(vintage_new) vintage_new = datenum(vintage_new,'yyyy-mm-dd'); end % Make sure datasets are the same size N = size(X_new,2); T_old = size(X_old,1); T_new = size(X_new,1); if T_new > T_old X_old = [X_old; NaN(T_new-T_old,N)]; end % append 1 year (12 months) of data to each dataset to allow for % forecasting at different horizons X_old = [X_old; NaN(12,N)]; X_new = [X_new; NaN(12,N)]; [y, m, d] = datevec(Time(end)); Time = [Time; datenum(y,(m+1:m+12)',d)]; i_series = find(strcmp(series,Spec.SeriesID)); series_name = Spec.SeriesName{i_series}; freq = Spec.Frequency{i_series}; switch freq case 'm' [y,m] = strtok(period,freq); y = str2double(y); m = str2double(strrep(m,freq,'')); d = 1; t_nowcast = find(Time==datenum(y,m,d)); case 'q' [y,q] = strtok(period,freq); y = str2double(y); q = str2double(strrep(q,freq,'')); m = 3*q; d = 1; t_nowcast = find(Time==datenum(y,m,d)); end if isempty(t_nowcast) error('Period is out of nowcasting horizon (up to one year ahead).'); end % Update nowcast for target variable 'series' (i) at horizon 'period' (t) % > Relate nowcast update into news from data releases: % a. Compute the impact from data revisions % b. Compute the impact from new data releases X_rev = X_new; X_rev(isnan(X_old)) = NaN; % Compute news -------------------------------------------------------- % Compute impact from data revisions [y_old] = News_DFM(X_old,X_rev,Res,t_nowcast,i_series); % Compute impact from data releases [y_rev,y_new,~,actual,forecast,weight] = News_DFM(X_rev,X_new,Res,t_nowcast,i_series); % Display output fprintf('\n\n\n'); fprintf('Nowcast Update: %s \n', datestr(vintage_new, 'mmmm dd, yyyy')) fprintf('Nowcast for %s (%s), %s \n',Spec.SeriesName{i_series},Spec.UnitsTransformed{i_series},datestr(Time(t_nowcast),'YYYY:QQ')); if(isempty(forecast)) % Only display table output if a forecast is made fprintf('\n No forecast was made.\n') else impact_revisions = y_rev - y_old; % Impact from revisions news = actual - forecast; % News from releases impact_releases = weight .* (news); % Impact of releases % Store results news_table = array2table([forecast, actual, weight, impact_releases],... 'VariableNames', {'Forecast', 'Actual', 'Weight', 'Impact'},... 'RowNames', Spec.SeriesID); % Select only series with updates data_released = any(isnan(X_old) & ~isnan(X_new), 1); % Display the impact decomposition fprintf('\n Nowcast Impact Decomposition \n') fprintf(' Note: The displayed output is subject to rounding error\n\n') fprintf(' %s nowcast: %5.2f\n', ... datestr(vintage_old, 'mmm dd'), y_old) fprintf(' Impact from data revisions: %5.2f\n', impact_revisions) fprintf(' Impact from data releases: %5.2f\n', sum(news_table.Impact,'omitnan')) fprintf(' +_________\n') fprintf(' Total impact: %5.2f\n', ... impact_revisions + sum(news_table.Impact,'omitnan')) fprintf(' %s nowcast: %5.2f\n\n', ... datestr(vintage_new, 'mmm dd'), y_new) % Display the table output fprintf('\n Nowcast Detail Table \n\n') disp(news_table(data_released, :)) % Output results to structure Res.impact_revisions = impact_revisions; Res.weight = weight; Res.news_table = news_table; end end function [y_old,y_new,singlenews,actual,forecast,weight,t_miss,v_miss,innov] = News_DFM(X_old,X_new,Res,t_fcst,v_news) %News_DFM() Calculates changes in news % % Syntax: % [y_old, y_new, singlenews, actual, fore, weight ,t_miss, v_miss, innov] = ... % News_DFM(X_old, X_new, Q, t_fcst, v_news) % % Description: % News DFM() inputs two datasets, DFM parameters, target time index, and % target variable index. The function then produces Nowcast updates and % decomposes the changes into news. % % Input Arguments: % X_old: Old data matrix (old vintage) % X_new: New data matrix (new vintage) % Res: DFM() output results (see DFM for more details) % t_fcst: Index for target time % v_news: Index for target variable % % Output Arguments: % y_old: Old nowcast % y_new: New nowcast % single_news: News for each data series % actual: Observed series release values % fore: Forecasted series values % weight: News weight % t_miss: Time index for data releases % v_miss: Series index for data releases % innov: Difference between observed and predicted series values ("innovation") %% Initialize variables r = size(Res.C,2); [~, N] = size(X_new); singlenews = zeros(1,N); % Initialize news vector (will store news for each series) %% NO FORECAST CASE: Already values for variables v_news at time t_fcst if ~isnan(X_new(t_fcst,v_news)) Res_old = para_const(X_old, Res, 0); % Apply Kalman filter for old data for i=1:size(v_news,2) % Loop for each target variable % (Observed value) - (predicted value) singlenews(:,v_news(i)) = X_new(t_fcst,v_news(i)) ... - Res_old.X_sm(t_fcst,v_news(i)); % Set predicted and observed y values y_old(1,i) = Res_old.X_sm(t_fcst,v_news(i)); y_new(1,i) = X_new(t_fcst,v_news(i)); end % Forecast-related output set to empty actual=[];forecast=[];weight=[];t_miss=[];v_miss=[];innov=[]; else %% FORECAST CASE (these are broken down into (A) and (B)) % Initialize series mean/standard deviation respectively Mx = Res.Mx; Wx = Res.Wx; % Calculate indicators for missing values (1 if missing, 0 otherwise) miss_old=isnan(X_old); miss_new=isnan(X_new); % Indicator for missing--combine above information to single matrix where: % (i) -1: Value is in the old data, but missing in new data % (ii) 1: Value is in the new data, but missing in old data % (iii) 0: Values are missing from/available in both datasets i_miss = miss_old - miss_new; % Time/variable indicies where case (b) is true [t_miss,v_miss]=find(i_miss==1); %% FORECAST SUBCASE (A): NO NEW INFORMATION if isempty(v_miss) % Fill in missing variables using a Kalman filter Res_old = para_const(X_old, Res, 0); Res_new = para_const(X_new, Res, 0); % Set predicted and observed y values. New y value is set to old y_old = Res_old.X_sm(t_fcst,v_news); y_new = y_old; % y_new = Res_new.X_sm(t_fcst,v_news); % No news, so nothing returned for news-related output groupnews=[];singlenews=[];gain=[];gainSer=[]; actual=[];forecast=[];weight=[];t_miss=[];v_miss=[];innov=[]; else %---------------------------------------------------------------------- % v_miss=[1:size(X_new,2)]'; % t_miss=t_miss(1)*ones(size(X_new,2),1); %---------------------------------------------------------------------- %% FORECAST SUBCASE (B): NEW INFORMATION % Difference between forecast time and new data time lag = t_fcst-t_miss; % Gives biggest time interval between forecast and new data k = max([abs(lag); max(lag)-min(lag)]); C = Res.C; % Observation matrix R = Res.R'; % Covariance for observation matrix residuals % Number of new events n_news = size(lag,1); % Smooth old dataset Res_old = para_const(X_old, Res, k); Plag = Res_old.Plag; % Smooth new dataset Res_new = para_const(X_new, Res, 0); % Subset for target variable and forecast time y_old = Res_old.X_sm(t_fcst,v_news); y_new = Res_new.X_sm(t_fcst,v_news); P = Res_old.P(:,:,2:end); P1=[]; % Initialize projection onto updates % Cycle through total number of updates for i=1:n_news h = abs(t_fcst-t_miss(i)); m = max([t_miss(i) t_fcst]); % If location of update is later than the forecasting date if t_miss(i)>t_fcst Pp=Plag{h+1}(:,:,m); %P(1:r,h*r+1:h*r+r,m)'; else Pp=Plag{h+1}(:,:,m)'; %P(1:r,h*r+1:h*r+r,m); end P1=[P1 Pp*C(v_miss(i),1:r)']; % Projection on updates end for i=1:size(t_miss,1) % Standardize predicted and observed values X_new_norm = (X_new(t_miss(i),v_miss(i)) - Mx(v_miss(i)))./Wx(v_miss(i)); X_sm_norm = (Res_old.X_sm(t_miss(i),v_miss(i))- Mx(v_miss(i)))./Wx(v_miss(i)); % Innovation: Gives [observed] data - [predicted data] innov(i)= X_new_norm - X_sm_norm; end ins=size(innov,2); P2=[]; p2=[]; % Gives non-standardized series weights for i=1:size(lag,1) for j=1:size(lag,1) h=abs(lag(i)-lag(j)); m=max([t_miss(i),t_miss(j)]); if t_miss(j)>t_miss(i) Pp=Plag{h+1}(:,:,m); %P(1:r,h*r+1:(h+1)*r,m)'; else Pp=Plag{h+1}(:,:,m)'; %P(1:r,h*r+1:(h+1)*r,m); end if v_miss(i)==v_miss(j) & t_miss(i)~=t_miss(j) WW(v_miss(i),v_miss(j))=0; else WW(v_miss(i),v_miss(j))=R(v_miss(i),v_miss(j)); end p2=[p2 C(v_miss(i),1:r)*Pp*C(v_miss(j),1:r)'+WW(v_miss(i),v_miss(j))]; end P2=[P2;p2]; p2=[]; end clear temp for i=1:size(v_news,2) % loop on v_news % Convert to real units (unstadardized data) totnews(1,i) = Wx(v_news(i))*C(v_news(i),1:r)*P1*inv(P2)*innov'; temp(1,:,i) = Wx(v_news(i))*C(v_news(i),1:r)*P1*inv(P2).*innov; gain(:,:,i) = Wx(v_news(i))*C(v_news(i),1:r)*P1*inv(P2); end % Initialize output objects singlenews = NaN(max(t_miss)-min(t_miss)+1,N); %,size(v_news,2) actual = NaN(N,1); % Actual forecasted values forecast = NaN(N,1); % Forecasted values weight = NaN(N,1,size(v_news,2)); % Fill in output values for i=1:size(innov,2) actual(v_miss(i),1) = X_new(t_miss(i),v_miss(i)); forecast(v_miss(i),1) = Res_old.X_sm(t_miss(i),v_miss(i)); for j=1:size(v_news,2) singlenews(t_miss(i)-min(t_miss)+1,v_miss(i),j) = temp(1,i,j); weight(v_miss(i),:,j) = gain(:,i,j)/Wx(v_miss(i)); end end singlenews = sum(singlenews,1); % Returns total news [v_miss, ~, ~] = unique(v_miss); end end end function Res = para_const(X, P, lag) %para_const() Implements Kalman filter for "News_DFM.m" % % Syntax: % Res = para_const(X,P,lag) % % Description: % para_const() implements the Kalman filter for the news calculation % step. This procedure smooths and fills in missing data for a given % data matrix X. In contrast to runKF(), this function is used when % model parameters are already estimated. % % Input parameters: % X: Data matrix. % P: Parameters from the dynamic factor model. % lag: Number of lags % % Output parameters: % Res [struc]: A structure containing the following: % Res.Plag: Smoothed factor covariance for transition matrix % Res.P: Smoothed factor covariance matrix % Res.X_sm: Smoothed data matrix % Res.F: Smoothed factors % % Kalman filter with specified paramaters % written for % "MAXIMUM LIKELIHOOD ESTIMATION OF FACTOR MODELS ON DATA SETS WITH % ARBITRARY PATTERN OF MISSING DATA." % by Marta Banbura and Michele Modugno %% Set model parameters and data preparation % Set model parameters Z_0 = P.Z_0; V_0 = P.V_0; A = P.A; C = P.C; Q = P.Q; R = P.R; Mx = P.Mx; Wx = P.Wx; % Prepare data [T,~] = size(X); % Standardise x Y = ((X-repmat(Mx,T,1))./repmat(Wx,T,1))'; %% Apply Kalman filter and smoother % See runKF() for details about FIS and SKF Sf = SKF(Y, A, C, Q, R, Z_0, V_0); % Kalman filter Ss = FIS(A, Sf); % Smoothing step %% Calculate parameter output Vs = Ss.VmT(:,:,2:end); % Smoothed factor covariance for transition matrix Vf = Sf.VmU(:,:,2:end); % Filtered factor posterior covariance Zsmooth = Ss.ZmT; % Smoothed factors Vsmooth = Ss.VmT; % Smoothed covariance values Plag{1} = Vs; for jk = 1:lag for jt = size(Plag{1},3):-1:lag+1 As = Vf(:,:,jt-jk)*A'*pinv(A*Vf(:,:,jt-jk)*A'+Q); Plag{jk+1}(:,:,jt) = As*Plag{jk}(:,:,jt); end end % Prepare data for output Zsmooth=Zsmooth'; x_sm = Zsmooth(2:end,:)*C'; % Factors to series representation X_sm = repmat(Wx,T,1).*x_sm+repmat(Mx,T,1); % Standardized to unstandardized %-------------------------------------------------------------------------- % Loading the structure with the results %-------------------------------------------------------------------------- Res.Plag = Plag; Res.P = Vsmooth; Res.X_sm = X_sm; Res.F = Zsmooth(2:end,:); end %______________________________________________________________________ function S = SKF(Y, A, C, Q, R, Z_0, V_0) %SKF Applies Kalman filter % % Syntax: % S = SKF(Y, A, C, Q, R, Z_0, V_0) % % Description: % SKF() applies a Kalman filter. This is a bayesian algorithm. Looping % forward in time, a 'prior' estimate is calculated from the previous % period. Then, using the observed data, a 'posterior' value is obtained. % % Input parameters: % y: Input data. % A: Transition matrix coefficients. % C: Observation matrix coefficients. % Q: Covariance matrix (factors and idiosyncratic component) % R: Variance-Covariance for observation equation residuals % Z_0: Initial factor values % V_0: Initial factor covariance matrix % % Output parameters: % S.Zm: Prior/predicted factor state vector (Z_t|t-1) % S.ZmU: Posterior/updated state vector (Z_t|t) % S.Vm: Prior/predicted covariance of factor state vector (V_t|t-1) % S.VmU: Posterior/updated covariance of factor state vector (V_t|t) % S.loglik: Value of likelihood function % S.k_t: Kalman gain % % Model: % Y_t = C_t Z_t + e_t, e_t ~ N(0, R) % Z_t = A Z_{t-1} + mu_t, mu_t ~ N(0, Q) %% INSTANTIATE OUTPUT VALUES --------------------------------------------- % Output structure & dimensions of state space matrix [~, m] = size(C); % Outputs time for data matrix. "number of observations" nobs = size(Y,2); % Initialize output S.Zm = NaN(m, nobs); % Z_t | t-1 (prior) S.Vm = NaN(m, m, nobs); % V_t | t-1 (prior) S.ZmU = NaN(m, nobs+1); % Z_t | t (posterior/updated) S.VmU = NaN(m, m, nobs+1); % V_t | t (posterior/updated) S.loglik = 0; %% SET INITIAL VALUES ---------------------------------------------------- Zu = Z_0; % Z_0|0 (In below loop, Zu gives Z_t | t) Vu = V_0; % V_0|0 (In below loop, Vu guvse V_t | t) % Store initial values S.ZmU(:,1) = Zu; S.VmU(:,:,1) = Vu; %% KALMAN FILTER PROCEDURE ---------------------------------------------- for t = 1:nobs %%% CALCULATING PRIOR DISTIBUTION---------------------------------- % Use transition eqn to create prior estimate for factor % i.e. Z = Z_t|t-1 Z = A * Zu; % Prior covariance matrix of Z (i.e. V = V_t|t-1) % Var(Z) = Var(A*Z + u_t) = Var(A*Z) + Var(\epsilon) = % A*Vu*A' + Q V = A * Vu* A' + Q; V = 0.5 * (V+V'); % Trick to make symmetric %%% CALCULATING POSTERIOR DISTRIBUTION ---------------------------- % Removes missing series: These are removed from Y, C, and R [Y_t, C_t, R_t, ~] = MissData(Y(:,t), C, R); % Check if y_t contains no data. If so, replace Zu and Vu with prior. if isempty(Y_t) Zu = Z; Vu = V; else % Steps for variance and population regression coefficients: % Var(c_t*Z_t + e_t) = c_t Var(A) c_t' + Var(u) = c_t*V *c_t' + R VC = V * C_t'; iF = inv(C_t * VC + R_t); % Matrix of population regression coefficients (QuantEcon eqn #4) VCF = VC*iF; % Gives difference between actual and predicted observation % matrix values innov = Y_t - C_t*Z; % Update estimate of factor values (posterior) Zu = Z + VCF * innov; % Update covariance matrix (posterior) for time t Vu = V - VCF * VC'; Vu = 0.5 * (Vu+Vu'); % Approximation trick to make symmetric % Update log likelihood S.loglik = S.loglik + 0.5*(log(det(iF)) - innov'*iF*innov); end %%% STORE OUTPUT---------------------------------------------------- % Store covariance and observation values for t-1 (priors) S.Zm(:,t) = Z; S.Vm(:,:,t) = V; % Store covariance and state values for t (posteriors) % i.e. Zu = Z_t|t & Vu = V_t|t S.ZmU(:,t+1) = Zu; S.VmU(:,:,t+1) = Vu; end % Store Kalman gain k_t if isempty(Y_t) S.k_t = zeros(m,m); else S.k_t = VCF * C_t; end end %______________________________________________________________________ function S = FIS(A, S) %FIS() Applies fixed-interval smoother % % Syntax: % S = FIS(A, S) % % Description: % SKF() applies a fixed-interval smoother, and is used in conjunction % with SKF(). Starting from the final value, this uses a set of % recursions and works backwards. Smoothers are advantageous in that % future values are used for estimation. See page 154 of 'Forecasting, % structural time series models and the Kalman filter' for more details % (Harvey, 1990). % % Input parameters: % A: Transition matrix coefficients. % S: Output from SKF() step. See SKF() for details. % % Output parameters: % S: In addition to the output from SKF(), FIS() adds the following % smoothed estimates. Note that t = 1...T gives time: % - S.ZmT: Smoothed estimate of factor values (Z_t|T) % - S.VmT: Smoothed estimate of factor covariance matrix (V_t|T = Cov(Z_t|T)) % - S.VmT_1: Smoothed estimate of Lag 1 factor covariance matrix (Cov(Z_tZ_t-1|T)) % % Model: % Y_t = C_t Z_t + e_t for e_t ~ N(0, R) % Z_t = A Z_{t-1} + mu_t for mu_t ~ N(0, Q) %% ORGANIZE INPUT --------------------------------------------------------- % Initialize output matrices [m, nobs] = size(S.Zm); S.ZmT = zeros(m,nobs+1); S.VmT = zeros(m,m,nobs+1); % Fill the final period of ZmT, VmT with SKF() posterior values S.ZmT(:,nobs+1) = squeeze(S.ZmU(:, nobs+1)); S.VmT(:,:,nobs+1) = squeeze(S.VmU(:,:, nobs+1)); % Initialize VmT_1 lag 1 covariance matrix for final period S.VmT_1(:,:,nobs) = (eye(m)-S.k_t) *A*squeeze(S.VmU(:,:,nobs)); % Used for recursion process. See companion file for details J_2 = squeeze(S.VmU(:,:,nobs)) * A' * pinv(squeeze(S.Vm(:,:,nobs))); %% RUN SMOOTHING ALGORITHM ---------------------------------------------- % Loop through time reverse-chronologically (starting at final period nobs) for t = nobs:-1:1 % Store posterior and prior factor covariance values VmU = squeeze(S.VmU(:,:,t)); Vm1 = squeeze(S.Vm(:,:,t)); % Store previous period smoothed factor covariance and lag-1 covariance V_T = squeeze(S.VmT(:,:,t+1)); V_T1 = squeeze(S.VmT_1(:,:,t)); J_1 = J_2; % Update smoothed factor estimate S.ZmT(:,t) = S.ZmU(:,t) + J_1 * (S.ZmT(:,t+1) - A * S.ZmU(:,t)) ; % Update smoothed factor covariance matrix S.VmT(:,:,t) = VmU + J_1 * (V_T - Vm1) * J_1'; if t>1 % Update weight J_2 = squeeze(S.VmU(:, :, t-1)) * A' * pinv(squeeze(S.Vm(:,:,t-1))); % Update lag 1 factor covariance matrix S.VmT_1(:,:,t-1) = VmU * J_2'+J_1 * (V_T1 - A * VmU) * J_2'; end end end function [y,C,R,L] = MissData(y,C,R) %______________________________________________________________________ % PROC missdata % PURPOSE: eliminates the rows in y & matrices Z, G that correspond to % missing data (NaN) in y % INPUT y vector of observations at time t % S KF system matrices (structure) % must contain Z & G % OUTPUT y vector of observations (reduced) % Z G KF system matrices (reduced) % L To restore standard dimensions % where # is the nr of available data in y %______________________________________________________________________ % Returns 1 for nonmissing series ix = ~isnan(y); % Index for columns with nonmissing variables e = eye(size(y,1)); L = e(:,ix); % Removes missing series y = y(ix); % Removes missing series from observation matrix C = C(ix,:); % Removes missing series from transition matrix R = R(ix,ix); end statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/test_DFM.m000066400000000000000000000101121400612667500331050ustar00rootroot00000000000000%%% Test for Dynamic factor model (DFM) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This script produces results for a variety of dynamic factor models (DFM) % using a panel of monthly and quarterly series that can be used for tests. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Clear workspace and set paths. close all; clear; clc; addpath('functions'); %% User inputs. vintage = '2016-06-29'; % vintage dataset to use for estimation country = 'US'; % United States macroeconomic data sample_start = datenum('2000-01-01','yyyy-mm-dd'); % estimation sample %% Load model specification and dataset. % Load model specification structure `Spec` Spec = load_spec('test_spec.xls'); % Load data datafile = fullfile('data',country,[vintage '.xls']); [X,Time,Z] = load_data(datafile,Spec,sample_start); % Basic settings threshold = 1e-4; % Set to 1e-5 for more robust estimates format long %% Test 1: p=1, k=1, max_iter=1 Spec.p = 1; Spec.k = 1; max_iter = 1; Res = dfm(X,Spec,threshold,max_iter); Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); kp = Spec.k * Spec.p; Lambda = Res.C(1:end, 1:Spec.k)'; f_A = Res.A(1:Spec.k, 1:kp)'; f_Q = Res.Q(1:Spec.k, 1:Spec.k); Ad = diag(Res.A); Qd = diag(Res.Q); idio = Spec.k * max(5, Spec.p) + 1; params = [Lambda(:)' f_A(:)' nonzeros(chol(f_Q)')' ... Ad(idio:idio+3)' Ad(idio+3+5) Qd(idio:idio+3)' Qd(idio+3+5)]'; save('test_dfm_111.mat','Res','Spec','params'); %% Test 2: p=1, k=1, max_iter=2 Spec.p = 1; Spec.k = 1; max_iter = 2; Res = dfm(X,Spec,threshold,max_iter); Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); kp = Spec.k * Spec.p; Lambda = Res.C(1:end, 1:Spec.k)'; f_A = Res.A(1:Spec.k, 1:kp)'; f_Q = Res.Q(1:Spec.k, 1:Spec.k); Ad = diag(Res.A); Qd = diag(Res.Q); idio = Spec.k * max(5, Spec.p) + 1; params = [Lambda(:)' f_A(:)' nonzeros(chol(f_Q)')' ... Ad(idio:idio+3)' Ad(idio+3+5) Qd(idio:idio+3)' Qd(idio+3+5)]'; save('test_dfm_112.mat','Res','Spec','params'); %% Test 3: p=1, k=1, max_iter=5000 Spec.p = 1; Spec.k = 1; max_iter = 5000; Res = dfm(X,Spec,threshold,max_iter); Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); kp = Spec.k * Spec.p; Lambda = Res.C(1:end, 1:Spec.k)'; f_A = Res.A(1:Spec.k, 1:kp)'; f_Q = Res.Q(1:Spec.k, 1:Spec.k); Ad = diag(Res.A); Qd = diag(Res.Q); idio = Spec.k * max(5, Spec.p) + 1; params = [Lambda(:)' f_A(:)' nonzeros(chol(f_Q)')' ... Ad(idio:idio+3)' Ad(idio+3+5) Qd(idio:idio+3)' Qd(idio+3+5)]'; save('test_dfm_11F.mat','Res','Spec','params'); %% Test 4: p=2, k=2, max_iter=1 Spec.p = 2; Spec.k = 2; max_iter = 1; Res = dfm(X,Spec,threshold,max_iter); Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); kp = Spec.k * Spec.p; Lambda = Res.C(1:end, 1:Spec.k)'; f_A = Res.A(1:Spec.k, 1:kp)'; f_Q = Res.Q(1:Spec.k, 1:Spec.k); Ad = diag(Res.A); Qd = diag(Res.Q); idio = Spec.k * max(5, Spec.p) + 1; params = [Lambda(:)' f_A(:)' nonzeros(chol(f_Q)')' ... Ad(idio:idio+3)' Ad(idio+3+5) Qd(idio:idio+3)' Qd(idio+3+5)]'; save('test_dfm_221.mat','Res','Spec','params'); %% Test 5: p=2, k=2, max_iter=2 Spec.p = 2; Spec.k = 2; max_iter = 2; Res = dfm(X,Spec,threshold,max_iter); Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); kp = Spec.k * Spec.p; Lambda = Res.C(1:end, 1:Spec.k)'; f_A = Res.A(1:Spec.k, 1:kp)'; f_Q = Res.Q(1:Spec.k, 1:Spec.k); Ad = diag(Res.A); Qd = diag(Res.Q); idio = Spec.k * max(5, Spec.p) + 1; params = [Lambda(:)' f_A(:)' nonzeros(chol(f_Q)')' ... Ad(idio:idio+3)' Ad(idio+3+5) Qd(idio:idio+3)' Qd(idio+3+5)]'; save('test_dfm_222.mat','Res','Spec','params'); %% Test 6: p=2, k=2, max_iter=5000 Spec.p = 2; Spec.k = 2; max_iter = 5000; Res = dfm(X,Spec,threshold,max_iter); Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); kp = Spec.k * Spec.p; Lambda = Res.C(1:end, 1:Spec.k)'; f_A = Res.A(1:Spec.k, 1:kp)'; f_Q = Res.Q(1:Spec.k, 1:Spec.k); Ad = diag(Res.A); Qd = diag(Res.Q); idio = Spec.k * max(5, Spec.p) + 1; params = [Lambda(:)' f_A(:)' nonzeros(chol(f_Q)')' ... Ad(idio:idio+3)' Ad(idio+3+5) Qd(idio:idio+3)' Qd(idio+3+5)]'; save('test_dfm_22F.mat','Res','Spec','params'); test_DFM_blocks.m000066400000000000000000000125501400612667500343730ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting%%% Test for Dynamic factor model (DFM) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This script produces results for a variety of dynamic factor models (DFM) % using a panel of monthly and quarterly series that can be used for tests. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Clear workspace and set paths. close all; clear; clc; addpath('functions'); %% User inputs. vintage = '2016-06-29'; % vintage dataset to use for estimation country = 'US'; % United States macroeconomic data sample_start = datenum('2000-01-01','yyyy-mm-dd'); % estimation sample %% Load model specification and dataset. % Load model specification structure `Spec` Spec = load_spec('test_spec_blocks.xls'); % Load data datafile = fullfile('data',country,[vintage '.xls']); [X,Time,Z] = load_data(datafile,Spec,sample_start); % Basic settings threshold = 1e-4; % Set to 1e-5 for more robust estimates format long %% Test 1: p=1, k=1, max_iter=1 Spec.p = 1; Spec.k = 1; max_iter = 1; Res = dfm(X,Spec,threshold,max_iter); Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); k = Spec.k; p = Spec.p; kp = k * p; p5 = max(5, Spec.p); kp5 = k * p5; Lambda = [Res.C(1:end, 1:k) ... Res.C(1:end, kp5 + 1:kp5 + k) ... Res.C(1:end, 2 * kp5 + 1:2 * kp5 + k)]'; mask = logical(Spec.Blocks'); Lambda = Lambda(mask)'; f_A1 = Res.A(1:k, 1:kp)'; f_A2 = Res.A(kp5 + 1:kp5 + k, kp5 + 1:kp5 + kp)'; f_A3 = Res.A(2 * kp5 + 1:2 * kp5 + k, 2 * kp5 + 1:2 * kp5 + kp)'; f_A = [f_A1 f_A2 f_A3]; f_Q1 = Res.Q(1:k, 1:k); f_Q2 = Res.Q(kp5 + 1:kp5 + k, kp5 + 1:kp5 + k); f_Q3 = Res.Q(2 * kp5 + 1:2 * kp5 + k, 2 * kp5 + 1:2 * kp5 + k); f_Q = [nonzeros(chol(f_Q1))' ... nonzeros(chol(f_Q2))' ... nonzeros(chol(f_Q3))']; Ad = diag(Res.A); Qd = diag(Res.Q); idio = 3 * kp5 + 1; params = [Lambda f_A f_Q ... Ad(idio:idio+6)' Ad(idio+6+5) Qd(idio:idio+6)' Qd(idio+6+5)]'; save('test_dfm_blocks_111.mat','Res','Spec','params'); %% Test 2: p=1, k=1, max_iter=1 Spec.p = 1; Spec.k = 1; max_iter = 2; Res = dfm(X,Spec,threshold,max_iter); Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); k = Spec.k; p = Spec.p; kp = k * p; p5 = max(5, Spec.p); kp5 = k * p5; Lambda = [Res.C(1:end, 1:k) ... Res.C(1:end, kp5 + 1:kp5 + k) ... Res.C(1:end, 2 * kp5 + 1:2 * kp5 + k)]'; mask = logical(Spec.Blocks'); Lambda = Lambda(mask)'; f_A1 = Res.A(1:k, 1:kp)'; f_A2 = Res.A(kp5 + 1:kp5 + k, kp5 + 1:kp5 + kp)'; f_A3 = Res.A(2 * kp5 + 1:2 * kp5 + k, 2 * kp5 + 1:2 * kp5 + kp)'; f_A = [f_A1 f_A2 f_A3]; f_Q1 = Res.Q(1:k, 1:k); f_Q2 = Res.Q(kp5 + 1:kp5 + k, kp5 + 1:kp5 + k); f_Q3 = Res.Q(2 * kp5 + 1:2 * kp5 + k, 2 * kp5 + 1:2 * kp5 + k); f_Q = [nonzeros(chol(f_Q1))' ... nonzeros(chol(f_Q2))' ... nonzeros(chol(f_Q3))']; Ad = diag(Res.A); Qd = diag(Res.Q); idio = 3 * kp5 + 1; params = [Lambda f_A f_Q ... Ad(idio:idio+6)' Ad(idio+6+5) Qd(idio:idio+6)' Qd(idio+6+5)]'; save('test_dfm_blocks_112.mat','Res','Spec','params'); %% Test 3: p=2, k=2, max_iter=1 Spec.p = 2; Spec.k = 2; max_iter = 1; Res = dfm(X,Spec,threshold,max_iter); Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); k = Spec.k; p = Spec.p; kp = k * p; p5 = max(5, Spec.p); kp5 = k * p5; Lambda1 = Res.C(1:end, 1:k); mask1 = repmat(logical(Spec.Blocks(:, 1)), 1, 2); Lambda2 = Res.C(1:end, kp5 + 1:kp5 + k); mask2 = repmat(logical(Spec.Blocks(:, 2)), 1, 2); Lambda3 = Res.C(1:end, 2 * kp5 + 1:2 * kp5 + k); mask3 = repmat(logical(Spec.Blocks(:, 3)), 1, 2); Lambda = [Lambda1 Lambda2 Lambda3]'; mask = [mask1 mask2 mask3]'; Lambda = Lambda(mask)'; f_A1 = Res.A(1:k, 1:kp)'; f_A2 = Res.A(kp5 + 1:kp5 + k, kp5 + 1:kp5 + kp)'; f_A3 = Res.A(2 * kp5 + 1:2 * kp5 + k, 2 * kp5 + 1:2 * kp5 + kp)'; f_A = [f_A1 f_A2 f_A3]; f_A = f_A(:)'; f_Q1 = Res.Q(1:k, 1:k); f_Q2 = Res.Q(kp5 + 1:kp5 + k, kp5 + 1:kp5 + k); f_Q3 = Res.Q(2 * kp5 + 1:2 * kp5 + k, 2 * kp5 + 1:2 * kp5 + k); f_Q = [nonzeros(chol(f_Q1))' ... nonzeros(chol(f_Q2))' ... nonzeros(chol(f_Q3))']; Ad = diag(Res.A); Qd = diag(Res.Q); idio = 3 * kp5 + 1; params = [Lambda f_A f_Q ... Ad(idio:idio+6)' Ad(idio+6+5) Qd(idio:idio+6)' Qd(idio+6+5)]'; save('test_dfm_blocks_221.mat','Res','Spec','params'); %% Test 3: p=2, k=2, max_iter=2 Spec.p = 2; Spec.k = 2; max_iter = 2; Res = dfm(X,Spec,threshold,max_iter); Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); k = Spec.k; p = Spec.p; kp = k * p; p5 = max(5, Spec.p); kp5 = k * p5; Lambda1 = Res.C(1:end, 1:k); mask1 = repmat(logical(Spec.Blocks(:, 1)), 1, 2); Lambda2 = Res.C(1:end, kp5 + 1:kp5 + k); mask2 = repmat(logical(Spec.Blocks(:, 2)), 1, 2); Lambda3 = Res.C(1:end, 2 * kp5 + 1:2 * kp5 + k); mask3 = repmat(logical(Spec.Blocks(:, 3)), 1, 2); Lambda = [Lambda1 Lambda2 Lambda3]'; mask = [mask1 mask2 mask3]'; Lambda = Lambda(mask)'; f_A1 = Res.A(1:k, 1:kp)'; f_A2 = Res.A(kp5 + 1:kp5 + k, kp5 + 1:kp5 + kp)'; f_A3 = Res.A(2 * kp5 + 1:2 * kp5 + k, 2 * kp5 + 1:2 * kp5 + kp)'; f_A = [f_A1 f_A2 f_A3]; f_A = f_A(:)'; f_Q1 = Res.Q(1:k, 1:k); f_Q2 = Res.Q(kp5 + 1:kp5 + k, kp5 + 1:kp5 + k); f_Q3 = Res.Q(2 * kp5 + 1:2 * kp5 + k, 2 * kp5 + 1:2 * kp5 + k); f_Q = [nonzeros(chol(f_Q1))' ... nonzeros(chol(f_Q2))' ... nonzeros(chol(f_Q3))']; Ad = diag(Res.A); Qd = diag(Res.Q); idio = 3 * kp5 + 1; params = [Lambda f_A f_Q ... Ad(idio:idio+6)' Ad(idio+6+5) Qd(idio:idio+6)' Qd(idio+6+5)]'; save('test_dfm_blocks_222.mat','Res','Spec','params'); statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/test_news.m000066400000000000000000000051571400612667500334700ustar00rootroot00000000000000%%% Dynamic factor model (DFM) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This script estimates a dynamic factor model (DFM) using a panel of % monthly and quarterly series. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Clear workspace and set paths. close all; clear; clc; addpath('functions'); %% User inputs. vintage_old = '2016-06-29'; % vintage dataset to use for estimation vintage_new = '2016-07-29'; % updated vintage dataset country = 'US'; % United States macroeconomic data sample_start = datenum('2000-01-01','yyyy-mm-dd'); % estimation sample series = 'GDPC1' ; % Nowcasting real GDP (GDPC1) period = '2016q3'; % Forecasting target quarter %% Load model specification and dataset. Spec = load_spec('test_spec.xls'); datafile_old = fullfile('data', country, [vintage_old '.xls']); datafile_new = fullfile('data', country, [vintage_new '.xls']); [X_old, ~] = load_data(datafile_old, Spec, sample_start); [X_new, Time] = load_data(datafile_new, Spec, sample_start); % Basic settings threshold = 1e-4; % Set to 1e-5 for more robust estimates format long %% Test 1: p=1, k=1, max_iter=2 Spec.p = 1; Spec.k = 1; max_iter = 2; % Run DFM model Res = dfm(X_old, Spec, threshold, max_iter); % Update nowcast Res = update_nowcast(X_old, X_new, Time, Spec, Res, series, period, ... vintage_old, vintage_new); % Store results Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); Res.news_table = Res.news_table{:,:}; kp = Spec.k * Spec.p; Lambda = Res.C(1:end, 1:Spec.k)'; f_A = Res.A(1:Spec.k, 1:kp)'; f_Q = Res.Q(1:Spec.k, 1:Spec.k); Ad = diag(Res.A); Qd = diag(Res.Q); idio = Spec.k * max(5, Spec.p) + 1; params = [Lambda(:)' f_A(:)' nonzeros(chol(f_Q)')' ... Ad(idio:idio+3)' Ad(idio+3+5) Qd(idio:idio+3)' Qd(idio+3+5)]'; save('test_news_112.mat','Res','Spec','params'); %% Test 2: p=2, k=2, max_iter=2 Spec.p = 2; Spec.k = 2; max_iter = 2; % Run DFM model Res = dfm(X_old, Spec, threshold, max_iter); % Update nowcast Res = update_nowcast(X_old, X_new, Time, Spec, Res, series, period, ... vintage_old, vintage_new); % Store results Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); Res.news_table = Res.news_table{:,:}; kp = Spec.k * Spec.p; Lambda = Res.C(1:end, 1:Spec.k)'; f_A = Res.A(1:Spec.k, 1:kp)'; f_Q = Res.Q(1:Spec.k, 1:Spec.k); Ad = diag(Res.A); Qd = diag(Res.Q); idio = Spec.k * max(5, Spec.p) + 1; params = [Lambda(:)' f_A(:)' nonzeros(chol(f_Q)')' ... Ad(idio:idio+3)' Ad(idio+3+5) Qd(idio:idio+3)' Qd(idio+3+5)]'; save('test_news_222.mat','Res','Spec','params'); test_news_blocks.m000066400000000000000000000074421400612667500347450ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting%%% Dynamic factor model (DFM) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This script estimates a dynamic factor model (DFM) using a panel of % monthly and quarterly series. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Clear workspace and set paths. close all; clear; clc; addpath('functions'); %% User inputs. vintage_old = '2016-06-29'; % vintage dataset to use for estimation vintage_new = '2016-07-29'; % updated vintage dataset country = 'US'; % United States macroeconomic data sample_start = datenum('2000-01-01','yyyy-mm-dd'); % estimation sample series = 'GDPC1' ; % Nowcasting real GDP (GDPC1) period = '2016q3'; % Forecasting target quarter %% Load model specification and dataset. Spec = load_spec('test_spec_blocks.xls'); datafile_old = fullfile('data', country, [vintage_old '.xls']); datafile_new = fullfile('data', country, [vintage_new '.xls']); [X_old, ~] = load_data(datafile_old, Spec, sample_start); [X_new, Time] = load_data(datafile_new, Spec, sample_start); % Basic settings threshold = 1e-4; % Set to 1e-5 for more robust estimates format long %% Test 1: p=1, k=1, max_iter=2 Spec.p = 1; Spec.k = 1; max_iter = 2; % Run DFM model Res = dfm(X_old, Spec, threshold, max_iter); % Update nowcast Res = update_nowcast(X_old, X_new, Time, Spec, Res, series, period, ... vintage_old, vintage_new); % Store results Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); Res.news_table = Res.news_table{:,:}; k = Spec.k; p = Spec.p; kp = k * p; p5 = max(5, Spec.p); kp5 = k * p5; Lambda = [Res.C(1:end, 1:k) ... Res.C(1:end, kp5 + 1:kp5 + k) ... Res.C(1:end, 2 * kp5 + 1:2 * kp5 + k)]'; mask = logical(Spec.Blocks'); Lambda = Lambda(mask)'; f_A1 = Res.A(1:k, 1:kp)'; f_A2 = Res.A(kp5 + 1:kp5 + k, kp5 + 1:kp5 + kp)'; f_A3 = Res.A(2 * kp5 + 1:2 * kp5 + k, 2 * kp5 + 1:2 * kp5 + kp)'; f_A = [f_A1 f_A2 f_A3]; f_Q1 = Res.Q(1:k, 1:k); f_Q2 = Res.Q(kp5 + 1:kp5 + k, kp5 + 1:kp5 + k); f_Q3 = Res.Q(2 * kp5 + 1:2 * kp5 + k, 2 * kp5 + 1:2 * kp5 + k); f_Q = [nonzeros(chol(f_Q1))' ... nonzeros(chol(f_Q2))' ... nonzeros(chol(f_Q3))']; Ad = diag(Res.A); Qd = diag(Res.Q); idio = 3 * kp5 + 1; params = [Lambda f_A f_Q ... Ad(idio:idio+6)' Ad(idio+6+5) Qd(idio:idio+6)' Qd(idio+6+5)]'; save('test_news_blocks_112.mat','Res','Spec','params'); %% Test 2: p=2, k=2, max_iter=2 Spec.p = 2; Spec.k = 2; max_iter = 2; % Run DFM model Res = dfm(X_old, Spec, threshold, max_iter); % Update nowcast Res = update_nowcast(X_old, X_new, Time, Spec, Res, series, period, ... vintage_old, vintage_new); % Store results Res = rmfield(Res, {'X_sm', 'Z', 'Vsmooth', 'VVsmooth'}); Res.news_table = Res.news_table{:,:}; k = Spec.k; p = Spec.p; kp = k * p; p5 = max(5, Spec.p); kp5 = k * p5; Lambda1 = Res.C(1:end, 1:k); mask1 = repmat(logical(Spec.Blocks(:, 1)), 1, 2); Lambda2 = Res.C(1:end, kp5 + 1:kp5 + k); mask2 = repmat(logical(Spec.Blocks(:, 2)), 1, 2); Lambda3 = Res.C(1:end, 2 * kp5 + 1:2 * kp5 + k); mask3 = repmat(logical(Spec.Blocks(:, 3)), 1, 2); Lambda = [Lambda1 Lambda2 Lambda3]'; mask = [mask1 mask2 mask3]'; Lambda = Lambda(mask)'; f_A1 = Res.A(1:k, 1:kp)'; f_A2 = Res.A(kp5 + 1:kp5 + k, kp5 + 1:kp5 + kp)'; f_A3 = Res.A(2 * kp5 + 1:2 * kp5 + k, 2 * kp5 + 1:2 * kp5 + kp)'; f_A = [f_A1 f_A2 f_A3]; f_A = f_A(:)'; f_Q1 = Res.Q(1:k, 1:k); f_Q2 = Res.Q(kp5 + 1:kp5 + k, kp5 + 1:kp5 + k); f_Q3 = Res.Q(2 * kp5 + 1:2 * kp5 + k, 2 * kp5 + 1:2 * kp5 + k); f_Q = [nonzeros(chol(f_Q1))' ... nonzeros(chol(f_Q2))' ... nonzeros(chol(f_Q3))']; Ad = diag(Res.A); Qd = diag(Res.Q); idio = 3 * kp5 + 1; params = [Lambda f_A f_Q ... Ad(idio:idio+6)' Ad(idio+6+5) Qd(idio:idio+6)' Qd(idio+6+5)]'; save('test_news_blocks_222.mat','Res','Spec','params'); statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/frbny_nowcast/Nowcasting/test_spec.xls000066400000000000000000000210001400612667500340010ustar00rootroot00000000000000ÐÏࡱá;þÿ  þÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿýÿÿÿÿÿÿÿ þÿÿÿþÿÿÿþÿÿÿþÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRoot Entryÿÿÿÿÿÿÿÿÿÿÿÿþÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿþÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿþÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿþÿÿÿ » Ìá°Áâ\p Chad Fulton B°aÀ=œ¯¼=@ 8ô@"·Ú1ÜCalibri1ÈÿArial1ÈÿArial1ÈÿArial1ܼCalibri1´Tahoma1´Tahoma ¤Generalà¤õÿ À àõÿ ôÀ àõÿ ôÀ àõÿ ôÀ àõÿ ôÀ àõÿ ôÀ àõÿ ôÀ àõÿ ôÀ àõÿ ôÀ àõÿ ôÀ àõÿ ôÀ àõÿ ôÀ àõÿ ôÀ àõÿ ôÀ àõÿ ôÀ ठÀ à+õÿ ðÀ à)õÿ ðÀ à,õÿ ðÀ à*õÿ ðÀ à õÿ ðÀ à¤!À à¤!À à¤!8À “€ÿ“€ÿ“€ÿ“€ÿ“€ÿ“€ÿ`… specŒÁÁTëZðRð3 ð¿ À@@ñ  ÷ü~&ModelSeriesID SeriesName Frequency Block1-GlobalTransformationUnitsCategoryGDPC1Real Gross Domestic ProductqpcaChained $, BillionsNational AccountsCPIAUCSLConsumer Price IndexmpchIndexPricesUNRATEUnemployment Ratechg%LaborULCNFBUnit Labor CostPAYEMSPayroll EmploymentThousands of Personsÿ ì cc » Ì dü©ñÒMbP?_€%<Á*+‚ƒ„&è?'è?(ð?)ð?¡"d,, ¶` ¶`à? ¶` ¶`à?U} ý‹} þ÷<€<<<<<ý ý ý ý ý ý ý ý ~ ý ý  ý  ~ ý  ý  ý  ~ ý ý ý ~ ý ý ý ~ ý ý ý ~ ý ý ý ~ ý ý ý  ~ ý  ý ý ~ ý ý ý ~ ý ý ý ìþð ððð( ð ð𮢠ð # ðl€…‡¿X€ÿÿÿƒ¿À4e¤ÁÂËš[Ö×ÿ?¿ ðÙÚð]4 )Gb˜FM}¾~_czxì ð¶.</0 = drop from model, 1 = include in estimation<.ì®𮢠ð # ðl€…‡¿X€ÿÿÿƒ¿À4e¤ÁÂËš[Ö×ÿ?¿ ðÁ ð]4 Äg˜””AîŒ}Í·Ë,)Xì ð¶<m = monthly, q = quarterly<ì®𮢠ð # ðl€…‡¿X€ÿÿÿƒ¿À4e¤ÁÂËš[Ö×ÿ?¿ ð¸Úð]4 ƒÈnÕ½L­”ÈS¨FQÅ´ì ð¶g<hFactor loading columns should be labeled "Block<#>-". 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,ÔÇÿòÈ™¢FND·µ¢cWfÅ/ÉãR’GÃÒvËI$ïvy4çbÈ(›ÌNLNóÈpüpåU„‹ë”„Ó±.gg¹.TZ}·Ï¾ßï¾ûn'bd Aèlº.ñÏÿJû÷ßDã?·Xf<3: H›¹tógfl(Ó¹8 š¡ÝÒðRÈo¾±ŠIL~R$šŸÁYê’¬ªu ¯F¿ º2KùV'aù» qjV6²^ÝZu§TÂAäæY³m0øÉJ“6E Æ” =këqÐP÷G9œÝt2kÂj .D¯É°æaMŪD]ìACÂzT™xtrÄ`áPíØ_gvK~Í} ã…ΙÆ0§@×? $©3Ø1op:ŠÜ¡› ÷aÍ&Aå 2 «Æõà}gòèÀ| .¸°zªà¤0„Òƃrâù‘šçàeÇIë¥Eï­ó¥eŸlHòF®ØCéÄ_€àEªGüãð¯÷ORÉ;º@éÍžƒº,7Ë+<¼¿#"ÏÌhBÅy$3«!¸)?$½nÀAB­\j5’s”eRòkèŒü9\I«Iëêî²»õ‚œE¡s8hŽðZäÜRÀâBÔ,®&[Jspš¡©»ÞÁ¶T%#Ó2g•NôO•€KŠóV=ÛøÜXºstatsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/kfas_helpers.R000066400000000000000000000050401400612667500270650ustar00rootroot00000000000000# Helper functions for working with KFAS objects cbind.fill <- function(...){ nm <- list(...) nm <- lapply(nm, as.matrix) n <- max(sapply(nm, nrow)) do.call(cbind, lapply(nm, function (x) rbind(x, matrix(, n-nrow(x), ncol(x))))) } flatten <- function(m) { f <- t(apply(m, 3, c)) dm <- dim(m) df <- dim(f) if(df[1] == 1 && dm[3] != 1) { f <- t(f) } f } kfas.output <- function(kf) { # Dimensions n = nrow(kf$model$y) p = ncol(kf$model$y) p2 = p^2 m = nrow(kf$model$T) m2 = m^2 mp = m * p r = nrow(kf$model$Q) r2 = r^2 # Construct the output dataframe # r = scaled_smoothed_estimator # N = scaled_smoothed_estimator_cov # m = forecasts # v = forecasts_error # F = forecasts_error_cov # a = predicted_state # P = predicted_state_cov # mu = filtered_forecasts # alphahat = smoothed_state # V = smoothed_state_cov # muhat = smoothed_forecasts # etahat = smoothed_state_disturbance # V_eta = smoothed_state_disturbance_cov # epshat = smoothed_measurement_disturbance # V_eps = smoothed_measurement_disturbance_cov out <- as.data.frame(with(kf, cbind.fill( t(r), t(r0), t(r1), flatten(N), flatten(N0), flatten(N1), flatten(N2), m, v, t(F), t(Finf), flatten(K), flatten(Kinf), a, flatten(P), flatten(Pinf), att, flatten(Ptt), alphahat, flatten(V), muhat, flatten(V_mu), etahat, flatten(V_eta), epshat, t(V_eps), logLik ))) names(out) <- c( paste('r', 1:m, sep='_'), paste('r0', 1:m, sep='_'), paste('r1', 1:m, sep='_'), paste('N', 1:m2, sep='_'), paste('N0', 1:m2, sep='_'), paste('N1', 1:m2, sep='_'), paste('N2', 1:m2, sep='_'), paste('m', 1:p, sep='_'), paste('v', 1:p, sep='_'), paste('F', 1:p, sep='_'), paste('Finf', 1:p, sep='_'), paste('K', 1:mp, sep='_'), paste('Kinf', 1:mp, sep='_'), paste('a', 1:m, sep='_'), paste('P', 1:m2, sep='_'), paste('Pinf', 1:m2, sep='_'), paste('att', 1:m, sep='_'), paste('Ptt', 1:m2, sep='_'), paste('alphahat', 1:m, sep='_'), paste('V', 1:m2, sep='_'), paste('muhat', 1:p, sep='_'), paste('Vmu', 1:p2, sep='_'), paste('etahat', 1:r, sep='_'), paste('Veta', 1:r2, sep='_'), paste('epshat', 1:p, sep='_'), paste('Veps', 1:p, sep='_'), 'llf' ) return(out) } kfas.llf <- function(kf) { # Dimensions n = nrow(kf$model$y) p = ncol(kf$model$y) m = nrow(kf$model$T) r = nrow(kf$model$Q) d = kf$d F = kf$F Finf = kf$Finf v = kf$v -((n * p / 2) * log(pi * 2) + 0.5 * sum(log(Finf[1:d])) + 0.5 * sum(log(F[(d+1):10]) + (v^2 / t(F))[(d+1):10])) } 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See also Stata time series documentation, in particular `dfactor`. Data from: http://www.jmulti.de/download/datasets/e1.dat Author: Chad Fulton License: Simplified-BSD """ lutkepohl_dfm = { 'params': [ .0063728, .00660177, .00636009, # Factor loadings .00203899, .00009016, .00005348, # Idiosyncratic variances .33101874, .63927819, # Factor transitions ], 'bse_oim': [ .002006, .0012514, .0012128, # Factor loadings .0003359, .0000184, .0000141, # Idiosyncratic variances .1196637, .1218577, # Factor transitions ], 'loglike': 594.0902026190786, 'aic': -1172.18, 'bic': -1153.641, } lutkepohl_dfm2 = { 'params': [ .03411188, .03478764, # Factor loadings: y1 .03553366, .0344871, # Factor loadings: y2 .03536757, .03433391, # Factor loadings: y3 .00224401, .00014678, .00010922, # Idiosyncratic variances .08845946, .08862982, # Factor transitions: Phi, row 1 .08754759, .08758589 # Phi, row 2 ], 'bse_oim': None, 'loglike': 496.379832917306, 'aic': -974.7597, 'bic': -953.9023, } lutkepohl_dfm_exog1 = { 'params': [ -.01254697, -.00734604, -.00671296, # Factor loadings .01803325, .02066737, .01983089, # Beta.constant .00198667, .00008426, .00005684, # Idiosyncratic variances .31140829, # Factor transition ], 'var_oim': [ .00004224, 2.730e-06, 3.625e-06, .00003087, 2.626e-06, 2.013e-06, 1.170e-07, 5.133e-10, 3.929e-10, .07412117 ], 'loglike': 596.9781590009525, 'aic': -1173.956, 'bic': -1150.781, } lutkepohl_dfm_exog2 = { 'params': [ .01249096, .00731147, .00680776, # Factor loadings .02187812, -.00009851, # Betas, y1 .02302646, -.00006045, # Betas, y2 .02009233, -6.683e-06, # Betas, y3 .0019856, .00008378, .00005581, # Idiosyncratic variances .2995768, # Factor transition ], 'var_oim': [ .00004278, 2.659e-06, 3.766e-06, .00013003, 6.536e-08, .00001079, 5.424e-09, 8.393e-06, 4.217e-09, 1.168e-07, 5.140e-10, 4.181e-10, .07578382, ], 'loglike': 597.4550537198315, 'aic': -1168.91, 'bic': -1138.783, } lutkepohl_dfm_gen = { 'params': [ .00312295, .00332555, .00318837, # Factor loadings # .00195462, # Covariance, lower triangle # 3.642e-06, .00010047, # .00007018, .00002565, .00006118 # Note: the following are the Cholesky of the covariance # matrix defined just above .04421108, # Cholesky, lower triangle .00008238, .01002313, .00158738, .00254603, .00722343, .987374, # Factor transition -.25613562, .00392166, .44859028, # Error transition parameters .01635544, -.249141, .08170863, -.02280001, .02059063, -.41808254 ], 'var_oim': [ 1.418e-06, 1.030e-06, 9.314e-07, # Factor loadings None, # Cholesky, lower triangle None, None, None, None, None, .00021421, # Factor transition .01307587, .29167522, .43204063, # Error transition parameters .00076899, .01742173, .0220161, .00055435, .01456365, .01707167 ], 'loglike': 607.7715711926285, 'aic': -1177.543, 'bic': -1133.511, } lutkepohl_dfm_ar2 = { 'params': [ .00419132, .0044007, .00422976, # Factor loadings .00188101, .0000786, .0000418, # Idiosyncratic variance .97855802, # Factor transition -.28856258, -.14910552, # Error transition parameters -.41544832, -.26706536, -.72661178, -.27278821, ], 'var_oim': [ 1.176e-06, 7.304e-07, 6.726e-07, # Factor loadings 9.517e-08, 2.300e-10, 1.389e-10, # Idiosyncratic variance .00041159, # Factor transition .0131511, .01296008, # Error transition parameters .01748435, .01616862, .03262051, .02546648, ], 'loglike': 607.4203109232711, 'aic': -1188.841, 'bic': -1158.713, } lutkepohl_dfm_scalar = { 'params': [ .04424851, .00114077, .00275081, # Factor loadings .01812298, .02071169, .01987196, # Beta.constant .00012067, # Idiosyncratic variance -.19915198, # Factor transition ], 'var_oim': [ .00001479, 1.664e-06, 1.671e-06, .00001985, 1.621e-06, 1.679e-06, 1.941e-10, .01409482 ], 'loglike': 588.7677809701966, 'aic': -1161.536, 'bic': -1142.996, } lutkepohl_sfm = { 'params': [ .02177607, .02089956, .02239669, # Factor loadings .00201477, .00013623, 7.452e-16 # Idiosyncratic variance ], 'var_oim': [ .00003003, 4.729e-06, 3.344e-06, 1.083e-07, 4.950e-10, 0 ], 'loglike': 532.2215594949788, 'aic': -1054.443, 'bic': -1042.856, } lutkepohl_sur = { 'params': [ .02169026, -.00009184, # Betas, y1 .0229165, -.00005654, # Betas, y2 .01998994, -3.049e-06, # Betas, y3 # .00215703, # Covariance, lower triangle # .0000484, .00014252, # .00012772, .00005642, .00010673, # Note: the following are the Cholesky of the covariance # matrix defined just above .04644384, # Cholesky, lower triangle .00104212, .0118926, .00274999, .00450315, .00888196, ], 'var_oim': [ .0001221, 6.137e-08, 8.067e-06, 4.055e-09, 6.042e-06, 3.036e-09, None, None, None, None, None, None ], 'loglike': 597.6181259116113, 'aic': -1171.236, 'bic': -1143.426, } lutkepohl_sur_auto = { 'params': [ .02243063, -.00011112, # Betas, y1 .02286952, -.0000554, # Betas, y2 .0020338, .00013843, # Idiosyncratic variance -.21127833, .50884609, # Error transition parameters .04292935, .00855789, ], 'var_oim': [ .00008357, 4.209e-08, 8.402e-06, 4.222e-09, 1.103e-07, 5.110e-10, .01259537, .19382105, .00085936, .01321035, ], 'loglike': 352.7250284160132, 'aic': -685.4501, 'bic': -662.2752 } statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/results_dynamic_factor_stata.csv000066400000000000000000001244021400612667500327540ustar00rootroot00000000000000predict_dfm_1,predict_dfm_2,predict_dfm_3,predict_dfm2_1,predict_dfm2_2,predict_dfm2_3,predict_dfm_exog1_1,predict_dfm_exog1_2,predict_dfm_exog1_3,predict_dfm_exog2_1,predict_dfm_exog2_2,predict_dfm_exog2_3,predict_dfm_gen_1,predict_dfm_gen_2,predict_dfm_gen_3,predict_dfm_ar2_1,predict_dfm_ar2_2,predict_dfm_ar2_3,predict_dfm_scalar_1,predict_dfm_scalar_2,predict_dfm_scalar_3,predict_sfm_1,predict_sfm_2,predict_sfm_3,predict_sur_1,predict_sur_2,predict_sur_3,predict_sur_auto_1,predict_sur_auto_2,dyn_predict_dfm_1,dyn_predict_dfm_2,dyn_predict_dfm_3,dyn_predict_dfm2_1,dyn_predict_dfm2_2,dyn_predict_dfm2_3,dyn_predict_dfm_exog1_1,dyn_predict_dfm_exog1_2,dyn_predict_dfm_exog1_3,dyn_predict_dfm_exog2_1,dyn_predict_dfm_exog2_2,dyn_predict_dfm_exog2_3,dyn_predict_dfm_gen_1,dyn_predict_dfm_gen_2,dyn_predict_dfm_gen_3,dyn_predict_dfm_ar2_1,dyn_predict_dfm_ar2_2,dyn_predict_dfm_ar2_3,dyn_predict_dfm_scalar_1,dyn_predict_dfm_scalar_2,dyn_predict_dfm_scalar_3,dyn_predict_sfm_1,dyn_predict_sfm_2,dyn_predict_sfm_3,dyn_predict_sur_1,dyn_predict_sur_2,dyn_predict_sur_3,dyn_predict_sur_auto_1,dyn_predict_sur_auto_2 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-3.43103618297003,-4.27196150084115,-5.29609942286875,0.0838517404088302,10.584681187332,12.0821673690361,12.9863234358394,4.23606797749979,-6.56428096310668,-8.10126730692002,-10.3226967726779,2.61803398874989,2.61803398874989,2.61803398874989,9.5277324404282,10.0753088214112,9.60654597476565,4.23606797749979,3.40723546272201,2.43509141526039,0.33337652363406,0.0916421794821756,4.40723546272201,4.43509141526039,3.33337652363406,0.0916421794821756,-3.43103618297003,-4.27196150084115,-5.29609942286875,0.177794334647952,-0.386835238496676,-0.45419135314428,-0.66974986047253,0.450849718747371,0.450849718747371,0.450849718747371 -2.46780125594993,-3.08099970860243,-3.74843496125432,0.0557280900008412,10.5277324404282,12.0753088214112,12.6065459747656,4.23606797749979,-6.51476808769632,-8.1031406992307,-10.1169333356148,2.61803398874989,2.61803398874989,2.61803398874989,9.50138433340872,10.0672924536641,9.35393731143888,4.23606797749979,3.97619927975198,3.16312991441925,1.03727710076531,0.105244939971399,4.97619927975198,5.16312991441925,4.03727710076531,0.105244939971399,-2.46780125594993,-3.08099970860243,-3.74843496125432,0.23606797749979,-0.963234927020107,-1.19096179223872,-1.54766446161443,0.472135954999579,0.472135954999579,0.472135954999579 0,0,0,0,10.5013843334087,12.0672924536641,12.3539373114389,4.23606797749979,-6.46078756555658,-8.06616195644968,-9.81353013318219,2.61803398874989,2.61803398874989,2.61803398874989,9.50839802380206,10.0821302058168,9.288842139511,4.23606797749979,5.50839802380206,5.08213020581682,3.288842139511,0.23606797749979,6.50839802380206,7.08213020581682,6.288842139511,0.23606797749979,0,0,0,1,-2.46780125594993,-3.08099970860243,-3.74843496125432,0.618033988749895,0.618033988749895,0.618033988749895 statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/results_kalman_filter.py000066400000000000000000001210341400612667500312410ustar00rootroot00000000000000""" Results for Kalman Filter Author: Chad Fulton License: Simplified-BSD Notes ----- There was an error in the loglikelihood computation in the GAUSS code from Kim and Nelson for the Clark 1989 model, omitting the exponent term on ``2 pi''. Therefore the loglikelihood in the test results for uc_bi is instead from the FKF R library, which can be replicated using the ``test_clark1989_r.R'' file. References ---------- Datasets produced using GAUSS code described in Kim and Nelson (1999) and found at http://econ.korea.ac.kr/~cjkim/SSMARKOV.htm Accessed 2013-11-18 Code was run using OxGauss 7. Kim, Chang-Jin, and Charles R. Nelson. 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications". MIT Press Books. The MIT Press. """ """ Clark's (1987) Univariate Unobserved Components model of GDP See http://econ.korea.ac.kr/~cjkim/MARKOV/prgmlist.htm#chapter3 Gauss Code: UC_UNI.OPT Dataset: GDP4795.PRN """ uc_uni = { 'data': [ 1239.5, 1247.19995117, 1255, 1269.5, 1284, 1295.69995117, 1303.80004883, 1316.40002441, 1305.30004883, 1302, 1312.59997559, 1301.90002441, 1350.90002441, 1393.5, 1445.19995117, 1484.5, 1504.09997559, 1548.30004883, 1585.40002441, 1596, 1607.69995117, 1612.09997559, 1621.90002441, 1657.80004883, 1687.30004883, 1695.30004883, 1687.90002441, 1671.19995117, 1660.80004883, 1658.40002441, 1677.69995117, 1698.30004883, 1742.5, 1758.59997559, 1778.19995117, 1793.90002441, 1787, 1798.5, 1802.19995117, 1826.59997559, 1836.40002441, 1834.80004883, 1851.19995117, 1830.5, 1790.09997559, 1804.40002441, 1840.90002441, 1880.90002441, 1904.90002441, 1937.5, 1930.80004883, 1941.90002441, 1976.90002441, 1971.69995117, 1973.69995117, 1961.09997559, 1977.40002441, 2006, 2035.19995117, 2076.5, 2103.80004883, 2125.69995117, 2142.60009766, 2140.19995117, 2170.89990234, 2199.5, 2237.60009766, 2254.5, 2311.10009766, 2329.89990234, 2357.39990234, 2364, 2410.10009766, 2442.80004883, 2485.5, 2543.80004883, 2596.80004883, 2601.39990234, 2626.10009766, 2640.5, 2657.19995117, 2669, 2699.5, 2715.10009766, 2752.10009766, 2796.89990234, 2816.80004883, 2821.69995117, 2864.60009766, 2867.80004883, 2884.5, 2875.10009766, 2867.80004883, 2859.5, 2895, 2873.30004883, 2939.89990234, 2944.19995117, 2962.30004883, 2977.30004883, 3037.30004883, 3089.69995117, 3125.80004883, 3175.5, 3253.30004883, 3267.60009766, 3264.30004883, 3289.10009766, 3259.39990234, 3267.60009766, 3239.10009766, 3226.39990234, 3154, 3190.39990234, 3249.89990234, 3292.5, 3356.69995117, 3369.19995117, 3381, 3416.30004883, 3466.39990234, 3525, 3574.39990234, 3567.19995117, 3591.80004883, 3707, 3735.60009766, 3779.60009766, 3780.80004883, 3784.30004883, 3807.5, 3814.60009766, 3830.80004883, 3732.60009766, 3733.5, 3808.5, 3860.5, 3844.39990234, 3864.5, 3803.10009766, 3756.10009766, 3771.10009766, 3754.39990234, 3759.60009766, 3783.5, 3886.5, 3944.39990234, 4012.10009766, 4089.5, 4144, 4166.39990234, 4194.20019531, 4221.79980469, 4254.79980469, 4309, 4333.5, 4390.5, 4387.70019531, 4412.60009766, 4427.10009766, 4460, 4515.29980469, 4559.29980469, 4625.5, 4655.29980469, 4704.79980469, 4734.5, 4779.70019531, 4817.60009766, 4839, 4839, 4856.70019531, 4898.29980469, 4917.10009766, 4906.5, 4867.20019531, 4842, 4867.89990234, 4879.89990234, 4880.79980469, 4918.5, 4947.5, 4990.5, 5060.70019531, 5075.29980469, 5105.39990234, 5139.39990234, 5218, 5261.10009766, 5314.10009766, 5367, 5433.79980469, 5470.10009766, 5487.79980469, 5544.60009766 ], 'start': 21-1, 'parameters': [0.005539, 0.006164, 0.000184, 1.531659, -0.585422], 'standard_errors': [0.000000, 0.000000, 0.000000, 0.000000, 0.000000], 'loglike': 578.520887, 'states': [ [7.369243, 0.013317, 0.018762], [7.374220, 0.011073, 0.016581], [7.385527, 0.005826, 0.015828], [7.416916, -0.003669, 0.017851], [7.434130, -0.003245, 0.017775], [7.433819, 0.001796, 0.015781], [7.427416, 0.003825, 0.013508], [7.419109, 0.002189, 0.011420], [7.419253, -0.004198, 0.010408], [7.424214, -0.010605, 0.009947], [7.443116, -0.017937, 0.010663], [7.455732, -0.018349, 0.010810], [7.483689, -0.020612, 0.012044], [7.484287, -0.012014, 0.011259], [7.493577, -0.010220, 0.011130], [7.500748, -0.008601, 0.010882], [7.493715, -0.005422, 0.009805], [7.504849, -0.010140, 0.009882], [7.507452, -0.010689, 0.009477], [7.524476, -0.014264, 0.009882], [7.527391, -0.011828, 0.009521], [7.525478, -0.010787, 0.008949], [7.537758, -0.014169, 0.009110], [7.523893, -0.011549, 0.008031], [7.504850, -0.014823, 0.006795], [7.524920, -0.026937, 0.007384], [7.547145, -0.029135, 0.008024], [7.563759, -0.024254, 0.008385], [7.569019, -0.016834, 0.008257], [7.582139, -0.012985, 0.008452], [7.573090, -0.007400, 0.007768], [7.581280, -0.009858, 0.007784], [7.600320, -0.011035, 0.008205], [7.593454, -0.006802, 0.007653], [7.596716, -0.009050, 0.007495], [7.592481, -0.011220, 0.007082], [7.605464, -0.015926, 0.007286], [7.619716, -0.015818, 0.007523], [7.630873, -0.012524, 0.007644], [7.647019, -0.008580, 0.007924], [7.654471, -0.002971, 0.007909], [7.661563, 0.000293, 0.007883], [7.667909, 0.001866, 0.007834], [7.666825, 0.001830, 0.007557], [7.683710, -0.000813, 0.007843], [7.695061, 0.000925, 0.007950], [7.709743, 0.003416, 0.008151], [7.714033, 0.006650, 0.008037], [7.737525, 0.007954, 0.008490], [7.740667, 0.012914, 0.008335], [7.751712, 0.013603, 0.008412], [7.754422, 0.013689, 0.008250], [7.775189, 0.012235, 0.008603], [7.785979, 0.014922, 0.008664], [7.801228, 0.017002, 0.008847], [7.820961, 0.020453, 0.009147], [7.836561, 0.025474, 0.009324], [7.835776, 0.028029, 0.009049], [7.848074, 0.025181, 0.009137], [7.855709, 0.023015, 0.009097], [7.864971, 0.020057, 0.009101], [7.872361, 0.017098, 0.009056], [7.886320, 0.014502, 0.009185], [7.893144, 0.013440, 0.009123], [7.908033, 0.012086, 0.009274], [7.923091, 0.013175, 0.009425], [7.928928, 0.014429, 0.009331], [7.932574, 0.012521, 0.009184], [7.950084, 0.010100, 0.009399], [7.951667, 0.009634, 0.009198], [7.960694, 0.006413, 0.009194], [7.960971, 0.002871, 0.008966], [7.964212, -0.002912, 0.008821], [7.967149, -0.008747, 0.008671], [7.983160, -0.012419, 0.008857], [7.977084, -0.013868, 0.008480], [8.002177, -0.016046, 0.008899], [8.000570, -0.012977, 0.008634], [8.007643, -0.013921, 0.008595], [8.013407, -0.014635, 0.008524], [8.032255, -0.013530, 0.008783], [8.044336, -0.008506, 0.008865], [8.051776, -0.004330, 0.008829], [8.064664, -0.001444, 0.008931], [8.084189, 0.003236, 0.009194], [8.084259, 0.007552, 0.008967], [8.085181, 0.005620, 0.008768], [8.096245, 0.002124, 0.008825], [8.090934, -0.001635, 0.008474], [8.099770, -0.007958, 0.008483], [8.096154, -0.013103, 0.008184], [8.099051, -0.019929, 0.008054], [8.084586, -0.028159, 0.007498], [8.104155, -0.036254, 0.007795], [8.120386, -0.034007, 0.008003], [8.127820, -0.028418, 0.007989], [8.141545, -0.022832, 0.008131], [8.140564, -0.018133, 0.007906], [8.143851, -0.017924, 0.007793], [8.154123, -0.017810, 0.007854], [8.166200, -0.015328, 0.007958], [8.178658, -0.011022, 0.008068], [8.187909, -0.006356, 0.008097], [8.184427, -0.004891, 0.007813], [8.193450, -0.007041, 0.007842], [8.222013, -0.004035, 0.008351], [8.222792, 0.002872, 0.008165], [8.232604, 0.004769, 0.008206], [8.232920, 0.004771, 0.008012], [8.237120, 0.001496, 0.007919], [8.246178, -0.001449, 0.007947], [8.250045, -0.003453, 0.007847], [8.256698, -0.005869, 0.007817], [8.236922, -0.012061, 0.007141], [8.247774, -0.022672, 0.007232], [8.269118, -0.024127, 0.007578], [8.277812, -0.019260, 0.007605], [8.271764, -0.017391, 0.007270], [8.279040, -0.019452, 0.007271], [8.266583, -0.023011, 0.006787], [8.262738, -0.031602, 0.006527], [8.272654, -0.037532, 0.006610], [8.270217, -0.039533, 0.006388], [8.273835, -0.041767, 0.006320], [8.280077, -0.041673, 0.006319], [8.301972, -0.036708, 0.006700], [8.307430, -0.027378, 0.006670], [8.317328, -0.020258, 0.006749], [8.329307, -0.013129, 0.006877], [8.336112, -0.006696, 0.006875], [8.338223, -0.003415, 0.006758], [8.344312, -0.002854, 0.006742], [8.350658, -0.002641, 0.006732], [8.358162, -0.002359, 0.006751], [8.369502, -0.001041, 0.006863], [8.373472, 0.000659, 0.006793], [8.385533, 0.001666, 0.006922], [8.384242, 0.002319, 0.006721], [8.391933, 0.000286, 0.006744], [8.396505, -0.001005, 0.006691], [8.404956, -0.002052, 0.006734], [8.416432, -0.001205, 0.006850], [8.424022, 0.000903, 0.006868], [8.436123, 0.003217, 0.006996], [8.440287, 0.005474, 0.006927], [8.450172, 0.006167, 0.007000], [8.455752, 0.006879, 0.006965], [8.465200, 0.006933, 0.007026], [8.472627, 0.007404, 0.007035], [8.477446, 0.007018, 0.006981], [8.479558, 0.004906, 0.006862], [8.486204, 0.001911, 0.006857], [8.496122, 0.000521, 0.006932], [8.500348, 0.000127, 0.006865], [8.500417, -0.002101, 0.006699], [8.497303, -0.007029, 0.006459], [8.498474, -0.013391, 0.006329], [8.507865, -0.017447, 0.006404], [8.511353, -0.018473, 0.006333], [8.512856, -0.019792, 0.006215], [8.521315, -0.020556, 0.006270], [8.526119, -0.019481, 0.006234], [8.533359, -0.018068, 0.006258], [8.544398, -0.015138, 0.006375], [8.544422, -0.012281, 0.006220], [8.550013, -0.011958, 0.006205], [8.556038, -0.011346, 0.006200], [8.569108, -0.009239, 0.006368], [8.573833, -0.005737, 0.006328], [8.581719, -0.003600, 0.006366], [8.589473, -0.001449, 0.006400], [8.599466, 0.000928, 0.006488], [8.604040, 0.003012, 0.006441], [8.607332, 0.002951, 0.006364], [8.618016, 0.002564, 0.006470] ] } """ Clark's (1989) Bivariate Unobserved Components model of GDP See http://econ.korea.ac.kr/~cjkim/MARKOV/prgmlist.htm#chapter3 Gauss Code: UC_BI.OPT Datasets: GDP4795.PRN, LHUR.PRN """ uc_bi = { 'data': [ [1239.5, 0], [1247.199951, 0], [1255, 0], [1269.5, 0], [1284, 3.733333349], [1295.699951, 3.666666667], [1303.800049, 3.766666651], [1316.400024, 3.833333333], [1305.300049, 4.666666667], [1302, 5.866666635], [1312.599976, 6.699999968], [1301.900024, 6.966666698], [1350.900024, 6.400000095], [1393.5, 5.566666762], [1445.199951, 4.633333365], [1484.5, 4.23333327], [1504.099976, 3.500000079], [1548.300049, 3.099999984], [1585.400024, 3.166666587], [1596, 3.366666635], [1607.699951, 3.066666683], [1612.099976, 2.966666698], [1621.900024, 3.233333349], [1657.800049, 2.833333333], [1687.300049, 2.699999968], [1695.300049, 2.566666683], [1687.900024, 2.733333349], [1671.199951, 3.699999968], [1660.800049, 5.266666571], [1658.400024, 5.800000032], [1677.699951, 5.966666698], [1698.300049, 5.333333333], [1742.5, 4.73333327], [1758.599976, 4.399999936], [1778.199951, 4.099999905], [1793.900024, 4.23333327], [1787, 4.033333302], [1798.5, 4.200000127], [1802.199951, 4.133333365], [1826.599976, 4.133333365], [1836.400024, 3.933333317], [1834.800049, 4.100000064], [1851.199951, 4.23333327], [1830.5, 4.933333238], [1790.099976, 6.300000032], [1804.400024, 7.366666794], [1840.900024, 7.333333333], [1880.900024, 6.366666476], [1904.900024, 5.833333333], [1937.5, 5.099999905], [1930.800049, 5.266666571], [1941.900024, 5.600000064], [1976.900024, 5.133333365], [1971.699951, 5.23333327], [1973.699951, 5.533333302], [1961.099976, 6.266666571], [1977.400024, 6.800000032], [2006, 7], [2035.199951, 6.766666571], [2076.5, 6.199999968], [2103.800049, 5.633333365], [2125.699951, 5.533333302], [2142.600098, 5.566666603], [2140.199951, 5.533333302], [2170.899902, 5.766666571], [2199.5, 5.73333327], [2237.600098, 5.5], [2254.5, 5.566666603], [2311.100098, 5.466666698], [2329.899902, 5.199999968], [2357.399902, 5], [2364, 4.966666698], [2410.100098, 4.899999936], [2442.800049, 4.666666667], [2485.5, 4.366666794], [2543.800049, 4.099999905], [2596.800049, 3.866666635], [2601.399902, 3.833333333], [2626.100098, 3.766666651], [2640.5, 3.699999968], [2657.199951, 3.833333333], [2669, 3.833333333], [2699.5, 3.799999952], [2715.100098, 3.900000016], [2752.100098, 3.733333349], [2796.899902, 3.566666683], [2816.800049, 3.533333381], [2821.699951, 3.400000095], [2864.600098, 3.400000095], [2867.800049, 3.433333397], [2884.5, 3.566666683], [2875.100098, 3.566666683], [2867.800049, 4.166666667], [2859.5, 4.76666673], [2895, 5.166666667], [2873.300049, 5.833333333], [2939.899902, 5.933333397], [2944.199951, 5.900000095], [2962.300049, 6.033333302], [2977.300049, 5.933333397], [3037.300049, 5.76666673], [3089.699951, 5.699999809], [3125.800049, 5.566666603], [3175.5, 5.366666635], [3253.300049, 4.933333397], [3267.600098, 4.933333397], [3264.300049, 4.800000191], [3289.100098, 4.76666673], [3259.399902, 5.133333206], [3267.600098, 5.199999968], [3239.100098, 5.633333365], [3226.399902, 6.599999905], [3154, 8.266667048], [3190.399902, 8.866666794], [3249.899902, 8.46666654], [3292.5, 8.299999873], [3356.699951, 7.73333327], [3369.199951, 7.566666603], [3381, 7.733333429], [3416.300049, 7.76666673], [3466.399902, 7.5], [3525, 7.133333206], [3574.399902, 6.900000095], [3567.199951, 6.666666826], [3591.800049, 6.333333492], [3707, 6], [3735.600098, 6.033333302], [3779.600098, 5.900000095], [3780.800049, 5.866666794], [3784.300049, 5.699999968], [3807.5, 5.866666635], [3814.600098, 5.966666698], [3830.800049, 6.300000191], [3732.600098, 7.333333333], [3733.5, 7.666666667], [3808.5, 7.399999936], [3860.5, 7.433333397], [3844.399902, 7.399999936], [3864.5, 7.399999936], [3803.100098, 8.233333429], [3756.100098, 8.833333333], [3771.100098, 9.433333397], [3754.399902, 9.900000254], [3759.600098, 10.66666667], [3783.5, 10.36666648], [3886.5, 10.13333352], [3944.399902, 9.366666476], [4012.100098, 8.53333346], [4089.5, 7.866666794], [4144, 7.433333238], [4166.399902, 7.433333397], [4194.200195, 7.300000032], [4221.799805, 7.23333327], [4254.799805, 7.300000032], [4309, 7.199999968], [4333.5, 7.033333302], [4390.5, 7.033333143], [4387.700195, 7.166666508], [4412.600098, 6.966666698], [4427.100098, 6.833333333], [4460, 6.599999905], [4515.299805, 6.26666673], [4559.299805, 6], [4625.5, 5.833333333], [4655.299805, 5.699999809], [4704.799805, 5.466666698], [4734.5, 5.466666698], [4779.700195, 5.333333492], [4817.600098, 5.199999968], [4839, 5.23333327], [4839, 5.23333327], [4856.700195, 5.366666794], [4898.299805, 5.300000032], [4917.100098, 5.333333333], [4906.5, 5.699999968], [4867.200195, 6.133333365], [4842, 6.600000064], [4867.899902, 6.833333333], [4879.899902, 6.866666794], [4880.799805, 7.100000064], [4918.5, 7.366666794], [4947.5, 7.600000064], [4990.5, 7.633333206], [5060.700195, 7.366666794], [5075.299805, 7.133333365], [5105.399902, 7.066666603], [5139.399902, 6.800000032], [5218, 6.633333365], [5261.100098, 6.633333206], [5314.100098, 6.199999968], [5367, 6], [5433.799805, 5.566666603], [5470.100098, 5.533333302], [5487.799805, 5.633333206], [5544.600098, 5.633333206] ], 'start': 21-4-1, 'parameters': [ 0.004863, 0.00668, 0.000295, 0.001518, 0.000306, 1.43859, -0.517385, -0.336789, -0.163511, -0.072012 ], 'standard_errors': [ 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000 ], # See Notes in the file docstring for more information on the loglikelihood # 'loglike': 1566.994602, 'loglike': 1485.41934, 'states': [ [7.359396, 0.023164, 0.013713, 0.044071], [7.362719, 0.022574, 0.012832, 0.043161], [7.373038, 0.018315, 0.012796, 0.044467], [7.393634, 0.019613, 0.012635, 0.037801], [7.408780, 0.022105, 0.012863, 0.038367], [7.414012, 0.021603, 0.012370, 0.038493], [7.414058, 0.017182, 0.011659, 0.039431], [7.416921, 0.004376, 0.011582, 0.044744], [7.429820, -0.014765, 0.012230, 0.051206], [7.435752, -0.022143, 0.011632, 0.048723], [7.447268, -0.022089, 0.011509, 0.047309], [7.450937, -0.013554, 0.010723, 0.043338], [7.467363, -0.004287, 0.010903, 0.041325], [7.472477, -0.000204, 0.010666, 0.042662], [7.480909, 0.002448, 0.010461, 0.041647], [7.491498, 0.000649, 0.010580, 0.043180], [7.487065, 0.001229, 0.009635, 0.041911], [7.495837, -0.001129, 0.009609, 0.042236], [7.497666, -0.000903, 0.009111, 0.041357], [7.510478, -0.000266, 0.009281, 0.040804], [7.513518, 0.002045, 0.008890, 0.040138], [7.516030, -0.001339, 0.008633, 0.041623], [7.526775, -0.003186, 0.008721, 0.041167], [7.526058, -0.013713, 0.008459, 0.045277], [7.524449, -0.034422, 0.008246, 0.050757], [7.544061, -0.046078, 0.008895, 0.051237], [7.558430, -0.040420, 0.009045, 0.048770], [7.563474, -0.023969, 0.008620, 0.045247], [7.568520, -0.016336, 0.008491, 0.046358], [7.575711, -0.006557, 0.008303, 0.044317], [7.576186, -0.010497, 0.008082, 0.047851], [7.587245, -0.015823, 0.008289, 0.048671], [7.596353, -0.007068, 0.008129, 0.045036], [7.595725, -0.009074, 0.007813, 0.047808], [7.602240, -0.014574, 0.007805, 0.048940], [7.606393, -0.025132, 0.007768, 0.051857], [7.620310, -0.030772, 0.008121, 0.052282], [7.634385, -0.030487, 0.008445, 0.052385], [7.643520, -0.025171, 0.008447, 0.051739], [7.653856, -0.015416, 0.008463, 0.050131], [7.658758, -0.007257, 0.008248, 0.049650], [7.668470, -0.006613, 0.008393, 0.050929], [7.677398, -0.007622, 0.008453, 0.051544], [7.676653, -0.007998, 0.007963, 0.051552], [7.693051, -0.010154, 0.008439, 0.052071], [7.704488, -0.008503, 0.008587, 0.051841], [7.717178, -0.004019, 0.008767, 0.051084], [7.726080, -0.005396, 0.008853, 0.052655], [7.747984, -0.002505, 0.009499, 0.051686], [7.752362, 0.001219, 0.009225, 0.051659], [7.761774, 0.003541, 0.009215, 0.051256], [7.765241, 0.002870, 0.008933, 0.051734], [7.782698, 0.004726, 0.009337, 0.050749], [7.792415, 0.008486, 0.009331, 0.050208], [7.805420, 0.012809, 0.009482, 0.049330], [7.824241, 0.017173, 0.009946, 0.048673], [7.841661, 0.020374, 0.010335, 0.048518], [7.845477, 0.018328, 0.010035, 0.049472], [7.855021, 0.018234, 0.009954, 0.048333], [7.860222, 0.018502, 0.009674, 0.047770], [7.869432, 0.015597, 0.009665, 0.048076], [7.874754, 0.014705, 0.009402, 0.047404], [7.885524, 0.015297, 0.009434, 0.046559], [7.893504, 0.013081, 0.009381, 0.047074], [7.904608, 0.015511, 0.009399, 0.045546], [7.917944, 0.018323, 0.009577, 0.044894], [7.925926, 0.017430, 0.009516, 0.045383], [7.927535, 0.017559, 0.009058, 0.044576], [7.942312, 0.017872, 0.009324, 0.043809], [7.945307, 0.015993, 0.009010, 0.044250], [7.954008, 0.013098, 0.008988, 0.044131], [7.952052, 0.011791, 0.008384, 0.043624], [7.959391, 0.001910, 0.008428, 0.045708], [7.965660, -0.007258, 0.008362, 0.046727], [7.981621, -0.010881, 0.008753, 0.046477], [7.984173, -0.020957, 0.008572, 0.049592], [8.005586, -0.019456, 0.009162, 0.047685], [8.005729, -0.018136, 0.008728, 0.048606], [8.014046, -0.020325, 0.008746, 0.049461], [8.017136, -0.018363, 0.008419, 0.048869], [8.032555, -0.013831, 0.008752, 0.048074], [8.047624, -0.011794, 0.009127, 0.048945], [8.057447, -0.010002, 0.009179, 0.049253], [8.069676, -0.006456, 0.009316, 0.048733], [8.086067, 0.001358, 0.009622, 0.047288], [8.091964, -0.000153, 0.009522, 0.049344], [8.091093, -0.000292, 0.008944, 0.048749], [8.097901, 0.000468, 0.008797, 0.048031], [8.095928, -0.006630, 0.008327, 0.050163], [8.099455, -0.007644, 0.008011, 0.048832], [8.097491, -0.014440, 0.007571, 0.050705], [8.107855, -0.028733, 0.007866, 0.053837], [8.110267, -0.053840, 0.007861, 0.059886], [8.125657, -0.057755, 0.008165, 0.057870], [8.132368, -0.045989, 0.007976, 0.055472], [8.141350, -0.041948, 0.008115, 0.057302], [8.151163, -0.032449, 0.008143, 0.055996], [8.152718, -0.030287, 0.007876, 0.057718], [8.159199, -0.033272, 0.007876, 0.059298], [8.168512, -0.032198, 0.007945, 0.059157], [8.177076, -0.026204, 0.007940, 0.058345], [8.187094, -0.019458, 0.008032, 0.057956], [8.197282, -0.015729, 0.008171, 0.058494], [8.193424, -0.013887, 0.007551, 0.058849], [8.195445, -0.009036, 0.007189, 0.057355], [8.219129, -0.001151, 0.007994, 0.055918], [8.228193, -0.002529, 0.008171, 0.058480], [8.238694, -0.001321, 0.008265, 0.057875], [8.239265, -0.001575, 0.007876, 0.058242], [8.238615, 0.000002, 0.007380, 0.057294], [8.247042, -0.002314, 0.007465, 0.057928], [8.250763, -0.004172, 0.007278, 0.058161], [8.259723, -0.008894, 0.007418, 0.059249], [8.251776, -0.026916, 0.006833, 0.064114], [8.255284, -0.030182, 0.006553, 0.061881], [8.266278, -0.021287, 0.006670, 0.059379], [8.278996, -0.020444, 0.007088, 0.061459], [8.276100, -0.021727, 0.006610, 0.062542], [8.280788, -0.021201, 0.006491, 0.062160], [8.278326, -0.034755, 0.006232, 0.066766], [8.274878, -0.043742, 0.005752, 0.067439], [8.284140, -0.049018, 0.005975, 0.068240], [8.284696, -0.054013, 0.005779, 0.070185], [8.295259, -0.063191, 0.006173, 0.073204], [8.294049, -0.055644, 0.005677, 0.070929], [8.312751, -0.047486, 0.006364, 0.070890], [8.314987, -0.034935, 0.006106, 0.070042], [8.319216, -0.022145, 0.005948, 0.068793], [8.328130, -0.011952, 0.006079, 0.068246], [8.335603, -0.006186, 0.006168, 0.068566], [8.342256, -0.007448, 0.006264, 0.070071], [8.347204, -0.005746, 0.006165, 0.069450], [8.352469, -0.004453, 0.006117, 0.069428], [8.361097, -0.005294, 0.006276, 0.069985], [8.371490, -0.003029, 0.006466, 0.069408], [8.374839, -0.000708, 0.006297, 0.069321], [8.387558, -0.000360, 0.006647, 0.069525], [8.389888, -0.003327, 0.006475, 0.070742], [8.392638, -0.000419, 0.006204, 0.069151], [8.393948, 0.001552, 0.005933, 0.068889], [8.398118, 0.004786, 0.005795, 0.067943], [8.405206, 0.010021, 0.005807, 0.066720], [8.411466, 0.013458, 0.005815, 0.066388], [8.423676, 0.015664, 0.006137, 0.066035], [8.429154, 0.016608, 0.006101, 0.066025], [8.436810, 0.019528, 0.006129, 0.064861], [8.443949, 0.018683, 0.006201, 0.065261], [8.452078, 0.020055, 0.006258, 0.064296], [8.458518, 0.021513, 0.006241, 0.063727], [8.464632, 0.019831, 0.006247, 0.063995], [8.466064, 0.018399, 0.005975, 0.063618], [8.472230, 0.015884, 0.005980, 0.063519], [8.479638, 0.017005, 0.006004, 0.062420], [8.484587, 0.015887, 0.005959, 0.062648], [8.489326, 0.008990, 0.005964, 0.064131], [8.488979, 0.001295, 0.005670, 0.064976], [8.490673, -0.005590, 0.005482, 0.065457], [8.497926, -0.007508, 0.005549, 0.064894], [8.500109, -0.007229, 0.005365, 0.064766], [8.503909, -0.010844, 0.005337, 0.065932], [8.514619, -0.013860, 0.005646, 0.066461], [8.522892, -0.016254, 0.005824, 0.067295], [8.530933, -0.015642, 0.005937, 0.067215], [8.539466, -0.010206, 0.006025, 0.066154], [8.539379, -0.007238, 0.005717, 0.066474], [8.544783, -0.006729, 0.005709, 0.066661], [8.547336, -0.002645, 0.005492, 0.065594], [8.559110, 0.000759, 0.005808, 0.065240], [8.567654, 0.000441, 0.005997, 0.066197], [8.571449, 0.006669, 0.005791, 0.064272], [8.578487, 0.009537, 0.005855, 0.064241], [8.584874, 0.015520, 0.005811, 0.062693], [8.592063, 0.014989, 0.005925, 0.063559], [8.598175, 0.012108, 0.005956, 0.064012], [8.608197, 0.012383, 0.006133, 0.063200] ] } """ Kim and Nelson's (1989) time-varying parameters model of monetary growth See http://econ.korea.ac.kr/~cjkim/MARKOV/prgmlist.htm#chapter3 Gauss Code: TVP.OPT Datasets: TVP.PRN """ tvp = { 'data': [ [59.300000, 0.751356, 0.226667, 0.191755, 0.103000, 0.828304], [59.400000, -0.869262, 0.540000, 0.496848, 0.044000, 0.751356], [60.100000, -0.259896, 0.690000, 0.608136, 0.058000, -0.869262], [60.200000, -0.165737, -0.356667, 0.113615, 0.188000, -0.259896], [60.300000, 0.943401, -0.880000, 0.603775, 0.126000, -0.165737], [60.400000, -0.046962, -0.633333, 0.037615, 0.087000, 0.943401], [61.100000, 0.538708, -0.053333, 0.637303, 0.096000, -0.046962], [61.200000, 0.767892, 0.043333, 0.223964, -0.004000, 0.538708], [61.300000, 0.600882, -0.046667, -0.037292, -0.043000, 0.767892], [61.400000, 0.940261, 0.000000, 0.409455, -0.034000, 0.600882], [62.100000, 0.637094, 0.156667, 0.111379, -0.059000, 0.940261], [62.200000, 0.700645, 0.263333, 0.407333, -0.201000, 0.637094], [62.300000, -0.112678, -0.010000, 0.368868, -0.169000, 0.700645], [62.400000, 0.562120, 0.126667, 0.257401, -0.145000, -0.112678], [63.100000, 1.026110, -0.026667, 0.256739, -0.122000, 0.562120], [63.200000, 0.949756, 0.093333, 0.329128, 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-0.8648, -0.0457], [1.4448, -0.4179, -0.3688, -0.7584, -0.0026], [1.4450, -0.4180, -0.3791, -0.7575, -0.0023], [1.4060, -0.4274, -0.5805, -0.6579, 0.0065], [1.3527, -0.4308, -0.7075, -0.5849, 0.0222], [1.3832, -0.4496, -0.6074, -0.6392, 0.0158], [1.4081, -0.4536, -0.3465, -0.6110, 0.0586], [1.2291, -0.4531, 0.1552, -0.7252, 0.0818] ] } """ Real GDP, 1947:1 - 2014:1 See http://research.stlouisfed.org/fred2/series/GDPC1 Stata Code: test_kalman_filter_gdp.do R Code: test_kalman_filter_gdp.R """ gdp = { 'stata_params': [ 0.40725515, 0.18782621, -0.01514009, -0.01027267, -0.03642297, 0.11576416, 0.02573029, -.00766572, 0.13506498, 0.08649569, 0.06942822, -0.10685783, 0.00008 ], 'stata_loglike': 883.1262237746861 } 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See also Stata time series documentation. Data from: https://www.stata-press.com/data/r12/wpi1 https://www.stata-press.com/data/r12/air2 https://www.stata-press.com/data/r12/friedman2 Author: Chad Fulton License: Simplified-BSD """ wpi1_data = [ 30.70000076, 30.79999924, 30.70000076, 30.70000076, 30.79999924, 30.5, 30.5, 30.60000038, 30.70000076, 30.60000038, 30.70000076, 30.70000076, 30.60000038, 30.5, 30.60000038, 30.70000076, 30.70000076, 30.60000038, 30.70000076, 30.70000076, 30.89999962, 31.20000076, 31.39999962, 31.60000038, 32.09999847, 32.20000076, 32.59999847, 32.40000153, 32.29999924, 32.29999924, 32.40000153, 32.5, 32.90000153, 33.09999847, 33.29999924, 33.40000153, 33.90000153, 34.40000153, 34.70000076, 35., 35.5, 35.70000076, 35.90000153, 35.90000153, 36.5, 36.90000153, 37.20000076, 37.20000076, 37.90000153, 38.29999924, 38.79999924, 39.20000076, 41.09999847, 43.09999847, 44.90000153, 45.29999924, 48.29999924, 50., 53.59999847, 55.40000153, 55.40000153, 56., 57.20000076, 57.79999924, 58.09999847, 59., 59.70000076, 60.20000076, 61.59999847, 63., 63.09999847, 63.90000153, 65.40000153, 67.40000153, 68.40000153, 70., 72.5, 75.09999847, 77.40000153, 80.19999695, 83.90000153, 85.59999847, 88.40000153, 90.40000153, 93.09999847, 95.19999695, 95.90000153, 95.80000305, 96.59999847, 96.69999695, 97.09999847, 97.19999695, 97.30000305, 97.59999847, 98.59999847, 99.09999847, 100.19999695, 100.80000305, 100.59999847, 100.30000305, 100.09999847, 100.19999695, 99.5, 100.09999847, 98.59999847, 96.80000305, 96.30000305, 96.69999695, 97.80000305, 99.40000153, 100.5, 101., 101.59999847, 103.19999695, 104.69999695, 105.19999695, 107.5, 109.40000153, 109., 109.40000153, 111., 110.80000305, 112.80000305, 116.19999695 ] wpi1_ar3 = { 'data': wpi1_data, 'params_ar': [.52707154, .09526127, .25803547], 'se_ar': [.09031296, .10143699, .09271067], 'params_ma': [], 'se_ma': [], 'params_mean': [], 'se_mean': [], 'params_variance': [.53074593], 'se_variance': [.067705], 'loglike': -136.21782, 'aic': 280.43565, 'bic': 291.68438, } wpi1_stationary = { 'data': wpi1_data, 'params_ar': [.8742288], 'se_ar_opg': [.0545435], 'se_ar_oim': [.0637705], 'se_ar_robust': [.0811246], 'params_ma': [-.4120458], 'se_ma_opg': [.1000284], 'se_ma_oim': [.1220756], 'se_ma_robust': [.1503862], 'params_mean': [.7498197], 'se_mean': [.3340968], 'se_mean_oim': [.2920992], 'params_variance': [.7250436**2], 'se_stddev_opg': [.0368065], 'se_stddev_oim': [.0462345], 'loglike': -135.35131, 'aic': 278.7026, 'bic': 289.9514, } wpi1_diffuse = { 'data': wpi1_data, 'initial_variance': 1e9, 'params_ar': [.864419], 'se_ar_opg': [.0563637], 'se_ar_oim': [.0716638], 'params_ma': [-.3960891], 'se_ma_opg': [.1018369], 'se_ma_oim': [.1384683], 'params_mean': [.8412064], 'se_mean_opg': [.3159328], 'se_mean_oim': [.3052621], 'params_variance': [.7282775**2], 'se_stddev_opg': [.0373227], 'se_stddev_oim': [.0468532], 'loglike': -154.29177, 'aic': 316.5835, 'bic': 327.8323, } wpi1_seasonal = { 'data': wpi1_data, 'params_ar': [.7806991], 'se_ar_opg': [.0944946], 'se_ar_oim': [.0811792], 'params_ma': [-.3990039, .3090813], 'se_ma_opg': [.1258753, .1200945], 'se_ma_oim': [.1058495, .1054576], 'params_mean': [.0110493], 'se_mean_opg': [.0048349], 'se_mean_oim': [.0037734], 'params_variance': [.0104394**2], 'se_stddev_opg': [.0004702], 'se_stddev_oim': [.0006658], 'loglike': 386.03357, 'aic': -762.0671, 'bic': -748.0062, } air2_data = [ 112, 118, 132, 129, 121, 135, 148, 148, 136, 119, 104, 118, 115, 126, 141, 135, 125, 149, 170, 170, 158, 133, 114, 140, 145, 150, 178, 163, 172, 178, 199, 199, 184, 162, 146, 166, 171, 180, 193, 181, 183, 218, 230, 242, 209, 191, 172, 194, 196, 196, 236, 235, 229, 243, 264, 272, 237, 211, 180, 201, 204, 188, 235, 227, 234, 264, 302, 293, 259, 229, 203, 229, 242, 233, 267, 269, 270, 315, 364, 347, 312, 274, 237, 278, 284, 277, 317, 313, 318, 374, 413, 405, 355, 306, 271, 306, 315, 301, 356, 348, 355, 422, 465, 467, 404, 347, 305, 336, 340, 318, 362, 348, 363, 435, 491, 505, 404, 359, 310, 337, 360, 342, 406, 396, 420, 472, 548, 559, 463, 407, 362, 405, 417, 391, 419, 461, 472, 535, 622, 606, 508, 461, 390, 432 ] air2_stationary = { 'data': air2_data, 'params_ma': [-.4018324], 'se_ma_opg': [.0730307], 'se_ma_oim': [.0896442], 'params_seasonal_ma': [-.5569342], 'se_seasonal_ma_opg': [.0963129], 'se_seasonal_ma_oim': [.0731055], 'params_variance': [.0367167**2], 'se_stddev_opg': [.0020132], 'se_stddev_oim': [.002277], 'loglike': 244.69651, 'aic': -483.393, 'bic': -474.7674, } friedman2_data = {'consump': [ 310.3999939, 316.3999939, 321.70001221, 323.79998779, 327.29998779, 333.20001221, 333.1000061, 335., 335.70001221, 340.6000061, 343.5, 350.70001221, 355.29998779, 361.29998779, 365.3999939, 371.70001221, 375.1000061, 379.3999939, 386.3999939, 391.1000061, 400.5, 408.29998779, 417.1000061, 419.79998779, 430.6000061, 437.79998779, 447.20001221, 461.5, 472., 477.1000061, 486.3999939, 492., 496.79998779, 506.20001221, 513.70001221, 521.20001221, 539.5, 553.20001221, 569.09997559, 577.5, 588.79998779, 599.40002441, 609.20001221, 621.09997559, 632.40002441, 642.70001221, 655.20001221, 662.09997559, 681.59997559, 695.79998779, 708.20001221, 724.5, 741.90002441, 759.90002441, 778.09997559, 802.90002441, 827.20001221, 842.09997559, 860.79998779, 876.09997559, 894.40002441, 922.40002441, 950.09997559, 957.79998779, 982.70001221, 1012.40002441, 1046.30004883, 1075.09997559, 1110.19995117, 1130.19995117, 1159.80004883, 1195., 1230.69995117, 1259.09997559, 1290.30004883, 1328.09997559, 1358.30004883, 1417.40002441, 1450.59997559, 1488.69995117, 1529.30004883, 1563.90002441, 1617.40002441, 1663.5, 1713.09997559, 1716.90002441, 1774.90002441, 1836.80004883, 1890.30004883, 1923.5, 1967.40002441, 1983.90002441 ], 'm2': [ 289.1499939, 294.04998779, 296.73001099, 297.79998779, 299.3500061, 302.32998657, 308.45001221, 312.36999512, 318.29000854, 324.29000854, 329.54000854, 335.5, 343.1000061, 349.25, 354.86999512, 362.72000122, 370.66000366, 378.42001343, 386.01998901, 393.23999023, 399.76000977, 407.07998657, 416.88000488, 424.73999023, 433.22000122, 440.1000061, 449.48999023, 459.17001343, 467.22000122, 471.1499939, 475.42999268, 480.16000366, 489.67001343, 502., 514.65997314, 524.77001953, 533.16998291, 542.60998535, 553.55999756, 566.84997559, 574.35998535, 578.4699707, 582.05999756, 587.90002441, 587.26000977, 595.15997314, 611.20001221, 626.54998779, 649.90002441, 672.96002197, 692.4699707, 710.26000977, 733.5, 749.66998291, 778.35998535, 802.2800293, 815.30999756, 833.22998047, 839.27001953, 855.52001953, 870.11999512, 877.82000732, 888.15997314, 902.41998291, 925.55999756, 963.30999756, 991.7199707, 1016.98999023, 1050.0300293, 1077.70996094, 1111.31005859, 1152.7800293, 1188.80004883, 1217.67004395, 1246.90002441, 1271.4699707, 1292.86999512, 1318.09997559, 1346.81005859, 1368.01000977, 1388.9699707, 1423.2199707, 1456.85998535, 1475.75, 1501.81994629, 1529.52001953, 1576.0300293, 1601.09997559, 1638., 1670.55004883, 1708.38000488, 1756.18994141 ]} friedman2_mle = { 'data': friedman2_data, 'params_exog': [-36.09872, 1.122029], 'se_exog_opg': [56.56703, .0363563], 'se_exog_oim': [33.95924, .0324069], 'params_ar': [.9348486], 'se_ar_opg': [.0411323], 'se_ar_oim': [.039903], 'params_ma': [.3090592], 'se_ma_opg': [.0885883], 'se_ma_oim': [.1125186], 'params_variance': [9.655308**2], 'se_stddev_opg': [.5635157], 'se_stddev_oim': [.7122745], 'loglike': -340.50774, 'aic': 691.0155, 'bic': 703.6244, } # 1959q1 - 1981q4 friedman2_prediction = [ 300.7722, 314.699, 318.3328, 322.1395, 324.1479, 329.3138, 338.3326, 334.2127, 340.1221, 340.1285, 345.7686, 348.9585, 358.8476, 360.8798, 367.4761, 373.4112, 380.132, 383.0179, 388.0034, 395.276, 398.8789, 410.393, 419.7131, 426.5234, 429.3965, 440.4875, 449.2072, 459.1391, 472.4367, 477.6227, 482.9371, 493.2135, 502.3943, 509.5284, 520.3149, 524.9484, 531.8344, 553.2029, 565.8674, 584.5371, 584.7531, 595.1661, 604.5025, 616.0223, 620.5868, 641.1515, 656.7986, 668.2184, 683.2755, 704.2855, 714.1062, 726.3972, 749.7296, 758.9711, 792.2435, 802.7343, 820.1996, 850.1489, 849.0018, 882.2756, 891.0745, 904.4603, 936.7991, 965.2041, 977.2533, 1020.77, 1038.109, 1072.798, 1107.716, 1137.204, 1161.788, 1201.592, 1230.821, 1261.099, 1289.544, 1316.565, 1352.555, 1384.148, 1450.45, 1466.267, 1508.321, 1560.003, 1589.353, 1631.959, 1683.234, 1731.301, 1745.414, 1792.131, 1866.122, 1907.568, 1944.034, 1999.784 ] # 1959q1 - 1981q4 # Dynamic after 1978q1 friedman2_dynamic_prediction = [ 300.7722, 314.699, 318.3328, 322.1395, 324.1479, 329.3138, 338.3326, 334.2127, 340.1221, 340.1285, 345.7686, 348.9585, 358.8476, 360.8798, 367.4761, 373.4112, 380.132, 383.0179, 388.0034, 395.276, 398.8789, 410.393, 419.7131, 426.5234, 429.3965, 440.4875, 449.2072, 459.1391, 472.4367, 477.6227, 482.9371, 493.2135, 502.3943, 509.5284, 520.3149, 524.9484, 531.8344, 553.2029, 565.8674, 584.5371, 584.7531, 595.1661, 604.5025, 616.0223, 620.5868, 641.1515, 656.7986, 668.2184, 683.2755, 704.2855, 714.1062, 726.3972, 749.7296, 758.9711, 792.2435, 802.7343, 820.1996, 850.1489, 849.0018, 882.2756, 891.0745, 904.4603, 936.7991, 965.2041, 977.2533, 1020.77, 1038.109, 1072.798, 1107.716, 1137.204, 1161.788, 1201.592, 1230.821, 1261.099, 1289.544, 1316.565, 1352.555, 1377.515, 1406.237, 1427.295, 1448.221, 1483.042, 1517.318, 1536.364, 1562.931, 1591.249, 1639.144, 1664.832, 1702.839, 1736.367, 1775.407, 1824.832 ] # 1959q1 - 1981q4 # Forecasts after 1978q1 friedman2_forecast = [ 300.7722, 314.699, 318.3328, 322.1395, 324.1479, 329.3138, 338.3326, 334.2127, 340.1221, 340.1285, 345.7686, 348.9585, 358.8476, 360.8798, 367.4761, 373.4112, 380.132, 383.0179, 388.0034, 395.276, 398.8789, 410.393, 419.7131, 426.5234, 429.3965, 440.4875, 449.2072, 459.1391, 472.4367, 477.6227, 482.9371, 493.2135, 502.3943, 509.5284, 520.3149, 524.9484, 531.8344, 553.2029, 565.8674, 584.5371, 584.7531, 595.1661, 604.5025, 616.0223, 620.5868, 641.1515, 656.7986, 668.2184, 683.2755, 704.2855, 714.1062, 726.3972, 749.7296, 758.9711, 792.2435, 802.7343, 820.1996, 850.1489, 849.0018, 882.2756, 891.0745, 904.4603, 936.7991, 965.2041, 977.2533, 1020.77, 1038.109, 1072.798, 1107.716, 1137.204, 1161.788, 1201.592, 1230.821, 1261.099, 1289.544, 1316.565, 1352.555, 1384.148, 1412.057, 1432.403, 1452.703, 1486.975, 1520.77, 1539.393, 1565.588, 1593.582, 1641.19, 1666.628, 1704.415, 1737.75, 1776.62, 1825.897 ] # 1959q1 - 1981q4 # Forecasts after 1978q1 (and dynamic) # This (the dynamic part) is not necessarily a sensible thing to do, but this # is just a unit test friedman2_dynamic_forecast = [ 300.7722, 314.699, 318.3328, 322.1395, 324.1479, 329.3138, 338.3326, 334.2127, 340.1221, 340.1285, 345.7686, 348.9585, 358.8476, 360.8798, 367.4761, 373.4112, 380.132, 383.0179, 388.0034, 395.276, 398.8789, 410.393, 419.7131, 426.5234, 429.3965, 440.4875, 449.2072, 459.1391, 472.4367, 477.6227, 482.9371, 493.2135, 502.3943, 509.5284, 520.3149, 524.9484, 531.8344, 553.2029, 565.8674, 584.5371, 584.7531, 595.1661, 604.5025, 616.0223, 620.5868, 641.1515, 656.7986, 668.2184, 683.2755, 704.2855, 714.1062, 726.3972, 749.7296, 758.9711, 792.2435, 802.7343, 820.1996, 850.1489, 849.0018, 882.2756, 891.0745, 904.4603, 936.7991, 965.2041, 977.2533, 1020.77, 1038.109, 1072.798, 1107.716, 1137.204, 1161.788, 1201.592, 1230.821, 1261.099, 1289.544, 1316.565, 1352.555, 1377.515, 1406.237, 1427.295, 1448.221, 1483.042, 1517.318, 1536.364, 1562.931, 1591.249, 1639.144, 1664.832, 1702.839, 1736.367, 1775.407, 1824.832 ] friedman2_predict = { 'data': friedman2_data, 'predict': friedman2_prediction, 'dynamic_predict': friedman2_dynamic_prediction, 'forecast': friedman2_forecast, 'dynamic_forecast': friedman2_dynamic_forecast, 'params_exog': [.66189, 1.037905], 'params_ar': [.8775207], 'params_ma': [.2770867], 'params_variance': [5.630046**2], 'loglike': -243.31642, 'aic': 496.6328, 'bic': 508.3519, } statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/results_sarimax_coverage.csv000066400000000000000000000141731400612667500321200ustar00rootroot00000000000000mod,llf,parameters "arima wpi, arima(3,0,0) noconstant vce(oim)",-145.917,"1.600047,-.3624836,-.2377553,.7515501" "arima wpi c, arima(3,0,0) noconstant vce(oim)",-145.1327,"78.60683,1.599097,-.3606729,-.2392393,.7511453" "arima wpi c t, arima(3,0,0) noconstant vce(oim)",-139.5423,"19.46176,.768438,1.528349,-.3448674,-.1935674,.7281097" "arima wpi c t3, arima(3,0,0) noconstant vce(oim)",-138.9533,"38.71439,.0000445,1.530887,-.3313616,-.2082853,.7239346" "arima wpi, arima(3,2,0) noconstant vce(oim)",-135.9354,"-.4536069,-.3408174,-.0977653,.7363397" "arima wpi, arima(3,0,0) sarima(0,2,0,4) noconstant vce(oim)",-194.9269,"1.179762,-.3453264,-.0898734,1.289575" "arima wpi, arima(3,0,0) noconstant vce(oim) diffuse",-159.3091,"1.641477,-.6359852,-.0014474,.7450104" "arima wpi x, arima(3,0,0) noconstant vce(oim)",-145.7514,".0806147,1.610143,-.382758,-.2275756,.7505294" "arima wpi, arima(0,0,3) noconstant vce(oim)",-540.8154,"-505.7114,-970.6211,-507.9258,.0357879" "arima wpi c, arima(0,0,3) noconstant vce(oim)",-379.8598,"62.99608,2.451664,2.39358,.8955524,4.920951" "arima wpi c t, arima(0,0,3) noconstant vce(oim)",-254.3036,"13.00193,.7996427,2.084224,2.038812,.8249226,1.800869" "arima wpi c t3, arima(0,0,3) noconstant vce(oim)",-278.1551,"38.14465,.0000501,2.115914,2.078889,.8569969,2.181463" "arima wpi, arima(0,2,3) noconstant vce(oim)",-136.14,"-.4584812,-.1298735,.0632101,.7375874" "arima wpi, arima(0,0,3) sarima(0,2,0,4) noconstant vce(oim)",-171.4663,"1.094744,1.094739,1.000001,-1.008989" "arima wpi, arima(0,0,3) noconstant vce(oim) diffuse",-587.4832,"-27.57705,-55.33257,-29.37171,.6453013" "arima wpi x, arima(0,0,3) noconstant vce(oim)",-476.4098,".9280385,2.378931,2.378931,.9999992,10.62952" "arima wpi, arima(3,0,3) noconstant vce(oim)",-142.1485,".9500802,.9998841,-.9501915,.6116305,-.5273701,-.1392938,.7241816" "arima wpi c, arima(3,0,2) noconstant vce(oim)",-141.6737,"80.5513,1.678086,-.4215884,-.2572052,-.1579189,-.2332231,.7297933" "arima wpi c t, arima(3,0,2) noconstant vce(oim)",-136.6645,"16.39083,.7941504,1.635404,-.3962173,-.2480547,-.1668943,-.2374508,.7109324" "arima wpi c t3, arima(3,0,2) noconstant vce(oim)",-135.8174,"37.6362,.0000484,1.6636,-.4328509,-.2383885,-.1989134,-.2353735,.7052346" "arima wpi, arima(3,2,2) noconstant vce(oim)",-134.3081,".6015591,.0150202,.2054096,-1.094043,.1107661,.7241633" "arima wpi, arima(3,0,2) sarima(0,2,0,4) noconstant vce(oim)",-179.129,"1.211058,-.7514844,.1956546,-.1231004,1,1.088146" "arima wpi, arima(3,2,2) sarima(0,2,0,4) noconstant vce(oim)",-190.8858,"-.3645584,.1081667,.1720293,9.66e-08,-1.000001,1.247552" "arima wpi, arima(3,0,2) noconstant vce(oim) diffuse",-155.478,"2.261425,-1.605342,.3449455,-.7905483,.1561876,.7256975" "arima wpi x, arima(3,0,2) noconstant vce(oim)",-142.1656,".1367752,1.632881,-.3357823,-.2972526,-.0898929,-.2674371,.7281773" "arima wpi, sarima(3,0,0,4) noconstant vce(oim)",-302.9966,"1.950329,-1.151533,.199516,2.442114" "arima wpi c, sarima(3,0,0,4) noconstant vce(oim)",-299.2088,"71.28411,1.937048,-1.128636,.182796,2.42974" "arima wpi c t, sarima(3,0,0,4) noconstant vce(oim)",-279.8638,"19.09781,.7348265,1.728363,-1.005377,.1971021,2.181769" "arima wpi c t3, sarima(3,0,0,4) noconstant vce(oim)",-284.7776,"40.37701,.0000402,1.771423,-.9909791,.1655766,2.250117" "arima wpi, arima(0,2,0) sarima(3,0,0,4) noconstant vce(oim)",-146.5967,".1093829,-.0753548,-.0933771,.8039928" "arima wpi, sarima(3,2,0,4) noconstant vce(oim)",-268.6161,".0712682,-.3369143,-.1180569,2.438388" "arima wpi, sarima(3,0,0,4) noconstant vce(oim) diffuse",-355.6312,"1.625832,-.61329,.0032626,2.456462" "arima wpi x, sarima(3,0,0,4) noconstant vce(oim)",-302.6354,"-.3005221,1.955475,-1.161604,.2044588,2.434233" "arima wpi, sarima(0,0,3,4) noconstant vce(oim)",-493.3605,"2.612943,2.61295,1.000004,10.63571" "arima wpi c, sarima(0,0,3,4) noconstant vce(oim)",-407.9579,"63.18759,2.716964,2.792693,1.128853,4.888196" "arima wpi c t, sarima(0,0,3,4) noconstant vce(oim)",-302.5591,"15.22961,.7746883,1.741946,1.4764,.6085909,2.620034" "arima wpi c t3, sarima(0,0,3,4) noconstant vce(oim)",-320.6151,"38.83094,.0000473,1.806445,1.633288,.7156993,2.992223" "arima wpi, arima(0,2,0) sarima(0,0,3,4) noconstant vce(oim)",-146.6127,".1181947,-.0550111,-.0974394,.8041813" "arima wpi, sarima(0,2,3,4) noconstant vce(oim)",-265.4803,"-.0022288,-.4547194,-.265093,2.352103" "arima wpi, sarima(0,0,3,4) noconstant vce(oim) diffuse",-594.3781,"2.523607,2.442817,.9009514,11.65001" "arima wpi x, sarima(0,0,3,4) noconstant vce(oim)",-493.3495,"-.07391,2.613046,2.613045,.9999989,10.63459" "arima wpi, sarima(3,0,2,4) noconstant vce(oim)",-298.2331,"2.290215,-1.620824,.3299609,1.239569,-1.690899,1.134022" "arima wpi c, sarima(3,0,2,4) noconstant vce(oim)",-297.3261,"71.09661,.8739118,.628973,-.5235254,3.822714,3.279209,.7281108" "arima wpi c t, sarima(3,0,2,4) noconstant vce(oim)",-277.6305,"18.52915,.7413986,.0106101,1.414883,-.6965621,1.775,.5448672,2.144826" "arima wpi c t3, sarima(3,0,2,4) noconstant vce(oim)",-274.1764,"39.50053,.000046,2.077418,-1.276982,.161876,-.487932,-.5120805,1.979523" "arima wpi, arima(0,2,0) sarima(3,0,2,4) noconstant vce(oim)",-144.272,"-1.510547,-.6593249,-.0585331,1.688265,.8242572,.780077" "arima wpi, sarima(3,2,2,4) noconstant vce(oim)",-265.2458,".963946,-.4554486,.1971574,-1.021818,.0216137,2.297261" "arima wpi, arima(0,2,0) sarima(3,2,2,4) noconstant vce(oim)",-166.3303,"-1.501011,-.7561807,-.2807991,.0000117,-.9999927,.9676953" "arima wpi, sarima(3,0,2,4) noconstant vce(oim) diffuse",-332.4084,"1.138662,-.1033737,-3.58e-08,.5722654,-.0668218,2.400033" "arima wpi x, sarima(3,0,2,4) noconstant vce(oim)",-300.3242,"-.3366271,1.468002,-.3188579,-.1517738,20.52264,36.0693,.0660329" "arima wpi 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0,0,0,0,-35.4580266729815,34.6874251999763,-85.3219999999974,2.28291641671433,124.295026672981,65.6635991477521,47.8366898577711,1.20692174722728,1.93376415332416,2.23304463594,60.8306117223583,0.657100689253895,-74.9594103438512,2.28291641671433,60.8306117223583,0.657100689253905,-74.9594103438512,-2.10089315196376e-18,60.8306117223583,0.657100689253905,-74.9594103438512,0.0196605678274483,0,0,0,1,28.0063882776412,2.32829753328047,0,0.0669217472272777,0.0367896959894586,0 statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/results_structural.py000066400000000000000000000223751400612667500306510ustar00rootroot00000000000000""" Results for structural tests Results from R, KFAS library using script `test_ucm.R`. See also Stata time series documentation. Author: Chad Fulton License: Simplified-BSD """ from numpy import pi LOG2PI = 0.9189385332046727 irregular = { 'models': [ {'irregular': True}, {'level': 'irregular'}, {'level': 'ntrend'}, ], 'params': [36.74687342], 'start_params': [30], 'llf': -653.8562525, 'kwargs': {} } # this model will issue a warning that there is no stochastic component, and # will then add an irregular component. Thus it's output will be just like # the "deterministic constant" model. fixed_intercept = { 'models': [ {'level': True}, {'level': 'fixed intercept'}, ], 'params': [2.127438969], 'start_params': [1.], 'llf': -365.5289923, 'kwargs': {} } deterministic_constant = { 'models': [ {'irregular': True, 'level': True}, {'level': 'deterministic constant'}, {'level': 'dconstant'}, ], 'params': [2.127438969], 'start_params': [1.], 'llf': -365.5289923, 'kwargs': {} } local_level = { 'models': [ {'irregular': True, 'level': True, 'stochastic_level': True}, {'level': 'local level'}, {'level': 'llevel'} ], 'params': [4.256647886e-06, 1.182078808e-01], 'start_params': [1e-4, 1e-2], 'llf': -70.97242557, 'kwargs': {} } random_walk = { 'models': [ {'level': True, 'stochastic_level': True}, {'level': 'random walk'}, {'level': 'rwalk'}, ], 'params': [0.1182174646], 'start_params': [0.5], 'llf': -70.96771641, 'kwargs': {} } # this model will issue a warning that there is no stochastic component, and # will then add an irregular component. Thus it's output will be just like # the "deterministic trend" model. fixed_slope = { 'models': [ {'level': True, 'trend': True}, {'level': 'fixed slope'}, ], 'params': [2.134137554], 'start_params': [1.], 'llf': -370.7758666, 'kwargs': {} } deterministic_trend = { 'models': [ {'irregular': True, 'level': True, 'trend': True}, {'level': 'deterministic trend'}, {'level': 'dtrend'}, ], 'params': [2.134137554], 'start_params': [1.], 'llf': -370.7758666, 'kwargs': {} } local_linear_deterministic_trend = { 'models': [ {'irregular': True, 'level': True, 'stochastic_level': True, 'trend': True}, {'level': 'local linear deterministic trend'}, {'level': 'lldtrend'}, ], 'params': [4.457592057e-06, 1.184455029e-01], 'start_params': [1e-5, 1e-2], 'llf': -73.47291031, 'kwargs': {} } random_walk_with_drift = { 'models': [ {'level': True, 'stochastic_level': True, 'trend': True}, {'level': 'random walk with drift'}, {'level': 'rwdrift'}, ], 'params': [0.1184499547], 'start_params': [0.5], 'llf': -73.46798576, 'kwargs': {} } local_linear_trend = { 'models': [ {'irregular': True, 'level': True, 'stochastic_level': True, 'trend': True, 'stochastic_trend': True}, {'level': 'local linear trend'}, {'level': 'lltrend'} ], 'params': [1.339852549e-06, 1.008704925e-02, 6.091760810e-02], 'start_params': [1e-5, 1e-4, 1e-4], 'llf': -31.15640107, 'kwargs': {} } smooth_trend = { 'models': [ {'irregular': True, 'level': True, 'trend': True, 'stochastic_trend': True}, {'level': 'smooth trend'}, {'level': 'strend'}, ], 'params': [0.0008824099119, 0.0753064234342], 'start_params': [1e-2, 1e-2], 'llf': -31.92261408, 'kwargs': {} } random_trend = { 'models': [ {'level': True, 'trend': True, 'stochastic_trend': True}, {'level': 'random trend'}, {'level': 'rtrend'}, ], 'params': [0.08054724989], 'start_params': [1e-2], 'llf': -32.05607557, 'kwargs': {} } cycle = { 'models': [{'irregular': True, 'cycle': True, 'stochastic_cycle': True, 'damped_cycle': True}], 'params': [37.57197079, 0.1, 2*pi/10, 1], 'start_params': [30, 0.001, 2*pi/20, 0.5], 'llf': -656.6568684, 'kwargs': {} } cycle_approx_diffuse = cycle.copy() cycle_approx_diffuse.update({ 'params': [37.57197224, 0.1, 2*pi/10, 1], 'llf': -672.3102588, 'kwargs': {'loglikelihood_burn': 0}}) seasonal = { 'models': [{'irregular': True, 'seasonal': 4}], 'params': [38.17043009, 0.1], 'start_params': [30, 0.001], 'llf': -655.3337155, 'kwargs': {}, 'rtol': 1e-6 } seasonal_approx_diffuse = seasonal.copy() seasonal_approx_diffuse.update({ 'params': [38.1704278, 0.1], 'llf': -678.8138005, 'kwargs': {'loglikelihood_burn': 0}}) freq_seasonal = { 'models': [{'irregular': True, 'freq_seasonal': [{'period': 5}]}], 'params': [38.95352534, 0.05], 'start_params': [30, 0.001], 'llf': -657.6629457, 'rtol': 1e-6, 'kwargs': {} } freq_seasonal_approx_diffuse = freq_seasonal.copy() freq_seasonal_approx_diffuse.update({ 'params': [38.95353592, 0.05], 'llf': -688.9697249, 'kwargs': {'loglikelihood_burn': 0}}) reg = { # Note: The test needs to fill in exog=np.log(dta['realgdp']) 'models': [ {'irregular': True, 'exog': True, 'mle_regression': False}, {'level': 'irregular', 'exog': True, 'mle_regression': False}, {'level': 'ntrend', 'exog': True, 'mle_regression': False}, {'level': 'ntrend', 'exog': 'numpy', 'mle_regression': False}, ], 'params': [2.215438082], 'start_params': [1.], 'llf': -371.7966543, 'kwargs': {} } reg_approx_diffuse = reg.copy() reg_approx_diffuse.update({ 'params': [2.215447924], 'llf': -379.6233483, 'kwargs': {'loglikelihood_burn': 0}}) rtrend_ar1 = { 'models': [ {'level': True, 'trend': True, 'stochastic_trend': True, 'autoregressive': 1}, {'level': 'random trend', 'autoregressive': 1}, {'level': 'rtrend', 'autoregressive': 1} ], 'params': [0.0609, 0.0097, 0.9592], 'start_params': [0.01, 0.001, 0.1], 'llf': -31.15629379, 'kwargs': {} } lltrend_cycle_seasonal_reg_ar1 = { # Note: The test needs to fill in exog=np.log(dta['realgdp']) 'models': [ # Complete specification {'irregular': True, 'level': True, 'stochastic_level': True, 'trend': True, 'stochastic_trend': True, 'cycle': True, 'stochastic_cycle': True, 'seasonal': 4, 'autoregressive': 1, 'exog': True, 'mle_regression': False}, ], 'params': [0.0001, 0.01, 0.06, 0.0001, 0.0001, 0.1, 2*pi / 10, 0.2], 'start_params': [0.0001, 0.01, 0.06, 0.0001, 0.0001, 0.1, 2*pi / 10, 0.2], 'llf': -105.8936568, 'kwargs': {}, # No need to try to find the maximum for this really weird model. 'maxiter': 5 } lltrend_cycle_seasonal_reg_ar1_approx_diffuse = { # Note: The test needs to fill in exog=np.log(dta['realgdp']) 'models': [ # Complete specification {'irregular': True, 'level': True, 'stochastic_level': True, 'trend': True, 'stochastic_trend': True, 'cycle': True, 'stochastic_cycle': True, 'seasonal': 4, 'autoregressive': 1, 'exog': True, 'mle_regression': False}, # Verbose string specification {'level': 'local linear trend', 'autoregressive': 1, 'cycle': True, 'stochastic_cycle': True, 'seasonal': 4, 'autoregressive': 1, 'exog': True, 'mle_regression': False}, # Abbreviated string specification {'level': 'lltrend', 'autoregressive': 1, 'cycle': True, 'stochastic_cycle': True, 'seasonal': 4, 'autoregressive': 1, 'exog': True, 'mle_regression': False}, # Numpy exog dataset {'level': 'lltrend', 'autoregressive': 1, 'cycle': True, 'stochastic_cycle': True, 'seasonal': 4, 'autoregressive': 1, 'exog': 'numpy', 'mle_regression': False}, # Annual frequency dataset {'level': 'lltrend', 'autoregressive': 1, 'cycle': True, 'stochastic_cycle': True, 'seasonal': 4, 'autoregressive': 1, 'exog': True, 'mle_regression': False, 'freq': 'AS'}, # Quarterly frequency dataset {'level': 'lltrend', 'autoregressive': 1, 'cycle': True, 'stochastic_cycle': True, 'seasonal': 4, 'autoregressive': 1, 'exog': True, 'mle_regression': False, 'freq': 'QS'}, # Monthly frequency dataset {'level': 'lltrend', 'autoregressive': 1, 'cycle': True, 'stochastic_cycle': True, 'seasonal': 4, 'autoregressive': 1, 'exog': True, 'mle_regression': False, 'freq': 'MS'}, # Minutely frequency dataset {'level': 'lltrend', 'autoregressive': 1, 'cycle': True, 'stochastic_cycle': True, 'seasonal': 4, 'autoregressive': 1, 'exog': True, 'mle_regression': False, 'freq': 'T', 'cycle_period_bounds': (1.5*12, 12*12)}, ], 'params': [0.0001, 0.01, 0.06, 0.0001, 0.0001, 0.1, 2*pi / 10, 0.2], 'start_params': [0.0001, 0.01, 0.06, 0.0001, 0.0001, 0.1, 2*pi / 10, 0.2], 'llf': -168.5258709, 'kwargs': { # Required due to the way KFAS estimated loglikelihood which P1inf is # set in the R code 'loglikelihood_burn': 0 }, # No need to try to find the maximum for this really weird model. 'maxiter': 5 } statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/results_var_R.py000066400000000000000000000127631400612667500275120ustar00rootroot00000000000000""" Results for VARMAX tests Results from R using script `test_var.R`. See also the packages "vars" and "MTS" Data from: https://www.stata-press.com/data/r14/lutkepohl2.dta Author: Chad Fulton License: Simplified-BSD """ res_basic = { 'llf': 596.164145004717, 'params': [-0.29883655890699, 0.0628044611244012, 0.659886869389918, -0.148082523252922, 0.0344024216201084, 0.626435414218001, 0.0243232147401712, -0.0743006500599362, 0.572632299564782, 0.0382739144340661, 0.0947818948355414, 0.280177703027101, -0.0184971989547667, 0.289109890254681, -0.0310399835571299, 0.0242429009692667, 0.416904807490799, 0.215822310109252, 0.0441917021237108, 0.000878653005437675, 0.0121587857077158, 0.00204049993421116, 0.0060703628735368, 0.00748745583771755] } res_c = { 'llf': 606.307040676657, 'params': [-0.016722145613102, 0.0157671932107926, 0.0129257858993457, -0.319631834481441, 0.145985129742841, 0.961228756482211, -0.160550841116343, 0.114600859415788, 0.934400111915348, 0.0439309334767638, -0.152731116093091, 0.288499158625839, 0.0500302034483248, 0.0191633532210331, -0.0102000393418508, -0.0024229889812185, 0.224813385583416, -0.263969465525517, 0.0338805880793048, 0.35491349008493, -0.0222264331018897, 0.0438795670052806, 0.00147561682483683, 0.0110449368419315, 0.00253927594913203, 0.00469160198527878, 0.00722432245241668] } res_ct = { 'llf': 607.438331754865, 'params': [ -0.0091687448890928, -0.000202696805258128, 0.0164700664012876, -0.0000188617227419232, 0.0116594765736253, 0.0000339816281660043, -0.33053195210291, 0.0991441034301294, 1.02497527768337, -0.168768113189076, 0.052065599978203, 1.01832964242176, 0.0429166353176552, -0.157089854999372, 0.294431019303797, 0.0492655544577624, 0.0133442051412007, -0.00239007148243754, -0.00059561067840422, 0.232666170125558, -0.274656415315255, 0.0352581938277472, 0.365397374775498, -0.0362970154881497, 0.043680752565187, 0.00144524803260901, 0.0110421281684084, 0.00261764677471134, 0.00471411575165134, 0.00714742282804776] } res_ct_as_exog0 = { 'llf': 607.438331754865, 'params': [ -0.33053195210291, 0.0991441034301291, 1.02497527768337, -0.168768113189076, 0.0520655999782025, 1.01832964242176, 0.0429166353176552, -0.157089854999372, 0.294431019303796, 0.0492655544577624, 0.0133442051412007, -0.00239007148243758, -0.000595610678404244, 0.232666170125558, -0.274656415315255, 0.0352581938277472, 0.365397374775498, -0.0362970154881497, -0.00937144169435092, -0.000202696805258128, 0.0164512046785456, -0.0000188617227419232, 0.0116934582017913, 0.0000339816281660044, 0.043680752565187, 0.00144524803260901, 0.0110421281684084, 0.00261764677471134, 0.00471411575165134, 0.00714742282804776] } res_ctt_as_exog1 = { 'llf': 609.490393107865, 'params': [ -0.337732421246314, 0.131516202959048, 1.02963148737009, -0.17420176313584, 0.0790611026384549, 1.0252507470967, 0.0465815476938576, -0.173566685306448, 0.29206109032178, 0.0520311868827124, -0.000396031756002358, -0.00591279224896053, 0.00084626300027174, 0.226183748313225, -0.275588808199104, 0.0363462669353941, 0.359991601352511, -0.0376829472183479, 0.00135916831998363, -0.00105584065752325, 0.0000109426769125814, 0.0111115434152017, 0.00041537351951475, -0.00000556963042921238, 0.00955129158661523, 0.000204821283222681, -0.00000219124025119403, 0.0434681194741622, 0.00166930018759676, 0.0107902800396133, 0.00271581816352387, 0.00457956681075423, 0.00714628937734587] } res_ct_exog = { 'llf': 608.068437908288, 'params': [ -0.00891774296871338, -0.000177588386858893, 0.0197390895235663, 0.000308147728766951, 0.0126534322433763, 0.000133409771140667, -0.330531447689365, 0.0984883875114303, 1.02556206489488, -0.168762569285516, 0.0515915213025295, 1.01893167456814, 0.0429232047476493, -0.165629831492911, 0.302073275424366, 0.0493377576859194, 0.00716985336647014, 0.00545073309741857, -0.000593613224747432, 0.230069566266306, -0.272332765858951, 0.035280147422236, 0.363520045761914, -0.0339129968146675, -0.00000107342140085188, -0.0000139801296102807, -0.00000425069770699759, 0.0436806162945145, 0.00144170298545239, 0.0109507769345455, 0.00261657568854817, 0.0046983621886579, 0.00714512825214436] } res_c_2exog = { 'llf': 609.051601848607, 'params': [ -0.0183154996756286, 0.0153812380370316, 0.0103369264061738, -0.337960592073415, 0.0503833175581312, 0.869221695835652, -0.177121478778926, -0.00828627855953333, 0.833693547676962, 0.0408338136200346, -0.168937622492442, 0.271586426539891, 0.0472115548647617, -0.00167581111974649, -0.0288652616238083, -0.00180977814169972, 0.226832537597882, -0.291808329427557, 0.0340137235903244, 0.357345372917494, -0.0561689416451492, -0.0000711052323565154, 0.000226083635596117, -0.0000123876692635146, 0.0000396928767974614, -0.00000605563782898125, 0.0000261698003981677, 0.0430020095866888, 0.00119895869898935, 0.0109748059062083, 0.00248803192377248, 0.00471772840157074, 0.00714511199868448] } 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statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/results_var_misc.py000066400000000000000000000130541400612667500302360ustar00rootroot00000000000000""" Results for VAR miscellaneous tests Results from Stata using script `test_var_misc_stata.do`. Data from: http://www.jmulti.de/download/datasets/e1.dat Author: Chad Fulton License: Simplified-BSD """ # See http://www.jmulti.de/download/datasets/e1.dat # 1960:Q1 - 1982Q4 lutkepohl_data = [ [180, 451, 415], [179, 465, 421], [185, 485, 434], [192, 493, 448], [211, 509, 459], [202, 520, 458], [207, 521, 479], [214, 540, 487], [231, 548, 497], [229, 558, 510], [234, 574, 516], [237, 583, 525], [206, 591, 529], [250, 599, 538], [259, 610, 546], [263, 627, 555], [264, 642, 574], [280, 653, 574], [282, 660, 586], [292, 694, 602], [286, 709, 617], [302, 734, 639], [304, 751, 653], [307, 763, 668], [317, 766, 679], [314, 779, 686], [306, 808, 697], [304, 785, 688], [292, 794, 704], [275, 799, 699], [273, 799, 709], [301, 812, 715], [280, 837, 724], [289, 853, 746], [303, 876, 758], [322, 897, 779], [315, 922, 798], [339, 949, 816], [364, 979, 837], [371, 988, 858], [375, 1025, 881], [432, 1063, 905], [453, 1104, 934], [460, 1131, 968], [475, 1137, 983], [496, 1178, 1013], [494, 1211, 1034], [498, 1256, 1064], [526, 1290, 1101], [519, 1314, 1102], [516, 1346, 1145], [531, 1385, 1173], [573, 1416, 1216], [551, 1436, 1229], [538, 1462, 1242], [532, 1493, 1267], [558, 1516, 1295], [524, 1557, 1317], [525, 1613, 1355], [519, 1642, 1371], [526, 1690, 1402], [510, 1759, 1452], [519, 1756, 1485], [538, 1780, 1516], [549, 1807, 1549], [570, 1831, 1567], [559, 1873, 1588], [584, 1897, 1631], [611, 1910, 1650], [597, 1943, 1685], [603, 1976, 1722], [619, 2018, 1752], [635, 2040, 1774], [658, 2070, 1807], [675, 2121, 1831], [700, 2132, 1842], [692, 2199, 1890], [759, 2253, 1958], [782, 2276, 1948], [816, 2318, 1994], [844, 2369, 2061], [830, 2423, 2056], [853, 2457, 2102], [852, 2470, 2121], [833, 2521, 2145], [860, 2545, 2164], [870, 2580, 2206], [830, 2620, 2225], [801, 2639, 2235], [824, 2618, 2237], [831, 2628, 2250], [830, 2651, 2271], ] lutkepohl_ar1 = { # intercept, AR, sigma^2 'params': [.02193629, -.19639897, .0020982049304637], 'loglike': 123.1654530510318, 'aic': -3.274741974352211, 'bic': -3.212469944806153, 'hqic': -3.249900896155949, 'fpe': .0022147718710451, 'estat_aic': -242.33091, 'estat_bic': -237.72278 } lutkepohl_ar1_lustats = { # intercept, AR, sigma^2 'params': [.02193629, -.19639897, .0020982049304637], 'loglike': 123.1654530510318, 'aic': -6.139646067788584, 'bic': -6.108510053015554, 'hqic': -6.127225528690452, 'fpe': .0022147718710451, 'estat_aic': -242.33091, 'estat_bic': -237.72278 } lutkepohl_ar1_lustats_dfk = { 'params': [.02193629, -.19639897, .00215649], # intercept, AR, sigma^2 'loglike': 123.1654530510318, 'loglike_dfk': 122.1516910060716, 'aic': -6.139646067788584, 'bic': -6.108510053015554, 'hqic': -6.127225528690452, 'fpe': .0022147718710451, 'estat_aic': -242.33091, 'estat_bic': -237.72278 } lutkepohl_var1 = { 'params': [ -.25155231, .27806257, .8357748, # Phi, row 1 .0226746, .1936755, .66011984, # Phi, row 2 -.01493575, .54067685, .2807106, # Phi, row 3 # 0.002010307675, # Covariance, lower triangle # 0.000063517318, 0.000184048720, # 0.000129337591, 0.000117178971, 0.000162533784 # Note: the following are the Cholesky of the covariance # matrix defined just above 0.0448364548, # Cholesky, lower triangle 0.0014166445, 0.0134922881, 0.0028846525, 0.0083820063, 0.0091626707 ], 'loglike': 580.6167823218026, 'aic': -15.44910222491358, 'bic': -15.16887809195632, 'hqic': -15.33731737303041, 'fpe': 3.91899792595e-11, 'estat_aic': -1143.2336, 'estat_bic': -1122.497 } lutkepohl_var1_lustats = { 'params': [ -.25155231, .27806257, .8357748, # Phi, row 1 .0226746, .1936755, .66011984, # Phi, row 2 -.01493575, .54067685, .2807106, # Phi, row 3 # 0.002010307675, # Covariance, lower triangle # 0.000063517318, 0.000184048720, # 0.000129337591, 0.000117178971, 0.000162533784 # Note: the following are the Cholesky of the covariance # matrix defined just above 0.0448364548, # Cholesky, lower triangle 0.0014166445, 0.0134922881, 0.0028846525, 0.0083820063, 0.0091626707 ], 'loglike': 580.6167823218026, 'aic': -23.96273342414162, 'bic': -23.68250929118436, 'hqic': -23.85094857225844, 'fpe': 3.91899792595e-11, 'estat_aic': -1143.2336, 'estat_bic': -1122.497 } lutkepohl_var1_lustats_dfk = { 'params': [ -.25155231, .27806257, .8357748, # Phi, row 1 .0226746, .1936755, .66011984, # Phi, row 2 -.01493575, .54067685, .2807106, # Phi, row 3 # .00209525, # Covariance, lower triangle # .0000662, .00019183, # .0001348, .00012213, .0001694 # Note: the following are the Cholesky of the covariance # matrix defined just above 0.0457739, # Cholesky, lower triangle 0.0014462, 0.0137746, 0.0029449, 0.0085572, 0.0093543 ], 'loglike': 580.6167823218026, 'loglike_dfk': 576.0230233277257, 'aic': -23.96273342414162, 'bic': -23.68250929118436, 'hqic': -23.85094857225844, 'fpe': 3.91899792595e-11, 'estat_aic': -1143.2336, 'estat_bic': -1122.497 } 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statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/results_varmax.py000066400000000000000000000210051400612667500277240ustar00rootroot00000000000000""" Results for VARMAX tests Results from Stata using script `test_varmax_stata.do`. See also Stata time series documentation, in particular `dfactor`. Data from: http://www.jmulti.de/download/datasets/e1.dat Author: Chad Fulton License: Simplified-BSD """ # See http://www.jmulti.de/download/datasets/e1.dat # 1960:Q1 - 1982Q4 lutkepohl_data = [ [180, 451, 415], [179, 465, 421], [185, 485, 434], [192, 493, 448], [211, 509, 459], [202, 520, 458], [207, 521, 479], [214, 540, 487], [231, 548, 497], [229, 558, 510], [234, 574, 516], [237, 583, 525], [206, 591, 529], [250, 599, 538], [259, 610, 546], [263, 627, 555], [264, 642, 574], [280, 653, 574], [282, 660, 586], [292, 694, 602], [286, 709, 617], [302, 734, 639], [304, 751, 653], [307, 763, 668], [317, 766, 679], [314, 779, 686], [306, 808, 697], [304, 785, 688], [292, 794, 704], [275, 799, 699], [273, 799, 709], [301, 812, 715], [280, 837, 724], [289, 853, 746], [303, 876, 758], [322, 897, 779], [315, 922, 798], [339, 949, 816], [364, 979, 837], [371, 988, 858], [375, 1025, 881], [432, 1063, 905], [453, 1104, 934], [460, 1131, 968], [475, 1137, 983], [496, 1178, 1013], [494, 1211, 1034], [498, 1256, 1064], [526, 1290, 1101], [519, 1314, 1102], [516, 1346, 1145], [531, 1385, 1173], [573, 1416, 1216], [551, 1436, 1229], [538, 1462, 1242], [532, 1493, 1267], [558, 1516, 1295], [524, 1557, 1317], [525, 1613, 1355], [519, 1642, 1371], [526, 1690, 1402], [510, 1759, 1452], [519, 1756, 1485], [538, 1780, 1516], [549, 1807, 1549], [570, 1831, 1567], [559, 1873, 1588], [584, 1897, 1631], [611, 1910, 1650], [597, 1943, 1685], [603, 1976, 1722], [619, 2018, 1752], [635, 2040, 1774], [658, 2070, 1807], [675, 2121, 1831], [700, 2132, 1842], [692, 2199, 1890], [759, 2253, 1958], [782, 2276, 1948], [816, 2318, 1994], [844, 2369, 2061], [830, 2423, 2056], [853, 2457, 2102], [852, 2470, 2121], [833, 2521, 2145], [860, 2545, 2164], [870, 2580, 2206], [830, 2620, 2225], [801, 2639, 2235], [824, 2618, 2237], [831, 2628, 2250], [830, 2651, 2271], ] lutkepohl_var1 = { 'params': [ -0.25034303, 0.28759168, 0.81626475, # Phi, row 1 0.023383, 0.19048278, 0.66502259, # Phi, row 2 -0.01492992, 0.53796097, 0.28114733, # Phi, row 3 # .00199294, # Covariance, lower triangle # .00006096, .00012986, # .00018523, .00011695, .00016188, # Note: the following are the Cholesky of the covariance # matrix defined just above 0.04464236, # Cholesky, lower triangle 0.00136552, 0.01354125, 0.0029089, 0.00834324, 0.00915471 ], 'var_oim': [ .01319669, .19413864, .2386643, .0012437, .01829378, .02234399, .00107749, .01584584, .01938099, 1.061e-07, 4.981e-09, 4.549e-09, 9.211e-10, 5.825e-10, 7.016e-10], 'loglike': 587.8481018831948, 'aic': -1145.696, 'bic': -1110.934, } lutkepohl_var1_diag = { 'params': [ -0.24817904, 0.29283012, 0.80794938, # Phi, row 1 0.02282985, 0.19672157, 0.66329776, # Phi, row 2 -0.01522531, 0.53500874, 0.28859213, # Phi, row 3 0.00199106, 0.00018529, 0.00016179 # Variances, diagonal ], 'var_oim': [ .01314245, .1902972, .23400828, .00124336, .01840132, .02229946, .00107322, .01558391, .01909303, 1.057e-07, 9.233e-10, 7.011e-10 ], 'loglike': 562.8168476509002, 'aic': -1101.634, 'bic': -1073.824 } lutkepohl_var1_diag_meas = { 'params': [ -0.24817904, 0.29283012, 0.80794938, # Phi, row 1 0.02282985, 0.19672157, 0.66329776, # Phi, row 2 -0.01522531, 0.53500874, 0.28859213, # Phi, row 3 0.00199106, 0.00018529, 0.00016179, # Variances, diagonal 0, 0, 0 # Measurement error variances ], 'var_oim': [ .01314245, .1902972, .23400828, .00124336, .01840132, .02229946, .00107322, .01558391, .01909303, 1.057e-07, 9.233e-10, 7.011e-10, None, None, None ], 'loglike': 562.8168476509002, 'aic': None, 'bic': None } lutkepohl_var1_obs_intercept = { 'params': [ -.24762, .25961003, .75992623, # Phi, row 1 .03186854, -.07271862, .23697765, # Phi, row 2 -.0053055, .2362571, -.19438311, # Phi, row 3 .00199116, .00013515, .00009937 # Variances, diagonal ], 'obs_intercept': [.01799302, .02065458, .01987525], # Intercepts 'var_oim': [ .01317874, .2311403, .33481866, .00090084, .0157839, .0229119, .00065737, .01149729, .01661236, # .00001802, 1.818e-06, 1.086e-06, # Intercept parameters 1.057e-07, 4.869e-10, 2.630e-10], 'loglike': 593.5252693885262, 'aic': -1101.634, 'bic': -1073.824 } lutkepohl_var1_exog = { 'params': [ -.25549409, .31149462, .92674046, # Phi, row 1 .02935715, .13699757, .5059042, # Phi, row 2 -.00540021, .4598014, .06065565, # Phi, row 3 -.00007533, .00012771, .00018224, # exog # .00200617, # Covariance, lower triangle # .00007053, .00017216, # .00013934, .00010021, .00013833 # Note: the following are the Cholesky of the covariance # matrix defined just above .04479029, # Cholesky, lower triangle .00157467, .01302614, .00311094, .00731692, .00866687 ], 'var_oim': [ .01350243, .20429977, .29684366, # Phi, row 1 .00115871, .01753203, .02547371, # Phi, row 2 .000931, .01408662, .02046759, # Phi, row 3 3.720e-08, 3.192e-09, 2.565e-09 # exog ], 'loglike': 587.4157014188437, 'aic': None, 'bic': None } lutkepohl_var1_exog2 = { 'params': [ -.2552236, .21722691, .81525457, # Phi, row 1 .02998355, -.08130972, .24772266, # Phi, row 2 -.00476998, .24016112, -.19910237, # Phi, row 3 .00811096, -.00015244, # exog, y1 .01878355, -.00005086, # exog, y2 .01889825, 2.577e-06, # exog, y3 # .00199918, # Covariance, lower triangle # .00005435, .00013469, # .00012306, .00006251, .00010039 # Note: the following are the Cholesky of the covariance # matrix defined just above .04471219, # Cholesky, lower triangle .00121555, .01102644, .00275227, .00536569, .00800152 ], 'var_oim': None, # 'loglike': 600.9801664685759, # From Stata 'loglike': 600.65449034396283, # From VARMAX (regression test) 'aic': None, 'bic': None } lutkepohl_var2 = { 'params': [ -.25244981, .62528114, # Phi_1, row 1 -.13011679, .58173748, # Phi_1, row 2 .05369178, .35716349, # Phi_2, row 1 .03861472, .43812606, # Phi_2, row 2 # .00197786, # Covariance, lower triangle # .00008091, .00018269 0.04447314, # Covariance cholesky, lower triangle 0.0018193, 0.01339329 ], 'var_oim': [ .01315844, .11805816, # Phi_1, row 1 .01321036, .11300702, # Phi_1, row 2 .00122666, .01064478, # Phi_2, row 1 .0012571, .0106738, # Phi_2, row 2 1.048e-07, # Covariance, lower triangle 4.994e-09, 8.940e-10 ], 'loglike': 343.3149718445623, 'aic': -664.6299, 'bic': -639.1376 } fred_varma11 = { 'params': [ .80580312, 0, # Phi_1, row 1 .17348681, -.48093755, # Phi_1, row 2 -.51890703, 0, # Theta_1, row 1 0, 0, # Theta_1, row 2 .0000582, .00003815, # Variances ], 'var_oim': [ .00272999, 0, # Phi_1, row 1 .00164152, .00248576, # Phi_1, row 2 .0049259, 0, # Theta_1, row 1 0, 0, # Theta_1, row 2 1.529e-11, 6.572e-12, # Variances ], 'loglike': 3156.056423235071, 'aic': -6300.113, 'bic': -6275.551 } fred_vma1 = { 'params': [ .24803941, 0, # Theta_1, row 1 0, 0, # Theta_1, row 2 .00006514, .00004621, # Variances ], 'var_oim': [ .00154773, 0, # Theta_1, row 1 0, 0, # Theta_1, row 2 1.916e-11, 9.639e-12, # Variances ], 'loglike': 3088.909619417645, 'aic': -6171.819, 'bic': -6159.539 } 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forecasts”Œforecasts_error”Œforecasts_error_cov”Œstandardized_forecasts_error”Œscaled_smoothed_estimator”Œscaled_smoothed_estimator_cov”Œsmoothing_error”Œsmoothed_state”Œsmoothed_state_cov”Œsmoothed_state_autocov”Œ smoothed_measurement_disturbance”Œsmoothed_state_disturbance”Œ$smoothed_measurement_disturbance_cov”Œsmoothed_state_disturbance_cov”Œfilter_results”Œsmoother_results”eŒnormalized_cov_params”NŒscale”G?ðhëNhìNh„Kúhh)”(Œcov_params_opg”h(h+K…”h-‡”R”(KKK†”h5‰C _‡šc¸Ên?Ê[‹gõ ¿Ì[‹gõ ¿2§&,uLz?”t”bŒ fittedvalues”NŒresid”NŒwresid”Nu}”h}”sbŒnobs_effective”KúŒdf_model”KŒdf_resid”GðŒcov_kwds”}”Œ description”ŒQCovariance matrix calculated using the outer product of gradients (complex-step).”sŒcov_type”Œopg”Œ_cov_approx_complex_step”ˆŒ_cov_approx_centered”‰Œ_rank”h&Œscalar”“”h˜C”†”R”Œcov_params_default”hóhÙNhÚNhÛNhÜNhÝNhÞNhßNhàNháNhâNhãNhäNhåNhæNhçNhèNhéNhêNŒ_data_attr_model”]”(hÖhheŒ data_in_cache”]”(h÷høhùh÷høhùeŒ _init_kwds”}”(hGhHhIhJhgNh@‰hA‰hB‰hC‰hDˆhEˆhF‰hKuŒ specification”Œstatsmodels.tools.tools”ŒBunch”“”)”(h?Kh@‰hA‰hC‰hDˆhEˆhF‰hGhHhIhJhqKhvKhoKhrKhtKhwKhpKhsKhgNh{Kh}KhB‰h~‰ujbhhhkhKhNhRhUhYh\h`hcŒpolynomial_reduced_ar”h(h+K…”h-‡”R”(KK…”h5‰Cð? e+¼ü°¿”t”bŒpolynomial_reduced_ma”h(h+K…”h-‡”R”(KK…”h5‰Cð?”t”bŒ model_orders”}”(hgKhKŒar”KŒma”KŒ seasonal_ar”KŒ seasonal_ma”KŒ reduced_ar”KŒ reduced_ma”KŒ exog_variance”KŒmeasurement_variance”KŒvariance”KuŒ param_terms”]”(j)j1eŒ _params_ar”h(h+K…”h-‡”R”(KK…”h5‰C e+¼ü°?”t”bŒ_params_variance”h(h+K…”h-‡”R”(KK…”h5‰CuÜéÖsdé?”t”bubŒ__doc__”Xg Class to hold results from fitting an SARIMAX model. Parameters ---------- model : SARIMAX instance The fitted model instance Attributes ---------- specification : dictionary Dictionary including all attributes from the SARIMAX model instance. polynomial_ar : array Array containing autoregressive lag polynomial coefficients, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). polynomial_ma : array Array containing moving average lag polynomial coefficients, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). polynomial_seasonal_ar : array Array containing seasonal autoregressive lag polynomial coefficients, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). polynomial_seasonal_ma : array Array containing seasonal moving average lag polynomial coefficients, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). polynomial_trend : array Array containing trend polynomial coefficients, ordered from lowest degree to highest. Initialized with ones, unless a coefficient is constrained to be zero (in which case it is zero). model_orders : list of int The orders of each of the polynomials in the model. param_terms : list of str List of parameters actually included in the model, in sorted order. See Also -------- statsmodels.tsa.statespace.kalman_filter.FilterResults statsmodels.tsa.statespace.mlemodel.MLEResults ”Œmlefit”Œstatsmodels.base.model”ŒLikelihoodModelResults”“”)”}”(h%h(h+K…”h-‡”R”(KK…”h5‰CìQÎDW±¿` $p`ì?”t”bh:h=hKh‡]”híNhîG?ðŒ mle_retvals”}”(Œfopt”j h5C¢µ‘n[Úô?”†”R”Œgopt”h(h+K…”h-‡”R”(KK…”h5‰Cÿÿÿÿ‘þ>>ÿÿÿ=h¾”t”bŒfcalls”KŒwarnflag”KŒ converged”ˆŒ iterations”KuŒ mle_settings”}”(Œ optimizer”Œlbfgs”Œ start_params”h(h+K…”h-‡”R”(KK…”h5‰Cõ=ñ椱¿%‘Ô]Žì?”t”bŒmaxiter”K2Œ full_output”KŒdisp”KŒfargs”}”(Œ transformed”‰Œ score_method”NŒapprox_complex_step”ˆu…”Œcallback”NŒretall”‰Œ approx_grad”ˆŒepsilon”G>äøµˆãhñŒextra_fit_funcs”}”Œbounds”]”(NN†”j~eŒiprint”KuubjQjRjbjcub.statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_clark1989_r.R000066400000000000000000000044521400612667500274340ustar00rootroot00000000000000library(FKF) library(KFAS) options(digits=10) # Observations df <- read.csv("clark1989.csv", header=FALSE) lgdp = log(df$V1[5:nrow(df)]) unemp = (df$V2 / 100)[5:nrow(df)] # True parameters params <- c( 0.004863, 0.00668, 0.000295, 0.001518, 0.000306, 1.43859, -0.517385, -0.336789, -0.163511, -0.072012 ) # Dimensions n = 2 k = 6 # Measurement equation H = matrix(rep(0, n*k), nrow=n) H[1,1] = 1 H[1,2] = 1 H[2,6] = 1 obs_intercept = matrix(rep(0,n), nrow=n) R = matrix(rep(0, n^2), nrow=n) # Transition equation mu = matrix(rep(0, k), nrow=k) F = matrix(rep(0, k^2), nrow=k) F[1,1] = 1 F[1,5] = 1 F[3,2] = 1 F[4,3] = 1 F[5,5] = 1 F[6,6] = 1 # Q = G Q_star G' Q = matrix(rep(0, k^2), nrow=k) # Update matrices with given parameters H[2,2] = params[8] H[2,3] = params[9] H[2,4] = params[10] F[2,2] = params[6] F[2,3] = params[7] R[2,2] = params[5]^2 Q[1,1] = params[1]^2 Q[2,2] = params[2]^2 Q[5,5] = params[3]^2 Q[6,6] = params[4]^2 # Initialization: Diffuse priors initial_state = c(mu) initial_state_cov = diag(k) * 100 initial_state_cov = (F %*% initial_state_cov) %*% (t(F)) # - FKF --------------------------------------------------------------------- # # Filter, complete dataset dta <- rbind(lgdp,unemp) ans <- fkf(a0=initial_state, P0=initial_state_cov, dt=mu, ct=obs_intercept, Tt=F, Zt=H, HHt=Q, GGt=R, yt=dta) # Filter, partially missing dataset (using KFAS) unemp2 = unemp n = length(unemp2) unemp2[(n-50):n] <- NaN dta2 <- rbind(lgdp,unemp2) ans2 <- fkf(a0=initial_state, P0=initial_state_cov, dt=mu, ct=obs_intercept, Tt=F, Zt=H, HHt=Q, GGt=R, yt=dta2) mod <- SSModel(t(dta2) ~ -1+SSMcustom(H, F, diag(6), Q, P1=initial_state_cov), H=R) fit <- KFS(mod, filtering="state", smoothing="state") # Recalculate Kalman gain # FKF defines the Kalman gain as P Z' F^{-1}, whereas Durbin and Koopman (2012) # use T P Z' F^{-1}, so premultiply the ans$Kt by the transition matrix Kt = ans$Kt for (i in 1:n) { Kt[,,i] = F %*% Kt[,,i] } # Create output columns # 1: sum of complete dataset Kalman gain sum_complete_Kt = colSums(Kt, dims=2) # 2-7: filtered states from incomplete dataset # t(ans2$att) # Print likelihood from partial missing model print(fit$logLik) out <- matrix(cbind(sum_complete_Kt, t(ans2$att))) write.csv(out, 'results_clark1989_R.csv', row.names=FALSE) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_dynamic_factor_stata.do000066400000000000000000000155751400612667500320530ustar00rootroot00000000000000// Helpful commands: // matrix list e(b) // matrix d = vecdiag(e(V)) // matrix list d webuse lutkepohl2, clear tsset // use lutkepohl2_s12, clear // tsset qtr // Dynamic factors dfactor (dln_inv dln_inc dln_consump = , noconstant ) (f = , ar(1/2)) if qtr<=tq(1978q4) // These are predict in-sample + forecast out-of-sample (1979q1 is first out-of sample obs) predict predict_dfm_1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_dfm_2, dynamic(tq(1979q1)) equation(dln_inc) predict predict_dfm_3, dynamic(tq(1979q1)) equation(dln_consump) // These are predict in-sample for first 3-observations (1960q2-1960q4), then // dynamic predict for the rest of in-sample observations (1961q1-1978q4), then // forecast for the remaining periods 1979q1 - 1982q4 predict dyn_predict_dfm_1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_dfm_2, dynamic(tq(1961q1)) equation(dln_inc) predict dyn_predict_dfm_3, dynamic(tq(1961q1)) equation(dln_consump) // Dynamic factors, with 2 factors // Note: this does not converge even if we do not enforce iter(#), but this is // good enough for testing dfactor (dln_inv dln_inc dln_consump = , noconstant ) (f1 f2 = , ar(1) arstructure(general)) if qtr<=tq(1978q4), iter(1) // predict + forecast, see above predict predict_dfm2_1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_dfm2_2, dynamic(tq(1979q1)) equation(dln_inc) predict predict_dfm2_3, dynamic(tq(1979q1)) equation(dln_consump) // predict + dynamic predict + forecast, see above predict dyn_predict_dfm2_1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_dfm2_2, dynamic(tq(1961q1)) equation(dln_inc) predict dyn_predict_dfm2_3, dynamic(tq(1961q1)) equation(dln_consump) // Dynamic factors, with 1 exog gen c = 1 dfactor (dln_inv dln_inc dln_consump = c, noconstant ) (f = , ar(1)) if qtr<=tq(1978q4) // predict + forecast, see above predict predict_dfm_exog1_1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_dfm_exog1_2, dynamic(tq(1979q1)) equation(dln_inc) predict predict_dfm_exog1_3, dynamic(tq(1979q1)) equation(dln_consump) // predict + dynamic predict + forecast, see above predict dyn_predict_dfm_exog1_1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_dfm_exog1_2, dynamic(tq(1961q1)) equation(dln_inc) predict dyn_predict_dfm_exog1_3, dynamic(tq(1961q1)) equation(dln_consump) // Dynamic factors, with 2 exog gen t = _n dfactor (dln_inv dln_inc dln_consump = c t, noconstant ) (f = , ar(1)) if qtr<=tq(1978q4) // predict + forecast, see above predict predict_dfm_exog2_1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_dfm_exog2_2, dynamic(tq(1979q1)) equation(dln_inc) predict predict_dfm_exog2_3, dynamic(tq(1979q1)) equation(dln_consump) // predict + dynamic predict + forecast, see above predict dyn_predict_dfm_exog2_1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_dfm_exog2_2, dynamic(tq(1961q1)) equation(dln_inc) predict dyn_predict_dfm_exog2_3, dynamic(tq(1961q1)) equation(dln_consump) // Dynamic factors, with general errors (VAR + unstructured), on demeaned data // (have to demean, otherwise get non-stationarity start params for the error // VAR) dfactor (dln_inv dln_inc dln_consump = , noconstant ar(1) arstructure(general) covstructure(unstructured)) (f = , ar(1)) if qtr<=tq(1978q4) // predict + forecast, see above predict predict_dfm_gen_1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_dfm_gen_2, dynamic(tq(1979q1)) equation(dln_inc) predict predict_dfm_gen_3, dynamic(tq(1979q1)) equation(dln_consump) // predict + dynamic predict + forecast, see above predict dyn_predict_dfm_gen_1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_dfm_gen_2, dynamic(tq(1961q1)) equation(dln_inc) predict dyn_predict_dfm_gen_3, dynamic(tq(1961q1)) equation(dln_consump) // Dynamic factors, with AR(2) errors dfactor (dln_inv dln_inc dln_consump = , noconstant ar(1/2)) (f = , ar(1)) if qtr<=tq(1978q4) // predict + forecast, see above predict predict_dfm_ar2_1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_dfm_ar2_2, dynamic(tq(1979q1)) equation(dln_inc) predict predict_dfm_ar2_3, dynamic(tq(1979q1)) equation(dln_consump) // predict + dynamic predict + forecast, see above predict dyn_predict_dfm_ar2_1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_dfm_ar2_2, dynamic(tq(1961q1)) equation(dln_inc) predict dyn_predict_dfm_ar2_3, dynamic(tq(1961q1)) equation(dln_consump) // Dynamic factors, with scalar error covariance + constant (1 exog) // Note: estimation does not converge w/o constant term dfactor (dln_inv dln_inc dln_consump = c, noconstant covstructure(dscalar)) (f = , ar(1)) if qtr<=tq(1978q4) // predict + forecast, see above predict predict_dfm_scalar_1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_dfm_scalar_2, dynamic(tq(1979q1)) equation(dln_inc) predict predict_dfm_scalar_3, dynamic(tq(1979q1)) equation(dln_consump) // predict + dynamic predict + forecast, see above predict dyn_predict_dfm_scalar_1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_dfm_scalar_2, dynamic(tq(1961q1)) equation(dln_inc) predict dyn_predict_dfm_scalar_3, dynamic(tq(1961q1)) equation(dln_consump) // Static factor (factor with no autocorrelation) // Note: estimation does not converge w/o constant term dfactor (dln_inv dln_inc dln_consump = , noconstant) (f = , ) if qtr<=tq(1978q4) // predict + forecast, see above predict predict_sfm_1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_sfm_2, dynamic(tq(1979q1)) equation(dln_inc) predict predict_sfm_3, dynamic(tq(1979q1)) equation(dln_consump) // predict + dynamic predict + forecast, see above predict dyn_predict_sfm_1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_sfm_2, dynamic(tq(1961q1)) equation(dln_inc) predict dyn_predict_sfm_3, dynamic(tq(1961q1)) equation(dln_consump) // SUR (exog, no autocorrelation, correlated innovations) dfactor (dln_inv dln_inc dln_consump = c t, noconstant covstructure(unstructured)) if qtr<=tq(1978q4) // predict + forecast, see above predict predict_sur_1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_sur_2, dynamic(tq(1979q1)) equation(dln_inc) predict predict_sur_3, dynamic(tq(1979q1)) equation(dln_consump) // predict + dynamic predict + forecast, see above predict dyn_predict_sur_1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_sur_2, dynamic(tq(1961q1)) equation(dln_inc) predict dyn_predict_sur_3, dynamic(tq(1961q1)) equation(dln_consump) // SUR (exog, vector error autocorrelation, uncorrelated innovations) dfactor (dln_inv dln_inc = c t, noconstant ar(1)) if qtr<=tq(1978q4) // predict + forecast, see above predict predict_sur_auto_1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_sur_auto_2, dynamic(tq(1979q1)) equation(dln_inc) // predict + dynamic predict + forecast, see above predict dyn_predict_sur_auto_1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_sur_auto_2, dynamic(tq(1961q1)) equation(dln_inc) outsheet pred* dyn* using results_dynamic_factor_stata.csv, comma replace statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_exact_diffuse_filtering.R000066400000000000000000000116211400612667500323340ustar00rootroot00000000000000library(KFAS) library(plyr) options(digits=10) # should run this from the statsmodels/statsmodels directory setwd('~/projects/statsmodels-0.9/statsmodels/') dta <- read.csv('datasets/macrodata/macrodata.csv') cbind.fill <- function(...){ nm <- list(...) nm <- lapply(nm, as.matrix) n <- max(sapply(nm, nrow)) do.call(cbind, lapply(nm, function (x) rbind(x, matrix(, n-nrow(x), ncol(x))))) } output <- function(kf) { # Dimensions n = nrow(kf$model$y) p = ncol(kf$model$y) m = nrow(kf$model$T) r = nrow(kf$model$Q) # Construct the output dataframe # r = scaled_smoothed_estimator # N = scaled_smoothed_estimator_cov # m = forecasts # v = forecasts_error # F = forecasts_error_cov # a = predicted_state # P = predicted_state_cov # mu = filtered_forecasts # alphahat = smoothed_state # V = smoothed_state_cov # muhat = smoothed_forecasts # etahat = smoothed_state_disturbance # V_eta = smoothed_state_disturbance_cov # epshat = smoothed_measurement_disturbance # V_eps = smoothed_measurement_disturbance_cov out <- as.data.frame(with(kf, cbind.fill( t(r), t(r0), t(r1), apply(N, 3, sum), apply(N0, 3, sum), apply(N1, 3, sum), apply(N2, 3, sum), m, v, t(F), t(Finf), a, apply(P, 3, sum), apply(Pinf, 3, sum), att, apply(Ptt, 3, sum), alphahat, apply(V, 3, sum), muhat, apply(V_mu, 3, sum), etahat, apply(V_eta, 3, sum), epshat, t(V_eps), logLik ))) names(out) <- c( paste('r', 1:m, sep='_'), paste('r0', 1:m, sep='_'), paste('r1', 1:m, sep='_'), 'sumN', 'sumN0', 'sumN1', 'sumN2', paste('m', 1:p, sep='_'), paste('v', 1:p, sep='_'), paste('F', 1:p, sep='_'), paste('Finf', 1:p, sep='_'), paste('a', 1:m, sep='_'), 'sumP', 'sumPinf', paste('att', 1:m, sep='_'), 'sumPtt', paste('alphahat', 1:m, sep='_'), 'sumV', paste('muhat', 1:p, sep='_'), 'sumVmu', paste('etahat', 1:r, sep='_'), 'sumVeta', paste('epshat', 1:p, sep='_'), paste('Veps', 1:p, sep='_'), 'llf' ) return(out) } llf <- function(kf) { # Dimensions n = nrow(kf$model$y) p = ncol(kf$model$y) m = nrow(kf$model$T) r = nrow(kf$model$Q) d = kf$d F = kf$F Finf = kf$Finf v = kf$v -((n * p / 2) * log(pi * 2) + 0.5 * sum(log(Finf[1:d])) + 0.5 * sum(log(F[(d+1):10]) + (v^2 / t(F))[(d+1):10])) } # Local level y1 <- 10.2394 sigma2_y <- 1.993 sigma2_mu <- 8.253 obs <- c(c(y1), rep(1, 9)) mod <- SSModel(obs ~ -1 + SSMcustom(Z=diag(1), T=diag(1), R=diag(1), Q=diag(1) * sigma2_mu, P1=diag(1) * 1e6), H=diag(1) * sigma2_y) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) write.csv(output(kf), 'tsa/statespace/tests/results/results_exact_initial_local_level_R.csv', row.names=FALSE) # Note: Apparent loglikelihood discrepancy print(llf(kf)) # -22.97437545 print(kf$logLik) # -21.13649839 print(-22.97437545 - -21.13649839) / kf$d # -0.9189385332 print(-0.5 * log(pi * 2)) # -0.9189385332 # Local linear trend y1 <- 10.2394 y2 <- 4.2039 y3 <- 6.123123 sigma2_y <- 1.993 sigma2_mu <- 8.253 sigma2_beta <- 2.334 obs <- c(c(y1, y2, y3), rep(1, 7)) mod <- SSModel(obs ~ -1 + SSMcustom(Z=t(as.matrix(c(1, 0))), T=as.matrix(cbind(c(1., 0), c(1, 1))), R=diag(2), Q=diag(c(sigma2_mu, sigma2_beta)), P1inf=diag(2)), H=diag(1) * sigma2_y) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) write.csv(output(kf), 'tsa/statespace/tests/results/results_exact_initial_local_linear_trend_R.csv', row.names=FALSE) # Local linear trend - missing obs[2] <- NA mod <- SSModel(obs ~ -1 + SSMcustom(Z=t(as.matrix(c(1, 0))), T=as.matrix(cbind(c(1., 0), c(1, 1))), R=diag(2), Q=diag(c(sigma2_mu, sigma2_beta)), P1inf=diag(2)), H=diag(1) * sigma2_y) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) write.csv(output(kf), 'tsa/statespace/tests/results/results_exact_initial_local_linear_trend_missing_R.csv', row.names=FALSE) # Common level y11 <- 10.2394 y21 <- 8.2304 theta <- 0.1111 sigma2_1 <- 1 sigma_12 <- 0 sigma2_2 <- 1 sigma2_mu <- 3.2324 obs <- cbind( c(c(y11), rep(1, 9)), c(c(y21), rep(1, 9)) ) mod <- SSModel(obs ~ -1 + SSMcustom( Z=as.matrix(cbind(c(1., theta), c(0, 1))), T=diag(2), R=as.matrix(c(1, 0)), Q=diag(1) * sigma2_mu, P1inf=diag(2)), H=diag(2)) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) write.csv(output(kf), 'tsa/statespace/tests/results/results_exact_initial_common_level_R.csv', row.names=FALSE) # Common level - restricted mod <- SSModel(obs ~ -1 + SSMcustom( Z=as.matrix(c(1, theta)), T=diag(1), R=diag(1), Q=diag(1) * sigma2_mu, P1inf=diag(1)), H=diag(2)) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) write.csv(output(kf), 'tsa/statespace/tests/results/results_exact_initial_common_level_restricted_R.csv', row.names=FALSE) test_exact_diffuse_filtering_multivariate.R000066400000000000000000000045231400612667500350460ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/statespace/tests/resultslibrary(KFAS) options(digits=10) # should run this from the statsmodels/statsmodels directory setwd('~/projects/statsmodels-0.9/statsmodels/') dta <- read.csv('datasets/macrodata/macrodata.csv') source('tsa/statespace/tests/results/kfas_helpers.R') # We use the following two observation datasets obs <- (diff(log(data.matrix(dta[c('realgdp', 'realcons')]))) * 400)[1:20,] obs_missing <- obs obs_missing[1:5,1] <- NA obs_missing[9:12,] <- NA # VAR(1) Z <- diag(2) T <- as.matrix(cbind(c(0.5, 0.2), c(0.3, 0.4))) R <- diag(2) Q <- diag(c(2, 3)) H <- diag(2) * 0 mod <- SSModel(obs ~ -1 + SSMcustom(Z=Z, T=T, R=R, Q=Q, P1inf=diag(2)), H=H) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) write.csv(kfas.output(kf), 'tsa/statespace/tests/results/results_exact_initial_var1_R.csv', row.names=FALSE) # VAR(1) + missing mod <- SSModel(obs_missing ~ -1 + SSMcustom(Z=Z, T=T, R=R, Q=Q, P1inf=diag(2)), H=H) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) write.csv(kfas.output(kf), 'tsa/statespace/tests/results/results_exact_initial_var1_missing_R.csv', row.names=FALSE) # VAR(1) + mixed initialization stationary_init <- 3.5714285714285716 mod <- SSModel(obs ~ -1 + SSMcustom(Z=Z, T=T, R=R, Q=Q, P1inf=diag(c(1, 0)), P1=diag(c(0, stationary_init))), H=H) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) write.csv(kfas.output(kf), 'tsa/statespace/tests/results/results_exact_initial_var1_mixed_R.csv', row.names=FALSE) # VAR(1) + measurement error H <- diag(c(4, 5)) mod <- SSModel(obs ~ -1 + SSMcustom(Z=Z, T=T, R=R, Q=Q, P1inf=diag(2)), H=H) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) write.csv(kfas.output(kf), 'tsa/statespace/tests/results/results_exact_initial_var1_measurement_error_R.csv', row.names=FALSE) # DFM Z <- matrix(c(0.5, 1, 0, 0), nrow=2) T <- matrix(c(0.9, 1, 0.1, 0), nrow=2) R <- matrix(c(1, 0), nrow=2) Q <- diag(1) H <- diag(c(1.5, 2)) mod <- SSModel(obs ~ -1 + SSMcustom(Z=Z, T=T, R=R, Q=Q, P1inf=diag(2)), H=H) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) write.csv(kfas.output(kf), 'tsa/statespace/tests/results/results_exact_initial_dfm_R.csv', row.names=FALSE) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_exact_diffuse_filtering_stata.do000066400000000000000000000050651400612667500337360ustar00rootroot00000000000000// Local level clear input x t 10.2394 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 end tsset t matrix define b0 = (8.253, 1.993) ucm x, model(llevel) from(b0) iterate(0) // e(ll) = -23.9352603142740605 disp %20.19g e(ll) // Local linear trend clear input x t 10.2394 1 4.2039 2 6.123123 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 end tsset t matrix define b0 = (8.253, 2.334, 1.993) ucm x, model(lltrend) from(b0) iterate(0) // e(ll) = -22.9743755748041529 disp %20.19g e(ll) // Local linear trend + missing // Have to skip this since Stata does not allow missing values, even using sspace // clear // input x t // 10.2394 1 // . 2 // 6.123123 3 // 1 4 // 1 5 // 1 6 // 1 7 // 1 8 // 1 9 // 1 10 // end // tsset t // // constraint 1 [x]u1 = 1 // constraint 2 [u1]L.u1 = 1 // constraint 3 [u1]L.u2 = 1 // constraint 4 [u2]L.u2 = 1 // // matrix define b0 = (1, 1, 1, 1, 8.253, 2.334, 1.993) // sspace (u1 L.u1 L.u2, state noconstant) /// // (u2 L.u2, state noconstant) /// // (x u1, noconstant), /// // constraints(1/4) covstate(diagonal) /// // from(b0) iterate(0) // // disp %20.19g e(ll) // Common trend clear input y1 y2 t 10.2394 8.2304 1 1 1 2 1 1 3 1 1 4 1 1 5 1 1 6 1 1 7 1 1 8 1 1 9 1 1 10 end tsset t constraint 1 [y1]u1 = 1 constraint 2 [y2]u2 = 1 constraint 3 [u1]L.u1 = 1 constraint 4 [u2]L.u2 = 1 matrix define b0 = (1, 1, 1, 0.1111, 1, 3.2324, 1, 1) sspace (u1 L.u1, state noconstant) /// (u2 L.u2, state noconstant noerror) /// (y1 u1, noconstant) /// (y2 u1 u2, noconstant), /// constraints(1/4) covstate(diagonal) /// from(b0) iterate(0) // -53.7830389463984773 disp %20.19g e(ll) // Dynamic Factor Model clear input y1 y2 t 9.9768523266 6.1144429663 1 -0.4771808443 4.1543910949 2 1.3978130617 0.4336043785 3 8.8760718057 3.8136603507 4 -1.8738213131 5.0289712198 5 0.6531520756 -1.5871706073 6 -5.1625439784 0.5372132872 7 2.3690365022 -0.1118599521 8 7.4138136616 5.9079363820 9 6.4126556647 1.9354521733 10 8.0611264188 7.9292248028 11 7.1109037147 4.2364664530 12 4.3922061400 4.8864935148 13 3.6816268854 3.2248106820 14 0.9708074857 5.6330208687 15 5.1940841814 2.6849177229 16 4.9811338373 3.8017109128 17 7.4616162956 5.4061666493 18 3.0295447157 3.3396476674 19 8.8783455475 7.8216699141 20 end tsset t constraint 1 [u2]L.u1 = 1 matrix define b0 = (0.9, 0.1, 1, 0.5, 1, 1, 1.5, 2.) sspace (u1 L.u1 L.u2, state noconstant) /// (u2 L.u1, state noconstant noerror) /// (y1 u1, noconstant) /// (y2 u1, noconstant), /// constraints(1) covstate(diagonal) /// from(b0) iterate(0) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_intercepts.R000066400000000000000000000041121400612667500276350ustar00rootroot00000000000000library(KFAS) library(MARSS) options(digits=20) # should run this from the statsmodels/statsmodels directory dta <- read.csv('datasets/macrodata/macrodata.csv') obs <- data.matrix(dta[c('realgdp','realcons','realinv')]) obs[,1] <- obs[,1] / sd(obs[,1], na.rm=TRUE) obs[,2] <- obs[,2] / sd(obs[,2], na.rm=TRUE) obs[,3] <- obs[,3] / sd(obs[,3], na.rm=TRUE) obs[1:50,1] <- NA obs[20:70,2] <- NA obs[40:90,3] <- NA obs[120:130,1] <- NA obs[120:130,3] <- NA Z <- diag(3) H <- diag(3) T <- diag(3) R <- diag(3) Q <- diag(3) P0 <- diag(3) * 1e6 d <- matrix(c(1,2,3),3,1) c <- matrix(c(4,5,6),3,1) ss <- list(Z=Z, R=H, B=T, Q=Q, V0=P0, A=d, U=c, x0="zero", tinitx=1) marssmod <- MARSS(t(obs), model=ss) marssout <- MARSSkfas(marssmod, return.kfas.model=TRUE) kf <- KFS(marssout$kfas.model, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) # kf$logLik # -7924.03893566 # r = scaled_smoothed_estimator # N = scaled_smoothed_estimator_cov # m = forecasts # v = forecasts_error # F = forecasts_error_cov # a = predicted_state # P = predicted_state_cov # mu = filtered_forecasts # alphahat = smoothed_state # V = smoothed_state_cov # muhat = smoothed_forecasts # etahat = smoothed_state_disturbance # V_eta = smoothed_state_disturbance_cov # epshat = smoothed_measurement_disturbance # V_eps = smoothed_measurement_disturbance_cov out <- as.data.frame(with(kf, cbind( t(r)[2:204,1:3], apply(N[1:3,1:3,], 3, det)[2:204], m, apply(P_mu, 3, det), v, t(F), a[2:204,1:3], apply(P[1:3,1:3,], 3, det)[2:204], alphahat[,1:3], apply(V[1:3,1:3,], 3, det), muhat, apply(V_mu, 3, det), etahat[,1:3], apply(V_eta[1:3,1:3,], 3, det), epshat, t(V_eps) ))) names(out) <- c( "r1", "r2", "r3", "detN", "m1", "m2", "m3", "detPmu", "v1", "v2", "v3", "F1", "F2", "F3", "a1", "a2", "a3", "detP", "alphahat1", "alphahat2", "alphahat3", "detV", "muhat1", "muhat2", "muhat3", "detVmu", "etahat1", "etahat2", "etahat3", "detVeta", "epshat1", "epshat2", "epshat3", "Veps1", "Veps2", "Veps3" ) write.csv(out, 'tsa/statespace/tests/results/results_intercepts_R.csv', row.names=FALSE) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_realgdpar_r.R000066400000000000000000000023531400612667500277440ustar00rootroot00000000000000library(FKF) # Observations df <- read.csv("results_kalman_filter_stata.csv") gdp = df$value lgdp = log(gdp) dlgdp = diff(lgdp) # Stata parameters params <- c( 0.40725515, 0.18782621, -0.01514009, -0.01027267, -0.03642297, 0.11576416, 0.02573029, -.00766572, 0.13506498, 0.08649569, 0.06942822, -0.10685783, 0.00008 ) # Measurement equation n = 1 H = matrix(rep(0, 12), nrow=1) H[1,1] = 1 R = matrix(c(0), nrow=1) # Transition equation k = 12 mu = matrix(rep(0,k), nrow=k) F = matrix(rep(0,k*k), nrow=k) for (i in 1:11) { F[i+1,i] = 1 } # Q = G Q_star G' Q = matrix(rep(0,k*k), nrow=k) # Update matrices with given parameters F[1,1:12] = params[1:12] Q[1,1] = params[13] # Initialization: Unconditional mean priors initial_state = c(solve(diag(k) - F) %*% mu) initial_state_cov = solve(diag(k^2) - F %x% F) %*% matrix(c(Q)) dim(initial_state_cov) <- c(k,k) # Filter ans <- fkf(a0=initial_state, P0=initial_state_cov, dt=mu, ct=matrix(0), Tt=F, Zt=H, HHt=Q, GGt=R, yt=rbind(dlgdp)) write.csv(t(ans$att), 'results_states_gdp_R.csv', row.names=FALSE) unlink('results_states_cov_gdp_R.csv') for (t in 1:length(dlgdp)) { write.table(t(ans$Ptt[,,t]), 'results_states_cov_gdp_R.csv', sep=",", append=TRUE, row.names=FALSE) }statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_realgdpar_stata.do000066400000000000000000000043671400612667500310270ustar00rootroot00000000000000clear insheet using results_realgdpar_stata.csv keep value gen lgdp = log(value) gen dlgdp = lgdp - lgdp[_n-1] gen quarter = _n tsset quarter // Estimate an ARMA(3,0) arima dlgdp if ~missing(dlgdp), arima(3,0,0) noconstant matrix b = e(b) matrix b = (b[1,1..3],1,1,1,b[1,4]^2) // Estimate via a state-space model constraint 1 [dlgdp]u1 = 1 constraint 2 [u2]L.u1 = 1 constraint 3 [u3]L.u2 = 1 sspace (u1 L.u1 L.u2 L.u3, state noconstant) /// (u2 L.u1, state noconstant noerror) /// (u3 L.u2, state noconstant noerror) /// (dlgdp u1, noconstant noerror) if ~missing(dlgdp), /// constraints(1/3) covstate(diagonal) from(b) // Estimate an ARMA(12,0) arima dlgdp if ~missing(dlgdp), arima(12,0,0) noconstant matrix b = e(b) matrix b = (b[1,1..12],1,1,1, 1,1,1, 1,1,1, 1,1,1,b[1,13]^2) // Estimate via a state-space model constraint 1 [dlgdp]u1 = 1 constraint 2 [u2]L.u1 = 1 constraint 3 [u3]L.u2 = 1 constraint 4 [u4]L.u3 = 1 constraint 5 [u5]L.u4 = 1 constraint 6 [u6]L.u5 = 1 constraint 7 [u7]L.u6 = 1 constraint 8 [u8]L.u7 = 1 constraint 9 [u9]L.u8 = 1 constraint 10 [u10]L.u9 = 1 constraint 11 [u11]L.u10 = 1 constraint 12 [u12]L.u11 = 1 sspace (u1 L.u1 L.u2 L.u3 L.u4 L.u5 L.u6 L.u7 L.u8 L.u9 L.u10 L.u11 L.u12, state noconstant) /// (u2 L.u1, state noconstant noerror) /// (u3 L.u2, state noconstant noerror) /// (u4 L.u3, state noconstant noerror) /// (u5 L.u4, state noconstant noerror) /// (u6 L.u5, state noconstant noerror) /// (u7 L.u6, state noconstant noerror) /// (u8 L.u7, state noconstant noerror) /// (u9 L.u8, state noconstant noerror) /// (u10 L.u9, state noconstant noerror) /// (u11 L.u10, state noconstant noerror) /// (u12 L.u11, state noconstant noerror) /// (dlgdp u1, noconstant noerror) if ~missing(dlgdp), /// constraints(1/12) covstate(diagonal) from (b) // Save the estimated states predict est_u1-est_u12, states equation(u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11 u12) // Save the filtered states predict u1-u12, states equation(u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11 u12) smethod(filter) // Save the standardized residuals predict rstd, rstandard // Output outsheet value u1-u12 est_u1-est_u12 rstd using results_realgdpar_stata.csv, comma replace statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_sarimax_coverage.do000066400000000000000000000150111400612667500311750ustar00rootroot00000000000000// Dataset use https://www.stata-press.com/data/r12/wpi1, clear rename t time set more off set maxiter 100 // 25, 43, 48, 52 // Create data for exog test gen x = (wpi - floor(wpi))^2 // Create data for deterministic trend tests gen c = 1 gen t = _n gen t2 = t^2 gen t3 = t^3 // Dummy column for saving LLFs gen mod = "" gen llf = . gen parameters = "" // Program to save the results program drop save_results program save_results args i replace mod = e(cmdline) in `i' replace llf = e(ll) in `i' matrix b = e(b) local params = "" local params = string(b[1,1]) local nparams = e(k) if `nparams' > 1 { foreach j of numlist 2/`nparams' { local params = "`params'," + string(b[1,`j']) } } replace parameters = "`params'" in `i' end // AR: (p,0,0) x (0,0,0,0) capture arima wpi, arima(3,0,0) noconstant vce(oim) save_results 1 // AR and deterministic trends ('nc', 'c', 'ct', polynomial) // 'c' capture arima wpi c, arima(3,0,0) noconstant vce(oim) save_results 2 // 'ct' capture arima wpi c t, arima(3,0,0) noconstant vce(oim) save_results 3 // polynomial [1,0,0,1] capture arima wpi c t3, arima(3,0,0) noconstant vce(oim) save_results 4 // AR and I(d): (p,d,0) x (0,0,0,0) capture arima wpi, arima(3,2,0) noconstant vce(oim) save_results 5 // AR and I(D): (p,0,0) x (0,D,0,s) capture arima wpi, arima(3,0,0) sarima(0,2,0,4) noconstant vce(oim) save_results 6 // AR and diffuse initialization capture arima wpi, arima(3,0,0) noconstant vce(oim) diffuse save_results 7 // ARX capture arima wpi x, arima(3,0,0) noconstant vce(oim) save_results 8 // MA: (0,0,q) x (0,0,0,0) capture arima wpi, arima(0,0,3) noconstant vce(oim) save_results 9 // MA and deterministic trends ('nc', 'c', 'ct', polynomial) // 'c' capture arima wpi c, arima(0,0,3) noconstant vce(oim) save_results 10 // 'ct' capture arima wpi c t, arima(0,0,3) noconstant vce(oim) save_results 11 // polynomial [1,0,0,1] capture arima wpi c t3, arima(0,0,3) noconstant vce(oim) save_results 12 // MA and I(d): (0,d,q) x (0,0,0,0) capture arima wpi, arima(0,2,3) noconstant vce(oim) save_results 13 // MA and I(D): (p,0,0) x (0,D,0,s) capture arima wpi, arima(0,0,3) sarima(0,2,0,4) noconstant vce(oim) save_results 14 // MA and diffuse initialization capture arima wpi, arima(0,0,3) noconstant vce(oim) diffuse save_results 15 // MAX capture arima wpi x, arima(0,0,3) noconstant vce(oim) save_results 16 // ARMA: (p,0,q) x (0,0,0,0) capture arima wpi, arima(3,0,3) noconstant vce(oim) save_results 17 // ARMA and deterministic trends ('nc', 'c', 'ct', polynomial) // 'c' capture arima wpi c, arima(3,0,2) noconstant vce(oim) save_results 18 // 'ct' capture arima wpi c t, arima(3,0,2) noconstant vce(oim) save_results 19 // polynomial [1,0,0,1] capture arima wpi c t3, arima(3,0,2) noconstant vce(oim) save_results 20 // ARMA and I(d): (p,d,q) x (0,0,0,0) capture arima wpi, arima(3,2,2) noconstant vce(oim) save_results 21 // ARMA and I(D): (p,0,q) x (0,D,0,s) capture arima wpi, arima(3,0,2) sarima(0,2,0,4) noconstant vce(oim) save_results 22 // ARMA and I(d) and I(D): (p,d,q) x (0,D,0,s) capture arima wpi, arima(3,2,2) sarima(0,2,0,4) noconstant vce(oim) save_results 23 // ARMA and diffuse initialization capture arima wpi, arima(3,0,2) noconstant vce(oim) diffuse save_results 24 // ARMAX capture arima wpi x, arima(3,0,2) noconstant vce(oim) save_results 25 // SAR: (0,0,0) x (P,0,0,s) capture arima wpi, sarima(3,0,0,4) noconstant vce(oim) save_results 26 // SAR and deterministic trends ('nc', 'c', 'ct', polynomial) // 'c' capture arima wpi c, sarima(3,0,0,4) noconstant vce(oim) save_results 27 // 'ct' capture arima wpi c t, sarima(3,0,0,4) noconstant vce(oim) save_results 28 // polynomial [1,0,0,1] capture arima wpi c t3, sarima(3,0,0,4) noconstant vce(oim) save_results 29 // SAR and I(d): (0,d,0) x (P,0,0,s) capture arima wpi, arima(0,2,0) sarima(3,0,0,4) noconstant vce(oim) save_results 30 // SAR and I(D): (0,0,0) x (P,D,0,s) capture arima wpi, sarima(3,2,0,4) noconstant vce(oim) save_results 31 // SAR and diffuse initialization capture arima wpi, sarima(3,0,0,4) noconstant vce(oim) diffuse save_results 32 // SARX capture arima wpi x, sarima(3,0,0,4) noconstant vce(oim) save_results 33 // SMA capture arima wpi, sarima(0,0,3,4) noconstant vce(oim) save_results 34 // SMA and deterministic trends ('nc', 'c', 'ct', polynomial) // 'c' capture arima wpi c, sarima(0,0,3,4) noconstant vce(oim) save_results 35 // 'ct' capture arima wpi c t, sarima(0,0,3,4) noconstant vce(oim) save_results 36 // polynomial [1,0,0,1] capture arima wpi c t3, sarima(0,0,3,4) noconstant vce(oim) save_results 37 // SMA and I(d): (0,d,0) x (0,0,Q,s) capture arima wpi, arima(0,2,0) sarima(0,0,3,4) noconstant vce(oim) save_results 38 // SAR and I(D): (0,0,0) x (0,D,Q,s) capture arima wpi, sarima(0,2,3,4) noconstant vce(oim) save_results 39 // SMA and diffuse initialization capture arima wpi, sarima(0,0,3,4) noconstant vce(oim) diffuse save_results 40 // SMAX capture arima wpi x, sarima(0,0,3,4) noconstant vce(oim) save_results 41 // SARMA: (0,0,0) x (P,0,Q,s) capture arima wpi, sarima(3,0,2,4) noconstant vce(oim) save_results 42 // SARMA and deterministic trends ('nc', 'c', 'ct', polynomial) // 'c' capture arima wpi c, sarima(3,0,2,4) noconstant vce(oim) save_results 43 // 'ct' capture arima wpi c t, sarima(3,0,2,4) noconstant vce(oim) save_results 44 // polynomial [1,0,0,1] capture arima wpi c t3, sarima(3,0,2,4) noconstant vce(oim) save_results 45 // SARMA and I(d): (0,d,0) x (P,0,Q,s) capture arima wpi, arima(0,2,0) sarima(3,0,2,4) noconstant vce(oim) save_results 46 // SARMA and I(D): (0,0,0) x (P,D,Q,s) capture arima wpi, sarima(3,2,2,4) noconstant vce(oim) save_results 47 // SARMA and I(d) and I(D): (0,d,0) x (P,D,Q,s) capture arima wpi, arima(0,2,0) sarima(3,2,2,4) noconstant vce(oim) save_results 48 // SARMA and diffuse initialization capture arima wpi, sarima(3,0,2,4) noconstant vce(oim) diffuse save_results 49 // SARMAX capture arima wpi x, sarima(3,0,2,4) noconstant vce(oim) save_results 50 // SARIMAX and exogenous capture arima wpi x, arima(3,2,2) sarima(3,2,2,4) noconstant vce(oim) save_results 51 // SARIMAX and exogenous and diffuse capture arima wpi x, arima(3,2,2) sarima(3,2,2,4) noconstant vce(oim) diffuse save_results 52 // ARMA and exogenous and trend polynomial and missing gen wpi2 = wpi gen t32 = (t-1)^3 replace wpi2 = . in 10/19 capture arima D.wpi2 t32 x, arima(3,0,2) noconstant vce(oim) save_results 53 // Write results outsheet mod llf parameters using "results_sarimax_coverage.csv" in 1/53, comma replace statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_sarimax_stata.do000066400000000000000000000040021400612667500305140ustar00rootroot00000000000000// Example 1: ARIMA model use https://www.stata-press.com/data/r12/wpi1, clear arima wpi, arima(1,1,1) vce(opg) arima wpi, arima(1,1,1) vce(oim) arima wpi, arima(1,1,1) vce(robust) arima wpi, arima(1,1,1) diffuse vce(opg) arima wpi, arima(1,1,1) diffuse vce(oim) // Estimate via a state-space model constraint 1 [D.wpi]u1 = 1 constraint 2 [u2]L.u1 = 1 constraint 3 [u3]L.u2 = 1 sspace (u1 L.u1 L.u2 L.u3, state noconstant) /// (u2 L.u1, state noconstant noerror) /// (u3 L.u2, state noconstant noerror) /// (D.wpi u1, noconstant noerror), /// constraints(1/3) covstate(diagonal) predict dep // Example 2: ARIMA model with additive seasonal effects arima D.ln_wpi, ar(1) ma(1 4) vce(opg) arima D.ln_wpi, ar(1) ma(1 4) vce(oim) // Example 3: Multiplicative SARIMA model use https://www.stata-press.com/data/r12/air2, clear generate lnair = ln(air) arima lnair, arima(0,1,1) sarima(0,1,1,12) noconstant vce(opg) arima lnair, arima(0,1,1) sarima(0,1,1,12) noconstant vce(oim) // Example 4: ARMAX model use https://www.stata-press.com/data/r12/friedman2, clear arima consump m2 if tin(, 1981q4), ar(1) ma(1) vce(opg) arima consump m2 if tin(, 1981q4), ar(1) ma(1) vce(oim) // Predict - Example 1: Predict, dynamic forecasts use https://www.stata-press.com/data/r12/friedman2, clear keep if time<=tq(1981q4) arima consump m2 if tin(, 1978q1), ar(1) ma(1) predict chat, y predict chatdy, dynamic(tq(1978q1)) y // Predict - Example 1, part 2: Forecasts // Note: in the previous example, because `consump` // was still non-missing for the "out-of-sample" component, it simply // amounts to in-sample prediction with fixed parameter (that happen // to have been defined by MLE on a subset of the observations) // Here make those observations missing so that we get true forecasts. use https://www.stata-press.com/data/r12/friedman2, clear keep if time<=tq(1981q4) & time>=tq(1959q1) arima consump m2 if tin(, 1978q1), ar(1) ma(1) replace consump = . if time>tq(1978q1) predict chat, y predict chatdy, dynamic(tq(1978q1)) y statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_simulation_smoothing.R000066400000000000000000000207331400612667500317370ustar00rootroot00000000000000library(KFAS) options(digits=10) # should run this from the statsmodels/statsmodels directory dta <- read.csv('datasets/macrodata/macrodata.csv') obs <- diff(log(data.matrix(dta[c('realgdp','realcons','realinv')])))[1:9,] T <- t(matrix( c(-0.1119908792, 0.8441841604, 0.0238725303, 0.2629347724, 0.4996718412, -0.0173023305, -3.2192369082, 4.1536028244, 0.4514379215), nrow=3, ncol=3)) Q <- t(matrix( c(0.0000640649, 0.0000388496, 0.0002148769, 0.0000388496, 0.0000572802, 0.000001555, 0.0002148769, 0.000001555, 0.0017088585), nrow=3, ncol=3)) H <- t(matrix( c(0.0000640649, 0., 0., 0., 0.0000572802, 0., 0., 0., 0.0017088585), nrow=3, ncol=3)) mod <- SSModel(obs ~ -1 + SSMcustom(Z=diag(3), T=T, R=diag(3), Q=Q, P1=diag(3)*1e6), H=H) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) kf$logLik # 39.01246166 # - Test 0 ------------------------------------------------------------------ # # use fixInNamespace(simHelper, 'KFAS') to set u to zeros # u <- rep(0, dfu * nsim) set.seed(1234) sim_eta <- simulateSSM(mod, type=c("eta")) sim_eps <- simulateSSM(mod, type=c("epsilon")) sim_state <- simulateSSM(mod, type=c("states")) sim_signal <- simulateSSM(mod, type=c("signals")) out <- as.data.frame(list(sim_eta, sim_eps, sim_state, sim_signal)) names(out) <- c( 'eta1', 'eta2', 'eta3', 'eps1', 'eps2', 'eps3', 'state1', 'state2', 'state3', 'signal1', 'signal2', 'signal3' ) write.csv(out, 'tsa/statespace/tests/results/results_simulation_smoothing0.csv', row.names=FALSE) # - Test 1 ------------------------------------------------------------------ # # use fixInNamespace(simHelper, 'KFAS') to set u to zeros, except set eps # variates to arange / 10 # u[1:(dfeps * nsim)] = (0:(dfeps * nsim - 1))/10 set.seed(1234) sim_eta <- simulateSSM(mod, type=c("eta")) sim_eps <- simulateSSM(mod, type=c("epsilon")) sim_state <- simulateSSM(mod, type=c("states")) sim_signal <- simulateSSM(mod, type=c("signals")) out <- as.data.frame(list(sim_eta, sim_eps, sim_state, sim_signal)) names(out) <- c( 'eta1', 'eta2', 'eta3', 'eps1', 'eps2', 'eps3', 'state1', 'state2', 'state3', 'signal1', 'signal2', 'signal3' ) write.csv(out, 'tsa/statespace/tests/results/results_simulation_smoothing1.csv', row.names=FALSE) # - Test 2 ------------------------------------------------------------------ # # use fixInNamespace(simHelper, 'KFAS') to set a1plus to zeros, set eps and eta # variates to arange / 10 # u[1:(dfeps * nsim)] = (0:(dfeps * nsim - 1))/10 # u[(dfeps * nsim + 1):(dfeps * nsim + dfeta * nsim)] = (0:(dfeps * nsim - 1))/10 set.seed(1234) sim_eta <- simulateSSM(mod, type=c("eta")) sim_eps <- simulateSSM(mod, type=c("epsilon")) sim_state <- simulateSSM(mod, type=c("states")) sim_signal <- simulateSSM(mod, type=c("signals")) out <- as.data.frame(list(sim_eta, sim_eps, sim_state, sim_signal)) names(out) <- c( 'eta1', 'eta2', 'eta3', 'eps1', 'eps2', 'eps3', 'state1', 'state2', 'state3', 'signal1', 'signal2', 'signal3' ) write.csv(out, 'tsa/statespace/tests/results/results_simulation_smoothing2.csv', row.names=FALSE) # - Test 3 ------------------------------------------------------------------ # # Reset obs to full dataset obs <- diff(log(data.matrix(dta[c('realgdp','realcons','realinv')]))) T <- t(matrix( c(-0.1119908792, 0.8441841604, 0.0238725303, 0.2629347724, 0.4996718412, -0.0173023305, -3.2192369082, 4.1536028244, 0.4514379215), nrow=3, ncol=3)) Q <- t(matrix( c(0.0000640649, 0.0000388496, 0.0002148769, 0.0000388496, 0.0000572802, 0.000001555, 0.0002148769, 0.000001555, 0.0017088585), nrow=3, ncol=3)) H <- t(matrix( c(0.0000640649, 0., 0., 0., 0.0000572802, 0., 0., 0., 0.0017088585), nrow=3, ncol=3)) mod <- SSModel(obs ~ -1 + SSMcustom(Z=diag(3), T=T, R=diag(3), Q=Q, P1=diag(3)*1e6), H=H) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) kf$logLik # 1695.34872 # if run sequentially, use fixInNamespace(simHelper, 'KFAS') to remove the # modifications to u # Instead, capture the actual variates drawn here set.seed(1234) variates <- rnorm(6 * nrow(obs) + 3, mean = 0, sd = 1) # Note: need to reset the seed before each call to make sure we always use # the same variates. set.seed(1234) sim_eta <- simulateSSM(mod, type=c("eta")) set.seed(1234) sim_eps <- simulateSSM(mod, type=c("epsilon")) set.seed(1234) sim_state <- simulateSSM(mod, type=c("states")) set.seed(1234) sim_signal <- simulateSSM(mod, type=c("signals")) out <- as.data.frame(list(sim_eta, sim_eps, sim_state, sim_signal)) names(out) <- c( 'eta1', 'eta2', 'eta3', 'eps1', 'eps2', 'eps3', 'state1', 'state2', 'state3', 'signal1', 'signal2', 'signal3' ) write.csv(variates, 'tsa/statespace/tests/results/results_simulation_smoothing3_variates.csv', row.names=FALSE) write.csv(out, 'tsa/statespace/tests/results/results_simulation_smoothing3.csv', row.names=FALSE) # - Test 4 ------------------------------------------------------------------ # # Now with some fully missing observations obs <- diff(log(data.matrix(dta[c('realgdp','realcons','realinv')]))) obs[1:50,] <- NaN mod <- SSModel(obs ~ -1 + SSMcustom(Z=diag(3), T=T, R=diag(3), Q=Q, P1=diag(3)*1e6), H=H) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) kf$logLik # 1305.739288 # The actual variates will be the same as in the Test 3 # Note: need to reset the seed before each call to make sure we always use # the same variates. set.seed(1234) sim_eta <- simulateSSM(mod, type=c("eta")) set.seed(1234) sim_eps <- simulateSSM(mod, type=c("epsilon")) set.seed(1234) sim_state <- simulateSSM(mod, type=c("states")) set.seed(1234) sim_signal <- simulateSSM(mod, type=c("signals")) out <- as.data.frame(list(sim_eta, sim_eps, sim_state, sim_signal)) names(out) <- c( 'eta1', 'eta2', 'eta3', 'eps1', 'eps2', 'eps3', 'state1', 'state2', 'state3', 'signal1', 'signal2', 'signal3' ) write.csv(out, 'tsa/statespace/tests/results/results_simulation_smoothing4.csv', row.names=FALSE) # - Test 5 ------------------------------------------------------------------ # # Now with some partially missing observations obs <- diff(log(data.matrix(dta[c('realgdp','realcons','realinv')]))) obs[1:50,1] <- NaN # The actual variates will be the same as in the Test 3 mod <- SSModel(obs ~ -1 + SSMcustom(Z=diag(3), T=T, R=diag(3), Q=Q, P1=diag(3)*1e6), H=H) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) kf$logLik # 1518.449598 # The actual variates will be the same as in the Test 3 # Note: need to reset the seed before each call to make sure we always use # the same variates. set.seed(1234) sim_eta <- simulateSSM(mod, type=c("eta")) set.seed(1234) sim_eps <- simulateSSM(mod, type=c("epsilon")) set.seed(1234) sim_state <- simulateSSM(mod, type=c("states")) set.seed(1234) sim_signal <- simulateSSM(mod, type=c("signals")) out <- as.data.frame(list(sim_eta, sim_eps, sim_state, sim_signal)) names(out) <- c( 'eta1', 'eta2', 'eta3', 'eps1', 'eps2', 'eps3', 'state1', 'state2', 'state3', 'signal1', 'signal2', 'signal3' ) write.csv(out, 'tsa/statespace/tests/results/results_simulation_smoothing5.csv', row.names=FALSE) # - Test 6 ------------------------------------------------------------------ # # Now with both fully and partially missing observations obs <- diff(log(data.matrix(dta[c('realgdp','realcons','realinv')]))) obs[1:50,1] <- NaN obs[20:70,2] <- NaN obs[40:90,3] <- NaN obs[120:130,1] <- NaN obs[120:130,3] <- NaN obs[193:202,] <- NaN mod <- SSModel(obs ~ -1 + SSMcustom(Z=diag(3), T=T, R=diag(3), Q=Q, P1=diag(3)*1e6), H=H) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) kf$logLik # 1108.341725 # The actual variates will be the same as in the Test 3 # Note: need to reset the seed before each call to make sure we always use # the same variates. set.seed(1234) sim_eta <- simulateSSM(mod, type=c("eta")) set.seed(1234) sim_eps <- simulateSSM(mod, type=c("epsilon")) set.seed(1234) sim_state <- simulateSSM(mod, type=c("states")) set.seed(1234) sim_signal <- simulateSSM(mod, type=c("signals")) out <- as.data.frame(list(sim_eta, sim_eps, sim_state, sim_signal)) names(out) <- c( 'eta1', 'eta2', 'eta3', 'eps1', 'eps2', 'eps3', 'state1', 'state2', 'state3', 'signal1', 'signal2', 'signal3' ) write.csv(out, 'tsa/statespace/tests/results/results_simulation_smoothing6.csv', row.names=FALSE) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_smoothing.R000066400000000000000000000032611400612667500274700ustar00rootroot00000000000000library(KFAS) options(digits=10) # should run this from the statsmodels/statsmodels directory dta <- read.csv('datasets/macrodata/macrodata.csv') obs <- diff(data.matrix(dta[c('realgdp','realcons','realinv')])) obs[1:50,1] <- NaN obs[20:70,2] <- NaN obs[40:90,3] <- NaN obs[120:130,1] <- NaN obs[120:130,3] <- NaN mod <- SSModel(obs ~ -1 + SSMcustom(Z=diag(3), T=diag(3), R=diag(3), Q=diag(3), P1=diag(3)*1e6), H=diag(3)) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) # kf$logLik = -205310.9767 # r = scaled_smoothed_estimator # N = scaled_smoothed_estimator_cov # m = forecasts # v = forecasts_error # F = forecasts_error_cov # a = predicted_state # P = predicted_state_cov # mu = filtered_forecasts # alphahat = smoothed_state # V = smoothed_state_cov # muhat = smoothed_forecasts # etahat = smoothed_state_disturbance # V_eta = smoothed_state_disturbance_cov # epshat = smoothed_measurement_disturbance # V_eps = smoothed_measurement_disturbance_cov out <- as.data.frame(with(kf, cbind( t(r)[2:203,], apply(N, 3, det)[2:203], m, apply(P_mu, 3, det), v, t(F), a[2:203,], apply(P, 3, det)[2:203], alphahat, apply(V, 3, det), muhat, apply(V_mu, 3, det), etahat, apply(V_eta, 3, det), epshat, t(V_eps) ))) names(out) <- c( "r1", "r2", "r3", "detN", "m1", "m2", "m3", "detPmu", "v1", "v2", "v3", "F1", "F2", "F3", "a1", "a2", "a3", "detP", "alphahat1", "alphahat2", "alphahat3", "detV", "muhat1", "muhat2", "muhat3", "detVmu", "etahat1", "etahat2", "etahat3", "detVeta", "epshat1", "epshat2", "epshat3", "Veps1", "Veps2", "Veps3" ) write.csv(out, 'tsa/statespace/tests/results/results_smoothing_R.csv', row.names=FALSE) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_smoothing2.R000066400000000000000000000046501400612667500275550ustar00rootroot00000000000000library(KFAS) options(digits=10) # should run this from the statsmodels/statsmodels directory dta <- read.csv('datasets/macrodata/macrodata.csv') obs <- diff(log(data.matrix(dta[c('realgdp','realcons','realinv')]))) #T <- t(matrix( # c(-0.1119908792, 0.8441841604, 0.0238725303, # 0.2629347724, 0.4996718412, -0.0173023305, # -3.2192369082, 4.1536028244, 0.4514379215), nrow=3, ncol=3)) #Q <- t(matrix( # c(0.0000640649, 0.0000388496, 0.0002148769, # 0.0000388496, 0.0000572802, 0.000001555, # 0.0002148769, 0.000001555, 0.0017088585), nrow=3, ncol=3)) #H <- matrix(0, 3, 3) T <- t(matrix( c(-0.1119908792, 0.8441841604, 0.0238725303, 0.2629347724, 0.4996718412, -0.0173023305, -3.2192369082, 4.1536028244, 0.4514379215), nrow=3, ncol=3)) Q <- t(matrix( c(0.0000640649, 0.0000388496, 0.0002148769, 0.0000388496, 0.0000572802, 0.000001555, 0.0002148769, 0.000001555, 0.0017088585), nrow=3, ncol=3)) H <- t(matrix( c(0.0000640649, 0., 0., 0., 0.0000572802, 0., 0., 0., 0.0017088585), nrow=3, ncol=3)) mod <- SSModel(obs ~ -1 + SSMcustom(Z=diag(3), T=T, R=diag(3), Q=Q, P1=diag(3)*1e6), H=H) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) # kf$logLik # 1695.34872 # r = scaled_smoothed_estimator # N = scaled_smoothed_estimator_cov # m = forecasts # v = forecasts_error # F = forecasts_error_cov # a = predicted_state # P = predicted_state_cov # mu = filtered_forecasts # alphahat = smoothed_state # V = smoothed_state_cov # muhat = smoothed_forecasts # etahat = smoothed_state_disturbance # V_eta = smoothed_state_disturbance_cov # epshat = smoothed_measurement_disturbance # V_eps = smoothed_measurement_disturbance_cov out <- as.data.frame(with(kf, cbind( t(r)[2:203,], apply(N, 3, det)[2:203], m, apply(P_mu, 3, det), v, t(F), a[2:203,], apply(P, 3, det)[2:203], alphahat, apply(V, 3, det), muhat, apply(V_mu, 3, det), etahat, apply(V_eta, 3, det), epshat, t(V_eps) ))) names(out) <- c( "r1", "r2", "r3", "detN", "m1", "m2", "m3", "detPmu", "v1", "v2", "v3", "F1", "F2", "F3", "a1", "a2", "a3", "detP", "alphahat1", "alphahat2", "alphahat3", "detV", "muhat1", "muhat2", "muhat3", "detVmu", "etahat1", "etahat2", "etahat3", "detVeta", "epshat1", "epshat2", "epshat3", "Veps1", "Veps2", "Veps3" ) write.csv(out, 'tsa/statespace/tests/results/results_smoothing2_R.csv', row.names=FALSE) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_smoothing3.R000066400000000000000000000040321400612667500275500ustar00rootroot00000000000000library(KFAS) options(digits=10) # should run this from the statsmodels/statsmodels directory dta <- read.csv('tsa/statespace/tests/results/results_wpi1_ar3_stata.csv') matlab <- read.csv('tsa/statespace/tests/results/results_wpi1_missing_ar3_matlab_ssm.csv') names(matlab) <- c( 'a1','a2','a3','detP','alphahat1','alphahat2','alphahat3', 'detV','eps','epsvar','eta','etavar') endog <- diff(dta$wpi) Z <- matrix(c(1, 0, 0), nrow=1, ncol=3) H <- matrix(0, nrow=1, ncol=1) T <- t(matrix( c(.5270715, .0952613, .2580355, 1, 0, 0, 0, 1, 0), nrow=3, ncol=3)) Q <- matrix(.5307459, nrow=1, ncol=1) R <- matrix(0, nrow=3, ncol=1) R[1,1] <- 1 P <- t(matrix( c(1.58276997, 1.24351589, 1.12706975, 1.24351589, 1.58276997, 1.24351589, 1.12706975, 1.24351589, 1.58276997), nrow=3, ncol=3)) mod <- SSModel(endog ~ -1 + SSMcustom(Z=Z, T=T, R=R, Q=Q, P1=P), H=H) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) # kf$logLik # -130.0310409 # r = scaled_smoothed_estimator # N = scaled_smoothed_estimator_cov # m = forecasts # v = forecasts_error # F = forecasts_error_cov # a = predicted_state # P = predicted_state_cov # mu = filtered_forecasts # alphahat = smoothed_state # V = smoothed_state_cov # muhat = smoothed_forecasts # etahat = smoothed_state_disturbance # V_eta = smoothed_state_disturbance_cov # epshat = smoothed_measurement_disturbance # V_eps = smoothed_measurement_disturbance_cov out <- as.data.frame(with(kf, cbind( t(r)[2:124,], apply(N, 3, det)[2:124], m, apply(P_mu, 3, det), v, t(F), a[2:124,], apply(P, 3, det)[2:124], alphahat, apply(V, 3, det), muhat, apply(V_mu, 3, det), etahat, apply(V_eta, 3, det), epshat, t(V_eps) ))) names(out) <- c( "r1", "r2", "r3", "detN", "m", "detPmu", "v", "F", "a1", "a2", "a3", "detP", "alphahat1", "alphahat2", "alphahat3", "detV", "muhat", "detVmu", "etahat", "detVeta", "epshat", "Veps" ) write.csv(out, 'tsa/statespace/tests/results/results_smoothing3_R.csv', row.names=FALSE) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_smoothing_generalobscov.R000066400000000000000000000046061400612667500324050ustar00rootroot00000000000000library(KFAS) options(digits=20) # should run this from the statsmodels/statsmodels directory dta <- read.csv('datasets/macrodata/macrodata.csv') obs <- diff(data.matrix(dta[c('realgdp','realcons','realinv')])) obs[1:50,1] <- NaN #obs[20:70,2] <- NaN #obs[40:90,3] <- NaN #obs[120:130,1] <- NaN #obs[120:130,3] <- NaN H <- diag(c(0.0000640649, 0.0000572802, 0.0017088585)) T <- t(matrix(c(-0.1119908792, 0.8441841604, 0.0238725303, 0.2629347724, 0.4996718412, -0.0173023305, -3.2192369082, 4.1536028244, 0.4514379215), 3, 3)) Q <- t(matrix(c(0.0000640649, 0.0000388496, 0.0002148769, 0.0000388496, 0.0000572802, 0.000001555, 0.0002148769, 0.000001555 , 0.0017088585), 3, 3)) mod <- list(Z=diag(3), H=H, T=T, R=diag(3), Q=Q, P0=diag(3)*1e6, a0=c(0,0,0)) testmod <- list(Z=ss$Z, H=ss$H, T=ss$T, R=ss$R, Q=ss$Q, P0=ss$P0, a0=ss$a0) ss <- list(Z=diag(3), R=H, B=T, Q=Q, V0=diag(3)*1e6, U="zero", x0="zero", tinitx=1) marssmod <- MARSS(t(obs), model=ss) marssout <- MARSSkfss(marssmod) mod <- SSModel(obs ~ -1 + SSMcustom(Z=diag(3), T=T, R=diag(3), Q=Q, P1=diag(3)*1e6), H=H) kf <- KFS(mod, c("state", "signal", "mean"), c("state", "signal", "mean", "disturbance"), simplify=FALSE) kf$logLik # r = scaled_smoothed_estimator # N = scaled_smoothed_estimator_cov # m = forecasts # v = forecasts_error # F = forecasts_error_cov # a = predicted_state # P = predicted_state_cov # mu = filtered_forecasts # alphahat = smoothed_state # V = smoothed_state_cov # muhat = smoothed_forecasts # etahat = smoothed_state_disturbance # V_eta = smoothed_state_disturbance_cov # epshat = smoothed_measurement_disturbance # V_eps = smoothed_measurement_disturbance_cov out <- as.data.frame(with(kf, cbind( t(r)[2:203,], apply(N, 3, det)[2:203], m, apply(P_mu, 3, det), v, t(F), a[2:203,], apply(P, 3, det)[2:203], alphahat, apply(V, 3, det), muhat, apply(V_mu, 3, det), etahat, apply(V_eta, 3, det), epshat, t(V_eps) ))) names(out) <- c( "r1", "r2", "r3", "detN", "m1", "m2", "m3", "detPmu", "v1", "v2", "v3", "F1", "F2", "F3", "a1", "a2", "a3", "detP", "alphahat1", "alphahat2", "alphahat3", "detV", "muhat1", "muhat2", "muhat3", "detVmu", "etahat1", "etahat2", "etahat3", "detVeta", "epshat1", "epshat2", "epshat3", "Veps1", "Veps2", "Veps3" ) write.csv(out, 'tsa/statespace/tests/results/results_smoothing_generalobscov_R.csv', row.names=FALSE) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_ucm.R000066400000000000000000000263421400612667500262520ustar00rootroot00000000000000library(KFAS) # library(rucm) options(digits=10) dta <- read.csv('datasets/macrodata/macrodata.csv') # Irregular (ntrend) mod_ntrend <- SSModel( dta$unemp ~ -1 + SSMcustom(Z=matrix(0), matrix(0), matrix(0), matrix(0)), H=matrix(NA)) res_ntrend <- fitSSM(inits=c(log(var(dta$unemp))), model=mod_ntrend, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_ntrend$optim.out$par)) # 36.74687342 print(res_ntrend$optim.out$value) # 653.8562525 # ---------------------------------------------------------------------------- # Irregular + Deterministic trend (dconstant) mod_dconstant <- SSModel(dta$unemp ~ SSMtrend(Q=matrix(0)), H=matrix(NA)) res_dconstant <- fitSSM(inits=c(log(var(dta$unemp))), model=mod_dconstant, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_dconstant$optim.out$par)) # 2.127438969 print(res_dconstant$optim.out$value) # 365.5289923 # ---------------------------------------------------------------------------- # Local level (llevel) mod_llevel <- SSModel(dta$unemp ~ SSMtrend(Q=matrix(NA)), H=matrix(NA)) res_llevel <- fitSSM(inits=c(log(var(dta$unemp)), log(var(dta$unemp))), model=mod_llevel, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_llevel$optim.out$par)) # [1.182078808e-01, 4.256647886e-06] print(res_llevel$optim.out$value) # 70.97242557 # ---------------------------------------------------------------------------- # Random walk (rwalk) mod_rwalk <- SSModel(dta$unemp ~ SSMtrend(Q=matrix(NA)), H=matrix(0)) res_rwalk <- fitSSM(inits=c(log(var(dta$unemp))), model=mod_rwalk, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_rwalk$optim.out$par)) # 0.1182174646 print(res_rwalk$optim.out$value) # 70.96771641 # ---------------------------------------------------------------------------- # Deterministic trend (dtrend) mod_dtrend <- SSModel(dta$unemp ~ SSMtrend(2, Q=list(matrix(0), matrix(0))), H=matrix(NA)) res_dtrend <- fitSSM(inits=c(log(var(dta$unemp))), model=mod_dtrend, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_dtrend$optim.out$par)) # 2.134137554 print(res_dtrend$optim.out$value) # 370.7758666 # ---------------------------------------------------------------------------- # Local level with deterministic trend (lldtrend) mod_lldtrend <- SSModel(dta$unemp ~ SSMtrend(2, Q=list(matrix(NA), matrix(0))), H=matrix(NA)) res_lldtrend <- fitSSM(inits=c(log(var(dta$unemp)), log(var(dta$unemp))), model=mod_lldtrend, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_lldtrend$optim.out$par)) # [1.184455029e-01, 4.457592057e-06] print(res_lldtrend$optim.out$value) # 73.47291031 # ---------------------------------------------------------------------------- # Random walk with drift (rwdrift) mod_rwdrift <- SSModel(dta$unemp ~ SSMtrend(2, Q=list(matrix(NA), matrix(0))), H=matrix(0)) res_rwdrift <- fitSSM(inits=c(log(var(dta$unemp))), model=mod_rwdrift, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_rwdrift$optim.out$par)) # [0.1184499547] print(res_rwdrift$optim.out$value) # 73.46798576 # ---------------------------------------------------------------------------- # Local linear trend (lltrend) mod_lltrend <- SSModel(dta$unemp ~ SSMtrend(2, Q=list(matrix(NA), matrix(NA))), H=matrix(NA)) res_lltrend <- fitSSM(inits=c(log(var(dta$unemp)), log(var(dta$unemp)), log(var(dta$unemp))), model=mod_lltrend, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_lltrend$optim.out$par)) # [1.008704925e-02, 6.091760810e-02, # 1.339852549e-06] print(res_lltrend$optim.out$value) # 31.15640107 # ---------------------------------------------------------------------------- # Smooth trend (strend) mod_strend <- SSModel(dta$unemp ~ SSMtrend(2, Q=list(matrix(0), matrix(NA))), H=matrix(NA)) res_strend <- fitSSM(inits=c(log(var(dta$unemp)), log(var(dta$unemp))), model=mod_strend, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_strend$optim.out$par)) # [0.0753064234342, 0.0008824099119] print(res_strend$optim.out$value) # 31.92261408 # ---------------------------------------------------------------------------- # Random trend (rtrend) mod_rtrend <- SSModel(dta$unemp ~ SSMtrend(2, Q=list(matrix(0), matrix(NA))), H=matrix(0)) res_rtrend <- fitSSM(inits=c(log(var(dta$unemp))), model=mod_rtrend, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_rtrend$optim.out$par)) # [0.08054724989] print(res_rtrend$optim.out$value) # 32.05607557 # ---------------------------------------------------------------------------- # Cycle (exact diffuse) (with fixed period=10, cycle variance=0.1) mod_cycle <- SSModel(dta$unemp ~ -1 + SSMcycle(10, Q=matrix(0.1)), H=matrix(NA)) res_cycle <- fitSSM(inits=c(log(var(dta$unemp))), model=mod_cycle, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_cycle$optim.out$par)) # [37.57197079] print(res_cycle$optim.out$value) # 656.6568684 # Cycle (approximate diffuse) (with fixed period=10, cycle variance=0.1) # Note: matching this requires setting loglikelihood_burn = 0 mod_cycle_approx_diffuse <- SSModel( dta$unemp ~ -1 + SSMcycle(10, Q=matrix(0.1), P1=diag(2)*1e6), H=matrix(NA)) res_cycle_approx_diffuse <- fitSSM(inits=c(log(var(dta$unemp))), model=mod_cycle_approx_diffuse, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_cycle_approx_diffuse$optim.out$par)) # [37.57197224] print(res_cycle_approx_diffuse$optim.out$value) # 672.3102588 # ---------------------------------------------------------------------------- # Seasonal (exact diffuse) (with fixed period=4, seasonal variance=0.1) mod_seasonal <- SSModel( dta$unemp ~ -1 + SSMseasonal(4, Q=matrix(0.1), sea.type='dummy'), H=matrix(NA)) res_seasonal <- fitSSM(inits=c(log(var(dta$unemp))), model=mod_seasonal, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_seasonal$optim.out$par)) # [38.17043009] print(res_seasonal$optim.out$value) # 655.3337155 # Seasonal (approximate diffuse) (with fixed period=4, seasonal variance=0.1) # Note: matching this requires setting loglikelihood_burn=0 mod_seasonal_approx_diffuse <- SSModel( dta$unemp ~ -1 + SSMseasonal(4, Q=matrix(0.1), sea.type='dummy', P1=diag(rep(1e6, 3))), H=matrix(NA)) res_seasonal_approx_diffuse <- fitSSM( inits=c(log(var(dta$unemp))), model=mod_seasonal_approx_diffuse, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_seasonal_approx_diffuse$optim.out$par)) # [38.1704278] print(res_seasonal_approx_diffuse$optim.out$value) # 678.8138005 # ---------------------------------------------------------------------------- # Trig Seasonal (exact diffuse) # (with fixed period=5, full number of harmonics, seasonal variance=.05) mod_trig_seasonal <- SSModel( dta$unemp ~ -1 + SSMseasonal(5, Q=0.05, sea.type='trigonometric'), H=matrix(NA)) res_trig_seasonal <- fitSSM( inits=c(log(var(dta$unemp))), model=mod_trig_seasonal, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_trig_seasonal$optim.out$par)) # [38.95353592] print(res_trig_seasonal$optim.out$value) # 657.6629457 # Trig Seasonal (approximate diffuse) # (with fixed period=5, full number of harmonics, seasonal variance=.05) # Note: matching this requires setting loglikelihood_burn=0 mod_trig_seasonal_approx_diffuse <- SSModel( dta$unemp ~ -1 + SSMseasonal(5, Q=0.05, sea.type='trigonometric', P1=diag(rep(1e6, 4))), H=matrix(NA)) res_trig_seasonal_approx_diffuse <- fitSSM( inits=c(log(var(dta$unemp))), model=mod_trig_seasonal_approx_diffuse, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_trig_seasonal_approx_diffuse$optim.out$par)) # [38.95352534] print(res_trig_seasonal_approx_diffuse$optim.out$value) # 688.9697249 # ---------------------------------------------------------------------------- # Regression (exact diffuse) # Note: matching this requires setting loglikelihood_burn = 0 mod_reg <- SSModel(dta$unemp ~ -1 + SSMregression(~-1+log(realgdp), data=dta), H=matrix(NA)) res_reg <- fitSSM(inits=c(log(var(dta$unemp))), model=mod_reg, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_reg$optim.out$par)) # [2.215438082] print(res_reg$optim.out$value) # 371.7966543 # Regression (approximate diffuse) # Note: matching this requires setting loglikelihood_burn = 0 mod_reg_approx_diffuse <- SSModel( dta$unemp ~ -1 + SSMregression(~-1+log(realgdp), data=dta, P1=diag(1)*1e6), H=matrix(NA)) res_reg_approx_diffuse <- fitSSM( inits=c(log(var(dta$unemp))), model=mod_reg_approx_diffuse, method="BFGS", control=list(REPORT=1, trace=1)) print(exp(res_reg_approx_diffuse$optim.out$par)) # [2.215447924] print(res_reg_approx_diffuse$optim.out$value) # 379.6233483 # ---------------------------------------------------------------------------- # Random trend + AR(1) # Note: KFAS does not want to estimate these parameters, so just fix them # to the MLE estimates from statsmodels and compare the loglikelihood # mod.update([]) mod_rtrend_ar1 <- SSModel( dta$unemp ~ SSMtrend(2, Q=list(matrix(0), matrix(0.0609))) + SSMarima(ar=c(0.9592), Q=matrix(0.0097)), H=matrix(0)) out_rtrend_ar1 <- KFS(mod_rtrend_ar1) print(out_rtrend_ar1$logLik) # -31.15629379 # ---------------------------------------------------------------------------- # Local linear trend + Cycle + Seasonal + Regression + AR(1) # (exact diffuse) # mod.update([0.0001, 0.01, 0.06, 0.0001, 0.0001, 0.1, 2*np.pi / 10, 0.2]) mod_lltrend_cycle_seasonal_reg_ar1 <- SSModel( dta$unemp ~ SSMtrend(2, Q=list(matrix(0.01), matrix(0.06))) + SSMcycle(10, Q=matrix(0.0001)) + SSMseasonal(4, Q=matrix(0.0001)) + SSMregression(~-1+log(realgdp), data=dta) + SSMarima(ar=c(0.2), Q=matrix(0.1)), H=matrix(0.0001)) out_lltrend_cycle_seasonal_reg_ar1 <- KFS(mod_lltrend_cycle_seasonal_reg_ar1) print(out_lltrend_cycle_seasonal_reg_ar1$logLik) # -105.8936568 # Local linear trend + Cycle + Seasonal + Regression + AR(1) # (approximate diffuse) # Note: matching this requires setting loglikelihood_burn = 0, and # mod.update([0.0001, 0.01, 0.06, 0.0001, 0.0001, 0.1, 2*np.pi / 10, 0.2]) mod_lltrend_cycle_seasonal_reg_ar1_approx_diffuse <- SSModel( dta$unemp ~ SSMtrend(2, Q=list(matrix(0.01), matrix(0.06)), P1=diag(2)*1e6) + SSMcycle(10, Q=matrix(0.0001), P1=diag(2)*1e6) + SSMseasonal(4, Q=matrix(0.0001), P1=diag(3)*1e6) + SSMregression(~-1+log(realgdp), data=dta, P1=diag(1)*1e6) + SSMarima(ar=c(0.2), Q=matrix(0.1)), H=matrix(0.0001)) out_lltrend_cycle_seasonal_reg_ar1_approx_diffuse <- ( KFS(mod_lltrend_cycle_seasonal_reg_ar1_approx_diffuse)) print(out_lltrend_cycle_seasonal_reg_ar1_approx_diffuse$logLik) # -168.5258709 statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_var.R000066400000000000000000000227131400612667500262540ustar00rootroot00000000000000library(plyr) library(vars) # library(MTS) library(readstata13) options(digits=15, scipen=999) dta <- read.dta13('~/projects/statsmodels/statsmodels/tsa/tests/results/lutkepohl2.dta') # TODO # predict(res, dumvar=exog_fcast) # vars::fevd(res) # vars::irf(res) extract_var_output <- function(res, k_trend=0, k_exog=0) { s <- summary(res) # Coefficient vectors coeffs <- vector("list", res$K) for(i in 1:res$K) { coeffs[[i]] <- t(res$varresult[[i]]$coefficients) } coeffs <- rbind.fill.matrix(coeffs) # Reorder k <- res$K * res$p k1 <- k + k_trend k2 <- ncol(coeffs) trend <- c() if (k_trend > 0) { trend <- t(coeffs[,(k + 1):k1]) } var <- t(coeffs[,1:k]) exog <- c() if (k_exog > 0) { exog <- t(coeffs[,(k1 + 1):k2]) } # Error variance # Have to compute this by hand since the definition used # in the log-likelihood computation is not the same as that # given by summary resids <- resid(res) Sigma <- (t(resids) %*% resids) / res$obs U <- chol(Sigma) params <- c(trend, var, exog, U[upper.tri(U, diag=TRUE)]) return(list(coeffs=coeffs, params=params, s=s)) } # "res_basic" endog <- dta[2:76,c('dln_inv', 'dln_inc', 'dln_consump')] res <- vars::VAR(endog, p=2, type="none") out <- extract_var_output(res, k_trend=0) cat(out$s$logLik) cat(out$params, sep=', ') fcasts_basic <- as.data.frame(predict(res)$fcst)[c(1,4,5,8,9,12)] names(fcasts_basic) <- paste0('basic.fcast.', names(fcasts_basic)) irfs_basic <- as.data.frame(vars::irf(res, ortho=FALSE, boot=FALSE)$irf) names(irfs_basic) <- paste0('basic.irf.', names(irfs_basic)) irfs_basic_ortho <- as.data.frame(vars::irf(res, ortho=TRUE, boot=FALSE)$irf) names(irfs_basic_ortho) <- paste0('basic.irf.ortho.', names(irfs_basic_ortho)) irfs_basic_cumu <- as.data.frame(vars::irf(res, cumulative=TRUE, boot=FALSE)$irf) names(irfs_basic_cumu) <- paste0('basic.irf.cumu.', names(irfs_basic_cumu)) fevd_basic <- vars::fevd(res) fevd_basic <- as.data.frame(cbind(fevd_basic[[1]], fevd_basic[[2]], fevd_basic[[3]])) names(fevd_basic) <- paste0('basic.fevd.', names(fevd_basic)) # "res_c" endog <- dta[2:76,c('dln_inv', 'dln_inc', 'dln_consump')] res <- vars::VAR(endog, p=2, type="const") out <- extract_var_output(res, k_trend=1) cat(out$s$logLik) cat(out$params, sep=', ') fcasts_c <- as.data.frame(predict(res)$fcst)[c(1,4,5,8,9,12)] names(fcasts_c) <- paste0('c.fcast.', names(fcasts_c)) irfs_c <- as.data.frame(vars::irf(res, ortho=FALSE, boot=FALSE)$irf) names(irfs_c) <- paste0('c.irf.', names(irfs_c)) irfs_c_ortho <- as.data.frame(vars::irf(res, ortho=TRUE, boot=FALSE)$irf) names(irfs_c_ortho) <- paste0('c.irf.ortho.', names(irfs_c_ortho)) irfs_c_cumu <- as.data.frame(vars::irf(res, cumulative=TRUE, boot=FALSE)$irf) names(irfs_c_cumu) <- paste0('c.irf.cumu.', names(irfs_c_cumu)) fevd_c <- vars::fevd(res) fevd_c <- as.data.frame(cbind(fevd_c[[1]], fevd_c[[2]], fevd_c[[3]])) names(fevd_c) <- paste0('c.fevd.', names(fevd_c)) # "res_ct" endog <- dta[2:76,c('dln_inv', 'dln_inc', 'dln_consump')] res <- vars::VAR(endog, p=2, type="both") out <- extract_var_output(res, k_trend=2) cat(out$s$logLik) cat(out$params, sep=', ') fcasts_ct <- as.data.frame(predict(res)$fcst)[c(1,4,5,8,9,12)] names(fcasts_ct) <- paste0('ct.fcast.', names(fcasts_ct)) irfs_ct <- as.data.frame(vars::irf(res, ortho=FALSE, boot=FALSE)$irf) names(irfs_ct) <- paste0('ct.irf.', names(irfs_ct)) irfs_ct_ortho <- as.data.frame(vars::irf(res, ortho=TRUE, boot=FALSE)$irf) names(irfs_ct_ortho) <- paste0('ct.irf.ortho.', names(irfs_ct_ortho)) irfs_ct_cumu <- as.data.frame(vars::irf(res, cumulative=TRUE, boot=FALSE)$irf) names(irfs_ct_cumu) <- paste0('ct.irf.cumu.', names(irfs_ct_cumu)) fevd_ct <- vars::fevd(res) fevd_ct <- as.data.frame(cbind(fevd_ct[[1]], fevd_ct[[2]], fevd_ct[[3]])) names(fevd_ct) <- paste0('ct.fevd.', names(fevd_ct)) # "res_ct_as_exog0" # here we start the trend at zero endog <- dta[2:76,c('dln_inv', 'dln_inc', 'dln_consump')] exog <- cbind(rep(1, 75), 0:74) exog_fcast <- cbind(rep(1, 10), 75:84) # exog <- cbind(rep(1, 75), 1:75, (1:75)^2) res <- vars::VAR(endog, p=2, type="none", exogen=exog) out <- extract_var_output(res, k_trend=0, k_exog=2) cat(out$s$logLik) cat(out$params, sep=', ') fcasts_ct_as_exog0 <- as.data.frame(predict(res, dumvar=exog_fcast)$fcst)[c(1,4,5,8,9,12)] names(fcasts_ct_as_exog0) <- paste0('ct_as_exog0.fcast.', names(fcasts_ct_as_exog0)) irfs_ct_as_exog0 <- as.data.frame(vars::irf(res, ortho=FALSE, boot=FALSE)$irf) names(irfs_ct_as_exog0) <- paste0('ct_as_exog0.irf.', names(irfs_ct_as_exog0)) irfs_ct_as_exog0_ortho <- as.data.frame(vars::irf(res, ortho=TRUE, boot=FALSE)$irf) names(irfs_ct_as_exog0_ortho) <- paste0('ct_as_exog0.irf.ortho.', names(irfs_ct_as_exog0_ortho)) irfs_ct_as_exog0_cumu <- as.data.frame(vars::irf(res, cumulative=TRUE, boot=FALSE)$irf) names(irfs_ct_as_exog0_cumu) <- paste0('ct_as_exog0.irf.cumu.', names(irfs_ct_as_exog0_cumu)) fevd_ct_as_exog0 <- vars::fevd(res) fevd_ct_as_exog0 <- as.data.frame(cbind(fevd_ct_as_exog0[[1]], fevd_ct_as_exog0[[2]], fevd_ct_as_exog0[[3]])) names(fevd_ct_as_exog0) <- paste0('ct_as_exog0.fevd.', names(fevd_ct_as_exog0)) # "res_ctt_as_exog1" endog <- dta[2:76,c('dln_inv', 'dln_inc', 'dln_consump')] exog <- cbind(rep(1, 75), 1:75, (1:75)^2) exog_fcast <- cbind(rep(1, 10), 76:85, (76:85)^2) res <- vars::VAR(endog, p=2, type='none', exogen=exog) out <- extract_var_output(res, k_trend=0, k_exog=3) cat(out$s$logLik) cat(out$params, sep=', ') fcasts_ctt_as_exog1 <- as.data.frame(predict(res, dumvar=exog_fcast)$fcst)[c(1,4,5,8,9,12)] names(fcasts_ctt_as_exog1) <- paste0('ctt_as_exog1.fcast.', names(fcasts_ctt_as_exog1)) irfs_ctt_as_exog1 <- as.data.frame(vars::irf(res, ortho=FALSE, boot=FALSE)$irf) names(irfs_ctt_as_exog1) <- paste0('ctt_as_exog1.irf.', names(irfs_ctt_as_exog1)) irfs_ctt_as_exog1_ortho <- as.data.frame(vars::irf(res, ortho=TRUE, boot=FALSE)$irf) names(irfs_ctt_as_exog1_ortho) <- paste0('ctt_as_exog1.irf.ortho.', names(irfs_ctt_as_exog1_ortho)) irfs_ctt_as_exog1_cumu <- as.data.frame(vars::irf(res, cumulative=TRUE, boot=FALSE)$irf) names(irfs_ctt_as_exog1_cumu) <- paste0('ctt_as_exog1.irf.cumu.', names(irfs_ctt_as_exog1_cumu)) fevd_ctt_as_exog1 <- vars::fevd(res) fevd_ctt_as_exog1 <- as.data.frame(cbind(fevd_ctt_as_exog1[[1]], fevd_ctt_as_exog1[[2]], fevd_ctt_as_exog1[[3]])) names(fevd_ctt_as_exog1) <- paste0('ctt_as_exog1.fevd.', names(fevd_ctt_as_exog1)) # "res_ct_exog" endog <- dta[2:76,c('dln_inv', 'dln_inc', 'dln_consump')] exog <- dta[2:76,c('inc')] exog_fcast <- matrix(dta[77:86,'inc'], nrow=10, ncol=1) names(exog_fcast) <- c('inc') res <- vars::VAR(endog, p=2, type='both', exogen=exog) out <- extract_var_output(res, k_trend=2, k_exog=1) cat(out$s$logLik) cat(out$params, sep=', ') fcasts_ct_exog <- as.data.frame(predict(res, dumvar=exog_fcast)$fcst)[c(1,4,5,8,9,12)] names(fcasts_ct_exog) <- paste0('ct_exog.fcast.', names(fcasts_ct_exog)) irfs_ct_exog <- as.data.frame(vars::irf(res, ortho=FALSE, boot=FALSE)$irf) names(irfs_ct_exog) <- paste0('ct_exog.irf.', names(irfs_ct_exog)) irfs_ct_exog_ortho <- as.data.frame(vars::irf(res, ortho=TRUE, boot=FALSE)$irf) names(irfs_ct_exog_ortho) <- paste0('ct_exog.irf.ortho.', names(irfs_ct_exog_ortho)) irfs_ct_exog_cumu <- as.data.frame(vars::irf(res, cumulative=TRUE, boot=FALSE)$irf) names(irfs_ct_exog_cumu) <- paste0('ct_exog.irf.cumu.', names(irfs_ct_exog_cumu)) fevd_ct_exog <- vars::fevd(res) fevd_ct_exog <- as.data.frame(cbind(fevd_ct_exog[[1]], fevd_ct_exog[[2]], fevd_ct_exog[[3]])) names(fevd_ct_exog) <- paste0('ct_exog.fevd.', names(fevd_ct_exog)) # "res_c_2exog" endog <- dta[2:76,c('dln_inv', 'dln_inc', 'dln_consump')] exog <- dta[2:76,c('inc', 'inv')] exog_fcast <- dta[77:86,c('inc', 'inv')] res <- vars::VAR(endog, p=2, type='const', exogen=exog) out <- extract_var_output(res, k_trend=1, k_exog=2) cat(out$s$logLik) cat(out$params, sep=', ') fcasts_c_2exog <- as.data.frame(predict(res, dumvar=exog_fcast)$fcst)[c(1,4,5,8,9,12)] names(fcasts_c_2exog) <- paste0('c_2exog.fcast.', names(fcasts_c_2exog)) irfs_c_2exog <- as.data.frame(vars::irf(res, ortho=FALSE, boot=FALSE)$irf) names(irfs_c_2exog) <- paste0('c_2exog.irf.', names(irfs_c_2exog)) irfs_c_2exog_ortho <- as.data.frame(vars::irf(res, ortho=TRUE, boot=FALSE)$irf) names(irfs_c_2exog_ortho) <- paste0('c_2exog.irf.ortho.', names(irfs_c_2exog_ortho)) irfs_c_2exog_cumu <- as.data.frame(vars::irf(res, cumulative=TRUE, boot=FALSE)$irf) names(irfs_c_2exog_cumu) <- paste0('c_2exog.irf.cumu.', names(irfs_c_2exog_cumu)) fevd_c_2exog <- vars::fevd(res) fevd_c_2exog <- as.data.frame(cbind(fevd_c_2exog[[1]], fevd_c_2exog[[2]], fevd_c_2exog[[3]])) names(fevd_c_2exog) <- paste0('c_2exog.fevd.', names(fevd_c_2exog)) cbind.fill <- function(...){ nm <- list(...) nm <- lapply(nm, as.matrix) n <- max(sapply(nm, nrow)) do.call(cbind, lapply(nm, function (x) rbind(x, matrix(, n-nrow(x), ncol(x))))) } # Combine forecasts, irfs, etc output <- cbind.fill( fcasts_basic, fcasts_c, fcasts_ct, fcasts_ct_as_exog0, fcasts_ctt_as_exog1, fcasts_ct_exog, fcasts_c_2exog, irfs_basic, irfs_c, irfs_ct, irfs_ct_as_exog0, irfs_ctt_as_exog1, irfs_ct_exog, irfs_c_2exog, irfs_basic_ortho, irfs_c_ortho, irfs_ct_ortho, irfs_ct_as_exog0_ortho, irfs_ctt_as_exog1_ortho, irfs_ct_exog_ortho, irfs_c_2exog_ortho, irfs_basic_cumu, irfs_c_cumu, irfs_ct_cumu, irfs_ct_as_exog0_cumu, irfs_ctt_as_exog1_cumu, irfs_ct_exog_cumu, irfs_c_2exog_cumu, fevd_basic, fevd_c, fevd_ct, fevd_ct_as_exog0, fevd_ctt_as_exog1, fevd_ct_exog, fevd_c_2exog) write.csv(output, '~/projects/statsmodels/statsmodels/tsa/statespace/tests/results/results_var_R_output.csv') statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_var_misc_stata.do000066400000000000000000000015151400612667500306610ustar00rootroot00000000000000webuse lutkepohl2, clear tsset // AR(1) // For results output, do: // matrix list e(b) // matrix list e(Sigma) // for loglike, aic, sbic, hqic, fpe: // ereturn list // for non-Lutkepohl IC, do: // estat ic // matrix list r(S) var dln_inv if qtr<=tq(1978q4), lags(1) estat ic var dln_inv if qtr<=tq(1978q4), lags(1) lutstats estat ic var dln_inv if qtr<=tq(1978q4), lags(1) lutstats dfk estat ic // VAR(1) // For results output, do: // matrix list e(b) // matrix list e(Sigma), format(%13.12f) // for loglike, aic, sbic, hqic, fpe: // ereturn list // for non-Lutkepohl IC, do: // estat ic // matrix list r(S) var dln_inv dln_inc dln_consump if qtr<=tq(1978q4), noconstant lags(1) var dln_inv dln_inc dln_consump if qtr<=tq(1978q4), noconstant lags(1) lutstats var dln_inv dln_inc dln_consump if qtr<=tq(1978q4), noconstant lags(1) lutstats dfk statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_varmax_stata.do000066400000000000000000000142471400612667500303620ustar00rootroot00000000000000webuse lutkepohl2, clear tsset // VAR(1) dfactor (dln_inv dln_inc dln_consump = , ar(1) arstructure(general) noconstant covstructure(unstructured)) if qtr<=tq(1978q4) estat ic // These are predict in-sample + forecast out-of-sample (1979q1 is first out-of sample obs) predict predict_1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_2, dynamic(tq(1979q1)) equation(dln_inc) predict predict_3, dynamic(tq(1979q1)) equation(dln_consump) // These are predict in-sample for first 3-observations (1960q2-1960q4), then // dynamic predict for the rest of in-sample observations (1961q1-1978q4), then // forecast for the remaining periods 1979q1 - 1982q4 predict dyn_predict_1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_2, dynamic(tq(1961q1)) equation(dln_inc) predict dyn_predict_3, dynamic(tq(1961q1)) equation(dln_consump) // VAR(1), diagonal covariance dfactor (dln_inv dln_inc dln_consump = , ar(1) arstructure(general) noconstant covstructure(diagonal)) if qtr<=tq(1978q4) estat ic // predict + forecast, see above predict predict_diag1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_diag2, dynamic(tq(1979q1)) equation(dln_inc) predict predict_diag3, dynamic(tq(1979q1)) equation(dln_consump) // predict + dynamic predict + forecast, see above predict dyn_predict_diag1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_diag2, dynamic(tq(1961q1)) equation(dln_inc) predict dyn_predict_diag3, dynamic(tq(1961q1)) equation(dln_consump) // VAR(1), diagonal covariance + observation intercept dfactor (dln_inv dln_inc dln_consump = , ar(1) arstructure(general) covstructure(diagonal)) if qtr<=tq(1978q4) estat ic // predict + forecast, see above predict predict_int1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_int2, dynamic(tq(1979q1)) equation(dln_inc) predict predict_int3, dynamic(tq(1979q1)) equation(dln_consump) // predict + dynamic predict + forecast, see above predict dyn_predict_int1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_int2, dynamic(tq(1961q1)) equation(dln_inc) predict dyn_predict_int3, dynamic(tq(1961q1)) equation(dln_consump) // VAR(1), diagonal covariance + 1 exog gen t = _n //dfactor (dln_inv dln_inc dln_consump = t, ar(1) arstructure(general) noconstant covstructure(diagonal)) if qtr<=tq(1978q4) var dln_inv dln_inc dln_consump if qtr<=tq(1978q4), lags(1) noconstant exog(t) // predict, see above (Note: uses actual data for forecasting, so we will want // to ignore the predictions after 1978q4, see below predict predict_exog1_1, equation(dln_inv) predict predict_exog1_2, equation(dln_inc) predict predict_exog1_3, equation(dln_consump) // We will want to use these values to compare for forecasting, but note that // this also includes in the columns the value for 1978q4 (i.e. a VAR(1) needs // 1 sample from which to compute forecasts. fcast compute fcast_exog1_ , dynamic(tq(1979q1)) step(16) replace // VAR(1), diagonal covariance + 2 exog gen c = 1 //dfactor (dln_inv dln_inc dln_consump = t, ar(1) arstructure(general) noconstant covstructure(diagonal)) if qtr<=tq(1978q4) var dln_inv dln_inc dln_consump if qtr<=tq(1978q4), lags(1) noconstant exog(c t) // predict, see above (Note: uses actual data for forecasting, so we will want // to ignore the predictions after 1978q4, see below predict predict_exog2_1, equation(dln_inv) predict predict_exog2_2, equation(dln_inc) predict predict_exog2_3, equation(dln_consump) // We will want to use these values to compare for forecasting, but note that // this also includes in the columns the value for 1978q4 (i.e. a VAR(1) needs // 1 sample from which to compute forecasts. fcast compute fcast_exog2_ , dynamic(tq(1979q1)) step(16) replace // VAR(2) dfactor (dln_inv dln_inc = , ar(1/2) arstructure(general) noconstant covstructure(unstructured)) if qtr<=tq(1978q4) estat ic // predict + forecast, see above predict predict_var2_1, dynamic(tq(1979q1)) equation(dln_inv) predict predict_var2_2, dynamic(tq(1979q1)) equation(dln_inc) // predict + dynamic predict + forecast, see above predict dyn_predict_var2_1, dynamic(tq(1961q1)) equation(dln_inv) predict dyn_predict_var2_2, dynamic(tq(1961q1)) equation(dln_inc) outsheet pred* dyn* fcas* using results_var_stata.csv, comma replace // VARMA(1,1) // Note: Stata does not have this built-in, so we need to create the state space form ourselves // This replicates example 4 from the Stata documentation use https://www.stata-press.com/data/r12/manufac, clear gen dlncaputil = D.lncaputil gen dlnhours = D.lnhours constraint 1 [u1]L.u2 = 1 constraint 2 [u1]e.u1 = 1 constraint 3 [u3]e.u3 = 1 constraint 4 [dlncaputil]u1 = 1 constraint 5 [dlnhours]u3 = 1 sspace (u1 L.u1 L.u2 e.u1, state noconstant) /// (u2 e.u1, state noconstant) /// (u3 L.u1 L.u3 e.u3, state noconstant) /// (dlncaputil u1, noconstant) /// (dlnhours u3, noconstant), /// constraints(1/5) technique(nr) covstate(diagonal) // in-sample predict + forecast 5 new observations (sample ends at 1999m12) tsappend, add(5) predict predict_varma11_1, dynamic(tm(2009m1)) equation(dlncaputil) predict predict_varma11_2, dynamic(tm(2009m1)) equation(dlnhours) // predict + dynamic predict + forecast predict dyn_predict_varma11_1, dynamic(tm(2000m1)) equation(dlncaputil) predict dyn_predict_varma11_2, dynamic(tm(2000m1)) equation(dlnhours) // VMA(1) // Note: Stata does not have this built-in, so we need to create the state space form ourselves constraint 1 [u1]L.u2 = 1 constraint 2 [u1]e.u1 = 1 constraint 3 [u3]e.u3 = 1 constraint 4 [dlncaputil]u1 = 1 constraint 5 [dlnhours]u3 = 1 sspace (u1 L.u2 e.u1, state noconstant) /// (u2 e.u1, state noconstant) /// (u3 e.u3, state noconstant) /// (dlncaputil u1, noconstant) /// (dlnhours u3, noconstant), /// constraints(1/5) technique(nr) covstate(diagonal) // in-sample predict + forecast 5 new observations (sample ends at 1999m12) predict predict_vma1_1, dynamic(tm(2009m1)) equation(dlncaputil) predict predict_vma1_2, dynamic(tm(2009m1)) equation(dlnhours) // predict + dynamic predict + forecast predict dyn_predict_vma1_1, dynamic(tm(2000m1)) equation(dlncaputil) predict dyn_predict_vma1_2, dynamic(tm(2000m1)) equation(dlnhours) outsheet pred* dyn* using results_varmax_stata.csv, comma replace statsmodels-0.12.2/statsmodels/tsa/statespace/tests/results/test_wpi1_stata.do000066400000000000000000000013511400612667500277340ustar00rootroot00000000000000use https://www.stata-press.com/data/r12/wpi1, clear gen dwpi = D.wpi // Estimate an AR(3) via a state-space model // (to test prediction, standardized residuals, predicted states) constraint 1 [dwpi]u1 = 1 constraint 2 [u2]L.u1 = 1 constraint 3 [u3]L.u2 = 1 sspace (u1 L.u1 L.u2 L.u3, state noconstant) /// (u2 L.u1, state noconstant noerror) /// (u3 L.u2, state noconstant noerror) /// (dwpi u1, noconstant noerror), /// constraints(1/3) covstate(diagonal) predict dep* predict sr*, rstandard predict sp*, states smethod(onestep) // predicted states predict sf*, states smethod(filter) // filtered states predict sm*, states smethod(smooth) // smoothed states outsheet using results_wpi1_ar3_stata.csv, comma statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_cfa_simulation_smoothing.py000066400000000000000000000153101400612667500312710ustar00rootroot00000000000000""" Tests for CFA simulation smoothing Author: Chad Fulton License: BSD-3 """ import os import numpy as np from numpy.testing import assert_allclose import pandas as pd from scipy.linalg import cho_solve_banded from statsmodels import datasets from statsmodels.tsa.statespace import (sarimax, structural, dynamic_factor, varmax) current_path = os.path.dirname(os.path.abspath(__file__)) dta = datasets.macrodata.load_pandas().data dta.index = pd.period_range('1959Q1', '2009Q3', freq='Q') dta = np.log(dta[['realcons', 'realgdp', 'cpi']]).diff().iloc[1:] * 400 class CheckPosteriorMoments(object): @classmethod def setup_class(cls, model_class, missing=None, mean_atol=0, cov_atol=0, use_complex=False, *args, **kwargs): cls.mean_atol = mean_atol cls.cov_atol = cov_atol endog = dta.copy() if missing == 'all': endog.iloc[0:50, :] = np.nan elif missing == 'partial': endog.iloc[0:50, 0] = np.nan elif missing == 'mixed': endog.iloc[0:50, 0] = np.nan endog.iloc[19:70, 1] = np.nan endog.iloc[39:90, 2] = np.nan endog.iloc[119:130, 0] = np.nan endog.iloc[119:130, 2] = np.nan endog.iloc[-10:, :] = np.nan if model_class in [sarimax.SARIMAX, structural.UnobservedComponents]: endog = endog.iloc[:, 2] cls.mod = model_class(endog, *args, **kwargs) params = cls.mod.start_params if use_complex: params = params + 0j cls.res = cls.mod.smooth(params) cls.sim_cfa = cls.mod.simulation_smoother(method='cfa') cls.sim_cfa.simulate() prefix = 'z' if use_complex else 'd' cls._sim_cfa = cls.sim_cfa._simulation_smoothers[prefix] def test_posterior_mean(self): # Test the values from the Cython results actual = np.array(self._sim_cfa.posterior_mean, copy=True) assert_allclose(actual, self.res.smoothed_state, atol=self.mean_atol) # Test the values from the CFASimulationSmoother wrapper results assert_allclose(self.sim_cfa.posterior_mean, self.res.smoothed_state, atol=self.mean_atol) def test_posterior_cov(self): # Test the values from the Cython results inv_chol = np.array(self._sim_cfa.posterior_cov_inv_chol, copy=True) actual = cho_solve_banded((inv_chol, True), np.eye(inv_chol.shape[1])) for t in range(self.mod.nobs): tm = t * self.mod.k_states t1m = tm + self.mod.k_states assert_allclose(actual[tm:t1m, tm:t1m], self.res.smoothed_state_cov[..., t], atol=self.cov_atol) # Test the values from the CFASimulationSmoother wrapper results actual = self.sim_cfa.posterior_cov for t in range(self.mod.nobs): tm = t * self.mod.k_states t1m = tm + self.mod.k_states assert_allclose(actual[tm:t1m, tm:t1m], self.res.smoothed_state_cov[..., t], atol=self.cov_atol) class TestDFM(CheckPosteriorMoments): @classmethod def setup_class(cls, missing=None, *args, **kwargs): kwargs['k_factors'] = 1 kwargs['factor_order'] = 1 super().setup_class(dynamic_factor.DynamicFactor, missing=missing, *args, **kwargs) class TestDFMComplex(CheckPosteriorMoments): @classmethod def setup_class(cls, missing=None, *args, **kwargs): kwargs['k_factors'] = 1 kwargs['factor_order'] = 1 super().setup_class(dynamic_factor.DynamicFactor, missing=missing, use_complex=True, *args, **kwargs) class TestDFMAllMissing(TestDFM): def setup_class(cls, missing='all', *args, **kwargs): super().setup_class(missing=missing, *args, **kwargs) class TestDFMPartialMissing(TestDFM): def setup_class(cls, missing='partial', *args, **kwargs): super().setup_class(missing=missing, *args, **kwargs) class TestDFMMixedMissing(TestDFM): def setup_class(cls, missing='mixed', *args, **kwargs): super().setup_class(missing=missing, *args, **kwargs) class TestVARME(CheckPosteriorMoments): # Test VAR model with Measurement Error # Note: this includes a trend # Note: have to use measurement error, due to the restriction that all # shocks must be non-degenerate for the CFA algorithm @classmethod def setup_class(cls, missing=None, *args, **kwargs): kwargs['order'] = (1, 0) kwargs['measurement_error'] = True super().setup_class(varmax.VARMAX, missing=missing, *args, **kwargs) class TestVARMEAllMissing(TestVARME): def setup_class(cls, missing='all', *args, **kwargs): super().setup_class(missing=missing, *args, **kwargs) class TestVARMEPartialMissing(TestVARME): def setup_class(cls, missing='partial', *args, **kwargs): super().setup_class(missing=missing, *args, **kwargs) class TestVARMEMixedMissing(TestVARME): def setup_class(cls, missing='mixed', *args, **kwargs): super().setup_class(missing=missing, *args, **kwargs) class TestSARIMAXME(CheckPosteriorMoments): # Test SARIMAX model with Measurement Error # Note: have to use measurement error, due to the restriction that all # shocks must be non-degenerate for the CFA algorithm @classmethod def setup_class(cls, missing=None, *args, **kwargs): kwargs['order'] = (1, 0, 0) kwargs['measurement_error'] = True super().setup_class(sarimax.SARIMAX, missing=missing, *args, **kwargs) class TestSARIMAXMEMissing(TestSARIMAXME): def setup_class(cls, missing='mixed', *args, **kwargs): super().setup_class(missing=missing, *args, **kwargs) class TestUnobservedComponents(CheckPosteriorMoments): # Test UC model, with exog @classmethod def setup_class(cls, missing=None, *args, **kwargs): kwargs['level'] = 'llevel' kwargs['exog'] = np.arange(dta.shape[0]) kwargs['autoregressive'] = 1 super().setup_class(structural.UnobservedComponents, missing=missing, *args, **kwargs) class TestUnobservedComponentsMissing(TestUnobservedComponents): def setup_class(cls, missing='mixed', *args, **kwargs): super().setup_class(missing=missing, *args, **kwargs) def test_dfm(missing=None): mod = dynamic_factor.DynamicFactor(dta, k_factors=2, factor_order=1) mod.update(mod.start_params) sim_cfa = mod.simulation_smoother(method='cfa') res = mod.ssm.smooth() # Test zero variates sim_cfa.simulate(np.zeros((mod.k_states, mod.nobs))) assert_allclose(sim_cfa.simulated_state, res.smoothed_state) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_cfa_tvpvar.py000066400000000000000000000166041400612667500263470ustar00rootroot00000000000000""" Tests for CFA simulation smoothing in a TVP-VAR model See "results/cfa_tvpvar_test.m" for Matlab file that generates the results. Based on "TVPVAR.m", found at http://joshuachan.org/code/code_TVPVAR.html. See [1]_ for details on the TVP-VAR model and the CFA method. References ---------- .. [1] Chan, Joshua CC, and Ivan Jeliazkov. "Efficient simulation and integrated likelihood estimation in state space models." International Journal of Mathematical Modelling and Numerical Optimisation 1, no. 1-2 (2009): 101-120. Author: Chad Fulton License: BSD-3 """ import os import numpy as np import pandas as pd from numpy.testing import assert_allclose from statsmodels import datasets from statsmodels.tools import add_constant from statsmodels.tsa.tsatools import lagmat from statsmodels.tsa.statespace import mlemodel dta = datasets.macrodata.load_pandas().data dta.index = pd.period_range('1959Q1', '2009Q3', freq='Q') endog = np.log(dta[['realcons', 'realgdp']]).diff().iloc[1:13] * 400 current_path = os.path.dirname(os.path.abspath(__file__)) results_path = os.path.join(current_path, 'results') results = { 'invP': pd.read_csv( os.path.join(results_path, 'cfa_tvpvar_invP.csv'), header=None), 'posterior_mean': pd.read_csv( os.path.join(results_path, 'cfa_tvpvar_posterior_mean.csv'), header=None), 'state_variates': pd.read_csv( os.path.join(results_path, 'cfa_tvpvar_state_variates.csv'), header=None), 'beta': pd.read_csv( os.path.join(results_path, 'cfa_tvpvar_beta.csv'), header=None), 'v10': pd.read_csv( os.path.join(results_path, 'cfa_tvpvar_v10.csv'), header=None), 'S10': pd.read_csv( os.path.join(results_path, 'cfa_tvpvar_S10.csv'), header=None), 'Omega_11': pd.read_csv( os.path.join(results_path, 'cfa_tvpvar_Omega_11.csv'), header=None), 'vi0': pd.read_csv( os.path.join(results_path, 'cfa_tvpvar_vi0.csv'), header=None), 'Si0': pd.read_csv( os.path.join(results_path, 'cfa_tvpvar_Si0.csv'), header=None), 'Omega_22': pd.read_csv( os.path.join(results_path, 'cfa_tvpvar_Omega_22.csv'), header=None)} class TVPVAR(mlemodel.MLEModel): def __init__(self, endog): if not isinstance(endog, pd.DataFrame): endog = pd.DataFrame(endog) k = endog.shape[1] augmented = lagmat(endog, 1, trim='both', original='in', use_pandas=True) endog = augmented.iloc[:, :k] exog = add_constant(augmented.iloc[:, k:]) k_states = k * (k + 1) super().__init__(endog, k_states=k_states) self.ssm.initialize('known', stationary_cov=np.eye(self.k_states) * 5) self['design'] = np.zeros((self.k_endog, self.k_states, self.nobs)) for i in range(self.k_endog): start = i * (self.k_endog + 1) end = start + self.k_endog + 1 self['design', i, start:end, :] = exog.T self['transition'] = np.eye(k_states) self['selection'] = np.eye(k_states) self._obs_cov_slice = np.s_[:self.k_endog * (self.k_endog + 1) // 2] self._obs_cov_tril = np.tril_indices(self.k_endog) self._state_cov_slice = np.s_[-self.k_states:] self._state_cov_ix = ('state_cov',) + np.diag_indices(self.k_states) @property def state_names(self): state_names = [] for i in range(self.k_endog): endog_name = self.endog_names[i] state_names += ['intercept.%s' % endog_name] state_names += ['L1.%s->%s' % (other_name, endog_name) for other_name in self.endog_names] return state_names def update_direct(self, obs_cov, state_cov_diag): self['obs_cov'] = obs_cov self[self._state_cov_ix] = state_cov_diag def test_tvpvar(): # This tests two MCMC iterations of the TVP-VAR model using the CFA # simulation smoother. # Create the model and the CFA simulation smoother mod = TVPVAR(endog.iloc[2:]) sim = mod.simulation_smoother(method='cfa') # Prior hyperparameters v10 = mod.k_endog + 3 S10 = np.eye(mod.k_endog) vi0 = np.ones(mod.k_states) * 6 / 2 Si0 = np.ones(mod.k_states) * 0.01 / 2 # - First iteration ------------------------------------------------------ # Update the model with initial parameterization initial_obs_cov = np.cov(endog.T) initial_state_cov_vars = np.ones(mod.k_states) * 0.01 mod.update_direct(initial_obs_cov, initial_state_cov_vars) res = mod.ssm.smooth() # Simulate the state using the given variates # (this also computes posterior moments) variates_1 = results['state_variates'].iloc[:6] sim.simulate(variates_1) # Check state posterior moments posterior_mean_1 = results['posterior_mean'].iloc[:6] assert_allclose(sim.posterior_mean, posterior_mean_1) assert_allclose(sim.posterior_mean, res.smoothed_state) posterior_cov_1 = np.linalg.inv(results['invP'].iloc[:54]) assert_allclose(sim.posterior_cov, posterior_cov_1) # Check simulated state simulated_state_1 = results['beta'].iloc[:6] assert_allclose(sim.simulated_state, simulated_state_1) # Posterior for obs cov fitted = np.matmul(mod['design'].transpose(2, 0, 1), sim.simulated_state.T[..., None])[..., 0] resid = mod.endog - fitted df = v10 + mod.nobs scale = S10 + np.dot(resid.T, resid) assert_allclose(df, results['v10'].iloc[:2]) assert_allclose(scale, results['S10'].iloc[:, :2]) # Posterior for state cov resid = sim.simulated_state.T[1:] - sim.simulated_state.T[:-1] sse = np.sum(resid**2, axis=0) shapes = vi0 + (mod.nobs - 1) / 2 scales = Si0 + sse / 2 assert_allclose(shapes, results['vi0'].values[0, 0]) assert_allclose(scales, results['Si0'].iloc[:, 0]) # - Second iteration ----------------------------------------------------- # Update the model with variates drawn in the previous iteration (here we # use the saved test case variates) mod.update_direct(results['Omega_11'].iloc[:, :2], results['Omega_22'].iloc[:, 0]) res = mod.ssm.smooth() # Simulate the state using the given variates # (this also computes posterior moments) variates_2 = results['state_variates'].iloc[6:] sim.simulate(variates_2) # Check state posterior moments posterior_mean_2 = results['posterior_mean'].iloc[6:] assert_allclose(sim.posterior_mean, posterior_mean_2) assert_allclose(sim.posterior_mean, res.smoothed_state) posterior_cov_2 = np.linalg.inv(results['invP'].iloc[54:]) assert_allclose(sim.posterior_cov, posterior_cov_2) # Check simulated state simulated_state_2 = results['beta'].iloc[6:] assert_allclose(sim.simulated_state, simulated_state_2) # Posterior for obs cov fitted = np.matmul(mod['design'].transpose(2, 0, 1), sim.simulated_state.T[..., None])[..., 0] resid = mod.endog - fitted df = v10 + mod.nobs scale = S10 + np.dot(resid.T, resid) assert_allclose(df, results['v10'].iloc[2:]) assert_allclose(scale, results['S10'].iloc[:, 2:]) # Posterior for state cov resid = sim.simulated_state.T[1:] - sim.simulated_state.T[:-1] sse = np.sum(resid**2, axis=0) shapes = vi0 + (mod.nobs - 1) / 2 scales = Si0 + sse / 2 assert_allclose(shapes, results['vi0'].values[0, 1]) assert_allclose(scales, results['Si0'].iloc[:, 1]) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_chandrasekhar.py000066400000000000000000000212421400612667500270040ustar00rootroot00000000000000""" Tests for Chandrasekhar recursions Author: Chad Fulton License: Simplified-BSD """ import numpy as np import pandas as pd from .results import results_varmax from statsmodels.tsa.statespace import sarimax, varmax from statsmodels.tsa.statespace.kalman_filter import ( MEMORY_CONSERVE, MEMORY_NO_LIKELIHOOD) from numpy.testing import assert_allclose import pytest def check_output(res_chand, res_orig, memory_conserve=False): # Test loglike params = res_orig.params assert_allclose(res_chand.llf, res_orig.llf) assert_allclose(res_chand.model.score_obs(params), res_orig.model.score_obs(params), atol=1e-10) # Test state space representation matrices for name in res_chand.model.ssm.shapes: if name == 'obs': continue assert_allclose(getattr(res_chand.filter_results, name), getattr(res_orig.filter_results, name)) # Test filter / smoother output filter_attr = ['predicted_state', 'filtered_state', 'forecasts', 'forecasts_error'] # Can only check kalman gain if we didn't use memory conservation if not memory_conserve: filter_attr += ['kalman_gain'] for name in filter_attr: actual = getattr(res_chand.filter_results, name) desired = getattr(res_orig.filter_results, name) assert_allclose(actual, desired, atol=1e-12) filter_attr_burn = ['predicted_state_cov', 'filtered_state_cov'] # Can only check kalman gain if we didn't use memory conservation if not memory_conserve: filter_attr += ['standardized_forecasts_error', 'tmp1', 'tmp2', 'tmp3', 'tmp4'] for name in filter_attr_burn: actual = getattr(res_chand.filter_results, name) desired = getattr(res_orig.filter_results, name) assert_allclose(actual, desired, atol=1e-12) if not memory_conserve: smoothed_attr = ['smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_state_disturbance', 'smoothed_state_disturbance_cov', 'smoothed_measurement_disturbance', 'smoothed_measurement_disturbance_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_forecasts', 'smoothed_forecasts_error', 'smoothed_forecasts_error_cov'] for name in smoothed_attr: actual = getattr(res_chand.filter_results, name) desired = getattr(res_orig.filter_results, name) assert_allclose(actual, desired, atol=1e-12) # Test prediction output nobs = res_chand.model.nobs if not memory_conserve: pred_chand = res_chand.get_prediction(start=10, end=nobs + 50, dynamic=40) pred_orig = res_chand.get_prediction(start=10, end=nobs + 50, dynamic=40) else: # In the memory conservation case, we can't do dynamic prediction pred_chand = res_chand.get_prediction(start=10, end=nobs + 50) pred_orig = res_chand.get_prediction(start=10, end=nobs + 50) assert_allclose(pred_chand.predicted_mean, pred_orig.predicted_mean) assert_allclose(pred_chand.se_mean, pred_orig.se_mean) def check_univariate_chandrasekhar(filter_univariate=False, **kwargs): # Test that Chandrasekhar recursions don't change the output index = pd.date_range('1960-01-01', '1982-10-01', freq='QS') dta = pd.DataFrame(results_varmax.lutkepohl_data, columns=['inv', 'inc', 'consump'], index=index) endog = np.log(dta['inv']).diff().loc['1960-04-01':'1978-10-01'] mod_orig = sarimax.SARIMAX(endog, **kwargs) mod_chand = sarimax.SARIMAX(endog, **kwargs) mod_chand.ssm.filter_chandrasekhar = True params = mod_orig.start_params mod_orig.ssm.filter_univariate = filter_univariate mod_chand.ssm.filter_univariate = filter_univariate res_chand = mod_chand.smooth(params) # Non-oncentrated model smoothing res_orig = mod_orig.smooth(params) check_output(res_chand, res_orig) def check_multivariate_chandrasekhar(filter_univariate=False, gen_obs_cov=False, memory_conserve=False, **kwargs): # Test that Chandrasekhar recursions don't change the output index = pd.date_range('1960-01-01', '1982-10-01', freq='QS') dta = pd.DataFrame(results_varmax.lutkepohl_data, columns=['inv', 'inc', 'consump'], index=index) dta['dln_inv'] = np.log(dta['inv']).diff() dta['dln_inc'] = np.log(dta['inc']).diff() dta['dln_consump'] = np.log(dta['consump']).diff() endog = dta.loc['1960-04-01':'1978-10-01', ['dln_inv', 'dln_inc']] mod_orig = varmax.VARMAX(endog, **kwargs) mod_chand = varmax.VARMAX(endog, **kwargs) mod_chand.ssm.filter_chandrasekhar = True params = mod_orig.start_params mod_orig.ssm.filter_univariate = filter_univariate mod_chand.ssm.filter_univariate = filter_univariate if gen_obs_cov: mod_orig['obs_cov'] = np.array([[1., 0.5], [0.5, 1.]]) mod_chand['obs_cov'] = np.array([[1., 0.5], [0.5, 1.]]) if memory_conserve: mod_orig.ssm.set_conserve_memory( MEMORY_CONSERVE & ~ MEMORY_NO_LIKELIHOOD) mod_chand.ssm.set_conserve_memory( MEMORY_CONSERVE & ~ MEMORY_NO_LIKELIHOOD) res_chand = mod_chand.filter(params) res_orig = mod_orig.filter(params) else: res_chand = mod_chand.smooth(params) res_orig = mod_orig.smooth(params) check_output(res_chand, res_orig, memory_conserve=memory_conserve) def test_chandrasekhar_conventional(): check_univariate_chandrasekhar(filter_univariate=False) check_univariate_chandrasekhar(filter_univariate=False, concentrate_scale=True) check_multivariate_chandrasekhar(filter_univariate=False) check_multivariate_chandrasekhar(filter_univariate=False, measurement_error=True) check_multivariate_chandrasekhar(filter_univariate=False, error_cov_type='diagonal') check_multivariate_chandrasekhar(filter_univariate=False, gen_obs_cov=True) check_multivariate_chandrasekhar(filter_univariate=False, gen_obs_cov=True, memory_conserve=True) def test_chandrasekhar_univariate(): check_univariate_chandrasekhar(filter_univariate=True) check_univariate_chandrasekhar(filter_univariate=True, concentrate_scale=True) check_multivariate_chandrasekhar(filter_univariate=True) check_multivariate_chandrasekhar(filter_univariate=True, measurement_error=True) check_multivariate_chandrasekhar(filter_univariate=True, error_cov_type='diagonal') check_multivariate_chandrasekhar(filter_univariate=True, gen_obs_cov=True) check_multivariate_chandrasekhar(filter_univariate=True, gen_obs_cov=True, memory_conserve=True) def test_invalid(): # Tests that trying to use the Chandrasekhar recursions in invalid # situations raises an error # Missing values endog = np.zeros(10) endog[1] = np.nan mod = sarimax.SARIMAX(endog) mod.ssm.filter_chandrasekhar = True with pytest.raises(RuntimeError, match=('Cannot use Chandrasekhar' ' recursions with missing data.')): mod.filter([0.5, 1.0]) # Alternative timing endog = np.zeros(10) mod = sarimax.SARIMAX(endog) mod.ssm.filter_chandrasekhar = True mod.ssm.timing_init_filtered = True with pytest.raises(RuntimeError, match=('Cannot use Chandrasekhar' ' recursions with filtered' ' timing.')): mod.filter([0.5, 1.0]) # Time-varying matrices endog = np.zeros(10) mod = sarimax.SARIMAX(endog) mod.ssm.filter_chandrasekhar = True mod['obs_cov'] = np.ones((1, 1, 10)) with pytest.raises(RuntimeError, match=('Cannot use Chandrasekhar' ' recursions with time-varying' r' system matrices \(except for' r' intercept terms\).')): mod.filter([0.5, 1.0]) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_collapsed.py000066400000000000000000000650121400612667500261570ustar00rootroot00000000000000""" Tests for collapsed observation vector These tests cannot be run for the Clark 1989 model since the dimension of observations (2) is smaller than the number of states (6). Author: Chad Fulton License: Simplified-BSD """ import numpy as np import pandas as pd import pytest import os from statsmodels import datasets from statsmodels.tsa.statespace import dynamic_factor from statsmodels.tsa.statespace.mlemodel import MLEModel from statsmodels.tsa.statespace.kalman_filter import ( FILTER_UNIVARIATE) from statsmodels.tsa.statespace.kalman_smoother import ( SMOOTH_CLASSICAL, SMOOTH_ALTERNATIVE, SMOOTH_UNIVARIATE) from statsmodels.tsa.statespace.tests.results import results_kalman_filter from numpy.testing import assert_equal, assert_allclose current_path = os.path.dirname(os.path.abspath(__file__)) class Trivariate(object): """ Tests collapsing three-dimensional observation data to two-dimensional """ @classmethod def setup_class(cls, dtype=float, alternate_timing=False, **kwargs): cls.results = results_kalman_filter.uc_bi # GDP and Unemployment, Quarterly, 1948.1 - 1995.3 data = pd.DataFrame( cls.results['data'], index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'), columns=['GDP', 'UNEMP'] )[4:] data['GDP'] = np.log(data['GDP']) data['UNEMP'] = (data['UNEMP']/100) data['X'] = np.exp(data['GDP']) * data['UNEMP'] k_states = 2 cls.mlemodel = MLEModel(data, k_states=k_states, **kwargs) cls.model = cls.mlemodel.ssm if alternate_timing: cls.model.timing_init_filtered = True # Statespace representation cls.model['selection'] = np.eye(cls.model.k_states) # Update matrices with test parameters cls.model['design'] = np.array([[0.5, 0.2], [0, 0.8], [1, -0.5]]) cls.model['transition'] = np.array([[0.4, 0.5], [1, 0]]) cls.model['obs_cov'] = np.diag([0.2, 1.1, 0.5]) cls.model['state_cov'] = np.diag([2., 1]) # Initialization cls.model.initialize_approximate_diffuse() def test_using_collapsed(self): # Test to make sure the results_b actually used a collapsed Kalman # filtering approach (i.e. that the flag being set actually caused the # filter to not use the conventional filter) assert not self.results_a.filter_collapsed assert self.results_b.filter_collapsed assert self.results_a.collapsed_forecasts is None assert self.results_b.collapsed_forecasts is not None assert_equal(self.results_a.forecasts.shape[0], 3) assert_equal(self.results_b.collapsed_forecasts.shape[0], 2) def test_forecasts(self): assert_allclose( self.results_a.forecasts[0, :], self.results_b.forecasts[0, :], ) def test_forecasts_error(self): assert_allclose( self.results_a.forecasts_error[0, :], self.results_b.forecasts_error[0, :] ) def test_forecasts_error_cov(self): assert_allclose( self.results_a.forecasts_error_cov[0, 0, :], self.results_b.forecasts_error_cov[0, 0, :] ) def test_filtered_state(self): assert_allclose( self.results_a.filtered_state, self.results_b.filtered_state ) def test_filtered_state_cov(self): assert_allclose( self.results_a.filtered_state_cov, self.results_b.filtered_state_cov ) def test_predicted_state(self): assert_allclose( self.results_a.predicted_state, self.results_b.predicted_state ) def test_predicted_state_cov(self): assert_allclose( self.results_a.predicted_state_cov, self.results_b.predicted_state_cov ) def test_loglike(self): assert_allclose( self.results_a.llf_obs, self.results_b.llf_obs ) def test_smoothed_states(self): assert_allclose( self.results_a.smoothed_state, self.results_b.smoothed_state ) def test_smoothed_states_cov(self): assert_allclose( self.results_a.smoothed_state_cov, self.results_b.smoothed_state_cov, atol=1e-4 ) def test_smoothed_states_autocov(self): assert_allclose( self.results_a.smoothed_state_autocov, self.results_b.smoothed_state_autocov ) # Skipped because "measurement" refers to different things; even different # dimensions @pytest.mark.skip def test_smoothed_measurement_disturbance(self): assert_allclose( self.results_a.smoothed_measurement_disturbance, self.results_b.smoothed_measurement_disturbance ) # Skipped because "measurement" refers to different things; even different # dimensions @pytest.mark.skip def test_smoothed_measurement_disturbance_cov(self): assert_allclose( self.results_a.smoothed_measurement_disturbance_cov, self.results_b.smoothed_measurement_disturbance_cov ) def test_smoothed_state_disturbance(self): assert_allclose( self.results_a.smoothed_state_disturbance, self.results_b.smoothed_state_disturbance ) def test_smoothed_state_disturbance_cov(self): assert_allclose( self.results_a.smoothed_state_disturbance_cov, self.results_b.smoothed_state_disturbance_cov ) def test_simulation_smoothed_state(self): assert_allclose( self.sim_a.simulated_state, self.sim_a.simulated_state ) def test_simulation_smoothed_measurement_disturbance(self): assert_allclose( self.sim_a.simulated_measurement_disturbance, self.sim_a.simulated_measurement_disturbance ) def test_simulation_smoothed_state_disturbance(self): assert_allclose( self.sim_a.simulated_state_disturbance, self.sim_a.simulated_state_disturbance ) class TestTrivariateConventional(Trivariate): @classmethod def setup_class(cls, dtype=float, **kwargs): super(TestTrivariateConventional, cls).setup_class(dtype, **kwargs) n_disturbance_variates = ( (cls.model.k_endog + cls.model.k_posdef) * cls.model.nobs ) # Collapsed filtering, smoothing, and simulation smoothing cls.model.filter_conventional = True cls.model.filter_collapsed = True cls.results_b = cls.model.smooth() cls.sim_b = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) # Conventional filtering, smoothing, and simulation smoothing cls.model.filter_collapsed = False cls.results_a = cls.model.smooth() cls.sim_a = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) class TestTrivariateConventionalAlternate(TestTrivariateConventional): @classmethod def setup_class(cls, *args, **kwargs): super(TestTrivariateConventionalAlternate, cls).setup_class( alternate_timing=True, *args, **kwargs) def test_using_alterate(self): assert(self.model._kalman_filter.filter_timing == 1) class TestTrivariateConventionalPartialMissing(Trivariate): @classmethod def setup_class(cls, dtype=float, **kwargs): super(TestTrivariateConventionalPartialMissing, cls).setup_class( dtype, **kwargs) n_disturbance_variates = ( (cls.model.k_endog + cls.model.k_posdef) * cls.model.nobs ) # Set partially missing data cls.model.endog[:2, 10:180] = np.nan # Collapsed filtering, smoothing, and simulation smoothing cls.model.filter_conventional = True cls.model.filter_collapsed = True cls.results_b = cls.model.smooth() cls.sim_b = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) # Conventional filtering, smoothing, and simulation smoothing cls.model.filter_collapsed = False cls.results_a = cls.model.smooth() cls.sim_a = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) class TestTrivariateConventionalPartialMissingAlternate( TestTrivariateConventionalPartialMissing): @classmethod def setup_class(cls, *args, **kwargs): super(TestTrivariateConventionalPartialMissingAlternate, cls).setup_class(alternate_timing=True, *args, **kwargs) def test_using_alterate(self): assert(self.model._kalman_filter.filter_timing == 1) class TestTrivariateConventionalAllMissing(Trivariate): @classmethod def setup_class(cls, dtype=float, **kwargs): super(TestTrivariateConventionalAllMissing, cls).setup_class( dtype, **kwargs) n_disturbance_variates = ( (cls.model.k_endog + cls.model.k_posdef) * cls.model.nobs ) # Set partially missing data cls.model.endog[:, 10:180] = np.nan # Collapsed filtering, smoothing, and simulation smoothing cls.model.filter_conventional = True cls.model.filter_collapsed = True cls.results_b = cls.model.smooth() cls.sim_b = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) # Conventional filtering, smoothing, and simulation smoothing cls.model.filter_collapsed = False cls.results_a = cls.model.smooth() cls.sim_a = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) class TestTrivariateConventionalAllMissingAlternate( TestTrivariateConventionalAllMissing): @classmethod def setup_class(cls, *args, **kwargs): super(TestTrivariateConventionalAllMissingAlternate, cls).setup_class( alternate_timing=True, *args, **kwargs) def test_using_alterate(self): assert(self.model._kalman_filter.filter_timing == 1) class TestTrivariateUnivariate(Trivariate): @classmethod def setup_class(cls, dtype=float, **kwargs): super(TestTrivariateUnivariate, cls).setup_class(dtype, **kwargs) n_disturbance_variates = ( (cls.model.k_endog + cls.model.k_posdef) * cls.model.nobs ) # Collapsed filtering, smoothing, and simulation smoothing cls.model.filter_univariate = True cls.model.filter_collapsed = True cls.results_b = cls.model.smooth() cls.sim_b = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) # Univariate filtering, smoothing, and simulation smoothing cls.model.filter_collapsed = False cls.results_a = cls.model.smooth() cls.sim_a = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) class TestTrivariateUnivariateAlternate(TestTrivariateUnivariate): @classmethod def setup_class(cls, *args, **kwargs): super(TestTrivariateUnivariateAlternate, cls).setup_class( alternate_timing=True, *args, **kwargs) def test_using_alterate(self): assert(self.model._kalman_filter.filter_timing == 1) class TestTrivariateUnivariatePartialMissing(Trivariate): @classmethod def setup_class(cls, dtype=float, **kwargs): super(TestTrivariateUnivariatePartialMissing, cls).setup_class( dtype, **kwargs) n_disturbance_variates = ( (cls.model.k_endog + cls.model.k_posdef) * cls.model.nobs ) # Set partially missing data cls.model.endog[:2, 10:180] = np.nan # Collapsed filtering, smoothing, and simulation smoothing cls.model.filter_univariate = True cls.model.filter_collapsed = True cls.results_b = cls.model.smooth() cls.sim_b = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) # Univariate filtering, smoothing, and simulation smoothing cls.model.filter_collapsed = False cls.results_a = cls.model.smooth() cls.sim_a = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) class TestTrivariateUnivariatePartialMissingAlternate( TestTrivariateUnivariatePartialMissing): @classmethod def setup_class(cls, *args, **kwargs): super(TestTrivariateUnivariatePartialMissingAlternate, cls).setup_class(alternate_timing=True, *args, **kwargs) def test_using_alterate(self): assert(self.model._kalman_filter.filter_timing == 1) class TestTrivariateUnivariateAllMissing(Trivariate): @classmethod def setup_class(cls, dtype=float, **kwargs): super(TestTrivariateUnivariateAllMissing, cls).setup_class( dtype, **kwargs) n_disturbance_variates = ( (cls.model.k_endog + cls.model.k_posdef) * cls.model.nobs ) # Set partially missing data cls.model.endog[:, 10:180] = np.nan # Univariate filtering, smoothing, and simulation smoothing cls.model.filter_univariate = True cls.model.filter_collapsed = True cls.results_b = cls.model.smooth() cls.sim_b = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) # Conventional filtering, smoothing, and simulation smoothing cls.model.filter_collapsed = False cls.results_a = cls.model.smooth() cls.sim_a = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) class TestTrivariateUnivariateAllMissingAlternate( TestTrivariateUnivariateAllMissing): @classmethod def setup_class(cls, *args, **kwargs): super(TestTrivariateUnivariateAllMissingAlternate, cls).setup_class( alternate_timing=True, *args, **kwargs) def test_using_alterate(self): assert(self.model._kalman_filter.filter_timing == 1) class TestDFM(object): @classmethod def create_model(cls, obs, **kwargs): # Create the model with typical state space mod = MLEModel(obs, k_states=2, k_posdef=2, **kwargs) mod['design'] = np.array([[-32.47143586, 17.33779024], [-7.40264169, 1.69279859], [-209.04702853, 125.2879374]]) mod['obs_cov'] = np.diag( np.array([0.0622668, 1.95666886, 58.37473642])) mod['transition'] = np.array([[0.29935707, 0.33289005], [-0.7639868, 1.2844237]]) mod['selection'] = np.eye(2) mod['state_cov'] = np.array([[1.2, -0.25], [-0.25, 1.1]]) mod.initialize_approximate_diffuse(1e6) return mod @classmethod def collapse(cls, obs, **kwargs): mod = cls.create_model(obs, **kwargs) mod.smooth([], return_ssm=True) _ss = mod.ssm._statespace out = np.zeros((mod.nobs, mod.k_states)) for t in range(mod.nobs): _ss.seek(t, mod.ssm.filter_univariate, 1) out[t] = np.array(_ss.collapse_obs) return out @classmethod def setup_class(cls, which='mixed', *args, **kwargs): # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') levels = dta[['realgdp', 'realcons', 'realinv']] obs = np.log(levels).diff().iloc[1:] * 400 if which == 'all': obs.iloc[:50, :] = np.nan obs.iloc[119:130, :] = np.nan elif which == 'partial': obs.iloc[0:50, 0] = np.nan obs.iloc[119:130, 0] = np.nan elif which == 'mixed': obs.iloc[0:50, 0] = np.nan obs.iloc[19:70, 1] = np.nan obs.iloc[39:90, 2] = np.nan obs.iloc[119:130, 0] = np.nan obs.iloc[119:130, 2] = np.nan mod = cls.create_model(obs, **kwargs) cls.model = mod.ssm n_disturbance_variates = ( (cls.model.k_endog + cls.model.k_posdef) * cls.model.nobs ) np.random.seed(1234) dv = np.random.normal(size=n_disturbance_variates) isv = np.random.normal(size=cls.model.k_states) # Collapsed filtering, smoothing, and simulation smoothing cls.model.filter_collapsed = True cls.results_b = cls.model.smooth() cls.sim_b = cls.model.simulation_smoother() cls.sim_b.simulate(disturbance_variates=dv, initial_state_variates=isv) # Conventional filtering, smoothing, and simulation smoothing cls.model.filter_collapsed = False cls.results_a = cls.model.smooth() cls.sim_a = cls.model.simulation_smoother() cls.sim_a.simulate(disturbance_variates=dv, initial_state_variates=isv) # Create the model with augmented state space kwargs.pop('filter_collapsed', None) mod = MLEModel(obs, k_states=4, k_posdef=2, **kwargs) mod['design', :3, :2] = np.array([[-32.47143586, 17.33779024], [-7.40264169, 1.69279859], [-209.04702853, 125.2879374]]) mod['obs_cov'] = np.diag( np.array([0.0622668, 1.95666886, 58.37473642])) mod['transition', :2, :2] = np.array([[0.29935707, 0.33289005], [-0.7639868, 1.2844237]]) mod['transition', 2:, :2] = np.eye(2) mod['selection', :2, :2] = np.eye(2) mod['state_cov'] = np.array([[1.2, -0.25], [-0.25, 1.1]]) mod.initialize_approximate_diffuse(1e6) cls.augmented_model = mod.ssm cls.augmented_results = mod.ssm.smooth() def test_using_collapsed(self): # Test to make sure the results_b actually used a collapsed Kalman # filtering approach (i.e. that the flag being set actually caused the # filter to not use the conventional filter) assert not self.results_a.filter_collapsed assert self.results_b.filter_collapsed assert self.results_a.collapsed_forecasts is None assert self.results_b.collapsed_forecasts is not None assert_equal(self.results_a.forecasts.shape[0], 3) assert_equal(self.results_b.collapsed_forecasts.shape[0], 2) def test_forecasts(self): assert_allclose( self.results_a.forecasts[0, :], self.results_b.forecasts[0, :], ) def test_forecasts_error(self): assert_allclose( self.results_a.forecasts_error[0, :], self.results_b.forecasts_error[0, :] ) def test_forecasts_error_cov(self): assert_allclose( self.results_a.forecasts_error_cov[0, 0, :], self.results_b.forecasts_error_cov[0, 0, :] ) def test_filtered_state(self): assert_allclose( self.results_a.filtered_state, self.results_b.filtered_state ) def test_filtered_state_cov(self): assert_allclose( self.results_a.filtered_state_cov, self.results_b.filtered_state_cov ) def test_predicted_state(self): assert_allclose( self.results_a.predicted_state, self.results_b.predicted_state ) def test_predicted_state_cov(self): assert_allclose( self.results_a.predicted_state_cov, self.results_b.predicted_state_cov ) def test_loglike(self): assert_allclose( self.results_a.llf_obs, self.results_b.llf_obs ) def test_smoothed_states(self): assert_allclose( self.results_a.smoothed_state, self.results_b.smoothed_state ) def test_smoothed_states_cov(self): assert_allclose( self.results_a.smoothed_state_cov, self.results_b.smoothed_state_cov, atol=1e-4 ) def test_smoothed_states_autocov(self): # Cov(\alpha_{t+1}, \alpha_t) # Test collapsed against non-collapsed assert_allclose( self.results_a.smoothed_state_autocov, self.results_b.smoothed_state_autocov ) # Directly test using the augmented model # Initialization makes these two methods slightly different for the # first few observations assert_allclose(self.results_a.smoothed_state_autocov[:, :, 0:5], self.augmented_results.smoothed_state_cov[:2, 2:, 1:6], atol=1e-4) assert_allclose(self.results_a.smoothed_state_autocov[:, :, 5:-1], self.augmented_results.smoothed_state_cov[:2, 2:, 6:], atol=1e-7) # Skipped because "measurement" refers to different things; even different # dimensions @pytest.mark.skip def test_smoothed_measurement_disturbance(self): assert_allclose( self.results_a.smoothed_measurement_disturbance, self.results_b.smoothed_measurement_disturbance ) # Skipped because "measurement" refers to different things; even different # dimensions @pytest.mark.skip def test_smoothed_measurement_disturbance_cov(self): assert_allclose( self.results_a.smoothed_measurement_disturbance_cov, self.results_b.smoothed_measurement_disturbance_cov ) def test_smoothed_state_disturbance(self): assert_allclose( self.results_a.smoothed_state_disturbance, self.results_b.smoothed_state_disturbance ) def test_smoothed_state_disturbance_cov(self): assert_allclose( self.results_a.smoothed_state_disturbance_cov, self.results_b.smoothed_state_disturbance_cov ) def test_simulation_smoothed_state(self): assert_allclose( self.sim_a.simulated_state, self.sim_b.simulated_state ) # Skipped because "measurement" refers to different things; even different # dimensions @pytest.mark.skip def test_simulation_smoothed_measurement_disturbance(self): assert_allclose( self.sim_a.simulated_measurement_disturbance, self.sim_b.simulated_measurement_disturbance ) def test_simulation_smoothed_state_disturbance(self): assert_allclose( self.sim_a.simulated_state_disturbance, self.sim_b.simulated_state_disturbance ) class TestDFMClassicalSmoothing(TestDFM): @classmethod def setup_class(cls, *args, **kwargs): super(TestDFMClassicalSmoothing, cls).setup_class( smooth_method=SMOOTH_CLASSICAL, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model._kalman_smoother.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model._kalman_smoother._smooth_method, SMOOTH_CLASSICAL) class TestDFMUnivariateSmoothing(TestDFM): @classmethod def setup_class(cls, *args, **kwargs): super(TestDFMUnivariateSmoothing, cls).setup_class( filter_method=FILTER_UNIVARIATE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.smooth_method, 0) assert_equal(self.model._kalman_smoother.smooth_method, 0) assert_equal(self.model._kalman_smoother._smooth_method, SMOOTH_UNIVARIATE) class TestDFMAlternativeSmoothing(TestDFM): @classmethod def setup_class(cls, *args, **kwargs): super(TestDFMAlternativeSmoothing, cls).setup_class( smooth_method=SMOOTH_ALTERNATIVE, **kwargs) def test_smooth_method(self): assert_equal(self.model.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model._kalman_smoother.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model._kalman_smoother._smooth_method, SMOOTH_ALTERNATIVE) class TestDFMMeasurementDisturbance(TestDFM): @classmethod def setup_class(cls, *args, **kwargs): super(TestDFMMeasurementDisturbance, cls).setup_class( smooth_method=SMOOTH_CLASSICAL, which='none', **kwargs) def test_smoothed_state_disturbance(self): assert_allclose( self.results_a.smoothed_state_disturbance, self.results_b.smoothed_state_disturbance, atol=1e-7) def test_smoothed_measurement_disturbance(self): assert_allclose( self.collapse(self.results_a.smoothed_measurement_disturbance.T).T, self.results_b.smoothed_measurement_disturbance, atol=1e-7) def test_simulation_smoothed_measurement_disturbance(self): assert_allclose( self.collapse(self.sim_a.simulated_measurement_disturbance.T), self.sim_b.simulated_measurement_disturbance.T, atol=1e-7) def test_simulation_smoothed_state_disturbance(self): assert_allclose( self.sim_a.simulated_state_disturbance, self.sim_b.simulated_state_disturbance, atol=1e-7) def test_dfm_missing(reset_randomstate): # This test is not captured by the TestTrivariate and TestDFM tests above # because it has k_states = 1 endog = np.random.normal(size=(100, 3)) endog[0, :1] = np.nan mod = dynamic_factor.DynamicFactor(endog, k_factors=1, factor_order=1) mod.ssm.filter_collapsed = True res = mod.smooth(mod.start_params) mod.ssm.filter_collapsed = False res2 = mod.smooth(mod.start_params) assert_allclose(res.llf, res2.llf) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_concentrated.py000066400000000000000000000271001400612667500266560ustar00rootroot00000000000000""" Tests for concentrating the scale out of the loglikelihood function Note: the univariate cases is well tested in test_sarimax.py Author: Chad Fulton License: Simplified-BSD """ import numpy as np import pandas as pd from statsmodels.tools.tools import Bunch from .results import results_varmax from statsmodels.tsa.statespace import sarimax, varmax from numpy.testing import assert_raises, assert_allclose def get_sarimax_models(endog, filter_univariate=False, **kwargs): kwargs.setdefault('tolerance', 0) # Construct a concentrated version of the given SARIMAX model, and get # the estimate of the scale mod_conc = sarimax.SARIMAX(endog, **kwargs) mod_conc.ssm.filter_concentrated = True mod_conc.ssm.filter_univariate = filter_univariate params_conc = mod_conc.start_params params_conc[-1] = 1 res_conc = mod_conc.smooth(params_conc) scale = res_conc.scale # Construct the non-concentrated version mod_orig = sarimax.SARIMAX(endog, **kwargs) mod_orig.ssm.filter_univariate = filter_univariate params_orig = params_conc.copy() k_vars = 1 + kwargs.get('measurement_error', False) params_orig[-k_vars:] = scale * params_conc[-k_vars:] res_orig = mod_orig.smooth(params_orig) return Bunch(**{'mod_conc': mod_conc, 'params_conc': params_conc, 'mod_orig': mod_orig, 'params_orig': params_orig, 'res_conc': res_conc, 'res_orig': res_orig, 'scale': scale}) def test_concentrated_loglike_sarimax(): # Note: we will not use the "concentrate_scale" option to SARIMAX for this # test, which is a lower-level test of the Kalman filter using the SARIMAX # model as an example nobs = 30 np.random.seed(28953) endog = np.random.normal(size=nobs) kwargs = {} # Typical model out = get_sarimax_models(endog) assert_allclose(out.res_conc.llf, out.res_orig.llf) assert_allclose(out.res_conc.llf_obs, out.res_orig.llf_obs) assert_allclose(out.mod_conc.loglike(out.params_conc), out.mod_orig.loglike(out.params_orig)) assert_allclose(out.mod_conc.loglikeobs(out.params_conc), out.mod_orig.loglikeobs(out.params_orig)) # Add missing entries endog[2:10] = np.nan out = get_sarimax_models(endog) assert_allclose(out.res_conc.llf, out.res_orig.llf) assert_allclose(out.res_conc.llf_obs, out.res_orig.llf_obs) assert_allclose(out.mod_conc.loglike(out.params_conc), out.mod_orig.loglike(out.params_orig)) assert_allclose(out.mod_conc.loglikeobs(out.params_conc), out.mod_orig.loglikeobs(out.params_orig)) # Add seasonal differencing # Note: now, due to differences in approximate diffuse initialization, # we may have differences in the first 2 observations (but notice that # this does not affect the computed joint log-likelihood because those # observations are not included there) kwargs['seasonal_order'] = (1, 1, 1, 2) out = get_sarimax_models(endog, **kwargs) assert_allclose(out.res_conc.llf, out.res_orig.llf) assert_allclose(out.res_conc.llf_obs[2:], out.res_orig.llf_obs[2:]) assert_allclose(out.mod_conc.loglike(out.params_conc), out.mod_orig.loglike(out.params_orig)) assert_allclose(out.mod_conc.loglikeobs(out.params_conc)[2:], out.mod_orig.loglikeobs(out.params_orig)[2:]) # Add loglikelihood burn, trend, and exog kwargs['loglikelihood_burn'] = 5 kwargs['trend'] = 'c' kwargs['exog'] = np.arange(nobs) out = get_sarimax_models(endog, **kwargs) assert_allclose(out.res_conc.llf, out.res_orig.llf) assert_allclose(out.res_conc.llf_obs[2:], out.res_orig.llf_obs[2:]) assert_allclose(out.mod_conc.loglike(out.params_conc), out.mod_orig.loglike(out.params_orig)) assert_allclose(out.mod_conc.loglikeobs(out.params_conc)[2:], out.mod_orig.loglikeobs(out.params_orig)[2:]) def test_concentrated_predict_sarimax(): # Note: we will not use the "concentrate_scale" option to SARIMAX for this # test, which is a lower-level test of the Kalman filter using the SARIMAX # model as an example nobs = 30 np.random.seed(28953) endog = np.random.normal(size=nobs) # Typical model out = get_sarimax_models(endog) assert_allclose(out.res_conc.predict(), out.res_orig.predict()) assert_allclose(out.res_conc.forecast(5), out.res_orig.forecast(5)) assert_allclose(out.res_conc.predict(start=0, end=45, dynamic=10), out.res_orig.predict(start=0, end=45, dynamic=10)) def test_fixed_scale_sarimax(): # Test that the fixed_scale context manager works nobs = 30 np.random.seed(28953) endog = np.random.normal(size=nobs) kwargs = { 'seasonal_order': (1, 1, 1, 2), 'trend': 'ct', 'exog': np.sin(np.arange(nobs)) } # Construct a concentrated version of the given SARIMAX model mod_conc = sarimax.SARIMAX(endog, concentrate_scale=True, **kwargs) # Construct the non-concentrated version mod_orig = sarimax.SARIMAX(endog, **kwargs) # Modify the scale parameter params = mod_orig.start_params params[-1] *= 1.2 # Test that these are not equal in the default computation assert_raises(AssertionError, assert_allclose, mod_conc.loglike(params[:-1]), mod_orig.loglike(params)) # Now test that the llf is equal when we use the fixed_scale decorator with mod_conc.ssm.fixed_scale(params[-1]): res1 = mod_conc.smooth(params[:-1]) llf1 = mod_conc.loglike(params[:-1]) llf_obs1 = mod_conc.loglikeobs(params[:-1]) res2 = mod_orig.smooth(params) llf2 = mod_orig.loglike(params) llf_obs2 = mod_orig.loglikeobs(params) assert_allclose(res1.llf, res2.llf) assert_allclose(res1.llf_obs[2:], res2.llf_obs[2:]) assert_allclose(llf1, llf2) assert_allclose(llf_obs1, llf_obs2) def check_concentrated_scale(filter_univariate=False, missing=False, **kwargs): # Test that concentrating the scale out of the likelihood function works index = pd.date_range('1960-01-01', '1982-10-01', freq='QS') dta = pd.DataFrame(results_varmax.lutkepohl_data, columns=['inv', 'inc', 'consump'], index=index) dta['dln_inv'] = np.log(dta['inv']).diff() dta['dln_inc'] = np.log(dta['inc']).diff() dta['dln_consump'] = np.log(dta['consump']).diff() endog = dta.loc['1960-04-01':'1978-10-01', ['dln_inv', 'dln_inc']] # Optionally add some missing observations if missing: endog.iloc[0, 0] = np.nan endog.iloc[3:5, :] = np.nan endog.iloc[8, 1] = np.nan # Sometimes we can have slight differences if the Kalman filters # converge at different observations, so disable convergence. kwargs.update({'tolerance': 0}) mod_orig = varmax.VARMAX(endog, **kwargs) mod_conc = varmax.VARMAX(endog, **kwargs) mod_conc.ssm.filter_concentrated = True mod_orig.ssm.filter_univariate = filter_univariate mod_conc.ssm.filter_univariate = filter_univariate # Since VARMAX does not explicitly allow concentrating out the scale, for # now we will simulate it by setting the first variance to be 1. # Note that start_scale will not be the scale used for the non-concentrated # model, because we need to use the MLE scale estimated by the # concentrated model. conc_params = mod_conc.start_params start_scale = conc_params[mod_conc._params_state_cov][0] if kwargs.get('error_cov_type', 'unstructured') == 'diagonal': conc_params[mod_conc._params_state_cov] /= start_scale else: conc_params[mod_conc._params_state_cov] /= start_scale**0.5 # Concentrated model smoothing res_conc = mod_conc.smooth(conc_params) scale = res_conc.scale # Map the concentrated parameters to the non-concentrated model orig_params = conc_params.copy() if kwargs.get('error_cov_type', 'unstructured') == 'diagonal': orig_params[mod_orig._params_state_cov] *= scale else: orig_params[mod_orig._params_state_cov] *= scale**0.5 # Measurement error variances also get rescaled orig_params[mod_orig._params_obs_cov] *= scale # Non-oncentrated model smoothing res_orig = mod_orig.smooth(orig_params) # Test loglike # Need to reduce the tolerance when we have measurement error. assert_allclose(res_conc.llf, res_orig.llf) # Test state space representation matrices for name in mod_conc.ssm.shapes: if name == 'obs': continue assert_allclose(getattr(res_conc.filter_results, name), getattr(res_orig.filter_results, name)) # Test filter / smoother output scale = res_conc.scale d = res_conc.loglikelihood_burn filter_attr = ['predicted_state', 'filtered_state', 'forecasts', 'forecasts_error', 'kalman_gain'] for name in filter_attr: actual = getattr(res_conc.filter_results, name) desired = getattr(res_orig.filter_results, name) assert_allclose(actual, desired, atol=1e-7) # Note: do not want to compare the elements from any diffuse # initialization for things like covariances, so only compare for # periods past the loglikelihood_burn period filter_attr_burn = ['standardized_forecasts_error', 'predicted_state_cov', 'filtered_state_cov', 'tmp1', 'tmp2', 'tmp3', 'tmp4'] for name in filter_attr_burn: actual = getattr(res_conc.filter_results, name)[..., d:] desired = getattr(res_orig.filter_results, name)[..., d:] assert_allclose(actual, desired, atol=1e-7) smoothed_attr = ['smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_state_disturbance', 'smoothed_state_disturbance_cov', 'smoothed_measurement_disturbance', 'smoothed_measurement_disturbance_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_forecasts', 'smoothed_forecasts_error', 'smoothed_forecasts_error_cov'] for name in smoothed_attr: actual = getattr(res_conc.filter_results, name) desired = getattr(res_orig.filter_results, name) assert_allclose(actual, desired, atol=1e-7) # Test prediction output nobs = mod_conc.nobs pred_conc = res_conc.get_prediction(start=10, end=nobs + 50, dynamic=40) pred_orig = res_conc.get_prediction(start=10, end=nobs + 50, dynamic=40) assert_allclose(pred_conc.predicted_mean, pred_orig.predicted_mean) assert_allclose(pred_conc.se_mean, pred_orig.se_mean) def test_concentrated_scale_conventional(): check_concentrated_scale(filter_univariate=False) check_concentrated_scale(filter_univariate=False, measurement_error=True) check_concentrated_scale(filter_univariate=False, error_cov_type='diagonal') check_concentrated_scale(filter_univariate=False, missing=True) check_concentrated_scale(filter_univariate=False, missing=True, loglikelihood_burn=10) def test_concentrated_scale_univariate(): check_concentrated_scale(filter_univariate=True) check_concentrated_scale(filter_univariate=True, measurement_error=True) check_concentrated_scale(filter_univariate=True, error_cov_type='diagonal') check_concentrated_scale(filter_univariate=True, missing=True) check_concentrated_scale(filter_univariate=True, missing=True, loglikelihood_burn=10) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_conserve_memory.py000066400000000000000000000324411400612667500274250ustar00rootroot00000000000000""" Tests for memory conservation in state space models Author: Chad Fulton License: BSD-3 """ import numpy as np import pandas as pd import pytest from numpy.testing import assert_equal, assert_allclose, assert_ from statsmodels.datasets import macrodata from statsmodels.tsa.statespace import ( sarimax, varmax, dynamic_factor) from statsmodels.tsa.statespace.kalman_filter import ( MEMORY_NO_FORECAST_MEAN, MEMORY_NO_FORECAST_COV, MEMORY_NO_PREDICTED_MEAN, MEMORY_NO_PREDICTED_COV, MEMORY_NO_PREDICTED, MEMORY_NO_SMOOTHING, MEMORY_NO_GAIN, MEMORY_CONSERVE) dta = macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-07-01', freq='QS') @pytest.mark.parametrize("concentrate", [True, False]) @pytest.mark.parametrize("univariate", [True, False]) @pytest.mark.parametrize("diffuse", [True, False]) @pytest.mark.parametrize("timing_init_filtered", [True, False]) def test_memory_no_likelihood(concentrate, univariate, diffuse, timing_init_filtered): # Basic test that covers a variety of special filtering cases with a # simple univariate model endog = dta['infl'].iloc[:20] mod = sarimax.SARIMAX(endog, order=(1, 0, 0), concentrate_scale=concentrate) if timing_init_filtered: mod.timing_init_filtered = True if diffuse: mod.ssm.initialize_diffuse() if univariate: mod.ssm.filter_univariate = True params = [0.85] if not concentrate: params.append(7.) res1 = mod.filter(params) mod.ssm.memory_no_likelihood = True res2 = mod.filter(params) # Check that we really did conserve memory in the second case assert_equal(len(res1.llf_obs), 20) assert_equal(res2.llf_obs, None) # Check that the loglikelihood computations are identical assert_allclose(res1.llf, res2.llf) @pytest.mark.parametrize("concentrate", [True, False]) @pytest.mark.parametrize("univariate", [True, False]) @pytest.mark.parametrize("diffuse", [True, False]) @pytest.mark.parametrize("timing_init_filtered", [True, False]) def test_memory_no_likelihood_extras(concentrate, univariate, diffuse, timing_init_filtered): # Test that adds extra features (missing data, exog variables) to the # variety of special filtering cases in a univariate model endog = dta['infl'].iloc[:20].copy() endog[0] = np.nan endog[4:6] = np.nan exog = dta['realint'].iloc[:20] mod = sarimax.SARIMAX(endog, order=(1, 0, 0), exog=exog, concentrate_scale=concentrate) if timing_init_filtered: mod.timing_init_filtered = True if diffuse: mod.ssm.initialize_diffuse() if univariate: mod.ssm.filter_univariate = True params = [1.2, 0.85] if not concentrate: params.append(7.) res1 = mod.filter(params) mod.ssm.memory_no_likelihood = True res2 = mod.filter(params) # Check that we really did conserve memory in the second case assert_equal(len(res1.llf_obs), 20) assert_equal(res2.llf_obs, None) # Check that the loglikelihood computations are identical assert_allclose(res1.llf, res2.llf) @pytest.mark.parametrize("univariate", [True, False]) @pytest.mark.parametrize("diffuse", [True, False]) def test_memory_no_likelihood_multivariate(univariate, diffuse): # Test with multivariate data, and also missing values, exog endog = dta[['infl', 'realint']].iloc[:20].copy() endog.iloc[0, 0] = np.nan endog.iloc[4:6, :] = np.nan exog = np.log(dta['realgdp'].iloc[:20]) mod = varmax.VARMAX(endog, order=(1, 0), exog=exog, trend='c') if diffuse: mod.ssm.initialize_diffuse() if univariate: mod.ssm.filter_univariate = True params = [1.4, 1.3, 0.1, 0.01, 0.02, 0.3, -0.001, 0.001, 1.0, -0.1, 0.6] res1 = mod.filter(params) mod.ssm.memory_no_likelihood = True res2 = mod.filter(params) # Check that we really did conserve memory in the second case assert_equal(len(res1.llf_obs), 20) assert_equal(res2.llf_obs, None) # Check that the loglikelihood computations are identical assert_allclose(res1.llf, res2.llf) @pytest.mark.parametrize("univariate", [True, False]) @pytest.mark.parametrize("diffuse", [True, False]) @pytest.mark.parametrize("collapsed", [True, False]) def test_memory_no_likelihood_multivariate_extra(univariate, diffuse, collapsed): # Test with multivariate data, missing values, and collapsed approach endog = dta[['infl', 'realint']].iloc[:20].copy() endog.iloc[0, 0] = np.nan endog.iloc[4:6, :] = np.nan mod = dynamic_factor.DynamicFactor(endog, k_factors=1, factor_order=1) if diffuse: mod.ssm.initialize_diffuse() if univariate: mod.ssm.filter_univariate = True if collapsed: mod.ssm.filter_collapsed = True params = [4, -4.5, 0.8, 0.9, -0.5] res1 = mod.filter(params) mod.ssm.memory_no_likelihood = True res2 = mod.filter(params) # Check that we really did conserve memory in the second case assert_equal(len(res1.llf_obs), 20) assert_equal(res2.llf_obs, None) # Check that the loglikelihood computations are identical assert_allclose(res1.llf, res2.llf) def test_fit(): # Test that fitting works regardless of the level of memory conservation # used endog = dta['infl'].iloc[:20] mod = sarimax.SARIMAX(endog, order=(1, 0, 0), concentrate_scale=True) res = mod.fit(disp=False) options_smooth = [ 'memory_no_forecast', 'memory_no_filtered', 'memory_no_likelihood', 'memory_no_std_forecast'] for option in options_smooth: mod.ssm.set_conserve_memory(0) setattr(mod.ssm, option, True) res2 = mod.fit(res.params, disp=False) # General check that smoothing results are available assert_allclose(res2.smoothed_state, res.smoothed_state, atol=1e-10) # Specific checks for each type if option == 'memory_no_forecast': assert_(res2.forecasts is None) assert_(res2.forecasts_error is None) assert_(res2.forecasts_error_cov is None) else: assert_allclose(res2.forecasts, res.forecasts) assert_allclose(res2.forecasts_error, res.forecasts_error) assert_allclose(res2.forecasts_error_cov, res.forecasts_error_cov) if option == 'memory_no_filtered': assert_(res2.filtered_state is None) assert_(res2.filtered_state_cov is None) else: assert_allclose(res2.filtered_state, res.filtered_state) assert_allclose(res2.filtered_state_cov, res.filtered_state_cov) assert_allclose(res2.llf, res.llf) if option == 'memory_no_likelihood': assert_(res2.llf_obs is None) else: assert_allclose(res2.llf_obs, res.llf_obs) if option == 'memory_no_std_forecast': assert_(res2.standardized_forecasts_error is None) else: assert_allclose(res2.standardized_forecasts_error, res.standardized_forecasts_error) options_filter_only = [ 'memory_no_predicted', 'memory_no_gain', 'memory_no_smoothing', 'memory_conserve'] for option in options_filter_only[2:]: mod.ssm.set_conserve_memory(0) setattr(mod.ssm, option, True) res2 = mod.fit(res.params, disp=False) # General check that smoothing results are not available assert_(res2.smoothed_state is None) # Specific checks for each type if option in ['memory_no_predicted', 'memory_conserve']: assert_(res2.predicted_state_cov is None) if option == 'memory_no_predicted': assert_(res2.predicted_state is None) else: assert_allclose(res2.predicted_state, res.predicted_state) assert_allclose(res2.predicted_state_cov, res.predicted_state_cov) if option in ['memory_no_gain', 'memory_conserve']: assert_(res2.filter_results._kalman_gain is None) else: assert_allclose(res2.filter_results.kalman_gain, res.filter_results.kalman_gain) def test_low_memory_filter(): endog = dta['infl'].iloc[:20] mod = sarimax.SARIMAX(endog, order=(1, 0, 0), concentrate_scale=True) mod.ssm.set_conserve_memory(MEMORY_NO_GAIN) res = mod.filter([0.5], low_memory=True) assert_equal(res.filter_results.conserve_memory, MEMORY_CONSERVE) assert_(res.llf_obs is None) assert_equal(mod.ssm.conserve_memory, MEMORY_NO_GAIN) def test_low_memory_fit(): endog = dta['infl'].iloc[:20] mod = sarimax.SARIMAX(endog, order=(1, 0, 0), concentrate_scale=True) mod.ssm.set_conserve_memory(MEMORY_NO_GAIN) res = mod.fit(low_memory=True, disp=False) assert_equal(res.filter_results.conserve_memory, MEMORY_CONSERVE) assert_(res.llf_obs is None) assert_equal(mod.ssm.conserve_memory, MEMORY_NO_GAIN) @pytest.mark.parametrize("conserve_memory", [ MEMORY_CONSERVE, MEMORY_NO_FORECAST_COV]) def test_fittedvalues_resid_predict(conserve_memory): # Basic test that as long as MEMORY_NO_FORECAST_MEAN is not set, we should # be able to use fittedvalues, resid, predict() with dynamic=False and # forecast endog = dta['infl'].iloc[:20] mod1 = sarimax.SARIMAX(endog, order=(1, 0, 0), concentrate_scale=True) mod2 = sarimax.SARIMAX(endog, order=(1, 0, 0), concentrate_scale=True) mod1.ssm.set_conserve_memory(conserve_memory) assert_equal(mod1.ssm.conserve_memory, conserve_memory) assert_equal(mod2.ssm.conserve_memory, 0) res1 = mod1.filter([0]) res2 = mod2.filter([0]) assert_equal(res1.filter_results.conserve_memory, conserve_memory | MEMORY_NO_SMOOTHING) assert_equal(res2.filter_results.conserve_memory, MEMORY_NO_SMOOTHING) # Test output against known values assert_allclose(res1.fittedvalues, 0) assert_allclose(res1.predict(), 0) assert_allclose(res1.predict(start=endog.index[10]), np.zeros(10)) assert_allclose(res1.resid, endog) assert_allclose(res1.forecast(3), np.zeros(3)) # Test output against results without memory conservation assert_allclose(res1.fittedvalues, res2.fittedvalues) assert_allclose(res1.predict(), res2.predict()) assert_allclose(res1.predict(start=endog.index[10]), res2.predict(start=endog.index[10])) assert_allclose(res1.resid, res2.resid) assert_allclose(res1.forecast(3), res2.forecast(3)) assert_allclose(res1.test_normality('jarquebera'), res2.test_normality('jarquebera')) assert_allclose(res1.test_heteroskedasticity('breakvar'), res2.test_heteroskedasticity('breakvar')) with pytest.warns(FutureWarning): actual = res1.test_serial_correlation('ljungbox') desired = res2.test_serial_correlation('ljungbox') assert_allclose(actual, desired) def test_get_prediction_memory_conserve(): endog = dta['infl'].iloc[:20] mod1 = sarimax.SARIMAX(endog, order=(1, 0, 0), concentrate_scale=True) mod2 = sarimax.SARIMAX(endog, order=(1, 0, 0), concentrate_scale=True) mod1.ssm.set_conserve_memory(MEMORY_CONSERVE) assert_equal(mod1.ssm.conserve_memory, MEMORY_CONSERVE) assert_equal(mod2.ssm.conserve_memory, 0) res1 = mod1.filter([0]) res2 = mod2.filter([0]) assert_equal(res1.filter_results.conserve_memory, MEMORY_CONSERVE) assert_equal(res2.filter_results.conserve_memory, MEMORY_NO_SMOOTHING) p1 = res1.get_prediction() p2 = res2.get_prediction() assert_allclose(p1.predicted_mean, p2.predicted_mean) assert_allclose(p1.se_mean, np.nan) assert_allclose(p1.conf_int(), np.nan) s1 = p1.summary_frame() s2 = p2.summary_frame() assert_allclose(s1['mean'], s2['mean']) assert_allclose(s1.mean_se, np.nan) assert_allclose(s1.mean_ci_lower, np.nan) assert_allclose(s1.mean_ci_upper, np.nan) def test_invalid_fittedvalues_resid_predict(): endog = dta['infl'].iloc[:20] mod = sarimax.SARIMAX(endog, order=(1, 0, 0), concentrate_scale=True) # Check that we can't do any prediction without forecast means res = mod.filter([0], conserve_memory=MEMORY_NO_FORECAST_MEAN) assert_equal(res.filter_results.conserve_memory, MEMORY_NO_FORECAST_MEAN) message = ('In-sample prediction is not available if memory conservation' ' has been used to avoid storing forecast means.') with pytest.raises(ValueError, match=message): res.predict() with pytest.raises(ValueError, match=message): res.get_prediction() # Check that we can't do dynamic prediction without predicted means, # predicted covs options = [ MEMORY_NO_PREDICTED_MEAN, MEMORY_NO_PREDICTED_COV, MEMORY_NO_PREDICTED] for option in options: res = mod.filter([0], conserve_memory=option) assert_equal(res.filter_results.conserve_memory, option) message = ('In-sample dynamic prediction is not available if' ' memory conservation has been used to avoid' ' storing forecasted or predicted state means' ' or covariances.') with pytest.raises(ValueError, match=message): res.predict(dynamic=True) with pytest.raises(ValueError, match=message): res.predict(start=endog.index[10], dynamic=True) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_dynamic_factor.py000066400000000000000000001137641400612667500272030ustar00rootroot00000000000000""" Tests for VARMAX models Author: Chad Fulton License: Simplified-BSD """ import os import re import warnings import numpy as np from numpy.testing import assert_equal, assert_raises, assert_allclose import pandas as pd import pytest from statsmodels.tsa.statespace import dynamic_factor from .results import results_varmax, results_dynamic_factor from statsmodels.iolib.summary import forg current_path = os.path.dirname(os.path.abspath(__file__)) output_path = os.path.join('results', 'results_dynamic_factor_stata.csv') output_results = pd.read_csv(os.path.join(current_path, output_path)) class CheckDynamicFactor(object): @classmethod def setup_class(cls, true, k_factors, factor_order, cov_type='approx', included_vars=['dln_inv', 'dln_inc', 'dln_consump'], demean=False, filter=True, **kwargs): cls.true = true # 1960:Q1 - 1982:Q4 dta = pd.DataFrame( results_varmax.lutkepohl_data, columns=['inv', 'inc', 'consump'], index=pd.date_range('1960-01-01', '1982-10-01', freq='QS')) dta['dln_inv'] = np.log(dta['inv']).diff() dta['dln_inc'] = np.log(dta['inc']).diff() dta['dln_consump'] = np.log(dta['consump']).diff() endog = dta.loc['1960-04-01':'1978-10-01', included_vars] if demean: endog -= dta.iloc[1:][included_vars].mean() cls.model = dynamic_factor.DynamicFactor(endog, k_factors=k_factors, factor_order=factor_order, **kwargs) if filter: cls.results = cls.model.smooth(true['params'], cov_type=cov_type) def test_params(self): # Smoke test to make sure the start_params are well-defined and # lead to a well-defined model self.model.filter(self.model.start_params) # Similarly a smoke test for param_names assert_equal(len(self.model.start_params), len(self.model.param_names)) # Finally make sure the transform and untransform do their job actual = self.model.transform_params( self.model.untransform_params(self.model.start_params)) assert_allclose(actual, self.model.start_params) # Also in the case of enforce stationarity = False self.model.enforce_stationarity = False actual = self.model.transform_params( self.model.untransform_params(self.model.start_params)) self.model.enforce_stationarity = True assert_allclose(actual, self.model.start_params) def test_results(self, close_figures): # Smoke test for creating the summary with warnings.catch_warnings(): warnings.simplefilter("ignore") self.results.summary() # Test cofficient matrix creation # (via a different, more direct, method) if self.model.factor_order > 0: model = self.model k_factors = model.k_factors pft_params = self.results.params[model._params_factor_transition] coefficients = np.array(pft_params).reshape( k_factors, k_factors * model.factor_order) coefficient_matrices = np.array([ coefficients[:self.model.k_factors, i*self.model.k_factors:(i+1)*self.model.k_factors] for i in range(self.model.factor_order) ]) assert_equal( self.results.coefficient_matrices_var, coefficient_matrices) else: assert_equal(self.results.coefficient_matrices_var, None) @pytest.mark.matplotlib def test_plot_coefficients_of_determination(self, close_figures): # Smoke test for plot_coefficients_of_determination self.results.plot_coefficients_of_determination() def test_no_enforce(self): return # Test that nothing goes wrong when we do not enforce stationarity params = self.model.untransform_params(self.true['params']) params[self.model._params_transition] = ( self.true['params'][self.model._params_transition]) self.model.enforce_stationarity = False results = self.model.filter(params, transformed=False) self.model.enforce_stationarity = True assert_allclose(results.llf, self.results.llf, rtol=1e-5) def test_mle(self, init_powell=True): with warnings.catch_warnings(record=True): warnings.simplefilter('always') start_params = self.model.start_params if init_powell: results = self.model.fit(method='powell', maxiter=100, disp=False) start_params = results.params results = self.model.fit(start_params, maxiter=1000, disp=False) results = self.model.fit(results.params, method='nm', maxiter=1000, disp=False) if not results.llf > self.results.llf: assert_allclose(results.llf, self.results.llf, rtol=1e-5) def test_loglike(self): assert_allclose(self.results.llf, self.true['loglike'], rtol=1e-6) def test_aic(self): # We only get 3 digits from Stata assert_allclose(self.results.aic, self.true['aic'], atol=3) def test_bic(self): # We only get 3 digits from Stata assert_allclose(self.results.bic, self.true['bic'], atol=3) def test_predict(self, **kwargs): # Tests predict + forecast self.results.predict(end='1982-10-01', **kwargs) assert_allclose( self.results.predict(end='1982-10-01', **kwargs), self.true['predict'], atol=1e-6) def test_dynamic_predict(self, **kwargs): # Tests predict + dynamic predict + forecast assert_allclose( self.results.predict(end='1982-10-01', dynamic='1961-01-01', **kwargs), self.true['dynamic_predict'], atol=1e-6) class TestDynamicFactor(CheckDynamicFactor): """ Test for a dynamic factor model with 1 AR(2) factor """ @classmethod def setup_class(cls): true = results_dynamic_factor.lutkepohl_dfm.copy() true['predict'] = output_results.iloc[1:][[ 'predict_dfm_1', 'predict_dfm_2', 'predict_dfm_3']] true['dynamic_predict'] = output_results.iloc[1:][[ 'dyn_predict_dfm_1', 'dyn_predict_dfm_2', 'dyn_predict_dfm_3']] super(TestDynamicFactor, cls).setup_class( true, k_factors=1, factor_order=2) def test_bse_approx(self): bse = self.results._cov_params_approx().diagonal()**0.5 assert_allclose(bse, self.true['bse_oim'], atol=1e-5) class TestDynamicFactor2(CheckDynamicFactor): """ Test for a dynamic factor model with two VAR(1) factors """ @classmethod def setup_class(cls): true = results_dynamic_factor.lutkepohl_dfm2.copy() true['predict'] = output_results.iloc[1:][[ 'predict_dfm2_1', 'predict_dfm2_2', 'predict_dfm2_3']] true['dynamic_predict'] = output_results.iloc[1:][[ 'dyn_predict_dfm2_1', 'dyn_predict_dfm2_2', 'dyn_predict_dfm2_3']] super(TestDynamicFactor2, cls).setup_class( true, k_factors=2, factor_order=1) def test_mle(self): # Stata's MLE on this model does not converge, so no reason to check pass def test_bse(self): # Stata's MLE on this model does not converge, and four of their # params do not even have bse (possibly they are still at starting # values?), so no reason to check this pass def test_aic(self): # Stata uses 9 df (i.e. 9 params) here instead of 13, because since the # model did not coverge, 4 of the parameters are not fully estimated # (possibly they are still at starting values?) so the AIC is off pass def test_bic(self): # Stata uses 9 df (i.e. 9 params) here instead of 13, because since the # model did not coverge, 4 of the parameters are not fully estimated # (possibly they are still at starting values?) so the BIC is off pass def test_summary(self): with warnings.catch_warnings(): warnings.simplefilter("ignore") summary = self.results.summary() tables = [str(table) for table in summary.tables] params = self.true['params'] # Make sure we have the right number of tables assert_equal( len(tables), 2 + self.model.k_endog + self.model.k_factors + 1) # Check the model overview table assert re.search( r'Model:.*DynamicFactor\(factors=2, order=1\)', tables[0]) # For each endogenous variable, check the output for i in range(self.model.k_endog): offset_loading = self.model.k_factors * i table = tables[i + 2] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Results for equation %s' % name, table) # -> Make sure it's the right size assert_equal(len(table.split('\n')), 7) # -> Check that we have the right coefficients assert re.search( 'loading.f1 +' + forg(params[offset_loading + 0], prec=4), table) assert re.search( 'loading.f2 +' + forg(params[offset_loading + 1], prec=4), table) # For each factor, check the output for i in range(self.model.k_factors): offset = (self.model.k_endog * (self.model.k_factors + 1) + i * self.model.k_factors) table = tables[self.model.k_endog + i + 2] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Results for factor equation f%d' % (i+1), table) # -> Make sure it's the right size assert_equal(len(table.split('\n')), 7) # -> Check that we have the right coefficients assert re.search('L1.f1 +' + forg(params[offset + 0], prec=4), table) assert re.search('L1.f2 +' + forg(params[offset + 1], prec=4), table) # Check the Error covariance matrix output table = tables[2 + self.model.k_endog + self.model.k_factors] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Error covariance matrix', table) # -> Make sure it's the right size assert_equal(len(table.split('\n')), 8) # -> Check that we have the right coefficients offset = self.model.k_endog * self.model.k_factors for i in range(self.model.k_endog): iname = self.model.endog_names[i] iparam = forg(params[offset + i], prec=4) assert re.search('sigma2.%s +%s' % (iname, iparam), table) class TestDynamicFactor_exog1(CheckDynamicFactor): """ Test for a dynamic factor model with 1 exogenous regressor: a constant """ @classmethod def setup_class(cls): true = results_dynamic_factor.lutkepohl_dfm_exog1.copy() true['predict'] = output_results.iloc[1:][[ 'predict_dfm_exog1_1', 'predict_dfm_exog1_2', 'predict_dfm_exog1_3']] true['dynamic_predict'] = output_results.iloc[1:][[ 'dyn_predict_dfm_exog1_1', 'dyn_predict_dfm_exog1_2', 'dyn_predict_dfm_exog1_3']] exog = np.ones((75, 1)) super(TestDynamicFactor_exog1, cls).setup_class( true, k_factors=1, factor_order=1, exog=exog) def test_predict(self): exog = np.ones((16, 1)) super(TestDynamicFactor_exog1, self).test_predict(exog=exog) def test_dynamic_predict(self): exog = np.ones((16, 1)) super(TestDynamicFactor_exog1, self).test_dynamic_predict(exog=exog) def test_bse_approx(self): bse = self.results._cov_params_approx().diagonal()**0.5 assert_allclose(bse**2, self.true['var_oim'], atol=1e-5) class TestDynamicFactor_exog2(CheckDynamicFactor): """ Test for a dynamic factor model with 2 exogenous regressors: a constant and a time-trend """ @classmethod def setup_class(cls): true = results_dynamic_factor.lutkepohl_dfm_exog2.copy() true['predict'] = output_results.iloc[1:][[ 'predict_dfm_exog2_1', 'predict_dfm_exog2_2', 'predict_dfm_exog2_3']] true['dynamic_predict'] = output_results.iloc[1:][[ 'dyn_predict_dfm_exog2_1', 'dyn_predict_dfm_exog2_2', 'dyn_predict_dfm_exog2_3']] exog = np.c_[np.ones((75, 1)), (np.arange(75) + 2)[:, np.newaxis]] super(TestDynamicFactor_exog2, cls).setup_class( true, k_factors=1, factor_order=1, exog=exog) def test_bse_approx(self): bse = self.results._cov_params_approx().diagonal()**0.5 assert_allclose(bse**2, self.true['var_oim'], atol=1e-5) def test_predict(self): exog = np.c_[np.ones((16, 1)), (np.arange(75, 75+16) + 2)[:, np.newaxis]] super(TestDynamicFactor_exog2, self).test_predict(exog=exog) def test_dynamic_predict(self): exog = np.c_[np.ones((16, 1)), (np.arange(75, 75+16) + 2)[:, np.newaxis]] super(TestDynamicFactor_exog2, self).test_dynamic_predict(exog=exog) def test_summary(self): with warnings.catch_warnings(): warnings.simplefilter("ignore") summary = self.results.summary() tables = [str(table) for table in summary.tables] params = self.true['params'] # Make sure we have the right number of tables assert_equal( len(tables), 2 + self.model.k_endog + self.model.k_factors + 1) # Check the model overview table assert re.search(r'Model:.*DynamicFactor\(factors=1, order=1\)', tables[0]) assert_equal(re.search(r'.*2 regressors', tables[0]) is None, False) # For each endogenous variable, check the output for i in range(self.model.k_endog): offset_loading = self.model.k_factors * i offset_exog = self.model.k_factors * self.model.k_endog table = tables[i + 2] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Results for equation %s' % name, table) # -> Make sure it's the right size assert_equal(len(table.split('\n')), 8) # -> Check that we have the right coefficients assert re.search( 'loading.f1 +' + forg(params[offset_loading + 0], prec=4), table) assert re.search( 'beta.const +' + forg(params[offset_exog + i*2 + 0], prec=4), table) assert re.search( 'beta.x1 +' + forg(params[offset_exog + i*2 + 1], prec=4), table) # For each factor, check the output for i in range(self.model.k_factors): offset = (self.model.k_endog * (self.model.k_factors + 3) + i * self.model.k_factors) table = tables[self.model.k_endog + i + 2] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Results for factor equation f%d' % (i+1), table) # -> Make sure it's the right size assert_equal(len(table.split('\n')), 6) # -> Check that we have the right coefficients assert re.search('L1.f1 +' + forg(params[offset + 0], prec=4), table) # Check the Error covariance matrix output table = tables[2 + self.model.k_endog + self.model.k_factors] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Error covariance matrix', table) # -> Make sure it's the right size assert_equal(len(table.split('\n')), 8) # -> Check that we have the right coefficients offset = self.model.k_endog * (self.model.k_factors + 2) for i in range(self.model.k_endog): iname = self.model.endog_names[i] iparam = forg(params[offset + i], prec=4) assert re.search('sigma2.%s +%s' % (iname, iparam), table) class TestDynamicFactor_general_errors(CheckDynamicFactor): """ Test for a dynamic factor model where errors are as general as possible, meaning: - Errors are vector autocorrelated, VAR(1) - Innovations are correlated """ @classmethod def setup_class(cls): true = results_dynamic_factor.lutkepohl_dfm_gen.copy() true['predict'] = output_results.iloc[1:][[ 'predict_dfm_gen_1', 'predict_dfm_gen_2', 'predict_dfm_gen_3']] true['dynamic_predict'] = output_results.iloc[1:][[ 'dyn_predict_dfm_gen_1', 'dyn_predict_dfm_gen_2', 'dyn_predict_dfm_gen_3']] super(TestDynamicFactor_general_errors, cls).setup_class( true, k_factors=1, factor_order=1, error_var=True, error_order=1, error_cov_type='unstructured') def test_bse_approx(self): bse = self.results._cov_params_approx().diagonal() assert_allclose(bse[:3], self.true['var_oim'][:3], atol=1e-5) assert_allclose(bse[-10:], self.true['var_oim'][-10:], atol=3e-4) @pytest.mark.skip("Known failure, no sequence of optimizers has been " "found which can achieve the maximum.") def test_mle(self): # The following gets us to llf=546.53, which is still not good enough # llf = 300.842477412 # res = mod.fit(method='lbfgs', maxiter=10000) # llf = 460.26576722 # res = mod.fit(res.params, method='nm', maxiter=10000, maxfev=10000) # llf = 542.245718508 # res = mod.fit(res.params, method='lbfgs', maxiter=10000) # llf = 544.035160955 # res = mod.fit(res.params, method='nm', maxiter=10000, maxfev=10000) # llf = 557.442240083 # res = mod.fit(res.params, method='lbfgs', maxiter=10000) # llf = 558.199513262 # res = mod.fit(res.params, method='nm', maxiter=10000, maxfev=10000) # llf = 559.049076604 # res = mod.fit(res.params, method='nm', maxiter=10000, maxfev=10000) # llf = 559.049076604 # ... pass def test_summary(self): with warnings.catch_warnings(): warnings.simplefilter("ignore") summary = self.results.summary() tables = [str(table) for table in summary.tables] params = self.true['params'] # Make sure we have the right number of tables assert_equal( len(tables), 2 + self.model.k_endog + self.model.k_factors + self.model.k_endog + 1) # Check the model overview table assert re.search(r'Model:.*DynamicFactor\(factors=1, order=1\)', tables[0]) assert re.search(r'.*VAR\(1\) errors', tables[0]) # For each endogenous variable, check the output for i in range(self.model.k_endog): offset_loading = self.model.k_factors * i table = tables[i + 2] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Results for equation %s' % name, table) # -> Make sure it's the right size assert_equal(len(table.split('\n')), 6) # -> Check that we have the right coefficients pattern = 'loading.f1 +' + forg(params[offset_loading + 0], prec=4) assert re.search(pattern, table) # For each factor, check the output for i in range(self.model.k_factors): offset = (self.model.k_endog * self.model.k_factors + 6 + i * self.model.k_factors) table = tables[2 + self.model.k_endog + i] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Results for factor equation f%d' % (i+1), table) # -> Make sure it's the right size assert_equal(len(table.split('\n')), 6) # -> Check that we have the right coefficients assert re.search('L1.f1 +' + forg(params[offset + 0], prec=4), table) # For each error equation, check the output for i in range(self.model.k_endog): offset = (self.model.k_endog * (self.model.k_factors + i) + 6 + self.model.k_factors) table = tables[2 + self.model.k_endog + self.model.k_factors + i] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search(r'Results for error equation e\(%s\)' % name, table) # -> Make sure it's the right size assert_equal(len(table.split('\n')), 8) # -> Check that we have the right coefficients for j in range(self.model.k_endog): name = self.model.endog_names[j] pattern = r'L1.e\(%s\) +%s' % (name, forg(params[offset + j], prec=4)) assert re.search(pattern, table) # Check the Error covariance matrix output table = tables[2 + self.model.k_endog + self.model.k_factors + self.model.k_endog] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Error covariance matrix', table) # -> Make sure it's the right size assert_equal(len(table.split('\n')), 11) # -> Check that we have the right coefficients offset = self.model.k_endog * self.model.k_factors assert re.search( r'cov.chol\[1,1\] +' + forg(params[offset + 0], prec=4), table) assert re.search( r'cov.chol\[2,1\] +' + forg(params[offset + 1], prec=4), table) assert re.search( r'cov.chol\[2,2\] +' + forg(params[offset + 2], prec=4), table) assert re.search( r'cov.chol\[3,1\] +' + forg(params[offset+3], prec=4), table) assert re.search( r'cov.chol\[3,2\] +' + forg(params[offset+4], prec=4), table) assert re.search( r'cov.chol\[3,3\] +' + forg(params[offset + 5], prec=4), table) class TestDynamicFactor_ar2_errors(CheckDynamicFactor): """ Test for a dynamic factor model where errors are as general as possible, meaning: - Errors are vector autocorrelated, VAR(1) - Innovations are correlated """ @classmethod def setup_class(cls): true = results_dynamic_factor.lutkepohl_dfm_ar2.copy() true['predict'] = output_results.iloc[1:][[ 'predict_dfm_ar2_1', 'predict_dfm_ar2_2', 'predict_dfm_ar2_3']] true['dynamic_predict'] = output_results.iloc[1:][[ 'dyn_predict_dfm_ar2_1', 'dyn_predict_dfm_ar2_2', 'dyn_predict_dfm_ar2_3']] super(TestDynamicFactor_ar2_errors, cls).setup_class( true, k_factors=1, factor_order=1, error_order=2) def test_bse_approx(self): bse = self.results._cov_params_approx().diagonal() assert_allclose(bse, self.true['var_oim'], atol=1e-5) def test_mle(self): with warnings.catch_warnings(record=True): # Depending on the system, this test can reach a greater precision, # but for cross-platform results keep it at 1e-2 mod = self.model res1 = mod.fit(maxiter=100, optim_score='approx', disp=False) res = mod.fit( res1.params, method='nm', maxiter=10000, optim_score='approx', disp=False) # Added rtol to catch spurious failures on some platforms assert_allclose(res.llf, self.results.llf, atol=1e-2, rtol=1e-4) class TestDynamicFactor_scalar_error(CheckDynamicFactor): """ Test for a dynamic factor model where innovations are uncorrelated and are forced to have the same variance. """ @classmethod def setup_class(cls): true = results_dynamic_factor.lutkepohl_dfm_scalar.copy() true['predict'] = output_results.iloc[1:][[ 'predict_dfm_scalar_1', 'predict_dfm_scalar_2', 'predict_dfm_scalar_3']] true['dynamic_predict'] = output_results.iloc[1:][[ 'dyn_predict_dfm_scalar_1', 'dyn_predict_dfm_scalar_2', 'dyn_predict_dfm_scalar_3']] exog = np.ones((75, 1)) super(TestDynamicFactor_scalar_error, cls).setup_class( true, k_factors=1, factor_order=1, exog=exog, error_cov_type='scalar') def test_bse_approx(self): bse = self.results._cov_params_approx().diagonal() assert_allclose(bse, self.true['var_oim'], atol=1e-5) def test_predict(self): exog = np.ones((16, 1)) super(TestDynamicFactor_scalar_error, self).test_predict(exog=exog) def test_dynamic_predict(self): exog = np.ones((16, 1)) super(TestDynamicFactor_scalar_error, self).test_dynamic_predict(exog=exog) class TestStaticFactor(CheckDynamicFactor): """ Test for a static factor model (i.e. factors are not autocorrelated). """ @classmethod def setup_class(cls): true = results_dynamic_factor.lutkepohl_sfm.copy() true['predict'] = output_results.iloc[1:][[ 'predict_sfm_1', 'predict_sfm_2', 'predict_sfm_3']] true['dynamic_predict'] = output_results.iloc[1:][[ 'dyn_predict_sfm_1', 'dyn_predict_sfm_2', 'dyn_predict_sfm_3']] super(TestStaticFactor, cls).setup_class( true, k_factors=1, factor_order=0) def test_bse_approx(self): bse = self.results._cov_params_approx().diagonal() assert_allclose(bse, self.true['var_oim'], atol=1e-5) def test_bic(self): # Stata uses 5 df (i.e. 5 params) here instead of 6, because one param # is basically zero. pass class TestSUR(CheckDynamicFactor): """ Test for a seemingly unrelated regression model (i.e. no factors) with errors cross-sectionally, but not auto-, correlated """ @classmethod def setup_class(cls): true = results_dynamic_factor.lutkepohl_sur.copy() true['predict'] = output_results.iloc[1:][[ 'predict_sur_1', 'predict_sur_2', 'predict_sur_3']] true['dynamic_predict'] = output_results.iloc[1:][[ 'dyn_predict_sur_1', 'dyn_predict_sur_2', 'dyn_predict_sur_3']] exog = np.c_[np.ones((75, 1)), (np.arange(75) + 2)[:, np.newaxis]] super(TestSUR, cls).setup_class( true, k_factors=0, factor_order=0, exog=exog, error_cov_type='unstructured') def test_bse_approx(self): bse = self.results._cov_params_approx().diagonal() assert_allclose(bse[:6], self.true['var_oim'][:6], atol=1e-5) def test_predict(self): exog = np.c_[np.ones((16, 1)), (np.arange(75, 75+16) + 2)[:, np.newaxis]] super(TestSUR, self).test_predict(exog=exog) def test_dynamic_predict(self): exog = np.c_[np.ones((16, 1)), (np.arange(75, 75+16) + 2)[:, np.newaxis]] super(TestSUR, self).test_dynamic_predict(exog=exog) class TestSUR_autocorrelated_errors(CheckDynamicFactor): """ Test for a seemingly unrelated regression model (i.e. no factors) where the errors are vector autocorrelated, but innovations are uncorrelated. """ @classmethod def setup_class(cls): true = results_dynamic_factor.lutkepohl_sur_auto.copy() true['predict'] = output_results.iloc[1:][[ 'predict_sur_auto_1', 'predict_sur_auto_2']] true['dynamic_predict'] = output_results.iloc[1:][[ 'dyn_predict_sur_auto_1', 'dyn_predict_sur_auto_2']] exog = np.c_[np.ones((75, 1)), (np.arange(75) + 2)[:, np.newaxis]] super(TestSUR_autocorrelated_errors, cls).setup_class( true, k_factors=0, factor_order=0, exog=exog, error_order=1, error_var=True, error_cov_type='diagonal', included_vars=['dln_inv', 'dln_inc']) def test_bse_approx(self): bse = self.results._cov_params_approx().diagonal() assert_allclose(bse, self.true['var_oim'], atol=1e-5) def test_predict(self): exog = np.c_[np.ones((16, 1)), (np.arange(75, 75+16) + 2)[:, np.newaxis]] super(TestSUR_autocorrelated_errors, self).test_predict(exog=exog) def test_dynamic_predict(self): exog = np.c_[np.ones((16, 1)), (np.arange(75, 75+16) + 2)[:, np.newaxis]] super(TestSUR_autocorrelated_errors, self).test_dynamic_predict(exog=exog) def test_mle(self): super(TestSUR_autocorrelated_errors, self).test_mle(init_powell=False) def test_misspecification(): # Tests for model specification and misspecification exceptions endog = np.arange(20).reshape(10, 2) # Too few endog assert_raises( ValueError, dynamic_factor.DynamicFactor, endog[:, 0], k_factors=0, factor_order=0) # Too many factors assert_raises( ValueError, dynamic_factor.DynamicFactor, endog, k_factors=2, factor_order=1) # Bad error_cov_type specification assert_raises( ValueError, dynamic_factor.DynamicFactor, endog, k_factors=1, factor_order=1, order=(1, 0), error_cov_type='') def test_miscellaneous(): # Initialization with 1-dimensional exog array exog = np.arange(75) mod = CheckDynamicFactor() mod.setup_class(true=None, k_factors=1, factor_order=1, exog=exog, filter=False) exog = pd.Series(np.arange(75), index=pd.date_range(start='1960-04-01', end='1978-10-01', freq='QS')) mod = CheckDynamicFactor() mod.setup_class( true=None, k_factors=1, factor_order=1, exog=exog, filter=False) def test_predict_custom_index(): np.random.seed(328423) endog = pd.DataFrame(np.random.normal(size=(50, 2))) mod = dynamic_factor.DynamicFactor(endog, k_factors=1, factor_order=1) res = mod.smooth(mod.start_params) out = res.predict(start=1, end=1, index=['a']) assert_equal(out.index.equals(pd.Index(['a'])), True) def test_forecast_exog(): # Test forecasting with various shapes of `exog` nobs = 100 endog = np.ones((nobs, 2)) * 2.0 exog = np.ones(nobs) mod = dynamic_factor.DynamicFactor(endog, exog=exog, k_factors=1, factor_order=1) res = mod.smooth(np.r_[[0] * 2, 2.0, 2.0, 1, 1., 0.]) # 1-step-ahead, valid exog_fcast_scalar = 1. exog_fcast_1dim = np.ones(1) exog_fcast_2dim = np.ones((1, 1)) assert_allclose(res.forecast(1, exog=exog_fcast_scalar), 2.) assert_allclose(res.forecast(1, exog=exog_fcast_1dim), 2.) assert_allclose(res.forecast(1, exog=exog_fcast_2dim), 2.) # h-steps-ahead, valid h = 10 exog_fcast_1dim = np.ones(h) exog_fcast_2dim = np.ones((h, 1)) assert_allclose(res.forecast(h, exog=exog_fcast_1dim), 2.) assert_allclose(res.forecast(h, exog=exog_fcast_2dim), 2.) # h-steps-ahead, invalid assert_raises(ValueError, res.forecast, h, exog=1.) assert_raises(ValueError, res.forecast, h, exog=[1, 2]) assert_raises(ValueError, res.forecast, h, exog=np.ones((h, 2))) def check_equivalent_models(mod, mod2): attrs = [ 'k_factors', 'factor_order', 'error_order', 'error_var', 'error_cov_type', 'enforce_stationarity', 'mle_regression', 'k_params'] ssm_attrs = [ 'nobs', 'k_endog', 'k_states', 'k_posdef', 'obs_intercept', 'design', 'obs_cov', 'state_intercept', 'transition', 'selection', 'state_cov'] for attr in attrs: assert_equal(getattr(mod2, attr), getattr(mod, attr)) for attr in ssm_attrs: assert_equal(getattr(mod2.ssm, attr), getattr(mod.ssm, attr)) assert_equal(mod2._get_init_kwds(), mod._get_init_kwds()) def test_recreate_model(): nobs = 100 endog = np.ones((nobs, 3)) * 2.0 exog = np.ones(nobs) k_factors = [0, 1, 2] factor_orders = [0, 1, 2] error_orders = [0, 1] error_vars = [False, True] error_cov_types = ['diagonal', 'scalar'] import itertools names = ['k_factors', 'factor_order', 'error_order', 'error_var', 'error_cov_type'] for element in itertools.product(k_factors, factor_orders, error_orders, error_vars, error_cov_types): kwargs = dict(zip(names, element)) mod = dynamic_factor.DynamicFactor(endog, exog=exog, **kwargs) mod2 = dynamic_factor.DynamicFactor(endog, exog=exog, **mod._get_init_kwds()) check_equivalent_models(mod, mod2) def test_append_results(): endog = np.arange(200).reshape(100, 2) exog = np.ones(100) params = [0.1, -0.2, 1., 2., 1., 1., 0.5, 0.1] mod1 = dynamic_factor.DynamicFactor( endog, k_factors=1, factor_order=2, exog=exog) res1 = mod1.smooth(params) mod2 = dynamic_factor.DynamicFactor( endog[:50], k_factors=1, factor_order=2, exog=exog[:50]) res2 = mod2.smooth(params) res3 = res2.append(endog[50:], exog=exog[50:]) assert_equal(res1.specification, res3.specification) assert_allclose(res3.cov_params_default, res2.cov_params_default) for attr in ['nobs', 'llf', 'llf_obs', 'loglikelihood_burn']: assert_equal(getattr(res3, attr), getattr(res1, attr)) for attr in [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov']: assert_equal(getattr(res3, attr), getattr(res1, attr)) assert_allclose(res3.forecast(10, exog=np.ones(10)), res1.forecast(10, exog=np.ones(10))) def test_extend_results(): endog = np.arange(200).reshape(100, 2) exog = np.ones(100) params = [0.1, -0.2, 1., 2., 1., 1., 0.5, 0.1] mod1 = dynamic_factor.DynamicFactor( endog, k_factors=1, factor_order=2, exog=exog) res1 = mod1.smooth(params) mod2 = dynamic_factor.DynamicFactor( endog[:50], k_factors=1, factor_order=2, exog=exog[:50]) res2 = mod2.smooth(params) res3 = res2.extend(endog[50:], exog=exog[50:]) assert_allclose(res3.llf_obs, res1.llf_obs[50:]) for attr in [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov']: desired = getattr(res1, attr) if desired is not None: desired = desired[..., 50:] assert_equal(getattr(res3, attr), desired) assert_allclose(res3.forecast(10, exog=np.ones(10)), res1.forecast(10, exog=np.ones(10))) def test_apply_results(): endog = np.arange(200).reshape(100, 2) exog = np.ones(100) params = [0.1, -0.2, 1., 2., 1., 1., 0.5, 0.1] mod1 = dynamic_factor.DynamicFactor( endog[:50], k_factors=1, factor_order=2, exog=exog[:50]) res1 = mod1.smooth(params) mod2 = dynamic_factor.DynamicFactor( endog[50:], k_factors=1, factor_order=2, exog=exog[50:]) res2 = mod2.smooth(params) res3 = res2.apply(endog[:50], exog=exog[:50]) assert_equal(res1.specification, res3.specification) assert_allclose(res3.cov_params_default, res2.cov_params_default) for attr in ['nobs', 'llf', 'llf_obs', 'loglikelihood_burn']: assert_equal(getattr(res3, attr), getattr(res1, attr)) for attr in [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov']: assert_equal(getattr(res3, attr), getattr(res1, attr)) assert_allclose(res3.forecast(10, exog=np.ones(10)), res1.forecast(10, exog=np.ones(10))) def test_start_params_nans(): ix = pd.date_range('1960-01-01', '1982-10-01', freq='QS') dta = np.log(pd.DataFrame( results_varmax.lutkepohl_data, columns=['inv', 'inc', 'consump'], index=ix)).diff().iloc[1:] endog1 = dta.iloc[:-1] mod1 = dynamic_factor.DynamicFactor(endog1, k_factors=1, factor_order=1) endog2 = dta.copy() endog2.iloc[-1:] = np.nan mod2 = dynamic_factor.DynamicFactor(endog2, k_factors=1, factor_order=1) assert_allclose(mod2.start_params, mod1.start_params) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_dynamic_factor_mq.py000066400000000000000000002425371400612667500277010ustar00rootroot00000000000000""" Basic tests for the BM model These test standard that the state space model is set up as desired, that expected exceptions are raised, etc. """ from statsmodels.compat.pandas import assert_frame_equal, assert_series_equal import numpy as np from numpy.testing import assert_, assert_allclose, assert_equal import pandas as pd import pytest from statsmodels.regression.linear_model import OLS from statsmodels.tools import add_constant from statsmodels.tsa.statespace import ( dynamic_factor, dynamic_factor_mq, sarimax, ) from statsmodels.tsa.statespace.tests import test_dynamic_factor_mq_monte_carlo def test_default(): # Includes 2 monthly and 2 quarterly series # Default is factors=1, factor_orders=1, idiosyncratic_ar1=True # Create the datasets index_M = pd.period_range(start='2000', periods=12, freq='M') index_Q = pd.period_range(start='2000', periods=4, freq='Q') dta_M = pd.DataFrame(np.zeros((12, 2)), index=index_M, columns=['M0', 'M1']) dta_Q = pd.DataFrame(np.zeros((4, 2)), index=index_Q, columns=['Q0', 'Q1']) # Add some noise so the variables aren't constants dta_M.iloc[0] = 1. dta_Q.iloc[1] = 1. # Create the model instance mod = dynamic_factor_mq.DynamicFactorMQ( dta_M, endog_quarterly=dta_Q, factors=1, factor_orders=1, idiosyncratic_ar1=True) # Test dimensions assert_equal(mod.k_endog, 2 + 2) assert_equal(mod.k_states, 5 + 2 + 2 * 5) assert_equal(mod.ssm.k_posdef, 1 + 2 + 2) # Test names assert_equal(mod.endog_names, ['M0', 'M1', 'Q0', 'Q1']) desired = (['0', 'L1.0', 'L2.0', 'L3.0', 'L4.0'] + ['eps_M.M0', 'eps_M.M1', 'eps_Q.Q0', 'eps_Q.Q1'] + ['L1.eps_Q.Q0', 'L1.eps_Q.Q1'] + ['L2.eps_Q.Q0', 'L2.eps_Q.Q1'] + ['L3.eps_Q.Q0', 'L3.eps_Q.Q1'] + ['L4.eps_Q.Q0', 'L4.eps_Q.Q1']) assert_equal(mod.state_names, desired) desired = [ 'loading.0->M0', 'loading.0->M1', 'loading.0->Q0', 'loading.0->Q1', 'L1.0->0', 'fb(0).cov.chol[1,1]', 'L1.eps_M.M0', 'L1.eps_M.M1', 'L1.eps_Q.Q0', 'L1.eps_Q.Q1', 'sigma2.M0', 'sigma2.M1', 'sigma2.Q0', 'sigma2.Q1'] assert_equal(mod.param_names, desired) # Test fixed elements of state space representation assert_allclose(mod['obs_intercept'], 0) assert_allclose(mod['design', :2, 5:7], np.eye(2)) assert_allclose(mod['design', 2:, 7:9], np.eye(2)) assert_allclose(mod['design', 2:, 9:11], 2 * np.eye(2)) assert_allclose(mod['design', 2:, 11:13], 3 * np.eye(2)) assert_allclose(mod['design', 2:, 13:15], 2 * np.eye(2)) assert_allclose(mod['design', 2:, 15:17], np.eye(2)) assert_allclose(np.sum(mod['design']), 20) assert_allclose(mod['obs_cov'], 0) assert_allclose(mod['state_intercept'], 0) assert_allclose(mod['transition', 1:5, :4], np.eye(4)) assert_allclose(mod['transition', 9:17, 7:15], np.eye(2 * 4)) assert_allclose(np.sum(mod['transition']), 12) assert_allclose(mod['selection', 0, 0], np.eye(1)) assert_allclose(mod['selection', 5:7, 1:3], np.eye(2)) assert_allclose(mod['selection', 7:9, 3:5], np.eye(2)) assert_allclose(np.sum(mod['selection']), 5) assert_allclose(mod['state_cov'], 0) # Test parameter entry mod.update(np.arange(mod.k_params) + 2) # -> obs_intercept assert_allclose(mod['obs_intercept'], 0) # -> design desired = np.array([ [2., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [3., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [4., 8., 12, 8., 4., 0., 0., 1., 0., 2., 0., 3., 0., 2., 0., 1., 0.], [5., 10, 15, 10, 5., 0., 0., 0., 1., 0., 2., 0., 3., 0., 2., 0., 1.]]) assert_allclose(mod['design'], desired) # -> obs_cov assert_allclose(mod['obs_cov'], 0) # -> state_intercept assert_allclose(mod['state_intercept'], 0) # -> transition desired = np.array([ [6., 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1., 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1., 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1., 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1., 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8., 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 9., 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 11., 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1., 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1., 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1., 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1., 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1., 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1., 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1., 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1., 0, 0]]) assert_allclose(mod['transition'], desired) # -> selection assert_allclose(np.sum(mod['selection']), 5) # -> state_cov desired = np.array([[49., 0., 0., 0., 0.], [0., 12., 0., 0., 0.], [0., 0., 13., 0., 0.], [0., 0., 0., 14., 0.], [0., 0., 0., 0., 15.]]) assert_allclose(mod['state_cov'], desired) def test_k_factors_gt1(): # Includes 2 monthly and 2 quarterly series # This case: k_factors=2, factor_orders=1, idiosyncratic_ar1=True # Create the datasets index_M = pd.period_range(start='2000', periods=12, freq='M') index_Q = pd.period_range(start='2000', periods=4, freq='Q') dta_M = pd.DataFrame(np.zeros((12, 2)), index=index_M, columns=['M0', 'M1']) dta_Q = pd.DataFrame(np.zeros((4, 2)), index=index_Q, columns=['Q0', 'Q1']) # Add some noise so the variables aren't constants dta_M.iloc[0] = 1. dta_Q.iloc[1] = 1. # Create the model instance mod = dynamic_factor_mq.DynamicFactorMQ( dta_M, endog_quarterly=dta_Q, factors=2, factor_orders={('0', '1'): 1}, idiosyncratic_ar1=True) # Test dimensions assert_equal(mod.k_endog, 2 + 2) assert_equal(mod.k_states, 5 * 2 + 2 + 2 * 5) assert_equal(mod.ssm.k_posdef, 2 + 2 + 2) # Test names assert_equal(mod.endog_names, ['M0', 'M1', 'Q0', 'Q1']) desired = (['0', '1', 'L1.0', 'L1.1', 'L2.0', 'L2.1', 'L3.0', 'L3.1', 'L4.0', 'L4.1'] + ['eps_M.M0', 'eps_M.M1', 'eps_Q.Q0', 'eps_Q.Q1'] + ['L1.eps_Q.Q0', 'L1.eps_Q.Q1'] + ['L2.eps_Q.Q0', 'L2.eps_Q.Q1'] + ['L3.eps_Q.Q0', 'L3.eps_Q.Q1'] + ['L4.eps_Q.Q0', 'L4.eps_Q.Q1']) assert_equal(mod.state_names, desired) desired = [ 'loading.0->M0', 'loading.1->M0', 'loading.0->M1', 'loading.1->M1', 'loading.0->Q0', 'loading.1->Q0', 'loading.0->Q1', 'loading.1->Q1', 'L1.0->0', 'L1.1->0', 'L1.0->1', 'L1.1->1', 'fb(0).cov.chol[1,1]', 'fb(0).cov.chol[2,1]', 'fb(0).cov.chol[2,2]', 'L1.eps_M.M0', 'L1.eps_M.M1', 'L1.eps_Q.Q0', 'L1.eps_Q.Q1', 'sigma2.M0', 'sigma2.M1', 'sigma2.Q0', 'sigma2.Q1'] assert_equal(mod.param_names, desired) # Test fixed elements of state space representation assert_allclose(mod['obs_intercept'], 0) assert_allclose(mod['design', :2, 10:12], np.eye(2)) assert_allclose(mod['design', 2:, 12:14], np.eye(2)) assert_allclose(mod['design', 2:, 14:16], 2 * np.eye(2)) assert_allclose(mod['design', 2:, 16:18], 3 * np.eye(2)) assert_allclose(mod['design', 2:, 18:20], 2 * np.eye(2)) assert_allclose(mod['design', 2:, 20:22], np.eye(2)) assert_allclose(np.sum(mod['design']), 20) assert_allclose(mod['obs_cov'], 0) assert_allclose(mod['state_intercept'], 0) assert_allclose(mod['transition', 2:10, :8], np.eye(8)) assert_allclose(mod['transition', 14:22, 12:20], np.eye(2 * 4)) assert_allclose(np.sum(mod['transition']), 16) assert_allclose(mod['selection', :2, :2], np.eye(2)) assert_allclose(mod['selection', 10:12, 2:4], np.eye(2)) assert_allclose(mod['selection', 12:14, 4:6], np.eye(2)) assert_allclose(np.sum(mod['selection']), 6) assert_allclose(mod['state_cov'], 0) # Test parameter entry mod.update(np.arange(mod.k_params) + 2) # -> obs_intercept assert_allclose(mod['obs_intercept'], 0) # -> design desired = np.array([ [2., 3., 0., 0., 0., 0., 0., 0., 0., 0.], [4., 5., 0., 0., 0., 0., 0., 0., 0., 0.], [6., 7., 12, 14, 18, 21, 12, 14, 6., 7.], [8., 9., 16, 18, 24, 27, 16, 18, 8., 9.]]) assert_allclose(mod['design', :, :10], desired) desired = np.array([ [1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 1., 0., 2., 0., 3., 0., 2., 0., 1., 0.], [0., 0., 0., 1., 0., 2., 0., 3., 0., 2., 0., 1.]]) assert_allclose(mod['design', :, 10:], desired) # -> obs_cov assert_allclose(mod['obs_cov'], 0) # -> state_intercept assert_allclose(mod['state_intercept'], 0) # -> transition desired = np.array([ [10, 11, 0., 0., 0., 0., 0., 0., 0., 0.], [12, 13, 0., 0., 0., 0., 0., 0., 0., 0.], [1., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 1., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 1., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 1., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 1., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 1., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 1., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 1., 0., 0.]]) assert_allclose(mod['transition', :10, :10], desired) assert_allclose(mod['transition', :10, 10:], 0) assert_allclose(mod['transition', 10:, :10], 0) desired = np.array([ [17, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 18, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 19, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 20, 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.]]) assert_allclose(mod['transition', 10:, 10:], desired) # -> selection assert_allclose(np.sum(mod['selection']), 6) # -> state_cov L = np.array([[14., 0], [15., 16.]]) desired = np.array([[0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0.], [0., 0., 21, 0., 0., 0.], [0., 0., 0., 22, 0., 0.], [0., 0., 0., 0., 23, 0.], [0., 0., 0., 0., 0., 24]]) desired[:2, :2] = np.dot(L, L.T) assert_allclose(mod['state_cov'], desired) def test_factor_order_gt1(): # Includes 2 monthly and 2 quarterly series # This case: factors=1, factor_orders=6, idiosyncratic_ar1=True # Create the datasets index_M = pd.period_range(start='2000', periods=12, freq='M') index_Q = pd.period_range(start='2000', periods=4, freq='Q') dta_M = pd.DataFrame(np.zeros((12, 2)), index=index_M, columns=['M0', 'M1']) dta_Q = pd.DataFrame(np.zeros((4, 2)), index=index_Q, columns=['Q0', 'Q1']) # Add some noise so the variables aren't constants dta_M.iloc[0] = 1. dta_Q.iloc[1] = 1. # Create the model instance mod = dynamic_factor_mq.DynamicFactorMQ( dta_M, endog_quarterly=dta_Q, factors=1, factor_orders=6, idiosyncratic_ar1=True) # Test dimensions assert_equal(mod.k_endog, 2 + 2) assert_equal(mod.k_states, 6 + 2 + 2 * 5) assert_equal(mod.ssm.k_posdef, 1 + 2 + 2) # Test names assert_equal(mod.endog_names, ['M0', 'M1', 'Q0', 'Q1']) desired = (['0', 'L1.0', 'L2.0', 'L3.0', 'L4.0', 'L5.0'] + ['eps_M.M0', 'eps_M.M1', 'eps_Q.Q0', 'eps_Q.Q1'] + ['L1.eps_Q.Q0', 'L1.eps_Q.Q1'] + ['L2.eps_Q.Q0', 'L2.eps_Q.Q1'] + ['L3.eps_Q.Q0', 'L3.eps_Q.Q1'] + ['L4.eps_Q.Q0', 'L4.eps_Q.Q1']) assert_equal(mod.state_names, desired) desired = [ 'loading.0->M0', 'loading.0->M1', 'loading.0->Q0', 'loading.0->Q1', 'L1.0->0', 'L2.0->0', 'L3.0->0', 'L4.0->0', 'L5.0->0', 'L6.0->0', 'fb(0).cov.chol[1,1]', 'L1.eps_M.M0', 'L1.eps_M.M1', 'L1.eps_Q.Q0', 'L1.eps_Q.Q1', 'sigma2.M0', 'sigma2.M1', 'sigma2.Q0', 'sigma2.Q1'] assert_equal(mod.param_names, desired) # Test fixed elements of state space representation assert_allclose(mod['obs_intercept'], 0) assert_allclose(mod['design', :2, 6:8], np.eye(2)) assert_allclose(mod['design', 2:, 8:10], np.eye(2)) assert_allclose(mod['design', 2:, 10:12], 2 * np.eye(2)) assert_allclose(mod['design', 2:, 12:14], 3 * np.eye(2)) assert_allclose(mod['design', 2:, 14:16], 2 * np.eye(2)) assert_allclose(mod['design', 2:, 16:18], np.eye(2)) assert_allclose(np.sum(mod['design']), 20) assert_allclose(mod['obs_cov'], 0) assert_allclose(mod['state_intercept'], 0) assert_allclose(mod['transition', 1:6, :5], np.eye(5)) assert_allclose(mod['transition', 10:18, 8:16], np.eye(2 * 4)) assert_allclose(np.sum(mod['transition']), 13) assert_allclose(mod['selection', 0, 0], np.eye(1)) assert_allclose(mod['selection', 6:8, 1:3], np.eye(2)) assert_allclose(mod['selection', 8:10, 3:5], np.eye(2)) assert_allclose(np.sum(mod['selection']), 5) assert_allclose(mod['state_cov'], 0) # Test parameter entry mod.update(np.arange(mod.k_params) + 2) # -> obs_intercept assert_allclose(mod['obs_intercept'], 0) # -> design desired = np.array([ [2., 0., 0., 0., 0., 0.], [3., 0., 0., 0., 0., 0.], [4., 8., 12, 8., 4., 0.], [5., 10, 15, 10, 5., 0.]]) assert_allclose(mod['design', :, :6], desired) desired = np.array([ [1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 1., 0., 2., 0., 3., 0., 2., 0., 1., 0.], [0., 0., 0., 1., 0., 2., 0., 3., 0., 2., 0., 1.]]) assert_allclose(mod['design', :, 6:], desired) # -> obs_cov assert_allclose(mod['obs_cov'], 0) # -> state_intercept assert_allclose(mod['state_intercept'], 0) # -> transition desired = np.array([ [6., 7., 8., 9., 10, 11, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0, 0], [1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0, 0], [0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0, 0], [0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0, 0], [0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0, 0], [0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0, 0], [0., 0., 0., 0., 0., 0., 13, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0, 0], [0., 0., 0., 0., 0., 0., 0., 14, 0., 0., 0., 0., 0., 0., 0., 0., 0, 0], [0., 0., 0., 0., 0., 0., 0., 0., 15, 0., 0., 0., 0., 0., 0., 0., 0, 0], [0., 0., 0., 0., 0., 0., 0., 0., 0., 16, 0., 0., 0., 0., 0., 0., 0, 0], [0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0, 0], [0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0, 0], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0, 0], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0, 0], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0, 0], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0, 0], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0, 0], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0, 0] ]) assert_allclose(mod['transition'], desired) # -> selection assert_allclose(np.sum(mod['selection']), 5) # -> state_cov desired = np.array([[144, 0., 0., 0., 0.], [0., 17., 0., 0., 0.], [0., 0., 18., 0., 0.], [0., 0., 0., 19., 0.], [0., 0., 0., 0., 20.]]) assert_allclose(mod['state_cov'], desired) def test_k_factors_gt1_factor_order_gt1(): # Includes 2 monthly and 2 quarterly series # This case: kactors=2, factor_orders=6, idiosyncratic_ar1=True # Create the datasets index_M = pd.period_range(start='2000', periods=12, freq='M') index_Q = pd.period_range(start='2000', periods=4, freq='Q') dta_M = pd.DataFrame(np.zeros((12, 2)), index=index_M, columns=['M0', 'M1']) dta_Q = pd.DataFrame(np.zeros((4, 2)), index=index_Q, columns=['Q0', 'Q1']) # Add some noise so the variables aren't constants dta_M.iloc[0] = 1. dta_Q.iloc[1] = 1. # Create the model instance mod = dynamic_factor_mq.DynamicFactorMQ( dta_M, endog_quarterly=dta_Q, factors=2, factor_orders={('0', '1'): 6}, idiosyncratic_ar1=True) # Test dimensions assert_equal(mod.k_endog, 2 + 2) assert_equal(mod.k_states, 6 * 2 + 2 + 2 * 5) assert_equal(mod.ssm.k_posdef, 2 + 2 + 2) # Test names assert_equal(mod.endog_names, ['M0', 'M1', 'Q0', 'Q1']) desired = (['0', '1', 'L1.0', 'L1.1', 'L2.0', 'L2.1', 'L3.0', 'L3.1', 'L4.0', 'L4.1', 'L5.0', 'L5.1'] + ['eps_M.M0', 'eps_M.M1', 'eps_Q.Q0', 'eps_Q.Q1'] + ['L1.eps_Q.Q0', 'L1.eps_Q.Q1'] + ['L2.eps_Q.Q0', 'L2.eps_Q.Q1'] + ['L3.eps_Q.Q0', 'L3.eps_Q.Q1'] + ['L4.eps_Q.Q0', 'L4.eps_Q.Q1']) assert_equal(mod.state_names, desired) desired = [ 'loading.0->M0', 'loading.1->M0', 'loading.0->M1', 'loading.1->M1', 'loading.0->Q0', 'loading.1->Q0', 'loading.0->Q1', 'loading.1->Q1', 'L1.0->0', 'L1.1->0', 'L2.0->0', 'L2.1->0', 'L3.0->0', 'L3.1->0', 'L4.0->0', 'L4.1->0', 'L5.0->0', 'L5.1->0', 'L6.0->0', 'L6.1->0', 'L1.0->1', 'L1.1->1', 'L2.0->1', 'L2.1->1', 'L3.0->1', 'L3.1->1', 'L4.0->1', 'L4.1->1', 'L5.0->1', 'L5.1->1', 'L6.0->1', 'L6.1->1', 'fb(0).cov.chol[1,1]', 'fb(0).cov.chol[2,1]', 'fb(0).cov.chol[2,2]', 'L1.eps_M.M0', 'L1.eps_M.M1', 'L1.eps_Q.Q0', 'L1.eps_Q.Q1', 'sigma2.M0', 'sigma2.M1', 'sigma2.Q0', 'sigma2.Q1'] assert_equal(mod.param_names, desired) # Test fixed elements of state space representation assert_allclose(mod['obs_intercept'], 0) assert_allclose(mod['design', :2, 12:14], np.eye(2)) assert_allclose(mod['design', 2:, 14:16], np.eye(2)) assert_allclose(mod['design', 2:, 16:18], 2 * np.eye(2)) assert_allclose(mod['design', 2:, 18:20], 3 * np.eye(2)) assert_allclose(mod['design', 2:, 20:22], 2 * np.eye(2)) assert_allclose(mod['design', 2:, 22:24], np.eye(2)) assert_allclose(np.sum(mod['design']), 20) assert_allclose(mod['obs_cov'], 0) assert_allclose(mod['state_intercept'], 0) assert_allclose(mod['transition', 2:12, :10], np.eye(10)) assert_allclose(mod['transition', 16:24, 14:22], np.eye(2 * 4)) assert_allclose(np.sum(mod['transition']), 18) assert_allclose(mod['selection', :2, :2], np.eye(2)) assert_allclose(mod['selection', 12:14, 2:4], np.eye(2)) assert_allclose(mod['selection', 14:16, 4:6], np.eye(2)) assert_allclose(np.sum(mod['selection']), 6) assert_allclose(mod['state_cov'], 0) # Test parameter entry mod.update(np.arange(mod.k_params) + 2) # -> obs_intercept assert_allclose(mod['obs_intercept'], 0) # -> design desired = np.array([ [2., 3., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [4., 5., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6., 7., 12, 14, 18, 21, 12, 14, 6., 7., 0., 0.], [8., 9., 16, 18, 24, 27, 16, 18, 8., 9., 0., 0.]]) assert_allclose(mod['design', :, :12], desired) desired = np.array([ [1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 1., 0., 2., 0., 3., 0., 2., 0., 1., 0.], [0., 0., 0., 1., 0., 2., 0., 3., 0., 2., 0., 1.]]) assert_allclose(mod['design', :, 12:], desired) # -> obs_cov assert_allclose(mod['obs_cov'], 0) # -> state_intercept assert_allclose(mod['state_intercept'], 0) # -> transition desired = np.array([ [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.]]) assert_allclose(mod['transition', :12, :12], desired) assert_allclose(mod['transition', :12, 12:], 0) assert_allclose(mod['transition', 12:, :12], 0) desired = np.array([ [37, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 38, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 39, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 40, 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.]]) assert_allclose(mod['transition', 12:, 12:], desired) # -> selection assert_allclose(np.sum(mod['selection']), 6) # -> state_cov L = np.array([[34., 0], [35., 36.]]) desired = np.array([[0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0.], [0., 0., 41, 0., 0., 0.], [0., 0., 0., 42, 0., 0.], [0., 0., 0., 0., 43, 0.], [0., 0., 0., 0., 0., 44]]) desired[:2, :2] = np.dot(L, L.T) assert_allclose(mod['state_cov'], desired) def test_k_factors_gt1_factor_order_gt1_no_idiosyncratic_ar1(): # Includes 2 monthly and 2 quarterly series # This case: factors=2, factor_orders=6, idiosyncratic_ar1=False # Create the datasets index_M = pd.period_range(start='2000', periods=12, freq='M') index_Q = pd.period_range(start='2000', periods=4, freq='Q') dta_M = pd.DataFrame(np.zeros((12, 2)), index=index_M, columns=['M0', 'M1']) dta_Q = pd.DataFrame(np.zeros((4, 2)), index=index_Q, columns=['Q0', 'Q1']) # Add some noise so the variables aren't constants dta_M.iloc[0] = 1. dta_Q.iloc[1] = 1. # Create the model instance mod = dynamic_factor_mq.DynamicFactorMQ( dta_M, endog_quarterly=dta_Q, factors=2, factor_orders={('0', '1'): 6}, idiosyncratic_ar1=False) # Test dimensions assert_equal(mod.k_endog, 2 + 2) assert_equal(mod.k_states, 6 * 2 + 2 * 5) assert_equal(mod.ssm.k_posdef, 2 + 2) # Test names assert_equal(mod.endog_names, ['M0', 'M1', 'Q0', 'Q1']) desired = (['0', '1', 'L1.0', 'L1.1', 'L2.0', 'L2.1', 'L3.0', 'L3.1', 'L4.0', 'L4.1', 'L5.0', 'L5.1'] + ['eps_Q.Q0', 'eps_Q.Q1'] + ['L1.eps_Q.Q0', 'L1.eps_Q.Q1'] + ['L2.eps_Q.Q0', 'L2.eps_Q.Q1'] + ['L3.eps_Q.Q0', 'L3.eps_Q.Q1'] + ['L4.eps_Q.Q0', 'L4.eps_Q.Q1']) assert_equal(mod.state_names, desired) desired = [ 'loading.0->M0', 'loading.1->M0', 'loading.0->M1', 'loading.1->M1', 'loading.0->Q0', 'loading.1->Q0', 'loading.0->Q1', 'loading.1->Q1', 'L1.0->0', 'L1.1->0', 'L2.0->0', 'L2.1->0', 'L3.0->0', 'L3.1->0', 'L4.0->0', 'L4.1->0', 'L5.0->0', 'L5.1->0', 'L6.0->0', 'L6.1->0', 'L1.0->1', 'L1.1->1', 'L2.0->1', 'L2.1->1', 'L3.0->1', 'L3.1->1', 'L4.0->1', 'L4.1->1', 'L5.0->1', 'L5.1->1', 'L6.0->1', 'L6.1->1', 'fb(0).cov.chol[1,1]', 'fb(0).cov.chol[2,1]', 'fb(0).cov.chol[2,2]', 'sigma2.M0', 'sigma2.M1', 'sigma2.Q0', 'sigma2.Q1'] assert_equal(mod.param_names, desired) # Test fixed elements of state space representation assert_allclose(mod['obs_intercept'], 0) assert_allclose(mod['design', 2:, 12:14], np.eye(2)) assert_allclose(mod['design', 2:, 14:16], 2 * np.eye(2)) assert_allclose(mod['design', 2:, 16:18], 3 * np.eye(2)) assert_allclose(mod['design', 2:, 18:20], 2 * np.eye(2)) assert_allclose(mod['design', 2:, 20:22], np.eye(2)) assert_allclose(np.sum(mod['design']), 18) assert_allclose(mod['obs_cov'], 0) assert_allclose(mod['state_intercept'], 0) assert_allclose(mod['transition', 2:12, :10], np.eye(10)) assert_allclose(mod['transition', 14:22, 12:20], np.eye(2 * 4)) assert_allclose(np.sum(mod['transition']), 18) assert_allclose(mod['selection', :2, :2], np.eye(2)) assert_allclose(mod['selection', 12:14, 2:4], np.eye(2)) assert_allclose(np.sum(mod['selection']), 4) assert_allclose(mod['state_cov'], 0) # Test parameter entry mod.update(np.arange(mod.k_params) + 2) # -> obs_intercept assert_allclose(mod['obs_intercept'], 0) # -> design desired = np.array([ [2., 3., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [4., 5., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6., 7., 12, 14, 18, 21, 12, 14, 6., 7., 0., 0.], [8., 9., 16, 18, 24, 27, 16, 18, 8., 9., 0., 0.]]) assert_allclose(mod['design', :, :12], desired) desired = np.array([ [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [1., 0., 2., 0., 3., 0., 2., 0., 1., 0.], [0., 1., 0., 2., 0., 3., 0., 2., 0., 1.]]) assert_allclose(mod['design', :, 12:], desired) # -> obs_cov assert_allclose(mod['obs_cov'], np.diag([37, 38, 0, 0])) # -> state_intercept assert_allclose(mod['state_intercept'], 0) # -> transition desired = np.array([ [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.]]) assert_allclose(mod['transition', :12, :12], desired) assert_allclose(mod['transition', :12, 12:], 0) assert_allclose(mod['transition', 12:, :12], 0) desired = np.array([ [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [1., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 1., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 1., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 1., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 1., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 1., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 1., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 1., 0., 0.]]) assert_allclose(mod['transition', 12:, 12:], desired) # -> selection assert_allclose(np.sum(mod['selection']), 4) # -> state_cov L = np.array([[34., 0], [35., 36.]]) desired = np.array([[0., 0., 0., 0.], [0., 0., 0., 0.], [0., 0., 39, 0.], [0., 0., 0., 40]]) desired[:2, :2] = np.dot(L, L.T) assert_allclose(mod['state_cov'], desired) def test_invalid_model_specification(): # Test for errors that can be raised for invalid model specifications # during __init__ dta = np.zeros((10, 2)) dta[0] = 1. dta_pd = pd.DataFrame(dta) dta_period_W = pd.DataFrame( dta, index=pd.period_range(start='2000', periods=10, freq='W')) dta_date_W = pd.DataFrame( dta, index=pd.date_range(start='2000', periods=10, freq='W')) dta_period_M = pd.DataFrame( dta, index=pd.period_range(start='2000', periods=10, freq='M')) dta_date_M = pd.DataFrame( dta, index=pd.date_range(start='2000', periods=10, freq='M')) dta_period_Q = pd.DataFrame( dta, index=pd.period_range(start='2000', periods=10, freq='Q')) # Error if k_factors == 0 msg = 'The model must contain at least one factor.' with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta, factors=0) # Error if k_factors, factor_multiplicities, or factor_orders is something # besides int or dict msg = ('`factors` argument must an integer number of factors, a list of' ' global factor names, or a dictionary, mapping observed variables' ' to factors.') with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta, factors=True) msg = '`factor_orders` argument must either be an integer or a dictionary.' with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta, factor_orders=True) msg = ('`factor_multiplicities` argument must either be an integer or a' ' dictionary.') with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta, factor_multiplicities=True) # Error if k_factors > k_endog_M msg = fr'Number of factors \({dta.shape[1] + 1}\) cannot be greater than' with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta, factors=dta.shape[1] + 1) # Error if factor assigned to more than one block factor_orders = {('a', 'b'): 1, 'b': 2} msg = ('Each factor can be assigned to at most one block of factors in' ' `factor_orders`.') with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta, factors=['a', 'b'], factor_orders=factor_orders) # Error if k_endog_monthly and endog_quarterly both specified msg = ('If `endog_quarterly` is specified, then `endog` must contain only' ' monthly variables, and so `k_endog_monthly` cannot be specified' ' since it will be inferred from the shape of `endog`.') with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta_period_M, k_endog_monthly=2, endog_quarterly=dta) # Error if invalid standardize msg = 'Invalid value passed for `standardize`.' with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta_period_M, standardize='a') # No factors for one endog msg = ('If a `factors` dictionary is provided, then it must include' ' entries for each observed variable.') with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta, factors={'y1': ['a']}) msg = ('Each observed variable must be mapped to at' ' least one factor in the `factors` dictionary.') with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ( dta, factors={'y1': ['a'], 'y2': []}) # Singular column of data + standardization msg = (r'Constant variable\(s\) found in observed variables, but constants' ' cannot be included in this model.') with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta * 0) # Non-pandas data when given both monthly and quarterly msg = 'Given monthly dataset is not a Pandas object.' with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta, endog_quarterly=dta) msg = 'Given quarterly dataset is not a Pandas object.' with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta_period_M, endog_quarterly=dta) # Pandas data without date index when given both monthly and quarterly msg = 'Given monthly dataset has an index with non-date values.' with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta_pd, endog_quarterly=dta_period_Q) msg = 'Given quarterly dataset has an index with non-date values.' # (test once with period index for monthly...) with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta_period_M, endog_quarterly=dta_pd) # (...and once with date index for monthly) with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ(dta_date_M, endog_quarterly=dta_pd) # Pandas data with date index of wrong freq msg = 'Index of given monthly dataset has a non-monthly frequency' # (test once with period index for monthly...) with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ( dta_period_W, endog_quarterly=dta_period_Q) # (...and once with date index for monthly) with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ( dta_date_W, endog_quarterly=dta_period_Q) msg = 'Index of given quarterly dataset has a non-quarterly frequency' # (test once with period index for quarterly...) with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ( dta_period_M, endog_quarterly=dta_period_W) # (and once with date index for quarterly...) with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ( dta_date_M, endog_quarterly=dta_date_W) @pytest.mark.parametrize('freq_Q', ['Q', 'Q-DEC', 'Q-JAN', 'QS', 'QS-DEC', 'QS-APR']) @pytest.mark.parametrize('freq_M', ['M', 'MS']) def test_date_indexes(reset_randomstate, freq_M, freq_Q): # Test that using either PeriodIndex or DatetimeIndex for monthly or # quarterly data, with a variety of DatetimeIndex frequencies, works # Monthly datasets nobs_M = 10 dates_M = pd.date_range(start='2000', periods=nobs_M, freq=freq_M) periods_M = pd.period_range(start='2000', periods=nobs_M, freq='M') dta_M = np.random.normal(size=(nobs_M, 2)) endog_period_M = pd.DataFrame(dta_M.copy(), index=periods_M) endog_date_M = pd.DataFrame(dta_M.copy(), index=dates_M) # Quarterly datasets nobs_Q = 3 dates_Q = pd.date_range(start='2000', periods=nobs_Q, freq=freq_Q) periods_Q = pd.period_range(start='2000', periods=nobs_Q, freq='Q') dta_Q = np.random.normal(size=(nobs_Q, 2)) endog_period_Q = pd.DataFrame(dta_Q.copy(), index=periods_Q) endog_date_Q = pd.DataFrame(dta_Q.copy(), index=dates_Q) # Baseline is monthly periods and quarterly periods mod_base = dynamic_factor_mq.DynamicFactorMQ( endog_period_M, endog_quarterly=endog_period_Q) # Test against monthly dates and quarterly dates mod = dynamic_factor_mq.DynamicFactorMQ( endog_date_M, endog_quarterly=endog_date_Q) assert_(mod._index.equals(mod_base._index)) assert_allclose(mod.endog, mod_base.endog) # Test against monthly dates and quarterly periods mod = dynamic_factor_mq.DynamicFactorMQ( endog_date_M, endog_quarterly=endog_period_Q) assert_(mod._index.equals(mod_base._index)) assert_allclose(mod.endog, mod_base.endog) # Test against monthly periods and quarterly dates mod = dynamic_factor_mq.DynamicFactorMQ( endog_period_M, endog_quarterly=endog_date_Q) assert_(mod._index.equals(mod_base._index)) assert_allclose(mod.endog, mod_base.endog) def gen_dfm_data(k_endog=2, nobs=1000): if k_endog > 10: raise ValueError('Only allows for k_endog <= 10') ix = pd.period_range(start='1950-01', periods=1, freq='M') faux = pd.DataFrame([[0] * k_endog], index=ix) mod = dynamic_factor.DynamicFactor(faux, k_factors=1, factor_order=1) loadings = [0.5, -0.9, 0.2, 0.7, -0.1, -0.1, 0.4, 0.4, 0.8, 0.8][:k_endog] phi = 0.5 sigma2 = 1.0 idio_ar1 = [0] * k_endog idio_var = [1.0, 0.2, 1.5, 0.8, 0.8, 1.4, 0.1, 0.2, 0.4, 0.5][:k_endog] params = np.r_[loadings, idio_var, phi] endog = mod.simulate(params, nobs) return endog, loadings, phi, sigma2, idio_ar1, idio_var def test_results_factors(reset_randomstate): # Tests for the `factors` attribute in the results object endog, _, _, _, _, _ = gen_dfm_data(k_endog=2, nobs=1000) mod_dfm = dynamic_factor_mq.DynamicFactorMQ( endog, factors=['global'], factor_multiplicities=2, standardize=False, idiosyncratic_ar1=False) res_dfm = mod_dfm.smooth(mod_dfm.start_params) assert_allclose(res_dfm.factors.smoothed, res_dfm.states.smoothed[['global.1', 'global.2']]) assert_allclose(res_dfm.factors.smoothed_cov.values, res_dfm.states.smoothed_cov.values, atol=1e-12) def test_coefficient_of_determination( reset_randomstate, close_figures): # Get simulated data, and add in some missing entries endog, _, _, _, _, _ = gen_dfm_data(k_endog=3, nobs=1000) endog.iloc[0, 10:20] = np.nan endog.iloc[2, 15:25] = np.nan # Setup the model and get the results factors = { 0: ['global', 'block'], 1: ['global', 'block'], 2: ['global'] } mod = dynamic_factor_mq.DynamicFactorMQ( endog, factors=factors, standardize=False, idiosyncratic_ar1=False) res = mod.smooth(mod.start_params) # For most of the tests, we'll use smoothed estimates, which are the # default factors = res.factors.smoothed # Test for method='individual' actual = res.get_coefficients_of_determination(method='individual') desired = pd.DataFrame(np.zeros((3, 2)), index=[0, 1, 2], columns=['global', 'block']) for i in range(3): for j in range(2): if i == 2 and j == 1: desired.iloc[i, j] = np.nan else: y = endog.iloc[:, i] X = add_constant(factors.iloc[:, j]) mod_ols = OLS(y, X, missing='drop') res_ols = mod_ols.fit() desired.iloc[i, j] = res_ols.rsquared assert_(actual.index.equals(desired.index)) assert_(actual.columns.equals(desired.columns)) assert_allclose(actual, desired) # Test for method='joint' actual = res.get_coefficients_of_determination(method='joint') desired = pd.Series(np.zeros(3), index=[0, 1, 2]) for i in range(3): y = endog.iloc[:, i] if i == 2: X = add_constant(factors.iloc[:, 0]) else: X = add_constant(factors) mod_ols = OLS(y, X, missing='drop') res_ols = mod_ols.fit() desired.iloc[i] = res_ols.rsquared assert_(actual.index.equals(desired.index)) assert_allclose(actual, desired) # Test for method='cumulative' actual = res.get_coefficients_of_determination(method='cumulative') desired = pd.DataFrame(np.zeros((3, 2)), index=[0, 1, 2], columns=['global', 'block']) for i in range(3): for j in range(2): if i == 2 and j == 1: desired.iloc[i, j] = np.nan else: y = endog.iloc[:, i] X = add_constant(factors.iloc[:, :j + 1]) mod_ols = OLS(y, X, missing='drop') res_ols = mod_ols.fit() desired.iloc[i, j] = res_ols.rsquared assert_(actual.index.equals(desired.index)) assert_(actual.columns.equals(desired.columns)) assert_allclose(actual, desired) # Test for method='individual', which='filtered' factors = res.factors.filtered actual = res.get_coefficients_of_determination( method='individual', which='filtered') desired = pd.DataFrame(np.zeros((3, 2)), index=[0, 1, 2], columns=['global', 'block']) for i in range(3): for j in range(2): if i == 2 and j == 1: desired.iloc[i, j] = np.nan else: y = endog.iloc[:, i] X = add_constant(factors.iloc[:, j]) mod_ols = OLS(y, X, missing='drop') res_ols = mod_ols.fit() desired.iloc[i, j] = res_ols.rsquared assert_allclose(actual, desired) # Optional smoke test for plot_coefficient_of_determination try: import matplotlib.pyplot as plt try: from pandas.plotting import register_matplotlib_converters register_matplotlib_converters() except ImportError: pass fig1 = plt.figure() res.plot_coefficients_of_determination(method='individual', fig=fig1) fig2 = plt.figure() res.plot_coefficients_of_determination(method='joint', fig=fig2) fig3 = plt.figure() res.plot_coefficients_of_determination(method='cumulative', fig=fig3) fig4 = plt.figure() res.plot_coefficients_of_determination(which='filtered', fig=fig4) except ImportError: pass @pytest.mark.filterwarnings("ignore:Log-likelihood decreased") def test_quasi_newton_fitting(reset_randomstate): # Test that the typical state space quasi-Newton fitting mechanisms work # here too, even if they aren't used much # Note: to match the quasi-Newton results, which use the stationary # initialization, we need to set em_initialization=False # Note: one thing that this test reveals is that there are some numerical # issues with the EM algorithm when em_initialization=False around the # true optimum, where apparently numerical issues case the EM algorithm to # decrease the log-likelihood. In particular, testing updating each block # of parameters shows that it is the updating of the factor autoregressive # coefficients and (it appears) the factor error variance term that are # to blame here. endog, _, _, _, _, _ = gen_dfm_data(k_endog=2, nobs=1000) # Create the test Dynamic Factor MQ models mod_dfm = dynamic_factor_mq.DynamicFactorMQ(endog, factor_orders=1, standardize=False, idiosyncratic_ar1=False) mod_dfm_ar1 = dynamic_factor_mq.DynamicFactorMQ(endog, factor_orders=1, standardize=False, idiosyncratic_ar1=True) # Check that transform and untransform works x = mod_dfm_ar1.start_params y = mod_dfm_ar1.untransform_params(x) z = mod_dfm_ar1.transform_params(y) assert_allclose(x, z) # Check lbfgs and em converge to the same thing: idiosyncratic_ar1=False res_lbfgs = mod_dfm.fit(method='lbfgs') params_lbfgs = res_lbfgs.params.copy() start_params = params_lbfgs.copy() start_params['L1.0->0'] += 1e-2 start_params['fb(0).cov.chol[1,1]'] += 1e-2 res_em = mod_dfm.fit(start_params, em_initialization=False) params_em = res_em.params.copy() assert_allclose(res_lbfgs.llf, res_em.llf, atol=5e-2, rtol=1e-5) assert_allclose(params_lbfgs, params_em, atol=5e-2, rtol=1e-5) # Check lbfgs and em converge to the same thing: idiosyncratic_ar1=True res_lbfgs = mod_dfm_ar1.fit(method='lbfgs') params_lbfgs = res_lbfgs.params.copy() start_params = params_lbfgs.copy() start_params['L1.0->0'] += 1e-2 start_params['fb(0).cov.chol[1,1]'] += 1e-2 res_em = mod_dfm_ar1.fit(params_lbfgs, em_initialization=False) params_em = res_em.params.copy() assert_allclose(res_lbfgs.llf, res_em.llf, atol=5e-2, rtol=1e-5) assert_allclose(params_lbfgs, params_em, atol=5e-2, rtol=1e-5) def test_summary(reset_randomstate): # Smoke tests for summaries endog, _, _, _, _, _ = gen_dfm_data(k_endog=10, nobs=100) # Create the test Dynamic Factor MQ models mod_dfm = dynamic_factor_mq.DynamicFactorMQ(endog, factor_orders=1, standardize=False, idiosyncratic_ar1=False) res_dfm = mod_dfm.smooth(mod_dfm.start_params) mod_dfm_ar1 = dynamic_factor_mq.DynamicFactorMQ(endog, factor_orders=1, standardize=False, idiosyncratic_ar1=True) res_dfm_ar1 = mod_dfm_ar1.smooth(mod_dfm_ar1.start_params) mod_dfm.summary() assert_equal(str(mod_dfm), str(mod_dfm.summary())) res_dfm.summary() mod_dfm_ar1.summary() res_dfm_ar1.summary() def test_append_extend_apply(reset_randomstate): # Most of `append`, `extend`, and `apply` are tested in # `test_standardized_{monthly,MQ}`, but here we test a couple of minor # things endog, loadings, phi, sigma2, _, idio_var = ( gen_dfm_data(k_endog=10, nobs=100)) endog1 = endog.iloc[:-10] endog2 = endog.iloc[-10:] mod = dynamic_factor_mq.DynamicFactorMQ(endog1, factor_orders=1, standardize=False, idiosyncratic_ar1=False) params = np.r_[loadings, phi, sigma2, idio_var] res = mod.smooth(params) # Test that error is raised if we try to extend the sample with a dataset # of a different dimension msg = 'Cannot append data of a different dimension to a model.' with pytest.raises(ValueError, match=msg): res.append(endog2.iloc[:, :3]) with pytest.raises(ValueError, match=msg): res.extend(endog2.iloc[:, :3]) # Test that copy_initialization works mod.initialize_known([0.1], [[1.0]]) res2 = mod.smooth(params) # These asserts just show that the initialization really is different assert_allclose(res.filter_results.initial_state, 0) assert_allclose(res.filter_results.initial_state_cov, 4 / 3.) assert_allclose(res2.filter_results.initial_state, 0.1) assert_allclose(res2.filter_results.initial_state_cov, 1.0) # Check append res3 = res2.append(endog2, copy_initialization=False) assert_allclose(res3.filter_results.initial_state, 0) assert_allclose(res3.filter_results.initial_state_cov, 4 / 3.) res4 = res2.append(endog2, copy_initialization=True) assert_allclose(res4.filter_results.initial_state, 0.1) assert_allclose(res4.filter_results.initial_state_cov, 1.0) # Check apply res5 = res2.apply(endog, copy_initialization=False) assert_allclose(res5.filter_results.initial_state, 0) assert_allclose(res5.filter_results.initial_state_cov, 4 / 3.) res6 = res2.apply(endog, copy_initialization=True) assert_allclose(res6.filter_results.initial_state, 0.1) assert_allclose(res6.filter_results.initial_state_cov, 1.0) def test_news_monthly(reset_randomstate): # Most of `news` is tested in `test_standardized_{monthly,MQ}`, but here # we test a couple of minor things endog, _, _, _, _, _ = gen_dfm_data(k_endog=10, nobs=100) endog_pre = endog.iloc[:-1].copy() endog_pre.iloc[-1, 0] *= 1.2 endog_pre.iloc[-1, 1] = np.nan # Base model mod = dynamic_factor_mq.DynamicFactorMQ(endog_pre, factor_orders=1, standardize=False, idiosyncratic_ar1=False) params = mod.start_params res = mod.smooth(params) # Updated results and desired news output (created using a results object) mod2 = mod.clone(endog) res2 = mod2.smooth(params) desired = res2.news(res, start=endog.index[-1], periods=1, comparison_type='previous') # Actual news output, created using the updated dataset actual = res.news(endog, start=endog.index[-1], periods=1, comparison_type='updated') attributes = [ 'total_impacts', 'update_impacts', 'revision_impacts', 'news', 'weights', 'update_forecasts', 'update_realized', 'prev_impacted_forecasts', 'post_impacted_forecasts', 'revisions_iloc', 'revisions_ix', 'updates_iloc', 'updates_ix'] for attr in attributes: w = getattr(actual, attr) x = getattr(desired, attr) if isinstance(x, pd.Series): assert_series_equal(w, x) else: assert_frame_equal(w, x) def test_news_MQ(reset_randomstate): # Most of `news` is tested in `test_standardized_{monthly,MQ}`, but here # we test a couple of minor things endog_M, endog_Q, f1 = test_dynamic_factor_mq_monte_carlo.gen_k_factor1( 100, k=2, idiosyncratic_ar1=False) endog_M_pre = endog_M.iloc[:-1].copy() endog_M_pre.iloc[-1, 0] *= 1.2 endog_M_pre.iloc[-1, 1] = np.nan endog_Q_pre = endog_Q.iloc[:-1].copy() endog_Q_pre.iloc[-1, 0] *= 1.2 endog_Q_pre.iloc[-1, 1] = np.nan # Base model mod = dynamic_factor_mq.DynamicFactorMQ( endog_M_pre, endog_quarterly=endog_Q_pre, factor_orders=1, standardize=False, idiosyncratic_ar1=False) params = mod.start_params res = mod.smooth(params) # Updated results and desired news output (created using a results object) mod2 = mod.clone(endog_M, endog_quarterly=endog_Q) res2 = mod2.smooth(params) desired = res2.news(res, start=endog_M.index[-1], periods=1, comparison_type='previous') # Actual news output, created using the updated dataset actual = res.news(endog_M, endog_quarterly=endog_Q, start=endog_M.index[-1], periods=1, comparison_type='updated') attributes = [ 'total_impacts', 'update_impacts', 'revision_impacts', 'news', 'weights', 'update_forecasts', 'update_realized', 'prev_impacted_forecasts', 'post_impacted_forecasts', 'revisions_iloc', 'revisions_ix', 'updates_iloc', 'updates_ix'] for attr in attributes: w = getattr(actual, attr) x = getattr(desired, attr) if isinstance(x, pd.Series): assert_series_equal(w, x) else: assert_frame_equal(w, x) def test_ar6_no_quarterly(reset_randomstate): # Test to make sure that an example with > 5 lags (which are the number of # lags that are always included in models with quarterly data) works, # for the case without quarterly data # Generate test data ix = pd.period_range(start='1950-01', periods=1, freq='M') faux = pd.Series([0], index=ix) mod = sarimax.SARIMAX(faux, order=(6, 0, 0)) params = np.r_[0., 0., 0., 0., 0., 0.5, 1.0] endog = mod.simulate(params, 100) # Create the baseline SARIMAX and the test Dynamic Factor MQ model mod_ar = sarimax.SARIMAX(endog, order=(6, 0, 0)) mod_dfm = dynamic_factor_mq.DynamicFactorMQ(endog, factor_orders=6, standardize=False, idiosyncratic_ar1=False) # Test that SARIMAX and DFM MQ produce the same loglike llf_ar = mod_ar.loglike(params) llf_dfm = mod_dfm.loglike(np.r_[1, params, 0.]) assert_allclose(llf_dfm, llf_ar) # Monte Carlo-type test, skipped by default if False: # Test for MLE fitting: this is a Monte Carlo test, which requires a # large sample size; e.g., use nobs=10000 for atol=1e-2 res_dfm = mod_dfm.fit() actual = res_dfm.params # normalize loading = 1, which requires us to multiply std. dev. of # factor (which is `actual[-2]`) by the estimated loading (`actual[0]`) actual[-2] *= actual[0] actual[0] = 1 assert_allclose(res_dfm.params[1:-1], params, atol=1e-2) def test_idiosyncratic_ar1_False(reset_randomstate): # Test the case with idiosyncratic_ar1=False (which is not tested in # the test_dynamic_factor_mq_frbny_nowcast) by comparison to a model with # idiosyncratic_ar1=True but no actual serial correlation in the # idiosyncratic component endog, loadings, phi, sigma2, idio_ar1, idio_var = gen_dfm_data( k_endog=10, nobs=1000) # Create the baseline SARIMAX and the test Dynamic Factor MQ model mod_base = dynamic_factor.DynamicFactor(endog, k_factors=1, factor_order=1) mod_dfm = dynamic_factor_mq.DynamicFactorMQ(endog, factor_orders=1, standardize=False, idiosyncratic_ar1=False) mod_dfm_ar1 = dynamic_factor_mq.DynamicFactorMQ(endog, factor_orders=1, standardize=False, idiosyncratic_ar1=True) params = np.r_[loadings, idio_var, phi] params_dfm = np.r_[loadings, phi, sigma2, idio_var] params_dfm_ar1 = np.r_[loadings, phi, sigma2, idio_ar1, idio_var] # Test that these models all produce the same loglikelihood llf_base = mod_base.loglike(params) llf_dfm = mod_dfm.loglike(params_dfm) llf_dfm_ar1 = mod_dfm_ar1.loglike(params_dfm_ar1) assert_allclose(llf_dfm_ar1, llf_dfm) assert_allclose(llf_dfm, llf_base) assert_allclose(llf_dfm_ar1, llf_base) # Test that these methods produce the same smoothed estimates of the # idiosyncratic disturbance res0_dfm = mod_dfm.smooth(params_dfm) res0_dfm_ar1 = mod_dfm_ar1.smooth(params_dfm_ar1) assert_allclose(res0_dfm.smoothed_measurement_disturbance, res0_dfm_ar1.smoothed_state[1:]) assert_allclose(res0_dfm.smoothed_measurement_disturbance_cov, res0_dfm_ar1.smoothed_state_cov[1:, 1:, :]) # Note: it is difficult to test the EM algorithm for the idiosyncratic # variance terms, because actually the EM algorithm is slightly different # depending on whether idiosyncratic_ar1 is True or False. # - If idiosyncratic_ar1=False, then the variance term is computed # conditional on the *updated estimate for the design matrix*, but the # smoothed moments that were generated conditional on the *previous* # estimate for the design matrix. # - If idiosyntratic_ar1=True, then the variance term is computed # conditional on the *previous estimate for the design matrix* (this is # because the estimated disturbance is part of the state vector, the # estimates of which are not modified to account for the updated design # matrix within this iteration) # # So instead, we'll just use a Monte Carlo-type test # Monte Carlo-type test, skipped by default if False: # Test for MLE fitting: this is a Monte Carlo test, which requires a # quite large sample size; e.g., use nobs=50000 for atol=1e-1 res_dfm = mod_dfm.fit() actual_dfm = res_dfm.params.copy() # normalize loadings and factor std dev. scalar = actual_dfm[0] / params_dfm[0] actual_dfm[11] *= scalar actual_dfm[:10] /= scalar assert_allclose(actual_dfm, params_dfm, atol=1e-1) res_dfm_ar1 = mod_dfm_ar1.fit() actual_dfm_ar1 = res_dfm_ar1.params.copy() # normalize loadings and factor std dev. scalar = actual_dfm_ar1[0] / params_dfm[0] actual_dfm_ar1[11] *= scalar actual_dfm_ar1[:10] /= scalar assert_allclose(actual_dfm_ar1, params_dfm_ar1, atol=1e-1) # Check the methods against each other desired = np.r_[actual_dfm_ar1[:12], actual_dfm_ar1[-10:]] assert_allclose(actual_dfm, desired, atol=1e-1) def test_invalid_standardize_1d(): endog = np.zeros(100) + 10 endog_pd = pd.Series(endog, name='y1') # Wrong shape options = [([], 10), (10, []), ([], []), ([1, 2], [1.]), ([1], [1, 2.])] msg = 'Invalid value passed for `standardize`: each element must be shaped' for standardize in options: with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ( endog, factors=1, factor_orders=1, idiosyncratic_ar1=False, standardize=standardize) # Wrong index: ndarray options = [ (pd.Series(10), pd.Series(10)), (pd.Series(10, index=['y']), pd.Series(10, index=['y1'])), (pd.Series(10, index=['y1']), pd.Series(10, index=['y1'])), (pd.Series([10], index=['y']), pd.Series([10, 1], index=['y1', 'y2']))] msg = ('Invalid value passed for `standardize`: if a Pandas Series, must' ' have index') for standardize in options: with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ( endog, factors=1, factor_orders=1, idiosyncratic_ar1=False, standardize=standardize) # Wrong index: pd.Series options = [ (pd.Series(10), pd.Series(10)), (pd.Series(10, index=['y']), pd.Series(10, index=['y1'])), (pd.Series(10, index=['y']), pd.Series(10, index=['y'])), (pd.Series([10], index=['y']), pd.Series([10, 1], index=['y1', 'y2']))] msg = ('Invalid value passed for `standardize`: if a Pandas Series, must' ' have index') for standardize in options: with pytest.raises(ValueError, match=msg): dynamic_factor_mq.DynamicFactorMQ( endog_pd, factors=1, factor_orders=1, idiosyncratic_ar1=False, standardize=standardize) @pytest.mark.parametrize('use_pandas', [True, False]) @pytest.mark.parametrize('standardize', [ (10, 10), ([10], [10]), (np.array(10), np.array(10)), (pd.Series([10], index=['y']), pd.Series([10], index=['y']))]) def test_simulate_standardized_1d(standardize, use_pandas): endog = np.zeros(100) + 10 if use_pandas: endog = pd.Series(endog, name='y') # Create the model, get the results mod = dynamic_factor_mq.DynamicFactorMQ( endog, factors=1, factor_orders=1, idiosyncratic_ar1=False, standardize=standardize) lambda1 = 2.0 phi = 0.5 params = [lambda1, phi, 0.0, 0] res = mod.smooth(params) # Desired value from the simulation mean = np.atleast_1d(standardize[0])[0] std = np.atleast_1d(standardize[1])[0] desired = phi**np.arange(10) * lambda1 * std + mean desired_nd = desired[:, None] if use_pandas else desired[:, None, None] # Test without repetitition actual = res.simulate(10, initial_state=[1.]) assert_equal(actual.shape, (10,)) assert_allclose(actual, desired) # Test with 1 repetitition actual = res.simulate(10, initial_state=[1.], repetitions=1) desired_shape = (10, 1) if use_pandas else (10, 1, 1) assert_equal(actual.shape, desired_shape) assert_allclose(actual, desired_nd) # Test with 2 repetititions actual = res.simulate(10, initial_state=[1.], repetitions=2) desired_shape = (10, 2) if use_pandas else (10, 1, 2) assert_equal(actual.shape, desired_shape) assert_allclose(actual, np.repeat(desired_nd, 2, axis=-1)) @pytest.mark.parametrize('use_pandas', [True, False]) @pytest.mark.parametrize('standardize', [ ([10, -4], [10., 10.]), (np.array([10, -4]), np.array([10, 10])), (pd.Series([10, -4], index=['y1', 'y2']), pd.Series([10, 10], index=['y1', 'y2']))]) def test_simulate_standardized_2d(standardize, use_pandas): endog = np.zeros((100, 2)) + [10, -4] if use_pandas: endog = pd.DataFrame(endog, columns=['y1', 'y2']) mod = dynamic_factor_mq.DynamicFactorMQ( endog, factors=1, factor_orders=1, idiosyncratic_ar1=False, standardize=standardize) lambda1 = 2.0 lambda2 = 0.5 phi = 0.5 params = [lambda1, lambda2, phi, 0.0, 0, 0.] res = mod.smooth(params) # Desired value from the simulation means = np.atleast_1d(standardize[0]) stds = np.atleast_1d(standardize[1]) desired = np.c_[phi**np.arange(10) * lambda1 * stds[0] + means[0], phi**np.arange(10) * lambda2 * stds[1] + means[1]] desired_nd = desired if use_pandas else desired[..., None] # Test without repetitition actual = res.simulate(10, initial_state=[1.]) assert_equal(actual.shape, (10, 2)) assert_allclose(actual, desired) # Test with 1 repetitition actual = res.simulate(10, initial_state=[1.], repetitions=1) desired_shape = (10, 2) if use_pandas else (10, 2, 1) assert_equal(actual.shape, desired_shape) assert_allclose(actual, desired_nd) # Test with 2 repetititions actual = res.simulate(10, initial_state=[1.], repetitions=2) desired_shape = (10, 4) if use_pandas else (10, 2, 2) assert_equal(actual.shape, desired_shape) assert_allclose(actual, np.repeat(desired_nd, 2, axis=-1)) def check_standardized_results(res1, res2, check_diagnostics=True): # res1 must be the standardized results, while res2 must be the # the "manual standardization" results. mod1 = res1.model mod2 = res2.model # - Test attributes ------------------------------------------------------ # The difference in the standard deviation (from standardization) results # in a difference in loglikelihood computation through the determinant # term. If we add that term in to the model that has been standardized, we # get back the loglikelihood from the model with "manual" standardization tmp = ((1 - res1.filter_results.missing.T) * np.array(mod1._endog_std)[None, :]**2) mask = res1.filter_results.missing.T.astype(bool) tmp[mask] = 1.0 llf_obs_diff = -0.5 * np.log(tmp).sum(axis=1) assert_allclose(res1.llf_obs + llf_obs_diff, res2.llf_obs) assert_allclose(res1.mae, res2.mae) assert_allclose(res1.mse, res2.mse) assert_allclose(res1.sse, res2.sse) # The reverse transformation has not been applied to the fittedvalues and # resid attributes std = np.array(mod1._endog_std) mean = np.array(mod1._endog_mean) if mod1.k_endog > 1: std = std[None, :] mean = mean[None, :] if mod1.k_endog == 1: assert_allclose(res1.fittedvalues.shape, (mod1.nobs,)) else: assert_allclose(res1.fittedvalues.shape, (mod1.nobs, mod1.k_endog)) actual = np.array(res1.fittedvalues) * std + mean assert_allclose(actual, res2.fittedvalues) actual = np.array(res1.resid) * std assert_allclose(actual, res2.resid) # - Test diagnostics ----------------------------------------------------- if check_diagnostics: actual = res1.test_normality(method='jarquebera') desired = res2.test_normality(method='jarquebera') assert_allclose(actual, desired) actual = res1.test_heteroskedasticity(method='breakvar') desired = res2.test_heteroskedasticity(method='breakvar') assert_allclose(actual, desired) lags = min(10, res1.nobs_effective // 5) actual = res1.test_serial_correlation(method='ljungbox', lags=lags) desired = res2.test_serial_correlation(method='ljungbox', lags=lags) assert_allclose(actual, desired) # - Test prediction/forecasting ------------------------------------------ # Baseline model start = res1.nobs // 10 dynamic = res1.nobs // 10 end = res1.nobs + 10 predict_actual = res1.predict() forecast_actual = res1.forecast(10) predict_dynamic_forecast_actual = res1.predict( start=start, end=end, dynamic=dynamic) get_predict_actual = res1.get_prediction() get_forecast_actual = res1.get_forecast(10) get_predict_dynamic_forecast_actual = res1.get_prediction( start=start, end=end, dynamic=dynamic) # "Manual" standardization predict_desired = res2.predict() forecast_desired = res2.forecast(10) predict_dynamic_forecast_desired = res2.predict( start=start, end=end, dynamic=dynamic) get_predict_desired = res2.get_prediction() get_forecast_desired = res2.get_forecast(10) get_predict_dynamic_forecast_desired = res2.get_prediction( start=start, end=end, dynamic=dynamic) assert_allclose(predict_actual, predict_desired) assert_allclose(forecast_actual, forecast_desired) assert_allclose(predict_dynamic_forecast_actual, predict_dynamic_forecast_desired) for i in range(mod1.k_endog): assert_allclose(get_predict_actual.summary_frame(endog=i), get_predict_desired.summary_frame(endog=i)) assert_allclose(get_forecast_actual.summary_frame(endog=i), get_forecast_desired.summary_frame(endog=i)) assert_allclose( get_predict_dynamic_forecast_actual.summary_frame(endog=i), get_predict_dynamic_forecast_desired.summary_frame(endog=i)) # - Test simulation ------------------------------------------------------ # Generate shocks np.random.seed(1234) nsimulations = 100 initial_state = np.random.multivariate_normal( res1.filter_results.initial_state, res1.filter_results.initial_state_cov) raw_measurement_shocks = np.random.multivariate_normal( np.zeros(mod1.k_endog), np.eye(mod1.k_endog), size=nsimulations) state_shocks = np.random.multivariate_normal( np.zeros(mod1.ssm.k_posdef), mod1['state_cov'], size=nsimulations) L1 = np.diag(mod1['obs_cov'].diagonal()**0.5) measurement_shocks1 = (L1 @ raw_measurement_shocks.T).T L2 = np.diag(mod2['obs_cov'].diagonal()**0.5) measurement_shocks2 = (L2 @ raw_measurement_shocks.T).T # Default simulation sim_actual = res1.simulate( nsimulations=nsimulations, initial_state=initial_state, measurement_shocks=measurement_shocks1, state_shocks=state_shocks) sim_desired = res2.simulate( nsimulations=nsimulations, initial_state=initial_state, measurement_shocks=measurement_shocks2, state_shocks=state_shocks) assert_allclose(sim_actual, sim_desired) # Anchored simulation sim_actual = res1.simulate( nsimulations=nsimulations, initial_state=initial_state, measurement_shocks=measurement_shocks1, state_shocks=state_shocks, anchor='end') sim_desired = res2.simulate( nsimulations=nsimulations, initial_state=initial_state, measurement_shocks=measurement_shocks2, state_shocks=state_shocks, anchor='end') assert_allclose(sim_actual, sim_desired) # - Test impulse responses ----------------------------------------------- irfs_actual = res1.impulse_responses(10) irfs_desired = res2.impulse_responses(10) assert_allclose(irfs_actual, irfs_desired) irfs_actual = res1.impulse_responses(10, orthogonalized=True) irfs_desired = res2.impulse_responses(10, orthogonalized=True) assert_allclose(irfs_actual, irfs_desired) irfs_actual = res1.impulse_responses(10, cumulative=True) irfs_desired = res2.impulse_responses(10, cumulative=True) assert_allclose(irfs_actual, irfs_desired) irfs_actual = res1.impulse_responses( 10, orthogonalized=True, cumulative=True) irfs_desired = res2.impulse_responses( 10, orthogonalized=True, cumulative=True) assert_allclose(irfs_actual, irfs_desired) irfs_actual = res1.impulse_responses( 10, orthogonalized=True, cumulative=True, anchor='end') irfs_desired = res2.impulse_responses( 10, orthogonalized=True, cumulative=True, anchor='end') assert_allclose(irfs_actual, irfs_desired) def check_identical_models(mod1, mod2, check_nobs=True): # Dimensions if check_nobs: assert_equal(mod2.nobs, mod1.nobs) assert_equal(mod2.k_endog, mod1.k_endog) assert_equal(mod2.k_endog_M, mod1.k_endog_M) assert_equal(mod2.k_endog_Q, mod1.k_endog_Q) assert_equal(mod2.k_states, mod1.k_states) assert_equal(mod2.ssm.k_posdef, mod1.ssm.k_posdef) # Standardization assert_allclose(mod2._endog_mean, mod1._endog_mean) assert_allclose(mod2._endog_std, mod1._endog_std) assert_allclose(mod2.standardize, mod1.standardize) # Parameterization assert_equal(mod2.factors, mod1.factors) assert_equal(mod2.factor_orders, mod1.factor_orders) assert_equal(mod2.factor_multiplicities, mod1.factor_multiplicities) assert_equal(mod2.idiosyncratic_ar1, mod1.idiosyncratic_ar1) assert_equal(mod2.init_t0, mod1.init_t0) assert_equal(mod2.obs_cov_diag, mod1.obs_cov_diag) # Other attributes assert_allclose(mod2.endog_factor_map, mod1.endog_factor_map) assert_allclose(mod2.factor_block_orders, mod1.factor_block_orders) assert_equal(mod2.endog_names, mod1.endog_names) assert_equal(mod2.factor_names, mod1.factor_names) assert_equal(mod2.k_factors, mod1.k_factors) assert_equal(mod2.k_factor_blocks, mod1.k_factor_blocks) assert_equal(mod2.max_factor_order, mod1.max_factor_order) def check_append(res1, res2, endog_M2, endog_Q2): # res1 is the usual results object # res2 is an "manually standardized" results object # endog_M2 is the monthly data to append # endog_Q2 is the quarterly data to append # Test for appending to the usual results object res1_append = res1.append(endog_M2, endog_quarterly=endog_Q2) mod1_append = res1_append.model mod1 = res1.model # Check that the models are the same check_identical_models(mod1, mod1_append, check_nobs=False) assert_equal(mod1_append.nobs, mod1.nobs + len(endog_M2)) assert_allclose(mod1_append.endog[:mod1.nobs], mod1.endog) # Check that the results are the same prior to the appended data assert_allclose(res1_append.filter_results.initial_state_cov, res1.filter_results.initial_state_cov) assert_allclose(res1_append.llf_obs[:mod1.nobs], res1.llf_obs) assert_allclose(res1_append.filter_results.forecasts[:, :mod1.nobs], res1.filter_results.forecasts) assert_allclose(res1_append.filter_results.forecasts_error[:, :mod1.nobs], res1.filter_results.forecasts_error) assert_allclose(res1_append.filter_results.initial_state, res1.filter_results.initial_state) assert_allclose(res1_append.filter_results.initial_state_cov, res1.filter_results.initial_state_cov) assert_allclose(res1_append.filter_results.filtered_state[:, :mod1.nobs], res1.filter_results.filtered_state) assert_allclose( res1_append.filter_results.filtered_state_cov[..., :mod1.nobs], res1.filter_results.filtered_state_cov) # Test that "manual standardization" continues to work with append res2_append = res2.append(endog_M2, endog_quarterly=endog_Q2) mod2_append = res2_append.model mod2 = res2.model # Because our mod2 has manual changes, we need to copy those over and # re-create the appended results object mod2_append.update(res2_append.params) mod2_append['obs_intercept'] = mod2['obs_intercept'] mod2_append['design'] = mod2['design'] mod2_append['obs_cov'] = mod2['obs_cov'] mod2_append.update = lambda params, **kwargs: params res2_append = mod2_append.smooth(res2_append.params) # Check output check_identical_models(mod2, mod2_append, check_nobs=False) # Check that the results are the same prior to the appended data assert_allclose(res2_append.filter_results.initial_state_cov, res2.filter_results.initial_state_cov) assert_allclose(res2_append.llf_obs[:mod2.nobs], res2.llf_obs) assert_allclose(res2_append.filter_results.forecasts[:, :mod2.nobs], res2.filter_results.forecasts) assert_allclose(res2_append.filter_results.forecasts_error[:, :mod2.nobs], res2.filter_results.forecasts_error) assert_allclose(res2_append.filter_results.initial_state, res2.filter_results.initial_state) assert_allclose(res2_append.filter_results.initial_state_cov, res2.filter_results.initial_state_cov) assert_allclose(res2_append.filter_results.filtered_state[:, :mod2.nobs], res2.filter_results.filtered_state) assert_allclose( res2_append.filter_results.filtered_state_cov[..., :mod2.nobs], res2.filter_results.filtered_state_cov) # Check res1_append vs res2_append check_standardized_results(res1_append, res2_append) def check_extend(res1, res2, endog_M2, endog_Q2): # res1 is the usual results object # endog_M2 is the monthly data to append # endog_Q2 is the, optional, quarterly data to append # res2 is an optional "manually standardized" results object # Test for extending to the usual results object res1_extend = res1.extend(endog_M2, endog_quarterly=endog_Q2) mod1_extend = res1_extend.model mod1 = res1.model # Check that the models are the same check_identical_models(mod1, mod1_extend, check_nobs=False) assert_equal(mod1_extend.nobs, len(endog_M2)) # Test that "manual standardization" continues to work with extend res2_extend = res2.extend(endog_M2, endog_quarterly=endog_Q2) mod2_extend = res2_extend.model mod2 = res2.model # Because our mod2 has manual changes, we need to copy those over and # re-create the extended results object mod2_extend.update(res2_extend.params) mod2_extend['obs_intercept'] = mod2['obs_intercept'] mod2_extend['design'] = mod2['design'] mod2_extend['obs_cov'] = mod2['obs_cov'] mod2_extend.update = lambda params, **kwargs: params res2_extend = mod2_extend.smooth(res2_extend.params) # Check that the models are the same check_identical_models(mod2, mod2_extend, check_nobs=False) # Check res1_extend vs res2_extend check_standardized_results(res1_extend, res2_extend, check_diagnostics=False) def check_apply(res1, res2, endog_M, endog_Q): # res1 is the usual results object # endog_M2 is the monthly data to append # endog_Q2 is the, optional, quarterly data to append # res2 is an optional "manually standardized" results object # Test for applying to the usual results object res1_apply = res1.apply(endog_M, endog_quarterly=endog_Q) mod1_apply = res1_apply.model mod1 = res1.model # Check that the models are the same check_identical_models(mod1, mod1_apply, check_nobs=False) assert_equal(mod1_apply.nobs, len(endog_M)) # Test that "manual standardization" continues to work with apply res2_apply = res2.apply(endog_M, endog_quarterly=endog_Q) mod2_apply = res2_apply.model mod2 = res2.model # Because our mod2 has manual changes, we need to copy those over and # re-create the applyed results object mod2_apply.update(res2_apply.params) mod2_apply['obs_intercept'] = mod2['obs_intercept'] mod2_apply['design'] = mod2['design'] mod2_apply['obs_cov'] = mod2['obs_cov'] mod2_apply.update = lambda params, **kwargs: params res2_apply = mod2_apply.smooth(res2_apply.params) # Check that the models are the same check_identical_models(mod2, mod2_apply, check_nobs=False) # Check res1_apply vs res2_apply check_standardized_results(res1_apply, res2_apply, check_diagnostics=False) @pytest.mark.parametrize('use_pandas', [True, False]) @pytest.mark.parametrize('k_endog', [1, 2]) @pytest.mark.parametrize('idiosyncratic_ar1', [True, False]) def test_standardized_monthly(reset_randomstate, idiosyncratic_ar1, k_endog, use_pandas): nobs = 100 k2 = 2 _, _, f2 = test_dynamic_factor_mq_monte_carlo.gen_k_factor2( nobs, k=k2, idiosyncratic_ar1=idiosyncratic_ar1) if k_endog == 1: endog = f2.iloc[:, 0] endog_mean = pd.Series([10], index=['f1']) endog_std = pd.Series([1], index=['f1']) else: endog = f2 endog_mean = pd.Series([10, -4], index=['f1', 'f2']) endog_std = pd.Series([1, 1], index=['f1', 'f2']) if not use_pandas: endog = endog.values endog_mean = endog_mean.values endog_std = endog_std.values # - Actual --------------------------------------------------------------- # Baseline model mod1 = dynamic_factor_mq.DynamicFactorMQ( endog, factors=1, factor_multiplicities=1, factor_orders=1, idiosyncratic_ar1=idiosyncratic_ar1, standardize=(endog_mean, endog_std)) params = pd.Series(mod1.start_params, index=mod1.param_names) res1 = mod1.smooth(params) # - Desired -------------------------------------------------------------- # Create an identical model, but without standardization mod2 = dynamic_factor_mq.DynamicFactorMQ( endog, factors=1, factor_multiplicities=1, factor_orders=1, idiosyncratic_ar1=idiosyncratic_ar1, standardize=False) # Start with the parameters from the standardized model mod2.update(params) # Update the observation equation to manually implement the standardization mod2['obs_intercept'] = np.array(endog_mean) mod2['design'] *= np.array(endog_std)[:, None] mod2['obs_cov'] *= np.array(endog_std)[:, None]**2 # Prevent the model from overwriting our changes mod2.update = lambda params, **kwargs: params # Create the results object based on the model with manual standardization res2 = mod2.smooth(params) # - Test results --------------------------------------------------------- check_standardized_results(res1, res2) @pytest.mark.parametrize('idiosyncratic_ar1', [True, False]) def test_standardized_MQ(reset_randomstate, idiosyncratic_ar1): nobs = 100 idiosyncratic_ar1 = False k1 = 2 k2 = 2 endog1_M, endog1_Q, f1 = test_dynamic_factor_mq_monte_carlo.gen_k_factor1( nobs, k=k1, idiosyncratic_ar1=idiosyncratic_ar1) endog2_M, endog2_Q, f2 = test_dynamic_factor_mq_monte_carlo.gen_k_factor2( nobs, k=k2, idiosyncratic_ar1=idiosyncratic_ar1) endog_M = pd.concat([endog1_M, f2, endog2_M], axis=1) endog_Q = pd.concat([endog1_Q, endog2_Q], axis=1) endog_M1 = endog_M.loc[:'1957-12'] endog_Q1 = endog_Q.loc[:'1957Q4'] endog_M2 = endog_M.loc['1958-01':] endog_Q2 = endog_Q.loc['1958Q1':] factors = {f'yM{i + 1}_f1': ['a'] for i in range(k1)} factors.update({f'f{i + 1}': ['b'] for i in range(2)}) factors.update({f'yM{i + 1}_f2': ['b'] for i in range(k2)}) factors.update({f'yQ{i + 1}_f1': ['a'] for i in range(k1)}) factors.update({f'yQ{i + 1}_f2': ['b'] for i in range(k2)}) factor_multiplicities = {'b': 2} # - Actual --------------------------------------------------------------- # Baseline model endog_mean = pd.Series( np.random.normal(size=len(factors)), index=factors.keys()) endog_std = pd.Series( np.abs(np.random.normal(size=len(factors))), index=factors.keys()) mod1 = dynamic_factor_mq.DynamicFactorMQ( endog_M1, endog_quarterly=endog_Q1, factors=factors, factor_multiplicities=factor_multiplicities, factor_orders=6, idiosyncratic_ar1=idiosyncratic_ar1, standardize=(endog_mean, endog_std)) params = pd.Series(mod1.start_params, index=mod1.param_names) res1 = mod1.smooth(params) # - Desired -------------------------------------------------------------- # Create an identical model, but without standardization mod2 = dynamic_factor_mq.DynamicFactorMQ( endog_M1, endog_quarterly=endog_Q1, factors=factors, factor_multiplicities=factor_multiplicities, factor_orders=6, idiosyncratic_ar1=idiosyncratic_ar1, standardize=False) # Start with the parameters from the standardized model mod2.update(params) # Update the observation equation to manually implement the standardization mod2['obs_intercept'] = endog_mean mod2['design'] *= np.array(endog_std)[:, None] mod2['obs_cov'] *= np.array(endog_std)[:, None]**2 # Prevent the model from overwriting our changes mod2.update = lambda params, **kwargs: params # Create the results object based on the model with manual standardization res2 = mod2.smooth(params) # - Test results --------------------------------------------------------- check_standardized_results(res1, res2) # - Test append, extend, apply ------------------------------------------- check_append(res1, res2, endog_M2, endog_Q2) check_extend(res1, res2, endog_M2, endog_Q2) check_apply(res1, res2, endog_M, endog_Q) # - Test news ------------------------------------------------------------ res1_apply = res1.apply(endog_M, endog_quarterly=endog_Q) res2_apply = res2.apply(endog_M, endog_quarterly=endog_Q) mod2_apply = res2_apply.model # Because our mod2 has manual changes, we need to copy those over and # re-create the applyed results object mod2_apply.update(res2_apply.params) mod2_apply['obs_intercept'] = mod2['obs_intercept'] mod2_apply['design'] = mod2['design'] mod2_apply['obs_cov'] = mod2['obs_cov'] mod2_apply.update = lambda params, **kwargs: params res2_apply = mod2_apply.smooth(res2_apply.params) news1 = res1_apply.news(res1, start='1958-01', end='1958-03', comparison_type='previous') news2 = res2_apply.news(res2, start='1958-01', end='1958-03', comparison_type='previous') attributes = [ 'total_impacts', 'update_impacts', 'revision_impacts', 'news', 'weights', 'update_forecasts', 'update_realized', 'prev_impacted_forecasts', 'post_impacted_forecasts', 'revisions_iloc', 'revisions_ix', 'updates_iloc', 'updates_ix'] for attr in attributes: w = getattr(news1, attr) x = getattr(news2, attr) if isinstance(x, pd.Series): assert_series_equal(w, x) else: assert_frame_equal(w, x) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_dynamic_factor_mq_frbny_nowcast.py000066400000000000000000000447011400612667500326300ustar00rootroot00000000000000import os import numpy as np import pandas as pd from scipy.io import matlab import pytest from numpy.testing import assert_allclose from statsmodels.tsa.statespace import initialization, dynamic_factor_mq # Load dataset current_path = os.path.dirname(os.path.abspath(__file__)) results_path = os.path.join(current_path, 'results', 'frbny_nowcast') data_path = os.path.join(results_path, 'Nowcasting', 'data', 'US') us_data = pd.read_csv(os.path.join(data_path, '2016-06-29.csv')) us_data.index = pd.PeriodIndex(us_data.Date.tolist(), freq='M') del us_data['Date'] us_data_update = pd.read_csv(os.path.join(data_path, '2016-07-29.csv')) us_data_update.index = pd.PeriodIndex(us_data_update.Date.tolist(), freq='M') del us_data_update['Date'] # Some definitions to re-use BLOCK_FACTORS_KP1 = { 'CPIAUCSL': ['global', 'test1'], 'UNRATE': ['global', 'test2'], 'PAYEMS': ['global', 'test2'], 'RSAFS': ['global', 'test1', 'test2'], 'TTLCONS': ['global', 'test1'], 'TCU': ['global', 'test2'], 'GDPC1': ['global', 'test1', 'test2'], 'ULCNFB': ['global'], } BLOCK_FACTOR_ORDERS_KP1 = { 'global': 1, 'test1': 1, 'test2': 1 } BLOCK_FACTOR_ORDERS_KP2 = { 'global': 2, 'test1': 2, 'test2': 2 } BLOCK_FACTOR_MULTIPLICITIES_KP2 = { 'global': 2, 'test1': 2, 'test2': 2 } @pytest.fixture(scope="module") def matlab_results(): # Get estimation output from FRBNY programs results = {} # DFM results with a single block of factors for run in ['111', '112', '11F', '221', '222', '22F']: res = matlab.loadmat(os.path.join(results_path, f'test_dfm_{run}.mat')) # The FRBNY version orders the idiosyncratic AR(1) factors differently, # so we need to re-order the initial state mean and covariance matrix k_factors = res['Spec']['k'][0, 0][0, 0] factor_orders = res['Spec']['p'][0, 0][0, 0] _factor_orders = max(5, factor_orders) idio = k_factors * _factor_orders + 3 ix = np.r_[np.arange(idio), idio + np.arange(10).reshape(2, 5).ravel(order='F')] initial_state = res['Res']['Z_0'][0, 0][:, 0][ix] initial_state_cov = res['Res']['V_0'][0, 0][ix][:, ix] # In the 2-factor case, we want both factors in a single block if k_factors == 2: factor_orders = {('0', '1'): factor_orders} results[run] = { 'k_endog_M': 3, 'factors': k_factors, 'factor_orders': factor_orders, 'factor_multiplicities': None, 'params': res['params'][:, 0], 'llf': res['Res']['loglik'][0, 0][0, 0], 'initial_state': initial_state, 'initial_state_cov': initial_state_cov, 'smoothed_forecasts': res['Res']['x_sm'][0, 0]} # News output with a single block of factors for run in ['112', '222']: res = matlab.loadmat(os.path.join(results_path, f'test_news_{run}.mat')) # The FRBNY version orders the idiosyncratic AR(1) factors differently, # so we need to re-order the initial state mean and covariance matrix k_factors = res['Spec']['k'][0, 0][0, 0] factor_orders = res['Spec']['p'][0, 0][0, 0] _factor_orders = max(5, factor_orders) idio = k_factors * _factor_orders + 3 ix = np.r_[np.arange(idio), idio + np.arange(10).reshape(2, 5).ravel(order='F')] initial_state = res['Res']['Z_0'][0, 0][:, 0][ix] initial_state_cov = res['Res']['V_0'][0, 0][ix][:, ix] # In the 2-factor case, we want both factors in a single block if k_factors == 2: factor_orders = {('0', '1'): factor_orders} results[f'news_{run}'] = { 'k_endog_M': 3, 'factors': k_factors, 'factor_orders': factor_orders, 'factor_multiplicities': None, 'params': res['params'][:, 0], 'initial_state': initial_state, 'initial_state_cov': initial_state_cov, 'revision_impacts': res['Res']['impact_revisions'][0, 0], 'weight': res['Res']['weight'], 'news_table': res['Res']['news_table'][0, 0]} # DFM results with three blocks of factors for run in ['111', '112', '221', '222']: res = matlab.loadmat(os.path.join(results_path, f'test_dfm_blocks_{run}.mat')) # The FRBNY version orders the idiosyncratic AR(1) factors differently, # so we need to re-order the initial state mean and covariance matrix k_factors = res['Spec']['k'][0, 0][0, 0] factor_order = res['Spec']['p'][0, 0][0, 0] _factor_order = max(5, factor_order) idio = 3 * k_factors * _factor_order + 6 ix = np.r_[np.arange(idio), idio + np.arange(10).reshape(2, 5).ravel(order='F')] initial_state = res['Res']['Z_0'][0, 0][:, 0][ix] initial_state_cov = res['Res']['V_0'][0, 0][ix][:, ix] # Setup factors / blocks if k_factors == 1: factors = BLOCK_FACTORS_KP1.copy() factor_orders = BLOCK_FACTOR_ORDERS_KP1.copy() factor_multiplicities = None else: factors = BLOCK_FACTORS_KP1.copy() factor_orders = BLOCK_FACTOR_ORDERS_KP2.copy() factor_multiplicities = BLOCK_FACTOR_MULTIPLICITIES_KP2.copy() results[f'block_{run}'] = { 'k_endog_M': 6, 'factors': factors, 'factor_orders': factor_orders, 'factor_multiplicities': factor_multiplicities, 'params': res['params'][:, 0], 'llf': res['Res']['loglik'][0, 0][0, 0], 'initial_state': initial_state, 'initial_state_cov': initial_state_cov, 'smoothed_forecasts': res['Res']['x_sm'][0, 0]} # News output with three blocks of factors for run in ['112', '222']: res = matlab.loadmat(os.path.join(results_path, f'test_news_blocks_{run}.mat')) # The FRBNY version orders the idiosyncratic AR(1) factors differently, # so we need to re-order the initial state mean and covariance matrix k_factors = res['Spec']['k'][0, 0][0, 0] factor_order = res['Spec']['p'][0, 0][0, 0] _factor_order = max(5, factor_order) idio = 3 * k_factors * _factor_order + 6 ix = np.r_[np.arange(idio), idio + np.arange(10).reshape(2, 5).ravel(order='F')] initial_state = res['Res']['Z_0'][0, 0][:, 0][ix] initial_state_cov = res['Res']['V_0'][0, 0][ix][:, ix] # Setup factors / blocks if k_factors == 1: factors = BLOCK_FACTORS_KP1.copy() factor_orders = BLOCK_FACTOR_ORDERS_KP1.copy() factor_multiplicities = None else: factors = BLOCK_FACTORS_KP1.copy() factor_orders = BLOCK_FACTOR_ORDERS_KP2.copy() factor_multiplicities = BLOCK_FACTOR_MULTIPLICITIES_KP2.copy() results[f'news_block_{run}'] = { 'k_endog_M': 6, 'factors': factors, 'factor_orders': factor_orders, 'factor_multiplicities': factor_multiplicities, 'params': res['params'][:, 0], 'initial_state': initial_state, 'initial_state_cov': initial_state_cov, 'revision_impacts': res['Res']['impact_revisions'][0, 0], 'weight': res['Res']['weight'], 'news_table': res['Res']['news_table'][0, 0]} # Construct the test dataset def get_data(us_data, mean_M=None, std_M=None, mean_Q=None, std_Q=None): dta_M = us_data[['CPIAUCSL', 'UNRATE', 'PAYEMS', 'RSAFS', 'TTLCONS', 'TCU']].copy() dta_Q = us_data[['GDPC1', 'ULCNFB']].copy().resample('Q').last() dta_M['CPIAUCSL'] = (dta_M['CPIAUCSL'] / dta_M['CPIAUCSL'].shift(1) - 1) * 100 dta_M['UNRATE'] = dta_M['UNRATE'].diff() dta_M['PAYEMS'] = dta_M['PAYEMS'].diff() dta_M['TCU'] = dta_M['TCU'].diff() dta_M['RSAFS'] = (dta_M['RSAFS'] / dta_M['RSAFS'].shift(1) - 1) * 100 dta_M['TTLCONS'] = (dta_M['TTLCONS'] / dta_M['TTLCONS'].shift(1) - 1) * 100 dta_Q = ((dta_Q / dta_Q.shift(1))**4 - 1) * 100 start = '2000' dta_M = dta_M.loc[start:] dta_Q = dta_Q.loc[start:] first_ix = dta_M.first_valid_index() last_ix = dta_M.last_valid_index() dta_M = dta_M.loc[first_ix:last_ix] first_ix = dta_Q.first_valid_index() last_ix = dta_Q.last_valid_index() dta_Q = dta_Q.loc[first_ix:last_ix] return dta_M, dta_Q # Usual test dataset endog_M, endog_Q = get_data(us_data) # Updated test dataset (for computing the news) updated_M, updated_Q = get_data(us_data_update) return endog_M, endog_Q, results, updated_M, updated_Q @pytest.mark.parametrize("run", ['111', '112', '11F', '221', '222', '22F', 'block_111', 'block_112', 'block_221', 'block_222']) def test_known(matlab_results, run): endog_M, endog_Q = matlab_results[:2] results = matlab_results[2][run] # Construct the model mod = dynamic_factor_mq.DynamicFactorMQ( endog_M.iloc[:, :results['k_endog_M']], endog_quarterly=endog_Q, factors=results['factors'], factor_orders=results['factor_orders'], factor_multiplicities=results['factor_multiplicities'], idiosyncratic_ar1=True, init_t0=True, obs_cov_diag=True, standardize=True) mod.initialize_known(results['initial_state'], results['initial_state_cov']) res = mod.smooth(results['params'], cov_type='none') assert_allclose(res.llf - mod.loglike_constant, results['llf']) assert_allclose(res.filter_results.smoothed_forecasts.T[1:], results['smoothed_forecasts'][:-1]) assert_allclose(res.forecast(1, original_scale=False).iloc[0], results['smoothed_forecasts'][-1]) @pytest.mark.parametrize("run", ['11', '22', 'block_11', 'block_22']) def test_emstep1(matlab_results, run): # Test that our EM step gets params2 from params1 # Uses our default method for the observation equation, which is an # optimized version of the method presented in BaÅ„bura and Modugno (2014) # (e.g. our version doesn't require the loop over T or the Kronecker # product) endog_M, endog_Q = matlab_results[:2] results1 = matlab_results[2][f'{run}1'] results2 = matlab_results[2][f'{run}2'] # Construct the model mod = dynamic_factor_mq.DynamicFactorMQ( endog_M.iloc[:, :results1['k_endog_M']], endog_quarterly=endog_Q, factors=results1['factors'], factor_orders=results1['factor_orders'], factor_multiplicities=results1['factor_multiplicities'], idiosyncratic_ar1=True, init_t0=True, obs_cov_diag=True, standardize=True) init = initialization.Initialization( mod.k_states, 'known', constant=results1['initial_state'], stationary_cov=results1['initial_state_cov']) res2, params2 = mod._em_iteration(results1['params'], init=init, mstep_method='missing') # Test parameters true2 = results2['params'] assert_allclose(params2[mod._p['loadings']], true2[mod._p['loadings']]) assert_allclose(params2[mod._p['factor_ar']], true2[mod._p['factor_ar']]) assert_allclose(params2[mod._p['factor_cov']], true2[mod._p['factor_cov']]) assert_allclose(params2[mod._p['idiosyncratic_ar1']], true2[mod._p['idiosyncratic_ar1']]) assert_allclose(params2[mod._p['idiosyncratic_var']], true2[mod._p['idiosyncratic_var']]) @pytest.mark.parametrize( "k_factors,factor_orders,factor_multiplicities,idiosyncratic_ar1", [(1, 1, 1, True), (3, 1, 1, True), (1, 6, 1, True), (3, 6, 1, True), (1, 1, 1, False), (3, 1, 1, False), (1, 6, 1, False), (3, 6, 1, False), (BLOCK_FACTORS_KP1.copy(), BLOCK_FACTOR_ORDERS_KP1.copy(), 1, True), (BLOCK_FACTORS_KP1.copy(), BLOCK_FACTOR_ORDERS_KP1.copy(), 1, False), (BLOCK_FACTORS_KP1.copy(), BLOCK_FACTOR_ORDERS_KP2.copy(), BLOCK_FACTOR_MULTIPLICITIES_KP2, True), (BLOCK_FACTORS_KP1.copy(), BLOCK_FACTOR_ORDERS_KP2.copy(), BLOCK_FACTOR_MULTIPLICITIES_KP2, False)]) @pytest.mark.filterwarnings('ignore::UserWarning') def test_emstep_methods_missing(matlab_results, k_factors, factor_orders, factor_multiplicities, idiosyncratic_ar1): # Test that in the case of missing data, the direct and optimized EM step # methods for the observation equation give identical results across a # variety of parameterizations endog_M = matlab_results[0].iloc[:, :10] endog_Q = matlab_results[1].iloc[:, :10] # Construct the model mod = dynamic_factor_mq.DynamicFactorMQ( endog_M, endog_quarterly=endog_Q, factors=k_factors, factor_orders=factor_orders, factor_multiplicities=factor_multiplicities, idiosyncratic_ar1=idiosyncratic_ar1, standardize=True) mod.ssm.filter_univariate = True params0 = mod.start_params _, params1 = mod._em_iteration(params0, mstep_method='missing') # Now double-check the observation equation M step for identical H and # Lambda directly mod.update(params1) res = mod.ssm.smooth() a = res.smoothed_state.T[..., None] cov_a = res.smoothed_state_cov.transpose(2, 0, 1) Eaa = cov_a + np.matmul(a, a.transpose(0, 2, 1)) Lambda, H = mod._em_maximization_obs_missing(res, Eaa, a, compute_H=True) @pytest.mark.parametrize( "k_factors,factor_orders,factor_multiplicities,idiosyncratic_ar1", [(1, 1, 1, True), (3, 1, 1, True), (1, 6, 1, True), (3, {('0', '1', '2'): 6}, 1, True), (1, 1, 1, False), (3, 1, 1, False), (1, 6, 1, False), (3, {('0', '1', '2'): 6}, 1, False), (BLOCK_FACTORS_KP1.copy(), BLOCK_FACTOR_ORDERS_KP1.copy(), 1, True), (BLOCK_FACTORS_KP1.copy(), BLOCK_FACTOR_ORDERS_KP1.copy(), 1, False), (BLOCK_FACTORS_KP1.copy(), BLOCK_FACTOR_ORDERS_KP2.copy(), BLOCK_FACTOR_MULTIPLICITIES_KP2, True), (BLOCK_FACTORS_KP1.copy(), BLOCK_FACTOR_ORDERS_KP2.copy(), BLOCK_FACTOR_MULTIPLICITIES_KP2, False)]) @pytest.mark.filterwarnings('ignore::UserWarning') def test_emstep_methods_nonmissing(matlab_results, k_factors, factor_orders, factor_multiplicities, idiosyncratic_ar1): # Test that in the case of non-missing data, our three EM step methods for # the observation equation (nonmissing, missing_direct, missing) give # identical results across a variety of parameterizations # Note that including quarterly series will always imply missing values, # so we have to only provide monthly series dta_M = matlab_results[0].iloc[:, :8] dta_M = (dta_M - dta_M.mean()) / dta_M.std() endog_M = dta_M.interpolate().fillna(method='backfill') # Remove the quarterly endog->factor maps if isinstance(k_factors, dict): if 'GDPC1' in k_factors: del k_factors['GDPC1'] if 'ULCNFB' in k_factors: del k_factors['ULCNFB'] # Construct the model mod = dynamic_factor_mq.DynamicFactorMQ( endog_M, factors=k_factors, factor_orders=factor_orders, factor_multiplicities=factor_multiplicities, idiosyncratic_ar1=idiosyncratic_ar1) mod.ssm.filter_univariate = True params0 = mod.start_params _, params1 = mod._em_iteration(params0, mstep_method='missing') _, params1_nonmissing = mod._em_iteration( params0, mstep_method='nonmissing') assert_allclose(params1_nonmissing, params1, atol=1e-13) # Now double-check the observation equation M step for identical H and # Lambda directly mod.update(params1) res = mod.ssm.smooth() a = res.smoothed_state.T[..., None] cov_a = res.smoothed_state_cov.transpose(2, 0, 1) Eaa = cov_a + np.matmul(a, a.transpose(0, 2, 1)) Lambda, H = mod._em_maximization_obs_missing(res, Eaa, a, compute_H=True) Lambda_nonmissing, H_nonmissing = mod._em_maximization_obs_nonmissing( res, Eaa, a, compute_H=True) assert_allclose(Lambda_nonmissing, Lambda, atol=1e-13) assert_allclose(H_nonmissing, H, atol=1e-13) @pytest.mark.parametrize("run", ['news_112', 'news_222', 'news_block_112', 'news_block_222']) def test_news(matlab_results, run): endog_M, endog_Q = matlab_results[:2] results = matlab_results[2][run] updated_M, updated_Q = matlab_results[-2:] # Construct the base model mod1 = dynamic_factor_mq.DynamicFactorMQ( endog_M.iloc[:, :results['k_endog_M']], endog_quarterly=endog_Q, factors=results['factors'], factor_orders=results['factor_orders'], factor_multiplicities=results['factor_multiplicities'], idiosyncratic_ar1=True, init_t0=True, obs_cov_diag=True, standardize=True) mod1.initialize_known(results['initial_state'], results['initial_state_cov']) res1 = mod1.smooth(results['params'], cov_type='none') # Construct the updated model res2 = res1.apply(updated_M.iloc[:, :results['k_endog_M']], endog_quarterly=updated_Q, retain_standardization=True) # Compute the news news = res2.news(res1, impact_date='2016-09', comparison_type='previous') print(news.revision_impacts.loc['2016-09', 'GDPC1']) assert_allclose(news.revision_impacts.loc['2016-09', 'GDPC1'], results['revision_impacts']) columns = ['forecast (prev)', 'observed', 'weight', 'impact'] actual = news.details_by_impact.loc['2016-09', 'GDPC1'][columns] assert_allclose(actual.loc[('2016-06', 'CPIAUCSL')], results['news_table'][0]) assert_allclose(actual.loc[('2016-06', 'UNRATE')], results['news_table'][1]) assert_allclose(actual.loc[('2016-06', 'PAYEMS')], results['news_table'][2]) if mod1.k_endog_M == 6: i = 6 assert_allclose(actual.loc[('2016-06', 'RSAFS')], results['news_table'][3]) assert_allclose(actual.loc[('2016-05', 'TTLCONS')], results['news_table'][4]) assert_allclose(actual.loc[('2016-06', 'TCU')], results['news_table'][5]) else: i = 3 assert_allclose(actual.loc[('2016-06', 'GDPC1')], results['news_table'][i]) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_dynamic_factor_mq_monte_carlo.py000066400000000000000000000566311400612667500322610ustar00rootroot00000000000000""" Monte Carlo-type tests for the BM model Note that that the actual tests that run are just regression tests against previously estimated values with small sample sizes that can be run quickly for continuous integration. However, this file can be used to re-run (slow) large-sample Monte Carlo tests. """ import numpy as np import pandas as pd import pytest from numpy.testing import assert_allclose from scipy.signal import lfilter from statsmodels.tsa.statespace import ( dynamic_factor_mq, sarimax, varmax, dynamic_factor) def simulate_k_factor1(nobs=1000): mod_sim = dynamic_factor.DynamicFactor(np.zeros((1, 4)), k_factors=1, factor_order=1, error_order=1) loadings = [1.0, -0.75, 0.25, -0.3, 0.5] p = np.r_[loadings[:mod_sim.k_endog], [10] * mod_sim.k_endog, 0.5, [0.] * mod_sim.k_endog] ix = pd.period_range(start='1935-01', periods=nobs, freq='M') endog = pd.DataFrame(mod_sim.simulate(p, nobs), index=ix) true = pd.Series(p, index=mod_sim.param_names) # Compute levels series (M and Q) ix = pd.period_range(start=endog.index[0] - 1, end=endog.index[-1], freq=endog.index.freq) levels_M = 1 + endog.reindex(ix) / 100 levels_M.iloc[0] = 100 levels_M = levels_M.cumprod() log_levels_M = np.log(levels_M) * 100 log_levels_Q = (np.log(levels_M).resample('Q', convention='e') .sum().iloc[:-1] * 100) # This is an alternative way to compute the quarterly levels # endog_M = endog.iloc[:, :3] # x = endog.iloc[:, 3:] # endog_Q = (x + 2 * x.shift(1) + 3 * x.shift(2) + 2 * x.shift(3) + # x.shift(4)).resample('Q', convention='e').last().iloc[:-1] / 3 # levels_Q = 1 + endog.iloc[:, 3:] / 100 # levels_Q.iloc[0] = 100 # Here is another alternative way to compute the quarterly levels # weights = np.array([1, 2, 3, 2, 1]) # def func(x, weights): # return np.sum(weights * x) # r = endog_M.rolling(5) # (r.apply(func, args=(weights,), raw=False).resample('Q', convention='e') # .last().iloc[:-1].tail()) # Compute the growth rate series that we'll actually run the model on endog_M = log_levels_M.iloc[:, :3].diff() endog_Q = log_levels_Q.iloc[:, 3:].diff() return endog_M, endog_Q, log_levels_M, log_levels_Q, true def simulate_k_factors3_blocks2(nobs=1000, idiosyncratic_ar1=False): # Simulate the first two factors ix = pd.period_range(start='2000-01', periods=1, freq='M') endog = pd.DataFrame(np.zeros((1, 2)), columns=['f1', 'f2'], index=ix) mod_f_12 = varmax.VARMAX(endog, order=(1, 0), trend='n') params = [0.5, 0.1, -0.2, 0.9, 1.0, 0, 1.0] f_12 = mod_f_12.simulate(params, nobs) # Simulate the third factor endog = pd.Series([0], name='f3', index=ix) mod_f_3 = sarimax.SARIMAX(endog, order=(2, 0, 0)) params = [0.7, 0.1, 1.] f_3 = mod_f_3.simulate(params, nobs) # Combine the factors f = pd.concat([f_12, f_3], axis=1) # Observed variables k_endog = 8 design = np.zeros((k_endog, 3)) design[0] = [1.0, 1.0, 1.0] design[1] = [0.5, -0.8, 0.0] design[2] = [1.0, 0.0, 0.0] design[3] = [0.2, 0.0, -0.1] design[4] = [0.5, 0.0, 0.0] design[5] = [-0.2, 0.0, 0.0] design[6] = [1.0, 1.0, 1.0] design[7] = [-1.0, 0.0, 0.0] rho = np.array([0.5, 0.2, -0.1, 0.0, 0.4, 0.9, 0.05, 0.05]) if not idiosyncratic_ar1: rho *= 0.0 eps = [lfilter([1], [1, -rho[i]], np.random.normal(size=nobs)) for i in range(k_endog)] endog = (design @ f.T).T + eps endog.columns = [f'y{i + 1}' for i in range(k_endog)] # True parameters tmp1 = design.ravel() tmp2 = np.linalg.cholesky(mod_f_12['state_cov']) tmp3 = rho if idiosyncratic_ar1 else [] true = np.r_[ tmp1[tmp1 != 0], mod_f_12['transition', :2, :].ravel(), mod_f_3['transition', :, 0], tmp2[np.tril_indices_from(tmp2)], mod_f_3['state_cov', 0, 0], tmp3, [1] * k_endog ] # Compute levels series (M and Q) ix = pd.period_range(endog.index[0] - 1, endog.index[-1], freq='M') levels_M = 1 + endog.reindex(ix) / 100 levels_M.iloc[0] = 100 levels_M = levels_M.cumprod() log_levels_M = np.log(levels_M) * 100 log_levels_Q = (np.log(levels_M).resample('Q', convention='e') .sum().iloc[:-1] * 100) # Compute the growth rate series that we'll actually run the model on endog_M = log_levels_M.iloc[:, :7].diff().iloc[1:] endog_Q = log_levels_Q.iloc[:, 7:].diff().iloc[2:] # Specification factor_names = np.array(['global', 'second', 'third']) factors = {endog.columns[i]: factor_names[design[i] != 0] for i in range(k_endog)} factor_orders = { ('global', 'second'): 1, 'third': 2, } return (endog_M, endog_Q, log_levels_M, log_levels_Q, factors, factor_orders, true, f) @pytest.mark.skip(reason="Monte carlo test, very slow, kept for manual runs") def test_k_factor1(reset_randomstate): # Fitted parameters for np.random.seed(1234) replicate the true parameters # pretty well (flipped signs on loadings are just from usual factor sign # identification issue): # True Fitted # loading.0->0 1.00 -0.98 # loading.0->1 -0.75 0.75 # loading.0)->2 0.25 -0.24 # loading.0->3 -0.30 0.31 # L1.0->0 0.50 0.50 # sigma2.0 10.00 10.07 # sigma2.1 10.00 10.06 # sigma2.2 10.00 9.94 # sigma2.3 10.00 11.60 np.random.seed(1234) endog_M, endog_Q, _, _, true_params, _ = simulate_k_factor1(nobs=100000) mod = dynamic_factor_mq.DynamicFactorMQ( endog_M, endog_quarterly=endog_Q, factors=1, factor_orders=1, idiosyncratic_ar1=False) # Fit the model with L-BFGS. Because the model doesn't impose identifying # assumptions on the factors, here we force identification by fixing the # factor error variance to be unity with mod.fix_params({'fb(0).cov.chol[1,1]': 1.}): mod.fit(method='lbfgs', disp=False) def gen_k_factor1_nonstationary(nobs=1000, k=1, idiosyncratic_ar1=False, idiosyncratic_var=0.4, k_ar=1): # Simulate univariate random walk ix = pd.period_range(start='1950-01', periods=1, freq='M') faux = pd.Series([0], index=ix) mod = sarimax.SARIMAX(faux, order=(k_ar, 0, 0), initialization='diffuse') params = np.r_[[0] * (k_ar - 1), [1.0001], 1.0] factor = mod.simulate(params, nobs) if idiosyncratic_ar1: mod_idio = sarimax.SARIMAX(faux, order=(1, 0, 0)) endog = pd.concat([ factor + mod_idio.simulate([0.7, idiosyncratic_var], nobs) for i in range(2 * k)], axis=1) else: endog = pd.concat([ factor + np.random.normal(scale=idiosyncratic_var**0.5, size=nobs) for i in range(2 * k)], axis=1) # Construct the quarterly variable levels_M = 1 + endog / 100 levels_M.iloc[0] = 100 levels_M = levels_M.cumprod() log_levels_M = np.log(levels_M) * 100 log_levels_Q = (np.log(levels_M).resample('Q', convention='e') .sum().iloc[:-1] * 100) # Compute the growth rate series that we'll actually run the model on endog_M = log_levels_M.diff().iloc[1:, :k] if k > 1: endog_M.columns = ['yM%d_f1' % (i + 1) for i in range(k)] else: endog_M.columns = ['yM_f1'] endog_Q = log_levels_Q.diff().iloc[1:, k:] if k > 1: endog_Q.columns = ['yQ%d_f1' % (i + 1) for i in range(k)] else: endog_Q.columns = ['yQ_f1'] return endog_M, endog_Q, factor def test_em_nonstationary(reset_randomstate): # Test that when the EM algorithm estimates non-stationary parameters, that # it warns the user and switches to a diffuse initialization. ix = pd.period_range(start='2000', periods=20, freq='M') endog_M = pd.Series(np.arange(20), index=ix) endog_M.iloc[10:12] += [0.4, -0.2] # add in a little noise ix = pd.period_range(start='2000', periods=5, freq='Q') endog_Q = pd.Series(np.arange(5), index=ix) mod = dynamic_factor_mq.DynamicFactorMQ( endog_M, endog_quarterly=endog_Q, idiosyncratic_ar1=False, standardize=False, factors=['global']) msg = ('Non-stationary parameters found at EM iteration 1, which is not' ' compatible with stationary initialization. Initialization was' r' switched to diffuse for the following: \["factor block:' r' \(\'global\',\)"\], and fitting was restarted.') with pytest.warns(UserWarning, match=msg): return mod.fit(maxiter=2, em_initialization=False) def gen_k_factor1(nobs=10000, k=1, idiosyncratic_ar1=False, idiosyncratic_var=0.4, k_ar=6): # Simulate univariate AR(6) ix = pd.period_range(start='1950-01', periods=1, freq='M') faux = pd.Series([0], index=ix) mod = sarimax.SARIMAX(faux, order=(k_ar, 0, 0)) params = np.r_[[0] * (k_ar - 1), [0.5], 1.0] factor = mod.simulate(params, nobs) if idiosyncratic_ar1: mod_idio = sarimax.SARIMAX(faux, order=(1, 0, 0)) endog = pd.concat([ factor + mod_idio.simulate([0.7, idiosyncratic_var], nobs) for i in range(2 * k)], axis=1) else: endog = pd.concat([ factor + np.random.normal(scale=idiosyncratic_var**0.5, size=nobs) for i in range(2 * k)], axis=1) # Construct the quarterly variable levels_M = 1 + endog / 100 levels_M.iloc[0] = 100 levels_M = levels_M.cumprod() log_levels_M = np.log(levels_M) * 100 log_levels_Q = (np.log(levels_M).resample('Q', convention='e') .sum().iloc[:-1] * 100) # Compute the growth rate series that we'll actually run the model on endog_M = log_levels_M.diff().iloc[1:, :k] if k > 1: endog_M.columns = ['yM%d_f1' % (i + 1) for i in range(k)] else: endog_M.columns = ['yM_f1'] endog_Q = log_levels_Q.diff().iloc[1:, k:] if k > 1: endog_Q.columns = ['yQ%d_f1' % (i + 1) for i in range(k)] else: endog_Q.columns = ['yQ_f1'] return endog_M, endog_Q, factor @pytest.mark.filterwarnings("ignore:Log-likelihood decreased") def test_k_factor1_factor_order_6(reset_randomstate): # This tests that the model is correctly set up when the lag order of the # factor is longer than 5 and we have a single factor. This is important # because 5 lags are always present when there is quarterly data, but we # want to check that, for example, we haven't accidentally relied on there # being exactly 5 lags available. # Note: as of 2020/07/25, the FRBNY code does not seem to work for 6 lags, # so we can't test against their code # Note: the case with only 100 nobs leads to issues with the EM algorithm # and a decrease in the log-likelihood # There is a description of the results from # a run with nobs=10000 that are a better indication of the model finding # the correct parameters. endog_M, endog_Q, _ = gen_k_factor1( nobs=100, idiosyncratic_var=0.0) # Construct and fit the model mod = dynamic_factor_mq.DynamicFactorMQ( endog_M, endog_quarterly=endog_Q, factor_orders=6, idiosyncratic_ar1=False, standardize=False) mod.fit() # From a run with 10000 observations, we get: # This results in the following fitted coefficients # True Fitted # loading.0->y1 1.00 1.15 # loading.0->y2 1.00 1.15 # L1.0->0 0.00 -0.01 # L2.0->0 0.00 -0.01 # L3.0->0 0.00 0.01 # L4.0->0 0.00 0.01 # L5.0->0 0.00 -0.00 # L6.0->0 0.50 0.50 # fb(0).cov.chol[1,1] 1.00 0.87 # sigma2.y1 0.00 -0.00 # sigma2.y2 0.00 0.00 # # Note that the fitted values are essentially exactly right, once we # account for the lack of factor identification. In particular, if we # normalize the loadings to one, then the estimated factor error variance # is (0.87 * 1.15)**2 = 1.0, as desired. def gen_k_factor2(nobs=10000, k=2, idiosyncratic_ar1=False, idiosyncratic_var=0.4, k_ar=6): # Simulate bivariate VAR(6) for the factor ix = pd.period_range(start='1950-01', periods=1, freq='M') faux = pd.DataFrame([[0, 0]], index=ix, columns=['f1', 'f2']) mod = varmax.VARMAX(faux, order=(k_ar, 0), trend='n') A = np.zeros((2, 2 * k_ar)) A[:, -2:] = np.array([[0.5, -0.2], [0.1, 0.3]]) Q = np.array([[1.5, 0.2], [0.2, 0.5]]) L = np.linalg.cholesky(Q) params = np.r_[A.ravel(), L[np.tril_indices_from(L)]] # Simulate the factors factors = mod.simulate(params, nobs) # Add in the idiosyncratic part faux = pd.Series([0], index=ix) mod_idio = sarimax.SARIMAX(faux, order=(1, 0, 0)) phi = [0.7, -0.2] if idiosyncratic_ar1 else [0, 0.] tmp = factors.iloc[:, 0] + factors.iloc[:, 1] # Monthly variables endog_M = pd.concat([tmp.copy() for i in range(k)], axis=1) columns = [] for i in range(k): endog_M.iloc[:, i] = ( endog_M.iloc[:, i] + mod_idio.simulate([phi[0], idiosyncratic_var], nobs)) columns += [f'yM{i + 1}_f2'] endog_M.columns = columns # Monthly versions of quarterly variables endog_Q_M = pd.concat([tmp.copy() for i in range(k)], axis=1) columns = [] for i in range(k): endog_Q_M.iloc[:, i] = ( endog_Q_M.iloc[:, i] + mod_idio.simulate([phi[0], idiosyncratic_var], nobs)) columns += [f'yQ{i + 1}_f2'] endog_Q_M.columns = columns # Create quarterly versions of quarterly variables levels_M = 1 + endog_Q_M / 100 levels_M.iloc[0] = 100 levels_M = levels_M.cumprod() # log_levels_M = np.log(levels_M) * 100 log_levels_Q = (np.log(levels_M).resample('Q', convention='e') .sum().iloc[:-1] * 100) # Compute the quarterly growth rate series endog_Q = log_levels_Q.diff() return endog_M, endog_Q, factors @pytest.mark.skip(reason="Monte carlo test, very slow, kept for manual runs") def test_k_factor2_factor_order_6(reset_randomstate): # This tests that the model is correctly set up when the lag order of the # factor is longer than 5 and we have two factors. This is important # because 5 lags are always present when there is quarterly data, but we # want to check that, for example, we haven't accidentally relied on there # being exactly 5 lags available. # Note: as of 2020/07/25, the FRBNY code does not seem to work for 6 lags, # so we can't test against their code endog_M, endog_Q, factors = gen_k_factor2() # Add the factors in to endog_M, which will allow us to identify them, # since endog_M and endog_Q are all the same linear combination of the # factors endog_M_aug = pd.concat([factors, endog_M], axis=1) mod = dynamic_factor_mq.DynamicFactorMQ( endog_M_aug, endog_quarterly=endog_Q, factor_multiplicities=2, factor_orders=6, idiosyncratic_ar1=False, standardize=False) res = mod.fit() # The identification for the VAR system means that it is harder to visually # check that the estimation procedure produced good estimates. # This is the invertible matrix that we'll use to transform the factors # and parameter matrices into the original form M = np.kron(np.eye(6), mod['design', :2, :2]) Mi = np.linalg.inv(M) # Get the estimated parameter matrices Z = mod['design', :, :12] A = mod['transition', :12, :12] R = mod['selection', :12, :2] Q = mod['state_cov', :2, :2] RQR = R @ Q @ R.T # Create the transformed matrices Z2 = Z @ Mi A2 = M @ A @ Mi Q2 = (M @ RQR @ M.T) # In this example, both endog_M and endog_Q are equal to the factors, # so we expect the loading matrix to look like, which can be confirmed # (up to some numerical precision) by printing Z2 # [ I 0 0 0 0 ] # [ I 2I 3I 2I I ] print(Z2.round(2)) desired = np.array([ [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 2, 2, 3, 3, 2, 2, 1, 1, 0, 0], [1, 1, 2, 2, 3, 3, 2, 2, 1, 1, 0, 0]]) assert_allclose(Z2, desired, atol=0.1) # Confirm that this is approximately: # [ 0 0 0 0 0 0 0 0 0 0 0.5 -0.2 ] # [ 0 0 0 0 0 0 0 0 0 0 0.1 0.3 ] print(A2.round(2)) desired = np.array([ [0, 0, 0.02, 0, 0.01, -0.03, 0.01, 0.02, 0, -0.01, 0.5, -0.2], [0, 0, 0, 0.02, 0, -0.01, 0, 0, 0, 0.01, 0.1, 0.3], [1., 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1., 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1., 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1., 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1., 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1., 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1., 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1., 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1., 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1., 0, 0]]) assert_allclose(A2, desired, atol=1e-2) # Confirm that this is approximately: # [ 1.5 0.2 ] # [ 0.2 0.5 ] # in the top left corner, and then zeros elsewhere print(Q2.round(2)) desired = np.array([[1.49, 0.21], [0.21, 0.49]]) assert_allclose(Q2[:2, :2], desired, atol=1e-2) assert_allclose(Q2[:2, 2:], 0, atol=1e-2) assert_allclose(Q2[2:, :2], 0, atol=1e-2) assert_allclose(Q2[2:, 2:], 0, atol=1e-2) # Finally, check that after the transformation, the factors are equal to # endog_M a = res.states.smoothed a2 = (M @ a.T.iloc[:12]).T assert_allclose(endog_M.values, a2.iloc[:, :2].values, atol=1e-10) @pytest.mark.skip(reason="Monte carlo test, very slow, kept for manual runs") def test_two_blocks_factor_orders_6(reset_randomstate): # This tests that the model is correctly set up when the lag order of the # factor is longer than 5 and we have two blocks of factors, one block with # a single factor and one block with two factors. # For the results below, we use nobs=1000, since nobs=10000 takes a very # long time and a large amount of memory. As a result, the results below # are noisier than they could be, although they still provide pretty good # evidence that the model is performing as it should nobs = 1000 idiosyncratic_ar1 = True k1 = 3 k2 = 10 endog1_M, endog1_Q, f1 = gen_k_factor1( nobs, k=k1, idiosyncratic_ar1=idiosyncratic_ar1) endog2_M, endog2_Q, f2 = gen_k_factor2( nobs, k=k2, idiosyncratic_ar1=idiosyncratic_ar1) endog_M = pd.concat([endog1_M, f2, endog2_M], axis=1) endog_Q = pd.concat([endog1_Q, endog2_Q], axis=1) factors = {f'yM{i + 1}_f1': ['a'] for i in range(k1)} factors.update({f'yQ{i + 1}_f1': ['a'] for i in range(k1)}) factors.update({f'f{i + 1}': ['b'] for i in range(2)}) factors.update({f'yM{i + 1}_f2': ['b'] for i in range(k2)}) factors.update({f'yQ{i + 1}_f2': ['b'] for i in range(k2)}) factor_multiplicities = {'b': 2} mod = dynamic_factor_mq.DynamicFactorMQ( endog_M, endog_quarterly=endog_Q, factors=factors, factor_multiplicities=factor_multiplicities, factor_orders=6, idiosyncratic_ar1=idiosyncratic_ar1, standardize=False) mod.fit() # For the 1-factor block: # From one run, the following fitted coefficients were estimated: # True Fitted # loading.a->yM1_f1 1.00 -0.86 # loading.a->yM2_f1 1.00 -0.85 # loading.a->yM3_f1 1.00 -0.86 # loading.a->yQ1_f1 1.00 -0.71 # loading.a->yQ2_f1 1.00 -0.47 # loading.a->yQ3_f1 1.00 -0.48 # L1.a->a 0.00 0.05 # L2.a->a 0.00 0.06 # L3.a->a 0.00 0.04 # L4.a->a 0.00 -0.03 # L5.a->a 0.00 -0.06 # L6.a->a 0.50 0.46 # fb(0).cov.chol[1,1] 1.00 1.63 # L1.eps_M.yM1_f1 0.70 0.65 # L1.eps_M.yM2_f1 0.70 0.67 # L1.eps_M.yM3_f1 0.70 0.68 # L1.eps_Q.yQ1_f1 0.70 0.76 # L1.eps_Q.yQ2_f1 0.70 0.59 # L1.eps_Q.yQ3_f1 0.70 0.62 # sigma2.yM1_f1 0.40 0.39 # sigma2.yM2_f1 0.40 0.41 # sigma2.yM3_f1 0.40 0.40 # sigma2.yQ1_f1 0.40 0.43 # sigma2.yQ2_f1 0.40 0.60 # sigma2.yQ3_f1 0.40 0.59 # These are pretty good: # 1. When we normalize the factor by the first loading, the monthly # variables then all have loading close to 1.0. However, the factor # standard deviation is 0.86 * 1.63 = 1.4, which is higher than it # should be (this is largely due to the existence of the quarterly # variables, which only have 1/3 the number of observations, and make # the estimation more noisy) # 2. Similarly, the idiosyncratic AR(1) and error variance are pretty-well # estimated, although more-so for monthly than quarterly variables # 3. The factor transition is pretty good, although there is some noise in # For the 2-factor block: # The identification for the VAR system means that it is harder to visually # check that the estimation procedure produced good estimates. # This is the invertible matrix that we'll use to transform the factors # and parameter matrices into the original form from scipy.linalg import block_diag M1 = np.kron(np.eye(6), mod['design', 3:5, :2]) M2 = np.kron(np.eye(6), mod['design', 0:1, 12:13]) M = block_diag(M1, M2) Mi = np.linalg.inv(M) # Get the estimated parameter matrices Z = mod['design', :, :18] A = mod['transition', :18, :18] R = mod['selection', :18, :3] Q = block_diag(mod['state_cov', :2, :2], mod['state_cov', 12:13, 12:13]) RQR = R @ Q @ R.T # Create the transformed matrices Z2 = Z @ Mi A2 = M @ A @ Mi Q2 = (M @ RQR @ M.T) # In this example, both endog_M and endog_Q are equal to the factors, # so we expect the loading matrix to look like, which can be confirmed # (up to some numerical precision) by printing Z2 # (where the 1's, 2's, etc. are actually vectors of 1's and 2's, etc.) # [ 0 0 0 0 0 0 0 0 0 0 | 1 0 0 0 0 ] # [ 0 0 0 0 0 0 0 0 0 0 | 1 2 3 2 1 ] # [ I 0 0 0 0 0 0 0 0 | 0 0 0 0 0 ] # [ 1 1 0 0 0 0 0 0 0 0 | 0 0 0 0 0 ] # [ 1 1 2 2 3 3 2 2 1 1 | 0 0 0 0 0 ] print(Z2.round(2)) # Confirm that for the first factor block this is approximately: # [ 0 0 0 0 0 0 0 0 0 0 0.5 -0.2 ] # [ 0 0 0 0 0 0 0 0 0 0 0.1 0.3 ] # and for the second factor block this is approximately # [ 0 0 0 0 0 0.5 ] print(A2.round(2)) # Confirm that this is approximately: # [ 1.5 0.2 ] # [ 0.2 0.5 ] # for the first factor block, and # [1.0] # for the second factor block (note: actually, this seems to be # about [0.3], underestimating this factor's error variance) print(Q2.round(2)) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_exact_diffuse_filtering.py000066400000000000000000001172331400612667500310700ustar00rootroot00000000000000""" Tests for exact diffuse initialization Notes ----- These tests are against four sources: - Koopman (1997) - The R package KFAS (v1.3.1): test_exact_diffuse_filtering.R - Stata: test_exact_diffuse_filtering_stata.do - statsmodels state space models using approximate diffuse filtering Koopman (1997) provides analytic results for a few cases that we can test against. More comprehensive tests are available against the R package KFAS, which also uses the Durbin and Koopman (2012) univariate diffuse filtering method. However, there are apparently some bugs in the KFAS output (see notes below), so some tests are run against Stata. KFAS v1.3.1 appears to have the following bugs: - Incorrect filtered covariance matrix (in their syntax, kf$Ptt). These matrices are not even symmetric, so they are clearly wrong. - Loglikelihood computation appears to be incorrect for the diffuse part of the state. See the section with "Note: Apparent loglikelihood discrepancy" in the R file. It appears that KFAS does not include the constant term (-0.5 * log(2 pi)) for the diffuse observations, whereas the loglikelihood function as given in e.g. section 7.2.5 of Durbin and Koopman (2012) shows that it should be included. To confirm this, we also check against the loglikelihood value computed by Stata. Stata uses the DeJong diffuse filtering method, which gives almost identical results but does imply some numerical differences for output at the 6th or 7th decimal place. Finally, we have tests against the same model using approximate (rather than exact) diffuse filtering. These will by definition have some discrepancies in the diffuse observations. Author: Chad Fulton License: Simplified-BSD """ from statsmodels.compat.platform import PLATFORM_WIN import numpy as np import pandas as pd import pytest import os from statsmodels import datasets from statsmodels.tsa.statespace.initialization import Initialization from statsmodels.tsa.statespace.kalman_smoother import KalmanSmoother from statsmodels.tsa.statespace.varmax import VARMAX from statsmodels.tsa.statespace.dynamic_factor import DynamicFactor from statsmodels.tsa.statespace.structural import UnobservedComponents from statsmodels.tsa.statespace.tests.test_impulse_responses import TVSS from numpy.testing import assert_equal, assert_allclose from . import kfas_helpers current_path = os.path.dirname(os.path.abspath(__file__)) macrodata = datasets.macrodata.load_pandas().data macrodata.index = pd.period_range(start='1959Q1', end='2009Q3', freq='Q') # - Model definitions -------------------------------------------------------- def model_local_level(endog=None, params=None, direct=False): if endog is None: y1 = 10.2394 endog = np.r_[y1, [1] * 9] if params is None: params = [1.993, 8.253] sigma2_y, sigma2_mu = params if direct: mod = None # Construct the basic representation ssm = KalmanSmoother(k_endog=1, k_states=1, k_posdef=1) ssm.bind(endog) init = Initialization(ssm.k_states, initialization_type='diffuse') ssm.initialize(init) # ssm.filter_univariate = True # should not be required # Fill in the system matrices for a local level model ssm['design', :] = 1 ssm['obs_cov', :] = sigma2_y ssm['transition', :] = 1 ssm['selection', :] = 1 ssm['state_cov', :] = sigma2_mu else: mod = UnobservedComponents(endog, 'llevel') mod.update(params) ssm = mod.ssm ssm.initialize(Initialization(ssm.k_states, 'diffuse')) return mod, ssm def model_local_linear_trend(endog=None, params=None, direct=False): if endog is None: y1 = 10.2394 y2 = 4.2039 y3 = 6.123123 endog = np.r_[y1, y2, y3, [1] * 7] if params is None: params = [1.993, 8.253, 2.334] sigma2_y, sigma2_mu, sigma2_beta = params if direct: mod = None # Construct the basic representation ssm = KalmanSmoother(k_endog=1, k_states=2, k_posdef=2) ssm.bind(endog) init = Initialization(ssm.k_states, initialization_type='diffuse') ssm.initialize(init) # ssm.filter_univariate = True # should not be required # Fill in the system matrices for a local level model ssm['design', 0, 0] = 1 ssm['obs_cov', 0, 0] = sigma2_y ssm['transition'] = np.array([[1, 1], [0, 1]]) ssm['selection'] = np.eye(2) ssm['state_cov'] = np.diag([sigma2_mu, sigma2_beta]) else: mod = UnobservedComponents(endog, 'lltrend') mod.update(params) ssm = mod.ssm ssm.initialize(Initialization(ssm.k_states, 'diffuse')) return mod, ssm def model_common_level(endog=None, params=None, restricted=False): if endog is None: y11 = 10.2394 y21 = 8.2304 endog = np.column_stack([np.r_[y11, [1] * 9], np.r_[y21, [1] * 9]]) if params is None: params = [0.1111, 3.2324] theta, sigma2_mu = params # sigma2_1 = 1 # sigma_12 = 0 # sigma2_2 = 1 if not restricted: # Construct the basic representation ssm = KalmanSmoother(k_endog=2, k_states=2, k_posdef=1) ssm.bind(endog.T) init = Initialization(ssm.k_states, initialization_type='diffuse') ssm.initialize(init) # ssm.filter_univariate = True # should not be required # Fill in the system matrices for a common trend model ssm['design'] = np.array([[1, 0], [theta, 1]]) ssm['obs_cov'] = np.eye(2) ssm['transition'] = np.eye(2) ssm['selection', 0, 0] = 1 ssm['state_cov', 0, 0] = sigma2_mu else: # Construct the basic representation ssm = KalmanSmoother(k_endog=2, k_states=1, k_posdef=1) ssm.bind(endog.T) init = Initialization(ssm.k_states, initialization_type='diffuse') ssm.initialize(init) # ssm.filter_univariate = True # should not be required # Fill in the system matrices for a local level model ssm['design'] = np.array([[1, theta]]).T ssm['obs_cov'] = np.eye(2) ssm['transition', :] = 1 ssm['selection', :] = 1 ssm['state_cov', :] = sigma2_mu return ssm def model_var1(endog=None, params=None, measurement_error=False, init=None): if endog is None: levels = macrodata[['realgdp', 'realcons']] endog = np.log(levels).iloc[:21].diff().iloc[1:] * 400 if params is None: params = np.r_[0.5, 0.3, 0.2, 0.4, 2**0.5, 0, 3**0.5] if measurement_error: params = np.r_[params, 4, 5] # Model mod = VARMAX(endog, order=(1, 0), trend='n', measurement_error=measurement_error) mod.update(params) ssm = mod.ssm if init is None: init = Initialization(ssm.k_states, 'diffuse') ssm.initialize(init) return mod, ssm def model_dfm(endog=None, params=None, factor_order=2): if endog is None: levels = macrodata[['realgdp', 'realcons']] endog = np.log(levels).iloc[:21].diff().iloc[1:] * 400 if params is None: params = np.r_[0.5, 1., 1.5, 2., 0.9, 0.1] # Model mod = DynamicFactor(endog, k_factors=1, factor_order=factor_order) mod.update(params) ssm = mod.ssm ssm.filter_univariate = True init = Initialization(ssm.k_states, 'diffuse') ssm.initialize(init) return mod, ssm # - Analytic tests (Koopman, 1997) ------------------------------------------- class TestLocalLevelAnalytic(object): @classmethod def setup_class(cls, **kwargs): cls.mod, cls.ssm = model_local_level(**kwargs) cls.res = cls.ssm.smooth() def test_results(self): ssm = self.ssm res = self.res y1 = ssm.endog[0, 0] sigma2_y = ssm['obs_cov', 0, 0] sigma2_mu = ssm['state_cov', 0, 0] # Basic initialization variables assert_allclose(res.predicted_state_cov[0, 0, 0], 0) assert_allclose(res.predicted_diffuse_state_cov[0, 0, 0], 1) # Output of the exact diffuse initialization, see Koopman (1997) assert_allclose(res.forecasts_error[0, 0], y1) assert_allclose(res.forecasts_error_cov[0, 0, 0], sigma2_y) assert_allclose(res.forecasts_error_diffuse_cov[0, 0, 0], 1) assert_allclose(res.kalman_gain[0, 0, 0], 1) assert_allclose(res.predicted_state[0, 1], y1) assert_allclose(res.predicted_state_cov[0, 0, 1], sigma2_y + sigma2_mu) assert_allclose(res.predicted_diffuse_state_cov[0, 0, 1], 0) # Miscellaneous assert_equal(res.nobs_diffuse, 1) class TestLocalLevelAnalyticDirect(TestLocalLevelAnalytic): @classmethod def setup_class(cls): super(TestLocalLevelAnalyticDirect, cls).setup_class(direct=True) class TestLocalLinearTrendAnalytic(object): @classmethod def setup_class(cls, **kwargs): cls.mod, cls.ssm = model_local_linear_trend(**kwargs) cls.res = cls.ssm.smooth() def test_results(self): ssm = self.ssm res = self.res y1, y2, y3 = ssm.endog[0, :3] sigma2_y = ssm['obs_cov', 0, 0] sigma2_mu, sigma2_beta = np.diagonal(ssm['state_cov']) # Basic initialization variables assert_allclose(res.predicted_state_cov[..., 0], np.zeros((2, 2))) assert_allclose(res.predicted_diffuse_state_cov[..., 0], np.eye(2)) # Output of the exact diffuse initialization, see Koopman (1997) q_mu = sigma2_mu / sigma2_y q_beta = sigma2_beta / sigma2_y assert_allclose(res.forecasts_error[0, 0], y1) assert_allclose(res.kalman_gain[:, 0, 0], [1, 0]) assert_allclose(res.predicted_state[:, 1], [y1, 0]) P2 = sigma2_y * np.array([[1 + q_mu, 0], [0, q_beta]]) assert_allclose(res.predicted_state_cov[:, :, 1], P2) assert_allclose(res.predicted_diffuse_state_cov[0, 0, 1], np.ones((2, 2))) # assert_allclose(res.kalman_gain[:, 0, 1], [2, 1]) assert_allclose(res.predicted_state[:, 2], [2 * y2 - y1, y2 - y1]) P3 = sigma2_y * np.array([[5 + 2 * q_mu + q_beta, 3 + q_mu + q_beta], [3 + q_mu + q_beta, 2 + q_mu + 2 * q_beta]]) assert_allclose(res.predicted_state_cov[:, :, 2], P3) assert_allclose(res.predicted_diffuse_state_cov[:, :, 2], np.zeros((2, 2))) # Miscellaneous assert_equal(res.nobs_diffuse, 2) class TestLocalLinearTrendAnalyticDirect(TestLocalLinearTrendAnalytic): @classmethod def setup_class(cls): super(TestLocalLinearTrendAnalyticDirect, cls).setup_class(direct=True) class TestLocalLinearTrendAnalyticMissing(TestLocalLinearTrendAnalytic): @classmethod def setup_class(cls): y1 = 10.2394 y2 = np.nan y3 = 6.123123 endog = np.r_[y1, y2, y3, [1] * 7] super(TestLocalLinearTrendAnalyticMissing, cls).setup_class( endog=endog) def test_results(self): ssm = self.ssm res = self.res y1, y2, y3 = ssm.endog[0, :3] sigma2_y = ssm['obs_cov', 0, 0] sigma2_mu, sigma2_beta = np.diagonal(ssm['state_cov']) # Test output q_mu = sigma2_mu / sigma2_y q_beta = sigma2_beta / sigma2_y a4 = [1.5 * y3 - 0.5 * y1, 0.5 * y3 - 0.5 * y1] assert_allclose(res.predicted_state[:, 3], a4) P4 = sigma2_y * np.array([ [2.5 + 1.5 * q_mu + 1.25 * q_beta, 1 + 0.5 * q_mu + 1.25 * q_beta], [1 + 0.5 * q_mu + 1.25 * q_beta, 0.5 + 0.5 * q_mu + 2.25 * q_beta]]) assert_allclose(res.predicted_state_cov[:, :, 3], P4) # Miscellaneous assert_equal(res.nobs_diffuse, 3) def test_common_level_analytic(): # Analytic test using results from Koopman (1997), section 5.3 mod = model_common_level() y11, y21 = mod.endog[:, 0] theta = mod['design', 1, 0] sigma2_mu = mod['state_cov', 0, 0] # Perform filtering res = mod.smooth() # Basic initialization variables assert_allclose(res.predicted_state_cov[..., 0], np.zeros((2, 2))) assert_allclose(res.predicted_diffuse_state_cov[..., 0], np.eye(2)) # Output of the exact diffuse initialization, see Koopman (1997) # Note: since Koopman (1997) did not apply the univariate method, # forecast errors and covariances, and the Kalman gain will not match # assert_allclose(res.forecasts_error[:, 0], [y11, y21]) # assert_allclose(res.forecasts_error_cov[:, :, 0], np.eye(2)) # F_inf1 = np.array([[1, theta], # [theta, 1 + theta**2]]) # assert_allclose(res.forecasts_error_diffuse_cov[:, :, 0], F_inf1) # K0 = np.array([[1, 0], # [-theta, 1]]) # assert_allclose(res.kalman_gain[..., 0], K0) assert_allclose(res.predicted_state[:, 1], [y11, y21 - theta * y11]) P2 = np.array([[1 + sigma2_mu, -theta], [-theta, 1 + theta**2]]) assert_allclose(res.predicted_state_cov[..., 1], P2) assert_allclose(res.predicted_diffuse_state_cov[..., 1], np.zeros((2, 2))) # Miscellaneous assert_equal(res.nobs_diffuse, 1) def test_common_level_restricted_analytic(): # Analytic test using results from Koopman (1997), section 5.3, # with the restriction mu_bar = 0 mod = model_common_level(restricted=True) y11, y21 = mod.endog[:, 0] theta = mod['design', 1, 0] sigma2_mu = mod['state_cov', 0, 0] # Perform filtering res = mod.smooth() # Basic initialization variables assert_allclose(res.predicted_state_cov[..., 0], 0) assert_allclose(res.predicted_diffuse_state_cov[..., 0], 1) # Output of the exact diffuse initialization, see Koopman (1997) phi = 1 / (1 + theta**2) # Note: since Koopman (1997) did not apply the univariate method, # forecast errors and covariances, and the Kalman gain will not match # assert_allclose(res.forecasts_error[:, 0], [y11, y21]) # assert_allclose(res.forecasts_error_cov[0, 0, 0], np.eye(2)) # F_inf1 = np.array([[1, theta], # [theta, theta**2]]) # assert_allclose(res.forecasts_error_diffuse_cov[0, 0, 0], F_inf1) # assert_allclose(res.kalman_gain[..., 0], phi * np.array([1, theta])) assert_allclose(res.predicted_state[:, 1], phi * (y11 + theta * y21)) # Note: Koopman (1997) actually has phi + sigma2_mu**0.5, but that appears # to be a typo assert_allclose(res.predicted_state_cov[..., 1], phi + sigma2_mu) assert_allclose(res.predicted_diffuse_state_cov[..., 1], 0) # Miscellaneous assert_equal(res.nobs_diffuse, 1) class CheckSSMResults(object): atol = 1e-14 rtol = 1e-07 atol_diffuse = 1e-7 rtol_diffuse = None def check_object(self, actual, desired, rtol_diffuse): # Short-circuit the test if desired is set to None (which allows us to # skip testing some objects where appropriate) if actual is None or desired is None: return # Optionally apply a different relative tolerance to the periods in the # diffuse observations. # This is especially useful when testing against approximate diffuse # initialization. By definition, the first few observations will be # quite different between the exact and approximate approach for many # quantities. # Note that the absolute tolerance is also pretty low (1e-7), mostly # for comparison against zero values in the approximate case d = None if rtol_diffuse is None: rtol_diffuse = self.rtol_diffuse if rtol_diffuse is not None: d = self.d if rtol_diffuse != np.inf: assert_allclose(actual.T[:d], desired.T[:d], rtol=rtol_diffuse, atol=self.atol_diffuse) assert_allclose(actual.T[d:], desired.T[d:], rtol=self.rtol, atol=self.atol) # - Filtered results tests ----------------------------------------------- def test_forecasts(self, rtol_diffuse=None): actual = self.results_a.forecasts desired = self.results_a.forecasts self.check_object(actual, desired, rtol_diffuse) def test_forecasts_error(self, rtol_diffuse=None): actual = self.results_a.forecasts_error desired = self.results_a.forecasts_error self.check_object(actual, desired, rtol_diffuse) def test_forecasts_error_cov(self, rtol_diffuse=None): actual = self.results_a.forecasts_error_cov desired = self.results_b.forecasts_error_cov self.check_object(actual, desired, rtol_diffuse) def test_filtered_state(self, rtol_diffuse=1e-5): # Note: we do want to check the diffuse values here, with a reduced # tolerance. See the note before the smoothed values for additional # details. actual = self.results_a.filtered_state desired = self.results_b.filtered_state self.check_object(actual, desired, rtol_diffuse) def test_filtered_state_cov(self, rtol_diffuse=None): actual = self.results_a.filtered_state_cov desired = self.results_b.filtered_state_cov self.check_object(actual, desired, rtol_diffuse) def test_predicted_state(self, rtol_diffuse=None): actual = self.results_a.predicted_state desired = self.results_b.predicted_state self.check_object(actual, desired, rtol_diffuse) def test_predicted_state_cov(self, rtol_diffuse=None): actual = self.results_a.predicted_state_cov desired = self.results_b.predicted_state_cov self.check_object(actual, desired, rtol_diffuse) def test_kalman_gain(self, rtol_diffuse=None): actual = self.results_a.kalman_gain desired = self.results_b.kalman_gain self.check_object(actual, desired, rtol_diffuse) def test_loglike(self, rtol_diffuse=None): if np.isscalar(self.results_b.llf_obs): actual = np.sum(self.results_a.llf_obs) desired = self.results_b.llf_obs assert_allclose(actual, desired) else: actual = self.results_a.llf_obs desired = self.results_b.llf_obs self.check_object(actual, desired, rtol_diffuse) # - Smoothed output tests ------------------------------------------------ # Note: for smoothed states, we do want to check some of the diffuse values # even in the approximate case, but with reduced precision. Note also that # there are cases that demonstrate the numerical error associated with the # approximate method, and so some specific tests are overridden in certain # cases, since they would not pass. def test_smoothed_state(self, rtol_diffuse=1e-5): actual = self.results_a.smoothed_state desired = self.results_b.smoothed_state self.check_object(actual, desired, rtol_diffuse) def test_smoothed_state_cov(self, rtol_diffuse=1e-5): actual = self.results_a.smoothed_state_cov desired = self.results_b.smoothed_state_cov self.check_object(actual, desired, rtol_diffuse) def test_smoothed_state_autocov(self, rtol_diffuse=None): actual = self.results_a.smoothed_state_autocov desired = self.results_b.smoothed_state_autocov self.check_object(actual, desired, rtol_diffuse) def test_smoothed_measurement_disturbance(self, rtol_diffuse=1e-5): actual = self.results_a.smoothed_measurement_disturbance desired = self.results_b.smoothed_measurement_disturbance self.check_object(actual, desired, rtol_diffuse) def test_smoothed_measurement_disturbance_cov(self, rtol_diffuse=1e-5): actual = self.results_a.smoothed_measurement_disturbance_cov desired = self.results_b.smoothed_measurement_disturbance_cov self.check_object(actual, desired, rtol_diffuse) def test_smoothed_state_disturbance(self, rtol_diffuse=1e-5): actual = self.results_a.smoothed_state_disturbance desired = self.results_b.smoothed_state_disturbance self.check_object(actual, desired, rtol_diffuse) def test_smoothed_state_disturbance_cov(self, rtol_diffuse=1e-5): actual = self.results_a.smoothed_state_disturbance_cov desired = self.results_b.smoothed_state_disturbance_cov self.check_object(actual, desired, rtol_diffuse) # - Smoothed intermediate tests ------------------------------------------ @pytest.mark.skip("This is not computed in the univariate method or " "by KFAS.") def test_smoothing_error(self, rtol_diffuse=None): actual = self.results_a.smoothing_error desired = self.results_b.smoothing_error self.check_object(actual, desired, rtol_diffuse) def test_scaled_smoothed_estimator(self, rtol_diffuse=1e-5): actual = self.results_a.scaled_smoothed_estimator desired = self.results_b.scaled_smoothed_estimator self.check_object(actual, desired, rtol_diffuse) def test_scaled_smoothed_estimator_cov(self, rtol_diffuse=1e-5): actual = self.results_a.scaled_smoothed_estimator_cov desired = self.results_b.scaled_smoothed_estimator_cov self.check_object(actual, desired, rtol_diffuse) # - Diffuse objects tests ------------------------------------------------ # Note: these cannot be checked against the approximate diffuse method. def test_forecasts_error_diffuse_cov(self, rtol_diffuse=None): actual = self.results_a.forecasts_error_diffuse_cov desired = self.results_b.forecasts_error_diffuse_cov self.check_object(actual, desired, rtol_diffuse) def test_predicted_diffuse_state_cov(self, rtol_diffuse=None): actual = self.results_a.predicted_diffuse_state_cov desired = self.results_b.predicted_diffuse_state_cov self.check_object(actual, desired, rtol_diffuse) # TODO: do something with this other than commenting it out? # We do not currently store this array # def test_kalman_gain_diffuse(self, rtol_diffuse=None): # actual = self.results_a. # desired = self.results_b. # self.check_object(actual, desired, rtol_diffuse) def test_scaled_smoothed_diffuse_estimator(self, rtol_diffuse=None): actual = self.results_a.scaled_smoothed_diffuse_estimator desired = self.results_b.scaled_smoothed_diffuse_estimator self.check_object(actual, desired, rtol_diffuse) def test_scaled_smoothed_diffuse1_estimator_cov(self, rtol_diffuse=None): actual = self.results_a.scaled_smoothed_diffuse1_estimator_cov desired = self.results_b.scaled_smoothed_diffuse1_estimator_cov self.check_object(actual, desired, rtol_diffuse) def test_scaled_smoothed_diffuse2_estimator_cov(self, rtol_diffuse=None): actual = self.results_a.scaled_smoothed_diffuse2_estimator_cov desired = self.results_b.scaled_smoothed_diffuse2_estimator_cov self.check_object(actual, desired, rtol_diffuse) # - Simulation smoother results tests ------------------------------------ @pytest.mark.xfail(reason="No sim_a attribute", raises=AttributeError, strict=True) def test_simulation_smoothed_state(self): assert_allclose( self.sim_a.simulated_state, self.sim_a.simulated_state) @pytest.mark.xfail(reason="No sim_a attribute", raises=AttributeError, strict=True) def test_simulation_smoothed_measurement_disturbance(self): assert_allclose( self.sim_a.simulated_measurement_disturbance, self.sim_a.simulated_measurement_disturbance) @pytest.mark.xfail(reason="No sim_a attribute", raises=AttributeError, strict=True) def test_simulation_smoothed_state_disturbance(self): assert_allclose( self.sim_a.simulated_state_disturbance, self.sim_a.simulated_state_disturbance) class CheckApproximateDiffuseMixin(object): """ Test the exact diffuse initialization against the approximate diffuse initialization. By definition, the first few observations will be quite different between the exact and approximate approach for many quantities, so we do not test them here. """ approximate_diffuse_variance = 1e6 @classmethod def setup_class(cls, *args, **kwargs): init_approx = kwargs.pop('init_approx', None) super(CheckApproximateDiffuseMixin, cls).setup_class(*args, **kwargs) # Get the approximate diffuse results kappa = cls.approximate_diffuse_variance if init_approx is None: init_approx = Initialization( cls.ssm.k_states, 'approximate_diffuse', approximate_diffuse_variance=kappa) cls.ssm.initialize(init_approx) cls.results_b = cls.ssm.smooth() # Instruct the tests not to test against the first d values cls.rtol_diffuse = np.inf def test_initialization_approx(self): kappa = self.approximate_diffuse_variance assert_allclose(self.results_b.initial_state_cov, np.eye(self.ssm.k_states) * kappa) assert_equal(self.results_b.initial_diffuse_state_cov, None) class CheckKFASMixin(object): """ Test against values from KFAS """ @classmethod def setup_class(cls, *args, **kwargs): kwargs.setdefault('filter_univariate', True) super(CheckKFASMixin, cls).setup_class(*args, **kwargs) # Get the KFAS results objects cls.results_b = kfas_helpers.parse(cls.results_path, cls.ssm) # Set some attributes that KFAS does not compute cls.results_b.smoothed_state_autocov = None # Remove the Kalman gain matrix since KFAS computes it using the # non-univariate method cls.results_b.kalman_gain = None # Remove the filtered_state_cov since KFAS v1.3.1 has a bug for these # matrices (they are not even symmetric) cls.results_b.filtered_state_cov = None # KFAS v1.3.1 seems to compute the loglikelihood incorrectly, so we # correct for it here # (we need to add back in the constant term for all of the non-missing # diffuse observations for which Finf is nonsingular) Finf = cls.results_b.forecasts_error_diffuse_cov.T Finf_nonsingular_obs = np.c_[[np.diag(Finf_t) for Finf_t in Finf]] > 0 nonmissing = ~np.isnan(cls.ssm.endog).T constant = (-0.5 * np.log(2 * np.pi) * (Finf_nonsingular_obs * nonmissing).sum(axis=1)) cls.results_b.llf_obs += constant[:cls.results_a.nobs_diffuse].sum() # - VAR(1) ------------------------------------------------------------------- class CheckVAR1(CheckSSMResults): @classmethod def setup_class(cls, **kwargs): filter_univariate = kwargs.pop('filter_univariate', False) cls.mod, cls.ssm = model_var1(**kwargs) if filter_univariate: cls.ssm.filter_univariate = True cls.results_a = cls.ssm.smooth() cls.d = cls.results_a.nobs_diffuse def test_nobs_diffuse(self): assert_allclose(self.d, 1) def test_initialization(self): assert_allclose(self.results_a.initial_state_cov, 0) assert_allclose(self.results_a.initial_diffuse_state_cov, np.eye(2)) class TestVAR1_Approx(CheckApproximateDiffuseMixin, CheckVAR1): pass class TestVAR1_KFAS(CheckKFASMixin, CheckVAR1): results_path = os.path.join( current_path, 'results', 'results_exact_initial_var1_R.csv') # - VAR(1) + Measurement error ----------------------------------------------- class CheckVAR1MeasurementError(CheckVAR1): @classmethod def setup_class(cls, **kwargs): kwargs['measurement_error'] = True super(CheckVAR1MeasurementError, cls).setup_class(**kwargs) class TestVAR1MeasurementError_Approx(CheckApproximateDiffuseMixin, CheckVAR1MeasurementError): # Note: somewhat fragile, we need to increase the approximate variance to # 1e9 for the tests to pass at the appropriate level of precision, but # we cannot increase too much more than this because then we start get # numerical errors (e.g. 1e10 is fine but 1e11 does not pass) approximate_diffuse_variance = 1e9 def test_smoothed_measurement_disturbance_cov(self, rtol_diffuse=None): # Note: this test would fail here with most rtol, because # this is an example where the numerical errors associated with the # approximate method result in noticeable errors # term: (x is the exact method, y is the approximate method) # x: array([[[3.355072, 0. ], # [0. , 4.221227]]]) # y: array([[[ 3.355072, -0.600856], # [-0.600856, 4.221227]]]) super(TestVAR1MeasurementError_Approx, self).test_smoothed_measurement_disturbance_cov( rtol_diffuse=rtol_diffuse) class TestVAR1MeasurementError_KFAS(CheckKFASMixin, CheckVAR1MeasurementError): results_path = os.path.join( current_path, 'results', 'results_exact_initial_var1_measurement_error_R.csv') # - VAR(1) + Missing data ---------------------------------------------------- class CheckVAR1Missing(CheckVAR1): @classmethod def setup_class(cls, **kwargs): levels = macrodata[['realgdp', 'realcons']] endog = np.log(levels).iloc[:21].diff().iloc[1:] * 400 endog.iloc[0:5, 0] = np.nan endog.iloc[8:12, :] = np.nan kwargs['endog'] = endog super(CheckVAR1Missing, cls).setup_class(**kwargs) def test_nobs_diffuse(self): assert_allclose(self.d, 2) class TestVAR1Missing_Approx(CheckApproximateDiffuseMixin, CheckVAR1Missing): # Note: somewhat fragile, we need to increase the approximate variance to # 1e10 for the tests to pass at the appropriate level of precision, but # we cannot increase it any more than this because then we start get # numerical errors (e.g. 1e11 does not pass) approximate_diffuse_variance = 1e10 def test_smoothed_state_cov(self, rtol_diffuse=None): # Note: this test would fail here with essentially any rtol, because # this is an example where the numerical errors associated with the # approximate method result in extreme errors: here a negative variance # term: (x is the exact method, y is the approximate method) # x: array([[[ 5.601218e+01, 0.000000e+00], # [ 0.000000e+00, 0.000000e+00]], # ... # y: array([[[-12.083676, 0. ], # [ 0. , 0. ]], super(TestVAR1Missing_Approx, self).test_smoothed_state_cov( rtol_diffuse=rtol_diffuse) class TestVAR1Missing_KFAS(CheckKFASMixin, CheckVAR1Missing): results_path = os.path.join( current_path, 'results', 'results_exact_initial_var1_missing_R.csv') def test_forecasts_error_cov(self): # TODO: fails for the general version of forecasts_error_cov because # (1) the routines in kalman_filter.py fill in values for all variables # regardless of missing status and also it uses the multivariate # approach rather than the univariate approach, and (2) KFAS fills in # values for all variables regardless of missing status (but does use # the univariate method). # Here we remove the off-diagonal elements so that the test passes (but # note that this is **not** a general solution since it depends on # which variables are missing). bak = self.results_a.forecasts_error_cov[:] self.results_a.forecasts_error_cov[0, 1, :] = 0 self.results_a.forecasts_error_cov[1, 0, :] = 0 super(TestVAR1Missing_KFAS, self).test_forecasts_error_cov() self.results_a.forecasts_error_cov = bak # - VAR(1) + Mixed stationary / diffuse initialization ----------------------- class CheckVAR1Mixed(CheckVAR1): @classmethod def setup_class(cls, **kwargs): k_states = 2 init = Initialization(k_states) init.set(0, 'diffuse') init.set(1, 'stationary') if kwargs.pop('approx', False): init_approx = Initialization(k_states) init_approx.set(0, 'approximate_diffuse') init_approx.set(1, 'stationary') kwargs['init_approx'] = init_approx super(CheckVAR1Mixed, cls).setup_class(init=init, **kwargs) def test_nobs_diffuse(self): assert_allclose(self.d, 1) def test_initialization(self): stationary_init = 3.5714285714285716 assert_allclose(self.results_a.initial_state_cov, np.diag([0, stationary_init])) assert_allclose(self.results_a.initial_diffuse_state_cov, np.diag([1, 0])) class TestVAR1Mixed_Approx(CheckVAR1Mixed, CheckApproximateDiffuseMixin, CheckVAR1): @classmethod def setup_class(cls, **kwargs): kwargs['approx'] = True super(TestVAR1Mixed_Approx, cls).setup_class(**kwargs) def test_initialization_approx(self): stationary_init = 3.5714285714285716 kappa = self.approximate_diffuse_variance assert_allclose(self.results_b.initial_state_cov, np.diag([kappa, stationary_init])) assert_equal(self.results_b.initial_diffuse_state_cov, None) class TestVAR1Mixed_KFAS(CheckVAR1Mixed, CheckKFASMixin, CheckVAR1): # TODO: fails results_path = os.path.join( current_path, 'results', 'results_exact_initial_var1_mixed_R.csv') # TODO: KFAS disagrees for the diffuse observations for all of these # states, but it appears that they have a bug (e.g. since the approximate # diffuse case agrees with us), so we should double-check against a third # package (RATS?) def test_predicted_state(self): super(TestVAR1Mixed_KFAS, self).test_predicted_state( rtol_diffuse=np.inf) def test_filtered_state(self): super(TestVAR1Mixed_KFAS, self).test_filtered_state( rtol_diffuse=np.inf) def test_smoothed_state(self): super(TestVAR1Mixed_KFAS, self).test_smoothed_state( rtol_diffuse=np.inf) # - DFM ---------------------------------------------------------------------- class CheckDFM(CheckSSMResults): @classmethod def setup_class(cls, **kwargs): filter_univariate = kwargs.pop('filter_univariate', False) cls.mod, cls.ssm = model_dfm(**kwargs) if filter_univariate: cls.ssm.filter_univariate = True cls.results_a = cls.ssm.smooth() cls.d = cls.results_a.nobs_diffuse def test_nobs_diffuse(self): assert_allclose(self.d, 2) def test_initialization(self): assert_allclose(self.results_a.initial_state_cov, 0) assert_allclose(self.results_a.initial_diffuse_state_cov, np.eye(2)) class TestDFM_Approx(CheckApproximateDiffuseMixin, CheckDFM): # Note: somewhat fragile, we need to increase the approximate variance to # 5e10 for the tests to pass at the appropriate level of precision, but # we cannot increase it too much more than this because then we start get # numerical errors (e.g. 1e11 works but 1e12 does not pass) approximate_diffuse_variance = 5e10 class TestDFM_KFAS(CheckKFASMixin, CheckDFM): results_path = os.path.join( current_path, 'results', 'results_exact_initial_dfm_R.csv') # TODO: KFAS disagrees for the diffuse observations for all of these # states, but it appears that they have a bug (e.g. since the approximate # diffuse case agrees with us), so we should double-check against a third # package (RATS?) def test_predicted_state(self): super(TestDFM_KFAS, self).test_predicted_state(rtol_diffuse=np.inf) def test_filtered_state(self): super(TestDFM_KFAS, self).test_filtered_state(rtol_diffuse=np.inf) def test_smoothed_state(self): super(TestDFM_KFAS, self).test_smoothed_state(rtol_diffuse=np.inf) # - DFM + Collapsed ---------------------------------------------------------- class CheckDFMCollapsed(CheckSSMResults): @classmethod def setup_class(cls, **kwargs): filter_univariate = kwargs.pop('filter_univariate', True) cls.mod, cls.ssm = model_dfm(factor_order=1, **kwargs) if filter_univariate: cls.ssm.filter_univariate = True cls.ssm.filter_collapsed = True cls.results_a = cls.ssm.smooth() cls.d = cls.results_a.nobs_diffuse def test_nobs_diffuse(self): assert_allclose(self.d, 1) def test_initialization(self): assert_allclose(self.results_a.initial_state_cov, 0) assert_allclose(self.results_a.initial_diffuse_state_cov, np.eye(1)) class TestDFMCollapsed_Approx(CheckApproximateDiffuseMixin, CheckDFMCollapsed): # Note: somewhat fragile, we need to increase the approximate variance to # 1e9 for the tests to pass at the appropriate level of precision, but # we cannot increase it too much more than this because then we start get # numerical errors (e.g. 1e10 does not pass) approximate_diffuse_variance = 1e9 # FIXME: do not leave this commented-out # Note: we cannot test against KFAS, since it does not support collapsed # filtering # class TestDFMCollapsed_KFAS(CheckKFASMixin, TestDFMCollapsed): # results_path = os.path.join( # current_path, 'results', '') # - TODO: additional tests --------------------------------------------------- # - Local level model, above # - Local linear trend model, above # - Common level model, above # - multivariate test with non-diagonal observation covariance matrix # - simulation smoother @pytest.mark.xfail def test_irrelevant_state(): # This test records a case in which exact diffuse initialization leads to # numerical problems, because the existence of an irrelevant state # initialized as diffuse means that there is never a transition to the # usual Kalman filter. endog = macrodata.infl spec = { 'freq_seasonal': [{'period': 8, 'harmonics': 6}, {'period': 36, 'harmonics': 6}] } # Approximate diffuse version mod = UnobservedComponents(endog, 'llevel', **spec) mod.ssm.initialization = Initialization(mod.k_states, 'approximate_diffuse') res = mod.smooth([3.4, 7.2, 0.01, 0.01]) # Exact diffuse version mod2 = UnobservedComponents(endog, 'llevel', **spec) mod2.ssm.filter_univariate = True mod2.ssm.initialization = Initialization(mod2.k_states, 'diffuse') res2 = mod2.smooth([3.4, 7.2, 0.01, 0.01]) # Check that e.g. the filtered state for the level is equal assert_allclose(res.filtered_state[0, 25:], res2.filtered_state[0, 25:], atol=1e-5) def test_nondiagonal_obs_cov(reset_randomstate): # All diffuse handling is done using the univariate filtering approach, # even if the usual multivariate filtering method is being used for the # other periods. This means that if the observation covariance matrix is # not a diagonal matrix during the diffuse periods, we need to transform # the observation equation as we would if we were using the univariate # filter. mod = TVSS(np.zeros((10, 2))) res1 = mod.smooth([]) mod.ssm.filter_univariate = True res2 = mod.smooth([]) atol = 0.002 if PLATFORM_WIN else 1e-5 rtol = 0.002 if PLATFORM_WIN else 1e-4 # Here we'll just test a few values assert_allclose(res1.llf, res2.llf, rtol=rtol, atol=atol) assert_allclose(res1.forecasts[0], res2.forecasts[0], rtol=rtol, atol=atol) assert_allclose(res1.filtered_state, res2.filtered_state, rtol=rtol, atol=atol) assert_allclose(res1.filtered_state_cov, res2.filtered_state_cov, rtol=rtol, atol=atol) assert_allclose(res1.smoothed_state, res2.smoothed_state, rtol=rtol, atol=atol) assert_allclose(res1.smoothed_state_cov, res2.smoothed_state_cov, rtol=rtol, atol=atol) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_exponential_smoothing.py000066400000000000000000001053031400612667500306240ustar00rootroot00000000000000r""" Tests for exponential smoothing models Notes ----- These tests are primarily against the `fpp` functions `ses`, `holt`, and `hw` and against the `forecast` function `ets`. There are a couple of details about how these packages work that are relevant for the tests: Trend smoothing parameterization ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Note that `fpp` and `ets` use different parameterizations for the trend smoothing parameter. Our implementation in `statespace.exponential_smoothing` uses the same parameterization as `ets`. The `fpp` package follows Holt's recursive equations directly, in which the trend updating is: .. math:: b_t = \beta^* (\ell_t - \ell_{t-1}) + (1 - \beta^*) b_{t-1} In our implementation, state updating is done by the Kalman filter, in which the trend updating equation is: .. math:: b_{t|t} = b_{t|t-1} + \beta (y_t - l_{t|t-1}) by rewriting the Kalman updating equation in the form of Holt's method, we find that we must have :math:`\beta = \beta^* \alpha`. This is the same parameterization used by `ets`, which does not use the Kalman fitler but instead uses an innovations state space framework. Loglikelihood ^^^^^^^^^^^^^ The `ets` package has a `loglik` output value, but it does not compute the loglikelihood itself, but rather a version without the constant parameters. It appears to compute: .. math:: -\frac{n}{2} \log \left (\sum_{t=1}^n \varepsilon_t^2 \right) while the loglikelihood is: .. math:: -\frac{n}{2} \log \left (2 \pi e \frac{1}{n} \sum_{t=1}^n \varepsilon_t^2 \right) See Hyndman et al. (2008), pages 68-69. In particular, the former equation - which is the value returned by `ets` - is -0.5 times equation (5.3), since for these models we have :math:`r(x_{t-1}) = 1`. The latter equation is the log of the likelihood formula given at the top of page 69. Confidence intervals ^^^^^^^^^^^^^^^^^^^^ The range of the confidence intervals depends on the estimated variance, sigma^2. In our default, we concentrate this variance out of the loglikelihood function, meaning that the default is to use the maximum likelihood estimate for forecasting purposes. forecast::ets uses a degree-of-freedom-corrected estimate of sigma^2, and so our default confidence bands will differ. To correct for this in the tests, we set `concentrate_scale=False` and use the estimated variance from forecast::ets. TODO: may want to add a parameter allowing specification of the variance estimator. Author: Chad Fulton License: BSD-3 """ from __future__ import division, absolute_import, print_function import numpy as np import pandas as pd import os import pytest from numpy.testing import assert_, assert_equal, assert_allclose from statsmodels.tsa.statespace.exponential_smoothing import ( ExponentialSmoothing) current_path = os.path.dirname(os.path.abspath(__file__)) results_path = os.path.join(current_path, 'results') params_path = os.path.join(results_path, 'exponential_smoothing_params.csv') predict_path = os.path.join(results_path, 'exponential_smoothing_predict.csv') states_path = os.path.join(results_path, 'exponential_smoothing_states.csv') results_params = pd.read_csv(params_path, index_col=[0]) results_predict = pd.read_csv(predict_path, index_col=[0]) results_states = pd.read_csv(states_path, index_col=[0]) # R, fpp: oildata <- window(oil,start=1996,end=2007) oildata = pd.Series([ 446.6565229, 454.4733065, 455.6629740, 423.6322388, 456.2713279, 440.5880501, 425.3325201, 485.1494479, 506.0481621, 526.7919833, 514.2688890, 494.2110193], index=pd.period_range(start='1996', end='2007', freq='A')) # R, fpp: air <- window(ausair,start=1990,end=2004) air = pd.Series([ 17.553400, 21.860100, 23.886600, 26.929300, 26.888500, 28.831400, 30.075100, 30.953500, 30.185700, 31.579700, 32.577569, 33.477398, 39.021581, 41.386432, 41.596552], index=pd.period_range(start='1990', end='2004', freq='A')) # R, fpp: aust <- window(austourists,start=2005) aust = pd.Series([ 41.727458, 24.041850, 32.328103, 37.328708, 46.213153, 29.346326, 36.482910, 42.977719, 48.901525, 31.180221, 37.717881, 40.420211, 51.206863, 31.887228, 40.978263, 43.772491, 55.558567, 33.850915, 42.076383, 45.642292, 59.766780, 35.191877, 44.319737, 47.913736], index=pd.period_range(start='2005Q1', end='2010Q4', freq='Q')) class CheckExponentialSmoothing(object): @classmethod def setup_class(cls, name, res): cls.name = name cls.res = res cls.nobs = res.nobs cls.nforecast = len(results_predict['%s_mean' % cls.name]) - cls.nobs cls.forecast = res.get_forecast(cls.nforecast) def test_fitted(self): assert_allclose(self.res.fittedvalues, results_predict['%s_mean' % self.name][:self.nobs]) def test_output(self): # There are two types of output, depending on some internal switch of # fpp::ses that appears to depend on if parameters are estimated. If # they are estimated, then llf and mse are available but sse is not. # Otherwise, sse is available and the other two aren't. has_llf = ~np.isnan(results_params[self.name]['llf']) if has_llf: assert_allclose(self.res.mse, results_params[self.name]['mse']) # As noted in the file docstring, `ets` does not return the actual # loglikelihood, but instead a transformation of it. Here we # compute that transformation based on our results, so as to # compare with the `ets` output. actual = -0.5 * self.nobs * np.log(np.sum(self.res.resid**2)) assert_allclose(actual, results_params[self.name]['llf']) else: assert_allclose(self.res.sse, results_params[self.name]['sse']) def test_forecasts(self): # Forecast mean assert_allclose(self.forecast.predicted_mean, results_predict['%s_mean' % self.name][self.nobs:]) def test_conf_int(self): # Forecast confidence intervals ci_95 = self.forecast.conf_int(alpha=0.05) assert_allclose(ci_95['lower y'], results_predict['%s_lower' % self.name][self.nobs:]) assert_allclose(ci_95['upper y'], results_predict['%s_upper' % self.name][self.nobs:]) def test_initial_states(self): mask = results_states.columns.str.startswith(self.name) desired = results_states.loc[:, mask].dropna().iloc[0] assert_allclose(self.res.initial_state.iloc[0], desired) def test_states(self): mask = results_states.columns.str.startswith(self.name) desired = results_states.loc[:, mask].dropna().iloc[1:] assert_allclose(self.res.filtered_state[1:].T, desired) def test_misc(self): mod = self.res.model assert_equal(mod.k_params, len(mod.start_params)) assert_equal(mod.k_params, len(mod.param_names)) # Smoke test for summary creation self.res.summary() class TestSESFPPFixed02(CheckExponentialSmoothing): @classmethod def setup_class(cls): # Test simple exponential smoothing (FPP: 7.1) against fpp::ses, with # a fixed coefficient 0.2 and simple initialization mod = ExponentialSmoothing(oildata, initialization_method='simple') res = mod.filter([results_params['oil_fpp1']['alpha']]) super().setup_class('oil_fpp1', res) class TestSESFPPFixed06(CheckExponentialSmoothing): @classmethod def setup_class(cls): # Test simple exponential smoothing (FPP: 7.1) against fpp::ses, with # a fixed coefficient 0.6 and simple initialization mod = ExponentialSmoothing(oildata, initialization_method='simple') res = mod.filter([results_params['oil_fpp2']['alpha']]) super().setup_class('oil_fpp2', res) class TestSESFPPEstimated(CheckExponentialSmoothing): @classmethod def setup_class(cls): # Test simple exponential smoothing (FPP: 7.1) against fpp::ses, with # estimated coefficients mod = ExponentialSmoothing(oildata, initialization_method='estimated', concentrate_scale=False) res = mod.filter([results_params['oil_fpp3']['alpha'], results_params['oil_fpp3']['sigma2'], results_params['oil_fpp3']['l0']]) super().setup_class('oil_fpp3', res) class TestSESETSEstimated(CheckExponentialSmoothing): @classmethod def setup_class(cls): # Test simple exponential smoothing (FPP: 7.1) against forecast::ets, # with estimated coefficients mod = ExponentialSmoothing(oildata, initialization_method='estimated', concentrate_scale=False) res = mod.filter([results_params['oil_ets']['alpha'], results_params['oil_ets']['sigma2'], results_params['oil_ets']['l0']]) super().setup_class('oil_ets', res) def test_mle_estimates(self): # Test that our fitted coefficients are at least as good as those from # `ets` mle_res = self.res.model.fit(disp=0) assert_(self.res.llf <= mle_res.llf) class TestHoltFPPFixed(CheckExponentialSmoothing): @classmethod def setup_class(cls): # Test Holt's linear trend method (FPP: 7.2) against fpp::holt, # with fixed coefficients and simple initialization mod = ExponentialSmoothing(air, trend=True, concentrate_scale=False, initialization_method='simple') # alpha, beta^* params = [results_params['air_fpp1']['alpha'], results_params['air_fpp1']['beta_star'], results_params['air_fpp1']['sigma2']] # beta = alpha * beta^* params[1] = params[0] * params[1] res = mod.filter(params) super().setup_class('air_fpp1', res) def test_conf_int(self): # Note: cannot test against the output of the `holt` command in this # case, as `holt` seems to have a bug: while it is parametrized in # terms of `beta_star`, its confidence intervals are computed as though # beta_star was actually beta = alpha * beta_star. # Instead, we'll compare against a direct computation as in # Hyndman et al. (2008) equation (6.1). j = np.arange(1, 14) alpha, beta, sigma2 = self.res.params c = np.r_[0, alpha + beta * j] se = (sigma2 * (1 + np.cumsum(c**2)))**0.5 assert_allclose(self.forecast.se_mean, se) class TestHoltDampedFPPEstimated(CheckExponentialSmoothing): @classmethod def setup_class(cls): # Test Holt's linear trend method (FPP: 7.2) with a damped trend # against fpp::holt, with estimated coefficients mod = ExponentialSmoothing(air, trend=True, damped_trend=True, concentrate_scale=False) params = [results_params['air_fpp2']['alpha'], results_params['air_fpp2']['beta'], results_params['air_fpp2']['phi'], results_params['air_fpp2']['sigma2'], results_params['air_fpp2']['l0'], results_params['air_fpp2']['b0']] res = mod.filter(params) super().setup_class('air_fpp2', res) class TestHoltDampedETSEstimated(CheckExponentialSmoothing): @classmethod def setup_class(cls): # Test Holt's linear trend method (FPP: 7.2) with a damped trend # against forecast::ets, with estimated coefficients mod = ExponentialSmoothing(air, trend=True, damped_trend=True, concentrate_scale=False) params = [results_params['air_ets']['alpha'], results_params['air_ets']['beta'], results_params['air_ets']['phi'], results_params['air_ets']['sigma2'], results_params['air_ets']['l0'], results_params['air_ets']['b0']] res = mod.filter(params) super().setup_class('air_ets', res) def test_mle_estimates(self): # Test that our fitted coefficients are at least as good as those from # `ets` mle_res = self.res.model.fit(disp=0) assert_(self.res.llf <= mle_res.llf) class TestHoltWintersFPPEstimated(CheckExponentialSmoothing): @classmethod def setup_class(cls): # Test Holt-Winters seasonal method (FPP: 7.5) against fpp::hw, # with estimated coefficients mod = ExponentialSmoothing(aust, trend=True, seasonal=4, concentrate_scale=False) params = np.r_[ results_params['aust_fpp1']['alpha'], results_params['aust_fpp1']['beta'], results_params['aust_fpp1']['gamma'], results_params['aust_fpp1']['sigma2'], results_params['aust_fpp1']['l0'], results_params['aust_fpp1']['b0'], results_params['aust_fpp1']['s0_0'], results_params['aust_fpp1']['s0_1'], results_params['aust_fpp1']['s0_2']] res = mod.filter(params) super().setup_class('aust_fpp1', res) class TestHoltWintersETSEstimated(CheckExponentialSmoothing): @classmethod def setup_class(cls): # Test Holt-Winters seasonal method (FPP: 7.5) against forecast::ets, # with estimated coefficients mod = ExponentialSmoothing(aust, trend=True, seasonal=4, concentrate_scale=False) params = np.r_[ results_params['aust_ets1']['alpha'], results_params['aust_ets1']['beta'], results_params['aust_ets1']['gamma'], results_params['aust_ets1']['sigma2'], results_params['aust_ets1']['l0'], results_params['aust_ets1']['b0'], results_params['aust_ets1']['s0_0'], results_params['aust_ets1']['s0_1'], results_params['aust_ets1']['s0_2']] res = mod.filter(params) super().setup_class('aust_ets1', res) class TestHoltWintersDampedETSEstimated(CheckExponentialSmoothing): @classmethod def setup_class(cls): # Test Holt-Winters seasonal method (FPP: 7.5) with a damped trend # against forecast::ets, with estimated coefficients mod = ExponentialSmoothing(aust, trend=True, damped_trend=True, seasonal=4, concentrate_scale=False) params = np.r_[ results_params['aust_ets2']['alpha'], results_params['aust_ets2']['beta'], results_params['aust_ets2']['gamma'], results_params['aust_ets2']['phi'], results_params['aust_ets2']['sigma2'], results_params['aust_ets2']['l0'], results_params['aust_ets2']['b0'], results_params['aust_ets2']['s0_0'], results_params['aust_ets2']['s0_1'], results_params['aust_ets2']['s0_2']] res = mod.filter(params) super().setup_class('aust_ets2', res) def test_mle_estimates(self): # Test that our fitted coefficients are at least as good as those from # `ets` mle_res = self.res.model.fit(disp=0, maxiter=100) assert_(self.res.llf <= mle_res.llf) class TestHoltWintersNoTrendETSEstimated(CheckExponentialSmoothing): @classmethod def setup_class(cls): # Test Holt-Winters seasonal method (FPP: 7.5) with no trend # against forecast::ets, with estimated coefficients mod = ExponentialSmoothing(aust, seasonal=4, concentrate_scale=False) params = np.r_[ results_params['aust_ets3']['alpha'], results_params['aust_ets3']['gamma'], results_params['aust_ets3']['sigma2'], results_params['aust_ets3']['l0'], results_params['aust_ets3']['s0_0'], results_params['aust_ets3']['s0_1'], results_params['aust_ets3']['s0_2']] res = mod.filter(params) super().setup_class('aust_ets3', res) def test_conf_int(self): # `forecast::ets` seems to have a bug in this case related to the # seasonal component of the standard error computation. From # Hyndman et al. (2008) Table 6.2, "d_{j,m} = 1 if j = 0 (mod m) and # 0 otherwise". This implies that the seasonal effect on the standard # error computation should only start when the j = m (here m = 4) term # is included in the standard error computation, which happens at the # fifth forecast (h=5). However, `ets` is starting it at the fourth # forecast (h=4). # Instead, we'll compare against a direct computation as in # Hyndman et al. (2008) equation (6.1). j = np.arange(1, 5) alpha, gamma, sigma2 = self.res.params[:3] c = np.r_[0, alpha + gamma * ((j % 4) == 0).astype(int)] se = (sigma2 * (1 + np.cumsum(c**2)))**0.5 assert_allclose(self.forecast.se_mean, se) def test_mle_estimates(self): # Test that our fitted coefficients are at least as good as those from # `ets` mle_res = self.res.model.fit(disp=0, maxiter=100) assert_(self.res.llf <= mle_res.llf) class CheckKnownInitialization(object): @classmethod def setup_class(cls, mod, start_params): # Base model, with estimated initialization # Note: we use start_params here that are pretty close to MLE so that # tests run quicker. cls.mod = mod cls.start_params = start_params endog = mod.data.orig_endog cls.res = cls.mod.fit(start_params, disp=0, maxiter=100) # Get the estimated initial parameters cls.initial_level = cls.res.params.get('initial_level', None) cls.initial_trend = cls.res.params.get('initial_trend', None) cls.initial_seasonal = None if cls.mod.seasonal: cls.initial_seasonal = [ cls.res.params['initial_seasonal.%d' % i] for i in range(cls.mod.seasonal_periods - 1)] # Get the estimated parameters cls.params = cls.res.params[:'initial_level'].drop('initial_level') cls.init_params = cls.res.params['initial_level':] # Create a model with the given known initialization cls.known_mod = cls.mod.clone(endog, initialization_method='known', initial_level=cls.initial_level, initial_trend=cls.initial_trend, initial_seasonal=cls.initial_seasonal) def test_given_params(self): # Test fixed initialization with given parameters # And filter with the given other parameters known_res = self.known_mod.filter(self.params) assert_allclose(known_res.llf, self.res.llf) assert_allclose(known_res.predicted_state, self.res.predicted_state) assert_allclose(known_res.predicted_state_cov, self.res.predicted_state_cov) assert_allclose(known_res.filtered_state, self.res.filtered_state) def test_estimated_params(self): # Now fit the original model with a fixed initial_level and make sure # that it gives the same result as the fitted second model fit_res1 = self.mod.fit_constrained( self.init_params.to_dict(), start_params=self.start_params, includes_fixed=True, disp=0) fit_res2 = self.known_mod.fit( self.start_params[:'initial_level'].drop('initial_level'), disp=0) assert_allclose( fit_res1.params[:'initial_level'].drop('initial_level'), fit_res2.params) assert_allclose(fit_res1.llf, fit_res2.llf) assert_allclose(fit_res1.scale, fit_res2.scale) assert_allclose(fit_res1.predicted_state, fit_res2.predicted_state) assert_allclose(fit_res1.predicted_state_cov, fit_res2.predicted_state_cov) assert_allclose(fit_res1.filtered_state, fit_res2.filtered_state) class TestSESKnownInitialization(CheckKnownInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(oildata) start_params = pd.Series([0.8, 440.], index=mod.param_names) super().setup_class(mod, start_params) class TestHoltKnownInitialization(CheckKnownInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(air, trend=True) start_params = pd.Series( [0.95, 0.0005, 15., 1.5], index=mod.param_names) super().setup_class(mod, start_params) class TestHoltDampedKnownInitialization(CheckKnownInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(air, trend=True, damped_trend=True) start_params = pd.Series( [0.9, 0.0005, 0.9, 14., 2.], index=mod.param_names) super().setup_class(mod, start_params) class TestHoltWintersKnownInitialization(CheckKnownInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(aust, trend=True, seasonal=4) start_params = pd.Series( [0.0005, 0.0004, 0.5, 33., 0.4, 2.5, -2., -9.], index=mod.param_names) super().setup_class(mod, start_params) class TestHoltWintersDampedKnownInitialization(CheckKnownInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(air, trend=True, damped_trend=True, seasonal=4) start_params = pd.Series( [0.0005, 0.0004, 0.0005, 0.95, 17.0, 1.5, -0.2, 0.1, 0.4], index=mod.param_names) super().setup_class(mod, start_params) class TestHoltWintersNoTrendKnownInitialization(CheckKnownInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(aust, seasonal=4) start_params = pd.Series( [0.5, 0.49, 30., 2., -2, -9], index=mod.param_names) super().setup_class(mod, start_params) class CheckHeuristicInitialization(object): @classmethod def setup_class(cls, mod): cls.mod = mod cls.res = cls.mod.filter(cls.mod.start_params) # Save the heuristic values init_heuristic = np.r_[cls.mod._initial_level] if cls.mod.trend: init_heuristic = np.r_[init_heuristic, cls.mod._initial_trend] if cls.mod.seasonal: init_heuristic = np.r_[init_heuristic, cls.mod._initial_seasonal] cls.init_heuristic = init_heuristic # Create a model with the given known initialization endog = cls.mod.data.orig_endog initial_seasonal = cls.mod._initial_seasonal if initial_seasonal is not None: initial_seasonal = initial_seasonal[:-1] cls.known_mod = cls.mod.clone(endog, initialization_method='known', initial_level=cls.mod._initial_level, initial_trend=cls.mod._initial_trend, initial_seasonal=initial_seasonal) cls.known_res = cls.mod.filter(cls.mod.start_params) class TestSESHeuristicInitialization(CheckHeuristicInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(oildata, initialization_method='heuristic') super().setup_class(mod) def test_heuristic(self): # See Hyndman et al. (2008), section 2.6 nobs = 10 exog = np.c_[np.ones(nobs), np.arange(nobs) + 1] desired = np.linalg.pinv(exog).dot(oildata.values[:nobs])[0] assert_allclose(self.init_heuristic, desired) class TestHoltHeuristicInitialization(CheckHeuristicInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(air, trend=True, initialization_method='heuristic') super().setup_class(mod) def test_heuristic(self): # See Hyndman et al. (2008), section 2.6 nobs = 10 exog = np.c_[np.ones(nobs), np.arange(nobs) + 1] desired = np.linalg.pinv(exog).dot(air.values[:nobs]) assert_allclose(self.init_heuristic, desired) class TestHoltDampedHeuristicInitialization(CheckHeuristicInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(air, trend=True, damped_trend=True, initialization_method='heuristic') super().setup_class(mod) def test_heuristic(self): TestHoltHeuristicInitialization.test_heuristic(self) class TestHoltWintersHeuristicInitialization(CheckHeuristicInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(aust, trend=True, seasonal=4, initialization_method='heuristic') super().setup_class(mod) def test_heuristic(self): # See Hyndman et al. (2008), section 2.6 # Get trend from 2x4 MA filter trend = (aust[:20].rolling(4).mean() .rolling(2).mean().shift(-2).dropna()) nobs = 10 exog = np.c_[np.ones(nobs), np.arange(nobs) + 1] desired = np.linalg.pinv(exog).dot(trend[:nobs]) if not self.mod.trend: desired = desired[:1] # Get seasonal initial states detrended = aust - trend initial_seasonal = np.nanmean(detrended.values.reshape(6, 4), axis=0) desired = np.r_[desired, initial_seasonal - np.mean(initial_seasonal)] assert_allclose(self.init_heuristic, desired) class TestHoltWintersDampedHeuristicInitialization( CheckHeuristicInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(aust, trend=True, damped_trend=True, seasonal=4, initialization_method='heuristic') super().setup_class(mod) def test_heuristic(self): TestHoltWintersHeuristicInitialization.test_heuristic(self) class TestHoltWintersNoTrendHeuristicInitialization( CheckHeuristicInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(aust, seasonal=4, initialization_method='heuristic') super().setup_class(mod) def test_heuristic(self): TestHoltWintersHeuristicInitialization.test_heuristic(self) def test_concentrated_initialization(): # Compare a model where initialization is concentrated out versus # numarical maximum likelihood estimation mod1 = ExponentialSmoothing(oildata, initialization_method='concentrated') mod2 = ExponentialSmoothing(oildata) # First, fix the other parameters at a particular value res1 = mod1.filter([0.1]) res2 = mod2.fit_constrained({'smoothing_level': 0.1}, disp=0) # Alternatively, estimate the remaining parameters res1 = mod1.fit(disp=0) res2 = mod2.fit(disp=0) assert_allclose(res1.llf, res2.llf) assert_allclose(res1.initial_state, res2.initial_state, rtol=1e-5) class CheckConcentratedInitialization(object): @classmethod def setup_class(cls, mod, start_params=None, atol=0, rtol=1e-7): # Note: because of the different computations methods (linear # regression in the concentrated case versus numerical MLE in the base # case), we have relatively large tolerances for these tests, # particularly when the other parameters are estimated, and we specify # start parameters relatively close to the MLE to avoid problems with # the methods finding different local maxima. cls.start_params = start_params cls.atol = atol cls.rtol = rtol # Compare a model where initialization is concentrated out versus # numarical maximum likelihood estimation cls.mod = mod cls.conc_mod = mod.clone(mod.data.orig_endog, initialization_method='concentrated') # Generate some fixed parameters cls.params = pd.Series([0.5, 0.2, 0.2, 0.95], index=[ 'smoothing_level', 'smoothing_trend', 'smoothing_seasonal', 'damping_trend']) drop = [] if not cls.mod.trend: drop += ['smoothing_trend', 'damping_trend'] elif not cls.mod.damped_trend: drop += ['damping_trend'] if not cls.mod.seasonal: drop += ['smoothing_seasonal'] cls.params.drop(drop, inplace=True) def test_given_params(self): # First, fix the other parameters at a particular value # (for the non-concentrated model, we need to fit the inital values # directly by MLE) res = self.mod.fit_constrained(self.params.to_dict(), disp=0) conc_res = self.conc_mod.filter(self.params.values) assert_allclose(conc_res.llf, res.llf, atol=self.atol, rtol=self.rtol) assert_allclose(conc_res.initial_state, res.initial_state, atol=self.atol, rtol=self.rtol) def test_estimated_params(self): # Alternatively, estimate the remaining parameters res = self.mod.fit(disp=0, maxiter=100) np.set_printoptions(suppress=True) conc_res = self.conc_mod.fit(self.start_params[:len(self.params)], disp=0) assert_allclose(conc_res.llf, res.llf, atol=self.atol, rtol=self.rtol) assert_allclose(conc_res.initial_state, res.initial_state, atol=self.atol, rtol=self.rtol) class TestSESConcentratedInitialization(CheckConcentratedInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(oildata) start_params = pd.Series([0.85, 445.], index=mod.param_names) super().setup_class(mod, start_params=start_params, rtol=1e-5) class TestHoltConcentratedInitialization(CheckConcentratedInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(air, trend=True) start_params = pd.Series( [0.95, 0.0005, 15., 1.5], index=mod.param_names) super().setup_class(mod, start_params=start_params, rtol=1e-4) class TestHoltDampedConcentratedInitialization( CheckConcentratedInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(air, trend=True, damped_trend=True) start_params = pd.Series( [0.95, 0.0005, 0.9, 15., 2.5], index=mod.param_names) super().setup_class(mod, start_params=start_params, rtol=1e-1) class TestHoltWintersConcentratedInitialization( CheckConcentratedInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(aust, trend=True, seasonal=4) start_params = pd.Series( [0.0005, 0.0004, 0.5, 33., 0.4, 2.5, -2., -9.], index=mod.param_names) super().setup_class(mod, start_params=start_params, rtol=1e-3) class TestHoltWintersDampedConcentratedInitialization( CheckConcentratedInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(aust, trend=True, damped_trend=True, seasonal=4) start_params = pd.Series( [0.0005, 0.0004, 0.0005, 0.95, 17.0, 1.5, -0.2, 0.1, 0.4], index=mod.param_names) super().setup_class(mod, start_params=start_params, rtol=1e-1) class TestHoltWintersNoTrendConcentratedInitialization( CheckConcentratedInitialization): @classmethod def setup_class(cls): mod = ExponentialSmoothing(aust, seasonal=4) start_params = pd.Series( [0.5, 0.49, 30., 2., -2, -9], index=mod.param_names) super().setup_class(mod, start_params=start_params, rtol=1e-4) class TestMultiIndex(CheckExponentialSmoothing): @classmethod def setup_class(cls): oildata_copy = oildata.copy() oildata_copy.name = ("oil", "data") mod = ExponentialSmoothing(oildata_copy, initialization_method='simple') res = mod.filter([results_params['oil_fpp2']['alpha']]) super().setup_class('oil_fpp2', res) def test_conf_int(self): # Forecast confidence intervals ci_95 = self.forecast.conf_int(alpha=0.05) assert_allclose(ci_95["lower ('oil', 'data')"], results_predict['%s_lower' % self.name][self.nobs:]) assert_allclose(ci_95["upper ('oil', 'data')"], results_predict['%s_upper' % self.name][self.nobs:]) def test_invalid(): # Tests for invalid model specifications that raise ValueErrors with pytest.raises( ValueError, match='Cannot have a seasonal period of 1.'): mod = ExponentialSmoothing(aust, seasonal=1) with pytest.raises(TypeError, match=( 'seasonal must be integer_like' r' \(int or np.integer, but not bool or timedelta64\) or None')): mod = ExponentialSmoothing(aust, seasonal=True) with pytest.raises( ValueError, match='Invalid initialization method "invalid".'): mod = ExponentialSmoothing(aust, initialization_method='invalid') with pytest.raises(ValueError, match=( '`initial_level` argument must be provided' ' when initialization method is set to' ' "known".')): mod = ExponentialSmoothing(aust, initialization_method='known') with pytest.raises(ValueError, match=( '`initial_trend` argument must be provided' ' for models with a trend component when' ' initialization method is set to "known".')): mod = ExponentialSmoothing( aust, trend=True, initialization_method='known', initial_level=0) with pytest.raises(ValueError, match=( '`initial_seasonal` argument must be provided' ' for models with a seasonal component when' ' initialization method is set to "known".')): mod = ExponentialSmoothing( aust, seasonal=4, initialization_method='known', initial_level=0) for arg in ['initial_level', 'initial_trend', 'initial_seasonal']: msg = ('Cannot give `%s` argument when initialization is "estimated"' % arg) with pytest.raises(ValueError, match=msg): mod = ExponentialSmoothing(aust, **{arg: 0}) with pytest.raises(ValueError, match=( 'Invalid length of initial seasonal values. Must be' ' one of s or s-1, where s is the number of seasonal' ' periods.')): mod = ExponentialSmoothing( aust, seasonal=4, initialization_method='known', initial_level=0, initial_seasonal=0) with pytest.raises(NotImplementedError, match='ExponentialSmoothing does not support `exog`.'): mod = ExponentialSmoothing(aust) mod.clone(aust, exog=air) def test_parameterless_model(reset_randomstate): # GH 6687 x = np.cumsum(np.random.standard_normal(1000)) ses = ExponentialSmoothing(x, initial_level=x[0], initialization_method="known") with ses.fix_params({'smoothing_level': 0.5}): res = ses.fit() assert np.isnan(res.bse).all() assert res.fixed_params == ["smoothing_level"] statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_fixed_params.py000066400000000000000000000613461400612667500266610ustar00rootroot00000000000000""" Tests for fixing the values of some parameters and estimating others Author: Chad Fulton License: Simplified-BSD """ from __future__ import division, absolute_import, print_function import numpy as np import pytest from statsmodels import datasets from statsmodels.tsa.statespace import ( initialization, mlemodel, sarimax, structural, dynamic_factor, varmax) from numpy.testing import assert_, assert_raises, assert_equal, assert_allclose macrodata = datasets.macrodata.load_pandas().data def test_fix_params(): # Just create a dummy model to test the basic `fix_params` mechanics mod = mlemodel.MLEModel([], 1) mod._param_names = ['a', 'b', 'c'] with mod.fix_params({'b': 1.}): assert_(mod._has_fixed_params) assert_equal(mod._fixed_params, {'b': 1.}) assert_equal(mod._fixed_params_index, [1]) assert_equal(mod._free_params_index, [0, 2]) assert_(not mod._has_fixed_params) assert_equal(mod._fixed_params, {}) assert_equal(mod._fixed_params_index, None) assert_equal(mod._free_params_index, None) def test_results_append(): endog = macrodata['infl'] endog1 = endog.iloc[:100] endog2 = endog.iloc[100:] mod_full = sarimax.SARIMAX(endog) with mod_full.fix_params({'ar.L1': 0.5}): res_full = mod_full.smooth([1.], includes_fixed=False) # Start pretty close to optimum to speed up test start_params = [10.3] res_full_fit = mod_full.fit(start_params, disp=False) mod = sarimax.SARIMAX(endog1) with mod.fix_params({'ar.L1': 0.5}): res1 = mod.smooth([1.], includes_fixed=False) # Append should work outside the context manager, since the results object # was created with fixed parameters res2 = res1.append(endog2) # Test to make sure refit works with fixed parameters res2_fit = res1.append(endog2, refit=True, fit_kwargs={ 'disp': False, 'start_params': res_full_fit.params}) # Check non-refit assert_allclose(res2.params, res_full.params) assert_equal(res2._fixed_params, res_full._fixed_params) assert_allclose(res2.llf_obs, res_full.llf_obs) # Check refit results assert_allclose(res2_fit.params, res_full_fit.params) assert_equal(res2_fit._fixed_params, res_full_fit._fixed_params) assert_allclose(res2_fit.llf_obs, res_full_fit.llf_obs) def test_results_extend(): endog = macrodata['infl'] endog1 = endog.iloc[:100] endog2 = endog.iloc[100:] mod_full = sarimax.SARIMAX(endog) with mod_full.fix_params({'ar.L1': 0.5}): res_full = mod_full.smooth([1.], includes_fixed=False) mod = sarimax.SARIMAX(endog1) with mod.fix_params({'ar.L1': 0.5}): res1 = mod.smooth([1.], includes_fixed=False) # Append should work outside the context manager, since the results object # was created with fixed parameters res2 = res1.append(endog2) # Check results assert_allclose(res2.params, res_full.params) assert_equal(res2._fixed_params, res_full._fixed_params) assert_allclose(res2.llf_obs, res_full.llf_obs) def test_results_apply(): endog = macrodata['infl'] mod = sarimax.SARIMAX(endog) with mod.fix_params({'ar.L1': 0.5}): res = mod.smooth([1.], includes_fixed=False) # Start pretty close to optimum to speed up test start_params = [10.3] res_fit = mod.fit(start_params, disp=False) res2 = res.apply(endog) # Test to make sure refit works with fixed parameters res2_fit = res.apply(endog, refit=True, fit_kwargs={ 'disp': False, 'start_params': res_fit.params}) # Check non-refit assert_allclose(res2.params, res.params) assert_equal(res2._fixed_params, res._fixed_params) assert_allclose(res2.llf_obs, res.llf_obs) # Check refit results assert_allclose(res2_fit.params, res_fit.params) assert_equal(res2_fit._fixed_params, res_fit._fixed_params) assert_allclose(res2_fit.llf_obs, res_fit.llf_obs) def test_sarimax_invalid(): # Test for invalid uses of parameter fixing endog = macrodata['infl'] mod1 = sarimax.SARIMAX(endog, order=(2, 0, 0)) # Try to fix invalid parameter assert_raises(ValueError, mod1.fit_constrained, {'AR.L1': 0.5}) # Cannot fix individual parameters that are part of a multivariate # transformation with pytest.raises(ValueError): with mod1.fix_params({'ar.L1': 0.5}): pass assert_raises(ValueError, mod1.fit_constrained, {'ar.L1': 0.5}) # But can fix the entire set of parameters that are part of a multivariate # transformation with mod1.fix_params({'ar.L1': 0.5, 'ar.L2': 0.2}): assert_(mod1._has_fixed_params) assert_equal(mod1._fixed_params, {'ar.L1': 0.5, 'ar.L2': 0.2}) assert_equal(mod1._fixed_params_index, [0, 1]) assert_equal(mod1._free_params_index, [2]) res = mod1.fit_constrained({'ar.L1': 0.5, 'ar.L2': 0.2}, start_params=[7.0], disp=False) assert_(res._has_fixed_params) assert_equal(res._fixed_params, {'ar.L1': 0.5, 'ar.L2': 0.2}) assert_equal(res._fixed_params_index, [0, 1]) assert_equal(res._free_params_index, [2]) def test_structural_invalid(): # Test for invalid uses of parameter fixing endog = macrodata['infl'] mod1 = structural.UnobservedComponents(endog, 'rwalk', ar=2) # Try to fix invalid parameter assert_raises(ValueError, mod1.fit_constrained, {'AR.L1': 0.5}) # Cannot fix parameters that are part of a multivariate transformation with pytest.raises(ValueError): with mod1.fix_params({'ar.L1': 0.5}): pass assert_raises(ValueError, mod1.fit_constrained, {'ar.L1': 0.5}) def test_dynamic_factor_invalid(): # Test for invalid uses of parameter fixing endog = np.log(macrodata[['cpi', 'realgdp', 'realinv']]).diff().iloc[1:] endog = (endog - endog.mean()) / endog.std() # Basic model mod1 = dynamic_factor.DynamicFactor( endog, k_factors=1, factor_order=1, error_cov_type='diagonal') # Check loading constraints = {'loading.f1.cpi': 0.5} with mod1.fix_params(constraints): assert_(mod1._has_fixed_params) assert_equal(mod1._fixed_params, constraints) assert_equal(mod1._fixed_params_index, [0]) assert_equal(mod1._free_params_index, [1, 2, 3, 4, 5, 6]) res1 = mod1.fit_constrained(constraints, disp=False) assert_(res1._has_fixed_params) assert_equal(res1._fixed_params, constraints) assert_equal(res1._fixed_params_index, [0]) assert_equal(res1._free_params_index, [1, 2, 3, 4, 5, 6]) # With k_factors=1 and factor_order=1, we can fix the factor AR coefficient # even with `enforce_stationarity=True`. # Fix factor AR coefficient with mod1.fix_params({'L1.f1.f1': 0.5}): assert_(mod1._has_fixed_params) assert_equal(mod1._fixed_params, {'L1.f1.f1': 0.5}) assert_equal(mod1._fixed_params_index, [6]) assert_equal(mod1._free_params_index, [0, 1, 2, 3, 4, 5]) # With k_factors > 1 or factor_order > 1, we can only fix the entire set of # factor AR coefficients when `enforce_stationarity=True`. mod2 = dynamic_factor.DynamicFactor( endog, k_factors=1, factor_order=2, error_cov_type='diagonal') with pytest.raises(ValueError): with mod2.fix_params({'L1.f1.f1': 0.5}): pass constraints = {'L1.f1.f1': 0.3, 'L2.f1.f1': 0.1} with mod2.fix_params(constraints): assert_(mod2._has_fixed_params) assert_equal(mod2._fixed_params, constraints) assert_equal(mod2._fixed_params_index, [6, 7]) assert_equal(mod2._free_params_index, [0, 1, 2, 3, 4, 5]) res2 = mod2.fit_constrained(constraints, disp=False) assert_(res2._has_fixed_params) assert_equal(res2._fixed_params, constraints) assert_equal(res2._fixed_params_index, [6, 7]) assert_equal(res2._free_params_index, [0, 1, 2, 3, 4, 5]) # (same as previous, now k_factors=2) mod3 = dynamic_factor.DynamicFactor( endog, k_factors=2, factor_order=1, error_cov_type='diagonal') with pytest.raises(ValueError): with mod3.fix_params({'L1.f1.f1': 0.3}): pass constraints = dict([('L1.f1.f1', 0.3), ('L1.f2.f1', 0.1), ('L1.f1.f2', -0.05), ('L1.f2.f2', 0.1)]) with mod3.fix_params(constraints): assert_(mod3._has_fixed_params) assert_equal(mod3._fixed_params, constraints) assert_equal(mod3._fixed_params_index, [9, 10, 11, 12]) assert_equal(mod3._free_params_index, [0, 1, 2, 3, 4, 5, 6, 7, 8]) res3 = mod3.fit_constrained(constraints, disp=False) assert_(res3._has_fixed_params) assert_equal(res3._fixed_params, constraints) assert_equal(res3._fixed_params_index, [9, 10, 11, 12]) assert_equal(res3._free_params_index, [0, 1, 2, 3, 4, 5, 6, 7, 8]) # Now, with enforce_stationarity=False, we can fix any of the factor AR # coefficients mod4 = dynamic_factor.DynamicFactor( endog, k_factors=1, factor_order=2, error_cov_type='diagonal', enforce_stationarity=False) with mod4.fix_params({'L1.f1.f1': 0.6}): assert_(mod4._has_fixed_params) assert_equal(mod4._fixed_params, {'L1.f1.f1': 0.6}) assert_equal(mod4._fixed_params_index, [6]) assert_equal(mod4._free_params_index, [0, 1, 2, 3, 4, 5, 7]) mod5 = dynamic_factor.DynamicFactor( endog, k_factors=2, factor_order=1, error_cov_type='diagonal', enforce_stationarity=False) with mod5.fix_params({'L1.f1.f1': 0.6}): assert_(mod5._has_fixed_params) assert_equal(mod5._fixed_params, {'L1.f1.f1': 0.6}) assert_equal(mod5._fixed_params_index, [9]) assert_equal(mod5._free_params_index, [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12]) # Check error variance # (mod1 has error_cov_type='diagonal', so we can fix any that we like) constraints = {'sigma2.cpi': 0.9, 'sigma2.realinv': 3} with mod1.fix_params(constraints): assert_(mod1._has_fixed_params) assert_equal(mod1._fixed_params, constraints) assert_equal(mod1._fixed_params_index, [3, 5]) assert_equal(mod1._free_params_index, [0, 1, 2, 4, 6]) res1 = mod1.fit_constrained(constraints, disp=False) assert_(res1._has_fixed_params) assert_equal(res1._fixed_params, constraints) assert_equal(res1._fixed_params_index, [3, 5]) assert_equal(res1._free_params_index, [0, 1, 2, 4, 6]) # Check unstructured error variance # (also reduce k_endog and fix some other parameters to make MLE go faster) mod6 = dynamic_factor.DynamicFactor( endog[['cpi', 'realgdp']], k_factors=1, factor_order=1, error_cov_type='unstructured') constraints = { 'loading.f1.cpi': 1., 'loading.f1.realgdp': 1., 'cov.chol[1,1]': 0.5, 'cov.chol[2,1]': 0.1} with mod6.fix_params(constraints): assert_(mod6._has_fixed_params) assert_equal(mod6._fixed_params, constraints) assert_equal(mod6._fixed_params_index, [0, 1, 2, 3]) assert_equal(mod6._free_params_index, [4, 5]) res6 = mod6.fit_constrained(constraints, disp=False) assert_(res6._has_fixed_params) assert_equal(res6._fixed_params, constraints) assert_equal(res6._fixed_params_index, [0, 1, 2, 3]) assert_equal(res6._free_params_index, [4, 5]) def test_varmax_invalid(): # Test for invalid uses of parameter fixing endog = np.log(macrodata[['cpi', 'realgdp']]).diff().iloc[1:] exog = np.log(macrodata[['realinv']]).diff().iloc[1:] # Basic model, VAR(1) + exog + measurement error mod1 = varmax.VARMAX(endog, order=(1, 0), exog=exog, measurement_error=True) # Check intercept, exog constraints = {'intercept.cpi': 0.5, 'intercept.realgdp': 1.1, 'beta.realinv.cpi': 0.2, 'beta.realinv.realgdp': 0.1, 'sqrt.var.cpi': 1.2, 'sqrt.cov.cpi.realgdp': -0.1, 'sqrt.var.realgdp': 2.3, 'measurement_variance.cpi': 0.4, 'measurement_variance.realgdp': 0.4} with mod1.fix_params(constraints): assert_(mod1._has_fixed_params) assert_equal(mod1._fixed_params, constraints) assert_equal(mod1._fixed_params_index, [0, 1, 6, 7, 8, 9, 10, 11, 12]) assert_equal(mod1._free_params_index, [2, 3, 4, 5]) res1 = mod1.fit_constrained(constraints, disp=False) assert_(res1._has_fixed_params) assert_equal(res1._fixed_params, constraints) assert_equal(res1._fixed_params_index, [0, 1, 6, 7, 8, 9, 10, 11, 12]) assert_equal(res1._free_params_index, [2, 3, 4, 5]) # With k_endog=1 we can fix the factor AR coefficient # even with `enforce_stationarity=True`. # Fix factor AR coefficient mod2 = varmax.VARMAX(endog[['cpi']], order=(1, 0), exog=exog, measurement_error=True) constraints = {'L1.cpi.cpi': 0.5} with mod2.fix_params(constraints): assert_(mod2._has_fixed_params) assert_equal(mod2._fixed_params, constraints) assert_equal(mod2._fixed_params_index, [1]) assert_equal(mod2._free_params_index, [0, 2, 3, 4]) # With k_ar > 1, we can only fix the entire set of AR coefficients when # `enforce_stationarity=True`. mod3 = varmax.VARMAX(endog[['cpi']], order=(2, 0)) with pytest.raises(ValueError): with mod3.fix_params({'L1.cpi.cpi': 0.5}): pass constraints = {'L1.cpi.cpi': 0.3, 'L2.cpi.cpi': 0.1} with mod3.fix_params(constraints): assert_(mod3._has_fixed_params) assert_equal(mod3._fixed_params, constraints) assert_equal(mod3._fixed_params_index, [1, 2]) assert_equal(mod3._free_params_index, [0, 3]) res3 = mod3.fit_constrained(constraints, start_params=[0, 1.], disp=False) assert_(res3._has_fixed_params) assert_equal(res3._fixed_params, constraints) assert_equal(res3._fixed_params_index, [1, 2]) assert_equal(res3._free_params_index, [0, 3]) # With k_endog > 1, we can only fix the entire set of AR coefficients when # `enforce_stationarity=True`. mod4 = varmax.VARMAX(endog, order=(1, 0)) with pytest.raises(ValueError): with mod4.fix_params({'L1.cpi.cpi': 0.3}): pass constraints = dict([('L1.cpi.cpi', 0.3), ('L1.realgdp.cpi', 0.1), ('L1.cpi.realgdp', -0.05), ('L1.realgdp.realgdp', 0.1)]) with mod4.fix_params(constraints): assert_(mod4._has_fixed_params) assert_equal(mod4._fixed_params, constraints) assert_equal(mod4._fixed_params_index, [2, 3, 4, 5]) assert_equal(mod4._free_params_index, [0, 1, 6, 7, 8]) res4 = mod4.fit_constrained(constraints, disp=False) assert_(res4._has_fixed_params) assert_equal(res4._fixed_params, constraints) assert_equal(res4._fixed_params_index, [2, 3, 4, 5]) assert_equal(res4._free_params_index, [0, 1, 6, 7, 8]) # Now, with enforce_stationarity=False, we can fix any of the AR # coefficients mod5 = varmax.VARMAX(endog[['cpi']], ar_order=(2, 0), enforce_stationarity=False) with mod5.fix_params({'L1.cpi.cpi': 0.6}): assert_(mod5._has_fixed_params) assert_equal(mod5._fixed_params, {'L1.cpi.cpi': 0.6}) assert_equal(mod5._fixed_params_index, [1]) assert_equal(mod5._free_params_index, [0, 2]) # Now, with enforce_stationarity=False, we can fix any of the AR # coefficients mod6 = varmax.VARMAX(endog, ar_order=(1, 0), enforce_stationarity=False) with mod6.fix_params({'L1.cpi.cpi': 0.6}): assert_(mod6._has_fixed_params) assert_equal(mod6._fixed_params, {'L1.cpi.cpi': 0.6}) assert_equal(mod6._fixed_params_index, [2]) assert_equal(mod6._free_params_index, [0, 1, 3, 4, 5, 6, 7, 8]) def check_results(res1, res2, check_lutkepohl=False, check_params=True): # Check other results assert_allclose(res2.nobs, res1.nobs) assert_allclose(res2.nobs_diffuse, res1.nobs_diffuse) assert_allclose(res2.nobs_effective, res1.nobs_effective) assert_allclose(res2.k_diffuse_states, res1.k_diffuse_states) assert_allclose(res2.df_model, res1.df_model) assert_allclose(res2.df_resid, res1.df_resid) assert_allclose(res2.llf, res1.llf) assert_allclose(res2.aic, res1.aic) assert_allclose(res2.bic, res1.bic) assert_allclose(res2.hqic, res1.hqic) if check_lutkepohl: assert_allclose(res2.info_criteria('aic', 'lutkepohl'), res1.info_criteria('aic', 'lutkepohl')) assert_allclose(res2.info_criteria('bic', 'lutkepohl'), res1.info_criteria('bic', 'lutkepohl')) assert_allclose(res2.info_criteria('hqic', 'lutkepohl'), res1.info_criteria('hqic', 'lutkepohl')) assert_allclose(res2.llf_obs, res1.llf_obs) assert_allclose(res2.fittedvalues, res1.fittedvalues) assert_allclose(res2.fittedvalues, res1.fittedvalues) if check_params: # Check parameter-related values mask_free = res2._free_params_index mask_fixed = res2._fixed_params_index assert_allclose(res2.pvalues[mask_free], res1.pvalues) assert_allclose(res2.pvalues[mask_fixed], np.nan) assert_allclose(res2.bse[mask_free], res1.bse) assert_allclose(res2.bse[mask_fixed], np.nan) assert_allclose(res2.zvalues[mask_free], res1.zvalues) assert_allclose(res2.zvalues[mask_fixed], np.nan) # Check parameter covariance matrix mask_free = np.ix_(res2._free_params_index, res2._free_params_index) mask_fixed = np.ix_(res2._fixed_params_index, res2._fixed_params_index) assert_allclose(res2.cov_params_default.values[mask_free], res1.cov_params_default) assert_allclose(res2.cov_params_default.values[mask_fixed], np.nan) assert_allclose(res2.cov_params_approx.values[mask_free], res1.cov_params_approx) assert_allclose(res2.cov_params_approx.values[mask_fixed], np.nan) assert_allclose(res2.cov_params_oim.values[mask_free], res1.cov_params_oim) assert_allclose(res2.cov_params_oim.values[mask_fixed], np.nan) assert_allclose(res2.cov_params_opg.values[mask_free], res1.cov_params_opg) assert_allclose(res2.cov_params_opg.values[mask_fixed], np.nan) assert_allclose(res2.cov_params_robust.values[mask_free], res1.cov_params_robust) assert_allclose(res2.cov_params_robust.values[mask_fixed], np.nan) assert_allclose(res2.cov_params_robust_oim.values[mask_free], res1.cov_params_robust_oim) assert_allclose(res2.cov_params_robust_oim.values[mask_fixed], np.nan) assert_allclose(res2.cov_params_robust_approx.values[mask_free], res1.cov_params_robust_approx) assert_allclose(res2.cov_params_robust_approx.values[mask_fixed], np.nan) # Check residual hypothesis tests assert_allclose(res2.test_normality('jarquebera'), res1.test_normality('jarquebera')) assert_allclose(res2.test_heteroskedasticity('breakvar'), res1.test_heteroskedasticity('breakvar')) with pytest.warns(FutureWarning): actual = res2.test_serial_correlation('ljungbox') desired = res1.test_serial_correlation('ljungbox') assert_allclose(actual, desired) def test_sarimax_nonconsecutive(): # SARIMAX allows using non-consecutive lag orders, which implicitly fix # AR coefficients to zeros, so we can test explicitly fixed AR coefficients # against this endog = macrodata['infl'] # y_t = \phi_1 y_{t-1} + \phi_4 y_{t-4} + \varepsilon_t # Note: because the transformation will not respect the parameter # constraints, we will need to set enforce_stationarity=False; set it to # False here too so that they both are the same model mod1 = sarimax.SARIMAX(endog, order=([1, 0, 0, 1], 0, 0), enforce_stationarity=False) mod2 = sarimax.SARIMAX(endog, order=(4, 0, 0), enforce_stationarity=False) # Start pretty close to optimum to speed up test start_params = [0.6, 0.2, 6.4] res1 = mod1.fit(start_params, disp=False) res2 = mod2.fit_constrained({'ar.L2': 0, 'ar.L3': 0}, res1.params, includes_fixed=False, disp=False) # Check that the right parameters were fixed assert_equal(res1.fixed_params, []) assert_equal(res2.fixed_params, ['ar.L2', 'ar.L3']) # Check that MLE finds the same parameters in either case desired = np.r_[res1.params[0], 0, 0, res1.params[1:]] assert_allclose(res2.params, desired) # Now smooth at the actual parameters (to allow high precision testing # below, even if there are small differences between MLE fitted parameters) with mod2.fix_params({'ar.L2': 0, 'ar.L3': 0}): res2 = mod2.smooth(res1.params) check_results(res1, res2, check_lutkepohl=True) # Check that results methods work within the context with mod2.fix_params({'ar.L2': 0, 'ar.L3': 0}): res3 = mod2.filter(res2.params, includes_fixed=True) check_results(res1, res3, check_lutkepohl=True) def test_structural(): # Many of the forms of UnobservedComponents are just special cases of the # most general model with parameter restrictions endog = macrodata['infl'] # Local linear trend is a pretty general model, so we can test fixing # parameters against other more specific models # Local level is local linear trend with sigma2.trend = 0 mod1 = structural.UnobservedComponents(endog, 'llevel') mod2 = structural.UnobservedComponents(endog, 'lltrend') # Note: have to reinitialize, so the estimate of the trend term stays at # zero. init = initialization.Initialization(mod2.k_states) init[0] = 'approximate_diffuse' init.set(1, 'known', constant=[0]) mod2.ssm.initialization = init mod2.ssm.loglikelihood_burn = 1 constraints = {'sigma2.trend': 0} # Start pretty close to optimum to speed up test start_params = [3.37, 0.74] res1 = mod1.fit(start_params, disp=False) res2 = mod2.fit_constrained(constraints, start_params=res1.params, includes_fixed=False, disp=False) # Check that the right parameters were fixed assert_equal(res1.fixed_params, []) assert_equal(res2.fixed_params, ['sigma2.trend']) # Check that MLE finds the same parameters in either case desired = np.r_[res1.params, 0] assert_allclose(res2.params, desired) # Now smooth at the actual parameters (to allow high precision testing # below, even if there are small differences between MLE fitted parameters) with mod2.fix_params(constraints): res2 = mod2.smooth(res1.params) check_results(res1, res2) def test_dynamic_factor_diag_error_cov(): # Can test fixing the off-diagonal error covariance parameters to zeros # with `error_cov_type='unstructured'` against the case # `error_cov_type='diagonal'`. endog = np.log(macrodata[['cpi', 'realgdp']]).diff().iloc[1:] endog = (endog - endog.mean()) / endog.std() # Basic model mod1 = dynamic_factor.DynamicFactor( endog, k_factors=1, factor_order=1, error_cov_type='diagonal') mod2 = dynamic_factor.DynamicFactor( endog, k_factors=1, factor_order=1, error_cov_type='unstructured') constraints = {'cov.chol[2,1]': 0} # Start pretty close to optimum to speed up test start_params = [-4.5e-06, -1.0e-05, 9.9e-01, 9.9e-01, -1.4e-01] res1 = mod1.fit(start_params=start_params, disp=False) res2 = mod2.fit_constrained(constraints, start_params=res1.params, includes_fixed=False, disp=False) # Check that the right parameters were fixed assert_equal(res1.fixed_params, []) assert_equal(res2.fixed_params, ['cov.chol[2,1]']) # Check that MLE finds the same parameters in either case # (need to account for the fact that diagonal params are variances but # unstructured params are standard deviations) params = np.r_[res1.params[:2], res1.params[2:4]**0.5, res1.params[4]] desired = np.r_[params[:3], 0, params[3:]] assert_allclose(res2.params, desired, atol=1e-5) # Now smooth at the actual parameters (to allow high precision testing # below, even if there are small differences between MLE fitted parameters) with mod2.fix_params(constraints): res2 = mod2.smooth(params) # Can't check some parameters-related values because of the different # parameterization (i.e. cov_params, bse, pvalues, etc. won't match). check_results(res1, res2, check_params=False) def test_score_shape(): # Test that the `score()` output for fixed params has the same shape as the # input vector endog = macrodata['infl'] mod = sarimax.SARIMAX(endog, order=(1, 0, 0)) with mod.fix_params({'ar.L1': 0.5}): score = mod.score([1.0]) assert_equal(score.shape, (1,)) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_forecasting.py000066400000000000000000000030511400612667500265100ustar00rootroot00000000000000r""" Tests for forecasting-related features not tested elsewhere """ import numpy as np import pandas as pd import pytest from numpy.testing import assert_allclose from statsmodels.tsa.statespace import sarimax @pytest.mark.parametrize('data', ['list', 'numpy', 'range', 'date', 'period']) def test_append_multistep(data): # Test that `MLEResults.append` works when called repeatedly endog = [1., 0.5, 1.5, 0.9, 0.2, 0.34] if data == 'numpy': endog = np.array(endog) elif data == 'range': endog = pd.Series(endog) elif data == 'date': index = pd.date_range(start='2000-01-01', periods=6, freq='MS') endog = pd.Series(endog, index=index) elif data == 'period': index = pd.period_range(start='2000-01', periods=6, freq='M') endog = pd.Series(endog, index=index) # Base model fitting mod = sarimax.SARIMAX(endog[:2], order=(1, 0, 0)) res = mod.smooth([0.5, 1.0]) assert_allclose(res.model.endog[:, 0], [1., 0.5]) assert_allclose(res.forecast(1), 0.25) # First append res1 = res.append(endog[2:3]) assert_allclose(res1.model.endog[:, 0], [1., 0.5, 1.5]) assert_allclose(res1.forecast(1), 0.75) # Second append res2 = res1.append(endog[3:5]) assert_allclose(res2.model.endog[:, 0], [1., 0.5, 1.5, 0.9, 0.2]) assert_allclose(res2.forecast(1), 0.1) # Third append res3 = res2.append(endog[5:6]) print(res3.model.endog) assert_allclose(res3.model.endog[:, 0], [1., 0.5, 1.5, 0.9, 0.2, 0.34]) assert_allclose(res3.forecast(1), 0.17) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_impulse_responses.py000066400000000000000000000632401400612667500277710ustar00rootroot00000000000000""" Tests for impulse responses of time series Author: Chad Fulton License: Simplified-BSD """ import warnings import numpy as np import pandas as pd from scipy.stats import ortho_group import pytest from numpy.testing import assert_, assert_allclose from statsmodels.tools.sm_exceptions import EstimationWarning from statsmodels.tsa.statespace import (mlemodel, sarimax, structural, varmax, dynamic_factor) def test_sarimax(): # AR(1) mod = sarimax.SARIMAX([0], order=(1, 0, 0)) phi = 0.5 actual = mod.impulse_responses([phi, 1], steps=10) desired = np.r_[[phi**i for i in range(11)]] assert_allclose(actual, desired) # MA(1) mod = sarimax.SARIMAX([0], order=(0, 0, 1)) theta = 0.5 actual = mod.impulse_responses([theta, 1], steps=10) desired = np.r_[1, theta, [0]*9] assert_allclose(actual, desired) # ARMA(2, 2) + constant # Stata: # webuse lutkepohl2 # arima dln_inc, arima(2, 0, 2) # irf create irf1, set(irf1) step(10) # irf table irf params = [.01928228, -.03656216, .7588994, .27070341, -.72928328, .01122177**0.5] mod = sarimax.SARIMAX([0], order=(2, 0, 2), trend='c') actual = mod.impulse_responses(params, steps=10) desired = [1, .234141, .021055, .17692, .00951, .133917, .002321, .101544, -.001951, .077133, -.004301] assert_allclose(actual, desired, atol=1e-6) # SARIMAX(1,1,1)x(1,0,1,4) + constant + exog # Stata: # webuse lutkepohl2 # gen exog = _n^2 # arima inc exog, arima(1,1,1) sarima(1,0,1,4) # irf create irf2, set(irf2) step(10) # irf table irf params = [.12853289, 12.207156, .86384742, -.71463236, .81878967, -.9533955, 14.043884**0.5] exog = np.arange(1, 92)**2 mod = sarimax.SARIMAX(np.zeros(91), order=(1, 1, 1), seasonal_order=(1, 0, 1, 4), trend='c', exog=exog, simple_differencing=True) actual = mod.impulse_responses(params, steps=10) desired = [1, .149215, .128899, .111349, -.038417, .063007, .054429, .047018, -.069598, .018641, .016103] assert_allclose(actual, desired, atol=1e-6) def test_structural(): steps = 10 # AR(1) mod = structural.UnobservedComponents([0], autoregressive=1) phi = 0.5 actual = mod.impulse_responses([1, phi], steps) desired = np.r_[[phi**i for i in range(steps + 1)]] assert_allclose(actual, desired) # ARX(1) # This is adequately tested in test_simulate.py, since in the time-varying # case `impulse_responses` just calls `simulate` # Irregular mod = structural.UnobservedComponents([0], 'irregular') actual = mod.impulse_responses([1.], steps) assert_allclose(actual, 0) # Fixed intercept # (in practice this is a deterministic constant, because an irregular # component must be added) with warnings.catch_warnings(): warnings.simplefilter("ignore") mod = structural.UnobservedComponents([0], 'fixed intercept') actual = mod.impulse_responses([1.], steps) assert_allclose(actual, 0) # Deterministic constant mod = structural.UnobservedComponents([0], 'deterministic constant') actual = mod.impulse_responses([1.], steps) assert_allclose(actual, 0) # Local level mod = structural.UnobservedComponents([0], 'local level') actual = mod.impulse_responses([1., 1.], steps) assert_allclose(actual, 1) # Random walk mod = structural.UnobservedComponents([0], 'random walk') actual = mod.impulse_responses([1.], steps) assert_allclose(actual, 1) # Fixed slope # (in practice this is a deterministic trend, because an irregular # component must be added) with warnings.catch_warnings(): warnings.simplefilter("ignore") mod = structural.UnobservedComponents([0], 'fixed slope') actual = mod.impulse_responses([1.], steps) assert_allclose(actual, 0) # Deterministic trend mod = structural.UnobservedComponents([0], 'deterministic trend') actual = mod.impulse_responses([1.], steps) assert_allclose(actual, 0) # Local linear deterministic trend mod = structural.UnobservedComponents( [0], 'local linear deterministic trend') actual = mod.impulse_responses([1., 1.], steps) assert_allclose(actual, 1) # Random walk with drift mod = structural.UnobservedComponents([0], 'random walk with drift') actual = mod.impulse_responses([1.], steps) assert_allclose(actual, 1) # Local linear trend mod = structural.UnobservedComponents([0], 'local linear trend') # - shock the level actual = mod.impulse_responses([1., 1., 1.], steps) assert_allclose(actual, 1) # - shock the trend actual = mod.impulse_responses([1., 1., 1.], steps, impulse=1) assert_allclose(actual, np.arange(steps + 1)) # Smooth trend mod = structural.UnobservedComponents([0], 'smooth trend') actual = mod.impulse_responses([1., 1.], steps) assert_allclose(actual, np.arange(steps + 1)) # Random trend mod = structural.UnobservedComponents([0], 'random trend') actual = mod.impulse_responses([1., 1.], steps) assert_allclose(actual, np.arange(steps + 1)) # Seasonal (deterministic) mod = structural.UnobservedComponents([0], 'irregular', seasonal=2, stochastic_seasonal=False) actual = mod.impulse_responses([1.], steps) assert_allclose(actual, 0) # Seasonal (stochastic) mod = structural.UnobservedComponents([0], 'irregular', seasonal=2) actual = mod.impulse_responses([1., 1.], steps) desired = np.r_[1, np.tile([-1, 1], steps // 2)] assert_allclose(actual, desired) # Cycle (deterministic) mod = structural.UnobservedComponents([0], 'irregular', cycle=True) actual = mod.impulse_responses([1., 1.2], steps) assert_allclose(actual, 0) # Cycle (stochastic) mod = structural.UnobservedComponents([0], 'irregular', cycle=True, stochastic_cycle=True) actual = mod.impulse_responses([1., 1., 1.2], steps=10) x1 = [np.cos(1.2), np.sin(1.2)] x2 = [-np.sin(1.2), np.cos(1.2)] T = np.array([x1, x2]) desired = np.zeros(steps + 1) states = [1, 0] for i in range(steps + 1): desired[i] += states[0] states = np.dot(T, states) assert_allclose(actual, desired) def test_varmax(): steps = 10 # Clear warnings varmax.__warningregistry__ = {} # VAR(2) - single series mod1 = varmax.VARMAX([[0]], order=(2, 0), trend='n') mod2 = sarimax.SARIMAX([0], order=(2, 0, 0)) actual = mod1.impulse_responses([0.5, 0.2, 1], steps) desired = mod2.impulse_responses([0.5, 0.2, 1], steps) assert_allclose(actual, desired) # VMA(2) - single series mod1 = varmax.VARMAX([[0]], order=(0, 2), trend='n') mod2 = sarimax.SARIMAX([0], order=(0, 0, 2)) actual = mod1.impulse_responses([0.5, 0.2, 1], steps) desired = mod2.impulse_responses([0.5, 0.2, 1], steps) assert_allclose(actual, desired) # VARMA(2, 2) - single series with warnings.catch_warnings(): warnings.simplefilter("ignore") mod1 = varmax.VARMAX([[0]], order=(2, 2), trend='n') mod2 = sarimax.SARIMAX([0], order=(2, 0, 2)) actual = mod1.impulse_responses([0.5, 0.2, 0.1, -0.2, 1], steps) desired = mod2.impulse_responses([0.5, 0.2, 0.1, -0.2, 1], steps) assert_allclose(actual, desired) # VARMA(2, 2) + trend - single series warning = EstimationWarning match = r'VARMA\(p,q\) models is not' with pytest.warns(warning, match=match): mod1 = varmax.VARMAX([[0]], order=(2, 2), trend='c') mod2 = sarimax.SARIMAX([0], order=(2, 0, 2), trend='c') actual = mod1.impulse_responses([10, 0.5, 0.2, 0.1, -0.2, 1], steps) desired = mod2.impulse_responses([10, 0.5, 0.2, 0.1, -0.2, 1], steps) assert_allclose(actual, desired) # VAR(2) + constant # Stata: # webuse lutkepohl2 # var dln_inv dln_inc, lags(1/2) # irf create irf3, set(irf3) step(10) # irf table irf # irf table oirf params = [-.00122728, .01503679, -.22741923, .71030531, -.11596357, .51494891, .05974659, .02094608, .05635125, .08332519, .04297918, .00159473, .01096298] irf_00 = [1, -.227419, -.021806, .093362, -.001875, -.00906, .009605, .001323, -.001041, .000769, .00032] irf_01 = [0, .059747, .044015, -.008218, .007845, .004629, .000104, .000451, .000638, .000063, .000042] irf_10 = [0, .710305, .36829, -.065697, .084398, .043038, .000533, .005755, .006051, .000548, .000526] irf_11 = [1, .020946, .126202, .066419, .028735, .007477, .009878, .003287, .001266, .000986, .0005] oirf_00 = [0.042979, -0.008642, -0.00035, 0.003908, 0.000054, -0.000321, 0.000414, 0.000066, -0.000035, 0.000034, 0.000015] oirf_01 = [0.001595, 0.002601, 0.002093, -0.000247, 0.000383, 0.000211, 0.00002, 0.000025, 0.000029, 4.30E-06, 2.60E-06] oirf_10 = [0, 0.007787, 0.004037, -0.00072, 0.000925, 0.000472, 5.80E-06, 0.000063, 0.000066, 6.00E-06, 5.80E-06] oirf_11 = [0.010963, 0.00023, 0.001384, 0.000728, 0.000315, 0.000082, 0.000108, 0.000036, 0.000014, 0.000011, 5.50E-06] mod = varmax.VARMAX([[0, 0]], order=(2, 0), trend='c') # IRFs actual = mod.impulse_responses(params, steps, impulse=0) assert_allclose(actual, np.c_[irf_00, irf_01], atol=1e-6) actual = mod.impulse_responses(params, steps, impulse=1) assert_allclose(actual, np.c_[irf_10, irf_11], atol=1e-6) # Orthogonalized IRFs actual = mod.impulse_responses(params, steps, impulse=0, orthogonalized=True) assert_allclose(actual, np.c_[oirf_00, oirf_01], atol=1e-6) actual = mod.impulse_responses(params, steps, impulse=1, orthogonalized=True) assert_allclose(actual, np.c_[oirf_10, oirf_11], atol=1e-6) # VARMA(2, 2) + trend + exog # TODO: This is just a smoke test with warnings.catch_warnings(): warnings.simplefilter("ignore") mod = varmax.VARMAX( np.random.normal(size=(steps, 2)), order=(2, 2), trend='c', exog=np.ones(steps), enforce_stationarity=False, enforce_invertibility=False) mod.impulse_responses(mod.start_params, steps) def test_dynamic_factor(): steps = 10 exog = np.random.normal(size=steps) # DFM: 2 series, AR(2) factor mod1 = dynamic_factor.DynamicFactor([[0, 0]], k_factors=1, factor_order=2) mod2 = sarimax.SARIMAX([0], order=(2, 0, 0)) actual = mod1.impulse_responses([-0.9, 0.8, 1., 1., 0.5, 0.2], steps) desired = mod2.impulse_responses([0.5, 0.2, 1], steps) assert_allclose(actual[:, 0], -0.9 * desired) assert_allclose(actual[:, 1], 0.8 * desired) # DFM: 2 series, AR(2) factor, exog mod1 = dynamic_factor.DynamicFactor(np.zeros((steps, 2)), k_factors=1, factor_order=2, exog=exog) mod2 = sarimax.SARIMAX([0], order=(2, 0, 0)) actual = mod1.impulse_responses( [-0.9, 0.8, 5, -2, 1., 1., 0.5, 0.2], steps) desired = mod2.impulse_responses([0.5, 0.2, 1], steps) assert_allclose(actual[:, 0], -0.9 * desired) assert_allclose(actual[:, 1], 0.8 * desired) # DFM, 3 series, VAR(2) factor, exog, error VAR # TODO: This is just a smoke test mod = dynamic_factor.DynamicFactor(np.random.normal(size=(steps, 3)), k_factors=2, factor_order=2, exog=exog, error_order=2, error_var=True, enforce_stationarity=False) mod.impulse_responses(mod.start_params, steps) def test_time_varying_ssm(): # Create an ad-hoc time-varying model mod = sarimax.SARIMAX([0] * 11, order=(1, 0, 0)) mod.update([0.5, 1.0]) T = np.zeros((1, 1, 11)) T[..., :5] = 0.5 T[..., 5:] = 0.2 mod['transition'] = T irfs = mod.ssm.impulse_responses() desired = np.cumprod(np.r_[1, [0.5] * 4, [0.2] * 5]).reshape(10, 1) assert_allclose(irfs, desired) class TVSS(mlemodel.MLEModel): """ Time-varying state space model for testing This creates a state space model with randomly generated time-varying system matrices. When used in a test, that test should use `reset_randomstate` to ensure consistent test runs. """ def __init__(self, endog, _k_states=None): k_states = 2 k_posdef = 2 # Allow subcasses to add additional states if _k_states is None: _k_states = k_states super(TVSS, self).__init__(endog, k_states=_k_states, k_posdef=k_posdef, initialization='diffuse') self['obs_intercept'] = np.random.normal( size=(self.k_endog, self.nobs)) self['design'] = np.zeros((self.k_endog, self.k_states, self.nobs)) self['transition'] = np.zeros( (self.k_states, self.k_states, self.nobs)) self['selection'] = np.zeros( (self.k_states, self.ssm.k_posdef, self.nobs)) self['design', :, :k_states, :] = np.random.normal( size=(self.k_endog, k_states, self.nobs)) # For the transition matrices, enforce eigenvalues not too far outside # unit circle. Otherwise, the random draws will often lead to large # eigenvalues that cause the covariance matrices to blow up to huge # values during long periods of missing data, which leads to numerical # problems and essentially spurious test failures D = [np.diag(d) for d in np.random.uniform(-1.1, 1.1, size=(self.nobs, k_states))] Q = ortho_group.rvs(k_states, size=self.nobs) self['transition', :k_states, :k_states, :] = ( Q @ D @ Q.transpose(0, 2, 1)).transpose(1, 2, 0) self['selection', :k_states, :, :] = np.random.normal( size=(k_states, self.ssm.k_posdef, self.nobs)) # Need to make sure the covariances are positive definite H05 = np.random.normal(size=(self.k_endog, self.k_endog, self.nobs)) Q05 = np.random.normal( size=(self.ssm.k_posdef, self.ssm.k_posdef, self.nobs)) H = np.zeros_like(H05) Q = np.zeros_like(Q05) for t in range(self.nobs): H[..., t] = np.dot(H05[..., t], H05[..., t].T) Q[..., t] = np.dot(Q05[..., t], Q05[..., t].T) self['obs_cov'] = H self['state_cov'] = Q def clone(self, endog, exog=None, **kwargs): mod = self.__class__(endog, **kwargs) for key in self.ssm.shapes.keys(): if key in ['obs', 'state_intercept']: continue n = min(self.nobs, mod.nobs) mod[key, ..., :n] = self.ssm[key, ..., :n] return mod def test_time_varying_in_sample(reset_randomstate): mod = TVSS(np.zeros((10, 2))) # Compute the max number of in-sample IRFs irfs = mod.impulse_responses([], steps=mod.nobs - 1) # Compute the same thing, but now with explicit anchor argument irfs_anchor = mod.impulse_responses([], steps=mod.nobs - 1, anchor=0) # Cumulative IRFs cirfs = mod.impulse_responses([], steps=mod.nobs - 1, cumulative=True) # Orthogonalized IRFs oirfs = mod.impulse_responses([], steps=mod.nobs - 1, orthogonalized=True) # Cumulative, orthogonalized IRFs coirfs = mod.impulse_responses([], steps=mod.nobs - 1, cumulative=True, orthogonalized=True) # Compute IRFs manually Z = mod['design'] T = mod['transition'] R = mod['selection'] Q = mod['state_cov', ..., 0] L = np.linalg.cholesky(Q) desired_irfs = np.zeros((mod.nobs - 1, 2)) * np.nan desired_oirfs = np.zeros((mod.nobs - 1, 2)) * np.nan tmp = R[..., 0] for i in range(1, mod.nobs): desired_irfs[i - 1] = Z[:, :, i].dot(tmp)[:, 0] desired_oirfs[i - 1] = Z[:, :, i].dot(tmp).dot(L)[:, 0] tmp = T[:, :, i].dot(tmp) assert_allclose(irfs, desired_irfs) assert_allclose(irfs_anchor, desired_irfs) assert_allclose(cirfs, np.cumsum(desired_irfs, axis=0)) assert_allclose(oirfs, desired_oirfs) assert_allclose(coirfs, np.cumsum(desired_oirfs, axis=0)) def test_time_varying_out_of_sample(reset_randomstate): mod = TVSS(np.zeros((10, 2))) # Compute all in-sample IRFs and also one out-of-sample IRF new_Z = np.random.normal(size=mod['design', :, :, -1].shape) new_T = np.random.normal(size=mod['transition', :, :, -1].shape) irfs = mod.impulse_responses( [], steps=mod.nobs, design=new_Z[:, :, None], transition=new_T[:, :, None]) # Compute the same thing, but now with explicit anchor argument irfs_anchor = mod.impulse_responses( [], steps=mod.nobs, anchor=0, design=new_Z[:, :, None], transition=new_T[:, :, None]) # Cumulative IRFs cirfs = mod.impulse_responses([], steps=mod.nobs, design=new_Z[:, :, None], transition=new_T[:, :, None], cumulative=True) # Orthogonalized IRFs oirfs = mod.impulse_responses([], steps=mod.nobs, design=new_Z[:, :, None], transition=new_T[:, :, None], orthogonalized=True) # Cumulative, orthogonalized IRFs coirfs = mod.impulse_responses( [], steps=mod.nobs, design=new_Z[:, :, None], transition=new_T[:, :, None], cumulative=True, orthogonalized=True) # Compute IRFs manually Z = mod['design'] T = mod['transition'] R = mod['selection'] Q = mod['state_cov', ..., 0] L = np.linalg.cholesky(Q) desired_irfs = np.zeros((mod.nobs, 2)) * np.nan desired_oirfs = np.zeros((mod.nobs, 2)) * np.nan tmp = R[..., 0] for i in range(1, mod.nobs): desired_irfs[i - 1] = Z[:, :, i].dot(tmp)[:, 0] desired_oirfs[i - 1] = Z[:, :, i].dot(tmp).dot(L)[:, 0] tmp = T[:, :, i].dot(tmp) desired_irfs[mod.nobs - 1] = new_Z.dot(tmp)[:, 0] desired_oirfs[mod.nobs - 1] = new_Z.dot(tmp).dot(L)[:, 0] assert_allclose(irfs, desired_irfs) assert_allclose(irfs_anchor, desired_irfs) assert_allclose(cirfs, np.cumsum(desired_irfs, axis=0)) assert_allclose(oirfs, desired_oirfs) assert_allclose(coirfs, np.cumsum(desired_oirfs, axis=0)) def test_time_varying_in_sample_anchored(reset_randomstate): mod = TVSS(np.zeros((10, 2))) # Compute the max number of in-sample IRFs anchor = 2 irfs = mod.impulse_responses( [], steps=mod.nobs - 1 - anchor, anchor=anchor) # Cumulative IRFs cirfs = mod.impulse_responses( [], steps=mod.nobs - 1 - anchor, anchor=anchor, cumulative=True) # Orthogonalized IRFs oirfs = mod.impulse_responses( [], steps=mod.nobs - 1 - anchor, anchor=anchor, orthogonalized=True) # Cumulative, orthogonalized IRFs coirfs = mod.impulse_responses( [], steps=mod.nobs - 1 - anchor, anchor=anchor, cumulative=True, orthogonalized=True) # Compute IRFs manually Z = mod['design'] T = mod['transition'] R = mod['selection'] Q = mod['state_cov', ..., anchor] L = np.linalg.cholesky(Q) desired_irfs = np.zeros((mod.nobs - anchor - 1, 2)) * np.nan desired_oirfs = np.zeros((mod.nobs - anchor - 1, 2)) * np.nan tmp = R[..., anchor] for i in range(1, mod.nobs - anchor): desired_irfs[i - 1] = Z[:, :, i + anchor].dot(tmp)[:, 0] desired_oirfs[i - 1] = Z[:, :, i + anchor].dot(tmp).dot(L)[:, 0] tmp = T[:, :, i + anchor].dot(tmp) assert_allclose(irfs, desired_irfs) assert_allclose(cirfs, np.cumsum(desired_irfs, axis=0)) assert_allclose(oirfs, desired_oirfs) assert_allclose(coirfs, np.cumsum(desired_oirfs, axis=0)) def test_time_varying_out_of_sample_anchored(reset_randomstate): mod = TVSS(np.zeros((10, 2))) # Compute all in-sample IRFs and also one out-of-sample IRF anchor = 2 new_Z = mod['design', :, :, -1] new_T = mod['transition', :, :, -1] irfs = mod.impulse_responses( [], steps=mod.nobs - anchor, anchor=anchor, design=new_Z[:, :, None], transition=new_T[:, :, None]) # Cumulative IRFs cirfs = mod.impulse_responses( [], steps=mod.nobs - anchor, anchor=anchor, design=new_Z[:, :, None], transition=new_T[:, :, None], cumulative=True) # Orthogonalized IRFs oirfs = mod.impulse_responses( [], steps=mod.nobs - anchor, anchor=anchor, design=new_Z[:, :, None], transition=new_T[:, :, None], orthogonalized=True) # Cumulative, orthogonalized IRFs coirfs = mod.impulse_responses( [], steps=mod.nobs - anchor, anchor=anchor, design=new_Z[:, :, None], transition=new_T[:, :, None], cumulative=True, orthogonalized=True) # Compute IRFs manually Z = mod['design'] T = mod['transition'] R = mod['selection'] Q = mod['state_cov', ..., anchor] L = np.linalg.cholesky(Q) desired_irfs = np.zeros((mod.nobs - anchor, 2)) * np.nan desired_oirfs = np.zeros((mod.nobs - anchor, 2)) * np.nan tmp = R[..., anchor] for i in range(1, mod.nobs - anchor): desired_irfs[i - 1] = Z[:, :, i + anchor].dot(tmp)[:, 0] desired_oirfs[i - 1] = Z[:, :, i + anchor].dot(tmp).dot(L)[:, 0] tmp = T[:, :, i + anchor].dot(tmp) desired_irfs[mod.nobs - anchor - 1] = new_Z.dot(tmp)[:, 0] desired_oirfs[mod.nobs - anchor - 1] = new_Z.dot(tmp).dot(L)[:, 0] assert_allclose(irfs, desired_irfs) assert_allclose(cirfs, np.cumsum(desired_irfs, axis=0)) assert_allclose(oirfs, desired_oirfs) assert_allclose(coirfs, np.cumsum(desired_oirfs, axis=0)) def test_time_varying_out_of_sample_anchored_end(reset_randomstate): mod = TVSS(np.zeros((10, 2))) # Cannot compute the any in-sample IRFs when anchoring at the end with pytest.raises(ValueError, match='Model has time-varying'): mod.impulse_responses([], steps=2, anchor='end') # Compute two out-of-sample IRFs new_Z = np.random.normal(size=mod['design', :, :, -2:].shape) new_T = np.random.normal(size=mod['transition', :, :, -2:].shape) irfs = mod.impulse_responses([], steps=2, anchor='end', design=new_Z, transition=new_T) # Cumulative IRFs cirfs = mod.impulse_responses( [], steps=2, anchor='end', design=new_Z, transition=new_T, cumulative=True) # Orthogonalized IRFs oirfs = mod.impulse_responses( [], steps=2, anchor='end', design=new_Z, transition=new_T, orthogonalized=True) # Cumulative, orthogonalized IRFs coirfs = mod.impulse_responses( [], steps=2, anchor='end', design=new_Z, transition=new_T, cumulative=True, orthogonalized=True) # Compute IRFs manually R = mod['selection'] Q = mod['state_cov', ..., -1] L = np.linalg.cholesky(Q) desired_irfs = np.zeros((2, 2)) * np.nan desired_oirfs = np.zeros((2, 2)) * np.nan # desired[0] = 0 # Z_{T+1} R_T tmp = R[..., -1] desired_irfs[0] = new_Z[:, :, 0].dot(tmp)[:, 0] desired_oirfs[0] = new_Z[:, :, 0].dot(tmp).dot(L)[:, 0] # T_{T+1} R_T tmp = new_T[..., 0].dot(tmp) # Z_{T+2} T_{T+1} R_T desired_irfs[1] = new_Z[:, :, 1].dot(tmp)[:, 0] desired_oirfs[1] = new_Z[:, :, 1].dot(tmp).dot(L)[:, 0] assert_allclose(irfs, desired_irfs) assert_allclose(cirfs, np.cumsum(desired_irfs, axis=0)) assert_allclose(oirfs, desired_oirfs) assert_allclose(coirfs, np.cumsum(desired_oirfs, axis=0)) def test_pandas_univariate_rangeindex(): # Impulse responses have RangeIndex endog = pd.Series(np.zeros(1)) mod = sarimax.SARIMAX(endog) res = mod.filter([0.5, 1.]) actual = res.impulse_responses(2) desired = pd.Series([1., 0.5, 0.25]) assert_allclose(res.impulse_responses(2), desired) assert_(actual.index.equals(desired.index)) def test_pandas_univariate_dateindex(): # Impulse responses still have RangeIndex (i.e. aren't wrapped with dates) ix = pd.date_range(start='2000', periods=1, freq='M') endog = pd.Series(np.zeros(1), index=ix) mod = sarimax.SARIMAX(endog) res = mod.filter([0.5, 1.]) actual = res.impulse_responses(2) desired = pd.Series([1., 0.5, 0.25]) assert_allclose(res.impulse_responses(2), desired) assert_(actual.index.equals(desired.index)) def test_pandas_multivariate_rangeindex(): # Impulse responses have RangeIndex endog = pd.DataFrame(np.zeros((1, 2))) mod = varmax.VARMAX(endog, trend='n') res = mod.filter([0.5, 0., 0., 0.2, 1., 0., 1.]) actual = res.impulse_responses(2) desired = pd.DataFrame([[1., 0.5, 0.25], [0., 0., 0.]]).T assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) def test_pandas_multivariate_dateindex(): # Impulse responses still have RangeIndex (i.e. aren't wrapped with dates) ix = pd.date_range(start='2000', periods=1, freq='M') endog = pd.DataFrame(np.zeros((1, 2)), index=ix) mod = varmax.VARMAX(endog, trend='n') res = mod.filter([0.5, 0., 0., 0.2, 1., 0., 1.]) actual = res.impulse_responses(2) desired = pd.DataFrame([[1., 0.5, 0.25], [0., 0., 0.]]).T assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) def test_pandas_anchor(): # Test that anchor with dates works ix = pd.date_range(start='2000', periods=10, freq='M') endog = pd.DataFrame(np.zeros((10, 2)), index=ix) mod = TVSS(endog) res = mod.filter([]) desired = res.impulse_responses(2, anchor=1) # Anchor to date actual = res.impulse_responses(2, anchor=ix[1]) assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) # Anchor to negative index actual = res.impulse_responses(2, anchor=-9) assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_initialization.py000066400000000000000000000327641400612667500272500ustar00rootroot00000000000000""" Tests for initialization Author: Chad Fulton License: Simplified-BSD """ import numpy as np from scipy.linalg import solve_discrete_lyapunov from statsmodels.tsa.statespace import sarimax, varmax from statsmodels.tsa.statespace.initialization import Initialization from numpy.testing import assert_allclose, assert_raises def check_initialization(mod, init, a_true, Pinf_true, Pstar_true): # Check the Python version a, Pinf, Pstar = init(model=mod) assert_allclose(a, a_true) assert_allclose(Pinf, Pinf_true) assert_allclose(Pstar, Pstar_true) # Check the Cython version mod.ssm._initialize_representation() init._initialize_initialization(prefix=mod.ssm.prefix) _statespace = mod.ssm._statespace _statespace.initialize(init) assert_allclose(np.array(_statespace.initial_state), a_true) assert_allclose(np.array(_statespace.initial_diffuse_state_cov), Pinf_true) assert_allclose(np.array(_statespace.initial_state_cov), Pstar_true) def test_global_known(): # Test for global known initialization # - 1-dimensional - endog = np.zeros(10) mod = sarimax.SARIMAX(endog, order=(1, 0, 0)) # Known, mean init = Initialization(mod.k_states, 'known', constant=[1.5]) check_initialization(mod, init, [1.5], np.diag([0]), np.diag([0])) # Known, covariance init = Initialization(mod.k_states, 'known', stationary_cov=np.diag([1])) check_initialization(mod, init, [0], np.diag([0]), np.diag([1])) # Known, both init = Initialization(mod.k_states, 'known', constant=[1.5], stationary_cov=np.diag([1])) check_initialization(mod, init, [1.5], np.diag([0]), np.diag([1])) # - n-dimensional - endog = np.zeros(10) mod = sarimax.SARIMAX(endog, order=(2, 0, 0)) # Known, mean init = Initialization(mod.k_states, 'known', constant=[1.5, -0.2]) check_initialization(mod, init, [1.5, -0.2], np.diag([0, 0]), np.diag([0, 0])) # Known, covariance init = Initialization(mod.k_states, 'known', stationary_cov=np.diag([1, 4.2])) check_initialization(mod, init, [0, 0], np.diag([0, 0]), np.diag([1, 4.2])) # Known, both init = Initialization(mod.k_states, 'known', constant=[1.5, -0.2], stationary_cov=np.diag([1, 4.2])) check_initialization(mod, init, [1.5, -0.2], np.diag([0, 0]), np.diag([1, 4.2])) def test_global_diffuse(): # Test for global diffuse initialization # - 1-dimensional - endog = np.zeros(10) mod = sarimax.SARIMAX(endog, order=(1, 0, 0)) init = Initialization(mod.k_states, 'diffuse') check_initialization(mod, init, [0], np.eye(1), np.diag([0])) # - n-dimensional - endog = np.zeros(10) mod = sarimax.SARIMAX(endog, order=(2, 0, 0)) init = Initialization(mod.k_states, 'diffuse') check_initialization(mod, init, [0, 0], np.eye(2), np.diag([0, 0])) def test_global_approximate_diffuse(): # Test for global approximate diffuse initialization # - 1-dimensional - endog = np.zeros(10) mod = sarimax.SARIMAX(endog, order=(1, 0, 0)) init = Initialization(mod.k_states, 'approximate_diffuse') check_initialization(mod, init, [0], np.diag([0]), np.eye(1) * 1e6) init = Initialization(mod.k_states, 'approximate_diffuse', constant=[1.2]) check_initialization(mod, init, [1.2], np.diag([0]), np.eye(1) * 1e6) init = Initialization(mod.k_states, 'approximate_diffuse', approximate_diffuse_variance=1e10) check_initialization(mod, init, [0], np.diag([0]), np.eye(1) * 1e10) # - n-dimensional - endog = np.zeros(10) mod = sarimax.SARIMAX(endog, order=(2, 0, 0)) init = Initialization(mod.k_states, 'approximate_diffuse') check_initialization(mod, init, [0, 0], np.diag([0, 0]), np.eye(2) * 1e6) init = Initialization(mod.k_states, 'approximate_diffuse', constant=[1.2, -0.2]) check_initialization(mod, init, [1.2, -0.2], np.diag([0, 0]), np.eye(2) * 1e6) init = Initialization(mod.k_states, 'approximate_diffuse', approximate_diffuse_variance=1e10) check_initialization(mod, init, [0, 0], np.diag([0, 0]), np.eye(2) * 1e10) def test_global_stationary(): # Test for global approximate diffuse initialization # - 1-dimensional - endog = np.zeros(10) mod = sarimax.SARIMAX(endog, order=(1, 0, 0), trend='c') # no intercept intercept = 0 phi = 0.5 sigma2 = 2. mod.update(np.r_[intercept, phi, sigma2]) init = Initialization(mod.k_states, 'stationary') check_initialization(mod, init, [0], np.diag([0]), np.eye(1) * sigma2 / (1 - phi**2)) # intercept intercept = 1.2 phi = 0.5 sigma2 = 2. mod.update(np.r_[intercept, phi, sigma2]) init = Initialization(mod.k_states, 'stationary') check_initialization(mod, init, [intercept / (1 - phi)], np.diag([0]), np.eye(1) * sigma2 / (1 - phi**2)) # - n-dimensional - endog = np.zeros(10) mod = sarimax.SARIMAX(endog, order=(2, 0, 0), trend='c') # no intercept intercept = 0 phi = [0.5, -0.2] sigma2 = 2. mod.update(np.r_[intercept, phi, sigma2]) init = Initialization(mod.k_states, 'stationary') T = np.array([[0.5, 1], [-0.2, 0]]) Q = np.diag([sigma2, 0]) desired_cov = solve_discrete_lyapunov(T, Q) check_initialization(mod, init, [0, 0], np.diag([0, 0]), desired_cov) # intercept intercept = 1.2 phi = [0.5, -0.2] sigma2 = 2. mod.update(np.r_[intercept, phi, sigma2]) init = Initialization(mod.k_states, 'stationary') desired_intercept = np.linalg.inv(np.eye(2) - T).dot([intercept, 0]) check_initialization(mod, init, desired_intercept, np.diag([0, 0]), desired_cov) def test_mixed_basic(): # Performs a number of tests for setting different initialization for # different blocks # - 2-dimensional - endog = np.zeros(10) mod = sarimax.SARIMAX(endog, order=(2, 0, 0)) phi = [0.5, -0.2] sigma2 = 2. mod.update(np.r_[phi, sigma2]) # known has constant init = Initialization(mod.k_states) init.set(0, 'known', constant=[1.2]) # > known has constant init.set(1, 'known', constant=[-0.2]) check_initialization(mod, init, [1.2, -0.2], np.diag([0, 0]), np.diag([0, 0])) # > diffuse init.unset(1) init.set(1, 'diffuse') check_initialization(mod, init, [1.2, 0], np.diag([0, 1]), np.diag([0, 0])) # > approximate diffuse init.unset(1) init.set(1, 'approximate_diffuse') check_initialization(mod, init, [1.2, 0], np.diag([0, 0]), np.diag([0, 1e6])) # > stationary init.unset(1) init.set(1, 'stationary') check_initialization(mod, init, [1.2, 0], np.diag([0, 0]), np.diag([0, 0])) # known has cov init = Initialization(mod.k_states) init.set(0, 'known', stationary_cov=np.diag([1])) init.set(1, 'diffuse') check_initialization(mod, init, [0, 0], np.diag([0, 1]), np.diag([1, 0])) # known has both init = Initialization(mod.k_states) init.set(0, 'known', constant=[1.2], stationary_cov=np.diag([1])) init.set(1, 'diffuse') check_initialization(mod, init, [1.2, 0], np.diag([0, 1]), np.diag([1, 0])) # - 3-dimensional - endog = np.zeros(10) mod = sarimax.SARIMAX(endog, order=(3, 0, 0)) # known has constant init = Initialization(mod.k_states) init.set((0, 2), 'known', constant=[1.2, -0.2]) init.set(2, 'diffuse') check_initialization(mod, init, [1.2, -0.2, 0], np.diag([0, 0, 1]), np.diag([0, 0, 0])) # known has cov init = Initialization(mod.k_states) init.set((0, 2), 'known', stationary_cov=np.diag([1, 4.2])) init.set(2, 'diffuse') check_initialization(mod, init, [0, 0, 0], np.diag([0, 0, 1]), np.diag([1, 4.2, 0])) # known has both init = Initialization(mod.k_states) init.set((0, 2), 'known', constant=[1.2, -0.2], stationary_cov=np.diag([1, 4.2])) init.set(2, 'diffuse') check_initialization(mod, init, [1.2, -0.2, 0], np.diag([0, 0, 1]), np.diag([1, 4.2, 0])) def test_mixed_stationary(): # More specific tests when one or more blocks are initialized as stationary endog = np.zeros(10) mod = sarimax.SARIMAX(endog, order=(2, 1, 0)) phi = [0.5, -0.2] sigma2 = 2. mod.update(np.r_[phi, sigma2]) init = Initialization(mod.k_states) init.set(0, 'diffuse') init.set((1, 3), 'stationary') desired_cov = np.zeros((3, 3)) T = np.array([[0.5, 1], [-0.2, 0]]) Q = np.diag([sigma2, 0]) desired_cov[1:, 1:] = solve_discrete_lyapunov(T, Q) check_initialization(mod, init, [0, 0, 0], np.diag([1, 0, 0]), desired_cov) init.clear() init.set(0, 'diffuse') init.set(1, 'stationary') init.set(2, 'approximate_diffuse') T = np.array([[0.5]]) Q = np.diag([sigma2]) desired_cov = np.diag([0, np.squeeze(solve_discrete_lyapunov(T, Q)), 1e6]) check_initialization(mod, init, [0, 0, 0], np.diag([1, 0, 0]), desired_cov) init.clear() init.set(0, 'diffuse') init.set(1, 'stationary') init.set(2, 'stationary') desired_cov[2, 2] = 0 check_initialization(mod, init, [0, 0, 0], np.diag([1, 0, 0]), desired_cov) # Test with a VAR model endog = np.zeros((10, 2)) mod = varmax.VARMAX(endog, order=(1, 0), ) intercept = [1.5, -0.1] transition = np.array([[0.5, -0.2], [0.1, 0.8]]) cov = np.array([[1.2, -0.4], [-0.4, 0.4]]) tril = np.tril_indices(2) params = np.r_[intercept, transition.ravel(), np.linalg.cholesky(cov)[tril]] mod.update(params) # > stationary, global init = Initialization(mod.k_states, 'stationary') desired_intercept = np.linalg.solve(np.eye(2) - transition, intercept) desired_cov = solve_discrete_lyapunov(transition, cov) check_initialization(mod, init, desired_intercept, np.diag([0, 0]), desired_cov) # > diffuse, global init.set(None, 'diffuse') check_initialization(mod, init, [0, 0], np.eye(2), np.diag([0, 0])) # > stationary, individually init.unset(None) init.set(0, 'stationary') init.set(1, 'stationary') a, Pinf, Pstar = init(model=mod) desired_intercept = [intercept[0] / (1 - transition[0, 0]), intercept[1] / (1 - transition[1, 1])] desired_cov = np.diag([cov[0, 0] / (1 - transition[0, 0]**2), cov[1, 1] / (1 - transition[1, 1]**2)]) check_initialization(mod, init, desired_intercept, np.diag([0, 0]), desired_cov) def test_nested(): endog = np.zeros(10) mod = sarimax.SARIMAX(endog, order=(6, 0, 0)) phi = [0.5, -0.2, 0.1, 0.0, 0.1, 0.0] sigma2 = 2. mod.update(np.r_[phi, sigma2]) # Create the initialization object as a series of nested objects init1_1 = Initialization(3) init1_1_1 = Initialization(2, 'stationary') init1_1_2 = Initialization(1, 'approximate_diffuse', approximate_diffuse_variance=1e9) init1_1.set((0, 2), init1_1_1) init1_1.set(2, init1_1_2) init1_2 = Initialization(3) init1_2_1 = Initialization(1, 'known', constant=[1], stationary_cov=[[2.]]) init1_2.set(0, init1_2_1) init1_2_2 = Initialization(1, 'diffuse') init1_2.set(1, init1_2_2) init1_2_3 = Initialization(1, 'approximate_diffuse') init1_2.set(2, init1_2_3) init = Initialization(6) init.set((0, 3), init1_1) init.set((3, 6), init1_2) # Check the output desired_cov = np.zeros((6, 6)) T = np.array([[0.5, 1], [-0.2, 0]]) Q = np.array([[sigma2, 0], [0, 0]]) desired_cov[:2, :2] = solve_discrete_lyapunov(T, Q) desired_cov[2, 2] = 1e9 desired_cov[3, 3] = 2. desired_cov[5, 5] = 1e6 check_initialization(mod, init, [0, 0, 0, 1, 0, 0], np.diag([0, 0, 0, 0, 1, 0]), desired_cov) def test_invalid(): # Invalid initializations (also tests for some invalid calls to set) assert_raises(ValueError, Initialization, 5, '') assert_raises(ValueError, Initialization, 5, 'stationary', constant=[1, 2]) assert_raises(ValueError, Initialization, 5, 'stationary', stationary_cov=[1, 2]) assert_raises(ValueError, Initialization, 5, 'known') assert_raises(ValueError, Initialization, 5, 'known', constant=[1]) assert_raises(ValueError, Initialization, 5, 'known', stationary_cov=[0]) # Invalid set() / unset() calls init = Initialization(5) assert_raises(ValueError, init.set, -1, 'diffuse') assert_raises(ValueError, init.unset, -1) assert_raises(ValueError, init.set, 5, 'diffuse') assert_raises(ValueError, init.set, 'x', 'diffuse') assert_raises(ValueError, init.unset, 'x') assert_raises(ValueError, init.set, (1, 2, 3), 'diffuse') assert_raises(ValueError, init.unset, (1, 2, 3)) init.set(None, 'diffuse') assert_raises(ValueError, init.set, 1, 'diffuse') init.clear() init.set(1, 'diffuse') assert_raises(ValueError, init.set, None, 'stationary') init.clear() assert_raises(ValueError, init.unset, 1) # Invalid __call__ init = Initialization(2) assert_raises(ValueError, init) init = Initialization(2, 'stationary') assert_raises(ValueError, init) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_kalman.py000066400000000000000000000652401400612667500254570ustar00rootroot00000000000000""" Tests for _representation and _kalman_filter modules Author: Chad Fulton License: Simplified-BSD References ---------- Kim, Chang-Jin, and Charles R. Nelson. 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications". MIT Press Books. The MIT Press. Hamilton, James D. 1994. Time Series Analysis. Princeton, N.J.: Princeton University Press. """ import copy import pickle import numpy as np import pandas as pd import os import pytest from scipy.linalg.blas import find_best_blas_type from scipy.linalg import solve_discrete_lyapunov from statsmodels.tsa.statespace.kalman_filter import ( MEMORY_NO_FORECAST, MEMORY_NO_PREDICTED, MEMORY_CONSERVE) from statsmodels.tsa.statespace.mlemodel import MLEModel from statsmodels.tsa.statespace import _representation, _kalman_filter from .results import results_kalman_filter from numpy.testing import assert_almost_equal, assert_allclose prefix_statespace_map = { 's': _representation.sStatespace, 'd': _representation.dStatespace, 'c': _representation.cStatespace, 'z': _representation.zStatespace } prefix_kalman_filter_map = { 's': _kalman_filter.sKalmanFilter, 'd': _kalman_filter.dKalmanFilter, 'c': _kalman_filter.cKalmanFilter, 'z': _kalman_filter.zKalmanFilter } current_path = os.path.dirname(os.path.abspath(__file__)) class Clark1987(object): """ Clark's (1987) univariate unobserved components model of real GDP (as presented in Kim and Nelson, 1999) Test data produced using GAUSS code described in Kim and Nelson (1999) and found at http://econ.korea.ac.kr/~cjkim/SSMARKOV.htm See `results.results_kalman_filter` for more information. """ @classmethod def setup_class(cls, dtype=float, conserve_memory=0, loglikelihood_burn=0): cls.true = results_kalman_filter.uc_uni cls.true_states = pd.DataFrame(cls.true['states']) # GDP, Quarterly, 1947.1 - 1995.3 data = pd.DataFrame( cls.true['data'], index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'), columns=['GDP'] ) data['lgdp'] = np.log(data['GDP']) # Parameters cls.conserve_memory = conserve_memory cls.loglikelihood_burn = loglikelihood_burn # Observed data cls.obs = np.array(data['lgdp'], ndmin=2, dtype=dtype, order="F") # Measurement equation cls.k_endog = k_endog = 1 # dimension of observed data # design matrix cls.design = np.zeros((k_endog, 4, 1), dtype=dtype, order="F") cls.design[:, :, 0] = [1, 1, 0, 0] # observation intercept cls.obs_intercept = np.zeros((k_endog, 1), dtype=dtype, order="F") # observation covariance matrix cls.obs_cov = np.zeros((k_endog, k_endog, 1), dtype=dtype, order="F") # Transition equation cls.k_states = k_states = 4 # dimension of state space # transition matrix cls.transition = np.zeros((k_states, k_states, 1), dtype=dtype, order="F") cls.transition[([0, 0, 1, 1, 2, 3], [0, 3, 1, 2, 1, 3], [0, 0, 0, 0, 0, 0])] = [1, 1, 0, 0, 1, 1] # state intercept cls.state_intercept = np.zeros((k_states, 1), dtype=dtype, order="F") # selection matrix cls.selection = np.asfortranarray(np.eye(k_states)[:, :, None], dtype=dtype) # state covariance matrix cls.state_cov = np.zeros((k_states, k_states, 1), dtype=dtype, order="F") # Initialization: Diffuse priors cls.initial_state = np.zeros((k_states,), dtype=dtype, order="F") cls.initial_state_cov = np.asfortranarray(np.eye(k_states)*100, dtype=dtype) # Update matrices with given parameters (sigma_v, sigma_e, sigma_w, phi_1, phi_2) = np.array( cls.true['parameters'], dtype=dtype ) cls.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2] cls.state_cov[ np.diag_indices(k_states)+(np.zeros(k_states, dtype=int),)] = [ sigma_v**2, sigma_e**2, 0, sigma_w**2 ] # Initialization: modification # Due to the difference in the way Kim and Nelson (1999) and Durbin # and Koopman (2012) define the order of the Kalman filter routines, # we need to modify the initial state covariance matrix to match # Kim and Nelson's results, since the *Statespace models follow Durbin # and Koopman. cls.initial_state_cov = np.asfortranarray( np.dot( np.dot(cls.transition[:, :, 0], cls.initial_state_cov), cls.transition[:, :, 0].T ) ) @classmethod def init_filter(cls): # Use the appropriate Statespace model prefix = find_best_blas_type((cls.obs,)) klass = prefix_statespace_map[prefix[0]] # Instantiate the statespace model model = klass( cls.obs, cls.design, cls.obs_intercept, cls.obs_cov, cls.transition, cls.state_intercept, cls.selection, cls.state_cov ) model.initialize_known(cls.initial_state, cls.initial_state_cov) # Initialize the appropriate Kalman filter klass = prefix_kalman_filter_map[prefix[0]] kfilter = klass(model, conserve_memory=cls.conserve_memory, loglikelihood_burn=cls.loglikelihood_burn) return model, kfilter @classmethod def run_filter(cls): # Filter the data cls.filter() # Get results return { 'loglike': lambda burn: np.sum(cls.filter.loglikelihood[burn:]), 'state': np.array(cls.filter.filtered_state), } def test_loglike(self): assert_almost_equal( self.result['loglike'](self.true['start']), self.true['loglike'], 5 ) def test_filtered_state(self): assert_almost_equal( self.result['state'][0][self.true['start']:], self.true_states.iloc[:, 0], 4 ) assert_almost_equal( self.result['state'][1][self.true['start']:], self.true_states.iloc[:, 1], 4 ) assert_almost_equal( self.result['state'][3][self.true['start']:], self.true_states.iloc[:, 2], 4 ) def test_pickled_filter(self): pickled = pickle.loads(pickle.dumps(self.filter)) # Run the filters self.filter() pickled() assert id(filter) != id(pickled) assert_allclose(np.array(self.filter.filtered_state), np.array(pickled.filtered_state)) assert_allclose(np.array(self.filter.loglikelihood), np.array(pickled.loglikelihood)) def test_copied_filter(self): copied = copy.deepcopy(self.filter) # Run the filters self.filter() copied() assert id(filter) != id(copied) assert_allclose(np.array(self.filter.filtered_state), np.array(copied.filtered_state)) assert_allclose(np.array(self.filter.loglikelihood), np.array(copied.loglikelihood)) class TestClark1987Single(Clark1987): """ Basic single precision test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): # TODO: Can we be more specific? How can a contributor help? pytest.skip('Not implemented') super(TestClark1987Single, cls).setup_class( dtype=np.float32, conserve_memory=0 ) cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() def test_loglike(self): assert_allclose( self.result['loglike'](self.true['start']), self.true['loglike'], rtol=1e-3 ) def test_filtered_state(self): assert_allclose( self.result['state'][0][self.true['start']:], self.true_states.iloc[:, 0], atol=1e-2 ) assert_allclose( self.result['state'][1][self.true['start']:], self.true_states.iloc[:, 1], atol=1e-2 ) assert_allclose( self.result['state'][3][self.true['start']:], self.true_states.iloc[:, 2], atol=1e-2 ) class TestClark1987Double(Clark1987): """ Basic double precision test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987Double, cls).setup_class( dtype=float, conserve_memory=0 ) cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() class TestClark1987SingleComplex(Clark1987): """ Basic single precision complex test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): # TODO: Can we be more specific? How can a contributor help? pytest.skip('Not implemented') super(TestClark1987SingleComplex, cls).setup_class( dtype=np.complex64, conserve_memory=0 ) cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() def test_loglike(self): assert_allclose( self.result['loglike'](self.true['start']), self.true['loglike'], rtol=1e-3 ) def test_filtered_state(self): assert_allclose( self.result['state'][0][self.true['start']:], self.true_states.iloc[:, 0], atol=1e-2 ) assert_allclose( self.result['state'][1][self.true['start']:], self.true_states.iloc[:, 1], atol=1e-2 ) assert_allclose( self.result['state'][3][self.true['start']:], self.true_states.iloc[:, 2], atol=1e-2 ) class TestClark1987DoubleComplex(Clark1987): """ Basic double precision complex test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987DoubleComplex, cls).setup_class( dtype=complex, conserve_memory=0 ) cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() class TestClark1987Conserve(Clark1987): """ Memory conservation test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987Conserve, cls).setup_class( dtype=float, conserve_memory=MEMORY_NO_FORECAST | MEMORY_NO_PREDICTED ) cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() class Clark1987Forecast(Clark1987): """ Forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls, dtype=float, nforecast=100, conserve_memory=0): super(Clark1987Forecast, cls).setup_class( dtype, conserve_memory ) cls.nforecast = nforecast # Add missing observations to the end (to forecast) cls._obs = cls.obs cls.obs = np.array(np.r_[cls.obs[0, :], [np.nan]*nforecast], ndmin=2, dtype=dtype, order="F") def test_filtered_state(self): assert_almost_equal( self.result['state'][0][self.true['start']:-self.nforecast], self.true_states.iloc[:, 0], 4 ) assert_almost_equal( self.result['state'][1][self.true['start']:-self.nforecast], self.true_states.iloc[:, 1], 4 ) assert_almost_equal( self.result['state'][3][self.true['start']:-self.nforecast], self.true_states.iloc[:, 2], 4 ) class TestClark1987ForecastDouble(Clark1987Forecast): """ Basic double forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987ForecastDouble, cls).setup_class() cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() class TestClark1987ForecastDoubleComplex(Clark1987Forecast): """ Basic double complex forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987ForecastDoubleComplex, cls).setup_class( dtype=complex ) cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() class TestClark1987ForecastConserve(Clark1987Forecast): """ Memory conservation forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987ForecastConserve, cls).setup_class( dtype=float, conserve_memory=MEMORY_NO_FORECAST | MEMORY_NO_PREDICTED ) cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() class TestClark1987ConserveAll(Clark1987): """ Memory conservation forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987ConserveAll, cls).setup_class( dtype=float, conserve_memory=MEMORY_CONSERVE ) cls.loglikelihood_burn = cls.true['start'] cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() def test_loglike(self): assert_almost_equal( self.result['loglike'](0), self.true['loglike'], 5 ) def test_filtered_state(self): end = self.true_states.shape[0] assert_almost_equal( self.result['state'][0][-1], self.true_states.iloc[end-1, 0], 4 ) assert_almost_equal( self.result['state'][1][-1], self.true_states.iloc[end-1, 1], 4 ) class Clark1989(object): """ Clark's (1989) bivariate unobserved components model of real GDP (as presented in Kim and Nelson, 1999) Tests two-dimensional observation data. Test data produced using GAUSS code described in Kim and Nelson (1999) and found at http://econ.korea.ac.kr/~cjkim/SSMARKOV.htm See `results.results_kalman_filter` for more information. """ @classmethod def setup_class(cls, dtype=float, conserve_memory=0, loglikelihood_burn=0): cls.true = results_kalman_filter.uc_bi cls.true_states = pd.DataFrame(cls.true['states']) # GDP and Unemployment, Quarterly, 1948.1 - 1995.3 data = pd.DataFrame( cls.true['data'], index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'), columns=['GDP', 'UNEMP'] )[4:] data['GDP'] = np.log(data['GDP']) data['UNEMP'] = (data['UNEMP']/100) # Observed data cls.obs = np.array(data, ndmin=2, dtype=dtype, order="C").T # Parameters cls.k_endog = k_endog = 2 # dimension of observed data cls.k_states = k_states = 6 # dimension of state space cls.conserve_memory = conserve_memory cls.loglikelihood_burn = loglikelihood_burn # Measurement equation # design matrix cls.design = np.zeros((k_endog, k_states, 1), dtype=dtype, order="F") cls.design[:, :, 0] = [[1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1]] # observation intercept cls.obs_intercept = np.zeros((k_endog, 1), dtype=dtype, order="F") # observation covariance matrix cls.obs_cov = np.zeros((k_endog, k_endog, 1), dtype=dtype, order="F") # Transition equation # transition matrix cls.transition = np.zeros((k_states, k_states, 1), dtype=dtype, order="F") cls.transition[([0, 0, 1, 1, 2, 3, 4, 5], [0, 4, 1, 2, 1, 2, 4, 5], [0, 0, 0, 0, 0, 0, 0, 0])] = [1, 1, 0, 0, 1, 1, 1, 1] # state intercept cls.state_intercept = np.zeros((k_states, 1), dtype=dtype, order="F") # selection matrix cls.selection = np.asfortranarray(np.eye(k_states)[:, :, None], dtype=dtype) # state covariance matrix cls.state_cov = np.zeros((k_states, k_states, 1), dtype=dtype, order="F") # Initialization: Diffuse priors cls.initial_state = np.zeros((k_states,), dtype=dtype) cls.initial_state_cov = np.asfortranarray(np.eye(k_states)*100, dtype=dtype) # Update matrices with given parameters (sigma_v, sigma_e, sigma_w, sigma_vl, sigma_ec, phi_1, phi_2, alpha_1, alpha_2, alpha_3) = np.array( cls.true['parameters'], dtype=dtype ) cls.design[([1, 1, 1], [1, 2, 3], [0, 0, 0])] = [ alpha_1, alpha_2, alpha_3 ] cls.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2] cls.obs_cov[1, 1, 0] = sigma_ec**2 cls.state_cov[ np.diag_indices(k_states)+(np.zeros(k_states, dtype=int),)] = [ sigma_v**2, sigma_e**2, 0, 0, sigma_w**2, sigma_vl**2 ] # Initialization: modification # Due to the difference in the way Kim and Nelson (1999) and Drubin # and Koopman (2012) define the order of the Kalman filter routines, # we need to modify the initial state covariance matrix to match # Kim and Nelson's results, since the *Statespace models follow Durbin # and Koopman. cls.initial_state_cov = np.asfortranarray( np.dot( np.dot(cls.transition[:, :, 0], cls.initial_state_cov), cls.transition[:, :, 0].T ) ) @classmethod def init_filter(cls): # Use the appropriate Statespace model prefix = find_best_blas_type((cls.obs,)) klass = prefix_statespace_map[prefix[0]] # Instantiate the statespace model model = klass( cls.obs, cls.design, cls.obs_intercept, cls.obs_cov, cls.transition, cls.state_intercept, cls.selection, cls.state_cov ) model.initialize_known(cls.initial_state, cls.initial_state_cov) # Initialize the appropriate Kalman filter klass = prefix_kalman_filter_map[prefix[0]] kfilter = klass(model, conserve_memory=cls.conserve_memory, loglikelihood_burn=cls.loglikelihood_burn) return model, kfilter @classmethod def run_filter(cls): # Filter the data cls.filter() # Get results return { 'loglike': lambda burn: np.sum(cls.filter.loglikelihood[burn:]), 'state': np.array(cls.filter.filtered_state), } def test_loglike(self): assert_almost_equal( # self.result['loglike'](self.true['start']), self.result['loglike'](0), self.true['loglike'], 2 ) def test_filtered_state(self): assert_almost_equal( self.result['state'][0][self.true['start']:], self.true_states.iloc[:, 0], 4 ) assert_almost_equal( self.result['state'][1][self.true['start']:], self.true_states.iloc[:, 1], 4 ) assert_almost_equal( self.result['state'][4][self.true['start']:], self.true_states.iloc[:, 2], 4 ) assert_almost_equal( self.result['state'][5][self.true['start']:], self.true_states.iloc[:, 3], 4 ) class TestClark1989(Clark1989): """ Basic double precision test for the loglikelihood and filtered states with two-dimensional observation vector. """ @classmethod def setup_class(cls): super(TestClark1989, cls).setup_class(dtype=float, conserve_memory=0) cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() class TestClark1989Conserve(Clark1989): """ Memory conservation test for the loglikelihood and filtered states with two-dimensional observation vector. """ @classmethod def setup_class(cls): super(TestClark1989Conserve, cls).setup_class( dtype=float, conserve_memory=MEMORY_NO_FORECAST | MEMORY_NO_PREDICTED ) cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() class Clark1989Forecast(Clark1989): """ Memory conservation test for the loglikelihood and filtered states with two-dimensional observation vector. """ @classmethod def setup_class(cls, dtype=float, nforecast=100, conserve_memory=0): super(Clark1989Forecast, cls).setup_class(dtype, conserve_memory) cls.nforecast = nforecast # Add missing observations to the end (to forecast) cls._obs = cls.obs cls.obs = np.array( np.c_[ cls._obs, np.r_[[np.nan, np.nan]*nforecast].reshape(2, nforecast) ], ndmin=2, dtype=dtype, order="F" ) cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() def test_filtered_state(self): assert_almost_equal( self.result['state'][0][self.true['start']:-self.nforecast], self.true_states.iloc[:, 0], 4 ) assert_almost_equal( self.result['state'][1][self.true['start']:-self.nforecast], self.true_states.iloc[:, 1], 4 ) assert_almost_equal( self.result['state'][4][self.true['start']:-self.nforecast], self.true_states.iloc[:, 2], 4 ) assert_almost_equal( self.result['state'][5][self.true['start']:-self.nforecast], self.true_states.iloc[:, 3], 4 ) class TestClark1989ForecastDouble(Clark1989Forecast): """ Basic double forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1989ForecastDouble, cls).setup_class() cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() class TestClark1989ForecastDoubleComplex(Clark1989Forecast): """ Basic double complex forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1989ForecastDoubleComplex, cls).setup_class( dtype=complex ) cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() class TestClark1989ForecastConserve(Clark1989Forecast): """ Memory conservation forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1989ForecastConserve, cls).setup_class( dtype=float, conserve_memory=MEMORY_NO_FORECAST | MEMORY_NO_PREDICTED ) cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() class TestClark1989ConserveAll(Clark1989): """ Memory conservation forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1989ConserveAll, cls).setup_class( dtype=float, conserve_memory=MEMORY_CONSERVE, ) # cls.loglikelihood_burn = cls.true['start'] cls.loglikelihood_burn = 0 cls.model, cls.filter = cls.init_filter() cls.result = cls.run_filter() def test_loglike(self): assert_almost_equal( self.result['loglike'](0), self.true['loglike'], 2 ) def test_filtered_state(self): end = self.true_states.shape[0] assert_almost_equal( self.result['state'][0][-1], self.true_states.iloc[end-1, 0], 4 ) assert_almost_equal( self.result['state'][1][-1], self.true_states.iloc[end-1, 1], 4 ) assert_almost_equal( self.result['state'][4][-1], self.true_states.iloc[end-1, 2], 4 ) assert_almost_equal( self.result['state'][5][-1], self.true_states.iloc[end-1, 3], 4 ) def check_stationary_initialization_1dim(dtype=float): endog = np.zeros(10, dtype=dtype) # 1-dimensional example mod = MLEModel(endog, k_states=1, k_posdef=1) mod.ssm.initialize_stationary() intercept = np.array([2.3], dtype=dtype) phi = np.diag([0.9]).astype(dtype) sigma2 = np.diag([1.3]).astype(dtype) mod['state_intercept'] = intercept mod['transition'] = phi mod['selection'] = np.eye(1).astype(dtype) mod['state_cov'] = sigma2 mod.ssm._initialize_filter() mod.ssm._initialize_state() _statespace = mod.ssm._statespace initial_state = np.array(_statespace.initial_state) initial_state_cov = np.array(_statespace.initial_state_cov) # precision reductions only required for float complex case # mean = intercept + phi * mean # intercept = (1 - phi) * mean # mean = intercept / (1 - phi) assert_allclose(initial_state, intercept / (1 - phi[0, 0])) desired = np.linalg.inv(np.eye(1) - phi).dot(intercept) assert_allclose(initial_state, desired) # var = phi**2 var + sigma2 # var = sigma2 / (1 - phi**2) assert_allclose(initial_state_cov, sigma2 / (1 - phi**2)) assert_allclose(initial_state_cov, solve_discrete_lyapunov(phi, sigma2)) def check_stationary_initialization_2dim(dtype=float): endog = np.zeros(10, dtype=dtype) # 2-dimensional example mod = MLEModel(endog, k_states=2, k_posdef=2) mod.ssm.initialize_stationary() intercept = np.array([2.3, -10.2], dtype=dtype) phi = np.array([[0.8, 0.1], [-0.2, 0.7]], dtype=dtype) sigma2 = np.array([[1.4, -0.2], [-0.2, 4.5]], dtype=dtype) mod['state_intercept'] = intercept mod['transition'] = phi mod['selection'] = np.eye(2).astype(dtype) mod['state_cov'] = sigma2 mod.ssm._initialize_filter() mod.ssm._initialize_state() _statespace = mod.ssm._statespace initial_state = np.array(_statespace.initial_state) initial_state_cov = np.array(_statespace.initial_state_cov) desired = np.linalg.solve(np.eye(2).astype(dtype) - phi, intercept) assert_allclose(initial_state, desired) desired = solve_discrete_lyapunov(phi, sigma2) # precision reductions only required for single precision float / complex assert_allclose(initial_state_cov, desired, atol=1e-5) def test_stationary_initialization(): check_stationary_initialization_1dim(np.float32) check_stationary_initialization_1dim(np.float64) check_stationary_initialization_1dim(np.complex64) check_stationary_initialization_1dim(np.complex128) check_stationary_initialization_2dim(np.float32) check_stationary_initialization_2dim(np.float64) check_stationary_initialization_2dim(np.complex64) check_stationary_initialization_2dim(np.complex128) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_mlemodel.py000066400000000000000000001323031400612667500260050ustar00rootroot00000000000000""" Tests for the generic MLEModel Author: Chad Fulton License: Simplified-BSD """ import os import re import warnings import numpy as np import pandas as pd import pytest from statsmodels.tsa.statespace import (sarimax, varmax, kalman_filter, kalman_smoother) from statsmodels.tsa.statespace.mlemodel import MLEModel, MLEResultsWrapper from statsmodels.datasets import nile from numpy.testing import ( assert_, assert_almost_equal, assert_equal, assert_allclose, assert_raises) from statsmodels.tsa.statespace.tests.results import ( results_sarimax, results_var_misc) current_path = os.path.dirname(os.path.abspath(__file__)) # Basic kwargs kwargs = { 'k_states': 1, 'design': [[1]], 'transition': [[1]], 'selection': [[1]], 'state_cov': [[1]], 'initialization': 'approximate_diffuse' } def get_dummy_mod(fit=True, pandas=False): # This tests time-varying parameters regression when in fact the parameters # are not time-varying, and in fact the regression fit is perfect endog = np.arange(100)*1.0 exog = 2*endog if pandas: index = pd.date_range('1960-01-01', periods=100, freq='MS') endog = pd.Series(endog, index=index) exog = pd.Series(exog, index=index) mod = sarimax.SARIMAX( endog, exog=exog, order=(0, 0, 0), time_varying_regression=True, mle_regression=False, use_exact_diffuse=True) if fit: with warnings.catch_warnings(): warnings.simplefilter("ignore") res = mod.fit(disp=-1) else: res = None return mod, res def test_init_matrices_time_invariant(): # Test setting state space system matrices in __init__, with time-invariant # matrices k_endog = 2 k_states = 3 k_posdef = 1 endog = np.zeros((10, 2)) obs_intercept = np.arange(k_endog) * 1.0 design = np.reshape( np.arange(k_endog * k_states) * 1.0, (k_endog, k_states)) obs_cov = np.reshape(np.arange(k_endog**2) * 1.0, (k_endog, k_endog)) state_intercept = np.arange(k_states) * 1.0 transition = np.reshape(np.arange(k_states**2) * 1.0, (k_states, k_states)) selection = np.reshape( np.arange(k_states * k_posdef) * 1.0, (k_states, k_posdef)) state_cov = np.reshape(np.arange(k_posdef**2) * 1.0, (k_posdef, k_posdef)) mod = MLEModel(endog, k_states=k_states, k_posdef=k_posdef, obs_intercept=obs_intercept, design=design, obs_cov=obs_cov, state_intercept=state_intercept, transition=transition, selection=selection, state_cov=state_cov) assert_allclose(mod['obs_intercept'], obs_intercept) assert_allclose(mod['design'], design) assert_allclose(mod['obs_cov'], obs_cov) assert_allclose(mod['state_intercept'], state_intercept) assert_allclose(mod['transition'], transition) assert_allclose(mod['selection'], selection) assert_allclose(mod['state_cov'], state_cov) def test_init_matrices_time_varying(): # Test setting state space system matrices in __init__, with time-varying # matrices nobs = 10 k_endog = 2 k_states = 3 k_posdef = 1 endog = np.zeros((10, 2)) obs_intercept = np.reshape(np.arange(k_endog * nobs) * 1.0, (k_endog, nobs)) design = np.reshape( np.arange(k_endog * k_states * nobs) * 1.0, (k_endog, k_states, nobs)) obs_cov = np.reshape( np.arange(k_endog**2 * nobs) * 1.0, (k_endog, k_endog, nobs)) state_intercept = np.reshape( np.arange(k_states * nobs) * 1.0, (k_states, nobs)) transition = np.reshape( np.arange(k_states**2 * nobs) * 1.0, (k_states, k_states, nobs)) selection = np.reshape( np.arange(k_states * k_posdef * nobs) * 1.0, (k_states, k_posdef, nobs)) state_cov = np.reshape( np.arange(k_posdef**2 * nobs) * 1.0, (k_posdef, k_posdef, nobs)) mod = MLEModel(endog, k_states=k_states, k_posdef=k_posdef, obs_intercept=obs_intercept, design=design, obs_cov=obs_cov, state_intercept=state_intercept, transition=transition, selection=selection, state_cov=state_cov) assert_allclose(mod['obs_intercept'], obs_intercept) assert_allclose(mod['design'], design) assert_allclose(mod['obs_cov'], obs_cov) assert_allclose(mod['state_intercept'], state_intercept) assert_allclose(mod['transition'], transition) assert_allclose(mod['selection'], selection) assert_allclose(mod['state_cov'], state_cov) def test_wrapping(): # Test the wrapping of various Representation / KalmanFilter / # KalmanSmoother methods / attributes mod, _ = get_dummy_mod(fit=False) # Test that we can get the design matrix assert_equal(mod['design', 0, 0], 2.0 * np.arange(100)) # Test that we can set individual elements of the design matrix mod['design', 0, 0, :] = 2 assert_equal(mod.ssm['design', 0, 0, :], 2) assert_equal(mod.ssm['design'].shape, (1, 1, 100)) # Test that we can set the entire design matrix mod['design'] = [[3.]] assert_equal(mod.ssm['design', 0, 0], 3.) # (Now it's no longer time-varying, so only 2-dim) assert_equal(mod.ssm['design'].shape, (1, 1)) # Test that we can change the following properties: loglikelihood_burn, # initial_variance, tolerance assert_equal(mod.loglikelihood_burn, 0) mod.loglikelihood_burn = 1 assert_equal(mod.ssm.loglikelihood_burn, 1) assert_equal(mod.tolerance, mod.ssm.tolerance) mod.tolerance = 0.123 assert_equal(mod.ssm.tolerance, 0.123) assert_equal(mod.initial_variance, 1e10) mod.initial_variance = 1e12 assert_equal(mod.ssm.initial_variance, 1e12) # Test that we can use the following wrappers: initialization, # initialize_known, initialize_stationary, initialize_approximate_diffuse # Initialization starts off as none assert_equal(isinstance(mod.initialization, object), True) # Since the SARIMAX model may be fully stationary or may have diffuse # elements, it uses a custom initialization by default, but it can be # overridden by users mod.initialize_default() # no-op here mod.initialize_approximate_diffuse(1e5) assert_equal(mod.initialization.initialization_type, 'approximate_diffuse') assert_equal(mod.initialization.approximate_diffuse_variance, 1e5) mod.initialize_known([5.], [[40]]) assert_equal(mod.initialization.initialization_type, 'known') assert_equal(mod.initialization.constant, [5.]) assert_equal(mod.initialization.stationary_cov, [[40]]) mod.initialize_stationary() assert_equal(mod.initialization.initialization_type, 'stationary') # Test that we can use the following wrapper methods: set_filter_method, # set_stability_method, set_conserve_memory, set_smoother_output # The defaults are as follows: assert_equal(mod.ssm.filter_method, kalman_filter.FILTER_CONVENTIONAL) assert_equal( mod.ssm.stability_method, kalman_filter.STABILITY_FORCE_SYMMETRY) assert_equal(mod.ssm.conserve_memory, kalman_filter.MEMORY_STORE_ALL) assert_equal(mod.ssm.smoother_output, kalman_smoother.SMOOTHER_ALL) # Now, create the Cython filter object and assert that they have # transferred correctly mod.ssm._initialize_filter() kf = mod.ssm._kalman_filter assert_equal(kf.filter_method, kalman_filter.FILTER_CONVENTIONAL) assert_equal(kf.stability_method, kalman_filter.STABILITY_FORCE_SYMMETRY) assert_equal(kf.conserve_memory, kalman_filter.MEMORY_STORE_ALL) # (the smoother object is so far not in Cython, so there is no # transferring) # Change the attributes in the model class mod.set_filter_method(100) mod.set_stability_method(101) mod.set_conserve_memory(102) mod.set_smoother_output(103) # Assert that the changes have occurred in the ssm class assert_equal(mod.ssm.filter_method, 100) assert_equal(mod.ssm.stability_method, 101) assert_equal(mod.ssm.conserve_memory, 102) assert_equal(mod.ssm.smoother_output, 103) # Assert that the changes have *not yet* occurred in the filter object assert_equal(kf.filter_method, kalman_filter.FILTER_CONVENTIONAL) assert_equal(kf.stability_method, kalman_filter.STABILITY_FORCE_SYMMETRY) assert_equal(kf.conserve_memory, kalman_filter.MEMORY_STORE_ALL) # Now, test the setting of the other two methods by resetting the # filter method to a valid value mod.set_filter_method(1) mod.ssm._initialize_filter() # Retrieve the new kalman filter object (a new object had to be created # due to the changing filter method) kf = mod.ssm._kalman_filter assert_equal(kf.filter_method, 1) assert_equal(kf.stability_method, 101) assert_equal(kf.conserve_memory, 102) def test_fit_misc(): true = results_sarimax.wpi1_stationary endog = np.diff(true['data'])[1:] mod = sarimax.SARIMAX(endog, order=(1, 0, 1), trend='c') # Test optim_hessian={'opg','oim','approx'} with warnings.catch_warnings(): warnings.simplefilter("ignore") res1 = mod.fit(method='ncg', disp=0, optim_hessian='opg', optim_complex_step=False) res2 = mod.fit(method='ncg', disp=0, optim_hessian='oim', optim_complex_step=False) # Check that the Hessians broadly result in the same optimum assert_allclose(res1.llf, res2.llf, rtol=1e-2) # Test return_params=True mod, _ = get_dummy_mod(fit=False) with warnings.catch_warnings(): warnings.simplefilter("ignore") res_params = mod.fit(disp=-1, return_params=True) # 5 digits necessary to accommodate 32-bit numpy/scipy with OpenBLAS 0.2.18 assert_almost_equal(res_params, [0, 0], 5) @pytest.mark.smoke def test_score_misc(): mod, res = get_dummy_mod() # Test that the score function works mod.score(res.params) def test_from_formula(): assert_raises(NotImplementedError, lambda: MLEModel.from_formula(1, 2, 3)) def test_score_analytic_ar1(): # Test the score against the analytic score for an AR(1) model with 2 # observations # Let endog = [1, 0.5], params=[0, 1] mod = sarimax.SARIMAX([1, 0.5], order=(1, 0, 0)) def partial_phi(phi, sigma2): return -0.5 * (phi**2 + 2*phi*sigma2 - 1) / (sigma2 * (1 - phi**2)) def partial_sigma2(phi, sigma2): return -0.5 * (2*sigma2 + phi - 1.25) / (sigma2**2) params = np.r_[0., 2] # Compute the analytic score analytic_score = np.r_[ partial_phi(params[0], params[1]), partial_sigma2(params[0], params[1])] # Check each of the approximations, transformed parameters approx_cs = mod.score(params, transformed=True, approx_complex_step=True) assert_allclose(approx_cs, analytic_score) approx_fd = mod.score(params, transformed=True, approx_complex_step=False) assert_allclose(approx_fd, analytic_score, atol=1e-5) approx_fd_centered = ( mod.score(params, transformed=True, approx_complex_step=False, approx_centered=True)) assert_allclose(approx_fd, analytic_score, atol=1e-5) harvey_cs = mod.score(params, transformed=True, method='harvey', approx_complex_step=True) assert_allclose(harvey_cs, analytic_score) harvey_fd = mod.score(params, transformed=True, method='harvey', approx_complex_step=False) assert_allclose(harvey_fd, analytic_score, atol=1e-5) harvey_fd_centered = mod.score(params, transformed=True, method='harvey', approx_complex_step=False, approx_centered=True) assert_allclose(harvey_fd_centered, analytic_score, atol=1e-5) # Check the approximations for untransformed parameters. The analytic # check now comes from chain rule with the analytic derivative of the # transformation # if L* is the likelihood evaluated at untransformed parameters and # L is the likelihood evaluated at transformed parameters, then we have: # L*(u) = L(t(u)) # and then # L'*(u) = L'(t(u)) * t'(u) def partial_transform_phi(phi): return -1. / (1 + phi**2)**(3./2) def partial_transform_sigma2(sigma2): return 2. * sigma2 uparams = mod.untransform_params(params) analytic_score = np.dot( np.diag(np.r_[partial_transform_phi(uparams[0]), partial_transform_sigma2(uparams[1])]), np.r_[partial_phi(params[0], params[1]), partial_sigma2(params[0], params[1])]) approx_cs = mod.score(uparams, transformed=False, approx_complex_step=True) assert_allclose(approx_cs, analytic_score) approx_fd = mod.score(uparams, transformed=False, approx_complex_step=False) assert_allclose(approx_fd, analytic_score, atol=1e-5) approx_fd_centered = ( mod.score(uparams, transformed=False, approx_complex_step=False, approx_centered=True)) assert_allclose(approx_fd_centered, analytic_score, atol=1e-5) harvey_cs = mod.score(uparams, transformed=False, method='harvey', approx_complex_step=True) assert_allclose(harvey_cs, analytic_score) harvey_fd = mod.score(uparams, transformed=False, method='harvey', approx_complex_step=False) assert_allclose(harvey_fd, analytic_score, atol=1e-5) harvey_fd_centered = mod.score(uparams, transformed=False, method='harvey', approx_complex_step=False, approx_centered=True) assert_allclose(harvey_fd_centered, analytic_score, atol=1e-5) # Check the Hessian: these approximations are not very good, particularly # when phi is close to 0 params = np.r_[0.5, 1.] def hessian(phi, sigma2): hessian = np.zeros((2, 2)) hessian[0, 0] = (-phi**2 - 1) / (phi**2 - 1)**2 hessian[1, 0] = hessian[0, 1] = -1 / (2 * sigma2**2) hessian[1, 1] = (sigma2 + phi - 1.25) / sigma2**3 return hessian analytic_hessian = hessian(params[0], params[1]) with warnings.catch_warnings(): warnings.simplefilter("ignore") assert_allclose(mod._hessian_complex_step(params) * 2, analytic_hessian, atol=1e-1) assert_allclose(mod._hessian_finite_difference(params) * 2, analytic_hessian, atol=1e-1) def test_cov_params(): mod, res = get_dummy_mod() # Smoke test for each of the covariance types with warnings.catch_warnings(): warnings.simplefilter("ignore") res = mod.fit(res.params, disp=-1, cov_type='none') assert_equal( res.cov_kwds['description'], 'Covariance matrix not calculated.') res = mod.fit(res.params, disp=-1, cov_type='approx') assert_equal(res.cov_type, 'approx') assert_equal( res.cov_kwds['description'], 'Covariance matrix calculated using numerical (complex-step) ' 'differentiation.') res = mod.fit(res.params, disp=-1, cov_type='oim') assert_equal(res.cov_type, 'oim') assert_equal( res.cov_kwds['description'], 'Covariance matrix calculated using the observed information ' 'matrix (complex-step) described in Harvey (1989).') res = mod.fit(res.params, disp=-1, cov_type='opg') assert_equal(res.cov_type, 'opg') assert_equal( res.cov_kwds['description'], 'Covariance matrix calculated using the outer product of ' 'gradients (complex-step).') res = mod.fit(res.params, disp=-1, cov_type='robust') assert_equal(res.cov_type, 'robust') assert_equal( res.cov_kwds['description'], 'Quasi-maximum likelihood covariance matrix used for robustness ' 'to some misspecifications; calculated using the observed ' 'information matrix (complex-step) described in Harvey (1989).') res = mod.fit(res.params, disp=-1, cov_type='robust_oim') assert_equal(res.cov_type, 'robust_oim') assert_equal( res.cov_kwds['description'], 'Quasi-maximum likelihood covariance matrix used for robustness ' 'to some misspecifications; calculated using the observed ' 'information matrix (complex-step) described in Harvey (1989).') res = mod.fit(res.params, disp=-1, cov_type='robust_approx') assert_equal(res.cov_type, 'robust_approx') assert_equal( res.cov_kwds['description'], 'Quasi-maximum likelihood covariance matrix used for robustness ' 'to some misspecifications; calculated using numerical ' '(complex-step) differentiation.') with pytest.raises(NotImplementedError): mod.fit(res.params, disp=-1, cov_type='invalid_cov_type') def test_transform(): # The transforms in MLEModel are noops mod = MLEModel([1, 2], **kwargs) # Test direct transform, untransform assert_allclose(mod.transform_params([2, 3]), [2, 3]) assert_allclose(mod.untransform_params([2, 3]), [2, 3]) # Smoke test for transformation in `filter`, `update`, `loglike`, # `loglikeobs` mod.filter([], transformed=False) mod.update([], transformed=False) mod.loglike([], transformed=False) mod.loglikeobs([], transformed=False) # Note that mod is an SARIMAX instance, and the two parameters are # variances mod, _ = get_dummy_mod(fit=False) # Test direct transform, untransform assert_allclose(mod.transform_params([2, 3]), [4, 9]) assert_allclose(mod.untransform_params([4, 9]), [2, 3]) # Test transformation in `filter` res = mod.filter([2, 3], transformed=True) assert_allclose(res.params, [2, 3]) res = mod.filter([2, 3], transformed=False) assert_allclose(res.params, [4, 9]) def test_filter(): endog = np.array([1., 2.]) mod = MLEModel(endog, **kwargs) # Test return of ssm object res = mod.filter([], return_ssm=True) assert_equal(isinstance(res, kalman_filter.FilterResults), True) # Test return of full results object res = mod.filter([]) assert_equal(isinstance(res, MLEResultsWrapper), True) assert_equal(res.cov_type, 'opg') # Test return of full results object, specific covariance type res = mod.filter([], cov_type='oim') assert_equal(isinstance(res, MLEResultsWrapper), True) assert_equal(res.cov_type, 'oim') def test_params(): mod = MLEModel([1, 2], **kwargs) # By default start_params raises NotImplementedError assert_raises(NotImplementedError, lambda: mod.start_params) # But param names are by default an empty array assert_equal(mod.param_names, []) # We can set them in the object if we want mod._start_params = [1] mod._param_names = ['a'] assert_equal(mod.start_params, [1]) assert_equal(mod.param_names, ['a']) def check_results(pandas): mod, res = get_dummy_mod(pandas=pandas) # Test fitted values assert_almost_equal(res.fittedvalues[2:], mod.endog[2:].squeeze()) # Test residuals assert_almost_equal(res.resid[2:], np.zeros(mod.nobs-2)) # Test loglikelihood_burn assert_equal(res.loglikelihood_burn, 0) def test_results(pandas=False): check_results(pandas=False) check_results(pandas=True) def test_predict(): dates = pd.date_range(start='1980-01-01', end='1981-01-01', freq='AS') endog = pd.Series([1, 2], index=dates) mod = MLEModel(endog, **kwargs) res = mod.filter([]) # Test that predict with start=None, end=None does prediction with full # dataset predict = res.predict() assert_equal(predict.shape, (mod.nobs,)) assert_allclose(res.get_prediction().predicted_mean, predict) # Test a string value to the dynamic option assert_allclose(res.predict(dynamic='1981-01-01'), res.predict()) # Test an invalid date string value to the dynamic option # assert_raises(ValueError, res.predict, dynamic='1982-01-01') # Test for passing a string to predict when dates are not set mod = MLEModel([1, 2], **kwargs) res = mod.filter([]) assert_raises(KeyError, res.predict, dynamic='string') def test_forecast(): # Numpy mod = MLEModel([1, 2], **kwargs) res = mod.filter([]) forecast = res.forecast(steps=10) assert_allclose(forecast, np.ones((10,)) * 2) assert_allclose(res.get_forecast(steps=10).predicted_mean, forecast) # Pandas index = pd.date_range('1960-01-01', periods=2, freq='MS') mod = MLEModel(pd.Series([1, 2], index=index), **kwargs) res = mod.filter([]) assert_allclose(res.forecast(steps=10), np.ones((10,)) * 2) assert_allclose(res.forecast(steps='1960-12-01'), np.ones((10,)) * 2) assert_allclose(res.get_forecast(steps=10).predicted_mean, np.ones((10,)) * 2) def test_summary(): dates = pd.date_range(start='1980-01-01', end='1984-01-01', freq='AS') endog = pd.Series([1, 2, 3, 4, 5], index=dates) mod = MLEModel(endog, **kwargs) res = mod.filter([]) # Get the summary txt = str(res.summary()) # Test res.summary when the model has dates assert_equal(re.search(r'Sample:\s+01-01-1980', txt) is not None, True) assert_equal(re.search(r'\s+- 01-01-1984', txt) is not None, True) # Test res.summary when `model_name` was not provided assert_equal(re.search(r'Model:\s+MLEModel', txt) is not None, True) # Smoke test that summary still works when diagnostic tests fail with warnings.catch_warnings(): warnings.simplefilter("ignore") res.filter_results._standardized_forecasts_error[:] = np.nan res.summary() res.filter_results._standardized_forecasts_error = 1 res.summary() res.filter_results._standardized_forecasts_error = 'a' res.summary() def check_endog(endog, nobs=2, k_endog=1, **kwargs): # create the model mod = MLEModel(endog, **kwargs) # the data directly available in the model is the statsmodels version of # the data; it should be 2-dim, C-contiguous, long-shaped: # (nobs, k_endog) == (2, 1) assert_equal(mod.endog.ndim, 2) assert_equal(mod.endog.flags['C_CONTIGUOUS'], True) assert_equal(mod.endog.shape, (nobs, k_endog)) # the data in the `ssm` object is the state space version of the data; it # should be 2-dim, F-contiguous, wide-shaped (k_endog, nobs) == (1, 2) # and it should share data with mod.endog assert_equal(mod.ssm.endog.ndim, 2) assert_equal(mod.ssm.endog.flags['F_CONTIGUOUS'], True) assert_equal(mod.ssm.endog.shape, (k_endog, nobs)) assert_equal(mod.ssm.endog.base is mod.endog, True) return mod def test_basic_endog(): # Test various types of basic python endog inputs (e.g. lists, scalars...) # Check cannot call with non-array_like # fails due to checks in statsmodels base classes assert_raises(ValueError, MLEModel, endog=1, k_states=1) assert_raises(ValueError, MLEModel, endog='a', k_states=1) assert_raises(ValueError, MLEModel, endog=True, k_states=1) # Check behavior with different types mod = MLEModel([1], **kwargs) res = mod.filter([]) assert_equal(res.filter_results.endog, [[1]]) mod = MLEModel([1.], **kwargs) res = mod.filter([]) assert_equal(res.filter_results.endog, [[1]]) mod = MLEModel([True], **kwargs) res = mod.filter([]) assert_equal(res.filter_results.endog, [[1]]) mod = MLEModel(['a'], **kwargs) # raises error due to inability coerce string to numeric assert_raises(ValueError, mod.filter, []) # Check that a different iterable tpyes give the expected result endog = [1., 2.] mod = check_endog(endog, **kwargs) mod.filter([]) endog = [[1.], [2.]] mod = check_endog(endog, **kwargs) mod.filter([]) endog = (1., 2.) mod = check_endog(endog, **kwargs) mod.filter([]) def test_numpy_endog(): # Test various types of numpy endog inputs # Check behavior of the link maintained between passed `endog` and # `mod.endog` arrays endog = np.array([1., 2.]) mod = MLEModel(endog, **kwargs) assert_equal(mod.endog.base is not mod.data.orig_endog, True) assert_equal(mod.endog.base is not endog, True) assert_equal(mod.data.orig_endog.base is not endog, True) endog[0] = 2 # there is no link to mod.endog assert_equal(mod.endog, np.r_[1, 2].reshape(2, 1)) # there remains a link to mod.data.orig_endog assert_equal(mod.data.orig_endog, endog) # Check behavior with different memory layouts / shapes # Example (failure): 0-dim array endog = np.array(1.) # raises error due to len(endog) failing in statsmodels base classes assert_raises(TypeError, check_endog, endog, **kwargs) # Example : 1-dim array, both C- and F-contiguous, length 2 endog = np.array([1., 2.]) assert_equal(endog.ndim, 1) assert_equal(endog.flags['C_CONTIGUOUS'], True) assert_equal(endog.flags['F_CONTIGUOUS'], True) assert_equal(endog.shape, (2,)) mod = check_endog(endog, **kwargs) mod.filter([]) # Example : 2-dim array, C-contiguous, long-shaped: (nobs, k_endog) endog = np.array([1., 2.]).reshape(2, 1) assert_equal(endog.ndim, 2) assert_equal(endog.flags['C_CONTIGUOUS'], True) # On newer numpy (>= 0.10), this array is (rightly) both C and F contiguous # assert_equal(endog.flags['F_CONTIGUOUS'], False) assert_equal(endog.shape, (2, 1)) mod = check_endog(endog, **kwargs) mod.filter([]) # Example : 2-dim array, C-contiguous, wide-shaped: (k_endog, nobs) endog = np.array([1., 2.]).reshape(1, 2) assert_equal(endog.ndim, 2) assert_equal(endog.flags['C_CONTIGUOUS'], True) # On newer numpy (>= 0.10), this array is (rightly) both C and F contiguous # assert_equal(endog.flags['F_CONTIGUOUS'], False) assert_equal(endog.shape, (1, 2)) # raises error because arrays are always interpreted as # (nobs, k_endog), which means that k_endog=2 is incompatibile with shape # of design matrix (1, 1) assert_raises(ValueError, check_endog, endog, **kwargs) # Example : 2-dim array, F-contiguous, long-shaped (nobs, k_endog) endog = np.array([1., 2.]).reshape(1, 2).transpose() assert_equal(endog.ndim, 2) # On newer numpy (>= 0.10), this array is (rightly) both C and F contiguous # assert_equal(endog.flags['C_CONTIGUOUS'], False) assert_equal(endog.flags['F_CONTIGUOUS'], True) assert_equal(endog.shape, (2, 1)) mod = check_endog(endog, **kwargs) mod.filter([]) # Example : 2-dim array, F-contiguous, wide-shaped (k_endog, nobs) endog = np.array([1., 2.]).reshape(2, 1).transpose() assert_equal(endog.ndim, 2) # On newer numpy (>= 0.10), this array is (rightly) both C and F contiguous # assert_equal(endog.flags['C_CONTIGUOUS'], False) assert_equal(endog.flags['F_CONTIGUOUS'], True) assert_equal(endog.shape, (1, 2)) # raises error because arrays are always interpreted as # (nobs, k_endog), which means that k_endog=2 is incompatibile with shape # of design matrix (1, 1) assert_raises(ValueError, check_endog, endog, **kwargs) # Example (failure): 3-dim array endog = np.array([1., 2.]).reshape(2, 1, 1) # raises error due to direct ndim check in statsmodels base classes assert_raises(ValueError, check_endog, endog, **kwargs) # Example : np.array with 2 columns # Update kwargs for k_endog=2 kwargs2 = { 'k_states': 1, 'design': [[1], [0.]], 'obs_cov': [[1, 0], [0, 1]], 'transition': [[1]], 'selection': [[1]], 'state_cov': [[1]], 'initialization': 'approximate_diffuse' } endog = np.array([[1., 2.], [3., 4.]]) mod = check_endog(endog, k_endog=2, **kwargs2) mod.filter([]) def test_pandas_endog(): # Test various types of pandas endog inputs (e.g. TimeSeries, etc.) # Example (failure): pandas.Series, no dates endog = pd.Series([1., 2.]) # raises error due to no dates warnings.simplefilter('always') # assert_raises(ValueError, check_endog, endog, **kwargs) # Example : pandas.Series dates = pd.date_range(start='1980-01-01', end='1981-01-01', freq='AS') endog = pd.Series([1., 2.], index=dates) mod = check_endog(endog, **kwargs) mod.filter([]) # Example : pandas.Series, string datatype endog = pd.Series(['a', 'b'], index=dates) # raises error due to direct type casting check in statsmodels base classes assert_raises(ValueError, check_endog, endog, **kwargs) # Example : pandas.Series endog = pd.Series([1., 2.], index=dates) mod = check_endog(endog, **kwargs) mod.filter([]) # Example : pandas.DataFrame with 1 column endog = pd.DataFrame({'a': [1., 2.]}, index=dates) mod = check_endog(endog, **kwargs) mod.filter([]) # Example (failure): pandas.DataFrame with 2 columns endog = pd.DataFrame({'a': [1., 2.], 'b': [3., 4.]}, index=dates) # raises error because 2-columns means k_endog=2, but the design matrix # set in **kwargs is shaped (1, 1) assert_raises(ValueError, check_endog, endog, **kwargs) # Check behavior of the link maintained between passed `endog` and # `mod.endog` arrays endog = pd.DataFrame({'a': [1., 2.]}, index=dates) mod = check_endog(endog, **kwargs) assert_equal(mod.endog.base is not mod.data.orig_endog, True) assert_equal(mod.endog.base is not endog, True) assert_equal(mod.data.orig_endog.values.base is not endog, True) endog.iloc[0, 0] = 2 # there is no link to mod.endog assert_equal(mod.endog, np.r_[1, 2].reshape(2, 1)) # there remains a link to mod.data.orig_endog assert_allclose(mod.data.orig_endog, endog) # Example : pandas.DataFrame with 2 columns # Update kwargs for k_endog=2 kwargs2 = { 'k_states': 1, 'design': [[1], [0.]], 'obs_cov': [[1, 0], [0, 1]], 'transition': [[1]], 'selection': [[1]], 'state_cov': [[1]], 'initialization': 'approximate_diffuse' } endog = pd.DataFrame({'a': [1., 2.], 'b': [3., 4.]}, index=dates) mod = check_endog(endog, k_endog=2, **kwargs2) mod.filter([]) def test_diagnostics(): mod, res = get_dummy_mod() # Override the standardized forecasts errors to get more reasonable values # for the tests to run (not necessary, but prevents some annoying warnings) shape = res.filter_results._standardized_forecasts_error.shape res.filter_results._standardized_forecasts_error = ( np.random.normal(size=shape)) # Make sure method=None selects the appropriate test actual = res.test_normality(method=None) desired = res.test_normality(method='jarquebera') assert_allclose(actual, desired) assert_raises(NotImplementedError, res.test_normality, method='invalid') actual = res.test_heteroskedasticity(method=None) desired = res.test_heteroskedasticity(method='breakvar') assert_allclose(actual, desired) with pytest.raises(ValueError): res.test_heteroskedasticity(method=None, alternative='invalid') with pytest.raises(NotImplementedError): res.test_heteroskedasticity(method='invalid') with pytest.warns(FutureWarning): actual = res.test_serial_correlation(method=None) with pytest.warns(FutureWarning): desired = res.test_serial_correlation(method='ljungbox') assert_allclose(actual, desired) with pytest.raises(NotImplementedError): res.test_serial_correlation(method='invalid') # Smoke tests for other options res.test_heteroskedasticity(method=None, alternative='d', use_f=False) with pytest.warns(FutureWarning): res.test_serial_correlation(method='boxpierce') def test_diagnostics_nile_eviews(): # Test the diagnostic tests using the Nile dataset. Results are from # "Fitting State Space Models with EViews" (Van den Bossche 2011, # Journal of Statistical Software). # For parameter values, see Figure 2 # For Ljung-Box and Jarque-Bera statistics and p-values, see Figure 5 # The Heteroskedasticity statistic is not provided in this paper. niledata = nile.data.load_pandas().data niledata.index = pd.date_range('1871-01-01', '1970-01-01', freq='AS') mod = MLEModel( niledata['volume'], k_states=1, initialization='approximate_diffuse', initial_variance=1e15, loglikelihood_burn=1) mod.ssm['design', 0, 0] = 1 mod.ssm['obs_cov', 0, 0] = np.exp(9.600350) mod.ssm['transition', 0, 0] = 1 mod.ssm['selection', 0, 0] = 1 mod.ssm['state_cov', 0, 0] = np.exp(7.348705) res = mod.filter([]) # Test Ljung-Box # Note: only 3 digits provided in the reference paper actual = res.test_serial_correlation(method='ljungbox', lags=10)[0, :, -1] assert_allclose(actual, [13.117, 0.217], atol=1e-3) # Test Jarque-Bera actual = res.test_normality(method='jarquebera')[0, :2] assert_allclose(actual, [0.041686, 0.979373], atol=1e-5) def test_diagnostics_nile_durbinkoopman(): # Test the diagnostic tests using the Nile dataset. Results are from # Durbin and Koopman (2012); parameter values reported on page 37; test # statistics on page 40 niledata = nile.data.load_pandas().data niledata.index = pd.date_range('1871-01-01', '1970-01-01', freq='AS') mod = MLEModel( niledata['volume'], k_states=1, initialization='approximate_diffuse', initial_variance=1e15, loglikelihood_burn=1) mod.ssm['design', 0, 0] = 1 mod.ssm['obs_cov', 0, 0] = 15099. mod.ssm['transition', 0, 0] = 1 mod.ssm['selection', 0, 0] = 1 mod.ssm['state_cov', 0, 0] = 1469.1 res = mod.filter([]) # Test Ljung-Box # Note: only 3 digits provided in the reference paper actual = res.test_serial_correlation(method='ljungbox', lags=9)[0, 0, -1] assert_allclose(actual, [8.84], atol=1e-2) # Test Jarque-Bera # Note: The book reports 0.09 for Kurtosis, because it is reporting the # statistic less the mean of the Kurtosis distribution (which is 3). norm = res.test_normality(method='jarquebera')[0] actual = [norm[0], norm[2], norm[3]] assert_allclose(actual, [0.05, -0.03, 3.09], atol=1e-2) # Test Heteroskedasticity # Note: only 2 digits provided in the book actual = res.test_heteroskedasticity(method='breakvar')[0, 0] assert_allclose(actual, [0.61], atol=1e-2) @pytest.mark.smoke def test_prediction_results(): # Just smoke tests for the PredictionResults class, which is copied from # elsewhere in statsmodels mod, res = get_dummy_mod() predict = res.get_prediction() predict.summary_frame() def test_lutkepohl_information_criteria(): # Setup dataset, use Lutkepohl data dta = pd.DataFrame( results_var_misc.lutkepohl_data, columns=['inv', 'inc', 'consump'], index=pd.date_range('1960-01-01', '1982-10-01', freq='QS')) dta['dln_inv'] = np.log(dta['inv']).diff() dta['dln_inc'] = np.log(dta['inc']).diff() dta['dln_consump'] = np.log(dta['consump']).diff() endog = dta.loc['1960-04-01':'1978-10-01', ['dln_inv', 'dln_inc', 'dln_consump']] # AR model - SARIMAX # (use loglikelihood_burn=1 to mimic conditional MLE used by Stata's var # command). true = results_var_misc.lutkepohl_ar1_lustats mod = sarimax.SARIMAX(endog['dln_inv'], order=(1, 0, 0), trend='c', loglikelihood_burn=1) res = mod.filter(true['params']) assert_allclose(res.llf, true['loglike']) # Test the Lutkepohl ICs # Note: for the Lutkepohl ICs, Stata only counts the AR coefficients as # estimated parameters for the purposes of information criteria, whereas we # count all parameters including scale and constant, so we need to adjust # for that aic = (res.info_criteria('aic', method='lutkepohl') - 2 * 2 / res.nobs_effective) bic = (res.info_criteria('bic', method='lutkepohl') - 2 * np.log(res.nobs_effective) / res.nobs_effective) hqic = (res.info_criteria('hqic', method='lutkepohl') - 2 * 2 * np.log(np.log(res.nobs_effective)) / res.nobs_effective) assert_allclose(aic, true['aic']) assert_allclose(bic, true['bic']) assert_allclose(hqic, true['hqic']) # Test the non-Lutkepohl ICs # Note: for the non-Lutkepohl ICs, Stata does not count the scale as an # estimated parameter, but does count the constant term, for the # purposes of information criteria, whereas we count both, so we need to # adjust for that true = results_var_misc.lutkepohl_ar1 aic = res.aic - 2 bic = res.bic - np.log(res.nobs_effective) assert_allclose(aic, true['estat_aic']) assert_allclose(bic, true['estat_bic']) aic = res.info_criteria('aic') - 2 bic = res.info_criteria('bic') - np.log(res.nobs_effective) assert_allclose(aic, true['estat_aic']) assert_allclose(bic, true['estat_bic']) # Note: could also test the "dfk" (degree of freedom corrections), but not # really necessary since they just rescale things a bit # VAR model - VARMAX # (use loglikelihood_burn=1 to mimic conditional MLE used by Stata's var # command). true = results_var_misc.lutkepohl_var1_lustats mod = varmax.VARMAX(endog, order=(1, 0), trend='n', error_cov_type='unstructured', loglikelihood_burn=1,) res = mod.filter(true['params']) assert_allclose(res.llf, true['loglike']) # Test the Lutkepohl ICs # Note: for the Lutkepohl ICs, Stata only counts the AR coefficients as # estimated parameters for the purposes of information criteria, whereas we # count all parameters including the elements of the covariance matrix, so # we need to adjust for that aic = (res.info_criteria('aic', method='lutkepohl') - 2 * 6 / res.nobs_effective) bic = (res.info_criteria('bic', method='lutkepohl') - 6 * np.log(res.nobs_effective) / res.nobs_effective) hqic = (res.info_criteria('hqic', method='lutkepohl') - 2 * 6 * np.log(np.log(res.nobs_effective)) / res.nobs_effective) assert_allclose(aic, true['aic']) assert_allclose(bic, true['bic']) assert_allclose(hqic, true['hqic']) # Test the non-Lutkepohl ICs # Note: for the non-Lutkepohl ICs, Stata does not count the elements of the # covariance matrix as estimated parameters for the purposes of information # criteria, whereas we count both, so we need to adjust for that true = results_var_misc.lutkepohl_var1 aic = res.aic - 2 * 6 bic = res.bic - 6 * np.log(res.nobs_effective) assert_allclose(aic, true['estat_aic']) assert_allclose(bic, true['estat_bic']) aic = res.info_criteria('aic') - 2 * 6 bic = res.info_criteria('bic') - 6 * np.log(res.nobs_effective) assert_allclose(aic, true['estat_aic']) assert_allclose(bic, true['estat_bic']) def test_append_extend_apply_invalid(): # Test for invalid options to append, extend, and apply niledata = nile.data.load_pandas().data['volume'] niledata.index = pd.date_range('1871-01-01', '1970-01-01', freq='AS') endog1 = niledata.iloc[:20] endog2 = niledata.iloc[20:40] mod = sarimax.SARIMAX(endog1, order=(1, 0, 0), concentrate_scale=True) res1 = mod.smooth([0.5]) assert_raises(ValueError, res1.append, endog2, fit_kwargs={'cov_type': 'approx'}) assert_raises(ValueError, res1.extend, endog2, fit_kwargs={'cov_type': 'approx'}) assert_raises(ValueError, res1.apply, endog2, fit_kwargs={'cov_type': 'approx'}) assert_raises(ValueError, res1.append, endog2, fit_kwargs={'cov_kwds': {}}) assert_raises(ValueError, res1.extend, endog2, fit_kwargs={'cov_kwds': {}}) assert_raises(ValueError, res1.apply, endog2, fit_kwargs={'cov_kwds': {}}) # Test for exception when given a different frequency wrong_freq = niledata.iloc[20:40] wrong_freq.index = pd.date_range( start=niledata.index[0], periods=len(wrong_freq), freq='MS') message = ('Given `endog` does not have an index that extends the index of' ' the model. Expected index frequency is') with pytest.raises(ValueError, match=message): res1.append(wrong_freq) with pytest.raises(ValueError, match=message): res1.extend(wrong_freq) message = ('Given `exog` does not have an index that extends the index of' ' the model. Expected index frequency is') with pytest.raises(ValueError, match=message): res1.append(endog2, exog=wrong_freq) message = 'The indices for endog and exog are not aligned' with pytest.raises(ValueError, match=message): res1.extend(endog2, exog=wrong_freq) # Test for exception when given the same frequency but not right after the # end of model not_cts = niledata.iloc[21:41] message = ('Given `endog` does not have an index that extends the index of' ' the model.$') with pytest.raises(ValueError, match=message): res1.append(not_cts) with pytest.raises(ValueError, match=message): res1.extend(not_cts) message = ('Given `exog` does not have an index that extends the index of' ' the model.$') with pytest.raises(ValueError, match=message): res1.append(endog2, exog=not_cts) message = 'The indices for endog and exog are not aligned' with pytest.raises(ValueError, match=message): res1.extend(endog2, exog=not_cts) # # Test for problems with non-date indexes endog3 = pd.Series(niledata.iloc[:20].values) endog4 = pd.Series(niledata.iloc[:40].values)[20:] mod2 = sarimax.SARIMAX(endog3, order=(1, 0, 0), exog=endog3, concentrate_scale=True) res2 = mod2.smooth([0.2, 0.5]) # Test for exception when given the same frequency but not right after the # end of model not_cts = pd.Series(niledata[:41].values)[21:] message = ('Given `endog` does not have an index that extends the index of' ' the model.$') with pytest.raises(ValueError, match=message): res2.append(not_cts) with pytest.raises(ValueError, match=message): res2.extend(not_cts) message = ('Given `exog` does not have an index that extends the index of' ' the model.$') with pytest.raises(ValueError, match=message): res2.append(endog4, exog=not_cts) message = 'The indices for endog and exog are not aligned' with pytest.raises(ValueError, match=message): res2.extend(endog4, exog=not_cts) def test_integer_params(): # See GH#6335 mod = sarimax.SARIMAX([1, 1, 1], order=(1, 0, 0), exog=[2, 2, 2], concentrate_scale=True) res = mod.filter([1, 0]) p = res.predict(end=5, dynamic=True, exog=[3, 3, 4]) assert_equal(p.dtype, np.float64) def check_states_index(states, ix, predicted_ix, cols): predicted_cov_ix = pd.MultiIndex.from_product( [predicted_ix, cols]).swaplevel() filtered_cov_ix = pd.MultiIndex.from_product([ix, cols]).swaplevel() smoothed_cov_ix = pd.MultiIndex.from_product([ix, cols]).swaplevel() # Predicted assert_(states.predicted.index.equals(predicted_ix)) assert_(states.predicted.columns.equals(cols)) assert_(states.predicted_cov.index.equals(predicted_cov_ix)) assert_(states.predicted.columns.equals(cols)) # Filtered assert_(states.filtered.index.equals(ix)) assert_(states.filtered.columns.equals(cols)) assert_(states.filtered_cov.index.equals(filtered_cov_ix)) assert_(states.filtered.columns.equals(cols)) # Smoothed assert_(states.smoothed.index.equals(ix)) assert_(states.smoothed.columns.equals(cols)) assert_(states.smoothed_cov.index.equals(smoothed_cov_ix)) assert_(states.smoothed.columns.equals(cols)) def test_states_index_periodindex(): nobs = 10 ix = pd.period_range(start='2000', periods=nobs, freq='M') endog = pd.Series(np.zeros(nobs), index=ix) mod = sarimax.SARIMAX(endog, order=(2, 0, 0)) res = mod.smooth([0.5, 0.1, 1.0]) predicted_ix = pd.period_range(start=ix[0], periods=nobs + 1, freq='M') cols = pd.Index(['state.0', 'state.1']) check_states_index(res.states, ix, predicted_ix, cols) def test_states_index_dateindex(): nobs = 10 ix = pd.date_range(start='2000', periods=nobs, freq='M') endog = pd.Series(np.zeros(nobs), index=ix) mod = sarimax.SARIMAX(endog, order=(2, 0, 0)) res = mod.smooth([0.5, 0.1, 1.0]) predicted_ix = pd.date_range(start=ix[0], periods=nobs + 1, freq='M') cols = pd.Index(['state.0', 'state.1']) check_states_index(res.states, ix, predicted_ix, cols) def test_states_index_int64index(): nobs = 10 ix = pd.Int64Index(np.arange(10)) endog = pd.Series(np.zeros(nobs), index=ix) mod = sarimax.SARIMAX(endog, order=(2, 0, 0)) res = mod.smooth([0.5, 0.1, 1.0]) predicted_ix = pd.Int64Index(np.arange(11)) cols = pd.Index(['state.0', 'state.1']) check_states_index(res.states, ix, predicted_ix, cols) def test_states_index_rangeindex(): nobs = 10 # Basic range index ix = pd.RangeIndex(10) endog = pd.Series(np.zeros(nobs), index=ix) mod = sarimax.SARIMAX(endog, order=(2, 0, 0)) res = mod.smooth([0.5, 0.1, 1.0]) predicted_ix = pd.RangeIndex(11) cols = pd.Index(['state.0', 'state.1']) check_states_index(res.states, ix, predicted_ix, cols) # More complex range index ix = pd.RangeIndex(2, 32, 3) endog = pd.Series(np.zeros(nobs), index=ix) mod = sarimax.SARIMAX(endog, order=(2, 0, 0)) res = mod.smooth([0.5, 0.1, 1.0]) predicted_ix = pd.RangeIndex(2, 35, 3) cols = pd.Index(['state.0', 'state.1']) check_states_index(res.states, ix, predicted_ix, cols) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_models.py000066400000000000000000000251211400612667500254710ustar00rootroot00000000000000""" Tests for miscellaneous models Author: Chad Fulton License: Simplified-BSD """ import numpy as np import pandas as pd import os import pytest from statsmodels.tsa.statespace import mlemodel, sarimax from statsmodels import datasets from numpy.testing import assert_equal, assert_allclose, assert_raises current_path = os.path.dirname(os.path.abspath(__file__)) class Intercepts(mlemodel.MLEModel): """ Test class for observation and state intercepts (which usually do not get tested in other models). """ def __init__(self, endog, **kwargs): k_states = 3 k_posdef = 3 super(Intercepts, self).__init__( endog, k_states=k_states, k_posdef=k_posdef, **kwargs) self['design'] = np.eye(3) self['obs_cov'] = np.eye(3) self['transition'] = np.eye(3) self['selection'] = np.eye(3) self['state_cov'] = np.eye(3) self.initialize_approximate_diffuse() @property def param_names(self): return ['d.1', 'd.2', 'd.3', 'c.1', 'c.2', 'c.3'] @property def start_params(self): return np.arange(6) def update(self, params, **kwargs): params = super(Intercepts, self).update(params, **kwargs) self['obs_intercept'] = params[:3] self['state_intercept'] = params[3:] class TestIntercepts(object): @classmethod def setup_class(cls, which='mixed', **kwargs): # Results path = current_path + os.sep + 'results/results_intercepts_R.csv' cls.desired = pd.read_csv(path) # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = dta[['realgdp', 'realcons', 'realinv']].copy() obs = obs / obs.std() if which == 'all': obs.iloc[:50, :] = np.nan obs.iloc[119:130, :] = np.nan elif which == 'partial': obs.iloc[0:50, 0] = np.nan obs.iloc[119:130, 0] = np.nan elif which == 'mixed': obs.iloc[0:50, 0] = np.nan obs.iloc[19:70, 1] = np.nan obs.iloc[39:90, 2] = np.nan obs.iloc[119:130, 0] = np.nan obs.iloc[119:130, 2] = np.nan mod = Intercepts(obs, **kwargs) cls.params = np.arange(6) + 1 cls.model = mod cls.results = mod.smooth(cls.params, return_ssm=True) # Calculate the determinant of the covariance matrices (for easy # comparison to other languages without having to store 2-dim arrays) cls.results.det_scaled_smoothed_estimator_cov = ( np.zeros((1, cls.model.nobs))) cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_disturbance_cov = ( np.zeros((1, cls.model.nobs))) for i in range(cls.model.nobs): cls.results.det_scaled_smoothed_estimator_cov[0, i] = ( np.linalg.det( cls.results.scaled_smoothed_estimator_cov[:, :, i])) cls.results.det_predicted_state_cov[0, i] = np.linalg.det( cls.results.predicted_state_cov[:, :, i+1]) cls.results.det_smoothed_state_cov[0, i] = np.linalg.det( cls.results.smoothed_state_cov[:, :, i]) cls.results.det_smoothed_state_disturbance_cov[0, i] = ( np.linalg.det( cls.results.smoothed_state_disturbance_cov[:, :, i])) def test_loglike(self): assert_allclose(np.sum(self.results.llf_obs), -7924.03893566) def test_scaled_smoothed_estimator(self): assert_allclose( self.results.scaled_smoothed_estimator.T, self.desired[['r1', 'r2', 'r3']] ) def test_scaled_smoothed_estimator_cov(self): assert_allclose( self.results.det_scaled_smoothed_estimator_cov.T, self.desired[['detN']] ) def test_forecasts(self): assert_allclose( self.results.forecasts.T, self.desired[['m1', 'm2', 'm3']] ) def test_forecasts_error(self): assert_allclose( self.results.forecasts_error.T, self.desired[['v1', 'v2', 'v3']] ) def test_forecasts_error_cov(self): assert_allclose( self.results.forecasts_error_cov.diagonal(), self.desired[['F1', 'F2', 'F3']] ) def test_predicted_states(self): assert_allclose( self.results.predicted_state[:, 1:].T, self.desired[['a1', 'a2', 'a3']] ) def test_predicted_states_cov(self): assert_allclose( self.results.det_predicted_state_cov.T, self.desired[['detP']] ) def test_smoothed_states(self): assert_allclose( self.results.smoothed_state.T, self.desired[['alphahat1', 'alphahat2', 'alphahat3']] ) def test_smoothed_states_cov(self): assert_allclose( self.results.det_smoothed_state_cov.T, self.desired[['detV']] ) def test_smoothed_forecasts(self): assert_allclose( self.results.smoothed_forecasts.T, self.desired[['muhat1', 'muhat2', 'muhat3']] ) def test_smoothed_state_disturbance(self): assert_allclose( self.results.smoothed_state_disturbance.T, self.desired[['etahat1', 'etahat2', 'etahat3']] ) def test_smoothed_state_disturbance_cov(self): assert_allclose( self.results.det_smoothed_state_disturbance_cov.T, self.desired[['detVeta']] ) def test_smoothed_measurement_disturbance(self): assert_allclose( self.results.smoothed_measurement_disturbance.T, self.desired[['epshat1', 'epshat2', 'epshat3']], atol=1e-9 ) def test_smoothed_measurement_disturbance_cov(self): assert_allclose( self.results.smoothed_measurement_disturbance_cov.diagonal(), self.desired[['Veps1', 'Veps2', 'Veps3']] ) class LargeStateCovAR1(mlemodel.MLEModel): """ Test class for k_posdef > k_states (which usually do not get tested in other models). This is just an AR(1) model with an extra unused state innovation """ def __init__(self, endog, **kwargs): k_states = 1 k_posdef = 2 super(LargeStateCovAR1, self).__init__( endog, k_states=k_states, k_posdef=k_posdef, **kwargs) self['design', 0, 0] = 1 self['selection', 0, 0] = 1 self['state_cov', 1, 1] = 1 self.initialize_stationary() @property def param_names(self): return ['phi', 'sigma2'] @property def start_params(self): return [0.5, 1] def update(self, params, **kwargs): params = super(LargeStateCovAR1, self).update(params, **kwargs) self['transition', 0, 0] = params[0] self['state_cov', 0, 0] = params[1] def test_large_kposdef(): assert_raises(ValueError, LargeStateCovAR1, np.arange(10)) class TestLargeStateCovAR1(object): @classmethod def setup_class(cls): pytest.skip( 'TODO: This test is skipped since an exception is currently ' 'raised if k_posdef > k_states. However, this test could be ' 'used if models of those types were allowed' ) # Data: just some sample data endog = [0.2, -1.5, -.3, -.1, 1.5, 0.2, -0.3, 0.2, 0.5, 0.8] # Params params = [0.5, 1] # Desired model: AR(1) mod_desired = sarimax.SARIMAX(endog) cls.res_desired = mod_desired.smooth(params) # Test class mod = LargeStateCovAR1(endog) cls.res = mod.smooth(params) def test_dimensions(self): assert_equal(self.res.filter_results.k_states, 1) assert_equal(self.res.filter_results.k_posdef, 2) assert_equal(self.res.smoothed_state_disturbance.shape, (2, 10)) assert_equal(self.res_desired.filter_results.k_states, 1) assert_equal(self.res_desired.filter_results.k_posdef, 1) assert_equal(self.res_desired.smoothed_state_disturbance.shape, (1, 10)) def test_loglike(self): assert_allclose(self.res.llf_obs, self.res_desired.llf_obs) def test_scaled_smoothed_estimator(self): assert_allclose(self.res.scaled_smoothed_estimator[0], self.res_desired.scaled_smoothed_estimator[0]) def test_scaled_smoothed_estimator_cov(self): assert_allclose(self.res.scaled_smoothed_estimator_cov[0], self.res_desired.scaled_smoothed_estimator_cov[0]) def test_forecasts(self): assert_allclose(self.res.forecasts, self.res_desired.forecasts) def test_forecasts_error(self): assert_allclose(self.res.forecasts_error, self.res_desired.forecasts_error) def test_forecasts_error_cov(self): assert_allclose(self.res.forecasts_error_cov, self.res_desired.forecasts_error_cov) def test_predicted_states(self): assert_allclose(self.res.predicted_state[0], self.res_desired.predicted_state[0]) def test_predicted_states_cov(self): assert_allclose(self.res.predicted_state_cov[0, 0], self.res_desired.predicted_state_cov[0, 0]) def test_smoothed_states(self): assert_allclose(self.res.smoothed_state[0], self.res_desired.smoothed_state[0]) def test_smoothed_states_cov(self): assert_allclose(self.res.smoothed_state_cov[0, 0], self.res_desired.smoothed_state_cov[0, 0]) def test_smoothed_state_disturbance(self): assert_allclose(self.res.smoothed_state_disturbance[0], self.res_desired.smoothed_state_disturbance[0]) assert_allclose(self.res.smoothed_state_disturbance[1], 0) def test_smoothed_state_disturbance_cov(self): assert_allclose(self.res.smoothed_state_disturbance_cov[0, 0], self.res_desired.smoothed_state_disturbance_cov[0, 0]) assert_allclose(self.res.smoothed_state_disturbance[1, 1], 0) def test_smoothed_measurement_disturbance(self): assert_allclose(self.res.smoothed_measurement_disturbance, self.res_desired.smoothed_measurement_disturbance) def test_smoothed_measurement_disturbance_cov(self): assert_allclose(self.res.smoothed_measurement_disturbance_cov, self.res_desired.smoothed_measurement_disturbance_cov) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_multivariate_switch_univariate.py000066400000000000000000000451011400612667500325240ustar00rootroot00000000000000""" Tests for automatic switching of the filter method from multivariate to univariate when the forecast error covariance matrix is singular. Author: Chad Fulton License: Simplified-BSD References ---------- Kim, Chang-Jin, and Charles R. Nelson. 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications". MIT Press Books. The MIT Press. Hamilton, James D. 1994. Time Series Analysis. Princeton, N.J.: Princeton University Press. """ import numpy as np import pytest from statsmodels.tsa.statespace import ( mlemodel, sarimax, structural, varmax, dynamic_factor) from statsmodels.tsa.statespace.tests.test_impulse_responses import TVSS from numpy.testing import assert_allclose def get_model(univariate, missing=None, init=None): if univariate: endog = np.array([0.5, 1.2, -0.2, 0.3, -0.1, 0.4, 1.4, 0.9]) if missing == 'init': endog[0:2] = np.nan elif missing == 'mixed': endog[2:4] = np.nan elif missing == 'all': endog[:] = np.nan mod = mlemodel.MLEModel(endog, k_states=1, k_posdef=1) mod['design', 0, 0] = 1. mod['transition', 0, 0] = 0.5 mod['selection', 0, 0] = 1. mod['state_cov', 0, 0] = 1. mod['state_intercept', 0, 0] = 1. else: endog = np.array([[0.5, 1.2, -0.2, 0.3, -0.1, 0.4, 1.4, 0.9], [-0.2, -0.3, -0.1, 0.1, 0.01, 0.05, -0.13, -0.2]]).T if missing == 'init': endog[0:2, :] = np.nan elif missing == 'mixed': endog[2:4, 0] = np.nan endog[3:6, 1] = np.nan elif missing == 'all': endog[:] = np.nan mod = mlemodel.MLEModel(endog, k_states=3, k_posdef=2) mod['obs_intercept'] = np.array([0.5, 0.2]) mod['design'] = np.array([[0.1, -0.1, 0], [0.2, 0.3, 0]]) mod['obs_cov'] = np.array([[5, -0.2], [-0.2, 3.]]) mod['transition', 0, 0] = 1 mod['transition', 1:, 1:] = np.array([[0.5, -0.1], [1., 0.]]) mod['selection', :2, :2] = np.eye(2) mod['state_cov'] = np.array([[1.2, 0.2], [0.2, 2.5]]) mod['state_intercept', :2] = np.array([1., -1.]) if init == 'diffuse': mod.ssm.initialize_diffuse() elif init == 'approximate_diffuse': mod.ssm.initialize_approximate_diffuse() elif init == 'stationary': mod.ssm.initialize_stationary() return mod def check_filter_output(mod, periods, atol=0): if isinstance(mod, mlemodel.MLEModel): # Multivariate filter res_mv = mod.ssm.filter() # Manually perform filtering with a switch mod.ssm.filter() kfilter = mod.ssm._kalman_filter kfilter.seek(0, True) kfilter.univariate_filter[periods] = 1 for _ in range(mod.nobs): next(kfilter) # Create the results object res_switch = mod.ssm.results_class(mod.ssm) res_switch.update_representation(mod.ssm) res_switch.update_filter(kfilter) # Univariate filter mod.ssm.filter_univariate = True res_uv = mod.ssm.filter() else: res_mv, res_switch, res_uv = mod # Test attributes that are the same regardless of the univariate or # multivariate method assert_allclose(res_switch.llf, res_mv.llf) assert_allclose(res_switch.llf, res_uv.llf) assert_allclose(res_switch.scale, res_mv.scale) assert_allclose(res_switch.scale, res_uv.scale) attrs = ['forecasts_error_diffuse_cov', 'predicted_state', 'predicted_state_cov', 'predicted_diffuse_state_cov', 'filtered_state', 'filtered_state_cov', 'llf_obs'] for attr in attrs: attr_mv = getattr(res_mv, attr) attr_uv = getattr(res_uv, attr) attr_switch = getattr(res_switch, attr) if attr_mv is None: continue assert_allclose(attr_switch, attr_mv, atol=atol) assert_allclose(attr_switch, attr_uv, atol=atol) # Test attributes that can differ for the univariate vs multivariate method attrs = ['forecasts_error', 'forecasts_error_cov', 'kalman_gain'] for attr in attrs: # Test all periods against the multivariate filter, except for periods # that were switched (it's easiest to just set those values to zero) actual = getattr(res_switch, attr).copy() desired = getattr(res_mv, attr).copy() actual[..., periods] = 0 desired[..., periods] = 0 assert_allclose(actual, desired, atol=atol) # Test switched periods against the univariate filter actual = getattr(res_switch, attr)[..., periods] desired = getattr(res_uv, attr)[..., periods] assert_allclose(actual, desired, atol=atol) def check_smoother_output(mod, periods, atol=1e-12): if isinstance(mod, mlemodel.MLEModel): # Multivariate filter / smoother res_mv = mod.ssm.smooth() # Manually perform filtering / smoothing with a switch kfilter = mod.ssm._kalman_filter kfilter.seek(0, True) kfilter.univariate_filter[periods] = 1 for _ in range(mod.nobs): next(kfilter) # Create the results object res_switch = mod.ssm.results_class(mod.ssm) res_switch.update_representation(mod.ssm) res_switch.update_filter(kfilter) mod.ssm._kalman_smoother.reset(True) smoother = mod.ssm._smooth() res_switch.update_smoother(smoother) # Univariate filter / smoother mod.ssm.filter_univariate = True res_uv = mod.ssm.smooth() else: res_mv, res_switch, res_uv = mod # Test attributes that are the same regardless of the univariate or # multivariate method attrs = ['scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_state_disturbance', 'smoothed_state_disturbance_cov', 'innovations_transition'] for attr in attrs: attr_mv = getattr(res_mv, attr) attr_uv = getattr(res_uv, attr) attr_switch = getattr(res_switch, attr) if attr_mv is None: continue assert_allclose(attr_uv, attr_mv, atol=atol) assert_allclose(attr_switch, attr_mv, atol=atol) assert_allclose(attr_switch, attr_uv, atol=atol) # Test attributes that can differ for the univariate vs multivariate method attrs = ['smoothing_error', 'smoothed_measurement_disturbance', 'smoothed_measurement_disturbance_cov'] for attr in attrs: attr_mv = getattr(res_mv, attr) attr_uv = getattr(res_uv, attr) attr_switch = getattr(res_switch, attr) if attr_mv is None: continue # Test all periods against the multivariate filter, except for periods # that were switched (it's easiest to just set those values to zero) actual = attr_switch.copy() desired = attr_mv.copy() actual[..., periods] = 0 desired[..., periods] = 0 assert_allclose(actual, desired) @pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all']) def test_basic(missing): # Test that the multivariate filter switches to the univariate filter # when it runs into problems mod = get_model(univariate=True, missing=missing) # Here, because of the known initialization with P_0 = [[0]], we will also # have F_0 = 0. # Then the Kalman filter gives P_0|0 = 0, and P_1 = Q = [[1.]] # so that F_1 != 0, and the rest of the periods do not have a singular # forecast error covariance matrix. mod.initialize_known([0], [[0]]) mod.ssm.filter() uf = np.array(mod.ssm._kalman_filter.univariate_filter) # As a result, we expect that in the period t=0, we had to fall back to the # univariate filter, while in the periods t >= 1, the multivariate filter # works as usual. # However, if the first period is missing (as in init and all), then we # essentially skip the forecast error and forecast error cov computation. # As a result, we don't need to switch to the univariate methods if missing in ['init', 'all']: assert_allclose(uf, 0) else: assert_allclose(uf[0], 1) assert_allclose(uf[1:], 0) @pytest.mark.parametrize('univariate', [True, False]) @pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all']) @pytest.mark.parametrize( 'init', ['stationary', 'diffuse', 'approximate_diffuse']) @pytest.mark.parametrize('periods', [np.s_[0], np.s_[4:6], np.s_[:]]) def test_filter_output(univariate, missing, init, periods): # Test the output when the multivariate filter switches to the univariate # filter mod = get_model(univariate, missing, init) check_filter_output(mod, periods) @pytest.mark.parametrize('univariate', [True, False]) @pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all']) @pytest.mark.parametrize('init', ['stationary', 'diffuse', 'approximate_diffuse']) @pytest.mark.parametrize('periods', [np.s_[0], np.s_[4:6], np.s_[:]]) @pytest.mark.parametrize('option', [None, 'alternate_timing']) def test_smoother_output(univariate, missing, init, periods, option): # Test the output when the multivariate filter switches to the univariate # filter mod = get_model(univariate, missing, init) if option == 'alternate_timing': # Can't use diffuse initialization with alternate timing if init == 'diffuse': return mod.ssm.timing_init_filtered = True atol = 1e-12 # Tolerance is lower for approximate diffuse for one attribute in this case if missing == 'init' and init == 'approximate_diffuse': atol = 1e-6 check_smoother_output(mod, periods, atol=atol) def test_invalid_options(): mod = get_model(univariate=True) mod.initialize_known([0], [[0]]) mod.ssm.set_inversion_method(0, solve_lu=True) msg = ('Singular forecast error covariance matrix detected, but' ' multivariate filter cannot fall back to univariate' ' filter when the inversion method is set to anything' ' other than INVERT_UNIVARIATE or SOLVE_CHOLESKY.') with pytest.raises(NotImplementedError, match=msg): mod.ssm.filter() mod = get_model(univariate=True) mod.initialize_known([0], [[0]]) mod.ssm.smooth_classical = True msg = ('Cannot use classical smoothing when the multivariate filter has' ' fallen back to univariate filtering.') with pytest.raises(NotImplementedError, match=msg): mod.ssm.smooth() mod = get_model(univariate=True) mod.initialize_known([0], [[0]]) mod.ssm.smooth_alternative = True msg = ('Cannot use alternative smoothing when the multivariate filter has' ' fallen back to univariate filtering.') with pytest.raises(NotImplementedError, match=msg): mod.ssm.smooth() @pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all']) @pytest.mark.parametrize('periods', [np.s_[0], np.s_[4:6], np.s_[:]]) @pytest.mark.parametrize('use_exact_diffuse', [False, True]) def test_sarimax(missing, periods, use_exact_diffuse): endog = np.array([0.5, 1.2, -0.2, 0.3, -0.1, 0.4, 1.4, 0.9]) exog = np.ones_like(endog) if missing == 'init': endog[0:2] = np.nan elif missing == 'mixed': endog[2:4] = np.nan elif missing == 'all': endog[:] = np.nan mod = sarimax.SARIMAX(endog, order=(1, 1, 1), trend='t', seasonal_order=(1, 1, 1, 2), exog=exog, use_exact_diffuse=use_exact_diffuse) mod.update([0.1, 0.3, 0.5, 0.2, 0.05, -0.1, 1.0]) check_filter_output(mod, periods, atol=1e-8) check_smoother_output(mod, periods) @pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all']) @pytest.mark.parametrize('periods', [np.s_[0], np.s_[4:6], np.s_[:]]) @pytest.mark.parametrize('use_exact_diffuse', [False, True]) def test_unobserved_components(missing, periods, use_exact_diffuse): endog = np.array([0.5, 1.2, -0.2, 0.3, -0.1, 0.4, 1.4, 0.9]) exog = np.ones_like(endog) if missing == 'init': endog[0:2] = np.nan elif missing == 'mixed': endog[2:4] = np.nan elif missing == 'all': endog[:] = np.nan mod = structural.UnobservedComponents( endog, 'llevel', exog=exog, seasonal=2, autoregressive=1, use_exact_diffuse=use_exact_diffuse) mod.update([1.0, 0.1, 0.3, 0.05, 0.15, 0.5]) check_filter_output(mod, periods) check_smoother_output(mod, periods) @pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all']) @pytest.mark.parametrize('periods', [np.s_[0], np.s_[4:6], np.s_[:]]) def test_varmax(missing, periods): endog = np.array([[0.5, 1.2, -0.2, 0.3, -0.1, 0.4, 1.4, 0.9], [-0.2, -0.3, -0.1, 0.1, 0.01, 0.05, -0.13, -0.2]]).T exog = np.ones_like(endog[:, 0]) if missing == 'init': endog[0:2, :] = np.nan elif missing == 'mixed': endog[2:4, 0] = np.nan endog[3:6, 1] = np.nan elif missing == 'all': endog[:] = np.nan mod = varmax.VARMAX(endog, order=(1, 0), trend='t', exog=exog) mod.update([0.1, -0.1, 0.5, 0.1, -0.05, 0.2, 0.4, 0.25, 1.2, 0.4, 2.3]) check_filter_output(mod, periods, atol=1e-12) check_smoother_output(mod, periods) @pytest.mark.parametrize('missing', [None, 'init', 'mixed', 'all']) @pytest.mark.parametrize('periods', [np.s_[0], np.s_[4:6], np.s_[:]]) def test_dynamic_factor(missing, periods): endog = np.array([[0.5, 1.2, -0.2, 0.3, -0.1, 0.4, 1.4, 0.9], [-0.2, -0.3, -0.1, 0.1, 0.01, 0.05, -0.13, -0.2]]).T exog = np.ones_like(endog[:, 0]) if missing == 'init': endog[0:2, :] = np.nan elif missing == 'mixed': endog[2:4, 0] = np.nan endog[3:6, 1] = np.nan elif missing == 'all': endog[:] = np.nan mod = dynamic_factor.DynamicFactor(endog, k_factors=1, factor_order=2, exog=exog) mod.update([1.0, -0.5, 0.3, -0.1, 1.2, 2.3, 0.5, 0.1]) check_filter_output(mod, periods) check_smoother_output(mod, periods) @pytest.mark.parametrize('missing', [None, 'mixed']) def test_simulation_smoothing(missing): # Test that the simulation smoother works when the multivariate filter # switches to the univariate filter when it runs into problems # (see test_basic for a description of the model used here) # Get the model where switching will occur mod_switch = get_model(univariate=True, missing=missing) mod_switch.initialize_known([0], [[0]]) sim_switch = mod_switch.simulation_smoother() # Get the model where we have specified univariate filtering (so there is # no need to switch) mod_uv = get_model(univariate=True, missing=missing) mod_uv.initialize_known([0], [[0]]) mod_uv.ssm.filter_univariate = True sim_uv = mod_uv.simulation_smoother() # Test for basic simulationg of a new observed series np.random.seed(1234) simulate_switch = mod_switch.simulate([], 10) np.random.seed(1234) simulate_uv = mod_uv.simulate([], 10) assert_allclose(simulate_switch, simulate_uv) # Perform simulation smoothing np.random.seed(1234) sim_switch.simulate() np.random.seed(1234) sim_uv.simulate() # Make sure that switching happened in the first model but not the second kfilter = sim_switch._simulation_smoother.simulated_kfilter uf_switch = np.array(kfilter.univariate_filter, copy=True) assert_allclose(uf_switch[0], 1) assert_allclose(uf_switch[1:], 0) kfilter = sim_uv._simulation_smoother.simulated_kfilter.univariate_filter uf_uv = np.array(kfilter, copy=True) assert_allclose(uf_uv, 1) if missing == 'mixed': kfilter = (sim_switch._simulation_smoother .secondary_simulated_kfilter.univariate_filter) uf_switch = np.array(kfilter, copy=True) assert_allclose(uf_switch[0], 1) assert_allclose(uf_switch[1:], 0) kfilter = (sim_uv._simulation_smoother .secondary_simulated_kfilter.univariate_filter) uf_uv = np.array(kfilter, copy=True) assert_allclose(uf_uv, 1) # Test all simulation smoothing output attrs = ['generated_measurement_disturbance', 'generated_state_disturbance', 'generated_obs', 'generated_state', 'simulated_state', 'simulated_measurement_disturbance', 'simulated_state_disturbance'] for attr in attrs: assert_allclose(getattr(sim_switch, attr), getattr(sim_uv, attr)) def test_time_varying_model(reset_randomstate): endog = np.array([[0.5, 1.2, -0.2, 0.3, -0.1, 0.4, 1.4, 0.9], [-0.2, -0.3, -0.1, 0.1, 0.01, 0.05, -0.13, -0.2]]).T # The basic model switches to the univariate method at observation 3, # because the forecast error covariance matrix will have a singular # component corresponding to the first endog variable np.random.seed(1234) mod_switch = TVSS(endog) mod_switch['design', ..., 3] = 0 mod_switch['obs_cov', ..., 3] = 0 mod_switch['obs_cov', 1, 1, 3] = 1. res_switch = mod_switch.ssm.smooth() kfilter = mod_switch.ssm._kalman_filter uf_switch = np.array(kfilter.univariate_filter, copy=True) # Next, this model only uses the univariate method np.random.seed(1234) mod_uv = TVSS(endog) mod_uv['design', ..., 3] = 0 mod_uv['obs_cov', ..., 3] = 0 mod_uv['obs_cov', 1, 1, 3] = 1. mod_uv.ssm.filter_univariate = True res_uv = mod_uv.ssm.smooth() kfilter = mod_uv.ssm._kalman_filter uf_uv = np.array(kfilter.univariate_filter, copy=True) # Finally, this model uses the multivariate method and gets around the # issue by setting the endog variable to NaN that would have contributed # to the singular part of the forecast error covariance matrix np.random.seed(1234) endog_mv = endog.copy() endog_mv[3, 0] = np.nan mod_mv = TVSS(endog_mv) mod_mv['design', ..., 3] = 0 mod_mv['obs_cov', ..., 3] = 0 mod_mv['obs_cov', 1, 1, 3] = 1. res_mv = mod_mv.ssm.smooth() kfilter = mod_mv.ssm._kalman_filter uf_mv = np.array(kfilter.univariate_filter, copy=True) # Make sure that switching happened in the switch model but not in the # other two models assert_allclose(uf_switch[:3], 0) assert_allclose(uf_switch[3], 1) assert_allclose(uf_switch[4:], 0) assert_allclose(uf_uv, 1) assert_allclose(uf_mv, 0) # Check filter and smoother output check_filter_output([res_mv, res_switch, res_uv], np.s_[3]) check_smoother_output([res_mv, res_switch, res_uv], np.s_[3]) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_news.py000066400000000000000000001251421400612667500251660ustar00rootroot00000000000000r""" Tests for news results Author: Chad Fulton License: BSD-3 """ from statsmodels.compat.pandas import ( assert_frame_equal, assert_series_equal, pandas_lt_25_0, ) import numpy as np from numpy.testing import assert_, assert_allclose, assert_equal import pandas as pd import pytest from statsmodels import datasets from statsmodels.tsa.statespace import ( dynamic_factor, sarimax, structural, varmax, ) dta = datasets.macrodata.load_pandas().data dta.index = pd.period_range(start='1959Q1', end='2009Q3', freq='Q') def check_impact_indices(news, impact_dates, impacted_variables): # Note: the index for impacts is only a time index, because we compute # impacts for all variables during these time periods. for attr in ['total_impacts', 'update_impacts', 'revision_impacts', 'post_impacted_forecasts', 'prev_impacted_forecasts']: val = getattr(news, attr) assert_(val.index.equals(impact_dates)) assert_equal(val.columns.tolist(), impacted_variables) def check_revision_indices(news, revisions_index): # Note: revision indices must be a MultiIndex, because for each time # period, not all variables necessarily revised. # If there are no revisions, we just check the length is zero if news.news_results.revision_impacts is None: assert_equal(len(news.revisions_iloc['revision date']), 0) assert_equal(len(news.revisions_iloc['revised variable']), 0) assert_equal(len(news.revisions_ix['revision date']), 0) assert_equal(len(news.revisions_ix['revised variable']), 0) # Otherwise, check that the revision indexes are correct else: # Get the integer locations of the given indexes dates = news.previous.model._index endog_names = news.previous.model.endog_names if isinstance(endog_names, str): endog_names = [endog_names] desired_ix = revisions_index.to_frame().reset_index(drop=True) desired_iloc = desired_ix.copy() desired_iloc['revision date'] = [ dates.get_loc(date) for date in desired_ix['revision date']] desired_iloc['revised variable'] = [ endog_names.index(name) for name in desired_ix['revised variable']] assert_(news.revisions_iloc.equals(desired_iloc)) assert_(news.revisions_ix.equals(desired_ix)) def check_update_indices(news, updates_index): # Note: update indices are also a MultiIndex, for the same reason as the # revision indices. # If there are no updates, we just check the length is zero if news.news_results.update_impacts is None: assert_equal(len(news.updates_iloc['update date']), 0) assert_equal(len(news.updates_iloc['updated variable']), 0) assert_equal(len(news.updates_ix['update date']), 0) assert_equal(len(news.updates_ix['updated variable']), 0) # Otherwise, check that the revision indexes are correct else: # Get the integer locations of the given indexes dates = news.updated.model._index endog_names = news.updated.model.endog_names if isinstance(endog_names, str): endog_names = [endog_names] desired_ix = updates_index.to_frame().reset_index(drop=True) desired_iloc = desired_ix.copy() desired_iloc['update date'] = [ dates.get_loc(date) for date in desired_ix['update date']] desired_iloc['updated variable'] = [ endog_names.index(name) for name in desired_ix['updated variable']] assert_(news.updates_iloc.equals(desired_iloc)) assert_(news.updates_ix.equals(desired_ix)) def check_news_indices(news, updates_index, impact_dates): # News are computed only from updates, so the news indices are the same as # the update indices if len(updates_index): news_index = updates_index else: news_index = pd.MultiIndex.from_product( [[], []], names=['update date', 'updated variable']) endog_names = news.previous.model.endog_names if isinstance(endog_names, str): endog_names = [endog_names] assert_(news.news.index.equals(news_index)) assert_(news.update_forecasts.index.equals(news_index)) assert_(news.update_realized.index.equals(news_index)) assert_(news.weights.index.equals(news_index)) weights_columns = pd.MultiIndex.from_product([impact_dates, endog_names]) assert_(news.weights.columns.equals(weights_columns)) def check_news(news, revisions, updates, impact_dates, impacted_variables, revisions_index, updates_index, revision_impacts, update_impacts, prev_impacted_forecasts, post_impacted_forecasts, update_forecasts, update_realized, news_desired, weights): # Note: we use atol=1e-12 to handle cases where impacts, etc. are equal to # zero, but numerical precision of the Kalman filter procedures gives an # answer of e.g. 1e-16. # Note: Here we set the tolerance to be slightly negative, since some of # the tests have weights or impacts exactly equal to zero, while we still # want to include those in tests. news.tolerance = -1e-10 # - Indexes -------------------------------------------------------------- # Index of impacts check_impact_indices(news, impact_dates, impacted_variables) # Reivision indices check_revision_indices(news, revisions_index) # Update indices check_update_indices(news, updates_index) # News indices check_news_indices(news, updates_index, impact_dates) # - Impacts -------------------------------------------------------------- if updates: assert_allclose(news.update_impacts, update_impacts, atol=1e-12) else: assert_(np.all(news.update_impacts.isnull())) # Impacts from revisions if revisions: assert_allclose(news.revision_impacts, revision_impacts, atol=1e-12) else: assert_(news.news_results.revision_impacts is None) assert_(np.all(news.revision_impacts.isnull())) # Total impacts total_impacts = (news.revision_impacts.fillna(0) + news.update_impacts.fillna(0)) assert_allclose(news.total_impacts, total_impacts, atol=1e-12) # - Impacted variable forecasts ------------------------------------------ assert_allclose(news.prev_impacted_forecasts, prev_impacted_forecasts, atol=1e-12) assert_allclose(news.post_impacted_forecasts, post_impacted_forecasts, atol=1e-12) # - News ----------------------------------------------------------------- assert_allclose(news.update_forecasts, update_forecasts, atol=1e-12) assert_allclose(news.update_realized, update_realized, atol=1e-12) # The "news" is simply the forecast error assert_allclose(news.news, news_desired, atol=1e-12) # The weight is zero on previously known data, and is geometrically # declining (according to the AR parameter) in the forecast period assert_allclose(news.weights, weights, atol=1e-12) # - Table: data revisions ------------------------------------------------ assert_equal(news.data_revisions.columns.tolist(), ['observed (prev)', 'revised']) assert_equal(news.data_revisions.index.names, ['revision date', 'revised variable']) assert_(news.data_revisions.index.equals(revisions_index)) # - Table: data updates -------------------------------------------------- assert_equal(news.data_updates.columns.tolist(), ['observed', 'forecast (prev)']) assert_equal(news.data_updates.index.names, ['update date', 'updated variable']) assert_(news.data_updates.index.equals(news.news.index)) assert_allclose(news.data_updates['forecast (prev)'], news.update_forecasts, atol=1e-12) assert_allclose(news.data_updates['observed'], news.update_realized, atol=1e-12) # - Table: details_by_impact --------------------------------------------- details_by_impact = news.details_by_impact desired = ['observed', 'forecast (prev)', 'news', 'weight', 'impact'] assert_equal(details_by_impact.columns.tolist(), desired) desired = ['impact date', 'impacted variable', 'update date', 'updated variable'] assert_equal(details_by_impact.index.names, desired) # Note: Pandas < 0.24 has problems with drop_duplicates if there is a # PeriodIndex (see e.g. https://github.com/pandas-dev/pandas/issues/22803) # However, the test is not quite as precise with the version that works # for Pandas < 0.24, so we special case it and will remove after we no # longer support Pandas 0.23 # See also one other case in the "details_by_update" section below if updates and pandas_lt_25_0: actual = (news.details_by_impact['forecast (prev)'] .reset_index() .drop_duplicates('forecast (prev)'))['forecast (prev)'] assert_allclose(actual, news.update_forecasts, atol=1e-12) actual = (news.details_by_impact['observed'] .reset_index() .drop_duplicates('observed'))['observed'] assert_allclose(actual, news.update_realized, atol=1e-12) actual = (news.details_by_impact['news'] .reset_index() .drop_duplicates('news')['news']) assert_allclose(actual, news.news, atol=1e-12) # Weights assert_allclose(details_by_impact['weight'].unstack([0, 1]), news.weights, atol=1e-12) # Impact of news actual = (news.details_by_impact['impact'] .unstack([2, 3]).sum(axis=1).unstack(1)) assert_allclose(actual, news.update_impacts, atol=1e-12) elif updates and not pandas_lt_25_0: actual = (news.details_by_impact['forecast (prev)'] .drop_duplicates() .reset_index([0, 1])['forecast (prev)']) assert_allclose(actual, news.update_forecasts, atol=1e-12) actual = (news.details_by_impact['observed'] .drop_duplicates().reset_index([0, 1])['observed']) assert_allclose(actual, news.update_realized, atol=1e-12) actual = (news.details_by_impact['news'] .drop_duplicates().reset_index([0, 1])['news']) assert_allclose(actual, news.news, atol=1e-12) # Weights assert_allclose(details_by_impact['weight'].unstack([0, 1]), news.weights, atol=1e-12) # Impact of news actual = (news.details_by_impact['impact'] .unstack([2, 3]).sum(axis=1).unstack(1)) assert_allclose(actual, news.update_impacts, atol=1e-12) # - Table: details_by_update --------------------------------------------- details_by_update = news.details_by_update desired = ['news', 'weight', 'impact'] assert_equal(details_by_update.columns.tolist(), desired) desired = ['update date', 'updated variable', 'observed', 'forecast (prev)', 'impact date', 'impacted variable'] assert_equal(details_by_update.index.names, desired) if updates: # News # Special case for Pandas = 0.23, see above if pandas_lt_25_0: actual = (news.details_by_update['news'] .reset_index().drop_duplicates('news')['news']) else: actual = (news.details_by_update['news'] .drop_duplicates().reset_index([2, 3, 4, 5])['news']) assert_allclose(actual, news.news, atol=1e-12) # Weights assert_allclose(news.details_by_update['weight'].unstack([4, 5]), news.weights, atol=1e-12) # Impact of news actual = (news.details_by_update['impact'] .unstack([4, 5]).sum(axis=0).unstack(1)) assert_allclose(actual, news.update_impacts, atol=1e-12) # - Table: impacts ------------------------------------------------------- impacts = news.impacts desired = ['estimate (prev)', 'impact of revisions', 'impact of news', 'total impact', 'estimate (new)'] assert_equal(impacts.columns.tolist(), desired) desired = ['impact date', 'impacted variable'] assert_equal(impacts.index.names, desired) assert_allclose(impacts.loc[:, 'estimate (prev)'], news.prev_impacted_forecasts.stack(), atol=1e-12) assert_allclose(impacts.loc[:, 'impact of revisions'], news.revision_impacts.fillna(0).stack(), atol=1e-12) assert_allclose(impacts.loc[:, 'impact of news'], news.update_impacts.fillna(0).stack(), atol=1e-12) assert_allclose(impacts.loc[:, 'total impact'], news.total_impacts.stack(), atol=1e-12) assert_allclose(impacts.loc[:, 'estimate (new)'], news.post_impacted_forecasts.stack(), atol=1e-12) @pytest.mark.parametrize('revisions', [True, False]) @pytest.mark.parametrize('updates', [True, False]) def test_sarimax_time_invariant(revisions, updates): # Construct previous and updated datasets endog = dta['infl'].copy() comparison_type = None if updates: endog1 = endog.loc[:'2009Q2'].copy() endog2 = endog.loc[:'2009Q3'].copy() else: endog1 = endog.loc[:'2009Q3'].copy() endog2 = endog.loc[:'2009Q3'].copy() # Without updates and without NaN values, we need to specify that # the type of the comparison object that we're passing is "updated" comparison_type = 'updated' if revisions: endog1.iloc[-1] = 0. # Get the previous results object and compute the news mod = sarimax.SARIMAX(endog1) res = mod.smooth([0.5, 1.0]) news = res.news(endog2, start='2009Q2', end='2010Q1', comparison_type=comparison_type) # Compute the true values for each combination of (revsions, updates) impact_dates = pd.period_range(start='2009Q2', end='2010Q1', freq='Q') impacted_variables = ['infl'] # Revisions if revisions and updates: revisions_index = pd.MultiIndex.from_arrays( [endog1.index[-1:], ['infl']], names=['revision date', 'revised variable']) # If we have updates, the revision is to 2009Q2 revision_impacts = endog2.iloc[-2] * 0.5**np.arange(4).reshape(4, 1) elif revisions: revisions_index = pd.MultiIndex.from_arrays( [endog1.index[-1:], ['infl']], names=['revision date', 'revised variable']) # With no updates, the revision is to 2009Q3 revision_impacts = np.r_[ 0, endog2.iloc[-1] * 0.5**np.arange(3)].reshape(4, 1) else: revisions_index = pd.MultiIndex.from_arrays( [[], []], names=['revision date', 'revised variable']) revision_impacts = None # Updates if updates: updates_index = pd.MultiIndex.from_arrays( [pd.period_range(start='2009Q3', periods=1, freq='Q'), ['infl']], names=['update date', 'updated variable']) update_impacts = np.array([[ 0, endog.loc['2009Q3'] - 0.5 * endog.loc['2009Q2'], 0.5 * endog.loc['2009Q3'] - 0.5**2 * endog.loc['2009Q2'], 0.5**2 * endog.loc['2009Q3'] - 0.5**3 * endog.loc['2009Q2']]]).T else: updates_index = pd.MultiIndex.from_arrays( [[], []], names=['update date', 'updated variable']) update_impacts = None # Impact forecasts if updates: prev_impacted_forecasts = np.r_[ endog1.iloc[-1] * 0.5**np.arange(4)].reshape(4, 1) else: prev_impacted_forecasts = np.r_[ endog1.iloc[-2], endog1.iloc[-1] * 0.5**np.arange(3)].reshape(4, 1) post_impacted_forecasts = np.r_[ endog2.iloc[-2], 0.5 ** np.arange(3) * endog2.iloc[-1]].reshape(4, 1) # News if updates: # Note: update_forecasts is created using the endog2 dataset even if # there were revisions, because it should be computed after revisions # have already been taken into account update_forecasts = [0.5 * endog2.loc['2009Q2']] update_realized = [endog2.loc['2009Q3']] news_desired = [update_realized[i] - update_forecasts[i] for i in range(len(update_forecasts))] weights = pd.DataFrame(np.r_[0, 0.5**np.arange(3)]).T else: update_forecasts = pd.Series([], dtype=np.float64) update_realized = pd.Series([], dtype=np.float64) news_desired = pd.Series([], dtype=np.float64) weights = pd.DataFrame(np.zeros((0, 4))) # Run unit tests check_news(news, revisions, updates, impact_dates, impacted_variables, revisions_index, updates_index, revision_impacts, update_impacts, prev_impacted_forecasts, post_impacted_forecasts, update_forecasts, update_realized, news_desired, weights) @pytest.mark.parametrize('revisions', [True, False]) @pytest.mark.parametrize('updates', [True, False]) @pytest.mark.parametrize('which', ['exog', 'trend']) def test_sarimax_time_varying(revisions, updates, which): # This is primarily a test that the `news` method works with a time-varying # setup (i.e. time-varying state space matrices). It tests a time-varying # SARIMAX model where the time-varying component has been set to zeros # against a time-invariant version of the model. # Construct previous and updated datasets endog = dta['infl'].copy() comparison_type = None if updates: endog1 = endog.loc[:'2009Q2'].copy() endog2 = endog.loc[:'2009Q3'].copy() else: endog1 = endog.loc[:'2009Q3'].copy() endog2 = endog.loc[:'2009Q3'].copy() # Without updates and without NaN values, we need to specify that # the type of the comparison object that we're passing is "updated" comparison_type = 'updated' if revisions: endog1.iloc[-1] = 0. exog1 = None exog2 = None trend = 'n' if which == 'exog': exog1 = np.ones_like(endog1) exog2 = np.ones_like(endog2) elif which == 'trend': trend = 't' # Compute the news from a model with a trend/exog term (so the model is # time-varying), but with the coefficient set to zero (so that it will be # equivalent to the time-invariant model) mod1 = sarimax.SARIMAX(endog1, exog=exog1, trend=trend) res1 = mod1.smooth([0., 0.5, 1.0]) news1 = res1.news(endog2, exog=exog2, start='2008Q1', end='2009Q3', comparison_type=comparison_type) # Compute the news from a model without a trend term mod2 = sarimax.SARIMAX(endog1) res2 = mod2.smooth([0.5, 1.0]) news2 = res2.news(endog2, start='2008Q1', end='2009Q3', comparison_type=comparison_type) attrs = ['total_impacts', 'update_impacts', 'revision_impacts', 'news', 'weights', 'update_forecasts', 'update_realized', 'prev_impacted_forecasts', 'post_impacted_forecasts', 'revisions_iloc', 'revisions_ix', 'updates_iloc', 'updates_ix'] for attr in attrs: w = getattr(news1, attr) x = getattr(news2, attr) if isinstance(x, pd.Series): assert_series_equal(w, x) else: assert_frame_equal(w, x) @pytest.mark.parametrize('revisions', [True, False]) @pytest.mark.parametrize('updates', [True, False]) def test_unobserved_components_time_varying(revisions, updates): # This is primarily a test that the `news` method works with a time-varying # setup (i.e. time-varying state space matrices). It tests a time-varying # UnobservedComponents model where the time-varying component has been set # to zeros against a time-invariant version of the model. # Construct previous and updated datasets endog = dta['infl'].copy() comparison_type = None if updates: endog1 = endog.loc[:'2009Q2'].copy() endog2 = endog.loc[:'2009Q3'].copy() else: endog1 = endog.loc[:'2009Q3'].copy() endog2 = endog.loc[:'2009Q3'].copy() # Without updates and without NaN values, we need to specify that # the type of the comparison object that we're passing is "updated" comparison_type = 'updated' if revisions: endog1.iloc[-1] = 0. exog1 = np.ones_like(endog1) exog2 = np.ones_like(endog2) # Compute the news from a model with a trend/exog term (so the model is # time-varying), but with the coefficient set to zero (so that it will be # equivalent to the time-invariant model) mod1 = structural.UnobservedComponents(endog1, 'llevel', exog=exog1) res1 = mod1.smooth([0.5, 0.2, 0.0]) news1 = res1.news(endog2, exog=exog2, start='2008Q1', end='2009Q3', comparison_type=comparison_type) # Compute the news from a model without a trend term mod2 = structural.UnobservedComponents(endog1, 'llevel') res2 = mod2.smooth([0.5, 0.2]) news2 = res2.news(endog2, start='2008Q1', end='2009Q3', comparison_type=comparison_type) attrs = ['total_impacts', 'update_impacts', 'revision_impacts', 'news', 'weights', 'update_forecasts', 'update_realized', 'prev_impacted_forecasts', 'post_impacted_forecasts', 'revisions_iloc', 'revisions_ix', 'updates_iloc', 'updates_ix'] for attr in attrs: w = getattr(news1, attr) x = getattr(news2, attr) if isinstance(x, pd.Series): assert_series_equal(w, x) else: assert_frame_equal(w, x) @pytest.mark.parametrize('revisions', [True, False]) @pytest.mark.parametrize('updates', [True, False]) def test_varmax_time_invariant(revisions, updates): # Construct previous and updated datasets endog = dta[['realgdp', 'unemp']].copy() endog['realgdp'] = np.log(endog['realgdp']).diff() * 400 endog = endog.iloc[1:] comparison_type = None if updates: endog1 = endog.loc[:'2009Q2'].copy() endog2 = endog.loc[:'2009Q3'].copy() else: endog1 = endog.loc[:'2009Q3'].copy() endog2 = endog.loc[:'2009Q3'].copy() # Without updates and without NaN values, we need to specify that # the type of the comparison object that we're passing is "updated" comparison_type = 'updated' if revisions: # TODO: add test for only one of the variables revising? endog1.iloc[-1] = 0. # Get the previous results object and compute the news mod = varmax.VARMAX(endog1, trend='n') params = np.r_[0.5, 0.1, 0.2, 0.9, 1., 0.1, 1.1] res = mod.smooth(params) news = res.news(endog2, start='2009Q2', end='2010Q1', comparison_type=comparison_type) # Compute the true values for each combination of (revsions, updates) impact_dates = pd.period_range(start='2009Q2', end='2010Q1', freq='Q') impacted_variables = ['realgdp', 'unemp'] # Matrix powers of transition matrix Z = np.zeros((2, 2)) T0 = np.eye(2) T1 = mod['transition'] T2 = T1 @ T1 T3 = T1 @ T2 # Revisions if revisions and updates: revisions_index = pd.MultiIndex.from_product( [endog1.index[-1:], ['realgdp', 'unemp']], names=['revision date', 'revised variable']) # If we have updates, the revision is to 2009Q2 # Note: this ".values" and all of those below are only required for # Pandas = 0.23, and can be removed once that is no longer a supported # dependency tmp = endog2.iloc[-2].values revision_impacts = np.c_[T0 @ tmp, T1 @ tmp, T2 @ tmp, T3 @ tmp].T elif revisions: revisions_index = pd.MultiIndex.from_product( [endog1.index[-1:], ['realgdp', 'unemp']], names=['revision date', 'revised variable']) # With no updates, the revision is to 2009Q3 tmp = endog2.iloc[-1].values revision_impacts = np.c_[Z @ tmp, T0 @ tmp, T1 @ tmp, T2 @ tmp].T else: revisions_index = pd.MultiIndex.from_product( [[], []], names=['revision date', 'revised variable']) revision_impacts = None # Impact forecasts if updates: tmp = endog1.iloc[-1].values prev_impacted_forecasts = np.c_[T0 @ tmp, T1 @ tmp, T2 @ tmp, T3 @ tmp].T tmp = endog2.iloc[-2].values rev_impacted_forecasts = np.c_[T0 @ tmp, T1 @ tmp, T2 @ tmp, T3 @ tmp].T else: tmp = endog1.iloc[-1].values prev_impacted_forecasts = np.c_[ T0 @ endog1.iloc[-2], T0 @ tmp, T1 @ tmp, T2 @ tmp].T tmp = endog2.iloc[-1].values rev_impacted_forecasts = np.c_[ T0 @ endog2.iloc[-2], T0 @ tmp, T1 @ tmp, T2 @ tmp].T tmp = endog2.iloc[-1].values post_impacted_forecasts = np.c_[ T0 @ endog2.iloc[-2], T0 @ tmp, T1 @ tmp, T2 @ tmp].T # Updates if updates: updates_index = pd.MultiIndex.from_product( [pd.period_range(start='2009Q3', periods=1, freq='Q'), ['realgdp', 'unemp']], names=['update date', 'updated variable']) update_impacts = post_impacted_forecasts - rev_impacted_forecasts else: updates_index = pd.MultiIndex.from_product( [[], []], names=['update date', 'updated variable']) update_impacts = None # News if updates: # Note: update_forecasts is created using the endog2 dataset even if # there were revisions, because it should be computed after revisions # have already been taken into account update_forecasts = T1 @ endog2.loc['2009Q2'].values update_realized = endog2.loc['2009Q3'].values news_desired = [update_realized[i] - update_forecasts[i] for i in range(len(update_forecasts))] columns = pd.MultiIndex.from_product( [impact_dates, impacted_variables], names=['impact dates', 'impacted variables']) weights = pd.DataFrame(np.zeros((2, 8)), index=updates_index, columns=columns) weights.loc[:, '2009Q2'] = Z weights.loc[:, '2009Q3'] = T0 weights.loc[:, '2009Q4'] = T1.T weights.loc[:, '2010Q1'] = T2.T else: update_forecasts = pd.Series([], dtype=np.float64) update_realized = pd.Series([], dtype=np.float64) news_desired = pd.Series([], dtype=np.float64) weights = pd.DataFrame(np.zeros((0, 8))) # Run unit tests check_news(news, revisions, updates, impact_dates, impacted_variables, revisions_index, updates_index, revision_impacts, update_impacts, prev_impacted_forecasts, post_impacted_forecasts, update_forecasts, update_realized, news_desired, weights) @pytest.mark.parametrize('revisions', [True, False]) @pytest.mark.parametrize('updates', [True, False]) @pytest.mark.parametrize('which', ['exog', 'trend']) def test_varmax_time_varying(revisions, updates, which): # This is primarily a test that the `news` method works with a time-varying # setup (i.e. time-varying state space matrices). It tests a time-varying # VARMAX model where the time-varying component has been set to zeros # against a time-invariant version of the model. # Construct previous and updated datasets endog = dta[['realgdp', 'unemp']].copy() endog['realgdp'] = np.log(endog['realgdp']).diff() * 400 endog = endog.iloc[1:] comparison_type = None if updates: endog1 = endog.loc[:'2009Q2'].copy() endog2 = endog.loc[:'2009Q3'].copy() else: endog1 = endog.loc[:'2009Q3'].copy() endog2 = endog.loc[:'2009Q3'].copy() # Without updates and without NaN values, we need to specify that # the type of the comparison object that we're passing is "updated" comparison_type = 'updated' if revisions: # TODO: add test for only one of the variables revising? endog1.iloc[-1] = 0. exog1 = None exog2 = None trend = 'n' if which == 'exog': exog1 = np.ones_like(endog1['realgdp']) exog2 = np.ones_like(endog2['realgdp']) params1 = np.r_[0.5, 0.1, 0.2, 0.9, 0., 0., 1., 0.1, 1.1] params2 = np.r_[0.5, 0.1, 0.2, 0.9, 1., 0.1, 1.1] elif which == 'trend': trend = 't' params1 = np.r_[0., 0., 0.5, 0.1, 0.2, 0.9, 1., 0.1, 1.1] params2 = np.r_[0.5, 0.1, 0.2, 0.9, 1., 0.1, 1.1] # Compute the news from a model with a trend/exog term (so the model is # time-varying), but with the coefficient set to zero (so that it will be # equivalent to the time-invariant model) mod1 = varmax.VARMAX(endog1, exog=exog1, trend=trend) res1 = mod1.smooth(params1) news1 = res1.news(endog2, exog=exog2, start='2008Q1', end='2009Q3', comparison_type=comparison_type) # Compute the news from a model without a trend term mod2 = varmax.VARMAX(endog1, trend='n') res2 = mod2.smooth(params2) news2 = res2.news(endog2, start='2008Q1', end='2009Q3', comparison_type=comparison_type) attrs = ['total_impacts', 'update_impacts', 'revision_impacts', 'news', 'weights', 'update_forecasts', 'update_realized', 'prev_impacted_forecasts', 'post_impacted_forecasts', 'revisions_iloc', 'revisions_ix', 'updates_iloc', 'updates_ix'] for attr in attrs: w = getattr(news1, attr) x = getattr(news2, attr) if isinstance(x, pd.Series): assert_series_equal(w, x) else: assert_frame_equal(w, x) @pytest.mark.parametrize('revisions', [True, False]) @pytest.mark.parametrize('updates', [True, False]) def test_dynamic_factor_time_varying(revisions, updates): # This is primarily a test that the `news` method works with a time-varying # setup (i.e. time-varying state space matrices). It tests a time-varying # DynamicFactor model where the time-varying component has been set to # zeros against a time-invariant version of the model. # Construct previous and updated datasets endog = dta[['realgdp', 'unemp']].copy() endog['realgdp'] = np.log(endog['realgdp']).diff() * 400 endog = endog.iloc[1:] comparison_type = None if updates: endog1 = endog.loc[:'2009Q2'].copy() endog2 = endog.loc[:'2009Q3'].copy() else: endog1 = endog.loc[:'2009Q3'].copy() endog2 = endog.loc[:'2009Q3'].copy() # Without updates and without NaN values, we need to specify that # the type of the comparison object that we're passing is "updated" comparison_type = 'updated' if revisions: # TODO: add test for only one of the variables revising? endog1.iloc[-1] = 0. exog1 = np.ones_like(endog1['realgdp']) exog2 = np.ones_like(endog2['realgdp']) params1 = np.r_[0.9, 0.2, 0.0, 0.0, 1.2, 1.1, 0.5, 0.2] params2 = np.r_[0.9, 0.2, 1.2, 1.1, 0.5, 0.2] # Compute the news from a model with an exog term (so the model is # time-varying), but with the coefficient set to zero (so that it will be # equivalent to the time-invariant model) mod1 = dynamic_factor.DynamicFactor(endog1, exog=exog1, k_factors=1, factor_order=2) res1 = mod1.smooth(params1) news1 = res1.news(endog2, exog=exog2, start='2008Q1', end='2009Q3', comparison_type=comparison_type) # Compute the news from a model without a trend term mod2 = dynamic_factor.DynamicFactor(endog1, k_factors=1, factor_order=2) res2 = mod2.smooth(params2) news2 = res2.news(endog2, start='2008Q1', end='2009Q3', comparison_type=comparison_type) attrs = ['total_impacts', 'update_impacts', 'revision_impacts', 'news', 'weights', 'update_forecasts', 'update_realized', 'prev_impacted_forecasts', 'post_impacted_forecasts', 'revisions_iloc', 'revisions_ix', 'updates_iloc', 'updates_ix'] for attr in attrs: w = getattr(news1, attr) x = getattr(news2, attr) if isinstance(x, pd.Series): assert_series_equal(w, x) else: assert_frame_equal(w, x) @pytest.mark.parametrize('revisions', [True, False]) @pytest.mark.parametrize('updates', [True, False]) def test_defaults(revisions, updates): # Construct previous and updated datasets endog = dta['infl'].copy() if updates: endog1 = endog.loc[:'2009Q2'].copy() endog2 = endog.loc[:'2009Q3'].copy() else: endog1 = endog.loc[:'2009Q3'].copy() endog2 = endog.loc[:'2009Q3'].copy() if revisions: # TODO: add test for only one of the variables revising? endog1.iloc[-1] = 0. # Get the previous results object and compute the news mod1 = sarimax.SARIMAX(endog1) res1 = mod1.smooth([0.5, 1.0]) mod2 = sarimax.SARIMAX(endog2) res2 = mod2.smooth([0.5, 1.0]) news_updated_data = res1.news(endog2, comparison_type='updated') news_previous_data = res2.news(endog1, comparison_type='previous') news_updated_results = res1.news(res2, comparison_type='updated') news_previous_results = res2.news(res1, comparison_type='previous') attrs = ['total_impacts', 'update_impacts', 'revision_impacts', 'news', 'weights', 'update_forecasts', 'update_realized', 'prev_impacted_forecasts', 'post_impacted_forecasts', 'revisions_iloc', 'revisions_ix', 'updates_iloc', 'updates_ix'] for attr in attrs: w = getattr(news_updated_data, attr) x = getattr(news_previous_data, attr) y = getattr(news_updated_results, attr) z = getattr(news_previous_results, attr) if isinstance(x, pd.Series): assert_series_equal(w, x) assert_series_equal(w, y) assert_series_equal(w, z) else: assert_frame_equal(w, x) assert_frame_equal(w, y) assert_frame_equal(w, z) def test_comparison_types(): endog = dta['infl'].copy() endog.iloc[-1] = np.nan msg = 'Could not automatically determine the type of comparison' mod = sarimax.SARIMAX(endog) res = mod.smooth([0.5, 1.0]) # Test that the comparison type cannot be determined if the given dataset # or results dataset is identical to the previous dataset with pytest.raises(ValueError, match=msg): res.news(endog) with pytest.raises(ValueError, match=msg): res.news(res) # Test that if the the comparison type is specified, the news can be # computed from data that has the same shape and number of NaNs (this can # happen if there are only revisions but no updates) news = res.news(endog, comparison_type='previous') assert_allclose(news.total_impacts, 0) news = res.news(endog, comparison_type='updated') assert_allclose(news.total_impacts, 0) news = res.news(res, comparison_type='updated') assert_allclose(news.total_impacts, 0) news = res.news(res, comparison_type='updated') assert_allclose(news.total_impacts, 0) @pytest.mark.parametrize('use_periods', [True, False]) def test_start_end_dates(use_periods): endog = dta['infl'].copy() if use_periods: index_range = pd.period_range else: def index_range(*args, **kwargs): return pd.period_range(*args, **kwargs).to_timestamp(freq='Q') endog = endog.to_timestamp(freq='Q') mod = sarimax.SARIMAX(endog.iloc[:-1]) res = mod.smooth([0.5, 1.0]) # Default is the first out-of-sample period news = res.news(endog) desired = index_range(start='2009Q2', periods=1, freq='Q') assert_(news.total_impacts.index.equals(desired)) # Start (dates), periods news = res.news(endog, start='2009Q1', periods=1) desired = index_range(start='2009Q1', periods=1, freq='Q') assert_(news.total_impacts.index.equals(desired)) news = res.news(endog, start='2009Q1', periods=2) desired = index_range(start='2009Q1', periods=2, freq='Q') assert_(news.total_impacts.index.equals(desired)) # Start (int), periods news = res.news(endog, start=mod.nobs - 1, periods=1) desired = index_range(start='2009Q2', periods=1, freq='Q') assert_(news.total_impacts.index.equals(desired)) news = res.news(endog, start=mod.nobs - 2, periods=2) desired = index_range(start='2009Q1', periods=2, freq='Q') assert_(news.total_impacts.index.equals(desired)) # End (dates), periods news = res.news(endog, end='2009Q1', periods=1) desired = index_range(end='2009Q1', periods=1, freq='Q') assert_(news.total_impacts.index.equals(desired)) news = res.news(endog, end='2009Q1', periods=2) desired = index_range(end='2009Q1', periods=2, freq='Q') assert_(news.total_impacts.index.equals(desired)) # End (int), periods news = res.news(endog, end=mod.nobs - 1, periods=1) desired = index_range(end='2009Q2', periods=1, freq='Q') assert_(news.total_impacts.index.equals(desired)) news = res.news(endog, end=mod.nobs - 2, periods=2) desired = index_range(end='2009Q1', periods=2, freq='Q') assert_(news.total_impacts.index.equals(desired)) # Start (dates), end (dates) news = res.news(endog, start='2009Q1', end='2009Q1') desired = index_range(start='2009Q1', end='2009Q1', freq='Q') assert_(news.total_impacts.index.equals(desired)) news = res.news(endog, start='2009Q1', end='2009Q2') desired = index_range(start='2009Q1', end='2009Q2', freq='Q') assert_(news.total_impacts.index.equals(desired)) # Start (dates), end (int) news = res.news(endog, start='2009Q1', end=mod.nobs - 2) desired = index_range(start='2009Q1', end='2009Q1', freq='Q') assert_(news.total_impacts.index.equals(desired)) predicted = res.predict(start='2009Q1', end=mod.nobs - 2) assert_(news.total_impacts.index.equals(predicted.index)) news = res.news(endog, start='2009Q1', end=mod.nobs - 1) desired = index_range(start='2009Q1', end='2009Q2', freq='Q') assert_(news.total_impacts.index.equals(desired)) predicted = res.predict(start='2009Q1', end=mod.nobs - 1) assert_(news.total_impacts.index.equals(predicted.index)) # Start (int), end (dates) news = res.news(endog, start=mod.nobs - 2, end='2009Q1') desired = index_range(start='2009Q1', end='2009Q1', freq='Q') assert_(news.total_impacts.index.equals(desired)) predicted = res.predict(start=mod.nobs - 2, end='2009Q1') assert_(news.total_impacts.index.equals(predicted.index)) news = res.news(endog, start=mod.nobs - 2, end='2009Q2') desired = index_range(start='2009Q1', end='2009Q2', freq='Q') assert_(news.total_impacts.index.equals(desired)) predicted = res.predict(start=mod.nobs - 2, end='2009Q2') assert_(news.total_impacts.index.equals(predicted.index)) # Negative indexes # Note that negative indexes are always computed relative to the updated # sample, which in this case is 1 observation more than is in `mod.nobs` total_nobs = len(endog) assert_equal(total_nobs, mod.nobs + 1) # Start (dates), end (int) desired = index_range(start='2009Q1', end='2009Q1', freq='Q') for end in [mod.nobs - 2, total_nobs - 3, -3]: news = res.news(endog, start='2009Q1', end=end) assert_(news.total_impacts.index.equals(desired)) # Note: predict does not allow negative indexing if end > 0: predicted = res.predict(start='2009Q1', end=end) assert_(news.total_impacts.index.equals(predicted.index)) # Start (int), end (dates) desired = index_range(start='2009Q1', end='2009Q1', freq='Q') for start in [mod.nobs - 2, total_nobs - 3, -3]: news = res.news(endog, start=start, end='2009Q1') assert_(news.total_impacts.index.equals(desired)) # Note: predict does not allow negative indexing if end > 0: predicted = res.predict(start=start, end='2009Q1') assert_(news.total_impacts.index.equals(predicted.index)) @pytest.mark.parametrize('which', ['range', 'range2', 'int64', 'numpy', 'list']) def test_start_end_int(which): endog = dta['infl'].copy() nobs = len(endog) if which == 'range': endog.index = pd.RangeIndex(nobs) endog_init = endog.iloc[:-1] index_plus2 = pd.RangeIndex(nobs + 2) if which == 'range2': endog.index = pd.RangeIndex(stop=nobs * 2, step=2) endog_init = endog.iloc[:-1] index_plus2 = pd.RangeIndex((nobs + 2) * 2, step=2) elif which == 'int64': endog.index = pd.Int64Index(np.arange(nobs)) endog_init = endog.iloc[:-1] index_plus2 = pd.Int64Index(np.arange(nobs + 2)) elif which == 'numpy': endog = endog.values endog_init = endog[:-1] index_plus2 = pd.RangeIndex(nobs + 2) elif which == 'list': endog = endog.tolist() endog_init = endog[:-1] index_plus2 = pd.RangeIndex(nobs + 2) mod = sarimax.SARIMAX(endog_init) res = mod.smooth([0.5, 1.0]) # Default is the last in-sample period news = res.news(endog) desired = index_plus2[-4:-3] assert_(news.total_impacts.index.equals(desired)) # Start, periods news = res.news(endog, start=mod.nobs - 1, periods=1) desired = index_plus2[-4:-3] assert_(news.total_impacts.index.equals(desired)) news = res.news(endog, start=mod.nobs - 2, periods=2) desired = index_plus2[-5:-3] assert_(news.total_impacts.index.equals(desired)) # End, periods news = res.news(endog, end=mod.nobs - 1, periods=1) desired = index_plus2[-4:-3] assert_(news.total_impacts.index.equals(desired)) news = res.news(endog, end=mod.nobs - 2, periods=2) desired = index_plus2[-6:-4] assert_(news.total_impacts.index.equals(desired)) # Start, end # Note: end is inclusive, like `get_prediction`. news = res.news(endog, start=mod.nobs - 2, end=mod.nobs - 1) desired = index_plus2[-5:-3] assert_(news.total_impacts.index.equals(desired)) if which not in ['numpy', 'list']: predicted = res.predict(start=mod.nobs - 2, end=mod.nobs - 1) assert_(news.total_impacts.index.equals(predicted.index)) news = res.news(endog, start=mod.nobs, end=mod.nobs) desired = index_plus2[-3:-2] assert_(news.total_impacts.index.equals(desired)) if which not in ['numpy', 'list']: predicted = res.predict(start=mod.nobs, end=mod.nobs) assert_(news.total_impacts.index.equals(predicted.index)) news = res.news(endog, start=mod.nobs, end=mod.nobs + 1) desired = index_plus2[-3:-1] assert_(news.total_impacts.index.equals(desired)) if which not in ['numpy', 'list']: predicted = res.predict(start=mod.nobs, end=mod.nobs + 1) assert_(news.total_impacts.index.equals(predicted.index)) def test_invalid(): endog = dta['infl'].copy() mod = sarimax.SARIMAX(endog.iloc[:-1]) res = mod.smooth([0.5, 1.0]) msg = 'The index associated with the updated results is not a superset' with pytest.raises(ValueError, match=msg): res.news(endog.values) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_options.py000066400000000000000000000222441400612667500257040ustar00rootroot00000000000000""" Tests for setting options in KalmanFilter, KalmanSmoother, SimulationSmoother (does not test the filtering, smoothing, or simulation smoothing for each option) Author: Chad Fulton License: Simplified-BSD """ import numpy as np from statsmodels.tsa.statespace.kalman_filter import ( FILTER_CONVENTIONAL, FILTER_EXACT_INITIAL, FILTER_AUGMENTED, FILTER_SQUARE_ROOT, FILTER_UNIVARIATE, FILTER_COLLAPSED, FILTER_EXTENDED, FILTER_UNSCENTED, FILTER_CONCENTRATED, FILTER_CHANDRASEKHAR, INVERT_UNIVARIATE, SOLVE_LU, INVERT_LU, SOLVE_CHOLESKY, INVERT_CHOLESKY, STABILITY_FORCE_SYMMETRY, MEMORY_STORE_ALL, MEMORY_NO_FORECAST, MEMORY_NO_PREDICTED, MEMORY_NO_FILTERED, MEMORY_NO_LIKELIHOOD, MEMORY_NO_GAIN, MEMORY_NO_SMOOTHING, MEMORY_NO_STD_FORECAST, MEMORY_CONSERVE ) from statsmodels.tsa.statespace.kalman_smoother import ( SMOOTHER_STATE, SMOOTHER_STATE_COV, SMOOTHER_STATE_AUTOCOV, SMOOTHER_DISTURBANCE, SMOOTHER_DISTURBANCE_COV, SMOOTHER_ALL ) from statsmodels.tsa.statespace.simulation_smoother import ( SimulationSmoother, SIMULATION_STATE, SIMULATION_ALL ) from numpy.testing import assert_equal class Options(object): @classmethod def setup_class(cls, *args, **kwargs): # Dummy data endog = np.arange(10) k_states = 1 cls.model = SimulationSmoother(k_endog=1, k_states=k_states, *args, **kwargs) cls.model.bind(endog) class TestOptions(Options): def test_filter_methods(self): model = self.model # TODO test FilterResults for accurante boolean versions of options # Clear the filter method model.filter_method = 0 # Try setting via boolean model.filter_conventional = True assert_equal(model.filter_method, FILTER_CONVENTIONAL) model.filter_collapsed = True assert_equal(model.filter_method, FILTER_CONVENTIONAL | FILTER_COLLAPSED) model.filter_conventional = False assert_equal(model.filter_method, FILTER_COLLAPSED) # Try setting directly via method model.set_filter_method(FILTER_AUGMENTED) assert_equal(model.filter_method, FILTER_AUGMENTED) # Try setting via boolean via method model.set_filter_method(filter_conventional=True, filter_augmented=False) assert_equal(model.filter_method, FILTER_CONVENTIONAL) # Try setting and unsetting all model.filter_method = 0 for name in model.filter_methods: setattr(model, name, True) assert_equal( model.filter_method, FILTER_CONVENTIONAL | FILTER_EXACT_INITIAL | FILTER_AUGMENTED | FILTER_SQUARE_ROOT | FILTER_UNIVARIATE | FILTER_COLLAPSED | FILTER_EXTENDED | FILTER_UNSCENTED | FILTER_CONCENTRATED | FILTER_CHANDRASEKHAR ) for name in model.filter_methods: setattr(model, name, False) assert_equal(model.filter_method, 0) def test_inversion_methods(self): model = self.model # Clear the inversion method model.inversion_method = 0 # Try setting via boolean model.invert_univariate = True assert_equal(model.inversion_method, INVERT_UNIVARIATE) model.invert_cholesky = True assert_equal(model.inversion_method, INVERT_UNIVARIATE | INVERT_CHOLESKY) model.invert_univariate = False assert_equal(model.inversion_method, INVERT_CHOLESKY) # Try setting directly via method model.set_inversion_method(INVERT_LU) assert_equal(model.inversion_method, INVERT_LU) # Try setting via boolean via method model.set_inversion_method(invert_cholesky=True, invert_univariate=True, invert_lu=False) assert_equal(model.inversion_method, INVERT_UNIVARIATE | INVERT_CHOLESKY) # Try setting and unsetting all model.inversion_method = 0 for name in model.inversion_methods: setattr(model, name, True) assert_equal( model.inversion_method, INVERT_UNIVARIATE | SOLVE_LU | INVERT_LU | SOLVE_CHOLESKY | INVERT_CHOLESKY ) for name in model.inversion_methods: setattr(model, name, False) assert_equal(model.inversion_method, 0) def test_stability_methods(self): model = self.model # Clear the stability method model.stability_method = 0 # Try setting via boolean model.stability_force_symmetry = True assert_equal(model.stability_method, STABILITY_FORCE_SYMMETRY) model.stability_force_symmetry = False assert_equal(model.stability_method, 0) # Try setting directly via method model.stability_method = 0 model.set_stability_method(STABILITY_FORCE_SYMMETRY) assert_equal(model.stability_method, STABILITY_FORCE_SYMMETRY) # Try setting via boolean via method model.stability_method = 0 model.set_stability_method(stability_method=True) assert_equal(model.stability_method, STABILITY_FORCE_SYMMETRY) # Try setting via keyword via method model.stability_method = 0 model.set_stability_method(stability_force_symmetry=True) assert_equal(model.stability_method, STABILITY_FORCE_SYMMETRY) def test_conserve_memory(self): model = self.model # Clear the filter method model.conserve_memory = MEMORY_STORE_ALL # Try setting via boolean model.memory_no_forecast = True assert_equal(model.conserve_memory, MEMORY_NO_FORECAST) model.memory_no_filtered = True assert_equal(model.conserve_memory, MEMORY_NO_FORECAST | MEMORY_NO_FILTERED) model.memory_no_forecast = False assert_equal(model.conserve_memory, MEMORY_NO_FILTERED) # Try setting directly via method model.set_conserve_memory(MEMORY_NO_PREDICTED) assert_equal(model.conserve_memory, MEMORY_NO_PREDICTED) # Try setting via boolean via method model.set_conserve_memory(memory_no_filtered=True, memory_no_predicted=False) assert_equal(model.conserve_memory, MEMORY_NO_FILTERED) # Try setting and unsetting all model.conserve_memory = 0 for name in model.memory_options: if name == 'memory_conserve': continue setattr(model, name, True) assert_equal( model.conserve_memory, MEMORY_NO_FORECAST | MEMORY_NO_PREDICTED | MEMORY_NO_FILTERED | MEMORY_NO_LIKELIHOOD | MEMORY_NO_GAIN | MEMORY_NO_SMOOTHING | MEMORY_NO_STD_FORECAST ) assert_equal(model.conserve_memory & MEMORY_CONSERVE, MEMORY_CONSERVE) for name in model.memory_options: if name == 'memory_conserve': continue setattr(model, name, False) assert_equal(model.conserve_memory, 0) def test_smoother_outputs(self): model = self.model # TODO test SmootherResults for accurante boolean versions of options # Clear the smoother output model.smoother_output = 0 # Try setting via boolean model.smoother_state = True assert_equal(model.smoother_output, SMOOTHER_STATE) model.smoother_disturbance = True assert_equal(model.smoother_output, SMOOTHER_STATE | SMOOTHER_DISTURBANCE) model.smoother_state = False assert_equal(model.smoother_output, SMOOTHER_DISTURBANCE) # Try setting directly via method model.set_smoother_output(SMOOTHER_DISTURBANCE_COV) assert_equal(model.smoother_output, SMOOTHER_DISTURBANCE_COV) # Try setting via boolean via method model.set_smoother_output(smoother_disturbance=True, smoother_disturbance_cov=False) assert_equal(model.smoother_output, SMOOTHER_DISTURBANCE) # Try setting and unsetting all model.smoother_output = 0 for name in model.smoother_outputs: if name == 'smoother_all': continue setattr(model, name, True) assert_equal( model.smoother_output, SMOOTHER_STATE | SMOOTHER_STATE_COV | SMOOTHER_STATE_AUTOCOV | SMOOTHER_DISTURBANCE | SMOOTHER_DISTURBANCE_COV ) assert_equal(model.smoother_output, SMOOTHER_ALL) for name in model.smoother_outputs: if name == 'smoother_all': continue setattr(model, name, False) assert_equal(model.smoother_output, 0) def test_simulation_outputs(self): # TODO test changing simulation options in SimulationSmoothResults # instance assert_equal( self.model.get_simulation_output(SIMULATION_STATE), SIMULATION_STATE) assert_equal( self.model.get_simulation_output(simulate_state=True, simulate_disturbance=True), SIMULATION_ALL) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_pickle.py000066400000000000000000000117661400612667500254670ustar00rootroot00000000000000""" Tests for python wrapper of state space representation and filtering Author: Chad Fulton License: Simplified-BSD References ---------- Kim, Chang-Jin, and Charles R. Nelson. 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications". MIT Press Books. The MIT Press. """ import pickle import numpy as np import pandas as pd from numpy.testing import assert_equal, assert_allclose import pytest from statsmodels.tsa.statespace import sarimax from statsmodels.tsa.statespace.kalman_filter import KalmanFilter from statsmodels.tsa.statespace.representation import Representation from statsmodels.tsa.statespace.structural import UnobservedComponents from .results import results_kalman_filter @pytest.fixture() def data(): true = results_kalman_filter.uc_uni data_ = pd.DataFrame( true['data'], index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'), columns=['GDP'] ) data_['lgdp'] = np.log(data_['GDP']) return data_ def test_pickle_fit_sarimax(data): # Fit an ARIMA(1,1,0) to log GDP mod = sarimax.SARIMAX(data['lgdp'], order=(1, 1, 0)) pkl_mod = pickle.loads(pickle.dumps(mod)) res = mod.fit(disp=-1, full_output=True, method='newton') pkl_res = pkl_mod.fit(disp=-1, full_output=True, method='newton') assert_allclose(res.llf_obs, pkl_res.llf_obs) assert_allclose(res.tvalues, pkl_res.tvalues) assert_allclose(res.smoothed_state, pkl_res.smoothed_state) assert_allclose(res.resid.values, pkl_res.resid.values) assert_allclose(res.impulse_responses(10), res.impulse_responses(10)) def test_unobserved_components_pickle(): # Tests for missing data nobs = 20 k_endog = 1 np.random.seed(1208) endog = np.random.normal(size=(nobs, k_endog)) endog[:4, 0] = np.nan exog2 = np.random.normal(size=(nobs, 2)) index = pd.date_range('1970-01-01', freq='QS', periods=nobs) endog_pd = pd.DataFrame(endog, index=index) exog2_pd = pd.DataFrame(exog2, index=index) models = [ UnobservedComponents(endog, 'llevel', exog=exog2), UnobservedComponents(endog_pd, 'llevel', exog=exog2_pd), ] for mod in models: # Smoke tests pkl_mod = pickle.loads(pickle.dumps(mod)) assert_equal(mod.start_params, pkl_mod.start_params) res = mod.fit(disp=False) pkl_res = pkl_mod.fit(disp=False) assert_allclose(res.llf_obs, pkl_res.llf_obs) assert_allclose(res.tvalues, pkl_res.tvalues) assert_allclose(res.smoothed_state, pkl_res.smoothed_state) assert_allclose(res.resid, pkl_res.resid) assert_allclose(res.impulse_responses(10), res.impulse_responses(10)) def test_kalman_filter_pickle(data): # Construct the statespace representation true = results_kalman_filter.uc_uni k_states = 4 model = KalmanFilter(k_endog=1, k_states=k_states) model.bind(data['lgdp'].values) model.design[:, :, 0] = [1, 1, 0, 0] model.transition[([0, 0, 1, 1, 2, 3], [0, 3, 1, 2, 1, 3], [0, 0, 0, 0, 0, 0])] = [1, 1, 0, 0, 1, 1] model.selection = np.eye(model.k_states) # Update matrices with given parameters (sigma_v, sigma_e, sigma_w, phi_1, phi_2) = np.array( true['parameters'] ) model.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2] model.state_cov[ np.diag_indices(k_states) + (np.zeros(k_states, dtype=int),)] = [ sigma_v ** 2, sigma_e ** 2, 0, sigma_w ** 2 ] # Initialization initial_state = np.zeros((k_states,)) initial_state_cov = np.eye(k_states) * 100 # Initialization: modification initial_state_cov = np.dot( np.dot(model.transition[:, :, 0], initial_state_cov), model.transition[:, :, 0].T ) model.initialize_known(initial_state, initial_state_cov) pkl_mod = pickle.loads(pickle.dumps(model)) results = model.filter() pkl_results = pkl_mod.filter() assert_allclose(results.llf_obs[true['start']:].sum(), pkl_results.llf_obs[true['start']:].sum()) assert_allclose(results.filtered_state[0][true['start']:], pkl_results.filtered_state[0][true['start']:]) assert_allclose(results.filtered_state[1][true['start']:], pkl_results.filtered_state[1][true['start']:]) assert_allclose(results.filtered_state[3][true['start']:], pkl_results.filtered_state[3][true['start']:]) def test_representation_pickle(): nobs = 10 k_endog = 2 arr = np.arange(nobs * k_endog).reshape(k_endog, nobs) * 1. endog = np.asfortranarray(arr) mod = Representation(endog, k_states=2) pkl_mod = pickle.loads(pickle.dumps(mod)) assert_equal(mod.nobs, pkl_mod.nobs) assert_equal(mod.k_endog, pkl_mod.k_endog) mod._initialize_representation() pkl_mod._initialize_representation() assert_equal(mod.design, pkl_mod.design) assert_equal(mod.obs_intercept, pkl_mod.obs_intercept) assert_equal(mod.initial_variance, pkl_mod.initial_variance) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_prediction.py000066400000000000000000000061351400612667500263520ustar00rootroot00000000000000""" Tests for prediction of state space models Author: Chad Fulton License: Simplified-BSD """ import numpy as np import pandas as pd from statsmodels.tsa.statespace import sarimax from numpy.testing import assert_equal, assert_raises, assert_allclose, assert_ def test_predict_dates(): index = pd.date_range(start='1950-01-01', periods=11, freq='D') np.random.seed(324328) endog = pd.Series(np.random.normal(size=10), index=index[:-1]) # Basic test mod = sarimax.SARIMAX(endog, order=(1, 0, 0)) res = mod.filter(mod.start_params) # In-sample prediction should have the same index pred = res.predict() assert_equal(len(pred), mod.nobs) assert_equal(pred.index.values, index[:-1].values) # Out-of-sample forecasting should extend the index appropriately fcast = res.forecast() assert_equal(fcast.index[0], index[-1]) # Simple differencing in the SARIMAX model should eliminate dates of # series eliminated due to differencing mod = sarimax.SARIMAX(endog, order=(1, 1, 0), simple_differencing=True) res = mod.filter(mod.start_params) pred = res.predict() # In-sample prediction should lose the first index value assert_equal(mod.nobs, endog.shape[0] - 1) assert_equal(len(pred), mod.nobs) assert_equal(pred.index.values, index[1:-1].values) # Out-of-sample forecasting should still extend the index appropriately fcast = res.forecast() assert_equal(fcast.index[0], index[-1]) # Simple differencing again, this time with a more complex differencing # structure mod = sarimax.SARIMAX(endog, order=(1, 2, 0), seasonal_order=(0, 1, 0, 4), simple_differencing=True) res = mod.filter(mod.start_params) pred = res.predict() # In-sample prediction should lose the first 6 index values assert_equal(mod.nobs, endog.shape[0] - (4 + 2)) assert_equal(len(pred), mod.nobs) assert_equal(pred.index.values, index[4 + 2:-1].values) # Out-of-sample forecasting should still extend the index appropriately fcast = res.forecast() assert_equal(fcast.index[0], index[-1]) def test_memory_no_predicted(): # Tests for forecasts with memory_no_predicted is set endog = [0.5, 1.2, 0.4, 0.6] mod = sarimax.SARIMAX(endog, order=(1, 0, 0)) res1 = mod.filter([0.5, 1.]) mod.ssm.memory_no_predicted = True res2 = mod.filter([0.5, 1.]) # Make sure we really didn't store all of the values in res2 assert_equal(res1.predicted_state.shape, (1, 5)) assert_(res2.predicted_state is None) assert_equal(res1.predicted_state_cov.shape, (1, 1, 5)) assert_(res2.predicted_state_cov is None) # Check that we can't do dynamic in-sample prediction assert_raises(ValueError, res2.predict, dynamic=True) assert_raises(ValueError, res2.get_prediction, dynamic=True) # Make sure the point forecasts are the same assert_allclose(res1.forecast(10), res2.forecast(10)) # Make sure the confidence intervals are the same fcast1 = res1.get_forecast(10) fcast2 = res1.get_forecast(10) assert_allclose(fcast1.summary_frame(), fcast2.summary_frame()) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_representation.py000066400000000000000000001341501400612667500272530ustar00rootroot00000000000000""" Tests for python wrapper of state space representation and filtering Author: Chad Fulton License: Simplified-BSD References ---------- Kim, Chang-Jin, and Charles R. Nelson. 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications". MIT Press Books. The MIT Press. """ import os import warnings import numpy as np import pandas as pd import pytest from statsmodels.tsa.statespace.representation import Representation from statsmodels.tsa.statespace.kalman_filter import ( KalmanFilter, FilterResults, PredictionResults) from statsmodels.tsa.statespace.simulation_smoother import SimulationSmoother from statsmodels.tsa.statespace import tools, sarimax from .results import results_kalman_filter from numpy.testing import ( assert_equal, assert_almost_equal, assert_raises, assert_allclose) current_path = os.path.dirname(os.path.abspath(__file__)) clark1989_path = os.path.join('results', 'results_clark1989_R.csv') clark1989_results = pd.read_csv(os.path.join(current_path, clark1989_path)) class Clark1987(object): """ Clark's (1987) univariate unobserved components model of real GDP (as presented in Kim and Nelson, 1999) Test data produced using GAUSS code described in Kim and Nelson (1999) and found at http://econ.korea.ac.kr/~cjkim/SSMARKOV.htm See `results.results_kalman_filter` for more information. """ @classmethod def setup_class(cls, dtype=float, **kwargs): cls.true = results_kalman_filter.uc_uni cls.true_states = pd.DataFrame(cls.true['states']) # GDP, Quarterly, 1947.1 - 1995.3 data = pd.DataFrame( cls.true['data'], index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'), columns=['GDP'] ) data['lgdp'] = np.log(data['GDP']) # Construct the statespace representation k_states = 4 cls.model = KalmanFilter(k_endog=1, k_states=k_states, **kwargs) cls.model.bind(data['lgdp'].values) cls.model.design[:, :, 0] = [1, 1, 0, 0] cls.model.transition[([0, 0, 1, 1, 2, 3], [0, 3, 1, 2, 1, 3], [0, 0, 0, 0, 0, 0])] = [1, 1, 0, 0, 1, 1] cls.model.selection = np.eye(cls.model.k_states) # Update matrices with given parameters (sigma_v, sigma_e, sigma_w, phi_1, phi_2) = np.array( cls.true['parameters'] ) cls.model.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2] cls.model.state_cov[ np.diag_indices(k_states)+(np.zeros(k_states, dtype=int),)] = [ sigma_v**2, sigma_e**2, 0, sigma_w**2 ] # Initialization initial_state = np.zeros((k_states,)) initial_state_cov = np.eye(k_states)*100 # Initialization: modification initial_state_cov = np.dot( np.dot(cls.model.transition[:, :, 0], initial_state_cov), cls.model.transition[:, :, 0].T ) cls.model.initialize_known(initial_state, initial_state_cov) @classmethod def run_filter(cls): # Filter the data return cls.model.filter() def test_loglike(self): assert_almost_equal( self.results.llf_obs[self.true['start']:].sum(), self.true['loglike'], 5 ) def test_filtered_state(self): assert_almost_equal( self.results.filtered_state[0][self.true['start']:], self.true_states.iloc[:, 0], 4 ) assert_almost_equal( self.results.filtered_state[1][self.true['start']:], self.true_states.iloc[:, 1], 4 ) assert_almost_equal( self.results.filtered_state[3][self.true['start']:], self.true_states.iloc[:, 2], 4 ) class TestClark1987Single(Clark1987): """ Basic single precision test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): pytest.skip('Not implemented') super(TestClark1987Single, cls).setup_class( dtype=np.float32, conserve_memory=0 ) cls.results = cls.run_filter() class TestClark1987Double(Clark1987): """ Basic double precision test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987Double, cls).setup_class( dtype=float, conserve_memory=0 ) cls.results = cls.run_filter() @pytest.mark.skip('Not implemented') class TestClark1987SingleComplex(Clark1987): """ Basic single precision complex test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987SingleComplex, cls).setup_class( dtype=np.complex64, conserve_memory=0 ) cls.results = cls.run_filter() class TestClark1987DoubleComplex(Clark1987): """ Basic double precision complex test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987DoubleComplex, cls).setup_class( dtype=complex, conserve_memory=0 ) cls.results = cls.run_filter() class TestClark1987Conserve(Clark1987): """ Memory conservation test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987Conserve, cls).setup_class( dtype=float, conserve_memory=0x01 | 0x02 ) cls.results = cls.run_filter() class Clark1987Forecast(Clark1987): """ Forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls, dtype=float, nforecast=100, conserve_memory=0): super(Clark1987Forecast, cls).setup_class( dtype=dtype, conserve_memory=conserve_memory ) cls.nforecast = nforecast # Add missing observations to the end (to forecast) cls.model.endog = np.array( np.r_[cls.model.endog[0, :], [np.nan]*nforecast], ndmin=2, dtype=dtype, order="F" ) cls.model.nobs = cls.model.endog.shape[1] def test_filtered_state(self): assert_almost_equal( self.results.filtered_state[0][self.true['start']:-self.nforecast], self.true_states.iloc[:, 0], 4 ) assert_almost_equal( self.results.filtered_state[1][self.true['start']:-self.nforecast], self.true_states.iloc[:, 1], 4 ) assert_almost_equal( self.results.filtered_state[3][self.true['start']:-self.nforecast], self.true_states.iloc[:, 2], 4 ) class TestClark1987ForecastDouble(Clark1987Forecast): """ Basic double forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987ForecastDouble, cls).setup_class() cls.results = cls.run_filter() class TestClark1987ForecastDoubleComplex(Clark1987Forecast): """ Basic double complex forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987ForecastDoubleComplex, cls).setup_class( dtype=complex ) cls.results = cls.run_filter() class TestClark1987ForecastConserve(Clark1987Forecast): """ Memory conservation forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987ForecastConserve, cls).setup_class( dtype=float, conserve_memory=0x01 | 0x02 ) cls.results = cls.run_filter() class TestClark1987ConserveAll(Clark1987): """ Memory conservation forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1987ConserveAll, cls).setup_class( dtype=float, conserve_memory=0x01 | 0x02 | 0x04 | 0x08 ) cls.model.loglikelihood_burn = cls.true['start'] cls.results = cls.run_filter() def test_loglike(self): assert_almost_equal( self.results.llf, self.true['loglike'], 5 ) def test_filtered_state(self): end = self.true_states.shape[0] assert_almost_equal( self.results.filtered_state[0][-1], self.true_states.iloc[end-1, 0], 4 ) assert_almost_equal( self.results.filtered_state[1][-1], self.true_states.iloc[end-1, 1], 4 ) class Clark1989(object): """ Clark's (1989) bivariate unobserved components model of real GDP (as presented in Kim and Nelson, 1999) Tests two-dimensional observation data. Test data produced using GAUSS code described in Kim and Nelson (1999) and found at http://econ.korea.ac.kr/~cjkim/SSMARKOV.htm See `results.results_kalman_filter` for more information. """ @classmethod def setup_class(cls, dtype=float, **kwargs): cls.true = results_kalman_filter.uc_bi cls.true_states = pd.DataFrame(cls.true['states']) # GDP and Unemployment, Quarterly, 1948.1 - 1995.3 data = pd.DataFrame( cls.true['data'], index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'), columns=['GDP', 'UNEMP'] )[4:] data['GDP'] = np.log(data['GDP']) data['UNEMP'] = (data['UNEMP']/100) k_states = 6 cls.model = KalmanFilter(k_endog=2, k_states=k_states, **kwargs) cls.model.bind(np.ascontiguousarray(data.values)) # Statespace representation cls.model.design[:, :, 0] = [[1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1]] cls.model.transition[ ([0, 0, 1, 1, 2, 3, 4, 5], [0, 4, 1, 2, 1, 2, 4, 5], [0, 0, 0, 0, 0, 0, 0, 0]) ] = [1, 1, 0, 0, 1, 1, 1, 1] cls.model.selection = np.eye(cls.model.k_states) # Update matrices with given parameters (sigma_v, sigma_e, sigma_w, sigma_vl, sigma_ec, phi_1, phi_2, alpha_1, alpha_2, alpha_3) = np.array( cls.true['parameters'], ) cls.model.design[([1, 1, 1], [1, 2, 3], [0, 0, 0])] = [ alpha_1, alpha_2, alpha_3 ] cls.model.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2] cls.model.obs_cov[1, 1, 0] = sigma_ec**2 cls.model.state_cov[ np.diag_indices(k_states)+(np.zeros(k_states, dtype=int),)] = [ sigma_v**2, sigma_e**2, 0, 0, sigma_w**2, sigma_vl**2 ] # Initialization initial_state = np.zeros((k_states,)) initial_state_cov = np.eye(k_states)*100 # Initialization: cls.modelification initial_state_cov = np.dot( np.dot(cls.model.transition[:, :, 0], initial_state_cov), cls.model.transition[:, :, 0].T ) cls.model.initialize_known(initial_state, initial_state_cov) @classmethod def run_filter(cls): # Filter the data return cls.model.filter() def test_loglike(self): assert_almost_equal( # self.results.llf_obs[self.true['start']:].sum(), self.results.llf_obs[0:].sum(), self.true['loglike'], 2 ) def test_filtered_state(self): assert_almost_equal( self.results.filtered_state[0][self.true['start']:], self.true_states.iloc[:, 0], 4 ) assert_almost_equal( self.results.filtered_state[1][self.true['start']:], self.true_states.iloc[:, 1], 4 ) assert_almost_equal( self.results.filtered_state[4][self.true['start']:], self.true_states.iloc[:, 2], 4 ) assert_almost_equal( self.results.filtered_state[5][self.true['start']:], self.true_states.iloc[:, 3], 4 ) class TestClark1989(Clark1989): """ Basic double precision test for the loglikelihood and filtered states with two-dimensional observation vector. """ @classmethod def setup_class(cls): super(TestClark1989, cls).setup_class(dtype=float, conserve_memory=0) cls.results = cls.run_filter() def test_kalman_gain(self): assert_allclose(self.results.kalman_gain.sum(axis=1).sum(axis=0), clark1989_results['V1'], atol=1e-4) class TestClark1989Conserve(Clark1989): """ Memory conservation test for the loglikelihood and filtered states with two-dimensional observation vector. """ @classmethod def setup_class(cls): super(TestClark1989Conserve, cls).setup_class( dtype=float, conserve_memory=0x01 | 0x02 ) cls.results = cls.run_filter() class Clark1989Forecast(Clark1989): """ Memory conservation test for the loglikelihood and filtered states with two-dimensional observation vector. """ @classmethod def setup_class(cls, dtype=float, nforecast=100, conserve_memory=0): super(Clark1989Forecast, cls).setup_class( dtype=dtype, conserve_memory=conserve_memory ) cls.nforecast = nforecast # Add missing observations to the end (to forecast) cls.model.endog = np.array( np.c_[ cls.model.endog, np.r_[[np.nan, np.nan]*nforecast].reshape(2, nforecast) ], ndmin=2, dtype=dtype, order="F" ) cls.model.nobs = cls.model.endog.shape[1] cls.results = cls.run_filter() def test_filtered_state(self): assert_almost_equal( self.results.filtered_state[0][self.true['start']:-self.nforecast], self.true_states.iloc[:, 0], 4 ) assert_almost_equal( self.results.filtered_state[1][self.true['start']:-self.nforecast], self.true_states.iloc[:, 1], 4 ) assert_almost_equal( self.results.filtered_state[4][self.true['start']:-self.nforecast], self.true_states.iloc[:, 2], 4 ) assert_almost_equal( self.results.filtered_state[5][self.true['start']:-self.nforecast], self.true_states.iloc[:, 3], 4 ) class TestClark1989ForecastDouble(Clark1989Forecast): """ Basic double forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1989ForecastDouble, cls).setup_class() cls.results = cls.run_filter() class TestClark1989ForecastDoubleComplex(Clark1989Forecast): """ Basic double complex forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1989ForecastDoubleComplex, cls).setup_class( dtype=complex ) cls.results = cls.run_filter() class TestClark1989ForecastConserve(Clark1989Forecast): """ Memory conservation forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1989ForecastConserve, cls).setup_class( dtype=float, conserve_memory=0x01 | 0x02 ) cls.results = cls.run_filter() class TestClark1989ConserveAll(Clark1989): """ Memory conservation forecasting test for the loglikelihood and filtered states. """ @classmethod def setup_class(cls): super(TestClark1989ConserveAll, cls).setup_class( dtype=float, conserve_memory=0x01 | 0x02 | 0x04 | 0x08 ) # cls.model.loglikelihood_burn = cls.true['start'] cls.model.loglikelihood_burn = 0 cls.results = cls.run_filter() def test_loglike(self): assert_almost_equal( self.results.llf, self.true['loglike'], 2 ) def test_filtered_state(self): end = self.true_states.shape[0] assert_almost_equal( self.results.filtered_state[0][-1], self.true_states.iloc[end-1, 0], 4 ) assert_almost_equal( self.results.filtered_state[1][-1], self.true_states.iloc[end-1, 1], 4 ) assert_almost_equal( self.results.filtered_state[4][-1], self.true_states.iloc[end-1, 2], 4 ) assert_almost_equal( self.results.filtered_state[5][-1], self.true_states.iloc[end-1, 3], 4 ) class TestClark1989PartialMissing(Clark1989): @classmethod def setup_class(cls): super(TestClark1989PartialMissing, cls).setup_class() endog = cls.model.endog endog[1, -51:] = np.NaN cls.model.bind(endog) cls.results = cls.run_filter() def test_loglike(self): assert_allclose(self.results.llf_obs[0:].sum(), 1232.113456) def test_filtered_state(self): # Could do this, but no need really. pass def test_predicted_state(self): assert_allclose( self.results.predicted_state.T[1:], clark1989_results.iloc[:, 1:], atol=1e-8 ) # Miscellaneous coverage-related tests def test_slice_notation(): # Test setting and getting state space representation matrices using the # slice notation. endog = np.arange(10)*1.0 mod = KalmanFilter(k_endog=1, k_states=2) mod.bind(endog) # Test invalid __setitem__ def set_designs(): mod['designs'] = 1 def set_designs2(): mod['designs', 0, 0] = 1 def set_designs3(): mod[0] = 1 assert_raises(IndexError, set_designs) assert_raises(IndexError, set_designs2) assert_raises(IndexError, set_designs3) # Test invalid __getitem__ assert_raises(IndexError, lambda: mod['designs']) assert_raises(IndexError, lambda: mod['designs', 0, 0, 0]) assert_raises(IndexError, lambda: mod[0]) # Test valid __setitem__, __getitem__ assert_equal(mod.design[0, 0, 0], 0) mod['design', 0, 0, 0] = 1 assert_equal(mod['design'].sum(), 1) assert_equal(mod.design[0, 0, 0], 1) assert_equal(mod['design', 0, 0, 0], 1) # Test valid __setitem__, __getitem__ with unspecified time index mod['design'] = np.zeros(mod['design'].shape) assert_equal(mod.design[0, 0], 0) mod['design', 0, 0] = 1 assert_equal(mod.design[0, 0], 1) assert_equal(mod['design', 0, 0], 1) def test_representation(): # Test Representation construction # Test an invalid number of states def zero_kstates(): Representation(1, 0) assert_raises(ValueError, zero_kstates) # Test an invalid endogenous array def empty_endog(): endog = np.zeros((0, 0)) Representation(endog, k_states=2) assert_raises(ValueError, empty_endog) # Test a Fortran-ordered endogenous array (which will be assumed to be in # wide format: k_endog x nobs) nobs = 10 k_endog = 2 arr = np.arange(nobs*k_endog).reshape(k_endog, nobs)*1. endog = np.asfortranarray(arr) mod = Representation(endog, k_states=2) assert_equal(mod.nobs, nobs) assert_equal(mod.k_endog, k_endog) # Test a C-ordered endogenous array (which will be assumed to be in # tall format: nobs x k_endog) nobs = 10 k_endog = 2 endog = np.arange(nobs*k_endog).reshape(nobs, k_endog)*1. mod = Representation(endog, k_states=2) assert_equal(mod.nobs, nobs) assert_equal(mod.k_endog, k_endog) # Test getting the statespace representation assert_equal(mod._statespace, None) mod._initialize_representation() assert_equal(mod._statespace is not None, True) def test_bind(): # Test binding endogenous data to Kalman filter mod = Representation(2, k_states=2) # Test invalid endogenous array (it must be ndarray) assert_raises(ValueError, lambda: mod.bind([1, 2, 3, 4])) # Test valid (nobs x 1) endogenous array mod.bind(np.arange(10).reshape((5, 2))*1.) assert_equal(mod.nobs, 5) # Test valid (k_endog x 0) endogenous array mod.bind(np.zeros((0, 2), dtype=np.float64)) # Test invalid (3-dim) endogenous array with pytest.raises(ValueError): mod.bind(np.arange(12).reshape(2, 2, 3)*1.) # Test valid F-contiguous mod.bind(np.asfortranarray(np.arange(10).reshape(2, 5))) assert_equal(mod.nobs, 5) # Test valid C-contiguous mod.bind(np.arange(10).reshape(5, 2)) assert_equal(mod.nobs, 5) # Test invalid F-contiguous with pytest.raises(ValueError): mod.bind(np.asfortranarray(np.arange(10).reshape(5, 2))) # Test invalid C-contiguous assert_raises(ValueError, lambda: mod.bind(np.arange(10).reshape(2, 5))) def test_initialization(): # Test Kalman filter initialization mod = Representation(1, k_states=2) # Test invalid state initialization assert_raises(RuntimeError, lambda: mod._initialize_state()) # Test valid initialization initial_state = np.zeros(2,) + 1.5 initial_state_cov = np.eye(2) * 3. mod.initialize_known(initial_state, initial_state_cov) assert_equal(mod.initialization.constant.sum(), 3) assert_equal(mod.initialization.stationary_cov.diagonal().sum(), 6) # Test invalid initial_state initial_state = np.zeros(10,) with pytest.raises(ValueError): mod.initialize_known(initial_state, initial_state_cov) initial_state = np.zeros((10, 10)) with pytest.raises(ValueError): mod.initialize_known(initial_state, initial_state_cov) # Test invalid initial_state_cov initial_state = np.zeros(2,) + 1.5 initial_state_cov = np.eye(3) with pytest.raises(ValueError): mod.initialize_known(initial_state, initial_state_cov) def test_init_matrices_time_invariant(): # Test setting state space system matrices in __init__, with time-invariant # matrices k_endog = 2 k_states = 3 k_posdef = 1 endog = np.zeros((10, 2)) obs_intercept = np.arange(k_endog) * 1.0 design = np.reshape( np.arange(k_endog * k_states) * 1.0, (k_endog, k_states)) obs_cov = np.reshape(np.arange(k_endog**2) * 1.0, (k_endog, k_endog)) state_intercept = np.arange(k_states) * 1.0 transition = np.reshape(np.arange(k_states**2) * 1.0, (k_states, k_states)) selection = np.reshape( np.arange(k_states * k_posdef) * 1.0, (k_states, k_posdef)) state_cov = np.reshape(np.arange(k_posdef**2) * 1.0, (k_posdef, k_posdef)) mod = Representation(endog, k_states=k_states, k_posdef=k_posdef, obs_intercept=obs_intercept, design=design, obs_cov=obs_cov, state_intercept=state_intercept, transition=transition, selection=selection, state_cov=state_cov) assert_allclose(mod['obs_intercept'], obs_intercept) assert_allclose(mod['design'], design) assert_allclose(mod['obs_cov'], obs_cov) assert_allclose(mod['state_intercept'], state_intercept) assert_allclose(mod['transition'], transition) assert_allclose(mod['selection'], selection) assert_allclose(mod['state_cov'], state_cov) def test_init_matrices_time_varying(): # Test setting state space system matrices in __init__, with time-varying # matrices nobs = 10 k_endog = 2 k_states = 3 k_posdef = 1 endog = np.zeros((10, 2)) obs_intercept = np.reshape(np.arange(k_endog * nobs) * 1.0, (k_endog, nobs)) design = np.reshape( np.arange(k_endog * k_states * nobs) * 1.0, (k_endog, k_states, nobs)) obs_cov = np.reshape( np.arange(k_endog**2 * nobs) * 1.0, (k_endog, k_endog, nobs)) state_intercept = np.reshape( np.arange(k_states * nobs) * 1.0, (k_states, nobs)) transition = np.reshape( np.arange(k_states**2 * nobs) * 1.0, (k_states, k_states, nobs)) selection = np.reshape( np.arange(k_states * k_posdef * nobs) * 1.0, (k_states, k_posdef, nobs)) state_cov = np.reshape( np.arange(k_posdef**2 * nobs) * 1.0, (k_posdef, k_posdef, nobs)) mod = Representation(endog, k_states=k_states, k_posdef=k_posdef, obs_intercept=obs_intercept, design=design, obs_cov=obs_cov, state_intercept=state_intercept, transition=transition, selection=selection, state_cov=state_cov) assert_allclose(mod['obs_intercept'], obs_intercept) assert_allclose(mod['design'], design) assert_allclose(mod['obs_cov'], obs_cov) assert_allclose(mod['state_intercept'], state_intercept) assert_allclose(mod['transition'], transition) assert_allclose(mod['selection'], selection) assert_allclose(mod['state_cov'], state_cov) def test_no_endog(): # Test for RuntimeError when no endog is provided by the time filtering # is initialized. mod = KalmanFilter(k_endog=1, k_states=1) # directly call the _initialize_filter function assert_raises(RuntimeError, mod._initialize_filter) # indirectly call it through filtering mod.initialize_approximate_diffuse() assert_raises(RuntimeError, mod.filter) def test_cython(): # Test the cython _kalman_filter creation, re-creation, calling, etc. # Check that datatypes are correct: for prefix, dtype in tools.prefix_dtype_map.items(): endog = np.array(1., ndmin=2, dtype=dtype) mod = KalmanFilter(k_endog=1, k_states=1, dtype=dtype) # Bind data and initialize the ?KalmanFilter object mod.bind(endog) mod._initialize_filter() # Check that the dtype and prefix are correct assert_equal(mod.prefix, prefix) assert_equal(mod.dtype, dtype) # Test that a dKalmanFilter instance was created assert_equal(prefix in mod._kalman_filters, True) kf = mod._kalman_filters[prefix] assert isinstance(kf, tools.prefix_kalman_filter_map[prefix]) # Test that the default returned _kalman_filter is the above instance assert_equal(mod._kalman_filter, kf) # Check that upcasting datatypes / ?KalmanFilter works (e.g. d -> z) mod = KalmanFilter(k_endog=1, k_states=1) # Default dtype is float assert_equal(mod.prefix, 'd') assert_equal(mod.dtype, np.float64) # Prior to initialization, no ?KalmanFilter exists assert_equal(mod._kalman_filter, None) # Bind data and initialize the ?KalmanFilter object endog = np.ascontiguousarray(np.array([1., 2.], dtype=np.float64)) mod.bind(endog) mod._initialize_filter() kf = mod._kalman_filters['d'] # Rebind data, still float, check that we have not changed mod.bind(endog) mod._initialize_filter() assert_equal(mod._kalman_filter, kf) # Force creating new ?Statespace and ?KalmanFilter, by changing the # time-varying character of an array mod.design = np.zeros((1, 1, 2)) mod._initialize_filter() assert_equal(mod._kalman_filter == kf, False) kf = mod._kalman_filters['d'] # Rebind data, now complex, check that the ?KalmanFilter instance has # changed endog = np.ascontiguousarray(np.array([1., 2.], dtype=np.complex128)) mod.bind(endog) assert_equal(mod._kalman_filter == kf, False) def test_filter(): # Tests of invalid calls to the filter function endog = np.ones((10, 1)) mod = KalmanFilter(endog, k_states=1, initialization='approximate_diffuse') mod['design', :] = 1 mod['selection', :] = 1 mod['state_cov', :] = 1 # Test default filter results res = mod.filter() assert_equal(isinstance(res, FilterResults), True) def test_loglike(): # Tests of invalid calls to the loglike function endog = np.ones((10, 1)) mod = KalmanFilter(endog, k_states=1, initialization='approximate_diffuse') mod['design', :] = 1 mod['selection', :] = 1 mod['state_cov', :] = 1 # Test that self.memory_no_likelihood = True raises an error mod.memory_no_likelihood = True assert_raises(RuntimeError, mod.loglikeobs) def test_predict(): # Tests of invalid calls to the predict function warnings.simplefilter("always") endog = np.ones((10, 1)) mod = KalmanFilter(endog, k_states=1, initialization='approximate_diffuse') mod['design', :] = 1 mod['obs_intercept'] = np.zeros((1, 10)) mod['selection', :] = 1 mod['state_cov', :] = 1 # Check that we need both forecasts and predicted output for dynamic # prediction mod.memory_no_forecast = True res = mod.filter() assert_raises(ValueError, res.predict) mod.memory_no_forecast = False mod.memory_no_predicted = True res = mod.filter() assert_raises(ValueError, res.predict, dynamic=True) mod.memory_no_predicted = False # Now get a clean filter object res = mod.filter() # Check that start < 0 is an error assert_raises(ValueError, res.predict, start=-1) # Check that end < start is an error assert_raises(ValueError, res.predict, start=2, end=1) # Check that dynamic < 0 is an error assert_raises(ValueError, res.predict, dynamic=-1) # Check that dynamic > end is an warning with warnings.catch_warnings(record=True) as w: res.predict(end=1, dynamic=2) message = ('Dynamic prediction specified to begin after the end of' ' prediction, and so has no effect.') assert_equal(str(w[0].message), message) # Check that dynamic > nobs is an warning with warnings.catch_warnings(record=True) as w: res.predict(end=11, dynamic=11, obs_intercept=np.zeros((1, 1))) message = ('Dynamic prediction specified to begin during' ' out-of-sample forecasting period, and so has no' ' effect.') assert_equal(str(w[0].message), message) # Check for a warning when providing a non-used statespace matrix with pytest.raises(ValueError): res.predict(end=res.nobs+1, design=True, obs_intercept=np.zeros((1, 1))) # Check that an error is raised when a new time-varying matrix is not # provided assert_raises(ValueError, res.predict, end=res.nobs+1) # Check that an error is raised when an obs_intercept with incorrect length # is given assert_raises(ValueError, res.predict, end=res.nobs+1, obs_intercept=np.zeros(2)) # Check that start=None gives start=0 and end=None gives end=nobs assert_equal(res.predict().forecasts.shape, (1, res.nobs)) # Check that dynamic=True begins dynamic prediction immediately # TODO just a smoke test res.predict(dynamic=True) # Check that on success, PredictionResults object is returned prediction_results = res.predict(start=3, end=5) assert_equal(isinstance(prediction_results, PredictionResults), True) # Check for correctly subset representation arrays # (k_endog, npredictions) = (1, 2) assert_equal(prediction_results.endog.shape, (1, 2)) # (k_endog, npredictions) = (1, 2) assert_equal(prediction_results.obs_intercept.shape, (1, 2)) # (k_endog, k_states) = (1, 1) assert_equal(prediction_results.design.shape, (1, 1)) # (k_endog, k_endog) = (1, 1) assert_equal(prediction_results.obs_cov.shape, (1, 1)) # (k_state,) = (1,) assert_equal(prediction_results.state_intercept.shape, (1,)) # (k_state, npredictions) = (1, 2) assert_equal(prediction_results.obs_intercept.shape, (1, 2)) # (k_state, k_state) = (1, 1) assert_equal(prediction_results.transition.shape, (1, 1)) # (k_state, k_posdef) = (1, 1) assert_equal(prediction_results.selection.shape, (1, 1)) # (k_posdef, k_posdef) = (1, 1) assert_equal(prediction_results.state_cov.shape, (1, 1)) # Check for correctly subset filter output arrays # (k_endog, npredictions) = (1, 2) assert_equal(prediction_results.forecasts.shape, (1, 2)) assert_equal(prediction_results.forecasts_error.shape, (1, 2)) # (k_states, npredictions) = (1, 2) assert_equal(prediction_results.filtered_state.shape, (1, 2)) assert_equal(prediction_results.predicted_state.shape, (1, 2)) # (k_endog, k_endog, npredictions) = (1, 1, 2) assert_equal(prediction_results.forecasts_error_cov.shape, (1, 1, 2)) # (k_states, k_states, npredictions) = (1, 1, 2) assert_equal(prediction_results.filtered_state_cov.shape, (1, 1, 2)) assert_equal(prediction_results.predicted_state_cov.shape, (1, 1, 2)) # Check for invalid attribute assert_raises(AttributeError, getattr, prediction_results, 'test') # Check that an error is raised when a non-two-dimensional obs_cov # is given # ...and... # Check that an error is raised when an obs_cov that is too short is given mod = KalmanFilter(endog, k_states=1, initialization='approximate_diffuse') mod['design', :] = 1 mod['obs_cov'] = np.zeros((1, 1, 10)) mod['selection', :] = 1 mod['state_cov', :] = 1 res = mod.filter() assert_raises(ValueError, res.predict, end=res.nobs + 2, obs_cov=np.zeros((1, 1))) assert_raises(ValueError, res.predict, end=res.nobs + 2, obs_cov=np.zeros((1, 1, 1))) def test_standardized_forecasts_error(): # Simple test that standardized forecasts errors are calculated correctly. # Just uses a different calculation method on a univariate series. # Get the dataset true = results_kalman_filter.uc_uni data = pd.DataFrame( true['data'], index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'), columns=['GDP'] ) data['lgdp'] = np.log(data['GDP']) # Fit an ARIMA(1, 1, 0) to log GDP mod = sarimax.SARIMAX(data['lgdp'], order=(1, 1, 0), use_exact_diffuse=True) res = mod.fit(disp=-1) d = np.maximum(res.loglikelihood_burn, res.nobs_diffuse) standardized_forecasts_error = ( res.filter_results.forecasts_error[0] / np.sqrt(res.filter_results.forecasts_error_cov[0, 0]) ) assert_allclose( res.filter_results.standardized_forecasts_error[0, d:], standardized_forecasts_error[..., d:], ) def test_simulate(): # Test for simulation of new time-series from scipy.signal import lfilter # Common parameters nsimulations = 10 sigma2 = 2 measurement_shocks = np.zeros(nsimulations) state_shocks = np.random.normal(scale=sigma2**0.5, size=nsimulations) # Random walk model, so simulated series is just the cumulative sum of # the shocks mod = SimulationSmoother(np.r_[0], k_states=1, initialization='diffuse') mod['design', 0, 0] = 1. mod['transition', 0, 0] = 1. mod['selection', 0, 0] = 1. actual = mod.simulate( nsimulations, measurement_shocks=measurement_shocks, state_shocks=state_shocks)[0].squeeze() desired = np.r_[0, np.cumsum(state_shocks)[:-1]] assert_allclose(actual, desired) # Local level model, so simulated series is just the cumulative sum of # the shocks plus the measurement shock mod = SimulationSmoother(np.r_[0], k_states=1, initialization='diffuse') mod['design', 0, 0] = 1. mod['transition', 0, 0] = 1. mod['selection', 0, 0] = 1. actual = mod.simulate( nsimulations, measurement_shocks=np.ones(nsimulations), state_shocks=state_shocks)[0].squeeze() desired = np.r_[1, np.cumsum(state_shocks)[:-1] + 1] assert_allclose(actual, desired) # Local level-like model with observation and state intercepts, so # simulated series is just the cumulative sum of the shocks minus the state # intercept, plus the observation intercept and the measurement shock mod = SimulationSmoother(np.zeros((1, 10)), k_states=1, initialization='diffuse') mod['obs_intercept', 0, 0] = 5. mod['design', 0, 0] = 1. mod['state_intercept', 0, 0] = -2. mod['transition', 0, 0] = 1. mod['selection', 0, 0] = 1. actual = mod.simulate( nsimulations, measurement_shocks=np.ones(nsimulations), state_shocks=state_shocks)[0].squeeze() desired = np.r_[1 + 5, np.cumsum(state_shocks - 2)[:-1] + 1 + 5] assert_allclose(actual, desired) # Model with time-varying observation intercept mod = SimulationSmoother(np.zeros((1, 10)), k_states=1, nobs=10, initialization='diffuse') mod['obs_intercept'] = (np.arange(10)*1.).reshape(1, 10) mod['design', 0, 0] = 1. mod['transition', 0, 0] = 1. mod['selection', 0, 0] = 1. actual = mod.simulate( nsimulations, measurement_shocks=measurement_shocks, state_shocks=state_shocks)[0].squeeze() desired = np.r_[0, np.cumsum(state_shocks)[:-1] + np.arange(1, 10)] assert_allclose(actual, desired) # Model with time-varying observation intercept, check that error is raised # if more simulations are requested than are nobs. mod = SimulationSmoother(np.zeros((1, 10)), k_states=1, nobs=10, initialization='diffuse') mod['obs_intercept'] = (np.arange(10)*1.).reshape(1, 10) mod['design', 0, 0] = 1. mod['transition', 0, 0] = 1. mod['selection', 0, 0] = 1. assert_raises(ValueError, mod.simulate, nsimulations+1, measurement_shocks, state_shocks) # ARMA(1, 1): phi = [0.1], theta = [0.5], sigma^2 = 2 phi = 0.1 theta = 0.5 mod = sarimax.SARIMAX([0], order=(1, 0, 1)) mod.update(np.r_[phi, theta, sigma2]) actual = mod.ssm.simulate( nsimulations, measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=np.zeros(mod.k_states))[0].squeeze() desired = lfilter([1, theta], [1, -phi], np.r_[0, state_shocks[:-1]]) assert_allclose(actual, desired) # SARIMAX(1, 0, 1)x(1, 0, 1, 4), this time using the results object call mod = sarimax.SARIMAX([0.1, 0.5, -0.2], order=(1, 0, 1), seasonal_order=(1, 0, 1, 4)) res = mod.filter([0.1, 0.5, 0.2, -0.3, 1]) actual = res.simulate( nsimulations, measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=np.zeros(mod.k_states)) desired = lfilter( res.polynomial_reduced_ma, res.polynomial_reduced_ar, np.r_[0, state_shocks[:-1]]) assert_allclose(actual, desired) def test_impulse_responses(): # Test for impulse response functions # Random walk: 1-unit impulse response (i.e. non-orthogonalized irf) is 1 # for all periods mod = SimulationSmoother(k_endog=1, k_states=1, initialization='diffuse') mod['design', 0, 0] = 1. mod['transition', 0, 0] = 1. mod['selection', 0, 0] = 1. mod['state_cov', 0, 0] = 2. actual = mod.impulse_responses(steps=10) desired = np.ones((11, 1)) assert_allclose(actual, desired) # Random walk: 2-unit impulse response (i.e. non-orthogonalized irf) is 2 # for all periods mod = SimulationSmoother(k_endog=1, k_states=1, initialization='diffuse') mod['design', 0, 0] = 1. mod['transition', 0, 0] = 1. mod['selection', 0, 0] = 1. mod['state_cov', 0, 0] = 2. actual = mod.impulse_responses(steps=10, impulse=[2]) desired = np.ones((11, 1)) * 2 assert_allclose(actual, desired) # Random walk: 1-standard-deviation response (i.e. orthogonalized irf) is # sigma for all periods (here sigma^2 = 2) mod = SimulationSmoother(k_endog=1, k_states=1, initialization='diffuse') mod['design', 0, 0] = 1. mod['transition', 0, 0] = 1. mod['selection', 0, 0] = 1. mod['state_cov', 0, 0] = 2. actual = mod.impulse_responses(steps=10, orthogonalized=True) desired = np.ones((11, 1)) * 2**0.5 assert_allclose(actual, desired) # Random walk: 1-standard-deviation cumulative response (i.e. cumulative # orthogonalized irf) mod = SimulationSmoother(k_endog=1, k_states=1, initialization='diffuse') mod['design', 0, 0] = 1. mod['transition', 0, 0] = 1. mod['selection', 0, 0] = 1. mod['state_cov', 0, 0] = 2. actual = mod.impulse_responses(steps=10, orthogonalized=True, cumulative=True) desired = np.cumsum(np.ones((11, 1)) * 2**0.5)[:, np.newaxis] actual = mod.impulse_responses(steps=10, impulse=[1], orthogonalized=True, cumulative=True) desired = np.cumsum(np.ones((11, 1)) * 2**0.5)[:, np.newaxis] assert_allclose(actual, desired) # Random walk: 1-unit impulse response (i.e. non-orthogonalized irf) is 1 # for all periods, even when intercepts are present mod = SimulationSmoother(k_endog=1, k_states=1, initialization='diffuse') mod['state_intercept', 0] = 100. mod['design', 0, 0] = 1. mod['obs_intercept', 0] = -1000. mod['transition', 0, 0] = 1. mod['selection', 0, 0] = 1. mod['state_cov', 0, 0] = 2. actual = mod.impulse_responses(steps=10) desired = np.ones((11, 1)) assert_allclose(actual, desired) # Univariate model (random walk): test that an error is thrown when # a multivariate or empty "impulse" is sent mod = SimulationSmoother(k_endog=1, k_states=1, initialization='diffuse') assert_raises(ValueError, mod.impulse_responses, impulse=1) assert_raises(ValueError, mod.impulse_responses, impulse=[1, 1]) assert_raises(ValueError, mod.impulse_responses, impulse=[]) # Univariate model with two uncorrelated shocks mod = SimulationSmoother(k_endog=1, k_states=2, initialization='diffuse') mod['design', 0, 0:2] = 1. mod['transition', :, :] = np.eye(2) mod['selection', :, :] = np.eye(2) mod['state_cov', :, :] = np.eye(2) desired = np.ones((11, 1)) actual = mod.impulse_responses(steps=10, impulse=0) assert_allclose(actual, desired) actual = mod.impulse_responses(steps=10, impulse=[1, 0]) assert_allclose(actual, desired) actual = mod.impulse_responses(steps=10, impulse=1) assert_allclose(actual, desired) actual = mod.impulse_responses(steps=10, impulse=[0, 1]) assert_allclose(actual, desired) # In this case (with sigma=sigma^2=1), orthogonalized is the same as not actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True) assert_allclose(actual, desired) actual = mod.impulse_responses( steps=10, impulse=[1, 0], orthogonalized=True) assert_allclose(actual, desired) actual = mod.impulse_responses( steps=10, impulse=[0, 1], orthogonalized=True) assert_allclose(actual, desired) # Univariate model with two correlated shocks mod = SimulationSmoother(k_endog=1, k_states=2, initialization='diffuse') mod['design', 0, 0:2] = 1. mod['transition', :, :] = np.eye(2) mod['selection', :, :] = np.eye(2) mod['state_cov', :, :] = np.array([[1, 0.5], [0.5, 1.25]]) desired = np.ones((11, 1)) # Non-orthogonalized (i.e. 1-unit) impulses still just generate 1's actual = mod.impulse_responses(steps=10, impulse=0) assert_allclose(actual, desired) actual = mod.impulse_responses(steps=10, impulse=1) assert_allclose(actual, desired) # Orthogonalized (i.e. 1-std-dev) impulses now generate different responses actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True) assert_allclose(actual, desired + desired * 0.5) actual = mod.impulse_responses(steps=10, impulse=1, orthogonalized=True) assert_allclose(actual, desired) # Multivariate model with two correlated shocks mod = SimulationSmoother(k_endog=2, k_states=2, initialization='diffuse') mod['design', :, :] = np.eye(2) mod['transition', :, :] = np.eye(2) mod['selection', :, :] = np.eye(2) mod['state_cov', :, :] = np.array([[1, 0.5], [0.5, 1.25]]) ones = np.ones((11, 1)) zeros = np.zeros((11, 1)) # Non-orthogonalized (i.e. 1-unit) impulses still just generate 1's, but # only for the appropriate series actual = mod.impulse_responses(steps=10, impulse=0) assert_allclose(actual, np.c_[ones, zeros]) actual = mod.impulse_responses(steps=10, impulse=1) assert_allclose(actual, np.c_[zeros, ones]) # Orthogonalized (i.e. 1-std-dev) impulses now generate different # responses, and only for the appropriate series actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True) assert_allclose(actual, np.c_[ones, ones * 0.5]) actual = mod.impulse_responses(steps=10, impulse=1, orthogonalized=True) assert_allclose(actual, np.c_[zeros, ones]) # AR(1) model generates a geometrically declining series mod = sarimax.SARIMAX([0.1, 0.5, -0.2], order=(1, 0, 0)) phi = 0.5 mod.update([phi, 1]) desired = np.cumprod(np.r_[1, [phi]*10]) # Test going through the model directly actual = mod.ssm.impulse_responses(steps=10) assert_allclose(actual[:, 0], desired) # Test going through the results object res = mod.filter([phi, 1.]) actual = res.impulse_responses(steps=10) assert_allclose(actual, desired) def test_missing(): # Datasets endog = np.arange(10).reshape(10, 1) endog_pre_na = np.ascontiguousarray(np.c_[ endog.copy() * np.nan, endog.copy() * np.nan, endog, endog]) endog_post_na = np.ascontiguousarray(np.c_[ endog, endog, endog.copy() * np.nan, endog.copy() * np.nan]) endog_inject_na = np.ascontiguousarray(np.c_[ endog, endog.copy() * np.nan, endog, endog.copy() * np.nan]) # Base model mod = KalmanFilter(np.ascontiguousarray(np.c_[endog, endog]), k_states=1, initialization='approximate_diffuse') mod['design', :, :] = 1 mod['obs_cov', :, :] = np.eye(mod.k_endog)*0.5 mod['transition', :, :] = 0.5 mod['selection', :, :] = 1 mod['state_cov', :, :] = 0.5 llf = mod.loglikeobs() # Model with prepended nans mod = KalmanFilter(endog_pre_na, k_states=1, initialization='approximate_diffuse') mod['design', :, :] = 1 mod['obs_cov', :, :] = np.eye(mod.k_endog)*0.5 mod['transition', :, :] = 0.5 mod['selection', :, :] = 1 mod['state_cov', :, :] = 0.5 llf_pre_na = mod.loglikeobs() assert_allclose(llf_pre_na, llf) # Model with appended nans mod = KalmanFilter(endog_post_na, k_states=1, initialization='approximate_diffuse') mod['design', :, :] = 1 mod['obs_cov', :, :] = np.eye(mod.k_endog)*0.5 mod['transition', :, :] = 0.5 mod['selection', :, :] = 1 mod['state_cov', :, :] = 0.5 llf_post_na = mod.loglikeobs() assert_allclose(llf_post_na, llf) # Model with injected nans mod = KalmanFilter(endog_inject_na, k_states=1, initialization='approximate_diffuse') mod['design', :, :] = 1 mod['obs_cov', :, :] = np.eye(mod.k_endog)*0.5 mod['transition', :, :] = 0.5 mod['selection', :, :] = 1 mod['state_cov', :, :] = 0.5 llf_inject_na = mod.loglikeobs() assert_allclose(llf_inject_na, llf) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_sarimax.py000066400000000000000000003114241400612667500256560ustar00rootroot00000000000000""" Tests for SARIMAX models Author: Chad Fulton License: Simplified-BSD """ import os import warnings from statsmodels.compat.platform import PLATFORM_WIN import numpy as np import pandas as pd import pytest from statsmodels.tsa.statespace import sarimax, tools from statsmodels.tsa import arima_model as arima from .results import results_sarimax from statsmodels.tools import add_constant from numpy.testing import ( assert_, assert_equal, assert_almost_equal, assert_raises, assert_allclose ) current_path = os.path.dirname(os.path.abspath(__file__)) realgdp_path = os.path.join('results', 'results_realgdpar_stata.csv') realgdp_results = pd.read_csv(current_path + os.sep + realgdp_path) coverage_path = os.path.join('results', 'results_sarimax_coverage.csv') coverage_results = pd.read_csv(os.path.join(current_path, coverage_path)) class TestSARIMAXStatsmodels(object): """ Test ARIMA model using SARIMAX class against statsmodels ARIMA class Notes ----- Standard errors are quite good for the OPG case. """ @classmethod def setup_class(cls): cls.true = results_sarimax.wpi1_stationary endog = cls.true['data'] cls.model_a = arima.ARIMA(endog, order=(1, 1, 1)) cls.result_a = cls.model_a.fit(disp=-1) cls.model_b = sarimax.SARIMAX(endog, order=(1, 1, 1), trend='c', simple_differencing=True, hamilton_representation=True) cls.result_b = cls.model_b.fit(disp=-1) def test_loglike(self): assert_allclose(self.result_b.llf, self.result_a.llf) def test_aic(self): assert_allclose(self.result_b.aic, self.result_a.aic) def test_bic(self): assert_allclose(self.result_b.bic, self.result_a.bic) def test_hqic(self): assert_allclose(self.result_b.hqic, self.result_a.hqic) def test_mle(self): # ARIMA estimates the mean of the process, whereas SARIMAX estimates # the intercept. Convert the mean to intercept to compare params_a = self.result_a.params.copy() params_a[0] = (1 - params_a[1]) * params_a[0] assert_allclose(self.result_b.params[:-1], params_a, atol=5e-5) def test_bse(self): # Test the complex step approximated BSE values cpa = self.result_b._cov_params_approx(approx_complex_step=True) bse = cpa.diagonal()**0.5 assert_allclose(bse[1:-1], self.result_a.bse[1:], atol=1e-5) def test_t_test(self): import statsmodels.tools._testing as smt # to trigger failure, un-comment the following: # self.result_b._cache['pvalues'] += 1 smt.check_ttest_tvalues(self.result_b) smt.check_ftest_pvalues(self.result_b) class TestRealGDPARStata(object): """ Includes tests of filtered states and standardized forecast errors. Notes ----- Could also test the usual things like standard errors, etc. but those are well-tested elsewhere. """ @classmethod def setup_class(cls): dlgdp = np.log(realgdp_results['value']).diff()[1:].values cls.model = sarimax.SARIMAX(dlgdp, order=(12, 0, 0), trend='n', hamilton_representation=True) # Estimated by Stata params = [ .40725515, .18782621, -.01514009, -.01027267, -.03642297, .11576416, .02573029, -.00766572, .13506498, .08649569, .06942822, -.10685783, .00007999607 ] cls.results = cls.model.filter(params) def test_filtered_state(self): for i in range(12): assert_allclose( realgdp_results.iloc[1:]['u%d' % (i+1)], self.results.filter_results.filtered_state[i], atol=1e-6 ) def test_standardized_forecasts_error(self): assert_allclose( realgdp_results.iloc[1:]['rstd'], self.results.filter_results.standardized_forecasts_error[0], atol=1e-3 ) class SARIMAXStataTests(object): def test_loglike(self): assert_almost_equal( self.result.llf, self.true['loglike'], 4 ) def test_aic(self): assert_almost_equal( self.result.aic, self.true['aic'], 3 ) def test_bic(self): assert_almost_equal( self.result.bic, self.true['bic'], 3 ) def test_hqic(self): hqic = ( -2*self.result.llf + 2*np.log(np.log(self.result.nobs_effective)) * self.result.params.shape[0] ) assert_almost_equal( self.result.hqic, hqic, 3 ) def test_standardized_forecasts_error(self): cython_sfe = self.result.standardized_forecasts_error self.result._standardized_forecasts_error = None python_sfe = self.result.standardized_forecasts_error assert_allclose(cython_sfe, python_sfe) class ARIMA(SARIMAXStataTests): """ ARIMA model Stata arima documentation, Example 1 """ @classmethod def setup_class(cls, true, *args, **kwargs): cls.true = true endog = true['data'] kwargs.setdefault('simple_differencing', True) kwargs.setdefault('hamilton_representation', True) cls.model = sarimax.SARIMAX(endog, order=(1, 1, 1), trend='c', *args, **kwargs) # Stata estimates the mean of the process, whereas SARIMAX estimates # the intercept of the process. Get the intercept. intercept = (1 - true['params_ar'][0]) * true['params_mean'][0] params = np.r_[intercept, true['params_ar'], true['params_ma'], true['params_variance']] cls.result = cls.model.filter(params) def test_mle(self): result = self.model.fit(disp=-1) assert_allclose( result.params, self.result.params, atol=1e-3 ) class TestARIMAStationary(ARIMA): """ Notes ----- Standard errors are very good for the OPG and complex step approximation cases. """ @classmethod def setup_class(cls): super(TestARIMAStationary, cls).setup_class( results_sarimax.wpi1_stationary ) def test_bse(self): # test defaults assert_equal(self.result.cov_type, 'opg') assert_equal(self.result._cov_approx_complex_step, True) assert_equal(self.result._cov_approx_centered, False) # default covariance type (opg) assert_allclose(self.result.bse[1], self.true['se_ar_opg'], atol=1e-7) assert_allclose(self.result.bse[2], self.true['se_ma_opg'], atol=1e-7) def test_bse_approx(self): # complex step bse = self.result._cov_params_approx( approx_complex_step=True).diagonal()**0.5 assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-7) assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-7) # The below tests pass irregularly; they give a sense of the precision # available with finite differencing # finite difference, non-centered # with warnings.catch_warnings(): # warnings.simplefilter("ignore") # bse = self.result._cov_params_approx( # approx_complex_step=False).diagonal()**0.5 # assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-2) # assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-1) # # finite difference, centered # cpa = self.result._cov_params_approx( # approx_complex_step=False, approx_centered=True) # bse = cpa.diagonal()**0.5 # assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-3) # assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-3) def test_bse_oim(self): # OIM covariance type oim_bse = self.result.cov_params_oim.diagonal()**0.5 assert_allclose(oim_bse[1], self.true['se_ar_oim'], atol=1e-3) assert_allclose(oim_bse[2], self.true['se_ma_oim'], atol=1e-2) def test_bse_robust(self): robust_oim_bse = self.result.cov_params_robust_oim.diagonal()**0.5 cpra = self.result.cov_params_robust_approx robust_approx_bse = cpra.diagonal()**0.5 true_robust_bse = np.r_[ self.true['se_ar_robust'], self.true['se_ma_robust'] ] assert_allclose(robust_oim_bse[1:3], true_robust_bse, atol=1e-2) assert_allclose(robust_approx_bse[1:3], true_robust_bse, atol=1e-3) class TestARIMADiffuse(ARIMA): """ Notes ----- Standard errors are very good for the OPG and quite good for the complex step approximation cases. """ @classmethod def setup_class(cls, **kwargs): kwargs['initialization'] = 'approximate_diffuse' kwargs['initial_variance'] = ( results_sarimax.wpi1_diffuse['initial_variance'] ) super(TestARIMADiffuse, cls).setup_class(results_sarimax.wpi1_diffuse, **kwargs) def test_bse(self): # test defaults assert_equal(self.result.cov_type, 'opg') assert_equal(self.result._cov_approx_complex_step, True) assert_equal(self.result._cov_approx_centered, False) # default covariance type (opg) assert_allclose(self.result.bse[1], self.true['se_ar_opg'], atol=1e-7) assert_allclose(self.result.bse[2], self.true['se_ma_opg'], atol=1e-7) def test_bse_approx(self): # complex step bse = self.result._cov_params_approx( approx_complex_step=True).diagonal()**0.5 assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-4) assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-4) # The below tests do not pass # with warnings.catch_warnings(): # warnings.simplefilter("ignore") # # finite difference, non-centered : failure # bse = self.result._cov_params_approx( # approx_complex_step=False).diagonal()**0.5 # assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-4) # assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-4) # # finite difference, centered : failure # cpa = self.result._cov_params_approx( # approx_complex_step=False, approx_centered=True) # bse = cpa.diagonal()**0.5 # assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-4) # assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-4) def test_bse_oim(self): # OIM covariance type bse = self.result._cov_params_oim().diagonal()**0.5 assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-2) assert_allclose(bse[2], self.true['se_ma_oim'], atol=1e-1) class AdditiveSeasonal(SARIMAXStataTests): """ ARIMA model with additive seasonal effects Stata arima documentation, Example 2 """ @classmethod def setup_class(cls, true, *args, **kwargs): cls.true = true endog = np.log(true['data']) kwargs.setdefault('simple_differencing', True) kwargs.setdefault('hamilton_representation', True) cls.model = sarimax.SARIMAX( endog, order=(1, 1, (1, 0, 0, 1)), trend='c', *args, **kwargs ) # Stata estimates the mean of the process, whereas SARIMAX estimates # the intercept of the process. Get the intercept. intercept = (1 - true['params_ar'][0]) * true['params_mean'][0] params = np.r_[intercept, true['params_ar'], true['params_ma'], true['params_variance']] cls.result = cls.model.filter(params) def test_mle(self): result = self.model.fit(disp=-1) assert_allclose( result.params, self.result.params, atol=1e-3 ) class TestAdditiveSeasonal(AdditiveSeasonal): """ Notes ----- Standard errors are very good for the OPG and quite good for the complex step approximation cases. """ @classmethod def setup_class(cls): super(TestAdditiveSeasonal, cls).setup_class( results_sarimax.wpi1_seasonal ) def test_bse(self): # test defaults assert_equal(self.result.cov_type, 'opg') assert_equal(self.result._cov_approx_complex_step, True) assert_equal(self.result._cov_approx_centered, False) # default covariance type (opg) assert_allclose(self.result.bse[1], self.true['se_ar_opg'], atol=1e-6) assert_allclose(self.result.bse[2:4], self.true['se_ma_opg'], atol=1e-5) def test_bse_approx(self): # complex step bse = self.result._cov_params_approx( approx_complex_step=True).diagonal()**0.5 assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-4) assert_allclose(bse[2:4], self.true['se_ma_oim'], atol=1e-4) # The below tests pass irregularly; they give a sense of the precision # available with finite differencing # with warnings.catch_warnings(): # warnings.simplefilter("ignore") # # finite difference, non-centered # bse = self.result._cov_params_approx( # approx_complex_step=False).diagonal()**0.5 # assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-2) # assert_allclose(bse[2:4], self.true['se_ma_oim'], atol=1e-2) # # finite difference, centered # cpa = self.result._cov_params_approx( # approx_complex_step=False, approx_centered=True) # bse = cpa.diagonal()**0.5 # assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-3) # assert_allclose(bse[2:4], self.true['se_ma_oim'], atol=1e-3) def test_bse_oim(self): # OIM covariance type bse = self.result._cov_params_oim().diagonal()**0.5 assert_allclose(bse[1], self.true['se_ar_oim'], atol=1e-2) assert_allclose(bse[2:4], self.true['se_ma_oim'], atol=1e-1) class Airline(SARIMAXStataTests): """ Multiplicative SARIMA model: "Airline" model Stata arima documentation, Example 3 """ @classmethod def setup_class(cls, true, *args, **kwargs): cls.true = true endog = np.log(true['data']) kwargs.setdefault('simple_differencing', True) kwargs.setdefault('hamilton_representation', True) cls.model = sarimax.SARIMAX( endog, order=(0, 1, 1), seasonal_order=(0, 1, 1, 12), trend='n', *args, **kwargs ) params = np.r_[true['params_ma'], true['params_seasonal_ma'], true['params_variance']] cls.result = cls.model.filter(params) def test_mle(self): with warnings.catch_warnings(): warnings.simplefilter("ignore") result = self.model.fit(disp=-1) assert_allclose( result.params, self.result.params, atol=1e-4 ) class TestAirlineHamilton(Airline): """ Notes ----- Standard errors are very good for the OPG and complex step approximation cases. """ @classmethod def setup_class(cls): super(TestAirlineHamilton, cls).setup_class( results_sarimax.air2_stationary ) def test_bse(self): # test defaults assert_equal(self.result.cov_type, 'opg') assert_equal(self.result._cov_approx_complex_step, True) assert_equal(self.result._cov_approx_centered, False) # default covariance type (opg) assert_allclose(self.result.bse[0], self.true['se_ma_opg'], atol=1e-6) assert_allclose(self.result.bse[1], self.true['se_seasonal_ma_opg'], atol=1e-6) def test_bse_approx(self): # complex step bse = self.result._cov_params_approx( approx_complex_step=True).diagonal()**0.5 assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-6) assert_allclose(bse[1], self.true['se_seasonal_ma_oim'], atol=1e-6) # The below tests pass irregularly; they give a sense of the precision # available with finite differencing # with warnings.catch_warnings(): # warnings.simplefilter("ignore") # # finite difference, non-centered # bse = self.result._cov_params_approx( # approx_complex_step=False).diagonal()**0.5 # assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-2) # assert_allclose(bse[1], self.true['se_seasonal_ma_oim'], # atol=1e-2) # # finite difference, centered # cpa = self.result._cov_params_approx( # approx_complex_step=False, approx_centered=True) # bse = cpa.diagonal()**0.5 # assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-4) # assert_allclose(bse[1], self.true['se_seasonal_ma_oim'], # atol=1e-4) def test_bse_oim(self): # OIM covariance type oim_bse = self.result.cov_params_oim.diagonal()**0.5 assert_allclose(oim_bse[0], self.true['se_ma_oim'], atol=1e-1) assert_allclose(oim_bse[1], self.true['se_seasonal_ma_oim'], atol=1e-1) class TestAirlineHarvey(Airline): """ Notes ----- Standard errors are very good for the OPG and complex step approximation cases. """ @classmethod def setup_class(cls): super(TestAirlineHarvey, cls).setup_class( results_sarimax.air2_stationary, hamilton_representation=False ) def test_bse(self): # test defaults assert_equal(self.result.cov_type, 'opg') assert_equal(self.result._cov_approx_complex_step, True) assert_equal(self.result._cov_approx_centered, False) # default covariance type (opg) assert_allclose(self.result.bse[0], self.true['se_ma_opg'], atol=1e-6) assert_allclose(self.result.bse[1], self.true['se_seasonal_ma_opg'], atol=1e-6) def test_bse_approx(self): # complex step bse = self.result._cov_params_approx( approx_complex_step=True).diagonal()**0.5 assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-6) assert_allclose(bse[1], self.true['se_seasonal_ma_oim'], atol=1e-6) # The below tests pass irregularly; they give a sense of the precision # available with finite differencing # with warnings.catch_warnings(): # warnings.simplefilter("ignore") # # finite difference, non-centered # bse = self.result._cov_params_approx( # approx_complex_step=False).diagonal()**0.5 # assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-2) # assert_allclose(bse[1], self.true['se_seasonal_ma_oim'], # atol=1e-2) # # finite difference, centered # cpa = self.result._cov_params_approx( # approx_complex_step=False, approx_centered=True) # bse = cpa.diagonal()**0.5 # assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-4) # assert_allclose(bse[1], self.true['se_seasonal_ma_oim'], # atol=1e-4) def test_bse_oim(self): # OIM covariance type oim_bse = self.result.cov_params_oim.diagonal()**0.5 assert_allclose(oim_bse[0], self.true['se_ma_oim'], atol=1e-1) assert_allclose(oim_bse[1], self.true['se_seasonal_ma_oim'], atol=1e-1) class TestAirlineStateDifferencing(Airline): """ Notes ----- Standard errors are very good for the OPG and quite good for the complex step approximation cases. """ @classmethod def setup_class(cls): super(TestAirlineStateDifferencing, cls).setup_class( results_sarimax.air2_stationary, simple_differencing=False, hamilton_representation=False ) def test_bic(self): # Due to diffuse component of the state (which technically changes the # BIC calculation - see Durbin and Koopman section 7.4), this is the # best we can do for BIC assert_almost_equal( self.result.bic, self.true['bic'], 0 ) def test_mle(self): result = self.model.fit(method='nm', maxiter=1000, disp=0) assert_allclose( result.params, self.result.params, atol=1e-3) def test_bse(self): # test defaults assert_equal(self.result.cov_type, 'opg') assert_equal(self.result._cov_approx_complex_step, True) assert_equal(self.result._cov_approx_centered, False) # default covariance type (opg) assert_allclose(self.result.bse[0], self.true['se_ma_opg'], atol=1e-6) assert_allclose(self.result.bse[1], self.true['se_seasonal_ma_opg'], atol=1e-6) def test_bse_approx(self): # complex step bse = self.result._cov_params_approx( approx_complex_step=True).diagonal()**0.5 assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-4) assert_allclose(bse[1], self.true['se_seasonal_ma_oim'], atol=1e-4) # The below tests do not pass # with warnings.catch_warnings(): # warnings.simplefilter("ignore") # # finite difference, non-centered : failure with NaNs # bse = self.result._cov_params_approx( # approx_complex_step=False).diagonal()**0.5 # assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-2) # assert_allclose(bse[1], self.true['se_seasonal_ma_oim'], # atol=1e-2) # # finite difference, centered : failure with NaNs # cpa = self.result._cov_params_approx( # approx_complex_step=False, approx_centered=True) # bse = cpa.diagonal()**0.5 # assert_allclose(bse[0], self.true['se_ma_oim'], atol=1e-4) # assert_allclose(bse[1], self.true['se_seasonal_ma_oim'], # atol=1e-4) def test_bse_oim(self): # OIM covariance type oim_bse = self.result.cov_params_oim.diagonal()**0.5 assert_allclose(oim_bse[0], self.true['se_ma_oim'], atol=1e-1) assert_allclose(oim_bse[1], self.true['se_seasonal_ma_oim'], atol=1e-1) class Friedman(SARIMAXStataTests): """ ARMAX model: Friedman quantity theory of money Stata arima documentation, Example 4 """ @classmethod def setup_class(cls, true, exog=None, *args, **kwargs): cls.true = true endog = np.r_[true['data']['consump']] if exog is None: exog = add_constant(true['data']['m2']) kwargs.setdefault('simple_differencing', True) kwargs.setdefault('hamilton_representation', True) cls.model = sarimax.SARIMAX( endog, exog=exog, order=(1, 0, 1), *args, **kwargs ) params = np.r_[true['params_exog'], true['params_ar'], true['params_ma'], true['params_variance']] cls.result = cls.model.filter(params) class TestFriedmanMLERegression(Friedman): """ Notes ----- Standard errors are very good for the OPG and complex step approximation cases. """ @classmethod def setup_class(cls): super(TestFriedmanMLERegression, cls).setup_class( results_sarimax.friedman2_mle ) def test_mle(self): result = self.model.fit(disp=-1) # Use ratio to make atol more meaningful parameter scale differs ratio = result.params / self.result.params assert_allclose(ratio, np.ones(5), atol=1e-2, rtol=1e-3) def test_bse(self): # test defaults assert_equal(self.result.cov_type, 'opg') assert_equal(self.result._cov_approx_complex_step, True) assert_equal(self.result._cov_approx_centered, False) # default covariance type (opg) assert_allclose(self.result.bse[0:2], self.true['se_exog_opg'], atol=1e-4) assert_allclose(self.result.bse[2], self.true['se_ar_opg'], atol=1e-6) assert_allclose(self.result.bse[3], self.true['se_ma_opg'], atol=1e-6) def test_bse_approx(self): # complex step bse = self.result._cov_params_approx( approx_complex_step=True).diagonal()**0.5 assert_allclose(bse[0:2], self.true['se_exog_oim'], atol=1e-4) assert_allclose(bse[2], self.true['se_ar_oim'], atol=1e-6) assert_allclose(bse[3], self.true['se_ma_oim'], atol=1e-6) # The below tests pass irregularly; they give a sense of the precision # available with finite differencing # with warnings.catch_warnings(): # warnings.simplefilter("ignore") # # finite difference, non-centered # bse = self.result._cov_params_approx( # approx_complex_step=False).diagonal()**0.5 # assert_allclose(bse[0], self.true['se_exog_oim'][0], rtol=1) # assert_allclose(bse[1], self.true['se_exog_oim'][1], atol=1e-2) # assert_allclose(bse[2], self.true['se_ar_oim'], atol=1e-2) # assert_allclose(bse[3], self.true['se_ma_oim'], atol=1e-2) # # finite difference, centered # cpa = self.result._cov_params_approx( # approx_complex_step=False, approx_centered=True) # bse = cpa.diagonal()**0.5 # assert_allclose(bse[0], self.true['se_exog_oim'][0], rtol=1) # assert_allclose(bse[1], self.true['se_exog_oim'][1], atol=1e-2) # assert_allclose(bse[2], self.true['se_ar_oim'], atol=1e-2) # assert_allclose(bse[3], self.true['se_ma_oim'], atol=1e-2) def test_bse_oim(self): # OIM covariance type bse = self.result.cov_params_oim.diagonal()**0.5 assert_allclose(bse[0], self.true['se_exog_oim'][0], rtol=1) assert_allclose(bse[1], self.true['se_exog_oim'][1], atol=1e-2) assert_allclose(bse[2], self.true['se_ar_oim'], atol=1e-2) assert_allclose(bse[3], self.true['se_ma_oim'], atol=1e-2) class TestFriedmanStateRegression(Friedman): """ Notes ----- MLE is not very close and standard errors are not very close for any set of parameters. This is likely because we're comparing against the model where the regression coefficients are also estimated by MLE. So this test should be considered just a very basic "sanity" test. """ @classmethod def setup_class(cls): # Remove the regression coefficients from the parameters, since they # will be estimated as part of the state vector true = dict(results_sarimax.friedman2_mle) exog = add_constant(true['data']['m2']) / 10. true['mle_params_exog'] = true['params_exog'][:] true['mle_se_exog'] = true['se_exog_opg'][:] true['params_exog'] = [] true['se_exog'] = [] super(TestFriedmanStateRegression, cls).setup_class( true, exog=exog, mle_regression=False ) cls.true_params = np.r_[true['params_exog'], true['params_ar'], true['params_ma'], true['params_variance']] cls.result = cls.model.filter(cls.true_params) def test_mle(self): result = self.model.fit(disp=-1) assert_allclose( result.params, self.result.params, atol=1e-1, rtol=2e-1 ) def test_regression_parameters(self): # The regression effects are integrated into the state vector as # the last two states (thus the index [-2:]). The filtered # estimates of the state vector produced by the Kalman filter and # stored in `filtered_state` for these state elements give the # recursive least squares estimates of the regression coefficients # at each time period. To get the estimates conditional on the # entire dataset, use the filtered states from the last time # period (thus the index [-1]). assert_almost_equal( self.result.filter_results.filtered_state[-2:, -1] / 10., self.true['mle_params_exog'], 1 ) # Loglikelihood (and so aic, bic) is slightly different when states are # integrated into the state vector def test_loglike(self): pass def test_aic(self): pass def test_bic(self): pass def test_bse(self): # test defaults assert_equal(self.result.cov_type, 'opg') assert_equal(self.result._cov_approx_complex_step, True) assert_equal(self.result._cov_approx_centered, False) # default covariance type (opg) assert_allclose(self.result.bse[0], self.true['se_ar_opg'], atol=1e-2) assert_allclose(self.result.bse[1], self.true['se_ma_opg'], atol=1e-2) def test_bse_approx(self): # complex step bse = self.result._cov_params_approx( approx_complex_step=True).diagonal()**0.5 assert_allclose(bse[0], self.true['se_ar_oim'], atol=1e-1) assert_allclose(bse[1], self.true['se_ma_oim'], atol=1e-1) # The below tests do not pass # with warnings.catch_warnings(): # warnings.simplefilter("ignore") # # finite difference, non-centered : # # failure (catastrophic cancellation) # bse = self.result._cov_params_approx( # approx_complex_step=False).diagonal()**0.5 # assert_allclose(bse[0], self.true['se_ar_oim'], atol=1e-3) # assert_allclose(bse[1], self.true['se_ma_oim'], atol=1e-2) # # finite difference, centered : failure (nan) # cpa = self.result._cov_params_approx( # approx_complex_step=False, approx_centered=True) # bse = cpa.diagonal()**0.5 # assert_allclose(bse[0], self.true['se_ar_oim'], atol=1e-3) # assert_allclose(bse[1], self.true['se_ma_oim'], atol=1e-3) def test_bse_oim(self): # OIM covariance type bse = self.result._cov_params_oim().diagonal()**0.5 assert_allclose(bse[0], self.true['se_ar_oim'], atol=1e-1) assert_allclose(bse[1], self.true['se_ma_oim'], atol=1e-1) class TestFriedmanPredict(Friedman): """ ARMAX model: Friedman quantity theory of money, prediction Stata arima postestimation documentation, Example 1 - Dynamic forecasts This follows the given Stata example, although it is not truly forecasting because it compares using the actual data (which is available in the example but just not used in the parameter MLE estimation) against dynamic prediction of that data. Here `test_predict` matches the first case, and `test_dynamic_predict` matches the second. """ @classmethod def setup_class(cls): super(TestFriedmanPredict, cls).setup_class( results_sarimax.friedman2_predict ) # loglike, aic, bic are not the point of this test (they could pass, but we # would have to modify the data so that they were calculated to # exclude the last 15 observations) def test_loglike(self): pass def test_aic(self): pass def test_bic(self): pass def test_predict(self): assert_almost_equal( self.result.predict(), self.true['predict'], 3 ) def test_dynamic_predict(self): dynamic = len(self.true['data']['consump'])-15-1 assert_almost_equal( self.result.predict(dynamic=dynamic), self.true['dynamic_predict'], 3 ) class TestFriedmanForecast(Friedman): """ ARMAX model: Friedman quantity theory of money, forecasts Variation on: Stata arima postestimation documentation, Example 1 - Dynamic forecasts This is a variation of the Stata example, in which the endogenous data is actually made to be missing so that the predict command must forecast. As another unit test, we also compare against the case in State when predict is used against missing data (so forecasting) with the dynamic option also included. Note, however, that forecasting in State space models amounts to running the Kalman filter against missing datapoints, so it is not clear whether "dynamic" forecasting (where instead of missing datapoints for lags, we plug in previous forecasted endog values) is meaningful. """ @classmethod def setup_class(cls): true = dict(results_sarimax.friedman2_predict) true['forecast_data'] = { 'consump': true['data']['consump'][-15:], 'm2': true['data']['m2'][-15:] } true['data'] = { 'consump': true['data']['consump'][:-15], 'm2': true['data']['m2'][:-15] } super(TestFriedmanForecast, cls).setup_class(true) cls.result = cls.model.filter(cls.result.params) # loglike, aic, bic are not the point of this test (they could pass, but we # would have to modify the data so that they were calculated to # exclude the last 15 observations) def test_loglike(self): pass def test_aic(self): pass def test_bic(self): pass def test_forecast(self): end = len(self.true['data']['consump'])+15-1 exog = add_constant(self.true['forecast_data']['m2']) assert_almost_equal( self.result.predict(end=end, exog=exog), self.true['forecast'], 3 ) def test_dynamic_forecast(self): end = len(self.true['data']['consump'])+15-1 dynamic = len(self.true['data']['consump'])-1 exog = add_constant(self.true['forecast_data']['m2']) assert_almost_equal( self.result.predict(end=end, dynamic=dynamic, exog=exog), self.true['dynamic_forecast'], 3 ) class SARIMAXCoverageTest(object): @classmethod def setup_class(cls, i, decimal=4, endog=None, *args, **kwargs): # Dataset if endog is None: endog = results_sarimax.wpi1_data # Loglikelihood, parameters cls.true_loglike = coverage_results.loc[i]['llf'] cls.true_params = np.array([ float(x) for x in coverage_results.loc[i]['parameters'].split(',')] ) # Stata reports the standard deviation; make it the variance cls.true_params[-1] = cls.true_params[-1]**2 # Test parameters cls.decimal = decimal # Compare using the Hamilton representation and simple differencing kwargs.setdefault('simple_differencing', True) kwargs.setdefault('hamilton_representation', True) cls.model = sarimax.SARIMAX(endog, *args, **kwargs) def test_loglike(self): self.result = self.model.filter(self.true_params) assert_allclose( self.result.llf, self.true_loglike, atol=0.7 * 10**(-self.decimal) ) def test_start_params(self): # just a quick test that start_params is not throwing an exception # (other than related to invertibility) stat = self.model.enforce_stationarity inv = self.model.enforce_invertibility self.model.enforce_stationarity = False self.model.enforce_invertibility = False self.model.start_params self.model.enforce_stationarity = stat self.model.enforce_invertibility = inv def test_transform_untransform(self): model = self.model stat, inv = model.enforce_stationarity, model.enforce_invertibility true_constrained = self.true_params # Sometimes the parameters given by Stata are not stationary and / or # invertible, so we need to skip those transformations for those # parameter sets model.update(self.true_params) par = model.polynomial_ar psar = model.polynomial_seasonal_ar contracted_psar = psar[psar.nonzero()] model.enforce_stationarity = ( (model.k_ar == 0 or tools.is_invertible(np.r_[1, -par[1:]])) and (len(contracted_psar) <= 1 or tools.is_invertible(np.r_[1, -contracted_psar[1:]])) ) pma = model.polynomial_ma psma = model.polynomial_seasonal_ma contracted_psma = psma[psma.nonzero()] model.enforce_invertibility = ( (model.k_ma == 0 or tools.is_invertible(np.r_[1, pma[1:]])) and (len(contracted_psma) <= 1 or tools.is_invertible(np.r_[1, contracted_psma[1:]])) ) unconstrained = model.untransform_params(true_constrained) constrained = model.transform_params(unconstrained) assert_almost_equal(constrained, true_constrained, 4) model.enforce_stationarity = stat model.enforce_invertibility = inv def test_results(self): self.result = self.model.filter(self.true_params) # Just make sure that no exceptions are thrown during summary self.result.summary() # Make sure no expections are thrown calculating any of the # covariance matrix types self.result.cov_params_default self.result.cov_params_approx self.result.cov_params_oim self.result.cov_params_opg self.result.cov_params_robust_oim self.result.cov_params_robust_approx @pytest.mark.matplotlib def test_plot_diagnostics(self, close_figures): # Make sure that no exceptions are thrown during plot_diagnostics self.result = self.model.filter(self.true_params) self.result.plot_diagnostics() def test_predict(self): result = self.model.filter(self.true_params) # Test predict does not throw exceptions, and produces the right shaped # output predict = result.predict() assert_equal(predict.shape, (self.model.nobs,)) predict = result.predict(start=10, end=20) assert_equal(predict.shape, (11,)) predict = result.predict(start=10, end=20, dynamic=10) assert_equal(predict.shape, (11,)) # Test forecasts if self.model.k_exog == 0: predict = result.predict(start=self.model.nobs, end=self.model.nobs+10, dynamic=-10) assert_equal(predict.shape, (11,)) predict = result.predict(start=self.model.nobs, end=self.model.nobs+10, dynamic=-10) forecast = result.forecast() assert_equal(forecast.shape, (1,)) forecast = result.forecast(10) assert_equal(forecast.shape, (10,)) else: k_exog = self.model.k_exog exog = np.r_[[0]*k_exog*11].reshape(11, k_exog) predict = result.predict(start=self.model.nobs, end=self.model.nobs+10, dynamic=-10, exog=exog) assert_equal(predict.shape, (11,)) predict = result.predict(start=self.model.nobs, end=self.model.nobs+10, dynamic=-10, exog=exog) exog = np.r_[[0]*k_exog].reshape(1, k_exog) forecast = result.forecast(exog=exog) assert_equal(forecast.shape, (1,)) def test_init_keys_replicate(self): mod1 = self.model kwargs = self.model._get_init_kwds() endog = mod1.data.orig_endog exog = mod1.data.orig_exog model2 = sarimax.SARIMAX(endog, exog, **kwargs) res1 = self.model.filter(self.true_params) res2 = model2.filter(self.true_params) rtol = 1e-6 if PLATFORM_WIN else 1e-13 assert_allclose(res2.llf, res1.llf, rtol=rtol) class Test_ar(SARIMAXCoverageTest): # // AR: (p, 0, 0) x (0, 0, 0, 0) # arima wpi, arima(3, 0, 0) noconstant vce(oim) # save_results 1 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 0) super(Test_ar, cls).setup_class(0, *args, **kwargs) class Test_ar_as_polynomial(SARIMAXCoverageTest): # // AR: (p, 0, 0) x (0, 0, 0, 0) # arima wpi, arima(3, 0, 0) noconstant vce(oim) # save_results 1 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = ([1, 1, 1], 0, 0) super(Test_ar_as_polynomial, cls).setup_class(0, *args, **kwargs) class Test_ar_trend_c(SARIMAXCoverageTest): # // 'c' # arima wpi c, arima(3, 0, 0) noconstant vce(oim) # save_results 2 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 0) kwargs['trend'] = 'c' super(Test_ar_trend_c, cls).setup_class(1, *args, **kwargs) # Modify true params to convert from mean to intercept form tps = cls.true_params cls.true_params[0] = (1 - tps[1:4].sum()) * tps[0] class Test_ar_trend_ct(SARIMAXCoverageTest): # // 'ct' # arima wpi c t, arima(3, 0, 0) noconstant vce(oim) # save_results 3 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 0) kwargs['trend'] = 'ct' super(Test_ar_trend_ct, cls).setup_class(2, *args, **kwargs) # Modify true params to convert from mean to intercept form tps = cls.true_params cls.true_params[:2] = (1 - tps[2:5].sum()) * tps[:2] class Test_ar_trend_polynomial(SARIMAXCoverageTest): # // polynomial [1, 0, 0, 1] # arima wpi c t3, arima(3, 0, 0) noconstant vce(oim) # save_results 4 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 0) kwargs['trend'] = [1, 0, 0, 1] super(Test_ar_trend_polynomial, cls).setup_class(3, *args, **kwargs) # Modify true params to convert from mean to intercept form tps = cls.true_params cls.true_params[:2] = (1 - tps[2:5].sum()) * tps[:2] class Test_ar_diff(SARIMAXCoverageTest): # // AR and I(d): (p, d, 0) x (0, 0, 0, 0) # arima wpi, arima(3, 2, 0) noconstant vce(oim) # save_results 5 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 2, 0) super(Test_ar_diff, cls).setup_class(4, *args, **kwargs) class Test_ar_seasonal_diff(SARIMAXCoverageTest): # // AR and I(D): (p, 0, 0) x (0, D, 0, s) # arima wpi, arima(3, 0, 0) sarima(0, 2, 0, 4) noconstant vce(oim) # save_results 6 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 0) kwargs['seasonal_order'] = (0, 2, 0, 4) super(Test_ar_seasonal_diff, cls).setup_class(5, *args, **kwargs) class Test_ar_diffuse(SARIMAXCoverageTest): # // AR and diffuse initialization # arima wpi, arima(3, 0, 0) noconstant vce(oim) diffuse # save_results 7 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 0) kwargs['initialization'] = 'approximate_diffuse' kwargs['initial_variance'] = 1e9 super(Test_ar_diffuse, cls).setup_class(6, *args, **kwargs) class Test_ar_no_enforce(SARIMAXCoverageTest): # // AR: (p, 0, 0) x (0, 0, 0, 0) # arima wpi, arima(3, 0, 0) noconstant vce(oim) # save_results 1 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 0) kwargs['enforce_stationarity'] = False kwargs['enforce_invertibility'] = False kwargs['initial_variance'] = 1e9 kwargs['loglikelihood_burn'] = 0 super(Test_ar_no_enforce, cls).setup_class(6, *args, **kwargs) # Reset loglikelihood burn, which gets automatically set to the number # of states if enforce_stationarity = False cls.model.ssm.loglikelihood_burn = 0 def test_init_keys_replicate(self): mod1 = self.model kwargs = self.model._get_init_kwds() endog = mod1.data.orig_endog exog = mod1.data.orig_exog model2 = sarimax.SARIMAX(endog, exog, **kwargs) # Fixes needed for edge case model model2.ssm.initialization = mod1.ssm.initialization res1 = self.model.filter(self.true_params) res2 = model2.filter(self.true_params) rtol = 1e-6 if PLATFORM_WIN else 1e-13 assert_allclose(res2.llf, res1.llf, rtol=rtol) class Test_ar_exogenous(SARIMAXCoverageTest): # // ARX # arima wpi x, arima(3, 0, 0) noconstant vce(oim) # save_results 8 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 0) endog = results_sarimax.wpi1_data kwargs['exog'] = (endog - np.floor(endog))**2 super(Test_ar_exogenous, cls).setup_class(7, *args, **kwargs) class Test_ar_exogenous_in_state(SARIMAXCoverageTest): # // ARX # arima wpi x, arima(3, 0, 0) noconstant vce(oim) # save_results 8 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 0) endog = results_sarimax.wpi1_data kwargs['exog'] = (endog - np.floor(endog))**2 kwargs['mle_regression'] = False super(Test_ar_exogenous_in_state, cls).setup_class(7, *args, **kwargs) cls.true_regression_coefficient = cls.true_params[0] cls.true_params = cls.true_params[1:] def test_loglike(self): # Regression in the state vector gives a different loglikelihood, so # just check that it's approximately the same self.result = self.model.filter(self.true_params) assert_allclose( self.result.llf, self.true_loglike, atol=2 ) def test_regression_coefficient(self): # Test that the regression coefficient (estimated as the last filtered # state estimate for the regression state) is the same as the Stata # MLE state self.result = self.model.filter(self.true_params) assert_allclose( self.result.filter_results.filtered_state[3][-1], self.true_regression_coefficient, self.decimal ) class Test_ma(SARIMAXCoverageTest): # // MA: (0, 0, q) x (0, 0, 0, 0) # arima wpi, arima(0, 0, 3) noconstant vce(oim) # save_results 9 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 3) super(Test_ma, cls).setup_class(8, *args, **kwargs) class Test_ma_as_polynomial(SARIMAXCoverageTest): # // MA: (0, 0, q) x (0, 0, 0, 0) # arima wpi, arima(0, 0, 3) noconstant vce(oim) # save_results 9 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, [1, 1, 1]) super(Test_ma_as_polynomial, cls).setup_class(8, *args, **kwargs) class Test_ma_trend_c(SARIMAXCoverageTest): # // 'c' # arima wpi c, arima(0, 0, 3) noconstant vce(oim) # save_results 10 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 3) kwargs['trend'] = 'c' super(Test_ma_trend_c, cls).setup_class(9, *args, **kwargs) class Test_ma_trend_ct(SARIMAXCoverageTest): # // 'ct' # arima wpi c t, arima(0, 0, 3) noconstant vce(oim) # save_results 11 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 3) kwargs['trend'] = 'ct' super(Test_ma_trend_ct, cls).setup_class(10, *args, **kwargs) class Test_ma_trend_polynomial(SARIMAXCoverageTest): # // polynomial [1, 0, 0, 1] # arima wpi c t3, arima(0, 0, 3) noconstant vce(oim) # save_results 12 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 3) kwargs['trend'] = [1, 0, 0, 1] super(Test_ma_trend_polynomial, cls).setup_class(11, *args, **kwargs) class Test_ma_diff(SARIMAXCoverageTest): # // MA and I(d): (0, d, q) x (0, 0, 0, 0) # arima wpi, arima(0, 2, 3) noconstant vce(oim) # save_results 13 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 2, 3) super(Test_ma_diff, cls).setup_class(12, *args, **kwargs) class Test_ma_seasonal_diff(SARIMAXCoverageTest): # // MA and I(D): (p, 0, 0) x (0, D, 0, s) # arima wpi, arima(0, 0, 3) sarima(0, 2, 0, 4) noconstant vce(oim) # save_results 14 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 3) kwargs['seasonal_order'] = (0, 2, 0, 4) super(Test_ma_seasonal_diff, cls).setup_class(13, *args, **kwargs) class Test_ma_diffuse(SARIMAXCoverageTest): # // MA and diffuse initialization # arima wpi, arima(0, 0, 3) noconstant vce(oim) diffuse # save_results 15 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 3) kwargs['initialization'] = 'approximate_diffuse' kwargs['initial_variance'] = 1e9 super(Test_ma_diffuse, cls).setup_class(14, *args, **kwargs) class Test_ma_exogenous(SARIMAXCoverageTest): # // MAX # arima wpi x, arima(0, 0, 3) noconstant vce(oim) # save_results 16 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 3) endog = results_sarimax.wpi1_data kwargs['exog'] = (endog - np.floor(endog))**2 super(Test_ma_exogenous, cls).setup_class(15, *args, **kwargs) class Test_arma(SARIMAXCoverageTest): # // ARMA: (p, 0, q) x (0, 0, 0, 0) # arima wpi, arima(3, 0, 3) noconstant vce(oim) # save_results 17 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 3) super(Test_arma, cls).setup_class(16, *args, **kwargs) class Test_arma_trend_c(SARIMAXCoverageTest): # // 'c' # arima wpi c, arima(3, 0, 2) noconstant vce(oim) # save_results 18 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 2) kwargs['trend'] = 'c' super(Test_arma_trend_c, cls).setup_class(17, *args, **kwargs) # Modify true params to convert from mean to intercept form tps = cls.true_params cls.true_params[:1] = (1 - tps[1:4].sum()) * tps[:1] class Test_arma_trend_ct(SARIMAXCoverageTest): # // 'ct' # arima wpi c t, arima(3, 0, 2) noconstant vce(oim) # save_results 19 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 2) kwargs['trend'] = 'ct' super(Test_arma_trend_ct, cls).setup_class(18, *args, **kwargs) # Modify true params to convert from mean to intercept form tps = cls.true_params cls.true_params[:2] = (1 - tps[2:5].sum()) * tps[:2] class Test_arma_trend_polynomial(SARIMAXCoverageTest): # // polynomial [1, 0, 0, 1] # arima wpi c t3, arima(3, 0, 2) noconstant vce(oim) # save_results 20 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 2) kwargs['trend'] = [1, 0, 0, 1] super(Test_arma_trend_polynomial, cls).setup_class(19, *args, **kwargs) # Modify true params to convert from mean to intercept form tps = cls.true_params cls.true_params[:2] = (1 - tps[2:5].sum()) * tps[:2] class Test_arma_diff(SARIMAXCoverageTest): # // ARMA and I(d): (p, d, q) x (0, 0, 0, 0) # arima wpi, arima(3, 2, 2) noconstant vce(oim) # save_results 21 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 2, 2) super(Test_arma_diff, cls).setup_class(20, *args, **kwargs) class Test_arma_seasonal_diff(SARIMAXCoverageTest): # // ARMA and I(D): (p, 0, q) x (0, D, 0, s) # arima wpi, arima(3, 0, 2) sarima(0, 2, 0, 4) noconstant vce(oim) # save_results 22 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 2) kwargs['seasonal_order'] = (0, 2, 0, 4) super(Test_arma_seasonal_diff, cls).setup_class(21, *args, **kwargs) class Test_arma_diff_seasonal_diff(SARIMAXCoverageTest): # // ARMA and I(d) and I(D): (p, d, q) x (0, D, 0, s) # arima wpi, arima(3, 2, 2) sarima(0, 2, 0, 4) noconstant vce(oim) # save_results 23 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 2, 2) kwargs['seasonal_order'] = (0, 2, 0, 4) super(Test_arma_diff_seasonal_diff, cls).setup_class( 22, *args, **kwargs) class Test_arma_diffuse(SARIMAXCoverageTest): # // ARMA and diffuse initialization # arima wpi, arima(3, 0, 2) noconstant vce(oim) diffuse # save_results 24 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 2) kwargs['initialization'] = 'approximate_diffuse' kwargs['initial_variance'] = 1e9 super(Test_arma_diffuse, cls).setup_class(23, *args, **kwargs) class Test_arma_exogenous(SARIMAXCoverageTest): # // ARMAX # arima wpi x, arima(3, 0, 2) noconstant vce(oim) # save_results 25 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 0, 2) endog = results_sarimax.wpi1_data kwargs['exog'] = (endog - np.floor(endog))**2 super(Test_arma_exogenous, cls).setup_class(24, *args, **kwargs) class Test_seasonal_ar(SARIMAXCoverageTest): # // SAR: (0, 0, 0) x (P, 0, 0, s) # arima wpi, sarima(3, 0, 0, 4) noconstant vce(oim) # save_results 26 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 0, 0, 4) super(Test_seasonal_ar, cls).setup_class(25, *args, **kwargs) class Test_seasonal_ar_as_polynomial(SARIMAXCoverageTest): # // SAR: (0, 0, 0) x (P, 0, 0, s) # arima wpi, sarima(3, 0, 0, 4) noconstant vce(oim) # save_results 26 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = ([1, 1, 1], 0, 0, 4) super(Test_seasonal_ar_as_polynomial, cls).setup_class( 25, *args, **kwargs) class Test_seasonal_ar_trend_c(SARIMAXCoverageTest): # // 'c' # arima wpi c, sarima(3, 0, 0, 4) noconstant vce(oim) # save_results 27 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 0, 0, 4) kwargs['trend'] = 'c' super(Test_seasonal_ar_trend_c, cls).setup_class(26, *args, **kwargs) # Modify true params to convert from mean to intercept form tps = cls.true_params cls.true_params[:1] = (1 - tps[1:4].sum()) * tps[:1] class Test_seasonal_ar_trend_ct(SARIMAXCoverageTest): # // 'ct' # arima wpi c t, sarima(3, 0, 0, 4) noconstant vce(oim) # save_results 28 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 0, 0, 4) kwargs['trend'] = 'ct' super(Test_seasonal_ar_trend_ct, cls).setup_class(27, *args, **kwargs) # Modify true params to convert from mean to intercept form tps = cls.true_params cls.true_params[:2] = (1 - tps[2:5].sum()) * tps[:2] class Test_seasonal_ar_trend_polynomial(SARIMAXCoverageTest): # // polynomial [1, 0, 0, 1] # arima wpi c t3, sarima(3, 0, 0, 4) noconstant vce(oim) # save_results 29 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 0, 0, 4) kwargs['trend'] = [1, 0, 0, 1] super(Test_seasonal_ar_trend_polynomial, cls).setup_class( 28, *args, **kwargs) # Modify true params to convert from mean to intercept form tps = cls.true_params cls.true_params[:2] = (1 - tps[2:5].sum()) * tps[:2] class Test_seasonal_ar_diff(SARIMAXCoverageTest): # // SAR and I(d): (0, d, 0) x (P, 0, 0, s) # arima wpi, arima(0, 2, 0) sarima(3, 0, 0, 4) noconstant vce(oim) # save_results 30 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 2, 0) kwargs['seasonal_order'] = (3, 0, 0, 4) super(Test_seasonal_ar_diff, cls).setup_class(29, *args, **kwargs) class Test_seasonal_ar_seasonal_diff(SARIMAXCoverageTest): # // SAR and I(D): (0, 0, 0) x (P, D, 0, s) # arima wpi, sarima(3, 2, 0, 4) noconstant vce(oim) # save_results 31 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 2, 0, 4) super(Test_seasonal_ar_seasonal_diff, cls).setup_class( 30, *args, **kwargs) class Test_seasonal_ar_diffuse(SARIMAXCoverageTest): # // SAR and diffuse initialization # arima wpi, sarima(3, 0, 0, 4) noconstant vce(oim) diffuse # save_results 32 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 0, 0, 4) kwargs['initialization'] = 'approximate_diffuse' kwargs['initial_variance'] = 1e9 super(Test_seasonal_ar_diffuse, cls).setup_class(31, *args, **kwargs) class Test_seasonal_ar_exogenous(SARIMAXCoverageTest): # // SARX # arima wpi x, sarima(3, 0, 0, 4) noconstant vce(oim) # save_results 33 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 0, 0, 4) endog = results_sarimax.wpi1_data kwargs['exog'] = (endog - np.floor(endog))**2 super(Test_seasonal_ar_exogenous, cls).setup_class(32, *args, **kwargs) class Test_seasonal_ma(SARIMAXCoverageTest): # // SMA # arima wpi, sarima(0, 0, 3, 4) noconstant vce(oim) # save_results 34 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (0, 0, 3, 4) super(Test_seasonal_ma, cls).setup_class(33, *args, **kwargs) class Test_seasonal_ma_as_polynomial(SARIMAXCoverageTest): # // SMA # arima wpi, sarima(0, 0, 3, 4) noconstant vce(oim) # save_results 34 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (0, 0, [1, 1, 1], 4) super(Test_seasonal_ma_as_polynomial, cls).setup_class( 33, *args, **kwargs) class Test_seasonal_ma_trend_c(SARIMAXCoverageTest): # // 'c' # arima wpi c, sarima(0, 0, 3, 4) noconstant vce(oim) # save_results 35 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (0, 0, 3, 4) kwargs['trend'] = 'c' kwargs['decimal'] = 3 super(Test_seasonal_ma_trend_c, cls).setup_class(34, *args, **kwargs) class Test_seasonal_ma_trend_ct(SARIMAXCoverageTest): # // 'ct' # arima wpi c t, sarima(0, 0, 3, 4) noconstant vce(oim) # save_results 36 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (0, 0, 3, 4) kwargs['trend'] = 'ct' super(Test_seasonal_ma_trend_ct, cls).setup_class(35, *args, **kwargs) class Test_seasonal_ma_trend_polynomial(SARIMAXCoverageTest): # // polynomial [1, 0, 0, 1] # arima wpi c t3, sarima(0, 0, 3, 4) noconstant vce(oim) # save_results 37 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (0, 0, 3, 4) kwargs['trend'] = [1, 0, 0, 1] kwargs['decimal'] = 3 super(Test_seasonal_ma_trend_polynomial, cls).setup_class( 36, *args, **kwargs) class Test_seasonal_ma_diff(SARIMAXCoverageTest): # // SMA and I(d): (0, d, 0) x (0, 0, Q, s) # arima wpi, arima(0, 2, 0) sarima(0, 0, 3, 4) noconstant vce(oim) # save_results 38 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 2, 0) kwargs['seasonal_order'] = (0, 0, 3, 4) super(Test_seasonal_ma_diff, cls).setup_class(37, *args, **kwargs) class Test_seasonal_ma_seasonal_diff(SARIMAXCoverageTest): # // SMA and I(D): (0, 0, 0) x (0, D, Q, s) # arima wpi, sarima(0, 2, 3, 4) noconstant vce(oim) # save_results 39 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (0, 2, 3, 4) super(Test_seasonal_ma_seasonal_diff, cls).setup_class( 38, *args, **kwargs) class Test_seasonal_ma_diffuse(SARIMAXCoverageTest): # // SMA and diffuse initialization # arima wpi, sarima(0, 0, 3, 4) noconstant vce(oim) diffuse # save_results 40 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (0, 0, 3, 4) kwargs['initialization'] = 'approximate_diffuse' kwargs['initial_variance'] = 1e9 super(Test_seasonal_ma_diffuse, cls).setup_class(39, *args, **kwargs) class Test_seasonal_ma_exogenous(SARIMAXCoverageTest): # // SMAX # arima wpi x, sarima(0, 0, 3, 4) noconstant vce(oim) # save_results 41 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (0, 0, 3, 4) endog = results_sarimax.wpi1_data kwargs['exog'] = (endog - np.floor(endog))**2 super(Test_seasonal_ma_exogenous, cls).setup_class(40, *args, **kwargs) class Test_seasonal_arma(SARIMAXCoverageTest): # // SARMA: (0, 0, 0) x (P, 0, Q, s) # arima wpi, sarima(3, 0, 2, 4) noconstant vce(oim) # save_results 42 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 0, 2, 4) super(Test_seasonal_arma, cls).setup_class(41, *args, **kwargs) class Test_seasonal_arma_trend_c(SARIMAXCoverageTest): # // 'c' # arima wpi c, sarima(3, 0, 2, 4) noconstant vce(oim) # save_results 43 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 0, 2, 4) kwargs['trend'] = 'c' super(Test_seasonal_arma_trend_c, cls).setup_class(42, *args, **kwargs) # Modify true params to convert from mean to intercept form tps = cls.true_params cls.true_params[:1] = (1 - tps[1:4].sum()) * tps[:1] class Test_seasonal_arma_trend_ct(SARIMAXCoverageTest): # // 'ct' # arima wpi c t, sarima(3, 0, 2, 4) noconstant vce(oim) # save_results 44 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 0, 2, 4) kwargs['trend'] = 'ct' super(Test_seasonal_arma_trend_ct, cls).setup_class( 43, *args, **kwargs) # Modify true params to convert from mean to intercept form tps = cls.true_params cls.true_params[:2] = (1 - tps[2:5].sum()) * tps[:2] class Test_seasonal_arma_trend_polynomial(SARIMAXCoverageTest): # // polynomial [1, 0, 0, 1] # arima wpi c t3, sarima(3, 0, 2, 4) noconstant vce(oim) # save_results 45 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 0, 2, 4) kwargs['trend'] = [1, 0, 0, 1] kwargs['decimal'] = 3 super(Test_seasonal_arma_trend_polynomial, cls).setup_class( 44, *args, **kwargs) # Modify true params to convert from mean to intercept form tps = cls.true_params cls.true_params[:2] = (1 - tps[2:5].sum()) * tps[:2] def test_results(self): self.result = self.model.filter(self.true_params) # Just make sure that no exceptions are thrown during summary self.result.summary() # Make sure no expections are thrown calculating any of the # covariance matrix types self.result.cov_params_default # Known failure due to the complex step inducing non-stationary # parameters, causing a failure in the solve_discrete_lyapunov call # self.result.cov_params_approx self.result.cov_params_oim self.result.cov_params_opg class Test_seasonal_arma_diff(SARIMAXCoverageTest): # // SARMA and I(d): (0, d, 0) x (P, 0, Q, s) # arima wpi, arima(0, 2, 0) sarima(3, 0, 2, 4) noconstant vce(oim) # save_results 46 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 2, 0) kwargs['seasonal_order'] = (3, 0, 2, 4) super(Test_seasonal_arma_diff, cls).setup_class(45, *args, **kwargs) class Test_seasonal_arma_seasonal_diff(SARIMAXCoverageTest): # // SARMA and I(D): (0, 0, 0) x (P, D, Q, s) # arima wpi, sarima(3, 2, 2, 4) noconstant vce(oim) # save_results 47 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 2, 2, 4) super(Test_seasonal_arma_seasonal_diff, cls).setup_class( 46, *args, **kwargs) class Test_seasonal_arma_diff_seasonal_diff(SARIMAXCoverageTest): # // SARMA and I(d) and I(D): (0, d, 0) x (P, D, Q, s) # arima wpi, arima(0, 2, 0) sarima(3, 2, 2, 4) noconstant vce(oim) # save_results 48 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 2, 0) kwargs['seasonal_order'] = (3, 2, 2, 4) super(Test_seasonal_arma_diff_seasonal_diff, cls).setup_class( 47, *args, **kwargs) def test_results(self): self.result = self.model.filter(self.true_params) # Just make sure that no exceptions are thrown during summary self.result.summary() # Make sure no expections are thrown calculating any of the # covariance matrix types self.result.cov_params_default # Known failure due to the complex step inducing non-stationary # parameters, causing a failure in the solve_discrete_lyapunov call # self.result.cov_params_approx self.result.cov_params_oim self.result.cov_params_opg class Test_seasonal_arma_diffuse(SARIMAXCoverageTest): # // SARMA and diffuse initialization # arima wpi, sarima(3, 0, 2, 4) noconstant vce(oim) diffuse # save_results 49 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 0, 2, 4) kwargs['decimal'] = 3 kwargs['initialization'] = 'approximate_diffuse' kwargs['initial_variance'] = 1e9 super(Test_seasonal_arma_diffuse, cls).setup_class(48, *args, **kwargs) class Test_seasonal_arma_exogenous(SARIMAXCoverageTest): # // SARMAX # arima wpi x, sarima(3, 0, 2, 4) noconstant vce(oim) # save_results 50 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (0, 0, 0) kwargs['seasonal_order'] = (3, 0, 2, 4) endog = results_sarimax.wpi1_data kwargs['exog'] = (endog - np.floor(endog))**2 super(Test_seasonal_arma_exogenous, cls).setup_class( 49, *args, **kwargs) class Test_sarimax_exogenous(SARIMAXCoverageTest): # // SARIMAX and exogenous # arima wpi x, arima(3, 2, 2) sarima(3, 2, 2, 4) noconstant vce(oim) # save_results 51 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 2, 2) kwargs['seasonal_order'] = (3, 2, 2, 4) endog = results_sarimax.wpi1_data kwargs['exog'] = (endog - np.floor(endog))**2 super(Test_sarimax_exogenous, cls).setup_class(50, *args, **kwargs) def test_results_params(self): result = self.model.filter(self.true_params) assert_allclose(self.true_params[1:4], result.arparams) assert_allclose(self.true_params[4:6], result.maparams) assert_allclose(self.true_params[6:9], result.seasonalarparams) assert_allclose(self.true_params[9:11], result.seasonalmaparams) class Test_sarimax_exogenous_not_hamilton(SARIMAXCoverageTest): # // SARIMAX and exogenous # arima wpi x, arima(3, 2, 2) sarima(3, 2, 2, 4) noconstant vce(oim) # save_results 51 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 2, 2) kwargs['seasonal_order'] = (3, 2, 2, 4) endog = results_sarimax.wpi1_data kwargs['exog'] = (endog - np.floor(endog))**2 kwargs['hamilton_representation'] = False kwargs['simple_differencing'] = False super(Test_sarimax_exogenous_not_hamilton, cls).setup_class( 50, *args, **kwargs) class Test_sarimax_exogenous_diffuse(SARIMAXCoverageTest): # // SARIMAX and exogenous diffuse # arima wpi x, arima(3, 2, 2) sarima(3, 2, 2, 4) noconstant vce(oim) # diffuse # save_results 52 @classmethod def setup_class(cls, *args, **kwargs): kwargs['order'] = (3, 2, 2) kwargs['seasonal_order'] = (3, 2, 2, 4) endog = results_sarimax.wpi1_data kwargs['exog'] = (endog - np.floor(endog))**2 kwargs['decimal'] = 2 kwargs['initialization'] = 'approximate_diffuse' kwargs['initial_variance'] = 1e9 super(Test_sarimax_exogenous_diffuse, cls).setup_class( 51, *args, **kwargs) class Test_arma_exog_trend_polynomial_missing(SARIMAXCoverageTest): # // ARMA and exogenous and trend polynomial and missing # gen wpi2 = wpi # replace wpi2 = . in 10/19 # arima wpi2 x c t3, arima(3, 0, 2) noconstant vce(oim) # save_results 53 @classmethod def setup_class(cls, *args, **kwargs): endog = np.r_[results_sarimax.wpi1_data] # Note we're using the non-missing exog data kwargs['exog'] = ((endog - np.floor(endog))**2)[1:] endog[9:19] = np.nan endog = endog[1:] - endog[:-1] endog[9] = np.nan kwargs['order'] = (3, 0, 2) kwargs['trend'] = [0, 0, 0, 1] kwargs['decimal'] = 1 super(Test_arma_exog_trend_polynomial_missing, cls).setup_class( 52, endog=endog, *args, **kwargs) # Modify true params to convert from mean to intercept form tps = cls.true_params cls.true_params[0] = (1 - tps[2:5].sum()) * tps[0] # Miscellaneous coverage tests def test_simple_time_varying(): # This tests time-varying parameters regression when in fact the parameters # are not time-varying, and in fact the regression fit is perfect endog = np.arange(100)*1.0 exog = 2*endog mod = sarimax.SARIMAX( endog, exog=exog, order=(0, 0, 0), time_varying_regression=True, mle_regression=False) # Ignore the warning that MLE does not converge with warnings.catch_warnings(): warnings.simplefilter("ignore") res = mod.fit(disp=-1) # Test that the estimated variances of the errors are essentially zero # 5 digits necessary to accommodate 32-bit numpy/scipy with OpenBLAS 0.2.18 assert_almost_equal(res.params, [0, 0], 5) # Test that the time-varying coefficients are all 0.5 (except the first # one) assert_almost_equal(res.filter_results.filtered_state[0][1:], [0.5]*99, 9) def test_invalid_time_varying(): assert_raises( ValueError, sarimax.SARIMAX, endog=[1, 2, 3], mle_regression=True, time_varying_regression=True) def test_manual_stationary_initialization(): endog = results_sarimax.wpi1_data # Create the first model to compare against mod1 = sarimax.SARIMAX(endog, order=(3, 0, 0)) res1 = mod1.filter([0.5, 0.2, 0.1, 1]) # Create a second model with "known" initialization mod2 = sarimax.SARIMAX(endog, order=(3, 0, 0)) mod2.ssm.initialize_known(res1.filter_results.initial_state, res1.filter_results.initial_state_cov) res2 = mod2.filter([0.5, 0.2, 0.1, 1]) # Create a third model with "known" initialization, but specified in kwargs mod3 = sarimax.SARIMAX( endog, order=(3, 0, 0), initialization='known', initial_state=res1.filter_results.initial_state, initial_state_cov=res1.filter_results.initial_state_cov) res3 = mod3.filter([0.5, 0.2, 0.1, 1]) # Create the forth model with stationary initialization specified in kwargs mod4 = sarimax.SARIMAX(endog, order=(3, 0, 0), initialization='stationary') res4 = mod4.filter([0.5, 0.2, 0.1, 1]) # Just test a couple of things to make sure the results are the same assert_almost_equal(res1.llf, res2.llf) assert_almost_equal(res1.filter_results.filtered_state, res2.filter_results.filtered_state) assert_almost_equal(res1.llf, res3.llf) assert_almost_equal(res1.filter_results.filtered_state, res3.filter_results.filtered_state) assert_almost_equal(res1.llf, res4.llf) assert_almost_equal(res1.filter_results.filtered_state, res4.filter_results.filtered_state) def test_manual_approximate_diffuse_initialization(): endog = results_sarimax.wpi1_data # Create the first model to compare against mod1 = sarimax.SARIMAX(endog, order=(3, 0, 0)) mod1.ssm.initialize_approximate_diffuse(1e9) res1 = mod1.filter([0.5, 0.2, 0.1, 1]) # Create a second model with "known" initialization mod2 = sarimax.SARIMAX(endog, order=(3, 0, 0)) mod2.ssm.initialize_known(res1.filter_results.initial_state, res1.filter_results.initial_state_cov) res2 = mod2.filter([0.5, 0.2, 0.1, 1]) # Create a third model with "known" initialization, but specified in kwargs mod3 = sarimax.SARIMAX( endog, order=(3, 0, 0), initialization='known', initial_state=res1.filter_results.initial_state, initial_state_cov=res1.filter_results.initial_state_cov) res3 = mod3.filter([0.5, 0.2, 0.1, 1]) # Create the forth model with approximate diffuse initialization specified # in kwargs mod4 = sarimax.SARIMAX(endog, order=(3, 0, 0), initialization='approximate_diffuse', initial_variance=1e9) res4 = mod4.filter([0.5, 0.2, 0.1, 1]) # Just test a couple of things to make sure the results are the same assert_almost_equal(res1.llf, res2.llf) assert_almost_equal(res1.filter_results.filtered_state, res2.filter_results.filtered_state) assert_almost_equal(res1.llf, res3.llf) assert_almost_equal(res1.filter_results.filtered_state, res3.filter_results.filtered_state) assert_almost_equal(res1.llf, res4.llf) assert_almost_equal(res1.filter_results.filtered_state, res4.filter_results.filtered_state) def test_results(): endog = results_sarimax.wpi1_data mod = sarimax.SARIMAX(endog, order=(1, 0, 1)) res = mod.filter([0.5, -0.5, 1], cov_type='oim') assert_almost_equal(res.arroots, 2.) assert_almost_equal(res.maroots, 2.) assert_almost_equal(res.arfreq, np.arctan2(0, 2) / (2*np.pi)) assert_almost_equal(res.mafreq, np.arctan2(0, 2) / (2*np.pi)) assert_almost_equal(res.arparams, [0.5]) assert_almost_equal(res.maparams, [-0.5]) def test_misc_exog(): # Tests for missing data nobs = 20 k_endog = 1 np.random.seed(1208) endog = np.random.normal(size=(nobs, k_endog)) endog[:4, 0] = np.nan exog1 = np.random.normal(size=(nobs, 1)) exog2 = np.random.normal(size=(nobs, 2)) index = pd.date_range('1970-01-01', freq='QS', periods=nobs) endog_pd = pd.DataFrame(endog, index=index) exog1_pd = pd.Series(exog1.squeeze(), index=index) exog2_pd = pd.DataFrame(exog2, index=index) models = [ sarimax.SARIMAX(endog, exog=exog1, order=(1, 1, 0)), sarimax.SARIMAX(endog, exog=exog2, order=(1, 1, 0)), sarimax.SARIMAX(endog, exog=exog2, order=(1, 1, 0), simple_differencing=False), sarimax.SARIMAX(endog_pd, exog=exog1_pd, order=(1, 1, 0)), sarimax.SARIMAX(endog_pd, exog=exog2_pd, order=(1, 1, 0)), sarimax.SARIMAX(endog_pd, exog=exog2_pd, order=(1, 1, 0), simple_differencing=False), ] for mod in models: # Smoke tests mod.start_params res = mod.fit(disp=False) res.summary() res.predict() res.predict(dynamic=True) res.get_prediction() oos_exog = np.random.normal(size=(1, mod.k_exog)) res.forecast(steps=1, exog=oos_exog) res.get_forecast(steps=1, exog=oos_exog) # Smoke tests for invalid exog oos_exog = np.random.normal(size=(2, mod.k_exog)) assert_raises(ValueError, res.forecast, steps=1, exog=oos_exog) oos_exog = np.random.normal(size=(1, mod.k_exog + 1)) assert_raises(ValueError, res.forecast, steps=1, exog=oos_exog) # Test invalid model specifications assert_raises(ValueError, sarimax.SARIMAX, endog, exog=np.zeros((10, 4)), order=(1, 1, 0)) @pytest.mark.smoke def test_datasets(): # Test that some unusual types of datasets work np.random.seed(232849) endog = np.random.binomial(1, 0.5, size=100) exog = np.random.binomial(1, 0.5, size=100) mod = sarimax.SARIMAX(endog, exog=exog, order=(1, 0, 0)) mod.fit(disp=-1) def test_predict_custom_index(): np.random.seed(328423) endog = pd.DataFrame(np.random.normal(size=50)) mod = sarimax.SARIMAX(endog, order=(1, 0, 0)) res = mod.smooth(mod.start_params) out = res.predict(start=1, end=1, index=['a']) assert_equal(out.index.equals(pd.Index(['a'])), True) def test_arima000(): # Test an ARIMA(0, 0, 0) with measurement error model (i.e. just estimating # a variance term) np.random.seed(328423) nobs = 50 endog = pd.DataFrame(np.random.normal(size=nobs)) mod = sarimax.SARIMAX(endog, order=(0, 0, 0), measurement_error=False) res = mod.smooth(mod.start_params) assert_allclose(res.smoothed_state, endog.T) # ARIMA(0, 1, 0) mod = sarimax.SARIMAX(endog, order=(0, 1, 0), measurement_error=False) res = mod.smooth(mod.start_params) assert_allclose(res.smoothed_state[1:, 1:], endog.diff()[1:].T) # Exogenous variables error = np.random.normal(size=nobs) endog = np.ones(nobs) * 10 + error exog = np.ones(nobs) # OLS mod = sarimax.SARIMAX(endog, order=(0, 0, 0), exog=exog) mod.ssm.filter_univariate = True res = mod.smooth([10., 1.]) assert_allclose(res.smoothed_state[0], error, atol=1e-10) # RLS mod = sarimax.SARIMAX(endog, order=(0, 0, 0), exog=exog, mle_regression=False) mod.ssm.filter_univariate = True mod.initialize_known([0., 10.], np.diag([1., 0.])) res = mod.smooth([1.]) assert_allclose(res.smoothed_state[0], error, atol=1e-10) assert_allclose(res.smoothed_state[1], 10, atol=1e-10) # RLS + TVP mod = sarimax.SARIMAX(endog, order=(0, 0, 0), exog=exog, mle_regression=False, time_varying_regression=True) mod.ssm.filter_univariate = True mod.initialize_known([10.], np.diag([0.])) res = mod.smooth([0., 1.]) assert_allclose(res.smoothed_state[0], 10, atol=1e-10) def check_concentrated_scale(filter_univariate=False): # Test that concentrating the scale out of the likelihood function works endog = np.diff(results_sarimax.wpi1_data) orders = [(1, 0, 0), (2, 2, 2)] seasonal_orders = [(0, 0, 0, 0), (1, 1, 1, 4)] simple_differencings = [True, False] exogs = [None, np.ones_like(endog)] trends = [None, 't'] # Disabled, see discussion below in setting k_snr for details time_varying_regressions = [True, False] measurement_errors = [True, False] import itertools names = ['exog', 'order', 'seasonal_order', 'trend', 'measurement_error', 'time_varying_regression', 'simple_differencing'] for element in itertools.product(exogs, orders, seasonal_orders, trends, measurement_errors, time_varying_regressions, simple_differencings): kwargs = dict(zip(names, element)) if kwargs.get('time_varying_regression', False): kwargs['mle_regression'] = False # Sometimes we can have slight differences if the Kalman filters # converge at different observations, so disable convergence. kwargs['tolerance'] = 0 mod_orig = sarimax.SARIMAX(endog, **kwargs) mod_conc = sarimax.SARIMAX(endog, concentrate_scale=True, **kwargs) mod_orig.ssm.filter_univariate = filter_univariate mod_conc.ssm.filter_univariate = filter_univariate # The base parameters are the starting parameters from the concentrated # model conc_params = mod_conc.start_params res_conc = mod_conc.smooth(conc_params) # We need to map the concentrated parameters to the non-concentrated # model # The first thing is to add an additional parameter for the scale # (here set to 1 because we will multiply by res_conc.scale below, but # because the scale is factored out of the entire obs_cov and state_cov # matrices we may need to multiply more parameters by res_conc.scale # also) orig_params = np.r_[conc_params, 1] k_snr = 1 # If we have time-varying regressions, then in the concentrated model # we actually are computing signal-to-noise ratios, and we # need to multiply it by the scale to get the variances # the non-concentrated model will expect as parameters if kwargs['time_varying_regression'] and kwargs['exog'] is not None: k_snr += 1 # Note: the log-likelihood is not exactly the same between concentrated # and non-concentrated models with time-varying regression, so this # combinations raises NotImplementedError. # If we have measurement error, then in the concentrated model # we actually are computing the signal-to-noise ratio, and we # need to multiply it by the scale to get the measurement error # variance that the non-concentrated model will expect as a # parameter if kwargs['measurement_error']: k_snr += 1 atol = 1e-5 if kwargs['measurement_error'] or kwargs['time_varying_regression']: atol = 1e-3 orig_params = np.r_[orig_params[:-k_snr], res_conc.scale * orig_params[-k_snr:]] res_orig = mod_orig.smooth(orig_params) # Test loglike # Need to reduce the tolerance when we have measurement error. assert_allclose(res_conc.llf, res_orig.llf, atol=atol) # Test state space representation matrices for name in mod_conc.ssm.shapes: if name == 'obs': continue assert_allclose(getattr(res_conc.filter_results, name), getattr(res_orig.filter_results, name)) # Test filter / smoother output d = res_conc.loglikelihood_burn filter_attr = ['predicted_state', 'filtered_state', 'forecasts', 'forecasts_error', 'kalman_gain'] for name in filter_attr: actual = getattr(res_conc.filter_results, name) desired = getattr(res_orig.filter_results, name) assert_allclose(actual, desired, atol=atol) # Note: do not want to compare the elements from any diffuse # initialization for things like covariances, so only compare for # periods past the loglikelihood_burn period filter_attr_burn = ['llf_obs', 'standardized_forecasts_error', 'predicted_state_cov', 'filtered_state_cov', 'tmp1', 'tmp2', 'tmp3', 'tmp4'] # Also need to ignore covariances of states with diffuse initialization # when time_varying_regression is True diffuse_mask = (res_orig.filter_results.initial_state_cov.diagonal() == mod_orig.ssm.initial_variance) ix = np.s_[~diffuse_mask, ~diffuse_mask, :] for name in filter_attr_burn: actual = getattr(res_conc.filter_results, name)[..., d:] desired = getattr(res_orig.filter_results, name)[..., d:] # Note: Cannot compare predicted or filtered cov for the time # varying regression state due to effects of approximate diffuse # initialization if (name in ['predicted_state_cov', 'filtered_state_cov'] and kwargs['time_varying_regression']): assert_allclose(actual[ix], desired[ix], atol=atol) else: assert_allclose(actual, desired, atol=atol) smoothed_attr = ['smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_state_disturbance', 'smoothed_state_disturbance_cov', 'smoothed_measurement_disturbance', 'smoothed_measurement_disturbance_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_forecasts', 'smoothed_forecasts_error', 'smoothed_forecasts_error_cov'] for name in smoothed_attr: actual = getattr(res_conc.filter_results, name)[..., d:] desired = getattr(res_orig.filter_results, name)[..., d:] if (name in ['smoothed_state_cov', 'smoothed_state_autocov'] and kwargs['time_varying_regression']): assert_allclose(actual[ix], desired[ix], atol=atol) else: assert_allclose(actual, desired, atol=atol) # Test non-covariance-matrix MLEResults output output = ['aic', 'bic', 'hqic', 'loglikelihood_burn'] for name in output: actual = getattr(res_conc, name) desired = getattr(res_orig, name) assert_allclose(actual, desired, atol=atol) # Test diagnostic output actual = res_conc.test_normality(method='jarquebera') desired = res_orig.test_normality(method='jarquebera') assert_allclose(actual, desired, rtol=1e-5, atol=atol) actual = res_conc.test_heteroskedasticity(method='breakvar') desired = res_orig.test_heteroskedasticity(method='breakvar') assert_allclose(actual, desired, rtol=1e-5, atol=atol) with pytest.warns(FutureWarning): actual = res_conc.test_serial_correlation(method='ljungbox') with pytest.warns(FutureWarning): desired = res_orig.test_serial_correlation(method='ljungbox') assert_allclose(actual, desired, rtol=1e-5, atol=atol) # Test predict exog = None if kwargs['exog'] is not None: exog = np.ones((130 - mod_conc.nobs + 1, 1)) actual = res_conc.get_prediction(start=100, end=130, dynamic=10, exog=exog) desired = res_orig.get_prediction(start=100, end=130, dynamic=10, exog=exog) assert_allclose(actual.predicted_mean, desired.predicted_mean, atol=atol) assert_allclose(actual.se_mean, desired.se_mean, atol=atol) # Test simulate # Simulate is currently broken for time-varying models, so do not try # to test it here np.random.seed(13847) if mod_conc.ssm.time_invariant: measurement_shocks = np.random.normal(size=10) state_shocks = np.random.normal(size=10) initial_state = np.random.normal(size=(mod_conc.k_states, 1)) actual = res_conc.simulate(10, measurement_shocks, state_shocks, initial_state) desired = res_orig.simulate(10, measurement_shocks, state_shocks, initial_state) assert_allclose(actual, desired, atol=atol) # Test impulse responses if mod_conc.ssm.time_invariant: actual = res_conc.impulse_responses(10) desired = res_orig.impulse_responses(10) assert_allclose(actual, desired, atol=atol) @pytest.mark.slow def test_concentrated_scale(): check_concentrated_scale(filter_univariate=False) check_concentrated_scale(filter_univariate=True) def test_forecast_exog(): # Test forecasting with various shapes of `exog` nobs = 100 endog = np.ones(nobs) * 2.0 exog = np.ones(nobs) mod = sarimax.SARIMAX(endog, exog=exog, order=(1, 0, 0)) res = mod.smooth([2.0, 0.0, 1.0]) # 1-step-ahead, valid exog_fcast_scalar = 1. exog_fcast_1dim = np.ones(1) exog_fcast_2dim = np.ones((1, 1)) assert_allclose(res.forecast(1, exog=exog_fcast_scalar), 2.) assert_allclose(res.forecast(1, exog=exog_fcast_1dim), 2.) assert_allclose(res.forecast(1, exog=exog_fcast_2dim), 2.) # h-steps-ahead, valid h = 10 exog_fcast_1dim = np.ones(h) exog_fcast_2dim = np.ones((h, 1)) assert_allclose(res.forecast(h, exog=exog_fcast_1dim), 2.) assert_allclose(res.forecast(h, exog=exog_fcast_2dim), 2.) # h-steps-ahead, invalid assert_raises(ValueError, res.forecast, h, exog=1.) assert_raises(ValueError, res.forecast, h, exog=[1, 2]) assert_raises(ValueError, res.forecast, h, exog=np.ones((h, 2))) def check_equivalent_models(mod, mod2): attrs = [ 'measurement_error', 'state_error', 'mle_regression', 'state_regression', 'time_varying_regression', 'simple_differencing', 'enforce_stationarity', 'enforce_invertibility', 'hamilton_representation', 'trend', 'polynomial_ar', 'polynomial_ma', 'polynomial_seasonal_ar', 'polynomial_seasonal_ma', 'polynomial_trend', 'k_ar', 'k_ar_params', 'k_diff', 'k_ma', 'k_ma_params', 'seasonal_periods', 'k_seasonal_ar', 'k_seasonal_ar_params', 'k_seasonal_diff', 'k_seasonal_ma', 'k_seasonal_ma_params', 'k_trend', 'k_exog'] ssm_attrs = [ 'nobs', 'k_endog', 'k_states', 'k_posdef', 'obs_intercept', 'design', 'obs_cov', 'state_intercept', 'transition', 'selection', 'state_cov'] for attr in attrs: print(attr) assert_equal(getattr(mod2, attr), getattr(mod, attr)) for attr in ssm_attrs: assert_equal(getattr(mod2.ssm, attr), getattr(mod.ssm, attr)) assert_equal(mod2._get_init_kwds(), mod._get_init_kwds()) def test_recreate_model(): nobs = 100 endog = np.ones(nobs) * 2.0 exog = np.ones(nobs) orders = [(1, 0, 0), (2, 2, 2)] seasonal_orders = [(0, 0, 0, 0), (1, 1, 1, 4)] simple_differencings = [True, False] exogs = [None, np.ones_like(endog)] trends = [None, 't'] # Disabled, see discussion below in setting k_snr for details time_varying_regressions = [True, False] measurement_errors = [True, False] import itertools names = ['exog', 'order', 'seasonal_order', 'trend', 'measurement_error', 'time_varying_regression', 'simple_differencing'] for element in itertools.product(exogs, orders, seasonal_orders, trends, measurement_errors, time_varying_regressions, simple_differencings): kwargs = dict(zip(names, element)) if kwargs.get('time_varying_regression', False): kwargs['mle_regression'] = False exog = kwargs.pop('exog', None) mod = sarimax.SARIMAX(endog, exog=exog, **kwargs) mod2 = sarimax.SARIMAX(endog, exog=exog, **mod._get_init_kwds()) check_equivalent_models(mod, mod2) def test_append_results(): endog = np.arange(100) exog = np.ones_like(endog) params = [1., 1., 0.1, 1.] mod1 = sarimax.SARIMAX(endog, exog=exog, order=(1, 0, 0), trend='t') res1 = mod1.smooth(params) mod2 = sarimax.SARIMAX(endog[:50], exog=exog[:50], order=(1, 0, 0), trend='t') res2 = mod2.smooth(params) res3 = res2.append(endog[50:], exog=exog[50:]) assert_equal(res1.specification, res3.specification) assert_allclose(res3.cov_params_default, res2.cov_params_default) for attr in ['nobs', 'llf', 'llf_obs', 'loglikelihood_burn']: assert_equal(getattr(res3, attr), getattr(res1, attr)) for attr in [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov']: assert_equal(getattr(res3, attr), getattr(res1, attr)) assert_allclose(res3.forecast(10, exog=np.ones(10)), res1.forecast(10, exog=np.ones(10))) # Check that we get an error if we try to append without exog with pytest.raises(ValueError, match='Cloning a model with an exogenous'): res2.append(endog[50:]) def test_extend_results(): endog = np.arange(100) exog = np.ones_like(endog) params = [1., 1., 0.1, 1.] mod1 = sarimax.SARIMAX(endog, exog=exog, order=(1, 0, 0), trend='t') res1 = mod1.smooth(params) mod2 = sarimax.SARIMAX(endog[:50], exog=exog[:50], order=(1, 0, 0), trend='t') res2 = mod2.smooth(params) res3 = res2.extend(endog[50:], exog=exog[50:]) assert_allclose(res3.llf_obs, res1.llf_obs[50:]) for attr in [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov']: desired = getattr(res1, attr) if desired is not None: desired = desired[..., 50:] assert_equal(getattr(res3, attr), desired) assert_allclose(res3.forecast(10, exog=np.ones(10)), res1.forecast(10, exog=np.ones(10))) # Check that we get an error if we try to extend without exog with pytest.raises(ValueError, match='Cloning a model with an exogenous'): res2.extend(endog[50:]) def test_apply_results(): endog = np.arange(100) exog = np.ones_like(endog) params = [1., 1., 0.1, 1.] mod1 = sarimax.SARIMAX(endog[:50], exog=exog[:50], order=(1, 0, 0), trend='t') res1 = mod1.smooth(params) mod2 = sarimax.SARIMAX(endog[50:], exog=exog[50:], order=(1, 0, 0), trend='t') res2 = mod2.smooth(params) res3 = res2.apply(endog[:50], exog=exog[:50]) assert_equal(res1.specification, res3.specification) assert_allclose(res3.cov_params_default, res2.cov_params_default) for attr in ['nobs', 'llf', 'llf_obs', 'loglikelihood_burn']: assert_equal(getattr(res3, attr), getattr(res1, attr)) for attr in [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov']: assert_equal(getattr(res3, attr), getattr(res1, attr)) assert_allclose(res3.forecast(10, exog=np.ones(10)), res1.forecast(10, exog=np.ones(10))) # Check that we get an error if we try to apply without exog with pytest.raises(ValueError, match='Cloning a model with an exogenous'): res2.apply(endog[50:]) def test_start_params_small_nobs(): # Test that starting parameters work even when nobs is very small, but # issues a warning. endog = np.log(realgdp_results['value']).diff()[1:].values # Regular ARMA mod = sarimax.SARIMAX(endog[:4], order=(4, 0, 0)) match = ('Too few observations to estimate starting parameters for ARMA' ' and trend.') with pytest.warns(UserWarning, match=match): start_params = mod.start_params assert_allclose(start_params, [0, 0, 0, 0, np.var(endog[:4])]) # Seasonal ARMA mod = sarimax.SARIMAX(endog[:4], order=(0, 0, 0), seasonal_order=(1, 0, 0, 4)) match = ('Too few observations to estimate starting parameters for' ' seasonal ARMA.') with pytest.warns(UserWarning, match=match): start_params = mod.start_params assert_allclose(start_params, [0, np.var(endog[:4])]) def test_simple_differencing_int64index(): values = np.log(realgdp_results['value']).values endog = pd.Series(values, index=pd.Int64Index(range(len(values)))) mod = sarimax.SARIMAX(endog, order=(1, 1, 0), simple_differencing=True) assert_(mod._index.equals(endog.index[1:])) def test_simple_differencing_rangeindex(): values = np.log(realgdp_results['value']).values endog = pd.Series(values, index=pd.RangeIndex(start=0, stop=len(values))) mod = sarimax.SARIMAX(endog, order=(1, 1, 0), simple_differencing=True) assert_(mod._index.equals(endog.index[1:])) def test_simple_differencing_dateindex(): values = np.log(realgdp_results['value']).values endog = pd.Series(values, index=pd.period_range( start='2000', periods=len(values), freq='M')) mod = sarimax.SARIMAX(endog, order=(1, 1, 0), simple_differencing=True) assert_(mod._index.equals(endog.index[1:])) def test_simple_differencing_strindex(): values = np.log(realgdp_results['value']).values index = pd.Int64Index(range(len(values))).map(str) endog = pd.Series(values, index=index) with pytest.warns(UserWarning): mod = sarimax.SARIMAX(endog, order=(1, 1, 0), simple_differencing=True) assert_(mod._index.equals(pd.RangeIndex(start=0, stop=len(values) - 1))) assert_(mod.data.row_labels.equals(index[1:])) def test_invalid_order(): endog = np.zeros(10) with pytest.raises(ValueError): sarimax.SARIMAX(endog, order=(1,)) with pytest.raises(ValueError): sarimax.SARIMAX(endog, order=(1, 2, 3, 4)) def test_invalid_seasonal_order(): endog = np.zeros(10) with pytest.raises(ValueError): sarimax.SARIMAX(endog, seasonal_order=(1,)) with pytest.raises(ValueError): sarimax.SARIMAX(endog, seasonal_order=(1, 2, 3, 4, 5)) with pytest.raises(ValueError): sarimax.SARIMAX(endog, seasonal_order=(1, 0, 0, 0)) with pytest.raises(ValueError): sarimax.SARIMAX(endog, seasonal_order=(0, 0, 1, 0)) with pytest.raises(ValueError): sarimax.SARIMAX(endog, seasonal_order=(1, 0, 1, 0)) with pytest.raises(ValueError): sarimax.SARIMAX(endog, seasonal_order=(0, 0, 0, 1)) def test_dynamic_str(): data = results_sarimax.wpi1_stationary["data"] index = pd.date_range("1980-1-1", freq="MS", periods=len(data)) series = pd.Series(data, index=index) mod = sarimax.SARIMAX(series, order=(1, 1, 0), trend="c") res = mod.fit() dynamic = index[-12] desired = res.get_prediction(index[-24], dynamic=12) actual = res.get_prediction(index[-24], dynamic=dynamic) assert_allclose(actual.predicted_mean, desired.predicted_mean) actual = res.get_prediction(index[-24], dynamic=dynamic.to_pydatetime()) assert_allclose(actual.predicted_mean, desired.predicted_mean) actual = res.get_prediction(index[-24], dynamic=dynamic.strftime("%Y-%m-%d")) assert_allclose(actual.predicted_mean, desired.predicted_mean) @pytest.mark.matplotlib def test_plot_too_few_obs(reset_randomstate): # GH 6173 # SO https://stackoverflow.com/questions/55930880/ # arima-models-plot-diagnostics-share-error/58051895#58051895 mod = sarimax.SARIMAX( np.random.normal(size=10), order=(10, 0, 0), enforce_stationarity=False ) results = mod.fit() with pytest.raises(ValueError, match="Length of endogenous"): results.plot_diagnostics(figsize=(15, 5)) y = np.random.standard_normal(9) mod = sarimax.SARIMAX( y, order=(1, 1, 1), seasonal_order=(1, 1, 0, 12), enforce_stationarity=False, enforce_invertibility=False, ) results = mod.fit() with pytest.raises(ValueError, match="Length of endogenous"): results.plot_diagnostics(figsize=(30, 15)) def test_sarimax_starting_values_few_obsevations(reset_randomstate): # GH 6396, 6801 y = np.random.standard_normal(17) sarimax_model = sarimax.SARIMAX( endog=y, order=(1, 1, 1), seasonal_order=(0, 1, 0, 12), trend="n" ).fit(disp=False) assert np.all( np.isfinite(sarimax_model.predict(start=len(y), end=len(y) + 11)) ) def test_sarimax_forecast_exog_trend(reset_randomstate): # Test that an error is not raised that the given `exog` for the forecast # period is a constant when forecating with an intercept # GH 7019 y = np.zeros(10) x = np.zeros(10) mod = sarimax.SARIMAX(endog=y, exog=x, order=(1, 0, 0), trend='c') res = mod.smooth([0.2, 0.4, 0.5, 1.0]) # Test for h=1 assert_allclose(res.forecast(1, exog=1), 0.2 + 0.4) # Test for h=2 assert_allclose(res.forecast(2, exog=[1., 1.]), 0.2 + 0.4, 0.2 + 0.4 + 0.5) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_save.py000066400000000000000000000104621400612667500251460ustar00rootroot00000000000000""" Tests of save / load / remove_data state space functionality. """ import pickle import os import tempfile import pytest from statsmodels import datasets from statsmodels.tsa.statespace import (sarimax, structural, varmax, dynamic_factor) from numpy.testing import assert_allclose current_path = os.path.dirname(os.path.abspath(__file__)) macrodata = datasets.macrodata.load_pandas().data @pytest.fixture() def temp_filename(): fd, filename = tempfile.mkstemp() yield filename try: os.close(fd) os.unlink(filename) except Exception: print("Couldn't close or delete file " "{filename}.".format(filename=filename)) def test_sarimax(temp_filename): mod = sarimax.SARIMAX(macrodata['realgdp'].values, order=(4, 1, 0)) res = mod.smooth(mod.start_params) res.summary() res.save(temp_filename) res2 = sarimax.SARIMAXResults.load(temp_filename) assert_allclose(res.params, res2.params) assert_allclose(res.bse, res2.bse) assert_allclose(res.llf, res2.llf) def test_sarimax_pickle(): mod = sarimax.SARIMAX(macrodata['realgdp'].values, order=(4, 1, 0)) pkl_mod = pickle.loads(pickle.dumps(mod)) res = mod.smooth(mod.start_params) pkl_res = pkl_mod.smooth(mod.start_params) assert_allclose(res.params, pkl_res.params) assert_allclose(res.bse, pkl_res.bse) assert_allclose(res.llf, pkl_res.llf) def test_structural(temp_filename): mod = structural.UnobservedComponents( macrodata['realgdp'].values, 'llevel') res = mod.smooth(mod.start_params) res.summary() res.save(temp_filename) res2 = structural.UnobservedComponentsResults.load(temp_filename) assert_allclose(res.params, res2.params) assert_allclose(res.bse, res2.bse) assert_allclose(res.llf, res2.llf) def test_structural_pickle(): mod = structural.UnobservedComponents( macrodata['realgdp'].values, 'llevel') pkl_mod = pickle.loads(pickle.dumps(mod)) res = mod.smooth(mod.start_params) pkl_res = pkl_mod.smooth(pkl_mod.start_params) assert_allclose(res.params, pkl_res.params) assert_allclose(res.bse, pkl_res.bse) assert_allclose(res.llf, pkl_res.llf) def test_dynamic_factor(temp_filename): mod = dynamic_factor.DynamicFactor( macrodata[['realgdp', 'realcons']].diff().iloc[1:].values, k_factors=1, factor_order=1) res = mod.smooth(mod.start_params) res.summary() res.save(temp_filename) res2 = dynamic_factor.DynamicFactorResults.load(temp_filename) assert_allclose(res.params, res2.params) assert_allclose(res.bse, res2.bse) assert_allclose(res.llf, res2.llf) def test_dynamic_factor_pickle(temp_filename): mod = varmax.VARMAX( macrodata[['realgdp', 'realcons']].diff().iloc[1:].values, order=(1, 0)) pkl_mod = pickle.loads(pickle.dumps(mod)) res = mod.smooth(mod.start_params) pkl_res = pkl_mod.smooth(mod.start_params) assert_allclose(res.params, pkl_res.params) assert_allclose(res.bse, pkl_res.bse) assert_allclose(res.llf, pkl_res.llf) res.summary() res.save(temp_filename) res2 = varmax.VARMAXResults.load(temp_filename) assert_allclose(res.params, res2.params) assert_allclose(res.bse, res2.bse) assert_allclose(res.llf, res2.llf) def test_varmax(temp_filename): mod = varmax.VARMAX( macrodata[['realgdp', 'realcons']].diff().iloc[1:].values, order=(1, 0)) res = mod.smooth(mod.start_params) res.summary() res.save(temp_filename) res2 = varmax.VARMAXResults.load(temp_filename) assert_allclose(res.params, res2.params) assert_allclose(res.bse, res2.bse) assert_allclose(res.llf, res2.llf) def test_varmax_pickle(temp_filename): mod = varmax.VARMAX( macrodata[['realgdp', 'realcons']].diff().iloc[1:].values, order=(1, 0)) res = mod.smooth(mod.start_params) res.summary() res.save(temp_filename) res2 = varmax.VARMAXResults.load(temp_filename) assert_allclose(res.params, res2.params) assert_allclose(res.bse, res2.bse) assert_allclose(res.llf, res2.llf) def test_existing_pickle(): pkl_file = os.path.join(current_path, 'results', 'sm-0.9-sarimax.pkl') loaded = sarimax.SARIMAXResults.load(pkl_file) assert isinstance(loaded, sarimax.SARIMAXResultsWrapper) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_simulate.py000066400000000000000000002134041400612667500260340ustar00rootroot00000000000000""" Tests for simulation of time series Author: Chad Fulton License: Simplified-BSD """ import numpy as np import pandas as pd from numpy.testing import assert_, assert_allclose, assert_equal import pytest from scipy.signal import lfilter from .test_impulse_responses import TVSS from statsmodels.tools.sm_exceptions import SpecificationWarning, \ EstimationWarning from statsmodels.tsa.statespace import (sarimax, structural, varmax, dynamic_factor) def test_arma_lfilter(): # Tests of an ARMA model simulation against scipy.signal.lfilter # Note: the first elements of the generated SARIMAX datasets are based on # the initial state, so we do not include them in the comparisons np.random.seed(10239) nobs = 100 eps = np.random.normal(size=nobs) # AR(1) mod = sarimax.SARIMAX([0], order=(1, 0, 0)) actual = mod.simulate([0.5, 1.], nobs + 1, state_shocks=np.r_[eps, 0], initial_state=np.zeros(mod.k_states)) desired = lfilter([1], [1, -0.5], eps) assert_allclose(actual[1:], desired) # MA(1) mod = sarimax.SARIMAX([0], order=(0, 0, 1)) actual = mod.simulate([0.5, 1.], nobs + 1, state_shocks=np.r_[eps, 0], initial_state=np.zeros(mod.k_states)) desired = lfilter([1, 0.5], [1], eps) assert_allclose(actual[1:], desired) # ARMA(1, 1) mod = sarimax.SARIMAX([0], order=(1, 0, 1)) actual = mod.simulate([0.5, 0.2, 1.], nobs + 1, state_shocks=np.r_[eps, 0], initial_state=np.zeros(mod.k_states)) desired = lfilter([1, 0.2], [1, -0.5], eps) assert_allclose(actual[1:], desired) def test_arma_direct(): # Tests of an ARMA model simulation against direct construction # This is useful for e.g. trend components # Note: the first elements of the generated SARIMAX datasets are based on # the initial state, so we do not include them in the comparisons np.random.seed(10239) nobs = 100 eps = np.random.normal(size=nobs) exog = np.random.normal(size=nobs) # AR(1) mod = sarimax.SARIMAX([0], order=(1, 0, 0)) actual = mod.simulate([0.5, 1.], nobs + 1, state_shocks=np.r_[eps, 0], initial_state=np.zeros(mod.k_states)) desired = np.zeros(nobs) for i in range(nobs): if i == 0: desired[i] = eps[i] else: desired[i] = 0.5 * desired[i - 1] + eps[i] assert_allclose(actual[1:], desired) # MA(1) mod = sarimax.SARIMAX([0], order=(0, 0, 1)) actual = mod.simulate([0.5, 1.], nobs + 1, state_shocks=np.r_[eps, 0], initial_state=np.zeros(mod.k_states)) desired = np.zeros(nobs) for i in range(nobs): if i == 0: desired[i] = eps[i] else: desired[i] = 0.5 * eps[i - 1] + eps[i] assert_allclose(actual[1:], desired) # ARMA(1, 1) mod = sarimax.SARIMAX([0], order=(1, 0, 1)) actual = mod.simulate([0.5, 0.2, 1.], nobs + 1, state_shocks=np.r_[eps, 0], initial_state=np.zeros(mod.k_states)) desired = np.zeros(nobs) for i in range(nobs): if i == 0: desired[i] = eps[i] else: desired[i] = 0.5 * desired[i - 1] + 0.2 * eps[i - 1] + eps[i] assert_allclose(actual[1:], desired) # ARMA(1, 1) + intercept mod = sarimax.SARIMAX([0], order=(1, 0, 1), trend='c') actual = mod.simulate([1.3, 0.5, 0.2, 1.], nobs + 1, state_shocks=np.r_[eps, 0], initial_state=np.zeros(mod.k_states)) desired = np.zeros(nobs) for i in range(nobs): trend = 1.3 if i == 0: desired[i] = trend + eps[i] else: desired[i] = (trend + 0.5 * desired[i - 1] + 0.2 * eps[i - 1] + eps[i]) assert_allclose(actual[1:], desired) # ARMA(1, 1) + intercept + time trend # Note: to allow time-varying SARIMAX to simulate 101 observations, need to # give it 101 observations up front mod = sarimax.SARIMAX(np.zeros(nobs + 1), order=(1, 0, 1), trend='ct') actual = mod.simulate([1.3, 0.2, 0.5, 0.2, 1.], nobs + 1, state_shocks=np.r_[eps, 0], initial_state=np.zeros(mod.k_states)) desired = np.zeros(nobs) for i in range(nobs): trend = 1.3 + 0.2 * (i + 1) if i == 0: desired[i] = trend + eps[i] else: desired[i] = (trend + 0.5 * desired[i - 1] + 0.2 * eps[i - 1] + eps[i]) assert_allclose(actual[1:], desired) # ARMA(1, 1) + intercept + time trend + exog # Note: to allow time-varying SARIMAX to simulate 101 observations, need to # give it 101 observations up front # Note: the model is regression with SARIMAX errors, so the exog is # introduced into the observation equation rather than the ARMA part mod = sarimax.SARIMAX(np.zeros(nobs + 1), exog=np.r_[0, exog], order=(1, 0, 1), trend='ct') actual = mod.simulate([1.3, 0.2, -0.5, 0.5, 0.2, 1.], nobs + 1, state_shocks=np.r_[eps, 0], initial_state=np.zeros(mod.k_states)) desired = np.zeros(nobs) for i in range(nobs): trend = 1.3 + 0.2 * (i + 1) if i == 0: desired[i] = trend + eps[i] else: desired[i] = (trend + 0.5 * desired[i - 1] + 0.2 * eps[i - 1] + eps[i]) desired = desired - 0.5 * exog assert_allclose(actual[1:], desired) def test_structural(): np.random.seed(38947) nobs = 100 eps = np.random.normal(size=nobs) exog = np.random.normal(size=nobs) eps1 = np.zeros(nobs) eps2 = np.zeros(nobs) eps2[49] = 1 eps3 = np.zeros(nobs) eps3[50:] = 1 # AR(1) mod1 = structural.UnobservedComponents([0], autoregressive=1) mod2 = sarimax.SARIMAX([0], order=(1, 0, 0)) actual = mod1.simulate([1, 0.5], nobs, state_shocks=eps, initial_state=np.zeros(mod1.k_states)) desired = mod2.simulate([0.5, 1], nobs, state_shocks=eps, initial_state=np.zeros(mod2.k_states)) assert_allclose(actual, desired) # ARX(1) mod1 = structural.UnobservedComponents(np.zeros(nobs), exog=exog, autoregressive=1) mod2 = sarimax.SARIMAX(np.zeros(nobs), exog=exog, order=(1, 0, 0)) actual = mod1.simulate([1, 0.5, 0.2], nobs, state_shocks=eps, initial_state=np.zeros(mod2.k_states)) desired = mod2.simulate([0.2, 0.5, 1], nobs, state_shocks=eps, initial_state=np.zeros(mod2.k_states)) assert_allclose(actual, desired) # Irregular mod = structural.UnobservedComponents([0], 'irregular') actual = mod.simulate([1.], nobs, measurement_shocks=eps, initial_state=np.zeros(mod.k_states)) assert_allclose(actual, eps) # Fixed intercept # (in practice this is a deterministic constant, because an irregular # component must be added) warning = SpecificationWarning match = 'irregular component added' with pytest.warns(warning, match=match): mod = structural.UnobservedComponents([0], 'fixed intercept') actual = mod.simulate([1.], nobs, measurement_shocks=eps, initial_state=[10]) assert_allclose(actual, 10 + eps) # Deterministic constant mod = structural.UnobservedComponents([0], 'deterministic constant') actual = mod.simulate([1.], nobs, measurement_shocks=eps, initial_state=[10]) assert_allclose(actual, 10 + eps) # Local level mod = structural.UnobservedComponents([0], 'local level') actual = mod.simulate([1., 1.], nobs, measurement_shocks=eps, state_shocks=eps2, initial_state=np.zeros(mod.k_states)) assert_allclose(actual, eps + eps3) # Random walk mod = structural.UnobservedComponents([0], 'random walk') actual = mod.simulate([1.], nobs, measurement_shocks=eps, state_shocks=eps2, initial_state=np.zeros(mod.k_states)) assert_allclose(actual, eps + eps3) # Fixed slope # (in practice this is a deterministic trend, because an irregular # component must be added) warning = SpecificationWarning match = 'irregular component added' with pytest.warns(warning, match=match): mod = structural.UnobservedComponents([0], 'fixed slope') actual = mod.simulate([1., 1.], nobs, measurement_shocks=eps, state_shocks=eps2, initial_state=[0, 1]) assert_allclose(actual, eps + np.arange(100)) # Deterministic trend mod = structural.UnobservedComponents([0], 'deterministic trend') actual = mod.simulate([1.], nobs, measurement_shocks=eps, state_shocks=eps2, initial_state=[0, 1]) assert_allclose(actual, eps + np.arange(100)) # Local linear deterministic trend mod = structural.UnobservedComponents( [0], 'local linear deterministic trend') actual = mod.simulate([1., 1.], nobs, measurement_shocks=eps, state_shocks=eps2, initial_state=[0, 1]) desired = eps + np.r_[np.arange(50), 1 + np.arange(50, 100)] assert_allclose(actual, desired) # Random walk with drift mod = structural.UnobservedComponents([0], 'random walk with drift') actual = mod.simulate([1.], nobs, state_shocks=eps2, initial_state=[0, 1]) desired = np.r_[np.arange(50), 1 + np.arange(50, 100)] assert_allclose(actual, desired) # Local linear trend mod = structural.UnobservedComponents([0], 'local linear trend') actual = mod.simulate([1., 1., 1.], nobs, measurement_shocks=eps, state_shocks=np.c_[eps2, eps1], initial_state=[0, 1]) desired = eps + np.r_[np.arange(50), 1 + np.arange(50, 100)] assert_allclose(actual, desired) actual = mod.simulate([1., 1., 1.], nobs, measurement_shocks=eps, state_shocks=np.c_[eps1, eps2], initial_state=[0, 1]) desired = eps + np.r_[np.arange(50), np.arange(50, 150, 2)] assert_allclose(actual, desired) # Smooth trend mod = structural.UnobservedComponents([0], 'smooth trend') actual = mod.simulate([1., 1.], nobs, measurement_shocks=eps, state_shocks=eps1, initial_state=[0, 1]) desired = eps + np.r_[np.arange(100)] assert_allclose(actual, desired) actual = mod.simulate([1., 1.], nobs, measurement_shocks=eps, state_shocks=eps2, initial_state=[0, 1]) desired = eps + np.r_[np.arange(50), np.arange(50, 150, 2)] assert_allclose(actual, desired) # Random trend mod = structural.UnobservedComponents([0], 'random trend') actual = mod.simulate([1., 1.], nobs, state_shocks=eps1, initial_state=[0, 1]) desired = np.r_[np.arange(100)] assert_allclose(actual, desired) actual = mod.simulate([1., 1.], nobs, state_shocks=eps2, initial_state=[0, 1]) desired = np.r_[np.arange(50), np.arange(50, 150, 2)] assert_allclose(actual, desired) # Seasonal (deterministic) mod = structural.UnobservedComponents([0], 'irregular', seasonal=2, stochastic_seasonal=False) actual = mod.simulate([1.], nobs, measurement_shocks=eps, initial_state=[10]) desired = eps + np.tile([10, -10], 50) assert_allclose(actual, desired) # Seasonal (stochastic) mod = structural.UnobservedComponents([0], 'irregular', seasonal=2) actual = mod.simulate([1., 1.], nobs, measurement_shocks=eps, state_shocks=eps2, initial_state=[10]) desired = eps + np.r_[np.tile([10, -10], 25), np.tile([11, -11], 25)] assert_allclose(actual, desired) # Cycle (deterministic) mod = structural.UnobservedComponents([0], 'irregular', cycle=True) actual = mod.simulate([1., 1.2], nobs, measurement_shocks=eps, initial_state=[1, 0]) x1 = [np.cos(1.2), np.sin(1.2)] x2 = [-np.sin(1.2), np.cos(1.2)] T = np.array([x1, x2]) desired = eps states = [1, 0] for i in range(nobs): desired[i] += states[0] states = np.dot(T, states) assert_allclose(actual, desired) # Cycle (stochastic) mod = structural.UnobservedComponents([0], 'irregular', cycle=True, stochastic_cycle=True) actual = mod.simulate([1., 1., 1.2], nobs, measurement_shocks=eps, state_shocks=np.c_[eps2, eps2], initial_state=[1, 0]) x1 = [np.cos(1.2), np.sin(1.2)] x2 = [-np.sin(1.2), np.cos(1.2)] T = np.array([x1, x2]) desired = eps states = [1, 0] for i in range(nobs): desired[i] += states[0] states = np.dot(T, states) + eps2[i] assert_allclose(actual, desired) def test_varmax(): np.random.seed(371934) nobs = 100 eps = np.random.normal(size=nobs) exog = np.random.normal(size=(nobs, 1)) eps1 = np.zeros(nobs) eps2 = np.zeros(nobs) eps2[49] = 1 eps3 = np.zeros(nobs) eps3[50:] = 1 # VAR(2) - single series mod1 = varmax.VARMAX([[0]], order=(2, 0), trend='n') mod2 = sarimax.SARIMAX([0], order=(2, 0, 0)) actual = mod1.simulate([0.5, 0.2, 1], nobs, state_shocks=eps, initial_state=np.zeros(mod1.k_states)) desired = mod2.simulate([0.5, 0.2, 1], nobs, state_shocks=eps, initial_state=np.zeros(mod2.k_states)) assert_allclose(actual, desired) # VMA(2) - single series mod1 = varmax.VARMAX([[0]], order=(0, 2), trend='n') mod2 = sarimax.SARIMAX([0], order=(0, 0, 2)) actual = mod1.simulate([0.5, 0.2, 1], nobs, state_shocks=eps, initial_state=np.zeros(mod1.k_states)) desired = mod2.simulate([0.5, 0.2, 1], nobs, state_shocks=eps, initial_state=np.zeros(mod2.k_states)) assert_allclose(actual, desired) # VARMA(2, 2) - single series warning = EstimationWarning match = r'VARMA\(p,q\) models is not' with pytest.warns(warning, match=match): mod1 = varmax.VARMAX([[0]], order=(2, 2), trend='n') mod2 = sarimax.SARIMAX([0], order=(2, 0, 2)) actual = mod1.simulate([0.5, 0.2, 0.1, -0.2, 1], nobs, state_shocks=eps, initial_state=np.zeros(mod1.k_states)) desired = mod2.simulate([0.5, 0.2, 0.1, -0.2, 1], nobs, state_shocks=eps, initial_state=np.zeros(mod2.k_states)) assert_allclose(actual, desired) # VARMA(2, 2) + trend - single series warning = EstimationWarning match = r'VARMA\(p,q\) models is not' with pytest.warns(warning, match=match): mod1 = varmax.VARMAX([[0]], order=(2, 2), trend='c') mod2 = sarimax.SARIMAX([0], order=(2, 0, 2), trend='c') actual = mod1.simulate([10, 0.5, 0.2, 0.1, -0.2, 1], nobs, state_shocks=eps, initial_state=np.zeros(mod1.k_states)) desired = mod2.simulate([10, 0.5, 0.2, 0.1, -0.2, 1], nobs, state_shocks=eps, initial_state=np.zeros(mod2.k_states)) assert_allclose(actual, desired) # VAR(1) transition = np.array([[0.5, 0.1], [-0.1, 0.2]]) mod = varmax.VARMAX([[0, 0]], order=(1, 0), trend='n') actual = mod.simulate(np.r_[transition.ravel(), 1., 0, 1.], nobs, state_shocks=np.c_[eps1, eps1], initial_state=np.zeros(mod.k_states)) assert_allclose(actual, 0) actual = mod.simulate(np.r_[transition.ravel(), 1., 0, 1.], nobs, state_shocks=np.c_[eps1, eps1], initial_state=[1, 1]) desired = np.zeros((nobs, 2)) state = np.r_[1, 1] for i in range(nobs): desired[i] = state state = np.dot(transition, state) assert_allclose(actual, desired) # VAR(1) + measurement error mod = varmax.VARMAX([[0, 0]], order=(1, 0), trend='n', measurement_error=True) actual = mod.simulate(np.r_[transition.ravel(), 1., 0, 1., 1., 1.], nobs, measurement_shocks=np.c_[eps, eps], state_shocks=np.c_[eps1, eps1], initial_state=np.zeros(mod.k_states)) assert_allclose(actual, np.c_[eps, eps]) # VARX(1) mod = varmax.VARMAX(np.zeros((nobs, 2)), order=(1, 0), trend='n', exog=exog) actual = mod.simulate(np.r_[transition.ravel(), 5, -2, 1., 0, 1.], nobs, state_shocks=np.c_[eps1, eps1], initial_state=[1, 1]) desired = np.zeros((nobs, 2)) state = np.r_[1, 1] for i in range(nobs): desired[i] = state if i < nobs - 1: state = exog[i + 1] * [5, -2] + np.dot(transition, state) assert_allclose(actual, desired) # VMA(1) # TODO: This is just a smoke test mod = varmax.VARMAX( np.random.normal(size=(nobs, 2)), order=(0, 1), trend='n') mod.simulate(mod.start_params, nobs) # VARMA(2, 2) + trend + exog # TODO: This is just a smoke test warning = EstimationWarning match = r"VARMA\(p,q\) models is not" with pytest.warns(warning, match=match): mod = varmax.VARMAX( np.random.normal(size=(nobs, 2)), order=(2, 2), trend='c', exog=exog) mod.simulate(mod.start_params, nobs) def test_dynamic_factor(): np.random.seed(93739) nobs = 100 eps = np.random.normal(size=nobs) exog = np.random.normal(size=(nobs, 1)) eps1 = np.zeros(nobs) eps2 = np.zeros(nobs) eps2[49] = 1 eps3 = np.zeros(nobs) eps3[50:] = 1 # DFM: 2 series, AR(2) factor mod1 = dynamic_factor.DynamicFactor([[0, 0]], k_factors=1, factor_order=2) mod2 = sarimax.SARIMAX([0], order=(2, 0, 0)) actual = mod1.simulate([-0.9, 0.8, 1., 1., 0.5, 0.2], nobs, measurement_shocks=np.c_[eps1, eps1], state_shocks=eps, initial_state=np.zeros(mod1.k_states)) desired = mod2.simulate([0.5, 0.2, 1], nobs, state_shocks=eps, initial_state=np.zeros(mod2.k_states)) assert_allclose(actual[:, 0], -0.9 * desired) assert_allclose(actual[:, 1], 0.8 * desired) # DFM: 2 series, AR(2) factor, exog mod1 = dynamic_factor.DynamicFactor(np.zeros((nobs, 2)), k_factors=1, factor_order=2, exog=exog) mod2 = sarimax.SARIMAX([0], order=(2, 0, 0)) actual = mod1.simulate([-0.9, 0.8, 5, -2, 1., 1., 0.5, 0.2], nobs, measurement_shocks=np.c_[eps1, eps1], state_shocks=eps, initial_state=np.zeros(mod1.k_states)) desired = mod2.simulate([0.5, 0.2, 1], nobs, state_shocks=eps, initial_state=np.zeros(mod2.k_states)) assert_allclose(actual[:, 0], -0.9 * desired + 5 * exog[:, 0]) assert_allclose(actual[:, 1], 0.8 * desired - 2 * exog[:, 0]) # DFM, 3 series, VAR(2) factor, exog, error VAR # TODO: This is just a smoke test mod = dynamic_factor.DynamicFactor(np.random.normal(size=(nobs, 3)), k_factors=2, factor_order=2, exog=exog, error_order=2, error_var=True) mod.simulate(mod.start_params, nobs) def test_known_initialization(): # Need to test that "known" initialization is taken into account in # time series simulation np.random.seed(38947) nobs = 100 eps = np.random.normal(size=nobs) eps1 = np.zeros(nobs) eps2 = np.zeros(nobs) eps2[49] = 1 eps3 = np.zeros(nobs) eps3[50:] = 1 # SARIMAX # (test that when state shocks are shut down, the initial state # geometrically declines according to the AR parameter) mod = sarimax.SARIMAX([0], order=(1, 0, 0)) mod.ssm.initialize_known([100], [[0]]) actual = mod.simulate([0.5, 1.], nobs, state_shocks=eps1) assert_allclose(actual, 100 * 0.5**np.arange(nobs)) # Unobserved components # (test that the initial level shifts the entire path) mod = structural.UnobservedComponents([0], 'local level') mod.ssm.initialize_known([100], [[0]]) actual = mod.simulate([1., 1.], nobs, measurement_shocks=eps, state_shocks=eps2) assert_allclose(actual, 100 + eps + eps3) # VARMAX # (here just test that with an independent VAR we have each initial state # geometrically declining at the appropriate rate) transition = np.diag([0.5, 0.2]) mod = varmax.VARMAX([[0, 0]], order=(1, 0), trend='n') mod.initialize_known([100, 50], np.diag([0, 0])) actual = mod.simulate(np.r_[transition.ravel(), 1., 0, 1.], nobs, measurement_shocks=np.c_[eps1, eps1], state_shocks=np.c_[eps1, eps1]) assert_allclose(actual, np.c_[100 * 0.5**np.arange(nobs), 50 * 0.2**np.arange(nobs)]) # Dynamic factor # (test that the initial state declines geometrically and then loads # correctly onto the series) mod = dynamic_factor.DynamicFactor([[0, 0]], k_factors=1, factor_order=1) mod.initialize_known([100], [[0]]) actual = mod.simulate([0.8, 0.2, 1.0, 1.0, 0.5], nobs, measurement_shocks=np.c_[eps1, eps1], state_shocks=eps1) tmp = 100 * 0.5**np.arange(nobs) assert_allclose(actual, np.c_[0.8 * tmp, 0.2 * tmp]) def test_sequential_simulate(): # Test that we can perform simulation, change the system matrices, and then # perform simulation again (i.e. check that everything updates correctly # in the simulation smoother). n_simulations = 100 mod = sarimax.SARIMAX([1], order=(0, 0, 0), trend='c') actual = mod.simulate([1, 0], n_simulations) assert_allclose(actual, np.ones(n_simulations)) actual = mod.simulate([10, 0], n_simulations) assert_allclose(actual, np.ones(n_simulations) * 10) def test_sarimax_end_time_invariant_noshocks(): # Test simulating values from the end of a time-invariant SARIMAX model # In this test, we suppress randomness by setting the shocks to zeros endog = np.arange(1, 11) mod = sarimax.SARIMAX(endog) res = mod.filter([0.5, 1.]) nsimulations = 10 measurement_shocks = np.zeros((nsimulations, mod.k_endog)) state_shocks = np.zeros((nsimulations, mod.k_states)) initial_state = res.predicted_state[..., -1] assert_allclose(initial_state, 5) actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # Compute the desired simulated values directly desired = 10 * 0.5**np.arange(1, nsimulations + 1) assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) # Alternatively, since we've shut down the shocks, we can compare against # the forecast values assert_allclose(actual, res.forecast(nsimulations)) def test_sarimax_simple_differencing_end_time_invariant_noshocks(): # Test simulating values from the end of a time-invariant SARIMAX model # in which simple differencing is used. # In this test, we suppress randomness by setting the shocks to zeros endog = np.cumsum(np.arange(0, 11)) mod = sarimax.SARIMAX(endog, order=(1, 1, 0), simple_differencing=True) res = mod.filter([0.5, 1.]) nsimulations = 10 measurement_shocks = np.zeros((nsimulations, mod.k_endog)) state_shocks = np.zeros((nsimulations, mod.k_states)) initial_state = res.predicted_state[..., -1] assert_allclose(initial_state, 5) actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # Compute the desired simulated values directly desired = 10 * 0.5**np.arange(1, nsimulations + 1) assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) # Alternatively, since we've shut down the shocks, we can compare against # the forecast values assert_allclose(actual, res.forecast(nsimulations)) def test_sarimax_time_invariant_shocks(reset_randomstate): # Test simulating values from the end of a time-invariant SARIMAX model, # with nonzero shocks endog = np.arange(1, 11) mod = sarimax.SARIMAX(endog) res = mod.filter([0.5, 1.]) nsimulations = 10 measurement_shocks = np.random.normal(size=nsimulations) state_shocks = np.random.normal(size=nsimulations) initial_state = res.predicted_state[:1, -1] actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) desired = ( lfilter([1], [1, -0.5], np.r_[initial_state, state_shocks])[:-1] + measurement_shocks) assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) def test_sarimax_simple_differencing_end_time_invariant_shocks(): # Test simulating values from the end of a time-invariant SARIMAX model # in which simple differencing is used. # In this test, we suppress randomness by setting the shocks to zeros endog = np.cumsum(np.arange(0, 11)) mod = sarimax.SARIMAX(endog, order=(1, 1, 0), simple_differencing=True) res = mod.filter([0.5, 1.]) nsimulations = 10 measurement_shocks = np.random.normal(size=nsimulations) state_shocks = np.random.normal(size=nsimulations) initial_state = res.predicted_state[:1, -1] actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) desired = ( lfilter([1], [1, -0.5], np.r_[initial_state, state_shocks])[:-1] + measurement_shocks) assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) def test_sarimax_time_varying_trend_noshocks(): # Test simulating values from the end of a time-varying SARIMAX model # In this test, we suppress randomness by setting the shocks to zeros endog = np.arange(1, 11) mod = sarimax.SARIMAX(endog, trend='t') res = mod.filter([1., 0.2, 1.]) nsimulations = 10 measurement_shocks = np.zeros((nsimulations, mod.k_endog)) state_shocks = np.zeros((nsimulations, mod.k_states)) initial_state = res.predicted_state[..., -1] assert_allclose(initial_state, 12) actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # Compute the desired simulated values directly desired = lfilter([1], [1, -0.2], np.r_[12, np.arange(11, 20)]) assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) # Alternatively, since we've shut down the shocks, we can compare against # the forecast values assert_allclose(actual, res.forecast(nsimulations)) def test_sarimax_simple_differencing_time_varying_trend_noshocks(): # Test simulating values from the end of a time-varying SARIMAX model # in which simple differencing is used. # In this test, we suppress randomness by setting the shocks to zeros endog = np.cumsum(np.arange(0, 11)) mod = sarimax.SARIMAX(endog, order=(1, 1, 0), trend='t', simple_differencing=True) res = mod.filter([1., 0.2, 1.]) nsimulations = 10 measurement_shocks = np.zeros((nsimulations, mod.k_endog)) state_shocks = np.zeros((nsimulations, mod.k_states)) initial_state = res.predicted_state[..., -1] assert_allclose(initial_state, 12) actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # Compute the desired simulated values directly desired = lfilter([1], [1, -0.2], np.r_[12, np.arange(11, 20)]) assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) # Alternatively, since we've shut down the shocks, we can compare against # the forecast values assert_allclose(actual, res.forecast(nsimulations)) def test_sarimax_time_varying_trend_shocks(reset_randomstate): # Test simulating values from the end of a time-varying SARIMAX model, # with nonzero shocks endog = np.arange(1, 11) mod = sarimax.SARIMAX(endog, trend='t') res = mod.filter([1., 0.2, 1.]) nsimulations = 10 measurement_shocks = np.random.normal(size=nsimulations) state_shocks = np.random.normal(size=nsimulations) initial_state = res.predicted_state[:1, -1] actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) x = np.r_[initial_state, state_shocks + np.arange(11, 21)] desired = lfilter([1], [1, -0.2], x)[:-1] + measurement_shocks assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) def test_sarimax_simple_differencing_time_varying_trend_shocks( reset_randomstate): # Test simulating values from the end of a time-varying SARIMAX model # in which simple differencing is used. # with nonzero shocks endog = np.cumsum(np.arange(0, 11)) mod = sarimax.SARIMAX(endog, order=(1, 1, 0), trend='t', simple_differencing=True) res = mod.filter([1., 0.2, 1.]) nsimulations = 10 measurement_shocks = np.random.normal(size=nsimulations) state_shocks = np.random.normal(size=nsimulations) initial_state = res.predicted_state[:1, -1] assert_allclose(initial_state, 12) actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) x = np.r_[initial_state, state_shocks + np.arange(11, 21)] desired = lfilter([1], [1, -0.2], x)[:-1] + measurement_shocks assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) def test_sarimax_time_varying_exog_noshocks(): # Test simulating values from the end of a time-varying SARIMAX model # In this test, we suppress randomness by setting the shocks to zeros # Note that `exog` here has basically the same effect as measurement shocks endog = np.arange(1, 11) exog = np.arange(1, 21)**2 mod = sarimax.SARIMAX(endog, exog=exog[:10]) res = mod.filter([1., 0.2, 1.]) nsimulations = 10 measurement_shocks = np.zeros((nsimulations, mod.k_endog)) state_shocks = np.zeros((nsimulations, mod.k_states)) initial_state = res.predicted_state[..., -1] actual = res.simulate(nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # Compute the desired simulated values directly desired = (lfilter([1], [1, -0.2], np.r_[initial_state, [0] * 9]) + exog[10:]) assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) # Alternatively, since we've shut down the shocks, we can compare against # the forecast values assert_allclose(actual, res.forecast(nsimulations, exog=exog[10:])) def test_sarimax_simple_differencing_time_varying_exog_noshocks(): # Test simulating values from the end of a time-varying SARIMAX model # with simple differencing # In this test, we suppress randomness by setting the shocks to zeros endog = np.cumsum(np.arange(0, 11)) exog = np.cumsum(np.arange(0, 21)**2) mod = sarimax.SARIMAX(endog, order=(1, 1, 0), exog=exog[:11], simple_differencing=True) res = mod.filter([1., 0.2, 1.]) nsimulations = 10 measurement_shocks = np.zeros((nsimulations, mod.k_endog)) state_shocks = np.zeros((nsimulations, mod.k_states)) initial_state = res.predicted_state[..., -1] actual = res.simulate(nsimulations, exog=exog[11:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # Compute the desired simulated values directly desired = (lfilter([1], [1, -0.2], np.r_[initial_state, [0] * 9]) + np.diff(exog)[10:]) assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, exog=exog[11:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) # Alternatively, since we've shut down the shocks, we can compare against # the forecast values assert_allclose(actual, res.forecast(nsimulations, exog=exog[11:])) def test_sarimax_time_varying_exog_shocks(reset_randomstate): # Test simulating values from the end of a time-varying SARIMAX model, # with nonzero shocks endog = np.arange(1, 11) exog = np.arange(1, 21)**2 mod = sarimax.SARIMAX(endog, exog=exog[:10]) res = mod.filter([1., 0.2, 1.]) nsimulations = 10 measurement_shocks = np.random.normal(size=nsimulations) state_shocks = np.random.normal(size=nsimulations) initial_state = res.predicted_state[:1, -1] actual = res.simulate(nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) x = np.r_[initial_state, state_shocks[:-1]] desired = lfilter([1], [1, -0.2], x) + exog[10:] + measurement_shocks assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) def test_sarimax_simple_differencing_time_varying_exog_shocks( reset_randomstate): # Test simulating values from the end of a time-varying SARIMAX model # Note that `exog` here has basically the same effect as measurement shocks endog = np.cumsum(np.arange(0, 11)) exog = np.cumsum(np.arange(0, 21)**2) mod = sarimax.SARIMAX(endog, order=(1, 1, 0), exog=exog[:11], simple_differencing=True) res = mod.filter([1., 0.2, 1.]) nsimulations = 10 measurement_shocks = np.random.normal(size=nsimulations) state_shocks = np.random.normal(size=nsimulations) initial_state = res.predicted_state[:1, -1] actual = res.simulate(nsimulations, exog=exog[11:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # Compute the desired simulated values directly x = np.r_[initial_state, state_shocks[:-1]] desired = (lfilter([1], [1, -0.2], x) + np.diff(exog)[10:] + measurement_shocks) assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, exog=exog[11:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) def test_unobserved_components_end_time_invariant_noshocks(): # Test simulating values from the end of a time-invariant # UnobservedComponents model # In this test, we suppress randomness by setting the shocks to zeros endog = np.arange(1, 11) mod = structural.UnobservedComponents(endog, 'llevel') res = mod.filter([1., 1.]) nsimulations = 10 measurement_shocks = np.zeros((nsimulations, mod.k_endog)) state_shocks = np.zeros((nsimulations, mod.k_states)) initial_state = res.predicted_state[..., -1] actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # The mean of the simulated local level values is just the last value desired = initial_state[0] assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) # Alternatively, since we've shut down the shocks, we can compare against # the forecast values assert_allclose(actual, res.forecast(nsimulations)) def test_unobserved_components_end_time_invariant_shocks(reset_randomstate): # Test simulating values from the end of a time-invariant # UnobservedComponents model, with nonzero shocks endog = np.arange(1, 11) mod = structural.UnobservedComponents(endog, 'llevel') res = mod.filter([1., 1.]) nsimulations = 10 measurement_shocks = np.random.normal(size=nsimulations) state_shocks = np.random.normal(size=nsimulations) initial_state = res.predicted_state[:1, -1] actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) desired = (initial_state + np.cumsum(np.r_[0, state_shocks[:-1]]) + measurement_shocks) assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) def test_unobserved_components_end_time_varying_exog_noshocks(): # Test simulating values from the end of a time-varying # UnobservedComponents model with exog # In this test, we suppress randomness by setting the shocks to zeros endog = np.arange(1, 11) exog = np.arange(1, 21)**2 mod = structural.UnobservedComponents(endog, 'llevel', exog=exog[:10]) res = mod.filter([1., 1., 1.]) nsimulations = 10 measurement_shocks = np.zeros((nsimulations, mod.k_endog)) state_shocks = np.zeros((nsimulations, mod.k_states)) initial_state = res.predicted_state[..., -1] actual = res.simulate(nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # The mean of the simulated local level values is just the last value desired = initial_state[0] + exog[10:] assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) # Alternatively, since we've shut down the shocks, we can compare against # the forecast values assert_allclose(actual, res.forecast(nsimulations, exog=exog[10:])) def test_unobserved_components_end_time_varying_exog_shocks(reset_randomstate): # Test simulating values from the end of a time-varying # UnobservedComponents model with exog endog = np.arange(1, 11) exog = np.arange(1, 21)**2 mod = structural.UnobservedComponents(endog, 'llevel', exog=exog[:10]) res = mod.filter([1., 1., 1.]) nsimulations = 10 measurement_shocks = np.random.normal(size=nsimulations) state_shocks = np.random.normal(size=nsimulations) initial_state = res.predicted_state[:1, -1] actual = res.simulate(nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) desired = (initial_state + np.cumsum(np.r_[0, state_shocks[:-1]]) + measurement_shocks + exog[10:]) assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) def test_varmax_end_time_invariant_noshocks(): # Test simulating values from the end of a time-invariant VARMAX model # In this test, we suppress randomness by setting the shocks to zeros endog = np.arange(1, 21).reshape(10, 2) mod = varmax.VARMAX(endog, trend='n') res = mod.filter([1., 1., 1., 1., 1., 0.5, 1.]) nsimulations = 10 measurement_shocks = np.zeros((nsimulations, mod.k_endog)) state_shocks = np.zeros((nsimulations, mod.k_states)) initial_state = res.predicted_state[:, -1] actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) desired = (initial_state[:, None] * 2 ** np.arange(10)).T assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) # Alternatively, since we've shut down the shocks, we can compare against # the forecast values assert_allclose(actual, res.forecast(nsimulations)) def test_varmax_end_time_invariant_shocks(reset_randomstate): # Test simulating values from the end of a time-invariant VARMAX model, # with nonzero shocks endog = np.arange(1, 21).reshape(10, 2) mod = varmax.VARMAX(endog, trend='n') res = mod.filter([1., 1., 1., 1., 1., 0.5, 1.]) nsimulations = 10 measurement_shocks = np.random.normal(size=(nsimulations, mod.k_endog)) state_shocks = np.random.normal(size=(nsimulations, mod.k_states)) initial_state = res.predicted_state[:, -1] actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) desired = np.zeros((nsimulations, mod.k_endog)) desired[0] = initial_state for i in range(1, nsimulations): desired[i] = desired[i - 1].sum() + state_shocks[i - 1] desired = desired + measurement_shocks assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) def test_varmax_end_time_varying_trend_noshocks(): # Test simulating values from the end of a time-varying VARMAX model # with a trend # In this test, we suppress randomness by setting the shocks to zeros endog = np.arange(1, 21).reshape(10, 2) mod = varmax.VARMAX(endog, trend='ct') res = mod.filter([1., 1., 1., 1., 1, 1, 1., 1., 1., 0.5, 1.]) nsimulations = 10 measurement_shocks = np.zeros((nsimulations, mod.k_endog)) state_shocks = np.zeros((nsimulations, mod.k_states)) # Need to set the final predicted state given the new trend with res._set_final_predicted_state(exog=None, out_of_sample=10): initial_state = res.predicted_state[:, -1].copy() # Simulation actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) desired = np.zeros((nsimulations, mod.k_endog)) desired[0] = initial_state tmp_trend = 1 + np.arange(11, 21) for i in range(1, nsimulations): desired[i] = desired[i - 1].sum() + tmp_trend[i] + state_shocks[i - 1] desired = desired + measurement_shocks assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) # Alternatively, since we've shut down the shocks, we can compare against # the forecast values assert_allclose(actual, res.forecast(nsimulations)) def test_varmax_end_time_varying_trend_shocks(reset_randomstate): # Test simulating values from the end of a time-varying VARMAX model # with a trend endog = np.arange(1, 21).reshape(10, 2) mod = varmax.VARMAX(endog, trend='ct') res = mod.filter([1., 1., 1., 1., 1, 1, 1., 1., 1., 0.5, 1.]) nsimulations = 10 measurement_shocks = np.random.normal(size=(nsimulations, mod.k_endog)) state_shocks = np.random.normal(size=(nsimulations, mod.k_states)) # Need to set the final predicted state given the new trend with res._set_final_predicted_state(exog=None, out_of_sample=10): initial_state = res.predicted_state[:, -1].copy() # Simulation actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) desired = np.zeros((nsimulations, mod.k_endog)) desired[0] = initial_state tmp_trend = 1 + np.arange(11, 21) for i in range(1, nsimulations): desired[i] = desired[i - 1].sum() + tmp_trend[i] + state_shocks[i - 1] desired = desired + measurement_shocks assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) def test_varmax_end_time_varying_exog_noshocks(): # Test simulating values from the end of a time-varying VARMAX model # with exog # In this test, we suppress randomness by setting the shocks to zeros endog = np.arange(1, 21).reshape(10, 2) exog = np.arange(1, 21)**2 mod = varmax.VARMAX(endog, trend='n', exog=exog[:10]) res = mod.filter([1., 1., 1., 1., 1., 1., 1., 0.5, 1.]) nsimulations = 10 measurement_shocks = np.zeros((nsimulations, mod.k_endog)) state_shocks = np.zeros((nsimulations, mod.k_states)) # Need to set the final predicted state given the new exog tmp_exog = mod._validate_out_of_sample_exog(exog[10:], out_of_sample=10) with res._set_final_predicted_state(exog=tmp_exog, out_of_sample=10): initial_state = res.predicted_state[:, -1].copy() # Simulation actual = res.simulate(nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) desired = np.zeros((nsimulations, mod.k_endog)) desired[0] = initial_state for i in range(1, nsimulations): desired[i] = desired[i - 1].sum() + exog[10 + i] + state_shocks[i - 1] desired = desired + measurement_shocks assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) # Alternatively, since we've shut down the shocks, we can compare against # the forecast values assert_allclose(actual, res.forecast(nsimulations, exog=exog[10:])) def test_varmax_end_time_varying_exog_shocks(reset_randomstate): # Test simulating values from the end of a time-varying VARMAX model # with exog endog = np.arange(1, 23).reshape(11, 2) exog = np.arange(1, 21)**2 mod = varmax.VARMAX(endog[:10], trend='n', exog=exog[:10]) res = mod.filter([1., 1., 1., 1., 1., 1., 1., 0.5, 1.]) mod2 = varmax.VARMAX(endog, trend='n', exog=exog[:11]) res2 = mod2.filter([1., 1., 1., 1., 1., 1., 1., 0.5, 1.]) nsimulations = 10 measurement_shocks = np.random.normal(size=(nsimulations, mod.k_endog)) state_shocks = np.random.normal(size=(nsimulations, mod.k_states)) # Need to set the final predicted state given the new exog tmp_exog = mod._validate_out_of_sample_exog(exog[10:], out_of_sample=10) with res._set_final_predicted_state(exog=tmp_exog, out_of_sample=10): initial_state = res.predicted_state[:, -1].copy() # Simulation actual = res.simulate(nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) actual2 = res2.simulate(nsimulations, exog=exog[11:], anchor=-1, measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=res2.predicted_state[:, -2]) desired = np.zeros((nsimulations, mod.k_endog)) desired[0] = initial_state for i in range(1, nsimulations): desired[i] = desired[i - 1].sum() + exog[10 + i] + state_shocks[i - 1] desired = desired + measurement_shocks assert_allclose(actual, desired) assert_allclose(actual2, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) def test_dynamic_factor_end_time_invariant_noshocks(): # Test simulating values from the end of a time-invariant dynamic factor # In this test, we suppress randomness by setting the shocks to zeros endog = np.arange(1, 21).reshape(10, 2) mod = dynamic_factor.DynamicFactor(endog, k_factors=1, factor_order=1) mod.ssm.filter_univariate = True res = mod.filter([1., 1., 1., 1., 1.]) nsimulations = 10 measurement_shocks = np.zeros((nsimulations, mod.k_endog)) state_shocks = np.zeros((nsimulations, mod.k_states)) initial_state = res.predicted_state[..., -1] # Simulation actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # Construct the simulation directly desired = np.zeros((nsimulations, mod.k_endog)) desired[0] = initial_state for i in range(1, nsimulations): desired[i] = desired[i - 1] + state_shocks[i - 1] desired = desired + measurement_shocks assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) # Alternatively, since we've shut down the shocks, we can compare against # the forecast values assert_allclose(actual, res.forecast(nsimulations)) def test_dynamic_factor_end_time_invariant_shocks(reset_randomstate): # Test simulating values from the end of a time-invariant dynamic factor endog = np.arange(1, 21).reshape(10, 2) mod = dynamic_factor.DynamicFactor(endog, k_factors=1, factor_order=1) mod.ssm.filter_univariate = True res = mod.filter([1., 1., 1., 1., 1., 1., 1.]) nsimulations = 10 measurement_shocks = np.random.normal(size=(nsimulations, mod.k_endog)) state_shocks = np.random.normal(size=(nsimulations, mod.k_states)) initial_state = res.predicted_state[..., -1] # Simulation actual = res.simulate(nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # Construct the simulation directly desired = np.zeros((nsimulations, mod.k_endog)) desired[0] = initial_state for i in range(1, nsimulations): desired[i] = desired[i - 1] + state_shocks[i - 1] desired = desired + measurement_shocks assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) def test_dynamic_factor_end_time_varying_exog_noshocks(): # Test simulating values from the end of a time-varying dynamic factor # model with exogenous inputs # In this test, we suppress randomness by setting the shocks to zeros endog = np.arange(1, 21).reshape(10, 2) exog = np.arange(1, 21)**2 mod = dynamic_factor.DynamicFactor(endog, k_factors=1, factor_order=1, exog=exog[:10]) mod.ssm.filter_univariate = True res = mod.filter([1., 1., 1., 1., 1., 1., 1.]) nsimulations = 10 measurement_shocks = np.zeros((nsimulations, mod.k_endog)) state_shocks = np.zeros((nsimulations, mod.k_states)) initial_state = res.predicted_state[..., -1] # Simulation actual = res.simulate(nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # Construct the simulation directly desired = np.zeros((nsimulations, mod.k_endog)) desired[0] = initial_state for i in range(1, nsimulations): desired[i] = desired[i - 1] + state_shocks[i - 1] desired = desired + measurement_shocks + exog[10:, None] assert_allclose(actual, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) # Alternatively, since we've shut down the shocks, we can compare against # the forecast values assert_allclose(actual, res.forecast(nsimulations, exog=exog[10:])) def test_dynamic_factor_end_time_varying_exog_shocks(reset_randomstate): # Test simulating values from the end of a time-varying dynamic factor # model with exogenous inputs endog = np.arange(1, 23).reshape(11, 2) exog = np.arange(1, 21)**2 mod = dynamic_factor.DynamicFactor( endog[:10], k_factors=1, factor_order=1, exog=exog[:10]) mod.ssm.filter_univariate = True res = mod.filter([1., 1., 1., 1., 1., 1., 1.]) mod2 = dynamic_factor.DynamicFactor( endog, k_factors=1, factor_order=1, exog=exog[:11]) mod2.ssm.filter_univariate = True res2 = mod2.filter([1., 1., 1., 1., 1., 1., 1.]) nsimulations = 10 measurement_shocks = np.random.normal(size=(nsimulations, mod.k_endog)) state_shocks = np.random.normal(size=(nsimulations, mod.k_states)) initial_state = res.predicted_state[..., -1] # Simulations actual = res.simulate(nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) actual2 = res2.simulate(nsimulations, exog=exog[11:], anchor=-1, measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) # Construct the simulation directly desired = np.zeros((nsimulations, mod.k_endog)) desired[0] = initial_state for i in range(1, nsimulations): desired[i] = desired[i - 1] + state_shocks[i - 1] desired = desired + measurement_shocks + exog[10:, None] assert_allclose(actual, desired) assert_allclose(actual2, desired) # Test using the model versus the results class mod_actual = mod.simulate( res.params, nsimulations, exog=exog[10:], anchor='end', measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(mod_actual, desired) def test_pandas_univariate_rangeindex(): # Simulate will also have RangeIndex endog = pd.Series(np.zeros(2)) mod = sarimax.SARIMAX(endog) res = mod.filter([0.5, 1.]) # Default simulate anchors to the start of the sample actual = res.simulate(2, state_shocks=np.zeros(2), initial_state=np.zeros(1)) desired = pd.Series([0, 0]) assert_allclose(actual, desired) # Alternative anchor changes the index actual = res.simulate(2, anchor=2, state_shocks=np.zeros(2), initial_state=np.zeros(1)) ix = pd.RangeIndex(2, 4) desired = pd.Series([0, 0], index=ix) assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) def test_pandas_univariate_rangeindex_repetitions(): # Simulate will also have RangeIndex endog = pd.Series(np.zeros(2)) mod = sarimax.SARIMAX(endog) res = mod.filter([0.5, 1.]) # Default simulate anchors to the start of the sample actual = res.simulate(2, state_shocks=np.zeros(2), initial_state=np.zeros(1), repetitions=2) columns = pd.MultiIndex.from_product([['y'], [0, 1]]) desired = pd.DataFrame(np.zeros((2, 2)), columns=columns) assert_allclose(actual, desired) assert_(actual.columns.equals(desired.columns)) # Alternative anchor changes the index actual = res.simulate(2, anchor=2, state_shocks=np.zeros(2), initial_state=np.zeros(1), repetitions=2) ix = pd.RangeIndex(2, 4) columns = pd.MultiIndex.from_product([['y'], [0, 1]]) desired = pd.DataFrame(np.zeros((2, 2)), index=ix, columns=columns) assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) assert_(actual.columns.equals(desired.columns)) def test_pandas_univariate_dateindex(): # Simulation will maintain have date index ix = pd.date_range(start='2000', periods=2, freq='M') endog = pd.Series(np.zeros(2), index=ix) mod = sarimax.SARIMAX(endog) res = mod.filter([0.5, 1.]) # Default simulate anchors to the start of the sample actual = res.simulate(2, state_shocks=np.zeros(2), initial_state=np.zeros(1)) ix = pd.date_range(start='2000-01', periods=2, freq='M') desired = pd.Series([0, 0], index=ix) assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) # Alternative anchor changes the index actual = res.simulate(2, anchor=2, state_shocks=np.zeros(2), initial_state=np.zeros(1)) ix = pd.date_range(start='2000-03', periods=2, freq='M') desired = pd.Series([0, 0], index=ix) assert_allclose(actual, desired) def test_pandas_univariate_dateindex_repetitions(): # Simulation will maintain have date index ix = pd.date_range(start='2000', periods=2, freq='M') endog = pd.Series(np.zeros(2), index=ix) mod = sarimax.SARIMAX(endog) res = mod.filter([0.5, 1.]) # Default simulate anchors to the start of the sample actual = res.simulate(2, state_shocks=np.zeros(2), initial_state=np.zeros(1), repetitions=2) ix = pd.date_range(start='2000-01', periods=2, freq='M') columns = pd.MultiIndex.from_product([['y'], [0, 1]]) desired = pd.DataFrame(np.zeros((2, 2)), index=ix, columns=columns) assert_allclose(actual, desired) assert_(actual.columns.equals(desired.columns)) # Alternative anchor changes the index actual = res.simulate(2, anchor=2, state_shocks=np.zeros(2), initial_state=np.zeros(1), repetitions=2) ix = pd.date_range(start='2000-03', periods=2, freq='M') columns = pd.MultiIndex.from_product([['y'], [0, 1]]) desired = pd.DataFrame(np.zeros((2, 2)), index=ix, columns=columns) assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) assert_(actual.columns.equals(desired.columns)) def test_pandas_multivariate_rangeindex(): # Simulate will also have RangeIndex endog = pd.DataFrame(np.zeros((2, 2))) mod = varmax.VARMAX(endog, trend='n') res = mod.filter([0.5, 0., 0., 0.2, 1., 0., 1.]) # Default simulate anchors to the start of the sample actual = res.simulate(2, state_shocks=np.zeros((2, 2)), initial_state=np.zeros(2)) desired = pd.DataFrame(np.zeros((2, 2))) assert_allclose(actual, desired) # Alternative anchor changes the index actual = res.simulate(2, anchor=2, state_shocks=np.zeros((2, 2)), initial_state=np.zeros(2)) ix = pd.RangeIndex(2, 4) desired = pd.DataFrame(np.zeros((2, 2)), index=ix) assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) def test_pandas_multivariate_rangeindex_repetitions(): # Simulate will also have RangeIndex endog = pd.DataFrame(np.zeros((2, 2)), columns=['y1', 'y2']) mod = varmax.VARMAX(endog, trend='n') res = mod.filter([0.5, 0., 0., 0.2, 1., 0., 1.]) # Default simulate anchors to the start of the sample actual = res.simulate(2, state_shocks=np.zeros((2, 2)), initial_state=np.zeros(2), repetitions=2) columns = pd.MultiIndex.from_product([['y1', 'y2'], [0, 1]]) desired = pd.DataFrame(np.zeros((2, 4)), columns=columns) assert_allclose(actual, desired) assert_(actual.columns.equals(desired.columns)) # Alternative anchor changes the index actual = res.simulate(2, anchor=2, state_shocks=np.zeros((2, 2)), initial_state=np.zeros(2), repetitions=2) ix = pd.RangeIndex(2, 4) columns = pd.MultiIndex.from_product([['y1', 'y2'], [0, 1]]) desired = pd.DataFrame(np.zeros((2, 4)), index=ix, columns=columns) assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) assert_(actual.columns.equals(desired.columns)) def test_pandas_multivariate_dateindex(): # Simulate will also have RangeIndex ix = pd.date_range(start='2000', periods=2, freq='M') endog = pd.DataFrame(np.zeros((2, 2)), index=ix) mod = varmax.VARMAX(endog, trend='n') res = mod.filter([0.5, 0., 0., 0.2, 1., 0., 1.]) # Default simulate anchors to the start of the sample actual = res.simulate(2, state_shocks=np.zeros((2, 2)), initial_state=np.zeros(2)) desired = pd.DataFrame(np.zeros((2, 2)), index=ix) assert_allclose(actual, desired) # Alternative anchor changes the index actual = res.simulate(2, anchor=2, state_shocks=np.zeros((2, 2)), initial_state=np.zeros(2)) ix = pd.date_range(start='2000-03', periods=2, freq='M') desired = pd.DataFrame(np.zeros((2, 2)), index=ix) assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) def test_pandas_multivariate_dateindex_repetitions(): # Simulate will also have RangeIndex ix = pd.date_range(start='2000', periods=2, freq='M') endog = pd.DataFrame(np.zeros((2, 2)), columns=['y1', 'y2'], index=ix) mod = varmax.VARMAX(endog, trend='n') res = mod.filter([0.5, 0., 0., 0.2, 1., 0., 1.]) # Default simulate anchors to the start of the sample actual = res.simulate(2, state_shocks=np.zeros((2, 2)), initial_state=np.zeros(2), repetitions=2) columns = pd.MultiIndex.from_product([['y1', 'y2'], [0, 1]]) desired = pd.DataFrame(np.zeros((2, 4)), columns=columns, index=ix) assert_allclose(actual, desired) assert_(actual.columns.equals(desired.columns)) # Alternative anchor changes the index actual = res.simulate(2, anchor=2, state_shocks=np.zeros((2, 2)), initial_state=np.zeros(2), repetitions=2) ix = pd.date_range(start='2000-03', periods=2, freq='M') columns = pd.MultiIndex.from_product([['y1', 'y2'], [0, 1]]) desired = pd.DataFrame(np.zeros((2, 4)), index=ix, columns=columns) assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) assert_(actual.columns.equals(desired.columns)) def test_pandas_anchor(): # Test that anchor with dates works ix = pd.date_range(start='2000', periods=2, freq='M') endog = pd.Series(np.zeros(2), index=ix) mod = sarimax.SARIMAX(endog) res = mod.filter([0.5, 1.]) desired = res.simulate(2, anchor=1, state_shocks=np.zeros(2), initial_state=np.zeros(1)) # Anchor to date actual = res.simulate(2, anchor=ix[1], state_shocks=np.zeros(2), initial_state=np.zeros(1)) assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) # Anchor to negative index actual = res.simulate(2, anchor=-1, state_shocks=np.zeros(2), initial_state=np.zeros(1)) assert_allclose(actual, desired) assert_(actual.index.equals(desired.index)) @pytest.mark.smoke def test_time_varying(reset_randomstate): mod = TVSS(np.zeros((10, 2))) mod.simulate([], 10) def test_time_varying_obs_cov(reset_randomstate): mod = TVSS(np.zeros((10, 2))) mod['obs_cov'] = np.zeros((mod.k_endog, mod.k_endog, mod.nobs)) mod['obs_cov', ..., 9] = np.eye(mod.k_endog) mod['state_intercept', :] = 0 mod['state_cov'] = mod['state_cov', :, :, 0] * 0 mod['selection'] = mod['selection', :, :, 0] assert_equal(mod['state_cov'].shape, (mod.ssm.k_posdef, mod.ssm.k_posdef)) assert_equal(mod['selection'].shape, (mod.k_states, mod.ssm.k_posdef)) sim = mod.simulate([], 10, initial_state=np.zeros(mod.k_states)) assert_allclose(sim[:9], mod['obs_intercept', :, :9].T) def test_time_varying_state_cov(reset_randomstate): mod = TVSS(np.zeros((10, 2))) mod['obs_cov'] = mod['obs_cov', :, :, 0] * 0 mod['selection'] = mod['selection', :, :, 0] mod['state_intercept', :] = 0 mod['state_cov'] = np.zeros((mod.ssm.k_posdef, mod.ssm.k_posdef, mod.nobs)) mod['state_cov', ..., -1] = np.eye(mod.ssm.k_posdef) assert_equal(mod['obs_cov'].shape, (mod.k_endog, mod.k_endog)) assert_equal(mod['selection'].shape, (mod.k_states, mod.ssm.k_posdef)) sim = mod.simulate([], 10) assert_allclose(sim, mod['obs_intercept'].T) @pytest.mark.smoke def test_time_varying_selection(reset_randomstate): mod = TVSS(np.zeros((10, 2))) mod['obs_cov'] = mod['obs_cov', :, :, 0] mod['state_cov'] = mod['state_cov', :, :, 0] assert_equal(mod['obs_cov'].shape, (mod.k_endog, mod.k_endog)) assert_equal(mod['state_cov'].shape, (mod.ssm.k_posdef, mod.ssm.k_posdef)) mod.simulate([], 10) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_simulation_smoothing.py000066400000000000000000000670341400612667500304720ustar00rootroot00000000000000""" Tests for simulation smoothing Author: Chad Fulton License: Simplified-BSD """ import os import numpy as np from numpy.testing import assert_allclose, assert_equal import pandas as pd from statsmodels import datasets from statsmodels.tsa.statespace import mlemodel, sarimax, structural from statsmodels.tsa.statespace.simulation_smoother import ( SIMULATION_STATE, SIMULATION_DISTURBANCE, SIMULATION_ALL) current_path = os.path.dirname(os.path.abspath(__file__)) class MultivariateVARKnown(object): """ Tests for simulation smoothing values in a couple of special cases of variates. Both computed values and KFAS values are used for comparison against the simulation smoother output. """ @classmethod def setup_class(cls, missing=None, test_against_KFAS=True, *args, **kwargs): cls.test_against_KFAS = test_against_KFAS # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = np.log(dta[['realgdp', 'realcons', 'realinv']]).diff().iloc[1:] if missing == 'all': obs.iloc[0:50, :] = np.nan elif missing == 'partial': obs.iloc[0:50, 0] = np.nan elif missing == 'mixed': obs.iloc[0:50, 0] = np.nan obs.iloc[19:70, 1] = np.nan obs.iloc[39:90, 2] = np.nan obs.iloc[119:130, 0] = np.nan obs.iloc[119:130, 2] = np.nan obs.iloc[-10:, :] = np.nan if test_against_KFAS: obs = obs.iloc[:9] # Create the model mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs) mod['design'] = np.eye(3) mod['obs_cov'] = np.array([ [0.0000640649, 0., 0.], [0., 0.0000572802, 0.], [0., 0., 0.0017088585]]) mod['transition'] = np.array([ [-0.1119908792, 0.8441841604, 0.0238725303], [0.2629347724, 0.4996718412, -0.0173023305], [-3.2192369082, 4.1536028244, 0.4514379215]]) mod['selection'] = np.eye(3) mod['state_cov'] = np.array([ [0.0000640649, 0.0000388496, 0.0002148769], [0.0000388496, 0.0000572802, 0.000001555], [0.0002148769, 0.000001555, 0.0017088585]]) mod.initialize_approximate_diffuse(1e6) mod.ssm.filter_univariate = True cls.model = mod cls.results = mod.smooth([], return_ssm=True) cls.sim = cls.model.simulation_smoother() def test_loglike(self): assert_allclose(np.sum(self.results.llf_obs), self.true_llf) def test_simulate_0(self): n = 10 # Test with all inputs as zeros measurement_shocks = np.zeros((n, self.model.k_endog)) state_shocks = np.zeros((n, self.model.ssm.k_posdef)) initial_state = np.zeros(self.model.k_states) obs, states = self.model.ssm.simulate( nsimulations=n, measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(obs, np.zeros((n, self.model.k_endog))) assert_allclose(states, np.zeros((n, self.model.k_states))) def test_simulate_1(self): n = 10 # Test with np.arange / 10 measurement shocks only measurement_shocks = np.reshape( np.arange(n * self.model.k_endog) / 10., (n, self.model.k_endog)) state_shocks = np.zeros((n, self.model.ssm.k_posdef)) initial_state = np.zeros(self.model.k_states) obs, states = self.model.ssm.simulate( nsimulations=n, measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) assert_allclose(obs, np.reshape( np.arange(n * self.model.k_endog) / 10., (n, self.model.k_endog))) assert_allclose(states, np.zeros((n, self.model.k_states))) def test_simulate_2(self): n = 10 Z = self.model['design'] T = self.model['transition'] # Test with non-zero state shocks and initial state measurement_shocks = np.zeros((n, self.model.k_endog)) state_shocks = np.ones((n, self.model.ssm.k_posdef)) initial_state = np.ones(self.model.k_states) * 2.5 obs, states = self.model.ssm.simulate( nsimulations=n, measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state) desired_obs = np.zeros((n, self.model.k_endog)) desired_state = np.zeros((n, self.model.k_states)) desired_state[0] = initial_state desired_obs[0] = np.dot(Z, initial_state) for i in range(1, n): desired_state[i] = np.dot(T, desired_state[i-1]) + state_shocks[i] desired_obs[i] = np.dot(Z, desired_state[i]) assert_allclose(obs, desired_obs) assert_allclose(states, desired_state) def test_simulation_smoothing_0(self): # Simulation smoothing when setting all variates to zeros # In this case: # - unconditional disturbances are zero, because they are simply # transformed to have the appropriate variance matrix, but keep the # same mean - of zero # - generated states are zeros, because initial state is # zeros and all state disturbances are zeros # - generated observations are zeros, because states are zeros and all # measurement disturbances are zeros # - The simulated state is equal to the smoothed state from the # original model, because # simulated state = (generated state - smoothed generated state + # smoothed state) # and here generated state = smoothed generated state = 0 # - The simulated measurement disturbance is equal to the smoothed # measurement disturbance for very similar reasons, because # simulated measurement disturbance = ( # generated measurement disturbance - # smoothed generated measurement disturbance + # smoothed measurement disturbance) # and here generated measurement disturbance and # smoothed generated measurement disturbance are zero. # - The simulated state disturbance is equal to the smoothed # state disturbance for exactly the same reason as above. sim = self.sim Z = self.model['design'] n_disturbance_variates = ( (self.model.k_endog + self.model.ssm.k_posdef) * self.model.nobs) # Test against known quantities (see above for description) sim.simulate(disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(self.model.k_states)) assert_allclose(sim.generated_measurement_disturbance, 0) assert_allclose(sim.generated_state_disturbance, 0) assert_allclose(sim.generated_state, 0) assert_allclose(sim.generated_obs, 0) assert_allclose(sim.simulated_state, self.results.smoothed_state) if not self.model.ssm.filter_collapsed: assert_allclose(sim.simulated_measurement_disturbance, self.results.smoothed_measurement_disturbance) assert_allclose(sim.simulated_state_disturbance, self.results.smoothed_state_disturbance) # Test against R package KFAS values if self.test_against_KFAS: path = os.path.join(current_path, 'results', 'results_simulation_smoothing0.csv') true = pd.read_csv(path) assert_allclose(sim.simulated_state, true[['state1', 'state2', 'state3']].T, atol=1e-7) assert_allclose(sim.simulated_measurement_disturbance, true[['eps1', 'eps2', 'eps3']].T, atol=1e-7) assert_allclose(sim.simulated_state_disturbance, true[['eta1', 'eta2', 'eta3']].T, atol=1e-7) signals = np.zeros((3, self.model.nobs)) for t in range(self.model.nobs): signals[:, t] = np.dot(Z, sim.simulated_state[:, t]) assert_allclose(signals, true[['signal1', 'signal2', 'signal3']].T, atol=1e-7) def test_simulation_smoothing_1(self): # Test with measurement disturbance as np.arange / 10., all other # disturbances are zeros sim = self.sim Z = self.model['design'] # Construct the variates measurement_disturbance_variates = np.reshape( np.arange(self.model.nobs * self.model.k_endog) / 10., (self.model.nobs, self.model.k_endog)) disturbance_variates = np.r_[ measurement_disturbance_variates.ravel(), np.zeros(self.model.nobs * self.model.ssm.k_posdef)] # Compute some additional known quantities generated_measurement_disturbance = np.zeros( measurement_disturbance_variates.shape) chol = np.linalg.cholesky(self.model['obs_cov']) for t in range(self.model.nobs): generated_measurement_disturbance[t] = np.dot( chol, measurement_disturbance_variates[t]) generated_model = mlemodel.MLEModel( generated_measurement_disturbance, k_states=self.model.k_states, k_posdef=self.model.ssm.k_posdef) for name in ['design', 'obs_cov', 'transition', 'selection', 'state_cov']: generated_model[name] = self.model[name] generated_model.initialize_approximate_diffuse(1e6) generated_model.ssm.filter_univariate = True generated_res = generated_model.ssm.smooth() simulated_state = ( 0 - generated_res.smoothed_state + self.results.smoothed_state) if not self.model.ssm.filter_collapsed: simulated_measurement_disturbance = ( generated_measurement_disturbance.T - generated_res.smoothed_measurement_disturbance + self.results.smoothed_measurement_disturbance) simulated_state_disturbance = ( 0 - generated_res.smoothed_state_disturbance + self.results.smoothed_state_disturbance) # Test against known values sim.simulate(disturbance_variates=disturbance_variates, initial_state_variates=np.zeros(self.model.k_states)) assert_allclose(sim.generated_measurement_disturbance, generated_measurement_disturbance) assert_allclose(sim.generated_state_disturbance, 0) assert_allclose(sim.generated_state, 0) assert_allclose(sim.generated_obs, generated_measurement_disturbance.T) assert_allclose(sim.simulated_state, simulated_state) if not self.model.ssm.filter_collapsed: assert_allclose(sim.simulated_measurement_disturbance, simulated_measurement_disturbance) assert_allclose(sim.simulated_state_disturbance, simulated_state_disturbance) # Test against R package KFAS values if self.test_against_KFAS: path = os.path.join(current_path, 'results', 'results_simulation_smoothing1.csv') true = pd.read_csv(path) assert_allclose(sim.simulated_state, true[['state1', 'state2', 'state3']].T, atol=1e-7) assert_allclose(sim.simulated_measurement_disturbance, true[['eps1', 'eps2', 'eps3']].T, atol=1e-7) assert_allclose(sim.simulated_state_disturbance, true[['eta1', 'eta2', 'eta3']].T, atol=1e-7) signals = np.zeros((3, self.model.nobs)) for t in range(self.model.nobs): signals[:, t] = np.dot(Z, sim.simulated_state[:, t]) assert_allclose(signals, true[['signal1', 'signal2', 'signal3']].T, atol=1e-7) def test_simulation_smoothing_2(self): # Test with measurement and state disturbances as np.arange / 10., # initial state variates are zeros. sim = self.sim Z = self.model['design'] T = self.model['transition'] # Construct the variates measurement_disturbance_variates = np.reshape( np.arange(self.model.nobs * self.model.k_endog) / 10., (self.model.nobs, self.model.k_endog)) state_disturbance_variates = np.reshape( np.arange(self.model.nobs * self.model.ssm.k_posdef) / 10., (self.model.nobs, self.model.ssm.k_posdef)) disturbance_variates = np.r_[ measurement_disturbance_variates.ravel(), state_disturbance_variates.ravel()] initial_state_variates = np.zeros(self.model.k_states) # Compute some additional known quantities generated_measurement_disturbance = np.zeros( measurement_disturbance_variates.shape) chol = np.linalg.cholesky(self.model['obs_cov']) for t in range(self.model.nobs): generated_measurement_disturbance[t] = np.dot( chol, measurement_disturbance_variates[t]) generated_state_disturbance = np.zeros( state_disturbance_variates.shape) chol = np.linalg.cholesky(self.model['state_cov']) for t in range(self.model.nobs): generated_state_disturbance[t] = np.dot( chol, state_disturbance_variates[t]) generated_obs = np.zeros((self.model.k_endog, self.model.nobs)) generated_state = np.zeros((self.model.k_states, self.model.nobs+1)) chol = np.linalg.cholesky(self.results.initial_state_cov) generated_state[:, 0] = ( self.results.initial_state + np.dot(chol, initial_state_variates)) for t in range(self.model.nobs): generated_state[:, t+1] = (np.dot(T, generated_state[:, t]) + generated_state_disturbance.T[:, t]) generated_obs[:, t] = (np.dot(Z, generated_state[:, t]) + generated_measurement_disturbance.T[:, t]) generated_model = mlemodel.MLEModel( generated_obs.T, k_states=self.model.k_states, k_posdef=self.model.ssm.k_posdef) for name in ['design', 'obs_cov', 'transition', 'selection', 'state_cov']: generated_model[name] = self.model[name] generated_model.initialize_approximate_diffuse(1e6) generated_model.ssm.filter_univariate = True generated_res = generated_model.ssm.smooth() simulated_state = ( generated_state[:, :-1] - generated_res.smoothed_state + self.results.smoothed_state) if not self.model.ssm.filter_collapsed: simulated_measurement_disturbance = ( generated_measurement_disturbance.T - generated_res.smoothed_measurement_disturbance + self.results.smoothed_measurement_disturbance) simulated_state_disturbance = ( generated_state_disturbance.T - generated_res.smoothed_state_disturbance + self.results.smoothed_state_disturbance) # Test against known values sim.simulate(disturbance_variates=disturbance_variates, initial_state_variates=np.zeros(self.model.k_states)) assert_allclose(sim.generated_measurement_disturbance, generated_measurement_disturbance) assert_allclose(sim.generated_state_disturbance, generated_state_disturbance) assert_allclose(sim.generated_state, generated_state) assert_allclose(sim.generated_obs, generated_obs) assert_allclose(sim.simulated_state, simulated_state) if not self.model.ssm.filter_collapsed: assert_allclose(sim.simulated_measurement_disturbance.T, simulated_measurement_disturbance.T) assert_allclose(sim.simulated_state_disturbance, simulated_state_disturbance) # Test against R package KFAS values if self.test_against_KFAS: path = os.path.join(current_path, 'results', 'results_simulation_smoothing2.csv') true = pd.read_csv(path) assert_allclose(sim.simulated_state.T, true[['state1', 'state2', 'state3']], atol=1e-7) assert_allclose(sim.simulated_measurement_disturbance, true[['eps1', 'eps2', 'eps3']].T, atol=1e-7) assert_allclose(sim.simulated_state_disturbance, true[['eta1', 'eta2', 'eta3']].T, atol=1e-7) signals = np.zeros((3, self.model.nobs)) for t in range(self.model.nobs): signals[:, t] = np.dot(Z, sim.simulated_state[:, t]) assert_allclose(signals, true[['signal1', 'signal2', 'signal3']].T, atol=1e-7) class TestMultivariateVARKnown(MultivariateVARKnown): @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariateVARKnown, cls).setup_class() cls.true_llf = 39.01246166 class TestMultivariateVARKnownMissingAll(MultivariateVARKnown): """ Notes ----- Cannot test against KFAS because they have a different behavior for missing entries. When an entry is missing, KFAS does not draw a simulation smoothed value for that entry, whereas we draw from the unconditional distribution. It appears there is nothing to definitively recommend one approach over the other, but it makes it difficult to line up the variates correctly in order to replicate results. """ @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariateVARKnownMissingAll, cls).setup_class( missing='all', test_against_KFAS=False) cls.true_llf = 1305.739288 class TestMultivariateVARKnownMissingPartial(MultivariateVARKnown): @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariateVARKnownMissingPartial, cls).setup_class( missing='partial', test_against_KFAS=False) cls.true_llf = 1518.449598 class TestMultivariateVARKnownMissingMixed(MultivariateVARKnown): @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariateVARKnownMissingMixed, cls).setup_class( missing='mixed', test_against_KFAS=False) cls.true_llf = 1117.265303 class TestDFM(TestMultivariateVARKnown): test_against_KFAS = False @classmethod def setup_class(cls, which='none', *args, **kwargs): # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') levels = dta[['realgdp', 'realcons', 'realinv']] obs = np.log(levels).diff().iloc[1:] * 400 if which == 'all': obs.iloc[:50, :] = np.nan obs.iloc[119:130, :] = np.nan elif which == 'partial': obs.iloc[0:50, 0] = np.nan obs.iloc[119:130, 0] = np.nan elif which == 'mixed': obs.iloc[0:50, 0] = np.nan obs.iloc[19:70, 1] = np.nan obs.iloc[39:90, 2] = np.nan obs.iloc[119:130, 0] = np.nan obs.iloc[119:130, 2] = np.nan # Create the model with typical state space mod = mlemodel.MLEModel(obs, k_states=2, k_posdef=2, **kwargs) mod['design'] = np.array([[-32.47143586, 17.33779024], [-7.40264169, 1.69279859], [-209.04702853, 125.2879374]]) mod['obs_cov'] = np.diag( np.array([0.0622668, 1.95666886, 58.37473642])) mod['transition'] = np.array([[0.29935707, 0.33289005], [-0.7639868, 1.2844237]]) mod['selection'] = np.eye(2) mod['state_cov'] = np.array([[1.2, -0.25], [-0.25, 1.1]]) mod.initialize_approximate_diffuse(1e6) mod.ssm.filter_univariate = True mod.ssm.filter_collapsed = True cls.model = mod cls.results = mod.smooth([], return_ssm=True) cls.sim = cls.model.simulation_smoother() def test_loglike(self): pass class MultivariateVAR(object): """ More generic tests for simulation smoothing; use actual N(0,1) variates """ @classmethod def setup_class(cls, missing='none', *args, **kwargs): # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = np.log(dta[['realgdp', 'realcons', 'realinv']]).diff().iloc[1:] if missing == 'all': obs.iloc[0:50, :] = np.nan elif missing == 'partial': obs.iloc[0:50, 0] = np.nan elif missing == 'mixed': obs.iloc[0:50, 0] = np.nan obs.iloc[19:70, 1] = np.nan obs.iloc[39:90, 2] = np.nan obs.iloc[119:130, 0] = np.nan obs.iloc[119:130, 2] = np.nan obs.iloc[-10:, :] = np.nan # Create the model mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs) mod['design'] = np.eye(3) mod['obs_cov'] = np.array([ [0.0000640649, 0., 0.], [0., 0.0000572802, 0.], [0., 0., 0.0017088585]]) mod['transition'] = np.array([ [-0.1119908792, 0.8441841604, 0.0238725303], [0.2629347724, 0.4996718412, -0.0173023305], [-3.2192369082, 4.1536028244, 0.4514379215]]) mod['selection'] = np.eye(3) mod['state_cov'] = np.array([ [0.0000640649, 0.0000388496, 0.0002148769], [0.0000388496, 0.0000572802, 0.000001555], [0.0002148769, 0.000001555, 0.0017088585]]) mod.initialize_approximate_diffuse(1e6) mod.ssm.filter_univariate = True cls.model = mod cls.results = mod.smooth([], return_ssm=True) cls.sim = cls.model.simulation_smoother() def test_loglike(self): assert_allclose(np.sum(self.results.llf_obs), self.true_llf) def test_simulation_smoothing(self): sim = self.sim Z = self.model['design'] # Simulate with known variates sim.simulate(disturbance_variates=self.variates[:-3], initial_state_variates=self.variates[-3:]) # Test against R package KFAS values assert_allclose(sim.simulated_state.T, self.true[['state1', 'state2', 'state3']], atol=1e-7) assert_allclose(sim.simulated_measurement_disturbance, self.true[['eps1', 'eps2', 'eps3']].T, atol=1e-7) assert_allclose(sim.simulated_state_disturbance, self.true[['eta1', 'eta2', 'eta3']].T, atol=1e-7) signals = np.zeros((3, self.model.nobs)) for t in range(self.model.nobs): signals[:, t] = np.dot(Z, sim.simulated_state[:, t]) assert_allclose(signals, self.true[['signal1', 'signal2', 'signal3']].T, atol=1e-7) class TestMultivariateVAR(MultivariateVAR): @classmethod def setup_class(cls): super(TestMultivariateVAR, cls).setup_class() path = os.path.join(current_path, 'results', 'results_simulation_smoothing3_variates.csv') cls.variates = pd.read_csv(path).values.squeeze() path = os.path.join(current_path, 'results', 'results_simulation_smoothing3.csv') cls.true = pd.read_csv(path) cls.true_llf = 1695.34872 def test_misc(): # Create the model and simulation smoother dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = np.log(dta[['realgdp', 'realcons', 'realinv']]).diff().iloc[1:] mod = sarimax.SARIMAX(obs['realgdp'], order=(1, 0, 0)) mod['design', 0, 0] = 0. mod['obs_cov', 0, 0] = 1. mod.update(np.r_[1., 1.]) sim = mod.simulation_smoother() # Test that the simulation smoother is drawing variates correctly np.random.seed(1234) n_disturbance_variates = mod.nobs * (mod.k_endog + mod.k_states) variates = np.random.normal(size=n_disturbance_variates) np.random.seed(1234) sim.simulate() assert_allclose(sim.generated_measurement_disturbance[:, 0], variates[:mod.nobs]) assert_allclose(sim.generated_state_disturbance[:, 0], variates[mod.nobs:]) # Test that we can change the options of the simulations smoother assert_equal(sim.simulation_output, mod.ssm.smoother_output) sim.simulation_output = 0 assert_equal(sim.simulation_output, 0) sim.simulate_state = True assert_equal(sim.simulation_output, SIMULATION_STATE) sim.simulate_state = False assert_equal(sim.simulation_output, 0) sim.simulate_disturbance = True assert_equal(sim.simulation_output, SIMULATION_DISTURBANCE) sim.simulate_disturbance = False assert_equal(sim.simulation_output, 0) sim.simulate_all = True assert_equal(sim.simulation_output, SIMULATION_ALL) sim.simulate_all = False assert_equal(sim.simulation_output, 0) def test_simulation_smoothing_obs_intercept(): nobs = 10 intercept = 100 endog = np.ones(nobs) * intercept mod = structural.UnobservedComponents(endog, 'rwalk', exog=np.ones(nobs)) mod.update([1, intercept]) sim = mod.simulation_smoother() sim.simulate(disturbance_variates=np.zeros(mod.nobs * 2), initial_state_variates=np.zeros(1)) assert_equal(sim.simulated_state[0], 0) def test_simulation_smoothing_state_intercept(): nobs = 10 intercept = 100 endog = np.ones(nobs) * intercept mod = sarimax.SARIMAX(endog, order=(0, 0, 0), trend='c', measurement_error=True) mod.initialize_known([100], [[0]]) mod.update([intercept, 1., 1.]) sim = mod.simulation_smoother() sim.simulate(disturbance_variates=np.zeros(mod.nobs * 2), initial_state_variates=np.zeros(1)) assert_equal(sim.simulated_state[0], intercept) def test_simulation_smoothing_state_intercept_diffuse(): nobs = 10 intercept = 100 endog = np.ones(nobs) * intercept # Test without missing values mod = sarimax.SARIMAX(endog, order=(0, 0, 0), trend='c', measurement_error=True, initialization='diffuse') mod.update([intercept, 1., 1.]) sim = mod.simulation_smoother() sim.simulate(disturbance_variates=np.zeros(mod.nobs * 2), initial_state_variates=np.zeros(1)) assert_equal(sim.simulated_state[0], intercept) # Test with missing values endog[5] = np.nan mod = sarimax.SARIMAX(endog, order=(0, 0, 0), trend='c', measurement_error=True, initialization='diffuse') mod.update([intercept, 1., 1.]) sim = mod.simulation_smoother() sim.simulate(disturbance_variates=np.zeros(mod.nobs * 2), initial_state_variates=np.zeros(1)) assert_equal(sim.simulated_state[0], intercept) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_smoothing.py000066400000000000000000001710351400612667500262230ustar00rootroot00000000000000r""" Tests for smoothing and estimation of unobserved states and disturbances - Predicted states: :math:`E(\alpha_t | Y_{t-1})` - Filtered states: :math:`E(\alpha_t | Y_t)` - Smoothed states: :math:`E(\alpha_t | Y_n)` - Smoothed disturbances :math:`E(\varepsilon_t | Y_n), E(\eta_t | Y_n)` Tested against R (FKF, KalmanRun / KalmanSmooth), Stata (sspace), and MATLAB (ssm toolbox) Author: Chad Fulton License: Simplified-BSD """ import os import numpy as np from numpy.testing import assert_allclose, assert_almost_equal, assert_equal import pandas as pd import pytest from statsmodels import datasets from statsmodels.tsa.statespace import mlemodel, sarimax, varmax from statsmodels.tsa.statespace.tests.test_impulse_responses import TVSS from statsmodels.tsa.statespace.kalman_filter import FILTER_UNIVARIATE from statsmodels.tsa.statespace.kalman_smoother import ( SMOOTH_CLASSICAL, SMOOTH_ALTERNATIVE, SMOOTH_UNIVARIATE) current_path = os.path.dirname(os.path.abspath(__file__)) class TestStatesAR3(object): @classmethod def setup_class(cls, alternate_timing=False, *args, **kwargs): # Dataset / Stata comparison path = os.path.join(current_path, 'results', 'results_wpi1_ar3_stata.csv') cls.stata = pd.read_csv(path) cls.stata.index = pd.date_range(start='1960-01-01', periods=124, freq='QS') # Matlab comparison path = os.path.join(current_path, 'results', 'results_wpi1_ar3_matlab_ssm.csv') matlab_names = [ 'a1', 'a2', 'a3', 'detP', 'alphahat1', 'alphahat2', 'alphahat3', 'detV', 'eps', 'epsvar', 'eta', 'etavar' ] cls.matlab_ssm = pd.read_csv(path, header=None, names=matlab_names) cls.model = sarimax.SARIMAX( cls.stata['wpi'], order=(3, 1, 0), simple_differencing=True, hamilton_representation=True, *args, **kwargs ) if alternate_timing: cls.model.ssm.timing_init_filtered = True # Parameters from from Stata's sspace MLE estimation params = np.r_[.5270715, .0952613, .2580355, .5307459] cls.results = cls.model.smooth(params, cov_type='none') # Calculate the determinant of the covariance matrices (for easy # comparison to other languages without having to store 2-dim arrays) cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs)) for i in range(cls.model.nobs): cls.results.det_predicted_state_cov[0, i] = np.linalg.det( cls.results.filter_results.predicted_state_cov[:, :, i]) cls.results.det_smoothed_state_cov[0, i] = np.linalg.det( cls.results.smoother_results.smoothed_state_cov[:, :, i]) # Perform simulation smoothing n_disturbance_variates = ( (cls.model.k_endog + cls.model.ssm.k_posdef) * cls.model.nobs ) cls.sim = cls.model.simulation_smoother(filter_timing=0) cls.sim.simulate( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) def test_predict_obs(self): assert_almost_equal( self.results.filter_results.predict().forecasts[0], self.stata.iloc[1:]['dep1'], 4 ) def test_standardized_residuals(self): assert_almost_equal( self.results.filter_results.standardized_forecasts_error[0], self.stata.iloc[1:]['sr1'], 4 ) def test_predicted_states(self): assert_almost_equal( self.results.filter_results.predicted_state[:, :-1].T, self.stata.iloc[1:][['sp1', 'sp2', 'sp3']], 4 ) assert_almost_equal( self.results.filter_results.predicted_state[:, :-1].T, self.matlab_ssm[['a1', 'a2', 'a3']], 4 ) def test_predicted_states_cov(self): assert_almost_equal( self.results.det_predicted_state_cov.T, self.matlab_ssm[['detP']], 4 ) def test_filtered_states(self): assert_almost_equal( self.results.filter_results.filtered_state.T, self.stata.iloc[1:][['sf1', 'sf2', 'sf3']], 4 ) def test_smoothed_states(self): assert_almost_equal( self.results.smoother_results.smoothed_state.T, self.stata.iloc[1:][['sm1', 'sm2', 'sm3']], 4 ) assert_almost_equal( self.results.smoother_results.smoothed_state.T, self.matlab_ssm[['alphahat1', 'alphahat2', 'alphahat3']], 4 ) def test_smoothed_states_cov(self): assert_almost_equal( self.results.det_smoothed_state_cov.T, self.matlab_ssm[['detV']], 4 ) def test_smoothed_measurement_disturbance(self): assert_almost_equal( self.results.smoother_results.smoothed_measurement_disturbance.T, self.matlab_ssm[['eps']], 4 ) def test_smoothed_measurement_disturbance_cov(self): res = self.results.smoother_results assert_almost_equal( res.smoothed_measurement_disturbance_cov[0].T, self.matlab_ssm[['epsvar']], 4 ) def test_smoothed_state_disturbance(self): assert_almost_equal( self.results.smoother_results.smoothed_state_disturbance.T, self.matlab_ssm[['eta']], 4 ) def test_smoothed_state_disturbance_cov(self): assert_almost_equal( self.results.smoother_results.smoothed_state_disturbance_cov[0].T, self.matlab_ssm[['etavar']], 4 ) class TestStatesAR3AlternateTiming(TestStatesAR3): @classmethod def setup_class(cls, *args, **kwargs): super(TestStatesAR3AlternateTiming, cls).setup_class( alternate_timing=True, *args, **kwargs) class TestStatesAR3AlternativeSmoothing(TestStatesAR3): @classmethod def setup_class(cls, *args, **kwargs): super(TestStatesAR3AlternativeSmoothing, cls).setup_class( smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs) def test_smoothed_states(self): # Initialization issues can change the first few smoothed states assert_almost_equal( self.results.smoother_results.smoothed_state.T[2:], self.stata.iloc[3:][['sm1', 'sm2', 'sm3']], 4 ) assert_almost_equal( self.results.smoother_results.smoothed_state.T[2:], self.matlab_ssm.iloc[2:][['alphahat1', 'alphahat2', 'alphahat3']], 4 ) def test_smoothed_states_cov(self): assert_almost_equal( self.results.det_smoothed_state_cov.T[1:], self.matlab_ssm.iloc[1:][['detV']], 4 ) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_ALTERNATIVE) class TestStatesAR3UnivariateSmoothing(TestStatesAR3): @classmethod def setup_class(cls, *args, **kwargs): super(TestStatesAR3UnivariateSmoothing, cls).setup_class( filter_method=FILTER_UNIVARIATE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_UNIVARIATE) class TestStatesMissingAR3(object): @classmethod def setup_class(cls, alternate_timing=False, *args, **kwargs): # Dataset path = os.path.join(current_path, 'results', 'results_wpi1_ar3_stata.csv') cls.stata = pd.read_csv(path) cls.stata.index = pd.date_range(start='1960-01-01', periods=124, freq='QS') # Matlab comparison path = os.path.join(current_path, 'results', 'results_wpi1_missing_ar3_matlab_ssm.csv') matlab_names = [ 'a1', 'a2', 'a3', 'detP', 'alphahat1', 'alphahat2', 'alphahat3', 'detV', 'eps', 'epsvar', 'eta', 'etavar' ] cls.matlab_ssm = pd.read_csv(path, header=None, names=matlab_names) # KFAS comparison path = os.path.join(current_path, 'results', 'results_smoothing3_R.csv') cls.R_ssm = pd.read_csv(path) # Create missing observations cls.stata['dwpi'] = cls.stata['wpi'].diff() cls.stata.loc[cls.stata.index[10:21], 'dwpi'] = np.nan cls.model = sarimax.SARIMAX( cls.stata.loc[cls.stata.index[1:], 'dwpi'], order=(3, 0, 0), hamilton_representation=True, *args, **kwargs ) if alternate_timing: cls.model.ssm.timing_init_filtered = True # Parameters from from Stata's sspace MLE estimation params = np.r_[.5270715, .0952613, .2580355, .5307459] cls.results = cls.model.smooth(params, return_ssm=True) # Calculate the determinant of the covariance matrices (for easy # comparison to other languages without having to store 2-dim arrays) cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs)) for i in range(cls.model.nobs): cls.results.det_predicted_state_cov[0, i] = np.linalg.det( cls.results.predicted_state_cov[:, :, i]) cls.results.det_smoothed_state_cov[0, i] = np.linalg.det( cls.results.smoothed_state_cov[:, :, i]) # Perform simulation smoothing n_disturbance_variates = ( (cls.model.k_endog + cls.model.k_posdef) * cls.model.nobs ) cls.sim = cls.model.simulation_smoother() cls.sim.simulate( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) def test_predicted_states(self): assert_almost_equal( self.results.predicted_state[:, :-1].T, self.matlab_ssm[['a1', 'a2', 'a3']], 4 ) def test_predicted_states_cov(self): assert_almost_equal( self.results.det_predicted_state_cov.T, self.matlab_ssm[['detP']], 4 ) def test_smoothed_states(self): assert_almost_equal( self.results.smoothed_state.T, self.matlab_ssm[['alphahat1', 'alphahat2', 'alphahat3']], 4 ) def test_smoothed_states_cov(self): assert_almost_equal( self.results.det_smoothed_state_cov.T, self.matlab_ssm[['detV']], 4 ) def test_smoothed_measurement_disturbance(self): assert_almost_equal( self.results.smoothed_measurement_disturbance.T, self.matlab_ssm[['eps']], 4 ) def test_smoothed_measurement_disturbance_cov(self): assert_almost_equal( self.results.smoothed_measurement_disturbance_cov[0].T, self.matlab_ssm[['epsvar']], 4 ) # There is a discrepancy between MATLAB ssm toolbox and # statsmodels.tsa.statespace on the following variables in the case of # missing data. Tests against the R package KFAS confirm our results def test_smoothed_state_disturbance(self): # See note above about why this assertion is invalid # assert_almost_equal( # self.results.smoothed_state_disturbance.T, # self.matlab_ssm[['eta']], 4 # ) assert_almost_equal( self.results.smoothed_state_disturbance.T, self.R_ssm[['etahat']], 9 ) def test_smoothed_state_disturbance_cov(self): # See note above about why this assertion is invalid # assert_almost_equal( # self.results.smoothed_state_disturbance_cov[0].T, # self.matlab_ssm[['etavar']], 4 # ) assert_almost_equal( self.results.smoothed_state_disturbance_cov[0, 0, :], self.R_ssm['detVeta'], 9 ) class TestStatesMissingAR3AlternateTiming(TestStatesMissingAR3): @classmethod def setup_class(cls, *args, **kwargs): super(TestStatesMissingAR3AlternateTiming, cls).setup_class(alternate_timing=True, *args, **kwargs) class TestStatesMissingAR3AlternativeSmoothing(TestStatesMissingAR3): @classmethod def setup_class(cls, *args, **kwargs): super(TestStatesMissingAR3AlternativeSmoothing, cls).setup_class( smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_ALTERNATIVE) class TestStatesMissingAR3UnivariateSmoothing(TestStatesMissingAR3): @classmethod def setup_class(cls, *args, **kwargs): super(TestStatesMissingAR3UnivariateSmoothing, cls).setup_class( filter_method=FILTER_UNIVARIATE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_UNIVARIATE) class TestMultivariateMissing(object): """ Tests for most filtering and smoothing variables against output from the R library KFAS. Note that KFAS uses the univariate approach which generally will result in different predicted values and covariance matrices associated with the measurement equation (e.g. forecasts, etc.). In this case, although the model is multivariate, each of the series is truly independent so the values will be the same regardless of whether the univariate approach is used or not. """ @classmethod def setup_class(cls, **kwargs): # Results path = os.path.join(current_path, 'results', 'results_smoothing_R.csv') cls.desired = pd.read_csv(path) # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = dta[['realgdp', 'realcons', 'realinv']].diff().iloc[1:] obs.iloc[0:50, 0] = np.nan obs.iloc[19:70, 1] = np.nan obs.iloc[39:90, 2] = np.nan obs.iloc[119:130, 0] = np.nan obs.iloc[119:130, 2] = np.nan # Create the model mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs) mod['design'] = np.eye(3) mod['obs_cov'] = np.eye(3) mod['transition'] = np.eye(3) mod['selection'] = np.eye(3) mod['state_cov'] = np.eye(3) mod.initialize_approximate_diffuse(1e6) cls.model = mod cls.results = mod.smooth([], return_ssm=True) # Calculate the determinant of the covariance matrices (for easy # comparison to other languages without having to store 2-dim arrays) cls.results.det_scaled_smoothed_estimator_cov = ( np.zeros((1, cls.model.nobs))) cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_disturbance_cov = ( np.zeros((1, cls.model.nobs))) for i in range(cls.model.nobs): cls.results.det_scaled_smoothed_estimator_cov[0, i] = ( np.linalg.det( cls.results.scaled_smoothed_estimator_cov[:, :, i])) cls.results.det_predicted_state_cov[0, i] = np.linalg.det( cls.results.predicted_state_cov[:, :, i+1]) cls.results.det_smoothed_state_cov[0, i] = np.linalg.det( cls.results.smoothed_state_cov[:, :, i]) cls.results.det_smoothed_state_disturbance_cov[0, i] = ( np.linalg.det( cls.results.smoothed_state_disturbance_cov[:, :, i])) def test_loglike(self): assert_allclose(np.sum(self.results.llf_obs), -205310.9767) def test_scaled_smoothed_estimator(self): assert_allclose( self.results.scaled_smoothed_estimator.T, self.desired[['r1', 'r2', 'r3']] ) def test_scaled_smoothed_estimator_cov(self): assert_allclose( self.results.det_scaled_smoothed_estimator_cov.T, self.desired[['detN']] ) def test_forecasts(self): assert_allclose( self.results.forecasts.T, self.desired[['m1', 'm2', 'm3']] ) def test_forecasts_error(self): assert_allclose( self.results.forecasts_error.T, self.desired[['v1', 'v2', 'v3']] ) def test_forecasts_error_cov(self): assert_allclose( self.results.forecasts_error_cov.diagonal(), self.desired[['F1', 'F2', 'F3']] ) def test_predicted_states(self): assert_allclose( self.results.predicted_state[:, 1:].T, self.desired[['a1', 'a2', 'a3']] ) def test_predicted_states_cov(self): assert_allclose( self.results.det_predicted_state_cov.T, self.desired[['detP']] ) def test_smoothed_states(self): assert_allclose( self.results.smoothed_state.T, self.desired[['alphahat1', 'alphahat2', 'alphahat3']] ) def test_smoothed_states_cov(self): assert_allclose( self.results.det_smoothed_state_cov.T, self.desired[['detV']] ) def test_smoothed_forecasts(self): assert_allclose( self.results.smoothed_forecasts.T, self.desired[['muhat1', 'muhat2', 'muhat3']] ) def test_smoothed_state_disturbance(self): assert_allclose( self.results.smoothed_state_disturbance.T, self.desired[['etahat1', 'etahat2', 'etahat3']] ) def test_smoothed_state_disturbance_cov(self): assert_allclose( self.results.det_smoothed_state_disturbance_cov.T, self.desired[['detVeta']] ) def test_smoothed_measurement_disturbance(self): assert_allclose( self.results.smoothed_measurement_disturbance.T, self.desired[['epshat1', 'epshat2', 'epshat3']] ) def test_smoothed_measurement_disturbance_cov(self): assert_allclose( self.results.smoothed_measurement_disturbance_cov.diagonal(), self.desired[['Veps1', 'Veps2', 'Veps3']] ) class TestMultivariateMissingClassicalSmoothing(TestMultivariateMissing): @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariateMissingClassicalSmoothing, cls).setup_class( smooth_method=SMOOTH_CLASSICAL, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_CLASSICAL) class TestMultivariateMissingAlternativeSmoothing(TestMultivariateMissing): @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariateMissingAlternativeSmoothing, cls).setup_class( smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_ALTERNATIVE) class TestMultivariateMissingUnivariateSmoothing(TestMultivariateMissing): @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariateMissingUnivariateSmoothing, cls).setup_class( filter_method=FILTER_UNIVARIATE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_UNIVARIATE) class TestMultivariateVAR(object): """ Tests for most filtering and smoothing variables against output from the R library KFAS. Note that KFAS uses the univariate approach which generally will result in different predicted values and covariance matrices associated with the measurement equation (e.g. forecasts, etc.). In this case, although the model is multivariate, each of the series is truly independent so the values will be the same regardless of whether the univariate approach is used or not. """ @classmethod def setup_class(cls, *args, **kwargs): # Results path = os.path.join(current_path, 'results', 'results_smoothing2_R.csv') cls.desired = pd.read_csv(path) # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = np.log(dta[['realgdp', 'realcons', 'realinv']]).diff().iloc[1:] # Create the model mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs) mod['design'] = np.eye(3) mod['obs_cov'] = np.array([ [0.0000640649, 0., 0.], [0., 0.0000572802, 0.], [0., 0., 0.0017088585]]) mod['transition'] = np.array([ [-0.1119908792, 0.8441841604, 0.0238725303], [0.2629347724, 0.4996718412, -0.0173023305], [-3.2192369082, 4.1536028244, 0.4514379215]]) mod['selection'] = np.eye(3) mod['state_cov'] = np.array([ [0.0000640649, 0.0000388496, 0.0002148769], [0.0000388496, 0.0000572802, 0.000001555], [0.0002148769, 0.000001555, 0.0017088585]]) mod.initialize_approximate_diffuse(1e6) cls.model = mod cls.results = mod.smooth([], return_ssm=True) # Calculate the determinant of the covariance matrices (for easy # comparison to other languages without having to store 2-dim arrays) cls.results.det_scaled_smoothed_estimator_cov = ( np.zeros((1, cls.model.nobs))) cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_disturbance_cov = ( np.zeros((1, cls.model.nobs))) for i in range(cls.model.nobs): cls.results.det_scaled_smoothed_estimator_cov[0, i] = ( np.linalg.det( cls.results.scaled_smoothed_estimator_cov[:, :, i])) cls.results.det_predicted_state_cov[0, i] = np.linalg.det( cls.results.predicted_state_cov[:, :, i+1]) cls.results.det_smoothed_state_cov[0, i] = np.linalg.det( cls.results.smoothed_state_cov[:, :, i]) cls.results.det_smoothed_state_disturbance_cov[0, i] = ( np.linalg.det( cls.results.smoothed_state_disturbance_cov[:, :, i])) def test_loglike(self): assert_allclose(np.sum(self.results.llf_obs), 1695.34872) def test_scaled_smoothed_estimator(self): assert_allclose( self.results.scaled_smoothed_estimator.T, self.desired[['r1', 'r2', 'r3']], atol=1e-4 ) def test_scaled_smoothed_estimator_cov(self): # Last obs is zero, so exclude it assert_allclose( np.log(self.results.det_scaled_smoothed_estimator_cov.T[:-1]), np.log(self.desired[['detN']][:-1]), atol=1e-6 ) def test_forecasts(self): assert_allclose( self.results.forecasts.T, self.desired[['m1', 'm2', 'm3']], atol=1e-6 ) def test_forecasts_error(self): assert_allclose( self.results.forecasts_error.T[:, 0], self.desired['v1'], atol=1e-6 ) def test_forecasts_error_cov(self): assert_allclose( self.results.forecasts_error_cov.diagonal()[:, 0], self.desired['F1'], atol=1e-6 ) def test_predicted_states(self): assert_allclose( self.results.predicted_state[:, 1:].T, self.desired[['a1', 'a2', 'a3']], atol=1e-6 ) def test_predicted_states_cov(self): assert_allclose( self.results.det_predicted_state_cov.T, self.desired[['detP']], atol=1e-16 ) def test_smoothed_states(self): assert_allclose( self.results.smoothed_state.T, self.desired[['alphahat1', 'alphahat2', 'alphahat3']], atol=1e-6 ) def test_smoothed_states_cov(self): assert_allclose( self.results.det_smoothed_state_cov.T, self.desired[['detV']], atol=1e-16 ) def test_smoothed_forecasts(self): assert_allclose( self.results.smoothed_forecasts.T, self.desired[['muhat1', 'muhat2', 'muhat3']], atol=1e-6 ) def test_smoothed_state_disturbance(self): assert_allclose( self.results.smoothed_state_disturbance.T, self.desired[['etahat1', 'etahat2', 'etahat3']], atol=1e-6 ) def test_smoothed_state_disturbance_cov(self): assert_allclose( self.results.det_smoothed_state_disturbance_cov.T, self.desired[['detVeta']], atol=1e-18 ) def test_smoothed_measurement_disturbance(self): assert_allclose( self.results.smoothed_measurement_disturbance.T, self.desired[['epshat1', 'epshat2', 'epshat3']], atol=1e-6 ) def test_smoothed_measurement_disturbance_cov(self): assert_allclose( self.results.smoothed_measurement_disturbance_cov.diagonal(), self.desired[['Veps1', 'Veps2', 'Veps3']], atol=1e-6 ) class TestMultivariateVARAlternativeSmoothing(TestMultivariateVAR): @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariateVARAlternativeSmoothing, cls).setup_class( smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_ALTERNATIVE) class TestMultivariateVARClassicalSmoothing(TestMultivariateVAR): @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariateVARClassicalSmoothing, cls).setup_class( smooth_method=SMOOTH_CLASSICAL, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_CLASSICAL) class TestMultivariateVARUnivariate(object): """ Tests for most filtering and smoothing variables against output from the R library KFAS. Note that KFAS uses the univariate approach which generally will result in different predicted values and covariance matrices associated with the measurement equation (e.g. forecasts, etc.). In this case, although the model is multivariate, each of the series is truly independent so the values will be the same regardless of whether the univariate approach is used or not. """ @classmethod def setup_class(cls, *args, **kwargs): # Results path = os.path.join(current_path, 'results', 'results_smoothing2_R.csv') cls.desired = pd.read_csv(path) # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = np.log(dta[['realgdp', 'realcons', 'realinv']]).diff().iloc[1:] # Create the model mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs) mod.ssm.filter_univariate = True mod['design'] = np.eye(3) mod['obs_cov'] = np.array([ [0.0000640649, 0., 0.], [0., 0.0000572802, 0.], [0., 0., 0.0017088585]]) mod['transition'] = np.array([ [-0.1119908792, 0.8441841604, 0.0238725303], [0.2629347724, 0.4996718412, -0.0173023305], [-3.2192369082, 4.1536028244, 0.4514379215]]) mod['selection'] = np.eye(3) mod['state_cov'] = np.array([ [0.0000640649, 0.0000388496, 0.0002148769], [0.0000388496, 0.0000572802, 0.000001555], [0.0002148769, 0.000001555, 0.0017088585]]) mod.initialize_approximate_diffuse(1e6) cls.model = mod cls.results = mod.smooth([], return_ssm=True) # Calculate the determinant of the covariance matrices (for easy # comparison to other languages without having to store 2-dim arrays) cls.results.det_scaled_smoothed_estimator_cov = ( np.zeros((1, cls.model.nobs))) cls.results.det_predicted_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_cov = np.zeros((1, cls.model.nobs)) cls.results.det_smoothed_state_disturbance_cov = ( np.zeros((1, cls.model.nobs))) for i in range(cls.model.nobs): cls.results.det_scaled_smoothed_estimator_cov[0, i] = ( np.linalg.det( cls.results.scaled_smoothed_estimator_cov[:, :, i])) cls.results.det_predicted_state_cov[0, i] = np.linalg.det( cls.results.predicted_state_cov[:, :, i+1]) cls.results.det_smoothed_state_cov[0, i] = np.linalg.det( cls.results.smoothed_state_cov[:, :, i]) cls.results.det_smoothed_state_disturbance_cov[0, i] = ( np.linalg.det( cls.results.smoothed_state_disturbance_cov[:, :, i])) def test_loglike(self): assert_allclose(np.sum(self.results.llf_obs), 1695.34872) def test_scaled_smoothed_estimator(self): assert_allclose( self.results.scaled_smoothed_estimator.T, self.desired[['r1', 'r2', 'r3']], atol=1e-4 ) def test_scaled_smoothed_estimator_cov(self): # Last obs is zero, so exclude it assert_allclose( np.log(self.results.det_scaled_smoothed_estimator_cov.T[:-1]), np.log(self.desired[['detN']][:-1]) ) def test_forecasts(self): assert_allclose( self.results.forecasts.T[:, 0], self.desired['m1'], atol=1e-6 ) def test_forecasts_error(self): assert_allclose( self.results.forecasts_error.T, self.desired[['v1', 'v2', 'v3']], atol=1e-6 ) def test_forecasts_error_cov(self): assert_allclose( self.results.forecasts_error_cov.diagonal(), self.desired[['F1', 'F2', 'F3']] ) def test_predicted_states(self): assert_allclose( self.results.predicted_state[:, 1:].T, self.desired[['a1', 'a2', 'a3']], atol=1e-8 ) def test_predicted_states_cov(self): assert_allclose( self.results.det_predicted_state_cov.T, self.desired[['detP']], atol=1e-18 ) def test_smoothed_states(self): assert_allclose( self.results.smoothed_state.T, self.desired[['alphahat1', 'alphahat2', 'alphahat3']], atol=1e-6 ) def test_smoothed_states_cov(self): assert_allclose( self.results.det_smoothed_state_cov.T, self.desired[['detV']], atol=1e-18 ) def test_smoothed_forecasts(self): assert_allclose( self.results.smoothed_forecasts.T, self.desired[['muhat1', 'muhat2', 'muhat3']], atol=1e-6 ) def test_smoothed_state_disturbance(self): assert_allclose( self.results.smoothed_state_disturbance.T, self.desired[['etahat1', 'etahat2', 'etahat3']], atol=1e-6 ) def test_smoothed_state_disturbance_cov(self): assert_allclose( self.results.det_smoothed_state_disturbance_cov.T, self.desired[['detVeta']], atol=1e-18 ) def test_smoothed_measurement_disturbance(self): assert_allclose( self.results.smoothed_measurement_disturbance.T, self.desired[['epshat1', 'epshat2', 'epshat3']], atol=1e-6 ) def test_smoothed_measurement_disturbance_cov(self): assert_allclose( self.results.smoothed_measurement_disturbance_cov.diagonal(), self.desired[['Veps1', 'Veps2', 'Veps3']] ) class TestMultivariateVARUnivariateSmoothing(TestMultivariateVARUnivariate): @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariateVARUnivariateSmoothing, cls).setup_class( filter_method=FILTER_UNIVARIATE, *args, **kwargs) def test_filter_method(self): assert_equal(self.model.ssm.filter_method, FILTER_UNIVARIATE) assert_equal(self.model.ssm._kalman_smoother.filter_method, FILTER_UNIVARIATE) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_UNIVARIATE) class TestVARAutocovariances(object): @classmethod def setup_class(cls, which='mixed', *args, **kwargs): # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = np.log(dta[['realgdp', 'realcons', 'realinv']]).diff().iloc[1:] if which == 'all': obs.iloc[:50, :] = np.nan obs.iloc[119:130, :] = np.nan elif which == 'partial': obs.iloc[0:50, 0] = np.nan obs.iloc[119:130, 0] = np.nan elif which == 'mixed': obs.iloc[0:50, 0] = np.nan obs.iloc[19:70, 1] = np.nan obs.iloc[39:90, 2] = np.nan obs.iloc[119:130, 0] = np.nan obs.iloc[119:130, 2] = np.nan # Create the model with typical state space mod = mlemodel.MLEModel(obs, k_states=3, k_posdef=3, **kwargs) mod['design'] = np.eye(3) mod['obs_cov'] = np.array([ [609.0746647855, 0., 0.], [0., 1.8774916622, 0.], [0., 0., 124.6768281675]]) mod['transition'] = np.array([ [-0.8110473405, 1.8005304445, 1.0215975772], [-1.9846632699, 2.4091302213, 1.9264449765], [0.9181658823, -0.2442384581, -0.6393462272]]) mod['selection'] = np.eye(3) mod['state_cov'] = np.array([ [1552.9758843938, 612.7185121905, 877.6157204992], [612.7185121905, 467.8739411204, 70.608037339], [877.6157204992, 70.608037339, 900.5440385836]]) mod.initialize_approximate_diffuse(1e6) cls.model = mod cls.results = mod.smooth([], return_ssm=True) # Create the model with augmented state space kwargs.pop('filter_collapsed', None) mod = mlemodel.MLEModel(obs, k_states=6, k_posdef=3, **kwargs) mod['design', :3, :3] = np.eye(3) mod['obs_cov'] = np.array([ [609.0746647855, 0., 0.], [0., 1.8774916622, 0.], [0., 0., 124.6768281675]]) mod['transition', :3, :3] = np.array([ [-0.8110473405, 1.8005304445, 1.0215975772], [-1.9846632699, 2.4091302213, 1.9264449765], [0.9181658823, -0.2442384581, -0.6393462272]]) mod['transition', 3:, :3] = np.eye(3) mod['selection', :3, :3] = np.eye(3) mod['state_cov'] = np.array([ [1552.9758843938, 612.7185121905, 877.6157204992], [612.7185121905, 467.8739411204, 70.608037339], [877.6157204992, 70.608037339, 900.5440385836]]) mod.initialize_approximate_diffuse(1e6) cls.augmented_model = mod cls.augmented_results = mod.smooth([], return_ssm=True) def test_smoothed_state_autocov(self): # Cov(\alpha_{t+1}, \alpha_t) # Initialization makes these two methods slightly different for the # first few observations assert_allclose(self.results.smoothed_state_autocov[:, :, 0:5], self.augmented_results.smoothed_state_cov[:3, 3:, 1:6], atol=1e-4) assert_allclose(self.results.smoothed_state_autocov[:, :, 5:-1], self.augmented_results.smoothed_state_cov[:3, 3:, 6:], atol=1e-7) class TestVARAutocovariancesAlternativeSmoothing(TestVARAutocovariances): @classmethod def setup_class(cls, *args, **kwargs): super(TestVARAutocovariancesAlternativeSmoothing, cls).setup_class( smooth_method=SMOOTH_ALTERNATIVE, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_ALTERNATIVE) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_ALTERNATIVE) class TestVARAutocovariancesClassicalSmoothing(TestVARAutocovariances): @classmethod def setup_class(cls, *args, **kwargs): super(TestVARAutocovariancesClassicalSmoothing, cls).setup_class( smooth_method=SMOOTH_CLASSICAL, *args, **kwargs) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model.ssm._kalman_smoother.smooth_method, SMOOTH_CLASSICAL) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_CLASSICAL) class TestVARAutocovariancesUnivariateSmoothing(TestVARAutocovariances): @classmethod def setup_class(cls, *args, **kwargs): super(TestVARAutocovariancesUnivariateSmoothing, cls).setup_class( filter_method=FILTER_UNIVARIATE, *args, **kwargs) def test_filter_method(self): assert_equal(self.model.ssm.filter_method, FILTER_UNIVARIATE) assert_equal(self.model.ssm._kalman_smoother.filter_method, FILTER_UNIVARIATE) def test_smooth_method(self): assert_equal(self.model.ssm.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother.smooth_method, 0) assert_equal(self.model.ssm._kalman_smoother._smooth_method, SMOOTH_UNIVARIATE) class TVSSWithLags(TVSS): def __init__(self, endog): # TVSS has 2 states, here we will add in 3 lags of those super().__init__(endog, _k_states=8) self['transition', 2:, :6] = np.eye(6)[..., None] # Can't use exact diffuse filtering self.ssm.initialize_approximate_diffuse(1e-4) def get_acov_model(missing, filter_univariate, tvp, oos=None, params=None, return_ssm=True): dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') endog = np.log(dta[['realgdp', 'realcons']]).diff().iloc[1:] if missing == 'all': endog.iloc[:5, :] = np.nan endog.iloc[11:13, :] = np.nan elif missing == 'partial': endog.iloc[0:5, 0] = np.nan endog.iloc[11:13, 0] = np.nan elif missing == 'mixed': endog.iloc[0:5, 0] = np.nan endog.iloc[1:7, 1] = np.nan endog.iloc[11:13, 0] = np.nan if oos is not None: new_ix = pd.date_range(start=endog.index[0], periods=len(endog) + oos, freq='QS') endog = endog.reindex(new_ix) if not tvp: mod = varmax.VARMAX(endog, order=(4, 0, 0), measurement_error=True, tolerance=0) mod.ssm.filter_univariate = filter_univariate if params is None: params = mod.start_params res = mod.smooth(params, return_ssm=return_ssm) else: mod = TVSSWithLags(endog) mod.ssm.filter_univariate = filter_univariate res = mod.smooth([], return_ssm=return_ssm) return mod, res @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_smoothed_state_autocovariances_backwards(missing, filter_univariate, tvp): r""" Test for Cov(t, t - lag) """ _, res = get_acov_model(missing, filter_univariate, tvp) cov = res.smoothed_state_cov.transpose(2, 0, 1) desired_acov1 = cov[:, :2, 2:4] desired_acov2 = cov[:, :2, 4:6] desired_acov3 = cov[:, :2, 6:8] # Test all "backward" autocovariances: Cov(t, t-lag) acov1 = res.smoothed_state_autocovariance(1).transpose(2, 0, 1) assert_allclose(acov1[1:, :2, :2], desired_acov1[1:], rtol=1e-6, atol=1e-6) assert_equal(acov1[:1], np.nan) acov2 = res.smoothed_state_autocovariance(2).transpose(2, 0, 1) assert_allclose(acov2[2:, :2, :2], desired_acov2[2:], rtol=1e-6, atol=1e-6) assert_equal(acov2[:2], np.nan) acov3 = res.smoothed_state_autocovariance(3).transpose(2, 0, 1) assert_allclose(acov3[3:, :2, :2], desired_acov3[3:], rtol=1e-6, atol=1e-6) assert_equal(acov3[:3], np.nan) # Test for specific autocovariances acov1 = res.smoothed_state_autocovariance(1, t=0) assert_allclose(acov1, np.nan) acov1 = res.smoothed_state_autocovariance(1, t=1) assert_allclose(acov1[:2, :2], desired_acov1[1], rtol=1e-6, atol=1e-6) acov1 = res.smoothed_state_autocovariance( 1, start=8, end=9).transpose(2, 0, 1) assert_allclose(acov1[:, :2, :2], desired_acov1[8:9], rtol=1e-6, atol=1e-6) acov2 = res.smoothed_state_autocovariance(2, t=0) assert_allclose(acov2, np.nan) acov2 = res.smoothed_state_autocovariance(2, t=1) assert_allclose(acov2, np.nan) acov2 = res.smoothed_state_autocovariance(2, t=2) assert_allclose(acov2[:2, :2], desired_acov2[2], rtol=1e-6, atol=1e-6) acov2 = res.smoothed_state_autocovariance( 2, start=8, end=9).transpose(2, 0, 1) assert_allclose(acov2[:, :2, :2], desired_acov2[8:9], rtol=1e-6, atol=1e-6) @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_smoothed_state_autocovariances_forwards(missing, filter_univariate, tvp): r""" Test for Cov(t, t + lag) """ # Out-of-sample model # Note: in TVP case, we need to first generate the larger model, and then # create the smaller model with the system matrices from the larger model # (otherwise they will be different, since the matrices are randomly # generated) mod_oos, res_oos = get_acov_model(missing, filter_univariate, tvp, oos=3) # Basic model names = ['obs_intercept', 'design', 'obs_cov', 'transition', 'selection', 'state_cov'] if not tvp: mod, res = get_acov_model(missing, filter_univariate, tvp, params=mod_oos.start_params) else: mod, _ = get_acov_model(missing, filter_univariate, tvp) for name in names: mod[name] = mod_oos[name, ..., :-3] res = mod.ssm.smooth() extend_kwargs1 = {} extend_kwargs2 = {} if tvp: keys = ['obs_intercept', 'design', 'obs_cov', 'transition', 'selection', 'state_cov'] for key in keys: extend_kwargs1[key] = mod_oos[key, ..., -3:-2] extend_kwargs2[key] = mod_oos[key, ..., -3:-1] assert_allclose(res_oos.llf, res.llf) cov = res.smoothed_state_cov.transpose(2, 0, 1) desired_acov1 = cov[:, 2:4, :2] desired_acov2 = cov[:, 4:6, :2] desired_acov3 = cov[:, 6:8, :2] oos_cov = np.concatenate( (res_oos.smoothed_state_cov, res_oos.predicted_state_cov[..., -1:]), axis=2).transpose(2, 0, 1) # Test all "forwards" autocovariances: Cov(t, t+lag) # For Cov(t, t+lag), the first out-of-sample forward covariance, # Cov(T, T+1), is already available, so we dno't need extend kwaargs acov1 = res.smoothed_state_autocovariance(-1).transpose(2, 0, 1) assert_allclose(acov1[:-1, :2, :2], desired_acov1[1:]) assert_allclose(acov1[-2:, :2, :2], oos_cov[-5:-3, 2:4, :2]) acov2 = res.smoothed_state_autocovariance( -2, extend_kwargs=extend_kwargs1).transpose(2, 0, 1) assert_allclose(acov2[:-2, :2, :2], desired_acov2[2:]) assert_allclose(acov2[-2:, :2, :2], oos_cov[-4:-2, 4:6, :2]) acov3 = res.smoothed_state_autocovariance( -3, extend_kwargs=extend_kwargs2).transpose(2, 0, 1) assert_allclose(acov3[:-3, :2, :2], desired_acov3[3:]) assert_allclose(acov3[-3:, :2, :2], oos_cov[-4:-1, 6:8, :2]) # Test for specific autocovariances acov1 = res.smoothed_state_autocovariance( -1, t=mod.nobs, extend_kwargs=extend_kwargs1) assert_allclose(acov1[:2, :2], oos_cov[-3, 2:4, :2]) acov1 = res.smoothed_state_autocovariance(-1, t=0) assert_allclose(acov1[:2, :2], desired_acov1[0 + 1]) acov1 = res.smoothed_state_autocovariance( -1, start=8, end=9).transpose(2, 0, 1) assert_allclose(acov1[:, :2, :2], desired_acov1[8 + 1:9 + 1]) acov2 = res.smoothed_state_autocovariance( -2, t=mod.nobs, extend_kwargs=extend_kwargs2) assert_allclose(acov2[:2, :2], oos_cov[-2, 4:6, :2]) acov2 = res.smoothed_state_autocovariance( -2, t=mod.nobs - 1, extend_kwargs=extend_kwargs1) assert_allclose(acov2[:2, :2], oos_cov[-3, 4:6, :2]) acov2 = res.smoothed_state_autocovariance(-2, t=0) assert_allclose(acov2[:2, :2], desired_acov2[0 + 2]) acov2 = res.smoothed_state_autocovariance( -2, start=8, end=9).transpose(2, 0, 1) assert_allclose(acov2[:, :2, :2], desired_acov2[8 + 2:9 + 2]) @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_smoothed_state_autocovariances_forwards_oos(missing, filter_univariate, tvp): # Out-of-sample model # Note: in TVP case, we need to first generate the larger model, and then # create the smaller model with the system matrices from the larger model # (otherwise they will be different, since the matrices are randomly # generated) mod_oos, res_oos = get_acov_model(missing, filter_univariate, tvp, oos=5) # Basic model names = ['obs_intercept', 'design', 'obs_cov', 'transition', 'selection', 'state_cov'] if not tvp: mod, res = get_acov_model(missing, filter_univariate, tvp, params=mod_oos.start_params) else: mod, _ = get_acov_model(missing, filter_univariate, tvp) for name in names: mod[name] = mod_oos[name, ..., :-5] res = mod.ssm.smooth() assert_allclose(res_oos.llf, res.llf) cov = np.concatenate( (res_oos.smoothed_state_cov, res_oos.predicted_state_cov[..., -1:]), axis=2).transpose(2, 0, 1) desired_acov1 = cov[:, 2:4, :2] desired_acov2 = cov[:, 4:6, :2] desired_acov3 = cov[:, 6:8, :2] # Test all "forwards" autocovariances: Cov(t, t+lag) extend_kwargs = {} if tvp: extend_kwargs = { 'obs_intercept': mod_oos['obs_intercept', ..., -5:], 'design': mod_oos['design', ..., -5:], 'obs_cov': mod_oos['obs_cov', ..., -5:], 'transition': mod_oos['transition', ..., -5:], 'selection': mod_oos['selection', ..., -5:], 'state_cov': mod_oos['state_cov', ..., -5:]} # Note: we can compute up to Cov(mod_oos.nobs, mod_oos.nobs + 1) using # a model that has state space matrices defined up to mod_oos.nobs. Since # mod_oos.nobs = mod.nobs + 5, we need to pass in 5 additional time points, # and that is what extend_kwargs, above, does. acov1 = res.smoothed_state_autocovariance( -1, end=mod_oos.nobs, extend_kwargs=extend_kwargs).transpose(2, 0, 1) assert_equal(acov1.shape, (mod_oos.nobs, mod.k_states, mod.k_states)) assert_allclose(acov1[:, :2, :2], desired_acov1[1:]) # Note: now we can compute up to Cov(mod_oos.nobs - 1, mod_oos.nobs + 1) # using a model that has state space matrices defined up to mod_oos.nobs. # We still need to pass in 5 additional time points for the extend kwargs. # This is why we have end = mod_oos.nobs - 1, because this function returns # values through Cov(end, end + 2). Because start=0 (the default), we # will have values for Cov(0, 2), Cov(1, 3), ..., # Cov(mod_oos.nobs - 1, mod_oos.nobs + 1), and that is a set of # mod_oos.nobs - 1 matrices. acov2 = res.smoothed_state_autocovariance( -2, end=mod_oos.nobs - 1, extend_kwargs=extend_kwargs).transpose(2, 0, 1) assert_equal(acov2.shape, (mod_oos.nobs - 1, mod.k_states, mod.k_states)) assert_allclose(acov2[:, :2, :2], desired_acov2[2:]) # Note: now we can compute up to Cov(mod_oos.nobs - 2, mod_oos.nobs + 1) # using a model that has state space matrices defined up to mod_oos.nobs. # We still need to pass in 5 additional time points for the extend kwargs. acov3 = res.smoothed_state_autocovariance( -3, end=mod_oos.nobs - 2, extend_kwargs=extend_kwargs).transpose(2, 0, 1) assert_equal(acov3.shape, (mod_oos.nobs - 2, mod.k_states, mod.k_states)) assert_allclose(acov3[:, :2, :2], desired_acov3[3:]) @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_smoothed_state_autocovariances_backwards_oos(missing, filter_univariate, tvp): # Out-of-sample model # Note: in TVP case, we need to first generate the larger model, and then # create the smaller model with the system matrices from the larger model # (otherwise they will be different, since the matrices are randomly # generated) mod_oos, res_oos = get_acov_model(missing, filter_univariate, tvp, oos=5) # Basic model names = ['obs_intercept', 'design', 'obs_cov', 'transition', 'selection', 'state_cov'] if not tvp: mod, res = get_acov_model(missing, filter_univariate, tvp, params=mod_oos.start_params) else: mod, _ = get_acov_model(missing, filter_univariate, tvp) for name in names: mod[name] = mod_oos[name, ..., :-5] res = mod.ssm.smooth() assert_allclose(res_oos.llf, res.llf) cov = np.concatenate( (res_oos.smoothed_state_cov, res_oos.predicted_state_cov[..., -1:]), axis=2).transpose(2, 0, 1) desired_acov1 = cov[:, :2, 2:4] desired_acov2 = cov[:, :2, 4:6] desired_acov3 = cov[:, :2, 6:8] # Test all "backwards" autocovariances: Cov(t, t - lag) end = mod_oos.nobs + 1 extend_kwargs = {} if tvp: extend_kwargs = { 'obs_intercept': mod_oos['obs_intercept', ..., -5:], 'design': mod_oos['design', ..., -5:], 'obs_cov': mod_oos['obs_cov', ..., -5:], 'transition': mod_oos['transition', ..., -5:], 'selection': mod_oos['selection', ..., -5:], 'state_cov': mod_oos['state_cov', ..., -5:]} # Note: we can compute up to Cov(mod_oos.nobs + 1, mod_oos.nobs) using # a model that has state space matrices defined up to mod_oos.nobs. Since # mod_oos.nobs = mod.nobs + 5, we need to pass in 5 additional time points, # and that is what extend_kwargs, above, does. acov1 = res.smoothed_state_autocovariance( 1, end=end, extend_kwargs=extend_kwargs).transpose(2, 0, 1) assert_equal(acov1.shape, (mod_oos.nobs + 1, mod.k_states, mod.k_states)) assert_allclose(acov1[1:, :2, :2], desired_acov1[1:]) # We cannot compute Cov(1, 0), so this is always NaNs assert_equal(acov1[:1], np.nan) # Note: we can compute up to Cov(mod_oos.nobs + 1, mod_oos.nobs - 1) using # a model that has state space matrices defined up to mod_oos.nobs, which # is why we don't need to change `end` here relative to the lag=1 case acov2 = res.smoothed_state_autocovariance( 2, end=end, extend_kwargs=extend_kwargs).transpose(2, 0, 1) assert_allclose(acov2[2:, :2, :2], desired_acov2[2:]) # We cannot compute Cov(1, -1) or Cov(2, 0), so this is always NaNs assert_equal(acov2[:2], np.nan) # Note: we can compute up to Cov(mod_oos.nobs + 1, mod_oos.nobs - 2) using # a model that has state space matrices defined up to mod_oos.nobs, which # is why we don't need to change `end` here relative to the lag=1 or lag=2 # cases acov3 = res.smoothed_state_autocovariance( 3, end=end, extend_kwargs=extend_kwargs).transpose(2, 0, 1) assert_allclose(acov3[3:, :2, :2], desired_acov3[3:]) # We cannot compute Cov(1, -2), Cov(2, -1), or Cov(3, 0), so this is always # NaNs assert_equal(acov3[:3], np.nan) def test_smoothed_state_autocovariances_invalid(): # Tests for invalid calls of `smoothed_state_autocovariance` _, res = get_acov_model(missing=False, filter_univariate=False, tvp=False) with pytest.raises(ValueError, match='Cannot specify both `t`'): res.smoothed_state_autocovariance(1, t=1, start=1) with pytest.raises(ValueError, match='Negative `t`'): res.smoothed_state_autocovariance(1, t=-1) with pytest.raises(ValueError, match='Negative `t`'): res.smoothed_state_autocovariance(1, start=-1) with pytest.raises(ValueError, match='Negative `t`'): res.smoothed_state_autocovariance(1, end=-1) with pytest.raises(ValueError, match='`end` must be after `start`'): res.smoothed_state_autocovariance(1, start=5, end=4) @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_news_basic(missing, filter_univariate, tvp): # Basic tests for news # Get the basic model mod, res = get_acov_model(missing, filter_univariate, tvp) params = [] if tvp else mod.start_params # Get an expanded model with one new observation and 9 additional NaN # datapoints (so that we can compute the desired value using the # `smoothed_forecasts` attribute). append = np.zeros((10, 2)) * np.nan append[0] = [0.1, -0.2] endog2 = np.concatenate((mod.endog, append), axis=0) mod2 = mod.clone(endog2) res2 = mod2.smooth(params, return_ssm=True) # Get an expanded model with only 10 additional NaN datapoints, to compute # the baseline `smoothed_forecasts`. endog3 = endog2.copy() endog3[-10:] = np.nan mod3 = mod2.clone(endog3) res3 = mod3.smooth(params, return_ssm=True) # Test the news computation at the start, middle, and end of the sample, as # well as out-of-sample. for t in [0, 1, 150, mod.nobs - 1, mod.nobs, mod.nobs + 1, mod.nobs + 9]: # Test with a time argument out = res2.news(res, t=t) desired = (res2.smoothed_forecasts[..., t] - res3.smoothed_forecasts[..., t]) # The "news" about the t=0 smoothed forecast from new data at # observation t=202 is almost identically zero, so we need to set an # "atol" to avoid problems with comparing floating point versions of # zero. assert_allclose(out.update_impacts, desired, atol=1e-14) assert_equal(out.revision_impacts, None) # Test with start/end arguments out = res2.news(res, start=t, end=t + 1) assert_allclose(out.update_impacts, desired[None, ...], atol=1e-14) @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_news_revisions(missing, filter_univariate, tvp): # Tests for news when there are revisions in the model # Get the basic model mod, res = get_acov_model(missing, filter_univariate, tvp, oos=10) params = [] if tvp else mod.start_params endog2 = mod.endog.copy() # Revise the last datapoint endog2[-11] = [0.0, 0.0] # Add a new datapoint endog2[-10] = [-0.3, -0.4] mod2 = mod.clone(endog2) res2 = mod2.smooth(params, return_ssm=True) # Test the news computation at the start, middle, and end of the sample, as # well as out-of-sample. nobs = mod.nobs - 10 for t in [0, 1, 150, nobs - 1, nobs, nobs + 1, nobs + 9]: out = res2.news(res, t=t) # Test for the news desired = (res2.smoothed_forecasts[..., t] - out.revision_results.smoothed_forecasts[..., t]) # Relaxed tolerance to 1e-10 after random failures assert_allclose(out.update_impacts, desired, atol=1e-10) # Test for the revisions desired = (out.revision_results.smoothed_forecasts[..., t] - res.smoothed_forecasts[..., t]) # Relaxed tolerance to 1e-10 after random failures assert_allclose(out.revision_impacts, desired, atol=1e-10) @pytest.mark.parametrize('missing', ['all', 'partial', 'mixed', None]) @pytest.mark.parametrize('filter_univariate', [True, False]) @pytest.mark.parametrize('tvp', [True, False]) def test_news_invalid(missing, filter_univariate, tvp): # Tests for invalid calls to news # (generic error message used below) error_ss = ('This results object has %s and so it does not appear to' ' by an extension of `previous`. Can only compute the' ' news by comparing this results set to previous results' ' objects.') # Basic model / results setup mod, res = get_acov_model(missing, filter_univariate, tvp, oos=1) params = [] if tvp else mod.start_params endog2 = mod.endog.copy() endog2[-1] = [0.2, 0.5] mod2 = mod.clone(endog2) res2_filtered = mod2.filter(params, return_ssm=True) res2_smoothed = mod2.smooth(params, return_ssm=True) # Test that news works with smoothing, but not with only filtering res2_smoothed.news(res, t=mod.nobs - 1) msg = ('Cannot compute news without having' ' applied the Kalman smoother first.') with pytest.raises(ValueError, match=msg): res2_filtered.news(res, t=mod.nobs - 1) # Test that if we want to request news for an out-of-sample period in a # time-varying model, then we need to provide a new design matrix if tvp: msg = ('Cannot compute the impacts of news on periods outside of the' ' sample in time-varying models.') with pytest.raises(RuntimeError, match=msg): res2_smoothed.news(res, t=mod.nobs + 2) # Test that news won't work when the calling model is is smaller mod, res = get_acov_model(missing, filter_univariate, tvp) params = [] if tvp else mod.start_params endog2 = mod.endog.copy()[:mod.nobs - 1] mod2 = mod.clone(endog2) res2 = mod2.smooth(params, return_ssm=True) msg = error_ss % 'fewer observations than `previous`' with pytest.raises(ValueError, match=msg): res2.news(res, t=mod.nobs - 1) # Test that news won't work when the state dimensions are different mod2 = sarimax.SARIMAX(np.zeros(mod.nobs)) res2 = mod2.smooth([0.5, 1.], return_ssm=True) msg = error_ss % 'different state space dimensions than `previous`' with pytest.raises(ValueError, match=msg): res2.news(res, t=mod.nobs - 1) # Test that news won't work when one of the models is time-varying and one # is time-invariant mod2, res2 = get_acov_model(missing, filter_univariate, not tvp, oos=1) if tvp: msg = 'time-invariant design while `previous` does not' else: msg = 'time-varying design while `previous` does not' with pytest.raises(ValueError, match=msg): res2.news(res, t=mod.nobs - 1) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_structural.py000066400000000000000000000626031400612667500264240ustar00rootroot00000000000000""" Tests for structural time series models Author: Chad Fulton License: Simplified-BSD """ import warnings import numpy as np from numpy.testing import assert_equal, assert_allclose, assert_raises import pandas as pd import pytest from statsmodels.datasets import macrodata from statsmodels.tools.sm_exceptions import SpecificationWarning from statsmodels.tsa.statespace import structural from statsmodels.tsa.statespace.structural import UnobservedComponents from statsmodels.tsa.statespace.tests.results import results_structural dta = macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-07-01', freq='QS') def run_ucm(name, use_exact_diffuse=False): true = getattr(results_structural, name) for model in true['models']: kwargs = model.copy() kwargs.update(true['kwargs']) kwargs['use_exact_diffuse'] = use_exact_diffuse # Make a copy of the data values = dta.copy() freq = kwargs.pop('freq', None) if freq is not None: values.index = pd.date_range(start='1959-01-01', periods=len(dta), freq=freq) # Test pandas exog if 'exog' in kwargs: # Default value here is pd.Series object exog = np.log(values['realgdp']) # Also allow a check with a 1-dim numpy array if kwargs['exog'] == 'numpy': exog = exog.values.squeeze() kwargs['exog'] = exog # Create the model mod = UnobservedComponents(values['unemp'], **kwargs) # Smoke test for starting parameters, untransform, transform # Also test that transform and untransform are inverses mod.start_params roundtrip = mod.transform_params( mod.untransform_params(mod.start_params)) assert_allclose(mod.start_params, roundtrip) # Fit the model at the true parameters res_true = mod.filter(true['params']) # Check that the cycle bounds were computed correctly freqstr = freq[0] if freq is not None else values.index.freqstr[0] if 'cycle_period_bounds' in kwargs: cycle_period_bounds = kwargs['cycle_period_bounds'] elif freqstr == 'A': cycle_period_bounds = (1.5, 12) elif freqstr == 'Q': cycle_period_bounds = (1.5*4, 12*4) elif freqstr == 'M': cycle_period_bounds = (1.5*12, 12*12) else: # If we have no information on data frequency, require the # cycle frequency to be between 0 and pi cycle_period_bounds = (2, np.inf) # Test that the cycle frequency bound is correct assert_equal(mod.cycle_frequency_bound, (2*np.pi / cycle_period_bounds[1], 2*np.pi / cycle_period_bounds[0])) # Test that the likelihood is correct rtol = true.get('rtol', 1e-7) atol = true.get('atol', 0) if use_exact_diffuse: # If we are using exact diffuse initialization, then we need to # adjust for the fact that KFAS does not include the constant in # the likelihood function for the diffuse periods # (see note to test_exact_diffuse_filtering.py for details). res_llf = (res_true.llf_obs.sum() + res_true.nobs_diffuse * 0.5 * np.log(2 * np.pi)) else: # If we are using approximate diffuse initialization, then we need # to ignore the first period, and this will agree with KFAS (since # it does not include the constant in the likelihood function for # diffuse periods). res_llf = res_true.llf_obs[res_true.loglikelihood_burn:].sum() assert_allclose(res_llf, true['llf'], rtol=rtol, atol=atol) # Optional smoke test for plot_components try: import matplotlib.pyplot as plt try: from pandas.plotting import register_matplotlib_converters register_matplotlib_converters() except ImportError: pass fig = plt.figure() res_true.plot_components(fig=fig) except ImportError: pass # Now fit the model via MLE with warnings.catch_warnings(record=True): fit_kwargs = {} if 'maxiter' in true: fit_kwargs['maxiter'] = true['maxiter'] res = mod.fit(start_params=true.get('start_params', None), disp=-1, **fit_kwargs) # If we found a higher likelihood, no problem; otherwise check # that we're very close to that found by R # See note above about these computation if use_exact_diffuse: res_llf = (res.llf_obs.sum() + res.nobs_diffuse * 0.5 * np.log(2 * np.pi)) else: res_llf = res.llf_obs[res_true.loglikelihood_burn:].sum() if res_llf <= true['llf']: assert_allclose(res_llf, true['llf'], rtol=1e-4) # Smoke test for summary res.summary() def test_irregular(close_figures): run_ucm('irregular') run_ucm('irregular', use_exact_diffuse=True) def test_fixed_intercept(close_figures): # Clear warnings structural.__warningregistry__ = {} warning = SpecificationWarning match = 'Specified model does not contain' with pytest.warns(warning, match=match): run_ucm('fixed_intercept') run_ucm('fixed_intercept', use_exact_diffuse=True) def test_deterministic_constant(close_figures): run_ucm('deterministic_constant') run_ucm('deterministic_constant', use_exact_diffuse=True) def test_random_walk(close_figures): run_ucm('random_walk') run_ucm('random_walk', use_exact_diffuse=True) def test_local_level(close_figures): run_ucm('local_level') run_ucm('local_level', use_exact_diffuse=True) def test_fixed_slope(close_figures): warning = SpecificationWarning match = 'irregular component added' with pytest.warns(warning, match=match): run_ucm('fixed_slope') run_ucm('fixed_slope', use_exact_diffuse=True) def test_fixed_slope_warn(close_figures): # Clear warnings structural.__warningregistry__ = {} warning = SpecificationWarning match = 'irregular component added' with pytest.warns(warning, match=match): run_ucm('fixed_slope') run_ucm('fixed_slope', use_exact_diffuse=True) def test_deterministic_trend(close_figures): run_ucm('deterministic_trend') run_ucm('deterministic_trend', use_exact_diffuse=True) def test_random_walk_with_drift(close_figures): run_ucm('random_walk_with_drift') run_ucm('random_walk_with_drift', use_exact_diffuse=True) def test_local_linear_deterministic_trend(close_figures): run_ucm('local_linear_deterministic_trend') run_ucm('local_linear_deterministic_trend', use_exact_diffuse=True) def test_local_linear_trend(close_figures): run_ucm('local_linear_trend') run_ucm('local_linear_trend', use_exact_diffuse=True) def test_smooth_trend(close_figures): run_ucm('smooth_trend') run_ucm('smooth_trend', use_exact_diffuse=True) def test_random_trend(close_figures): run_ucm('random_trend') run_ucm('random_trend', use_exact_diffuse=True) def test_cycle(close_figures): run_ucm('cycle_approx_diffuse') run_ucm('cycle', use_exact_diffuse=True) def test_seasonal(close_figures): run_ucm('seasonal_approx_diffuse') run_ucm('seasonal', use_exact_diffuse=True) def test_freq_seasonal(close_figures): run_ucm('freq_seasonal_approx_diffuse') run_ucm('freq_seasonal', use_exact_diffuse=True) def test_reg(close_figures): run_ucm('reg_approx_diffuse') run_ucm('reg', use_exact_diffuse=True) def test_rtrend_ar1(close_figures): run_ucm('rtrend_ar1') run_ucm('rtrend_ar1', use_exact_diffuse=True) @pytest.mark.slow def test_lltrend_cycle_seasonal_reg_ar1(close_figures): run_ucm('lltrend_cycle_seasonal_reg_ar1_approx_diffuse') run_ucm('lltrend_cycle_seasonal_reg_ar1', use_exact_diffuse=True) @pytest.mark.parametrize("use_exact_diffuse", [True, False]) def test_mle_reg(use_exact_diffuse): endog = np.arange(100)*1.0 exog = endog*2 # Make the fit not-quite-perfect endog[::2] += 0.01 endog[1::2] -= 0.01 with warnings.catch_warnings(record=True): mod1 = UnobservedComponents(endog, irregular=True, exog=exog, mle_regression=False, use_exact_diffuse=use_exact_diffuse) res1 = mod1.fit(disp=-1) mod2 = UnobservedComponents(endog, irregular=True, exog=exog, mle_regression=True, use_exact_diffuse=use_exact_diffuse) res2 = mod2.fit(disp=-1) assert_allclose(res1.regression_coefficients.filtered[0, -1], 0.5, atol=1e-5) assert_allclose(res2.params[1], 0.5, atol=1e-5) # When the regression component is part of the state vector with exact # diffuse initialization, we have two diffuse observations if use_exact_diffuse: print(res1.predicted_diffuse_state_cov) assert_equal(res1.nobs_diffuse, 2) assert_equal(res2.nobs_diffuse, 0) else: assert_equal(res1.loglikelihood_burn, 1) assert_equal(res2.loglikelihood_burn, 0) def test_specifications(): # Clear warnings structural.__warningregistry__ = {} endog = [1, 2] # Test that when nothing specified, a warning is issued and the model that # is fit is one with irregular=True and nothing else. warning = SpecificationWarning match = 'irregular component added' with pytest.warns(warning, match=match): mod = UnobservedComponents(endog) assert_equal(mod.trend_specification, 'irregular') # Test an invalid string trend specification with pytest.raises(ValueError): UnobservedComponents(endog, 'invalid spec') # Test that if a trend component is specified without a level component, # a warning is issued and a deterministic level component is added warning = SpecificationWarning match = 'Trend component specified without' with pytest.warns(warning, match=match): mod = UnobservedComponents(endog, trend=True, irregular=True) assert_equal(mod.trend_specification, 'deterministic trend') # Test that if a string specification is provided, a warning is issued if # the boolean attributes are also specified trend_attributes = ['irregular', 'trend', 'stochastic_level', 'stochastic_trend'] for attribute in trend_attributes: kwargs = {attribute: True} warning = SpecificationWarning match = 'may be overridden when the trend' with pytest.warns(warning, match=match): UnobservedComponents(endog, 'deterministic trend', **kwargs) # Test that a seasonal with period less than two is invalid with pytest.raises(ValueError): UnobservedComponents(endog, seasonal=1) def test_start_params(): # Test that the behavior is correct for multiple exogenous and / or # autoregressive components # Parameters nobs = int(1e4) beta = np.r_[10, -2] phi = np.r_[0.5, 0.1] # Generate data np.random.seed(1234) exog = np.c_[np.ones(nobs), np.arange(nobs)*1.0] eps = np.random.normal(size=nobs) endog = np.zeros(nobs+2) for t in range(1, nobs): endog[t+1] = phi[0] * endog[t] + phi[1] * endog[t-1] + eps[t] endog = endog[2:] endog += np.dot(exog, beta) # Now just test that the starting parameters are approximately what they # ought to be (could make this arbitrarily precise by increasing nobs, # but that would slow down the test for no real gain) mod = UnobservedComponents(endog, exog=exog, autoregressive=2) assert_allclose(mod.start_params, [1., 0.5, 0.1, 10, -2], atol=1e-1) def test_forecast(): endog = np.arange(50) + 10 exog = np.arange(50) mod = UnobservedComponents(endog, exog=exog, level='dconstant', seasonal=4) res = mod.smooth([1e-15, 0, 1]) actual = res.forecast(10, exog=np.arange(50, 60)[:, np.newaxis]) desired = np.arange(50, 60) + 10 assert_allclose(actual, desired) def test_misc_exog(): # Tests for missing data nobs = 20 k_endog = 1 np.random.seed(1208) endog = np.random.normal(size=(nobs, k_endog)) endog[:4, 0] = np.nan exog1 = np.random.normal(size=(nobs, 1)) exog2 = np.random.normal(size=(nobs, 2)) index = pd.date_range('1970-01-01', freq='QS', periods=nobs) endog_pd = pd.DataFrame(endog, index=index) exog1_pd = pd.Series(exog1.squeeze(), index=index) exog2_pd = pd.DataFrame(exog2, index=index) models = [ UnobservedComponents(endog, 'llevel', exog=exog1), UnobservedComponents(endog, 'llevel', exog=exog2), UnobservedComponents(endog, 'llevel', exog=exog2), UnobservedComponents(endog_pd, 'llevel', exog=exog1_pd), UnobservedComponents(endog_pd, 'llevel', exog=exog2_pd), UnobservedComponents(endog_pd, 'llevel', exog=exog2_pd), ] for mod in models: # Smoke tests mod.start_params res = mod.fit(disp=False) res.summary() res.predict() res.predict(dynamic=True) res.get_prediction() oos_exog = np.random.normal(size=(1, mod.k_exog)) res.forecast(steps=1, exog=oos_exog) res.get_forecast(steps=1, exog=oos_exog) # Smoke tests for invalid exog oos_exog = np.random.normal(size=(2, mod.k_exog)) with pytest.raises(ValueError): res.forecast(steps=1, exog=oos_exog) oos_exog = np.random.normal(size=(1, mod.k_exog + 1)) with pytest.raises(ValueError): res.forecast(steps=1, exog=oos_exog) # Test invalid model specifications with pytest.raises(ValueError): UnobservedComponents(endog, 'llevel', exog=np.zeros((10, 4))) def test_predict_custom_index(): np.random.seed(328423) endog = pd.DataFrame(np.random.normal(size=50)) mod = structural.UnobservedComponents(endog, 'llevel') res = mod.smooth(mod.start_params) out = res.predict(start=1, end=1, index=['a']) assert_equal(out.index.equals(pd.Index(['a'])), True) def test_matrices_somewhat_complicated_model(): values = dta.copy() model = UnobservedComponents(values['unemp'], level='lltrend', freq_seasonal=[{'period': 4}, {'period': 9, 'harmonics': 3}], cycle=True, cycle_period_bounds=[2, 30], damped_cycle=True, stochastic_freq_seasonal=[True, False], stochastic_cycle=True ) # Selected parameters params = [1, # irregular_var 3, 4, # lltrend parameters: level_var, trend_var 5, # freq_seasonal parameters: freq_seasonal_var_0 # cycle parameters: cycle_var, cycle_freq, cycle_damp 6, 2*np.pi/30., .9 ] model.update(params) # Check scalar properties assert_equal(model.k_states, 2 + 4 + 6 + 2) assert_equal(model.k_state_cov, 2 + 1 + 0 + 1) assert_equal(model.loglikelihood_burn, 2 + 4 + 6 + 2) assert_allclose(model.ssm.k_posdef, 2 + 4 + 0 + 2) assert_equal(model.k_params, len(params)) # Check the statespace model matrices against hand-constructed answers # We group the terms by the component expected_design = np.r_[[1, 0], [1, 0, 1, 0], [1, 0, 1, 0, 1, 0], [1, 0]].reshape(1, 14) assert_allclose(model.ssm.design[:, :, 0], expected_design) expected_transition = __direct_sum([ np.array([[1, 1], [0, 1]]), np.array([[0, 1, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, -1]]), np.array([[np.cos(2*np.pi*1/9.), np.sin(2*np.pi*1/9.), 0, 0, 0, 0], [-np.sin(2*np.pi*1/9.), np.cos(2*np.pi*1/9.), 0, 0, 0, 0], [0, 0, np.cos(2*np.pi*2/9.), np.sin(2*np.pi*2/9.), 0, 0], [0, 0, -np.sin(2*np.pi*2/9.), np.cos(2*np.pi*2/9.), 0, 0], [0, 0, 0, 0, np.cos(2*np.pi/3.), np.sin(2*np.pi/3.)], [0, 0, 0, 0, -np.sin(2*np.pi/3.), np.cos(2*np.pi/3.)]]), np.array([[.9*np.cos(2*np.pi/30.), .9*np.sin(2*np.pi/30.)], [-.9*np.sin(2*np.pi/30.), .9*np.cos(2*np.pi/30.)]]) ]) assert_allclose( model.ssm.transition[:, :, 0], expected_transition, atol=1e-7) # Since the second seasonal term is not stochastic, # the dimensionality of the state disturbance is 14 - 6 = 8 expected_selection = np.zeros((14, 14 - 6)) expected_selection[0:2, 0:2] = np.eye(2) expected_selection[2:6, 2:6] = np.eye(4) expected_selection[-2:, -2:] = np.eye(2) assert_allclose(model.ssm.selection[:, :, 0], expected_selection) expected_state_cov = __direct_sum([ np.diag(params[1:3]), np.eye(4)*params[3], np.eye(2)*params[4] ]) assert_allclose(model.ssm.state_cov[:, :, 0], expected_state_cov) def __direct_sum(square_matrices): """Compute the matrix direct sum of an iterable of square numpy 2-d arrays """ new_shape = np.sum([m.shape for m in square_matrices], axis=0) new_array = np.zeros(new_shape) offset = 0 for m in square_matrices: rows, cols = m.shape assert rows == cols new_array[offset:offset + rows, offset:offset + rows] = m offset += rows return new_array def test_forecast_exog(): # Test forecasting with various shapes of `exog` nobs = 100 endog = np.ones(nobs) * 2.0 exog = np.ones(nobs) mod = UnobservedComponents(endog, 'irregular', exog=exog) res = mod.smooth([1.0, 2.0]) # 1-step-ahead, valid exog_fcast_scalar = 1. exog_fcast_1dim = np.ones(1) exog_fcast_2dim = np.ones((1, 1)) assert_allclose(res.forecast(1, exog=exog_fcast_scalar), 2.) assert_allclose(res.forecast(1, exog=exog_fcast_1dim), 2.) assert_allclose(res.forecast(1, exog=exog_fcast_2dim), 2.) # h-steps-ahead, valid h = 10 exog_fcast_1dim = np.ones(h) exog_fcast_2dim = np.ones((h, 1)) assert_allclose(res.forecast(h, exog=exog_fcast_1dim), 2.) assert_allclose(res.forecast(h, exog=exog_fcast_2dim), 2.) # h-steps-ahead, invalid assert_raises(ValueError, res.forecast, h, exog=1.) assert_raises(ValueError, res.forecast, h, exog=[1, 2]) assert_raises(ValueError, res.forecast, h, exog=np.ones((h, 2))) def check_equivalent_models(mod, mod2): attrs = [ 'level', 'trend', 'seasonal_periods', 'seasonal', 'freq_seasonal_periods', 'freq_seasonal_harmonics', 'freq_seasonal', 'cycle', 'ar_order', 'autoregressive', 'irregular', 'stochastic_level', 'stochastic_trend', 'stochastic_seasonal', 'stochastic_freq_seasonal', 'stochastic_cycle', 'damped_cycle', 'mle_regression', 'trend_specification', 'trend_mask', 'regression', 'cycle_frequency_bound'] ssm_attrs = [ 'nobs', 'k_endog', 'k_states', 'k_posdef', 'obs_intercept', 'design', 'obs_cov', 'state_intercept', 'transition', 'selection', 'state_cov'] for attr in attrs: assert_equal(getattr(mod2, attr), getattr(mod, attr)) for attr in ssm_attrs: assert_equal(getattr(mod2.ssm, attr), getattr(mod.ssm, attr)) assert_equal(mod2._get_init_kwds(), mod._get_init_kwds()) def test_recreate_model(): nobs = 100 endog = np.ones(nobs) * 2.0 exog = np.ones(nobs) levels = [ 'irregular', 'ntrend', 'fixed intercept', 'deterministic constant', 'dconstant', 'local level', 'llevel', 'random walk', 'rwalk', 'fixed slope', 'deterministic trend', 'dtrend', 'local linear deterministic trend', 'lldtrend', 'random walk with drift', 'rwdrift', 'local linear trend', 'lltrend', 'smooth trend', 'strend', 'random trend', 'rtrend'] for level in levels: # Note: have to add in some stochastic component, otherwise we have # problems with entirely deterministic models # level + stochastic seasonal mod = UnobservedComponents(endog, level=level, seasonal=2, stochastic_seasonal=True, exog=exog) mod2 = UnobservedComponents(endog, exog=exog, **mod._get_init_kwds()) check_equivalent_models(mod, mod2) # level + autoregressive mod = UnobservedComponents(endog, level=level, exog=exog, autoregressive=1) mod2 = UnobservedComponents(endog, exog=exog, **mod._get_init_kwds()) check_equivalent_models(mod, mod2) # level + stochastic cycle mod = UnobservedComponents(endog, level=level, exog=exog, cycle=True, stochastic_cycle=True, damped_cycle=True) mod2 = UnobservedComponents(endog, exog=exog, **mod._get_init_kwds()) check_equivalent_models(mod, mod2) def test_append_results(): endog = np.arange(100) exog = np.ones_like(endog) params = [1., 1., 0.1, 1.] mod1 = UnobservedComponents(endog, 'llevel', exog=exog) res1 = mod1.smooth(params) mod2 = UnobservedComponents(endog[:50], 'llevel', exog=exog[:50]) res2 = mod2.smooth(params) res3 = res2.append(endog[50:], exog=exog[50:]) assert_equal(res1.specification, res3.specification) assert_allclose(res3.cov_params_default, res2.cov_params_default) for attr in ['nobs', 'llf', 'llf_obs', 'loglikelihood_burn']: assert_equal(getattr(res3, attr), getattr(res1, attr)) for attr in [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov']: assert_equal(getattr(res3, attr), getattr(res1, attr)) assert_allclose(res3.forecast(10, exog=np.ones(10)), res1.forecast(10, exog=np.ones(10))) def test_extend_results(): endog = np.arange(100) exog = np.ones_like(endog) params = [1., 1., 0.1, 1.] mod1 = UnobservedComponents(endog, 'llevel', exog=exog) res1 = mod1.smooth(params) mod2 = UnobservedComponents(endog[:50], 'llevel', exog=exog[:50]) res2 = mod2.smooth(params) res3 = res2.extend(endog[50:], exog=exog[50:]) assert_allclose(res3.llf_obs, res1.llf_obs[50:]) for attr in [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov']: desired = getattr(res1, attr) if desired is not None: desired = desired[..., 50:] assert_equal(getattr(res3, attr), desired) assert_allclose(res3.forecast(10, exog=np.ones(10)), res1.forecast(10, exog=np.ones(10))) def test_apply_results(): endog = np.arange(100) exog = np.ones_like(endog) params = [1., 1., 0.1, 1.] mod1 = UnobservedComponents(endog[:50], 'llevel', exog=exog[:50]) res1 = mod1.smooth(params) mod2 = UnobservedComponents(endog[50:], 'llevel', exog=exog[50:]) res2 = mod2.smooth(params) res3 = res2.apply(endog[:50], exog=exog[:50]) assert_equal(res1.specification, res3.specification) assert_allclose(res3.cov_params_default, res2.cov_params_default) for attr in ['nobs', 'llf', 'llf_obs', 'loglikelihood_burn']: assert_equal(getattr(res3, attr), getattr(res1, attr)) for attr in [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov']: assert_equal(getattr(res3, attr), getattr(res1, attr)) assert_allclose(res3.forecast(10, exog=np.ones(10)), res1.forecast(10, exog=np.ones(10))) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_tools.py000066400000000000000000000733431400612667500253570ustar00rootroot00000000000000""" Tests for tools Author: Chad Fulton License: Simplified-BSD """ import pytest import numpy as np from numpy.testing import (assert_allclose, assert_equal, assert_array_less, assert_array_equal, assert_almost_equal) import pandas as pd from scipy.linalg import solve_discrete_lyapunov from statsmodels.tsa.statespace import tools from statsmodels.tsa.api import acovf class TestCompanionMatrix(object): cases = [ (2, np.array([[0, 1], [0, 0]])), ([1, -1, -2], np.array([[1, 1], [2, 0]])), ([1, -1, -2, -3], np.array([[1, 1, 0], [2, 0, 1], [3, 0, 0]])), ([1, -np.array([[1, 2], [3, 4]]), -np.array([[5, 6], [7, 8]])], np.array([[1, 2, 5, 6], [3, 4, 7, 8], [1, 0, 0, 0], [0, 1, 0, 0]]).T), # GH 5570 (np.int64(2), np.array([[0, 1], [0, 0]])) ] def test_cases(self): for polynomial, result in self.cases: assert_equal(tools.companion_matrix(polynomial), result) class TestDiff(object): x = np.arange(10) cases = [ # diff = 1 ([1, 2, 3], 1, None, 1, [1, 1]), # diff = 2 (x, 2, None, 1, [0]*8), # diff = 1, seasonal_diff=1, seasonal_periods=4 (x, 1, 1, 4, [0]*5), (x**2, 1, 1, 4, [8]*5), (x**3, 1, 1, 4, [60, 84, 108, 132, 156]), # diff = 1, seasonal_diff=2, seasonal_periods=2 (x, 1, 2, 2, [0]*5), (x**2, 1, 2, 2, [0]*5), (x**3, 1, 2, 2, [24]*5), (x**4, 1, 2, 2, [240, 336, 432, 528, 624]), ] # TODO: use pytest.mark.parametrize? def test_cases(self): # Basic cases for series, diff, seas_diff, seasonal_periods, result in self.cases: seasonal_diff = seas_diff # Test numpy array x = tools.diff(series, diff, seasonal_diff, seasonal_periods) assert_almost_equal(x, result) # Test as Pandas Series series = pd.Series(series) # Rewrite to test as n-dimensional array series = np.c_[series, series] result = np.c_[result, result] # Test Numpy array x = tools.diff(series, diff, seasonal_diff, seasonal_periods) assert_almost_equal(x, result) # Test as Pandas DataFrame series = pd.DataFrame(series) x = tools.diff(series, diff, seasonal_diff, seasonal_periods) assert_almost_equal(x, result) class TestSolveDiscreteLyapunov(object): def solve_dicrete_lyapunov_direct(self, a, q, complex_step=False): # This is the discrete Lyapunov solver as "real function of real # variables": the difference between this and the usual, complex, # version is that in the Kronecker product the second argument is # *not* conjugated here. if not complex_step: lhs = np.kron(a, a.conj()) lhs = np.eye(lhs.shape[0]) - lhs x = np.linalg.solve(lhs, q.flatten()) else: lhs = np.kron(a, a) lhs = np.eye(lhs.shape[0]) - lhs x = np.linalg.solve(lhs, q.flatten()) return np.reshape(x, q.shape) def test_univariate(self): # Real case a = np.array([[0.5]]) q = np.array([[10.]]) actual = tools.solve_discrete_lyapunov(a, q) desired = solve_discrete_lyapunov(a, q) assert_allclose(actual, desired) # Complex case (where the Lyapunov equation is taken as a complex # function) a = np.array([[0.5+1j]]) q = np.array([[10.]]) actual = tools.solve_discrete_lyapunov(a, q) desired = solve_discrete_lyapunov(a, q) assert_allclose(actual, desired) # Complex case (where the Lyapunov equation is taken as a real # function) a = np.array([[0.5+1j]]) q = np.array([[10.]]) actual = tools.solve_discrete_lyapunov(a, q, complex_step=True) desired = self.solve_dicrete_lyapunov_direct(a, q, complex_step=True) assert_allclose(actual, desired) def test_multivariate(self): # Real case a = tools.companion_matrix([1, -0.4, 0.5]) q = np.diag([10., 5.]) actual = tools.solve_discrete_lyapunov(a, q) desired = solve_discrete_lyapunov(a, q) assert_allclose(actual, desired) # Complex case (where the Lyapunov equation is taken as a complex # function) a = tools.companion_matrix([1, -0.4+0.1j, 0.5]) q = np.diag([10., 5.]) actual = tools.solve_discrete_lyapunov(a, q, complex_step=False) desired = self.solve_dicrete_lyapunov_direct(a, q, complex_step=False) assert_allclose(actual, desired) # Complex case (where the Lyapunov equation is taken as a real # function) a = tools.companion_matrix([1, -0.4+0.1j, 0.5]) q = np.diag([10., 5.]) actual = tools.solve_discrete_lyapunov(a, q, complex_step=True) desired = self.solve_dicrete_lyapunov_direct(a, q, complex_step=True) assert_allclose(actual, desired) class TestConcat(object): x = np.arange(10) valid = [ (((1, 2, 3), (4,)), (1, 2, 3, 4)), (((1, 2, 3), [4]), (1, 2, 3, 4)), (([1, 2, 3], np.r_[4]), (1, 2, 3, 4)), ((np.r_[1, 2, 3], pd.Series([4])), 0, True, (1, 2, 3, 4)), ((pd.Series([1, 2, 3]), pd.Series([4])), 0, True, (1, 2, 3, 4)), ((np.c_[x[:2], x[:2]], np.c_[x[2:3], x[2:3]]), np.c_[x[:3], x[:3]]), ((np.c_[x[:2], x[:2]].T, np.c_[x[2:3], x[2:3]].T), 1, np.c_[x[:3], x[:3]].T), ((pd.DataFrame(np.c_[x[:2], x[:2]]), np.c_[x[2:3], x[2:3]]), 0, True, np.c_[x[:3], x[:3]]), ] invalid = [ (((1, 2, 3), pd.Series([4])), ValueError), (((1, 2, 3), np.array([[1, 2]])), ValueError) ] def test_valid(self): for args in self.valid: assert_array_equal(tools.concat(*args[:-1]), args[-1]) def test_invalid(self): for args in self.invalid: with pytest.raises(args[-1]): tools.concat(*args[:-1]) class TestIsInvertible(object): cases = [ ([1, -0.5], True), ([1, 1-1e-9], True), ([1, 1], False), ([1, 0.9, 0.1], True), (np.array([1, 0.9, 0.1]), True), (pd.Series([1, 0.9, 0.1]), True) ] def test_cases(self): for polynomial, invertible in self.cases: assert_equal(tools.is_invertible(polynomial), invertible) class TestConstrainStationaryUnivariate(object): cases = [ (np.array([2.]), -2./((1+2.**2)**0.5)) ] def test_cases(self): for unconstrained, constrained in self.cases: result = tools.constrain_stationary_univariate(unconstrained) assert_equal(result, constrained) class TestUnconstrainStationaryUnivariate(object): cases = [ (np.array([-2./((1+2.**2)**0.5)]), np.array([2.])) ] def test_cases(self): for constrained, unconstrained in self.cases: result = tools.unconstrain_stationary_univariate(constrained) assert_allclose(result, unconstrained) class TestStationaryUnivariate(object): # Test that the constraint and unconstrained functions are inverses constrained_cases = [ np.array([0]), np.array([0.1]), np.array([-0.5]), np.array([0.999])] unconstrained_cases = [ np.array([10.]), np.array([-40.42]), np.array([0.123])] def test_cases(self): for constrained in self.constrained_cases: unconstrained = tools.unconstrain_stationary_univariate(constrained) # noqa:E501 reconstrained = tools.constrain_stationary_univariate(unconstrained) # noqa:E501 assert_allclose(reconstrained, constrained) for unconstrained in self.unconstrained_cases: constrained = tools.constrain_stationary_univariate(unconstrained) reunconstrained = tools.unconstrain_stationary_univariate(constrained) # noqa:E501 assert_allclose(reunconstrained, unconstrained) class TestValidateMatrixShape(object): # name, shape, nrows, ncols, nobs valid = [ ('TEST', (5, 2), 5, 2, None), ('TEST', (5, 2), 5, 2, 10), ('TEST', (5, 2, 10), 5, 2, 10), ] invalid = [ ('TEST', (5,), 5, None, None), ('TEST', (5, 1, 1, 1), 5, 1, None), ('TEST', (5, 2), 10, 2, None), ('TEST', (5, 2), 5, 1, None), ('TEST', (5, 2, 10), 5, 2, None), ('TEST', (5, 2, 10), 5, 2, 5), ] def test_valid_cases(self): for args in self.valid: # Just testing that no exception is raised tools.validate_matrix_shape(*args) def test_invalid_cases(self): for args in self.invalid: with pytest.raises(ValueError): tools.validate_matrix_shape(*args) class TestValidateVectorShape(object): # name, shape, nrows, ncols, nobs valid = [ ('TEST', (5,), 5, None), ('TEST', (5,), 5, 10), ('TEST', (5, 10), 5, 10), ] invalid = [ ('TEST', (5, 2, 10), 5, 10), ('TEST', (5,), 10, None), ('TEST', (5, 10), 5, None), ('TEST', (5, 10), 5, 5), ] def test_valid_cases(self): for args in self.valid: # Just testing that no exception is raised tools.validate_vector_shape(*args) def test_invalid_cases(self): for args in self.invalid: with pytest.raises(ValueError): tools.validate_vector_shape(*args) def test_multivariate_acovf(): _acovf = tools._compute_multivariate_acovf_from_coefficients # Test for a VAR(1) process. From Lutkepohl (2007), pages 27-28. # See (2.1.14) for Phi_1, (2.1.33) for Sigma_u, and (2.1.34) for Gamma_0 Sigma_u = np.array([[2.25, 0, 0], [0, 1.0, 0.5], [0, 0.5, 0.74]]) Phi_1 = np.array([[0.5, 0, 0], [0.1, 0.1, 0.3], [0, 0.2, 0.3]]) Gamma_0 = np.array([[3.0, 0.161, 0.019], [0.161, 1.172, 0.674], [0.019, 0.674, 0.954]]) assert_allclose(_acovf([Phi_1], Sigma_u)[0], Gamma_0, atol=1e-3) # Test for a VAR(2) process. From Lutkepohl (2007), pages 28-29 # See (2.1.40) for Phi_1, Phi_2, (2.1.14) for Sigma_u, and (2.1.42) for # Gamma_0, Gamma_1 Sigma_u = np.diag([0.09, 0.04]) Phi_1 = np.array([[0.5, 0.1], [0.4, 0.5]]) Phi_2 = np.array([[0, 0], [0.25, 0]]) Gamma_0 = np.array([[0.131, 0.066], [0.066, 0.181]]) Gamma_1 = np.array([[0.072, 0.051], [0.104, 0.143]]) Gamma_2 = np.array([[0.046, 0.040], [0.113, 0.108]]) Gamma_3 = np.array([[0.035, 0.031], [0.093, 0.083]]) assert_allclose( _acovf([Phi_1, Phi_2], Sigma_u, maxlag=0), [Gamma_0], atol=1e-3) assert_allclose( _acovf([Phi_1, Phi_2], Sigma_u, maxlag=1), [Gamma_0, Gamma_1], atol=1e-3) assert_allclose( _acovf([Phi_1, Phi_2], Sigma_u), [Gamma_0, Gamma_1], atol=1e-3) assert_allclose( _acovf([Phi_1, Phi_2], Sigma_u, maxlag=2), [Gamma_0, Gamma_1, Gamma_2], atol=1e-3) assert_allclose( _acovf([Phi_1, Phi_2], Sigma_u, maxlag=3), [Gamma_0, Gamma_1, Gamma_2, Gamma_3], atol=1e-3) # Test sample acovf in the univariate case against sm.tsa.acovf x = np.arange(20)*1.0 assert_allclose( np.squeeze(tools._compute_multivariate_sample_acovf(x, maxlag=4)), acovf(x, fft=False)[:5]) def test_multivariate_pacf(): # Test sample acovf in the univariate case against sm.tsa.acovf np.random.seed(1234) x = np.arange(10000) y = np.random.normal(size=10000) # Note: could make this test more precise with higher nobs, but no need to assert_allclose( tools._compute_multivariate_sample_pacf(np.c_[x, y], maxlag=1)[0], np.diag([1, 0]), atol=1e-2) class TestConstrainStationaryMultivariate(object): cases = [ # This is the same test as the univariate case above, except notice # the sign difference; this is an array input / output (np.array([[2.]]), np.eye(1), np.array([[2./((1+2.**2)**0.5)]])), # Same as above, but now a list input / output ([np.array([[2.]])], np.eye(1), [np.array([[2./((1+2.**2)**0.5)]])]) ] eigval_cases = [ [np.array([[0]])], [np.array([[100]]), np.array([[50]])], [np.array([[30, 1], [-23, 15]]), np.array([[10, .3], [.5, -30]])], ] def test_cases(self): # Test against known results for unconstrained, error_variance, constrained in self.cases: result = tools.constrain_stationary_multivariate( unconstrained, error_variance) assert_allclose(result[0], constrained) # Test that the constrained results correspond to companion matrices # with eigenvalues less than 1 in modulus for unconstrained in self.eigval_cases: if type(unconstrained) == list: cov = np.eye(unconstrained[0].shape[0]) else: cov = np.eye(unconstrained.shape[0]) constrained, _ = tools.constrain_stationary_multivariate(unconstrained, cov) # noqa:E501 companion = tools.companion_matrix( [1] + [-np.squeeze(constrained[i]) for i in range(len(constrained))] ).T assert_array_less(np.abs(np.linalg.eigvals(companion)), 1) class TestUnconstrainStationaryMultivariate(object): cases = [ # This is the same test as the univariate case above, except notice # the sign difference; this is an array input / output (np.array([[2./((1+2.**2)**0.5)]]), np.eye(1), np.array([[2.]])), # Same as above, but now a list input / output ([np.array([[2./((1+2.**2)**0.5)]])], np.eye(1), [np.array([[2.]])]) ] def test_cases(self): for constrained, error_variance, unconstrained in self.cases: result = tools.unconstrain_stationary_multivariate( constrained, error_variance) assert_allclose(result[0], unconstrained) class TestStationaryMultivariate(object): # Test that the constraint and unconstrained functions are inverses constrained_cases = [ np.array([[0]]), np.array([[0.1]]), np.array([[-0.5]]), np.array([[0.999]]), [np.array([[0]])], np.array([[0.8, -0.2]]), [np.array([[0.8]]), np.array([[-0.2]])], [np.array([[0.3, 0.01], [-0.23, 0.15]]), np.array([[0.1, 0.03], [0.05, -0.3]])], np.array([[0.3, 0.01, 0.1, 0.03], [-0.23, 0.15, 0.05, -0.3]]) ] unconstrained_cases = [ np.array([[0]]), np.array([[-40.42]]), np.array([[0.123]]), [np.array([[0]])], np.array([[100, 50]]), [np.array([[100]]), np.array([[50]])], [np.array([[30, 1], [-23, 15]]), np.array([[10, .3], [.5, -30]])], np.array([[30, 1, 10, .3], [-23, 15, .5, -30]]) ] def test_cases(self): for constrained in self.constrained_cases: if type(constrained) == list: cov = np.eye(constrained[0].shape[0]) else: cov = np.eye(constrained.shape[0]) unconstrained, _ = tools.unconstrain_stationary_multivariate(constrained, cov) # noqa:E501 reconstrained, _ = tools.constrain_stationary_multivariate(unconstrained, cov) # noqa:E501 assert_allclose(reconstrained, constrained) for unconstrained in self.unconstrained_cases: if type(unconstrained) == list: cov = np.eye(unconstrained[0].shape[0]) else: cov = np.eye(unconstrained.shape[0]) constrained, _ = tools.constrain_stationary_multivariate(unconstrained, cov) # noqa:E501 reunconstrained, _ = tools.unconstrain_stationary_multivariate(constrained, cov) # noqa:E501 # Note: low tolerance comes from last example in # unconstrained_cases, but is not a real problem assert_allclose(reunconstrained, unconstrained, atol=1e-4) def test_reorder_matrix_rows(): nobs = 5 k_endog = 3 k_states = 3 missing = np.zeros((k_endog, nobs)) given = np.zeros((k_endog, k_states, nobs)) given[:, :, :] = np.array([[11, 12, 13], [21, 22, 23], [31, 32, 33]])[:, :, np.newaxis] desired = given.copy() missing[0, 0] = 1 given[:, :, 0] = np.array([[21, 22, 23], [31, 32, 33], [0, 0, 0]]) desired[0, :, 0] = 0 missing[:2, 1] = 1 given[:, :, 1] = np.array([[31, 32, 33], [0, 0, 0], [0, 0, 0]]) desired[:2, :, 1] = 0 missing[0, 2] = 1 missing[2, 2] = 1 given[:, :, 2] = np.array([[21, 22, 23], [0, 0, 0], [0, 0, 0]]) desired[0, :, 2] = 0 desired[2, :, 2] = 0 missing[1, 3] = 1 given[:, :, 3] = np.array([[11, 12, 13], [31, 32, 33], [0, 0, 0]]) desired[1, :, 3] = 0 missing[2, 4] = 1 given[:, :, 4] = np.array([[11, 12, 13], [21, 22, 23], [0, 0, 0]]) desired[2, :, 4] = 0 actual = np.asfortranarray(given) missing = np.asfortranarray(missing.astype(np.int32)) tools.reorder_missing_matrix(actual, missing, True, False, False, inplace=True) assert_equal(actual, desired) def test_reorder_matrix_cols(): nobs = 5 k_endog = 3 k_states = 3 missing = np.zeros((k_endog, nobs)) given = np.zeros((k_endog, k_states, nobs)) given[:, :, :] = np.array([[11, 12, 13], [21, 22, 23], [31, 32, 33]])[:, :, np.newaxis] desired = given.copy() missing[0, 0] = 1 given[:, :, :] = np.array([[12, 13, 0], [22, 23, 0], [32, 33, 0]])[:, :, np.newaxis] desired[:, 0, 0] = 0 missing[:2, 1] = 1 given[:, :, 1] = np.array([[13, 0, 0], [23, 0, 0], [33, 0, 0]]) desired[:, :2, 1] = 0 missing[0, 2] = 1 missing[2, 2] = 1 given[:, :, 2] = np.array([[12, 0, 0], [22, 0, 0], [32, 0, 0]]) desired[:, 0, 2] = 0 desired[:, 2, 2] = 0 missing[1, 3] = 1 given[:, :, 3] = np.array([[11, 13, 0], [21, 23, 0], [31, 33, 0]]) desired[:, 1, 3] = 0 missing[2, 4] = 1 given[:, :, 4] = np.array([[11, 12, 0], [21, 22, 0], [31, 32, 0]]) desired[:, 2, 4] = 0 actual = np.asfortranarray(given) missing = np.asfortranarray(missing.astype(np.int32)) tools.reorder_missing_matrix(actual, missing, False, True, False, inplace=True) assert_equal(actual[:, :, 4], desired[:, :, 4]) def test_reorder_submatrix(): nobs = 5 k_endog = 3 missing = np.zeros((k_endog, nobs)) missing[0, 0] = 1 missing[:2, 1] = 1 missing[0, 2] = 1 missing[2, 2] = 1 missing[1, 3] = 1 missing[2, 4] = 1 given = np.zeros((k_endog, k_endog, nobs)) given[:, :, :] = np.array([[11, 12, 13], [21, 22, 23], [31, 32, 33]])[:, :, np.newaxis] desired = given.copy() given[:, :, 0] = np.array([[22, 23, 0], [32, 33, 0], [0, 0, 0]]) desired[0, :, 0] = 0 desired[:, 0, 0] = 0 given[:, :, 1] = np.array([[33, 0, 0], [0, 0, 0], [0, 0, 0]]) desired[:2, :, 1] = 0 desired[:, :2, 1] = 0 given[:, :, 2] = np.array([[22, 0, 0], [0, 0, 0], [0, 0, 0]]) desired[0, :, 2] = 0 desired[:, 0, 2] = 0 desired[2, :, 2] = 0 desired[:, 2, 2] = 0 given[:, :, 3] = np.array([[11, 13, 0], [31, 33, 0], [0, 0, 0]]) desired[1, :, 3] = 0 desired[:, 1, 3] = 0 given[:, :, 4] = np.array([[11, 12, 0], [21, 22, 0], [0, 0, 0]]) desired[2, :, 4] = 0 desired[:, 2, 4] = 0 actual = np.asfortranarray(given) missing = np.asfortranarray(missing.astype(np.int32)) tools.reorder_missing_matrix(actual, missing, True, True, False, inplace=True) assert_equal(actual, desired) def test_reorder_diagonal_submatrix(): nobs = 5 k_endog = 3 missing = np.zeros((k_endog, nobs)) missing[0, 0] = 1 missing[:2, 1] = 1 missing[0, 2] = 1 missing[2, 2] = 1 missing[1, 3] = 1 missing[2, 4] = 1 given = np.zeros((k_endog, k_endog, nobs)) given[:, :, :] = np.array([[11, 00, 00], [00, 22, 00], [00, 00, 33]])[:, :, np.newaxis] desired = given.copy() given[:, :, 0] = np.array([[22, 00, 0], [00, 33, 0], [0, 0, 0]]) desired[0, :, 0] = 0 desired[:, 0, 0] = 0 given[:, :, 1] = np.array([[33, 0, 0], [0, 0, 0], [0, 0, 0]]) desired[:2, :, 1] = 0 desired[:, :2, 1] = 0 given[:, :, 2] = np.array([[22, 0, 0], [0, 0, 0], [0, 0, 0]]) desired[0, :, 2] = 0 desired[:, 0, 2] = 0 desired[2, :, 2] = 0 desired[:, 2, 2] = 0 given[:, :, 3] = np.array([[11, 00, 0], [00, 33, 0], [0, 0, 0]]) desired[1, :, 3] = 0 desired[:, 1, 3] = 0 given[:, :, 4] = np.array([[11, 00, 0], [00, 22, 0], [0, 0, 0]]) desired[2, :, 4] = 0 desired[:, 2, 4] = 0 actual = np.asfortranarray(given.copy()) missing = np.asfortranarray(missing.astype(np.int32)) tools.reorder_missing_matrix(actual, missing, True, True, False, inplace=True) assert_equal(actual, desired) actual = np.asfortranarray(given.copy()) tools.reorder_missing_matrix(actual, missing, True, True, True, inplace=True) assert_equal(actual, desired) def test_reorder_vector(): nobs = 5 k_endog = 3 missing = np.zeros((k_endog, nobs)) missing[0, 0] = 1 missing[:2, 1] = 1 missing[0, 2] = 1 missing[2, 2] = 1 missing[1, 3] = 1 missing[2, 4] = 1 given = np.zeros((k_endog, nobs)) given[:, :] = np.array([1, 2, 3])[:, np.newaxis] desired = given.copy() given[:, 0] = [2, 3, 0] desired[:, 0] = [0, 2, 3] given[:, 1] = [3, 0, 0] desired[:, 1] = [0, 0, 3] given[:, 2] = [2, 0, 0] desired[:, 2] = [0, 2, 0] given[:, 3] = [1, 3, 0] desired[:, 3] = [1, 0, 3] given[:, 4] = [1, 2, 0] desired[:, 4] = [1, 2, 0] actual = np.asfortranarray(given.copy()) missing = np.asfortranarray(missing.astype(np.int32)) tools.reorder_missing_vector(actual, missing, inplace=True) assert_equal(actual, desired) def test_copy_missing_matrix_rows(): nobs = 5 k_endog = 3 k_states = 2 missing = np.zeros((k_endog, nobs)) missing[0, 0] = 1 missing[:2, 1] = 1 missing[0, 2] = 1 missing[2, 2] = 1 missing[1, 3] = 1 missing[2, 4] = 1 A = np.zeros((k_endog, k_states, nobs)) for t in range(nobs): n = int(k_endog - np.sum(missing[:, t])) A[:n, :, t] = 1. B = np.zeros((k_endog, k_states, nobs), order='F') missing = np.asfortranarray(missing.astype(np.int32)) tools.copy_missing_matrix(A, B, missing, True, False, False, inplace=True) assert_equal(B, A) def test_copy_missing_matrix_cols(): nobs = 5 k_endog = 3 k_states = 2 missing = np.zeros((k_endog, nobs)) missing[0, 0] = 1 missing[:2, 1] = 1 missing[0, 2] = 1 missing[2, 2] = 1 missing[1, 3] = 1 missing[2, 4] = 1 A = np.zeros((k_states, k_endog, nobs)) for t in range(nobs): n = int(k_endog - np.sum(missing[:, t])) A[:, :n, t] = 1. B = np.zeros((k_states, k_endog, nobs), order='F') missing = np.asfortranarray(missing.astype(np.int32)) tools.copy_missing_matrix(A, B, missing, False, True, False, inplace=True) assert_equal(B, A) def test_copy_missing_submatrix(): nobs = 5 k_endog = 3 missing = np.zeros((k_endog, nobs)) missing[0, 0] = 1 missing[:2, 1] = 1 missing[0, 2] = 1 missing[2, 2] = 1 missing[1, 3] = 1 missing[2, 4] = 1 A = np.zeros((k_endog, k_endog, nobs)) for t in range(nobs): n = int(k_endog - np.sum(missing[:, t])) A[:n, :n, t] = 1. B = np.zeros((k_endog, k_endog, nobs), order='F') missing = np.asfortranarray(missing.astype(np.int32)) tools.copy_missing_matrix(A, B, missing, True, True, False, inplace=True) assert_equal(B, A) def test_copy_missing_diagonal_submatrix(): nobs = 5 k_endog = 3 missing = np.zeros((k_endog, nobs)) missing[0, 0] = 1 missing[:2, 1] = 1 missing[0, 2] = 1 missing[2, 2] = 1 missing[1, 3] = 1 missing[2, 4] = 1 A = np.zeros((k_endog, k_endog, nobs)) for t in range(nobs): n = int(k_endog - np.sum(missing[:, t])) A[:n, :n, t] = np.eye(n) B = np.zeros((k_endog, k_endog, nobs), order='F') missing = np.asfortranarray(missing.astype(np.int32)) tools.copy_missing_matrix(A, B, missing, True, True, False, inplace=True) assert_equal(B, A) B = np.zeros((k_endog, k_endog, nobs), order='F') tools.copy_missing_matrix(A, B, missing, True, True, True, inplace=True) assert_equal(B, A) def test_copy_missing_vector(): nobs = 5 k_endog = 3 missing = np.zeros((k_endog, nobs)) missing[0, 0] = 1 missing[:2, 1] = 1 missing[0, 2] = 1 missing[2, 2] = 1 missing[1, 3] = 1 missing[2, 4] = 1 A = np.zeros((k_endog, nobs)) for t in range(nobs): n = int(k_endog - np.sum(missing[:, t])) A[:n, t] = 1. B = np.zeros((k_endog, nobs), order='F') missing = np.asfortranarray(missing.astype(np.int32)) tools.copy_missing_vector(A, B, missing, inplace=True) assert_equal(B, A) def test_copy_index_matrix_rows(): nobs = 5 k_endog = 3 k_states = 2 index = np.zeros((k_endog, nobs)) index[0, 0] = 1 index[:2, 1] = 1 index[0, 2] = 1 index[2, 2] = 1 index[1, 3] = 1 index[2, 4] = 1 A = np.zeros((k_endog, k_states, nobs)) for t in range(nobs): for i in range(k_endog): if index[i, t]: A[i, :, t] = 1. B = np.zeros((k_endog, k_states, nobs), order='F') index = np.asfortranarray(index.astype(np.int32)) tools.copy_index_matrix(A, B, index, True, False, False, inplace=True) assert_equal(B, A) def test_copy_index_matrix_cols(): nobs = 5 k_endog = 3 k_states = 2 index = np.zeros((k_endog, nobs)) index[0, 0] = 1 index[:2, 1] = 1 index[0, 2] = 1 index[2, 2] = 1 index[1, 3] = 1 index[2, 4] = 1 A = np.zeros((k_states, k_endog, nobs)) for t in range(nobs): for i in range(k_endog): if index[i, t]: A[:, i, t] = 1. B = np.zeros((k_states, k_endog, nobs), order='F') index = np.asfortranarray(index.astype(np.int32)) tools.copy_index_matrix(A, B, index, False, True, False, inplace=True) assert_equal(B, A) def test_copy_index_submatrix(): nobs = 5 k_endog = 3 index = np.zeros((k_endog, nobs)) index[0, 0] = 1 index[:2, 1] = 1 index[0, 2] = 1 index[2, 2] = 1 index[1, 3] = 1 index[2, 4] = 1 A = np.zeros((k_endog, k_endog, nobs)) for t in range(nobs): for i in range(k_endog): if index[i, t]: A[i, :, t] = 1. A[:, i, t] = 1. B = np.zeros((k_endog, k_endog, nobs), order='F') index = np.asfortranarray(index.astype(np.int32)) tools.copy_index_matrix(A, B, index, True, True, False, inplace=True) assert_equal(B, A) def test_copy_index_diagonal_submatrix(): nobs = 5 k_endog = 3 index = np.zeros((k_endog, nobs)) index[0, 0] = 1 index[:2, 1] = 1 index[0, 2] = 1 index[2, 2] = 1 index[1, 3] = 1 index[2, 4] = 1 A = np.zeros((k_endog, k_endog, nobs)) for t in range(nobs): for i in range(k_endog): if index[i, t]: A[i, i, t] = 1. B = np.zeros((k_endog, k_endog, nobs), order='F') index = np.asfortranarray(index.astype(np.int32)) tools.copy_index_matrix(A, B, index, True, True, False, inplace=True) assert_equal(B, A) B = np.zeros((k_endog, k_endog, nobs), order='F') tools.copy_index_matrix(A, B, index, True, True, True, inplace=True) assert_equal(B, A) def test_copy_index_vector(): nobs = 5 k_endog = 3 index = np.zeros((k_endog, nobs)) index[0, 0] = 1 index[:2, 1] = 1 index[0, 2] = 1 index[2, 2] = 1 index[1, 3] = 1 index[2, 4] = 1 A = np.zeros((k_endog, nobs)) for t in range(nobs): for i in range(k_endog): if index[i, t]: A[i, t] = 1. B = np.zeros((k_endog, nobs), order='F') index = np.asfortranarray(index.astype(np.int32)) tools.copy_index_vector(A, B, index, inplace=True) assert_equal(B, A) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_univariate.py000066400000000000000000000650621400612667500263650ustar00rootroot00000000000000""" Tests for univariate treatment of multivariate models TODO skips the tests for measurement disturbance and measurement disturbance covariance, which do not pass. The univariate smoother *appears* to be correctly implemented against Durbin and Koopman (2012) chapter 6, yet still gives a different answer from the conventional smoother. It's not clear if this is intended (i.e. it has to be at least slightly different, since the conventional smoother can return a non-diagonal covariance matrix whereas the univariate smoother must return a diagonal covariance matrix). Author: Chad Fulton License: Simplified-BSD """ import os import numpy as np from numpy.testing import assert_almost_equal, assert_allclose import pandas as pd import pytest from statsmodels import datasets from statsmodels.tsa.statespace.mlemodel import MLEModel from statsmodels.tsa.statespace.tests.results import results_kalman_filter from statsmodels.tsa.statespace.sarimax import SARIMAX current_path = os.path.dirname(os.path.abspath(__file__)) class TestClark1989(object): """ Clark's (1989) bivariate unobserved components model of real GDP (as presented in Kim and Nelson, 1999) Tests two-dimensional observation data. Test data produced using GAUSS code described in Kim and Nelson (1999) and found at http://econ.korea.ac.kr/~cjkim/SSMARKOV.htm See `results.results_kalman_filter` for more information. """ @classmethod def setup_class(cls, dtype=float, alternate_timing=False, **kwargs): cls.true = results_kalman_filter.uc_bi cls.true_states = pd.DataFrame(cls.true['states']) # GDP and Unemployment, Quarterly, 1948.1 - 1995.3 data = pd.DataFrame( cls.true['data'], index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'), columns=['GDP', 'UNEMP'] )[4:] data['GDP'] = np.log(data['GDP']) data['UNEMP'] = (data['UNEMP']/100) k_states = 6 cls.mlemodel = MLEModel(data, k_states=k_states, **kwargs) cls.model = cls.mlemodel.ssm # Statespace representation cls.model.design[:, :, 0] = [[1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1]] cls.model.transition[ ([0, 0, 1, 1, 2, 3, 4, 5], [0, 4, 1, 2, 1, 2, 4, 5], [0, 0, 0, 0, 0, 0, 0, 0]) ] = [1, 1, 0, 0, 1, 1, 1, 1] cls.model.selection = np.eye(cls.model.k_states) # Update matrices with given parameters (sigma_v, sigma_e, sigma_w, sigma_vl, sigma_ec, phi_1, phi_2, alpha_1, alpha_2, alpha_3) = np.array( cls.true['parameters'], ) cls.model.design[([1, 1, 1], [1, 2, 3], [0, 0, 0])] = [ alpha_1, alpha_2, alpha_3 ] cls.model.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2] cls.model.obs_cov[1, 1, 0] = sigma_ec**2 cls.model.state_cov[ np.diag_indices(k_states)+(np.zeros(k_states, dtype=int),)] = [ sigma_v**2, sigma_e**2, 0, 0, sigma_w**2, sigma_vl**2 ] # Initialization initial_state = np.zeros((k_states,)) initial_state_cov = np.eye(k_states)*100 # Initialization: cls.modification if not alternate_timing: initial_state_cov = np.dot( np.dot(cls.model.transition[:, :, 0], initial_state_cov), cls.model.transition[:, :, 0].T ) else: cls.model.timing_init_filtered = True cls.model.initialize_known(initial_state, initial_state_cov) # Conventional filtering, smoothing, and simulation smoothing cls.model.filter_conventional = True cls.conventional_results = cls.model.smooth() n_disturbance_variates = ( (cls.model.k_endog + cls.model.k_posdef) * cls.model.nobs ) cls.conventional_sim = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) # Univariate filtering, smoothing, and simulation smoothing cls.model.filter_univariate = True cls.univariate_results = cls.model.smooth() cls.univariate_sim = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) def test_using_univariate(self): # Regression test to make sure the univariate_results actually # used the univariate Kalman filtering approach (i.e. that the flag # being set actually caused the filter to not use the conventional # filter) assert not self.conventional_results.filter_univariate assert self.univariate_results.filter_univariate assert_allclose( self.conventional_results.forecasts_error_cov[1, 1, 0], 143.03724478030821 ) assert_allclose( self.univariate_results.forecasts_error_cov[1, 1, 0], 120.66208525029386 ) def test_forecasts(self): assert_almost_equal( self.conventional_results.forecasts[0, :], self.univariate_results.forecasts[0, :], 9 ) def test_forecasts_error(self): assert_almost_equal( self.conventional_results.forecasts_error[0, :], self.univariate_results.forecasts_error[0, :], 9 ) def test_forecasts_error_cov(self): assert_almost_equal( self.conventional_results.forecasts_error_cov[0, 0, :], self.univariate_results.forecasts_error_cov[0, 0, :], 9 ) def test_filtered_state(self): assert_almost_equal( self.conventional_results.filtered_state, self.univariate_results.filtered_state, 8 ) def test_filtered_state_cov(self): assert_almost_equal( self.conventional_results.filtered_state_cov, self.univariate_results.filtered_state_cov, 9 ) def test_predicted_state(self): assert_almost_equal( self.conventional_results.predicted_state, self.univariate_results.predicted_state, 8 ) def test_predicted_state_cov(self): assert_almost_equal( self.conventional_results.predicted_state_cov, self.univariate_results.predicted_state_cov, 9 ) def test_loglike(self): assert_allclose( self.conventional_results.llf_obs, self.univariate_results.llf_obs ) def test_smoothed_states(self): assert_almost_equal( self.conventional_results.smoothed_state, self.univariate_results.smoothed_state, 7 ) def test_smoothed_states_cov(self): assert_almost_equal( self.conventional_results.smoothed_state_cov, self.univariate_results.smoothed_state_cov, 6 ) def test_smoothed_measurement_disturbance(self): assert_almost_equal( self.conventional_results.smoothed_measurement_disturbance, self.univariate_results.smoothed_measurement_disturbance, 9 ) def test_smoothed_measurement_disturbance_cov(self): conv = self.conventional_results univ = self.univariate_results assert_almost_equal( conv.smoothed_measurement_disturbance_cov.diagonal(), univ.smoothed_measurement_disturbance_cov.diagonal(), 9 ) def test_smoothed_state_disturbance(self): assert_allclose( self.conventional_results.smoothed_state_disturbance, self.univariate_results.smoothed_state_disturbance, atol=1e-7 ) def test_smoothed_state_disturbance_cov(self): assert_almost_equal( self.conventional_results.smoothed_state_disturbance_cov, self.univariate_results.smoothed_state_disturbance_cov, 9 ) def test_simulation_smoothed_state(self): assert_almost_equal( self.conventional_sim.simulated_state, self.univariate_sim.simulated_state, 9 ) def test_simulation_smoothed_measurement_disturbance(self): assert_almost_equal( self.conventional_sim.simulated_measurement_disturbance, self.univariate_sim.simulated_measurement_disturbance, 9 ) def test_simulation_smoothed_state_disturbance(self): assert_almost_equal( self.conventional_sim.simulated_state_disturbance, self.univariate_sim.simulated_state_disturbance, 9 ) class TestClark1989Alternate(TestClark1989): @classmethod def setup_class(cls, *args, **kwargs): super(TestClark1989Alternate, cls).setup_class(alternate_timing=True, *args, **kwargs) def test_using_alterate(self): assert(self.model._kalman_filter.filter_timing == 1) class MultivariateMissingGeneralObsCov(object): @classmethod def setup_class(cls, which, dtype=float, alternate_timing=False, **kwargs): # Results path = os.path.join(current_path, 'results', 'results_smoothing_generalobscov_R.csv') cls.desired = pd.read_csv(path) # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = dta[['realgdp', 'realcons', 'realinv']].diff().iloc[1:] if which == 'all': obs.iloc[:50, :] = np.nan obs.iloc[119:130, :] = np.nan elif which == 'partial': obs.iloc[0:50, 0] = np.nan obs.iloc[119:130, 0] = np.nan elif which == 'mixed': obs.iloc[0:50, 0] = np.nan obs.iloc[19:70, 1] = np.nan obs.iloc[39:90, 2] = np.nan obs.iloc[119:130, 0] = np.nan obs.iloc[119:130, 2] = np.nan # Create the model mod = MLEModel(obs, k_states=3, k_posdef=3, **kwargs) mod['design'] = np.eye(3) X = (np.arange(9) + 1).reshape((3, 3)) / 10. mod['obs_cov'] = np.dot(X, X.T) mod['transition'] = np.eye(3) mod['selection'] = np.eye(3) mod['state_cov'] = np.eye(3) mod.initialize_approximate_diffuse(1e6) cls.model = mod.ssm # Conventional filtering, smoothing, and simulation smoothing cls.model.filter_conventional = True cls.conventional_results = cls.model.smooth() n_disturbance_variates = ( (cls.model.k_endog + cls.model.k_posdef) * cls.model.nobs ) cls.conventional_sim = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) # Univariate filtering, smoothing, and simulation smoothing cls.model.filter_univariate = True cls.univariate_results = cls.model.smooth() cls.univariate_sim = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) def test_using_univariate(self): # Regression test to make sure the univariate_results actually # used the univariate Kalman filtering approach (i.e. that the flag # being set actually caused the filter to not use the conventional # filter) assert not self.conventional_results.filter_univariate assert self.univariate_results.filter_univariate assert_allclose( self.conventional_results.forecasts_error_cov[1, 1, 0], 1000000.77 ) assert_allclose( self.univariate_results.forecasts_error_cov[1, 1, 0], 1000000.77 ) def test_forecasts(self): assert_almost_equal( self.conventional_results.forecasts[0, :], self.univariate_results.forecasts[0, :], 9 ) def test_forecasts_error(self): assert_almost_equal( self.conventional_results.forecasts_error[0, :], self.univariate_results.forecasts_error[0, :], 9 ) def test_forecasts_error_cov(self): assert_almost_equal( self.conventional_results.forecasts_error_cov[0, 0, :], self.univariate_results.forecasts_error_cov[0, 0, :], 9 ) def test_filtered_state(self): assert_almost_equal( self.conventional_results.filtered_state, self.univariate_results.filtered_state, 8 ) def test_filtered_state_cov(self): assert_almost_equal( self.conventional_results.filtered_state_cov, self.univariate_results.filtered_state_cov, 9 ) def test_predicted_state(self): assert_almost_equal( self.conventional_results.predicted_state, self.univariate_results.predicted_state, 8 ) def test_predicted_state_cov(self): assert_almost_equal( self.conventional_results.predicted_state_cov, self.univariate_results.predicted_state_cov, 9 ) def test_loglike(self): assert_allclose( self.conventional_results.llf_obs, self.univariate_results.llf_obs ) def test_smoothed_states(self): assert_almost_equal( self.conventional_results.smoothed_state, self.univariate_results.smoothed_state, 7 ) def test_smoothed_states_cov(self): assert_almost_equal( self.conventional_results.smoothed_state_cov, self.univariate_results.smoothed_state_cov, 6 ) @pytest.mark.skip def test_smoothed_measurement_disturbance(self): assert_almost_equal( self.conventional_results.smoothed_measurement_disturbance, self.univariate_results.smoothed_measurement_disturbance, 9 ) @pytest.mark.skip def test_smoothed_measurement_disturbance_cov(self): conv = self.conventional_results univ = self.univariate_results assert_almost_equal( conv.smoothed_measurement_disturbance_cov.diagonal(), univ.smoothed_measurement_disturbance_cov.diagonal(), 9 ) def test_smoothed_state_disturbance(self): assert_allclose( self.conventional_results.smoothed_state_disturbance, self.univariate_results.smoothed_state_disturbance, atol=1e-7 ) def test_smoothed_state_disturbance_cov(self): assert_almost_equal( self.conventional_results.smoothed_state_disturbance_cov, self.univariate_results.smoothed_state_disturbance_cov, 9 ) def test_simulation_smoothed_state(self): assert_almost_equal( self.conventional_sim.simulated_state, self.univariate_sim.simulated_state, 9 ) @pytest.mark.skip def test_simulation_smoothed_measurement_disturbance(self): assert_almost_equal( self.conventional_sim.simulated_measurement_disturbance, self.univariate_sim.simulated_measurement_disturbance, 9 ) def test_simulation_smoothed_state_disturbance(self): assert_almost_equal( self.conventional_sim.simulated_state_disturbance, self.univariate_sim.simulated_state_disturbance, 9 ) class TestMultivariateGeneralObsCov(MultivariateMissingGeneralObsCov): """ This class tests the univariate method when the observation covariance matrix is not diagonal and all data is available. Tests are against the conventional smoother. """ @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariateGeneralObsCov, cls).setup_class('none') class TestMultivariateAllMissingGeneralObsCov( MultivariateMissingGeneralObsCov): """ This class tests the univariate method when the observation covariance matrix is not diagonal and there are cases of fully missing data only. Tests are against the conventional smoother. """ @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariateAllMissingGeneralObsCov, cls).setup_class('all') class TestMultivariatePartialMissingGeneralObsCov( MultivariateMissingGeneralObsCov): """ This class tests the univariate method when the observation covariance matrix is not diagonal and there are cases of partially missing data only. Tests are against the conventional smoother. """ @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariatePartialMissingGeneralObsCov, cls).setup_class('partial') def test_forecasts(self): assert_almost_equal( self.conventional_results.forecasts[0, :], self.univariate_results.forecasts[0, :], 8 ) def test_forecasts_error(self): assert_almost_equal( self.conventional_results.forecasts_error[0, :], self.univariate_results.forecasts_error[0, :], 8 ) class TestMultivariateMixedMissingGeneralObsCov( MultivariateMissingGeneralObsCov): """ This class tests the univariate method when the observation covariance matrix is not diagonal and there are cases of both partially missing and fully missing data. Tests are against the conventional smoother. """ @classmethod def setup_class(cls, *args, **kwargs): super(TestMultivariateMixedMissingGeneralObsCov, cls).setup_class('mixed') def test_forecasts(self): assert_almost_equal( self.conventional_results.forecasts[0, :], self.univariate_results.forecasts[0, :], 8 ) def test_forecasts_error(self): assert_almost_equal( self.conventional_results.forecasts_error[0, :], self.univariate_results.forecasts_error[0, :], 8 ) class TestMultivariateVAR(object): @classmethod def setup_class(cls, which='none', **kwargs): # Results path = os.path.join(current_path, 'results', 'results_smoothing_generalobscov_R.csv') cls.desired = pd.read_csv(path) # Data dta = datasets.macrodata.load_pandas().data dta.index = pd.date_range(start='1959-01-01', end='2009-7-01', freq='QS') obs = dta[['realgdp', 'realcons', 'realinv']].diff().iloc[1:] if which == 'all': obs.iloc[:50, :] = np.nan obs.iloc[119:130, :] = np.nan elif which == 'partial': obs.iloc[0:50, 0] = np.nan obs.iloc[119:130, 0] = np.nan elif which == 'mixed': obs.iloc[0:50, 0] = np.nan obs.iloc[19:70, 1] = np.nan obs.iloc[39:90, 2] = np.nan obs.iloc[119:130, 0] = np.nan obs.iloc[119:130, 2] = np.nan # Create the model mod = MLEModel(obs, k_states=3, k_posdef=3, **kwargs) mod['design'] = np.eye(3) mod['obs_cov'] = np.array([ [609.0746647855, 0., 0.], [0., 1.8774916622, 0.], [0., 0., 124.6768281675]]) mod['transition'] = np.array([ [-0.8110473405, 1.8005304445, 1.0215975772], [-1.9846632699, 2.4091302213, 1.9264449765], [0.9181658823, -0.2442384581, -0.6393462272]]) mod['selection'] = np.eye(3) mod['state_cov'] = np.array([ [1552.9758843938, 612.7185121905, 877.6157204992], [612.7185121905, 467.8739411204, 70.608037339], [877.6157204992, 70.608037339, 900.5440385836]]) mod.initialize_approximate_diffuse(1e6) cls.model = mod.ssm # Conventional filtering, smoothing, and simulation smoothing cls.model.filter_conventional = True cls.conventional_results = cls.model.smooth() n_disturbance_variates = ( (cls.model.k_endog + cls.model.k_posdef) * cls.model.nobs ) cls.conventional_sim = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) # Univariate filtering, smoothing, and simulation smoothing cls.model.filter_univariate = True cls.univariate_results = cls.model.smooth() cls.univariate_sim = cls.model.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(cls.model.k_states) ) def test_forecasts(self): assert_almost_equal( self.conventional_results.forecasts[0, :], self.univariate_results.forecasts[0, :], 9 ) def test_forecasts_error(self): assert_almost_equal( self.conventional_results.forecasts_error[0, :], self.univariate_results.forecasts_error[0, :], 9 ) def test_forecasts_error_cov(self): assert_almost_equal( self.conventional_results.forecasts_error_cov[0, 0, :], self.univariate_results.forecasts_error_cov[0, 0, :], 9 ) def test_filtered_state(self): assert_almost_equal( self.conventional_results.filtered_state, self.univariate_results.filtered_state, 8 ) def test_filtered_state_cov(self): assert_almost_equal( self.conventional_results.filtered_state_cov, self.univariate_results.filtered_state_cov, 9 ) def test_predicted_state(self): assert_almost_equal( self.conventional_results.predicted_state, self.univariate_results.predicted_state, 8 ) def test_predicted_state_cov(self): assert_almost_equal( self.conventional_results.predicted_state_cov, self.univariate_results.predicted_state_cov, 9 ) def test_loglike(self): assert_allclose( self.conventional_results.llf_obs, self.univariate_results.llf_obs ) def test_smoothed_states(self): assert_allclose( self.conventional_results.smoothed_state, self.univariate_results.smoothed_state ) def test_smoothed_states_cov(self): assert_allclose( self.conventional_results.smoothed_state_cov, self.univariate_results.smoothed_state_cov, atol=1e-9 ) @pytest.mark.skip def test_smoothed_measurement_disturbance(self): assert_almost_equal( self.conventional_results.smoothed_measurement_disturbance, self.univariate_results.smoothed_measurement_disturbance, 9 ) @pytest.mark.skip def test_smoothed_measurement_disturbance_cov(self): conv = self.self.conventional_results univ = self.univariate_results assert_almost_equal( conv.smoothed_measurement_disturbance_cov.diagonal(), univ.smoothed_measurement_disturbance_cov.diagonal(), 9 ) def test_smoothed_state_disturbance(self): assert_allclose( self.conventional_results.smoothed_state_disturbance, self.univariate_results.smoothed_state_disturbance, atol=1e-7 ) def test_smoothed_state_disturbance_cov(self): assert_almost_equal( self.conventional_results.smoothed_state_disturbance_cov, self.univariate_results.smoothed_state_disturbance_cov, 9 ) def test_simulation_smoothed_state(self): assert_almost_equal( self.conventional_sim.simulated_state, self.univariate_sim.simulated_state, 9 ) @pytest.mark.skip def test_simulation_smoothed_measurement_disturbance(self): assert_almost_equal( self.conventional_sim.simulated_measurement_disturbance, self.univariate_sim.simulated_measurement_disturbance, 9 ) def test_simulation_smoothed_state_disturbance(self): assert_almost_equal( self.conventional_sim.simulated_state_disturbance, self.univariate_sim.simulated_state_disturbance, 9 ) def test_time_varying_transition(): # Test for correct univariate filtering/smoothing when we have a # time-varying transition matrix endog = np.array([10, 5, 2.5, 1.25, 2.5, 5, 10]) transition = np.ones((1, 1, 7)) transition[..., :5] = 0.5 transition[..., 5:] = 2 # Conventional filter / smoother mod1 = SARIMAX(endog, order=(1, 0, 0), measurement_error=True) mod1.update([2., 1., 1.]) mod1.ssm['transition'] = transition res1 = mod1.ssm.smooth() # Univariate filter / smoother mod2 = SARIMAX(endog, order=(1, 0, 0), measurement_error=True) mod2.ssm.filter_univariate = True mod2.update([2., 1., 1.]) mod2.ssm['transition'] = transition res2 = mod2.ssm.smooth() # Simulation smoothers n_disturbance_variates = (mod1.k_endog + mod1.k_posdef) * mod1.nobs sim1 = mod1.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(mod1.k_states)) sim2 = mod2.simulation_smoother( disturbance_variates=np.zeros(n_disturbance_variates), initial_state_variates=np.zeros(mod2.k_states)) # Test for correctness assert_allclose(res1.forecasts[0, :], res2.forecasts[0, :]) assert_allclose(res1.forecasts_error[0, :], res2.forecasts_error[0, :]) assert_allclose(res1.forecasts_error_cov[0, 0, :], res2.forecasts_error_cov[0, 0, :]) assert_allclose(res1.filtered_state, res2.filtered_state) assert_allclose(res1.filtered_state_cov, res2.filtered_state_cov) assert_allclose(res1.predicted_state, res2.predicted_state) assert_allclose(res1.predicted_state_cov, res2.predicted_state_cov) assert_allclose(res1.llf_obs, res2.llf_obs) assert_allclose(res1.smoothed_state, res2.smoothed_state) assert_allclose(res1.smoothed_state_cov, res2.smoothed_state_cov) assert_allclose(res1.smoothed_measurement_disturbance, res2.smoothed_measurement_disturbance) assert_allclose(res1.smoothed_measurement_disturbance_cov.diagonal(), res2.smoothed_measurement_disturbance_cov.diagonal()) assert_allclose(res1.smoothed_state_disturbance, res2.smoothed_state_disturbance) assert_allclose(res1.smoothed_state_disturbance_cov, res2.smoothed_state_disturbance_cov) assert_allclose(sim1.simulated_state, sim2.simulated_state) assert_allclose(sim1.simulated_measurement_disturbance, sim2.simulated_measurement_disturbance) assert_allclose(sim1.simulated_state_disturbance, sim2.simulated_state_disturbance) statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_var.py000066400000000000000000000204501400612667500247760ustar00rootroot00000000000000""" Tests for VAR models (via VARMAX) These are primarily tests of VAR results from the VARMAX state space approach compared to the output of estimation via CSS loglikelihood_burn = k_ar is required, since the loglikelihood reported by the CSS approach is the conditional loglikelihood. Author: Chad Fulton License: Simplified-BSD """ import os import numpy as np from numpy.testing import assert_allclose import pandas as pd from statsmodels.tsa.statespace import varmax from .results import results_var_R current_path = os.path.dirname(os.path.abspath(__file__)) results_var_R_output = pd.read_csv( os.path.join(current_path, 'results', 'results_var_R_output.csv')) up2 = os.path.split(os.path.split(current_path)[0])[0] dta = pd.read_stata(os.path.join(up2, 'tests', 'results', 'lutkepohl2.dta')) dta.index = pd.PeriodIndex(dta.qtr, freq='Q') endog = dta[['dln_inv', 'dln_inc', 'dln_consump']].loc['1960Q2':'1978'] # Note that we start the time-trend at 0 here, to match time_trend0 = np.arange(len(endog)) exog0 = np.c_[np.ones(len(endog)), time_trend0, time_trend0**2] time_trend0_fcast = np.arange(len(endog), len(endog) + 10) exog0_fcast = np.c_[np.ones(10), time_trend0_fcast, time_trend0_fcast**2] # And here we start the time-trend at 1 time_trend1 = np.arange(1, len(endog) + 1) time_trend1_fcast = np.arange(len(endog) + 1, len(endog) + 1 + 10) exog1 = np.c_[np.ones(len(endog)), time_trend1, time_trend1**2] exog1_fcast = np.c_[np.ones(10), time_trend1_fcast, time_trend1_fcast**2] def check_irf(test, mod, results, params=None): # Note that 'vars' uses an estimator of Sigma_u with k_params fewer degrees # of freedom to compute impulse responses, so we need to reset the # state_cov matrix for this part of the test Sigma_u_mle = mod['state_cov'] nobs_effective = mod.nobs - mod.k_ar df_resid = (nobs_effective - (mod.k_ar * mod.k_endog + mod.k_trend + mod.k_exog)) Sigma_u = Sigma_u_mle * nobs_effective / df_resid L = np.linalg.cholesky(Sigma_u) if params is None: params = np.copy(results['params']) params[-6:] = L[np.tril_indices_from(L)] res = mod.smooth(params) for i in range(3): impulse_to = endog.columns[i] # Non-orthogonalized columns = ['%s.irf.%s.%s' % (test, impulse_to, name) for name in endog.columns] assert_allclose(res.impulse_responses(10, i), results_var_R_output[columns]) # Orthogonalized columns = ['%s.irf.ortho.%s.%s' % (test, impulse_to, name) for name in endog.columns] assert_allclose(res.impulse_responses(10, i, orthogonalized=True), results_var_R_output[columns]) # Orthogonalized, cumulated columns = ['%s.irf.cumu.%s.%s' % (test, impulse_to, name) for name in endog.columns] result = res.impulse_responses(10, i, orthogonalized=True, cumulative=True) assert_allclose(result, results_var_R_output[columns]) def test_var_basic(): test = 'basic' # VAR(2), no trend or exog results = results_var_R.res_basic mod = varmax.VARMAX(endog, order=(2, 0), trend='n', loglikelihood_burn=2) res = mod.smooth(results['params']) assert_allclose(res.llf, results['llf']) # Forecast columns = ['%s.fcast.%s.fcst' % (test, name) for name in endog.columns] assert_allclose(res.forecast(10), results_var_R_output[columns].iloc[:10]) # IRF check_irf(test, mod, results) # FEVD: TODO def test_var_c(): test = 'c' # VAR(2), constant trend, no exog results = results_var_R.res_c mod = varmax.VARMAX(endog, order=(2, 0), trend='c', loglikelihood_burn=2) res = mod.smooth(results['params']) assert_allclose(res.llf, results['llf']) # Forecast columns = ['%s.fcast.%s.fcst' % (test, name) for name in endog.columns] assert_allclose(res.forecast(10), results_var_R_output[columns].iloc[:10]) # IRF check_irf(test, mod, results) # FEVD: TODO def test_var_ct(): test = 'ct' # VAR(2), constant and time trend, no exog results = results_var_R.res_ct mod = varmax.VARMAX(endog, order=(2, 0), trend='ct', loglikelihood_burn=2) res = mod.smooth(results['params']) assert_allclose(res.llf, results['llf']) # Forecast columns = ['%s.fcast.%s.fcst' % (test, name) for name in endog.columns] assert_allclose(res.forecast(10), results_var_R_output[columns].iloc[:10]) # IRF check_irf(test, mod, results) # FEVD: TODO def test_var_ct_as_exog0(): test = 'ct_as_exog0' # VAR(2), no built-in trend, constant and time trend as exog # Here we start the time-trend at 0 results = results_var_R.res_ct_as_exog0 mod = varmax.VARMAX(endog, order=(2, 0), exog=exog0[:, :2], trend='n', loglikelihood_burn=2) res = mod.smooth(results['params']) assert_allclose(res.llf, results['llf']) # Forecast columns = ['%s.fcast.%s.fcst' % (test, name) for name in endog.columns] assert_allclose(res.forecast(10, exog=exog0_fcast[:, :2]), results_var_R_output[columns].iloc[:10]) # IRF check_irf(test, mod, results) # FEVD: TODO def test_var_ct_as_exog1(): test = 'ct' # VAR(2), no built-in trend, constant and time trend as exog # Here we start the time-trend at 1 and so we can compare to the built-in # trend results "res_ct" results = results_var_R.res_ct mod = varmax.VARMAX(endog, order=(2, 0), exog=exog1[:, :2], trend='n', loglikelihood_burn=2) # Since the params were given for the built-in trend case, we need to # re-order them params = results['params'] params = np.r_[params[6:-6], params[:6], params[-6:]] res = mod.smooth(params) assert_allclose(res.llf, results['llf']) # Forecast columns = ['%s.fcast.%s.fcst' % (test, name) for name in endog.columns] assert_allclose(res.forecast(10, exog=exog1_fcast[:, :2]), results_var_R_output[columns].iloc[:10]) # IRF check_irf(test, mod, results, params) # FEVD: TODO def test_var_ctt(): test = 'ctt_as_exog1' # VAR(2), constant, trend, and trend**2, no exog # Note that this is comparing against trend as exog in the R package, # since it does not have a built-in option for trend**2 results = results_var_R.res_ctt_as_exog1 mod = varmax.VARMAX(endog, order=(2, 0), trend='ctt', loglikelihood_burn=2) params = results['params'] params = np.r_[params[-(6+9):-6], params[:-(6+9)], params[-6:]] res = mod.smooth(params) assert_allclose(res.llf, results['llf']) # Forecast columns = ['%s.fcast.%s.fcst' % (test, name) for name in endog.columns] assert_allclose(res.forecast(10), results_var_R_output[columns].iloc[:10]) # IRF check_irf(test, mod, results, params) # FEVD: TODO def test_var_ct_exog(): test = 'ct_exog' # VAR(2), constant and trend, 'inc' variable as exog results = results_var_R.res_ct_exog exog = dta['inc'].loc['1960Q2':'1978'] exog_fcast = dta[['inc']].loc['1979Q1':'1981Q2'] mod = varmax.VARMAX(endog, order=(2, 0), exog=exog, trend='ct', loglikelihood_burn=2) res = mod.smooth(results['params']) assert_allclose(res.llf, results['llf']) # Forecast columns = ['%s.fcast.%s.fcst' % (test, name) for name in endog.columns] assert_allclose(res.forecast(10, exog=exog_fcast), results_var_R_output[columns].iloc[:10]) # IRF check_irf(test, mod, results) # FEVD: TODO def test_var_c_2exog(): test = 'c_2exog' # VAR(2), constant, 'inc', 'inv' variables as exog results = results_var_R.res_c_2exog exog = dta[['inc', 'inv']].loc['1960Q2':'1978'] exog_fcast = dta[['inc', 'inv']].loc['1979Q1':'1981Q2'] mod = varmax.VARMAX(endog, order=(2, 0), exog=exog, trend='c', loglikelihood_burn=2) res = mod.smooth(results['params']) assert_allclose(res.llf, results['llf']) # Forecast columns = ['%s.fcast.%s.fcst' % (test, name) for name in endog.columns] assert_allclose(res.forecast(10, exog=exog_fcast), results_var_R_output[columns].iloc[:10]) # IRF check_irf(test, mod, results) # FEVD: TODO statsmodels-0.12.2/statsmodels/tsa/statespace/tests/test_varmax.py000066400000000000000000001406251400612667500255130ustar00rootroot00000000000000""" Tests for VARMAX models Author: Chad Fulton License: Simplified-BSD """ import os import re import warnings import numpy as np from numpy.testing import assert_equal, assert_allclose, assert_raises import pandas as pd import pytest from statsmodels.tsa.statespace import varmax, sarimax from statsmodels.iolib.summary import forg from .results import results_varmax current_path = os.path.dirname(os.path.abspath(__file__)) var_path = os.path.join('results', 'results_var_stata.csv') var_results = pd.read_csv(os.path.join(current_path, var_path)) varmax_path = os.path.join('results', 'results_varmax_stata.csv') varmax_results = pd.read_csv(os.path.join(current_path, varmax_path)) class CheckVARMAX(object): """ Test Vector Autoregression against Stata's `dfactor` code (Stata's `var` function uses OLS and not state space / MLE, so we cannot get equivalent log-likelihoods) """ def test_mle(self): with warnings.catch_warnings(record=True): warnings.simplefilter('always') # Fit with all transformations # results = self.model.fit(method='powell', disp=-1) results = self.model.fit(maxiter=100, disp=False) # Fit now without transformations self.model.enforce_stationarity = False self.model.enforce_invertibility = False results = self.model.fit(results.params, method='nm', maxiter=1000, disp=False) self.model.enforce_stationarity = True self.model.enforce_invertibility = True assert_allclose(results.llf, self.results.llf, rtol=1e-5) @pytest.mark.smoke def test_params(self): # Smoke test to make sure the start_params are well-defined and # lead to a well-defined model model = self.model model.filter(model.start_params) # Similarly a smoke test for param_names assert len(model.start_params) == len(model.param_names) # Finally make sure the transform and untransform do their job actual = model.transform_params( model.untransform_params(model.start_params)) assert_allclose(actual, model.start_params) # Also in the case of enforce invertibility and stationarity = False model.enforce_stationarity = False model.enforce_invertibility = False actual = model.transform_params( model.untransform_params(model.start_params)) model.enforce_stationarity = True model.enforce_invertibility = True assert_allclose(actual, model.start_params) @pytest.mark.smoke def test_results(self): # Smoke test for creating the summary self.results.summary() model = self.model # Test cofficient matrix creation # (via a different, more direct, method) if model.k_ar > 0: params_ar = np.array(self.results.params[model._params_ar]) coefficients = params_ar.reshape(model.k_endog, model.k_endog * model.k_ar) coefficient_matrices = np.array([ coefficients[:model.k_endog, i*model.k_endog:(i+1)*model.k_endog] for i in range(model.k_ar) ]) assert_equal(self.results.coefficient_matrices_var, coefficient_matrices) else: assert_equal(self.results.coefficient_matrices_var, None) if model.k_ma > 0: params_ma = np.array(self.results.params[model._params_ma]) coefficients = params_ma.reshape(model.k_endog, model.k_endog * model.k_ma) coefficient_matrices = np.array([ coefficients[:model.k_endog, i*model.k_endog:(i+1)*model.k_endog] for i in range(model.k_ma) ]) assert_equal(self.results.coefficient_matrices_vma, coefficient_matrices) else: assert_equal(self.results.coefficient_matrices_vma, None) def test_loglike(self): assert_allclose(self.results.llf, self.true['loglike'], rtol=1e-6) def test_aic(self): # We only get 3 digits from Stata assert_allclose(self.results.aic, self.true['aic'], atol=3) def test_bic(self): # We only get 3 digits from Stata assert_allclose(self.results.bic, self.true['bic'], atol=3) def test_predict(self, end, atol=1e-6, **kwargs): # Tests predict + forecast assert_allclose( self.results.predict(end=end, **kwargs), self.true['predict'], atol=atol) def test_dynamic_predict(self, end, dynamic, atol=1e-6, **kwargs): # Tests predict + dynamic predict + forecast assert_allclose( self.results.predict(end=end, dynamic=dynamic, **kwargs), self.true['dynamic_predict'], atol=atol) def test_standardized_forecasts_error(self): cython_sfe = self.results.standardized_forecasts_error self.results._standardized_forecasts_error = None python_sfe = self.results.standardized_forecasts_error assert_allclose(cython_sfe, python_sfe) class CheckLutkepohl(CheckVARMAX): @classmethod def setup_class(cls, true, order, trend, error_cov_type, cov_type='approx', included_vars=['dln_inv', 'dln_inc', 'dln_consump'], **kwargs): cls.true = true # 1960:Q1 - 1982:Q4 dta = pd.DataFrame( results_varmax.lutkepohl_data, columns=['inv', 'inc', 'consump'], index=pd.date_range('1960-01-01', '1982-10-01', freq='QS')) dta['dln_inv'] = np.log(dta['inv']).diff() dta['dln_inc'] = np.log(dta['inc']).diff() dta['dln_consump'] = np.log(dta['consump']).diff() endog = dta.loc['1960-04-01':'1978-10-01', included_vars] cls.model = varmax.VARMAX(endog, order=order, trend=trend, error_cov_type=error_cov_type, **kwargs) cls.results = cls.model.smooth(true['params'], cov_type=cov_type) def test_predict(self, **kwargs): super(CheckLutkepohl, self).test_predict(end='1982-10-01', **kwargs) def test_dynamic_predict(self, **kwargs): super(CheckLutkepohl, self).test_dynamic_predict(end='1982-10-01', dynamic='1961-01-01', **kwargs) class TestVAR(CheckLutkepohl): @classmethod def setup_class(cls): true = results_varmax.lutkepohl_var1.copy() true['predict'] = var_results.iloc[1:][['predict_1', 'predict_2', 'predict_3']] true['dynamic_predict'] = var_results.iloc[1:][['dyn_predict_1', 'dyn_predict_2', 'dyn_predict_3']] super(TestVAR, cls).setup_class( true, order=(1, 0), trend='n', error_cov_type="unstructured") def test_bse_approx(self): bse = self.results._cov_params_approx().diagonal()**0.5 assert_allclose(bse**2, self.true['var_oim'], atol=1e-4) def test_bse_oim(self): bse = self.results._cov_params_oim().diagonal()**0.5 assert_allclose(bse**2, self.true['var_oim'], atol=1e-2) def test_summary(self): summary = self.results.summary() tables = [str(table) for table in summary.tables] params = self.true['params'] # Check the model overview table assert re.search(r'Model:.*VAR\(1\)', tables[0]) # For each endogenous variable, check the output for i in range(self.model.k_endog): offset = i * self.model.k_endog table = tables[i+2] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Results for equation %s' % name, table) # -> Make sure it's the right size assert len(table.split('\n')) == 8 # -> Check that we have the right coefficients assert re.search('L1.dln_inv +%.4f' % params[offset + 0], table) assert re.search('L1.dln_inc +%.4f' % params[offset + 1], table) assert re.search('L1.dln_consump +%.4f' % params[offset + 2], table) # Test the error covariance matrix table table = tables[-1] assert re.search('Error covariance matrix', table) assert len(table.split('\n')) == 11 params = params[self.model._params_state_cov] names = self.model.param_names[self.model._params_state_cov] for i in range(len(names)): assert re.search('%s +%.4f' % (names[i], params[i]), table) class TestVAR_diagonal(CheckLutkepohl): @classmethod def setup_class(cls): true = results_varmax.lutkepohl_var1_diag.copy() true['predict'] = var_results.iloc[1:][['predict_diag1', 'predict_diag2', 'predict_diag3']] true['dynamic_predict'] = var_results.iloc[1:][['dyn_predict_diag1', 'dyn_predict_diag2', 'dyn_predict_diag3']] super(TestVAR_diagonal, cls).setup_class( true, order=(1, 0), trend='n', error_cov_type="diagonal") def test_bse_approx(self): bse = self.results._cov_params_approx().diagonal()**0.5 assert_allclose(bse**2, self.true['var_oim'], atol=1e-5) def test_bse_oim(self): bse = self.results._cov_params_oim().diagonal()**0.5 assert_allclose(bse**2, self.true['var_oim'], atol=1e-2) def test_summary(self): summary = self.results.summary() tables = [str(table) for table in summary.tables] params = self.true['params'] # Check the model overview table assert re.search(r'Model:.*VAR\(1\)', tables[0]) # For each endogenous variable, check the output for i in range(self.model.k_endog): offset = i * self.model.k_endog table = tables[i+2] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Results for equation %s' % name, table) # -> Make sure it's the right size assert len(table.split('\n')) == 8 # -> Check that we have the right coefficients assert re.search('L1.dln_inv +%.4f' % params[offset + 0], table) assert re.search('L1.dln_inc +%.4f' % params[offset + 1], table) assert re.search('L1.dln_consump +%.4f' % params[offset + 2], table) # Test the error covariance matrix table table = tables[-1] assert re.search('Error covariance matrix', table) assert len(table.split('\n')) == 8 params = params[self.model._params_state_cov] names = self.model.param_names[self.model._params_state_cov] for i in range(len(names)): assert re.search('%s +%.4f' % (names[i], params[i]), table) class TestVAR_measurement_error(CheckLutkepohl): """ Notes ----- There does not appear to be a way to get Stata to estimate a VAR with measurement errors. Thus this test is mostly a smoke test that measurement errors are setup correctly: it uses the same params from TestVAR_diagonal and sets the measurement errors variance params to zero to check that the loglike and predict are the same. It also checks that the state-space representation with positive measurement errors is correct. """ @classmethod def setup_class(cls): true = results_varmax.lutkepohl_var1_diag_meas.copy() true['predict'] = var_results.iloc[1:][['predict_diag1', 'predict_diag2', 'predict_diag3']] true['dynamic_predict'] = var_results.iloc[1:][['dyn_predict_diag1', 'dyn_predict_diag2', 'dyn_predict_diag3']] super(TestVAR_measurement_error, cls).setup_class( true, order=(1, 0), trend='n', error_cov_type="diagonal", measurement_error=True) # Create another filter results with positive measurement errors cls.true_measurement_error_variances = [1., 2., 3.] params = np.r_[true['params'][:-3], cls.true_measurement_error_variances] cls.results2 = cls.model.smooth(params) def test_mle(self): # With the additional measurment error parameters, this would not be # a meaningful test pass def test_bse_approx(self): # This would just test the same thing # as TestVAR_diagonal.test_bse_approx pass def test_bse_oim(self): # This would just test the same thing as TestVAR_diagonal.test_bse_oim pass def test_aic(self): # Since the measurement error is added, the number # of parameters, and hence the aic and bic, will be off pass def test_bic(self): # Since the measurement error is added, the number # of parameters, and hence the aic and bic, will be off pass def test_representation(self): # Test that the state space representation in the measurement error # case is correct for name in self.model.ssm.shapes.keys(): if name == 'obs': pass elif name == 'obs_cov': actual = self.results2.filter_results.obs_cov desired = np.diag( self.true_measurement_error_variances)[:, :, np.newaxis] assert_equal(actual, desired) else: assert_equal(getattr(self.results2.filter_results, name), getattr(self.results.filter_results, name)) def test_summary(self): summary = self.results.summary() tables = [str(table) for table in summary.tables] params = self.true['params'] # Check the model overview table assert re.search(r'Model:.*VAR\(1\)', tables[0]) # For each endogenous variable, check the output for i in range(self.model.k_endog): offset = i * self.model.k_endog table = tables[i+2] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Results for equation %s' % name, table) # -> Make sure it's the right size assert len(table.split('\n')) == 9 # -> Check that we have the right coefficients assert re.search('L1.dln_inv +%.4f' % params[offset + 0], table) assert re.search('L1.dln_inc +%.4f' % params[offset + 1], table) assert re.search('L1.dln_consump +%.4f' % params[offset + 2], table) assert re.search('measurement_variance +%.4g' % params[-(i+1)], table) # Test the error covariance matrix table table = tables[-1] assert re.search('Error covariance matrix', table) assert len(table.split('\n')) == 8 params = params[self.model._params_state_cov] names = self.model.param_names[self.model._params_state_cov] for i in range(len(names)): assert re.search('%s +%.4f' % (names[i], params[i]), table) class TestVAR_obs_intercept(CheckLutkepohl): @classmethod def setup_class(cls): true = results_varmax.lutkepohl_var1_obs_intercept.copy() true['predict'] = var_results.iloc[1:][['predict_int1', 'predict_int2', 'predict_int3']] true['dynamic_predict'] = var_results.iloc[1:][['dyn_predict_int1', 'dyn_predict_int2', 'dyn_predict_int3']] super(TestVAR_obs_intercept, cls).setup_class( true, order=(1, 0), trend='n', error_cov_type="diagonal", obs_intercept=true['obs_intercept']) def test_bse_approx(self): bse = self.results._cov_params_approx().diagonal()**0.5 assert_allclose(bse**2, self.true['var_oim'], atol=1e-4) def test_bse_oim(self): bse = self.results._cov_params_oim().diagonal()**0.5 assert_allclose(bse**2, self.true['var_oim'], atol=1e-2) def test_aic(self): # Since the obs_intercept is added in in an ad-hoc way here, the number # of parameters, and hence the aic and bic, will be off pass def test_bic(self): # Since the obs_intercept is added in in an ad-hoc way here, the number # of parameters, and hence the aic and bic, will be off pass class TestVAR_exog(CheckLutkepohl): # Note: unlike the other tests in this file, this is against the Stata # var function rather than the Stata dfactor function @classmethod def setup_class(cls): true = results_varmax.lutkepohl_var1_exog.copy() true['predict'] = var_results.iloc[1:76][['predict_exog1_1', 'predict_exog1_2', 'predict_exog1_3']] true['predict'].iloc[0, :] = 0 true['fcast'] = var_results.iloc[76:][['fcast_exog1_dln_inv', 'fcast_exog1_dln_inc', 'fcast_exog1_dln_consump']] exog = np.arange(75) + 2 super(TestVAR_exog, cls).setup_class( true, order=(1, 0), trend='n', error_cov_type='unstructured', exog=exog, initialization='approximate_diffuse', loglikelihood_burn=1) def test_mle(self): pass def test_aic(self): # Stata's var calculates AIC differently pass def test_bic(self): # Stata's var calculates BIC differently pass def test_bse_approx(self): # Exclude the covariance cholesky terms bse = self.results._cov_params_approx().diagonal()**0.5 assert_allclose(bse[:-6]**2, self.true['var_oim'], atol=1e-5) def test_bse_oim(self): # Exclude the covariance cholesky terms bse = self.results._cov_params_oim().diagonal()**0.5 assert_allclose(bse[:-6]**2, self.true['var_oim'], atol=1e-5) def test_predict(self): super(CheckLutkepohl, self).test_predict(end='1978-10-01', atol=1e-3) def test_dynamic_predict(self): # Stata's var cannot subsequently use dynamic pass def test_forecast(self): # Tests forecast exog = (np.arange(75, 75+16) + 2)[:, np.newaxis] # Test it through the results class wrapper desired = self.results.forecast(steps=16, exog=exog) assert_allclose(desired, self.true['fcast'], atol=1e-6) # Test it directly (i.e. without the wrapping done in # VARMAXResults.get_prediction which converts exog to state_intercept) # beta = self.results.params[-9:-6] # state_intercept = np.concatenate([ # exog*beta[0], exog*beta[1], exog*beta[2]], axis=1).T # desired = mlemodel.MLEResults.get_prediction( # self.results._results, start=75, end=75+15, # state_intercept=state_intercept).predicted_mean # assert_allclose(desired, self.true['fcast'], atol=1e-6) def test_summary(self): summary = self.results.summary() tables = [str(table) for table in summary.tables] params = self.true['params'] # Check the model overview table assert re.search(r'Model:.*VARX\(1\)', tables[0]) # For each endogenous variable, check the output for i in range(self.model.k_endog): offset = i * self.model.k_endog table = tables[i+2] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Results for equation %s' % name, table) # -> Make sure it's the right size assert len(table.split('\n')) == 9 # -> Check that we have the right coefficients assert re.search('L1.dln_inv +%.4f' % params[offset + 0], table) assert re.search('L1.dln_inc +%.4f' % params[offset + 1], table) assert re.search( 'L1.dln_consump +%.4f' % params[offset + 2], table) assert re.search( 'beta.x1 +' + forg(params[self.model._params_regression][i], prec=4), table) # Test the error covariance matrix table table = tables[-1] assert re.search('Error covariance matrix', table) assert len(table.split('\n')) == 11 params = params[self.model._params_state_cov] names = self.model.param_names[self.model._params_state_cov] for i in range(len(names)): assert re.search('%s +%.4f' % (names[i], params[i]), table) class TestVAR_exog2(CheckLutkepohl): # This is a regression test, to make sure that the setup with multiple exog # works correctly. The params are from Stata, but the loglike is from # this model. Likely the small discrepancy (see the results file) is from # the approximate diffuse initialization. @classmethod def setup_class(cls): true = results_varmax.lutkepohl_var1_exog2.copy() true['predict'] = var_results.iloc[1:76][['predict_exog2_1', 'predict_exog2_2', 'predict_exog2_3']] true['predict'].iloc[0, :] = 0 true['fcast'] = var_results.iloc[76:][['fcast_exog2_dln_inv', 'fcast_exog2_dln_inc', 'fcast_exog2_dln_consump']] exog = np.c_[np.ones((75, 1)), (np.arange(75) + 2)[:, np.newaxis]] super(TestVAR_exog2, cls).setup_class( true, order=(1, 0), trend='n', error_cov_type='unstructured', exog=exog, initialization='approximate_diffuse', loglikelihood_burn=1) def test_mle(self): pass def test_aic(self): pass def test_bic(self): pass def test_bse_approx(self): pass def test_bse_oim(self): pass def test_predict(self): super(CheckLutkepohl, self).test_predict(end='1978-10-01', atol=1e-3) def test_dynamic_predict(self): # Stata's var cannot subsequently use dynamic pass def test_forecast(self): # Tests forecast exog = np.c_[np.ones((16, 1)), (np.arange(75, 75+16) + 2)[:, np.newaxis]] desired = self.results.forecast(steps=16, exog=exog) assert_allclose(desired, self.true['fcast'], atol=1e-6) class TestVAR2(CheckLutkepohl): @classmethod def setup_class(cls): true = results_varmax.lutkepohl_var2.copy() true['predict'] = var_results.iloc[1:][['predict_var2_1', 'predict_var2_2']] true['dynamic_predict'] = var_results.iloc[1:][['dyn_predict_var2_1', 'dyn_predict_var2_2']] super(TestVAR2, cls).setup_class( true, order=(2, 0), trend='n', error_cov_type='unstructured', included_vars=['dln_inv', 'dln_inc']) def test_bse_approx(self): # Exclude the covariance cholesky terms bse = self.results._cov_params_approx().diagonal()**0.5 assert_allclose(bse[:-3]**2, self.true['var_oim'][:-3], atol=1e-5) def test_bse_oim(self): # Exclude the covariance cholesky terms bse = self.results._cov_params_oim().diagonal()**0.5 assert_allclose(bse[:-3]**2, self.true['var_oim'][:-3], atol=1e-2) def test_summary(self): summary = self.results.summary() tables = [str(table) for table in summary.tables] params = self.true['params'] # Check the model overview table assert re.search(r'Model:.*VAR\(2\)', tables[0]) # For each endogenous variable, check the output for i in range(self.model.k_endog): offset = i * self.model.k_endog * self.model.k_ar table = tables[i+2] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Results for equation %s' % name, table) # -> Make sure it's the right size assert len(table.split('\n')) == 9 # -> Check that we have the right coefficients assert re.search('L1.dln_inv +%.4f' % params[offset + 0], table) assert re.search('L1.dln_inc +%.4f' % params[offset + 1], table) assert re.search('L2.dln_inv +%.4f' % params[offset + 2], table) assert re.search('L2.dln_inc +%.4f' % params[offset + 3], table) # Test the error covariance matrix table table = tables[-1] assert re.search('Error covariance matrix', table) assert len(table.split('\n')) == 8 params = params[self.model._params_state_cov] names = self.model.param_names[self.model._params_state_cov] for i in range(len(names)): assert re.search('%s +%.4f' % (names[i], params[i]), table) class CheckFREDManufacturing(CheckVARMAX): @classmethod def setup_class(cls, true, order, trend, error_cov_type, cov_type='approx', **kwargs): cls.true = true # 1960:Q1 - 1982:Q4 path = os.path.join(current_path, 'results', 'manufac.dta') with open(path, 'rb') as test_data: dta = pd.read_stata(test_data) dta.index = pd.DatetimeIndex(dta.month, freq='MS') dta['dlncaputil'] = dta['lncaputil'].diff() dta['dlnhours'] = dta['lnhours'].diff() endog = dta.loc['1972-02-01':, ['dlncaputil', 'dlnhours']] with warnings.catch_warnings(record=True): warnings.simplefilter('always') cls.model = varmax.VARMAX(endog, order=order, trend=trend, error_cov_type=error_cov_type, **kwargs) cls.results = cls.model.smooth(true['params'], cov_type=cov_type) class TestVARMA(CheckFREDManufacturing): """ Test against the sspace VARMA example with some params set to zeros. """ @classmethod def setup_class(cls): true = results_varmax.fred_varma11.copy() true['predict'] = varmax_results.iloc[1:][['predict_varma11_1', 'predict_varma11_2']] true['dynamic_predict'] = varmax_results.iloc[1:][[ 'dyn_predict_varma11_1', 'dyn_predict_varma11_2']] super(TestVARMA, cls).setup_class( true, order=(1, 1), trend='n', error_cov_type='diagonal') def test_mle(self): # Since the VARMA model here is generic (we're just forcing zeros # in some params) whereas Stata's is restricted, the MLE test is not # meaninful pass @pytest.mark.skip('Known failure: standard errors do not match.') def test_bse_approx(self): # Standard errors do not match Stata's pass @pytest.mark.skip('Known failure: standard errors do not match.') def test_bse_oim(self): # Standard errors do not match Stata's pass def test_aic(self): # Since the VARMA model here is generic (we're just putting in zeros # for some params), Stata assumes a different estimated number of # parameters; hence the aic and bic, will be off pass def test_bic(self): # Since the VARMA model here is generic (we're just putting in zeros # for some params), Stata assumes a different estimated number of # parameters; hence the aic and bic, will be off pass def test_predict(self): super(TestVARMA, self).test_predict(end='2009-05-01', atol=1e-4) def test_dynamic_predict(self): super(TestVARMA, self).test_dynamic_predict(end='2009-05-01', dynamic='2000-01-01') def test_summary(self): summary = self.results.summary() tables = [str(table) for table in summary.tables] params = self.true['params'] # Check the model overview table assert re.search(r'Model:.*VARMA\(1,1\)', tables[0]) # For each endogenous variable, check the output for i in range(self.model.k_endog): offset_ar = i * self.model.k_endog offset_ma = (self.model.k_endog**2 * self.model.k_ar + i * self.model.k_endog) table = tables[i+2] # -> Make sure we have the right table / table name name = self.model.endog_names[i] assert re.search('Results for equation %s' % name, table) # -> Make sure it's the right size assert len(table.split('\n')) == 9 # -> Check that we have the right coefficients assert re.search( 'L1.dlncaputil +' + forg(params[offset_ar + 0], prec=4), table) assert re.search( 'L1.dlnhours +' + forg(params[offset_ar + 1], prec=4), table) assert re.search( r'L1.e\(dlncaputil\) +' + forg(params[offset_ma + 0], prec=4), table) assert re.search( r'L1.e\(dlnhours\) +' + forg(params[offset_ma + 1], prec=4), table) # Test the error covariance matrix table table = tables[-1] assert re.search('Error covariance matrix', table) assert len(table.split('\n')) == 7 params = params[self.model._params_state_cov] names = self.model.param_names[self.model._params_state_cov] for i in range(len(names)): assert re.search('%s +%s' % (names[i], forg(params[i], prec=4)), table) class TestVMA1(CheckFREDManufacturing): """ Test against the sspace VARMA example with some params set to zeros. """ @classmethod def setup_class(cls): true = results_varmax.fred_vma1.copy() true['predict'] = varmax_results.iloc[1:][['predict_vma1_1', 'predict_vma1_2']] true['dynamic_predict'] = varmax_results.iloc[1:][[ 'dyn_predict_vma1_1', 'dyn_predict_vma1_2']] super(TestVMA1, cls).setup_class( true, order=(0, 1), trend='n', error_cov_type='diagonal') def test_mle(self): # Since the VARMA model here is generic (we're just forcing zeros # in some params) whereas Stata's is restricted, the MLE test is not # meaninful pass @pytest.mark.skip('Known failure: standard errors do not match.') def test_bse_approx(self): # Standard errors do not match Stata's pass @pytest.mark.skip('Known failure: standard errors do not match.') def test_bse_oim(self): # Standard errors do not match Stata's pass def test_aic(self): # Since the VARMA model here is generic (we're just putting in zeros # for some params), Stata assumes a different estimated number of # parameters; hence the aic and bic, will be off pass def test_bic(self): # Since the VARMA model here is generic (we're just putting in zeros # for some params), Stata assumes a different estimated number of # parameters; hence the aic and bic, will be off pass def test_predict(self): super(TestVMA1, self).test_predict(end='2009-05-01', atol=1e-4) def test_dynamic_predict(self): super(TestVMA1, self).test_dynamic_predict(end='2009-05-01', dynamic='2000-01-01') def test_specifications(): # Tests for model specification and state space creation endog = np.arange(20).reshape(10, 2) exog = np.arange(10) exog2 = pd.Series(exog, index=pd.date_range('2000-01-01', '2009-01-01', freq='AS')) # Test successful model creation varmax.VARMAX(endog, exog=exog, order=(1, 0)) # Test successful model creation with pandas exog varmax.VARMAX(endog, exog=exog2, order=(1, 0)) def test_misspecifications(): varmax.__warningregistry__ = {} # Tests for model specification and misspecification exceptions endog = np.arange(20).reshape(10, 2) # Bad trend specification with pytest.raises(ValueError): varmax.VARMAX(endog, order=(1, 0), trend='') # Bad error_cov_type specification with pytest.raises(ValueError): varmax.VARMAX(endog, order=(1, 0), error_cov_type='') # Bad order specification with pytest.raises(ValueError): varmax.VARMAX(endog, order=(0, 0)) with warnings.catch_warnings(record=True) as w: warnings.simplefilter('always') varmax.VARMAX(endog, order=(1, 1)) # Warning with VARMA specification with warnings.catch_warnings(record=True) as w: warnings.simplefilter('always') varmax.VARMAX(endog, order=(1, 1)) message = ('Estimation of VARMA(p,q) models is not generically robust,' ' due especially to identification issues.') assert str(w[0].message) == message warnings.resetwarnings() def test_misc_exog(): # Tests for missing data nobs = 20 k_endog = 2 np.random.seed(1208) endog = np.random.normal(size=(nobs, k_endog)) endog[:4, 0] = np.nan endog[2:6, 1] = np.nan exog1 = np.random.normal(size=(nobs, 1)) exog2 = np.random.normal(size=(nobs, 2)) index = pd.date_range('1970-01-01', freq='QS', periods=nobs) endog_pd = pd.DataFrame(endog, index=index) exog1_pd = pd.Series(exog1.squeeze(), index=index) exog2_pd = pd.DataFrame(exog2, index=index) models = [ varmax.VARMAX(endog, exog=exog1, order=(1, 0)), varmax.VARMAX(endog, exog=exog2, order=(1, 0)), varmax.VARMAX(endog_pd, exog=exog1_pd, order=(1, 0)), varmax.VARMAX(endog_pd, exog=exog2_pd, order=(1, 0)), ] for mod in models: # Smoke tests mod.start_params res = mod.fit(disp=False) res.summary() res.predict() res.predict(dynamic=True) res.get_prediction() oos_exog = np.random.normal(size=(1, mod.k_exog)) res.forecast(steps=1, exog=oos_exog) res.get_forecast(steps=1, exog=oos_exog) # Smoke tests for invalid exog oos_exog = np.random.normal(size=(2, mod.k_exog)) with pytest.raises(ValueError): res.forecast(steps=1, exog=oos_exog) oos_exog = np.random.normal(size=(1, mod.k_exog + 1)) with pytest.raises(ValueError): res.forecast(steps=1, exog=oos_exog) # Test invalid model specifications with pytest.raises(ValueError): varmax.VARMAX(endog, exog=np.zeros((10, 4)), order=(1, 0)) def test_predict_custom_index(): np.random.seed(328423) endog = pd.DataFrame(np.random.normal(size=(50, 2))) mod = varmax.VARMAX(endog, order=(1, 0)) res = mod.smooth(mod.start_params) out = res.predict(start=1, end=1, index=['a']) assert out.index.equals(pd.Index(['a'])) def test_forecast_exog(): # Test forecasting with various shapes of `exog` nobs = 100 endog = np.ones((nobs, 2)) * 2.0 exog = np.ones(nobs) mod = varmax.VARMAX(endog, order=(1, 0), exog=exog, trend='n') res = mod.smooth(np.r_[[0] * 4, 2.0, 2.0, 1, 0, 1]) # 1-step-ahead, valid exog_fcast_scalar = 1. exog_fcast_1dim = np.ones(1) exog_fcast_2dim = np.ones((1, 1)) assert_allclose(res.forecast(1, exog=exog_fcast_scalar), 2.) assert_allclose(res.forecast(1, exog=exog_fcast_1dim), 2.) assert_allclose(res.forecast(1, exog=exog_fcast_2dim), 2.) # h-steps-ahead, valid h = 10 exog_fcast_1dim = np.ones(h) exog_fcast_2dim = np.ones((h, 1)) assert_allclose(res.forecast(h, exog=exog_fcast_1dim), 2.) assert_allclose(res.forecast(h, exog=exog_fcast_2dim), 2.) # h-steps-ahead, invalid assert_raises(ValueError, res.forecast, h, exog=1.) assert_raises(ValueError, res.forecast, h, exog=[1, 2]) assert_raises(ValueError, res.forecast, h, exog=np.ones((h, 2))) def check_equivalent_models(mod, mod2): attrs = [ 'order', 'trend', 'error_cov_type', 'measurement_error', 'enforce_stationarity', 'enforce_invertibility', 'k_params'] ssm_attrs = [ 'nobs', 'k_endog', 'k_states', 'k_posdef', 'obs_intercept', 'design', 'obs_cov', 'state_intercept', 'transition', 'selection', 'state_cov'] for attr in attrs: assert_equal(getattr(mod2, attr), getattr(mod, attr)) for attr in ssm_attrs: assert_equal(getattr(mod2.ssm, attr), getattr(mod.ssm, attr)) assert_equal(mod2._get_init_kwds(), mod._get_init_kwds()) def test_recreate_model(): nobs = 100 endog = np.ones((nobs, 3)) * 2.0 exog = np.ones(nobs) orders = [(1, 0), (1, 1)] trends = ['t', 'n'] error_cov_types = ['diagonal', 'unstructured'] measurement_errors = [False, True] enforce_stationarities = [False, True] enforce_invertibilities = [False, True] import itertools names = ['order', 'trend', 'error_cov_type', 'measurement_error', 'enforce_stationarity', 'enforce_invertibility'] for element in itertools.product(orders, trends, error_cov_types, measurement_errors, enforce_stationarities, enforce_invertibilities): kwargs = dict(zip(names, element)) with warnings.catch_warnings(record=False): warnings.simplefilter('ignore') mod = varmax.VARMAX(endog, exog=exog, **kwargs) mod2 = varmax.VARMAX(endog, exog=exog, **mod._get_init_kwds()) check_equivalent_models(mod, mod2) def test_append_results(): endog = np.arange(200).reshape(100, 2) exog = np.ones(100) params = [0.1, 0.2, 0.5, -0.1, 0.0, 0.2, 1., 2., 1., 0., 1.] mod1 = varmax.VARMAX(endog, order=(1, 0), trend='t', exog=exog) res1 = mod1.smooth(params) mod2 = varmax.VARMAX(endog[:50], order=(1, 0), trend='t', exog=exog[:50]) res2 = mod2.smooth(params) res3 = res2.append(endog[50:], exog=exog[50:]) assert_equal(res1.specification, res3.specification) assert_allclose(res3.cov_params_default, res2.cov_params_default) for attr in ['nobs', 'llf', 'llf_obs', 'loglikelihood_burn']: assert_equal(getattr(res3, attr), getattr(res1, attr)) for attr in [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov']: assert_equal(getattr(res3, attr), getattr(res1, attr)) assert_allclose(res3.forecast(10, exog=np.ones(10)), res1.forecast(10, exog=np.ones(10))) @pytest.mark.parametrize('trend', ['n', 'c', 'ct']) @pytest.mark.parametrize('forecast', [True, False]) def test_extend_results(trend, forecast): endog = np.arange(200).reshape(100, 2) trend_params = [] if trend == 'c': trend_params = [0.1, 0.2] if trend == 'ct': trend_params = [0.1, 0.2, 1., 2.] params = np.r_[trend_params, 0.5, -0.1, 0.0, 0.2, 1., 0., 1.] mod1 = varmax.VARMAX(endog, order=(1, 0), trend=trend) res1 = mod1.smooth(params) if forecast: # Call `forecast` to trigger the _set_final_exog and # _set_final_predicted_state context managers res1.forecast() mod2 = mod1.clone(endog[:50]) res2 = mod2.smooth(params) if forecast: # Call `forecast` to trigger the _set_final_exog and # _set_final_predicted_state context managers res2.forecast() res3 = res2.extend(endog[50:]) assert_allclose(res3.llf_obs, res1.llf_obs[50:]) for attr in [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov']: desired = getattr(res1, attr) if desired is not None: desired = desired[..., 50:] assert_allclose(getattr(res3, attr), desired, atol=1e-12) assert_allclose(res3.forecast(10), res1.forecast(10)) def test_extend_results_exog(): endog = np.arange(200).reshape(100, 2) exog = np.ones(100) params = [0.1, 0.2, 0.5, -0.1, 0.0, 0.2, 1., 2., 1., 0., 1.] mod1 = varmax.VARMAX(endog, order=(1, 0), trend='t', exog=exog) res1 = mod1.smooth(params) mod2 = varmax.VARMAX(endog[:50], order=(1, 0), trend='t', exog=exog[:50]) res2 = mod2.smooth(params) res3 = res2.extend(endog[50:], exog=exog[50:]) assert_allclose(res3.llf_obs, res1.llf_obs[50:]) for attr in [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov']: desired = getattr(res1, attr) if desired is not None: desired = desired[..., 50:] assert_equal(getattr(res3, attr), desired) assert_allclose(res3.forecast(10, exog=np.ones(10)), res1.forecast(10, exog=np.ones(10))) def test_apply_results(): endog = np.arange(200).reshape(100, 2) exog = np.ones(100) params = [0.1, 0.2, 0.5, -0.1, 0.0, 0.2, 1., 2., 1., 0., 1.] mod1 = varmax.VARMAX(endog[:50], order=(1, 0), trend='t', exog=exog[:50]) res1 = mod1.smooth(params) mod2 = varmax.VARMAX(endog[50:], order=(1, 0), trend='t', exog=exog[50:]) res2 = mod2.smooth(params) res3 = res2.apply(endog[:50], exog=exog[:50]) assert_equal(res1.specification, res3.specification) assert_allclose(res3.cov_params_default, res2.cov_params_default) for attr in ['nobs', 'llf', 'llf_obs', 'loglikelihood_burn']: assert_equal(getattr(res3, attr), getattr(res1, attr)) for attr in [ 'filtered_state', 'filtered_state_cov', 'predicted_state', 'predicted_state_cov', 'forecasts', 'forecasts_error', 'forecasts_error_cov', 'standardized_forecasts_error', 'forecasts_error_diffuse_cov', 'predicted_diffuse_state_cov', 'scaled_smoothed_estimator', 'scaled_smoothed_estimator_cov', 'smoothing_error', 'smoothed_state', 'smoothed_state_cov', 'smoothed_state_autocov', 'smoothed_measurement_disturbance', 'smoothed_state_disturbance', 'smoothed_measurement_disturbance_cov', 'smoothed_state_disturbance_cov']: assert_equal(getattr(res3, attr), getattr(res1, attr)) assert_allclose(res3.forecast(10, exog=np.ones(10)), res1.forecast(10, exog=np.ones(10))) def test_vma1_exog(): # Test the VMAX(1) case against univariate MAX(1) models dta = pd.DataFrame( results_varmax.lutkepohl_data, columns=['inv', 'inc', 'consump'], index=pd.date_range('1960-01-01', '1982-10-01', freq='QS')) dta = np.log(dta).diff().iloc[1:] endog = dta.iloc[:, :2] exog = dta.iloc[:, 2] ma_params1 = [-0.01, 1.4, -0.3, 0.002] ma_params2 = [0.004, 0.8, -0.5, 0.0001] vma_params = [ma_params1[0], ma_params2[0], ma_params1[2], 0, 0, ma_params2[2], ma_params1[1], ma_params2[1], ma_params1[3], ma_params2[3]] # Joint VMA model mod_vma = varmax.VARMAX(endog, exog=exog, order=(0, 1), error_cov_type='diagonal') mod_vma.ssm.initialize_diffuse() res_mva = mod_vma.smooth(vma_params) # Smoke test that start_params does not raise an error sp = mod_vma.start_params assert_equal(len(sp), len(mod_vma.param_names)) # Univariate MA models mod_ma1 = sarimax.SARIMAX(endog.iloc[:, 0], exog=exog, order=(0, 0, 1), trend='c') mod_ma1.ssm.initialize_diffuse() mod_ma2 = sarimax.SARIMAX(endog.iloc[:, 1], exog=exog, order=(0, 0, 1), trend='c') mod_ma2.ssm.initialize_diffuse() res_ma1 = mod_ma1.smooth(ma_params1) res_ma2 = mod_ma2.smooth(ma_params2) # Have to ignore first 2 observations due to differences in initialization assert_allclose(res_mva.llf_obs[2:], (res_ma1.llf_obs + res_ma2.llf_obs)[2:]) def test_param_names_trend(): endog = np.zeros((3, 2)) base_names = ['L1.y1.y1', 'L1.y2.y1', 'L1.y1.y2', 'L1.y2.y2', 'sqrt.var.y1', 'sqrt.cov.y1.y2', 'sqrt.var.y2'] base_params = [0.5, 0, 0, 0.4, 1.0, 0.0, 1.0] # No trend mod = varmax.VARMAX(endog, order=(1, 0), trend='n') desired = base_names assert_equal(mod.param_names, desired) # Intercept mod = varmax.VARMAX(endog, order=(1, 0), trend=[1]) desired = ['intercept.y1', 'intercept.y2'] + base_names assert_equal(mod.param_names, desired) mod.update([1.2, -0.5] + base_params) assert_allclose(mod['state_intercept'], [1.2, -0.5]) # Intercept + drift mod = varmax.VARMAX(endog, order=(1, 0), trend=[1, 1]) desired = (['intercept.y1', 'drift.y1', 'intercept.y2', 'drift.y2'] + base_names) assert_equal(mod.param_names, desired) mod.update([1.2, 0, -0.5, 0] + base_params) assert_allclose(mod['state_intercept', 0], 1.2) assert_allclose(mod['state_intercept', 1], -0.5) mod.update([0, 1, 0, 1.1] + base_params) assert_allclose(mod['state_intercept', 0], np.arange(2, 5)) assert_allclose(mod['state_intercept', 1], 1.1 * np.arange(2, 5)) mod.update([1.2, 1, -0.5, 1.1] + base_params) assert_allclose(mod['state_intercept', 0], 1.2 + np.arange(2, 5)) assert_allclose(mod['state_intercept', 1], -0.5 + 1.1 * np.arange(2, 5)) # Drift only mod = varmax.VARMAX(endog, order=(1, 0), trend=[0, 1]) desired = ['drift.y1', 'drift.y2'] + base_names assert_equal(mod.param_names, desired) mod.update([1, 1.1] + base_params) assert_allclose(mod['state_intercept', 0], np.arange(2, 5)) assert_allclose(mod['state_intercept', 1], 1.1 * np.arange(2, 5)) # Intercept + third order mod = varmax.VARMAX(endog, order=(1, 0), trend=[1, 0, 1]) desired = (['intercept.y1', 'trend.2.y1', 'intercept.y2', 'trend.2.y2'] + base_names) assert_equal(mod.param_names, desired) mod.update([1.2, 0, -0.5, 0] + base_params) assert_allclose(mod['state_intercept', 0], 1.2) assert_allclose(mod['state_intercept', 1], -0.5) mod.update([0, 1, 0, 1.1] + base_params) assert_allclose(mod['state_intercept', 0], np.arange(2, 5)**2) assert_allclose(mod['state_intercept', 1], 1.1 * np.arange(2, 5)**2) mod.update([1.2, 1, -0.5, 1.1] + base_params) assert_allclose(mod['state_intercept', 0], 1.2 + np.arange(2, 5)**2) assert_allclose(mod['state_intercept', 1], -0.5 + 1.1 * np.arange(2, 5)**2) statsmodels-0.12.2/statsmodels/tsa/statespace/tools.py000066400000000000000000002007411400612667500231500ustar00rootroot00000000000000""" Statespace Tools Author: Chad Fulton License: Simplified-BSD """ import numpy as np from scipy.linalg import solve_sylvester import pandas as pd from statsmodels.compat.pandas import Appender from statsmodels.tools.data import _is_using_pandas from scipy.linalg.blas import find_best_blas_type from . import (_initialization, _representation, _kalman_filter, _kalman_smoother, _simulation_smoother, _cfa_simulation_smoother, _tools) compatibility_mode = False has_trmm = True prefix_dtype_map = { 's': np.float32, 'd': np.float64, 'c': np.complex64, 'z': np.complex128 } prefix_initialization_map = { 's': _initialization.sInitialization, 'd': _initialization.dInitialization, 'c': _initialization.cInitialization, 'z': _initialization.zInitialization } prefix_statespace_map = { 's': _representation.sStatespace, 'd': _representation.dStatespace, 'c': _representation.cStatespace, 'z': _representation.zStatespace } prefix_kalman_filter_map = { 's': _kalman_filter.sKalmanFilter, 'd': _kalman_filter.dKalmanFilter, 'c': _kalman_filter.cKalmanFilter, 'z': _kalman_filter.zKalmanFilter } prefix_kalman_smoother_map = { 's': _kalman_smoother.sKalmanSmoother, 'd': _kalman_smoother.dKalmanSmoother, 'c': _kalman_smoother.cKalmanSmoother, 'z': _kalman_smoother.zKalmanSmoother } prefix_simulation_smoother_map = { 's': _simulation_smoother.sSimulationSmoother, 'd': _simulation_smoother.dSimulationSmoother, 'c': _simulation_smoother.cSimulationSmoother, 'z': _simulation_smoother.zSimulationSmoother } prefix_cfa_simulation_smoother_map = { 's': _cfa_simulation_smoother.sCFASimulationSmoother, 'd': _cfa_simulation_smoother.dCFASimulationSmoother, 'c': _cfa_simulation_smoother.cCFASimulationSmoother, 'z': _cfa_simulation_smoother.zCFASimulationSmoother } prefix_pacf_map = { 's': _tools._scompute_coefficients_from_multivariate_pacf, 'd': _tools._dcompute_coefficients_from_multivariate_pacf, 'c': _tools._ccompute_coefficients_from_multivariate_pacf, 'z': _tools._zcompute_coefficients_from_multivariate_pacf } prefix_sv_map = { 's': _tools._sconstrain_sv_less_than_one, 'd': _tools._dconstrain_sv_less_than_one, 'c': _tools._cconstrain_sv_less_than_one, 'z': _tools._zconstrain_sv_less_than_one } prefix_reorder_missing_matrix_map = { 's': _tools.sreorder_missing_matrix, 'd': _tools.dreorder_missing_matrix, 'c': _tools.creorder_missing_matrix, 'z': _tools.zreorder_missing_matrix } prefix_reorder_missing_vector_map = { 's': _tools.sreorder_missing_vector, 'd': _tools.dreorder_missing_vector, 'c': _tools.creorder_missing_vector, 'z': _tools.zreorder_missing_vector } prefix_copy_missing_matrix_map = { 's': _tools.scopy_missing_matrix, 'd': _tools.dcopy_missing_matrix, 'c': _tools.ccopy_missing_matrix, 'z': _tools.zcopy_missing_matrix } prefix_copy_missing_vector_map = { 's': _tools.scopy_missing_vector, 'd': _tools.dcopy_missing_vector, 'c': _tools.ccopy_missing_vector, 'z': _tools.zcopy_missing_vector } prefix_copy_index_matrix_map = { 's': _tools.scopy_index_matrix, 'd': _tools.dcopy_index_matrix, 'c': _tools.ccopy_index_matrix, 'z': _tools.zcopy_index_matrix } prefix_copy_index_vector_map = { 's': _tools.scopy_index_vector, 'd': _tools.dcopy_index_vector, 'c': _tools.ccopy_index_vector, 'z': _tools.zcopy_index_vector } def set_mode(compatibility=None): if compatibility: raise NotImplementedError('Compatibility mode is only available in' ' statsmodels <= 0.9') def companion_matrix(polynomial): r""" Create a companion matrix Parameters ---------- polynomial : array_like or list If an iterable, interpreted as the coefficients of the polynomial from which to form the companion matrix. Polynomial coefficients are in order of increasing degree, and may be either scalars (as in an AR(p) model) or coefficient matrices (as in a VAR(p) model). If an integer, it is interpreted as the size of a companion matrix of a scalar polynomial, where the polynomial coefficients are initialized to zeros. If a matrix polynomial is passed, :math:`C_0` may be set to the scalar value 1 to indicate an identity matrix (doing so will improve the speed of the companion matrix creation). Returns ------- companion_matrix : ndarray Notes ----- Given coefficients of a lag polynomial of the form: .. math:: c(L) = c_0 + c_1 L + \dots + c_p L^p returns a matrix of the form .. math:: \begin{bmatrix} \phi_1 & 1 & 0 & \cdots & 0 \\ \phi_2 & 0 & 1 & & 0 \\ \vdots & & & \ddots & 0 \\ & & & & 1 \\ \phi_n & 0 & 0 & \cdots & 0 \\ \end{bmatrix} where some or all of the :math:`\phi_i` may be non-zero (if `polynomial` is None, then all are equal to zero). If the coefficients provided are scalars :math:`(c_0, c_1, \dots, c_p)`, then the companion matrix is an :math:`n \times n` matrix formed with the elements in the first column defined as :math:`\phi_i = -\frac{c_i}{c_0}, i \in 1, \dots, p`. If the coefficients provided are matrices :math:`(C_0, C_1, \dots, C_p)`, each of shape :math:`(m, m)`, then the companion matrix is an :math:`nm \times nm` matrix formed with the elements in the first column defined as :math:`\phi_i = -C_0^{-1} C_i', i \in 1, \dots, p`. It is important to understand the expected signs of the coefficients. A typical AR(p) model is written as: .. math:: y_t = a_1 y_{t-1} + \dots + a_p y_{t-p} + \varepsilon_t This can be rewritten as: .. math:: (1 - a_1 L - \dots - a_p L^p )y_t = \varepsilon_t \\ (1 + c_1 L + \dots + c_p L^p )y_t = \varepsilon_t \\ c(L) y_t = \varepsilon_t The coefficients from this form are defined to be :math:`c_i = - a_i`, and it is the :math:`c_i` coefficients that this function expects to be provided. """ identity_matrix = False if isinstance(polynomial, (int, np.integer)): # GH 5570, allow numpy integer types, but coerce to python int n = int(polynomial) m = 1 polynomial = None else: n = len(polynomial) - 1 if n < 1: raise ValueError("Companion matrix polynomials must include at" " least two terms.") if isinstance(polynomial, list) or isinstance(polynomial, tuple): try: # Note: cannot use polynomial[0] because of the special # behavior associated with matrix polynomials and the constant # 1, see below. m = len(polynomial[1]) except TypeError: m = 1 # Check if we just have a scalar polynomial if m == 1: polynomial = np.asanyarray(polynomial) # Check if 1 was passed as the first argument (indicating an # identity matrix) elif polynomial[0] == 1: polynomial[0] = np.eye(m) identity_matrix = True else: m = 1 polynomial = np.asanyarray(polynomial) matrix = np.zeros((n * m, n * m), dtype=np.asanyarray(polynomial).dtype) idx = np.diag_indices((n - 1) * m) idx = (idx[0], idx[1] + m) matrix[idx] = 1 if polynomial is not None and n > 0: if m == 1: matrix[:, 0] = -polynomial[1:] / polynomial[0] elif identity_matrix: for i in range(n): matrix[i * m:(i + 1) * m, :m] = -polynomial[i+1].T else: inv = np.linalg.inv(polynomial[0]) for i in range(n): matrix[i * m:(i + 1) * m, :m] = -np.dot(inv, polynomial[i+1]).T return matrix def diff(series, k_diff=1, k_seasonal_diff=None, seasonal_periods=1): r""" Difference a series simply and/or seasonally along the zero-th axis. Given a series (denoted :math:`y_t`), performs the differencing operation .. math:: \Delta^d \Delta_s^D y_t where :math:`d =` `diff`, :math:`s =` `seasonal_periods`, :math:`D =` `seasonal\_diff`, and :math:`\Delta` is the difference operator. Parameters ---------- series : array_like The series to be differenced. diff : int, optional The number of simple differences to perform. Default is 1. seasonal_diff : int or None, optional The number of seasonal differences to perform. Default is no seasonal differencing. seasonal_periods : int, optional The seasonal lag. Default is 1. Unused if there is no seasonal differencing. Returns ------- differenced : ndarray The differenced array. """ pandas = _is_using_pandas(series, None) differenced = np.asanyarray(series) if not pandas else series # Seasonal differencing if k_seasonal_diff is not None: while k_seasonal_diff > 0: if not pandas: differenced = (differenced[seasonal_periods:] - differenced[:-seasonal_periods]) else: sdiffed = differenced.diff(seasonal_periods) differenced = sdiffed[seasonal_periods:] k_seasonal_diff -= 1 # Simple differencing if not pandas: differenced = np.diff(differenced, k_diff, axis=0) else: while k_diff > 0: differenced = differenced.diff()[1:] k_diff -= 1 return differenced def concat(series, axis=0, allow_mix=False): """ Concatenate a set of series. Parameters ---------- series : iterable An iterable of series to be concatenated axis : int, optional The axis along which to concatenate. Default is 1 (columns). allow_mix : bool Whether or not to allow a mix of pandas and non-pandas objects. Default is False. If true, the returned object is an ndarray, and additional pandas metadata (e.g. column names, indices, etc) is lost. Returns ------- concatenated : array or pd.DataFrame The concatenated array. Will be a DataFrame if series are pandas objects. """ is_pandas = np.r_[[_is_using_pandas(s, None) for s in series]] ndim = np.r_[[np.ndim(s) for s in series]] max_ndim = np.max(ndim) if max_ndim > 2: raise ValueError('`tools.concat` does not support arrays with 3 or' ' more dimensions.') # Make sure the iterable is mutable if isinstance(series, tuple): series = list(series) # Standardize ndim for i in range(len(series)): if ndim[i] == 0 and max_ndim == 1: series[i] = np.atleast_1d(series[i]) elif ndim[i] == 0 and max_ndim == 2: series[i] = np.atleast_2d(series[i]) elif ndim[i] == 1 and max_ndim == 2 and is_pandas[i]: name = series[i].name series[i] = series[i].to_frame() series[i].columns = [name] elif ndim[i] == 1 and max_ndim == 2 and not is_pandas[i]: series[i] = np.atleast_2d(series[i]).T if np.all(is_pandas): if isinstance(series[0], pd.DataFrame): base_columns = series[0].columns else: base_columns = pd.Index([series[0].name]) for i in range(1, len(series)): s = series[i] if isinstance(s, pd.DataFrame): # Handle case where we were passed a dataframe and a series # to concatenate, and the series did not have a name. if s.columns.equals(pd.Index([None])): s.columns = base_columns[:1] s_columns = s.columns else: s_columns = pd.Index([s.name]) if axis == 0 and not base_columns.equals(s_columns): raise ValueError('Columns must match to concatenate along' ' rows.') elif axis == 1 and not series[0].index.equals(s.index): raise ValueError('Index must match to concatenate along' ' columns.') concatenated = pd.concat(series, axis=axis) elif np.all(~is_pandas) or allow_mix: concatenated = np.concatenate(series, axis=axis) else: raise ValueError('Attempted to concatenate Pandas objects with' ' non-Pandas objects with `allow_mix=False`.') return concatenated def is_invertible(polynomial, threshold=1 - 1e-10): r""" Determine if a polynomial is invertible. Requires all roots of the polynomial lie inside the unit circle. Parameters ---------- polynomial : array_like or tuple, list Coefficients of a polynomial, in order of increasing degree. For example, `polynomial=[1, -0.5]` corresponds to the polynomial :math:`1 - 0.5x` which has root :math:`2`. If it is a matrix polynomial (in which case the coefficients are coefficient matrices), a tuple or list of matrices should be passed. threshold : number Allowed threshold for `is_invertible` to return True. Default is 1. See Also -------- companion_matrix Notes ----- If the coefficients provided are scalars :math:`(c_0, c_1, \dots, c_n)`, then the corresponding polynomial is :math:`c_0 + c_1 L + \dots + c_n L^n`. If the coefficients provided are matrices :math:`(C_0, C_1, \dots, C_n)`, then the corresponding polynomial is :math:`C_0 + C_1 L + \dots + C_n L^n`. There are three equivalent methods of determining if the polynomial represented by the coefficients is invertible: The first method factorizes the polynomial into: .. math:: C(L) & = c_0 + c_1 L + \dots + c_n L^n \\ & = constant (1 - \lambda_1 L) (1 - \lambda_2 L) \dots (1 - \lambda_n L) In order for :math:`C(L)` to be invertible, it must be that each factor :math:`(1 - \lambda_i L)` is invertible; the condition is then that :math:`|\lambda_i| < 1`, where :math:`\lambda_i` is a root of the polynomial. The second method factorizes the polynomial into: .. math:: C(L) & = c_0 + c_1 L + \dots + c_n L^n \\ & = constant (L - \zeta_1) (L - \zeta_2) \dots (L - \zeta_3) The condition is now :math:`|\zeta_i| > 1`, where :math:`\zeta_i` is a root of the polynomial with reversed coefficients and :math:`\lambda_i = \frac{1}{\zeta_i}`. Finally, a companion matrix can be formed using the coefficients of the polynomial. Then the eigenvalues of that matrix give the roots of the polynomial. This last method is the one actually used. """ # First method: # np.all(np.abs(np.roots(np.r_[1, params])) < 1) # Second method: # np.all(np.abs(np.roots(np.r_[1, params][::-1])) > 1) # Final method: eigvals = np.linalg.eigvals(companion_matrix(polynomial)) return np.all(np.abs(eigvals) < threshold) def solve_discrete_lyapunov(a, q, complex_step=False): r""" Solves the discrete Lyapunov equation using a bilinear transformation. Notes ----- This is a modification of the version in Scipy (see https://github.com/scipy/scipy/blob/master/scipy/linalg/_solvers.py) which allows passing through the complex numbers in the matrix a (usually the transition matrix) in order to allow complex step differentiation. """ eye = np.eye(a.shape[0], dtype=a.dtype) if not complex_step: aH = a.conj().transpose() aHI_inv = np.linalg.inv(aH + eye) b = np.dot(aH - eye, aHI_inv) c = 2*np.dot(np.dot(np.linalg.inv(a + eye), q), aHI_inv) return solve_sylvester(b.conj().transpose(), b, -c) else: aH = a.transpose() aHI_inv = np.linalg.inv(aH + eye) b = np.dot(aH - eye, aHI_inv) c = 2*np.dot(np.dot(np.linalg.inv(a + eye), q), aHI_inv) return solve_sylvester(b.transpose(), b, -c) def constrain_stationary_univariate(unconstrained): """ Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation Parameters ---------- unconstrained : ndarray Unconstrained parameters used by the optimizer, to be transformed to stationary coefficients of, e.g., an autoregressive or moving average component. Returns ------- constrained : ndarray Constrained parameters of, e.g., an autoregressive or moving average component, to be transformed to arbitrary parameters used by the optimizer. References ---------- .. [*] Monahan, John F. 1984. "A Note on Enforcing Stationarity in Autoregressive-moving Average Models." Biometrika 71 (2) (August 1): 403-404. """ n = unconstrained.shape[0] y = np.zeros((n, n), dtype=unconstrained.dtype) r = unconstrained/((1 + unconstrained**2)**0.5) for k in range(n): for i in range(k): y[k, i] = y[k - 1, i] + r[k] * y[k - 1, k - i - 1] y[k, k] = r[k] return -y[n - 1, :] def unconstrain_stationary_univariate(constrained): """ Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer Parameters ---------- constrained : ndarray Constrained parameters of, e.g., an autoregressive or moving average component, to be transformed to arbitrary parameters used by the optimizer. Returns ------- unconstrained : ndarray Unconstrained parameters used by the optimizer, to be transformed to stationary coefficients of, e.g., an autoregressive or moving average component. References ---------- .. [*] Monahan, John F. 1984. "A Note on Enforcing Stationarity in Autoregressive-moving Average Models." Biometrika 71 (2) (August 1): 403-404. """ n = constrained.shape[0] y = np.zeros((n, n), dtype=constrained.dtype) y[n-1:] = -constrained for k in range(n-1, 0, -1): for i in range(k): y[k-1, i] = (y[k, i] - y[k, k]*y[k, k-i-1]) / (1 - y[k, k]**2) r = y.diagonal() x = r / ((1 - r**2)**0.5) return x def _constrain_sv_less_than_one_python(unconstrained, order=None, k_endog=None): """ Transform arbitrary matrices to matrices with singular values less than one. Parameters ---------- unconstrained : list Arbitrary matrices. Should be a list of length `order`, where each element is an array sized `k_endog` x `k_endog`. order : int, optional The order of the autoregression. k_endog : int, optional The dimension of the data vector. Returns ------- constrained : list Partial autocorrelation matrices. Should be a list of length `order`, where each element is an array sized `k_endog` x `k_endog`. See Also -------- constrain_stationary_multivariate Notes ----- Corresponds to Lemma 2.2 in Ansley and Kohn (1986). See `constrain_stationary_multivariate` for more details. """ from scipy import linalg constrained = [] # P_s, s = 1, ..., p if order is None: order = len(unconstrained) if k_endog is None: k_endog = unconstrained[0].shape[0] eye = np.eye(k_endog) for i in range(order): A = unconstrained[i] B, lower = linalg.cho_factor(eye + np.dot(A, A.T), lower=True) constrained.append(linalg.solve_triangular(B, A, lower=lower)) return constrained def _compute_coefficients_from_multivariate_pacf_python( partial_autocorrelations, error_variance, transform_variance=False, order=None, k_endog=None): """ Transform matrices with singular values less than one to matrices corresponding to a stationary (or invertible) process. Parameters ---------- partial_autocorrelations : list Partial autocorrelation matrices. Should be a list of length `order`, where each element is an array sized `k_endog` x `k_endog`. error_variance : ndarray The variance / covariance matrix of the error term. Should be sized `k_endog` x `k_endog`. This is used as input in the algorithm even if is not transformed by it (when `transform_variance` is False). The error term variance is required input when transformation is used either to force an autoregressive component to be stationary or to force a moving average component to be invertible. transform_variance : bool, optional Whether or not to transform the error variance term. This option is not typically used, and the default is False. order : int, optional The order of the autoregression. k_endog : int, optional The dimension of the data vector. Returns ------- coefficient_matrices : list Transformed coefficient matrices leading to a stationary VAR representation. See Also -------- constrain_stationary_multivariate Notes ----- Corresponds to Lemma 2.1 in Ansley and Kohn (1986). See `constrain_stationary_multivariate` for more details. """ from scipy import linalg if order is None: order = len(partial_autocorrelations) if k_endog is None: k_endog = partial_autocorrelations[0].shape[0] # If we want to keep the provided variance but with the constrained # coefficient matrices, we need to make a copy here, and then after the # main loop we will transform the coefficients to match the passed variance if not transform_variance: initial_variance = error_variance # Need to make the input variance large enough that the recursions # do not lead to zero-matrices due to roundoff error, which would case # exceptions from the Cholesky decompositions. # Note that this will still not always ensure positive definiteness, # and for k_endog, order large enough an exception may still be raised error_variance = np.eye(k_endog) * (order + k_endog)**10 forward_variances = [error_variance] # \Sigma_s backward_variances = [error_variance] # \Sigma_s^*, s = 0, ..., p autocovariances = [error_variance] # \Gamma_s # \phi_{s,k}, s = 1, ..., p # k = 1, ..., s+1 forwards = [] # \phi_{s,k}^* backwards = [] error_variance_factor = linalg.cholesky(error_variance, lower=True) forward_factors = [error_variance_factor] backward_factors = [error_variance_factor] # We fill in the entries as follows: # [1,1] # [2,2], [2,1] # [3,3], [3,1], [3,2] # ... # [p,p], [p,1], ..., [p,p-1] # the last row, correctly ordered, is then used as the coefficients for s in range(order): # s = 0, ..., p-1 prev_forwards = forwards prev_backwards = backwards forwards = [] backwards = [] # Create the "last" (k = s+1) matrix # Note: this is for k = s+1. However, below we then have to fill # in for k = 1, ..., s in order. # P L*^{-1} = x # x L* = P # L*' x' = P' forwards.append( linalg.solve_triangular( backward_factors[s], partial_autocorrelations[s].T, lower=True, trans='T')) forwards[0] = np.dot(forward_factors[s], forwards[0].T) # P' L^{-1} = x # x L = P' # L' x' = P backwards.append( linalg.solve_triangular( forward_factors[s], partial_autocorrelations[s], lower=True, trans='T')) backwards[0] = np.dot(backward_factors[s], backwards[0].T) # Update the variance # Note: if s >= 1, this will be further updated in the for loop # below # Also, this calculation will be re-used in the forward variance tmp = np.dot(forwards[0], backward_variances[s]) autocovariances.append(tmp.copy().T) # Create the remaining k = 1, ..., s matrices, # only has an effect if s >= 1 for k in range(s): forwards.insert(k, prev_forwards[k] - np.dot( forwards[-1], prev_backwards[s-(k+1)])) backwards.insert(k, prev_backwards[k] - np.dot( backwards[-1], prev_forwards[s-(k+1)])) autocovariances[s+1] += np.dot(autocovariances[k+1], prev_forwards[s-(k+1)].T) # Create forward and backwards variances forward_variances.append( forward_variances[s] - np.dot(tmp, forwards[s].T) ) backward_variances.append( backward_variances[s] - np.dot( np.dot(backwards[s], forward_variances[s]), backwards[s].T ) ) # Cholesky factors forward_factors.append( linalg.cholesky(forward_variances[s+1], lower=True) ) backward_factors.append( linalg.cholesky(backward_variances[s+1], lower=True) ) # If we do not want to use the transformed variance, we need to # adjust the constrained matrices, as presented in Lemma 2.3, see above variance = forward_variances[-1] if not transform_variance: # Here, we need to construct T such that: # variance = T * initial_variance * T' # To do that, consider the Cholesky of variance (L) and # input_variance (M) to get: # L L' = T M M' T' = (TM) (TM)' # => L = T M # => L M^{-1} = T initial_variance_factor = np.linalg.cholesky(initial_variance) transformed_variance_factor = np.linalg.cholesky(variance) transform = np.dot(initial_variance_factor, np.linalg.inv(transformed_variance_factor)) inv_transform = np.linalg.inv(transform) for i in range(order): forwards[i] = ( np.dot(np.dot(transform, forwards[i]), inv_transform) ) return forwards, variance def constrain_stationary_multivariate_python(unconstrained, error_variance, transform_variance=False, prefix=None): r""" Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation for a vector autoregression. Parameters ---------- unconstrained : array or list Arbitrary matrices to be transformed to stationary coefficient matrices of the VAR. If a list, should be a list of length `order`, where each element is an array sized `k_endog` x `k_endog`. If an array, should be the matrices horizontally concatenated and sized `k_endog` x `k_endog * order`. error_variance : ndarray The variance / covariance matrix of the error term. Should be sized `k_endog` x `k_endog`. This is used as input in the algorithm even if is not transformed by it (when `transform_variance` is False). The error term variance is required input when transformation is used either to force an autoregressive component to be stationary or to force a moving average component to be invertible. transform_variance : bool, optional Whether or not to transform the error variance term. This option is not typically used, and the default is False. prefix : {'s','d','c','z'}, optional The appropriate BLAS prefix to use for the passed datatypes. Only use if absolutely sure that the prefix is correct or an error will result. Returns ------- constrained : array or list Transformed coefficient matrices leading to a stationary VAR representation. Will match the type of the passed `unconstrained` variable (so if a list was passed, a list will be returned). Notes ----- In the notation of [1]_, the arguments `(variance, unconstrained)` are written as :math:`(\Sigma, A_1, \dots, A_p)`, where :math:`p` is the order of the vector autoregression, and is here determined by the length of the `unconstrained` argument. There are two steps in the constraining algorithm. First, :math:`(A_1, \dots, A_p)` are transformed into :math:`(P_1, \dots, P_p)` via Lemma 2.2 of [1]_. Second, :math:`(\Sigma, P_1, \dots, P_p)` are transformed into :math:`(\Sigma, \phi_1, \dots, \phi_p)` via Lemmas 2.1 and 2.3 of [1]_. If `transform_variance=True`, then only Lemma 2.1 is applied in the second step. While this function can be used even in the univariate case, it is much slower, so in that case `constrain_stationary_univariate` is preferred. References ---------- .. [1] Ansley, Craig F., and Robert Kohn. 1986. "A Note on Reparameterizing a Vector Autoregressive Moving Average Model to Enforce Stationarity." Journal of Statistical Computation and Simulation 24 (2): 99-106. .. [*] Ansley, Craig F, and Paul Newbold. 1979. "Multivariate Partial Autocorrelations." In Proceedings of the Business and Economic Statistics Section, 349-53. American Statistical Association """ use_list = type(unconstrained) == list if not use_list: k_endog, order = unconstrained.shape order //= k_endog unconstrained = [ unconstrained[:k_endog, i*k_endog:(i+1)*k_endog] for i in range(order) ] order = len(unconstrained) k_endog = unconstrained[0].shape[0] # Step 1: convert from arbitrary matrices to those with singular values # less than one. sv_constrained = _constrain_sv_less_than_one_python( unconstrained, order, k_endog) # Step 2: convert matrices from our "partial autocorrelation matrix" space # (matrices with singular values less than one) to the space of stationary # coefficient matrices constrained, var = _compute_coefficients_from_multivariate_pacf_python( sv_constrained, error_variance, transform_variance, order, k_endog) if not use_list: constrained = np.concatenate(constrained, axis=1).reshape( k_endog, k_endog * order) return constrained, var @Appender(constrain_stationary_multivariate_python.__doc__) def constrain_stationary_multivariate(unconstrained, variance, transform_variance=False, prefix=None): use_list = type(unconstrained) == list if use_list: unconstrained = np.concatenate(unconstrained, axis=1) k_endog, order = unconstrained.shape order //= k_endog if order < 1: raise ValueError('Must have order at least 1') if k_endog < 1: raise ValueError('Must have at least 1 endogenous variable') if prefix is None: prefix, dtype, _ = find_best_blas_type( [unconstrained, variance]) dtype = prefix_dtype_map[prefix] unconstrained = np.asfortranarray(unconstrained, dtype=dtype) variance = np.asfortranarray(variance, dtype=dtype) # Step 1: convert from arbitrary matrices to those with singular values # less than one. # sv_constrained = _constrain_sv_less_than_one(unconstrained, order, # k_endog, prefix) sv_constrained = prefix_sv_map[prefix](unconstrained, order, k_endog) # Step 2: convert matrices from our "partial autocorrelation matrix" # space (matrices with singular values less than one) to the space of # stationary coefficient matrices constrained, variance = prefix_pacf_map[prefix]( sv_constrained, variance, transform_variance, order, k_endog) constrained = np.array(constrained, dtype=dtype) variance = np.array(variance, dtype=dtype) if use_list: constrained = [ constrained[:k_endog, i*k_endog:(i+1)*k_endog] for i in range(order) ] return constrained, variance def _unconstrain_sv_less_than_one(constrained, order=None, k_endog=None): """ Transform matrices with singular values less than one to arbitrary matrices. Parameters ---------- constrained : list The partial autocorrelation matrices. Should be a list of length `order`, where each element is an array sized `k_endog` x `k_endog`. order : int, optional The order of the autoregression. k_endog : int, optional The dimension of the data vector. Returns ------- unconstrained : list Unconstrained matrices. A list of length `order`, where each element is an array sized `k_endog` x `k_endog`. See Also -------- unconstrain_stationary_multivariate Notes ----- Corresponds to the inverse of Lemma 2.2 in Ansley and Kohn (1986). See `unconstrain_stationary_multivariate` for more details. """ from scipy import linalg unconstrained = [] # A_s, s = 1, ..., p if order is None: order = len(constrained) if k_endog is None: k_endog = constrained[0].shape[0] eye = np.eye(k_endog) for i in range(order): P = constrained[i] # B^{-1} B^{-1}' = I - P P' B_inv, lower = linalg.cho_factor(eye - np.dot(P, P.T), lower=True) # A = BP # B^{-1} A = P unconstrained.append(linalg.solve_triangular(B_inv, P, lower=lower)) return unconstrained def _compute_multivariate_sample_acovf(endog, maxlag): r""" Computer multivariate sample autocovariances Parameters ---------- endog : array_like Sample data on which to compute sample autocovariances. Shaped `nobs` x `k_endog`. maxlag : int Maximum lag to use when computing the sample autocovariances. Returns ------- sample_autocovariances : list A list of the first `maxlag` sample autocovariance matrices. Each matrix is shaped `k_endog` x `k_endog`. Notes ----- This function computes the forward sample autocovariances: .. math:: \hat \Gamma(s) = \frac{1}{n} \sum_{t=1}^{n-s} (Z_t - \bar Z) (Z_{t+s} - \bar Z)' See page 353 of Wei (1990). This function is primarily implemented for checking the partial autocorrelation functions below, and so is quite slow. References ---------- .. [*] Wei, William. 1990. Time Series Analysis : Univariate and Multivariate Methods. Boston: Pearson. """ # Get the (demeaned) data as an array endog = np.array(endog) if endog.ndim == 1: endog = endog[:, np.newaxis] endog -= np.mean(endog, axis=0) # Dimensions nobs, k_endog = endog.shape sample_autocovariances = [] for s in range(maxlag + 1): sample_autocovariances.append(np.zeros((k_endog, k_endog))) for t in range(nobs - s): sample_autocovariances[s] += np.outer(endog[t], endog[t+s]) sample_autocovariances[s] /= nobs return sample_autocovariances def _compute_multivariate_acovf_from_coefficients( coefficients, error_variance, maxlag=None, forward_autocovariances=False): r""" Compute multivariate autocovariances from vector autoregression coefficient matrices Parameters ---------- coefficients : array or list The coefficients matrices. If a list, should be a list of length `order`, where each element is an array sized `k_endog` x `k_endog`. If an array, should be the coefficient matrices horizontally concatenated and sized `k_endog` x `k_endog * order`. error_variance : ndarray The variance / covariance matrix of the error term. Should be sized `k_endog` x `k_endog`. maxlag : int, optional The maximum autocovariance to compute. Default is `order`-1. Can be zero, in which case it returns the variance. forward_autocovariances : bool, optional Whether or not to compute forward autocovariances :math:`E(y_t y_{t+j}')`. Default is False, so that backward autocovariances :math:`E(y_t y_{t-j}')` are returned. Returns ------- autocovariances : list A list of the first `maxlag` autocovariance matrices. Each matrix is shaped `k_endog` x `k_endog`. Notes ----- Computes .. math:: \Gamma(j) = E(y_t y_{t-j}') for j = 1, ..., `maxlag`, unless `forward_autocovariances` is specified, in which case it computes: .. math:: E(y_t y_{t+j}') = \Gamma(j)' Coefficients are assumed to be provided from the VAR model: .. math:: y_t = A_1 y_{t-1} + \dots + A_p y_{t-p} + \varepsilon_t Autocovariances are calculated by solving the associated discrete Lyapunov equation of the state space representation of the VAR process. """ from scipy import linalg # Convert coefficients to a list of matrices, for use in # `companion_matrix`; get dimensions if type(coefficients) == list: order = len(coefficients) k_endog = coefficients[0].shape[0] else: k_endog, order = coefficients.shape order //= k_endog coefficients = [ coefficients[:k_endog, i*k_endog:(i+1)*k_endog] for i in range(order) ] if maxlag is None: maxlag = order-1 # Start with VAR(p): w_{t+1} = phi_1 w_t + ... + phi_p w_{t-p+1} + u_{t+1} # Then stack the VAR(p) into a VAR(1) in companion matrix form: # z_{t+1} = F z_t + v_t companion = companion_matrix( [1] + [-np.squeeze(coefficients[i]) for i in range(order)] ).T # Compute the error variance matrix for the stacked form: E v_t v_t' selected_variance = np.zeros(companion.shape) selected_variance[:k_endog, :k_endog] = error_variance # Compute the unconditional variance of z_t: E z_t z_t' stacked_cov = linalg.solve_discrete_lyapunov(companion, selected_variance) # The first (block) row of the variance of z_t gives the first p-1 # autocovariances of w_t: \Gamma_i = E w_t w_t+i with \Gamma_0 = Var(w_t) # Note: these are okay, checked against ArmaProcess autocovariances = [ stacked_cov[:k_endog, i*k_endog:(i+1)*k_endog] for i in range(min(order, maxlag+1)) ] for i in range(maxlag - (order-1)): stacked_cov = np.dot(companion, stacked_cov) autocovariances += [ stacked_cov[:k_endog, -k_endog:] ] if forward_autocovariances: for i in range(len(autocovariances)): autocovariances[i] = autocovariances[i].T return autocovariances def _compute_multivariate_sample_pacf(endog, maxlag): """ Computer multivariate sample partial autocorrelations Parameters ---------- endog : array_like Sample data on which to compute sample autocovariances. Shaped `nobs` x `k_endog`. maxlag : int Maximum lag for which to calculate sample partial autocorrelations. Returns ------- sample_pacf : list A list of the first `maxlag` sample partial autocorrelation matrices. Each matrix is shaped `k_endog` x `k_endog`. """ sample_autocovariances = _compute_multivariate_sample_acovf(endog, maxlag) return _compute_multivariate_pacf_from_autocovariances( sample_autocovariances) def _compute_multivariate_pacf_from_autocovariances(autocovariances, order=None, k_endog=None): """ Compute multivariate partial autocorrelations from autocovariances. Parameters ---------- autocovariances : list Autocorrelations matrices. Should be a list of length `order` + 1, where each element is an array sized `k_endog` x `k_endog`. order : int, optional The order of the autoregression. k_endog : int, optional The dimension of the data vector. Returns ------- pacf : list List of first `order` multivariate partial autocorrelations. See Also -------- unconstrain_stationary_multivariate Notes ----- Note that this computes multivariate partial autocorrelations. Corresponds to the inverse of Lemma 2.1 in Ansley and Kohn (1986). See `unconstrain_stationary_multivariate` for more details. Computes sample partial autocorrelations if sample autocovariances are given. """ from scipy import linalg if order is None: order = len(autocovariances)-1 if k_endog is None: k_endog = autocovariances[0].shape[0] # Now apply the Ansley and Kohn (1986) algorithm, except that instead of # calculating phi_{s+1, s+1} = L_s P_{s+1} {L_s^*}^{-1} (which requires # the partial autocorrelation P_{s+1} which is what we're trying to # calculate here), we calculate it as in Ansley and Newbold (1979), using # the autocovariances \Gamma_s and the forwards and backwards residual # variances \Sigma_s, \Sigma_s^*: # phi_{s+1, s+1} = [ \Gamma_{s+1}' - \phi_{s,1} \Gamma_s' - ... - # \phi_{s,s} \Gamma_1' ] {\Sigma_s^*}^{-1} # Forward and backward variances forward_variances = [] # \Sigma_s backward_variances = [] # \Sigma_s^*, s = 0, ..., p # \phi_{s,k}, s = 1, ..., p # k = 1, ..., s+1 forwards = [] # \phi_{s,k}^* backwards = [] forward_factors = [] # L_s backward_factors = [] # L_s^*, s = 0, ..., p # Ultimately we want to construct the partial autocorrelation matrices # Note that this is "1-indexed" in the sense that it stores P_1, ... P_p # rather than starting with P_0. partial_autocorrelations = [] # We fill in the entries of phi_{s,k} as follows: # [1,1] # [2,2], [2,1] # [3,3], [3,1], [3,2] # ... # [p,p], [p,1], ..., [p,p-1] # the last row, correctly ordered, should be the same as the coefficient # matrices provided in the argument `constrained` for s in range(order): # s = 0, ..., p-1 prev_forwards = list(forwards) prev_backwards = list(backwards) forwards = [] backwards = [] # Create forward and backwards variances Sigma_s, Sigma*_s forward_variance = autocovariances[0].copy() backward_variance = autocovariances[0].T.copy() for k in range(s): forward_variance -= np.dot(prev_forwards[k], autocovariances[k+1]) backward_variance -= np.dot(prev_backwards[k], autocovariances[k+1].T) forward_variances.append(forward_variance) backward_variances.append(backward_variance) # Cholesky factors forward_factors.append( linalg.cholesky(forward_variances[s], lower=True) ) backward_factors.append( linalg.cholesky(backward_variances[s], lower=True) ) # Create the intermediate sum term if s == 0: # phi_11 = \Gamma_1' \Gamma_0^{-1} # phi_11 \Gamma_0 = \Gamma_1' # \Gamma_0 phi_11' = \Gamma_1 forwards.append(linalg.cho_solve( (forward_factors[0], True), autocovariances[1]).T) # backwards.append(forwards[-1]) # phi_11_star = \Gamma_1 \Gamma_0^{-1} # phi_11_star \Gamma_0 = \Gamma_1 # \Gamma_0 phi_11_star' = \Gamma_1' backwards.append(linalg.cho_solve( (backward_factors[0], True), autocovariances[1].T).T) else: # G := \Gamma_{s+1}' - # \phi_{s,1} \Gamma_s' - .. - \phi_{s,s} \Gamma_1' tmp_sum = autocovariances[s+1].T.copy() for k in range(s): tmp_sum -= np.dot(prev_forwards[k], autocovariances[s-k].T) # Create the "last" (k = s+1) matrix # Note: this is for k = s+1. However, below we then have to # fill in for k = 1, ..., s in order. # phi = G Sigma*^{-1} # phi Sigma* = G # Sigma*' phi' = G' # Sigma* phi' = G' # (because Sigma* is symmetric) forwards.append(linalg.cho_solve( (backward_factors[s], True), tmp_sum.T).T) # phi = G' Sigma^{-1} # phi Sigma = G' # Sigma' phi' = G # Sigma phi' = G # (because Sigma is symmetric) backwards.append(linalg.cho_solve( (forward_factors[s], True), tmp_sum).T) # Create the remaining k = 1, ..., s matrices, # only has an effect if s >= 1 for k in range(s): forwards.insert(k, prev_forwards[k] - np.dot( forwards[-1], prev_backwards[s-(k+1)])) backwards.insert(k, prev_backwards[k] - np.dot( backwards[-1], prev_forwards[s-(k+1)])) # Partial autocorrelation matrix: P_{s+1} # P = L^{-1} phi L* # L P = (phi L*) partial_autocorrelations.append(linalg.solve_triangular( forward_factors[s], np.dot(forwards[s], backward_factors[s]), lower=True)) return partial_autocorrelations def _compute_multivariate_pacf_from_coefficients(constrained, error_variance, order=None, k_endog=None): r""" Transform matrices corresponding to a stationary (or invertible) process to matrices with singular values less than one. Parameters ---------- constrained : array or list The coefficients matrices. If a list, should be a list of length `order`, where each element is an array sized `k_endog` x `k_endog`. If an array, should be the coefficient matrices horizontally concatenated and sized `k_endog` x `k_endog * order`. error_variance : ndarray The variance / covariance matrix of the error term. Should be sized `k_endog` x `k_endog`. order : int, optional The order of the autoregression. k_endog : int, optional The dimension of the data vector. Returns ------- pacf : list List of first `order` multivariate partial autocorrelations. See Also -------- unconstrain_stationary_multivariate Notes ----- Note that this computes multivariate partial autocorrelations. Corresponds to the inverse of Lemma 2.1 in Ansley and Kohn (1986). See `unconstrain_stationary_multivariate` for more details. Notes ----- Coefficients are assumed to be provided from the VAR model: .. math:: y_t = A_1 y_{t-1} + \dots + A_p y_{t-p} + \varepsilon_t """ if type(constrained) == list: order = len(constrained) k_endog = constrained[0].shape[0] else: k_endog, order = constrained.shape order //= k_endog # Get autocovariances for the process; these are defined to be # E z_t z_{t-j}' # However, we want E z_t z_{t+j}' = (E z_t z_{t-j}')' _acovf = _compute_multivariate_acovf_from_coefficients autocovariances = [ autocovariance.T for autocovariance in _acovf(constrained, error_variance, maxlag=order)] return _compute_multivariate_pacf_from_autocovariances(autocovariances) def unconstrain_stationary_multivariate(constrained, error_variance): """ Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer Parameters ---------- constrained : array or list Constrained parameters of, e.g., an autoregressive or moving average component, to be transformed to arbitrary parameters used by the optimizer. If a list, should be a list of length `order`, where each element is an array sized `k_endog` x `k_endog`. If an array, should be the coefficient matrices horizontally concatenated and sized `k_endog` x `k_endog * order`. error_variance : ndarray The variance / covariance matrix of the error term. Should be sized `k_endog` x `k_endog`. This is used as input in the algorithm even if is not transformed by it (when `transform_variance` is False). Returns ------- unconstrained : ndarray Unconstrained parameters used by the optimizer, to be transformed to stationary coefficients of, e.g., an autoregressive or moving average component. Will match the type of the passed `constrained` variable (so if a list was passed, a list will be returned). Notes ----- Uses the list representation internally, even if an array is passed. References ---------- .. [*] Ansley, Craig F., and Robert Kohn. 1986. "A Note on Reparameterizing a Vector Autoregressive Moving Average Model to Enforce Stationarity." Journal of Statistical Computation and Simulation 24 (2): 99-106. """ use_list = type(constrained) == list if not use_list: k_endog, order = constrained.shape order //= k_endog constrained = [ constrained[:k_endog, i*k_endog:(i+1)*k_endog] for i in range(order) ] else: order = len(constrained) k_endog = constrained[0].shape[0] # Step 1: convert matrices from the space of stationary # coefficient matrices to our "partial autocorrelation matrix" space # (matrices with singular values less than one) partial_autocorrelations = _compute_multivariate_pacf_from_coefficients( constrained, error_variance, order, k_endog) # Step 2: convert from arbitrary matrices to those with singular values # less than one. unconstrained = _unconstrain_sv_less_than_one( partial_autocorrelations, order, k_endog) if not use_list: unconstrained = np.concatenate(unconstrained, axis=1) return unconstrained, error_variance def validate_matrix_shape(name, shape, nrows, ncols, nobs): """ Validate the shape of a possibly time-varying matrix, or raise an exception Parameters ---------- name : str The name of the matrix being validated (used in exception messages) shape : array_like The shape of the matrix to be validated. May be of size 2 or (if the matrix is time-varying) 3. nrows : int The expected number of rows. ncols : int The expected number of columns. nobs : int The number of observations (used to validate the last dimension of a time-varying matrix) Raises ------ ValueError If the matrix is not of the desired shape. """ ndim = len(shape) # Enforce dimension if ndim not in [2, 3]: raise ValueError('Invalid value for %s matrix. Requires a' ' 2- or 3-dimensional array, got %d dimensions' % (name, ndim)) # Enforce the shape of the matrix if not shape[0] == nrows: raise ValueError('Invalid dimensions for %s matrix: requires %d' ' rows, got %d' % (name, nrows, shape[0])) if not shape[1] == ncols: raise ValueError('Invalid dimensions for %s matrix: requires %d' ' columns, got %d' % (name, ncols, shape[1])) # If we do not yet know `nobs`, do not allow time-varying arrays if nobs is None and not (ndim == 2 or shape[-1] == 1): raise ValueError('Invalid dimensions for %s matrix: time-varying' ' matrices cannot be given unless `nobs` is specified' ' (implicitly when a dataset is bound or else set' ' explicity)' % name) # Enforce time-varying array size if ndim == 3 and nobs is not None and not shape[-1] in [1, nobs]: raise ValueError('Invalid dimensions for time-varying %s' ' matrix. Requires shape (*,*,%d), got %s' % (name, nobs, str(shape))) def validate_vector_shape(name, shape, nrows, nobs): """ Validate the shape of a possibly time-varying vector, or raise an exception Parameters ---------- name : str The name of the vector being validated (used in exception messages) shape : array_like The shape of the vector to be validated. May be of size 1 or (if the vector is time-varying) 2. nrows : int The expected number of rows (elements of the vector). nobs : int The number of observations (used to validate the last dimension of a time-varying vector) Raises ------ ValueError If the vector is not of the desired shape. """ ndim = len(shape) # Enforce dimension if ndim not in [1, 2]: raise ValueError('Invalid value for %s vector. Requires a' ' 1- or 2-dimensional array, got %d dimensions' % (name, ndim)) # Enforce the shape of the vector if not shape[0] == nrows: raise ValueError('Invalid dimensions for %s vector: requires %d' ' rows, got %d' % (name, nrows, shape[0])) # If we do not yet know `nobs`, do not allow time-varying arrays if nobs is None and not (ndim == 1 or shape[-1] == 1): raise ValueError('Invalid dimensions for %s vector: time-varying' ' vectors cannot be given unless `nobs` is specified' ' (implicitly when a dataset is bound or else set' ' explicity)' % name) # Enforce time-varying array size if ndim == 2 and not shape[1] in [1, nobs]: raise ValueError('Invalid dimensions for time-varying %s' ' vector. Requires shape (*,%d), got %s' % (name, nobs, str(shape))) def reorder_missing_matrix(matrix, missing, reorder_rows=False, reorder_cols=False, is_diagonal=False, inplace=False, prefix=None): """ Reorder the rows or columns of a time-varying matrix where all non-missing values are in the upper left corner of the matrix. Parameters ---------- matrix : array_like The matrix to be reordered. Must have shape (n, m, nobs). missing : array_like of bool The vector of missing indices. Must have shape (k, nobs) where `k = n` if `reorder_rows is True` and `k = m` if `reorder_cols is True`. reorder_rows : bool, optional Whether or not the rows of the matrix should be re-ordered. Default is False. reorder_cols : bool, optional Whether or not the columns of the matrix should be re-ordered. Default is False. is_diagonal : bool, optional Whether or not the matrix is diagonal. If this is True, must also have `n = m`. Default is False. inplace : bool, optional Whether or not to reorder the matrix in-place. prefix : {'s', 'd', 'c', 'z'}, optional The Fortran prefix of the vector. Default is to automatically detect the dtype. This parameter should only be used with caution. Returns ------- reordered_matrix : array_like The reordered matrix. """ if prefix is None: prefix = find_best_blas_type((matrix,))[0] reorder = prefix_reorder_missing_matrix_map[prefix] if not inplace: matrix = np.copy(matrix, order='F') reorder(matrix, np.asfortranarray(missing), reorder_rows, reorder_cols, is_diagonal) return matrix def reorder_missing_vector(vector, missing, inplace=False, prefix=None): """ Reorder the elements of a time-varying vector where all non-missing values are in the first elements of the vector. Parameters ---------- vector : array_like The vector to be reordered. Must have shape (n, nobs). missing : array_like of bool The vector of missing indices. Must have shape (n, nobs). inplace : bool, optional Whether or not to reorder the matrix in-place. Default is False. prefix : {'s', 'd', 'c', 'z'}, optional The Fortran prefix of the vector. Default is to automatically detect the dtype. This parameter should only be used with caution. Returns ------- reordered_vector : array_like The reordered vector. """ if prefix is None: prefix = find_best_blas_type((vector,))[0] reorder = prefix_reorder_missing_vector_map[prefix] if not inplace: vector = np.copy(vector, order='F') reorder(vector, np.asfortranarray(missing)) return vector def copy_missing_matrix(A, B, missing, missing_rows=False, missing_cols=False, is_diagonal=False, inplace=False, prefix=None): """ Copy the rows or columns of a time-varying matrix where all non-missing values are in the upper left corner of the matrix. Parameters ---------- A : array_like The matrix from which to copy. Must have shape (n, m, nobs) or (n, m, 1). B : array_like The matrix to copy to. Must have shape (n, m, nobs). missing : array_like of bool The vector of missing indices. Must have shape (k, nobs) where `k = n` if `reorder_rows is True` and `k = m` if `reorder_cols is True`. missing_rows : bool, optional Whether or not the rows of the matrix are a missing dimension. Default is False. missing_cols : bool, optional Whether or not the columns of the matrix are a missing dimension. Default is False. is_diagonal : bool, optional Whether or not the matrix is diagonal. If this is True, must also have `n = m`. Default is False. inplace : bool, optional Whether or not to copy to B in-place. Default is False. prefix : {'s', 'd', 'c', 'z'}, optional The Fortran prefix of the vector. Default is to automatically detect the dtype. This parameter should only be used with caution. Returns ------- copied_matrix : array_like The matrix B with the non-missing submatrix of A copied onto it. """ if prefix is None: prefix = find_best_blas_type((A, B))[0] copy = prefix_copy_missing_matrix_map[prefix] if not inplace: B = np.copy(B, order='F') # We may have been given an F-contiguous memoryview; in that case, we do # not want to alter it or convert it to a numpy array try: if not A.is_f_contig(): raise ValueError() except (AttributeError, ValueError): A = np.asfortranarray(A) copy(A, B, np.asfortranarray(missing), missing_rows, missing_cols, is_diagonal) return B def copy_missing_vector(a, b, missing, inplace=False, prefix=None): """ Reorder the elements of a time-varying vector where all non-missing values are in the first elements of the vector. Parameters ---------- a : array_like The vector from which to copy. Must have shape (n, nobs) or (n, 1). b : array_like The vector to copy to. Must have shape (n, nobs). missing : array_like of bool The vector of missing indices. Must have shape (n, nobs). inplace : bool, optional Whether or not to copy to b in-place. Default is False. prefix : {'s', 'd', 'c', 'z'}, optional The Fortran prefix of the vector. Default is to automatically detect the dtype. This parameter should only be used with caution. Returns ------- copied_vector : array_like The vector b with the non-missing subvector of b copied onto it. """ if prefix is None: prefix = find_best_blas_type((a, b))[0] copy = prefix_copy_missing_vector_map[prefix] if not inplace: b = np.copy(b, order='F') # We may have been given an F-contiguous memoryview; in that case, we do # not want to alter it or convert it to a numpy array try: if not a.is_f_contig(): raise ValueError() except (AttributeError, ValueError): a = np.asfortranarray(a) copy(a, b, np.asfortranarray(missing)) return b def copy_index_matrix(A, B, index, index_rows=False, index_cols=False, is_diagonal=False, inplace=False, prefix=None): """ Copy the rows or columns of a time-varying matrix where all non-index values are in the upper left corner of the matrix. Parameters ---------- A : array_like The matrix from which to copy. Must have shape (n, m, nobs) or (n, m, 1). B : array_like The matrix to copy to. Must have shape (n, m, nobs). index : array_like of bool The vector of index indices. Must have shape (k, nobs) where `k = n` if `reorder_rows is True` and `k = m` if `reorder_cols is True`. index_rows : bool, optional Whether or not the rows of the matrix are a index dimension. Default is False. index_cols : bool, optional Whether or not the columns of the matrix are a index dimension. Default is False. is_diagonal : bool, optional Whether or not the matrix is diagonal. If this is True, must also have `n = m`. Default is False. inplace : bool, optional Whether or not to copy to B in-place. Default is False. prefix : {'s', 'd', 'c', 'z'}, optional The Fortran prefix of the vector. Default is to automatically detect the dtype. This parameter should only be used with caution. Returns ------- copied_matrix : array_like The matrix B with the non-index submatrix of A copied onto it. """ if prefix is None: prefix = find_best_blas_type((A, B))[0] copy = prefix_copy_index_matrix_map[prefix] if not inplace: B = np.copy(B, order='F') # We may have been given an F-contiguous memoryview; in that case, we do # not want to alter it or convert it to a numpy array try: if not A.is_f_contig(): raise ValueError() except (AttributeError, ValueError): A = np.asfortranarray(A) copy(A, B, np.asfortranarray(index), index_rows, index_cols, is_diagonal) return B def copy_index_vector(a, b, index, inplace=False, prefix=None): """ Reorder the elements of a time-varying vector where all non-index values are in the first elements of the vector. Parameters ---------- a : array_like The vector from which to copy. Must have shape (n, nobs) or (n, 1). b : array_like The vector to copy to. Must have shape (n, nobs). index : array_like of bool The vector of index indices. Must have shape (n, nobs). inplace : bool, optional Whether or not to copy to b in-place. Default is False. prefix : {'s', 'd', 'c', 'z'}, optional The Fortran prefix of the vector. Default is to automatically detect the dtype. This parameter should only be used with caution. Returns ------- copied_vector : array_like The vector b with the non-index subvector of b copied onto it. """ if prefix is None: prefix = find_best_blas_type((a, b))[0] copy = prefix_copy_index_vector_map[prefix] if not inplace: b = np.copy(b, order='F') # We may have been given an F-contiguous memoryview; in that case, we do # not want to alter it or convert it to a numpy array try: if not a.is_f_contig(): raise ValueError() except (AttributeError, ValueError): a = np.asfortranarray(a) copy(a, b, np.asfortranarray(index)) return b def prepare_exog(exog): k_exog = 0 if exog is not None: exog_is_using_pandas = _is_using_pandas(exog, None) if not exog_is_using_pandas: exog = np.asarray(exog) # Make sure we have 2-dimensional array if exog.ndim == 1: if not exog_is_using_pandas: exog = exog[:, None] else: exog = pd.DataFrame(exog) k_exog = exog.shape[1] return (k_exog, exog) def prepare_trend_spec(trend): # Trend if trend is None or trend == 'n': polynomial_trend = np.ones(0) elif trend == 'c': polynomial_trend = np.r_[1] elif trend == 't': polynomial_trend = np.r_[0, 1] elif trend == 'ct': polynomial_trend = np.r_[1, 1] elif trend == 'ctt': # TODO deprecate ctt? polynomial_trend = np.r_[1, 1, 1] else: trend = np.array(trend) if trend.ndim > 0: polynomial_trend = (trend > 0).astype(int) else: raise ValueError('Invalid trend method.') # Note: k_trend is not the degree of the trend polynomial, because e.g. # k_trend = 1 corresponds to the degree zero polynomial (with only a # constant term). k_trend = int(np.sum(polynomial_trend)) return polynomial_trend, k_trend def prepare_trend_data(polynomial_trend, k_trend, nobs, offset=1): # Cache the arrays for calculating the intercept from the trend # components time_trend = np.arange(offset, nobs + offset) trend_data = np.zeros((nobs, k_trend)) i = 0 for k in polynomial_trend.nonzero()[0]: if k == 0: trend_data[:, i] = np.ones(nobs,) else: trend_data[:, i] = time_trend**k i += 1 return trend_data statsmodels-0.12.2/statsmodels/tsa/statespace/varmax.py000066400000000000000000001415611400612667500233120ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Vector Autoregressive Moving Average with eXogenous regressors model Author: Chad Fulton License: Simplified-BSD """ import contextlib from warnings import warn import pandas as pd import numpy as np from statsmodels.compat.pandas import Appender from statsmodels.tools.tools import Bunch from statsmodels.tools.data import _is_using_pandas from statsmodels.tsa.vector_ar import var_model import statsmodels.base.wrapper as wrap from statsmodels.tools.sm_exceptions import EstimationWarning from .kalman_filter import INVERT_UNIVARIATE, SOLVE_LU from .mlemodel import MLEModel, MLEResults, MLEResultsWrapper from .initialization import Initialization from .tools import ( is_invertible, concat, prepare_exog, constrain_stationary_multivariate, unconstrain_stationary_multivariate, prepare_trend_spec, prepare_trend_data ) class VARMAX(MLEModel): r""" Vector Autoregressive Moving Average with eXogenous regressors model Parameters ---------- endog : array_like The observed time-series process :math:`y`, , shaped nobs x k_endog. exog : array_like, optional Array of exogenous regressors, shaped nobs x k. order : iterable The (p,q) order of the model for the number of AR and MA parameters to use. trend : str{'n','c','t','ct'} or iterable, optional Parameter controlling the deterministic trend polynomial :math:`A(t)`. Can be specified as a string where 'c' indicates a constant (i.e. a degree zero component of the trend polynomial), 't' indicates a linear trend with time, and 'ct' is both. Can also be specified as an iterable defining the non-zero polynomial exponents to include, in increasing order. For example, `[1,1,0,1]` denotes :math:`a + bt + ct^3`. Default is a constant trend component. error_cov_type : {'diagonal', 'unstructured'}, optional The structure of the covariance matrix of the error term, where "unstructured" puts no restrictions on the matrix and "diagonal" requires it to be a diagonal matrix (uncorrelated errors). Default is "unstructured". measurement_error : bool, optional Whether or not to assume the endogenous observations `endog` were measured with error. Default is False. enforce_stationarity : bool, optional Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. Default is True. enforce_invertibility : bool, optional Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. Default is True. trend_offset : int, optional The offset at which to start time trend values. Default is 1, so that if `trend='t'` the trend is equal to 1, 2, ..., nobs. Typically is only set when the model created by extending a previous dataset. **kwargs Keyword arguments may be used to provide default values for state space matrices or for Kalman filtering options. See `Representation`, and `KalmanFilter` for more details. Attributes ---------- order : iterable The (p,q) order of the model for the number of AR and MA parameters to use. trend : str{'n','c','t','ct'} or iterable Parameter controlling the deterministic trend polynomial :math:`A(t)`. Can be specified as a string where 'c' indicates a constant (i.e. a degree zero component of the trend polynomial), 't' indicates a linear trend with time, and 'ct' is both. Can also be specified as an iterable defining the non-zero polynomial exponents to include, in increasing order. For example, `[1,1,0,1]` denotes :math:`a + bt + ct^3`. error_cov_type : {'diagonal', 'unstructured'}, optional The structure of the covariance matrix of the error term, where "unstructured" puts no restrictions on the matrix and "diagonal" requires it to be a diagonal matrix (uncorrelated errors). Default is "unstructured". measurement_error : bool, optional Whether or not to assume the endogenous observations `endog` were measured with error. Default is False. enforce_stationarity : bool, optional Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. Default is True. enforce_invertibility : bool, optional Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. Default is True. Notes ----- Generically, the VARMAX model is specified (see for example chapter 18 of [1]_): .. math:: y_t = A(t) + A_1 y_{t-1} + \dots + A_p y_{t-p} + B x_t + \epsilon_t + M_1 \epsilon_{t-1} + \dots M_q \epsilon_{t-q} where :math:`\epsilon_t \sim N(0, \Omega)`, and where :math:`y_t` is a `k_endog x 1` vector. Additionally, this model allows considering the case where the variables are measured with error. Note that in the full VARMA(p,q) case there is a fundamental identification problem in that the coefficient matrices :math:`\{A_i, M_j\}` are not generally unique, meaning that for a given time series process there may be multiple sets of matrices that equivalently represent it. See Chapter 12 of [1]_ for more information. Although this class can be used to estimate VARMA(p,q) models, a warning is issued to remind users that no steps have been taken to ensure identification in this case. References ---------- .. [1] Lütkepohl, Helmut. 2007. New Introduction to Multiple Time Series Analysis. Berlin: Springer. """ def __init__(self, endog, exog=None, order=(1, 0), trend='c', error_cov_type='unstructured', measurement_error=False, enforce_stationarity=True, enforce_invertibility=True, trend_offset=1, **kwargs): # Model parameters self.error_cov_type = error_cov_type self.measurement_error = measurement_error self.enforce_stationarity = enforce_stationarity self.enforce_invertibility = enforce_invertibility # Save the given orders self.order = order # Model orders self.k_ar = int(order[0]) self.k_ma = int(order[1]) # Check for valid model if error_cov_type not in ['diagonal', 'unstructured']: raise ValueError('Invalid error covariance matrix type' ' specification.') if self.k_ar == 0 and self.k_ma == 0: raise ValueError('Invalid VARMAX(p,q) specification; at least one' ' p,q must be greater than zero.') # Warn for VARMA model if self.k_ar > 0 and self.k_ma > 0: warn('Estimation of VARMA(p,q) models is not generically robust,' ' due especially to identification issues.', EstimationWarning) # Trend self.trend = trend self.trend_offset = trend_offset self.polynomial_trend, self.k_trend = prepare_trend_spec(self.trend) self._trend_is_const = (self.polynomial_trend.size == 1 and self.polynomial_trend[0] == 1) # Exogenous data (self.k_exog, exog) = prepare_exog(exog) # Note: at some point in the future might add state regression, as in # SARIMAX. self.mle_regression = self.k_exog > 0 # We need to have an array or pandas at this point if not _is_using_pandas(endog, None): endog = np.asanyarray(endog) # Model order # Used internally in various places _min_k_ar = max(self.k_ar, 1) self._k_order = _min_k_ar + self.k_ma # Number of states k_endog = endog.shape[1] k_posdef = k_endog k_states = k_endog * self._k_order # By default, initialize as stationary kwargs.setdefault('initialization', 'stationary') # By default, use LU decomposition kwargs.setdefault('inversion_method', INVERT_UNIVARIATE | SOLVE_LU) # Initialize the state space model super(VARMAX, self).__init__( endog, exog=exog, k_states=k_states, k_posdef=k_posdef, **kwargs ) # Set as time-varying model if we have time-trend or exog if self.k_exog > 0 or (self.k_trend > 0 and not self._trend_is_const): self.ssm._time_invariant = False # Initialize the parameters self.parameters = {} self.parameters['trend'] = self.k_endog * self.k_trend self.parameters['ar'] = self.k_endog**2 * self.k_ar self.parameters['ma'] = self.k_endog**2 * self.k_ma self.parameters['regression'] = self.k_endog * self.k_exog if self.error_cov_type == 'diagonal': self.parameters['state_cov'] = self.k_endog # These parameters fill in a lower-triangular matrix which is then # dotted with itself to get a positive definite matrix. elif self.error_cov_type == 'unstructured': self.parameters['state_cov'] = ( int(self.k_endog * (self.k_endog + 1) / 2) ) self.parameters['obs_cov'] = self.k_endog * self.measurement_error self.k_params = sum(self.parameters.values()) # Initialize trend data: we create trend data with one more observation # than we actually have, to make it easier to insert the appropriate # trend component into the final state intercept. trend_data = prepare_trend_data( self.polynomial_trend, self.k_trend, self.nobs + 1, offset=self.trend_offset) self._trend_data = trend_data[:-1] self._final_trend = trend_data[-1:] # Initialize known elements of the state space matrices # If we have exog effects, then the state intercept needs to be # time-varying if (self.k_trend > 0 and not self._trend_is_const) or self.k_exog > 0: self.ssm['state_intercept'] = np.zeros((self.k_states, self.nobs)) # self.ssm['obs_intercept'] = np.zeros((self.k_endog, self.nobs)) # The design matrix is just an identity for the first k_endog states idx = np.diag_indices(self.k_endog) self.ssm[('design',) + idx] = 1 # The transition matrix is described in four blocks, where the upper # left block is in companion form with the autoregressive coefficient # matrices (so it is shaped k_endog * k_ar x k_endog * k_ar) ... if self.k_ar > 0: idx = np.diag_indices((self.k_ar - 1) * self.k_endog) idx = idx[0] + self.k_endog, idx[1] self.ssm[('transition',) + idx] = 1 # ... and the lower right block is in companion form with zeros as the # coefficient matrices (it is shaped k_endog * k_ma x k_endog * k_ma). idx = np.diag_indices((self.k_ma - 1) * self.k_endog) idx = (idx[0] + (_min_k_ar + 1) * self.k_endog, idx[1] + _min_k_ar * self.k_endog) self.ssm[('transition',) + idx] = 1 # The selection matrix is described in two blocks, where the upper # block selects the all k_posdef errors in the first k_endog rows # (the upper block is shaped k_endog * k_ar x k) and the lower block # also selects all k_posdef errors in the first k_endog rows (the lower # block is shaped k_endog * k_ma x k). idx = np.diag_indices(self.k_endog) self.ssm[('selection',) + idx] = 1 idx = idx[0] + _min_k_ar * self.k_endog, idx[1] if self.k_ma > 0: self.ssm[('selection',) + idx] = 1 # Cache some indices if self._trend_is_const and self.k_exog == 0: self._idx_state_intercept = np.s_['state_intercept', :k_endog, :] elif self.k_trend > 0 or self.k_exog > 0: self._idx_state_intercept = np.s_['state_intercept', :k_endog, :-1] if self.k_ar > 0: self._idx_transition = np.s_['transition', :k_endog, :] else: self._idx_transition = np.s_['transition', :k_endog, k_endog:] if self.error_cov_type == 'diagonal': self._idx_state_cov = ( ('state_cov',) + np.diag_indices(self.k_endog)) elif self.error_cov_type == 'unstructured': self._idx_lower_state_cov = np.tril_indices(self.k_endog) if self.measurement_error: self._idx_obs_cov = ('obs_cov',) + np.diag_indices(self.k_endog) # Cache some slices def _slice(key, offset): length = self.parameters[key] param_slice = np.s_[offset:offset + length] offset += length return param_slice, offset offset = 0 self._params_trend, offset = _slice('trend', offset) self._params_ar, offset = _slice('ar', offset) self._params_ma, offset = _slice('ma', offset) self._params_regression, offset = _slice('regression', offset) self._params_state_cov, offset = _slice('state_cov', offset) self._params_obs_cov, offset = _slice('obs_cov', offset) # Variable holding optional final `exog` # (note: self._final_trend was set earlier) self._final_exog = None # Update _init_keys attached by super self._init_keys += ['order', 'trend', 'error_cov_type', 'measurement_error', 'enforce_stationarity', 'enforce_invertibility'] + list(kwargs.keys()) def clone(self, endog, exog=None, **kwargs): return self._clone_from_init_kwds(endog, exog=exog, **kwargs) @property def _res_classes(self): return {'fit': (VARMAXResults, VARMAXResultsWrapper)} @property def start_params(self): params = np.zeros(self.k_params, dtype=np.float64) # A. Run a multivariate regression to get beta estimates endog = pd.DataFrame(self.endog.copy()) endog = endog.interpolate() endog = endog.fillna(method='backfill').values exog = None if self.k_trend > 0 and self.k_exog > 0: exog = np.c_[self._trend_data, self.exog] elif self.k_trend > 0: exog = self._trend_data elif self.k_exog > 0: exog = self.exog # Although the Kalman filter can deal with missing values in endog, # conditional sum of squares cannot if np.any(np.isnan(endog)): mask = ~np.any(np.isnan(endog), axis=1) endog = endog[mask] if exog is not None: exog = exog[mask] # Regression and trend effects via OLS trend_params = np.zeros(0) exog_params = np.zeros(0) if self.k_trend > 0 or self.k_exog > 0: trendexog_params = np.linalg.pinv(exog).dot(endog) endog -= np.dot(exog, trendexog_params) if self.k_trend > 0: trend_params = trendexog_params[:self.k_trend].T if self.k_endog > 0: exog_params = trendexog_params[self.k_trend:].T # B. Run a VAR model on endog to get trend, AR parameters ar_params = [] k_ar = self.k_ar if self.k_ar > 0 else 1 mod_ar = var_model.VAR(endog) res_ar = mod_ar.fit(maxlags=k_ar, ic=None, trend='nc') if self.k_ar > 0: ar_params = np.array(res_ar.params).T.ravel() endog = res_ar.resid # Test for stationarity if self.k_ar > 0 and self.enforce_stationarity: coefficient_matrices = ( ar_params.reshape( self.k_endog * self.k_ar, self.k_endog ).T ).reshape(self.k_endog, self.k_endog, self.k_ar).T stationary = is_invertible([1] + list(-coefficient_matrices)) if not stationary: warn('Non-stationary starting autoregressive parameters' ' found. Using zeros as starting parameters.') ar_params *= 0 # C. Run a VAR model on the residuals to get MA parameters ma_params = [] if self.k_ma > 0: mod_ma = var_model.VAR(endog) res_ma = mod_ma.fit(maxlags=self.k_ma, ic=None, trend='nc') ma_params = np.array(res_ma.params.T).ravel() # Test for invertibility if self.enforce_invertibility: coefficient_matrices = ( ma_params.reshape( self.k_endog * self.k_ma, self.k_endog ).T ).reshape(self.k_endog, self.k_endog, self.k_ma).T invertible = is_invertible([1] + list(-coefficient_matrices)) if not invertible: warn('Non-stationary starting moving-average parameters' ' found. Using zeros as starting parameters.') ma_params *= 0 # Transform trend / exog params from mean form to intercept form if self.k_ar > 0 and (self.k_trend > 0 or self.mle_regression): coefficient_matrices = ( ar_params.reshape( self.k_endog * self.k_ar, self.k_endog ).T ).reshape(self.k_endog, self.k_endog, self.k_ar).T tmp = np.eye(self.k_endog) - np.sum(coefficient_matrices, axis=0) if self.k_trend > 0: trend_params = np.dot(tmp, trend_params) if self.mle_regression > 0: exog_params = np.dot(tmp, exog_params) # 1. Intercept terms if self.k_trend > 0: params[self._params_trend] = trend_params.ravel() # 2. AR terms if self.k_ar > 0: params[self._params_ar] = ar_params # 3. MA terms if self.k_ma > 0: params[self._params_ma] = ma_params # 4. Regression terms if self.mle_regression: params[self._params_regression] = exog_params.ravel() # 5. State covariance terms if self.error_cov_type == 'diagonal': params[self._params_state_cov] = res_ar.sigma_u.diagonal() elif self.error_cov_type == 'unstructured': cov_factor = np.linalg.cholesky(res_ar.sigma_u) params[self._params_state_cov] = ( cov_factor[self._idx_lower_state_cov].ravel()) # 5. Measurement error variance terms if self.measurement_error: if self.k_ma > 0: params[self._params_obs_cov] = res_ma.sigma_u.diagonal() else: params[self._params_obs_cov] = res_ar.sigma_u.diagonal() return params @property def param_names(self): param_names = [] endog_names = self.endog_names if not isinstance(self.endog_names, list): endog_names = [endog_names] # 1. Intercept terms if self.k_trend > 0: for j in range(self.k_endog): for i in self.polynomial_trend.nonzero()[0]: if i == 0: param_names += ['intercept.%s' % endog_names[j]] elif i == 1: param_names += ['drift.%s' % endog_names[j]] else: param_names += ['trend.%d.%s' % (i, endog_names[j])] # 2. AR terms param_names += [ 'L%d.%s.%s' % (i+1, endog_names[k], endog_names[j]) for j in range(self.k_endog) for i in range(self.k_ar) for k in range(self.k_endog) ] # 3. MA terms param_names += [ 'L%d.e(%s).%s' % (i+1, endog_names[k], endog_names[j]) for j in range(self.k_endog) for i in range(self.k_ma) for k in range(self.k_endog) ] # 4. Regression terms param_names += [ 'beta.%s.%s' % (self.exog_names[j], endog_names[i]) for i in range(self.k_endog) for j in range(self.k_exog) ] # 5. State covariance terms if self.error_cov_type == 'diagonal': param_names += [ 'sigma2.%s' % endog_names[i] for i in range(self.k_endog) ] elif self.error_cov_type == 'unstructured': param_names += [ ('sqrt.var.%s' % endog_names[i] if i == j else 'sqrt.cov.%s.%s' % (endog_names[j], endog_names[i])) for i in range(self.k_endog) for j in range(i+1) ] # 5. Measurement error variance terms if self.measurement_error: param_names += [ 'measurement_variance.%s' % endog_names[i] for i in range(self.k_endog) ] return param_names def transform_params(self, unconstrained): """ Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation Parameters ---------- unconstrained : array_like Array of unconstrained parameters used by the optimizer, to be transformed. Returns ------- constrained : array_like Array of constrained parameters which may be used in likelihood evaluation. Notes ----- Constrains the factor transition to be stationary and variances to be positive. """ unconstrained = np.array(unconstrained, ndmin=1) constrained = np.zeros(unconstrained.shape, dtype=unconstrained.dtype) # 1. Intercept terms: nothing to do constrained[self._params_trend] = unconstrained[self._params_trend] # 2. AR terms: optionally force to be stationary if self.k_ar > 0 and self.enforce_stationarity: # Create the state covariance matrix if self.error_cov_type == 'diagonal': state_cov = np.diag(unconstrained[self._params_state_cov]**2) elif self.error_cov_type == 'unstructured': state_cov_lower = np.zeros(self.ssm['state_cov'].shape, dtype=unconstrained.dtype) state_cov_lower[self._idx_lower_state_cov] = ( unconstrained[self._params_state_cov]) state_cov = np.dot(state_cov_lower, state_cov_lower.T) # Transform the parameters coefficients = unconstrained[self._params_ar].reshape( self.k_endog, self.k_endog * self.k_ar) coefficient_matrices, variance = ( constrain_stationary_multivariate(coefficients, state_cov)) constrained[self._params_ar] = coefficient_matrices.ravel() else: constrained[self._params_ar] = unconstrained[self._params_ar] # 3. MA terms: optionally force to be invertible if self.k_ma > 0 and self.enforce_invertibility: # Transform the parameters, using an identity variance matrix state_cov = np.eye(self.k_endog, dtype=unconstrained.dtype) coefficients = unconstrained[self._params_ma].reshape( self.k_endog, self.k_endog * self.k_ma) coefficient_matrices, variance = ( constrain_stationary_multivariate(coefficients, state_cov)) constrained[self._params_ma] = coefficient_matrices.ravel() else: constrained[self._params_ma] = unconstrained[self._params_ma] # 4. Regression terms: nothing to do constrained[self._params_regression] = ( unconstrained[self._params_regression]) # 5. State covariance terms # If we have variances, force them to be positive if self.error_cov_type == 'diagonal': constrained[self._params_state_cov] = ( unconstrained[self._params_state_cov]**2) # Otherwise, nothing needs to be done elif self.error_cov_type == 'unstructured': constrained[self._params_state_cov] = ( unconstrained[self._params_state_cov]) # 5. Measurement error variance terms if self.measurement_error: # Force these to be positive constrained[self._params_obs_cov] = ( unconstrained[self._params_obs_cov]**2) return constrained def untransform_params(self, constrained): """ Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer. Parameters ---------- constrained : array_like Array of constrained parameters used in likelihood evaluation, to be transformed. Returns ------- unconstrained : array_like Array of unconstrained parameters used by the optimizer. """ constrained = np.array(constrained, ndmin=1) unconstrained = np.zeros(constrained.shape, dtype=constrained.dtype) # 1. Intercept terms: nothing to do unconstrained[self._params_trend] = constrained[self._params_trend] # 2. AR terms: optionally were forced to be stationary if self.k_ar > 0 and self.enforce_stationarity: # Create the state covariance matrix if self.error_cov_type == 'diagonal': state_cov = np.diag(constrained[self._params_state_cov]) elif self.error_cov_type == 'unstructured': state_cov_lower = np.zeros(self.ssm['state_cov'].shape, dtype=constrained.dtype) state_cov_lower[self._idx_lower_state_cov] = ( constrained[self._params_state_cov]) state_cov = np.dot(state_cov_lower, state_cov_lower.T) # Transform the parameters coefficients = constrained[self._params_ar].reshape( self.k_endog, self.k_endog * self.k_ar) unconstrained_matrices, variance = ( unconstrain_stationary_multivariate(coefficients, state_cov)) unconstrained[self._params_ar] = unconstrained_matrices.ravel() else: unconstrained[self._params_ar] = constrained[self._params_ar] # 3. MA terms: optionally were forced to be invertible if self.k_ma > 0 and self.enforce_invertibility: # Transform the parameters, using an identity variance matrix state_cov = np.eye(self.k_endog, dtype=constrained.dtype) coefficients = constrained[self._params_ma].reshape( self.k_endog, self.k_endog * self.k_ma) unconstrained_matrices, variance = ( unconstrain_stationary_multivariate(coefficients, state_cov)) unconstrained[self._params_ma] = unconstrained_matrices.ravel() else: unconstrained[self._params_ma] = constrained[self._params_ma] # 4. Regression terms: nothing to do unconstrained[self._params_regression] = ( constrained[self._params_regression]) # 5. State covariance terms # If we have variances, then these were forced to be positive if self.error_cov_type == 'diagonal': unconstrained[self._params_state_cov] = ( constrained[self._params_state_cov]**0.5) # Otherwise, nothing needs to be done elif self.error_cov_type == 'unstructured': unconstrained[self._params_state_cov] = ( constrained[self._params_state_cov]) # 5. Measurement error variance terms if self.measurement_error: # These were forced to be positive unconstrained[self._params_obs_cov] = ( constrained[self._params_obs_cov]**0.5) return unconstrained def _validate_can_fix_params(self, param_names): super(VARMAX, self)._validate_can_fix_params(param_names) ix = np.cumsum(list(self.parameters.values()))[:-1] (_, ar_names, ma_names, _, _, _) = [ arr.tolist() for arr in np.array_split(self.param_names, ix)] if self.enforce_stationarity and self.k_ar > 0: if self.k_endog > 1 or self.k_ar > 1: fix_all = param_names.issuperset(ar_names) fix_any = ( len(param_names.intersection(ar_names)) > 0) if fix_any and not fix_all: raise ValueError( 'Cannot fix individual autoregressive parameters' ' when `enforce_stationarity=True`. In this case,' ' must either fix all autoregressive parameters or' ' none.') if self.enforce_invertibility and self.k_ma > 0: if self.k_endog or self.k_ma > 1: fix_all = param_names.issuperset(ma_names) fix_any = ( len(param_names.intersection(ma_names)) > 0) if fix_any and not fix_all: raise ValueError( 'Cannot fix individual moving average parameters' ' when `enforce_invertibility=True`. In this case,' ' must either fix all moving average parameters or' ' none.') def update(self, params, transformed=True, includes_fixed=False, complex_step=False): params = self.handle_params(params, transformed=transformed, includes_fixed=includes_fixed) # 1. State intercept # - Exog if self.mle_regression: exog_params = params[self._params_regression].reshape( self.k_endog, self.k_exog).T intercept = np.dot(self.exog[1:], exog_params) self.ssm[self._idx_state_intercept] = intercept.T if self._final_exog is not None: self.ssm['state_intercept', :self.k_endog, -1] = np.dot( self._final_exog, exog_params) # - Trend if self.k_trend > 0: # If we did not set the intercept above, zero it out so we can # just += later if not self.mle_regression: zero = np.array(0, dtype=params.dtype) self.ssm['state_intercept', :] = zero trend_params = params[self._params_trend].reshape( self.k_endog, self.k_trend).T if self._trend_is_const: intercept = trend_params else: intercept = np.dot(self._trend_data[1:], trend_params) self.ssm[self._idx_state_intercept] += intercept.T if self._final_trend is not None and not self._trend_is_const: self.ssm['state_intercept', :self.k_endog, -1:] += np.dot( self._final_trend, trend_params).T # Need to set the last state intercept to np.nan (with appropriate # dtype) if we don't have the final exog if self.mle_regression and self._final_exog is None: nan = np.array(np.nan, dtype=params.dtype) self.ssm['state_intercept', :self.k_endog, -1] = nan # 2. Transition ar = params[self._params_ar].reshape( self.k_endog, self.k_endog * self.k_ar) ma = params[self._params_ma].reshape( self.k_endog, self.k_endog * self.k_ma) self.ssm[self._idx_transition] = np.c_[ar, ma] # 3. State covariance if self.error_cov_type == 'diagonal': self.ssm[self._idx_state_cov] = ( params[self._params_state_cov] ) elif self.error_cov_type == 'unstructured': state_cov_lower = np.zeros(self.ssm['state_cov'].shape, dtype=params.dtype) state_cov_lower[self._idx_lower_state_cov] = ( params[self._params_state_cov]) self.ssm['state_cov'] = np.dot(state_cov_lower, state_cov_lower.T) # 4. Observation covariance if self.measurement_error: self.ssm[self._idx_obs_cov] = params[self._params_obs_cov] @contextlib.contextmanager def _set_final_exog(self, exog): """ Set the final state intercept value using out-of-sample `exog` / trend Parameters ---------- exog : ndarray Out-of-sample `exog` values, usually produced by `_validate_out_of_sample_exog` to ensure the correct shape (this method does not do any additional validation of its own). out_of_sample : int Number of out-of-sample periods. Notes ----- We need special handling for simulating or forecasting with `exog` or trend, because if we had these then the last predicted_state has been set to NaN since we did not have the appropriate `exog` to create it. Since we handle trend in the same way as `exog`, we still have this issue when only trend is used without `exog`. """ cache_value = self._final_exog if self.k_exog > 0: if exog is not None: exog = np.atleast_1d(exog) if exog.ndim == 2: exog = exog[:1] try: exog = np.reshape(exog[:1], (self.k_exog,)) except ValueError: raise ValueError('Provided exogenous values are not of the' ' appropriate shape. Required %s, got %s.' % (str((self.k_exog,)), str(exog.shape))) self._final_exog = exog try: yield finally: self._final_exog = cache_value @Appender(MLEModel.simulate.__doc__) def simulate(self, params, nsimulations, measurement_shocks=None, state_shocks=None, initial_state=None, anchor=None, repetitions=None, exog=None, extend_model=None, extend_kwargs=None, transformed=True, includes_fixed=False, **kwargs): with self._set_final_exog(exog): out = super(VARMAX, self).simulate( params, nsimulations, measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state, anchor=anchor, repetitions=repetitions, exog=exog, extend_model=extend_model, extend_kwargs=extend_kwargs, transformed=transformed, includes_fixed=includes_fixed, **kwargs) return out class VARMAXResults(MLEResults): """ Class to hold results from fitting an VARMAX model. Parameters ---------- model : VARMAX instance The fitted model instance Attributes ---------- specification : dictionary Dictionary including all attributes from the VARMAX model instance. coefficient_matrices_var : ndarray Array containing autoregressive lag polynomial coefficient matrices, ordered from lowest degree to highest. coefficient_matrices_vma : ndarray Array containing moving average lag polynomial coefficients, ordered from lowest degree to highest. See Also -------- statsmodels.tsa.statespace.kalman_filter.FilterResults statsmodels.tsa.statespace.mlemodel.MLEResults """ def __init__(self, model, params, filter_results, cov_type=None, cov_kwds=None, **kwargs): super(VARMAXResults, self).__init__(model, params, filter_results, cov_type, cov_kwds, **kwargs) self.specification = Bunch(**{ # Set additional model parameters 'error_cov_type': self.model.error_cov_type, 'measurement_error': self.model.measurement_error, 'enforce_stationarity': self.model.enforce_stationarity, 'enforce_invertibility': self.model.enforce_invertibility, 'trend_offset': self.model.trend_offset, 'order': self.model.order, # Model order 'k_ar': self.model.k_ar, 'k_ma': self.model.k_ma, # Trend / Regression 'trend': self.model.trend, 'k_trend': self.model.k_trend, 'k_exog': self.model.k_exog, }) # Polynomials / coefficient matrices self.coefficient_matrices_var = None self.coefficient_matrices_vma = None if self.model.k_ar > 0: ar_params = np.array(self.params[self.model._params_ar]) k_endog = self.model.k_endog k_ar = self.model.k_ar self.coefficient_matrices_var = ( ar_params.reshape(k_endog * k_ar, k_endog).T ).reshape(k_endog, k_endog, k_ar).T if self.model.k_ma > 0: ma_params = np.array(self.params[self.model._params_ma]) k_endog = self.model.k_endog k_ma = self.model.k_ma self.coefficient_matrices_vma = ( ma_params.reshape(k_endog * k_ma, k_endog).T ).reshape(k_endog, k_endog, k_ma).T def extend(self, endog, exog=None, **kwargs): # If we have exog, then the last element of predicted_state and # predicted_state_cov are nan (since they depend on the exog associated # with the first out-of-sample point), so we need to compute them here if exog is not None: fcast = self.get_prediction(self.nobs, self.nobs, exog=exog[:1]) fcast_results = fcast.prediction_results initial_state = fcast_results.predicted_state[..., 0] initial_state_cov = fcast_results.predicted_state_cov[..., 0] else: initial_state = self.predicted_state[..., -1] initial_state_cov = self.predicted_state_cov[..., -1] kwargs.setdefault('trend_offset', self.nobs + self.model.trend_offset) mod = self.model.clone(endog, exog=exog, **kwargs) mod.ssm.initialization = Initialization( mod.k_states, 'known', constant=initial_state, stationary_cov=initial_state_cov) if self.smoother_results is not None: res = mod.smooth(self.params) else: res = mod.filter(self.params) return res @contextlib.contextmanager def _set_final_predicted_state(self, exog, out_of_sample): """ Set the final predicted state value using out-of-sample `exog` / trend Parameters ---------- exog : ndarray Out-of-sample `exog` values, usually produced by `_validate_out_of_sample_exog` to ensure the correct shape (this method does not do any additional validation of its own). out_of_sample : int Number of out-of-sample periods. Notes ----- We need special handling for forecasting with `exog`, because if we had these then the last predicted_state has been set to NaN since we did not have the appropriate `exog` to create it. """ flag = out_of_sample and self.model.k_exog > 0 if flag: tmp_endog = concat([ self.model.endog[-1:], np.zeros((1, self.model.k_endog))]) if self.model.k_exog > 0: tmp_exog = concat([self.model.exog[-1:], exog[:1]]) else: tmp_exog = None tmp_trend_offset = self.model.trend_offset + self.nobs - 1 tmp_mod = self.model.clone(tmp_endog, exog=tmp_exog, trend_offset=tmp_trend_offset) constant = self.filter_results.predicted_state[:, -2] stationary_cov = self.filter_results.predicted_state_cov[:, :, -2] tmp_mod.ssm.initialize_known(constant=constant, stationary_cov=stationary_cov) tmp_res = tmp_mod.filter(self.params, transformed=True, includes_fixed=True, return_ssm=True) # Patch up `predicted_state` self.filter_results.predicted_state[:, -1] = ( tmp_res.predicted_state[:, -2]) try: yield finally: if flag: self.filter_results.predicted_state[:, -1] = np.nan @Appender(MLEResults.get_prediction.__doc__) def get_prediction(self, start=None, end=None, dynamic=False, index=None, exog=None, **kwargs): if start is None: start = 0 # Handle end (e.g. date) _start, _end, out_of_sample, _ = ( self.model._get_prediction_index(start, end, index, silent=True)) # Normalize `exog` exog = self.model._validate_out_of_sample_exog(exog, out_of_sample) # Handle trend offset for extended model extend_kwargs = {} if self.model.k_trend > 0: extend_kwargs['trend_offset'] = ( self.model.trend_offset + self.nobs) # Get the prediction with self.model._set_final_exog(exog): with self._set_final_predicted_state(exog, out_of_sample): out = super(VARMAXResults, self).get_prediction( start=start, end=end, dynamic=dynamic, index=index, exog=exog, extend_kwargs=extend_kwargs, **kwargs) return out @Appender(MLEResults.simulate.__doc__) def simulate(self, nsimulations, measurement_shocks=None, state_shocks=None, initial_state=None, anchor=None, repetitions=None, exog=None, extend_model=None, extend_kwargs=None, **kwargs): if anchor is None or anchor == 'start': iloc = 0 elif anchor == 'end': iloc = self.nobs else: iloc, _, _ = self.model._get_index_loc(anchor) if iloc < 0: iloc = self.nobs + iloc if iloc > self.nobs: raise ValueError('Cannot anchor simulation after the estimated' ' sample.') out_of_sample = max(iloc + nsimulations - self.nobs, 0) # Normalize `exog` exog = self.model._validate_out_of_sample_exog(exog, out_of_sample) with self._set_final_predicted_state(exog, out_of_sample): out = super(VARMAXResults, self).simulate( nsimulations, measurement_shocks=measurement_shocks, state_shocks=state_shocks, initial_state=initial_state, anchor=anchor, repetitions=repetitions, exog=exog, extend_model=extend_model, extend_kwargs=extend_kwargs, **kwargs) return out def _news_previous_results(self, previous, start, end, periods): # We need to figure out the out-of-sample exog, so that we can add back # in the last exog, predicted state exog = None out_of_sample = self.nobs - previous.nobs if self.model.k_exog > 0 and out_of_sample > 0: exog = self.model.exog[-out_of_sample:] # We also need to manually compute the `revised` results, rev_endog = self.model.endog[:previous.nobs].copy() rev_endog[previous.filter_results.missing.astype(bool).T] = np.nan has_revisions = not np.allclose(rev_endog, previous.model.endog, equal_nan=True) revised_results = None if has_revisions: rev_exog = None if self.model.exog is not None: rev_exog = self.model.exog[:previous.nobs].copy() rev_mod = previous.model.clone(rev_endog, exog=rev_exog) revised = rev_mod.smooth(self.params) # Compute the news with contextlib.ExitStack() as stack: stack.enter_context(previous.model._set_final_exog(exog)) stack.enter_context(previous._set_final_predicted_state( exog, out_of_sample)) if has_revisions: stack.enter_context(revised.model._set_final_exog(exog)) stack.enter_context(revised._set_final_predicted_state( exog, out_of_sample)) revised_results = revised.smoother_results out = self.smoother_results.news( previous.smoother_results, start=start, end=end, revised=revised_results) return out @Appender(MLEResults.summary.__doc__) def summary(self, alpha=.05, start=None, separate_params=True): from statsmodels.iolib.summary import summary_params # Create the model name spec = self.specification if spec.k_ar > 0 and spec.k_ma > 0: model_name = 'VARMA' order = '(%s,%s)' % (spec.k_ar, spec.k_ma) elif spec.k_ar > 0: model_name = 'VAR' order = '(%s)' % (spec.k_ar) else: model_name = 'VMA' order = '(%s)' % (spec.k_ma) if spec.k_exog > 0: model_name += 'X' model_name = [model_name + order] if spec.k_trend > 0: model_name.append('intercept') if spec.measurement_error: model_name.append('measurement error') summary = super(VARMAXResults, self).summary( alpha=alpha, start=start, model_name=model_name, display_params=not separate_params ) if separate_params: indices = np.arange(len(self.params)) def make_table(self, mask, title, strip_end=True): res = (self, self.params[mask], self.bse[mask], self.zvalues[mask], self.pvalues[mask], self.conf_int(alpha)[mask]) param_names = [] for name in np.array(self.data.param_names)[mask].tolist(): if strip_end: param_name = '.'.join(name.split('.')[:-1]) else: param_name = name if name in self.fixed_params: param_name = '%s (fixed)' % param_name param_names.append(param_name) return summary_params(res, yname=None, xname=param_names, alpha=alpha, use_t=False, title=title) # Add parameter tables for each endogenous variable k_endog = self.model.k_endog k_ar = self.model.k_ar k_ma = self.model.k_ma k_trend = self.model.k_trend k_exog = self.model.k_exog endog_masks = [] for i in range(k_endog): masks = [] offset = 0 # 1. Intercept terms if k_trend > 0: masks.append(np.arange(i, i + k_endog * k_trend, k_endog)) offset += k_endog * k_trend # 2. AR terms if k_ar > 0: start = i * k_endog * k_ar end = (i + 1) * k_endog * k_ar masks.append( offset + np.arange(start, end)) offset += k_ar * k_endog**2 # 3. MA terms if k_ma > 0: start = i * k_endog * k_ma end = (i + 1) * k_endog * k_ma masks.append( offset + np.arange(start, end)) offset += k_ma * k_endog**2 # 4. Regression terms if k_exog > 0: masks.append( offset + np.arange(i * k_exog, (i + 1) * k_exog)) offset += k_endog * k_exog # 5. Measurement error variance terms if self.model.measurement_error: masks.append( np.array(self.model.k_params - i - 1, ndmin=1)) # Create the table mask = np.concatenate(masks) endog_masks.append(mask) endog_names = self.model.endog_names if not isinstance(endog_names, list): endog_names = [endog_names] title = "Results for equation %s" % endog_names[i] table = make_table(self, mask, title) summary.tables.append(table) # State covariance terms state_cov_mask = ( np.arange(len(self.params))[self.model._params_state_cov]) table = make_table(self, state_cov_mask, "Error covariance matrix", strip_end=False) summary.tables.append(table) # Add a table for all other parameters masks = [] for m in (endog_masks, [state_cov_mask]): m = np.array(m).flatten() if len(m) > 0: masks.append(m) masks = np.concatenate(masks) inverse_mask = np.array(list(set(indices).difference(set(masks)))) if len(inverse_mask) > 0: table = make_table(self, inverse_mask, "Other parameters", strip_end=False) summary.tables.append(table) return summary class VARMAXResultsWrapper(MLEResultsWrapper): _attrs = {} _wrap_attrs = wrap.union_dicts(MLEResultsWrapper._wrap_attrs, _attrs) _methods = {} _wrap_methods = wrap.union_dicts(MLEResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(VARMAXResultsWrapper, VARMAXResults) # noqa:E305 statsmodels-0.12.2/statsmodels/tsa/stattools.py000066400000000000000000002415561400612667500217210ustar00rootroot00000000000000""" Statistical tools for time series analysis """ from statsmodels.compat.numpy import lstsq from statsmodels.compat.pandas import deprecate_kwarg from statsmodels.compat.python import lrange, lzip from statsmodels.compat.scipy import _next_regular import warnings import numpy as np from numpy.linalg import LinAlgError import pandas as pd from scipy import stats from statsmodels.regression.linear_model import OLS, yule_walker from statsmodels.tools.sm_exceptions import ( CollinearityWarning, InfeasibleTestError, InterpolationWarning, MissingDataError, ) from statsmodels.tools.tools import Bunch, add_constant from statsmodels.tools.validation import ( array_like, bool_like, dict_like, float_like, int_like, string_like, ) from statsmodels.tsa._bds import bds from statsmodels.tsa._innovations import innovations_algo, innovations_filter from statsmodels.tsa.adfvalues import mackinnoncrit, mackinnonp from statsmodels.tsa.arima_model import ARMA from statsmodels.tsa.tsatools import add_trend, lagmat, lagmat2ds __all__ = [ "acovf", "acf", "pacf", "pacf_yw", "pacf_ols", "ccovf", "ccf", "q_stat", "coint", "arma_order_select_ic", "adfuller", "kpss", "bds", "pacf_burg", "innovations_algo", "innovations_filter", "levinson_durbin_pacf", "levinson_durbin", "zivot_andrews", ] SQRTEPS = np.sqrt(np.finfo(np.double).eps) def _autolag( mod, endog, exog, startlag, maxlag, method, modargs=(), fitargs=(), regresults=False, ): """ Returns the results for the lag length that maximizes the info criterion. Parameters ---------- mod : Model class Model estimator class endog : array_like nobs array containing endogenous variable exog : array_like nobs by (startlag + maxlag) array containing lags and possibly other variables startlag : int The first zero-indexed column to hold a lag. See Notes. maxlag : int The highest lag order for lag length selection. method : {"aic", "bic", "t-stat"} aic - Akaike Information Criterion bic - Bayes Information Criterion t-stat - Based on last lag modargs : tuple, optional args to pass to model. See notes. fitargs : tuple, optional args to pass to fit. See notes. regresults : bool, optional Flag indicating to return optional return results Returns ------- icbest : float Best information criteria. bestlag : int The lag length that maximizes the information criterion. results : dict, optional Dictionary containing all estimation results Notes ----- Does estimation like mod(endog, exog[:,:i], *modargs).fit(*fitargs) where i goes from lagstart to lagstart+maxlag+1. Therefore, lags are assumed to be in contiguous columns from low to high lag length with the highest lag in the last column. """ # TODO: can tcol be replaced by maxlag + 2? # TODO: This could be changed to laggedRHS and exog keyword arguments if # this will be more general. results = {} method = method.lower() for lag in range(startlag, startlag + maxlag + 1): mod_instance = mod(endog, exog[:, :lag], *modargs) results[lag] = mod_instance.fit() if method == "aic": icbest, bestlag = min((v.aic, k) for k, v in results.items()) elif method == "bic": icbest, bestlag = min((v.bic, k) for k, v in results.items()) elif method == "t-stat": # stop = stats.norm.ppf(.95) stop = 1.6448536269514722 # Default values to ensure that always set bestlag = startlag + maxlag icbest = 0.0 for lag in range(startlag + maxlag, startlag - 1, -1): icbest = np.abs(results[lag].tvalues[-1]) bestlag = lag if np.abs(icbest) >= stop: # Break for first lag with a significant t-stat break else: raise ValueError(f"Information Criterion {method} not understood.") if not regresults: return icbest, bestlag else: return icbest, bestlag, results # this needs to be converted to a class like HetGoldfeldQuandt, # 3 different returns are a mess # See: # Ng and Perron(2001), Lag length selection and the construction of unit root # tests with good size and power, Econometrica, Vol 69 (6) pp 1519-1554 # TODO: include drift keyword, only valid with regression == "c" # just changes the distribution of the test statistic to a t distribution # TODO: autolag is untested def adfuller( x, maxlag=None, regression="c", autolag="AIC", store=False, regresults=False, ): """ Augmented Dickey-Fuller unit root test. The Augmented Dickey-Fuller test can be used to test for a unit root in a univariate process in the presence of serial correlation. Parameters ---------- x : array_like, 1d The data series to test. maxlag : int Maximum lag which is included in test, default 12*(nobs/100)^{1/4}. regression : {"c","ct","ctt","nc"} Constant and trend order to include in regression. * "c" : constant only (default). * "ct" : constant and trend. * "ctt" : constant, and linear and quadratic trend. * "nc" : no constant, no trend. autolag : {"AIC", "BIC", "t-stat", None} Method to use when automatically determining the lag length among the values 0, 1, ..., maxlag. * If "AIC" (default) or "BIC", then the number of lags is chosen to minimize the corresponding information criterion. * "t-stat" based choice of maxlag. Starts with maxlag and drops a lag until the t-statistic on the last lag length is significant using a 5%-sized test. * If None, then the number of included lags is set to maxlag. store : bool If True, then a result instance is returned additionally to the adf statistic. Default is False. regresults : bool, optional If True, the full regression results are returned. Default is False. Returns ------- adf : float The test statistic. pvalue : float MacKinnon"s approximate p-value based on MacKinnon (1994, 2010). usedlag : int The number of lags used. nobs : int The number of observations used for the ADF regression and calculation of the critical values. critical values : dict Critical values for the test statistic at the 1 %, 5 %, and 10 % levels. Based on MacKinnon (2010). icbest : float The maximized information criterion if autolag is not None. resstore : ResultStore, optional A dummy class with results attached as attributes. Notes ----- The null hypothesis of the Augmented Dickey-Fuller is that there is a unit root, with the alternative that there is no unit root. If the pvalue is above a critical size, then we cannot reject that there is a unit root. The p-values are obtained through regression surface approximation from MacKinnon 1994, but using the updated 2010 tables. If the p-value is close to significant, then the critical values should be used to judge whether to reject the null. The autolag option and maxlag for it are described in Greene. References ---------- .. [1] W. Green. "Econometric Analysis," 5th ed., Pearson, 2003. .. [2] Hamilton, J.D. "Time Series Analysis". Princeton, 1994. .. [3] MacKinnon, J.G. 1994. "Approximate asymptotic distribution functions for unit-root and cointegration tests. `Journal of Business and Economic Statistics` 12, 167-76. .. [4] MacKinnon, J.G. 2010. "Critical Values for Cointegration Tests." Queen"s University, Dept of Economics, Working Papers. Available at http://ideas.repec.org/p/qed/wpaper/1227.html Examples -------- See example notebook """ x = array_like(x, "x") maxlag = int_like(maxlag, "maxlag", optional=True) regression = string_like( regression, "regression", options=("c", "ct", "ctt", "nc") ) autolag = string_like( autolag, "autolag", optional=True, options=("aic", "bic", "t-stat") ) store = bool_like(store, "store") regresults = bool_like(regresults, "regresults") if regresults: store = True trenddict = {None: "nc", 0: "c", 1: "ct", 2: "ctt"} if regression is None or isinstance(regression, int): regression = trenddict[regression] regression = regression.lower() nobs = x.shape[0] ntrend = len(regression) if regression != "nc" else 0 if maxlag is None: # from Greene referencing Schwert 1989 maxlag = int(np.ceil(12.0 * np.power(nobs / 100.0, 1 / 4.0))) # -1 for the diff maxlag = min(nobs // 2 - ntrend - 1, maxlag) if maxlag < 0: raise ValueError( "sample size is too short to use selected " "regression component" ) elif maxlag > nobs // 2 - ntrend - 1: raise ValueError( "maxlag must be less than (nobs/2 - 1 - ntrend) " "where n trend is the number of included " "deterministic regressors" ) xdiff = np.diff(x) xdall = lagmat(xdiff[:, None], maxlag, trim="both", original="in") nobs = xdall.shape[0] xdall[:, 0] = x[-nobs - 1 : -1] # replace 0 xdiff with level of x xdshort = xdiff[-nobs:] if store: from statsmodels.stats.diagnostic import ResultsStore resstore = ResultsStore() if autolag: if regression != "nc": fullRHS = add_trend(xdall, regression, prepend=True) else: fullRHS = xdall startlag = fullRHS.shape[1] - xdall.shape[1] + 1 # 1 for level # search for lag length with smallest information criteria # Note: use the same number of observations to have comparable IC # aic and bic: smaller is better if not regresults: icbest, bestlag = _autolag( OLS, xdshort, fullRHS, startlag, maxlag, autolag ) else: icbest, bestlag, alres = _autolag( OLS, xdshort, fullRHS, startlag, maxlag, autolag, regresults=regresults, ) resstore.autolag_results = alres bestlag -= startlag # convert to lag not column index # rerun ols with best autolag xdall = lagmat(xdiff[:, None], bestlag, trim="both", original="in") nobs = xdall.shape[0] xdall[:, 0] = x[-nobs - 1 : -1] # replace 0 xdiff with level of x xdshort = xdiff[-nobs:] usedlag = bestlag else: usedlag = maxlag icbest = None if regression != "nc": resols = OLS( xdshort, add_trend(xdall[:, : usedlag + 1], regression) ).fit() else: resols = OLS(xdshort, xdall[:, : usedlag + 1]).fit() adfstat = resols.tvalues[0] # adfstat = (resols.params[0]-1.0)/resols.bse[0] # the "asymptotically correct" z statistic is obtained as # nobs/(1-np.sum(resols.params[1:-(trendorder+1)])) (resols.params[0] - 1) # I think this is the statistic that is used for series that are integrated # for orders higher than I(1), ie., not ADF but cointegration tests. # Get approx p-value and critical values pvalue = mackinnonp(adfstat, regression=regression, N=1) critvalues = mackinnoncrit(N=1, regression=regression, nobs=nobs) critvalues = { "1%": critvalues[0], "5%": critvalues[1], "10%": critvalues[2], } if store: resstore.resols = resols resstore.maxlag = maxlag resstore.usedlag = usedlag resstore.adfstat = adfstat resstore.critvalues = critvalues resstore.nobs = nobs resstore.H0 = ( "The coefficient on the lagged level equals 1 - " "unit root" ) resstore.HA = "The coefficient on the lagged level < 1 - stationary" resstore.icbest = icbest resstore._str = "Augmented Dickey-Fuller Test Results" return adfstat, pvalue, critvalues, resstore else: if not autolag: return adfstat, pvalue, usedlag, nobs, critvalues else: return adfstat, pvalue, usedlag, nobs, critvalues, icbest @deprecate_kwarg("unbiased", "adjusted") def acovf(x, adjusted=False, demean=True, fft=None, missing="none", nlag=None): """ Estimate autocovariances. Parameters ---------- x : array_like Time series data. Must be 1d. adjusted : bool, default False If True, then denominators is n-k, otherwise n. demean : bool, default True If True, then subtract the mean x from each element of x. fft : bool, default None If True, use FFT convolution. This method should be preferred for long time series. missing : str, default "none" A string in ["none", "raise", "conservative", "drop"] specifying how the NaNs are to be treated. "none" performs no checks. "raise" raises an exception if NaN values are found. "drop" removes the missing observations and then estimates the autocovariances treating the non-missing as contiguous. "conservative" computes the autocovariance using nan-ops so that nans are removed when computing the mean and cross-products that are used to estimate the autocovariance. When using "conservative", n is set to the number of non-missing observations. nlag : {int, None}, default None Limit the number of autocovariances returned. Size of returned array is nlag + 1. Setting nlag when fft is False uses a simple, direct estimator of the autocovariances that only computes the first nlag + 1 values. This can be much faster when the time series is long and only a small number of autocovariances are needed. Returns ------- ndarray The estimated autocovariances. References ----------- .. [1] Parzen, E., 1963. On spectral analysis with missing observations and amplitude modulation. Sankhya: The Indian Journal of Statistics, Series A, pp.383-392. """ adjusted = bool_like(adjusted, "adjusted") demean = bool_like(demean, "demean") fft = bool_like(fft, "fft", optional=True) missing = string_like( missing, "missing", options=("none", "raise", "conservative", "drop") ) nlag = int_like(nlag, "nlag", optional=True) if fft is None: msg = ( "fft=True will become the default after the release of the 0.12 " "release of statsmodels. To suppress this warning, explicitly " "set fft=False." ) warnings.warn(msg, FutureWarning) fft = False x = array_like(x, "x", ndim=1) missing = missing.lower() if missing == "none": deal_with_masked = False else: deal_with_masked = has_missing(x) if deal_with_masked: if missing == "raise": raise MissingDataError("NaNs were encountered in the data") notmask_bool = ~np.isnan(x) # bool if missing == "conservative": # Must copy for thread safety x = x.copy() x[~notmask_bool] = 0 else: # "drop" x = x[notmask_bool] # copies non-missing notmask_int = notmask_bool.astype(int) # int if demean and deal_with_masked: # whether "drop" or "conservative": xo = x - x.sum() / notmask_int.sum() if missing == "conservative": xo[~notmask_bool] = 0 elif demean: xo = x - x.mean() else: xo = x n = len(x) lag_len = nlag if nlag is None: lag_len = n - 1 elif nlag > n - 1: raise ValueError("nlag must be smaller than nobs - 1") if not fft and nlag is not None: acov = np.empty(lag_len + 1) acov[0] = xo.dot(xo) for i in range(lag_len): acov[i + 1] = xo[i + 1 :].dot(xo[: -(i + 1)]) if not deal_with_masked or missing == "drop": if adjusted: acov /= n - np.arange(lag_len + 1) else: acov /= n else: if adjusted: divisor = np.empty(lag_len + 1, dtype=np.int64) divisor[0] = notmask_int.sum() for i in range(lag_len): divisor[i + 1] = notmask_int[i + 1 :].dot( notmask_int[: -(i + 1)] ) divisor[divisor == 0] = 1 acov /= divisor else: # biased, missing data but npt "drop" acov /= notmask_int.sum() return acov if adjusted and deal_with_masked and missing == "conservative": d = np.correlate(notmask_int, notmask_int, "full") d[d == 0] = 1 elif adjusted: xi = np.arange(1, n + 1) d = np.hstack((xi, xi[:-1][::-1])) elif deal_with_masked: # biased and NaNs given and ("drop" or "conservative") d = notmask_int.sum() * np.ones(2 * n - 1) else: # biased and no NaNs or missing=="none" d = n * np.ones(2 * n - 1) if fft: nobs = len(xo) n = _next_regular(2 * nobs + 1) Frf = np.fft.fft(xo, n=n) acov = np.fft.ifft(Frf * np.conjugate(Frf))[:nobs] / d[nobs - 1 :] acov = acov.real else: acov = np.correlate(xo, xo, "full")[n - 1 :] / d[n - 1 :] if nlag is not None: # Copy to allow gc of full array rather than view return acov[: lag_len + 1].copy() return acov def q_stat(x, nobs, type=None): """ Compute Ljung-Box Q Statistic. Parameters ---------- x : array_like Array of autocorrelation coefficients. Can be obtained from acf. nobs : int, optional Number of observations in the entire sample (ie., not just the length of the autocorrelation function results. Returns ------- q-stat : ndarray Ljung-Box Q-statistic for autocorrelation parameters. p-value : ndarray P-value of the Q statistic. Notes ----- Designed to be used with acf. """ x = array_like(x, "x") nobs = int_like(nobs, "nobs") if type is not None: warnings.warn( "The `type` argument is deprecated and has no effect. This " "argument will be removed after the 0.12 release.", FutureWarning, ) ret = ( nobs * (nobs + 2) * np.cumsum((1.0 / (nobs - np.arange(1, len(x) + 1))) * x ** 2) ) chi2 = stats.chi2.sf(ret, np.arange(1, len(x) + 1)) return ret, chi2 # NOTE: Changed unbiased to False # see for example # http://www.itl.nist.gov/div898/handbook/eda/section3/autocopl.htm @deprecate_kwarg("unbiased", "adjusted") def acf( x, adjusted=False, nlags=None, qstat=False, fft=None, alpha=None, missing="none", ): """ Calculate the autocorrelation function. Parameters ---------- x : array_like The time series data. adjusted : bool, default False If True, then denominators for autocovariance are n-k, otherwise n. nlags : int, default 40 Number of lags to return autocorrelation for. qstat : bool, default False If True, returns the Ljung-Box q statistic for each autocorrelation coefficient. See q_stat for more information. fft : bool, default None If True, computes the ACF via FFT. alpha : scalar, default None If a number is given, the confidence intervals for the given level are returned. For instance if alpha=.05, 95 % confidence intervals are returned where the standard deviation is computed according to Bartlett"s formula. missing : str, default "none" A string in ["none", "raise", "conservative", "drop"] specifying how the NaNs are to be treated. "none" performs no checks. "raise" raises an exception if NaN values are found. "drop" removes the missing observations and then estimates the autocovariances treating the non-missing as contiguous. "conservative" computes the autocovariance using nan-ops so that nans are removed when computing the mean and cross-products that are used to estimate the autocovariance. When using "conservative", n is set to the number of non-missing observations. Returns ------- acf : ndarray The autocorrelation function. confint : ndarray, optional Confidence intervals for the ACF. Returned if alpha is not None. qstat : ndarray, optional The Ljung-Box Q-Statistic. Returned if q_stat is True. pvalues : ndarray, optional The p-values associated with the Q-statistics. Returned if q_stat is True. Notes ----- The acf at lag 0 (ie., 1) is returned. For very long time series it is recommended to use fft convolution instead. When fft is False uses a simple, direct estimator of the autocovariances that only computes the first nlag + 1 values. This can be much faster when the time series is long and only a small number of autocovariances are needed. If adjusted is true, the denominator for the autocovariance is adjusted for the loss of data. References ---------- .. [1] Parzen, E., 1963. On spectral analysis with missing observations and amplitude modulation. Sankhya: The Indian Journal of Statistics, Series A, pp.383-392. """ adjusted = bool_like(adjusted, "adjusted") nlags = int_like(nlags, "nlags", optional=True) qstat = bool_like(qstat, "qstat") fft = bool_like(fft, "fft", optional=True) alpha = float_like(alpha, "alpha", optional=True) missing = string_like( missing, "missing", options=("none", "raise", "conservative", "drop") ) if nlags is None: warnings.warn( "The default number of lags is changing from 40 to" "min(int(10 * np.log10(nobs)), nobs - 1) after 0.12" "is released. Set the number of lags to an integer to " " silence this warning.", FutureWarning, ) nlags = 40 if fft is None: warnings.warn( "fft=True will become the default after the release of the 0.12 " "release of statsmodels. To suppress this warning, explicitly " "set fft=False.", FutureWarning, ) fft = False x = array_like(x, "x") nobs = len(x) # TODO: should this shrink for missing="drop" and NaNs in x? avf = acovf(x, adjusted=adjusted, demean=True, fft=fft, missing=missing) acf = avf[: nlags + 1] / avf[0] if not (qstat or alpha): return acf if alpha is not None: varacf = np.ones_like(acf) / nobs varacf[0] = 0 varacf[1] = 1.0 / nobs varacf[2:] *= 1 + 2 * np.cumsum(acf[1:-1] ** 2) interval = stats.norm.ppf(1 - alpha / 2.0) * np.sqrt(varacf) confint = np.array(lzip(acf - interval, acf + interval)) if not qstat: return acf, confint if qstat: qstat, pvalue = q_stat(acf[1:], nobs=nobs) # drop lag 0 if alpha is not None: return acf, confint, qstat, pvalue else: return acf, qstat, pvalue def pacf_yw(x, nlags=None, method="adjusted"): """ Partial autocorrelation estimated with non-recursive yule_walker. Parameters ---------- x : array_like The observations of time series for which pacf is calculated. nlags : int, default 40 The largest lag for which pacf is returned. method : {"adjusted", "mle"}, default "adjusted" The method for the autocovariance calculations in yule walker. Returns ------- ndarray The partial autocorrelations, maxlag+1 elements. See Also -------- statsmodels.tsa.stattools.pacf Partial autocorrelation estimation. statsmodels.tsa.stattools.pacf_ols Partial autocorrelation estimation using OLS. statsmodels.tsa.stattools.pacf_burg Partial autocorrelation estimation using Burg"s method. Notes ----- This solves yule_walker for each desired lag and contains currently duplicate calculations. """ x = array_like(x, "x") nlags = int_like(nlags, "nlags", optional=True) if nlags is None: warnings.warn( "The default number of lags is changing from 40 to" "min(int(10 * np.log10(nobs)), nobs - 1) after 0.12" "is released. Set the number of lags to an integer to " " silence this warning.", FutureWarning, ) nlags = 40 method = string_like( method, "method", options=("adjusted", "unbiased", "mle") ) if method == "unbiased": warnings.warn( "unbiased is deprecated in factor of adjusted to reflect that the " "term is adjusting the sample size used in the autocovariance " "calculation rather than estimating an unbiased autocovariance. " "After release 0.13, using 'unbiased' will raise.", FutureWarning, ) method = "adjusted" pacf = [1.0] for k in range(1, nlags + 1): pacf.append(yule_walker(x, k, method=method)[0][-1]) return np.array(pacf) def pacf_burg(x, nlags=None, demean=True): """ Calculate Burg"s partial autocorrelation estimator. Parameters ---------- x : array_like Observations of time series for which pacf is calculated. nlags : int, optional Number of lags to compute the partial autocorrelations. If omitted, uses the smaller of 10(log10(nobs)) or nobs - 1. demean : bool, optional Flag indicating to demean that data. Set to False if x has been previously demeaned. Returns ------- pacf : ndarray Partial autocorrelations for lags 0, 1, ..., nlag. sigma2 : ndarray Residual variance estimates where the value in position m is the residual variance in an AR model that includes m lags. See Also -------- statsmodels.tsa.stattools.pacf Partial autocorrelation estimation. statsmodels.tsa.stattools.pacf_yw Partial autocorrelation estimation using Yule-Walker. statsmodels.tsa.stattools.pacf_ols Partial autocorrelation estimation using OLS. References ---------- .. [1] Brockwell, P.J. and Davis, R.A., 2016. Introduction to time series and forecasting. Springer. """ x = array_like(x, "x") if demean: x = x - x.mean() nobs = x.shape[0] p = nlags if nlags is not None else min(int(10 * np.log10(nobs)), nobs - 1) if p > nobs - 1: raise ValueError("nlags must be smaller than nobs - 1") d = np.zeros(p + 1) d[0] = 2 * x.dot(x) pacf = np.zeros(p + 1) u = x[::-1].copy() v = x[::-1].copy() d[1] = u[:-1].dot(u[:-1]) + v[1:].dot(v[1:]) pacf[1] = 2 / d[1] * v[1:].dot(u[:-1]) last_u = np.empty_like(u) last_v = np.empty_like(v) for i in range(1, p): last_u[:] = u last_v[:] = v u[1:] = last_u[:-1] - pacf[i] * last_v[1:] v[1:] = last_v[1:] - pacf[i] * last_u[:-1] d[i + 1] = (1 - pacf[i] ** 2) * d[i] - v[i] ** 2 - u[-1] ** 2 pacf[i + 1] = 2 / d[i + 1] * v[i + 1 :].dot(u[i:-1]) sigma2 = (1 - pacf ** 2) * d / (2.0 * (nobs - np.arange(0, p + 1))) pacf[0] = 1 # Insert the 0 lag partial autocorrel return pacf, sigma2 @deprecate_kwarg("unbiased", "adjusted") def pacf_ols(x, nlags=None, efficient=True, adjusted=False): """ Calculate partial autocorrelations via OLS. Parameters ---------- x : array_like Observations of time series for which pacf is calculated. nlags : int Number of lags for which pacf is returned. Lag 0 is not returned. efficient : bool, optional If true, uses the maximum number of available observations to compute each partial autocorrelation. If not, uses the same number of observations to compute all pacf values. adjusted : bool, optional Adjust each partial autocorrelation by n / (n - lag). Returns ------- ndarray The partial autocorrelations, (maxlag,) array corresponding to lags 0, 1, ..., maxlag. See Also -------- statsmodels.tsa.stattools.pacf Partial autocorrelation estimation. statsmodels.tsa.stattools.pacf_yw Partial autocorrelation estimation using Yule-Walker. statsmodels.tsa.stattools.pacf_burg Partial autocorrelation estimation using Burg"s method. Notes ----- This solves a separate OLS estimation for each desired lag using method in [1]_. Setting efficient to True has two effects. First, it uses `nobs - lag` observations of estimate each pacf. Second, it re-estimates the mean in each regression. If efficient is False, then the data are first demeaned, and then `nobs - maxlag` observations are used to estimate each partial autocorrelation. The inefficient estimator appears to have better finite sample properties. This option should only be used in time series that are covariance stationary. OLS estimation of the pacf does not guarantee that all pacf values are between -1 and 1. References ---------- .. [1] Box, G. E., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis: forecasting and control. John Wiley & Sons, p. 66 """ x = array_like(x, "x") nlags = int_like(nlags, "nlags", optional=True) efficient = bool_like(efficient, "efficient") adjusted = bool_like(adjusted, "adjusted") if nlags is None: warnings.warn( "The default number of lags is changing from 40 to" "min(int(10 * np.log10(nobs)), nobs - 1) after 0.12" "is released. Set the number of lags to an integer to " " silence this warning.", FutureWarning, ) nlags = 40 pacf = np.empty(nlags + 1) pacf[0] = 1.0 if efficient: xlags, x0 = lagmat(x, nlags, original="sep") xlags = add_constant(xlags) for k in range(1, nlags + 1): params = lstsq(xlags[k:, : k + 1], x0[k:], rcond=None)[0] pacf[k] = params[-1] else: x = x - np.mean(x) # Create a single set of lags for multivariate OLS xlags, x0 = lagmat(x, nlags, original="sep", trim="both") for k in range(1, nlags + 1): params = lstsq(xlags[:, :k], x0, rcond=None)[0] # Last coefficient corresponds to PACF value (see [1]) pacf[k] = params[-1] if adjusted: n = len(x) pacf *= n / (n - np.arange(nlags + 1)) return pacf def pacf(x, nlags=None, method="ywadjusted", alpha=None): """ Partial autocorrelation estimate. Parameters ---------- x : array_like Observations of time series for which pacf is calculated. nlags : int The largest lag for which the pacf is returned. The default is currently 40, but will change to min(int(10 * np.log10(nobs)), nobs // 2 - 1) in the future method : str, default "ywunbiased" Specifies which method for the calculations to use. - "yw" or "ywadjusted" : Yule-Walker with sample-size adjustment in denominator for acovf. Default. - "ywm" or "ywmle" : Yule-Walker without adjustment. - "ols" : regression of time series on lags of it and on constant. - "ols-inefficient" : regression of time series on lags using a single common sample to estimate all pacf coefficients. - "ols-adjusted" : regression of time series on lags with a bias adjustment. - "ld" or "ldadjusted" : Levinson-Durbin recursion with bias correction. - "ldb" or "ldbiased" : Levinson-Durbin recursion without bias correction. alpha : float, optional If a number is given, the confidence intervals for the given level are returned. For instance if alpha=.05, 95 % confidence intervals are returned where the standard deviation is computed according to 1/sqrt(len(x)). Returns ------- pacf : ndarray Partial autocorrelations, nlags elements, including lag zero. confint : ndarray, optional Confidence intervals for the PACF. Returned if confint is not None. See Also -------- statsmodels.tsa.stattools.acf Estimate the autocorrelation function. statsmodels.tsa.stattools.pacf Partial autocorrelation estimation. statsmodels.tsa.stattools.pacf_yw Partial autocorrelation estimation using Yule-Walker. statsmodels.tsa.stattools.pacf_ols Partial autocorrelation estimation using OLS. statsmodels.tsa.stattools.pacf_burg Partial autocorrelation estimation using Burg"s method. Notes ----- Based on simulation evidence across a range of low-order ARMA models, the best methods based on root MSE are Yule-Walker (MLW), Levinson-Durbin (MLE) and Burg, respectively. The estimators with the lowest bias included included these three in addition to OLS and OLS-adjusted. Yule-Walker (adjusted) and Levinson-Durbin (adjusted) performed consistently worse than the other options. """ nlags = int_like(nlags, "nlags", optional=True) renames = { "ydu": "yda", "ywu": "ywa", "ywunbiased": "ywadjusted", "ldunbiased": "ldadjusted", "ld_unbiased": "ld_adjusted", "ldu": "lda", "ols-unbiased": "ols-adjusted", } if method in renames: warnings.warn( f"{method} has been renamed {renames[method]}. After release 0.13, " "using the old name will raise.", FutureWarning, ) method = renames[method] methods = ( "ols", "ols-inefficient", "ols-adjusted", "yw", "ywa", "ld", "ywadjusted", "yw_adjusted", "ywm", "ywmle", "yw_mle", "lda", "ldadjusted", "ld_adjusted", "ldb", "ldbiased", "ld_biased", ) x = array_like(x, "x", maxdim=2) method = string_like(method, "method", options=methods) alpha = float_like(alpha, "alpha", optional=True) if nlags is None: warnings.warn( "The default number of lags is changing from 40 to" "min(int(10 * np.log10(nobs)), nobs // 2 - 1) after 0.12" "is released. Set the number of lags to an integer to " " silence this warning.", FutureWarning, ) nlags = 40 if nlags >= x.shape[0] // 2: raise ValueError( "Can only compute partial correlations for lags up to 50% of the " f"sample size. The requested nlags {nlags} must be < " f"{x.shape[0] // 2}." ) if method in ("ols", "ols-inefficient", "ols-adjusted"): efficient = "inefficient" not in method adjusted = "adjusted" in method ret = pacf_ols(x, nlags=nlags, efficient=efficient, adjusted=adjusted) elif method in ("yw", "ywa", "ywadjusted", "yw_adjusted"): ret = pacf_yw(x, nlags=nlags, method="adjusted") elif method in ("ywm", "ywmle", "yw_mle"): ret = pacf_yw(x, nlags=nlags, method="mle") elif method in ("ld", "lda", "ldadjusted", "ld_adjusted"): acv = acovf(x, adjusted=True, fft=False) ld_ = levinson_durbin(acv, nlags=nlags, isacov=True) ret = ld_[2] # inconsistent naming with ywmle else: # method in ("ldb", "ldbiased", "ld_biased") acv = acovf(x, adjusted=False, fft=False) ld_ = levinson_durbin(acv, nlags=nlags, isacov=True) ret = ld_[2] if alpha is not None: varacf = 1.0 / len(x) # for all lags >=1 interval = stats.norm.ppf(1.0 - alpha / 2.0) * np.sqrt(varacf) confint = np.array(lzip(ret - interval, ret + interval)) confint[0] = ret[0] # fix confidence interval for lag 0 to varpacf=0 return ret, confint else: return ret @deprecate_kwarg("unbiased", "adjusted") def ccovf(x, y, adjusted=True, demean=True): """ Calculate the crosscovariance between two series. Parameters ---------- x, y : array_like The time series data to use in the calculation. adjusted : bool, optional If True, then denominators for autocovariance is n-k, otherwise n. demean : bool, optional Flag indicating whether to demean x and y. Returns ------- ndarray The estimated crosscovariance function. Notes ----- This uses np.correlate which does full convolution. For very long time series it is recommended to use fft convolution instead. """ x = array_like(x, "x") y = array_like(y, "y") adjusted = bool_like(adjusted, "adjusted") demean = bool_like(demean, "demean") n = len(x) if demean: xo = x - x.mean() yo = y - y.mean() else: xo = x yo = y if adjusted: xi = np.ones(n) d = np.correlate(xi, xi, "full") else: d = n return (np.correlate(xo, yo, "full") / d)[n - 1 :] @deprecate_kwarg("unbiased", "adjusted") def ccf(x, y, adjusted=True): """ The cross-correlation function. Parameters ---------- x, y : array_like The time series data to use in the calculation. adjusted : bool If True, then denominators for autocovariance is n-k, otherwise n. Returns ------- ndarray The cross-correlation function of x and y. Notes ----- This is based np.correlate which does full convolution. For very long time series it is recommended to use fft convolution instead. If adjusted is true, the denominator for the autocovariance is adjusted. """ x = array_like(x, "x") y = array_like(y, "y") adjusted = bool_like(adjusted, "adjusted") cvf = ccovf(x, y, adjusted=adjusted, demean=True) return cvf / (np.std(x) * np.std(y)) # moved from sandbox.tsa.examples.try_ld_nitime, via nitime # TODO: check what to return, for testing and trying out returns everything def levinson_durbin(s, nlags=10, isacov=False): """ Levinson-Durbin recursion for autoregressive processes. Parameters ---------- s : array_like If isacov is False, then this is the time series. If iasacov is true then this is interpreted as autocovariance starting with lag 0. nlags : int, optional The largest lag to include in recursion or order of the autoregressive process. isacov : bool, optional Flag indicating whether the first argument, s, contains the autocovariances or the data series. Returns ------- sigma_v : float The estimate of the error variance. arcoefs : ndarray The estimate of the autoregressive coefficients for a model including nlags. pacf : ndarray The partial autocorrelation function. sigma : ndarray The entire sigma array from intermediate result, last value is sigma_v. phi : ndarray The entire phi array from intermediate result, last column contains autoregressive coefficients for AR(nlags). Notes ----- This function returns currently all results, but maybe we drop sigma and phi from the returns. If this function is called with the time series (isacov=False), then the sample autocovariance function is calculated with the default options (biased, no fft). """ s = array_like(s, "s") nlags = int_like(nlags, "nlags") isacov = bool_like(isacov, "isacov") order = nlags if isacov: sxx_m = s else: sxx_m = acovf(s, fft=False)[: order + 1] # not tested phi = np.zeros((order + 1, order + 1), "d") sig = np.zeros(order + 1) # initial points for the recursion phi[1, 1] = sxx_m[1] / sxx_m[0] sig[1] = sxx_m[0] - phi[1, 1] * sxx_m[1] for k in range(2, order + 1): phi[k, k] = ( sxx_m[k] - np.dot(phi[1:k, k - 1], sxx_m[1:k][::-1]) ) / sig[k - 1] for j in range(1, k): phi[j, k] = phi[j, k - 1] - phi[k, k] * phi[k - j, k - 1] sig[k] = sig[k - 1] * (1 - phi[k, k] ** 2) sigma_v = sig[-1] arcoefs = phi[1:, -1] pacf_ = np.diag(phi).copy() pacf_[0] = 1.0 return sigma_v, arcoefs, pacf_, sig, phi # return everything def levinson_durbin_pacf(pacf, nlags=None): """ Levinson-Durbin algorithm that returns the acf and ar coefficients. Parameters ---------- pacf : array_like Partial autocorrelation array for lags 0, 1, ... p. nlags : int, optional Number of lags in the AR model. If omitted, returns coefficients from an AR(p) and the first p autocorrelations. Returns ------- arcoefs : ndarray AR coefficients computed from the partial autocorrelations. acf : ndarray The acf computed from the partial autocorrelations. Array returned contains the autocorrelations corresponding to lags 0, 1, ..., p. References ---------- .. [1] Brockwell, P.J. and Davis, R.A., 2016. Introduction to time series and forecasting. Springer. """ pacf = array_like(pacf, "pacf") nlags = int_like(nlags, "nlags", optional=True) pacf = np.squeeze(np.asarray(pacf)) if pacf[0] != 1: raise ValueError( "The first entry of the pacf corresponds to lags 0 " "and so must be 1." ) pacf = pacf[1:] n = pacf.shape[0] if nlags is not None: if nlags > n: raise ValueError( "Must provide at least as many values from the " "pacf as the number of lags." ) pacf = pacf[:nlags] n = pacf.shape[0] acf = np.zeros(n + 1) acf[1] = pacf[0] nu = np.cumprod(1 - pacf ** 2) arcoefs = pacf.copy() for i in range(1, n): prev = arcoefs[: -(n - i)].copy() arcoefs[: -(n - i)] = prev - arcoefs[i] * prev[::-1] acf[i + 1] = arcoefs[i] * nu[i - 1] + prev.dot(acf[1 : -(n - i)][::-1]) acf[0] = 1 return arcoefs, acf def grangercausalitytests(x, maxlag, addconst=True, verbose=True): """ Four tests for granger non causality of 2 time series. All four tests give similar results. `params_ftest` and `ssr_ftest` are equivalent based on F test which is identical to lmtest:grangertest in R. Parameters ---------- x : array_like The data for test whether the time series in the second column Granger causes the time series in the first column. Missing values are not supported. maxlag : {int, Iterable[int]} If an integer, computes the test for all lags up to maxlag. If an iterable, computes the tests only for the lags in maxlag. addconst : bool Include a constant in the model. verbose : bool Print results. Returns ------- dict All test results, dictionary keys are the number of lags. For each lag the values are a tuple, with the first element a dictionary with test statistic, pvalues, degrees of freedom, the second element are the OLS estimation results for the restricted model, the unrestricted model and the restriction (contrast) matrix for the parameter f_test. Notes ----- TODO: convert to class and attach results properly The Null hypothesis for grangercausalitytests is that the time series in the second column, x2, does NOT Granger cause the time series in the first column, x1. Grange causality means that past values of x2 have a statistically significant effect on the current value of x1, taking past values of x1 into account as regressors. We reject the null hypothesis that x2 does not Granger cause x1 if the pvalues are below a desired size of the test. The null hypothesis for all four test is that the coefficients corresponding to past values of the second time series are zero. `params_ftest`, `ssr_ftest` are based on F distribution `ssr_chi2test`, `lrtest` are based on chi-square distribution References ---------- .. [1] https://en.wikipedia.org/wiki/Granger_causality .. [2] Greene: Econometric Analysis Examples -------- >>> import statsmodels.api as sm >>> from statsmodels.tsa.stattools import grangercausalitytests >>> import numpy as np >>> data = sm.datasets.macrodata.load_pandas() >>> data = data.data[["realgdp", "realcons"]].pct_change().dropna() All lags up to 4 >>> gc_res = grangercausalitytests(data, 4) Only lag 4 >>> gc_res = grangercausalitytests(data, [4]) """ x = array_like(x, "x", ndim=2) if not np.isfinite(x).all(): raise ValueError("x contains NaN or inf values.") addconst = bool_like(addconst, "addconst") verbose = bool_like(verbose, "verbose") try: maxlag = int_like(maxlag, "maxlag") if maxlag <= 0: raise ValueError("maxlag must a a positive integer") lags = np.arange(1, maxlag + 1) except TypeError: lags = np.array([int(lag) for lag in maxlag]) maxlag = lags.max() if lags.min() <= 0 or lags.size == 0: raise ValueError( "maxlag must be a non-empty list containing only " "positive integers" ) if x.shape[0] <= 3 * maxlag + int(addconst): raise ValueError( "Insufficient observations. Maximum allowable " "lag is {0}".format(int((x.shape[0] - int(addconst)) / 3) - 1) ) resli = {} for mlg in lags: result = {} if verbose: print("\nGranger Causality") print("number of lags (no zero)", mlg) mxlg = mlg # create lagmat of both time series dta = lagmat2ds(x, mxlg, trim="both", dropex=1) # add constant if addconst: dtaown = add_constant(dta[:, 1 : (mxlg + 1)], prepend=False) dtajoint = add_constant(dta[:, 1:], prepend=False) if ( dtajoint.shape[1] == (dta.shape[1] - 1) or (dtajoint.max(0) == dtajoint.min(0)).sum() != 1 ): raise InfeasibleTestError( "The x values include a column with constant values and so" " the test statistic cannot be computed." ) else: raise NotImplementedError("Not Implemented") # dtaown = dta[:, 1:mxlg] # dtajoint = dta[:, 1:] # Run ols on both models without and with lags of second variable res2down = OLS(dta[:, 0], dtaown).fit() res2djoint = OLS(dta[:, 0], dtajoint).fit() # print results # for ssr based tests see: # http://support.sas.com/rnd/app/examples/ets/granger/index.htm # the other tests are made-up # Granger Causality test using ssr (F statistic) if res2djoint.model.k_constant: tss = res2djoint.centered_tss else: tss =res2djoint.centered_tss if ( tss == 0 or res2djoint.ssr == 0 or np.isnan(res2djoint.rsquared) or (res2djoint.ssr / tss) < np.finfo(float).eps or res2djoint.params.shape[0] != dtajoint.shape[1] ): raise InfeasibleTestError( "The Granger causality test statistic cannot be compute " "because the VAR has a perfect fit of the data." ) fgc1 = ( (res2down.ssr - res2djoint.ssr) / res2djoint.ssr / mxlg * res2djoint.df_resid ) if verbose: print( "ssr based F test: F=%-8.4f, p=%-8.4f, df_denom=%d," " df_num=%d" % ( fgc1, stats.f.sf(fgc1, mxlg, res2djoint.df_resid), res2djoint.df_resid, mxlg, ) ) result["ssr_ftest"] = ( fgc1, stats.f.sf(fgc1, mxlg, res2djoint.df_resid), res2djoint.df_resid, mxlg, ) # Granger Causality test using ssr (ch2 statistic) fgc2 = res2down.nobs * (res2down.ssr - res2djoint.ssr) / res2djoint.ssr if verbose: print( "ssr based chi2 test: chi2=%-8.4f, p=%-8.4f, " "df=%d" % (fgc2, stats.chi2.sf(fgc2, mxlg), mxlg) ) result["ssr_chi2test"] = (fgc2, stats.chi2.sf(fgc2, mxlg), mxlg) # likelihood ratio test pvalue: lr = -2 * (res2down.llf - res2djoint.llf) if verbose: print( "likelihood ratio test: chi2=%-8.4f, p=%-8.4f, df=%d" % (lr, stats.chi2.sf(lr, mxlg), mxlg) ) result["lrtest"] = (lr, stats.chi2.sf(lr, mxlg), mxlg) # F test that all lag coefficients of exog are zero rconstr = np.column_stack( (np.zeros((mxlg, mxlg)), np.eye(mxlg, mxlg), np.zeros((mxlg, 1))) ) ftres = res2djoint.f_test(rconstr) if verbose: print( "parameter F test: F=%-8.4f, p=%-8.4f, df_denom=%d," " df_num=%d" % (ftres.fvalue, ftres.pvalue, ftres.df_denom, ftres.df_num) ) result["params_ftest"] = ( np.squeeze(ftres.fvalue)[()], np.squeeze(ftres.pvalue)[()], ftres.df_denom, ftres.df_num, ) resli[mxlg] = (result, [res2down, res2djoint, rconstr]) return resli def coint( y0, y1, trend="c", method="aeg", maxlag=None, autolag="aic", return_results=None, ): """ Test for no-cointegration of a univariate equation. The null hypothesis is no cointegration. Variables in y0 and y1 are assumed to be integrated of order 1, I(1). This uses the augmented Engle-Granger two-step cointegration test. Constant or trend is included in 1st stage regression, i.e. in cointegrating equation. **Warning:** The autolag default has changed compared to statsmodels 0.8. In 0.8 autolag was always None, no the keyword is used and defaults to "aic". Use `autolag=None` to avoid the lag search. Parameters ---------- y0 : array_like The first element in cointegrated system. Must be 1-d. y1 : array_like The remaining elements in cointegrated system. trend : str {"c", "ct"} The trend term included in regression for cointegrating equation. * "c" : constant. * "ct" : constant and linear trend. * also available quadratic trend "ctt", and no constant "nc". method : {"aeg"} Only "aeg" (augmented Engle-Granger) is available. maxlag : None or int Argument for `adfuller`, largest or given number of lags. autolag : str Argument for `adfuller`, lag selection criterion. * If None, then maxlag lags are used without lag search. * If "AIC" (default) or "BIC", then the number of lags is chosen to minimize the corresponding information criterion. * "t-stat" based choice of maxlag. Starts with maxlag and drops a lag until the t-statistic on the last lag length is significant using a 5%-sized test. return_results : bool For future compatibility, currently only tuple available. If True, then a results instance is returned. Otherwise, a tuple with the test outcome is returned. Set `return_results=False` to avoid future changes in return. Returns ------- coint_t : float The t-statistic of unit-root test on residuals. pvalue : float MacKinnon"s approximate, asymptotic p-value based on MacKinnon (1994). crit_value : dict Critical values for the test statistic at the 1 %, 5 %, and 10 % levels based on regression curve. This depends on the number of observations. Notes ----- The Null hypothesis is that there is no cointegration, the alternative hypothesis is that there is cointegrating relationship. If the pvalue is small, below a critical size, then we can reject the hypothesis that there is no cointegrating relationship. P-values and critical values are obtained through regression surface approximation from MacKinnon 1994 and 2010. If the two series are almost perfectly collinear, then computing the test is numerically unstable. However, the two series will be cointegrated under the maintained assumption that they are integrated. In this case the t-statistic will be set to -inf and the pvalue to zero. TODO: We could handle gaps in data by dropping rows with nans in the Auxiliary regressions. Not implemented yet, currently assumes no nans and no gaps in time series. References ---------- .. [1] MacKinnon, J.G. 1994 "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests." Journal of Business & Economics Statistics, 12.2, 167-76. .. [2] MacKinnon, J.G. 2010. "Critical Values for Cointegration Tests." Queen"s University, Dept of Economics Working Papers 1227. http://ideas.repec.org/p/qed/wpaper/1227.html """ y0 = array_like(y0, "y0") y1 = array_like(y1, "y1", ndim=2) trend = string_like(trend, "trend", options=("c", "nc", "ct", "ctt")) method = string_like(method, "method", options=("aeg",)) maxlag = int_like(maxlag, "maxlag", optional=True) autolag = string_like( autolag, "autolag", optional=True, options=("aic", "bic", "t-stat") ) return_results = bool_like(return_results, "return_results", optional=True) nobs, k_vars = y1.shape k_vars += 1 # add 1 for y0 if trend == "nc": xx = y1 else: xx = add_trend(y1, trend=trend, prepend=False) res_co = OLS(y0, xx).fit() if res_co.rsquared < 1 - 100 * SQRTEPS: res_adf = adfuller( res_co.resid, maxlag=maxlag, autolag=autolag, regression="nc" ) else: warnings.warn( "y0 and y1 are (almost) perfectly colinear." "Cointegration test is not reliable in this case.", CollinearityWarning, ) # Edge case where series are too similar res_adf = (-np.inf,) # no constant or trend, see egranger in Stata and MacKinnon if trend == "nc": crit = [np.nan] * 3 # 2010 critical values not available else: crit = mackinnoncrit(N=k_vars, regression=trend, nobs=nobs - 1) # nobs - 1, the -1 is to match egranger in Stata, I do not know why. # TODO: check nobs or df = nobs - k pval_asy = mackinnonp(res_adf[0], regression=trend, N=k_vars) return res_adf[0], pval_asy, crit def _safe_arma_fit(y, order, model_kw, trend, fit_kw, start_params=None): try: return ARMA(y, order=order, **model_kw).fit( disp=0, trend=trend, start_params=start_params, **fit_kw ) except LinAlgError: # SVD convergence failure on badly misspecified models return except ValueError as error: if start_params is not None: # do not recurse again # user supplied start_params only get one chance return # try a little harder, should be handled in fit really elif "initial" not in error.args[0] or "initial" in str(error): start_params = [0.1] * sum(order) if trend == "c": start_params = [0.1] + start_params return _safe_arma_fit( y, order, model_kw, trend, fit_kw, start_params ) else: return except: # no idea what happened return def arma_order_select_ic( y, max_ar=4, max_ma=2, ic="bic", trend="c", model_kw=None, fit_kw=None ): """ Compute information criteria for many ARMA models. Parameters ---------- y : array_like Array of time-series data. max_ar : int Maximum number of AR lags to use. Default 4. max_ma : int Maximum number of MA lags to use. Default 2. ic : str, list Information criteria to report. Either a single string or a list of different criteria is possible. trend : str The trend to use when fitting the ARMA models. model_kw : dict Keyword arguments to be passed to the ``ARMA`` model. fit_kw : dict Keyword arguments to be passed to ``ARMA.fit``. Returns ------- Bunch Dict-like object with attribute access. Each ic is an attribute with a DataFrame for the results. The AR order used is the row index. The ma order used is the column index. The minimum orders are available as ``ic_min_order``. Notes ----- This method can be used to tentatively identify the order of an ARMA process, provided that the time series is stationary and invertible. This function computes the full exact MLE estimate of each model and can be, therefore a little slow. An implementation using approximate estimates will be provided in the future. In the meantime, consider passing {method : "css"} to fit_kw. Examples -------- >>> from statsmodels.tsa.arima_process import arma_generate_sample >>> import statsmodels.api as sm >>> import numpy as np >>> arparams = np.array([.75, -.25]) >>> maparams = np.array([.65, .35]) >>> arparams = np.r_[1, -arparams] >>> maparam = np.r_[1, maparams] >>> nobs = 250 >>> np.random.seed(2014) >>> y = arma_generate_sample(arparams, maparams, nobs) >>> res = sm.tsa.arma_order_select_ic(y, ic=["aic", "bic"], trend="nc") >>> res.aic_min_order >>> res.bic_min_order """ max_ar = int_like(max_ar, "max_ar") max_ma = int_like(max_ma, "max_ma") trend = string_like(trend, "trend", options=("nc", "c")) model_kw = dict_like(model_kw, "model_kw", optional=True) fit_kw = dict_like(fit_kw, "fit_kw", optional=True) ar_range = lrange(0, max_ar + 1) ma_range = lrange(0, max_ma + 1) if isinstance(ic, str): ic = [ic] elif not isinstance(ic, (list, tuple)): raise ValueError("Need a list or a tuple for ic if not a string.") results = np.zeros((len(ic), max_ar + 1, max_ma + 1)) model_kw = {} if model_kw is None else model_kw fit_kw = {} if fit_kw is None else fit_kw y_arr = array_like(y, "y", contiguous=True) for ar in ar_range: for ma in ma_range: if ar == 0 and ma == 0 and trend == "nc": results[:, ar, ma] = np.nan continue mod = _safe_arma_fit(y_arr, (ar, ma), model_kw, trend, fit_kw) if mod is None: results[:, ar, ma] = np.nan continue for i, criteria in enumerate(ic): results[i, ar, ma] = getattr(mod, criteria) dfs = [ pd.DataFrame(res, columns=ma_range, index=ar_range) for res in results ] res = dict(zip(ic, dfs)) # add the minimums to the results dict min_res = {} for i, result in res.items(): mins = np.where(result.min().min() == result) min_res.update({i + "_min_order": (mins[0][0], mins[1][0])}) res.update(min_res) return Bunch(**res) def has_missing(data): """ Returns True if "data" contains missing entries, otherwise False """ return np.isnan(np.sum(data)) @deprecate_kwarg("lags", "nlags") def kpss(x, regression="c", nlags=None, store=False): """ Kwiatkowski-Phillips-Schmidt-Shin test for stationarity. Computes the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test for the null hypothesis that x is level or trend stationary. Parameters ---------- x : array_like, 1d The data series to test. regression : str{"c", "ct"} The null hypothesis for the KPSS test. * "c" : The data is stationary around a constant (default). * "ct" : The data is stationary around a trend. nlags : {None, str, int}, optional Indicates the number of lags to be used. If None (default), lags is calculated using the legacy method. If "auto", lags is calculated using the data-dependent method of Hobijn et al. (1998). See also Andrews (1991), Newey & West (1994), and Schwert (1989). If set to "legacy", uses int(12 * (n / 100)**(1 / 4)) , as outlined in Schwert (1989). store : bool If True, then a result instance is returned additionally to the KPSS statistic (default is False). Returns ------- kpss_stat : float The KPSS test statistic. p_value : float The p-value of the test. The p-value is interpolated from Table 1 in Kwiatkowski et al. (1992), and a boundary point is returned if the test statistic is outside the table of critical values, that is, if the p-value is outside the interval (0.01, 0.1). lags : int The truncation lag parameter. crit : dict The critical values at 10%, 5%, 2.5% and 1%. Based on Kwiatkowski et al. (1992). resstore : (optional) instance of ResultStore An instance of a dummy class with results attached as attributes. Notes ----- To estimate sigma^2 the Newey-West estimator is used. If lags is None, the truncation lag parameter is set to int(12 * (n / 100) ** (1 / 4)), as outlined in Schwert (1989). The p-values are interpolated from Table 1 of Kwiatkowski et al. (1992). If the computed statistic is outside the table of critical values, then a warning message is generated. Missing values are not handled. References ---------- .. [1] Andrews, D.W.K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59: 817-858. .. [2] Hobijn, B., Frances, B.H., & Ooms, M. (2004). Generalizations of the KPSS-test for stationarity. Statistica Neerlandica, 52: 483-502. .. [3] Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54: 159-178. .. [4] Newey, W.K., & West, K.D. (1994). Automatic lag selection in covariance matrix estimation. Review of Economic Studies, 61: 631-653. .. [5] Schwert, G. W. (1989). Tests for unit roots: A Monte Carlo investigation. Journal of Business and Economic Statistics, 7 (2): 147-159. """ x = array_like(x, "x") regression = string_like(regression, "regression", options=("c", "ct")) store = bool_like(store, "store") nobs = x.shape[0] hypo = regression # if m is not one, n != m * n if nobs != x.size: raise ValueError("x of shape {0} not understood".format(x.shape)) if hypo == "ct": # p. 162 Kwiatkowski et al. (1992): y_t = beta * t + r_t + e_t, # where beta is the trend, r_t a random walk and e_t a stationary # error term. resids = OLS(x, add_constant(np.arange(1, nobs + 1))).fit().resid crit = [0.119, 0.146, 0.176, 0.216] elif hypo == "c": # special case of the model above, where beta = 0 (so the null # hypothesis is that the data is stationary around r_0). resids = x - x.mean() crit = [0.347, 0.463, 0.574, 0.739] if nlags is None: nlags = "legacy" msg = ( "The behavior of using nlags=None will change in release 0.13." "Currently nlags=None is the same as " 'nlags="legacy", and so a sample-size lag length is used. ' "After the next release, the default will change to be the " 'same as nlags="auto" which uses an automatic lag length ' "selection method. To silence this warning, either use " '"auto" or "legacy"' ) warnings.warn(msg, FutureWarning) if nlags == "legacy": nlags = int(np.ceil(12.0 * np.power(nobs / 100.0, 1 / 4.0))) nlags = min(nlags, nobs - 1) elif nlags == "auto": # autolag method of Hobijn et al. (1998) nlags = _kpss_autolag(resids, nobs) nlags = min(nlags, nobs - 1) else: nlags = int(nlags) if nlags >= nobs: raise ValueError( "lags ({}) must be < number of observations ({})".format( nlags, nobs ) ) pvals = [0.10, 0.05, 0.025, 0.01] eta = np.sum(resids.cumsum() ** 2) / (nobs ** 2) # eq. 11, p. 165 s_hat = _sigma_est_kpss(resids, nobs, nlags) kpss_stat = eta / s_hat p_value = np.interp(kpss_stat, crit, pvals) warn_msg = """\ The test statistic is outside of the range of p-values available in the look-up table. The actual p-value is {direction} than the p-value returned. """ if p_value == pvals[-1]: warnings.warn( warn_msg.format(direction="smaller"), InterpolationWarning ) elif p_value == pvals[0]: warnings.warn( warn_msg.format(direction="greater"), InterpolationWarning ) crit_dict = {"10%": crit[0], "5%": crit[1], "2.5%": crit[2], "1%": crit[3]} if store: from statsmodels.stats.diagnostic import ResultsStore rstore = ResultsStore() rstore.lags = nlags rstore.nobs = nobs stationary_type = "level" if hypo == "c" else "trend" rstore.H0 = "The series is {0} stationary".format(stationary_type) rstore.HA = "The series is not {0} stationary".format(stationary_type) return kpss_stat, p_value, crit_dict, rstore else: return kpss_stat, p_value, nlags, crit_dict def _sigma_est_kpss(resids, nobs, lags): """ Computes equation 10, p. 164 of Kwiatkowski et al. (1992). This is the consistent estimator for the variance. """ s_hat = np.sum(resids ** 2) for i in range(1, lags + 1): resids_prod = np.dot(resids[i:], resids[: nobs - i]) s_hat += 2 * resids_prod * (1.0 - (i / (lags + 1.0))) return s_hat / nobs def _kpss_autolag(resids, nobs): """ Computes the number of lags for covariance matrix estimation in KPSS test using method of Hobijn et al (1998). See also Andrews (1991), Newey & West (1994), and Schwert (1989). Assumes Bartlett / Newey-West kernel. """ covlags = int(np.power(nobs, 2.0 / 9.0)) s0 = np.sum(resids ** 2) / nobs s1 = 0 for i in range(1, covlags + 1): resids_prod = np.dot(resids[i:], resids[: nobs - i]) resids_prod /= nobs / 2.0 s0 += resids_prod s1 += i * resids_prod s_hat = s1 / s0 pwr = 1.0 / 3.0 gamma_hat = 1.1447 * np.power(s_hat * s_hat, pwr) autolags = int(gamma_hat * np.power(nobs, pwr)) return autolags class ZivotAndrewsUnitRoot(object): """ Class wrapper for Zivot-Andrews structural-break unit-root test """ def __init__(self): """ Critical values for the three different models specified for the Zivot-Andrews unit-root test. Notes ----- The p-values are generated through Monte Carlo simulation using 100,000 replications and 2000 data points. """ self._za_critical_values = {} # constant-only model self._c = ( (0.001, -6.78442), (0.100, -5.83192), (0.200, -5.68139), (0.300, -5.58461), (0.400, -5.51308), (0.500, -5.45043), (0.600, -5.39924), (0.700, -5.36023), (0.800, -5.33219), (0.900, -5.30294), (1.000, -5.27644), (2.500, -5.03340), (5.000, -4.81067), (7.500, -4.67636), (10.000, -4.56618), (12.500, -4.48130), (15.000, -4.40507), (17.500, -4.33947), (20.000, -4.28155), (22.500, -4.22683), (25.000, -4.17830), (27.500, -4.13101), (30.000, -4.08586), (32.500, -4.04455), (35.000, -4.00380), (37.500, -3.96144), (40.000, -3.92078), (42.500, -3.88178), (45.000, -3.84503), (47.500, -3.80549), (50.000, -3.77031), (52.500, -3.73209), (55.000, -3.69600), (57.500, -3.65985), (60.000, -3.62126), (65.000, -3.54580), (70.000, -3.46848), (75.000, -3.38533), (80.000, -3.29112), (85.000, -3.17832), (90.000, -3.04165), (92.500, -2.95146), (95.000, -2.83179), (96.000, -2.76465), (97.000, -2.68624), (98.000, -2.57884), (99.000, -2.40044), (99.900, -1.88932), ) self._za_critical_values["c"] = np.asarray(self._c) # trend-only model self._t = ( (0.001, -83.9094), (0.100, -13.8837), (0.200, -9.13205), (0.300, -6.32564), (0.400, -5.60803), (0.500, -5.38794), (0.600, -5.26585), (0.700, -5.18734), (0.800, -5.12756), (0.900, -5.07984), (1.000, -5.03421), (2.500, -4.65634), (5.000, -4.40580), (7.500, -4.25214), (10.000, -4.13678), (12.500, -4.03765), (15.000, -3.95185), (17.500, -3.87945), (20.000, -3.81295), (22.500, -3.75273), (25.000, -3.69836), (27.500, -3.64785), (30.000, -3.59819), (32.500, -3.55146), (35.000, -3.50522), (37.500, -3.45987), (40.000, -3.41672), (42.500, -3.37465), (45.000, -3.33394), (47.500, -3.29393), (50.000, -3.25316), (52.500, -3.21244), (55.000, -3.17124), (57.500, -3.13211), (60.000, -3.09204), (65.000, -3.01135), (70.000, -2.92897), (75.000, -2.83614), (80.000, -2.73893), (85.000, -2.62840), (90.000, -2.49611), (92.500, -2.41337), (95.000, -2.30820), (96.000, -2.25797), (97.000, -2.19648), (98.000, -2.11320), (99.000, -1.99138), (99.900, -1.67466), ) self._za_critical_values["t"] = np.asarray(self._t) # constant + trend model self._ct = ( (0.001, -38.17800), (0.100, -6.43107), (0.200, -6.07279), (0.300, -5.95496), (0.400, -5.86254), (0.500, -5.77081), (0.600, -5.72541), (0.700, -5.68406), (0.800, -5.65163), (0.900, -5.60419), (1.000, -5.57556), (2.500, -5.29704), (5.000, -5.07332), (7.500, -4.93003), (10.000, -4.82668), (12.500, -4.73711), (15.000, -4.66020), (17.500, -4.58970), (20.000, -4.52855), (22.500, -4.47100), (25.000, -4.42011), (27.500, -4.37387), (30.000, -4.32705), (32.500, -4.28126), (35.000, -4.23793), (37.500, -4.19822), (40.000, -4.15800), (42.500, -4.11946), (45.000, -4.08064), (47.500, -4.04286), (50.000, -4.00489), (52.500, -3.96837), (55.000, -3.93200), (57.500, -3.89496), (60.000, -3.85577), (65.000, -3.77795), (70.000, -3.69794), (75.000, -3.61852), (80.000, -3.52485), (85.000, -3.41665), (90.000, -3.28527), (92.500, -3.19724), (95.000, -3.08769), (96.000, -3.03088), (97.000, -2.96091), (98.000, -2.85581), (99.000, -2.71015), (99.900, -2.28767), ) self._za_critical_values["ct"] = np.asarray(self._ct) def _za_crit(self, stat, model="c"): """ Linear interpolation for Zivot-Andrews p-values and critical values Parameters ---------- stat : float The ZA test statistic model : {"c","t","ct"} The model used when computing the ZA statistic. "c" is default. Returns ------- pvalue : float The interpolated p-value cvdict : dict Critical values for the test statistic at the 1%, 5%, and 10% levels Notes ----- The p-values are linear interpolated from the quantiles of the simulated ZA test statistic distribution """ table = self._za_critical_values[model] pcnts = table[:, 0] stats = table[:, 1] # ZA cv table contains quantiles multiplied by 100 pvalue = np.interp(stat, stats, pcnts) / 100.0 cv = [1.0, 5.0, 10.0] crit_value = np.interp(cv, pcnts, stats) cvdict = { "1%": crit_value[0], "5%": crit_value[1], "10%": crit_value[2], } return pvalue, cvdict def _quick_ols(self, endog, exog): """ Minimal implementation of LS estimator for internal use """ xpxi = np.linalg.inv(exog.T.dot(exog)) xpy = exog.T.dot(endog) nobs, k_exog = exog.shape b = xpxi.dot(xpy) e = endog - exog.dot(b) sigma2 = e.T.dot(e) / (nobs - k_exog) return b / np.sqrt(np.diag(sigma2 * xpxi)) def _format_regression_data(self, series, nobs, const, trend, cols, lags): """ Create the endog/exog data for the auxiliary regressions from the original (standardized) series under test. """ # first-diff y and standardize for numerical stability endog = np.diff(series, axis=0) endog /= np.sqrt(endog.T.dot(endog)) series /= np.sqrt(series.T.dot(series)) # reserve exog space exog = np.zeros((endog[lags:].shape[0], cols + lags)) exog[:, 0] = const # lagged y and dy exog[:, cols - 1] = series[lags : (nobs - 1)] exog[:, cols:] = lagmat(endog, lags, trim="none")[ lags : exog.shape[0] + lags ] return endog, exog def _update_regression_exog( self, exog, regression, period, nobs, const, trend, cols, lags ): """ Update the exog array for the next regression. """ cutoff = period - (lags + 1) if regression != "t": exog[:cutoff, 1] = 0 exog[cutoff:, 1] = const exog[:, 2] = trend[(lags + 2) : (nobs + 1)] if regression == "ct": exog[:cutoff, 3] = 0 exog[cutoff:, 3] = trend[1 : (nobs - period + 1)] else: exog[:, 1] = trend[(lags + 2) : (nobs + 1)] exog[: (cutoff - 1), 2] = 0 exog[(cutoff - 1) :, 2] = trend[0 : (nobs - period + 1)] return exog def run(self, x, trim=0.15, maxlag=None, regression="c", autolag="AIC"): """ Zivot-Andrews structural-break unit-root test. The Zivot-Andrews test tests for a unit root in a univariate process in the presence of serial correlation and a single structural break. Parameters ---------- x : array_like The data series to test. trim : float The percentage of series at begin/end to exclude from break-period calculation in range [0, 0.333] (default=0.15). maxlag : int The maximum lag which is included in test, default is 12*(nobs/100)^{1/4} (Schwert, 1989). regression : {"c","t","ct"} Constant and trend order to include in regression. * "c" : constant only (default). * "t" : trend only. * "ct" : constant and trend. autolag : {"AIC", "BIC", "t-stat", None} The method to select the lag length when using automatic selection. * if None, then maxlag lags are used, * if "AIC" (default) or "BIC", then the number of lags is chosen to minimize the corresponding information criterion, * "t-stat" based choice of maxlag. Starts with maxlag and drops a lag until the t-statistic on the last lag length is significant using a 5%-sized test. Returns ------- zastat : float The test statistic. pvalue : float The pvalue based on MC-derived critical values. cvdict : dict The critical values for the test statistic at the 1%, 5%, and 10% levels. bpidx : int The index of x corresponding to endogenously calculated break period with values in the range [0..nobs-1]. baselag : int The number of lags used for period regressions. Notes ----- H0 = unit root with a single structural break Algorithm follows Baum (2004/2015) approximation to original Zivot-Andrews method. Rather than performing an autolag regression at each candidate break period (as per the original paper), a single autolag regression is run up-front on the base model (constant + trend with no dummies) to determine the best lag length. This lag length is then used for all subsequent break-period regressions. This results in significant run time reduction but also slightly more pessimistic test statistics than the original Zivot-Andrews method, although no attempt has been made to characterize the size/power trade-off. References ---------- .. [1] Baum, C.F. (2004). ZANDREWS: Stata module to calculate Zivot-Andrews unit root test in presence of structural break," Statistical Software Components S437301, Boston College Department of Economics, revised 2015. .. [2] Schwert, G.W. (1989). Tests for unit roots: A Monte Carlo investigation. Journal of Business & Economic Statistics, 7: 147-159. .. [3] Zivot, E., and Andrews, D.W.K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business & Economic Studies, 10: 251-270. """ x = array_like(x, "x") trim = float_like(trim, "trim") maxlag = int_like(maxlag, "maxlag", optional=True) regression = string_like( regression, "regression", options=("c", "t", "ct") ) autolag = string_like( autolag, "autolag", options=("aic", "bic", "t-stat"), optional=True ) if trim < 0 or trim > (1.0 / 3.0): raise ValueError("trim value must be a float in range [0, 1/3)") nobs = x.shape[0] if autolag: adf_res = adfuller( x, maxlag=maxlag, regression="ct", autolag=autolag ) baselags = adf_res[2] elif maxlag: baselags = maxlag else: baselags = int(12.0 * np.power(nobs / 100.0, 1 / 4.0)) trimcnt = int(nobs * trim) start_period = trimcnt end_period = nobs - trimcnt if regression == "ct": basecols = 5 else: basecols = 4 # normalize constant and trend terms for stability c_const = 1 / np.sqrt(nobs) t_const = np.arange(1.0, nobs + 2) t_const *= np.sqrt(3) / nobs ** (3 / 2) # format the auxiliary regression data endog, exog = self._format_regression_data( x, nobs, c_const, t_const, basecols, baselags ) # iterate through the time periods stats = np.full(end_period + 1, np.inf) for bp in range(start_period + 1, end_period + 1): # update intercept dummy / trend / trend dummy exog = self._update_regression_exog( exog, regression, bp, nobs, c_const, t_const, basecols, baselags, ) # check exog rank on first iteration if bp == start_period + 1: o = OLS(endog[baselags:], exog, hasconst=1).fit() if o.df_model < exog.shape[1] - 1: raise ValueError( "ZA: auxiliary exog matrix is not full rank.\n" " cols (exc intercept) = {} rank = {}".format( exog.shape[1] - 1, o.df_model ) ) stats[bp] = o.tvalues[basecols - 1] else: stats[bp] = self._quick_ols(endog[baselags:], exog)[ basecols - 1 ] # return best seen zastat = np.min(stats) bpidx = np.argmin(stats) - 1 crit = self._za_crit(zastat, regression) pval = crit[0] cvdict = crit[1] return zastat, pval, cvdict, baselags, bpidx def __call__( self, x, trim=0.15, maxlag=None, regression="c", autolag="AIC" ): return self.run( x, trim=trim, maxlag=maxlag, regression=regression, autolag=autolag ) zivot_andrews = ZivotAndrewsUnitRoot() zivot_andrews.__doc__ = zivot_andrews.run.__doc__ statsmodels-0.12.2/statsmodels/tsa/tests/000077500000000000000000000000001400612667500204405ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/tests/__init__.py000066400000000000000000000000001400612667500225370ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/tests/arima.do000066400000000000000000000116201400612667500220550ustar00rootroot00000000000000insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv" gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate /* here for safe keeping arima cpi, arima(4,1,1) from(0.92687596 -0.5558627 0.32086541 0.25225289 0.11362493 0.93914412 0.78437817334640536, copy) predict xb, xb dynamic(.) predict y, y dynamic(.) */ arima cpi, arima(1,1,1) mat llf=e(ll) mat nobs=e(N) // number of parameters mat k=e(k) // number of dependent variables mat k_exog=e(k_dv) mat sigma=e(sigma) mat chi2=e(chi2) mat df_model=e(df_m) mat k_ar=e(ar_max) mat k_ma=e(ma_max) mat params=e(b) mat cov_params=e(V) // do not append because you'll rewrite the bunch class // mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima_results.py") format("%16.0g") replace predict xb predict y, y predict resid, resid predict yr, yr predict mse, mse predict stdp, stdp estat ic mat icstats=r(S) mkmat xb xb mkmat y y mkmat yr yr mkmat mse mse mkmat stdp stdp mkmat resid resid mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params xb y resid yr mse stdp icstats, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima111_results.py") format("%16.0g") replace clear /* do it with no constant */ insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv" gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate arima cpi, arima(1,1,1) noconstant mat llf=e(ll) mat nobs=e(N) // number of parameters mat k=e(k) // number of dependent variables mat k_exog=e(k_dv) mat sigma=e(sigma) mat chi2=e(chi2) mat df_model=e(df_m) mat k_ar=e(ar_max) mat k_ma=e(ma_max) mat params=e(b) mat cov_params=e(V) // do not append because you'll rewrite the bunch class // mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima_results.py") format("%16.0g") replace predict xb predict y, y predict resid, resid predict yr, yr predict mse, mse /*predict stdp, stdp*/ estat ic mat icstats=r(S) mkmat xb xb mkmat y y mkmat yr yr mkmat mse mse /*mkmat stdp stdp*/ mkmat resid resid mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params xb y resid yr mse stdp icstats, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima111nc_results.py") format("%16.0g") replace clear /* Now do conditional */ insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv" gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate arima cpi, arima(1,1,1) condition mat llf=e(ll) mat nobs=e(N) // number of parameters mat k=e(k) // number of dependent variables mat k_exog=e(k_dv) mat sigma=e(sigma) mat chi2=e(chi2) mat df_model=e(df_m) mat k_ar=e(ar_max) mat k_ma=e(ma_max) mat params=e(b) mat cov_params=e(V) // do not append because you'll rewrite the bunch class // mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima_results.py") format("%16.0g") replace predict xb predict y, y predict resid, resid predict yr, yr predict mse, mse predict stdp, stdp estat ic mat icstats=r(S) mkmat xb xb mkmat y y mkmat yr yr mkmat mse mse mkmat stdp stdp mkmat resid resid mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params xb y resid yr mse stdp icstats, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima111_css_results.py") format("%16.0g") replace clear /* do it with no constant */ insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv" gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate arima cpi, arima(1,1,1) noconstant condition mat llf=e(ll) mat nobs=e(N) // number of parameters mat k=e(k) // number of dependent variables mat k_exog=e(k_dv) mat sigma=e(sigma) mat chi2=e(chi2) mat df_model=e(df_m) mat k_ar=e(ar_max) mat k_ma=e(ma_max) mat params=e(b) mat cov_params=e(V) // do not append because you'll rewrite the bunch class // mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima_results.py") format("%16.0g") replace predict xb predict y, y predict resid, resid predict yr, yr predict mse, mse predict stdp, stdp estat ic mat icstats=r(S) mkmat xb xb mkmat y y mkmat yr yr mkmat mse mse mkmat stdp stdp mkmat resid resid mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params xb y resid yr mse stdp icstats, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima111nc_css_results.py") format("%16.0g") replace statsmodels-0.12.2/statsmodels/tsa/tests/arima112.do000066400000000000000000000115071400612667500223050ustar00rootroot00000000000000insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv" gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate arima cpi, arima(1,1,2) mat llf=e(ll) mat nobs=e(N) // number of parameters mat k=e(k) // number of dependent variables mat k_exog=e(k_dv) mat sigma=e(sigma) mat chi2=e(chi2) mat df_model=e(df_m) mat k_ar=e(ar_max) mat k_ma=e(ma_max) mat params=e(b) mat cov_params=e(V) // do not append because you'll rewrite the bunch class // mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima_results.py") format("%16.0g") replace predict xb predict y, y predict resid, resid predict yr, yr predict mse, mse predict stdp, stdp estat ic mat icstats=r(S) mkmat xb xb mkmat y y mkmat yr yr mkmat mse mse mkmat stdp stdp mkmat resid resid mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params xb y resid yr mse stdp icstats, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima112_results.py") format("%16.0g") replace /* Do it with no constant */ clear insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv" gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate arima cpi, arima(1,1,2) noconstant mat llf=e(ll) mat nobs=e(N) // number of parameters mat k=e(k) // number of dependent variables mat k_exog=e(k_dv) mat sigma=e(sigma) mat chi2=e(chi2) mat df_model=e(df_m) mat k_ar=e(ar_max) mat k_ma=e(ma_max) mat params=e(b) mat cov_params=e(V) // do not append because you'll rewrite the bunch class // mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima_results.py") format("%16.0g") replace predict xb predict y, y predict resid, resid predict yr, yr predict mse, mse /*predict stdp, stdp*/ estat ic mat icstats=r(S) mkmat xb xb mkmat y y mkmat yr yr mkmat mse mse /*mkmat stdp stdp*/ mkmat resid resid mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params xb y resid yr mse icstats, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima112nc_results.py") format("%16.0g") replace clear /* now do conditional */ insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv" gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate /* still converges to different than x-12-arima */ arima cpi, arima(1,1,2) condition from(.905322 -.692425 1.07366 0.172024 0.682072819129, copy) gtolerance(.0001) vce(oim) mat llf=e(ll) mat nobs=e(N) // number of parameters mat k=e(k) // number of dependent variables mat k_exog=e(k_dv) mat sigma=e(sigma) mat chi2=e(chi2) mat df_model=e(df_m) mat k_ar=e(ar_max) mat k_ma=e(ma_max) mat params=e(b) mat cov_params=e(V) // do not append because you'll rewrite the bunch class // mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima_results.py") format("%16.0g") replace predict xb predict y, y predict resid, resid predict yr, yr predict mse, mse predict stdp, stdp estat ic mat icstats=r(S) mkmat xb xb mkmat y y mkmat yr yr mkmat mse mse mkmat stdp stdp mkmat resid resid mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params xb y resid yr mse stdp icstats, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima112_css_results.py") format("%16.0g") replace /* Do it with no constant */ clear insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv" gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate arima cpi, arima(1,1,2) noconstant condition mat llf=e(ll) mat nobs=e(N) // number of parameters mat k=e(k) // number of dependent variables mat k_exog=e(k_dv) mat sigma=e(sigma) mat chi2=e(chi2) mat df_model=e(df_m) mat k_ar=e(ar_max) mat k_ma=e(ma_max) mat params=e(b) mat cov_params=e(V) // do not append because you'll rewrite the bunch class // mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima_results.py") format("%16.0g") replace predict xb predict y, y predict resid, resid predict yr, yr predict mse, mse predict stdp, stdp estat ic mat icstats=r(S) mkmat xb xb mkmat y y mkmat yr yr mkmat mse mse mkmat stdp stdp mkmat resid resid mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params xb y resid yr mse stdp icstats, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima112nc_css_results.py") format("%16.0g") replace statsmodels-0.12.2/statsmodels/tsa/tests/arima211.do000066400000000000000000000113371400612667500223060ustar00rootroot00000000000000insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv" gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate arima cpi, arima(2,1,1) mat llf=e(ll) mat nobs=e(N) // number of parameters mat k=e(k) // number of dependent variables mat k_exog=e(k_dv) mat sigma=e(sigma) mat chi2=e(chi2) mat df_model=e(df_m) mat k_ar=e(ar_max) mat k_ma=e(ma_max) mat params=e(b) mat cov_params=e(V) // do not append because you'll rewrite the bunch class // mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima_results.py") format("%16.0g") replace predict xb predict y, y predict resid, resid predict yr, yr predict mse, mse predict stdp, stdp estat ic mat icstats=r(S) mkmat xb xb mkmat y y mkmat yr yr mkmat mse mse mkmat stdp stdp mkmat resid resid mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params xb y resid yr mse stdp icstats, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima211_results.py") format("%16.0g") replace clear /* do it with no constant */ insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv" gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate arima cpi, arima(2,1,1) noconstant mat llf=e(ll) mat nobs=e(N) // number of parameters mat k=e(k) // number of dependent variables mat k_exog=e(k_dv) mat sigma=e(sigma) mat chi2=e(chi2) mat df_model=e(df_m) mat k_ar=e(ar_max) mat k_ma=e(ma_max) mat params=e(b) mat cov_params=e(V) // do not append because you'll rewrite the bunch class // mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima_results.py") format("%16.0g") replace predict xb predict y, y predict resid, resid predict yr, yr predict mse, mse /* cannot do stdp without a constant predict stdp, stdp */ estat ic mat icstats=r(S) mkmat xb xb mkmat y y mkmat yr yr mkmat mse mse /*mkmat stdp stdp*/ mkmat resid resid mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params xb y resid yr mse icstats, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima211nc_results.py") format("%16.0g") replace /* now do conditional */ clear insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv" gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate arima cpi, arima(2,1,1) condition mat llf=e(ll) mat nobs=e(N) // number of parameters mat k=e(k) // number of dependent variables mat k_exog=e(k_dv) mat sigma=e(sigma) mat chi2=e(chi2) mat df_model=e(df_m) mat k_ar=e(ar_max) mat k_ma=e(ma_max) mat params=e(b) mat cov_params=e(V) // do not append because you'll rewrite the bunch class // mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima_results.py") format("%16.0g") replace predict xb predict y, y predict resid, resid predict yr, yr predict mse, mse predict stdp, stdp estat ic mat icstats=r(S) mkmat xb xb mkmat y y mkmat yr yr mkmat mse mse mkmat stdp stdp mkmat resid resid mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params xb y resid yr mse stdp icstats, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima211_css_results.py") format("%16.0g") replace /* do it with no constant */ clear insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv" gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate arima cpi, arima(2,1,1) condition noconstant mat llf=e(ll) mat nobs=e(N) // number of parameters mat k=e(k) // number of dependent variables mat k_exog=e(k_dv) mat sigma=e(sigma) mat chi2=e(chi2) mat df_model=e(df_m) mat k_ar=e(ar_max) mat k_ma=e(ma_max) mat params=e(b) mat cov_params=e(V) // do not append because you'll rewrite the bunch class // mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima_results.py") format("%16.0g") replace predict xb predict y, y predict resid, resid predict yr, yr predict mse, mse predict stdp, stdp estat ic mat icstats=r(S) mkmat xb xb mkmat y y mkmat yr yr mkmat mse mse mkmat stdp stdp mkmat resid resid mat2nparray llf nobs k k_exog sigma chi2 df_model k_ar k_ma params cov_params xb y resid yr mse stdp icstats, saving("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/arima211nc_css_results.py") format("%16.0g") replace 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statsmodels-0.12.2/statsmodels/tsa/tests/results/__init__.py000066400000000000000000000000001400612667500242400ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/tests/results/arima.R000066400000000000000000000012611400612667500233550ustar00rootroot00000000000000dta <- read.csv("/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv") cpi <- dta$cpi /* this automatically suppresses the constant */ mod111 <- arima(cpi, order=c(1,1,1), method="CSS") /*you can use xreg=1:length(cpi)*/ dcpi <- diff(cpi) mod111 <- arima(dcpi, order=c(1,0,1), method="CSS") bse <- sqrt(diag(mod111$var.coef)) tvalues <- mod111$coef / bse pvalues <- (1 - pt(abs(tvalues), 198)) * 2 /* use starting values from X-ARIMA */ mod112 <- arima(dcpi, order=c(1,0,2), method="CSS", init=c(-0.692425, 1.07366, 0.172024, 0.905322)) bse <- sqrt(diag(mod112$var.coef)) tvalues <- mod112$coef / bse pvalues <- (1 - pt(abs(tvalues), 198)) * 2 statsmodels-0.12.2/statsmodels/tsa/tests/results/arima111_css_results.py000066400000000000000000000645351400612667500264750ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch llf = np.array([-242.06033399744]) nobs = np.array([202]) k = np.array([4]) k_exog = np.array([1]) sigma = np.array([.80201496146073]) chi2 = np.array([348.43324197088]) df_model = np.array([2]) k_ar = np.array([1]) k_ma = np.array([1]) params = np.array([ .82960638524364, .93479332833705, -.75728342544279, .64322799840686]) cov_params = np.array([ .14317811930738, -.01646077810033, .01510986837498, -.00280799533479, -.01646077810033, .00321032468661, -.00353027620719, .00097645385252, .01510986837498, -.00353027620719, .00484312817753, -.00112050648944, -.00280799533479, .00097645385252, -.00112050648944, .0007715609499]).reshape(4, 4) xb = np.array([ .82960641384125, .82960641384125, .697261095047, .61113905906677, .51607495546341, .47362637519836, .41342103481293, 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.64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199, .64322799444199]) stdp = np.array([ .82960641384125, .82960641384125, .697261095047, .61113905906677, .51607495546341, .47362637519836, .41342103481293, .40238001942635, .37454023957253, .33222004771233, .32514902949333, .31093680858612, .30019253492355, .31159669160843, .29182952642441, .30349296331406, .29457464814186, .28427124023438, .30664679408073, .29696446657181, .31270903348923, .29268020391464, .28816330432892, .29006817936897, .30216124653816, .30066826939583, .31728908419609, .30679926276207, .3272570669651, .37292611598969, .36668366193771, .40278288722038, .36799272894859, .36827209591866, .38623574376106, .39983862638474, .42789059877396, .43138384819031, .46953064203262, .48066720366478, .48910140991211, .53098994493484, .54496067762375, .55554050207138, .58130383491516, .60081332921982, .58008605241776, .58214038610458, .58369606733322, .53162068128586, .54543834924698, .52040082216263, .50143963098526, .48708060383797, .47620677947998, .48572361469269, .51068127155304, .61833620071411, .61110657453537, .76539021730423, .84672522544861, .92606955766678, .96840506792068, 1.0892199277878, 1.1097067594528, 1.0187155008316, 1.0030621290207, .97345739603043, .95103752613068, .82755368947983, .84054774045944, .85038793087006, .84008830785751, .92104357481003, .89359468221664, .87280809879303, .91032028198242, .95647835731506, 1.0624366998672, 1.1426770687103, 1.1679404973984, 1.311328291893, 1.473167181015, 1.5602221488953, 1.7326545715332, 1.8809853792191, 1.7803012132645, 1.7750589847565, 1.8420933485031, 1.7863517999649, 1.8328944444656, 1.7793855667114, 1.5791050195694, 1.3564316034317, 1.5250737667084, 1.3155146837234, 1.014811873436, .98235523700714, .97552710771561, .97035628557205, 1.0196926593781, 1.0393049716949, .98315137624741, .97613000869751, .89980864524841, .96626943349838, .91009211540222, .88530200719833, .97303456068039, .57794612646103, .63377332687378, .65829831361771, .76562696695328, .86465454101563, .90414637327194, .95180231332779, .95238989591599, .98833626508713, 1.0333099365234, 1.0851185321808, 1.1066001653671, 1.2293750047684, 1.233595252037, 1.1480363607407, 1.2962552309036, 1.2842413187027, 1.3106474876404, 1.5614050626755, 1.4672855138779, 1.2362524271011, 1.1855486631393, 1.1294020414352, 1.1046353578568, 1.0858771800995, 1.0716745853424, 1.0786685943604, 1.0662157535553, 1.0390332937241, .96519494056702, .9802839756012, .92070508003235, .91108840703964, .95705932378769, .95637094974518, .97360169887543, 1.0221517086029, .9701629281044, .94854199886322, .98542231321335, 1.048855304718, 1.0081344842911, 1.0305507183075, 1.0475262403488, .93612504005432, .85176283121109, .89438372850418, .820152759552, .71068543195724, .76979607343674, .76130604743958, .77262878417969, .85220617055893, .84146595001221, .93983960151672, .97883212566376, 1.0793634653091, 1.1909983158112, 1.1690304279327, 1.2411522865295, 1.1360056400299, 1.0918840169907, .9164656996727, .76586949825287, .918093085289, .87360894680023, .92867678403854, 1.00588285923, .92233866453171, .84132260084152, .90422683954239, .9873673915863, .99707210063934, 1.1109310388565, 1.1971517801285, 1.138188958168, 1.2710473537445, 1.1763968467712, 1.7437561750412, 1.4101150035858, 1.3527159690857, 1.4335050582886, .99765706062317, 1.1067585945129, 1.3086627721786, 1.2968333959579, 1.3547962903976, 1.6768488883972, 1.5905654430389, 2.0774590969086, 1.3218278884888, .21813294291496, .30750840902328, .60612773895264]) icstats = np.array([ 202, np.nan, -242.06033399744, 4, 492.12066799488, 505.35373878448]) results = Bunch( llf=llf, nobs=nobs, k=k, k_exog=k_exog, sigma=sigma, chi2=chi2, df_model=df_model, k_ar=k_ar, k_ma=k_ma, params=params, cov_params=cov_params, xb=xb, y=y, resid=resid, yr=yr, mse=mse, stdp=stdp, icstats=icstats ) statsmodels-0.12.2/statsmodels/tsa/tests/results/arima111_forecasts.csv000066400000000000000000000146711400612667500262540ustar00rootroot00000000000000dates, cpi, predict, stderr, conf1, conf2 1950:1, 28.980,,,, 1950:2, 29.150, 29.861 ,,, 1950:3, 29.350, 29.803 ,,, 1950:4, 29.370, 29.904 ,,, 1951:1, 29.540, 29.829 ,,, 1951:2, 29.550, 29.968 ,,, 1951:3, 29.750, 29.928 ,,, 1951:4, 29.840, 30.127 ,,, 1952:1, 29.810, 30.197 ,,, 1952:2, 29.920, 30.132 ,,, 1952:3, 29.980, 30.239 ,,, 1952:4, 30.040, 30.289 ,,, 1953:1, 30.210, 30.341 ,,, 1953:2, 30.220, 30.524 ,,, 1953:3, 30.380, 30.517 ,,, 1953:4, 30.440, 30.689 ,,, 1954:1, 30.480, 30.741 ,,, 1954:2, 30.690, 30.772 ,,, 1954:3, 30.750, 31.003 ,,, 1954:4, 30.940, 31.055 ,,, 1955:1, 30.950, 31.260 ,,, 1955:2, 31.020, 31.251 ,,, 1955:3, 31.120, 31.317 ,,, 1955:4, 31.280, 31.419 ,,, 1956:1, 31.380, 31.590 ,,, 1956:2, 31.580, 31.689 ,,, 1956:3, 31.650, 31.905 ,,, 1956:4, 31.880, 31.965 ,,, 1957:1, 32.280, 32.215 ,,, 1957:2, 32.450, 32.659 ,,, 1957:3, 32.850, 32.824 ,,, 1957:4, 32.900, 33.259 ,,, 1958:1, 33.100, 33.276 ,,, 1958:2, 33.400, 33.477 ,,, 1958:3, 33.700, 33.794 ,,, 1958:4, 34.100, 34.108 ,,, 1959:1, 34.400, 34.535 ,,, 1959:2, 34.900, 34.839 ,,, 1959:3, 35.300, 35.376 ,,, 1959:4, 35.700, 35.787 ,,, 1960:1, 36.300, 36.196 ,,, 1960:2, 36.800, 36.837 ,,, 1960:3, 37.300, 37.351 ,,, 1960:4, 37.900, 37.862 ,,, 1961:1, 38.500, 38.488 ,,, 1961:2, 38.900, 39.108 ,,, 1961:3, 39.400, 39.489 ,,, 1961:4, 39.900, 39.991 ,,, 1962:1, 40.100, 40.493 ,,, 1962:2, 40.600, 40.644 ,,, 1962:3, 40.900, 41.157 ,,, 1962:4, 41.200, 41.433 ,,, 1963:1, 41.500, 41.715 ,,, 1963:2, 41.800, 42.000 ,,, 1963:3, 42.200, 42.289 ,,, 1963:4, 42.700, 42.698 ,,, 1964:1, 43.700, 43.221 ,,, 1964:2, 44.200, 44.324 ,,, 1964:3, 45.600, 44.818 ,,, 1964:4, 46.800, 46.366 ,,, 1965:1, 48.100, 47.646 ,,, 1965:2, 49.300, 49.025 ,,, 1965:3, 51.000, 50.269 ,,, 1965:4, 52.300, 52.087 ,,, 1966:1, 53.000, 53.411 ,,, 1966:2, 54.000, 54.027 ,,, 1966:3, 54.900, 55.014 ,,, 1966:4, 55.800, 55.887 ,,, 1967:1, 56.100, 56.766 ,,, 1967:2, 57.000, 56.948 ,,, 1967:3, 57.900, 57.859 ,,, 1967:4, 58.700, 58.767 ,,, 1968:1, 60.000, 59.557 ,,, 1968:2, 60.800, 60.933 ,,, 1968:3, 61.600, 61.707 ,,, 1968:4, 62.700, 62.488 ,,, 1969:1, 63.900, 63.623 ,,, 1969:2, 65.500, 64.867 ,,, 1969:3, 67.100, 66.569 ,,, 1969:4, 68.500, 68.247 ,,, 1970:1, 70.600, 69.674 ,,, 1970:2, 73.000, 71.913 ,,, 1970:3, 75.200, 74.471 ,,, 1970:4, 78.000, 76.758 ,,, 1971:1, 80.900, 79.727 ,,, 1971:2, 82.600, 82.775 ,,, 1971:3, 84.700, 84.385 ,,, 1971:4, 87.200, 86.484 ,,, 1972:1, 89.100, 89.051 ,,, 1972:2, 91.500, 90.901 ,,, 1972:3, 93.400, 93.347 ,,, 1972:4, 94.400, 95.198 ,,, 1973:1, 95.000, 96.008 ,,, 1973:2, 97.500, 96.394 ,,, 1973:3, 98.100, 99.050 ,,, 1973:4, 97.900, 99.449 ,,, 1974:1, 98.800, 98.959 ,,, 1974:2, 99.800, 99.822 ,,, 1974:3, 100.800, 100.810 ,,, 1974:4, 102.100, 101.800 ,,, 1975:1, 103.300, 103.144 ,,, 1975:2, 104.100, 104.360 ,,, 1975:3, 105.100, 105.106 ,,, 1975:4, 105.700, 106.097 ,,, 1976:1, 107.000, 106.623 ,,, 1976:2, 107.700, 107.984 ,,, 1976:3, 108.500, 108.630 ,,, 1976:4, 109.900, 109.405 ,,, 1977:1, 108.700, 110.887 ,,, 1977:2, 109.500, 109.311 ,,, 1977:3, 110.200, 110.159 ,,, 1977:4, 111.400, 110.880 ,,, 1978:1, 112.700, 112.180 ,,, 1978:2, 113.800, 113.574 ,,, 1978:3, 115.000, 114.712 ,,, 1978:4, 116.000, 115.959 ,,, 1979:1, 117.200, 116.961 ,,, 1979:2, 118.500, 118.197 ,,, 1979:3, 119.900, 119.541 ,,, 1979:4, 121.200, 120.992 ,,, 1980:1, 123.100, 122.314 ,,, 1980:2, 124.500, 124.333 ,,, 1980:3, 125.400, 125.740 ,,, 1980:4, 127.500, 126.561 ,,, 1981:1, 128.900, 128.803 ,,, 1981:2, 130.500, 130.194 ,,, 1981:3, 133.400, 131.821 ,,, 1981:4, 134.700, 134.961 ,,, 1982:1, 135.100, 136.176 ,,, 1982:2, 136.200, 136.359 ,,, 1982:3, 137.200, 137.409 ,,, 1982:4, 138.300, 138.354 ,,, 1983:1, 139.400, 139.428 ,,, 1983:2, 140.500, 140.509 ,,, 1983:3, 141.700, 141.594 ,,, 1983:4, 142.800, 142.799 ,,, 1984:1, 143.800, 143.886 ,,, 1984:2, 144.500, 144.859 ,,, 1984:3, 145.600, 145.488 ,,, 1984:4, 146.300, 146.600 ,,, 1985:1, 147.200, 147.242 ,,, 1985:2, 148.400, 148.131 ,,, 1985:3, 149.400, 149.374 ,,, 1985:4, 150.500, 150.373 ,,, 1986:1, 151.800, 151.489 ,,, 1986:2, 152.600, 152.835 ,,, 1986:3, 153.500, 153.586 ,,, 1986:4, 154.700, 154.465 ,,, 1987:1, 156.100, 155.700 ,,, 1987:2, 157.000, 157.160 ,,, 1987:3, 158.200, 158.022 ,,, 1987:4, 159.400, 159.244 ,,, 1988:1, 159.900, 160.460 ,,, 1988:2, 160.400, 160.855 ,,, 1988:3, 161.500, 161.274 ,,, 1988:4, 162.000, 162.412 ,,, 1989:1, 162.200, 162.841 ,,, 1989:2, 163.200, 162.935 ,,, 1989:3, 163.900, 163.988 ,,, 1989:4, 164.700, 164.679 ,,, 1990:1, 165.900, 165.489 ,,, 1990:2, 166.700, 166.764 ,,, 1990:3, 168.100, 167.554 ,,, 1990:4, 169.300, 169.048 ,,, 1991:1, 170.900, 170.286 ,,, 1991:2, 172.700, 171.984 ,,, 1991:3, 173.900, 173.893 ,,, 1991:4, 175.600, 175.075 ,,, 1992:1, 176.400, 176.846 ,,, 1992:2, 177.400, 177.549 ,,, 1992:3, 177.600, 178.508 ,,, 1992:4, 177.700, 178.541 ,,, 1993:1, 179.300, 178.495 ,,, 1993:2, 180.000, 180.236 ,,, 1993:3, 181.200, 180.893 ,,, 1993:4, 182.600, 182.144 ,,, 1994:1, 183.200, 183.617 ,,, 1994:2, 183.700, 184.139 ,,, 1994:3, 184.900, 184.561 ,,, 1994:4, 186.300, 185.819 ,,, 1995:1, 187.400, 187.298 ,,, 1995:2, 189.100, 188.408 ,,, 1995:3, 190.800, 190.218 ,,, 1995:4, 191.800, 192.002 ,,, 1996:1, 193.800, 192.948 ,,, 1996:2, 194.700, 195.076 ,,, 1996:3, 199.200, 195.889 ,,, 1996:4, 199.400, 200.930 ,,, 1997:1, 200.700, 200.820 ,,, 1997:2, 202.700, 202.068 ,,, 1997:3, 201.900, 204.145 ,,, 1997:4, 203.574, 202.932 ,,, 1998:1, 205.920, 204.705 ,,, 1998:2, 207.338, 207.241 ,,, 1998:3, 209.133, 208.649 ,,, 1998:4, 212.495, 210.500 ,,, 1999:1, 213.997, 214.170 ,,, 1999:2, 218.610, 215.595 ,,, 1999:3, 216.889, 220.674 ,,, 1999:4, 212.174, 218.243 ,,, 2000:1, 212.671, 212.474 ,,, 2000:2, 214.469, 213.039 ,,, 2000:3, 216.385, 215.110 ,,, 2000:4,, 217.255, 0.7999, 215.688, 218.823 2001:1,, 218.127, 1.2305, 215.715, 220.538 2001:2,, 218.998, 1.6254, 215.813, 222.184 2001:3,, 219.870, 2.0093, 215.932, 223.809 2001:4,, 220.743, 2.3897, 216.060, 225.427 2002:1,, 221.616, 2.7691, 216.189, 227.044 2002:2,, 222.490, 3.1483, 216.320, 228.661 2002:3,, 223.364, 3.5276, 216.450, 230.278 2002:4,, 224.239, 3.9067, 216.582, 231.896 2003:1,, 225.114, 4.2853, 216.715, 233.513 2003:2,, 225.989, 4.6630, 216.850, 235.128 2003:3,, 226.865, 5.0394, 216.988, 236.742 2003:4,, 227.741, 5.4142, 217.129, 238.352 2004:1,, 228.617, 5.7870, 217.274, 239.959 2004:2,, 229.493, 6.1576, 217.425, 241.562 2004:3,, 230.370, 6.5257, 217.580, 243.160 2004:4,, 231.247, 6.8911, 217.741, 244.753 2005:1,, 232.124, 7.2535, 217.908, 246.341 2005:2,, 233.002, 7.6128, 218.081, 247.923 2005:3,, 233.879, 7.9689, 218.261, 249.498 statsmodels-0.12.2/statsmodels/tsa/tests/results/arima111_results.py000066400000000000000000000645231400612667500256220ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch llf = np.array([-241.75576160303]) nobs = np.array([202]) k = np.array([4]) k_exog = np.array([1]) sigma = np.array([.79987660416529]) chi2 = np.array([342.91413339514]) df_model = np.array([2]) k_ar = np.array([1]) k_ma = np.array([1]) params = np.array([ .88084748605315, .93989719451385, -.7709851377434, .79987660416529]) cov_params = np.array([ .15020189867396, -.01642122563089, .01456018801049, -.00156750041014, -.01642122563089, .0032067778715, -.00350387326241, .00059634328354, .01456018801049, -.00350387326241, .00480028434835, -.00068065418463, -.00156750041014, .00059634328354, -.00068065418463, .00029322997097]).reshape(4, 4) xb = np.array([ .88084751367569, .88084751367569, .65303039550781, .55365419387817, .45908725261688, .42810925841331, .37837743759155, .37686342000961, .35719576478004, .3220648765564, .31943875551224, .30907514691353, .30120712518692, .31383177638054, .29652059078217, .30856171250343, .30095273256302, .29171526432037, .31331890821457, .30463594198227, .31990340352058, .30126947164536, .29703867435455, .29884466528893, .31037190556526, .30912432074547, .32505416870117, .31537705659866, .33494210243225, .37874156236649, .37366089224815, .40859284996986, .37640652060509, .37692713737488, .39422073960304, .40755322575569, .43472331762314, .43878075480461, .47569087147713, .48725643754005, .49617394804955, .53683114051819, .55128628015518, .56243091821671, .58791494369507, .60756206512451, .58892780542374, .59145200252533, .59339815378189, .54422444105148, .55698639154434, .53304374217987, .51458370685577, .50035130977631, .48937830328941, .49780988693237, .52120143175125, .62369203567505, .6182547211647, .76608312129974, .84627467393875, .92499214410782, .96879118680954, 1.0870156288147, 1.1105998754501, 1.0274360179901, 1.013991355896, .98673474788666, .96571969985962, .84817039966583, .85888928174973, .86715340614319, .85663330554962, .93297851085663, .90738350152969, .88765007257462, .92311006784439, .96734017133713, 1.0690053701401, 1.1473876237869, 1.1740373373032, 1.3128218650818, 1.4704967737198, 1.5582785606384, 1.7273052930832, 1.8745132684708, 1.7853132486343, 1.7841064929962, 1.850741147995, 1.800768494606, 1.8466963768005, 1.7976499795914, 1.6078149080276, 1.3938897848129, 1.5498898029327, 1.3492304086685, 1.059396147728, 1.0217411518097, 1.0096007585526, 1.0002405643463, 1.0436969995499, 1.0603114366531, 1.0055546760559, .99712115526199, .92305397987366, .9841884970665, .92997401952744, .90506774187088, .9872123003006, .61137217283249, .65943044424057, .67959040403366, .77959072589874, .87357920408249, .91226226091385, .95897603034973, .96120971441269, .99671375751495, 1.0409790277481, 1.0919979810715, 1.1144404411316, 1.2330915927887, 1.2401138544083, 1.161071896553, 1.3028255701065, 1.2938764095306, 1.3207612037659, 1.5610725879669, 1.4760913848877, 1.258552312851, 1.2090681791306, 1.1540271043777, 1.12848341465, 1.1087870597839, 1.0936040878296, 1.0987877845764, 1.0858948230743, 1.0590622425079, .98770052194595, 1.0002481937408, .94235575199127, .93150353431702, .97381073236465, .9726470708847, .98864215612411, 1.0347559452057, .98585307598114, .96503925323486, .9996662735939, 1.0601476430893, 1.022319316864, 1.043828368187, 1.0604115724564, .95495897531509, .87365657091141, .91232192516327, .84078407287598, .73495537042618, .78849309682846, .77909576892853, .78874284029007, .8637443780899, .8540056347847, .94784545898438, .98641014099121, 1.0837067365646, 1.1925053596497, 1.1750392913818, 1.2460317611694, 1.1487410068512, 1.1075156927109, .94060403108597, .7950227856636, .93615245819092, .89293897151947, .94407802820206, 1.0172899961472, .93860250711441, .86104601621628, .91948908567429, .99833220243454, 1.008442401886, 1.1175880432129, 1.2017351388931, 1.1483734846115, 1.2761443853378, 1.188849568367, 1.7296310663223, 1.4202431440353, 1.3675138950348, 1.445098400116, 1.031960606575, 1.1313284635544, 1.3214453458786, 1.3112732172012, 1.367110490799, 1.674845457077, 1.5979281663895, 2.064112663269, 1.3536450862885, .30015936493874, .36831066012383, .64060544967651]) y = np.array([ np.nan, 29.860847473145, 29.803030014038, 29.903654098511, 29.82908821106, 29.968111038208, 29.928377151489, 30.126863479614, 30.197195053101, 30.132064819336, 30.23943901062, 30.289073944092, 30.341207504272, 30.523830413818, 30.516519546509, 30.68856048584, 30.740953445435, 30.771715164185, 31.003318786621, 31.054636001587, 31.25990486145, 31.251270294189, 31.317039489746, 31.418846130371, 31.590372085571, 31.689123153687, 31.905054092407, 31.965375900269, 32.214942932129, 32.658740997314, 32.823661804199, 33.258590698242, 33.27640914917, 33.47692489624, 33.7942237854, 34.107555389404, 34.534721374512, 34.83878326416, 35.375694274902, 35.787254333496, 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.63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139, .63980257511139]) stdp = np.array([ .88084751367569, .88084751367569, .65303039550781, .55365419387817, .45908725261688, .42810925841331, .37837743759155, .37686342000961, .35719576478004, .3220648765564, .31943875551224, .30907514691353, .30120712518692, .31383177638054, .29652059078217, .30856171250343, .30095273256302, .29171526432037, .31331890821457, .30463594198227, .31990340352058, .30126947164536, .29703867435455, .29884466528893, .31037190556526, .30912432074547, .32505416870117, .31537705659866, .33494210243225, .37874156236649, .37366089224815, .40859284996986, .37640652060509, .37692713737488, .39422073960304, .40755322575569, .43472331762314, .43878075480461, .47569087147713, .48725643754005, .49617394804955, .53683114051819, .55128628015518, .56243091821671, .58791494369507, .60756206512451, .58892780542374, .59145200252533, .59339815378189, .54422444105148, .55698639154434, .53304374217987, .51458370685577, .50035130977631, .48937830328941, .49780988693237, .52120143175125, .62369203567505, .6182547211647, .76608312129974, .84627467393875, .92499214410782, .96879118680954, 1.0870156288147, 1.1105998754501, 1.0274360179901, 1.013991355896, .98673474788666, .96571969985962, .84817039966583, .85888928174973, .86715340614319, .85663330554962, .93297851085663, .90738350152969, .88765007257462, .92311006784439, .96734017133713, 1.0690053701401, 1.1473876237869, 1.1740373373032, 1.3128218650818, 1.4704967737198, 1.5582785606384, 1.7273052930832, 1.8745132684708, 1.7853132486343, 1.7841064929962, 1.850741147995, 1.800768494606, 1.8466963768005, 1.7976499795914, 1.6078149080276, 1.3938897848129, 1.5498898029327, 1.3492304086685, 1.059396147728, 1.0217411518097, 1.0096007585526, 1.0002405643463, 1.0436969995499, 1.0603114366531, 1.0055546760559, .99712115526199, .92305397987366, .9841884970665, .92997401952744, .90506774187088, .9872123003006, .61137217283249, .65943044424057, .67959040403366, .77959072589874, .87357920408249, .91226226091385, .95897603034973, .96120971441269, .99671375751495, 1.0409790277481, 1.0919979810715, 1.1144404411316, 1.2330915927887, 1.2401138544083, 1.161071896553, 1.3028255701065, 1.2938764095306, 1.3207612037659, 1.5610725879669, 1.4760913848877, 1.258552312851, 1.2090681791306, 1.1540271043777, 1.12848341465, 1.1087870597839, 1.0936040878296, 1.0987877845764, 1.0858948230743, 1.0590622425079, .98770052194595, 1.0002481937408, .94235575199127, .93150353431702, .97381073236465, .9726470708847, .98864215612411, 1.0347559452057, .98585307598114, .96503925323486, .9996662735939, 1.0601476430893, 1.022319316864, 1.043828368187, 1.0604115724564, .95495897531509, .87365657091141, .91232192516327, .84078407287598, .73495537042618, .78849309682846, .77909576892853, .78874284029007, .8637443780899, .8540056347847, .94784545898438, .98641014099121, 1.0837067365646, 1.1925053596497, 1.1750392913818, 1.2460317611694, 1.1487410068512, 1.1075156927109, .94060403108597, .7950227856636, .93615245819092, .89293897151947, .94407802820206, 1.0172899961472, .93860250711441, .86104601621628, .91948908567429, .99833220243454, 1.008442401886, 1.1175880432129, 1.2017351388931, 1.1483734846115, 1.2761443853378, 1.188849568367, 1.7296310663223, 1.4202431440353, 1.3675138950348, 1.445098400116, 1.031960606575, 1.1313284635544, 1.3214453458786, 1.3112732172012, 1.367110490799, 1.674845457077, 1.5979281663895, 2.064112663269, 1.3536450862885, .30015936493874, .36831066012383, .64060544967651]) icstats = np.array([ 202, np.nan, -241.75576160303, 4, 491.51152320605, 504.74459399566]) results = Bunch( llf=llf, nobs=nobs, k=k, k_exog=k_exog, sigma=sigma, chi2=chi2, df_model=df_model, k_ar=k_ar, k_ma=k_ma, params=params, cov_params=cov_params, xb=xb, y=y, resid=resid, yr=yr, mse=mse, stdp=stdp, icstats=icstats ) statsmodels-0.12.2/statsmodels/tsa/tests/results/arima111nc_css_results.py000066400000000000000000000641141400612667500270070ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch llf = np.array([-242.89663276735]) nobs = np.array([202]) k = np.array([3]) k_exog = np.array([1]) sigma = np.array([.8053519404535]) chi2 = np.array([15723.381396967]) df_model = np.array([2]) k_ar = np.array([1]) k_ma = np.array([1]) params = np.array([ .99479180506163, -.84461527652809, .64859174799221]) cov_params = np.array([ .00008904968254, -.00023560410507, .00012795903324, -.00023560410507, .00131628534915, -.00022462340695, .00012795903324, -.00022462340695, .0005651128627]).reshape(3, 3) xb = np.array([ 0, 0, .02869686298072, .05651443824172, .0503994859755, .06887971609831, .05940540507436, .08067328482866, .08167565613985, .06429278105497, .07087650150061, .06886467337608, .06716959923506, .08230647444725, .07099691033363, .08401278406382, .07996553182602, .07354256510735, .09366323798895, .08811800926924, .10296355187893, .08846370875835, .0852297320962, .08700425922871, .09751411527395, .09737934917212, .11228405684233, .1053489819169, .12352022528648, .16439816355705, .1643835157156, .19891132414341, .17551273107529, .17827558517456, .19562774896622, .21028305590153, .23767858743668, .24580039083958, .28269505500793, .29883882403374, .31247469782829, .35402658581734, .37410452961922, .39106267690659, .42040377855301, .44518512487411, .43608102202415, .44340893626213, .44959822297096, .40977239608765, .42118826508522, .40079545974731, .38357082009315, .36902260780334, .35673499107361, .36137464642525, .38031083345413, .47139286994934, .47323387861252, .60994738340378, .69538277387619, .7825602889061, .84117436408997, .9657689332962, 1.0109325647354, .95897275209427, .96013957262039, .9461076259613, .9342554807663, .83413934707642, .83968591690063, .84437066316605, .83330947160721, .8990553021431, .87949693202972, .86297762393951, .89407861232758, .93536442518234, 1.0303052663803, 1.1104937791824, 1.1481873989105, 1.2851470708847, 1.4458787441254, 1.5515991449356, 1.7309991121292, 1.8975404500961, 1.8579913377762, 1.8846583366394, 1.9672524929047, 1.9469071626663, 2.0048115253448, 1.9786299467087, 1.8213576078415, 1.6284521818161, 1.7508568763733, 1.5689061880112, 1.2950873374939, 1.2290096282959, 1.1882168054581, 1.1537625789642, 1.1697143316269, 1.1681711673737, 1.106795668602, 1.0849931240082, 1.006507396698, 1.0453414916992, .98803448677063, .95465070009232, 1.0165599584579, .67838954925537, .69311982393265, .69054269790649, .76345545053482, .84005492925644, .87471830844879, .91901183128357, .92638796567917, .96265280246735, 1.0083012580872, 1.0618740320206, 1.0921038389206, 1.2077431678772, 1.2303256988525, 1.174311041832, 1.3072115182877, 1.314337015152, 1.3503924608231, 1.5760731697083, 1.5264053344727, 1.34929728508, 1.304829955101, 1.2522557973862, 1.222869515419, 1.198047041893, 1.1770839691162, 1.1743944883347, 1.1571066379547, 1.1274864673615, 1.0574153661728, 1.058304309845, .99898308515549, .9789143204689, 1.0070173740387, 1.000718832016, 1.0104174613953, 1.0486439466476, 1.0058424472809, .98470783233643, 1.0119106769562, 1.0649236440659, 1.0346088409424, 1.0540577173233, 1.0704846382141, .97923594713211, .90216588973999, .9271782040596, .85819715261459, .75488126277924, .78776079416275, .77047789096832, .77089905738831, .8313245177269, .82229107618332, .90476810932159, .94439232349396, 1.0379292964935, 1.1469690799713, 1.1489590406418, 1.2257302999496, 1.1554099321365, 1.1260533332825, .9811190366745, .8436843752861, .95287209749222, .90993344783783, .94875508546829, 1.0115815401077, .94450175762177, .87282890081406, .91741597652435, .98511207103729, .9972335100174, 1.0975805521011, 1.1823329925537, 1.1487929821014, 1.270641207695, 1.2083609104156, 1.696394443512, 1.4628355503082, 1.4307631254196, 1.5087975263596, 1.1542117595673, 1.2262620925903, 1.3880327939987, 1.3853038549423, 1.4396153688431, 1.7208145856857, 1.678991317749, 2.110867023468, 1.524417757988, .57946246862411, .56406193971634, .74643105268478]) y = np.array([ np.nan, 28.979999542236, 29.178695678711, 29.40651512146, 29.420400619507, 29.608880996704, 29.609405517578, 29.830673217773, 29.921676635742, 29.874292373657, 29.990877151489, 30.048864364624, 30.10717010498, 30.292304992676, 30.290996551514, 30.464012145996, 30.519966125488, 30.553541183472, 30.783664703369, 30.838117599487, 31.042964935303, 31.038463592529, 31.105230331421, 31.207004547119, 31.377513885498, 31.477378845215, 31.692283630371, 31.755348205566, 32.003520965576, 32.444396972656, 32.61438369751, 33.048908233643, 33.07551574707, 33.278274536133, 33.595630645752, 33.91028213501, 34.337677001953, 34.645801544189, 35.182697296143, 35.598838806152, 36.012474060059, 36.654026031494, 37.174102783203, 37.691062927246, 38.320404052734, 38.94518661499, 39.336082458496, 39.843410491943, 40.349597930908, 40.509769439697, 41.021186828613, 41.300796508789, 41.583572387695, 41.869022369385, 42.156734466553, 42.561374664307, 43.080310821533, 44.171394348145, 44.673233032227, 46.209945678711, 47.495380401611, 48.882556915283, 50.141174316406, 51.965770721436, 53.310932159424, 53.958972930908, 54.960140228271, 55.84610748291, 56.734252929688, 56.934139251709, 57.839687347412, 58.744373321533, 59.533309936523, 60.899055480957, 61.679496765137, 62.46297454834, 63.594078063965, 64.83536529541, 66.530303955078, 68.210494995117, 69.64818572998, 71.885147094727, 74.445877075195, 76.751594543457, 79.731002807617, 82.797538757324, 84.457992553711, 86.584655761719, 89.167251586914, 91.046905517578, 93.504814147949, 95.378631591797, 96.22135925293, 96.628448486328, 99.250854492188, 99.668907165527, 99.195091247559, 100.0290145874, 100.98822021484, 101.95376586914, 103.26971435547, 104.46817779541, 105.20679473877, 106.1849899292, 106.70650482178, 108.0453414917, 108.68803405762, 109.45465087891, 110.91656494141, 109.37838745117, 110.19312286377, 110.89054107666, 112.16345977783, 113.54005432129, 114.67472076416, 115.91901397705, 116.92639160156, 118.16265106201, 119.50830078125, 120.96187591553, 122.29209899902, 124.30773925781, 125.7303237915, 126.57431030273, 128.8072052002, 130.21432495117, 131.85038757324, 134.97607421875, 136.22640991211, 136.44931030273, 137.50482177734, 138.45225524902, 139.5228729248, 140.59803771973, 141.67707824707, 142.87438964844, 143.95710754395, 144.92749023438, 145.55741882324, 146.65830993652, 147.29898071289, 148.17890930176, 149.40701293945, 150.40071105957, 151.51042175293, 152.84864807129, 153.60585021973, 154.48471069336, 155.7119140625, 157.16493225098, 158.03460693359, 159.25405883789, 160.47047424316, 160.87922668457, 161.30215454102, 162.42718505859, 162.85820007324, 162.95487976074, 163.98776245117, 164.67047119141, 165.47090148926, 166.73132324219, 167.52229309082, 169.00477600098, 170.24440002441, 171.93792724609, 173.84696960449, 175.04895019531, 176.82572937012, 177.55540466309, 178.52604675293, 178.58113098145, 178.54368591309, 180.25286865234, 180.90992736816, 182.14875793457, 183.61158752441, 184.14450073242, 184.5728302002, 185.81741333008, 187.28511047363, 188.39723205566, 190.19758605957, 191.98233032227, 192.94879150391, 195.07064819336, 195.90835571289, 200.89639282227, 200.86282348633, 202.13075256348, 204.20880126953, 203.05419921875, 204.80026245117, 207.3080291748, 208.72329711914, 210.57261657715, 214.21580505371, 215.67597961426, 220.72087097168, 218.41342163086, 212.75346374512, 213.23506164551, 215.21542358398]) resid = np.array([ np.nan, .17000007629395, .17130389809608, -.03651398047805, .11960058659315, -.05888139456511, .14059536159039, .00932686589658, -.11167634278536, .04570783302188, -.0108770346269, -.00886330008507, .10282856971025, -.07230624556541, .08900293707848, -.0240114107728, -.03996651992202, .13645842671394, -.03366377204657, .10188252478838, -.09296332299709, -.01846401393414, .01477065030485, .0729955881834, .00248436117545, .10262141376734, -.04228436201811, .12465056031942, .27647939324379, .00560382334515, .23561419546604, -.1489082723856, .02448422275484, .12172746658325, .10437148809433, .18971465528011, .06232447177172, .25419962406158, .11730266362429, .10116269439459, .2875237762928, .14597341418266, .12589547038078, .20893961191177, .17959471046925, -.04518361017108, .06391899287701, .05659105628729, -.24960128962994, .09022761881351, -.12118522822857, -.10079623758793, -.08357158303261, -.06902338564396, .04326653853059, .13862533867359, .61968916654587, .02860714122653, .92676383256912, .59005337953568, .60461646318436, .41744044423103, .85882639884949, .33423033356667, -.31093180179596, .04102724045515, -.06013804674149, -.04610994458199, -.63425624370575, .06586220860481, .06031560897827, -.04437142238021, .46668976545334, -.09905604273081, -.07949769496918, .23702463507652, .30592212080956, .66463404893875, .56969320774078, .28950771689415, .95181107521057, 1.1148544549942, .75411820411682, 1.2484039068222, 1.1690024137497, -.1975435167551, .24200716614723, .6153416633606, -.06725100427866, .45309436321259, -.10480991750956, -.97863000631332, -1.2213591337204, .8715478181839, -1.1508584022522, -1.7689031362534, -.39508575201035, -.22900961339474, -.18821682035923, .14623281359673, .03029025532305, -.36817568540573, -.10679569840431, -.48499462008476, .29349562525749, -.34534454345703, -.18803144991398, .44535079598427, -2.2165644168854, .12161350995302, .00687709869817, .50946187973022, .53653997182846, .25995117425919, .32527860999107, .08098815381527, .27360898256302, .33735024929047, .39170032739639, .23812144994736, .80789774656296, .19225835800171, -.33032417297363, .92568749189377, .09278241544962, .28566908836365, 1.5496014356613, -.27607008814812, -1.1263961791992, -.24930645525455, -.30482992529869, -.15224970877171, -.12287864089012, -.09804095327854, .02291300706565, -.07438835501671, -.15710659325123, -.42748948931694, .04259072244167, -.35830733180046, -.09898918122053, .22108262777328, -.00701736938208, .0992873236537, .28958559036255, -.24864092469215, -.10584850609303, .21528913080692, .38809850811958, -.16492980718613, .16538816690445, .1459391862154, -.57048463821411, -.47923597693443, .19784018397331, -.4271782040596, -.65820020437241, .24511873722076, -.0877638310194, .02952514961362, .42909786105156, -.03132146969438, .57771807909012, .29522883892059, .6555985212326, .76207375526428, .05302781611681, .55105316638947, -.42574247717857, -.15540990233421, -.92604118585587, -.88112819194794, .75632172822952, -.25287514925003, .29006350040436, .45125409960747, -.41159069538116, -.44450175762177, .32716807723045, .48259317874908, .11487878113985, .70277869701385, .60241633653641, -.18233296275139, .85120695829391, -.37064728140831, 3.2916390895844, -1.4963974952698, -.16283248364925, .56923681497574, -2.3088004589081, .51979947090149, 1.1197309494019, .02996650896966, .40969428420067, 1.9223841428757, -.21881568431854, 2.9340152740479, -3.8318600654602, -6.239429473877, -.08245316892862, 1.2339268922806, 1.1695692539215]) yr = np.array([ np.nan, .17000007629395, .17130389809608, -.03651398047805, .11960058659315, -.05888139456511, .14059536159039, .00932686589658, -.11167634278536, .04570783302188, -.0108770346269, -.00886330008507, .10282856971025, -.07230624556541, .08900293707848, -.0240114107728, -.03996651992202, .13645842671394, -.03366377204657, .10188252478838, -.09296332299709, -.01846401393414, .01477065030485, .0729955881834, .00248436117545, .10262141376734, -.04228436201811, .12465056031942, .27647939324379, .00560382334515, .23561419546604, -.1489082723856, .02448422275484, .12172746658325, .10437148809433, .18971465528011, .06232447177172, .25419962406158, .11730266362429, .10116269439459, .2875237762928, .14597341418266, .12589547038078, .20893961191177, .17959471046925, -.04518361017108, .06391899287701, .05659105628729, -.24960128962994, .09022761881351, -.12118522822857, -.10079623758793, -.08357158303261, -.06902338564396, .04326653853059, .13862533867359, .61968916654587, .02860714122653, .92676383256912, .59005337953568, .60461646318436, .41744044423103, .85882639884949, .33423033356667, -.31093180179596, .04102724045515, -.06013804674149, -.04610994458199, -.63425624370575, .06586220860481, .06031560897827, -.04437142238021, .46668976545334, -.09905604273081, -.07949769496918, .23702463507652, .30592212080956, .66463404893875, .56969320774078, .28950771689415, .95181107521057, 1.1148544549942, .75411820411682, 1.2484039068222, 1.1690024137497, -.1975435167551, .24200716614723, .6153416633606, -.06725100427866, .45309436321259, -.10480991750956, -.97863000631332, -1.2213591337204, .8715478181839, -1.1508584022522, -1.7689031362534, -.39508575201035, -.22900961339474, -.18821682035923, .14623281359673, .03029025532305, -.36817568540573, -.10679569840431, -.48499462008476, .29349562525749, -.34534454345703, -.18803144991398, .44535079598427, -2.2165644168854, .12161350995302, .00687709869817, .50946187973022, .53653997182846, .25995117425919, .32527860999107, .08098815381527, .27360898256302, .33735024929047, .39170032739639, .23812144994736, .80789774656296, .19225835800171, -.33032417297363, .92568749189377, .09278241544962, .28566908836365, 1.5496014356613, -.27607008814812, -1.1263961791992, -.24930645525455, -.30482992529869, -.15224970877171, -.12287864089012, -.09804095327854, .02291300706565, -.07438835501671, -.15710659325123, -.42748948931694, .04259072244167, -.35830733180046, -.09898918122053, .22108262777328, -.00701736938208, .0992873236537, .28958559036255, -.24864092469215, -.10584850609303, .21528913080692, .38809850811958, -.16492980718613, .16538816690445, .1459391862154, -.57048463821411, -.47923597693443, .19784018397331, -.4271782040596, -.65820020437241, .24511873722076, -.0877638310194, .02952514961362, .42909786105156, -.03132146969438, .57771807909012, .29522883892059, .6555985212326, .76207375526428, .05302781611681, .55105316638947, -.42574247717857, -.15540990233421, -.92604118585587, -.88112819194794, .75632172822952, -.25287514925003, .29006350040436, .45125409960747, -.41159069538116, -.44450175762177, .32716807723045, .48259317874908, .11487878113985, .70277869701385, .60241633653641, -.18233296275139, .85120695829391, -.37064728140831, 3.2916390895844, -1.4963974952698, -.16283248364925, .56923681497574, -2.3088004589081, .51979947090149, 1.1197309494019, .02996650896966, .40969428420067, 1.9223841428757, -.21881568431854, 2.9340152740479, -3.8318600654602, -6.239429473877, -.08245316892862, 1.2339268922806, 1.1695692539215]) mse = np.array([ 1.1112809181213, .6632194519043, .65879660844803, .65575885772705, .65364873409271, .65217137336731, .65113133192062, .6503963470459, .64987552165985, .64950579404831, .64924287796021, .64905577898026, .64892256259918, .64882761240005, .64875996112823, .64871168136597, .64867728948593, .64865279197693, .64863526821136, .64862281084061, .64861387014389, .64860755205154, .64860302209854, .64859980344772, .64859747886658, .64859586954117, .64859467744827, .64859384298325, .6485932469368, .64859282970428, .64859253168106, .64859229326248, .64859211444855, .64859199523926, .64859193563461, .64859187602997, .64859187602997, .64859181642532, .64859181642532, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068, .64859175682068]) stdp = np.array([ 0, 0, .02869686298072, .05651443824172, .0503994859755, .06887971609831, .05940540507436, .08067328482866, .08167565613985, .06429278105497, .07087650150061, .06886467337608, .06716959923506, .08230647444725, .07099691033363, .08401278406382, .07996553182602, .07354256510735, .09366323798895, .08811800926924, .10296355187893, .08846370875835, .0852297320962, .08700425922871, .09751411527395, .09737934917212, .11228405684233, .1053489819169, .12352022528648, .16439816355705, .1643835157156, .19891132414341, .17551273107529, .17827558517456, .19562774896622, .21028305590153, .23767858743668, .24580039083958, .28269505500793, .29883882403374, .31247469782829, .35402658581734, .37410452961922, .39106267690659, .42040377855301, .44518512487411, .43608102202415, .44340893626213, .44959822297096, .40977239608765, .42118826508522, .40079545974731, .38357082009315, .36902260780334, .35673499107361, .36137464642525, .38031083345413, .47139286994934, .47323387861252, .60994738340378, .69538277387619, .7825602889061, .84117436408997, .9657689332962, 1.0109325647354, .95897275209427, .96013957262039, .9461076259613, .9342554807663, .83413934707642, .83968591690063, .84437066316605, .83330947160721, .8990553021431, .87949693202972, .86297762393951, .89407861232758, .93536442518234, 1.0303052663803, 1.1104937791824, 1.1481873989105, 1.2851470708847, 1.4458787441254, 1.5515991449356, 1.7309991121292, 1.8975404500961, 1.8579913377762, 1.8846583366394, 1.9672524929047, 1.9469071626663, 2.0048115253448, 1.9786299467087, 1.8213576078415, 1.6284521818161, 1.7508568763733, 1.5689061880112, 1.2950873374939, 1.2290096282959, 1.1882168054581, 1.1537625789642, 1.1697143316269, 1.1681711673737, 1.106795668602, 1.0849931240082, 1.006507396698, 1.0453414916992, .98803448677063, .95465070009232, 1.0165599584579, .67838954925537, .69311982393265, .69054269790649, .76345545053482, .84005492925644, .87471830844879, .91901183128357, .92638796567917, .96265280246735, 1.0083012580872, 1.0618740320206, 1.0921038389206, 1.2077431678772, 1.2303256988525, 1.174311041832, 1.3072115182877, 1.314337015152, 1.3503924608231, 1.5760731697083, 1.5264053344727, 1.34929728508, 1.304829955101, 1.2522557973862, 1.222869515419, 1.198047041893, 1.1770839691162, 1.1743944883347, 1.1571066379547, 1.1274864673615, 1.0574153661728, 1.058304309845, .99898308515549, .9789143204689, 1.0070173740387, 1.000718832016, 1.0104174613953, 1.0486439466476, 1.0058424472809, .98470783233643, 1.0119106769562, 1.0649236440659, 1.0346088409424, 1.0540577173233, 1.0704846382141, .97923594713211, .90216588973999, .9271782040596, .85819715261459, .75488126277924, .78776079416275, .77047789096832, .77089905738831, .8313245177269, .82229107618332, .90476810932159, .94439232349396, 1.0379292964935, 1.1469690799713, 1.1489590406418, 1.2257302999496, 1.1554099321365, 1.1260533332825, .9811190366745, .8436843752861, .95287209749222, .90993344783783, .94875508546829, 1.0115815401077, .94450175762177, .87282890081406, .91741597652435, .98511207103729, .9972335100174, 1.0975805521011, 1.1823329925537, 1.1487929821014, 1.270641207695, 1.2083609104156, 1.696394443512, 1.4628355503082, 1.4307631254196, 1.5087975263596, 1.1542117595673, 1.2262620925903, 1.3880327939987, 1.3853038549423, 1.4396153688431, 1.7208145856857, 1.678991317749, 2.110867023468, 1.524417757988, .57946246862411, .56406193971634, .74643105268478]) icstats = np.array([ 202, np.nan, -242.89663276735, 3, 491.79326553469, 501.7180686269]) results = Bunch( llf=llf, nobs=nobs, k=k, k_exog=k_exog, sigma=sigma, chi2=chi2, df_model=df_model, k_ar=k_ar, k_ma=k_ma, params=params, cov_params=cov_params, xb=xb, y=y, resid=resid, yr=yr, mse=mse, stdp=stdp, icstats=icstats ) statsmodels-0.12.2/statsmodels/tsa/tests/results/arima111nc_results.py000066400000000000000000000641171400612667500261420ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch llf = np.array([-243.77512585356]) nobs = np.array([202]) k = np.array([3]) k_exog = np.array([1]) sigma = np.array([.80556855709271]) chi2 = np.array([14938.241729056]) df_model = np.array([2]) k_ar = np.array([1]) k_ma = np.array([1]) params = np.array([ .99034248845249, -.83659509233745, .80556855709271]) cov_params = np.array([ .00009906057555, -.00026616895902, .00007867120825, -.00026616895902, .00137590666911, -.0001403880509, .00007867120825, -.0001403880509, .0002129852258]).reshape(3, 3) xb = np.array([ 0, 0, .10457526892424, .14047028124332, .10415132343769, .11891452968121, .09492295235395, .11409470438957, .1086763292551, .08389142900705, .08740901201963, .08212262392044, .07780049741268, .09159570932388, .07793674618006, .08996207267046, .08444581180811, .07675409317017, .09658851474524, .09001308679581, .10454939305782, .08898131549358, .08520055562258, .08665482699871, .09710033237934, .09660832583904, .11157563328743, .10410477221012, .12245775014162, .16395011544228, .16329728066921, .19811384379864, .1734282374382, .17583830654621, .19323042035103, .20777989923954, .23532645404339, .24299769103527, .28016451001167, .29588291049004, .30903342366219, .35078409314156, .37033796310425, .38669663667679, .41575729846954, .44006872177124, .42965853214264, .43632391095161, .44190016388893, .40044051408768, .41188025474548, .3907016813755, .37298321723938, .3581600189209, .3457590341568, .35075950622559, .37031736969948, .46355310082436, .46467992663383, .60399496555328, .68979620933533, .77695161104202, .8344908952713, .95950168371201, 1.0025858879089, .94638174772263, .94548571109772, .92936158180237, .91587167978287, .81233781576157, .81797075271606, .8226832151413, .81125050783157, .87855970859528, .85799652338028, .84079349040985, .87252616882324, .9144481420517, 1.0110183954239, 1.0918086767197, 1.1286484003067, 1.2670909166336, 1.4290360212326, 1.533768415451, 1.7136362791061, 1.8794873952866, 1.8337399959564, 1.8569672107697, 1.9378981590271, 1.9133563041687, 1.969698548317, 1.939960360527, 1.7767087221146, 1.5786340236664, 1.7050459384918, 1.5186812877655, 1.2397723197937, 1.1755603551865, 1.1372153759003, 1.1051361560822, 1.1244224309921, 1.1251838207245, 1.06432056427, 1.0441527366638, .96578127145767, 1.0078399181366, .95077663660049, .91841346025467, .98358678817749, .63836628198624, .65705251693726, .65730959177017, .73439955711365, .81426596641541, .85033398866653, .89588165283203, .90323758125305, .94014054536819, .98638904094696, 1.040454864502, 1.0703103542328, 1.1875365972519, 1.2087339162827, 1.1495937108994, 1.2846138477325, 1.2899470329285, 1.3251601457596, 1.5544888973236, 1.5003498792648, 1.316685795784, 1.2706536054611, 1.2167699337006, 1.1870667934418, 1.1622149944305, 1.1414264440536, 1.1394081115723, 1.1223464012146, 1.0926969051361, 1.0217674970627, 1.0239287614822, .96423649787903, .94504725933075, .97511827945709, .96952658891678, .98022425174713, 1.0199228525162, .97626084089279, .95510673522949, .98353403806686, 1.0380674600601, 1.0068138837814, 1.0267919301987, 1.0435055494308, .94986528158188, .87152636051178, .89823776483536, .82833498716354, .72372996807098, .75921636819839, .74277937412262, .74440395832062, .80726110935211, .79834908246994, .88314270973206, .92332923412323, 1.0184471607208, 1.12877368927, 1.1288229227066, 1.2057402133942, 1.1317123174667, 1.100532412529, .95145136117935, .81135284900665, .92477059364319, .88128125667572, .92177194356918, .98639768362045, .91746246814728, .84441828727722, .89093261957169, .96059763431549, .97275197505951, 1.0751719474792, 1.1608537435532, 1.124911904335, 1.2485905885696, 1.1829364299774, 1.6815021038055, 1.4374854564667, 1.4024653434753, 1.4807903766632, 1.1158236265182, 1.1908674240112, 1.3569641113281, 1.3532432317734, 1.4080929756165, 1.6949023008347, 1.6488753557205, 2.0886788368225, 1.4827802181244, .51556593179703, .5077338218689, .70120370388031]) y = np.array([ np.nan, 28.979999542236, 29.25457572937, 29.49047088623, 29.474151611328, 29.65891456604, 29.64492225647, 29.864093780518, 29.948677062988, 29.893890380859, 30.00740814209, 30.062122344971, 30.11780166626, 30.301595687866, 30.29793548584, 30.469961166382, 30.524446487427, 30.556753158569, 30.786588668823, 30.840013504028, 31.044549942017, 31.038982391357, 31.105201721191, 31.206655502319, 31.377101898193, 31.476608276367, 31.691576004028, 31.754104614258, 32.002456665039, 32.443950653076, 32.613296508789, 33.048110961914, 33.073429107666, 33.27583694458, 33.593231201172, 33.907779693604, 34.33532333374, 34.642997741699, 35.180164337158, 35.595882415771, 36.009033203125, 36.650783538818, 37.170337677002, 37.686695098877, 38.315757751465, 38.94006729126, 39.329658508301, 39.836326599121, 40.341899871826, 40.500438690186, 41.011878967285, 41.290702819824, 41.572982788086, 41.85816192627, 42.14575958252, 42.550758361816, 43.070316314697, 44.163555145264, 44.664680480957, 46.203994750977, 47.489795684814, 48.876949310303, 50.134490966797, 51.959503173828, 53.302585601807, 53.946380615234, 54.945484161377, 55.829364776611, 56.715869903564, 56.912334442139, 57.817970275879, 58.722682952881, 59.511249542236, 60.878559112549, 61.657997131348, 62.44079208374, 63.572528839111, 64.814453125, 66.511016845703, 68.19181060791, 69.628646850586, 71.867088317871, 74.429039001465, 76.733764648438, 79.713638305664, 82.779487609863, 84.433738708496, 86.55696105957, 89.137893676758, 91.01335144043, 93.469696044922, 95.339958190918, 96.176712036133, 96.578636169434, 99.205047607422, 99.618682861328, 99.139770507813, 99.975563049316, 100.9372177124, 101.9051361084, 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.47569087147713, .48725643754005, .49617394804955, .53683114051819, .55128628015518, .56243091821671, .58791494369507, .60756206512451, .58892780542374, .59145200252533, .59339815378189, .54422444105148, .55698639154434, .53304374217987, .51458370685577, .50035130977631, .48937830328941, .49780988693237, .52120143175125, .62369203567505, .6182547211647, .76608312129974, .84627467393875, .92499214410782, .96879118680954, 1.0870156288147, 1.1105998754501, 1.0274360179901, 1.013991355896, .98673474788666, .96571969985962, .84817039966583, .85888928174973, .86715340614319, .85663330554962, .93297851085663, .90738350152969, .88765007257462, .92311006784439, .96734017133713, 1.0690053701401, 1.1473876237869, 1.1740373373032, 1.3128218650818, 1.4704967737198, 1.5582785606384, 1.7273052930832, 1.8745132684708, 1.7853132486343, 1.7841064929962, 1.850741147995, 1.800768494606, 1.8466963768005, 1.7976499795914, 1.6078149080276, 1.3938897848129, 1.5498898029327, 1.3492304086685, 1.059396147728, 1.0217411518097, 1.0096007585526, 1.0002405643463, 1.0436969995499, 1.0603114366531, 1.0055546760559, .99712115526199, .92305397987366, .9841884970665, .92997401952744, .90506774187088, .9872123003006, .61137217283249, .65943044424057, .67959040403366, .77959072589874, .87357920408249, .91226226091385, .95897603034973, .96120971441269, .99671375751495, 1.0409790277481, 1.0919979810715, 1.1144404411316, 1.2330915927887, 1.2401138544083, 1.161071896553, 1.3028255701065, 1.2938764095306, 1.3207612037659, 1.5610725879669, 1.4760913848877, 1.258552312851, 1.2090681791306, 1.1540271043777, 1.12848341465, 1.1087870597839, 1.0936040878296, 1.0987877845764, 1.0858948230743, 1.0590622425079, .98770052194595, 1.0002481937408, .94235575199127, .93150353431702, .97381073236465, .9726470708847, .98864215612411, 1.0347559452057, .98585307598114, .96503925323486, .9996662735939, 1.0601476430893, 1.022319316864, 1.043828368187, 1.0604115724564, .95495897531509, .87365657091141, .91232192516327, .84078407287598, .73495537042618, .78849309682846, .77909576892853, .78874284029007, .8637443780899, .8540056347847, .94784545898438, .98641014099121, 1.0837067365646, 1.1925053596497, 1.1750392913818, 1.2460317611694, 1.1487410068512, 1.1075156927109, .94060403108597, .7950227856636, .93615245819092, .89293897151947, .94407802820206, 1.0172899961472, .93860250711441, .86104601621628, .91948908567429, .99833220243454, 1.008442401886, 1.1175880432129, 1.2017351388931, 1.1483734846115, 1.2761443853378, 1.188849568367, 1.7296310663223, 1.4202431440353, 1.3675138950348, 1.445098400116, 1.031960606575, 1.1313284635544, 1.3214453458786, 1.3112732172012, 1.367110490799, 1.674845457077, 1.5979281663895, 2.064112663269, 1.3536450862885, .30015936493874, .36831066012383, .64060544967651]) icstats = np.array([ 202, np.nan, -243.77512585356, 3, 493.55025170713, 503.47505479933]) results = Bunch( llf=llf, nobs=nobs, k=k, k_exog=k_exog, sigma=sigma, chi2=chi2, df_model=df_model, k_ar=k_ar, k_ma=k_ma, params=params, cov_params=cov_params, xb=xb, y=y, resid=resid, yr=yr, mse=mse, stdp=stdp, icstats=icstats ) statsmodels-0.12.2/statsmodels/tsa/tests/results/arima112_css_results.py000066400000000000000000000650461400612667500264740ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch llf = np.array([-244.3852892951]) nobs = np.array([202]) k = np.array([5]) k_exog = np.array([1]) sigma = np.array([.81130812929037]) chi2 = np.array([73901.783883385]) df_model = np.array([3]) k_ar = np.array([1]) k_ma = np.array([2]) params = np.array([ .91963917600489, -.89804855498306, 1.3032353997768, .30230174935463, .65822088065264]) cov_params = np.array([ .00622027554245, .00026933156699, -.00014478009121, -.00010527901395, .00006880952561, .00026933156699, .0023661521973, -.00263264462948, -.00241927046074, -.00069258998629, -.00014478009121, -.00263264462948, .003637275855, .0033625395431, .00072507981262, -.00010527901395, -.00241927046074, .0033625395431, .00312013997649, .00067166747844, .00006880952561, -.00069258998629, .00072507981262, .00067166747844, .00108477120916]).reshape(5, 5) xb = np.array([ .91963917016983, .91963917016983, .69261693954468, .76115423440933, .63710719347, .77478265762329, .61527073383331, .80501782894135, .62182641029358, .72158020734787, .66619211435318, .72980058193207, .64935982227325, .77660953998566, .6069877743721, .79818457365036, .60795724391937, .7583304643631, .68147450685501, .72765469551086, .69699174165726, .69102382659912, .67753201723099, .72617518901825, .69977235794067, .713603079319, .72478419542313, .68503832817078, .75677126646042, .79034942388535, .68609654903412, .83208250999451, .60605573654175, .80849212408066, .69862711429596, .80978256464005, .7383074760437, .78789436817169, .79390448331833, .79169547557831, .76283228397369, .87939429283142, .75783687829971, .85010063648224, .80657452344894, .86508285999298, .72368890047073, .86846202611923, .75351697206497, .74047154188156, .82022970914841, .73184186220169, .7623735666275, .74929028749466, .75702118873596, .79036456346512, .81429827213287, 1.0007030963898, .70464313030243, 1.2375881671906, .82733017206192, 1.1780800819397, .83767229318619, 1.3407131433487, .7835128903389, .99667322635651, .82677388191223, 1.0330017805099, .78713357448578, .80603551864624, .91298097372055, .94862020015717, .83088356256485, 1.1405943632126, .72683191299438, 1.0197489261627, .88344657421112, 1.1016070842743, 1.0485582351685, 1.1717364788055, .94894939661026, 1.418029665947, 1.2063212394714, 1.3504880666733, 1.4053744077682, 1.5106836557388, .91192328929901, 1.4546687602997, 1.2100585699081, 1.2459771633148, 1.2914154529572, 1.1733019351959, .80550068616867, .88859277963638, 1.5257360935211, .49089628458023, .75268715620041, .92090040445328, .99410575628281, .87882828712463, 1.1253950595856, .89082646369934, .9317963719368, .90858340263367, .82737028598785, 1.0978132486343, .74325948953629, .98125350475311, 1.0478370189667, .03625157848001, 1.3422871828079, .51377469301224, 1.3643686771393, .70055514574051, 1.2559896707535, .71517109870911, 1.1997950077057, .75360465049744, 1.2862613201141, .79965251684189, 1.2606881856918, 1.018030166626, 1.1752370595932, .69517260789871, 1.597958445549, .65335071086884, 1.4763361215591, 1.2708671092987, 1.0432199239731, .561203956604, 1.2630445957184, .66821777820587, 1.2384748458862, .70777904987335, 1.2246036529541, .75373476743698, 1.199233174324, .69312900304794, 1.0659650564194, .80386221408844, .99243313074112, .78622406721115, 1.1766475439072, .74267518520355, 1.1679803133011, .85658311843872, .99335825443268, .79920876026154, 1.1595865488052, .92043119668961, .98299539089203, .94316083192825, 1.0661553144455, .6393609046936, .9456650018692, .91597771644592, .80332309007645, .65838772058487, 1.1093089580536, .68860310316086, 1.0485997200012, .89771980047226, .94581252336502, 1.0480616092682, 1.0014315843582, 1.1307729482651, 1.1770483255386, .89873492717743, 1.2652103900909, .66434383392334, 1.1431220769882, .44322970509529, .9269899725914, 1.0786435604095, .82789659500122, 1.0368362665176, 1.0712716579437, .70438456535339, .88966482877731, 1.009087562561, 1.0887442827225, .88976800441742, 1.2735350131989, 1.0157470703125, .95522791147232, 1.3003809452057, .73179203271866, 2.4736785888672, -.25176140666008, 1.9082181453705, .53501582145691, .7591078877449, 1.0281100273132, 1.6240043640137, .60095232725143, 1.6211705207825, 1.344465970993, 1.124480009079, 2.1775946617126, -.71973150968552, -.37754261493683, 1.2329530715942, 1.127131819725]) y = np.array([ np.nan, 29.899639129639, 29.842617034912, 30.111154556274, 30.007108688354, 30.314783096313, 30.165269851685, 30.555017471313, 30.461826324463, 30.531579971313, 30.586193084717, 30.709800720215, 30.689361572266, 30.986608505249, 30.826986312866, 31.178184509277, 31.047958374023, 31.238330841064, 31.371475219727, 31.477655410767, 31.636991500854, 31.641023635864, 31.697532653809, 31.846176147461, 31.979772567749, 32.093601226807, 32.304782867432, 32.335037231445, 32.636772155762, 33.070346832275, 33.136096954346, 33.682079315186, 33.506057739258, 33.908489227295, 34.098628997803, 34.509784698486, 34.838306427002, 35.187896728516, 35.693904876709, 36.091693878174, 36.462833404541, 37.179393768311, 37.557834625244, 38.150100708008, 38.706577301025, 39.365081787109, 39.623691558838, 40.268463134766, 40.653518676758, 40.840469360352, 41.420227050781, 41.631843566895, 41.962375640869, 42.249290466309, 42.557022094727, 42.990364074707, 43.514297485352, 44.700702667236, 44.904644012451, 46.837585449219, 47.627330780029, 49.278079986572, 50.137672424316, 52.340713500977, 53.083511352539, 53.996673583984, 54.826774597168, 55.933002471924, 56.587131500244, 56.906032562256, 57.912979125977, 58.848621368408, 59.530883789063, 61.140594482422, 61.526832580566, 62.619747161865, 63.583446502686, 65.001609802246, 66.548561096191, 68.27173614502, 69.448951721191, 72.018028259277, 74.206321716309, 76.550483703613, 79.405372619629, 82.410682678223, 83.511924743652, 86.154663085938, 88.410057067871, 90.345977783203, 92.791412353516, 94.573303222656, 95.205505371094, 95.888595581055, 99.025733947754, 98.590896606445, 98.652687072754, 99.720901489258, 100.79410552979, 101.67883300781, 103.22539520264, 104.19082641602, 105.03179168701, 106.00858306885, 106.52736663818, 108.09781646729, 108.44326019287, 109.48125457764, 110.94783782959, 108.73625183105, 110.84228515625, 110.71376800537, 112.7643737793, 113.40055084229, 115.05599212646, 115.71517181396, 117.19979858398, 117.95359802246, 119.78626251221, 120.69965362549, 122.46068572998, 124.1180267334, 125.67523956299, 126.09517669678, 129.09796142578, 129.55334472656, 131.97633361816, 134.67086791992, 135.74320983887, 135.66120910645, 137.46304321289, 137.86820983887, 139.53848266602, 140.10777282715, 141.724609375, 142.45373535156, 143.99923706055, 144.49313354492, 145.56596374512, 146.40386962891, 147.29243469238, 147.98622131348, 149.57664489746, 150.14266967773, 151.66798400879, 152.65658569336, 153.59336853027, 154.29920959473, 155.85958862305, 157.02043151855, 157.98300170898, 159.14315795898, 160.46615600586, 160.53935241699, 161.34565734863, 162.41598510742, 162.80332946777, 162.85838317871, 164.30931091309, 164.5885925293, 165.74859619141, 166.7977142334, 167.64581298828, 169.14807128906, 170.30143737793, 172.03076171875, 173.87704467773, 174.79872131348, 176.86521911621, 177.06433105469, 178.54312133789, 178.0432434082, 178.62698364258, 180.37864685059, 180.82789611816, 182.23683166504, 183.67127990723, 183.90438842773, 184.58966064453, 185.90908813477, 187.38874816895, 188.2897644043, 190.37353515625, 191.81575012207, 192.75523376465, 195.10038757324, 195.43179321289, 201.67367553711, 199.14823913574, 202.60821533203, 203.23501586914, 202.65910339355, 204.60211181641, 207.54400634766, 207.93894958496, 210.75416564941, 213.83946228027, 215.12147521973, 220.78759765625, 216.16928100586, 211.79644775391, 213.90396118164, 215.59613037109]) resid = np.array([ np.nan, -.74963909387589, -.49261617660522, -.74115377664566, -.46710711717606, -.76478433609009, -.41527000069618, -.71501767635345, -.65182709693909, -.61157959699631, -.6061926484108, -.66979920864105, -.47936165332794, -.76660931110382, -.44698792695999, -.73818320035934, -.56795823574066, -.54832947254181, -.62147504091263, -.53765416145325, -.68699151277542, -.6210241317749, -.57753163576126, -.56617534160614, -.59977388381958, -.51360231637955, -.65478450059891, -.45503878593445, -.35677161812782, -.62034744024277, -.2860988676548, -.78207945823669, -.40605875849724, -.50848907232285, -.39862787723541, -.40978488326073, -.43830442428589, -.28789436817169, -.39390674233437, -.3916939496994, -.16283383965492, -.37939432263374, -.25783684849739, -.25009834766388, -.20657606422901, -.46508130431175, -.22368888556957, -.36846202611923, -.55352002382278, -.24047155678272, -.52022665739059, -.43184259533882, -.46237435936928, -.44929105043411, -.35701966285706, -.29036456346512, .1857016980648, -.50070303678513, .69535458087921, -.03758737072349, .47266906499863, .02192067168653, .86232846975327, -.04071394726634, -.08351214230061, .0033267585095, .07322765141726, -.13300403952599, -.48713436722755, .09396601468325, -.01297946088016, -.14862097799778, .4691156744957, -.34059509634972, .073167309165, .08025334775448, .31655418872833, .49839133024216, .55144023895264, .22826506197453, 1.1510490179062, .9819718003273, .9936757683754, 1.4495149850845, 1.4946271181107, .18931329250336, 1.1880751848221, 1.0453312397003, .68994289636612, 1.1540243625641, .60858601331711, -.17330189049244, -.20550219714642, 1.611407160759, -.92573761940002, -.69089323282242, .14731439948082, .07909959554672, .00589422974735, .42116710543633, .07460948079824, -.09083105623722, .06820363551378, -.30858492851257, .47263273596764, -.39781630039215, .05674355849624, .41874802112579, -2.2478415966034, .76375144720078, -.64229023456573, .68622988462448, -.06437320262194, .39945095777512, -.0559926815331, .28482890129089, .00020190737268, .54639840126038, .11374024301767, .50034290552139, .63931334018707, .38197138905525, -.27523550391197, 1.404825925827, -.1979645639658, .94665539264679, 1.4236577749252, .02913599461317, -.643210709095, .53878688812256, -.26304465532303, .43178829550743, -.13848400115967, .39222705364227, -.02460673451424, .34627133607864, -.19923311471939, .00686796056107, .03404098749161, -.10386525094509, -.09243924915791, .41377285122871, -.17664749920368, .35733091831207, .13202276825905, -.05658006668091, -.09336434304714, .40078815817833, .24042254686356, -.02043732441962, .217001542449, .25683608651161, -.56615537405014, -.13936093449593, .15434110164642, -.41597774624825, -.60332614183426, .34161224961281, -.40931203961372, .11139994114637, .15139718353748, -.09771674126387, .45419663190842, .15193535387516, .5985592007637, .66923010349274, .02294866926968, .80127727985382, -.46522265672684, .33565619587898, -.94310986995697, -.34323886036873, .67301613092422, -.37864658236504, .37210035324097, .3631728887558, -.47128081321716, -.20438456535339, .3103321492672, .3909215927124, .01124659087509, .81024420261383, .42646199464798, -.01574708521366, 1.044772028923, -.40038701891899, 3.768208026886, -2.273681640625, 1.5517644882202, .09178187698126, -1.3350188732147, .91490334272385, 1.317883014679, -.20600511133671, 1.1940457820892, 1.7408289909363, .15753293037415, 3.4885265827179, -3.8985877037048, -3.9952800273895, .87455189228058, .56503582000732, .78886848688126]) yr = np.array([ np.nan, -.74963909387589, -.49261617660522, -.74115377664566, -.46710711717606, -.76478433609009, -.41527000069618, -.71501767635345, -.65182709693909, -.61157959699631, -.6061926484108, -.66979920864105, -.47936165332794, -.76660931110382, -.44698792695999, -.73818320035934, -.56795823574066, -.54832947254181, -.62147504091263, -.53765416145325, 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.31655418872833, .49839133024216, .55144023895264, .22826506197453, 1.1510490179062, .9819718003273, .9936757683754, 1.4495149850845, 1.4946271181107, .18931329250336, 1.1880751848221, 1.0453312397003, .68994289636612, 1.1540243625641, .60858601331711, -.17330189049244, -.20550219714642, 1.611407160759, -.92573761940002, -.69089323282242, .14731439948082, .07909959554672, .00589422974735, .42116710543633, .07460948079824, -.09083105623722, .06820363551378, -.30858492851257, .47263273596764, -.39781630039215, .05674355849624, .41874802112579, -2.2478415966034, .76375144720078, -.64229023456573, .68622988462448, -.06437320262194, .39945095777512, -.0559926815331, .28482890129089, .00020190737268, .54639840126038, .11374024301767, .50034290552139, .63931334018707, .38197138905525, -.27523550391197, 1.404825925827, -.1979645639658, .94665539264679, 1.4236577749252, .02913599461317, -.643210709095, .53878688812256, -.26304465532303, .43178829550743, -.13848400115967, .39222705364227, -.02460673451424, .34627133607864, -.19923311471939, .00686796056107, .03404098749161, -.10386525094509, -.09243924915791, .41377285122871, -.17664749920368, .35733091831207, .13202276825905, -.05658006668091, -.09336434304714, .40078815817833, .24042254686356, -.02043732441962, .217001542449, .25683608651161, -.56615537405014, -.13936093449593, .15434110164642, -.41597774624825, -.60332614183426, .34161224961281, -.40931203961372, .11139994114637, .15139718353748, -.09771674126387, .45419663190842, .15193535387516, .5985592007637, .66923010349274, .02294866926968, .80127727985382, -.46522265672684, .33565619587898, -.94310986995697, -.34323886036873, .67301613092422, -.37864658236504, .37210035324097, .3631728887558, -.47128081321716, -.20438456535339, .3103321492672, .3909215927124, .01124659087509, .81024420261383, .42646199464798, -.01574708521366, 1.044772028923, -.40038701891899, 3.768208026886, -2.273681640625, 1.5517644882202, .09178187698126, -1.3350188732147, .91490334272385, 1.317883014679, -.20600511133671, 1.1940457820892, 1.7408289909363, .15753293037415, 3.4885265827179, -3.8985877037048, -3.9952800273895, .87455189228058, .56503582000732, .78886848688126]) mse = np.array([ 1.8363103866577, .82643759250641, .69298559427261, .67553198337555, .67162227630615, .67045229673386, .66999220848083, .66973727941513, .66954612731934, .66937738656998, .66921871900558, .66906636953354, .66891890764236, .66877597570419, .66863715648651, .66850233078003, .66837131977081, .66824388504028, .6681199669838, .66799944639206, .6678820848465, .66776782274246, .66765648126602, .66754806041718, .66744232177734, .66733926534653, .66723877191544, .66714072227478, .66704499721527, .66695153713226, .66686034202576, .66677123308182, .66668421030045, .66659909486771, .66651594638824, .66643464565277, .66635513305664, .66627734899521, .66620123386383, .66612672805786, .6660538315773, .66598242521286, .66591250896454, .66584402322769, .66577690839767, .66571110486984, .66564667224884, .66558349132538, .66552156209946, .66546076536179, .66540116071701, .66534268856049, .66528534889221, .6652290225029, .66517376899719, .6651194691658, .66506624221802, .6650139093399, .66496247053146, .66491198539734, .66486239433289, .66481363773346, .6647657752037, .66471868753433, .66467237472534, .66462683677673, .66458207368851, .66453808546066, .66449475288391, .6644521355629, .66441023349762, .66436898708344, .66432839632034, .66428846120834, .66424912214279, .66421037912369, .66417229175568, .66413474082947, .66409778594971, .66406136751175, .66402548551559, .66399013996124, .66395533084869, .6639209985733, .66388720273972, .66385388374329, .66382104158401, .66378861665726, .6637567281723, .66372525691986, .66369420289993, .66366362571716, .66363340616226, .66360366344452, .66357427835464, .66354531049728, .66351670026779, .66348850727081, .6634606719017, .66343319416046, .66340607404709, .66337931156158, .66335290670395, .66332685947418, .66330111026764, .66327565908432, .66325056552887, .66322582960129, .66320133209229, .66317713260651, .6631532907486, .66312968730927, .66310638189316, .66308337450027, .66306066513062, .66303819417953, .66301596164703, .66299402713776, .6629723906517, .66295093297958, .66292977333069, .66290885210037, .66288816928864, .66286766529083, .66284745931625, .66282749176025, .66280770301819, .6627881526947, .66276878118515, .66274970769882, .66273081302643, .66271209716797, .66269356012344, .6626752614975, .66265720129013, .66263926029205, .66262155771255, .66260403394699, .66258668899536, .66256952285767, .66255259513855, .66253578662872, .66251915693283, .66250270605087, .6624863743782, .66247028112411, .66245430707932, .66243851184845, .66242289543152, .66240739822388, .66239207983017, .6623769402504, .66236186027527, .66234701871872, .66233229637146, .66231769323349, .66230326890945, .66228896379471, .66227477788925, .66226077079773, .6622468829155, .66223311424255, .6622194647789, .66220593452454, .66219258308411, .66217935085297, .66216617822647, .66215318441391, .66214030981064, .66212749481201, .66211485862732, .66210234165192, .66208988428116, .66207760572433, .66206538677216, .66205328702927, .66204130649567, .66202944517136, .66201764345169, .66200596094131, .66199439764023, .66198295354843, .66197156906128, .66196030378342, .66194915771484, .66193807125092, .66192710399628, .66191619634628, .66190540790558, .66189467906952, .66188406944275, .66187357902527, .66186314821243, .66185277700424, .66184252500534, .66183233261108, .66182225942612, .66181224584579, .66180229187012, .66179245710373, .66178268194199, .66177302598953, .66176337003708]) stdp = np.array([ .91963917016983, .91963917016983, .69261693954468, .76115423440933, .63710719347, .77478265762329, .61527073383331, .80501782894135, .62182641029358, .72158020734787, .66619211435318, .72980058193207, .64935982227325, .77660953998566, .6069877743721, .79818457365036, .60795724391937, .7583304643631, .68147450685501, .72765469551086, .69699174165726, .69102382659912, .67753201723099, .72617518901825, .69977235794067, .713603079319, .72478419542313, .68503832817078, .75677126646042, .79034942388535, .68609654903412, .83208250999451, .60605573654175, .80849212408066, .69862711429596, .80978256464005, .7383074760437, .78789436817169, .79390448331833, .79169547557831, .76283228397369, .87939429283142, .75783687829971, .85010063648224, .80657452344894, .86508285999298, .72368890047073, .86846202611923, .75351697206497, .74047154188156, .82022970914841, .73184186220169, .7623735666275, .74929028749466, .75702118873596, .79036456346512, .81429827213287, 1.0007030963898, .70464313030243, 1.2375881671906, .82733017206192, 1.1780800819397, .83767229318619, 1.3407131433487, .7835128903389, .99667322635651, .82677388191223, 1.0330017805099, .78713357448578, .80603551864624, .91298097372055, .94862020015717, .83088356256485, 1.1405943632126, .72683191299438, 1.0197489261627, .88344657421112, 1.1016070842743, 1.0485582351685, 1.1717364788055, .94894939661026, 1.418029665947, 1.2063212394714, 1.3504880666733, 1.4053744077682, 1.5106836557388, .91192328929901, 1.4546687602997, 1.2100585699081, 1.2459771633148, 1.2914154529572, 1.1733019351959, .80550068616867, .88859277963638, 1.5257360935211, .49089628458023, .75268715620041, .92090040445328, .99410575628281, .87882828712463, 1.1253950595856, .89082646369934, .9317963719368, .90858340263367, .82737028598785, 1.0978132486343, .74325948953629, .98125350475311, 1.0478370189667, .03625157848001, 1.3422871828079, .51377469301224, 1.3643686771393, .70055514574051, 1.2559896707535, .71517109870911, 1.1997950077057, .75360465049744, 1.2862613201141, .79965251684189, 1.2606881856918, 1.018030166626, 1.1752370595932, .69517260789871, 1.597958445549, .65335071086884, 1.4763361215591, 1.2708671092987, 1.0432199239731, .561203956604, 1.2630445957184, .66821777820587, 1.2384748458862, .70777904987335, 1.2246036529541, .75373476743698, 1.199233174324, .69312900304794, 1.0659650564194, .80386221408844, .99243313074112, .78622406721115, 1.1766475439072, .74267518520355, 1.1679803133011, .85658311843872, .99335825443268, .79920876026154, 1.1595865488052, .92043119668961, .98299539089203, .94316083192825, 1.0661553144455, .6393609046936, .9456650018692, .91597771644592, .80332309007645, .65838772058487, 1.1093089580536, .68860310316086, 1.0485997200012, .89771980047226, .94581252336502, 1.0480616092682, 1.0014315843582, 1.1307729482651, 1.1770483255386, .89873492717743, 1.2652103900909, .66434383392334, 1.1431220769882, .44322970509529, .9269899725914, 1.0786435604095, .82789659500122, 1.0368362665176, 1.0712716579437, .70438456535339, .88966482877731, 1.009087562561, 1.0887442827225, .88976800441742, 1.2735350131989, 1.0157470703125, .95522791147232, 1.3003809452057, .73179203271866, 2.4736785888672, -.25176140666008, 1.9082181453705, .53501582145691, .7591078877449, 1.0281100273132, 1.6240043640137, .60095232725143, 1.6211705207825, 1.344465970993, 1.124480009079, 2.1775946617126, -.71973150968552, -.37754261493683, 1.2329530715942, 1.127131819725]) icstats = np.array([ 202, np.nan, -244.3852892951, 5, 498.7705785902, 515.31191707721]) results = Bunch( llf=llf, nobs=nobs, k=k, k_exog=k_exog, sigma=sigma, chi2=chi2, df_model=df_model, k_ar=k_ar, k_ma=k_ma, params=params, cov_params=cov_params, xb=xb, y=y, resid=resid, yr=yr, mse=mse, stdp=stdp, icstats=icstats ) statsmodels-0.12.2/statsmodels/tsa/tests/results/arima112_results.py000066400000000000000000000650501400612667500256170ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch llf = np.array([-245.40783909604]) nobs = np.array([202]) k = np.array([5]) k_exog = np.array([1]) sigma = np.array([.8100467417583]) chi2 = np.array([2153.20304012]) df_model = np.array([3]) k_ar = np.array([1]) k_ma = np.array([2]) params = np.array([ .92817025087557, -.89593490671979, 1.3025011610587, .30250063082791, .8100467417583]) cov_params = np.array([ .00638581549851, .0001858475428, 2.8222806545671, .8538806860364, -1.1429127085819, .0001858475428, .00132037832566, -.14420925344502, -.04447007102804, .0576156187095, 2.8222806545671, -.14420925344502, 40397.568324803, 12222.977216556, -16359.547340433, .8538806860364, -.04447007102804, 12222.977216556, 3698.2722243412, -4949.8609964351, -1.1429127085819, .0576156187095, -16359.547340433, -4949.8609964351, 6625.0231409853]).reshape(5, 5) xb = np.array([ .92817026376724, .92817026376724, .69511789083481, .77192437648773, .66135895252228, .77525061368942, .64687132835388, .79659670591354, .65842008590698, .71215486526489, .69971066713333, .72092038393021, .68201982975006, .76510280370712, .64253836870193, .78239262104034, .64609551429749, .74087703227997, .71774411201477, .7119727730751, .73067259788513, .67785596847534, .70898467302322, .71334755420685, .72984194755554, .7017787694931, .75292426347733, .67507487535477, .78219056129456, .78040039539337, .71250075101852, .82028061151505, .63505899906158, .79452306032181, .72773635387421, .79555094242096, .76685506105423, .77427339553833, .82101213932037, .77917188405991, .78917801380157, .86641925573349, .78457218408585, .83697980642319, .83281791210175, .85224026441574, .75030690431595, .8551008105278, .78025943040848, .72790426015854, .84552866220474, .72061747312546, .78669738769531, .73868823051453, .78071022033691, .78002023696899, .83737623691559, .98988044261932, .72882527112961, 1.2245427370071, .85331875085831, 1.1637357473373, .86477434635162, 1.3248475790024, .81245219707489, .98008638620377, .85591268539429, 1.0162551403046, .8165408372879, .78947591781616, .94166398048401, .93266606330872, .85924750566483, 1.1245046854019, .75576168298721, 1.0030617713928, .91267073154449, 1.0848042964935, 1.0778224468231, 1.1551086902618, .97817331552505, 1.4012540578842, 1.2360861301422, 1.3335381746292, 1.4352362155914, 1.4941285848618, .9415163397789, 1.437669634819, 1.2404690980911, 1.2285294532776, 1.3219480514526, 1.1560415029526, .83524394035339, .87116771936417, 1.5561962127686, .47358739376068, .78093349933624, .90549737215042, 1.0217791795731, .86397403478622, 1.1526786088943, .87662625312805, .95803648233414, .89513635635376, .85281348228455, 1.0852742195129, .76808404922485, .96872144937515, 1.0732915401459, .02145584858954, 1.3687089681625, .50049883127213, 1.3895837068558, .6889950633049, 1.2795144319534, .7050421833992, 1.2218985557556, .74481928348541, 1.3074514865875, .7919961810112, 1.2807723283768, 1.0120536088943, 1.1938916444778, .68923074007034, 1.6174983978271, .64740318059921, 1.4949930906296, 1.2678960561752, 1.0586776733398, .55762887001038, 1.2790743112564, .66515874862671, 1.2538269758224, .70554333925247, 1.2391568422318, .75241559743881, 1.2129040956497, .69235223531723, 1.0785228013992, .8043577671051, 1.0037930011749, .78750842809677, 1.1880930662155, .74399447441101, 1.1791603565216, .85870295763016, 1.0032330751419, .8019300699234, 1.1696527004242, .92376220226288, .99186056852341, .94733852148056, 1.0748032331467, .64247089624405, .95419937372208, .92043441534042, .8104555606842, .66252142190933, 1.1178470849991, .69223344326019, 1.0570795536041, .90239083766937, .95320242643356, 1.0541093349457, 1.0082466602325, 1.1376332044601, 1.1841852664948, .90440809726715, 1.2733660936356, .66835701465607, 1.1515763998032, .44600257277489, .93500959873199, 1.0847823619843, .83353632688522, 1.0442448854446, 1.077241897583, .71010553836823, .89557945728302, 1.0163468122482, 1.094814658165, .89641278982162, 1.2808450460434, 1.0223702192307, .96094745397568, 1.309353351593, .73499941825867, 2.4902238845825, -.2579345703125, 1.9272556304932, .53125941753387, .7708500623703, 1.0312130451202, 1.6360099315643, .6022145152092, 1.6338716745377, 1.3494771718979, 1.1322995424271, 2.1901025772095, -.72639065980911, -.37026473879814, 1.2391144037247, 1.1353877782822]) y = np.array([ np.nan, 29.908170700073, 29.84511756897, 30.121925354004, 30.031360626221, 30.315252304077, 30.196870803833, 30.5465965271, 30.498420715332, 30.52215385437, 30.619710922241, 30.70092010498, 30.722021102905, 30.975101470947, 30.862537384033, 31.162391662598, 31.086095809937, 31.220876693726, 31.407745361328, 31.461973190308, 31.670673370361, 31.627857208252, 31.728984832764, 31.833349227905, 32.009841918945, 32.08177947998, 32.33292388916, 32.325073242188, 32.662189483643, 33.060398101807, 33.162502288818, 33.670280456543, 33.535060882568, 33.894519805908, 34.127738952637, 34.495552062988, 34.866851806641, 35.17427444458, 35.721012115479, 36.079170227051, 36.489177703857, 37.16641998291, 37.584571838379, 38.136978149414, 38.732818603516, 39.352241516113, 39.65030670166, 40.255104064941, 40.68025970459, 40.827903747559, 41.445526123047, 41.620620727539, 41.986698150635, 42.238689422607, 42.580707550049, 42.98002243042, 43.537376403809, 44.689880371094, 44.928825378418, 46.824542999268, 47.653316497803, 49.263732910156, 50.164772033691, 52.324848175049, 53.112449645996, 53.980087280273, 54.855911254883, 55.916255950928, 56.616539001465, 56.889472961426, 57.941665649414, 58.832668304443, 59.55924987793, 61.124504089355, 61.555759429932, 62.603061676025, 63.612670898438, 64.984802246094, 66.577819824219, 68.255104064941, 69.478172302246, 72.001251220703, 74.236083984375, 76.533538818359, 79.435234069824, 82.39412689209, 83.541511535645, 86.137664794922, 88.440467834473, 90.32852935791, 92.82194519043, 94.556045532227, 95.235244750977, 95.871170043945, 99.056198120117, 98.573585510254, 98.680938720703, 99.705497741699, 100.82178497314, 101.66397857666, 103.25267791748, 104.17662811279, 105.0580368042, 105.99513244629, 106.55281066895, 108.08527374268, 108.46807861328, 109.46871948242, 110.97328948975, 108.72145080566, 110.86870574951, 110.70049285889, 112.78958892822, 113.38899230957, 115.0795211792, 115.70503997803, 117.22190093994, 117.94481658936, 119.80744934082, 120.69200134277, 122.48076629639, 124.11205291748, 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stdp = np.array([ .92817026376724, .92817026376724, .69511789083481, .77192437648773, .66135895252228, .77525061368942, .64687132835388, .79659670591354, .65842008590698, .71215486526489, .69971066713333, .72092038393021, .68201982975006, .76510280370712, .64253836870193, .78239262104034, .64609551429749, .74087703227997, .71774411201477, .7119727730751, .73067259788513, .67785596847534, .70898467302322, .71334755420685, .72984194755554, .7017787694931, .75292426347733, .67507487535477, .78219056129456, .78040039539337, .71250075101852, .82028061151505, .63505899906158, .79452306032181, .72773635387421, .79555094242096, .76685506105423, .77427339553833, .82101213932037, .77917188405991, .78917801380157, .86641925573349, .78457218408585, .83697980642319, .83281791210175, .85224026441574, .75030690431595, .8551008105278, .78025943040848, .72790426015854, .84552866220474, .72061747312546, .78669738769531, .73868823051453, .78071022033691, .78002023696899, .83737623691559, .98988044261932, 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.74481928348541, 1.3074514865875, .7919961810112, 1.2807723283768, 1.0120536088943, 1.1938916444778, .68923074007034, 1.6174983978271, .64740318059921, 1.4949930906296, 1.2678960561752, 1.0586776733398, .55762887001038, 1.2790743112564, .66515874862671, 1.2538269758224, .70554333925247, 1.2391568422318, .75241559743881, 1.2129040956497, .69235223531723, 1.0785228013992, .8043577671051, 1.0037930011749, .78750842809677, 1.1880930662155, .74399447441101, 1.1791603565216, .85870295763016, 1.0032330751419, .8019300699234, 1.1696527004242, .92376220226288, .99186056852341, .94733852148056, 1.0748032331467, .64247089624405, .95419937372208, .92043441534042, .8104555606842, .66252142190933, 1.1178470849991, .69223344326019, 1.0570795536041, .90239083766937, .95320242643356, 1.0541093349457, 1.0082466602325, 1.1376332044601, 1.1841852664948, .90440809726715, 1.2733660936356, .66835701465607, 1.1515763998032, .44600257277489, .93500959873199, 1.0847823619843, .83353632688522, 1.0442448854446, 1.077241897583, .71010553836823, .89557945728302, 1.0163468122482, 1.094814658165, .89641278982162, 1.2808450460434, 1.0223702192307, .96094745397568, 1.309353351593, .73499941825867, 2.4902238845825, -.2579345703125, 1.9272556304932, .53125941753387, .7708500623703, 1.0312130451202, 1.6360099315643, .6022145152092, 1.6338716745377, 1.3494771718979, 1.1322995424271, 2.1901025772095, -.72639065980911, -.37026473879814, 1.2391144037247, 1.1353877782822]) icstats = np.array([ 202, np.nan, -245.40783909604, 5, 500.81567819208, 517.35701667909]) results = Bunch( llf=llf, nobs=nobs, k=k, k_exog=k_exog, sigma=sigma, chi2=chi2, df_model=df_model, k_ar=k_ar, k_ma=k_ma, params=params, cov_params=cov_params, xb=xb, y=y, resid=resid, yr=yr, mse=mse, stdp=stdp, icstats=icstats ) statsmodels-0.12.2/statsmodels/tsa/tests/results/arima112nc_css_results.py000066400000000000000000000641561400612667500270160ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch llf = np.array([-239.75290561974]) nobs = np.array([202]) k = np.array([4]) k_exog = np.array([1]) sigma = np.array([.79291203639424]) chi2 = np.array([35036.682546665]) df_model = np.array([3]) k_ar = np.array([1]) k_ma = np.array([2]) params = np.array([ .99954097483478, -.69022779461512, -.20477682541104, .62870949745886]) cov_params = np.array([ .00007344276568, -.00016074342677, -.00018478942445, 8.040251506e-06, -.00016074342677, .00094099304774, .00017233777676, -.0000145011098, -.00018478942445, .00017233777676, .00103352686916, .00030686101903, 8.040251506e-06, -.0000145011098, .00030686101903, .00067796985496]).reshape(4, 4) xb = np.array([ 0, 0, .05104803293943, .06663129478693, .02164618112147, .0773858949542, .02606418170035, .09391833096743, .05710592120886, .03083370067179, .07319989800453, .05287836492062, .05776296555996, .09105986356735, .04293738678098, .09576436132193, .06068528071046, .06157376244664, .11172580718994, .06527806818485, .11443704366684, .05653077363968, .08205550909042, .08481238037348, .10436166077852, .0875685736537, .12320486456156, .08366665989161, .13979130983353, .1902572363615, .1306214183569, .21803694963455, .11079790443182, .17274764180183, .1937662512064, .20047917962074, .24034893512726, .21783453226089, .29279819130898, .26804205775261, .28678458929062, .35651323199272, .33659368753433, .35760068893433, .39895334839821, .41131839156151, .36645981669426, .40991494059563, .41024547815323, .32657703757286, .42312324047089, .34933325648308, .35912537574768, .35077446699142, .34701564908028, .37364318966866, .40170526504517, .56070649623871, .41915491223335, .73478156328201, .67748892307281, .7744625210762, .77825599908829, .97586625814438, .88692498207092, .76232481002808, .87376874685287, .83281141519547, .84783887863159, .66423743963242, .84904235601425, .81613594293594, .80033475160599, .95782464742661, .80624777078629, .83626395463943, .91873735189438, .95130664110184, 1.0939226150513, 1.1171194314957, 1.1004731655121, 1.3512066602707, 1.4703129529953, 1.4805699586868, 1.7385860681534, 1.8268398046494, 1.5489361286163, 1.7446503639221, 1.864644408226, 1.7200467586517, 1.9223358631134, 1.775306224823, 1.5392524003983, 1.4067870378494, 1.9366238117218, 1.2984343767166, 1.1080636978149, 1.3500427007675, 1.2837564945221, 1.2670782804489, 1.3347851037979, 1.2857422828674, 1.1625040769577, 1.2111755609512, 1.0548515319824, 1.2553508281708, 1.0327949523926, 1.0740388631821, 1.222040772438, .40555971860886, 1.0233588218689, .84209614992142, 1.0186324119568, 1.0319027900696, .99487775564194, 1.0439211130142, .98785293102264, 1.0620124340057, 1.0916963815689, 1.1378232240677, 1.1243290901184, 1.3305295705795, 1.1925677061081, 1.0872994661331, 1.4599523544312, 1.2333589792252, 1.3584797382355, 1.7595859766006, 1.3009568452835, 1.1157965660095, 1.2948887348175, 1.2063180208206, 1.2332669496536, 1.2132470607758, 1.2049551010132, 1.2260574102402, 1.1875206232071, 1.1547852754593, 1.0519831180573, 1.1594845056534, 1.0069926977158, 1.0675266981125, 1.1299223899841, 1.0620901584625, 1.0999356508255, 1.1535499095917, 1.0026944875717, 1.0428657531738, 1.1120204925537, 1.1684119701385, 1.0258769989014, 1.1342295408249, 1.1183958053589, .91313683986664, .91156214475632, 1.0540328025818, .84359037876129, .75758427381516, .96401190757751, .83226495981216, .8759680390358, .98239886760712, .85917687416077, 1.0634194612503, .99442666769028, 1.153311252594, 1.2288066148758, 1.0869039297104, 1.281947016716, 1.0067318677902, 1.1028815507889, .82448446750641, .78489726781845, 1.1850204467773, .86753690242767, 1.0692945718765, 1.1030179262161, .8791960477829, .86451041698456, 1.0455346107483, 1.085998415947, 1.0172398090363, 1.2250980138779, 1.2316122055054, 1.062157869339, 1.3991860151291, 1.0520887374878, 2.2203133106232, .88833123445511, 1.4289729595184, 1.5206423997879, .68520504236221, 1.4659557342529, 1.5350053310394, 1.3178979158401, 1.4888265132904, 1.9698411226273, 1.4406447410583, 2.517040014267, .55537897348404, -.20722626149654, 1.0899519920349, 1.164245724678]) y = np.array([ np.nan, 28.979999542236, 29.201047897339, 29.416631698608, 29.391647338867, 29.617385864258, 29.576063156128, 29.84391784668, 29.897106170654, 29.84083366394, 29.993200302124, 30.032876968384, 30.097763061523, 30.3010597229, 30.262937545776, 30.475763320923, 30.500686645508, 30.541572570801, 30.801725387573, 30.815279006958, 31.054437637329, 31.006530761719, 31.102056503296, 31.20481300354, 31.384363174438, 31.467567443848, 31.703205108643, 31.733665466309, 32.019790649414, 32.47025680542, 32.580623626709, 33.068035125732, 33.010799407959, 33.272747039795, 33.593769073486, 33.900478363037, 34.340347290039, 34.617835998535, 35.192798614502, 35.568042755127, 35.986785888672, 36.656513214111, 37.13659286499, 37.657600402832, 38.29895401001, 38.911319732666, 39.266460418701, 39.809917449951, 40.310245513916, 40.426574707031, 41.023120880127, 41.249336242676, 41.559127807617, 41.850772857666, 42.14701461792, 42.573642730713, 43.101707458496, 44.260707855225, 44.619155883789, 46.334781646729, 47.477489471436, 48.874462127686, 50.078254699707, 51.9758644104, 53.186923980713, 53.762325286865, 54.873767852783, 55.732814788818, 56.647838592529, 56.764236450195, 57.849040985107, 58.716136932373, 59.500335693359, 60.957824707031, 61.606246948242, 62.436264038086, 63.61873626709, 64.85131072998, 66.593925476074, 68.21711730957, 69.600471496582, 71.951202392578, 74.470314025879, 76.680564880371, 79.738586425781, 82.726844787598, 84.148933410645, 86.444648742676, 89.064643859863, 90.820045471191, 93.422332763672, 95.175308227539, 95.939254760742, 96.406784057617, 99.436622619629, 99.398429870605, 99.00806427002, 100.15004730225, 101.08376312256, 102.06707763672, 103.43478393555, 104.58574676514, 105.26250457764, 106.31117248535, 106.75485229492, 108.25534820557, 108.73279571533, 109.57403564453, 111.12203979492, 109.10556030273, 110.52336120605, 111.04209136963, 112.41863250732, 113.73190307617, 114.79488372803, 116.04392242432, 116.98785400391, 118.26200866699, 119.59169769287, 121.03782653809, 122.32432556152, 124.4305267334, 125.69256591797, 126.4873046875, 128.95994567871, 130.13334655762, 131.85847473145, 135.15957641602, 136.00096130371, 136.21580505371, 137.49488830566, 138.40631103516, 139.53326416016, 140.61323547363, 141.70495605469, 142.9260559082, 143.98751831055, 144.95478820801, 145.55198669434, 146.7594909668, 147.30699157715, 148.26751708984, 149.52992248535, 150.46208190918, 151.59992980957, 152.95355224609, 153.60270690918, 154.54286193848, 155.81201171875, 157.2684173584, 158.02587890625, 159.33422851563, 160.51838684082, 160.81312561035, 161.31155395508, 162.55403137207, 162.84359741211, 162.95758056641, 164.16400146484, 164.73225402832, 165.57595825195, 166.88238525391, 167.55917358398, 169.16342163086, 170.29443359375, 172.0532989502, 173.92880249023, 174.9868927002, 176.88195800781, 177.40672302246, 178.50286865234, 178.42448425293, 178.48489379883, 180.48501586914, 180.86753845215, 182.26928710938, 183.70301818848, 184.07919311523, 184.56451416016, 185.94552612305, 187.38600158691, 188.41723632813, 190.32510375977, 192.03161621094, 192.8621673584, 195.19918823242, 195.7520904541, 201.42030334473, 200.28833007813, 202.12896728516, 204.22064208984, 202.58520507813, 205.03996276855, 207.45500183105, 208.65589904785, 210.62182617188, 214.46484375, 215.4376373291, 221.12704467773, 217.44438171387, 211.96676635742, 213.76095581055, 215.63323974609]) resid = np.array([ np.nan, .17000007629395, .14895272254944, -.04663083329797, .14835388958454, -.067387573421, .17393657565117, -.00391817837954, -.08710660785437, .07916691154242, -.01320043392479, .00712300790474, .11223520338535, -.08105963468552, .11706246435642, -.03576298803091, -.0206862706691, .14842723309994, -.05172633752227, .12472246587276, -.104436814785, .01346892025322, .01794487424195, .07518746703863, -.00436318712309, .11243218928576, -.05320516973734, .14633287489414, .26020830869675, -.02025525644422, .26937630772591, -.16803389787674, .08919904381037, .12725540995598, .10623299330473, .1995185315609, .05965411290526, .28216546773911, .10719951242208, .13195945322514, .31321388483047, .14348678290844, .16340629756451, .24240159988403, .20104511082172, -.01131687406451, .13354018330574, .09008505195379, -.21024852991104, .1734229773283, -.12312019616365, -.04933403432369, -.05912613496184, -.05077522993088, .05298588424921, .12635681033134, .59829473495483, -.06070650368929, .98084276914597, .46521919965744, .62251031398773, .42553821206093, .92174476385117, .32413294911385, -.18692423403263, .23767517507076, .02623280882835, .06718628853559, -.54783964157104, .23576405644417, .05095916613936, -.01613672077656, .49966445565224, -.1578253954649, -.00624855514616, .26373836398125, .28126338124275, .64869183301926, .50607579946518, .28288212418556, .99952530860901, 1.0487948656082, .72968405485153, 1.319433093071, 1.1614154577255, -.126842841506, .55106240510941, .75534957647324, .03535716608167, .67995470762253, -.02233435213566, -.775306224823, -.93925392627716, 1.0932129621506, -1.3366253376007, -1.4984313249588, -.20806217193604, -.35004270076752, -.28375649452209, .03291719779372, -.13478049635887, -.48574689030647, -.16250413656235, -.61117708683014, .24515150487423, -.55535387992859, -.23279193043709, .32596263289452, -2.4220454692841, .39444333314896, -.32336190342903, .3579084277153, .28136301040649, .06810333579779, .20511920750141, -.04392115399241, .2121440321207, .23799060285091, .30830511450768, .16217225790024, .77567237615585, .06947190314531, -.29256621003151, 1.012699007988, -.05995841696858, .36664715409279, 1.5415141582489, -.45958289504051, -.90094763040543, -.01580573618412, -.29488867521286, -.10631188750267, -.13327611982822, -.11324090510607, -.00495810527354, -.12605135142803, -.18752062320709, -.45478835701942, .04802301898599, -.45948752760887, -.1069987937808, .13247023522854, -.12992236018181, .0379159450531, .20006743073463, -.35354685783386, -.10270062834024, .15713113546371, .28798860311508, -.26841807365417, .17411996424198, .06576746702194, -.61839586496353, -.41313683986664, .18844394385815, -.55403280258179, -.6435934305191, .24241572618484, -.26401495933533, -.03226193040609, .32402887940407, -.1823958158493, .54083228111267, .13657745718956, .60556417703629, .64669179916382, -.02880969829857, .61310833692551, -.48195922374725, -.00673185009509, -.90286934375763, -.72449362277985, .81510883569717, -.48502343893051, .33246004581451, .33071464300156, -.50302714109421, -.3791960477829, .33548650145531, .35447460412979, .01399240642786, .682772397995, .474898904562, -.23161220550537, .93784213066101, -.49919214844704, 3.4479112625122, -2.020316362381, .41167178750038, .57102704048157, -2.3206453323364, .98880618810654, .8800373673439, -.11700607091188, .47710022330284, 1.8731729984283, -.46784225106239, 3.1723618507385, -4.2380332946777, -5.2703905105591, .70423555374146, .70803683996201, .7517546415329]) yr = np.array([ np.nan, .17000007629395, .14895272254944, -.04663083329797, .14835388958454, -.067387573421, .17393657565117, -.00391817837954, -.08710660785437, .07916691154242, -.01320043392479, .00712300790474, .11223520338535, -.08105963468552, .11706246435642, -.03576298803091, -.0206862706691, .14842723309994, -.05172633752227, .12472246587276, -.104436814785, .01346892025322, .01794487424195, .07518746703863, -.00436318712309, .11243218928576, -.05320516973734, .14633287489414, .26020830869675, -.02025525644422, .26937630772591, -.16803389787674, .08919904381037, .12725540995598, .10623299330473, .1995185315609, .05965411290526, .28216546773911, .10719951242208, .13195945322514, .31321388483047, .14348678290844, .16340629756451, .24240159988403, .20104511082172, -.01131687406451, .13354018330574, .09008505195379, -.21024852991104, .1734229773283, -.12312019616365, -.04933403432369, -.05912613496184, -.05077522993088, .05298588424921, .12635681033134, .59829473495483, -.06070650368929, .98084276914597, .46521919965744, .62251031398773, .42553821206093, .92174476385117, .32413294911385, -.18692423403263, .23767517507076, .02623280882835, .06718628853559, -.54783964157104, .23576405644417, .05095916613936, -.01613672077656, .49966445565224, -.1578253954649, -.00624855514616, .26373836398125, .28126338124275, .64869183301926, .50607579946518, .28288212418556, .99952530860901, 1.0487948656082, .72968405485153, 1.319433093071, 1.1614154577255, -.126842841506, .55106240510941, .75534957647324, .03535716608167, .67995470762253, -.02233435213566, -.775306224823, -.93925392627716, 1.0932129621506, -1.3366253376007, -1.4984313249588, -.20806217193604, -.35004270076752, -.28375649452209, .03291719779372, -.13478049635887, -.48574689030647, -.16250413656235, -.61117708683014, .24515150487423, -.55535387992859, -.23279193043709, .32596263289452, -2.4220454692841, .39444333314896, -.32336190342903, .3579084277153, .28136301040649, .06810333579779, .20511920750141, -.04392115399241, .2121440321207, .23799060285091, .30830511450768, .16217225790024, .77567237615585, .06947190314531, -.29256621003151, 1.012699007988, -.05995841696858, .36664715409279, 1.5415141582489, -.45958289504051, -.90094763040543, -.01580573618412, -.29488867521286, -.10631188750267, -.13327611982822, -.11324090510607, -.00495810527354, -.12605135142803, -.18752062320709, -.45478835701942, .04802301898599, -.45948752760887, -.1069987937808, .13247023522854, -.12992236018181, .0379159450531, .20006743073463, -.35354685783386, -.10270062834024, .15713113546371, .28798860311508, -.26841807365417, .17411996424198, .06576746702194, -.61839586496353, -.41313683986664, .18844394385815, -.55403280258179, -.6435934305191, .24241572618484, -.26401495933533, -.03226193040609, .32402887940407, -.1823958158493, .54083228111267, .13657745718956, .60556417703629, .64669179916382, -.02880969829857, .61310833692551, -.48195922374725, -.00673185009509, -.90286934375763, -.72449362277985, .81510883569717, -.48502343893051, .33246004581451, .33071464300156, -.50302714109421, -.3791960477829, .33548650145531, .35447460412979, .01399240642786, .682772397995, .474898904562, -.23161220550537, .93784213066101, -.49919214844704, 3.4479112625122, -2.020316362381, .41167178750038, .57102704048157, -2.3206453323364, .98880618810654, .8800373673439, -.11700607091188, .47710022330284, 1.8731729984283, -.46784225106239, 3.1723618507385, -4.2380332946777, -5.2703905105591, .70423555374146, .70803683996201, .7517546415329]) mse = np.array([ .95459979772568, .71522510051727, .63122135400772, .6314896941185, .63029319047928, .63014930486679, .62988424301147, .62969470024109, .62953060865402, .6293950676918, .62928181886673, .62918740510941, .62910866737366, .62904292345047, .62898802757263, .6289421916008, .62890386581421, .62887191772461, .62884521484375, .6288229227066, .62880426645279, .6287887096405, .6287756562233, .62876480817795, .62875574827194, .62874811887741, .62874180078506, .62873649597168, .62873202562332, .62872833013535, .62872523069382, .62872266769409, .62872052192688, .62871867418289, .62871718406677, .62871593236923, .62871485948563, .62871396541595, .62871325016022, .62871265411377, .62871211767197, .62871170043945, .62871134281158, .62871104478836, .62871074676514, .6287105679512, .62871038913727, .62871026992798, .62871015071869, .6287100315094, .62870991230011, .62870985269547, .62870979309082, .62870973348618, .62870973348618, .62870967388153, .62870967388153, .62870961427689, .62870961427689, .62870955467224, .62870955467224, .62870955467224, .62870955467224, .62870955467224, .62870955467224, .62870955467224, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676, .6287094950676]) stdp = np.array([ 0, 0, .05104803293943, .06663129478693, .02164618112147, .0773858949542, .02606418170035, .09391833096743, .05710592120886, .03083370067179, .07319989800453, .05287836492062, .05776296555996, .09105986356735, .04293738678098, .09576436132193, .06068528071046, .06157376244664, .11172580718994, .06527806818485, .11443704366684, .05653077363968, .08205550909042, .08481238037348, .10436166077852, .0875685736537, .12320486456156, .08366665989161, .13979130983353, .1902572363615, .1306214183569, .21803694963455, .11079790443182, .17274764180183, .1937662512064, .20047917962074, .24034893512726, .21783453226089, .29279819130898, .26804205775261, .28678458929062, .35651323199272, .33659368753433, .35760068893433, .39895334839821, .41131839156151, .36645981669426, .40991494059563, .41024547815323, .32657703757286, .42312324047089, .34933325648308, .35912537574768, .35077446699142, .34701564908028, .37364318966866, .40170526504517, .56070649623871, .41915491223335, .73478156328201, .67748892307281, .7744625210762, .77825599908829, .97586625814438, .88692498207092, .76232481002808, .87376874685287, .83281141519547, .84783887863159, .66423743963242, .84904235601425, .81613594293594, .80033475160599, .95782464742661, .80624777078629, .83626395463943, .91873735189438, .95130664110184, 1.0939226150513, 1.1171194314957, 1.1004731655121, 1.3512066602707, 1.4703129529953, 1.4805699586868, 1.7385860681534, 1.8268398046494, 1.5489361286163, 1.7446503639221, 1.864644408226, 1.7200467586517, 1.9223358631134, 1.775306224823, 1.5392524003983, 1.4067870378494, 1.9366238117218, 1.2984343767166, 1.1080636978149, 1.3500427007675, 1.2837564945221, 1.2670782804489, 1.3347851037979, 1.2857422828674, 1.1625040769577, 1.2111755609512, 1.0548515319824, 1.2553508281708, 1.0327949523926, 1.0740388631821, 1.222040772438, .40555971860886, 1.0233588218689, .84209614992142, 1.0186324119568, 1.0319027900696, .99487775564194, 1.0439211130142, .98785293102264, 1.0620124340057, 1.0916963815689, 1.1378232240677, 1.1243290901184, 1.3305295705795, 1.1925677061081, 1.0872994661331, 1.4599523544312, 1.2333589792252, 1.3584797382355, 1.7595859766006, 1.3009568452835, 1.1157965660095, 1.2948887348175, 1.2063180208206, 1.2332669496536, 1.2132470607758, 1.2049551010132, 1.2260574102402, 1.1875206232071, 1.1547852754593, 1.0519831180573, 1.1594845056534, 1.0069926977158, 1.0675266981125, 1.1299223899841, 1.0620901584625, 1.0999356508255, 1.1535499095917, 1.0026944875717, 1.0428657531738, 1.1120204925537, 1.1684119701385, 1.0258769989014, 1.1342295408249, 1.1183958053589, .91313683986664, .91156214475632, 1.0540328025818, .84359037876129, .75758427381516, .96401190757751, .83226495981216, .8759680390358, .98239886760712, .85917687416077, 1.0634194612503, .99442666769028, 1.153311252594, 1.2288066148758, 1.0869039297104, 1.281947016716, 1.0067318677902, 1.1028815507889, .82448446750641, .78489726781845, 1.1850204467773, .86753690242767, 1.0692945718765, 1.1030179262161, .8791960477829, .86451041698456, 1.0455346107483, 1.085998415947, 1.0172398090363, 1.2250980138779, 1.2316122055054, 1.062157869339, 1.3991860151291, 1.0520887374878, 2.2203133106232, .88833123445511, 1.4289729595184, 1.5206423997879, .68520504236221, 1.4659557342529, 1.5350053310394, 1.3178979158401, 1.4888265132904, 1.9698411226273, 1.4406447410583, 2.517040014267, .55537897348404, -.20722626149654, 1.0899519920349, 1.164245724678]) icstats = np.array([ 202, np.nan, -239.75290561974, 4, 487.50581123949, 500.73888202909]) results = Bunch( llf=llf, nobs=nobs, k=k, k_exog=k_exog, sigma=sigma, chi2=chi2, df_model=df_model, k_ar=k_ar, k_ma=k_ma, params=params, cov_params=cov_params, xb=xb, y=y, resid=resid, yr=yr, mse=mse, stdp=stdp, icstats=icstats ) statsmodels-0.12.2/statsmodels/tsa/tests/results/arima112nc_results.py000066400000000000000000000541311400612667500261360ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch llf = np.array([-240.79351748413]) nobs = np.array([202]) k = np.array([4]) k_exog = np.array([1]) sigma = np.array([.79349479007541]) chi2 = np.array([31643.977146904]) df_model = np.array([3]) k_ar = np.array([1]) k_ma = np.array([2]) params = np.array([ .99502750401315, -.68630179255403, -.19840894739396, .79349479007541]) cov_params = np.array([ .00010016992219, -.00021444523598, -.00023305572854, -6.768123591e-06, -.00021444523598, .00104186449549, .00023669747281, 3.902897504e-06, -.00023305572854, .00023669747281, .0010810935718, .00020764808165, -6.768123591e-06, 3.902897504e-06, .00020764808165, .0002668504612]).reshape(4, 4) xb = np.array([ 0, 0, .11361486464739, .14230862259865, .07256115227938, .13274206221104, .06747215241194, .13822889328003, .09585004299879, .06099047139287, .10120190680027, .07761032879353, .07942545413971, .11177492141724, .06088993698359, .11208334565163, .0755797252059, .07422959059477, .12350624799728, .07623053342104, .12391770631075, .06531815230846, .08897981792688, .09103457629681, .10980048775673, .09255626052618, .12732291221619, .08764986693859, .14262486994267, .19330270588398, .13410428166389, .2202503234148, .1138079687953, .17364008724689, .19471970200539, .20120698213577, .24072274565697, .21839858591557, .29251739382744, .26838713884354, .28637075424194, .3556769490242, .33624804019928, .35650280117989, .3974232673645, .40968126058578, .36446389555931, .40641778707504, .40639826655388, .32208651304245, .41636437177658, .34307014942169, .3511538207531, .34216031432152, .33759200572968, .36354607343674, .39148297905922, .55032896995544, .4113195836544, .7244918346405, .67152947187424, .76787060499191, .77276849746704, .96944856643677, .88270664215088, .7563271522522, .86404490470886, .82250237464905, .83520317077637, .65044301748276, .83044308423996, .79827356338501, .78103590011597, .93702721595764, .78709679841995, .81435388326645, .89593154191971, .92867535352707, 1.0709822177887, 1.0957812070847, 1.0792914628983, 1.3286831378937, 1.4503024816513, 1.4619816541672, 1.7190475463867, 1.8096150159836, 1.5324629545212, 1.721804857254, 1.8408879041672, 1.6955831050873, 1.8928952217102, 1.7459137439728, 1.5055395364761, 1.3664853572845, 1.8893030881882, 1.256967663765, 1.0567245483398, 1.2921603918076, 1.2266329526901, 1.2085332870483, 1.275726556778, 1.2278587818146, 1.1046848297119, 1.1517647504807, .99646359682083, 1.194694519043, .97580307722092, 1.0148292779922, 1.1635760068893, .35167038440704, .95728904008865, .78414303064346, .95968008041382, .97746151685715, .94291216135025, .99327826499939, .93940645456314, 1.013852596283, 1.0454497337341, 1.0929356813431, 1.0810794830322, 1.2874436378479, 1.1533098220825, 1.0470397472382, 1.4171674251556, 1.1959022283554, 1.3181202411652, 1.7197531461716, 1.2677561044693, 1.0768386125565, 1.2508004903793, 1.1625586748123, 1.1872273683548, 1.1668027639389, 1.1576874256134, 1.1782459020615, 1.1398378610611, 1.1065219640732, 1.0032601356506, 1.1087976694107, .95788156986237, 1.0163568258286, 1.079482793808, 1.0131409168243, 1.0506906509399, 1.1052004098892, .95601671934128, .99452114105225, 1.0641269683838, 1.1217628717422, .98107707500458, 1.0877858400345, 1.0735836029053, .86890149116516, .86449563503265, 1.0060983896255, .79812264442444, .70991164445877, .91461282968521, .78625136613846, .8291689157486, .93680161237717, .81633454561234, 1.0196126699448, .95442569255829, 1.1131925582886, 1.1916073560715, 1.05200278759, 1.2451642751694, .97296446561813, 1.0647999048233, .78715896606445, .74267995357513, 1.1400059461594, .82839399576187, 1.0262999534607, 1.0628409385681, .84051495790482, .82304340600967, 1.0028872489929, 1.0457111597061, .97847640514374, 1.1855980157852, 1.195351600647, 1.0270363092422, 1.3610677719116, 1.0189098119736, 2.1800265312195, .86722087860107, 1.3893752098083, 1.4851142168045, .65110164880753, 1.417050242424, 1.4938380718231, 1.2786860466003, 1.446773648262, 1.9284181594849, 1.4071846008301, 2.4745123386383, .53088372945786, -.25887301564217, 1.0166070461273, 1.1028108596802]) y = np.array([ np.nan, 28.979999542236, 29.263614654541, 29.492309570313, 29.442562103271, 29.672742843628, 29.617471694946, 29.888229370117, 29.935850143433, 29.870990753174, 30.021202087402, 30.057609558105, 30.119426727295, 30.321773529053, 30.280889511108, 30.492082595825, 30.515581130981, 30.554229736328, 30.813507080078, 30.826231002808, 31.063919067383, 31.015319824219, 31.108980178833, 31.21103477478, 31.389801025391, 31.472555160522, 31.707323074341, 31.737649917603, 32.022624969482, 32.473300933838, 32.584106445313, 33.070247650146, 33.013809204102, 33.273639678955, 33.594722747803, 33.901206970215, 34.340721130371, 34.61840057373, 35.192520141602, 35.568386077881, 35.98637008667, 36.65567779541, 37.136245727539, 37.65650177002, 38.297424316406, 38.909679412842, 39.264465332031, 39.806419372559, 40.306400299072, 40.42208480835, 41.016361236572, 41.243072509766, 41.551155090332, 41.84215927124, 42.137592315674, 42.563545227051, 43.091484069824, 44.250328063965, 44.611320495605, 46.324489593506, 47.471527099609, 48.867870330811, 50.072769165039, 51.9694480896, 53.182704925537, 53.756328582764, 54.864044189453, 55.722503662109, 56.635204315186, 56.750442504883, 57.830444335938, 58.698276519775, 59.481037139893, 60.937026977539, 61.587097167969, 62.414352416992, 63.595932006836, 64.828674316406, 66.570983886719, 68.195777893066, 69.579292297363, 71.928680419922, 74.450302124023, 76.661979675293, 79.719047546387, 82.709617614746, 84.132461547852, 86.421798706055, 89.040885925293, 90.79557800293, 93.39289855957, 95.14591217041, 95.905540466309, 96.366485595703, 99.389305114746, 99.356964111328, 98.956726074219, 100.09216308594, 101.02663421631, 102.00853729248, 103.37572479248, 104.52786254883, 105.20468139648, 106.25176239014, 106.69645690918, 108.19469451904, 108.67579650879, 109.51483154297, 111.06357574463, 109.05166625977, 110.45729064941, 110.98413848877, 112.35968017578, 113.6774597168, 114.74291229248, 115.99327850342, 116.93940734863, 118.21385192871, 119.54544830322, 120.99293518066, 122.28107452393, 124.38744354248, 125.65331268311, 126.44704437256, 128.91716003418, 130.09590148926, 131.81811523438, 135.11975097656, 135.96775817871, 136.17684936523, 137.45079040527, 138.36254882813, 139.48722839355, 140.56680297852, 141.65768432617, 142.87825012207, 143.93983459473, 144.9065246582, 145.50326538086, 146.70880126953, 147.25788879395, 148.21635437012, 149.47947692871, 150.41313171387, 151.55068969727, 152.90519714355, 153.55603027344, 154.49452209473, 155.76412963867, 157.22177124023, 157.98107910156, 159.28778076172, 160.47357177734, 160.76889038086, 161.26449584961, 162.50610351563, 162.7981262207, 162.90991210938, 164.11460876465, 164.6862487793, 165.5291595459, 166.83679199219, 167.5163269043, 169.11961364746, 170.25442504883, 172.01318359375, 173.8916015625, 174.95199584961, 176.84516906738, 177.37295532227, 178.46479797363, 178.38716125488, 178.44267272949, 180.44000244141, 180.8283996582, 182.22630310059, 183.66284179688, 184.04051208496, 184.52304077148, 185.90287780762, 187.34571838379, 188.37846374512, 190.28559875488, 191.99536132813, 192.82704162598, 195.16107177734, 195.71890258789, 201.3800201416, 200.26721191406, 202.08937072754, 204.18510437012, 202.55110168457, 204.99105834961, 207.41383361816, 208.61668395996, 210.57977294922, 214.4234161377, 215.40417480469, 221.08451843262, 217.41989135742, 211.91511535645, 213.68760681152, 215.57180786133]) resid = np.array([ np.nan, .17000007629395, .08638589829206, -.12230817228556, .09743892401457, -.12274374067783, .13252860307693, -.04822873324156, -.12585072219372, .04901013895869, -.04120244085789, -.01760895550251, .0905727148056, -.1017746925354, .09910991042852, -.05208196863532, -.03558072075248, .13577139377594, -.0635067820549, .11377000063658, -.11391747742891, .00468154205009, .01102056354284, .0689652711153, -.00980201456696, .10744450241327, -.05732321739197, .14234967529774, .25737473368645, -.02330071851611, .26589342951775, 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np.array([ np.nan, .17000007629395, .08638589829206, -.12230817228556, .09743892401457, -.12274374067783, .13252860307693, -.04822873324156, -.12585072219372, .04901013895869, -.04120244085789, -.01760895550251, .0905727148056, -.1017746925354, .09910991042852, -.05208196863532, -.03558072075248, .13577139377594, -.0635067820549, .11377000063658, -.11391747742891, .00468154205009, .01102056354284, .0689652711153, -.00980201456696, .10744450241327, -.05732321739197, .14234967529774, .25737473368645, -.02330071851611, .26589342951775, -.17024727165699, .08618897944689, .12636296451092, .10527954250574, .19879072904587, .05928030610085, .28160139918327, .10748030990362, .13161440193653, .31362771987915, .14432306587696, .16375194489956, .24349948763847, .20257519185543, -.00967973750085, .13553610444069, .09358221292496, -.20640131831169, .17791347205639, -.11636133491993, -.04307091236115, -.05115458369255, -.04216108098626, .06240950897336, .13645392656326, .60851699113846, 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.00672172475606, .26059049367905, .28615045547485, .35455179214478, .2070597410202, .81892204284668, .11255792528391, -.25330832600594, 1.0529587268829, -.0171735137701, .40410390496254, 1.5818736553192, -.41975006461143, -.86774694919586, .02315225638449, -.25080046057701, -.06255260109901, -.08723650127649, -.06679660826921, .04230948910117, -.07823982834816, -.13983787596226, -.40652501583099, .09674594551325, -.40880066156387, -.05788768827915, .1836401373148, -.07948285341263, .08686522394419, .24931237101555, -.30519738793373, -.05602284148335, .20547580718994, .33588215708733, -.22176894545555, .21891987323761, .11221113055944, -.57358360290527, -.36890152096748, .23551045358181, -.50609844923019, -.59812569618225, .29008835554123, -.21461589634418, .013751687482, .37082800269127, -.13679853081703, .5836746096611, .18038421869278, .64556515216827, .68681055307388, .00838960427791, .64800941944122, -.44517654180527, .02703555487096, -.8647877573967, -.68716812133789, .85732614994049, -.44000896811485, .37160298228264, .37370926141739, -.46285009384155, -.34051498770714, .37695357203484, .3971218764782, .05427964404225, .72153580188751, .51439893245697, -.19535164535046, .97296363115311, -.46107393503189, 3.4810900688171, -1.9800295829773, .43278217315674, .61062479019165, -2.2851173877716, 1.0229095220566, .92894279956818, -.07583882659674, .51631212234497, 1.9152258634567, -.42641922831535, 3.2058219909668, -4.1955056190491, -5.2458953857422, .75588232278824, .7813817858696, .81318950653076]) mse = np.array([ 1.4407075643539, 1.4407075643539, .79720854759216, .75209444761276, .71109557151794, .68920749425888, .67417079210281, .66374856233597, .65616118907928, .65050256252289, .64619332551956, .64286160469055, .64025497436523, .63819670677185, .63655960559845, .6352499127388, .63419729471207, .63334810733795, .63266098499298, .63210368156433, .63165074586868, .63128209114075, .63098156452179, .63073641061783, .63053613901138, .63037252426147, .6302387714386, .63012927770615, .63003975152969, .62996637821198, .62990635633469, .62985718250275, .62981688976288, .62978386878967, .62975686788559, .62973469495773, .62971651554108, .62970167398453, .62968945503235, .62967944145203, .62967127561569, .62966454029083, .62965905666351, .62965452671051, .62965083122253, .62964779138565, .62964528799057, .62964326143265, .62964159250259, .62964022159576, .62963908910751, .62963819503784, .62963742017746, .62963682413101, .62963628768921, .6296358704567, .62963551282883, .62963527441025, .62963503599167, .62963485717773, .6296346783638, .62963455915451, .62963443994522, .62963438034058, .62963432073593, .62963426113129, .62963420152664, .629634141922, .629634141922, .62963408231735, .62963408231735, .62963408231735, .62963402271271, .62963402271271, .62963402271271, .62963402271271, .62963402271271, .62963402271271, .62963402271271, .62963402271271, .62963402271271, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806, .62963396310806]) icstats = np.array([ 202, np.nan, -240.79351748413, 4, 489.58703496826, 502.82010575786]) results = Bunch( llf=llf, nobs=nobs, k=k, k_exog=k_exog, sigma=sigma, chi2=chi2, df_model=df_model, k_ar=k_ar, k_ma=k_ma, params=params, cov_params=cov_params, xb=xb, y=y, resid=resid, yr=yr, mse=mse, icstats=icstats ) statsmodels-0.12.2/statsmodels/tsa/tests/results/arima211_css_results.py000066400000000000000000000650341400612667500264710ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch llf = np.array([-240.29558272688]) nobs = np.array([202]) k = np.array([5]) k_exog = np.array([1]) sigma = np.array([.79494581155191]) chi2 = np.array([1213.6019521322]) df_model = np.array([3]) k_ar = np.array([2]) k_ma = np.array([1]) params = np.array([ .72428568600554, 1.1464248419014, -.17024528879204, -.87113675466923, .63193884330392]) cov_params = np.array([ .31218565961764, -.01618380799341, .00226345462929, .01386291798401, -.0036338799176, -.01618380799341, .00705713030623, -.00395404914463, -.00685704952799, -.00018629958479, .00226345462929, -.00395404914463, .00255884492061, .00363586332269, .00039879711931, .01386291798401, -.00685704952799, .00363586332269, .00751765532203, .00008982556101, -.0036338799176, -.00018629958479, .00039879711931, .00008982556101, .00077550533053]).reshape(5, 5) xb = np.array([ .72428566217422, .72428566217422, .56208884716034, .53160965442657, .45030161738396, .45229381322861, .38432359695435, .40517011284828, .36063131690025, .30754271149635, .32044330239296, .29408219456673, .27966624498367, .29743707180023, .25011941790581, .27747189998627, .24822402000427, .23426930606365, .27233305573463, .23524768650532, .26427435874939, .21787133812904, .22461311519146, .22853142023087, .24335558712482, .22953669726849, .25524401664734, .22482520341873, .26450532674789, .31863233447075, .27352628111839, .33670437335968, .25623551011086, .28701293468475, .315819054842, 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.63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688, .63193881511688]) stdp = np.array([ .72428566217422, .72428566217422, .56208884716034, .53160965442657, .45030161738396, .45229381322861, .38432359695435, .40517011284828, .36063131690025, .30754271149635, .32044330239296, .29408219456673, .27966624498367, .29743707180023, .25011941790581, .27747189998627, .24822402000427, .23426930606365, .27233305573463, .23524768650532, .26427435874939, .21787133812904, .22461311519146, .22853142023087, .24335558712482, .22953669726849, .25524401664734, .22482520341873, .26450532674789, .31863233447075, .27352628111839, .33670437335968, .25623551011086, .28701293468475, .315819054842, .3238864839077, .35844340920448, .34399557113647, .40348997712135, .39373970031738, .4022718667984, .46476069092751, .45762005448341, .46842387318611, .50536489486694, .52051961421967, .47866532206535, .50378143787384, .50863671302795, .4302790760994, .49568024277687, .44652271270752, .43774726986885, .43010330200195, .42344436049461, .44517293572426, .47460499405861, .62086409330368, .52550911903381, .77532315254211, .78466820716858, .85438597202301, .87056696414948, 1.0393311977386, .99110960960388, .85202795267105, .91560190916061, .89238166809082, .88917690515518, .72121334075928, .84221452474594, .8454754948616, .82078683376312, .95394861698151, .84718400239944, .839300096035, .91501939296722, .95743554830551, 1.0874761343002, 1.1326615810394, 1.1169674396515, 1.3300451040268, 1.4790810346603, 1.5027786493301, 1.7226468324661, 1.8395622968674, 1.5940405130386, 1.694568157196, 1.8241587877274, 1.7037791013718, 1.838702917099, 1.7334734201431, 1.4791669845581, 1.3007366657257, 1.7364456653595, 1.2694935798645, .96595168113708, 1.1405370235443, 1.1328836679459, 1.1091921329498, 1.171138882637, 1.1465038061142, 1.0319484472275, 1.055313706398, .93150246143341, 1.0844472646713, .93333613872528, .93137633800507, 1.0778160095215, .38748729228973, .77933365106583, .75266307592392, .88410103321075, .94100385904312, .91849637031555, .96046274900436, .92494148015976, .98310285806656, 1.0272513628006, 1.0762135982513, 1.0743116140366, 1.254854798317, 1.1723403930664, 1.0479376316071, 1.3550333976746, 1.2255589962006, 1.2870025634766, 1.6643482446671, 1.3312928676605, 1.0657893419266, 1.1804157495499, 1.1335761547089, 1.137326002121, 1.1235628128052, 1.1115798950195, 1.1286649703979, 1.0989991426468, 1.0626485347748, .96542054414749, 1.0419135093689, .93033194541931, .95628559589386, 1.027433514595, .98328214883804, 1.0063992738724, 1.0645687580109, .94354963302612, .95077443122864, 1.0226324796677, 1.089217543602, .97552293539047, 1.0441918373108, 1.052937746048, .86785578727722, .82579529285431, .95432937145233, .79897737503052, .68320548534393, .85365778207779, .78336101770401, .80072748661041, .9089440703392, .82500487565994, .98515397310257, .96745657920837, 1.0962044000626, 1.195325255394, 1.0824474096298, 1.2239117622375, 1.0142554044724, 1.0399018526077, .80796521902084, .7145761847496, 1.0631860494614, .86374056339264, .98086261749268, 1.0528303384781, .86123734712601, .80300676822662, .96200370788574, 1.0364016294479, .98456978797913, 1.1556725502014, 1.2025715112686, 1.0507286787033, 1.312912106514, 1.0682457685471, 2.0334177017212, 1.0775905847549, 1.2798084020615, 1.461397767067, .72960823774338, 1.2498733997345, 1.466894865036, 1.286082983017, 1.3903408050537, 1.8483582735062, 1.4685434103012, 2.3107523918152, .7711226940155, -.31598940491676, .68151205778122, 1.0212944746017]) icstats = np.array([ 202, np.nan, -240.29558272688, 5, 490.59116545376, 507.13250394077]) results = Bunch( llf=llf, nobs=nobs, k=k, k_exog=k_exog, sigma=sigma, chi2=chi2, df_model=df_model, k_ar=k_ar, k_ma=k_ma, params=params, cov_params=cov_params, xb=xb, y=y, resid=resid, yr=yr, mse=mse, stdp=stdp, icstats=icstats ) statsmodels-0.12.2/statsmodels/tsa/tests/results/arima211_results.py000066400000000000000000000650251400612667500256210ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch llf = np.array([-239.91961140777]) nobs = np.array([202]) k = np.array([5]) k_exog = np.array([1]) sigma = np.array([.79249918716869]) chi2 = np.array([907.36856676748]) df_model = np.array([3]) k_ar = np.array([2]) k_ma = np.array([1]) params = np.array([ .86132870569126, 1.1429974468925, -.16912378249242, -.87400688606796, .79249918716869]) cov_params = np.array([ .22693223682292, -.00989623843683, -.00092349277863, .00706357033712, -.00195332705416, -.00989623843683, .00771565502349, -.00405286187622, -.00748374882497, -.00006513770699, -.00092349277863, -.00405286187622, .00252946620109, .00372566422545, .00024079697522, .00706357033712, -.00748374882497, .00372566422545, .00812286034649, 8.202907726e-06, -.00195332705416, -.00006513770699, .00024079697522, 8.202907726e-06, .00031052148013]).reshape(5, 5) xb = np.array([ .86132872104645, .86132872104645, .58931648731232, .53695642948151, .43875110149384, .43893754482269, .36897498369217, .39383068680763, .35268598794937, .30327013134956, .3206245303154, .29862868785858, .2883597612381, .30968201160431, .26627779006958, .29635512828827, .27021989226341, .25900682806969, .29855474829674, .26389503479004, .2940701842308, .24996083974838, .25805163383484, .26306444406509, .27853038907051, .26575443148613, .29165366292, .262396723032, .30186694860458, .35503962635994, .31088310480118, .37306407094002, .29435822367668, .32511350512505, .35352823138237, .36144828796387, .39527052640915, .38102087378502, .43927636742592, .42946752905846, .43780836462975, .49889534711838, .49156260490417, .50206583738327, .53814554214478, .55276554822922, .51174682378769, .53661912679672, .54144555330276, .4649658203125, .52955776453018, .48147654533386, .47327646613121, .46611019968987, .45984682440758, .48127228021622, .50998419523239, .65266174077988, .5583056807518, .80249065160751, .80990171432495, .87710189819336, .89202457666397, 1.0564744472504, 1.0080462694168, .87197554111481, .93521976470947, .9128600358963, .91022855043411, .7465353012085, .866335272789, .86956661939621, .84549117088318, .97585707902908, .87074065208435, .86343002319336, .93773847818375, .97884559631348, 1.1054569482803, 1.1484670639038, 1.1322609186172, 1.3402134180069, 1.4842771291733, 1.5056529045105, 1.719556927681, 1.8319338560104, 1.5904501676559, 1.6899375915527, 1.8168371915817, 1.6987046003342, 1.8314251899719, 1.7283667325974, 1.4807628393173, 1.308970451355, 1.7375549077988, 1.2797228097916, .98571860790253, 1.1599444150925, 1.1530816555023, 1.13017141819, 1.1908437013626, 1.1662386655807, 1.0540459156036, 1.0774390697479, .95646268129349, 1.1066728830338, .95817422866821, .95676136016846, 1.1000070571899, .42435362935066, .81153392791748, .78478264808655, .91281259059906, .9670450091362, .94373846054077, .98408794403076, .9486455321312, 1.0052901506424, 1.0478744506836, 1.095078587532, 1.0925225019455, 1.2685979604721, 1.1865184307098, 1.0648469924927, 1.3658550977707, 1.2376955747604, 1.2978720664978, 1.6663243770599, 1.338112950325, 1.0797605514526, 1.1944576501846, 1.1494234800339, 1.153874874115, 1.1408479213715, 1.1294689178467, 1.1464176177979, 1.1174235343933, 1.0820926427841, .98742854595184, 1.0630278587341, .95385235548019, .97988063097, 1.049503326416, 1.0058189630508, 1.0283635854721, 1.0849515199661, .96609032154083, .97366327047348, 1.0440692901611, 1.1086683273315, .99680209159851, 1.0642927885056, 1.0725424289703, .8914600610733, .85157895088196, .97811859846115, .8258438706398, .71353197097778, .88130152225494, .81193578243256, .82894796133041, .9344978928566, .85150623321533, 1.0080153942108, .9895287156105, 1.1147927045822, 1.2104271650314, 1.0987895727158, 1.23719227314, 1.0314946174622, 1.0577303171158, .8316445350647, .74243623018265, 1.0848734378815, .88838368654251, 1.0033586025238, 1.0730868577957, .88500571250916, .82902699708939, .98530465364456, 1.057307600975, 1.0057097673416, 1.1727533340454, 1.2172684669495, 1.0678850412369, 1.3246995210648, 1.0841422080994, 2.0282983779907, 1.0879902839661, 1.289278626442, 1.4674614667892, .75163400173187, 1.2650294303894, 1.4760826826096, 1.2972749471664, 1.3993507623672, 1.8463147878647, 1.4716247320175, 2.2955448627472, .7857254743576, -.26799991726875, .71938097476959, 1.0508332252502]) y = np.array([ np.nan, 29.841327667236, 29.739316940308, 29.886957168579, 29.808752059937, 29.978939056396, 29.918973922729, 30.143831253052, 30.192686080933, 30.113269805908, 30.24062538147, 30.27862739563, 30.32836151123, 30.519681930542, 30.486276626587, 30.67635345459, 30.710220336914, 30.73900604248, 30.988555908203, 31.01389503479, 31.234069824219, 31.199960708618, 31.278051376343, 31.383066177368, 31.558530807495, 31.645753860474, 31.871654510498, 31.912395477295, 32.181865692139, 32.635040283203, 32.760883331299, 33.223064422607, 33.194358825684, 33.425113677979, 33.753528594971, 34.061447143555, 34.495269775391, 34.781021118164, 35.339279174805, 35.729465484619, 36.137809753418, 36.798892974854, 37.291561126709, 37.802066802979, 38.438148498535, 39.052764892578, 39.41174697876, 39.936618804932, 40.44144821167, 40.564964294434, 41.129554748535, 41.381477355957, 41.673278808594, 41.966110229492, 42.259845733643, 42.681274414063, 43.209983825684, 44.352661132813, 44.758304595947, 46.402488708496, 47.609901428223, 48.977100372314, 50.192024230957, 52.05647277832, 53.308044433594, 53.871974945068, 54.935218811035, 55.81286239624, 56.710227966309, 56.846534729004, 57.86633682251, 58.769569396973, 59.545490264893, 60.975856781006, 61.670738220215, 62.463428497314, 63.637741088867, 64.878845214844, 66.605453491211, 68.248466491699, 69.632263183594, 71.940208435059, 74.484275817871, 76.70565032959, 79.71955871582, 82.73193359375, 84.190444946289, 86.389930725098, 89.016830444336, 90.798706054688, 93.331428527832, 95.128364562988, 95.880767822266, 96.308967590332, 99.23755645752, 99.379722595215, 98.885719299316, 99.959945678711, 100.95308685303, 101.93017578125, 103.29084014893, 104.4662399292, 105.15404510498, 106.17743682861, 106.65645599365, 108.10667419434, 108.65817260742, 109.45676422119, 111.00000762939, 109.12435150146, 110.31153106689, 110.98477935791, 112.31281280518, 113.66704559326, 114.74374389648, 115.98408508301, 116.94864654541, 118.20528411865, 119.54787445068, 120.99507904053, 122.29251861572, 124.36859893799, 125.68651580811, 126.46485137939, 128.86585998535, 130.1376953125, 131.79786682129, 135.06631469727, 136.03811645508, 136.17976379395, 137.39445495605, 138.34942626953, 139.45387268066, 140.54084777832, 141.6294708252, 142.84642028809, 143.91741943359, 144.88209533691, 145.48742675781, 146.66304016113, 147.25386047363, 148.17987060547, 149.4494934082, 150.40580749512, 151.52836608887, 152.88494873047, 153.56610107422, 154.47366333008, 155.74406433105, 157.20867919922, 157.9967956543, 159.26428222656, 160.47253417969, 160.79145812988, 161.25157165527, 162.47811889648, 162.82585144043, 162.91352844238, 164.08129882813, 164.71192932129, 165.52894592285, 166.83448791504, 167.55149841309, 169.10801696777, 170.28953552246, 172.0147857666, 173.9104309082, 174.99877929688, 176.83720397949, 177.43148803711, 178.45771789551, 178.43165588379, 178.44242858887, 180.38487243652, 180.88838195801, 182.20335388184, 183.67309570313, 184.08500671387, 184.5290222168, 185.88529968262, 187.35731506348, 188.40570068359, 190.27276611328, 192.01727294922, 192.8678894043, 195.12471008301, 195.78413391113, 201.22830200195, 200.48799133301, 201.98927307129, 204.16746520996, 202.65162658691, 204.83903503418, 207.39608764648, 208.63526916504, 210.53234863281, 214.34130859375, 215.4686126709, 220.9055480957, 217.67472839355, 211.90599060059, 213.39038085938, 215.51982116699]) resid = np.array([ np.nan, -.6913286447525, -.38931575417519, -.51695597171783, -.26875102519989, -.42893922328949, -.16897420585155, -.30383053421974, -.38268667459488, -.19326950609684, -.26062506437302, -.2386272996664, -.11836158484221, -.29968178272247, -.10627794265747, -.23635374009609, -.2302208840847, -.04900583252311, -.23855529725552, -.07389451563358, -.28406995534897, -.17996114492416, -.15805125236511, -.10306460410357, -.17853192985058, -.06575367599726, -.22165396809578, -.03239719197154, .09813265502453, -.18503764271736, .08911459892988, -.32306101918221, -.09436126798391, -.02511045895517, -.05352900549769, .03854943066835, -.09526748210192, .11897913366556, -.0392786487937, -.02946598827839, .16219010949135, .00110464950558, .00843739509583, .09793642908335, .06185294687748, -.15276403725147, -.01174682471901, -.03661911562085, -.34144860506058, .0350341796875, -.22955468297005, -.18147730827332, -.17327722907066, -.16611096262932, -.05984530970454, .01872771047056, .49001583456993, -.15266172587872, .84169203042984, .39751008152962, .4900975227356, .32289886474609, .80797618627548, .24352477490902, -.30804550647736, .12802444398403, -.03521826863289, -.01286232378334, -.61022931337357, .15346619486809, .03366623818874, -.06956738233566, .45450806617737, -.17585784196854, -.07074139267206, .236572265625, .26226228475571, .62115287780762, .49454152584076, .2515344619751, .96773761510849, 1.059788107872, .71571981906891, 1.2943501472473, 1.1804445981979, -.13193695247173, .50954836606979, .81006240844727, .08316437155008, .70129698514938, .0685763657093, -.72836673259735, -.88076442480087, 1.191029548645, -1.1375564336777, -1.4797197580338, -.08571709692478, -.15994438529015, -.15308164060116, .16982398927212, .00916088558733, -.36624330282211, -.0540459305048, -.47744059562683, .34354037046432, -.40667590498924, -.15817116200924, .44324016571045, -2.3000116348267, .37564942240715, -.11153698712587, .41522192955017, .38718286156654, .13296109437943, .25625845789909, .01591204665601, .25135138630867, .2947128713131, .35212710499763, .20491683483124, .80747896432877, .13140361011028, -.28651690483093, 1.0351514816284, .03413881734014, .36231052875519, 1.6021218299866, -.36632135510445, -.93810379505157, .02023027092218, -.19445763528347, -.04941740259528, -.05388405546546, -.04084182903171, .0705279931426, -.04641156643629, -.11742353439331, -.38209563493729, .11257757246494, -.36303088068962, -.05385848507285, .22011630237103, -.04950327426195, .09418711811304, .27163949608803, -.28494849801064, -.06609643250704, .22633366286755, .35593989491463, -.20867441594601, .20319482684135, .13570418953896, -.57254236936569, -.3914600610733, .24842712283134, -.47811862826347, -.62584692239761, .28646802902222, -.18130460381508, -.01193272508681, .37104898691177, -.13449484109879, .54850292205811, .19198158383369, .61046212911606, .6852103471756, -.01043024007231, .60122263431549, -.43720445036888, -.03149457275867, -.85771811008453, -.73165369033813, .85756987333298, -.38487648963928, .31161326169968, .39665061235428, -.47309604287148, -.38500571250916, .3709699511528, .4147045314312, .04268322139978, .69430238008499, .52724367380142, -.2172684520483, .93211495876312, -.42470565438271, 3.4158577919006, -1.8283013105392, .21201276779175, .7107213139534, -2.2674646377563, .92237722873688, 1.0809636116028, -.05808337032795, .49772322177887, 1.9626487493515, -.34431591629982, 3.1413819789886, -4.016538143158, -5.5007371902466, .76500922441483, 1.078607916832, .86516714096069]) yr = np.array([ np.nan, -.6913286447525, -.38931575417519, -.51695597171783, -.26875102519989, -.42893922328949, -.16897420585155, -.30383053421974, -.38268667459488, -.19326950609684, -.26062506437302, -.2386272996664, -.11836158484221, -.29968178272247, -.10627794265747, -.23635374009609, -.2302208840847, -.04900583252311, -.23855529725552, -.07389451563358, -.28406995534897, -.17996114492416, -.15805125236511, -.10306460410357, -.17853192985058, -.06575367599726, -.22165396809578, -.03239719197154, .09813265502453, -.18503764271736, .08911459892988, -.32306101918221, -.09436126798391, -.02511045895517, -.05352900549769, .03854943066835, -.09526748210192, .11897913366556, -.0392786487937, -.02946598827839, .16219010949135, .00110464950558, .00843739509583, .09793642908335, .06185294687748, -.15276403725147, -.01174682471901, -.03661911562085, -.34144860506058, .0350341796875, -.22955468297005, -.18147730827332, -.17327722907066, -.16611096262932, -.05984530970454, .01872771047056, .49001583456993, -.15266172587872, .84169203042984, .39751008152962, .4900975227356, .32289886474609, .80797618627548, .24352477490902, -.30804550647736, .12802444398403, -.03521826863289, -.01286232378334, -.61022931337357, .15346619486809, .03366623818874, -.06956738233566, .45450806617737, -.17585784196854, -.07074139267206, .236572265625, .26226228475571, .62115287780762, .49454152584076, .2515344619751, .96773761510849, 1.059788107872, .71571981906891, 1.2943501472473, 1.1804445981979, -.13193695247173, .50954836606979, .81006240844727, .08316437155008, .70129698514938, .0685763657093, -.72836673259735, -.88076442480087, 1.191029548645, -1.1375564336777, -1.4797197580338, -.08571709692478, -.15994438529015, -.15308164060116, .16982398927212, .00916088558733, -.36624330282211, -.0540459305048, -.47744059562683, .34354037046432, -.40667590498924, -.15817116200924, .44324016571045, -2.3000116348267, .37564942240715, -.11153698712587, .41522192955017, .38718286156654, .13296109437943, .25625845789909, .01591204665601, .25135138630867, .2947128713131, .35212710499763, .20491683483124, .80747896432877, .13140361011028, -.28651690483093, 1.0351514816284, .03413881734014, .36231052875519, 1.6021218299866, -.36632135510445, -.93810379505157, .02023027092218, -.19445763528347, -.04941740259528, -.05388405546546, -.04084182903171, .0705279931426, -.04641156643629, -.11742353439331, -.38209563493729, .11257757246494, -.36303088068962, -.05385848507285, .22011630237103, -.04950327426195, .09418711811304, .27163949608803, -.28494849801064, -.06609643250704, .22633366286755, .35593989491463, -.20867441594601, .20319482684135, .13570418953896, -.57254236936569, -.3914600610733, .24842712283134, -.47811862826347, -.62584692239761, .28646802902222, -.18130460381508, -.01193272508681, .37104898691177, -.13449484109879, .54850292205811, .19198158383369, .61046212911606, .6852103471756, -.01043024007231, .60122263431549, -.43720445036888, -.03149457275867, -.85771811008453, -.73165369033813, .85756987333298, -.38487648963928, .31161326169968, .39665061235428, -.47309604287148, -.38500571250916, .3709699511528, .4147045314312, .04268322139978, .69430238008499, .52724367380142, -.2172684520483, .93211495876312, -.42470565438271, 3.4158577919006, -1.8283013105392, .21201276779175, .7107213139534, -2.2674646377563, .92237722873688, 1.0809636116028, -.05808337032795, .49772322177887, 1.9626487493515, -.34431591629982, 3.1413819789886, -4.016538143158, -5.5007371902466, .76500922441483, 1.078607916832, .86516714096069]) mse = np.array([ .80370712280273, .80370712280273, .67928272485733, .66423606872559, .65418779850006, .64722007513046, .64226144552231, .63866710662842, .63602674007416, .63406819105148, .6326048374176, .63150554895401, .63067644834518, .63004916906357, .62957346439362, .62921214103699, .62893730401993, .62872803211212, .6285685300827, .62844693660736, .62835419178009, .62828344106674, .62822943925858, .62818819284439, .62815672159195, .6281327009201, .62811434268951, .62810027599335, .62808960676193, .6280814409256, .6280751824379, .62807041406631, .62806677818298, .62806397676468, .62806183099747, .62806022167206, .62805896997452, .6280580163002, .62805730104446, .62805676460266, .62805634737015, .62805598974228, .6280557513237, .62805557250977, .62805545330048, .62805533409119, .6280552148819, .62805515527725, .62805509567261, .62805509567261, .62805503606796, .62805503606796, .62805503606796, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332, .62805497646332]) stdp = np.array([ .86132872104645, .86132872104645, .58931648731232, .53695642948151, .43875110149384, .43893754482269, .36897498369217, .39383068680763, .35268598794937, .30327013134956, .3206245303154, .29862868785858, .2883597612381, .30968201160431, .26627779006958, .29635512828827, .27021989226341, .25900682806969, .29855474829674, .26389503479004, .2940701842308, .24996083974838, .25805163383484, .26306444406509, .27853038907051, .26575443148613, .29165366292, .262396723032, .30186694860458, .35503962635994, .31088310480118, .37306407094002, .29435822367668, .32511350512505, .35352823138237, .36144828796387, .39527052640915, .38102087378502, .43927636742592, .42946752905846, .43780836462975, .49889534711838, .49156260490417, .50206583738327, .53814554214478, .55276554822922, .51174682378769, .53661912679672, .54144555330276, .4649658203125, .52955776453018, .48147654533386, .47327646613121, .46611019968987, .45984682440758, .48127228021622, .50998419523239, .65266174077988, .5583056807518, .80249065160751, .80990171432495, .87710189819336, .89202457666397, 1.0564744472504, 1.0080462694168, .87197554111481, .93521976470947, .9128600358963, .91022855043411, .7465353012085, .866335272789, .86956661939621, .84549117088318, .97585707902908, .87074065208435, .86343002319336, .93773847818375, .97884559631348, 1.1054569482803, 1.1484670639038, 1.1322609186172, 1.3402134180069, 1.4842771291733, 1.5056529045105, 1.719556927681, 1.8319338560104, 1.5904501676559, 1.6899375915527, 1.8168371915817, 1.6987046003342, 1.8314251899719, 1.7283667325974, 1.4807628393173, 1.308970451355, 1.7375549077988, 1.2797228097916, .98571860790253, 1.1599444150925, 1.1530816555023, 1.13017141819, 1.1908437013626, 1.1662386655807, 1.0540459156036, 1.0774390697479, .95646268129349, 1.1066728830338, .95817422866821, .95676136016846, 1.1000070571899, .42435362935066, .81153392791748, .78478264808655, .91281259059906, .9670450091362, .94373846054077, .98408794403076, .9486455321312, 1.0052901506424, 1.0478744506836, 1.095078587532, 1.0925225019455, 1.2685979604721, 1.1865184307098, 1.0648469924927, 1.3658550977707, 1.2376955747604, 1.2978720664978, 1.6663243770599, 1.338112950325, 1.0797605514526, 1.1944576501846, 1.1494234800339, 1.153874874115, 1.1408479213715, 1.1294689178467, 1.1464176177979, 1.1174235343933, 1.0820926427841, .98742854595184, 1.0630278587341, .95385235548019, .97988063097, 1.049503326416, 1.0058189630508, 1.0283635854721, 1.0849515199661, .96609032154083, .97366327047348, 1.0440692901611, 1.1086683273315, .99680209159851, 1.0642927885056, 1.0725424289703, .8914600610733, .85157895088196, .97811859846115, .8258438706398, .71353197097778, .88130152225494, .81193578243256, .82894796133041, .9344978928566, .85150623321533, 1.0080153942108, .9895287156105, 1.1147927045822, 1.2104271650314, 1.0987895727158, 1.23719227314, 1.0314946174622, 1.0577303171158, .8316445350647, .74243623018265, 1.0848734378815, .88838368654251, 1.0033586025238, 1.0730868577957, .88500571250916, .82902699708939, .98530465364456, 1.057307600975, 1.0057097673416, 1.1727533340454, 1.2172684669495, 1.0678850412369, 1.3246995210648, 1.0841422080994, 2.0282983779907, 1.0879902839661, 1.289278626442, 1.4674614667892, .75163400173187, 1.2650294303894, 1.4760826826096, 1.2972749471664, 1.3993507623672, 1.8463147878647, 1.4716247320175, 2.2955448627472, .7857254743576, -.26799991726875, .71938097476959, 1.0508332252502]) icstats = np.array([ 202, np.nan, -239.91961140777, 5, 489.83922281554, 506.38056130255]) results = Bunch( llf=llf, nobs=nobs, k=k, k_exog=k_exog, sigma=sigma, chi2=chi2, df_model=df_model, k_ar=k_ar, k_ma=k_ma, params=params, cov_params=cov_params, xb=xb, y=y, resid=resid, yr=yr, mse=mse, stdp=stdp, icstats=icstats ) statsmodels-0.12.2/statsmodels/tsa/tests/results/arima211nc_css_results.py000066400000000000000000000643561400612667500270200ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch llf = np.array([-240.21658671417]) nobs = np.array([202]) k = np.array([4]) k_exog = np.array([1]) sigma = np.array([.79473430527544]) chi2 = np.array([54633.096432541]) df_model = np.array([3]) k_ar = np.array([2]) k_ma = np.array([1]) params = np.array([ 1.1970355174119, -.19724105359909, -.91770441432171, .63160261598163]) cov_params = np.array([ .00182362158934, -.00163271308366, -.00140915922719, -.00044400541718, -.00163271308366, .00148731108625, .00117094734518, .00044939207189, -.00140915922719, .00117094734518, .00181742086472, .00032737864417, -.00044400541718, .00044939207189, .00032737864417, .00071193796554]).reshape(4, 4) xb = np.array([ 0, 0, .04999904707074, .06866559386253, .02903163060546, .07047952711582, .03383458778262, .08519082516432, .06387747824192, .0323903337121, .0664371997118, .056028008461, .05634552612901, .08741936087608, .04945361241698, .0881454795599, .06608437746763, .05997726693749, .1058451384306, .07246486097574, .10775856673717, .06419499218464, .07649331539869, .08432687073946, .10236189514399, .09031195193529, .11902847886086, .08933536708355, .13242828845978, .18790599703789, .1410321444273, .2076324224472, .12561346590519, .16128000617027, .19236192107201, .20115886628628, .23716603219509, .22255305945873, .28473255038261, .27441227436066, .28466689586639, .34994292259216, .3424659371376, .35532799363136, .39506548643112, .41180691123009, .37130555510521, .40151777863503, .40951976180077, .33306270837784, .40587121248245, .35764938592911, .35284259915352, .34843212366104, .34438464045525, .36860400438309, .3990384042263, .54691004753113, .44432625174522, .70020270347595, .70163971185684, .77033877372742, .78572767972946, .95923948287964, 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1.0992801189423, 1.4178918600082, 1.2780615091324, 1.3436778783798, 1.727570772171, 1.376532793045, 1.1185711622238, 1.2548811435699, 1.2139776945114, 1.22409760952, 1.2136551141739, 1.2040791511536, 1.2232189178467, 1.1931306123734, 1.1573059558868, 1.0603547096252, 1.1422899961472, 1.0268490314484, 1.0556720495224, 1.1264756917953, 1.0764141082764, 1.0978548526764, 1.1536711454391, 1.025780916214, 1.034966468811, 1.1074740886688, 1.1707112789154, 1.0496238470078, 1.1209251880646, 1.1271858215332, .93740028142929, .90130144357681, 1.0357736349106, .87323325872421, .75861483812332, .93606770038605, .85732334852219, .87216699123383, .97779452800751, .88410341739655, 1.0446182489395, 1.0177079439163, 1.144193649292, 1.2372444868088, 1.1155867576599, 1.2619564533234, 1.0462523698807, 1.0816910266876, .85130125284195, .76972281932831, 1.1335872411728, .92024201154709, 1.0416384935379, 1.1102936267853, .91037821769714, .85678082704544, 1.022847533226, 1.0930491685867, 1.0342184305191, 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.63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035, .63160264492035]) stdp = np.array([ 0, 0, .04999904707074, .06866559386253, .02903163060546, .07047952711582, .03383458778262, .08519082516432, .06387747824192, .0323903337121, .0664371997118, .056028008461, .05634552612901, .08741936087608, .04945361241698, .0881454795599, .06608437746763, .05997726693749, .1058451384306, .07246486097574, .10775856673717, .06419499218464, .07649331539869, .08432687073946, .10236189514399, .09031195193529, .11902847886086, .08933536708355, .13242828845978, .18790599703789, .1410321444273, .2076324224472, .12561346590519, .16128000617027, .19236192107201, .20115886628628, .23716603219509, .22255305945873, .28473255038261, .27441227436066, .28466689586639, .34994292259216, .3424659371376, .35532799363136, .39506548643112, .41180691123009, .37130555510521, .40151777863503, .40951976180077, .33306270837784, .40587121248245, .35764938592911, .35284259915352, .34843212366104, .34438464045525, .36860400438309, .3990384042263, .54691004753113, .44432625174522, .70020270347595, .70163971185684, .77033877372742, .78572767972946, .95923948287964, .90811860561371, .77250319719315, .85019183158875, .83438217639923, .83959633111954, .67678385972977, .81331378221512, .8202628493309, .79870623350143, .93831378221512, .8281461596489, .8256653547287, .9071888923645, .95076316595078, 1.0827594995499, 1.1249971389771, 1.1078934669495, 1.3271758556366, 1.4741442203522, 1.4939774274826, 1.7192279100418, 1.8355281352997, 1.5873348712921, 1.7079899311066, 1.8515517711639, 1.7368041276932, 1.8895095586777, 1.7913619279861, 1.5485136508942, 1.3914349079132, 1.8569093942642, 1.378589630127, 1.0909280776978, 1.2919955253601, 1.2874838113785, 1.2636196613312, 1.3255174160004, 1.2952193021774, 1.1754019260406, 1.2002106904984, 1.0717958211899, 1.2283787727356, 1.0664055347443, 1.0640426874161, 1.2097471952438, .49885395169258, .91795635223389, .88015007972717, 1.0048481225967, 1.0485925674438, 1.0131514072418, 1.0480036735535, 1.0044000148773, 1.0596977472305, 1.0989319086075, 1.1431447267532, 1.1360602378845, 1.316884636879, 1.2248164415359, 1.0992801189423, 1.4178918600082, 1.2780615091324, 1.3436778783798, 1.727570772171, 1.376532793045, 1.1185711622238, 1.2548811435699, 1.2139776945114, 1.22409760952, 1.2136551141739, 1.2040791511536, 1.2232189178467, 1.1931306123734, 1.1573059558868, 1.0603547096252, 1.1422899961472, 1.0268490314484, 1.0556720495224, 1.1264756917953, 1.0764141082764, 1.0978548526764, 1.1536711454391, 1.025780916214, 1.034966468811, 1.1074740886688, 1.1707112789154, 1.0496238470078, 1.1209251880646, 1.1271858215332, .93740028142929, .90130144357681, 1.0357736349106, .87323325872421, .75861483812332, .93606770038605, .85732334852219, .87216699123383, .97779452800751, .88410341739655, 1.0446182489395, 1.0177079439163, 1.144193649292, 1.2372444868088, 1.1155867576599, 1.2619564533234, 1.0462523698807, 1.0816910266876, .85130125284195, .76972281932831, 1.1335872411728, .92024201154709, 1.0416384935379, 1.1102936267853, .91037821769714, .85678082704544, 1.022847533226, 1.0930491685867, 1.0342184305191, 1.2070096731186, 1.2472279071808, 1.0886085033417, 1.3604420423508, 1.1053978204727, 2.0939025878906, 1.0898643732071, 1.3238569498062, 1.5171576738358, .77435439825058, 1.3360253572464, 1.5512014627457, 1.3569095134735, 1.4669530391693, 1.9312930107117, 1.52878677845, 2.3952746391296, .80755305290222, -.2365039139986, .85178333520889, 1.1858888864517]) icstats = np.array([ 202, np.nan, -240.21658671417, 4, 488.43317342834, 501.66624421795]) results = Bunch( llf=llf, nobs=nobs, k=k, k_exog=k_exog, sigma=sigma, chi2=chi2, df_model=df_model, k_ar=k_ar, k_ma=k_ma, params=params, cov_params=cov_params, xb=xb, y=y, resid=resid, yr=yr, mse=mse, stdp=stdp, icstats=icstats ) statsmodels-0.12.2/statsmodels/tsa/tests/results/arima211nc_results.py000066400000000000000000000541321400612667500261370ustar00rootroot00000000000000import numpy as np from statsmodels.tools.tools import Bunch llf = np.array([-241.25977940638]) nobs = np.array([202]) k = np.array([4]) k_exog = np.array([1]) sigma = np.array([.79533686587485]) chi2 = np.array([48655.961417345]) df_model = np.array([3]) k_ar = np.array([2]) k_ma = np.array([1]) params = np.array([ 1.1870704073154, -.19095698898571, -.90853757573555, .79533686587485]) cov_params = np.array([ .00204336743511, -.00177522179187, -.00165894353702, -.00031352141782, -.00177522179187, .00157376214003, .00132907629148, .00030367391511, -.00165894353702, .00132907629148, .00210988984438, .00024199988464, -.00031352141782, .00030367391511, .00024199988464, .00027937875185]).reshape(4, 4) xb = np.array([ 0, 0, .11248598247766, .14283391833305, .0800810828805, .12544548511505, .07541109621525, .1297073662281, .10287435352802, .06303016841412, .09501431882381, .08120259642601, .07862555980682, .10874316096306, .06787430495024, .10527064651251, .08142036944628, .07337106764317, .11828763782978, .08380854874849, .11801292747259, .07338324189186, .0842502862215, .09106454998255, .10832596570253, .09570593386889, .1236881390214, .09362822026014, .13587079942226, .19111332297325, .14459040760994, .21043147146702, .12866979837418, .16308072209358, .19356986880302, .20215991139412, .23782986402512, .22326464951038, .28485587239265, .27474755048752, .28465977311134, .34938132762909, .3421268761158, .35463020205498, .39384591579437, .41037485003471, .36968034505844, .39875456690788, .40607318282127, .32915702462196, .40012913942337, .35161358118057, .34572568535805, .34037715196609, .3355179131031, .35895752906799, .38901025056839, .53648668527603, .43572762608528, .69034379720688, .69410443305969, .76356476545334, .77972346544266, .95276647806168, .9030898809433, .76722019910812, .84191131591797, .82463103532791, .82802563905716, .66399103403091, .79665386676788, .80260843038559, .78016436100006, .91813576221466, .80874294042587, .80483394861221, .8848432302475, .92809981107712, 1.0597171783447, 1.1029140949249, 1.0864543914795, 1.3046631813049, 1.4528053998947, 1.4744025468826, 1.6993381977081, 1.816978096962, 1.5705223083496, 1.6871707439423, 1.8281806707382, 1.7127912044525, 1.8617957830429, 1.7624272108078, 1.5169456005096, 1.3543643951416, 1.8122490644455, 1.3362231254578, 1.0437293052673, 1.2371381521225, 1.2306576967239, 1.2056746482849, 1.2665351629257, 1.2366921901703, 1.1172571182251, 1.1408381462097, 1.0126565694809, 1.1675561666489, 1.0074961185455, 1.0045058727264, 1.1498116254807, .44306626915932, .85451871156693, .81856834888458, .94427144527435, .99084824323654, .95836746692657, .994897544384, .95328682661057, 1.0093784332275, 1.0500040054321, 1.0956697463989, 1.090208530426, 1.2714649438858, 1.1823015213013, 1.0575052499771, 1.373840212822, 1.2371203899384, 1.3022859096527, 1.6853868961334, 1.3395566940308, 1.0802086591721, 1.2114092111588, 1.1690926551819, 1.1775953769684, 1.1662193536758, 1.1558910608292, 1.1743551492691, 1.1441857814789, 1.1080147027969, 1.0106881856918, 1.0909667015076, .97610247135162, 1.0038343667984, 1.0743995904922, 1.0255174636841, 1.0471519231796, 1.1034165620804, .97707790136337, .9856236577034, 1.0578545331955, 1.1219012737274, 1.0026258230209, 1.0733016729355, 1.0802255868912, .89154416322708, .85378932952881, .98660898208618, .82558387517929, .71030122041702, .88567733764648, .80868631601334, .82387971878052, .92999804019928, .83861750364304, .99909782409668, .97461491823196, 1.1019765138626, 1.1970175504684, 1.0780508518219, 1.2238110303879, 1.0100719928741, 1.0434579849243, .81277370452881, .72809249162674, 1.0880596637726, .87798285484314, .99824965000153, 1.0677480697632, .86986482143402, .81499886512756, .97921711206436, 1.0504562854767, .99342101812363, 1.1660186052322, 1.208247423172, 1.0516448020935, 1.3215674161911, 1.0694575309753, 2.0531799793243, 1.0617904663086, 1.2885792255402, 1.4795436859131, .73947989940643, 1.290878534317, 1.506583571434, 1.3157633543015, 1.424609541893, 1.8879710435867, 1.4916514158249, 2.3532779216766, .77780252695084, -.27798706293106, .7862361073494, 1.1202166080475]) y = np.array([ np.nan, 28.979999542236, 29.26248550415, 29.492834091187, 29.450082778931, 29.665447235107, 29.625410079956, 29.879707336426, 29.942874908447, 29.873029708862, 30.015014648438, 30.06120300293, 30.118625640869, 30.318742752075, 30.287874221802, 30.485269546509, 30.521421432495, 30.553371429443, 30.808288574219, 30.833808898926, 31.058013916016, 31.023384094238, 31.104249954224, 31.211065292358, 31.388326644897, 31.475704193115, 31.703687667847, 31.743627548218, 32.015869140625, 32.471111297607, 32.594593048096, 33.060428619385, 33.028671264648, 33.263080596924, 33.593570709229, 33.902160644531, 34.337829589844, 34.623264312744, 35.184856414795, 35.574745178223, 35.984661102295, 36.649379730225, 37.142127990723, 37.654628753662, 38.293846130371, 38.910373687744, 39.269680023193, 39.798755645752, 40.306076049805, 40.42915725708, 41.00012588501, 41.251613616943, 41.545726776123, 41.840377807617, 42.135517120361, 42.558959960938, 43.089012145996, 44.236488342285, 44.635726928711, 46.290340423584, 47.494102478027, 48.863563537598, 50.079723358154, 51.952766418457, 53.203090667725, 53.767219543457, 54.841911315918, 55.724632263184, 56.628025054932, 56.763988494873, 57.796653747559, 58.702610015869, 59.480163574219, 60.91813659668, 61.608741760254, 62.404830932617, 63.584842681885, 64.828102111816, 66.559715270996, 68.202911376953, 69.586456298828, 71.904663085938, 74.45280456543, 76.67440032959, 79.699340820313, 82.716979980469, 84.170516967773, 86.387168884277, 89.028175354004, 90.812789916992, 93.361793518066, 95.16242980957, 95.916946411133, 96.354362487793, 99.31224822998, 99.436218261719, 98.943733215332, 100.03713989258, 101.03066253662, 102.00567626953, 103.36653137207, 104.5366973877, 105.21725463867, 106.24083709717, 106.71265411377, 108.1675567627, 108.70749664307, 109.50450897217, 111.04981231689, 109.14306640625, 110.35451507568, 111.01856231689, 112.34427642822, 113.6908416748, 114.7583694458, 115.99489593506, 116.95328521729, 118.20937347412, 119.55000305176, 120.9956741333, 122.29020690918, 124.37145996094, 125.68230438232, 126.45750427246, 128.87384033203, 130.13711547852, 131.80229187012, 135.08538818359, 136.03955078125, 136.18022155762, 137.4114074707, 138.36909484863, 139.47760009766, 140.56620788574, 141.65588378906, 142.87435913086, 143.94418334961, 144.90802001953, 145.51068115234, 146.69097900391, 147.27610778809, 148.2038269043, 149.47439575195, 150.4255065918, 151.5471496582, 152.90342712402, 153.57708740234, 154.4856262207, 155.75785827637, 157.22190856934, 158.00262451172, 159.2733001709, 160.48022460938, 160.79153442383, 161.25378417969, 162.4866027832, 162.82557678223, 162.9102935791, 164.08567810059, 164.70867919922, 165.52388000488, 166.82998657227, 167.53861999512, 169.09910583496, 170.27461242676, 172.00196838379, 173.89701843262, 174.97804260254, 176.82382202148, 177.41006469727, 178.44345092773, 178.41278076172, 178.42808532715, 180.38806152344, 180.87797546387, 182.1982421875, 183.66775512695, 184.06985473633, 184.51499938965, 185.87921142578, 187.35046386719, 188.3934173584, 190.26602172852, 192.00825500488, 192.85165405273, 195.12156677246, 195.76945495605, 201.25317382813, 200.4617767334, 201.98857116699, 204.17953491211, 202.63948059082, 204.86488342285, 207.42657470703, 208.65376281738, 210.55760192871, 214.38296508789, 215.48864746094, 220.96327209473, 217.66680908203, 211.89601135254, 213.45724487305, 215.58921813965]) resid = np.array([ np.nan, .17000007629395, .08751478046179, -.12283346056938, .08991899341345, -.11544716358185, .12458966672421, -.03970721364021, -.13287504017353, .04697044193745, -.03501485288143, -.02120122499764, .09137260913849, -.09874293208122, .09212554246187, -.04526927694678, -.04142136126757, .13662992417812, -.0582881718874, .10619198530912, -.10801269859076, -.00338354869746, .01575009897351, .06893529742956, -.00832748971879, .10429482907057, -.05368844047189, .13637132942677, .26412883400917, -.02111134678125, .2554073035717, -.16042841970921, .07132714986801, .13692232966423, .1064293757081, .19783779978752, .0621731877327, .27673536539078, .11514183133841, .12525399029255, .31533870100975, .15061867237091, .15787313878536, .24537208676338, .20615255832672, -.01037331111729, .13031965494156, .10124543309212, -.20607624948025, .1708429902792, -.10012608766556, -.05161434784532, -.04572645947337, -.04037792980671, .06448362022638, .14104247093201, .61098974943161, -.03648666664958, .96427005529404, .50965696573257, .60589480400085, .43643599748611, .9202772974968, .34723278880119, -.20308908820152, .23277981579304, .05809023976326, .07536666095257, -.52802640199661, .23601049184799, .1033476293087, -.00260917330161, .51983487606049, -.11813650280237, -.00874368380755, .29516834020615, .31515756249428, .67189866304398, .54028129577637, .29708743095398, 1.0135440826416, 1.095338344574, .74719160795212, 1.3256005048752, 1.2006633281708, -.11698111891747, .52947622537613, .81282931566238, .07182084023952, .68721032142639, .03820572793484, -.7624272108078, -.91694712638855, 1.1456356048584, -1.2122505903244, -1.5362200737, -.14372782409191, -.23713812232018, -.2306577116251, .09432080388069, -.06653053313494, -.43669676780701, -.11725706607103, -.54083967208862, .28734645247459, -.467559248209, -.20749309659004, .39549562335014, -2.3498160839081, .3569367825985, -.15452179312706, .38143622875214, .35572397708893, .1091578528285, .24162948131561, .00510244909674, .24671010673046, .29062458872795, .34999752044678, .20432561635971, .80979299545288, .12853652238846, -.28230002522469, 1.042493224144, .02615367434919, .36288577318192, 1.5977079868317, -.38538381457329, -.93954759836197, .01978221163154, -.21140915155411, -.06908652186394, -.07760456204414, -.06621328741312, .0441059358418, -.07434900850058, -.14418575167656, -.40801778435707, .08931794017553, -.39096972346306, -.07610860466957, .19616261124611, -.07439963519573, .07448863238096, .25285106897354, -.30341354012489, -.07708399742842, .21437329053879, .34215462207794, -.22190742194653, .19737112522125, .12669529020786, -.58022564649582, -.3915441930294, .24621678888798, -.48660898208618, -.6255869269371, .28969877958298, -.18568041920662, -.00868325773627, .37611722946167, -.12999498844147, .5613916516304, .20089910924435, .6253759264946, .69802659749985, .00297940592282, .621961414814, -.42382326722145, -.01007199659944, -.84344571828842, -.71278285980225, .87191361188889, -.38806268572807, .32201409339905, .40175950527191, -.4677571952343, -.36986482143402, .38499811291695, .42079201340675, .04953457415104, .70659118890762, .53397834300995, -.20824746787548, .94835525751114, -.42157354950905, 3.4305424690247, -1.8531830310822, .23821261525154, .71142077445984, -2.2795467376709, .93453133106232, 1.0551145076752, -.08858433365822, .47923478484154, 1.9373899698257, -.38597220182419, 3.1213552951813, -4.0742712020874, -5.4928140640259, .77499634027481, 1.0117527246475, .79578375816345]) yr = np.array([ np.nan, .17000007629395, .08751478046179, -.12283346056938, .08991899341345, -.11544716358185, .12458966672421, -.03970721364021, -.13287504017353, .04697044193745, -.03501485288143, -.02120122499764, .09137260913849, -.09874293208122, .09212554246187, -.04526927694678, -.04142136126757, .13662992417812, -.0582881718874, .10619198530912, -.10801269859076, -.00338354869746, .01575009897351, .06893529742956, -.00832748971879, .10429482907057, -.05368844047189, .13637132942677, .26412883400917, -.02111134678125, .2554073035717, -.16042841970921, .07132714986801, .13692232966423, .1064293757081, .19783779978752, .0621731877327, .27673536539078, .11514183133841, .12525399029255, .31533870100975, .15061867237091, .15787313878536, .24537208676338, .20615255832672, -.01037331111729, .13031965494156, .10124543309212, -.20607624948025, .1708429902792, -.10012608766556, -.05161434784532, -.04572645947337, -.04037792980671, .06448362022638, .14104247093201, .61098974943161, -.03648666664958, .96427005529404, .50965696573257, .60589480400085, .43643599748611, .9202772974968, .34723278880119, -.20308908820152, .23277981579304, .05809023976326, .07536666095257, -.52802640199661, .23601049184799, .1033476293087, -.00260917330161, .51983487606049, -.11813650280237, -.00874368380755, .29516834020615, .31515756249428, .67189866304398, .54028129577637, .29708743095398, 1.0135440826416, 1.095338344574, .74719160795212, 1.3256005048752, 1.2006633281708, -.11698111891747, .52947622537613, .81282931566238, .07182084023952, .68721032142639, .03820572793484, -.7624272108078, -.91694712638855, 1.1456356048584, -1.2122505903244, -1.5362200737, -.14372782409191, -.23713812232018, -.2306577116251, .09432080388069, -.06653053313494, -.43669676780701, -.11725706607103, -.54083967208862, .28734645247459, -.467559248209, -.20749309659004, .39549562335014, -2.3498160839081, .3569367825985, -.15452179312706, .38143622875214, .35572397708893, .1091578528285, .24162948131561, .00510244909674, .24671010673046, .29062458872795, .34999752044678, .20432561635971, .80979299545288, .12853652238846, -.28230002522469, 1.042493224144, .02615367434919, .36288577318192, 1.5977079868317, -.38538381457329, -.93954759836197, .01978221163154, -.21140915155411, -.06908652186394, -.07760456204414, -.06621328741312, .0441059358418, -.07434900850058, -.14418575167656, -.40801778435707, .08931794017553, -.39096972346306, -.07610860466957, .19616261124611, -.07439963519573, .07448863238096, .25285106897354, -.30341354012489, -.07708399742842, .21437329053879, .34215462207794, -.22190742194653, .19737112522125, .12669529020786, -.58022564649582, -.3915441930294, .24621678888798, -.48660898208618, -.6255869269371, .28969877958298, -.18568041920662, -.00868325773627, .37611722946167, -.12999498844147, .5613916516304, .20089910924435, .6253759264946, .69802659749985, .00297940592282, .621961414814, -.42382326722145, -.01007199659944, -.84344571828842, -.71278285980225, .87191361188889, -.38806268572807, .32201409339905, .40175950527191, -.4677571952343, -.36986482143402, .38499811291695, .42079201340675, .04953457415104, .70659118890762, .53397834300995, -.20824746787548, .94835525751114, -.42157354950905, 3.4305424690247, -1.8531830310822, .23821261525154, .71142077445984, -2.2795467376709, .93453133106232, 1.0551145076752, -.08858433365822, .47923478484154, 1.9373899698257, -.38597220182419, 3.1213552951813, -4.0742712020874, -5.4928140640259, .77499634027481, 1.0117527246475, .79578375816345]) mse = np.array([ 1.4402351379395, 1.4402351379395, .80966705083847, .74677377939224, .71241801977158, .69108927249908, .67678099870682, .66667699813843, .6592805981636, .6537224650383, .64946305751801, .64614951610565, .64354157447815, .64147007465363, .639812707901, .63847899436951, .63740062713623, .63652545213699, .63581293821335, .63523155450821, .63475602865219, .63436657190323, .63404709100723, .63378477096558, .63356912136078, .63339179754257, .63324582576752, .63312560319901, .63302659988403, .63294500112534, .63287770748138, .63282227516174, .63277649879456, .63273876905441, .63270765542984, .63268196582794, .63266080617905, .63264334201813, .63262891769409, .63261699676514, .63260716199875, .63259905576706, .63259238004684, .63258683681488, .63258230686188, .63257849216461, .63257539272308, .63257282972336, .63257074356079, .63256901502609, .63256752490997, .63256633281708, .63256537914276, .63256454467773, .63256388902664, .63256335258484, .63256287574768, .63256251811981, .63256222009659, .63256192207336, .63256174325943, .6325615644455, .63256138563156, .63256126642227, .63256120681763, .63256108760834, .63256102800369, .63256096839905, .63256096839905, .6325609087944, .63256084918976, .63256084918976, .63256084918976, .63256078958511, .63256078958511, .63256078958511, .63256078958511, .63256078958511, .63256078958511, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047, .63256072998047]) icstats = np.array([ 202, np.nan, -241.25977940638, 4, 490.51955881276, 503.75262960236]) results = Bunch( llf=llf, nobs=nobs, k=k, k_exog=k_exog, sigma=sigma, chi2=chi2, df_model=df_model, k_ar=k_ar, k_ma=k_ma, params=params, cov_params=cov_params, xb=xb, y=y, resid=resid, yr=yr, mse=mse, icstats=icstats ) statsmodels-0.12.2/statsmodels/tsa/tests/results/arima212_forecast.csv000066400000000000000000000142151400612667500260650ustar00rootroot00000000000000dates, cpi, predict, stderr, conf1, conf2 1950:1, 28.980,,,, 1950:2, 29.150, 29.848,, 1950:3, 29.350, 29.751,, 1950:4, 29.370, 29.925,, 1951:1, 29.540, 29.788,, 1951:2, 29.550, 30.005,, 1951:3, 29.750, 29.872,, 1951:4, 29.840, 30.181,, 1952:1, 29.810, 30.125,, 1952:2, 29.920, 30.154,, 1952:3, 29.980, 30.203,, 1952:4, 30.040, 30.290,, 1953:1, 30.210, 30.306,, 1953:2, 30.220, 30.535,, 1953:3, 30.380, 30.450,, 1953:4, 30.440, 30.721,, 1954:1, 30.480, 30.657,, 1954:2, 30.690, 30.793,, 1954:3, 30.750, 30.955,, 1954:4, 30.940, 31.034,, 1955:1, 30.950, 31.237,, 1955:2, 31.020, 31.194,, 1955:3, 31.120, 31.310,, 1955:4, 31.280, 31.371,, 1956:1, 31.380, 31.588,, 1956:2, 31.580, 31.629,, 1956:3, 31.650, 31.915,, 1956:4, 31.880, 31.882,, 1957:1, 32.280, 32.248,, 1957:2, 32.450, 32.601,, 1957:3, 32.850, 32.794,, 1957:4, 32.900, 33.245,, 1958:1, 33.100, 33.179,, 1958:2, 33.400, 33.502,, 1958:3, 33.700, 33.723,, 1958:4, 34.100, 34.119,, 1959:1, 34.400, 34.481,, 1959:2, 34.900, 34.819,, 1959:3, 35.300, 35.358,, 1959:4, 35.700, 35.737,, 1960:1, 36.300, 36.176,, 1960:2, 36.800, 36.821,, 1960:3, 37.300, 37.301,, 1960:4, 37.900, 37.844,, 1961:1, 38.500, 38.456,, 1961:2, 38.900, 39.082,, 1961:3, 39.400, 39.423,, 1961:4, 39.900, 39.995,, 1962:1, 40.100, 40.436,, 1962:2, 40.600, 40.599,, 1962:3, 40.900, 41.175,, 1962:4, 41.200, 41.354,, 1963:1, 41.500, 41.738,, 1963:2, 41.800, 41.936,, 1963:3, 42.200, 42.311,, 1963:4, 42.700, 42.658,, 1964:1, 43.700, 43.247,, 1964:2, 44.200, 44.354,, 1964:3, 45.600, 44.715,, 1964:4, 46.800, 46.538,, 1965:1, 48.100, 47.464,, 1965:2, 49.300, 49.162,, 1965:3, 51.000, 50.071,, 1965:4, 52.300, 52.276,, 1966:1, 53.000, 53.138,, 1966:2, 54.000, 54.101,, 1966:3, 54.900, 54.875,, 1966:4, 55.800, 55.948,, 1967:1, 56.100, 56.663,, 1967:2, 57.000, 56.919,, 1967:3, 57.900, 57.917,, 1967:4, 58.700, 58.733,, 1968:1, 60.000, 59.585,, 1968:2, 60.800, 60.985,, 1968:3, 61.600, 61.618,, 1968:4, 62.700, 62.545,, 1969:1, 63.900, 63.602,, 1969:2, 65.500, 64.917,, 1969:3, 67.100, 66.596,, 1969:4, 68.500, 68.249,, 1970:1, 70.600, 69.639,, 1970:2, 73.000, 72.023,, 1970:3, 75.200, 74.438,, 1970:4, 78.000, 76.768,, 1971:1, 80.900, 79.775,, 1971:2, 82.600, 82.748,, 1971:3, 84.700, 84.201,, 1971:4, 87.200, 86.591,, 1972:1, 89.100, 88.976,, 1972:2, 91.500, 90.888,, 1972:3, 93.400, 93.401,, 1972:4, 94.400, 95.103,, 1973:1, 95.000, 95.950,, 1973:2, 97.500, 96.342,, 1973:3, 98.100, 99.392,, 1973:4, 97.900, 99.031,, 1974:1, 98.800, 99.216,, 1974:2, 99.800, 99.751,, 1974:3, 100.800, 101.044,, 1974:4, 102.100, 101.727 ,, 1975:1, 103.300, 103.382 ,, 1975:2, 104.100, 104.251 ,, 1975:3, 105.100, 105.233 ,, 1975:4, 105.700, 106.052 ,, 1976:1, 107.000, 106.667 ,, 1976:2, 107.700, 108.081 ,, 1976:3, 108.500, 108.538 ,, 1976:4, 109.900, 109.523 ,, 1977:1, 108.700, 110.907 ,, 1977:2, 109.500, 108.963 ,, 1977:3, 110.200, 110.651 ,, 1977:4, 111.400, 110.524 ,, 1978:1, 112.700, 112.660 ,, 1978:2, 113.800, 113.230 ,, 1978:3, 115.000, 115.051 ,, 1978:4, 116.000, 115.662 ,, 1979:1, 117.200, 117.204 ,, 1979:2, 118.500, 117.975 ,, 1979:3, 119.900, 119.754 ,, 1979:4, 121.200, 120.802 ,, 1980:1, 123.100, 122.467 ,, 1980:2, 124.500, 124.261 ,, 1980:3, 125.400, 125.749 ,, 1980:4, 127.500, 126.429 ,, 1981:1, 128.900, 129.043 ,, 1981:2, 130.500, 129.915 ,, 1981:3, 133.400, 132.075 ,, 1981:4, 134.700, 134.922 ,, 1982:1, 135.100, 136.050 ,, 1982:2, 136.200, 136.239 ,, 1982:3, 137.200, 137.516 ,, 1982:4, 138.300, 138.258 ,, 1983:1, 139.400, 139.559 ,, 1983:2, 140.500, 140.434 ,, 1983:3, 141.700, 141.711 ,, 1983:4, 142.800, 142.753 ,, 1984:1, 143.800, 143.966 ,, 1984:2, 144.500, 144.807 ,, 1984:3, 145.600, 145.519 ,, 1984:4, 146.300, 146.646 ,, 1985:1, 147.200, 147.195 ,, 1985:2, 148.400, 148.223 ,, 1985:3, 149.400, 149.379 ,, 1985:4, 150.500, 150.396 ,, 1986:1, 151.800, 151.507 ,, 1986:2, 152.600, 152.878 ,, 1986:3, 153.500, 153.502 ,, 1986:4, 154.700, 154.540 ,, 1987:1, 156.100, 155.683 ,, 1987:2, 157.000, 157.240 ,, 1987:3, 158.200, 157.903 ,, 1987:4, 159.400, 159.379 ,, 1988:1, 159.900, 160.350 ,, 1988:2, 160.400, 160.856 ,, 1988:3, 161.500, 161.226 ,, 1988:4, 162.000, 162.540 ,, 1989:1, 162.200, 162.682 ,, 1989:2, 163.200, 163.025 ,, 1989:3, 163.900, 164.017 ,, 1989:4, 164.700, 164.677 ,, 1990:1, 165.900, 165.527 ,, 1990:2, 166.700, 166.815 ,, 1990:3, 168.100, 167.488 ,, 1990:4, 169.300, 169.190 ,, 1991:1, 170.900, 170.157 ,, 1991:2, 172.700, 172.157 ,, 1991:3, 173.900, 173.775 ,, 1991:4, 175.600, 175.092 ,, 1992:1, 176.400, 176.843 ,, 1992:2, 177.400, 177.401 ,, 1992:3, 177.600, 178.590 ,, 1992:4, 177.700, 178.310 ,, 1993:1, 179.300, 178.624 ,, 1993:2, 180.000, 180.330 ,, 1993:3, 181.200, 180.791 ,, 1993:4, 182.600, 182.320 ,, 1994:1, 183.200, 183.535 ,, 1994:2, 183.700, 184.132 ,, 1994:3, 184.900, 184.510 ,, 1994:4, 186.300, 185.955 ,, 1995:1, 187.400, 187.256 ,, 1995:2, 189.100, 188.443 ,, 1995:3, 190.800, 190.274 ,, 1995:4, 191.800, 191.988 ,, 1996:1, 193.800, 192.858 ,, 1996:2, 194.700, 195.254 ,, 1996:3, 199.200, 195.589 ,, 1996:4, 199.400, 201.698 ,, 1997:1, 200.700, 199.660 ,, 1997:2, 202.700, 203.065 ,, 1997:3, 201.900, 203.288 ,, 1997:4, 203.574, 203.327 ,, 1998:1, 205.920, 204.543 ,, 1998:2, 207.338, 207.635 ,, 1998:3, 209.133, 208.278 ,, 1998:4, 212.495, 210.909 ,, 1999:1, 213.997, 214.077 ,, 1999:2, 218.610, 215.531 ,, 1999:3, 216.889, 221.137 ,, 1999:4, 212.174, 217.006 ,, 2000:1, 212.671, 212.741 ,, 2000:2, 214.469, 213.240 ,, 2000:3, 216.385, 215.464,,, 2000:4,, 217.291, 0.7691, 215.784, 218.799 2001:1,, 218.197, 1.2775, 215.693, 220.701 2001:2,, 219.100, 1.6382, 215.889, 222.311 2001:3,, 220.002, 2.0322, 216.019, 223.985 2001:4,, 220.902, 2.3838, 216.230, 225.574 2002:1,, 221.801, 2.7544, 216.403, 227.200 2002:2,, 222.699, 3.1082, 216.607, 228.791 2002:3,, 223.595, 3.4721, 216.790, 230.400 2002:4,, 224.490, 3.8288, 216.986, 231.994 2003:1,, 225.384, 4.1908, 217.170, 233.598 2003:2,, 226.276, 4.5494, 217.360, 235.193 2003:3,, 227.168, 4.9105, 217.544, 236.793 2003:4,, 228.059, 5.2698, 217.730, 238.387 2004:1,, 228.948, 5.6300, 217.914, 239.983 2004:2,, 229.837, 5.9888, 218.099, 241.574 2004:3,, 230.724, 6.3475, 218.283, 243.165 2004:4,, 231.611, 6.7049, 218.470, 244.752 2005:1,, 232.497, 7.0614, 218.657, 246.337 2005:2,, 233.382, 7.4165, 218.846, 247.918 2005:3,, 234.266, 7.7704, 219.037, 249.496 statsmodels-0.12.2/statsmodels/tsa/tests/results/arima_forecast.inp000066400000000000000000000013441400612667500256320ustar00rootroot00000000000000open /home/skipper/statsmodels/statsmodels/statsmodels/datasets/macrodata/macrodata.csv setobs 4 1959:1 --time-series dataset addobs 25 # (1,1,1) arima 1 1 1 ; cpi --nc fcast 2000:1 2015:04 fc111nc fcast 2000:1 2015:04 fc111ncdyn --dynamic arima 1 1 1 ; cpi fcast 2000:1 2015:04 fc111c fcast 2000:1 2015:04 fc111cdyn --dynamic # (2,1,1) arima 2 1 1 ; cpi --nc fcast 2000:1 2015:04 fc211nc fcast 2000:1 2015:04 fc211ncdyn --dynamic arima 2 1 1 ; cpi fcast 2000:1 2015:04 fc211c fcast 2000:1 2015:04 fc211cdyn --dynamic smpl 2000:1 2015:04 store '/home/skipper/statsmodels/statsmodels-skipper/statsmodels/tsa/tests/results/results_arima_forecasts.csv' fc111nc fc111ncdyn fc111c fc111cdyn fc211nc fc211ncdyn fc211c fc211cdyn --omit-obs statsmodels-0.12.2/statsmodels/tsa/tests/results/arma_forecast.inp000066400000000000000000000013121400612667500254540ustar00rootroot00000000000000open \ /home/skipper/statsmodels/statsmodels/statsmodels/tsa/tests/results/y_arma_data.csv setobs 12 1980:01 --time-series dataset addobs 10 # (0,0) arima 1 0 1 ; 1 --nc fcast 2000:11 2001:08 # (4,1) arima 4 0 1 ; 3 --nc fcast 2000:11 2001:08 # (5,0) arima 5 0 0 ; 5 --nc fcast 2000:11 2001:08 # (1,1) c arima 1 0 1 ; 7 fcast 2000:11 2001:08 # (4,1) c arima 4 0 1 ; 9 fcast 2000:11 2001:08 # (5,0) c arima 5 0 0 ; 11 fcast 2000:11 2001:08 smpl 2000:11 2001:08 #store '/home/skipper/statsmodels/statsmodels-git/scikits/statsmodels/tsa/tests/results/results_arma_forecasts.csv' fc11 fe11 fc41 fe41 fc50 fe50 fc11c fe11c fc41c fe41c fc50c fe50c --omit-obs # no way to capture errors as far as I can tell statsmodels-0.12.2/statsmodels/tsa/tests/results/bds_data.csv000066400000000000000000000076031400612667500244250ustar00rootroot000000000000001,0.585528817843856,1.80509751881082,1770.7 2,0.709466017509524,-0.481647363694637,1768 3,-0.109303314681054,0.620379801298422,1766.5 4,-0.453497173462763,0.612123492650849,1793.3 5,0.605887455840394,-0.162310976918126,1821.8 6,-1.81795596770373,0.81187317855386,1855.3 7,0.630098551068391,2.19683354634753,1865.3 8,-0.276184105225216,2.04919033740619,1868.2 9,-0.284159743943371,1.63244563948047,1842.2 10,-0.919322002474128,0.254271192814055,1835.5 11,-0.116247806352002,0.491188279272559,1856.1 12,1.81731204370422,-0.324086578737118,1838.7 13,0.370627864257954,-1.66205024385863,1913 14,0.520216457554957,1.76773385087297,1971.2 15,-0.750531994502331,0.0258010486478081,2048.4 16,0.816899839520583,1.12851083359018,2084.4 17,-0.886357521243213,-2.38035806139704,2110.7 18,-0.331577589942552,-1.06026555215253,2145.7 19,1.12071265166956,0.937140540182908,2188.5 20,0.298723699267293,0.854451720330554,2192.2 21,0.779621924555324,1.46072940310409,2214.3 22,1.45578508247686,-1.41309877788919,2216.7 23,-0.644328429231302,0.567403253424482,2231.6 24,-1.55313740522969,0.583187653435685,2305.3 25,-1.59770951669631,-1.30679883346442,2348.4 ,,0.294465403072536,2366.2 ,,0.617253665579483,2351.8 ,,0.974274127278477,2314.6 ,,0.618212037952617,2303.5 ,,0.521369193447754,2306.4 ,,0.902503795921803,2332.4 ,,0.637454432668164,2379.1 ,,0.864301132969558,2447.7 ,,0.251117740990594,2488.1 ,,0.21506908070296,2521.4 ,,0.609476044774055,2535.5 ,,0.383444635430351,2523.9 ,,0.755271044559777,2543.8 ,,0.379736242815852,2540.6 ,,0.794972063507885,2582.1 ,,0.905691135907546,2597.9 ,,0.984026173362508,2591.7 ,,0.587947973515838,2616.6 ,,0.00946405157446861,2589.1 ,,0.320792069192976,2519 ,,0.559456733288243,2534.5 ,,0.514917560154572,2593.9 ,,0.0897118621505797,2654.3 ,,0.683250573696569,2708 ,,0.709972049575299,2776.4 ,,,2773.1 ,,,2782.8 ,,,2845.3 ,,,2832 ,,,2836.6 ,,,2800.2 ,,,2816.9 ,,,2869.6 ,,,2915.9 ,,,2975.3 ,,,3028.7 ,,,3062.1 ,,,3090.4 ,,,3097.9 ,,,3138.4 ,,,3177.7 ,,,3237.6 ,,,3262.2 ,,,3335.4 ,,,3373.7 ,,,3419.5 ,,,3429 ,,,3513.3 ,,,3560.9 ,,,3633.2 ,,,3720.8 ,,,3812.2 ,,,3824.9 ,,,3850 ,,,3881.2 ,,,3915.4 ,,,3916.2 ,,,3947.5 ,,,3977.6 ,,,4059.5 ,,,4128.5 ,,,4156.7 ,,,4174.7 ,,,4240.5 ,,,4252.8 ,,,4279.7 ,,,4259.6 ,,,4252.9 ,,,4260.7 ,,,4298.6 ,,,4253 ,,,4370.3 ,,,4395.1 ,,,4430.2 ,,,4442.5 ,,,4521.9 ,,,4629.1 ,,,4673.5 ,,,4750.5 ,,,4872 ,,,4928.4 ,,,4902.1 ,,,4948.8 ,,,4905.4 ,,,4918 ,,,4869.4 ,,,4850.2 ,,,4791.2 ,,,4827.8 ,,,4909.1 ,,,4973.3 ,,,5086.3 ,,,5124.6 ,,,5149.7 ,,,5187.1 ,,,5247.3 ,,,5351.6 ,,,5447.3 ,,,5446.1 ,,,5464.7 ,,,5679.7 ,,,5735.4 ,,,5811.3 ,,,5821 ,,,5826.4 ,,,5868.3 ,,,5884.5 ,,,5903.4 ,,,5782.4 ,,,5771.7 ,,,5878.4 ,,,6000.6 ,,,5952.7 ,,,6025 ,,,5950 ,,,5852.3 ,,,5884 ,,,5861.4 ,,,5866 ,,,5938.9 ,,,6072.4 ,,,6192.2 ,,,6320.2 ,,,6442.8 ,,,6554 ,,,6617.7 ,,,6671.6 ,,,6734.5 ,,,6791.5 ,,,6897.6 ,,,6950 ,,,7016.8 ,,,7045 ,,,7112.9 ,,,7147.3 ,,,7186.9 ,,,7263.3 ,,,7326.3 ,,,7451.7 ,,,7490.2 ,,,7586.4 ,,,7625.6 ,,,7727.4 ,,,7799.9 ,,,7858.3 ,,,7920.6 ,,,7937.9 ,,,8020.8 ,,,8052.7 ,,,8052.6 ,,,7982 ,,,7943.4 ,,,7997 ,,,8030.7 ,,,8062.2 ,,,8150.7 ,,,8237.3 ,,,8322.3 ,,,8409.8 ,,,8425.3 ,,,8479.2 ,,,8523.8 ,,,8636.4 ,,,8720.5 ,,,8839.8 ,,,8896.7 ,,,8995.5 ,,,9017.6 ,,,9037 ,,,9112.9 ,,,9176.4 ,,,9239.3 ,,,9399 ,,,9480.8 ,,,9584.3 ,,,9658 ,,,9801.2 ,,,9924.2 ,,,10000.3 ,,,10094.8 ,,,10185.6 ,,,10320 ,,,10498.6 ,,,10592.1 ,,,10674.9 ,,,10810.7 ,,,11004.8 ,,,11033.6 ,,,11248.8 ,,,11258.3 ,,,11325 ,,,11287.8 ,,,11361.7 ,,,11330.4 ,,,11370 ,,,11467.1 ,,,11528.1 ,,,11586.6 ,,,11590.6 ,,,11638.9 ,,,11737.5 ,,,11930.7 ,,,12038.6 ,,,12117.9 ,,,12195.9 ,,,12286.7 ,,,12387.2 ,,,12515 ,,,12570.7 ,,,12670.5 ,,,12735.6 ,,,12896.4 ,,,12948.7 ,,,12950.4 ,,,13038.4 ,,,13056.1 ,,,13173.6 ,,,13269.8 ,,,13326 ,,,13266.8 ,,,13310.5 ,,,13186.9 ,,,12883.5 ,,,12711 ,,,12701 ,,,12746.7 ,,,12873.1 ,,,12947.6 ,,,13019.6 ,,,13103.5 ,,,13181.2 ,,,13183.8 ,,,13264.7 ,,,13306.9 ,,,13441 ,,,13506.4 ,,,13548.5 ,,,13652.5 ,,,13665.4 ,,,13725.7 statsmodels-0.12.2/statsmodels/tsa/tests/results/bds_results.csv000066400000000000000000000026711400612667500252150ustar00rootroot000000000000001.00000000,1.00000000,NaN,NaN,NaN,0.69666667,0.49898551 1.00000000,2.00000000,36.40567147,0.00000000,0.71739130,0.71739130,0.49898551 1.00000000,3.00000000,37.73419833,0.00000000,0.73913043,0.73913043,0.49898551 1.00000000,4.00000000,39.98711582,0.00000000,0.76190476,0.76190476,0.49898551 1.00000000,5.00000000,43.69162614,0.00000000,0.78571429,0.78571429,0.49898551 2.00000000,1.00000000,NaN,NaN,NaN,0.69666667,0.50681159 2.00000000,2.00000000,2.15098566,0.03147733,0.49275362,0.68840580,0.50681159 2.00000000,3.00000000,2.28830079,0.02212001,0.35177866,0.68379447,0.50681159 2.00000000,4.00000000,1.53581933,0.12458270,0.23376623,0.67532468,0.50681159 2.00000000,5.00000000,1.15344705,0.24872694,0.14285714,0.65714286,0.50681159 3.00000000,1.00000000,NaN,NaN,NaN,0.73877551,0.59656463 3.00000000,2.00000000,0.67088078,0.50229648,0.56207483,0.74319728,0.59656463 3.00000000,3.00000000,0.04274706,0.96590317,0.41400709,0.74468085,0.59656463 3.00000000,4.00000000,0.26226100,0.79312022,0.30804810,0.74005550,0.59656463 3.00000000,5.00000000,0.97965854,0.32725470,0.24830918,0.73526570,0.59656463 4.00000000,1.00000000,NaN,NaN,NaN,0.68170383,0.48895534 4.00000000,2.00000000,72.16152400,0.00000000,0.68069478,0.68222145,0.48895534 4.00000000,3.00000000,79.04282276,0.00000000,0.68026006,0.68275622,0.48895534 4.00000000,4.00000000,87.73840060,0.00000000,0.67997426,0.68330847,0.48895534 4.00000000,5.00000000,100.08086806,0.00000000,0.67975243,0.68387857,0.48895534 statsmodels-0.12.2/statsmodels/tsa/tests/results/corrgram.do000066400000000000000000000011231400612667500242760ustar00rootroot00000000000000* Stata do file for getting test results insheet using "/home/skipper/statsmodels/statsmodels-skipper/statsmodels/datasets/macrodata/macrodata.csv", double clear gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate ac realgdp, gen(acvar) ac realgdp, gen(acvarfft) fft corrgram realgdp matrix Q = r(Q)' svmat Q, names(Q) matrix PAC = r(PAC)' svmat PAC, names(PAC) rename PAC1 PACOLS pac realgdp, yw gen(PACYW) outsheet acvar acvarfft Q1 PACOLS PACYW using "/home/skipper/statsmodels/statsmodels-skipper/scikits/statsmodels/sandbox/tsa/tests/results/results_corrgram.csv", comma replace statsmodels-0.12.2/statsmodels/tsa/tests/results/datamlw_tls.py000066400000000000000000000146251400612667500250360ustar00rootroot00000000000000from numpy import array from statsmodels.tools.testing import Holder mlpacf = Holder() mlpacf.comment = 'mlab.parcorr(x, [], 2, nout=3)' mlpacf.name = 'mlpacf' mlpacf.lags1000 = array([ [0.], [1.], [2.], [3.], [4.], [5.], [6.], [7.], [8.], [9.], [10.], [11.], [12.], [13.], [14.], [15.], [16.], [17.], [18.], [19.], [20.]]) mlpacf.bounds1000 = array([ [0.06334064], [-0.06334064]]) mlpacf.lags100 = array([ [0.], [1.], [2.], [3.], [4.], [5.], [6.], [7.], [8.], [9.], [10.], [11.], [12.], [13.], [14.], [15.], [16.], [17.], [18.], [19.], [20.]]) mlpacf.pacf100 = array([ [1.], [0.47253777], [-0.49466966], [-0.02689319], [-0.00122204], [0.08419183], [0.03220774], [0.10404012], [0.05304617], [-0.04129564], [-0.04049451], [0.11727754], [0.11804158], [-0.05864957], [-0.15681802], [0.11828684], [0.05156002], [0.00694629], [0.01668964], [0.02236851], [-0.0909443]]) mlpacf.pacf1000 = array([ [1.00000000e+00], [5.29288262e-01], [-5.31849027e-01], [1.17440051e-02], [-5.37941905e-02], [-4.11119348e-02], [-2.40367432e-02], [2.24289891e-02], [3.33007235e-02], [4.59658302e-02], [6.65850553e-03], [-3.76714278e-02], [5.27229738e-02], [2.50796558e-02], [-4.42597301e-02], [-1.95819186e-02], [4.70451394e-02], [-1.70963705e-03], [3.04262524e-04], [-6.22001614e-03], [-1.16694989e-02]]) mlpacf.bounds100 = array([ [0.20306923], [-0.20306923]]) mlacf = Holder() mlacf.comment = 'mlab.autocorr(x, [], 2, nout=3)' mlacf.name = 'mlacf' mlacf.acf1000 = array([ [1.], [0.5291635], [-0.10186759], [-0.35798372], [-0.25894203], [-0.06398397], [0.0513664], [0.08222289], [0.08115406], [0.07674254], [0.04540619], [-0.03024699], [-0.05886634], [-0.01422948], [0.01277825], [-0.01013384], [-0.00765693], [0.02183677], [0.03618889], [0.01622553], [-0.02073507]]) mlacf.lags1000 = array([ [0.], [1.], [2.], [3.], [4.], [5.], [6.], [7.], [8.], [9.], [10.], [11.], [12.], [13.], [14.], [15.], [16.], [17.], [18.], [19.], [20.]]) mlacf.bounds1000 = array([ [0.0795181], [-0.0795181]]) mlacf.lags100 = array([ [0.], [1.], [2.], [3.], [4.], [5.], [6.], [7.], [8.], [9.], [10.], [11.], [12.], [13.], [14.], [15.], [16.], [17.], [18.], [19.], [20.]]) mlacf.bounds100 = array([ [0.24319646], [-0.24319646]]) mlacf.acf100 = array([ [1.], [0.47024791], [-0.1348087], [-0.32905777], [-0.18632437], [0.06223404], [0.16645194], [0.12589966], [0.04805397], [-0.03785273], [-0.0956997], [0.00644021], [0.17157144], [0.12370327], [-0.07597526], [-0.13865131], [0.02730275], [0.13624193], [0.10417949], [0.01114516], [-0.09727938]]) mlccf = Holder() mlccf.comment = 'mlab.crosscorr(x[4:], x[:-4], [], 2, nout=3)' mlccf.name = 'mlccf' mlccf.ccf100 = array([ [0.20745123], [0.12351939], [-0.03436893], [-0.14550879], [-0.10570855], [0.0108839], [0.1108941], [0.14562415], [0.02872607], [-0.14976649], [-0.08274954], [0.13158485], [0.18350343], [0.00633845], [-0.10359988], [-0.0416147], [0.05056298], [0.13438945], [0.17832125], [0.06665153], [-0.19999538], [-0.31700548], [-0.09727956], [0.46547234], [0.92934645], [0.44480271], [-0.09228691], [-0.21627289], [-0.05447732], [0.13786254], [0.15409039], [0.07466298], [-0.01000896], [-0.06744264], [-0.0607185], [0.04338471], [0.12336618], [0.07712367], [-0.08739259], [-0.09319212], [0.04426167]]) mlccf.lags1000 = array([ [-20.], [-19.], [-18.], [-17.], [-16.], [-15.], [-14.], [-13.], [-12.], [-11.], [-10.], [-9.], [-8.], [-7.], [-6.], [-5.], [-4.], [-3.], [-2.], [-1.], [0.], [1.], [2.], [3.], [4.], [5.], [6.], [7.], [8.], [9.], [10.], [11.], [12.], [13.], [14.], [15.], [16.], [17.], [18.], [19.], [20.]]) mlccf.bounds1000 = array([ [0.06337243], [-0.06337243]]) mlccf.ccf1000 = array([ [0.02733339], [0.04372407], [0.01082335], [-0.02755073], [-0.02076039], [0.01624263], [0.03622844], [0.02186092], [-0.00766506], [-0.0101448], [0.01279167], [-0.01424596], [-0.05893064], [-0.03028013], [0.04545462], [0.076825], [0.08124118], [0.08231121], [0.05142144], [-0.06405412], [-0.25922346], [-0.35806674], [-0.1017256], [0.5293535], [0.99891094], [0.52941977], [-0.10127572], [-0.35691466], [-0.25943369], [-0.06458511], [0.05026194], [0.08196501], [0.08242852], [0.07775845], [0.04590431], [-0.03195209], [-0.06162966], [-0.01395345], [0.01448736], [-0.00952503], [-0.00927344]]) mlccf.lags100 = array([ [-20.], [-19.], [-18.], [-17.], [-16.], [-15.], [-14.], [-13.], [-12.], [-11.], [-10.], [-9.], [-8.], [-7.], [-6.], [-5.], [-4.], [-3.], [-2.], [-1.], [0.], [1.], [2.], [3.], [4.], [5.], [6.], [7.], [8.], [9.], [10.], [11.], [12.], [13.], [14.], [15.], [16.], [17.], [18.], [19.], [20.]]) mlccf.bounds100 = array([ [0.20412415], [-0.20412415]]) mlywar = Holder() mlywar.comment = "mlab.ar(x100-x100.mean(), 10, 'yw').a.ravel()" mlywar.arcoef100 = array([ 1., -0.66685531, 0.43519425, -0.00399862, 0.05521524, -0.09366752, 0.01093454, -0.00688404, -0.04739089, 0.00127931, 0.03946846]) mlywar.arcoef1000 = array([ 1., -0.81230253, 0.55766432, -0.02370962, 0.02688963, 0.01110911, 0.02239171, -0.01891209, -0.00240527, -0.01752532, -0.06348611, 0.0609686, -0.00717163, -0.0467326, -0.00122755, 0.06004768, -0.04893984, 0.00575949, 0.00249315, -0.00560358, 0.01248498]) mlywar.name = 'mlywar' statsmodels-0.12.2/statsmodels/tsa/tests/results/fit_ets.R000066400000000000000000000037131400612667500237250ustar00rootroot00000000000000library(fpp2) library(forecast) library(jsonlite) concat <- function(...) { return(paste(..., sep="")) } # get variable or NaN get_var <- function(named, name) { if (name %in% names(named)) val <- c(named[name]) else val <- c(NaN) names(val) <- c(name) return(val) } # innov from np.random.seed(0); np.random.randn(4) innov <- c(1.76405235, 0.40015721, 0.97873798, 2.2408932) # fit all models and add fit results to list obtain_model_results <- function(models, data) { results = list() for (damped in c(TRUE, FALSE)) { results_damped = list() for (model in models) { fitted <- tryCatch((function(){ fit <- ets(data, model = model, damped = damped) pars <- list() # alpha, beta, gamma, phi for (name in c("alpha", "beta", "gamma", "phi")) { pars[name] <- get_var(fit$par, name) } pars$initstate <- fit$initstate pars$states <- fit$states pars$residuals <- fit$residuals pars$fitted <- fit$fitted pars$sigma2 <- fit$sigma2 pars$loglik <- fit$loglik pars$forecast <- forecast(fit, 4, PI = FALSE)$mean pars$simulation <- simulate(fit, 4, innov = innov) return(pars) })(), error = function(e) list()) results_damped[[model]] <- fitted } results[[as.character(damped)]] <- results_damped } return(results) } error <- c("A", "M") trend <- c("A", "M", "N") seasonal <- c("A", "M") models_seasonal <- outer(error, trend, FUN = "concat") %>% outer(seasonal, FUN = "concat") %>% as.vector results <- obtain_model_results(models_seasonal, austourists) sink("fit_ets_results_seasonal.json") cat(toJSON(results, pretty = TRUE, digits = 8)) sink() models_nonseasonal <- outer(error, trend, FUN = "concat") %>% outer(c("N"), FUN = "concat") %>% as.vector results <- obtain_model_results(models_nonseasonal, oil) sink("fit_ets_results_nonseasonal.json") cat(toJSON(results, pretty = TRUE, digits = 8)) sink() statsmodels-0.12.2/statsmodels/tsa/tests/results/fit_ets_results.json000066400000000000000000003473401400612667500262650ustar00rootroot00000000000000{ "TRUE": { "AAA": { "alpha": [0.35445427], "beta": [0.03200749], "gamma": [0.39993387], 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117LSF \ 4 Dec 2016 14:31
ã^“òØ ò 7Fcoùÿùÿùÿ÷ÿ÷ÿ÷ÿ÷ÿ÷ÿ÷ÿ÷ÿinvstment¶Ûm¶Ûm¶Ûm¶Ûm¶Ûm¶Ûm¶Ûmincmentšxà“ž@ª8jconsumpion’’©h™›0qtrmptionfq€i€¢è‘hln_invmentbà…À¢H‘°¬ˆdln_invmentm¶Ûm¶Ûm¶Ûm¶Ûm¶Ûm¶Ûmln_incentÛm¶Ûm¶Ûm¶Ûm¶Ûm¶Ûm¶Ûmdln_incÛm¶Ûm¶Ûm¶Ûm¶Ûm¶Ûm¶Ûm¶Ûmln_consumpnm¶Ûm¶Ûm¶Ûm¶Ûm¶Ûm¶Ûmdln_consumpn¶Ûm¶Ûm¶Ûm¶Ûm¶Ûm¶Ûm«04X:­ôt%8.0gUÿÿÿÿ%8.0gUÿÿÿÿ%8.0gUÿÿÿÿ%tqgUÿÿÿÿ%%8.0gÿÿÿÿ%9.0gUÿÿÿÿ%9.0gUÿÿÿÿ%9.0gUÿÿÿÿ%9%8.0gÿÿÿÿ%9.0gUÿÿÿÿ%tq%9.0g%9.0g%9.0g%9.0g%9.0g%9.0g­sP¯&«048È­sT­sL­sHÿÿ­sD¯'«048̯'0« 48Я°« @y:د'`« 48Ôÿÿÿÿÿÿÿÿ¯'€« 048Øÿÿÿÿÿÿ¯' «P48ÜHHsh¯'Ы0investment(ĉ\ÿ 4O°kB N Ðincomeent(ĉ\ÿ 4O°kB N Ðconsumption(ĉ\ÿ 4O°kB N Ðquarterion(ĉ\ÿ 4O°kB N Ðlog investment(ĉ\ÿ 4O°kB N Ðfirst-difference of ln_inv\ÿ 4O°kB N Ðlog incomerence of ln_inv\ÿ 4O°kB N Ðfirst-difference of ln_inc\ÿ 4O°kB N Ðlog consumption of ln_inc\ÿ 4O°kB N Ðfirst-difference of ln_consump 4O°kB N ÐF_dta_TStvarâÜÂÐE\ùŒNÐqtrD_dta_TSitrvlÜÂÐE\ùŒNÐ1F_dtatisÿâÜÂÐE\ùŒNÐqtr´ÃŸ´,¦@$‘Ã@¨çÀ@³Ñ¥€?ÿ¥@Œ¶»’‹Ä@nú<@]Á@0k<¹å²@( §@€ =ŒäÅ@},=aVÂ@!ù<ÀíÀ@@g=¨@€=’jÆ@† Aþ‘®@ñ°<½HË@—ç<àÇ@ ?<íG 0AYú®@¶P<0ÈË@æ~<ÂmÈ@§<ÎO@Aö}ª@`Œ¾Ö7Ì@L_<ð«È@¸ø;úWPAϯ°@ ;F>ü¥Ì@L\<#6É@3Š<b"`A‰Ñ±@Ý=;Í@•<¯É@Öq<s+pAO²@{<<Î@.á<ý4Ê@ï…<‚>€A-n²@¸x;èÝÎ@¬Á<½HË@à =>ˆA2P´@€q=iÏ@,‹<½HË@”JAŠ´@<é;nÀÏ@´.<<òË@©<$¶Z˜Aø§µ@€»=î[Ñ@ÀM=éÎÌ@­Ü<Åi Aãý´@ª¼ Ò@-¯<‡˜Í@žÉ<.Þ¨AÑ»¶@÷^=ü&Ó@€ð =Š·Î@€=0ï°Aäñ¶@LØ;ŽâÓ@’»<iÏ@Š±<3ûœ¸AVB·@ä Óß@=šÚÙ@-Ü<ÅP¦(BcµÃ@lB=Ù6à@=þÜÚ@2=ÌkÈ,B3Ä@>{<Éüà@ðÅ<çÜ@€t=Ûq×0Bà9Å@o=!(á@`­;ßÜ@ð{<ðšõ4BEœÆ@€21=TJâ@€=$vÝ@Eö<î» 8B,{Æ@d„»©,ã@Uâ<;Þ@¨<òè(w ¢Bë×@‰¼N^ù@£¸<Ñô@0»U™ 6¤B×õ×@ìß<7Àõ@~< ±®Bë×@Ê@½¨Þû@|<ñ£ö@„ [ ߶Bë×@àº?ü@Ä<“K÷@4< statsmodels-0.12.2/statsmodels/tsa/tests/results/make_arma.py000066400000000000000000000035231400612667500244330ustar00rootroot00000000000000import numpy as np from statsmodels.tsa.arima_process import arma_generate_sample from statsmodels.iolib import savetxt np.random.seed(12345) # no constant y_arma11 = arma_generate_sample([1., -.75], [1., .35], nsample=250) y_arma14 = arma_generate_sample([1., -.75], [1., .35, -.75, .1, .35], nsample=250) y_arma41 = arma_generate_sample([1., -.75, .25, .25, -.75], [1., .35], nsample=250) y_arma22 = arma_generate_sample([1., -.75, .45], [1., .35, -.9], nsample=250) y_arma50 = arma_generate_sample([1., -.75, .35, -.3, -.2, .1], [1.], nsample=250) y_arma02 = arma_generate_sample([1.], [1., .35, -.75], nsample=250) # constant constant = 4.5 y_arma11c = arma_generate_sample([1., -.75], [1., .35], nsample=250) + constant y_arma14c = arma_generate_sample([1., -.75], [1., .35, -.75, .1, .35], nsample=250) + constant y_arma41c = arma_generate_sample([1., -.75, .25, .25, -.75], [1., .35], nsample=250) + constant y_arma22c = arma_generate_sample([1., -.75, .45], [1., .35, -.9], nsample=250) + constant y_arma50c = arma_generate_sample([1., -.75, .35, -.3, -.2, .1], [1.], nsample=250) + constant y_arma02c = arma_generate_sample([1.], [1., .35, -.75], nsample=250) + constant savetxt( 'y_arma_data.csv', np.column_stack((y_arma11, y_arma14, y_arma41, y_arma22, y_arma50, y_arma02, y_arma11c, y_arma14c, y_arma41c, y_arma22c, y_arma50c, y_arma02c)), names=['y_arma11', 'y_arma14', 'y_arma41', 'y_arma22', 'y_arma50', 'y_arma02', 'y_arma11c', 'y_arma14c', 'y_arma41c', 'y_arma22c', 'y_arma50c', 'y_arma02c'], delimiter=",") statsmodels-0.12.2/statsmodels/tsa/tests/results/rand10000.csv000066400000000000000000003615001400612667500241700ustar00rootroot00000000000000RAND10000 0 1.259113978 1.103351908 0.304648282 -0.256822186 -0.793623817 0.276240773 1.258717736 1.023375177 0.266912662 0.787009975 0.07932412 1.501039627 1.002943507 0.178014113 0.369162792 0.428018616 1.191724188 0.823192493 2.612305175 1.636512755 1.88534769 2.426631194 2.043392893 2.184948387 2.398270484 2.088821963 2.341701754 2.720855131 2.812856689 3.263658109 4.78401526 3.75468432 4.057548858 3.749539419 4.166395224 3.383377854 4.469708524 3.739546936 3.592604039 3.681372249 3.998210994 3.601921117 1.939222179 2.519517645 4.92559958 4.167487869 4.056720179 2.854898662 4.024112148 4.320935975 4.146995855 4.612796305 5.747658556 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-0.9297695920,-0.2147646615,0.2226420326,0.4155209017,-0.4025136167,1.2699764920 1.5520045711,0.9490810942,-0.4636747808,2.2503671983,-0.2346598245,-0.8542840206 -0.6104665251,-0.0369750570,-0.0718750263,-0.3645384358,0.0577303028,-1.1965566103 -2.3444748918,-1.8625407115,-1.4432198913,0.8588460949,0.0235767637,0.4572494498 -0.8802265307,-1.1860625649,1.0873505807,-0.0776431517,0.5309276800,-1.5730941995 0.3756041114,-0.0946943315,-0.0781043471,-0.2557330565,-0.0055637314,1.4109350393 0.0762942030,0.0623884486,-0.2492628234,-0.0719879835,-0.4455953506,-1.9626100016 0.1349729302,-0.3853985614,-1.4885562589,-1.2542048528,0.3643667912,-0.2617745557 -1.3248533169,-0.5362571292,0.2285475719,0.3678037275,-0.8001339176,-1.1250722261 0.1021162434,0.8216924054,-1.0050056147,0.3538765236,-0.1108005750,-1.6268770378 0.9893796578,-0.5445479923,-0.6985699887,0.4275870899,0.7186676814,0.8831142972 -0.6528904987,1.0281908499,0.1322170128,0.8972593946,-1.1487894432,1.2361729916 1.1052174274,0.7304291994,1.7398796530,1.3531171804,0.1718537295,-2.6784704740 -1.1416939473,0.0578815886,0.7495743571,-1.7551145060,0.9450348217,0.0463244383 0.5130557203,2.2522998596,-1.5798575447,1.7569742951,1.1897796354,-1.0059329497 -0.2635734004,0.6064424763,-0.6732565922,-2.7690659217,-0.2960408405,1.1480267708 0.6768033834,1.5538048490,-0.9729001401,1.8032642048,1.4887937090,0.8395074269 -0.3741392058,1.1962552335,1.0153800771,0.4098058451,0.5662269008,1.1278183643 statsmodels-0.12.2/statsmodels/tsa/tests/results/results_ar.py000066400000000000000000000222171400612667500247020ustar00rootroot00000000000000import numpy as np import os cur_dir = os.path.dirname(os.path.abspath(__file__)) class ARLagResults(object): """ Results are from R vars::VARselect for sunspot data. Comands run were var_select <- VARselect(SUNACTIVITY, lag.max=16, type=c("const")) """ def __init__(self, type="const"): # order of results is AIC, HQ, SC, FPE if type == "const": ic = [ 6.311751824815273, 6.321813007357017, 6.336872456958734, 551.009492543133547, 5.647615009344886, 5.662706783157502, 5.685295957560077, 283.614444209634655, 5.634199640773091, 5.654322005856580, 5.684440905060013, 279.835333966272003, 5.639415797766900, 5.664568754121261, 5.702217378125553, 281.299267441683185, 5.646102475432464, 5.676286023057697, 5.721464371862848, 283.187210932784524, 5.628416873122441, 5.663631012018546, 5.716339085624555, 278.223839284844701, 5.584204185137150, 5.624448915304128, 5.684686713710994, 266.191975554941564, 5.541163244029505, 5.586438565467356, 5.654206088675081, 254.979353737235556, 5.483155367013447, 5.533461279722170, 5.608758527730753, 240.611088468544949, 5.489939895595428, 5.545276399575022, 5.628103372384465, 242.251199397394288, 5.496713895370946, 5.557080990621412, 5.647437688231713, 243.900349905069504, 5.503539311586831, 5.568936998108170, 5.666823420519329, 245.573823561989144, 5.510365149977393, 5.580793427769605, 5.686209574981622, 247.259396991133599, 5.513740912139918, 5.589199781203001, 5.702145653215877, 248.099655693709479, 5.515627471325321, 5.596116931659277, 5.716592528473011, 248.572915484827206, 5.515935627515806, 5.601455679120634, 5.729461000735226, 248.654927915301300] self.ic = np.asarray(ic).reshape(4, -1, order='F') class ARResultsOLS(object): """ Results of fitting an AR(9) model to the sunspot data. Results were taken from Stata using the var command. """ def __init__(self, constant=True): self.avobs = 300. if constant: self.params = [ 6.7430535917332, 1.1649421971129, -.40535742259304, -.16653934246587, .14980629416032, -.09462417064796, .00491001240749, .0504665930841, -.08635349190816, .25349103194757] # These are returned by stata VAR, using the (V)AR scale/sigma # we return the true OLS bse by default # the stata residuals can be achieved # by np.sqrt(np.diag(res1.cov_params())) self.bse_stata = [ 2.413485601, .0560359041, .0874490762, .0900894414, .0899348339, .0900100797, .0898385666, .0896997939, .0869773089, .0559505756] # The below are grom gretl's ARIMA command with conditional # maximum likelihood self.bse_gretl = [ 2.45474, 0.0569939, 0.0889440, 0.0916295, 0.0914723, 0.0915488, 0.0913744, 0.0912332, 0.0884642, 0.0569071] self.rmse = 15.1279294937327 self.fpe = 236.4827257929261 self.llf = -1235.559128419549 # NOTE: we use a different definition of these ic than Stata # but our order selection results agree with R VARselect # close to Stata for Lutkepohl but we penalize the ic for # the trend terms # self.bic = 8.427186938618863 # self.aic = 8.30372752279699 # self.hqic = 8.353136159250697 # NOTE: predictions were taken from gretl, but agree with Stata # test predict # TODO: remove one of the files filename = os.path.join(cur_dir, "AROLSConstantPredict.csv") predictresults = np.loadtxt(filename) fv = predictresults[:300, 0] pv = predictresults[300:, 1] del predictresults # cases - in sample predict # n = -1, start = 0 (fitted values) self.FVOLSnneg1start0 = fv # n=-1, start=9 self.FVOLSnneg1start9 = fv # n=-1, start=100 self.FVOLSnneg1start100 = fv[100-9:] # n = 200, start = 0 self.FVOLSn200start0 = fv[:192] # n = 200, start = 200 self.FVOLSn200start200 = np.hstack((fv[200-9:], pv[:101-9])) # n = 200, start = -109 use above self.FVOLSn200startneg109 = self.FVOLSn200start200 # n = 100, start = 325, post-sample forecasting self.FVOLSn100start325 = np.hstack((fv[-1], pv)) # n = 301, start = 9 self.FVOLSn301start9 = np.hstack((fv, pv[:2])) # n = 301, start = 0 self.FVOLSdefault = fv # n = 4, start = 312 self.FVOLSn4start312 = np.hstack((fv[-1], pv[:8])) # n = 15, start = 312 self.FVOLSn15start312 = np.hstack((fv[-1], pv[:19])) elif not constant: self.params = [ 1.19582389902985, -0.40591818219637, -0.15813796884843, 0.16620079925202, -0.08570200254617, 0.01876298948686, 0.06130211910707, -0.08461507700047, 0.27995084653313] self.bse_stata = [ .055645055, .088579237, .0912031179, .0909032462, .0911161784, .0908611473, .0907743174, .0880993504, .0558560278] self.bse_gretl = [ 0.0564990, 0.0899386, 0.0926027, 0.0922983, 0.0925145, 0.0922555, 0.0921674, 0.0894513, 0.0567132] self.rmse = 15.29712618677774 self.sigma = 226.9820074869752 self.llf = -1239.41217278661 # See note above; TODO: be more specific about "above" # self.bic = 8.433861292817106 # self.hqic = 8.367215591385756 # self.aic = 8.322747818577421 self.fpe = 241.0221316614273 filename = os.path.join(cur_dir, "AROLSNoConstantPredict.csv") predictresults = np.loadtxt(filename) fv = predictresults[:300, 0] pv = predictresults[300:, 1] del predictresults # cases - in sample predict # n = -1, start = 0 (fitted values) self.FVOLSnneg1start0 = fv # n=-1, start=9 self.FVOLSnneg1start9 = fv # n=-1, start=100 self.FVOLSnneg1start100 = fv[100-9:] # n = 200, start = 0 self.FVOLSn200start0 = fv[:192] # n = 200, start = 200 self.FVOLSn200start200 = np.hstack((fv[200-9:], pv[:101-9])) # n = 200, start = -109 use above self.FVOLSn200startneg109 = self.FVOLSn200start200 # n = 100, start = 325, post-sample forecasting self.FVOLSn100start325 = np.hstack((fv[-1], pv)) # n = 301, start = 9 self.FVOLSn301start9 = np.hstack((fv, pv[:2])) # n = 301, start = 0 self.FVOLSdefault = fv # n = 4, start = 312 self.FVOLSn4start312 = np.hstack((fv[-1], pv[:8])) # n = 15, start = 312 self.FVOLSn15start312 = np.hstack((fv[-1], pv[:19])) class ARResultsMLE(object): """ Results of fitting an AR(9) model to the sunspot data using exact MLE. Results were taken from gretl. """ def __init__(self, constant=True): self.avobs = 300 if constant: # NOTE: Stata's estimated parameters differ from gretl filename = os.path.join(cur_dir, "ARMLEConstantPredict.csv") filename2 = os.path.join(cur_dir, 'results_ar_forecast_mle_dynamic.csv') predictresults = np.loadtxt(filename, delimiter=",") pv = predictresults[:, 1] dynamicpv = np.genfromtxt(filename2, delimiter=",", skip_header=1) # cases - in sample predict # start = 0 (fitted values) self.FVMLEdefault = pv[:309] # start=9 self.FVMLEstart9end308 = pv[9:309] # start=100, end=309 self.FVMLEstart100end308 = pv[100:309] # start = 0, end self.FVMLEstart0end200 = pv[:201] # n = 200, start = 200 self.FVMLEstart200end334 = pv[200:] # start = 309, end=334 post-sample forecasting self.FVMLEstart308end334 = pv[308:] # end = 310, start = 9 self.FVMLEstart9end309 = pv[9:310] # end = 301, start = 0 self.FVMLEstart0end301 = pv[:302] # end = 312, start = 4 self.FVMLEstart4end312 = pv[4:313] # end = 7, start = 2 self.FVMLEstart2end7 = pv[2:8] self.fcdyn = dynamicpv[:, 0] self.fcdyn2 = dynamicpv[:, 1] self.fcdyn3 = dynamicpv[:, 2] self.fcdyn4 = dynamicpv[:, 3] else: pass statsmodels-0.12.2/statsmodels/tsa/tests/results/results_ar_forecast_mle_dynamic.csv000066400000000000000000000244321400612667500312750ustar00rootroot00000000000000fcdyn,fcdyn2,fcdyn3,fcdyn4,year,index NA,NA,NA,NA,1700,0 NA,NA,NA,NA,1701,1 NA,NA,NA,NA,1702,2 NA,NA,NA,NA,1703,3 NA,NA,NA,NA,1704,4 NA,NA,NA,NA,1705,5 NA,NA,NA,NA,1706,6 NA,NA,NA,NA,1707,7 NA,NA,NA,NA,1708,8 11.23047,NA,NA,NA,1709,9 13.23731,NA,NA,NA,1710,10 19.66407,NA,NA,NA,1711,11 27.00373,NA,NA,NA,1712,12 33.57858,NA,NA,NA,1713,13 44.90784,NA,NA,NA,1714,14 47.95866,NA,NA,NA,1715,15 45.09347,NA,NA,NA,1716,16 36.50656,NA,NA,NA,1717,17 28.78818,NA,NA,NA,1718,18 23.48711,NA,NA,NA,1719,19 22.53206,NA,NA,NA,1720,20 25.68737,NA,NA,NA,1721,21 31.07822,NA,NA,NA,1722,22 38.54836,NA,NA,NA,1723,23 45.41845,NA,NA,NA,1724,24 49.67139,NA,NA,NA,1725,25 49.37283,NA,NA,NA,1726,26 45.30287,NA,NA,NA,1727,27 39.27502,NA,NA,NA,1728,28 33.76503,NA,NA,NA,1729,29 30.76819,NA,NA,NA,1730,30 31.00231,NA,NA,NA,1731,31 34.36712,NA,NA,NA,1732,32 39.73509,NA,NA,NA,1733,33 45.49821,NA,NA,NA,1734,34 49.73386,NA,NA,NA,1735,35 51.13904,NA,NA,NA,1736,36 49.42444,NA,NA,NA,1737,37 45.44374,NA,NA,NA,1738,38 40.80805,NA,NA,NA,1739,39 37.19994,NA,NA,NA,1740,40 35.84322,NA,NA,NA,1741,41 37.12242,NA,NA,NA,1742,42 40.5707,NA,NA,NA,1743,43 45.0109,NA,NA,NA,1744,44 48.97761,NA,NA,NA,1745,45 51.20812,NA,NA,NA,1746,46 51.08132,NA,NA,NA,1747,47 48.81563,NA,NA,NA,1748,48 45.34622,NA,NA,NA,1749,49 41.96479,NA,NA,NA,1750,50 39.85285,NA,NA,NA,1751,51 39.70252,NA,NA,NA,1752,52 41.51253,NA,NA,NA,1753,53 44.62548,NA,NA,NA,1754,54 47.97401,NA,NA,NA,1755,55 50.45678,NA,NA,NA,1756,56 51.31412,NA,NA,NA,1757,57 50.37143,NA,NA,NA,1758,58 48.07163,NA,NA,NA,1759,59 45.29209,NA,NA,NA,1760,60 43.02564,NA,NA,NA,1761,61 42.04014,NA,NA,NA,1762,62 42.63295,NA,NA,NA,1763,63 44.55469,NA,NA,NA,1764,64 47.11933,NA,NA,NA,1765,65 49.45578,NA,NA,NA,1766,66 50.81053,NA,NA,NA,1767,67 50.79702,NA,NA,NA,1768,68 49.50859,NA,NA,NA,1769,69 47.46335,NA,NA,NA,1770,70 45.40802,NA,NA,NA,1771,71 44.05476,NA,NA,NA,1772,72 43.84306,NA,NA,NA,1773,73 44.80533,NA,NA,NA,1774,74 46.57591,NA,NA,NA,1775,75 48.53369,NA,NA,NA,1776,76 50.02399,NA,NA,NA,1777,77 50.58108,NA,NA,NA,1778,78 50.07622,NA,NA,NA,1779,79 48.74461,NA,NA,NA,1780,80 47.0881,NA,NA,NA,1781,81 45.69285,NA,NA,NA,1782,82 45.02758,NA,NA,NA,1783,83 45.29136,NA,NA,NA,1784,84 46.35975,NA,NA,NA,1785,85 47.84262,NA,NA,NA,1786,86 49.22875,NA,NA,NA,1787,87 50.06412,NA,NA,NA,1788,88 50.10232,NA,NA,NA,1789,89 49.37749,NA,NA,NA,1790,90 48.17905,NA,NA,NA,1791,91 46.94158,NA,NA,NA,1792,92 46.09115,NA,NA,NA,1793,93 45.9021,NA,NA,NA,1794,94 46.41197,NA,NA,NA,1795,95 47.4205,NA,NA,NA,1796,96 48.5688,NA,NA,NA,1797,97 49.46817,NA,NA,NA,1798,98 49.83268,NA,NA,NA,1799,99 49.57053,25.74347,NA,NA,1800,100 48.80555,45.07553,NA,NA,1801,101 47.82483,56.26223,NA,NA,1802,102 46.97392,58.91456,NA,NA,1803,103 46.53746,51.91183,NA,NA,1804,104 46.64617,41.38568,NA,NA,1805,105 47.24034,29.44033,NA,NA,1806,106 48.09929,20.594,NA,NA,1807,107 48.92374,15.65894,NA,NA,1808,108 49.44053,18.22081,NA,NA,1809,109 49.49352,27.80714,NA,NA,1810,110 49.09048,40.67458,NA,NA,1811,111 48.39246,52.10051,NA,NA,1812,112 47.65195,57.96601,NA,NA,1813,113 47.12326,57.18009,NA,NA,1814,114 46.97669,50.58997,NA,NA,1815,115 47.24521,41.19133,NA,NA,1816,116 47.82008,31.97262,NA,NA,1817,117 48.49449,26.00973,NA,NA,1818,118 49.0381,25.3424,NA,NA,1819,119 49.2759,30.23195,NA,NA,1820,120 49.14449,38.94292,NA,NA,1821,121 48.708,48.32435,NA,NA,1822,122 48.13022,55.21302,NA,NA,1823,123 47.61448,57.45876,NA,NA,1824,124 47.33314,54.73303,NA,NA,1825,125 47.371,48.31932,NA,NA,1826,126 47.70098,40.61562,NA,NA,1827,127 48.19876,34.30102,NA,NA,1828,128 48.68947,31.49938,NA,NA,1829,129 49.00915,33.09014,NA,NA,1830,130 49.05949,38.4097,NA,NA,1831,131 48.83779,45.54427,NA,NA,1832,132 48.43316,52.02924,NA,NA,1833,133 47.99199,55.75885,NA,NA,1834,134 47.66576,55.67565,NA,NA,1835,135 47.55974,52.06329,NA,NA,1836,136 47.6997,46.36284,NA,NA,1837,137 48.02718,40.63523,NA,NA,1838,138 48.42331,36.8523,NA,NA,1839,139 48.75186,36.24014,NA,NA,1840,140 48.90604,38.89879,NA,NA,1841,141 48.84306,43.81192,NA,NA,1842,142 48.59544,49.24557,NA,NA,1843,143 48.25633,53.37311,NA,NA,1844,144 47.94516,54.90133,NA,NA,1845,145 47.76602,53.47803,NA,NA,1846,146 47.77337,49.76026,NA,NA,1847,147 47.95608,45.14231,NA,NA,1848,148 48.2444,41.25146,NA,NA,1849,149 48.53638,39.3907,NA,NA,1850,150 48.73379,40.11474,NA,NA,1851,151 48.77512,43.07797,NA,NA,1852,152 48.65446,47.194,NA,NA,1853,153 48.42082,51.03932,NA,NA,1854,154 48.15889,53.35115,NA,NA,1855,155 47.95871,53.44565,NA,NA,1856,156 47.88509,51.41935,NA,NA,1857,157 47.95695,48.07774,NA,NA,1858,158 48.14322,44.62913,NA,NA,1859,159 48.37574,42.25802,NA,NA,1860,160 48.5741,41.72712,NA,NA,1861,161 48.67334,43.14053,NA,NA,1862,162 48.64509,45.94062,NA,NA,1863,163 48.50536,49.1286,NA,NA,1864,164 48.30696,51.62327,NA,NA,1865,165 48.11988,52.62979,NA,NA,1866,166 48.00684,51.8937,NA,NA,1867,167 48.00254,49.76002,NA,NA,1868,168 48.10326,47.0275,NA,NA,1869,169 48.27007,44.65717,NA,NA,1870,170 48.44363,43.44038,NA,NA,1871,171 48.56524,43.74025,NA,NA,1872,172 48.59658,45.3902,NA,NA,1873,173 48.53167,47.77605,NA,NA,1874,174 48.39723,50.06516,NA,NA,1875,175 48.24216,51.49802,NA,NA,1876,176 48.11987,51.64078,NA,NA,1877,177 48.07012,50.51556,NA,NA,1878,178 48.10623,48.57068,NA,NA,1879,179 48.21193,46.50852,NA,NA,1880,180 48.34826,45.03631,NA,NA,1881,181 48.46784,44.62735,NA,NA,1882,182 48.53126,45.37293,NA,NA,1883,183 48.51997,46.97024,NA,NA,1884,184 48.44153,48.84385,NA,NA,1885,185 48.32577,50.35313,NA,NA,1886,186 48.21362,51.01153,NA,NA,1887,187 48.14281,50.64309,NA,NA,1888,188 48.13525,49.42654,NA,NA,1889,189 48.19046,47.81766,NA,NA,1890,190 48.28681,46.382,NA,NA,1891,191 48.38984,45.59878,NA,NA,1892,192 48.46454,45.70354,NA,NA,1893,193 48.48717,46.62066,NA,NA,1894,194 48.45269,48.00411,NA,NA,1895,195 48.37559,49.36743,NA,NA,1896,196 48.284,50.25469,NA,NA,1897,197 48.20957,50.39271,NA,NA,1898,198 48.1766,49.77424,NA,NA,1899,199 48.19421,48.64739,NA,NA,1900,200 48.25402,47.41943,NA,NA,1901,201 48.33384,46.51162,NA,NA,1902,202 48.40579,46.21651,NA,NA,1903,203 48.44604,46.6056,NA,NA,1904,204 48.4426,47.51603,NA,NA,1905,205 48.3988,48.61704,NA,NA,1906,206 48.33142,49.52975,NA,NA,1907,207 48.26437,49.95725,NA,NA,1908,208 48.22027,49.78077,NA,NA,1909,209 48.21289,49.09095,NA,NA,1910,210 48.24294,48.14704,NA,NA,1911,211 48.29848,47.28117,NA,NA,1912,212 48.35955,46.78283,NA,NA,1913,213 48.4053,46.8033,NA,NA,1914,214 48.42108,47.31141,NA,NA,1915,215 48.40305,48.11303,NA,NA,1916,216 48.35898,48.92453,NA,NA,1917,217 48.30501,49.4728,NA,NA,1918,218 48.25985,49.58682,NA,NA,1919,219 48.23831,49.25039,NA,NA,1920,220 48.24652,48.59994,NA,NA,1921,221 48.28025,47.87108,NA,NA,1922,222 48.3269,47.31424,NA,NA,1923,223 48.37012,47.10955,NA,NA,1924,224 48.3955,47.30951,NA,NA,1925,225 48.39538,47.82753,NA,NA,1926,226 48.37106,48.474,NA,NA,1927,227 48.33194,49.02525,NA,NA,1928,228 48.29195,49.30067,NA,NA,1929,229 48.26462,49.22147,NA,NA,1930,230 48.25856,48.83232,NA,NA,1931,231 48.27478,48.28018,NA,NA,1932,232 48.30673,47.75973,NA,NA,1933,233 48.34286,47.44541,NA,NA,1934,234 48.3708,47.43357,NA,NA,1935,235 48.38153,47.7138,NA,NA,1936,236 48.37229,48.17769,NA,NA,1937,237 48.34718,48.66019,NA,NA,1938,238 48.31544,48.99806,NA,NA,1939,239 48.28812,49.0848,NA,NA,1940,240 48.27422,48.90384,NA,NA,1941,241 48.27777,48.52964,NA,NA,1942,242 48.29672,48.09819,NA,NA,1943,243 48.32394,47.75808,NA,NA,1944,244 48.34984,47.61982,NA,NA,1945,245 48.36576,47.7204,NA,NA,1946,246 48.36682,48.01445,NA,NA,1947,247 48.3534,48.39355,NA,NA,1948,248 48.33074,48.72594,NA,NA,1949,249 48.30694,48.90203,NA,NA,1950,250 48.29008,48.87032,NA,NA,1951,251 48.28551,48.6519,NA,NA,1952,252 48.29417,48.32977,NA,NA,1953,253 48.3125,48.01783,NA,NA,1954,254 48.33385,47.82096,NA,NA,1955,255 48.35086,47.80007,NA,NA,1956,256 48.35802,47.95373,NA,NA,1957,257 48.3534,48.22171,NA,NA,1958,258 48.33914,48.50819,NA,NA,1959,259 48.32052,48.71578,NA,NA,1960,260 48.30403,48.77848,NA,NA,1961,261 48.29514,48.68238,NA,NA,1962,262 48.29647,48.46779,NA,NA,1963,263 48.30708,48.21301,NA,NA,1964,264 48.32293,48.00602,NA,NA,1965,265 48.33842,47.9144,NA,NA,1966,266 48.34835,47.96348,NA,NA,1967,267 48.34964,48.12991,NA,NA,1968,268 48.34229,48.35188,NA,NA,1969,269 48.3292,48.55192,NA,NA,1970,270 48.31506,48.66372,NA,NA,1971,271 48.3047,48.65398,NA,NA,1972,272 48.30142,48.53202,NA,NA,1973,273 48.30599,48.34455,NA,NA,1974,274 48.31648,48.15806,NA,NA,1975,275 48.32907,48.03546,NA,NA,1976,276 48.3394,48.01503,NA,NA,1977,277 48.34411,48.09869,NA,NA,1978,278 48.34188,48.25319,NA,NA,1979,279 48.33381,48.42301,NA,NA,1980,280 48.3229,48.55017,NA,NA,1981,281 48.31298,48.59394,NA,NA,1982,282 48.30734,48.54369,NA,NA,1983,283 48.30768,48.42102,NA,NA,1984,284 48.31358,48.27089,NA,NA,1985,285 48.32279,48.14532,NA,NA,1986,286 48.33204,48.08548,NA,NA,1987,287 48.3382,48.10837,NA,NA,1988,288 48.33936,48.20225,NA,NA,1989,289 48.33537,48.332,NA,NA,1990,290 48.32782,48.45215,NA,NA,1991,291 48.31944,48.52268,NA,NA,1992,292 48.31309,48.52226,NA,NA,1993,293 48.31082,48.45455,NA,NA,1994,294 48.31319,48.3457,NA,NA,1995,295 48.31918,48.23446,NA,NA,1996,296 48.32658,48.15849,NA,NA,1997,297 48.33284,48.1417,NA,NA,1998,298 48.3359,48.18687,NA,NA,1999,299 48.33488,48.27574,NA,NA,2000,300 48.33033,48.37623,NA,NA,2001,301 48.32396,48.4539,NA,NA,2002,302 48.318,48.48368,NA,NA,2003,303 48.31445,48.45791,NA,NA,2004,304 48.31438,48.38801,NA,NA,2005,305 48.31765,48.29974,NA,NA,2006,306 48.32299,48.22377,NA,NA,2007,307 48.3285,48.18514,23.47364,NA,2008,308 48.33231,48.19506,54.73861,30.85857,2009,309 48.33322,48.24781,80.91882,61.33544,2010,310 48.33107,48.32352,96.89133,87.02467,2011,311 48.32673,48.39553,94.15365,91.32123,2012,312 48.32178,48.43977,77.70128,79.9216,2013,313 48.3179,48.44268,56.33983,60.7995,2014,314 48.31637,48.40531,36.52842,40.37485,2015,315 48.31757,48.34226,21.34622,24.52903,2016,316 48.32098,48.27606,15.74889,13.53051,2017,317 48.32533,48.22919,23.33969,14.44262,2018,318 48.32911,48.21651,40.86964,26.82511,2019,319 48.33107,48.24065,61.94895,47.5587,2020,320 48.33065,48.29165,78.24312,67.30043,2021,321 48.3281,48.35101,84.08843,78.69045,2022,322 48.32438,48.3983,78.31338,78.43595,2023,323 48.32081,48.41819,64.1858,67.94477,2024,324 48.31858,48.4053,46.7631,52.09101,2025,325 48.31839,48.36561,31.46734,35.70807,2026,326 48.32018,48.31381,23.18735,24.0176,2027,327 48.32327,48.26797,24.45816,20.48491,2028,328 48.32655,48.24327,34.63706,26.46583,2029,329 48.3289,48.247,49.85213,39.67762,2030,330 48.32957,48.27651,64.55238,55.23003,2031,331 48.32843,48.3206,73.5886,67.49796,2032,332 48.32594,48.36368,74.20407,72.37827,2033,333 statsmodels-0.12.2/statsmodels/tsa/tests/results/results_arima.py000066400000000000000000000555241400612667500254000ustar00rootroot00000000000000import os import numpy as np from numpy import genfromtxt cur_dir = os.path.dirname(os.path.abspath(__file__)) path = os.path.join(cur_dir, "results_arima_forecasts.csv") with open(path, "rb") as fd: forecast_results = genfromtxt(fd, names=True, delimiter=",", dtype=float) # NOTE: # stata gives no indication of no convergence for 112 CSS but gives a # different answer than x12arima, gretl simply fails to converge # redid stata with starting parameters from x12arima # it looks like stata uses a different formula for the CSS likelihood # they appear to be using a larger sample than R, gretl, or us. # CSS results are therefore taken from R and gretl class ARIMA111(object): def __init__(self, method="mle"): self.k_ar = 1 self.k_diff = 1 self.k_ma = 1 if method == "mle": # from stata from .arima111_results import results # unpack stata results self.__dict__.update(results) self.resid = self.resid[1:] self.params = self.params[:-1] self.sigma2 = self.sigma**2 self.aic = self.icstats[4] self.bic = self.icstats[5] self.fittedvalues = self.xb[1:] # no idea why this initial value self.linear = self.y[1:] # stata bse are OPG # self.bse = np.diag(self.cov_params) ** .5 # from gretl self.arroots = [1.0640 + 0j] self.maroots = [1.2971 + 0j] self.hqic = 496.8653 self.aic_gretl = 491.5112 self.bic_gretl = 504.7442 self.tvalues = [4.280, 20.57, -8.590] self.pvalues = [1.87e-5, 5.53e-94, 8.73e-18] self.cov_params = [[0.0423583, -0.00167449, 0.00262911], [-0.00167449, 0.00208858, -0.0035068], [0.00262911, -0.0035068, 0.00805622]] self.bse = np.sqrt(np.diag(self.cov_params)) # these bse are approx [.205811, .0457010, .0897565] # from stata # forecast = genfromtxt(open(cur_dir+"/arima111_forecasts.csv"), # delimiter=",", skip_header=1, usecols=[1,2,3,4,5]) # self.forecast = forecast[203:,1] # self.fcerr = forecast[203:,2] # self.fc_conf_int = forecast[203:,3:] # from gretl self.forecast = forecast_results['fc111c'][-25:] self.forecasterr = forecast_results['fc111cse'][-25:] self.forecast_dyn = forecast_results['fc111cdyn'] self.forecasterr_dyn = forecast_results['fc111cdynse'] else: # coefs, bse, tvalues, and pvalues taken from R because gretl # uses mean not constant self.bse = [0.21583833, 0.03844939, 0.08566390] self.params = [1.0087257, 0.9455393, -0.8021834] self.sigma2 = 0.6355913 self.tvalues = [4.673524, 24.591788, -9.364311] self.pvalues = [5.464467e-06, 0, 0] self.cov_params = np.array([ [0.046586183, 0.002331183, -0.004647432], [0.002331183, 0.001478356, -0.002726201], [-0.004647432, -0.002726201, 0.007338304]]) # from gretl self.llf = -239.6601 self.aic = 487.3202 self.bic = 500.5334 self.hqic = 492.6669 self.arroots = [1.0578 + 0j] self.maroots = [1.2473 + 0j] # cov_params = np.array([[0.00369569, -0.00271777, 0.00269806], # [0, 0.00209573, -0.00224559], # [0, 0, 0.00342769]]) # self.cov_params = cov_params + cov_params.T - \ # np.diag(np.diag(cov_params)) # self.bse = np.sqrt(np.diag(self.cov_params)) self.resid = [-0.015830, -0.236884, -0.093946, -0.281152, -0.089983, -0.226336, -0.351666, -0.198703, -0.258418, -0.259026, -0.149513, -0.325703, -0.165703, -0.279229, -0.295711, -0.120018, -0.289870, -0.154243, -0.348403, -0.273902, -0.240894, -0.182791, -0.252930, -0.152441, -0.296412, -0.128941, 0.024068, -0.243972, -0.011436, -0.392437, -0.217022, -0.118190, -0.133489, -0.045755, -0.169953, 0.025010, -0.107754, -0.119661, 0.070794, -0.065586, -0.080390, 0.007741, -0.016138, -0.235283, -0.121907, -0.125546, -0.428463, -0.087713, -0.298131, -0.277757, -0.261422, -0.248326, -0.137826, -0.043771, 0.437100, -0.150051, 0.751890, 0.424180, 0.450514, 0.277089, 0.732583, 0.225086, -0.403648, -0.040509, -0.132975, -0.112572, -0.696214, 0.003079, -0.003491, -0.108758, 0.401383, -0.162302, -0.141547, 0.175094, 0.245346, 0.607134, 0.519045, 0.248419, 0.920521, 1.097613, 0.755983, 1.271156, 1.216969, -0.121014, 0.340712, 0.732750, 0.068915, 0.603912, 0.060157, -0.803110, -1.044392, 1.040311, -0.984497, -1.611668, -0.258198, -0.112970, -0.091071, 0.226487, 0.097475, -0.311423, -0.061105, -0.449488, 0.317277, -0.329734, -0.181248, 0.443263, -2.223262, 0.096836, -0.033782, 0.456032, 0.476052, 0.197564, 0.263362, 0.021578, 0.216803, 0.284249, 0.343786, 0.196981, 0.773819, 0.169070, -0.343097, 0.918962, 0.096363, 0.298610, 1.571685, -0.236620, -1.073822, -0.194208, -0.250742, -0.101530, -0.076437, -0.056319, 0.059811, -0.041620, -0.128404, -0.403446, 0.059654, -0.347208, -0.095257, 0.217668, -0.015057, 0.087431, 0.275062, -0.263580, -0.122746, 0.195629, 0.367272, -0.184188, 0.146368, 0.127777, -0.587128, -0.498538, 0.172490, -0.456741, -0.694000, 0.199392, -0.140634, -0.029636, 0.364818, -0.097080, 0.510745, 0.230842, 0.595504, 0.709721, 0.012218, 0.520223, -0.445174, -0.168341, -0.935465, -0.894203, 0.733417, -0.279707, 0.258861, 0.417969, -0.443542, -0.477955, 0.288992, 0.442126, 0.075826, 0.665759, 0.571509, -0.204055, 0.835901, -0.375693, 3.292828, -1.469299, -0.122206, 0.617909, -2.250468, 0.570871, 1.166013, 0.079873, 0.463372, 1.981434, -0.142869, 3.023376, -3.713161, -6.120150, -0.007487, 1.267027, 1.176930] self.linear = [ 29.3658, 29.6069, 29.6339, 29.8312, 29.8400, 30.0663, 30.1617, 30.1187, 30.2384, 30.2990, 30.3595, 30.5457, 30.5457, 30.7192, 30.7757, 30.8100, 31.0399, 31.0942, 31.2984, 31.2939, 31.3609, 31.4628, 31.6329, 31.7324, 31.9464, 32.0089, 32.2559, 32.6940, 32.8614, 33.2924, 33.3170, 33.5182, 33.8335, 34.1458, 34.5700, 34.8750, 35.4078, 35.8197, 36.2292, 36.8656, 37.3804, 37.8923, 38.5161, 39.1353, 39.5219, 40.0255, 40.5285, 40.6877, 41.1981, 41.4778, 41.7614, 42.0483, 42.3378, 42.7438, 43.2629, 44.3501, 44.8481, 46.3758, 47.6495, 49.0229, 50.2674, 52.0749, 53.4036, 54.0405, 55.0330, 55.9126, 56.7962, 56.9969, 57.9035, 58.8088, 59.5986, 60.9623, 61.7415, 62.5249, 63.6547, 64.8929, 66.5810, 68.2516, 69.6795, 71.9024, 74.4440, 76.7288, 79.6830, 82.7210, 84.3593, 86.4672, 89.0311, 90.8961, 93.3398, 95.2031, 96.0444, 96.4597, 99.0845, 99.5117, 99.0582, 99.9130, 100.8911, 101.8735, 103.2025, 104.4114, 105.1611, 106.1495, 106.6827, 108.0297, 108.6812, 109.4567, 110.9233, 109.4032, 110.2338, 110.9440, 112.2239, 113.6024, 114.7366, 115.9784, 116.9832, 118.2158, 119.5562, 121.0030, 122.3262, 124.3309, 125.7431, 126.5810, 128.8036, 130.2014, 131.8283, 134.9366, 136.1738, 136.3942, 137.4507, 138.4015, 139.4764, 140.5563, 141.6402, 142.8416, 143.9284, 144.9034, 145.5403, 146.6472, 147.2953, 148.1823, 149.4151, 150.4126, 151.5249, 152.8636, 153.6227, 154.5044, 155.7327, 157.1842, 158.0536, 159.2722, 160.4871, 160.8985, 161.3275, 162.4567, 162.8940, 163.0006, 164.0406, 164.7296, 165.5352, 166.7971, 167.5893, 169.0692, 170.3045, 171.9903, 173.8878, 175.0798, 176.8452, 177.5683, 178.5355, 178.5942, 178.5666, 180.2797, 180.9411, 182.1820, 183.6435, 184.1780, 184.6110, 185.8579, 187.3242, 188.4342, 190.2285, 192.0041, 192.9641, 195.0757, 195.9072, 200.8693, 200.8222, 202.0821, 204.1505, 203.0031, 204.7540, 207.2581, 208.6696, 210.5136, 214.1399, 215.5866, 220.6022, 218.2942, 212.6785, 213.2020, 215.2081] # forecasting is not any different for css # except you lose the first p+1 observations for in-sample # these results are from x-12 arima self.forecast = forecast_results['fc111c_css'][-25:] self.forecasterr = forecast_results['fc111cse_css'][-25:] self.forecast_dyn = forecast_results['fc111cdyn_css'] self.forecasterr_dyn = forecast_results['fc111cdynse_css'] class ARIMA211(object): def __init__(self, method="mle"): if method == 'mle': # from stata from .arima111_results import results self.__dict__.update(results) self.resid = self.resid[1:] self.params = self.params[:-1] self.sigma2 = self.sigma**2 self.aic = self.icstats[4] self.bic = self.icstats[5] self.fittedvalues = self.xb[1:] # no idea why this initial value self.linear = self.y[1:] self.k_diff = 1 # stata bse are OPG # self.bse = np.diag(self.cov_params) ** .5 # from gretl self.arroots = [1.027 + 0j, 5.7255 + 0j] self.maroots = [1.1442+0j] self.hqic = 496.5314 self.aic_gretl = 489.8388 self.bic_gretl = 506.3801 self.tvalues = [3.468, 11.14, -1.941, 12.55] self.pvalues = [.0005, 8.14e-29, .0522, 3.91e-36] cov_params = np.array([ [0.0616906, -0.00250187, 0.0010129, 0.00260485], [0, 0.0105302, -0.00867819, -0.00525614], [0, 0, 0.00759185, 0.00361962], [0, 0, 0, 0.00484898]]) self.cov_params = ( cov_params + cov_params.T - np.diag(np.diag(cov_params))) self.bse = np.sqrt(np.diag(self.cov_params)) # these bse are approx [0.248376, 0.102617, 0.0871312, 0.0696346] self.forecast = forecast_results['fc211c'][-25:] self.forecasterr = forecast_results['fc211cse'][-25:] self.forecast_dyn = forecast_results['fc211cdyn'][-25:] self.forecasterr_dyn = forecast_results['fc211cdynse'][-25:] else: from .arima211_css_results import results self.__dict__.update(results) self.resid = self.resid[1:] self.params = self.params[:-1] self.sigma2 = self.sigma**2 self.aic = self.icstats[4] self.bic = self.icstats[5] self.fittedvalues = self.xb[1:] # no idea why this initial value self.linear = self.y[1:] self.k_diff = 1 # from gretl self.arroots = [1.0229 + 0j, 4.4501 + 0j] self.maroots = [1.0604 + 0j] self.hqic = 489.3225 self.aic_gretl = 482.6486 self.bic_gretl = 499.1402 self.tvalues = [.7206, 22.54, -19.04] self.pvalues = [.4712, 1.52e-112, 2.19e-10, 8.00e-81] cov_params = np.array([ [8.20496e-04, -0.0011992, 4.57078e-04, 0.00109907], [0, 0.00284432, -0.0016752, -0.00220223], [0, 0, 0.00119783, 0.00108868], [0, 0, 0, 0.00245324]]) self.cov_params = ( cov_params + cov_params.T - np.diag(np.diag(cov_params))) self.bse = np.sqrt(np.diag(self.cov_params)) # forecasting is not any different for css # except you lose the first p+1 observations for in-sample self.forecast = forecast_results['fc111c_css'][-25:] self.forecasterr = forecast_results['fc111cse_css'][-25:] self.forecast_dyn = forecast_results['fc111cdyn_css'] self.forecasterr_dyn = forecast_results['fc111cdynse_css'] class ARIMA112(object): def __init__(self, method="mle"): self.df_model = 3 self.k = 5 self.k_ar = 1 self.k_ma = 2 self.k_exog = 1 self.k_diff = 1 if method == "mle": from .arima112_results import results # from gretl self.arroots = [1.0324 + 0j] self.maroots = [1.1447 + 0j, -4.8613+0j] self.hqic = 495.5852 self.aic_gretl = 488.8925 self.bic_gretl = 505.4338 self.tvalues = [3.454, 31.10, -7.994, -2.127] self.pvalues = [0.0006, 2.1e-212, 1.31e-15, .0334] cov_params = np.array([ [0.0620096, -0.00172172, 0.00181301, 0.00103271], [0, 9.69682e-04, -9.70767e-04, -8.99814e-04], [0, 0, 0.00698068, -0.00443871], [0, 0, 0, 0.00713662]]) self.cov_params = ( cov_params + cov_params.T - np.diag(np.diag(cov_params))) self.bse = np.sqrt(np.diag(self.cov_params)) # from gretl self.forecast = forecast_results['fc112c'][-25:] self.forecasterr = forecast_results['fc112cse'][-25:] self.forecast_dyn = forecast_results['fc112cdyn'] self.forecasterr_dyn = forecast_results['fc112cdynse'] # unpack stata results self.__dict__ = results self.resid = self.resid[1:] self.params = self.params[:-1] self.sigma2 = self.sigma**2 self.aic = self.icstats[4] self.bic = self.icstats[5] self.fittedvalues = self.xb[1:] # no idea why this initial value self.linear = self.y[1:] # stata bse are OPG # self.bse = np.diag(self.cov_params) ** .5 else: # NOTE: this looks like a "hard" problem # unable to replicate stata's results even with their starting # values # unable to replicate x12 results in stata using their starting # values. x-12 has better likelihood and we can replicate so # use their results # taken from R using X12-arima values as init params self.bse = [0.07727588, 0.09356658, 0.10503567, 0.07727970] self.params = [0.9053219, -0.692412, 1.0736728, 0.1720008] self.sigma2 = 0.6820727 self.tvalues = [11.715452, -7.400215, 10.221983, 2.225692] self.pvalues = [0, 3.791634e-12, 0, 2.716275e-02] self.cov_params = np.array([ [0.0059715623, 0.001327824, -0.001592129, -0.0008061933], [0.0013278238, 0.008754705, -0.008024634, -0.0045933413], [-0.0015921293, -0.008024634, 0.011032492, 0.0072509641], [-0.0008061933, -0.004593341, 0.007250964, 0.0059721516]]) # from x12arima via gretl # gretl did not converge for this model... self.llf = -246.7534 self.nobs = 202 # self.params = [.905322, -.692425, 1.07366, 0.172024] # self.sigma2 = 0.682072819129 # self.bse = [0.0756430, 0.118440, 0.140691, 0.105266] self.resid = [ -1.214477, -0.069772, -1.064510, -0.249555, -0.874206, -0.322177, -1.003579, -0.310040, -0.890506, -0.421211, -0.715219, -0.564119, -0.636560, -0.580912, -0.717440, -0.424277, -0.747835, -0.424739, -0.805958, -0.516877, -0.690127, -0.473072, -0.694766, -0.435627, -0.736474, -0.388060, -0.429596, -0.557224, -0.342308, -0.741842, -0.442199, -0.491319, -0.420884, -0.388057, -0.466176, -0.257193, -0.429646, -0.349683, -0.205870, -0.335547, -0.290300, -0.216572, -0.234272, -0.427951, -0.255446, -0.338097, -0.579033, -0.213860, -0.556756, -0.389907, -0.510060, -0.409759, -0.396778, -0.258727, 0.160063, -0.467109, 0.688004, -0.021120, 0.503044, 0.031500, 0.878365, -0.003548, -0.079327, 0.038289, 0.032773, -0.050780, -0.560124, 0.185655, -0.111981, -0.020714, 0.363254, -0.218484, -0.006161, 0.165950, 0.252365, 0.599220, 0.488921, 0.347677, 1.079814, 1.102745, 0.959907, 1.570836, 1.454934, 0.343521, 1.125826, 1.154059, 0.666141, 1.269685, 0.551831, -0.027476, -0.305192, 1.715665, -0.990662, -0.548239, -0.011636, 0.197796, -0.050128, 0.480031, 0.061198, -0.049562, 0.064436, -0.300420, 0.494730, -0.411527, 0.109242, 0.375255, -2.184482, 0.717733, -0.673064, 0.751681, -0.092543, 0.438016, -0.024881, 0.250085, 0.096010, 0.452618, 0.265491, 0.374299, 0.820424, 0.238176, -0.059646, 1.214061, 0.028679, 0.797567, 1.614444, -0.094717, -0.408067, 0.299198, -0.021561, 0.231915, 0.084190, 0.199192, 0.201132, 0.148509, 0.035431, -0.203352, 0.264744, -0.319785, 0.150305, 0.184628, 0.074637, 0.148340, 0.357372, -0.241250, 0.119294, 0.204413, 0.458730, -0.190477, 0.416587, 0.084216, -0.363361, -0.310339, 0.309728, -0.549677, -0.449092, 0.183025, -0.259015, -0.000883, 0.267255, -0.188068, 0.577697, 0.049310, 0.746401, 0.565829, 0.178270, 0.709983, -0.348012, 0.273262, -0.873288, -0.403100, 0.720072, -0.428076, 0.488246, 0.248152, -0.313214, -0.323137, 0.414843, 0.308909, 0.134180, 0.732275, 0.535639, -0.056128, 1.128355, -0.449151, 3.879123, -2.303860, 1.712549, -0.074407, -1.162052, 0.848316, 1.262031, 0.009320, 1.017563, 1.978597, -0.001637, 3.782223, -4.119563, -3.666488, 0.345244, 0.869998, 0.635321] self.linear = [ 30.5645, 29.4398, 30.6045, 29.7996, 30.6242, 30.1622, 30.8136, 30.2300, 30.8705, 30.4612, 30.9252, 30.7841, 31.0166, 31.0209, 31.1974, 31.1143, 31.4978, 31.3647, 31.7560, 31.5369, 31.8101, 31.7531, 32.0748, 32.0156, 32.3865, 32.2681, 32.7096, 33.0072, 33.1923, 33.6418, 33.5422, 33.8913, 34.1209, 34.4881, 34.8662, 35.1572, 35.7296, 36.0497, 36.5059, 37.1355, 37.5903, 38.1166, 38.7343, 39.3280, 39.6554, 40.2381, 40.6790, 40.8139, 41.4568, 41.5899, 42.0101, 42.2098, 42.5968, 42.9587, 43.5399, 44.6671, 44.9120, 46.8211, 47.5970, 49.2685, 50.1216, 52.3035, 53.0793, 53.9617, 54.8672, 55.8508, 56.6601, 56.8143, 58.0120, 58.7207, 59.6367, 61.0185, 61.6062, 62.5340, 63.6476, 64.9008, 66.6111, 68.1523, 69.5202, 71.8973, 74.2401, 76.4292, 79.4451, 82.2565, 83.5742, 86.0459, 88.4339, 90.2303, 92.8482, 94.4275, 95.3052, 95.7843, 99.0907, 98.4482, 98.8116, 99.6022, 100.8501, 101.6200, 103.2388, 104.1496, 105.0356, 106.0004, 106.5053, 108.1115, 108.3908, 109.5247, 110.8845, 108.7823, 110.8731, 110.6483, 112.7925, 113.3620, 115.0249, 115.7499, 117.1040, 118.0474, 119.6345, 120.8257, 122.2796, 124.2618, 125.4596, 126.2859, 128.8713, 129.7024, 131.7856, 134.7947, 135.5081, 135.9008, 137.2216, 138.0681, 139.3158, 140.3008, 141.4989, 142.6515, 143.7646, 144.7034, 145.3353, 146.6198, 147.0497, 148.2154, 149.3254, 150.3517, 151.4426, 152.8413, 153.3807, 154.4956, 155.6413, 157.1905, 157.7834, 159.3158, 160.2634, 160.7103, 161.1903, 162.5497, 162.6491, 163.0170, 164.1590, 164.7009, 165.6327, 166.8881, 167.5223, 169.2507, 170.1536, 172.1342, 173.7217, 174.8900, 176.7480, 177.1267, 178.4733, 178.1031, 178.5799, 180.4281, 180.7118, 182.3518, 183.5132, 184.0231, 184.4852, 185.9911, 187.2658, 188.3677, 190.2644, 191.8561, 192.6716, 195.1492, 195.3209, 201.7039, 198.9875, 202.7744, 203.0621, 202.7257, 204.6580, 207.3287, 208.1154, 210.5164, 213.9986, 214.8278, 221.0086, 215.8405, 212.3258, 213.5990, 215.7497] self.yr = [] self.arroots = [-1.4442 + 0j] self.maroots = [-1.1394 + 0j, -5.1019+0j] self.hqic = 510.1902 self.aic = 503.5069 self.bic = 520.0234 # TODO: Document source for these non-used results # (and why they are not used) # self.tvalues = [11.97, -5.846, 7.631, 1.634] # self.pvalues = [5.21e-33, 5.03e-9, 2.32e-14, .1022] # cov_params = np.array([ # [0.0620096, -0.00172172, 0.00181301, 0.00103271], # [0, 9.69682e-04, -9.70767e-04, -8.99814e-04], # [0, 0, 0.00698068, -0.00443871], # [0, 0, 0, 0.00713662]]) # self.cov_params = cov_params + cov_params.T - \ # np.diag(np.diag(cov_params)) # self.bse = np.sqrt(np.diag(self.cov_params)) self.forecast = forecast_results['fc112c_css'][-25:] self.forecasterr = forecast_results['fc112cse_css'][-25:] self.forecast_dyn = forecast_results['fc112cdyn_css'] self.forecasterr_dyn = forecast_results['fc112cdynse_css'] statsmodels-0.12.2/statsmodels/tsa/tests/results/results_arima_exog_forecasts_css.csv000066400000000000000000000104221400612667500314720ustar00rootroot00000000000000orig_index,year,quarter,y,predict,std_err,lower,upper 0,1950,1,3.198371,,,, 1,1950,2,0.951462,,,, 2,1950,3,2.044147,1.637865,,, 3,1950,4,5.387144,3.026386,,, 4,1951,1,4.278298,4.758931,,, 5,1951,2,2.608896,2.744609,,, 6,1951,3,2.2891,2.190297,,, 7,1951,4,0.542828,2.572409,,, 8,1952,1,1.818848,1.464508,,, 9,1952,2,1.141287,2.995619,,, 10,1952,3,1.390376,1.964605,,, 11,1952,4,3.519065,2.452368,,, 12,1953,1,2.687199,3.739905,,, 13,1953,2,2.72044,2.352415,,, 14,1953,3,3.640325,2.782552,,, 15,1953,4,3.388688,3.337867,,, 16,1954,1,1.285691,2.807582,,, 17,1954,2,1.193271,1.532043,,, 18,1954,3,4.125089,2.281349,,, 19,1954,4,1.826838,4.190755,,, 20,1955,1,1.211262,1.496953,,, 21,1955,2,1.494882,2.104899,,, 22,1955,3,2.407813,2.42813,,, 23,1955,4,3.476123,2.908037,,, 24,1956,1,4.683225,3.270582,,, 25,1956,2,3.209492,3.687261,,, 26,1956,3,3.045272,2.260033,,, 27,1956,4,3.189591,2.771537,,, 28,1957,1,3.223306,2.86421,,, 29,1957,2,2.160318,2.825037,,, 30,1957,3,1.084407,2.10187,,, 31,1957,4,0.698262,1.797678,,, 32,1958,1,1.121673,1.916263,,, 33,1958,2,2.538408,2.308136,,, 34,1958,3,3.671068,3.072406,,, 35,1958,4,3.45499,3.284601,,, 36,1959,1,2.136544,2.743738,,, 37,1959,2,3.821324,1.982434,,, 38,1959,3,4.975221,3.611985,,, 39,1959,4,3.157348,3.662564,,, 40,1960,1,1.30047,2.059906,,, 41,1960,2,1.802575,1.56944,,, 42,1960,3,3.772872,2.555923,,, 43,1960,4,3.770009,3.604042,,, 44,1961,1,3.359749,2.847162,,, 45,1961,2,2.440787,2.64582,,, 46,1961,3,2.682876,2.180379,,, 47,1961,4,4.210082,2.684437,,, 48,1962,1,3.215831,3.570286,,, 49,1962,2,2.501961,2.311421,,, 50,1962,3,2.597237,2.281679,,, 51,1962,4,2.865064,2.576134,,, 52,1963,1,1.27064,2.688936,,, 53,1963,2,-0.23313,1.51842,,, 54,1963,3,0.276246,1.147103,,, 55,1963,4,2.197587,2.011094,,, 56,1964,1,3.4989,3.036608,,, 57,1964,2,2.577512,3.170317,,, 58,1964,3,3.582812,2.110702,,, 59,1964,4,3.0313,3.186722,,, 60,1965,1,2.467222,2.374814,,, 61,1965,2,2.161508,2.255183,,, 62,1965,3,2.460806,2.24175,,, 63,1965,4,3.291564,2.537855,,, 64,1966,1,3.637327,2.960457,,, 65,1966,2,2.015331,2.872379,,, 66,1966,3,3.386468,1.678517,,, 67,1966,4,2.153601,3.241487,,, 68,1967,1,2.037476,1.80477,,, 69,1967,2,2.115952,2.270841,,, 70,1967,3,1.352658,2.308425,,, 71,1967,4,1.847239,1.76327,,, 72,1968,1,1.741011,2.393571,,, 73,1968,2,2.28343,2.091623,,, 74,1968,3,3.006313,2.514739,,, 75,1968,4,4.314375,2.772906,,, 76,1969,1,3.718064,3.380456,,, 77,1969,2,2.029417,2.48767,,, 78,1969,3,1.500418,1.638736,,, 79,1969,4,2.249069,1.917292,,, 80,1970,1,2.751434,2.556965,,, 81,1970,2,4.149486,2.578243,,, 82,1970,3,4.793702,3.342115,,, 83,1970,4,2.970161,3.233744,,, 84,1971,1,1.535665,1.809793,,, 85,1971,2,-0.690842,1.585436,,, 86,1971,3,0.372726,0.581896,,, 87,1971,4,1.280042,2.116903,,, 88,1972,1,1.981304,2.214855,,, 89,1972,2,2.909937,2.372742,,, 90,1972,3,3.050076,2.743802,,, 91,1972,4,2.641661,2.491526,,, 92,1973,1,2.621315,2.193228,,, 93,1973,2,2.422996,2.338137,,, 94,1973,3,2.613121,2.192145,,, 95,1973,4,-0.631347,2.393736,,, 96,1974,1,0.308662,0.135852,,, 97,1974,2,2.14549,2.048404,,, 98,1974,3,2.530416,2.769812,,, 99,1974,4,2.333179,2.349218,,, 100,1975,1,,2.129509,0.943872,0.279554,3.979465 101,1975,2,,2.074884,1.135543,-0.150738,4.300507 102,1975,3,,2.105186,1.136638,-0.122583,4.332955 103,1975,4,,2.134998,1.15044,-0.119824,4.389819 104,1976,1,,2.136828,1.156371,-0.129617,4.403272 105,1976,2,,2.12296,1.156401,-0.143544,4.389463 106,1976,3,,2.109324,1.156884,-0.158127,4.376774 107,1976,4,,2.100939,1.157087,-0.166909,4.368787 108,1977,1,,2.095456,1.157087,-0.172394,4.363306 109,1977,2,,2.089903,1.157105,-0.17798,4.357787 110,1977,3,,2.083365,1.157111,-0.184532,4.351262 111,1977,4,,2.076291,1.157111,-0.191606,4.344188 112,1978,1,,2.069235,1.157112,-0.198663,4.337133 113,1978,2,,2.062363,1.157112,-0.205535,4.330262 114,1978,3,,2.055591,1.157112,-0.212308,4.323489 115,1978,4,,2.048814,1.157112,-0.219084,4.316713 116,1979,1,,2.042003,1.157112,-0.225896,4.309901 117,1979,2,,2.035173,1.157112,-0.232725,4.303072 118,1979,3,,2.028345,1.157112,-0.239554,4.296243 119,1979,4,,2.021522,1.157112,-0.246376,4.289421 120,1980,1,,2.014704,1.157112,-0.253195,4.282602 121,1980,2,,2.007885,1.157112,-0.260014,4.275783 122,1980,3,,2.001064,1.157112,-0.266834,4.268963 123,1980,4,,1.994244,1.157112,-0.273655,4.262142 124,1981,1,,1.987423,1.157112,-0.280476,4.255321 ,,,,1.980602,1.157112,-0.287296,4.248501 statsmodels-0.12.2/statsmodels/tsa/tests/results/results_arima_exog_forecasts_mle.csv000066400000000000000000000110341400612667500314570ustar00rootroot00000000000000orig_index,year,quarter,y,predict,std_err,lower,upper 0,1950,1,3.198371,2.786912,0,0,0 1,1950,2,0.951462,2.974749,0,0,0 2,1950,3,2.044147,1.436963,0,0,0 3,1950,4,5.387144,3.04366,0,0,0 4,1951,1,4.278298,4.703375,0,0,0 5,1951,2,2.608896,2.671842,0,0,0 6,1951,3,2.2891,2.179081,0,0,0 7,1951,4,0.542828,2.559835,0,0,0 8,1952,1,1.818848,1.44334,0,0,0 9,1952,2,1.141287,2.994511,0,0,0 10,1952,3,1.390376,1.924747,0,0,0 11,1952,4,3.519065,2.444375,0,0,0 12,1953,1,2.687199,3.708894,0,0,0 13,1953,2,2.72044,2.302143,0,0,0 14,1953,3,3.640325,2.772049,0,0,0 15,1953,4,3.388688,3.306912,0,0,0 16,1954,1,1.285691,2.76964,0,0,0 17,1954,2,1.193271,1.515752,0,0,0 18,1954,3,4.125089,2.28757,0,0,0 19,1954,4,1.826838,4.162606,0,0,0 20,1955,1,1.211262,1.441483,0,0,0 21,1955,2,1.494882,2.122148,0,0,0 22,1955,3,2.407813,2.41238,0,0,0 23,1955,4,3.476123,2.886529,0,0,0 24,1956,1,4.683225,3.238772,0,0,0 25,1956,2,3.209492,3.650045,0,0,0 26,1956,3,3.045272,2.223427,0,0,0 27,1956,4,3.189591,2.769419,0,0,0 28,1957,1,3.223306,2.84062,0,0,0 29,1957,2,2.160318,2.802709,0,0,0 30,1957,3,1.084407,2.084095,0,0,0 31,1957,4,0.698262,1.797552,0,0,0 32,1958,1,1.121673,1.917181,0,0,0 33,1958,2,2.538408,2.301813,0,0,0 34,1958,3,3.671068,3.054365,0,0,0 35,1958,4,3.45499,3.251589,0,0,0 36,1959,1,2.136544,2.71492,0,0,0 37,1959,2,3.821324,1.972191,0,0,0 38,1959,3,4.975221,3.609349,0,0,0 39,1959,4,3.157348,3.617571,0,0,0 40,1960,1,1.30047,2.032269,0,0,0 41,1960,2,1.802575,1.581756,0,0,0 42,1960,3,3.772872,2.56424,0,0,0 43,1960,4,3.770009,3.580948,0,0,0 44,1961,1,3.359749,2.809913,0,0,0 45,1961,2,2.440787,2.635187,0,0,0 46,1961,3,2.682876,2.172471,0,0,0 47,1961,4,4.210082,2.68386,0,0,0 48,1962,1,3.215831,3.551058,0,0,0 49,1962,2,2.501961,2.281018,0,0,0 50,1962,3,2.597237,2.286959,0,0,0 51,1962,4,2.865064,2.572783,0,0,0 52,1963,1,1.27064,2.677956,0,0,0 53,1963,2,-0.23313,1.511573,0,0,0 54,1963,3,0.276246,1.169244,0,0,0 55,1963,4,2.197587,2.029432,0,0,0 56,1964,1,3.4989,3.027459,0,0,0 57,1964,2,2.577512,3.143262,0,0,0 58,1964,3,3.582812,2.093742,0,0,0 59,1964,4,3.0313,3.192262,0,0,0 60,1965,1,2.467222,2.353064,0,0,0 61,1965,2,2.161508,2.260144,0,0,0 62,1965,3,2.460806,2.244168,0,0,0 63,1965,4,3.291564,2.538462,0,0,0 64,1966,1,3.637327,2.952329,0,0,0 65,1966,2,2.015331,2.85753,0,0,0 66,1966,3,3.386468,1.674466,0,0,0 67,1966,4,2.153601,3.258153,0,0,0 68,1967,1,2.037476,1.783801,0,0,0 69,1967,2,2.115952,2.291254,0,0,0 70,1967,3,1.352658,2.308358,0,0,0 71,1967,4,1.847239,1.767768,0,0,0 72,1968,1,1.741011,2.40798,0,0,0 73,1968,2,2.28343,2.089385,0,0,0 74,1968,3,3.006313,2.522133,0,0,0 75,1968,4,4.314375,2.768106,0,0,0 76,1969,1,3.718064,3.37106,0,0,0 77,1969,2,2.029417,2.471187,0,0,0 78,1969,3,1.500418,1.651553,0,0,0 79,1969,4,2.249069,1.942538,0,0,0 80,1970,1,2.751434,2.566664,0,0,0 81,1970,2,4.149486,2.574459,0,0,0 82,1970,3,4.793702,3.339428,0,0,0 83,1970,4,2.970161,3.215612,0,0,0 84,1971,1,1.535665,1.806844,0,0,0 85,1971,2,-0.690842,1.616034,0,0,0 86,1971,3,0.372726,0.611575,0,0,0 87,1971,4,1.280042,2.159702,0,0,0 88,1972,1,1.981304,2.213886,0,0,0 89,1972,2,2.909937,2.379235,0,0,0 90,1972,3,3.050076,2.747067,0,0,0 91,1972,4,2.641661,2.490161,0,0,0 92,1973,1,2.621315,2.202678,0,0,0 93,1973,2,2.422996,2.352931,0,0,0 94,1973,3,2.613121,2.20254,0,0,0 95,1973,4,-0.631347,2.407679,0,0,0 96,1974,1,0.308662,0.15372,0,0,0 97,1974,2,2.14549,2.110661,0,0,0 98,1974,3,2.530416,2.769133,0,0,0 99,1974,4,2.333179,2.346634,0,0,0 100,1975,1,,2.143652,0.954284,0.273289,4.014014 101,1975,2,,2.102544,1.146611,-0.144772,4.34986 102,1975,3,,2.136329,1.147121,-0.111987,4.384644 103,1975,4,,2.16265,1.161904,-0.11464,4.43994 104,1976,1,,2.161075,1.167047,-0.126294,4.448444 105,1976,2,,2.147009,1.167047,-0.140361,4.434379 106,1976,3,,2.135191,1.16758,-0.153225,4.423606 107,1976,4,,2.12856,1.167729,-0.160146,4.417266 108,1977,1,,2.123977,1.167729,-0.16473,4.412685 109,1977,2,,2.11883,1.167748,-0.169914,4.407575 110,1977,3,,2.112729,1.167753,-0.176024,4.401481 111,1977,4,,2.106298,1.167753,-0.182456,4.395051 112,1978,1,,2.099996,1.167753,-0.188758,4.388751 113,1978,2,,2.093869,1.167753,-0.194886,4.382623 114,1978,3,,2.087793,1.167753,-0.200962,4.376548 115,1978,4,,2.081689,1.167753,-0.207066,4.370444 116,1979,1,,2.075554,1.167753,-0.213201,4.364308 117,1979,2,,2.069411,1.167753,-0.219344,4.358165 118,1979,3,,2.063273,1.167753,-0.225481,4.352028 119,1979,4,,2.057142,1.167753,-0.231613,4.345896 120,1980,1,,2.051011,1.167753,-0.237744,4.339766 121,1980,2,,2.044879,1.167753,-0.243875,4.333634 122,1980,3,,2.038747,1.167753,-0.250008,4.327501 123,1980,4,,2.032614,1.167753,-0.256141,4.321369 124,1981,1,,2.026481,1.167753,-0.262273,4.315236 statsmodels-0.12.2/statsmodels/tsa/tests/results/results_arima_forecasts.csv000066400000000000000000000563051400612667500276120ustar00rootroot00000000000000year,quarter,fc111nc,fc111ncse,fc111ncconf1,fc111ncconf2,fc111ncdyn,fc111ncdynse,fc111ncdynconf1,fc111ncdynconf2,fc111c,fc111cse,fc111cconf1,fc111cconf2,fc111cdyn,fc111cdynse,fc111cdynconf1,fc111cdynconf2,fc211nc,fc211ncse,fc211ncconf1,fc211ncconf2,fc211ncdyn,fc211ncdynse,fc211ncdynconf1,fc211ncdynconf2,fc211c,fc211cse,fc211cconf1,fc211cconf2,fc211cdyn,fc211cdynse,fc211cdynconf1,fc211ncdynconf2,fc111c_css,fc111cse_css,fc111cconf1_css,fc111cconf2_css,fc111cdyn_css,fc111cdynse_css,fc111cdynconf1_css,fc111cdynconf2_css,fc112c_css,fc112cse_css,fc112cconf1_css,fc112cconf2_css,fc112cdyn_css,fc112cdynse_css,fc112cdynconf1_css,fc112cdynconf2_css 2000,1,170.2233243826,,,,170.2233243826,0.8056,168.644,171.802,170.2864191564,,,,170.2864191564,0.7999,168.719,171.854,170.2746065512,,,,170.2746065512,0.7953,168.716,171.833,170.2895305662,,,,170.2895305662,0.7925,168.736,171.843,170.304,,,,170.304,0.7972,168.742,171.867,170.154,,,,170.154,0.8259,168.535,171.772 2000,2,171.9184524902,,,,171.1377283933,1.23,168.727,173.549,171.9837202702,,,,171.2664932271,1.2305,168.855,173.678,172.0019713519,,,,171.2023842717,1.291,168.672,173.733,172.0147981675,,,,171.2401153995,1.2804,168.731,173.75,171.99,,,,171.309,1.211,168.935,173.682,172.134,,,,171.103,1.4083,168.343,173.863 2000,3,173.828787093,,,,172.0432982132,1.6186,168.871,175.216,173.892520498,,,,172.2406036174,1.6254,169.055,175.426,173.897011282,,,,172.1176130768,1.7143,168.758,175.478,173.9104306451,,,,172.1817815353,1.698,168.854,175.51,173.888,,,,172.313,1.5831,169.21,175.416,173.722,,,,171.978,1.8547,168.343,175.613 2000,4,175.0288317109,,,,172.9401191906,1.9993,169.021,176.859,175.0750500309,,,,173.2091088061,2.0093,169.271,177.147,174.9780464837,,,,173.0268876834,2.1027,168.906,177.148,174.9987913625,,,,173.1198404087,2.0819,169.039,177.2,175.08,,,,173.318,1.9403,169.515,177.121,174.89,,,,172.904,2.1881,168.616,177.193 2001,1,176.8057511331,,,,173.8282758494,2.3815,169.161,178.496,176.8460409347,,,,174.1723457236,2.3897,169.489,178.856,176.823803435,,,,173.9314905347,2.4735,169.084,178.779,176.837192481,,,,174.0552845768,2.4481,169.257,178.854,176.845,,,,174.323,2.2912,169.833,178.814,176.748,,,,173.795,2.4921,168.911,178.679 2001,2,177.5317122,,,,174.7078518968,2.7692,169.28,180.135,177.5487445729,,,,175.1306310477,2.7691,169.703,180.558,177.4100697987,,,,174.8316846814,2.8356,169.274,180.389,177.4314962031,,,,174.9883502198,2.8046,169.491,180.485,177.568,,,,175.328,2.6392,170.156,180.501,177.127,,,,174.711,2.7534,169.314,180.107 2001,3,178.5005259429,,,,175.5789302315,3.1643,169.377,181.781,178.5075160891,,,,176.0842624201,3.1483,169.914,182.255,178.4434523593,,,,175.7275374931,3.194,169.467,181.988,178.4577307847,,,,175.9191394228,3.1554,169.735,182.104,178.535,,,,176.334,2.9858,170.482,182.186,178.473,,,,175.609,2.998,169.733,181.485 2001,4,178.551424957,,,,176.4415929509,3.5677,169.449,183.434,178.5405940261,,,,177.0335195914,3.5276,170.12,183.947,178.4127628861,,,,176.6190787111,3.5515,169.658,183.58,178.431638159,,,,176.8477289245,3.503,169.982,183.713,178.594,,,,177.34,3.3315,170.81,183.869,178.103,,,,176.519,3.2202,170.207,182.831 2002,1,178.5113144309,,,,177.2959213597,3.9799,169.495,185.096,178.4950101925,,,,177.9786654965,3.9067,170.322,185.636,178.4280846262,,,,177.5063307758,3.91,169.843,185.17,178.4424347618,,,,177.7741891719,3.8486,170.231,185.317,178.567,,,,178.345,3.6766,171.139,185.551,178.58,,,,177.421,3.4306,170.697,184.145 2002,2,180.2247478027,,,,178.1419959768,4.4009,169.516,186.768,180.2361498037,,,,178.9199472648,4.2853,170.521,187.319,180.3880488337,,,,178.3893146464,4.2706,170.019,186.76,180.384875915,,,,178.6985877074,4.1932,170.48,186.917,180.28,,,,179.351,4.021,171.47,187.232,180.428,,,,178.329,3.6271,171.22,185.438 2002,3,180.8812555147,,,,178.9798965432,4.8306,169.512,188.448,180.8929359533,,,,179.8575971709,4.663,170.718,188.997,180.8779742943,,,,179.2680509174,4.6342,170.185,188.351,180.8883836647,,,,179.6209898179,4.5371,170.728,188.514,180.941,,,,180.357,4.3645,171.803,188.912,180.712,,,,179.232,3.8146,171.756,186.709 2002,4,182.1217530645,,,,179.8097020298,5.2691,169.483,190.137,182.1440794946,,,,180.7918335272,5.0394,170.915,190.669,182.1982416071,,,,180.1425600339,5.0013,170.34,189.945,182.2033611924,,,,180.5414587027,4.8808,170.975,190.108,182.182,,,,181.364,4.707,172.138,190.589,182.352,,,,180.139,3.9926,172.313,187.964 2003,1,183.5863851269,,,,180.6314906442,5.7159,169.428,191.835,183.6172936436,,,,181.7228615235,5.4142,171.111,192.334,183.6677376966,,,,181.0128623329,5.3723,170.483,191.542,183.6730872079,,,,181.4600555571,5.2243,171.221,191.699,183.644,,,,182.37,5.0481,172.476,192.264,183.513,,,,181.043,4.1635,172.883,189.204 2003,2,184.1174433192,,,,181.4453398387,6.171,169.35,193.54,184.138603356,,,,182.6508740151,5.787,171.308,193.993,184.0698585717,,,,181.8789780516,5.7474,170.614,193.144,184.0850064378,,,,182.376839639,5.5676,171.464,193.289,184.178,,,,183.376,5.3878,172.817,193.936,184.023,,,,181.949,4.3273,173.468,190.43 2003,3,184.5443919305,,,,182.251326317,6.6341,169.249,195.254,184.561043527,,,,183.5760522653,6.1576,171.507,195.645,184.5149896099,,,,182.7409273298,6.1268,170.733,194.749,184.5290257015,,,,183.2918683299,5.9109,171.707,194.877,184.611,,,,184.383,5.7256,173.161,195.605,184.485,,,,182.854,4.4853,174.063,191.645 2003,4,185.790913924,,,,183.0495260422,7.1048,169.124,196.975,185.8194914079,,,,184.4985666411,6.5257,171.708,197.289,185.879208987,,,,183.5987302099,6.5106,170.838,196.359,185.885307579,,,,184.2051971955,6.2541,171.947,196.463,185.858,,,,185.39,6.0616,173.509,197.27,185.991,,,,183.76,4.6378,174.67,192.85 2004,1,187.2605858834,,,,183.840014243,7.583,168.978,198.702,187.2983369795,,,,185.4185772689,6.8911,171.912,198.925,187.3504459251,,,,184.4524066383,6.8989,170.931,197.974,187.3573082078,,,,185.1168800421,6.5971,172.187,198.047,187.324,,,,186.397,6.3954,173.862,198.931,187.266,,,,184.665,4.7856,175.285,194.044 2004,2,188.3727424216,,,,184.6228654218,8.0684,168.809,200.437,188.4084484474,,,,186.3362346499,7.2535,172.12,200.553,188.3934156532,,,,185.3019764651,7.2916,171.011,199.593,188.4057130567,,,,186.026968973,6.9399,172.425,199.629,188.434,,,,187.403,6.727,174.219,200.588,188.368,,,,185.57,4.9288,175.91,195.231 2004,3,190.1751707887,,,,185.3981533608,8.5607,168.619,202.177,190.217596201,,,,187.2516802385,7.6128,172.331,202.173,190.2660090321,,,,186.1474594451,7.6889,171.078,201.217,190.2727541662,,,,186.9355144424,7.2823,172.662,201.209,190.228,,,,188.41,7.0562,174.581,202.24,190.264,,,,186.476,5.0681,176.542,196.409 2004,4,191.9608597652,,,,186.1659511297,9.0598,168.409,203.923,192.0017457862,,,,188.1650469862,7.9689,172.546,203.784,192.0082426728,,,,186.9888752382,8.0906,171.132,202.846,192.0172722694,,,,187.8425653072,7.6243,172.899,202.786,192.004,,,,189.418,7.3829,174.947,203.888,191.856,,,,187.381,5.2036,177.182,197.58 2005,1,192.9249100574,,,,186.9263310921,9.5653,168.179,205.674,192.9483784061,,,,189.076459853,8.3216,172.766,205.387,192.8516392196,,,,187.8262434093,8.4968,171.173,204.48,192.867884817,,,,188.7481688778,7.9659,173.135,204.361,192.964,,,,190.425,7.7069,175.32,205.53,192.672,,,,188.286,5.3357,177.828,198.744 2005,2,195.0485996347,,,,187.6793649125,10.077,167.929,207.43,195.0761539867,,,,189.9860362873,8.6709,172.991,206.981,195.1215629644,,,,188.6595834296,8.9073,171.202,206.118,195.1247041843,,,,189.6523709671,8.3068,173.371,205.933,195.076,,,,191.432,8.0282,175.697,207.167,195.149,,,,189.192,5.4645,178.481,199.902 2005,3,195.8829345899,,,,188.425123563,10.5947,167.66,209.19,195.8888528366,,,,190.8938866775,9.0167,173.222,208.566,195.769454439,,,,189.4889146764,9.3223,171.218,207.76,195.7841430678,,,,190.5552159377,8.6471,173.607,207.503,195.907,,,,192.439,8.3467,176.08,208.798,195.321,,,,190.097,5.5904,179.14,201.054 2005,4,200.881551968,,,,189.1636773301,11.1182,167.372,210.955,200.9296590393,,,,191.8001147769,9.3588,173.457,210.143,201.2531803919,,,,190.3142564339,9.7415,171.221,209.407,201.2283148262,,,,191.4567467481,8.9866,173.843,209.07,200.869,,,,193.447,8.6623,176.469,210.424,201.704,,,,191.002,5.7136,179.804,202.201 2006,1,200.8374966075,,,,189.8950958213,11.6472,167.067,212.723,200.8202472437,,,,192.7048181018,9.6974,173.698,211.711,200.4617908111,,,,191.1356278936,10.165,171.212,211.059,200.4879862602,,,,192.3570049969,9.3252,174.08,210.634,200.822,,,,194.454,8.975,176.863,212.045,198.987,,,,191.907,5.8341,180.473,203.342 2006,2,202.1024666878,,,,190.6194479714,12.1817,166.744,214.495,202.0675124183,,,,193.6080883069,10.0323,173.945,213.271,201.9885761817,,,,191.9530481544,10.5927,171.192,212.714,201.9892792336,,,,193.256030966,9.663,174.317,212.195,202.082,,,,195.462,9.2848,177.264,213.66,202.774,,,,192.813,5.9522,181.147,204.479 2006,3,204.1807964789,,,,191.3368020496,12.7213,166.404,216.27,204.1450996188,,,,194.5100115376,10.3635,174.198,214.822,204.179541508,,,,192.7665362236,11.0246,171.159,214.374,204.1674660761,,,,194.1538636621,9.9997,174.555,213.753,204.15,,,,196.469,9.5916,177.67,215.268,203.062,,,,193.718,6.068,181.825,205.611 2006,4,203.0157854602,,,,192.0472256651,13.2659,166.046,218.048,202.9319404185,,,,195.410668761,10.6911,174.457,216.365,202.6394746314,,,,193.5761110169,11.4604,171.114,216.038,202.6516262814,,,,195.0505408572,10.3355,174.793,215.308,203.003,,,,197.477,9.8954,178.082,216.872,202.726,,,,194.623,6.1816,182.508,206.739 2007,1,204.7648391013,,,,192.7507857741,13.8154,165.673,219.828,204.7053158681,,,,196.3101360771,11.015,174.721,217.899,204.864868405,,,,194.3817913592,11.9003,171.058,217.706,204.8390307301,,,,195.9460991278,10.67,175.033,216.859,204.754,,,,198.485,10.1962,178.5,218.469,204.658,,,,195.529,6.2932,183.194,207.863 2007,2,207.2769566127,,,,193.447548686,14.3694,165.284,221.611,207.2414456805,,,,197.2084850116,11.3352,174.992,219.425,207.4265796922,,,,195.1835959846,12.3441,170.99,219.378,207.3960909405,,,,196.8405738924,11.0034,175.274,218.407,207.258,,,,199.492,10.494,178.924,220.06,207.329,,,,196.434,6.4029,183.885,208.983 2007,3,208.6912331435,,,,194.1375800696,14.928,164.879,223.396,208.6492720137,,,,198.105782791,11.6518,175.269,220.943,208.6537586221,,,,195.9815435372,12.7917,170.91,221.053,208.6352773018,,,,197.7339994486,11.3356,175.517,219.951,208.67,,,,200.5,10.7888,179.355,221.646,208.115,,,,197.339,6.5107,184.579,210.1 2007,4,210.5410872839,,,,194.8209449591,15.4908,164.459,225.182,210.500111343,,,,199.0020926004,11.9647,175.552,222.453,210.5576053658,,,,196.7756525715,13.2432,170.819,222.732,210.532355268,,,,198.626409008,11.6665,175.761,221.492,210.514,,,,201.508,11.0805,179.791,223.225,210.516,,,,198.245,6.6167,185.276,211.213 2008,1,214.1899253565,,,,195.4977077604,16.0578,164.025,226.971,214.1698597159,,,,199.8974738271,12.2741,175.841,223.954,214.3829696128,,,,197.5659415525,13.6983,170.718,224.414,214.3413261881,,,,199.5178347313,11.996,176.006,223.03,214.14,,,,202.516,11.3693,180.232,224.799,213.999,,,,199.15,6.721,185.977,212.323 2008,2,215.6458854232,,,,196.1679322573,16.6289,163.576,228.76,215.5949327403,,,,200.7919822885,12.58,176.136,225.448,215.4886503677,,,,198.3524288567,14.1572,170.605,226.1,215.4686267913,,,,200.4083077608,12.3242,176.253,224.563,215.587,,,,203.524,11.6551,180.68,226.367,214.828,,,,200.055,6.8238,186.681,213.43 2008,3,220.6987299825,,,,196.8316816174,17.2038,163.113,230.55,220.6741351366,,,,201.6856704468,12.8823,176.437,226.935,220.9632787766,,,,199.1351327719,14.6196,170.481,227.789,220.9055597068,,,,201.2978582533,12.6509,176.503,226.093,220.602,,,,204.532,11.9379,181.134,227.93,221.009,,,,200.961,6.925,187.388,214.534 2008,4,218.3717504048,,,,197.4890183978,17.7824,162.636,232.342,218.2426223953,,,,202.5785876106,13.1812,176.744,228.413,217.6667975573,,,,199.9140714981,15.0855,170.347,229.481,217.6747091231,,,,202.186515411,12.9761,176.754,227.619,218.294,,,,205.54,12.2178,181.593,229.486,215.84,,,,201.866,7.0248,188.098,215.634 2009,1,212.6894332539,,,,198.1400045515,18.3646,162.146,234.134,212.4740916853,,,,203.4707801248,13.4766,177.057,229.884,211.8959992321,,,,200.6892631477,15.5549,170.202,231.176,211.9059766187,,,,203.0743075115,13.2999,177.007,229.142,212.678,,,,206.548,12.4947,182.059,231.037,212.326,,,,202.771,7.1232,188.81,216.733 2009,2,213.1786192035,,,,198.7847014328,18.9502,161.643,235.926,213.0392637652,,,,204.3622915483,13.7687,177.376,231.348,213.4572131423,,,,201.460725746,16.0277,170.047,232.874,213.3903799208,,,,203.9612619376,13.6221,177.262,230.66,213.202,,,,207.556,12.7688,182.529,232.582,213.599,,,,203.677,7.2203,189.525,217.828 2009,3,215.1701293805,,,,199.4231698032,19.5392,161.127,237.719,215.1095875387,,,,205.2531628216,14.0574,177.701,232.805,215.5892010821,,,,202.2284772315,16.5038,169.882,234.575,215.5198428062,,,,204.847405205,13.9428,177.52,232.175,215.208,,,,208.564,13.04,183.006,234.122,215.75,,,,204.582,7.316,190.243,218.921 2009,4,217.2661592661,0.8056,215.687,218.845,200.0554698373,20.1314,160.599,239.512,217.2554734364,0.7999,215.688,218.823,206.1434324244,14.3429,178.032,234.255,217.5930744392,0.7953,216.034,219.152,202.9925354565,16.9832,169.706,236.279,217.5372491403,0.7925,215.984,219.091,205.7327629904,14.2619,177.78,233.686,217.308,0.7972,215.745,218.871,209.572,13.3085,183.488,235.656,217.422,0.8259,215.804,219.041,205.487,7.4105,190.963,220.012 2010,1,218.1388055236,1.23,215.728,220.55,200.6816611283,20.7267,160.058,241.305,218.1265713231,1.2305,215.715,220.538,207.0331365232,14.6251,178.368,235.698,218.6612703593,1.291,216.131,221.192,203.7529181874,17.4658,169.521,237.985,218.5527257447,1.2804,216.043,221.062,206.6173601574,14.5794,178.042,235.192,218.236,1.211,215.862,220.609,210.58,13.5741,183.975,237.185,218.346,1.4083,215.585,221.106,206.393,7.5039,191.685,221.1 2010,2,219.003021018,1.6186,215.831,222.175,201.3018026937,21.3249,159.506,243.098,218.9982561241,1.6254,215.813,222.184,207.9223091109,14.9042,178.711,237.134,219.6986031575,1.7143,216.339,223.059,204.5096431051,17.9516,169.325,239.694,219.5410430132,1.698,216.213,222.869,207.5012207828,14.8952,178.307,236.695,219.168,1.5831,216.065,222.271,211.588,13.837,184.468,238.708,219.238,1.8547,215.603,222.874,207.298,7.596,192.41,222.186 2010,3,219.8588872002,1.9993,215.94,223.778,201.9159529807,21.9261,158.942,244.89,219.8704925599,2.0093,215.932,223.809,208.8109821365,15.1802,179.058,238.564,220.7260098869,2.1027,216.605,224.847,205.2627278056,18.4404,169.12,241.405,220.5214492212,2.0819,216.441,224.602,208.3843681813,15.2095,178.574,238.194,220.104,1.9403,216.301,223.907,212.597,14.0972,184.967,240.226,220.152,2.1881,215.864,224.441,208.203,7.6871,193.137,223.27 2010,4,220.706484734,2.3815,216.039,225.374,202.524169872,22.5299,158.366,246.682,220.7432474715,2.3897,216.06,225.427,209.6991856291,15.4531,179.412,239.987,221.7475271771,2.4735,216.9,226.595,206.0121897999,18.9323,168.905,243.119,221.4974064825,2.4481,216.699,226.296,209.2668249293,15.522,178.844,239.689,221.044,2.2912,216.553,225.535,213.605,14.3547,185.47,241.739,221.052,2.4921,216.167,225.936,209.109,7.7771,193.866,224.351 2011,1,221.545893504,2.7692,216.118,226.973,203.126510691,23.1365,157.78,248.473,221.6164896931,2.7691,216.189,227.044,210.5869478123,15.723,179.771,241.403,222.7639487392,2.8356,217.206,228.322,206.7580465151,19.4272,168.681,244.835,222.4696165704,2.8046,216.973,227.967,210.1486128889,15.8329,179.117,241.18,221.988,2.6392,216.815,227.161,214.613,14.6096,185.979,243.247,221.961,2.7534,216.565,227.358,210.014,7.8661,194.597,225.431 2011,2,222.3771926233,3.1643,216.175,228.579,203.7230322072,23.7456,157.183,250.264,222.4901899324,3.1483,216.32,228.661,211.4742952135,15.9899,180.135,242.814,223.775445946,3.194,217.515,230.036,207.5003152945,19.9251,168.448,246.553,223.4382960718,3.1554,217.254,229.623,211.0297532299,16.1421,179.392,242.668,222.935,2.9858,217.083,228.787,215.621,14.8619,186.493,244.75,222.864,2.998,216.988,228.74,210.919,7.9541,195.33,226.509 2011,3,223.2004604401,3.5677,216.208,230.193,204.3137906419,24.3571,156.575,252.053,223.3643206578,3.5276,216.45,230.278,212.3612527653,16.2539,180.504,244.218,224.7820706652,3.5515,217.821,231.743,208.2390133976,20.4258,168.205,248.273,224.4035738561,3.503,217.538,231.269,211.9102664522,16.4495,179.67,244.151,223.886,3.3315,217.357,230.416,216.63,15.1116,187.011,246.248,223.771,3.2202,217.459,230.082,211.825,8.0411,196.064,227.585 2011,4,224.0157745462,3.9799,216.215,231.816,204.8988416729,24.9711,155.956,253.841,224.2388559925,3.9067,216.582,231.896,213.2478439017,16.5152,180.879,245.617,225.7838517429,3.91,218.12,233.447,208.9741580012,20.9293,167.954,249.995,225.3655605905,3.8486,217.822,232.909,212.7901724066,16.7553,179.95,245.63,224.84,3.6766,217.634,232.046,217.638,15.3588,187.535,247.741,224.675,3.4306,217.951,231.399,212.73,8.1272,196.801,228.659 2012,1,224.8232117835,4.4009,216.198,233.449,205.4782404403,25.5873,155.328,255.628,225.1137716155,4.2853,216.715,233.513,214.134090648,16.7736,181.258,247.01,226.7808135168,4.2706,218.411,235.151,209.7057661993,21.4356,167.693,251.719,226.3243609722,4.1932,218.106,234.543,213.6694903158,17.0594,180.234,247.105,225.797,4.021,217.916,233.678,218.646,15.6036,188.064,249.229,225.581,3.6271,218.472,232.69,213.635,8.2124,197.539,229.731 2012,2,225.6228482515,4.8306,216.155,235.091,206.0520415515,26.2056,154.69,257.414,225.9890446675,4.663,216.85,235.128,215.0200137057,17.0293,181.643,248.397,227.7729793693,4.6342,218.69,236.856,210.4338550039,21.9446,167.423,253.444,227.2800759537,4.5371,218.387,236.173,214.5482387938,17.3618,180.52,248.577,226.757,4.3645,218.202,235.311,219.654,15.8459,188.597,250.712,226.486,3.8146,219.009,233.962,214.541,8.2967,198.279,230.802 2012,3,226.4147593147,5.2691,216.088,236.742,206.6202990863,26.8261,154.042,259.198,226.8646536632,5.0394,216.988,236.742,215.9056325317,17.2823,182.033,249.778,228.7603724093,5.0013,218.958,238.563,211.1584413449,22.4563,167.145,255.172,228.2328032167,4.8808,218.667,237.799,215.4264358655,17.6624,180.809,250.044,227.719,4.707,218.494,236.945,220.663,16.0859,189.135,252.191,227.392,3.9926,219.566,235.217,215.446,8.3802,199.021,231.871 2012,4,227.1990196094,5.7159,215.996,238.402,207.183066602,27.4486,153.385,260.981,227.740578409,5.4142,217.129,238.352,216.7909654136,17.5327,182.428,251.154,229.7430156036,5.3723,219.213,240.273,211.8795420709,22.9706,166.858,256.901,229.1826373376,5.2243,218.943,239.422,216.304098985,17.9613,181.101,251.508,228.684,5.0481,218.79,238.578,221.671,16.3234,189.678,253.665,228.297,4.1635,220.136,236.457,216.351,8.4628,199.764,232.938 2013,1,227.9757030506,6.171,215.881,240.071,207.7403971383,28.073,152.718,262.762,228.6167999251,5.787,217.274,239.959,217.6760295396,17.7805,182.827,252.525,230.7209318028,5.7474,219.456,241.986,212.5971739494,23.4874,166.563,258.632,230.1296698969,5.5676,219.217,241.042,217.1812450544,18.2585,181.395,252.967,229.651,5.3878,219.091,240.211,222.68,16.5587,190.225,255.134,229.202,4.3273,220.721,237.683,217.257,8.5447,200.509,234.004 2013,2,228.7448828395,6.6341,215.742,241.747,208.2923432229,28.6993,152.043,264.542,229.4933003724,6.1576,217.425,241.562,218.5608410646,18.0257,183.231,253.891,231.6941437462,6.1268,219.686,243.702,213.3113536672,24.0068,166.259,260.364,231.0739895756,5.9109,219.489,242.659,218.0578904402,18.5539,181.693,254.423,230.621,5.7256,219.399,241.843,223.688,16.7917,190.777,256.599,230.107,4.4853,221.316,238.898,218.162,8.6257,201.256,235.068 2013,3,229.50663147,7.1048,215.581,243.432,208.8389568756,29.3273,151.358,266.319,230.3700629844,6.5257,217.58,243.16,219.4454151726,18.2686,183.64,255.251,232.6626740638,6.5106,219.902,245.423,214.0220978309,24.5287,165.947,262.097,232.0156822477,6.2541,219.758,244.274,218.9340509913,18.8477,181.993,255.875,231.592,6.0616,219.712,243.473,224.696,17.0225,191.333,258.06,231.013,4.6378,221.923,240.103,219.067,8.706,202.004,236.131 2013,4,230.2610207356,7.583,215.399,245.123,209.3802896139,29.957,150.666,268.095,231.2470720022,6.8911,217.741,244.753,220.3297661348,18.5089,184.053,256.607,233.6265452764,6.8989,220.105,247.148,214.7294229673,25.053,165.626,263.832,232.9548310688,6.5971,220.025,245.885,219.8097420547,19.1397,182.297,257.323,232.566,6.3954,220.031,245.101,225.705,17.2511,191.893,259.516,231.918,4.7856,222.538,241.298,219.972,8.7856,202.753,237.192 2014,1,231.0081217362,8.0684,215.194,246.822,209.9163924575,30.5884,149.964,269.869,232.1243126143,7.2535,217.908,246.341,221.2139073645,18.747,184.471,257.957,234.5857797965,7.2916,220.294,248.877,215.4333455235,25.5797,165.298,265.569,233.8915165624,6.9399,220.29,247.493,220.6849784915,19.43,182.603,258.767,233.542,6.727,220.357,246.726,226.713,17.4776,192.458,260.969,232.823,4.9288,223.163,242.484,220.878,8.8645,203.504,238.252 2014,2,231.7480048848,8.5607,214.969,248.527,210.4473159331,31.2213,149.255,271.64,233.0017708995,7.6128,218.081,247.923,222.0978514689,18.9827,184.893,259.303,235.5403999291,7.6889,220.471,250.61,216.1338818676,26.1088,164.962,267.306,234.8258167029,7.2823,220.553,249.099,221.5597746927,19.7186,182.912,260.208,234.519,7.0562,220.689,248.349,227.722,17.7019,193.027,262.417,233.729,5.0681,223.795,243.662,221.783,8.9426,204.256,239.31 2014,3,232.480739914,9.0598,214.724,250.238,210.9731100793,31.8558,148.537,273.409,233.8794337734,7.9689,218.261,249.498,222.9816102973,19.2161,185.319,260.644,236.4904278715,8.0906,220.633,252.348,216.8310482889,26.6402,164.617,269.045,235.7578069968,7.6243,220.814,250.701,222.4341445934,20.0055,183.224,261.644,235.498,7.3829,221.028,249.968,228.73,17.9242,193.599,263.861,234.634,5.2036,224.435,244.833,222.688,9.0201,205.009,240.368 2014,4,233.206395883,9.5653,214.459,251.954,211.4938244514,32.4916,147.811,275.176,234.7572889381,8.3216,218.447,251.067,223.8651949865,19.4472,185.749,261.981,237.4358857144,8.4968,220.783,254.089,217.5248609985,27.1738,164.265,270.785,236.6875605602,7.9659,221.075,252.3,223.3081016879,20.2907,183.539,263.077,236.479,7.7069,221.374,251.584,229.739,18.1444,194.176,265.301,235.539,5.3357,225.082,245.997,223.594,9.097,205.764,241.423 2015,1,233.9250411836,10.077,214.175,253.676,212.0095081258,33.1288,147.078,276.941,235.6353248348,8.6709,218.641,252.63,224.7486160043,19.6762,186.184,263.313,238.3767954422,8.9073,220.919,255.835,218.2153361293,27.7096,163.905,272.525,237.6151481949,8.3068,221.334,253.896,224.1816590432,20.5741,183.857,264.506,237.461,8.0282,221.726,253.196,230.747,18.3627,194.757,266.737,236.445,5.4645,225.734,247.155,224.499,9.1731,206.52,242.478 2015,2,234.6367435468,10.5947,213.872,255.402,212.5202097049,33.7673,146.338,278.703,236.5135305999,9.0167,218.841,254.186,225.6318831888,19.9031,186.623,264.641,239.3131789336,9.3223,221.042,257.585,218.9024897366,28.2477,163.538,274.267,238.5406384615,8.6471,221.593,255.489,225.0548293128,20.8559,184.178,265.932,238.445,8.3467,222.086,254.804,231.755,18.5789,195.341,268.17,237.35,5.5904,226.393,248.307,225.404,9.2487,207.277,243.532 2015,3,235.3415700494,11.1182,213.55,257.133,213.0259773212,34.407,145.589,280.463,237.3918960223,9.3588,219.049,255.735,226.5150057872,20.1278,187.065,265.965,240.245057962,9.7415,221.152,259.338,219.5863377988,28.7878,163.163,276.009,239.4640977504,8.9866,221.851,257.077,225.9276247493,21.136,184.502,267.354,239.43,8.6623,222.452,256.408,232.764,18.7933,195.93,269.598,238.255,5.7136,227.057,249.454,226.31,9.3237,208.036,244.584 2015,4,236.0395871201,11.6472,213.211,258.868,213.5268586427,35.0479,144.834,282.22,238.2704115052,9.6974,219.264,257.277,227.3979924905,20.3505,187.512,267.284,241.1724541961,10.165,221.249,261.096,220.2668962169,29.3301,162.781,277.753,240.3855903505,9.3252,222.108,258.663,226.800057218,21.4145,184.828,268.772,240.416,8.975,222.825,258.007,233.772,19.0058,196.522,271.023,239.161,5.8341,227.726,250.595,227.215,9.398,208.795,245.635 statsmodels-0.12.2/statsmodels/tsa/tests/results/results_arima_forecasts_all_css.csv000066400000000000000000000353441400612667500313120ustar00rootroot00000000000000fc,fcdyn,fcdyn2,fcdyn3,fcdyn4,orig_index,year,quarter,,,,,, NA,NA,NA,NA,NA,0,1959,1,,,,,, NA,NA,NA,NA,NA,1,1959,2,,,,,, NA,NA,NA,NA,NA,2,1959,3,,,,,, NA,NA,NA,NA,NA,3,1959,4,,,,,, NA,NA,NA,NA,NA,4,1960,1,,,,,, 29.7575819218,29.7575819218,NA,NA,NA,5,1960,2,,,,,, 29.6889197051,29.9572171332,NA,NA,NA,6,1960,3,,,,,, 29.9626330839,30.1680969792,NA,NA,NA,7,1960,4,,,,,, 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31.7379939232,34.411282142,31.6823961791,NA,NA,26,1965,3,,,,,, 31.7603857461,34.6369229685,31.8187238201,NA,NA,27,1965,4,,,,,, 32.0533148842,34.8627580301,31.9539331921,NA,NA,28,1966,1,,,,,, 32.4829850845,35.088787485,32.0898712134,NA,NA,29,1966,2,,,,,, 32.6081136012,35.3150114973,32.2260104566,NA,NA,30,1966,3,,,,,, 33.1082366398,35.5414302325,32.3621085756,NA,NA,31,1966,4,,,,,, 33.0256737089,35.7680438567,32.4983553035,NA,NA,32,1967,1,,,,,, 33.3102788967,35.9948525371,32.634744717,NA,NA,33,1967,2,,,,,, 33.5898710208,36.2218564413,32.7712370524,NA,NA,34,1967,3,,,,,, 33.9093400596,36.4490557371,32.9078459341,NA,NA,35,1967,4,,,,,, 34.3561409186,36.6764505927,33.044575937,NA,NA,36,1968,1,,,,,, 34.6307558557,36.9040411762,33.1814227831,NA,NA,37,1968,2,,,,,, 35.2106795469,37.1318276561,33.3183869295,NA,NA,38,1968,3,,,,,, 35.5711327549,37.3598102011,33.4554693153,NA,NA,39,1968,4,,,,,, 36.0080894273,37.5879889798,33.5926696993,NA,NA,40,1969,1,,,,,, 36.6606355815,37.8163641612,33.7299881027,NA,NA,41,1969,2,,,,,, 37.1360332408,38.0449359144,33.8674247253,NA,NA,42,1969,3,,,,,, 37.6751991393,38.2737044085,34.0049796551,NA,NA,43,1969,4,,,,,, 38.3005703403,38.5026698128,34.1426529764,NA,NA,44,1970,1,,,,,, 38.9079571589,38.7318322969,34.280444799,NA,NA,45,1970,2,,,,,, 39.2733991806,38.9611920304,34.4183552264,NA,NA,46,1970,3,,,,,, 39.8148885174,39.190749183,34.5563843583,NA,NA,47,1970,4,,,,,, 40.2915758461,39.4205039248,34.6945322972,NA,NA,48,1971,1,,,,,, 40.4225895126,39.6504564257,34.8327991459,NA,NA,49,1971,2,,,,,, 41.0185075749,39.880606856,34.9711850064,NA,NA,50,1971,3,,,,,, 41.2142853032,40.110955386,35.1096899812,NA,NA,51,1971,4,,,,,, 41.5594233571,40.3415021864,35.2483141727,NA,NA,52,1972,1,,,,,, 41.8323265312,40.5722474276,35.3870576838,NA,NA,53,1972,2,,,,,, 42.1305292337,40.8031912806,35.5259206169,NA,NA,54,1972,3,,,,,, 42.5580908985,41.0343339163,35.664903075,NA,NA,55,1972,4,,,,,, 43.0849626521,41.2656755057,35.8040051609,NA,NA,56,1973,1,,,,,, 44.2451877539,41.4972162202,35.9432269775,NA,NA,57,1973,2,,,,,, 44.6132865443,41.7289562311,36.082568628,NA,NA,58,1973,3,,,,,, 46.3671644035,41.96089571,36.2220302155,NA,NA,59,1973,4,,,,,, 47.4424883646,42.1930348285,36.3616118431,NA,NA,60,1974,1,,,,,, 48.9233461033,42.4253737585,36.5013136143,NA,NA,61,1974,2,,,,,, 50.0952378443,42.6579126721,36.6411356325,NA,NA,62,1974,3,,,,,, 51.9839926027,42.8906517412,36.7810780011,NA,NA,63,1974,4,,,,,, 53.1741129397,43.1235911382,36.9211408237,NA,NA,64,1975,1,,,,,, 53.8053193308,43.3567310356,37.0613242041,NA,NA,65,1975,2,,,,,, 54.8708705552,43.5900716059,37.2016282459,NA,NA,66,1975,3,,,,,, 55.6636550103,43.8236130218,37.3420530531,NA,NA,67,1975,4,,,,,, 56.6131925387,44.0573554562,37.4825987296,NA,NA,68,1976,1,,,,,, 56.7317375164,44.2912990822,37.6232653794,NA,NA,69,1976,2,,,,,, 57.8182142576,44.5254440728,37.7640531066,NA,NA,70,1976,3,,,,,, 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1.594814571946,0.926875951549,0.926875951549,1.594814571946,NA,196,2008,1 1.576157878722,0.926875951549,0.926875951549,1.576157878722,NA,197,2008,2 2.627374926492,0.926875951549,0.926875951549,2.627374926492,NA,198,2008,3 -0.080501465061,0.926875951549,0.926875951549,-0.080501465061,NA,199,2008,4 -0.143905364796,0.926875951549,0.926875951549,-0.143905364796,NA,200,2009,1 -0.291651949853,0.926875951549,0.926875951549,-0.291651949853,NA,201,2009,2 0.543157406421,0.926875951549,0.926875951549,0.543157406423,NA,202,2009,3 1.196374008885,0.926875951549,0.926875951549,0.670188970211,1.196374008885,203,2009,4 1.265346864378,0.926875951549,0.926875951549,1.117335644106,1.265346864378,204,2010,1 1.173696210516,0.926875951549,0.926875951549,0.740831804756,1.173696210516,205,2010,2 1.078652308679,0.926875951549,0.926875951549,0.983052812221,1.078652308679,206,2010,3 1.037707266894,0.926875951549,0.926875951549,0.85483217265,1.037707266894,207,2010,4 1.014688660435,0.926875951549,0.926875951549,0.959658388297,1.014688660435,208,2011,1 0.979957079474,0.926875951549,0.926875951549,0.878568582037,0.979957079474,209,2011,2 0.970749320849,0.926875951549,0.926875951549,0.952456798029,0.970749320849,210,2011,3 0.954264512229,0.926875951549,0.926875951549,0.89723984453,0.954264512229,211,2011,4 0.949096714807,0.926875951549,0.926875951549,0.943096789796,0.949096714807,212,2012,1 0.940410834647,0.926875951549,0.926875951549,0.909314112718,0.940410834647,213,2012,2 0.938376248966,0.926875951549,0.926875951549,0.937273453716,0.938376248966,214,2012,3 0.933543521689,0.926875951549,0.926875951549,0.91618573467,0.933543521689,215,2012,4 0.932798795546,0.926875951549,0.926875951549,0.933567508384,0.932798795546,216,2013,1 0.930161942404,0.926875951549,0.926875951549,0.920353581631,0.930161942404,217,2013,2 0.929938463825,0.926875951549,0.926875951549,0.931133359137,0.929938463825,218,2013,3 0.928479634179,0.926875951549,0.926875951549,0.922889904339,0.928479634179,219,2013,4 0.928469062843,0.926875951549,0.926875951549,0.929572741746,0.928469062843,220,2014,1 0.927650865487,0.926875951549,0.926875951549,0.924430761588,0.927650865487,221,2014,2 0.927708891911,0.926875951549,0.926875951549,0.928578703482,0.927708891911,222,2014,3 0.927245679784,0.926875951549,0.926875951549,0.925372237336,0.927245679784,223,2014,4 0.927314186847,0.926875951549,0.926875951549,0.927947780535,0.927314186847,224,2015,1 0.927049147244,0.926875951549,0.926875951549,0.925949361587,0.927049147244,225,2015,2 0.927108200998,0.926875951549,0.926875951549,0.927549079877,0.927108200998,226,2015,3 0.926954981816,0.926875951549,0.926875951549,0.92630398656,0.926954981816,227,2015,4 statsmodels-0.12.2/statsmodels/tsa/tests/results/results_arma.py000066400000000000000000001230171400612667500252200ustar00rootroot00000000000000""" Results for ARMA models. Produced by gretl. """ import os from numpy import genfromtxt current_path = os.path.dirname(os.path.abspath(__file__)) with open(current_path+"/yhat_exact_nc.csv", "rb") as fd: yhat_mle = genfromtxt(fd, delimiter=",", skip_header=1, dtype=float) with open(current_path+"/yhat_css_nc.csv", "rb") as fd: yhat_css = genfromtxt(fd, delimiter=",", skip_header=1, dtype=float) with open(current_path+"/yhat_exact_c.csv", "rb") as fd: yhatc_mle = genfromtxt(fd, delimiter=",", skip_header=1, dtype=float) with open(current_path+"/yhat_css_c.csv", "rb") as fd: yhatc_css = genfromtxt(fd, delimiter=",", skip_header=1, dtype=float) with open(current_path+"/resids_exact_nc.csv", "rb") as fd: resids_mle = genfromtxt(fd, delimiter=",", skip_header=1, dtype=float) with open(current_path+"/resids_css_nc.csv", "rb") as fd: resids_css = genfromtxt(fd, delimiter=",", skip_header=1, dtype=float) with open(current_path+"/resids_exact_c.csv", "rb") as fd: residsc_mle = genfromtxt(fd, delimiter=",", skip_header=1, dtype=float) with open(current_path+"/resids_css_c.csv", "rb") as fd: residsc_css = genfromtxt(fd, delimiter=",", skip_header=1, dtype=float) with open(current_path+"/results_arma_forecasts.csv", "rb") as fd: forecast_results = genfromtxt(fd, names=True, delimiter=",", dtype=float) class Y_arma11(object): def __init__(self, method="mle"): if method == "mle": self.params = [0.788452102751, 0.381793815167] self.aic = 714.489820273473 self.bic = 725.054203027060 self.arroots = 1.2683 + 0j self.maroots = -2.6192 + 0j self.bse = [0.042075906061, 0.060925105865] self.hqic = 718.741675179309 self.llf = -354.244910136737 self.resid = resids_mle[:, 0] self.fittedvalues = yhat_mle[:, 0] self.pvalues = [2.39e-78, 3.69e-10] self.tvalues = [18.74, 6.267] self.sigma2 = 0.994743350844 ** 2 self.cov_params = [[0.0017704, -0.0010612], [-0.0010612, 0.0037119]] self.forecast = forecast_results['fc11'] self.forecasterr = forecast_results['fe11'] elif method == "css": self.params = [0.791515576984, 0.383078056824] self.aic = 710.994047176570 self.bic = 721.546405865964 self.arroots = [1.2634 + 0.0000j] self.maroots = [-2.6104 + 0.0000j] # NOTE: bse, cov_params, tvalues taken from R; commented-out # versions below are from [TODO: finish this sentence] # self.bse = [0.042369318062, 0.065703859674] self.bse = [0.0424015620491, 0.0608752234378] # self.cov_params = [ # [0.0017952, -0.0010996], # [-0.0010996, 0.0043170]] self.cov_params = [ [0.00179789246421, -0.00106195321540], [-0.00106195321540, 0.00370579282860]] self.hqic = 715.241545108550 self.llf = -352.497023588285 self.resid = resids_css[1:, 0] self.fittedvalues = yhat_css[1:, 0] self.pvalues = [7.02e-78, 5.53e-09] # self.tvalues = [18.68, 5.830] self.tvalues = [18.6671317239, 6.2928857557] self.sigma2 = 0.996717562780**2 class Y_arma14(object): def __init__(self, method="mle"): if method == "mle": self.params = [0.763798613302, 0.306453049063, -0.835653786888, 0.151382611965, 0.421169903784] self.aic = 736.001094752429 self.bic = 757.129860259603 self.arroots = 1.3092 + 0j self.maroots = [1.0392 - 0.7070j, 1.0392 + 0.7070j, -1.2189 - 0.1310j, -1.2189 + 0.1310j] self.bse = [0.064888368113, 0.078031359430, 0.076246826219, 0.069267771804, 0.071567389557] self.cov_params = [ [0.0042105, -0.0031074, -0.0027947, -0.00027766, -0.00037373], [-0.0031074, 0.0060889, 0.0033958, -0.0026825, -0.00062289], [-0.0027947, 0.0033958, 0.0058136, -0.00063747, -0.0028984], [-0.00027766, -0.0026825, -0.00063747, 0.0047980, 0.0026998], [-0.00037373, -0.00062289, -0.0028984, 0.0026998, 0.0051219]] self.hqic = 744.504804564101 self.llf = -362.000547376215 self.resid = resids_mle[:, 1] self.fittedvalues = yhat_mle[:, 1] self.pvalues = [5.51e-32, 8.59e-05, 5.96e-28, 0.0289, 3.98e-09] self.tvalues = [11.77, 3.927, -10.96, 2.185, 5.885] self.sigma2 = 1.022607088673 ** 2 self.bse = [0.064888368113, 0.078031359430, 0.076246826219, 0.069267771804, 0.071567389557] elif method == "css": self.params = [0.772072791055, 0.283961556581, -0.834797380642, 0.157773469382, 0.431616426021] self.aic = 734.294057687460 self.bic = 755.398775066249 self.arroots = [1.2952 + 0.0000j] self.maroots = [1.0280 - 0.6987j, 1.0280 + 0.6987j, -1.2108 - 0.1835j, -1.2108 + 0.1835j] # NOTE: bse, cov_params, tvalues taken from R; commented-out # versions below are from [TODO: finish this sentence] # self.bse = [0.083423762397, 0.086852297123, 0.093883465705, # 0.068170451942, 0.065938183073] self.bse = [0.06106330, 0.07381130, 0.07257705, 0.06857992, 0.07046048] # self.cov_params = [ # [0.0069595, -0.0053083, -0.0054522, -0.0016324, -0.00099984], # [-0.0053083, 0.0075433, 0.0052442, -0.00071680, 0.0010335], # [-0.0054522, 0.0052442, 0.0088141, 0.0019754, -0.0018231], # [-0.0016324, -0.00071680, 0.0019754, 0.0046472, 0.0011853], # [-0.00099984, 0.0010335, -0.0018231, 0.0011853, 0.0043478]] self.cov_params = [ [0.0037287270, -0.0025337305, -0.0023475489, -0.0001894180, -0.0002716368], [-0.0025337305, 0.0054481087, 0.0029356374, -0.0027307668, -0.0008073432], [-0.0023475489, 0.0029356374, 0.0052674275, -0.0007578638, -0.0028534882], [-0.0001894180, -0.0027307668, -0.0007578638, 0.0047032056, 0.0026710177], [-0.0002716368, -0.0008073432, -0.0028534882, 0.0026710177, 0.0049646795] ] self.hqic = 742.789053551421 self.llf = -361.147028843730 self.resid = resids_css[1:, 1] self.fittedvalues = yhat_css[1:, 1] self.pvalues = [2.15e-20, 0.0011, 6.01e-19, 0.0206, 5.92e-11] # self.tvalues = [9.255, 3.269, -8.892, 2.314, 6.546] self.tvalues = [12.643194, 3.847252, -11.501785, 2.301399, 6.126120] self.sigma2 = 1.031950951582**2 class Y_arma41(object): def __init__(self, method="mle"): if method == "mle": self.params = [0.859167822255, -0.445990454620, -0.094364739597, 0.633504596270, 0.039251240870] self.aic = 680.801215465509 self.bic = 701.929980972682 self.arroots = [1.0209-0j, 0.2966-0.9835j, 0.2966+0.9835j, -1.4652 + 0.0000j] self.maroots = [-25.4769 + 0.0000] self.bse = [0.097363938243, 0.136020728785, 0.128467873077, 0.081059611396, 0.138536155409] self.cov_params = [ [0.0094797, -0.012908, 0.011870, -0.0073247, -0.011669], [-0.012908, 0.018502, -0.017103, 0.010456, 0.015892], [0.011870, -0.017103, 0.016504, -0.010091, -0.014626], [-0.0073247, 0.010456, -0.010091, 0.0065707, 0.0089767], [-0.011669, 0.015892, -0.014626, 0.0089767, 0.019192]] self.hqic = 689.304925277181 self.llf = -334.400607732754 self.resid = resids_mle[:, 2] self.fittedvalues = yhat_mle[:, 2] self.pvalues = [1.10e-18, 0.0010, 0.4626, 5.48e-15, 0.7769] self.tvalues = [8.824, -3.279, -.7345, 7.815, .2833] self.sigma2 = 0.911409665692 ** 2 self.forecast = forecast_results['fc41'] self.forecasterr = forecast_results['fe41'] elif method == "css": self.params = [0.868370308475, -0.459433478113, -0.086098063077, 0.635050245511, 0.033645204508] self.aic = 666.171731561927 self.bic = 687.203720777521 self.arroots = [1.0184+0.0000j, 0.2960-0.9803j, 0.2960+0.9803j, -1.4747+0.0000j] self.maroots = [-29.7219 + 0.0000j] # NOTE: bse, cov_params, tvalues taken from R; commented-out # versions below are from [TODO: finish this sentence] # self.bse = [0.077822066628, 0.112199961491, 0.104986211369, # 0.068394652456, 0.113996438269] self.bse = [0.09554032, 0.13387533, 0.12691479, 0.08045129, 0.13456419] # self.cov_params = [ # [0.0060563, -0.0083712, 0.0076270, -0.0047067, -0.0070610], # [-0.0083712, 0.012589, -0.011391, 0.0069576, 0.0098601], # [0.0076270, -0.011391, 0.011022, -0.0067771, -0.0089971], # [-0.0047067, 0.0069576, -0.0067771, 0.0046778, 0.0054205], # [-0.0070610, 0.0098601, -0.0089971, 0.0054205, 0.012995] # ] self.cov_params = [ [.009127952, -.01243259, .011488329, -.007070855, -.011031907], [-.012432590, .01792260, -.016597806, .010136298, .015053122], [.011488329, -.01659781, .016107364, -.009851695, -.013923062], [-.007070855, .01013630, -.009851695, .006472410, .008562476], [-.011031907, .01505312, -.013923062, .008562476, .018107521] ] self.hqic = 674.640335476392 self.llf = -327.085865780964 self.resid = resids_css[4:, 2] self.fittedvalues = yhat_css[4:, 2] self.pvalues = [6.51e-29, 4.23e-05, 0.4122, 1.62e-20, 0.7679] # self.tvalues = [11.16, -4.095, -0.8201, 9.285, 0.2951] self.tvalues = [9.0887381, -3.4315100, -0.6786792, 7.8938778, 0.2503143] self.sigma2 = 0.914551777765**2 class Y_arma22(object): def __init__(self, method="mle"): if method == "mle": self.params = [0.810898877154, -0.535753742985, 0.101765385197, -0.691891368356] self.aic = 756.286535543453 self.bic = 773.893840132765 self.arroots = [0.7568 - 1.1375j, 0.7568 + 1.1375j] self.maroots = [-1.1309, 1.2780] self.bse = [0.065073834100, 0.060522519771, 0.065569474599, 0.071275323591] self.cov_params = [ [0.0042346, -0.0012416, -0.0024319, -0.0012756], [-0.0012416, 0.0036630, -0.00022460, -0.0019999], [-0.0024319, -0.00022460, 0.0042994, 0.0017842], [-0.0012756, -0.0019999, 0.0017842, 0.0050802]] self.hqic = 763.372960386513 self.llf = -373.143267771727 self.resid = resids_mle[:, 3] self.fittedvalues = yhat_mle[:, 3] self.pvalues = [1.22e-35, 8.59e-19, 0.1207, 2.81e-22] self.tvalues = [12.46, -8.852, 1.552, -9.707] self.sigma2 = 1.069529754715**2 elif method == "css": self.params = [0.811172493623, -0.538952207139, 0.108020549805, -0.697398037845] self.aic = 749.652327535412 self.bic = 767.219471266237 self.arroots = [0.7525 - 1.1354j, 0.7525 + 1.1354j] self.maroots = [-1.1225 + 0.0000j, 1.2774 + 0.0000j] # NOTE: bse, cov_params, tvalues taken from R; commented-out # versions below are from [TODO: finish this sentence] # self.bse = [0.063356402845, 0.064719801680, 0.058293106832, # 0.061453528114] self.bse = [0.06549657, 0.06127495, 0.06514116, 0.07148213] # self.cov_params = [ # [0.0040140, -0.0016670, -0.0019069, -0.0011369], # [-0.0016670, 0.0041887, -0.00019356, -0.0014322], # [-0.0019069, -0.00019356, 0.0033981, 0.0020063], # [-0.0011369, -0.0014322, 0.0020063, 0.0037765]] self.cov_params = [ [0.004289801, -0.0012980774, -0.0024461381, -0.001244467], [-0.001298077, 0.0037546193, -0.0001725373, -0.002039177], [-0.002446138, -0.0001725373, 0.0042433713, 0.001720042], [-0.001244467, -0.0020391767, 0.0017200417, 0.005109695] ] self.hqic = 756.724194601530 self.llf = -369.826163767706 self.resid = resids_css[2:, 3] self.fittedvalues = yhat_css[2:, 3] self.pvalues = [1.57e-37, 8.26e-17, 0.0639, 7.55e-30] # self.tvalues = [12.80, -8.327, 1.853, -11.35] self.tvalues = [12.385077, -8.795883, 1.657944, -9.755738] self.sigma2 = 1.074973483083**2 class Y_arma50(object): def __init__(self, method="mle"): if method == "mle": self.params = [0.726892679311, -0.312619864536, 0.323740181610, 0.226499145083, -0.089562902305] self.aic = 691.422630427314 self.bic = 712.551395934487 self.arroots = [1.0772 + 0.0000j, 0.0087 - 1.2400j, 0.0087 + 1.2400j, -1.9764 + 0.0000j, 3.4107 + 0.0000j] self.maroots = None # TODO: empty array? self.bse = [0.062942787895, 0.076539691571, 0.076608230545, 0.077330717503, 0.063499540628] self.cov_params = [ [0.0039618, -0.0028252, 0.0013351, -0.0013901, -0.00066624], [-0.0028252, 0.0058583, -0.0040200, 0.0026059, -0.0014275], [0.0013351, -0.0040200, 0.0058688, -0.0041018, 0.0013917], [-0.0013901, 0.0026059, -0.0041018, 0.0059800, -0.0028959], [-0.00066624, -0.0014275, 0.0013917, -0.0028959, 0.0040322]] self.hqic = 699.926340238986 self.llf = -339.711315213657 self.resid = resids_mle[:, 4] self.fittedvalues = yhat_mle[:, 4] self.pvalues = [7.51e-31, 4.42e-05, 2.38e-05, 0.0034, 0.1584] self.tvalues = [11.55, -4.084, 4.226, 2.929, -1.410] self.sigma2 = 0.938374940397 ** 2 self.forecast = forecast_results['fc50'] self.forecasterr = forecast_results['fe50'] elif method == "css": # NOTE: some results use x-12 arima because gretl uses # LS estimates for AR CSS self.params = [0.725706505843, -0.305501865989, 0.320719417706, 0.226552951649, -0.089852608091] # self.aic = 674.817286564674 self.aic = 676.8173 # self.bic = 692.323577617397 self.bic = 697.8248 self.arroots = [1.0755 + 0.0000j, 0.0075-1.2434j, 0.0075 + 1.2434j, -1.9686 + 0.0000j, 3.3994 + 0.0000j] self.maroots = None self.bse = [0.064344956583, 0.078060866211, 0.077980166982, 0.078390791831, 0.064384559496] self.cov_params = [ [0.0041403, -0.0029335, 0.0013775, -0.0014298, -0.00068813], [-0.0029335, 0.0060935, -0.0041786, 0.0026980, -0.0014765], [0.0013775, -0.0041786, 0.0060809, -0.0042177, 0.0014572], [-0.0014298, 0.0026980, -0.0042177, 0.0061451, -0.0029853], [-0.00068813, -0.0014765, 0.0014572, -0.0029853, 0.0041454]] # self.hqic = 681.867054880965 self.hqic = 685.2770 self.llf = -332.408643282337 self.resid = resids_css[5:, 4] self.fittedvalues = yhat_css[5:, 4] self.pvalues = [1.68e-29, 9.09e-05, 3.91e-05, 0.0039, 0.1628] self.tvalues = [11.28, -3.914, 4.113, 2.890, -1.396] # self.sigma2 = 0.949462810435**2 self.sigma2 = .939724 ** 2 class Y_arma02(object): def __init__(self, method="mle"): if method == "mle": self.params = [0.169096401142, -0.683713393265] self.aic = 775.017701544762 self.bic = 785.582084298349 self.arroots = None self.maroots = [-1.0920 + 0j, 1.3393 + 0j] self.bse = [0.049254112414, 0.050541821979] self.cov_params = [[0.0024260, 0.00078704], [0.00078704, 0.0025545]] self.hqic = 779.269556450598 self.llf = -384.508850772381 self.resid = resids_mle[:, 5] self.fittedvalues = yhat_mle[:, 5] self.pvalues = [.0006, 1.07e-41] self.tvalues = [3.433, -13.53] self.sigma2 = 1.122887152869 ** 2 elif method == "css": # NOTE: bse, cov_params, tvalues taken from R; commented-out # versions below are from [TODO: finish this sentence] self.params = [0.175605240783, -0.688421349504] self.aic = 773.725350463014 self.bic = 784.289733216601 self.arroots = None self.maroots = [-1.0844 + 0.j, 1.3395 + 0.j] # self.bse = [0.044465497496, 0.045000813836] self.bse = [0.04850046, 0.05023068] # self.cov_params = [ # [0.0019772, 0.00090016], # [0.00090016, 0.0020251]] self.cov_params = [ [0.0023522942, 0.0007545702], [0.0007545702, 0.0025231209] ] self.hqic = 777.977205368850 self.llf = -383.862675231507 self.resid = resids_css[:, 5] self.fittedvalues = yhat_css[:, 5] self.pvalues = [7.84e-05, 7.89e-53] # self.tvalues = [3.949, -15.30] self.tvalues = [3.620967, -13.705514] self.sigma2 = 1.123571177436**2 class Y_arma11c(object): def __init__(self, method="mle"): if method == "mle": self.params = [4.856475759430, 0.664363281011, 0.407547531124] self.aic = 737.922644877973 self.bic = 752.008488549422 self.arroots = [1.5052 + 0j] self.maroots = [-2.4537 + 0j] self.bse = [0.273164176960, 0.055495689209, 0.068249092654] self.cov_params = [ [0.074619, -0.00012834, 1.5413e-05], [-0.00012834, 0.0030798, -0.0020242], [1.5413e-05, -0.0020242, 0.0046579]] self.hqic = 743.591784752421 self.llf = -364.961322438987 self.resid = residsc_mle[:, 0] self.fittedvalues = yhatc_mle[:, 0] self.pvalues = [1.04e-70, 5.02e-33, 2.35e-9] self.tvalues = [17.78, 11.97, 5.971] self.sigma2 = 1.039168068701 ** 2 self.forecast = forecast_results['fc11c'] self.forecasterr = forecast_results['fe11c'] elif method == "css": # NOTE: params, bse, cov_params, tvalues taken from R; # commented-out versions below are from gretl # NOTE: gretl gives the intercept not the mean, x-12-arima # and R agree with us # self.params = [1.625462134333, 0.666386002049, 0.409512270580] self.params = [4.872477127267, 0.666395534262, 0.409517026658] self.aic = 734.613526514951 self.bic = 748.683338100810 self.arroots = [1.5006 + 0.0000j] self.maroots = [-2.4419 + 0.0000] # self.bse = [0.294788633992, 0.057503298669, 0.063059352497] self.bse = [0.2777238133284, 0.0557583459688, 0.0681432545482] # self.cov_params = [ # [0.086900, -0.016074, 0.010536], # [-0.016074, 0.0033066, -0.0021977], # [0.010536, -0.0021977, 0.0039765] # ] self.cov_params = [ [7.71305164897e-02, 5.65375305967e-06, 1.29481824075e-06], [5.65375305967e-06, 3.10899314518e-03, -2.02754322743e-03], [1.29481824075e-06, -2.02754322743e-03, 4.64350314042e-03] ] self.hqic = 740.276857090925 self.llf = -363.306763257476 self.resid = residsc_css[1:, 0] self.fittedvalues = yhatc_css[1:, 0] self.pvalues = [3.51e-08, 4.70e-31, 8.35e-11] # self.tvalues = [5.514, 11.59, 6.494] self.tvalues = [17.544326, 11.951494, 6.009649] self.sigma2 = 1.040940645447**2 class Y_arma14c(object): def __init__(self, method="mle"): if method == "mle": self.params = [4.773779823083, 0.591149657917, 0.322267595204, -0.702933089342, 0.116129490967, 0.323009574097] self.aic = 720.814886758937 self.bic = 745.465113183973 self.arroots = [1.6916 + 0.0000j] # TODO: had to change order in maroots? self.maroots = [1.1071 - 0.7821j, 1.1071 + 0.7821j, -1.2868 - 0.1705j, -1.2868 + 0.1705j] self.bse = [0.160891073193, 0.151756542096, 0.152996852330, 0.140231020145, 0.064663675882, 0.065045468010] self.cov_params = [ [0.025886, 0.00026606, -0.00020969, -0.00021435, 4.2558e-05, 5.2904e-05], [0.00026606, 0.023030, -0.021269, -0.018787, 0.0015423, 0.0011363], [-0.00020969, -0.021269, 0.023408, 0.018469, -0.0035048, -0.0010750], [-0.00021435, -0.018787, 0.018469, 0.019665, -0.00085717, -0.0033840], [4.2558e-05, 0.0015423, -0.0035048, -0.00085717, 0.0041814, 0.0014543], [5.2904e-05, 0.0011363, -0.0010750, -0.0033840, 0.0014543, 0.0042309]] self.hqic = 730.735881539221 self.llf = -353.407443379469 self.resid = residsc_mle[:, 1] self.fittedvalues = yhatc_mle[:, 1] self.pvalues = [1.82e-193, 9.80e-05, 0.0352, 5.37e-07, 0.0725, 6.84e-07] self.tvalues = [29.67, 3.895, 2.106, -5.013, 1.796, 4.966] self.sigma2 = 0.990262659233 ** 2 elif method == "css": # NOTE: params, bse, cov_params, tvalues taken from R; # commented-out versions below are from # [TODO: Finish this sentence] # self.params = [1.502401748545, 0.683090744792, 0.197636417391, # -0.763847295045, 0.137000823589, 0.304781097398] self.params = [4.740785760452, 0.683056278882, 0.197681128402, -0.763804443884, 0.136991271488, 0.304776424257] self.aic = 719.977407193363 self.bic = 744.599577468616 self.arroots = [1.4639 + 0.0000j] self.maroots = [1.1306-0.7071j, 1.1306+0.7071j, -1.3554 - 0.0896j, -1.3554 + 0.0896j] # self.bse = [0.534723749868, 0.111273280223, 0.119840296133, # 0.111263606843, 0.070759105676, 0.061783181500] self.bse = [0.1750455599911, 0.0942341854820, 0.0999988749541, 0.0929630759694, 0.0628352649371, 0.0645444272345] # self.cov_params = [ # [0.28593, -0.059175, 0.053968, # 0.046974, 0.00085168, 0.0028000], # [-0.059175, 0.012382, -0.011333, # -0.0098375, -0.00012631, -0.00058518], # [0.053968, -0.011333, 0.014362, # 0.010298, -0.0028117, -0.00011132], # [0.046974, -0.0098375, 0.010298, # 0.012380, 0.00031018, -0.0021617], # [0.00085168, -0.00012631, -0.0028117, # 0.00031018, 0.0050069, 0.00079958], # [.0028000, -0.00058518, -0.00011132, # -0.0021617, 0.00079958, 0.0038172]] self.cov_params = [ [0.030640948072601, -1.61599091345e-03, 0.001707084515950, 0.001163372764659, -1.78587340563e-04, 0.000116062673743], [-0.001615990913449, 8.88008171345e-03, -0.007454252059003, -0.006468410832237, 5.66645379098e-05, -0.000381880917361], [0.001707084515950, -7.45425205900e-03, 0.009999774992092, 0.005860013051220, -2.27726197200e-03, 0.000757683049669], [0.001163372764659, -6.46841083224e-03, 0.005860013051220, 0.008642133493695, 4.40550745987e-04, -0.002170706208320], [-0.000178587340563, 5.66645379098e-05, -0.002277261972002, 0.000440550745987, 3.94827051971e-03, 0.000884171120090], [0.000116062673743, -3.81880917361e-04, 0.000757683049669, -0.002170706208320, 8.84171120090e-04, 0.004165983087027] ] self.hqic = 729.888235701317 self.llf = -352.988703596681 self.resid = residsc_css[1:, 1] self.fittedvalues = yhatc_css[1:, 1] self.pvalues = [.0050, 8.31e-10, .0991, 6.64e-12, .0528, 8.09e-7] # self.tvalues = [2.810, 6.139, 1.649, -6.865, 1.936, 4.933] self.tvalues = [27.08315344127, 7.24849772286, 1.97683352430, -8.21621311385, 2.18016541548, 4.72196341831] self.sigma2 = 0.998687642867**2 class Y_arma41c(object): def __init__(self, method="mle"): if method == "mle": self.params = [1.062980233899, 0.768972932892, -0.264824839032, -0.279936544064, 0.756963578430, 0.231557444097] self.aic = 686.468309958027 self.bic = 711.118536383063 self.arroots = [1.0077 + 0j, .3044-.9793j, .3044+.9793j, -1.2466 + 0j] self.maroots = [-4.3186 + 0.j] self.bse = [2.781653916478, 0.063404432598, 0.091047664068, 0.084679571389, 0.054747989396, 0.098952817806] self.cov_params = [ [7.7376, 0.0080220, -0.0039840, 0.0064925, 0.0022936, -0.0098015], [0.0080220, 0.0040201, -0.0054843, 0.0046548, -0.0029922, -0.0047964], [-0.0039840, -0.0054843, 0.0082897, -0.0072913, 0.0043566, 0.0067289], [0.0064925, 0.0046548, -0.0072913, 0.0071706, -0.0043610, -0.0057962], [0.0022936, -0.0029922, 0.0043566, -0.0043610, 0.0029973, 0.0036193], [-0.0098015, -0.0047964, 0.0067289, -0.0057962, 0.0036193, 0.0097917]] self.hqic = 696.389304738311 self.llf = -336.234154979014 self.resid = residsc_mle[:, 2] self.fittedvalues = yhatc_mle[:, 2] self.pvalues = [0.7024, 7.50e-34, 0.0036, 0.0009, 1.77e-43, 0.0193] self.tvalues = [0.3821, 12.13, -2.909, -3.306, 13.83, 2.340] self.sigma2 = 0.915487643192 ** 2 self.forecast = forecast_results['fc41c'] self.forecasterr = forecast_results['fe41c'] elif method == "css": # NOTE: params, bse, cov_params, tvalues taken from R; # commented-out versions below are from # [TODO: Finish this sentence] # self.params = [-0.077068926631, 0.763816531155, -0.270949972390, # -0.284496499726, 0.757135838677, 0.225247299659] self.params = [-2.234160612756, 0.763815335585, -0.270946894536, -0.284497190744, 0.757136686518, 0.225260672575] self.aic = 668.907200379791 self.bic = 693.444521131318 self.arroots = [1.0141+0.0000j, 0.3036-0.9765j, 0.3036+0.9765j, -1.2455+0.0000j] self.maroots = [-4.4396+0.0000j] # self.bse = [0.076048453921, 0.067854052128, 0.098041415680, # 0.090698349822, 0.057331126067, 0.099985455449] self.bse = [2.1842857865614, 0.0644148863289, 0.0923502391706, 0.0860004491012, 0.0558014467639, 0.1003832271008] # self.cov_params = [ # [0.0057834, 0.00052477, -0.00079965, # 0.00061291, -0.00013618, -0.0018963], # [0.00052477, 0.0046042, -0.0062505, # 0.0053416, -0.0032941, -0.0047957], # [-0.00079965, -0.0062505, 0.0096121, # -0.0084500, 0.0047967, 0.0064755], # [0.00061291, 0.0053416, -0.0084500, # 0.0082262, -0.0048029, -0.0057908], # [-0.00013618, -0.0032941, 0.0047967, # -0.0048029, 0.0032869, 0.0035716], # [-0.0018963, -0.0047957, 0.0064755, # -0.0057908, 0.0035716, 0.0099971] # ] self.cov_params = [ [4.77110439737413, -0.00908682223670, 0.00330914414276, -0.00684678121434, -0.00232348925409, 0.00950558295301], [-0.00908682223670, -0.00562941039954, 0.00852856667488, -0.00749429397372, -0.00304322809665, -0.00494984519949], [0.00330914414276, -0.00562941039954, 0.00852856667488, -0.00749429397372, 0.00443590637587, 0.00693146988144], [-0.00684678121434, 0.00482359594764, -0.00749429397372, 0.00739607724561, -0.00448059420947, -0.00600908311031], [-0.00232348925409, -0.00304322809665, 0.00443590637587, -0.00448059420947, 0.00311380146095, 0.00373734623817], [0.00950558295301, -0.00494984519949, 0.00693146988144, -0.00600908311031, 0.00373734623817, 0.01007679228317]] self.hqic = 678.787238280001 self.llf = -327.453600189896 self.resid = residsc_css[4:, 2] self.fittedvalues = yhatc_css[4:, 2] self.pvalues = [0.3109, 2.15e-29, 0.0057, 0.0017, 8.06e-40, 0.0243] # self.tvalues = [-1.013, 11.26, -2.764, -3.137, 13.21, 2.253] self.tvalues = [-1.02283347101, 11.85774561000, -2.93390571556, -3.30808959392, 13.56840602577, 2.24400708246] self.sigma2 = 0.915919923456**2 class Y_arma22c(object): def __init__(self, method="mle"): if method == "mle": self.params = [4.507728587708, 0.788365037622, -0.358656861792, 0.035886565643, -0.699600200796] self.aic = 813.417242529788 self.bic = 834.546008036962 self.arroots = [1.0991 - 1.2571j, 1.0991 + 1.2571j] self.maroots = [-1.1702 + 0.0000j, 1.2215 + 0.0000j] self.bse = [0.045346684035, 0.078382496509, 0.07004802526, 0.069227816205, 0.070668181454] self.cov_params = [ [0.0020563, -2.3845e-05, -6.3775e-06, 4.6698e-05, 5.8515e-05], [-2.3845e-05, 0.0061438, -0.0014403, -0.0035405, -0.0019265], [-6.3775e-06, -0.0014403, 0.0049067, -0.00059888, -0.0025716], [4.6698e-05, -0.0035405, -0.00059888, 0.0047925, 0.0022931], [5.8515e-05, -0.0019265, -0.0025716, 0.0022931, 0.0049940]] self.hqic = 821.920952341460 self.llf = -400.708621264894 self.resid = residsc_mle[:, 3] self.fittedvalues = yhatc_mle[:, 3] self.pvalues = [0.0000, 8.48e-24, 3.05e-07, 0.6042, 4.17e-23] self.tvalues = [99.41, 10.06, -5.120, 0.5184, -9.900] self.sigma2 = 1.196309833136 ** 2 elif method == "css": # NOTE: params, bse, cov_params, tvalues taken from R; # commented-out versions below are from # [TODO: Finish this sentence] # self.params = [2.571274348147, 0.793030965872, -0.363511071688, # 0.033543918525, -0.702593972949] self.params = [4.507207454494, 0.793055048760, -0.363521072479, 0.033519062805, -0.702595834943] self.aic = 806.807171655455 self.bic = 827.887744132445 # self.bse = [0.369201481343, 0.076041378729, 0.070029488852, # 0.062547355221, 0.068166970089] self.bse = [0.0446913896589, 0.0783060902603, 0.0697866176073, 0.0681463870772, 0.068958002297] # self.cov_params = [ # [0.13631, -0.017255, -0.012852, 0.014091, 0.017241], # [-0.017255, 0.0057823, -0.0020013, -0.0026493, -0.0014131], # [-0.012852, -0.0020013, 0.0049041, -0.00042960, -0.0023845], # [0.014091, -0.0026493, -0.00042960, 0.0039122, 0.0022028], # [0.017241, -0.0014131, -0.0023845, 0.0022028, 0.0046467] # ] self.cov_params = [ [1.99732030964e-03, -2.22972353619e-05, -0.000009957435095, 4.64825632252e-05, 5.98134427402e-05], [-2.22972353619e-05, 6.13184377186e-03, -0.001435210779968, -3.47284237940e-03, -1.95077811843e-03], [-9.95743509501e-06, -1.43521077997e-03, 0.004870171997068, -6.54767224831e-04, -2.44459075151e-03], [4.64825632252e-05, -3.47284237940e-03, -0.000654767224831, 4.64393007167e-03, 2.34032945541e-03], [5.98134427402e-05, -1.95077811843e-03, -0.002444590751509, 2.34032945541e-03, 4.75520608091e-03]] self.arroots = [1.0908 - 1.2494j, 1.0908 + 1.2494j] self.maroots = [-1.1694 + 0.0000j, 1.2171 + 0.0000j] self.hqic = 815.293412134796 self.llf = -397.403585827727 self.resid = residsc_css[2:, 3] self.fittedvalues = yhatc_css[2:, 3] self.pvalues = [3.30e-12, 1.83e-25, 2.09e-07, 0.5918, 6.55e-25] # self.tvalues = [6.964, 10.43, -5.191, 0.5363, -10.31] self.tvalues = [100.851808120009, 10.127629231947, -5.209036989363, 0.491868523669, -10.188749840927] self.sigma2 = 1.201409294941**2 class Y_arma50c(object): def __init__(self, method="mle"): if method == "mle": self.params = [4.562207236168, 0.754284447885, -0.305849188005, 0.253824706641, 0.281161230244, -0.172263847479] self.aic = 711.817562780112 self.bic = 736.467789205148 self.arroots = [-1.6535 + 0.j, .0129 - 1.2018j, .0129 + 1.2018j, 1.1546 + 0.j, 2.1052 + 0j] self.maroots = None self.bse = [0.318447388812, 0.062272737541, 0.076600312879, 0.077310728819, 0.076837326995, 0.062642955733] self.cov_params = [ [0.10141, -6.6930e-05, -7.3157e-05, -4.4815e-05, 7.7676e-05, -0.00013170], [-6.6930e-05, 0.0038779, -0.0028465, 0.0013770, -0.0012194, -0.00058978], [-7.3157e-05, -0.0028465, 0.0058676, -0.0040145, 0.0024694, -0.0012307], [-4.4815e-05, 0.0013770, -0.0040145, 0.0059769, -0.0040413, 0.0013481], [7.7676e-05, -0.0012194, 0.0024694, -0.0040413, 0.0059040, -0.0028575], [-0.00013170, -0.00058978, -0.0012307, 0.0013481, -0.0028575, 0.0039241]] self.hqic = 721.738557560396 self.llf = -348.908781390056 self.resid = residsc_mle[:, 4] self.fittedvalues = yhatc_mle[:, 4] self.pvalues = [1.50e-46, 9.06e-34, 6.53e-05, .0010, .0003, .0060] self.tvalues = [14.33, 12.11, -3.993, 3.283, 3.659, -2.750] self.sigma2 = 0.973930886014 ** 2 self.forecast = forecast_results['fc50c'] self.forecasterr = forecast_results['fe50c'] elif method == "css": # NOTE: params, bse, cov_params, tvalues taken from R; # commented-out versions below are from # [TODO: Finish this sentence] # likelihood based results from x-12 arima # self.params = [0.843173779572, 0.755433266689, -0.296886816205, # 0.253572751789, 0.276975022313, -0.172637420881] self.params = [4.593494860193, 0.755427402630, -0.296867127441, 0.253556723526, 0.276987447724, -0.172647993470] # self.aic = 694.843378847617 self.aic = 696.8434 # self.bic = 715.850928110886 self.bic = 721.3522 self.arroots = [-1.6539+0.0000j, 0.0091-1.2069j, 0.0091+1.2069j, 1.1508+0.0000j, 2.0892+0.0000j] self.maroots = None # self.bse = [0.236922950898, 0.063573574389, 0.078206936773, # 0.078927252266, 0.078183651496, 0.063596048046] self.bse = [0.3359627893565, 0.0621593755265, 0.0764672280408, 0.0771715117870, 0.0764444608104, 0.0621813373935] # self.cov_params = [ # [0.056132, -0.0028895, -0.0012291, # -0.0031424, -0.0012502, -0.0028739], # [-0.0028895, 0.0040416, -0.0029508, # 0.0014229, -0.0012546, -0.00062818], # [-0.0012291, -0.0029508, 0.0061163, # -0.0041939, 0.0025537, -0.0012585], # [-0.0031424, 0.0014229, -0.0041939, # 0.0062295, -0.0041928, 0.0014204], # [-0.0012502, -0.0012546, 0.0025537, # -0.0041928, 0.0061127, -0.0029479], # [-0.0028739, -0.00062818, -0.0012585, # 0.0014204, -0.0029479, 0.0040445] # ] self.cov_params = [ [1.12870995832e-01, 4.32810158586e-05, -1.89697385245e-05, 0.0000465331836881, -0.000024151327384, 0.000109807500875], [4.32810158586e-05, 3.86378796585e-03, -2.82098637123e-03, 0.001360256141301, -0.001199382243647, -0.000600542191229], [-1.89697385245e-05, -2.82098637123e-03, 5.84723696424e-03, -0.004009391809667, 0.002441359768335, -0.001203154760767], [4.65331836880e-05, 1.36025614130e-03, -4.00939180967e-03, 0.005955442231484, -0.004008307295820, 0.001357917028471], [-2.41513273840e-05, -1.19938224365e-03, 2.44135976834e-03, -0.004008307295820, 0.005843755588588, -0.002818181279545], [1.09807500875e-04, -6.00542191229e-04, -1.20315476077e-03, 0.001357917028471, -0.002818181279545, 0.003866518720043]] # self.hqic = 703.303100827167 self.hqic = 706.7131 self.llf = -341.421689423809 self.resid = residsc_css[5:, 4] self.fittedvalues = yhatc_css[5:, 4] self.pvalues = [0.0004, 1.45e-32, 0.0001, 0.0013, 0.0004, 0.0066] # self.tvalues = [3.559, 11.88, -3.796, 3.213, 3.543, -2.715] self.tvalues = [13.67262984389, 12.15307258528, -3.88227918086, 3.28562597329, 3.62338153462, -2.77652428699] # self.sigma2 = 0.987100631424**2 self.sigma2 = 0.974939 ** 2 class Y_arma02c(object): def __init__(self, method="mle"): if method == "mle": self.params = [4.519277801954, 0.200385403960, -0.643766305844] self.aic = 758.051194540770 self.bic = 772.137038212219 self.arroots = None self.maroots = [-1.1004 + 0.j, 1.4117 + 0.j] self.bse = [0.038397713362, 0.049314652466, 0.048961366071] self.cov_params = [ [0.0014744, 6.2363e-05, 6.4093e-05], [6.2363e-05, 0.0024319, 0.0014083], [6.4093e-05, 0.0014083, 0.0023972]] self.hqic = 763.720334415218 self.llf = -375.025597270385 self.resid = residsc_mle[:, 5] self.fittedvalues = yhatc_mle[:, 5] self.pvalues = [0.0000, 4.84e-5, 1.74e-39] self.tvalues = [117.7, 4.063, -13.15] self.sigma2 = 1.081406299967 ** 2 elif method == "css": # NOTE: cov_params, tvalues taken from R; commented-out # versions below are from [TODO: Finish this sentence] self.params = [4.519869870853, 0.202414429306, -0.647482560461] self.aic = 756.679105324347 self.bic = 770.764948995796 self.arroots = None self.maroots = [-1.0962 + 0.0000j, 1.4089 + 0.0000j] self.bse = [0.038411589816, 0.047983057239, 0.043400749866] # self.cov_params = [ # [0.0014755, 9.0191e-05, 7.3561e-06], # [9.0191e-05, 0.0023024, 0.0012479], # [7.3561e-06, 0.0012479, 0.0018836]] self.cov_params = [ [1.46121526606e-03, 5.30770136338e-05, 5.34796521051e-05], [5.30770136338e-05, 2.37105883909e-03, 1.41090983316e-03], [5.34796521051e-05, 1.41090983316e-03, 2.35584355080e-03]] self.hqic = 762.348245198795 self.llf = -374.339552662174 self.resid = residsc_css[:, 5] self.fittedvalues = yhatc_css[:, 5] self.pvalues = [0.0000, 2.46e-05, 2.49e-50] # self.tvalues = [117.7, 4.218, -14.92] self.tvalues = [118.24120637494, 4.15691796413, -13.33981086206] self.sigma2 = 1.081576475937**2 statsmodels-0.12.2/statsmodels/tsa/tests/results/results_arma_acf.py000066400000000000000000000037251400612667500260340ustar00rootroot00000000000000""" ARMA autocorrelation results (from R's ARMAacf function) These numbers are printed out when running the R script results/test_arma_acf.R """ bd_example_3_3_2 = [ 1.00000000000, 0.87500000000, 0.62500000000, 0.40625000000, 0.25000000000, 0.14843750000, 0.08593750000, 0.04882812500, 0.02734375000, 0.01513671875] custom_example_1 = [ 1.00000000000000000, 0.89043062200956924, 0.65657894736842093, 0.43397129186602867, 0.26982655502392344, 0.16133373205741627, 0.09387709330143541, 0.05354366028708134, 0.03007438696172249, 0.01668847188995216] custom_example_2 = [ 1.0000000000000000, 0.9092437831227068, 0.7142784345699144, 0.5076054830819404, 0.3290358744394619, 0.2021345036689768, 0.1198755350591113, 0.0693419091418671, 0.0393730253770893, 0.0220375480916225] custom_example_3 = [ 1.00000000000000000, 0.88441824705279337, 0.64345207585853414, 0.39159405433111233, 0.20382175807278322, 0.10592324449000515, 0.05496780497180934, 0.02848699384930806, 0.01474504260635572, 0.00762329414402871] custom_example_4 = [ 1.000000000000000000, 0.879686150302332326, 0.625215951626835631, 0.359037575583069424, 0.159975165562913885, 0.062441513101065334, 0.022447721710336863, 0.006837343435070529, 0.001225413007486314, -0.000483922851281319] custom_example_5 = [ 1.000000000000000, 0.929315745090953, 0.784137453318877, 0.651808517046139, 0.548705728225515, 0.464167344295868, 0.392171763944103, 0.331000500692688, 0.279374294136249, 0.235841345357487] custom_example_6 = [ 1.0000000000000000, 0.9136917896587146, 0.7322751541352182, 0.5581676172376039, 0.4164680076696708, 0.3044690292908558, 0.2195550313904376, 0.1571761939728106, 0.1119109386708032, 0.0793489418521015] custom_example_7 = [ 1.000000000000000, 0.918273770449316, 0.747774138591147, 0.587247490228175, 0.460496808034306, 0.362548660813911, 0.287125976307581, 0.228131600167948, 0.181325081575292, 0.144087282284054] statsmodels-0.12.2/statsmodels/tsa/tests/results/results_arma_forecasts.csv000066400000000000000000000024421400612667500274320ustar00rootroot00000000000000"fc11","fe11","fc41","fe41","fc50","fe50","fc11c","fe11c","fc41c","fe41c","fc50c","fe50c" -0.0931139795,0.994743,-0.4298095393,0.91141,1.24361,0.938375,4.2276592922,1.03917,-1.3985445949,0.915488,4.779739852,0.973931 -0.073415913,1.53122,-1.4961938371,1.22521,0.484195,1.16009,4.4387131881,1.52336,3.0228581596,1.29504,4.692859693,1.21992 -0.057884931,1.78523,-3.770193621,1.2607,0.722602,1.17762,4.5789296469,1.6936,4.071345984,1.37495,3.8280155603,1.24654 -0.0456394955,1.92633,-3.6148341892,1.27585,1.09664,1.20138,4.6720843135,1.76352,0.8457602276,1.38243,3.9467079457,1.26508 -0.0359845562,2.00905,-1.5553772244,1.29131,0.854109,1.31833,4.7339728534,1.79351,-2.3126724383,1.39737,4.5998286564,1.37737 -0.028372099,2.05881,-0.3162209074,1.49296,0.510239,1.39506,4.7750893268,1.80659,-0.833875753,1.5901,4.59173986,1.4486 -0.0223700411,2.08914,-1.6253254747,1.67599,0.579206,1.41288,4.802405602,1.81234,2.8363368346,1.83677,4.1878148976,1.45879 -0.017637706,2.10777,-3.3986372227,1.68533,0.721688,1.43171,4.8205535323,1.81487,3.7095186811,1.86802,4.2337457799,1.46621 -0.0139064864,2.11928,-3.150618693,1.69048,0.60394,1.47332,4.8326103507,1.81598,0.6042207231,1.86845,4.553063531,1.49431 -0.0109645984,2.1264,-1.2381045022,1.70353,0.43997,1.50507,4.8406204582,1.81647,-1.9229410947,1.87871,4.562562544,1.51482 statsmodels-0.12.2/statsmodels/tsa/tests/results/results_corrgram.csv000066400000000000000000000057671400612667500262720ustar00rootroot00000000000000acvar,acvarfft,Q1,PACOLS,PACYW,acvar_lb,acvar_ub 0.98685781,0.98685781,200.6355,1.002988,0.98685781,-0.1375625,0.1375625 0.97371846,0.97371846,396.9356,-0.3956237,-0.00650592,-0.23618231,0.23618231 0.96014366,0.96014366,588.7549,-0.1769759,-0.0233345,-0.30276354,0.30276354 0.94568545,0.94568545,775.7759,0.0742275,-0.04078457,-0.35574695,0.35574695 0.93054425,0.93054425,957.7706,-0.0580367,-0.0334311,-0.40050362,0.40050362 0.91484806,0.91484806,1134.57,0.0935246,-0.02818214,-0.43951706,0.43951706 0.89901438,0.89901438,1306.174,0.0034315,-0.01168091,-0.47418465,0.47418465 0.8827679,0.8827679,1472.48,0.0385079,-0.02192074,-0.50541068,0.50541068 0.86649857,0.86649857,1633.539,0.1050301,-0.00748351,-0.53379138,0.53379138 0.8503736,0.8503736,1789.463,-0.1834061,-0.00143193,-0.55977623,0.55977623 0.83435254,0.83435254,1940.348,-0.0210358,-0.00310717,-0.58371041,0.58371041 0.81829961,0.81829961,2086.244,0.0992143,-0.00921395,-0.60585868,0.60585868 0.80240987,0.80240987,2227.266,0.2540452,-0.0025009,-0.62642442,0.62642442 0.78635609,0.78635609,2363.419,-0.0080142,-0.01557323,-0.64558168,0.64558168 0.77024519,0.77024519,2494.745,-0.0524568,-0.01164751,-0.66345953,0.66345953 0.75437469,0.75437469,2621.388,0.11607,-0.00030521,-0.68017076,0.68017076 0.73850631,0.73850631,2743.412,-0.1211871,-0.00893237,-0.6958234,0.6958234 0.72274736,0.72274736,2860.916,0.092306,-0.00507808,-0.71050094,0.71050094 0.70701465,0.70701465,2973.971,0.0317384,-0.00829011,-0.72427993,0.72427993 0.69141553,0.69141553,3082.682,-0.0422092,-0.00460458,-0.73722448,0.73722448 0.67600225,0.67600225,3187.173,0.0628712,-0.00246537,-0.74939498,0.74939498 0.66067686,0.66067686,3287.53,0.0086186,-0.00610282,-0.76084695,0.76084695 0.64543953,0.64543953,3383.844,-0.0044266,-0.0068184,-0.77162686,0.77162686 0.63020869,0.63020869,3476.178,0.001695,-0.00994534,-0.78177665,0.78177665 0.61518569,0.61518569,3564.658,-0.128714,-0.00216407,-0.79133186,0.79133186 0.60054983,0.60054983,3649.454,0.0279399,0.00497323,-0.8003308,0.8003308 0.58608693,0.58608693,3730.674,0.0982797,-0.00302243,-0.80881349,0.80881349 0.57172016,0.57172016,3808.402,0.0937156,-0.00642863,-0.81681061,0.81681061 0.55730727,0.55730727,3882.685,-0.1677933,-0.0125645,-0.82434845,0.82434845 0.54281535,0.54281535,3953.562,-0.116249,-0.01382639,-0.8314477,0.8314477 0.5282993,0.5282993,4021.09,0.1120091,-0.01135471,-0.83812696,0.83812696 0.51386026,0.51386026,4085.351,-0.1551635,-0.00700203,-0.84440504,0.84440504 0.49934969,0.49934969,4146.39,-0.0644834,-0.01242531,-0.85030197,0.85030197 0.48452688,0.48452688,4204.199,0.2141102,-0.02166683,-0.85583326,0.85583326 0.4697521,0.4697521,4258.86,0.0573164,-0.0078988,-0.86100856,0.86100856 0.45473224,0.45473224,4310.389,0.1685996,-0.01871847,-0.86584485,0.86584485 0.43987621,0.43987621,4358.896,-0.0405992,-0.00300827,-0.87035242,0.87035242 0.42500013,0.42500013,4404.451,0.041648,-0.0100618,-0.87454923,0.87454923 0.41057995,0.41057995,4447.228,0.1566605,0.0076425,-0.87844889,0.87844889 0.3960725,0.3960725,4487.278,-0.0708302,-0.01332486,-0.88207286,0.88207286 statsmodels-0.12.2/statsmodels/tsa/tests/results/results_process.py000066400000000000000000000025431400612667500257560ustar00rootroot00000000000000from numpy import array from statsmodels.tools.testing import Holder armarep = Holder() armarep.comment = ('mlab.garchma(-res_armarep.ar[1:], res_armarep.ma[1:], 20)' 'mlab.garchar(-res_armarep.ar[1:], res_armarep.ma[1:], 20)') armarep.marep = array([ [-0.1], [-0.77], [-0.305], [0.4635], [0.47575], [-0.132925], [-0.4470625], [-0.11719125], [0.299054375], [0.2432801875], [-0.11760340625], [-0.253425853125], [-0.0326302015625], [0.18642558171875], [0.11931695210938], [-0.08948198932031], [-0.14019455634766], [0.00148831328242], [0.11289980171934], [0.05525925023373]]) armarep.ar = array([1., -0.5, 0.8]) armarep.ma = array([1., -0.6, 0.08]) armarep.name = 'armarep' armarep.arrep = array([ [-1.00000000000000e-01], [-7.80000000000000e-01], [-4.60000000000000e-01], [-2.13600000000000e-01], [-9.13600000000000e-02], [-3.77280000000000e-02], [-1.53280000000000e-02], [-6.17856000000000e-03], [-2.48089600000000e-03], [-9.94252799999999e-04], [-3.98080000000000e-04], [-1.59307776000000e-04], [-6.37382655999999e-05], [-2.54983372800000e-05], [-1.01999411200000e-05], [-4.08009768959999e-06], [-1.63206332416000e-06], [-6.52830179327999e-07], [-2.61133041663999e-07], [-1.04453410652160e-07]]) statsmodels-0.12.2/statsmodels/tsa/tests/results/rgnp.csv000066400000000000000000000013471400612667500236310ustar00rootroot00000000000000REAL_GNP 4.76046307 4.788324729 4.813809051 4.86907173 4.878246106 4.833102254 4.824305716 4.900076104 4.906755164 5.022563865 4.986342602 4.941642423 4.850466542 4.997212274 5.111385197 5.108971195 5.18961795 5.247024072 5.245970886 5.251749731 5.316157285 5.212214667 5.131672289 4.971201225 4.952299717 5.038898759 5.132852927 5.262690189 5.314190716 5.26217192 5.344246298 5.425830687 5.574812093 5.69642212 5.820379622 5.889708638 5.872681011 5.744924418 5.736249665 5.779817161 5.78105211 5.872962503 5.949078831 5.979138897 6.022963214 6.008813185 6.08221891 6.100543142 6.114787763 6.10322951 6.165207748 6.189700463 6.20899236 6.272499577 6.311734809 6.364750757 6.42616478 6.489356895 6.515008943 6.560464735 6.585757776 6.579251212 statsmodels-0.12.2/statsmodels/tsa/tests/results/rgnpq.csv000066400000000000000000000035571400612667500240170ustar00rootroot00000000000000REAL_GNP_QTR 7.574046546 7.57317714 7.572137692 7.587975262 7.603009239 7.619338958 7.624913865 7.625972074 7.612026853 7.608513919 7.619217216 7.609736821 7.64895235 7.678893988 7.717463415 7.73645774 7.749721523 7.767782914 7.788308983 7.790875916 7.800935406 7.8030438 7.810091498 7.842072945 7.860306964 7.868384758 7.862151487 7.846961044 7.842783365 7.843791774 7.855082556 7.875000688 7.903106698 7.919044506 7.932385485 7.938487648 7.935347643 7.943431673 7.942781482 7.95805334 7.965516753 7.963850387 7.973146129 7.961410647 7.935454998 7.942091057 7.964597902 7.987517347 8.005806077 8.029696649 8.028198203 8.032465371 8.054128313 8.05048684 8.053219665 8.041480496 8.048602324 8.066533731 8.083106671 8.103186306 8.120874428 8.132150812 8.141632748 8.146526533 8.157127075 8.169702797 8.189029344 8.196320487 8.21820963 8.229634045 8.243249382 8.246225322 8.27136017 8.28508533 8.304486486 8.326986468 8.351440805 8.355512029 8.362415749 8.371183352 8.380181005 8.380869561 8.390058212 8.397823448 8.41796075 8.434729422 8.442058354 8.446418305 8.461771175 8.464704024 8.470614241 8.46626341 8.464664819 8.466637309 8.475306255 8.464482261 8.491824715 8.497852357 8.504897103 8.50814498 8.526099017 8.548729067 8.558398664 8.574709175 8.599925325 8.611635358 8.607636091 8.616896616 8.610370189 8.612338267 8.60170767 8.596322251 8.582833543 8.590508149 8.60737954 8.622181478 8.644035336 8.651846629 8.656963829 8.664596128 8.677385526 8.696406422 8.713664336 8.712645988 8.717480723 8.753594548 8.763996862 8.778508906 8.780721086 8.783162795 8.792464873 8.794915378 8.79834841 8.777076072 8.774829064 8.790719847 8.811642862 8.803792328 8.815690419 8.80535145 8.788048535 8.794778715 8.789314013 8.789882583 8.80264999 8.825624208 8.845012672 8.865598516 8.884287327 8.901584056 8.911186752 8.918036033 8.926040175 8.935421568 8.949569717 8.957637981 8.966070473 8.969101967 8.979542602 statsmodels-0.12.2/statsmodels/tsa/tests/results/savedrvs.py000066400000000000000000000455501400612667500243610ustar00rootroot00000000000000'''Generated Random Processes for tests autogenerated by savervs.py ''' from numpy import array from statsmodels.tools.testing import Holder rvsdata = Holder() rvsdata.comment = 'generated data, divide by 1000, see savervs' rvsdata.xarma32 = array([ -1271, -1222, -840, -169, -1016, -980, -1272, -926, 445, 833, -91, -1974, -2231, -549, 424, 238, -1665, -1815, 685, 3361, 1912, -1931, -3555, -1817, 387, 730, -1154, -702, 973, 1340, -161, 276, 200, 1785, 834, -1469, -1593, -134, 555, -422, -2314, -1326, -2268, -3579, -3049, -930, 1155, 962, -644, -217, -561, 224, 810, 2445, 2710, 2152, 502, 21, 164, -499, -1093, -492, 531, -605, -1535, -2081, -3816, -2257, 487, 2134, 1785, 1495, 1259, 1895, 1339, 617, 1143, 385, -1220, -738, 1171, 1047, -234, -107, -1458, -1244, -2737, 33, 2373, 2749, 2725, 3331, 1054, 418, 1231, -1171, -1446, -1187, 863, 1386, 757, 734, 283, -735, 550, 417, -236, 324, 318, -102, 2126, 3246, 2358, 2156, 726, -983, -803, -242, -500, -13, 49, 308, -227, 243, -612, -2329, -2476, -3441, -5435, -4693, -2538, -2159, -2656, -906, -211, -288, 1777, 1363, 564, -2035, -1134, -609, -1112, 560, 658, 1533, 796, 523, 456, 76, -1164, -749, -1084, -3218, -2107, -310, -686, -1625, 2008, 4155, 1650, -1086, -673, 1634, 1999, 449, -1077, -648, -155, -327, 228, 1295, 2036, 542, -197, -451, -1554, -2416, -2066, -2146, -1524, -1976, -2962, -2621, -2313, -2052, -3314, -2363, -1522, -3305, -3445, -3206, -1501, 2029, 1963, 1168, 2050, 2927, 2019, 84, 213, 1783, 617, -767, -425, 739, 281, 506, -749, -938, -284, -147, 51, 1296, 3033, 2263, 1409, -1702, -819, -1295, -1831, -539, 1327, 1954, 1473, -1535, -1187, -1310, 380, 1621, 2035, 2234, 559, 51, -1071, 590, 2128, 1483, 848, 1198, 2707, 1447, -629, 237, 909, 453, -734, -802, 1026, 521, -9, 919, 441, -118, -1073, -2428, 98, 823, 102, -438, -233, -613, 440, 1143, -743, -1345, 186, -1999, -2351, -887, -584, -883, -623, -1522, 974, 2318, 1329, -523, -2599, -1555, 826, -859, -2790, -2753, 807, 1889, -95, -1454, 443, 845, -291, 1516, 2804, 1018, 402, -446, -1721, -1824, 1678, 2889, -663, -560, 628, 1213, 520, -1344, -3029, -3100, -1603, -1480, -1667, -3356, -4405, -2556, 532, 1602, -15, 646, 2279, 1893, -945, -258, 344, -316, 1130, 1119, 695, 276, 56, -682, -610, 412, 1058, 259, 746, 1197, 1959, 1896, 127, -1301, 1036, 3094, 5213, 3846, 1728, 40, -520, -173, 330, -480, 649, 1621, 1622, -1011, -1851, -2687, -756, 401, 1888, 2372, 4153, 2531, -150, 485, 2600, 2193, -1238, -2702, -184, 1336, 370, -1196, -1737, 637, 634, 77, -1314, -688, -1375, -1973, -1229, -1414, -2230, -1922, -584, 93, 180, 2158, 2976, 1433, -173, -1073, -1362, -446, 242, 7, 354, 332, 2003, 1866, -729, -1446, -294, 2438, 3955, 1829, 485, 1028, 981, 1335, 513, -1386, -2583, -1063, 465, 1104, 85, -892, -78, 766, 1995, 891, -170, 2, -428, -562, -1078, -2591, -2077, -135, -238, -1150, -1207, -185, -46, -1319, -1829, -1409, -926, 576, 1119, 454, -747, -538, -739, -2994, -3052, -1626, -2472, -1340, -254, -972, -1182, -258, 831, 876, -244, -724, -208, -428, -110, 188, -2187, -2695, -1161, 597, 1492, 1594, -403, 695, 1834, 1737, 586, -740, 259, -714, -1607, -1082, -365, 2040, 604, -1253, -1269, -419, -713, -482, 1379, 2335, 1730, 325, -1377, -1721, -1762, -602, -1224, -839, 70, -1058, -118, -691, -1397, -245, -291, -648, -1489, -1088, -1083, -160, 1310, 169, -1539, -1558, -2095, -3421, -1609, -465, -867, 311, 272, -157, -936, -1003, -492, -1526, -2179, -1237, -662, -144, 638, 596, -629, -1893, -671, 324, 408, 367, 1438, 4568, 2576, 677, 701, 2667, 1288, 449, -357, 776, 2250, 2324, 968, 245, 1432, 1597, 843, 88, -274, -256, 830, 348, 534, 140, -560, -1582, -2012, -287, 1470, -729, -2398, -1433, -1409, -1547, 70, 1438, 2246, 408, -293, -566, 374, 1793, 2355, 1104, 358, 2301, 2994, 572, 278, 508, -2406, -2767, -1216, -231, -1717, -1038, 2015, 1469, 1471, 1395, 860, 1148, 1211, 1189, 494, -536, 383, -136, -2171, -2334, -1181, -294, -841, -2051, -3304, -2254, -926, -811, 160, 1960, 2945, 2466, 1922, 2833, 2421, 1197, 3025, 4033, 3210, 1497, 1912, 1138, 174, -630, -2423, -999, 296, 1519, 2061, 1400, -424, -609, -978, -1747, -1637, -2454, -1547, 885, 2065, 1530, -1956, 846, 2811, 3105, 2220, 2732, 4631, 3504, 1996, 246, -419, -1541, -1955, -3171, -2742, -811, -318, -1303, -2002, -997, -487, -2089, -3453, -3373, -1940, -620, 384, 365, -133, -1300, -833, -1544, -1711, -1981, -315, -155, -1995, -2384, -4010, -5394, -6186, -3794, -1829, -2637, -4255, -2014, 282, -174, -2623, -2023, -749, -168, -2387, -3959, -4101, -2004, -2070, -2468, -1831, -1518, 606, 305, 684, 2183, 1218, -1008, -2261, -1276, -99, 889, 740, -525, -1786, -1716, -452, -872, -1384, -1867, -547, -900, -1464, -1898, -1493, -990, 965, 810, 636, -335, -57, 1761, 2837, 773, 215, 920, 483, -234, 1301, 2610, 3083, 2329, 920, -827, 22, 4317, 5366, 3711, 2220, 1356, 198, -1385, 656, 1163, -370, -1721, -1005, -832, -1455, -1485, 221, -1445, -1502, -79, -4, -599, -850, -507, 902, 1909, 1642, -326, -3379, -5642, -7068, -4275, -1044, 528, 548, 249, -1384, -2485, -1533, -1776, -2930, -2058, -1721, -475, -166, -1761, -2550, -1586, -240, -1584, -1954, 623, 3826, 2094, -1004, -1782, -267, 2490, 3336, 2293, 189, -108, -315, -965, -125, 1201, 360, -544, -1602, -2150, -901, 1430, 968, -1100, 505, 2880, 2554, 928, 918, 689, -2829, -2478, -2904, -1615, -242, 243, -1668, -877, 2385, 543, -2462, -1762, 470, 1344, 1493, 1624, 257, -1833, -1947, -805, -413, 905, 2909, 3272, 1148, -1473, -2368, -1054, -2143, -4330, -3257, -1939, -1831, -414, -1157, -1212, -1644, -1360, -2409, -4136, -5747, -3415, -1752, 373, -1680, -1267, 2267, 2701, 1101, -1714, -3138, -3153, -3256, -3328, -2661, -879, 2115, 1795, -324, -1930, -1432, -1613, -2301, -1401, 88, 1369, 1063, -854, -2125, 243, 1683, 2011, 2646, 1289, -938, -1205, -1214, 562, 2641, 3335, 2858, 2650, 1965, 478, 1391, 486, 255, -1764, -813, 84, -453, -809, -1203, -1590, 730, 2059, 234, -319, 0, 624, 1273, 1470, 1882, 2215, 1611, 485, -16, 397, 593, -95, 125, 1435, 2673, 3073, 2262, 1803, 983, 666, 1516, 2821, 2395, 299, 86, 1150, 1214, 751, -1096, -962, -39, -366, -2125, -2086, -1032, -966, -863, -1522, -1793, 1228, 207, -2243, -1916, -1320, -1530, -2318, -1050, -663, -1137, -2035, -1198, -246, 753, -185, -709, -231, -1111, -1121, -11, 976, 555, -1947, -1304, 807, 529, 231, -285, -553, -695, -2006, -1090, -424, 318, -1113]) rvsdata.name = 'rvsdata' rvsdata.xnormal = array([ -1271, 176, -296, 327, -973, 228, -819, 107, 975, 82, -477, -1492, -403, 695, 212, 91, -1549, -45, 1557, 1947, -785, -2139, -1264, 295, 806, 278, -1244, 787, 752, 173, -738, 969, -646, 1811, -990, -1369, 72, 408, 169, -587, -1517, 720, -2150, -1233, -121, 682, 1268, -29, -802, 679, -1041, 934, 344, 1788, 486, 460, -834, 40, -93, -751, -374, 345, 500, -1167, -387, -966, -2369, 1119, 1148, 1193, 411, 626, 45, 960, -293, 11, 806, -866, -1043, 574, 1072, -328, -381, 433, -1857, 409, -2190, 2614, 1005, 864, 1243, 1268, -1701, 680, 560, -2567, 639, -663, 1513, 215, 69, 498, -504, -771, 1392, -739, -131, 744, -382, -158, 2394, 712, 162, 1064, -1146, -1062, 248, -171, -411, 665, -236, 350, -503, 645, -1105, -1447, -337, -2050, -2539, -151, 85, -840, -555, 1235, -427, 106, 2227, -828, 252, -2248, 992, -737, -559, 1801, -593, 1438, -583, 342, -10, -331, -1053, 466, -1020, -2163, 1003, 224, -794, -406, 3338, 1021, -1157, -788, 242, 1219, 267, -455, -843, 183, -196, -181, 699, 822, 825, -920, 110, -482, -1332, -843, -256, -989, 232, -1082, -1221, -200, -800, -344, -1779, 559, -485, -2241, -84, -1173, 701, 2685, -395, 644, 1374, 741, -144, -788, 542, 1044, -1150, -296, 281, 485, -495, 829, -1385, 80, 192, -237, 340, 1213, 1634, -264, 479, -2698, 1282, -1759, -422, 1003, 1015, 668, 332, -2367, 835, -1347, 1532, 828, 766, 907, -1122, 265, -1357, 1658, 879, -199, 433, 532, 1482, -925, -812, 1081, -191, -126, -637, -45, 1306, -863, 326, 954, -806, 42, -885, -1504, 2167, -496, -63, -19, -61, -654, 1153, 340, -1586, 97, 836, -2868, 439, 380, -652, -34, 197, -1342, 2507, 481, -228, -748, -1941, 596, 1137, -1978, -857, -546, 2208, 151, -864, -446, 1297, -507, -417, 2265, 596, -1011, 719, -1112, -1279, -184, 2721, 371, -2244, 1511, -127, 365, -53, -1399, -1628, -736, 312, -785, -182, -2070, -1452, 640, 1479, 648, -754, 1396, 1005, -183, -1661, 1296, -547, -532, 1901, -511, 232, -27, -191, -734, 140, 647, 406, -449, 997, 204, 1035, 352, -1083, -788, 2025, 1127, 2903, -184, -197, -888, -536, 82, 279, -775, 1426, 490, 362, -1900, -219, -1753, 1342, 166, 1677, 753, 2518, -1078, -990, 1138, 1235, -197, -2026, -747, 1329, 255, -323, -722, -716, 1677, -746, 298, -1190, 509, -1420, -498, 302, -996, -883, -12, 443, 139, 260, 2131, 620, -535, -443, -870, -671, 535, 213, -172, 612, -169, 1841, -195, -1629, -3, 265, 2091, 1611, -929, 225, 486, -338, 922, -582, -1433, -1072, 765, 424, 696, -541, -524, 612, 278, 1405, -777, -163, 188, -805, 36, -692, -1680, 268, 810, -688, -359, -120, 386, -248, -1015, -387, -273, -158, 1263, 271, -209, -716, 208, -738, -2268, -37, 5, -1793, 1277, 46, -967, 151, 427, 579, 178, -621, -189, 167, -563, 481, 93, -2388, -120, 359, 751, 946, 613, -1484, 1690, 387, 285, -258, -870, 936, -1574, -400, 204, -70, 2254, -1548, -593, -89, -66, -599, 452, 1518, 658, 195, -496, -1363, -468, -759, 681, -1159, 579, 368, -1393, 1360, -1277, -474, 959, -779, -77, -864, 141, -632, 770, 1119, -1125, -857, -153, -1451, -1597, 1318, -337, -436, 1453, -619, -64, -625, -214, 78, -1334, -519, 313, -293, 446, 719, -93, -860, -1006, 823, 57, 199, 332, 1112, 3079, -1616, 338, 298, 1515, -1213, 603, -811, 1023, 1171, 464, -372, -24, 1105, -43, -1, -208, -340, -102, 970, -632, 743, -459, -520, -977, -671, 1096, 974, -1956, -601, 251, -1197, -108, 1305, 661, 1135, -1164, 195, -628, 708, 1211, 773, -470, 102, 1923, 405, -1286, 932, -349, -2927, 277, 144, -19, -1333, 988, 2027, -952, 1495, 91, -288, 784, 127, 341, -324, -670, 967, -1015, -1599, -98, -9, 157, -541, -1040, -1576, 297, 67, -285, 1094, 1433, 1051, 440, 491, 1410, -145, -138, 2498, 764, 408, -237, 1099, -888, -184, -541, -1975, 1272, 87, 1229, 908, -97, -1121, 168, -949, -891, -88, -1521, 596, 1512, 747, 259, -2640, 3297, 236, 1135, 500, 1288, 2137, -399, 380, -1022, -439, -1345, -514, -1828, -69, 770, -307, -693, -606, 370, -290, -1584, -1193, -834, 148, 404, 771, 18, -207, -1068, 393, -1392, -163, -807, 1152, -564, -1495, -210, -2692, -1930, -2043, 660, -58, -1329, -1511, 1339, 458, -536, -1669, 511, -210, 167, -2028, -1333, -1271, 661, -1274, -334, 64, -619, 1818, -811, 1078, 1446, -927, -1106, -984, 181, 235, 902, 44, -836, -1021, -298, 479, -916, -219, -811, 804, -1060, -300, -710, -163, -115, 1647, -480, 582, -807, 412, 1486, 972, -1188, 649, 326, -605, -109, 1607, 847, 1140, 266, -492, -1229, 912, 3582, 914, 580, 283, -375, -834, -1206, 1985, -468, -814, -702, 211, -700, -608, -113, 1086, -2231, 662, 581, -565, -131, -197, -39, 1113, 863, 236, -1199, -2557, -2587, -2859, 948, 822, 911, 448, 71, -1579, -959, 292, -1273, -1206, 474, -908, 929, -126, -1497, -608, 106, 371, -1552, 61, 1758, 2286, -1107, -1079, -534, 404, 2099, 1035, 219, -997, 143, -666, -652, 850, 788, -780, -118, -1156, -878, 675, 1530, -576, -1022, 1862, 1282, 75, -105, 604, -507, -3169, 907, -2181, 792, 540, 180, -1660, 1113, 2179, -2179, -1223, 567, 560, 544, 906, 580, -1054, -1474, -186, 110, -189, 1452, 1823, 684, -856, -1508, -974, 353, -1953, -1918, 418, -598, -513, 1332, -1457, 226, -905, -78, -1575, -1908, -2347, 923, -460, 1745, -2262, 1119, 2445, -200, 25, -1892, -1465, -1012, -1193, -797, -204, 784, 2291, -382, -782, -1097, -103, -1085, -802, 521, 547, 1020, 17, -1255, -948, 1733, 352, 971, 1444, -955, -1251, -38, -844, 1473, 1673, 1071, 687, 818, -109, -758, 1446, -1260, 507, -2043, 1091, -143, -573, 40, -705, -693, 1992, 582, -1145, 532, -176, 341, 802, 455, 858, 713, -47, -389, -137, 288, 63, -443, 499, 1048, 1202, 1044, 157, 472, -423, 135, 978, 1325, 104, -958, 465, 564, -14, 220, -1498, 330, 158, -601, -1414, -14, -29, -535, 186, -954, -468, 2492, -1869, -1194, 345, -835, -578, -838, 802, -596, -418, -898, 414, 91, 851, -824, -34, 193, -1276, 208, 593, 538, -175, -1954, 860, 843, -610, 617, -511, -339, -261, -1495, 833, -298, 637, -1384]) rvsdata.xar2 = array([ -1271, -841, -333, 481, -422, -350, -889, -428, 1077, 1158, -89, -2142, -2073, 108, 1335, 1105, -1332, -1663, 892, 3493, 1563, -2635, -4154, -1710, 1515, 2345, -125, -486, 426, 757, -346, 314, -222, 1476, 302, -1866, -1571, 84, 1022, 189, -1877, -876, -1912, -2325, -1025, 1024, 2600, 1539, -871, -787, -1235, 339, 1233, 2604, 1953, 721, -1234, -1307, -522, -514, -525, 183, 908, -532, -1267, -1713, -3107, -509, 2294, 3282, 1890, 497, -502, 310, 206, 21, 720, -301, -1644, -591, 1421, 1104, -209, -286, -1981, -1033, -2026, 1509, 3226, 2689, 1781, 1348, -1514, -1205, 353, -1682, -883, -529, 1531, 1704, 667, 180, -694, -1416, 607, 454, -71, 460, 22, -371, 2086, 2567, 1172, 719, -1157, -2347, -1052, 161, 243, 779, 266, 174, -497, 160, -729, -2110, -1661, -2324, -3568, -1843, 394, 397, -434, 689, 342, 35, 2084, 822, -133, -2765, -1154, -277, -204, 1777, 931, 1294, -13, -315, -256, -379, -1228, -327, -667, -2533, -690, 938, 302, -633, 2681, 3483, 289, -2298, -1741, 975, 1918, 592, -1329, -1176, -472, 29, 959, 1575, 1606, -423, -1031, -1095, -1693, -1649, -729, -748, -1, -709, -1788, -1275, -926, -447, -1674, -557, -93, -2038, -1667, -1488, 345, 3705, 2396, 709, 743, 981, 269, -1063, -443, 1222, 48, -868, -438, 569, 180, 689, -924, -1003, -148, 146, 531, 1564, 2620, 1050, 9, -3216, -1295, -1187, -725, 1016, 2190, 1911, 766, -2710, -1716, -1364, 1298, 2549, 2156, 1357, -1114, -1305, -1844, 835, 2470, 1359, 286, 81, 1404, 157, -1388, -108, 416, 261, -636, -685, 1076, 340, 60, 831, -170, -510, -1208, -2215, 999, 1410, 565, -272, -561, -967, 660, 1351, -835, -1247, 256, -2040, -1321, 344, 283, 21, 72, -1294, 1436, 2277, 876, -1185, -3327, -1474, 1622, 57, -1623, -1873, 1521, 2304, 219, -1423, 50, 244, -246, 1946, 2276, -164, -550, -1471, -2180, -1193, 2857, 3253, -1070, -971, -369, 556, 576, -1216, -2889, -2439, -195, 279, 139, -2099, -3201, -871, 2383, 2990, 447, 258, 989, 479, -1772, -361, 50, -312, 1627, 947, 176, -360, -567, -1008, -383, 845, 1273, 147, 478, 513, 1206, 1061, -837, -1988, 853, 2803, 4719, 2190, -804, -2626, -2234, -392, 1083, 288, 1115, 1238, 795, -1883, -2123, -2510, 395, 1737, 2869, 2179, 2827, 94, -2329, -772, 1781, 1614, -1626, -2855, -142, 1569, 1003, -705, -1781, 605, 628, 498, -1106, -624, -1367, -1280, -38, -387, -1173, -757, 423, 856, 732, 2289, 2085, -11, -1494, -2060, -1572, 308, 1245, 670, 525, -84, 1511, 1056, -1540, -1763, -375, 2672, 3936, 884, -1037, -785, -447, 957, 407, -1586, -2544, -477, 1314, 1986, 391, -1204, -547, 443, 2033, 628, -676, -667, -1001, -431, -537, -1894, -979, 974, 581, -382, -716, 4, 113, -926, -1185, -757, -172, 1504, 1560, 287, -1266, -948, -864, -2485, -1593, -27, -1018, 476, 936, -456, -682, 109, 1007, 929, -382, -959, -409, -410, 357, 584, -2100, -2092, -265, 1585, 2346, 1697, -1299, -198, 879, 1087, 172, -1276, -171, -1072, -1172, -197, 358, 2639, 384, -1606, -1566, -516, -229, 528, 2055, 2038, 798, -876, -2463, -2000, -1127, 780, 28, 212, 523, -1080, 234, -549, -1030, 410, 64, -231, -1080, -608, -578, 611, 1897, 87, -1736, -1585, -1852, -2285, 415, 1138, 267, 1097, 125, -512, -1097, -836, -42, -949, -1257, -219, 161, 683, 1185, 513, -1042, -2096, -333, 839, 1037, 742, 1187, 3658, 717, -917, -794, 1338, 255, 138, -828, 291, 1818, 1772, 137, -801, 396, 674, 341, -273, -729, -548, 895, 358, 582, -172, -949, -1650, -1517, 708, 2298, -472, -2127, -1215, -1106, -385, 1550, 2094, 2035, -583, -1289, -1367, 258, 2102, 2325, 339, -790, 1122, 1697, -490, -308, -350, -3053, -1991, 78, 1039, -541, 36, 2326, 890, 1044, 481, -425, 204, 502, 641, -62, -1041, 166, -362, -1971, -1494, -219, 729, 151, -1283, -2678, -1204, 443, 671, 1409, 2225, 2127, 1029, 251, 1096, 606, -201, 2034, 2492, 1384, -376, 106, -615, -729, -816, -2263, -130, 1114, 2185, 2099, 490, -1779, -1501, -1260, -1148, -377, -1248, -214, 1965, 2425, 1216, -2880, 385, 1984, 2530, 1532, 1249, 2370, 873, -107, -1544, -1620, -1870, -1200, -1853, -952, 936, 917, -427, -1407, -542, -20, -1329, -2246, -1967, -303, 1145, 1838, 916, -393, -1841, -883, -1178, -664, -749, 885, 518, -1523, -1687, -3280, -3711, -3372, -182, 1482, -52, -2294, -470, 1229, 683, -1737, -1220, -317, 524, -1451, -2756, -2751, -161, -27, -275, -142, -595, 1413, 617, 865, 1829, 103, -1938, -2586, -919, 793, 1996, 1244, -839, -2314, -1730, 252, 150, -225, -1066, 63, -476, -713, -1042, -641, -107, 1883, 1079, 504, -944, -595, 1482, 2455, 36, -550, -132, -435, -391, 1512, 2252, 2185, 888, -874, -2372, -549, 4330, 4652, 2136, -334, -1711, -2035, -1979, 1419, 1657, -198, -1689, -1041, -688, -639, -279, 1182, -1146, -845, 477, 240, -178, -459, -318, 1088, 1893, 1206, -1180, -4105, -5281, -5031, -437, 2988, 3519, 1770, -273, -2682, -2968, -741, -383, -1141, -248, -535, 625, 641, -1297, -1966, -818, 700, -584, -756, 1445, 3821, 1227, -2007, -2753, -795, 2840, 3704, 1762, -1440, -1890, -1458, -873, 881, 1929, 323, -824, -1976, -2047, 26, 2574, 1471, -1132, 221, 2024, 1584, 150, -68, -636, -3644, -1691, -1712, 268, 1610, 1334, -1398, -672, 2340, 29, -2370, -1343, 670, 1752, 1973, 1282, -1015, -2927, -2020, -43, 787, 2103, 3111, 2122, -715, -3141, -3129, -580, -852, -2310, -1003, -246, -208, 1288, -322, -675, -1284, -768, -1547, -2762, -3783, -722, 853, 2789, -458, -641, 2161, 1850, 424, -2477, -3659, -2700, -1523, -666, 25, 1137, 3188, 1600, -1096, -2774, -1774, -1117, -809, 432, 1297, 1841, 842, -1502, -2570, 428, 1979, 2341, 2327, -264, -2626, -2007, -1137, 1567, 3495, 3083, 1406, 401, -491, -1351, 610, -96, 125, -1895, -487, 415, 2, -166, -838, -1281, 1387, 2332, 27, -612, -680, 103, 1224, 1383, 1353, 1104, 160, -813, -868, 0, 498, -45, 214, 1242, 2089, 2094, 787, 55, -773, -511, 956, 2346, 1502, -929, -1029, 205, 664, 649, -1310, -1042, -21, -96, -1481, -1150, -208, -127, 189, -739, -1154, 1938, 258, -1957, -1349, -936, -653, -892, 414, 182, -480, -1372, -444, 422, 1411, 93, -665, -386, -1252, -600, 739, 1429, 599, -2190, -1192, 985, 774, 744, -302, -953, -872, -1716, -103, 477, 1071, -766]) statsmodels-0.12.2/statsmodels/tsa/tests/results/stkprc.csv000066400000000000000000000022671400612667500241730ustar00rootroot00000000000000STOCK_PRICES 1.545432582 1.615419984 1.568615918 1.519513205 1.492904096 1.401182974 1.1442228 1.217875709 1.415853163 1.650579856 1.832581464 1.774952351 1.728109442 1.553925203 1.526056303 1.678963975 1.710187816 1.648658626 1.671473303 1.662030363 1.615419984 1.713797928 1.564440547 1.479329227 1.510721939 1.442201993 1.492904096 1.619388243 1.838961071 1.816452082 2.059238834 2.130609828 1.975468951 1.953027617 2.196112848 2.265921109 2.059238834 2.051556338 2.273156282 2.235376343 2.223541886 2.254444718 2.141241943 2.089391873 2.117459609 2.248128907 2.140066163 2.020222182 2.172476408 2.076938411 1.925707442 2.129421474 2.148267733 2.202764758 2.411439498 2.532902848 2.730463796 2.993229143 3.258865473 3.04594999 2.614471854 1.935859813 2.192770227 2.286455711 2.360854001 2.738902665 2.735016649 2.441477092 2.489894191 2.399711804 2.284421122 2.159868791 2.442347035 2.52332576 2.71866038 2.837908188 2.719319793 2.742773637 2.723267167 2.912350665 3.106378794 3.198673118 3.208017082 3.390810289 3.70105503 3.842029634 3.792788918 3.833845224 4.049695811 4.022669526 4.193737306 4.133244711 4.246636373 4.399006655 4.479266769 4.445705411 4.521027418 4.592084946 4.583333491 4.428671642 statsmodels-0.12.2/statsmodels/tsa/tests/results/stl-fixed.f90000066400000000000000000000335271400612667500243720ustar00rootroot00000000000000! fixed partition sort July 2019 ! Converted to double July 2019 ! Converted to FORTRAN90 ! Otherwise unmodified from original subroutine ma(x, n, len, ave) integer n, len, i, j, k, m, newn real(kind=8) x(n), ave(n), flen, v newn = n - len + 1 flen = dble(len) v = dble(0.0) do i = 1, len v = v + x(i) end do ave(1) = v / flen if(.not.(newn > 1))goto 23085 k = len m = 0 do j = 2, newn k = k + 1 m = m + 1 v = v - x(m) + x(k) ave(j) = v / flen end do 23085 continue return end subroutine ess(y, n, len, ideg, njump, userw, rw, ys, res) integer n, len, ideg, njump, newnj, nleft, nright, nsh, k, i, j real(kind=8) y(n), rw(n), ys(n), res(n), delta logical ok, userw if(.not.(n < 2))goto 23019 ys(1) = y(1) return 23019 continue newnj = min0(njump, n - 1) if(.not.(len >= n))goto 23021 nleft = 1 nright = n do i = 1, n, newnj call est(y, n, len, ideg, dble(i), ys(i), nleft, nright, res, userw, rw, ok) if(.not.(.not. ok))goto 23025 ys(i) = y(i) 23025 continue end do goto 23022 23021 continue if(.not.(newnj == 1))goto 23027 nsh = (len + 1) / 2 nleft = 1 nright = len do i = 1, n if(.not.(i > nsh .and. nright /= n))goto 23031 nleft = nleft + 1 nright = nright + 1 23031 continue call est(y, n, len, ideg, dble(i), ys(i), nleft, nright, res, userw, rw, ok) if(.not.(.not. ok))goto 23033 ys(i) = y(i) 23033 continue end do goto 23028 23027 continue nsh = (len + 1) / 2 do i = 1, n, newnj if(.not.(i < nsh))goto 23037 nleft = 1 nright = len goto 23038 23037 continue if(.not.(i >= n - nsh + 1))goto 23039 nleft = n - len + 1 nright = n goto 23040 23039 continue nleft = i - nsh + 1 nright = len + i - nsh 23040 continue 23038 continue call est(y, n, len, ideg, dble(i), ys(i), nleft, nright, res, userw, rw, ok) if(.not.(.not. ok))goto 23041 ys(i) = y(i) 23041 continue end do 23028 continue 23022 continue if(.not.(newnj /= 1))goto 23043 do i = 1, n - newnj, newnj delta = (ys(i + newnj) - ys(i)) / dble(newnj) do j = i + 1, i + newnj - 1 ys(j) = ys(i) + delta * dble(j - i) end do end do k = ((n - 1) / newnj) * newnj + 1 if(.not.(k /= n))goto 23049 call est(y, n, len, ideg, dble(n), ys(n), nleft, nright, res, userw, rw, ok) if(.not.(.not. ok))goto 23051 ys(n) = y(n) 23051 continue if(.not.(k /= n - 1))goto 23053 delta = (ys(n) - ys(k)) / dble(n - k) do j = k + 1, n - 1 ys(j) = ys(k) + delta * dble(j - k) end do 23053 continue 23049 continue 23043 continue return end subroutine est(y, n, len, ideg, xs, ys, nleft, nright, w, userw, rw, ok) integer n, len, ideg, nleft, nright, j real(kind=8) y(n), w(n), rw(n), xs, ys, range, h, h1, h9, a, b, c, r logical userw, ok range = dble(n) - dble(1) h = amax1(xs - dble(nleft), dble(nright) - xs) if(.not.(len > n))goto 23057 h = h + dble((len - n) / 2) 23057 continue h9 = .999 * h h1 = .001 * h a = 0.0 do j = nleft, nright w(j) = 0. r = abs(dble(j) - xs) if(.not.(r <= h9))goto 23061 if(.not.(r <= h1))goto 23063 w(j) = 1. goto 23064 23063 continue w(j) = (1.0 - (r / h)**3)**3 23064 continue if(.not.(userw))goto 23065 w(j) = rw(j) * w(j) 23065 continue a = a + w(j) 23061 continue end do if(.not.(a <= 0.0))goto 23067 ok = .false. goto 23068 23067 continue ok = .true. do j = nleft, nright w(j) = w(j) / a end do if(.not.((h > 0.) .and. (ideg > 0)))goto 23071 a = 0.0 do j = nleft, nright a = a + w(j) * dble(j) end do b = xs - a c = 0.0 do j = nleft, nright c = c + w(j) * (dble(j) - a)**2 end do if(.not.(sqrt(c) > .001 * range))goto 23077 b = b / c do j = nleft, nright w(j) = w(j) * (b * (dble(j) - a) + 1.0) end do 23077 continue 23071 continue ys = 0.0 do j = nleft, nright ys = ys + w(j) * y(j) end do 23068 continue return end subroutine fts(x, n, np, trend, work) integer n, np real(kind=8) x(n), trend(n), work(n) call ma(x, n, np, trend) call ma(trend, n - np + 1, np, work) call ma(work, n - 2 * np + 2, 3, trend) return end subroutine rwts(y, n, fit, rw) integer mid(2), n real(kind=8) y(n), fit(n), rw(n), cmad, c9, c1, r do i = 1, n rw(i) = abs(y(i) - fit(i)) end do ! TODO: psort does not work correctly, reorder mid mid(2) = n / 2 + 1 mid(1) = n - mid(2) + 1 call psort(rw, n, mid, 2) cmad = 3.0 * (rw(mid(1)) + rw(mid(2))) c9 = .999 * cmad c1 = .001 * cmad do i = 1, n r = abs(y(i) - fit(i)) if(.not.(r <= c1))goto 23101 rw(i) = 1. goto 23102 23101 continue if(.not.(r <= c9))goto 23103 rw(i) = (1.0 - (r / cmad)**2)**2 goto 23104 23103 continue rw(i) = 0. 23104 continue 23102 continue end do return end subroutine ss(y, n, np, ns, isdeg, nsjump, userw, rw, season, work1, work2, work3, work4) integer n, np, ns, isdeg, nsjump, nright, nleft, i, j, k real(kind=8) y(n), rw(n), season(n + 2 * np), work1(n), work2(n), work3(n), work4(n), xs logical userw, ok j = 1 23105 if(.not.(j <= np))goto 23107 k = (n - j) / np + 1 do i = 1, k work1(i) = y((i - 1) * np + j) end do if(.not.(userw))goto 23110 do i = 1, k work3(i) = rw((i - 1) * np + j) end do 23110 continue call ess(work1, k, ns, isdeg, nsjump, userw, work3, work2(2), work4) xs = 0 nright = min0(ns, k) call est(work1, k, ns, isdeg, xs, work2(1), 1, nright, work4, userw, work3, ok) if(.not.(.not. ok))goto 23114 work2(1) = work2(2) 23114 continue xs = k + 1 nleft = max0(1, k - ns + 1) call est(work1, k, ns, isdeg, xs, work2(k + 2), nleft, k, work4, userw, work3, ok) if(.not.(.not. ok))goto 23116 work2(k + 2) = work2(k + 1) 23116 continue do m = 1, k + 2 season((m - 1) * np + j) = work2(m) end do j = j + 1 goto 23105 23107 continue return end subroutine onestp(y, n, np, ns, nt,nl, isdeg, itdeg, ildeg, nsjump,ntjump, nljump, ni, userw,rw, season, trend, work) integer n, ni, np, ns, nt, nsjump, ntjump, nl, nljump, isdeg, itdeg, ildeg real(kind=8) y(n), rw(n), season(n), trend(n), work(n + 2 * np, 5) logical userw do j = 1, ni do i = 1, n work(i, 1) = y(i) - trend(i) end do call ss(work(1, 1), n, np, ns, isdeg, nsjump, userw, rw, work(1, 2), work(1, 3), work(1, 4), work(1, 5), season) call fts(work(1, 2), n + 2 * np, np, work(1, 3), work(1, 1)) call ess(work(1, 3), n, nl, ildeg, nljump, .false., work(1, 4), work(1, 1), work(1, 5)) do i = 1, n season(i) = work(np + i, 2) - work(i, 1) end do do i = 1, n work(i, 1) = y(i) - season(i) end do call ess(work(1, 1), n, nt, itdeg, ntjump, userw, rw, trend, work(1, 3)) end do return end subroutine stl(y, n, np, ns, nt,nl, isdeg, itdeg, ildeg, nsjump,ntjump, nljump, ni, no,rw, season, trend, work) integer n, np, ns, nt, nl, isdeg, itdeg, ildeg, nsjump, ntjump, nljump, ni, no, k integer newns, newnt, newnl, newnp real(kind=8) y(n), rw(n), season(n), trend(n), work(n + 2 * np, 5) logical userw userw = .false. k = 0 do i = 1, n trend(i) = 0.0 end do newns = max0(3, ns) newnt = max0(3, nt) newnl = max0(3, nl) newnp = max0(2, np) if(.not.(mod(newns, 2) == 0))goto 23002 newns = newns + 1 23002 continue if(.not.(mod(newnt, 2) == 0))goto 23004 newnt = newnt + 1 23004 continue if(.not.(mod(newnl, 2) == 0))goto 23006 newnl = newnl + 1 23006 continue 23008 continue call onestp(y, n, newnp, newns, newnt, newnl, isdeg, itdeg, ildeg, nsjump, ntjump, nljump, ni, userw, rw,season, trend, work) k = k + 1 if(.not.(k > no))goto 23011 goto 23010 23011 continue do i = 1, n work(i, 1) = trend(i) + season(i) end do call rwts(y, n, work(1, 1), rw) userw = .true. 23009 goto 23008 23010 continue if(.not.(no <= 0))goto 23015 do i = 1, n rw(i) = 1.0 end do 23015 continue return end subroutine stlez(y, n, np, ns, isdeg, itdeg, robust, no, rw, season, trend, work) logical robust integer n, i, j, np, ns, no, nt, nl, ni, nsjump, ntjump, nljump, newns, newnp integer isdeg, itdeg, ildeg real(kind=8) y(n), rw(n), season(n), trend(n), work(n + 2 * np, 7) real(kind=8) maxs, mins, maxt, mint, maxds, maxdt, difs, dift ildeg = itdeg newns = max0(3, ns) if(.not.(mod(newns, 2) == 0))goto 23120 newns = newns + 1 23120 continue newnp = max0(2, np) nt = (1.5 * newnp) / (1 - 1.5 / newns) + 0.5 nt = max0(3, nt) if(.not.(mod(nt, 2) == 0))goto 23122 nt = nt + 1 23122 continue nl = newnp if(.not.(mod(nl, 2) == 0))goto 23124 nl = nl + 1 23124 continue if(.not.(robust))goto 23126 ni = 1 goto 23127 23126 continue ni = 2 23127 continue nsjump = max0(1, int(dble(newns) / 10 + 0.9)) ntjump = max0(1, int(dble(nt) / 10 + 0.9)) nljump = max0(1, int(dble(nl) / 10 + 0.9)) do i = 1, n trend(i) = 0.0 end do call onestp(y, n, newnp, newns, nt, nl, isdeg, itdeg, ildeg, nsjump, ntjump, nljump, ni, .false., rw, season, trend, work) no = 0 if(.not.(robust))goto 23130 j = 1 23132 if(.not.(j <= 15))goto 23134 do i = 1, n work(i, 6) = season(i) work(i, 7) = trend(i) work(i, 1) = trend(i) + season(i) end do call rwts(y, n, work(1, 1), rw) call onestp(y, n, newnp, newns, nt, nl, isdeg, itdeg, ildeg, nsjump, ntjump, nljump, ni, .true., rw, season, trend, work) no = no + 1 maxs = work(1, 6) mins = work(1, 6) maxt = work(1, 7) mint = work(1, 7) maxds = abs(work(1, 6) - season(1)) maxdt = abs(work(1, 7) - trend(1)) do i = 2, n if(.not.(maxs < work(i, 6)))goto 23139 maxs = work(i, 6) 23139 continue if(.not.(maxt < work(i, 7)))goto 23141 maxt = work(i, 7) 23141 continue if(.not.(mins > work(i, 6)))goto 23143 mins = work(i, 6) 23143 continue if(.not.(mint > work(i, 7)))goto 23145 mint = work(i, 7) 23145 continue difs = abs(work(i, 6) - season(i)) dift = abs(work(i, 7) - trend(i)) if(.not.(maxds < difs))goto 23147 maxds = difs 23147 continue if(.not.(maxdt < dift))goto 23149 maxdt = dift 23149 continue end do if(.not.((maxds / (maxs - mins) < .01) .and. (maxdt / (maxt - mint) < .01)))goto 23151 goto 23134 23151 continue j = j + 1 goto 23132 23134 continue 23130 continue if(.not.(.not. robust))goto 23153 do i = 1, n rw(i) = 1.0 end do 23153 continue return end subroutine psort(a, n, ind, ni) real(kind=8) a(n) integer n, ind(ni), ni integer indu(16), indl(16), iu(16), il(16), p, jl, ju, i, j, m, k, ij, l real(kind=8) t, tt if(.not.(n < 0 .or. ni < 0))goto 23157 return 23157 continue if(.not.(n < 2 .or. ni == 0))goto 23159 return 23159 continue jl = 1 ju = ni indl(1) = 1 indu(1) = ni i = 1 j = n m = 1 23161 continue if(.not.(i < j))goto 23164 go to 10 23164 continue 23166 continue m = m - 1 if(.not.(m == 0))goto 23169 goto 23163 23169 continue i = il(m) j = iu(m) jl = indl(m) ju = indu(m) if(.not.(jl <= ju))goto 23171 23173 if(.not.(j - i > 10))goto 23174 10 k = i ij = (i + j) / 2 t = a(ij) if(.not.(a(i) > t))goto 23175 a(ij) = a(i) a(i) = t t = a(ij) 23175 continue l = j if(.not.(a(j) < t))goto 23177 a(ij) = a(j) a(j) = t t = a(ij) if(.not.(a(i) > t))goto 23179 a(ij) = a(i) a(i) = t t = a(ij) 23179 continue 23177 continue 23181 continue l = l - 1 if(.not.(a(l) <= t))goto 23184 tt = a(l) 23186 continue k = k + 1 23187 if(.not.(a(k) >= t))goto 23186 if(.not.(k > l))goto 23189 goto 23183 23189 continue a(l) = a(k) a(k) = tt 23184 continue 23182 goto 23181 23183 continue indl(m) = jl indu(m) = ju p = m m = m + 1 if(.not.(l - i <= j - k))goto 23191 il(p) = k iu(p) = j j = l 23193 continue if(.not.(jl > ju))goto 23196 goto 23167 23196 continue if(.not.(ind(ju) <= j))goto 23198 goto 23195 23198 continue ju = ju - 1 23194 goto 23193 23195 continue indl(p) = ju + 1 goto 23192 23191 continue il(p) = i iu(p) = l i = k 23200 continue if(.not.(jl > ju))goto 23203 goto 23167 23203 continue if(.not.(ind(jl) >= i))goto 23205 goto 23202 23205 continue jl = jl + 1 23201 goto 23200 23202 continue indu(p) = jl - 1 23192 continue goto 23173 23174 continue if(.not.(i == 1))goto 23207 goto 23168 23207 continue i = i - 1 23209 continue i = i + 1 if(.not.(i == j))goto 23212 goto 23211 23212 continue t = a(i + 1) if(.not.(a(i) > t))goto 23214 k = i 23216 continue a(k + 1) = a(k) k = k - 1 23217 if(.not.(t >= a(k)))goto 23216 a(k + 1) = t 23214 continue 23210 goto 23209 23211 continue 23171 continue 23167 goto 23166 23168 continue 23162 goto 23161 23163 continue return end statsmodels-0.12.2/statsmodels/tsa/tests/results/stl_co2000066400000000000000000000046641400612667500234430ustar00rootroot00000000000000315.58 316.39 316.79 317.82 318.39 318.22 316.68 315.01 314.02 313.55 315.02 315.75 316.52 317.1 317.79 319.22 320.08 319.7 318.27 315.99 314.24 314.05 315.05 316.23 316.92 317.76 318.54 319.49 320.64 319.85 318.7 316.96 315.17 315.47 316.19 317.17 318.12 318.72 319.79 320.68 321.28 320.89 319.79 317.56 316.46 315.59 316.85 317.87 318.87 319.25 320.13 321.49 322.34 321.62 319.85 317.87 316.36 316.24 317.13 318.46 319.57 320.23 320.89 321.54 322.2 321.9 320.42 318.6 316.73 317.15 317.94 318.91 319.73 320.78 321.23 322.49 322.59 322.35 321.61 319.24 318.23 317.76 319.36 319.5 320.35 321.4 322.22 323.45 323.8 323.5 322.16 320.09 318.26 317.66 319.47 320.7 322.06 322.23 322.78 324.1 324.63 323.79 322.34 320.73 319 318.99 320.41 321.68 322.3 322.89 323.59 324.65 325.3 325.15 323.88 321.8 319.99 319.86 320.88 322.36 323.59 324.23 325.34 326.33 327.03 326.24 325.39 323.16 321.87 321.31 322.34 323.74 324.61 325.58 326.55 327.81 327.82 327.53 326.29 324.66 323.12 323.09 324.01 325.1 326.12 326.62 327.16 327.94 329.15 328.79 327.53 325.65 323.6 323.78 325.13 326.26 326.93 327.84 327.96 329.93 330.25 329.24 328.13 326.42 324.97 325.29 326.56 327.73 328.73 329.7 330.46 331.7 332.66 332.22 331.02 329.39 327.58 327.27 328.3 328.81 329.44 330.89 331.62 332.85 333.29 332.44 331.35 329.58 327.58 327.55 328.56 329.73 330.45 330.98 331.63 332.88 333.63 333.53 331.9 330.08 328.59 328.31 329.44 330.64 331.62 332.45 333.36 334.46 334.84 334.29 333.04 330.88 329.23 328.83 330.18 331.5 332.8 333.22 334.54 335.82 336.45 335.97 334.65 332.4 331.28 330.73 332.05 333.54 334.65 335.06 336.32 337.39 337.66 337.56 336.24 334.39 332.43 332.22 333.61 334.78 335.88 336.43 337.61 338.53 339.06 338.92 337.39 335.72 333.64 333.65 335.07 336.53 337.82 338.19 339.89 340.56 341.22 340.92 339.26 337.27 335.66 335.54 336.71 337.79 338.79 340.06 340.93 342.02 342.65 341.8 340.01 337.94 336.17 336.28 337.76 339.05 340.18 341.04 342.16 343.01 343.64 342.91 341.72 339.52 337.75 337.68 339.14 340.37 341.32 342.45 343.05 344.91 345.77 345.3 343.98 342.41 339.89 340.03 341.19 342.87 343.74 344.55 345.28 347 347.37 346.74 345.36 343.19 340.97 341.2 342.76 343.96 344.82 345.82 347.24 348.09 348.66 347.9 346.27 344.21 342.88 342.58 343.99 345.31 345.98 346.72 347.63 349.24 349.83 349.1 347.52 345.43 344.48 343.89 345.29 346.54 347.66 348.07 349.12 350.55 351.34 350.8 349.1 347.54 346.2 346.2 347.44 348.67 statsmodels-0.12.2/statsmodels/tsa/tests/results/stl_co2.csv000066400000000000000000000045351400612667500242320ustar00rootroot00000000000000315.58 316.39 316.79 317.82 318.39 318.22 316.68 315.01 314.02 313.55 315.02 315.75 316.52 317.1 317.79 319.22 320.08 319.7 318.27 315.99 314.24 314.05 315.05 316.23 316.92 317.76 318.54 319.49 320.64 319.85 318.7 316.96 315.17 315.47 316.19 317.17 318.12 318.72 319.79 320.68 321.28 320.89 319.79 317.56 316.46 315.59 316.85 317.87 318.87 319.25 320.13 321.49 322.34 321.62 319.85 317.87 316.36 316.24 317.13 318.46 319.57 320.23 320.89 321.54 322.2 321.9 320.42 318.6 316.73 317.15 317.94 318.91 319.73 320.78 321.23 322.49 322.59 322.35 321.61 319.24 318.23 317.76 319.36 319.5 320.35 321.4 322.22 323.45 323.8 323.5 322.16 320.09 318.26 317.66 319.47 320.7 322.06 322.23 322.78 324.1 324.63 323.79 322.34 320.73 319 318.99 320.41 321.68 322.3 322.89 323.59 324.65 325.3 325.15 323.88 321.8 319.99 319.86 320.88 322.36 323.59 324.23 325.34 326.33 327.03 326.24 325.39 323.16 321.87 321.31 322.34 323.74 324.61 325.58 326.55 327.81 327.82 327.53 326.29 324.66 323.12 323.09 324.01 325.1 326.12 326.62 327.16 327.94 329.15 328.79 327.53 325.65 323.6 323.78 325.13 326.26 326.93 327.84 327.96 329.93 330.25 329.24 328.13 326.42 324.97 325.29 326.56 327.73 328.73 329.7 330.46 331.7 332.66 332.22 331.02 329.39 327.58 327.27 328.3 328.81 329.44 330.89 331.62 332.85 333.29 332.44 331.35 329.58 327.58 327.55 328.56 329.73 330.45 330.98 331.63 332.88 333.63 333.53 331.9 330.08 328.59 328.31 329.44 330.64 331.62 332.45 333.36 334.46 334.84 334.29 333.04 330.88 329.23 328.83 330.18 331.5 332.8 333.22 334.54 335.82 336.45 335.97 334.65 332.4 331.28 330.73 332.05 333.54 334.65 335.06 336.32 337.39 337.66 337.56 336.24 334.39 332.43 332.22 333.61 334.78 335.88 336.43 337.61 338.53 339.06 338.92 337.39 335.72 333.64 333.65 335.07 336.53 337.82 338.19 339.89 340.56 341.22 340.92 339.26 337.27 335.66 335.54 336.71 337.79 338.79 340.06 340.93 342.02 342.65 341.8 340.01 337.94 336.17 336.28 337.76 339.05 340.18 341.04 342.16 343.01 343.64 342.91 341.72 339.52 337.75 337.68 339.14 340.37 341.32 342.45 343.05 344.91 345.77 345.3 343.98 342.41 339.89 340.03 341.19 342.87 343.74 344.55 345.28 347 347.37 346.74 345.36 343.19 340.97 341.2 342.76 343.96 344.82 345.82 347.24 348.09 348.66 347.9 346.27 344.21 342.88 342.58 343.99 345.31 345.98 346.72 347.63 349.24 349.83 349.1 347.52 345.43 344.48 343.89 345.29 346.54 347.66 348.07 349.12 350.55 351.34 350.8 349.1 347.54 346.2 346.2 347.44 348.67 statsmodels-0.12.2/statsmodels/tsa/tests/results/stl_test_data.f90000066400000000000000000000047101400612667500253150ustar00rootroot00000000000000! data are 348 monthly values (29 years) in file stl_co2 ! gfortran stl-fixed.f90 stl_test_data.f90 -o stl_test ! ./stl_test < co2 > stl_test_results.csv real(kind=8) y(348), season(348), trend(348), rw(348), work(372, 7), & y_short(347), season_short(347), trend_short(347), rw_short(347), & work_short(371, 7) logical robust, ok, userw read(5, *)(y(i), i = 1, 348) print *, "scenario,idx,season,trend,rw" n = 348 np = 12 ns = 35 nt = 19 nl = 13 no = 2 ni = 1 nsjump = 4 ntjump = 2 nljump = 2 isdeg = 1 itdeg = 1 ildeg = 1 trend = 0.0 season = 0.0 rw = 1.0 work = 0.0 call stl(y, n, np, ns, nt, nl, isdeg, itdeg, ildeg, nsjump, ntjump, & nljump, ni, no, rw, season, trend, work) do i = 1, n print *, "baseline,", i-1, ",", season(i), ",", trend(i), ",", rw(i) end do nljump = 1 trend = 0.0 season = 0.0 rw = 1.0 work = 0.0 call stl(y, n, np, ns, nt, nl, isdeg, itdeg, ildeg, nsjump, ntjump, & nljump, ni, no, rw, season, trend, work) do i = 1, n print *, "nljump-1,", i-1, ",", season(i), ",", trend(i), ",", rw(i) end do nljump = 2 ntjump = 1 trend = 0.0 season = 0.0 rw = 1.0 work = 0.0 call stl(y, n, np, ns, nt, nl, isdeg, itdeg, ildeg, nsjump, ntjump, & nljump, ni, no, rw, season, trend, work) do i = 1, n print *, "ntjump-1,", i-1, ",", season(i), ",", trend(i), ",", rw(i) end do rw = 1.0 nljump = 1 ntjump = 1 trend = 0.0 season = 0.0 rw = 1.0 work = 0.0 call stl(y, n, np, ns, nt, nl, isdeg, itdeg, ildeg, nsjump, ntjump, & nljump, ni, no, rw, season, trend, work) do i = 1, n print *, "nljump-1-ntjump-1,", i-1, ",", season(i), ",", trend(i), ",", rw(i) end do do i = 1, n-1 y_short(i) = y(i) end do ntjump = 2 nljump = 2 rw_short = 1.0 trend_short = 0.0 season_short = 0.0 work_short = 0.0 call stl(y_short, n-1, np, ns, nt, nl, isdeg, itdeg, ildeg, nsjump, ntjump, & nljump, ni, no, rw_short, season_short, trend_short, work_short) do i = 1, n-1 print *, "short,", i-1, ",", season_short(i), ",", trend_short(i), ",", rw_short(i) end do season = 0.0 trend = 0.0 rw = 1.0 robust = .false. call stlez(y, n, np, ns, isdeg, itdeg, robust, nconv, rw, season, trend, work) do i = 1, n print *, "stlez,", i-1, ",", season(i), ",", trend(i), ",", rw(i) end do season = 0.0 trend = 0.0 rw = 1.0 robust = .true. call stlez(y, n, np, ns, isdeg, itdeg, robust, nconv, rw, season, trend, work) do i = 1, n print *, "stlez-robust,", i-1, ",", season(i), ",", trend(i), ",", rw(i) end do end statsmodels-0.12.2/statsmodels/tsa/tests/results/stl_test_results.csv000066400000000000000000010015461400612667500263070ustar00rootroot00000000000000 scenario,idx,season,trend,rw baseline, 0 , -0.13125464336066284 , 315.55193972532356 , 0.94748803176461716 baseline, 1 , 0.51706942811097434 , 315.64448157233920 , 0.88239070760993688 baseline, 2 , 1.0818206758492068 , 315.73702341935484 , 0.99815764718888089 baseline, 3 , 2.1332663735877313 , 315.83101934204581 , 0.95241860894780928 baseline, 4 , 2.7337554687412702 , 315.92501526473671 , 0.81727078927394348 baseline, 5 , 2.2399777683589441 , 316.01787137000565 , 0.99688505140950301 baseline, 6 , 0.92969951525655825 , 316.11072747527453 , 0.72808569510215149 baseline, 7 , -1.1144470742040518 , 316.20201977879987 , 0.99085198230576710 baseline, 8 , -2.6757382124558076 , 316.29331208232520 , 0.63788491165242378 baseline, 9 , -2.8785633048873667 , 316.39895719429785 , 0.99007288070955068 baseline, 10 , -1.9020978585318979 , 316.50460230627056 , 0.59576256569904962 baseline, 11 , -0.96028839684688216 , 316.61629618651364 , 0.97271181609259205 baseline, 12 , -0.12730959950617737 , 316.72799006675666 , 0.96585667671289366 baseline, 13 , 0.51912397162898372 , 316.80792580508808 , 0.84149981556861897 baseline, 14 , 1.0984583359589664 , 316.88786154341949 , 0.88652323298010016 baseline, 15 , 2.1537774509239207 , 316.93114104451831 , 0.96514697611660816 baseline, 16 , 2.7417827983113332 , 316.97442054561714 , 0.74166827782285516 baseline, 17 , 2.2439065462740442 , 317.00910734971956 , 0.59183799131206560 baseline, 18 , 0.92703494771659856 , 317.04379415382203 , 0.79219397067008412 baseline, 19 , -1.1184057488104602 , 317.07992943776253 , 0.99764100260221000 baseline, 20 , -2.6942160810219318 , 317.11606472170308 , 0.91271025136602180 baseline, 21 , -2.8983258456476011 , 317.14570699375537 , 0.92880720949843298 baseline, 22 , -1.9124665030340955 , 317.17534926580765 , 0.89823785023254366 baseline, 23 , -0.96045943231597519 , 317.21732342668167 , 0.99926629661261768 baseline, 24 , -0.12332361457262232 , 317.25929758755564 , 0.85188637731325900 baseline, 25 , 0.52121807074356397 , 317.33356080383544 , 0.96421576266831432 baseline, 26 , 1.1151341661827983 , 317.40782402011519 , 0.99996528926836548 baseline, 27 , 2.1743236918615110 , 317.50317724038814 , 0.90864140147557115 baseline, 28 , 2.7498422849701241 , 317.59853046066115 , 0.82326076076722132 baseline, 29 , 2.2478640289756506 , 317.69326345723539 , 0.97761131584791239 baseline, 30 , 0.92439563266092273 , 317.78799645380963 , 0.99997434958375975 baseline, 31 , -1.1223443263911230 , 317.87782206857133 , 0.88956735116624275 baseline, 32 , -2.7126790080208485 , 317.96764768333304 , 0.98148811785824253 baseline, 33 , -2.9180777658917858 , 318.05056799352451 , 0.69261640342633901 baseline, 34 , -1.9228288480714004 , 318.13348830371598 , 0.99979930055436661 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0.82003186428867003 baseline, 249 , -3.2783192691159111 , 337.09101301273370 , 0.92752798144456161 baseline, 250 , -2.0900212512066600 , 337.25695792544394 , 0.96950663305779272 baseline, 251 , -0.95621527008616847 , 337.42058141430931 , 0.99306747613365964 baseline, 252 , -7.6590343260986626E-002 , 337.58420490317468 , 0.76204941416880612 baseline, 253 , 0.54830330583281073 , 337.74054594472830 , 0.97674440224280423 baseline, 254 , 1.4018981766210834 , 337.89688698628197 , 0.32107463175539702 baseline, 255 , 2.5605940447330164 , 338.04260373321802 , 0.99657758930875184 baseline, 256 , 3.0221644939335737 , 338.18832048015406 , 0.99989220222395825 baseline, 257 , 2.3724949300455616 , 338.31052325102075 , 0.86730559269148277 baseline, 258 , 0.81288209549921264 , 338.43272602188750 , 0.99976968852061465 baseline, 259 , -1.2874816269534932 , 338.54413009818381 , 0.99959050354909429 baseline, 260 , -3.0278858029687585 , 338.65553417448007 , 0.99831721874694201 baseline, 261 , 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0.90766746009658905 baseline, 274 , -2.1036912341348839 , 339.88299593395578 , 0.99833498650058605 baseline, 275 , -0.95482840670139968 , 339.99712614426323 , 0.99998960665779446 baseline, 276 , -7.5973886727610726E-002 , 340.11125635457074 , 0.93259446506073407 baseline, 277 , 0.54701826193883685 , 340.23599061134780 , 0.82491219175044672 baseline, 278 , 1.4255054146578319 , 340.36072486812486 , 0.66809680566550933 baseline, 279 , 2.5994707908362016 , 340.47373038717626 , 0.99435090530737125 baseline, 280 , 3.0675785134514952 , 340.58673590622760 , 0.99988206297316629 baseline, 281 , 2.3917705555532160 , 340.68915818139249 , 0.93229305020491460 baseline, 282 , 0.79011593682655756 , 340.79158045655731 , 0.95309315019950369 baseline, 283 , -1.3171706182124037 , 340.90072736022125 , 0.98070566201966836 baseline, 284 , -3.0519343519751843 , 341.00987426388514 , 0.89260195909420481 baseline, 285 , -3.3349397312634084 , 341.15487239677691 , 0.94521759412358530 baseline, 286 , 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0.87334739308830944 baseline, 299 , -0.95340389521823143 , 343.63719186589020 , 0.93740278182867687 baseline, 300 , -7.6024513393407059E-002 , 343.76655762813982 , 0.99102420171982197 baseline, 301 , 0.54623943103083716 , 343.88635091135700 , 0.96019832068468125 baseline, 302 , 1.4487640250649803 , 344.00614419457412 , 0.93189580774492109 baseline, 303 , 2.6388850632353908 , 344.11505715271687 , 0.83609966115670087 baseline, 304 , 3.1143443745742063 , 344.22397011085968 , 0.99489696566110142 baseline, 305 , 2.4109713200003271 , 344.32375174225280 , 0.99955552132966841 baseline, 306 , 0.76666698570029690 , 344.42353337364591 , 0.92570514259134407 baseline, 307 , -1.3482445858565708 , 344.52647108929443 , 0.99970597657567095 baseline, 308 , -3.0763025671198156 , 344.62940880494295 , 0.33735768865839794 baseline, 309 , -3.3724751285996524 , 344.73518444780603 , 0.92720151242670701 baseline, 310 , -2.1236761093458711 , 344.84096009066911 , 0.99723349377131043 baseline, 311 , 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nljump-1, 52 , 2.7659519458718496 , 319.06784781978519 , 0.50441811360999045 nljump-1, 53 , 2.2557654011749184 , 319.11128613520941 , 0.85799095099581424 nljump-1, 54 , 0.91909433045619315 , 319.15472445063358 , 0.88011489419053135 nljump-1, 55 , -1.1302503950545393 , 319.20171928021227 , 0.90047712240466093 nljump-1, 56 , -2.7496454866282511 , 319.24871410979102 , 0.94583381640565767 nljump-1, 57 , -2.9576209798933020 , 319.28477298642997 , 0.98857522124382446 nljump-1, 58 , -1.9435998748317873 , 319.32083186306897 , 0.85736154925411512 nljump-1, 59 , -0.96100253586566242 , 319.35716903020193 , 0.98773535937713386 nljump-1, 60 , -0.11166271269165844 , 319.39350619733489 , 0.83485298277624898 nljump-1, 61 , 0.52704205449487662 , 319.44077652213593 , 0.86060976632630692 nljump-1, 62 , 1.1659170704897810 , 319.48804684693692 , 0.87662878972723024 nljump-1, 63 , 2.2357282115811841 , 319.53622817877869 , 0.86773098497939360 nljump-1, 64 , 2.7755805968101432 , 319.58440951062045 , 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0.53960544655608011 ntjump-1, 333 , -3.4094640894232837 , 347.23210899806202 , 0.99436598488496841 ntjump-1, 334 , -2.1367346139140850 , 347.35385144049792 , 0.99188407947185175 ntjump-1, 335 , -0.94927251755442665 , 347.47917697784845 , 0.99990559238362309 ntjump-1, 336 , -7.7521356609403222E-002 , 347.61299655944629 , 0.94408554845821424 ntjump-1, 337 , 0.54671173687608887 , 347.75821709485473 , 0.89429360957016890 ntjump-1, 338 , 1.4834224815145793 , 347.91598177298886 , 0.83693730344320327 ntjump-1, 339 , 2.6974207085587629 , 348.11207639282361 , 0.86955624273989429 ntjump-1, 340 , 3.1860259413039191 , 348.30689393685043 , 0.95826788902383719 ntjump-1, 341 , 2.4389773781874990 , 348.49979689905842 , 0.95992797813602804 ntjump-1, 342 , 0.73012212362945261 , 348.69343076726636 , 0.76829192694125392 ntjump-1, 343 , -1.3942459724769820 , 348.88921160842176 , 0.99885794632647784 ntjump-1, 344 , -3.1143890741716178 , 349.08794233757794 , 0.87285894549401644 ntjump-1, 345 , 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nljump-1-ntjump-1, 9 , -2.8776152464842242 , 316.39367952533217 , 0.98857200843673076 nljump-1-ntjump-1, 10 , -1.9015882795527757 , 316.50530275161913 , 0.60070224014339257 nljump-1-ntjump-1, 11 , -0.96026479213923899 , 316.62061491884282 , 0.97509033782219956 nljump-1-ntjump-1, 12 , -0.12718903541154405 , 316.72882898903561 , 0.96587919656529586 nljump-1-ntjump-1, 13 , 0.51899245274912609 , 316.81980124772059 , 0.82896814250680184 nljump-1-ntjump-1, 14 , 1.0983000068958224 , 316.88878406351120 , 0.88715916925658522 nljump-1-ntjump-1, 15 , 2.1529568800110868 , 316.93764437641477 , 0.96901759676856114 nljump-1-ntjump-1, 16 , 2.7419337042215286 , 316.97532093030338 , 0.74498804492084658 nljump-1-ntjump-1, 17 , 2.2436205097216870 , 317.00980080605814 , 0.59702657834061879 nljump-1-ntjump-1, 18 , 0.92672144099671117 , 317.04453497988970 , 0.79484125439730924 nljump-1-ntjump-1, 19 , -1.1190977393372472 , 317.08149340934614 , 0.99781885220592870 nljump-1-ntjump-1, 20 , -2.6934837496806332 , 317.11645906763789 , 0.91331381381918342 nljump-1-ntjump-1, 21 , -2.8974575136928999 , 317.14706524871423 , 0.92944097740098697 nljump-1-ntjump-1, 22 , -1.9119949999749826 , 317.17550753934938 , 0.89914813513134195 nljump-1-ntjump-1, 23 , -0.96037764493326994 , 317.20980958424457 , 0.99975478492028447 nljump-1-ntjump-1, 24 , -0.12320596688030695 , 317.25931464996296 , 0.85353198996353075 nljump-1-ntjump-1, 25 , 0.52110761845204212 , 317.32583365775719 , 0.96882398447739526 nljump-1-ntjump-1, 26 , 1.1149467969448852 , 317.40785062219175 , 0.99996307308625920 nljump-1-ntjump-1, 27 , 2.1734741990339468 , 317.50105141264959 , 0.91170952588490639 nljump-1-ntjump-1, 28 , 2.7499772486111871 , 317.59867995686466 , 0.82506626621039514 nljump-1-ntjump-1, 29 , 2.2474994057053039 , 317.69522461142475 , 0.97712365990203021 nljump-1-ntjump-1, 30 , 0.92407850685059090 , 317.78821156167663 , 0.99997257262547024 nljump-1-ntjump-1, 31 , -1.1228015318157765 , 317.87909368094131 , 0.89142066666767494 nljump-1-ntjump-1, 32 , -2.7119826151289526 , 317.96788881815280 , 0.98153558992232826 nljump-1-ntjump-1, 33 , -2.9172896016702792 , 318.05266266904266 , 0.69841309301346843 nljump-1-ntjump-1, 34 , -1.9223954189867716 , 318.13374294708660 , 0.99978419426753706 nljump-1-ntjump-1, 35 , -0.96048699837090279 , 318.21190224187217 , 0.98887106516386925 nljump-1-ntjump-1, 36 , -0.11922119593091825 , 318.28715230120650 , 0.98688470836151909 nljump-1-ntjump-1, 37 , 0.52322347773923750 , 318.36099197906401 , 0.91785087905361917 nljump-1-ntjump-1, 38 , 1.1315938063255124 , 318.42991785350557 , 0.88556046511732145 nljump-1-ntjump-1, 39 , 2.1939915661154261 , 318.49324119542428 , 0.99963684075442494 nljump-1-ntjump-1, 40 , 2.7580207984286500 , 318.55173654704396 , 0.99445227958335969 nljump-1-ntjump-1, 41 , 2.2513783016889208 , 318.60643920169844 , 0.99820614107868810 nljump-1-ntjump-1, 42 , 0.92143557270447074 , 318.65785282737500 , 0.88834428363176043 nljump-1-ntjump-1, 43 , -1.1265053176420727 , 318.70546219391395 , 0.99952497908525029 nljump-1-ntjump-1, 44 , -2.7304814189519848 , 318.75131960219943 , 0.59009157485628638 nljump-1-ntjump-1, 45 , -2.9371214352109756 , 318.79868664205452 , 0.85640616031168992 nljump-1-ntjump-1, 46 , -1.9327951714881257 , 318.84839906248965 , 0.99107724490133653 nljump-1-ntjump-1, 47 , -0.96059507239612141 , 318.89698396360092 , 0.99118900605280980 nljump-1-ntjump-1, 48 , -0.11523459599599445 , 318.93901788092552 , 0.99934387632309796 nljump-1-ntjump-1, 49 , 0.52534110245669341 , 318.97384698878494 , 0.82220181209671162 nljump-1-ntjump-1, 50 , 1.1482412133583768 , 319.00452004897414 , 0.99647940449475225 nljump-1-ntjump-1, 51 , 2.2145061378024025 , 319.03452345511636 , 0.87349605667431518 nljump-1-ntjump-1, 52 , 2.7660564222000881 , 319.06805694043521 , 0.50886499361276072 nljump-1-ntjump-1, 53 , 2.2552425166956356 , 319.10876004320329 , 0.85628340535718694 nljump-1-ntjump-1, 54 , 0.91877022467893288 , 319.15488943850886 , 0.88134789410626158 nljump-1-ntjump-1, 55 , -1.1302393402177042 , 319.20341813666590 , 0.90009583555156791 nljump-1-ntjump-1, 56 , -2.7490174102400178 , 319.24878808578688 , 0.94633488263519949 nljump-1-ntjump-1, 57 , -2.9569957061458196 , 319.28753601882011 , 0.98782314429484697 nljump-1-ntjump-1, 58 , -1.9432404050705898 , 319.32082307587217 , 0.85875857809204759 nljump-1-ntjump-1, 59 , -0.96074930085563404 , 319.35437172894456 , 0.98688211078697163 nljump-1-ntjump-1, 60 , -0.11155920005840798 , 319.39348854833122 , 0.83645206786810344 nljump-1-ntjump-1, 61 , 0.52699123824446148 , 319.43844116137416 , 0.85987809162978013 nljump-1-ntjump-1, 62 , 1.1656518058070000 , 319.48806553675240 , 0.87781819643960646 nljump-1-ntjump-1, 63 , 2.2347895141491110 , 319.53795449290953 , 0.86755400960924711 nljump-1-ntjump-1, 64 , 2.7756673033010255 , 319.58441074189119 , 0.92589744022071174 nljump-1-ntjump-1, 65 , 2.2604238655696194 , 319.62577570151797 , 0.99963204907399217 nljump-1-ntjump-1, 66 , 0.91580990374896742 , 319.66421468018081 , 0.94339645830558561 nljump-1-ntjump-1, 67 , -1.1349858541247411 , 319.70322582184201 , 0.99678647122050679 nljump-1-ntjump-1, 68 , -2.7679515111465789 , 319.74805947546037 , 0.85000188706061908 nljump-1-ntjump-1, 69 , -2.9776408214933383 , 319.79930753992750 , 0.71700083663543801 nljump-1-ntjump-1, 70 , -1.9541541104625053 , 319.85520964362422 , 0.99446759533874951 nljump-1-ntjump-1, 71 , -0.96116629026578848 , 319.91484055864049 , 0.99747984427709391 nljump-1-ntjump-1, 72 , -0.10776417330330074 , 319.97668258493906 , 0.94135351122942912 nljump-1-ntjump-1, 73 , 0.52875826521143254 , 320.04356129026348 , 0.91181619948473591 nljump-1-ntjump-1, 74 , 1.1831730337840953 , 320.11744865983462 , 0.98537119956695607 nljump-1-ntjump-1, 75 , 2.2551742666705579 , 320.19644997427088 , 0.99700207018478559 nljump-1-ntjump-1, 76 , 2.7853678787117824 , 320.27486273927673 , 0.50025214537799789 nljump-1-ntjump-1, 77 , 2.2656814661624853 , 320.34637222844492 , 0.82948614688931821 nljump-1-ntjump-1, 78 , 0.91291139498167029 , 320.41187639863301 , 0.81376331160239024 nljump-1-ntjump-1, 79 , -1.1396850720882603 , 320.47664234008420 , 0.97324310431545813 nljump-1-ntjump-1, 80 , -2.7868518635328781 , 320.54498114374258 , 0.55126317209432840 nljump-1-ntjump-1, 81 , -2.9982637592806509 , 320.61790819264280 , 0.94463183203216816 nljump-1-ntjump-1, 82 , -1.9650545644873698 , 320.69528020853681 , 0.27108682069321360 nljump-1-ntjump-1, 83 , -0.96157618251181676 , 320.77177506227781 , 0.77650773199897716 nljump-1-ntjump-1, 84 , -0.10396581448204725 , 320.84102519866548 , 0.62737726842842201 nljump-1-ntjump-1, 85 , 0.53052660895922210 , 320.89871783203176 , 0.99347668116408439 nljump-1-ntjump-1, 86 , 1.2006946691515135 , 320.94810282525805 , 0.99061476679004923 nljump-1-ntjump-1, 87 , 2.2755591064089744 , 320.99732479648122 , 0.92445603299730417 nljump-1-ntjump-1, 88 , 2.7950684636193590 , 321.05252857551818 , 0.99231989729648928 nljump-1-ntjump-1, 89 , 2.2709390667553522 , 321.11834291396775 , 0.96598201851033572 nljump-1-ntjump-1, 90 , 0.91001288621437304 , 321.19130658512813 , 0.98689470593277040 nljump-1-ntjump-1, 91 , -1.1443842880561708 , 321.26335839948894 , 0.99907144138987980 nljump-1-ntjump-1, 92 , -2.8057522131478128 , 321.32962797524266 , 0.84204190942780688 nljump-1-ntjump-1, 93 , -3.0188867502267529 , 321.38935929964737 , 0.18223205308310841 nljump-1-ntjump-1, 94 , -1.9759553519659387 , 321.44281178337224 , 0.99946434141851181 nljump-1-ntjump-1, 95 , -0.96198722171223716 , 321.49189270257307 , 0.91768546019412012 nljump-1-ntjump-1, 96 , -0.10017037896114045 , 321.53973497864644 , 0.28855659695070701 nljump-1-ntjump-1, 97 , 0.53228882328702953 , 321.58802402694556 , 0.97454435570330844 nljump-1-ntjump-1, 98 , 1.2182051847867581 , 321.63890473919656 , 0.98568906130661427 nljump-1-ntjump-1, 99 , 2.2959260205656409 , 321.69216250202510 , 0.96754911694640011 nljump-1-ntjump-1, 100 , 2.8047429221436442 , 321.74719649787522 , 0.98913786105929102 nljump-1-ntjump-1, 101 , 2.2761617739455517 , 321.80547547805827 , 0.80284003665998938 nljump-1-ntjump-1, 102 , 0.90707117337466048 , 321.86743267304269 , 0.59943194838751024 nljump-1-ntjump-1, 103 , -1.1491336026102639 , 321.93182920731800 , 0.99334674787107868 nljump-1-ntjump-1, 104 , -2.8247073978643931 , 321.99708268154495 , 0.92714663264523500 nljump-1-ntjump-1, 105 , -3.0395666214959163 , 322.06321823062547 , 0.99951483580514544 nljump-1-ntjump-1, 106 , -1.9869119916641222 , 322.13516470015958 , 0.83276655010274281 nljump-1-ntjump-1, 107 , -0.96244975275276634 , 322.21707227217320 , 0.59085669609409353 nljump-1-ntjump-1, 108 , -9.6498616364324760E-002 , 322.30835276944413 , 0.98467128279237659 nljump-1-ntjump-1, 109 , 0.53452117200473714 , 322.40120324004175 , 0.99228302287946479 nljump-1-ntjump-1, 110 , 1.2363026270154944 , 322.48696728081165 , 0.95589801959328247 nljump-1-ntjump-1, 111 , 2.3165876156796248 , 322.56287732356861 , 0.87883842179481708 nljump-1-ntjump-1, 112 , 2.8152547901389395 , 322.63333610483471 , 0.93980361526095679 nljump-1-ntjump-1, 113 , 2.2817345833749081 , 322.70741761522891 , 0.93514553201308070 nljump-1-ntjump-1, 114 , 0.90378382003212976 , 322.79486713556037 , 0.91535936281071040 nljump-1-ntjump-1, 115 , -1.1551208298761975 , 322.90049565319890 , 0.99279419741896957 nljump-1-ntjump-1, 116 , -2.8444045221908292 , 323.02114008817796 , 0.91489386841340725 nljump-1-ntjump-1, 117 , -3.0608754960237214 , 323.14993498272236 , 0.89354824449867365 nljump-1-ntjump-1, 118 , -1.9978111470228885 , 323.27937945570420 , 0.65042463094191538 nljump-1-ntjump-1, 119 , -0.96262849927908156 , 323.40692699140379 , 0.98598303306693291 nljump-1-ntjump-1, 120 , -9.2714461094074441E-002 , 323.53352577524061 , 0.95007163805202299 nljump-1-ntjump-1, 121 , 0.53685780757263879 , 323.66366769662466 , 0.99887121792756850 nljump-1-ntjump-1, 122 , 1.2544938255119165 , 323.79747152455451 , 0.80682236648305228 nljump-1-ntjump-1, 123 , 2.3373305371003239 , 323.92944506876540 , 0.98868867862224386 nljump-1-ntjump-1, 124 , 2.8258342267031389 , 324.05239897661642 , 0.95052965452026728 nljump-1-ntjump-1, 125 , 2.2873606813633569 , 324.16229675574277 , 0.89705388856651980 nljump-1-ntjump-1, 126 , 0.90053593988635094 , 324.26223207441842 , 0.87361835938689669 nljump-1-ntjump-1, 127 , -1.1610809791605214 , 324.35909988692941 , 0.99552734494818440 nljump-1-ntjump-1, 128 , -2.8640848081922003 , 324.45750267276117 , 0.82652229183990278 nljump-1-ntjump-1, 129 , -3.0821751940007771 , 324.55698909874133 , 0.94447176474805616 nljump-1-ntjump-1, 130 , -2.0087061630098799 , 324.65503791327330 , 0.78419158793321064 nljump-1-ntjump-1, 131 , -0.96280587774808513 , 324.75162843893338 , 0.99543999719571996 nljump-1-ntjump-1, 132 , -8.8930111098353734E-002 , 324.85006283967584 , 0.94131454167062856 nljump-1-ntjump-1, 133 , 0.53919433537151706 , 324.95504518083897 , 0.98495366170514864 nljump-1-ntjump-1, 134 , 1.2726849340281774 , 325.06993234182625 , 0.89665772494752294 nljump-1-ntjump-1, 135 , 2.3580734282502620 , 325.19517962407434 , 0.83759050427566828 nljump-1-ntjump-1, 136 , 2.8364136591184166 , 325.32501777521878 , 0.72440768491689578 nljump-1-ntjump-1, 137 , 2.2929867793518057 , 325.45202057137936 , 0.89391340972293365 nljump-1-ntjump-1, 138 , 0.89728805974057213 , 325.56822676174795 , 0.92976154366655184 nljump-1-ntjump-1, 139 , -1.1670410755874208 , 325.67132276720520 , 0.94383323653134876 nljump-1-ntjump-1, 140 , -2.8837646835591113 , 325.76450509027779 , 0.86345126759651647 nljump-1-ntjump-1, 141 , -3.1034732133514384 , 325.85014732571801 , 0.70163736167799606 nljump-1-ntjump-1, 142 , -2.0195961972687906 , 325.93274938454044 , 0.97122315175316332 nljump-1-ntjump-1, 143 , -0.96297159083645878 , 326.01625834745028 , 0.98940901801799197 nljump-1-ntjump-1, 144 , -8.5123206225531961E-002 , 326.10009246892861 , 0.96566947327649955 nljump-1-ntjump-1, 145 , 0.54156832478836014 , 326.17795577241600 , 0.98100201860848257 nljump-1-ntjump-1, 146 , 1.2909317270701681 , 326.24943421295302 , 0.70524714707279279 nljump-1-ntjump-1, 147 , 2.3788933425867995 , 326.32009566021208 , 0.11450482500150178 nljump-1-ntjump-1, 148 , 2.8470948855458005 , 326.39643548796806 , 0.98358234428163360 nljump-1-ntjump-1, 149 , 2.2987427986559075 , 326.47977753039942 , 0.99734505921750638 nljump-1-ntjump-1, 150 , 0.89420044256988196 , 326.56981482441137 , 0.98227296728721136 nljump-1-ntjump-1, 151 , -1.1728101241327782 , 326.66576193768287 , 0.93458609146156979 nljump-1-ntjump-1, 152 , -2.9032238765685001 , 326.76628094382147 , 0.84856861906959480 nljump-1-ntjump-1, 153 , -3.1245235873323733 , 326.86513294626951 , 0.99039493084269381 nljump-1-ntjump-1, 154 , -2.0302168786914461 , 326.95561164467256 , 0.88700829617056454 nljump-1-ntjump-1, 155 , -0.96285519609504044 , 327.03547208994604 , 0.89590851804760474 nljump-1-ntjump-1, 156 , -8.3153854699882901E-002 , 327.10844282686685 , 0.98644097090850547 nljump-1-ntjump-1, 157 , 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nljump-1-ntjump-1, 191 , -0.96020493547812680 , 330.59340904438943 , 0.97421669490640717 nljump-1-ntjump-1, 192 , -7.7615732405695692E-002 , 330.63841043028702 , 0.97644205599681144 nljump-1-ntjump-1, 193 , 0.55087062520754748 , 330.69328106043389 , 0.84616949186151225 nljump-1-ntjump-1, 194 , 1.3477467198259745 , 330.75577267713203 , 0.54717833977972841 nljump-1-ntjump-1, 195 , 2.4618761771216455 , 330.82582954880115 , 0.66327048988847270 nljump-1-ntjump-1, 196 , 2.9121734470335459 , 330.90356864451593 , 0.92198918404235441 nljump-1-ntjump-1, 197 , 2.3262386313175862 , 330.98993400554872 , 0.87937354733360984 nljump-1-ntjump-1, 198 , 0.86720401084396881 , 331.08862944767520 , 0.99405443155824624 nljump-1-ntjump-1, 199 , -1.2142133960548294 , 331.20031625360411 , 0.98284061089929775 nljump-1-ntjump-1, 200 , -2.9699156126661794 , 331.31978972242018 , 0.86474864556129993 nljump-1-ntjump-1, 201 , -3.2049974322239541 , 331.43614014527640 , 0.98324895060363915 nljump-1-ntjump-1, 202 , 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nljump-1-ntjump-1, 236 , -3.0045749625898290 , 335.47014596334191 , 0.99604079970032455 nljump-1-ntjump-1, 237 , -3.2598593563776963 , 335.57547187583498 , 0.97575385615145105 nljump-1-ntjump-1, 238 , -2.0835040280893660 , 335.67739878465858 , 0.99983658773534501 nljump-1-ntjump-1, 239 , -0.95621379890424973 , 335.77862101520958 , 0.99452737961116466 nljump-1-ntjump-1, 240 , -7.6967926018416469E-002 , 335.88145181689822 , 0.98097977746609211 nljump-1-ntjump-1, 241 , 0.54945532763389815 , 335.98671564429907 , 0.97606856522962449 nljump-1-ntjump-1, 242 , 1.3900548525827034 , 336.09693929025610 , 0.95904345399590873 nljump-1-ntjump-1, 243 , 2.5399155611188835 , 336.21392265547343 , 0.89432310446045582 nljump-1-ntjump-1, 244 , 2.9992611314999129 , 336.33869703043996 , 0.82375456385088752 nljump-1-ntjump-1, 245 , 2.3619037948567012 , 336.47183665348979 , 0.97955375818769441 nljump-1-ntjump-1, 246 , 0.82394501649926721 , 336.61348967259556 , 0.99465883666843546 nljump-1-ntjump-1, 247 , 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nljump-1-ntjump-1, 281 , 2.3908496735137672 , 340.69026523394740 , 0.93264047897605096 nljump-1-ntjump-1, 282 , 0.78974404864245706 , 340.79166110238481 , 0.95348782010772115 nljump-1-ntjump-1, 283 , -1.3145945568465116 , 340.89529452963569 , 0.98245913285593556 nljump-1-ntjump-1, 284 , -3.0525444320290704 , 341.00970100635237 , 0.89417024058903960 nljump-1-ntjump-1, 285 , -3.3347209631109163 , 341.14340413159363 , 0.95332762160783924 nljump-1-ntjump-1, 286 , -2.1107670017666340 , 341.29951643642755 , 0.99180215984308284 nljump-1-ntjump-1, 287 , -0.95326717547587836 , 341.47558170342950 , 0.93785809496016914 nljump-1-ntjump-1, 288 , -7.6010525732747136E-002 , 341.66709929603786 , 0.85228220599905358 nljump-1-ntjump-1, 289 , 0.54697794576473047 , 341.86803512472397 , 0.99441011574979599 nljump-1-ntjump-1, 290 , 1.4373388990353211 , 342.07021324861438 , 0.55817544766452198 nljump-1-ntjump-1, 291 , 2.6175220853790622 , 342.26755980188284 , 0.99775237145416595 nljump-1-ntjump-1, 292 , 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0.94639391088725133 stlez-robust, 174 , 0.88095524684639204 , 329.90185203752259 , 0.85430173930448894 stlez-robust, 175 , -1.1956505355469738 , 329.99451770721475 , 0.32480055589216539 stlez-robust, 176 , -2.9368389510685233 , 330.08718337690686 , 0.58348848591283697 stlez-robust, 177 , -3.1650045656072541 , 330.15660631173142 , 0.79362028993598044 stlez-robust, 178 , -2.0471361071826975 , 330.22602924655598 , 0.95764306685145029 stlez-robust, 179 , -0.96176693145810588 , 330.26562653432495 , 0.51564788604923784 stlez-robust, 180 , -7.9466364577659862E-002 , 330.30522382209386 , 7.5879882065641627E-002 stlez-robust, 181 , 0.54837198928219155 , 330.32336680520120 , 0.99686752158983671 stlez-robust, 182 , 1.3338191251601221 , 330.34150978830860 , 0.99731497400279179 stlez-robust, 183 , 2.4422890330471212 , 330.36846449707912 , 0.98959866416443487 stlez-robust, 184 , 2.8959379815291766 , 330.39541920584963 , 0.99980399547645038 stlez-robust, 185 , 2.3202558260047721 , 330.43309745267811 , 0.79130638185802127 stlez-robust, 186 , 0.87411829632329086 , 330.47077569950665 , 0.99955693165913473 stlez-robust, 187 , -1.2062459899430491 , 330.49567573662534 , 0.81266408929968448 stlez-robust, 188 , -2.9535530351456125 , 330.52057577374399 , 0.99967069830810718 stlez-robust, 189 , -3.1852253064850213 , 330.54052384471100 , 0.90095593264204643 stlez-robust, 190 , -2.0555721153089985 , 330.56047191567802 , 0.99243077475662700 stlez-robust, 191 , -0.96090776336406458 , 330.59988868879736 , 0.97668480531979585 stlez-robust, 192 , -7.7578762077474106E-002 , 330.63930546191665 , 0.97593596090246948 stlez-robust, 193 , 0.55067915424068270 , 330.69812857408317 , 0.83941998249754080 stlez-robust, 194 , 1.3480377202968647 , 330.75695168624969 , 0.54188154191124738 stlez-robust, 195 , 2.4631359147019616 , 330.83081160011443 , 0.65075376071005220 stlez-robust, 196 , 2.9123346873338760 , 330.90467151397917 , 0.92059043844240640 stlez-robust, 197 , 2.3273016352116280 , 330.99703806496359 , 0.88560785973215816 stlez-robust, 198 , 0.86756191186786913 , 331.08940461594796 , 0.99386172323772826 stlez-robust, 199 , -1.2165090605441555 , 331.20486852110707 , 0.98378852422190044 stlez-robust, 200 , -2.9698829177004438 , 331.32033242626613 , 0.86380086601385619 stlez-robust, 201 , -3.2050204228315806 , 331.43066835567885 , 0.98069199713234834 stlez-robust, 202 , -2.0635410758951438 , 331.54100428509156 , 0.99561585631750671 stlez-robust, 203 , -0.95956649351236722 , 331.62679990669005 , 0.99803509906714982 stlez-robust, 204 , -7.7302190522983136E-002 , 331.71259552828849 , 0.99981171475843500 stlez-robust, 205 , 0.55035793523180954 , 331.78159941527952 , 0.96498892404314041 stlez-robust, 206 , 1.3586696309189810 , 331.85060330227054 , 0.94149553370121852 stlez-robust, 207 , 2.4827519570734968 , 331.91079307814067 , 0.98544893500585540 stlez-robust, 208 , 2.9342198915017437 , 331.97098285401080 , 0.98909180627940085 stlez-robust, 209 , 2.3362808974875851 , 332.03766184183723 , 0.98472662804956468 stlez-robust, 210 , 0.85681400616396375 , 332.10434082966367 , 0.98386584018297163 stlez-robust, 211 , -1.2304789011020054 , 332.18860043707997 , 0.97831468992041515 stlez-robust, 212 , -2.9813294946716549 , 332.27286004449627 , 0.98971306301279727 stlez-robust, 213 , -3.2233121743210802 , 332.38463149440429 , 0.74869023141322677 stlez-robust, 214 , -2.0701370378678221 , 332.49640294431225 , 0.85039264543750337 stlez-robust, 215 , -0.95871047739294735 , 332.63158555465492 , 0.92672981727402681 stlez-robust, 216 , -7.7125370965373224E-002 , 332.76676816499759 , 0.96405552322188681 stlez-robust, 217 , 0.54992674542014042 , 332.91815247976649 , 0.85817417976471499 stlez-robust, 218 , 1.3691813519323861 , 333.06953679453545 , 0.97194253248424045 stlez-robust, 219 , 2.5022544009460468 , 333.22934202313814 , 0.97556406703751930 stlez-robust, 220 , 2.9559980882803534 , 333.38914725174084 , 0.97305996067454781 stlez-robust, 221 , 2.3451697136697676 , 333.54586630544406 , 0.98289031345802447 stlez-robust, 222 , 0.84599221566176841 , 333.70258535914729 , 0.97454424847702059 stlez-robust, 223 , -1.2445060754985160 , 333.84858638899834 , 0.88030222526137469 stlez-robust, 224 , -2.9928168545218972 , 333.99458741884933 , 0.82363342084226165 stlez-robust, 225 , -3.2416324769157057 , 334.12666019601943 , 0.93934653596799644 stlez-robust, 226 , -2.0767493191717223 , 334.25873297318952 , 0.95233555579336082 stlez-robust, 227 , -0.95786406465608909 , 334.38767172590599 , 0.97213352848097678 stlez-robust, 228 , -7.6951438841664999E-002 , 334.51661047862245 , 0.88206936248816814 stlez-robust, 229 , 0.54949411151233940 , 334.64800963975790 , 0.95724469129646272 stlez-robust, 230 , 1.3796930721874292 , 334.77940880089341 , 0.93199665513256613 stlez-robust, 231 , 2.5217568496857923 , 334.90272534662483 , 0.99875958199678794 stlez-robust, 232 , 2.9777762955517155 , 335.02604189235620 , 0.73052040308292743 stlez-robust, 233 , 2.3540585350983259 , 335.13941794417576 , 0.98744508811119913 stlez-robust, 234 , 0.83517042515957307 , 335.25279399599532 , 0.94307794772866349 stlez-robust, 235 , -1.2585332514198133 , 335.36145825435676 , 0.83079626617127056 stlez-robust, 236 , -3.0043042174217129 , 335.47012251271815 , 0.99596258230996593 stlez-robust, 237 , -3.2599528408701572 , 335.57379021481222 , 0.97639706746735089 stlez-robust, 238 , -2.0833617201457004 , 335.67745791690623 , 0.99984274130657147 stlez-robust, 239 , -0.95701850964070856 , 335.77951135325202 , 0.99439619191116602 stlez-robust, 240 , -7.6779102490833945E-002 , 335.88156478959786 , 0.98086671113520996 stlez-robust, 241 , 0.54905698080965570 , 335.98935951265838 , 0.97478315485401557 stlez-robust, 242 , 1.3901973946255843 , 336.09715423571890 , 0.95874110559112169 stlez-robust, 243 , 2.5412459951089286 , 336.21806561000329 , 0.88767355080561483 stlez-robust, 244 , 2.9995352940067477 , 336.33897698428768 , 0.82157343607876721 stlez-robust, 245 , 2.3629208196836258 , 336.47635725664190 , 0.98165577547838134 stlez-robust, 246 , 0.82431476978718954 , 336.61373752899607 , 0.99452559897308590 stlez-robust, 247 , -1.2725998590240157 , 336.76940281450976 , 0.90225379920939408 stlez-robust, 248 , -3.0158365788171513 , 336.92506810002345 , 0.82003186428867003 stlez-robust, 249 , -3.2783192691159111 , 337.09101301273370 , 0.92752798144456161 stlez-robust, 250 , -2.0900212512066600 , 337.25695792544394 , 0.96950663305779272 stlez-robust, 251 , -0.95621527008616847 , 337.42058141430931 , 0.99306747613365964 stlez-robust, 252 , -7.6590343260986626E-002 , 337.58420490317468 , 0.76204941416880612 stlez-robust, 253 , 0.54830330583281073 , 337.74054594472830 , 0.97674440224280423 stlez-robust, 254 , 1.4018981766210834 , 337.89688698628197 , 0.32107463175539702 stlez-robust, 255 , 2.5605940447330164 , 338.04260373321802 , 0.99657758930875184 stlez-robust, 256 , 3.0221644939335737 , 338.18832048015406 , 0.99989220222395825 stlez-robust, 257 , 2.3724949300455616 , 338.31052325102075 , 0.86730559269148277 stlez-robust, 258 , 0.81288209549921264 , 338.43272602188750 , 0.99976968852061465 stlez-robust, 259 , -1.2874816269534932 , 338.54413009818381 , 0.99959050354909429 stlez-robust, 260 , -3.0278858029687585 , 338.65553417448007 , 0.99831721874694201 stlez-robust, 261 , -3.2972042367876111 , 338.76544295954409 , 0.99028361183962732 stlez-robust, 262 , -2.0968607203814607 , 338.87535174460811 , 0.98461556545702056 stlez-robust, 263 , -0.95552459349447882 , 338.96673119433160 , 0.87362920096749441 stlez-robust, 264 , -7.6283147484999508E-002 , 339.05811064405503 , 0.92508562175839049 stlez-robust, 265 , 0.54766020764790746 , 339.12807253722144 , 0.64993580242511939 stlez-robust, 266 , 1.4137016756543257 , 339.19803443038791 , 0.75276150341047154 stlez-robust, 267 , 2.5800323563487040 , 339.26837946615836 , 0.91520468472882377 stlez-robust, 268 , 3.0448715008058564 , 339.33872450192882 , 0.82206109807618011 stlez-robust, 269 , 2.3821327413560498 , 339.42403947712671 , 0.99999366612313212 stlez-robust, 270 , 0.80149901616288499 , 339.50935445232454 , 0.79448449641851349 stlez-robust, 271 , -1.3023261535369419 , 339.59958085024823 , 0.67967826877293391 stlez-robust, 272 , -3.0399101393799586 , 339.68980724817192 , 0.51227912832841704 stlez-robust, 273 , -3.3160722828784182 , 339.78640159106385 , 0.90766746009658905 stlez-robust, 274 , -2.1036912341348839 , 339.88299593395578 , 0.99833498650058605 stlez-robust, 275 , -0.95482840670139968 , 339.99712614426323 , 0.99998960665779446 stlez-robust, 276 , -7.5973886727610726E-002 , 340.11125635457074 , 0.93259446506073407 stlez-robust, 277 , 0.54701826193883685 , 340.23599061134780 , 0.82491219175044672 stlez-robust, 278 , 1.4255054146578319 , 340.36072486812486 , 0.66809680566550933 stlez-robust, 279 , 2.5994707908362016 , 340.47373038717626 , 0.99435090530737125 stlez-robust, 280 , 3.0675785134514952 , 340.58673590622760 , 0.99988206297316629 stlez-robust, 281 , 2.3917705555532160 , 340.68915818139249 , 0.93229305020491460 stlez-robust, 282 , 0.79011593682655756 , 340.79158045655731 , 0.95309315019950369 stlez-robust, 283 , -1.3171706182124037 , 340.90072736022125 , 0.98070566201966836 stlez-robust, 284 , -3.0519343519751843 , 341.00987426388514 , 0.89260195909420481 stlez-robust, 285 , -3.3349397312634084 , 341.15487239677691 , 0.94521759412358530 stlez-robust, 286 , -2.1105206762926469 , 341.29987052966868 , 0.99155605141388981 stlez-robust, 287 , -0.95413005756272995 , 341.48347276180777 , 0.93091637312839992 stlez-robust, 288 , -7.5661372874700442E-002 , 341.66707499394687 , 0.85051292277826829 stlez-robust, 289 , 0.54638041381069868 , 341.86824215310889 , 0.99445294995604250 stlez-robust, 290 , 1.4373140957276815 , 342.06940931227098 , 0.55470537283138399 stlez-robust, 291 , 2.6189143594322815 , 342.26445621457799 , 0.99755273420775015 stlez-robust, 292 , 3.0902908522479557 , 342.45950311688506 , 0.88970520745361314 stlez-robust, 293 , 2.4014146767289675 , 342.65044948726523 , 0.86763691338054971 stlez-robust, 294 , 0.77874014529657820 , 342.84139585764541 , 0.73305443100043699 stlez-robust, 295 , -1.3320048040165433 , 343.02125345426180 , 0.18934318107264755 stlez-robust, 296 , -3.0639452946341135 , 343.20111105087824 , 0.82689020308394123 stlez-robust, 297 , -3.3537891192302642 , 343.35446857725941 , 0.99999005942521546 stlez-robust, 298 , -2.1173272675504373 , 343.50782610364058 , 0.87334739308830944 stlez-robust, 299 , -0.95340389521823143 , 343.63719186589020 , 0.93740278182867687 stlez-robust, 300 , -7.6024513393407059E-002 , 343.76655762813982 , 0.99102420171982197 stlez-robust, 301 , 0.54623943103083716 , 343.88635091135700 , 0.96019832068468125 stlez-robust, 302 , 1.4487640250649803 , 344.00614419457412 , 0.93189580774492109 stlez-robust, 303 , 2.6388850632353908 , 344.11505715271687 , 0.83609966115670087 stlez-robust, 304 , 3.1143443745742063 , 344.22397011085968 , 0.99489696566110142 stlez-robust, 305 , 2.4109713200003271 , 344.32375174225280 , 0.99955552132966841 stlez-robust, 306 , 0.76666698570029690 , 344.42353337364591 , 0.92570514259134407 stlez-robust, 307 , -1.3482445858565708 , 344.52647108929443 , 0.99970597657567095 stlez-robust, 308 , -3.0763025671198156 , 344.62940880494295 , 0.33735768865839794 stlez-robust, 309 , -3.3724751285996524 , 344.73518444780603 , 0.92720151242670701 stlez-robust, 310 , -2.1236761093458711 , 344.84096009066911 , 0.99723349377131043 stlez-robust, 311 , -0.95232381046758074 , 344.94083007541724 , 0.99618078062297277 stlez-robust, 312 , -7.6352065370696665E-002 , 345.04070006016531 , 0.96511551348089919 stlez-robust, 313 , 0.54612743275626918 , 345.14282560209313 , 0.94521450462101930 stlez-robust, 314 , 1.4602363348714484 , 345.24495114402094 , 0.40065242405704649 stlez-robust, 315 , 2.6588722367375559 , 345.35325841423889 , 0.97891024641686075 stlez-robust, 316 , 3.1384084558293992 , 345.46156568445690 , 0.98819784382267173 stlez-robust, 317 , 2.4205336894717462 , 345.56174259832460 , 0.98348898178260624 stlez-robust, 318 , 0.75459471957519175 , 345.66191951219236 , 0.94478622981909677 stlez-robust, 319 , -1.3644861651509281 , 345.74718330079207 , 0.89873153952422824 stlez-robust, 320 , -3.0886643279853536 , 345.83244708939179 , 0.95810729581130105 stlez-robust, 321 , -3.3911656938938064 , 345.91832151946159 , 0.99702019412633991 stlez-robust, 322 , -2.1300295746110014 , 346.00419594953138 , 0.97504235866389666 stlez-robust, 323 , -0.95124701118736332 , 346.10077900447999 , 0.94905861698620841 stlez-robust, 324 , -7.6681564819156806E-002 , 346.19736205942860 , 0.96645717919889307 stlez-robust, 325 , 0.54601430836807052 , 346.29959356179097 , 0.97150907691529442 stlez-robust, 326 , 1.4717083399218265 , 346.40182506415334 , 0.86693720288978193 stlez-robust, 327 , 2.6788592539865799 , 346.51218610275578 , 0.99040461319969664 stlez-robust, 328 , 3.1624725293344005 , 346.62254714135815 , 0.99286212186597456 stlez-robust, 329 , 2.4300960550680695 , 346.74406165265196 , 0.98591020096949877 stlez-robust, 330 , 0.74252245345008672 , 346.86557616394578 , 0.97850674293191675 stlez-robust, 331 , -1.3807276977116538 , 346.98850088895483 , 0.89203300954537967 stlez-robust, 332 , -3.1010259953836288 , 347.11142561396395 , 0.53604535847752643 stlez-robust, 333 , -3.4098556504568371 , 347.23265735512166 , 0.99429400044873473 stlez-robust, 334 , -2.1363819158811475 , 347.35388909627932 , 0.99189380107645830 stlez-robust, 335 , -0.95016708486963330 , 347.48349416046210 , 0.99977683487531410 stlez-robust, 336 , -7.7005934187575842E-002 , 347.61309922464494 , 0.94366986620520510 stlez-robust, 337 , 0.54591059745987858 , 347.76465776149735 , 0.88787344054877848 stlez-robust, 338 , 1.4831940418521767 , 347.91621629834981 , 0.83515531555310352 stlez-robust, 339 , 2.6988672663959825 , 348.11170488756818 , 0.86567219371461301 stlez-robust, 340 , 3.1865648962801858 , 348.30719347678649 , 0.95762804301047100 stlez-robust, 341 , 2.4396976845411769 , 348.50045999022370 , 0.95871744071791232 stlez-robust, 342 , 0.73050042163776618 , 348.69372650366097 , 0.76541101645714449 stlez-robust, 343 , -1.3969070531105792 , 348.89098306968299 , 0.99879671454096575 stlez-robust, 344 , -3.1133135427710874 , 349.08823963570507 , 0.87220449106762565 stlez-robust, 345 , -3.4284602097186672 , 349.29172700436311 , 0.75215910012056453 stlez-robust, 346 , -2.1426375825597082 , 349.49521437302110 , 0.98284553390023988 stlez-robust, 347 , -0.94898196289088432 , 349.70269160292088 , 0.98071842215379312 statsmodels-0.12.2/statsmodels/tsa/tests/results/test_arma_acf.R000066400000000000000000000020061400612667500250520ustar00rootroot00000000000000options(digits=15, scipen=999) # Example 3.3.2 from Brockwell and Davis ar_params = c(1, -0.25) ma_params = c(1) print(ARMAacf(ar_params, ma_params, lag.max=9)) # Custom example 1 ar_params = c(1, -0.25) ma_params = c(1, 0.2) print(ARMAacf(ar_params, ma_params, lag.max=9)) # Custom example 2 ar_params = c(1, -0.25) ma_params = c(1, 0.2, 0.3) print(ARMAacf(ar_params, ma_params, lag.max=9)) # Custom example 3 ar_params = c(1, -0.25) ma_params = c(1, 0.2, 0.3, -0.35) print(ARMAacf(ar_params, ma_params, lag.max=9)) # Custom example 4 ar_params = c(1, -0.25) ma_params = c(1, 0.2, 0.3, -0.35, -0.1) print(ARMAacf(ar_params, ma_params, lag.max=9)) # Custom example 5 ar_params = c(1, -0.25, 0.1) ma_params = c(1, 0.2) print(ARMAacf(ar_params, ma_params, lag.max=9)) # Custom example 6 ar_params = c(1, -0.25, 0.1, -0.05) ma_params = c(1, 0.2) print(ARMAacf(ar_params, ma_params, lag.max=9)) # Custom example 7 ar_params = c(1, -0.25, 0.1, -0.05, 0.02) ma_params = c(1, 0.2) print(ARMAacf(ar_params, ma_params, lag.max=9)) statsmodels-0.12.2/statsmodels/tsa/tests/results/test_bds.m000066400000000000000000000023121400612667500241240ustar00rootroot00000000000000% % BDS test for IID time series % % Calculates and outputs BDS test statistics and p-values for several % datasets. % % Requires bds function, from Kanzler. % % References % ---------- % % Kanzler, Ludwig. 1998. % BDS: MATLAB Module to Calculate Brock, Dechert & Scheinkman Test for % Independence. % Statistical Software Components. Boston College Department of Economics. % http://ideas.repec.org/c/boc/bocode/t871803.html. % % in = csvread('bds_data.csv'); sequence = in(1:25,1); normal = in(1:25,2); combined = in(1:50,3); gdpc1 = in(1:end,4); [w_s, sig_s, c_s, c1_s, k_s] = bds(sequence, 5); [w_n, sig_n, c_n, c1_n, k_n] = bds(normal, 5); [w_c, sig_c, c_c, c1_c, k_c] = bds(combined, 5); [w_g, sig_g, c_g, c1_g, k_g] = bds(gdpc1, 5); out_s = [repmat(1,1,5); 1:5; ... NaN w_s; NaN sig_s; NaN c_s; c1_s; repmat(k_s,1,5)]'; out_n = [repmat(2,1,5); 1:5; ... NaN w_n; NaN sig_n; NaN c_n; c1_n; repmat(k_n,1,5)]'; out_c = [repmat(3,1,5); 1:5; ... NaN w_c; NaN sig_c; NaN c_c; c1_c; repmat(k_c,1,5)]'; out_g = [repmat(4,1,5); 1:5; ... 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statsmodels.tsa.stattools as tsast from statsmodels.datasets import macrodata def test_adf_autolag(): #see issue #246 #this is mostly a unit test d2 = macrodata.load_pandas().data for k_trend, tr in enumerate(['nc', 'c', 'ct', 'ctt']): #[None:'nc', 0:'c', 1:'ct', 2:'ctt'] x = np.log(d2['realgdp'].values) xd = np.diff(x) #check exog adf3 = tsast.adfuller(x, maxlag=None, autolag='aic', regression=tr, store=True, regresults=True) st2 = adf3[-1] assert_equal(len(st2.autolag_results), 15 + 1) #+1 for lagged level for i, res in sorted(st2.autolag_results.items())[:5]: lag = i - k_trend #assert correct design matrices in _autolag assert_equal(res.model.exog[-10:,k_trend], x[-11:-1]) assert_equal(res.model.exog[-1,k_trend+1:], xd[-lag:-1][::-1]) #min-ic lag of dfgls in Stata is also 2, or 9 for maic with notrend assert_equal(st2.usedlag, 2) #same result with lag fixed at usedlag of autolag adf2 = tsast.adfuller(x, maxlag=2, autolag=None, regression=tr) assert_almost_equal(adf3[:2], adf2[:2], decimal=12) tr = 'c' #check maxlag with autolag adf3 = tsast.adfuller(x, maxlag=5, autolag='aic', regression=tr, store=True, regresults=True) assert_equal(len(adf3[-1].autolag_results), 5 + 1) adf3 = tsast.adfuller(x, maxlag=0, autolag='aic', regression=tr, store=True, regresults=True) assert_equal(len(adf3[-1].autolag_results), 0 + 1) statsmodels-0.12.2/statsmodels/tsa/tests/test_ar.py000066400000000000000000001415431400612667500224630ustar00rootroot00000000000000""" Test AR Model """ from itertools import product import numpy as np import numpy.testing as npt from numpy.testing import assert_allclose, assert_almost_equal import pandas as pd from pandas import Index, Series, date_range, period_range from pandas.testing import assert_series_equal import pytest import statsmodels.api as sm from statsmodels.iolib.summary import Summary from statsmodels.regression.linear_model import OLS from statsmodels.tools.testing import assert_equal from statsmodels.tools.tools import Bunch from statsmodels.tsa.ar_model import AR, AutoReg, ar_select_order from statsmodels.tsa.arima.model import ARIMA from statsmodels.tsa.deterministic import ( DeterministicProcess, Seasonality, TimeTrend, ) from statsmodels.tsa.statespace.sarimax import SARIMAX from statsmodels.tsa.tests.results import results_ar DECIMAL_6 = 6 DECIMAL_5 = 5 DECIMAL_4 = 4 def gen_ar_data(nobs): rs = np.random.RandomState(982739) idx = pd.date_range("1-1-1900", freq="M", periods=nobs) return pd.Series(rs.standard_normal(nobs), index=idx), rs def gen_ols_regressors(ar, seasonal, trend, exog): nobs = 500 y, rs = gen_ar_data(nobs) maxlag = ar if isinstance(ar, int) else max(ar) reg = [] if "c" in trend: const = pd.Series(np.ones(nobs), index=y.index, name="const") reg.append(const) if "t" in trend: time = np.arange(1, nobs + 1) time = pd.Series(time, index=y.index, name="time") reg.append(time) if isinstance(ar, int) and ar: lags = np.arange(1, ar + 1) elif ar == 0: lags = None else: lags = ar if seasonal: seasons = np.zeros((500, 12)) for i in range(12): seasons[i::12, i] = 1 cols = ["s.{0}".format(i) for i in range(12)] seasons = pd.DataFrame(seasons, columns=cols, index=y.index) if "c" in trend: seasons = seasons.iloc[:, 1:] reg.append(seasons) if maxlag: for lag in lags: reg.append(y.shift(lag)) if exog: x = rs.standard_normal((nobs, exog)) cols = ["x.{0}".format(i) for i in range(exog)] x = pd.DataFrame(x, columns=cols, index=y.index) reg.append(x) else: x = None reg.insert(0, y) df = pd.concat(reg, 1).dropna() endog = df.iloc[:, 0] exog = df.iloc[:, 1:] return y, x, endog, exog ar = [0, 3, [1, 3], [3]] seasonal = [True, False] trend = ["n", "c", "t", "ct"] exog = [None, 2] covs = ["nonrobust", "HC0"] params = list(product(ar, seasonal, trend, exog, covs)) final = [] for param in params: if param[0] != 0 or param[1] or param[2] != "n" or param[3]: final.append(param) params = final names = ("AR", "Seasonal", "Trend", "Exog", "Cov Type") ids = [ ", ".join([n + ": " + str(p) for n, p in zip(names, param)]) for param in params ] @pytest.fixture(scope="module", params=params, ids=ids) def ols_autoreg_result(request): ar, seasonal, trend, exog, cov_type = request.param y, x, endog, exog = gen_ols_regressors(ar, seasonal, trend, exog) ar_mod = AutoReg( y, ar, seasonal=seasonal, trend=trend, exog=x, old_names=False ) ar_res = ar_mod.fit(cov_type=cov_type) ols = OLS(endog, exog) ols_res = ols.fit(cov_type=cov_type, use_t=False) return ar_res, ols_res attributes = [ "bse", "cov_params", "df_model", "df_resid", "fittedvalues", "llf", "nobs", "params", "resid", "scale", "tvalues", "use_t", ] def fix_ols_attribute(val, attrib, res): """ fixes to correct for df adjustment b/t OLS and AutoReg with nonrobust cov """ nparam = res.k_constant + res.df_model nobs = nparam + res.df_resid df_correction = (nobs - nparam) / nobs if attrib in ("scale",): return val * df_correction elif attrib == "df_model": return val + res.k_constant elif res.cov_type != "nonrobust": return val elif attrib in ("bse", "conf_int"): return val * np.sqrt(df_correction) elif attrib in ("cov_params", "scale"): return val * df_correction elif attrib in ("f_test",): return val / df_correction elif attrib in ("tvalues",): return val / np.sqrt(df_correction) return val @pytest.mark.parametrize("attribute", attributes) def test_equiv_ols_autoreg(ols_autoreg_result, attribute): a, o = ols_autoreg_result ols_a = getattr(o, attribute) ar_a = getattr(a, attribute) if callable(ols_a): ols_a = ols_a() ar_a = ar_a() ols_a = fix_ols_attribute(ols_a, attribute, o) assert_allclose(ols_a, ar_a) def test_conf_int_ols_autoreg(ols_autoreg_result): a, o = ols_autoreg_result a_ci = a.conf_int() o_ci = o.conf_int() if o.cov_type == "nonrobust": spread = o_ci.T - o.params spread = fix_ols_attribute(spread, "conf_int", o) o_ci = (spread + o.params).T assert_allclose(a_ci, o_ci) def test_f_test_ols_autoreg(ols_autoreg_result): a, o = ols_autoreg_result r = np.eye(a.params.shape[0]) a_f = a.f_test(r).fvalue o_f = o.f_test(r).fvalue o_f = fix_ols_attribute(o_f, "f_test", o) assert_allclose(a_f, o_f) @pytest.mark.smoke def test_other_tests_autoreg(ols_autoreg_result): a, _ = ols_autoreg_result r = np.ones_like(a.params) a.t_test(r) r = np.eye(a.params.shape[0]) a.wald_test(r) # TODO: test likelihood for ARX model? class CheckARMixin(object): def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, DECIMAL_6) def test_bse(self): bse = np.sqrt(np.diag(self.res1.cov_params())) # no dof correction for compatability with Stata assert_almost_equal(bse, self.res2.bse_stata, DECIMAL_6) assert_almost_equal(self.res1.bse, self.res2.bse_gretl, DECIMAL_5) def test_llf(self): assert_almost_equal(self.res1.llf, self.res2.llf, DECIMAL_6) def test_fpe(self): assert_almost_equal(self.res1.fpe, self.res2.fpe, DECIMAL_6) def test_pickle(self): from io import BytesIO fh = BytesIO() # test wrapped results load save pickle self.res1.save(fh) fh.seek(0, 0) res_unpickled = self.res1.__class__.load(fh) assert type(res_unpickled) is type(self.res1) # noqa: E721 @pytest.mark.smoke def test_summary(self): assert isinstance(self.res1.summary().as_text(), str) @pytest.mark.smoke def test_pvalues(self): assert isinstance(self.res1.pvalues, (np.ndarray, pd.Series)) class CheckAutoRegMixin(CheckARMixin): def test_bse(self): assert_almost_equal(self.res1.bse, self.res2.bse_stata, DECIMAL_6) class TestAROLSConstant(CheckARMixin): """ Test AR fit by OLS with a constant. """ @classmethod def setup_class(cls): data = sm.datasets.sunspots.load(as_pandas=False) with pytest.warns(FutureWarning): cls.res1 = AR(data.endog).fit(maxlag=9, method="cmle") cls.res2 = results_ar.ARResultsOLS(constant=True) def test_predict(self): model = self.res1.model params = self.res1.params assert_almost_equal( model.predict(params), self.res2.FVOLSnneg1start0, DECIMAL_4 ) assert_almost_equal( model.predict(params), self.res2.FVOLSnneg1start9, DECIMAL_4 ) assert_almost_equal( model.predict(params, start=100), self.res2.FVOLSnneg1start100, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=9, end=200), self.res2.FVOLSn200start0, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=200, end=400), self.res2.FVOLSn200start200, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=308, end=424), self.res2.FVOLSn100start325, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=9, end=310), self.res2.FVOLSn301start9, DECIMAL_4, ) assert_almost_equal( model.predict(params), self.res2.FVOLSdefault, DECIMAL_4 ) assert_almost_equal( model.predict(params, start=308, end=316), self.res2.FVOLSn4start312, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=308, end=327), self.res2.FVOLSn15start312, DECIMAL_4, ) class TestAROLSNoConstant(CheckARMixin): """f Test AR fit by OLS without a constant. """ @classmethod def setup_class(cls): data = sm.datasets.sunspots.load(as_pandas=False) with pytest.warns(FutureWarning): cls.res1 = AR(data.endog).fit(maxlag=9, method="cmle", trend="nc") cls.res2 = results_ar.ARResultsOLS(constant=False) def test_predict(self): model = self.res1.model params = self.res1.params assert_almost_equal( model.predict(params), self.res2.FVOLSnneg1start0, DECIMAL_4 ) assert_almost_equal( model.predict(params), self.res2.FVOLSnneg1start9, DECIMAL_4 ) assert_almost_equal( model.predict(params, start=100), self.res2.FVOLSnneg1start100, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=9, end=200), self.res2.FVOLSn200start0, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=200, end=400), self.res2.FVOLSn200start200, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=308, end=424), self.res2.FVOLSn100start325, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=9, end=310), self.res2.FVOLSn301start9, DECIMAL_4, ) assert_almost_equal( model.predict(params), self.res2.FVOLSdefault, DECIMAL_4 ) assert_almost_equal( model.predict(params, start=308, end=316), self.res2.FVOLSn4start312, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=308, end=327), self.res2.FVOLSn15start312, DECIMAL_4, ) def test_mle(self): # check predict with no constant, #3945 res1 = self.res1 endog = res1.model.endog with pytest.warns(FutureWarning): res0 = AR(endog).fit(maxlag=9, method="mle", trend="nc", disp=0) assert_allclose( res0.fittedvalues[-10:], res0.fittedvalues[-10:], rtol=0.015 ) res_arma = ARIMA(endog, order=(9, 0, 0), trend="n").fit() assert_allclose(res0.params, res_arma.params[:-1], rtol=1e-2) assert_allclose( res0.fittedvalues[-10:], res_arma.fittedvalues[-10:], rtol=1e-4 ) class TestARMLEConstant(object): @classmethod def setup_class(cls): data = sm.datasets.sunspots.load(as_pandas=False) with pytest.warns(FutureWarning): cls.res1 = AR(data.endog).fit(maxlag=9, method="mle", disp=-1) cls.res2 = results_ar.ARResultsMLE(constant=True) def test_predict(self): model = self.res1.model # for some reason convergence is off in 1 out of 10 runs on # some platforms. i've never been able to replicate. see #910 params = np.array( [ 5.66817602, 1.16071069, -0.39538222, -0.16634055, 0.15044614, -0.09439266, 0.00906289, 0.05205291, -0.08584362, 0.25239198, ] ) assert_almost_equal( model.predict(params), self.res2.FVMLEdefault, DECIMAL_4 ) assert_almost_equal( model.predict(params, start=9, end=308), self.res2.FVMLEstart9end308, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=100, end=308), self.res2.FVMLEstart100end308, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=0, end=200), self.res2.FVMLEstart0end200, DECIMAL_4, ) # Note: factor 0.5 in below two tests needed to meet precision on OS X. assert_almost_equal( 0.5 * model.predict(params, start=200, end=333), 0.5 * self.res2.FVMLEstart200end334, DECIMAL_4, ) assert_almost_equal( 0.5 * model.predict(params, start=308, end=333), 0.5 * self.res2.FVMLEstart308end334, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=9, end=309), self.res2.FVMLEstart9end309, DECIMAL_4, ) assert_almost_equal( model.predict(params, end=301), self.res2.FVMLEstart0end301, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=4, end=312), self.res2.FVMLEstart4end312, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=2, end=7), self.res2.FVMLEstart2end7, DECIMAL_4, ) def test_dynamic_predict(self): # for some reason convergence is off in 1 out of 10 runs on # some platforms. i've never been able to replicate. see #910 params = np.array( [ 5.66817602, 1.16071069, -0.39538222, -0.16634055, 0.15044614, -0.09439266, 0.00906289, 0.05205291, -0.08584362, 0.25239198, ] ) res1 = self.res1 res2 = self.res2 rtol = 8e-6 # assert_raises pre-sample start, end = 9, 51 fv = res1.model.predict(params, start, end, dynamic=True) assert_allclose(fv, res2.fcdyn[start : end + 1], rtol=rtol) start, end = 9, 308 fv = res1.model.predict(params, start, end, dynamic=True) assert_allclose(fv, res2.fcdyn[start : end + 1], rtol=rtol) start, end = 9, 333 fv = res1.model.predict(params, start, end, dynamic=True) assert_allclose(fv, res2.fcdyn[start : end + 1], rtol=rtol) start, end = 100, 151 fv = res1.model.predict(params, start, end, dynamic=True) assert_allclose(fv, res2.fcdyn2[start : end + 1], rtol=rtol) start, end = 100, 308 fv = res1.model.predict(params, start, end, dynamic=True) assert_allclose(fv, res2.fcdyn2[start : end + 1], rtol=rtol) start, end = 100, 333 fv = res1.model.predict(params, start, end, dynamic=True) assert_allclose(fv, res2.fcdyn2[start : end + 1], rtol=rtol) start, end = 308, 308 fv = res1.model.predict(params, start, end, dynamic=True) assert_allclose(fv, res2.fcdyn3[start : end + 1], rtol=rtol) start, end = 308, 333 fv = res1.model.predict(params, start, end, dynamic=True) assert_allclose(fv, res2.fcdyn3[start : end + 1], rtol=rtol) start, end = 309, 333 fv = res1.model.predict(params, start, end, dynamic=True) assert_allclose(fv, res2.fcdyn4[start : end + 1], rtol=rtol) # start, end = None, None fv = res1.model.predict(params, dynamic=True) assert_allclose(fv, res2.fcdyn[9:309], rtol=rtol) class TestAutolagAR(object): @classmethod def setup_class(cls): data = sm.datasets.sunspots.load(as_pandas=False) endog = data.endog results = [] for lag in range(1, 16 + 1): endog_tmp = endog[16 - lag :] with pytest.warns(FutureWarning): r = AR(endog_tmp).fit(maxlag=lag) # See issue #324 for why we're doing these corrections vs. R # results k_ar = r.k_ar k_trend = r.k_trend log_sigma2 = np.log(r.sigma2) aic = r.aic aic = (aic - log_sigma2) * (1 + k_ar) / (1 + k_ar + k_trend) aic += log_sigma2 hqic = r.hqic hqic = (hqic - log_sigma2) * (1 + k_ar) / (1 + k_ar + k_trend) hqic += log_sigma2 bic = r.bic bic = (bic - log_sigma2) * (1 + k_ar) / (1 + k_ar + k_trend) bic += log_sigma2 results.append([aic, hqic, bic, r.fpe]) res1 = np.asarray(results).T.reshape(4, -1, order="C") # aic correction to match R cls.res1 = res1 cls.res2 = results_ar.ARLagResults("const").ic def test_ic(self): npt.assert_almost_equal(self.res1, self.res2, DECIMAL_6) def test_ar_dates(): # just make sure they work data = sm.datasets.sunspots.load(as_pandas=False) dates = date_range(start="1700", periods=len(data.endog), freq="A") endog = Series(data.endog, index=dates) with pytest.warns(FutureWarning): ar_model = AR(endog, freq="A").fit(maxlag=9, method="mle", disp=-1) pred = ar_model.predict(start="2005", end="2015") predict_dates = date_range(start="2005", end="2016", freq="A")[:11] assert_equal(ar_model.data.predict_dates, predict_dates) assert_equal(pred.index, predict_dates) def test_ar_named_series(reset_randomstate): dates = period_range(start="2011-1", periods=72, freq="M") y = Series(np.random.randn(72), name="foobar", index=dates) with pytest.warns(FutureWarning): results = AR(y).fit(2) idx = Index(["const", "L1.foobar", "L2.foobar"]) assert results.params.index.equals(idx) @pytest.mark.smoke def test_ar_start_params(): # fix GH#236 data = sm.datasets.sunspots.load(as_pandas=False) with pytest.warns(FutureWarning): AR(data.endog).fit( maxlag=9, start_params=0.1 * np.ones(10), method="mle", disp=-1, maxiter=100, ) @pytest.mark.smoke def test_ar_series(): # GH#773 dta = sm.datasets.macrodata.load_pandas().data["cpi"].diff().dropna() dates = period_range(start="1959Q1", periods=len(dta), freq="Q") dta.index = dates with pytest.warns(FutureWarning): ar = AR(dta).fit(maxlags=15) ar.bse def test_ar_select_order(): # GH#2118 np.random.seed(12345) y = sm.tsa.arma_generate_sample([1, -0.75, 0.3], [1], 100) ts = Series(y, index=date_range(start="1/1/1990", periods=100, freq="M")) with pytest.warns(FutureWarning): ar = AR(ts) with pytest.warns(FutureWarning): res = ar.select_order(maxlag=12, ic="aic") assert res == 2 # GH 2658 def test_ar_select_order_tstat(): rs = np.random.RandomState(123) tau = 25 y = rs.randn(tau) ts = Series(y, index=date_range(start="1/1/1990", periods=tau, freq="M")) with pytest.warns(FutureWarning): ar = AR(ts) with pytest.warns(FutureWarning): res = ar.select_order(maxlag=5, ic="t-stat") assert_equal(res, 0) def test_constant_column_trend(): # GH#5258, after calling lagmat, the sample below has a constant column, # which used to cause the result.k_trend attribute to be set incorrectly # See also GH#5538 sample = np.array( [ 0.46341460943222046, 0.46341460943222046, 0.39024388790130615, 0.4146341383457184, 0.4146341383457184, 0.4146341383457184, 0.3414634168148041, 0.4390243887901306, 0.46341460943222046, 0.4390243887901306, ] ) with pytest.warns(FutureWarning): model = AR(sample) # Fitting with a constant and maxlag=7 raises because of regressor # collinearity. with pytest.raises(ValueError, match="trend='c' is not allowed"): model.fit(trend="c") res = model.fit(trend="nc") assert res.k_trend == 0 assert res.k_ar == 7 assert len(res.params) == 7 pred = res.predict(start=10, end=12) # expected numbers are regression-test expected = np.array([0.44687422, 0.45608137, 0.47046381]) assert_allclose(pred, expected) def test_summary_corner(): data = sm.datasets.macrodata.load_pandas().data["cpi"].diff().dropna() dates = period_range(start="1959Q1", periods=len(data), freq="Q") data.index = dates with pytest.warns(FutureWarning): res = AR(data).fit(maxlag=4) summ = res.summary().as_text() assert "AR(4)" in summ assert "L4.cpi" in summ assert "03-31-1959" in summ with pytest.warns(FutureWarning): res = AR(data).fit(maxlag=0) summ = res.summary().as_text() assert "const" in summ assert "AR(0)" in summ def test_at_repeated_fit(): data = sm.datasets.sunspots.load_pandas() with pytest.warns(FutureWarning): ar = AR(data.endog) ar.fit() with pytest.raises(RuntimeError): ar.fit(maxlag=1) with pytest.raises(RuntimeError): ar.fit(method="mle") with pytest.raises(RuntimeError): ar.fit(ic="aic") with pytest.raises(RuntimeError): ar.fit(trend="nc") def test_ar_errors(reset_randomstate): with pytest.raises(ValueError, match="Only the univariate case"): with pytest.warns(FutureWarning): AR(np.empty((1000, 2))) with pytest.warns(FutureWarning): ar = AR(np.random.standard_normal(1000)) with pytest.raises(ValueError, match="Method yw not"): ar.fit(method="yw") with pytest.raises(ValueError, match="ic option fpic not"): ar.fit(ic="fpic") res = ar.fit() with pytest.raises(ValueError, match="Start must be >= k_ar"): res.predict(start=0) with pytest.raises(ValueError, match="Prediction must have `end` after"): res.predict(start=100, end=99) with pytest.raises(ValueError, match="Length of start params"): with pytest.warns(FutureWarning): AR(np.random.standard_normal(1000)).fit( maxlag=2, method="mle", start_params=[1, 1] ) @pytest.mark.smoke def test_ar_score(): data = sm.datasets.sunspots.load_pandas() with pytest.warns(FutureWarning): ar = AR(np.asarray(data.endog)) res = ar.fit(3) score = ar.score(res.params) assert isinstance(score, np.ndarray) assert score.shape == (4,) assert ar.information(res.params) is None @pytest.mark.smoke def test_bestlag_stop(): data = sm.datasets.sunspots.load_pandas() with pytest.warns(FutureWarning): ar = AR(np.asarray(data.endog)) with pytest.warns(FutureWarning): ar.fit(2, ic="t-stat") assert ar.k_ar == 2 def test_roots(): data = sm.datasets.sunspots.load_pandas() with pytest.warns(FutureWarning): ar = AR(np.asarray(data.endog)) res = ar.fit(1) assert_almost_equal(res.roots, np.array([1.0 / res.params[-1]])) def test_resids_mle(): data = sm.datasets.sunspots.load_pandas() with pytest.warns(FutureWarning): ar = AR(np.asarray(data.endog)) res = ar.fit(1, method="mle", disp=-1) assert res.resid.shape[0] == data.endog.shape[0] def test_ar_repeated_fit(): data = sm.datasets.sunspots.load(as_pandas=False) with pytest.warns(FutureWarning): mod = AR(data.endog) res = mod.fit(maxlag=2, method="cmle") repeat = mod.fit(maxlag=2, method="cmle") assert_allclose(res.params, repeat.params) assert isinstance(res.summary().as_text(), str) assert isinstance(repeat.summary().as_text(), str) def test_ar_predict_no_fit(): data = sm.datasets.sunspots.load(as_pandas=False) with pytest.warns(FutureWarning): mod = AR(data.endog) with pytest.raises(RuntimeError, match="Model must be fit"): mod.predict([0.1]) params = product( [0, 1, 3, [1, 3]], ["n", "c", "t", "ct"], [True, False], [0, 2], [None, 11], ["none", "drop"], [True, False], [None, 12], ) params = list(params) params = [ param for param in params if (param[0] or param[1] != "n" or param[2] or param[3]) ] params = [ param for param in params if not param[2] or (param[2] and (param[4] or param[6])) ] param_fmt = """\ lags: {0}, trend: {1}, seasonal: {2}, nexog: {3}, periods: {4}, \ missing: {5}, pandas: {6}, hold_back{7}""" ids = [param_fmt.format(*param) for param in params] def gen_data(nobs, nexog, pandas, seed=92874765): rs = np.random.RandomState(seed) endog = rs.standard_normal((nobs)) exog = rs.standard_normal((nobs, nexog)) if nexog else None if pandas: index = pd.date_range("31-12-1999", periods=nobs, freq="M") endog = pd.Series(endog, name="endog", index=index) if nexog: cols = ["exog.{0}".format(i) for i in range(exog.shape[1])] exog = pd.DataFrame(exog, columns=cols, index=index) from collections import namedtuple DataSet = namedtuple("DataSet", ["endog", "exog"]) return DataSet(endog=endog, exog=exog) @pytest.fixture(scope="module", params=params, ids=ids) def ar_data(request): lags, trend, seasonal = request.param[:3] nexog, period, missing, use_pandas, hold_back = request.param[3:] data = gen_data(250, nexog, use_pandas) return Bunch( trend=trend, lags=lags, seasonal=seasonal, period=period, endog=data.endog, exog=data.exog, missing=missing, hold_back=hold_back, ) params = product( [0, 3, [1, 3]], ["c"], [True, False], [0], [None, 11], ["drop"], [True, False], [None, 12], ) params = list(params) params = [ param for param in params if (param[0] or param[1] != "n" or param[2] or param[3]) ] params = [ param for param in params if not param[2] or (param[2] and (param[4] or param[6])) ] param_fmt = """\ lags: {0}, trend: {1}, seasonal: {2}, nexog: {3}, periods: {4}, \ missing: {5}, pandas: {6}, hold_back: {7}""" ids = [param_fmt.format(*param) for param in params] # Only test 1/3 to save time @pytest.fixture(scope="module", params=params[::3], ids=ids[::3]) def plot_data(request): lags, trend, seasonal = request.param[:3] nexog, period, missing, use_pandas, hold_back = request.param[3:] data = gen_data(250, nexog, use_pandas) return Bunch( trend=trend, lags=lags, seasonal=seasonal, period=period, endog=data.endog, exog=data.exog, missing=missing, hold_back=hold_back, ) @pytest.mark.matplotlib @pytest.mark.smoke def test_autoreg_smoke_plots(plot_data, close_figures): from matplotlib.figure import Figure mod = AutoReg( plot_data.endog, plot_data.lags, trend=plot_data.trend, seasonal=plot_data.seasonal, exog=plot_data.exog, hold_back=plot_data.hold_back, period=plot_data.period, missing=plot_data.missing, old_names=False, ) res = mod.fit() fig = res.plot_diagnostics() assert isinstance(fig, Figure) if plot_data.exog is None: fig = res.plot_predict(end=300) assert isinstance(fig, Figure) fig = res.plot_predict(end=300, alpha=None, in_sample=False) assert isinstance(fig, Figure) assert isinstance(res.summary(), Summary) @pytest.mark.smoke def test_autoreg_predict_smoke(ar_data): mod = AutoReg( ar_data.endog, ar_data.lags, trend=ar_data.trend, seasonal=ar_data.seasonal, exog=ar_data.exog, hold_back=ar_data.hold_back, period=ar_data.period, missing=ar_data.missing, old_names=False, ) res = mod.fit() exog_oos = None if ar_data.exog is not None: exog_oos = np.empty((1, ar_data.exog.shape[1])) mod.predict(res.params, 0, 250, exog_oos=exog_oos) if ar_data.lags == 0 and ar_data.exog is None: mod.predict(res.params, 0, 350, exog_oos=exog_oos) if isinstance(ar_data.endog, pd.Series) and ( not ar_data.seasonal or ar_data.period is not None ): ar_data.endog.index = list(range(ar_data.endog.shape[0])) if ar_data.exog is not None: ar_data.exog.index = list(range(ar_data.endog.shape[0])) mod = AutoReg( ar_data.endog, ar_data.lags, trend=ar_data.trend, seasonal=ar_data.seasonal, exog=ar_data.exog, period=ar_data.period, missing=ar_data.missing, old_names=False, ) mod.predict(res.params, 0, 250, exog_oos=exog_oos) @pytest.mark.matplotlib def test_parameterless_autoreg(): data = gen_data(250, 0, False) mod = AutoReg( data.endog, 0, trend="n", seasonal=False, exog=None, old_names=False ) res = mod.fit() for attr in dir(res): if attr.startswith("_"): continue # TODO if attr in ( "predict", "f_test", "t_test", "initialize", "load", "remove_data", "save", "t_test", "t_test_pairwise", "wald_test", "wald_test_terms", ): continue warning = None if attr != "test_serial_correlation" else FutureWarning attr = getattr(res, attr) if callable(attr): with pytest.warns(warning): attr() else: assert isinstance(attr, object) def test_predict_errors(): data = gen_data(250, 2, True) mod = AutoReg(data.endog, 3, old_names=False) res = mod.fit() with pytest.raises(ValueError, match="exog and exog_oos cannot be used"): mod.predict(res.params, exog=data.exog) with pytest.raises(ValueError, match="exog and exog_oos cannot be used"): mod.predict(res.params, exog_oos=data.exog) with pytest.raises(ValueError, match="hold_back must be >= lags"): AutoReg(data.endog, 3, hold_back=1, old_names=False) with pytest.raises(ValueError, match="freq cannot be inferred"): AutoReg(data.endog.values, 3, seasonal=True, old_names=False) mod = AutoReg(data.endog, 3, exog=data.exog, old_names=False) res = mod.fit() with pytest.raises(ValueError, match=r"The shape of exog \(200, 2\)"): mod.predict(res.params, exog=data.exog.iloc[:200]) with pytest.raises(ValueError, match="The number of columns in exog_oos"): mod.predict(res.params, exog_oos=data.exog.iloc[:, :1]) with pytest.raises(ValueError, match="Prediction must have `end` after"): mod.predict(res.params, start=200, end=199) with pytest.raises(ValueError, match="exog_oos must be provided"): mod.predict(res.params, end=250, exog_oos=None) mod = AutoReg(data.endog, 0, exog=data.exog, old_names=False) res = mod.fit() with pytest.raises(ValueError, match="start and end indicate that 10"): mod.predict(res.params, end=259, exog_oos=data.exog.iloc[:5]) def test_spec_errors(): data = gen_data(250, 2, True) with pytest.raises(ValueError, match="lags must be a positive scalar"): AutoReg(data.endog, -1, old_names=False) with pytest.raises(ValueError, match="All values in lags must be pos"): AutoReg(data.endog, [1, 1, 1], old_names=False) with pytest.raises(ValueError, match="All values in lags must be pos"): AutoReg(data.endog, [1, -2, 3], old_names=False) @pytest.mark.smoke def test_dynamic_forecast_smoke(ar_data): mod = AutoReg( ar_data.endog, ar_data.lags, trend=ar_data.trend, seasonal=ar_data.seasonal, exog=ar_data.exog, hold_back=ar_data.hold_back, period=ar_data.period, missing=ar_data.missing, old_names=False, ) res = mod.fit() res.predict(dynamic=True) if ar_data.exog is None: res.predict(end=260, dynamic=True) @pytest.mark.smoke def test_ar_select_order_smoke(): data = sm.datasets.sunspots.load(as_pandas=True).data["SUNACTIVITY"] ar_select_order(data, 4, glob=True, trend="n", old_names=False) ar_select_order(data, 4, glob=False, trend="n", old_names=False) ar_select_order(data, 4, seasonal=True, period=12, old_names=False) ar_select_order(data, 4, seasonal=False, old_names=False) ar_select_order(data, 4, glob=True, old_names=False) ar_select_order( data, 4, glob=True, seasonal=True, period=12, old_names=False ) class TestAutoRegOLSConstant(CheckAutoRegMixin): """ Test AutoReg fit by OLS with a constant. """ @classmethod def setup_class(cls): data = sm.datasets.sunspots.load(as_pandas=True) data.endog.index = list(range(len(data.endog))) cls.res1 = AutoReg(data.endog, lags=9, old_names=False).fit() cls.res2 = results_ar.ARResultsOLS(constant=True) def test_predict(self): model = self.res1.model params = self.res1.params assert_almost_equal( model.predict(params), self.res2.FVOLSnneg1start0, DECIMAL_4 ) assert_almost_equal( model.predict(params), self.res2.FVOLSnneg1start9, DECIMAL_4 ) assert_almost_equal( model.predict(params, start=100), self.res2.FVOLSnneg1start100, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=9, end=200), self.res2.FVOLSn200start0, DECIMAL_4, ) assert_almost_equal( model.predict(params), self.res2.FVOLSdefault, DECIMAL_4 ) assert_almost_equal( model.predict(params, start=200, end=400), self.res2.FVOLSn200start200, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=308, end=424), self.res2.FVOLSn100start325, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=9, end=310), self.res2.FVOLSn301start9, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=308, end=316), self.res2.FVOLSn4start312, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=308, end=327), self.res2.FVOLSn15start312, DECIMAL_4, ) class TestAutoRegOLSNoConstant(CheckAutoRegMixin): """f Test AR fit by OLS without a constant. """ @classmethod def setup_class(cls): data = sm.datasets.sunspots.load(as_pandas=False) cls.res1 = AutoReg( data.endog, lags=9, trend="n", old_names=False ).fit() cls.res2 = results_ar.ARResultsOLS(constant=False) def test_predict(self): model = self.res1.model params = self.res1.params assert_almost_equal( model.predict(params), self.res2.FVOLSnneg1start0, DECIMAL_4 ) assert_almost_equal( model.predict(params), self.res2.FVOLSnneg1start9, DECIMAL_4 ) assert_almost_equal( model.predict(params, start=100), self.res2.FVOLSnneg1start100, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=9, end=200), self.res2.FVOLSn200start0, DECIMAL_4, ) assert_almost_equal( model.predict(params), self.res2.FVOLSdefault, DECIMAL_4 ) assert_almost_equal( model.predict(params, start=200, end=400), self.res2.FVOLSn200start200, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=308, end=424), self.res2.FVOLSn100start325, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=9, end=310), self.res2.FVOLSn301start9, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=308, end=316), self.res2.FVOLSn4start312, DECIMAL_4, ) assert_almost_equal( model.predict(params, start=308, end=327), self.res2.FVOLSn15start312, DECIMAL_4, ) @pytest.mark.parametrize("lag", list(np.arange(1, 16 + 1))) def test_autoreg_info_criterion(lag): data = sm.datasets.sunspots.load(as_pandas=False) endog = data.endog endog_tmp = endog[16 - lag :] r = AutoReg(endog_tmp, lags=lag, old_names=False).fit() # See issue #324 for the corrections vs. R k_ar = len(r.model.ar_lags) k_trend = 1 log_sigma2 = np.log(r.sigma2) aic = r.aic aic = (aic - log_sigma2) * (1 + k_ar) / (1 + k_ar + k_trend) aic += log_sigma2 hqic = r.hqic hqic = (hqic - log_sigma2) * (1 + k_ar) / (1 + k_ar + k_trend) hqic += log_sigma2 bic = r.bic bic = (bic - log_sigma2) * (1 + k_ar) / (1 + k_ar + k_trend) bic += log_sigma2 res1 = np.array([aic, hqic, bic, r.fpe]) # aic correction to match R res2 = results_ar.ARLagResults("const").ic.T assert_almost_equal(res1, res2[lag - 1, :], DECIMAL_6) r2 = AutoReg(endog, lags=lag, hold_back=16, old_names=False).fit() assert_allclose(r.aic, r2.aic) assert_allclose(r.bic, r2.bic) assert_allclose(r.hqic, r2.hqic) assert_allclose(r.fpe, r2.fpe) @pytest.mark.parametrize("old_names", [True, False]) def test_autoreg_named_series(reset_randomstate, old_names): dates = period_range(start="2011-1", periods=72, freq="M") y = Series(np.random.randn(72), name="foobar", index=dates) results = AutoReg(y, lags=2, old_names=old_names).fit() if old_names: idx = Index(["intercept", "foobar.L1", "foobar.L2"]) else: idx = Index(["const", "foobar.L1", "foobar.L2"]) assert results.params.index.equals(idx) @pytest.mark.smoke def test_autoreg_series(): # GH#773 dta = sm.datasets.macrodata.load_pandas().data["cpi"].diff().dropna() dates = period_range(start="1959Q1", periods=len(dta), freq="Q") dta.index = dates ar = AutoReg(dta, lags=15, old_names=False).fit() ar.bse def test_ar_order_select(): # GH#2118 np.random.seed(12345) y = sm.tsa.arma_generate_sample([1, -0.75, 0.3], [1], 100) ts = Series(y, index=date_range(start="1/1/1990", periods=100, freq="M")) res = ar_select_order(ts, maxlag=12, ic="aic", old_names=False) assert tuple(res.ar_lags) == (1, 2) assert isinstance(res.aic, dict) assert isinstance(res.bic, dict) assert isinstance(res.hqic, dict) assert isinstance(res.model, AutoReg) assert not res.seasonal assert res.trend == "c" assert res.period is None def test_autoreg_constant_column_trend(): sample = np.array( [ 0.46341460943222046, 0.46341460943222046, 0.39024388790130615, 0.4146341383457184, 0.4146341383457184, 0.4146341383457184, 0.3414634168148041, 0.4390243887901306, 0.46341460943222046, 0.4390243887901306, ] ) with pytest.raises(ValueError, match="The model specification cannot"): AutoReg(sample, lags=7, old_names=False) with pytest.raises(ValueError, match="The model specification cannot"): AutoReg(sample, lags=7, trend="n", old_names=False) @pytest.mark.parametrize("old_names", [True, False]) def test_autoreg_summary_corner(old_names): data = sm.datasets.macrodata.load_pandas().data["cpi"].diff().dropna() dates = period_range(start="1959Q1", periods=len(data), freq="Q") data.index = dates res = AutoReg(data, lags=4, old_names=old_names).fit() summ = res.summary().as_text() assert "AutoReg(4)" in summ assert "cpi.L4" in summ assert "03-31-1960" in summ res = AutoReg(data, lags=0, old_names=old_names).fit() summ = res.summary().as_text() if old_names: assert "intercept" in summ else: assert "const" in summ assert "AutoReg(0)" in summ @pytest.mark.smoke def test_autoreg_score(): data = sm.datasets.sunspots.load_pandas() ar = AutoReg(np.asarray(data.endog), 3, old_names=False) res = ar.fit() score = ar.score(res.params) assert isinstance(score, np.ndarray) assert score.shape == (4,) assert ar.information(res.params).shape == (4, 4) def test_autoreg_roots(): data = sm.datasets.sunspots.load_pandas() ar = AutoReg(np.asarray(data.endog), lags=1, old_names=False) res = ar.fit() assert_almost_equal(res.roots, np.array([1.0 / res.params[-1]])) def test_equiv_dynamic(reset_randomstate): e = np.random.standard_normal(1001) y = np.empty(1001) y[0] = e[0] * np.sqrt(1.0 / (1 - 0.9 ** 2)) for i in range(1, 1001): y[i] = 0.9 * y[i - 1] + e[i] mod = AutoReg(y, 1, old_names=False) res = mod.fit() pred0 = res.predict(500, 800, dynamic=0) pred1 = res.predict(500, 800, dynamic=True) idx = pd.date_range("31-01-2000", periods=1001, freq="M") y = pd.Series(y, index=idx) mod = AutoReg(y, 1, old_names=False) res = mod.fit() pred2 = res.predict(idx[500], idx[800], dynamic=idx[500]) pred3 = res.predict(idx[500], idx[800], dynamic=0) pred4 = res.predict(idx[500], idx[800], dynamic=True) assert_allclose(pred0, pred1) assert_allclose(pred0, pred2) assert_allclose(pred0, pred3) assert_allclose(pred0, pred4) def test_dynamic_against_sarimax(): rs = np.random.RandomState(12345678) e = rs.standard_normal(1001) y = np.empty(1001) y[0] = e[0] * np.sqrt(1.0 / (1 - 0.9 ** 2)) for i in range(1, 1001): y[i] = 0.9 * y[i - 1] + e[i] smod = SARIMAX(y, order=(1, 0, 0), trend="c") sres = smod.fit(disp=False) mod = AutoReg(y, 1, old_names=False) spred = sres.predict(900, 1100) pred = mod.predict(sres.params[:2], 900, 1100) assert_allclose(spred, pred) spred = sres.predict(900, 1100, dynamic=True) pred = mod.predict(sres.params[:2], 900, 1100, dynamic=True) assert_allclose(spred, pred) spred = sres.predict(900, 1100, dynamic=50) pred = mod.predict(sres.params[:2], 900, 1100, dynamic=50) assert_allclose(spred, pred) def test_predict_seasonal(): rs = np.random.RandomState(12345678) e = rs.standard_normal(1001) y = np.empty(1001) y[0] = e[0] * np.sqrt(1.0 / (1 - 0.9 ** 2)) effects = 10 * np.cos(np.arange(12) / 11 * 2 * np.pi) for i in range(1, 1001): y[i] = 10 + 0.9 * y[i - 1] + e[i] + effects[i % 12] ys = pd.Series(y, index=pd.date_range("1-1-1950", periods=1001, freq="M")) mod = AutoReg(ys, 1, seasonal=True, old_names=False) res = mod.fit() c = res.params.iloc[0] seasons = np.zeros(12) seasons[1:] = res.params.iloc[1:-1] ar = res.params.iloc[-1] pred = res.predict(900, 1100, True) direct = np.zeros(201) direct[0] = y[899] * ar + c + seasons[900 % 12] for i in range(1, 201): direct[i] = direct[i - 1] * ar + c + seasons[(900 + i) % 12] direct = pd.Series( direct, index=pd.date_range(ys.index[900], periods=201, freq="M") ) assert_series_equal(pred, direct) pred = res.predict(900, dynamic=False) direct = y[899:-1] * ar + c + seasons[np.arange(900, 1001) % 12] direct = pd.Series( direct, index=pd.date_range(ys.index[900], periods=101, freq="M") ) assert_series_equal(pred, direct) def test_predict_exog(): rs = np.random.RandomState(12345678) e = rs.standard_normal(1001) y = np.empty(1001) x = rs.standard_normal((1001, 2)) y[:3] = e[:3] * np.sqrt(1.0 / (1 - 0.9 ** 2)) + x[:3].sum(1) for i in range(3, 1001): y[i] = 10 + 0.9 * y[i - 1] - 0.5 * y[i - 3] + e[i] + x[i].sum() ys = pd.Series(y, index=pd.date_range("1-1-1950", periods=1001, freq="M")) xdf = pd.DataFrame(x, columns=["x0", "x1"], index=ys.index) mod = AutoReg(ys, [1, 3], trend="c", exog=xdf, old_names=False) res = mod.fit() pred = res.predict(900) c = res.params.iloc[0] ar = res.params.iloc[1:3] ex = np.asarray(res.params.iloc[3:]) direct = c + ar[0] * y[899:-1] + ar[1] * y[897:-3] direct += ex[0] * x[900:, 0] + ex[1] * x[900:, 1] idx = pd.date_range(ys.index[900], periods=101, freq="M") direct = pd.Series(direct, index=idx) assert_series_equal(pred, direct) exog_oos = rs.standard_normal((100, 2)) pred = res.predict(900, 1100, dynamic=True, exog_oos=exog_oos) direct = np.zeros(201) direct[0] = c + ar[0] * y[899] + ar[1] * y[897] + x[900] @ ex direct[1] = c + ar[0] * direct[0] + ar[1] * y[898] + x[901] @ ex direct[2] = c + ar[0] * direct[1] + ar[1] * y[899] + x[902] @ ex for i in range(3, 201): direct[i] = c + ar[0] * direct[i - 1] + ar[1] * direct[i - 3] if 900 + i < x.shape[0]: direct[i] += x[900 + i] @ ex else: direct[i] += exog_oos[i - 101] @ ex direct = pd.Series( direct, index=pd.date_range(ys.index[900], periods=201, freq="M") ) assert_series_equal(pred, direct) def test_predict_irregular_ar(): rs = np.random.RandomState(12345678) e = rs.standard_normal(1001) y = np.empty(1001) y[:3] = e[:3] * np.sqrt(1.0 / (1 - 0.9 ** 2)) for i in range(3, 1001): y[i] = 10 + 0.9 * y[i - 1] - 0.5 * y[i - 3] + e[i] ys = pd.Series(y, index=pd.date_range("1-1-1950", periods=1001, freq="M")) mod = AutoReg(ys, [1, 3], trend="ct", old_names=False) res = mod.fit() c = res.params.iloc[0] t = res.params.iloc[1] ar = np.asarray(res.params.iloc[2:]) pred = res.predict(900, 1100, True) direct = np.zeros(201) direct[0] = c + t * 901 + ar[0] * y[899] + ar[1] * y[897] direct[1] = c + t * 902 + ar[0] * direct[0] + ar[1] * y[898] direct[2] = c + t * 903 + ar[0] * direct[1] + ar[1] * y[899] for i in range(3, 201): direct[i] = ( c + t * (901 + i) + ar[0] * direct[i - 1] + ar[1] * direct[i - 3] ) direct = pd.Series( direct, index=pd.date_range(ys.index[900], periods=201, freq="M") ) assert_series_equal(pred, direct) pred = res.predict(900) direct = ( c + t * np.arange(901, 901 + 101) + ar[0] * y[899:-1] + ar[1] * y[897:-3] ) idx = pd.date_range(ys.index[900], periods=101, freq="M") direct = pd.Series(direct, index=idx) assert_series_equal(pred, direct) @pytest.mark.parametrize("dynamic", [True, False]) def test_forecast_start_end_equiv(dynamic): rs = np.random.RandomState(12345678) e = rs.standard_normal(1001) y = np.empty(1001) y[0] = e[0] * np.sqrt(1.0 / (1 - 0.9 ** 2)) effects = 10 * np.cos(np.arange(12) / 11 * 2 * np.pi) for i in range(1, 1001): y[i] = 10 + 0.9 * y[i - 1] + e[i] + effects[i % 12] ys = pd.Series(y, index=pd.date_range("1-1-1950", periods=1001, freq="M")) mod = AutoReg(ys, 1, seasonal=True, old_names=False) res = mod.fit() pred_int = res.predict(1000, 1020, dynamic=dynamic) dates = pd.date_range("1-1-1950", periods=1021, freq="M") pred_dates = res.predict(dates[1000], dates[1020], dynamic=dynamic) assert_series_equal(pred_int, pred_dates) @pytest.mark.parametrize("start", [21, 25]) def test_autoreg_start(start): y_train = pd.Series(np.random.normal(size=20)) m = AutoReg(y_train, lags=2, old_names=False) mf = m.fit() end = start + 5 pred = mf.predict(start=start, end=end) assert pred.shape[0] == end - start + 1 def test_deterministic(reset_randomstate): y = pd.Series(np.random.normal(size=200)) terms = [TimeTrend(constant=True, order=1), Seasonality(12)] dp = DeterministicProcess(y.index, additional_terms=terms) m = AutoReg(y, trend="n", seasonal=False, lags=2, deterministic=dp) res = m.fit() m2 = AutoReg( y, trend="ct", seasonal=True, lags=2, period=12, old_names=False ) res2 = m2.fit() assert_almost_equal(np.asarray(res.params), np.asarray(res2.params)) with pytest.warns(RuntimeWarning, match="When using deterministic, trend"): AutoReg(y, trend="ct", seasonal=False, lags=2, deterministic=dp) def test_autoreg_predict_forecast_equiv(reset_randomstate): e = np.random.normal(size=1000) nobs = e.shape[0] idx = pd.date_range("2020-1-1", freq="D", periods=nobs) for i in range(1, nobs): e[i] = 0.95 * e[i - 1] + e[i] y = pd.Series(e, index=idx) m = AutoReg(y, trend="c", lags=1, old_names=False) res = m.fit() a = res.forecast(12) b = res.predict(nobs, nobs + 11) c = res.forecast("2022-10-08") assert_series_equal(a, b) assert_series_equal(a, c) sarimax_res = SARIMAX(y, order=(1, 0, 0), trend="c").fit(disp=False) d = sarimax_res.forecast(12) pd.testing.assert_index_equal(a.index, d.index) def test_autoreg_forecast_period_index(): pi = pd.period_range("1990-1-1", periods=524, freq="M") y = np.random.RandomState(0).standard_normal(500) ys = pd.Series(y, index=pi[:500], name="y") mod = AutoReg(ys, 3, seasonal=True, old_names=False) res = mod.fit() fcast = res.forecast(24) assert isinstance(fcast.index, pd.PeriodIndex) pd.testing.assert_index_equal(fcast.index, pi[-24:]) @pytest.mark.matplotlib def test_autoreg_plot_err(): y = np.random.standard_normal(100) mod = AutoReg(y, lags=[1, 3], old_names=False) res = mod.fit() with pytest.raises(ValueError): res.plot_predict(0, end=50, in_sample=False) statsmodels-0.12.2/statsmodels/tsa/tests/test_arima.py000066400000000000000000003215241400612667500231510ustar00rootroot00000000000000from statsmodels.compat.platform import (PLATFORM_OSX, PLATFORM_WIN, PLATFORM_WIN32) from statsmodels.compat.python import lrange import os import pickle import warnings from io import BytesIO import numpy as np import pandas as pd import pytest from numpy.testing import assert_almost_equal, assert_allclose, assert_raises from pandas import DatetimeIndex, date_range, period_range import statsmodels.sandbox.tsa.fftarma as fa from statsmodels.datasets.macrodata import load_pandas as load_macrodata_pandas from statsmodels.regression.linear_model import OLS from statsmodels.tools.sm_exceptions import ( ValueWarning, HessianInversionWarning, SpecificationWarning, MissingDataError) from statsmodels.tools.testing import assert_equal from statsmodels.tsa.ar_model import AutoReg from statsmodels.tsa.arima_model import ARMA, ARIMA from statsmodels.tsa.arima_process import arma_generate_sample from statsmodels.tsa.arma_mle import Arma from statsmodels.tsa.tests.results import results_arma, results_arima DECIMAL_4 = 4 DECIMAL_3 = 3 DECIMAL_2 = 2 DECIMAL_1 = 1 current_path = os.path.dirname(os.path.abspath(__file__)) ydata_path = os.path.join(current_path, 'results', 'y_arma_data.csv') with open(ydata_path, "rb") as fd: y_arma = np.genfromtxt(fd, delimiter=",", skip_header=1, dtype=float) cpi_dates = period_range(start='1959q1', end='2009q3', freq='Q') sun_dates = period_range(start='1700', end='2008', freq='A') cpi_predict_dates = period_range(start='2009q3', end='2015q4', freq='Q') sun_predict_dates = period_range(start='2008', end='2033', freq='A') def test_compare_arma(): # this is a preliminary test to compare arma_kf, arma_cond_ls # and arma_cond_mle # the results returned by the fit methods are incomplete # for now without random.seed np.random.seed(9876565) x = fa.ArmaFft([1, -0.5], [1., 0.4], 40).generate_sample(nsample=200, burnin=1000) modkf = ARMA(x, (1, 1)) reskf = modkf.fit(trend='nc', disp=-1) dres = reskf modc = Arma(x) resls = modc.fit(order=(1, 1)) rescm = modc.fit_mle(order=(1, 1), start_params=[0.4, 0.4, 1.], disp=0) # decimal 1 corresponds to threshold of 5% difference # still different sign corrcted assert_almost_equal(resls[0] / dres.params, np.ones(dres.params.shape), decimal=1) # rescm also contains variance estimate as last element of params assert_almost_equal(rescm.params[:-1] / dres.params, np.ones(dres.params.shape), decimal=1) class CheckArmaResultsMixin(object): """ res2 are the results from gretl. They are in results/results_arma. res1 are from statsmodels """ decimal_params = DECIMAL_4 def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, self.decimal_params) decimal_aic = DECIMAL_4 def test_aic(self): assert_almost_equal(self.res1.aic, self.res2.aic, self.decimal_aic) decimal_bic = DECIMAL_4 def test_bic(self): assert_almost_equal(self.res1.bic, self.res2.bic, self.decimal_bic) decimal_arroots = DECIMAL_4 def test_arroots(self): assert_almost_equal(self.res1.arroots, self.res2.arroots, self.decimal_arroots) decimal_maroots = DECIMAL_4 def test_maroots(self): assert_almost_equal(self.res1.maroots, self.res2.maroots, self.decimal_maroots) decimal_bse = DECIMAL_2 def test_bse(self): assert_almost_equal(self.res1.bse, self.res2.bse, self.decimal_bse) decimal_cov_params = DECIMAL_4 def test_covparams(self): assert_almost_equal(self.res1.cov_params(), self.res2.cov_params, self.decimal_cov_params) decimal_hqic = DECIMAL_4 def test_hqic(self): assert_almost_equal(self.res1.hqic, self.res2.hqic, self.decimal_hqic) decimal_llf = DECIMAL_4 def test_llf(self): assert_almost_equal(self.res1.llf, self.res2.llf, self.decimal_llf) decimal_resid = DECIMAL_4 def test_resid(self): assert_almost_equal(self.res1.resid, self.res2.resid, self.decimal_resid) decimal_fittedvalues = DECIMAL_4 def test_fittedvalues(self): assert_almost_equal(self.res1.fittedvalues, self.res2.fittedvalues, self.decimal_fittedvalues) decimal_pvalues = DECIMAL_2 def test_pvalues(self): assert_almost_equal(self.res1.pvalues, self.res2.pvalues, self.decimal_pvalues) decimal_t = DECIMAL_2 # only 2 decimal places in gretl output def test_tvalues(self): assert_almost_equal(self.res1.tvalues, self.res2.tvalues, self.decimal_t) decimal_sigma2 = DECIMAL_4 def test_sigma2(self): assert_almost_equal(self.res1.sigma2, self.res2.sigma2, self.decimal_sigma2) @pytest.mark.smoke def test_summary(self): self.res1.summary() @pytest.mark.smoke def test_summary2(self): self.res1.summary2() class CheckForecastMixin(object): decimal_forecast = DECIMAL_4 def test_forecast(self): assert_almost_equal(self.res1.forecast_res, self.res2.forecast, self.decimal_forecast) decimal_forecasterr = DECIMAL_4 def test_forecasterr(self): assert_almost_equal(self.res1.forecast_err, self.res2.forecasterr, self.decimal_forecasterr) class CheckDynamicForecastMixin(object): decimal_forecast_dyn = 4 def test_dynamic_forecast(self): assert_almost_equal(self.res1.forecast_res_dyn, self.res2.forecast_dyn, self.decimal_forecast_dyn) def test_forecasterr(self): assert_almost_equal(self.res1.forecast_err_dyn, self.res2.forecasterr_dyn, DECIMAL_4) class CheckArimaResultsMixin(CheckArmaResultsMixin): def test_order(self): assert self.res1.k_diff == self.res2.k_diff assert self.res1.k_ar == self.res2.k_ar assert self.res1.k_ma == self.res2.k_ma decimal_predict_levels = DECIMAL_4 def test_predict_levels(self): assert_almost_equal(self.res1.predict(typ='levels'), self.res2.linear, self.decimal_predict_levels) class Test_Y_ARMA11_NoConst(CheckArmaResultsMixin, CheckForecastMixin): @classmethod def setup_class(cls): endog = y_arma[:, 0] cls.res1 = ARMA(endog, order=(1, 1)).fit(trend='nc', disp=-1) (cls.res1.forecast_res, cls.res1.forecast_err, confint) = cls.res1.forecast(10) cls.res2 = results_arma.Y_arma11() def test_pickle(self): fh = BytesIO() # test wrapped results load save pickle self.res1.save(fh) fh.seek(0, 0) res_unpickled = self.res1.__class__.load(fh) assert type(res_unpickled) is type(self.res1) # noqa: E721 class Test_Y_ARMA14_NoConst(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 1] cls.res1 = ARMA(endog, order=(1, 4)).fit(trend='nc', disp=-1) cls.res2 = results_arma.Y_arma14() @pytest.mark.slow class Test_Y_ARMA41_NoConst(CheckArmaResultsMixin, CheckForecastMixin): @classmethod def setup_class(cls): endog = y_arma[:, 2] cls.res1 = ARMA(endog, order=(4, 1)).fit(trend='nc', disp=-1) (cls.res1.forecast_res, cls.res1.forecast_err, confint) = cls.res1.forecast(10) cls.res2 = results_arma.Y_arma41() cls.decimal_maroots = DECIMAL_3 class Test_Y_ARMA22_NoConst(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 3] cls.res1 = ARMA(endog, order=(2, 2)).fit(trend='nc', disp=-1) cls.res2 = results_arma.Y_arma22() class Test_Y_ARMA50_NoConst(CheckArmaResultsMixin, CheckForecastMixin): @classmethod def setup_class(cls): endog = y_arma[:, 4] cls.res1 = ARMA(endog, order=(5, 0)).fit(trend='nc', disp=-1) (cls.res1.forecast_res, cls.res1.forecast_err, confint) = cls.res1.forecast(10) cls.res2 = results_arma.Y_arma50() class Test_Y_ARMA02_NoConst(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 5] cls.res1 = ARMA(endog, order=(0, 2)).fit(trend='nc', disp=-1) cls.res2 = results_arma.Y_arma02() class Test_Y_ARMA11_Const(CheckArmaResultsMixin, CheckForecastMixin): @classmethod def setup_class(cls): endog = y_arma[:, 6] cls.res1 = ARMA(endog, order=(1, 1)).fit(trend="c", disp=-1) (cls.res1.forecast_res, cls.res1.forecast_err, confint) = cls.res1.forecast(10) cls.res2 = results_arma.Y_arma11c() class Test_Y_ARMA14_Const(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 7] cls.res1 = ARMA(endog, order=(1, 4)).fit(trend="c", disp=-1) cls.res2 = results_arma.Y_arma14c() class Test_Y_ARMA41_Const(CheckArmaResultsMixin, CheckForecastMixin): @classmethod def setup_class(cls): endog = y_arma[:, 8] cls.res2 = results_arma.Y_arma41c() cls.res1 = ARMA(endog, order=(4, 1)).fit(trend="c", disp=-1, start_params=cls.res2.params) (cls.res1.forecast_res, cls.res1.forecast_err, confint) = cls.res1.forecast(10) cls.decimal_cov_params = DECIMAL_3 cls.decimal_fittedvalues = DECIMAL_3 cls.decimal_resid = DECIMAL_3 cls.decimal_params = DECIMAL_3 class Test_Y_ARMA22_Const(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 9] cls.res1 = ARMA(endog, order=(2, 2)).fit(trend="c", disp=-1) cls.res2 = results_arma.Y_arma22c() def test_summary(self): # regression test for html of roots table #4434 # we ignore whitespace in the assert summ = self.res1.summary() summ_roots = """\ Roots RealImaginaryModulusFrequency AR.11.0991-1.2571j1.6698-0.1357 AR.21.0991+1.2571j1.66980.1357 MA.1-1.1702+0.0000j1.17020.5000 MA.21.2215+0.0000j1.22150.0000 """ assert_equal(summ.tables[2]._repr_html_().replace(' ', ''), summ_roots.replace(' ', '')) class Test_Y_ARMA50_Const(CheckArmaResultsMixin, CheckForecastMixin): @classmethod def setup_class(cls): endog = y_arma[:, 10] cls.res1 = ARMA(endog, order=(5, 0)).fit(trend="c", disp=-1) (cls.res1.forecast_res, cls.res1.forecast_err, confint) = cls.res1.forecast(10) cls.res2 = results_arma.Y_arma50c() class Test_Y_ARMA02_Const(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 11] cls.res1 = ARMA(endog, order=(0, 2)).fit(trend="c", disp=-1) cls.res2 = results_arma.Y_arma02c() # cov_params and tvalues are off still but not as much vs. R class Test_Y_ARMA11_NoConst_CSS(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 0] cls.res1 = ARMA(endog, order=(1, 1)).fit(method="css", trend='nc', disp=-1) cls.res2 = results_arma.Y_arma11("css") cls.decimal_t = DECIMAL_1 # better vs. R class Test_Y_ARMA14_NoConst_CSS(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 1] cls.res1 = ARMA(endog, order=(1, 4)).fit(method="css", trend='nc', disp=-1) cls.res2 = results_arma.Y_arma14("css") cls.decimal_fittedvalues = DECIMAL_3 cls.decimal_resid = DECIMAL_3 cls.decimal_t = DECIMAL_1 # bse, etc. better vs. R # maroot is off because maparams is off a bit (adjust tolerance?) class Test_Y_ARMA41_NoConst_CSS(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 2] cls.res1 = ARMA(endog, order=(4, 1)).fit(method="css", trend='nc', disp=-1) cls.res2 = results_arma.Y_arma41("css") cls.decimal_t = DECIMAL_1 cls.decimal_pvalues = 0 cls.decimal_cov_params = DECIMAL_3 cls.decimal_maroots = DECIMAL_1 # same notes as above class Test_Y_ARMA22_NoConst_CSS(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 3] cls.res1 = ARMA(endog, order=(2, 2)).fit(method="css", trend='nc', disp=-1) cls.res2 = results_arma.Y_arma22("css") cls.decimal_t = DECIMAL_1 cls.decimal_resid = DECIMAL_3 cls.decimal_pvalues = DECIMAL_1 cls.decimal_fittedvalues = DECIMAL_3 # NOTE: gretl just uses least squares for AR CSS # so BIC, etc. is # -2*res1.llf + np.log(nobs)*(res1.q+res1.p+res1.k) # with no adjustment for p and no extra sigma estimate # NOTE: so our tests use x-12 arima results which agree with us and are # consistent with the rest of the models class Test_Y_ARMA50_NoConst_CSS(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 4] cls.res1 = ARMA(endog, order=(5, 0)).fit(method="css", trend='nc', disp=-1) cls.res2 = results_arma.Y_arma50("css") cls.decimal_t = 0 cls.decimal_llf = DECIMAL_1 # looks like rounding error? class Test_Y_ARMA02_NoConst_CSS(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 5] cls.res1 = ARMA(endog, order=(0, 2)).fit(method="css", trend='nc', disp=-1) cls.res2 = results_arma.Y_arma02("css") # NOTE: our results are close to --x-12-arima option and R class Test_Y_ARMA11_Const_CSS(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 6] cls.res1 = ARMA(endog, order=(1, 1)).fit(trend="c", method="css", disp=-1) cls.res2 = results_arma.Y_arma11c("css") cls.decimal_params = DECIMAL_3 cls.decimal_cov_params = DECIMAL_3 cls.decimal_t = DECIMAL_1 class Test_Y_ARMA14_Const_CSS(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 7] cls.res1 = ARMA(endog, order=(1, 4)).fit(trend="c", method="css", disp=-1) cls.res2 = results_arma.Y_arma14c("css") cls.decimal_t = DECIMAL_1 cls.decimal_pvalues = DECIMAL_1 class Test_Y_ARMA41_Const_CSS(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 8] cls.res1 = ARMA(endog, order=(4, 1)).fit(trend="c", method="css", disp=-1) cls.res2 = results_arma.Y_arma41c("css") cls.decimal_t = DECIMAL_1 cls.decimal_cov_params = DECIMAL_1 cls.decimal_maroots = DECIMAL_3 cls.decimal_bse = DECIMAL_1 class Test_Y_ARMA22_Const_CSS(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 9] cls.res1 = ARMA(endog, order=(2, 2)).fit(trend="c", method="css", disp=-1) cls.res2 = results_arma.Y_arma22c("css") cls.decimal_t = 0 cls.decimal_pvalues = DECIMAL_1 class Test_Y_ARMA50_Const_CSS(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 10] cls.res1 = ARMA(endog, order=(5, 0)).fit(trend="c", method="css", disp=-1) cls.res2 = results_arma.Y_arma50c("css") cls.decimal_t = DECIMAL_1 cls.decimal_params = DECIMAL_3 cls.decimal_cov_params = DECIMAL_2 class Test_Y_ARMA02_Const_CSS(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 11] cls.res1 = ARMA(endog, order=(0, 2)).fit(trend="c", method="css", disp=-1) cls.res2 = results_arma.Y_arma02c("css") def test_reset_trend_error(): endog = y_arma[:, 0] mod = ARMA(endog, order=(1, 1)) mod.fit(trend="c", disp=-1) with pytest.raises(RuntimeError): mod.fit(trend="nc", disp=-1) @pytest.mark.slow def test_start_params_bug(): data = np.array([1368., 1187, 1090, 1439, 2362, 2783, 2869, 2512, 1804, 1544, 1028, 869, 1737, 2055, 1947, 1618, 1196, 867, 997, 1862, 2525, 3250, 4023, 4018, 3585, 3004, 2500, 2441, 2749, 2466, 2157, 1847, 1463, 1146, 851, 993, 1448, 1719, 1709, 1455, 1950, 1763, 2075, 2343, 3570, 4690, 3700, 2339, 1679, 1466, 998, 853, 835, 922, 851, 1125, 1299, 1105, 860, 701, 689, 774, 582, 419, 846, 1132, 902, 1058, 1341, 1551, 1167, 975, 786, 759, 751, 649, 876, 720, 498, 553, 459, 543, 447, 415, 377, 373, 324, 320, 306, 259, 220, 342, 558, 825, 994, 1267, 1473, 1601, 1896, 1890, 2012, 2198, 2393, 2825, 3411, 3406, 2464, 2891, 3685, 3638, 3746, 3373, 3190, 2681, 2846, 4129, 5054, 5002, 4801, 4934, 4903, 4713, 4745, 4736, 4622, 4642, 4478, 4510, 4758, 4457, 4356, 4170, 4658, 4546, 4402, 4183, 3574, 2586, 3326, 3948, 3983, 3997, 4422, 4496, 4276, 3467, 2753, 2582, 2921, 2768, 2789, 2824, 2482, 2773, 3005, 3641, 3699, 3774, 3698, 3628, 3180, 3306, 2841, 2014, 1910, 2560, 2980, 3012, 3210, 3457, 3158, 3344, 3609, 3327, 2913, 2264, 2326, 2596, 2225, 1767, 1190, 792, 669, 589, 496, 354, 246, 250, 323, 495, 924, 1536, 2081, 2660, 2814, 2992, 3115, 2962, 2272, 2151, 1889, 1481, 955, 631, 288, 103, 60, 82, 107, 185, 618, 1526, 2046, 2348, 2584, 2600, 2515, 2345, 2351, 2355, 2409, 2449, 2645, 2918, 3187, 2888, 2610, 2740, 2526, 2383, 2936, 2968, 2635, 2617, 2790, 3906, 4018, 4797, 4919, 4942, 4656, 4444, 3898, 3908, 3678, 3605, 3186, 2139, 2002, 1559, 1235, 1183, 1096, 673, 389, 223, 352, 308, 365, 525, 779, 894, 901, 1025, 1047, 981, 902, 759, 569, 519, 408, 263, 156, 72, 49, 31, 41, 192, 423, 492, 552, 564, 723, 921, 1525, 2768, 3531, 3824, 3835, 4294, 4533, 4173, 4221, 4064, 4641, 4685, 4026, 4323, 4585, 4836, 4822, 4631, 4614, 4326, 4790, 4736, 4104, 5099, 5154, 5121, 5384, 5274, 5225, 4899, 5382, 5295, 5349, 4977, 4597, 4069, 3733, 3439, 3052, 2626, 1939, 1064, 713, 916, 832, 658, 817, 921, 772, 764, 824, 967, 1127, 1153, 824, 912, 957, 990, 1218, 1684, 2030, 2119, 2233, 2657, 2652, 2682, 2498, 2429, 2346, 2298, 2129, 1829, 1816, 1225, 1010, 748, 627, 469, 576, 532, 475, 582, 641, 605, 699, 680, 714, 670, 666, 636, 672, 679, 446, 248, 134, 160, 178, 286, 413, 676, 1025, 1159, 952, 1398, 1833, 2045, 2072, 1798, 1799, 1358, 727, 353, 347, 844, 1377, 1829, 2118, 2272, 2745, 4263, 4314, 4530, 4354, 4645, 4547, 5391, 4855, 4739, 4520, 4573, 4305, 4196, 3773, 3368, 2596, 2596, 2305, 2756, 3747, 4078, 3415, 2369, 2210, 2316, 2263, 2672, 3571, 4131, 4167, 4077, 3924, 3738, 3712, 3510, 3182, 3179, 2951, 2453, 2078, 1999, 2486, 2581, 1891, 1997, 1366, 1294, 1536, 2794, 3211, 3242, 3406, 3121, 2425, 2016, 1787, 1508, 1304, 1060, 1342, 1589, 2361, 3452, 2659, 2857, 3255, 3322, 2852, 2964, 3132, 3033, 2931, 2636, 2818, 3310, 3396, 3179, 3232, 3543, 3759, 3503, 3758, 3658, 3425, 3053, 2620, 1837, 923, 712, 1054, 1376, 1556, 1498, 1523, 1088, 728, 890, 1413, 2524, 3295, 4097, 3993, 4116, 3874, 4074, 4142, 3975, 3908, 3907, 3918, 3755, 3648, 3778, 4293, 4385, 4360, 4352, 4528, 4365, 3846, 4098, 3860, 3230, 2820, 2916, 3201, 3721, 3397, 3055, 2141, 1623, 1825, 1716, 2232, 2939, 3735, 4838, 4560, 4307, 4975, 5173, 4859, 5268, 4992, 5100, 5070, 5270, 4760, 5135, 5059, 4682, 4492, 4933, 4737, 4611, 4634, 4789, 4811, 4379, 4689, 4284, 4191, 3313, 2770, 2543, 3105, 2967, 2420, 1996, 2247, 2564, 2726, 3021, 3427, 3509, 3759, 3324, 2988, 2849, 2340, 2443, 2364, 1252, 623, 742, 867, 684, 488, 348, 241, 187, 279, 355, 423, 678, 1375, 1497, 1434, 2116, 2411, 1929, 1628, 1635, 1609, 1757, 2090, 2085, 1790, 1846, 2038, 2360, 2342, 2401, 2920, 3030, 3132, 4385, 5483, 5865, 5595, 5485, 5727, 5553, 5560, 5233, 5478, 5159, 5155, 5312, 5079, 4510, 4628, 4535, 3656, 3698, 3443, 3146, 2562, 2304, 2181, 2293, 1950, 1930, 2197, 2796, 3441, 3649, 3815, 2850, 4005, 5305, 5550, 5641, 4717, 5131, 2831, 3518, 3354, 3115, 3515, 3552, 3244, 3658, 4407, 4935, 4299, 3166, 3335, 2728, 2488, 2573, 2002, 1717, 1645, 1977, 2049, 2125, 2376, 2551, 2578, 2629, 2750, 3150, 3699, 4062, 3959, 3264, 2671, 2205, 2128, 2133, 2095, 1964, 2006, 2074, 2201, 2506, 2449, 2465, 2064, 1446, 1382, 983, 898, 489, 319, 383, 332, 276, 224, 144, 101, 232, 429, 597, 750, 908, 960, 1076, 951, 1062, 1183, 1404, 1391, 1419, 1497, 1267, 963, 682, 777, 906, 1149, 1439, 1600, 1876, 1885, 1962, 2280, 2711, 2591, 2411]) with warnings.catch_warnings(): warnings.simplefilter("ignore") ARMA(data, order=(4, 1)).fit(start_ar_lags=5, disp=-1) class Test_ARIMA101(CheckArmaResultsMixin): @classmethod def setup_class(cls): endog = y_arma[:, 6] cls.res1 = ARIMA(endog, (1, 0, 1)).fit(trend="c", disp=-1) (cls.res1.forecast_res, cls.res1.forecast_err, confint) = cls.res1.forecast(10) cls.res2 = results_arma.Y_arma11c() cls.res2.k_diff = 0 cls.res2.k_ar = 1 cls.res2.k_ma = 1 class Test_ARIMA111(CheckArimaResultsMixin, CheckForecastMixin, CheckDynamicForecastMixin): @classmethod def setup_class(cls): cpi = load_macrodata_pandas().data['cpi'].values cls.res1 = ARIMA(cpi, (1, 1, 1)).fit(disp=-1) cls.res2 = results_arima.ARIMA111() # make sure endog names changes to D.cpi cls.decimal_llf = 3 cls.decimal_aic = 3 cls.decimal_bic = 3 # TODO: why has dec_cov_params changed, used to be better cls.decimal_cov_params = 2 cls.decimal_t = 0 (cls.res1.forecast_res, cls.res1.forecast_err, conf_int) = cls.res1.forecast(25) # TODO: fix the indexing for the end here, I do not think this is right # if we're going to treat it like indexing # the forecast from 2005Q1 through 2009Q4 is indices # 184 through 227 not 226 # note that the first one counts in the count so 164 + 64 is 65 # predictions cls.res1.forecast_res_dyn = cls.res1.predict(start=164, end=164 + 63, typ='levels', dynamic=True) def test_freq(self): assert_almost_equal(self.res1.arfreq, [0.0000], 4) assert_almost_equal(self.res1.mafreq, [0.0000], 4) class Test_ARIMA111CSS(CheckArimaResultsMixin, CheckForecastMixin, CheckDynamicForecastMixin): @classmethod def setup_class(cls): cpi = load_macrodata_pandas().data['cpi'].values cls.res1 = ARIMA(cpi, (1, 1, 1)).fit(disp=-1, method='css') cls.res2 = results_arima.ARIMA111(method='css') cls.res2.fittedvalues = - cpi[1:-1] + cls.res2.linear # make sure endog names changes to D.cpi (cls.res1.forecast_res, cls.res1.forecast_err, conf_int) = cls.res1.forecast(25) cls.decimal_forecast = 2 cls.decimal_forecast_dyn = 2 cls.decimal_forecasterr = 3 cls.res1.forecast_res_dyn = cls.res1.predict(start=164, end=164 + 63, typ='levels', dynamic=True) # precisions cls.decimal_arroots = 3 cls.decimal_cov_params = 3 cls.decimal_hqic = 3 cls.decimal_maroots = 3 cls.decimal_t = 1 cls.decimal_fittedvalues = 2 # because of rounding when copying cls.decimal_resid = 2 cls.decimal_predict_levels = DECIMAL_2 class Test_ARIMA112CSS(CheckArimaResultsMixin): @classmethod def setup_class(cls): cpi = load_macrodata_pandas().data['cpi'].values cls.res1 = ARIMA(cpi, (1, 1, 2)).fit(disp=-1, method='css', start_params=[.905322, -.692425, 1.07366, 0.172024]) cls.res2 = results_arima.ARIMA112(method='css') cls.res2.fittedvalues = - cpi[1:-1] + cls.res2.linear # make sure endog names changes to D.cpi cls.decimal_llf = 3 cls.decimal_aic = 3 cls.decimal_bic = 3 # TODO: fix the indexing for the end here, I do not think this is right # if we're going to treat it like indexing # the forecast from 2005Q1 through 2009Q4 is indices # 184 through 227 not 226 # note that the first one counts in the count so 164 + 64 is 65 # predictions # cls.res1.forecast_res_dyn = self.predict(start=164, end=164+63, # typ='levels', dynamic=True) # since we got from gretl do not have linear prediction in differences cls.decimal_arroots = 3 cls.decimal_maroots = 2 cls.decimal_t = 1 cls.decimal_resid = 2 cls.decimal_fittedvalues = 3 cls.decimal_predict_levels = DECIMAL_3 def test_freq(self): assert_almost_equal(self.res1.arfreq, [0.5000], 4) assert_almost_equal(self.res1.mafreq, [0.5000, 0.5000], 4) def test_arima_predict_mle_dates(): cpi = load_macrodata_pandas().data['cpi'].values res1 = ARIMA(cpi, (4, 1, 1), dates=cpi_dates, freq='Q').fit(disp=-1) file_path = os.path.join(current_path, 'results', 'results_arima_forecasts_all_mle.csv') with open(file_path, "rb") as test_data: arima_forecasts = np.genfromtxt(test_data, delimiter=",", skip_header=1, dtype=float) fc = arima_forecasts[:, 0] fcdyn = arima_forecasts[:, 1] fcdyn2 = arima_forecasts[:, 2] start, end = 2, 51 fv = res1.predict('1959Q3', '1971Q4', typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) assert_equal(res1.data.predict_dates, cpi_dates[start:end + 1]) start, end = 202, 227 fv = res1.predict('2009Q3', '2015Q4', typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) assert_equal(res1.data.predict_dates, cpi_predict_dates) # make sure dynamic works start, end = '1960q2', '1971q4' fv = res1.predict(start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn[5:51 + 1], DECIMAL_4) start, end = '1965q1', '2015q4' fv = res1.predict(start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn2[24:227 + 1], DECIMAL_4) def test_arma_predict_mle_dates(): from statsmodels.datasets.sunspots import load_pandas sunspots = load_pandas().data['SUNACTIVITY'].values mod = ARMA(sunspots, (9, 0), dates=sun_dates, freq='A') mod.method = 'mle' assert_raises(ValueError, mod._get_prediction_index, '1701', '1751', True) start, end = 2, 51 mod._get_prediction_index('1702', '1751', False) assert_equal(mod.data.predict_dates, sun_dates[start:end + 1]) start, end = 308, 333 mod._get_prediction_index('2008', '2033', False) assert_equal(mod.data.predict_dates, sun_predict_dates) def test_arima_predict_css_dates(): cpi = load_macrodata_pandas().data['cpi'].values res1 = ARIMA(cpi, (4, 1, 1), dates=cpi_dates, freq='Q').fit(disp=-1, method='css', trend='nc') params = np.array([1.231272508473910, -0.282516097759915, 0.170052755782440, -0.118203728504945, -0.938783134717947]) file_path = os.path.join(current_path, 'results', 'results_arima_forecasts_all_css.csv') with open(file_path, "rb") as test_data: arima_forecasts = np.genfromtxt(test_data, delimiter=",", skip_header=1, dtype=float) fc = arima_forecasts[:, 0] fcdyn = arima_forecasts[:, 1] fcdyn2 = arima_forecasts[:, 2] start, end = 5, 51 fv = res1.model.predict(params, '1960Q2', '1971Q4', typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) assert_equal(res1.data.predict_dates, cpi_dates[start:end + 1]) start, end = 202, 227 fv = res1.model.predict(params, '2009Q3', '2015Q4', typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) assert_equal(res1.data.predict_dates, cpi_predict_dates) # make sure dynamic works start, end = 5, 51 fv = res1.model.predict(params, '1960Q2', '1971Q4', typ='levels', dynamic=True) assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4) start, end = '1965q1', '2015q4' fv = res1.model.predict(params, start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn2[24:227 + 1], DECIMAL_4) def test_arma_predict_css_dates(): from statsmodels.datasets.sunspots import load_pandas sunspots = load_pandas().data['SUNACTIVITY'].values mod = ARMA(sunspots, (9, 0), dates=sun_dates, freq='A') mod.method = 'css' assert_raises(ValueError, mod._get_prediction_index, '1701', '1751', False) def test_arima_predict_mle(): cpi = load_macrodata_pandas().data['cpi'].values res1 = ARIMA(cpi, (4, 1, 1)).fit(disp=-1) # fit the model so that we get correct endog length but use file_path = os.path.join(current_path, 'results', 'results_arima_forecasts_all_mle.csv') with open(file_path, "rb") as test_data: arima_forecasts = np.genfromtxt(test_data, delimiter=",", skip_header=1, dtype=float) fc = arima_forecasts[:, 0] fcdyn = arima_forecasts[:, 1] fcdyn2 = arima_forecasts[:, 2] fcdyn3 = arima_forecasts[:, 3] fcdyn4 = arima_forecasts[:, 4] # 0 indicates the first sample-observation below # ie., the index after the pre-sample, these are also differenced once # so the indices are moved back once from the cpi in levels # start < p, end

0 1959q3 - 1971q4 start, end = 2, 51 fv = res1.predict(start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start < p, end nobs 1959q3 - 2009q3 start, end = 2, 202 fv = res1.predict(start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start < p, end >nobs 1959q3 - 2015q4 start, end = 2, 227 fv = res1.predict(start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start 0, end >0 1960q1 - 1971q4 start, end = 4, 51 fv = res1.predict(start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start 0, end nobs 1960q1 - 2009q3 start, end = 4, 202 fv = res1.predict(start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start 0, end >nobs 1960q1 - 2015q4 start, end = 4, 227 fv = res1.predict(start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >p, end >0 1965q1 - 1971q4 start, end = 24, 51 fv = res1.predict(start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >p, end nobs 1965q1 - 2009q3 start, end = 24, 202 fv = res1.predict(start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >p, end >nobs 1965q1 - 2015q4 start, end = 24, 227 fv = res1.predict(start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start nobs, end nobs 2009q3 - 2009q3 start, end = 202, 202 fv = res1.predict(start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_3) # start nobs, end >nobs 2009q3 - 2015q4 start, end = 202, 227 fv = res1.predict(start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_3) # start >nobs, end >nobs 2009q4 - 2015q4 start, end = 203, 227 fv = res1.predict(start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # defaults start, end = None, None fv = res1.predict(start, end, typ='levels') assert_almost_equal(fv, fc[1:203], DECIMAL_4) # Dynamic # start < p, end

0 1959q3 - 1971q4 start, end = 2, 51 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.predict(start, end, dynamic=True, typ='levels') # start < p, end nobs 1959q3 - 2009q3 start, end = 2, 202 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.predict(start, end, dynamic=True, typ='levels') # start < p, end >nobs 1959q3 - 2015q4 start, end = 2, 227 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.predict(start, end, dynamic=True, typ='levels') # start 0, end >0 1960q1 - 1971q4 start, end = 5, 51 fv = res1.predict(start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4) # start 0, end nobs 1960q1 - 2009q3 start, end = 5, 202 fv = res1.predict(start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4) # start 0, end >nobs 1960q1 - 2015q4 start, end = 5, 227 fv = res1.predict(start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4) # start >p, end >0 1965q1 - 1971q4 start, end = 24, 51 fv = res1.predict(start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4) # start >p, end nobs 1965q1 - 2009q3 start, end = 24, 202 fv = res1.predict(start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4) # start >p, end >nobs 1965q1 - 2015q4 start, end = 24, 227 fv = res1.predict(start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4) # start nobs, end nobs 2009q3 - 2009q3 start, end = 202, 202 fv = res1.predict(start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn3[start:end + 1], DECIMAL_4) # start nobs, end >nobs 2009q3 - 2015q4 start, end = 202, 227 fv = res1.predict(start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn3[start:end + 1], DECIMAL_4) # start >nobs, end >nobs 2009q4 - 2015q4 start, end = 203, 227 fv = res1.predict(start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn4[start:end + 1], DECIMAL_4) # defaults start, end = None, None fv = res1.predict(start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn[5:203], DECIMAL_4) def _check_start(model, given, expected, dynamic): start, _, _, _ = model._get_prediction_index(given, None, dynamic) assert_equal(start, expected) def _check_end(model, given, end_expect, out_of_sample_expect): _, end, out_of_sample, _ = model._get_prediction_index(None, given, False) assert_equal((end, out_of_sample), (end_expect, out_of_sample_expect)) def test_arma_predict_indices(): from statsmodels.datasets.sunspots import load_pandas sunspots = load_pandas().data['SUNACTIVITY'].values model = ARMA(sunspots, (9, 0), dates=sun_dates, freq='A') model.method = 'mle' # raises - pre-sample + dynamic with pytest.raises(ValueError): model._get_prediction_index(0, None, True) with pytest.raises(ValueError): model._get_prediction_index(8, None, True) with pytest.raises(ValueError): model._get_prediction_index('1700', None, True) with pytest.raises(ValueError): model._get_prediction_index('1708', None, True) # raises - start out of sample # works - in-sample # None start_test_cases = [ # given, expected, dynamic (None, 9, True), # all start get moved back by k_diff (9, 9, True), (10, 10, True), # what about end of sample start - last value is first # forecast (309, 309, True), (308, 308, True), (0, 0, False), (1, 1, False), (4, 4, False), # all start get moved back by k_diff ('1709', 9, True), ('1710', 10, True), # what about end of sample start - last value is first # forecast ('2008', 308, True), ('2009', 309, True), ('1700', 0, False), ('1708', 8, False), ('1709', 9, False), ] for case in start_test_cases: _check_start(*((model,) + case)) # the length of sunspot is 309, so last index is 208 end_test_cases = [(None, 308, 0), (307, 307, 0), (308, 308, 0), (309, 308, 1), (312, 308, 4), (51, 51, 0), (333, 308, 25), ('2007', 307, 0), ('2008', 308, 0), ('2009', 308, 1), ('2012', 308, 4), ('1815', 115, 0), ('2033', 308, 25), ] for case in end_test_cases: _check_end(*((model,) + case)) def test_arima_predict_indices(): cpi = load_macrodata_pandas().data['cpi'].values model = ARIMA(cpi, (4, 1, 1), dates=cpi_dates, freq='Q') model.method = 'mle' # starting indices # raises - pre-sample + dynamic with pytest.raises(ValueError): model._get_prediction_index(0, None, True) with pytest.raises(ValueError): model._get_prediction_index(4, None, True) with pytest.raises(KeyError): model._get_prediction_index('1959Q1', None, True) with pytest.raises(ValueError): model._get_prediction_index('1960Q1', None, True) # raises - index differenced away with pytest.raises(ValueError): model._get_prediction_index(0, None, False) with pytest.raises(KeyError): model._get_prediction_index('1959Q1', None, False) # raises - start out of sample # works - in-sample # None start_test_cases = [ # given, expected, dynamic (None, 4, True), # all start get moved back by k_diff (5, 4, True), (6, 5, True), # what about end of sample start - last value is first # forecast (203, 202, True), (1, 0, False), (4, 3, False), (5, 4, False), # all start get moved back by k_diff ('1960Q2', 4, True), ('1960Q3', 5, True), # what about end of sample start - last value is first # forecast ('2009Q4', 202, True), ('1959Q2', 0, False), ('1960Q1', 3, False), ('1960Q2', 4, False), ] for case in start_test_cases: _check_start(*((model,) + case)) # TODO: make sure dates are passing through unmolested # the length of diff(cpi) is 202, so last index is 201 end_test_cases = [(None, 201, 0), (201, 200, 0), (202, 201, 0), (203, 201, 1), (204, 201, 2), (51, 50, 0), (164 + 63, 201, 25), ('2009Q2', 200, 0), ('2009Q3', 201, 0), ('2009Q4', 201, 1), ('2010Q1', 201, 2), ('1971Q4', 50, 0), ('2015Q4', 201, 25), ] for case in end_test_cases: _check_end(*((model,) + case)) # check higher k_diff # model.k_diff = 2 model = ARIMA(cpi, (4, 2, 1), dates=cpi_dates, freq='Q') model.method = 'mle' # raises - pre-sample + dynamic assert_raises(ValueError, model._get_prediction_index, 0, None, True) assert_raises(ValueError, model._get_prediction_index, 5, None, True) assert_raises(KeyError, model._get_prediction_index, '1959Q1', None, True) assert_raises(ValueError, model._get_prediction_index, '1960Q1', None, True) # raises - index differenced away assert_raises(ValueError, model._get_prediction_index, 1, None, False) assert_raises(KeyError, model._get_prediction_index, '1959Q2', None, False) start_test_cases = [(None, 4, True), # all start get moved back by k_diff (6, 4, True), # what about end of sample start - last value is first # forecast (203, 201, True), (2, 0, False), (4, 2, False), (5, 3, False), ('1960Q3', 4, True), # what about end of sample start - last value is first # forecast ('2009Q4', 201, True), ('2009Q4', 201, True), ('1959Q3', 0, False), ('1960Q1', 2, False), ('1960Q2', 3, False), ] for case in start_test_cases: _check_start(*((model,) + case)) end_test_cases = [(None, 200, 0), (201, 199, 0), (202, 200, 0), (203, 200, 1), (204, 200, 2), (51, 49, 0), (164 + 63, 200, 25), ('2009Q2', 199, 0), ('2009Q3', 200, 0), ('2009Q4', 200, 1), ('2010Q1', 200, 2), ('1971Q4', 49, 0), ('2015Q4', 200, 25), ] for case in end_test_cases: _check_end(*((model,) + case)) def test_arima_predict_indices_css(): cpi = load_macrodata_pandas().data['cpi'].values # NOTE: Doing no-constant for now to kick the conditional exogenous # issue 274 down the road # go ahead and git the model to set up necessary variables model = ARIMA(cpi, (4, 1, 1)) model.method = 'css' assert_raises(ValueError, model._get_prediction_index, 0, None, False) assert_raises(ValueError, model._get_prediction_index, 0, None, True) assert_raises(ValueError, model._get_prediction_index, 2, None, False) assert_raises(ValueError, model._get_prediction_index, 2, None, True) def test_arima_predict_css(): cpi = load_macrodata_pandas().data['cpi'].values # NOTE: Doing no-constant for now to kick the conditional exogenous # issue 274 down the road # go ahead and git the model to set up necessary variables res1 = ARIMA(cpi, (4, 1, 1)).fit(disp=-1, method="css", trend="nc") # but use gretl parameters to predict to avoid precision problems params = np.array([1.231272508473910, -0.282516097759915, 0.170052755782440, -0.118203728504945, -0.938783134717947]) file_path = os.path.join(current_path, 'results', 'results_arima_forecasts_all_css.csv') with open(file_path, "rb") as test_data: arima_forecasts = np.genfromtxt(test_data, delimiter=",", skip_header=1, dtype=float) fc = arima_forecasts[:, 0] fcdyn = arima_forecasts[:, 1] fcdyn2 = arima_forecasts[:, 2] fcdyn3 = arima_forecasts[:, 3] fcdyn4 = arima_forecasts[:, 4] start, end = 1, 3 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.model.predict(params, start, end) # start < p, end 0 1959q3 - 1960q1 start, end = 2, 4 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.model.predict(params, start, end) # start < p, end >0 1959q3 - 1971q4 start, end = 2, 51 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.model.predict(params, start, end) # start < p, end nobs 1959q3 - 2009q3 start, end = 2, 202 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.model.predict(params, start, end) # start < p, end >nobs 1959q3 - 2015q4 start, end = 2, 227 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.model.predict(params, start, end) # start 0, end >0 1960q1 - 1971q4 start, end = 5, 51 fv = res1.model.predict(params, start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start 0, end nobs 1960q1 - 2009q3 start, end = 5, 202 fv = res1.model.predict(params, start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start 0, end >nobs 1960q1 - 2015q4 # TODO: why detoriating precision? fv = res1.model.predict(params, start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >p, end >0 1965q1 - 1971q4 start, end = 24, 51 fv = res1.model.predict(params, start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >p, end nobs 1965q1 - 2009q3 start, end = 24, 202 fv = res1.model.predict(params, start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >p, end >nobs 1965q1 - 2015q4 start, end = 24, 227 fv = res1.model.predict(params, start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start nobs, end nobs 2009q3 - 2009q3 start, end = 202, 202 fv = res1.model.predict(params, start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start nobs, end >nobs 2009q3 - 2015q4 start, end = 202, 227 fv = res1.model.predict(params, start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >nobs, end >nobs 2009q4 - 2015q4 start, end = 203, 227 fv = res1.model.predict(params, start, end, typ='levels') assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # defaults start, end = None, None fv = res1.model.predict(params, start, end, typ='levels') assert_almost_equal(fv, fc[5:203], DECIMAL_4) # Dynamic # start < p, end

0 1959q3 - 1971q4 start, end = 2, 51 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.predict(start, end, dynamic=True) # start < p, end nobs 1959q3 - 2009q3 start, end = 2, 202 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.predict(start, end, dynamic=True) # start < p, end >nobs 1959q3 - 2015q4 start, end = 2, 227 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.predict(start, end, dynamic=True) # start 0, end >0 1960q1 - 1971q4 start, end = 5, 51 fv = res1.model.predict(params, start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4) # start 0, end nobs 1960q1 - 2009q3 start, end = 5, 202 fv = res1.model.predict(params, start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4) # start 0, end >nobs 1960q1 - 2015q4 start, end = 5, 227 fv = res1.model.predict(params, start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4) # start >p, end >0 1965q1 - 1971q4 start, end = 24, 51 fv = res1.model.predict(params, start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4) # start >p, end nobs 1965q1 - 2009q3 start, end = 24, 202 fv = res1.model.predict(params, start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4) # start >p, end >nobs 1965q1 - 2015q4 start, end = 24, 227 fv = res1.model.predict(params, start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4) # start nobs, end nobs 2009q3 - 2009q3 start, end = 202, 202 fv = res1.model.predict(params, start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn3[start:end + 1], DECIMAL_4) # start nobs, end >nobs 2009q3 - 2015q4 start, end = 202, 227 fv = res1.model.predict(params, start, end, dynamic=True, typ='levels') # start >nobs, end >nobs 2009q4 - 2015q4 start, end = 203, 227 fv = res1.model.predict(params, start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn4[start:end + 1], DECIMAL_4) # defaults start, end = None, None fv = res1.model.predict(params, start, end, dynamic=True, typ='levels') assert_almost_equal(fv, fcdyn[5:203], DECIMAL_4) def test_arima_predict_css_diffs(): cpi = load_macrodata_pandas().data['cpi'].values # NOTE: Doing no-constant for now to kick the conditional exogenous # issue 274 down the road # go ahead and git the model to set up necessary variables res1 = ARIMA(cpi, (4, 1, 1)).fit(disp=-1, method="css", trend="c") # but use gretl parameters to predict to avoid precision problems params = np.array([0.78349893861244, -0.533444105973324, 0.321103691668809, 0.264012463189186, 0.107888256920655, 0.920132542916995]) # we report mean, should we report constant? params[0] = params[0] / (1 - params[1:5].sum()) file_path = os.path.join(current_path, 'results', 'results_arima_forecasts_all_css_diff.csv') with open(file_path, "rb") as test_data: arima_forecasts = np.genfromtxt(test_data, delimiter=",", skip_header=1, dtype=float) fc = arima_forecasts[:, 0] fcdyn = arima_forecasts[:, 1] fcdyn2 = arima_forecasts[:, 2] fcdyn3 = arima_forecasts[:, 3] fcdyn4 = arima_forecasts[:, 4] start, end = 1, 3 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.model.predict(params, start, end) # start < p, end 0 1959q3 - 1960q1 start, end = 2, 4 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.model.predict(params, start, end) # start < p, end >0 1959q3 - 1971q4 start, end = 2, 51 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.model.predict(params, start, end) # start < p, end nobs 1959q3 - 2009q3 start, end = 2, 202 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.model.predict(params, start, end) # start < p, end >nobs 1959q3 - 2015q4 start, end = 2, 227 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.model.predict(params, start, end) # start 0, end >0 1960q1 - 1971q4 start, end = 5, 51 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start 0, end nobs 1960q1 - 2009q3 start, end = 5, 202 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start 0, end >nobs 1960q1 - 2015q4 # TODO: why detoriating precision? fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >p, end >0 1965q1 - 1971q4 start, end = 24, 51 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >p, end nobs 1965q1 - 2009q3 start, end = 24, 202 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >p, end >nobs 1965q1 - 2015q4 start, end = 24, 227 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start nobs, end nobs 2009q3 - 2009q3 start, end = 202, 202 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start nobs, end >nobs 2009q3 - 2015q4 start, end = 202, 227 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >nobs, end >nobs 2009q4 - 2015q4 start, end = 203, 227 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # defaults start, end = None, None fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[5:203], DECIMAL_4) # Dynamic # start < p, end

0 1959q3 - 1971q4 start, end = 2, 51 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.predict(start, end, dynamic=True) # start < p, end nobs 1959q3 - 2009q3 start, end = 2, 202 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.predict(start, end, dynamic=True) # start < p, end >nobs 1959q3 - 2015q4 start, end = 2, 227 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.predict(start, end, dynamic=True) # start 0, end >0 1960q1 - 1971q4 start, end = 5, 51 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4) # start 0, end nobs 1960q1 - 2009q3 start, end = 5, 202 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4) # start 0, end >nobs 1960q1 - 2015q4 start, end = 5, 227 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4) # start >p, end >0 1965q1 - 1971q4 start, end = 24, 51 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4) # start >p, end nobs 1965q1 - 2009q3 start, end = 24, 202 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4) # start >p, end >nobs 1965q1 - 2015q4 start, end = 24, 227 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4) # start nobs, end nobs 2009q3 - 2009q3 start, end = 202, 202 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn3[start:end + 1], DECIMAL_4) # start nobs, end >nobs 2009q3 - 2015q4 start, end = 202, 227 fv = res1.model.predict(params, start, end, dynamic=True) # start >nobs, end >nobs 2009q4 - 2015q4 start, end = 203, 227 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn4[start:end + 1], DECIMAL_4) # defaults start, end = None, None fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn[5:203], DECIMAL_4) def test_arima_predict_mle_diffs(): cpi = load_macrodata_pandas().data['cpi'].values # NOTE: Doing no-constant for now to kick the conditional exogenous # issue 274 down the road # go ahead and git the model to set up necessary variables res1 = ARIMA(cpi, (4, 1, 1)).fit(disp=-1, trend="c") # but use gretl parameters to predict to avoid precision problems params = np.array([0.926875951549299, -0.555862621524846, 0.320865492764400, 0.252253019082800, 0.113624958031799, 0.939144026934634]) file_path = os.path.join(current_path, 'results', 'results_arima_forecasts_all_mle_diff.csv') with open(file_path, "rb") as test_data: arima_forecasts = np.genfromtxt(test_data, delimiter=",", skip_header=1, dtype=float) fc = arima_forecasts[:, 0] fcdyn = arima_forecasts[:, 1] fcdyn2 = arima_forecasts[:, 2] fcdyn3 = arima_forecasts[:, 3] fcdyn4 = arima_forecasts[:, 4] start, end = 1, 3 res1.model.predict(params, start, end) # start < p, end 0 1959q3 - 1960q1 start, end = 2, 4 res1.model.predict(params, start, end) # start < p, end >0 1959q3 - 1971q4 start, end = 2, 51 res1.model.predict(params, start, end) # start < p, end nobs 1959q3 - 2009q3 start, end = 2, 202 res1.model.predict(params, start, end) # start < p, end >nobs 1959q3 - 2015q4 start, end = 2, 227 res1.model.predict(params, start, end) # start 0, end >0 1960q1 - 1971q4 start, end = 5, 51 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start 0, end nobs 1960q1 - 2009q3 start, end = 5, 202 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start 0, end >nobs 1960q1 - 2015q4 # TODO: why detoriating precision? fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >p, end >0 1965q1 - 1971q4 start, end = 24, 51 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >p, end nobs 1965q1 - 2009q3 start, end = 24, 202 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >p, end >nobs 1965q1 - 2015q4 start, end = 24, 227 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start nobs, end nobs 2009q3 - 2009q3 start, end = 202, 202 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start nobs, end >nobs 2009q3 - 2015q4 start, end = 202, 227 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # start >nobs, end >nobs 2009q4 - 2015q4 start, end = 203, 227 fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4) # defaults start, end = None, None fv = res1.model.predict(params, start, end) assert_almost_equal(fv, fc[1:203], DECIMAL_4) # Dynamic # NOTE: should raise # start < p, end

0 1959q3 - 1971q4 start, end = 2, 51 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.predict(start, end, dynamic=True) # start < p, end nobs 1959q3 - 2009q3 start, end = 2, 202 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.predict(start, end, dynamic=True) # start < p, end >nobs 1959q3 - 2015q4 start, end = 2, 227 with pytest.raises(ValueError, match='Start must be >= k_ar'): res1.predict(start, end, dynamic=True) # start 0, end >0 1960q1 - 1971q4 start, end = 5, 51 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4) # start 0, end nobs 1960q1 - 2009q3 start, end = 5, 202 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4) # start 0, end >nobs 1960q1 - 2015q4 start, end = 5, 227 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4) # start >p, end >0 1965q1 - 1971q4 start, end = 24, 51 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4) # start >p, end nobs 1965q1 - 2009q3 start, end = 24, 202 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4) # start >p, end >nobs 1965q1 - 2015q4 start, end = 24, 227 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4) # start nobs, end nobs 2009q3 - 2009q3 start, end = 202, 202 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn3[start:end + 1], DECIMAL_4) # start nobs, end >nobs 2009q3 - 2015q4 start, end = 202, 227 fv = res1.model.predict(params, start, end, dynamic=True) # start >nobs, end >nobs 2009q4 - 2015q4 start, end = 203, 227 fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn4[start:end + 1], DECIMAL_4) # defaults start, end = None, None fv = res1.model.predict(params, start, end, dynamic=True) assert_almost_equal(fv, fcdyn[5:203], DECIMAL_4) def test_arima_wrapper(): cpi = load_macrodata_pandas().data['cpi'] cpi.index = pd.Index(cpi_dates) res = ARIMA(cpi, (4, 1, 1), freq='Q').fit(disp=-1) assert_equal(res.params.index, pd.Index(['const', 'ar.L1.D.cpi', 'ar.L2.D.cpi', 'ar.L3.D.cpi', 'ar.L4.D.cpi', 'ma.L1.D.cpi'])) assert_equal(res.model.endog_names, 'D.cpi') @pytest.mark.smoke def test_1dexog(): # smoke test, this will raise an error if broken dta = load_macrodata_pandas().data endog = dta['realcons'].values exog = dta['m1'].values.squeeze() with warnings.catch_warnings(): warnings.simplefilter("ignore") mod = ARMA(endog, (1, 1), exog).fit(disp=-1) mod.predict(193, 203, exog[-10:]) # check for dynamic is true and pandas Series see #2589 mod.predict(193, 202, exog[-10:], dynamic=True) dta.index = pd.Index(cpi_dates) mod = ARMA(dta['realcons'], (1, 1), dta['m1']).fit(disp=-1) mod.predict(dta.index[-10], dta.index[-1], exog=dta['m1'][-10:], dynamic=True) mod = ARMA(dta['realcons'], (1, 1), dta['m1']).fit(trend='nc', disp=-1) mod.predict(dta.index[-10], dta.index[-1], exog=dta['m1'][-10:], dynamic=True) def test_arima_predict_bug(): # predict_start_date was not getting set on start = None from statsmodels.datasets import sunspots dta = sunspots.load_pandas().data.SUNACTIVITY dta.index = pd.date_range(start='1700', end='2009', freq='A')[:309] arma_mod20 = ARMA(dta, (2, 0)).fit(disp=-1) arma_mod20.predict(None, None) # test prediction with time stamp, see #2587 predict = arma_mod20.predict(dta.index[-20], dta.index[-1]) assert predict.index.equals(dta.index[-20:]) predict = arma_mod20.predict(dta.index[-20], dta.index[-1], dynamic=True) assert predict.index.equals(dta.index[-20:]) # partially out of sample predict_dates = pd.date_range(start='2000', end='2015', freq='A') predict = arma_mod20.predict(predict_dates[0], predict_dates[-1]) assert predict.index.equals(predict_dates) def test_arima_predict_q2(): # bug with q > 1 for arima predict inv = load_macrodata_pandas().data['realinv'].values arima_mod = ARIMA(np.log(inv), (1, 1, 2)).fit(start_params=[0, 0, 0, 0], disp=-1) fc, stderr, conf_int = arima_mod.forecast(5) # values copy-pasted from gretl assert_almost_equal(fc, [7.306320, 7.313825, 7.321749, 7.329827, 7.337962], 5) def test_arima_predict_pandas_nofreq(): # this is issue 712 dates = ["2010-01-04", "2010-01-05", "2010-01-06", "2010-01-07", "2010-01-08", "2010-01-11", "2010-01-12", "2010-01-11", "2010-01-12", "2010-01-13", "2010-01-17"] close = [626.75, 623.99, 608.26, 594.1, 602.02, 601.11, 590.48, 587.09, 589.85, 580.0, 587.62] data = pd.DataFrame(close, index=DatetimeIndex(dates), columns=["close"]) # TODO: fix this names bug for non-string names names with pytest.warns(ValueWarning, match="it has no associated frequency"): arma = ARMA(data, order=(1, 0)).fit(disp=-1) # first check that in-sample prediction works predict = arma.predict() assert predict.index.equals(data.index) # check that this raises an exception when date not on index assert_raises(KeyError, arma.predict, start="2010-1-9", end=10) assert_raises(KeyError, arma.predict, start="2010-1-9", end="2010-1-17") # raise because end not on index assert_raises(KeyError, arma.predict, start="2010-1-4", end="2010-1-10") # raise because end not on index assert_raises(KeyError, arma.predict, start=3, end="2010-1-10") predict = arma.predict(start="2010-1-7", end=10) # should be of length 10 assert len(predict) == 8 assert predict.index.equals(data.index[3:10 + 1]) with pytest.warns(ValueWarning, match="No supported index is available"): predict = arma.predict(start="2010-1-7", end=14) assert predict.index.equals(pd.Index(lrange(3, 15))) with pytest.warns(ValueWarning, match="No supported index is available"): predict = arma.predict(start=3, end=14) assert predict.index.equals(pd.Index(lrange(3, 15))) # end can be a date if it's in the sample and on the index # predict dates is just a slice of the dates index then predict = arma.predict(start="2010-1-6", end="2010-1-13") assert predict.index.equals(data.index[2:10]) predict = arma.predict(start=2, end="2010-1-13") assert predict.index.equals(data.index[2:10]) def test_arima_predict_exog(): # check 625 and 626 # from statsmodels.tsa.arima_process import arma_generate_sample # arparams = np.array([1, -.45, .25]) # maparams = np.array([1, .15]) # nobs = 100 # np.random.seed(123) # y = arma_generate_sample(arparams, maparams, nobs, burnin=100) # make an exogenous trend # X = np.array(lrange(nobs)) / 20.0 # add a constant # y += 2.5 from pandas import read_csv file_name = "/results/results_arima_exog_forecasts_mle.csv" arima_forecasts = read_csv(current_path + file_name) y = arima_forecasts["y"].dropna() X = np.arange(len(y) + 25) / 20. predict_expected = arima_forecasts["predict"] arma_res = ARMA(y.values, order=(2, 1), exog=X[:100]).fit(trend="c", disp=-1) # params from gretl params = np.array([2.786912485145725, -0.122650190196475, 0.533223846028938, -0.319344321763337, 0.132883233000064]) assert_almost_equal(arma_res.params, params, 5) # no exog for in-sample predict = arma_res.predict() assert_almost_equal(predict, predict_expected.values[:100], 5) # check 626 assert len(arma_res.model.exog_names) == 5 # exog for out-of-sample and in-sample dynamic predict = arma_res.model.predict(params, end=124, exog=X[100:]) assert_almost_equal(predict, predict_expected.values, 6) # conditional sum of squares # arima_forecasts = read_csv(current_path + "/results/" # "results_arima_exog_forecasts_css.csv") # predict_expected = arima_forecasts["predict"].dropna() # arma_res = ARMA(y.values, order=(2,1), exog=X[:100]).fit(trend="c", # method="css", # disp=-1) # params = np.array([2.152350033809826, -0.103602399018814, # 0.566716580421188, -0.326208009247944, # 0.102142932143421]) # predict = arma_res.model.predict(params) # in-sample # assert_almost_equal(predict, predict_expected.values[:98], 6) # predict = arma_res.model.predict(params, end=124, exog=X[100:]) # exog for out-of-sample and in-sample dynamic # assert_almost_equal(predict, predict_expected.values, 3) @pytest.mark.smoke def test_arima_no_diff(): # GH#736 # smoke test, predict will break if we have ARIMAResults but # ARMA model, need ARIMA(p, 0, q) to return an ARMA in init. ar = [1, -.75, .15, .35] ma = [1, .25, .9] np.random.seed(12345) y = arma_generate_sample(ar, ma, 100) mod = ARIMA(y, (3, 0, 2)) assert type(mod) is ARMA res = mod.fit(disp=-1) # smoke test just to be sure res.predict() @pytest.mark.smoke def test_arima_predict_noma(): # GH#657 ar = [1, .75] ma = [1] np.random.seed(12345) data = arma_generate_sample(ar, ma, 100) arma = ARMA(data, order=(0, 1)) arma_res = arma.fit(disp=-1) arma_res.forecast(1) def test_arimax(): dta = load_macrodata_pandas().data dta.index = cpi_dates dta = dta[["realdpi", "m1", "realgdp"]] y = dta.pop("realdpi") # 1 exog # X = dta.iloc[1:]["m1"] # res = ARIMA(y, (2, 1, 1), X).fit(disp=-1) # params = [23.902305009084373, 0.024650911502790, -0.162140641341602, # 0.165262136028113, -0.066667022903974] # assert_almost_equal(res.params.values, params, 6) # 2 exog X = dta res = ARIMA(y, (2, 1, 1), X).fit(disp=False, solver="nm", maxiter=1000, ftol=1e-12, xtol=1e-12) # from gretl # params = [13.113976653926638, -0.003792125069387, 0.004123504809217, # -0.199213760940898, 0.151563643588008, -0.033088661096699] # from stata using double stata_llf = -1076.108614859121 params = [13.1259220104, -0.00376814509403812, 0.00411970083135622, -0.19921477896158524, 0.15154396192855729, -0.03308400760360837] # we can get close assert_almost_equal(res.params.values, params, 4) # This shows that it's an optimizer problem and not a problem in the code assert_almost_equal(res.model.loglike(np.array(params)), stata_llf, 6) X = dta.diff() X.iloc[0] = 0 res = ARIMA(y, (2, 1, 1), X).fit(disp=False) # gretl will not estimate this - looks like maybe a bug on their part, # but we can just fine, we're close to Stata's answer # from Stata params = [19.5656863783347, 0.32653841355833396198, 0.36286527042965188716, -1.01133792126884, -0.15722368379307766206, 0.69359822544092153418] assert_almost_equal(res.params.values, params, 3) def test_bad_start_params(): endog = np.array([ 820.69093, 781.0103028, 785.8786988, 767.64282267, 778.9837648, 824.6595702, 813.01877867, 751.65598567, 753.431091, 746.920813, 795.6201904, 772.65732833, 793.4486454, 868.8457766, 823.07226547, 783.09067747, 791.50723847, 770.93086347, 835.34157333, 810.64147947, 738.36071367, 776.49038513, 822.93272333, 815.26461227, 773.70552987, 777.3726522, 811.83444853, 840.95489133, 777.51031933, 745.90077307, 806.95113093, 805.77521973, 756.70927733, 749.89091773, 1694.2266924, 2398.4802244, 1434.6728516, 909.73940427, 929.01291907, 769.07561453, 801.1112548, 796.16163313, 817.2496376, 857.73046447, 838.849345, 761.92338873, 731.7842242, 770.4641844]) mod = ARMA(endog, (15, 0)) with pytest.raises(ValueError, match="pass your own start_params"): with pytest.warns(RuntimeWarning, match="encountered in sqrt"): # numpy warns "invalid value encountered in sqrt" mod.fit() inv = load_macrodata_pandas().data['realinv'].values arima_mod = ARIMA(np.log(inv), (1, 1, 2)) with pytest.raises(ValueError): arima_mod.fit() def test_arima_small_data_bug(): # Issue 1038, too few observations with given order import statsmodels.api as sm vals = [96.2, 98.3, 99.1, 95.5, 94.0, 87.1, 87.9, 86.7402777504474] dr = pd.date_range("1990", periods=len(vals), freq='Q') ts = pd.Series(vals, index=dr) df = pd.DataFrame(ts) mod = sm.tsa.ARIMA(df, (2, 0, 2)) assert_raises(ValueError, mod.fit) @pytest.mark.smoke def test_arima_dataframe_integer_name(): # Smoke Test for Issue GH#1038 import statsmodels.api as sm vals = [96.2, 98.3, 99.1, 95.5, 94.0, 87.1, 87.9, 86.7402777504474, 94.0, 96.5, 93.3, 97.5, 96.3, 92.] dr = pd.date_range("1990", periods=len(vals), freq='Q') ts = pd.Series(vals, index=dr) df = pd.DataFrame(ts) sm.tsa.ARIMA(df, (2, 0, 2)) def test_arima_exog_predict_1d(): # test 1067 np.random.seed(12345) y = np.random.random(100) x = np.random.random(100) mod = ARMA(y, (2, 1), x).fit(disp=-1) newx = np.random.random(10) mod.forecast(steps=10, alpha=0.05, exog=newx) with pytest.raises(ValueError): mod.forecast(steps=10, alpha=0.05, exog=newx[:5]) with pytest.raises(ValueError): mod.forecast(steps=10, alpha=0.05) too_many = pd.DataFrame(np.zeros((10, 2)), columns=['x1', 'x2']) with pytest.raises(ValueError): mod.forecast(steps=10, alpha=0.05, exog=too_many) def test_arima_1123(): # test ARMAX predict when trend is none np.random.seed(12345) arparams = np.array([.75, -.25]) maparams = np.array([.65, .35]) nobs = 20 np.random.seed(12345) y = arma_generate_sample(arparams, maparams, nobs) X = np.random.randn(nobs) y += 5 * X mod = ARMA(y[:-1], order=(1, 0), exog=X[:-1]) res = mod.fit(trend='nc', disp=False) fc = res.forecast(exog=X[-1:]) # results from gretl assert_almost_equal(fc[0], 2.200393, 6) assert_almost_equal(fc[1], 1.030743, 6) assert_almost_equal(fc[2][0, 0], 0.180175, 6) assert_almost_equal(fc[2][0, 1], 4.220611, 6) mod = ARMA(y[:-1], order=(1, 1), exog=X[:-1]) res = mod.fit(trend='nc', disp=False) fc = res.forecast(exog=X[-1:]) assert_almost_equal(fc[0], 2.765688, 6) assert_almost_equal(fc[1], 0.835048, 6) assert_almost_equal(fc[2][0, 0], 1.129023, 6) assert_almost_equal(fc[2][0, 1], 4.402353, 6) # make sure this works to. code looked fishy. mod = ARMA(y[:-1], order=(1, 0), exog=X[:-1]) res = mod.fit(trend='c', disp=False) fc = res.forecast(exog=X[-1:]) assert_almost_equal(fc[0], 2.481219, 6) assert_almost_equal(fc[1], 0.968759, 6) assert_almost_equal(fc[2][0], [0.582485, 4.379952], 6) def test_small_data(): # 1146 y = [-1214.360173, -1848.209905, -2100.918158, -3647.483678, -4711.186773] # refuse to estimate these assert_raises(ValueError, ARIMA, y, (2, 0, 3)) assert_raises(ValueError, ARIMA, y, (1, 1, 3)) mod = ARIMA(y, (1, 0, 3)) assert_raises(ValueError, mod.fit, trend="c") # try to estimate these...leave it up to the user to check for garbage # and be clear, these are garbage parameters. # X-12 arima will estimate, gretl refuses to estimate likely a problem # in start params regression. mod.fit(trend="nc", disp=0, start_params=[.1, .1, .1, .1]) mod = ARIMA(y, (1, 0, 2)) import warnings with warnings.catch_warnings(): warnings.simplefilter("ignore") mod.fit(disp=0, start_params=[np.mean(y), .1, .1, .1]) class TestARMA00(object): @classmethod def setup_class(cls): from statsmodels.datasets.sunspots import load_pandas sunspots = load_pandas().data['SUNACTIVITY'].values cls.y = y = sunspots cls.arma_00_model = ARMA(y, order=(0, 0)) cls.arma_00_res = cls.arma_00_model.fit(disp=-1) def test_parameters(self): params = self.arma_00_res.params assert_almost_equal(self.y.mean(), params) def test_predictions(self): predictions = self.arma_00_res.predict() assert_almost_equal(self.y.mean() * np.ones_like(predictions), predictions) def test_arroots(self): # regression test; older implementation of arroots returned None # instead of en empty array roots = self.arma_00_res.arroots assert_equal(roots.size, 0) def test_maroots(self): # regression test; older implementation of arroots returned None # instead of en empty array roots = self.arma_00_res.maroots assert_equal(roots.size, 0) @pytest.mark.skip("This test is invalid since the ICs differ due to " "df_model differences between OLS and ARIMA") def test_information_criteria(self): res = self.arma_00_res y = self.y ols_res = OLS(y, np.ones_like(y)).fit(disp=-1) ols_ic = np.array([ols_res.aic, ols_res.bic]) arma_ic = np.array([res.aic, res.bic]) assert_almost_equal(ols_ic, arma_ic, DECIMAL_4) def test_arma_00_nc(self): arma_00 = ARMA(self.y, order=(0, 0)) assert_raises(ValueError, arma_00.fit, trend='nc', disp=-1) def test_css(self): arma = ARMA(self.y, order=(0, 0)) fit = arma.fit(method='css', disp=-1) predictions = fit.predict() assert_almost_equal(self.y.mean() * np.ones_like(predictions), predictions) def test_arima(self): yi = np.cumsum(self.y) arima = ARIMA(yi, order=(0, 1, 0)) fit = arima.fit(disp=-1) assert_almost_equal(np.diff(yi).mean(), fit.params, DECIMAL_4) def test_arma_ols(self): y = self.y y_lead = y[1:] y_lag = y[:-1] T = y_lag.shape[0] X = np.hstack((np.ones((T, 1)), y_lag[:, None])) ols_res = OLS(y_lead, X).fit() arma_res = ARMA(y_lead, order=(0, 0), exog=y_lag).fit(trend='c', disp=-1) assert_almost_equal(ols_res.params, arma_res.params) def test_arma_exog_no_constant(self): y = self.y y_lead = y[1:] y_lag = y[:-1] X = y_lag[:, None] ols_res = OLS(y_lead, X).fit() arma_res = ARMA(y_lead, order=(0, 0), exog=y_lag).fit(trend='nc', disp=-1) assert_almost_equal(ols_res.params, arma_res.params) def test_arima_dates_startatend(): # bug np.random.seed(18) x = pd.Series(np.random.random(36), index=pd.date_range(start='1/1/1990', periods=36, freq='M')) res = ARIMA(x, (1, 0, 0)).fit(disp=0) pred = res.predict(start=len(x), end=len(x)) assert pred.index[0] == x.index.shift(1)[-1] fc = res.forecast()[0] assert_almost_equal(pred.values[0], fc) def test_arma_missing(): from statsmodels.tools.sm_exceptions import MissingDataError # bug 1343 y = np.random.random(40) y[-1] = np.nan assert_raises(MissingDataError, ARMA, y, (1, 0), missing='raise') @pytest.mark.matplotlib def test_plot_predict(close_figures): from statsmodels.datasets.sunspots import load_pandas dta = load_pandas().data[['SUNACTIVITY']] dta.index = date_range(start='1700', end='2009', freq='A')[:309] res = ARMA(dta, (3, 0)).fit(disp=-1) res.plot_predict('1990', '2012', dynamic=True, plot_insample=False) res.plot_predict('1990', '2012', dynamic=True, plot_insample=True) res = ARIMA(dta, (3, 1, 0)).fit(disp=-1) res.plot_predict('1990', '2012', dynamic=True, plot_insample=False) res.plot_predict('1990', '2012', dynamic=True, plot_insample=True) def test_arima_diff2(): dta = load_macrodata_pandas().data['cpi'] dta.index = cpi_dates mod = ARIMA(dta, (3, 2, 1)).fit(disp=-1) fc, fcerr, conf_int = mod.forecast(10) # forecasts from gretl conf_int_res = [(216.139, 219.231), (216.472, 221.520), (217.064, 223.649), (217.586, 225.727), (218.119, 227.770), (218.703, 229.784), (219.306, 231.777), (219.924, 233.759), (220.559, 235.735), (221.206, 237.709)] fc_res = [217.685, 218.996, 220.356, 221.656, 222.945, 224.243, 225.541, 226.841, 228.147, 229.457] fcerr_res = [0.7888, 1.2878, 1.6798, 2.0768, 2.4620, 2.8269, 3.1816, 3.52950, 3.8715, 4.2099] assert_almost_equal(fc, fc_res, 3) assert_almost_equal(fcerr, fcerr_res, 3) assert_almost_equal(conf_int, conf_int_res, 3) predicted = mod.predict('2008Q1', '2012Q1', typ='levels') predicted_res = [214.464, 215.478, 221.277, 217.453, 212.419, 213.530, 215.087, 217.685, 218.996, 220.356, 221.656, 222.945, 224.243, 225.541, 226.841, 228.147, 229.457] assert_almost_equal(predicted, predicted_res, 3) def test_arima111_predict_exog_2127(): # regression test for issue #2127 ef = [0.03005, 0.03917, 0.02828, 0.03644, 0.03379, 0.02744, 0.03343, 0.02621, 0.03050, 0.02455, 0.03261, 0.03507, 0.02734, 0.05373, 0.02677, 0.03443, 0.03331, 0.02741, 0.03709, 0.02113, 0.03343, 0.02011, 0.03675, 0.03077, 0.02201, 0.04844, 0.05518, 0.03765, 0.05433, 0.03049, 0.04829, 0.02936, 0.04421, 0.02457, 0.04007, 0.03009, 0.04504, 0.05041, 0.03651, 0.02719, 0.04383, 0.02887, 0.03440, 0.03348, 0.02364, 0.03496, 0.02549, 0.03284, 0.03523, 0.02579, 0.03080, 0.01784, 0.03237, 0.02078, 0.03508, 0.03062, 0.02006, 0.02341, 0.02223, 0.03145, 0.03081, 0.02520, 0.02683, 0.01720, 0.02225, 0.01579, 0.02237, 0.02295, 0.01830, 0.02356, 0.02051, 0.02932, 0.03025, 0.02390, 0.02635, 0.01863, 0.02994, 0.01762, 0.02837, 0.02421, 0.01951, 0.02149, 0.02079, 0.02528, 0.02575, 0.01634, 0.02563, 0.01719, 0.02915, 0.01724, 0.02804, 0.02750, 0.02099, 0.02522, 0.02422, 0.03254, 0.02095, 0.03241, 0.01867, 0.03998, 0.02212, 0.03034, 0.03419, 0.01866, 0.02623, 0.02052] ue = [4.9, 5.0, 5.0, 5.0, 4.9, 4.7, 4.8, 4.7, 4.7, 4.6, 4.6, 4.7, 4.7, 4.5, 4.4, 4.5, 4.4, 4.6, 4.5, 4.4, 4.5, 4.4, 4.6, 4.7, 4.6, 4.7, 4.7, 4.7, 5.0, 5.0, 4.9, 5.1, 5.0, 5.4, 5.6, 5.8, 6.1, 6.1, 6.5, 6.8, 7.3, 7.8, 8.3, 8.7, 9.0, 9.4, 9.5, 9.5, 9.6, 9.8, 10., 9.9, 9.9, 9.7, 9.8, 9.9, 9.9, 9.6, 9.4, 9.5, 9.5, 9.5, 9.5, 9.8, 9.4, 9.1, 9.0, 9.0, 9.1, 9.0, 9.1, 9.0, 9.0, 9.0, 8.8, 8.6, 8.5, 8.2, 8.3, 8.2, 8.2, 8.2, 8.2, 8.2, 8.1, 7.8, 7.8, 7.8, 7.9, 7.9, 7.7, 7.5, 7.5, 7.5, 7.5, 7.3, 7.2, 7.2, 7.2, 7.0, 6.7, 6.6, 6.7, 6.7, 6.3, 6.3] ue = np.array(ue) / 100 model = ARIMA(ef, (1, 1, 1), exog=ue) res = model.fit(transparams=False, pgtol=1e-8, iprint=0, disp=0) if not PLATFORM_WIN32: # Random failures on Win32 assert_equal(res.mle_retvals['warnflag'], 0) predicts = res.predict(start=len(ef), end=len(ef) + 10, exog=ue[-11:], typ='levels') # regression test, not verified numbers predicts_res = np.array([ 0.02591095, 0.02321325, 0.02436579, 0.02368759, 0.02389753, 0.02372, 0.0237481, 0.0236738, 0.023644, 0.0236283, 0.02362267]) assert_allclose(predicts, predicts_res, atol=5e-6) # Smoke check of forecast with exog in ARIMA res.forecast(steps=10, exog=np.empty(10)) with pytest.raises(ValueError): res.forecast(steps=10) with pytest.raises(ValueError): res.forecast(steps=10, exog=np.empty((10, 2))) with pytest.raises(ValueError): res.forecast(steps=10, exog=np.empty(100)) def test_arima_exog_predict(): # test forecasting and dynamic prediction with exog against Stata dta = load_macrodata_pandas().data cpi_dates = period_range(start='1959Q1', end='2009Q3', freq='Q') dta.index = cpi_dates data = dta data['loginv'] = np.log(data['realinv']) data['loggdp'] = np.log(data['realgdp']) data['logcons'] = np.log(data['realcons']) forecast_period = period_range(start='2008Q2', end='2009Q4', freq='Q') end = forecast_period[0] data_sample = data.loc[dta.index < end] exog_full = data[['loggdp', 'logcons']] # pandas mod = ARIMA(data_sample['loginv'], (1, 0, 1), exog=data_sample[['loggdp', 'logcons']]) with warnings.catch_warnings(): warnings.simplefilter("ignore") res = mod.fit(disp=0, solver='bfgs', maxiter=5000) predicted_arma_fp = res.predict(start=197, end=202, exog=exog_full.values[197:]).values predicted_arma_dp = res.predict(start=193, end=202, exog=exog_full[197:], dynamic=True) # numpy mod2 = ARIMA(np.asarray(data_sample['loginv']), (1, 0, 1), exog=np.asarray(data_sample[['loggdp', 'logcons']])) res2 = mod2.fit(start_params=res.params, disp=0, solver='bfgs', maxiter=5000) exog_full = data[['loggdp', 'logcons']] predicted_arma_f = res2.predict(start=197, end=202, exog=exog_full.values[197:]) predicted_arma_d = res2.predict(start=193, end=202, exog=exog_full[197:], dynamic=True) endog_scale = 100 ex_scale = 1000 # ARIMA(1, 1, 1) ex = ex_scale * np.asarray(data_sample[['loggdp', 'logcons']].diff()) # The first observation is not (supposed to be) used, # but I get a Lapack problem # Intel MKL ERROR: Parameter 5 was incorrect on entry to DLASCL. ex[0] = 0 mod111 = ARIMA(100 * np.asarray(data_sample['loginv']), (1, 1, 1), # Stata differences also the exog exog=ex) sv = [-0.94771574, 0.5869353, -0.32651653, 0.78066562, -0.68747501] res111 = mod111.fit(start_params=sv, disp=0, solver='bfgs', maxiter=5000) exog_full_d = ex_scale * data[['loggdp', 'logcons']].diff() res111.predict(start=197, end=202, exog=exog_full_d.values[197:]) predicted_arima_f = res111.predict(start=196, end=202, exog=exog_full_d.values[197:], typ='levels') predicted_arima_d = res111.predict(start=193, end=202, exog=exog_full_d.values[197:], typ='levels', dynamic=True) res_f101 = np.array( [7.73975859954, 7.71660108543, 7.69808978329, 7.70872117504, 7.65183927580, 7.69784279784, 7.70290907856, 7.69237782644, 7.65017785174, 7.66061689028, 7.65980022857, 7.61505314129, 7.51697158428, 7.51657606630, 7.5271053284]) res_f111 = np.array( [7.74460013693, 7.71958207517, 7.69629561172, 7.71208186737, 7.65758850178, 7.69223472572, 7.70411775588, 7.68896109499, 7.64016249001, 7.64871881901, 7.62550283402, 7.55814609462, 7.44431310053, 7.42963968062, 7.43554675427]) res_d111 = np.array( [7.74460013693, 7.71958207517, 7.69629561172, 7.71208186737, 7.65758850178, 7.69223472572, 7.71870821151, 7.72994302150, 7.71439447355, 7.72544001101, 7.70521902623, 7.64020040524, 7.52819271910, 7.51494426940, 7.52196378005]) res_d101 = np.array( [7.73975859954, 7.71660108543, 7.69808978329, 7.70872117504, 7.65183927580, 7.69784279784, 7.72522142662, 7.73962377858, 7.73245950636, 7.74935432862, 7.74449584691, 7.69589103679, 7.59412746880, 7.59021764836, 7.59739267775]) # Relax tolerance on OSX due to frequent small failures # GH 4657 tol = 1e-2 if PLATFORM_OSX or PLATFORM_WIN else 1e-4 assert_allclose(predicted_arma_dp, res_d101[-len(predicted_arma_d):], rtol=tol, atol=tol) assert_allclose(predicted_arma_fp, res_f101[-len(predicted_arma_f):], rtol=tol, atol=tol) assert_allclose(predicted_arma_d, res_d101[-len(predicted_arma_d):], rtol=tol, atol=tol) assert_allclose(predicted_arma_f, res_f101[-len(predicted_arma_f):], rtol=tol, atol=tol) assert_allclose(predicted_arima_d / endog_scale, res_d111[-len(predicted_arima_d):], rtol=tol, atol=tol) assert_allclose(predicted_arima_f / endog_scale, res_f111[-len(predicted_arima_f):], rtol=tol, atol=tol) # test for forecast with 0 ar fix in #2457 numbers again from Stata res_f002 = np.array( [7.70178181209, 7.67445481224, 7.67153737650, 7.67729153190, 7.61173201163, 7.67913499878, 7.67276092120, 7.66275451925, 7.65199799315, 7.65149983741, 7.65554131408, 7.62213286298, 7.53795983357, 7.53626130154, 7.54539963934]) res_d002 = np.array( [7.70178181209, 7.67445481224, 7.67153737650, 7.67729153190, 7.61173201163, 7.67913499878, 7.67306697759, 7.65287924998, 7.64904451605, 7.66580449603, 7.66252081172, 7.62213286298, 7.53795983357, 7.53626130154, 7.54539963934]) mod_002 = ARIMA(np.asarray(data_sample['loginv']), (0, 0, 2), exog=np.asarray(data_sample[['loggdp', 'logcons']])) # does not converge with default starting values start_params = np.concatenate((res.params[[0, 1, 2, 4]], [0])) res_002 = mod_002.fit(start_params=start_params, disp=0, solver='bfgs', maxiter=5000) # forecast fpredict_002 = res_002.predict(start=197, end=202, exog=exog_full.values[197:]) forecast_002 = res_002.forecast(steps=len(exog_full.values[197:]), exog=exog_full.values[197:]) # TODO: Checking other results forecast_002 = forecast_002[0] assert_allclose(fpredict_002, res_f002[-len(fpredict_002):], rtol=tol, atol=tol / 100.0) assert_allclose(forecast_002, res_f002[-len(forecast_002):], rtol=tol, atol=tol / 100.0) # dynamic predict dpredict_002 = res_002.predict(start=193, end=202, exog=exog_full.values[197:], dynamic=True) assert_allclose(dpredict_002, res_d002[-len(dpredict_002):], rtol=tol, atol=tol / 100.0) # in-sample dynamic predict should not need exog, #2982 predict_3a = res_002.predict(start=100, end=120, dynamic=True) predict_3b = res_002.predict(start=100, end=120, exog=exog_full.values[100:120], dynamic=True) assert_allclose(predict_3a, predict_3b, rtol=1e-10) h = len(exog_full.values[197:]) with pytest.raises(ValueError): res_002.forecast(steps=h) with pytest.raises(ValueError): res_002.forecast(steps=h, exog=np.empty((h, 20))) with pytest.raises(ValueError): res_002.forecast(steps=h, exog=np.empty(20)) def test_arima_fit_multiple_calls(): y = [-1214.360173, -1848.209905, -2100.918158, -3647.483678, -4711.186773] mod = ARIMA(y, (1, 0, 2)) # Make multiple calls to fit with pytest.warns(HessianInversionWarning, match="no bse or cov"): mod.fit(disp=0, start_params=[np.mean(y), .1, .1, .1]) assert_equal(mod.exog_names, ['const', 'ar.L1.y', 'ma.L1.y', 'ma.L2.y']) with pytest.warns(HessianInversionWarning, match="no bse or cov"): res = mod.fit(disp=0, start_params=[np.mean(y), .1, .1, .1]) assert_equal(mod.exog_names, ['const', 'ar.L1.y', 'ma.L1.y', 'ma.L2.y']) # ensure summary() works # TODO: separate and pytest.mark.smoke res.summary() res.summary2() # test multiple calls when there is only a constant term mod = ARIMA(y, (0, 0, 0)) # Make multiple calls to fit mod.fit(disp=0, start_params=[np.mean(y)]) assert_equal(mod.exog_names, ['const']) with pytest.raises(RuntimeError): mod.fit(disp=0, start_params=[np.mean(y)]) def test_long_ar_start_params(): np.random.seed(12345) arparams = np.array([1, -.75, .25]) maparams = np.array([1, .65, .35]) nobs = 30 np.random.seed(12345) y = arma_generate_sample(arparams, maparams, nobs) model = ARMA(y, order=(2, 2)) model.fit(method='css', start_ar_lags=10, disp=0) with pytest.raises(RuntimeError): model.fit(method='css-mle', start_ar_lags=10, disp=0) with pytest.raises(RuntimeError): model.fit(method='mle', start_ar_lags=10, disp=0) with pytest.raises(RuntimeError): model.fit(ValueError, start_ar_lags=nobs + 5, disp=0) def test_start_params_too_large(): np.random.seed(12345) arparams = np.array([1, -.75, .25]) maparams = np.array([1, .65, .35]) nobs = 30 np.random.seed(12345) y = arma_generate_sample(arparams, maparams, nobs) model = ARMA(y, order=(2, 2)) with pytest.raises(ValueError): model.fit(start_ar_lags=nobs + 5, disp=0) def test_arma_pickle(): np.random.seed(9876565) x = fa.ArmaFft([1, -0.5], [1., 0.4], 40).generate_sample(nsample=200, burnin=1000) mod = ARMA(x, (1, 1)) pkl_mod = pickle.loads(pickle.dumps(mod)) res = mod.fit(trend="c", disp=-1, solver='newton') pkl_res = pkl_mod.fit(trend="c", disp=-1, solver='newton') assert_allclose(res.params, pkl_res.params) assert_allclose(res.llf, pkl_res.llf) assert_almost_equal(res.resid, pkl_res.resid) assert_almost_equal(res.fittedvalues, pkl_res.fittedvalues) assert_almost_equal(res.pvalues, pkl_res.pvalues) def test_arima_pickle(): endog = y_arma[:, 6] mod = ARIMA(endog, (1, 1, 1)) pkl_mod = pickle.loads(pickle.dumps(mod)) res = mod.fit(trend="c", disp=-1, solver='newton') pkl_res = pkl_mod.fit(trend="c", disp=-1, solver='newton') assert_allclose(res.params, pkl_res.params) assert_allclose(res.llf, pkl_res.llf) assert_almost_equal(res.resid, pkl_res.resid) assert_almost_equal(res.fittedvalues, pkl_res.fittedvalues) assert_almost_equal(res.pvalues, pkl_res.pvalues) def test_arima_not_implemented(): formula = ' WUE ~ 1 + SFO3 ' data = [-1214.360173, -1848.209905, -2100.918158] assert_raises(NotImplementedError, ARIMA.from_formula, formula, data) def test_endog_int(): # int endog should produce same result as float, #3504 np.random.seed(123987) y = np.random.randint(0, 16, size=100) yf = y.astype(np.float64) res = AutoReg(y, 5, old_names=False).fit() resf = AutoReg(yf, 5, old_names=False).fit() assert_allclose(res.params, resf.params, atol=1e-5) assert_allclose(res.bse, resf.bse, atol=1e-5) res = ARMA(y, order=(2, 1)).fit(disp=-1) resf = ARMA(yf, order=(2, 1)).fit(disp=-1) assert_allclose(res.params, resf.params, atol=1e-5) assert_allclose(res.bse, resf.bse, atol=1e-5) res = ARIMA(y.cumsum(), order=(1, 1, 1)).fit(disp=-1) resf = ARIMA(yf.cumsum(), order=(1, 1, 1)).fit(disp=-1) assert_allclose(res.params, resf.params, rtol=1e-6, atol=1e-5) assert_allclose(res.bse, resf.bse, rtol=1e-6, atol=1e-5) def test_multidim_endog(reset_randomstate): y = np.random.randn(1000, 2) with pytest.raises(ValueError): ARMA(y, order=(1, 1)) y = np.random.randn(1000, 1, 2) with pytest.raises(ValueError): ARMA(y, order=(1, 1)) y = np.random.randn(1, 1, 1000) with pytest.raises(ValueError): ARMA(y, order=(1, 1)) def test_arima_no_full_output(): # GH 2752 endog = y_arma[:, 6] mod = ARIMA(endog, (1, 0, 1)) res = mod.fit(trend="c", disp=-1, full_output=False) assert res.mle_retvals is None def test_arima_summary_no_lags(reset_randomstate): y_train = pd.Series(np.random.randn(1000), name='y_train') x_train = pd.DataFrame(np.random.randn(1000, 2), columns=['x1', 'x2']) res = ARIMA(endog=y_train.values, exog=x_train, order=(0, 1, 0)).fit(disp=-1) summ = res.summary().as_text() assert 'const ' in summ assert 'x1 ' in summ assert 'x2 ' in summ def test_constant_column_trend(): # GH#3343 analogous to GH#5258 for AR, when the user passes a constant exog # and also passes trend="c", raise instead _make_arma_exog used to # silently drop a column and return an inconsistenct k_trend value. exog = np.array([0.5, 0.5, 0.5, 0.5, 0.5]) endog = np.array([-0.011866, 0.003380, 0.015357, 0.004451, -0.020889]) model = ARIMA(endog=endog, order=(1, 1, 0), exog=exog) # Fitting with a constant and constant exog raises because of colinearity with pytest.raises(ValueError, match="x contains one or more constant"): model.fit(trend="c", disp=-1) # FIXME: calling model.fit(trend="nc") raises for orthogonal reasons def test_arima_d0_forecast(reset_randomstate): arparams = np.array([1, -.75]) maparams = np.array([1, .65]) y = arma_generate_sample(arparams, maparams, 250) mod = ARIMA(y, (1, 0, 1)) assert isinstance(mod, ARMA) res = mod.fit(disp=-1) pred = res.predict(start=200, end=300) pred_typ = res.predict(start=200, end=300, typ='linear') assert_allclose(pred, pred_typ) pred_mod = mod.predict(res.params, start=200, end=300, typ='linear') assert_allclose(pred, pred_mod) def test_predict_exog_adjust(reset_randomstate): df = pd.DataFrame(np.random.standard_normal((1000, 2)), index=pd.date_range('31-12-2000', periods=1000), columns=['y', 'x']) y = df.y.iloc[:750] x = df.x.iloc[:750] mod = ARMA(y, (2, 0), exog=x) res = mod.fit(disp=-1) pred_adj = res.predict(end=df.index[-1], exog=df.x) pred = res.predict(end=df.index[-1], exog=df.x.iloc[750:]) assert_allclose(pred, pred_adj) def test_predict_wrong_exog_len(reset_randomstate): df = pd.DataFrame(np.random.standard_normal((1000, 2)), index=pd.date_range('31-12-2000', periods=1000), columns=['y', 'x']) y = df.y.iloc[:750] x = df.x.iloc[:750] mod = ARMA(y, (2, 0), exog=x) res = mod.fit(disp=-1) with pytest.warns(SpecificationWarning, match='of observations in exog'): res.predict(end=df.index[-1], exog=df.x.iloc[500:]) def test_invalid_method(reset_randomstate): ar, ma = [1, -0.5], [1., 0.4] x = fa.ArmaFft(ar, ma, 40).generate_sample(nsample=1000, burnin=1000) mod = ARMA(x, (1, 1)) with pytest.raises(ValueError, match='Method unknown not understood'): mod.fit(method='unknown') @pytest.mark.matplotlib def test_summary_plots_no_dates(reset_randomstate, close_figures): ar, ma = [1, -0.5], [1., 0.4] x = fa.ArmaFft(ar, ma, 40).generate_sample(nsample=1000, burnin=1000) res = ARMA(x, (1, 1)).fit(disp=-1) res.plot_predict() res.plot_predict(plot_insample=True) assert isinstance(res.summary().as_text(), str) assert isinstance(res.summary2().as_text(), str) def test_predict_exog_missing(): dta = load_macrodata_pandas().data res = ARMA(dta['realcons'], (1, 1), dta['m1']).fit(disp=-1) with pytest.raises(ValueError, match='You must provide exog for ARMAX'): res.predict(start=203, end=210) def test_too_few_obs_starting_values(reset_randomstate): ar, ma = [1, -0.5], [1., 0.4] x = fa.ArmaFft(ar, ma, 40).generate_sample(nsample=5, burnin=100) with pytest.raises(ValueError, match='Insufficient degrees of freedom'): ARMA(x, (1, 6)).fit(disp=-1) def test_repeated_fit_error(reset_randomstate): ar, ma = [1, -0.5], [1., 0.4] x = fa.ArmaFft(ar, ma, 40).generate_sample(nsample=1000, burnin=100) arma = ARMA(x, (1, 1)) arma.fit(disp=-1) with pytest.raises(RuntimeError): arma.fit(trend='nc') with pytest.raises(RuntimeError): arma.fit(method='css') def test_predict_no_fit(): ar, ma = [1, -0.5], [1., 0.4] x = fa.ArmaFft(ar, ma, 40).generate_sample(nsample=1000, burnin=100) arma = ARMA(x, (1, 1)) with pytest.raises(RuntimeError, match='Model must be fit'): arma.predict([.1, .1]) arima = ARIMA(x, (1, 1, 1)) with pytest.raises(RuntimeError, match='Model must be fit'): arima.predict([.1, .1]) def test_arma_repeated_fit(): ar, ma = [1, -0.5], [1., 0.4] x = fa.ArmaFft(ar, ma, 40).generate_sample(nsample=1000, burnin=100) arma = ARMA(x, (1, 1)) res = arma.fit(trend='c', disp=-1) repeat = arma.fit(trend='c', disp=-1) rtol = 1e-4 if PLATFORM_WIN32 else 1e-7 assert_allclose(res.params, repeat.params, rtol=rtol) assert isinstance(res.summary().as_text(), str) assert isinstance(repeat.summary().as_text(), str) def test_arima_repeated_fit(reset_randomstate): ar, ma = [1, -0.5], [1., 0.4] n = 1000 arma_fft = fa.ArmaFft(ar, ma, 40) x = 4 * np.arange(n) + arma_fft.generate_sample(nsample=n, burnin=100) arma = ARIMA(x, (1, 1, 1)) res = arma.fit(trend='c', disp=-1) repeat = arma.fit(trend='c', disp=-1) tol = 1e-3 if PLATFORM_WIN32 else 1e-6 assert_allclose(res.params, repeat.params, atol=tol, rtol=tol) assert isinstance(res.summary().as_text(), str) assert isinstance(repeat.summary().as_text(), str) def test_arma_ttest_ftest(): # GH947 ar, ma = [1, -0.5], [1., 0.4] x = 2 + fa.ArmaFft(ar, ma, 40).generate_sample(nsample=1000, burnin=100) arma = ARMA(x, (1, 1)) res = arma.fit(disp=-1) r = np.array([0, 1, 1]) t_test = res.t_test(r) c = res.cov_params() v = r @ c @ r numerator = res.params @ r denom = np.sqrt(v) stat = numerator / denom assert_allclose(stat, t_test.statistic) f_test = res.f_test(r) assert_allclose(stat**2, f_test.statistic) def test_nan_exog_arima_d1(): # GH2746, verify raises on missing df = pd.DataFrame(np.random.standard_normal((1000, 2)), index=pd.date_range('31-12-2000', periods=1000), columns=['y', 'x']) y = df.y.iloc[:750] x = df.x.iloc[:750] x.iloc[0] = np.nan with pytest.raises(MissingDataError): ARIMA(y, (0, 1, 1), exog=x) def test_arma_exog_const_trend_nc(reset_randomstate): x = np.ones((1000, 1)) y = arma_generate_sample([1, -1.2, 0.5], [1, 0.7], 1000, distrvs=np.random.standard_normal) y += 1 res = ARMA(y, (2, 1), exog=x).fit(trend='nc', disp=-1) assert res.params.shape[0] == 4 statsmodels-0.12.2/statsmodels/tsa/tests/test_arima_process.py000066400000000000000000000343231400612667500247050ustar00rootroot00000000000000 from statsmodels.tsa.arima_model import ARMA from unittest import TestCase import numpy as np from numpy.testing import (assert_array_almost_equal, assert_almost_equal, assert_allclose, assert_equal, assert_raises, assert_) import pytest from statsmodels.tsa.arima_process import (arma_generate_sample, arma_acovf, arma_acf, arma_impulse_response, lpol_fiar, lpol_fima, ArmaProcess, lpol2index, index2lpol) from statsmodels.sandbox.tsa.fftarma import ArmaFft from statsmodels.tsa.tests.results.results_process import armarep # benchmarkdata from statsmodels.tsa.tests.results import results_arma_acf arlist = [[1.], [1, -0.9], # ma representation will need many terms to get high precision [1, 0.9], [1, -0.9, 0.3]] malist = [[1.], [1, 0.9], [1, -0.9], [1, 0.9, -0.3]] DECIMAL_4 = 4 def test_arma_acovf(): # Check for specific AR(1) N = 20 phi = 0.9 sigma = 1 # rep 1: from module function rep1 = arma_acovf([1, -phi], [1], N) # rep 2: manually rep2 = [1. * sigma * phi ** i / (1 - phi ** 2) for i in range(N)] assert_allclose(rep1, rep2) def test_arma_acovf_persistent(): # Test arma_acovf in case where there is a near-unit root. # .999 is high enough to trigger the "while ir[-1] > 5*1e-5:" clause, # but not high enough to trigger the "nobs_ir > 50000" clause. ar = np.array([1, -.9995]) ma = np.array([1]) process = ArmaProcess(ar, ma) res = process.acovf(10) # Theoretical variance sig2 given by: # sig2 = .9995**2 * sig2 + 1 sig2 = 1/(1-.9995**2) corrs = .9995**np.arange(10) expected = sig2*corrs assert_equal(res.ndim, 1) assert_allclose(res, expected) def test_arma_acf(): # Check for specific AR(1) N = 20 phi = 0.9 sigma = 1 # rep 1: from module function rep1 = arma_acf([1, -phi], [1], N) # rep 2: manually acovf = np.array([1. * sigma * phi ** i / (1 - phi ** 2) for i in range(N)]) rep2 = acovf / (1. / (1 - phi ** 2)) assert_allclose(rep1, rep2) def test_arma_acf_compare_R_ARMAacf(): # Test specific cases against output from R's ARMAacf bd_example_3_3_2 = arma_acf([1, -1, 0.25], [1, 1]) assert_allclose(bd_example_3_3_2, results_arma_acf.bd_example_3_3_2) example_1 = arma_acf([1, -1, 0.25], [1, 1, 0.2]) assert_allclose(example_1, results_arma_acf.custom_example_1) example_2 = arma_acf([1, -1, 0.25], [1, 1, 0.2, 0.3]) assert_allclose(example_2, results_arma_acf.custom_example_2) example_3 = arma_acf([1, -1, 0.25], [1, 1, 0.2, 0.3, -0.35]) assert_allclose(example_3, results_arma_acf.custom_example_3) example_4 = arma_acf([1, -1, 0.25], [1, 1, 0.2, 0.3, -0.35, -0.1]) assert_allclose(example_4, results_arma_acf.custom_example_4) example_5 = arma_acf([1, -1, 0.25, -0.1], [1, 1, 0.2]) assert_allclose(example_5, results_arma_acf.custom_example_5) example_6 = arma_acf([1, -1, 0.25, -0.1, 0.05], [1, 1, 0.2]) assert_allclose(example_6, results_arma_acf.custom_example_6) example_7 = arma_acf([1, -1, 0.25, -0.1, 0.05, -0.02], [1, 1, 0.2]) assert_allclose(example_7, results_arma_acf.custom_example_7) def test_arma_acov_compare_theoretical_arma_acov(): # Test against the older version of this function, which used a different # approach that nicely shows the theoretical relationship # See GH:5324 when this was removed for full version of the function # including documentation and inline comments def arma_acovf_historical(ar, ma, nobs=10): if np.abs(np.sum(ar) - 1) > 0.9: nobs_ir = max(1000, 2 * nobs) else: nobs_ir = max(100, 2 * nobs) ir = arma_impulse_response(ar, ma, leads=nobs_ir) while ir[-1] > 5 * 1e-5: nobs_ir *= 10 ir = arma_impulse_response(ar, ma, leads=nobs_ir) if nobs_ir > 50000 and nobs < 1001: end = len(ir) acovf = np.array([np.dot(ir[:end-nobs-t], ir[t:end-nobs]) for t in range(nobs)]) else: acovf = np.correlate(ir, ir, 'full')[len(ir) - 1:] return acovf[:nobs] assert_allclose(arma_acovf([1, -0.5], [1, 0.2]), arma_acovf_historical([1, -0.5], [1, 0.2])) assert_allclose(arma_acovf([1, -0.99], [1, 0.2]), arma_acovf_historical([1, -0.99], [1, 0.2])) def _manual_arma_generate_sample(ar, ma, eta): T = len(eta) ar = ar[::-1] ma = ma[::-1] p, q = len(ar), len(ma) rep2 = [0] * max(p, q) # initialize with zeroes for t in range(T): yt = eta[t] if p: yt += np.dot(rep2[-p:], ar) if q: # left pad shocks with zeros yt += np.dot([0] * (q - t) + list(eta[max(0, t - q):t]), ma) rep2.append(yt) return np.array(rep2[max(p, q):]) @pytest.mark.parametrize('ar', arlist) @pytest.mark.parametrize('ma', malist) @pytest.mark.parametrize('dist', [np.random.standard_normal]) def test_arma_generate_sample(dist, ar, ma): # Test that this generates a true ARMA process # (amounts to just a test that scipy.signal.lfilter does what we want) T = 100 np.random.seed(1234) eta = dist(T) # rep1: from module function np.random.seed(1234) rep1 = arma_generate_sample(ar, ma, T, distrvs=dist) # rep2: "manually" create the ARMA process ar_params = -1 * np.array(ar[1:]) ma_params = np.array(ma[1:]) rep2 = _manual_arma_generate_sample(ar_params, ma_params, eta) assert_array_almost_equal(rep1, rep2, 13) def test_fi(): # test identity of ma and ar representation of fi lag polynomial n = 100 mafromar = arma_impulse_response(lpol_fiar(0.4, n=n), [1], n) assert_array_almost_equal(mafromar, lpol_fima(0.4, n=n), 13) def test_arma_impulse_response(): arrep = arma_impulse_response(armarep.ma, armarep.ar, leads=21)[1:] marep = arma_impulse_response(armarep.ar, armarep.ma, leads=21)[1:] assert_array_almost_equal(armarep.marep.ravel(), marep, 14) # difference in sign convention to matlab for AR term assert_array_almost_equal(-armarep.arrep.ravel(), arrep, 14) @pytest.mark.parametrize('ar', arlist) @pytest.mark.parametrize('ma', malist) def test_spectrum(ar, ma): nfreq = 20 w = np.linspace(0, np.pi, nfreq, endpoint=False) arma = ArmaFft(ar, ma, 20) spdr, wr = arma.spdroots(w) spdp, wp = arma.spdpoly(w, 200) spdd, wd = arma.spddirect(nfreq * 2) assert_equal(w, wr) assert_equal(w, wp) assert_almost_equal(w, wd[:nfreq], decimal=14) assert_almost_equal(spdr, spdd[:nfreq], decimal=7, err_msg='spdr spdd not equal for %s, %s' % (ar, ma)) assert_almost_equal(spdr, spdp, decimal=7, err_msg='spdr spdp not equal for %s, %s' % (ar, ma)) @pytest.mark.parametrize('ar', arlist) @pytest.mark.parametrize('ma', malist) def test_armafft(ar, ma): # test other methods nfreq = 20 w = np.linspace(0, np.pi, nfreq, endpoint=False) arma = ArmaFft(ar, ma, 20) ac1 = arma.invpowerspd(1024)[:10] ac2 = arma.acovf(10)[:10] assert_allclose(ac1, ac2, atol=1e-15, err_msg='acovf not equal for %s, %s' % (ar, ma)) def test_lpol2index_index2lpol(): process = ArmaProcess([1, 0, 0, -0.8]) coefs, locs = lpol2index(process.arcoefs) assert_almost_equal(coefs, [0.8]) assert_equal(locs, [2]) process = ArmaProcess([1, .1, .1, -0.8]) coefs, locs = lpol2index(process.arcoefs) assert_almost_equal(coefs, [-.1, -.1, 0.8]) assert_equal(locs, [0, 1, 2]) ar = index2lpol(coefs, locs) assert_equal(process.arcoefs, ar) class TestArmaProcess(TestCase): def test_empty_coeff(self): process = ArmaProcess() assert_equal(process.arcoefs, np.array([])) assert_equal(process.macoefs, np.array([])) process = ArmaProcess([1, -0.8]) assert_equal(process.arcoefs, np.array([0.8])) assert_equal(process.macoefs, np.array([])) process = ArmaProcess(ma=[1, -0.8]) assert_equal(process.arcoefs, np.array([])) assert_equal(process.macoefs, np.array([-0.8])) def test_from_coeff(self): ar = [1.8, -0.9] ma = [0.3] process = ArmaProcess.from_coeffs(np.array(ar), np.array(ma)) ar.insert(0, -1) ma.insert(0, 1) ar_p = -1 * np.array(ar) ma_p = ma process_direct = ArmaProcess(ar_p, ma_p) assert_equal(process.arcoefs, process_direct.arcoefs) assert_equal(process.macoefs, process_direct.macoefs) assert_equal(process.nobs, process_direct.nobs) assert_equal(process.maroots, process_direct.maroots) assert_equal(process.arroots, process_direct.arroots) assert_equal(process.isinvertible, process_direct.isinvertible) assert_equal(process.isstationary, process_direct.isstationary) def test_from_model(self): process = ArmaProcess([1, -.8], [1, .3], 1000) t = 1000 rs = np.random.RandomState(12345) y = process.generate_sample(t, burnin=100, distrvs=rs.standard_normal) res = ARMA(y, (1, 1)).fit(disp=False) process_model = ArmaProcess.from_estimation(res) process_coef = ArmaProcess.from_coeffs(res.arparams, res.maparams, t) assert_equal(process_model.arcoefs, process_coef.arcoefs) assert_equal(process_model.macoefs, process_coef.macoefs) assert_equal(process_model.nobs, process_coef.nobs) assert_equal(process_model.isinvertible, process_coef.isinvertible) assert_equal(process_model.isstationary, process_coef.isstationary) def test_process_multiplication(self): process1 = ArmaProcess.from_coeffs([.9]) process2 = ArmaProcess.from_coeffs([.7]) process3 = process1 * process2 assert_equal(process3.arcoefs, np.array([1.6, -0.7 * 0.9])) assert_equal(process3.macoefs, np.array([])) process1 = ArmaProcess.from_coeffs([.9], [.2]) process2 = ArmaProcess.from_coeffs([.7]) process3 = process1 * process2 assert_equal(process3.arcoefs, np.array([1.6, -0.7 * 0.9])) assert_equal(process3.macoefs, np.array([0.2])) process1 = ArmaProcess.from_coeffs([.9], [.2]) process2 = process1 * (np.array([1.0, -0.7]), np.array([1.0])) assert_equal(process2.arcoefs, np.array([1.6, -0.7 * 0.9])) assert_raises(TypeError, process1.__mul__, [3]) def test_str_repr(self): process1 = ArmaProcess.from_coeffs([.9], [.2]) out = process1.__str__() print(out) assert_(out.find('AR: [1.0, -0.9]') != -1) assert_(out.find('MA: [1.0, 0.2]') != -1) out = process1.__repr__() assert_(out.find('nobs=100') != -1) assert_(out.find('at ' + str(hex(id(process1)))) != -1) def test_acf(self): process1 = ArmaProcess.from_coeffs([.9]) acf = process1.acf(10) expected = np.array(0.9) ** np.arange(10.0) assert_array_almost_equal(acf, expected) acf = process1.acf() assert_(acf.shape[0] == process1.nobs) def test_pacf(self): process1 = ArmaProcess.from_coeffs([.9]) pacf = process1.pacf(10) expected = np.array([1, 0.9] + [0] * 8) assert_array_almost_equal(pacf, expected) pacf = process1.pacf() assert_(pacf.shape[0] == process1.nobs) def test_isstationary(self): process1 = ArmaProcess.from_coeffs([1.1]) assert_equal(process1.isstationary, False) process1 = ArmaProcess.from_coeffs([1.8, -0.9]) assert_equal(process1.isstationary, True) process1 = ArmaProcess.from_coeffs([1.5, -0.5]) print(np.abs(process1.arroots)) assert_equal(process1.isstationary, False) def test_arma2ar(self): process1 = ArmaProcess.from_coeffs([], [0.8]) vals = process1.arma2ar(100) assert_almost_equal(vals, (-0.8) ** np.arange(100.0)) def test_invertroots(self): process1 = ArmaProcess.from_coeffs([], [2.5]) process2 = process1.invertroots(True) assert_almost_equal(process2.ma, np.array([1.0, 0.4])) process1 = ArmaProcess.from_coeffs([], [0.4]) process2 = process1.invertroots(True) assert_almost_equal(process2.ma, np.array([1.0, 0.4])) process1 = ArmaProcess.from_coeffs([], [2.5]) roots, invertable = process1.invertroots(False) assert_equal(invertable, False) assert_almost_equal(roots, np.array([1, 0.4])) def test_generate_sample(self): process = ArmaProcess.from_coeffs([0.9]) np.random.seed(12345) sample = process.generate_sample() np.random.seed(12345) expected = np.random.randn(100) for i in range(1, 100): expected[i] = 0.9 * expected[i - 1] + expected[i] assert_almost_equal(sample, expected) process = ArmaProcess.from_coeffs([1.6, -0.9]) np.random.seed(12345) sample = process.generate_sample() np.random.seed(12345) expected = np.random.randn(100) expected[1] = 1.6 * expected[0] + expected[1] for i in range(2, 100): expected[i] = 1.6 * expected[i - 1] - 0.9 * expected[i - 2] + expected[i] assert_almost_equal(sample, expected) process = ArmaProcess.from_coeffs([1.6, -0.9]) np.random.seed(12345) sample = process.generate_sample(burnin=100) np.random.seed(12345) expected = np.random.randn(200) expected[1] = 1.6 * expected[0] + expected[1] for i in range(2, 200): expected[i] = 1.6 * expected[i - 1] - 0.9 * expected[i - 2] + expected[i] assert_almost_equal(sample, expected[100:]) np.random.seed(12345) sample = process.generate_sample(nsample=(100,5)) assert_equal(sample.shape, (100,5)) def test_impulse_response(self): process = ArmaProcess.from_coeffs([0.9]) ir = process.impulse_response(10) assert_almost_equal(ir, 0.9 ** np.arange(10)) def test_periodogram(self): process = ArmaProcess() pg = process.periodogram() assert_almost_equal(pg[0], np.linspace(0,np.pi,100,False)) assert_almost_equal(pg[1], np.sqrt(2 / np.pi) / 2 * np.ones(100)) statsmodels-0.12.2/statsmodels/tsa/tests/test_bds.py000066400000000000000000000051611400612667500226240ustar00rootroot00000000000000""" Test for BDS test for IID time series References ---------- Kanzler, Ludwig. 1998. BDS: MATLAB Module to Calculate Brock, Dechert & Scheinkman Test for Independence. Statistical Software Components. Boston College Department of Economics. http://ideas.repec.org/c/boc/bocode/t871803.html. """ import os import numpy as np import pandas as pd from statsmodels.tsa.stattools import bds from numpy.testing import assert_almost_equal DECIMAL_8 = 8 DECIMAL_6 = 6 DECIMAL_5 = 5 DECIMAL_4 = 4 DECIMAL_3 = 3 DECIMAL_2 = 2 DECIMAL_1 = 1 curdir = os.path.dirname(os.path.abspath(__file__)) data_file = os.path.join(curdir, "results", "bds_data.csv") data = pd.read_csv(data_file, header=None) res_file = os.path.join(curdir, "results", "bds_results.csv") results = pd.read_csv(res_file, header=None) class CheckBDS(object): """ Test BDS Test values from Kanzler's MATLAB program bds. """ def test_stat(self): assert_almost_equal(self.res[0], self.bds_stats, DECIMAL_8) def test_pvalue(self): assert_almost_equal(self.res[1], self.pvalues, DECIMAL_8) class TestBDSSequence(CheckBDS): """ BDS Test on np.arange(1,26) """ @classmethod def setup_class(cls): cls.results = results[results[0] == 1] cls.bds_stats = np.array(cls.results[2][1:]) cls.pvalues = np.array(cls.results[3][1:]) cls.data = data[0][data[0].notnull()] cls.res = bds(cls.data, 5) class TestBDSNormal(CheckBDS): """ BDS Test on np.random.normal(size=25) """ @classmethod def setup_class(cls): cls.results = results[results[0] == 2] cls.bds_stats = np.array(cls.results[2][1:]) cls.pvalues = np.array(cls.results[3][1:]) cls.data = data[1][data[1].notnull()] cls.res = bds(cls.data, 5) class TestBDSCombined(CheckBDS): """ BDS Test on np.r_[np.random.normal(size=25), np.random.uniform(size=25)] """ @classmethod def setup_class(cls): cls.results = results[results[0] == 3] cls.bds_stats = np.array(cls.results[2][1:]) cls.pvalues = np.array(cls.results[3][1:]) cls.data = data[2][data[2].notnull()] cls.res = bds(cls.data, 5) class TestBDSGDPC1(CheckBDS): """ BDS Test on GDPC1: 1947Q1 - 2013Q1 References ---------- http://research.stlouisfed.org/fred2/series/GDPC1 """ @classmethod def setup_class(cls): cls.results = results[results[0] == 4] cls.bds_stats = np.array(cls.results[2][1:]) cls.pvalues = np.array(cls.results[3][1:]) cls.data = data[3][data[3].notnull()] cls.res = bds(cls.data, 5) statsmodels-0.12.2/statsmodels/tsa/tests/test_deterministic.py000066400000000000000000000540071400612667500247220ustar00rootroot00000000000000from statsmodels.compat.pandas import pandas_lt_1_0_0 from typing import Hashable, Tuple import numpy as np import pandas as pd import pytest from statsmodels.tsa.deterministic import ( CalendarFourier, CalendarSeasonality, CalendarTimeTrend, DeterministicProcess, DeterministicTerm, Fourier, Seasonality, TimeTrend, ) @pytest.fixture(scope="module", params=[True, False]) def time_index(request): idx = pd.date_range("2000-01-01", periods=833, freq="B") if request.param: return idx.to_period("B") return idx @pytest.fixture( scope="module", params=["range", "period", "datetime", "fib", "int64"] ) def index(request): param = request.param if param in ("period", "datetime"): idx = pd.date_range("2000-01-01", periods=137, freq="M") if param == "period": idx = idx.to_period("M") elif param == "range": idx = pd.RangeIndex(0, 123) elif param == "int64": idx = pd.Int64Index(np.arange(123)) elif param == "fib": fib = [0, 1] for _ in range(113): fib.append(fib[-2] + fib[-1]) idx = pd.Index(fib) else: raise NotImplementedError() return idx @pytest.fixture(scope="module", params=[None, "period", False, "list"]) def forecast_index(request): idx = pd.date_range("2000-01-01", periods=400, freq="B") if request.param is None: return None elif request.param == "period": return idx.to_period("B") elif request.param == "list": return list(idx) return idx @pytest.mark.smoke def test_time_trend_smoke(index, forecast_index): tt = TimeTrend(True, 2) tt.in_sample(index) steps = 83 if forecast_index is None else len(forecast_index) warn = None if type(index) is pd.Int64Index and np.any(np.diff(index) != 1): warn = UserWarning with pytest.warns(warn): tt.out_of_sample(steps, index, forecast_index) str(tt) hash(tt) assert isinstance(tt.order, int) assert isinstance(tt._constant, bool) assert TimeTrend.from_string("ctt") == tt assert TimeTrend.from_string("ct") != tt assert TimeTrend.from_string("t") != tt assert TimeTrend.from_string("n") != tt assert Seasonality(12) != tt tt0 = TimeTrend(False, 0) tt0.in_sample(index) str(tt0) @pytest.mark.smoke def test_seasonality_smoke(index, forecast_index): s = Seasonality(12) s.in_sample(index) steps = 83 if forecast_index is None else len(forecast_index) warn = None if type(index) is pd.Int64Index and np.any(np.diff(index) != 1): warn = UserWarning with pytest.warns(warn): s.out_of_sample(steps, index, forecast_index) assert isinstance(s.period, int) str(s) hash(s) if isinstance(index, (pd.DatetimeIndex, pd.PeriodIndex)) and index.freq: s = Seasonality.from_index(index) s.in_sample(index) s.out_of_sample(steps, index, forecast_index) Seasonality.from_index(list(index)) @pytest.mark.smoke def test_fourier_smoke(index, forecast_index): f = Fourier(12, 2) f.in_sample(index) steps = 83 if forecast_index is None else len(forecast_index) warn = None if type(index) is pd.Int64Index and np.any(np.diff(index) != 1): warn = UserWarning with pytest.warns(warn): f.out_of_sample(steps, index, forecast_index) assert isinstance(f.period, float) assert isinstance(f.order, int) str(f) hash(f) with pytest.raises(ValueError, match=r"2 \* order must be <= period"): Fourier(12, 7) @pytest.mark.smoke def test_calendar_time_trend_smoke(time_index, forecast_index): ct = CalendarTimeTrend("A", order=2) ct.in_sample(time_index) steps = 83 if forecast_index is None else len(forecast_index) ct.out_of_sample(steps, time_index, forecast_index) str(ct) hash(ct) assert isinstance(ct.order, int) assert isinstance(ct.constant, bool) assert isinstance(ct.freq, str) assert ct.base_period is None @pytest.mark.smoke def test_calendar_fourier_smoke(time_index, forecast_index): cf = CalendarFourier("A", 2) cf.in_sample(time_index) steps = 83 if forecast_index is None else len(forecast_index) cf.out_of_sample(steps, time_index, forecast_index) assert isinstance(cf.order, int) assert isinstance(cf.freq, str) str(cf) repr(cf) hash(cf) params = CalendarSeasonality._supported cs_params = [(k, k2) for k, v in params.items() for k2 in v.keys()] @pytest.mark.parametrize("freq_period", cs_params) def test_calendar_seasonality(time_index, forecast_index, freq_period): freq, period = freq_period cs = CalendarSeasonality(period, freq) cs.in_sample(time_index) steps = 83 if forecast_index is None else len(forecast_index) cs.out_of_sample(steps, time_index, forecast_index) assert isinstance(cs.period, str) assert isinstance(cs.freq, str) str(cs) repr(cs) hash(cs) cs2 = CalendarSeasonality(period, freq) assert cs == cs2 def test_forbidden_index(): index = pd.RangeIndex(0, 10) ct = CalendarTimeTrend("A", order=2) with pytest.raises(TypeError, match="CalendarTimeTrend terms can only"): ct.in_sample(index) def test_calendar_time_trend_base(time_index): ct = CalendarTimeTrend("M", True, order=3, base_period="1960-1-1") ct2 = CalendarTimeTrend("M", True, order=3) assert ct != ct2 str(ct) str(ct2) assert ct.base_period is not None assert ct2.base_period is None def test_invalid_freq_period(time_index): with pytest.raises(ValueError, match="The combination of freq="): CalendarSeasonality("H", "A") cs = CalendarSeasonality("B", "W") with pytest.raises(ValueError, match="freq is B but index contains"): cs.in_sample(pd.date_range("2000-1-1", periods=10, freq="D")) def test_check_index_type(): ct = CalendarTimeTrend("A", True, order=3) idx = pd.RangeIndex(0, 20) with pytest.raises(TypeError, match="CalendarTimeTrend terms can only"): ct._check_index_type(idx, pd.DatetimeIndex) with pytest.raises(TypeError, match="CalendarTimeTrend terms can only"): ct._check_index_type(idx, (pd.DatetimeIndex,)) with pytest.raises(TypeError, match="CalendarTimeTrend terms can only"): ct._check_index_type(idx, (pd.DatetimeIndex, pd.PeriodIndex)) idx = pd.Index([0, 1, 1, 2, 3, 5, 8, 13]) with pytest.raises(TypeError, match="CalendarTimeTrend terms can only"): types = (pd.DatetimeIndex, pd.PeriodIndex, pd.RangeIndex) ct._check_index_type(idx, types) def test_unknown_freq(): with pytest.raises(ValueError, match="freq is not understood by pandas"): CalendarTimeTrend("unknown", True, order=3) def test_invalid_formcast_index(index): tt = TimeTrend(order=4) with pytest.raises(ValueError, match="The number of values in forecast_"): tt.out_of_sample(10, index, pd.RangeIndex(11)) def test_seasonal_from_index_err(): index = pd.Index([0, 1, 1, 2, 3, 5, 8, 12]) with pytest.raises(TypeError): Seasonality.from_index(index) index = pd.date_range("2000-1-1", periods=10)[[0, 1, 2, 3, 5, 8]] with pytest.raises(ValueError): Seasonality.from_index(index) def test_time_trend(index): tt = TimeTrend(constant=True) const = tt.in_sample(index) assert const.shape == (index.shape[0], 1) assert np.all(const == 1) pd.testing.assert_index_equal(const.index, index) warn = None if type(index) is pd.Int64Index and np.any(np.diff(index) != 1): warn = UserWarning with pytest.warns(warn): const_fcast = tt.out_of_sample(23, index) assert np.all(const_fcast == 1) tt = TimeTrend(constant=False) empty = tt.in_sample(index) assert empty.shape == (index.shape[0], 0) tt = TimeTrend(constant=False, order=2) t2 = tt.in_sample(index) assert t2.shape == (index.shape[0], 2) assert list(t2.columns) == ["trend", "trend_squared"] tt = TimeTrend(constant=True, order=2) final = tt.in_sample(index) expected = pd.concat([const, t2], axis=1) pd.testing.assert_frame_equal(final, expected) tt = TimeTrend(constant=True, order=2) short = tt.in_sample(index[:-50]) with pytest.warns(warn): remainder = tt.out_of_sample(50, index[:-50]) with pytest.warns(warn): direct = tt.out_of_sample( steps=50, index=index[:-50], forecast_index=index[-50:] ) combined = pd.concat([short, remainder], axis=0) if isinstance(index, (pd.DatetimeIndex, pd.RangeIndex)): pd.testing.assert_frame_equal(combined, final) combined = pd.concat([short, direct], axis=0) pd.testing.assert_frame_equal(combined, final) def test_seasonality(index): s = Seasonality(period=12) exog = s.in_sample(index) assert s.is_dummy assert exog.shape == (index.shape[0], 12) pd.testing.assert_index_equal(exog.index, index) assert np.all(exog.sum(1) == 1.0) assert list(exog.columns) == [f"s({i},12)" for i in range(1, 13)] expected = np.zeros((index.shape[0], 12)) for i in range(12): expected[i::12, i] = 1.0 np.testing.assert_equal(expected, np.asarray(exog)) warn = None if type(index) is pd.Int64Index and np.any(np.diff(index) != 1): warn = UserWarning with pytest.warns(warn): fcast = s.out_of_sample(steps=12, index=index) assert fcast.iloc[0, len(index) % 12] == 1.0 assert np.all(fcast.sum(1) == 1) s = Seasonality(period=7, initial_period=3) exog = s.in_sample(index) assert exog.iloc[0, 2] == 1.0 assert exog.iloc[0].sum() == 1.0 assert s.initial_period == 3 with pytest.raises(ValueError, match="initial_period must be in"): Seasonality(period=12, initial_period=-3) with pytest.raises(ValueError, match="period must be >= 2"): Seasonality(period=1) def test_seasonality_time_index(time_index): tt = Seasonality.from_index(time_index) assert tt.period == 5 fcast = tt.out_of_sample(steps=12, index=time_index) new_idx = DeterministicTerm._extend_index(time_index, 12) pd.testing.assert_index_equal(fcast.index, new_idx) def test_fourier(index): f = Fourier(period=12, order=3) terms = f.in_sample(index) assert f.order == 3 assert terms.shape == (index.shape[0], 2 * f.order) loc = np.arange(index.shape[0]) / 12 for i, col in enumerate(terms): j = i // 2 + 1 fn = np.cos if (i % 2) else np.sin expected = fn(2 * np.pi * j * loc) np.testing.assert_allclose(terms[col], expected, atol=1e-8) cols = [] for i in range(2 * f.order): fn = "cos" if (i % 2) else "sin" cols.append(f"{fn}({(i // 2) + 1},12)") assert list(terms.columns) == cols @pytest.mark.skipif(pandas_lt_1_0_0, reason="bug in old pandas") def test_index_like(): idx = np.empty((100, 2)) with pytest.raises(TypeError, match="index must be a pandas"): DeterministicTerm._index_like(idx) def test_calendar_fourier(reset_randomstate): inc = np.abs(np.random.standard_normal(1000)) inc = np.cumsum(inc) inc = 10 * inc / inc[-1] offset = (24 * 3600 * inc).astype(np.int64) base = pd.Timestamp("2000-1-1") index = [base + pd.Timedelta(val, unit="s") for val in offset] index = pd.Index(index) cf = CalendarFourier("D", 2) assert cf.order == 2 terms = cf.in_sample(index) cols = [] for i in range(2 * cf.order): fn = "cos" if (i % 2) else "sin" cols.append(f"{fn}({(i // 2) + 1},freq=D)") assert list(terms.columns) == cols inc = offset / (24 * 3600) loc = 2 * np.pi * (inc - np.floor(inc)) expected = [] for i in range(4): scale = i // 2 + 1 fn = np.cos if (i % 2) else np.sin expected.append(fn(scale * loc)) expected = np.column_stack(expected) np.testing.assert_allclose(expected, terms.values) def test_calendar_time_trend(reset_randomstate): inc = np.abs(np.random.standard_normal(1000)) inc = np.cumsum(inc) inc = 10 * inc / inc[-1] offset = (24 * 3600 * inc).astype(np.int64) base = pd.Timestamp("2000-1-1") index = [base + pd.Timedelta(val, "s") for val in offset] index = pd.Index(index) ctt = CalendarTimeTrend("D", True, order=3, base_period=base) assert ctt.order == 3 terms = ctt.in_sample(index) cols = ["const", "trend", "trend_squared", "trend_cubed"] assert list(terms.columns) == cols inc = 1 + offset / (24 * 3600) expected = [] for i in range(4): expected.append(inc ** i) expected = np.column_stack(expected) np.testing.assert_allclose(expected, terms.values) ctt = CalendarTimeTrend("D", True, order=2, base_period=base) ctt2 = CalendarTimeTrend.from_string("D", trend="ctt", base_period=base) pd.testing.assert_frame_equal(ctt.in_sample(index), ctt2.in_sample(index)) ct = CalendarTimeTrend("D", True, order=1, base_period=base) ct2 = CalendarTimeTrend.from_string("D", trend="ct", base_period=base) pd.testing.assert_frame_equal(ct.in_sample(index), ct2.in_sample(index)) ctttt = CalendarTimeTrend("D", True, order=4, base_period=base) assert ctttt.order == 4 terms = ctttt.in_sample(index) cols = ["const", "trend", "trend_squared", "trend_cubed", "trend**4"] assert list(terms.columns) == cols def test_calendar_seasonal_period_w(): period = "W" index = pd.date_range("2000-01-03", freq="H", periods=600) cs = CalendarSeasonality("H", period=period) terms = cs.in_sample(index) assert np.all(terms.sum(1) == 1.0) for i in range(index.shape[0]): assert terms.iloc[i, i % 168] == 1.0 index = pd.date_range("2000-01-03", freq="B", periods=600) cs = CalendarSeasonality("B", period=period) terms = cs.in_sample(index) assert np.all(terms.sum(1) == 1.0) for i in range(index.shape[0]): assert terms.iloc[i, i % 5] == 1.0 index = pd.date_range("2000-01-03", freq="D", periods=600) cs = CalendarSeasonality("D", period=period) terms = cs.in_sample(index) assert np.all(terms.sum(1) == 1.0) for i in range(index.shape[0]): assert terms.iloc[i, i % 7] == 1.0 def test_calendar_seasonal_period_d(): period = "D" index = pd.date_range("2000-01-03", freq="H", periods=600) cs = CalendarSeasonality("H", period=period) terms = cs.in_sample(index) assert np.all(terms.sum(1) == 1.0) for i in range(index.shape[0]): assert terms.iloc[i, i % 24] == 1.0 def test_calendar_seasonal_period_q(): period = "Q" index = pd.date_range("2000-01-01", freq="M", periods=600) cs = CalendarSeasonality("M", period=period) terms = cs.in_sample(index) assert np.all(terms.sum(1) == 1.0) for i in range(index.shape[0]): assert terms.iloc[i, i % 3] == 1.0 def test_calendar_seasonal_period_a(): period = "A" index = pd.date_range("2000-01-01", freq="M", periods=600) cs = CalendarSeasonality("M", period=period) terms = cs.in_sample(index) assert np.all(terms.sum(1) == 1.0) for i in range(index.shape[0]): assert terms.iloc[i, i % 12] == 1.0 cs = CalendarSeasonality("Q", period=period) terms = cs.in_sample(index) assert np.all(terms.sum(1) == 1.0) for i in range(index.shape[0]): assert terms.iloc[i, (i % 12) // 3] == 1.0 @pytest.mark.parametrize("constant", [True, False]) @pytest.mark.parametrize("order", [0, 1]) @pytest.mark.parametrize("seasonal", [True, False]) @pytest.mark.parametrize("fourier", [0, 1]) @pytest.mark.parametrize("period", [None, 10]) @pytest.mark.parametrize("drop", [True, False]) def test_deterministic_process( time_index, constant, order, seasonal, fourier, period, drop ): if seasonal and fourier: return dp = DeterministicProcess( time_index, constant=constant, order=order, seasonal=seasonal, fourier=fourier, period=period, drop=drop, ) terms = dp.in_sample() pd.testing.assert_index_equal(terms.index, time_index) terms = dp.out_of_sample(23) assert isinstance(terms, pd.DataFrame) def test_deterministic_process_errors(time_index): with pytest.raises(ValueError, match="seasonal and fourier"): DeterministicProcess(time_index, seasonal=True, fourier=2, period=5) with pytest.raises(TypeError, match="All additional terms"): DeterministicProcess(time_index, seasonal=True, additional_terms=[1]) def test_range_error(): idx = pd.Index([0, 1, 1, 2, 3, 5, 8, 13]) dp = DeterministicProcess( idx, constant=True, order=2, seasonal=True, period=2 ) with pytest.raises(TypeError, match="The index in the deterministic"): dp.range(0, 12) def test_range_index_basic(): idx = pd.date_range("2000-1-1", freq="M", periods=120) dp = DeterministicProcess(idx, constant=True, order=1, seasonal=True) dp.range("2001-1-1", "2008-1-1") dp.range("2001-1-1", "2015-1-1") dp.range("2013-1-1", "2008-1-1") dp.range(0, 100) dp.range(100, 150) dp.range(130, 150) with pytest.raises(ValueError): dp.range("1990-1-1", "2010-1-1") idx = pd.period_range("2000-1-1", freq="M", periods=120) dp = DeterministicProcess(idx, constant=True, order=1, seasonal=True) dp.range("2001-1-1", "2008-1-1") dp.range("2001-1-1", "2015-1-1") dp.range("2013-1-1", "2008-1-1") with pytest.raises(ValueError, match="start must be non-negative"): dp.range(-7, 200) dp.range(0, 100) dp.range(100, 150) dp.range(130, 150) idx = pd.RangeIndex(0, 120) dp = DeterministicProcess( idx, constant=True, order=1, seasonal=True, period=12 ) dp.range(0, 100) dp.range(100, 150) dp.range(120, 150) dp.range(130, 150) with pytest.raises(ValueError): dp.range(-10, 0) def test_range_casting(): idx = np.arange(120) dp = DeterministicProcess( idx, constant=True, order=1, seasonal=True, period=12 ) idx = pd.RangeIndex(0, 120) dp2 = DeterministicProcess( idx, constant=True, order=1, seasonal=True, period=12 ) pd.testing.assert_frame_equal(dp.in_sample(), dp2.in_sample()) pd.testing.assert_frame_equal(dp.range(100, 150), dp2.range(100, 150)) def test_non_unit_range(): idx = pd.RangeIndex(0, 700, 7) dp = DeterministicProcess(idx, constant=True) with pytest.raises(ValueError, match="The step of the index is not 1"): dp.range(11, 900) def test_additional_terms(time_index): add_terms = [TimeTrend(True, order=1)] dp = DeterministicProcess(time_index, additional_terms=add_terms) dp2 = DeterministicProcess(time_index, constant=True, order=1) pd.testing.assert_frame_equal(dp.in_sample(), dp2.in_sample()) with pytest.raises( ValueError, match="One or more terms in additional_terms" ): DeterministicProcess( time_index, additional_terms=add_terms + add_terms ) with pytest.raises( ValueError, match="One or more terms in additional_terms" ): DeterministicProcess( time_index, constant=True, order=1, additional_terms=add_terms ) def test_drop_two_consants(time_index): tt = TimeTrend(constant=True, order=1) dp = DeterministicProcess( time_index, constant=True, additional_terms=[tt], drop=True ) assert dp.in_sample().shape[1] == 2 dp2 = DeterministicProcess(time_index, additional_terms=[tt], drop=True) pd.testing.assert_frame_equal(dp.in_sample(), dp2.in_sample()) @pytest.mark.parametrize( "index", [ pd.RangeIndex(0, 200), pd.Int64Index(np.arange(200)), pd.date_range("2000-1-1", freq="M", periods=200), pd.period_range("2000-1-1", freq="M", periods=200), ], ) def test_determintic_term_equiv(index): base = DeterministicProcess(pd.RangeIndex(0, 200), constant=True, order=2) dp = DeterministicProcess(index, constant=True, order=2) np.testing.assert_array_equal(base.in_sample(), dp.in_sample()) np.testing.assert_array_equal(base.out_of_sample(37), dp.out_of_sample(37)) np.testing.assert_array_equal(base.range(200, 237), dp.range(200, 237)) np.testing.assert_array_equal(base.range(50, 150), dp.range(50, 150)) np.testing.assert_array_equal(base.range(50, 250), dp.range(50, 250)) class DummyTerm(DeterministicTerm): @property def _eq_attr(self) -> Tuple[Hashable, ...]: return ("Dummy",) def __str__(self) -> str: return "Dummy" columns = [ "const1", "const2", "trend1", "trend2", "normal1", "normal2", "dummy1_1", "dummy1_2", "always_drop1", "always_drop2", "dummy2_1", "dummy2_2", ] def in_sample(self, index: pd.Index) -> pd.DataFrame: nobs = index.shape[0] terms = np.empty((index.shape[0], 12)) for i in range(0, 12, 2): if i == 0: value = 1 elif i == 2: value = np.arange(nobs) elif i == 4: value = np.random.standard_normal(nobs) elif i == 6: value = np.zeros(nobs) value[::2] = 1 elif i == 8: value = 0 else: # elif i == 8: value = np.zeros(nobs) value[1::2] = 1 terms[:, i] = terms[:, i + 1] = value return pd.DataFrame(terms, columns=self.columns, index=index) def out_of_sample( self, steps: int, index: pd.Index, forecast_index: pd.Index = None, ) -> pd.DataFrame: fcast_index = self._extend_index(index, steps, forecast_index) terms = np.random.standard_normal((steps, 12)) return pd.DataFrame(terms, columns=self.columns, index=fcast_index) def test_drop(): index = pd.RangeIndex(0, 200) dummy = DummyTerm() str(dummy) assert dummy != TimeTrend() dp = DeterministicProcess(index, additional_terms=[dummy], drop=True) in_samp = dp.in_sample() assert in_samp.shape == (200, 4) oos = dp.out_of_sample(37) assert oos.shape == (37, 4) assert list(oos.columns) == list(in_samp.columns) valid = ("const", "trend", "dummy", "normal") for valid_col in valid: assert sum([1 for col in oos if valid_col in col]) == 1 statsmodels-0.12.2/statsmodels/tsa/tests/test_exponential_smoothing.py000066400000000000000000000744061400612667500265010ustar00rootroot00000000000000""" Author: Samuel Scherrer """ from statsmodels.compat.platform import PLATFORM_WIN, PLATFORM_LINUX32 from itertools import product import json import pathlib import numpy as np from numpy.testing import assert_allclose, assert_almost_equal import pandas as pd import pytest import scipy.stats from statsmodels.tsa.exponential_smoothing.ets import ETSModel import statsmodels.tsa.holtwinters as holtwinters import statsmodels.tsa.statespace.exponential_smoothing as statespace # This contains tests for the exponential smoothing implementation in # tsa/exponential_smoothing/ets.py. # # Tests are mostly done by comparing results with the R implementation in the # package forecast for the datasets `oildata` (non-seasonal) and `austourists` # (seasonal). # # Therefore, a parametrized pytest fixture ``setup_model`` is provided, which # returns a constructed model, model parameters from R in the format expected # by ETSModel, and a dictionary of reference results. Use like this: # # def test_(setup_model): # model, params, results_R = setup_model # # perform some tests # ... ############################################################################### # UTILS ############################################################################### # Below I define parameter lists for all possible model and data combinations # (for data, see below). These are used for parametrizing the pytest fixture # ``setup_model``, which should be used for all tests comparing to R output. def remove_invalid_models_from_list(modellist): # remove invalid models (no trend but damped) for i, model in enumerate(modellist): if model[1] is None and model[3]: del modellist[i] ERRORS = ("add", "mul") TRENDS = ("add", "mul", None) SEASONALS = ("add", "mul", None) DAMPED = (True, False) MODELS_DATA_SEASONAL = list( product(ERRORS, TRENDS, ("add", "mul"), DAMPED, ("austourists",),) ) MODELS_DATA_NONSEASONAL = list( product(ERRORS, TRENDS, (None,), DAMPED, ("oildata",),) ) remove_invalid_models_from_list(MODELS_DATA_SEASONAL) remove_invalid_models_from_list(MODELS_DATA_NONSEASONAL) def short_model_name(error, trend, seasonal, damped=False): short_name = {"add": "A", "mul": "M", None: "N", True: "d", False: ""} return ( short_name[error] + short_name[trend] + short_name[damped] + short_name[seasonal] ) ALL_MODELS_AND_DATA = MODELS_DATA_NONSEASONAL + MODELS_DATA_SEASONAL ALL_MODEL_IDS = [ short_model_name(*mod[:3], mod[3]) for mod in ALL_MODELS_AND_DATA ] @pytest.fixture(params=ALL_MODELS_AND_DATA, ids=ALL_MODEL_IDS) def setup_model( request, austourists, oildata, ets_austourists_fit_results_R, ets_oildata_fit_results_R, ): params = request.param error, trend, seasonal, damped = params[0:4] data = params[4] if data == "austourists": data = austourists seasonal_periods = 4 results = ets_austourists_fit_results_R[damped] else: data = oildata seasonal_periods = None results = ets_oildata_fit_results_R[damped] name = short_model_name(error, trend, seasonal) if name not in results: pytest.skip(f"model {name} not implemented or not converging in R") results_R = results[name] params = get_params_from_R(results_R) model = ETSModel( data, seasonal_periods=seasonal_periods, error=error, trend=trend, seasonal=seasonal, damped_trend=damped, ) return model, params, results_R @pytest.fixture def austourists_model(austourists): return ETSModel( austourists, seasonal_periods=4, error="add", trend="add", seasonal="add", damped_trend=True, ) @pytest.fixture def austourists_model_fit(austourists_model): return austourists_model.fit(disp=False) @pytest.fixture def oildata_model(oildata): return ETSModel(oildata, error="add", trend="add", damped_trend=True,) ############################################################################# # DATA ############################################################################# @pytest.fixture def austourists(): # austourists dataset from fpp2 package # https://cran.r-project.org/web/packages/fpp2/index.html data = [ 30.05251300, 19.14849600, 25.31769200, 27.59143700, 32.07645600, 23.48796100, 28.47594000, 35.12375300, 36.83848500, 25.00701700, 30.72223000, 28.69375900, 36.64098600, 23.82460900, 29.31168300, 31.77030900, 35.17787700, 19.77524400, 29.60175000, 34.53884200, 41.27359900, 26.65586200, 28.27985900, 35.19115300, 42.20566386, 24.64917133, 32.66733514, 37.25735401, 45.24246027, 29.35048127, 36.34420728, 41.78208136, 49.27659843, 31.27540139, 37.85062549, 38.83704413, 51.23690034, 31.83855162, 41.32342126, 42.79900337, 55.70835836, 33.40714492, 42.31663797, 45.15712257, 59.57607996, 34.83733016, 44.84168072, 46.97124960, 60.01903094, 38.37117851, 46.97586413, 50.73379646, 61.64687319, 39.29956937, 52.67120908, 54.33231689, 66.83435838, 40.87118847, 51.82853579, 57.49190993, 65.25146985, 43.06120822, 54.76075713, 59.83447494, 73.25702747, 47.69662373, 61.09776802, 66.05576122, ] index = pd.date_range("1999-01-01", "2015-12-31", freq="Q") return pd.Series(data, index) @pytest.fixture def oildata(): # oildata dataset from fpp2 package # https://cran.r-project.org/web/packages/fpp2/index.html data = [ 111.0091346, 130.8284341, 141.2870879, 154.2277747, 162.7408654, 192.1664835, 240.7997253, 304.2173901, 384.0045673, 429.6621566, 359.3169299, 437.2518544, 468.4007898, 424.4353365, 487.9794299, 509.8284478, 506.3472527, 340.1842374, 240.2589210, 219.0327876, 172.0746632, 252.5900922, 221.0710774, 276.5187735, 271.1479517, 342.6186005, 428.3558357, 442.3945534, 432.7851482, 437.2497186, 437.2091599, 445.3640981, 453.1950104, 454.4096410, 422.3789058, 456.0371217, 440.3866047, 425.1943725, 486.2051735, 500.4290861, 521.2759092, 508.9476170, 488.8888577, 509.8705750, 456.7229123, 473.8166029, 525.9508706, 549.8338076, 542.3404698, ] return pd.Series(data, index=pd.date_range("1965", "2013", freq="AS")) ############################################################################# # REFERENCE RESULTS ############################################################################# def obtain_R_results(path): with path.open("r") as f: R_results = json.load(f) # remove invalid models results = {} for damped in R_results: new_key = damped == "TRUE" results[new_key] = {} for model in R_results[damped]: if len(R_results[damped][model]): results[new_key][model] = R_results[damped][model] # get correct types for damped in results: for model in results[damped]: for key in ["alpha", "beta", "gamma", "phi", "sigma2"]: results[damped][model][key] = float( results[damped][model][key][0] ) for key in [ "states", "initstate", "residuals", "fitted", "forecast", "simulation", ]: results[damped][model][key] = np.asarray( results[damped][model][key] ) return results @pytest.fixture def ets_austourists_fit_results_R(): """ Dictionary of ets fit results obtained with script ``results/fit_ets.R``. """ path = ( pathlib.Path(__file__).parent / "results" / "fit_ets_results_seasonal.json" ) return obtain_R_results(path) @pytest.fixture def ets_oildata_fit_results_R(): """ Dictionary of ets fit results obtained with script ``results/fit_ets.R``. """ path = ( pathlib.Path(__file__).parent / "results" / "fit_ets_results_nonseasonal.json" ) return obtain_R_results(path) def fit_austourists_with_R_params(model, results_R, set_state=False): """ Fit the model with params as found by R's forecast package """ params = get_params_from_R(results_R) with model.fix_params(dict(zip(model.param_names, params))): fit = model.fit(disp=False) if set_state: states_R = get_states_from_R(results_R, model._k_states) fit.states = states_R return fit def get_params_from_R(results_R): # get params from R params = [results_R[name] for name in ["alpha", "beta", "gamma", "phi"]] # in R, initial states are order l[-1], b[-1], s[-1], s[-2], ..., s[-m] params += list(results_R["initstate"]) params = list(filter(np.isfinite, params)) return params def get_states_from_R(results_R, k_states): if k_states > 1: xhat_R = results_R["states"][1:, 0:k_states] else: xhat_R = results_R["states"][1:] xhat_R = np.reshape(xhat_R, (len(xhat_R), 1)) return xhat_R ############################################################################# # BASIC TEST CASES ############################################################################# def test_fit_model_austouritsts(setup_model): model, params, results_R = setup_model model.fit(disp=False) ############################################################################# # TEST OF MODEL EQUATIONS VS R ############################################################################# def test_smooth_vs_R(setup_model): model, params, results_R = setup_model yhat, xhat = model.smooth(params, return_raw=True) yhat_R = results_R["fitted"] xhat_R = get_states_from_R(results_R, model._k_states) assert_allclose(xhat, xhat_R, rtol=1e-5, atol=1e-5) assert_allclose(yhat, yhat_R, rtol=1e-5, atol=1e-5) def test_residuals_vs_R(setup_model): model, params, results_R = setup_model yhat = model.smooth(params, return_raw=True)[0] residuals = model._residuals(yhat) assert_allclose(residuals, results_R["residuals"], rtol=1e-5, atol=1e-5) def test_loglike_vs_R(setup_model): model, params, results_R = setup_model loglike = model.loglike(params) # the calculation of log likelihood in R is only up to a constant: const = -model.nobs / 2 * (np.log(2 * np.pi / model.nobs) + 1) loglike_R = results_R["loglik"][0] + const assert_allclose(loglike, loglike_R, rtol=1e-5, atol=1e-5) def test_forecast_vs_R(setup_model): model, params, results_R = setup_model fit = fit_austourists_with_R_params(model, results_R, set_state=True) fcast = fit.forecast(4) expected = np.asarray(results_R["forecast"]) assert_allclose(expected, fcast.values, rtol=1e-3, atol=1e-4) def test_simulate_vs_R(setup_model): model, params, results_R = setup_model fit = fit_austourists_with_R_params(model, results_R, set_state=True) innov = np.asarray([[1.76405235, 0.40015721, 0.97873798, 2.2408932]]).T sim = fit.simulate(4, anchor="end", repetitions=1, random_errors=innov) expected = np.asarray(results_R["simulation"]) assert_allclose(expected, sim.values, rtol=1e-5, atol=1e-5) def test_fit_vs_R(setup_model, reset_randomstate): model, params, results_R = setup_model if PLATFORM_WIN and model.short_name == "AAdA": start = params else: start = None fit = model.fit(disp=True, tol=1e-8, start_params=start) # check log likelihood: we want to have a fit that is better, i.e. a fit # that has a **higher** log-likelihood const = -model.nobs / 2 * (np.log(2 * np.pi / model.nobs) + 1) loglike_R = results_R["loglik"][0] + const loglike = fit.llf try: assert loglike >= loglike_R - 1e-4 except AssertionError: fit = model.fit(disp=True, tol=1e-8, start_params=params) loglike = fit.llf try: assert loglike >= loglike_R - 1e-4 except AssertionError: if PLATFORM_LINUX32: # Linux32 often fails to produce the correct solution. # Fixing this is low priority given the rareness of # its application pytest.xfail("Known to fail on 32-bit Linux") else: raise def test_predict_vs_R(setup_model): model, params, results_R = setup_model fit = fit_austourists_with_R_params(model, results_R, set_state=True) n = fit.nobs prediction = fit.predict(end=n + 3, dynamic=n) yhat_R = results_R["fitted"] assert_allclose(prediction[:n], yhat_R, rtol=1e-5, atol=1e-5) forecast_R = results_R["forecast"] assert_allclose(prediction[n:], forecast_R, rtol=1e-3, atol=1e-4) ############################################################################# # OTHER TESTS ############################################################################# def test_initialization_known(austourists): initial_level, initial_trend = [36.46466837, 34.72584983] model = ETSModel( austourists, error="add", trend="add", damped_trend=True, initialization_method="known", initial_level=initial_level, initial_trend=initial_trend, ) internal_params = model._internal_params(model._start_params) assert initial_level == internal_params[4] assert initial_trend == internal_params[5] assert internal_params[6] == 0 def test_initialization_heuristic(oildata): model_estimated = ETSModel( oildata, error="add", trend="add", damped_trend=True, initialization_method="estimated", ) model_heuristic = ETSModel( oildata, error="add", trend="add", damped_trend=True, initialization_method="heuristic", ) fit_estimated = model_estimated.fit(disp=False) fit_heuristic = model_heuristic.fit(disp=False) yhat_estimated = fit_estimated.fittedvalues.values yhat_heuristic = fit_heuristic.fittedvalues.values # this test is mostly just to see if it works, so we only test whether the # result is not totally off assert_allclose(yhat_estimated[10:], yhat_heuristic[10:], rtol=0.5) def test_bounded_fit(oildata): beta = [0.99, 0.99] model1 = ETSModel( oildata, error="add", trend="add", damped_trend=True, bounds={"smoothing_trend": beta}, ) fit1 = model1.fit(disp=False) assert fit1.smoothing_trend == 0.99 # same using with fix_params semantic model2 = ETSModel(oildata, error="add", trend="add", damped_trend=True,) with model2.fix_params({"smoothing_trend": 0.99}): fit2 = model2.fit(disp=False) assert fit2.smoothing_trend == 0.99 assert_allclose(fit1.params, fit2.params) fit2.summary() # check if summary runs without failing # using fit_constrained fit3 = model2.fit_constrained({"smoothing_trend": 0.99}) assert fit3.smoothing_trend == 0.99 assert_allclose(fit1.params, fit3.params) fit3.summary() def test_seasonal_periods(austourists): # test auto-deduction of period model = ETSModel(austourists, error="add", trend="add", seasonal="add") assert model.seasonal_periods == 4 # test if seasonal period raises error try: model = ETSModel(austourists, seasonal="add", seasonal_periods=0) except ValueError: pass def test_simulate_keywords(austourists_model_fit): """ check whether all keywords are accepted and work without throwing errors. """ fit = austourists_model_fit # test anchor assert_almost_equal( fit.simulate(4, anchor=-1, random_state=0).values, fit.simulate(4, anchor="2015-12-31", random_state=0).values, ) assert_almost_equal( fit.simulate(4, anchor="end", random_state=0).values, fit.simulate(4, anchor="2015-12-31", random_state=0).values, ) # test different random error options fit.simulate(4, repetitions=10) fit.simulate(4, repetitions=10, random_errors=scipy.stats.norm) fit.simulate(4, repetitions=10, random_errors=scipy.stats.norm()) fit.simulate(4, repetitions=10, random_errors=np.random.randn(4, 10)) fit.simulate(4, repetitions=10, random_errors="bootstrap") # test seeding res = fit.simulate(4, repetitions=10, random_state=10).values res2 = fit.simulate( 4, repetitions=10, random_state=np.random.RandomState(10) ).values assert np.all(res == res2) def test_predict_ranges(austourists_model_fit): # in total 68 observations fit = austourists_model_fit # first prediction is 0, last is 10 -> 11 predictions pred = fit.predict(start=0, end=10) assert len(pred) == 11 pred = fit.predict(start=10, end=20) assert len(pred) == 11 pred = fit.predict(start=10, dynamic=10, end=30) assert len(pred) == 21 # try boolean dynamic pred = fit.predict(start=0, dynamic=True, end=70) assert len(pred) == 71 pred = fit.predict(start=0, dynamic=True, end=70) assert len(pred) == 71 # try only out oof sample prediction pred = fit.predict(start=80, end=84) assert len(pred) == 5 def test_summary(austourists_model): # just try to run summary to see if it works fit = austourists_model.fit(disp=False) fit.summary() # now without estimated initial states austourists_model.set_initialization_method("heuristic") fit = austourists_model.fit(disp=False) fit.summary() # and with fixed params fit = austourists_model.fit_constrained({"smoothing_trend": 0.9}) fit.summary() def test_score(austourists_model_fit): score_cs = austourists_model_fit.model.score(austourists_model_fit.params) score_fd = austourists_model_fit.model.score( austourists_model_fit.params, approx_complex_step=False, approx_centered=True, ) assert_almost_equal(score_cs, score_fd, 4) def test_hessian(austourists_model_fit): # The hessian approximations are not very consistent, but the test makes # sure they run austourists_model_fit.model.hessian(austourists_model_fit.params) austourists_model_fit.model.hessian( austourists_model_fit.params, approx_complex_step=False, approx_centered=True, ) def test_prediction_results(austourists_model_fit): # simple test case starting at 0 pred = austourists_model_fit.get_prediction(start=0, dynamic=30, end=40,) summary = pred.summary_frame() assert len(summary["mean"].values) == 41 assert np.all(~np.isnan(summary["mean"])) # simple test case starting at not 0 pred = austourists_model_fit.get_prediction(start=10, dynamic=30, end=40) summary = pred.summary_frame() assert len(summary["mean"].values) == 31 assert np.all(~np.isnan(summary["mean"])) # long out of sample prediction pred = austourists_model_fit.get_prediction(start=0, dynamic=30, end=80) summary = pred.summary_frame() assert len(summary["mean"].values) == 81 assert np.all(~np.isnan(summary["mean"])) # long out of sample, starting in-sample pred = austourists_model_fit.get_prediction(start=67, end=80) summary = pred.summary_frame() assert len(summary["mean"].values) == 14 assert np.all(~np.isnan(summary["mean"])) # long out of sample, starting at end of sample pred = austourists_model_fit.get_prediction(start=68, end=80) summary = pred.summary_frame() assert len(summary["mean"].values) == 13 assert np.all(~np.isnan(summary["mean"])) # long out of sample, starting just out of sample pred = austourists_model_fit.get_prediction(start=69, end=80) summary = pred.summary_frame() assert len(summary["mean"].values) == 12 assert np.all(~np.isnan(summary["mean"])) # long out of sample, starting long out of sample pred = austourists_model_fit.get_prediction(start=79, end=80) summary = pred.summary_frame() assert len(summary["mean"].values) == 2 assert np.all(~np.isnan(summary["mean"])) # long out of sample, `start`== `end` pred = austourists_model_fit.get_prediction(start=80, end=80) summary = pred.summary_frame() assert len(summary["mean"].values) == 1 assert np.all(~np.isnan(summary["mean"])) @pytest.fixture def statespace_comparison(austourists): ets_model = ETSModel( austourists, seasonal_periods=4, error="add", trend="add", seasonal="add", damped_trend=True, ) ets_results = ets_model.fit(disp=False) statespace_model = statespace.ExponentialSmoothing( austourists, trend=True, damped_trend=True, seasonal=4, initialization_method="known", initial_level=ets_results.initial_level, initial_trend=ets_results.initial_trend, initial_seasonal=ets_results.initial_seasonal, ) with statespace_model.fix_params( { "smoothing_level": ets_results.smoothing_level, "smoothing_trend": ets_results.smoothing_trend, "smoothing_seasonal": ets_results.smoothing_seasonal, "damping_trend": ets_results.damping_trend, } ): statespace_results = statespace_model.fit() return ets_results, statespace_results def test_results_vs_statespace(statespace_comparison): ets_results, statespace_results = statespace_comparison assert_almost_equal(ets_results.llf, statespace_results.llf) assert_almost_equal(ets_results.scale, statespace_results.scale) assert_almost_equal( ets_results.fittedvalues.values, statespace_results.fittedvalues.values ) # compare diagnostics with pytest.warns(FutureWarning): assert_almost_equal( ets_results.test_serial_correlation(method="ljungbox"), statespace_results.test_serial_correlation(method="ljungbox"), ) assert_almost_equal( ets_results.test_normality(method="jarquebera"), statespace_results.test_normality(method="jarquebera"), ) # heteroskedasticity is somewhat different, because of burn in period? ets_het = ets_results.test_heteroskedasticity(method="breakvar")[0] statespace_het = statespace_results.test_heteroskedasticity( method="breakvar" )[0] # het[0] is test statistic, het[1] p-value if not PLATFORM_LINUX32: # Skip on Linux-32 bit due to random failures. These values are not # close at all in any way so it isn't clear what this is testing assert_allclose(ets_het[0], statespace_het[0], rtol=0.2) assert_allclose(ets_het[1], statespace_het[1], rtol=0.7) def test_prediction_results_vs_statespace(statespace_comparison): ets_results, statespace_results = statespace_comparison # comparison of two predictions ets_pred = ets_results.get_prediction(start=10, dynamic=10, end=40) statespace_pred = statespace_results.get_prediction( start=10, dynamic=10, end=40 ) statespace_summary = statespace_pred.summary_frame() ets_summary = ets_pred.summary_frame() # import matplotlib.pyplot as plt # plt.switch_backend('TkAgg') # plt.plot(ets_summary["mean"] - statespace_summary["mean"]) # plt.grid() # plt.show() assert_almost_equal( ets_summary["mean"].values[:-10], statespace_summary["mean"].values[:-10], ) assert_almost_equal( ets_summary["mean"].values[-10:], statespace_summary["mean"].values[-10:], 4, ) # comparison of dynamic prediction at end of sample -> this works ets_pred = ets_results.get_prediction(start=60, end=80,) statespace_pred = statespace_results.get_prediction(start=60, end=80) statespace_summary = statespace_pred.summary_frame() ets_summary = ets_pred.summary_frame() assert_almost_equal( ets_summary["mean"].values, statespace_summary["mean"].values, 4 ) @pytest.mark.skip def test_prediction_results_slow_AAN(oildata): # slow test with high number of simulation repetitions for comparison # Note: runs succesfull with specified tolerance fit = ETSModel(oildata, error="add", trend="add").fit(disp=False) pred_exact = fit.get_prediction(start=40, end=55) summary_exact = pred_exact.summary_frame() pred_sim = fit.get_prediction( start=40, end=55, simulate_repetitions=int(1e6), random_state=11, method="simulated", ) summary_sim = pred_sim.summary_frame() # check if mean converges to expected mean assert_allclose( summary_sim["mean"].values, summary_sim["mean_numerical"].values, rtol=1e-3, atol=1e-3, ) import matplotlib.pyplot as plt plt.switch_backend("TkAgg") for i in range(1000): plt.plot( pred_sim._results.simulation_results.iloc[:, i], color="grey", alpha=0.1, ) plt.plot(oildata[40:], "-", label="data") plt.plot(summary_exact["mean"], "--", label="mean") plt.plot(summary_sim["pi_lower"], ":", label="sim lower") plt.plot(summary_exact["pi_lower"], ".-", label="exact lower") plt.plot(summary_sim["pi_upper"], ":", label="sim upper") plt.plot(summary_exact["pi_upper"], ".-", label="exact upper") # plt.legend() plt.show() # check if prediction intervals are equal assert_allclose( summary_sim["pi_lower"].values, summary_exact["pi_lower"].values, rtol=1e-4, atol=1e-4, ) assert_allclose( summary_sim["pi_upper"].values, summary_exact["pi_upper"].values, rtol=1e-4, atol=1e-4, ) @pytest.mark.skip def test_prediction_results_slow_AAdA(austourists): # slow test with high number of simulation repetitions for comparison # Note: succesfull with specified tolerance fit = ETSModel( austourists, error="add", trend="add", seasonal="add", damped_trend=True, seasonal_periods=4, ).fit(disp=False) pred_exact = fit.get_prediction(start=60, end=75) summary_exact = pred_exact.summary_frame() pred_sim = fit.get_prediction( start=60, end=75, simulate_repetitions=int(1e6), random_state=11, method="simulated", ) summary_sim = pred_sim.summary_frame() # check if mean converges to expected mean assert_allclose( summary_sim["mean"].values, summary_sim["mean_numerical"].values, rtol=1e-3, atol=1e-3, ) import matplotlib.pyplot as plt plt.switch_backend("TkAgg") for i in range(1000): plt.plot( pred_sim._results.simulation_results.iloc[:, i], color="grey", alpha=0.1, ) plt.plot(fit.endog[60:], "-", label="data") plt.plot(summary_exact["mean"], "--", label="mean") plt.plot(summary_sim["pi_lower"], ":", label="sim lower") plt.plot(summary_exact["pi_lower"], ".-", label="exact lower") plt.plot(summary_sim["pi_upper"], ":", label="sim upper") plt.plot(summary_exact["pi_upper"], ".-", label="exact upper") plt.show() # check if prediction intervals are equal assert_allclose( summary_sim["pi_lower"].values, summary_exact["pi_lower"].values, rtol=2e-2, atol=1e-4, ) assert_allclose( summary_sim["pi_upper"].values, summary_exact["pi_upper"].values, rtol=2e-2, atol=1e-4, ) def test_convergence_simple(): # issue 6883 gen = np.random.RandomState(0) e = gen.standard_normal(12000) y = e.copy() for i in range(1, e.shape[0]): y[i] = y[i - 1] - 0.2 * e[i - 1] + e[i] y = y[200:] mod = holtwinters.ExponentialSmoothing( y, initialization_method="estimated" ) res = mod.fit() ets_res = ETSModel(y).fit() # the smoothing level should be very similar, the initial state might be # different as it doesn't influence the final result too much assert_allclose( res.params["smoothing_level"], ets_res.smoothing_level, rtol=1e-4, atol=1e-4, ) # the first few values are influenced by differences in initial state, so # we don't test them here assert_allclose( res.fittedvalues[10:], ets_res.fittedvalues[10:], rtol=1e-4, atol=1e-4 ) def test_exact_prediction_intervals(austourists_model_fit): fit = austourists_model_fit._results class DummyModel: def __init__(self, short_name): self.short_name = short_name # compare AAdN with AAN fit.damping_trend = 1 - 1e-3 fit.model = DummyModel("AAdN") steps = 5 s_AAdN = fit._relative_forecast_variance(steps) fit.model = DummyModel("AAN") s_AAN = fit._relative_forecast_variance(steps) assert_almost_equal(s_AAdN, s_AAN, 2) # compare AAdA with AAA fit.damping_trend = 1 - 1e-3 fit.model = DummyModel("AAdA") steps = 5 s_AAdA = fit._relative_forecast_variance(steps) fit.model = DummyModel("AAA") s_AAA = fit._relative_forecast_variance(steps) assert_almost_equal(s_AAdA, s_AAA, 2) def test_one_step_ahead(setup_model): model, params, results_R = setup_model model2 = ETSModel( pd.Series(model.endog), seasonal_periods=model.seasonal_periods, error=model.error, trend=model.trend, seasonal=model.seasonal, damped_trend=model.damped_trend, ) res = model2.smooth(params) fcast1 = res.forecast(steps=1) fcast2 = res.forecast(steps=2) assert_allclose(fcast1.iloc[0], fcast2.iloc[0]) pred1 = res.get_prediction(start=model2.nobs, end=model2.nobs, simulate_repetitions=2) pred2 = res.get_prediction(start=model2.nobs, end=model2.nobs + 1, simulate_repetitions=2) df1 = pred1.summary_frame(alpha=0.05) df2 = pred1.summary_frame(alpha=0.05) assert_allclose(df1.iloc[0, 0], df2.iloc[0, 0]) statsmodels-0.12.2/statsmodels/tsa/tests/test_seasonal.py000066400000000000000000000367331400612667500236720ustar00rootroot00000000000000import numpy as np import pandas as pd import pytest from numpy.testing import (assert_almost_equal, assert_equal, assert_raises, assert_allclose) from statsmodels.tsa.seasonal import seasonal_decompose # Verification values for tests SEASONAL = [62.46, 86.17, -88.38, -60.25, 62.46, 86.17, -88.38, -60.25, 62.46, 86.17, -88.38, -60.25, 62.46, 86.17, -88.38, -60.25, 62.46, 86.17, -88.38, -60.25, 62.46, 86.17, -88.38, -60.25, 62.46, 86.17, -88.38, -60.25, 62.46, 86.17, -88.38, -60.25] TREND = [np.nan, np.nan, 159.12, 204.00, 221.25, 245.12, 319.75, 451.50, 561.12, 619.25, 615.62, 548.00, 462.12, 381.12, 316.62, 264.00, 228.38, 210.75, 188.38, 199.00, 207.12, 191.00, 166.88, 72.00, -9.25, -33.12, -36.75, 36.25, 103.00, 131.62, np.nan, np.nan] RANDOM = [np.nan, np.nan, 78.254, 70.254, -36.710, -94.299, -6.371, -62.246, 105.415, 103.576, 2.754, 1.254, 15.415, -10.299, -33.246, -27.746, 46.165, -57.924, 28.004, -36.746, -37.585, 151.826, -75.496, 86.254, -10.210, -194.049, 48.129, 11.004, -40.460, 143.201, np.nan, np.nan] MULT_SEASONAL = [1.0815, 1.5538, 0.6716, 0.6931, 1.0815, 1.5538, 0.6716, 0.6931, 1.0815, 1.5538, 0.6716, 0.6931, 1.0815, 1.5538, 0.6716, 0.6931, 1.0815, 1.5538, 0.6716, 0.6931, 1.0815, 1.5538, 0.6716, 0.6931, 1.0815, 1.5538, 0.6716, 0.6931, 1.0815, 1.5538, 0.6716, 0.6931] MULT_TREND = [np.nan, np.nan, 171.62, 204.00, 221.25, 245.12, 319.75, 451.50, 561.12, 619.25, 615.62, 548.00, 462.12, 381.12, 316.62, 264.00, 228.38, 210.75, 188.38, 199.00, 207.12, 191.00, 166.88, 107.25, 80.50, 79.12, 78.75, 116.50, 140.00, 157.38, np.nan, np.nan] MULT_RANDOM = [np.nan, np.nan, 1.29263, 1.51360, 1.03223, 0.62226, 1.04771, 1.05139, 1.20124, 0.84080, 1.28182, 1.28752, 1.08043, 0.77172, 0.91697, 0.96191, 1.36441, 0.72986, 1.01171, 0.73956, 1.03566, 1.44556, 0.02677, 1.31843, 0.49390, 1.14688, 1.45582, 0.16101, 0.82555, 1.47633, np.nan, np.nan] class TestDecompose: @classmethod def setup_class(cls): # even data = [-50, 175, 149, 214, 247, 237, 225, 329, 729, 809, 530, 489, 540, 457, 195, 176, 337, 239, 128, 102, 232, 429, 3, 98, 43, -141, -77, -13, 125, 361, -45, 184] cls.data = pd.DataFrame(data, pd.date_range(start='1/1/1951', periods=len(data), freq='Q')) def test_ndarray(self): res_add = seasonal_decompose(self.data.values, period=4) assert_almost_equal(res_add.seasonal, SEASONAL, 2) assert_almost_equal(res_add.trend, TREND, 2) assert_almost_equal(res_add.resid, RANDOM, 3) res_mult = seasonal_decompose(np.abs(self.data.values), 'm', period=4) assert_almost_equal(res_mult.seasonal, MULT_SEASONAL, 4) assert_almost_equal(res_mult.trend, MULT_TREND, 2) assert_almost_equal(res_mult.resid, MULT_RANDOM, 4) # test odd res_add = seasonal_decompose(self.data.values[:-1], period=4) seasonal = [68.18, 69.02, -82.66, -54.54, 68.18, 69.02, -82.66, -54.54, 68.18, 69.02, -82.66, -54.54, 68.18, 69.02, -82.66, -54.54, 68.18, 69.02, -82.66, -54.54, 68.18, 69.02, -82.66, -54.54, 68.18, 69.02, -82.66, -54.54, 68.18, 69.02, -82.66] trend = [np.nan, np.nan, 159.12, 204.00, 221.25, 245.12, 319.75, 451.50, 561.12, 619.25, 615.62, 548.00, 462.12, 381.12, 316.62, 264.00, 228.38, 210.75, 188.38, 199.00, 207.12, 191.00, 166.88, 72.00, -9.25, -33.12, -36.75, 36.25, 103.00, np.nan, np.nan] random = [np.nan, np.nan, 72.538, 64.538, -42.426, -77.150, -12.087, -67.962, 99.699, 120.725, -2.962, -4.462, 9.699, 6.850, -38.962, -33.462, 40.449, -40.775, 22.288, -42.462, -43.301, 168.975, -81.212, 80.538, -15.926, -176.900, 42.413, 5.288, -46.176, np.nan, np.nan] assert_almost_equal(res_add.seasonal, seasonal, 2) assert_almost_equal(res_add.trend, trend, 2) assert_almost_equal(res_add.resid, random, 3) def test_pandas(self): res_add = seasonal_decompose(self.data, period=4) freq_override_data = self.data.copy() freq_override_data.index = pd.date_range( start='1/1/1951', periods=len(freq_override_data), freq='A') res_add_override = seasonal_decompose(freq_override_data, period=4) assert_almost_equal(res_add.seasonal.values.squeeze(), SEASONAL, 2) assert_almost_equal(res_add.trend.values.squeeze(), TREND, 2) assert_almost_equal(res_add.resid.values.squeeze(), RANDOM, 3) assert_almost_equal(res_add_override.seasonal.values.squeeze(), SEASONAL, 2) assert_almost_equal(res_add_override.trend.values.squeeze(), TREND, 2) assert_almost_equal(res_add_override.resid.values.squeeze(), RANDOM, 3) assert_equal(res_add.seasonal.index.values.squeeze(), self.data.index.values) res_mult = seasonal_decompose(np.abs(self.data), 'm', period=4) res_mult_override = seasonal_decompose(np.abs(freq_override_data), 'm', period=4) assert_almost_equal(res_mult.seasonal.values.squeeze(), MULT_SEASONAL, 4) assert_almost_equal(res_mult.trend.values.squeeze(), MULT_TREND, 2) assert_almost_equal(res_mult.resid.values.squeeze(), MULT_RANDOM, 4) assert_almost_equal(res_mult_override.seasonal.values.squeeze(), MULT_SEASONAL, 4) assert_almost_equal(res_mult_override.trend.values.squeeze(), MULT_TREND, 2) assert_almost_equal(res_mult_override.resid.values.squeeze(), MULT_RANDOM, 4) assert_equal(res_mult.seasonal.index.values.squeeze(), self.data.index.values) def test_pandas_nofreq(self, reset_randomstate): # issue #3503 nobs = 100 dta = pd.Series([x % 3 for x in range(nobs)] + np.random.randn(nobs)) res_np = seasonal_decompose(dta.values, period=3) res = seasonal_decompose(dta, period=3) atol = 1e-8 rtol = 1e-10 assert_allclose(res.seasonal.values.squeeze(), res_np.seasonal, atol=atol, rtol=rtol) assert_allclose(res.trend.values.squeeze(), res_np.trend, atol=atol, rtol=rtol) assert_allclose(res.resid.values.squeeze(), res_np.resid, atol=atol, rtol=rtol) def test_filt(self): filt = np.array([1 / 8., 1 / 4., 1. / 4, 1 / 4., 1 / 8.]) res_add = seasonal_decompose(self.data.values, filt=filt, period=4) assert_almost_equal(res_add.seasonal, SEASONAL, 2) assert_almost_equal(res_add.trend, TREND, 2) assert_almost_equal(res_add.resid, RANDOM, 3) def test_one_sided_moving_average_in_stl_decompose(self): res_add = seasonal_decompose(self.data.values, period=4, two_sided=False) seasonal = np.array([76.76, 90.03, -114.4, -52.4, 76.76, 90.03, -114.4, -52.4, 76.76, 90.03, -114.4, -52.4, 76.76, 90.03, -114.4, -52.4, 76.76, 90.03, -114.4, -52.4, 76.76, 90.03, -114.4, -52.4, 76.76, 90.03, -114.4, -52.4, 76.76, 90.03, -114.4, -52.4]) trend = np.array([np.nan, np.nan, np.nan, np.nan, 159.12, 204., 221.25, 245.12, 319.75, 451.5, 561.12, 619.25, 615.62, 548., 462.12, 381.12, 316.62, 264., 228.38, 210.75, 188.38, 199., 207.12, 191., 166.88, 72., -9.25, -33.12, -36.75, 36.25, 103., 131.62]) resid = np.array([np.nan, np.nan, np.nan, np.nan, 11.112, -57.031, 118.147, 136.272, 332.487, 267.469, 83.272, -77.853, -152.388, -181.031, -152.728, -152.728, -56.388, -115.031, 14.022, -56.353, -33.138, 139.969, -89.728, -40.603, -200.638, -303.031, 46.647, 72.522, 84.987, 234.719, -33.603, 104.772]) assert_almost_equal(res_add.seasonal, seasonal, 2) assert_almost_equal(res_add.trend, trend, 2) assert_almost_equal(res_add.resid, resid, 3) res_mult = seasonal_decompose(np.abs(self.data.values), 'm', period=4, two_sided=False) seasonal = np.array([1.1985, 1.5449, 0.5811, 0.6755, 1.1985, 1.5449, 0.5811, 0.6755, 1.1985, 1.5449, 0.5811, 0.6755, 1.1985, 1.5449, 0.5811, 0.6755, 1.1985, 1.5449, 0.5811, 0.6755, 1.1985, 1.5449, 0.5811, 0.6755, 1.1985, 1.5449, 0.5811, 0.6755, 1.1985, 1.5449, 0.5811, 0.6755]) trend = np.array([np.nan, np.nan, np.nan, np.nan, 171.625, 204., 221.25, 245.125, 319.75, 451.5, 561.125, 619.25, 615.625, 548., 462.125, 381.125, 316.625, 264., 228.375, 210.75, 188.375, 199., 207.125, 191., 166.875, 107.25, 80.5, 79.125, 78.75, 116.5, 140., 157.375]) resid = np.array([np.nan, np.nan, np.nan, np.nan, 1.2008, 0.752, 1.75, 1.987, 1.9023, 1.1598, 1.6253, 1.169, 0.7319, 0.5398, 0.7261, 0.6837, 0.888, 0.586, 0.9645, 0.7165, 1.0276, 1.3954, 0.0249, 0.7596, 0.215, 0.851, 1.646, 0.2432, 1.3244, 2.0058, 0.5531, 1.7309]) assert_almost_equal(res_mult.seasonal, seasonal, 4) assert_almost_equal(res_mult.trend, trend, 2) assert_almost_equal(res_mult.resid, resid, 4) # test odd res_add = seasonal_decompose(self.data.values[:-1], period=4, two_sided=False) seasonal = np.array([81.21, 94.48, -109.95, -65.74, 81.21, 94.48, -109.95, -65.74, 81.21, 94.48, -109.95, -65.74, 81.21, 94.48, -109.95, -65.74, 81.21, 94.48, -109.95, -65.74, 81.21, 94.48, -109.95, -65.74, 81.21, 94.48, -109.95, -65.74, 81.21, 94.48, -109.95]) trend = [np.nan, np.nan, np.nan, np.nan, 159.12, 204., 221.25, 245.12, 319.75, 451.5, 561.12, 619.25, 615.62, 548., 462.12, 381.12, 316.62, 264., 228.38, 210.75, 188.38, 199., 207.12, 191., 166.88, 72., -9.25, -33.12, -36.75, 36.25, 103.] random = [np.nan, np.nan, np.nan, np.nan, 6.663, -61.48, 113.699, 149.618, 328.038, 263.02, 78.824, -64.507, -156.837, -185.48, -157.176, -139.382, -60.837, -119.48, 9.574, -43.007, -37.587, 135.52, -94.176, -27.257, -205.087, -307.48, 42.199, 85.868, 80.538, 230.27, -38.051] assert_almost_equal(res_add.seasonal, seasonal, 2) assert_almost_equal(res_add.trend, trend, 2) assert_almost_equal(res_add.resid, random, 3) def test_2d(self): x = np.tile(np.arange(6), (2, 1)).T trend = seasonal_decompose(x, period=2).trend expected = np.tile(np.arange(6, dtype=float), (2, 1)).T expected[0] = expected[-1] = np.nan assert_equal(trend, expected) def test_interpolate_trend(self): x = np.arange(12) freq = 4 trend = seasonal_decompose(x, period=freq).trend assert_equal(trend[0], np.nan) trend = seasonal_decompose(x, period=freq, extrapolate_trend=5).trend assert_almost_equal(trend, x) trend = seasonal_decompose(x, period=freq, extrapolate_trend='freq').trend assert_almost_equal(trend, x) trend = seasonal_decompose(x[:, None], period=freq, extrapolate_trend=5).trend assert_almost_equal(trend, x) # 2d case x = np.tile(np.arange(12), (2, 1)).T trend = seasonal_decompose(x, period=freq, extrapolate_trend=1).trend assert_almost_equal(trend, x) trend = seasonal_decompose(x, period=freq, extrapolate_trend='freq').trend assert_almost_equal(trend, x) def test_raises(self): assert_raises(ValueError, seasonal_decompose, self.data.values) assert_raises(ValueError, seasonal_decompose, self.data, 'm', period=4) x = self.data.astype(float).copy() x.iloc[2] = np.nan assert_raises(ValueError, seasonal_decompose, x) def test_seasonal_decompose_too_short(reset_randomstate): dates = pd.date_range('31-1-2000', periods=4, freq='Q') y = np.sin(np.arange(4) / 4 * 2 * np.pi) y += np.random.standard_normal(y.size) y = pd.Series(y, name='y', index=dates) with pytest.raises(ValueError): seasonal_decompose(y) dates = pd.date_range('31-1-2000', periods=12, freq='M') y = np.sin(np.arange(12) / 12 * 2 * np.pi) y += np.random.standard_normal(y.size) y = pd.Series(y, name='y', index=dates) with pytest.raises(ValueError): seasonal_decompose(y) with pytest.raises(ValueError): seasonal_decompose(y.values, period=12) @pytest.mark.smoke def test_seasonal_decompose_smoke(): x = np.array([-50, 175, 149, 214, 247, 237, 225, 329, 729, 809, 530, 489, 540, 457, 195, 176, 337, 239, 128, 102, 232, 429, 3, 98, 43, -141, -77, -13, 125, 361, -45, 184]) seasonal_decompose(x, period=4) data = pd.DataFrame(x, pd.date_range(start='1/1/1951', periods=len(x), freq='Q')) seasonal_decompose(data) def test_seasonal_decompose_multiple(): x = np.array([-50, 175, 149, 214, 247, 237, 225, 329, 729, 809, 530, 489, 540, 457, 195, 176, 337, 239, 128, 102, 232, 429, 3, 98, 43, -141, -77, -13, 125, 361, -45, 184]) x = np.c_[x, x] res = seasonal_decompose(x, period=4) assert_allclose(res.trend[:, 0], res.trend[:, 1]) assert_allclose(res.seasonal[:, 0], res.seasonal[:, 1]) assert_allclose(res.resid[:, 0], res.resid[:, 1]) @pytest.mark.matplotlib @pytest.mark.parametrize('model', ['additive', 'multiplicative']) @pytest.mark.parametrize('freq', [4, 12]) @pytest.mark.parametrize('two_sided', [True, False]) @pytest.mark.parametrize('extrapolate_trend', [True, False]) def test_seasonal_decompose_plot(model, freq, two_sided, extrapolate_trend): x = np.array([-50, 175, 149, 214, 247, 237, 225, 329, 729, 809, 530, 489, 540, 457, 195, 176, 337, 239, 128, 102, 232, 429, 3, 98, 43, -141, -77, -13, 125, 361, -45, 184]) x -= x.min() + 1 x2 = np.r_[x[12:], x[:12]] x = np.c_[x, x2] res = seasonal_decompose(x, period=freq, two_sided=two_sided, extrapolate_trend=extrapolate_trend) res.plot() statsmodels-0.12.2/statsmodels/tsa/tests/test_stattools.py000066400000000000000000001141771400612667500241200ustar00rootroot00000000000000from statsmodels.compat.numpy import lstsq from statsmodels.compat.pandas import assert_index_equal from statsmodels.compat.platform import PLATFORM_WIN from statsmodels.compat.python import lrange import os import warnings import numpy as np from numpy.testing import ( assert_, assert_allclose, assert_almost_equal, assert_equal, assert_raises, ) import pandas as pd from pandas import DataFrame, Series, date_range import pytest from statsmodels.datasets import macrodata, modechoice, nile, randhie, sunspots from statsmodels.tools.sm_exceptions import ( CollinearityWarning, InfeasibleTestError, InterpolationWarning, MissingDataError ) from statsmodels.tsa.arima_process import arma_acovf from statsmodels.tsa.statespace.sarimax import SARIMAX from statsmodels.tsa.stattools import ( acf, acovf, adfuller, arma_order_select_ic, coint, grangercausalitytests, innovations_algo, innovations_filter, kpss, levinson_durbin, levinson_durbin_pacf, pacf, pacf_burg, pacf_ols, pacf_yw, zivot_andrews, ) DECIMAL_8 = 8 DECIMAL_6 = 6 DECIMAL_5 = 5 DECIMAL_4 = 4 DECIMAL_3 = 3 DECIMAL_2 = 2 DECIMAL_1 = 1 CURR_DIR = os.path.dirname(os.path.abspath(__file__)) @pytest.fixture(scope="module") def acovf_data(): rnd = np.random.RandomState(12345) return rnd.randn(250) class CheckADF(object): """ Test Augmented Dickey-Fuller Test values taken from Stata. """ levels = ["1%", "5%", "10%"] data = macrodata.load_pandas() x = data.data["realgdp"].values y = data.data["infl"].values def test_teststat(self): assert_almost_equal(self.res1[0], self.teststat, DECIMAL_5) def test_pvalue(self): assert_almost_equal(self.res1[1], self.pvalue, DECIMAL_5) def test_critvalues(self): critvalues = [self.res1[4][lev] for lev in self.levels] assert_almost_equal(critvalues, self.critvalues, DECIMAL_2) class TestADFConstant(CheckADF): """ Dickey-Fuller test for unit root """ @classmethod def setup_class(cls): cls.res1 = adfuller(cls.x, regression="c", autolag=None, maxlag=4) cls.teststat = 0.97505319 cls.pvalue = 0.99399563 cls.critvalues = [-3.476, -2.883, -2.573] class TestADFConstantTrend(CheckADF): """""" @classmethod def setup_class(cls): cls.res1 = adfuller(cls.x, regression="ct", autolag=None, maxlag=4) cls.teststat = -1.8566374 cls.pvalue = 0.67682968 cls.critvalues = [-4.007, -3.437, -3.137] # FIXME: do not leave commented-out # class TestADFConstantTrendSquared(CheckADF): # """ # """ # pass # TODO: get test values from R? class TestADFNoConstant(CheckADF): """""" @classmethod def setup_class(cls): cls.res1 = adfuller(cls.x, regression="nc", autolag=None, maxlag=4) cls.teststat = 3.5227498 cls.pvalue = 0.99999 # Stata does not return a p-value for noconstant. # Tau^max in MacKinnon (1994) is missing, so it is # assumed that its right-tail is well-behaved cls.critvalues = [-2.587, -1.950, -1.617] # No Unit Root class TestADFConstant2(CheckADF): @classmethod def setup_class(cls): cls.res1 = adfuller(cls.y, regression="c", autolag=None, maxlag=1) cls.teststat = -4.3346988 cls.pvalue = 0.00038661 cls.critvalues = [-3.476, -2.883, -2.573] class TestADFConstantTrend2(CheckADF): @classmethod def setup_class(cls): cls.res1 = adfuller(cls.y, regression="ct", autolag=None, maxlag=1) cls.teststat = -4.425093 cls.pvalue = 0.00199633 cls.critvalues = [-4.006, -3.437, -3.137] class TestADFNoConstant2(CheckADF): @classmethod def setup_class(cls): cls.res1 = adfuller(cls.y, regression="nc", autolag=None, maxlag=1) cls.teststat = -2.4511596 cls.pvalue = 0.013747 # Stata does not return a p-value for noconstant # this value is just taken from our results cls.critvalues = [-2.587, -1.950, -1.617] _, _1, _2, cls.store = adfuller( cls.y, regression="nc", autolag=None, maxlag=1, store=True ) def test_store_str(self): assert_equal( self.store.__str__(), "Augmented Dickey-Fuller Test Results" ) class CheckCorrGram(object): """ Set up for ACF, PACF tests. """ data = macrodata.load_pandas() x = data.data["realgdp"] filename = os.path.join(CURR_DIR, "results", "results_corrgram.csv") results = pd.read_csv(filename, delimiter=",") class TestACF(CheckCorrGram): """ Test Autocorrelation Function """ @classmethod def setup_class(cls): cls.acf = cls.results["acvar"] # cls.acf = np.concatenate(([1.], cls.acf)) cls.qstat = cls.results["Q1"] cls.res1 = acf(cls.x, nlags=40, qstat=True, alpha=0.05, fft=False) cls.confint_res = cls.results[["acvar_lb", "acvar_ub"]].values def test_acf(self): assert_almost_equal(self.res1[0][1:41], self.acf, DECIMAL_8) def test_confint(self): centered = self.res1[1] - self.res1[1].mean(1)[:, None] assert_almost_equal(centered[1:41], self.confint_res, DECIMAL_8) def test_qstat(self): assert_almost_equal(self.res1[2][:40], self.qstat, DECIMAL_3) # 3 decimal places because of stata rounding # FIXME: enable/xfail/skip or delete # def pvalue(self): # pass # NOTE: should not need testing if Q stat is correct class TestACF_FFT(CheckCorrGram): # Test Autocorrelation Function using FFT @classmethod def setup_class(cls): cls.acf = cls.results["acvarfft"] cls.qstat = cls.results["Q1"] cls.res1 = acf(cls.x, nlags=40, qstat=True, fft=True) def test_acf(self): assert_almost_equal(self.res1[0][1:], self.acf, DECIMAL_8) def test_qstat(self): # todo why is res1/qstat 1 short assert_almost_equal(self.res1[1], self.qstat, DECIMAL_3) class TestACFMissing(CheckCorrGram): # Test Autocorrelation Function using Missing @classmethod def setup_class(cls): cls.x = np.concatenate((np.array([np.nan]), cls.x)) cls.acf = cls.results["acvar"] # drop and conservative cls.qstat = cls.results["Q1"] cls.res_drop = acf( cls.x, nlags=40, qstat=True, alpha=0.05, missing="drop", fft=False ) cls.res_conservative = acf( cls.x, nlags=40, qstat=True, alpha=0.05, fft=False, missing="conservative", ) cls.acf_none = np.empty(40) * np.nan # lags 1 to 40 inclusive cls.qstat_none = np.empty(40) * np.nan cls.res_none = acf( cls.x, nlags=40, qstat=True, alpha=0.05, missing="none", fft=False ) def test_raise(self): with pytest.raises(MissingDataError): acf( self.x, nlags=40, qstat=True, fft=False, alpha=0.05, missing="raise", ) def test_acf_none(self): assert_almost_equal(self.res_none[0][1:41], self.acf_none, DECIMAL_8) def test_acf_drop(self): assert_almost_equal(self.res_drop[0][1:41], self.acf, DECIMAL_8) def test_acf_conservative(self): assert_almost_equal( self.res_conservative[0][1:41], self.acf, DECIMAL_8 ) def test_qstat_none(self): # todo why is res1/qstat 1 short assert_almost_equal(self.res_none[2], self.qstat_none, DECIMAL_3) # FIXME: enable/xfail/skip or delete # how to do this test? the correct q_stat depends on whether nobs=len(x) is # used when x contains NaNs or whether nobs= 3 where" " low_pass > period" ) with pytest.raises(ValueError, match=match): STL(endog=endog, period=period, low_pass=14) with pytest.raises(ValueError, match=match): STL(endog=endog, period=period, low_pass=7) with pytest.raises(ValueError, match=match): STL(endog=endog, period=period, low_pass=-19) with pytest.raises(ValueError, match=match): STL(endog=endog, period=period, low_pass=19.0) def test_jump_errors(default_kwargs): class_kwargs, _, _ = _to_class_kwargs(default_kwargs) endog = class_kwargs["endog"] period = class_kwargs["period"] with pytest.raises(ValueError, match="low_pass_jump must be a positve"): STL(endog=endog, period=period, low_pass_jump=0) with pytest.raises(ValueError, match="low_pass_jump must be a positve"): STL(endog=endog, period=period, low_pass_jump=1.0) with pytest.raises(ValueError, match="seasonal_jump must be a positve"): STL(endog=endog, period=period, seasonal_jump=0) with pytest.raises(ValueError, match="seasonal_jump must be a positve"): STL(endog=endog, period=period, seasonal_jump=1.0) with pytest.raises(ValueError, match="trend_jump must be a positve"): STL(endog=endog, period=period, trend_jump=0) with pytest.raises(ValueError, match="trend_jump must be a positve"): STL(endog=endog, period=period, trend_jump=1.0) def test_defaults_smoke(default_kwargs, robust): class_kwargs, _, _ = _to_class_kwargs(default_kwargs, robust) endog = class_kwargs["endog"] period = class_kwargs["period"] mod = STL(endog=endog, period=period) mod.fit() def test_pandas(default_kwargs, robust): class_kwargs, _, _ = _to_class_kwargs(default_kwargs, robust) endog = pd.Series(class_kwargs["endog"], name="y") period = class_kwargs["period"] mod = STL(endog=endog, period=period) res = mod.fit() assert isinstance(res.trend, pd.Series) assert isinstance(res.seasonal, pd.Series) assert isinstance(res.resid, pd.Series) assert isinstance(res.weights, pd.Series) def test_period_detection(default_kwargs): class_kwargs, _, _ = _to_class_kwargs(default_kwargs) mod = STL(**class_kwargs) res = mod.fit() del class_kwargs["period"] endog = class_kwargs["endog"] index = pd.date_range("1-1-1959", periods=348, freq="M") class_kwargs["endog"] = pd.Series(endog, index=index) mod = STL(**class_kwargs) res_implicit_period = mod.fit() assert_allclose(res.seasonal, res_implicit_period.seasonal) def test_no_period(default_kwargs): class_kwargs, _, _ = _to_class_kwargs(default_kwargs) del class_kwargs["period"] class_kwargs["endog"] = pd.Series(class_kwargs["endog"]) with pytest.raises(ValueError, match="Unable to determine period from"): STL(**class_kwargs) @pytest.mark.matplotlib def test_plot(default_kwargs): class_kwargs, outer, inner = _to_class_kwargs(default_kwargs) res = STL(**class_kwargs).fit(outer_iter=outer, inner_iter=inner) res.plot() class_kwargs["endog"] = pd.Series(class_kwargs["endog"], name="CO2") res = STL(**class_kwargs).fit() res.plot() def test_default_trend(default_kwargs): # GH 6686 class_kwargs, _, _ = _to_class_kwargs(default_kwargs) class_kwargs["seasonal"] = 17 class_kwargs["trend"] = None mod = STL(**class_kwargs) period = class_kwargs["period"] seasonal = class_kwargs["seasonal"] expected = int(np.ceil(1.5 * period / (1 - 1.5 / seasonal))) expected += 1 if expected % 2 == 0 else 0 assert mod.config["trend"] == expected class_kwargs["seasonal"] = 7 mod = STL(**class_kwargs) period = class_kwargs["period"] seasonal = class_kwargs["seasonal"] expected = int(np.ceil(1.5 * period / (1 - 1.5 / seasonal))) expected += 1 if expected % 2 == 0 else 0 assert mod.config["trend"] == expected def test_pickle(default_kwargs): class_kwargs, outer, inner = _to_class_kwargs(default_kwargs) mod = STL(**class_kwargs) res = mod.fit() pkl = pickle.dumps(mod) reloaded = pickle.loads(pkl) res2 = reloaded.fit() assert_allclose(res.trend, res2.trend) assert_allclose(res.seasonal, res2.seasonal) assert mod.config == reloaded.config statsmodels-0.12.2/statsmodels/tsa/tests/test_tsa_tools.py000066400000000000000000000666421400612667500240760ustar00rootroot00000000000000'''tests for some time series analysis functions ''' from statsmodels.compat.pandas import assert_frame_equal, assert_series_equal import pytest import numpy as np from numpy.testing import (assert_array_almost_equal, assert_equal, assert_raises, assert_array_equal) import pandas as pd import statsmodels.api as sm import statsmodels.tsa.stattools as tsa import statsmodels.tsa.tsatools as tools from statsmodels.tsa.tsatools import vec, vech from statsmodels.tsa.tests.results import savedrvs from statsmodels.tsa.tests.results.datamlw_tls import mlacf, mlccf, mlpacf, \ mlywar xo = savedrvs.rvsdata.xar2 x100 = xo[-100:] / 1000. x1000 = xo / 1000. def test_acf(): acf_x = tsa.acf(x100, adjusted=False, fft=False, nlags=20) assert_array_almost_equal(mlacf.acf100.ravel(), acf_x, 8) # why only dec=8 acf_x = tsa.acf(x1000, adjusted=False, fft=False, nlags=20) assert_array_almost_equal(mlacf.acf1000.ravel(), acf_x, 8) # why only dec=9 def test_ccf(): ccf_x = tsa.ccf(x100[4:], x100[:-4], adjusted=False)[:21] assert_array_almost_equal(mlccf.ccf100.ravel()[:21][::-1], ccf_x, 8) ccf_x = tsa.ccf(x1000[4:], x1000[:-4], adjusted=False)[:21] assert_array_almost_equal(mlccf.ccf1000.ravel()[:21][::-1], ccf_x, 8) def test_pacf_yw(): pacfyw = tsa.pacf_yw(x100, 20, method='mle') assert_array_almost_equal(mlpacf.pacf100.ravel(), pacfyw, 1) pacfyw = tsa.pacf_yw(x1000, 20, method='mle') assert_array_almost_equal(mlpacf.pacf1000.ravel(), pacfyw, 2) # assert False def test_pacf_ols(): pacfols = tsa.pacf_ols(x100, 20) assert_array_almost_equal(mlpacf.pacf100.ravel(), pacfols, 8) pacfols = tsa.pacf_ols(x1000, 20) assert_array_almost_equal(mlpacf.pacf1000.ravel(), pacfols, 8) # assert False def test_ywcoef(): assert_array_almost_equal(mlywar.arcoef100[1:], - sm.regression.yule_walker(x100, 10, method='mle')[ 0], 8) assert_array_almost_equal(mlywar.arcoef1000[1:], -sm.regression.yule_walker(x1000, 20, method='mle')[0], 8) @pytest.mark.smoke def test_yule_walker_inter(): # see 1869 x = np.array([1, -1, 2, 2, 0, -2, 1, 0, -3, 0, 0]) # it works sm.regression.yule_walker(x, 3) def test_duplication_matrix(reset_randomstate): for k in range(2, 10): m = tools.unvech(np.random.randn(k * (k + 1) // 2)) Dk = tools.duplication_matrix(k) assert (np.array_equal(vec(m), np.dot(Dk, vech(m)))) def test_elimination_matrix(reset_randomstate): for k in range(2, 10): m = np.random.randn(k, k) Lk = tools.elimination_matrix(k) assert (np.array_equal(vech(m), np.dot(Lk, vec(m)))) def test_commutation_matrix(reset_randomstate): m = np.random.randn(4, 3) K = tools.commutation_matrix(4, 3) assert (np.array_equal(vec(m.T), np.dot(K, vec(m)))) def test_vec(): arr = np.array([[1, 2], [3, 4]]) assert (np.array_equal(vec(arr), [1, 3, 2, 4])) def test_vech(): arr = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) assert (np.array_equal(vech(arr), [1, 4, 7, 5, 8, 9])) def test_ar_transparams(): arr = np.array([-1000.0, -100.0, -10.0, 1.0, 0.0, 1.0, 10.0, 100.0, 1000.0]) assert (not np.isnan(tools._ar_transparams(arr)).any()) class TestLagmat(object): @classmethod def setup_class(cls): data = sm.datasets.macrodata.load_pandas() cls.macro_df = data.data[['year', 'quarter', 'realgdp', 'cpi']] cols = list(cls.macro_df.columns) cls.realgdp_loc = cols.index('realgdp') cls.cpi_loc = cols.index('cpi') np.random.seed(12345) cls.random_data = np.random.randn(100) index = [str(int(yr)) + '-Q' + str(int(qu)) for yr, qu in zip(cls.macro_df.year, cls.macro_df.quarter)] cls.macro_df.index = index cls.series = cls.macro_df.cpi def test_add_lag_insert(self): data = self.macro_df.values nddata = data.astype(float) lagmat = sm.tsa.lagmat(nddata[:, 2], 3, trim='Both') results = np.column_stack((nddata[3:, :3], lagmat, nddata[3:, -1])) lag_data = sm.tsa.add_lag(data, self.realgdp_loc, 3) assert_equal(lag_data, results) def test_add_lag_noinsert(self): data = self.macro_df.values nddata = data.astype(float) lagmat = sm.tsa.lagmat(nddata[:, 2], 3, trim='Both') results = np.column_stack((nddata[3:, :], lagmat)) lag_data = sm.tsa.add_lag(data, self.realgdp_loc, 3, insert=False) assert_equal(lag_data, results) def test_add_lag_noinsert_atend(self): data = self.macro_df.values nddata = data.astype(float) lagmat = sm.tsa.lagmat(nddata[:, -1], 3, trim='Both') results = np.column_stack((nddata[3:, :], lagmat)) lag_data = sm.tsa.add_lag(data, self.cpi_loc, 3, insert=False) assert_equal(lag_data, results) # should be the same as insert lag_data2 = sm.tsa.add_lag(data, self.cpi_loc, 3, insert=True) assert_equal(lag_data2, results) def test_add_lag_ndarray(self): data = self.macro_df.values nddata = data.astype(float) lagmat = sm.tsa.lagmat(nddata[:, 2], 3, trim='Both') results = np.column_stack((nddata[3:, :3], lagmat, nddata[3:, -1])) lag_data = sm.tsa.add_lag(nddata, 2, 3) assert_equal(lag_data, results) def test_add_lag_noinsert_ndarray(self): data = self.macro_df.values nddata = data.astype(float) lagmat = sm.tsa.lagmat(nddata[:, 2], 3, trim='Both') results = np.column_stack((nddata[3:, :], lagmat)) lag_data = sm.tsa.add_lag(nddata, 2, 3, insert=False) assert_equal(lag_data, results) def test_add_lag_noinsertatend_ndarray(self): data = self.macro_df.values nddata = data.astype(float) lagmat = sm.tsa.lagmat(nddata[:, -1], 3, trim='Both') results = np.column_stack((nddata[3:, :], lagmat)) lag_data = sm.tsa.add_lag(nddata, 3, 3, insert=False) assert_equal(lag_data, results) # should be the same as insert also check negative col number lag_data2 = sm.tsa.add_lag(nddata, -1, 3, insert=True) assert_equal(lag_data2, results) def test_sep_return(self): data = self.random_data n = data.shape[0] lagmat, leads = sm.tsa.lagmat(data, 3, trim='none', original='sep') expected = np.zeros((n + 3, 4)) for i in range(4): expected[i:i + n, i] = data expected_leads = expected[:, :1] expected_lags = expected[:, 1:] assert_equal(expected_lags, lagmat) assert_equal(expected_leads, leads) def test_add_lag1d(self): data = self.random_data lagmat = sm.tsa.lagmat(data, 3, trim='Both') results = np.column_stack((data[3:], lagmat)) lag_data = sm.tsa.add_lag(data, lags=3, insert=True) assert_equal(results, lag_data) # add index data = data[:, None] lagmat = sm.tsa.lagmat(data, 3, trim='Both') # test for lagmat too results = np.column_stack((data[3:], lagmat)) lag_data = sm.tsa.add_lag(data, lags=3, insert=True) assert_equal(results, lag_data) def test_add_lag1d_drop(self): data = self.random_data lagmat = sm.tsa.lagmat(data, 3, trim='Both') lag_data = sm.tsa.add_lag(data, lags=3, drop=True, insert=True) assert_equal(lagmat, lag_data) # no insert, should be the same lag_data = sm.tsa.add_lag(data, lags=3, drop=True, insert=False) assert_equal(lagmat, lag_data) def test_add_lag1d_struct(self): data = np.zeros(100, dtype=[('variable', float)]) nddata = self.random_data data['variable'] = nddata lagmat = sm.tsa.lagmat(nddata, 3, trim='Both', original='in') lag_data = sm.tsa.add_lag(data, 'variable', lags=3, insert=True) assert_equal(lagmat, lag_data.view((float, 4))) lag_data = sm.tsa.add_lag(data, 'variable', lags=3, insert=False) assert_equal(lagmat, lag_data.view((float, 4))) lag_data = sm.tsa.add_lag(data, lags=3, insert=True) assert_equal(lagmat, lag_data.view((float, 4))) def test_add_lag_1d_drop_struct(self): data = np.zeros(100, dtype=[('variable', float)]) nddata = self.random_data data['variable'] = nddata lagmat = sm.tsa.lagmat(nddata, 3, trim='Both') lag_data = sm.tsa.add_lag(data, lags=3, drop=True) assert_equal(lagmat, lag_data.view((float, 3))) def test_add_lag_drop_insert(self): data = self.macro_df.values nddata = data.astype(float) lagmat = sm.tsa.lagmat(nddata[:, 2], 3, trim='Both') results = np.column_stack((nddata[3:, :2], lagmat, nddata[3:, -1])) lag_data = sm.tsa.add_lag(data, self.realgdp_loc, 3, drop=True) assert_equal(lag_data, results) def test_add_lag_drop_noinsert(self): data = self.macro_df.values nddata = data.astype(float) lagmat = sm.tsa.lagmat(nddata[:, 2], 3, trim='Both') results = np.column_stack((nddata[3:, np.array([0, 1, 3])], lagmat)) lag_data = sm.tsa.add_lag(data, self.realgdp_loc, 3, insert=False, drop=True) assert_equal(lag_data, results) def test_dataframe_without_pandas(self): data = self.macro_df both = sm.tsa.lagmat(data, 3, trim='both', original='in') both_np = sm.tsa.lagmat(data.values, 3, trim='both', original='in') assert_equal(both, both_np) lags = sm.tsa.lagmat(data, 3, trim='none', original='ex') lags_np = sm.tsa.lagmat(data.values, 3, trim='none', original='ex') assert_equal(lags, lags_np) lags, lead = sm.tsa.lagmat(data, 3, trim='forward', original='sep') lags_np, lead_np = sm.tsa.lagmat(data.values, 3, trim='forward', original='sep') assert_equal(lags, lags_np) assert_equal(lead, lead_np) def test_dataframe_both(self): data = self.macro_df columns = list(data.columns) n = data.shape[0] values = np.zeros((n + 3,16)) values[:n,:4] = data.values for lag in range(1,4): new_cols = [col + '.L.' + str(lag) for col in data] columns.extend(new_cols) values[lag:n+lag,4*lag:4*(lag+1)] = data.values index = data.index values = values[:n] expected = pd.DataFrame(values,columns=columns, index=index) expected = expected.iloc[3:] both = sm.tsa.lagmat(self.macro_df, 3, trim='both', original='in', use_pandas=True) assert_frame_equal(both, expected) lags = sm.tsa.lagmat(self.macro_df, 3, trim='both', original='ex', use_pandas=True) assert_frame_equal(lags, expected.iloc[:, 4:]) lags, lead = sm.tsa.lagmat(self.macro_df, 3, trim='both', original='sep', use_pandas=True) assert_frame_equal(lags, expected.iloc[:, 4:]) assert_frame_equal(lead, expected.iloc[:, :4]) def test_too_few_observations(self): assert_raises(ValueError, sm.tsa.lagmat, self.macro_df, 300, use_pandas=True) assert_raises(ValueError, sm.tsa.lagmat, self.macro_df.values, 300) def test_unknown_trim(self): assert_raises(ValueError, sm.tsa.lagmat, self.macro_df, 3, trim='unknown', use_pandas=True) assert_raises(ValueError, sm.tsa.lagmat, self.macro_df.values, 3, trim='unknown') def test_dataframe_forward(self): data = self.macro_df columns = list(data.columns) n = data.shape[0] values = np.zeros((n + 3,16)) values[:n,:4] = data.values for lag in range(1,4): new_cols = [col + '.L.' + str(lag) for col in data] columns.extend(new_cols) values[lag:n+lag,4*lag:4*(lag+1)] = data.values index = data.index values = values[:n] expected = pd.DataFrame(values,columns=columns, index=index) both = sm.tsa.lagmat(self.macro_df, 3, trim='forward', original='in', use_pandas=True) assert_frame_equal(both, expected) lags = sm.tsa.lagmat(self.macro_df, 3, trim='forward', original='ex', use_pandas=True) assert_frame_equal(lags, expected.iloc[:, 4:]) lags, lead = sm.tsa.lagmat(self.macro_df, 3, trim='forward', original='sep', use_pandas=True) assert_frame_equal(lags, expected.iloc[:, 4:]) assert_frame_equal(lead, expected.iloc[:, :4]) def test_pandas_errors(self): assert_raises(ValueError, sm.tsa.lagmat, self.macro_df, 3, trim='none', use_pandas=True) assert_raises(ValueError, sm.tsa.lagmat, self.macro_df, 3, trim='backward', use_pandas=True) assert_raises(ValueError, sm.tsa.lagmat, self.series, 3, trim='none', use_pandas=True) assert_raises(ValueError, sm.tsa.lagmat, self.series, 3, trim='backward', use_pandas=True) def test_series_forward(self): expected = pd.DataFrame(index=self.series.index, columns=['cpi', 'cpi.L.1', 'cpi.L.2', 'cpi.L.3']) expected['cpi'] = self.series for lag in range(1, 4): expected['cpi.L.' + str(int(lag))] = self.series.shift(lag) expected = expected.fillna(0.0) both = sm.tsa.lagmat(self.series, 3, trim='forward', original='in', use_pandas=True) assert_frame_equal(both, expected) lags = sm.tsa.lagmat(self.series, 3, trim='forward', original='ex', use_pandas=True) assert_frame_equal(lags, expected.iloc[:, 1:]) lags, lead = sm.tsa.lagmat(self.series, 3, trim='forward', original='sep', use_pandas=True) assert_frame_equal(lead, expected.iloc[:, :1]) assert_frame_equal(lags, expected.iloc[:, 1:]) def test_series_both(self): expected = pd.DataFrame(index=self.series.index, columns=['cpi', 'cpi.L.1', 'cpi.L.2', 'cpi.L.3']) expected['cpi'] = self.series for lag in range(1, 4): expected['cpi.L.' + str(int(lag))] = self.series.shift(lag) expected = expected.iloc[3:] both = sm.tsa.lagmat(self.series, 3, trim='both', original='in', use_pandas=True) assert_frame_equal(both, expected) lags = sm.tsa.lagmat(self.series, 3, trim='both', original='ex', use_pandas=True) assert_frame_equal(lags, expected.iloc[:, 1:]) lags, lead = sm.tsa.lagmat(self.series, 3, trim='both', original='sep', use_pandas=True) assert_frame_equal(lead, expected.iloc[:, :1]) assert_frame_equal(lags, expected.iloc[:, 1:]) def test_freq_to_period(): from pandas.tseries.frequencies import to_offset freqs = ['A', 'AS-MAR', 'Q', 'QS', 'QS-APR', 'W', 'W-MON', 'B', 'D', 'H'] expected = [1, 1, 4, 4, 4, 52, 52, 5, 7, 24] for i, j in zip(freqs, expected): assert_equal(tools.freq_to_period(i), j) assert_equal(tools.freq_to_period(to_offset(i)), j) class TestDetrend(object): @classmethod def setup_class(cls): cls.data_1d = np.arange(5.0) cls.data_2d = np.arange(10.0).reshape(5, 2) def test_detrend_1d(self): data = self.data_1d assert_array_almost_equal(sm.tsa.detrend(data, order=1), np.zeros_like(data)) assert_array_almost_equal(sm.tsa.detrend(data, order=0), [-2, -1, 0, 1, 2]) def test_detrend_2d(self): data = self.data_2d assert_array_almost_equal(sm.tsa.detrend(data, order=1, axis=0), np.zeros_like(data)) assert_array_almost_equal(sm.tsa.detrend(data, order=0, axis=0), [[-4, -4], [-2, -2], [0, 0], [2, 2], [4, 4]]) assert_array_almost_equal(sm.tsa.detrend(data, order=0, axis=1), [[-0.5, 0.5], [-0.5, 0.5], [-0.5, 0.5], [-0.5, 0.5], [-0.5, 0.5]]) def test_detrend_series(self): data = pd.Series(self.data_1d, name='one') detrended = sm.tsa.detrend(data, order=1) assert_array_almost_equal(detrended.values, np.zeros_like(data)) assert_series_equal(detrended, pd.Series(detrended.values, name='one')) detrended = sm.tsa.detrend(data, order=0) assert_array_almost_equal(detrended.values, pd.Series([-2, -1, 0, 1, 2])) assert_series_equal(detrended, pd.Series(detrended.values, name='one')) def test_detrend_dataframe(self): columns = ['one', 'two'] index = [c for c in 'abcde'] data = pd.DataFrame(self.data_2d, columns=columns, index=index) detrended = sm.tsa.detrend(data, order=1, axis=0) assert_array_almost_equal(detrended.values, np.zeros_like(data)) assert_frame_equal(detrended, pd.DataFrame(detrended.values, columns=columns, index=index)) detrended = sm.tsa.detrend(data, order=0, axis=0) assert_array_almost_equal(detrended.values, [[-4, -4], [-2, -2], [0, 0], [2, 2], [4, 4]]) assert_frame_equal(detrended, pd.DataFrame(detrended.values, columns=columns, index=index)) detrended = sm.tsa.detrend(data, order=0, axis=1) assert_array_almost_equal(detrended.values, [[-0.5, 0.5], [-0.5, 0.5], [-0.5, 0.5], [-0.5, 0.5], [-0.5, 0.5]]) assert_frame_equal(detrended, pd.DataFrame(detrended.values, columns=columns, index=index)) def test_detrend_dim_too_large(self): assert_raises(NotImplementedError, sm.tsa.detrend, np.ones((3, 3, 3))) class TestAddTrend(object): @classmethod def setup_class(cls): cls.n = 200 cls.arr_1d = np.arange(float(cls.n)) cls.arr_2d = np.tile(np.arange(float(cls.n))[:, None], 2) cls.c = np.ones(cls.n) cls.t = np.arange(1.0, cls.n + 1) def test_series(self): s = pd.Series(self.arr_1d) appended = tools.add_trend(s) expected = pd.DataFrame(s) expected['const'] = self.c assert_frame_equal(expected, appended) prepended = tools.add_trend(s, prepend=True) expected = pd.DataFrame(s) expected.insert(0, 'const', self.c) assert_frame_equal(expected, prepended) s = pd.Series(self.arr_1d) appended = tools.add_trend(s, trend='ct') expected = pd.DataFrame(s) expected['const'] = self.c expected['trend'] = self.t assert_frame_equal(expected, appended) def test_dataframe(self): df = pd.DataFrame(self.arr_2d) appended = tools.add_trend(df) expected = df.copy() expected['const'] = self.c assert_frame_equal(expected, appended) prepended = tools.add_trend(df, prepend=True) expected = df.copy() expected.insert(0, 'const', self.c) assert_frame_equal(expected, prepended) df = pd.DataFrame(self.arr_2d) appended = tools.add_trend(df, trend='t') expected = df.copy() expected['trend'] = self.t assert_frame_equal(expected, appended) df = pd.DataFrame(self.arr_2d) appended = tools.add_trend(df, trend='ctt') expected = df.copy() expected['const'] = self.c expected['trend'] = self.t expected['trend_squared'] = self.t ** 2 assert_frame_equal(expected, appended) def test_recarray(self): recarray = pd.DataFrame(self.arr_2d).to_records(index=False) with pytest.warns(FutureWarning, match="recarray support"): appended = tools.add_trend(recarray) expected = pd.DataFrame(self.arr_2d) expected['const'] = self.c expected = expected.to_records(index=False) assert_equal(expected, appended) with pytest.warns(FutureWarning, match="recarray support"): prepended = tools.add_trend(recarray, prepend=True) expected = pd.DataFrame(self.arr_2d) expected.insert(0, 'const', self.c) expected = expected.to_records(index=False) assert_equal(expected, prepended) with pytest.warns(FutureWarning, match="recarray support"): appended = tools.add_trend(recarray, trend='ctt') expected = pd.DataFrame(self.arr_2d) expected['const'] = self.c expected['trend'] = self.t expected['trend_squared'] = self.t ** 2 expected = expected.to_records(index=False) assert_equal(expected, appended) def test_duplicate_const(self): assert_raises(ValueError, tools.add_trend, x=self.c, trend='c', has_constant='raise') assert_raises(ValueError, tools.add_trend, x=self.c, trend='ct', has_constant='raise') df = pd.DataFrame(self.c) assert_raises(ValueError, tools.add_trend, x=df, trend='c', has_constant='raise') assert_raises(ValueError, tools.add_trend, x=df, trend='ct', has_constant='raise') skipped = tools.add_trend(self.c, trend='c') assert_equal(skipped, self.c[:,None]) skipped_const = tools.add_trend(self.c, trend='ct', has_constant='skip') expected = np.vstack((self.c, self.t)).T assert_equal(skipped_const, expected) added = tools.add_trend(self.c, trend='c', has_constant='add') expected = np.vstack((self.c, self.c)).T assert_equal(added, expected) added = tools.add_trend(self.c, trend='ct', has_constant='add') expected = np.vstack((self.c, self.c, self.t)).T assert_equal(added, expected) def test_mixed_recarray(self): dt = np.dtype([('c0', np.float64), ('c1', np.int8), ('c2', 'S4')]) ra = np.array([(1.0, 1, 'aaaa'), (1.1, 2, 'bbbb')], dtype=dt).view(np.recarray) with pytest.warns(FutureWarning, match="recarray support"): added = tools.add_trend(ra, trend='ct') dt = np.dtype([('c0', np.float64), ('c1', np.int8), ('c2', 'S4'), ('const', np.float64), ('trend', np.float64)]) expected = np.array([(1.0, 1, 'aaaa', 1.0, 1.0), (1.1, 2, 'bbbb', 1.0, 2.0)], dtype=dt).view(np.recarray) assert_equal(added, expected) def test_dataframe_duplicate(self): df = pd.DataFrame(self.arr_2d, columns=['const', 'trend']) tools.add_trend(df, trend='ct') tools.add_trend(df, trend='ct', prepend=True) def test_array(self): base = np.vstack((self.arr_1d, self.c, self.t, self.t ** 2)).T assert_equal(tools.add_trend(self.arr_1d), base[:, :2]) assert_equal(tools.add_trend(self.arr_1d, trend='t'), base[:, [0, 2]]) assert_equal(tools.add_trend(self.arr_1d, trend='ct'), base[:, :3]) assert_equal(tools.add_trend(self.arr_1d, trend='ctt'), base) base = np.hstack((self.c[:, None], self.t[:, None], self.t[:, None] ** 2, self.arr_2d)) assert_equal(tools.add_trend(self.arr_2d, prepend=True), base[:, [0, 3, 4]]) assert_equal(tools.add_trend(self.arr_2d, trend='t', prepend=True), base[:, [1, 3, 4]]) assert_equal(tools.add_trend(self.arr_2d, trend='ct', prepend=True), base[:, [0, 1, 3, 4]]) assert_equal(tools.add_trend(self.arr_2d, trend='ctt', prepend=True), base) def test_unknown_trend(self): assert_raises(ValueError, tools.add_trend, x=self.arr_1d, trend='unknown') def test_trend_n(self): assert_equal(tools.add_trend(self.arr_1d, 'n'), self.arr_1d) assert tools.add_trend(self.arr_1d, 'n') is not self.arr_1d assert_equal(tools.add_trend(self.arr_2d, 'n'), self.arr_2d) assert tools.add_trend(self.arr_2d, 'n') is not self.arr_2d class TestLagmat2DS(object): @classmethod def setup_class(cls): data = sm.datasets.macrodata.load_pandas() cls.macro_df = data.data[['year', 'quarter', 'realgdp', 'cpi']] np.random.seed(12345) cls.random_data = np.random.randn(100) index = [str(int(yr)) + '-Q' + str(int(qu)) for yr, qu in zip(cls.macro_df.year, cls.macro_df.quarter)] cls.macro_df.index = index cls.series = cls.macro_df.cpi @staticmethod def _prepare_expected(data, lags, trim='front'): t, k = data.shape expected = np.zeros((t + lags, (lags + 1) * k)) for col in range(k): for i in range(lags + 1): if i < lags: expected[i:-lags + i, (lags + 1) * col + i] = data[:, col] else: expected[i:, (lags + 1) * col + i] = data[:, col] if trim == 'front': expected = expected[:-lags] return expected def test_lagmat2ds_numpy(self): data = self.macro_df npdata = data.values lagmat = sm.tsa.lagmat2ds(npdata, 2) expected = self._prepare_expected(npdata, 2) assert_array_equal(lagmat, expected) lagmat = sm.tsa.lagmat2ds(npdata[:, :2], 3) expected = self._prepare_expected(npdata[:, :2], 3) assert_array_equal(lagmat, expected) npdata = self.series.values lagmat = sm.tsa.lagmat2ds(npdata, 5) expected = self._prepare_expected(npdata[:, None], 5) assert_array_equal(lagmat, expected) def test_lagmat2ds_pandas(self): data = self.macro_df lagmat = sm.tsa.lagmat2ds(data, 2) expected = self._prepare_expected(data.values, 2) assert_array_equal(lagmat, expected) lagmat = sm.tsa.lagmat2ds(data.iloc[:, :2], 3, trim='both') expected = self._prepare_expected(data.values[:, :2], 3) expected = expected[3:] assert_array_equal(lagmat, expected) data = self.series lagmat = sm.tsa.lagmat2ds(data, 5) expected = self._prepare_expected(data.values[:, None], 5) assert_array_equal(lagmat, expected) def test_lagmat2ds_use_pandas(self): data = self.macro_df lagmat = sm.tsa.lagmat2ds(data, 2, use_pandas=True) expected = self._prepare_expected(data.values, 2) cols = [] for c in data: for lags in range(3): if lags == 0: cols.append(c) else: cols.append(c + '.L.' + str(lags)) expected = pd.DataFrame(expected, index=data.index, columns=cols) assert_frame_equal(lagmat, expected) lagmat = sm.tsa.lagmat2ds(data.iloc[:, :2], 3, use_pandas=True, trim='both') expected = self._prepare_expected(data.values[:, :2], 3) cols = [] for c in data.iloc[:, :2]: for lags in range(4): if lags == 0: cols.append(c) else: cols.append(c + '.L.' + str(lags)) expected = pd.DataFrame(expected, index=data.index, columns=cols) expected = expected.iloc[3:] assert_frame_equal(lagmat, expected) data = self.series lagmat = sm.tsa.lagmat2ds(data, 5, use_pandas=True) expected = self._prepare_expected(data.values[:, None], 5) cols = [] c = data.name for lags in range(6): if lags == 0: cols.append(c) else: cols.append(c + '.L.' + str(lags)) expected = pd.DataFrame(expected, index=data.index, columns=cols) assert_frame_equal(lagmat, expected) def test_3d_error(self): data = np.array(2) with pytest.raises(ValueError): sm.tsa.lagmat2ds(data, 5) data = np.zeros((100, 2, 2)) with pytest.raises(ValueError): sm.tsa.lagmat2ds(data, 5) statsmodels-0.12.2/statsmodels/tsa/tests/test_x13.py000066400000000000000000000027571400612667500224770ustar00rootroot00000000000000import pandas as pd import pytest from statsmodels.datasets import macrodata, co2 from statsmodels.tsa.x13 import (_find_x12, x13_arima_select_order, x13_arima_analysis) x13path = _find_x12() pytestmark = pytest.mark.skipif(x13path is False, reason='X13/X12 not available') dta = macrodata.load_pandas().data index = pd.period_range(start='1959Q1', end='2009Q3', freq='Q') dta.index = index quarterly_data = dta.dropna() dta = co2.load_pandas().data dta['co2'] = dta.co2.interpolate() monthly_data = dta.resample('M') # change in pandas 0.18 resample is deferred object if not isinstance(monthly_data, (pd.DataFrame, pd.Series)): monthly_data = monthly_data.mean() monthly_start_data = dta.resample('MS') if not isinstance(monthly_start_data, (pd.DataFrame, pd.Series)): monthly_start_data = monthly_start_data.mean() data = (monthly_data, monthly_start_data, monthly_data.co2, monthly_start_data.co2, quarterly_data.realgdp, quarterly_data[['realgdp']]) ids = ('monthly', 'monthly_start', 'monthly_co2', 'monthly_start_co2', 'series', 'dataframe') @pytest.fixture(params=data, ids=ids) def dataset(request): return request.param def test_x13_arima_select_order(dataset): res = x13_arima_select_order(dataset) assert isinstance(res.order, tuple) assert isinstance(res.sorder, tuple) @pytest.mark.matplotlib def test_x13_arima_plot(dataset): res = x13_arima_analysis(dataset) res.plot() statsmodels-0.12.2/statsmodels/tsa/tsatools.py000066400000000000000000000610761400612667500215320ustar00rootroot00000000000000from statsmodels.compat.python import lrange, lzip from statsmodels.compat.numpy import recarray_select import numpy as np import numpy.lib.recfunctions as nprf import pandas as pd from pandas import DataFrame from pandas.tseries import offsets from pandas.tseries.frequencies import to_offset from statsmodels.tools.validation import int_like, bool_like, string_like from statsmodels.tools.sm_exceptions import ValueWarning from statsmodels.tools.data import _is_using_pandas, _is_recarray from statsmodels.tools.validation import array_like def add_trend(x, trend="c", prepend=False, has_constant='skip'): """ Add a trend and/or constant to an array. Parameters ---------- x : array_like Original array of data. trend : str {'n', 'c', 't', 'ct', 'ctt'} The trend to add. * 'n' add no trend. * 'c' add constant only. * 't' add trend only. * 'ct' add constant and linear trend. * 'ctt' add constant and linear and quadratic trend. prepend : bool If True, prepends the new data to the columns of X. has_constant : str {'raise', 'add', 'skip'} Controls what happens when trend is 'c' and a constant column already exists in x. 'raise' will raise an error. 'add' will add a column of 1s. 'skip' will return the data without change. 'skip' is the default. Returns ------- array_like The original data with the additional trend columns. If x is a recarray or pandas Series or DataFrame, then the trend column names are 'const', 'trend' and 'trend_squared'. See Also -------- statsmodels.tools.tools.add_constant Add a constant column to an array. Notes ----- Returns columns as ['ctt','ct','c'] whenever applicable. There is currently no checking for an existing trend. """ prepend = bool_like(prepend, 'prepend') trend = string_like(trend, 'trend', options=('n', 'c', 't', 'ct', 'ctt')) has_constant = string_like(has_constant, 'has_constant', options=('raise', 'add', 'skip')) # TODO: could be generalized for trend of aribitrary order columns = ['const', 'trend', 'trend_squared'] if trend == 'n': return x.copy() elif trend == "c": # handles structured arrays columns = columns[:1] trendorder = 0 elif trend == "ct" or trend == "t": columns = columns[:2] if trend == "t": columns = columns[1:2] trendorder = 1 elif trend == "ctt": trendorder = 2 is_recarray = _is_recarray(x) is_pandas = _is_using_pandas(x, None) or is_recarray if is_pandas or is_recarray: if is_recarray: # deprecated: remove recarray support after 0.12 import warnings from statsmodels.tools.sm_exceptions import recarray_warning warnings.warn(recarray_warning, FutureWarning) descr = x.dtype.descr x = pd.DataFrame.from_records(x) elif isinstance(x, pd.Series): x = pd.DataFrame(x) else: x = x.copy() else: x = np.asanyarray(x) nobs = len(x) trendarr = np.vander(np.arange(1, nobs + 1, dtype=np.float64), trendorder + 1) # put in order ctt trendarr = np.fliplr(trendarr) if trend == "t": trendarr = trendarr[:, 1] if "c" in trend: if is_pandas or is_recarray: # Mixed type protection def safe_is_const(s): try: return np.ptp(s) == 0.0 and np.any(s != 0.0) except: return False col_const = x.apply(safe_is_const, 0) else: ptp0 = np.ptp(np.asanyarray(x), axis=0) col_is_const = ptp0 == 0 nz_const = col_is_const & (x[0] != 0) col_const = nz_const if np.any(col_const): if has_constant == 'raise': if x.ndim == 1: base_err = "x is constant." else: columns = np.arange(x.shape[1])[col_const] if isinstance(x, pd.DataFrame): columns = x.columns const_cols = ", ".join([str(c) for c in columns]) base_err = ( "x contains one or more constant columns. Column(s) " f"{const_cols} are constant." ) msg = ( f"{base_err} Adding a constant with trend='{trend}' is not allowed." ) raise ValueError(msg) elif has_constant == 'skip': columns = columns[1:] trendarr = trendarr[:, 1:] order = 1 if prepend else -1 if is_recarray or is_pandas: trendarr = pd.DataFrame(trendarr, index=x.index, columns=columns) x = [trendarr, x] x = pd.concat(x[::order], 1) else: x = [trendarr, x] x = np.column_stack(x[::order]) if is_recarray: x = x.to_records(index=False) new_descr = x.dtype.descr extra_col = len(new_descr) - len(descr) if prepend: descr = new_descr[:extra_col] + descr else: descr = descr + new_descr[-extra_col:] x = x.astype(np.dtype(descr)) return x def add_lag(x, col=None, lags=1, drop=False, insert=True): """ Returns an array with lags included given an array. Parameters ---------- x : array_like An array or NumPy ndarray subclass. Can be either a 1d or 2d array with observations in columns. col : 'string', int, or None If data is a structured array or a recarray, `col` can be a string that is the name of the column containing the variable. Or `col` can be an int of the zero-based column index. If it's a 1d array `col` can be None. lags : int The number of lags desired. drop : bool Whether to keep the contemporaneous variable for the data. insert : bool or int If True, inserts the lagged values after `col`. If False, appends the data. If int inserts the lags at int. Returns ------- array : ndarray Array with lags Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.macrodata.load(as_pandas=False) >>> data = data.data[['year','quarter','realgdp','cpi']] >>> data = sm.tsa.add_lag(data, 'realgdp', lags=2) Notes ----- Trims the array both forward and backward, so that the array returned so that the length of the returned array is len(`X`) - lags. The lags are returned in increasing order, ie., t-1,t-2,...,t-lags """ lags = int_like(lags, 'lags') drop = bool_like(drop, 'drop') if x.dtype.names: names = x.dtype.names if not col and np.squeeze(x).ndim > 1: raise IndexError("col is None and the input array is not 1d") elif len(names) == 1: col = names[0] if isinstance(col, int): col = x.dtype.names[col] contemp = x[col] # make names for lags tmp_names = [col + '_'+'L(%i)' % i for i in range(1, lags+1)] ndlags = lagmat(contemp, maxlag=lags, trim='Both') # get index for return if insert is True: ins_idx = list(names).index(col) + 1 elif insert is False: ins_idx = len(names) + 1 else: # insert is an int if insert > len(names): import warnings warnings.warn("insert > number of variables, inserting at the" " last position", ValueWarning) ins_idx = insert first_names = list(names[:ins_idx]) last_names = list(names[ins_idx:]) if drop: if col in first_names: first_names.pop(first_names.index(col)) else: last_names.pop(last_names.index(col)) if first_names: # only do this if x is not "empty" # Workaround to avoid NumPy FutureWarning _x = recarray_select(x, first_names) first_arr = nprf.append_fields(_x[lags:], tmp_names, ndlags.T, usemask=False) else: first_arr = np.zeros(len(x)-lags, dtype=lzip(tmp_names, (x[col].dtype,)*lags)) for i,name in enumerate(tmp_names): first_arr[name] = ndlags[:,i] if last_names: return nprf.append_fields(first_arr, last_names, [x[name][lags:] for name in last_names], usemask=False) else: # lags for last variable return first_arr else: # we have an ndarray if x.ndim == 1: # make 2d if 1d x = x[:,None] if col is None: col = 0 # handle negative index if col < 0: col = x.shape[1] + col contemp = x[:,col] if insert is True: ins_idx = col + 1 elif insert is False: ins_idx = x.shape[1] else: if insert < 0: # handle negative index insert = x.shape[1] + insert + 1 if insert > x.shape[1]: insert = x.shape[1] import warnings warnings.warn("insert > number of variables, inserting at the" " last position", ValueWarning) ins_idx = insert ndlags = lagmat(contemp, lags, trim='Both') first_cols = lrange(ins_idx) last_cols = lrange(ins_idx,x.shape[1]) if drop: if col in first_cols: first_cols.pop(first_cols.index(col)) else: last_cols.pop(last_cols.index(col)) return np.column_stack((x[lags:,first_cols],ndlags, x[lags:,last_cols])) def detrend(x, order=1, axis=0): """ Detrend an array with a trend of given order along axis 0 or 1. Parameters ---------- x : array_like, 1d or 2d Data, if 2d, then each row or column is independently detrended with the same trendorder, but independent trend estimates. order : int The polynomial order of the trend, zero is constant, one is linear trend, two is quadratic trend. axis : int Axis can be either 0, observations by rows, or 1, observations by columns. Returns ------- ndarray The detrended series is the residual of the linear regression of the data on the trend of given order. """ order = int_like(order, 'order') axis = int_like(axis, 'axis') if x.ndim == 2 and int(axis) == 1: x = x.T elif x.ndim > 2: raise NotImplementedError('x.ndim > 2 is not implemented until it is needed') nobs = x.shape[0] if order == 0: # Special case demean resid = x - x.mean(axis=0) else: trends = np.vander(np.arange(float(nobs)), N=order + 1) beta = np.linalg.pinv(trends).dot(x) resid = x - np.dot(trends, beta) if x.ndim == 2 and int(axis) == 1: resid = resid.T return resid def lagmat(x, maxlag, trim='forward', original='ex', use_pandas=False): """ Create 2d array of lags. Parameters ---------- x : array_like Data; if 2d, observation in rows and variables in columns. maxlag : int All lags from zero to maxlag are included. trim : {'forward', 'backward', 'both', 'none', None} The trimming method to use. * 'forward' : trim invalid observations in front. * 'backward' : trim invalid initial observations. * 'both' : trim invalid observations on both sides. * 'none', None : no trimming of observations. original : {'ex','sep','in'} How the original is treated. * 'ex' : drops the original array returning only the lagged values. * 'in' : returns the original array and the lagged values as a single array. * 'sep' : returns a tuple (original array, lagged values). The original array is truncated to have the same number of rows as the returned lagmat. use_pandas : bool If true, returns a DataFrame when the input is a pandas Series or DataFrame. If false, return numpy ndarrays. Returns ------- lagmat : ndarray The array with lagged observations. y : ndarray, optional Only returned if original == 'sep'. Notes ----- When using a pandas DataFrame or Series with use_pandas=True, trim can only be 'forward' or 'both' since it is not possible to consistently extend index values. Examples -------- >>> from statsmodels.tsa.tsatools import lagmat >>> import numpy as np >>> X = np.arange(1,7).reshape(-1,2) >>> lagmat(X, maxlag=2, trim="forward", original='in') array([[ 1., 2., 0., 0., 0., 0.], [ 3., 4., 1., 2., 0., 0.], [ 5., 6., 3., 4., 1., 2.]]) >>> lagmat(X, maxlag=2, trim="backward", original='in') array([[ 5., 6., 3., 4., 1., 2.], [ 0., 0., 5., 6., 3., 4.], [ 0., 0., 0., 0., 5., 6.]]) >>> lagmat(X, maxlag=2, trim="both", original='in') array([[ 5., 6., 3., 4., 1., 2.]]) >>> lagmat(X, maxlag=2, trim="none", original='in') array([[ 1., 2., 0., 0., 0., 0.], [ 3., 4., 1., 2., 0., 0.], [ 5., 6., 3., 4., 1., 2.], [ 0., 0., 5., 6., 3., 4.], [ 0., 0., 0., 0., 5., 6.]]) """ maxlag = int_like(maxlag, 'maxlag') use_pandas = bool_like(use_pandas, 'use_pandas') trim = string_like(trim, 'trim', optional=True, options=('forward', 'backward', 'both', 'none')) original = string_like(original, 'original', options=('ex', 'sep', 'in')) # TODO: allow list of lags additional to maxlag orig = x x = array_like(x, 'x', ndim=2, dtype=None) is_pandas = _is_using_pandas(orig, None) and use_pandas trim = 'none' if trim is None else trim trim = trim.lower() if is_pandas and trim in ('none', 'backward'): raise ValueError("trim cannot be 'none' or 'forward' when used on " "Series or DataFrames") dropidx = 0 nobs, nvar = x.shape if original in ['ex', 'sep']: dropidx = nvar if maxlag >= nobs: raise ValueError("maxlag should be < nobs") lm = np.zeros((nobs + maxlag, nvar * (maxlag + 1))) for k in range(0, int(maxlag + 1)): lm[maxlag - k:nobs + maxlag - k, nvar * (maxlag - k):nvar * (maxlag - k + 1)] = x if trim in ('none', 'forward'): startobs = 0 elif trim in ('backward', 'both'): startobs = maxlag else: raise ValueError('trim option not valid') if trim in ('none', 'backward'): stopobs = len(lm) else: stopobs = nobs if is_pandas: x = orig x_columns = x.columns if isinstance(x, DataFrame) else [x.name] columns = [str(col) for col in x_columns] for lag in range(maxlag): lag_str = str(lag + 1) columns.extend([str(col) + '.L.' + lag_str for col in x_columns]) lm = DataFrame(lm[:stopobs], index=x.index, columns=columns) lags = lm.iloc[startobs:] if original in ('sep', 'ex'): leads = lags[x_columns] lags = lags.drop(x_columns, 1) else: lags = lm[startobs:stopobs, dropidx:] if original == 'sep': leads = lm[startobs:stopobs, :dropidx] if original == 'sep': return lags, leads else: return lags def lagmat2ds(x, maxlag0, maxlagex=None, dropex=0, trim='forward', use_pandas=False): """ Generate lagmatrix for 2d array, columns arranged by variables. Parameters ---------- x : array_like Data, 2d. Observations in rows and variables in columns. maxlag0 : int The first variable all lags from zero to maxlag are included. maxlagex : {None, int} The max lag for all other variables all lags from zero to maxlag are included. dropex : int Exclude first dropex lags from other variables. For all variables, except the first, lags from dropex to maxlagex are included. trim : str The trimming method to use. * 'forward' : trim invalid observations in front. * 'backward' : trim invalid initial observations. * 'both' : trim invalid observations on both sides. * 'none' : no trimming of observations. use_pandas : bool If true, returns a DataFrame when the input is a pandas Series or DataFrame. If false, return numpy ndarrays. Returns ------- ndarray The array with lagged observations, columns ordered by variable. Notes ----- Inefficient implementation for unequal lags, implemented for convenience. """ maxlag0 = int_like(maxlag0, 'maxlag0') maxlagex = int_like(maxlagex, 'maxlagex', optional=True) trim = string_like(trim, 'trim', optional=True, options=('forward', 'backward', 'both', 'none')) if maxlagex is None: maxlagex = maxlag0 maxlag = max(maxlag0, maxlagex) is_pandas = _is_using_pandas(x, None) if x.ndim == 1: if is_pandas: x = pd.DataFrame(x) else: x = x[:, None] elif x.ndim == 0 or x.ndim > 2: raise ValueError('Only supports 1 and 2-dimensional data.') nobs, nvar = x.shape if is_pandas and use_pandas: lags = lagmat(x.iloc[:, 0], maxlag, trim=trim, original='in', use_pandas=True) lagsli = [lags.iloc[:, :maxlag0 + 1]] for k in range(1, nvar): lags = lagmat(x.iloc[:, k], maxlag, trim=trim, original='in', use_pandas=True) lagsli.append(lags.iloc[:, dropex:maxlagex + 1]) return pd.concat(lagsli, axis=1) elif is_pandas: x = np.asanyarray(x) lagsli = [lagmat(x[:, 0], maxlag, trim=trim, original='in')[:, :maxlag0 + 1]] for k in range(1, nvar): lagsli.append(lagmat(x[:, k], maxlag, trim=trim, original='in')[:, dropex:maxlagex + 1]) return np.column_stack(lagsli) def vec(mat): return mat.ravel('F') def vech(mat): # Gets Fortran-order return mat.T.take(_triu_indices(len(mat))) # tril/triu/diag, suitable for ndarray.take def _tril_indices(n): rows, cols = np.tril_indices(n) return rows * n + cols def _triu_indices(n): rows, cols = np.triu_indices(n) return rows * n + cols def _diag_indices(n): rows, cols = np.diag_indices(n) return rows * n + cols def unvec(v): k = int(np.sqrt(len(v))) assert(k * k == len(v)) return v.reshape((k, k), order='F') def unvech(v): # quadratic formula, correct fp error rows = .5 * (-1 + np.sqrt(1 + 8 * len(v))) rows = int(np.round(rows)) result = np.zeros((rows, rows)) result[np.triu_indices(rows)] = v result = result + result.T # divide diagonal elements by 2 result[np.diag_indices(rows)] /= 2 return result def duplication_matrix(n): """ Create duplication matrix D_n which satisfies vec(S) = D_n vech(S) for symmetric matrix S Returns ------- D_n : ndarray """ n = int_like(n, 'n') tmp = np.eye(n * (n + 1) // 2) return np.array([unvech(x).ravel() for x in tmp]).T def elimination_matrix(n): """ Create the elimination matrix L_n which satisfies vech(M) = L_n vec(M) for any matrix M Parameters ---------- Returns ------- """ n = int_like(n, 'n') vech_indices = vec(np.tril(np.ones((n, n)))) return np.eye(n * n)[vech_indices != 0] def commutation_matrix(p, q): """ Create the commutation matrix K_{p,q} satisfying vec(A') = K_{p,q} vec(A) Parameters ---------- p : int q : int Returns ------- K : ndarray (pq x pq) """ p = int_like(p, 'p') q = int_like(q, 'q') K = np.eye(p * q) indices = np.arange(p * q).reshape((p, q), order='F') return K.take(indices.ravel(), axis=0) def _ar_transparams(params): """ Transforms params to induce stationarity/invertability. Parameters ---------- params : array_like The AR coefficients Reference --------- Jones(1980) """ newparams = np.tanh(params/2) tmp = np.tanh(params/2) for j in range(1,len(params)): a = newparams[j] for kiter in range(j): tmp[kiter] -= a * newparams[j-kiter-1] newparams[:j] = tmp[:j] return newparams def _ar_invtransparams(params): """ Inverse of the Jones reparameterization Parameters ---------- params : array_like The transformed AR coefficients """ params = params.copy() tmp = params.copy() for j in range(len(params)-1,0,-1): a = params[j] for kiter in range(j): tmp[kiter] = (params[kiter] + a * params[j-kiter-1])/\ (1-a**2) params[:j] = tmp[:j] invarcoefs = 2*np.arctanh(params) return invarcoefs def _ma_transparams(params): """ Transforms params to induce stationarity/invertability. Parameters ---------- params : ndarray The ma coeffecients of an (AR)MA model. Reference --------- Jones(1980) """ newparams = ((1-np.exp(-params))/(1+np.exp(-params))).copy() tmp = ((1-np.exp(-params))/(1+np.exp(-params))).copy() # levinson-durbin to get macf for j in range(1,len(params)): b = newparams[j] for kiter in range(j): tmp[kiter] += b * newparams[j-kiter-1] newparams[:j] = tmp[:j] return newparams def _ma_invtransparams(macoefs): """ Inverse of the Jones reparameterization Parameters ---------- params : ndarray The transformed MA coefficients """ tmp = macoefs.copy() for j in range(len(macoefs)-1,0,-1): b = macoefs[j] for kiter in range(j): tmp[kiter] = (macoefs[kiter]-b *macoefs[j-kiter-1])/(1-b**2) macoefs[:j] = tmp[:j] invmacoefs = -np.log((1-macoefs)/(1+macoefs)) return invmacoefs def unintegrate_levels(x, d): """ Returns the successive differences needed to unintegrate the series. Parameters ---------- x : array_like The original series d : int The number of differences of the differenced series. Returns ------- y : array_like The increasing differences from 0 to d-1 of the first d elements of x. See Also -------- unintegrate """ d = int_like(d, 'd') x = x[:d] return np.asarray([np.diff(x, d - i)[0] for i in range(d, 0, -1)]) def unintegrate(x, levels): """ After taking n-differences of a series, return the original series Parameters ---------- x : array_like The n-th differenced series levels : list A list of the first-value in each differenced series, for [first-difference, second-difference, ..., n-th difference] Returns ------- y : array_like The original series de-differenced Examples -------- >>> x = np.array([1, 3, 9., 19, 8.]) >>> levels = unintegrate_levels(x, 2) >>> levels array([ 1., 2.]) >>> unintegrate(np.diff(x, 2), levels) array([ 1., 3., 9., 19., 8.]) """ levels = list(levels)[:] # copy if len(levels) > 1: x0 = levels.pop(-1) return unintegrate(np.cumsum(np.r_[x0, x]), levels) x0 = levels[0] return np.cumsum(np.r_[x0, x]) def freq_to_period(freq): """ Convert a pandas frequency to a periodicity Parameters ---------- freq : str or offset Frequency to convert Returns ------- period : int Periodicity of freq Notes ----- Annual maps to 1, quarterly maps to 4, monthly to 12, weekly to 52. """ if not isinstance(freq, offsets.DateOffset): freq = to_offset(freq) # go ahead and standardize freq = freq.rule_code.upper() if freq == 'A' or freq.startswith(('A-', 'AS-')): return 1 elif freq == 'Q' or freq.startswith(('Q-', 'QS-')): return 4 elif freq == 'M' or freq.startswith(('M-', 'MS')): return 12 elif freq == 'W' or freq.startswith('W-'): return 52 elif freq == 'D': return 7 elif freq == 'B': return 5 elif freq == 'H': return 24 else: # pragma : no cover raise ValueError("freq {} not understood. Please report if you " "think this is in error.".format(freq)) __all__ = ['lagmat', 'lagmat2ds','add_trend', 'duplication_matrix', 'elimination_matrix', 'commutation_matrix', 'vec', 'vech', 'unvec', 'unvech', 'freq_to_period'] statsmodels-0.12.2/statsmodels/tsa/varma_process.py000066400000000000000000000464301400612667500225230ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Helper and filter functions for VAR and VARMA, and basic VAR class Created on Mon Jan 11 11:04:23 2010 Author: josef-pktd License: BSD This is a new version, I did not look at the old version again, but similar ideas. not copied/cleaned yet: * fftn based filtering, creating samples with fft * Tests: I ran examples but did not convert them to tests examples look good for parameter estimate and forecast, and filter functions main TODOs: * result statistics * see whether Bayesian dummy observation can be included without changing the single call to linalg.lstsq * impulse response function does not treat correlation, see Hamilton and jplv Extensions * constraints, Bayesian priors/penalization * Error Correction Form and Cointegration * Factor Models Stock-Watson, ??? see also VAR section in Notes.txt """ import numpy as np from scipy import signal from statsmodels.tsa.tsatools import lagmat def varfilter(x, a): '''apply an autoregressive filter to a series x Warning: I just found out that convolve does not work as I thought, this likely does not work correctly for nvars>3 x can be 2d, a can be 1d, 2d, or 3d Parameters ---------- x : array_like data array, 1d or 2d, if 2d then observations in rows a : array_like autoregressive filter coefficients, ar lag polynomial see Notes Returns ------- y : ndarray, 2d filtered array, number of columns determined by x and a Notes ----- In general form this uses the linear filter :: y = a(L)x where x : nobs, nvars a : nlags, nvars, npoly Depending on the shape and dimension of a this uses different Lag polynomial arrays case 1 : a is 1d or (nlags,1) one lag polynomial is applied to all variables (columns of x) case 2 : a is 2d, (nlags, nvars) each series is independently filtered with its own lag polynomial, uses loop over nvar case 3 : a is 3d, (nlags, nvars, npoly) the ith column of the output array is given by the linear filter defined by the 2d array a[:,:,i], i.e. :: y[:,i] = a(.,.,i)(L) * x y[t,i] = sum_p sum_j a(p,j,i)*x(t-p,j) for p = 0,...nlags-1, j = 0,...nvars-1, for all t >= nlags Note: maybe convert to axis=1, Not TODO: initial conditions ''' x = np.asarray(x) a = np.asarray(a) if x.ndim == 1: x = x[:,None] if x.ndim > 2: raise ValueError('x array has to be 1d or 2d') nvar = x.shape[1] nlags = a.shape[0] ntrim = nlags//2 # for x is 2d with ncols >1 if a.ndim == 1: # case: identical ar filter (lag polynomial) return signal.convolve(x, a[:,None], mode='valid') # alternative: #return signal.lfilter(a,[1],x.astype(float),axis=0) elif a.ndim == 2: if min(a.shape) == 1: # case: identical ar filter (lag polynomial) return signal.convolve(x, a, mode='valid') # case: independent ar #(a bit like recserar in gauss, but no x yet) #(no, reserar is inverse filter) result = np.zeros((x.shape[0]-nlags+1, nvar)) for i in range(nvar): # could also use np.convolve, but easier for swiching to fft result[:,i] = signal.convolve(x[:,i], a[:,i], mode='valid') return result elif a.ndim == 3: # case: vector autoregressive with lag matrices # Note: we must have shape[1] == shape[2] == nvar yf = signal.convolve(x[:,:,None], a) yvalid = yf[ntrim:-ntrim, yf.shape[1]//2,:] return yvalid def varinversefilter(ar, nobs, version=1): '''creates inverse ar filter (MA representation) recursively The VAR lag polynomial is defined by :: ar(L) y_t = u_t or y_t = -ar_{-1}(L) y_{t-1} + u_t the returned lagpolynomial is arinv(L)=ar^{-1}(L) in :: y_t = arinv(L) u_t Parameters ---------- ar : ndarray, (nlags,nvars,nvars) matrix lagpolynomial, currently no exog first row should be identity Returns ------- arinv : ndarray, (nobs,nvars,nvars) Notes ----- ''' nlags, nvars, nvarsex = ar.shape if nvars != nvarsex: print('exogenous variables not implemented not tested') arinv = np.zeros((nobs+1, nvarsex, nvars)) arinv[0,:,:] = ar[0] arinv[1:nlags,:,:] = -ar[1:] if version == 1: for i in range(2,nobs+1): tmp = np.zeros((nvars,nvars)) for p in range(1,nlags): tmp += np.dot(-ar[p],arinv[i-p,:,:]) arinv[i,:,:] = tmp if version == 0: for i in range(nlags+1,nobs+1): print(ar[1:].shape, arinv[i-1:i-nlags:-1,:,:].shape) #arinv[i,:,:] = np.dot(-ar[1:],arinv[i-1:i-nlags:-1,:,:]) #print(np.tensordot(-ar[1:],arinv[i-1:i-nlags:-1,:,:],axes=([2],[1])).shape #arinv[i,:,:] = np.tensordot(-ar[1:],arinv[i-1:i-nlags:-1,:,:],axes=([2],[1])) raise NotImplementedError('waiting for generalized ufuncs or something') return arinv def vargenerate(ar, u, initvalues=None): '''generate an VAR process with errors u similar to gauss uses loop Parameters ---------- ar : array (nlags,nvars,nvars) matrix lagpolynomial u : array (nobs,nvars) exogenous variable, error term for VAR Returns ------- sar : array (1+nobs,nvars) sample of var process, inverse filtered u does not trim initial condition y_0 = 0 Examples -------- # generate random sample of VAR nobs, nvars = 10, 2 u = numpy.random.randn(nobs,nvars) a21 = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[-0.8, 0. ], [ 0., -0.6]]]) vargenerate(a21,u) # Impulse Response to an initial shock to the first variable imp = np.zeros((nobs, nvars)) imp[0,0] = 1 vargenerate(a21,imp) ''' nlags, nvars, nvarsex = ar.shape nlagsm1 = nlags - 1 nobs = u.shape[0] if nvars != nvarsex: print('exogenous variables not implemented not tested') if u.shape[1] != nvars: raise ValueError('u needs to have nvars columns') if initvalues is None: sar = np.zeros((nobs+nlagsm1, nvars)) start = nlagsm1 else: start = max(nlagsm1, initvalues.shape[0]) sar = np.zeros((nobs+start, nvars)) sar[start-initvalues.shape[0]:start] = initvalues #sar[nlagsm1:] = u sar[start:] = u #if version == 1: for i in range(start,start+nobs): for p in range(1,nlags): sar[i] += np.dot(sar[i-p,:],-ar[p]) return sar def padone(x, front=0, back=0, axis=0, fillvalue=0): '''pad with zeros along one axis, currently only axis=0 can be used sequentially to pad several axis Examples -------- >>> padone(np.ones((2,3)),1,3,axis=1) array([[ 0., 1., 1., 1., 0., 0., 0.], [ 0., 1., 1., 1., 0., 0., 0.]]) >>> padone(np.ones((2,3)),1,1, fillvalue=np.nan) array([[ NaN, NaN, NaN], [ 1., 1., 1.], [ 1., 1., 1.], [ NaN, NaN, NaN]]) ''' #primitive version shape = np.array(x.shape) shape[axis] += (front + back) shapearr = np.array(x.shape) out = np.empty(shape) out.fill(fillvalue) startind = np.zeros(x.ndim) startind[axis] = front endind = startind + shapearr myslice = [slice(startind[k], endind[k]) for k in range(len(endind))] #print(myslice #print(out.shape #print(out[tuple(myslice)].shape out[tuple(myslice)] = x return out def trimone(x, front=0, back=0, axis=0): '''trim number of array elements along one axis Examples -------- >>> xp = padone(np.ones((2,3)),1,3,axis=1) >>> xp array([[ 0., 1., 1., 1., 0., 0., 0.], [ 0., 1., 1., 1., 0., 0., 0.]]) >>> trimone(xp,1,3,1) array([[ 1., 1., 1.], [ 1., 1., 1.]]) ''' shape = np.array(x.shape) shape[axis] -= (front + back) #print(shape, front, back shapearr = np.array(x.shape) startind = np.zeros(x.ndim) startind[axis] = front endind = startind + shape myslice = [slice(startind[k], endind[k]) for k in range(len(endind))] #print(myslice #print(shape, endind #print(x[tuple(myslice)].shape return x[tuple(myslice)] def ar2full(ar): '''make reduced lagpolynomial into a right side lagpoly array ''' nlags, nvar,nvarex = ar.shape return np.r_[np.eye(nvar,nvarex)[None,:,:],-ar] def ar2lhs(ar): '''convert full (rhs) lagpolynomial into a reduced, left side lagpoly array this is mainly a reminder about the definition ''' return -ar[1:] class _Var(object): '''obsolete VAR class, use tsa.VAR instead, for internal use only Examples -------- >>> v = Var(ar2s) >>> v.fit(1) >>> v.arhat array([[[ 1. , 0. ], [ 0. , 1. ]], [[-0.77784898, 0.01726193], [ 0.10733009, -0.78665335]]]) ''' def __init__(self, y): self.y = y self.nobs, self.nvars = y.shape def fit(self, nlags): '''estimate parameters using ols Parameters ---------- nlags : int number of lags to include in regression, same for all variables Returns ------- None, but attaches arhat : array (nlags, nvar, nvar) full lag polynomial array arlhs : array (nlags-1, nvar, nvar) reduced lag polynomial for left hand side other statistics as returned by linalg.lstsq : need to be completed This currently assumes all parameters are estimated without restrictions. In this case SUR is identical to OLS estimation results are attached to the class instance ''' self.nlags = nlags # without current period nvars = self.nvars #TODO: ar2s looks like a module variable, bug? #lmat = lagmat(ar2s, nlags, trim='both', original='in') lmat = lagmat(self.y, nlags, trim='both', original='in') self.yred = lmat[:,:nvars] self.xred = lmat[:,nvars:] res = np.linalg.lstsq(self.xred, self.yred, rcond=-1) self.estresults = res self.arlhs = res[0].reshape(nlags, nvars, nvars) self.arhat = ar2full(self.arlhs) self.rss = res[1] self.xredrank = res[2] def predict(self): '''calculate estimated timeseries (yhat) for sample ''' if not hasattr(self, 'yhat'): self.yhat = varfilter(self.y, self.arhat) return self.yhat def covmat(self): ''' covariance matrix of estimate # not sure it's correct, need to check orientation everywhere # looks ok, display needs getting used to >>> v.rss[None,None,:]*np.linalg.inv(np.dot(v.xred.T,v.xred))[:,:,None] array([[[ 0.37247445, 0.32210609], [ 0.1002642 , 0.08670584]], [[ 0.1002642 , 0.08670584], [ 0.45903637, 0.39696255]]]) >>> >>> v.rss[0]*np.linalg.inv(np.dot(v.xred.T,v.xred)) array([[ 0.37247445, 0.1002642 ], [ 0.1002642 , 0.45903637]]) >>> v.rss[1]*np.linalg.inv(np.dot(v.xred.T,v.xred)) array([[ 0.32210609, 0.08670584], [ 0.08670584, 0.39696255]]) ''' #check if orientation is same as self.arhat self.paramcov = (self.rss[None,None,:] * np.linalg.inv(np.dot(self.xred.T, self.xred))[:,:,None]) def forecast(self, horiz=1, u=None): '''calculates forcast for horiz number of periods at end of sample Parameters ---------- horiz : int (optional, default=1) forecast horizon u : array (horiz, nvars) error term for forecast periods. If None, then u is zero. Returns ------- yforecast : array (nobs+horiz, nvars) this includes the sample and the forecasts ''' if u is None: u = np.zeros((horiz, self.nvars)) return vargenerate(self.arhat, u, initvalues=self.y) class VarmaPoly(object): '''class to keep track of Varma polynomial format Examples -------- ar23 = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[-0.6, 0. ], [ 0.2, -0.6]], [[-0.1, 0. ], [ 0.1, -0.1]]]) ma22 = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[ 0.4, 0. ], [ 0.2, 0.3]]]) ''' def __init__(self, ar, ma=None): self.ar = ar self.ma = ma nlags, nvarall, nvars = ar.shape self.nlags, self.nvarall, self.nvars = nlags, nvarall, nvars self.isstructured = not (ar[0,:nvars] == np.eye(nvars)).all() if self.ma is None: self.ma = np.eye(nvars)[None,...] self.isindependent = True else: self.isindependent = not (ma[0] == np.eye(nvars)).all() self.malags = ar.shape[0] self.hasexog = nvarall > nvars self.arm1 = -ar[1:] #@property def vstack(self, a=None, name='ar'): '''stack lagpolynomial vertically in 2d array ''' if a is not None: a = a elif name == 'ar': a = self.ar elif name == 'ma': a = self.ma else: raise ValueError('no array or name given') return a.reshape(-1, self.nvarall) #@property def hstack(self, a=None, name='ar'): '''stack lagpolynomial horizontally in 2d array ''' if a is not None: a = a elif name == 'ar': a = self.ar elif name == 'ma': a = self.ma else: raise ValueError('no array or name given') return a.swapaxes(1,2).reshape(-1, self.nvarall).T #@property def stacksquare(self, a=None, name='ar', orientation='vertical'): '''stack lagpolynomial vertically in 2d square array with eye ''' if a is not None: a = a elif name == 'ar': a = self.ar elif name == 'ma': a = self.ma else: raise ValueError('no array or name given') astacked = a.reshape(-1, self.nvarall) lenpk, nvars = astacked.shape #[0] amat = np.eye(lenpk, k=nvars) amat[:,:nvars] = astacked return amat #@property def vstackarma_minus1(self): '''stack ar and lagpolynomial vertically in 2d array ''' a = np.concatenate((self.ar[1:], self.ma[1:]),0) return a.reshape(-1, self.nvarall) #@property def hstackarma_minus1(self): '''stack ar and lagpolynomial vertically in 2d array this is the Kalman Filter representation, I think ''' a = np.concatenate((self.ar[1:], self.ma[1:]),0) return a.swapaxes(1,2).reshape(-1, self.nvarall) def getisstationary(self, a=None): '''check whether the auto-regressive lag-polynomial is stationary Returns ------- isstationary : bool *attaches* areigenvalues : complex array eigenvalues sorted by absolute value References ---------- formula taken from NAG manual ''' if a is not None: a = a else: if self.isstructured: a = -self.reduceform(self.ar)[1:] else: a = -self.ar[1:] amat = self.stacksquare(a) ev = np.sort(np.linalg.eigvals(amat))[::-1] self.areigenvalues = ev return (np.abs(ev) < 1).all() def getisinvertible(self, a=None): '''check whether the auto-regressive lag-polynomial is stationary Returns ------- isinvertible : bool *attaches* maeigenvalues : complex array eigenvalues sorted by absolute value References ---------- formula taken from NAG manual ''' if a is not None: a = a else: if self.isindependent: a = self.reduceform(self.ma)[1:] else: a = self.ma[1:] if a.shape[0] == 0: # no ma lags self.maeigenvalues = np.array([], np.complex) return True amat = self.stacksquare(a) ev = np.sort(np.linalg.eigvals(amat))[::-1] self.maeigenvalues = ev return (np.abs(ev) < 1).all() def reduceform(self, apoly): ''' this assumes no exog, todo ''' if apoly.ndim != 3: raise ValueError('apoly needs to be 3d') nlags, nvarsex, nvars = apoly.shape a = np.empty_like(apoly) try: a0inv = np.linalg.inv(a[0,:nvars, :]) except np.linalg.LinAlgError: raise ValueError('matrix not invertible', 'ask for implementation of pinv') for lag in range(nlags): a[lag] = np.dot(a0inv, apoly[lag]) return a if __name__ == "__main__": # some example lag polynomials a21 = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[-0.8, 0. ], [ 0., -0.6]]]) a22 = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[-0.8, 0. ], [ 0.1, -0.8]]]) a23 = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[-0.8, 0.2], [ 0.1, -0.6]]]) a24 = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[-0.6, 0. ], [ 0.2, -0.6]], [[-0.1, 0. ], [ 0.1, -0.1]]]) a31 = np.r_[np.eye(3)[None,:,:], 0.8*np.eye(3)[None,:,:]] a32 = np.array([[[ 1. , 0. , 0. ], [ 0. , 1. , 0. ], [ 0. , 0. , 1. ]], [[ 0.8, 0. , 0. ], [ 0.1, 0.6, 0. ], [ 0. , 0. , 0.9]]]) ######## ut = np.random.randn(1000,2) ar2s = vargenerate(a22,ut) #res = np.linalg.lstsq(lagmat(ar2s,1)[:,1:], ar2s) res = np.linalg.lstsq(lagmat(ar2s,1), ar2s, rcond=-1) bhat = res[0].reshape(1,2,2) arhat = ar2full(bhat) #print(maxabs(arhat - a22) v = _Var(ar2s) v.fit(1) v.forecast() v.forecast(25)[-30:] ar23 = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[-0.6, 0. ], [ 0.2, -0.6]], [[-0.1, 0. ], [ 0.1, -0.1]]]) ma22 = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[ 0.4, 0. ], [ 0.2, 0.3]]]) ar23ns = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[-1.9, 0. ], [ 0.4, -0.6]], [[ 0.3, 0. ], [ 0.1, -0.1]]]) vp = VarmaPoly(ar23, ma22) print(vars(vp)) print(vp.vstack()) print(vp.vstack(a24)) print(vp.hstackarma_minus1()) print(vp.getisstationary()) print(vp.getisinvertible()) vp2 = VarmaPoly(ar23ns) print(vp2.getisstationary()) print(vp2.getisinvertible()) # no ma lags statsmodels-0.12.2/statsmodels/tsa/vector_ar/000077500000000000000000000000001400612667500212625ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/__init__.py000066400000000000000000000001131400612667500233660ustar00rootroot00000000000000from statsmodels.tools._testing import PytestTester test = PytestTester() statsmodels-0.12.2/statsmodels/tsa/vector_ar/api.py000066400000000000000000000002301400612667500224000ustar00rootroot00000000000000# pylint: disable=W0611 __all__ = ["VAR", "SVAR", "DynamicVAR"] from .dynamic import DynamicVAR from .svar_model import SVAR from .var_model import VAR statsmodels-0.12.2/statsmodels/tsa/vector_ar/hypothesis_test_results.py000066400000000000000000000166771400612667500266740ustar00rootroot00000000000000import numpy as np from statsmodels.iolib.table import SimpleTable class HypothesisTestResults(object): """ Results class for hypothesis tests. Parameters ---------- test_statistic : float crit_value : float pvalue : float, 0 <= `pvalue` <= 1 df : int Degrees of freedom. signif : float, 0 < `signif` < 1 Significance level. method : str The kind of test (e.g. ``"f"`` for F-test, ``"wald"`` for Wald-test). title : str A title describing the test. It will be part of the summary. h0 : str A string describing the null hypothesis. It will be used in the summary. """ def __init__(self, test_statistic, crit_value, pvalue, df, signif, method, title, h0): self.test_statistic = test_statistic self.crit_value = crit_value self.pvalue = pvalue self.df = df self.signif = signif self.method = method.capitalize() if test_statistic < crit_value: self.conclusion = "fail to reject" else: self.conclusion = "reject" self.title = title self.h0 = h0 self.conclusion_str = "Conclusion: %s H_0" % self.conclusion self.signif_str = " at {:.0%} significance level".format(self.signif) def summary(self): """Return summary""" title = self.title + ". " + self.h0 + ". " \ + self.conclusion_str + self.signif_str + "." data_fmt = {"data_fmts": ["%#0.4g", "%#0.4g", "%#0.3F", "%s"]} html_data_fmt = dict(data_fmt) html_data_fmt["data_fmts"] = ["" + i + "" for i in html_data_fmt["data_fmts"]] return SimpleTable(data=[[self.test_statistic, self.crit_value, self.pvalue, str(self.df)]], headers=['Test statistic', 'Critical value', 'p-value', 'df'], title=title, txt_fmt=data_fmt, html_fmt=html_data_fmt, ltx_fmt=data_fmt) def __str__(self): return "<" + self.__module__ + "." + self.__class__.__name__ \ + " object. " + self.h0 + ": " + self.conclusion \ + self.signif_str \ + ". Test statistic: {:.3f}".format(self.test_statistic) \ + ", critical value: {:.3f}>".format(self.crit_value) \ + ", p-value: {:.3f}>".format(self.pvalue) def __eq__(self, other): if not isinstance(other, self.__class__): return False return np.allclose(self.test_statistic, other.test_statistic) \ and np.allclose(self.crit_value, other.crit_value) \ and np.allclose(self.pvalue, other.pvalue) \ and np.allclose(self.signif, other.signif) class CausalityTestResults(HypothesisTestResults): """ Results class for Granger-causality and instantaneous causality. Parameters ---------- causing : list of str This list contains the potentially causing variables. caused : list of str This list contains the potentially caused variables. test_statistic : float crit_value : float pvalue : float df : int Degrees of freedom. signif : float Significance level. test : str {``"granger"``, ``"inst"``}, default: ``"granger"`` If ``"granger"``, Granger-causality has been tested. If ``"inst"``, instantaneous causality has been tested. method : str {``"f"``, ``"wald"``} The kind of test. ``"f"`` indicates an F-test, ``"wald"`` indicates a Wald-test. """ def __init__(self, causing, caused, test_statistic, crit_value, pvalue, df, signif, test="granger", method=None): self.causing = causing self.caused = caused self.test = test if method is None or method.lower() not in ["f", "wald"]: raise ValueError('The method ("f" for F-test, "wald" for ' "Wald-test) must not be None.") method = method.capitalize() # attributes used in summary and string representation: title = "Granger" if self.test == "granger" else "Instantaneous" title += " causality %s-test" % method h0 = "H_0: " if len(self.causing) == 1: h0 += "{} does not ".format(self.causing[0]) else: h0 += "{} do not ".format(self.causing) h0 += "Granger-" if self.test == "granger" else "instantaneously " h0 += "cause " if len(self.caused) == 1: h0 += self.caused[0] else: h0 += "[" + ", ".join(caused) + "]" super(CausalityTestResults, self).__init__(test_statistic, crit_value, pvalue, df, signif, method, title, h0) def __eq__(self, other): basic_test = super(CausalityTestResults, self).__eq__(other) if not basic_test: return False test = self.test == other.test variables = (self.causing == other.causing and self.caused == other.caused) # instantaneous causality is a symmetric relation ==> causing and # caused may be swapped if not variables and self.test == "inst": variables = (self.causing == other.caused and self.caused == other.causing) return test and variables class NormalityTestResults(HypothesisTestResults): """ Results class for the Jarque-Bera-test for nonnormality. Parameters ---------- test_statistic : float The test's test statistic. crit_value : float The test's critical value. pvalue : float The test's p-value. df : int Degrees of freedom. signif : float Significance level. """ def __init__(self, test_statistic, crit_value, pvalue, df, signif): method = "Jarque-Bera" title = "normality (skew and kurtosis) test" h0 = 'H_0: data generated by normally-distributed process' super(NormalityTestResults, self).__init__(test_statistic, crit_value, pvalue, df, signif, method, title, h0) class WhitenessTestResults(HypothesisTestResults): """ Results class for the Portmanteau-test for residual autocorrelation. Parameters ---------- test_statistic : float The test's test statistic. crit_value : float The test's critical value. pvalue : float The test's p-value. df : int Degrees of freedom. signif : float Significance level. nlags : int Number of lags tested. """ def __init__(self, test_statistic, crit_value, pvalue, df, signif, nlags, adjusted): self.lags = nlags self.adjusted = adjusted method = "Portmanteau" title = "{}-test for residual autocorrelation".format(method) if adjusted: title = "Adjusted " + title h0 = "H_0: residual autocorrelation up to lag {} is zero".format(nlags) super(WhitenessTestResults, self).__init__(test_statistic, crit_value, pvalue, df, signif, method, title, h0) statsmodels-0.12.2/statsmodels/tsa/vector_ar/irf.py000066400000000000000000000574441400612667500224320ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Impulse reponse-related code """ import numpy as np import numpy.linalg as la import scipy.linalg as L from statsmodels.tools.decorators import cache_readonly import statsmodels.tsa.tsatools as tsa import statsmodels.tsa.vector_ar.plotting as plotting import statsmodels.tsa.vector_ar.util as util mat = np.array class BaseIRAnalysis(object): """ Base class for plotting and computing IRF-related statistics, want to be able to handle known and estimated processes """ def __init__(self, model, P=None, periods=10, order=None, svar=False, vecm=False): self.model = model self.periods = periods self.neqs, self.lags, self.T = model.neqs, model.k_ar, model.nobs self.order = order if P is None: sigma = model.sigma_u # TODO, may be difficult at the moment # if order is not None: # indexer = [model.get_eq_index(name) for name in order] # sigma = sigma[:, indexer][indexer, :] # if sigma.shape != model.sigma_u.shape: # raise ValueError('variable order is wrong length') P = la.cholesky(sigma) self.P = P self.svar = svar self.irfs = model.ma_rep(periods) if svar: self.svar_irfs = model.svar_ma_rep(periods, P=P) else: self.orth_irfs = model.orth_ma_rep(periods, P=P) self.cum_effects = self.irfs.cumsum(axis=0) if svar: self.svar_cum_effects = self.svar_irfs.cumsum(axis=0) else: self.orth_cum_effects = self.orth_irfs.cumsum(axis=0) # long-run effects may be infinite for VECMs. if not vecm: self.lr_effects = model.long_run_effects() if svar: self.svar_lr_effects = np.dot(model.long_run_effects(), P) else: self.orth_lr_effects = np.dot(model.long_run_effects(), P) # auxiliary stuff if vecm: self._A = util.comp_matrix(model.var_rep) else: self._A = util.comp_matrix(model.coefs) def _choose_irfs(self, orth=False, svar=False): if orth: return self.orth_irfs elif svar: return self.svar_irfs else: return self.irfs def cov(self, *args, **kwargs): raise NotImplementedError def cum_effect_cov(self, *args, **kwargs): raise NotImplementedError def plot(self, orth=False, *, impulse=None, response=None, signif=0.05, plot_params=None, figsize=(10, 10), subplot_params=None, plot_stderr=True, stderr_type='asym', repl=1000, seed=None, component=None): """ Plot impulse responses Parameters ---------- orth : bool, default False Compute orthogonalized impulse responses impulse : {str, int} variable providing the impulse response : {str, int} variable affected by the impulse signif : float (0 < signif < 1) Significance level for error bars, defaults to 95% CI subplot_params : dict To pass to subplot plotting funcions. Example: if fonts are too big, pass {'fontsize' : 8} or some number to your taste. plot_params : dict figsize : (float, float), default (10, 10) Figure size (width, height in inches) plot_stderr : bool, default True Plot standard impulse response error bands stderr_type : str 'asym': default, computes asymptotic standard errors 'mc': monte carlo standard errors (use rpl) repl : int, default 1000 Number of replications for Monte Carlo and Sims-Zha standard errors seed : int np.random.seed for Monte Carlo replications component: array or vector of principal component indices """ periods = self.periods model = self.model svar = self.svar if orth and svar: raise ValueError("For SVAR system, set orth=False") irfs = self._choose_irfs(orth, svar) if orth: title = 'Impulse responses (orthogonalized)' elif svar: title = 'Impulse responses (structural)' else: title = 'Impulse responses' if plot_stderr is False: stderr = None elif stderr_type not in ['asym', 'mc', 'sz1', 'sz2','sz3']: raise ValueError("Error type must be either 'asym', 'mc','sz1','sz2', or 'sz3'") else: if stderr_type == 'asym': stderr = self.cov(orth=orth) if stderr_type == 'mc': stderr = self.errband_mc(orth=orth, svar=svar, repl=repl, signif=signif, seed=seed) if stderr_type == 'sz1': stderr = self.err_band_sz1(orth=orth, svar=svar, repl=repl, signif=signif, seed=seed, component=component) if stderr_type == 'sz2': stderr = self.err_band_sz2(orth=orth, svar=svar, repl=repl, signif=signif, seed=seed, component=component) if stderr_type == 'sz3': stderr = self.err_band_sz3(orth=orth, svar=svar, repl=repl, signif=signif, seed=seed, component=component) fig = plotting.irf_grid_plot(irfs, stderr, impulse, response, self.model.names, title, signif=signif, subplot_params=subplot_params, plot_params=plot_params, figsize=figsize, stderr_type=stderr_type) return fig def plot_cum_effects(self, orth=False, *, impulse=None, response=None, signif=0.05, plot_params=None, figsize=(10, 10), subplot_params=None, plot_stderr=True, stderr_type='asym', repl=1000, seed=None): """ Plot cumulative impulse response functions Parameters ---------- orth : bool, default False Compute orthogonalized impulse responses impulse : {str, int} variable providing the impulse response : {str, int} variable affected by the impulse signif : float (0 < signif < 1) Significance level for error bars, defaults to 95% CI subplot_params : dict To pass to subplot plotting funcions. Example: if fonts are too big, pass {'fontsize' : 8} or some number to your taste. plot_params : dict figsize: (float, float), default (10, 10) Figure size (width, height in inches) plot_stderr : bool, default True Plot standard impulse response error bands stderr_type : str 'asym': default, computes asymptotic standard errors 'mc': monte carlo standard errors (use rpl) repl : int, default 1000 Number of replications for monte carlo standard errors seed : int np.random.seed for Monte Carlo replications """ if orth: title = 'Cumulative responses responses (orthogonalized)' cum_effects = self.orth_cum_effects lr_effects = self.orth_lr_effects else: title = 'Cumulative responses' cum_effects = self.cum_effects lr_effects = self.lr_effects if stderr_type not in ['asym', 'mc']: raise ValueError("`stderr_type` must be one of 'asym', 'mc'") else: if stderr_type == 'asym': stderr = self.cum_effect_cov(orth=orth) if stderr_type == 'mc': stderr = self.cum_errband_mc(orth=orth, repl=repl, signif=signif, seed=seed) if not plot_stderr: stderr = None fig = plotting.irf_grid_plot(cum_effects, stderr, impulse, response, self.model.names, title, signif=signif, hlines=lr_effects, subplot_params=subplot_params, plot_params=plot_params, figsize=figsize, stderr_type=stderr_type) return fig class IRAnalysis(BaseIRAnalysis): """ Impulse response analysis class. Computes impulse responses, asymptotic standard errors, and produces relevant plots Parameters ---------- model : VAR instance Notes ----- Using Lütkepohl (2005) notation """ def __init__(self, model, P=None, periods=10, order=None, svar=False, vecm=False): BaseIRAnalysis.__init__(self, model, P=P, periods=periods, order=order, svar=svar, vecm=vecm) if vecm: self.cov_a = model.cov_var_repr else: self.cov_a = model._cov_alpha self.cov_sig = model._cov_sigma # memoize dict for G matrix function self._g_memo = {} def cov(self, orth=False): """ Compute asymptotic standard errors for impulse response coefficients Notes ----- Lütkepohl eq 3.7.5 Returns ------- """ if orth: return self._orth_cov() covs = self._empty_covm(self.periods + 1) covs[0] = np.zeros((self.neqs ** 2, self.neqs ** 2)) for i in range(1, self.periods + 1): Gi = self.G[i - 1] covs[i] = Gi @ self.cov_a @ Gi.T return covs def errband_mc(self, orth=False, svar=False, repl=1000, signif=0.05, seed=None, burn=100): """ IRF Monte Carlo integrated error bands """ model = self.model periods = self.periods if svar: return model.sirf_errband_mc(orth=orth, repl=repl, steps=periods, signif=signif, seed=seed, burn=burn, cum=False) else: return model.irf_errband_mc(orth=orth, repl=repl, steps=periods, signif=signif, seed=seed, burn=burn, cum=False) def err_band_sz1(self, orth=False, svar=False, repl=1000, signif=0.05, seed=None, burn=100, component=None): """ IRF Sims-Zha error band method 1. Assumes symmetric error bands around mean. Parameters ---------- orth : bool, default False Compute orthogonalized impulse responses repl : int, default 1000 Number of MC replications signif : float (0 < signif < 1) Significance level for error bars, defaults to 95% CI seed : int, default None np.random seed burn : int, default 100 Number of initial simulated obs to discard component : neqs x neqs array, default to largest for each Index of column of eigenvector/value to use for each error band Note: period of impulse (t=0) is not included when computing principle component References ---------- Sims, Christopher A., and Tao Zha. 1999. "Error Bands for Impulse Response". Econometrica 67: 1113-1155. """ model = self.model periods = self.periods irfs = self._choose_irfs(orth, svar) neqs = self.neqs irf_resim = model.irf_resim(orth=orth, repl=repl, steps=periods, seed=seed, burn=burn) q = util.norm_signif_level(signif) W, eigva, k =self._eigval_decomp_SZ(irf_resim) if component is not None: if np.shape(component) != (neqs,neqs): raise ValueError("Component array must be " + str(neqs) + " x " + str(neqs)) if np.argmax(component) >= neqs*periods: raise ValueError("Atleast one of the components does not exist") else: k = component # here take the kth column of W, which we determine by finding the largest eigenvalue of the covaraince matrix lower = np.copy(irfs) upper = np.copy(irfs) for i in range(neqs): for j in range(neqs): lower[1:,i,j] = irfs[1:,i,j] + W[i,j,:,k[i,j]]*q*np.sqrt(eigva[i,j,k[i,j]]) upper[1:,i,j] = irfs[1:,i,j] - W[i,j,:,k[i,j]]*q*np.sqrt(eigva[i,j,k[i,j]]) return lower, upper def err_band_sz2(self, orth=False, svar=False, repl=1000, signif=0.05, seed=None, burn=100, component=None): """ IRF Sims-Zha error band method 2. This method Does not assume symmetric error bands around mean. Parameters ---------- orth : bool, default False Compute orthogonalized impulse responses repl : int, default 1000 Number of MC replications signif : float (0 < signif < 1) Significance level for error bars, defaults to 95% CI seed : int, default None np.random seed burn : int, default 100 Number of initial simulated obs to discard component : neqs x neqs array, default to largest for each Index of column of eigenvector/value to use for each error band Note: period of impulse (t=0) is not included when computing principle component References ---------- Sims, Christopher A., and Tao Zha. 1999. "Error Bands for Impulse Response". Econometrica 67: 1113-1155. """ model = self.model periods = self.periods irfs = self._choose_irfs(orth, svar) neqs = self.neqs irf_resim = model.irf_resim(orth=orth, repl=repl, T=periods, seed=seed, burn=100) W, eigva, k = self._eigval_decomp_SZ(irf_resim) if component is not None: if np.shape(component) != (neqs,neqs): raise ValueError("Component array must be " + str(neqs) + " x " + str(neqs)) if np.argmax(component) >= neqs*periods: raise ValueError("Atleast one of the components does not exist") else: k = component gamma = np.zeros((repl, periods+1, neqs, neqs)) for p in range(repl): for i in range(neqs): for j in range(neqs): gamma[p,1:,i,j] = W[i,j,k[i,j],:] * irf_resim[p,1:,i,j] gamma_sort = np.sort(gamma, axis=0) #sort to get quantiles indx = round(signif/2*repl)-1,round((1-signif/2)*repl)-1 lower = np.copy(irfs) upper = np.copy(irfs) for i in range(neqs): for j in range(neqs): lower[:,i,j] = irfs[:,i,j] + gamma_sort[indx[0],:,i,j] upper[:,i,j] = irfs[:,i,j] + gamma_sort[indx[1],:,i,j] return lower, upper def err_band_sz3(self, orth=False, svar=False, repl=1000, signif=0.05, seed=None, burn=100, component=None): """ IRF Sims-Zha error band method 3. Does not assume symmetric error bands around mean. Parameters ---------- orth : bool, default False Compute orthogonalized impulse responses repl : int, default 1000 Number of MC replications signif : float (0 < signif < 1) Significance level for error bars, defaults to 95% CI seed : int, default None np.random seed burn : int, default 100 Number of initial simulated obs to discard component : vector length neqs, default to largest for each Index of column of eigenvector/value to use for each error band Note: period of impulse (t=0) is not included when computing principle component References ---------- Sims, Christopher A., and Tao Zha. 1999. "Error Bands for Impulse Response". Econometrica 67: 1113-1155. """ model = self.model periods = self.periods irfs = self._choose_irfs(orth, svar) neqs = self.neqs irf_resim = model.irf_resim(orth=orth, repl=repl, T=periods, seed=seed, burn=100) stack = np.zeros((neqs, repl, periods*neqs)) #stack left to right, up and down for p in range(repl): for i in range(neqs): stack[i, p,:] = np.ravel(irf_resim[p,1:,:,i].T) stack_cov=np.zeros((neqs, periods*neqs, periods*neqs)) W = np.zeros((neqs, periods*neqs, periods*neqs)) eigva = np.zeros((neqs, periods*neqs)) k = np.zeros((neqs)) if component is not None: if np.size(component) != (neqs): raise ValueError("Component array must be of length " + str(neqs)) if np.argmax(component) >= neqs*periods: raise ValueError("Atleast one of the components does not exist") else: k = component #compute for eigen decomp for each stack for i in range(neqs): stack_cov[i] = np.cov(stack[i],rowvar=0) W[i], eigva[i], k[i] = util.eigval_decomp(stack_cov[i]) gamma = np.zeros((repl, periods+1, neqs, neqs)) for p in range(repl): c = 0 for j in range(neqs): for i in range(neqs): gamma[p,1:,i,j] = W[j,k[j],i*periods:(i+1)*periods] * irf_resim[p,1:,i,j] if i == neqs-1: gamma[p,1:,i,j] = W[j,k[j],i*periods:] * irf_resim[p,1:,i,j] gamma_sort = np.sort(gamma, axis=0) #sort to get quantiles indx = round(signif/2*repl)-1,round((1-signif/2)*repl)-1 lower = np.copy(irfs) upper = np.copy(irfs) for i in range(neqs): for j in range(neqs): lower[:,i,j] = irfs[:,i,j] + gamma_sort[indx[0],:,i,j] upper[:,i,j] = irfs[:,i,j] + gamma_sort[indx[1],:,i,j] return lower, upper def _eigval_decomp_SZ(self, irf_resim): """ Returns ------- W: array of eigenvectors eigva: list of eigenvalues k: matrix indicating column # of largest eigenvalue for each c_i,j """ neqs = self.neqs periods = self.periods cov_hold = np.zeros((neqs, neqs, periods, periods)) for i in range(neqs): for j in range(neqs): cov_hold[i,j,:,:] = np.cov(irf_resim[:,1:,i,j],rowvar=0) W = np.zeros((neqs, neqs, periods, periods)) eigva = np.zeros((neqs, neqs, periods, 1)) k = np.zeros((neqs, neqs)) for i in range(neqs): for j in range(neqs): W[i,j,:,:], eigva[i,j,:,0], k[i,j] = util.eigval_decomp(cov_hold[i,j,:,:]) return W, eigva, k @cache_readonly def G(self): # Gi matrices as defined on p. 111 K = self.neqs # nlags = self.model.p # J = np.hstack((np.eye(K),) + (np.zeros((K, K)),) * (nlags - 1)) def _make_g(i): # p. 111 Lutkepohl G = 0. for m in range(i): # be a bit cute to go faster idx = i - 1 - m if idx in self._g_memo: apow = self._g_memo[idx] else: apow = la.matrix_power(self._A.T, idx) # apow = np.dot(J, apow) apow = apow[:K] self._g_memo[idx] = apow # take first K rows piece = np.kron(apow, self.irfs[m]) G = G + piece return G return [_make_g(i) for i in range(1, self.periods + 1)] def _orth_cov(self): # Lutkepohl 3.7.8 Ik = np.eye(self.neqs) PIk = np.kron(self.P.T, Ik) H = self.H covs = self._empty_covm(self.periods + 1) for i in range(self.periods + 1): if i == 0: apiece = 0 else: Ci = np.dot(PIk, self.G[i-1]) apiece = Ci @ self.cov_a @ Ci.T Cibar = np.dot(np.kron(Ik, self.irfs[i]), H) bpiece = (Cibar @ self.cov_sig @ Cibar.T) / self.T # Lutkepohl typo, cov_sig correct covs[i] = apiece + bpiece return covs def cum_effect_cov(self, orth=False): """ Compute asymptotic standard errors for cumulative impulse response coefficients Parameters ---------- orth : bool Notes ----- eq. 3.7.7 (non-orth), 3.7.10 (orth) Returns ------- """ Ik = np.eye(self.neqs) PIk = np.kron(self.P.T, Ik) F = 0. covs = self._empty_covm(self.periods + 1) for i in range(self.periods + 1): if i > 0: F = F + self.G[i - 1] if orth: if i == 0: apiece = 0 else: Bn = np.dot(PIk, F) apiece = Bn @ self.cov_a @ Bn.T Bnbar = np.dot(np.kron(Ik, self.cum_effects[i]), self.H) bpiece = (Bnbar @ self.cov_sig @ Bnbar.T) / self.T covs[i] = apiece + bpiece else: if i == 0: covs[i] = np.zeros((self.neqs**2, self.neqs**2)) continue covs[i] = F @ self.cov_a @ F.T return covs def cum_errband_mc(self, orth=False, repl=1000, signif=0.05, seed=None, burn=100): """ IRF Monte Carlo integrated error bands of cumulative effect """ model = self.model periods = self.periods return model.irf_errband_mc(orth=orth, repl=repl, T=periods, signif=signif, seed=seed, burn=burn, cum=True) def lr_effect_cov(self, orth=False): """ Returns ------- """ lre = self.lr_effects Finfty = np.kron(np.tile(lre.T, self.lags), lre) Ik = np.eye(self.neqs) if orth: Binf = np.dot(np.kron(self.P.T, np.eye(self.neqs)), Finfty) Binfbar = np.dot(np.kron(Ik, lre), self.H) return (Binf @ self.cov_a @ Binf.T + Binfbar @ self.cov_sig @ Binfbar.T) else: return Finfty @ self.cov_a @ Finfty.T def stderr(self, orth=False): return np.array([tsa.unvec(np.sqrt(np.diag(c))) for c in self.cov(orth=orth)]) def cum_effect_stderr(self, orth=False): return np.array([tsa.unvec(np.sqrt(np.diag(c))) for c in self.cum_effect_cov(orth=orth)]) def lr_effect_stderr(self, orth=False): cov = self.lr_effect_cov(orth=orth) return tsa.unvec(np.sqrt(np.diag(cov))) def _empty_covm(self, periods): return np.zeros((periods, self.neqs ** 2, self.neqs ** 2), dtype=float) @cache_readonly def H(self): k = self.neqs Lk = tsa.elimination_matrix(k) Kkk = tsa.commutation_matrix(k, k) Ik = np.eye(k) # B = Lk @ (np.eye(k**2) + commutation_matrix(k, k)) @ \ # np.kron(self.P, np.eye(k)) @ Lk.T # return Lk.T @ L.inv(B) B = Lk @ (np.kron(Ik, self.P) @ Kkk + np.kron(self.P, Ik)) @ Lk.T return np.dot(Lk.T, L.inv(B)) def fevd_table(self): raise NotImplementedError statsmodels-0.12.2/statsmodels/tsa/vector_ar/output.py000066400000000000000000000154411400612667500232010ustar00rootroot00000000000000from statsmodels.compat.python import lzip from io import StringIO import numpy as np from statsmodels.iolib import SimpleTable mat = np.array _default_table_fmt = dict( empty_cell = '', colsep=' ', row_pre = '', row_post = '', table_dec_above='=', table_dec_below='=', header_dec_below='-', header_fmt = '%s', stub_fmt = '%s', title_align='c', header_align = 'r', data_aligns = 'r', stubs_align = 'l', fmt = 'txt' ) class VARSummary(object): default_fmt = dict( #data_fmts = ["%#12.6g","%#12.6g","%#10.4g","%#5.4g"], #data_fmts = ["%#10.4g","%#10.4g","%#10.4g","%#6.4g"], data_fmts = ["%#15.6F","%#15.6F","%#15.3F","%#14.3F"], empty_cell = '', #colwidths = 10, colsep=' ', row_pre = '', row_post = '', table_dec_above='=', table_dec_below='=', header_dec_below='-', header_fmt = '%s', stub_fmt = '%s', title_align='c', header_align = 'r', data_aligns = 'r', stubs_align = 'l', fmt = 'txt' ) part1_fmt = dict( default_fmt, data_fmts = ["%s"], colwidths = 15, colsep=' ', table_dec_below='', header_dec_below=None, ) part2_fmt = dict( default_fmt, data_fmts = ["%#12.6g","%#12.6g","%#10.4g","%#5.4g"], colwidths = None, colsep=' ', table_dec_above='-', table_dec_below='-', header_dec_below=None, ) def __init__(self, estimator): self.model = estimator self.summary = self.make() def __repr__(self): return self.summary def make(self, endog_names=None, exog_names=None): """ Summary of VAR model """ buf = StringIO() buf.write(self._header_table() + '\n') buf.write(self._stats_table() + '\n') buf.write(self._coef_table() + '\n') buf.write(self._resid_info() + '\n') return buf.getvalue() def _header_table(self): import time model = self.model t = time.localtime() # TODO: change when we allow coef restrictions # ncoefs = len(model.beta) # Header information part1title = "Summary of Regression Results" part1data = [[model._model_type], ["OLS"], #TODO: change when fit methods change [time.strftime("%a, %d, %b, %Y", t)], [time.strftime("%H:%M:%S", t)]] part1header = None part1stubs = ('Model:', 'Method:', 'Date:', 'Time:') part1 = SimpleTable(part1data, part1header, part1stubs, title=part1title, txt_fmt=self.part1_fmt) return str(part1) def _stats_table(self): # TODO: do we want individual statistics or should users just # use results if wanted? # Handle overall fit statistics model = self.model part2Lstubs = ('No. of Equations:', 'Nobs:', 'Log likelihood:', 'AIC:') part2Rstubs = ('BIC:', 'HQIC:', 'FPE:', 'Det(Omega_mle):') part2Ldata = [[model.neqs], [model.nobs], [model.llf], [model.aic]] part2Rdata = [[model.bic], [model.hqic], [model.fpe], [model.detomega]] part2Lheader = None part2L = SimpleTable(part2Ldata, part2Lheader, part2Lstubs, txt_fmt = self.part2_fmt) part2R = SimpleTable(part2Rdata, part2Lheader, part2Rstubs, txt_fmt = self.part2_fmt) part2L.extend_right(part2R) return str(part2L) def _coef_table(self): model = self.model k = model.neqs Xnames = self.model.exog_names data = lzip(model.params.T.ravel(), model.stderr.T.ravel(), model.tvalues.T.ravel(), model.pvalues.T.ravel()) header = ('coefficient','std. error','t-stat','prob') buf = StringIO() dim = k * model.k_ar + model.k_trend + model.k_exog_user for i in range(k): section = "Results for equation %s" % model.names[i] buf.write(section + '\n') table = SimpleTable(data[dim * i : dim * (i + 1)], header, Xnames, title=None, txt_fmt = self.default_fmt) buf.write(str(table) + '\n') if i < k - 1: buf.write('\n') return buf.getvalue() def _resid_info(self): buf = StringIO() names = self.model.names buf.write("Correlation matrix of residuals" + '\n') buf.write(pprint_matrix(self.model.resid_corr, names, names) + '\n') return buf.getvalue() def normality_summary(results): title = "Normality skew/kurtosis Chi^2-test" null_hyp = 'H_0: data generated by normally-distributed process' return hypothesis_test_table(results, title, null_hyp) def hypothesis_test_table(results, title, null_hyp): fmt = dict(_default_table_fmt, data_fmts=["%#15.6F","%#15.6F","%#15.3F", "%s"]) buf = StringIO() table = SimpleTable([[results['statistic'], results['crit_value'], results['pvalue'], str(results['df'])]], ['Test statistic', 'Critical Value', 'p-value', 'df'], [''], title=None, txt_fmt=fmt) buf.write(title + '\n') buf.write(str(table) + '\n') buf.write(null_hyp + '\n') buf.write("Conclusion: %s H_0" % results['conclusion']) buf.write(" at %.2f%% significance level" % (results['signif'] * 100)) return buf.getvalue() def pprint_matrix(values, rlabels, clabels, col_space=None): buf = StringIO() T, K = len(rlabels), len(clabels) if col_space is None: min_space = 10 col_space = [max(len(str(c)) + 2, min_space) for c in clabels] else: col_space = (col_space,) * K row_space = max([len(str(x)) for x in rlabels]) + 2 head = _pfixed('', row_space) for j, h in enumerate(clabels): head += _pfixed(h, col_space[j]) buf.write(head + '\n') for i, rlab in enumerate(rlabels): line = ('%s' % rlab).ljust(row_space) for j in range(K): line += _pfixed(values[i,j], col_space[j]) buf.write(line + '\n') return buf.getvalue() def _pfixed(s, space, nanRep=None, float_format=None): if isinstance(s, float): if float_format: formatted = float_format(s) else: formatted = "%#8.6F" % s return formatted.rjust(space) else: return ('%s' % s)[:space].rjust(space) statsmodels-0.12.2/statsmodels/tsa/vector_ar/plotting.py000066400000000000000000000165061400612667500235040ustar00rootroot00000000000000from statsmodels.compat.python import lrange import numpy as np import statsmodels.tsa.vector_ar.util as util class MPLConfigurator(object): def __init__(self): self._inverse_actions = [] def revert(self): for action in self._inverse_actions: action() def set_fontsize(self, size): import matplotlib as mpl old_size = mpl.rcParams['font.size'] mpl.rcParams['font.size'] = size def revert(): mpl.rcParams['font.size'] = old_size self._inverse_actions.append(revert) #------------------------------------------------------------------------------- # Plotting functions def plot_mts(Y, names=None, index=None): """ Plot multiple time series """ import matplotlib.pyplot as plt k = Y.shape[1] rows, cols = k, 1 fig = plt.figure(figsize=(10, 10)) for j in range(k): ts = Y[:, j] ax = fig.add_subplot(rows, cols, j+1) if index is not None: ax.plot(index, ts) else: ax.plot(ts) if names is not None: ax.set_title(names[j]) return fig def plot_var_forc(prior, forc, err_upper, err_lower, index=None, names=None, plot_stderr=True, legend_options=None): import matplotlib.pyplot as plt n, k = prior.shape rows, cols = k, 1 fig = plt.figure(figsize=(10, 10)) prange = np.arange(n) rng_f = np.arange(n - 1, n + len(forc)) rng_err = np.arange(n, n + len(forc)) for j in range(k): ax = plt.subplot(rows, cols, j+1) p1 = ax.plot(prange, prior[:, j], 'k', label='Observed') p2 = ax.plot(rng_f, np.r_[prior[-1:, j], forc[:, j]], 'k--', label='Forecast') if plot_stderr: p3 = ax.plot(rng_err, err_upper[:, j], 'k-.', label='Forc 2 STD err') ax.plot(rng_err, err_lower[:, j], 'k-.') if names is not None: ax.set_title(names[j]) if legend_options is None: legend_options = {"loc": "upper right"} ax.legend(**legend_options) return fig def plot_with_error(y, error, x=None, axes=None, value_fmt='k', error_fmt='k--', alpha=0.05, stderr_type = 'asym'): """ Make plot with optional error bars Parameters ---------- y : error : array or None """ import matplotlib.pyplot as plt if axes is None: axes = plt.gca() x = x if x is not None else lrange(len(y)) plot_action = lambda y, fmt: axes.plot(x, y, fmt) plot_action(y, value_fmt) #changed this if error is not None: if stderr_type == 'asym': q = util.norm_signif_level(alpha) plot_action(y - q * error, error_fmt) plot_action(y + q * error, error_fmt) if stderr_type in ('mc','sz1','sz2','sz3'): plot_action(error[0], error_fmt) plot_action(error[1], error_fmt) def plot_full_acorr(acorr, fontsize=8, linewidth=8, xlabel=None, err_bound=None): """ Parameters ---------- """ import matplotlib.pyplot as plt config = MPLConfigurator() config.set_fontsize(fontsize) k = acorr.shape[1] fig, axes = plt.subplots(k, k, figsize=(10, 10), squeeze=False) for i in range(k): for j in range(k): ax = axes[i][j] acorr_plot(acorr[:, i, j], linewidth=linewidth, xlabel=xlabel, ax=ax) if err_bound is not None: ax.axhline(err_bound, color='k', linestyle='--') ax.axhline(-err_bound, color='k', linestyle='--') adjust_subplots() config.revert() return fig def acorr_plot(acorr, linewidth=8, xlabel=None, ax=None): import matplotlib.pyplot as plt if ax is None: ax = plt.gca() if xlabel is None: xlabel = np.arange(len(acorr)) ax.vlines(xlabel, [0], acorr, lw=linewidth) ax.axhline(0, color='k') ax.set_ylim([-1, 1]) # hack? ax.set_xlim([-1, xlabel[-1] + 1]) def plot_acorr_with_error(): raise NotImplementedError def adjust_subplots(**kwds): import matplotlib.pyplot as plt passed_kwds = dict(bottom=0.05, top=0.925, left=0.05, right=0.95, hspace=0.2) passed_kwds.update(kwds) plt.subplots_adjust(**passed_kwds) #------------------------------------------------------------------------------- # Multiple impulse response (cum_effects, etc.) cplots def irf_grid_plot(values, stderr, impcol, rescol, names, title, signif=0.05, hlines=None, subplot_params=None, plot_params=None, figsize=(10,10), stderr_type='asym'): """ Reusable function to make flexible grid plots of impulse responses and comulative effects values : (T + 1) x k x k stderr : T x k x k hlines : k x k """ import matplotlib.pyplot as plt if subplot_params is None: subplot_params = {} if plot_params is None: plot_params = {} nrows, ncols, to_plot = _get_irf_plot_config(names, impcol, rescol) fig, axes = plt.subplots(nrows=nrows, ncols=ncols, sharex=True, squeeze=False, figsize=figsize) # fill out space adjust_subplots() fig.suptitle(title, fontsize=14) subtitle_temp = r'%s$\rightarrow$%s' k = len(names) rng = lrange(len(values)) for (j, i, ai, aj) in to_plot: ax = axes[ai][aj] # HACK? if stderr is not None: if stderr_type == 'asym': sig = np.sqrt(stderr[:, j * k + i, j * k + i]) plot_with_error(values[:, i, j], sig, x=rng, axes=ax, alpha=signif, value_fmt='b', stderr_type=stderr_type) if stderr_type in ('mc','sz1','sz2','sz3'): errs = stderr[0][:, i, j], stderr[1][:, i, j] plot_with_error(values[:, i, j], errs, x=rng, axes=ax, alpha=signif, value_fmt='b', stderr_type=stderr_type) else: plot_with_error(values[:, i, j], None, x=rng, axes=ax, value_fmt='b') ax.axhline(0, color='k') if hlines is not None: ax.axhline(hlines[i,j], color='k') sz = subplot_params.get('fontsize', 12) ax.set_title(subtitle_temp % (names[j], names[i]), fontsize=sz) return fig def _get_irf_plot_config(names, impcol, rescol): nrows = ncols = k = len(names) if impcol is not None and rescol is not None: # plot one impulse-response pair nrows = ncols = 1 j = util.get_index(names, impcol) i = util.get_index(names, rescol) to_plot = [(j, i, 0, 0)] elif impcol is not None: # plot impacts of impulse in one variable ncols = 1 j = util.get_index(names, impcol) to_plot = [(j, i, i, 0) for i in range(k)] elif rescol is not None: # plot only things having impact on particular variable ncols = 1 i = util.get_index(names, rescol) to_plot = [(j, i, j, 0) for j in range(k)] else: # plot everything to_plot = [(j, i, i, j) for i in range(k) for j in range(k)] return nrows, ncols, to_plot #------------------------------------------------------------------------------- # Forecast error variance decomposition statsmodels-0.12.2/statsmodels/tsa/vector_ar/svar_model.py000066400000000000000000000544471400612667500240050ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Vector Autoregression (VAR) processes References ---------- Lütkepohl (2005) New Introduction to Multiple Time Series Analysis """ from statsmodels.compat.pandas import deprecate_kwarg import numpy as np import numpy.linalg as npl from numpy.linalg import slogdet from statsmodels.tools.decorators import deprecated_alias from statsmodels.tools.numdiff import approx_fprime, approx_hess import statsmodels.tsa.base.tsa_model as tsbase from statsmodels.tsa.vector_ar.irf import IRAnalysis import statsmodels.tsa.vector_ar.util as util from statsmodels.tsa.vector_ar.var_model import VARProcess, VARResults def svar_ckerr(svar_type, A, B): if A is None and (svar_type == 'A' or svar_type == 'AB'): raise ValueError('SVAR of type A or AB but A array not given.') if B is None and (svar_type == 'B' or svar_type == 'AB'): raise ValueError('SVAR of type B or AB but B array not given.') class SVAR(tsbase.TimeSeriesModel): r""" Fit VAR and then estimate structural components of A and B, defined: .. math:: Ay_t = A_1 y_{t-1} + \ldots + A_p y_{t-p} + B\var(\epsilon_t) Parameters ---------- endog : array_like 1-d endogenous response variable. The independent variable. dates : array_like must match number of rows of endog svar_type : str "A" - estimate structural parameters of A matrix, B assumed = I "B" - estimate structural parameters of B matrix, A assumed = I "AB" - estimate structural parameters indicated in both A and B matrix A : array_like neqs x neqs with unknown parameters marked with 'E' for estimate B : array_like neqs x neqs with unknown parameters marked with 'E' for estimate References ---------- Hamilton (1994) Time Series Analysis """ y = deprecated_alias("y", "endog", remove_version="0.11.0") def __init__(self, endog, svar_type, dates=None, freq=None, A=None, B=None, missing='none'): super(SVAR, self).__init__(endog, None, dates, freq, missing=missing) #(self.endog, self.names, # self.dates) = data_util.interpret_data(endog, names, dates) self.neqs = self.endog.shape[1] types = ['A', 'B', 'AB'] if svar_type not in types: raise ValueError('SVAR type not recognized, must be in ' + str(types)) self.svar_type = svar_type svar_ckerr(svar_type, A, B) self.A_original = A self.B_original = B # initialize A, B as I if not given # Initialize SVAR masks if A is None: A = np.identity(self.neqs) self.A_mask = A_mask = np.zeros(A.shape, dtype=bool) else: A_mask = np.logical_or(A == 'E', A == 'e') self.A_mask = A_mask if B is None: B = np.identity(self.neqs) self.B_mask = B_mask = np.zeros(B.shape, dtype=bool) else: B_mask = np.logical_or(B == 'E', B == 'e') self.B_mask = B_mask # convert A and B to numeric #TODO: change this when masked support is better or with formula #integration Anum = np.zeros(A.shape, dtype=float) Anum[~A_mask] = A[~A_mask] Anum[A_mask] = np.nan self.A = Anum Bnum = np.zeros(B.shape, dtype=float) Bnum[~B_mask] = B[~B_mask] Bnum[B_mask] = np.nan self.B = Bnum #LikelihoodModel.__init__(self, endog) #super(SVAR, self).__init__(endog) def fit(self, A_guess=None, B_guess=None, maxlags=None, method='ols', ic=None, trend='c', verbose=False, s_method='mle', solver="bfgs", override=False, maxiter=500, maxfun=500): """ Fit the SVAR model and solve for structural parameters Parameters ---------- A_guess : array_like, optional A vector of starting values for all parameters to be estimated in A. B_guess : array_like, optional A vector of starting values for all parameters to be estimated in B. maxlags : int Maximum number of lags to check for order selection, defaults to 12 * (nobs/100.)**(1./4), see select_order function method : {'ols'} Estimation method to use ic : {'aic', 'fpe', 'hqic', 'bic', None} Information criterion to use for VAR order selection. aic : Akaike fpe : Final prediction error hqic : Hannan-Quinn bic : Bayesian a.k.a. Schwarz verbose : bool, default False Print order selection output to the screen trend, str {"c", "ct", "ctt", "nc"} "c" - add constant "ct" - constant and trend "ctt" - constant, linear and quadratic trend "nc" - co constant, no trend Note that these are prepended to the columns of the dataset. s_method : {'mle'} Estimation method for structural parameters solver : {'nm', 'newton', 'bfgs', 'cg', 'ncg', 'powell'} Solution method See statsmodels.base for details override : bool, default False If True, returns estimates of A and B without checking order or rank condition maxiter : int, default 500 Number of iterations to perform in solution method maxfun : int Number of function evaluations to perform Notes ----- Lütkepohl pp. 146-153 Hamilton pp. 324-336 Returns ------- est : SVARResults """ lags = maxlags if ic is not None: selections = self.select_order(maxlags=maxlags, verbose=verbose) if ic not in selections: raise ValueError("%s not recognized, must be among %s" % (ic, sorted(selections))) lags = selections[ic] if verbose: print('Using %d based on %s criterion' % (lags, ic)) else: if lags is None: lags = 1 self.nobs = len(self.endog) - lags # initialize starting parameters start_params = self._get_init_params(A_guess, B_guess) return self._estimate_svar(start_params, lags, trend=trend, solver=solver, override=override, maxiter=maxiter, maxfun=maxfun) def _get_init_params(self, A_guess, B_guess): """ Returns either the given starting or .1 if none are given. """ var_type = self.svar_type.lower() n_masked_a = self.A_mask.sum() if var_type in ['ab', 'a']: if A_guess is None: A_guess = np.array([.1]*n_masked_a) else: if len(A_guess) != n_masked_a: msg = 'len(A_guess) = %s, there are %s parameters in A' raise ValueError(msg % (len(A_guess), n_masked_a)) else: A_guess = [] n_masked_b = self.B_mask.sum() if var_type in ['ab', 'b']: if B_guess is None: B_guess = np.array([.1]*n_masked_b) else: if len(B_guess) != n_masked_b: msg = 'len(B_guess) = %s, there are %s parameters in B' raise ValueError(msg % (len(B_guess), n_masked_b)) else: B_guess = [] return np.r_[A_guess, B_guess] def _estimate_svar(self, start_params, lags, maxiter, maxfun, trend='c', solver="nm", override=False): """ lags : int trend : {str, None} As per above """ k_trend = util.get_trendorder(trend) y = self.endog z = util.get_var_endog(y, lags, trend=trend, has_constant='raise') y_sample = y[lags:] # Lutkepohl p75, about 5x faster than stated formula var_params = np.linalg.lstsq(z, y_sample, rcond=-1)[0] resid = y_sample - np.dot(z, var_params) # Unbiased estimate of covariance matrix $\Sigma_u$ of the white noise # process $u$ # equivalent definition # .. math:: \frac{1}{T - Kp - 1} Y^\prime (I_T - Z (Z^\prime Z)^{-1} # Z^\prime) Y # Ref: Lutkepohl p.75 # df_resid right now is T - Kp - 1, which is a suggested correction avobs = len(y_sample) df_resid = avobs - (self.neqs * lags + k_trend) sse = np.dot(resid.T, resid) #TODO: should give users the option to use a dof correction or not omega = sse / df_resid self.sigma_u = omega A, B = self._solve_AB(start_params, override=override, solver=solver, maxiter=maxiter, maxfun=maxfun) A_mask = self.A_mask B_mask = self.B_mask return SVARResults(y, z, var_params, omega, lags, names=self.endog_names, trend=trend, dates=self.data.dates, model=self, A=A, B=B, A_mask=A_mask, B_mask=B_mask) def loglike(self, params): """ Loglikelihood for SVAR model Notes ----- This method assumes that the autoregressive parameters are first estimated, then likelihood with structural parameters is estimated """ #TODO: this does not look robust if A or B is None A = self.A B = self.B A_mask = self.A_mask B_mask = self.B_mask A_len = len(A[A_mask]) B_len = len(B[B_mask]) if A is not None: A[A_mask] = params[:A_len] if B is not None: B[B_mask] = params[A_len:A_len+B_len] nobs = self.nobs neqs = self.neqs sigma_u = self.sigma_u W = np.dot(npl.inv(B),A) trc_in = np.dot(np.dot(W.T,W),sigma_u) sign, b_logdet = slogdet(B**2) #numpy 1.4 compat b_slogdet = sign * b_logdet likl = -nobs/2. * (neqs * np.log(2 * np.pi) - np.log(npl.det(A)**2) + b_slogdet + np.trace(trc_in)) return likl def score(self, AB_mask): """ Return the gradient of the loglike at AB_mask. Parameters ---------- AB_mask : unknown values of A and B matrix concatenated Notes ----- Return numerical gradient """ loglike = self.loglike return approx_fprime(AB_mask, loglike, epsilon=1e-8) def hessian(self, AB_mask): """ Returns numerical hessian. """ loglike = self.loglike return approx_hess(AB_mask, loglike) def _solve_AB(self, start_params, maxiter, maxfun, override=False, solver='bfgs'): """ Solves for MLE estimate of structural parameters Parameters ---------- override : bool, default False If True, returns estimates of A and B without checking order or rank condition solver : str or None, optional Solver to be used. The default is 'nm' (Nelder-Mead). Other choices are 'bfgs', 'newton' (Newton-Raphson), 'cg' conjugate, 'ncg' (non-conjugate gradient), and 'powell'. maxiter : int, optional The maximum number of iterations. Default is 500. maxfun : int, optional The maximum number of function evalutions. Returns ------- A_solve, B_solve: ML solutions for A, B matrices """ #TODO: this could stand a refactor A_mask = self.A_mask B_mask = self.B_mask A = self.A B = self.B A_len = len(A[A_mask]) A[A_mask] = start_params[:A_len] B[B_mask] = start_params[A_len:] if not override: J = self._compute_J(A, B) self.check_order(J) self.check_rank(J) else: #TODO: change to a warning? print("Order/rank conditions have not been checked") retvals = super(SVAR, self).fit(start_params=start_params, method=solver, maxiter=maxiter, maxfun=maxfun, ftol=1e-20, disp=0).params A[A_mask] = retvals[:A_len] B[B_mask] = retvals[A_len:] return A, B def _compute_J(self, A_solve, B_solve): #first compute appropriate duplication matrix # taken from Magnus and Neudecker (1980), #"The Elimination Matrix: Some Lemmas and Applications # the creation of the D_n matrix follows MN (1980) directly, #while the rest follows Hamilton (1994) neqs = self.neqs sigma_u = self.sigma_u A_mask = self.A_mask B_mask = self.B_mask #first generate duplication matrix, see MN (1980) for notation D_nT = np.zeros([int((1.0 / 2) * (neqs) * (neqs + 1)), neqs**2]) for j in range(neqs): i=j while j <= i < neqs: u=np.zeros([int((1.0/2)*neqs*(neqs+1)), 1]) u[int(j * neqs + (i + 1) - (1.0 / 2) * (j + 1) * j - 1)] = 1 Tij=np.zeros([neqs,neqs]) Tij[i,j]=1 Tij[j,i]=1 D_nT=D_nT+np.dot(u,(Tij.ravel('F')[:,None]).T) i=i+1 D_n=D_nT.T D_pl=npl.pinv(D_n) #generate S_B S_B = np.zeros((neqs**2, len(A_solve[A_mask]))) S_D = np.zeros((neqs**2, len(B_solve[B_mask]))) j = 0 j_d = 0 if len(A_solve[A_mask]) != 0: A_vec = np.ravel(A_mask, order='F') for k in range(neqs**2): if A_vec[k]: S_B[k,j] = -1 j += 1 if len(B_solve[B_mask]) != 0: B_vec = np.ravel(B_mask, order='F') for k in range(neqs**2): if B_vec[k]: S_D[k,j_d] = 1 j_d +=1 #now compute J invA = npl.inv(A_solve) J_p1i = np.dot(np.dot(D_pl, np.kron(sigma_u, invA)), S_B) J_p1 = -2.0 * J_p1i J_p2 = np.dot(np.dot(D_pl, np.kron(invA, invA)), S_D) J = np.append(J_p1, J_p2, axis=1) return J def check_order(self, J): if np.size(J, axis=0) < np.size(J, axis=1): raise ValueError("Order condition not met: " "solution may not be unique") def check_rank(self, J): rank = np.linalg.matrix_rank(J) if rank < np.size(J, axis=1): raise ValueError("Rank condition not met: " "solution may not be unique.") class SVARProcess(VARProcess): """ Class represents a known SVAR(p) process Parameters ---------- coefs : ndarray (p x k x k) intercept : ndarray (length k) sigma_u : ndarray (k x k) names : sequence (length k) A : neqs x neqs np.ndarray with unknown parameters marked with 'E' A_mask : neqs x neqs mask array with known parameters masked B : neqs x neqs np.ndarry with unknown parameters marked with 'E' B_mask : neqs x neqs mask array with known parameters masked """ def __init__(self, coefs, intercept, sigma_u, A_solve, B_solve, names=None): self.k_ar = len(coefs) self.neqs = coefs.shape[1] self.coefs = coefs self.intercept = intercept self.sigma_u = sigma_u self.A_solve = A_solve self.B_solve = B_solve self.names = names def orth_ma_rep(self, maxn=10, P=None): """ Unavailable for SVAR """ raise NotImplementedError def svar_ma_rep(self, maxn=10, P=None): """ Compute Structural MA coefficient matrices using MLE of A, B """ if P is None: A_solve = self.A_solve B_solve = self.B_solve P = np.dot(npl.inv(A_solve), B_solve) ma_mats = self.ma_rep(maxn=maxn) return np.array([np.dot(coefs, P) for coefs in ma_mats]) class SVARResults(SVARProcess, VARResults): """ Estimate VAR(p) process with fixed number of lags Parameters ---------- endog : ndarray endog_lagged : ndarray params : ndarray sigma_u : ndarray lag_order : int model : VAR model instance trend : str {'nc', 'c', 'ct'} names : array_like List of names of the endogenous variables in order of appearance in `endog`. dates Attributes ---------- aic bic bse coefs : ndarray (p x K x K) Estimated A_i matrices, A_i = coefs[i-1] cov_params dates detomega df_model : int df_resid : int endog endog_lagged fittedvalues fpe intercept info_criteria k_ar : int k_trend : int llf model names neqs : int Number of variables (equations) nobs : int n_totobs : int params k_ar : int Order of VAR process params : ndarray (Kp + 1) x K A_i matrices and intercept in stacked form [int A_1 ... A_p] pvalue names : list variables names resid sigma_u : ndarray (K x K) Estimate of white noise process variance Var[u_t] sigma_u_mle stderr trenorder tvalues y : ys_lagged """ _model_type = 'SVAR' y = deprecated_alias("y", "endog", remove_version="0.11.0") ys_lagged = deprecated_alias("ys_lagged", "endog_lagged", remove_version="0.11.0") def __init__(self, endog, endog_lagged, params, sigma_u, lag_order, A=None, B=None, A_mask=None, B_mask=None, model=None, trend='c', names=None, dates=None): self.model = model self.endog = endog self.endog_lagged = endog_lagged self.dates = dates self.n_totobs, self.neqs = self.endog.shape self.nobs = self.n_totobs - lag_order k_trend = util.get_trendorder(trend) if k_trend > 0: # make this the polynomial trend order trendorder = k_trend - 1 else: trendorder = None self.k_trend = k_trend self.k_exog = k_trend # now (0.9) required by VARProcess self.trendorder = trendorder self.exog_names = util.make_lag_names(names, lag_order, k_trend) self.params = params self.sigma_u = sigma_u # Each matrix needs to be transposed reshaped = self.params[self.k_trend:] reshaped = reshaped.reshape((lag_order, self.neqs, self.neqs)) # Need to transpose each coefficient matrix intercept = self.params[0] coefs = reshaped.swapaxes(1, 2).copy() #SVAR components #TODO: if you define these here, you do not also have to define #them in SVAR process, but I left them for now -ss self.A = A self.B = B self.A_mask = A_mask self.B_mask = B_mask super(SVARResults, self).__init__(coefs, intercept, sigma_u, A, B, names=names) def irf(self, periods=10, var_order=None): """ Analyze structural impulse responses to shocks in system Parameters ---------- periods : int Returns ------- irf : IRAnalysis """ A = self.A B= self.B P = np.dot(npl.inv(A), B) return IRAnalysis(self, P=P, periods=periods, svar=True) @deprecate_kwarg('T', 'steps') def sirf_errband_mc(self, orth=False, repl=1000, steps=10, signif=0.05, seed=None, burn=100, cum=False): """ Compute Monte Carlo integrated error bands assuming normally distributed for impulse response functions Parameters ---------- orth : bool, default False Compute orthogonalized impulse response error bands repl : int number of Monte Carlo replications to perform steps : int, default 10 number of impulse response periods signif : float (0 < signif <1) Significance level for error bars, defaults to 95% CI seed : int np.random.seed for replications burn : int number of initial observations to discard for simulation cum : bool, default False produce cumulative irf error bands Notes ----- Lütkepohl (2005) Appendix D Returns ------- Tuple of lower and upper arrays of ma_rep monte carlo standard errors """ neqs = self.neqs mean = self.mean() k_ar = self.k_ar coefs = self.coefs sigma_u = self.sigma_u intercept = self.intercept df_model = self.df_model nobs = self.nobs ma_coll = np.zeros((repl, steps + 1, neqs, neqs)) A = self.A B = self.B A_mask = self.A_mask B_mask = self.B_mask A_pass = self.model.A_original B_pass = self.model.B_original s_type = self.model.svar_type g_list = [] def agg(impulses): if cum: return impulses.cumsum(axis=0) return impulses opt_A = A[A_mask] opt_B = B[B_mask] for i in range(repl): # discard first hundred to correct for starting bias sim = util.varsim(coefs, intercept, sigma_u, seed=seed, steps=nobs + burn) sim = sim[burn:] smod = SVAR(sim, svar_type=s_type, A=A_pass, B=B_pass) if i == 10: # Use first 10 to update starting val for remainder of fits mean_AB = np.mean(g_list, axis=0) split = len(A[A_mask]) opt_A = mean_AB[:split] opt_B = mean_AB[split:] sres = smod.fit(maxlags=k_ar, A_guess=opt_A, B_guess=opt_B) if i < 10: # save estimates for starting val if in first 10 g_list.append(np.append(sres.A[A_mask].tolist(), sres.B[B_mask].tolist())) ma_coll[i] = agg(sres.svar_ma_rep(maxn=steps)) ma_sort = np.sort(ma_coll, axis=0) # sort to get quantiles index = (int(round(signif / 2 * repl) - 1), int(round((1 - signif / 2) * repl) - 1)) lower = ma_sort[index[0], :, :, :] upper = ma_sort[index[1], :, :, :] return lower, upper statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/000077500000000000000000000000001400612667500224245ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/000077500000000000000000000000001400612667500253515ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/__init__.py000066400000000000000000000000001400612667500274500ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_c.txt000077500000000000000000000066541400612667500317510ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:23:21 *** VAR ESTIMATION RESULTS endogenous variables: realcons realgdp realinv exogenous variables: deterministic variables: CONST endogenous lags: 4 exogenous lags: 0 sample range: [1960 Q1, 2009 Q3], T = 199 modulus of the eigenvalues of the reverse characteristic polynomial : |z| = ( 1.5287 1.5287 2.1209 2.1209 4.1522 4.1522 1.5245 1.5245 1.0538 1.0538 1.3179 0.9958 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= realcons realgdp realinv ------------------------------------------- realcons(t-1)| 1.399 1.268 0.936 | (0.112) (0.192) (0.138) | {0.000} {0.000} {0.000} | [12.442] [6.610] [6.765] realgdp (t-1)| -0.238 0.566 -0.153 | (0.089) (0.152) (0.109) | {0.007} {0.000} {0.160} | [-2.680] [3.735] [-1.404] realinv (t-1)| 0.285 0.324 1.159 | (0.104) (0.177) (0.128) | {0.006} {0.068} {0.000} | [2.740] [1.827] [9.061] realcons(t-2)| -0.070 -0.617 -0.613 | (0.189) (0.322) (0.232) | {0.711} {0.055} {0.008} | [-0.371] [-1.915] [-2.642] realgdp (t-2)| 0.016 0.343 0.180 | (0.127) (0.216) (0.156) | {0.901} {0.112} {0.249} | [0.125] [1.587] [1.153] realinv (t-2)| -0.107 -0.424 -0.312 | (0.163) (0.278) (0.200) | {0.510} {0.127} {0.120} | [-0.659] [-1.525] [-1.555] realcons(t-3)| 0.100 -0.116 -0.145 | (0.193) (0.329) (0.237) | {0.605} {0.725} {0.539} | [0.518] [-0.352] [-0.614] realgdp (t-3)| 0.012 -0.164 -0.208 | (0.126) (0.215) (0.155) | {0.922} {0.445} {0.179} | [0.099] [-0.764] [-1.343] realinv (t-3)| -0.072 0.109 0.243 | (0.160) (0.273) (0.197) | {0.653} {0.691} {0.218} | [-0.450] [0.398] [1.231] realcons(t-4)| -0.446 -0.444 -0.117 | (0.129) (0.219) (0.158) | {0.001} {0.043} {0.460} | [-3.470] [-2.025] [-0.739] realgdp (t-4)| 0.225 0.206 0.153 | (0.092) (0.157) (0.113) | {0.014} {0.189} {0.176} | [2.451] [1.314] [1.353] realinv (t-4)| -0.113 -0.119 -0.196 | (0.110) (0.187) (0.135) | {0.303} {0.525} {0.146} | [-1.029] [-0.636] [-1.453] ------------------------------------------- Deterministic term: =================== realcons realgdp realinv --------------------------------------- CONST | 3.263 17.568 -7.535 | (10.803) (18.426) (13.283) | {0.763} {0.340} {0.571} | [0.302] [0.953] [-0.567] --------------------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_c_Sigmau.txt000077500000000000000000000012051400612667500332410ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:23:21 *** VAR MODEL STATISTICS sample range: [1960 Q1, 2009 Q3], T = 199 Log Likelihood: -2.781153e+03 Determinant (Cov): 3.184027e+08 Covariance: 7.223846e+02 6.705143e+02 -3.969719e-01 6.705143e+02 2.101811e+03 1.037008e+03 -3.969719e-01 1.037008e+03 1.092267e+03 Correlation: 1.000000e+00 5.441604e-01 -4.469009e-04 5.441604e-01 1.000000e+00 6.844175e-01 -4.469009e-04 6.844175e-01 1.000000e+00 AIC: 1.997079e+01 FPE: 4.714607e+08 SC: 2.061621e+01 HQ: 2.023201e+01 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_c_diag.txt000077500000000000000000000043051400612667500327240ustar00rootroot00000000000000*** Fri, 7 Oct 2016 13:04:15 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 150. tested order: 16 test statistic: 110.1008 p-value: 0.4257 adjusted test statistic: 115.6053 p-value: 0.2908 degrees of freedom: 108.0000 *** Fri, 7 Oct 2016 13:04:15 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags Reference: Doornik (1996), LM test and LMF test (with F-approximation) LM statistic: 49.5891 p-value: 0.2953 df: 45.0000 LMF statistic: 1.0343 p-value: 0.4149 df1: 45.0000 df2: 502.0000 *** Fri, 7 Oct 2016 13:04:15 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 84.2158 p-value: 0.0000 degrees of freedom: 6.0000 skewness only: 10.2312 p-value: 0.0167 kurtosis only: 73.9847 p-value: 0.0000 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 41.7946 p-value: 0.0000 degrees of freedom: 6.0000 skewness only: 3.0251 p-value: 0.3878 kurtosis only: 38.7696 p-value: 0.0000 *** Fri, 7 Oct 2016 13:04:15 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 19.4703 0.0001 -0.2678 4.4358 u2 5.6573 0.0591 0.2730 3.6199 u3 52.1664 0.0000 -0.3199 5.4253 *** Fri, 7 Oct 2016 13:04:15 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 9.6251 0.8855 0.6350 0.8521 u2 24.1933 0.0854 1.7424 0.0434 u3 19.1173 0.2626 1.3342 0.1819 *** Fri, 7 Oct 2016 13:04:15 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 277.2551 p-value(chi^2): 0.0000 degrees of freedom: 180.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_c_fc5.txt000077500000000000000000000027231400612667500324770ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:43:26 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals realcons time forecast lower CI upper CI +/- 2009 Q4 9306.8633 9254.1849 9359.5416 52.6784 2010 Q1 9337.0637 9254.9076 9419.2198 82.1561 2010 Q2 9382.3601 9270.0264 9494.6937 112.3336 2010 Q3 9417.3212 9269.3713 9565.2711 147.9499 2010 Q4 9451.9627 9272.1622 9631.7632 179.8005 realgdp time forecast lower CI upper CI +/- 2009 Q4 13125.8383 13035.9827 13215.6938 89.8556 2010 Q1 13239.5173 13095.5534 13383.4812 143.9639 2010 Q2 13351.9136 13150.7526 13553.0747 201.1610 2010 Q3 13448.5115 13193.1668 13703.8561 255.3446 2010 Q4 13534.5814 13227.7124 13841.4505 306.8690 realinv time forecast lower CI upper CI +/- 2009 Q4 1535.2526 1470.4769 1600.0284 64.7757 2010 Q1 1591.4234 1489.9846 1692.8621 101.4387 2010 Q2 1642.9390 1505.1358 1780.7421 137.8032 2010 Q3 1688.4049 1517.0684 1859.7415 171.3366 2010 Q4 1726.1592 1520.8135 1931.5049 205.3457 macrodata_jmulti_c_granger_causality_realcons.txt000077500000000000000000000005211400612667500373260ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:23:44 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons" do not Granger-cause "realgdp, realinv" Test statistic l = 11.1446 pval-F( l; 8, 558) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons" and "realgdp, realinv" Test statistic: c = 71.2453 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_c_granger_causality_realcons_realgdp.txt000077500000000000000000000005211400612667500410240ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:24:00 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons, realgdp" do not Granger-cause "realinv" Test statistic l = 16.6303 pval-F( l; 8, 558) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons, realgdp" and "realinv" Test statistic: c = 79.5492 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_c_granger_causality_realcons_realinv.txt000077500000000000000000000005211400612667500410460ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:24:15 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons, realinv" do not Granger-cause "realgdp" Test statistic l = 10.6974 pval-F( l; 8, 558) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons, realinv" and "realgdp" Test statistic: c = 86.2439 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_c_granger_causality_realgdp.txt000077500000000000000000000005201400612667500371350ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:24:41 *** TEST FOR GRANGER-CAUSALITY: H0: "realgdp" do not Granger-cause "realcons, realinv" Test statistic l = 3.7090 pval-F( l; 8, 558) = 0.0003 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realgdp" and "realcons, realinv" Test statistic: c = 86.2439 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_c_granger_causality_realgdp_realinv.txt000077500000000000000000000005201400612667500406550ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:24:28 *** TEST FOR GRANGER-CAUSALITY: H0: "realgdp, realinv" do not Granger-cause "realcons" Test statistic l = 3.4756 pval-F( l; 8, 558) = 0.0006 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realgdp, realinv" and "realcons" Test statistic: c = 71.2453 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_c_granger_causality_realinv.txt000077500000000000000000000005201400612667500371570ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:24:52 *** TEST FOR GRANGER-CAUSALITY: H0: "realinv" do not Granger-cause "realcons, realgdp" Test statistic l = 3.6508 pval-F( l; 8, 558) = 0.0004 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realinv" and "realcons, realgdp" Test statistic: c = 79.5492 pval-Chi( c; 2) = 0.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_c_ir.txt000077500000000000000000000112031400612667500324250ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:25:11 *** VAR Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time realcons realgdp realinv realcons realgdp realinv realcons realgdp realinv ->realcons ->realcons ->realcons ->realgdp ->realgdp ->realgdp ->realinv ->realinv ->realinv point estimate 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 1 point estimate 1.3995 -0.2382 0.2850 1.2682 0.5662 0.3242 0.9357 -0.1534 1.1587 2 point estimate 1.8530 -0.4960 0.5444 2.1793 0.3123 0.4967 1.5857 -0.3076 1.2481 3 point estimate 2.4475 -0.8017 0.7879 3.1582 -0.3098 0.9294 2.1697 -0.7807 1.6445 4 point estimate 2.6677 -0.9784 1.0217 3.8166 -0.7777 1.2851 2.7240 -1.1184 1.8430 5 point estimate 2.8997 -1.1401 1.2175 4.2116 -1.1114 1.5505 2.9670 -1.3359 1.9754 6 point estimate 3.0939 -1.2365 1.3481 4.4067 -1.3180 1.7394 3.0262 -1.4779 2.0793 7 point estimate 3.1796 -1.2828 1.4493 4.4671 -1.4016 1.8301 3.0309 -1.5197 2.0796 8 point estimate 3.2676 -1.3138 1.5188 4.4403 -1.4003 1.8442 2.9141 -1.4769 2.0188 9 point estimate 3.3340 -1.3194 1.5552 4.3663 -1.3489 1.8064 2.7534 -1.3972 1.9241 10 point estimate 3.3643 -1.3092 1.5737 4.2700 -1.2680 1.7302 2.5898 -1.2905 1.7928 11 point estimate 3.3861 -1.2909 1.5742 4.1580 -1.1711 1.6295 2.4022 -1.1665 1.6442 12 point estimate 3.3890 -1.2603 1.5571 4.0354 -1.0667 1.5139 2.2127 -1.0405 1.4894 13 point estimate 3.3706 -1.2200 1.5273 3.9047 -0.9577 1.3882 2.0279 -0.9139 1.3294 14 point estimate 3.3391 -1.1719 1.4849 3.7655 -0.8455 1.2558 1.8402 -0.7880 1.1702 15 point estimate 3.2924 -1.1151 1.4307 3.6195 -0.7310 1.1192 1.6563 -0.6661 1.0143 16 point estimate 3.2319 -1.0515 1.3672 3.4687 -0.6151 0.9798 1.4776 -0.5479 0.8622 17 point estimate 3.1613 -0.9821 1.2951 3.3146 -0.4986 0.8392 1.3033 -0.4340 0.7158 18 point estimate 3.0813 -0.9078 1.2157 3.1596 -0.3826 0.6987 1.1361 -0.3256 0.5759 19 point estimate 2.9934 -0.8298 1.1307 3.0054 -0.2683 0.5596 0.9772 -0.2232 0.4430 20 point estimate 2.8997 -0.7492 1.0411 2.8538 -0.1566 0.4231 0.8269 -0.1271 0.3180 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_c_lagorder.txt000077500000000000000000000006741400612667500336240ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:23:07 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: realcons realgdp realinv deterministic variables: CONST sample range: [1961 Q3, 2009 Q3], T = 193 optimal number of lags (searched up to 10 lags of levels): Akaike Info Criterion: 4 Final Prediction Error: 4 Hannan-Quinn Criterion: 2 Schwarz Criterion: 2 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_cs.txt000077500000000000000000000076411400612667500321310ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:25:42 *** VAR ESTIMATION RESULTS endogenous variables: realcons realgdp realinv exogenous variables: deterministic variables: CONST S1 S2 S3 endogenous lags: 4 exogenous lags: 0 sample range: [1960 Q1, 2009 Q3], T = 199 modulus of the eigenvalues of the reverse characteristic polynomial : |z| = ( 1.4992 1.4992 2.0185 2.0185 3.5410 6.3965 1.5057 1.5057 1.0509 1.0509 1.3257 0.9958 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= realcons realgdp realinv ------------------------------------------- realcons(t-1)| 1.436 1.305 0.953 | (0.114) (0.195) (0.141) | {0.000} {0.000} {0.000} | [12.621] [6.693] [6.758] realgdp (t-1)| -0.266 0.543 -0.164 | (0.090) (0.154) (0.111) | {0.003} {0.000} {0.142} | [-2.954] [3.525] [-1.469] realinv (t-1)| 0.308 0.345 1.169 | (0.104) (0.179) (0.129) | {0.003} {0.053} {0.000} | [2.953] [1.932] [9.038] realcons(t-2)| -0.138 -0.686 -0.649 | (0.193) (0.330) (0.239) | {0.474} {0.037} {0.006} | [-0.717] [-2.082] [-2.722] realgdp (t-2)| 0.058 0.400 0.208 | (0.129) (0.221) (0.160) | {0.650} {0.071} {0.193} | [0.453] [1.809] [1.300] realinv (t-2)| -0.154 -0.470 -0.335 | (0.164) (0.282) (0.204) | {0.349} {0.095} {0.100} | [-0.936] [-1.669] [-1.644] realcons(t-3)| 0.160 -0.107 -0.139 | (0.197) (0.337) (0.244) | {0.416} {0.750} {0.569} | [0.814] [-0.318] [-0.570] realgdp (t-3)| -0.011 -0.179 -0.218 | (0.128) (0.219) (0.159) | {0.930} {0.415} {0.170} | [-0.087] [-0.815] [-1.371] realinv (t-3)| -0.041 0.123 0.252 | (0.162) (0.277) (0.200) | {0.799} {0.656} {0.209} | [-0.255] [0.445] [1.256] realcons(t-4)| -0.474 -0.419 -0.105 | (0.130) (0.223) (0.161) | {0.000} {0.060} {0.515} | [-3.649] [-1.884] [-0.651] realgdp (t-4)| 0.233 0.188 0.145 | (0.093) (0.159) (0.115) | {0.012} {0.238} {0.208} | [2.507] [1.179] [1.258] realinv (t-4)| -0.121 -0.108 -0.191 | (0.110) (0.189) (0.136) | {0.271} {0.567} {0.161} | [-1.101] [-0.572] [-1.403] ------------------------------------------- Deterministic term: =================== realcons realgdp realinv --------------------------------------- CONST | 0.514 8.866 -12.124 | (11.320) (19.393) (14.032) | {0.964} {0.648} {0.388} | [0.045] [0.457] [-0.864] S1 (t)| 4.472 7.218 4.147 | (5.541) (9.493) (6.869) | {0.420} {0.447} {0.546} | [0.807] [0.760] [0.604] S2 (t)| -1.636 13.947 7.368 | (5.458) (9.350) (6.766) | {0.764} {0.136} {0.276} | [-0.300] [1.492] [1.089] S3 (t)| 8.790 12.807 6.307 | (5.523) (9.462) (6.846) | {0.112} {0.176} {0.357} | [1.591] [1.354] [0.921] --------------------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_cs_Sigmau.txt000077500000000000000000000012051400612667500334240ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:25:42 *** VAR MODEL STATISTICS sample range: [1960 Q1, 2009 Q3], T = 199 Log Likelihood: -2.774606e+03 Determinant (Cov): 2.980264e+08 Covariance: 7.170910e+02 6.757978e+02 -2.843256e+00 6.757978e+02 2.104500e+03 1.037849e+03 -2.843256e+00 1.037849e+03 1.101882e+03 Correlation: 1.000000e+00 5.501171e-01 -3.198611e-03 5.501171e-01 1.000000e+00 6.815414e-01 -3.198611e-03 6.815414e-01 1.000000e+00 AIC: 1.999510e+01 FPE: 4.833001e+08 SC: 2.078947e+01 HQ: 2.031660e+01 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_cs_diag.txt000077500000000000000000000043051400612667500331070ustar00rootroot00000000000000*** Fri, 7 Oct 2016 13:04:33 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 150. tested order: 16 test statistic: 113.6746 p-value: 0.3355 adjusted test statistic: 119.4159 p-value: 0.2130 degrees of freedom: 108.0000 *** Fri, 7 Oct 2016 13:04:33 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags Reference: Doornik (1996), LM test and LMF test (with F-approximation) LM statistic: 50.4880 p-value: 0.2656 df: 45.0000 LMF statistic: 1.0343 p-value: 0.4149 df1: 45.0000 df2: 493.0000 *** Fri, 7 Oct 2016 13:04:33 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 84.2349 p-value: 0.0000 degrees of freedom: 6.0000 skewness only: 10.1638 p-value: 0.0172 kurtosis only: 74.0711 p-value: 0.0000 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 36.3134 p-value: 0.0000 degrees of freedom: 6.0000 skewness only: 2.2185 p-value: 0.5283 kurtosis only: 34.0949 p-value: 0.0000 *** Fri, 7 Oct 2016 13:04:33 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 13.5542 0.0011 -0.2252 4.1966 u2 5.9071 0.0522 0.3103 3.5722 u3 51.1882 0.0000 -0.3042 5.4090 *** Fri, 7 Oct 2016 13:04:33 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 8.2029 0.9426 0.5367 0.9244 u2 26.2402 0.0507 1.9145 0.0222 u3 19.1961 0.2586 1.3404 0.1784 *** Fri, 7 Oct 2016 13:04:33 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 274.5865 p-value(chi^2): 0.0000 degrees of freedom: 180.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_cs_fc5.txt000077500000000000000000000027231400612667500326620ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:41:18 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals realcons time forecast lower CI upper CI +/- 2009 Q4 9306.9285 9254.4435 9359.4135 52.4850 2010 Q1 9336.1807 9253.9213 9418.4401 82.2594 2010 Q2 9377.4893 9265.4763 9489.5023 112.0130 2010 Q3 9416.8644 9269.3094 9564.4193 147.5549 2010 Q4 9446.9244 9267.4228 9626.4261 179.5017 realgdp time forecast lower CI upper CI +/- 2009 Q4 13118.7690 13028.8560 13208.6820 89.9130 2010 Q1 13232.9915 13088.6807 13377.3023 144.3108 2010 Q2 13350.0139 13147.8661 13552.1617 202.1478 2010 Q3 13446.4530 13190.4794 13702.4266 255.9736 2010 Q4 13527.0975 13219.5730 13834.6220 307.5245 realinv time forecast lower CI upper CI +/- 2009 Q4 1531.5958 1466.5355 1596.6560 65.0602 2010 Q1 1587.9116 1486.0592 1689.7640 101.8524 2010 Q2 1641.5994 1503.0576 1780.1413 138.5419 2010 Q3 1685.8940 1514.0876 1857.7004 171.8064 2010 Q4 1722.4866 1516.8585 1928.1147 205.6281 macrodata_jmulti_cs_granger_causality_realcons.txt000077500000000000000000000005211400612667500375110ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:26:39 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons" do not Granger-cause "realgdp, realinv" Test statistic l = 10.9780 pval-F( l; 8, 549) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons" and "realgdp, realinv" Test statistic: c = 72.2185 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_cs_granger_causality_realcons_realgdp.txt000077500000000000000000000005211400612667500412070ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:28:25 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons, realgdp" do not Granger-cause "realinv" Test statistic l = 16.5166 pval-F( l; 8, 549) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons, realgdp" and "realinv" Test statistic: c = 79.8044 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_cs_granger_causality_realcons_realinv.txt000077500000000000000000000005211400612667500412310ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:28:41 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons, realinv" do not Granger-cause "realgdp" Test statistic l = 10.6470 pval-F( l; 8, 549) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons, realinv" and "realgdp" Test statistic: c = 86.5410 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_cs_granger_causality_realgdp.txt000077500000000000000000000005201400612667500373200ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:29:17 *** TEST FOR GRANGER-CAUSALITY: H0: "realgdp" do not Granger-cause "realcons, realinv" Test statistic l = 3.9150 pval-F( l; 8, 549) = 0.0002 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realgdp" and "realcons, realinv" Test statistic: c = 86.5410 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_cs_granger_causality_realgdp_realinv.txt000077500000000000000000000005201400612667500410400ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:29:07 *** TEST FOR GRANGER-CAUSALITY: H0: "realgdp, realinv" do not Granger-cause "realcons" Test statistic l = 3.6527 pval-F( l; 8, 549) = 0.0004 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realgdp, realinv" and "realcons" Test statistic: c = 72.2185 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_cs_granger_causality_realinv.txt000077500000000000000000000005201400612667500373420ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:29:28 *** TEST FOR GRANGER-CAUSALITY: H0: "realinv" do not Granger-cause "realcons, realgdp" Test statistic l = 3.7582 pval-F( l; 8, 549) = 0.0003 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realinv" and "realcons, realgdp" Test statistic: c = 79.8044 pval-Chi( c; 2) = 0.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_cs_ir.txt000077500000000000000000000112031400612667500326100ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:29:38 *** VAR Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time realcons realgdp realinv realcons realgdp realinv realcons realgdp realinv ->realcons ->realcons ->realcons ->realgdp ->realgdp ->realgdp ->realinv ->realinv ->realinv point estimate 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 1 point estimate 1.4362 -0.2655 0.3080 1.3048 0.5429 0.3453 0.9532 -0.1638 1.1688 2 point estimate 1.8720 -0.5175 0.5569 2.2251 0.2914 0.5228 1.6201 -0.3255 1.2682 3 point estimate 2.4885 -0.8385 0.8084 3.1902 -0.3321 0.9487 2.1939 -0.7989 1.6595 4 point estimate 2.7272 -1.0326 1.0551 3.8899 -0.8266 1.3147 2.7696 -1.1506 1.8618 5 point estimate 2.9583 -1.1993 1.2523 4.3027 -1.1807 1.5901 3.0313 -1.3862 2.0049 6 point estimate 3.1720 -1.3097 1.3934 4.5141 -1.4074 1.7914 3.0963 -1.5393 2.1146 7 point estimate 3.2644 -1.3635 1.5028 4.5944 -1.5093 1.8953 3.1142 -1.5929 2.1230 8 point estimate 3.3558 -1.3982 1.5768 4.5747 -1.5173 1.9202 3.0035 -1.5572 2.0708 9 point estimate 3.4315 -1.4089 1.6192 4.5049 -1.4709 1.8907 2.8413 -1.4782 1.9799 10 point estimate 3.4651 -1.4007 1.6419 4.4121 -1.3910 1.8197 2.6788 -1.3706 1.8511 11 point estimate 3.4906 -1.3836 1.6451 4.3005 -1.2921 1.7221 2.4891 -1.2431 1.7038 12 point estimate 3.4984 -1.3542 1.6307 4.1782 -1.1847 1.6078 2.2959 -1.1120 1.5479 13 point estimate 3.4824 -1.3140 1.6026 4.0479 -1.0721 1.4820 2.1089 -0.9802 1.3861 14 point estimate 3.4531 -1.2655 1.5611 3.9081 -0.9558 1.3487 1.9178 -0.8487 1.2243 15 point estimate 3.4081 -1.2079 1.5073 3.7609 -0.8371 1.2103 1.7296 -0.7210 1.0650 16 point estimate 3.3476 -1.1425 1.4433 3.6079 -0.7164 1.0684 1.5469 -0.5971 0.9092 17 point estimate 3.2763 -1.0708 1.3701 3.4504 -0.5947 0.9244 1.3673 -0.4774 0.7585 18 point estimate 3.1946 -0.9935 1.2889 3.2908 -0.4730 0.7799 1.1943 -0.3630 0.6140 19 point estimate 3.1040 -0.9118 1.2014 3.1310 -0.3524 0.6360 1.0292 -0.2543 0.4760 20 point estimate 3.0069 -0.8270 1.1086 2.9727 -0.2339 0.4939 0.8720 -0.1518 0.3456 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_cs_lagorder.txt000077500000000000000000000007051400612667500340020ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:26:11 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: realcons realgdp realinv deterministic variables: CONST S1 S2 S3 sample range: [1961 Q3, 2009 Q3], T = 193 optimal number of lags (searched up to 10 lags of levels): Akaike Info Criterion: 4 Final Prediction Error: 4 Hannan-Quinn Criterion: 2 Schwarz Criterion: 2 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_cst.txt000077500000000000000000000101131400612667500323010ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:34:05 *** VAR ESTIMATION RESULTS endogenous variables: realcons realgdp realinv exogenous variables: deterministic variables: CONST S1 S2 S3 TREND endogenous lags: 4 exogenous lags: 0 sample range: [1960 Q1, 2009 Q3], T = 199 modulus of the eigenvalues of the reverse characteristic polynomial : |z| = ( 1.5030 1.5030 1.9859 1.9859 8.0600 3.3058 1.5023 1.5023 1.0605 1.0605 1.2661 1.0124 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= realcons realgdp realinv ------------------------------------------- realcons(t-1)| 1.426 1.290 0.956 | (0.114) (0.196) (0.142) | {0.000} {0.000} {0.000} | [12.492] [6.592] [6.737] realgdp (t-1)| -0.268 0.540 -0.163 | (0.090) (0.154) (0.112) | {0.003} {0.000} {0.145} | [-2.982] [3.500] [-1.459] realinv (t-1)| 0.309 0.347 1.168 | (0.104) (0.179) (0.130) | {0.003} {0.052} {0.000} | [2.966] [1.940] [9.012] realcons(t-2)| -0.134 -0.681 -0.650 | (0.192) (0.330) (0.239) | {0.485} {0.039} {0.007} | [-0.698] [-2.065] [-2.718] realgdp (t-2)| 0.054 0.394 0.209 | (0.129) (0.221) (0.160) | {0.675} {0.075} {0.192} | [0.420] [1.779] [1.304] realinv (t-2)| -0.150 -0.465 -0.336 | (0.164) (0.282) (0.204) | {0.362} {0.099} {0.100} | [-0.912] [-1.648] [-1.644] realcons(t-3)| 0.160 -0.107 -0.139 | (0.197) (0.337) (0.245) | {0.415} {0.751} {0.570} | [0.815] [-0.317] [-0.568] realgdp (t-3)| -0.014 -0.183 -0.217 | (0.128) (0.220) (0.159) | {0.913} {0.405} {0.173} | [-0.110] [-0.832] [-1.362] realinv (t-3)| -0.038 0.127 0.251 | (0.162) (0.277) (0.201) | {0.813} {0.645} {0.212} | [-0.236] [0.460] [1.248] realcons(t-4)| -0.449 -0.384 -0.112 | (0.132) (0.226) (0.164) | {0.001} {0.089} {0.495} | [-3.402] [-1.698] [-0.683] realgdp (t-4)| 0.218 0.167 0.149 | (0.094) (0.161) (0.117) | {0.020} {0.301} {0.201} | [2.318] [1.034] [1.278] realinv (t-4)| -0.104 -0.084 -0.196 | (0.111) (0.191) (0.138) | {0.352} {0.661} {0.155} | [-0.931] [-0.438] [-1.421] ------------------------------------------- Deterministic term: =================== realcons realgdp realinv --------------------------------------- CONST | 24.900 42.506 -18.948 | (24.888) (42.686) (30.949) | {0.317} {0.319} {0.540} | [1.000] [0.996] [-0.612] S1 (t)| 4.467 7.211 4.148 | (5.538) (9.499) (6.887) | {0.420} {0.448} {0.547} | [0.807] [0.759] [0.602] S2 (t)| -1.542 14.076 7.342 | (5.455) (9.357) (6.784) | {0.777} {0.132} {0.279} | [-0.283] [1.504] [1.082] S3 (t)| 8.801 12.824 6.303 | (5.520) (9.467) (6.864) | {0.111} {0.176} {0.358} | [1.594] [1.355] [0.918] TREND(t)| 0.386 0.532 -0.108 | (0.351) (0.602) (0.436) | {0.271} {0.376} {0.804} | [1.100] [0.885] [-0.248] --------------------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_cst_Sigmau.txt000077500000000000000000000012051400612667500336100ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:34:05 *** VAR MODEL STATISTICS sample range: [1960 Q1, 2009 Q3], T = 199 Log Likelihood: -2.773442e+03 Determinant (Cov): 2.945441e+08 Covariance: 7.162689e+02 6.729414e+02 -1.526202e+00 6.729414e+02 2.107000e+03 1.045390e+03 -1.526202e+00 1.045390e+03 1.107563e+03 Correlation: 1.000000e+00 5.477809e-01 -1.713522e-03 5.477809e-01 1.000000e+00 6.843241e-01 -1.713522e-03 6.843241e-01 1.000000e+00 AIC: 2.001350e+01 FPE: 4.923766e+08 SC: 2.085751e+01 HQ: 2.035510e+01 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_cst_diag.txt000077500000000000000000000043051400612667500332730ustar00rootroot00000000000000*** Fri, 7 Oct 2016 13:09:15 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 150. tested order: 16 test statistic: 111.6858 p-value: 0.3847 adjusted test statistic: 117.3291 p-value: 0.2539 degrees of freedom: 108.0000 *** Fri, 7 Oct 2016 13:09:15 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags Reference: Doornik (1996), LM test and LMF test (with F-approximation) LM statistic: 51.3776 p-value: 0.2381 df: 45.0000 LMF statistic: 1.0489 p-value: 0.3901 df1: 45.0000 df2: 490.0000 *** Fri, 7 Oct 2016 13:09:15 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 87.8036 p-value: 0.0000 degrees of freedom: 6.0000 skewness only: 9.3168 p-value: 0.0254 kurtosis only: 78.4868 p-value: 0.0000 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 40.2734 p-value: 0.0000 degrees of freedom: 6.0000 skewness only: 3.1095 p-value: 0.3751 kurtosis only: 37.1639 p-value: 0.0000 *** Fri, 7 Oct 2016 13:09:15 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 16.7497 0.0002 -0.2775 4.3084 u2 4.6787 0.0964 0.2814 3.4976 u3 52.6188 0.0000 -0.2999 5.4467 *** Fri, 7 Oct 2016 13:09:15 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 8.0644 0.9469 0.5273 0.9300 u2 25.1012 0.0681 1.8182 0.0324 u3 19.3453 0.2512 1.3520 0.1719 *** Fri, 7 Oct 2016 13:09:15 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 277.0829 p-value(chi^2): 0.0000 degrees of freedom: 180.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_cst_fc5.txt000077500000000000000000000027231400612667500330460ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:36:29 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals realcons time forecast lower CI upper CI +/- 2009 Q4 9300.6496 9248.1947 9353.1045 52.4549 2010 Q1 9321.5224 9239.7531 9403.2917 81.7693 2010 Q2 9352.1985 9241.4242 9462.9729 110.7743 2010 Q3 9380.6350 9235.4295 9525.8404 145.2055 2010 Q4 9399.9545 9223.8058 9576.1033 176.1488 realgdp time forecast lower CI upper CI +/- 2009 Q4 13110.1070 13020.1406 13200.0734 89.9664 2010 Q1 13209.0014 13065.3335 13352.6692 143.6678 2010 Q2 13303.1382 13103.1689 13503.1075 199.9693 2010 Q3 13374.8516 13123.4596 13626.2435 251.3920 2010 Q4 13430.1995 13129.9346 13730.4644 300.2649 realinv time forecast lower CI upper CI +/- 2009 Q4 1533.3529 1468.1252 1598.5806 65.2277 2010 Q1 1587.7720 1485.5726 1689.9714 102.1994 2010 Q2 1636.0621 1497.1493 1774.9749 138.9128 2010 Q3 1673.6534 1501.6651 1845.6417 171.9883 2010 Q4 1703.1185 1497.8072 1908.4298 205.3113 macrodata_jmulti_cst_granger_causality_realcons.txt000077500000000000000000000005211400612667500376750ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:34:46 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons" do not Granger-cause "realgdp, realinv" Test statistic l = 10.4761 pval-F( l; 8, 546) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons" and "realgdp, realinv" Test statistic: c = 71.9870 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_cst_granger_causality_realcons_realgdp.txt000077500000000000000000000005211400612667500413730ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:34:58 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons, realgdp" do not Granger-cause "realinv" Test statistic l = 15.6399 pval-F( l; 8, 546) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons, realgdp" and "realinv" Test statistic: c = 79.9025 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_cst_granger_causality_realcons_realinv.txt000077500000000000000000000005211400612667500414150ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:35:08 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons, realinv" do not Granger-cause "realgdp" Test statistic l = 10.1078 pval-F( l; 8, 546) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons, realinv" and "realgdp" Test statistic: c = 86.5484 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_cst_granger_causality_realgdp.txt000077500000000000000000000005201400612667500375040ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:35:30 *** TEST FOR GRANGER-CAUSALITY: H0: "realgdp" do not Granger-cause "realcons, realinv" Test statistic l = 3.3656 pval-F( l; 8, 546) = 0.0009 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realgdp" and "realcons, realinv" Test statistic: c = 86.5484 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_cst_granger_causality_realgdp_realinv.txt000077500000000000000000000005201400612667500412240ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:35:21 *** TEST FOR GRANGER-CAUSALITY: H0: "realgdp, realinv" do not Granger-cause "realcons" Test statistic l = 3.3096 pval-F( l; 8, 546) = 0.0011 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realgdp, realinv" and "realcons" Test statistic: c = 71.9870 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_cst_granger_causality_realinv.txt000077500000000000000000000005201400612667500375260ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:35:39 *** TEST FOR GRANGER-CAUSALITY: H0: "realinv" do not Granger-cause "realcons, realgdp" Test statistic l = 2.7676 pval-F( l; 8, 546) = 0.0053 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realinv" and "realcons, realgdp" Test statistic: c = 79.9025 pval-Chi( c; 2) = 0.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_cst_ir.txt000077500000000000000000000112031400612667500327740ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:36:00 *** VAR Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time realcons realgdp realinv realcons realgdp realinv realcons realgdp realinv ->realcons ->realcons ->realcons ->realgdp ->realgdp ->realgdp ->realinv ->realinv ->realinv point estimate 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 1 point estimate 1.4257 -0.2680 0.3092 1.2903 0.5395 0.3469 0.9562 -0.1631 1.1684 2 point estimate 1.8482 -0.5230 0.5594 2.1861 0.2823 0.5269 1.6196 -0.3257 1.2684 3 point estimate 2.4455 -0.8464 0.8125 3.1113 -0.3476 0.9565 2.1853 -0.8015 1.6605 4 point estimate 2.6811 -1.0539 1.0756 3.7901 -0.8631 1.3465 2.7449 -1.1520 1.8597 5 point estimate 2.9139 -1.2333 1.2913 4.1960 -1.2435 1.6579 2.9987 -1.3934 2.0092 6 point estimate 3.1347 -1.3590 1.4537 4.4207 -1.5050 1.9076 3.0667 -1.5558 2.1320 7 point estimate 3.2446 -1.4339 1.5901 4.5331 -1.6490 2.0681 3.0892 -1.6163 2.1521 8 point estimate 3.3565 -1.4908 1.6919 4.5587 -1.7052 2.1546 2.9911 -1.5916 2.1149 9 point estimate 3.4539 -1.5255 1.7629 4.5427 -1.7116 2.1897 2.8459 -1.5248 2.0397 10 point estimate 3.5112 -1.5430 1.8158 4.5064 -1.6865 2.1838 2.6991 -1.4285 1.9247 11 point estimate 3.5593 -1.5514 1.8489 4.4500 -1.6428 2.1504 2.5247 -1.3131 1.7907 12 point estimate 3.5881 -1.5474 1.8642 4.3794 -1.5891 2.0986 2.3445 -1.1929 1.6467 13 point estimate 3.5923 -1.5323 1.8657 4.2959 -1.5276 2.0325 2.1670 -1.0706 1.4952 14 point estimate 3.5816 -1.5080 1.8532 4.1980 -1.4594 1.9561 1.9829 -0.9476 1.3427 15 point estimate 3.5540 -1.4739 1.8280 4.0879 -1.3856 1.8716 1.7996 -0.8271 1.1919 16 point estimate 3.5100 -1.4316 1.7922 3.9679 -1.3069 1.7806 1.6200 -0.7095 1.0436 17 point estimate 3.4543 -1.3825 1.7467 3.8397 -1.2243 1.6848 1.4427 -0.5955 0.9002 18 point estimate 3.3873 -1.3273 1.6928 3.7062 -1.1392 1.5857 1.2714 -0.4866 0.7627 19 point estimate 3.3106 -1.2675 1.6321 3.5694 -1.0531 1.4847 1.1078 -0.3833 0.6318 20 point estimate 3.2265 -1.2041 1.5658 3.4313 -0.9671 1.3833 0.9521 -0.2865 0.5086 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_cst_lagorder.txt000077500000000000000000000007131400612667500341650ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:33:45 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: realcons realgdp realinv deterministic variables: CONST S1 S2 S3 TREND sample range: [1961 Q3, 2009 Q3], T = 193 optimal number of lags (searched up to 10 lags of levels): Akaike Info Criterion: 4 Final Prediction Error: 4 Hannan-Quinn Criterion: 2 Schwarz Criterion: 2 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_ct.txt000077500000000000000000000071261400612667500321300ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:31:19 *** VAR ESTIMATION RESULTS endogenous variables: realcons realgdp realinv exogenous variables: deterministic variables: CONST TREND endogenous lags: 4 exogenous lags: 0 sample range: [1960 Q1, 2009 Q3], T = 199 modulus of the eigenvalues of the reverse characteristic polynomial : |z| = ( 1.5310 1.5310 2.0836 2.0836 4.4365 4.4365 1.5170 1.5170 1.0625 1.0625 1.2673 1.0127 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= realcons realgdp realinv ------------------------------------------- realcons(t-1)| 1.389 1.254 0.939 | (0.113) (0.193) (0.139) | {0.000} {0.000} {0.000} | [12.311] [6.508] [6.746] realgdp (t-1)| -0.241 0.563 -0.153 | (0.089) (0.152) (0.110) | {0.007} {0.000} {0.164} | [-2.710] [3.708] [-1.393] realinv (t-1)| 0.286 0.326 1.158 | (0.104) (0.178) (0.128) | {0.006} {0.066} {0.000} | [2.754] [1.835] [9.035] realcons(t-2)| -0.066 -0.612 -0.614 | (0.189) (0.322) (0.233) | {0.725} {0.058} {0.008} | [-0.352] [-1.899] [-2.640] realgdp (t-2)| 0.011 0.338 0.181 | (0.127) (0.217) (0.156) | {0.929} {0.119} {0.247} | [0.090] [1.558] [1.158] realinv (t-2)| -0.103 -0.419 -0.313 | (0.163) (0.278) (0.201) | {0.525} {0.132} {0.120} | [-0.635] [-1.505] [-1.557] realcons(t-3)| 0.101 -0.115 -0.146 | (0.193) (0.329) (0.238) | {0.602} {0.728} {0.540} | [0.522] [-0.348] [-0.613] realgdp (t-3)| 0.009 -0.168 -0.207 | (0.126) (0.215) (0.155) | {0.941} {0.434} {0.182} | [0.074] [-0.783] [-1.334] realinv (t-3)| -0.069 0.113 0.242 | (0.160) (0.273) (0.197) | {0.668} {0.679} {0.221} | [-0.429] [0.414] [1.223] realcons(t-4)| -0.420 -0.410 -0.124 | (0.130) (0.223) (0.161) | {0.001} {0.066} {0.440} | [-3.223] [-1.841] [-0.772] realgdp (t-4)| 0.210 0.186 0.157 | (0.093) (0.159) (0.115) | {0.024} {0.242} {0.169} | [2.259] [1.170] [1.374] realinv (t-4)| -0.095 -0.095 -0.201 | (0.111) (0.189) (0.137) | {0.391} {0.614} {0.141} | [-0.859] [-0.505] [-1.473] ------------------------------------------- Deterministic term: =================== realcons realgdp realinv --------------------------------------- CONST | 28.164 50.455 -14.771 | (24.747) (42.269) (30.527) | {0.255} {0.233} {0.628} | [1.138] [1.194] [-0.484] TREND(t)| 0.394 0.520 -0.114 | (0.352) (0.601) (0.434) | {0.263} {0.387} {0.792} | [1.118] [0.865] [-0.263] --------------------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_ct_Sigmau.txt000077500000000000000000000012051400612667500334250ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:31:19 *** VAR MODEL STATISTICS sample range: [1960 Q1, 2009 Q3], T = 199 Log Likelihood: -2.780012e+03 Determinant (Cov): 3.147519e+08 Covariance: 7.214135e+02 6.676988e+02 1.017747e+00 6.676988e+02 2.104667e+03 1.044485e+03 1.017747e+00 1.044485e+03 1.097759e+03 Correlation: 1.000000e+00 5.418721e-01 1.143653e-03 5.418721e-01 1.000000e+00 6.871588e-01 1.143653e-03 6.871588e-01 1.000000e+00 AIC: 1.998941e+01 FPE: 4.803878e+08 SC: 2.068448e+01 HQ: 2.027072e+01 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_ct_diag.txt000077500000000000000000000043051400612667500331100ustar00rootroot00000000000000*** Fri, 7 Oct 2016 13:04:53 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 150. tested order: 16 test statistic: 108.1183 p-value: 0.4787 adjusted test statistic: 113.5296 p-value: 0.3390 degrees of freedom: 108.0000 *** Fri, 7 Oct 2016 13:04:53 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags Reference: Doornik (1996), LM test and LMF test (with F-approximation) LM statistic: 50.1452 p-value: 0.2767 df: 45.0000 LMF statistic: 1.0420 p-value: 0.4016 df1: 45.0000 df2: 499.0000 *** Fri, 7 Oct 2016 13:04:53 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 87.7787 p-value: 0.0000 degrees of freedom: 6.0000 skewness only: 9.5406 p-value: 0.0229 kurtosis only: 78.2381 p-value: 0.0000 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 47.1375 p-value: 0.0000 degrees of freedom: 6.0000 skewness only: 4.1429 p-value: 0.2464 kurtosis only: 42.9945 p-value: 0.0000 *** Fri, 7 Oct 2016 13:04:53 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 24.0615 0.0000 -0.3235 4.5759 u2 4.3888 0.1114 0.2430 3.5413 u3 53.4128 0.0000 -0.3149 5.4587 *** Fri, 7 Oct 2016 13:04:53 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 9.5118 0.8909 0.6271 0.8588 u2 23.3007 0.1059 1.6688 0.0572 u3 19.2513 0.2558 1.3447 0.1759 *** Fri, 7 Oct 2016 13:04:53 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 280.5029 p-value(chi^2): 0.0000 degrees of freedom: 180.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_ct_fc5.txt000077500000000000000000000027231400612667500326630ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:40:54 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals realcons time forecast lower CI upper CI +/- 2009 Q4 9300.5029 9247.8600 9353.1459 52.6430 2010 Q1 9322.0298 9240.3880 9403.6716 81.6418 2010 Q2 9356.1011 9245.0642 9467.1379 111.0368 2010 Q3 9379.3785 9233.8884 9524.8686 145.4901 2010 Q4 9402.3839 9226.1128 9578.6549 176.2710 realgdp time forecast lower CI upper CI +/- 2009 Q4 13117.4378 13027.5212 13207.3544 89.9166 2010 Q1 13215.8562 13072.5158 13359.1967 143.3404 2010 Q2 13305.2187 13106.2154 13504.2220 199.0033 2010 Q3 13376.5086 13125.7352 13627.2820 250.7734 2010 Q4 13436.4822 13136.8901 13736.0743 299.5921 realinv time forecast lower CI upper CI +/- 2009 Q4 1537.1008 1472.1624 1602.0393 64.9384 2010 Q1 1591.4194 1489.6343 1693.2045 101.7851 2010 Q2 1637.4995 1499.3243 1775.6747 138.1752 2010 Q3 1675.8552 1504.3435 1847.3669 171.5117 2010 Q4 1705.8688 1500.8749 1910.8627 204.9939 macrodata_jmulti_ct_granger_causality_realcons.txt000077500000000000000000000005211400612667500375120ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:31:48 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons" do not Granger-cause "realgdp, realinv" Test statistic l = 10.6287 pval-F( l; 8, 555) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons" and "realgdp, realinv" Test statistic: c = 71.0006 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_ct_granger_causality_realcons_realgdp.txt000077500000000000000000000005211400612667500412100ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:32:02 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons, realgdp" do not Granger-cause "realinv" Test statistic l = 15.7489 pval-F( l; 8, 555) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons, realgdp" and "realinv" Test statistic: c = 79.6426 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_ct_granger_causality_realcons_realinv.txt000077500000000000000000000005211400612667500412320ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:32:25 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons, realinv" do not Granger-cause "realgdp" Test statistic l = 10.1522 pval-F( l; 8, 555) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons, realinv" and "realgdp" Test statistic: c = 86.2497 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_ct_granger_causality_realgdp.txt000077500000000000000000000005201400612667500373210ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:32:51 *** TEST FOR GRANGER-CAUSALITY: H0: "realgdp" do not Granger-cause "realcons, realinv" Test statistic l = 3.1668 pval-F( l; 8, 555) = 0.0016 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realgdp" and "realcons, realinv" Test statistic: c = 86.2497 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_ct_granger_causality_realgdp_realinv.txt000077500000000000000000000005201400612667500410410ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:32:35 *** TEST FOR GRANGER-CAUSALITY: H0: "realgdp, realinv" do not Granger-cause "realcons" Test statistic l = 3.1404 pval-F( l; 8, 555) = 0.0017 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realgdp, realinv" and "realcons" Test statistic: c = 71.0006 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_ct_granger_causality_realinv.txt000077500000000000000000000005201400612667500373430ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:33:00 *** TEST FOR GRANGER-CAUSALITY: H0: "realinv" do not Granger-cause "realcons, realgdp" Test statistic l = 2.6620 pval-F( l; 8, 555) = 0.0071 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realinv" and "realcons, realgdp" Test statistic: c = 79.6426 pval-Chi( c; 2) = 0.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_ct_ir.txt000077500000000000000000000112031400612667500326110ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:33:09 *** VAR Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time realcons realgdp realinv realcons realgdp realinv realcons realgdp realinv ->realcons ->realcons ->realcons ->realgdp ->realgdp ->realgdp ->realinv ->realinv ->realinv point estimate 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 1 point estimate 1.3888 -0.2407 0.2862 1.2541 0.5628 0.3258 0.9388 -0.1527 1.1584 2 point estimate 1.8291 -0.5021 0.5472 2.1412 0.3027 0.5012 1.5853 -0.3076 1.2481 3 point estimate 2.4039 -0.8108 0.7928 3.0812 -0.3266 0.9381 2.1613 -0.7834 1.6456 4 point estimate 2.6206 -1.0017 1.0436 3.7186 -0.8163 1.3181 2.6990 -1.1202 1.8410 5 point estimate 2.8535 -1.1768 1.2585 4.1059 -1.1770 1.6197 2.9336 -1.3440 1.9801 6 point estimate 3.0546 -1.2894 1.4117 4.3132 -1.4189 1.8575 2.9947 -1.4957 2.0974 7 point estimate 3.1576 -1.3580 1.5415 4.4045 -1.5453 2.0056 3.0032 -1.5452 2.1103 8 point estimate 3.2662 -1.4125 1.6407 4.4219 -1.5927 2.0827 2.8986 -1.5143 2.0658 9 point estimate 3.3552 -1.4437 1.7082 4.4009 -1.5951 2.1114 2.7547 -1.4478 1.9884 10 point estimate 3.4102 -1.4612 1.7596 4.3610 -1.5701 2.1026 2.6073 -1.3539 1.8728 11 point estimate 3.4560 -1.4704 1.7929 4.3049 -1.5298 2.0690 2.4360 -1.2434 1.7400 12 point estimate 3.4819 -1.4673 1.8087 4.2352 -1.4808 2.0190 2.2612 -1.1304 1.5997 13 point estimate 3.4857 -1.4545 1.8117 4.1532 -1.4250 1.9564 2.0880 -1.0153 1.4529 14 point estimate 3.4752 -1.4330 1.8016 4.0582 -1.3631 1.8844 1.9099 -0.8999 1.3057 15 point estimate 3.4483 -1.4023 1.7793 3.9521 -1.2959 1.8052 1.7334 -0.7873 1.1609 16 point estimate 3.4068 -1.3641 1.7470 3.8370 -1.2243 1.7202 1.5605 -0.6775 1.0190 17 point estimate 3.3540 -1.3196 1.7056 3.7150 -1.1493 1.6310 1.3908 -0.5712 0.8821 18 point estimate 3.2908 -1.2696 1.6564 3.5886 -1.0722 1.5390 1.2276 -0.4700 0.7512 19 point estimate 3.2189 -1.2153 1.6008 3.4599 -0.9944 1.4456 1.0722 -0.3743 0.6270 20 point estimate 3.1401 -1.1579 1.5400 3.3304 -0.9170 1.3520 0.9249 -0.2847 0.5103 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_ct_lagorder.txt000077500000000000000000000007021400612667500340000ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:30:57 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: realcons realgdp realinv deterministic variables: CONST TREND sample range: [1961 Q3, 2009 Q3], T = 193 optimal number of lags (searched up to 10 lags of levels): Akaike Info Criterion: 4 Final Prediction Error: 4 Hannan-Quinn Criterion: 2 Schwarz Criterion: 2 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_nc.txt000077500000000000000000000061421400612667500321170ustar00rootroot00000000000000*** Sat, 3 Sep 2016 21:52:15 *** VAR ESTIMATION RESULTS endogenous variables: realcons realgdp realinv exogenous variables: deterministic variables: endogenous lags: 4 exogenous lags: 0 sample range: [1960 Q1, 2009 Q3], T = 199 modulus of the eigenvalues of the reverse characteristic polynomial : |z| = ( 1.5237 1.5237 2.1188 2.1188 4.0128 4.0128 1.5233 1.5233 1.1578 1.1578 1.0233 0.9937 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= realcons realgdp realinv ------------------------------------------- realcons(t-1)| 1.396 1.251 0.943 | (0.112) (0.191) (0.137) | {0.000} {0.000} {0.000} | [12.500] [6.550] [6.862] realgdp (t-1)| -0.234 0.591 -0.164 | (0.087) (0.149) (0.107) | {0.007} {0.000} {0.127} | [-2.674] [3.956] [-1.526] realinv (t-1)| 0.280 0.297 1.170 | (0.102) (0.175) (0.126) | {0.006} {0.090} {0.000} | [2.734] [1.696] [9.292] realcons(t-2)| -0.070 -0.617 -0.613 | (0.188) (0.322) (0.232) | {0.710} {0.055} {0.008} | [-0.372] [-1.918] [-2.646] realgdp (t-2)| 0.017 0.348 0.178 | (0.127) (0.216) (0.156) | {0.896} {0.108} {0.253} | [0.131] [1.608] [1.144] realinv (t-2)| -0.107 -0.424 -0.311 | (0.162) (0.278) (0.200) | {0.509} {0.127} {0.119} | [-0.661] [-1.526] [-1.558] realcons(t-3)| 0.100 -0.115 -0.146 | (0.192) (0.329) (0.237) | {0.604} {0.725} {0.538} | [0.519] [-0.351] [-0.615] realgdp (t-3)| 0.012 -0.165 -0.207 | (0.126) (0.215) (0.155) | {0.923} {0.442} {0.179} | [0.097] [-0.769] [-1.343] realinv (t-3)| -0.071 0.113 0.241 | (0.160) (0.273) (0.197) | {0.655} {0.679} {0.221} | [-0.446] [0.414] [1.224] realcons(t-4)| -0.448 -0.454 -0.112 | (0.128) (0.219) (0.158) | {0.000} {0.038} {0.475} | [-3.497] [-2.075] [-0.714] realgdp (t-4)| 0.224 0.201 0.155 | (0.092) (0.157) (0.113) | {0.014} {0.200} {0.169} | [2.448] [1.282] [1.376] realinv (t-4)| -0.111 -0.108 -0.201 | (0.109) (0.187) (0.134) | {0.310} {0.561} {0.136} | [-1.016] [-0.581] [-1.492] ------------------------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_nc_Sigmau.txt000077500000000000000000000012051400612667500334170ustar00rootroot00000000000000*** Sat, 3 Sep 2016 21:52:15 *** VAR MODEL STATISTICS sample range: [1960 Q1, 2009 Q3], T = 199 Log Likelihood: -2.784455e+03 Determinant (Cov): 3.292006e+08 Covariance: 7.188741e+02 6.688264e+02 -1.208885e+00 6.688264e+02 2.100788e+03 1.027081e+03 -1.208885e+00 1.027081e+03 1.088305e+03 Correlation: 1.000000e+00 5.442468e-01 -1.366731e-03 5.442468e-01 1.000000e+00 6.792632e-01 -1.366731e-03 6.792632e-01 1.000000e+00 AIC: 1.997399e+01 FPE: 4.729151e+08 SC: 2.056976e+01 HQ: 2.021511e+01 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_nc_diag.txt000077500000000000000000000043051400612667500331020ustar00rootroot00000000000000*** Fri, 7 Oct 2016 13:03:06 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 150. tested order: 16 test statistic: 109.2188 p-value: 0.4491 adjusted test statistic: 114.6298 p-value: 0.3130 degrees of freedom: 108.0000 *** Fri, 7 Oct 2016 13:03:06 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags Reference: Doornik (1996), LM test and LMF test (with F-approximation) LM statistic: 50.8056 p-value: 0.2556 df: 45.0000 LMF statistic: 1.0662 p-value: 0.3614 df1: 45.0000 df2: 505.0000 *** Fri, 7 Oct 2016 13:03:06 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 78.5845 p-value: 0.0000 degrees of freedom: 6.0000 skewness only: 8.0544 p-value: 0.0449 kurtosis only: 70.5301 p-value: 0.0000 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 39.3298 p-value: 0.0000 degrees of freedom: 6.0000 skewness only: 2.7843 p-value: 0.4261 kurtosis only: 36.5456 p-value: 0.0000 *** Fri, 7 Oct 2016 13:03:06 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 19.9339 0.0000 -0.2845 4.4424 u2 5.8476 0.0537 0.2463 3.6802 u3 51.4284 0.0000 -0.3003 5.4169 *** Fri, 7 Oct 2016 13:03:06 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 9.7285 0.8804 0.6422 0.8458 u2 22.5410 0.1266 1.6067 0.0718 u3 19.1264 0.2622 1.3349 0.1815 *** Fri, 7 Oct 2016 13:03:06 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 285.2274 p-value(chi^2): 0.0000 degrees of freedom: 180.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_nc_fc5.txt000077500000000000000000000027231400612667500326550ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:42:40 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals realcons time forecast lower CI upper CI +/- 2009 Q4 9307.2247 9254.6745 9359.7749 52.5502 2010 Q1 9337.0319 9255.0721 9418.9918 81.9599 2010 Q2 9381.8009 9269.7311 9493.8707 112.0698 2010 Q3 9415.8372 9268.1582 9563.5162 147.6790 2010 Q4 9449.2250 9269.6139 9628.8361 179.6111 realgdp time forecast lower CI upper CI +/- 2009 Q4 13127.7840 13037.9503 13217.6176 89.8337 2010 Q1 13241.6877 13097.6300 13385.7454 144.0577 2010 Q2 13354.9804 13153.6395 13556.3213 201.3409 2010 Q3 13451.5405 13196.0598 13707.0212 255.4807 2010 Q4 13537.4984 13230.8448 13844.1520 306.6536 realinv time forecast lower CI upper CI +/- 2009 Q4 1534.4180 1469.7599 1599.0762 64.6582 2010 Q1 1590.1180 1488.8167 1691.4194 101.3014 2010 Q2 1640.8075 1503.1521 1778.4630 137.6554 2010 Q3 1684.3150 1512.8783 1855.7517 171.4367 2010 Q4 1719.8102 1513.8136 1925.8068 205.9966 macrodata_jmulti_nc_granger_causality_realcons.txt000077500000000000000000000005211400612667500375040ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:13:24 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons" do not Granger-cause "realgdp, realinv" Test statistic l = 11.6835 pval-F( l; 8, 561) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons" and "realgdp, realinv" Test statistic: c = 70.7644 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_nc_granger_causality_realcons_realgdp.txt000077500000000000000000000005211400612667500412020ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:13:00 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons, realgdp" do not Granger-cause "realinv" Test statistic l = 17.1550 pval-F( l; 8, 561) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons, realgdp" and "realinv" Test statistic: c = 78.9052 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_nc_granger_causality_realcons_realinv.txt000077500000000000000000000005211400612667500412240ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:13:35 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons, realinv" do not Granger-cause "realgdp" Test statistic l = 11.1461 pval-F( l; 8, 561) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons, realinv" and "realgdp" Test statistic: c = 85.8428 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_nc_granger_causality_realgdp.txt000077500000000000000000000005201400612667500373130ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:14:19 *** TEST FOR GRANGER-CAUSALITY: H0: "realgdp" do not Granger-cause "realcons, realinv" Test statistic l = 4.7662 pval-F( l; 8, 561) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realgdp" and "realcons, realinv" Test statistic: c = 85.8428 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_nc_granger_causality_realgdp_realinv.txt000077500000000000000000000005201400612667500410330ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:13:48 *** TEST FOR GRANGER-CAUSALITY: H0: "realgdp, realinv" do not Granger-cause "realcons" Test statistic l = 3.7899 pval-F( l; 8, 561) = 0.0002 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realgdp, realinv" and "realcons" Test statistic: c = 70.7644 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_nc_granger_causality_realinv.txt000077500000000000000000000005201400612667500373350ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:14:51 *** TEST FOR GRANGER-CAUSALITY: H0: "realinv" do not Granger-cause "realcons, realgdp" Test statistic l = 4.3984 pval-F( l; 8, 561) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realinv" and "realcons, realgdp" Test statistic: c = 78.9052 pval-Chi( c; 2) = 0.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_nc_ir.txt000077500000000000000000000112031400612667500326030ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:15:13 *** VAR Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time realcons realgdp realinv realcons realgdp realinv realcons realgdp realinv ->realcons ->realcons ->realcons ->realgdp ->realgdp ->realgdp ->realinv ->realinv ->realinv point estimate 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 1 point estimate 1.3962 -0.2336 0.2799 1.2508 0.5908 0.2968 0.9431 -0.1640 1.1705 2 point estimate 1.8511 -0.4934 0.5417 2.1480 0.3559 0.4489 1.6025 -0.3311 1.2739 3 point estimate 2.4527 -0.8087 0.7963 3.1178 -0.2512 0.8680 2.1967 -0.8193 1.6856 4 point estimate 2.6844 -1.0039 1.0506 3.7713 -0.7229 1.2333 2.7734 -1.1844 1.9115 5 point estimate 2.9346 -1.1898 1.2715 4.1750 -1.0719 1.5186 3.0452 -1.4392 2.0818 6 point estimate 3.1521 -1.3160 1.4314 4.3863 -1.3045 1.7365 3.1378 -1.6255 2.2299 7 point estimate 3.2644 -1.3953 1.5642 4.4689 -1.4202 1.8596 3.1837 -1.7157 2.2761 8 point estimate 3.3824 -1.4618 1.6666 4.4703 -1.4546 1.9063 3.1101 -1.7229 2.2622 9 point estimate 3.4809 -1.5042 1.7368 4.4252 -1.4394 1.9000 2.9935 -1.6928 2.2135 10 point estimate 3.5446 -1.5315 1.7901 4.3582 -1.3934 1.8531 2.8753 -1.6337 2.1259 11 point estimate 3.6011 -1.5508 1.8259 4.2745 -1.3291 1.7794 2.7318 -1.5544 2.0193 12 point estimate 3.6397 -1.5576 1.8447 4.1782 -1.2540 1.6888 2.5853 -1.4700 1.9046 13 point estimate 3.6579 -1.5544 1.8513 4.0723 -1.1711 1.5860 2.4428 -1.3816 1.7828 14 point estimate 3.6639 -1.5427 1.8455 3.9564 -1.0817 1.4748 2.2960 -1.2905 1.6601 15 point estimate 3.6556 -1.5216 1.8282 3.8323 -0.9868 1.3575 2.1518 -1.2004 1.5392 16 point estimate 3.6341 -1.4927 1.8013 3.7024 -0.8874 1.2358 2.0121 -1.1110 1.4205 17 point estimate 3.6030 -1.4570 1.7657 3.5681 -0.7844 1.1111 1.8754 -1.0232 1.3057 18 point estimate 3.5624 -1.4151 1.7222 3.4317 -0.6792 0.9846 1.7447 -0.9382 1.1957 19 point estimate 3.5139 -1.3679 1.6723 3.2947 -0.5728 0.8574 1.6206 -0.8563 1.0907 20 point estimate 3.4589 -1.3164 1.6166 3.1583 -0.4661 0.7304 1.5032 -0.7782 0.9913 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_nc_lagorder.txt000077500000000000000000000006331400612667500337750ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:22:50 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: realcons realgdp realinv sample range: [1961 Q3, 2009 Q3], T = 193 optimal number of lags (searched up to 10 lags of levels): Akaike Info Criterion: 4 Final Prediction Error: 4 Hannan-Quinn Criterion: 2 Schwarz Criterion: 2 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_ncs.txt000077500000000000000000000073671400612667500323140ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:15:59 *** VAR ESTIMATION RESULTS endogenous variables: realcons realgdp realinv exogenous variables: deterministic variables: S1 S2 S3 endogenous lags: 4 exogenous lags: 0 sample range: [1960 Q1, 2009 Q3], T = 199 modulus of the eigenvalues of the reverse characteristic polynomial : |z| = ( 1.4985 1.4985 2.0225 2.0225 3.9001 5.4939 1.5053 1.5053 1.1995 1.1181 1.0330 0.9947 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= realcons realgdp realinv ------------------------------------------- realcons(t-1)| 1.436 1.300 0.960 | (0.113) (0.194) (0.141) | {0.000} {0.000} {0.000} | [12.671] [6.693] [6.819] realgdp (t-1)| -0.265 0.553 -0.177 | (0.089) (0.152) (0.110) | {0.003} {0.000} {0.108} | [-2.984] [3.632] [-1.606] realinv (t-1)| 0.307 0.335 1.183 | (0.103) (0.177) (0.128) | {0.003} {0.058} {0.000} | [2.980] [1.892] [9.237] realcons(t-2)| -0.138 -0.695 -0.638 | (0.192) (0.329) (0.238) | {0.470} {0.034} {0.007} | [-0.722] [-2.116] [-2.679] realgdp (t-2)| 0.059 0.407 0.198 | (0.128) (0.220) (0.159) | {0.646} {0.064} {0.214} | [0.459] [1.850] [1.243] realinv (t-2)| -0.154 -0.475 -0.328 | (0.164) (0.281) (0.203) | {0.347} {0.091} {0.107} | [-0.941] [-1.692] [-1.612] realcons(t-3)| 0.160 -0.102 -0.146 | (0.196) (0.336) (0.244) | {0.413} {0.762} {0.548} | [0.818] [-0.303] [-0.601] realgdp (t-3)| -0.011 -0.183 -0.211 | (0.128) (0.219) (0.159) | {0.928} {0.402} {0.182} | [-0.090] [-0.839] [-1.333] realinv (t-3)| -0.041 0.129 0.243 | (0.161) (0.276) (0.200) | {0.800} {0.640} {0.223} | [-0.254] [0.468] [1.218] realcons(t-4)| -0.475 -0.424 -0.098 | (0.129) (0.222) (0.161) | {0.000} {0.056} {0.541} | [-3.666] [-1.912] [-0.611] realgdp (t-4)| 0.233 0.186 0.148 | (0.093) (0.159) (0.115) | {0.012} {0.242} {0.199} | [2.514] [1.170] [1.284] realinv (t-4)| -0.121 -0.104 -0.197 | (0.110) (0.188) (0.136) | {0.270} {0.581} {0.148} | [-1.103] [-0.552] [-1.448] ------------------------------------------- Deterministic term: =================== realcons realgdp realinv --------------------------------------- S1(t)| 4.537 8.340 2.612 | (5.338) (9.150) (6.631) | {0.395} {0.362} {0.694} | [0.850] [0.912] [0.394] S2(t)| -1.573 15.042 5.870 | (5.261) (9.018) (6.535) | {0.765} {0.095} {0.369} | [-0.299] [1.668] [0.898] S3(t)| 8.851 13.868 4.856 | (5.340) (9.153) (6.633) | {0.097} {0.130} {0.464} | [1.658] [1.515] [0.732] --------------------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_ncs_Sigmau.txt000077500000000000000000000012051400612667500336020ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:15:59 *** VAR MODEL STATISTICS sample range: [1960 Q1, 2009 Q3], T = 199 Log Likelihood: -2.777424e+03 Determinant (Cov): 3.066325e+08 Covariance: 7.132018e+02 6.722637e+02 -3.017500e+00 6.722637e+02 2.095453e+03 1.028940e+03 -3.017500e+00 1.028940e+03 1.100364e+03 Correlation: 1.000000e+00 5.499136e-01 -3.406222e-03 5.499136e-01 1.000000e+00 6.776146e-01 -3.406222e-03 6.776146e-01 1.000000e+00 AIC: 1.999342e+01 FPE: 4.823986e+08 SC: 2.073814e+01 HQ: 2.029483e+01 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_ncs_diag.txt000077500000000000000000000043051400612667500332650ustar00rootroot00000000000000*** Fri, 7 Oct 2016 13:03:56 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 150. tested order: 16 test statistic: 112.7721 p-value: 0.3575 adjusted test statistic: 118.4273 p-value: 0.2318 degrees of freedom: 108.0000 *** Fri, 7 Oct 2016 13:03:56 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags Reference: Doornik (1996), LM test and LMF test (with F-approximation) LM statistic: 56.9945 p-value: 0.1083 df: 45.0000 LMF statistic: 1.1906 p-value: 0.1917 df1: 45.0000 df2: 496.0000 *** Fri, 7 Oct 2016 13:03:56 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 75.0261 p-value: 0.0000 degrees of freedom: 6.0000 skewness only: 8.7314 p-value: 0.0331 kurtosis only: 66.2947 p-value: 0.0000 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 32.5281 p-value: 0.0000 degrees of freedom: 6.0000 skewness only: 1.8515 p-value: 0.6038 kurtosis only: 30.6767 p-value: 0.0000 *** Fri, 7 Oct 2016 13:03:57 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 13.6053 0.0011 -0.2267 4.1980 u2 5.9939 0.0499 0.3008 3.6008 u3 48.6717 0.0000 -0.2748 5.3596 *** Fri, 7 Oct 2016 13:03:57 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 8.2197 0.9421 0.5379 0.9237 u2 25.7500 0.0576 1.8729 0.0262 u3 19.1633 0.2603 1.3378 0.1798 *** Fri, 7 Oct 2016 13:03:57 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 283.5096 p-value(chi^2): 0.0000 degrees of freedom: 180.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_ncs_fc5.txt000077500000000000000000000027231400612667500330400ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:44:08 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals realcons time forecast lower CI upper CI +/- 2009 Q4 9306.9499 9254.6074 9359.2924 52.3425 2010 Q1 9335.9848 9253.9221 9418.0474 82.0627 2010 Q2 9376.8357 9265.0928 9488.5785 111.7429 2010 Q3 9415.1694 9267.8597 9562.4791 147.3097 2010 Q4 9443.4785 9264.0520 9622.9050 179.4265 realgdp time forecast lower CI upper CI +/- 2009 Q4 13119.1377 13029.4182 13208.8573 89.7195 2010 Q1 13233.5032 13089.3639 13377.6426 144.1393 2010 Q2 13350.9043 13149.0350 13552.7736 201.8693 2010 Q3 13447.0691 13191.4843 13702.6540 255.5849 2010 Q4 13525.7034 13218.7890 13832.6178 306.9144 realinv time forecast lower CI upper CI +/- 2009 Q4 1531.0916 1466.0762 1596.1070 65.0154 2010 Q1 1586.6564 1484.8673 1688.4454 101.7890 2010 Q2 1638.8190 1500.3294 1777.3085 138.4895 2010 Q3 1680.7507 1508.6052 1852.8962 172.1455 2010 Q4 1715.6945 1509.0410 1922.3480 206.6535 macrodata_jmulti_ncs_granger_causality_realcons.txt000077500000000000000000000005211400612667500376670ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:16:34 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons" do not Granger-cause "realgdp, realinv" Test statistic l = 11.4249 pval-F( l; 8, 552) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons" and "realgdp, realinv" Test statistic: c = 71.7504 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_ncs_granger_causality_realcons_realgdp.txt000077500000000000000000000005211400612667500413650ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:16:49 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons, realgdp" do not Granger-cause "realinv" Test statistic l = 16.6367 pval-F( l; 8, 552) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons, realgdp" and "realinv" Test statistic: c = 79.2548 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_ncs_granger_causality_realcons_realinv.txt000077500000000000000000000005211400612667500414070ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:20:03 *** TEST FOR GRANGER-CAUSALITY: H0: "realcons, realinv" do not Granger-cause "realgdp" Test statistic l = 10.8067 pval-F( l; 8, 552) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realcons, realinv" and "realgdp" Test statistic: c = 86.1955 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_ncs_granger_causality_realgdp.txt000077500000000000000000000005201400612667500374760ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:20:51 *** TEST FOR GRANGER-CAUSALITY: H0: "realgdp" do not Granger-cause "realcons, realinv" Test statistic l = 4.8888 pval-F( l; 8, 552) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realgdp" and "realcons, realinv" Test statistic: c = 86.1955 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_ncs_granger_causality_realgdp_realinv.txt000077500000000000000000000005201400612667500412160ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:20:25 *** TEST FOR GRANGER-CAUSALITY: H0: "realgdp, realinv" do not Granger-cause "realcons" Test statistic l = 3.7293 pval-F( l; 8, 552) = 0.0003 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realgdp, realinv" and "realcons" Test statistic: c = 71.7504 pval-Chi( c; 2) = 0.0000 macrodata_jmulti_ncs_granger_causality_realinv.txt000077500000000000000000000005201400612667500375200ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Sat, 3 Sep 2016 22:21:06 *** TEST FOR GRANGER-CAUSALITY: H0: "realinv" do not Granger-cause "realcons, realgdp" Test statistic l = 4.3526 pval-F( l; 8, 552) = 0.0000 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "realinv" and "realcons, realgdp" Test statistic: c = 79.2548 pval-Chi( c; 2) = 0.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_ncs_ir.txt000077500000000000000000000112031400612667500327660ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:21:22 *** VAR Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time realcons realgdp realinv realcons realgdp realinv realcons realgdp realinv ->realcons ->realcons ->realcons ->realgdp ->realgdp ->realgdp ->realinv ->realinv ->realinv point estimate 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 1 point estimate 1.4360 -0.2650 0.3074 1.3001 0.5527 0.3346 0.9598 -0.1772 1.1834 2 point estimate 1.8741 -0.5225 0.5624 2.2115 0.3085 0.5053 1.6460 -0.3637 1.3083 3 point estimate 2.5015 -0.8588 0.8298 3.1824 -0.3207 0.9375 2.2355 -0.8614 1.7242 4 point estimate 2.7548 -1.0752 1.0997 3.8888 -0.8320 1.3233 2.8363 -1.2466 1.9585 5 point estimate 3.0072 -1.2706 1.3250 4.3222 -1.2160 1.6296 3.1346 -1.5279 2.1452 6 point estimate 3.2472 -1.4151 1.4988 4.5619 -1.4822 1.8703 3.2373 -1.7302 2.3021 7 point estimate 3.3696 -1.5065 1.6435 4.6751 -1.6282 2.0166 3.2992 -1.8363 2.3591 8 point estimate 3.4944 -1.5813 1.7545 4.6941 -1.6841 2.0851 3.2358 -1.8549 2.3572 9 point estimate 3.6060 -1.6339 1.8355 4.6646 -1.6858 2.0988 3.1209 -1.8287 2.3154 10 point estimate 3.6776 -1.6685 1.8981 4.6128 -1.6529 2.0699 3.0070 -1.7719 2.2340 11 point estimate 3.7428 -1.6947 1.9422 4.5425 -1.5992 2.0128 2.8656 -1.6926 2.1326 12 point estimate 3.7920 -1.7089 1.9698 4.4608 -1.5342 1.9379 2.7197 -1.6062 2.0209 13 point estimate 3.8190 -1.7123 1.9846 4.3707 -1.4615 1.8501 2.5797 -1.5161 1.9016 14 point estimate 3.8341 -1.7071 1.9866 4.2707 -1.3823 1.7538 2.4347 -1.4232 1.7808 15 point estimate 3.8349 -1.6925 1.9771 4.1629 -1.2980 1.6512 2.2919 -1.3309 1.6611 16 point estimate 3.8213 -1.6694 1.9575 4.0489 -1.2093 1.5439 2.1536 -1.2397 1.5432 17 point estimate 3.7978 -1.6392 1.9288 3.9300 -1.1169 1.4333 2.0175 -1.1498 1.4288 18 point estimate 3.7644 -1.6023 1.8919 3.8082 -1.0219 1.3205 1.8864 -1.0624 1.3185 19 point estimate 3.7223 -1.5598 1.8481 3.6851 -0.9254 1.2066 1.7616 -0.9780 1.2128 20 point estimate 3.6733 -1.5126 1.7982 3.5620 -0.8283 1.0924 1.6424 -0.8970 1.1122 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/macrodata_jmulti_ncs_lagorder.txt000077500000000000000000000006771400612667500341700ustar00rootroot00000000000000*** Sat, 3 Sep 2016 22:22:28 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: realcons realgdp realinv deterministic variables: S1 S2 S3 sample range: [1961 Q3, 2009 Q3], T = 193 optimal number of lags (searched up to 10 lags of levels): Akaike Info Criterion: 4 Final Prediction Error: 4 Hannan-Quinn Criterion: 2 Schwarz Criterion: 2 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/parse_jmulti_var_output.py000066400000000000000000000431051400612667500327140ustar00rootroot00000000000000from io import open import os import re import numpy as np from .parse_jmulti_vecm_output import stringify_var_names, sublists debug_mode = False here = os.path.dirname(os.path.realpath(__file__)) def print_debug_output(results, dt): print("\n\n\nDETERMINISTIC TERMS: " + dt) coefs = results["est"]["Lagged endogenous term"] print("coefs:") print(str(type(coefs)) + str(coefs.shape)) print(coefs) print("se: ") print(results["se"]["Lagged endogenous term"]) print("t: ") print(results["t"]["Lagged endogenous term"]) print("p: ") print(results["p"]["Lagged endogenous term"]) def dt_s_tup_to_string(dt_s_tup): """ Parameters ---------- dt_s_tup : tuple A tuple of length 2. The first entry is a string specifying the deterministic term without any information about seasonal terms (for example "nc" or "c"). The second entry is an int specifying the number of seasons. Returns ------- dt_string : str Returns dt_s_tup[0], if dt_s_tup[1] is 0 (i.e. no seasons). If dt_s_tup[1] is > 0 (i.e. there are seasons) add an "s" to the string in dt_s_tup[0] like in the following examples: "nc" --> "ncs" "c" --> "cs" "ct" --> "cst" """ dt_string = dt_s_tup[0] # string for identifying the file to parse. if dt_s_tup[1] > 0: # if there are seasons in the model if dt_string == "nc": dt_string = dt_string[:2] + "s" if dt_string == "c" or dt_string == "ct": dt_string = dt_string[:1] + "s" + dt_string[1:] return dt_string def load_results_jmulti(dataset, dt_s_list): """ Parameters ---------- dataset : module A data module in the statsmodels/datasets directory that defines a __str__() method returning the dataset's name. dt_s_list : list A list of strings where each string represents a combination of deterministic terms. Returns ------- result : dict A dict (keys: tuples of deterministic terms and seasonal terms) of dicts (keys: strings "est" (for estimators), "se" (for standard errors), "t" (for t-values), "p" (for p-values)) of dicts (keys: strings "alpha", "beta", "Gamma" and other results) """ source = "jmulti" results_dict_per_det_terms = dict.fromkeys(dt_s_list) for dt_s in dt_s_list: dt_string = dt_s_tup_to_string(dt_s) params_file = dataset.__str__()+"_"+source+"_"+dt_string+".txt" params_file = os.path.join(here, params_file) # sections in jmulti output: section_headers = ["Lagged endogenous term", # parameter matrices "Deterministic term"] # c, s, ct if dt_string == "nc": del section_headers[-1] results = dict() results["est"] = dict.fromkeys(section_headers) results["se"] = dict.fromkeys(section_headers) results["t"] = dict.fromkeys(section_headers) results["p"] = dict.fromkeys(section_headers) result = [] result_se = [] result_t = [] result_p = [] rows = 0 started_reading_section = False start_end_mark = "-----" # --------------------------------------------------------------------- # parse information about \alpha, \beta, \Gamma, deterministic of VECM # and A_i and deterministic of corresponding VAR: section = -1 params_file = open(params_file, encoding='latin_1') for line in params_file: if section == -1 and section_headers[section+1] not in line: continue if section < len(section_headers)-1 \ and section_headers[section+1] in line: # new section section += 1 continue if not started_reading_section: if line.startswith(start_end_mark): started_reading_section = True continue if started_reading_section: if line.startswith(start_end_mark): if result == []: # no values collected in section "Legend" started_reading_section = False continue results["est"][section_headers[section]] = np.column_stack( result) result = [] results["se"][section_headers[section]] = np.column_stack( result_se) result_se = [] results["t"][section_headers[section]] = np.column_stack( result_t) result_t = [] results["p"][section_headers[section]] = np.column_stack( result_p) result_p = [] started_reading_section = False continue str_number = r"-?\d+\.\d{3}" regex_est = re.compile(str_number + r"[^\)\]\}]") est_col = re.findall(regex_est, line) # standard errors in parantheses in JMulTi output: regex_se = re.compile(r"\(" + str_number + r"\)") se_col = re.findall(regex_se, line) # t-values in brackets in JMulTi output: regex_t_value = re.compile(r"\[" + str_number + r"\]") t_col = re.findall(regex_t_value, line) # p-values in braces in JMulTi output: regex_p_value = re.compile(r"\{" + str_number + r"\}") p_col = re.findall(regex_p_value, line) if result == [] and est_col != []: rows = len(est_col) if est_col != []: est_col = [float(el) for el in est_col] result.append(est_col) elif se_col != []: for i in range(rows): se_col[i] = se_col[i].replace("(", "").replace(")", "") se_col = [float(el) for el in se_col] result_se.append(se_col) elif t_col != []: for i in range(rows): t_col[i] = t_col[i].replace("[", "").replace("]", "") t_col = [float(el) for el in t_col] result_t.append(t_col) elif p_col != []: for i in range(rows): p_col[i] = p_col[i].replace("{", "").replace("}", "") p_col = [float(el) for el in p_col] result_p.append(p_col) params_file.close() # --------------------------------------------------------------------- # parse information regarding \Sigma_u sigmau_file = dataset.__str__() + "_" + source + "_" + dt_string \ + "_Sigmau" + ".txt" sigmau_file = os.path.join(here, sigmau_file) rows_to_parse = 0 # all numbers of Sigma_u in notation with e (e.g. 2.283862e-05) regex_est = re.compile(r"\s+\S+e\S+") sigmau_section_reached = False sigmau_file = open(sigmau_file, encoding='latin_1') for line in sigmau_file: if line.startswith("Log Likelihood:"): line = line[len("Log Likelihood:"):] results["log_like"] = float(re.findall(regex_est, line)[0]) continue if not sigmau_section_reached and "Covariance:" not in line: continue if "Covariance:" in line: sigmau_section_reached = True row = re.findall(regex_est, line) rows_to_parse = len(row) # Sigma_u quadratic ==> #rows==#cols sigma_u = np.empty((rows_to_parse, rows_to_parse)) row = re.findall(regex_est, line) rows_to_parse -= 1 sigma_u[rows_to_parse] = row # rows are added in reverse order... if rows_to_parse == 0: break sigmau_file.close() results["est"]["Sigma_u"] = sigma_u[::-1] # ...and reversed again here # --------------------------------------------------------------------- # parse forecast related output: fc_file = dataset.__str__() + "_" + source + "_" + dt_string \ + "_fc5" + ".txt" fc_file = os.path.join(here, fc_file) fc, lower, upper, plu_min = [], [], [], [] fc_file = open(fc_file, encoding='latin_1') for line in fc_file: str_number = r"(\s+-?\d+\.\d{3}\s*)" regex_number = re.compile(str_number) numbers = re.findall(regex_number, line) if numbers == []: continue fc.append(float(numbers[0])) lower.append(float(numbers[1])) upper.append(float(numbers[2])) plu_min.append(float(numbers[3])) fc_file.close() neqs = len(results["est"]["Sigma_u"]) fc = np.hstack(np.vsplit(np.array(fc)[:, None], neqs)) lower = np.hstack(np.vsplit(np.array(lower)[:, None], neqs)) upper = np.hstack(np.vsplit(np.array(upper)[:, None], neqs)) results["fc"] = dict.fromkeys(["fc", "lower", "upper"]) results["fc"]["fc"] = fc results["fc"]["lower"] = lower results["fc"]["upper"] = upper # --------------------------------------------------------------------- # parse output related to Granger-caus. and instantaneous causality: results["granger_caus"] = dict.fromkeys(["p", "test_stat"]) results["granger_caus"]["p"] = dict() results["granger_caus"]["test_stat"] = dict() results["inst_caus"] = dict.fromkeys(["p", "test_stat"]) results["inst_caus"]["p"] = dict() results["inst_caus"]["test_stat"] = dict() vn = dataset.variable_names # all possible combinations of potentially causing variables # (at least 1 variable and not all variables together): var_combs = sublists(vn, 1, len(vn)-1) if debug_mode: print("\n\n\n" + dt_string) for causing in var_combs: caused = tuple(name for name in vn if name not in causing) causality_file = dataset.__str__() + "_" + source + "_" \ + dt_string + "_granger_causality_" \ + stringify_var_names(causing, "_") + ".txt" causality_file = os.path.join(here, causality_file) causality_file = open(causality_file) causality_results = [] for line in causality_file: str_number = r"\d+\.\d{4}" regex_number = re.compile(str_number) number = re.search(regex_number, line) if number is None: continue number = float(number.group(0)) causality_results.append(number) causality_file.close() results["granger_caus"]["test_stat"][(causing, caused)] = \ causality_results[0] results["granger_caus"]["p"][(causing, caused)] =\ causality_results[1] results["inst_caus"]["test_stat"][(causing, caused)] = \ causality_results[2] results["inst_caus"]["p"][(causing, caused)] = \ causality_results[3] # --------------------------------------------------------------------- # parse output related to impulse-response analysis: ir_file = dataset.__str__() + "_" + source + "_" + dt_string \ + "_ir" + ".txt" ir_file = os.path.join(here, ir_file) ir_file = open(ir_file, encoding='latin_1') causing = None caused = None data = None regex_vars = re.compile(r"\w+") regex_vals = re.compile(r"-?\d+\.\d{4}") line_start_causing = "time" data_line_indicator = "point estimate" data_rows_read = 0 for line in ir_file: if causing is None and not line.startswith(line_start_causing): continue # no relevant info in the header if line.startswith(line_start_causing): line = line[4:] causing = re.findall(regex_vars, line) # 21 periods shown in JMulTi output data = np.empty((21, len(causing))) continue if caused is None: caused = re.findall(regex_vars, line) continue # now start collecting the values: if data_line_indicator not in line: continue start = line.find(data_line_indicator) + len(data_line_indicator) line = line[start:] data[data_rows_read] = re.findall(regex_vals, line) data_rows_read += 1 ir_file.close() results["ir"] = data # --------------------------------------------------------------------- # parse output related to lag order selection: lagorder_file = dataset.__str__() + "_" + source + "_" + dt_string \ + "_lagorder" + ".txt" lagorder_file = os.path.join(here, lagorder_file) lagorder_file = open(lagorder_file, encoding='latin_1') results["lagorder"] = dict() aic_start = "Akaike Info Criterion:" fpe_start = "Final Prediction Error:" hqic_start = "Hannan-Quinn Criterion:" bic_start = "Schwarz Criterion:" for line in lagorder_file: if line.startswith(aic_start): results["lagorder"]["aic"] = int(line[len(aic_start):]) elif line.startswith(fpe_start): results["lagorder"]["fpe"] = int(line[len(fpe_start):]) elif line.startswith(hqic_start): results["lagorder"]["hqic"] = int(line[len(hqic_start):]) elif line.startswith(bic_start): results["lagorder"]["bic"] = int(line[len(bic_start):]) lagorder_file.close() # --------------------------------------------------------------------- # parse output related to non-normality-test: test_norm_file = dataset.__str__() + "_" + source + "_" + dt_string \ + "_diag" + ".txt" test_norm_file = os.path.join(here, test_norm_file) test_norm_file = open(test_norm_file, encoding='latin_1') results["test_norm"] = dict() section_start_marker = "TESTS FOR NONNORMALITY" section_reached = False subsection_start_marker = "Introduction to Multiple Time Series A" subsection_reached = False line_start_statistic = "joint test statistic:" line_start_pvalue = " p-value:" for line in test_norm_file: if not section_reached: if section_start_marker in line: section_reached = True # section w/ relevant results found continue if not subsection_reached: if subsection_start_marker in line: subsection_reached = True continue if "joint_pvalue" in results["test_norm"].keys(): break if line.startswith(line_start_statistic): line_end = line[len(line_start_statistic):] results["test_norm"]["joint_test_statistic"] = float(line_end) if line.startswith(line_start_pvalue): line_end = line[len(line_start_pvalue):] results["test_norm"]["joint_pvalue"] = float(line_end) test_norm_file.close() # --------------------------------------------------------------------- # parse output related to testing the whiteness of the residuals: whiteness_file = dataset.__str__() + "_" + source + "_" + dt_string \ + "_diag" + ".txt" whiteness_file = os.path.join(here, whiteness_file) whiteness_file = open(whiteness_file, encoding='latin_1') results["whiteness"] = dict() section_start_marker = "PORTMANTEAU TEST" order_start = "tested order:" statistic_start = "test statistic:" p_start = " p-value:" adj_statistic_start = "adjusted test statistic:" unadjusted_finished = False in_section = False for line in whiteness_file: if not in_section and section_start_marker not in line: continue if not in_section and section_start_marker in line: in_section = True continue if line.startswith(order_start): results["whiteness"]["tested order"] = int( line[len(order_start):]) continue if line.startswith(statistic_start): results["whiteness"]["test statistic"] = float( line[len(statistic_start):]) continue if line.startswith(adj_statistic_start): results["whiteness"]["test statistic adj."] = float( line[len(adj_statistic_start):]) continue if line.startswith(p_start): # same for unadjusted and adjusted if not unadjusted_finished: results["whiteness"]["p-value"] = \ float(line[len(p_start):]) unadjusted_finished = True else: results["whiteness"]["p-value adjusted"] = \ float(line[len(p_start):]) break whiteness_file.close() # --------------------------------------------------------------------- if debug_mode: print_debug_output(results, dt_string) results_dict_per_det_terms[dt_s] = results return results_dict_per_det_terms statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/parse_jmulti_vecm_output.py000066400000000000000000000560561400612667500330670ustar00rootroot00000000000000from io import open import itertools import os import re import numpy as np debug_mode = False here = os.path.dirname(os.path.realpath(__file__)) def print_debug_output(results, dt): print("\n\n\nDETERMINISTIC TERMS: " + dt) alpha = results["est"]["alpha"] print("alpha:") print(str(type(alpha)) + str(alpha.shape)) print(alpha) print("se: ") print(results["se"]["alpha"]) print("t: ") print(results["t"]["alpha"]) print("p: ") print(results["p"]["alpha"]) beta = results["est"]["beta"] print("beta:") print(str(type(beta)) + str(beta.shape)) print(beta) gamma = results["est"]["Gamma"] print("Gamma:") print(str(type(gamma)) + str(gamma.shape)) print(gamma) if "co" in dt or "s" in dt or "lo" in dt: c = results["est"]["C"] print("C:") print(str(type(c)) + str(c.shape)) print(c) print("se: ") print(results["se"]["C"]) def dt_s_tup_to_string(dt_s_tup): dt_string = dt_s_tup[0] # string for identifying the file to parse. if dt_s_tup[1] > 0: # if there are seasons in the model if "co" in dt_string or "ci" in dt_string or "nc" in dt_string: dt_string = dt_string[:2] + "s" + dt_string[2:] else: dt_string = "s" + dt_string return dt_string def sublists(lst, min_elmts=0, max_elmts=None): """Build a list of all possible sublists of a given list. Restrictions on the length of the sublists can be posed via the min_elmts and max_elmts parameters. All sublists have will have at least min_elmts elements and not more than max_elmts elements. Parameters ---------- lst : list Original list from which sublists are generated. min_elmts : int Lower bound for the length of sublists. max_elmts : int or None If int, then max_elmts are the upper bound for the length of sublists. If None, sublists' length is not restricted. In this case the longest sublist will be of the same length as the original list lst. Returns ------- result : list A list of all sublists of lst fulfilling the length restrictions. """ if max_elmts is None: max_elmts = len(lst) # for the following see also the definition of powerset() in # https://docs.python.org/dev/library/itertools.html#itertools-recipes result = itertools.chain.from_iterable( itertools.combinations(lst, sublist_len) for sublist_len in range(min_elmts, max_elmts+1)) if type(result) != list: result = list(result) return result def stringify_var_names(var_list, delimiter=""): """ Parameters ---------- var_list : list[str] Each list element is the name of a variable. Returns ------- result : str Concatenated variable names. """ result = var_list[0] for var_name in var_list[1:]: result += delimiter + var_name return result.lower() def load_results_jmulti(dataset): """ Parameters ---------- dataset : module A data module in the statsmodels/datasets directory that defines a __str__() method returning the dataset's name. dt_s_list : list A list of strings where each string represents a combination of deterministic terms. Returns ------- result : dict A dict (keys: tuples of deterministic terms and seasonal terms) of dicts (keys: strings "est" (for estimators), "se" (for standard errors), "t" (for t-values), "p" (for p-values)) of dicts (keys: strings "alpha", "beta", "Gamma" and other results) """ source = "jmulti" results_dict_per_det_terms = dict.fromkeys(dataset.dt_s_list) for dt_s in dataset.dt_s_list: dt_string = dt_s_tup_to_string(dt_s) params_file = "vecm_"+dataset.__str__()+"_"+source+"_"+dt_string+".txt" params_file = os.path.join(here, params_file) # sections in jmulti output: section_header = ["Lagged endogenous term", # Gamma "Deterministic term", # co, s, lo "Loading coefficients", # alpha "Estimated cointegration relation", # beta "Legend", "Lagged endogenous term", # VAR representation "Deterministic term"] # VAR representation # the following "sections" will serve as key for the corresponding # result values sections = ["Gamma", "C", # Here all deterministic term coefficients are # collected. (const and linear trend which belong # to cointegration relation as well as seasonal # components which are outside the cointegration # relation. Later, we will strip the terms related # to the cointegration relation from C. "alpha", "beta", "Legend", "VAR A", # VAR parameter matrices "VAR deterministic"] # VAR deterministic terms if "co" not in dt_string and "lo" not in dt_string \ and "s" not in dt_string: # JMulTi: no deterministic terms section in VEC representation del(section_header[1]) del(sections[1]) if "ci" not in dt_string and "li" not in dt_string: # JMulTi: no deterministic section in VAR repr. del(section_header[-1]) del(sections[-1]) results = dict() results["est"] = dict.fromkeys(sections) results["se"] = dict.fromkeys(sections) results["t"] = dict.fromkeys(sections) results["p"] = dict.fromkeys(sections) section = -1 result = [] result_se = [] result_t = [] result_p = [] rows = 0 started_reading_section = False start_end_mark = "-----" # --------------------------------------------------------------------- # parse information about \alpha, \beta, \Gamma, deterministic of VECM # and A_i and deterministic of corresponding VAR: params_file = open(params_file) for line in params_file: if section == -1 and section_header[section+1] not in line: continue if section < len(section_header)-1 \ and section_header[section+1] in line: # new section section += 1 continue if not started_reading_section: if line.startswith(start_end_mark): started_reading_section = True continue if started_reading_section: if line.startswith(start_end_mark): if result == []: # no values collected in section "Legend" started_reading_section = False continue results["est"][sections[section]] = np.column_stack( result) result = [] results["se"][sections[section]] = np.column_stack( result_se) result_se = [] results["t"][sections[section]] = np.column_stack( result_t) result_t = [] results["p"][sections[section]] = np.column_stack( result_p) result_p = [] started_reading_section = False continue str_number = r"-?\d+\.\d{3}" regex_est = re.compile(str_number + r"[^\)\]\}]") est_col = re.findall(regex_est, line) # standard errors in parantheses in JMulTi output: regex_se = re.compile(r"\(" + str_number + r"\)") se_col = re.findall(regex_se, line) # t-values in brackets in JMulTi output: regex_t_value = re.compile(r"\[" + str_number + r"\]") t_col = re.findall(regex_t_value, line) # p-values in braces in JMulTi output: regex_p_value = re.compile(r"\{" + str_number + r"\}") p_col = re.findall(regex_p_value, line) if result == [] and est_col != []: rows = len(est_col) if est_col != []: est_col = [float(el) for el in est_col] result.append(est_col) elif se_col != []: for i in range(rows): se_col[i] = se_col[i].replace("(", "").replace(")", "") se_col = [float(el) for el in se_col] result_se.append(se_col) elif t_col != []: for i in range(rows): t_col[i] = t_col[i].replace("[", "").replace("]", "") t_col = [float(el) for el in t_col] result_t.append(t_col) elif p_col != []: for i in range(rows): p_col[i] = p_col[i].replace("{", "").replace("}", "") p_col = [float(el) for el in p_col] result_p.append(p_col) params_file.close() # delete "Legend"-section of JMulTi: del results["est"]["Legend"] del results["se"]["Legend"] del results["t"]["Legend"] del results["p"]["Legend"] # JMulTi outputs beta.T results["est"]["beta"] = results["est"]["beta"].T results["se"]["beta"] = results["se"]["beta"].T results["t"]["beta"] = results["t"]["beta"].T results["p"]["beta"] = results["p"]["beta"].T # split information about beta and deterministic terms inside coint. alpha = results["est"]["alpha"] beta = results["est"]["beta"] alpha_rows = alpha.shape[0] if beta.shape[0] > alpha_rows: results["est"]["beta"], results["est"]["det_coint"] = np.vsplit( results["est"]["beta"], [alpha_rows]) results["se"]["beta"], results["se"]["det_coint"] = np.vsplit( results["se"]["beta"], [alpha_rows]) results["t"]["beta"], results["t"]["det_coint"] = np.vsplit( results["t"]["beta"], [alpha_rows]) results["p"]["beta"], results["p"]["det_coint"] = np.vsplit( results["p"]["beta"], [alpha_rows]) # --------------------------------------------------------------------- # parse information regarding \Sigma_u sigmau_file = "vecm_" + dataset.__str__() + "_" + source + "_" + \ dt_string + "_Sigmau" + ".txt" sigmau_file = os.path.join(here, sigmau_file) rows_to_parse = 0 # all numbers of Sigma_u in notation with e (e.g. 2.283862e-05) regex_est = re.compile(r"\s+\S+e\S+") sigmau_section_reached = False sigmau_file = open(sigmau_file) for line in sigmau_file: if line.startswith("Log Likelihood:"): line = line.split("Log Likelihood:")[1] results["log_like"] = float(re.findall(regex_est, line)[0]) if not sigmau_section_reached and "Covariance:" not in line: continue if "Covariance:" in line: sigmau_section_reached = True row = re.findall(regex_est, line) rows_to_parse = len(row) # Sigma_u quadratic ==> #rows==#cols sigma_u = np.empty((rows_to_parse, rows_to_parse)) row = re.findall(regex_est, line) rows_to_parse -= 1 sigma_u[rows_to_parse] = row # rows are added in reverse order if rows_to_parse == 0: break sigmau_file.close() results["est"]["Sigma_u"] = sigma_u[::-1] # --------------------------------------------------------------------- # parse forecast related output: fc_file = "vecm_" + dataset.__str__() + "_" + source + "_" + \ dt_string + "_fc5" + ".txt" fc_file = os.path.join(here, fc_file) fc, lower, upper, plu_min = [], [], [], [] fc_file = open(fc_file, encoding='latin_1') for line in fc_file: str_number = r"(\s+-?\d+\.\d{4}\s*?)" regex_number = re.compile(str_number) numbers = re.findall(regex_number, line) if numbers == []: continue fc.append(float(numbers[0])) lower.append(float(numbers[1])) upper.append(float(numbers[2])) plu_min.append(float(numbers[3])) fc_file.close() variables = alpha.shape[0] fc = np.hstack(np.vsplit(np.array(fc)[:, None], variables)) lower = np.hstack(np.vsplit(np.array(lower)[:, None], variables)) upper = np.hstack(np.vsplit(np.array(upper)[:, None], variables)) # plu_min = np.hstack(np.vsplit(np.array(plu_min)[:, None], variables)) results["fc"] = dict.fromkeys(["fc", "lower", "upper"]) results["fc"]["fc"] = fc results["fc"]["lower"] = lower results["fc"]["upper"] = upper # --------------------------------------------------------------------- # parse output related to Granger-causality: results["granger_caus"] = dict.fromkeys(["p", "test_stat"]) results["granger_caus"]["p"] = dict() results["granger_caus"]["test_stat"] = dict() vn = dataset.variable_names # all possible combinations of potentially causing variables # (at least 1 variable and not all variables together): var_combs = sublists(vn, 1, len(vn)-1) for causing in var_combs: caused = tuple(el for el in vn if el not in causing) granger_file = "vecm_" + dataset.__str__() + "_" + source + "_" \ + dt_string + "_granger_causality_" \ + stringify_var_names(causing) + "_" \ + stringify_var_names(caused) + ".txt" granger_file = os.path.join(here, granger_file) granger_file = open(granger_file) granger_results = [] for line in granger_file: str_number = r"\d+\.\d{4}" regex_number = re.compile(str_number) number = re.search(regex_number, line) if number is None: continue number = float(number.group(0)) granger_results.append(number) granger_file.close() results["granger_caus"]["test_stat"][(causing, caused)] = \ granger_results[0] results["granger_caus"]["p"][(causing, caused)] =\ granger_results[1] # --------------------------------------------------------------------- # parse output related to instant causality: results["inst_caus"] = dict.fromkeys(["p", "test_stat"]) results["inst_caus"]["p"] = dict() results["inst_caus"]["test_stat"] = dict() vn = dataset.variable_names # all possible combinations of potentially causing variables # (at least 1 variable and not all variables together): var_combs = sublists(vn, 1, len(vn)-1) for causing in var_combs: caused = tuple(el for el in vn if el not in causing) # Though Granger- and instantaneous causality results are in the # same file we use two separate files, since JMulTi is basing both # tests on a VAR(p+1) model (where p is the number of lags in # levels). According to Lutkepohl, Granger-causality tests are # based on VAR(p+1) *but* tests for instantaneous causality are # based on VAR(p)! Thus we have this separate file with JMulTi # results for a VECM with the lag order reduced by one. inst_file = "vecm_" + dataset.__str__() + "_" + source + "_" \ + dt_string + "_inst_causality_" \ + stringify_var_names(causing) + "_" \ + stringify_var_names(caused) + ".txt" inst_file = os.path.join(here, inst_file) inst_file = open(inst_file) inst_results = [] for line in inst_file: str_number = r"\d+\.\d{4}" regex_number = re.compile(str_number) number = re.search(regex_number, line) if number is None: continue number = float(number.group(0)) inst_results.append(number) inst_file.close() results["inst_caus"]["test_stat"][(causing, caused)] = \ inst_results[2] results["inst_caus"]["p"][(causing, caused)] = \ inst_results[3] # --------------------------------------------------------------------- # parse output related to impulse-response analysis: ir_file = "vecm_" + dataset.__str__() + "_" + source + "_" + \ dt_string + "_ir" + ".txt" ir_file = os.path.join(here, ir_file) ir_file = open(ir_file, encoding='latin_1') causing = None caused = None data = None regex_vars = re.compile(r"\w+") regex_vals = re.compile(r"-?\d+\.\d{4}") line_start_causing = "time" data_line_indicator = "point estimate" data_rows_read = 0 for line in ir_file: if causing is None and not line.startswith(line_start_causing): continue # no relevant info in the header if line.startswith(line_start_causing): line = line[4:] causing = re.findall(regex_vars, line) # 21 periods shown in JMulTi output data = np.empty((21, len(causing))) continue if caused is None: caused = re.findall(regex_vars, line) continue # now start collecting the values: if data_line_indicator not in line: continue start = line.find(data_line_indicator) + len(data_line_indicator) line = line[start:] data[data_rows_read] = re.findall(regex_vals, line) data_rows_read += 1 ir_file.close() results["ir"] = data # --------------------------------------------------------------------- # parse output related to lag order selection: lagorder_file = "vecm_" + dataset.__str__() + "_" + source + "_" + \ dt_string + "_lagorder" + ".txt" lagorder_file = os.path.join(here, lagorder_file) lagorder_file = open(lagorder_file, encoding='latin_1') results["lagorder"] = dict() aic_start = "Akaike Info Criterion:" fpe_start = "Final Prediction Error:" hqic_start = "Hannan-Quinn Criterion:" bic_start = "Schwarz Criterion:" for line in lagorder_file: if line.startswith(aic_start): results["lagorder"]["aic"] = int(line[len(aic_start):]) elif line.startswith(fpe_start): results["lagorder"]["fpe"] = int(line[len(fpe_start):]) elif line.startswith(hqic_start): results["lagorder"]["hqic"] = int(line[len(hqic_start):]) elif line.startswith(bic_start): results["lagorder"]["bic"] = int(line[len(bic_start):]) lagorder_file.close() # --------------------------------------------------------------------- # parse output related to non-normality-test: test_norm_file = "vecm_" + dataset.__str__() + "_" + source + "_" + \ dt_string + "_diag" + ".txt" test_norm_file = os.path.join(here, test_norm_file) test_norm_file = open(test_norm_file, encoding='latin_1') results["test_norm"] = dict() reading_values = False line_start_statistic = "joint test statistic:" line_start_pvalue = " p-value:" for line in test_norm_file: if not reading_values: if "Introduction to Multiple Time Series Analysis" in line: reading_values = True # section w/ relevant results found continue if "joint_pvalue" in results["test_norm"].keys(): break if line.startswith(line_start_statistic): line_end = line[len(line_start_statistic):] results["test_norm"]["joint_test_statistic"] = float(line_end) if line.startswith(line_start_pvalue): line_end = line[len(line_start_pvalue):] results["test_norm"]["joint_pvalue"] = float(line_end) test_norm_file.close() # --------------------------------------------------------------------- # parse output related to testing the whiteness of the residuals: whiteness_file = "vecm_" + dataset.__str__() + "_" + source + "_" + \ dt_string + "_diag" + ".txt" whiteness_file = os.path.join(here, whiteness_file) whiteness_file = open(whiteness_file, encoding='latin_1') results["whiteness"] = dict() section_start_marker = "PORTMANTEAU TEST" order_start = "tested order:" statistic_start = "test statistic:" p_start = " p-value:" adj_statistic_start = "adjusted test statistic:" unadjusted_finished = False in_section = False for line in whiteness_file: if not in_section and section_start_marker not in line: continue if not in_section and section_start_marker in line: in_section = True continue if line.startswith(order_start): results["whiteness"]["tested order"] = int( line[len(order_start):]) continue if line.startswith(statistic_start): results["whiteness"]["test statistic"] = float( line[len(statistic_start):]) continue if line.startswith(adj_statistic_start): results["whiteness"]["test statistic adj."] = float( line[len(adj_statistic_start):]) continue if line.startswith(p_start): # same for unadjusted and adjusted if not unadjusted_finished: results["whiteness"]["p-value"] = \ float(line[len(p_start):]) unadjusted_finished = True else: results["whiteness"]["p-value adjusted"] = \ float(line[len(p_start):]) break whiteness_file.close() # --------------------------------------------------------------------- if debug_mode: print_debug_output(results, dt_string) results_dict_per_det_terms[dt_s] = results return results_dict_per_det_terms statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_ci.txt000066400000000000000000000072721400612667500315050ustar00rootroot00000000000000*** Mon, 25 Jul 2016 14:17:28 *** VEC REPRESENTATION endogenous variables: Dp R exogenous variables: deterministic variables: CONST endogenous lags (diffs): 3 exogenous lags: 0 sample range: [1973 Q2, 1998 Q4], T = 103 estimation procedure: One stage. Johansen approach Lagged endogenous term: ======================= d(Dp) d(R) ------------------------------ d(Dp)(t-1)| -0.516 -0.322 | (0.154) (0.133) | {0.001} {0.016} | [-3.358] [-2.416] d(R) (t-1)| 0.049 0.258 | (0.116) (0.101) | {0.673} {0.011} | [0.422] [2.558] d(Dp)(t-2)| -0.655 -0.200 | (0.105) (0.091) | {0.000} {0.028} | [-6.235] [-2.198] d(R) (t-2)| 0.121 0.015 | (0.116) (0.101) | {0.299} {0.878} | [1.039] [0.153] d(Dp)(t-3)| -0.803 -0.070 | (0.056) (0.048) | {0.000} {0.148} | [-14.430] [-1.448] d(R) (t-3)| -0.050 0.224 | (0.114) (0.098) | {0.658} {0.023} | [-0.442] [2.272] ------------------------------ Loading coefficients: ===================== d(Dp) d(R) ----------------------------- ec1(t-1)| -0.639 0.423 | (0.201) (0.175) | {0.001} {0.015} | [-3.176] [2.426] ----------------------------- Estimated cointegration relation(s): ==================================== ec1(t-1) ------------------- Dp(t-1)| 1.000 | (0.000) | {0.000} | [0.000] R (t-1)| -0.273 | (0.050) | {0.000} | [-5.423] CONST | 0.012 | (0.004) | {0.002} | [3.146] ------------------- VAR REPRESENTATION modulus of the eigenvalues of the reverse characteristic polynomial: |z| = ( 1.0095 1.0117 1.0117 1.0000 1.3287 1.3287 1.7308 1.7308 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= Dp R ----------------------------- Dp(t-1)| -0.155 0.102 | (0.253) (0.220) | {0.540} {0.643} | [-0.613] [0.463] R (t-1)| 0.224 1.142 | (0.129) (0.112) | {0.082} {0.000} | [1.738] [10.236] Dp(t-2)| -0.139 0.122 | (0.056) (0.049) | {0.013} {0.013} | [-2.475] [2.497] R (t-2)| 0.072 -0.243 | (0.170) (0.147) | {0.673} {0.099} | [0.422] [-1.648] Dp(t-3)| -0.148 0.130 | (0.057) (0.049) | {0.009} {0.008} | [-2.618] [2.658] R (t-3)| -0.171 0.208 | (0.170) (0.147) | {0.315} {0.158} | [-1.006] [1.412] Dp(t-4)| 0.803 0.070 | (0.056) (0.048) | {0.000} {0.148} | [14.430] [1.448] R (t-4)| 0.050 -0.224 | (0.114) (0.098) | {0.658} {0.023} | [0.442] [-2.272] ----------------------------- Deterministic term: =================== Dp R ----------------------------- CONST | -0.008 0.005 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] ----------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_ci_Sigmau.txt000066400000000000000000000005631400612667500330060ustar00rootroot00000000000000*** Mon, 25 Jul 2016 14:17:28 *** VECM MODEL STATISTICS sample range: [1973 Q2, 1998 Q4], T = 103 Log Likelihood: 7.693576e+02 Determinant (Cov): 9.627791e-10 Covariance: 3.584925e-05 -1.729222e-06 -1.729222e-06 2.693974e-05 Correlation: 1.000000e+00 -5.564344e-02 -5.564344e-02 1.000000e+00 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_ci_diag.txt000066400000000000000000000034331400612667500324640ustar00rootroot00000000000000*** Mon, 25 Jul 2016 13:43:33 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) tested order: 16 test statistic: 47.2544 p-value: 0.5842 adjusted test statistic: 52.1375 p-value: 0.3908 degrees of freedom: 50.0000 *** Mon, 25 Jul 2016 13:43:33 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags LM statistic: 23.9801 p-value: 0.2433 df: 20.0000 *** Mon, 25 Jul 2016 13:43:33 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 0.7129 p-value: 0.9497 degrees of freedom: 4.0000 skewness only: 0.1626 p-value: 0.9219 kurtosis only: 0.5503 p-value: 0.7595 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 0.5689 p-value: 0.9665 degrees of freedom: 4.0000 skewness only: 0.1453 p-value: 0.9299 kurtosis only: 0.4237 p-value: 0.8091 *** Mon, 25 Jul 2016 13:43:33 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 0.1450 0.9301 0.0918 3.0065 u2 0.7066 0.7024 -0.0009 3.4057 *** Mon, 25 Jul 2016 13:43:33 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 18.6742 0.2859 1.4861 0.1299 u2 27.1235 0.0401 2.4631 0.0051 *** Mon, 25 Jul 2016 13:43:33 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 73.0452 p-value(chi^2): 0.0051 degrees of freedom: 45.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_ci_fc5.txt000077500000000000000000000020531400612667500322350ustar00rootroot00000000000000*** Thu, 28 Jul 2016 16:41:32 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals Dp time forecast lower CI upper CI +/- 1999 Q1 -0.0175 -0.0293 -0.0058 0.0117 1999 Q2 -0.0035 -0.0156 0.0086 0.0121 1999 Q3 0.0010 -0.0115 0.0136 0.0125 1999 Q4 0.0216 0.0090 0.0342 0.0126 2000 Q1 -0.0176 -0.0342 -0.0010 0.0166 R time forecast lower CI upper CI +/- 1999 Q1 0.0393 0.0292 0.0495 0.0102 1999 Q2 0.0402 0.0248 0.0556 0.0154 1999 Q3 0.0411 0.0220 0.0602 0.0191 1999 Q4 0.0411 0.0181 0.0641 0.0230 2000 Q1 0.0423 0.0159 0.0688 0.0264 vecm_e6_jmulti_ci_granger_causality_dp_r.txt000066400000000000000000000004461400612667500362110ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 11:25:22 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 1.4382 pval-F( l; 4, 182) = 0.2231 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.9998 pval-Chi( c; 1) = 0.3174 vecm_e6_jmulti_ci_granger_causality_r_dp.txt000066400000000000000000000004461400612667500362110ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 13:43:55 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.8185 pval-F( l; 4, 182) = 0.0053 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.9998 pval-Chi( c; 1) = 0.3174 vecm_e6_jmulti_ci_inst_causality_dp_r.txt000077500000000000000000000004461400612667500355440ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:45:45 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 1.7371 pval-F( l; 3, 188) = 0.1609 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.5489 pval-Chi( c; 1) = 0.4588 vecm_e6_jmulti_ci_inst_causality_r_dp.txt000077500000000000000000000004461400612667500355440ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:46:00 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 4.1789 pval-F( l; 3, 188) = 0.0068 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.5489 pval-Chi( c; 1) = 0.4588 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_ci_ir.txt000077500000000000000000000046111400612667500321740ustar00rootroot00000000000000*** Tue, 16 Aug 2016 19:30:32 *** VECM Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time Dp R Dp R ->Dp ->Dp ->R ->R point estimate 1.0000 0.0000 0.0000 1.0000 1 point estimate -0.1552 0.2238 0.1017 1.1424 2 point estimate -0.0921 0.2927 0.2220 1.0852 3 point estimate -0.0551 0.0773 0.3310 1.2277 4 point estimate 0.9197 0.1217 0.3782 1.2260 5 point estimate -0.1705 0.3410 0.4393 1.1486 6 point estimate -0.0871 0.3433 0.5101 1.1076 7 point estimate -0.0455 0.1257 0.5672 1.0649 8 point estimate 0.8901 0.1629 0.5579 1.0201 9 point estimate -0.1554 0.3531 0.5694 0.9811 10 point estimate -0.0667 0.3458 0.5995 0.9433 11 point estimate -0.0282 0.1345 0.6231 0.9219 12 point estimate 0.8642 0.1670 0.5910 0.9135 13 point estimate -0.1421 0.3462 0.5864 0.8999 14 point estimate -0.0502 0.3373 0.6044 0.8845 15 point estimate -0.0155 0.1354 0.6201 0.8837 16 point estimate 0.8357 0.1682 0.5859 0.8895 17 point estimate -0.1325 0.3394 0.5802 0.8863 18 point estimate -0.0374 0.3302 0.5972 0.8790 19 point estimate -0.0057 0.1380 0.6125 0.8829 20 point estimate 0.8066 0.1712 0.5806 0.8910 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_ci_lagorder.txt000077500000000000000000000006601400612667500333610ustar00rootroot00000000000000*** Sun, 21 Aug 2016 09:36:25 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: Dp R deterministic variables: CONST sample range: [1975 Q1, 1998 Q4], T = 96 optimal number of lags (searched up to 10 lags of 1. differences): Akaike Info Criterion: 3 Final Prediction Error: 3 Hannan-Quinn Criterion: 3 Schwarz Criterion: 3 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cili.txt000066400000000000000000000077471400612667500320410ustar00rootroot00000000000000*** Mon, 25 Jul 2016 21:32:41 *** VEC REPRESENTATION endogenous variables: Dp R exogenous variables: deterministic variables: CONST TREND endogenous lags (diffs): 3 exogenous lags: 0 sample range: [1973 Q2, 1998 Q4], T = 103 estimation procedure: One stage. Johansen approach Lagged endogenous term: ======================= d(Dp) d(R) ------------------------------ d(Dp)(t-1)| -0.531 -0.324 | (0.151) (0.131) | {0.000} {0.013} | [-3.514] [-2.479] d(R) (t-1)| 0.051 0.260 | (0.117) (0.101) | {0.660} {0.010} | [0.440] [2.581] d(Dp)(t-2)| -0.665 -0.202 | (0.103) (0.089) | {0.000} {0.024} | [-6.427] [-2.254] d(R) (t-2)| 0.122 0.017 | (0.116) (0.101) | {0.295} {0.863} | [1.047] [0.172] d(Dp)(t-3)| -0.808 -0.071 | (0.055) (0.047) | {0.000} {0.137} | [-14.712] [-1.487] d(R) (t-3)| -0.050 0.226 | (0.114) (0.098) | {0.659} {0.022} | [-0.441] [2.295] ------------------------------ Loading coefficients: ===================== d(Dp) d(R) ----------------------------- ec1(t-1)| -0.619 0.426 | (0.198) (0.171) | {0.002} {0.013} | [-3.127] [2.490] ----------------------------- Estimated cointegration relation(s): ==================================== ec1(t-1) -------------------- Dp(t-1) | 1.000 | (0.000) | {0.000} | [0.000] R (t-1) | -0.281 | (0.063) | {0.000} | [-4.429] CONST | 0.013 | (0.006) | {0.032} | [2.150] TREND(t-1)| 0.000 | (0.000) | {0.901} | [-0.124] -------------------- VAR REPRESENTATION modulus of the eigenvalues of the reverse characteristic polynomial: |z| = ( 1.0095 1.0117 1.0117 1.0000 1.3224 1.3224 1.7259 1.7259 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= Dp R ----------------------------- Dp(t-1)| -0.150 0.102 | (0.249) (0.215) | {0.547} {0.634} | [-0.603] [0.475] R (t-1)| 0.225 1.140 | (0.129) (0.112) | {0.081} {0.000} | [1.745] [10.216] Dp(t-2)| -0.134 0.122 | (0.055) (0.048) | {0.016} {0.011} | [-2.415] [2.552] R (t-2)| 0.071 -0.243 | (0.170) (0.147) | {0.678} {0.099} | [0.415] [-1.649] Dp(t-3)| -0.143 0.131 | (0.056) (0.048) | {0.010} {0.007} | [-2.561] [2.716] R (t-3)| -0.172 0.208 | (0.170) (0.147) | {0.312} {0.157} | [-1.011] [1.415] Dp(t-4)| 0.808 0.071 | (0.055) (0.047) | {0.000} {0.137} | [14.712] [1.487] R (t-4)| 0.050 -0.226 | (0.114) (0.098) | {0.659} {0.022} | [0.441] [-2.295] ----------------------------- Deterministic term: =================== Dp R --------------------------------- CONST (t)| -0.008 0.006 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] TREND(t-1)(t)| 0.000 0.000 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] --------------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cili_Sigmau.txt000066400000000000000000000005631400612667500333330ustar00rootroot00000000000000*** Mon, 25 Jul 2016 21:32:41 *** VECM MODEL STATISTICS sample range: [1973 Q2, 1998 Q4], T = 103 Log Likelihood: 7.693615e+02 Determinant (Cov): 9.627057e-10 Covariance: 3.594755e-05 -1.704602e-06 -1.704602e-06 2.686168e-05 Correlation: 1.000000e+00 -5.485571e-02 -5.485571e-02 1.000000e+00 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cili_diag.txt000066400000000000000000000034331400612667500330110ustar00rootroot00000000000000*** Mon, 25 Jul 2016 11:45:40 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) tested order: 16 test statistic: 47.3477 p-value: 0.5804 adjusted test statistic: 52.2349 p-value: 0.3872 degrees of freedom: 50.0000 *** Mon, 25 Jul 2016 11:45:40 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags LM statistic: 23.8022 p-value: 0.2511 df: 20.0000 *** Mon, 25 Jul 2016 11:45:40 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 0.7086 p-value: 0.9503 degrees of freedom: 4.0000 skewness only: 0.1543 p-value: 0.9257 kurtosis only: 0.5543 p-value: 0.7579 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 0.5669 p-value: 0.9667 degrees of freedom: 4.0000 skewness only: 0.1378 p-value: 0.9334 kurtosis only: 0.4292 p-value: 0.8069 *** Mon, 25 Jul 2016 11:45:40 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 0.1374 0.9336 0.0895 3.0024 u2 0.7101 0.7011 -0.0000 3.4068 *** Mon, 25 Jul 2016 11:45:40 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 18.5181 0.2944 1.4703 0.1362 u2 27.1756 0.0396 2.4700 0.0050 *** Mon, 25 Jul 2016 11:45:40 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 73.2472 p-value(chi^2): 0.0049 degrees of freedom: 45.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cili_fc5.txt000077500000000000000000000020531400612667500325620ustar00rootroot00000000000000*** Thu, 28 Jul 2016 16:43:15 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals Dp time forecast lower CI upper CI +/- 1999 Q1 -0.0175 -0.0292 -0.0057 0.0118 1999 Q2 -0.0035 -0.0156 0.0086 0.0121 1999 Q3 0.0011 -0.0115 0.0136 0.0125 1999 Q4 0.0216 0.0090 0.0342 0.0126 2000 Q1 -0.0175 -0.0341 -0.0009 0.0166 R time forecast lower CI upper CI +/- 1999 Q1 0.0394 0.0292 0.0495 0.0102 1999 Q2 0.0402 0.0248 0.0556 0.0154 1999 Q3 0.0412 0.0221 0.0602 0.0190 1999 Q4 0.0412 0.0183 0.0641 0.0229 2000 Q1 0.0425 0.0162 0.0688 0.0263 vecm_e6_jmulti_cili_granger_causality_dp_r.txt000066400000000000000000000004461400612667500365360ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 11:46:09 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 1.0026 pval-F( l; 4, 180) = 0.4076 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 1.2890 pval-Chi( c; 1) = 0.2562 vecm_e6_jmulti_cili_granger_causality_r_dp.txt000066400000000000000000000004461400612667500365360ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 11:46:25 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.3839 pval-F( l; 4, 180) = 0.0107 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 1.2890 pval-Chi( c; 1) = 0.2562 vecm_e6_jmulti_cili_inst_causality_dp_r.txt000077500000000000000000000004461400612667500360710ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:46:38 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 0.8349 pval-F( l; 3, 186) = 0.4763 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.8433 pval-Chi( c; 1) = 0.3585 vecm_e6_jmulti_cili_inst_causality_r_dp.txt000077500000000000000000000004461400612667500360710ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:46:24 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.6151 pval-F( l; 3, 186) = 0.0143 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.8433 pval-Chi( c; 1) = 0.3585 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cili_ir.txt000077500000000000000000000046111400612667500325210ustar00rootroot00000000000000*** Tue, 16 Aug 2016 19:31:54 *** VECM Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time Dp R Dp R ->Dp ->Dp ->R ->R point estimate 1.0000 0.0000 0.0000 1.0000 1 point estimate -0.1501 0.2253 0.1024 1.1402 2 point estimate -0.0882 0.2937 0.2236 1.0805 3 point estimate -0.0520 0.0776 0.3337 1.2212 4 point estimate 0.9222 0.1222 0.3824 1.2155 5 point estimate -0.1637 0.3425 0.4444 1.1338 6 point estimate -0.0817 0.3436 0.5159 1.0893 7 point estimate -0.0411 0.1253 0.5736 1.0432 8 point estimate 0.8937 0.1627 0.5645 0.9954 9 point estimate -0.1480 0.3537 0.5759 0.9541 10 point estimate -0.0607 0.3451 0.6057 0.9146 11 point estimate -0.0233 0.1333 0.6289 0.8921 12 point estimate 0.8683 0.1660 0.5966 0.8830 13 point estimate -0.1346 0.3460 0.5915 0.8691 14 point estimate -0.0442 0.3361 0.6091 0.8537 15 point estimate -0.0104 0.1337 0.6245 0.8530 16 point estimate 0.8399 0.1667 0.5900 0.8591 17 point estimate -0.1253 0.3389 0.5840 0.8562 18 point estimate -0.0314 0.3287 0.6008 0.8491 19 point estimate -0.0006 0.1361 0.6161 0.8533 20 point estimate 0.8109 0.1698 0.5842 0.8617 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cili_lagorder.txt000077500000000000000000000006661400612667500337140ustar00rootroot00000000000000*** Sun, 21 Aug 2016 09:35:07 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: Dp R deterministic variables: CONST TREND sample range: [1975 Q1, 1998 Q4], T = 96 optimal number of lags (searched up to 10 lags of 1. differences): Akaike Info Criterion: 3 Final Prediction Error: 3 Hannan-Quinn Criterion: 3 Schwarz Criterion: 3 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cis.txt000066400000000000000000000110561400612667500316630ustar00rootroot00000000000000*** Mon, 25 Jul 2016 14:16:09 *** VEC REPRESENTATION endogenous variables: Dp R exogenous variables: deterministic variables: CONST S1 S2 S3 endogenous lags (diffs): 3 exogenous lags: 0 sample range: [1973 Q2, 1998 Q4], T = 103 estimation procedure: One stage. Johansen approach Lagged endogenous term: ======================= d(Dp) d(R) ------------------------------ d(Dp)(t-1)| -0.334 -0.202 | (0.141) (0.150) | {0.018} {0.177} | [-2.364] [-1.350] d(R) (t-1)| 0.068 0.272 | (0.095) (0.101) | {0.474} {0.007} | [0.715] [2.709] d(Dp)(t-2)| -0.387 -0.218 | (0.114) (0.121) | {0.001} {0.072} | [-3.399] [-1.802] d(R) (t-2)| -0.003 -0.016 | (0.095) (0.101) | {0.975} {0.872} | [-0.032] [-0.162] d(Dp)(t-3)| -0.346 -0.106 | (0.076) (0.081) | {0.000} {0.193} | [-4.524] [-1.301] d(R) (t-3)| 0.020 0.225 | (0.092) (0.098) | {0.824} {0.021} | [0.222] [2.303] ------------------------------ Deterministic term: =================== d(Dp) d(R) ----------------------------- S1(t)| -0.034 0.002 | (0.005) (0.005) | {0.000} {0.750} | [-7.464] [0.318] S2(t)| -0.018 0.009 | (0.005) (0.005) | {0.000} {0.074} | [-3.814] [1.786] S3(t)| -0.016 0.000 | (0.005) (0.005) | {0.000} {0.934} | [-3.632] [-0.082] ----------------------------- Loading coefficients: ===================== d(Dp) d(R) ----------------------------- ec1(t-1)| -0.632 0.397 | (0.167) (0.177) | {0.000} {0.025} | [-3.791] [2.245] ----------------------------- Estimated cointegration relation(s): ==================================== ec1(t-1) ------------------- Dp(t-1)| 1.000 | (0.000) | {0.000} | [0.000] R (t-1)| -0.251 | (0.044) | {0.000} | [-5.671] CONST | 0.011 | (0.003) | {0.002} | [3.142] ------------------- VAR REPRESENTATION modulus of the eigenvalues of the reverse characteristic polynomial: |z| = ( 1.3732 1.2831 1.2831 1.0000 1.3977 1.3977 1.7293 1.7293 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= Dp R ----------------------------- Dp(t-1)| 0.034 0.195 | (0.218) (0.232) | {0.875} {0.401} | [0.157] [0.840] R (t-1)| 0.226 1.173 | (0.103) (0.110) | {0.029} {0.000} | [2.185] [10.671] Dp(t-2)| -0.054 -0.016 | (0.079) (0.084) | {0.499} {0.852} | [-0.677] [-0.186] R (t-2)| -0.071 -0.289 | (0.141) (0.150) | {0.616} {0.054} | [-0.502] [-1.931] Dp(t-3)| 0.042 0.112 | (0.079) (0.084) | {0.598} {0.181} | [0.527] [1.337] R (t-3)| 0.023 0.242 | (0.141) (0.150) | {0.868} {0.107} | [0.166] [1.613] Dp(t-4)| 0.346 0.106 | (0.076) (0.081) | {0.000} {0.193} | [4.524] [1.301] R (t-4)| -0.020 -0.225 | (0.092) (0.098) | {0.824} {0.021} | [-0.222] [-2.303] ----------------------------- Deterministic term: =================== Dp R ----------------------------- S1 (t)| -0.034 0.002 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] S2 (t)| -0.018 0.009 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] S3 (t)| -0.016 0.000 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] CONST | -0.007 0.004 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] ----------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cis_Sigmau.txt000066400000000000000000000005631400612667500331710ustar00rootroot00000000000000*** Mon, 25 Jul 2016 14:16:09 *** VECM MODEL STATISTICS sample range: [1973 Q2, 1998 Q4], T = 103 Log Likelihood: 7.936180e+02 Determinant (Cov): 5.983229e-10 Covariance: 2.307334e-05 -1.398990e-06 -1.398990e-06 2.601618e-05 Correlation: 1.000000e+00 -5.710022e-02 -5.710022e-02 1.000000e+00 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cis_diag.txt000066400000000000000000000034331400612667500326470ustar00rootroot00000000000000*** Mon, 25 Jul 2016 13:46:16 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) tested order: 16 test statistic: 47.3961 p-value: 0.5785 adjusted test statistic: 52.9667 p-value: 0.3604 degrees of freedom: 50.0000 *** Mon, 25 Jul 2016 13:46:16 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags LM statistic: 15.6596 p-value: 0.7375 df: 20.0000 *** Mon, 25 Jul 2016 13:46:16 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 2.3854 p-value: 0.6653 degrees of freedom: 4.0000 skewness only: 0.2816 p-value: 0.8687 kurtosis only: 2.1038 p-value: 0.3493 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 2.1178 p-value: 0.7141 degrees of freedom: 4.0000 skewness only: 0.3071 p-value: 0.8577 kurtosis only: 1.8107 p-value: 0.4044 *** Mon, 25 Jul 2016 13:46:16 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 0.5789 0.7487 -0.0320 2.6383 u2 2.1556 0.3403 -0.1199 3.6669 *** Mon, 25 Jul 2016 13:46:16 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 15.5911 0.4818 1.1872 0.2999 u2 26.4160 0.0484 2.3709 0.0070 *** Mon, 25 Jul 2016 13:46:16 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 77.5396 p-value(chi^2): 0.0018 degrees of freedom: 45.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cis_fc5.txt000077500000000000000000000020531400612667500324200ustar00rootroot00000000000000*** Thu, 28 Jul 2016 16:42:33 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals Dp time forecast lower CI upper CI +/- 1999 Q1 -0.0224 -0.0318 -0.0129 0.0094 1999 Q2 -0.0039 -0.0136 0.0058 0.0097 1999 Q3 0.0033 -0.0066 0.0132 0.0099 1999 Q4 0.0244 0.0143 0.0345 0.0101 2000 Q1 -0.0249 -0.0359 -0.0139 0.0110 R time forecast lower CI upper CI +/- 1999 Q1 0.0396 0.0296 0.0496 0.0100 1999 Q2 0.0408 0.0253 0.0562 0.0154 1999 Q3 0.0402 0.0210 0.0594 0.0192 1999 Q4 0.0388 0.0158 0.0619 0.0231 2000 Q1 0.0400 0.0134 0.0666 0.0266 vecm_e6_jmulti_cis_granger_causality_dp_r.txt000066400000000000000000000004461400612667500363740ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 11:30:46 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 0.7474 pval-F( l; 4, 176) = 0.5610 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.4071 pval-Chi( c; 1) = 0.5235 vecm_e6_jmulti_cis_granger_causality_r_dp.txt000066400000000000000000000004461400612667500363740ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 11:30:58 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.5314 pval-F( l; 4, 176) = 0.0084 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.4071 pval-Chi( c; 1) = 0.5235 vecm_e6_jmulti_cis_inst_causality_dp_r.txt000077500000000000000000000004461400612667500357270ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:47:54 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 2.1104 pval-F( l; 3, 182) = 0.1005 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.6068 pval-Chi( c; 1) = 0.4360 vecm_e6_jmulti_cis_inst_causality_r_dp.txt000077500000000000000000000004461400612667500357270ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:47:43 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 4.2498 pval-F( l; 3, 182) = 0.0063 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.6068 pval-Chi( c; 1) = 0.4360 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cis_ir.txt000077500000000000000000000046111400612667500323570ustar00rootroot00000000000000*** Tue, 16 Aug 2016 19:30:53 *** VECM Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time Dp R Dp R ->Dp ->Dp ->R ->R point estimate 1.0000 0.0000 0.0000 1.0000 1 point estimate 0.0343 0.2262 0.1949 1.1727 2 point estimate -0.0083 0.2023 0.2196 1.1306 3 point estimate 0.0755 0.1911 0.3116 1.2648 4 point estimate 0.4097 0.2183 0.4733 1.2744 5 point estimate 0.1077 0.2852 0.5556 1.2246 6 point estimate 0.0771 0.2694 0.5629 1.2141 7 point estimate 0.1328 0.2612 0.6113 1.1860 8 point estimate 0.2484 0.2670 0.6620 1.1509 9 point estimate 0.1502 0.2849 0.6771 1.1331 10 point estimate 0.1332 0.2774 0.6723 1.1187 11 point estimate 0.1600 0.2713 0.6807 1.1029 12 point estimate 0.1993 0.2720 0.6909 1.0937 13 point estimate 0.1658 0.2773 0.6907 1.0893 14 point estimate 0.1573 0.2742 0.6848 1.0857 15 point estimate 0.1685 0.2714 0.6847 1.0829 16 point estimate 0.1817 0.2716 0.6865 1.0818 17 point estimate 0.1699 0.2734 0.6852 1.0817 18 point estimate 0.1660 0.2723 0.6824 1.0818 19 point estimate 0.1704 0.2713 0.6819 1.0817 20 point estimate 0.1749 0.2715 0.6825 1.0819 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cis_lagorder.txt000077500000000000000000000006711400612667500335460ustar00rootroot00000000000000*** Sun, 21 Aug 2016 09:36:02 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: Dp R deterministic variables: CONST S1 S2 S3 sample range: [1975 Q1, 1998 Q4], T = 96 optimal number of lags (searched up to 10 lags of 1. differences): Akaike Info Criterion: 3 Final Prediction Error: 3 Hannan-Quinn Criterion: 0 Schwarz Criterion: 0 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cisli.txt000066400000000000000000000116271400612667500322140ustar00rootroot00000000000000*** Mon, 25 Jul 2016 14:20:40 *** VEC REPRESENTATION endogenous variables: Dp R exogenous variables: deterministic variables: CONST S1 S2 S3 TREND endogenous lags (diffs): 3 exogenous lags: 0 sample range: [1973 Q2, 1998 Q4], T = 103 estimation procedure: One stage. Johansen approach Lagged endogenous term: ======================= d(Dp) d(R) ------------------------------ d(Dp)(t-1)| -0.296 -0.185 | (0.145) (0.156) | {0.042} {0.236} | [-2.034] [-1.184] d(R) (t-1)| 0.063 0.265 | (0.094) (0.101) | {0.502} {0.009} | [0.672] [2.624] d(Dp)(t-2)| -0.362 -0.206 | (0.116) (0.125) | {0.002} {0.097} | [-3.114] [-1.657] d(R) (t-2)| -0.004 -0.023 | (0.095) (0.102) | {0.969} {0.819} | [-0.039] [-0.229] d(Dp)(t-3)| -0.333 -0.100 | (0.077) (0.083) | {0.000} {0.225} | [-4.328] [-1.215] d(R) (t-3)| 0.022 0.218 | (0.091) (0.098) | {0.808} {0.026} | [0.243] [2.229] ------------------------------ Deterministic term: =================== d(Dp) d(R) ----------------------------- S1(t)| -0.034 0.002 | (0.005) (0.005) | {0.000} {0.746} | [-7.490] [0.324] S2(t)| -0.018 0.009 | (0.005) (0.005) | {0.000} {0.074} | [-3.840] [1.788] S3(t)| -0.016 0.000 | (0.005) (0.005) | {0.000} {0.939} | [-3.641] [-0.077] ----------------------------- Loading coefficients: ===================== d(Dp) d(R) ----------------------------- ec1(t-1)| -0.684 0.374 | (0.174) (0.186) | {0.000} {0.044} | [-3.940] [2.011] ----------------------------- Estimated cointegration relation(s): ==================================== ec1(t-1) -------------------- Dp(t-1) | 1.000 | (0.000) | {0.000} | [0.000] R (t-1) | -0.229 | (0.052) | {0.000} | [-4.395] CONST | 0.008 | (0.005) | {0.090} | [1.693] TREND(t-1)| 0.000 | (0.000) | {0.642} | [0.466] -------------------- VAR REPRESENTATION modulus of the eigenvalues of the reverse characteristic polynomial: |z| = ( 1.3775 1.2878 1.2878 1.7459 1.7459 1.0000 1.4263 1.4263 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= Dp R ----------------------------- Dp(t-1)| 0.020 0.190 | (0.226) (0.243) | {0.929} {0.435} | [0.089] [0.781] R (t-1)| 0.220 1.179 | (0.102) (0.110) | {0.032} {0.000} | [2.148] [10.758] Dp(t-2)| -0.066 -0.022 | (0.080) (0.085) | {0.408} {0.799} | [-0.827] [-0.255] R (t-2)| -0.067 -0.288 | (0.140) (0.150) | {0.633} {0.055} | [-0.478] [-1.918] Dp(t-3)| 0.029 0.106 | (0.080) (0.086) | {0.721} {0.215} | [0.357] [1.239] R (t-3)| 0.026 0.242 | (0.140) (0.151) | {0.854} {0.108} | [0.184] [1.606] Dp(t-4)| 0.333 0.100 | (0.077) (0.083) | {0.000} {0.225} | [4.328] [1.215] R (t-4)| -0.022 -0.218 | (0.091) (0.098) | {0.808} {0.026} | [-0.243] [-2.229] ----------------------------- Deterministic term: =================== Dp R --------------------------------- S1 (t)| -0.034 0.002 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] S2 (t)| -0.018 0.009 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] S3 (t)| -0.016 0.000 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] CONST (t)| -0.006 0.003 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] TREND(t-1)(t)| 0.000 0.000 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] --------------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cisli_Sigmau.txt000066400000000000000000000005631400612667500335160ustar00rootroot00000000000000*** Mon, 25 Jul 2016 14:20:40 *** VECM MODEL STATISTICS sample range: [1973 Q2, 1998 Q4], T = 103 Log Likelihood: 7.936778e+02 Determinant (Cov): 5.976211e-10 Covariance: 2.284983e-05 -1.539185e-06 -1.539185e-06 2.625798e-05 Correlation: 1.000000e+00 -6.283749e-02 -6.283749e-02 1.000000e+00 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cisli_diag.txt000066400000000000000000000034331400612667500331740ustar00rootroot00000000000000*** Mon, 25 Jul 2016 11:41:17 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) tested order: 16 test statistic: 47.0532 p-value: 0.5924 adjusted test statistic: 52.6125 p-value: 0.3732 degrees of freedom: 50.0000 *** Mon, 25 Jul 2016 11:41:17 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags LM statistic: 15.5903 p-value: 0.7417 df: 20.0000 *** Mon, 25 Jul 2016 11:41:17 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 2.1348 p-value: 0.7110 degrees of freedom: 4.0000 skewness only: 0.2728 p-value: 0.8725 kurtosis only: 1.8620 p-value: 0.3942 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 1.8624 p-value: 0.7610 degrees of freedom: 4.0000 skewness only: 0.2989 p-value: 0.8612 kurtosis only: 1.5636 p-value: 0.4576 *** Mon, 25 Jul 2016 11:41:17 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 0.5197 0.7712 -0.0429 2.6627 u2 1.9722 0.3730 -0.1153 3.6375 *** Mon, 25 Jul 2016 11:41:17 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 14.8383 0.5365 1.1181 0.3563 u2 26.3504 0.0493 2.3624 0.0072 *** Mon, 25 Jul 2016 11:41:17 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 75.1732 p-value(chi^2): 0.0032 degrees of freedom: 45.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cisli_fc5.txt000077500000000000000000000020531400612667500327450ustar00rootroot00000000000000*** Thu, 28 Jul 2016 16:44:02 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals Dp time forecast lower CI upper CI +/- 1999 Q1 -0.0224 -0.0318 -0.0131 0.0094 1999 Q2 -0.0039 -0.0136 0.0057 0.0096 1999 Q3 0.0033 -0.0065 0.0131 0.0098 1999 Q4 0.0244 0.0143 0.0344 0.0100 2000 Q1 -0.0250 -0.0358 -0.0141 0.0108 R time forecast lower CI upper CI +/- 1999 Q1 0.0396 0.0295 0.0496 0.0100 1999 Q2 0.0407 0.0251 0.0562 0.0155 1999 Q3 0.0400 0.0207 0.0594 0.0194 1999 Q4 0.0386 0.0153 0.0619 0.0233 2000 Q1 0.0397 0.0128 0.0667 0.0270 vecm_e6_jmulti_cisli_granger_causality_dp_r.txt000066400000000000000000000004461400612667500367210ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 11:42:24 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 0.4480 pval-F( l; 4, 174) = 0.7738 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.6101 pval-Chi( c; 1) = 0.4348 vecm_e6_jmulti_cisli_granger_causality_r_dp.txt000066400000000000000000000004461400612667500367210ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 11:42:07 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.0268 pval-F( l; 4, 174) = 0.0191 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.6101 pval-Chi( c; 1) = 0.4348 vecm_e6_jmulti_cisli_inst_causality_dp_r.txt000077500000000000000000000004461400612667500362540ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:47:09 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 1.4258 pval-F( l; 3, 180) = 0.2368 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.9332 pval-Chi( c; 1) = 0.3340 vecm_e6_jmulti_cisli_inst_causality_r_dp.txt000077500000000000000000000004461400612667500362540ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:47:23 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.6535 pval-F( l; 3, 180) = 0.0137 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.9332 pval-Chi( c; 1) = 0.3340 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cisli_ir.txt000077500000000000000000000046111400612667500327040ustar00rootroot00000000000000*** Tue, 16 Aug 2016 19:31:35 *** VECM Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time Dp R Dp R ->Dp ->Dp ->R ->R point estimate 1.0000 0.0000 0.0000 1.0000 1 point estimate 0.0202 0.2197 0.1896 1.1795 2 point estimate -0.0238 0.1966 0.2057 1.1445 3 point estimate 0.0592 0.1878 0.2892 1.2841 4 point estimate 0.3913 0.2109 0.4418 1.3058 5 point estimate 0.0888 0.2751 0.5184 1.2677 6 point estimate 0.0570 0.2614 0.5212 1.2663 7 point estimate 0.1110 0.2544 0.5652 1.2480 8 point estimate 0.2243 0.2592 0.6137 1.2209 9 point estimate 0.1274 0.2769 0.6287 1.2083 10 point estimate 0.1100 0.2708 0.6241 1.1982 11 point estimate 0.1356 0.2656 0.6327 1.1857 12 point estimate 0.1737 0.2662 0.6435 1.1782 13 point estimate 0.1414 0.2715 0.6446 1.1747 14 point estimate 0.1330 0.2690 0.6398 1.1717 15 point estimate 0.1435 0.2666 0.6402 1.1690 16 point estimate 0.1563 0.2667 0.6426 1.1678 17 point estimate 0.1452 0.2685 0.6420 1.1674 18 point estimate 0.1414 0.2676 0.6396 1.1672 19 point estimate 0.1455 0.2667 0.6394 1.1670 20 point estimate 0.1498 0.2668 0.6401 1.1669 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cisli_lagorder.txt000077500000000000000000000006771400612667500341010ustar00rootroot00000000000000*** Sun, 21 Aug 2016 09:35:29 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: Dp R deterministic variables: CONST S1 S2 S3 TREND sample range: [1975 Q1, 1998 Q4], T = 96 optimal number of lags (searched up to 10 lags of 1. differences): Akaike Info Criterion: 3 Final Prediction Error: 3 Hannan-Quinn Criterion: 0 Schwarz Criterion: 0 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_co.txt000066400000000000000000000075451400612667500315160ustar00rootroot00000000000000*** Tue, 21 Jun 2016 11:28:38 *** VEC REPRESENTATION endogenous variables: Dp R exogenous variables: deterministic variables: CONST endogenous lags (diffs): 3 exogenous lags: 0 sample range: [1973 Q2, 1998 Q4], T = 103 estimation procedure: One stage. Johansen approach Lagged endogenous term: ======================= d(Dp) d(R) ------------------------------ d(Dp)(t-1)| -0.515 -0.321 | (0.153) (0.133) | {0.001} {0.016} | [-3.359] [-2.418] d(R) (t-1)| 0.045 0.253 | (0.117) (0.101) | {0.701} {0.012} | [0.384] [2.507] d(Dp)(t-2)| -0.655 -0.200 | (0.105) (0.091) | {0.000} {0.028} | [-6.239] [-2.202] d(R) (t-2)| 0.118 0.013 | (0.116) (0.101) | {0.308} {0.900} | [1.019] [0.126] d(Dp)(t-3)| -0.803 -0.070 | (0.056) (0.048) | {0.000} {0.146} | [-14.446] [-1.453] d(R) (t-3)| -0.053 0.220 | (0.114) (0.098) | {0.640} {0.025} | [-0.468] [2.238] ------------------------------ Deterministic term: =================== d(Dp) d(R) ----------------------------- CONST | -0.008 0.005 | (0.003) (0.002) | {0.001} {0.028} | [-3.207] [2.196] ----------------------------- Loading coefficients: ===================== d(Dp) d(R) ----------------------------- ec1(t-1)| -0.640 0.423 | (0.201) (0.174) | {0.001} {0.015} | [-3.183] [2.426] ----------------------------- Estimated cointegration relation(s): ==================================== ec1(t-1) ------------------- Dp(t-1)| 1.000 | (0.000) | {0.000} | [0.000] R (t-1)| -0.273 | (0.050) | {0.000} | [-5.422] ------------------- VAR REPRESENTATION modulus of the eigenvalues of the reverse characteristic polynomial: |z| = ( 1.0095 1.0117 1.0117 1.0000 1.3347 1.3347 1.7356 1.7356 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= Dp R ----------------------------- Dp(t-1)| -0.156 0.101 | (0.253) (0.219) | {0.538} {0.644} | [-0.615] [0.463] R (t-1)| 0.220 1.138 | (0.129) (0.112) | {0.088} {0.000} | [1.705] [10.193] Dp(t-2)| -0.139 0.121 | (0.056) (0.049) | {0.013} {0.013} | [-2.482] [2.497] R (t-2)| 0.074 -0.240 | (0.170) (0.147) | {0.664} {0.102} | [0.434] [-1.635] Dp(t-3)| -0.148 0.130 | (0.056) (0.049) | {0.009} {0.008} | [-2.624] [2.660] R (t-3)| -0.172 0.207 | (0.170) (0.147) | {0.312} {0.159} | [-1.011] [1.410] Dp(t-4)| 0.803 0.070 | (0.056) (0.048) | {0.000} {0.146} | [14.446] [1.453] R (t-4)| 0.053 -0.220 | (0.114) (0.098) | {0.640} {0.025} | [0.468] [-2.238] ----------------------------- Deterministic term: =================== Dp R ----------------------------- CONST | -0.008 0.005 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] ----------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_co_Sigmau.txt000066400000000000000000000005631400612667500330140ustar00rootroot00000000000000*** Tue, 21 Jun 2016 11:28:38 *** VECM MODEL STATISTICS sample range: [1973 Q2, 1998 Q4], T = 103 Log Likelihood: 7.697274e+02 Determinant (Cov): 9.558234e-10 Covariance: 3.576095e-05 -1.831235e-06 -1.831235e-06 2.682190e-05 Correlation: 1.000000e+00 -5.912821e-02 -5.912821e-02 1.000000e+00 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_co_diag.txt000066400000000000000000000034331400612667500324720ustar00rootroot00000000000000*** Mon, 25 Jul 2016 13:41:39 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) tested order: 16 test statistic: 47.5770 p-value: 0.5712 adjusted test statistic: 52.5065 p-value: 0.3771 degrees of freedom: 50.0000 *** Mon, 25 Jul 2016 13:41:39 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags LM statistic: 22.9164 p-value: 0.2929 df: 20.0000 *** Mon, 25 Jul 2016 13:41:39 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 0.6897 p-value: 0.9526 degrees of freedom: 4.0000 skewness only: 0.1654 p-value: 0.9206 kurtosis only: 0.5243 p-value: 0.7694 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 0.5506 p-value: 0.9684 degrees of freedom: 4.0000 skewness only: 0.1476 p-value: 0.9288 kurtosis only: 0.4030 p-value: 0.8175 *** Mon, 25 Jul 2016 13:41:39 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 0.1473 0.9290 0.0926 3.0035 u2 0.6764 0.7130 0.0088 3.3966 *** Mon, 25 Jul 2016 13:41:39 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 18.8623 0.2759 1.5052 0.1226 u2 27.0631 0.0408 2.4552 0.0052 *** Mon, 25 Jul 2016 13:41:39 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 73.3027 p-value(chi^2): 0.0049 degrees of freedom: 45.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_co_fc5.txt000077500000000000000000000020531400612667500322430ustar00rootroot00000000000000*** Thu, 28 Jul 2016 16:36:26 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals Dp time forecast lower CI upper CI +/- 1999 Q1 -0.0178 -0.0295 -0.0061 0.0117 1999 Q2 -0.0038 -0.0159 0.0083 0.0121 1999 Q3 0.0006 -0.0119 0.0131 0.0125 1999 Q4 0.0212 0.0086 0.0337 0.0125 2000 Q1 -0.0183 -0.0348 -0.0018 0.0165 R time forecast lower CI upper CI +/- 1999 Q1 0.0390 0.0289 0.0492 0.0102 1999 Q2 0.0395 0.0241 0.0548 0.0154 1999 Q3 0.0399 0.0210 0.0589 0.0189 1999 Q4 0.0394 0.0166 0.0622 0.0228 2000 Q1 0.0401 0.0140 0.0663 0.0261 vecm_e6_jmulti_co_granger_causality_dp_r.txt000066400000000000000000000004461400612667500362170ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 10:26:21 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 1.4382 pval-F( l; 4, 182) = 0.2231 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.9998 pval-Chi( c; 1) = 0.3174 vecm_e6_jmulti_co_granger_causality_r_dp.txt000066400000000000000000000004461400612667500362170ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 10:26:53 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.8185 pval-F( l; 4, 182) = 0.0053 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.9998 pval-Chi( c; 1) = 0.3174 vecm_e6_jmulti_co_inst_causality_dp_r.txt000077500000000000000000000004461400612667500355520ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:40:32 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 1.7371 pval-F( l; 3, 188) = 0.1609 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.5489 pval-Chi( c; 1) = 0.4588 vecm_e6_jmulti_co_inst_causality_r_dp.txt000077500000000000000000000004461400612667500355520ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:40:16 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 4.1789 pval-F( l; 3, 188) = 0.0068 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.5489 pval-Chi( c; 1) = 0.4588 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_co_ir.txt000077500000000000000000000046111400612667500322020ustar00rootroot00000000000000*** Tue, 16 Aug 2016 19:24:50 *** VECM Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time Dp R Dp R ->Dp ->Dp ->R ->R point estimate 1.0000 0.0000 0.0000 1.0000 1 point estimate -0.1556 0.2197 0.1013 1.1377 2 point estimate -0.0928 0.2894 0.2208 1.0761 3 point estimate -0.0561 0.0730 0.3287 1.2140 4 point estimate 0.9185 0.1197 0.3746 1.2094 5 point estimate -0.1723 0.3356 0.4339 1.1308 6 point estimate -0.0890 0.3390 0.5033 1.0889 7 point estimate -0.0476 0.1208 0.5593 1.0463 8 point estimate 0.8881 0.1606 0.5491 1.0023 9 point estimate -0.1582 0.3479 0.5597 0.9642 10 point estimate -0.0693 0.3417 0.5892 0.9275 11 point estimate -0.0308 0.1300 0.6125 0.9072 12 point estimate 0.8619 0.1650 0.5804 0.8995 13 point estimate -0.1453 0.3413 0.5756 0.8867 14 point estimate -0.0530 0.3336 0.5936 0.8719 15 point estimate -0.0182 0.1311 0.6095 0.8714 16 point estimate 0.8333 0.1663 0.5754 0.8774 17 point estimate -0.1359 0.3349 0.5697 0.8744 18 point estimate -0.0403 0.3266 0.5868 0.8672 19 point estimate -0.0084 0.1338 0.6024 0.8711 20 point estimate 0.8044 0.1694 0.5706 0.8791 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_co_lagorder.txt000077500000000000000000000006601400612667500333670ustar00rootroot00000000000000*** Sun, 21 Aug 2016 09:33:20 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: Dp R deterministic variables: CONST sample range: [1975 Q1, 1998 Q4], T = 96 optimal number of lags (searched up to 10 lags of 1. differences): Akaike Info Criterion: 3 Final Prediction Error: 3 Hannan-Quinn Criterion: 3 Schwarz Criterion: 3 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_colo.txt000066400000000000000000000101431400612667500320350ustar00rootroot00000000000000*** Tue, 21 Jun 2016 11:34:28 *** VEC REPRESENTATION endogenous variables: Dp R exogenous variables: deterministic variables: CONST TREND endogenous lags (diffs): 3 exogenous lags: 0 sample range: [1973 Q2, 1998 Q4], T = 103 estimation procedure: One stage. Johansen approach Lagged endogenous term: ======================= d(Dp) d(R) ------------------------------ d(Dp)(t-1)| -0.519 -0.318 | (0.154) (0.133) | {0.001} {0.017} | [-3.377] [-2.395] d(R) (t-1)| 0.044 0.252 | (0.117) (0.101) | {0.707} {0.013} | [0.376] [2.482] d(Dp)(t-2)| -0.657 -0.198 | (0.105) (0.091) | {0.000} {0.029} | [-6.254] [-2.180] d(R) (t-2)| 0.118 0.012 | (0.117) (0.101) | {0.313} {0.908} | [1.008] [0.115] d(Dp)(t-3)| -0.804 -0.069 | (0.056) (0.048) | {0.000} {0.151} | [-14.467] [-1.437] d(R) (t-3)| -0.055 0.219 | (0.114) (0.099) | {0.633} {0.026} | [-0.478] [2.221] ------------------------------ Deterministic term: =================== d(Dp) d(R) ----------------------------- CONST | -0.008 0.005 | (0.003) (0.002) | {0.003} {0.028} | [-3.011] [2.195] TREND(t)| 0.000 0.000 | (0.000) (0.000) | {0.937} {0.791} | [-0.080] [-0.264] ----------------------------- Loading coefficients: ===================== d(Dp) d(R) ----------------------------- ec1(t-1)| -0.635 0.419 | (0.201) (0.174) | {0.002} {0.016} | [-3.154] [2.402] ----------------------------- Estimated cointegration relation(s): ==================================== ec1(t-1) ------------------- Dp(t-1)| 1.000 | (0.000) | {0.000} | [0.000] R (t-1)| -0.276 | (0.063) | {0.000} | [-4.400] ------------------- VAR REPRESENTATION modulus of the eigenvalues of the reverse characteristic polynomial: |z| = ( 1.0094 1.0116 1.0116 1.0000 1.3356 1.3356 1.7369 1.7369 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= Dp R ----------------------------- Dp(t-1)| -0.154 0.100 | (0.253) (0.219) | {0.542} {0.647} | [-0.609] [0.458] R (t-1)| 0.220 1.136 | (0.130) (0.112) | {0.090} {0.000} | [1.693] [10.121] Dp(t-2)| -0.138 0.120 | (0.056) (0.049) | {0.014} {0.013} | [-2.456] [2.473] R (t-2)| 0.074 -0.240 | (0.170) (0.147) | {0.665} {0.102} | [0.433] [-1.633] Dp(t-3)| -0.147 0.129 | (0.057) (0.049) | {0.009} {0.008} | [-2.597] [2.635] R (t-3)| -0.172 0.207 | (0.170) (0.147) | {0.311} {0.158} | [-1.013] [1.411] Dp(t-4)| 0.804 0.069 | (0.056) (0.048) | {0.000} {0.151} | [14.467] [1.437] R (t-4)| 0.055 -0.219 | (0.114) (0.099) | {0.633} {0.026} | [0.478] [-2.221] ----------------------------- Deterministic term: =================== Dp R ----------------------------- CONST | -0.008 0.005 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] TREND(t)| 0.000 0.000 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] ----------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_colo_Sigmau.txt000066400000000000000000000005631400612667500333470ustar00rootroot00000000000000*** Tue, 21 Jun 2016 11:34:28 *** VECM MODEL STATISTICS sample range: [1973 Q2, 1998 Q4], T = 103 Log Likelihood: 7.697651e+02 Determinant (Cov): 9.551175e-10 Covariance: 3.579404e-05 -1.829322e-06 -1.829322e-06 2.677719e-05 Correlation: 1.000000e+00 -5.908841e-02 -5.908841e-02 1.000000e+00 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_colo_diag.txt000066400000000000000000000034331400612667500330250ustar00rootroot00000000000000*** Mon, 25 Jul 2016 13:46:58 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) tested order: 16 test statistic: 47.6914 p-value: 0.5665 adjusted test statistic: 52.6457 p-value: 0.3720 degrees of freedom: 50.0000 *** Mon, 25 Jul 2016 13:46:58 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags LM statistic: 23.0235 p-value: 0.2876 df: 20.0000 *** Mon, 25 Jul 2016 13:46:58 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 0.6397 p-value: 0.9586 degrees of freedom: 4.0000 skewness only: 0.1148 p-value: 0.9442 kurtosis only: 0.5248 p-value: 0.7692 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 0.5085 p-value: 0.9727 degrees of freedom: 4.0000 skewness only: 0.1036 p-value: 0.9495 kurtosis only: 0.4049 p-value: 0.8167 *** Mon, 25 Jul 2016 13:46:58 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 0.0980 0.9522 0.0756 3.0028 u2 0.6770 0.7128 -0.0133 3.3963 *** Mon, 25 Jul 2016 13:46:58 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 19.1284 0.2621 1.5325 0.1129 u2 26.9344 0.0422 2.4383 0.0055 *** Mon, 25 Jul 2016 13:46:58 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 73.4375 p-value(chi^2): 0.0047 degrees of freedom: 45.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_colo_fc5.txt000077500000000000000000000020531400612667500325760ustar00rootroot00000000000000*** Thu, 28 Jul 2016 16:38:11 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals Dp time forecast lower CI upper CI +/- 1999 Q1 -0.0179 -0.0297 -0.0062 0.0117 1999 Q2 -0.0040 -0.0161 0.0081 0.0121 1999 Q3 0.0004 -0.0121 0.0129 0.0125 1999 Q4 0.0210 0.0084 0.0335 0.0125 2000 Q1 -0.0187 -0.0352 -0.0022 0.0165 R time forecast lower CI upper CI +/- 1999 Q1 0.0388 0.0287 0.0490 0.0101 1999 Q2 0.0390 0.0237 0.0544 0.0153 1999 Q3 0.0392 0.0203 0.0581 0.0189 1999 Q4 0.0384 0.0157 0.0611 0.0227 2000 Q1 0.0388 0.0128 0.0648 0.0260 vecm_e6_jmulti_colo_granger_causality_dp_r.txt000066400000000000000000000004461400612667500365520ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 13:47:29 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 1.0026 pval-F( l; 4, 180) = 0.4076 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 1.2890 pval-Chi( c; 1) = 0.2562 vecm_e6_jmulti_colo_granger_causality_r_dp.txt000066400000000000000000000004461400612667500365520ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 10:58:59 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.3839 pval-F( l; 4, 180) = 0.0107 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 1.2890 pval-Chi( c; 1) = 0.2562 vecm_e6_jmulti_colo_inst_causality_dp_r.txt000077500000000000000000000004461400612667500361050ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:40:57 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 0.8349 pval-F( l; 3, 186) = 0.4763 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.8433 pval-Chi( c; 1) = 0.3585 vecm_e6_jmulti_colo_inst_causality_r_dp.txt000077500000000000000000000004461400612667500361050ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:41:11 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.6151 pval-F( l; 3, 186) = 0.0143 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.8433 pval-Chi( c; 1) = 0.3585 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_colo_ir.txt000077500000000000000000000046111400612667500325350ustar00rootroot00000000000000*** Tue, 16 Aug 2016 19:25:18 *** VECM Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time Dp R Dp R ->Dp ->Dp ->R ->R point estimate 1.0000 0.0000 0.0000 1.0000 1 point estimate -0.1544 0.2197 0.1003 1.1359 2 point estimate -0.0922 0.2892 0.2187 1.0723 3 point estimate -0.0561 0.0720 0.3256 1.2083 4 point estimate 0.9185 0.1200 0.3706 1.2021 5 point estimate -0.1714 0.3360 0.4291 1.1223 6 point estimate -0.0888 0.3390 0.4977 1.0794 7 point estimate -0.0479 0.1202 0.5530 1.0363 8 point estimate 0.8878 0.1611 0.5424 0.9920 9 point estimate -0.1577 0.3484 0.5526 0.9538 10 point estimate -0.0693 0.3418 0.5819 0.9170 11 point estimate -0.0314 0.1295 0.6050 0.8968 12 point estimate 0.8615 0.1656 0.5729 0.8893 13 point estimate -0.1449 0.3419 0.5681 0.8766 14 point estimate -0.0531 0.3338 0.5860 0.8619 15 point estimate -0.0188 0.1307 0.6019 0.8616 16 point estimate 0.8330 0.1669 0.5679 0.8676 17 point estimate -0.1356 0.3354 0.5622 0.8647 18 point estimate -0.0404 0.3268 0.5793 0.8575 19 point estimate -0.0090 0.1334 0.5948 0.8614 20 point estimate 0.8042 0.1699 0.5632 0.8695 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_colo_lagorder.txt000077500000000000000000000006661400612667500337300ustar00rootroot00000000000000*** Sun, 21 Aug 2016 09:34:48 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: Dp R deterministic variables: CONST TREND sample range: [1975 Q1, 1998 Q4], T = 96 optimal number of lags (searched up to 10 lags of 1. differences): Akaike Info Criterion: 3 Final Prediction Error: 3 Hannan-Quinn Criterion: 3 Schwarz Criterion: 3 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cos.txt000066400000000000000000000111261400612667500316670ustar00rootroot00000000000000*** Tue, 21 Jun 2016 11:30:21 *** VEC REPRESENTATION endogenous variables: Dp R exogenous variables: deterministic variables: CONST S1 S2 S3 endogenous lags (diffs): 3 exogenous lags: 0 sample range: [1973 Q2, 1998 Q4], T = 103 estimation procedure: One stage. Johansen approach Lagged endogenous term: ======================= d(Dp) d(R) ------------------------------ d(Dp)(t-1)| -0.339 -0.210 | (0.141) (0.149) | {0.016} {0.159} | [-2.404] [-1.407] d(R) (t-1)| 0.065 0.269 | (0.095) (0.100) | {0.490} {0.007} | [0.690] [2.678] d(Dp)(t-2)| -0.391 -0.223 | (0.114) (0.121) | {0.001} {0.064} | [-3.432] [-1.849] d(R) (t-2)| -0.004 -0.018 | (0.095) (0.101) | {0.964} {0.860} | [-0.045] [-0.176] d(Dp)(t-3)| -0.347 -0.108 | (0.076) (0.081) | {0.000} {0.183} | [-4.549] [-1.332] d(R) (t-3)| 0.018 0.223 | (0.092) (0.098) | {0.842} {0.022} | [0.200] [2.284] ------------------------------ Deterministic term: =================== d(Dp) d(R) ----------------------------- CONST | -0.007 0.004 | (0.002) (0.002) | {0.000} {0.040} | [-3.801] [2.054] S1 (t)| -0.034 0.001 | (0.005) (0.005) | {0.000} {0.759} | [-7.474] [0.307] S2 (t)| -0.018 0.009 | (0.005) (0.005) | {0.000} {0.074} | [-3.821] [1.784] S3 (t)| -0.016 0.000 | (0.005) (0.005) | {0.000} {0.931} | [-3.636] [-0.086] ----------------------------- Loading coefficients: ===================== d(Dp) d(R) ----------------------------- ec1(t-1)| -0.625 0.408 | (0.167) (0.176) | {0.000} {0.021} | [-3.752] [2.312] ----------------------------- Estimated cointegration relation(s): ==================================== ec1(t-1) ------------------- Dp(t-1)| 1.000 | (0.000) | {0.000} | [0.000] R (t-1)| -0.252 | (0.044) | {0.000} | [-5.697] ------------------- VAR REPRESENTATION modulus of the eigenvalues of the reverse characteristic polynomial: |z| = ( 1.3729 1.0000 1.4004 1.4004 1.2824 1.2824 1.7310 1.7310 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= Dp R ----------------------------- Dp(t-1)| 0.036 0.197 | (0.218) (0.231) | {0.869} {0.393} | [0.165] [0.854] R (t-1)| 0.223 1.166 | (0.104) (0.110) | {0.031} {0.000} | [2.152] [10.621] Dp(t-2)| -0.052 -0.013 | (0.079) (0.084) | {0.514} {0.879} | [-0.653] [-0.152] R (t-2)| -0.070 -0.287 | (0.141) (0.149) | {0.621} {0.055} | [-0.495] [-1.923] Dp(t-3)| 0.044 0.115 | (0.079) (0.084) | {0.582} {0.169} | [0.551] [1.376] R (t-3)| 0.023 0.241 | (0.141) (0.149) | {0.872} {0.107} | [0.161] [1.612] Dp(t-4)| 0.347 0.108 | (0.076) (0.081) | {0.000} {0.183} | [4.549] [1.332] R (t-4)| -0.018 -0.223 | (0.092) (0.098) | {0.842} {0.022} | [-0.200] [-2.284] ----------------------------- Deterministic term: =================== Dp R ----------------------------- CONST | -0.007 0.004 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] S1 (t)| -0.034 0.001 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] S2 (t)| -0.018 0.009 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] S3 (t)| -0.016 0.000 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] ----------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cos_Sigmau.txt000066400000000000000000000005631400612667500331770ustar00rootroot00000000000000*** Tue, 21 Jun 2016 11:30:21 *** VECM MODEL STATISTICS sample range: [1973 Q2, 1998 Q4], T = 103 Log Likelihood: 7.940801e+02 Determinant (Cov): 5.929254e-10 Covariance: 2.303948e-05 -1.480276e-06 -1.480276e-06 2.583030e-05 Correlation: 1.000000e+00 -6.067946e-02 -6.067946e-02 1.000000e+00 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cos_diag.txt000066400000000000000000000034331400612667500326550ustar00rootroot00000000000000*** Mon, 25 Jul 2016 13:48:53 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) tested order: 16 test statistic: 47.8463 p-value: 0.5602 adjusted test statistic: 53.4707 p-value: 0.3425 degrees of freedom: 50.0000 *** Mon, 25 Jul 2016 13:48:53 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags LM statistic: 14.4330 p-value: 0.8079 df: 20.0000 *** Mon, 25 Jul 2016 13:48:53 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 2.2794 p-value: 0.6845 degrees of freedom: 4.0000 skewness only: 0.2422 p-value: 0.8860 kurtosis only: 2.0372 p-value: 0.3611 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 2.0208 p-value: 0.7319 degrees of freedom: 4.0000 skewness only: 0.2670 p-value: 0.8750 kurtosis only: 1.7539 p-value: 0.4161 *** Mon, 25 Jul 2016 13:48:53 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 0.5649 0.7539 -0.0341 2.6436 u2 2.0538 0.3581 -0.1097 3.6561 *** Mon, 25 Jul 2016 13:48:53 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 15.4552 0.4916 1.1746 0.3096 u2 26.4312 0.0483 2.3728 0.0070 *** Mon, 25 Jul 2016 13:48:53 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 77.4668 p-value(chi^2): 0.0019 degrees of freedom: 45.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cos_fc5.txt000077500000000000000000000020531400612667500324260ustar00rootroot00000000000000*** Thu, 28 Jul 2016 16:37:09 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals Dp time forecast lower CI upper CI +/- 1999 Q1 -0.0226 -0.0320 -0.0132 0.0094 1999 Q2 -0.0042 -0.0139 0.0054 0.0097 1999 Q3 0.0029 -0.0070 0.0128 0.0099 1999 Q4 0.0239 0.0138 0.0339 0.0101 2000 Q1 -0.0256 -0.0365 -0.0146 0.0109 R time forecast lower CI upper CI +/- 1999 Q1 0.0393 0.0293 0.0492 0.0100 1999 Q2 0.0399 0.0246 0.0553 0.0153 1999 Q3 0.0389 0.0199 0.0579 0.0190 1999 Q4 0.0370 0.0142 0.0597 0.0228 2000 Q1 0.0376 0.0113 0.0638 0.0262 vecm_e6_jmulti_cos_granger_causality_dp_r.txt000066400000000000000000000004461400612667500364020ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 10:42:29 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 0.7474 pval-F( l; 4, 176) = 0.5610 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.4071 pval-Chi( c; 1) = 0.5235 vecm_e6_jmulti_cos_granger_causality_r_dp.txt000066400000000000000000000004461400612667500364020ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 13:49:28 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.5314 pval-F( l; 4, 176) = 0.0084 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.4071 pval-Chi( c; 1) = 0.5235 vecm_e6_jmulti_cos_inst_causality_dp_r.txt000077500000000000000000000004461400612667500357350ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:42:09 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 2.1104 pval-F( l; 3, 182) = 0.1005 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.6068 pval-Chi( c; 1) = 0.4360 vecm_e6_jmulti_cos_inst_causality_r_dp.txt000077500000000000000000000004461400612667500357350ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:42:26 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 4.2498 pval-F( l; 3, 182) = 0.0063 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.6068 pval-Chi( c; 1) = 0.4360 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cos_ir.txt000077500000000000000000000046111400612667500323650ustar00rootroot00000000000000*** Tue, 16 Aug 2016 19:24:23 *** VECM Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time Dp R Dp R ->Dp ->Dp ->R ->R point estimate 1.0000 0.0000 0.0000 1.0000 1 point estimate 0.0360 0.2231 0.1973 1.1659 2 point estimate -0.0063 0.1984 0.2244 1.1168 3 point estimate 0.0778 0.1862 0.3188 1.2448 4 point estimate 0.4119 0.2141 0.4820 1.2490 5 point estimate 0.1098 0.2800 0.5641 1.1952 6 point estimate 0.0793 0.2633 0.5710 1.1816 7 point estimate 0.1353 0.2548 0.6191 1.1514 8 point estimate 0.2508 0.2608 0.6692 1.1154 9 point estimate 0.1524 0.2784 0.6833 1.0972 10 point estimate 0.1353 0.2705 0.6776 1.0827 11 point estimate 0.1623 0.2644 0.6855 1.0671 12 point estimate 0.2015 0.2652 0.6952 1.0582 13 point estimate 0.1678 0.2704 0.6946 1.0541 14 point estimate 0.1593 0.2672 0.6884 1.0509 15 point estimate 0.1705 0.2644 0.6881 1.0484 16 point estimate 0.1837 0.2647 0.6899 1.0475 17 point estimate 0.1718 0.2665 0.6885 1.0476 18 point estimate 0.1679 0.2654 0.6856 1.0478 19 point estimate 0.1724 0.2644 0.6852 1.0479 20 point estimate 0.1768 0.2646 0.6859 1.0481 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_cos_lagorder.txt000077500000000000000000000006711400612667500335540ustar00rootroot00000000000000*** Sun, 21 Aug 2016 09:33:58 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: Dp R deterministic variables: CONST S1 S2 S3 sample range: [1975 Q1, 1998 Q4], T = 96 optimal number of lags (searched up to 10 lags of 1. differences): Akaike Info Criterion: 3 Final Prediction Error: 3 Hannan-Quinn Criterion: 0 Schwarz Criterion: 0 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_coslo.txt000066400000000000000000000115241400612667500322240ustar00rootroot00000000000000*** Tue, 21 Jun 2016 11:32:53 *** VEC REPRESENTATION endogenous variables: Dp R exogenous variables: deterministic variables: CONST S1 S2 S3 TREND endogenous lags (diffs): 3 exogenous lags: 0 sample range: [1973 Q2, 1998 Q4], T = 103 estimation procedure: One stage. Johansen approach Lagged endogenous term: ======================= d(Dp) d(R) ------------------------------ d(Dp)(t-1)| -0.302 -0.193 | (0.146) (0.156) | {0.039} {0.216} | [-2.069] [-1.238] d(R) (t-1)| 0.061 0.260 | (0.095) (0.101) | {0.521} {0.010} | [0.642] [2.571] d(Dp)(t-2)| -0.366 -0.212 | (0.117) (0.125) | {0.002} {0.089} | [-3.139] [-1.701] d(R) (t-2)| -0.005 -0.025 | (0.095) (0.102) | {0.956} {0.804} | [-0.055] [-0.249] d(Dp)(t-3)| -0.335 -0.103 | (0.077) (0.082) | {0.000} {0.212} | [-4.350] [-1.247] d(R) (t-3)| 0.020 0.215 | (0.092) (0.098) | {0.831} {0.028} | [0.214] [2.193] ------------------------------ Deterministic term: =================== d(Dp) d(R) ----------------------------- CONST | -0.006 0.003 | (0.002) (0.002) | {0.000} {0.088} | [-3.541] [1.708] S1 (t)| -0.034 0.002 | (0.005) (0.005) | {0.000} {0.752} | [-7.493] [0.316] S2 (t)| -0.018 0.009 | (0.005) (0.005) | {0.000} {0.075} | [-3.845] [1.782] S3 (t)| -0.016 0.000 | (0.005) (0.005) | {0.000} {0.936} | [-3.644] [-0.081] TREND(t)| 0.000 0.000 | (0.000) (0.000) | {0.589} {0.936} | [-0.540] [0.080] ----------------------------- Loading coefficients: ===================== d(Dp) d(R) ----------------------------- ec1(t-1)| -0.675 0.385 | (0.175) (0.187) | {0.000} {0.040} | [-3.856] [2.058] ----------------------------- Estimated cointegration relation(s): ==================================== ec1(t-1) ------------------- Dp(t-1)| 1.000 | (0.000) | {0.000} | [0.000] R (t-1)| -0.232 | (0.052) | {0.000} | [-4.430] ------------------- VAR REPRESENTATION modulus of the eigenvalues of the reverse characteristic polynomial: |z| = ( 1.3768 1.2868 1.2868 1.7489 1.7489 1.0000 1.4303 1.4303 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= Dp R ----------------------------- Dp(t-1)| 0.022 0.192 | (0.228) (0.244) | {0.923} {0.431} | [0.097] [0.787] R (t-1)| 0.217 1.171 | (0.103) (0.110) | {0.035} {0.000} | [2.106] [10.629] Dp(t-2)| -0.064 -0.018 | (0.080) (0.085) | {0.426} {0.828} | [-0.797] [-0.217] R (t-2)| -0.066 -0.286 | (0.140) (0.150) | {0.637} {0.056} | [-0.472] [-1.908] Dp(t-3)| 0.031 0.109 | (0.080) (0.086) | {0.701} {0.202} | [0.384] [1.275] R (t-3)| 0.025 0.240 | (0.140) (0.150) | {0.859} {0.109} | [0.177] [1.603] Dp(t-4)| 0.335 0.103 | (0.077) (0.082) | {0.000} {0.212} | [4.350] [1.247] R (t-4)| -0.020 -0.215 | (0.092) (0.098) | {0.831} {0.028} | [-0.214] [-2.193] ----------------------------- Deterministic term: =================== Dp R ----------------------------- CONST | -0.006 0.003 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] S1 (t)| -0.034 0.002 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] S2 (t)| -0.018 0.009 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] S3 (t)| -0.016 0.000 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] TREND(t)| 0.000 0.000 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] ----------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_coslo_Sigmau.txt000066400000000000000000000005631400612667500335320ustar00rootroot00000000000000*** Tue, 21 Jun 2016 11:32:53 *** VECM MODEL STATISTICS sample range: [1973 Q2, 1998 Q4], T = 103 Log Likelihood: 7.941435e+02 Determinant (Cov): 5.921885e-10 Covariance: 2.283862e-05 -1.599784e-06 -1.599784e-06 2.604132e-05 Correlation: 1.000000e+00 -6.559867e-02 -6.559867e-02 1.000000e+00 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_coslo_diag.txt000066400000000000000000000034331400612667500332100ustar00rootroot00000000000000*** Mon, 25 Jul 2016 13:50:25 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) tested order: 16 test statistic: 47.5281 p-value: 0.5731 adjusted test statistic: 53.1533 p-value: 0.3537 degrees of freedom: 50.0000 *** Mon, 25 Jul 2016 13:50:25 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags LM statistic: 14.4240 p-value: 0.8084 df: 20.0000 *** Mon, 25 Jul 2016 13:50:25 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 2.1499 p-value: 0.7082 degrees of freedom: 4.0000 skewness only: 0.3098 p-value: 0.8565 kurtosis only: 1.8401 p-value: 0.3985 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 1.8898 p-value: 0.7560 degrees of freedom: 4.0000 skewness only: 0.3385 p-value: 0.8443 kurtosis only: 1.5513 p-value: 0.4604 *** Mon, 25 Jul 2016 13:50:25 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 0.4993 0.7791 -0.0475 2.6724 u2 1.9942 0.3690 -0.1221 3.6364 *** Mon, 25 Jul 2016 13:50:25 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 14.6214 0.5525 1.0984 0.3735 u2 26.1501 0.0520 2.3368 0.0079 *** Mon, 25 Jul 2016 13:50:25 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 74.6546 p-value(chi^2): 0.0036 degrees of freedom: 45.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_coslo_fc5.txt000077500000000000000000000020531400612667500327610ustar00rootroot00000000000000*** Thu, 28 Jul 2016 16:39:52 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals Dp time forecast lower CI upper CI +/- 1999 Q1 -0.0227 -0.0321 -0.0133 0.0094 1999 Q2 -0.0043 -0.0139 0.0053 0.0096 1999 Q3 0.0028 -0.0070 0.0126 0.0098 1999 Q4 0.0237 0.0138 0.0337 0.0100 2000 Q1 -0.0258 -0.0366 -0.0150 0.0108 R time forecast lower CI upper CI +/- 1999 Q1 0.0390 0.0290 0.0490 0.0100 1999 Q2 0.0395 0.0240 0.0549 0.0154 1999 Q3 0.0382 0.0190 0.0573 0.0191 1999 Q4 0.0359 0.0130 0.0589 0.0230 2000 Q1 0.0362 0.0098 0.0627 0.0265 vecm_e6_jmulti_coslo_granger_causality_dp_r.txt000066400000000000000000000004461400612667500367350ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 13:50:44 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 0.4480 pval-F( l; 4, 174) = 0.7738 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.6101 pval-Chi( c; 1) = 0.4348 vecm_e6_jmulti_coslo_granger_causality_r_dp.txt000066400000000000000000000004461400612667500367350ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 13:50:53 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.0268 pval-F( l; 4, 174) = 0.0191 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.6101 pval-Chi( c; 1) = 0.4348 vecm_e6_jmulti_coslo_inst_causality_dp_r.txt000077500000000000000000000004461400612667500362700ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:41:45 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 1.4258 pval-F( l; 3, 180) = 0.2368 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.9332 pval-Chi( c; 1) = 0.3340 vecm_e6_jmulti_coslo_inst_causality_r_dp.txt000077500000000000000000000004461400612667500362700ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:41:33 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.6535 pval-F( l; 3, 180) = 0.0137 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.9332 pval-Chi( c; 1) = 0.3340 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_coslo_ir.txt000077500000000000000000000046111400612667500327200ustar00rootroot00000000000000*** Tue, 16 Aug 2016 19:25:44 *** VECM Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time Dp R Dp R ->Dp ->Dp ->R ->R point estimate 1.0000 0.0000 0.0000 1.0000 1 point estimate 0.0221 0.2173 0.1917 1.1713 2 point estimate -0.0215 0.1932 0.2102 1.1279 3 point estimate 0.0619 0.1830 0.2961 1.2598 4 point estimate 0.3939 0.2071 0.4502 1.2750 5 point estimate 0.0912 0.2706 0.5263 1.2323 6 point estimate 0.0595 0.2559 0.5285 1.2272 7 point estimate 0.1138 0.2483 0.5723 1.2062 8 point estimate 0.2273 0.2536 0.6201 1.1778 9 point estimate 0.1299 0.2709 0.6340 1.1645 10 point estimate 0.1125 0.2644 0.6285 1.1541 11 point estimate 0.1382 0.2591 0.6366 1.1415 12 point estimate 0.1765 0.2599 0.6470 1.1343 13 point estimate 0.1438 0.2651 0.6475 1.1310 14 point estimate 0.1353 0.2624 0.6424 1.1282 15 point estimate 0.1460 0.2600 0.6427 1.1258 16 point estimate 0.1588 0.2602 0.6450 1.1247 17 point estimate 0.1475 0.2620 0.6443 1.1246 18 point estimate 0.1438 0.2611 0.6418 1.1245 19 point estimate 0.1479 0.2602 0.6416 1.1243 20 point estimate 0.1523 0.2603 0.6424 1.1243 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_coslo_lagorder.txt000077500000000000000000000006771400612667500341150ustar00rootroot00000000000000*** Sun, 21 Aug 2016 09:34:22 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: Dp R deterministic variables: CONST S1 S2 S3 TREND sample range: [1975 Q1, 1998 Q4], T = 96 optimal number of lags (searched up to 10 lags of 1. differences): Akaike Info Criterion: 3 Final Prediction Error: 3 Hannan-Quinn Criterion: 0 Schwarz Criterion: 0 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_nc.txt000066400000000000000000000065421400612667500315110ustar00rootroot00000000000000*** Tue, 21 Jun 2016 11:25:25 *** VEC REPRESENTATION endogenous variables: Dp R exogenous variables: deterministic variables: endogenous lags (diffs): 3 exogenous lags: 0 sample range: [1973 Q2, 1998 Q4], T = 103 estimation procedure: One stage. Johansen approach Lagged endogenous term: ======================= d(Dp) d(R) ------------------------------ d(Dp)(t-1)| -0.588 -0.082 | (0.144) (0.127) | {0.000} {0.518} | [-4.072] [-0.646] d(R) (t-1)| 0.117 0.186 | (0.112) (0.099) | {0.296} {0.060} | [1.046] [1.880] d(Dp)(t-2)| -0.704 -0.040 | (0.099) (0.087) | {0.000} {0.644} | [-7.124] [-0.462] d(R) (t-2)| 0.187 -0.045 | (0.113) (0.100) | {0.098} {0.655} | [1.653] [-0.446] d(Dp)(t-3)| -0.825 0.009 | (0.053) (0.047) | {0.000} {0.846} | [-15.489] [0.194] d(R) (t-3)| 0.023 0.172 | (0.112) (0.099) | {0.836} {0.080} | [0.207] [1.748] ------------------------------ Loading coefficients: ===================== d(Dp) d(R) ----------------------------- ec1(t-1)| -0.546 0.106 | (0.190) (0.167) | {0.004} {0.527} | [-2.880] [0.632] ----------------------------- Estimated cointegration relation(s): ==================================== ec1(t-1) ------------------- Dp(t-1)| 1.000 | (0.000) | {0.000} | [0.000] R (t-1)| -0.111 | (0.014) | {0.000} | [-7.798] ------------------- VAR REPRESENTATION modulus of the eigenvalues of the reverse characteristic polynomial: |z| = ( 1.0098 1.0121 1.0121 1.0000 1.1621 1.8586 1.8586 1.6916 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= Dp R ----------------------------- Dp(t-1)| -0.134 0.023 | (0.238) (0.210) | {0.575} {0.911} | [-0.561] [0.112] R (t-1)| 0.178 1.174 | (0.114) (0.101) | {0.119} {0.000} | [1.557] [11.665] Dp(t-2)| -0.116 0.042 | (0.054) (0.047) | {0.031} {0.375} | [-2.158] [0.886] R (t-2)| 0.070 -0.231 | (0.171) (0.151) | {0.682} {0.127} | [0.410] [-1.526] Dp(t-3)| -0.122 0.049 | (0.053) (0.047) | {0.022} {0.293} | [-2.291] [1.052] R (t-3)| -0.164 0.217 | (0.172) (0.151) | {0.338} {0.152} | [-0.958] [1.433] Dp(t-4)| 0.825 -0.009 | (0.053) (0.047) | {0.000} {0.846} | [15.489] [-0.194] R (t-4)| -0.023 -0.172 | (0.112) (0.099) | {0.836} {0.080} | [-0.207] [-1.748] ----------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_nc_Sigmau.txt000066400000000000000000000005631400612667500330130ustar00rootroot00000000000000*** Tue, 21 Jun 2016 11:25:25 *** VECM MODEL STATISTICS sample range: [1973 Q2, 1998 Q4], T = 103 Log Likelihood: 7.663536e+02 Determinant (Cov): 1.021192e-09 Covariance: 3.642544e-05 -3.485125e-06 -3.485125e-06 2.836858e-05 Correlation: 1.000000e+00 -1.084170e-01 -1.084170e-01 1.000000e+00 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_nc_diag.txt000066400000000000000000000034331400612667500324710ustar00rootroot00000000000000*** Mon, 25 Jul 2016 10:05:54 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) tested order: 16 test statistic: 48.8795 p-value: 0.5184 adjusted test statistic: 53.9964 p-value: 0.3243 degrees of freedom: 50.0000 *** Mon, 25 Jul 2016 10:05:54 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags LM statistic: 41.7097 p-value: 0.0030 df: 20.0000 *** Mon, 25 Jul 2016 10:05:54 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 2.6293 p-value: 0.6216 degrees of freedom: 4.0000 skewness only: 2.2140 p-value: 0.3306 kurtosis only: 0.4153 p-value: 0.8125 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 2.3763 p-value: 0.6669 degrees of freedom: 4.0000 skewness only: 2.1432 p-value: 0.3425 kurtosis only: 0.2331 p-value: 0.8900 *** Mon, 25 Jul 2016 10:05:54 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 2.1830 0.3357 0.3524 3.1089 u2 0.5265 0.7685 0.0020 3.3502 *** Mon, 25 Jul 2016 10:05:54 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 12.0814 0.7384 0.8769 0.5971 u2 26.0997 0.0526 2.3303 0.0081 *** Mon, 25 Jul 2016 10:05:54 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 62.4334 p-value(chi^2): 0.0435 degrees of freedom: 45.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_nc_fc5.txt000077500000000000000000000020531400612667500322420ustar00rootroot00000000000000*** Thu, 28 Jul 2016 16:35:11 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals Dp time forecast lower CI upper CI +/- 1999 Q1 -0.0145 -0.0263 -0.0027 0.0118 1999 Q2 -0.0012 -0.0133 0.0109 0.0121 1999 Q3 0.0031 -0.0094 0.0156 0.0125 1999 Q4 0.0233 0.0108 0.0358 0.0125 2000 Q1 -0.0134 -0.0297 0.0029 0.0163 R time forecast lower CI upper CI +/- 1999 Q1 0.0380 0.0275 0.0484 0.0104 1999 Q2 0.0374 0.0213 0.0535 0.0161 1999 Q3 0.0369 0.0168 0.0569 0.0200 1999 Q4 0.0355 0.0112 0.0597 0.0242 2000 Q1 0.0355 0.0073 0.0636 0.0282 vecm_e6_jmulti_nc_granger_causality_dp_r.txt000066400000000000000000000004461400612667500362160ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 09:57:00 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 0.8755 pval-F( l; 4, 184) = 0.4797 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 1.5808 pval-Chi( c; 1) = 0.2086 vecm_e6_jmulti_nc_granger_causality_r_dp.txt000066400000000000000000000004461400612667500362160ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 09:58:26 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.3765 pval-F( l; 4, 184) = 0.0108 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 1.5808 pval-Chi( c; 1) = 0.2086 vecm_e6_jmulti_nc_inst_causality_dp_r.txt000077500000000000000000000004461400612667500355510ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:37:21 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 0.5527 pval-F( l; 3, 190) = 0.6469 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 1.2429 pval-Chi( c; 1) = 0.2649 vecm_e6_jmulti_nc_inst_causality_r_dp.txt000077500000000000000000000004461400612667500355510ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:39:22 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.2345 pval-F( l; 3, 190) = 0.0235 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 1.2429 pval-Chi( c; 1) = 0.2649 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_nc_ir.txt000077500000000000000000000046111400612667500322010ustar00rootroot00000000000000*** Tue, 16 Aug 2016 19:20:13 *** VECM Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time Dp R Dp R ->Dp ->Dp ->R ->R point estimate 1.0000 0.0000 0.0000 1.0000 1 point estimate -0.1337 0.1776 0.0235 1.1743 2 point estimate -0.0938 0.2550 0.0664 1.1525 3 point estimate -0.0803 0.0681 0.1142 1.3129 4 point estimate 0.8843 0.0377 0.1023 1.3794 5 point estimate -0.1932 0.2232 0.1181 1.3795 6 point estimate -0.1364 0.2675 0.1579 1.3959 7 point estimate -0.1164 0.0777 0.1938 1.4110 8 point estimate 0.8085 0.0526 0.1731 1.4203 9 point estimate -0.2218 0.2257 0.1816 1.4232 10 point estimate -0.1535 0.2634 0.2124 1.4182 11 point estimate -0.1308 0.0822 0.2398 1.4197 12 point estimate 0.7532 0.0594 0.2143 1.4278 13 point estimate -0.2341 0.2240 0.2178 1.4275 14 point estimate -0.1573 0.2582 0.2428 1.4200 15 point estimate -0.1338 0.0851 0.2650 1.4211 16 point estimate 0.7097 0.0650 0.2373 1.4283 17 point estimate -0.2376 0.2220 0.2381 1.4275 18 point estimate -0.1542 0.2530 0.2596 1.4203 19 point estimate -0.1310 0.0877 0.2784 1.4213 20 point estimate 0.6731 0.0701 0.2500 1.4281 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_nc_lagorder.txt000077500000000000000000000006171400612667500333700ustar00rootroot00000000000000*** Sun, 21 Aug 2016 09:32:02 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: Dp R sample range: [1975 Q1, 1998 Q4], T = 96 optimal number of lags (searched up to 10 lags of 1. differences): Akaike Info Criterion: 3 Final Prediction Error: 3 Hannan-Quinn Criterion: 3 Schwarz Criterion: 3 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_ncs.txt000066400000000000000000000105301400612667500316640ustar00rootroot00000000000000*** Tue, 21 Jun 2016 11:36:47 *** VEC REPRESENTATION endogenous variables: Dp R exogenous variables: deterministic variables: S1 S2 S3 endogenous lags (diffs): 3 exogenous lags: 0 sample range: [1973 Q2, 1998 Q4], T = 103 estimation procedure: One stage. Johansen approach Lagged endogenous term: ======================= d(Dp) d(R) ------------------------------ d(Dp)(t-1)| -0.417 0.027 | (0.132) (0.142) | {0.002} {0.848} | [-3.164] [0.192] d(R) (t-1)| 0.130 0.207 | (0.092) (0.099) | {0.156} {0.035} | [1.419] [2.103] d(Dp)(t-2)| -0.442 -0.065 | (0.109) (0.118) | {0.000} {0.578} | [-4.038] [-0.556] d(R) (t-2)| 0.055 -0.067 | (0.094) (0.101) | {0.558} {0.507} | [0.586] [-0.663] d(Dp)(t-3)| -0.368 -0.034 | (0.076) (0.081) | {0.000} {0.675} | [-4.855] [-0.420] d(R) (t-3)| 0.085 0.181 | (0.091) (0.098) | {0.352} {0.064} | [0.931] [1.854] ------------------------------ Deterministic term: =================== d(Dp) d(R) ----------------------------- S1(t)| -0.034 0.002 | (0.005) (0.005) | {0.000} {0.697} | [-7.472] [0.390] S2(t)| -0.018 0.009 | (0.005) (0.005) | {0.000} {0.074} | [-3.797] [1.788] S3(t)| -0.017 0.000 | (0.005) (0.005) | {0.000} {0.980} | [-3.624] [-0.025] ----------------------------- Loading coefficients: ===================== d(Dp) d(R) ----------------------------- ec1(t-1)| -0.518 0.090 | (0.151) (0.162) | {0.001} {0.580} | [-3.431] [0.554] ----------------------------- Estimated cointegration relation(s): ==================================== ec1(t-1) ------------------- Dp(t-1)| 1.000 | (0.000) | {0.000} | [0.000] R (t-1)| -0.108 | (0.012) | {0.000} | [-8.905] ------------------- VAR REPRESENTATION modulus of the eigenvalues of the reverse characteristic polynomial: |z| = ( 1.3631 1.2805 1.2805 1.8318 1.8318 1.0000 1.2153 1.7166 ) Legend: ======= Equation 1 Equation 2 ... ------------------------------------------ Variable 1 | Coefficient ... | (Std. Dev.) | {p - Value} | [t - Value] Variable 2 | ... ... ------------------------------------------ Lagged endogenous term: ======================= Dp R ----------------------------- Dp(t-1)| 0.065 0.117 | (0.201) (0.215) | {0.747} {0.587} | [0.322] [0.543] R (t-1)| 0.186 1.198 | (0.093) (0.100) | {0.046} {0.000} | [1.996] [11.961] Dp(t-2)| -0.025 -0.093 | (0.078) (0.084) | {0.748} {0.268} | [-0.321] [-1.109] R (t-2)| -0.075 -0.274 | (0.142) (0.153) | {0.597} {0.073} | [-0.529] [-1.794] Dp(t-3)| 0.074 0.031 | (0.077) (0.083) | {0.339} {0.707} | [0.956] [0.376] R (t-3)| 0.030 0.248 | (0.143) (0.153) | {0.834} {0.105} | [0.209] [1.620] Dp(t-4)| 0.368 0.034 | (0.076) (0.081) | {0.000} {0.675} | [4.855] [0.420] R (t-4)| -0.085 -0.181 | (0.091) (0.098) | {0.352} {0.064} | [-0.931] [-1.854] ----------------------------- Deterministic term: =================== Dp R ----------------------------- S1(t)| -0.034 0.002 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] S2(t)| -0.018 0.009 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] S3(t)| -0.017 0.000 | (0.000) (0.000) | {0.000} {0.000} | [0.000] [0.000] ----------------------------- statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_ncs_Sigmau.txt000066400000000000000000000005631400612667500331760ustar00rootroot00000000000000*** Tue, 21 Jun 2016 11:36:47 *** VECM MODEL STATISTICS sample range: [1973 Q2, 1998 Q4], T = 103 Log Likelihood: 7.907212e+02 Determinant (Cov): 6.332912e-10 Covariance: 2.359687e-05 -2.956435e-06 -2.956435e-06 2.720835e-05 Correlation: 1.000000e+00 -1.166783e-01 -1.166783e-01 1.000000e+00 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_ncs_diag.txt000066400000000000000000000034331400612667500326540ustar00rootroot00000000000000*** Mon, 25 Jul 2016 13:55:40 *** PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0) tested order: 16 test statistic: 48.0815 p-value: 0.5507 adjusted test statistic: 53.8138 p-value: 0.3305 degrees of freedom: 50.0000 *** Mon, 25 Jul 2016 13:55:40 *** LM-TYPE TEST FOR AUTOCORRELATION with 5 lags LM statistic: 23.5983 p-value: 0.2604 df: 20.0000 *** Mon, 25 Jul 2016 13:55:40 *** TESTS FOR NONNORMALITY Reference: Doornik & Hansen (1994) joint test statistic: 1.2601 p-value: 0.8681 degrees of freedom: 4.0000 skewness only: 0.2625 p-value: 0.8770 kurtosis only: 0.9976 p-value: 0.6073 Reference: Lütkepohl (1993), Introduction to Multiple Time Series Analysis, 2ed, p. 153 joint test statistic: 1.0210 p-value: 0.9066 degrees of freedom: 4.0000 skewness only: 0.2477 p-value: 0.8835 kurtosis only: 0.7733 p-value: 0.6793 *** Mon, 25 Jul 2016 13:55:40 *** JARQUE-BERA TEST variable teststat p-Value(Chi^2) skewness kurtosis u1 0.5868 0.7457 0.0939 2.6815 u2 1.1219 0.5707 -0.0883 3.4798 *** Mon, 25 Jul 2016 13:55:40 *** ARCH-LM TEST with 16 lags variable teststat p-Value(Chi^2) F stat p-Value(F) u1 15.5197 0.4870 1.1806 0.3050 u2 26.9092 0.0425 2.4350 0.0056 *** Mon, 25 Jul 2016 13:55:40 *** MULTIVARIATE ARCH-LM TEST with 5 lags VARCHLM test statistic: 73.4831 p-value(chi^2): 0.0047 degrees of freedom: 45.0000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_ncs_fc5.txt000077500000000000000000000020531400612667500324250ustar00rootroot00000000000000*** Thu, 28 Jul 2016 16:35:44 *** FORECASTING Reference: Lütkepohl (1993), IMTSA, 2ed, ch. 5.2.6, ch. 10.5 CI coverage: 0.95 forecast horizon: 5 periods using standard confidence intervals Dp time forecast lower CI upper CI +/- 1999 Q1 -0.0199 -0.0294 -0.0104 0.0095 1999 Q2 -0.0016 -0.0113 0.0081 0.0097 1999 Q3 0.0058 -0.0040 0.0157 0.0099 1999 Q4 0.0271 0.0171 0.0371 0.0100 2000 Q1 -0.0214 -0.0321 -0.0107 0.0107 R time forecast lower CI upper CI +/- 1999 Q1 0.0386 0.0284 0.0488 0.0102 1999 Q2 0.0393 0.0234 0.0552 0.0159 1999 Q3 0.0381 0.0182 0.0581 0.0199 1999 Q4 0.0359 0.0118 0.0600 0.0241 2000 Q1 0.0364 0.0084 0.0644 0.0280 vecm_e6_jmulti_ncs_granger_causality_dp_r.txt000066400000000000000000000004461400612667500364010ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 10:14:12 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 0.2675 pval-F( l; 4, 178) = 0.8986 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 0.9519 pval-Chi( c; 1) = 0.3292 vecm_e6_jmulti_ncs_granger_causality_r_dp.txt000066400000000000000000000004461400612667500364010ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Mon, 25 Jul 2016 10:14:36 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 2.8553 pval-F( l; 4, 178) = 0.0251 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 0.9519 pval-Chi( c; 1) = 0.3292 vecm_e6_jmulti_ncs_inst_causality_dp_r.txt000077500000000000000000000004461400612667500357340ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:44:12 *** TEST FOR GRANGER-CAUSALITY: H0: "Dp" do not Granger-cause "R" Test statistic l = 1.2025 pval-F( l; 3, 184) = 0.3103 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "Dp" and "R" Test statistic: c = 1.4168 pval-Chi( c; 1) = 0.2339 vecm_e6_jmulti_ncs_inst_causality_r_dp.txt000077500000000000000000000004461400612667500357340ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results*** Fri, 26 Aug 2016 11:43:59 *** TEST FOR GRANGER-CAUSALITY: H0: "R" do not Granger-cause "Dp" Test statistic l = 3.1771 pval-F( l; 3, 184) = 0.0254 TEST FOR INSTANTANEOUS CAUSALITY: H0: No instantaneous causality between "R" and "Dp" Test statistic: c = 1.4168 pval-Chi( c; 1) = 0.2339 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_ncs_ir.txt000077500000000000000000000046111400612667500323640ustar00rootroot00000000000000*** Tue, 16 Aug 2016 19:23:53 *** VECM Forecast Error Impulse Responses Selected Impulse Responses: "impulse variable -> response variable" time Dp R Dp R ->Dp ->Dp ->R ->R point estimate 1.0000 0.0000 0.0000 1.0000 1 point estimate 0.0646 0.1861 0.1170 1.1977 2 point estimate 0.0010 0.1597 0.0551 1.1820 3 point estimate 0.0739 0.1654 0.0593 1.3370 4 point estimate 0.3881 0.1312 0.1297 1.4035 5 point estimate 0.0585 0.1788 0.1723 1.4019 6 point estimate 0.0193 0.1741 0.1488 1.4311 7 point estimate 0.0692 0.1666 0.1639 1.4491 8 point estimate 0.1646 0.1526 0.1961 1.4500 9 point estimate 0.0458 0.1689 0.2111 1.4542 10 point estimate 0.0279 0.1668 0.2057 1.4610 11 point estimate 0.0526 0.1619 0.2139 1.4625 12 point estimate 0.0807 0.1575 0.2273 1.4630 13 point estimate 0.0372 0.1630 0.2333 1.4645 14 point estimate 0.0298 0.1620 0.2324 1.4661 15 point estimate 0.0407 0.1598 0.2364 1.4666 16 point estimate 0.0485 0.1584 0.2420 1.4668 17 point estimate 0.0324 0.1603 0.2445 1.4674 18 point estimate 0.0295 0.1598 0.2446 1.4679 19 point estimate 0.0339 0.1589 0.2464 1.4682 20 point estimate 0.0359 0.1584 0.2488 1.4683 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/JMulTi_results/vecm_e6_jmulti_ncs_lagorder.txt000077500000000000000000000006631400612667500335540ustar00rootroot00000000000000*** Sun, 21 Aug 2016 09:33:01 *** OPTIMAL ENDOGENOUS LAGS FROM INFORMATION CRITERIA endogenous variables: Dp R deterministic variables: S1 S2 S3 sample range: [1975 Q1, 1998 Q4], T = 96 optimal number of lags (searched up to 10 lags of 1. differences): Akaike Info Criterion: 3 Final Prediction Error: 3 Hannan-Quinn Criterion: 0 Schwarz Criterion: 0 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/Matlab_results/000077500000000000000000000000001400612667500254055ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/Matlab_results/__init__.py000066400000000000000000000000001400612667500275040ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/Matlab_results/test_coint.csv000066400000000000000000000534551400612667500303110ustar00rootroot00000000000000 2.8300000e+02 9.9000000e+01 5.6500000e+02 1.2000000e+02 3.1200000e+02 4.8100000e+02 9.2000000e+01 6.9700000e+02 2.8200000e+02 9.9000000e+01 5.5800000e+02 1.2100000e+02 3.0900000e+02 4.7200000e+02 9.2000000e+01 6.9300000e+02 2.7700000e+02 1.0100000e+02 5.6000000e+02 1.1700000e+02 3.0600000e+02 4.7500000e+02 9.6000000e+01 6.9600000e+02 2.8000000e+02 1.0600000e+02 5.6300000e+02 1.1400000e+02 3.1000000e+02 4.8700000e+02 9.8000000e+01 6.8900000e+02 2.8000000e+02 1.0800000e+02 5.4900000e+02 1.1000000e+02 3.1400000e+02 4.7600000e+02 9.7000000e+01 6.6700000e+02 2.7300000e+02 1.0800000e+02 5.4500000e+02 1.0300000e+02 3.1500000e+02 4.7100000e+02 9.7000000e+01 6.5300000e+02 2.7400000e+02 1.0800000e+02 5.1800000e+02 1.0000000e+02 3.0900000e+02 4.5800000e+02 9.3000000e+01 6.4000000e+02 2.6900000e+02 1.0500000e+02 5.0900000e+02 9.7000000e+01 2.9600000e+02 4.4700000e+02 9.1000000e+01 6.2300000e+02 2.6300000e+02 1.0400000e+02 5.0500000e+02 9.5000000e+01 3.0300000e+02 4.5500000e+02 8.9000000e+01 6.0100000e+02 2.6000000e+02 1.0300000e+02 5.0600000e+02 9.2000000e+01 2.9500000e+02 4.4900000e+02 8.8000000e+01 5.8100000e+02 2.5600000e+02 1.0100000e+02 4.9100000e+02 8.7000000e+01 2.8600000e+02 4.2100000e+02 8.6000000e+01 5.5100000e+02 2.5100000e+02 1.0000000e+02 4.7200000e+02 9.3000000e+01 2.8200000e+02 3.9000000e+02 8.5000000e+01 5.2500000e+02 2.3600000e+02 9.3000000e+01 4.3900000e+02 8.6000000e+01 2.6600000e+02 3.8900000e+02 7.7000000e+01 4.9900000e+02 2.3300000e+02 9.2000000e+01 4.2800000e+02 8.1000000e+01 2.5400000e+02 3.5800000e+02 7.6000000e+01 4.8300000e+02 2.3800000e+02 9.5000000e+01 4.2000000e+02 8.2000000e+01 2.5000000e+02 3.7900000e+02 7.7000000e+01 4.9000000e+02 2.4300000e+02 9.6000000e+01 4.1300000e+02 8.4000000e+01 2.5100000e+02 3.8400000e+02 8.0000000e+01 4.9200000e+02 2.4400000e+02 9.7000000e+01 4.1800000e+02 9.1000000e+01 2.5500000e+02 3.8700000e+02 8.0000000e+01 4.8600000e+02 2.4900000e+02 9.8000000e+01 4.1500000e+02 9.4000000e+01 2.6900000e+02 3.9900000e+02 8.0000000e+01 4.8700000e+02 2.5300000e+02 1.0000000e+02 4.2000000e+02 9.2000000e+01 2.7200000e+02 4.0000000e+02 7.7000000e+01 4.7400000e+02 2.5000000e+02 1.0000000e+02 4.2200000e+02 9.6000000e+01 2.7200000e+02 3.9700000e+02 7.9000000e+01 4.8000000e+02 2.5100000e+02 1.0100000e+02 4.2600000e+02 9.5000000e+01 2.7300000e+02 4.0300000e+02 8.1000000e+01 4.8700000e+02 2.5100000e+02 9.9000000e+01 4.2400000e+02 9.4000000e+01 2.7500000e+02 4.0000000e+02 8.1000000e+01 4.8500000e+02 2.5300000e+02 9.9000000e+01 4.2600000e+02 9.5000000e+01 2.7600000e+02 3.9800000e+02 8.0000000e+01 4.8600000e+02 2.4900000e+02 9.6000000e+01 4.2700000e+02 8.9000000e+01 2.7300000e+02 3.8900000e+02 8.0000000e+01 4.8200000e+02 2.4600000e+02 9.3000000e+01 4.2300000e+02 8.8000000e+01 2.7000000e+02 3.7900000e+02 7.5000000e+01 4.9700000e+02 2.4500000e+02 9.3000000e+01 4.2500000e+02 8.7000000e+01 2.6700000e+02 3.7300000e+02 7.5000000e+01 4.9400000e+02 2.5200000e+02 9.5000000e+01 4.3100000e+02 8.9000000e+01 2.6700000e+02 3.7900000e+02 7.7000000e+01 4.9900000e+02 2.5800000e+02 1.0000000e+02 4.3900000e+02 1.0000000e+02 2.7000000e+02 3.9000000e+02 8.1000000e+01 5.0000000e+02 2.6700000e+02 1.0300000e+02 4.5000000e+02 1.0400000e+02 2.7800000e+02 3.9500000e+02 8.1000000e+01 5.0300000e+02 2.7300000e+02 1.0600000e+02 4.6600000e+02 1.0700000e+02 2.8400000e+02 4.0200000e+02 8.3000000e+01 5.1500000e+02 2.6900000e+02 1.0800000e+02 4.7600000e+02 1.0600000e+02 2.9100000e+02 4.0500000e+02 8.3000000e+01 5.1800000e+02 2.7500000e+02 1.0900000e+02 4.8300000e+02 1.0600000e+02 2.8900000e+02 4.0400000e+02 8.2000000e+01 5.1100000e+02 2.7700000e+02 1.1000000e+02 4.8900000e+02 1.0400000e+02 2.8700000e+02 4.0500000e+02 8.1000000e+01 5.0900000e+02 2.7400000e+02 1.0600000e+02 4.7900000e+02 1.0500000e+02 2.8400000e+02 3.8100000e+02 8.2000000e+01 4.6300000e+02 2.7400000e+02 1.0500000e+02 4.5100000e+02 1.0300000e+02 2.7900000e+02 3.6600000e+02 8.2000000e+01 4.2800000e+02 2.7100000e+02 1.0100000e+02 4.5400000e+02 9.8000000e+01 2.7300000e+02 3.4700000e+02 8.0000000e+01 4.2200000e+02 2.6300000e+02 9.7000000e+01 4.2500000e+02 9.3000000e+01 2.6500000e+02 3.5900000e+02 7.3000000e+01 4.3700000e+02 2.6300000e+02 9.4000000e+01 4.1700000e+02 9.2000000e+01 2.5800000e+02 3.5100000e+02 7.2000000e+01 4.3700000e+02 2.6500000e+02 9.7000000e+01 4.2900000e+02 9.2000000e+01 2.6000000e+02 3.6400000e+02 7.7000000e+01 4.4500000e+02 2.7700000e+02 1.0300000e+02 4.4200000e+02 9.7000000e+01 2.6200000e+02 3.7300000e+02 7.8000000e+01 4.5100000e+02 2.8300000e+02 1.0500000e+02 4.4500000e+02 1.0300000e+02 2.6400000e+02 3.7300000e+02 7.8000000e+01 4.5300000e+02 2.8700000e+02 1.0600000e+02 4.4700000e+02 1.0500000e+02 2.6500000e+02 3.7800000e+02 7.9000000e+01 4.5800000e+02 2.8400000e+02 1.0700000e+02 4.4100000e+02 1.0400000e+02 2.6500000e+02 3.7400000e+02 7.8000000e+01 4.5300000e+02 2.8200000e+02 1.0500000e+02 4.4500000e+02 1.0600000e+02 2.5900000e+02 3.6200000e+02 7.8000000e+01 4.5200000e+02 2.8400000e+02 1.0500000e+02 4.4500000e+02 9.5000000e+01 2.6000000e+02 3.6000000e+02 7.9000000e+01 4.5300000e+02 2.8000000e+02 1.0000000e+02 4.4300000e+02 9.6000000e+01 2.5800000e+02 3.6300000e+02 7.8000000e+01 4.5000000e+02 2.7600000e+02 9.8000000e+01 4.3800000e+02 1.0300000e+02 2.5800000e+02 3.5700000e+02 8.0000000e+01 4.4400000e+02 2.7100000e+02 9.3000000e+01 4.2900000e+02 1.0100000e+02 2.5400000e+02 3.4400000e+02 7.9000000e+01 4.4600000e+02 2.6000000e+02 8.9000000e+01 4.1200000e+02 9.6000000e+01 2.4700000e+02 3.3600000e+02 7.5000000e+01 4.2900000e+02 2.5000000e+02 8.8000000e+01 4.0500000e+02 9.8000000e+01 2.3800000e+02 3.3500000e+02 7.3000000e+01 4.1700000e+02 2.4600000e+02 8.9000000e+01 4.0700000e+02 9.6000000e+01 2.3100000e+02 3.3800000e+02 7.5000000e+01 4.1800000e+02 2.5000000e+02 8.9000000e+01 4.0700000e+02 1.0100000e+02 2.2600000e+02 3.4200000e+02 6.9000000e+01 4.1100000e+02 2.5100000e+02 9.1000000e+01 4.0700000e+02 1.0300000e+02 2.2500000e+02 3.4100000e+02 7.0000000e+01 4.0700000e+02 2.5200000e+02 9.1000000e+01 4.0300000e+02 1.0100000e+02 2.2500000e+02 3.4200000e+02 7.0000000e+01 4.0700000e+02 2.5400000e+02 9.2000000e+01 4.0600000e+02 9.8000000e+01 2.2400000e+02 3.3900000e+02 7.1000000e+01 4.0600000e+02 2.5200000e+02 9.0000000e+01 4.0100000e+02 9.2000000e+01 2.1900000e+02 3.3400000e+02 7.0000000e+01 4.0100000e+02 2.5100000e+02 9.0000000e+01 4.0000000e+02 9.1000000e+01 2.1800000e+02 3.3600000e+02 7.0000000e+01 3.9900000e+02 2.5100000e+02 8.9000000e+01 3.9200000e+02 9.2000000e+01 2.1800000e+02 3.3200000e+02 7.2000000e+01 3.9100000e+02 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statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/__init__.py000066400000000000000000000000001400612667500245230ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/example_svar.py000066400000000000000000000017471400612667500254750ustar00rootroot00000000000000import numpy as np import pandas as pd import statsmodels.api as sm from statsmodels.tsa.vector_ar.svar_model import SVAR mdatagen = sm.datasets.macrodata.load(as_pandas=False).data mdata = mdatagen[['realgdp','realcons','realinv']] names = mdata.dtype.names start = pd.datetime(1959, 3, 31) end = pd.datetime(2009, 9, 30) #qtr = pd.DatetimeIndex(start=start, end=end, freq=pd.datetools.BQuarterEnd()) qtr = pd.date_range(start=start, end=end, freq='BQ-MAR') data = pd.DataFrame(mdata, index=qtr) data = (np.log(data)).diff().dropna() #define structural inputs A = np.asarray([[1, 0, 0],['E', 1, 0],['E', 'E', 1]]) B = np.asarray([['E', 0, 0], [0, 'E', 0], [0, 0, 'E']]) A_guess = np.asarray([0.5, 0.25, -0.38]) B_guess = np.asarray([0.5, 0.1, 0.05]) mymodel = SVAR(data, svar_type='AB', A=A, B=B, freq='Q') res = mymodel.fit(maxlags=3, maxiter=10000, maxfun=10000, solver='bfgs') res.irf(periods=30).plot(impulse='realgdp', plot_stderr=True, stderr_type='mc', repl=100) statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/results/000077500000000000000000000000001400612667500241255ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/results/__init__.py000066400000000000000000000000001400612667500262240ustar00rootroot00000000000000statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/results/e1.dat000066400000000000000000000050531400612667500251270ustar00rootroot00000000000000/*quarterly, seasonally adjusted, West German fixed investment, disposable income, consumption expenditures in billions of DM, 1960Q1-1982Q4; source: Deutsche Bundesbank */ <1960 Q1> invest income cons 180 451 415 179 465 421 185 485 434 192 493 448 211 509 459 202 520 458 207 521 479 214 540 487 231 548 497 229 558 510 234 574 516 237 583 525 206 591 529 250 599 538 259 610 546 263 627 555 264 642 574 280 653 574 282 660 586 292 694 602 286 709 617 302 734 639 304 751 653 307 763 668 317 766 679 314 779 686 306 808 697 304 785 688 292 794 704 275 799 699 273 799 709 301 812 715 280 837 724 289 853 746 303 876 758 322 897 779 315 922 798 339 949 816 364 979 837 371 988 858 375 1025 881 432 1063 905 453 1104 934 460 1131 968 475 1137 983 496 1178 1013 494 1211 1034 498 1256 1064 526 1290 1101 519 1314 1102 516 1346 1145 531 1385 1173 573 1416 1216 551 1436 1229 538 1462 1242 532 1493 1267 558 1516 1295 524 1557 1317 525 1613 1355 519 1642 1371 526 1690 1402 510 1759 1452 519 1756 1485 538 1780 1516 549 1807 1549 570 1831 1567 559 1873 1588 584 1897 1631 611 1910 1650 597 1943 1685 603 1976 1722 619 2018 1752 635 2040 1774 658 2070 1807 675 2121 1831 700 2132 1842 692 2199 1890 759 2253 1958 782 2276 1948 816 2318 1994 844 2369 2061 830 2423 2056 853 2457 2102 852 2470 2121 833 2521 2145 860 2545 2164 870 2580 2206 830 2620 2225 801 2639 2235 824 2618 2237 831 2628 2250 830 2651 2271 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/results/e2.dat000066400000000000000000000040041400612667500251230ustar00rootroot00000000000000/*quarterly, seasonally adjusted, U.S. fixed investment (y1), change in business inventories (y2), 1947Q1-1972Q4; source: U.S. Department of Commerce, Bureau of Economic Analysis, The National Income and Product Accounts of the United States, 1929-1974 */ <1947 Q1> y1 y2 69.6 0.1 67.6 -0.9 69.5 -2.9 74.7 2.7 77.1 4.1 77.4 5.6 76.6 6.9 76.1 5.3 71.8 -0.3 68.9 -7.1 68.5 -2.5 70.6 -7.7 75.4 4.4 82.3 7.7 88.2 8.0 86.9 22.1 83.4 13.4 80.3 19.9 79.4 14.6 78.6 7.0 79.3 7.3 80.3 -2.7 75.3 5.4 80.6 7.2 83.9 3.9 84.2 5.1 84.4 1.9 83.8 -5.0 82.8 -3.4 84.1 -4.1 87.0 -2.7 88.5 1.5 92.1 5.9 96.1 8.0 98.3 7.8 98.8 9.2 96.6 7.5 97.4 5.5 97.6 4.9 96.6 5.4 96.2 2.5 95.3 2.9 96.4 3.7 94.9 -3.0 90.0 -6.8 87.2 -6.2 88.0 0.3 93.0 5.3 98.3 5.0 101.6 13.0 102.6 -0.4 101.4 8.2 104.9 13.5 101.8 4.9 98.8 3.0 98.6 -3.9 97.7 -3.8 99.2 1.9 101.3 6.6 104.6 6.7 106.1 10.6 109.9 9.2 111.1 8.0 110.1 4.7 110.7 7.6 116.0 7.0 118.5 9.3 122.0 7.1 124.0 6.1 124.0 8.0 124.9 7.3 126.4 7.9 133.4 13.4 137.9 10.6 140.1 12.4 143.8 8.8 147.5 13.5 146.2 17.8 145.0 15.1 139.7 20.5 136.4 14.6 139.6 7.5 141.1 12.2 145.5 13.8 148.9 6.3 148.9 11.8 150.7 9.2 155.0 7.6 159.1 9.8 158.4 12.2 158.1 13.4 154.3 6.8 151.8 2.9 150.0 4.8 150.4 6.3 149.5 3.3 154.3 7.9 158.4 10.0 162.1 5.0 166.0 3.7 174.3 4.8 176.1 10.1 178.2 12.1 186.7 10.8 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/results/e3.dat000066400000000000000000000167031400612667500251350ustar00rootroot00000000000000/*quarterly, seasonally adjusted real U.S. money (M1), GNP in 1982 Dollars, discount rate on 91-day treasury bills (rd), yield on long term treasury bonds (rb), 1954Q1-1987Q4; source: Business Conditions Digest */ <1954 Q1> M1 gnp rd rb 450.9 1406.8 0.010800000 0.026133333 453.0 1401.2 0.0081333333 0.025233333 459.1 1418.0 0.0087000000 0.024900000 464.6 1438.8 0.010366667 0.025666667 469.6 1469.6 0.012600000 0.027466667 473.1 1485.7 0.015133333 0.028166667 474.6 1505.5 0.018633333 0.029266667 474.3 1518.7 0.023466667 0.028900000 475.4 1515.7 0.023800000 0.028866667 472.9 1522.6 0.025966667 0.029900000 468.7 1523.7 0.025966667 0.031266667 467.5 1540.6 0.030633333 0.033000000 464.7 1553.3 0.031700000 0.032733333 461.2 1552.4 0.031566667 0.034333333 457.1 1561.5 0.033800000 0.036300000 453.0 1537.3 0.033433333 0.035333333 447.5 1506.1 0.018366667 0.032566667 449.6 1514.2 0.010200000 0.031533333 454.2 1550.0 0.017100000 0.035700000 458.5 1586.7 0.027866667 0.037533333 464.1 1606.4 0.028000000 0.039166667 466.3 1637.0 0.030200000 0.040600000 468.1 1629.5 0.035333333 0.041566667 460.0 1643.4 0.043000000 0.041666667 459.2 1671.6 0.039433333 0.042233333 455.7 1666.8 0.030900000 0.041066667 459.5 1668.4 0.023933333 0.038300000 455.9 1654.1 0.023600000 0.039066667 458.0 1671.3 0.023766667 0.038266667 461.5 1692.1 0.023266667 0.038033333 462.2 1716.3 0.023233333 0.039733333 465.4 1754.9 0.024766667 0.040066667 467.4 1777.9 0.027400000 0.040600000 468.5 1796.4 0.027166667 0.038900000 466.5 1813.1 0.028566667 0.039800000 467.7 1810.1 0.028033333 0.038766667 471.9 1834.6 0.029100000 0.039133333 474.8 1860.0 0.029433333 0.039800000 477.7 1892.5 0.032800000 0.040133333 479.9 1906.1 0.034966667 0.041066667 481.9 1948.7 0.035366667 0.041566667 484.8 1965.4 0.034800000 0.041633333 491.3 1985.2 0.035066667 0.041433333 495.6 1993.7 0.036866667 0.041400000 498.3 2036.9 0.039000000 0.041500000 497.6 2066.4 0.038800000 0.041433333 501.7 2099.3 0.038600000 0.041966667 507.8 2147.6 0.041566667 0.043500000 511.8 2190.1 0.046333333 0.045566667 511.8 2195.8 0.045966667 0.045833333 506.2 2218.3 0.050500000 0.047800000 503.1 2229.2 0.045800000 0.046966667 507.1 2241.8 0.045266667 0.044400000 510.8 2255.2 0.036566667 0.047100000 518.0 2287.7 0.043466667 0.049333333 521.3 2300.6 0.047866667 0.053300000 521.9 2327.3 0.050633333 0.052433333 525.4 2366.9 0.055066667 0.053033333 528.3 2385.3 0.052266667 0.050733333 533.8 2383.0 0.055800000 0.054200000 536.5 2416.5 0.061400000 0.058833333 532.8 2419.8 0.062400000 0.059133333 527.6 2433.2 0.070466667 0.061366667 523.2 2423.5 0.073166667 0.065333333 521.4 2408.6 0.072600000 0.065633333 518.1 2406.5 0.067533333 0.068200000 519.4 2435.8 0.063833333 0.066500000 521.2 2413.8 0.053600000 0.062666667 524.7 2478.6 0.038600000 0.058233333 530.8 2478.4 0.042066667 0.058833333 534.1 2491.1 0.050500000 0.057500000 536.5 2491.0 0.042333333 0.055200000 542.6 2545.6 0.034333333 0.056500000 547.8 2595.1 0.037466667 0.056566667 554.4 2622.1 0.042400000 0.056266667 562.5 2671.3 0.048500000 0.056100000 565.2 2734.0 0.056400000 0.061000000 560.1 2741.0 0.066100000 0.062266667 556.1 2738.3 0.083900000 0.065966667 548.5 2762.8 0.074633333 0.063000000 542.1 2747.4 0.076033333 0.066366667 532.8 2755.2 0.082666667 0.070500000 522.8 2719.3 0.082833333 0.072700000 511.9 2695.4 0.073333333 0.069733333 505.3 2642.7 0.058700000 0.067033333 506.8 2669.6 0.054000000 0.069733333 505.5 2714.9 0.063333333 0.070933333 501.0 2752.7 0.056833333 0.072233333 502.2 2804.4 0.049533333 0.069100000 505.5 2816.9 0.051666667 0.068866667 502.6 2828.6 0.051700000 0.067900000 505.3 2856.8 0.046966667 0.065500000 508.1 2896.0 0.046233333 0.070133333 507.7 2942.7 0.048266667 0.070966667 509.4 3001.8 0.054733333 0.069766667 513.0 2994.1 0.061366667 0.071600000 513.7 3020.5 0.064100000 0.075800000 514.1 3115.9 0.064833333 0.078500000 512.5 3142.6 0.073166667 0.079333333 509.7 3181.6 0.086800000 0.081966667 503.3 3181.7 0.093600000 0.084366667 496.1 3178.9 0.093733333 0.084366667 497.2 3207.4 0.096300000 0.084833333 487.6 3201.3 0.11803333 0.096066667 474.0 3233.4 0.13460000 0.11150000 451.2 3157.0 0.10050000 0.10016667 464.9 3159.1 0.092366667 0.10433333 465.3 3199.2 0.13710000 0.11640000 455.3 3261.1 0.14366667 0.12010000 453.7 3250.2 0.14830000 0.12656667 448.9 3264.6 0.15086667 0.13600000 447.1 3219.3 0.12023333 0.13230000 451.2 3170.4 0.12893333 0.13446667 447.1 3179.9 0.12360000 0.12943333 449.1 3154.5 0.097066667 0.12200000 464.9 3159.3 0.079333333 0.10340000 475.8 3186.6 0.080800000 0.10436667 484.3 3258.3 0.084200000 0.10346667 493.6 3306.4 0.091866667 0.11260000 496.4 3365.1 0.087933333 0.11323333 497.5 3451.7 0.091333333 0.11543333 500.4 3498.0 0.098433333 0.12686667 501.5 3520.6 0.10343333 0.12340000 502.2 3535.2 0.089733333 0.11373333 511.0 3577.5 0.081833333 0.11426667 518.2 3599.2 0.075233333 0.10913333 533.9 3635.8 0.071033333 0.10590000 543.2 3662.4 0.071466667 0.10080000 553.4 3719.3 0.068866667 0.089033333 576.8 3711.6 0.061300000 0.079466667 598.0 3721.3 0.055333333 0.078866667 620.0 3734.7 0.053400000 0.078400000 631.9 3776.7 0.055333333 0.076366667 634.8 3823.0 0.057333333 0.085766667 630.1 3865.3 0.060333333 0.090833333 630.5 3923.0 0.060033333 0.092400000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/results/e4.dat000066400000000000000000000062551400612667500251370ustar00rootroot00000000000000/*quarterly, unadjusted, West German real per capita disposable income, personal consumption expenditures, 1960Q1-1987Q4; source: Deutsches Institut fuer Wirtschaftsforschung, Berlin */ <1960 Q1> inc cons 1684.6080 1505.3198 1757.2068 1632.8338 1842.7211 1655.8021 2027.3177 1889.8641 1859.0561 1600.8018 1832.6429 1686.0382 1893.5360 1739.6939 2098.9234 1958.8067 1873.2676 1645.0461 1908.6426 1798.0200 1989.5797 1805.1480 2203.5812 2038.5067 1931.2619 1673.9302 1980.3270 1829.8065 2065.5097 1848.9135 2256.8667 2065.9135 2040.4667 1758.5866 2098.8673 1894.7205 2145.8642 1910.8631 2427.6995 2165.6707 2178.3079 1830.4957 2268.4690 2024.4865 2313.5771 2040.4966 2548.2016 2274.2020 2239.8707 1919.7148 2286.0157 2070.1321 2379.5459 2085.6752 2535.5248 2269.4856 2247.8021 1942.0016 2311.8334 2063.5617 2332.9532 2088.5606 2579.1389 2320.2063 2348.2887 1965.2127 2404.7787 2164.5546 2478.4108 2182.9295 2808.6086 2467.3345 2535.4286 2121.2628 2605.4529 2307.8719 2688.1167 2333.5107 2998.7831 2626.8251 2695.4440 2252.5326 2764.9544 2445.3018 2879.4832 2484.5415 3255.6348 2810.1885 2825.4761 2383.4010 2877.2233 2575.9185 2955.7203 2578.9525 3378.4279 2872.9650 3014.1083 2517.0234 3030.1896 2645.5602 3092.0762 2682.6305 3491.3989 2962.6573 3098.3107 2607.4582 3091.6898 2755.3575 3144.9089 2732.3144 3535.0880 2988.6982 3096.3842 2606.4549 3110.8586 2748.4852 3222.0775 2775.8346 3613.9943 3012.7843 3233.5315 2647.7614 3319.4594 2854.9956 3323.1825 2880.3328 3723.1654 3164.0112 3312.5138 2808.3615 3324.6223 2965.6652 3418.3893 2978.0314 3824.4625 3280.6247 3414.6557 2914.1164 3438.2362 3095.7771 3487.2942 3122.1189 3973.8991 3438.6965 3546.9684 3053.1464 3553.1513 3216.7262 3655.2346 3254.8354 4102.7937 3543.8848 3680.9675 3130.1370 3783.8147 3406.7708 3755.9600 3327.0867 4261.4059 3669.2334 3797.3271 3279.6486 3786.5219 3324.2316 3790.9261 3369.4241 4282.9525 3682.5376 3848.1635 3250.4014 3764.6489 3308.7353 3759.0830 3339.1146 4294.2124 3661.0499 3811.5833 3224.8444 3709.8919 3291.6504 3641.5356 3260.4145 4180.7126 3611.8419 3734.1328 3259.6856 3698.3154 3361.7589 3664.9417 3347.9925 4237.3911 3700.2983 3847.0869 3323.8678 3766.3393 3424.4785 3783.3845 3430.6044 4327.6089 3753.7867 3887.8617 3335.6273 3839.1482 3469.0466 3859.0148 3533.5180 4431.0216 3859.7411 4049.0191 3452.2034 4053.1962 3669.5399 4077.4384 3673.5696 4653.9432 3999.3784 4191.4281 3540.2152 4163.4328 3750.5110 4177.7770 3775.5819 4811.1361 4150.3215 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/results/e5.dat000066400000000000000000000266301400612667500251370ustar00rootroot00000000000000/*monthly West German interest rate on 3-months loans in the money market (i_short), yields on bonds outstanding for total fixed interest securities (i_long), 1960M1-1987M12; source: Deutsche Bundesbank */ <1960 M1> i_short i_long 4.3600000 6.2000000 4.4700000 6.2000000 4.7100000 6.2000000 4.5900000 6.2000000 4.6400000 6.2000000 5.2500000 6.4000000 5.5800000 6.6000000 5.4400000 6.5000000 5.6100000 6.4000000 6.1000000 6.4000000 5.3800000 6.2000000 5.0600000 6.2000000 4.6600000 6.1000000 4.1300000 6.1000000 3.7300000 6.0000000 3.3400000 5.8000000 3.2300000 5.7000000 3.1300000 5.7000000 3.1600000 5.8000000 3.0900000 5.9000000 3.0600000 6.0000000 4.0500000 6.0000000 3.7100000 6.0000000 3.8300000 6.0000000 2.9300000 5.9000000 2.9400000 5.9000000 3.0200000 5.8000000 3.0800000 5.8000000 3.0800000 5.9000000 3.1300000 6.0000000 3.2900000 6.0000000 3.2600000 6.1000000 3.2000000 6.1000000 4.4500000 6.2000000 4.3300000 6.2000000 4.3500000 6.2000000 3.2900000 6.1000000 3.3100000 6.1000000 3.5300000 6.1000000 3.5600000 6.1000000 3.6000000 6.1000000 3.8300000 6.1000000 3.9800000 6.1000000 3.8100000 6.1000000 3.7500000 6.1000000 5.1300000 6.1000000 5.0000000 6.1000000 4.9800000 6.1000000 3.3300000 6.0000000 3.3300000 6.0000000 3.4600000 6.0000000 3.5500000 6.1000000 3.6900000 6.2000000 3.7500000 6.2000000 3.6900000 6.3000000 3.9100000 6.3000000 4.0800000 6.3000000 5.4200000 6.3000000 5.5000000 6.3000000 5.3600000 6.3000000 3.8800000 6.3000000 3.9500000 6.4000000 4.2800000 6.4000000 4.5200000 6.5000000 4.6900000 6.7000000 4.8000000 6.8000000 5.0800000 6.9000000 5.2700000 7.0000000 5.3600000 7.1000000 6.6600000 7.2000000 6.5800000 7.3000000 6.5500000 7.4000000 5.2300000 7.3000000 5.3600000 7.3000000 5.6900000 7.4000000 6.2100000 7.6000000 6.3500000 7.7000000 6.8100000 7.9000000 6.8900000 8.1000000 7.0000000 8.1000000 6.8000000 8.1000000 7.8800000 8.0000000 7.7300000 7.9000000 7.5700000 7.6000000 5.6900000 7.4000000 5.5600000 7.3000000 5.0400000 7.2000000 4.4800000 6.9000000 3.6900000 6.8000000 3.9800000 6.9000000 3.5100000 6.9000000 3.5600000 6.9000000 3.4300000 6.9000000 4.2000000 6.9000000 4.0000000 7.0000000 4.0700000 7.0000000 3.3200000 6.9000000 3.4500000 7.0000000 3.5200000 7.0000000 3.6400000 6.9000000 3.6800000 6.7000000 3.7200000 6.7000000 3.5900000 6.7000000 3.5500000 6.6000000 3.5400000 6.5000000 4.7500000 6.5000000 4.5000000 6.6000000 4.4400000 6.5000000 3.8700000 6.5000000 3.9100000 6.5000000 4.2100000 6.6000000 4.4000000 6.7000000 4.3800000 6.8000000 5.5000000 6.9000000 5.7800000 7.1000000 6.5000000 7.1000000 6.9400000 7.2000000 7.4200000 7.3000000 7.6900000 7.3000000 8.8300000 7.4000000 9.2900000 7.5000000 9.5100000 7.6000000 9.8100000 7.9000000 9.8600000 8.0000000 9.9300000 8.2000000 9.8800000 8.6000000 9.5900000 8.6000000 9.1600000 8.4000000 9.3600000 8.4000000 9.5300000 8.5000000 8.8400000 8.6000000 8.1200000 8.3000000 7.5000000 7.9000000 7.4700000 7.9000000 7.4600000 8.0000000 6.3600000 8.0000000 6.1600000 8.1000000 6.8000000 8.3000000 7.6600000 8.5000000 7.5600000 8.5000000 7.5900000 8.4000000 7.8000000 8.3000000 6.7900000 8.2000000 6.6300000 8.1000000 5.1900000 7.9000000 4.8800000 7.7000000 4.8000000 7.8000000 4.7800000 8.0000000 4.7100000 8.2000000 4.6500000 8.3000000 4.6500000 8.4000000 4.8000000 8.3000000 5.3200000 8.3000000 6.8800000 8.4000000 8.0700000 8.6000000 8.6000000 8.7000000 7.8900000 8.6000000 7.9600000 8.6000000 8.7700000 8.7000000 10.620000 8.9000000 12.420000 9.4000000 13.620000 10.200000 14.300000 10.300000 14.570000 10.100000 14.250000 9.8000000 14.490000 9.9000000 13.620000 9.6000000 13.200000 9.7000000 12.090000 9.7000000 10.670000 10.000000 11.200000 10.700000 10.070000 10.800000 9.1000000 10.800000 9.4600000 10.900000 9.4800000 10.900000 9.6500000 10.900000 9.6900000 10.800000 9.7800000 10.900000 9.0400000 10.600000 8.6000000 9.9000000 7.7400000 9.4000000 6.4300000 9.0000000 5.7100000 8.9000000 4.8900000 8.8000000 4.9900000 8.5000000 4.8800000 8.4000000 4.6600000 8.4000000 3.8800000 8.6000000 3.9300000 8.7000000 4.0700000 8.7000000 4.1200000 8.7000000 4.2100000 8.6000000 3.9300000 8.4000000 3.7200000 8.2000000 3.7400000 7.8000000 3.6200000 7.8000000 3.7700000 8.0000000 4.1400000 8.3000000 4.4700000 8.4000000 4.5600000 8.3000000 4.5600000 8.1000000 4.8500000 8.0000000 4.6900000 7.6000000 4.9300000 7.4000000 4.7800000 7.2000000 4.7100000 7.1000000 4.7300000 7.0000000 4.6200000 6.6000000 4.4400000 6.4000000 4.2800000 6.4000000 4.2900000 6.3000000 4.1200000 6.1000000 4.1500000 6.0000000 4.1300000 6.0000000 4.1500000 6.0000000 3.9800000 6.0000000 3.5800000 5.8000000 3.4600000 5.7000000 3.5100000 5.6000000 3.5600000 5.6000000 3.6000000 5.8000000 3.6800000 6.0000000 3.7500000 6.3000000 3.7000000 6.6000000 3.7000000 6.4000000 3.9500000 6.3000000 3.8500000 6.6000000 4.0600000 6.6000000 3.8900000 6.7000000 4.1500000 7.0000000 4.4700000 7.1000000 5.5400000 7.2000000 5.9200000 7.6000000 6.4600000 8.0000000 6.8400000 7.9000000 7.0900000 7.7000000 7.8900000 7.8000000 8.7600000 7.9000000 9.6500000 8.3000000 9.5800000 8.0000000 8.8600000 8.1000000 8.9700000 8.5000000 9.6400000 9.5000000 10.220000 9.6000000 10.260000 8.8000000 10.110000 8.3000000 9.7000000 8.0000000 8.9800000 7.9000000 8.9700000 8.3000000 9.0800000 8.5000000 9.4500000 9.0000000 10.200000 9.1000000 9.4700000 9.2000000 10.670000 9.9000000 13.600000 10.400000 13.190000 10.400000 13.200000 11.000000 13.090000 11.100000 12.960000 11.200000 12.900000 11.500000 12.500000 11.300000 11.780000 10.600000 11.080000 10.200000 10.820000 9.9000000 10.460000 10.000000 10.270000 9.9000000 9.8700000 9.6000000 9.3300000 9.1000000 9.1800000 8.9000000 9.2800000 9.2000000 9.4600000 9.5000000 9.0000000 9.2000000 8.1800000 8.8000000 7.5800000 8.4000000 7.3100000 8.2000000 6.6200000 8.0000000 5.8200000 7.7000000 5.8300000 7.7000000 5.4500000 7.4000000 5.2000000 7.4000000 5.3300000 7.7000000 5.5700000 8.1000000 5.5700000 8.2000000 5.7100000 8.3000000 5.8800000 8.4000000 6.1800000 8.2000000 6.3000000 8.2000000 6.4800000 8.3000000 6.1200000 8.2000000 5.9500000 8.1000000 5.8600000 7.9000000 5.8400000 7.9000000 6.1000000 8.0000000 6.1300000 8.1000000 6.1300000 8.1000000 6.0200000 7.9000000 5.8200000 7.7000000 6.0700000 7.4000000 5.9600000 7.2000000 5.8300000 7.0000000 5.8700000 7.1000000 6.1600000 7.5000000 6.3900000 7.7000000 6.0200000 7.3000000 5.8400000 7.1000000 5.6800000 7.0000000 5.3400000 6.8000000 4.7900000 6.5000000 4.6900000 6.4000000 4.8100000 6.6000000 4.8400000 6.7000000 4.8300000 6.6000000 4.6700000 6.4000000 4.4900000 6.3000000 4.5400000 6.0000000 4.4900000 5.6000000 4.6000000 5.9000000 4.6000000 6.0000000 4.6300000 6.0000000 4.5700000 5.8000000 4.5000000 5.8000000 4.5900000 6.0000000 4.6900000 6.1000000 4.8100000 6.0000000 4.4900000 5.9000000 3.9700000 5.7000000 3.9900000 5.6000000 3.8900000 5.5000000 3.7600000 5.4000000 3.7000000 5.5000000 3.8300000 5.8000000 3.9500000 6.0000000 3.9900000 6.2000000 4.7000000 6.5000000 3.9400000 6.0000000 3.6500000 5.8000000 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/results/e6.dat000066400000000000000000000117271400612667500251410ustar00rootroot00000000000000/* sample: 1972Q2 -- 1998Q4 West German data until 1990Q2, all of Germany aferwards Dp - \Delta log gdp deflator (source: Deutsches Institut für Wirtschaftsforschung, Volkswirtschaftliche Gesamtrechnung) R - nominal long term interest rate (Umlaufsrendite) (source: Monatsberichte der Deutschen Bundesbank, quarterly values are values of last month of quarter) */ <1972 Q2> Dp R -0.00313258 0.083 0.0188713 0.083 0.0248036 0.087 0.0162776 0.087 2.89679E-4 0.102 0.016829 0.098 0.0385835 0.097 -0.00144386 0.107 0.0127239 0.109 0.0238972 0.108 0.0427728 0.099 -0.0103779 0.089 0.00558424 0.084 0.00870609 0.087 0.0389199 0.086 -0.0196176 0.078 0.00731993 0.083 0.0180764 0.081 0.0237775 0.074 -0.0144377 0.07 0.0110059 0.064 0.0104017 0.06 0.0354648 0.06 -0.0157599 0.056 0.0100193 0.06 0.0180621 0.064 0.0256915 0.066 -0.0170689 0.071 0.00350475 0.08 0.0256438 0.078 0.0315075 0.08 -0.0132775 0.095 0.0130968 0.083 0.0151458 0.083 0.0312119 0.091 -0.0207896 0.104 0.0104489 0.111 0.018106 0.113 0.0405002 0.099 -0.0201483 0.096 0.00380802 0.092 0.0215569 0.088 0.0327106 0.08 -0.0201726 0.074 -0.00333166 0.081 0.0192871 0.084 0.0345473 0.083 -0.0262156 0.079 -0.00519753 0.081 0.0132318 0.077 0.0374279 0.07 -0.0291948 0.077 -0.00261354 0.07 0.0172353 0.064 0.0376387 0.066 -0.0204763 0.06 9.00269E-4 0.06 0.0125732 0.058 0.0344677 0.06 -0.0220394 0.056 -0.00202703 0.055 0.00173426 0.062 0.0365901 0.058 -0.0252557 0.056 9.2268E-4 0.06 0.00451374 0.063 0.0383272 0.062 -0.0211368 0.07 -5.33104E-4 0.071 0.00981092 0.071 0.0373549 0.078 -0.016232 0.09 0.00197124 0.09 0.00687361 0.091 0.0274582 0.09 -0.0140786 0.086 0.0166497 0.086 0.0144682 0.088 0.043004 0.087 -0.0127769 0.082 0.00927353 0.084 0.0179157 0.082 0.030508 0.074 -0.0105906 0.065 0.00747108 0.067 0.00467587 0.061 0.0310678 0.056 -0.0153685 0.062 8.10146E-4 0.069 0.00806475 0.074 0.0287657 0.074 -0.0183783 0.071 0.00449467 0.064 0.00988674 0.061 0.0245948 0.055 -0.0185189 0.058 -0.00590181 0.059 0.00581503 0.055 0.0243654 0.051 -0.0157485 0.051 -0.00749254 0.05 0.00388288 0.051 0.0242448 0.051 -0.014647 0.047 -0.00204897 0.047 0.00247526 0.041 0.0239234 0.038 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/results/results_svar.py000066400000000000000000000006131400612667500272330ustar00rootroot00000000000000""" Test Results for the SVAR model. Obtained from R using svartest.R """ class SVARdataResults(object): def __init__(self): self.A = ([ [1.0, 0.0, 0], [-0.506802245, 1.0, 0], [-5.536056520, 3.04117686, 1.0]]) self.B = ([ [0.0075756676, 0.0, 0.0], [0.0, 0.00512051886, 0.0], [0.0, 0.0, 0.020708948]]) statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/results/results_svar_st.py000066400000000000000000001217151400612667500277500ustar00rootroot00000000000000import numpy as np from statsmodels.tools.testing import ParamsTableTestBunch est = dict( mlag_var=3, fpe_var=7.47593408072e-13, aic_var=-19.4085401106207, hqic_var=-19.20760258859687, sbic_var=-18.91206199634062, tparms_var=30, k_var=30, df_eq_var=10, k_aux=18, k_eq=18, k_eq_var=3, k_dv_var=3, neqs_var=3, k_dv=3, neqs=3, N_cns=12, ic_ml=9, rc_ml=0, oid_df=0, N=199, rank=6, F_3_var=9.018236399703298, df_r3_var=189, df_m3_var=9, ll_3_var=364.1156201942387, r2_3_var=.3004252574875596, rmse_3_var=.0398398997327694, k_3_var=10, obs_3_var=199, F_2_var=5.002566602091567, df_r2_var=189, df_m2_var=9, ll_2_var=728.0001662442413, r2_2_var=.1923874161594955, rmse_2_var=.0064000343524738, k_2_var=10, obs_2_var=199, F_1_var=8.356742395485949, df_r1_var=189, df_m1_var=9, ll_1_var=694.4411801251371, r2_1_var=.2846617748967589, rmse_1_var=.0075756675969815, k_1_var=10, obs_1_var=199, df_r=193, df_r_var=189, ll=1945.759734821802, ll_var=1961.149741006759, detsig_ml_var=5.52855987611e-13, detsig_var=6.45335912865e-13, T_var=199, N_gaps_var=0, tmin=0, tmax=198, cmd="svar", cmdline="svar gdp cons inv, aeq(A) beq(B) lags(1/3) var dfk small", predict="svar_p", dfk_var="dfk", vcetype="EIM", lags_var="1 2 3", depvar_var="gdp cons inv", eqnames_var="gdp cons inv", endog_var="gdp cons inv", timevar="qtrdate", tsfmt="%tq", small="small", title="Structural vector autoregression", cns_b="[b_1_2]_cons = 0:[b_1_3]_cons = 0:[b_2_1]_cons = 0:[b_2_3]_cons = 0:[b_3_1]_cons = 0:[b_3_2]_cons = 0", # noqa:E501 cns_a="[a_1_1]_cons = 1:[a_1_2]_cons = 0:[a_1_3]_cons = 0:[a_2_2]_cons = 1:[a_2_3]_cons = 0:[a_3_3]_cons = 1", # noqa:E501 properties="b V", ) params_table = np.array([ 1, np.nan, np.nan, np.nan, np.nan, np.nan, 193, 1.9723316757957, 0, -.50680224519119, .04791445158754, -10.577231469827, 6.466439125e-21, -.60130543578568, -.41229905459671, 193, 1.9723316757957, 0, -5.5360565201616, .24220266982262, -22.857124259679, 8.232580974e-57, -6.013760517815, -5.0583525225081, 193, 1.9723316757957, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, 193, 1.9723316757957, 0, 1, np.nan, np.nan, np.nan, np.nan, np.nan, 193, 1.9723316757957, 0, 3.0411768648574, .28669329203947, 10.607771263929, 5.260805180e-21, 2.4757226037298, 3.606631125985, 193, 1.9723316757957, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, 193, 1.9723316757957, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, 193, 1.9723316757957, 0, 1, np.nan, np.nan, np.nan, np.nan, np.nan, 193, 1.9723316757957, 0, .00757566759698, .00037973390425, 19.94993734326, 8.739086225e-49, .00682670638925, .00832462880472, 193, 1.9723316757957, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, 193, 1.9723316757957, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, 193, 1.9723316757957, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, 193, 1.9723316757957, 0, .00512051886486, .00025666841839, 19.94993734326, 8.739086225e-49, .00461428361309, .00562675411662, 193, 1.9723316757957, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, 193, 1.9723316757957, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, 193, 1.9723316757957, 0, 0, np.nan, np.nan, np.nan, np.nan, np.nan, 193, 1.9723316757957, 0, .02070894812762, .00103804577284, 19.94993734326, 8.739086225e-49, .01866157756892, .02275631868632, 193, 1.9723316757957, 0]).reshape(18, 9) params_table_colnames = 'b se t pvalue ll ul df crit eform'.split() params_table_rownames = [ '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons'] b = np.array([ 1, -.50680224519119, -5.5360565201616, 0, 1, 3.0411768648574, 0, 0, 1, .00757566759698, 0, 0, 0, .00512051886486, 0, 0, 0, .02070894812762]) b_colnames = [ '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons'] b_rownames = 'y1'.split() cov = np.array([ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, .00229579467093, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, .0586621332692, 0, 0, -.04165561908647, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -.04165561908647, 0, 0, .08219304370043, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.441978380e-07, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6.587867700e-08, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.077539027e-06 ]).reshape(18, 18) cov_colnames = [ '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons'] cov_rownames = [ '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons'] constraints = np.array([ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]).reshape(12, 19) constraints_colnames = [ '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_cons', '_r'] constraints_rownames = 'r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12'.split() Sigma = np.array([ .00005739073954, .00002908575565, .00022926345064, .00002908575565, .00004096043971, .0000364524456, .00022926345064, .0000364524456, .00158721761072]).reshape(3, 3) Sigma_colnames = 'gdp cons inv'.split() Sigma_rownames = 'gdp cons inv'.split() G_var = np.array([ 1, .00772119249309, .00832845872247, .00812414768988, .00772450051084, .00839168407728, .00810118500591, .00793331513676, .00846090823295, .009386666817, .00772119249309, .00013590038218, .00010436399127, .00039355021854, .00008395547668, .00009296949447, .0001468047815, .00007985818625, .00008622263703, .00012491817455, .00832845872247, .00010436399127, .0001177915254, .0001572415776, .00008140583018, .00008416323485, .00014479739125, .00007884622137, .0000839417926, .00012879456896, .00812414768988, .00039355021854, .0001572415776, .00222357091844, .0001852293649, .00023227850984, .00042852108282, .00014155595459, .00015686829612, .00027431611677, .00772450051084, .00008395547668, .00008140583018, .0001852293649, .00013589031191, .00010428130248, .00039335411738, .00008365141811, .00009289191013, .0001446903813, .00839168407728, .00009296949447, .00008416323485, .00023227850984, .00010428130248, .000118309348, .00015273148978, .00008252427592, .00008497769731, .00014704611828, .00810118500591, .0001468047815, .00014479739125, .00042852108282, .00039335411738, .00015273148978, .00222677863348, .00017054880362, .0002272506141, .00033983014403, .00793331513676, .00007985818625, .00007884622137, .00014155595459, .00008365141811, .00008252427592, .00017054880362, .00013762976929, .00010632331501, .00038874930061, .00846090823295, .00008622263703, .0000839417926, .00015686829612, .00009289191013, .00008497769731, .0002272506141, .00010632331501, .000119472079, .00016022586575, .009386666817, .00012491817455, .00012879456896, .00027431611677, .0001446903813, .00014704611828, .00033983014403, .00038874930061, .00016022586575, .00210416228523 ]).reshape(10, 10) G_var_colnames = [ '_cons', 'L.gdp', 'L.cons', 'L.inv', 'L2.gdp', 'L2.cons', 'L2.inv', 'L3.gdp', 'L3.cons', 'L3.inv'] G_var_rownames = [ '_cons', 'L.gdp', 'L.cons', 'L.inv', 'L2.gdp', 'L2.cons', 'L2.inv', 'L3.gdp', 'L3.cons', 'L3.inv'] bf_var = np.array([ -.28614799058891, .02569110476595, -.18003096181942, .6738689560015, .29544106895159, .18370240194258, .03057777928182, -.01444291994803, .01263245201514, .00128149319157, -.12715587337617, -.08663431448056, -.35906668730993, .25639388994688, .20570668527827, .41845237867104, .02404284475263, .00384555072972, .04190581088286, .00483719365525, -1.8625374877103, .33142498594011, -.48831009148236, 4.4033743272466, .87819807698004, -.12378698529172, .22371717935155, -.09655522236577, .03345298758638, -.02059735685585]) bf_var_colnames = [ 'L.gdp', 'L2.gdp', 'L3.gdp', 'L.cons', 'L2.cons', 'L3.cons', 'L.inv', 'L2.inv', 'L3.inv', '_cons', 'L.gdp', 'L2.gdp', 'L3.gdp', 'L.cons', 'L2.cons', 'L3.cons', 'L.inv', 'L2.inv', 'L3.inv', '_cons', 'L.gdp', 'L2.gdp', 'L3.gdp', 'L.cons', 'L2.cons', 'L3.cons', 'L.inv', 'L2.inv', 'L3.inv', '_cons'] bf_var_rownames = 'r1'.split() B = np.array([ .00757566759698, 0, 0, 0, .00512051886486, 0, 0, 0, .02070894812762]).reshape(3, 3) B_colnames = 'gdp cons inv'.split() B_rownames = 'gdp cons inv'.split() A = np.array([ 1, 0, 0, -.50680224519119, 1, 0, -5.5360565201616, 3.0411768648574, 1]).reshape(3, 3) A_colnames = 'gdp cons inv'.split() A_rownames = 'gdp cons inv'.split() beq = np.array([ np.nan, 0, 0, 0, np.nan, 0, 0, 0, np.nan]).reshape(3, 3) beq_colnames = 'c1 c2 c3'.split() beq_rownames = 'r1 r2 r3'.split() aeq = np.array([ 1, 0, 0, np.nan, 1, 0, np.nan, np.nan, 1]).reshape(3, 3) aeq_colnames = 'c1 c2 c3'.split() aeq_rownames = 'r1 r2 r3'.split() V_var = np.array([ .02944043907167, -.00139167936464, -.0010606099932, -.01749947940302, .00202095994301, -.00138072504574, -.00385176007523, .00038731129816, .00020334459451, -.00004143863419, .01492048062093, -.00070530622659, -.00053751952583, -.00886877545113, .00102422703656, -.00069975455317, -.00195208065406, .0001962902355, .00010305549704, -.00002100119285, .11760811420253, -.00555945464168, -.00423690492187, -.06990659232715, .00807329290157, 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-.00002632026649, -.00002980084833, -.0000313877223, -.00001119725114, -.00001779264303, -.00001437627996, 6.908586346e-06, 6.744287298e-06, 5.690575137e-06, 1.065631164e-06, -.00114604081571, -.00129759280914, -.00136668870299, -.00048755231406, -.00077472981275, -.00062597404237, .00030081465683, .00029366072412, .00024777983816, .00004639986487 ]).reshape(30, 30) V_var_colnames = [ 'L.gdp', 'L2.gdp', 'L3.gdp', 'L.cons', 'L2.cons', 'L3.cons', 'L.inv', 'L2.inv', 'L3.inv', '_cons', 'L.gdp', 'L2.gdp', 'L3.gdp', 'L.cons', 'L2.cons', 'L3.cons', 'L.inv', 'L2.inv', 'L3.inv', '_cons', 'L.gdp', 'L2.gdp', 'L3.gdp', 'L.cons', 'L2.cons', 'L3.cons', 'L.inv', 'L2.inv', 'L3.inv', '_cons'] V_var_rownames = [ 'L.gdp', 'L2.gdp', 'L3.gdp', 'L.cons', 'L2.cons', 'L3.cons', 'L.inv', 'L2.inv', 'L3.inv', '_cons', 'L.gdp', 'L2.gdp', 'L3.gdp', 'L.cons', 'L2.cons', 'L3.cons', 'L.inv', 'L2.inv', 'L3.inv', '_cons', 'L.gdp', 'L2.gdp', 'L3.gdp', 'L.cons', 'L2.cons', 'L3.cons', 'L.inv', 'L2.inv', 'L3.inv', '_cons'] b_var = np.array([ -.28614799058891, .02569110476595, -.18003096181942, .6738689560015, .29544106895159, .18370240194258, .03057777928182, -.01444291994803, .01263245201514, .00128149319157, -.12715587337617, -.08663431448056, -.35906668730993, .25639388994688, .20570668527827, .41845237867104, .02404284475263, .00384555072972, .04190581088286, .00483719365525, -1.8625374877103, .33142498594011, -.48831009148236, 4.4033743272466, .87819807698004, -.12378698529172, .22371717935155, -.09655522236577, .03345298758638, -.02059735685585]) b_var_colnames = [ 'L.gdp', 'L2.gdp', 'L3.gdp', 'L.cons', 'L2.cons', 'L3.cons', 'L.inv', 'L2.inv', 'L3.inv', '_cons', 'L.gdp', 'L2.gdp', 'L3.gdp', 'L.cons', 'L2.cons', 'L3.cons', 'L.inv', 'L2.inv', 'L3.inv', '_cons', 'L.gdp', 'L2.gdp', 'L3.gdp', 'L.cons', 'L2.cons', 'L3.cons', 'L.inv', 'L2.inv', 'L3.inv', '_cons'] b_var_rownames = 'y1'.split() results_svar1_small = ParamsTableTestBunch( params_table=params_table, params_table_colnames=params_table_colnames, params_table_rownames=params_table_rownames, b=b, b_colnames=b_colnames, b_rownames=b_rownames, cov=cov, cov_colnames=cov_colnames, cov_rownames=cov_rownames, constraints=constraints, constraints_colnames=constraints_colnames, constraints_rownames=constraints_rownames, Sigma=Sigma, Sigma_colnames=Sigma_colnames, Sigma_rownames=Sigma_rownames, G_var=G_var, G_var_colnames=G_var_colnames, G_var_rownames=G_var_rownames, bf_var=bf_var, bf_var_colnames=bf_var_colnames, bf_var_rownames=bf_var_rownames, B=B, B_colnames=B_colnames, B_rownames=B_rownames, A=A, A_colnames=A_colnames, A_rownames=A_rownames, beq=beq, beq_colnames=beq_colnames, beq_rownames=beq_rownames, aeq=aeq, aeq_colnames=aeq_colnames, aeq_rownames=aeq_rownames, V_var=V_var, V_var_colnames=V_var_colnames, V_var_rownames=V_var_rownames, b_var=b_var, b_var_colnames=b_var_colnames, b_var_rownames=b_var_rownames, **est ) results_svar1_small.__doc__ = """ Scalars e(N) number of observations e(N_cns) number of constraints e(k_eq) number of equations in e(b) e(k_dv) number of dependent variables e(k_aux) number of auxiliary parameters e(ll) log likelihood from svar e(ll_#) log likelihood for equation # e(N_gaps_var) number of gaps in the sample e(k_var) number of coefficients in VAR e(k_eq_var) number of equations in underlying VAR e(k_dv_var) number of dependent variables in underlying VAR e(df_eq_var) average number of parameters in an equation e(df_m_var) model degrees of freedom e(df_r_var) if small, residual degrees of freedom e(obs_#_var) number of observations on equation # e(k_#_var) number of coefficients in equation # e(df_m#_var) model degrees of freedom for equation # e(df_r#_var) residual degrees of freedom for equation # (small only) e(r2_#_var) R-squared for equation # e(ll_#_var) log likelihood for equation # VAR e(chi2_#_var) chi-squared statistic for equation # e(F_#_var) F statistic for equation # (small only) e(rmse_#_var) root mean squared error for equation # e(mlag_var) highest lag in VAR e(tparms_var) number of parameters in all equations e(aic_var) Akaike information criterion e(hqic_var) Hannan-Quinn information criterion e(sbic_var) Schwarz-Bayesian information criterion e(fpe_var) final prediction error e(ll_var) log likelihood from var e(detsig_var) determinant of e(Sigma) e(detsig_ml_var) determinant of Sigma_ml hat e(tmin) first time period in the sample e(tmax) maximum time e(chi2_oid) overidentification test e(oid_df) number of overidentifying restrictions e(rank) rank of e(V) e(ic_ml) number of iterations e(rc_ml) return code from ml Matrices e(b) coefficient vector e(Cns) constraints matrix e(Sigma) Sigma hat matrix e(V) variance-covariance matrix of the estimators e(b_var) coefficient vector of underlying VAR model e(V_var) VCE of underlying VAR model e(bf_var) full coefficient vector with zeros in dropped lags e(G_var) Gamma matrix saved by var; see Methods and formulas in [TS] var svar e(aeq) aeq(matrix), if specified e(acns) acns(matrix), if specified e(beq) beq(matrix), if specified e(bcns) bcns(matrix), if specified e(lreq) lreq(matrix), if specified e(lrcns) lrcns(matrix), if specified e(Cns_var) constraint matrix from var, if varconstraints() is specified e(A) estimated A matrix, if a short-run model e(B) estimated B matrix e(C) estimated C matrix, if a long-run model e(A1) estimated A bar matrix, if a long-run model """ # noqa:E501 statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/results/results_var.py000066400000000000000000000051371400612667500270560ustar00rootroot00000000000000""" Test Results for the VAR model. Obtained from Stata using datasets/macrodata/var.do """ import numpy as np class MacrodataResults(object): def __init__(self): params = [ -0.2794863875, 0.0082427826, 0.6750534746, 0.2904420695, 0.0332267098, -0.0073250059, 0.0015269951, -0.1004938623, -0.1231841792, 0.2686635768, 0.2325045441, 0.0257430635, 0.0235035714, 0.0054596064, -1.97116e+00, 0.3809752365, 4.4143364022, 0.8001168377, 0.2255078864, -0.1241109271, -0.0239026118] params = np.asarray(params).reshape(3, -1) params = np.hstack((params[:, -1][:, None], params[:, :-1:2], params[:, 1::2])) self.params = params self.neqs = 3 self.nobs = 200 self.df_eq = 7 self.nobs_1 = 200 self.df_model_1 = 6 self.rmse_1 = .0075573716985351 self.rsquared_1 = .2739094844780006 self.llf_1 = 696.8213727557811 self.nobs_2 = 200 self.rmse_2 = .0065444260782597 self.rsquared_2 = .1423626064753714 self.llf_2 = 725.6033255319256 self.nobs_3 = 200 self.rmse_3 = .0395942039671031 self.rsquared_3 = .2955406949737428 self.llf_3 = 365.5895183036045 # These are from Stata. They use the LL based definition # We return Lutkepohl statistics. See Stata TS manual page 436 # self.bic = -19.06939794312953 # self.aic = -19.41572126661708 # self.hqic = -19.27556951526737 # These are from R. See var.R in macrodata folder self.bic = -2.758301611618373e+01 self.aic = -2.792933943967127e+01 self.hqic = -2.778918768832157e+01 self.fpe = 7.421287668357018e-13 self.detsig = 6.01498432283e-13 self.llf = 1962.572126661708 self.chi2_1 = 75.44775165699033 # do not know how they calculate this; it's not -2 * (ll1 - ll0) self.chi2_2 = 33.19878716815366 self.chi2_3 = 83.90568280242312 bse = [ .1666662376, .1704584393, .1289691456, .1433308696, .0257313781, .0253307796, .0010992645, .1443272761, .1476111934, .1116828804, .1241196435, .0222824956, .021935591, .0009519255, .8731894193, .8930573331, .6756886998, .7509319263, .1348105496, .1327117543, .0057592114] bse = np.asarray(bse).reshape(3, -1) bse = np.hstack((bse[:, -1][:, None], bse[:, :-1:2], bse[:, 1::2])) self.bse = bse statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/results/results_var_data.py000066400000000000000000000151721400612667500300470ustar00rootroot00000000000000from numpy import array, rec from statsmodels.tools.testing import Holder var_results = Holder() var_results.comment = 'VAR test data converted from vars_results.npz' var_results.causality = array([ (9.317172089406967e-08,), (0.5183914225971917,), (4.8960835385969403e-14,)], dtype=[('causedby', 'float')]) var_results.name = 'var_results' var_results.orthirf = array({ 'realgdp': rec.array([ (0.007557357219752236, 0.003948403413668315, 0.02972434157321242), (0.0015408726821578582, 0.0010664916255201816, 0.00923575489996933), (0.0015874964105555918, 0.0010551760558416706, 0.006102514196485799), (0.0007262051539604352, 0.0005562787500837443, 0.003199064883156089), (0.0005537000868358786, 0.0003520396722562061, 0.0024372344590635623), (0.0003079984190444812, 0.00021674897409108682, .0013369479853037147)], dtype=[('realgdp', 'float'), ('realcons', 'float'), ('realinv', 'float')]), 'realinv': rec.array([ (.0, 0.0, 0.020741992721114832), (.0006890376065674764, .0005338724781743238, 0.004676882806534488), (.00017134455810606506, .000682084896451223, -0.0005205835547221123), (.0005217378718553543, .00030179909990059973, 0.0026650577026759623), (.00034979575853114173, .00022249591743758265, 0.0015804716569096742), (.00017738402507880077, .00013384975583249413, 0.0007585745605878197)], dtype=[('realgdp', 'float'), ('realcons', 'float'), ('realinv', 'float')]), 'realcons': rec.array([ (.0, 0.005219256972675799, -0.01593559385372415), (.0029937089930834665, 0.000991936965470755, 0.019445506482528015), (.002111631850388755, 0.0013051320985438103, 0.00901674690789421), (.000760821255683657, 0.0006894587307924545, 0.0031531908594739904), (.0006879775935656037, 0.0004452087814044681, 0.0029845646103117077), (.0003908528054047277, 0.00026799713044743445, 0.0017324202804285334)], dtype=[('realgdp', 'float'), ('realcons', 'float'), ('realinv', 'float')]) }, dtype=object) var_results.detomega = array([6.69357627913858242322e-13]) var_results.nirfs = array([5.]) var_results.loglike = array([1962.57082404432503608405]) var_results.stderr = array([ (0.0011190205021849168, 0.0009690469778955306, 0.0058627441569700095), (0.169662667084976, 0.14692411307869205, 0.8888923913067142), (0.13128502534984174, 0.11368992508162204, 0.6878252130006585), (0.02619387125804535, 0.022683312533087908, 0.13723427351570822), (0.17352233516355128, 0.15026650017519333, 0.9091138675275061), (0.14590394087772843, 0.12634958224138662, 0.7644162686828472), (0.02578605367156698, 0.022330151532965133, 0.13509764584216039)], dtype=[('realgdp', 'float'), ('realcons', 'float'), ('realinv', 'float')]) var_results.crit = array({ 'sic': [-27.583016116183746], 'hqic': [-27.789187688321583], 'fpe': [7.421287668356912e-13], 'aic': [-27.92933943967129] }, dtype=object) var_results.phis = array([ [[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]], [[-0.27943473587305184269, 0.67501575174854244743, .03321945079394677397], [-0.10046797808205484848, 0.26863955252271337626, .02573872652220415141], [-1.97097367379580989954, 4.41416232699026434005, .22547895322388852857]], [[-.04698727419951594098, 0.42980675754266339794, 0.00826075683324488733], [-.17281970983411520937, 0.35046409430422942322, 0.03288425107568751504], [0.04364931246903419604, 1.65096193457053663778, -.02509804924346402399]], [[-.11912577490062775665, 0.22257198988626961111, 0.02515370046023775175], [-.07584698388980917749, 0.17652397885529469423, 0.01455014973529403233], [-.60265240582682233494, 0.99644320159959076655, 0.12848609767194643649]], [[-.08883245330826733399, 0.18330532474980901214, 0.01686413466798001443], [-.05728563445875266974, 0.11805267650029765969, 0.01072683422606196188], [-.39750493711843060129, 0.80448318531634888107, 0.07619671254154830597]], [[-.04564844379524263945, 0.10099768165139233478, .00855192784337583181], [-.03382143062494445684, 0.07105049775782870669, .00645308084098585207], [-.19869441802790854812, 0.44359103295144985957, .03657192299636715521]]]) var_results.nahead = array([5.]) var_results.totobs = array([202.]) var_results.type = array(['const'], dtype='|S5') var_results.obs = array([200.]) var_results.irf = array({ 'realgdp': rec.array([ (1.0, 0.0, 0.0), (-0.27943473587305184, -0.10046797808205485, -1.97097367379581), (-0.04698727419951594, -0.1728197098341152, 0.043649312469034196), (-0.11912577490062776, -0.07584698388980918, -0.6026524058268223), (-0.08883245330826733, -0.05728563445875267, -0.3975049371184306), (-0.04564844379524264, -0.03382143062494446, -0.19869441802790855)], dtype=[('realgdp', 'float'), ('realcons', 'float'), ('realinv', 'float')]), 'realinv': rec.array([ (0.0, 0.0, 1.0), (0.033219450793946774, 0.02573872652220415, 0.22547895322388853), (0.008260756833244887, 0.032884251075687515, -0.025098049243464024), (0.025153700460237752, 0.014550149735294032, 0.12848609767194644), (0.016864134667980014, 0.010726834226061962, 0.0761967125415483), (0.008551927843375832, 0.006453080840985852, 0.036571922996367155)], dtype=[('realgdp', 'float'), ('realcons', 'float'), ('realinv', 'float')]), 'realcons': rec.array([ (0.0, 1.0, 0.0), (0.6750157517485424, 0.2686395525227134, 4.414162326990264), (0.4298067575426634, 0.3504640943042294, 1.6509619345705366), (0.2225719898862696, 0.1765239788552947, 0.9964432015995908), (0.183305324749809, 0.11805267650029766, 0.8044831853163489), (0.10099768165139233, 0.0710504977578287, 0.44359103295144986)], dtype=[('realgdp', 'float'), ('realcons', 'float'), ('realinv', 'float')]) }, dtype=object) var_results.coefs = array([ (0.0015269723529158544, 0.005459603048402539, -0.02390252088527764), (-0.27943473587305184, -0.10046797808205485, -1.97097367379581), (0.6750157517485424, 0.2686395525227134, 4.414162326990264), (0.033219450793946774, 0.02573872652220415, 0.22547895322388853), (0.008221084912580555, -0.12317392770605443, 0.3807858492371746), (0.29045762812920883, 0.23249943591732136, 0.8002809175290293), (-0.007320907532428127, 0.023503761040979707, -0.12407906157659883)], dtype=[('realgdp', 'float'), ('realcons', 'float'), ('realinv', 'float')]) statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/results/vars_results.npz000066400000000000000000000131001400612667500274050ustar00rootroot00000000000000PKô’L>>¬Ûxx causality.npy“NUMPYV{'descr': [('causedby', 'ŒžÒ›©–à?+=PKô’L>U(C¹VV orthirf.npy“NUMPYF{'descr': '|O8', 'fortran_order': False, 'shape': (), } €cnumpy.core.multiarray _reconstruct qcnumpy ndarray qK…Ub‡Rq(K)cnumpy dtype qUO8KK‡Rq(KU|NNNJÿÿÿÿJÿÿÿÿK?tb‰]q}q(Urealgdphcnumpy.core.records recarray qK…Ub‡Rq (KK…hcnumpy.core.records record q KK‡Rq (KU|NUrealgdpq Urealconsq Urealinvq‡q}q(h hUf8KK‡Rq(KUY?ÇÙË©0yQ?Žqþ 2ê‚?§XJqZ?E믩ºIQ?›D[.óþx?ÿw±ÙËG?5:…g:B?šG¡áì4j?˜hãáÅ$B?çŠá>7?bjkI@÷c?×v#[/4?ʱ¤‚ãh,?.®ä÷çU?tbUrealinvhhK…Ub‡Rq(KK…hh KK‡Rq(KU|NUrealgdpqUrealconsqUrealinvq‡q}q(hhK†hhK†hhK†uKKKtb‰U“q‘c=•?\¬2þ”F?üIÀjr~A?3|8+(s?ûÍü‹^u&?,¦c)¾YF?µ­Ò«øA¿ËÆ`Œ§A?yÑ—CYÇ3?«(™õÕe? 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irf.npyPKô’L>¾Ò›(( €Òcoefs.npyPK !statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/svar.do000066400000000000000000000006611400612667500237260ustar00rootroot00000000000000insheet using "/home/skipper/statsmodels/statsmodels-skipper/scikits/statsmodels/datasets/macrodata/macrodata.csv", double clear gen qtrdate=yq(year,quarter) format qtrdate %tq tsset qtrdate gen lgdp = log(realgdp) gen lcons = log(realcons) gen linv = log(realinv) gen gdp = D.lgdp gen cons = D.lcons gen inv = D.linv matrix A = (1,0,0\.,1,0\.,.,1) matrix B = (.,0,0\0,.,0\0,0,.) svar gdp cons inv, aeq(A) beq(B) lags(1/3) var statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/svartest.R000066400000000000000000000014461400612667500244270ustar00rootroot00000000000000library("vars") #data <- read.csv("/home/skipper/statsmodels/statsmodels-skipper/scikits/statsmodels/datasets/macrodata/macrodata.csv") #data <- read.csv("/home/bart/statsmodels/scikits/statsmodels/datasets/macrodata/macrodata.csv") data <- read.csv("C:\\statsmodels\\statsmodels-bartbkr\\scikits\\statsmodels\\datasets\\macrodata\\macrodata.csv") names <- colnames(data) data <- log(data[c('realgdp','realcons','realinv')]) data <- sapply(data, diff) data = ts(data, start=c(1959,2), frequency=4) var <-VAR(data, p=3, type= "const") amat <- matrix(0,3,3) amat[1,1] <- 1 amat[2,1] <- NA amat[3,1] <- NA amat[2,2] <- 1 amat[3,2] <- NA amat[3,3] <- 1 bmat <- diag(3) diag(bmat) <- NA svar <- SVAR(var, estmethod = 'scoring', Bmat=bmat, Amat=amat) plot(irf(svar, n.ahead=30, impulse = 'realgdp', runs=100)) statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/test_coint.py000066400000000000000000000233231400612667500251540ustar00rootroot00000000000000# -*- coding: utf-8 -*- """Test Johansen's Cointegration test against jplv, Spatial Econometrics Toolbox Created on Thu Aug 30 21:51:08 2012 Author: Josef Perktold """ import os import warnings import numpy as np from numpy.testing import assert_almost_equal, assert_equal import pandas as pd import pytest from statsmodels.tools.sm_exceptions import HypothesisTestWarning from statsmodels.tsa.vector_ar.vecm import coint_johansen current_path = os.path.dirname(os.path.abspath(__file__)) dta_path = os.path.join(current_path, "Matlab_results", "test_coint.csv") with open(dta_path, "rb") as fd: dta = np.genfromtxt(fd) class CheckCointJoh(object): def test_basic(self): assert_equal(self.res.ind, np.arange(len(self.res.ind), dtype=int)) assert_equal(self.res.r0t.shape, (self.nobs_r, 8)) def test_table_trace(self): table1 = np.column_stack((self.res.lr1, self.res.cvt)) assert_almost_equal(table1, self.res1_m.reshape(table1.shape, order='F')) def test_table_maxeval(self): table2 = np.column_stack((self.res.lr2, self.res.cvm)) assert_almost_equal(table2, self.res2_m.reshape(table2.shape, order='F')) def test_normalization(self): # GH 5517 evec = self.res.evec non_zero = evec.flat != 0 assert evec.flat[non_zero][0] > 0 class TestCointJoh12(CheckCointJoh): @classmethod def setup_class(cls): cls.res = coint_johansen(dta, 1, 2) cls.nobs_r = 173 - 1 - 2 cls.res1_m = np.array([241.985452556075, 166.4781461662553, 110.3298006342814, 70.79801574443575, 44.90887371527634, 27.22385073668511, 11.74205493173769, 3.295435325623445, 169.0618, 133.7852, 102.4674, 75.1027, 51.6492, 32.0645, 16.1619, 2.7055, 175.1584, 139.278, 107.3429, 79.34220000000001, 55.2459, 35.0116, 18.3985, 3.8415, 187.1891, 150.0778, 116.9829, 87.7748, 62.5202, 41.0815, 23.1485, 6.6349]) cls.res2_m = np.array([75.50730638981975, 56.14834553197396, 39.5317848898456, 25.8891420291594, 17.68502297859124, 15.48179580494741, 8.446619606114249, 3.295435325623445, 52.5858, 46.5583, 40.5244, 34.4202, 28.2398, 21.8731, 15.0006, 2.7055, 55.7302, 49.5875, 43.4183, 37.1646, 30.8151, 24.2522, 17.1481, 3.8415, 62.1741, 55.8171, 49.4095, 42.8612, 36.193, 29.2631, 21.7465, 6.6349,]) evec = np.array([ 0.01102517075074406, -0.2185481584930077, 0.04565819524210763, -0.06556394587400775, 0.04711496306104131, -0.1500111976629196, 0.03775327003706507, 0.03479475877437702, 0.007517888890275335, -0.2014629352546497, 0.01526001455616041, 0.0707900418057458, -0.002388919695513273, 0.04486516694838273, -0.02936314422571188, 0.009900554050392113, 0.02846074144367176, 0.02021385478834498, -0.04276914888645468, 0.1738024290422287, 0.07821155002012749, -0.1066523077111768, -0.3011042488399306, 0.04965189679477353, 0.07141291326159237, -0.01406702689857725, -0.07842109866080313, -0.04773566072362181, -0.04768640728128824, -0.04428737926285261, 0.4143225656833862, 0.04512787132114879, -0.06817130121837202, 0.2246249779872569, -0.009356548567565763, 0.006685350535849125, -0.02040894506833539, 0.008131690308487425, -0.2503209797396666, 0.01560186979508953, 0.03327070126502506, -0.263036624535624, -0.04669882107497259, 0.0146457545413255, 0.01408691619062709, 0.1004753600191269, -0.02239205763487946, -0.02169291468272568, 0.08782313160608619, -0.07696508791577318, 0.008925177304198475, -0.06230900392092828, -0.01548907461158638, 0.04574831652028973, -0.2972228156126774, 0.003469819004961912, -0.001868995544352928, 0.05993345996347871, 0.01213394328069316, 0.02096614212178651, -0.08624395993789938, 0.02108183181049973, -0.08470307289295617, -5.135072530480897e-005]) cls.evec_m = evec.reshape(cls.res.evec.shape, order='F') cls.eig_m = np.array([0.3586376068088151, 0.2812806889719111, 0.2074818815675726, 0.141259991767926, 0.09880133062878599, 0.08704563854307619, 0.048471840356709, 0.01919823444066367]) def test_evec(self): for col in range(self.evec_m.shape[1]): try: assert_almost_equal(self.res.evec[:, col], self.evec_m[:, col]) except AssertionError: assert_almost_equal(self.res.evec[:, col], -self.evec_m[:, col]) def test_evals(self): assert_almost_equal(self.res.eig, self.eig_m) class TestCointJoh09(CheckCointJoh): @classmethod def setup_class(cls): cls.res = coint_johansen(dta, 0, 9) cls.nobs_r = 173 - 1 - 9 #fprintf(1, '%18.16g, ', r1) cls.res1_m = np.array([307.6888935095814, 205.3839229398245, 129.1330243009336, 83.3101865760208, 52.51955460357912, 30.20027050520502, 13.84158157562689, 0.4117390188204866, 153.6341, 120.3673, 91.109, 65.8202, 44.4929, 27.0669, 13.4294, 2.7055, 159.529, 125.6185, 95.7542, 69.8189, 47.8545, 29.7961, 15.4943, 3.8415, 171.0905, 135.9825, 104.9637, 77.8202, 54.6815, 35.4628, 19.9349, 6.6349]) #r2 = [res.lr2 res.cvm] cls.res2_m = np.array([102.3049705697569, 76.25089863889085, 45.82283772491284, 30.7906319724417, 22.31928409837409, 16.35868892957814, 13.4298425568064, 0.4117390188204866, 49.2855, 43.2947, 37.2786, 31.2379, 25.1236, 18.8928, 12.2971, 2.7055, 52.3622, 46.2299, 40.0763, 33.8777, 27.5858, 21.1314, 14.2639, 3.8415, 58.6634, 52.3069, 45.8662, 39.3693, 32.7172, 25.865, 18.52, 6.6349]) class TestCointJohMin18(CheckCointJoh): @classmethod def setup_class(cls): cls.res = coint_johansen(dta, -1, 8) cls.nobs_r = 173 - 1 - 8 cls.res1_m = np.array([260.6786029744658, 162.7966072512681, 105.8253545950566, 71.16133060790817, 47.68490211260372, 28.11843682526138, 13.03968537077271, 2.25398078597622, 137.9954, 106.7351, 79.5329, 56.2839, 37.0339, 21.7781, 10.4741, 2.9762, 143.6691, 111.7797, 83.9383, 60.0627, 40.1749, 24.2761, 12.3212, 4.1296, 154.7977, 121.7375, 92.7136, 67.63670000000001, 46.5716, 29.5147, 16.364, 6.9406]) cls.res2_m = np.array([97.88199572319769, 56.97125265621156, 34.66402398714837, 23.47642849530445, 19.56646528734234, 15.07875145448866, 10.7857045847965, 2.25398078597622, 45.893, 39.9085, 33.9271, 27.916, 21.837, 15.7175, 9.4748, 2.9762, 48.8795, 42.7679, 36.6301, 30.4428, 24.1592, 17.7961, 11.2246, 4.1296, 55.0335, 48.6606, 42.2333, 35.7359, 29.0609, 22.2519, 15.0923, 6.9406]) class TestCointJoh25(CheckCointJoh): @classmethod def setup_class(cls): with warnings.catch_warnings(): warnings.simplefilter("ignore", category=HypothesisTestWarning) cls.res = coint_johansen(dta, 2, 5) cls.nobs_r = 173 - 1 - 5 # Note: critical values not available if trend>1 cls.res1_m = np.array([270.1887263915158, 171.6870096307863, 107.8613367358704, 70.82424032233558, 44.62551818267534, 25.74352073857572, 14.17882426926978, 4.288656185006764, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) cls.res1_m[cls.res1_m == 0] = np.nan cls.res2_m = np.array([98.50171676072955, 63.82567289491584, 37.03709641353485, 26.19872213966024, 18.88199744409963, 11.56469646930594, 9.890168084263012, 4.288656185006764, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) cls.res2_m[cls.res2_m == 0] = np.nan @pytest.mark.smoke def test_coint_johansen_0lag(reset_randomstate): # GH 5731 x_diff = np.random.normal(0, 1, 1000) x = pd.Series(np.cumsum(x_diff)) e1 = np.random.normal(0, 1, 1000) y = x + 5 + e1 data = pd.concat([x, y], axis=1) result = coint_johansen(data, det_order=-1, k_ar_diff=0) assert result.eig.shape == (2,) statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/test_svar.py000066400000000000000000000054601400612667500250150ustar00rootroot00000000000000""" Test SVAR estimation """ from statsmodels.compat.platform import PLATFORM_WIN import numpy as np from numpy.testing import assert_allclose, assert_almost_equal import pytest import statsmodels.datasets.macrodata from statsmodels.tsa.vector_ar.svar_model import SVAR DECIMAL_6 = 6 DECIMAL_5 = 5 DECIMAL_4 = 4 class TestSVAR(object): @classmethod def setup_class(cls): mdata = statsmodels.datasets.macrodata.load_pandas().data mdata = mdata[['realgdp', 'realcons', 'realinv']] data = mdata.values data = np.diff(np.log(data), axis=0) A = np.asarray([[1, 0, 0], ['E', 1, 0], ['E', 'E', 1]]) B = np.asarray([['E', 0, 0], [0, 'E', 0], [0, 0, 'E']]) results = SVAR(data, svar_type='AB', A=A, B=B).fit(maxlags=3) cls.res1 = results #cls.res2 = results_svar.SVARdataResults() from .results import results_svar_st cls.res2 = results_svar_st.results_svar1_small def _reformat(self, x): return x[[1, 4, 7, 2, 5, 8, 3, 6, 9, 0], :].ravel("F") def test_A(self): assert_almost_equal(self.res1.A, self.res2.A, DECIMAL_4) def test_B(self): # see issue #3148, adding np.abs to make solution positive # general case will need positive sqrt of covariance matrix assert_almost_equal(np.abs(self.res1.B), self.res2.B, DECIMAL_4) def test_basic(self): res1 = self.res1 res2 = self.res2 assert_allclose(self._reformat(res1.params), res2.b_var, atol=1e-12) bse_st = np.sqrt(np.diag(res2.V_var)) assert_allclose(self._reformat(res1.bse), bse_st, atol=1e-12) def test_llf_ic(self): res1 = self.res1 res2 = self.res2 assert_allclose(res1.llf, res2.ll_var, atol=1e-12) # different definition, missing constant term ? corr_const = -8.51363119922803 assert_allclose(res1.fpe, res2.fpe_var, atol=1e-12) assert_allclose(res1.aic - corr_const, res2.aic_var, atol=1e-12) assert_allclose(res1.bic - corr_const, res2.sbic_var, atol=1e-12) assert_allclose(res1.hqic - corr_const, res2.hqic_var, atol=1e-12) @pytest.mark.smoke def test_irf(self): # mostly SMOKE, API test # this only checks that the methods work and produce the same result res1 = self.res1 errband1 = res1.sirf_errband_mc(orth=False, repl=50, steps=10, signif=0.05, seed=987123, burn=100, cum=False) irf = res1.irf() errband2 = irf.errband_mc(orth=False, svar=True, repl=50, signif=0.05, seed=987123, burn=100) # Windows precision limits require non-zero atol atol = 1e-6 if PLATFORM_WIN else 1e-8 assert_allclose(errband1, errband2, rtol=1e-8, atol=atol) statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/test_var.py000066400000000000000000000715061400612667500246360ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Test VAR Model """ from statsmodels.compat.pandas import assert_index_equal from statsmodels.compat.python import lrange from io import BytesIO, StringIO import os import sys import warnings import numpy as np from numpy.testing import assert_allclose, assert_almost_equal, assert_equal import pandas as pd import pytest import statsmodels.api as sm import statsmodels.tools.data as data_util from statsmodels.tools.sm_exceptions import ValueWarning from statsmodels.tsa.base.datetools import dates_from_str import statsmodels.tsa.vector_ar.util as util from statsmodels.tsa.vector_ar.var_model import VAR, var_acf DECIMAL_12 = 12 DECIMAL_6 = 6 DECIMAL_5 = 5 DECIMAL_4 = 4 DECIMAL_3 = 3 DECIMAL_2 = 2 @pytest.fixture() def bivariate_var_data(reset_randomstate): """A bivariate dataset for VAR estimation""" e = np.random.standard_normal((252, 2)) y = np.zeros_like(e) y[:2] = e[:2] for i in range(2, 252): y[i] = .2 * y[i - 1] + .1 * y[i - 2] + e[i] return y @pytest.fixture() def bivariate_var_result(bivariate_var_data): """A bivariate VARResults for reuse""" mod = VAR(bivariate_var_data) return mod.fit() class CheckVAR(object): # FIXME: not inherited, so these tests are never run! # just so pylint will not complain res1 = None res2 = None def test_params(self): assert_almost_equal(self.res1.params, self.res2.params, DECIMAL_3) def test_neqs(self): assert_equal(self.res1.neqs, self.res2.neqs) def test_nobs(self): assert_equal(self.res1.avobs, self.res2.nobs) def test_df_eq(self): assert_equal(self.res1.df_eq, self.res2.df_eq) def test_rmse(self): results = self.res1.results for i in range(len(results)): assert_almost_equal(results[i].mse_resid ** .5, eval('self.res2.rmse_' + str(i + 1)), DECIMAL_6) def test_rsquared(self): results = self.res1.results for i in range(len(results)): assert_almost_equal(results[i].rsquared, eval('self.res2.rsquared_' + str(i + 1)), DECIMAL_3) def test_llf(self): results = self.res1.results assert_almost_equal(self.res1.llf, self.res2.llf, DECIMAL_2) for i in range(len(results)): assert_almost_equal(results[i].llf, eval('self.res2.llf_' + str(i + 1)), DECIMAL_2) def test_aic(self): assert_almost_equal(self.res1.aic, self.res2.aic) def test_bic(self): assert_almost_equal(self.res1.bic, self.res2.bic) def test_hqic(self): assert_almost_equal(self.res1.hqic, self.res2.hqic) def test_fpe(self): assert_almost_equal(self.res1.fpe, self.res2.fpe) def test_detsig(self): assert_almost_equal(self.res1.detomega, self.res2.detsig) def test_bse(self): assert_almost_equal(self.res1.bse, self.res2.bse, DECIMAL_4) def get_macrodata(): data = sm.datasets.macrodata.load_pandas().data[['realgdp', 'realcons', 'realinv']] data = data.to_records(index=False) nd = data.view((float, 3), type=np.ndarray) nd = np.diff(np.log(nd), axis=0) return nd.ravel().view(data.dtype, type=np.ndarray) def generate_var(): # FIXME: make a test? import pandas.rpy.common as prp from rpy2.robjects import r r.source('tests/var.R') return prp.convert_robj(r['result'], use_pandas=False) def write_generate_var(): # FIXME: make a test? result = generate_var() np.savez('tests/results/vars_results.npz', **result) class RResults(object): """ Simple interface with results generated by "vars" package in R. """ def __init__(self): # data = np.load(resultspath + 'vars_results.npz') from .results.results_var_data import var_results data = var_results.__dict__ self.names = data['coefs'].dtype.names self.params = data['coefs'].view((float, len(self.names)), type=np.ndarray) self.stderr = data['stderr'].view((float, len(self.names)), type=np.ndarray) self.irf = data['irf'].item() self.orth_irf = data['orthirf'].item() self.nirfs = int(data['nirfs'][0]) self.nobs = int(data['obs'][0]) self.totobs = int(data['totobs'][0]) crit = data['crit'].item() self.aic = crit['aic'][0] self.sic = self.bic = crit['sic'][0] self.hqic = crit['hqic'][0] self.fpe = crit['fpe'][0] self.detomega = data['detomega'][0] self.loglike = data['loglike'][0] self.nahead = int(data['nahead'][0]) self.ma_rep = data['phis'] self.causality = data['causality'] _orig_stdout = None def setup_module(): global _orig_stdout _orig_stdout = sys.stdout sys.stdout = StringIO() class CheckIRF(object): ref = None res = None irf = None k = None # --------------------------------------------------------------------------- # IRF tests def test_irf_coefs(self): self._check_irfs(self.irf.irfs, self.ref.irf) self._check_irfs(self.irf.orth_irfs, self.ref.orth_irf) def _check_irfs(self, py_irfs, r_irfs): for i, name in enumerate(self.res.names): ref_irfs = r_irfs[name].view((float, self.k), type=np.ndarray) res_irfs = py_irfs[:, :, i] assert_almost_equal(ref_irfs, res_irfs) @pytest.mark.matplotlib def test_plot_irf(self, close_figures): self.irf.plot() self.irf.plot(plot_stderr=False) self.irf.plot(impulse=0, response=1) self.irf.plot(impulse=0) self.irf.plot(response=0) self.irf.plot(orth=True) self.irf.plot(impulse=0, response=1, orth=True) @pytest.mark.matplotlib def test_plot_cum_effects(self, close_figures): self.irf.plot_cum_effects() self.irf.plot_cum_effects(plot_stderr=False) self.irf.plot_cum_effects(impulse=0, response=1) self.irf.plot_cum_effects(orth=True) self.irf.plot_cum_effects(impulse=0, response=1, orth=True) @pytest.mark.matplotlib def test_plot_figsizes(self): assert_equal(self.irf.plot().get_size_inches(), (10, 10)) assert_equal( self.irf.plot(figsize=(14, 10)).get_size_inches(), (14, 10)) assert_equal(self.irf.plot_cum_effects().get_size_inches(), (10, 10)) assert_equal( self.irf.plot_cum_effects(figsize=(14, 10)).get_size_inches(), (14, 10)) @pytest.mark.smoke class CheckFEVD(object): fevd = None # --------------------------------------------------------------------------- # FEVD tests @pytest.mark.matplotlib def test_fevd_plot(self, close_figures): self.fevd.plot() def test_fevd_repr(self): self.fevd def test_fevd_summary(self): self.fevd.summary() @pytest.mark.xfail(reason="FEVD.cov() is not implemented", raises=NotImplementedError, strict=True) def test_fevd_cov(self): # test does not crash # not implemented covs = self.fevd.cov() raise NotImplementedError class TestVARResults(CheckIRF, CheckFEVD): @classmethod def setup_class(cls): cls.p = 2 cls.data = get_macrodata() cls.model = VAR(cls.data) cls.names = cls.model.endog_names cls.ref = RResults() cls.k = len(cls.ref.names) cls.res = cls.model.fit(maxlags=cls.p) cls.irf = cls.res.irf(cls.ref.nirfs) cls.nahead = cls.ref.nahead cls.fevd = cls.res.fevd() def test_constructor(self): # make sure this works with no names ndarr = self.data.view((float, 3), type=np.ndarray) model = VAR(ndarr) res = model.fit(self.p) def test_names(self): assert_equal(self.model.endog_names, self.ref.names) model2 = VAR(self.data) assert_equal(model2.endog_names, self.ref.names) def test_get_eq_index(self): assert type(self.res.names) is list # noqa: E721 for i, name in enumerate(self.names): idx = self.res.get_eq_index(i) idx2 = self.res.get_eq_index(name) assert_equal(idx, i) assert_equal(idx, idx2) with pytest.raises(Exception): self.res.get_eq_index('foo') @pytest.mark.smoke def test_repr(self): # just want this to work foo = str(self.res) bar = repr(self.res) def test_params(self): assert_almost_equal(self.res.params, self.ref.params, DECIMAL_3) @pytest.mark.smoke def test_cov_params(self): # do nothing for now self.res.cov_params @pytest.mark.smoke def test_cov_ybar(self): self.res.cov_ybar() @pytest.mark.smoke def test_tstat(self): self.res.tvalues @pytest.mark.smoke def test_pvalues(self): self.res.pvalues @pytest.mark.smoke def test_summary(self): summ = self.res.summary() def test_detsig(self): assert_almost_equal(self.res.detomega, self.ref.detomega) def test_aic(self): assert_almost_equal(self.res.aic, self.ref.aic) def test_bic(self): assert_almost_equal(self.res.bic, self.ref.bic) def test_hqic(self): assert_almost_equal(self.res.hqic, self.ref.hqic) def test_fpe(self): assert_almost_equal(self.res.fpe, self.ref.fpe) def test_lagorder_select(self): ics = ['aic', 'fpe', 'hqic', 'bic'] for ic in ics: res = self.model.fit(maxlags=10, ic=ic, verbose=True) with pytest.raises(Exception): self.model.fit(ic='foo') def test_nobs(self): assert_equal(self.res.nobs, self.ref.nobs) def test_stderr(self): assert_almost_equal(self.res.stderr, self.ref.stderr, DECIMAL_4) def test_loglike(self): assert_almost_equal(self.res.llf, self.ref.loglike) def test_ma_rep(self): ma_rep = self.res.ma_rep(self.nahead) assert_almost_equal(ma_rep, self.ref.ma_rep) # -------------------------------------------------- # Lots of tests to make sure stuff works...need to check correctness def test_causality(self): causedby = self.ref.causality['causedby'] for i, name in enumerate(self.names): variables = self.names[:i] + self.names[i + 1:] result = self.res.test_causality(name, variables, kind='f') assert_almost_equal(result.pvalue, causedby[i], DECIMAL_4) rng = lrange(self.k) rng.remove(i) result2 = self.res.test_causality(i, rng, kind='f') assert_almost_equal(result.pvalue, result2.pvalue, DECIMAL_12) # make sure works result = self.res.test_causality(name, variables, kind='wald') # corner cases _ = self.res.test_causality(self.names[0], self.names[1]) _ = self.res.test_causality(0, 1) with pytest.raises(Exception): self.res.test_causality(0, 1, kind='foo') def test_causality_no_lags(self): res = VAR(self.data).fit(maxlags=0) with pytest.raises(RuntimeError, match="0 lags"): res.test_causality(0, 1) @pytest.mark.smoke def test_select_order(self): result = self.model.fit(10, ic='aic', verbose=True) result = self.model.fit(10, ic='fpe', verbose=True) # bug model = VAR(self.model.endog) model.select_order() def test_is_stable(self): # may not necessarily be true for other datasets assert (self.res.is_stable(verbose=True)) def test_acf(self): # test that it works...for now acfs = self.res.acf(10) # defaults to nlags=lag_order acfs = self.res.acf() assert (len(acfs) == self.p + 1) def test_acf_2_lags(self): c = np.zeros((2, 2, 2)) c[0] = np.array([[.2, .1], [.15, .15]]) c[1] = np.array([[.1, .9], [0, .1]]) acf = var_acf(c, np.eye(2), 3) gamma = np.zeros((6, 6)) gamma[:2, :2] = acf[0] gamma[2:4, 2:4] = acf[0] gamma[4:6, 4:6] = acf[0] gamma[2:4, :2] = acf[1].T gamma[4:, :2] = acf[2].T gamma[:2, 2:4] = acf[1] gamma[:2, 4:] = acf[2] recovered = np.dot(gamma[:2, 2:], np.linalg.inv(gamma[:4, :4])) recovered = [recovered[:, 2 * i:2 * (i + 1)] for i in range(2)] recovered = np.array(recovered) assert_allclose(recovered, c, atol=1e-7) @pytest.mark.smoke def test_acorr(self): acorrs = self.res.acorr(10) @pytest.mark.smoke def test_forecast(self): self.res.forecast(self.res.endog[-5:], 5) @pytest.mark.smoke def test_forecast_interval(self): y = self.res.endog[:-self.p:] point, lower, upper = self.res.forecast_interval(y, 5) @pytest.mark.matplotlib def test_plot_sim(self, close_figures): self.res.plotsim(steps=100) @pytest.mark.matplotlib def test_plot(self, close_figures): self.res.plot() @pytest.mark.matplotlib def test_plot_acorr(self, close_figures): self.res.plot_acorr() @pytest.mark.matplotlib def test_plot_forecast(self, close_figures): self.res.plot_forecast(5) def test_reorder(self): # manually reorder data = self.data.view((float, 3), type=np.ndarray) names = self.names data2 = np.append(np.append(data[:, 2, None], data[:, 0, None], axis=1), data[:, 1, None], axis=1) names2 = [] names2.append(names[2]) names2.append(names[0]) names2.append(names[1]) res2 = VAR(data2).fit(maxlags=self.p) # use reorder function res3 = self.res.reorder(['realinv', 'realgdp', 'realcons']) # check if the main results match assert_almost_equal(res2.params, res3.params) assert_almost_equal(res2.sigma_u, res3.sigma_u) assert_almost_equal(res2.bic, res3.bic) assert_almost_equal(res2.stderr, res3.stderr) def test_pickle(self): fh = BytesIO() # test wrapped results load save pickle del self.res.model.data.orig_endog self.res.save(fh) fh.seek(0, 0) res_unpickled = self.res.__class__.load(fh) assert type(res_unpickled) is type(self.res) # noqa: E721 class E1_Results(object): """ Results from Lütkepohl (2005) using E2 dataset """ def __init__(self): # Lutkepohl p. 120 results # I asked the author about these results and there is probably rounding # error in the book, so I adjusted these test results to match what is # coming out of the Python (double-checked) calculations self.irf_stderr = np.array([[[.125, 0.546, 0.664], [0.032, 0.139, 0.169], [0.026, 0.112, 0.136]], [[0.129, 0.547, 0.663], [0.032, 0.134, 0.163], [0.026, 0.108, 0.131]], [[0.084, .385, .479], [.016, .079, .095], [.016, .078, .103]]]) self.cum_irf_stderr = np.array([[[.125, 0.546, 0.664], [0.032, 0.139, 0.169], [0.026, 0.112, 0.136]], [[0.149, 0.631, 0.764], [0.044, 0.185, 0.224], [0.033, 0.140, 0.169]], [[0.099, .468, .555], [.038, .170, .205], [.033, .150, .185]]]) self.lr_stderr = np.array([[.134, .645, .808], [.048, .230, .288], [.043, .208, .260]]) basepath = os.path.split(sm.__file__)[0] resultspath = basepath + '/tsa/vector_ar/tests/results/' def get_lutkepohl_data(name='e2'): path = resultspath + '%s.dat' % name return util.parse_lutkepohl_data(path) def test_lutkepohl_parse(): files = ['e%d' % i for i in range(1, 7)] for f in files: get_lutkepohl_data(f) class TestVARResultsLutkepohl(object): """ Verify calculations using results from Lütkepohl's book """ @classmethod def setup_class(cls): cls.p = 2 sdata, dates = get_lutkepohl_data('e1') data = data_util.struct_to_ndarray(sdata) adj_data = np.diff(np.log(data), axis=0) # est = VAR(adj_data, p=2, dates=dates[1:], names=names) cls.model = VAR(adj_data[:-16], dates=dates[1:-16], freq='BQ-MAR') cls.res = cls.model.fit(maxlags=cls.p) cls.irf = cls.res.irf(10) cls.lut = E1_Results() def test_approx_mse(self): # 3.5.18, p. 99 mse2 = np.array([[25.12, .580, 1.300], [.580, 1.581, .586], [1.300, .586, 1.009]]) * 1e-4 assert_almost_equal(mse2, self.res.forecast_cov(3)[1], DECIMAL_3) def test_irf_stderr(self): irf_stderr = self.irf.stderr(orth=False) for i in range(1, 1 + len(self.lut.irf_stderr)): assert_almost_equal(np.round(irf_stderr[i], 3), self.lut.irf_stderr[i - 1]) def test_cum_irf_stderr(self): stderr = self.irf.cum_effect_stderr(orth=False) for i in range(1, 1 + len(self.lut.cum_irf_stderr)): assert_almost_equal(np.round(stderr[i], 3), self.lut.cum_irf_stderr[i - 1]) def test_lr_effect_stderr(self): stderr = self.irf.lr_effect_stderr(orth=False) orth_stderr = self.irf.lr_effect_stderr(orth=True) assert_almost_equal(np.round(stderr, 3), self.lut.lr_stderr) def test_get_trendorder(): results = { 'c': 1, 'nc': 0, 'ct': 2, 'ctt': 3 } for t, trendorder in results.items(): assert (util.get_trendorder(t) == trendorder) def test_var_constant(): # see 2043 import datetime from pandas import DataFrame, DatetimeIndex series = np.array([[2., 2.], [1, 2.], [1, 2.], [1, 2.], [1., 2.]]) data = DataFrame(series) d = datetime.datetime.now() delta = datetime.timedelta(days=1) index = [] for i in range(data.shape[0]): index.append(d) d += delta data.index = DatetimeIndex(index) # with pytest.warns(ValueWarning): #does not silence warning in test output with warnings.catch_warnings(): warnings.simplefilter("ignore", category=ValueWarning) model = VAR(data) with pytest.raises(ValueError): model.fit(1) def test_var_trend(): # see 2271 data = get_macrodata().view((float, 3), type=np.ndarray) model = sm.tsa.VAR(data) results = model.fit(4) # , trend = 'c') irf = results.irf(10) data_nc = data - data.mean(0) model_nc = sm.tsa.VAR(data_nc) results_nc = model_nc.fit(4, trend='nc') with pytest.raises(ValueError): model.fit(4, trend='t') def test_irf_trend(): # test for irf with different trend see #1636 # this is a rough comparison by adding trend or subtracting mean to data # to get similar AR coefficients and IRF data = get_macrodata().view((float, 3), type=np.ndarray) model = sm.tsa.VAR(data) results = model.fit(4) # , trend = 'c') irf = results.irf(10) data_nc = data - data.mean(0) model_nc = sm.tsa.VAR(data_nc) results_nc = model_nc.fit(4, trend='nc') irf_nc = results_nc.irf(10) assert_allclose(irf_nc.stderr()[1:4], irf.stderr()[1:4], rtol=0.01) trend = 1e-3 * np.arange(len(data)) / (len(data) - 1) # for pandas version, currently not used, if data is a pd.DataFrame # data_t = pd.DataFrame(data.values + trend[:,None], index=data.index, columns=data.columns) data_t = data + trend[:, None] model_t = sm.tsa.VAR(data_t) results_t = model_t.fit(4, trend='ct') irf_t = results_t.irf(10) assert_allclose(irf_t.stderr()[1:4], irf.stderr()[1:4], rtol=0.03) class TestVARExtras(object): @classmethod def setup_class(cls): mdata = sm.datasets.macrodata.load_pandas().data mdata = mdata[['realgdp', 'realcons', 'realinv']] data = mdata.values data = np.diff(np.log(data), axis=0) * 400 cls.res0 = sm.tsa.VAR(data).fit(maxlags=2) def test_process(self, close_figures): res0 = self.res0 k_ar = res0.k_ar fc20 = res0.forecast(res0.endog[-k_ar:], 20) mean_lr = res0.mean() assert_allclose(mean_lr, fc20[-1], rtol=5e-4) ysim = res0.simulate_var(seed=987128) assert_allclose(ysim.mean(0), mean_lr, rtol=0.1) # initialization does not use long run intercept, see #4542 assert_allclose(ysim[0], res0.intercept, rtol=1e-10) assert_allclose(ysim[1], res0.intercept, rtol=1e-10) n_sim = 900 ysimz = res0.simulate_var(steps=n_sim, offset=np.zeros((n_sim, 3)), seed=987128) zero3 = np.zeros(3) assert_allclose(ysimz.mean(0), zero3, atol=0.4) # initialization does not use long run intercept, see #4542 assert_allclose(ysimz[0], zero3, atol=1e-10) assert_allclose(ysimz[1], zero3, atol=1e-10) # check attributes assert_equal(res0.k_trend, 1) assert_equal(res0.k_exog_user, 0) assert_equal(res0.k_exog, 1) assert_equal(res0.k_ar, 2) irf = res0.irf() @pytest.mark.matplotlib def test_process_plotting(self, close_figures): # Partially a smoke test res0 = self.res0 k_ar = res0.k_ar fc20 = res0.forecast(res0.endog[-k_ar:], 20) irf = res0.irf() res0.plotsim() res0.plot_acorr() fig = res0.plot_forecast(20) fcp = fig.axes[0].get_children()[1].get_ydata()[-20:] # Note values are equal, but keep rtol buffer assert_allclose(fc20[:, 0], fcp, rtol=1e-13) fcp = fig.axes[1].get_children()[1].get_ydata()[-20:] assert_allclose(fc20[:, 1], fcp, rtol=1e-13) fcp = fig.axes[2].get_children()[1].get_ydata()[-20:] assert_allclose(fc20[:, 2], fcp, rtol=1e-13) fig_asym = irf.plot() fig_mc = irf.plot(stderr_type='mc', repl=1000, seed=987128) for k in range(3): a = fig_asym.axes[1].get_children()[k].get_ydata() m = fig_mc.axes[1].get_children()[k].get_ydata() # use m as desired because it is larger # a is for some irf much smaller than m assert_allclose(a, m, atol=0.1, rtol=0.9) def test_forecast_cov(self): # forecast_cov can include parameter uncertainty if contant-only res = self.res0 covfc1 = res.forecast_cov(3) assert_allclose(covfc1, res.mse(3), rtol=1e-13) # ignore warning, TODO: assert OutputWarning with warnings.catch_warnings(): warnings.simplefilter("ignore") covfc2 = res.forecast_cov(3, method='auto') assert_allclose(covfc2, covfc1, rtol=0.05) # regression test, TODO: replace with verified numbers (Stata) res_covfc2 = np.array([[[9.45802013, 4.94142038, 37.1999646], [4.94142038, 7.09273624, 5.66215089], [37.1999646, 5.66215089, 259.61275869]], [[11.30364479, 5.72569141, 49.28744123], [5.72569141, 7.409761, 10.98164091], [49.28744123, 10.98164091, 336.4484723]], [[12.36188803, 6.44426905, 53.54588026], [6.44426905, 7.88850029, 13.96382545], [53.54588026, 13.96382545, 352.19564327]]]) assert_allclose(covfc2, res_covfc2, atol=1e-6) def test_exog(self): # check that trend and exog are equivalent for basics and varsim data = self.res0.model.endog res_lin_trend = sm.tsa.VAR(data).fit(maxlags=2, trend='ct') ex = np.arange(len(data)) res_lin_trend1 = sm.tsa.VAR(data, exog=ex).fit(maxlags=2) ex2 = np.arange(len(data))[:, None] ** [0, 1] res_lin_trend2 = sm.tsa.VAR(data, exog=ex2).fit(maxlags=2, trend='nc') # TODO: intercept differs by 4e-3, others are < 1e-12 assert_allclose(res_lin_trend.params, res_lin_trend1.params, rtol=5e-3) assert_allclose(res_lin_trend.params, res_lin_trend2.params, rtol=5e-3) assert_allclose(res_lin_trend1.params, res_lin_trend2.params, rtol=1e-10) y1 = res_lin_trend.simulate_var(seed=987128) y2 = res_lin_trend1.simulate_var(seed=987128) y3 = res_lin_trend2.simulate_var(seed=987128) assert_allclose(y2.mean(0), y1.mean(0), rtol=1e-12) assert_allclose(y3.mean(0), y1.mean(0), rtol=1e-12) assert_allclose(y3.mean(0), y2.mean(0), rtol=1e-12) h = 10 fc1 = res_lin_trend.forecast(res_lin_trend.endog[-2:], h) exf = np.arange(len(data), len(data) + h) fc2 = res_lin_trend1.forecast(res_lin_trend1.endog[-2:], h, exog_future=exf) with pytest.raises(ValueError, match="exog_future only has"): wrong_exf = np.arange(len(data), len(data) + h // 2) res_lin_trend1.forecast(res_lin_trend1.endog[-2:], h, exog_future=wrong_exf) exf2 = exf[:, None] ** [0, 1] fc3 = res_lin_trend2.forecast(res_lin_trend2.endog[-2:], h, exog_future=exf2) assert_allclose(fc2, fc1, rtol=1e-12) assert_allclose(fc3, fc1, rtol=1e-12) assert_allclose(fc3, fc2, rtol=1e-12) fci1 = res_lin_trend.forecast_interval(res_lin_trend.endog[-2:], h) exf = np.arange(len(data), len(data) + h) fci2 = res_lin_trend1.forecast_interval(res_lin_trend1.endog[-2:], h, exog_future=exf) exf2 = exf[:, None] ** [0, 1] fci3 = res_lin_trend2.forecast_interval(res_lin_trend2.endog[-2:], h, exog_future=exf2) assert_allclose(fci2, fci1, rtol=1e-12) assert_allclose(fci3, fci1, rtol=1e-12) assert_allclose(fci3, fci2, rtol=1e-12) @pytest.mark.parametrize('attr', ['y', 'ys_lagged']) def test_deprecated_attributes_varresults(bivariate_var_result, attr): with pytest.warns(FutureWarning): getattr(bivariate_var_result, attr) def test_var_cov_params_pandas(bivariate_var_data): df = pd.DataFrame(bivariate_var_data, columns=['x', 'y']) mod = VAR(df) res = mod.fit(2) cov = res.cov_params() assert isinstance(cov, pd.DataFrame) exog_names = ('const', 'L1.x', 'L1.y', 'L2.x', 'L2.y') index = pd.MultiIndex.from_product((exog_names, ('x', 'y'))) assert_index_equal(cov.index, cov.columns) assert_index_equal(cov.index, index) def test_summaries_exog(reset_randomstate): y = np.random.standard_normal((500, 6)) df = pd.DataFrame(y) cols = (["endog_{0}".format(i) for i in range(2)] + ["exog_{0}".format(i) for i in range(4)]) df.columns = cols df.index = pd.date_range('1-1-1950', periods=500, freq="MS") endog = df.iloc[:, :2] exog = df.iloc[:, 2:] res = VAR(endog=endog, exog=exog).fit(maxlags=0) summ = res.summary().summary assert 'exog_0' in summ assert 'exog_1' in summ assert 'exog_2' in summ assert 'exog_3' in summ res = VAR(endog=endog, exog=exog).fit(maxlags=2) summ = res.summary().summary assert 'exog_0' in summ assert 'exog_1' in summ assert 'exog_2' in summ assert 'exog_3' in summ def test_whiteness_nlag(reset_randomstate): # GH 6686 y = np.random.standard_normal((200, 2)) res = VAR(y).fit(maxlags=1, ic=None) with pytest.raises(ValueError, match="The whiteness test can only"): res.test_whiteness(1) def test_var_maxlag(reset_randomstate): y = np.random.standard_normal((22, 10)) VAR(y).fit(maxlags=None, ic="aic") with pytest.raises(ValueError, match="maxlags is too large"): VAR(y).fit(maxlags=8, ic="aic") def test_from_formula(): with pytest.raises(NotImplementedError): VAR.from_formula("y ~ x", None) def test_correct_nobs(): # GH6748 mdata = sm.datasets.macrodata.load_pandas().data # prepare the dates index dates = mdata[['year', 'quarter']].astype(int).astype(str) quarterly = dates["year"] + "Q" + dates["quarter"] quarterly = dates_from_str(quarterly) mdata = mdata[['realgdp', 'realcons', 'realinv']] mdata.index = pd.DatetimeIndex(quarterly) data = np.log(mdata).diff().dropna() data_exog = pd.DataFrame(index=data.index) data_exog['exovar1'] = np.random.normal(size=data_exog.shape[0]) # make a VAR model model = VAR(endog=data, exog=data_exog) results = model.fit(maxlags=1) irf = results.irf_resim(orth=False, repl=100, steps=10, seed=1, burn=100, cum=False) assert irf.shape == (100, 11, 3, 3) statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/test_var_jmulti.py000066400000000000000000000572511400612667500262230ustar00rootroot00000000000000 import numpy as np from numpy.testing import assert_, assert_allclose, assert_raises import statsmodels.datasets.macrodata.data as macro from statsmodels.tsa.vector_ar.tests.JMulTi_results.parse_jmulti_vecm_output import ( sublists, ) from statsmodels.tsa.vector_ar.var_model import VAR from .JMulTi_results.parse_jmulti_var_output import ( dt_s_tup_to_string, load_results_jmulti, ) atol = 0.001 # absolute tolerance rtol = 0.01 # relative tolerance datasets = [] data = {} results_ref = {} results_sm = {} debug_mode = False dont_test_se_t_p = False deterministic_terms_list = ["nc", "c", "ct"] seasonal_list = [0, 4] dt_s_list = [(det, s) for det in deterministic_terms_list for s in seasonal_list] all_tests = ["coefs", "det", "Sigma_u", "log_like", "fc", "causality", "impulse-response", "lag order", "test normality", "whiteness", "exceptions"] to_test = all_tests #["coefs", "det", "Sigma_u", "log_like", "fc", "causality"] # all_tests def load_data(dataset, data_dict): dtset = dataset.load_pandas() variables = dataset.variable_names loaded = dtset.data[variables].astype(float).values data_dict[dataset] = loaded.reshape((-1, len(variables))) def reorder_jmultis_det_terms(jmulti_output, constant, seasons): """ In case of seasonal terms and a trend term we have to reorder them to make the outputs from JMulTi and statsmodels comparable. JMulTi's ordering is: [constant], [seasonal terms], [trend term] while in statsmodels it is: [constant], [trend term], [seasonal terms] Parameters ---------- jmulti_output : ndarray (neqs x number_of_deterministic_terms) constant : bool Indicates whether there is a constant term or not in jmulti_output. seasons : int Number of seasons in the model. That means there are seasons-1 columns for seasonal terms in jmulti_output Returns ------- reordered : ndarray (neqs x number_of_deterministic_terms) jmulti_output reordered such that the order of deterministic terms matches that of statsmodels. """ if seasons == 0: return jmulti_output constant = int(constant) const_column = jmulti_output[:, :constant] season_columns = jmulti_output[:, constant:constant+seasons-1].copy() trend_columns = jmulti_output[:, constant+seasons-1:].copy() return np.hstack((const_column, trend_columns, season_columns)) def generate_exog_from_season(seasons, endog_len): """ Translate seasons to exog matrix. Parameters ---------- seasons : int Number of seasons. endog_len : int Number of observations. Returns ------- exog : ndarray or None If seasonal deterministic terms exist, the corresponding exog-matrix is returned. Otherwise, None is returned. """ exog_stack = [] if seasons > 0: season_exog = np.zeros((seasons - 1, endog_len)) for i in range(seasons - 1): season_exog[i, i::seasons] = 1 # season_exog = season_exog[:, ::-1] # season_exog = np.hstack((season_exog[:, 3:4], # season_exog[:, :-1])) # season_exog = np.hstack((season_exog[:, 2:4], # season_exog[:, :-2])) # season_exog = np.hstack((season_exog[:, 1:4], season_exog[:, :-3])) # season_exog[1] = -season_exog[1] # the following line is commented out because seasonal terms are # *not* centered in JMulTi's VAR-framework (in contrast to VECM) # season_exog -= 1 / seasons season_exog = season_exog.T exog_stack.append(season_exog) if exog_stack != []: exog = np.column_stack(exog_stack) else: exog = None return exog def load_results_statsmodels(dataset): results_per_deterministic_terms = dict.fromkeys(dt_s_list) for dt_s_tup in dt_s_list: endog = data[dataset] exog = generate_exog_from_season(dt_s_tup[1], len(endog)) model = VAR(endog, exog) results_per_deterministic_terms[dt_s_tup] = model.fit( maxlags=4, trend=dt_s_tup[0], method="ols") return results_per_deterministic_terms def build_err_msg(ds, dt_s, parameter_str): dt = dt_s_tup_to_string(dt_s) seasons = dt_s[1] err_msg = "Error in " + parameter_str + " for:\n" err_msg += "- Dataset: " + ds.__str__() + "\n" err_msg += "- Deterministic terms: " err_msg += (dt_s[0] if dt != "nc" else "no det. terms") if seasons > 0: err_msg += ", seasons: " + str(seasons) return err_msg def setup(): datasets.append(macro) # TODO: append more data sets for more test cases. for ds in datasets: load_data(ds, data) results_ref[ds] = load_results_jmulti(ds, dt_s_list) results_sm[ds] = load_results_statsmodels(ds) setup() def test_ols_coefs(): if debug_mode: if "coefs" not in to_test: return print("\n\nESTIMATED PARAMETER MATRICES FOR LAGGED ENDOG", end="") for ds in datasets: for dt_s in dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt_s) + ": ", end="") # estimated parameter vector err_msg = build_err_msg(ds, dt_s, "PARAMETER MATRICES ENDOG") obtained = np.hstack(results_sm[ds][dt_s].coefs) desired = results_ref[ds][dt_s]["est"]["Lagged endogenous term"] assert_allclose(obtained, desired, rtol, atol, False, err_msg) if debug_mode and dont_test_se_t_p: continue # standard errors obt = results_sm[ds][dt_s].stderr_endog_lagged des = results_ref[ds][dt_s]["se"]["Lagged endogenous term"].T assert_allclose(obt, des, rtol, atol, False, "STANDARD ERRORS\n" + err_msg) # t-values obt = results_sm[ds][dt_s].tvalues_endog_lagged des = results_ref[ds][dt_s]["t"]["Lagged endogenous term"].T assert_allclose(obt, des, rtol, atol, False, "t-VALUES\n" + err_msg) # p-values obt = results_sm[ds][dt_s].pvalues_endog_lagged des = results_ref[ds][dt_s]["p"]["Lagged endogenous term"].T assert_allclose(obt, des, rtol, atol, False, "p-VALUES\n" + err_msg) def test_ols_det_terms(): if debug_mode: if "det" not in to_test: return print("\n\nESTIMATED PARAMETERS FOR DETERMINISTIC TERMS", end="") for ds in datasets: for dt_s in dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt_s) + ": ", end="") err_msg = build_err_msg(ds, dt_s, "PARAMETER MATRICES EXOG") det_key_ref = "Deterministic term" # If there are no det. terms, just make sure we do not compute any: if det_key_ref not in results_ref[ds][dt_s]["est"].keys(): assert_((results_sm[ds][dt_s].coefs_exog.size == 0 and results_sm[ds][dt_s].stderr_dt.size == 0 and results_sm[ds][dt_s].tvalues_dt.size == 0 and results_sm[ds][dt_s].pvalues_dt.size == 0), err_msg) continue obtained = results_sm[ds][dt_s].coefs_exog desired = results_ref[ds][dt_s]["est"][det_key_ref] desired = reorder_jmultis_det_terms( desired, dt_s[0].startswith("c"), dt_s[1]) assert_allclose(obtained, desired, rtol, atol, False, err_msg) if debug_mode and dont_test_se_t_p: continue # standard errors obt = results_sm[ds][dt_s].stderr_dt des = results_ref[ds][dt_s]["se"][det_key_ref] des = reorder_jmultis_det_terms(des, dt_s[0].startswith("c"), dt_s[1]).T assert_allclose(obt, des, rtol, atol, False, "STANDARD ERRORS\n" + err_msg) # t-values obt = results_sm[ds][dt_s].tvalues_dt des = results_ref[ds][dt_s]["t"][det_key_ref] des = reorder_jmultis_det_terms(des, dt_s[0].startswith("c"), dt_s[1]).T assert_allclose(obt, des, rtol, atol, False, "t-VALUES\n" + err_msg) # p-values obt = results_sm[ds][dt_s].pvalues_dt des = results_ref[ds][dt_s]["p"][det_key_ref] des = reorder_jmultis_det_terms(des, dt_s[0].startswith("c"), dt_s[1]).T assert_allclose(obt, des, rtol, atol, False, "p-VALUES\n" + err_msg) def test_ols_sigma(): if debug_mode: if "Sigma_u" not in to_test: return print("\n\nSIGMA_U", end="") for ds in datasets: for dt in dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") err_msg = build_err_msg(ds, dt, "Sigma_u") obtained = results_sm[ds][dt].sigma_u desired = results_ref[ds][dt]["est"]["Sigma_u"] assert_allclose(obtained, desired, rtol, atol, False, err_msg) def test_log_like(): if debug_mode: if "log_like" not in to_test: return else: print("\n\nLOG LIKELIHOOD", end="") for ds in datasets: for dt in dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") err_msg = build_err_msg(ds, dt, "Log Likelihood") obtained = results_sm[ds][dt].llf desired = results_ref[ds][dt]["log_like"] assert_allclose(obtained, desired, rtol, atol, False, err_msg) def test_fc(): if debug_mode: if "fc" not in to_test: return else: print("\n\nFORECAST", end="") for ds in datasets: for dt in dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") steps = 5 # parsed JMulTi output comprises 5 steps last_observations = results_sm[ds][dt].endog[ -results_sm[ds][dt].k_ar:] seasons = dt[1] if seasons == 0: exog_future = None else: exog_future = np.zeros((steps, seasons-1)) # the following line is appropriate only if the last # observation was in the next to last season (this is the case # for macrodata) exog_future[1:seasons] = np.identity(seasons-1) err_msg = build_err_msg(ds, dt, "FORECAST") # test point forecast functionality of forecast method obtained = results_sm[ds][dt].forecast( y=last_observations, steps=steps, exog_future=exog_future) desired = results_ref[ds][dt]["fc"]["fc"] assert_allclose(obtained, desired, rtol, atol, False, err_msg) # test forecast method with confidence interval calculation err_msg = build_err_msg(ds, dt, "FORECAST WITH INTERVALS") obtained = results_sm[ds][dt].forecast_interval( y=last_observations, steps=steps, alpha=0.05, exog_future=exog_future) obt = obtained[0] # forecast obt_l = obtained[1] # lower bound obt_u = obtained[2] # upper bound des = results_ref[ds][dt]["fc"]["fc"] des_l = results_ref[ds][dt]["fc"]["lower"] des_u = results_ref[ds][dt]["fc"]["upper"] assert_allclose(obt, des, rtol, atol, False, err_msg) assert_allclose(obt_l, des_l, rtol, atol, False, err_msg) assert_allclose(obt_u, des_u, rtol, atol, False, err_msg) def test_causality(): # test Granger- and instantaneous causality if debug_mode: if "causality" not in to_test: return else: print("\n\nCAUSALITY", end="") for ds in datasets: for dt in dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") err_msg_g_p = build_err_msg(ds, dt, "GRANGER CAUS. - p-VALUE") err_msg_g_t = build_err_msg(ds, dt, "GRANGER CAUS. - TEST STAT.") err_msg_i_p = build_err_msg(ds, dt, "INSTANT. CAUS. - p-VALUE") err_msg_i_t = build_err_msg(ds, dt, "INSTANT. CAUS. - TEST STAT.") v_ind = range(len(ds.variable_names)) for causing_ind in sublists(v_ind, 1, len(v_ind)-1): causing_names = ["y" + str(i+1) for i in causing_ind] causing_key = tuple(ds.variable_names[i] for i in causing_ind) caused_ind = [i for i in v_ind if i not in causing_ind] caused_names = ["y" + str(i+1) for i in caused_ind] caused_key = tuple(ds.variable_names[i] for i in caused_ind) # test Granger-causality ###################################### granger_sm_ind = results_sm[ds][ dt].test_causality(caused_ind, causing_ind) granger_sm_str = results_sm[ds][ dt].test_causality(caused_names, causing_names) # test test-statistic for Granger non-causality: g_t_obt = granger_sm_ind.test_statistic g_t_des = results_ref[ds][dt]["granger_caus"][ "test_stat"][(causing_key, caused_key)] assert_allclose(g_t_obt, g_t_des, rtol, atol, False, err_msg_g_t) # check whether string sequences as args work in the same way: g_t_obt_str = granger_sm_str.test_statistic assert_allclose(g_t_obt_str, g_t_obt, 1e-07, 0, False, err_msg_g_t + " - sequences of integers and ".upper() + "strings as arguments do not yield the same result!".upper()) # check if int (e.g. 0) as index and list of int ([0]) yield # the same result: if len(causing_ind) == 1 or len(caused_ind) == 1: ci = causing_ind[0] if len(causing_ind)==1 else causing_ind ce = caused_ind[0] if len(caused_ind) == 1 else caused_ind granger_sm_single_ind = results_sm[ds][ dt].test_causality(ce, ci) g_t_obt_single = granger_sm_single_ind.test_statistic assert_allclose(g_t_obt_single, g_t_obt, 1e-07, 0, False, err_msg_g_t + " - list of int and int as ".upper() + "argument do not yield the same result!".upper()) # test p-value for Granger non-causality: g_p_obt = granger_sm_ind.pvalue g_p_des = results_ref[ds][dt]["granger_caus"]["p"][( causing_key, caused_key)] assert_allclose(g_p_obt, g_p_des, rtol, atol, False, err_msg_g_p) # check whether string sequences as args work in the same way: g_p_obt_str = granger_sm_str.pvalue assert_allclose(g_p_obt_str, g_p_obt, 1e-07, 0, False, err_msg_g_t + " - sequences of integers and ".upper() + "strings as arguments do not yield the same result!".upper()) # check if int (e.g. 0) as index and list of int ([0]) yield # the same result: if len(causing_ind) == 1: g_p_obt_single = granger_sm_single_ind.pvalue assert_allclose(g_p_obt_single, g_p_obt, 1e-07, 0, False, err_msg_g_t + " - list of int and int as ".upper() + \ "argument do not yield the same result!".upper()) # test instantaneous causality ################################ inst_sm_ind = results_sm[ds][dt].test_inst_causality( causing_ind) inst_sm_str = results_sm[ds][dt].test_inst_causality( causing_names) # test test-statistic for instantaneous non-causality t_obt = inst_sm_ind.test_statistic t_des = results_ref[ds][dt]["inst_caus"][ "test_stat"][(causing_key, caused_key)] assert_allclose(t_obt, t_des, rtol, atol, False, err_msg_i_t) # check whether string sequences as args work in the same way: t_obt_str = inst_sm_str.test_statistic assert_allclose(t_obt_str, t_obt, 1e-07, 0, False, err_msg_i_t + " - sequences of integers and ".upper() + "strings as arguments do not yield the same result!".upper()) # check if int (e.g. 0) as index and list of int ([0]) yield # the same result: if len(causing_ind) == 1: inst_sm_single_ind = results_sm[ds][ dt].test_inst_causality(causing_ind[0]) t_obt_single = inst_sm_single_ind.test_statistic assert_allclose(t_obt_single, t_obt, 1e-07, 0, False, err_msg_i_t + " - list of int and int as ".upper() + "argument do not yield the same result!".upper()) # test p-value for instantaneous non-causality p_obt = results_sm[ds][dt].test_inst_causality( causing_ind).pvalue p_des = results_ref[ds][dt]["inst_caus"]["p"][( causing_key, caused_key)] assert_allclose(p_obt, p_des, rtol, atol, False, err_msg_i_p) # check whether string sequences as args work in the same way: p_obt_str = inst_sm_str.pvalue assert_allclose(p_obt_str, p_obt, 1e-07, 0, False, err_msg_i_p + " - sequences of integers and ".upper() + "strings as arguments do not yield the same result!".upper()) # check if int (e.g. 0) as index and list of int ([0]) yield # the same result: if len(causing_ind) == 1: inst_sm_single_ind = results_sm[ds][ dt].test_inst_causality(causing_ind[0]) p_obt_single = inst_sm_single_ind.pvalue assert_allclose(p_obt_single, p_obt, 1e-07, 0, False, err_msg_i_p + " - list of int and int as ".upper() + "argument do not yield the same result!".upper()) def test_impulse_response(): if debug_mode: if "impulse-response" not in to_test: return else: print("\n\nIMPULSE-RESPONSE", end="") for ds in datasets: for dt in dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") err_msg = build_err_msg(ds, dt, "IMULSE-RESPONSE") periods = 20 obtained_all = results_sm[ds][dt].irf(periods=periods).irfs # flatten inner arrays to make them comparable to parsed results: obtained_all = obtained_all.reshape(periods+1, -1) desired_all = results_ref[ds][dt]["ir"] assert_allclose(obtained_all, desired_all, rtol, atol, False, err_msg) def test_lag_order_selection(): if debug_mode: if "lag order" not in to_test: return else: print("\n\nLAG ORDER SELECTION", end="") for ds in datasets: for dt in dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") endog_tot = data[ds] exog = generate_exog_from_season(dt[1], len(endog_tot)) model = VAR(endog_tot, exog) obtained_all = model.select_order(10, trend=dt[0]) for ic in ["aic", "fpe", "hqic", "bic"]: err_msg = build_err_msg(ds, dt, "LAG ORDER SELECTION - " + ic.upper()) obtained = getattr(obtained_all, ic) desired = results_ref[ds][dt]["lagorder"][ic] assert_allclose(obtained, desired, rtol, atol, False, err_msg) def test_normality(): if debug_mode: if "test normality" not in to_test: return else: print("\n\nTEST NON-NORMALITY", end="") for ds in datasets: for dt in dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") obtained = results_sm[ds][dt].test_normality(signif=0.05) err_msg = build_err_msg(ds, dt, "TEST NON-NORMALITY - STATISTIC") obt_statistic = obtained.test_statistic des_statistic = results_ref[ds][dt]["test_norm"][ "joint_test_statistic"] assert_allclose(obt_statistic, des_statistic, rtol, atol, False, err_msg) err_msg = build_err_msg(ds, dt, "TEST NON-NORMALITY - P-VALUE") obt_pvalue = obtained.pvalue des_pvalue = results_ref[ds][dt]["test_norm"]["joint_pvalue"] assert_allclose(obt_pvalue, des_pvalue, rtol, atol, False, err_msg) # call methods to assure they do not raise exceptions obtained.summary() str(obtained) # __str__() def test_whiteness(): if debug_mode: if "whiteness" not in to_test: return else: print("\n\nTEST WHITENESS OF RESIDUALS", end="") for ds in datasets: for dt in dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") lags = results_ref[ds][dt]["whiteness"]["tested order"] obtained = results_sm[ds][dt].test_whiteness(nlags=lags) # test statistic err_msg = build_err_msg(ds, dt, "WHITENESS OF RESIDUALS - " "TEST STATISTIC") desired = results_ref[ds][dt]["whiteness"]["test statistic"] assert_allclose(obtained.test_statistic, desired, rtol, atol, False, err_msg) # p-value err_msg = build_err_msg(ds, dt, "WHITENESS OF RESIDUALS - " "P-VALUE") desired = results_ref[ds][dt]["whiteness"]["p-value"] assert_allclose(obtained.pvalue, desired, rtol, atol, False, err_msg) obtained = results_sm[ds][dt].test_whiteness(nlags=lags, adjusted=True) # test statistic (adjusted Portmanteau test) err_msg = build_err_msg(ds, dt, "WHITENESS OF RESIDUALS - " "TEST STATISTIC (ADJUSTED TEST)") desired = results_ref[ds][dt]["whiteness"]["test statistic adj."] assert_allclose(obtained.test_statistic, desired, rtol, atol, False, err_msg) # p-value (adjusted Portmanteau test) err_msg = build_err_msg(ds, dt, "WHITENESS OF RESIDUALS - " "P-VALUE (ADJUSTED TEST)") desired = results_ref[ds][dt]["whiteness"]["p-value adjusted"] assert_allclose(obtained.pvalue, desired, rtol, atol, False, err_msg) def test_exceptions(): if debug_mode: if "exceptions" not in to_test: return else: print("\n\nEXCEPTIONS\n", end="") for ds in datasets: for dt in dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") # instant causality: ### 0 0: err_msg += ", seasons: " + str(seasons) return err_msg def setup(): datasets.append( DataSet(e6, [0, 4], [0, 1], ["Dp", "R"]), # DataSet(...) TODO: append more data sets for more test cases. ) for ds in datasets: load_data(ds, data) results_ref[ds] = load_results_jmulti(ds) results_sm[ds] = load_results_statsmodels(ds) results_sm_exog[ds] = load_results_statsmodels_exog(ds) results_sm_exog_coint[ds] = load_results_statsmodels_exog_coint(ds) setup() def test_ml_gamma(): if debug_mode: if "Gamma" not in to_test: # pragma: no cover return print("\n\nGAMMA", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") exog = (results_sm_exog[ds][dt].exog is not None) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) # estimated parameter vector err_msg = build_err_msg(ds, dt, "Gamma") obtained = results_sm[ds][dt].gamma obtained_exog = results_sm_exog[ds][dt].gamma obtained_exog_coint = results_sm_exog_coint[ds][dt].gamma desired = results_ref[ds][dt]["est"]["Gamma"] assert_allclose(obtained, desired, rtol, atol, False, err_msg) if exog: assert_equal(obtained_exog, obtained, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(obtained_exog_coint, obtained, "WITH EXOG_COINT: " + err_msg) if debug_mode and dont_test_se_t_p: # pragma: no cover continue # standard errors obt = results_sm[ds][dt].stderr_gamma obt_exog = results_sm_exog[ds][dt].stderr_gamma obt_exog_coint = results_sm_exog_coint[ds][dt].stderr_gamma des = results_ref[ds][dt]["se"]["Gamma"] assert_allclose(obt, des, rtol, atol, False, "STANDARD ERRORS\n" + err_msg) if exog: assert_equal(obt_exog, obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(obt_exog_coint, obt, "WITH EXOG_COINT: " + err_msg) # t-values obt = results_sm[ds][dt].tvalues_gamma obt_exog = results_sm_exog[ds][dt].tvalues_gamma obt_exog_coint = results_sm_exog_coint[ds][dt].tvalues_gamma des = results_ref[ds][dt]["t"]["Gamma"] assert_allclose(obt, des, rtol, atol, False, "t-VALUES\n" + err_msg) if exog: assert_equal(obt_exog, obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(obt_exog_coint, obt, "WITH EXOG_COINT: " + err_msg) # p-values obt = results_sm[ds][dt].pvalues_gamma obt_exog = results_sm_exog[ds][dt].pvalues_gamma obt_exog_coint = results_sm_exog_coint[ds][dt].pvalues_gamma des = results_ref[ds][dt]["p"]["Gamma"] assert_allclose(obt, des, rtol, atol, False, "p-VALUES\n" + err_msg) if exog: assert_equal(obt_exog, obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(obt_exog_coint, obt, "WITH EXOG_COINT: " + err_msg) def test_ml_alpha(): if debug_mode: if "alpha" not in to_test: # pragma: no cover return print("\n\nALPHA", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") exog = (results_sm_exog[ds][dt].exog is not None) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) err_msg = build_err_msg(ds, dt, "alpha") obtained = results_sm[ds][dt].alpha obtained_exog = results_sm_exog[ds][dt].alpha obtained_exog_coint = results_sm_exog_coint[ds][dt].alpha desired = results_ref[ds][dt]["est"]["alpha"] assert_allclose(obtained, desired, rtol, atol, False, err_msg) if exog: assert_equal(obtained_exog, obtained, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(obtained_exog_coint, obtained, "WITH EXOG_COINT: " + err_msg) if debug_mode and dont_test_se_t_p: # pragma: no cover continue # standard errors obt = results_sm[ds][dt].stderr_alpha obt_exog = results_sm_exog[ds][dt].stderr_alpha obt_exog_coint = results_sm_exog_coint[ds][dt].stderr_alpha des = results_ref[ds][dt]["se"]["alpha"] assert_allclose(obt, des, rtol, atol, False, "STANDARD ERRORS\n" + err_msg) if exog: assert_equal(obt_exog, obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(obt_exog_coint, obt, "WITH EXOG_COINT: " + err_msg) # t-values obt = results_sm[ds][dt].tvalues_alpha obt_exog = results_sm_exog[ds][dt].tvalues_alpha obt_exog_coint = results_sm_exog_coint[ds][dt].tvalues_alpha des = results_ref[ds][dt]["t"]["alpha"] assert_allclose(obt, des, rtol, atol, False, "t-VALUES\n" + err_msg) if exog: assert_equal(obt_exog, obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(obt_exog_coint, obt, "WITH EXOG_COINT: " + err_msg) # p-values obt = results_sm[ds][dt].pvalues_alpha obt_exog = results_sm_exog[ds][dt].pvalues_alpha obt_exog_coint = results_sm_exog_coint[ds][dt].pvalues_alpha des = results_ref[ds][dt]["p"]["alpha"] assert_allclose(obt, des, rtol, atol, False, "p-VALUES\n" + err_msg) if exog: assert_equal(obt_exog, obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(obt_exog_coint, obt, "WITH EXOG_COINT: " + err_msg) def test_ml_beta(): if debug_mode: if "beta" not in to_test: # pragma: no cover return print("\n\nBETA", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") exog = (results_sm_exog[ds][dt].exog is not None) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) err_msg = build_err_msg(ds, dt, "beta") desired = results_ref[ds][dt]["est"]["beta"] rows = desired.shape[0] # - first coint_rank rows in JMulTi output have se=t_val=p_val=0 # - beta includes deterministic terms in cointegration relation in # sm, so we compare only the elements belonging to beta. obtained = results_sm[ds][dt].beta[coint_rank:rows] obtained_exog = results_sm_exog[ds][dt].beta[coint_rank:rows] obtained_exog_coint = results_sm_exog_coint[ds][dt].beta[ coint_rank:rows] desired = desired[coint_rank:] assert_allclose(obtained, desired, rtol, atol, False, err_msg) if exog: assert_equal(obtained_exog, obtained, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(obtained_exog_coint, obtained, "WITH EXOG_COINT: " + err_msg) if debug_mode and dont_test_se_t_p: # pragma: no cover continue # standard errors obt = results_sm[ds][dt].stderr_beta[coint_rank:rows] obt_exog = results_sm_exog[ds][dt].stderr_beta[coint_rank:rows] obt_exog_coint = results_sm_exog_coint[ds][dt].stderr_beta[ coint_rank:rows] des = results_ref[ds][dt]["se"]["beta"][coint_rank:] assert_allclose(obt, des, rtol, atol, False, "STANDARD ERRORS\n" + err_msg) if exog: assert_equal(obt_exog, obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(obt_exog_coint, obt, "WITH EXOG_COINT: " + err_msg) # t-values obt = results_sm[ds][dt].tvalues_beta[coint_rank:rows] obt_exog = results_sm_exog[ds][dt].tvalues_beta[coint_rank:rows] obt_exog_coint = results_sm_exog_coint[ds][dt].tvalues_beta[ coint_rank:rows] des = results_ref[ds][dt]["t"]["beta"][coint_rank:] assert_allclose(obt, des, rtol, atol, False, "t-VALUES\n" + err_msg) if exog: assert_equal(obt_exog, obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(obt_exog_coint, obt, "WITH EXOG_COINT: " + err_msg) # p-values obt = results_sm[ds][dt].pvalues_beta[coint_rank:rows] obt_exog = results_sm_exog[ds][dt].pvalues_beta[coint_rank:rows] obt_exog_coint = results_sm_exog_coint[ds][dt].pvalues_beta[ coint_rank:rows] des = results_ref[ds][dt]["p"]["beta"][coint_rank:] assert_allclose(obt, des, rtol, atol, False, "p-VALUES\n" + err_msg) if exog: assert_equal(obt_exog, obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(obt_exog_coint, obt, "WITH EXOG_COINT: " + err_msg) def test_ml_c(): # test deterministic terms outside coint relation if debug_mode: if "C" not in to_test: # pragma: no cover return print("\n\nDET_COEF", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") exog = (results_sm_exog[ds][dt].exog is not None) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) C_obt = results_sm[ds][dt].det_coef C_obt_exog = results_sm_exog[ds][dt].det_coef C_obt_exog_coint = results_sm_exog_coint[ds][dt].det_coef se_C_obt = results_sm[ds][dt].stderr_det_coef se_C_obt_exog = results_sm_exog[ds][dt].stderr_det_coef se_C_obt_exog_coint = results_sm_exog_coint[ds][dt].stderr_det_coef t_C_obt = results_sm[ds][dt].tvalues_det_coef t_C_obt_exog = results_sm_exog[ds][dt].tvalues_det_coef t_C_obt_exog_coint = results_sm_exog_coint[ds][dt].tvalues_det_coef p_C_obt = results_sm[ds][dt].pvalues_det_coef p_C_obt_exog = results_sm_exog[ds][dt].pvalues_det_coef p_C_obt_exog_coint = results_sm_exog_coint[ds][dt].pvalues_det_coef if "C" not in results_ref[ds][dt]["est"].keys(): # case: there are no deterministic terms if C_obt.size == 0 and se_C_obt.size == 0 \ and t_C_obt.size == 0 and p_C_obt.size == 0: assert_(True) continue desired = results_ref[ds][dt]["est"]["C"] dt_string = dt_s_tup_to_string(dt) if "co" in dt_string: err_msg = build_err_msg(ds, dt, "CONST") const_obt = C_obt[:, :1] const_obt_exog = C_obt_exog[:, :1] const_obt_exog_coint = C_obt_exog_coint[:, :1] const_des = desired[:, :1] C_obt = C_obt[:, 1:] C_obt_exog = C_obt_exog[:, 1:] C_obt_exog_coint = C_obt_exog_coint[:, 1:] desired = desired[:, 1:] assert_allclose(const_obt, const_des, rtol, atol, False, err_msg) if exog: assert_equal(const_obt_exog, const_obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(const_obt_exog_coint, const_obt, "WITH EXOG_COINT: " + err_msg) if "s" in dt_string: err_msg = build_err_msg(ds, dt, "SEASONAL") if "lo" in dt_string: seas_obt = C_obt[:, :-1] seas_obt_exog = C_obt_exog[:, :-1] seas_obt_exog_coint = C_obt_exog_coint[:, :-1] seas_des = desired[:, :-1] else: seas_obt = C_obt seas_obt_exog = C_obt_exog seas_obt_exog_coint = C_obt_exog_coint seas_des = desired assert_allclose(seas_obt, seas_des, rtol, atol, False, err_msg) if exog: assert_equal(seas_obt_exog, seas_obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(seas_obt_exog_coint, seas_obt, "WITH EXOG_COINT: " + err_msg) if "lo" in dt_string: err_msg = build_err_msg(ds, dt, "LINEAR TREND") lt_obt = C_obt[:, -1:] lt_obt_exog = C_obt_exog[:, -1:] lt_obt_exog_coint = C_obt_exog_coint[:, -1:] lt_des = desired[:, -1:] assert_allclose(lt_obt, lt_des, rtol, atol, False, err_msg) if exog: assert_equal(lt_obt_exog, lt_obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(lt_obt_exog_coint, lt_obt, "WITH EXOG_COINT: " + err_msg) if debug_mode and dont_test_se_t_p: # pragma: no cover continue # standard errors se_desired = results_ref[ds][dt]["se"]["C"] if "co" in dt_string: err_msg = build_err_msg(ds, dt, "SE CONST") se_const_obt = se_C_obt[:, 0][:, None] se_C_obt = se_C_obt[:, 1:] se_const_obt_exog = se_C_obt_exog[:, 0][:, None] se_C_obt_exog = se_C_obt_exog[:, 1:] se_const_obt_exog_coint = se_C_obt_exog_coint[:, 0][:, None] se_C_obt_exog_coint = se_C_obt_exog_coint[:, 1:] se_const_des = se_desired[:, 0][:, None] se_desired = se_desired[:, 1:] assert_allclose(se_const_obt, se_const_des, rtol, atol, False, err_msg) if exog: assert_equal(se_const_obt_exog, se_const_obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(se_const_obt_exog_coint, se_const_obt, "WITH EXOG_COINT: " + err_msg) if "s" in dt_string: err_msg = build_err_msg(ds, dt, "SE SEASONAL") if "lo" in dt_string: se_seas_obt = se_C_obt[:, :-1] se_seas_obt_exog = se_C_obt_exog[:, :-1] se_seas_obt_exog_coint = se_C_obt_exog_coint[:, :-1] se_seas_des = se_desired[:, :-1] else: se_seas_obt = se_C_obt se_seas_obt_exog = se_C_obt_exog se_seas_obt_exog_coint = se_C_obt_exog_coint se_seas_des = se_desired assert_allclose(se_seas_obt, se_seas_des, rtol, atol, False, err_msg) if exog: assert_equal(se_seas_obt_exog, se_seas_obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(se_seas_obt_exog_coint, se_seas_obt, "WITH EXOG_COINT: " + err_msg) if "lo" in dt_string: err_msg = build_err_msg(ds, dt, "SE LIN. TREND") se_lt_obt = se_C_obt[:, -1:] se_lt_obt_exog = se_C_obt_exog[:, -1:] se_lt_obt_exog_coint = se_C_obt_exog_coint[:, -1:] se_lt_des = se_desired[:, -1:] assert_allclose(se_lt_obt, se_lt_des, rtol, atol, False, err_msg) if exog: assert_equal(se_lt_obt_exog, se_lt_obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(se_lt_obt_exog_coint, se_lt_obt, "WITH EXOG_COINT: " + err_msg) # t-values t_desired = results_ref[ds][dt]["t"]["C"] if "co" in dt_string: t_const_obt = t_C_obt[:, 0][:, None] t_C_obt = t_C_obt[:, 1:] t_const_obt_exog = t_C_obt_exog[:, 0][:, None] t_C_obt_exog = t_C_obt_exog[:, 1:] t_const_obt_exog_coint = t_C_obt_exog_coint[:, 0][:, None] t_C_obt_exog_coint = t_C_obt_exog_coint[:, 1:] t_const_des = t_desired[:, 0][:, None] t_desired = t_desired[:, 1:] assert_allclose(t_const_obt, t_const_des, rtol, atol, False, build_err_msg(ds, dt, "T CONST")) if exog: assert_equal(t_const_obt_exog, t_const_obt, "WITH EXOG: " + err_msg) if exog_coint: assert_equal(t_const_obt_exog_coint, t_const_obt, "WITH EXOG_COINT: " + err_msg) if "s" in dt_string: if "lo" in dt_string: t_seas_obt = t_C_obt[:, :-1] t_seas_obt_exog = t_C_obt_exog[:, :-1] t_seas_obt_exog_coint = t_C_obt_exog_coint[:, :-1] t_seas_des = t_desired[:, :-1] else: t_seas_obt = t_C_obt t_seas_obt_exog = t_C_obt_exog t_seas_obt_exog_coint = t_C_obt_exog_coint t_seas_des = t_desired assert_allclose(t_seas_obt, t_seas_des, rtol, atol, False, build_err_msg(ds, dt, "T SEASONAL")) if exog: assert_equal(t_seas_obt_exog, t_seas_obt, "WITH EXOG" + err_msg) if exog_coint: assert_equal(t_seas_obt_exog_coint, t_seas_obt, "WITH EXOG_COINT" + err_msg) if "lo" in dt_string: t_lt_obt = t_C_obt[:, -1:] t_lt_obt_exog = t_C_obt_exog[:, -1:] t_lt_obt_exog_coint = t_C_obt_exog_coint[:, -1:] t_lt_des = t_desired[:, -1:] assert_allclose(t_lt_obt, t_lt_des, rtol, atol, False, build_err_msg(ds, dt, "T LIN. TREND")) if exog: assert_equal(t_lt_obt_exog, t_lt_obt, "WITH EXOG" + err_msg) if exog_coint: assert_equal(t_lt_obt_exog_coint, t_lt_obt, "WITH EXOG_COINT" + err_msg) # p-values p_desired = results_ref[ds][dt]["p"]["C"] if "co" in dt_string: p_const_obt = p_C_obt[:, 0][:, None] p_C_obt = p_C_obt[:, 1:] p_const_obt_exog = p_C_obt_exog[:, 0][:, None] p_C_obt_exog = p_C_obt_exog[:, 1:] p_const_obt_exog_coint = p_C_obt_exog_coint[:, 0][:, None] p_C_obt_exo_cointg = p_C_obt_exog_coint[:, 1:] p_const_des = p_desired[:, 0][:, None] p_desired = p_desired[:, 1:] assert_allclose(p_const_obt, p_const_des, rtol, atol, False, build_err_msg(ds, dt, "P CONST")) if exog: assert_equal(p_const_obt, p_const_obt_exog, "WITH EXOG" + err_msg) if exog_coint: assert_equal(p_const_obt, p_const_obt_exog_coint, "WITH EXOG_COINT" + err_msg) if "s" in dt_string: if "lo" in dt_string: p_seas_obt = p_C_obt[:, :-1] p_seas_obt_exog = p_C_obt_exog[:, :-1] p_seas_obt_exog_coint = p_C_obt_exog_coint[:, :-1] p_seas_des = p_desired[:, :-1] else: p_seas_obt = p_C_obt p_seas_obt_exog = p_C_obt_exog p_seas_obt_exog_coint = p_C_obt_exog_coint p_seas_des = p_desired assert_allclose(p_seas_obt, p_seas_des, rtol, atol, False, build_err_msg(ds, dt, "P SEASONAL")) if exog: assert_equal(p_seas_obt_exog, p_seas_obt, "WITH EXOG" + err_msg) if exog_coint: assert_equal(p_seas_obt_exog_coint, p_seas_obt, "WITH EXOG_COINT" + err_msg) if "lo" in dt_string: p_lt_obt = p_C_obt[:, -1:] p_lt_obt_exog = p_C_obt_exog[:, -1:] p_lt_obt_exog_coint = p_C_obt_exog_coint[:, -1:] p_lt_des = p_desired[:, -1:] assert_allclose(p_lt_obt, p_lt_des, rtol, atol, False, build_err_msg(ds, dt, "P LIN. TREND")) if exog: assert_equal(p_lt_obt_exog, p_lt_obt, "WITH EXOG" + err_msg) if exog_coint: assert_equal(p_lt_obt_exog_coint, p_lt_obt, "WITH EXOG_COINT" + err_msg) def test_ml_det_terms_in_coint_relation(): if debug_mode: if "det_coint" not in to_test: # pragma: no cover return print("\n\nDET_COEF_COINT", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") exog = (results_sm_exog[ds][dt].exog is not None) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) err_msg = build_err_msg(ds, dt, "det terms in coint relation") dt_string = dt_s_tup_to_string(dt) obtained = results_sm[ds][dt].det_coef_coint obtained_exog = results_sm_exog[ds][dt].det_coef_coint obtained_exog_coint = results_sm_exog_coint[ds][dt].det_coef_coint if "ci" not in dt_string and "li" not in dt_string: if obtained.size > 0: assert_(False, build_err_msg(ds, dt, "There should not be any det terms in " + "cointegration for deterministic terms " + dt_string)) else: assert_(True) continue desired = results_ref[ds][dt]["est"]["det_coint"] assert_allclose(obtained, desired, rtol, atol, False, err_msg) if exog: assert_equal(obtained_exog, obtained, "WITH EXOG" + err_msg) if exog_coint: assert_equal(obtained_exog_coint, obtained, "WITH EXOG_COINT" + err_msg) # standard errors se_obtained = results_sm[ds][dt].stderr_det_coef_coint se_obtained_exog = results_sm_exog[ds][dt].stderr_det_coef_coint se_obtained_exog_coint = results_sm_exog_coint[ds][ dt].stderr_det_coef_coint se_desired = results_ref[ds][dt]["se"]["det_coint"] assert_allclose(se_obtained, se_desired, rtol, atol, False, "STANDARD ERRORS\n" + err_msg) if exog: assert_equal(se_obtained_exog, se_obtained, "WITH EXOG" + err_msg) if exog_coint: assert_equal(se_obtained_exog_coint, se_obtained, "WITH EXOG_COINT" + err_msg) # t-values t_obtained = results_sm[ds][dt].tvalues_det_coef_coint t_obtained_exog = results_sm_exog[ds][dt].tvalues_det_coef_coint t_obtained_exog_coint = results_sm_exog_coint[ds][ dt].tvalues_det_coef_coint t_desired = results_ref[ds][dt]["t"]["det_coint"] assert_allclose(t_obtained, t_desired, rtol, atol, False, "t-VALUES\n" + err_msg) if exog: assert_equal(t_obtained_exog, t_obtained, "WITH EXOG" + err_msg) if exog_coint: assert_equal(t_obtained_exog_coint, t_obtained, "WITH EXOG_COINT" + err_msg) # p-values p_obtained = results_sm[ds][dt].pvalues_det_coef_coint p_obtained_exog = results_sm_exog[ds][dt].pvalues_det_coef_coint p_obtained_exog_coint = results_sm_exog_coint[ds][ dt].pvalues_det_coef_coint p_desired = results_ref[ds][dt]["p"]["det_coint"] assert_allclose(p_obtained, p_desired, rtol, atol, False, "p-VALUES\n" + err_msg) if exog: assert_equal(p_obtained_exog, p_obtained, "WITH EXOG" + err_msg) if exog_coint: assert_equal(p_obtained_exog_coint, p_obtained, "WITH EXOG_COINT" + err_msg) def test_ml_sigma(): if debug_mode: if "Sigma_u" not in to_test: # pragma: no cover return print("\n\nSIGMA_U", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") exog = (results_sm_exog[ds][dt].exog is not None) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) err_msg = build_err_msg(ds, dt, "Sigma_u") obtained = results_sm[ds][dt].sigma_u obtained_exog = results_sm_exog[ds][dt].sigma_u obtained_exog_coint = results_sm_exog_coint[ds][dt].sigma_u desired = results_ref[ds][dt]["est"]["Sigma_u"] assert_allclose(obtained, desired, rtol, atol, False, err_msg) if exog: assert_equal(obtained_exog, obtained, "WITH EXOG" + err_msg) if exog_coint: assert_equal(obtained_exog_coint, obtained, "WITH EXOG_COINT" + err_msg) def test_var_rep(): if debug_mode: if "VAR repr. A" not in to_test: # pragma: no cover return print("\n\nVAR REPRESENTATION", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") exog = (results_sm_exog[ds][dt].exog is not None) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) err_msg = build_err_msg(ds, dt, "VAR repr. A") obtained = results_sm[ds][dt].var_rep obtained_exog = results_sm_exog[ds][dt].var_rep obtained_exog_coint = results_sm_exog_coint[ds][dt].var_rep p = obtained.shape[0] desired = np.hsplit(results_ref[ds][dt]["est"]["VAR A"], p) assert_allclose(obtained, desired, rtol, atol, False, err_msg) if exog: assert_equal(obtained_exog, obtained, "WITH EXOG" + err_msg) if exog_coint: assert_equal(obtained_exog_coint, obtained, "WITH EXOG_COINT" + err_msg) def test_var_to_vecm(): if debug_mode: if "VAR to VEC representation" not in to_test: # pragma: no cover return print("\n\nVAR TO VEC", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") err_msg = build_err_msg(ds, dt, "VAR to VEC representation") sigma_u = results_sm[ds][dt].sigma_u coefs = results_sm[ds][dt].var_rep intercept = np.zeros(len(sigma_u)) # Note: _params_info k_trend, k_exog, ... is inferred with defaults var = VARProcess(coefs, intercept, sigma_u) vecm_results = var.to_vecm() obtained_pi = vecm_results["Pi"] obtained_gamma = vecm_results["Gamma"] desired_pi = np.dot(results_sm[ds][dt].alpha, results_sm[ds][dt].beta.T) desired_gamma = results_sm[ds][dt].gamma assert_allclose(obtained_pi, desired_pi, rtol, atol, False, err_msg + " Pi") assert_allclose(obtained_gamma, desired_gamma, rtol, atol, False, err_msg + " Gamma") # Commented out since JMulTi shows the same det. terms for both VEC & VAR repr. # def test_var_rep_det(): # for ds in datasets: # for dt in dt_s_list: # if dt != "nc": # err_msg = build_err_msg(ds, dt, "VAR repr. deterministic") # obtained = 0 # not implemented since the same values as VECM # desired = results_ref[ds][dt]["est"]["VAR deterministic"] # assert_allclose(obtained, desired, rtol, atol, False, err_msg) def test_log_like(): if debug_mode: if "log_like" not in to_test: # pragma: no cover return else: print("\n\nLOG LIKELIHOOD", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") exog = (results_sm_exog[ds][dt].exog is not None) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) err_msg = build_err_msg(ds, dt, "Log Likelihood") obtained = results_sm[ds][dt].llf obtained_exog = results_sm_exog[ds][dt].llf obtained_exog_coint = results_sm_exog_coint[ds][dt].llf # JMulTi's llf seems to have a bug (Stata and tsdyn suggest that # our code is correct). We use nobs to correct this inconsistency. nobs = results_sm[ds][dt].nobs desired = results_ref[ds][dt]["log_like"] * nobs / (nobs-1) assert_allclose(obtained, desired, rtol, atol, False, err_msg) if exog: assert_equal(obtained_exog, obtained, "WITH EXOG" + err_msg) if exog_coint: assert_equal(obtained_exog_coint, obtained, "WITH EXOG_COINT" + err_msg) def test_fc(): if debug_mode: if "fc" not in to_test: # pragma: no cover return else: print("\n\nFORECAST", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") STEPS = 5 ALPHA = 0.05 err_msg = build_err_msg(ds, dt, "FORECAST") # test point forecast functionality of predict method obtained = results_sm[ds][dt].predict(steps=STEPS) desired = results_ref[ds][dt]["fc"]["fc"] assert_allclose(obtained, desired, rtol, atol, False, err_msg) # ----------------------------------------------------------------- # with exog: exog = (results_sm_exog[ds][dt].exog is not None) exog_fc = None if exog: # build future values of exog and test: seasons = dt[1] exog_model = results_sm_exog[ds][dt].exog exog_seasons_fc = exog_model[-seasons:, :seasons-1] exog_seasons_fc = np.pad(exog_seasons_fc, ((0, STEPS-exog_seasons_fc.shape[0]), (0, 0)), "wrap") # if linear trend in exog if exog_seasons_fc.shape[1] + 1 == exog_model.shape[1]: exog_lt_fc = exog_model[-1, -1] + 1 + np.arange(STEPS) exog_fc = np.column_stack((exog_seasons_fc, exog_lt_fc)) else: exog_fc = exog_seasons_fc obtained_exog = results_sm_exog[ds][dt].predict( steps=STEPS, exog_fc=exog_fc) assert_allclose(obtained_exog, obtained, 1e-07, 0, False, "WITH EXOG" + err_msg) # test predict method with confidence interval calculation err_msg = build_err_msg(ds, dt, "FORECAST WITH INTERVALS") obtained_w_intervals = results_sm[ds][dt].predict( steps=STEPS, alpha=ALPHA) obtained_w_intervals_exog = results_sm_exog[ds][dt].predict( steps=STEPS, alpha=ALPHA, exog_fc=exog_fc) obt = obtained_w_intervals[0] # forecast obt_l = obtained_w_intervals[1] # lower bound obt_u = obtained_w_intervals[2] # upper bound obt_exog = obtained_w_intervals_exog[0] obt_exog_l = obtained_w_intervals_exog[1] obt_exog_u = obtained_w_intervals_exog[2] des = results_ref[ds][dt]["fc"]["fc"] des_l = results_ref[ds][dt]["fc"]["lower"] des_u = results_ref[ds][dt]["fc"]["upper"] assert_allclose(obt, des, rtol, atol, False, err_msg) assert_allclose(obt_l, des_l, rtol, atol, False, err_msg) assert_allclose(obt_u, des_u, rtol, atol, False, err_msg) if exog: assert_allclose(obt_exog, obt, 1e-07, 0, False, "WITH EXOG" + err_msg) assert_allclose(obt_exog_l, obt_l, 1e-07, 0, False, "WITH EXOG" + err_msg) assert_allclose(obt_exog_u, obt_u, 1e-07, 0, False, "WITH EXOG" + err_msg) # ----------------------------------------------------------------- # with exog_coint: exog_coint_model = results_sm_exog_coint[ds][dt].exog_coint exog_coint = (exog_coint_model is not None) exog_coint_fc = None if exog_coint: # build future values of exog_coint and test: # const is in exog_coint in all tests that have exog_coint exog_coint_fc = np.ones(STEPS-1) # if linear trend in exog_coint if exog_coint_model.shape[1] == 2: exog_coint_fc = np.column_stack( (exog_coint_fc, exog_coint_model[-1, -1] + 1 + np.arange(STEPS-1)) ) obtained_exog_coint = results_sm_exog_coint[ds][dt].predict( steps=STEPS, exog_coint_fc=exog_coint_fc) assert_allclose(obtained_exog_coint, obtained, 1e-07, 0, False, "WITH EXOG_COINT" + err_msg) # test predict method with confidence interval calculation err_msg = build_err_msg(ds, dt, "FORECAST WITH INTERVALS") obtained_w_intervals = results_sm[ds][dt].predict( steps=STEPS, alpha=ALPHA) obtained_w_intervals_exog_coint = results_sm_exog_coint[ds][ dt].predict(steps=STEPS, alpha=ALPHA, exog_coint_fc=exog_coint_fc) obt = obtained_w_intervals[0] # forecast obt_l = obtained_w_intervals[1] # lower bound obt_u = obtained_w_intervals[2] # upper bound obt_exog_coint = obtained_w_intervals_exog_coint[0] obt_exog_coint_l = obtained_w_intervals_exog_coint[1] obt_exog_coint_u = obtained_w_intervals_exog_coint[2] des = results_ref[ds][dt]["fc"]["fc"] des_l = results_ref[ds][dt]["fc"]["lower"] des_u = results_ref[ds][dt]["fc"]["upper"] assert_allclose(obt, des, rtol, atol, False, err_msg) assert_allclose(obt_l, des_l, rtol, atol, False, err_msg) assert_allclose(obt_u, des_u, rtol, atol, False, err_msg) if exog_coint: assert_allclose(obt_exog_coint, obt, 1e-07, 0, False, "WITH EXOG_COINT" + err_msg) assert_allclose(obt_exog_coint_l, obt_l, 1e-07, 0, False, "WITH EXOG_COINT" + err_msg) assert_allclose(obt_exog_coint_u, obt_u, 1e-07, 0, False, "WITH EXOG_COINT" + err_msg) def test_granger_causality(): if debug_mode: if "granger" not in to_test: # pragma: no cover return else: print("\n\nGRANGER", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") exog = (results_sm_exog[ds][dt].exog is not None) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) err_msg_g_p = build_err_msg(ds, dt, "GRANGER CAUS. - p-VALUE") err_msg_g_t = build_err_msg(ds, dt, "GRANGER CAUS. - TEST STAT.") v_ind = range(len(ds.variable_names)) for causing_ind in sublists(v_ind, 1, len(v_ind)-1): causing_names = ["y" + str(i+1) for i in causing_ind] causing_key = tuple(ds.variable_names[i] for i in causing_ind) caused_ind = [i for i in v_ind if i not in causing_ind] caused_names = ["y" + str(i+1) for i in caused_ind] caused_key = tuple(ds.variable_names[i] for i in caused_ind) granger_sm_ind = results_sm[ds][ dt].test_granger_causality(caused_ind, causing_ind) granger_sm_ind_exog = results_sm_exog[ds][ dt].test_granger_causality(caused_ind, causing_ind) granger_sm_ind_exog_coint = results_sm_exog_coint[ds][ dt].test_granger_causality(caused_ind, causing_ind) granger_sm_str = results_sm[ds][ dt].test_granger_causality(caused_names, causing_names) # call methods to assure they do not raise exceptions granger_sm_ind.summary() str(granger_sm_ind) # __str__() assert_(granger_sm_ind == granger_sm_str) # __eq__() # test test-statistic for Granger non-causality: g_t_obt = granger_sm_ind.test_statistic g_t_obt_exog = granger_sm_ind_exog.test_statistic g_t_obt_exog_coint = granger_sm_ind_exog_coint.test_statistic g_t_des = results_ref[ds][dt]["granger_caus"][ "test_stat"][(causing_key, caused_key)] assert_allclose(g_t_obt, g_t_des, rtol, atol, False, err_msg_g_t) if exog: assert_allclose(g_t_obt_exog, g_t_obt, 1e-07, 0, False, "WITH EXOG" + err_msg_g_t) if exog_coint: assert_allclose(g_t_obt_exog_coint, g_t_obt, 1e-07, 0, False, "WITH EXOG_COINT" + err_msg_g_t) # check whether string sequences as args work in the same way: g_t_obt_str = granger_sm_str.test_statistic assert_allclose(g_t_obt_str, g_t_obt, 1e-07, 0, False, err_msg_g_t + " - sequences of integers and ".upper() + "strings as arguments do not yield the same result!".upper()) # check if int (e.g. 0) as index and list of int ([0]) yield # the same result: if len(causing_ind) == 1 or len(caused_ind) == 1: ci = causing_ind[0] if len(causing_ind)==1 else causing_ind ce = caused_ind[0] if len(caused_ind) == 1 else caused_ind granger_sm_single_ind = results_sm[ds][ dt].test_granger_causality(ce, ci) g_t_obt_single = granger_sm_single_ind.test_statistic assert_allclose(g_t_obt_single, g_t_obt, 1e-07, 0, False, err_msg_g_t + " - list of int and int as ".upper() + "argument do not yield the same result!".upper()) # test p-value for Granger non-causality: g_p_obt = granger_sm_ind.pvalue g_p_des = results_ref[ds][dt]["granger_caus"]["p"][( causing_key, caused_key)] assert_allclose(g_p_obt, g_p_des, rtol, atol, False, err_msg_g_p) # check whether string sequences as args work in the same way: g_p_obt_str = granger_sm_str.pvalue assert_allclose(g_p_obt_str, g_p_obt, 1e-07, 0, False, err_msg_g_t + " - sequences of integers and ".upper() + \ "strings as arguments do not yield the same result!".upper()) # check if int (e.g. 0) as index and list of int ([0]) yield # the same result: if len(causing_ind) == 1: g_p_obt_single = granger_sm_single_ind.pvalue assert_allclose(g_p_obt_single, g_p_obt, 1e-07, 0, False, err_msg_g_t + " - list of int and int as ".upper() + \ "argument do not yield the same result!".upper()) def test_inst_causality(): # test instantaneous causality if debug_mode: if "inst. causality" not in to_test: # pragma: no cover return else: print("\n\nINST. CAUSALITY", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") exog = (results_sm_exog[ds][dt].exog is not None) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) err_msg_i_p = build_err_msg(ds, dt, "INSTANT. CAUS. - p-VALUE") err_msg_i_t = build_err_msg(ds, dt, "INSTANT. CAUS. - TEST STAT.") v_ind = range(len(ds.variable_names)) for causing_ind in sublists(v_ind, 1, len(v_ind)-1): causing_names = ["y" + str(i+1) for i in causing_ind] causing_key = tuple(ds.variable_names[i] for i in causing_ind) caused_ind = [i for i in v_ind if i not in causing_ind] caused_key = tuple(ds.variable_names[i] for i in caused_ind) inst_sm_ind = results_sm[ds][dt].test_inst_causality( causing_ind) inst_sm_ind_exog = results_sm_exog[ds][ dt].test_inst_causality(causing_ind) inst_sm_ind_exog_coint = results_sm_exog_coint[ds][ dt].test_inst_causality(causing_ind) inst_sm_str = results_sm[ds][dt].test_inst_causality( causing_names) # call methods to assure they do not raise exceptions inst_sm_ind.summary() str(inst_sm_ind) # __str__() assert_(inst_sm_ind == inst_sm_str) # __eq__() # test test-statistic for instantaneous non-causality t_obt = inst_sm_ind.test_statistic t_obt_exog = inst_sm_ind_exog.test_statistic t_obt_exog_coint = inst_sm_ind_exog_coint.test_statistic t_des = results_ref[ds][dt]["inst_caus"][ "test_stat"][(causing_key, caused_key)] assert_allclose(t_obt, t_des, rtol, atol, False, err_msg_i_t) if exog: assert_allclose(t_obt_exog, t_obt, 1e-07, 0, False, "WITH EXOG" + err_msg_i_t) if exog_coint: assert_allclose(t_obt_exog_coint, t_obt, 1e-07, 0, False, "WITH EXOG_COINT" + err_msg_i_t) # check whether string sequences as args work in the same way: t_obt_str = inst_sm_str.test_statistic assert_allclose(t_obt_str, t_obt, 1e-07, 0, False, err_msg_i_t + " - sequences of integers and ".upper() + "strings as arguments do not yield the same result!".upper()) # check if int (e.g. 0) as index and list of int ([0]) yield # the same result: if len(causing_ind) == 1: inst_sm_single_ind = results_sm[ds][ dt].test_inst_causality(causing_ind[0]) t_obt_single = inst_sm_single_ind.test_statistic assert_allclose(t_obt_single, t_obt, 1e-07, 0, False, err_msg_i_t + " - list of int and int as ".upper() + "argument do not yield the same result!".upper()) # test p-value for instantaneous non-causality p_obt = results_sm[ds][dt].test_inst_causality( causing_ind).pvalue p_des = results_ref[ds][dt]["inst_caus"]["p"][( causing_key, caused_key)] assert_allclose(p_obt, p_des, rtol, atol, False, err_msg_i_p) # check whether string sequences as args work in the same way: p_obt_str = inst_sm_str.pvalue assert_allclose(p_obt_str, p_obt, 1e-07, 0, False, err_msg_i_p + " - sequences of integers and ".upper() + "strings as arguments do not yield the same result!".upper()) # check if int (e.g. 0) as index and list of int ([0]) yield # the same result: if len(causing_ind) == 1: inst_sm_single_ind = results_sm[ds][ dt].test_inst_causality(causing_ind[0]) p_obt_single = inst_sm_single_ind.pvalue assert_allclose(p_obt_single, p_obt, 1e-07, 0, False, err_msg_i_p + " - list of int and int as ".upper() + "argument do not yield the same result!".upper()) def test_impulse_response(): if debug_mode: if "impulse-response" not in to_test: # pragma: no cover return else: print("\n\nIMPULSE-RESPONSE", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") exog = (results_sm_exog[ds][dt].exog is not None) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) err_msg = build_err_msg(ds, dt, "IMULSE-RESPONSE") periods = 20 obtained_all = results_sm[ds][dt].irf(periods=periods).irfs obtained_all_exog = results_sm_exog[ds][dt].irf( periods=periods).irfs obtained_all_exog_coint = results_sm_exog_coint[ds][dt].irf( periods=periods).irfs # flatten inner arrays to make them comparable to parsed results: obtained_all = obtained_all.reshape(periods+1, -1) obtained_all_exog = obtained_all_exog.reshape(periods+1, -1) obtained_all_exog_coint = obtained_all_exog_coint.reshape( periods+1, -1) desired_all = results_ref[ds][dt]["ir"] assert_allclose(obtained_all, desired_all, rtol, atol, False, err_msg) if exog: assert_equal(obtained_all_exog, obtained_all, "WITH EXOG" + err_msg) if exog_coint: assert_equal(obtained_all_exog_coint, obtained_all, "WITH EXOG_COINT" + err_msg) def test_lag_order_selection(): if debug_mode: if "lag order" not in to_test: # pragma: no cover return else: print("\n\nLAG ORDER SELECTION", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") deterministic = dt[0] endog_tot = data[ds] obtained_all = select_order(endog_tot, 10, dt[0], dt[1]) deterministic_outside_exog = "" # "co" is not in exog in any test case if "co" in deterministic: deterministic_outside_exog += "co" # "lo" is is in exog only in test cases with seasons>0 if "lo" in deterministic and dt[1] == 0: deterministic_outside_exog += "lo" exog_model = results_sm_exog[ds][dt].exog exog = (exog_model is not None) exog_coint_model = results_sm_exog_coint[ds][dt].exog_coint exog_coint = (exog_coint_model is not None) obtained_all_exog = select_order(endog_tot, 10, deterministic_outside_exog, seasons=0, exog=exog_model) # "ci" and "li" are always in exog_coint, so pass "nc" as det. term obtained_all_exog_coint = select_order(endog_tot, 10, "nc", seasons=dt[1], exog_coint=exog_coint_model) for ic in ["aic", "fpe", "hqic", "bic"]: err_msg = build_err_msg(ds, dt, "LAG ORDER SELECTION - " + ic.upper()) obtained = getattr(obtained_all, ic) desired = results_ref[ds][dt]["lagorder"][ic] assert_allclose(obtained, desired, rtol, atol, False, err_msg) if exog: assert_equal(getattr(obtained_all_exog, ic), getattr(obtained_all, ic), "WITH EXOG" + err_msg) if exog_coint: assert_equal(getattr(obtained_all_exog_coint, ic), getattr(obtained_all, ic), "WITH EXOG_COINT" + err_msg) # call methods to assure they do not raise exceptions obtained_all.summary() str(obtained_all) # __str__() def test_normality(): if debug_mode: if "test_norm" not in to_test: # pragma: no cover return else: print("\n\nTEST NON-NORMALITY", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") exog = (results_sm_exog[ds][dt].exog is not None) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) obtained = results_sm[ds][dt].test_normality(signif=0.05) obtained_exog = results_sm_exog[ds][dt].test_normality(signif=0.05) obtained_exog_coint = results_sm_exog_coint[ds][dt].test_normality( signif=0.05) err_msg = build_err_msg(ds, dt, "TEST NON-NORMALITY - STATISTIC") obt_statistic = obtained.test_statistic obt_statistic_exog = obtained_exog.test_statistic obt_statistic_exog_coint = obtained_exog_coint.test_statistic des_statistic = results_ref[ds][dt]["test_norm"][ "joint_test_statistic"] assert_allclose(obt_statistic, des_statistic, rtol, atol, False, err_msg) if exog: assert_equal(obt_statistic_exog, obt_statistic, "WITH EXOG" + err_msg) if exog_coint: assert_equal(obt_statistic_exog_coint, obt_statistic, "WITH EXOG_COINT" + err_msg) err_msg = build_err_msg(ds, dt, "TEST NON-NORMALITY - P-VALUE") obt_pvalue = obtained.pvalue des_pvalue = results_ref[ds][dt]["test_norm"]["joint_pvalue"] assert_allclose(obt_pvalue, des_pvalue, rtol, atol, False, err_msg) # call methods to assure they do not raise exceptions obtained.summary() str(obtained) # __str__() assert_(obtained == obtained_exog) # __eq__() def test_whiteness(): if debug_mode: if "whiteness" not in to_test: # pragma: no cover return else: print("\n\nTEST WHITENESS OF RESIDUALS", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") exog = (results_sm_exog[ds][dt].exog is not None) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) lags = results_ref[ds][dt]["whiteness"]["tested order"] obtained = results_sm[ds][dt].test_whiteness(nlags=lags) obtained_exog = results_sm_exog[ds][dt].test_whiteness(nlags=lags) obtained_exog_coint = results_sm_exog_coint[ds][dt].test_whiteness( nlags=lags) # test statistic err_msg = build_err_msg(ds, dt, "WHITENESS OF RESIDUALS - " "TEST STATISTIC") desired = results_ref[ds][dt]["whiteness"]["test statistic"] assert_allclose(obtained.test_statistic, desired, rtol, atol, False, err_msg) if exog: assert_equal(obtained_exog.test_statistic, obtained.test_statistic, "WITH EXOG" + err_msg) if exog_coint: assert_equal(obtained_exog_coint.test_statistic, obtained.test_statistic, "WITH EXOG_COINT" + err_msg) # p-value err_msg = build_err_msg(ds, dt, "WHITENESS OF RESIDUALS - " "P-VALUE") desired = results_ref[ds][dt]["whiteness"]["p-value"] assert_allclose(obtained.pvalue, desired, rtol, atol, False, err_msg) obtained = results_sm[ds][dt].test_whiteness(nlags=lags, adjusted=True) obtained_exog = results_sm_exog[ds][dt].test_whiteness( nlags=lags, adjusted=True) obtained_exog_coint = results_sm_exog_coint[ds][dt].test_whiteness( nlags=lags, adjusted=True) # test statistic (adjusted Portmanteau test) err_msg = build_err_msg(ds, dt, "WHITENESS OF RESIDUALS - " "TEST STATISTIC (ADJUSTED TEST)") desired = results_ref[ds][dt]["whiteness"]["test statistic adj."] assert_allclose(obtained.test_statistic, desired, rtol, atol, False, err_msg) if exog: assert_equal(obtained_exog.test_statistic, obtained.test_statistic, "WITH EXOG" + err_msg) if exog_coint: assert_equal(obtained_exog_coint.test_statistic, obtained.test_statistic, "WITH EXOG_COINT" + err_msg) # p-value (adjusted Portmanteau test) err_msg = build_err_msg(ds, dt, "WHITENESS OF RESIDUALS - " "P-VALUE (ADJUSTED TEST)") desired = results_ref[ds][dt]["whiteness"]["p-value adjusted"] assert_allclose(obtained.pvalue, desired, rtol, atol, False, err_msg) # call methods to assure they do not raise exceptions obtained.summary() str(obtained) # __str__() assert_(obtained == obtained_exog) # __eq__() def test_summary(): if debug_mode: if "summary" not in to_test: # pragma: no cover return else: print("\n\nSUMMARY", end="") for ds in datasets: for dt in ds.dt_s_list: if debug_mode: print("\n" + dt_s_tup_to_string(dt) + ": ", end="") # see if summary gets printed results_sm[ds][dt].summary(alpha=0.05) exog = (results_sm_exog[ds][dt].exog is not None) if exog is not None: results_sm_exog[ds][dt].summary(alpha=0.05) exog_coint = (results_sm_exog_coint[ds][dt].exog_coint is not None) if exog_coint is not None: results_sm_exog_coint[ds][dt].summary(alpha=0.05) def test_exceptions(): if debug_mode: if "exceptions" not in to_test: # pragma: no cover return else: print("\n\nEXCEPTIONS\n", end="") ds = datasets[0] dt = ds.dt_s_list[0] endog = data[datasets[0]] # select_coint_rank: # method argument cannot be "my_method" assert_raises(ValueError, select_coint_rank, endog, 0, 3, "my_method", 0.05) # det_order has to be -1, 0, or 1: assert_raises(ValueError, select_coint_rank, endog, 2, 3) assert_raises(ValueError, select_coint_rank, endog, 0.5, 3) # 0.025 is not possible (must be 0.1, 0.05, or 0.01) assert_raises(ValueError, select_coint_rank, endog, 0, 3, "trace", 0.025) # Granger_causality: # ### 0 0: assert_equal(r_1[0], r_1[1]) for i in range(rank): assert_(test_stats[i] > crit_vals[i]) if rank < neqs: assert_(test_stats[rank] < crit_vals[rank]) maxeig_result = select_coint_rank(endog, 0, 3, method="maxeig", signif=0.1) rank = maxeig_result.rank r_1 = maxeig_result.r_1 test_stats = maxeig_result.test_stats crit_vals = maxeig_result.crit_vals if maxeig_result.rank > 0: assert_equal(r_1[0], r_1[1] - 1) for i in range(rank): assert_(test_stats[i] > crit_vals[i]) if rank < neqs: assert_(test_stats[rank] < crit_vals[rank]) def test_VECM_seasonal_forecast(): # timing of seasonal dummies, VAR forecast horizon np.random.seed(964255) nobs = 200 seasons = 6 fact = np.cumsum(0.1 + np.random.randn(nobs, 2),0) xx = np.random.randn(nobs+2, 3) xx = xx[2:] + 0.6 * xx[1:-1] + 0.25 * xx[:-2] xx[:,:2] += fact[:,0][:,None] xx[:,2:] += fact[:,1][:,None] # add large seasonal effect xx += 3 * np.log(0.1 + (np.arange(nobs)[:, None] % seasons)) res0 = VECM(xx, k_ar_diff=0, coint_rank=2, deterministic='co', seasons=seasons, first_season=0).fit() res2 = VECM(xx, k_ar_diff=2, coint_rank=2, deterministic='co', seasons=seasons, first_season=0).fit() res4 = VECM(xx, k_ar_diff=4, coint_rank=2, deterministic='co', seasons=seasons, first_season=0).fit() # check that seasonal dummy are independent of number of lags assert_allclose(res2._delta_x.T[-2 * seasons:, -seasons:], res0._delta_x.T[-2 * seasons:, -seasons:], rtol=1e-10) assert_allclose(res4._delta_x.T[-2 * seasons:, -seasons:], res0._delta_x.T[-2 * seasons:, -seasons:], rtol=1e-10) # check location of smallest seasonal coefficient assert_array_equal(np.argmin(res0.det_coef, axis=1), [1, 1, 1]) assert_array_equal(np.argmin(res2.det_coef, axis=1), [1, 1, 1]) assert_array_equal(np.argmin(res4.det_coef, axis=1), [1, 1, 1]) # predict 3 cycles, check location of dips dips_true = np.array([[ 4, 4, 4], [10, 10, 10], [16, 16, 16]]) for res in [res0, res2, res4]: forecast = res.predict(steps=3*seasons) dips = np.sort(np.argsort(forecast, axis=0)[:3], axis=0) assert_array_equal(dips, dips_true) # res2.plot_forecast(steps=18, alpha=0.1, n_last_obs=4*seasons) statsmodels-0.12.2/statsmodels/tsa/vector_ar/tests/var.R000066400000000000000000000037661400612667500233530ustar00rootroot00000000000000library(vars) data <- read.csv('/home/wesm/code/statsmodels/scikits/statsmodels/datasets/macrodata/macrodata.csv') names <- colnames(data) data <- log(data[c('realgdp', 'realcons', 'realinv')]) data <- sapply(data, diff) reorder.coefs <- function(coefs) { n <- dim(coefs)[1] # put constant first... coefs[c(n, seq(1:(n-1))),] } extract.mat <- function(lst, i) { sapply(lst, function(x) x[,i]) } get.coefs <- function(est) { reorder.coefs(extract.mat(coef(est), 1)) } get.stderr <- function(est) { reorder.coefs(extract.mat(coef(est), 2)) } reorder.phi <- function(phis) { # Puts things in more proper C order for comparison purposes in Python k <- dim(phis)[1] n <- dim(phis)[3] arr <- array(dim=c(n, k, k)) for (i in 1:n) arr[i,,] <- phis[,,i] arr } causality.matrix <- function(est) { names <- colnames(est$y) K <- est$K # p-values result <- matrix(0, nrow=K, ncol=) for (i in 1:K) { ## # causes ## result[i,1] <- causality(est, cause=names[i])$Granger$p.value # caused by others result[i,1] <- causality(est, cause=names[-i])$Granger$p.value } colnames(result) <- c("causedby") result } get.results <- function(data, p=1) { sel <- VARselect(data, p) # do at most p est <- VAR(data, p=p) K <- ncol(data) nirfs <- 5 orth.irf <- irf(est, n.ahead=nirfs, boot=F)$irf irf <- irf(est, n.ahead=nirfs, boot=F, orth=F)$irf crit <- t(sel$criteria) colnames(crit) <- c('aic', 'hqic', 'sic', 'fpe') resid <- resid(est) detomega <- det(crossprod(resid) / (est$obs - K * p - 1)) n.ahead <- 5 list(coefs=get.coefs(est), stderr=get.stderr(est), obs=est$obs, totobs=est$totobs, type=est$type, crit=as.list(crit[p,]), nirfs=nirfs, orthirf=orth.irf, irf=irf, causality=causality.matrix(est), detomega=detomega, loglike=as.numeric(logLik(est)), nahead=n.ahead, phis=Phi(est, n.ahead)) } k <- dim(data)[2] result <- get.results(data, p=2) est = VAR(data, p=2) statsmodels-0.12.2/statsmodels/tsa/vector_ar/util.py000066400000000000000000000226131400612667500226150ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Miscellaneous utility code for VAR estimation """ from statsmodels.compat.pandas import frequencies from statsmodels.compat.python import asbytes import numpy as np import pandas as pd import scipy.linalg.decomp as decomp import scipy.stats as stats import statsmodels.tsa.tsatools as tsa #------------------------------------------------------------------------------- # Auxiliary functions for estimation def get_var_endog(y, lags, trend='c', has_constant='skip'): """ Make predictor matrix for VAR(p) process Z := (Z_0, ..., Z_T).T (T x Kp) Z_t = [1 y_t y_{t-1} ... y_{t - p + 1}] (Kp x 1) Ref: Lütkepohl p.70 (transposed) has_constant can be 'raise', 'add', or 'skip'. See add_constant. """ nobs = len(y) # Ravel C order, need to put in descending order Z = np.array([y[t-lags : t][::-1].ravel() for t in range(lags, nobs)]) # Add constant, trend, etc. if trend != 'nc': Z = tsa.add_trend(Z, prepend=True, trend=trend, has_constant=has_constant) return Z def get_trendorder(trend='c'): # Handle constant, etc. if trend == 'c': trendorder = 1 elif trend in ('n', 'nc'): trendorder = 0 elif trend == 'ct': trendorder = 2 elif trend == 'ctt': trendorder = 3 return trendorder def make_lag_names(names, lag_order, trendorder=1, exog=None): """ Produce list of lag-variable names. Constant / trends go at the beginning Examples -------- >>> make_lag_names(['foo', 'bar'], 2, 1) ['const', 'L1.foo', 'L1.bar', 'L2.foo', 'L2.bar'] """ lag_names = [] if isinstance(names, str): names = [names] # take care of lagged endogenous names for i in range(1, lag_order + 1): for name in names: if not isinstance(name, str): name = str(name) # will need consistent unicode handling lag_names.append('L'+str(i)+'.'+name) # handle the constant name if trendorder != 0: lag_names.insert(0, 'const') if trendorder > 1: lag_names.insert(1, 'trend') if trendorder > 2: lag_names.insert(2, 'trend**2') if exog is not None: if isinstance(exog, pd.Series): exog = pd.DataFrame(exog) elif not hasattr(exog, 'ndim'): exog = np.asarray(exog) if exog.ndim == 1: exog = exog[:, None] for i in range(exog.shape[1]): if isinstance(exog, pd.DataFrame): exog_name = str(exog.columns[i]) else: exog_name = "exog" + str(i) lag_names.insert(trendorder + i, exog_name) return lag_names def comp_matrix(coefs): """ Return compansion matrix for the VAR(1) representation for a VAR(p) process (companion form) A = [A_1 A_2 ... A_p-1 A_p I_K 0 0 0 0 I_K ... 0 0 0 ... I_K 0] """ p, k1, k2 = coefs.shape if k1 != k2: raise ValueError('coefs must be 3-d with shape (p, k, k).') kp = k1 * p result = np.zeros((kp, kp)) result[:k1] = np.concatenate(coefs, axis=1) # Set I_K matrices if p > 1: result[np.arange(k1, kp), np.arange(kp-k1)] = 1 return result #------------------------------------------------------------------------------- # Miscellaneous stuff def parse_lutkepohl_data(path): # pragma: no cover """ Parse data files from Lütkepohl (2005) book Source for data files: www.jmulti.de """ from collections import deque from datetime import datetime import re regex = re.compile(asbytes(r'<(.*) (\w)([\d]+)>.*')) with open(path, 'rb') as f: lines = deque(f) to_skip = 0 while asbytes('*/') not in lines.popleft(): #while '*/' not in lines.popleft(): to_skip += 1 while True: to_skip += 1 line = lines.popleft() m = regex.match(line) if m: year, freq, start_point = m.groups() break data = (pd.read_csv(path, delimiter=r"\s+", header=to_skip+1) .to_records(index=False)) n = len(data) # generate the corresponding date range (using pandas for now) start_point = int(start_point) year = int(year) offsets = { asbytes('Q'): frequencies.BQuarterEnd(), asbytes('M'): frequencies.BMonthEnd(), asbytes('A'): frequencies.BYearEnd() } # create an instance offset = offsets[freq] inc = offset * (start_point - 1) start_date = offset.rollforward(datetime(year, 1, 1)) + inc offset = offsets[freq] date_range = pd.date_range(start=start_date, freq=offset, periods=n) return data, date_range def norm_signif_level(alpha=0.05): return stats.norm.ppf(1 - alpha / 2) def acf_to_acorr(acf): diag = np.diag(acf[0]) # numpy broadcasting sufficient return acf / np.sqrt(np.outer(diag, diag)) def varsim(coefs, intercept, sig_u, steps=100, initvalues=None, seed=None): """ Simulate VAR(p) process, given coefficients and assuming Gaussian noise Parameters ---------- coefs : ndarray Coefficients for the VAR lags of endog. intercept : None or ndarray 1-D (neqs,) or (steps, neqs) This can be either the intercept for each equation or an offset. If None, then the VAR process has a zero intercept. If intercept is 1-D, then the same (endog specific) intercept is added to all observations. If intercept is 2-D, then it is treated as an offset and is added as an observation specific intercept to the autoregression. In this case, the intercept/offset should have same number of rows as steps, and the same number of columns as endogenous variables (neqs). sig_u : ndarray Covariance matrix of the residuals or innovations. If sig_u is None, then an identity matrix is used. steps : {None, int} number of observations to simulate, this includes the initial observations to start the autoregressive process. If offset is not None, then exog of the model are used if they were provided in the model seed : {None, int} If seed is not None, then it will be used with for the random variables generated by numpy.random. Returns ------- endog_simulated : nd_array Endog of the simulated VAR process """ rs = np.random.RandomState(seed=seed) rmvnorm = rs.multivariate_normal p, k, k = coefs.shape if sig_u is None: sig_u = np.eye(k) ugen = rmvnorm(np.zeros(len(sig_u)), sig_u, steps) result = np.zeros((steps, k)) if intercept is not None: # intercept can be 2-D like an offset variable if np.ndim(intercept) > 1: if not len(intercept) == len(ugen): raise ValueError('2-D intercept needs to have length `steps`') # add intercept/offset also to intial values result += intercept result[p:] += ugen[p:] else: result[p:] = ugen[p:] # add in AR terms for t in range(p, steps): ygen = result[t] for j in range(p): ygen += np.dot(coefs[j], result[t-j-1]) return result def get_index(lst, name): try: result = lst.index(name) except Exception: if not isinstance(name, int): raise result = name return result #method used repeatedly in Sims-Zha error bands def eigval_decomp(sym_array): """ Returns ------- W: array of eigenvectors eigva: list of eigenvalues k: largest eigenvector """ #check if symmetric, do not include shock period eigva, W = decomp.eig(sym_array, left=True, right=False) k = np.argmax(eigva) return W, eigva, k def vech(A): """ Simple vech operator Returns ------- vechvec: vector of all elements on and below diagonal """ length=A.shape[1] vechvec=[] for i in range(length): b=i while b < length: vechvec.append(A[b,i]) b=b+1 vechvec=np.asarray(vechvec) return vechvec def seasonal_dummies(n_seasons, len_endog, first_period=0, centered=False): """ Parameters ---------- n_seasons : int >= 0 Number of seasons (e.g. 12 for monthly data and 4 for quarterly data). len_endog : int >= 0 Total number of observations. first_period : int, default: 0 Season of the first observation. As an example, suppose we have monthly data and the first observation is in March (third month of the year). In this case we pass 2 as first_period. (0 for the first season, 1 for the second, ..., n_seasons-1 for the last season). An integer greater than n_seasons-1 are treated in the same way as the integer modulo n_seasons. centered : bool, default: False If True, center (demean) the dummy variables. That is useful in order to get seasonal dummies that are orthogonal to the vector of constant dummy variables (a vector of ones). Returns ------- seasonal_dummies : ndarray (len_endog x n_seasons-1) """ if n_seasons == 0: return np.empty((len_endog, 0)) if n_seasons > 0: season_exog = np.zeros((len_endog, n_seasons - 1)) for i in range(n_seasons - 1): season_exog[(i-first_period) % n_seasons::n_seasons, i] = 1 if centered: season_exog -= 1 / n_seasons return season_exog statsmodels-0.12.2/statsmodels/tsa/vector_ar/var_model.py000066400000000000000000002257001400612667500236120ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Vector Autoregression (VAR) processes References ---------- Lütkepohl (2005) New Introduction to Multiple Time Series Analysis """ from statsmodels.compat.pandas import deprecate_kwarg from statsmodels.compat.python import lrange from collections import defaultdict from io import StringIO import numpy as np import pandas as pd import scipy.stats as stats import statsmodels.base.wrapper as wrap from statsmodels.iolib.table import SimpleTable from statsmodels.tools.decorators import cache_readonly, deprecated_alias from statsmodels.tools.linalg import logdet_symm from statsmodels.tools.sm_exceptions import OutputWarning from statsmodels.tools.validation import array_like from statsmodels.tsa.base.tsa_model import ( TimeSeriesModel, TimeSeriesResultsWrapper, ) import statsmodels.tsa.tsatools as tsa from statsmodels.tsa.tsatools import duplication_matrix, unvec, vec from statsmodels.tsa.vector_ar import output, plotting, util from statsmodels.tsa.vector_ar.hypothesis_test_results import ( CausalityTestResults, NormalityTestResults, WhitenessTestResults, ) from statsmodels.tsa.vector_ar.irf import IRAnalysis from statsmodels.tsa.vector_ar.output import VARSummary # ------------------------------------------------------------------------------- # VAR process routines def ma_rep(coefs, maxn=10): r""" MA(\infty) representation of VAR(p) process Parameters ---------- coefs : ndarray (p x k x k) maxn : int Number of MA matrices to compute Notes ----- VAR(p) process as .. math:: y_t = A_1 y_{t-1} + \ldots + A_p y_{t-p} + u_t can be equivalently represented as .. math:: y_t = \mu + \sum_{i=0}^\infty \Phi_i u_{t-i} e.g. can recursively compute the \Phi_i matrices with \Phi_0 = I_k Returns ------- phis : ndarray (maxn + 1 x k x k) """ p, k, k = coefs.shape phis = np.zeros((maxn+1, k, k)) phis[0] = np.eye(k) # recursively compute Phi matrices for i in range(1, maxn + 1): for j in range(1, i+1): if j > p: break phis[i] += np.dot(phis[i-j], coefs[j-1]) return phis def is_stable(coefs, verbose=False): """ Determine stability of VAR(p) system by examining the eigenvalues of the VAR(1) representation Parameters ---------- coefs : ndarray (p x k x k) Returns ------- is_stable : bool """ A_var1 = util.comp_matrix(coefs) eigs = np.linalg.eigvals(A_var1) if verbose: print('Eigenvalues of VAR(1) rep') for val in np.abs(eigs): print(val) return (np.abs(eigs) <= 1).all() def var_acf(coefs, sig_u, nlags=None): """ Compute autocovariance function ACF_y(h) up to nlags of stable VAR(p) process Parameters ---------- coefs : ndarray (p x k x k) Coefficient matrices A_i sig_u : ndarray (k x k) Covariance of white noise process u_t nlags : int, optional Defaults to order p of system Notes ----- Ref: Lütkepohl p.28-29 Returns ------- acf : ndarray, (p, k, k) """ p, k, _ = coefs.shape if nlags is None: nlags = p # p x k x k, ACF for lags 0, ..., p-1 result = np.zeros((nlags + 1, k, k)) result[:p] = _var_acf(coefs, sig_u) # yule-walker equations for h in range(p, nlags + 1): # compute ACF for lag=h # G(h) = A_1 G(h-1) + ... + A_p G(h-p) for j in range(p): result[h] += np.dot(coefs[j], result[h-j-1]) return result def _var_acf(coefs, sig_u): """ Compute autocovariance function ACF_y(h) for h=1,...,p Notes ----- Lütkepohl (2005) p.29 """ p, k, k2 = coefs.shape assert(k == k2) A = util.comp_matrix(coefs) # construct VAR(1) noise covariance SigU = np.zeros((k*p, k*p)) SigU[:k, :k] = sig_u # vec(ACF) = (I_(kp)^2 - kron(A, A))^-1 vec(Sigma_U) vecACF = np.linalg.solve(np.eye((k*p)**2) - np.kron(A, A), vec(SigU)) acf = unvec(vecACF) acf = [acf[:k, k * i:k * (i + 1)] for i in range(p)] acf = np.array(acf) return acf def forecast_cov(ma_coefs, sigma_u, steps): r""" Compute theoretical forecast error variance matrices Parameters ---------- steps : int Number of steps ahead Notes ----- .. math:: \mathrm{MSE}(h) = \sum_{i=0}^{h-1} \Phi \Sigma_u \Phi^T Returns ------- forc_covs : ndarray (steps x neqs x neqs) """ neqs = len(sigma_u) forc_covs = np.zeros((steps, neqs, neqs)) prior = np.zeros((neqs, neqs)) for h in range(steps): # Sigma(h) = Sigma(h-1) + Phi Sig_u Phi' phi = ma_coefs[h] var = phi @ sigma_u @ phi.T forc_covs[h] = prior = prior + var return forc_covs mse = forecast_cov def forecast(y, coefs, trend_coefs, steps, exog=None): """ Produce linear minimum MSE forecast Parameters ---------- y : ndarray (k_ar x neqs) coefs : ndarray (k_ar x neqs x neqs) trend_coefs : ndarray (1 x neqs) or (neqs) steps : int exog : ndarray (trend_coefs.shape[1] x neqs) Returns ------- forecasts : ndarray (steps x neqs) Notes ----- Lütkepohl p. 37 """ p = len(coefs) k = len(coefs[0]) # initial value forcs = np.zeros((steps, k)) if exog is not None and trend_coefs is not None: forcs += np.dot(exog, trend_coefs) # to make existing code (with trend_coefs=intercept and without exog) work: elif exog is None and trend_coefs is not None: forcs += trend_coefs # h=0 forecast should be latest observation # forcs[0] = y[-1] # make indices easier to think about for h in range(1, steps + 1): # y_t(h) = intercept + sum_1^p A_i y_t_(h-i) f = forcs[h - 1] for i in range(1, p + 1): # slightly hackish if h - i <= 0: # e.g. when h=1, h-1 = 0, which is y[-1] prior_y = y[h - i - 1] else: # e.g. when h=2, h-1=1, which is forcs[0] prior_y = forcs[h - i - 1] # i=1 is coefs[0] f = f + np.dot(coefs[i - 1], prior_y) forcs[h - 1] = f return forcs def _forecast_vars(steps, ma_coefs, sig_u): """_forecast_vars function used by VECMResults. Note that the definition of the local variable covs is the same as in VARProcess and as such it differs from the one in VARResults! Parameters ---------- steps ma_coefs sig_u Returns ------- """ covs = mse(ma_coefs, sig_u, steps) # Take diagonal for each cov neqs = len(sig_u) inds = np.arange(neqs) return covs[:, inds, inds] def forecast_interval(y, coefs, trend_coefs, sig_u, steps=5, alpha=0.05, exog=1): assert(0 < alpha < 1) q = util.norm_signif_level(alpha) point_forecast = forecast(y, coefs, trend_coefs, steps, exog) ma_coefs = ma_rep(coefs, steps) sigma = np.sqrt(_forecast_vars(steps, ma_coefs, sig_u)) forc_lower = point_forecast - q * sigma forc_upper = point_forecast + q * sigma return point_forecast, forc_lower, forc_upper def var_loglike(resid, omega, nobs): r""" Returns the value of the VAR(p) log-likelihood. Parameters ---------- resid : ndarray (T x K) omega : ndarray Sigma hat matrix. Each element i,j is the average product of the OLS residual for variable i and the OLS residual for variable j or np.dot(resid.T,resid)/nobs. There should be no correction for the degrees of freedom. nobs : int Returns ------- llf : float The value of the loglikelihood function for a VAR(p) model Notes ----- The loglikelihood function for the VAR(p) is .. math:: -\left(\frac{T}{2}\right) \left(\ln\left|\Omega\right|-K\ln\left(2\pi\right)-K\right) """ logdet = logdet_symm(np.asarray(omega)) neqs = len(omega) part1 = - (nobs * neqs / 2) * np.log(2 * np.pi) part2 = - (nobs / 2) * (logdet + neqs) return part1 + part2 def _reordered(self, order): # Create new arrays to hold rearranged results from .fit() endog = self.endog endog_lagged = self.endog_lagged params = self.params sigma_u = self.sigma_u names = self.names k_ar = self.k_ar endog_new = np.zeros([np.size(endog, 0), np.size(endog, 1)]) endog_lagged_new = np.zeros([np.size(endog_lagged, 0), np.size(endog_lagged, 1)]) params_new_inc, params_new = [np.zeros([np.size(params, 0), np.size(params, 1)]) for i in range(2)] sigma_u_new_inc, sigma_u_new = [np.zeros([np.size(sigma_u, 0), np.size(sigma_u, 1)]) for i in range(2)] num_end = len(self.params[0]) names_new = [] # Rearrange elements and fill in new arrays k = self.k_trend for i, c in enumerate(order): endog_new[:, i] = self.endog[:, c] if k > 0: params_new_inc[0, i] = params[0, i] endog_lagged_new[:, 0] = endog_lagged[:, 0] for j in range(k_ar): params_new_inc[i+j*num_end+k, :] = self.params[c+j*num_end+k, :] endog_lagged_new[:, i+j*num_end+k] = endog_lagged[:, c+j*num_end+k] sigma_u_new_inc[i, :] = sigma_u[c, :] names_new.append(names[c]) for i, c in enumerate(order): params_new[:, i] = params_new_inc[:, c] sigma_u_new[:, i] = sigma_u_new_inc[:, c] return VARResults(endog=endog_new, endog_lagged=endog_lagged_new, params=params_new, sigma_u=sigma_u_new, lag_order=self.k_ar, model=self.model, trend='c', names=names_new, dates=self.dates) def orth_ma_rep(results, maxn=10, P=None): r"""Compute Orthogonalized MA coefficient matrices using P matrix such that :math:`\Sigma_u = PP^\prime`. P defaults to the Cholesky decomposition of :math:`\Sigma_u` Parameters ---------- results : VARResults or VECMResults maxn : int Number of coefficient matrices to compute P : ndarray (neqs x neqs), optional Matrix such that Sigma_u = PP', defaults to the Cholesky decomposition. Returns ------- coefs : ndarray (maxn x neqs x neqs) """ if P is None: P = results._chol_sigma_u ma_mats = results.ma_rep(maxn=maxn) return np.array([np.dot(coefs, P) for coefs in ma_mats]) def test_normality(results, signif=0.05): """ Test assumption of normal-distributed errors using Jarque-Bera-style omnibus Chi^2 test Parameters ---------- results : VARResults or statsmodels.tsa.vecm.vecm.VECMResults signif : float The test's significance level. Notes ----- H0 (null) : data are generated by a Gaussian-distributed process Returns ------- result : NormalityTestResults References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. .. [2] Kilian, L. & Demiroglu, U. (2000). "Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence." Journal of Business & Economic Statistics """ resid_c = results.resid - results.resid.mean(0) sig = np.dot(resid_c.T, resid_c) / results.nobs Pinv = np.linalg.inv(np.linalg.cholesky(sig)) w = np.dot(Pinv, resid_c.T) b1 = (w**3).sum(1)[:, None] / results.nobs b2 = (w**4).sum(1)[:, None] / results.nobs - 3 lam_skew = results.nobs * np.dot(b1.T, b1) / 6 lam_kurt = results.nobs * np.dot(b2.T, b2) / 24 lam_omni = float(lam_skew + lam_kurt) omni_dist = stats.chi2(results.neqs * 2) omni_pvalue = float(omni_dist.sf(lam_omni)) crit_omni = float(omni_dist.ppf(1 - signif)) return NormalityTestResults(lam_omni, crit_omni, omni_pvalue, results.neqs*2, signif) class LagOrderResults: """ Results class for choosing a model's lag order. Parameters ---------- ics : dict The keys are the strings ``"aic"``, ``"bic"``, ``"hqic"``, and ``"fpe"``. A corresponding value is a list of information criteria for various numbers of lags. selected_orders : dict The keys are the strings ``"aic"``, ``"bic"``, ``"hqic"``, and ``"fpe"``. The corresponding value is an integer specifying the number of lags chosen according to a given criterion (key). vecm : bool, default: `False` `True` indicates that the model is a VECM. In case of a VAR model this argument must be `False`. Notes ----- In case of a VECM the shown lags are lagged differences. """ def __init__(self, ics, selected_orders, vecm=False): self.title = ("VECM" if vecm else "VAR") + " Order Selection" self.title += " (* highlights the minimums)" self.ics = ics self.selected_orders = selected_orders self.vecm = vecm self.aic = selected_orders["aic"] self.bic = selected_orders["bic"] self.hqic = selected_orders["hqic"] self.fpe = selected_orders["fpe"] def summary(self): # basically copied from (now deleted) print_ic_table() cols = sorted(self.ics) # ["aic", "bic", "hqic", "fpe"] str_data = np.array([["%#10.4g" % v for v in self.ics[c]] for c in cols], dtype=object).T # mark minimum with an asterisk for i, col in enumerate(cols): idx = int(self.selected_orders[col]), i str_data[idx] += '*' return SimpleTable(str_data, [col.upper() for col in cols], lrange(len(str_data)), title=self.title) def __str__(self): return "<" + self.__module__ + "." + self.__class__.__name__ \ + " object. Selected orders are: AIC -> " + str(self.aic) \ + ", BIC -> " + str(self.bic) \ + ", FPE -> " + str(self.fpe) \ + ", HQIC -> " + str(self.hqic) + ">" # ------------------------------------------------------------------------------- # VARProcess class: for known or unknown VAR process class VAR(TimeSeriesModel): r""" Fit VAR(p) process and do lag order selection .. math:: y_t = A_1 y_{t-1} + \ldots + A_p y_{t-p} + u_t Parameters ---------- endog : array_like 2-d endogenous response variable. The independent variable. exog : array_like 2-d exogenous variable. dates : array_like must match number of rows of endog References ---------- Lütkepohl (2005) New Introduction to Multiple Time Series Analysis """ y = deprecated_alias("y", "endog", remove_version="0.11.0") def __init__(self, endog, exog=None, dates=None, freq=None, missing='none'): super(VAR, self).__init__(endog, exog, dates, freq, missing=missing) if self.endog.ndim == 1: raise ValueError("Only gave one variable to VAR") self.neqs = self.endog.shape[1] self.n_totobs = len(endog) def predict(self, params, start=None, end=None, lags=1, trend='c'): """ Returns in-sample predictions or forecasts """ params = np.array(params) if start is None: start = lags # Handle start, end start, end, out_of_sample, prediction_index = ( self._get_prediction_index(start, end)) if end < start: raise ValueError("end is before start") if end == start + out_of_sample: return np.array([]) k_trend = util.get_trendorder(trend) k = self.neqs k_ar = lags predictedvalues = np.zeros((end + 1 - start + out_of_sample, k)) if k_trend != 0: intercept = params[:k_trend] predictedvalues += intercept y = self.endog x = util.get_var_endog(y, lags, trend=trend, has_constant='raise') fittedvalues = np.dot(x, params) fv_start = start - k_ar pv_end = min(len(predictedvalues), len(fittedvalues) - fv_start) fv_end = min(len(fittedvalues), end - k_ar + 1) predictedvalues[:pv_end] = fittedvalues[fv_start:fv_end] if not out_of_sample: return predictedvalues # fit out of sample y = y[-k_ar:] coefs = params[k_trend:].reshape((k_ar, k, k)).swapaxes(1, 2) predictedvalues[pv_end:] = forecast(y, coefs, intercept, out_of_sample) return predictedvalues def fit(self, maxlags=None, method='ols', ic=None, trend='c', verbose=False): # todo: this code is only supporting deterministic terms as exog. # This means that all exog-variables have lag 0. If dealing with # different exogs is necessary, a `lags_exog`-parameter might make # sense (e.g. a sequence of ints specifying lags). # Alternatively, leading zeros for exog-variables with smaller number # of lags than the maximum number of exog-lags might work. """ Fit the VAR model Parameters ---------- maxlags : {int, None}, default None Maximum number of lags to check for order selection, defaults to 12 * (nobs/100.)**(1./4), see select_order function method : {'ols'} Estimation method to use ic : {'aic', 'fpe', 'hqic', 'bic', None} Information criterion to use for VAR order selection. aic : Akaike fpe : Final prediction error hqic : Hannan-Quinn bic : Bayesian a.k.a. Schwarz verbose : bool, default False Print order selection output to the screen trend : str {"c", "ct", "ctt", "nc", "n"} "c" - add constant "ct" - constant and trend "ctt" - constant, linear and quadratic trend "n", "nc" - co constant, no trend Note that these are prepended to the columns of the dataset. Returns ------- VARResults Estimation results Notes ----- See Lütkepohl pp. 146-153 for implementation details. """ lags = maxlags if trend not in ['c', 'ct', 'ctt', 'nc', 'n']: raise ValueError("trend '{}' not supported for VAR".format(trend)) if ic is not None: selections = self.select_order(maxlags=maxlags) if not hasattr(selections, ic): raise ValueError("%s not recognized, must be among %s" % (ic, sorted(selections))) lags = getattr(selections, ic) if verbose: print(selections) print('Using %d based on %s criterion' % (lags, ic)) else: if lags is None: lags = 1 k_trend = util.get_trendorder(trend) orig_exog_names = self.exog_names self.exog_names = util.make_lag_names(self.endog_names, lags, k_trend) self.nobs = self.n_totobs - lags # add exog to data.xnames (necessary because the length of xnames also # determines the allowed size of VARResults.params) if self.exog is not None: if orig_exog_names: x_names_to_add = orig_exog_names else: x_names_to_add = [("exog%d" % i) for i in range(self.exog.shape[1])] self.data.xnames = (self.data.xnames[:k_trend] + x_names_to_add + self.data.xnames[k_trend:]) self.data.cov_names = pd.MultiIndex.from_product((self.data.xnames, self.data.ynames)) return self._estimate_var(lags, trend=trend) def _estimate_var(self, lags, offset=0, trend='c'): """ lags : int Lags of the endogenous variable. offset : int Periods to drop from beginning-- for order selection so it's an apples-to-apples comparison trend : {str, None} As per above """ # have to do this again because select_order does not call fit self.k_trend = k_trend = util.get_trendorder(trend) if offset < 0: # pragma: no cover raise ValueError('offset must be >= 0') nobs = self.n_totobs - lags - offset endog = self.endog[offset:] exog = None if self.exog is None else self.exog[offset:] z = util.get_var_endog(endog, lags, trend=trend, has_constant='raise') if exog is not None: # TODO: currently only deterministic terms supported (exoglags==0) # and since exoglags==0, x will be an array of size 0. x = util.get_var_endog(exog[-nobs:], 0, trend="n", has_constant="raise") x_inst = exog[-nobs:] x = np.column_stack((x, x_inst)) del x_inst # free memory temp_z = z z = np.empty((x.shape[0], x.shape[1]+z.shape[1])) z[:, :self.k_trend] = temp_z[:, :self.k_trend] z[:, self.k_trend:self.k_trend+x.shape[1]] = x z[:, self.k_trend+x.shape[1]:] = temp_z[:, self.k_trend:] del temp_z, x # free memory # the following modification of z is necessary to get the same results # as JMulTi for the constant-term-parameter... for i in range(self.k_trend): if (np.diff(z[:, i]) == 1).all(): # modify the trend-column z[:, i] += lags # make the same adjustment for the quadratic term if (np.diff(np.sqrt(z[:, i])) == 1).all(): z[:, i] = (np.sqrt(z[:, i]) + lags)**2 y_sample = endog[lags:] # Lütkepohl p75, about 5x faster than stated formula params = np.linalg.lstsq(z, y_sample, rcond=1e-15)[0] resid = y_sample - np.dot(z, params) # Unbiased estimate of covariance matrix $\Sigma_u$ of the white noise # process $u$ # equivalent definition # .. math:: \frac{1}{T - Kp - 1} Y^\prime (I_T - Z (Z^\prime Z)^{-1} # Z^\prime) Y # Ref: Lütkepohl p.75 # df_resid right now is T - Kp - 1, which is a suggested correction avobs = len(y_sample) if exog is not None: k_trend += exog.shape[1] df_resid = avobs - (self.neqs * lags + k_trend) sse = np.dot(resid.T, resid) omega = sse / df_resid varfit = VARResults(endog, z, params, omega, lags, names=self.endog_names, trend=trend, dates=self.data.dates, model=self, exog=self.exog) return VARResultsWrapper(varfit) def select_order(self, maxlags=None, trend="c"): """ Compute lag order selections based on each of the available information criteria Parameters ---------- maxlags : int if None, defaults to 12 * (nobs/100.)**(1./4) trend : str {"nc", "c", "ct", "ctt"} * "nc" - no deterministic terms * "c" - constant term * "ct" - constant and linear term * "ctt" - constant, linear, and quadratic term Returns ------- selections : LagOrderResults """ ntrend = len(trend) if trend.startswith("c") else 0 max_estimable = (self.n_totobs - self.neqs - ntrend) // (1 + self.neqs) if maxlags is None: maxlags = int(round(12*(len(self.endog)/100.)**(1/4.))) # TODO: This expression shows up in a bunch of places, but # in some it is `int` and in others `np.ceil`. Also in some # it multiplies by 4 instead of 12. Let's put these all in # one place and document when to use which variant. # Ensure enough obs to estimate model with maxlags maxlags = min(maxlags, max_estimable) else: if maxlags > max_estimable: raise ValueError( "maxlags is too large for the number of observations and " "the number of equations. The largest model cannot be " "estimated." ) ics = defaultdict(list) p_min = 0 if self.exog is not None or trend != "nc" else 1 for p in range(p_min, maxlags + 1): # exclude some periods to same amount of data used for each lag # order result = self._estimate_var(p, offset=maxlags - p, trend=trend) for k, v in result.info_criteria.items(): ics[k].append(v) selected_orders = dict((k, np.array(v).argmin() + p_min) for k, v in ics.items()) return LagOrderResults(ics, selected_orders, vecm=False) @classmethod def from_formula(cls, formula, data, subset=None, drop_cols=None, *args, **kwargs): """ Not implemented. Formulas are not supported for VAR models. """ raise NotImplementedError("formulas are not supported for VAR models.") class VARProcess(object): """ Class represents a known VAR(p) process Parameters ---------- coefs : ndarray (p x k x k) coefficients for lags of endog, part or params reshaped coefs_exog : ndarray parameters for trend and user provided exog sigma_u : ndarray (k x k) residual covariance names : sequence (length k) _params_info : dict internal dict to provide information about the composition of `params`, specifically `k_trend` (trend order) and `k_exog_user` (the number of exog variables provided by the user). If it is None, then coefs_exog are assumed to be for the intercept and trend. """ def __init__(self, coefs, coefs_exog, sigma_u, names=None, _params_info=None): self.k_ar = len(coefs) self.neqs = coefs.shape[1] self.coefs = coefs self.coefs_exog = coefs_exog # Note reshaping 1-D coefs_exog to 2_D makes unit tests fail self.sigma_u = sigma_u self.names = names if _params_info is None: _params_info = {} self.k_exog_user = _params_info.get('k_exog_user', 0) if self.coefs_exog is not None: k_ex = self.coefs_exog.shape[0] if self.coefs_exog.ndim != 1 else 1 k_c = k_ex - self.k_exog_user else: k_c = 0 self.k_trend = _params_info.get('k_trend', k_c) # TODO: we need to distinguish exog including trend and exog_user self.k_exog = self.k_trend + self.k_exog_user if self.k_trend > 0: if coefs_exog.ndim == 2: self.intercept = coefs_exog[:, 0] else: self.intercept = coefs_exog else: self.intercept = np.zeros(self.neqs) def get_eq_index(self, name): """Return integer position of requested equation name""" return util.get_index(self.names, name) def __str__(self): output = ('VAR(%d) process for %d-dimensional response y_t' % (self.k_ar, self.neqs)) output += '\nstable: %s' % self.is_stable() output += '\nmean: %s' % self.mean() return output def is_stable(self, verbose=False): """Determine stability based on model coefficients Parameters ---------- verbose : bool Print eigenvalues of the VAR(1) companion Notes ----- Checks if det(I - Az) = 0 for any mod(z) <= 1, so all the eigenvalues of the companion matrix must lie outside the unit circle """ return is_stable(self.coefs, verbose=verbose) def simulate_var(self, steps=None, offset=None, seed=None): """ simulate the VAR(p) process for the desired number of steps Parameters ---------- steps : None or int number of observations to simulate, this includes the initial observations to start the autoregressive process. If offset is not None, then exog of the model are used if they were provided in the model offset : None or ndarray (steps, neqs) If not None, then offset is added as an observation specific intercept to the autoregression. If it is None and either trend (including intercept) or exog were used in the VAR model, then the linear predictor of those components will be used as offset. This should have the same number of rows as steps, and the same number of columns as endogenous variables (neqs). seed : {None, int} If seed is not None, then it will be used with for the random variables generated by numpy.random. Returns ------- endog_simulated : nd_array Endog of the simulated VAR process """ steps_ = None if offset is None: if self.k_exog_user > 0 or self.k_trend > 1: # if more than intercept # endog_lagged contains all regressors, trend, exog_user # and lagged endog, trimmed initial observations offset = self.endog_lagged[:,:self.k_exog].dot( self.coefs_exog.T) steps_ = self.endog_lagged.shape[0] else: offset = self.intercept else: steps_ = offset.shape[0] # default, but over written if exog or offset are used if steps is None: if steps_ is None: steps = 1000 else: steps = steps_ else: if steps_ is not None and steps != steps_: raise ValueError('if exog or offset are used, then steps must' 'be equal to their length or None') y = util.varsim(self.coefs, offset, self.sigma_u, steps=steps, seed=seed) return y def plotsim(self, steps=None, offset=None, seed=None): """ Plot a simulation from the VAR(p) process for the desired number of steps """ y = self.simulate_var(steps=steps, offset=offset, seed=seed) return plotting.plot_mts(y) def intercept_longrun(self): r""" Long run intercept of stable VAR process Lütkepohl eq. 2.1.23 .. math:: \mu = (I - A_1 - \dots - A_p)^{-1} \alpha where \alpha is the intercept (parameter of the constant) """ return np.linalg.solve(self._char_mat, self.intercept) def mean(self): r""" Long run intercept of stable VAR process Warning: trend and exog except for intercept are ignored for this. This might change in future versions. Lütkepohl eq. 2.1.23 .. math:: \mu = (I - A_1 - \dots - A_p)^{-1} \alpha where \alpha is the intercept (parameter of the constant) """ return self.intercept_longrun() def ma_rep(self, maxn=10): r""" Compute MA(:math:`\infty`) coefficient matrices Parameters ---------- maxn : int Number of coefficient matrices to compute Returns ------- coefs : ndarray (maxn x k x k) """ return ma_rep(self.coefs, maxn=maxn) def orth_ma_rep(self, maxn=10, P=None): r""" Compute orthogonalized MA coefficient matrices using P matrix such that :math:`\Sigma_u = PP^\prime`. P defaults to the Cholesky decomposition of :math:`\Sigma_u` Parameters ---------- maxn : int Number of coefficient matrices to compute P : ndarray (k x k), optional Matrix such that Sigma_u = PP', defaults to Cholesky descomp Returns ------- coefs : ndarray (maxn x k x k) """ return orth_ma_rep(self, maxn, P) def long_run_effects(self): r"""Compute long-run effect of unit impulse .. math:: \Psi_\infty = \sum_{i=0}^\infty \Phi_i """ return np.linalg.inv(self._char_mat) @cache_readonly def _chol_sigma_u(self): return np.linalg.cholesky(self.sigma_u) @cache_readonly def _char_mat(self): """Characteristic matrix of the VAR""" return np.eye(self.neqs) - self.coefs.sum(0) def acf(self, nlags=None): """Compute theoretical autocovariance function Returns ------- acf : ndarray (p x k x k) """ return var_acf(self.coefs, self.sigma_u, nlags=nlags) def acorr(self, nlags=None): """ Autocorrelation function Parameters ---------- nlags : int or None The number of lags to include in the autocovariance function. The default is the number of lags included in the model. Returns ------- acorr : ndarray Autocorrelation and cross correlations (nlags, neqs, neqs) """ return util.acf_to_acorr(self.acf(nlags=nlags)) def plot_acorr(self, nlags=10, linewidth=8): """Plot theoretical autocorrelation function""" fig = plotting.plot_full_acorr(self.acorr(nlags=nlags), linewidth=linewidth) return fig def forecast(self, y, steps, exog_future=None): """Produce linear minimum MSE forecasts for desired number of steps ahead, using prior values y Parameters ---------- y : ndarray (p x k) steps : int Returns ------- forecasts : ndarray (steps x neqs) Notes ----- Lütkepohl pp 37-38 """ if self.exog is None and exog_future is not None: raise ValueError("No exog in model, so no exog_future supported " "in forecast method.") if self.exog is not None and exog_future is None: raise ValueError("Please provide an exog_future argument to " "the forecast method.") exog_future = array_like(exog_future, "exog_future", optional=True, ndim=2) if exog_future is not None: if exog_future.shape[0] != steps: err_msg = f"""\ exog_future only has {exog_future.shape[0]} observations. It must have \ steps ({steps}) observations. """ raise ValueError(err_msg) trend_coefs = None if self.coefs_exog.size == 0 else self.coefs_exog.T exogs = [] if self.trend.startswith("c"): # constant term exogs.append(np.ones(steps)) exog_lin_trend = np.arange(self.n_totobs + 1, self.n_totobs + 1 + steps) if "t" in self.trend: exogs.append(exog_lin_trend) if "tt" in self.trend: exogs.append(exog_lin_trend**2) if exog_future is not None: exogs.append(exog_future) if not exogs: exog_future = None else: exog_future = np.column_stack(exogs) return forecast(y, self.coefs, trend_coefs, steps, exog_future) # TODO: use `mse` module-level function? def mse(self, steps): r""" Compute theoretical forecast error variance matrices Parameters ---------- steps : int Number of steps ahead Notes ----- .. math:: \mathrm{MSE}(h) = \sum_{i=0}^{h-1} \Phi \Sigma_u \Phi^T Returns ------- forc_covs : ndarray (steps x neqs x neqs) """ ma_coefs = self.ma_rep(steps) k = len(self.sigma_u) forc_covs = np.zeros((steps, k, k)) prior = np.zeros((k, k)) for h in range(steps): # Sigma(h) = Sigma(h-1) + Phi Sig_u Phi' phi = ma_coefs[h] var = phi @ self.sigma_u @ phi.T forc_covs[h] = prior = prior + var return forc_covs forecast_cov = mse def _forecast_vars(self, steps): covs = self.forecast_cov(steps) # Take diagonal for each cov inds = np.arange(self.neqs) return covs[:, inds, inds] def forecast_interval(self, y, steps, alpha=0.05, exog_future=None): """ Construct forecast interval estimates assuming the y are Gaussian Parameters ---------- y : {ndarray, None} The initial values to use for the forecasts. If None, the last k_ar values of the original endogenous variables are used. steps : int Number of steps ahead to forecast alpha : float, optional The significance level for the confidence intervals. exog_future : ndarray, optional Forecast values of the exogenous variables. Should include constant, trend, etc. as needed, including extrapolating out of sample. Returns ------- point : ndarray Mean value of forecast lower : ndarray Lower bound of confidence interval upper : ndarray Upper bound of confidence interval Notes ----- Lütkepohl pp. 39-40 """ if not 0 < alpha < 1: raise ValueError('alpha must be between 0 and 1') q = util.norm_signif_level(alpha) point_forecast = self.forecast(y, steps, exog_future=exog_future) sigma = np.sqrt(self._forecast_vars(steps)) forc_lower = point_forecast - q * sigma forc_upper = point_forecast + q * sigma return point_forecast, forc_lower, forc_upper def to_vecm(self): """to_vecm""" k = self.coefs.shape[1] p = self.coefs.shape[0] A = self.coefs pi = -(np.identity(k) - np.sum(A, 0)) gamma = np.zeros((p-1, k, k)) for i in range(p-1): gamma[i] = -(np.sum(A[i+1:], 0)) gamma = np.concatenate(gamma, 1) return {"Gamma": gamma, "Pi": pi} # ------------------------------------------------------------------------------- # VARResults class class VARResults(VARProcess): """Estimate VAR(p) process with fixed number of lags Parameters ---------- endog : ndarray endog_lagged : ndarray params : ndarray sigma_u : ndarray lag_order : int model : VAR model instance trend : str {'nc', 'c', 'ct'} names : array_like List of names of the endogenous variables in order of appearance in `endog`. dates exog : ndarray Attributes ---------- coefs : ndarray (p x K x K) Estimated A_i matrices, A_i = coefs[i-1] dates endog endog_lagged k_ar : int Order of VAR process k_trend : int model names neqs : int Number of variables (equations) nobs : int n_totobs : int params : ndarray (Kp + 1) x K A_i matrices and intercept in stacked form [int A_1 ... A_p] names : list variables names resid sigma_u : ndarray (K x K) Estimate of white noise process variance Var[u_t] tvalues y : ys_lagged """ _model_type = 'VAR' y = deprecated_alias("y", "endog", remove_version="0.11.0") ys_lagged = deprecated_alias("ys_lagged", "endog_lagged", remove_version="0.11.0") def __init__(self, endog, endog_lagged, params, sigma_u, lag_order, model=None, trend='c', names=None, dates=None, exog=None): self.model = model self.endog = endog self.endog_lagged = endog_lagged self.dates = dates self.n_totobs, neqs = self.endog.shape self.nobs = self.n_totobs - lag_order self.trend = trend k_trend = util.get_trendorder(trend) self.exog_names = util.make_lag_names(names, lag_order, k_trend, model.data.orig_exog) self.params = params self.exog = exog # Initialize VARProcess parent class # construct coefficient matrices # Each matrix needs to be transposed endog_start = k_trend if exog is not None: k_exog_user = exog.shape[1] endog_start += k_exog_user else: k_exog_user = 0 reshaped = self.params[endog_start:] reshaped = reshaped.reshape((lag_order, neqs, neqs)) # Need to transpose each coefficient matrix coefs = reshaped.swapaxes(1, 2).copy() self.coefs_exog = params[:endog_start].T self.k_exog = self.coefs_exog.shape[1] self.k_exog_user = k_exog_user # maybe change to params class, distinguish exog_all versus exog_user # see issue #4535 _params_info = {'k_trend': k_trend, 'k_exog_user': k_exog_user, 'k_ar': lag_order} super(VARResults, self).__init__(coefs, self.coefs_exog, sigma_u, names=names, _params_info=_params_info) def plot(self): """Plot input time series""" return plotting.plot_mts(self.endog, names=self.names, index=self.dates) @property def df_model(self): """ Number of estimated parameters, including the intercept / trends """ return self.neqs * self.k_ar + self.k_exog @property def df_resid(self): """Number of observations minus number of estimated parameters""" return self.nobs - self.df_model @cache_readonly def fittedvalues(self): """ The predicted insample values of the response variables of the model. """ return np.dot(self.endog_lagged, self.params) @cache_readonly def resid(self): """ Residuals of response variable resulting from estimated coefficients """ return self.endog[self.k_ar:] - self.fittedvalues def sample_acov(self, nlags=1): """Sample acov""" return _compute_acov(self.endog[self.k_ar:], nlags=nlags) def sample_acorr(self, nlags=1): """Sample acorr""" acovs = self.sample_acov(nlags=nlags) return _acovs_to_acorrs(acovs) def plot_sample_acorr(self, nlags=10, linewidth=8): """ Plot sample autocorrelation function Parameters ---------- nlags : int The number of lags to use in compute the autocorrelation. Does not count the zero lag, which will be returned. linewidth : int The linewidth for the plots. Returns ------- Figure The figure that contains the plot axes. """ fig = plotting.plot_full_acorr(self.sample_acorr(nlags=nlags), linewidth=linewidth) return fig def resid_acov(self, nlags=1): """ Compute centered sample autocovariance (including lag 0) Parameters ---------- nlags : int Returns ------- """ return _compute_acov(self.resid, nlags=nlags) def resid_acorr(self, nlags=1): """ Compute sample autocorrelation (including lag 0) Parameters ---------- nlags : int Returns ------- """ acovs = self.resid_acov(nlags=nlags) return _acovs_to_acorrs(acovs) @cache_readonly def resid_corr(self): """ Centered residual correlation matrix """ return self.resid_acorr(0)[0] @cache_readonly def sigma_u_mle(self): """(Biased) maximum likelihood estimate of noise process covariance """ return self.sigma_u * self.df_resid / self.nobs def cov_params(self): """Estimated variance-covariance of model coefficients Notes ----- Covariance of vec(B), where B is the matrix [params_for_deterministic_terms, A_1, ..., A_p] with the shape (K x (Kp + number_of_deterministic_terms)) Adjusted to be an unbiased estimator Ref: Lütkepohl p.74-75 """ z = self.endog_lagged return np.kron(np.linalg.inv(z.T @ z), self.sigma_u) def cov_ybar(self): r"""Asymptotically consistent estimate of covariance of the sample mean .. math:: \sqrt(T) (\bar{y} - \mu) \rightarrow {\cal N}(0, \Sigma_{\bar{y}})\\ \Sigma_{\bar{y}} = B \Sigma_u B^\prime, \text{where } B = (I_K - A_1 - \cdots - A_p)^{-1} Notes ----- Lütkepohl Proposition 3.3 """ Ainv = np.linalg.inv(np.eye(self.neqs) - self.coefs.sum(0)) return Ainv @ self.sigma_u @ Ainv.T # ------------------------------------------------------------ # Estimation-related things @cache_readonly def _zz(self): # Z'Z return np.dot(self.endog_lagged.T, self.endog_lagged) @property def _cov_alpha(self): """ Estimated covariance matrix of model coefficients w/o exog """ # drop exog kn = self.k_exog * self.neqs return self.cov_params()[kn:, kn:] @cache_readonly def _cov_sigma(self): """ Estimated covariance matrix of vech(sigma_u) """ D_K = tsa.duplication_matrix(self.neqs) D_Kinv = np.linalg.pinv(D_K) sigxsig = np.kron(self.sigma_u, self.sigma_u) return 2 * D_Kinv @ sigxsig @ D_Kinv.T @cache_readonly def llf(self): "Compute VAR(p) loglikelihood" return var_loglike(self.resid, self.sigma_u_mle, self.nobs) @cache_readonly def stderr(self): """Standard errors of coefficients, reshaped to match in size """ stderr = np.sqrt(np.diag(self.cov_params())) return stderr.reshape((self.df_model, self.neqs), order='C') bse = stderr # statsmodels interface? @cache_readonly def stderr_endog_lagged(self): """Stderr_endog_lagged""" start = self.k_exog return self.stderr[start:] @cache_readonly def stderr_dt(self): """Stderr_dt""" end = self.k_exog return self.stderr[:end] @cache_readonly def tvalues(self): """Compute t-statistics. Use Student-t(T - Kp - 1) = t(df_resid) to test significance. """ return self.params / self.stderr @cache_readonly def tvalues_endog_lagged(self): """tvalues_endog_lagged""" start = self.k_exog return self.tvalues[start:] @cache_readonly def tvalues_dt(self): """tvalues_dt""" end = self.k_exog return self.tvalues[:end] @cache_readonly def pvalues(self): """Two-sided p-values for model coefficients from Student t-distribution """ # return stats.t.sf(np.abs(self.tvalues), self.df_resid)*2 return 2 * stats.norm.sf(np.abs(self.tvalues)) @cache_readonly def pvalues_endog_lagged(self): """pvalues_endog_laggd""" start = self.k_exog return self.pvalues[start:] @cache_readonly def pvalues_dt(self): """pvalues_dt""" end = self.k_exog return self.pvalues[:end] # todo: -------------------------------------------------------------------- def plot_forecast(self, steps, alpha=0.05, plot_stderr=True): """ Plot forecast """ mid, lower, upper = self.forecast_interval(self.endog[-self.k_ar:], steps, alpha=alpha) fig = plotting.plot_var_forc(self.endog, mid, lower, upper, names=self.names, plot_stderr=plot_stderr) return fig # Forecast error covariance functions def forecast_cov(self, steps=1, method='mse'): r"""Compute forecast covariance matrices for desired number of steps Parameters ---------- steps : int Notes ----- .. math:: \Sigma_{\hat y}(h) = \Sigma_y(h) + \Omega(h) / T Ref: Lütkepohl pp. 96-97 Returns ------- covs : ndarray (steps x k x k) """ fc_cov = self.mse(steps) if method == 'mse': pass elif method == 'auto': if self.k_exog == 1 and self.k_trend < 2: # currently only supported if no exog and trend in ['nc', 'c'] fc_cov += self._omega_forc_cov(steps) / self.nobs import warnings warnings.warn('forecast cov takes parameter uncertainty into' 'account', OutputWarning) else: raise ValueError("method has to be either 'mse' or 'auto'") return fc_cov # Monte Carlo irf standard errors @deprecate_kwarg('T', 'steps') def irf_errband_mc(self, orth=False, repl=1000, steps=10, signif=0.05, seed=None, burn=100, cum=False): """ Compute Monte Carlo integrated error bands assuming normally distributed for impulse response functions Parameters ---------- orth : bool, default False Compute orthogonalized impulse response error bands repl : int number of Monte Carlo replications to perform steps : int, default 10 number of impulse response periods signif : float (0 < signif <1) Significance level for error bars, defaults to 95% CI seed : int np.random.seed for replications burn : int number of initial observations to discard for simulation cum : bool, default False produce cumulative irf error bands Notes ----- Lütkepohl (2005) Appendix D Returns ------- Tuple of lower and upper arrays of ma_rep monte carlo standard errors """ ma_coll = self.irf_resim(orth=orth, repl=repl, steps=steps, seed=seed, burn=burn, cum=cum) ma_sort = np.sort(ma_coll, axis=0) # sort to get quantiles # python 2: round returns float low_idx = int(round(signif / 2 * repl) - 1) upp_idx = int(round((1 - signif / 2) * repl) - 1) lower = ma_sort[low_idx, :, :, :] upper = ma_sort[upp_idx, :, :, :] return lower, upper @deprecate_kwarg('T', 'steps') def irf_resim(self, orth=False, repl=1000, steps=10, seed=None, burn=100, cum=False): """ Simulates impulse response function, returning an array of simulations. Used for Sims-Zha error band calculation. Parameters ---------- orth : bool, default False Compute orthogonalized impulse response error bands repl : int number of Monte Carlo replications to perform steps : int, default 10 number of impulse response periods signif : float (0 < signif <1) Significance level for error bars, defaults to 95% CI seed : int np.random.seed for replications burn : int number of initial observations to discard for simulation cum : bool, default False produce cumulative irf error bands Notes ----- .. [*] Sims, Christoper A., and Tao Zha. 1999. "Error Bands for Impulse Response." Econometrica 67: 1113-1155. Returns ------- Array of simulated impulse response functions """ neqs = self.neqs k_ar = self.k_ar coefs = self.coefs sigma_u = self.sigma_u intercept = self.intercept nobs = self.nobs nobs_original = nobs + k_ar ma_coll = np.zeros((repl, steps + 1, neqs, neqs)) def fill_coll(sim): ret = VAR(sim, exog=self.exog).fit(maxlags=k_ar, trend=self.trend) ret = ret.orth_ma_rep(maxn=steps) if orth else ret.ma_rep(maxn=steps) return ret.cumsum(axis=0) if cum else ret for i in range(repl): # discard first burn to eliminate correct for starting bias sim = util.varsim(coefs, intercept, sigma_u, seed=seed, steps=nobs_original+burn) sim = sim[burn:] ma_coll[i, :, :, :] = fill_coll(sim) return ma_coll def _omega_forc_cov(self, steps): # Approximate MSE matrix \Omega(h) as defined in Lut p97 G = self._zz Ginv = np.linalg.inv(G) # memoize powers of B for speedup # TODO: see if can memoize better # TODO: much lower-hanging fruit in caching `np.trace` below. B = self._bmat_forc_cov() _B = {} def bpow(i): if i not in _B: _B[i] = np.linalg.matrix_power(B, i) return _B[i] phis = self.ma_rep(steps) sig_u = self.sigma_u omegas = np.zeros((steps, self.neqs, self.neqs)) for h in range(1, steps + 1): if h == 1: omegas[h-1] = self.df_model * self.sigma_u continue om = omegas[h-1] for i in range(h): for j in range(h): Bi = bpow(h - 1 - i) Bj = bpow(h - 1 - j) mult = np.trace(Bi.T @ Ginv @ Bj @ G) om += mult * phis[i] @ sig_u @ phis[j].T omegas[h-1] = om return omegas def _bmat_forc_cov(self): # B as defined on p. 96 of Lut upper = np.zeros((self.k_exog, self.df_model)) upper[:, :self.k_exog] = np.eye(self.k_exog) lower_dim = self.neqs * (self.k_ar - 1) eye = np.eye(lower_dim) lower = np.column_stack((np.zeros((lower_dim, self.k_exog)), eye, np.zeros((lower_dim, self.neqs)))) return np.vstack((upper, self.params.T, lower)) def summary(self): """Compute console output summary of estimates Returns ------- summary : VARSummary """ return VARSummary(self) def irf(self, periods=10, var_decomp=None, var_order=None): """Analyze impulse responses to shocks in system Parameters ---------- periods : int var_decomp : ndarray (k x k), lower triangular Must satisfy Omega = P P', where P is the passed matrix. Defaults to Cholesky decomposition of Omega var_order : sequence Alternate variable order for Cholesky decomposition Returns ------- irf : IRAnalysis """ if var_order is not None: raise NotImplementedError('alternate variable order not implemented' ' (yet)') return IRAnalysis(self, P=var_decomp, periods=periods) def fevd(self, periods=10, var_decomp=None): """ Compute forecast error variance decomposition ("fevd") Returns ------- fevd : FEVD instance """ return FEVD(self, P=var_decomp, periods=periods) def reorder(self, order): """Reorder variables for structural specification """ if len(order) != len(self.params[0, :]): raise ValueError("Reorder specification length should match " "number of endogenous variables") # This converts order to list of integers if given as strings if isinstance(order[0], str): order_new = [] for i, nam in enumerate(order): order_new.append(self.names.index(order[i])) order = order_new return _reordered(self, order) # -------------------------------------------------------------------------- # VAR Diagnostics: Granger-causality, whiteness of residuals, normality, etc def test_causality(self, caused, causing=None, kind='f', signif=0.05): """ Test Granger causality Parameters ---------- caused : int or str or sequence of int or str If int or str, test whether the variable specified via this index (int) or name (str) is Granger-caused by the variable(s) specified by `causing`. If a sequence of int or str, test whether the corresponding variables are Granger-caused by the variable(s) specified by `causing`. causing : int or str or sequence of int or str or None, default: None If int or str, test whether the variable specified via this index (int) or name (str) is Granger-causing the variable(s) specified by `caused`. If a sequence of int or str, test whether the corresponding variables are Granger-causing the variable(s) specified by `caused`. If None, `causing` is assumed to be the complement of `caused`. kind : {'f', 'wald'} Perform F-test or Wald (chi-sq) test signif : float, default 5% Significance level for computing critical values for test, defaulting to standard 0.05 level Notes ----- Null hypothesis is that there is no Granger-causality for the indicated variables. The degrees of freedom in the F-test are based on the number of variables in the VAR system, that is, degrees of freedom are equal to the number of equations in the VAR times degree of freedom of a single equation. Test for Granger-causality as described in chapter 7.6.3 of [1]_. Test H0: "`causing` does not Granger-cause the remaining variables of the system" against H1: "`causing` is Granger-causal for the remaining variables". Returns ------- results : CausalityTestResults References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. """ if not (0 < signif < 1): raise ValueError("signif has to be between 0 and 1") allowed_types = (str, int) if isinstance(caused, allowed_types): caused = [caused] if not all(isinstance(c, allowed_types) for c in caused): raise TypeError("caused has to be of type string or int (or a " "sequence of these types).") caused = [self.names[c] if type(c) == int else c for c in caused] caused_ind = [util.get_index(self.names, c) for c in caused] if causing is not None: if isinstance(causing, allowed_types): causing = [causing] if not all(isinstance(c, allowed_types) for c in causing): raise TypeError("causing has to be of type string or int (or " "a sequence of these types) or None.") causing = [self.names[c] if type(c) == int else c for c in causing] causing_ind = [util.get_index(self.names, c) for c in causing] if causing is None: causing_ind = [i for i in range(self.neqs) if i not in caused_ind] causing = [self.names[c] for c in caused_ind] k, p = self.neqs, self.k_ar if p == 0: err = "Cannot test Granger Causality in a model with 0 lags." raise RuntimeError(err) # number of restrictions num_restr = len(causing) * len(caused) * p num_det_terms = self.k_exog # Make restriction matrix C = np.zeros((num_restr, k * num_det_terms + k**2 * p), dtype=float) cols_det = k * num_det_terms row = 0 for j in range(p): for ing_ind in causing_ind: for ed_ind in caused_ind: C[row, cols_det + ed_ind + k * ing_ind + k**2 * j] = 1 row += 1 # Lütkepohl 3.6.5 Cb = np.dot(C, vec(self.params.T)) middle = np.linalg.inv(C @ self.cov_params() @ C.T) # wald statistic lam_wald = statistic = Cb @ middle @ Cb if kind.lower() == 'wald': df = num_restr dist = stats.chi2(df) elif kind.lower() == 'f': statistic = lam_wald / num_restr df = (num_restr, k * self.df_resid) dist = stats.f(*df) else: raise ValueError('kind %s not recognized' % kind) pvalue = dist.sf(statistic) crit_value = dist.ppf(1 - signif) return CausalityTestResults(causing, caused, statistic, crit_value, pvalue, df, signif, test="granger", method=kind) def test_inst_causality(self, causing, signif=0.05): """ Test for instantaneous causality Parameters ---------- causing : If int or str, test whether the corresponding variable is causing the variable(s) specified in caused. If sequence of int or str, test whether the corresponding variables are causing the variable(s) specified in caused. signif : float between 0 and 1, default 5 % Significance level for computing critical values for test, defaulting to standard 0.05 level verbose : bool If True, print a table with the results. Returns ------- results : dict A dict holding the test's results. The dict's keys are: "statistic" : float The calculated test statistic. "crit_value" : float The critical value of the Chi^2-distribution. "pvalue" : float The p-value corresponding to the test statistic. "df" : float The degrees of freedom of the Chi^2-distribution. "conclusion" : str {"reject", "fail to reject"} Whether H0 can be rejected or not. "signif" : float Significance level Notes ----- Test for instantaneous causality as described in chapters 3.6.3 and 7.6.4 of [1]_. Test H0: "No instantaneous causality between caused and causing" against H1: "Instantaneous causality between caused and causing exists". Instantaneous causality is a symmetric relation (i.e. if causing is "instantaneously causing" caused, then also caused is "instantaneously causing" causing), thus the naming of the parameters (which is chosen to be in accordance with test_granger_causality()) may be misleading. This method is not returning the same result as JMulTi. This is because the test is based on a VAR(k_ar) model in statsmodels (in accordance to pp. 104, 320-321 in [1]_) whereas JMulTi seems to be using a VAR(k_ar+1) model. References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. """ if not (0 < signif < 1): raise ValueError("signif has to be between 0 and 1") allowed_types = (str, int) if isinstance(causing, allowed_types): causing = [causing] if not all(isinstance(c, allowed_types) for c in causing): raise TypeError("causing has to be of type string or int (or a " + "a sequence of these types).") causing = [self.names[c] if type(c) == int else c for c in causing] causing_ind = [util.get_index(self.names, c) for c in causing] caused_ind = [i for i in range(self.neqs) if i not in causing_ind] caused = [self.names[c] for c in caused_ind] # Note: JMulTi seems to be using k_ar+1 instead of k_ar k, t, p = self.neqs, self.nobs, self.k_ar num_restr = len(causing) * len(caused) # called N in Lütkepohl sigma_u = self.sigma_u vech_sigma_u = util.vech(sigma_u) sig_mask = np.zeros(sigma_u.shape) # set =1 twice to ensure, that all the ones needed are below the main # diagonal: sig_mask[causing_ind, caused_ind] = 1 sig_mask[caused_ind, causing_ind] = 1 vech_sig_mask = util.vech(sig_mask) inds = np.nonzero(vech_sig_mask)[0] # Make restriction matrix C = np.zeros((num_restr, len(vech_sigma_u)), dtype=float) for row in range(num_restr): C[row, inds[row]] = 1 Cs = np.dot(C, vech_sigma_u) d = np.linalg.pinv(duplication_matrix(k)) Cd = np.dot(C, d) middle = np.linalg.inv(Cd @ np.kron(sigma_u, sigma_u) @ Cd.T) / 2 wald_statistic = t * (Cs.T @ middle @ Cs) df = num_restr dist = stats.chi2(df) pvalue = dist.sf(wald_statistic) crit_value = dist.ppf(1 - signif) return CausalityTestResults(causing, caused, wald_statistic, crit_value, pvalue, df, signif, test="inst", method="wald") def test_whiteness(self, nlags=10, signif=0.05, adjusted=False): """ Residual whiteness tests using Portmanteau test Parameters ---------- nlags : int > 0 The number of lags tested must be larger than the number of lags included in the VAR model. signif : float, between 0 and 1 The significance level of the test. adjusted : bool, default False Flag indicating to apply small-sample adjustments. Returns ------- WhitenessTestResults The test results. Notes ----- Test the whiteness of the residuals using the Portmanteau test as described in [1]_, chapter 4.4.3. References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. """ if nlags - self.k_ar <= 0: raise ValueError("The whiteness test can only be used when nlags " "is larger than the number of lags included in " f"the model ({self.k_ar}).") statistic = 0 u = np.asarray(self.resid) acov_list = _compute_acov(u, nlags) cov0_inv = np.linalg.inv(acov_list[0]) for t in range(1, nlags+1): ct = acov_list[t] to_add = np.trace(ct.T @ cov0_inv @ ct @ cov0_inv) if adjusted: to_add /= (self.nobs - t) statistic += to_add statistic *= self.nobs**2 if adjusted else self.nobs df = self.neqs**2 * (nlags - self.k_ar) dist = stats.chi2(df) pvalue = dist.sf(statistic) crit_value = dist.ppf(1 - signif) return WhitenessTestResults(statistic, crit_value, pvalue, df, signif, nlags, adjusted) def plot_acorr(self, nlags=10, resid=True, linewidth=8): r""" Plot autocorrelation of sample (endog) or residuals Sample (Y) or Residual autocorrelations are plotted together with the standard :math:`2 / \sqrt{T}` bounds. Parameters ---------- nlags : int number of lags to display (excluding 0) resid : bool If True, then the autocorrelation of the residuals is plotted If False, then the autocorrelation of endog is plotted. linewidth : int width of vertical bars Returns ------- Figure Figure instance containing the plot. """ if resid: acorrs = self.resid_acorr(nlags) else: acorrs = self.sample_acorr(nlags) bound = 2 / np.sqrt(self.nobs) fig = plotting.plot_full_acorr(acorrs[1:], xlabel=np.arange(1, nlags+1), err_bound=bound, linewidth=linewidth) fig.suptitle(r"ACF plots for residuals with $2 / \sqrt{T}$ bounds ") return fig def test_normality(self, signif=0.05): """ Test assumption of normal-distributed errors using Jarque-Bera-style omnibus Chi^2 test. Parameters ---------- signif : float Test significance level. Returns ------- result : NormalityTestResults Notes ----- H0 (null) : data are generated by a Gaussian-distributed process """ return test_normality(self, signif=signif) @cache_readonly def detomega(self): r""" Return determinant of white noise covariance with degrees of freedom correction: .. math:: \hat \Omega = \frac{T}{T - Kp - 1} \hat \Omega_{\mathrm{MLE}} """ return np.linalg.det(self.sigma_u) @cache_readonly def info_criteria(self): "information criteria for lagorder selection" nobs = self.nobs neqs = self.neqs lag_order = self.k_ar free_params = lag_order * neqs ** 2 + neqs * self.k_exog ld = logdet_symm(self.sigma_u_mle) # See Lütkepohl pp. 146-150 aic = ld + (2. / nobs) * free_params bic = ld + (np.log(nobs) / nobs) * free_params hqic = ld + (2. * np.log(np.log(nobs)) / nobs) * free_params fpe = ((nobs + self.df_model) / self.df_resid) ** neqs * np.exp(ld) return { 'aic': aic, 'bic': bic, 'hqic': hqic, 'fpe': fpe } @property def aic(self): """Akaike information criterion""" return self.info_criteria['aic'] @property def fpe(self): """Final Prediction Error (FPE) Lütkepohl p. 147, see info_criteria """ return self.info_criteria['fpe'] @property def hqic(self): """Hannan-Quinn criterion""" return self.info_criteria['hqic'] @property def bic(self): """Bayesian a.k.a. Schwarz info criterion""" return self.info_criteria['bic'] @cache_readonly def roots(self): """ The roots of the VAR process are the solution to (I - coefs[0]*z - coefs[1]*z**2 ... - coefs[p-1]*z**k_ar) = 0. Note that the inverse roots are returned, and stability requires that the roots lie outside the unit circle. """ neqs = self.neqs k_ar = self.k_ar p = neqs * k_ar arr = np.zeros((p, p)) arr[:neqs, :] = np.column_stack(self.coefs) arr[neqs:, :-neqs] = np.eye(p-neqs) roots = np.linalg.eig(arr)[0]**-1 idx = np.argsort(np.abs(roots))[::-1] # sort by reverse modulus return roots[idx] class VARResultsWrapper(wrap.ResultsWrapper): _attrs = {'bse': 'columns_eq', 'cov_params': 'cov', 'params': 'columns_eq', 'pvalues': 'columns_eq', 'tvalues': 'columns_eq', 'sigma_u': 'cov_eq', 'sigma_u_mle': 'cov_eq', 'stderr': 'columns_eq'} _wrap_attrs = wrap.union_dicts(TimeSeriesResultsWrapper._wrap_attrs, _attrs) _methods = {'conf_int': 'multivariate_confint'} _wrap_methods = wrap.union_dicts(TimeSeriesResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(VARResultsWrapper, VARResults) # noqa:E305 class FEVD(object): """ Compute and plot Forecast error variance decomposition and asymptotic standard errors """ def __init__(self, model, P=None, periods=None): self.periods = periods self.model = model self.neqs = model.neqs self.names = model.model.endog_names self.irfobj = model.irf(var_decomp=P, periods=periods) self.orth_irfs = self.irfobj.orth_irfs # cumulative impulse responses irfs = (self.orth_irfs[:periods] ** 2).cumsum(axis=0) rng = lrange(self.neqs) mse = self.model.mse(periods)[:, rng, rng] # lag x equation x component fevd = np.empty_like(irfs) for i in range(periods): fevd[i] = (irfs[i].T / mse[i]).T # switch to equation x lag x component self.decomp = fevd.swapaxes(0, 1) def summary(self): buf = StringIO() rng = lrange(self.periods) for i in range(self.neqs): ppm = output.pprint_matrix(self.decomp[i], rng, self.names) buf.write('FEVD for %s\n' % self.names[i]) buf.write(ppm + '\n') print(buf.getvalue()) def cov(self): """Compute asymptotic standard errors Returns ------- """ raise NotImplementedError def plot(self, periods=None, figsize=(10, 10), **plot_kwds): """Plot graphical display of FEVD Parameters ---------- periods : int, default None Defaults to number originally specified. Can be at most that number """ import matplotlib.pyplot as plt k = self.neqs periods = periods or self.periods fig, axes = plt.subplots(nrows=k, figsize=figsize) fig.suptitle('Forecast error variance decomposition (FEVD)') colors = [str(c) for c in np.arange(k, dtype=float) / k] ticks = np.arange(periods) limits = self.decomp.cumsum(2) for i in range(k): ax = axes[i] this_limits = limits[i].T handles = [] for j in range(k): lower = this_limits[j - 1] if j > 0 else 0 upper = this_limits[j] handle = ax.bar(ticks, upper - lower, bottom=lower, color=colors[j], label=self.names[j], **plot_kwds) handles.append(handle) ax.set_title(self.names[i]) # just use the last axis to get handles for plotting handles, labels = ax.get_legend_handles_labels() fig.legend(handles, labels, loc='upper right') plotting.adjust_subplots(right=0.85) return fig # ------------------------------------------------------------------------------- def _compute_acov(x, nlags=1): x = x - x.mean(0) result = [] for lag in range(nlags + 1): if lag > 0: r = np.dot(x[lag:].T, x[:-lag]) else: r = np.dot(x.T, x) result.append(r) return np.array(result) / len(x) def _acovs_to_acorrs(acovs): sd = np.sqrt(np.diag(acovs[0])) return acovs / np.outer(sd, sd) if __name__ == '__main__': import statsmodels.tools.data as data_util from statsmodels.tsa.vector_ar.util import parse_lutkepohl_data np.set_printoptions(linewidth=140, precision=5) sdata, dates = parse_lutkepohl_data('data/%s.dat' % 'e1') names = sdata.dtype.names data = data_util.struct_to_ndarray(sdata) adj_data = np.diff(np.log(data), axis=0) # est = VAR(adj_data, p=2, dates=dates[1:], names=names) model = VAR(adj_data[:-16], dates=dates[1:-16], names=names) # model = VAR(adj_data[:-16], dates=dates[1:-16], names=names) est = model.fit(maxlags=2) irf = est.irf() y = est.endog[-2:] """ # irf.plot_irf() # i = 2; j = 1 # cv = irf.cum_effect_cov(orth=True) # print np.sqrt(cv[:, j * 3 + i, j * 3 + i]) / 1e-2 # data = np.genfromtxt('Canada.csv', delimiter=',', names=True) # data = data.view((float, 4)) """ ''' mdata = sm.datasets.macrodata.load(as_pandas=False).data mdata2 = mdata[['realgdp','realcons','realinv']] names = mdata2.dtype.names data = mdata2.view((float,3)) data = np.diff(np.log(data), axis=0) import pandas as pn df = pn.DataFrame.fromRecords(mdata) df = np.log(df.reindex(columns=names)) df = (df - df.shift(1)).dropna() model = VAR(df) est = model.fit(maxlags=2) irf = est.irf() ''' statsmodels-0.12.2/statsmodels/tsa/vector_ar/vecm.py000066400000000000000000002650231400612667500225760ustar00rootroot00000000000000# -*- coding: utf-8 -*- from collections import defaultdict import numpy as np from numpy import hstack, vstack from numpy.linalg import inv, svd import scipy import scipy.stats from statsmodels.iolib.summary import Summary from statsmodels.iolib.table import SimpleTable from statsmodels.tools.decorators import cache_readonly from statsmodels.tools.sm_exceptions import HypothesisTestWarning import statsmodels.tsa.base.tsa_model as tsbase from statsmodels.tsa.coint_tables import c_sja, c_sjt from statsmodels.tsa.tsatools import duplication_matrix, lagmat, vec from statsmodels.tsa.vector_ar.hypothesis_test_results import ( CausalityTestResults, WhitenessTestResults, ) import statsmodels.tsa.vector_ar.irf as irf import statsmodels.tsa.vector_ar.plotting as plot from statsmodels.tsa.vector_ar.util import get_index, seasonal_dummies from statsmodels.tsa.vector_ar.var_model import ( VAR, LagOrderResults, _compute_acov, forecast, forecast_interval, ma_rep, orth_ma_rep, test_normality, ) def select_order(data, maxlags, deterministic="nc", seasons=0, exog=None, exog_coint=None): """ Compute lag order selections based on each of the available information criteria. Parameters ---------- data : array_like (nobs_tot x neqs) The observed data. maxlags : int All orders until maxlag will be compared according to the information criteria listed in the Results-section of this docstring. deterministic : str {``"nc"``, ``"co"``, ``"ci"``, ``"lo"``, ``"li"``} * ``"nc"`` - no deterministic terms * ``"co"`` - constant outside the cointegration relation * ``"ci"`` - constant within the cointegration relation * ``"lo"`` - linear trend outside the cointegration relation * ``"li"`` - linear trend within the cointegration relation Combinations of these are possible (e.g. ``"cili"`` or ``"colo"`` for linear trend with intercept). See the docstring of the :class:`VECM`-class for more information. seasons : int, default: 0 Number of periods in a seasonal cycle. exog : ndarray (nobs_tot x neqs) or `None`, default: `None` Deterministic terms outside the cointegration relation. exog_coint : ndarray (nobs_tot x neqs) or `None`, default: `None` Deterministic terms inside the cointegration relation. Returns ------- selected_orders : :class:`statsmodels.tsa.vector_ar.var_model.LagOrderResults` """ ic = defaultdict(list) for p in range(1, maxlags + 2): # +2 because k_ar_VECM == k_ar_VAR - 1 exogs = [] if "co" in deterministic or "ci" in deterministic: exogs.append(np.ones(len(data)).reshape(-1, 1)) if "lo" in deterministic or "li" in deterministic: exogs.append(1 + np.arange(len(data)).reshape(-1, 1)) if exog_coint is not None: exogs.append(exog_coint) if seasons > 0: exogs.append(seasonal_dummies(seasons, len(data) ).reshape(-1, seasons-1)) if exog is not None: exogs.append(exog) exogs = hstack(exogs) if exogs else None var_model = VAR(data, exogs) # exclude some periods ==> same amount of data used for each lag order var_result = var_model._estimate_var(lags=p, offset=maxlags+1-p) for k, v in var_result.info_criteria.items(): ic[k].append(v) # -1+1 in the following line is only here for clarification. # -1 because k_ar_VECM == k_ar_VAR - 1 # +1 because p == index +1 (we start with p=1, not p=0) selected_orders = dict((ic_name, np.array(ic_value).argmin() - 1 + 1) for ic_name, ic_value in ic.items()) return LagOrderResults(ic, selected_orders, True) def _linear_trend(nobs, k_ar, coint=False): """ Construct an ndarray representing a linear trend in a VECM. Parameters ---------- nobs : int Number of observations excluding the presample. k_ar : int Number of lags in levels. coint : bool, default: False If True (False), the returned array represents a linear trend inside (outside) the cointegration relation. Returns ------- ret : ndarray (nobs) An ndarray representing a linear trend in a VECM Notes ----- The returned array's size is nobs and not nobs_tot so it cannot be used to construct the exog-argument of VECM's __init__ method. """ ret = np.arange(nobs) + k_ar if not coint: ret += 1 return ret def _num_det_vars(det_string, seasons=0): """Gives the number of deterministic variables specified by det_string and seasons. Parameters ---------- det_string : str {"nc", "co", "ci", "lo", "li"} * "nc" - no deterministic terms * "co" - constant outside the cointegration relation * "ci" - constant within the cointegration relation * "lo" - linear trend outside the cointegration relation * "li" - linear trend within the cointegration relation Combinations of these are possible (e.g. "cili" or "colo" for linear trend with intercept). See the docstring of the :class:`VECM`-class for more information. seasons : int Number of periods in a seasonal cycle. Returns ------- num : int Number of deterministic terms and number dummy variables for seasonal terms. """ num = 0 if "ci" in det_string or "co" in det_string: num += 1 if "li" in det_string or "lo" in det_string: num += 1 if seasons > 0: num += seasons - 1 return num def _deterministic_to_exog(deterministic, seasons, nobs_tot, first_season=0, seasons_centered=False, exog=None, exog_coint=None): """ Translate all information about deterministic terms into a single array. These information is taken from `deterministic` and `seasons` as well as from the `exog` and `exog_coint` arrays. The resulting array form can then be used e.g. in VAR's __init__ method. Parameters ---------- deterministic : str A string specifying the deterministic terms in the model. See VECM's docstring for more information. seasons : int Number of periods in a seasonal cycle. nobs_tot : int Number of observations including the presample. first_season : int, default: 0 Season of the first observation. seasons_centered : bool, default: False If True, the seasonal dummy variables are demeaned such that they are orthogonal to an intercept term. exog : ndarray (nobs_tot x #det_terms) or None, default: None An ndarray representing deterministic terms outside the cointegration relation. exog_coint : ndarray (nobs_tot x #det_terms_coint) or None, default: None An ndarray representing deterministic terms inside the cointegration relation. Returns ------- exog : ndarray or None None, if the function's arguments do not contain deterministic terms. Otherwise, an ndarray representing these deterministic terms. """ exogs = [] if "co" in deterministic or "ci" in deterministic: exogs.append(np.ones(nobs_tot)) if exog_coint is not None: exogs.append(exog_coint) if "lo" in deterministic or "li" in deterministic: exogs.append(np.arange(nobs_tot)) if seasons > 0: exogs.append(seasonal_dummies(seasons, nobs_tot, first_period=first_season, centered=seasons_centered)) if exog is not None: exogs.append(exog) return np.column_stack(exogs) if exogs else None def _mat_sqrt(_2darray): """Calculates the square root of a matrix. Parameters ---------- _2darray : ndarray A 2-dimensional ndarray representing a square matrix. Returns ------- result : ndarray Square root of the matrix given as function argument. """ u_, s_, v_ = svd(_2darray, full_matrices=False) s_ = np.sqrt(s_) return u_.dot(s_[:, None] * v_) def _endog_matrices(endog, exog, exog_coint, diff_lags, deterministic, seasons=0, first_season=0): """ Returns different matrices needed for parameter estimation. Compare p. 186 in [1]_. The returned matrices consist of elements of the data as well as elements representing deterministic terms. A tuple of consisting of these matrices is returned. Parameters ---------- endog : ndarray (neqs x nobs_tot) The whole sample including the presample. exog : ndarray (nobs_tot x neqs) or None Deterministic terms outside the cointegration relation. exog_coint : ndarray (nobs_tot x neqs) or None Deterministic terms inside the cointegration relation. diff_lags : int Number of lags in the VEC representation. deterministic : str {``"nc"``, ``"co"``, ``"ci"``, ``"lo"``, ``"li"``} * ``"nc"`` - no deterministic terms * ``"co"`` - constant outside the cointegration relation * ``"ci"`` - constant within the cointegration relation * ``"lo"`` - linear trend outside the cointegration relation * ``"li"`` - linear trend within the cointegration relation Combinations of these are possible (e.g. ``"cili"`` or ``"colo"`` for linear trend with intercept). See the docstring of the :class:`VECM`-class for more information. seasons : int, default: 0 Number of periods in a seasonal cycle. 0 (default) means no seasons. first_season : int, default: 0 The season of the first observation. `0` means first season, `1` means second season, ..., `seasons-1` means the last season. Returns ------- y_1_T : ndarray (neqs x nobs) The (transposed) data without the presample. `.. math:: (y_1, \\ldots, y_T) delta_y_1_T : ndarray (neqs x nobs) The first differences of endog. `.. math:: (y_1, \\ldots, y_T) - (y_0, \\ldots, y_{T-1}) y_lag1 : ndarray (neqs x nobs) (dimensions assuming no deterministic terms are given) Endog of the previous period (lag 1). `.. math:: (y_0, \\ldots, y_{T-1}) delta_x : ndarray (k_ar_diff*neqs x nobs) (dimensions assuming no deterministic terms are given) Lagged differenced endog, used as regressor for the short term equation. References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. """ # p. 286: p = diff_lags+1 y = endog K = y.shape[0] y_1_T = y[:, p:] T = y_1_T.shape[1] delta_y = np.diff(y) delta_y_1_T = delta_y[:, p-1:] y_lag1 = y[:, p-1:-1] if "co" in deterministic and "ci" in deterministic: raise ValueError("Both 'co' and 'ci' as deterministic terms given. " + "Please choose one of the two.") y_lag1_stack = [y_lag1] if "ci" in deterministic: # pp. 257, 299, 306, 307 y_lag1_stack.append(np.ones(T)) if "li" in deterministic: # p. 299 y_lag1_stack.append(_linear_trend(T, p, coint=True)) if exog_coint is not None: y_lag1_stack.append(exog_coint[-T-1:-1].T) y_lag1 = np.row_stack(y_lag1_stack) # p. 286: delta_x = np.zeros((diff_lags*K, T)) if diff_lags > 0: for j in range(delta_x.shape[1]): delta_x[:, j] = (delta_y[:, j+p-2:None if j-1 < 0 else j-1:-1] .T.reshape(K*(p-1))) delta_x_stack = [delta_x] # p. 299, p. 303: if "co" in deterministic: delta_x_stack.append(np.ones(T)) if seasons > 0: delta_x_stack.append(seasonal_dummies(seasons, delta_x.shape[1], first_period=first_season + diff_lags + 1, centered=True).T) if "lo" in deterministic: delta_x_stack.append(_linear_trend(T, p)) if exog is not None: delta_x_stack.append(exog[-T:].T) delta_x = np.row_stack(delta_x_stack) return y_1_T, delta_y_1_T, y_lag1, delta_x def _r_matrices(delta_y_1_T, y_lag1, delta_x): """Returns two ndarrays needed for parameter estimation as well as the calculation of standard errors. Parameters ---------- delta_y_1_T : ndarray (neqs x nobs) The first differences of endog. `.. math:: (y_1, \\ldots, y_T) - (y_0, \\ldots, y_{T-1}) y_lag1 : ndarray (neqs x nobs) (dimensions assuming no deterministic terms are given) Endog of the previous period (lag 1). `.. math:: (y_0, \\ldots, y_{T-1}) delta_x : ndarray (k_ar_diff*neqs x nobs) (dimensions assuming no deterministic terms are given) Lagged differenced endog, used as regressor for the short term equation. Returns ------- result : tuple A tuple of two ndarrays. (See p. 292 in [1]_ for the definition of R_0 and R_1.) References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. """ # todo: rewrite m such that a big (TxT) matrix is avoided nobs = y_lag1.shape[1] m = np.identity(nobs) - ( delta_x.T.dot(inv(delta_x.dot(delta_x.T))).dot(delta_x)) # p. 291 r0 = delta_y_1_T.dot(m) # p. 292 r1 = y_lag1.dot(m) return r0, r1 def _sij(delta_x, delta_y_1_T, y_lag1): """Returns matrices and eigenvalues and -vectors used for parameter estimation and the calculation of a models loglikelihood. Parameters ---------- delta_x : ndarray (k_ar_diff*neqs x nobs) (dimensions assuming no deterministic terms are given) delta_y_1_T : ndarray (neqs x nobs) :math:`(y_1, \\ldots, y_T) - (y_0, \\ldots, y_{T-1})` y_lag1 : ndarray (neqs x nobs) (dimensions assuming no deterministic terms are given) :math:`(y_0, \\ldots, y_{T-1})` Returns ------- result : tuple A tuple of five ndarrays as well as eigenvalues and -vectors of a certain (matrix) product of some of the returned ndarrays. (See pp. 294-295 in [1]_ for more information on :math:`S_0, S_1, \\lambda_i, \\v_i` for :math:`i \\in \\{1, \\dots, K\\}`.) References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. """ nobs = y_lag1.shape[1] r0, r1 = _r_matrices(delta_y_1_T, y_lag1, delta_x) s00 = np.dot(r0, r0.T) / nobs s01 = np.dot(r0, r1.T) / nobs s10 = s01.T s11 = np.dot(r1, r1.T) / nobs s11_ = inv(_mat_sqrt(s11)) # p. 295: s01_s11_ = np.dot(s01, s11_) eig = np.linalg.eig(s01_s11_.T @ inv(s00) @ s01_s11_) lambd = eig[0] v = eig[1] # reorder eig_vals to make them decreasing (and order eig_vecs accordingly) lambd_order = np.argsort(lambd)[::-1] lambd = lambd[lambd_order] v = v[:, lambd_order] return s00, s01, s10, s11, s11_, lambd, v class CointRankResults: """A class for holding the results from testing the cointegration rank. Parameters ---------- rank : int (0 <= `rank` <= `neqs`) The rank to choose according to the Johansen cointegration rank test. neqs : int Number of variables in the time series. test_stats : array_like (`rank` + 1 if `rank` < `neqs` else `rank`) A one-dimensional array-like object containing the test statistics of the conducted tests. crit_vals : array_like (`rank` +1 if `rank` < `neqs` else `rank`) A one-dimensional array-like object containing the critical values corresponding to the entries in the `test_stats` argument. method : str, {``"trace"``, ``"maxeig"``}, default: ``"trace"`` If ``"trace"``, the trace test statistic is used. If ``"maxeig"``, the maximum eigenvalue test statistic is used. signif : float, {0.1, 0.05, 0.01}, default: 0.05 The test's significance level. """ def __init__(self, rank, neqs, test_stats, crit_vals, method="trace", signif=0.05): self.rank = rank self.neqs = neqs self.r_1 = [neqs if method == "trace" else i+1 for i in range(min(rank+1, neqs))] self.test_stats = test_stats self.crit_vals = crit_vals self.method = method self.signif = signif def summary(self): headers = ["r_0", "r_1", "test statistic", "critical value"] title = "Johansen cointegration test using " + \ ("trace" if self.method == "trace" else "maximum eigenvalue") + \ " test statistic with {:.0%}".format(self.signif) + \ " significance level" num_tests = min(self.rank, self.neqs-1) data = [[i, self.r_1[i], self.test_stats[i], self.crit_vals[i]] for i in range(num_tests + 1)] data_fmt = {"data_fmts": ["%s", "%s", "%#0.4g", "%#0.4g"], "data_aligns": "r"} html_data_fmt = dict(data_fmt) html_data_fmt["data_fmts"] = ["" + i + "" for i in html_data_fmt["data_fmts"]] return SimpleTable(data=data, headers=headers, title=title, txt_fmt=data_fmt, html_fmt=html_data_fmt, ltx_fmt=data_fmt) def __str__(self): return self.summary().as_text() def select_coint_rank(endog, det_order, k_ar_diff, method="trace", signif=0.05): """Calculate the cointegration rank of a VECM. Parameters ---------- endog : array_like (nobs_tot x neqs) The data with presample. det_order : int * -1 - no deterministic terms * 0 - constant term * 1 - linear trend k_ar_diff : int, nonnegative Number of lagged differences in the model. method : str, {``"trace"``, ``"maxeig"``}, default: ``"trace"`` If ``"trace"``, the trace test statistic is used. If ``"maxeig"``, the maximum eigenvalue test statistic is used. signif : float, {0.1, 0.05, 0.01}, default: 0.05 The test's significance level. Returns ------- rank : :class:`CointRankResults` A :class:`CointRankResults` object containing the cointegration rank suggested by the test and allowing a summary to be printed. """ if method not in ["trace", "maxeig"]: raise ValueError("The method argument has to be either 'trace' or" "'maximum eigenvalue'.") if det_order not in [-1, 0, 1]: if type(det_order) == int and det_order > 1: raise ValueError("A det_order greather than 1 is not supported." "Use a value of -1, 0, or 1.") else: raise ValueError("det_order must be -1, 0, or 1.") possible_signif_values = [0.1, 0.05, 0.01] if signif not in possible_signif_values: raise ValueError("Please choose a significance level from {0.1, 0.05," "0.01}") coint_result = coint_johansen(endog, det_order, k_ar_diff) test_stat = coint_result.lr1 if method == "trace" else coint_result.lr2 crit_vals = coint_result.cvt if method == "trace" else coint_result.cvm signif_index = possible_signif_values.index(signif) neqs = endog.shape[1] r_0 = 0 # rank in null hypothesis while r_0 < neqs: if test_stat[r_0] < crit_vals[r_0, signif_index]: break # we accept current rank else: r_0 += 1 # we reject current rank and test next possible rank return CointRankResults(r_0, neqs, test_stat[:r_0 + 1], crit_vals[:r_0 + 1, signif_index], method, signif) def coint_johansen(endog, det_order, k_ar_diff): """ Johansen cointegration test of the cointegration rank of a VECM Parameters ---------- endog : array_like (nobs_tot x neqs) Data to test det_order : int * -1 - no deterministic terms * 0 - constant term * 1 - linear trend k_ar_diff : int, nonnegative Number of lagged differences in the model. Returns ------- result : JohansenTestResult An object containing the test's results. The most important attributes of the result class are: * trace_stat and trace_stat_crit_vals * max_eig_stat and max_eig_stat_crit_vals Notes ----- The implementation might change to make more use of the existing VECM framework. See Also -------- statsmodels.tsa.vector_ar.vecm.select_coint_rank References ---------- .. [1] Lütkepohl, H. 2005. New Introduction to Multiple Time Series Analysis. Springer. """ import warnings if det_order not in [-1, 0, 1]: warnings.warn("Critical values are only available for a det_order of " "-1, 0, or 1.", category=HypothesisTestWarning) if endog.shape[1] > 12: # todo: test with a time series of 13 variables warnings.warn("Critical values are only available for time series " "with 12 variables at most.", category=HypothesisTestWarning) from statsmodels.regression.linear_model import OLS def detrend(y, order): if order == -1: return y return OLS(y, np.vander(np.linspace(-1, 1, len(y)), order+1)).fit().resid def resid(y, x): if x.size == 0: return y r = y - np.dot(x, np.dot(np.linalg.pinv(x), y)) return r endog = np.asarray(endog) nobs, neqs = endog.shape # why this? f is detrend transformed series, det_order is detrend data if det_order > -1: f = 0 else: f = det_order endog = detrend(endog, det_order) dx = np.diff(endog, 1, axis=0) z = lagmat(dx, k_ar_diff) z = z[k_ar_diff:] z = detrend(z, f) dx = dx[k_ar_diff:] dx = detrend(dx, f) r0t = resid(dx, z) # GH 5731, [:-0] does not work, need [:t-0] lx = endog[:(endog.shape[0]-k_ar_diff)] lx = lx[1:] dx = detrend(lx, f) rkt = resid(dx, z) # level on lagged diffs # Level covariance after filtering k_ar_diff skk = np.dot(rkt.T, rkt) / rkt.shape[0] # Covariacne between filtered and unfiltered sk0 = np.dot(rkt.T, r0t) / rkt.shape[0] s00 = np.dot(r0t.T, r0t) / r0t.shape[0] sig = np.dot(sk0, np.dot(inv(s00), sk0.T)) tmp = inv(skk) au, du = np.linalg.eig(np.dot(tmp, sig)) # au is eval, du is evec temp = inv(np.linalg.cholesky(np.dot(du.T, np.dot(skk, du)))) dt = np.dot(du, temp) # JP: the next part can be done much easier auind = np.argsort(au) aind = np.flipud(auind) a = au[aind] d = dt[:, aind] # Normalize by first non-zero element of d, usually [0, 0] # GH 5517 non_zero_d = d.flat != 0 if np.any(non_zero_d): d *= np.sign(d.flat[non_zero_d][0]) # Compute the trace and max eigenvalue statistics lr1 = np.zeros(neqs) lr2 = np.zeros(neqs) cvm = np.zeros((neqs, 3)) cvt = np.zeros((neqs, 3)) iota = np.ones(neqs) t, junk = rkt.shape for i in range(0, neqs): tmp = np.log(iota - a)[i:] lr1[i] = -t * np.sum(tmp, 0) lr2[i] = -t * np.log(1-a[i]) cvm[i, :] = c_sja(neqs - i, det_order) cvt[i, :] = c_sjt(neqs - i, det_order) aind[i] = i return JohansenTestResult(rkt, r0t, a, d, lr1, lr2, cvt, cvm, aind) class JohansenTestResult(object): """ Results class for Johansen's cointegration test Notes ----- See p. 292 in [1]_ for r0t and rkt References ---------- .. [1] Lütkepohl, H. 2005. New Introduction to Multiple Time Series Analysis. Springer. """ def __init__(self, rkt, r0t, eig, evec, lr1, lr2, cvt, cvm, ind): self._meth = 'johansen' self._rkt = rkt self._r0t = r0t self._eig = eig self._evec = evec self._lr1 = lr1 self._lr2 = lr2 self._cvt = cvt self._cvm = cvm self._ind = ind @property def rkt(self): """Residuals for :math:`Y_{-1}`""" return self._rkt @property def r0t(self): """Residuals for :math:`\\Delta Y`.""" return self._r0t @property def eig(self): """Eigenvalues of VECM coefficient matrix""" return self._eig @property def evec(self): """Eigenvectors of VECM coefficient matrix""" return self._evec @property def trace_stat(self): """Trace statistic""" return self._lr1 @property def lr1(self): """Trace statistic""" return self._lr1 @property def max_eig_stat(self): """Maximum eigenvalue statistic""" return self._lr2 @property def lr2(self): """Maximum eigenvalue statistic""" return self._lr2 @property def trace_stat_crit_vals(self): """Critical values (90%, 95%, 99%) of trace statistic""" return self._cvt @property def cvt(self): """Critical values (90%, 95%, 99%) of trace statistic""" return self._cvt @property def cvm(self): """Critical values (90%, 95%, 99%) of maximum eigenvalue statistic.""" return self._cvm @property def max_eig_stat_crit_vals(self): """Critical values (90%, 95%, 99%) of maximum eigenvalue statistic.""" return self._cvm @property def ind(self): """Order of eigenvalues""" return self._ind @property def meth(self): """Test method""" return self._meth class VECM(tsbase.TimeSeriesModel): """ Class representing a Vector Error Correction Model (VECM). A VECM(:math:`k_{ar}-1`) has the following form .. math:: \\Delta y_t = \\Pi y_{t-1} + \\Gamma_1 \\Delta y_{t-1} + \\ldots + \\Gamma_{k_{ar}-1} \\Delta y_{t-k_{ar}+1} + u_t where .. math:: \\Pi = \\alpha \\beta' as described in chapter 7 of [1]_. Parameters ---------- endog : array_like (nobs_tot x neqs) 2-d endogenous response variable. exog : ndarray (nobs_tot x neqs) or None Deterministic terms outside the cointegration relation. exog_coint : ndarray (nobs_tot x neqs) or None Deterministic terms inside the cointegration relation. dates : array_like of datetime, optional See :class:`statsmodels.tsa.base.tsa_model.TimeSeriesModel` for more information. freq : str, optional See :class:`statsmodels.tsa.base.tsa_model.TimeSeriesModel` for more information. missing : str, optional See :class:`statsmodels.base.model.Model` for more information. k_ar_diff : int Number of lagged differences in the model. Equals :math:`k_{ar} - 1` in the formula above. coint_rank : int Cointegration rank, equals the rank of the matrix :math:`\\Pi` and the number of columns of :math:`\\alpha` and :math:`\\beta`. deterministic : str {``"nc"``, ``"co"``, ``"ci"``, ``"lo"``, ``"li"``} * ``"nc"`` - no deterministic terms * ``"co"`` - constant outside the cointegration relation * ``"ci"`` - constant within the cointegration relation * ``"lo"`` - linear trend outside the cointegration relation * ``"li"`` - linear trend within the cointegration relation Combinations of these are possible (e.g. ``"cili"`` or ``"colo"`` for linear trend with intercept). When using a constant term you have to choose whether you want to restrict it to the cointegration relation (i.e. ``"ci"``) or leave it unrestricted (i.e. ``"co"``). Do not use both ``"ci"`` and ``"co"``. The same applies for ``"li"`` and ``"lo"`` when using a linear term. See the Notes-section for more information. seasons : int, default: 0 Number of periods in a seasonal cycle. 0 means no seasons. first_season : int, default: 0 Season of the first observation. Notes ----- A VECM(:math:`k_{ar} - 1`) with deterministic terms has the form .. math:: \\Delta y_t = \\alpha \\begin{pmatrix}\\beta' & \\eta'\\end{pmatrix} \\begin{pmatrix}y_{t-1}\\\\D^{co}_{t-1}\\end{pmatrix} + \\Gamma_1 \\Delta y_{t-1} + \\dots + \\Gamma_{k_{ar}-1} \\Delta y_{t-k_{ar}+1} + C D_t + u_t. In :math:`D^{co}_{t-1}` we have the deterministic terms which are inside the cointegration relation (or restricted to the cointegration relation). :math:`\\eta` is the corresponding estimator. To pass a deterministic term inside the cointegration relation, we can use the `exog_coint` argument. For the two special cases of an intercept and a linear trend there exists a simpler way to declare these terms: we can pass ``"ci"`` and ``"li"`` respectively to the `deterministic` argument. So for an intercept inside the cointegration relation we can either pass ``"ci"`` as `deterministic` or `np.ones(len(data))` as `exog_coint` if `data` is passed as the `endog` argument. This ensures that :math:`D_{t-1}^{co} = 1` for all :math:`t`. We can also use deterministic terms outside the cointegration relation. These are defined in :math:`D_t` in the formula above with the corresponding estimators in the matrix :math:`C`. We specify such terms by passing them to the `exog` argument. For an intercept and/or linear trend we again have the possibility to use `deterministic` alternatively. For an intercept we pass ``"co"`` and for a linear trend we pass ``"lo"`` where the `o` stands for `outside`. The following table shows the five cases considered in [2]_. The last column indicates which string to pass to the `deterministic` argument for each of these cases. ==== =============================== =================================== ============= Case Intercept Slope of the linear trend `deterministic` ==== =============================== =================================== ============= I 0 0 ``"nc"`` II :math:`- \\alpha \\beta^T \\mu` 0 ``"ci"`` III :math:`\\neq 0` 0 ``"co"`` IV :math:`\\neq 0` :math:`- \\alpha \\beta^T \\gamma` ``"coli"`` V :math:`\\neq 0` :math:`\\neq 0` ``"colo"`` ==== =============================== =================================== ============= References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. .. [2] Johansen, S. 1995. *Likelihood-Based Inference in Cointegrated * *Vector Autoregressive Models*. Oxford University Press. """ def __init__(self, endog, exog=None, exog_coint=None, dates=None, freq=None, missing="none", k_ar_diff=1, coint_rank=1, deterministic="nc", seasons=0, first_season=0): super(VECM, self).__init__(endog, exog, dates, freq, missing=missing) if exog_coint is not None and \ not exog_coint.shape[0] == endog.shape[0]: raise ValueError("exog_coint must have as many rows as enodg_tot!") if self.endog.ndim == 1: raise ValueError("Only gave one variable to VECM") self.y = self.endog.T self.exog_coint = exog_coint self.neqs = self.endog.shape[1] self.k_ar = k_ar_diff + 1 self.k_ar_diff = k_ar_diff self.coint_rank = coint_rank self.deterministic = deterministic self.seasons = seasons self.first_season = first_season self.load_coef_repr = "ec" # name for loading coef. (alpha) in summary def fit(self, method="ml"): """ Estimates the parameters of a VECM. The estimation procedure is described on pp. 269-304 in [1]_. Parameters ---------- method : str {"ml"}, default: "ml" Estimation method to use. "ml" stands for Maximum Likelihood. Returns ------- est : :class:`VECMResults` References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. """ if method == "ml": return self._estimate_vecm_ml() else: raise ValueError("%s not recognized, must be among %s" % (method, "ml")) def _estimate_vecm_ml(self): y_1_T, delta_y_1_T, y_lag1, delta_x = _endog_matrices( self.y, self.exog, self.exog_coint, self.k_ar_diff, self.deterministic, self.seasons, self.first_season) T = y_1_T.shape[1] s00, s01, s10, s11, s11_, _, v = _sij(delta_x, delta_y_1_T, y_lag1) beta_tilde = (v[:, :self.coint_rank].T.dot(s11_)).T beta_tilde = np.real_if_close(beta_tilde) # normalize beta tilde such that eye(r) forms the first r rows of it: beta_tilde = np.dot(beta_tilde, inv(beta_tilde[:self.coint_rank])) alpha_tilde = s01.dot(beta_tilde).dot( inv(beta_tilde.T.dot(s11).dot(beta_tilde))) gamma_tilde = (delta_y_1_T - alpha_tilde.dot(beta_tilde.T).dot(y_lag1) ).dot(delta_x.T).dot(inv(np.dot(delta_x, delta_x.T))) temp = (delta_y_1_T - alpha_tilde.dot(beta_tilde.T).dot(y_lag1) - gamma_tilde.dot(delta_x)) sigma_u_tilde = temp.dot(temp.T) / T return VECMResults(self.y, self.exog, self.exog_coint, self.k_ar, self.coint_rank, alpha_tilde, beta_tilde, gamma_tilde, sigma_u_tilde, deterministic=self.deterministic, seasons=self.seasons, delta_y_1_T=delta_y_1_T, y_lag1=y_lag1, delta_x=delta_x, model=self, names=self.endog_names, dates=self.data.dates, first_season=self.first_season) @property def _lagged_param_names(self): """ Returns parameter names (for Gamma and deterministics) for the summary. Returns ------- param_names : list of str Returns a list of parameter names for the lagged endogenous parameters which are called :math:`\\Gamma` in [1]_ (see chapter 6). If present in the model, also names for deterministic terms outside the cointegration relation are returned. They name the elements of the matrix C in [1]_ (p. 299). References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. """ param_names = [] # 1. Deterministic terms outside cointegration relation if "co" in self.deterministic: param_names += ["const.%s" % n for n in self.endog_names] if self.seasons > 0: param_names += ["season%d.%s" % (s, n) for s in range(1, self.seasons) for n in self.endog_names] if "lo" in self.deterministic: param_names += ["lin_trend.%s" % n for n in self.endog_names] if self.exog is not None: param_names += ["exog%d.%s" % (exog_no, n) for exog_no in range(1, self.exog.shape[1] + 1) for n in self.endog_names] # 2. lagged endogenous terms param_names += [ "L%d.%s.%s" % (i+1, n1, n2) for n2 in self.endog_names for i in range(self.k_ar_diff) for n1 in self.endog_names] return param_names @property def _load_coef_param_names(self): """ Returns parameter names (for alpha) for the summary. Returns ------- param_names : list of str Returns a list of parameter names for the loading coefficients which are called :math:`\\alpha` in [1]_ (see chapter 6). References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. """ param_names = [] if self.coint_rank == 0: return None # loading coefficients (alpha) # called "ec" in JMulTi, "ECT" in tsDyn, param_names += [ # and "_ce" in Stata self.load_coef_repr + "%d.%s" % (i+1, self.endog_names[j]) for j in range(self.neqs) for i in range(self.coint_rank) ] return param_names @property def _coint_param_names(self): """ Returns parameter names (for beta and deterministics) for the summary. Returns ------- param_names : list of str Returns a list of parameter names for the cointegration matrix as well as deterministic terms inside the cointegration relation (if present in the model). """ # 1. cointegration matrix/vector param_names = [] param_names += [("beta.%d." + self.load_coef_repr + "%d") % (j+1, i+1) for i in range(self.coint_rank) for j in range(self.neqs)] # 2. deterministic terms inside cointegration relation if "ci" in self.deterministic: param_names += ["const." + self.load_coef_repr + "%d" % (i+1) for i in range(self.coint_rank)] if "li" in self.deterministic: param_names += ["lin_trend." + self.load_coef_repr + "%d" % (i+1) for i in range(self.coint_rank)] if self.exog_coint is not None: param_names += ["exog_coint%d.%s" % (n+1, exog_no) for exog_no in range(1, self.exog_coint.shape[1]+1) for n in range(self.neqs)] return param_names class VECMResults(object): """Class for holding estimation related results of a vector error correction model (VECM). Parameters ---------- endog : ndarray (neqs x nobs_tot) Array of observations. exog : ndarray (nobs_tot x neqs) or `None` Deterministic terms outside the cointegration relation. exog_coint : ndarray (nobs_tot x neqs) or `None` Deterministic terms inside the cointegration relation. k_ar : int, >= 1 Lags in the VAR representation. This implies that the number of lags in the VEC representation (=lagged differences) equals :math:`k_{ar} - 1`. coint_rank : int, 0 <= `coint_rank` <= neqs Cointegration rank, equals the rank of the matrix :math:`\\Pi` and the number of columns of :math:`\\alpha` and :math:`\\beta`. alpha : ndarray (neqs x `coint_rank`) Estimate for the parameter :math:`\\alpha` of a VECM. beta : ndarray (neqs x `coint_rank`) Estimate for the parameter :math:`\\beta` of a VECM. gamma : ndarray (neqs x neqs*(k_ar-1)) Array containing the estimates of the :math:`k_{ar}-1` parameter matrices :math:`\\Gamma_1, \\dots, \\Gamma_{k_{ar}-1}` of a VECM(:math:`k_{ar}-1`). The submatrices are stacked horizontally from left to right. sigma_u : ndarray (neqs x neqs) Estimate of white noise process covariance matrix :math:`\\Sigma_u`. deterministic : str {``"nc"``, ``"co"``, ``"ci"``, ``"lo"``, ``"li"``} * ``"nc"`` - no deterministic terms * ``"co"`` - constant outside the cointegration relation * ``"ci"`` - constant within the cointegration relation * ``"lo"`` - linear trend outside the cointegration relation * ``"li"`` - linear trend within the cointegration relation Combinations of these are possible (e.g. ``"cili"`` or ``"colo"`` for linear trend with intercept). See the docstring of the :class:`VECM`-class for more information. seasons : int, default: 0 Number of periods in a seasonal cycle. 0 means no seasons. first_season : int, default: 0 Season of the first observation. delta_y_1_T : ndarray or `None`, default: `None` Auxiliary array for internal computations. It will be calculated if not given as parameter. y_lag1 : ndarray or `None`, default: `None` Auxiliary array for internal computations. It will be calculated if not given as parameter. delta_x : ndarray or `None`, default: `None` Auxiliary array for internal computations. It will be calculated if not given as parameter. model : :class:`VECM` An instance of the :class:`VECM`-class. names : list of str Each str in the list represents the name of a variable of the time series. dates : array_like For example a DatetimeIndex of length nobs_tot. Attributes ---------- nobs : int Number of observations (excluding the presample). model : see Parameters y_all : see `endog` in Parameters exog : see Parameters exog_coint : see Parameters names : see Parameters dates : see Parameters neqs : int Number of variables in the time series. k_ar : see Parameters deterministic : see Parameters seasons : see Parameters first_season : see Parameters alpha : see Parameters beta : see Parameters gamma : see Parameters sigma_u : see Parameters det_coef_coint : ndarray (#(determinist. terms inside the coint. rel.) x `coint_rank`) Estimated coefficients for the all deterministic terms inside the cointegration relation. const_coint : ndarray (1 x `coint_rank`) If there is a constant deterministic term inside the cointegration relation, then `const_coint` is the first row of `det_coef_coint`. Otherwise it's an ndarray of zeros. lin_trend_coint : ndarray (1 x `coint_rank`) If there is a linear deterministic term inside the cointegration relation, then `lin_trend_coint` contains the corresponding estimated coefficients. As such it represents the corresponding row of `det_coef_coint`. If there is no linear deterministic term inside the cointegration relation, then `lin_trend_coint` is an ndarray of zeros. exog_coint_coefs : ndarray (exog_coint.shape[1] x `coint_rank`) or `None` If deterministic terms inside the cointegration relation are passed via the `exog_coint` parameter, then `exog_coint_coefs` contains the corresponding estimated coefficients. As such `exog_coint_coefs` represents the last rows of `det_coef_coint`. If no deterministic terms were passed via the `exog_coint` parameter, this attribute is `None`. det_coef : ndarray (neqs x #(deterministic terms outside the coint. rel.)) Estimated coefficients for the all deterministic terms outside the cointegration relation. const : ndarray (neqs x 1) or (neqs x 0) If a constant deterministic term outside the cointegration is specified within the deterministic parameter, then `const` is the first column of `det_coef_coint`. Otherwise it's an ndarray of size zero. seasonal : ndarray (neqs x seasons) If the `seasons` parameter is > 0, then seasonal contains the estimated coefficients corresponding to the seasonal terms. Otherwise it's an ndarray of size zero. lin_trend : ndarray (neqs x 1) or (neqs x 0) If a linear deterministic term outside the cointegration is specified within the deterministic parameter, then `lin_trend` contains the corresponding estimated coefficients. As such it represents the corresponding column of `det_coef_coint`. If there is no linear deterministic term outside the cointegration relation, then `lin_trend` is an ndarray of size zero. exog_coefs : ndarray (neqs x exog_coefs.shape[1]) If deterministic terms outside the cointegration relation are passed via the `exog` parameter, then `exog_coefs` contains the corresponding estimated coefficients. As such `exog_coefs` represents the last columns of `det_coef`. If no deterministic terms were passed via the `exog` parameter, this attribute is an ndarray of size zero. _delta_y_1_T : see delta_y_1_T in Parameters _y_lag1 : see y_lag1 in Parameters _delta_x : see delta_x in Parameters coint_rank : int Cointegration rank, equals the rank of the matrix :math:`\\Pi` and the number of columns of :math:`\\alpha` and :math:`\\beta`. llf : float The model's log-likelihood. cov_params : ndarray (d x d) Covariance matrix of the parameters. The number of rows and columns, d (used in the dimension specification of this argument), is equal to neqs * (neqs+num_det_coef_coint + neqs*(k_ar-1)+number of deterministic dummy variables outside the cointegration relation). For the case with no deterministic terms this matrix is defined on p. 287 in [1]_ as :math:`\\Sigma_{co}` and its relationship to the ML-estimators can be seen in eq. (7.2.21) on p. 296 in [1]_. cov_params_wo_det : ndarray Covariance matrix of the parameters :math:`\\tilde{\\Pi}, \\tilde{\\Gamma}` where :math:`\\tilde{\\Pi} = \\tilde{\\alpha} \\tilde{\\beta'}`. Equals `cov_params` without the rows and columns related to deterministic terms. This matrix is defined as :math:`\\Sigma_{co}` on p. 287 in [1]_. stderr_params : ndarray (d) Array containing the standard errors of :math:`\\Pi`, :math:`\\Gamma`, and estimated parameters related to deterministic terms. stderr_coint : ndarray (neqs+num_det_coef_coint x `coint_rank`) Array containing the standard errors of :math:`\\beta` and estimated parameters related to deterministic terms inside the cointegration relation. stderr_alpha : ndarray (neqs x `coint_rank`) The standard errors of :math:`\\alpha`. stderr_beta : ndarray (neqs x `coint_rank`) The standard errors of :math:`\\beta`. stderr_det_coef_coint : ndarray (num_det_coef_coint x `coint_rank`) The standard errors of estimated the parameters related to deterministic terms inside the cointegration relation. stderr_gamma : ndarray (neqs x neqs*(k_ar-1)) The standard errors of :math:`\\Gamma_1, \\ldots, \\Gamma_{k_{ar}-1}`. stderr_det_coef : ndarray (neqs x det. terms outside the coint. relation) The standard errors of estimated the parameters related to deterministic terms outside the cointegration relation. tvalues_alpha : ndarray (neqs x `coint_rank`) tvalues_beta : ndarray (neqs x `coint_rank`) tvalues_det_coef_coint : ndarray (num_det_coef_coint x `coint_rank`) tvalues_gamma : ndarray (neqs x neqs*(k_ar-1)) tvalues_det_coef : ndarray (neqs x det. terms outside the coint. relation) pvalues_alpha : ndarray (neqs x `coint_rank`) pvalues_beta : ndarray (neqs x `coint_rank`) pvalues_det_coef_coint : ndarray (num_det_coef_coint x `coint_rank`) pvalues_gamma : ndarray (neqs x neqs*(k_ar-1)) pvalues_det_coef : ndarray (neqs x det. terms outside the coint. relation) var_rep : (k_ar x neqs x neqs) KxK parameter matrices :math:`A_i` of the corresponding VAR representation. If the return value is assigned to a variable ``A``, these matrices can be accessed via ``A[i]`` for :math:`i=0, \\ldots, k_{ar}-1`. cov_var_repr : ndarray (neqs**2 * k_ar x neqs**2 * k_ar) This matrix is called :math:`\\Sigma^{co}_{\\alpha}` on p. 289 in [1]_. It is needed e.g. for impulse-response-analysis. fittedvalues : ndarray (nobs x neqs) The predicted in-sample values of the models' endogenous variables. resid : ndarray (nobs x neqs) The residuals. References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. """ def __init__(self, endog, exog, exog_coint, k_ar, coint_rank, alpha, beta, gamma, sigma_u, deterministic='nc', seasons=0, first_season=0, delta_y_1_T=None, y_lag1=None, delta_x=None, model=None, names=None, dates=None): self.model = model self.y_all = endog self.exog = exog self.exog_coint = exog_coint self.names = names self.dates = dates self.neqs = endog.shape[0] self.k_ar = k_ar self.deterministic = deterministic self.seasons = seasons self.first_season = first_season self.coint_rank = coint_rank if alpha.dtype == np.complex128 and np.all(np.imag(alpha) == 0): alpha = np.real_if_close(alpha) if beta.dtype == np.complex128 and np.all(np.imag(beta) == 0): beta = np.real_if_close(beta) if gamma.dtype == np.complex128 and np.all(np.imag(gamma) == 0): gamma = np.real_if_close(gamma) self.alpha = alpha self.beta, self.det_coef_coint = np.vsplit(beta, [self.neqs]) self.gamma, self.det_coef = np.hsplit(gamma, [self.neqs * (self.k_ar - 1)]) if "ci" in deterministic: self.const_coint = self.det_coef_coint[:1, :] else: self.const_coint = np.zeros(coint_rank).reshape((1, -1)) if "li" in deterministic: start = 1 if "ci" in deterministic else 0 self.lin_trend_coint = self.det_coef_coint[start:start+1, :] else: self.lin_trend_coint = np.zeros(coint_rank).reshape(1, -1) if self.exog_coint is not None: start = ("ci" in deterministic) + ("li" in deterministic) self.exog_coint_coefs = self.det_coef_coint[start:, :] else: self.exog_coint_coefs = None split_const_season = 1 if "co" in deterministic else 0 split_season_lin = split_const_season + ((seasons-1) if seasons else 0) if "lo" in deterministic: split_lin_exog = split_season_lin + 1 else: split_lin_exog = split_season_lin self.const, self.seasonal, self.lin_trend, self.exog_coefs = \ np.hsplit(self.det_coef, [split_const_season, split_season_lin, split_lin_exog]) self.sigma_u = sigma_u if y_lag1 is not None and delta_x is not None \ and delta_y_1_T is not None: self._delta_y_1_T = delta_y_1_T self._y_lag1 = y_lag1 self._delta_x = delta_x else: _y_1_T, self._delta_y_1_T, self._y_lag1, self._delta_x = \ _endog_matrices(endog, self.exog, k_ar, deterministic, seasons) self.nobs = self._y_lag1.shape[1] @cache_readonly def llf(self): # Lutkepohl p. 295 (7.2.20) """ Compute the VECM's loglikelihood. """ K = self.neqs T = self.nobs r = self.coint_rank s00, _, _, _, _, lambd, _ = _sij(self._delta_x, self._delta_y_1_T, self._y_lag1) return - K * T * np.log(2*np.pi) / 2 \ - T * (np.log(np.linalg.det(s00)) + sum(np.log(1-lambd)[:r])) / 2 \ - K * T / 2 @cache_readonly def _cov_sigma(self): sigma_u = self.sigma_u d = duplication_matrix(self.neqs) d_K_plus = np.linalg.pinv(d) # compare p. 93, 297 Lutkepohl (2005) return 2 * (d_K_plus @ np.kron(sigma_u, sigma_u) @ d_K_plus.T) @cache_readonly def cov_params_default(self): # p.296 (7.2.21) # Sigma_co described on p. 287 beta = self.beta if self.det_coef_coint.size > 0: beta = vstack((beta, self.det_coef_coint)) dt = self.deterministic num_det = ("co" in dt) + ("lo" in dt) num_det += (self.seasons-1) if self.seasons else 0 if self.exog is not None: num_det += self.exog.shape[1] b_id = scipy.linalg.block_diag(beta, np.identity(self.neqs * (self.k_ar-1) + num_det)) y_lag1 = self._y_lag1 b_y = beta.T.dot(y_lag1) omega11 = b_y.dot(b_y.T) omega12 = b_y.dot(self._delta_x.T) omega21 = omega12.T omega22 = self._delta_x.dot(self._delta_x.T) omega = np.bmat([[omega11, omega12], [omega21, omega22]]).A mat1 = b_id.dot(inv(omega)).dot(b_id.T) return np.kron(mat1, self.sigma_u) @cache_readonly def cov_params_wo_det(self): # rows & cols to be dropped (related to deterministic terms inside the # cointegration relation) start_i = self.neqs**2 # first elements belong to alpha @ beta.T end_i = start_i + self.neqs * self.det_coef_coint.shape[0] to_drop_i = np.arange(start_i, end_i) # rows & cols to be dropped (related to deterministic terms outside of # the cointegration relation) cov = self.cov_params_default cov_size = len(cov) to_drop_o = np.arange(cov_size-self.det_coef.size, cov_size) to_drop = np.union1d(to_drop_i, to_drop_o) mask = np.ones(cov.shape, dtype=bool) mask[to_drop] = False mask[:, to_drop] = False cov_size_new = mask.sum(axis=0)[0] return cov[mask].reshape((cov_size_new, cov_size_new)) # standard errors: @cache_readonly def stderr_params(self): return np.sqrt(np.diag(self.cov_params_default)) @cache_readonly def stderr_coint(self): """ Standard errors of beta and deterministic terms inside the cointegration relation. Notes ----- See p. 297 in [1]_. Using the rule .. math:: vec(B R) = (B' \\otimes I) vec(R) for two matrices B and R which are compatible for multiplication. This is rule (3) on p. 662 in [1]_. References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. """ r = self.coint_rank _, r1 = _r_matrices(self._delta_y_1_T, self._y_lag1, self._delta_x) r12 = r1[r:] if r12.size == 0: return np.zeros((r, r)) mat1 = inv(r12.dot(r12.T)) mat1 = np.kron(mat1.T, np.identity(r)) det = self.det_coef_coint.shape[0] mat2 = np.kron(np.identity(self.neqs-r+det), inv(self.alpha.T @ inv(self.sigma_u) @ self.alpha)) first_rows = np.zeros((r, r)) last_rows_1d = np.sqrt(np.diag(mat1.dot(mat2))) last_rows = last_rows_1d.reshape((self.neqs-r+det, r), order="F") return vstack((first_rows, last_rows)) @cache_readonly def stderr_alpha(self): ret_1dim = self.stderr_params[:self.alpha.size] return ret_1dim.reshape(self.alpha.shape, order="F") @cache_readonly def stderr_beta(self): ret_1dim = self.stderr_coint[:self.beta.shape[0]] return ret_1dim.reshape(self.beta.shape, order="F") @cache_readonly def stderr_det_coef_coint(self): if self.det_coef_coint.size == 0: return self.det_coef_coint # 0-size array ret_1dim = self.stderr_coint[self.beta.shape[0]:] return ret_1dim.reshape(self.det_coef_coint.shape, order="F") @cache_readonly def stderr_gamma(self): start = self.alpha.shape[0] * (self.beta.shape[0] + self.det_coef_coint.shape[0]) ret_1dim = self.stderr_params[start:start+self.gamma.size] return ret_1dim.reshape(self.gamma.shape, order="F") @cache_readonly def stderr_det_coef(self): if self.det_coef.size == 0: return self.det_coef # 0-size array ret1_1dim = self.stderr_params[-self.det_coef.size:] return ret1_1dim.reshape(self.det_coef.shape, order="F") # t-values: @cache_readonly def tvalues_alpha(self): return self.alpha / self.stderr_alpha @cache_readonly def tvalues_beta(self): r = self.coint_rank first_rows = np.zeros((r, r)) last_rows = self.beta[r:] / self.stderr_beta[r:] return vstack((first_rows, last_rows)) @cache_readonly def tvalues_det_coef_coint(self): if self.det_coef_coint.size == 0: return self.det_coef_coint # 0-size array return self.det_coef_coint / self.stderr_det_coef_coint @cache_readonly def tvalues_gamma(self): return self.gamma / self.stderr_gamma @cache_readonly def tvalues_det_coef(self): if self.det_coef.size == 0: return self.det_coef # 0-size array return self.det_coef / self.stderr_det_coef # p-values: @cache_readonly def pvalues_alpha(self): return (1-scipy.stats.norm.cdf(abs(self.tvalues_alpha))) * 2 @cache_readonly def pvalues_beta(self): first_rows = np.zeros((self.coint_rank, self.coint_rank)) tval_last = self.tvalues_beta[self.coint_rank:] last_rows = (1-scipy.stats.norm.cdf(abs(tval_last))) * 2 # student-t return vstack((first_rows, last_rows)) @cache_readonly def pvalues_det_coef_coint(self): if self.det_coef_coint.size == 0: return self.det_coef_coint # 0-size array return (1-scipy.stats.norm.cdf(abs(self.tvalues_det_coef_coint))) * 2 @cache_readonly def pvalues_gamma(self): return (1-scipy.stats.norm.cdf(abs(self.tvalues_gamma))) * 2 @cache_readonly def pvalues_det_coef(self): if self.det_coef.size == 0: return self.det_coef # 0-size array return (1-scipy.stats.norm.cdf(abs(self.tvalues_det_coef))) * 2 # confidence intervals def _make_conf_int(self, est, stderr, alpha): struct_arr = np.zeros(est.shape, dtype=[("lower", float), ("upper", float)]) struct_arr["lower"] = est - scipy.stats.norm.ppf(1 - alpha/2) * stderr struct_arr["upper"] = est + scipy.stats.norm.ppf(1 - alpha/2) * stderr return struct_arr def conf_int_alpha(self, alpha=0.05): return self._make_conf_int(self.alpha, self.stderr_alpha, alpha) def conf_int_beta(self, alpha=0.05): return self._make_conf_int(self.beta, self.stderr_beta, alpha) def conf_int_det_coef_coint(self, alpha=0.05): return self._make_conf_int(self.det_coef_coint, self.stderr_det_coef_coint, alpha) def conf_int_gamma(self, alpha=0.05): return self._make_conf_int(self.gamma, self.stderr_gamma, alpha) def conf_int_det_coef(self, alpha=0.05): return self._make_conf_int(self.det_coef, self.stderr_det_coef, alpha) @cache_readonly def var_rep(self): pi = self.alpha.dot(self.beta.T) gamma = self.gamma K = self.neqs A = np.zeros((self.k_ar, K, K)) A[0] = pi + np.identity(K) if self.gamma.size > 0: A[0] += gamma[:, :K] A[self.k_ar-1] = - gamma[:, K*(self.k_ar-2):] for i in range(1, self.k_ar-1): A[i] = gamma[:, K*i:K*(i+1)] - gamma[:, K*(i-1):K*i] return A @cache_readonly def cov_var_repr(self): """ Gives the covariance matrix of the corresponding VAR-representation. More precisely, the covariance matrix of the vector consisting of the columns of the corresponding VAR coefficient matrices (i.e. vec(self.var_rep)). Returns ------- cov : array (neqs**2 * k_ar x neqs**2 * k_ar) """ # This implementation is using the fact that for a random variable x # with covariance matrix Sigma_x the following holds: # B @ x with B being a suitably sized matrix has the covariance matrix # B @ Sigma_x @ B.T. The arrays called vecm_var_transformation and # self.cov_params_wo_det in the code play the roles of B and Sigma_x # respectively. The elements of the random variable x are the elements # of the estimated matrices Pi (alpha @ beta.T) and Gamma. # Alternatively the following code (commented out) would yield the same # result (following p. 289 in Lutkepohl): # K, p = self.neqs, self.k_ar # w = np.identity(K * p) # w[np.arange(K, len(w)), np.arange(K, len(w))] *= (-1) # w[np.arange(K, len(w)), np.arange(len(w)-K)] = 1 # # w_eye = np.kron(w, np.identity(K)) # # return w_eye.T @ self.cov_params_default @ w_eye if self.k_ar - 1 == 0: return self.cov_params_wo_det vecm_var_transformation = np.zeros((self.neqs**2 * self.k_ar, self.neqs**2 * self.k_ar)) eye = np.identity(self.neqs**2) # for A_1: vecm_var_transformation[:self.neqs**2, :2*self.neqs**2] = hstack( (eye, eye)) # for A_i, where i = 2, ..., k_ar-1 for i in range(2, self.k_ar): start_row = self.neqs**2 + (i-2) * self.neqs**2 start_col = self.neqs**2 + (i-2) * self.neqs**2 vecm_var_transformation[start_row:start_row+self.neqs**2, start_col:start_col+2*self.neqs**2] = hstack((-eye, eye)) # for A_p: vecm_var_transformation[-self.neqs**2:, -self.neqs**2:] = -eye vvt = vecm_var_transformation return vvt @ self.cov_params_wo_det @ vvt.T def ma_rep(self, maxn=10): return ma_rep(self.var_rep, maxn) @cache_readonly def _chol_sigma_u(self): return np.linalg.cholesky(self.sigma_u) def orth_ma_rep(self, maxn=10, P=None): """Compute orthogonalized MA coefficient matrices. For this purpose a matrix P is used which fulfills :math:`\\Sigma_u = PP^\\prime`. P defaults to the Cholesky decomposition of :math:`\\Sigma_u` Parameters ---------- maxn : int Number of coefficient matrices to compute P : ndarray (neqs x neqs), optional Matrix such that :math:`\\Sigma_u = PP'`. Defaults to Cholesky decomposition. Returns ------- coefs : ndarray (maxn x neqs x neqs) """ return orth_ma_rep(self, maxn, P) def predict(self, steps=5, alpha=None, exog_fc=None, exog_coint_fc=None): """ Calculate future values of the time series. Parameters ---------- steps : int Prediction horizon. alpha : float, 0 < `alpha` < 1 or None If None, compute point forecast only. If float, compute confidence intervals too. In this case the argument stands for the confidence level. exog : ndarray (steps x self.exog.shape[1]) If self.exog is not None, then information about the future values of exog have to be passed via this parameter. The ndarray may be larger in it's first dimension. In this case only the first steps rows will be considered. Returns ------- forecast - ndarray (steps x neqs) or three ndarrays In case of a point forecast: each row of the returned ndarray represents the forecast of the neqs variables for a specific period. The first row (index [0]) is the forecast for the next period, the last row (index [steps-1]) is the steps-periods-ahead- forecast. """ if self.exog is not None and exog_fc is None: raise ValueError("exog_fc is None: Please pass the future values " "of the VECM's exog terms via the exog_fc " "argument!") if self.exog is None and exog_fc is not None: raise ValueError("This VECMResult-instance's exog attribute is " "None. Please do not pass a non-None value as the " "method's exog_fc-argument.") if exog_fc is not None and exog_fc.shape[0] < steps: raise ValueError("The argument exog_fc must have at least steps " "elements in its first dimension") if self.exog_coint is not None and exog_coint_fc is None: raise ValueError("exog_coint_fc is None: Please pass the future " "values of the VECM's exog_coint terms via the " "exog_coint_fc argument!") if self.exog_coint is None and exog_coint_fc is not None: raise ValueError("This VECMResult-instance's exog_coint attribute " "is None. Please do not pass a non-None value as " "the method's exog_coint_fc-argument.") if exog_coint_fc is not None and exog_coint_fc.shape[0] < steps - 1: raise ValueError("The argument exog_coint_fc must have at least " "steps elements in its first dimension") last_observations = self.y_all.T[-self.k_ar:] exog = [] trend_coefs = [] # adding deterministic terms outside cointegration relation exog_const = np.ones(steps) nobs_tot = self.nobs + self.k_ar if self.const.size > 0: exog.append(exog_const) trend_coefs.append(self.const.T) if self.seasons > 0: first_future_season = (self.first_season + nobs_tot) % self.seasons exog_seasonal = seasonal_dummies(self.seasons, steps, first_future_season, True) exog.append(exog_seasonal) trend_coefs.append(self.seasonal.T) exog_lin_trend = _linear_trend(self.nobs, self.k_ar) exog_lin_trend = exog_lin_trend[-1] + 1 + np.arange(steps) if self.lin_trend.size > 0: exog.append(exog_lin_trend) trend_coefs.append(self.lin_trend.T) if exog_fc is not None: exog.append(exog_fc[:steps]) trend_coefs.append(self.exog_coefs.T) # adding deterministic terms inside cointegration relation if "ci" in self.deterministic: exog.append(exog_const) trend_coefs.append(self.alpha.dot(self.const_coint.T).T) exog_lin_trend_coint = _linear_trend(self.nobs, self.k_ar, coint=True) exog_lin_trend_coint = exog_lin_trend_coint[-1] + 1 + np.arange(steps) if "li" in self.deterministic: exog.append(exog_lin_trend_coint) trend_coefs.append(self.alpha.dot(self.lin_trend_coint.T).T) if exog_coint_fc is not None: if exog_coint_fc.ndim == 1: exog_coint_fc = exog_coint_fc[:, None] # make 2-D exog_coint_fc = np.vstack((self.exog_coint[-1:], exog_coint_fc[:steps-1])) exog.append(exog_coint_fc) trend_coefs.append(self.alpha.dot(self.exog_coint_coefs.T).T) # glueing all deterministics together exog = np.column_stack(exog) if exog != [] else None if trend_coefs != []: trend_coefs = np.row_stack(trend_coefs) else: trend_coefs = None # call the forecasting function of the VAR-module if alpha is not None: return forecast_interval(last_observations, self.var_rep, trend_coefs, self.sigma_u, steps, alpha=alpha, exog=exog) else: return forecast(last_observations, self.var_rep, trend_coefs, steps, exog) def plot_forecast(self, steps, alpha=0.05, plot_conf_int=True, n_last_obs=None): """ Plot the forecast. Parameters ---------- steps : int Prediction horizon. alpha : float, 0 < `alpha` < 1 The confidence level. plot_conf_int : bool, default: True If True, plot bounds of confidence intervals. n_last_obs : int or None, default: None If int, restrict plotted history to n_last_obs observations. If None, include the whole history in the plot. """ mid, lower, upper = self.predict(steps, alpha=alpha) y = self.y_all.T y = y[self.k_ar:] if n_last_obs is None else y[-n_last_obs:] plot.plot_var_forc(y, mid, lower, upper, names=self.names, plot_stderr=plot_conf_int, legend_options={"loc": "lower left"}) def test_granger_causality(self, caused, causing=None, signif=0.05): r""" Test for Granger-causality. The concept of Granger-causality is described in chapter 7.6.3 of [1]_. Test |H0|: "The variables in `causing` do not Granger-cause those in `caused`" against |H1|: "`causing` is Granger-causal for `caused`". Parameters ---------- caused : int or str or sequence of int or str If int or str, test whether the variable specified via this index (int) or name (str) is Granger-caused by the variable(s) specified by `causing`. If a sequence of int or str, test whether the corresponding variables are Granger-caused by the variable(s) specified by `causing`. causing : int or str or sequence of int or str or `None`, default: `None` If int or str, test whether the variable specified via this index (int) or name (str) is Granger-causing the variable(s) specified by `caused`. If a sequence of int or str, test whether the corresponding variables are Granger-causing the variable(s) specified by `caused`. If `None`, `causing` is assumed to be the complement of `caused` (the remaining variables of the system). signif : float, 0 < `signif` < 1, default 5 % Significance level for computing critical values for test, defaulting to standard 0.05 level. Returns ------- results : :class:`statsmodels.tsa.vector_ar.hypothesis_test_results.CausalityTestResults` References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. .. |H0| replace:: H\ :sub:`0` .. |H1| replace:: H\ :sub:`1` """ if not (0 < signif < 1): raise ValueError("signif has to be between 0 and 1") allowed_types = (str, int) if isinstance(caused, allowed_types): caused = [caused] if not all(isinstance(c, allowed_types) for c in caused): raise TypeError("caused has to be of type string or int (or a " "sequence of these types).") caused = [self.names[c] if type(c) == int else c for c in caused] caused_ind = [get_index(self.names, c) for c in caused] if causing is not None: if isinstance(causing, allowed_types): causing = [causing] if not all(isinstance(c, allowed_types) for c in causing): raise TypeError("causing has to be of type string or int (or " "a sequence of these types) or None.") causing = [self.names[c] if type(c) == int else c for c in causing] causing_ind = [get_index(self.names, c) for c in causing] if causing is None: causing_ind = [i for i in range(self.neqs) if i not in caused_ind] causing = [self.names[c] for c in causing_ind] y, k, t, p = self.y_all, self.neqs, self.nobs - 1, self.k_ar + 1 exog = _deterministic_to_exog(self.deterministic, self.seasons, nobs_tot=self.nobs + self.k_ar, first_season=self.first_season, seasons_centered=True, exog=self.exog, exog_coint=self.exog_coint) var_results = VAR(y.T, exog).fit(maxlags=p, trend="n") # num_restr is called N in Lutkepohl num_restr = len(causing) * len(caused) * (p - 1) num_det_terms = _num_det_vars(self.deterministic, self.seasons) if self.exog is not None: num_det_terms += self.exog.shape[1] if self.exog_coint is not None: num_det_terms += self.exog_coint.shape[1] # Make restriction matrix C = np.zeros((num_restr, k*num_det_terms + k**2 * (p-1)), dtype=float) cols_det = k * num_det_terms row = 0 for j in range(p-1): for ing_ind in causing_ind: for ed_ind in caused_ind: C[row, cols_det + ed_ind + k * ing_ind + k**2 * j] = 1 row += 1 Ca = np.dot(C, vec(var_results.params[:-k].T)) x_min_p_components = [] if exog is not None: x_min_p_components.append(exog[-t:].T) x_min_p = np.zeros((k * p, t)) for i in range(p-1): # fll first k * k_ar rows of x_min_p x_min_p[i*k:(i+1)*k, :] = y[:, p-1-i:-1-i] - y[:, :-p] x_min_p[-k:, :] = y[:, :-p] # fill last rows of x_min_p x_min_p_components.append(x_min_p) x_min_p = np.row_stack(x_min_p_components) x_x = np.dot(x_min_p, x_min_p.T) # k*k_ar x k*k_ar x_x_11 = inv(x_x)[:k*(p-1) + num_det_terms, :k*(p-1) + num_det_terms] # k*(k_ar-1) x k*(k_ar-1) # For VAR-models with parameter restrictions the denominator in the # calculation of sigma_u is nobs and not (nobs-k*k_ar-num_det_terms). # Testing for Granger-causality means testing for restricted # parameters, thus the former of the two denominators is used. As # Lutkepohl states, both variants of the estimated sigma_u are # possible. (see Lutkepohl, p.198) # The choice of the denominator T has also the advantage of getting the # same results as the reference software JMulTi. sigma_u = var_results.sigma_u * (t-k*p-num_det_terms) / t sig_alpha_min_p = t * np.kron(x_x_11, sigma_u) # k**2*(p-1)xk**2*(p-1) middle = inv(C @ sig_alpha_min_p @ C.T) wald_statistic = t * (Ca.T @ middle @ Ca) f_statistic = wald_statistic / num_restr df = (num_restr, k * var_results.df_resid) f_distribution = scipy.stats.f(*df) pvalue = f_distribution.sf(f_statistic) crit_value = f_distribution.ppf(1 - signif) return CausalityTestResults(causing, caused, f_statistic, crit_value, pvalue, df, signif, test="granger", method="f") def test_inst_causality(self, causing, signif=0.05): r""" Test for instantaneous causality. The concept of instantaneous causality is described in chapters 3.6.3 and 7.6.4 of [1]_. Test |H0|: "No instantaneous causality between the variables in `caused` and those in `causing`" against |H1|: "Instantaneous causality between `caused` and `causing` exists". Note that instantaneous causality is a symmetric relation (i.e. if `causing` is "instantaneously causing" `caused`, then also `caused` is "instantaneously causing" `causing`), thus the naming of the parameters (which is chosen to be in accordance with :meth:`test_granger_causality()`) may be misleading. Parameters ---------- causing : int or str or sequence of int or str If int or str, test whether the corresponding variable is causing the variable(s) specified in caused. If sequence of int or str, test whether the corresponding variables are causing the variable(s) specified in caused. signif : float, 0 < `signif` < 1, default 5 % Significance level for computing critical values for test, defaulting to standard 0.05 level. Returns ------- results : :class:`statsmodels.tsa.vector_ar.hypothesis_test_results.CausalityTestResults` Notes ----- This method is not returning the same result as `JMulTi`. This is because the test is based on a VAR(k_ar) model in `statsmodels` (in accordance to pp. 104, 320-321 in [1]_) whereas `JMulTi` seems to be using a VAR(k_ar+1) model. Reducing the lag order by one in `JMulTi` leads to equal results in `statsmodels` and `JMulTi`. References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. .. |H0| replace:: H\ :sub:`0` .. |H1| replace:: H\ :sub:`1` """ exog = _deterministic_to_exog(self.deterministic, self.seasons, nobs_tot=self.nobs + self.k_ar, first_season=self.first_season, seasons_centered=True, exog=self.exog, exog_coint=self.exog_coint) # Note: JMulTi seems to be using k_ar+1 instead of k_ar k, t, p = self.neqs, self.nobs, self.k_ar # fit with trend "nc" because all trend information is already in exog var_results = VAR(self.y_all.T, exog).fit(maxlags=p, trend="n") var_results._results.names = self.names return var_results.test_inst_causality(causing=causing, signif=signif) def irf(self, periods=10): return irf.IRAnalysis(self, periods=periods, vecm=True) @cache_readonly def fittedvalues(self): """ Return the in-sample values of endog calculated by the model. Returns ------- fitted : array (nobs x neqs) The predicted in-sample values of the models' endogenous variables. """ beta = self.beta if self.det_coef_coint.size > 0: beta = vstack((beta, self.det_coef_coint)) pi = np.dot(self.alpha, beta.T) gamma = self.gamma if self.det_coef.size > 0: gamma = hstack((gamma, self.det_coef)) delta_y = np.dot(pi, self._y_lag1) + np.dot(gamma, self._delta_x) return (delta_y + self._y_lag1[:self.neqs]).T @cache_readonly def resid(self): """ Return the difference between observed and fitted values. Returns ------- resid : array (nobs x neqs) The residuals. """ return self.y_all.T[self.k_ar:] - self.fittedvalues def test_normality(self, signif=0.05): r""" Test assumption of normal-distributed errors using Jarque-Bera-style omnibus :math:`\\chi^2` test. Parameters ---------- signif : float The test's significance level. Returns ------- result : :class:`statsmodels.tsa.vector_ar.hypothesis_test_results.NormalityTestResults` Notes ----- |H0| : data are generated by a Gaussian-distributed process .. |H0| replace:: H\ :sub:`0` """ return test_normality(self, signif=signif) def test_whiteness(self, nlags=10, signif=0.05, adjusted=False): """ Test the whiteness of the residuals using the Portmanteau test. This test is described in [1]_, chapter 8.4.1. Parameters ---------- nlags : int > 0 signif : float, 0 < `signif` < 1 adjusted : bool, default False Returns ------- result : :class:`statsmodels.tsa.vector_ar.hypothesis_test_results.WhitenessTestResults` References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. """ statistic = 0 u = np.asarray(self.resid) acov_list = _compute_acov(u, nlags) # self.sigma_u instead of cov(0) is necessary to get the same # result as JMulTi. The difference between the two is that sigma_u is # calculated with the usual residuals while in cov(0) the # residuals are demeaned. To me JMulTi's behaviour seems a bit strange # because it uses the usual residuals here but demeaned residuals in # the calculation of autocovariances with lag > 0. (used in the # argument of trace() four rows below this comment.) c0_inv = inv(self.sigma_u) # instead of inv(cov(0)) if c0_inv.dtype == np.complex128 and np.all(np.imag(c0_inv) == 0): c0_inv = np.real(c0_inv) for t in range(1, nlags+1): ct = acov_list[t] to_add = np.trace(ct.T @ c0_inv @ ct @ c0_inv) if adjusted: to_add /= (self.nobs - t) statistic += to_add statistic *= self.nobs**2 if adjusted else self.nobs df = self.neqs**2 * (nlags - self.k_ar + 1) - self.neqs*self.coint_rank dist = scipy.stats.chi2(df) pvalue = dist.sf(statistic) crit_value = dist.ppf(1 - signif) return WhitenessTestResults(statistic, crit_value, pvalue, df, signif, nlags, adjusted) def plot_data(self, with_presample=False): """ Plot the input time series. Parameters ---------- with_presample : bool, default: `False` If `False`, the pre-sample data (the first `k_ar` values) will not be plotted. """ y = self.y_all if with_presample else self.y_all[:, self.k_ar:] names = self.names dates = self.dates if with_presample else self.dates[self.k_ar:] plot.plot_mts(y.T, names=names, index=dates) def summary(self, alpha=.05): """ Return a summary of the estimation results. Parameters ---------- alpha : float 0 < `alpha` < 1, default 0.05 Significance level of the shown confidence intervals. Returns ------- summary : :class:`statsmodels.iolib.summary.Summary` A summary containing information about estimated parameters. """ from statsmodels.iolib.summary import summary_params summary = Summary() def make_table(self, params, std_err, t_values, p_values, conf_int, mask, names, title, strip_end=True): res = (self, params[mask], std_err[mask], t_values[mask], p_values[mask], conf_int[mask] ) param_names = [ '.'.join(name.split('.')[:-1]) if strip_end else name for name in np.array(names)[mask].tolist()] return summary_params(res, yname=None, xname=param_names, alpha=alpha, use_t=False, title=title) # --------------------------------------------------------------------- # Add tables with gamma and det_coef for each endogenous variable: lagged_params_components = [] stderr_lagged_params_components = [] tvalues_lagged_params_components = [] pvalues_lagged_params_components = [] conf_int_lagged_params_components = [] if self.det_coef.size > 0: lagged_params_components.append(self.det_coef.flatten(order="F")) stderr_lagged_params_components.append( self.stderr_det_coef.flatten(order="F")) tvalues_lagged_params_components.append( self.tvalues_det_coef.flatten(order="F")) pvalues_lagged_params_components.append( self.pvalues_det_coef.flatten(order="F")) conf_int = self.conf_int_det_coef(alpha=alpha) lower = conf_int["lower"].flatten(order="F") upper = conf_int["upper"].flatten(order="F") conf_int_lagged_params_components.append(np.column_stack( (lower, upper))) if self.k_ar - 1 > 0: lagged_params_components.append(self.gamma.flatten()) stderr_lagged_params_components.append(self.stderr_gamma.flatten()) tvalues_lagged_params_components.append( self.tvalues_gamma.flatten()) pvalues_lagged_params_components.append( self.pvalues_gamma.flatten()) conf_int = self.conf_int_gamma(alpha=alpha) lower = conf_int["lower"].flatten() upper = conf_int["upper"].flatten() conf_int_lagged_params_components.append(np.column_stack( (lower, upper))) # if gamma or det_coef exists, then make a summary-table for them: if len(lagged_params_components) != 0: lagged_params = hstack(lagged_params_components) stderr_lagged_params = hstack(stderr_lagged_params_components) tvalues_lagged_params = hstack(tvalues_lagged_params_components) pvalues_lagged_params = hstack(pvalues_lagged_params_components) conf_int_lagged_params = vstack(conf_int_lagged_params_components) for i in range(self.neqs): masks = [] offset = 0 # 1. Deterministic terms outside cointegration relation if "co" in self.deterministic: masks.append(offset + np.array(i, ndmin=1)) offset += self.neqs if self.seasons > 0: for _ in range(self.seasons-1): masks.append(offset + np.array(i, ndmin=1)) offset += self.neqs if "lo" in self.deterministic: masks.append(offset + np.array(i, ndmin=1)) offset += self.neqs if self.exog is not None: for _ in range(self.exog.shape[1]): masks.append(offset + np.array(i, ndmin=1)) offset += self.neqs # 2. Lagged endogenous terms if self.k_ar - 1 > 0: start = i * self.neqs * (self.k_ar-1) end = (i+1) * self.neqs * (self.k_ar-1) masks.append(offset + np.arange(start, end)) # offset += self.neqs**2 * (self.k_ar-1) # Create the table mask = np.concatenate(masks) eq_name = self.model.endog_names[i] title = "Det. terms outside the coint. relation " + \ "& lagged endog. parameters for equation %s" % eq_name table = make_table(self, lagged_params, stderr_lagged_params, tvalues_lagged_params, pvalues_lagged_params, conf_int_lagged_params, mask, self.model._lagged_param_names, title) summary.tables.append(table) # --------------------------------------------------------------------- # Loading coefficients (alpha): a = self.alpha.flatten() se_a = self.stderr_alpha.flatten() t_a = self.tvalues_alpha.flatten() p_a = self.pvalues_alpha.flatten() ci_a = self.conf_int_alpha(alpha=alpha) lower = ci_a["lower"].flatten() upper = ci_a["upper"].flatten() ci_a = np.column_stack((lower, upper)) a_names = self.model._load_coef_param_names alpha_masks = [] for i in range(self.neqs): if self.coint_rank > 0: start = i * self.coint_rank end = start + self.coint_rank mask = np.arange(start, end) # Create the table alpha_masks.append(mask) eq_name = self.model.endog_names[i] title = "Loading coefficients (alpha) for equation %s" % eq_name table = make_table(self, a, se_a, t_a, p_a, ci_a, mask, a_names, title) summary.tables.append(table) # --------------------------------------------------------------------- # Cointegration matrix/vector (beta) and det. terms inside coint. rel.: coint_components = [] stderr_coint_components = [] tvalues_coint_components = [] pvalues_coint_components = [] conf_int_coint_components = [] if self.coint_rank > 0: coint_components.append(self.beta.T.flatten()) stderr_coint_components.append(self.stderr_beta.T.flatten()) tvalues_coint_components.append(self.tvalues_beta.T.flatten()) pvalues_coint_components.append(self.pvalues_beta.T.flatten()) conf_int = self.conf_int_beta(alpha=alpha) lower = conf_int["lower"].T.flatten() upper = conf_int["upper"].T.flatten() conf_int_coint_components.append(np.column_stack( (lower, upper))) if self.det_coef_coint.size > 0: coint_components.append(self.det_coef_coint.flatten()) stderr_coint_components.append( self.stderr_det_coef_coint.flatten()) tvalues_coint_components.append( self.tvalues_det_coef_coint.flatten()) pvalues_coint_components.append( self.pvalues_det_coef_coint.flatten()) conf_int = self.conf_int_det_coef_coint(alpha=alpha) lower = conf_int["lower"].flatten() upper = conf_int["upper"].flatten() conf_int_coint_components.append(np.column_stack((lower, upper))) coint = hstack(coint_components) stderr_coint = hstack(stderr_coint_components) tvalues_coint = hstack(tvalues_coint_components) pvalues_coint = hstack(pvalues_coint_components) conf_int_coint = vstack(conf_int_coint_components) coint_names = self.model._coint_param_names for i in range(self.coint_rank): masks = [] offset = 0 # 1. Cointegration matrix (beta) if self.coint_rank > 0: start = i * self.neqs end = start + self.neqs masks.append(offset + np.arange(start, end)) offset += self.neqs * self.coint_rank # 2. Deterministic terms inside cointegration relation if "ci" in self.deterministic: masks.append(offset + np.array(i, ndmin=1)) offset += self.coint_rank if "li" in self.deterministic: masks.append(offset + np.array(i, ndmin=1)) offset += self.coint_rank if self.exog_coint is not None: for _ in range(self.exog_coint.shape[1]): masks.append(offset + np.array(i, ndmin=1)) offset += self.coint_rank # Create the table mask = np.concatenate(masks) title = "Cointegration relations for " + \ "loading-coefficients-column %d" % (i+1) table = make_table(self, coint, stderr_coint, tvalues_coint, pvalues_coint, conf_int_coint, mask, coint_names, title) summary.tables.append(table) return summary statsmodels-0.12.2/statsmodels/tsa/x13.py000066400000000000000000000541371400612667500202750ustar00rootroot00000000000000""" Run x12/x13-arima specs in a subprocess from Python and curry results back into python. Notes ----- Many of the functions are called x12. However, they are also intended to work for x13. If this is not the case, it's a bug. """ from statsmodels.compat.pandas import deprecate_kwarg import os import subprocess import tempfile import re from warnings import warn import pandas as pd from statsmodels.tools.tools import Bunch from statsmodels.tools.sm_exceptions import (X13NotFoundError, IOWarning, X13Error, X13Warning) __all__ = ["x13_arima_select_order", "x13_arima_analysis"] _binary_names = ('x13as.exe', 'x13as', 'x12a.exe', 'x12a') class _freq_to_period: def __getitem__(self, key): if key.startswith('M'): return 12 elif key.startswith('Q'): return 4 elif key.startswith('W'): return 52 _freq_to_period = _freq_to_period() _period_to_freq = {12: 'M', 4: 'Q'} _log_to_x12 = {True: 'log', False: 'none', None: 'auto'} _bool_to_yes_no = lambda x: 'yes' if x else 'no' # noqa:E731 def _find_x12(x12path=None, prefer_x13=True): """ If x12path is not given, then either x13as[.exe] or x12a[.exe] must be found on the PATH. Otherwise, the environmental variable X12PATH or X13PATH must be defined. If prefer_x13 is True, only X13PATH is searched for. If it is false, only X12PATH is searched for. """ global _binary_names if x12path is not None and x12path.endswith(_binary_names): # remove binary from path if given x12path = os.path.dirname(x12path) if not prefer_x13: # search for x12 first _binary_names = _binary_names[::-1] if x12path is None: x12path = os.getenv("X12PATH", "") if not x12path: x12path = os.getenv("X13PATH", "") elif x12path is None: x12path = os.getenv("X13PATH", "") if not x12path: x12path = os.getenv("X12PATH", "") for binary in _binary_names: x12 = os.path.join(x12path, binary) try: subprocess.check_call(x12, stdout=subprocess.PIPE, stderr=subprocess.PIPE) return x12 except OSError: pass else: return False def _check_x12(x12path=None): x12path = _find_x12(x12path) if not x12path: raise X13NotFoundError("x12a and x13as not found on path. Give the " "path, put them on PATH, or set the " "X12PATH or X13PATH environmental variable.") return x12path def _clean_order(order): """ Takes something like (1 1 0)(0 1 1) and returns a arma order, sarma order tuple. Also accepts (1 1 0) and return arma order and (0, 0, 0) """ order = re.findall(r"\([0-9 ]*?\)", order) def clean(x): return tuple(map(int, re.sub("[()]", "", x).split(" "))) if len(order) > 1: order, sorder = map(clean, order) else: order = clean(order[0]) sorder = (0, 0, 0) return order, sorder def run_spec(x12path, specpath, outname=None, meta=False, datameta=False): if meta and datameta: raise ValueError("Cannot specify both meta and datameta.") if meta: args = [x12path, "-m " + specpath] elif datameta: args = [x12path, "-d " + specpath] else: args = [x12path, specpath] if outname: args += [outname] return subprocess.Popen(args, stdout=subprocess.PIPE, stderr=subprocess.STDOUT) def _make_automdl_options(maxorder, maxdiff, diff): options = "\n" options += "maxorder = ({0} {1})\n".format(maxorder[0], maxorder[1]) if maxdiff is not None: # maxdiff always takes precedence options += "maxdiff = ({0} {1})\n".format(maxdiff[0], maxdiff[1]) else: options += "diff = ({0} {1})\n".format(diff[0], diff[1]) return options def _make_var_names(exog): if hasattr(exog, "name"): var_names = exog.name elif hasattr(exog, "columns"): var_names = exog.columns else: raise ValueError("exog is not a Series or DataFrame or is unnamed.") try: var_names = " ".join(var_names) except TypeError: # cannot have names that are numbers, pandas default from statsmodels.base.data import _make_exog_names if exog.ndim == 1: var_names = "x1" else: var_names = " ".join(_make_exog_names(exog)) return var_names def _make_regression_options(trading, exog): if not trading and exog is None: # start regression spec return "" reg_spec = "regression{\n" if trading: reg_spec += " variables = (td)\n" if exog is not None: var_names = _make_var_names(exog) reg_spec += " user = ({0})\n".format(var_names) reg_spec += " data = ({0})\n".format("\n".join(map(str, exog.values.ravel().tolist()))) reg_spec += "}\n" # close out regression spec return reg_spec def _make_forecast_options(forecast_periods): if forecast_periods is None: return "" forecast_spec = "forecast{\n" forecast_spec += "maxlead = ({0})\n}}\n".format(forecast_periods) return forecast_spec def _check_errors(errors): errors = errors[errors.find("spc:")+4:].strip() if errors and 'ERROR' in errors: raise X13Error(errors) elif errors and 'WARNING' in errors: warn(errors, X13Warning) def _convert_out_to_series(x, dates, name): """ Convert x to a DataFrame where x is a string in the format given by x-13arima-seats output. """ from io import StringIO from pandas import read_csv out = read_csv(StringIO(x), skiprows=2, header=None, sep='\t', engine='python') return out.set_index(dates).rename(columns={1: name})[name] def _open_and_read(fname): # opens a file, reads it, and make sure it's closed with open(fname, 'r') as fin: fout = fin.read() return fout class Spec(object): @property def spec_name(self): return self.__class__.__name__.replace("Spec", "") def create_spec(self, **kwargs): spec = """{name} {{ {options} }} """ return spec.format(name=self.spec_name, options=self.options) def set_options(self, **kwargs): options = "" for key, value in kwargs.items(): options += "{0}={1}\n".format(key, value) self.__dict__.update({key: value}) self.options = options class SeriesSpec(Spec): """ Parameters ---------- data appendbcst : bool appendfcst : bool comptype compwt decimals modelspan name period precision to_print to_save span start title type Notes ----- Rarely used arguments divpower missingcode missingval saveprecision trimzero """ def __init__(self, data, name='Unnamed Series', appendbcst=False, appendfcst=False, comptype=None, compwt=1, decimals=0, modelspan=(), period=12, precision=0, to_print=[], to_save=[], span=(), start=(1, 1), title='', series_type=None, divpower=None, missingcode=-99999, missingval=1000000000): appendbcst, appendfcst = map(_bool_to_yes_no, [appendbcst, appendfcst, ]) series_name = "\"{0}\"".format(name[:64]) # trim to 64 characters title = "\"{0}\"".format(title[:79]) # trim to 79 characters self.set_options(data=data, appendbcst=appendbcst, appendfcst=appendfcst, period=period, start=start, title=title, name=series_name, ) def pandas_to_series_spec(x): # from statsmodels.tools.data import _check_period_index # check_period_index(x) if hasattr(x, 'columns'): # convert to series if len(x.columns) > 1: raise ValueError("Does not handle DataFrame with more than one " "column") x = x[x.columns[0]] data = "({0})".format("\n".join(map(str, x.values.tolist()))) # get periodicity # get start / first data # give it a title try: period = _freq_to_period[x.index.freqstr] except (AttributeError, ValueError): from pandas.tseries.api import infer_freq period = _freq_to_period[infer_freq(x.index)] start_date = x.index[0] if period == 12: year, stperiod = start_date.year, start_date.month elif period == 4: year, stperiod = start_date.year, start_date.quarter else: # pragma: no cover raise ValueError("Only monthly and quarterly periods are supported." " Please report or send a pull request if you want " "this extended.") if hasattr(x, 'name'): name = x.name or "Unnamed Series" else: name = 'Unnamed Series' series_spec = SeriesSpec(data=data, name=name, period=period, title=name, start="{0}.{1}".format(year, stperiod)) return series_spec @deprecate_kwarg('forecast_years', 'forecast_periods') def x13_arima_analysis(endog, maxorder=(2, 1), maxdiff=(2, 1), diff=None, exog=None, log=None, outlier=True, trading=False, forecast_periods=None, retspec=False, speconly=False, start=None, freq=None, print_stdout=False, x12path=None, prefer_x13=True): """ Perform x13-arima analysis for monthly or quarterly data. Parameters ---------- endog : array_like, pandas.Series The series to model. It is best to use a pandas object with a DatetimeIndex or PeriodIndex. However, you can pass an array-like object. If your object does not have a dates index then ``start`` and ``freq`` are not optional. maxorder : tuple The maximum order of the regular and seasonal ARMA polynomials to examine during the model identification. The order for the regular polynomial must be greater than zero and no larger than 4. The order for the seasonal polynomial may be 1 or 2. maxdiff : tuple The maximum orders for regular and seasonal differencing in the automatic differencing procedure. Acceptable inputs for regular differencing are 1 and 2. The maximum order for seasonal differencing is 1. If ``diff`` is specified then ``maxdiff`` should be None. Otherwise, ``diff`` will be ignored. See also ``diff``. diff : tuple Fixes the orders of differencing for the regular and seasonal differencing. Regular differencing may be 0, 1, or 2. Seasonal differencing may be 0 or 1. ``maxdiff`` must be None, otherwise ``diff`` is ignored. exog : array_like Exogenous variables. log : bool or None If None, it is automatically determined whether to log the series or not. If False, logs are not taken. If True, logs are taken. outlier : bool Whether or not outliers are tested for and corrected, if detected. trading : bool Whether or not trading day effects are tested for. forecast_periods : int Number of forecasts produced. The default is None. retspec : bool Whether to return the created specification file. Can be useful for debugging. speconly : bool Whether to create the specification file and then return it without performing the analysis. Can be useful for debugging. start : str, datetime Must be given if ``endog`` does not have date information in its index. Anything accepted by pandas.DatetimeIndex for the start value. freq : str Must be givein if ``endog`` does not have date information in its index. Anything accepted by pandas.DatetimeIndex for the freq value. print_stdout : bool The stdout from X12/X13 is suppressed. To print it out, set this to True. Default is False. x12path : str or None The path to x12 or x13 binary. If None, the program will attempt to find x13as or x12a on the PATH or by looking at X13PATH or X12PATH depending on the value of prefer_x13. prefer_x13 : bool If True, will look for x13as first and will fallback to the X13PATH environmental variable. If False, will look for x12a first and will fallback to the X12PATH environmental variable. If x12path points to the path for the X12/X13 binary, it does nothing. Returns ------- Bunch A bunch object containing the listed attributes. - results : str The full output from the X12/X13 run. - seasadj : pandas.Series The final seasonally adjusted ``endog``. - trend : pandas.Series The trend-cycle component of ``endog``. - irregular : pandas.Series The final irregular component of ``endog``. - stdout : str The captured stdout produced by x12/x13. - spec : str, optional Returned if ``retspec`` is True. The only thing returned if ``speconly`` is True. Notes ----- This works by creating a specification file, writing it to a temporary directory, invoking X12/X13 in a subprocess, and reading the output directory, invoking exog12/X13 in a subprocess, and reading the output back in. """ x12path = _check_x12(x12path) if not isinstance(endog, (pd.DataFrame, pd.Series)): if start is None or freq is None: raise ValueError("start and freq cannot be none if endog is not " "a pandas object") endog = pd.Series(endog, index=pd.DatetimeIndex(start=start, periods=len(endog), freq=freq)) spec_obj = pandas_to_series_spec(endog) spec = spec_obj.create_spec() spec += "transform{{function={0}}}\n".format(_log_to_x12[log]) if outlier: spec += "outlier{}\n" options = _make_automdl_options(maxorder, maxdiff, diff) spec += "automdl{{{0}}}\n".format(options) spec += _make_regression_options(trading, exog) spec += _make_forecast_options(forecast_periods) spec += "x11{ save=(d11 d12 d13) }" if speconly: return spec # write it to a tempfile # TODO: make this more robust - give the user some control? ftempin = tempfile.NamedTemporaryFile(delete=False, suffix='.spc') ftempout = tempfile.NamedTemporaryFile(delete=False) try: ftempin.write(spec.encode('utf8')) ftempin.close() ftempout.close() # call x12 arima p = run_spec(x12path, ftempin.name[:-4], ftempout.name) p.wait() stdout = p.stdout.read() if print_stdout: print(p.stdout.read()) # check for errors errors = _open_and_read(ftempout.name + '.err') _check_errors(errors) # read in results results = _open_and_read(ftempout.name + '.out') seasadj = _open_and_read(ftempout.name + '.d11') trend = _open_and_read(ftempout.name + '.d12') irregular = _open_and_read(ftempout.name + '.d13') finally: try: # sometimes this gives a permission denied error? # not sure why. no process should have these open os.remove(ftempin.name) os.remove(ftempout.name) except OSError: if os.path.exists(ftempin.name): warn("Failed to delete resource {0}".format(ftempin.name), IOWarning) if os.path.exists(ftempout.name): warn("Failed to delete resource {0}".format(ftempout.name), IOWarning) seasadj = _convert_out_to_series(seasadj, endog.index, 'seasadj') trend = _convert_out_to_series(trend, endog.index, 'trend') irregular = _convert_out_to_series(irregular, endog.index, 'irregular') # NOTE: there is not likely anything in stdout that's not in results # so may be safe to just suppress and remove it if not retspec: res = X13ArimaAnalysisResult(observed=endog, results=results, seasadj=seasadj, trend=trend, irregular=irregular, stdout=stdout) else: res = X13ArimaAnalysisResult(observed=endog, results=results, seasadj=seasadj, trend=trend, irregular=irregular, stdout=stdout, spec=spec) return res @deprecate_kwarg('forecast_years', 'forecast_periods') def x13_arima_select_order(endog, maxorder=(2, 1), maxdiff=(2, 1), diff=None, exog=None, log=None, outlier=True, trading=False, forecast_periods=None, start=None, freq=None, print_stdout=False, x12path=None, prefer_x13=True): """ Perform automatic seasonal ARIMA order identification using x12/x13 ARIMA. Parameters ---------- endog : array_like, pandas.Series The series to model. It is best to use a pandas object with a DatetimeIndex or PeriodIndex. However, you can pass an array-like object. If your object does not have a dates index then ``start`` and ``freq`` are not optional. maxorder : tuple The maximum order of the regular and seasonal ARMA polynomials to examine during the model identification. The order for the regular polynomial must be greater than zero and no larger than 4. The order for the seasonal polynomial may be 1 or 2. maxdiff : tuple The maximum orders for regular and seasonal differencing in the automatic differencing procedure. Acceptable inputs for regular differencing are 1 and 2. The maximum order for seasonal differencing is 1. If ``diff`` is specified then ``maxdiff`` should be None. Otherwise, ``diff`` will be ignored. See also ``diff``. diff : tuple Fixes the orders of differencing for the regular and seasonal differencing. Regular differencing may be 0, 1, or 2. Seasonal differencing may be 0 or 1. ``maxdiff`` must be None, otherwise ``diff`` is ignored. exog : array_like Exogenous variables. log : bool or None If None, it is automatically determined whether to log the series or not. If False, logs are not taken. If True, logs are taken. outlier : bool Whether or not outliers are tested for and corrected, if detected. trading : bool Whether or not trading day effects are tested for. forecast_periods : int Number of forecasts produced. The default is None. start : str, datetime Must be given if ``endog`` does not have date information in its index. Anything accepted by pandas.DatetimeIndex for the start value. freq : str Must be givein if ``endog`` does not have date information in its index. Anything accepted by pandas.DatetimeIndex for the freq value. print_stdout : bool The stdout from X12/X13 is suppressed. To print it out, set this to True. Default is False. x12path : str or None The path to x12 or x13 binary. If None, the program will attempt to find x13as or x12a on the PATH or by looking at X13PATH or X12PATH depending on the value of prefer_x13. prefer_x13 : bool If True, will look for x13as first and will fallback to the X13PATH environmental variable. If False, will look for x12a first and will fallback to the X12PATH environmental variable. If x12path points to the path for the X12/X13 binary, it does nothing. Returns ------- Bunch A bunch object containing the listed attributes. - order : tuple The regular order. - sorder : tuple The seasonal order. - include_mean : bool Whether to include a mean or not. - results : str The full results from the X12/X13 analysis. - stdout : str The captured stdout from the X12/X13 analysis. Notes ----- This works by creating a specification file, writing it to a temporary directory, invoking X12/X13 in a subprocess, and reading the output back in. """ results = x13_arima_analysis(endog, x12path=x12path, exog=exog, log=log, outlier=outlier, trading=trading, forecast_periods=forecast_periods, maxorder=maxorder, maxdiff=maxdiff, diff=diff, start=start, freq=freq, prefer_x13=prefer_x13) model = re.search("(?<=Final automatic model choice : ).*", results.results) order = model.group() if re.search("Mean is not significant", results.results): include_mean = False elif re.search("Constant", results.results): include_mean = True else: include_mean = False order, sorder = _clean_order(order) res = Bunch(order=order, sorder=sorder, include_mean=include_mean, results=results.results, stdout=results.stdout) return res class X13ArimaAnalysisResult(object): def __init__(self, **kwargs): for key, value in kwargs.items(): setattr(self, key, value) def plot(self): from statsmodels.graphics.utils import _import_mpl plt = _import_mpl() fig, axes = plt.subplots(4, 1, sharex=True) self.observed.plot(ax=axes[0], legend=False) axes[0].set_ylabel('Observed') self.seasadj.plot(ax=axes[1], legend=False) axes[1].set_ylabel('Seas. Adjusted') self.trend.plot(ax=axes[2], legend=False) axes[2].set_ylabel('Trend') self.irregular.plot(ax=axes[3], legend=False) axes[3].set_ylabel('Irregular') fig.tight_layout() return fig statsmodels-0.12.2/tools/000077500000000000000000000000001400612667500153055ustar00rootroot00000000000000statsmodels-0.12.2/tools/R2nparray/000077500000000000000000000000001400612667500171655ustar00rootroot00000000000000statsmodels-0.12.2/tools/R2nparray/DESCRIPTION000066400000000000000000000006021400612667500206710ustar00rootroot00000000000000Package: R2nparray Version: 0.1 Date: 2011-08-23 Title: R to Numpy Arrays Author: Skipper Seabold Maintainer: Skipper Seabold Description: Writes R matrices, vectors, and scalars to a file as numpy arrays License: BSD URL: https://www.github.com/statsmodels/statsmodels Repository: github Collate: 'R2nparray-package.R' 'R2nparray.R' statsmodels-0.12.2/tools/R2nparray/NAMESPACE000066400000000000000000000000251400612667500204010ustar00rootroot00000000000000exportPattern( "." ) statsmodels-0.12.2/tools/R2nparray/R/000077500000000000000000000000001400612667500173665ustar00rootroot00000000000000statsmodels-0.12.2/tools/R2nparray/R/R2nparray-package.R000066400000000000000000000000751400612667500227640ustar00rootroot00000000000000#' R2nparray #' #' @name R2nparray #' @docType package NULL statsmodels-0.12.2/tools/R2nparray/R/R2nparray.R000066400000000000000000000162241400612667500213760ustar00rootroot00000000000000#' Print R object contents to python expression #' #' @param object with names attribute names(object) will be written as python assignments #' @param prefix string string that is prepended to the variable names #' @param blacklist list of strings names that are in the blacklist are ignored #' @param trans named list (dict_like) names that are in trans will be replaced by the corresponding value #' @param strict skip content that cannot be pretty-printed. Otherwise, will print as str(deparse(x)) #' @note currently limited type inference, mainly numerical #' @export #' @examples #' mod = lm(rnorm(100) ~ rnorm(100)) #' cat_items(mod) cat_items <- function(object, prefix="", strict=TRUE, trans=list(), blacklist=NULL){ out = convert_items(object, prefix, strict, trans, blacklist) cat(out) } #' Same as cat_items() except it returns a string instead of printing it #' #' @export #' @examples #' mod = lm(rnorm(100) ~ rnorm(100)) #' convert_items(mod) convert_items <- function(object, prefix="", strict=TRUE, trans=list(), blacklist=NULL){ out = list() for (n in names(object)){ if (n %in% blacklist) next newname = sanitize_name(n) if (newname %in% names(trans)){ newname = trans[[newname]] } newname = paste(prefix, newname, sep='') tmp = try(convert(object[[n]], name=newname, strict=strict)) if (class(tmp) != 'try-error'){ out[[newname]] = tmp } } out = paste(out, collapse='\n') return(out) } convert <- function (x, name='default', strict=TRUE) { UseMethod("convert", x) } convert.default <- function(X, name='default', strict=TRUE){ head = paste(name, '= ') mid = paste(deparse(X), collapse='\n') out = paste(head, "'''", mid, "'''") if(!strict){ return(out) } } convert.data.frame <- function(X, name='default', strict=TRUE){ X = as.matrix(X) out = convert(X, name=name) return(out) } convert.numeric <- function(X, name='default', strict=TRUE) { if (length(X) > 1){ head = paste(name, '= np.array([\n') mid = strwrap(paste(X, collapse=', '), width=79, indent=3, exdent=4) mid = paste(mid, collapse='\n') tail = "\n ])" if (is.matrix(X)) { i <- nrow(X) j <- ncol(X) tail = paste(tail, ".reshape(", i, ", ", j, ", order='F')\n", sep='') } out = paste(head, mid, tail, collapse='\n') }else{ out = paste(name, '=', X) } return(out) } convert.character <- function(X, name='default', strict=TRUE) { if (length(X) > 1){ head = paste(name, '= np.array([\n') mid = paste("'", X, "'", sep='') mid = paste(mid, collapse=', ') tail = "\n ])" out = paste(head, mid, tail) }else{ out = paste(name, " = '", X, "'", sep='') } return(out) } sanitize_name <- function(name) { #"[%s]" % "]|[".join(map(re.escape, list(string.punctuation.replace("_","") punctuation <- '[\\!]|[\\"]|[\\#]|[\\$]|[\\%]|[\\&]|[\\\']|[\\(]|[\\)]|[\\*]|[\\+]|[\\,]|[\\-]|[\\.]|[\\/]|[\\:]|[\\;]|[\\<]|[\\=]|[\\>]|[\\?]|[\\@]|[\\[]|[\\\\]|[\\]]|[\\^]|[\\`]|[\\{]|[\\|]|[\\}]|[\\~]' # handle spaces,tabs,etc. and periods specially name <- gsub("[[:blank:]\\.]", "_", name) name <- gsub(punctuation, "", name) return(name) } get_dimnames <- function(mat, prefix="", asstring=FALSE) { dimension_names = c('rownames', 'colnames', 3:100) dimn = dimnames(mat) if(is.null(dimn)){ dimn = names(mat) if(is.null(dimn)){ dimn = NULL }else{ dimn = list(dimn) } } for (i in 1:length(dimn)){ pref = paste(prefix, dimension_names[i], sep='') dimn[[i]] = sapply(dimn[[i]], sanitize_name) dimn[[i]] = paste(dimn[[i]], collapse="', '") dimn[[i]] = paste(pref, " = ['", dimn[[i]], "']", sep='') } dimn = paste(dimn, collapse='\n')[1] return(dimn) } # Dictionary of lambda functions d = list() d$df_resid = function(x) x$df.residual d$deviance = function(x) x$deviance d$null_deviance = function(x) x$null.deviance d$rank = function(x) x$rank d$aic = function(x) x$aic d$nobs = function(x) dim(model.matrix(x))[1] d$conf_int = function(x) as.matrix(confint(x)) d$resid = function(x) resid(x) d$predict = function(x) predict(x) d$fittedvalues = function(x) predict(x) d$params = function(x) summary(x)$coefficients[,1] d$bse = function(x) summary(x)$coefficients[,2] d$tvalues = function(x) summary(x)$coefficients[,3] d$pvalues = function(x) summary(x)$coefficients[,4] d$rsquared = function(x) summary(x)$r.squared[1] d$rsquared_adj = function(x) summary(x)$r.squared[2] d$fvalue = function(x) summary(x)$fstatistic$statistic d$f_pvalue = function(x) summary(x)$fstatistic$p.value d$fstatistic = function(x) summary(x)$fstatistic #' Applies functions to an object (skips on error) #' #' @param object an object on which we want to apply the lambda functions #' @param lambdas a named list of lambda functions #' @export #' @examples #' mod = lm(rnorm(100) ~ rnorm(100)) #' cat_items(apply_functions(mod)) apply_functions = function(object, lambdas=d){ out = list() for (n in names(lambdas)){ tmp = try(lambdas[[n]](object)) if (class(tmp) != 'try-error'){ out[[n]] = tmp } } return(out) } mkhtest <- function(ht, name, distr="f") { #function to write results of a statistical test of class htest to a python dict # #Parameters #---------- #ht : instance of ht # return of many statistical tests #name : string # name of variable that holds results dict #distr : string # distribution of the test statistic # cat(name); cat(" = dict("); cat("statistic="); cat(ht$statistic); cat(", "); cat("pvalue="); cat(ht$p.value); cat(", "); cat("parameters=("); cat(ht$parameter, sep=","); cat(",), "); cat("distr='"); cat(distr); cat("'"); cat(")"); cat("\n\n") } header = " import numpy as np from statsmodels.tools.tools import Bunch " write_header = function(){ cat(header) } # Example #library(plm) #library(systemfit) #data(Grunfeld) #panel <- plm.data(Grunfeld, c('firm','year')) #SUR <- systemfit(inv ~ value + capital, method='SUR',data=panel) ##translation table for names (could be dict in python) #translate = list(coefficients="params", #coefCov="cov_params", #residCovEst="resid_cov_est", #residCov="resid_cov", #df_residual="df_resid", #df_residual_sys="df_resid_sys", ##nCoef="k_vars", #not sure about this #fitted_values="fittedvalues" #) #fname = "tmp_sur_0.py" #append = FALSE #TRUE #sink(file=fname, append=append) #redirect output to file #cat(header) #cat("\nsur = Bunch()\n") #cat_items(SUR, prefix="sur.", blacklist=c("eq", "control"), trans=translate) #equations = SUR[["eq"]] #for (ii in c(1:length(equations))) { #equ_name = paste("sur.equ", ii, sep="") #cat("\n\n", equ_name, sep=""); cat(" = Bunch()\n") #cat_items(equations[[ii]], prefix=paste(equ_name, ".", sep=""), trans=translate) #} #sink() statsmodels-0.12.2/tools/R2nparray/R/ex_sur.R000066400000000000000000000031211400612667500210130ustar00rootroot00000000000000data <- read.csv('E:\\path_to_repo\\statsmodels\\datasets\\grunfeld\\grunfeld.csv') #data <- read.csv('../../../statsmodels/datasets/grunfeld/grunfeld.csv') data <- data[data$firm %in% c('General Motors','Chrysler','General Electric','Westinghouse','US Steel'),] attach(data) library('plm') library('systemfit') panel <- plm.data(data,c('firm','year')) formula <- invest ~ value + capital SUR <- systemfit(formula,method='SUR',data=panel) f <- fitted(SUR) ff <- c(f[,'Chrysler'],f[,'General.Electric'],f[,'General.Motors'],f[,'US.Steel'],f[,'Westinghouse']) #save results to python module #load functions, (windows path separators) source("E:\\path_to_repo\\tools\\R2nparray\\R\\R2nparray.R") #source("R2nparray.R") #translation table for names (could be dict in python) translate = list(coefficients="params", coefCov="cov_params", residCovEst="resid_cov_est", residCov="resid_cov", df_residual="df_resid", df_residual_sys="df_resid_sys", #nCoef="k_vars", #not sure about this fitted_values="fittedvalues" ) fname = "tmp_sur_0.py" append = FALSE #TRUE #redirect output to file sink(file=fname, append=append) write_header() cat("\nsur = Bunch()\n") cat_items(SUR, prefix="sur.", blacklist=c("eq", "control"), trans=translate) equations = SUR[["eq"]] for (ii in c(1:length(equations))) { equ_name = paste("sur.equ", ii, sep="") cat("\n\n", equ_name, sep=""); cat(" = Bunch()\n") cat_items(equations[[ii]], prefix=paste(equ_name, ".", sep=""), trans=translate) } sink() statsmodels-0.12.2/tools/R2nparray/README.txt000066400000000000000000000020041400612667500206570ustar00rootroot00000000000000Using without installing ------------------------ To use this script from an R session: source('statsmodels/tools/R2nparray/R/R2nparray.R') The 3 most useful commands are: cat_items(), convert_items() and apply_functions(). To print the content of an R regression to file in a format readable in python, you can: sink(file='tmp.py') data(iris) mod = lm(Sepal.Length ~ Sepal.Width, data=iris) cat_items(mod) sink() Install the R2nparray package ----------------------------- To make full use of the package's functions (including reading docs), you can install R2nparray in your R library. This first requires installing the devtools and roxygen2 packages: install.packages(c('devtools', 'roxygen2')) Then, you need to create a directory to host the documentation. The ``man`` directory should be located here: mkdir statsmodels/tools/R2nparray/man Finally, run ``R`` inside the ``statsmodels.tools.R2nparray`` folder, and execute: library(devtools) document() install() statsmodels-0.12.2/tools/README.rst000066400000000000000000000002231400612667500167710ustar00rootroot00000000000000Developers ---------- This directory is only of interest to developers. Many of the files are substantially out of date and subject to clean-up. statsmodels-0.12.2/tools/ci/000077500000000000000000000000001400612667500157005ustar00rootroot00000000000000statsmodels-0.12.2/tools/ci/README.md000066400000000000000000000003121400612667500171530ustar00rootroot00000000000000# Continuous Integration Tools These scripts are used to implement Continuous Integration on Travis, AppVeyor and Azure. They should not be removed without careful consideration of the consequences. statsmodels-0.12.2/tools/ci/appveyor_conda.bat000066400000000000000000000010011400612667500213710ustar00rootroot00000000000000REM Install required conda version and libraries @echo on curl -fsS -o c:\Miniconda.exe "https://repo.anaconda.com/miniconda/Miniconda3-latest-Windows-%PYTHON_ARCH%.exe" START /WAIT C:\Miniconda.exe /S /D=C:\Py set PATH=C:\Py;C:\Py\Scripts;C:\Py\Library\bin;%PATH% conda config --set always_yes yes conda update conda --quiet IF Defined SCIPY ( conda install numpy=%NUMPY% scipy=%SCIPY% icc_rt cython pandas pip nose patsy --quiet ) else ( conda install numpy scipy cython pandas pip nose patsy --quiet ) statsmodels-0.12.2/tools/ci/appveyor_pip.bat000066400000000000000000000003671400612667500211130ustar00rootroot00000000000000REM Install packages using pip set PATH=%PYTHON%;%PYTHON%\Scripts;%PATH% python -m pip install -U pip IF Defined SCIPY ( pip install numpy scipy==%SCIPY% cython pandas nose patsy ) else ( pip install numpy scipy cython pandas nose patsy ) statsmodels-0.12.2/tools/ci/azure_template.yml000066400000000000000000000032711400612667500214470ustar00rootroot00000000000000# Python package # Create and test a Python package on multiple Python versions. # Add steps that analyze code, save the dist with the build record, publish to a PyPI-compatible index, and more: # https://docs.microsoft.com/azure/devops/pipelines/languages/python parameters: # defaults for any parameters that are not specified name: '' vmImage: '' jobs: - job: ${{ parameters.name }}Test pool: vmImage: ${{ parameters.vmImage }} strategy: matrix: Python36: python.version: '3.6' Python37: python.version: '3.7' Python38: python.version: '3.8' maxParallel: 4 steps: - task: UsePythonVersion@0 inputs: versionSpec: '$(python.version)' architecture: 'x64' - script: | python -m pip install --upgrade pip "setuptools<50.0" pip install -r requirements.txt pip install -r requirements-dev.txt displayName: 'Install dependencies' - script: | pip install -e . displayName: 'Build Cython Extensions' - script: | pytest statsmodels --junitxml=junit/test-results.xml --skip-examples -n 2 --durations=25 displayName: 'pytest' - ${{ if eq(parameters.name, 'Linux') }}: # Only lint on Linux - script: | LINT=true ./lint.sh displayName: 'Checking code format (linting)' - task: PublishTestResults@2 inputs: testResultsFiles: '**/test-results.xml' testRunTitle: 'Python $(python.version)' condition: succeededOrFailed() - job: ${{ parameters.name }}Publish dependsOn: ${{ parameters.name }}Test pool: vmImage: ${{ parameters.vmImage }} steps: - task: UsePythonVersion@0 inputs: versionSpec: '3.x' architecture: 'x64' statsmodels-0.12.2/tools/ci/docbuild.sh000066400000000000000000000067071400612667500200330ustar00rootroot00000000000000# Change to doc directory cd "$SRCDIR"/docs # Run notebooks as tests pytest ../statsmodels/examples/tests set -e # Build documentation echo '========================================================================' echo '= Building documentation =' echo '========================================================================' echo 'make html 2>&1 | tee doc_build.log' # Multithreaded build export O="-j auto" make html 2>&1 | tee doc_build.log set +e # Info echo '========================================================================' echo '= Opportunities To Improve (Warnings) =' echo '========================================================================' grep -E '(WARNING)' doc_build.log | grep -v '(noindex|toctree)' # Check log echo '========================================================================' echo '= Broken Behavior (Errors and Warnings to be Fixed) =' echo '========================================================================' grep -E '(SEVERE|ERROR|WARNING)' doc_build.log | grep -Ev '(noindex|toctree)' # Check that docbuild succeeded. Exit 1 if not. echo "Checking if index.html exists" if [ -f "build/html/index.html" ]; then echo "docbuild succeeded."; else echo "docbuild failed. Aborting doctr."; echo "contents of build" ls build echo "contents of build/html" ls build/html exit 1; fi; # Build documentation echo '========================================================================' echo '= Checking Spelling =' echo '========================================================================' echo 'make spelling > doc_spelling.log 2>&1' make spelling > /dev/null echo '========================================================================' echo '= Spelling Mistakes =' echo '========================================================================' if [ -f "build/spelling/output.txt" ]; then cat build/spelling/output.txt fi; # Deploy with doctr cd "$SRCDIR" if [[ -z "$TRAVIS_TAG" ]]; then doctr deploy --built-docs docs/build/html/ --deploy-repo statsmodels/statsmodels.github.io devel > /dev/null; else if [[ "$TRAVIS_TAG" != *"dev"* ]]; then # do not push on dev tags echo doctr deploy --build-tags --built-docs docs/build/html/ --deploy-repo statsmodels/statsmodels.github.io "$TRAVIS_TAG" > /dev/null; doctr deploy --build-tags --built-docs docs/build/html/ --deploy-repo statsmodels/statsmodels.github.io "$TRAVIS_TAG" > /dev/null; if [[ "$TRAVIS_TAG" != *"rc"* ]]; then # do not push on main on rc echo doctr deploy --build-tags --built-docs docs/build/html/ --deploy-repo statsmodels/statsmodels.github.io stable > /dev/null; doctr deploy --build-tags --built-docs docs/build/html/ --deploy-repo statsmodels/statsmodels.github.io stable > /dev/null; fi; fi; fi; # Script to text examples and build docs on travis echo '========================================================================' echo '= Checking Doc Strings =' echo '========================================================================' cd "$SRCDIR" pip install numpydoc --upgrade python "$SRCDIR"/tools/validate_docstrings.py --errors=GL03,GL04,GL05,GL06,GL07,GL08,GL09,SS01,SS04,SS05,SS06,PR01,PR02,PR03,PR04,PR05,PR06,PR07,PR08,PR10,EX04,RT01,RT02,RT03,RT04,RT05,SA05,EX04 || true statsmodels-0.12.2/tools/ci/docbuild_install.sh000066400000000000000000000012541400612667500215510ustar00rootroot00000000000000# Additional installation requirements for travis docbuilds # Install system dependencies echo sudo apt-get update sudo apt-get update echo sudo apt-get install graphviz libgfortran3 enchant pandoc -qq sudo apt-get install graphviz libgfortran3 enchant pandoc -qq # doctr and pdr echo pip install sphinx jupyter nbconvert numpydoc pyyaml doctr pandas-datareader simplegeneric seaborn sphinxcontrib-spelling nbsphinx pip install sphinx sphinx-material jupyter nbconvert numpydoc pyyaml doctr pandas-datareader simplegeneric seaborn sphinxcontrib-spelling nbsphinx # Add pymc3 and theano for statespace_sarimax_pymc3. echo conda install theano pymc3 -y conda install theano pymc3 -y statsmodels-0.12.2/tools/ci/run_test.bat000066400000000000000000000011171400612667500202330ustar00rootroot00000000000000@echo on @IF not Defined PYTEST_DIRECTIVES GOTO :RUN_FROM_INSTALL @echo Running test from %CD% @echo pytest -n auto -r s statsmodels --skip-examples %PYTEST_DIRECTIVES% pytest -n auto -r s statsmodels --skip-examples %PYTEST_DIRECTIVES% @GOTO :End :RUN_FROM_INSTALL mkdir test-run cd test-run @echo PYTEST_DIRECTIVES is not defined, testing using install @echo Running test from %CD% @echo python -c "import statsmodels;statsmodels.test(['-r s', '-n 2', '--skip-examples'], exit=True) python -c "import statsmodels;statsmodels.test(['-r s', '-n 2', '--skip-examples'], exit=True) :End statsmodels-0.12.2/tools/ci/travis_conda.sh000066400000000000000000000026371400612667500207200ustar00rootroot00000000000000# Source to configure conda CI builds if [ "$TRAVIS_OS_NAME" = "linux" ]; then CONDA_FILE="Miniconda3-latest-Linux-x86_64.sh"; fi if [ "$TRAVIS_OS_NAME" = "osx" ]; then CONDA_FILE="Miniconda3-latest-MacOSX-x86_64.sh"; fi wget https://repo.continuum.io/miniconda/"$CONDA_FILE" -O miniconda.sh -nv chmod +x miniconda.sh ./miniconda.sh -b -p "$HOME"/miniconda export PATH="$HOME"/miniconda/bin:$PATH conda config --set always_yes yes conda update --quiet conda # Build package list to avoid empty package=versions; only needed for versioned packages PKGS="numpy"; if [ ${NUMPY} ]; then PKGS="${PKGS}=${NUMPY}"; fi PKGS="${PKGS} scipy"; if [ ${SCIPY} ]; then PKGS="${PKGS}=${SCIPY}"; fi PKGS="${PKGS} patsy"; if [ ${PATSY} ]; then PKGS="${PKGS}=${PATSY}"; fi PKGS="${PKGS} pandas"; if [ ${PANDAS} ]; then PKGS="${PKGS}=${PANDAS}"; fi PKGS="${PKGS} Cython"; if [ ${CYTHON} ]; then PKGS="${PKGS}=${CYTHON}"; fi if [ ${USE_MATPLOTLIB} = true ]; then PKGS="${PKGS} matplotlib"; if [ ${MATPLOTLIB} ]; then PKGS="${PKGS}=${MATPLOTLIB}"; fi; fi if [ ${COVERAGE} = true ]; then export COVERAGE_OPTS=" --cov=statsmodels "; else export COVERAGE_OPTS=""; fi echo conda create --yes --quiet -n statsmodels-test python=${PYTHON} ${BLAS} ${PKGS} ${OPTIONAL} ${DEPEND_ALWAYS} conda create --yes --quiet -n statsmodels-test python=${PYTHON} ${BLAS} ${PKGS} ${OPTIONAL} ${DEPEND_ALWAYS} source activate statsmodels-test python -m pip install --upgrade pip statsmodels-0.12.2/tools/ci/travis_pip.sh000066400000000000000000000033601400612667500204160ustar00rootroot00000000000000# Source to configure pip CI builds # Wheelhouse for various packages missing from pypi. EXTRA_WHEELS="https://5cf40426d9f06eb7461d-6fe47d9331aba7cd62fc36c7196769e4.ssl.cf2.rackcdn.com" # Wheelhouse for daily builds of some packages. PRE_WHEELS="https://7933911d6844c6c53a7d-47bd50c35cd79bd838daf386af554a83.ssl.cf2.rackcdn.com" EXTRA_PIP_FLAGS="--find-links=$EXTRA_WHEELS" # Build package list to avoid empty package=versions; only needed for versioned packages PKGS="${PKGS} numpy"; if [ ${NUMPY} ]; then PKGS="${PKGS}==${NUMPY}"; fi PKGS="${PKGS} scipy"; if [ ${SCIPY} ]; then PKGS="${PKGS}==${SCIPY}"; fi PKGS="${PKGS} patsy"; if [ ${PATSY} ]; then PKGS="${PKGS}==${PATSY}"; fi PKGS="${PKGS} pandas"; if [ ${PANDAS} ]; then PKGS="${PKGS}==${PANDAS}"; fi PKGS="${PKGS} Cython"; if [ ${CYTHON} ]; then PKGS="${PKGS}==${CYTHON}"; fi if [ ${USE_MATPLOTLIB} = true ]; then PKGS="${PKGS} matplotlib" if [ ${MATPLOTLIB} ]; then PKGS="${PKGS}==${MATPLOTLIB}" fi fi if [ "${PIP_PRE}" = true ]; then EXTRA_PIP_FLAGS="--pre $EXTRA_PIP_FLAGS --find-links $PRE_WHEELS" fi # travis osx python support is limited. Use homebrew/pyenv to install python. if [ "$TRAVIS_OS_NAME" = "osx" ]; then brew update && brew upgrade pyenv eval "$(pyenv init -)" pyenv install "$PYTHON" pyenv shell "$PYTHON" fi # Install in our own virtualenv python -m pip install --upgrade pip pip install --upgrade virtualenv virtualenv --python=python venv source venv/bin/activate python --version # just to check python -m pip install --upgrade pip pip install ${EXTRA_PIP_FLAGS} ${PKGS} ${DEPEND_ALWAYS} if [ "${PIP_PRE}" = true ]; then pip install -i https://pypi.anaconda.org/scipy-wheels-nightly/simple numpy pandas scipy --upgrade --use-deprecated=legacy-resolver fi statsmodels-0.12.2/tools/dataset_rst.py000077500000000000000000000046321400612667500202040ustar00rootroot00000000000000#!/usr/bin/env python3 """ Run this script to convert dataset documentation to ReST files. Relies on the meta-information from the datasets of the currently installed version. Ie., it imports the datasets package to scrape the meta-information. """ import glob import inspect import os from os.path import dirname, join, realpath from string import Template import statsmodels.api as sm file_path = dirname(__file__) dest_dir = realpath(join(file_path, '..', 'docs', 'source', 'datasets', 'generated')) datasets = dict(inspect.getmembers(sm.datasets, inspect.ismodule)) datasets.pop('utils') last_mod_time = {} for dataset in datasets: root = os.path.abspath(os.path.split(datasets[dataset].__file__)[0]) files = glob.glob(os.path.join(root, '*')) if not files: raise NotImplementedError('Must be files to read the date') mtime = 0.0 for f in files: if f.startswith('__') and f != '__init__.py': continue mtime = max(mtime, os.path.getmtime(f)) last_mod_time[dataset] = mtime doc_template = Template(u"""$TITLE $title_ Description ----------- $DESCRIPTION Notes ----- $NOTES Source ------ $SOURCE Copyright --------- $COPYRIGHT\ """) if __name__ == "__main__": if not os.path.exists(dest_dir): os.makedirs(dest_dir) for dataset in datasets: rst_file_name = dataset + '.rst' write_pth = join(dest_dir, rst_file_name) if os.path.exists(write_pth): rst_mtime = os.path.getmtime(write_pth) if rst_mtime > last_mod_time[dataset]: print('Skipping creation of {0} since the rst file is newer ' 'than the data files.'.format(rst_file_name)) continue data_mod = datasets[dataset] title = getattr(data_mod, 'TITLE') descr = getattr(data_mod, 'DESCRLONG') copyr = getattr(data_mod, 'COPYRIGHT') notes = getattr(data_mod, 'NOTE') source = getattr(data_mod, 'SOURCE') write_file = doc_template.substitute(TITLE=title, title_='=' * len(title), DESCRIPTION=descr, NOTES=notes, SOURCE=source, COPYRIGHT=copyr) print('Writing {0}.'.format(rst_file_name)) with open(os.path.realpath(write_pth), 'w') as rst_file: rst_file.write(write_file) statsmodels-0.12.2/tools/estmat2nparray.ado000066400000000000000000000075671400612667500207650ustar00rootroot00000000000000* * Save estimation results and matrices to a Python module * * Based on mat2nparray by Skipper * Changes by Josef * * changes * ------- * write also column and row names of matrices to py module * replace missing values by np.nan in matrices * make namelist optional * add estimation results from e(), e(scalars) and e(macros), not the matrices in e * make estimation result optional * add aliases for params_table * do not split col or row names if only 1 - changed my mind: always list * Issues * ------ * row and colum names if only a single row or column - list or string capture program drop estmat2nparray program define estmat2nparray version 11.0 syntax [namelist(min=1)], SAVing(str) [ Format(str) APPend REPlace NOEst] if "`format'"=="" local format "%16.0g" local saving: subinstr local saving "." ".", count(local ext) if !`ext' local saving "`saving'.py" tempname myfile file open `myfile' using "`saving'", write text `append' `replace' file write `myfile' "import numpy as np" _n _n /* get results from e()*/ if "`noest'" == "" { file write `myfile' "est = dict(" _n local escalars : e(scalars) foreach ii in `escalars'{ file write `myfile' " " "`ii'" " = " "`e(`ii')'" "," _n } local emacros : e(macros) foreach ii in `emacros' { file write `myfile' " " "`ii'" " = " `"""' "`e(`ii')'" `"""' "," _n } file write `myfile' " )" _n _n } /* end write e()*/ foreach mat of local namelist { mkarray `mat' `myfile' `format' } file write `myfile' "from statsmodels.tools.tools import Bunch" _n if "`noest'" == "" { file write `myfile' " for i,att in enumerate(['params', 'bse', 'tvalues', 'pvalues']):" _n file write `myfile' " self[att] = self.params_table[:,i]" _n _n } file write `myfile' "" _n file write `myfile' "results = Bunch(" _n foreach mat of local namelist { file write `myfile' " `mat'=`mat', " _n file write `myfile' " `mat'_colnames=`mat'_colnames, " _n file write `myfile' " `mat'_rownames=`mat'_rownames, " _n } if "`noest'" == "" { file write `myfile' " **est" _n } file write `myfile' " )" _n _n file close `myfile' end capture program drop mkarray program define mkarray args mat myfile fmt local nrows = rowsof(`mat') local ncols = colsof(`mat') local i 1 local j 1 file write `myfile' "`mat' = np.array([" local justifyn = length("`mat' = np.array([") forvalues i=1/`nrows' { forvalues j = 1/`ncols' { if `i' > 1 | `j' > 1 { // then we need to indent forvalues k=1/`justifyn' { file write `myfile' " " } } if `i' < `nrows' | `j' < `ncols' { if mi(`mat'[`i',`j']) { file write `myfile' "np.nan" ", " _n } else { file write `myfile' `fmt' (`mat'[`i',`j']) ", " _n } } else { if mi(`mat'[`i',`j']) { file write `myfile' "np.nan" } else { file write `myfile' `fmt' (`mat'[`i',`j']) } } } } if `nrows' == 1 | `ncols' == 1 { file write `myfile' "])" _n _n } else { file write `myfile' "]).reshape(`nrows',`ncols')" _n _n } capture drop colnms local colnms: coln `mat' capture file write `myfile' "`mat'_colnames = '" "`colnms'" "'" * always split -> return list for single column * set > 1 to avoid list for single column if `ncols' > 0 { file write `myfile' ".split()" _n _n } else { file write `myfile' _n _n } capture drop rownms local rownms: rown `mat' capture file write `myfile' "`mat'_rownames = '" "`rownms'" "'" * always split -> return list for single row if `nrows' > 0 { file write `myfile' ".split()" _n _n } else { file write `myfile' _n _n } end statsmodels-0.12.2/tools/export_notebooks_to_python.py000066400000000000000000000112441400612667500233700ustar00rootroot00000000000000#!/usr/bin/env python # -*- coding: utf-8 -*- import argparse import glob import logging import os import textwrap import nbconvert from yapf.yapflib.yapf_api import FormatCode BASE_PATH = os.path.split(os.path.abspath(__file__))[0] DO_NOT_EDIT = """ # DO NOT EDIT # Autogenerated from the notebook {notebook}. # Edit the notebook and then sync the output with this file. # # flake8: noqa # DO NOT EDIT """ logger = logging.getLogger('notebook-exporter') logger.setLevel(logging.INFO) ch = logging.StreamHandler() ch.setLevel(logging.INFO) logger.addHandler(ch) parser = argparse.ArgumentParser(description=""" Sync notebooks to python by exporting. The exported files are always written in ../python relative to the notebooks. Requires nbconvert and yapf. """) parser.add_argument('--full-path', '-fp', type=str, default=None, help='Full Path to notebook to convert. Converts all ' 'notebooks in FULL_PATH by default. If not ' 'specified, searches for examples in ' '../examples/notebooks (relative to this file).') parser.add_argument('--notebook', '-nb', type=str, default=None, help='Name of a single notebook to export. If not ' 'provided, all notebooks found are exported. Appends ' '.ipynb if NOTEBOOK does not end with this ' 'extension.') parser.add_argument('--force', '-f', action='store_true', help='Force conversion if python file in destination ' 'exists and is newer than notebook.') def is_newer(file1, file2, strict=True): """ Determine if file1 has been modified after file2 Parameters ---------- file1 : str File path. May not exist, in which case False is returned. file1 : str File path. Must exist. strict : bool Use strict inequality test (>). If False, then returns True for files with the same modified time. Returns ------- newer : bool True if file1 is strictly newer than file 2 """ try: t1 = os.path.getmtime(file1) t2 = os.path.getmtime(file2) except FileNotFoundError: return False if strict: return t1 > t2 return t1 >= t2 def main(): args = parser.parse_args() full_path = args.full_path force = args.force if full_path is None: full_path = os.path.join(BASE_PATH, '..', 'examples', 'notebooks') notebook = args.notebook if notebook is None: notebooks = glob.glob(os.path.join(full_path, '*.ipynb')) else: if not notebook.endswith('.ipynb'): notebook = notebook + '.ipynb' notebook = os.path.abspath(os.path.join(full_path, notebook)) if not os.path.exists(notebook): raise FileNotFoundError('Notebook {0} not found.'.format(notebook)) notebooks = [notebook] if not notebooks: import warnings warnings.warn('No notebooks found', UserWarning) for nb in notebooks: nb_full_name = os.path.split(nb)[1] nb_name = os.path.splitext(nb_full_name)[0] py_name = nb_name + '.py' # Get base directory to notebook out_file = os.path.split(nb)[0] # Write to ../python out_file = os.path.join(out_file, '..', 'python', py_name) if is_newer(out_file, nb) and not force: logger.info('Skipping {0}, exported version newer than ' 'notebook'.format(nb_name)) continue logger.info('Converting {0}'.format(nb_name)) with open(nb, 'r') as nb_file: converter = nbconvert.PythonExporter() python = converter.from_file(nb_file) code = python[0].split('\n') code_out = [] for i, block in enumerate(code): if 'get_ipython' in block: continue elif block.startswith('# In[ ]:'): continue if block.startswith('#'): # Wrap comments from Markdown block = textwrap.fill(block, width=74) block = block.replace('\n', '\n# ') code_out.append(block) if not code_out[0]: code_out = code_out[1:] loc = 0 if 'coding' in code_out[0]: loc = 1 code_out.insert(loc, DO_NOT_EDIT.format(notebook=nb_full_name)) code_out = '\n'.join(code_out) code_out, success = FormatCode(code_out, style_config='pep8') with open(out_file, 'w') as of: of.write(code_out) if __name__ == '__main__': main() statsmodels-0.12.2/tools/generate_formula_api.py000077500000000000000000000052151400612667500220350ustar00rootroot00000000000000#!/usr/bin/env python """ This will generate an API file for formula in dir/statsmodels/formula/api.py It first builds statsmodels in place, then generates the file. It's to be run by developers to add files to the formula API without having to maintain this by hand. usage generate_formula_api /home/skipper/statsmodels/statsmodels/ """ import os import sys def iter_subclasses(cls, _seen=None, template_classes=[]): """ Generator to iterate over all the subclasses of Model. Based on http://code.activestate.com/recipes/576949-find-all-subclasses-of-a-given-class/ Yields class """ if not isinstance(cls, type): raise TypeError('itersubclasses must be called with ' 'new-style classes, not %.100r' % cls) if _seen is None: _seen = set() try: subs = cls.__subclasses__() except TypeError: # fails only when cls is type subs = cls.__subclasses__(cls) for sub in subs: if sub not in _seen and sub.__name__ not in template_classes: _seen.add(sub) # we do not want to yield the templates, but we do want to # recurse on them yield sub for sub in iter_subclasses(sub, _seen, template_classes): yield sub def write_formula_api(directory): template_classes = ['DiscreteModel', 'BinaryModel', 'MultinomialModel', 'OrderedModel', 'CountModel', 'LikelihoodModel', 'GenericLikelihoodModel', 'TimeSeriesModel', # this class should really be deleted 'ARIMAProcess', # these need some more work, so do not expose them 'ARIMA', 'VAR', 'SVAR', 'AR', 'NBin', 'NbReg', 'ARMA', ] path = os.path.join(directory, 'statsmodels', 'formula', 'api.py') fout = open(path, 'w') for model in iter_subclasses(Model, template_classes=template_classes): print("Generating API for %s" % model.__name__) fout.write( 'from ' + model.__module__ + ' import ' + model.__name__ + '\n' ) fout.write( model.__name__.lower() + ' = ' + model.__name__ + '.from_formula\n' ) fout.close() if __name__ == "__main__": import statsmodels.api as sm print("Generating formula API for statsmodels version %s" % sm.version.full_version) directory = sys.argv[1] cur_dir = os.path.dirname(__file__) os.chdir(directory) # it needs to be installed to walk the whole subclass chain? from statsmodels.base.model import Model write_formula_api(directory) statsmodels-0.12.2/tools/nbgenerate.py000077500000000000000000000220731400612667500200000ustar00rootroot00000000000000#!/usr/bin/env python3 # -*- coding: utf-8 -*- import argparse from functools import partial import hashlib import io import json import os import shutil import sys from colorama import Fore, init from nbconvert import HTMLExporter, RSTExporter from nbconvert.preprocessors import ExecutePreprocessor import nbformat try: from concurrent import futures has_futures = True except ImportError: has_futures = False init() here = os.path.dirname(__file__) pkgdir = os.path.split(here)[0] EXAMPLE_DIR = os.path.abspath(os.path.join(pkgdir, "examples")) SOURCE_DIR = os.path.join(EXAMPLE_DIR, "notebooks") DOC_SRC_DIR = os.path.join(pkgdir, "docs", "source") DST_DIR = os.path.abspath(os.path.join(DOC_SRC_DIR, "examples", "notebooks", "generated")) EXECUTED_DIR = DST_DIR error_message = """ ****************************************************************************** ERROR: Error occurred when running {notebook} {exception} {message} ****************************************************************************** """ for dname in [EXECUTED_DIR, DST_DIR]: if not os.path.exists(dname): os.makedirs(dname) def execute_nb(src, dst, allow_errors=False, timeout=1000, kernel_name=None): """ Execute notebook in `src` and write the output to `dst` Parameters ---------- src, dst: str path to notebook allow_errors: bool timeout: int kernel_name: str defualts to value set in notebook metadata Returns ------- dst: str """ with io.open(src, encoding='utf-8') as f: nb = nbformat.read(f, as_version=4) ep = ExecutePreprocessor(allow_errors=False, timeout=timeout, kernel_name=kernel_name) ep.preprocess(nb, {'metadata': {'path': SOURCE_DIR}}) with io.open(dst, 'wt', encoding='utf-8') as f: nbformat.write(nb, f) return dst def convert(src, dst, to='rst'): """ Convert a notebook `src`. Parameters ---------- src, dst: str filepaths to: {'rst', 'html'} format to export to """ dispatch = {'rst': RSTExporter, 'html': HTMLExporter} exporter = dispatch[to.lower()]() (body, resources) = exporter.from_filename(src) with io.open(dst, 'wt', encoding='utf-8') as f: f.write(body) return dst def find_notebooks(directory=None): if directory is None: directory = SOURCE_DIR nbs = (os.path.join(directory, x) for x in os.listdir(directory) if x.endswith('.ipynb')) return nbs def do_one(nb, to=None, execute=None, timeout=None, kernel_name=None, report_error=True, error_fail=False, skip_existing=False, execute_only=False): from traitlets.traitlets import TraitError import jupyter_client os.chdir(SOURCE_DIR) name = os.path.basename(nb) dst = os.path.join(EXECUTED_DIR, name) hash_file = f"{os.path.splitext(dst)[0]}.json" existing_hash = "" if os.path.exists(hash_file): with open(hash_file, encoding="utf-8") as hf: existing_hash = json.load(hf) with io.open(nb, mode="rb") as f: current_hash = hashlib.sha512(f.read()).hexdigest() update_needed = existing_hash != current_hash update_needed = update_needed or not skip_existing if not update_needed: print('Skipping {0}'.format(nb)) if execute and update_needed: print("Executing %s to %s" % (nb, dst)) try: nb = execute_nb(nb, dst, timeout=timeout, kernel_name=kernel_name) except Exception as e: if report_error: print(Fore.RED + error_message.format(notebook=nb, exception=str(e), message=str(e.args[0]))) print(Fore.RESET) if error_fail: raise elif not execute: print("Copying (without executing) %s to %s" % (nb, dst)) shutil.copy(nb, dst) if execute_only: with open(hash_file, encoding="utf-8", mode="w") as hf: json.dump(current_hash, hf) return dst dst = os.path.splitext(os.path.join(DST_DIR, name))[0] + '.' + to print("Converting %s to %s" % (nb, dst)) try: convert(nb, dst, to=to) except TraitError: kernels = jupyter_client.kernelspec.find_kernel_specs() msg = ('Could not find kernel named `%s`, Available kernels:\n %s' % kernel_name, kernels) raise ValueError(msg) with open(hash_file, encoding="utf-8", mode="w") as hf: json.dump(current_hash, hf) return dst def do(fp=None, directory=None, to='html', execute=True, timeout=1000, kernel_name='', parallel=False, report_errors=True, error_fail=False, skip_existing=False, execute_only=False, skip_specific=()): if fp is None: nbs = find_notebooks(directory) else: nbs = [fp] nbs = list(nbs) skip = set() for nb in nbs: for skip_nb in skip_specific: if skip_nb in nb: skip.add(nb) nbs = [nb for nb in nbs if nb not in skip] if kernel_name is None: kernel_name = find_kernel_name() func = partial(do_one, to=to, execute=execute, timeout=timeout, kernel_name=kernel_name, report_error=report_errors, error_fail=error_fail, skip_existing=skip_existing, execute_only=execute_only) if parallel and has_futures: with futures.ProcessPoolExecutor() as pool: for dst in pool.map(func, nbs): print("Finished %s" % dst) else: for nb in nbs: func(nb) print("Finished %s" % nb) skip_func = partial(do_one, to=to, execute=False, timeout=timeout, kernel_name=kernel_name, report_error=report_errors, error_fail=error_fail, skip_existing=skip_existing, execute_only=execute_only) for nb in skip: skip_func(nb) print("Finished (without execution) %s" % nb) def find_kernel_name(): import jupyter_client kernels = jupyter_client.kernelspec.find_kernel_specs() kernel_name = 'python%s' % sys.version_info.major if kernel_name not in kernels: return '' return kernel_name parser = argparse.ArgumentParser(description="Process example notebooks") parser.add_argument("--fp", type=str, default=None, help="Path to notebook to convert. Converts all notebooks " "in `directory` by default.") parser.add_argument("--directory", type=str, default=None, help="Path to notebook directory to convert") parser.add_argument("--to", type=str, default="html", help="Type to convert to. One of `{'html', 'rst'}`") parser.add_argument("--timeout", type=int, default=1000, help="Seconds to allow for each cell before timing out") parser.add_argument("--kernel_name", type=str, default=None, help="Name of kernel to execute with") parser.add_argument("--skip-execution", dest='skip_execution', action='store_true', help="Skip execution notebooks before converting") parser.add_argument("--execute-only", dest='execute_only', action='store_true', help="Execute notebooks but do not convert to html") parser.add_argument('--parallel', dest='parallel', action='store_true', help='Execute notebooks in parallel') parser.add_argument('--report-errors', dest='report_errors', action='store_true', help='Report errors that occur when executing notebooks') parser.add_argument('--fail-on-error', dest='error_fail', action='store_true', help='Fail when an error occurs when executing a cell ' 'in a notebook.') parser.add_argument('--skip-existing', dest='skip_existing', action='store_true', help='Skip execution of an executed file exists and ' 'is newer than the notebook.') parser.add_argument('--execution-blacklist', type=str, default=None, help='Comma separated list of notebook names to skip, e.g,' 'slow-notebook.ipynb,other-notebook.ipynb') parser.set_defaults(parallel=True, skip_execution=False, report_errors=True, error_fail=False, skip_existing=False) def main(): args = parser.parse_args() skip_nb_exec = args.execution_blacklist skip_specific = skip_nb_exec.split(",") if skip_nb_exec else [] do(fp=args.fp, directory=args.directory, to=args.to, execute=not args.skip_execution, timeout=args.timeout, kernel_name=args.kernel_name, parallel=args.parallel, report_errors=args.report_errors, error_fail=args.error_fail, skip_existing=args.skip_existing, execute_only=args.execute_only, skip_specific=skip_specific) if __name__ == '__main__': main() statsmodels-0.12.2/tools/releasing/000077500000000000000000000000001400612667500172565ustar00rootroot00000000000000statsmodels-0.12.2/tools/releasing/enumerate-api.py000066400000000000000000000235101400612667500223650ustar00rootroot00000000000000""" This tool is used in generating meaningful release notes. This tool simplifies reading the current statsmodels API to a JSON file. It can also be used against any installed statsmodels package to read the API. The typical use would be source venv/legacy-statsmodels/activate python enumerate-api.py -of statsmodels-legacy.json source venv/legacy-statsmodels/deactivate python enumerate-api.py --diff statsmodels-legacy.json which produces a RST file that can be included in the docs or edited. """ from setuptools import find_packages import argparse import importlib import inspect import json import logging import os from pkgutil import iter_modules import sys def find_modules(path): modules = set() for pkg in find_packages(path): modules.add(pkg) pkgpath = path + "/" + pkg.replace(".", "/") if sys.version_info.major == 2 or ( sys.version_info.major == 3 and sys.version_info.minor < 6 ): for _, name, ispkg in iter_modules([pkgpath]): if not ispkg: modules.add(pkg + "." + name) else: for info in iter_modules([pkgpath]): if not info.ispkg: modules.add(pkg + "." + info.name) return modules def update_class(func, funcs, class_name, full_name): logger = logging.getLogger("enumerate-api") class_api = {} for v2 in dir(func): if v2.startswith("_") and v2 != "__init__": continue method = getattr(func, v2) if not ( inspect.isfunction(method) or inspect.isclass(method) or inspect.ismethod(method) or isinstance(method, property) ): continue if isinstance(method, property): try: name = f"{method.fget.__module__}.{class_name}.{v2}" class_api[name] = tuple() except Exception: name = "" else: sig = inspect.signature(method) name = f"{method.__module__}.{class_name}.{v2}" class_api[name] = tuple(k for k in sig.parameters.keys()) logger.info(name) funcs[full_name] = class_api def walk_modules(path): logger = logging.getLogger("enumerate-api") modules = find_modules(path) api = {"functions": {}, "classes": {}} for mod in modules: module = f"statsmodels.{mod}" logger.info(module) if ( ".sandbox" in module or module.endswith(".tests") or ".tests." in module ): continue try: lib = importlib.import_module(module) except (ImportError, OSError): lib = None if lib is None: continue for v in dir(lib): if v.startswith("_"): continue func = getattr(lib, v) if not (inspect.isfunction(func) or inspect.isclass(func)): continue if "statsmodels" not in func.__module__: continue name = f"{func.__module__}.{v}" try: if inspect.isfunction(func): d = api["functions"] else: d = api["classes"] sig = inspect.signature(func) d[name] = tuple(k for k in sig.parameters.keys()) except Exception: d[name] = tuple() if inspect.isclass(func): update_class(func, api["classes"], v, name) logger.info(f"{module}.{v}") return api def generate_diff(api, other): api_classes = set(api["classes"].keys()) other_classes = set(other["classes"].keys()) new_classes = api_classes.difference(other_classes) removed_classes = set(other_classes).difference(api_classes) new_methods = {} removed_methods = {} changed_methods = {} expanded_methods = {} expanded_funcs = {} changed_funcs = {} common = api_classes.intersection(other_classes) for key in common: current_class = api["classes"][key] other_class = other["classes"][key] new = set(current_class.keys()).difference(other_class.keys()) for meth in new: new_methods[meth] = current_class[meth] removed = set(other_class.keys()).difference(current_class.keys()) for meth in removed: removed_methods[meth] = tuple(other_class[meth]) common_methods = set(other_class.keys()).intersection( current_class.keys() ) for meth in common_methods: if current_class[meth] != tuple(other_class[meth]): if set(current_class[meth]).issuperset(other_class[meth]): expanded_methods[key] = set( current_class[meth] ).difference(other_class[meth]) else: changed_methods[key] = { "current": current_class[meth], "other": tuple(other_class[meth]), } api_funcs = set(api["functions"].keys()) other_funcs = set(other["functions"].keys()) new_funcs = api_funcs.difference(other_funcs) removed_funcs = set(other_funcs).difference(api_funcs) common_funcs = api_funcs.intersection(other_funcs) for key in common_funcs: current_func = api["functions"][key] other_func = other["functions"][key] if current_func == tuple(other_func): continue elif set(current_func).issuperset(other_func): expanded_funcs[key] = set(current_func).difference(other_func) else: changed_funcs[key] = { "current": current_func, "other": tuple(other_func), } def header(v, first=False): return ( "\n\n" * (not first) + f"\n{v}\n" + "-" * len(v) + "\n" ) with open("api-differences.rst", "w") as rst: rst.write(header("New Classes", first=True)) for val in sorted(new_classes): rst.write(f"* :class:`{val}`\n") rst.write(header("Removed Classes")) for val in sorted(removed_classes): rst.write(f"* ``{val}``\n") rst.write(header("New Methods")) for val in sorted(new_methods): rst.write(f"* :meth:`{val}`\n") rst.write(header("Removed Methods")) for val in sorted(removed_methods): rst.write(f"* ``{val}``\n") rst.write(header("Methods with New Arguments")) for val in sorted(expanded_methods): args = map(lambda v: f"``{v}``", expanded_methods[val]) rst.write(f"* :meth:`{val}`: " + ", ".join(args) + "\n") rst.write(header("Methods with Changed Arguments")) for val in sorted(changed_methods): rst.write(f"* :meth:`{val}`\n") name = val.split(".")[-1] args = ", ".join(changed_methods[val]["current"]) if args.startswith("self"): args = args[4:] if args.startswith(", "): args = args[2:] rst.write(f" * New: ``{name}({args})``\n") args = ", ".join(changed_methods[val]["other"]) if args.startswith("self"): args = args[4:] if args.startswith(", "): args = args[2:] rst.write(f" * Old: ``{name}({args})``\n") rst.write(header("New Functions")) for val in sorted(new_funcs): rst.write(f"* :func:`{val}`\n") rst.write(header("Removed Functions")) for val in sorted(removed_funcs): rst.write(f"* ``{val}``\n") rst.write(header("Functions with New Arguments")) for val in sorted(expanded_funcs): args = map(lambda v: f"``{v}``", expanded_funcs[val]) rst.write(f"* :func:`{val}`: " + ", ".join(args) + "\n") rst.write(header("Functions with Changed Arguments")) for val in sorted(changed_funcs): rst.write(f"* :func:`{val}`\n") name = val.split(".")[-1] args = ", ".join(changed_funcs[val]["current"]) rst.write(f" * New: ``{name}({args})``\n") args = ", ".join(changed_funcs[val]["other"]) rst.write(f" * Old: ``{name}({args})``\n") parser = argparse.ArgumentParser( description=""" Store the current visible API as json, or read the API of any version into a JSON file, or compare the current API to a different version. """ ) parser.add_argument( "--file-path", "-fp", type=str, default=None, help="Path to the root directory. If not provided, assumed to be be" "the import location of statsmodels.", ) parser.add_argument( "--out-file", "-of", type=str, default=None, help="Name of output json file. Default is statsmodels-{version}-api.json", ) parser.add_argument( "--diff", "-d", type=str, default=None, help="json file to diff" ) def main(): args = parser.parse_args() logger = logging.getLogger("enumerate-api") logger.setLevel(logging.INFO) ch = logging.StreamHandler() formatter = logging.Formatter( "%(asctime)s - %(name)s - %(levelname)s - %(message)s" ) ch.setFormatter(formatter) logger.addHandler(ch) file_path = args.file_path if file_path is None: import statsmodels file_path = os.path.dirname(statsmodels.__file__) current_api = walk_modules(file_path) out_file = args.out_file if out_file is None: import statsmodels out_file = f"statsmodels-{statsmodels.__version__}-api.json" with open(out_file, "w") as api: json.dump(current_api, api, indent=2, sort_keys=True) if args.diff is not None: with open(args.diff, "r") as other: other_api = json.load(other) generate_diff(current_api, other_api) if __name__ == "__main__": main() statsmodels-0.12.2/tools/releasing/release_note.py000066400000000000000000000141321400612667500222760ustar00rootroot00000000000000""" Generate a release note template. The key parameters are RELEASE, VERSION, MILESTONE BRANCH, and LAST_COMMIT_SHA. LAST_COMMIT_SHA is the sha of the commit used to produce the previous version. This is used to determine the time stamp where commits in the current release begin. Requires PyGitHub, dateparser and jinja2 """ from collections import defaultdict import datetime as dt import os import dateparser from github import Github from jinja2 import Template # Full release version RELEASE = "0.12.2" # The current milestone and short version VERSION = MILESTONE = "0.12" # This is the final commit from the previous release LAST_COMMIT_SHA = "6691939be971981cb617cd5ecda5fed0ad201e1c" # Branch, usually master but can be a maintenance branch as well BRANCH = "maintenance/0.12.x" # Provide access token using command line to keep out of repo ACCESS_TOKEN = os.environ.get("GITHUB_ACCESS_TOKEN", None) if not ACCESS_TOKEN: raise RuntimeError("Must set environment variable GITHUB_ACCESS_TOKEN " "containing a valid GitHub access token before running" "this program.") # Using an access token g = Github(ACCESS_TOKEN) # Get the repo statsmodels = g.get_user("statsmodels").get_repo("statsmodels") # Look up the modification time of the commit used to tag the previous release last_modified = statsmodels.get_commit(LAST_COMMIT_SHA).commit.last_modified last_modified = dateparser.parse(last_modified) # Look for times creater than this time plus 1 second first_commit_time = last_modified + dt.timedelta(seconds=1) first_commit_time_iso = first_commit_time.isoformat() # General search for sm/sm, PR, merged, merged> first commit time and branch query_parts = ("repo:statsmodels/statsmodels", "is:pr", "is:merged", "merged:>{}".format(first_commit_time_iso), "base:{}".format(BRANCH)) query = " ".join(query_parts) merged_pull_data = [] merged_pulls = g.search_issues(query) # Get the milestone for the current release or create if it does not exist milestone = None for ms in statsmodels.get_milestones(): if ms.title == MILESTONE: milestone = ms if milestone is None: description = "Release {} issues and pull requests".format(MILESTONE) milestone = statsmodels.create_milestone(MILESTONE, state="open", description=description) # Get PR data and set the milestone if needed for pull in merged_pulls: merged_pull_data.append({"number": pull.number, "title": pull.title, "login": pull.user.login, "labels": pull.labels, "milestone": pull.milestone} ) if pull.milestone is None or pull.milestone != milestone: pull.edit(milestone=milestone) merged_pull_data = sorted(merged_pull_data, key=lambda x: x["number"]) # Robust name resolutions using commits and GitHub lookup names = defaultdict(set) extra_names = set() for pull in merged_pull_data: print("Reading commit data for PR#{}".format(pull["number"])) pr = statsmodels.get_pull(pull["number"]) for commit in pr.get_commits(): name = commit.commit.author.name if name and commit.author: names[commit.author.login].update([name]) elif name: extra_names.update([name]) for login in names: user = g.get_user(login) if user.name: names[login].update([user.name]) # Continue trying to resolve to human names contributors = [] for login in names: print("Reading user data for {}".format(login)) user_names = list(names[login]) if len(user_names) == 1: name = user_names[0] if " " in name: name = name.title() contributors.append(name) else: valid = [name for name in user_names if " " in name] if len(valid) == 0: contributors.append(login) else: contributors.append(valid[0].title()) contributors = sorted(set(contributors)) # Get all issues closed since first_commit_time_iso query_parts = ("repo:statsmodels/statsmodels", "is:issue", "is:closed", "closed:>{}".format(first_commit_time_iso)) query = " ".join(query_parts) closed_issues = g.search_issues(query) # Set the milestone for these issues if needed for issue in closed_issues: if issue.milestone is None or issue.milestone != milestone: issue.edit(milestone=milestone) issues_closed = closed_issues.totalCount # Create a What's New Dictionary to automatically populate the template # Structure is dict[module, dict[pr number, sanitized title]] whats_new = defaultdict(dict) for pull in merged_pull_data: if pull["labels"]: labels = [lab.name for lab in pull["labels"] if not lab.name.startswith("type")] if "maintenance" in labels and len(labels) > 1: labels.remove("maintenance") elif "comp-docs" in labels and len(labels) > 1: labels.remove("comp-docs") for label in labels: label = label.split("comp-")[-1].replace("-", ".") number = pull["number"] title = pull["title"] if ": " in title: title = ": ".join(title.split(": ")[1:]) title = title[:1].upper() + title[1:] whats_new[label][number] = title whats_new = {key: whats_new[key] for key in sorted(whats_new)} # Variables for the template variables = {"milestone": MILESTONE, "release": RELEASE, "version": VERSION, "issues_closed": issues_closed, "pulls_merged": len(merged_pull_data), "contributors": contributors, "pulls": merged_pull_data, "whats_new": whats_new, } # Read the template and generate the output with open("release_note.tmpl", encoding="utf-8") as tmpl: tmpl_data = tmpl.read() t = Template(tmpl_data) rendered = t.render(**variables) file_name = "version{}.rst".format(VERSION) with open(file_name, encoding="utf-8", mode="w") as out: out.write(rendered) statsmodels-0.12.2/tools/releasing/release_note.tmpl000066400000000000000000000061741400612667500226310ustar00rootroot00000000000000:orphan: {% set release_header = "Release " + release -%} {%- set release_marker = "=" * release_header|length -%} {{ release_marker }} {{ release_header }} {{ release_marker }} Release summary =============== statsmodels is using github to store the updated documentation. Two version are available: - `Stable `_, the latest release - `Development `_, the latest build of the master branch **Warning** API stability is not guaranteed for new features, although even in this case changes will be made in a backwards compatible way if possible. The stability of a new feature depends on how much time it was already in statsmodels master and how much usage it has already seen. If there are specific known problems or limitations, then they are mentioned in the docstrings. Stats ----- **Issues Closed**: {{ issues_closed }} **Pull Requests Merged**: {{ pulls_merged }} The Highlights ============== What's new - an overview ======================== The following lists the main new features of statsmodels {{ release }}. In addition, release {{ release }} includes bug fixes, refactorings and improvements in many areas. Submodules ---------- {% for comp in whats_new %} {% set pull_requests = whats_new[comp] %} {%- set comp_marker = "~" * (comp|length + 4) -%} ``{{comp}}`` {{comp_marker}} {% for number in pull_requests -%} - {{ pull_requests[number] }} (:pr:`{{ number }}`) {% endfor %} {% endfor %} bug-wrong --------- A new issue label `type-bug-wrong` indicates bugs that cause that incorrect numbers are returned without warnings. (Regular bugs are mostly usability bugs or bugs that raise an exception for unsupported use cases.) `see tagged issues `_ Major Bugs Fixed ================ See github issues for a list of bug fixes included in this release - `Closed bugs `_ - `Closed bugs (wrong result) `_ Development summary and credits =============================== Besides receiving contributions for new and improved features and for bugfixes, important contributions to general maintenance for this release came from - Chad Fulton - Brock Mendel - Peter Quackenbush - Kerby Shedden - Kevin Sheppard and the general maintainer and code reviewer - Josef Perktold Additionally, many users contributed by participation in github issues and providing feedback. Thanks to all of the contributors for the {{ release }} release (based on git log): {% for contributor in contributors -%} - {{ contributor }} {% endfor %} These lists of names are automatically generated based on git log, and may not be complete. Merged Pull Requests -------------------- The following Pull Requests were merged since the last release: {% for pull in pulls -%} - :pr:`{{ pull.number }}`: {{ pull.title }} {% endfor %} statsmodels-0.12.2/tools/validate_docstrings.py000066400000000000000000001157371400612667500217250ustar00rootroot00000000000000#!/usr/bin/env python """ Analyze docstrings to detect errors. If no argument is provided, it does a quick check of docstrings and returns a csv with all API functions and results of basic checks. If a function or method is provided in the form 'pandas.function', 'pandas.module.class.method', etc. a list of all errors in the docstring for the specified function or method. Usage:: $ ./validate_docstrings.py $ ./validate_docstrings.py pandas.DataFrame.head """ import argparse import ast import collections import doctest import functools import glob import importlib import inspect from io import StringIO import json import os import pydoc import re import string import sys import tempfile import textwrap import flake8.main.application import matplotlib import numpy from numpydoc.docscrape import NumpyDocString import pandas from pandas.io.formats.printing import pprint_thing import statsmodels.api # Template backend makes matplotlib to not plot anything. This is useful # to avoid that plot windows are open from the doctests while running the # script. Setting here before matplotlib is loaded. # We don't warn for the number of open plots, as none is actually being opened matplotlib.use('agg') matplotlib.rc('figure', max_open_warning=10000) BASE_PATH = os.path.dirname(os.path.dirname(os.path.abspath(__file__))) sys.path.insert(0, os.path.join(BASE_PATH)) # TODO: Single-line ignore GL01, GL02 # TODO: Complete import location list # TODO: Recurse through module to find classes # TODO: Separate data from code NO_RETURN_WHITELIST = { 'bse', 'aic', 'bic', 'params', 'tvalues', 'pvalues', 'fvalue', 'fittedvalues', 'mse_model', 'mse_resid', 'mse_total', 'ssr', 'nobs', 'rsquared_adj', 'rsquared', 'resid', 'prsquared', 'zvalues', 'uncentered_tss', 'llf', 'hqic', 'ess', 'centered_tss', 'wresid', 'f_pvalue', 'eigenvals', 'condition_number', 'scale', 'llr', 'llr_pvalue', 'llnull', 'resid_response', 'resid_pearson', 'resid_generalized', 'resid_dev', 'save'} MODULES = ('api', 'tsa.api', 'discrete.conditional_models', 'discrete.count_model', 'discrete.discrete_model', 'duration.hazard_regression', 'regression.linear_model', 'regression.mixed_linear_model', 'regression.process_regression', 'regression.quantile_regression', 'regression.recursive_ls', 'robust.robust_linear_model', 'robust.norms', 'stats.anova', 'stats.mediation', 'tsa.seasonal') ALLOW_SINGLE_LINE_DOCSTRINGS = True members = [] for mod in MODULES: imp = importlib.import_module('statsmodels.' + mod) members += inspect.getmembers(imp) API_CLASSES = [] for member in members: if not member[0]: continue if member[0][0] in string.ascii_uppercase: if not type(member[1]) is type: continue name = str(member[1]).split('\'')[1] if not name.startswith('statsmodels.'): continue API_CLASSES.append((name, member[1])) API_CLASSES = sorted(set(API_CLASSES), key=lambda v: v[0]) RUN_DOCTESTS = False sys.path.insert(1, os.path.join(BASE_PATH, 'doc', 'sphinxext')) PRIVATE_CLASSES = [] DIRECTIVES = ['versionadded', 'versionchanged', 'deprecated'] ALLOWED_SECTIONS = [ 'Parameters', 'Attributes', 'Methods', 'Returns', 'Yields', 'Other Parameters', 'Raises', 'Warns', 'See Also', 'Notes', 'References', 'Examples', ] ERROR_MSGS = { 'GL01': 'Docstring text (summary) should start in the line immediately ' 'after the opening quotes (not in the same line, or leaving a ' 'blank line in between)', 'GL02': 'Closing quotes should be placed in the line after the last text ' 'in the docstring (do not close the quotes in the same line as ' 'the text, or leave a blank line between the last text and the ' 'quotes)', 'GL03': 'Double line break found; please use only one blank line to ' 'separate sections or paragraphs, and do not leave blank lines ' 'at the end of docstrings', 'GL04': 'Private classes ({mentioned_private_classes}) should not be ' 'mentioned in public docstrings', 'GL05': 'Tabs found at the start of line "{line_with_tabs}", please use ' 'whitespace only', 'GL06': 'Found unknown section "{section}". Allowed sections are: ' '{allowed_sections}', 'GL07': 'Sections are in the wrong order. ' 'Correct order is: {correct_sections}', 'GL08': 'The object does not have a docstring', 'GL09': 'Deprecation warning should precede extended summary', 'SS01': 'No summary found (a short summary in a single line should be ' 'present at the beginning of the docstring)', 'SS02': 'Summary does not start with a capital letter', 'SS03': 'Summary does not end with a period', 'SS04': 'Summary contains heading whitespaces', 'SS05': 'Summary must start with infinitive verb, not third person ' '(e.g. use "Generate" instead of "Generates")', 'SS06': 'Summary should fit in a single line', 'ES01': 'No extended summary found', 'PR01': 'Parameters {missing_params} not documented', 'PR02': 'Unknown parameters {unknown_params}', 'PR03': 'Wrong parameters order. Actual: {actual_params}. ' 'Documented: {documented_params}', 'PR04': 'Parameter "{param_name}" has no type', 'PR05': 'Parameter "{param_name}" type should not finish with "."', 'PR06': 'Parameter "{param_name}" type should use "{right_type}" instead ' 'of "{wrong_type}"', 'PR07': 'Parameter "{param_name}" has no description', 'PR08': 'Parameter "{param_name}" description should start with a ' 'capital letter', 'PR09': 'Parameter "{param_name}" description should finish with "."', 'PR10': 'Parameter "{param_name}" requires a space before the colon ' 'separating the parameter name and type', 'RT01': 'No Returns section found', 'RT02': 'The first line of the Returns section should contain only the ' 'type, unless multiple values are being returned', 'RT03': 'Return value has no description', 'RT04': 'Return value description should start with a capital letter', 'RT05': 'Return value description should finish with "."', 'YD01': 'No Yields section found', 'SA01': 'See Also section not found', 'SA02': 'Missing period at end of description for See Also ' '"{reference_name}" reference', 'SA03': 'Description should be capitalized for See Also ' '"{reference_name}" reference', 'SA04': 'Missing description for See Also "{reference_name}" reference', 'SA05': '{reference_name} in `See Also` section does not need `pandas` ' 'prefix, use {right_reference} instead.', 'EX01': 'No examples section found', 'EX02': 'Examples do not pass tests:\n{doctest_log}', 'EX03': 'flake8 error: {error_code} {error_message}{times_happening}', 'EX04': 'Do not import {imported_library}, as it is imported ' 'automatically for the examples (numpy as np, pandas as pd)', } def error(code, **kwargs): """ Return a tuple with the error code and the message with variables replaced. This is syntactic sugar so instead of: - `('EX02', ERROR_MSGS['EX02'].format(doctest_log=log))` We can simply use: - `error('EX02', doctest_log=log)` Parameters ---------- code : str Error code. **kwargs Values for the variables in the error messages Returns ------- code : str Error code. message : str Error message with variables replaced. """ return (code, ERROR_MSGS[code].format(**kwargs)) def get_api_items(api_doc_fd): """ Yield information about all public API items. Parse api.rst file from the documentation, and extract all the functions, methods, classes, attributes... This should include all pandas public API. Parameters ---------- api_doc_fd : file descriptor A file descriptor of the API documentation page, containing the table of contents with all the public API. Yields ------ name : str The name of the object (e.g. 'pandas.Series.str.upper). func : function The object itself. In most cases this will be a function or method, but it can also be classes, properties, cython objects... section : str The name of the section in the API page where the object item is located. subsection : str The name of the subsection in the API page where the object item is located. """ current_module = 'statsmodels' previous_line = current_section = current_subsection = '' position = None for line in api_doc_fd: line = line.strip() if len(line) == len(previous_line): if set(line) == set('-'): current_section = previous_line continue if set(line) == set('~'): current_subsection = previous_line continue if line.startswith('.. currentmodule::'): current_module = line.replace('.. currentmodule::', '').strip() continue if line == '.. autosummary::': position = 'autosummary' continue if position == 'autosummary': if line == '': position = 'items' continue if position == 'items': if line == '': position = None continue item = line.strip() if item.startswith('~statsmodels.'): path = item.replace('~', '').split('.') item = path[-1] current_module = '.'.join(path[:-1]) func = importlib.import_module(current_module) for part in item.split('.'): func = getattr(func, part) yield ( '.'.join([current_module, item]), func, current_section, current_subsection, ) previous_line = line class Docstring(object): def __init__(self, name): self.name = name obj = self._load_obj(name) self.obj = obj self.code_obj = self._to_original_callable(obj) self.raw_doc = obj.__doc__ or '' self.clean_doc = pydoc.getdoc(obj) self.doc = NumpyDocString(self.clean_doc) def __len__(self): return len(self.raw_doc) @staticmethod def _load_obj(name): """ Import Python object from its name as string. Parameters ---------- name : str Object name to import (e.g. pandas.Series.str.upper) Returns ------- object Python object that can be a class, method, function... Examples -------- >>> Docstring._load_obj('pandas.Series') """ for maxsplit in range(1, name.count('.') + 1): func_name_split = name.rsplit('.', maxsplit) module, *func_parts = func_name_split try: obj = importlib.import_module(module) except ImportError: pass else: continue if 'obj' not in locals(): raise ImportError('No module can be imported ' 'from "{}"'.format(name)) for part in func_parts: obj = getattr(obj, part) return obj @staticmethod def _to_original_callable(obj): """ Find the Python object that contains the source code of the object. This is useful to find the place in the source code (file and line number) where a docstring is defined. It does not currently work for all cases, but it should help find some (properties...). """ while True: if inspect.isfunction(obj) or inspect.isclass(obj): f = inspect.getfile(obj) if f.startswith('<') and f.endswith('>'): return None return obj if inspect.ismethod(obj): obj = obj.__func__ elif isinstance(obj, functools.partial): obj = obj.func elif isinstance(obj, property): obj = obj.fget else: return None @property def type(self): return type(self.obj).__name__ @property def is_function_or_method(self): return inspect.isfunction(self.obj) or inspect.ismethod(self.obj) @property def source_file_name(self): """ File name where the object is implemented (e.g. pandas/core/frame.py). """ try: fname = inspect.getsourcefile(self.code_obj) except TypeError: # In some cases the object is something complex like a cython # object that can't be easily introspected. An it's better to # return the source code file of the object as None, than crash pass else: if fname: fname = os.path.relpath(fname, BASE_PATH) return fname @property def source_file_def_line(self): """ Number of line where the object is defined in its file. """ try: return inspect.getsourcelines(self.code_obj)[-1] except (OSError, TypeError): # In some cases the object is something complex like a cython # object that can't be easily introspected. An it's better to # return the line number as None, than crash pass @property def github_url(self): url = 'https://github.com/statsmodels/statsmodels/master/' url += '{}#L{}'.format(self.source_file_name, self.source_file_def_line) return url @property def start_blank_lines(self): i = None if self.raw_doc: for i, row in enumerate(self.raw_doc.split('\n')): if row.strip(): break return i @property def end_blank_lines(self): i = None if self.raw_doc: for i, row in enumerate(reversed(self.raw_doc.split('\n'))): if row.strip(): break return i @property def single_line_docstring(self): return (self.raw_doc and '\n' not in self.raw_doc and ALLOW_SINGLE_LINE_DOCSTRINGS) @property def double_blank_lines(self): prev = True for row in self.raw_doc.split('\n'): if not prev and not row.strip(): return True prev = row.strip() return False @property def section_titles(self): sections = [] self.doc._doc.reset() while not self.doc._doc.eof(): content = self.doc._read_to_next_section() if ( len(content) > 1 and len(content[0]) == len(content[1]) and set(content[1]) == {'-'} ): sections.append(content[0]) return sections @property def summary(self): return ' '.join(self.doc['Summary']) @property def num_summary_lines(self): return len(self.doc['Summary']) @property def extended_summary(self): if not self.doc['Extended Summary'] and len(self.doc['Summary']) > 1: return ' '.join(self.doc['Summary']) return ' '.join(self.doc['Extended Summary']) @property def needs_summary(self): return not (bool(self.summary) and bool(self.extended_summary)) @property def doc_parameters(self): return collections.OrderedDict( (name, (type_, ''.join(desc))) for name, type_, desc in self.doc['Parameters'] ) @property def signature_parameters(self): if inspect.isclass(self.obj): if hasattr(self.obj, '_accessors') and ( self.name.split('.')[-1] in self.obj._accessors ): # accessor classes have a signature but don't want to show this return tuple() try: sig = inspect.signature(self.obj) except (TypeError, ValueError): # Some objects, mainly in C extensions do not support introspection # of the signature try: from numpydoc.docscrape import FunctionDoc doc = FunctionDoc(self.obj) if 'Signature' in doc: sig = doc['Signature'].split('(')[-1].split(')')[0] sig = sig.split(',') params = [] for param in sig: if param.strip() in ('*', '/'): continue param = param.split('=')[0] params.append(param) return tuple([param.name for param in doc['Parameters']]) except Exception as exc: print('!! numpydoc failed on {0}!!'.format(str(self.obj))) print(exc) return tuple() params = list(sig.parameters.keys()) out_params = params[:] kind = inspect.Parameter.VAR_POSITIONAL varargs = [key for key in params if sig.parameters[key].kind == kind] if varargs: out_params = ['*' + param if param == varargs[0] else param for param in out_params] kind = inspect.Parameter.VAR_KEYWORD varkw = [key for key in params if sig.parameters[key].kind == kind] if varkw: out_params = ['**' + param if param == varkw[0] else param for param in out_params] params = tuple(out_params) if params and params[0] in ('self', 'cls'): return params[1:] return params @property def parameter_mismatches(self): errs = [] signature_params = self.signature_parameters doc_params = tuple(self.doc_parameters) missing = set(signature_params) - set(doc_params) if missing: errs.append(error('PR01', missing_params=pprint_thing(missing))) extra = set(doc_params) - set(signature_params) if extra: errs.append(error('PR02', unknown_params=pprint_thing(extra))) if ( not missing and not extra and signature_params != doc_params and not (not signature_params and not doc_params) ): errs.append( error('PR03', actual_params=signature_params, documented_params=doc_params) ) return errs @property def correct_parameters(self): return not bool(self.parameter_mismatches) def parameter_type(self, param): return self.doc_parameters[param][0] def parameter_desc(self, param): desc = self.doc_parameters[param][1] # Find and strip out any sphinx directives for directive in DIRECTIVES: full_directive = '.. {}'.format(directive) if full_directive in desc: # Only retain any description before the directive desc = desc[: desc.index(full_directive)] return desc @property def see_also(self): result = collections.OrderedDict() for funcs, desc in self.doc['See Also']: for func, _ in funcs: result[func] = ''.join(desc) return result @property def examples(self): return self.doc['Examples'] @property def returns(self): return self.doc['Returns'] @property def yields(self): return self.doc['Yields'] @property def method_source(self): try: source = inspect.getsource(self.obj) except TypeError: return '' return textwrap.dedent(source) @property def method_returns_something(self): """ Check if the docstrings method can return something. Bare returns, returns valued None and returns from nested functions are disconsidered. Returns ------- bool Whether the docstrings method can return something. """ def get_returns_not_on_nested_functions(node): returns = [node] if isinstance(node, ast.Return) else [] for child in ast.iter_child_nodes(node): # Ignore nested functions and its subtrees. if not isinstance(child, ast.FunctionDef): child_returns = get_returns_not_on_nested_functions(child) returns.extend(child_returns) return returns tree = ast.parse(self.method_source).body if tree: returns = get_returns_not_on_nested_functions(tree[0]) return_values = [r.value for r in returns] # Replace NameConstant nodes valued None for None. for i, v in enumerate(return_values): if isinstance(v, ast.NameConstant) and v.value is None: return_values[i] = None return any(return_values) else: return False @property def no_return_whitelisted(self): method = self.name.split('.')[-1] return 'Results' in self.name and method in NO_RETURN_WHITELIST @property def first_line_ends_in_dot(self): if self.doc: return self.doc.split('\n')[0][-1] == '.' @property def deprecated(self): return '.. deprecated:: ' in (self.summary + self.extended_summary) @property def mentioned_private_classes(self): return [klass for klass in PRIVATE_CLASSES if klass in self.raw_doc] @property def examples_errors(self): flags = doctest.NORMALIZE_WHITESPACE | doctest.IGNORE_EXCEPTION_DETAIL finder = doctest.DocTestFinder() runner = doctest.DocTestRunner(optionflags=flags) context = {'np': numpy, 'pd': pandas, 'sm': statsmodels.api} error_msgs = '' for test in finder.find(self.raw_doc, self.name, globs=context): f = StringIO() runner.run(test, out=f.write) error_msgs += f.getvalue() return error_msgs @property def examples_source_code(self): lines = doctest.DocTestParser().get_examples(self.raw_doc) return [line.source for line in lines] def validate_pep8(self): if not self.examples: return # F401 is needed to not generate flake8 errors in examples # that do not user numpy or pandas content = ''.join( ( 'import numpy as np # noqa: F401\n', 'import pandas as pd # noqa: F401\n', 'import statsmodels.api as sm # noqa: F401\n', *self.examples_source_code, ) ) application = flake8.main.application.Application() application.initialize(['--quiet']) with tempfile.NamedTemporaryFile(mode='w', encoding='utf-8') as file: file.write(content) file.flush() application.run_checks([file.name]) # We need this to avoid flake8 printing the names of the files to # the standard output application.formatter.write = lambda line, source: None application.report() yield from application.guide.stats.statistics_for('') def get_validation_data(doc): """ Validate the docstring. Parameters ---------- doc : Docstring A Docstring object with the given function name. Returns ------- tuple errors : list of tuple Errors occurred during validation. warnings : list of tuple Warnings occurred during validation. examples_errs : str Examples usage displayed along the error, otherwise empty string. Notes ----- The errors codes are defined as: - First two characters: Section where the error happens: * GL: Global (no section, like section ordering errors) * SS: Short summary * ES: Extended summary * PR: Parameters * RT: Returns * YD: Yields * RS: Raises * WN: Warns * SA: See Also * NT: Notes * RF: References * EX: Examples - Last two characters: Numeric error code inside the section For example, EX02 is the second codified error in the Examples section (which in this case is assigned to examples that do not pass the tests). The error codes, their corresponding error messages, and the details on how they are validated, are not documented more than in the source code of this function. """ errs = [] wrns = [] if not doc.raw_doc: errs.append(error('GL08')) return errs, wrns, '' if doc.start_blank_lines != 1 and not doc.single_line_docstring: errs.append(error('GL01')) if doc.end_blank_lines != 1 and not doc.single_line_docstring: errs.append(error('GL02')) if doc.double_blank_lines: errs.append(error('GL03')) mentioned_errs = doc.mentioned_private_classes if mentioned_errs: errs.append(error('GL04', mentioned_private_classes=', '.join(mentioned_errs))) for line in doc.raw_doc.splitlines(): if re.match('^ *\t', line): errs.append(error('GL05', line_with_tabs=line.lstrip())) unexpected_sections = [section for section in doc.section_titles if section not in ALLOWED_SECTIONS] for section in unexpected_sections: errs.append(error('GL06', section=section, allowed_sections=', '.join(ALLOWED_SECTIONS))) correct_order = [section for section in ALLOWED_SECTIONS if section in doc.section_titles] if correct_order != doc.section_titles: errs.append(error('GL07', correct_sections=', '.join(correct_order))) if (doc.deprecated and not doc.extended_summary.startswith('.. deprecated:: ')): errs.append(error('GL09')) if not doc.summary: errs.append(error('SS01')) else: if not doc.summary[0].isupper(): errs.append(error('SS02')) if (doc.summary[-1] != '.' and not doc.single_line_docstring and ALLOW_SINGLE_LINE_DOCSTRINGS): errs.append(error('SS03')) if doc.summary != doc.summary.lstrip(): errs.append(error('SS04')) elif (doc.is_function_or_method and doc.summary.split(' ')[0][-1] == 's'): errs.append(error('SS05')) if doc.num_summary_lines > 1: errs.append(error('SS06')) if not doc.extended_summary: wrns.append(('ES01', 'No extended summary found')) # PR01: Parameters not documented # PR02: Unknown parameters # PR03: Wrong parameters order errs += doc.parameter_mismatches for param in doc.doc_parameters: if not param.startswith('*'): # Check can ignore var / kwargs if not doc.parameter_type(param): if ':' in param: errs.append(error('PR10', param_name=param.split(':')[0])) else: errs.append(error('PR04', param_name=param)) else: if doc.parameter_type(param)[-1] == '.': errs.append(error('PR05', param_name=param)) common_type_errors = [ ('integer', 'int'), ('boolean', 'bool'), ('string', 'str'), ] for wrong_type, right_type in common_type_errors: if wrong_type in doc.parameter_type(param): errs.append( error( 'PR06', param_name=param, right_type=right_type, wrong_type=wrong_type, ) ) if not doc.parameter_desc(param): errs.append(error('PR07', param_name=param)) else: if not doc.parameter_desc(param)[0].isupper(): errs.append(error('PR08', param_name=param)) if doc.parameter_desc(param)[-1] != '.': errs.append(error('PR09', param_name=param)) if doc.is_function_or_method: if not doc.returns: if doc.method_returns_something and not doc.no_return_whitelisted: errs.append(error('RT01')) else: if len(doc.returns) == 1 and doc.returns[0].name: errs.append(error('RT02')) for name_or_type, type_, desc in doc.returns: if not desc: errs.append(error('RT03')) else: desc = ' '.join(desc) if not desc[0].isupper(): errs.append(error('RT04')) if not desc.endswith('.'): errs.append(error('RT05')) if not doc.yields and 'yield' in doc.method_source: errs.append(error('YD01')) if not doc.see_also: wrns.append(error('SA01')) else: for rel_name, rel_desc in doc.see_also.items(): if rel_desc: if not rel_desc.endswith('.'): errs.append(error('SA02', reference_name=rel_name)) if not rel_desc[0].isupper(): errs.append(error('SA03', reference_name=rel_name)) else: errs.append(error('SA04', reference_name=rel_name)) # TODO: Change to statsmodels if rel_name.startswith('pandas.'): errs.append( error( 'SA05', reference_name=rel_name, right_reference=rel_name[len('pandas.'):], ) ) examples_errs = '' if not doc.examples: wrns.append(error('EX01')) elif RUN_DOCTESTS: examples_errs = doc.examples_errors if examples_errs: errs.append(error('EX02', doctest_log=examples_errs)) for err in doc.validate_pep8(): errs.append( error( 'EX03', error_code=err.error_code, error_message=err.message, times_happening=' ({} times)'.format(err.count) if err.count > 1 else '', ) ) examples_source_code = ''.join(doc.examples_source_code) for wrong_import in ('numpy', 'pandas'): if 'import {}'.format(wrong_import) in examples_source_code: errs.append(error('EX04', imported_library=wrong_import)) return errs, wrns, examples_errs def validate_one(func_name): """ Validate the docstring for the given func_name Parameters ---------- func_name : function Function whose docstring will be evaluated (e.g. pandas.read_csv). Returns ------- dict A dictionary containing all the information obtained from validating the docstring. """ doc = Docstring(func_name) errs, wrns, examples_errs = get_validation_data(doc) return { 'type': doc.type, 'docstring': doc.clean_doc, 'deprecated': doc.deprecated, 'file': doc.source_file_name, 'file_line': doc.source_file_def_line, 'github_link': doc.github_url, 'errors': errs, 'warnings': wrns, 'examples_errors': examples_errs, } def validate_all(prefix, ignore_deprecated=False): """ Execute the validation of all docstrings, and return a dict with the results. Parameters ---------- prefix : str or None If provided, only the docstrings that start with this pattern will be validated. If None, all docstrings will be validated. ignore_deprecated: bool, default False If True, deprecated objects are ignored when validating docstrings. Returns ------- dict A dictionary with an item for every function/method... containing all the validation information. """ result = {} seen = {} # functions from the API docs api_doc_fnames = os.path.join(BASE_PATH, 'docs', 'source', '*.rst') api_items = [] for api_doc_fname in glob.glob(api_doc_fnames): if 'sandbox' in api_doc_fname: continue with open(api_doc_fname, encoding='utf8') as f: api_items += list(get_api_items(f)) for func_name, func_obj, section, subsection in api_items: if prefix and not func_name.startswith(prefix): continue doc_info = validate_one(func_name) if ignore_deprecated and doc_info['deprecated']: continue result[func_name] = doc_info shared_code_key = doc_info['file'], doc_info['file_line'] shared_code = seen.get(shared_code_key, '') result[func_name].update( { 'in_api': True, 'section': section, 'subsection': subsection, 'shared_code_with': shared_code, } ) seen[shared_code_key] = func_name # functions from introspecting Series and DataFrame api_item_names = set(list(zip(*api_items))[0]) for class_name, class_ in API_CLASSES: for member in inspect.getmembers(class_): func_name = class_name + '.' + member[0] if (not member[0].startswith('_') and func_name not in api_item_names): if prefix and not func_name.startswith(prefix): continue doc_info = validate_one(func_name) if ignore_deprecated and doc_info['deprecated']: continue result[func_name] = doc_info result[func_name]['in_api'] = False return result def main(func_name, prefix, errors, output_format, ignore_deprecated): def header(title, width=80, char='#'): full_line = char * width side_len = (width - len(title) - 2) // 2 adj = '' if len(title) % 2 == 0 else ' ' title_line = '{side} {title}{adj} {side}'.format( side=char * side_len, title=title, adj=adj ) return '\n{full_line}\n{title_line}\n{full_line}\n\n'.format( full_line=full_line, title_line=title_line ) exit_status = 0 if func_name is None: result = validate_all(prefix, ignore_deprecated) if output_format == 'json': output = json.dumps(result) else: if output_format == 'default': output_format = '{text}\n' elif output_format == 'azure': output_format = ( '##vso[task.logissue type=error;' 'sourcepath={path};' 'linenumber={row};' 'code={code};' ']{text}\n' ) else: raise ValueError( 'Unknown output_format "{}"'.format(output_format)) output = [] for name, res in result.items(): for err_code, err_desc in res['errors']: # The script would be faster if instead of filtering the # errors after validating them, it didn't validate them # initially. But that would complicate the code too much if errors and err_code not in errors: continue exit_status += 1 output.append(output_format.format( name=name, path=res['file'], row=res['file_line'], code=err_code, text='{}: {}'.format(name, err_desc)) ) output = ''.join(sorted(output)) sys.stdout.write(output) else: result = validate_one(func_name) sys.stderr.write(header('Docstring ({})'.format(func_name))) sys.stderr.write('{}\n'.format(result['docstring'])) sys.stderr.write(header('Validation')) if result['errors']: sys.stderr.write( '{} Errors found:\n'.format(len(result['errors']))) for err_code, err_desc in result['errors']: # Failing examples are printed at the end if err_code == 'EX02': sys.stderr.write('\tExamples do not pass tests\n') continue sys.stderr.write('\t{}\n'.format(err_desc)) if result['warnings']: sys.stderr.write( '{} Warnings found:\n'.format(len(result['warnings']))) for wrn_code, wrn_desc in result['warnings']: sys.stderr.write('\t{}\n'.format(wrn_desc)) if not result['errors']: sys.stderr.write( 'Docstring for "{}" correct. :)\n'.format(func_name)) if result['examples_errors']: sys.stderr.write(header('Doctests')) sys.stderr.write(result['examples_errors']) return exit_status if __name__ == '__main__': format_opts = 'default', 'json', 'azure' func_help = ( 'function or method to validate (e.g. pandas.DataFrame.head) ' 'if not provided, all docstrings are validated and returned ' 'as JSON' ) argparser = argparse.ArgumentParser( description='validate pandas docstrings') argparser.add_argument('function', nargs='?', default=None, help=func_help) argparser.add_argument( '--format', default='default', choices=format_opts, help='format of the output when validating ' 'multiple docstrings (ignored when validating one).' 'It can be {}'.format(str(format_opts)[1:-1]), ) argparser.add_argument( '--prefix', default=None, help='pattern for the ' 'docstring names, in order to decide which ones ' 'will be validated. A prefix "pandas.Series.str."' 'will make the script validate all the docstrings' 'of methods starting by this pattern. It is ' 'ignored if parameter function is provided', ) argparser.add_argument( '--errors', default=None, help='comma separated ' 'list of error codes to validate. By default it ' 'validates all errors (ignored when validating ' 'a single docstring)', ) argparser.add_argument( '--ignore_deprecated', default=False, action='store_true', help='if this flag is set, ' 'deprecated objects are ignored when validating ' 'all docstrings', ) args = argparser.parse_args() sys.exit( main( args.function, args.prefix, args.errors.split(',') if args.errors else None, args.format, args.ignore_deprecated, ) ) statsmodels-0.12.2/tox.ini000066400000000000000000000027101400612667500154600ustar00rootroot00000000000000############################################################################## # Intended to simplify local generation of coverage of Cython files # # tox -e cython-coverage # # will produce a HTML report showing line-by-line coverage # # can be used to run standard tests on Python 2.7, 3.5, 3.6, and 3.7 or a # run with coverage but without coverage of Cython files using # # tox -e ENV # # where env is one of the values in envlist or all environments (slow) # # tox # ############################################################################## [tox] envlist = py27 py35 py36 py37 coverage cython-coverage [testenv] deps = -rrequirements.txt cython matplotlib joblib pytest>=3 pytest-xdist setenv = MKL_NUM_THREADS=1 NUMEXPR_NUM_THREADS=1 OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 changedir = {homedir} commands = python -c "import statsmodels;statsmodels.test(['-n 2'], exit=True)" [testenv:coverage] usedevelop = True deps = {[testenv]deps} pytest-cov setenv = {[testenv]setenv} SM_CYTHON_COVERAGE=false changedir = {toxinidir} commands = coverage erase pytest -n 2 --cov-report html --cov=statsmodels statsmodels [testenv:cython-coverage] usedevelop = True deps = {[testenv]deps} pytest-cov setenv = {[testenv]setenv} SM_CYTHON_COVERAGE=true changedir = {toxinidir} commands = coverage erase pytest -n 2 --cov-report html --cov=statsmodels statsmodels statsmodels-0.12.2/versioneer.py000066400000000000000000002060361400612667500167070ustar00rootroot00000000000000 # Version: 0.18 """The Versioneer - like a rocketeer, but for versions. The Versioneer ============== * like a rocketeer, but for versions! * https://github.com/warner/python-versioneer * Brian Warner * License: Public Domain * Compatible With: python2.6, 2.7, 3.2, 3.3, 3.4, 3.5, 3.6, and pypy * [![Latest Version] (https://pypip.in/version/versioneer/badge.svg?style=flat) ](https://pypi.python.org/pypi/versioneer/) * [![Build Status] (https://travis-ci.org/warner/python-versioneer.png?branch=master) ](https://travis-ci.org/warner/python-versioneer) This is a tool for managing a recorded version number in distutils-based python projects. The goal is to remove the tedious and error-prone "update the embedded version string" step from your release process. Making a new release should be as easy as recording a new tag in your version-control system, and maybe making new tarballs. ## Quick Install * `pip install versioneer` to somewhere to your $PATH * add a `[versioneer]` section to your setup.cfg (see below) * run `versioneer install` in your source tree, commit the results ## Version Identifiers Source trees come from a variety of places: * a version-control system checkout (mostly used by developers) * a nightly tarball, produced by build automation * a snapshot tarball, produced by a web-based VCS browser, like github's "tarball from tag" feature * a release tarball, produced by "setup.py sdist", distributed through PyPI Within each source tree, the version identifier (either a string or a number, this tool is format-agnostic) can come from a variety of places: * ask the VCS tool itself, e.g. "git describe" (for checkouts), which knows about recent "tags" and an absolute revision-id * the name of the directory into which the tarball was unpacked * an expanded VCS keyword ($Id$, etc) * a `_version.py` created by some earlier build step For released software, the version identifier is closely related to a VCS tag. Some projects use tag names that include more than just the version string (e.g. "myproject-1.2" instead of just "1.2"), in which case the tool needs to strip the tag prefix to extract the version identifier. For unreleased software (between tags), the version identifier should provide enough information to help developers recreate the same tree, while also giving them an idea of roughly how old the tree is (after version 1.2, before version 1.3). Many VCS systems can report a description that captures this, for example `git describe --tags --dirty --always` reports things like "0.7-1-g574ab98-dirty" to indicate that the checkout is one revision past the 0.7 tag, has a unique revision id of "574ab98", and is "dirty" (it has uncommitted changes. The version identifier is used for multiple purposes: * to allow the module to self-identify its version: `myproject.__version__` * to choose a name and prefix for a 'setup.py sdist' tarball ## Theory of Operation Versioneer works by adding a special `_version.py` file into your source tree, where your `__init__.py` can import it. This `_version.py` knows how to dynamically ask the VCS tool for version information at import time. `_version.py` also contains `$Revision$` markers, and the installation process marks `_version.py` to have this marker rewritten with a tag name during the `git archive` command. As a result, generated tarballs will contain enough information to get the proper version. To allow `setup.py` to compute a version too, a `versioneer.py` is added to the top level of your source tree, next to `setup.py` and the `setup.cfg` that configures it. This overrides several distutils/setuptools commands to compute the version when invoked, and changes `setup.py build` and `setup.py sdist` to replace `_version.py` with a small static file that contains just the generated version data. ## Installation See [INSTALL.md](./INSTALL.md) for detailed installation instructions. ## Version-String Flavors Code which uses Versioneer can learn about its version string at runtime by importing `_version` from your main `__init__.py` file and running the `get_versions()` function. From the "outside" (e.g. in `setup.py`), you can import the top-level `versioneer.py` and run `get_versions()`. Both functions return a dictionary with different flavors of version information: * `['version']`: A condensed version string, rendered using the selected style. This is the most commonly used value for the project's version string. The default "pep440" style yields strings like `0.11`, `0.11+2.g1076c97`, or `0.11+2.g1076c97.dirty`. See the "Styles" section below for alternative styles. * `['full-revisionid']`: detailed revision identifier. For Git, this is the full SHA1 commit id, e.g. "1076c978a8d3cfc70f408fe5974aa6c092c949ac". * `['date']`: Date and time of the latest `HEAD` commit. For Git, it is the commit date in ISO 8601 format. This will be None if the date is not available. * `['dirty']`: a boolean, True if the tree has uncommitted changes. Note that this is only accurate if run in a VCS checkout, otherwise it is likely to be False or None * `['error']`: if the version string could not be computed, this will be set to a string describing the problem, otherwise it will be None. It may be useful to throw an exception in setup.py if this is set, to avoid e.g. creating tarballs with a version string of "unknown". Some variants are more useful than others. Including `full-revisionid` in a bug report should allow developers to reconstruct the exact code being tested (or indicate the presence of local changes that should be shared with the developers). `version` is suitable for display in an "about" box or a CLI `--version` output: it can be easily compared against release notes and lists of bugs fixed in various releases. The installer adds the following text to your `__init__.py` to place a basic version in `YOURPROJECT.__version__`: from ._version import get_versions __version__ = get_versions()['version'] del get_versions ## Styles The setup.cfg `style=` configuration controls how the VCS information is rendered into a version string. The default style, "pep440", produces a PEP440-compliant string, equal to the un-prefixed tag name for actual releases, and containing an additional "local version" section with more detail for in-between builds. For Git, this is TAG[+DISTANCE.gHEX[.dirty]] , using information from `git describe --tags --dirty --always`. For example "0.11+2.g1076c97.dirty" indicates that the tree is like the "1076c97" commit but has uncommitted changes (".dirty"), and that this commit is two revisions ("+2") beyond the "0.11" tag. For released software (exactly equal to a known tag), the identifier will only contain the stripped tag, e.g. "0.11". Other styles are available. See [details.md](details.md) in the Versioneer source tree for descriptions. ## Debugging Versioneer tries to avoid fatal errors: if something goes wrong, it will tend to return a version of "0+unknown". To investigate the problem, run `setup.py version`, which will run the version-lookup code in a verbose mode, and will display the full contents of `get_versions()` (including the `error` string, which may help identify what went wrong). ## Known Limitations Some situations are known to cause problems for Versioneer. This details the most significant ones. More can be found on Github [issues page](https://github.com/warner/python-versioneer/issues). ### Subprojects Versioneer has limited support for source trees in which `setup.py` is not in the root directory (e.g. `setup.py` and `.git/` are *not* siblings). The are two common reasons why `setup.py` might not be in the root: * Source trees which contain multiple subprojects, such as [Buildbot](https://github.com/buildbot/buildbot), which contains both "master" and "slave" subprojects, each with their own `setup.py`, `setup.cfg`, and `tox.ini`. Projects like these produce multiple PyPI distributions (and upload multiple independently-installable tarballs). * Source trees whose main purpose is to contain a C library, but which also provide bindings to Python (and perhaps other langauges) in subdirectories. Versioneer will look for `.git` in parent directories, and most operations should get the right version string. However `pip` and `setuptools` have bugs and implementation details which frequently cause `pip install .` from a subproject directory to fail to find a correct version string (so it usually defaults to `0+unknown`). `pip install --editable .` should work correctly. `setup.py install` might work too. Pip-8.1.1 is known to have this problem, but hopefully it will get fixed in some later version. [Bug #38](https://github.com/warner/python-versioneer/issues/38) is tracking this issue. The discussion in [PR #61](https://github.com/warner/python-versioneer/pull/61) describes the issue from the Versioneer side in more detail. [pip PR#3176](https://github.com/pypa/pip/pull/3176) and [pip PR#3615](https://github.com/pypa/pip/pull/3615) contain work to improve pip to let Versioneer work correctly. Versioneer-0.16 and earlier only looked for a `.git` directory next to the `setup.cfg`, so subprojects were completely unsupported with those releases. ### Editable installs with setuptools <= 18.5 `setup.py develop` and `pip install --editable .` allow you to install a project into a virtualenv once, then continue editing the source code (and test) without re-installing after every change. "Entry-point scripts" (`setup(entry_points={"console_scripts": ..})`) are a convenient way to specify executable scripts that should be installed along with the python package. These both work as expected when using modern setuptools. When using setuptools-18.5 or earlier, however, certain operations will cause `pkg_resources.DistributionNotFound` errors when running the entrypoint script, which must be resolved by re-installing the package. This happens when the install happens with one version, then the egg_info data is regenerated while a different version is checked out. Many setup.py commands cause egg_info to be rebuilt (including `sdist`, `wheel`, and installing into a different virtualenv), so this can be surprising. [Bug #83](https://github.com/warner/python-versioneer/issues/83) describes this one, but upgrading to a newer version of setuptools should probably resolve it. ### Unicode version strings While Versioneer works (and is continually tested) with both Python 2 and Python 3, it is not entirely consistent with bytes-vs-unicode distinctions. Newer releases probably generate unicode version strings on py2. It's not clear that this is wrong, but it may be surprising for applications when then write these strings to a network connection or include them in bytes-oriented APIs like cryptographic checksums. [Bug #71](https://github.com/warner/python-versioneer/issues/71) investigates this question. ## Updating Versioneer To upgrade your project to a new release of Versioneer, do the following: * install the new Versioneer (`pip install -U versioneer` or equivalent) * edit `setup.cfg`, if necessary, to include any new configuration settings indicated by the release notes. See [UPGRADING](./UPGRADING.md) for details. * re-run `versioneer install` in your source tree, to replace `SRC/_version.py` * commit any changed files ## Future Directions This tool is designed to make it easily extended to other version-control systems: all VCS-specific components are in separate directories like src/git/ . The top-level `versioneer.py` script is assembled from these components by running make-versioneer.py . In the future, make-versioneer.py will take a VCS name as an argument, and will construct a version of `versioneer.py` that is specific to the given VCS. It might also take the configuration arguments that are currently provided manually during installation by editing setup.py . Alternatively, it might go the other direction and include code from all supported VCS systems, reducing the number of intermediate scripts. ## License To make Versioneer easier to embed, all its code is dedicated to the public domain. The `_version.py` that it creates is also in the public domain. Specifically, both are released under the Creative Commons "Public Domain Dedication" license (CC0-1.0), as described in https://creativecommons.org/publicdomain/zero/1.0/ . """ from __future__ import print_function try: import configparser except ImportError: import ConfigParser as configparser import errno import json import os import re import subprocess import sys class VersioneerConfig: """Container for Versioneer configuration parameters.""" def get_root(): """Get the project root directory. We require that all commands are run from the project root, i.e. the directory that contains setup.py, setup.cfg, and versioneer.py . """ root = os.path.realpath(os.path.abspath(os.getcwd())) setup_py = os.path.join(root, "setup.py") versioneer_py = os.path.join(root, "versioneer.py") if not (os.path.exists(setup_py) or os.path.exists(versioneer_py)): # allow 'python path/to/setup.py COMMAND' root = os.path.dirname(os.path.realpath(os.path.abspath(sys.argv[0]))) setup_py = os.path.join(root, "setup.py") versioneer_py = os.path.join(root, "versioneer.py") if not (os.path.exists(setup_py) or os.path.exists(versioneer_py)): err = ("Versioneer was unable to run the project root directory. " "Versioneer requires setup.py to be executed from " "its immediate directory (like 'python setup.py COMMAND'), " "or in a way that lets it use sys.argv[0] to find the root " "(like 'python path/to/setup.py COMMAND').") raise VersioneerBadRootError(err) try: # Certain runtime workflows (setup.py install/develop in a setuptools # tree) execute all dependencies in a single python process, so # "versioneer" may be imported multiple times, and python's shared # module-import table will cache the first one. So we cannot use # os.path.dirname(__file__), as that will find whichever # versioneer.py was first imported, even in later projects. me = os.path.realpath(os.path.abspath(__file__)) me_dir = os.path.normcase(os.path.splitext(me)[0]) vsr_dir = os.path.normcase(os.path.splitext(versioneer_py)[0]) if me_dir != vsr_dir: print("Warning: build in %s is using versioneer.py from %s" % (os.path.dirname(me), versioneer_py)) except NameError: pass return root def get_config_from_root(root): """Read the project setup.cfg file to determine Versioneer config.""" # This might raise EnvironmentError (if setup.cfg is missing), or # configparser.NoSectionError (if it lacks a [versioneer] section), or # configparser.NoOptionError (if it lacks "VCS="). See the docstring at # the top of versioneer.py for instructions on writing your setup.cfg . setup_cfg = os.path.join(root, "setup.cfg") parser = configparser.SafeConfigParser() with open(setup_cfg, "r") as f: parser.readfp(f) VCS = parser.get("versioneer", "VCS") # mandatory def get(parser, name): if parser.has_option("versioneer", name): return parser.get("versioneer", name) return None cfg = VersioneerConfig() cfg.VCS = VCS cfg.style = get(parser, "style") or "" cfg.versionfile_source = get(parser, "versionfile_source") cfg.versionfile_build = get(parser, "versionfile_build") cfg.tag_prefix = get(parser, "tag_prefix") if cfg.tag_prefix in ("''", '""'): cfg.tag_prefix = "" cfg.parentdir_prefix = get(parser, "parentdir_prefix") cfg.verbose = get(parser, "verbose") return cfg class NotThisMethod(Exception): """Exception raised if a method is not valid for the current scenario.""" # these dictionaries contain VCS-specific tools LONG_VERSION_PY = {} HANDLERS = {} def register_vcs_handler(vcs, method): # decorator """Decorator to mark a method as the handler for a particular VCS.""" def decorate(f): """Store f in HANDLERS[vcs][method].""" if vcs not in HANDLERS: HANDLERS[vcs] = {} HANDLERS[vcs][method] = f return f return decorate def run_command(commands, args, cwd=None, verbose=False, hide_stderr=False, env=None): """Call the given command(s).""" assert isinstance(commands, list) p = None for c in commands: try: dispcmd = str([c] + args) # remember shell=False, so use git.cmd on windows, not just git p = subprocess.Popen([c] + args, cwd=cwd, env=env, stdout=subprocess.PIPE, stderr=(subprocess.PIPE if hide_stderr else None)) break except EnvironmentError: e = sys.exc_info()[1] if e.errno == errno.ENOENT: continue if verbose: print("unable to run %s" % dispcmd) print(e) return None, None else: if verbose: print("unable to find command, tried %s" % (commands,)) return None, None stdout = p.communicate()[0].strip() if sys.version_info[0] >= 3: stdout = stdout.decode() if p.returncode != 0: if verbose: print("unable to run %s (error)" % dispcmd) print("stdout was %s" % stdout) return None, p.returncode return stdout, p.returncode LONG_VERSION_PY['git'] = ''' # This file helps to compute a version number in source trees obtained from # git-archive tarball (such as those provided by githubs download-from-tag # feature). Distribution tarballs (built by setup.py sdist) and build # directories (produced by setup.py build) will contain a much shorter file # that just contains the computed version number. # This file is released into the public domain. Generated by # versioneer-0.18 (https://github.com/warner/python-versioneer) """Git implementation of _version.py.""" import errno import os import re import subprocess import sys def get_keywords(): """Get the keywords needed to look up the version information.""" # these strings will be replaced by git during git-archive. # setup.py/versioneer.py will grep for the variable names, so they must # each be defined on a line of their own. _version.py will just call # get_keywords(). git_refnames = "%(DOLLAR)sFormat:%%d%(DOLLAR)s" git_full = "%(DOLLAR)sFormat:%%H%(DOLLAR)s" git_date = "%(DOLLAR)sFormat:%%ci%(DOLLAR)s" keywords = {"refnames": git_refnames, "full": git_full, "date": git_date} return keywords class VersioneerConfig: """Container for Versioneer configuration parameters.""" def get_config(): """Create, populate and return the VersioneerConfig() object.""" # these strings are filled in when 'setup.py versioneer' creates # _version.py cfg = VersioneerConfig() cfg.VCS = "git" cfg.style = "%(STYLE)s" cfg.tag_prefix = "%(TAG_PREFIX)s" cfg.parentdir_prefix = "%(PARENTDIR_PREFIX)s" cfg.versionfile_source = "%(VERSIONFILE_SOURCE)s" cfg.verbose = False return cfg class NotThisMethod(Exception): """Exception raised if a method is not valid for the current scenario.""" LONG_VERSION_PY = {} HANDLERS = {} def register_vcs_handler(vcs, method): # decorator """Decorator to mark a method as the handler for a particular VCS.""" def decorate(f): """Store f in HANDLERS[vcs][method].""" if vcs not in HANDLERS: HANDLERS[vcs] = {} HANDLERS[vcs][method] = f return f return decorate def run_command(commands, args, cwd=None, verbose=False, hide_stderr=False, env=None): """Call the given command(s).""" assert isinstance(commands, list) p = None for c in commands: try: dispcmd = str([c] + args) # remember shell=False, so use git.cmd on windows, not just git p = subprocess.Popen([c] + args, cwd=cwd, env=env, stdout=subprocess.PIPE, stderr=(subprocess.PIPE if hide_stderr else None)) break except EnvironmentError: e = sys.exc_info()[1] if e.errno == errno.ENOENT: continue if verbose: print("unable to run %%s" %% dispcmd) print(e) return None, None else: if verbose: print("unable to find command, tried %%s" %% (commands,)) return None, None stdout = p.communicate()[0].strip() if sys.version_info[0] >= 3: stdout = stdout.decode() if p.returncode != 0: if verbose: print("unable to run %%s (error)" %% dispcmd) print("stdout was %%s" %% stdout) return None, p.returncode return stdout, p.returncode def versions_from_parentdir(parentdir_prefix, root, verbose): """Try to determine the version from the parent directory name. Source tarballs conventionally unpack into a directory that includes both the project name and a version string. We will also support searching up two directory levels for an appropriately named parent directory """ rootdirs = [] for i in range(3): dirname = os.path.basename(root) if dirname.startswith(parentdir_prefix): return {"version": dirname[len(parentdir_prefix):], "full-revisionid": None, "dirty": False, "error": None, "date": None} else: rootdirs.append(root) root = os.path.dirname(root) # up a level if verbose: print("Tried directories %%s but none started with prefix %%s" %% (str(rootdirs), parentdir_prefix)) raise NotThisMethod("rootdir does not start with parentdir_prefix") @register_vcs_handler("git", "get_keywords") def git_get_keywords(versionfile_abs): """Extract version information from the given file.""" # the code embedded in _version.py can just fetch the value of these # keywords. When used from setup.py, we do not want to import _version.py, # so we do it with a regexp instead. This function is not used from # _version.py. keywords = {} try: f = open(versionfile_abs, "r") for line in f.readlines(): if line.strip().startswith("git_refnames ="): mo = re.search(r'=\s*"(.*)"', line) if mo: keywords["refnames"] = mo.group(1) if line.strip().startswith("git_full ="): mo = re.search(r'=\s*"(.*)"', line) if mo: keywords["full"] = mo.group(1) if line.strip().startswith("git_date ="): mo = re.search(r'=\s*"(.*)"', line) if mo: keywords["date"] = mo.group(1) f.close() except EnvironmentError: pass return keywords @register_vcs_handler("git", "keywords") def git_versions_from_keywords(keywords, tag_prefix, verbose): """Get version information from git keywords.""" if not keywords: raise NotThisMethod("no keywords at all, weird") date = keywords.get("date") if date is not None: # git-2.2.0 added "%%cI", which expands to an ISO-8601 -compliant # datestamp. However we prefer "%%ci" (which expands to an "ISO-8601 # -like" string, which we must then edit to make compliant), because # it's been around since git-1.5.3, and it's too difficult to # discover which version we're using, or to work around using an # older one. date = date.strip().replace(" ", "T", 1).replace(" ", "", 1) refnames = keywords["refnames"].strip() if refnames.startswith("$Format"): if verbose: print("keywords are unexpanded, not using") raise NotThisMethod("unexpanded keywords, not a git-archive tarball") refs = set([r.strip() for r in refnames.strip("()").split(",")]) # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of # just "foo-1.0". If we see a "tag: " prefix, prefer those. TAG = "tag: " tags = set([r[len(TAG):] for r in refs if r.startswith(TAG)]) if not tags: # Either we're using git < 1.8.3, or there really are no tags. We use # a heuristic: assume all version tags have a digit. The old git %%d # expansion behaves like git log --decorate=short and strips out the # refs/heads/ and refs/tags/ prefixes that would let us distinguish # between branches and tags. By ignoring refnames without digits, we # filter out many common branch names like "release" and # "stabilization", as well as "HEAD" and "master". tags = set([r for r in refs if re.search(r'\d', r)]) if verbose: print("discarding '%%s', no digits" %% ",".join(refs - tags)) if verbose: print("likely tags: %%s" %% ",".join(sorted(tags))) for ref in sorted(tags): # sorting will prefer e.g. "2.0" over "2.0rc1" if ref.startswith(tag_prefix): r = ref[len(tag_prefix):] if verbose: print("picking %%s" %% r) return {"version": r, "full-revisionid": keywords["full"].strip(), "dirty": False, "error": None, "date": date} # no suitable tags, so version is "0+unknown", but full hex is still there if verbose: print("no suitable tags, using unknown + full revision id") return {"version": "0+unknown", "full-revisionid": keywords["full"].strip(), "dirty": False, "error": "no suitable tags", "date": None} @register_vcs_handler("git", "pieces_from_vcs") def git_pieces_from_vcs(tag_prefix, root, verbose, run_command=run_command): """Get version from 'git describe' in the root of the source tree. This only gets called if the git-archive 'subst' keywords were *not* expanded, and _version.py has not already been rewritten with a short version string, meaning we're inside a checked out source tree. """ GITS = ["git"] if sys.platform == "win32": GITS = ["git.cmd", "git.exe"] out, rc = run_command(GITS, ["rev-parse", "--git-dir"], cwd=root, hide_stderr=True) if rc != 0: if verbose: print("Directory %%s not under git control" %% root) raise NotThisMethod("'git rev-parse --git-dir' returned error") # if there is a tag matching tag_prefix, this yields TAG-NUM-gHEX[-dirty] # if there is not one, this yields HEX[-dirty] (no NUM) describe_out, rc = run_command(GITS, ["describe", "--tags", "--dirty", "--always", "--long", "--match", "%%s*" %% tag_prefix], cwd=root) # --long was added in git-1.5.5 if describe_out is None: raise NotThisMethod("'git describe' failed") describe_out = describe_out.strip() full_out, rc = run_command(GITS, ["rev-parse", "HEAD"], cwd=root) if full_out is None: raise NotThisMethod("'git rev-parse' failed") full_out = full_out.strip() pieces = {} pieces["long"] = full_out pieces["short"] = full_out[:7] # maybe improved later pieces["error"] = None # parse describe_out. It will be like TAG-NUM-gHEX[-dirty] or HEX[-dirty] # TAG might have hyphens. git_describe = describe_out # look for -dirty suffix dirty = git_describe.endswith("-dirty") pieces["dirty"] = dirty if dirty: git_describe = git_describe[:git_describe.rindex("-dirty")] # now we have TAG-NUM-gHEX or HEX if "-" in git_describe: # TAG-NUM-gHEX mo = re.search(r'^(.+)-(\d+)-g([0-9a-f]+)$', git_describe) if not mo: # unparseable. Maybe git-describe is misbehaving? pieces["error"] = ("unable to parse git-describe output: '%%s'" %% describe_out) return pieces # tag full_tag = mo.group(1) if not full_tag.startswith(tag_prefix): if verbose: fmt = "tag '%%s' does not start with prefix '%%s'" print(fmt %% (full_tag, tag_prefix)) pieces["error"] = ("tag '%%s' does not start with prefix '%%s'" %% (full_tag, tag_prefix)) return pieces pieces["closest-tag"] = full_tag[len(tag_prefix):] # distance: number of commits since tag pieces["distance"] = int(mo.group(2)) # commit: short hex revision ID pieces["short"] = mo.group(3) else: # HEX: no tags pieces["closest-tag"] = None count_out, rc = run_command(GITS, ["rev-list", "HEAD", "--count"], cwd=root) pieces["distance"] = int(count_out) # total number of commits # commit date: see ISO-8601 comment in git_versions_from_keywords() date = run_command(GITS, ["show", "-s", "--format=%%ci", "HEAD"], cwd=root)[0].strip() pieces["date"] = date.strip().replace(" ", "T", 1).replace(" ", "", 1) return pieces def plus_or_dot(pieces): """Return a + if we do not already have one, else return a .""" if "+" in pieces.get("closest-tag", ""): return "." return "+" def render_pep440(pieces): """Build up version string, with post-release "local version identifier". Our goal: TAG[+DISTANCE.gHEX[.dirty]] . Note that if you get a tagged build and then dirty it, you'll get TAG+0.gHEX.dirty Exceptions: 1: no tags. git_describe was just HEX. 0+untagged.DISTANCE.gHEX[.dirty] """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"] or pieces["dirty"]: rendered += plus_or_dot(pieces) rendered += "%%d.g%%s" %% (pieces["distance"], pieces["short"]) if pieces["dirty"]: rendered += ".dirty" else: # exception #1 rendered = "0+untagged.%%d.g%%s" %% (pieces["distance"], pieces["short"]) if pieces["dirty"]: rendered += ".dirty" return rendered def render_pep440_pre(pieces): """TAG[.post.devDISTANCE] -- No -dirty. Exceptions: 1: no tags. 0.post.devDISTANCE """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"]: rendered += ".post.dev%%d" %% pieces["distance"] else: # exception #1 rendered = "0.post.dev%%d" %% pieces["distance"] return rendered def render_pep440_post(pieces): """TAG[.postDISTANCE[.dev0]+gHEX] . The ".dev0" means dirty. Note that .dev0 sorts backwards (a dirty tree will appear "older" than the corresponding clean one), but you should not be releasing software with -dirty anyways. Exceptions: 1: no tags. 0.postDISTANCE[.dev0] """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"] or pieces["dirty"]: rendered += ".post%%d" %% pieces["distance"] if pieces["dirty"]: rendered += ".dev0" rendered += plus_or_dot(pieces) rendered += "g%%s" %% pieces["short"] else: # exception #1 rendered = "0.post%%d" %% pieces["distance"] if pieces["dirty"]: rendered += ".dev0" rendered += "+g%%s" %% pieces["short"] return rendered def render_pep440_old(pieces): """TAG[.postDISTANCE[.dev0]] . The ".dev0" means dirty. Eexceptions: 1: no tags. 0.postDISTANCE[.dev0] """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"] or pieces["dirty"]: rendered += ".post%%d" %% pieces["distance"] if pieces["dirty"]: rendered += ".dev0" else: # exception #1 rendered = "0.post%%d" %% pieces["distance"] if pieces["dirty"]: rendered += ".dev0" return rendered def render_git_describe(pieces): """TAG[-DISTANCE-gHEX][-dirty]. Like 'git describe --tags --dirty --always'. Exceptions: 1: no tags. HEX[-dirty] (note: no 'g' prefix) """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"]: rendered += "-%%d-g%%s" %% (pieces["distance"], pieces["short"]) else: # exception #1 rendered = pieces["short"] if pieces["dirty"]: rendered += "-dirty" return rendered def render_git_describe_long(pieces): """TAG-DISTANCE-gHEX[-dirty]. Like 'git describe --tags --dirty --always -long'. The distance/hash is unconditional. Exceptions: 1: no tags. HEX[-dirty] (note: no 'g' prefix) """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] rendered += "-%%d-g%%s" %% (pieces["distance"], pieces["short"]) else: # exception #1 rendered = pieces["short"] if pieces["dirty"]: rendered += "-dirty" return rendered def render(pieces, style): """Render the given version pieces into the requested style.""" if pieces["error"]: return {"version": "unknown", "full-revisionid": pieces.get("long"), "dirty": None, "error": pieces["error"], "date": None} if not style or style == "default": style = "pep440" # the default if style == "pep440": rendered = render_pep440(pieces) elif style == "pep440-pre": rendered = render_pep440_pre(pieces) elif style == "pep440-post": rendered = render_pep440_post(pieces) elif style == "pep440-old": rendered = render_pep440_old(pieces) elif style == "git-describe": rendered = render_git_describe(pieces) elif style == "git-describe-long": rendered = render_git_describe_long(pieces) else: raise ValueError("unknown style '%%s'" %% style) return {"version": rendered, "full-revisionid": pieces["long"], "dirty": pieces["dirty"], "error": None, "date": pieces.get("date")} def get_versions(): """Get version information or return default if unable to do so.""" # I am in _version.py, which lives at ROOT/VERSIONFILE_SOURCE. If we have # __file__, we can work backwards from there to the root. Some # py2exe/bbfreeze/non-CPython implementations do not do __file__, in which # case we can only use expanded keywords. cfg = get_config() verbose = cfg.verbose try: return git_versions_from_keywords(get_keywords(), cfg.tag_prefix, verbose) except NotThisMethod: pass try: root = os.path.realpath(__file__) # versionfile_source is the relative path from the top of the source # tree (where the .git directory might live) to this file. Invert # this to find the root from __file__. for i in cfg.versionfile_source.split('/'): root = os.path.dirname(root) except NameError: return {"version": "0+unknown", "full-revisionid": None, "dirty": None, "error": "unable to find root of source tree", "date": None} try: pieces = git_pieces_from_vcs(cfg.tag_prefix, root, verbose) return render(pieces, cfg.style) except NotThisMethod: pass try: if cfg.parentdir_prefix: return versions_from_parentdir(cfg.parentdir_prefix, root, verbose) except NotThisMethod: pass return {"version": "0+unknown", "full-revisionid": None, "dirty": None, "error": "unable to compute version", "date": None} ''' @register_vcs_handler("git", "get_keywords") def git_get_keywords(versionfile_abs): """Extract version information from the given file.""" # the code embedded in _version.py can just fetch the value of these # keywords. When used from setup.py, we do not want to import _version.py, # so we do it with a regexp instead. This function is not used from # _version.py. keywords = {} try: f = open(versionfile_abs, "r") for line in f.readlines(): if line.strip().startswith("git_refnames ="): mo = re.search(r'=\s*"(.*)"', line) if mo: keywords["refnames"] = mo.group(1) if line.strip().startswith("git_full ="): mo = re.search(r'=\s*"(.*)"', line) if mo: keywords["full"] = mo.group(1) if line.strip().startswith("git_date ="): mo = re.search(r'=\s*"(.*)"', line) if mo: keywords["date"] = mo.group(1) f.close() except EnvironmentError: pass return keywords @register_vcs_handler("git", "keywords") def git_versions_from_keywords(keywords, tag_prefix, verbose): """Get version information from git keywords.""" if not keywords: raise NotThisMethod("no keywords at all, weird") date = keywords.get("date") if date is not None: # git-2.2.0 added "%cI", which expands to an ISO-8601 -compliant # datestamp. However we prefer "%ci" (which expands to an "ISO-8601 # -like" string, which we must then edit to make compliant), because # it's been around since git-1.5.3, and it's too difficult to # discover which version we're using, or to work around using an # older one. date = date.strip().replace(" ", "T", 1).replace(" ", "", 1) refnames = keywords["refnames"].strip() if refnames.startswith("$Format"): if verbose: print("keywords are unexpanded, not using") raise NotThisMethod("unexpanded keywords, not a git-archive tarball") refs = set([r.strip() for r in refnames.strip("()").split(",")]) # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of # just "foo-1.0". If we see a "tag: " prefix, prefer those. TAG = "tag: " tags = set([r[len(TAG):] for r in refs if r.startswith(TAG)]) if not tags: # Either we're using git < 1.8.3, or there really are no tags. We use # a heuristic: assume all version tags have a digit. The old git %d # expansion behaves like git log --decorate=short and strips out the # refs/heads/ and refs/tags/ prefixes that would let us distinguish # between branches and tags. By ignoring refnames without digits, we # filter out many common branch names like "release" and # "stabilization", as well as "HEAD" and "master". tags = set([r for r in refs if re.search(r'\d', r)]) if verbose: print("discarding '%s', no digits" % ",".join(refs - tags)) if verbose: print("likely tags: %s" % ",".join(sorted(tags))) for ref in sorted(tags): # sorting will prefer e.g. "2.0" over "2.0rc1" if ref.startswith(tag_prefix): r = ref[len(tag_prefix):] if verbose: print("picking %s" % r) return {"version": r, "full-revisionid": keywords["full"].strip(), "dirty": False, "error": None, "date": date} # no suitable tags, so version is "0+unknown", but full hex is still there if verbose: print("no suitable tags, using unknown + full revision id") return {"version": "0+unknown", "full-revisionid": keywords["full"].strip(), "dirty": False, "error": "no suitable tags", "date": None} @register_vcs_handler("git", "pieces_from_vcs") def git_pieces_from_vcs(tag_prefix, root, verbose, run_command=run_command): """Get version from 'git describe' in the root of the source tree. This only gets called if the git-archive 'subst' keywords were *not* expanded, and _version.py has not already been rewritten with a short version string, meaning we're inside a checked out source tree. """ GITS = ["git"] if sys.platform == "win32": GITS = ["git.cmd", "git.exe"] out, rc = run_command(GITS, ["rev-parse", "--git-dir"], cwd=root, hide_stderr=True) if rc != 0: if verbose: print("Directory %s not under git control" % root) raise NotThisMethod("'git rev-parse --git-dir' returned error") # if there is a tag matching tag_prefix, this yields TAG-NUM-gHEX[-dirty] # if there is not one, this yields HEX[-dirty] (no NUM) describe_out, rc = run_command(GITS, ["describe", "--tags", "--dirty", "--always", "--long", "--match", "%s*" % tag_prefix], cwd=root) # --long was added in git-1.5.5 if describe_out is None: raise NotThisMethod("'git describe' failed") describe_out = describe_out.strip() full_out, rc = run_command(GITS, ["rev-parse", "HEAD"], cwd=root) if full_out is None: raise NotThisMethod("'git rev-parse' failed") full_out = full_out.strip() pieces = {} pieces["long"] = full_out pieces["short"] = full_out[:7] # maybe improved later pieces["error"] = None # parse describe_out. It will be like TAG-NUM-gHEX[-dirty] or HEX[-dirty] # TAG might have hyphens. git_describe = describe_out # look for -dirty suffix dirty = git_describe.endswith("-dirty") pieces["dirty"] = dirty if dirty: git_describe = git_describe[:git_describe.rindex("-dirty")] # now we have TAG-NUM-gHEX or HEX if "-" in git_describe: # TAG-NUM-gHEX mo = re.search(r'^(.+)-(\d+)-g([0-9a-f]+)$', git_describe) if not mo: # unparseable. Maybe git-describe is misbehaving? pieces["error"] = ("unable to parse git-describe output: '%s'" % describe_out) return pieces # tag full_tag = mo.group(1) if not full_tag.startswith(tag_prefix): if verbose: fmt = "tag '%s' does not start with prefix '%s'" print(fmt % (full_tag, tag_prefix)) pieces["error"] = ("tag '%s' does not start with prefix '%s'" % (full_tag, tag_prefix)) return pieces pieces["closest-tag"] = full_tag[len(tag_prefix):] # distance: number of commits since tag pieces["distance"] = int(mo.group(2)) # commit: short hex revision ID pieces["short"] = mo.group(3) else: # HEX: no tags pieces["closest-tag"] = None count_out, rc = run_command(GITS, ["rev-list", "HEAD", "--count"], cwd=root) pieces["distance"] = int(count_out) # total number of commits # commit date: see ISO-8601 comment in git_versions_from_keywords() date = run_command(GITS, ["show", "-s", "--format=%ci", "HEAD"], cwd=root)[0].strip() pieces["date"] = date.strip().replace(" ", "T", 1).replace(" ", "", 1) return pieces def do_vcs_install(manifest_in, versionfile_source, ipy): """Git-specific installation logic for Versioneer. For Git, this means creating/changing .gitattributes to mark _version.py for export-subst keyword substitution. """ GITS = ["git"] if sys.platform == "win32": GITS = ["git.cmd", "git.exe"] files = [manifest_in, versionfile_source] if ipy: files.append(ipy) try: me = __file__ if me.endswith(".pyc") or me.endswith(".pyo"): me = os.path.splitext(me)[0] + ".py" versioneer_file = os.path.relpath(me) except NameError: versioneer_file = "versioneer.py" files.append(versioneer_file) present = False try: f = open(".gitattributes", "r") for line in f.readlines(): if line.strip().startswith(versionfile_source): if "export-subst" in line.strip().split()[1:]: present = True f.close() except EnvironmentError: pass if not present: f = open(".gitattributes", "a+") f.write("%s export-subst\n" % versionfile_source) f.close() files.append(".gitattributes") run_command(GITS, ["add", "--"] + files) def versions_from_parentdir(parentdir_prefix, root, verbose): """Try to determine the version from the parent directory name. Source tarballs conventionally unpack into a directory that includes both the project name and a version string. We will also support searching up two directory levels for an appropriately named parent directory """ rootdirs = [] for i in range(3): dirname = os.path.basename(root) if dirname.startswith(parentdir_prefix): return {"version": dirname[len(parentdir_prefix):], "full-revisionid": None, "dirty": False, "error": None, "date": None} else: rootdirs.append(root) root = os.path.dirname(root) # up a level if verbose: print("Tried directories %s but none started with prefix %s" % (str(rootdirs), parentdir_prefix)) raise NotThisMethod("rootdir does not start with parentdir_prefix") SHORT_VERSION_PY = """ # This file was generated by 'versioneer.py' (0.18) from # revision-control system data, or from the parent directory name of an # unpacked source archive. Distribution tarballs contain a pre-generated copy # of this file. import json version_json = ''' %s ''' # END VERSION_JSON def get_versions(): return json.loads(version_json) """ def versions_from_file(filename): """Try to determine the version from _version.py if present.""" try: with open(filename) as f: contents = f.read() except EnvironmentError: raise NotThisMethod("unable to read _version.py") mo = re.search(r"version_json = '''\n(.*)''' # END VERSION_JSON", contents, re.M | re.S) if not mo: mo = re.search(r"version_json = '''\r\n(.*)''' # END VERSION_JSON", contents, re.M | re.S) if not mo: raise NotThisMethod("no version_json in _version.py") return json.loads(mo.group(1)) def write_to_version_file(filename, versions): """Write the given version number to the given _version.py file.""" os.unlink(filename) contents = json.dumps(versions, sort_keys=True, indent=1, separators=(",", ": ")) with open(filename, "w") as f: f.write(SHORT_VERSION_PY % contents) print("set %s to '%s'" % (filename, versions["version"])) def plus_or_dot(pieces): """Return a + if we do not already have one, else return a .""" if "+" in pieces.get("closest-tag", ""): return "." return "+" def render_pep440(pieces): """Build up version string, with post-release "local version identifier". Our goal: TAG[+DISTANCE.gHEX[.dirty]] . Note that if you get a tagged build and then dirty it, you'll get TAG+0.gHEX.dirty Exceptions: 1: no tags. git_describe was just HEX. 0+untagged.DISTANCE.gHEX[.dirty] """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"] or pieces["dirty"]: rendered += plus_or_dot(pieces) rendered += "%d.g%s" % (pieces["distance"], pieces["short"]) if pieces["dirty"]: rendered += ".dirty" else: # exception #1 rendered = "0+untagged.%d.g%s" % (pieces["distance"], pieces["short"]) if pieces["dirty"]: rendered += ".dirty" return rendered def render_pep440_pre(pieces): """TAG[.post.devDISTANCE] -- No -dirty. Exceptions: 1: no tags. 0.post.devDISTANCE """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"]: rendered += ".post.dev%d" % pieces["distance"] else: # exception #1 rendered = "0.post.dev%d" % pieces["distance"] return rendered def render_pep440_post(pieces): """TAG[.postDISTANCE[.dev0]+gHEX] . The ".dev0" means dirty. Note that .dev0 sorts backwards (a dirty tree will appear "older" than the corresponding clean one), but you should not be releasing software with -dirty anyways. Exceptions: 1: no tags. 0.postDISTANCE[.dev0] """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"] or pieces["dirty"]: rendered += ".post%d" % pieces["distance"] if pieces["dirty"]: rendered += ".dev0" rendered += plus_or_dot(pieces) rendered += "g%s" % pieces["short"] else: # exception #1 rendered = "0.post%d" % pieces["distance"] if pieces["dirty"]: rendered += ".dev0" rendered += "+g%s" % pieces["short"] return rendered def render_pep440_old(pieces): """TAG[.postDISTANCE[.dev0]] . The ".dev0" means dirty. Eexceptions: 1: no tags. 0.postDISTANCE[.dev0] """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"] or pieces["dirty"]: rendered += ".post%d" % pieces["distance"] if pieces["dirty"]: rendered += ".dev0" else: # exception #1 rendered = "0.post%d" % pieces["distance"] if pieces["dirty"]: rendered += ".dev0" return rendered def render_git_describe(pieces): """TAG[-DISTANCE-gHEX][-dirty]. Like 'git describe --tags --dirty --always'. Exceptions: 1: no tags. HEX[-dirty] (note: no 'g' prefix) """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] if pieces["distance"]: rendered += "-%d-g%s" % (pieces["distance"], pieces["short"]) else: # exception #1 rendered = pieces["short"] if pieces["dirty"]: rendered += "-dirty" return rendered def render_git_describe_long(pieces): """TAG-DISTANCE-gHEX[-dirty]. Like 'git describe --tags --dirty --always -long'. The distance/hash is unconditional. Exceptions: 1: no tags. HEX[-dirty] (note: no 'g' prefix) """ if pieces["closest-tag"]: rendered = pieces["closest-tag"] rendered += "-%d-g%s" % (pieces["distance"], pieces["short"]) else: # exception #1 rendered = pieces["short"] if pieces["dirty"]: rendered += "-dirty" return rendered def render(pieces, style): """Render the given version pieces into the requested style.""" if pieces["error"]: return {"version": "unknown", "full-revisionid": pieces.get("long"), "dirty": None, "error": pieces["error"], "date": None} if not style or style == "default": style = "pep440" # the default if style == "pep440": rendered = render_pep440(pieces) elif style == "pep440-pre": rendered = render_pep440_pre(pieces) elif style == "pep440-post": rendered = render_pep440_post(pieces) elif style == "pep440-old": rendered = render_pep440_old(pieces) elif style == "git-describe": rendered = render_git_describe(pieces) elif style == "git-describe-long": rendered = render_git_describe_long(pieces) else: raise ValueError("unknown style '%s'" % style) return {"version": rendered, "full-revisionid": pieces["long"], "dirty": pieces["dirty"], "error": None, "date": pieces.get("date")} class VersioneerBadRootError(Exception): """The project root directory is unknown or missing key files.""" def get_versions(verbose=False): """Get the project version from whatever source is available. Returns dict with two keys: 'version' and 'full'. """ if "versioneer" in sys.modules: # see the discussion in cmdclass.py:get_cmdclass() del sys.modules["versioneer"] root = get_root() cfg = get_config_from_root(root) assert cfg.VCS is not None, "please set [versioneer]VCS= in setup.cfg" handlers = HANDLERS.get(cfg.VCS) assert handlers, "unrecognized VCS '%s'" % cfg.VCS verbose = verbose or cfg.verbose assert cfg.versionfile_source is not None, \ "please set versioneer.versionfile_source" assert cfg.tag_prefix is not None, "please set versioneer.tag_prefix" versionfile_abs = os.path.join(root, cfg.versionfile_source) # extract version from first of: _version.py, VCS command (e.g. 'git # describe'), parentdir. This is meant to work for developers using a # source checkout, for users of a tarball created by 'setup.py sdist', # and for users of a tarball/zipball created by 'git archive' or github's # download-from-tag feature or the equivalent in other VCSes. get_keywords_f = handlers.get("get_keywords") from_keywords_f = handlers.get("keywords") if get_keywords_f and from_keywords_f: try: keywords = get_keywords_f(versionfile_abs) ver = from_keywords_f(keywords, cfg.tag_prefix, verbose) if verbose: print("got version from expanded keyword %s" % ver) return ver except NotThisMethod: pass try: ver = versions_from_file(versionfile_abs) if verbose: print("got version from file %s %s" % (versionfile_abs, ver)) return ver except NotThisMethod: pass from_vcs_f = handlers.get("pieces_from_vcs") if from_vcs_f: try: pieces = from_vcs_f(cfg.tag_prefix, root, verbose) ver = render(pieces, cfg.style) if verbose: print("got version from VCS %s" % ver) return ver except NotThisMethod: pass try: if cfg.parentdir_prefix: ver = versions_from_parentdir(cfg.parentdir_prefix, root, verbose) if verbose: print("got version from parentdir %s" % ver) return ver except NotThisMethod: pass if verbose: print("unable to compute version") return {"version": "0+unknown", "full-revisionid": None, "dirty": None, "error": "unable to compute version", "date": None} def get_version(): """Get the short version string for this project.""" return get_versions()["version"] def get_cmdclass(): """Get the custom setuptools/distutils subclasses used by Versioneer.""" if "versioneer" in sys.modules: del sys.modules["versioneer"] # this fixes the "python setup.py develop" case (also 'install' and # 'easy_install .'), in which subdependencies of the main project are # built (using setup.py bdist_egg) in the same python process. Assume # a main project A and a dependency B, which use different versions # of Versioneer. A's setup.py imports A's Versioneer, leaving it in # sys.modules by the time B's setup.py is executed, causing B to run # with the wrong versioneer. Setuptools wraps the sub-dep builds in a # sandbox that restores sys.modules to it's pre-build state, so the # parent is protected against the child's "import versioneer". By # removing ourselves from sys.modules here, before the child build # happens, we protect the child from the parent's versioneer too. # Also see https://github.com/warner/python-versioneer/issues/52 cmds = {} # we add "version" to both distutils and setuptools from distutils.core import Command class cmd_version(Command): description = "report generated version string" user_options = [] boolean_options = [] def initialize_options(self): pass def finalize_options(self): pass def run(self): vers = get_versions(verbose=True) print("Version: %s" % vers["version"]) print(" full-revisionid: %s" % vers.get("full-revisionid")) print(" dirty: %s" % vers.get("dirty")) print(" date: %s" % vers.get("date")) if vers["error"]: print(" error: %s" % vers["error"]) cmds["version"] = cmd_version # we override "build_py" in both distutils and setuptools # # most invocation pathways end up running build_py: # distutils/build -> build_py # distutils/install -> distutils/build ->.. # setuptools/bdist_wheel -> distutils/install ->.. # setuptools/bdist_egg -> distutils/install_lib -> build_py # setuptools/install -> bdist_egg ->.. # setuptools/develop -> ? # pip install: # copies source tree to a tempdir before running egg_info/etc # if .git is not copied too, 'git describe' will fail # then does setup.py bdist_wheel, or sometimes setup.py install # setup.py egg_info -> ? # we override different "build_py" commands for both environments if "setuptools" in sys.modules: from setuptools.command.build_py import build_py as _build_py else: from distutils.command.build_py import build_py as _build_py class cmd_build_py(_build_py): def run(self): root = get_root() cfg = get_config_from_root(root) versions = get_versions() _build_py.run(self) # now locate _version.py in the new build/ directory and replace # it with an updated value if cfg.versionfile_build: target_versionfile = os.path.join(self.build_lib, cfg.versionfile_build) print("UPDATING %s" % target_versionfile) write_to_version_file(target_versionfile, versions) cmds["build_py"] = cmd_build_py if "cx_Freeze" in sys.modules: # cx_freeze enabled? from cx_Freeze.dist import build_exe as _build_exe # nczeczulin reports that py2exe will not like the pep440-style string # as FILEVERSION, but it can be used for PRODUCTVERSION, e.g. # setup(console=[{ # "version": versioneer.get_version().split("+", 1)[0], # FILEVERSION # "product_version": versioneer.get_version(), # ... class cmd_build_exe(_build_exe): def run(self): root = get_root() cfg = get_config_from_root(root) versions = get_versions() target_versionfile = cfg.versionfile_source print("UPDATING %s" % target_versionfile) write_to_version_file(target_versionfile, versions) _build_exe.run(self) os.unlink(target_versionfile) with open(cfg.versionfile_source, "w") as f: LONG = LONG_VERSION_PY[cfg.VCS] f.write(LONG % {"DOLLAR": "$", "STYLE": cfg.style, "TAG_PREFIX": cfg.tag_prefix, "PARENTDIR_PREFIX": cfg.parentdir_prefix, "VERSIONFILE_SOURCE": cfg.versionfile_source, }) cmds["build_exe"] = cmd_build_exe del cmds["build_py"] if 'py2exe' in sys.modules: # py2exe enabled? try: from py2exe.distutils_buildexe import py2exe as _py2exe # py3 except ImportError: from py2exe.build_exe import py2exe as _py2exe # py2 class cmd_py2exe(_py2exe): def run(self): root = get_root() cfg = get_config_from_root(root) versions = get_versions() target_versionfile = cfg.versionfile_source print("UPDATING %s" % target_versionfile) write_to_version_file(target_versionfile, versions) _py2exe.run(self) os.unlink(target_versionfile) with open(cfg.versionfile_source, "w") as f: LONG = LONG_VERSION_PY[cfg.VCS] f.write(LONG % {"DOLLAR": "$", "STYLE": cfg.style, "TAG_PREFIX": cfg.tag_prefix, "PARENTDIR_PREFIX": cfg.parentdir_prefix, "VERSIONFILE_SOURCE": cfg.versionfile_source, }) cmds["py2exe"] = cmd_py2exe # we override different "sdist" commands for both environments if "setuptools" in sys.modules: from setuptools.command.sdist import sdist as _sdist else: from distutils.command.sdist import sdist as _sdist class cmd_sdist(_sdist): def run(self): versions = get_versions() self._versioneer_generated_versions = versions # unless we update this, the command will keep using the old # version self.distribution.metadata.version = versions["version"] return _sdist.run(self) def make_release_tree(self, base_dir, files): root = get_root() cfg = get_config_from_root(root) _sdist.make_release_tree(self, base_dir, files) # now locate _version.py in the new base_dir directory # (remembering that it may be a hardlink) and replace it with an # updated value target_versionfile = os.path.join(base_dir, cfg.versionfile_source) print("UPDATING %s" % target_versionfile) write_to_version_file(target_versionfile, self._versioneer_generated_versions) cmds["sdist"] = cmd_sdist return cmds CONFIG_ERROR = """ setup.cfg is missing the necessary Versioneer configuration. You need a section like: [versioneer] VCS = git style = pep440 versionfile_source = src/myproject/_version.py versionfile_build = myproject/_version.py tag_prefix = parentdir_prefix = myproject- You will also need to edit your setup.py to use the results: import versioneer setup(version=versioneer.get_version(), cmdclass=versioneer.get_cmdclass(), ...) Please read the docstring in ./versioneer.py for configuration instructions, edit setup.cfg, and re-run the installer or 'python versioneer.py setup'. """ SAMPLE_CONFIG = """ # See the docstring in versioneer.py for instructions. Note that you must # re-run 'versioneer.py setup' after changing this section, and commit the # resulting files. [versioneer] #VCS = git #style = pep440 #versionfile_source = #versionfile_build = #tag_prefix = #parentdir_prefix = """ INIT_PY_SNIPPET = """ from ._version import get_versions __version__ = get_versions()['version'] del get_versions """ def do_setup(): """Main VCS-independent setup function for installing Versioneer.""" root = get_root() try: cfg = get_config_from_root(root) except (EnvironmentError, configparser.NoSectionError, configparser.NoOptionError) as e: if isinstance(e, (EnvironmentError, configparser.NoSectionError)): print("Adding sample versioneer config to setup.cfg", file=sys.stderr) with open(os.path.join(root, "setup.cfg"), "a") as f: f.write(SAMPLE_CONFIG) print(CONFIG_ERROR, file=sys.stderr) return 1 print(" creating %s" % cfg.versionfile_source) with open(cfg.versionfile_source, "w") as f: LONG = LONG_VERSION_PY[cfg.VCS] f.write(LONG % {"DOLLAR": "$", "STYLE": cfg.style, "TAG_PREFIX": cfg.tag_prefix, "PARENTDIR_PREFIX": cfg.parentdir_prefix, "VERSIONFILE_SOURCE": cfg.versionfile_source, }) ipy = os.path.join(os.path.dirname(cfg.versionfile_source), "__init__.py") if os.path.exists(ipy): try: with open(ipy, "r") as f: old = f.read() except EnvironmentError: old = "" if INIT_PY_SNIPPET not in old: print(" appending to %s" % ipy) with open(ipy, "a") as f: f.write(INIT_PY_SNIPPET) else: print(" %s unmodified" % ipy) else: print(" %s does not exist, ok" % ipy) ipy = None # Make sure both the top-level "versioneer.py" and versionfile_source # (PKG/_version.py, used by runtime code) are in MANIFEST.in, so # they'll be copied into source distributions. Pip will not be able to # install the package without this. manifest_in = os.path.join(root, "MANIFEST.in") simple_includes = set() try: with open(manifest_in, "r") as f: for line in f: if line.startswith("include "): for include in line.split()[1:]: simple_includes.add(include) except EnvironmentError: pass # That does not cover everything MANIFEST.in can do # (http://docs.python.org/2/distutils/sourcedist.html#commands), so # it might give some false negatives. Appending redundant 'include' # lines is safe, though. if "versioneer.py" not in simple_includes: print(" appending 'versioneer.py' to MANIFEST.in") with open(manifest_in, "a") as f: f.write("include versioneer.py\n") else: print(" 'versioneer.py' already in MANIFEST.in") if cfg.versionfile_source not in simple_includes: print(" appending versionfile_source ('%s') to MANIFEST.in" % cfg.versionfile_source) with open(manifest_in, "a") as f: f.write("include %s\n" % cfg.versionfile_source) else: print(" versionfile_source already in MANIFEST.in") # Make VCS-specific changes. For git, this means creating/changing # .gitattributes to mark _version.py for export-subst keyword # substitution. do_vcs_install(manifest_in, cfg.versionfile_source, ipy) return 0 def scan_setup_py(): """Validate the contents of setup.py against Versioneer's expectations.""" found = set() setters = False errors = 0 with open("setup.py", "r") as f: for line in f.readlines(): if "import versioneer" in line: found.add("import") if "versioneer.get_cmdclass()" in line: found.add("cmdclass") if "versioneer.get_version()" in line: found.add("get_version") if "versioneer.VCS" in line: setters = True if "versioneer.versionfile_source" in line: setters = True if len(found) != 3: print("") print("Your setup.py appears to be missing some important items") print("(but I might be wrong). Please make sure it has something") print("roughly like the following:") print("") print(" import versioneer") print(" setup( version=versioneer.get_version(),") print(" cmdclass=versioneer.get_cmdclass(), ...)") print("") errors += 1 if setters: print("You should remove lines like 'versioneer.VCS = ' and") print("'versioneer.versionfile_source = ' . This configuration") print("now lives in setup.cfg, and should be removed from setup.py") print("") errors += 1 return errors if __name__ == "__main__": cmd = sys.argv[1] if cmd == "setup": errors = do_setup() errors += scan_setup_py() if errors: sys.exit(1)